LMFDB - Embedded newform 605.2.s.b.416.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(16,605)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("605.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.s (of order $55$, degree $40$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$880$
Relative dimension:	$22$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			416.3
Character	$\chi$	$=$	605.416
Dual form			605.2.s.b.16.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03821 + 0.233862i) q^{2} +(0.653999 - 0.475158i) q^{3} +(2.15157 - 0.500325i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-1.22186 + 1.12142i) q^{6} +(-0.0770600 + 0.0792929i) q^{7} +(-0.403791 + 0.144072i) q^{8} +(-0.725112 + 2.23166i) q^{9} +O(q^{10})$	\(q+(-2.03821 + 0.233862i) q^{2} +(0.653999 - 0.475158i) q^{3} +(2.15157 - 0.500325i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-1.22186 + 1.12142i) q^{6} +(-0.0770600 + 0.0792929i) q^{7} +(-0.403791 + 0.144072i) q^{8} +(-0.725112 + 2.23166i) q^{9} +(1.34350 + 1.55048i) q^{10} +(-3.07435 - 1.24433i) q^{11} +(1.16939 - 1.34955i) q^{12} +(0.978429 + 1.62254i) q^{13} +(0.138521 - 0.179637i) q^{14} +(-0.761375 - 0.271658i) q^{15} +(-3.17534 + 1.56121i) q^{16} +(-2.66596 - 2.17994i) q^{17} +(0.956024 - 4.71817i) q^{18} +(-0.367122 + 0.0209928i) q^{19} +(-1.62744 - 1.49365i) q^{20} +(-0.0127205 + 0.0884732i) q^{21} +(6.55717 + 1.81722i) q^{22} +(0.539872 + 3.75489i) q^{23} +(-0.195622 + 0.286088i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(-2.37369 - 3.07826i) q^{26} +(1.33559 + 4.11051i) q^{27} +(-0.126127 + 0.209159i) q^{28} +(-0.153525 - 0.394327i) q^{29} +(1.61537 + 0.375638i) q^{30} +(-4.52370 + 1.91173i) q^{31} +(6.82822 - 4.38823i) q^{32} +(-2.60188 + 0.647015i) q^{33} +(5.94357 + 3.81970i) q^{34} +(0.108950 + 0.0188546i) q^{35} +(-0.443567 + 5.16436i) q^{36} +(0.422389 + 4.91779i) q^{37} +(0.743360 - 0.128643i) q^{38} +(1.41086 + 0.596233i) q^{39} +(0.346845 + 0.251997i) q^{40} +(-7.16134 - 4.04420i) q^{41} +(0.00523650 - 0.183301i) q^{42} +(6.37251 + 1.87114i) q^{43} +(-7.23724 - 1.13908i) q^{44} +(2.25146 - 0.661088i) q^{45} +(-1.97850 - 7.52699i) q^{46} +(0.457072 + 2.25574i) q^{47} +(-1.33485 + 2.52982i) q^{48} +(0.199543 + 6.98492i) q^{49} +(0.521549 - 1.98418i) q^{50} +(-2.77935 - 0.158929i) q^{51} +(2.91695 + 3.00147i) q^{52} +(1.70367 + 0.837637i) q^{53} +(-3.68349 - 8.06573i) q^{54} +(0.708141 + 3.24014i) q^{55} +(0.0196922 - 0.0431200i) q^{56} +(-0.230122 + 0.188170i) q^{57} +(0.405135 + 0.767816i) q^{58} +(-6.63921 + 3.74933i) q^{59} +(-1.77407 - 0.203555i) q^{60} +(-12.3361 - 1.41543i) q^{61} +(8.77314 - 4.95442i) q^{62} +(-0.121078 - 0.229468i) q^{63} +(-7.41265 + 6.06129i) q^{64} +(0.787095 - 1.72350i) q^{65} +(5.15185 - 1.92723i) q^{66} +(0.779681 + 1.70726i) q^{67} +(-6.82666 - 3.35644i) q^{68} +(2.13724 + 2.19917i) q^{69} +(-0.226472 - 0.0129501i) q^{70} +(-2.13187 + 8.11049i) q^{71} +(-0.0287275 - 1.00559i) q^{72} +(-4.29019 + 8.13081i) q^{73} +(-2.01100 - 9.92468i) q^{74} +(0.205507 + 0.781829i) q^{75} +(-0.779383 + 0.228847i) q^{76} +(0.335576 - 0.147887i) q^{77} +(-3.01505 - 0.885299i) q^{78} +(-0.414663 + 14.5151i) q^{79} +(3.08104 + 1.73994i) q^{80} +(-2.86848 - 2.08407i) q^{81} +(15.5421 + 6.56813i) q^{82} +(-14.3771 + 2.48806i) q^{83} +(0.0168963 + 0.196720i) q^{84} +(-0.294700 + 3.43113i) q^{85} +(-13.4261 - 2.32347i) q^{86} +(-0.287773 - 0.184941i) q^{87} +(1.42067 + 0.0595188i) q^{88} +(2.96984 - 1.90860i) q^{89} +(-4.43433 + 1.87397i) q^{90} +(-0.204054 - 0.0474507i) q^{91} +(3.04024 + 7.80879i) q^{92} +(-2.05012 + 3.39974i) q^{93} +(-1.45914 - 4.49077i) q^{94} +(0.224548 + 0.291199i) q^{95} +(2.38055 - 6.11438i) q^{96} +(-1.19286 + 1.74450i) q^{97} +(-2.04022 - 14.1900i) q^{98} +(5.00617 - 5.95865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) $ 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{53}{55}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.03821	+	0.233862i	−1.44123	+	0.165366i	−0.799085	−	0.601218i	$-0.794682\pi$
$2$	−2.03821	+	0.233862i	−1.44123	+	0.165366i	−0.642144	+	0.766584i	$0.721955\pi$
$3$	0.653999	−	0.475158i	0.377586	−	0.274333i	−0.382763	−	0.923846i	$-0.625028\pi$
$3$	0.653999	−	0.475158i	0.377586	−	0.274333i	0.760350	+	0.649514i	$0.225028\pi$
$4$	2.15157	−	0.500325i	1.07578	−	0.250163i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$6$	−1.22186	+	1.12142i	−0.498823	+	0.457816i
$7$	−0.0770600	+	0.0792929i	−0.0291260	+	0.0299699i	−0.731538	−	0.681800i	$-0.761197\pi$
$7$	−0.0770600	+	0.0792929i	−0.0291260	+	0.0299699i	0.702412	+	0.711770i	$0.252106\pi$
$8$	−0.403791	+	0.144072i	−0.142762	+	0.0509372i
$9$	−0.725112	+	2.23166i	−0.241704	+	0.743888i
$10$	1.34350	+	1.55048i	0.424851	+	0.490305i
$11$	−3.07435	−	1.24433i	−0.926952	−	0.375179i
$11$	−3.07435	−	1.24433i	−0.926952	−	0.375179i
$12$	1.16939	−	1.34955i	0.337573	−	0.389580i
$13$	0.978429	+	1.62254i	0.271367	+	0.450012i	0.961944	−	0.273247i	$-0.0880977\pi$
$13$	0.978429	+	1.62254i	0.271367	+	0.450012i	−0.690577	+	0.723259i	$0.742643\pi$
$14$	0.138521	−	0.179637i	0.0370212	−	0.0480099i
$15$	−0.761375	−	0.271658i	−0.196586	−	0.0701418i
$16$	−3.17534	+	1.56121i	−0.793835	+	0.390303i
$17$	−2.66596	−	2.17994i	−0.646589	−	0.528714i	0.251875	−	0.967760i	$-0.418953\pi$
$17$	−2.66596	−	2.17994i	−0.646589	−	0.528714i	−0.898464	+	0.439046i	$0.855316\pi$
$18$	0.956024	−	4.71817i	0.225337	−	1.11208i
$19$	−0.367122	+	0.0209928i	−0.0842235	+	0.00481607i	−0.0991497	−	0.995073i	$-0.531612\pi$
$19$	−0.367122	+	0.0209928i	−0.0842235	+	0.00481607i	0.0149263	+	0.999889i	$0.495249\pi$
$20$	−1.62744	−	1.49365i	−0.363907	−	0.333991i
$21$	−0.0127205	+	0.0884732i	−0.00277585	+	0.0193064i
$22$	6.55717	+	1.81722i	1.39799	+	0.387432i
$23$	0.539872	+	3.75489i	0.112571	+	0.782949i	0.965403	+	0.260763i	$0.0839742\pi$
$23$	0.539872	+	3.75489i	0.112571	+	0.782949i	−0.852832	+	0.522186i	$0.825117\pi$
$24$	−0.195622	+	0.286088i	−0.0399311	+	0.0583974i
$25$	−0.362808	+	0.931864i	−0.0725615	+	0.186373i
$26$	−2.37369	−	3.07826i	−0.465519	−	0.603696i
$27$	1.33559	+	4.11051i	0.257034	+	0.791069i
$28$	−0.126127	+	0.209159i	−0.0238359	+	0.0395273i
$29$	−0.153525	−	0.394327i	−0.0285090	−	0.0732247i	0.916890	−	0.399140i	$-0.130691\pi$
$29$	−0.153525	−	0.394327i	−0.0285090	−	0.0732247i	−0.945399	+	0.325915i	$0.894328\pi$
$30$	1.61537	+	0.375638i	0.294925	+	0.0685818i
$31$	−4.52370	+	1.91173i	−0.812480	+	0.343357i	−0.755607	−	0.655025i	$-0.772658\pi$
$31$	−4.52370	+	1.91173i	−0.812480	+	0.343357i	−0.0568722	+	0.998381i	$0.518113\pi$
$32$	6.82822	−	4.38823i	1.20707	−	0.775737i
$33$	−2.60188	+	0.647015i	−0.452929	+	0.112631i
$34$	5.94357	+	3.81970i	1.01931	+	0.655074i
$35$	0.108950	+	0.0188546i	0.0184159	+	0.00318700i
$36$	−0.443567	+	5.16436i	−0.0739279	+	0.860727i
$37$	0.422389	+	4.91779i	0.0694403	+	0.808479i	0.945361	+	0.326025i	$0.105709\pi$
$37$	0.422389	+	4.91779i	0.0694403	+	0.808479i	−0.875921	+	0.482455i	$0.839745\pi$
$38$	0.743360	−	0.128643i	0.120589	−	0.0208687i
$39$	1.41086	+	0.596233i	0.225918	+	0.0954736i
$40$	0.346845	+	0.251997i	0.0548410	+	0.0398443i
$41$	−7.16134	−	4.04420i	−1.11841	−	0.631597i	−0.182282	−	0.983246i	$-0.558348\pi$
$41$	−7.16134	−	4.04420i	−1.11841	−	0.631597i	−0.936132	+	0.351649i	$0.885621\pi$
$42$	0.00523650	−	0.183301i	0.000808009	−	0.0282840i
$43$	6.37251	+	1.87114i	0.971799	+	0.285346i	0.728835	−	0.684689i	$-0.240062\pi$
$43$	6.37251	+	1.87114i	0.971799	+	0.285346i	0.242964	+	0.970035i	$0.421880\pi$
$44$	−7.23724	−	1.13908i	−1.09106	−	0.171722i
$45$	2.25146	−	0.661088i	0.335628	−	0.0985492i
$46$	−1.97850	−	7.52699i	−0.291714	−	1.10979i
$47$	0.457072	+	2.25574i	0.0666708	+	0.329033i	0.999511	−	0.0312560i	$-0.00995072\pi$
$47$	0.457072	+	2.25574i	0.0666708	+	0.329033i	−0.932841	+	0.360289i	$0.882678\pi$
$48$	−1.33485	+	2.52982i	−0.192669	+	0.365148i
$49$	0.199543	+	6.98492i	0.0285062	+	0.997846i
$50$	0.521549	−	1.98418i	0.0737581	−	0.280605i
$51$	−2.77935	−	0.158929i	−0.389187	−	0.0222545i
$52$	2.91695	+	3.00147i	0.404509	+	0.416229i
$53$	1.70367	+	0.837637i	0.234017	+	0.115058i	0.554463	−	0.832208i	$-0.312924\pi$
$53$	1.70367	+	0.837637i	0.234017	+	0.115058i	−0.320446	+	0.947267i	$0.603833\pi$
$54$	−3.68349	−	8.06573i	−0.501260	−	1.09761i
$55$	0.708141	+	3.24014i	0.0954857	+	0.436901i
$56$	0.0196922	−	0.0431200i	0.00263148	−	0.00576215i
$57$	−0.230122	+	0.188170i	−0.0304804	+	0.0249237i
$58$	0.405135	+	0.767816i	0.0531968	+	0.100819i
$59$	−6.63921	+	3.74933i	−0.864351	+	0.488121i	−0.859066	−	0.511865i	$-0.828955\pi$
$59$	−6.63921	+	3.74933i	−0.864351	+	0.488121i	−0.00528481	+	0.999986i	$0.501682\pi$
$60$	−1.77407	−	0.203555i	−0.229031	−	0.0262788i
$61$	−12.3361	−	1.41543i	−1.57947	−	0.181228i	−0.720575	−	0.693377i	$-0.756122\pi$
$61$	−12.3361	−	1.41543i	−1.57947	−	0.181228i	−0.858897	+	0.512149i	$0.828850\pi$
$62$	8.77314	−	4.95442i	1.11419	−	0.629212i
$63$	−0.121078	−	0.229468i	−0.0152544	−	0.0289103i
$64$	−7.41265	+	6.06129i	−0.926581	+	0.757662i
$65$	0.787095	−	1.72350i	0.0976272	−	0.213774i
$66$	5.15185	−	1.92723i	0.634148	−	0.237226i
$67$	0.779681	+	1.70726i	0.0952532	+	0.208576i	0.951261	−	0.308388i	$-0.0997895\pi$
$67$	0.779681	+	1.70726i	0.0952532	+	0.208576i	−0.856007	+	0.516964i	$0.827062\pi$
$68$	−6.82666	−	3.35644i	−0.827854	−	0.407028i
$69$	2.13724	+	2.19917i	0.257294	+	0.264749i
$70$	−0.226472	−	0.0129501i	−0.0270686	−	0.00154784i
$71$	−2.13187	+	8.11049i	−0.253007	+	0.962538i	0.712397	+	0.701777i	$0.247610\pi$
$71$	−2.13187	+	8.11049i	−0.253007	+	0.962538i	−0.965403	+	0.260761i	$0.916027\pi$
