LMFDB - Embedded newform 690.2.m.d.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			541.2
Root			$-0.0296794 - 0.00871465i$ of defining polynomial
Character	$\chi$	$=$	690.541
Dual form			690.2.m.d.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(2.25922 + 2.60728i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(2.25922 + 2.60728i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.654861 - 0.755750i) q^{10} +(3.00554 + 1.93155i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(1.91026 - 2.20456i) q^{13} +(3.31018 + 0.971955i) q^{14} +(-0.142315 - 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.831833 + 1.82146i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(-0.366972 + 0.803556i) q^{19} +(0.142315 - 0.989821i) q^{20} +(2.90226 - 1.86517i) q^{21} +3.57270 q^{22} +(-4.56059 - 1.48358i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.415140 - 2.88736i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(3.31018 - 0.971955i) q^{28} +(-1.83516 - 4.01845i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(-0.254124 - 1.76747i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(2.33962 - 2.70006i) q^{33} +(1.68454 + 1.08259i) q^{34} +(2.90226 + 1.86517i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(2.67890 + 0.786596i) q^{37} +(0.125719 + 0.874394i) q^{38} +(-1.91026 - 2.20456i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(-7.69951 + 2.26078i) q^{41} +(1.43315 - 3.13816i) q^{42} +(0.474462 - 3.29995i) q^{43} +(3.00554 - 1.93155i) q^{44} -1.00000 q^{45} +(-4.63870 + 1.21757i) q^{46} -6.66271 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.697621 + 4.85206i) q^{49} +(0.415415 - 0.909632i) q^{50} +(1.92130 - 0.564145i) q^{51} +(-1.21179 - 2.65345i) q^{52} +(-2.06575 - 2.38401i) q^{53} +(0.142315 + 0.989821i) q^{54} +(3.42798 + 1.00654i) q^{55} +(2.25922 - 2.60728i) q^{56} +(0.743151 + 0.477594i) q^{57} +(-3.71638 - 2.38837i) q^{58} +(-1.49817 + 1.72898i) q^{59} +(-0.959493 - 0.281733i) q^{60} +(-0.0614036 - 0.427072i) q^{61} +(-1.16935 - 1.34950i) q^{62} +(-1.43315 - 3.13816i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(1.21179 - 2.65345i) q^{65} +(0.508448 - 3.53633i) q^{66} +(-4.69226 + 3.01553i) q^{67} +2.00241 q^{68} +(-2.11752 + 4.30303i) q^{69} +3.44992 q^{70} +(3.86069 - 2.48112i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-0.637855 + 1.39671i) q^{73} +(2.67890 - 0.786596i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(0.578494 + 0.667618i) q^{76} +(1.75410 + 12.2001i) q^{77} +(-2.79889 - 0.821829i) q^{78} +(-3.67678 + 4.24323i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-5.25497 + 6.06456i) q^{82} +(16.0001 + 4.69805i) q^{83} +(-0.490975 - 3.41481i) q^{84} +(1.31130 + 1.51332i) q^{85} +(-1.38495 - 3.03261i) q^{86} +(-4.23872 + 1.24460i) q^{87} +(1.48415 - 3.24984i) q^{88} +(1.55693 - 10.8287i) q^{89} +(-0.841254 + 0.540641i) q^{90} +10.0636 q^{91} +(-3.24405 + 3.53216i) q^{92} -1.78565 q^{93} +(-5.60503 + 3.60214i) q^{94} +(-0.125719 + 0.874394i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-3.16425 + 0.929106i) q^{97} +(2.03635 + 4.45898i) q^{98} +(-2.33962 - 2.70006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$6$	−0.415415	−	0.909632i	−0.169592	−	0.371356i
$7$	2.25922	+	2.60728i	0.853904	+	0.985458i	0.999993	−	0.00381361i	$-0.00121391\pi$
$7$	2.25922	+	2.60728i	0.853904	+	0.985458i	−0.146089	+	0.989272i	$0.546668\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	0.654861	−	0.755750i	0.207085	−	0.238989i
$11$	3.00554	+	1.93155i	0.906205	+	0.582383i	0.908624	−	0.417614i	$-0.137134\pi$
$11$	3.00554	+	1.93155i	0.906205	+	0.582383i	−0.00241910	+	0.999997i	$0.500770\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	1.91026	−	2.20456i	0.529812	−	0.611436i	−0.426248	−	0.904606i	$-0.640165\pi$
$13$	1.91026	−	2.20456i	0.529812	−	0.611436i	0.956060	+	0.293171i	$0.0947104\pi$
$14$	3.31018	+	0.971955i	0.884682	+	0.259766i
$15$	−0.142315	−	0.989821i	−0.0367455	−	0.255571i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	0.831833	+	1.82146i	0.201749	+	0.441769i	0.983281	−	0.182097i	$-0.0582885\pi$
$17$	0.831833	+	1.82146i	0.201749	+	0.441769i	−0.781531	+	0.623866i	$0.785561\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	−0.366972	+	0.803556i	−0.0841891	+	0.184348i	−0.947044	−	0.321103i	$-0.895947\pi$
$19$	−0.366972	+	0.803556i	−0.0841891	+	0.184348i	0.862855	+	0.505451i	$0.168674\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	2.90226	−	1.86517i	0.633325	−	0.407013i
$22$	3.57270			0.761701
$23$	−4.56059	−	1.48358i	−0.950949	−	0.309348i
$23$	−4.56059	−	1.48358i	−0.950949	−	0.309348i
$24$	−1.00000			−0.204124
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.415140	−	2.88736i	0.0814157	−	0.566259i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	3.31018	−	0.971955i	0.625564	−	0.183682i
$29$	−1.83516	−	4.01845i	−0.340782	−	0.746207i	0.659202	−	0.751966i	$-0.270894\pi$
$29$	−1.83516	−	4.01845i	−0.340782	−	0.746207i	−0.999983	+	0.00575855i	$0.998167\pi$
$30$	−0.654861	−	0.755750i	−0.119561	−	0.137980i
$31$	−0.254124	−	1.76747i	−0.0456421	−	0.317448i	−0.999833	−	0.0182507i	$-0.994190\pi$
$31$	−0.254124	−	1.76747i	−0.0456421	−	0.317448i	0.954191	−	0.299197i	$-0.0967188\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	2.33962	−	2.70006i	0.407275	−	0.470021i
$34$	1.68454	+	1.08259i	0.288896	+	0.185662i
$35$	2.90226	+	1.86517i	0.490571	+	0.315271i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	2.67890	+	0.786596i	0.440408	+	0.129316i	0.494417	−	0.869225i	$-0.335382\pi$
$37$	2.67890	+	0.786596i	0.440408	+	0.129316i	−0.0540085	+	0.998540i	$0.517200\pi$
$38$	0.125719	+	0.874394i	0.0203943	+	0.141845i
$39$	−1.91026	−	2.20456i	−0.305887	−	0.353013i
$40$	−0.415415	−	0.909632i	−0.0656829	−	0.143825i
$41$	−7.69951	+	2.26078i	−1.20246	+	0.353074i	−0.820793	−	0.571225i	$-0.806468\pi$
$41$	−7.69951	+	2.26078i	−1.20246	+	0.353074i	−0.381668	+	0.924300i	$0.624650\pi$
$42$	1.43315	−	3.13816i	0.221140	−	0.484228i
$43$	0.474462	−	3.29995i	0.0723547	−	0.503238i	−0.921128	−	0.389259i	$-0.872731\pi$
$43$	0.474462	−	3.29995i	0.0723547	−	0.503238i	0.993483	−	0.113979i	$-0.0363598\pi$
$44$	3.00554	−	1.93155i	0.453103	−	0.291191i