$72$	−0.0287275	−	1.00559i	−0.00338557	−	0.118510i
$73$	−4.29019	+	8.13081i	−0.502129	+	0.951639i	0.494467	+	0.869196i	$0.335363\pi$
$73$	−4.29019	+	8.13081i	−0.502129	+	0.951639i	−0.996596	+	0.0824432i	$0.973728\pi$
$74$	−2.01100	−	9.92468i	−0.233774	−	1.15372i
$75$	0.205507	+	0.781829i	0.0237299	+	0.0902779i
$76$	−0.779383	+	0.228847i	−0.0894013	+	0.0262506i
$77$	0.335576	−	0.147887i	0.0382424	−	0.0168532i
$78$	−3.01505	−	0.885299i	−0.341387	−	0.100240i
$79$	−0.414663	+	14.5151i	−0.0466532	+	1.63307i	0.553260	+	0.833009i	$0.313384\pi$
$79$	−0.414663	+	14.5151i	−0.0466532	+	1.63307i	−0.599913	+	0.800065i	$0.704798\pi$
$80$	3.08104	+	1.73994i	0.344470	+	0.194531i
$81$	−2.86848	−	2.08407i	−0.318720	−	0.231564i
$82$	15.5421	+	6.56813i	1.71633	+	0.725329i
$83$	−14.3771	+	2.48806i	−1.57809	+	0.273100i	−0.891184	−	0.453642i	$-0.850124\pi$
$83$	−14.3771	+	2.48806i	−1.57809	+	0.273100i	−0.686911	+	0.726742i	$0.741034\pi$
$84$	0.0168963	+	0.196720i	0.00184354	+	0.0214639i
$85$	−0.294700	+	3.43113i	−0.0319647	+	0.372158i
$86$	−13.4261	−	2.32347i	−1.44777	−	0.250547i
$87$	−0.287773	−	0.184941i	−0.0308525	−	0.0198277i
$88$	1.42067	+	0.0595188i	0.151444	+	0.00634472i
$89$	2.96984	−	1.90860i	0.314802	−	0.202311i	−0.373692	−	0.927553i	$-0.621908\pi$
$89$	2.96984	−	1.90860i	0.314802	−	0.202311i	0.688494	+	0.725242i	$0.258272\pi$
$90$	−4.43433	+	1.87397i	−0.467420	+	0.197533i
$91$	−0.204054	−	0.0474507i	−0.0213907	−	0.00497418i
$92$	3.04024	+	7.80879i	0.316967	+	0.814122i
$93$	−2.05012	+	3.39974i	−0.212587	+	0.352537i
$94$	−1.45914	−	4.49077i	−0.150499	−	0.463187i
$95$	0.224548	+	0.291199i	0.0230382	+	0.0298764i
$96$	2.38055	−	6.11438i	0.242963	−	0.624047i
$97$	−1.19286	+	1.74450i	−0.121116	+	0.177127i	−0.881265	−	0.472622i	$-0.843308\pi$
$97$	−1.19286	+	1.74450i	−0.121116	+	0.177127i	0.760149	+	0.649749i	$0.225126\pi$
$98$	−2.04022	−	14.1900i	−0.206093	−	1.43341i
$99$	5.00617	−	5.95865i	0.503139	−	0.598867i
$100$	−0.314370	+	2.18649i	−0.0314370	+	0.218649i
$101$	−5.71038	−	5.24094i	−0.568204	−	0.521493i	0.339776	−	0.940506i	$-0.389649\pi$
$101$	−5.71038	−	5.24094i	−0.568204	−	0.521493i	−0.907980	+	0.419013i	$0.862376\pi$
$102$	5.70205	−	0.326055i	0.564587	−	0.0322843i
$103$	1.07137	−	5.28741i	0.105565	−	0.520984i	−0.892049	−	0.451939i	$-0.850732\pi$
$103$	1.07137	−	5.28741i	0.105565	−	0.520984i	0.997614	−	0.0690443i	$-0.0219950\pi$
$104$	−0.628844	−	0.514203i	−0.0616632	−	0.0504218i
$105$	0.0802121	−	0.0394376i	0.00782790	−	0.00384872i
$106$	−3.66832	−	1.30885i	−0.356299	−	0.127127i
$107$	9.05826	−	11.7470i	0.875695	−	1.13562i	−0.114149	−	0.993464i	$-0.536414\pi$
$107$	9.05826	−	11.7470i	0.875695	−	1.13562i	0.989844	−	0.142158i	$-0.0454040\pi$
$108$	4.93020	+	8.17581i	0.474408	+	0.786718i
$109$	4.48798	−	5.17941i	0.429871	−	0.496098i	−0.498948	−	0.866632i	$-0.666280\pi$
$109$	4.48798	−	5.17941i	0.429871	−	0.496098i	0.928819	+	0.370535i	$0.120825\pi$
$110$	−2.20108	−	6.43847i	−0.209865	−	0.613884i
$111$	2.61297	+	3.01553i	0.248012	+	0.286221i
$112$	0.120899	−	0.372089i	0.0114239	−	0.0351591i
$113$	0.379319	−	0.135341i	0.0356833	−	0.0127318i	−0.318147	−	0.948041i	$-0.603061\pi$
$113$	0.379319	−	0.135341i	0.0356833	−	0.0127318i	0.353831	+	0.935309i	$0.384879\pi$
$114$	0.425031	−	0.437346i	0.0398078	−	0.0409612i
$115$	2.79483	−	2.56507i	0.260619	−	0.239194i
$116$	−0.527612	−	0.771608i	−0.0489875	−	0.0716420i
$117$	−4.33044	+	1.00700i	−0.400349	+	0.0930972i
$118$	12.6552	−	9.19457i	1.16501	−	0.846429i
$119$	0.378293	−	0.0434050i	0.0346780	−	0.00397893i
$120$	0.346575			0.0316378
$121$	7.90330	+	7.65100i	0.718482	+	0.695546i
$122$	25.4745			2.30635
$123$	−6.60514	+	0.757870i	−0.595566	+	0.0683348i
$124$	−8.77654	+	6.37653i	−0.788157	+	0.572629i
$125$	0.974012	−	0.226497i	0.0871183	−	0.0202585i
$126$	0.300446	+	0.439388i	0.0267658	+	0.0391438i
$127$	10.7345	−	9.85201i	0.952530	−	0.874225i	−0.0396275	−	0.999215i	$-0.512617\pi$
$127$	10.7345	−	9.85201i	0.952530	−	0.874225i	0.992158	+	0.124990i	$0.0398899\pi$
$128$	2.37730	−	2.44618i	0.210126	−	0.216214i
$129$	5.05670	−	1.80423i	0.445218	−	0.158853i
$130$	−1.20120	+	3.69692i	−0.105352	+	0.324241i
$131$	10.0005	+	11.5412i	0.873750	+	1.00836i	0.999866	+	0.0163463i	$0.00520342\pi$
$131$	10.0005	+	11.5412i	0.873750	+	1.00836i	−0.126116	+	0.992016i	$0.540251\pi$
$132$	−5.27439	+	2.69388i	−0.459077	+	0.234472i
$133$	0.0266258	−	0.0307278i	0.00230875	−	0.00266444i
$134$	−1.98842	−	3.29742i	−0.171773	−	0.284853i
$135$	2.63925	−	3.42264i	0.227151	−	0.294574i
$136$	1.39056	+	0.496150i	0.119239	+	0.0425445i
$137$	−3.18176	+	1.56436i	−0.271836	+	0.133653i	−0.572049	−	0.820219i	$-0.693851\pi$
$137$	−3.18176	+	1.56436i	−0.271836	+	0.133653i	0.300213	+	0.953872i	$0.402942\pi$
$138$	−4.87044	−	3.98254i	−0.414600	−	0.339017i
$139$	0.277739	−	1.37070i	0.0235575	−	0.116261i	−0.966578	−	0.256371i	$-0.917473\pi$
$139$	0.277739	−	1.37070i	0.0235575	−	0.116261i	0.990136	+	0.140110i	$0.0447457\pi$
$140$	0.243847	−	0.0139437i	0.0206088	−	0.00117845i
$141$	1.37076	+	1.25807i	0.115439	+	0.105949i
$142$	2.44846	−	17.0294i	0.205470	−	1.42908i
$143$	−0.989063	−	6.20575i	−0.0827096	−	0.518951i
$144$	−1.18162	−	8.21835i	−0.0984683	−	0.684862i
$145$	−0.238849	+	0.349306i	−0.0198354	+	0.0290083i
$146$	6.84280	−	17.5756i	0.566314	−	1.45457i
$147$	3.44944	+	4.47332i	0.284505	+	0.368953i
$148$	3.36929	+	10.3696i	0.276954	+	0.852377i
$149$	9.59750	−	15.9157i	0.786258	−	1.30386i	−0.162136	−	0.986768i	$-0.551838\pi$
$149$	9.59750	−	15.9157i	0.786258	−	1.30386i	0.948394	−	0.317094i	$-0.102707\pi$
$150$	−0.601706	−	1.54547i	−0.0491290	−	0.126187i
$151$	−7.13552	−	1.65929i	−0.580681	−	0.135031i	−0.0741404	−	0.997248i	$-0.523621\pi$
$151$	−7.13552	−	1.65929i	−0.580681	−	0.135031i	−0.506540	+	0.862216i	$0.669076\pi$
$152$	0.145216	−	0.0613687i	0.0117786	−	0.00497766i
$153$	6.79801	−	4.36882i	0.549587	−	0.353198i
$154$	−0.649388	+	0.379902i	−0.0523292	+	0.0306133i
$155$	4.13145	+	2.65512i	0.331846	+	0.213264i
$156$	3.33386	+	0.576947i	0.266922	+	0.0461927i
$157$	−0.375534	+	4.37227i	−0.0299709	+	0.348945i	0.965951	+	0.258725i	$0.0833024\pi$
$157$	−0.375534	+	4.37227i	−0.0299709	+	0.348945i	−0.995922	+	0.0902197i	$0.971243\pi$
$158$	−2.54936	−	29.6817i	−0.202816	−	2.36135i
$159$	1.51221	−	0.261698i	0.119926	−	0.0207540i
$160$	−7.47650	−	3.15960i	−0.591070	−	0.249788i
$161$	−0.339339	−	0.246544i	−0.0267436	−	0.0194304i
$162$	6.33394	+	3.57694i	0.497642	+	0.281031i
$163$	−0.114764	+	4.01725i	−0.00898898	+	0.314655i	0.982639	+	0.185528i	$0.0593995\pi$
$163$	−0.114764	+	4.01725i	−0.00898898	+	0.314655i	−0.991628	+	0.129127i	$0.958782\pi$
$164$	−17.4315	−	5.11835i	−1.36117	−	0.399676i
$165$	2.00270	+	1.78257i	0.155910	+	0.138773i
$166$	28.7217	−	8.43344i	2.22923	−	0.654562i
$167$	−2.23629	−	8.50771i	−0.173049	−	0.658347i	−0.995930	−	0.0901326i	$-0.971271\pi$
$167$	−2.23629	−	8.50771i	−0.173049	−	0.658347i	0.822881	−	0.568214i	$-0.192365\pi$
$168$	−0.00761010	−	0.0375573i	−0.000587132	−	0.00289761i
$169$	4.39136	−	8.32254i	0.337797	−	0.640196i
$170$	−0.201752	−	7.06226i	−0.0154737	−	0.541650i
$171$	0.219355	−	0.834514i	0.0167745	−	0.0638169i
$172$	14.6471	+	0.837549i	1.11683	+	0.0638625i
$173$	2.79251	+	2.87342i	0.212310	+	0.218462i	0.814919	−	0.579574i	$-0.196781\pi$
$173$	2.79251	+	2.87342i	0.212310	+	0.218462i	−0.602609	+	0.798037i	$0.705872\pi$
$174$	0.629792	+	0.309648i	0.0477444	+	0.0234743i
$175$	−0.0459322	−	0.100578i	−0.00347215	−	0.00760295i
$176$	11.7048	−	0.848549i	0.882281	−	0.0639618i
$177$	−2.56051	+	5.60673i	−0.192460	+	0.421428i
$178$	−5.60679	+	4.58465i	−0.420246	+	0.343634i
$179$	−6.12053	−	11.5997i	−0.457470	−	0.867002i	−0.999643	−	0.0267350i	$-0.991489\pi$
$179$	−6.12053	−	11.5997i	−0.457470	−	0.867002i	0.542172	−	0.840267i	$-0.317602\pi$
$180$	4.51340	−	2.54884i	0.336409	−	0.189979i
$181$	18.7071	+	2.14644i	1.39049	+	0.159544i	0.776672	−	0.629905i	$-0.216906\pi$
$181$	18.7071	+	2.14644i	1.39049	+	0.159544i	0.613816	+	0.789449i	$0.289634\pi$
$182$	0.427001	+	0.0489938i	0.0316514	+	0.00363166i
$183$	−8.74033	+	4.93589i	−0.646104	+	0.364872i
$184$	−0.758971	−	1.43841i	−0.0559521	−	0.106041i
$185$	3.82108	−	3.12448i	0.280931	−	0.229716i
$186$	3.38349	−	7.40881i	0.248090	−	0.543240i
$187$	5.48353	+	10.0192i	0.400996	+	0.732679i
$188$	2.11202	+	4.62468i	0.154035	+	0.337290i
$189$	−0.428855	−	0.210854i	−0.0311946	−	0.0153374i
$190$	−0.525776	−	0.541011i	−0.0381438	−	0.0392490i
$191$	−12.8693	−	0.735894i	−0.931191	−	0.0532474i	−0.415095	−	0.909778i	$-0.636252\pi$
$191$	−12.8693	−	0.735894i	−0.931191	−	0.0532474i	−0.516096	+	0.856531i	$0.672615\pi$
$192$	−1.96779	+	7.48626i	−0.142013	+	0.540274i
$193$	−0.760520	−	26.6217i	−0.0547434	−	1.91627i	−0.312260	−	0.949997i	$-0.601086\pi$
$193$	−0.760520	−	26.6217i	−0.0547434	−	1.91627i	0.257516	−	0.966274i	$-0.417096\pi$
$194$	2.02332	−	3.83461i	0.145266	−	0.275309i
$195$	−0.304175	−	1.50116i	−0.0217824	−	0.107500i
$196$	3.92406	+	14.9287i	0.280290	+	1.06633i
$197$	−2.48512	+	0.729696i	−0.177057	+	0.0519887i	−0.369059	−	0.929406i	$-0.620320\pi$
$197$	−2.48512	+	0.729696i	−0.177057	+	0.0519887i	0.192002	+	0.981394i	$0.438502\pi$
$198$	−8.81010	+	13.3157i	−0.626106	+	0.946306i
$199$	−1.64494	−	0.482999i	−0.116607	−	0.0342389i	0.222908	−	0.974839i	$-0.428445\pi$
$199$	−1.64494	−	0.482999i	−0.116607	−	0.0342389i	−0.339515	+	0.940600i	$0.610263\pi$
$200$	0.0122427	−	0.428549i	0.000865686	−	0.0303030i
$201$	1.32113	+	0.746077i	0.0931854	+	0.0526242i
$202$	12.8646	+	9.34667i	0.905149	+	0.657629i
$203$	0.0430980	+	0.0182134i	0.00302489	+	0.00127833i
$204$	−6.05947	+	1.04863i	−0.424248	+	0.0734190i
$205$	0.703801	+	8.19421i	0.0491556	+	0.572308i
$206$	−0.947142	+	11.0274i	−0.0659905	+	0.768314i
$207$	−8.77112	−	1.51790i	−0.609635	−	0.105502i
$208$	−5.63998	−	3.62459i	−0.391062	−	0.251320i
$209$	1.15478	+	0.392280i	0.0798780	+	0.0271346i
$210$	−0.154266	+	0.0991406i	−0.0106454	+	0.00684135i
$211$	2.95225	−	1.24763i	0.203241	−	0.0858905i	−0.285273	−	0.958446i	$-0.592084\pi$
$211$	2.95225	−	1.24763i	0.203241	−	0.0858905i	0.488515	+	0.872556i	$0.337539\pi$
$212$	4.08465	+	0.949844i	0.280535	+	0.0652355i
$213$	2.45952	+	6.31723i	0.168524	+	0.432849i
$214$	−15.7154	+	26.0611i	−1.07428	+	1.78150i
$215$	−2.05235	−	6.31648i	−0.139969	−	0.430781i
$216$	−1.13151	−	1.46737i	−0.0769894	−	0.0998417i
$217$	0.197010	−	0.506015i	0.0133739	−	0.0343505i
$218$	−7.93617	+	11.6063i	−0.537505	+	0.786076i
$219$	1.05764	+	7.35606i	0.0714688	+	0.497076i
$220$	3.14474	+	6.61708i	0.212018	+	0.446124i
$221$	0.928599	−	6.45855i	0.0624643	−	0.434449i
$222$	−6.03098	−	5.53519i	−0.404773	−	0.371497i
$223$	2.49831	−	0.142858i	0.167299	−	0.00956650i	0.0267614	−	0.999642i	$-0.491481\pi$
$223$	2.49831	−	0.142858i	0.167299	−	0.00956650i	0.140538	+	0.990075i	$0.455117\pi$
$224$	−0.178227	+	0.879587i	−0.0119083	+	0.0587698i
$225$	−1.81653	−	1.48537i	−0.121102	−	0.0990247i
$226$	−0.741479	+	0.364561i	−0.0493224	+	0.0242502i
$227$	−2.75311	−	0.982308i	−0.182730	−	0.0651981i	0.243099	−	0.970001i	$-0.421836\pi$
$227$	−2.75311	−	0.982308i	−0.182730	−	0.0651981i	−0.425830	+	0.904803i	$0.640018\pi$
$228$	−0.400977	+	0.519996i	−0.0265553	+	0.0344376i
$229$	−2.67295	−	4.43259i	−0.176634	−	0.292914i	0.755415	−	0.655246i	$-0.227435\pi$
$229$	−2.67295	−	4.43259i	−0.176634	−	0.292914i	−0.932049	+	0.362332i	$0.881981\pi$
$230$	−5.09657	+	5.88175i	−0.336058	+	0.387831i
$231$	0.149197	−	0.256169i	0.00981644	−	0.0168547i
$232$	0.118804	+	0.137107i	0.00779985	+	0.00900151i
$233$	−2.06136	+	6.34421i	−0.135044	+	0.415623i	−0.995597	−	0.0937383i	$-0.970118\pi$
$233$	−2.06136	+	6.34421i	−0.135044	+	0.415623i	0.860553	+	0.509361i	$0.170118\pi$
$234$	8.59082	−	3.06520i	0.561600	−	0.200378i
$235$	1.60406	−	1.65054i	0.104637	−	0.107669i
$236$	−12.4088	+	11.3887i	−0.807744	+	0.741341i
$237$	6.62577	+	9.68988i	0.430390	+	0.629425i
$238$	−0.760887	+	0.176937i	−0.0493210	+	0.0114691i
$239$	−7.65207	+	5.55955i	−0.494971	+	0.359618i	−0.807093	−	0.590425i	$-0.798960\pi$
$239$	−7.65207	+	5.55955i	−0.494971	+	0.359618i	0.312122	+	0.950042i	$0.398960\pi$
$240$	2.84174	−	0.326059i	0.183434	−	0.0210470i
$241$	−9.41726			−0.606619			−0.303309	−	0.952892i	$-0.598092\pi$
$241$	−9.41726			−0.606619			−0.303309	+	0.952892i	$0.598092\pi$
$242$	−17.8978	−	13.7460i	−1.15052	−	0.883628i
$243$	−15.8324			−1.01565
$244$	−27.2500	+	3.12665i	−1.74451	+	0.200163i
$245$	5.65323	−	4.10731i	0.361172	−	0.262406i
$246$	13.2854	−	3.08939i	0.847046	−	0.196972i
$247$	−0.393264	−	0.575130i	−0.0250228	−	0.0365947i
$248$	1.55120	−	1.42368i	0.0985013	−	0.0904036i
$249$	−8.22040	+	8.45860i	−0.520947	+	0.536042i
$250$	−1.93227	+	0.689432i	−0.122207	+	0.0436035i
$251$	−8.81308	+	27.1239i	−0.556277	+	1.71204i	0.136271	+	0.990672i	$0.456488\pi$
$251$	−8.81308	+	27.1239i	−0.556277	+	1.71204i	−0.692547	+	0.721372i	$0.743512\pi$
$252$	−0.375316	−	0.433138i	−0.0236427	−	0.0272851i
$253$	3.01256	−	12.2156i	0.189398	−	0.767991i
$254$	−19.5750	+	22.5908i	−1.22825	+	1.41747i
$255$	1.43759	+	2.38398i	0.0900256	+	0.149291i
$256$	7.42094	−	9.62364i	0.463809	−	0.601478i
$257$	−7.00716	−	2.50015i	−0.437095	−	0.155955i	0.108330	−	0.994115i	$-0.465450\pi$
$257$	−7.00716	−	2.50015i	−0.437095	−	0.155955i	−0.545425	+	0.838160i	$0.683632\pi$
$258$	−9.88466	+	4.85996i	−0.615392	+	0.302568i
$259$	−0.422495	−	0.345472i	−0.0262526	−	0.0214666i
$260$	0.831178	−	4.10202i	0.0515475	−	0.254397i
$261$	0.991328	−	0.0566862i	0.0613617	−	0.00350879i
$262$	−23.0822	−	21.1846i	−1.42602	−	1.30879i
$263$	0.387129	−	2.69254i	0.0238714	−	0.166029i	−0.974398	−	0.224828i	$-0.927818\pi$
$263$	0.387129	−	2.69254i	0.0238714	−	0.166029i	0.998270	+	0.0587988i	$0.0187270\pi$
$264$	0.957397	−	0.636117i	0.0589237	−	0.0391503i
$265$	−0.270178	−	1.87913i	−0.0165969	−	0.115434i
$266$	−0.0470828	+	0.0688564i	−0.00288683	+	0.00422186i
$267$	1.03538	−	2.65936i	0.0633645	−	0.162750i
$268$	2.53172	+	3.28320i	0.154650	+	0.200553i
$269$	8.04657	+	24.7648i	0.490608	+	1.50994i	0.823691	+	0.567039i	$0.191911\pi$
$269$	8.04657	+	24.7648i	0.490608	+	1.50994i	−0.333082	+	0.942898i	$0.608089\pi$
$270$	−4.57891	+	7.59327i	−0.278664	+	0.462112i
$271$	0.687350	+	1.76544i	0.0417535	+	0.107243i	0.951197	−	0.308585i	$-0.0998554\pi$
$271$	0.687350	+	1.76544i	0.0417535	+	0.107243i	−0.909443	+	0.415828i	$0.863492\pi$
$272$	11.8687	+	2.75994i	0.719644	+	0.167346i
$273$	−0.155998	+	0.0659251i	−0.00944140	+	0.00398997i
$274$	6.11923	−	3.93259i	0.369676	−	0.237576i
$275$	2.27494	−	2.41343i	0.137184	−	0.145535i
$276$	5.69872	+	3.66234i	0.343023	+	0.220447i
$277$	−29.6632	−	5.13343i	−1.78229	−	0.308438i	−0.818383	−	0.574673i	$-0.805129\pi$
$277$	−29.6632	−	5.13343i	−1.78229	−	0.308438i	−0.963908	+	0.266235i	$0.914220\pi$
$278$	−0.245535	+	2.85871i	−0.0147262	+	0.171454i
$279$	−0.986154	−	11.4816i	−0.0590395	−	0.687384i
$280$	−0.0467095	+	0.00808339i	−0.00279142	+	0.000483075i
$281$	−11.7732	−	4.97540i	−0.702331	−	0.296808i	0.00870609	−	0.999962i	$-0.497229\pi$
$281$	−11.7732	−	4.97540i	−0.702331	−	0.296808i	−0.711037	+	0.703155i	$0.751774\pi$
$282$	−3.08810	−	2.24363i	−0.183894	−	0.133607i
$283$	20.4113	+	11.5268i	1.21332	+	0.685196i	0.959406	−	0.282030i	$-0.0910078\pi$
$283$	20.4113	+	11.5268i	1.21332	+	0.685196i	0.253918	+	0.967226i	$0.418281\pi$
$284$	−0.528985	+	18.5169i	−0.0313895	+	1.09877i
$285$	0.285220	+	0.0837481i	0.0168950	+	0.00496081i
$286$	3.46721	+	12.4173i	0.205020	+	0.734250i
$287$	0.872529	−	0.256198i	0.0515038	−	0.0151229i
$288$	4.84183	+	18.4202i	0.285308	+	1.08542i
$289$	−1.02086	−	5.03814i	−0.0600506	−	0.296361i
$290$	0.405135	−	0.767816i	0.0237903	−	0.0450877i
$291$	0.0487850	+	1.70770i	0.00285983	+	0.100107i
$292$	−5.16257	+	19.6405i	−0.302117	+	1.14937i
$293$	23.4987	+	1.34371i	1.37281	+	0.0785002i	0.727861	−	0.685725i	$-0.240515\pi$
$293$	23.4987	+	1.34371i	1.37281	+	0.0785002i	0.644950	+	0.764225i	$0.276878\pi$
$294$	−8.07682	−	8.31085i	−0.471050	−	0.484699i
$295$	6.84242	+	3.36419i	0.398381	+	0.195871i
$296$	−0.879074	−	1.92490i	−0.0510951	−	0.111883i
$297$	1.00876	−	14.2991i	0.0585341	−	0.829717i
$298$	−15.8396	+	34.6839i	−0.917563	+	2.00918i
$299$	−5.56425	+	4.54986i	−0.321789	+	0.263125i
$300$	0.833330	+	1.57934i	0.0481123	+	0.0911830i
$301$	−0.639434	+	0.361105i	−0.0368564	+	0.0208138i
$302$	14.9317	+	1.71325i	0.859223	+	0.0985867i
$303$	−6.22486	−	0.714236i	−0.357609	−	0.0410318i
$304$	1.13296	−	0.639813i	0.0649798	−	0.0366958i
$305$	5.79461	+	10.9820i	0.331798	+	0.628828i
$306$	−12.8340	+	10.4943i	−0.733673	+	0.599922i
$307$	−6.77144	+	14.8274i	−0.386466	+	0.846243i	0.611999	+	0.790859i	$0.290366\pi$
$307$	−6.77144	+	14.8274i	−0.386466	+	0.846243i	−0.998465	+	0.0553844i	$0.982362\pi$
$308$	0.648023	−	0.486085i	0.0369245	−	0.0276972i
$309$	−1.81168	−	3.96703i	−0.103063	−	0.225676i
$310$	−9.04167	−	4.44549i	−0.513532	−	0.252487i
$311$	−4.90131	−	5.04333i	−0.277928	−	0.285981i	0.563768	−	0.825933i	$-0.309351\pi$
$311$	−4.90131	−	5.04333i	−0.277928	−	0.285981i	−0.841695	+	0.539952i	$0.818442\pi$
$312$	−0.655591	−	0.0374881i	−0.0371155	−	0.00212234i
$313$	3.94639	−	15.0136i	0.223063	−	0.848621i	−0.757568	−	0.652757i	$-0.773612\pi$
$313$	3.94639	−	15.0136i	0.223063	−	0.848621i	0.980631	−	0.195864i	$-0.0627512\pi$
$314$	−0.257092	−	8.99940i	−0.0145085	−	0.507865i
$315$	−0.121078	+	0.229468i	−0.00682197	+	0.0129291i
$316$	6.37009	+	31.4376i	0.358345	+	1.76850i
$317$	−5.03412	−	19.1518i	−0.282744	−	1.07567i	−0.945179	−	0.326551i	$-0.894113\pi$
$317$	−5.03412	−	19.1518i	−0.282744	−	1.07567i	0.662435	−	0.749119i	$-0.269523\pi$
$318$	−3.02099	+	0.887042i	−0.169409	+	0.0497429i
$319$	−0.0186802	+	1.40334i	−0.00104589	+	0.0785718i
$320$	9.18745	+	2.69768i	0.513594	+	0.150805i
$321$	0.342430	−	11.9866i	0.0191126	−	0.669027i
$322$	0.749300	+	0.423149i	0.0417568	+	0.0235812i
$323$	1.02449	+	0.744338i	0.0570043	+	0.0414161i
$324$	−7.21444	−	3.04885i	−0.400802	−	0.169381i
$325$	−1.86697	+	0.323092i	−0.103561	+	0.0179219i
$326$	−0.705571	−	8.21482i	−0.0390780	−	0.454977i
$327$	0.474099	−	5.51983i	0.0262177	−	0.305247i
$328$	3.47434	+	0.601258i	0.191838	+	0.0331989i
$329$	−0.214086	−	0.137585i	−0.0118029	−	0.00758529i
$330$	−4.49880	−	3.16489i	−0.247651	−	0.174222i
$331$	21.8894	−	14.0675i	1.20315	−	0.773218i	0.223652	−	0.974669i	$-0.428202\pi$
$331$	21.8894	−	14.0675i	1.20315	−	0.773218i	0.979499	+	0.201451i	$0.0645656\pi$
$332$	−29.6885	+	12.5465i	−1.62937	+	0.688576i
$333$	−11.2811	−	2.62331i	−0.618202	−	0.143757i
$334$	6.54764	+	16.8175i	0.358271	+	0.920212i
$335$	0.969213	−	1.60726i	0.0529537	−	0.0878139i
$336$	−0.0977332	−	0.300792i	−0.00533178	−	0.0164095i
$337$	13.1741	+	17.0845i	0.717640	+	0.930652i	0.999586	−	0.0287783i	$-0.00916167\pi$
$337$	13.1741	+	17.0845i	0.717640	+	0.930652i	−0.281946	+	0.959430i	$0.590980\pi$
$338$	−7.00415	+	17.9900i	−0.380976	+	0.978528i
$339$	0.183766	−	0.268749i	0.00998080	−	0.0145965i
$340$	1.08261	+	7.52974i	0.0587129	+	0.408357i
$341$	16.2863	−	0.248376i	0.881950	−	0.0134503i
$342$	−0.251930	+	1.75221i	−0.0136228	+	0.0947486i
$343$	−1.13946	−	1.04579i	−0.0615250	−	0.0564672i