$45$	−1.00000			−0.149071
$46$	−4.63870	+	1.21757i	−0.683939	+	0.179521i
$47$	−6.66271			−0.971857			−0.485928	−	0.873999i	$-0.661518\pi$
$47$	−6.66271			−0.971857			−0.485928	+	0.873999i	$0.661518\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	−0.697621	+	4.85206i	−0.0996602	+	0.693152i
$50$	0.415415	−	0.909632i	0.0587486	−	0.128641i
$51$	1.92130	−	0.564145i	0.269036	−	0.0789961i
$52$	−1.21179	−	2.65345i	−0.168045	−	0.367967i
$53$	−2.06575	−	2.38401i	−0.283753	−	0.327469i	0.595923	−	0.803041i	$-0.296786\pi$
$53$	−2.06575	−	2.38401i	−0.283753	−	0.327469i	−0.879676	+	0.475573i	$0.842241\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	3.42798	+	1.00654i	0.462228	+	0.135722i
$56$	2.25922	−	2.60728i	0.301901	−	0.348412i
$57$	0.743151	+	0.477594i	0.0984328	+	0.0632589i
$58$	−3.71638	−	2.38837i	−0.487984	−	0.313608i
$59$	−1.49817	+	1.72898i	−0.195045	+	0.225094i	−0.844845	−	0.535012i	$-0.820307\pi$
$59$	−1.49817	+	1.72898i	−0.195045	+	0.225094i	0.649800	+	0.760105i	$0.274853\pi$
$60$	−0.959493	−	0.281733i	−0.123870	−	0.0363715i
$61$	−0.0614036	−	0.427072i	−0.00786193	−	0.0546809i	0.985513	−	0.169601i	$-0.0542479\pi$
$61$	−0.0614036	−	0.427072i	−0.00786193	−	0.0546809i	−0.993375	+	0.114920i	$0.963339\pi$
$62$	−1.16935	−	1.34950i	−0.148508	−	0.171387i
$63$	−1.43315	−	3.13816i	−0.180560	−	0.395371i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	1.21179	−	2.65345i	0.150304	−	0.329120i
$66$	0.508448	−	3.53633i	0.0625856	−	0.435292i
$67$	−4.69226	+	3.01553i	−0.573250	+	0.368406i	−0.794918	−	0.606717i	$-0.792486\pi$
$67$	−4.69226	+	3.01553i	−0.573250	+	0.368406i	0.221668	+	0.975122i	$0.428850\pi$
$68$	2.00241			0.242828
$69$	−2.11752	+	4.30303i	−0.254919	+	0.518025i
$70$	3.44992			0.412344
$71$	3.86069	−	2.48112i	0.458180	−	0.294454i	−0.291118	−	0.956687i	$-0.594027\pi$
$71$	3.86069	−	2.48112i	0.458180	−	0.294454i	0.749298	+	0.662233i	$0.230391\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	−0.637855	+	1.39671i	−0.0746553	+	0.163472i	−0.943280	−	0.331998i	$-0.892277\pi$
$73$	−0.637855	+	1.39671i	−0.0746553	+	0.163472i	0.868625	+	0.495471i	$0.165004\pi$
$74$	2.67890	−	0.786596i	0.311416	−	0.0914399i
$75$	−0.415415	−	0.909632i	−0.0479680	−	0.105035i
$76$	0.578494	+	0.667618i	0.0663579	+	0.0765811i
$77$	1.75410	+	12.2001i	0.199899	+	1.39033i
$78$	−2.79889	−	0.821829i	−0.316912	−	0.0930539i
$79$	−3.67678	+	4.24323i	−0.413670	+	0.477400i	−0.923898	−	0.382639i	$-0.875015\pi$
$79$	−3.67678	+	4.24323i	−0.413670	+	0.477400i	0.510228	+	0.860039i	$0.329561\pi$
$80$	−0.841254	−	0.540641i	−0.0940550	−	0.0604455i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−5.25497	+	6.06456i	−0.580314	+	0.669718i
$83$	16.0001	+	4.69805i	1.75624	+	0.515678i	0.991663	−	0.128856i	$-0.0411304\pi$
$83$	16.0001	+	4.69805i	1.75624	+	0.515678i	0.764576	+	0.644534i	$0.222949\pi$
$84$	−0.490975	−	3.41481i	−0.0535698	−	0.372586i
$85$	1.31130	+	1.51332i	0.142231	+	0.164143i
$86$	−1.38495	−	3.03261i	−0.149343	−	0.327015i
$87$	−4.23872	+	1.24460i	−0.454438	+	0.133435i
$88$	1.48415	−	3.24984i	0.158211	−	0.346434i
$89$	1.55693	−	10.8287i	0.165034	−	1.14784i	−0.723934	−	0.689870i	$-0.757668\pi$
$89$	1.55693	−	10.8287i	0.165034	−	1.14784i	0.888968	−	0.457970i	$-0.151423\pi$
$90$	−0.841254	+	0.540641i	−0.0886759	+	0.0569885i
$91$	10.0636			1.05495
$92$	−3.24405	+	3.53216i	−0.338216	+	0.368253i
$93$	−1.78565			−0.185163
$94$	−5.60503	+	3.60214i	−0.578115	+	0.371532i
$95$	−0.125719	+	0.874394i	−0.0128985	+	0.0897109i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	−3.16425	+	0.929106i	−0.321280	+	0.0943365i	−0.438396	−	0.898782i	$-0.644453\pi$
$97$	−3.16425	+	0.929106i	−0.321280	+	0.0943365i	0.117116	+	0.993118i	$0.462635\pi$
$98$	2.03635	+	4.45898i	0.205702	+	0.450425i
$99$	−2.33962	−	2.70006i	−0.235140	−	0.271367i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	−14.1575	−	4.15703i	−1.40873	−	0.413640i	−0.513055	−	0.858355i	$-0.671486\pi$
$101$	−14.1575	−	4.15703i	−1.40873	−	0.413640i	−0.895672	+	0.444716i	$0.853305\pi$
$102$	1.31130	−	1.51332i	0.129838	−	0.149841i
$103$	13.1280	+	8.43685i	1.29354	+	0.831307i	0.992493	−	0.122302i	$-0.0390277\pi$
$103$	13.1280	+	8.43685i	1.29354	+	0.831307i	0.301047	+	0.953609i	$0.402664\pi$
$104$	−2.45398	−	1.57708i	−0.240633	−	0.154645i
$105$	2.25922	−	2.60728i	0.220477	−	0.254444i
$106$	−3.02671	−	0.888723i	−0.293980	−	0.0863205i
$107$	1.25180	+	8.70647i	0.121016	+	0.841686i	0.956408	+	0.292032i	$0.0943314\pi$
$107$	1.25180	+	8.70647i	0.121016	+	0.841686i	−0.835392	+	0.549654i	$0.814759\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	6.12051	+	13.4020i	0.586239	+	1.28368i	0.937689	+	0.347477i	$0.112961\pi$
$109$	6.12051	+	13.4020i	0.586239	+	1.28368i	−0.351450	+	0.936207i	$0.614311\pi$
$110$	3.42798	−	1.00654i	0.326845	−	0.0959703i
$111$	1.15984	−	2.53969i	0.110087	−	0.241057i
$112$	0.490975	−	3.41481i	0.0463928	−	0.322669i
$113$	−15.4704	+	9.94222i	−1.45533	+	0.935285i	−0.456368	+	0.889791i	$0.650850\pi$
$113$	−15.4704	+	9.94222i	−1.45533	+	0.935285i	−0.998965	+	0.0454943i	$0.985514\pi$
$114$	0.883386			0.0827366
$115$	−4.79383	−	0.138618i	−0.447027	−	0.0129262i
$116$	−4.41767			−0.410170
$117$	−2.45398	+	1.57708i	−0.226871	+	0.145801i
$118$	−0.325583	+	2.26448i	−0.0299724	+	0.208462i
$119$	−2.86976	+	6.28389i	−0.263070	+	0.576044i
$120$	−0.959493	+	0.281733i	−0.0875893	+	0.0257185i
$121$	0.732857	+	1.60473i	0.0666233	+	0.145885i
$122$	−0.282548	−	0.326078i	−0.0255807	−	0.0295217i
$123$	1.14201	+	7.94288i	0.102972	+	0.716186i
$124$	−1.71332	−	0.503076i	−0.153860	−	0.0451775i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	−2.90226	−	1.86517i	−0.258554	−	0.166162i
$127$	16.9584	+	10.8985i	1.50482	+	0.967087i	0.994231	+	0.107260i	$0.0342076\pi$
$127$	16.9584	+	10.8985i	1.50482	+	0.967087i	0.510585	+	0.859827i	$0.329429\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	−3.19884	−	0.939265i	−0.281642	−	0.0826977i
$130$	−0.415140	−	2.88736i	−0.0364102	−	0.253239i
$131$	−8.00078	−	9.23340i	−0.699032	−	0.806726i	0.289590	−	0.957151i	$-0.406481\pi$
$131$	−8.00078	−	9.23340i	−0.699032	−	0.806726i	−0.988621	+	0.150425i	$0.951936\pi$
$132$	−1.48415	−	3.24984i	−0.129179	−	0.282862i
$133$	−2.92416	+	0.858611i	−0.253557	+	0.0744510i