$344$	−2.84274	+	0.162554i	−0.153270	+	0.00876432i
$345$	0.609002	−	3.00554i	0.0327875	−	0.161813i
$346$	−6.36369	−	5.20356i	−0.342114	−	0.279745i
$347$	−4.72312	+	2.32220i	−0.253551	+	0.124662i	−0.563571	−	0.826067i	$-0.690573\pi$
$347$	−4.72312	+	2.32220i	−0.253551	+	0.124662i	0.310021	+	0.950730i	$0.399664\pi$
$348$	−0.711693	−	0.253932i	−0.0381508	−	0.0136122i
$349$	8.60351	−	11.1572i	0.460535	−	0.597233i	−0.503175	−	0.864185i	$-0.667835\pi$
$349$	8.60351	−	11.1572i	0.460535	−	0.597233i	0.963710	+	0.266952i	$0.0860165\pi$
$350$	0.117141	+	0.194256i	0.00626143	+	0.0103834i
$351$	−5.36271	+	6.18889i	−0.286240	+	0.330339i
$352$	−26.4528	+	4.99443i	−1.40994	+	0.266204i
$353$	−12.7070	−	14.6646i	−0.676323	−	0.780518i	0.309029	−	0.951053i	$-0.399996\pi$
$353$	−12.7070	−	14.6646i	−0.676323	−	0.780518i	−0.985352	+	0.170534i	$0.945451\pi$
$354$	3.90764	−	12.0265i	0.207689	−	0.639200i
$355$	7.89830	−	2.81811i	0.419198	−	0.149570i
$356$	5.43488	−	5.59236i	0.288048	−	0.296394i
$357$	0.226779	−	0.208136i	0.0120024	−	0.0110157i
$358$	15.1876	+	22.2112i	0.802691	+	1.17390i
$359$	14.9394	−	3.47401i	0.788471	−	0.183351i	0.187121	−	0.982337i	$-0.440084\pi$
$359$	14.9394	−	3.47401i	0.788471	−	0.183351i	0.601350	+	0.798986i	$0.294630\pi$
$360$	−0.813874	+	0.591314i	−0.0428950	+	0.0311650i
$361$	−18.7418	+	2.15042i	−0.986411	+	0.113180i
$362$	−38.6309			−2.03040
$363$	8.80419	+	1.24843i	0.462100	+	0.0655257i
$364$	−0.462776			−0.0242561
$365$	9.13332	−	1.04795i	0.478060	−	0.0548523i
$366$	16.6603	−	12.1044i	0.870846	−	0.632707i
$367$	−16.6521	+	3.87228i	−0.869233	+	0.202131i	−0.637314	−	0.770604i	$-0.719955\pi$
$367$	−16.6521	+	3.87228i	−0.869233	+	0.202131i	−0.231918	+	0.972735i	$0.574500\pi$
$368$	−7.57645	−	11.0802i	−0.394950	−	0.577596i
$369$	14.2181	−	13.0492i	0.740162	−	0.679315i
$370$	−7.05745	+	7.26194i	−0.366899	+	0.377530i
$371$	−0.197703	+	0.0705404i	−0.0102643	+	0.00366228i
$372$	−2.70999	+	8.34049i	−0.140506	+	0.432434i
$373$	−4.53006	−	5.22796i	−0.234557	−	0.270694i	0.626252	−	0.779620i	$-0.284588\pi$
$373$	−4.53006	−	5.22796i	−0.234557	−	0.270694i	−0.860810	+	0.508927i	$0.830042\pi$
$374$	−13.5197	−	19.1389i	−0.699086	−	0.989647i
$375$	0.529381	−	0.610938i	0.0273371	−	0.0315487i
$376$	−0.509551	−	0.844995i	−0.0262781	−	0.0435773i
$377$	0.489598	−	0.634923i	0.0252156	−	0.0327002i
$378$	0.923405	+	0.329470i	0.0474948	+	0.0169461i
$379$	1.26733	−	0.623104i	0.0650983	−	0.0320067i	−0.408382	−	0.912811i	$-0.633907\pi$
$379$	1.26733	−	0.623104i	0.0650983	−	0.0320067i	0.473480	+	0.880805i	$0.342998\pi$
$380$	0.628825	+	0.514187i	0.0322580	+	0.0263773i
$381$	2.33907	−	11.5438i	0.119834	−	0.591406i
$382$	26.4024	−	1.50974i	1.35086	−	0.0772452i
$383$	12.2867	+	11.2766i	0.627820	+	0.576208i	0.925636	−	0.378415i	$-0.123531\pi$
$383$	12.2867	+	11.2766i	0.627820	+	0.576208i	−0.297816	+	0.954623i	$0.596258\pi$
$384$	0.392428	−	2.72940i	0.0200260	−	0.139284i
$385$	−0.311490	−	0.193535i	−0.0158750	−	0.00986346i
$386$	7.77590	+	54.0826i	0.395783	+	2.75273i
$387$	−8.79654	+	12.8645i	−0.447153	+	0.653941i
$388$	−1.69370	+	4.35022i	−0.0859844	+	0.220849i
$389$	−2.66568	−	3.45692i	−0.135155	−	0.175273i	0.719460	−	0.694533i	$-0.244389\pi$
$389$	−2.66568	−	3.45692i	−0.135155	−	0.175273i	−0.854616	+	0.519261i	$0.826207\pi$
$390$	0.971035	+	2.98854i	0.0491703	+	0.151331i
$391$	6.74617	−	11.1873i	0.341169	−	0.565765i
$392$	−1.08691	−	2.79170i	−0.0548971	−	0.141002i
$393$	12.0242	+	2.79612i	0.606543	+	0.141046i
$394$	4.89453	−	2.06844i	0.246583	−	0.104207i
$395$	12.2158	−	7.85065i	0.614646	−	0.395009i
$396$	7.78984	−	15.3251i	0.391454	−	0.770117i
$397$	−26.0587	−	16.7469i	−1.30785	−	0.840502i	−0.313803	−	0.949488i	$-0.601603\pi$
$397$	−26.0587	−	16.7469i	−1.30785	−	0.840502i	−0.994043	+	0.108986i	$0.965240\pi$
$398$	3.46569	+	0.599761i	0.173719	+	0.0300633i
$399$	0.00281268	−	0.0327474i	0.000140810	−	0.00163942i
$400$	−0.302797	−	3.52541i	−0.0151399	−	0.176270i
$401$	10.2752	−	1.77819i	0.513117	−	0.0887984i	0.0919180	−	0.995767i	$-0.470700\pi$
$401$	10.2752	−	1.77819i	0.513117	−	0.0887984i	0.421199	+	0.906968i	$0.361609\pi$
$402$	−2.86722	−	1.21170i	−0.143004	−	0.0604339i
$403$	−7.52798	−	5.46939i	−0.374995	−	0.272450i
$404$	−14.9084	−	8.41918i	−0.741722	−	0.418870i
$405$	−0.101249	+	3.54419i	−0.00503113	+	0.176112i
$406$	−0.0921020	−	0.0270436i	−0.00457095	−	0.00134215i
$407$	4.82076	−	15.6446i	0.238956	−	0.775474i
$408$	1.14517	−	0.336253i	0.0566945	−	0.0166470i
$409$	−1.49961	−	5.70512i	−0.0741511	−	0.282100i	0.919731	−	0.392550i	$-0.128407\pi$
$409$	−1.49961	−	5.70512i	−0.0741511	−	0.282100i	−0.993882	+	0.110450i	$0.964771\pi$
$410$	−3.35081	−	16.5369i	−0.165485	−	0.816698i
$411$	−1.33755	+	2.53493i	−0.0659762	+	0.125039i
$412$	−0.340305	−	11.9122i	−0.0167656	−	0.586874i
$413$	0.214322	−	0.815365i	0.0105461	−	0.0401215i
$414$	18.2323	+	1.04256i	0.896070	+	0.0512392i
$415$	10.1689	+	10.4635i	0.499171	+	0.513635i
$416$	13.8010	+	6.78550i	0.676651	+	0.332687i
$417$	−0.469656	−	1.02840i	−0.0229992	−	0.0503611i
$418$	−2.44543	−	0.529487i	−0.119610	−	0.0258981i
$419$	−13.2090	+	28.9236i	−0.645300	+	1.41301i	0.250309	+	0.968166i	$0.419468\pi$
$419$	−13.2090	+	28.9236i	−0.645300	+	1.41301i	−0.895609	+	0.444843i	$0.853259\pi$
$420$	0.152850	−	0.124985i	0.00745832	−	0.00609864i
$421$	−17.5432	−	33.2480i	−0.855002	−	1.62041i	−0.782171	−	0.623064i	$-0.785888\pi$
$421$	−17.5432	−	33.2480i	−0.855002	−	1.62041i	−0.0728306	−	0.997344i	$-0.523203\pi$
$422$	−5.72552	+	3.23335i	−0.278714	+	0.157397i
$423$	−5.36548	−	0.615631i	−0.260878	−	0.0299330i
$424$	−0.808606	−	0.0927789i	−0.0392694	−	0.00450574i
$425$	2.99864	−	1.69341i	0.145455	−	0.0821424i
$426$	−6.49037	−	12.3006i	−0.314460	−	0.595967i
$427$	1.06285	−	0.869089i	0.0514350	−	0.0420582i
$428$	13.6121	−	29.8064i	0.657968	−	1.44075i
$429$	−3.59556	−	3.58860i	−0.173595	−	0.173259i
$430$	5.66030	+	12.3943i	0.272964	+	0.597707i
$431$	4.02937	+	1.98111i	0.194088	+	0.0954266i	0.535678	−	0.844423i	$-0.320056\pi$
$431$	4.02937	+	1.98111i	0.194088	+	0.0954266i	−0.341590	+	0.939849i	$0.610965\pi$
$432$	−10.6583	−	10.9672i	−0.512799	−	0.527657i
$433$	25.1587	+	1.43863i	1.20905	+	0.0691360i	0.649958	−	0.759970i	$-0.274786\pi$
$433$	25.1587	+	1.43863i	1.20905	+	0.0691360i	0.559092	+	0.829106i	$0.311150\pi$
$434$	−0.283208	+	1.07744i	−0.0135944	+	0.0517185i
$435$	0.00976836	+	0.341937i	0.000468357	+	0.0163946i
$436$	7.06480	−	13.3893i	0.338343	−	0.641231i
$437$	−0.277024	−	1.36717i	−0.0132519	−	0.0654005i
$438$	−3.87600	−	14.7458i	−0.185202	−	0.704582i
$439$	−26.4567	+	7.76839i	−1.26271	+	0.370765i	−0.843502	−	0.537125i	$-0.819510\pi$
$439$	−26.4567	+	7.76839i	−1.26271	+	0.370765i	−0.419207	+	0.907890i	$0.637692\pi$
$440$	−0.752756	−	1.20632i	−0.0358862	−	0.0575089i
$441$	−15.7327	−	4.61954i	−0.749176	−	0.219978i
$442$	−0.382265	+	13.3810i	−0.0181825	+	0.636470i
$443$	30.9142	+	17.4581i	1.46878	+	0.829458i	0.998589	−	0.0531067i	$-0.0169124\pi$
$443$	30.9142	+	17.4581i	1.46878	+	0.829458i	0.470191	+	0.882565i	$0.344185\pi$
$444$	7.13072	+	5.18077i	0.338409	+	0.245868i
$445$	−3.25180	−	1.37422i	−0.154150	−	0.0651443i
$446$	−5.05865	+	0.875434i	−0.239534	+	0.0414530i
$447$	−1.28570	−	14.9692i	−0.0608116	−	0.708017i
$448$	0.0906015	−	1.05485i	0.00428052	−	0.0498372i
$449$	21.7328	+	3.76101i	1.02563	+	0.177493i	0.658426	−	0.752646i	$-0.271223\pi$
$449$	21.7328	+	3.76101i	1.02563	+	0.177493i	0.367208	+	0.930139i	$0.380314\pi$
$450$	4.04984	+	2.60267i	0.190911	+	0.122691i
$451$	16.9842	+	21.3443i	0.799755	+	1.00507i
$452$	0.748415	−	0.480977i	0.0352025	−	0.0226233i
$453$	−5.45505	+	2.30532i	−0.256301	+	0.108314i
$454$	5.84113	+	1.35830i	0.274138	+	0.0637480i
$455$	0.0760076	+	0.195224i	0.00356329	+	0.00915224i
$456$	0.0658112	−	0.109136i	0.00308189	−	0.00511074i
$457$	0.837829	+	2.57857i	0.0391920	+	0.120621i	0.968738	−	0.248085i	$-0.0798012\pi$
$457$	0.837829	+	2.57857i	0.0391920	+	0.120621i	−0.929546	+	0.368705i	$0.879801\pi$
$458$	6.48464	+	8.40943i	0.303007	+	0.392947i
$459$	5.40006	−	13.8700i	0.252053	−	0.647394i
$460$	4.72989	−	6.91725i	0.220532	−	0.322518i
$461$	4.99873	+	34.7669i	0.232814	+	1.61926i	0.685835	+	0.727757i	$0.259437\pi$
$461$	4.99873	+	34.7669i	0.232814	+	1.61926i	−0.453021	+	0.891500i	$0.649654\pi$
$462$	−0.244186	+	0.557017i	−0.0113605	+	0.0259148i
$463$	1.87443	−	13.0369i	0.0871120	−	0.605877i	−0.898768	−	0.438424i	$-0.855537\pi$
$463$	1.87443	−	13.0369i	0.0871120	−	0.605877i	0.985880	−	0.167453i	$-0.0535542\pi$
$464$	1.10312	+	1.01244i	0.0512112	+	0.0470012i
$465$	3.96356	−	0.226645i	0.183806	−	0.0105104i
$466$	2.71780	−	13.4129i	0.125900	−	0.621339i
$467$	25.9394	+	21.2106i	1.20033	+	0.981508i	0.999998	+	0.00178020i	$0.000566655\pi$
$467$	25.9394	+	21.2106i	1.20033	+	0.981508i	0.200335	+	0.979727i	$0.435797\pi$
$468$	−8.81340	+	4.33325i	−0.407399	+	0.200305i
$469$	−0.195456	−	0.0697386i	−0.00902533	−	0.00322023i
$470$	−2.88340	+	3.73926i	−0.133001	+	0.172479i
$471$	1.83192	+	3.03790i	0.0844103	+	0.139979i
$472$	2.14068	−	2.47047i	0.0985326	−	0.113713i
$473$	−17.2631	−	13.6820i	−0.793756	−	0.629101i
$474$	−15.7708	−	18.2004i	−0.724376	−	0.835974i
$475$	0.113632	−	0.349724i	0.00521380	−	0.0160464i
$476$	0.792205	−	0.282658i	0.0363106	−	0.0129556i
$477$	−3.10467	+	3.19463i	−0.142153	+	0.146272i
$478$	14.2963	−	13.1210i	0.653898	−	0.600142i
$479$	12.0396	+	17.6073i	0.550103	+	0.804499i	0.995883	−	0.0906427i	$-0.0288921\pi$
$479$	12.0396	+	17.6073i	0.550103	+	0.804499i	−0.445781	+	0.895142i	$0.647074\pi$
$480$	−6.39093	+	1.48615i	−0.291705	+	0.0678331i
$481$	−7.56604	+	5.49705i	−0.344982	+	0.250644i
$482$	19.1943	−	2.20234i	0.874276	−	0.100314i
$483$	−0.339075			−0.0154284
$484$	20.8325	+	12.5074i	0.946930	+	0.568519i
$485$	2.11334			0.0959617
$486$	32.2697	−	3.70260i	1.46378	−	0.167953i
$487$	−26.3683	+	19.1577i	−1.19486	+	0.868117i	−0.993769	−	0.111456i	$-0.964449\pi$
$487$	−26.3683	+	19.1577i	−1.19486	+	0.868117i	−0.201091	+	0.979573i	$0.564449\pi$
$488$	5.18512	−	1.20575i	0.234719	−	0.0545816i
$489$	1.83377	+	2.68181i	0.0829261	+	0.121276i
$490$	−10.5619	+	9.69362i	−0.477138	+	0.437913i
$491$	−23.2944	+	23.9693i	−1.05126	+	1.08172i	−0.0547293	+	0.998501i	$0.517430\pi$
$491$	−23.2944	+	23.9693i	−1.05126	+	1.08172i	−0.996531	+	0.0832203i	$0.973479\pi$
$492$	−13.8322	+	4.93533i	−0.623605	+	0.222502i
$493$	−0.450318	+	1.38594i	−0.0202813	+	0.0624194i
$494$	0.936054	+	1.08026i	0.0421151	+	0.0486034i
$495$	−7.74439	−	0.769134i	−0.348085	−	0.0345700i
$496$	11.3797	−	13.1328i	0.510962	−	0.589682i
$497$	−0.478822	−	0.794037i	−0.0214781	−	0.0356174i
$498$	14.7767	−	19.1628i	0.662161	−	0.858705i
$499$	20.7669	+	7.40962i	0.929654	+	0.331700i	0.757099	−	0.653300i	$-0.226616\pi$
$499$	20.7669	+	7.40962i	0.929654	+	0.331700i	0.172555	+	0.985000i	$0.444798\pi$
$500$	1.98233	−	0.974645i	0.0886524	−	0.0435875i
$501$	−5.50504	−	4.50145i	−0.245947	−	0.201110i
$502$	11.6196	−	57.3451i	0.518609	−	2.55944i
$503$	−1.07748	+	0.0616123i	−0.0480423	+	0.00274716i	−0.0810934	−	0.996707i	$-0.525841\pi$
$503$	−1.07748	+	0.0616123i	−0.0480423	+	0.00274716i	0.0330512	+	0.999454i	$0.489478\pi$
$504$	0.0819502	+	0.0752132i	0.00365035	+	0.00335026i
$505$	−1.10306	+	7.67197i	−0.0490857	+	0.341398i
$506$	−3.28343	+	25.6025i	−0.145966	+	1.13817i
$507$	−1.08258	−	7.52952i	−0.0480792	−	0.334398i
$508$	18.1667	−	26.5680i	0.806018	−	1.17876i
$509$	7.72788	−	19.8489i	0.342532	−	0.879787i	−0.650235	−	0.759733i	$-0.725330\pi$
$509$	7.72788	−	19.8489i	0.342532	−	0.879787i	0.992767	−	0.120054i	$-0.0383068\pi$
$510$	−3.48763	−	4.52284i	−0.154435	−	0.200275i
$511$	−0.314114	−	0.966742i	−0.0138956	−	0.0427662i
$512$	−16.3977	+	27.1926i	−0.724684	+	1.20175i
$513$	−0.576614	−	1.48102i	−0.0254581	−	0.0653887i
$514$	14.8667	+	3.45711i	0.655743	+	0.152487i
$515$	−4.96933	+	2.10006i	−0.218975	+	0.0925396i
$516$	9.97713	−	6.41191i	0.439219	−	0.282269i
$517$	1.40168	−	7.50368i	0.0616456	−	0.330012i
$518$	0.941924	+	0.605338i	0.0413858	+	0.0265970i
$519$	3.19163	+	0.552332i	0.140097	+	0.0242447i
$520$	−0.0695136	+	0.809332i	−0.00304837	+	0.0354915i
$521$	−1.95058	−	22.7102i	−0.0854564	−	0.994951i	−0.905975	−	0.423331i	$-0.860861\pi$
$521$	−1.95058	−	22.7102i	−0.0854564	−	0.994951i	0.820519	−	0.571620i	$-0.193685\pi$
$522$	−2.00727	+	0.347372i	−0.0878560	+	0.0152041i
$523$	−19.4462	−	8.21802i	−0.850322	−	0.359349i	−0.0798374	−	0.996808i	$-0.525440\pi$
$523$	−19.4462	−	8.21802i	−0.850322	−	0.359349i	−0.770484	+	0.637459i	$0.779986\pi$
$524$	27.2912	+	19.8282i	1.19222	+	0.866199i
$525$	−0.0778299	−	0.0439525i	−0.00339677	−	0.00191825i
$526$	−0.159365	+	5.57849i	−0.00694863	+	0.243234i
$527$	16.2274	+	4.76480i	0.706878	+	0.207558i
$528$	7.25172	−	6.11657i	0.315591	−	0.266190i
$529$	8.26058	−	2.42553i	0.359156	−	0.105458i
$530$	0.990136	+	3.76687i	0.0430087	+	0.163622i
$531$	−3.55308	−	17.5352i	−0.154191	−	0.760961i
$532$	0.0419133	−	0.0794345i	0.00181717	−	0.00344392i
$533$	−0.444986	−	15.5765i	−0.0192745	−	0.674695i
$534$	−1.48840	+	5.66247i	−0.0644094	+	0.245039i
$535$	−14.8097	−	0.846847i	−0.640277	−	0.0366124i
$536$	−0.560798	−	0.577047i	−0.0242228	−	0.0249246i
$537$	−9.51451	−	4.67797i	−0.410582	−	0.201869i
$538$	−22.1921	−	48.5940i	−0.956770	−	2.09504i
$539$	8.07806	−	21.7224i	0.347947	−	0.935651i
$540$	3.96609	−	8.68452i	0.170673	−	0.373722i
$541$	30.8589	−	25.2332i	1.32673	−	1.08486i	0.337059	−	0.941483i	$-0.390568\pi$
$541$	30.8589	−	25.2332i	1.32673	−	1.08486i	0.989668	−	0.143376i	$-0.0457959\pi$
$542$	−1.81383	−	3.43759i	−0.0779107	−	0.147657i
$543$	13.2543	−	7.48506i	0.568798	−	0.321215i
$544$	−27.7698	−	3.18629i	−1.19062	−	0.136611i
$545$	−6.80867	−	0.781222i	−0.291651	−	0.0334639i
$546$	0.302538	−	0.170851i	0.0129474	−	0.00731174i
$547$	15.0611	+	28.5439i	0.643965	+	1.22045i	0.962176	+	0.272430i	$0.0878273\pi$
$547$	15.0611	+	28.5439i	0.643965	+	1.22045i	−0.318210	+	0.948020i	$0.603082\pi$
$548$	−6.06307	+	4.95775i	−0.259001	+	0.211784i
$549$	12.1038	−	26.5036i	0.516577	−	1.13115i
$550$	−4.07239	+	5.45109i	−0.173647	+	0.232435i
$551$	0.0646405	+	0.141543i	0.00275378	+	0.00602994i
$552$	−1.17984	−	0.580088i	−0.0502173	−	0.0246902i
$553$	−1.11899	−	1.15141i	−0.0475843	−	0.0489630i
$554$	61.6603	+	3.52586i	2.61969	+	0.149800i
$555$	1.01436	−	3.85903i	0.0430572	−	0.163807i
$556$	−0.0882200	−	3.08810i	−0.00374136	−	0.130965i
$557$	16.1069	−	30.5260i	0.682472	−	1.29343i	−0.262073	−	0.965048i	$-0.584406\pi$
$557$	16.1069	−	30.5260i	0.682472	−	1.29343i	0.944545	−	0.328381i	$-0.106503\pi$
$558$	4.69509	+	23.1712i	0.198759	+	0.980915i
$559$	3.19905	+	12.1705i	0.135305	+	0.514755i
$560$	−0.375390	+	0.110224i	−0.0158631	+	0.00465783i
$561$	8.34694	+	3.94702i	0.352408	+	0.166643i
$562$	25.1598	+	7.38758i	1.06130	+	0.311626i
$563$	−0.956398	+	33.4783i	−0.0403074	+	1.41094i	0.688010	+	0.725702i	$0.258485\pi$
$563$	−0.956398	+	33.4783i	−0.0403074	+	1.41094i	−0.728317	+	0.685240i	$0.759697\pi$
$564$	3.57872	+	2.02099i	0.150691	+	0.0850992i
$565$	−0.325824	−	0.236725i	−0.0137075	−	0.00995910i
$566$	−44.2980	−	18.7205i	−1.86199	−	0.786881i
$567$	0.386298	−	0.0668515i	0.0162230	−	0.00280750i
$568$	−0.307666	−	3.58209i	−0.0129094	−	0.150301i
$569$	−1.59765	+	18.6011i	−0.0669769	+	0.779798i	0.883384	+	0.468649i	$0.155259\pi$
$569$	−1.59765	+	18.6011i	−0.0669769	+	0.779798i	−0.950361	+	0.311149i	$0.899286\pi$
$570$	−0.600922	−	0.103994i	−0.0251699	−	0.00435582i
$571$	−15.8239	−	10.1694i	−0.662212	−	0.425578i	0.165899	−	0.986143i	$-0.446948\pi$
$571$	−15.8239	−	10.1694i	−0.662212	−	0.425578i	−0.828110	+	0.560565i	$0.810584\pi$
$572$	−5.23293	−	12.8572i	−0.218800	−	0.537588i
$573$	−8.76618	+	5.63368i	−0.366213	+	0.235350i
$574$	−1.71848	+	0.726235i	−0.0717279	+	0.0303125i
$575$	−3.69492	−	0.859217i	−0.154089	−	0.0358318i
$576$	−8.15177	−	20.9377i	−0.339657	−	0.872402i
$577$	15.1275	−	25.0862i	0.629768	−	1.04435i	−0.363840	−	0.931462i	$-0.618534\pi$
$577$	15.1275	−	25.0862i	0.629768	−	1.04435i	0.993607	−	0.112891i	$-0.0360110\pi$
$578$	3.25895	+	10.0300i	0.135555	+	0.417194i
$579$	−13.1469	−	17.0492i	−0.546366	−	0.708540i
$580$	−0.339134	+	0.871058i	−0.0140818	+	0.0361687i
$581$	0.910616	−	1.33173i	0.0377787	−	0.0552496i
$582$	−0.498800	−	3.46923i	−0.0206759	−	0.143804i
$583$	−4.19538	−	4.69511i	−0.173755	−	0.194452i
$584$	0.560914	−	3.90124i	0.0232108	−	0.161435i
$585$	3.27554	+	3.00626i	0.135427	+	0.124294i
$586$	−48.2095	+	2.75672i	−1.99152	+	0.113879i
$587$	−6.38767	+	31.5244i	−0.263647	+	1.30115i	0.601193	+	0.799104i	$0.294692\pi$
$587$	−6.38767	+	31.5244i	−0.263647	+	1.30115i	−0.864841	+	0.502047i	$0.832581\pi$
$588$	9.65982	+	7.89880i	0.398364	+	0.325741i
$589$	1.62061	−	0.796802i	0.0667762	−	0.0328317i
$590$	−14.7330	−	5.25673i	−0.606549	−	0.216416i
$591$	−1.27854	+	1.65804i	−0.0525922	+	0.0682028i
$592$	−9.01893	−	14.9562i	−0.370676	−	0.614697i
$593$	−18.1620	+	20.9600i	−0.745823	+	0.860726i	−0.994156	−	0.107949i	$-0.965572\pi$
$593$	−18.1620	+	20.9600i	−0.745823	+	0.860726i	0.248333	+	0.968675i	$0.420117\pi$
$594$	1.28796	+	29.3804i	0.0528457	+	1.20549i
$595$	−0.249354	−	0.287770i	−0.0102225	−	0.0117974i
$596$	12.6866	−	39.0455i	0.519665	−	1.59936i
$597$	−1.30529	+	0.465728i	−0.0534221	+	0.0190610i
$598$	10.2770	−	10.5748i	0.420259	−	0.432436i
$599$	6.18112	−	5.67298i	0.252554	−	0.231792i	−0.539892	−	0.841734i	$-0.681535\pi$
$599$	6.18112	−	5.67298i	0.252554	−	0.231792i	0.792445	+	0.609943i	$0.208808\pi$
$600$	−0.195622	−	0.286088i	−0.00798622	−	0.0116795i
$601$	−25.6392	+	5.96214i	−1.04584	+	0.243201i	−0.714009	−	0.700137i	$-0.753122\pi$
$601$	−25.6392	+	5.96214i	−1.04584	+	0.243201i	−0.331835	+	0.943337i	$0.607668\pi$
$602$	1.21885	−	0.885546i	0.0496766	−	0.0360922i
$603$	−4.37540	+	0.502030i	−0.178180	+	0.0204442i
$604$	−16.1827			−0.658466
$605$	1.85472	−	10.8425i	0.0754053	−	0.440811i
$606$	12.8546			0.522181
$607$	0.414184	−	0.0475231i	0.0168112	−	0.00192890i	−0.105582	−	0.994411i	$-0.533670\pi$
$607$	0.414184	−	0.0475231i	0.0168112	−	0.00192890i	0.122393	+	0.992482i	$0.460943\pi$
$608$	−2.41467	+	1.75436i	−0.0979276	+	0.0711486i
$609$	0.0368403	−	0.00856684i	0.00149284	−	0.000347146i
$610$	−14.3789	−	21.0285i	−0.582184	−	0.851417i
$611$	−3.21282	+	2.94870i	−0.129977	+	0.119292i
$612$	12.4405	−	12.8010i	0.502879	−	0.517450i
$613$	−0.837146	+	0.298693i	−0.0338120	+	0.0120641i	−0.352901	−	0.935661i	$-0.614805\pi$
$613$	−0.837146	+	0.298693i	−0.0338120	+	0.0120641i	0.319089	+	0.947725i	$0.396623\pi$
$614$	10.3340	−	31.8048i	0.417047	−	1.28354i
$615$	4.35383	+	5.02459i	0.175563	+	0.202611i
$616$	−0.114196	+	0.108062i	−0.00460110	+	0.00435396i
$617$	−23.6743	+	27.3216i	−0.953091	+	1.09993i	0.0418162	+	0.999125i	$0.486686\pi$
$617$	−23.6743	+	27.3216i	−0.953091	+	1.09993i	−0.994907	+	0.100800i	$0.967860\pi$
$618$	4.62032	+	7.66193i	0.185856	+	0.308208i
$619$	−26.3122	+	34.1222i	−1.05758	+	1.37149i	−0.132728	+	0.991153i	$0.542374\pi$
$619$	−26.3122	+	34.1222i	−1.05758	+	1.37149i	−0.924848	+	0.380336i	$0.875808\pi$
$620$	10.2175	+	3.64560i	0.410345	+	0.146411i
$621$	−14.7135	+	7.23414i	−0.590432	+	0.290296i