$134$	−2.31706	+	5.07365i	−0.200163	+	0.438297i
$135$	−0.142315	+	0.989821i	−0.0122485	+	0.0851903i
$136$	1.68454	−	1.08259i	0.144448	−	0.0928310i
$137$	−14.6636			−1.25280			−0.626399	−	0.779502i	$-0.715472\pi$
$137$	−14.6636			−1.25280			−0.626399	+	0.779502i	$0.715472\pi$
$138$	0.545025	+	4.76476i	0.0463956	+	0.405603i
$139$	8.25897			0.700517			0.350258	−	0.936653i	$-0.386094\pi$
$139$	8.25897			0.700517			0.350258	+	0.936653i	$0.386094\pi$
$140$	2.90226	−	1.86517i	0.245286	−	0.157635i
$141$	−0.948203	+	6.59490i	−0.0798531	+	0.555391i
$142$	1.90643	−	4.17449i	0.159984	−	0.350316i
$143$	9.99960	−	2.93615i	0.836208	−	0.245533i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−2.89296	−	3.33865i	−0.240247	−	0.277260i
$146$	0.218519	+	1.51984i	0.0180848	+	0.125783i
$147$	4.70339	+	1.38104i	0.387929	+	0.113906i
$148$	1.82837	−	2.11005i	0.150291	−	0.173445i
$149$	−16.6276	−	10.6859i	−1.36219	−	0.875426i	−0.363763	−	0.931492i	$-0.618508\pi$
$149$	−16.6276	−	10.6859i	−1.36219	−	0.875426i	−0.998427	+	0.0560651i	$0.982145\pi$
$150$	−0.841254	−	0.540641i	−0.0686881	−	0.0441431i
$151$	6.27561	−	7.24244i	0.510702	−	0.589381i	−0.440577	−	0.897715i	$-0.645226\pi$
$151$	6.27561	−	7.24244i	0.510702	−	0.589381i	0.951278	+	0.308334i	$0.0997714\pi$
$152$	0.847602	+	0.248878i	0.0687496	+	0.0201867i
$153$	−0.284973	−	1.98203i	−0.0230387	−	0.160238i
$154$	8.07150	+	9.31501i	0.650420	+	0.750625i
$155$	−0.741785	−	1.62428i	−0.0595816	−	0.130466i
$156$	−2.79889	+	0.821829i	−0.224091	+	0.0657990i
$157$	−5.41793	+	11.8636i	−0.432398	+	0.946819i	0.560534	+	0.828131i	$0.310596\pi$
$157$	−5.41793	+	11.8636i	−0.432398	+	0.946819i	−0.992932	+	0.118687i	$0.962131\pi$
$158$	−0.799040	+	5.55744i	−0.0635682	+	0.442126i
$159$	−2.65373	+	1.70545i	−0.210454	+	0.135251i
$160$	−1.00000			−0.0790569
$161$	−6.43526	−	15.2425i	−0.507170	−	1.20127i
$162$	1.00000			0.0785674
$163$	−4.37597	+	2.81226i	−0.342752	+	0.220273i	−0.700680	−	0.713476i	$-0.747120\pi$
$163$	−4.37597	+	2.81226i	−0.342752	+	0.220273i	0.357928	+	0.933749i	$0.383483\pi$
$164$	−1.14201	+	7.94288i	−0.0891763	+	0.620235i
$165$	1.48415	−	3.24984i	0.115541	−	0.253000i
$166$	16.0001	−	4.69805i	1.24185	−	0.364640i
$167$	−0.0607807	−	0.133091i	−0.00470335	−	0.0102989i	0.907266	−	0.420558i	$-0.138166\pi$
$167$	−0.0607807	−	0.133091i	−0.00470335	−	0.0102989i	−0.911969	+	0.410259i	$0.865438\pi$
$168$	−2.25922	−	2.60728i	−0.174302	−	0.201156i
$169$	0.639106	+	4.44508i	0.0491620	+	0.341929i
$170$	1.92130	+	0.564145i	0.147357	+	0.0432680i
$171$	0.578494	−	0.667618i	0.0442386	−	0.0510540i
$172$	−2.80465	−	1.80244i	−0.213852	−	0.137434i
$173$	15.2612	+	9.80780i	1.16029	+	0.745673i	0.971662	−	0.236375i	$-0.0759595\pi$
$173$	15.2612	+	9.80780i	1.16029	+	0.745673i	0.188628	+	0.982049i	$0.439596\pi$
$174$	−2.89296	+	3.33865i	−0.219314	+	0.253102i
$175$	3.31018	+	0.971955i	0.250226	+	0.0734729i
$176$	−0.508448	−	3.53633i	−0.0383257	−	0.266561i
$177$	1.49817	+	1.72898i	0.112609	+	0.129958i
$178$	−4.54466	−	9.95142i	−0.340637	−	0.745890i
$179$	−0.962409	+	0.282589i	−0.0719338	+	0.0211217i	−0.317501	−	0.948258i	$-0.602844\pi$
$179$	−0.962409	+	0.282589i	−0.0719338	+	0.0211217i	0.245568	+	0.969379i	$0.421026\pi$
$180$	−0.415415	+	0.909632i	−0.0309632	+	0.0678000i
$181$	1.70529	−	11.8606i	0.126753	−	0.881588i	−0.822878	−	0.568218i	$-0.807633\pi$
$181$	1.70529	−	11.8606i	0.126753	−	0.881588i	0.949631	−	0.313370i	$-0.101458\pi$
$182$	8.46605	−	5.44080i	0.627545	−	0.403299i
$183$	−0.431463			−0.0318947
$184$	−0.819440	+	4.72531i	−0.0604099	+	0.348354i
$185$	2.79200			0.205272
$186$	−1.50218	+	0.965395i	−0.110145	+	0.0707862i
$187$	−1.01812	+	7.08120i	−0.0744525	+	0.517829i
$188$	−2.76779	+	6.06062i	−0.201862	+	0.442016i
$189$	−3.31018	+	0.971955i	−0.240780	+	0.0706993i
$190$	0.366972	+	0.803556i	0.0266229	+	0.0582961i
$191$	−11.5452	−	13.3238i	−0.835380	−	0.964080i	0.164371	−	0.986399i	$-0.447441\pi$
$191$	−11.5452	−	13.3238i	−0.835380	−	0.964080i	−0.999751	+	0.0223188i	$0.992895\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	−15.2647	−	4.48213i	−1.09878	−	0.322631i	−0.318412	−	0.947952i	$-0.603150\pi$
$193$	−15.2647	−	4.48213i	−1.09878	−	0.322631i	−0.780367	+	0.625322i	$0.784968\pi$
$194$	−2.15962	+	2.49233i	−0.155052	+	0.178939i
$195$	−2.45398	−	1.57708i	−0.175733	−	0.112937i
$196$	4.12379	+	2.65020i	0.294556	+	0.189300i
$197$	−13.3507	+	15.4075i	−0.951196	+	1.09774i	0.0439205	+	0.999035i	$0.486015\pi$
$197$	−13.3507	+	15.4075i	−0.951196	+	1.09774i	−0.995117	+	0.0987041i	$0.968530\pi$
$198$	−3.42798	−	1.00654i	−0.243616	−	0.0715320i
$199$	0.586462	+	4.07893i	0.0415732	+	0.289148i	0.999993	+	0.00378534i	$0.00120492\pi$
$199$	0.586462	+	4.07893i	0.0415732	+	0.289148i	−0.958420	+	0.285363i	$0.907886\pi$
$200$	−0.654861	−	0.755750i	−0.0463056	−	0.0534396i
$201$	2.31706	+	5.07365i	0.163433	+	0.357868i
$202$	−14.1575	+	4.15703i	−0.996120	+	0.292487i
$203$	6.33117	−	13.8633i	0.444361	−	0.973015i
$204$	0.284973	−	1.98203i	0.0199521	−	0.138770i
$205$	−6.75069	+	4.33840i	−0.471489	+	0.303007i
$206$	15.6053			1.08727
$207$	3.95788	+	2.70835i	0.275092	+	0.188243i
$208$	−2.91706			−0.202261
$209$	−2.65505	+	1.70630i	−0.183654	+	0.118027i
$210$	0.490975	−	3.41481i	0.0338805	−	0.235644i
$211$	4.76636	−	10.4369i	0.328130	−	0.718503i	−0.671620	−	0.740896i	$-0.734401\pi$
$211$	4.76636	−	10.4369i	0.328130	−	0.718503i	0.999749	+	0.0223926i	$0.00712838\pi$
$212$	−3.02671	+	0.888723i	−0.207876	+	0.0610378i
$213$	−1.90643	−	4.17449i	−0.130626	−	0.286032i
$214$	5.76016	+	6.64758i	0.393756	+	0.454419i
$215$	−0.474462	−	3.29995i	−0.0323580	−	0.225055i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	4.03417	−	4.65568i	0.273857	−	0.316048i
$218$	12.3946	+	7.96552i	0.839468	+	0.539493i
$219$	1.29172	+	0.830135i	0.0872861	+	0.0560953i
$220$	2.33962	−	2.70006i	0.157737	−	0.182038i
$221$	5.60454	+	1.64564i	0.377002	+	0.110698i
$222$	−0.397342	−	2.76358i	−0.0266679	−	0.185479i
$223$	2.74294	+	3.16552i	0.183681	+	0.211979i	0.840121	−	0.542399i	$-0.182484\pi$
$223$	2.74294	+	3.16552i	0.183681	+	0.211979i	−0.656440	+	0.754378i	$0.727939\pi$
$224$	−1.43315	−	3.13816i	−0.0957563	−	0.209677i
$225$	−0.959493	+	0.281733i	−0.0639662	+	0.0187822i
$226$	−7.63936	+	16.7279i	−0.508162	+	1.11272i
$227$	−2.31335	+	16.0897i	−0.153543	+	1.06791i	0.756677	+	0.653788i	$0.226821\pi$
$227$	−2.31335	+	16.0897i	−0.153543	+	1.06791i	−0.910220	+	0.414125i	$0.864088\pi$
$228$	0.743151	−	0.477594i	0.0492164	−	0.0316295i
$229$	5.86649			0.387668			0.193834	−	0.981034i	$-0.437908\pi$
$229$	5.86649			0.387668			0.193834	+	0.981034i	$0.437908\pi$
$230$	−4.10777	+	2.47513i	−0.270858	+	0.163205i
$231$	12.3255			0.810960
$232$	−3.71638	+	2.38837i	−0.243992	+	0.156804i
$233$	3.14011	−	21.8399i	0.205715	−	1.43078i	−0.581220	−	0.813746i	$-0.697424\pi$
$233$	3.14011	−	21.8399i	0.205715	−	1.43078i	0.786935	−	0.617035i	$-0.211666\pi$
$234$	−1.21179	+	2.65345i	−0.0792171	+	0.173461i
$235$	−6.39283	+	1.87710i	−0.417022	+	0.122449i
$236$	0.950372	+	2.08103i	0.0618640	+	0.135463i
$237$	3.67678	+	4.24323i	0.238832	+	0.275627i
$238$	0.983135	+	6.83786i	0.0637272	+	0.443232i
$239$	−6.00657	−	1.76369i	−0.388533	−	0.114084i	0.0816311	−	0.996663i	$-0.473987\pi$
$239$	−6.00657	−	1.76369i	−0.388533	−	0.114084i	−0.470164	+	0.882579i	$0.655805\pi$
$240$	−0.654861	+	0.755750i	−0.0422711	+	0.0487834i
$241$	0.270609	+	0.173910i	0.0174315	+	0.0112025i	0.549328	−	0.835607i	$-0.314884\pi$
$241$	0.270609	+	0.173910i	0.0174315	+	0.0112025i	−0.531896	+	0.846810i	$0.678520\pi$
$242$	1.48410	+	0.953774i	0.0954017	+	0.0613109i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−0.413986	−	0.121557i	−0.0265027	−	0.00778190i
$245$	0.697621	+	4.85206i	0.0445694	+	0.309987i
$246$	5.25497	+	6.06456i	0.335045	+	0.386662i
$247$	1.07048	+	2.34402i	0.0681128	+	0.149146i
$248$	−1.71332	+	0.503076i	−0.108796	+	0.0319453i
$249$	6.92728	−	15.1686i	0.438999	−	0.961273i
$250$	0.142315	−	0.989821i	0.00900078	−	0.0626018i
$251$	8.02082	−	5.15467i	0.506270	−	0.325360i	−0.262450	−	0.964946i	$-0.584531\pi$
$251$	8.02082	−	5.15467i	0.506270	−	0.325360i	0.768720	+	0.639586i	$0.220894\pi$
$252$	−3.44992			−0.217325
$253$	−10.8414	−	13.2680i	−0.681596	−	0.834149i
$254$	20.1585			1.26486
$255$	1.68454	−	1.08259i	0.105490	−	0.0677942i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	4.76678	−	10.4378i	0.297343	−	0.651091i	−0.700711	−	0.713446i	$-0.747134\pi$
$257$	4.76678	−	10.4378i	0.297343	−	0.651091i	0.998054	+	0.0623542i	$0.0198608\pi$
$258$	−3.19884	+	0.939265i	−0.199151	+	0.0584761i
$259$	4.00135	+	8.76172i	0.248631	+	0.544427i
$260$	−1.91026	−	2.20456i	−0.118470	−	0.136721i
$261$	0.628699	+	4.37270i	0.0389155	+	0.270663i
$262$	−11.7226	−	3.44208i	−0.724227	−	0.212652i
$263$	10.9849	−	12.6773i	0.677360	−	0.781715i	−0.308149	−	0.951338i	$-0.599710\pi$
$263$	10.9849	−	12.6773i	0.677360	−	0.781715i	0.985509	+	0.169623i	$0.0542551\pi$
$264$	−3.00554	−	1.93155i	−0.184978	−	0.118878i
$265$	−2.65373	−	1.70545i	−0.163017	−	0.104765i
$266$	−1.99576	+	2.30323i	−0.122368	+	0.141220i
$267$	−10.4969	−	3.08217i	−0.642400	−	0.188626i
$268$	0.793789	+	5.52092i	0.0484884	+	0.337244i
$269$	−5.43013	−	6.26670i	−0.331081	−	0.382088i	0.565664	−	0.824636i	$-0.308620\pi$
$269$	−5.43013	−	6.26670i	−0.331081	−	0.382088i	−0.896745	+	0.442548i	$0.854075\pi$
$270$	0.415415	+	0.909632i	0.0252814	+	0.0553584i
$271$	−10.5618	+	3.10122i	−0.641584	+	0.188386i	−0.586312	−	0.810085i	$-0.699421\pi$
$271$	−10.5618	+	3.10122i	−0.641584	+	0.188386i	−0.0552717	+	0.998471i	$0.517602\pi$
$272$	0.831833	−	1.82146i	0.0504373	−	0.110442i
$273$	1.43220	−	9.96118i	0.0866808	−	0.602878i
$274$	−12.3358	+	7.92776i	−0.745235	+	0.478933i
$275$	3.57270			0.215442
$276$	3.03453	+	3.71371i	0.182657	+	0.223539i
$277$	17.1728			1.03181			0.515906	−	0.856645i	$-0.327455\pi$
$277$	17.1728			1.03181			0.515906	+	0.856645i	$0.327455\pi$
$278$	6.94789	−	4.46514i	0.416707	−	0.267801i
$279$	−0.254124	+	1.76747i	−0.0152140	+	0.105816i
$280$	1.43315	−	3.13816i	0.0856470	−	0.187541i
$281$	8.09556	−	2.37707i	0.482941	−	0.141804i	−0.0311944	−	0.999513i	$-0.509931\pi$
$281$	8.09556	−	2.37707i	0.482941	−	0.141804i	0.514135	+	0.857709i	$0.328113\pi$
$282$	2.76779	+	6.06062i	0.164820	+	0.360905i
$283$	−14.5793	−	16.8254i	−0.866646	−	1.00016i	−0.999959	−	0.00908927i	$-0.997107\pi$
$283$	−14.5793	−	16.8254i	−0.866646	−	1.00016i	0.133312	−	0.991074i	$-0.457439\pi$
$284$	−0.653113	−	4.54250i	−0.0387551	−	0.269548i
$285$	0.847602	+	0.248878i	0.0502076	+	0.0147423i
$286$	6.82480	−	7.87623i	0.403559	−	0.465731i
$287$	−23.2893	−	14.9672i	−1.37473	−	0.883483i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	8.50686	−	9.81744i	0.500404	−	0.577497i
$290$	−4.23872	−	1.24460i	−0.248906	−	0.0730854i
$291$	0.469330	+	3.26426i	0.0275126	+	0.191355i
$292$	1.00552	+	1.16043i	0.0588434	+	0.0679089i
$293$	4.83241	+	10.5815i	0.282312	+	0.618178i	0.996664	−	0.0816087i	$-0.0260058\pi$
$293$	4.83241	+	10.5815i	0.282312	+	0.618178i	−0.714352	+	0.699786i	$0.753279\pi$
$294$	4.70339	−	1.38104i	0.274307	−	0.0805439i
$295$	−0.950372	+	2.08103i	−0.0553328	+	0.121162i
$296$	0.397342	−	2.76358i	0.0230951	−	0.160630i
$297$	−3.00554	+	1.93155i	−0.174399	+	0.112080i
$298$	−19.7653			−1.14497
$299$	−11.9826	+	7.22008i	−0.692971	+	0.417548i
$300$	−1.00000			−0.0577350
$301$	9.67581	−	6.21826i	0.557704	−	0.358415i
$302$	1.36382	−	9.48557i	0.0784790	−	0.545833i
$303$	−6.12954	+	13.4218i	−0.352133	+	0.771064i
$304$	0.847602	−	0.248878i	0.0486133	−	0.0142742i
$305$	−0.179236	−	0.392473i	−0.0102630	−	0.0224729i
$306$	−1.31130	−	1.51332i	−0.0749622	−	0.0865109i
$307$	3.30356	+	22.9768i	0.188544	+	1.31135i	0.835781	+	0.549063i	$0.185015\pi$
$307$	3.30356	+	22.9768i	0.188544	+	1.31135i	−0.647237	+	0.762289i	$0.724075\pi$
$308$	11.8262	+	3.47250i	0.673863	+	0.197864i
$309$	10.2193	−	11.7937i	0.581355	−	0.670919i
$310$	−1.50218	−	0.965395i	−0.0853183	−	0.0548307i
$311$	11.6288	+	7.47339i	0.659410	+	0.423777i	0.827094	−	0.562064i	$-0.189993\pi$
$311$	11.6288	+	7.47339i	0.659410	+	0.423777i	−0.167684	+	0.985841i	$0.553629\pi$
$312$	−1.91026	+	2.20456i	−0.108147	+	0.124809i
$313$	−27.3925	−	8.04316i	−1.54832	−	0.454627i	−0.607719	−	0.794152i	$-0.707915\pi$
$313$	−27.3925	−	8.04316i	−1.54832	−	0.454627i	−0.940597	+	0.339526i	$0.889733\pi$
$314$	1.85610	+	12.9095i	0.104746	+	0.728523i
$315$	−2.25922	−	2.60728i	−0.127293	−	0.146903i