$622$	11.1693	+	9.13310i	0.447849	+	0.366204i
$623$	−0.0775174	+	0.382564i	−0.00310567	+	0.0153271i
$624$	−5.41079	+	0.309400i	−0.216605	+	0.0123859i
$625$	−0.736741	−	0.676175i	−0.0294696	−	0.0270470i
$626$	−4.53244	+	31.5238i	−0.181153	+	1.25994i
$627$	0.941622	−	0.292154i	0.0376048	−	0.0116675i
$628$	1.37957	+	9.59510i	0.0550507	+	0.382886i
$629$	9.59442	−	14.0314i	0.382555	−	0.559468i
$630$	0.193118	−	0.496019i	0.00769400	−	0.0197619i
$631$	4.30988	+	5.58916i	0.171574	+	0.222501i	0.869836	−	0.493342i	$-0.164225\pi$
$631$	4.30988	+	5.58916i	0.171574	+	0.222501i	−0.698262	+	0.715842i	$0.746043\pi$
$632$	−1.92378	−	5.92080i	−0.0765240	−	0.235517i
$633$	1.33795	−	2.21874i	0.0531786	−	0.0881868i
$634$	14.7394	+	37.8579i	0.585378	+	1.50353i
$635$	−14.1916	−	3.30011i	−0.563175	−	0.130961i
$636$	3.12268	−	1.31966i	0.123822	−	0.0523277i
$637$	−11.1381	+	7.15802i	−0.441307	+	0.283611i
$638$	−0.290113	−	2.86466i	−0.0114857	−	0.113413i
$639$	−16.5540	−	10.6386i	−0.654868	−	0.420858i
$640$	−3.36111	−	0.581663i	−0.132859	−	0.0229922i
$641$	−2.78929	+	32.4751i	−0.110170	+	1.28269i	0.707380	+	0.706833i	$0.249877\pi$
$641$	−2.78929	+	32.4751i	−0.110170	+	1.28269i	−0.817550	+	0.575857i	$0.804668\pi$
$642$	2.10527	+	24.5112i	0.0830885	+	0.967381i
$643$	−1.68677	+	0.291907i	−0.0665197	+	0.0115117i	−0.203685	−	0.979037i	$-0.565292\pi$
$643$	−1.68677	+	0.291907i	−0.0665197	+	0.0115117i	0.137165	+	0.990548i	$0.456201\pi$
$644$	−0.853462	−	0.360676i	−0.0336311	−	0.0142126i
$645$	−4.34356	−	3.15578i	−0.171028	−	0.124259i
$646$	−2.26220	−	1.27752i	−0.0890051	−	0.0502635i
$647$	0.941113	−	32.9433i	0.0369990	−	1.29513i	−0.742974	−	0.669320i	$-0.766586\pi$
$647$	0.941113	−	32.9433i	0.0369990	−	1.29513i	0.779973	−	0.625813i	$-0.215233\pi$
$648$	1.45852	+	0.428262i	0.0572963	+	0.0168237i
$649$	25.0767	−	3.26543i	0.984345	−	0.128179i
$650$	3.72971	−	1.09514i	0.146291	−	0.0429550i
$651$	−0.111593	−	0.424544i	−0.00437367	−	0.0166392i
$652$	1.76301	+	8.70079i	0.0690448	+	0.340749i
$653$	3.50232	−	6.63764i	0.137057	−	0.259751i	−0.806317	−	0.591484i	$-0.798542\pi$
$653$	3.50232	−	6.63764i	0.137057	−	0.259751i	0.943373	+	0.331733i	$0.107633\pi$
$654$	0.324570	+	11.3614i	0.0126917	+	0.444267i
$655$	3.88223	−	14.7695i	0.151691	−	0.577093i
$656$	29.0535	+	1.66134i	1.13435	+	0.0648645i
$657$	−15.0344	−	15.4700i	−0.586547	−	0.603542i
$658$	0.468527	+	0.230359i	0.0182651	+	0.00898034i
$659$	−5.05605	−	11.0712i	−0.196956	−	0.431273i	0.785225	−	0.619210i	$-0.212547\pi$
$659$	−5.05605	−	11.0712i	−0.196956	−	0.431273i	−0.982181	+	0.187937i	$0.939820\pi$
$660$	5.20082	+	2.83332i	0.202441	+	0.110287i
$661$	−4.00447	+	8.76857i	−0.155756	+	0.341058i	−0.971382	−	0.237521i	$-0.923665\pi$
$661$	−4.00447	+	8.76857i	−0.155756	+	0.341058i	0.815627	+	0.578579i	$0.196392\pi$
$662$	−41.3253	+	33.7915i	−1.60615	+	1.31334i
$663$	−2.46153	−	4.66511i	−0.0955978	−	0.181178i
$664$	5.44689	−	3.07600i	0.211380	−	0.119372i
$665$	−0.0403937	−	0.00463475i	−0.00156640	−	0.000179728i
$666$	23.6067	+	2.70862i	0.914743	+	0.104957i
$667$	1.39777	−	0.789358i	0.0541219	−	0.0305641i
$668$	−9.06814	−	17.1860i	−0.350857	−	0.664948i
$669$	1.56601	−	1.28052i	0.0605454	−	0.0495077i
$670$	−1.59958	+	3.50259i	−0.0617971	+	0.135317i
$671$	36.1642	+	19.7016i	1.39610	+	0.760574i
$672$	0.301382	+	0.659935i	0.0116261	+	0.0254575i
$673$	34.7406	+	17.0808i	1.33915	+	0.658416i	0.963341	−	0.268281i	$-0.0864556\pi$
$673$	34.7406	+	17.0808i	1.33915	+	0.658416i	0.375809	+	0.926697i	$0.377365\pi$
$674$	−30.8470	−	31.7408i	−1.18818	−	1.22261i
$675$	−4.31500	−	0.246741i	−0.166084	−	0.00949705i
$676$	5.28431	−	20.1036i	0.203243	−	0.773216i
$677$	−0.477185	−	16.7037i	−0.0183397	−	0.641973i	−0.955823	−	0.293943i	$-0.905032\pi$
$677$	−0.477185	−	16.7037i	−0.0183397	−	0.641973i	0.937483	−	0.348030i	$-0.113149\pi$
$678$	−0.311703	+	0.590742i	−0.0119709	+	0.0226873i
$679$	−0.0464048	−	0.229016i	−0.00178085	−	0.00878885i
$680$	−0.375333	−	1.42792i	−0.0143934	−	0.0547580i
$681$	−2.26728	+	0.665735i	−0.0868825	+	0.0255110i
$682$	−33.1366	+	4.31498i	−1.26887	+	0.165229i
$683$	−4.19112	−	1.23062i	−0.160369	−	0.0470885i	0.200563	−	0.979681i	$-0.435723\pi$
$683$	−4.19112	−	1.23062i	−0.160369	−	0.0470885i	−0.360931	+	0.932592i	$0.617541\pi$
$684$	0.0544289	−	1.90526i	0.00208114	−	0.0728495i
$685$	3.08726	+	1.74346i	0.117958	+	0.0666140i
$686$	2.56702	+	1.86505i	0.0980094	+	0.0712080i
$687$	−3.85429	−	1.62884i	−0.147050	−	0.0621440i
$688$	−23.1562	+	4.00733i	−0.882820	+	0.152778i
$689$	0.307817	+	3.58384i	0.0117269	+	0.136534i
$690$	−0.538388	+	6.26833i	−0.0204961	+	0.238631i
$691$	−7.06362	−	1.22241i	−0.268713	−	0.0465026i	0.0345732	−	0.999402i	$-0.488993\pi$
$691$	−7.06362	−	1.22241i	−0.268713	−	0.0465026i	−0.303286	+	0.952900i	$0.598084\pi$
$692$	7.44590	+	4.78519i	0.283051	+	0.181906i
$693$	0.0867029	+	0.856127i	0.00329357	+	0.0325216i
$694$	9.08362	−	5.83769i	0.344810	−	0.221596i
$695$	−1.28824	+	0.544414i	−0.0488657	+	0.0206508i
$696$	0.142845	+	0.0332172i	0.00541453	+	0.00125909i
$697$	10.2757	+	26.3930i	0.389220	+	0.999705i
$698$	−14.9265	+	24.7528i	−0.564975	+	0.936906i
$699$	1.66638	+	5.12858i	0.0630281	+	0.193981i
$700$	−0.149148	−	0.193418i	−0.00563725	−	0.00731052i
$701$	−16.1730	+	41.5399i	−0.610845	+	1.56894i	0.197545	+	0.980294i	$0.436703\pi$
$701$	−16.1730	+	41.5399i	−0.610845	+	1.56894i	−0.808390	+	0.588648i	$0.799660\pi$
$702$	9.48295	−	13.8684i	0.357911	−	0.523428i
$703$	−0.258306	−	1.79656i	−0.00974220	−	0.0677585i
$704$	30.3313	−	9.41080i	1.14316	−	0.354683i
$705$	0.264786	−	1.84163i	0.00997243	−	0.0693598i
$706$	29.3289	+	26.9178i	1.10381	+	1.01306i
$707$	0.855611	−	0.0489256i	0.0321786	−	0.00184004i
$708$	−2.70391	+	13.3443i	−0.101619	+	0.501511i
$709$	13.6425	+	11.1555i	0.512357	+	0.418952i	0.853526	−	0.521050i	$-0.174459\pi$
$709$	13.6425	+	11.1555i	0.512357	+	0.418952i	−0.341170	+	0.940002i	$0.610823\pi$
$710$	−15.4393	+	7.59100i	−0.579427	+	0.284885i
$711$	−32.0921	−	11.4504i	−1.20355	−	0.429425i
$712$	−0.924217	+	1.19855i	−0.0346365	+	0.0449174i
$713$	−9.62056	−	15.9539i	−0.360293	−	0.597478i
$714$	−0.413547	+	0.477258i	−0.0154766	+	0.0178609i
$715$	−4.56441	+	4.31924i	−0.170699	+	0.161530i
$716$	−18.9723	−	21.8953i	−0.709030	−	0.818264i
$717$	−2.36278	+	7.27188i	−0.0882396	+	0.271573i
$718$	−29.6371	+	10.5745i	−1.10605	+	0.394637i
$719$	−25.0006	+	25.7250i	−0.932364	+	0.959380i	−0.999263	−	0.0383797i	$-0.987780\pi$
$719$	−25.0006	+	25.7250i	−0.932364	+	0.959380i	0.0668990	+	0.997760i	$0.478689\pi$
$720$	−6.11706	+	5.61418i	−0.227969	+	0.209228i
$721$	0.336694	+	0.492400i	0.0125391	+	0.0183379i
$722$	37.6968	−	8.76601i	1.40293	−	0.326237i
$723$	−6.15888	+	4.47469i	−0.229051	+	0.166415i
$724$	41.3235	−	4.74143i	1.53578	−	0.176214i
$725$	0.423159			0.0157157
$726$	−18.2367	−	0.485593i	−0.676827	−	0.0180220i
$727$	−0.0264828			−0.000982191			−0.000491096	−	1.00000i	$-0.500156\pi$
$727$	−0.0264828			−0.000982191			−0.000491096		1.00000i	$0.500156\pi$
$728$	0.0892314	−	0.0102384i	0.00330714	−	0.000379459i
$729$	−1.74893	+	1.27067i	−0.0647750	+	0.0470618i
$730$	−18.3705	+	4.27188i	−0.679923	+	0.158109i
$731$	−12.9099	−	18.8801i	−0.477489	−	0.698305i
$732$	−16.3358	+	14.9929i	−0.603790	+	0.554154i
$733$	7.91078	−	8.14000i	0.292191	−	0.300658i	−0.555103	−	0.831782i	$-0.687321\pi$
$733$	7.91078	−	8.14000i	0.292191	−	0.300658i	0.847294	+	0.531124i	$0.178230\pi$
$734$	33.0348	−	11.7868i	1.21934	−	0.435059i
$735$	1.74558	−	5.37235i	0.0643868	−	0.198162i
$736$	20.1637	+	23.2701i	0.743244	+	0.857749i
$737$	−0.272621	−	6.21891i	−0.0100421	−	0.229077i
$738$	−25.9276	+	29.9220i	−0.954408	+	1.10145i
$739$	20.9600	+	34.7583i	0.771027	+	1.27861i	0.955273	+	0.295725i	$0.0955612\pi$
$739$	20.9600	+	34.7583i	0.771027	+	1.27861i	−0.184246	+	0.982880i	$0.558984\pi$
$740$	6.65805	−	8.63431i	0.244755	−	0.317404i
$741$	−0.530472	−	0.189272i	−0.0194874	−	0.00695308i
$742$	0.386463	−	0.190011i	0.0141875	−	0.00697553i
$743$	3.91767	+	3.20346i	0.143725	+	0.117524i	0.702142	−	0.712037i	$-0.252227\pi$
$743$	3.91767	+	3.20346i	0.143725	+	0.117524i	−0.558416	+	0.829561i	$0.688591\pi$
$744$	0.338011	−	1.66815i	0.0123921	−	0.0611573i
$745$	−18.5552	+	1.06102i	−0.679809	+	0.0388729i
$746$	10.4558	+	9.59626i	0.382814	+	0.351344i
$747$	4.87251	−	33.8890i	0.178276	−	1.23993i
$748$	16.8111	+	18.8135i	0.614673	+	0.687889i
$749$	0.233421	+	1.62348i	0.00852901	+	0.0593205i
$750$	−0.936112	+	1.36902i	−0.0341820	+	0.0499895i
$751$	12.8933	−	33.1161i	0.470483	−	1.20843i	−0.474193	−	0.880421i	$-0.657260\pi$
$751$	12.8933	−	33.1161i	0.470483	−	1.20843i	0.944676	−	0.328004i	$-0.106376\pi$
$752$	−4.97304	−	6.44915i	−0.181348	−	0.235176i
$753$	7.12438	+	21.9266i	0.259627	+	0.799050i
$754$	−0.849418	+	1.40860i	−0.0309340	+	0.0512982i
$755$	2.65790	+	6.82675i	0.0967307	+	0.248451i
$756$	−1.02821	−	0.239099i	−0.0373955	−	0.00869594i
$757$	−1.40946	+	0.595643i	−0.0512277	+	0.0216490i	−0.414733	−	0.909943i	$-0.636125\pi$
$757$	−1.40946	+	0.595643i	−0.0512277	+	0.0216490i	0.363506	+	0.931592i	$0.381580\pi$
$758$	−2.43736	+	1.56639i	−0.0885288	+	0.0568940i
$759$	−3.83415	−	9.42046i	−0.139171	−	0.341941i
$760$	−0.132624	−	0.0852324i	−0.00481079	−	0.00309171i
$761$	−30.6500	−	5.30419i	−1.11106	−	0.192277i	−0.414694	−	0.909961i	$-0.636111\pi$
$761$	−30.6500	−	5.30419i	−1.11106	−	0.192277i	−0.696369	+	0.717684i	$0.745202\pi$
$762$	−2.06786	+	24.0756i	−0.0749105	+	0.872167i
$763$	0.0648462	+	0.754991i	0.00234759	+	0.0273325i
$764$	−28.0574	+	4.85552i	−1.01508	+	0.175666i
$765$	−7.44343	−	3.14562i	−0.269118	−	0.113730i