$316$	2.33239	+	5.10721i	0.131207	+	0.287303i
$317$	−3.41259	+	1.00203i	−0.191670	+	0.0562794i	−0.376159	−	0.926555i	$-0.622755\pi$
$317$	−3.41259	+	1.00203i	−0.191670	+	0.0562794i	0.184489	+	0.982835i	$0.440937\pi$
$318$	−1.31042	+	2.86943i	−0.0734849	+	0.160910i
$319$	2.24615	−	15.6223i	0.125760	−	0.874682i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	8.79600			0.490945
$322$	−13.6544	−	9.34360i	−0.760929	−	0.520699i
$323$	−1.76890			−0.0984244
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	0.415140	−	2.88736i	0.0230278	−	0.160162i
$326$	−2.16087	+	4.73165i	−0.119680	+	0.262062i
$327$	14.1367	−	4.15090i	0.781760	−	0.229545i
$328$	3.33352	+	7.29940i	0.184063	+	0.403042i
$329$	−15.0525	−	17.3715i	−0.829872	−	0.957724i
$330$	−0.508448	−	3.53633i	−0.0279891	−	0.194669i
$331$	−11.4186	−	3.35282i	−0.627625	−	0.184287i	−0.0475744	−	0.998868i	$-0.515149\pi$
$331$	−11.4186	−	3.35282i	−0.627625	−	0.184287i	−0.580051	+	0.814580i	$0.696967\pi$
$332$	10.9202	−	12.6026i	0.599323	−	0.691655i
$333$	−2.34878	−	1.50947i	−0.128712	−	0.0827183i
$334$	−0.123087	−	0.0791029i	−0.00673500	−	0.00432832i
$335$	−3.65261	+	4.21534i	−0.199564	+	0.230309i
$336$	−3.31018	−	0.971955i	−0.180585	−	0.0530245i
$337$	−4.36046	−	30.3277i	−0.237529	−	1.65205i	−0.664133	−	0.747615i	$-0.731199\pi$
$337$	−4.36046	−	30.3277i	−0.237529	−	1.65205i	0.426603	−	0.904439i	$-0.359710\pi$
$338$	2.94084	+	3.39391i	0.159961	+	0.184605i
$339$	7.63936	+	16.7279i	0.414913	+	0.908532i
$340$	1.92130	−	0.564145i	0.104197	−	0.0305951i
$341$	2.65017	−	5.80307i	0.143515	−	0.314254i
$342$	0.125719	−	0.874394i	0.00679810	−	0.0472818i
$343$	6.08906	−	3.91320i	0.328779	−	0.211293i
$344$	−3.33389			−0.179751
$345$	−0.819440	+	4.72531i	−0.0441172	+	0.254402i
$346$	18.1411			0.975270
$347$	16.3505	−	10.5078i	0.877739	−	0.564089i	−0.0223714	−	0.999750i	$-0.507122\pi$
$347$	16.3505	−	10.5078i	0.877739	−	0.564089i	0.900111	+	0.435661i	$0.143485\pi$
$348$	−0.628699	+	4.37270i	−0.0337018	+	0.234401i
$349$	3.93021	−	8.60596i	0.210379	−	0.460666i	−0.774797	−	0.632210i	$-0.782148\pi$
$349$	3.93021	−	8.60596i	0.210379	−	0.460666i	0.985177	+	0.171543i	$0.0548754\pi$
$350$	3.31018	−	0.971955i	0.176936	−	0.0519532i
$351$	1.21179	+	2.65345i	0.0646805	+	0.141631i
$352$	−2.33962	−	2.70006i	−0.124702	−	0.143914i
$353$	4.96524	+	34.5340i	0.264273	+	1.83806i	0.499737	+	0.866177i	$0.333430\pi$
$353$	4.96524	+	34.5340i	0.264273	+	1.83806i	−0.235463	+	0.971883i	$0.575661\pi$
$354$	2.19510	+	0.644538i	0.116668	+	0.0342568i
$355$	3.00530	−	3.46830i	0.159505	−	0.184078i
$356$	−9.20335	−	5.91464i	−0.487777	−	0.313475i
$357$	5.81152	+	3.73484i	0.307578	+	0.197669i
$358$	−0.656851	+	0.758046i	−0.0347157	+	0.0400640i
$359$	18.4440	+	5.41566i	0.973439	+	0.285827i	0.729513	−	0.683967i	$-0.239747\pi$
$359$	18.4440	+	5.41566i	0.973439	+	0.285827i	0.243925	+	0.969794i	$0.421565\pi$
$360$	0.142315	+	0.989821i	0.00750065	+	0.0521682i
$361$	11.9313	+	13.7695i	0.627964	+	0.724709i
$362$	−4.97772	−	10.8997i	−0.261623	−	0.572875i
$363$	1.69269	−	0.497020i	0.0888434	−	0.0260868i
$364$	4.18057	−	9.15418i	0.219122	−	0.479809i
$365$	−0.218519	+	1.51984i	−0.0114378	+	0.0795519i
$366$	−0.362970	+	0.233267i	−0.0189727	+	0.0121930i
$367$	22.9467			1.19781			0.598905	−	0.800820i	$-0.295603\pi$
$367$	22.9467			1.19781			0.598905	+	0.800820i	$0.295603\pi$
$368$	1.86534	+	4.41820i	0.0972374	+	0.230315i
$369$	8.02456			0.417742
$370$	2.34878	−	1.50947i	0.122107	−	0.0784734i
$371$	1.54878	−	10.7720i	0.0804085	−	0.559253i
$372$	−0.741785	+	1.62428i	−0.0384598	+	0.0842152i
$373$	−17.2684	+	5.07045i	−0.894122	+	0.262538i	−0.696343	−	0.717709i	$-0.745191\pi$
$373$	−17.2684	+	5.07045i	−0.894122	+	0.262538i	−0.197778	+	0.980247i	$0.563373\pi$
$374$	2.97189	+	6.50752i	0.153673	+	0.336496i
$375$	−0.654861	−	0.755750i	−0.0338169	−	0.0390267i
$376$	0.948203	+	6.59490i	0.0488998	+	0.340106i
$377$	−12.3646	−	3.63057i	−0.636808	−	0.186984i
$378$	−2.25922	+	2.60728i	−0.116202	+	0.134104i
$379$	−26.8009	−	17.2239i	−1.37667	−	0.884731i	−0.377520	−	0.926001i	$-0.623223\pi$
$379$	−26.8009	−	17.2239i	−1.37667	−	0.884731i	−0.999148	+	0.0412703i	$0.986860\pi$
$380$	0.743151	+	0.477594i	0.0381229	+	0.0245001i
$381$	13.2010	−	15.2348i	0.676309	−	0.780502i
$382$	−16.9158	−	4.96694i	−0.865490	−	0.254131i
$383$	1.32646	+	9.22570i	0.0677787	+	0.471411i	0.995237	+	0.0974848i	$0.0310797\pi$
$383$	1.32646	+	9.22570i	0.0677787	+	0.471411i	−0.927458	+	0.373927i	$0.878011\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	5.12021	+	11.2117i	0.260950	+	0.571400i
$386$	−15.2647	+	4.48213i	−0.776955	+	0.228134i
$387$	−1.38495	+	3.03261i	−0.0704008	+	0.154156i
$388$	−0.469330	+	3.26426i	−0.0238266	+	0.165718i
$389$	19.4127	−	12.4758i	0.984264	−	0.632548i	0.0536535	−	0.998560i	$-0.482913\pi$
$389$	19.4127	−	12.4758i	0.984264	−	0.632548i	0.930610	+	0.366012i	$0.119277\pi$
$390$	−2.91706			−0.147711
$391$	−1.09137	−	9.54102i	−0.0551928	−	0.482510i
$392$	4.90196			0.247586
$393$	−10.2780	+	6.60530i	−0.518459	+	0.333193i
$394$	−2.90138	+	20.1795i	−0.146169	+	1.01663i
$395$	−2.33239	+	5.10721i	−0.117355	+	0.256972i
$396$	−3.42798	+	1.00654i	−0.172262	+	0.0505808i
$397$	7.77143	+	17.0170i	0.390037	+	0.854061i	0.998184	+	0.0602371i	$0.0191857\pi$
$397$	7.77143	+	17.0170i	0.390037	+	0.854061i	−0.608147	+	0.793824i	$0.708087\pi$
$398$	2.69860	+	3.11435i	0.135269	+	0.156108i
$399$	0.433720	+	3.01659i	0.0217132	+	0.151018i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−12.6891	+	14.6440i	−0.633661	+	0.731284i	−0.978241	−	0.207473i	$-0.933476\pi$
$401$	−12.6891	+	14.6440i	−0.633661	+	0.731284i	0.344579	+	0.938757i	$0.388022\pi$
$402$	4.69226	+	3.01553i	0.234028	+	0.150401i
$403$	−4.38195	−	2.81611i	−0.218281	−	0.140280i
$404$	−9.66262	+	11.1513i	−0.480733	+	0.554796i
$405$	0.959493	+	0.281733i	0.0476776	+	0.0139994i
$406$	−2.16896	−	15.0855i	−0.107644	−	0.748679i
$407$	6.53220	+	7.53856i	0.323789	+	0.373673i
$408$	−0.831833	−	1.82146i	−0.0411819	−	0.0901757i
$409$	15.0320	−	4.41380i	0.743286	−	0.218248i	0.111902	−	0.993719i	$-0.464306\pi$
$409$	15.0320	−	4.41380i	0.743286	−	0.218248i	0.631383	+	0.775471i	$0.282487\pi$
$410$	−3.33352	+	7.29940i	−0.164631	+	0.360491i
$411$	−2.08685	+	14.5144i	−0.102937	+	0.715941i
$412$	13.1280	−	8.43685i	0.646770	−	0.415654i
$413$	−7.89261			−0.388370
$414$	4.79383	+	0.138618i	0.235604	+	0.00681272i
$415$	16.6756			0.818572
$416$	−2.45398	+	1.57708i	−0.120316	+	0.0773227i
$417$	1.17537	−	8.17490i	0.0575583	−	0.400327i
$418$	−1.31108	+	2.87086i	−0.0641269	+	0.140418i
$419$	−0.259147	+	0.0760924i	−0.0126601	+	0.00371735i	−0.288056	−	0.957613i	$-0.593009\pi$
$419$	−0.259147	+	0.0760924i	−0.0126601	+	0.00371735i	0.275396	+	0.961331i	$0.411191\pi$
$420$	−1.43315	−	3.13816i	−0.0699305	−	0.153126i
$421$	−11.7970	−	13.6144i	−0.574948	−	0.663526i	0.391562	−	0.920152i	$-0.371935\pi$
$421$	−11.7970	−	13.6144i	−0.574948	−	0.663526i	−0.966511	+	0.256626i	$0.917389\pi$
$422$	−1.63288	−	11.3569i	−0.0794874	−	0.552847i
$423$	6.39283	+	1.87710i	0.310830	+	0.0912679i
$424$	−2.06575	+	2.38401i	−0.100322	+	0.115778i
$425$	1.68454	+	1.08259i	0.0817121	+	0.0525132i
$426$	−3.86069	−	2.48112i	−0.187051	−	0.120210i
$427$	0.974769	−	1.12494i	0.0471724	−	0.0544399i
$428$	8.43970	+	2.47812i	0.407948	+	0.119784i
$429$	−1.48317	−	10.3157i	−0.0716081	−	0.498045i
$430$	−2.18323	−	2.51958i	−0.105285	−	0.121505i
$431$	−9.47823	−	20.7544i	−0.456550	−	0.999706i	−0.988260	−	0.152779i	$-0.951178\pi$
$431$	−9.47823	−	20.7544i	−0.456550	−	0.999706i	0.531710	−	0.846926i	$-0.321550\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	8.04525	−	17.6166i	0.386630	−	0.846602i	−0.611823	−	0.790995i	$-0.709563\pi$
$433$	8.04525	−	17.6166i	0.386630	−	0.846602i	0.998453	−	0.0556068i	$-0.0177093\pi$
$434$	0.876709	−	6.09765i	0.0420834	−	0.292696i
$435$	−3.71638	+	2.38837i	−0.178187	+	0.114514i
$436$	14.7335			0.705606
$437$	2.86575	−	3.12026i	0.137087	−	0.149262i
$438$	1.53547			0.0733674
$439$	30.9917	−	19.9171i	1.47915	−	0.950593i	0.481921	−	0.876215i	$-0.339939\pi$
$439$	30.9917	−	19.9171i	1.47915	−	0.950593i	0.997230	−	0.0743777i	$-0.0236970\pi$
$440$	0.508448	−	3.53633i	0.0242393	−	0.168588i
$441$	2.03635	−	4.45898i	0.0969689	−	0.212332i
$442$	5.60454	−	1.64564i	0.266581	−	0.0782752i
$443$	14.2737	+	31.2551i	0.678165	+	1.48497i	0.864576	+	0.502502i	$0.167587\pi$
$443$	14.2737	+	31.2551i	0.678165	+	1.48497i	−0.186411	+	0.982472i	$0.559685\pi$
$444$	−1.82837	−	2.11005i	−0.0867705	−	0.100138i
$445$	−1.55693	−	10.8287i	−0.0738056	−	0.513329i
$446$	4.01891	+	1.18006i	0.190301	+	0.0558774i
$447$	−12.9435	+	14.9376i	−0.612208	+	0.706526i
$448$	−2.90226	−	1.86517i	−0.137119	−	0.0881209i
$449$	−22.6309	−	14.5440i	−1.06802	−	0.686375i	−0.116260	−	0.993219i	$-0.537091\pi$
$449$	−22.6309	−	14.5440i	−1.06802	−	0.686375i	−0.951760	+	0.306844i	$0.900727\pi$
$450$	−0.654861	+	0.755750i	−0.0308704	+	0.0356264i
$451$	−27.5080	−	8.07708i	−1.29530	−	0.380335i
$452$	2.61713	+	18.2025i	0.123099	+	0.856174i
$453$	−6.27561	−	7.24244i	−0.294854	−	0.340279i
$454$	6.75265	+	14.7862i	0.316918	+	0.693953i
$455$	9.65596	−	2.83525i	0.452679	−	0.132918i
$456$	0.366972	−	0.803556i	0.0171850	−	0.0376299i
$457$	3.96111	−	27.5501i	0.185293	−	1.28874i	−0.658709	−	0.752398i	$-0.728897\pi$
$457$	3.96111	−	27.5501i	0.185293	−	1.28874i	0.844001	−	0.536341i	$-0.180194\pi$
$458$	4.93520	−	3.17166i	0.230607	−	0.148202i
$459$	−2.00241			−0.0934647
$460$	−2.11752	+	4.30303i	−0.0987299	+	0.200630i
$461$	13.8343			0.644327			0.322163	−	0.946684i	$-0.395590\pi$
$461$	13.8343			0.644327			0.322163	+	0.946684i	$0.395590\pi$
$462$	10.3689	−	6.66368i	0.482404	−	0.310022i
$463$	3.60814	−	25.0952i	0.167685	−	1.16627i	−0.715970	−	0.698131i	$-0.754015\pi$
$463$	3.60814	−	25.0952i	0.167685	−	1.16627i	0.883654	−	0.468140i	$-0.155076\pi$
$464$	−1.83516	+	4.01845i	−0.0851954	+	0.186552i
$465$	−1.71332	+	0.503076i	−0.0794532	+	0.0233296i
$466$	−9.16593	−	20.0706i	−0.424604	−	0.929752i
$467$	−11.7828	−	13.5981i	−0.545245	−	0.629246i	0.414524	−	0.910039i	$-0.363948\pi$
$467$	−11.7828	−	13.5981i	−0.545245	−	0.629246i	−0.959769	+	0.280792i	$0.909403\pi$
$468$	0.415140	+	2.88736i	0.0191899	+	0.133468i
$469$	−18.4631	−	5.42127i	−0.852549	−	0.250331i
$470$	−4.36315	+	5.03534i	−0.201257	+	0.232263i
$471$	10.9718	+	7.05115i	0.505554	+	0.324900i
$472$	1.92459	+	1.23686i	0.0885865	+	0.0569311i
$473$	7.80003	−	9.00171i	0.358646	−	0.413899i
$474$	5.38716	+	1.58181i	0.247441	+	0.0726551i
$475$	0.125719	+	0.874394i	0.00576838	+	0.0401199i
$476$	4.52389	+	5.22085i	0.207352	+	0.239297i
$477$	1.31042	+	2.86943i	0.0600002	+	0.131382i
$478$	−6.00657	+	1.76369i	−0.274734	+	0.0806693i
$479$	7.02663	−	15.3862i	0.321055	−	0.703012i	−0.678445	−	0.734652i	$-0.737346\pi$
$479$	7.02663	−	15.3862i	0.321055	−	0.703012i	0.999499	+	0.0316398i	$0.0100729\pi$
$480$	−0.142315	+	0.989821i	−0.00649575	+	0.0451790i
$481$	6.85151	−	4.40320i	0.312402	−	0.200768i
$482$	0.321674			0.0146518
$483$	−16.0031	+	4.20053i	−0.728168	+	0.191131i
$484$	1.76416			0.0801889
$485$	−2.77431	+	1.78294i	−0.125975	+	0.0809592i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	−13.2410	+	28.9938i	−0.600009	+	1.31384i	0.329193	+	0.944263i	$0.393223\pi$
$487$	−13.2410	+	28.9938i	−0.600009	+	1.31384i	−0.929202	+	0.369573i	$0.879504\pi$
$488$	−0.413986	+	0.121557i	−0.0187403	+	0.00550264i
$489$	2.16087	+	4.73165i	0.0977181	+	0.213973i
$490$	3.21010	+	3.70465i	0.145017	+	0.167359i
$491$	−3.09971	−	21.5590i	−0.139888	−	0.972942i	−0.931972	−	0.362530i	$-0.881913\pi$
$491$	−3.09971	−	21.5590i	−0.139888	−	0.972942i	0.792084	−	0.610412i	$-0.208996\pi$
$492$	7.69951	+	2.26078i	0.347121	+	0.101924i
$493$	5.79290	−	6.68536i	0.260899	−	0.301093i
$494$	2.16781	+	1.39317i	0.0975345	+	0.0626816i
$495$	−3.00554	−	1.93155i	−0.135089	−	0.0868165i
$496$	−1.16935	+	1.34950i	−0.0525054	+	0.0605945i
$497$	15.1911	+	4.46051i	0.681414	+	0.200081i
$498$	−2.37318	−	16.5058i	−0.106345	−	0.739645i
$499$	−5.34372	−	6.16699i	−0.239218	−	0.276072i	0.623428	−	0.781881i	$-0.285740\pi$
$499$	−5.34372	−	6.16699i	−0.239218	−	0.276072i	−0.862646	+	0.505809i	$0.831194\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	−0.140387	+	0.0412212i	−0.00627201	+	0.00184163i
$502$	3.96072	−	8.67276i	0.176775	−	0.387084i
$503$	−0.132378	+	0.920708i	−0.00590243	+	0.0410523i	−0.992560	−	0.121758i	$-0.961147\pi$
$503$	−0.132378	+	0.920708i	−0.00590243	+	0.0410523i	0.986657	+	0.162810i	$0.0520559\pi$