$766$	−27.6800	−	20.1107i	−1.00012	−	0.726628i
$767$	−12.5794	−	7.10394i	−0.454217	−	0.256508i
$768$	0.280534	−	9.81997i	0.0101229	−	0.354348i
$769$	9.69757	+	2.84746i	0.349703	+	0.102682i	0.451867	−	0.892085i	$-0.350758\pi$
$769$	9.69757	+	2.84746i	0.349703	+	0.102682i	−0.102163	+	0.994768i	$0.532576\pi$
$770$	0.680141	+	0.321619i	0.0245106	+	0.0115903i
$771$	−5.77065	+	1.69441i	−0.207825	+	0.0610228i
$772$	−14.9558	−	56.8978i	−0.538271	−	2.04780i
$773$	4.25297	+	20.9893i	0.152969	+	0.754931i	0.980963	+	0.194194i	$0.0622093\pi$
$773$	4.25297	+	20.9893i	0.152969	+	0.754931i	−0.827994	+	0.560737i	$0.810518\pi$
$774$	14.9206	−	28.2777i	0.536311	−	1.01642i
$775$	−0.140241	−	4.90906i	−0.00503759	−	0.176339i
$776$	0.230331	−	0.876271i	0.00826841	−	0.0314563i
$777$	−0.440465	−	0.0251867i	−0.0158016	−	0.000903568i
$778$	6.24165	+	6.42250i	0.223774	+	0.230258i
$779$	2.71398	+	1.33438i	0.0972385	+	0.0478089i
$780$	−1.40552	−	3.07766i	−0.0503257	−	0.110198i
$781$	16.6462	−	22.2818i	0.595649	−	0.797304i
$782$	−11.1338	+	24.3796i	−0.398144	+	0.871814i
$783$	1.41584	−	1.15773i	0.0505980	−	0.0413738i
$784$	−11.5386	−	21.8680i	−0.412091	−	0.781000i
$785$	3.82115	−	2.15790i	0.136383	−	0.0770188i
$786$	−25.1618	−	2.88705i	−0.897491	−	0.102978i
$787$	28.6866	+	3.29148i	1.02257	+	0.117328i	0.609020	−	0.793155i	$-0.291563\pi$
$787$	28.6866	+	3.29148i	1.02257	+	0.117328i	0.413546	+	0.910483i	$0.364290\pi$
$788$	−4.98180	+	2.81335i	−0.177469	+	0.100222i
$789$	−1.02620	−	1.94487i	−0.0365337	−	0.0692391i
$790$	−23.0624	+	18.8581i	−0.820524	+	0.670940i
$791$	−0.0184988	+	0.0405067i	−0.000657741	+	0.00144025i
$792$	−1.16297	+	3.12730i	−0.0413243	+	0.111124i
$793$	−9.77337	−	21.4007i	−0.347063	−	0.759961i
$794$	57.0294	+	28.0394i	2.02390	+	0.995083i
$795$	−1.06958	−	1.10057i	−0.0379341	−	0.0390332i
$796$	−3.78086	−	0.216198i	−0.134009	−	0.00766292i
$797$	0.793091	−	3.01723i	0.0280927	−	0.106876i	−0.951623	−	0.307268i	$-0.900585\pi$
$797$	0.793091	−	3.01723i	0.0280927	−	0.106876i	0.979716	+	0.200392i	$0.0642216\pi$
$798$	0.00192557	+	0.0674038i	6.81645e−5	+	0.00238607i
$799$	3.69884	−	7.01009i	0.130856	−	0.247999i
$800$	1.61190	+	7.95506i	0.0569894	+	0.281254i
$801$	2.10589	+	8.01162i	0.0744078	+	0.283077i
$802$	−20.5270	+	6.02728i	−0.724835	+	0.212831i
$803$	23.3069	−	19.6586i	0.822484	−	0.693737i
$804$	3.21578	+	0.944239i	0.113412	+	0.0333007i
$805$	−0.0119777	+	0.419275i	−0.000422159	+	0.0147775i
$806$	16.6226	+	9.38724i	0.585508	+	0.330651i
$807$	17.0297	+	12.3728i	0.599472	+	0.435542i
$808$	3.06087	+	1.29354i	0.107681	+	0.0455064i
$809$	6.92609	−	1.19861i	0.243509	−	0.0421408i	−0.0474612	−	0.998873i	$-0.515113\pi$
$809$	6.92609	−	1.19861i	0.243509	−	0.0421408i	0.290970	+	0.956732i	$0.406022\pi$
$810$	−0.622486	−	7.24747i	−0.0218719	−	0.254650i
$811$	0.610182	−	7.10421i	0.0214264	−	0.249463i	−0.977780	−	0.209633i	$-0.932773\pi$
$811$	0.610182	−	7.10421i	0.0214264	−	0.249463i	0.999206	−	0.0398296i	$-0.0126815\pi$
$812$	0.101841	+	0.0176242i	0.00357391	+	0.000618490i
$813$	1.28839	+	0.827998i	0.0451858	+	0.0290392i
$814$	−6.16702	+	33.0143i	−0.216154	+	1.15715i
$815$	3.38090	−	2.17277i	0.118428	−	0.0761090i
$816$	9.07351	−	3.83450i	0.317636	−	0.134234i
$817$	−2.37877	−	0.553159i	−0.0832225	−	0.0193526i
$818$	4.39073	+	11.2775i	0.153518	+	0.394309i
$819$	0.253856	−	0.420973i	0.00887044	−	0.0147100i
$820$	5.61404	+	17.2782i	0.196051	+	0.603382i
$821$	−7.02567	−	9.11105i	−0.245197	−	0.317978i	0.653179	−	0.757203i	$-0.273435\pi$
$821$	−7.02567	−	9.11105i	−0.245197	−	0.317978i	−0.898377	+	0.439225i	$0.855253\pi$
$822$	2.13337	−	5.47951i	0.0744097	−	0.191120i
$823$	18.3865	−	26.8894i	0.640913	−	0.937306i	−0.359079	−	0.933307i	$-0.616909\pi$
$823$	18.3865	−	26.8894i	0.640913	−	0.937306i	0.999992	−	0.00399852i	$-0.00127277\pi$
$824$	0.329160	+	2.28936i	0.0114668	+	0.0797537i
$825$	0.341051	−	2.65934i	0.0118739	−	0.0925862i
$826$	−0.246149	+	1.71200i	−0.00856462	+	0.0595682i
$827$	11.2985	+	10.3697i	0.392887	+	0.360589i	0.848139	−	0.529774i	$-0.177723\pi$
$827$	11.2985	+	10.3697i	0.392887	+	0.360589i	−0.455251	+	0.890363i	$0.650451\pi$
$828$	−19.6311	+	1.12255i	−0.682228	+	0.0390112i
$829$	−10.0824	+	49.7585i	−0.350175	+	1.72818i	0.287414	+	0.957806i	$0.407204\pi$
$829$	−10.0824	+	49.7585i	−0.350175	+	1.72818i	−0.637589	+	0.770377i	$0.720068\pi$
$830$	−23.1733	−	18.9487i	−0.804358	−	0.657720i
$831$	−21.8389	+	10.7375i	−0.757584	+	0.372479i
$832$	−17.0875	−	6.09679i	−0.592401	−	0.211368i
$833$	14.6948	−	19.0565i	0.509143	−	0.660268i
$834$	1.19776	+	1.98626i	0.0414751	+	0.0687787i
$835$	−5.76062	+	6.64811i	−0.199355	+	0.230067i
$836$	2.68086	+	0.266249i	0.0927195	+	0.00920842i
$837$	−13.9000	−	16.0414i	−0.480454	−	0.554473i
$838$	20.1584	−	62.0413i	0.696361	−	2.14318i
$839$	−15.1452	+	5.40379i	−0.522869	+	0.186559i	−0.584278	−	0.811553i	$-0.698622\pi$
$839$	−15.1452	+	5.40379i	−0.522869	+	0.186559i	0.0614091	+	0.998113i	$0.480441\pi$
$840$	−0.0267071	+	0.0274809i	−0.000921481	+	0.000948181i
$841$	21.2336	−	19.4880i	0.732192	−	0.672000i
$842$	43.5320	+	63.6636i	1.50021	+	2.19399i
$843$	−10.0638	+	2.34023i	−0.346615	+	0.0806018i
$844$	5.72774	−	4.16145i	0.197157	−	0.143243i
$845$	−9.34870	+	1.07266i	−0.321605	+	0.0369007i
$846$	11.0799			0.380935
$847$	−1.21570	+	0.0370890i	−0.0417719	+	0.00127439i
$848$	−6.71746			−0.230678
$849$	18.8260	−	2.16008i	0.646106	−	0.0741338i
$850$	−5.71582	+	4.15278i	−0.196051	+	0.142439i
$851$	−18.2377	+	4.24100i	−0.625181	+	0.145380i
$852$	8.45249	+	12.3614i	0.289578	+	0.423494i
$853$	19.8924	−	18.2570i	0.681102	−	0.625109i	−0.259051	−	0.965864i	$-0.583410\pi$
$853$	19.8924	−	18.2570i	0.681102	−	0.625109i	0.940152	+	0.340754i	$0.110682\pi$
$854$	−1.96306	+	2.01994i	−0.0671746	+	0.0691211i
$855$	−0.812681	+	0.289964i	−0.0277931	+	0.00991656i
$856$	−1.96523	+	6.04836i	−0.0671702	+	0.206729i
$857$	23.3040	+	26.8942i	0.796049	+	0.918689i	0.998158	−	0.0606740i	$-0.0193250\pi$
$857$	23.3040	+	26.8942i	0.796049	+	0.918689i	−0.202109	+	0.979363i	$0.564780\pi$
$858$	8.16773	+	6.47343i	0.278842	+	0.220999i
$859$	−28.4793	+	32.8669i	−0.971703	+	1.12140i	0.0208738	+	0.999782i	$0.493355\pi$
$859$	−28.4793	+	32.8669i	−0.971703	+	1.12140i	−0.992576	+	0.121622i	$0.961190\pi$
$860$	−7.57606	−	12.5635i	−0.258342	−	0.428411i
$861$	0.448899	−	0.582142i	0.0152984	−	0.0198394i
$862$	−8.67599	−	3.09559i	−0.295505	−	0.105436i
$863$	2.52529	−	1.24160i	0.0859620	−	0.0422647i	−0.397734	−	0.917501i	$-0.630203\pi$
$863$	2.52529	−	1.24160i	0.0859620	−	0.0422647i	0.483696	+	0.875236i	$0.339294\pi$
$864$	27.1576	+	22.2066i	0.923919	+	0.755485i
$865$	0.795717	−	3.92702i	0.0270552	−	0.133523i
$866$	−51.6150	+	2.95145i	−1.75395	+	0.100295i
$867$	−3.06156	−	2.80987i	−0.103976	−	0.0954282i
$868$	0.170707	−	1.18729i	0.00579417	−	0.0402993i
$869$	19.3363	−	44.1085i	0.655940	−	1.49628i
$870$	−0.0998761	−	0.694654i	−0.00338612	−	0.0235510i
$871$	−2.00725	+	2.93550i	−0.0680129	+	0.0994657i
$872$	−1.06600	+	2.73799i	−0.0360992	+	0.0927201i
$873$	−3.02818	−	3.92702i	−0.102488	−	0.132909i
$874$	0.884361	+	2.72178i	0.0299140	+	0.0920657i
$875$	−0.0570978	+	0.0946861i	−0.00193026	+	0.00320097i
$876$	5.95601	+	15.2979i	0.201235	+	0.516868i
$877$	32.9862	+	7.67061i	1.11386	+	0.259018i	0.742750	−	0.669569i	$-0.233521\pi$
$877$	32.9862	+	7.67061i	1.11386	+	0.259018i	0.371114	+	0.928587i	$0.378976\pi$
$878$	52.1075	−	22.0208i	1.75854	−	0.743166i
$879$	16.0066	−	10.2868i	0.539890	−	0.346966i
$880$	−7.30714	−	9.18301i	−0.246324	−	0.309559i
$881$	6.03401	+	3.87782i	0.203291	+	0.130647i	0.638325	−	0.769767i	$-0.279627\pi$
$881$	6.03401	+	3.87782i	0.203291	+	0.130647i	−0.435034	+	0.900414i	$0.643264\pi$
$882$	33.1468	+	5.73628i	1.11611	+	0.193151i
$883$	−4.98838	+	58.0787i	−0.167873	+	1.95450i	0.110113	+	0.993919i	$0.464879\pi$
$883$	−4.98838	+	58.0787i	−0.167873	+	1.95450i	−0.277986	+	0.960585i	$0.589667\pi$
$884$	−1.23343	−	14.3606i	−0.0414848	−	0.482999i
$885$	6.07346	−	1.05105i	0.204157	−	0.0353308i
$886$	−67.0923	−	28.3535i	−2.25401	−	0.952553i
$887$	−20.8654	−	15.1596i	−0.700593	−	0.509011i	0.179532	−	0.983752i	$-0.442542\pi$
$887$	−20.8654	−	15.1596i	−0.700593	−	0.509011i	−0.880125	+	0.474742i	$0.842542\pi$
$888$	−1.48955	−	0.841186i	−0.0499859	−	0.0282283i
$889$	−0.0460044	+	1.61036i	−0.00154294	+	0.0540099i
$890$	6.94921	+	2.04047i	0.232938	+	0.0683968i
$891$	6.22546	+	9.97651i	0.208561	+	0.334226i
$892$	5.30379	−	1.55733i	0.177584	−	0.0521434i
$893$	−0.215155	−	0.818535i	−0.00719989	−	0.0273912i
$894$	6.12125	+	30.2095i	0.204725	+	1.01036i
$895$	−6.12053	+	11.5997i	−0.204587	+	0.387735i
$896$	0.0107702	+	0.377006i	0.000359807	+	0.0125949i
$897$	−1.47711	+	5.61950i	−0.0493192	+	0.187630i
$898$	−45.1754	−	2.58323i	−1.50752	−	0.0862034i
$899$	1.44835	+	1.49032i	0.0483052	+	0.0497048i
$900$	−4.65155	−	2.28702i	−0.155052	−	0.0762338i
$901$	−2.71591	−	5.94700i	−0.0904799	−	0.198123i
$902$	−39.6089	−	39.5322i	−1.31883	−	1.31628i
$903$	−0.246607	+	0.539995i	−0.00820658	+	0.0179699i
$904$	−0.133667	+	0.109299i	−0.00444569	+	0.00363522i
$905$	−8.78727	−	16.6537i	−0.292099	−	0.553589i
$906$	10.5794	−	5.97446i	0.351477	−	0.198488i
$907$	14.5707	+	1.67183i	0.483812	+	0.0555123i	0.352467	−	0.935824i	$-0.385343\pi$
$907$	14.5707	+	1.67183i	0.483812	+	0.0555123i	0.131346	+	0.991337i	$0.458070\pi$
$908$	−6.41497	−	0.736050i	−0.212888	−	0.0244267i
$909$	15.8367	−	8.94338i	0.525269	−	0.296633i
$910$	−0.200575	−	0.380131i	−0.00664898	−	0.0126012i
$911$	−19.9708	+	16.3301i	−0.661663	+	0.541039i	−0.903129	−	0.429370i	$-0.858736\pi$