$504$	−2.90226	+	1.86517i	−0.129277	+	0.0830812i
$505$	−14.7552			−0.656599
$506$	−16.2936	−	5.30038i	−0.724339	−	0.235631i
$507$	4.49079			0.199443
$508$	16.9584	−	10.8985i	0.752408	−	0.483543i
$509$	−3.04140	+	21.1534i	−0.134807	+	0.937607i	0.804359	+	0.594144i	$0.202509\pi$
$509$	−3.04140	+	21.1534i	−0.134807	+	0.937607i	−0.939166	+	0.343463i	$0.888400\pi$
$510$	0.831833	−	1.82146i	0.0368342	−	0.0806556i
$511$	−5.08266	+	1.49240i	−0.224844	+	0.0660200i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−0.578494	−	0.667618i	−0.0255412	−	0.0294761i
$514$	−1.63303	−	11.3579i	−0.0720297	−	0.500977i
$515$	14.9732	+	4.39651i	0.659796	+	0.193734i
$516$	−2.18323	+	2.51958i	−0.0961115	+	0.110919i
$517$	−20.0251	−	12.8693i	−0.880702	−	0.565993i
$518$	8.10309	+	5.20754i	0.356029	+	0.228806i
$519$	11.8799	−	13.7101i	0.521468	−	0.601807i
$520$	−2.79889	−	0.821829i	−0.122740	−	0.0360396i
$521$	0.446868	+	3.10803i	0.0195776	+	0.136165i	0.997266	−	0.0738951i	$-0.0235430\pi$
$521$	0.446868	+	3.10803i	0.0195776	+	0.136165i	−0.977688	+	0.210060i	$0.932634\pi$
$522$	2.89296	+	3.33865i	0.126621	+	0.146129i
$523$	13.6560	+	29.9025i	0.597136	+	1.30755i	0.931033	+	0.364936i	$0.118909\pi$
$523$	13.6560	+	29.9025i	0.597136	+	1.30755i	−0.333897	+	0.942610i	$0.608364\pi$
$524$	−11.7226	+	3.44208i	−0.512106	+	0.150368i
$525$	1.43315	−	3.13816i	0.0625478	−	0.136960i
$526$	2.38725	−	16.6037i	0.104089	−	0.723956i
$527$	3.00799	−	1.93312i	0.131030	−	0.0842080i
$528$	−3.57270			−0.155482
$529$	18.5980	+	13.5320i	0.808608	+	0.588348i
$530$	−3.15449			−0.137022
$531$	1.92459	−	1.23686i	0.0835202	−	0.0536751i
$532$	−0.433720	+	3.01659i	−0.0188042	+	0.130786i
$533$	−9.72407	+	21.2927i	−0.421196	+	0.922291i
$534$	−10.4969	+	3.08217i	−0.454245	+	0.133378i
$535$	3.65399	+	8.00113i	0.157976	+	0.345919i
$536$	3.65261	+	4.21534i	0.157769	+	0.182075i
$537$	0.142747	+	0.992830i	0.00616000	+	0.0428438i
$538$	−7.95615	−	2.33614i	−0.343014	−	0.100718i
$539$	−11.4687	+	13.2356i	−0.493992	+	0.570097i
$540$	0.841254	+	0.540641i	0.0362018	+	0.0232655i
$541$	−16.0471	−	10.3129i	−0.689921	−	0.443385i	0.148137	−	0.988967i	$-0.452672\pi$
$541$	−16.0471	−	10.3129i	−0.689921	−	0.443385i	−0.838058	+	0.545582i	$0.816309\pi$
$542$	−7.20850	+	8.31905i	−0.309632	+	0.357334i
$543$	−11.4971	−	3.37587i	−0.493390	−	0.144872i
$544$	−0.284973	−	1.98203i	−0.0122181	−	0.0849789i
$545$	9.64838	+	11.1348i	0.413291	+	0.476963i
$546$	−4.18057	−	9.15418i	−0.178912	−	0.391763i
$547$	−1.10924	+	0.325702i	−0.0474276	+	0.0139260i	−0.305360	−	0.952237i	$-0.598777\pi$
$547$	−1.10924	+	0.325702i	−0.0474276	+	0.0139260i	0.257933	+	0.966163i	$0.416959\pi$
$548$	−6.09149	+	13.3385i	−0.260216	+	0.569793i
$549$	−0.0614036	+	0.427072i	−0.00262064	+	0.0182270i
$550$	3.00554	−	1.93155i	0.128157	−	0.0823614i
$551$	3.90250			0.166252
$552$	4.56059	+	1.48358i	0.194112	+	0.0631454i
$553$	−19.3699			−0.823692
$554$	14.4466	−	9.28430i	0.613779	−	0.394452i
$555$	0.397342	−	2.76358i	0.0168662	−	0.117307i
$556$	3.43090	−	7.51262i	0.145503	−	0.318606i
$557$	19.4224	−	5.70293i	0.822954	−	0.241641i	0.156966	−	0.987604i	$-0.449829\pi$
$557$	19.4224	−	5.70293i	0.822954	−	0.241641i	0.665987	+	0.745963i	$0.268010\pi$
$558$	0.741785	+	1.62428i	0.0314023	+	0.0687614i
$559$	−6.36861	−	7.34977i	−0.269364	−	0.310862i
$560$	−0.490975	−	3.41481i	−0.0207475	−	0.144302i
$561$	6.86423	+	2.01552i	0.289808	+	0.0850953i
$562$	5.52528	−	6.37651i	0.233070	−	0.268977i
$563$	33.5785	+	21.5796i	1.41517	+	0.909473i	1.00000		0.000272706i	$-8.68051e-5\pi$
$563$	33.5785	+	21.5796i	1.41517	+	0.909473i	0.415167	+	0.909745i	$0.363723\pi$
$564$	5.60503	+	3.60214i	0.236014	+	0.151677i
$565$	−12.0427	+	13.8980i	−0.506640	+	0.584693i
$566$	−21.3613	−	6.27225i	−0.897883	−	0.263642i
$567$	0.490975	+	3.41481i	0.0206190	+	0.143408i
$568$	−3.00530	−	3.46830i	−0.126099	−	0.145526i
$569$	10.5859	+	23.1800i	0.443785	+	0.971754i	0.990888	+	0.134689i	$0.0430035\pi$
$569$	10.5859	+	23.1800i	0.443785	+	0.971754i	−0.547103	+	0.837066i	$0.684269\pi$
$570$	0.847602	−	0.248878i	0.0355021	−	0.0104244i
$571$	−18.0824	+	39.5950i	−0.756727	+	1.65700i	−0.00283969	+	0.999996i	$0.500904\pi$
$571$	−18.0824	+	39.5950i	−0.756727	+	1.65700i	−0.753887	+	0.657004i	$0.771823\pi$
$572$	1.48317	−	10.3157i	0.0620144	−	0.431320i
$573$	−14.8313	+	9.53149i	−0.619586	+	0.398184i
$574$	−27.6841			−1.15551
$575$	−4.63870	+	1.21757i	−0.193447	+	0.0507763i
$576$	1.00000			0.0416667
$577$	31.4207	−	20.1928i	1.30806	−	0.840639i	0.313995	−	0.949425i	$-0.398333\pi$
$577$	31.4207	−	20.1928i	1.30806	−	0.840639i	0.994065	+	0.108786i	$0.0346962\pi$
$578$	1.84872	−	12.8581i	0.0768965	−	0.534827i
$579$	−6.60891	+	14.4715i	−0.274657	+	0.601414i
$580$	−4.23872	+	1.24460i	−0.176003	+	0.0516792i
$581$	23.8986	+	52.3306i	0.991480	+	2.17104i
$582$	2.15962	+	2.49233i	0.0895191	+	0.103311i
$583$	−1.60389	−	11.1553i	−0.0664265	−	0.462007i
$584$	1.47327	+	0.432591i	0.0609643	+	0.0179007i
$585$	−1.91026	+	2.20456i	−0.0789797	+	0.0911475i
$586$	9.78607	+	6.28912i	0.404259	+	0.259801i
$587$	6.11634	+	3.93073i	0.252448	+	0.162239i	0.660745	−	0.750611i	$-0.270241\pi$
$587$	6.11634	+	3.93073i	0.252448	+	0.162239i	−0.408296	+	0.912849i	$0.633877\pi$
$588$	3.21010	−	3.70465i	0.132382	−	0.152777i
$589$	1.51352	+	0.444410i	0.0623635	+	0.0183116i
$590$	0.325583	+	2.26448i	0.0134040	+	0.0932272i
$591$	13.3507	+	15.4075i	0.549173	+	0.633780i
$592$	−1.15984	−	2.53969i	−0.0476690	−	0.104381i
$593$	−39.1398	+	11.4925i	−1.60728	+	0.471940i	−0.957560	−	0.288235i	$-0.906932\pi$
$593$	−39.1398	+	11.4925i	−1.60728	+	0.471940i	−0.649719	+	0.760174i	$0.725113\pi$
$594$	−1.48415	+	3.24984i	−0.0608955	+	0.133342i
$595$	−0.983135	+	6.83786i	−0.0403046	+	0.280325i
$596$	−16.6276	+	10.6859i	−0.681095	+	0.437713i
$597$	4.12088			0.168656
$598$	−6.17692	+	12.5522i	−0.252593	+	0.513297i
$599$	45.3874			1.85448			0.927239	−	0.374470i	$-0.122175\pi$
$599$	45.3874			1.85448			0.927239	+	0.374470i	$0.122175\pi$
$600$	−0.841254	+	0.540641i	−0.0343440	+	0.0220716i
$601$	−4.69569	+	32.6593i	−0.191541	+	1.33220i	0.636389	+	0.771368i	$0.280427\pi$
$601$	−4.69569	+	32.6593i	−0.191541	+	1.33220i	−0.827930	+	0.560831i	$0.810482\pi$