$911$	−19.9708	+	16.3301i	−0.661663	+	0.541039i	0.241466	+	0.970409i	$0.422372\pi$
$912$	0.436944	−	0.956773i	0.0144687	−	0.0316819i
$913$	47.2963	+	10.2407i	1.56528	+	0.338917i
$914$	−2.31070	−	5.05972i	−0.0764311	−	0.167361i
$915$	9.00786	+	4.42887i	0.297791	+	0.146414i
$916$	−7.96877	−	8.19967i	−0.263295	−	0.270925i
$917$	−1.68578	−	0.0963963i	−0.0556693	−	0.00318329i
$918$	−7.76278	+	29.5327i	−0.256210	+	0.974724i
$919$	−1.14926	−	40.2294i	−0.0379107	−	1.32705i	−0.766566	−	0.642166i	$-0.778036\pi$
$919$	−1.14926	−	40.2294i	−0.0379107	−	1.32705i	0.728655	−	0.684881i	$-0.240146\pi$
$920$	−0.758971	+	1.43841i	−0.0250225	+	0.0474230i
$921$	2.61684	+	12.9146i	0.0862277	+	0.425550i
$922$	−18.3191	−	69.6931i	−0.603308	−	2.29522i
$923$	−15.2455	+	4.47648i	−0.501812	+	0.147345i
$924$	0.192839	−	0.625812i	0.00634394	−	0.0205877i
$925$	−4.73596	−	1.39060i	−0.155717	−	0.0457227i
$926$	−0.771622	+	27.0103i	−0.0253571	+	0.887613i
$927$	11.0229	+	6.22489i	0.362038	+	0.204452i
$928$	−2.77870	−	2.01885i	−0.0912154	−	0.0662719i
$929$	20.4543	+	8.64405i	0.671083	+	0.283602i	0.698065	−	0.716034i	$-0.254044\pi$
$929$	20.4543	+	8.64405i	0.671083	+	0.283602i	−0.0269827	+	0.999636i	$0.508590\pi$
$930$	−8.02556	+	1.38888i	−0.263168	+	0.0455431i
$931$	−0.219890	−	2.56013i	−0.00720659	−	0.0839048i
$932$	−1.26098	+	14.6813i	−0.0413048	+	0.480903i
$933$	−5.60183	−	0.969435i	−0.183396	−	0.0317379i
$934$	−57.8302	−	37.1652i	−1.89226	−	1.21608i
$935$	5.17545	−	10.1818i	0.169255	−	0.332980i
$936$	1.60351	−	1.03051i	0.0524124	−	0.0336834i
$937$	−35.3724	+	14.9485i	−1.15557	+	0.488347i	−0.880951	−	0.473207i	$-0.843096\pi$
$937$	−35.3724	+	14.9485i	−1.15557	+	0.488347i	−0.274616	+	0.961554i	$0.588551\pi$
$938$	0.414689	+	0.0964318i	0.0135401	+	0.00314861i
$939$	−4.55291	−	11.6941i	−0.148579	−	0.381621i
$940$	2.62543	−	4.35379i	0.0856321	−	0.142005i
$941$	−4.33185	−	13.3321i	−0.141214	−	0.434613i	0.855291	−	0.518149i	$-0.173379\pi$
$941$	−4.33185	−	13.3321i	−0.141214	−	0.434613i	−0.996505	+	0.0835360i	$0.973379\pi$
$942$	−4.44427	−	5.76344i	−0.144802	−	0.187783i
$943$	11.3193	−	29.0734i	0.368608	−	0.946761i
$944$	15.2282	−	22.2706i	0.495637	−	0.724846i
$945$	0.0680104	+	0.473023i	0.00221238	+	0.0153874i
$946$	38.3854	+	23.8496i	1.24802	+	0.775418i
$947$	−2.83488	+	19.7170i	−0.0921213	+	0.640718i	0.890484	+	0.455014i	$0.150366\pi$
$947$	−2.83488	+	19.7170i	−0.0921213	+	0.640718i	−0.982606	+	0.185704i	$0.940543\pi$
$948$	19.1039	+	17.5334i	0.620465	+	0.569457i
$949$	−17.3902	+	0.994409i	−0.564511	+	0.0322799i
$950$	−0.149818	+	0.739383i	−0.00486075	+	0.0239888i
$951$	−12.3924	−	10.1332i	−0.401852	−	0.328593i
$952$	−0.146498	+	0.0720280i	−0.00474802	+	0.00233444i
$953$	4.68468	+	1.67149i	0.151752	+	0.0541449i	0.410833	−	0.911711i	$-0.365238\pi$
$953$	4.68468	+	1.67149i	0.151752	+	0.0541449i	−0.259081	+	0.965856i	$0.583420\pi$
$954$	5.58086	−	7.23739i	0.180687	−	0.234319i
$955$	6.65654	+	11.0386i	0.215400	+	0.357201i
$956$	−13.6823	+	15.7903i	−0.442518	+	0.510694i
$957$	0.654590	+	0.926657i	0.0211599	+	0.0299546i
$958$	−28.6568	−	33.0717i	−0.925860	−	1.06850i
$959$	0.121143	−	0.372841i	0.00391192	−	0.0120397i
$960$	7.29041	−	2.60121i	0.235297	−	0.0839537i
$961$	−4.79596	+	4.93492i	−0.154708	+	0.159191i
$962$	14.1356	−	12.9735i	0.455750	−	0.418283i
$963$	19.6470	+	28.7328i	0.633116	+	0.925903i
$964$	−20.2618	+	4.71169i	−0.652590	+	0.151753i
$965$	−21.5462	+	15.6542i	−0.693596	+	0.503927i
$966$	0.691104	−	0.0792968i	0.0222359	−	0.00255133i
$967$	29.5409			0.949973			0.474986	−	0.879993i	$-0.342453\pi$
$967$	29.5409			0.949973			0.474986	+	0.879993i	$0.342453\pi$
$968$	−4.29358	−	1.95076i	−0.138001	−	0.0626998i
$969$	1.02370			0.0328858
$970$	−4.30741	+	0.494230i	−0.138303	+	0.0158688i
$971$	18.7719	−	13.6386i	0.602420	−	0.437684i	−0.244317	−	0.969695i	$-0.578564\pi$
$971$	18.7719	−	13.6386i	0.602420	−	0.437684i	0.846737	+	0.532012i	$0.178564\pi$
$972$	−34.0645	+	7.92135i	−1.09262	+	0.254077i
$973$	0.0872839	+	0.127649i	0.00279819	+	0.00409223i
$974$	49.2637	−	45.2138i	1.57851	−	1.44874i
$975$	−1.06748	+	1.09841i	−0.0341866	+	0.0351772i
$976$	41.3810	−	14.7647i	1.32457	−	0.472607i
$977$	5.61153	−	17.2705i	0.179529	−	0.552533i	−0.820282	−	0.571959i	$-0.806184\pi$
$977$	5.61153	−	17.2705i	0.179529	−	0.552533i	0.999811	+	0.0194256i	$0.00618375\pi$
$978$	−4.36478	−	5.03722i	−0.139570	−	0.161073i
$979$	−11.5052	+	2.17226i	−0.367709	+	0.0694256i
$980$	10.1083	−	11.6656i	0.322898	−	0.372644i
$981$	8.30441	+	13.7713i	0.265139	+	0.439684i
$982$	41.8732	−	54.3021i	1.33623	−	1.73285i
$983$	37.4813	+	13.3733i	1.19547	+	0.426542i	0.857435	−	0.514593i	$-0.172057\pi$
$983$	37.4813	+	13.3733i	1.19547	+	0.426542i	0.338032	+	0.941135i	$0.390239\pi$
$984$	2.55791	−	1.25764i	0.0815431	−	0.0400921i
$985$	2.00505	+	1.63952i	0.0638862	+	0.0522395i
$986$	0.593722	−	2.93013i	0.0189080	−	0.0933144i
$987$	−0.205386	+	0.0117444i	−0.00653752	+	0.000373829i
$988$	−1.13389	−	1.04067i	−0.0360737	−	0.0331081i
$989$	−3.58558	+	24.9383i	−0.114015	+	0.792991i
$990$	15.9645	−	0.243469i	0.507386	−	0.00773797i
$991$	−6.42721	−	44.7023i	−0.204167	−	1.42001i	−0.791748	−	0.610848i	$-0.790829\pi$
$991$	−6.42721	−	44.7023i	−0.204167	−	1.42001i	0.587581	−	0.809166i	$-0.300081\pi$
$992$	−22.4997	+	32.9047i	−0.714365	+	1.04473i
$993$	7.63138	−	19.6010i	0.242175	−	0.622020i
$994$	1.16163	+	1.50643i	0.0368448	+	0.0477811i
$995$	0.529776	+	1.63048i	0.0167950	+	0.0516897i
$996$	−13.4547	+	22.3121i	−0.426328	+	0.706986i
$997$	4.10582	+	10.5457i	0.130033	+	0.333986i	0.981795	−	0.189941i	$-0.0608298\pi$
$997$	4.10582	+	10.5457i	0.130033	+	0.333986i	−0.851763	+	0.523928i	$0.824466\pi$
$998$	−44.0600	−	10.2457i	−1.39470	−	0.324323i
$999$	−19.6505	+	8.30437i	−0.621714	+	0.262739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.s.b.416.3	yes	880
121.16	even	55	inner	605.2.s.b.16.3	✓	880

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.s.b.16.3	✓	880	121.16	even	55	inner
605.2.s.b.416.3	yes	880	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.s (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03821 + 0.233862i) q^{2} +(0.653999 - 0.475158i) q^{3} +(2.15157 - 0.500325i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-1.22186 + 1.12142i) q^{6} +(-0.0770600 + 0.0792929i) q^{7} +(-0.403791 + 0.144072i) q^{8} +(-0.725112 + 2.23166i) q^{9} +O(q^{10})\)	\(q+(-2.03821 + 0.233862i) q^{2} +(0.653999 - 0.475158i) q^{3} +(2.15157 - 0.500325i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-1.22186 + 1.12142i) q^{6} +(-0.0770600 + 0.0792929i) q^{7} +(-0.403791 + 0.144072i) q^{8} +(-0.725112 + 2.23166i) q^{9} +(1.34350 + 1.55048i) q^{10} +(-3.07435 - 1.24433i) q^{11} +(1.16939 - 1.34955i) q^{12} +(0.978429 + 1.62254i) q^{13} +(0.138521 - 0.179637i) q^{14} +(-0.761375 - 0.271658i) q^{15} +(-3.17534 + 1.56121i) q^{16} +(-2.66596 - 2.17994i) q^{17} +(0.956024 - 4.71817i) q^{18} +(-0.367122 + 0.0209928i) q^{19} +(-1.62744 - 1.49365i) q^{20} +(-0.0127205 + 0.0884732i) q^{21} +(6.55717 + 1.81722i) q^{22} +(0.539872 + 3.75489i) q^{23} +(-0.195622 + 0.286088i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(-2.37369 - 3.07826i) q^{26} +(1.33559 + 4.11051i) q^{27} +(-0.126127 + 0.209159i) q^{28} +(-0.153525 - 0.394327i) q^{29} +(1.61537 + 0.375638i) q^{30} +(-4.52370 + 1.91173i) q^{31} +(6.82822 - 4.38823i) q^{32} +(-2.60188 + 0.647015i) q^{33} +(5.94357 + 3.81970i) q^{34} +(0.108950 + 0.0188546i) q^{35} +(-0.443567 + 5.16436i) q^{36} +(0.422389 + 4.91779i) q^{37} +(0.743360 - 0.128643i) q^{38} +(1.41086 + 0.596233i) q^{39} +(0.346845 + 0.251997i) q^{40} +(-7.16134 - 4.04420i) q^{41} +(0.00523650 - 0.183301i) q^{42} +(6.37251 + 1.87114i) q^{43} +(-7.23724 - 1.13908i) q^{44} +(2.25146 - 0.661088i) q^{45} +(-1.97850 - 7.52699i) q^{46} +(0.457072 + 2.25574i) q^{47} +(-1.33485 + 2.52982i) q^{48} +(0.199543 + 6.98492i) q^{49} +(0.521549 - 1.98418i) q^{50} +(-2.77935 - 0.158929i) q^{51} +(2.91695 + 3.00147i) q^{52} +(1.70367 + 0.837637i) q^{53} +(-3.68349 - 8.06573i) q^{54} +(0.708141 + 3.24014i) q^{55} +(0.0196922 - 0.0431200i) q^{56} +(-0.230122 + 0.188170i) q^{57} +(0.405135 + 0.767816i) q^{58} +(-6.63921 + 3.74933i) q^{59} +(-1.77407 - 0.203555i) q^{60} +(-12.3361 - 1.41543i) q^{61} +(8.77314 - 4.95442i) q^{62} +(-0.121078 - 0.229468i) q^{63} +(-7.41265 + 6.06129i) q^{64} +(0.787095 - 1.72350i) q^{65} +(5.15185 - 1.92723i) q^{66} +(0.779681 + 1.70726i) q^{67} +(-6.82666 - 3.35644i) q^{68} +(2.13724 + 2.19917i) q^{69} +(-0.226472 - 0.0129501i) q^{70} +(-2.13187 + 8.11049i) q^{71} +(-0.0287275 - 1.00559i) q^{72} +(-4.29019 + 8.13081i) q^{73} +(-2.01100 - 9.92468i) q^{74} +(0.205507 + 0.781829i) q^{75} +(-0.779383 + 0.228847i) q^{76} +(0.335576 - 0.147887i) q^{77} +(-3.01505 - 0.885299i) q^{78} +(-0.414663 + 14.5151i) q^{79} +(3.08104 + 1.73994i) q^{80} +(-2.86848 - 2.08407i) q^{81} +(15.5421 + 6.56813i) q^{82} +(-14.3771 + 2.48806i) q^{83} +(0.0168963 + 0.196720i) q^{84} +(-0.294700 + 3.43113i) q^{85} +(-13.4261 - 2.32347i) q^{86} +(-0.287773 - 0.184941i) q^{87} +(1.42067 + 0.0595188i) q^{88} +(2.96984 - 1.90860i) q^{89} +(-4.43433 + 1.87397i) q^{90} +(-0.204054 - 0.0474507i) q^{91} +(3.04024 + 7.80879i) q^{92} +(-2.05012 + 3.39974i) q^{93} +(-1.45914 - 4.49077i) q^{94} +(0.224548 + 0.291199i) q^{95} +(2.38055 - 6.11438i) q^{96} +(-1.19286 + 1.74450i) q^{97} +(-2.04022 - 14.1900i) q^{98} +(5.00617 - 5.95865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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