$602$	4.77796	−	10.4623i	0.194735	−	0.426410i
$603$	5.35176	−	1.57142i	0.217940	−	0.0639931i
$604$	−3.98097	−	8.71711i	−0.161983	−	0.354694i
$605$	1.15528	+	1.33326i	0.0469687	+	0.0542047i
$606$	2.09989	+	14.6050i	0.0853021	+	0.593289i
$607$	−42.3421	−	12.4328i	−1.71861	−	0.504631i	−0.733967	−	0.679186i	$-0.762333\pi$
$607$	−42.3421	−	12.4328i	−1.71861	−	0.504631i	−0.984647	+	0.174555i	$0.944151\pi$
$608$	0.578494	−	0.667618i	0.0234610	−	0.0270755i
$609$	−12.8212	−	8.23969i	−0.519542	−	0.333889i
$610$	−0.362970	−	0.233267i	−0.0146962	−	0.00944469i
$611$	−12.7275	+	14.6884i	−0.514901	+	0.594228i
$612$	−1.92130	−	0.564145i	−0.0776640	−	0.0228042i
$613$	−3.54682	−	24.6687i	−0.143255	−	0.996360i	−0.926942	−	0.375204i	$-0.877573\pi$
$613$	−3.54682	−	24.6687i	−0.143255	−	0.996360i	0.783687	−	0.621155i	$-0.213336\pi$
$614$	15.2013	+	17.5432i	0.613475	+	0.707987i
$615$	3.33352	+	7.29940i	0.134421	+	0.294340i
$616$	11.8262	−	3.47250i	0.476493	−	0.139911i
$617$	−0.150510	+	0.329570i	−0.00605929	+	0.0132680i	−0.912637	−	0.408770i	$-0.865958\pi$
$617$	−0.150510	+	0.329570i	−0.00605929	+	0.0132680i	0.906578	+	0.422038i	$0.138685\pi$
$618$	2.22086	−	15.4464i	0.0893362	−	0.621347i
$619$	−19.5685	+	12.5759i	−0.786526	+	0.505470i	−0.871194	−	0.490940i	$-0.836654\pi$
$619$	−19.5685	+	12.5759i	−0.786526	+	0.505470i	0.0846675	+	0.996409i	$0.473017\pi$
$620$	−1.78565			−0.0717134
$621$	3.24405	−	3.53216i	0.130179	−	0.141741i
$622$	13.8232			0.554260
$623$	31.7508	−	20.4050i	1.27207	−	0.817510i
$624$	−0.415140	+	2.88736i	−0.0166189	+	0.115587i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−27.3925	+	8.04316i	−1.09482	+	0.321470i
$627$	1.31108	+	2.87086i	0.0523594	+	0.114651i
$628$	8.54083	+	9.85664i	0.340816	+	0.393323i
$629$	0.795644	+	5.53382i	0.0317244	+	0.220648i
$630$	−3.31018	−	0.971955i	−0.131881	−	0.0387236i
$631$	−25.6469	+	29.5981i	−1.02099	+	1.17828i	−0.0371333	+	0.999310i	$0.511823\pi$
$631$	−25.6469	+	29.5981i	−1.02099	+	1.17828i	−0.983854	+	0.178972i	$0.942723\pi$
$632$	4.72329	+	3.03548i	0.187883	+	0.120745i
$633$	−9.65231	−	6.20316i	−0.383645	−	0.246554i
$634$	−2.32912	+	2.68794i	−0.0925010	+	0.106752i
$635$	19.3419	+	5.67931i	0.767562	+	0.225376i
$636$	0.448931	+	3.12239i	0.0178013	+	0.123811i
$637$	9.36404	+	10.8067i	0.371017	+	0.428176i
$638$	−6.55649	−	14.3567i	−0.259574	−	0.568387i
$639$	−4.40332	+	1.29293i	−0.174193	+	0.0511475i
$640$	−0.415415	+	0.909632i	−0.0164207	+	0.0359564i
$641$	−3.23735	+	22.5163i	−0.127868	+	0.889340i	0.820382	+	0.571816i	$0.193761\pi$
$641$	−3.23735	+	22.5163i	−0.127868	+	0.889340i	−0.948250	+	0.317525i	$0.897148\pi$
$642$	7.39967	−	4.75548i	0.292042	−	0.187684i
$643$	0.617140			0.0243376			0.0121688	−	0.999926i	$-0.496126\pi$
$643$	0.617140			0.0243376			0.0121688	+	0.999926i	$0.496126\pi$
$644$	−16.5383	−	0.478223i	−0.651701	−	0.0188446i
$645$	−3.33389			−0.131272
$646$	−1.48810	+	0.956341i	−0.0585484	+	0.0376268i
$647$	−0.753992	+	5.24413i	−0.0296425	+	0.206168i	−0.999260	−	0.0384570i	$-0.987756\pi$
$647$	−0.753992	+	5.24413i	−0.0296425	+	0.206168i	0.969618	+	0.244625i	$0.0786648\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	−7.84241	+	2.30274i	−0.307841	+	0.0903904i
$650$	−1.21179	−	2.65345i	−0.0475303	−	0.104077i
$651$	−4.03417	−	4.65568i	−0.158112	−	0.182471i
$652$	0.740282	+	5.14878i	0.0289917	+	0.201642i
$653$	−28.6830	−	8.42208i	−1.12245	−	0.329582i	−0.332715	−	0.943027i	$-0.607965\pi$
$653$	−28.6830	−	8.42208i	−1.12245	−	0.329582i	−0.789737	+	0.613446i	$0.789783\pi$
$654$	9.64838	−	11.1348i	0.377282	−	0.435406i
$655$	−10.2780	−	6.60530i	−0.401596	−	0.258090i
$656$	6.75069	+	4.33840i	0.263570	+	0.169386i
$657$	1.00552	−	1.16043i	0.0392289	−	0.0452726i
$658$	−22.0548	−	6.47586i	−0.859784	−	0.252455i
$659$	1.47779	+	10.2782i	0.0575664	+	0.400383i	0.998149	+	0.0608177i	$0.0193708\pi$
$659$	1.47779	+	10.2782i	0.0575664	+	0.400383i	−0.940583	+	0.339565i	$0.889720\pi$
$660$	−2.33962	−	2.70006i	−0.0910695	−	0.105100i
$661$	−1.23883	−	2.71266i	−0.0481849	−	0.105510i	0.884008	−	0.467471i	$-0.154835\pi$
$661$	−1.23883	−	2.71266i	−0.0481849	−	0.105510i	−0.932193	+	0.361961i	$0.882107\pi$
$662$	−11.4186	+	3.35282i	−0.443798	+	0.130311i
$663$	2.42650	−	5.31330i	0.0942375	−	0.206351i
$664$	2.37318	−	16.5058i	0.0920973	−	0.640551i
$665$	−2.56381	+	1.64766i	−0.0994204	+	0.0638936i
$666$	−2.79200			−0.108188
$667$	2.40774	+	21.0491i	0.0932281	+	0.815025i
$668$	−0.146313			−0.00566103
$669$	3.52366	−	2.26452i	0.136233	−	0.0875513i
$670$	−0.793789	+	5.52092i	−0.0306667	+	0.213292i
$671$	0.640357	−	1.40219i	0.0247207	−	0.0541308i
$672$	−3.31018	+	0.971955i	−0.127693	+	0.0374940i
$673$	0.691741	+	1.51470i	0.0266647	+	0.0583875i	0.922496	−	0.386007i	$-0.126146\pi$
$673$	0.691741	+	1.51470i	0.0266647	+	0.0583875i	−0.895831	+	0.444395i	$0.853419\pi$
$674$	−20.0646	−	23.1558i	−0.772861	−	0.891929i
$675$	0.142315	+	0.989821i	0.00547770	+	0.0380982i
$676$	4.30888	+	1.26520i	0.165726	+	0.0486616i
$677$	−10.9338	+	12.6183i	−0.420220	+	0.484960i	−0.925904	−	0.377759i	$-0.876695\pi$
$677$	−10.9338	+	12.6183i	−0.420220	+	0.484960i	0.505684	+	0.862719i	$0.331240\pi$
$678$	15.4704	+	9.94222i	0.594137	+	0.381829i
$679$	−9.57116	−	6.15101i	−0.367307	−	0.236054i
$680$	1.31130	−	1.51332i	0.0502861	−	0.0580333i
$681$	15.5967	+	4.57962i	0.597668	+	0.175491i
$682$	−0.907909	−	6.31465i	−0.0347656	−	0.241800i
$683$	13.1410	+	15.1655i	0.502825	+	0.580291i	0.949247	−	0.314532i	$-0.101847\pi$
$683$	13.1410	+	15.1655i	0.502825	+	0.580291i	−0.446422	+	0.894823i	$0.647302\pi$
$684$	−0.366972	−	0.803556i	−0.0140315	−	0.0307247i
$685$	−14.0696	+	4.13122i	−0.537574	+	0.157846i
$686$	3.00681	−	6.58399i	0.114800	−	0.251378i
$687$	0.834888	−	5.80677i	0.0318530	−	0.221542i
$688$	−2.80465	+	1.80244i	−0.106926	+	0.0687172i
$689$	−9.20183			−0.350562
$690$	1.86534	+	4.41820i	0.0710121	+	0.168198i
$691$	−42.5140			−1.61731			−0.808654	−	0.588284i	$-0.799804\pi$
$691$	−42.5140			−1.61731			−0.808654	+	0.588284i	$0.799804\pi$
$692$	15.2612	−	9.80780i	0.580145	−	0.372837i
$693$	1.75410	−	12.2001i	0.0666329	−	0.463442i
$694$	8.07394	−	17.6795i	0.306483	−	0.671103i
$695$	7.92442	−	2.32682i	0.300591	−	0.0882613i
$696$	1.83516	+	4.01845i	0.0695617	+	0.152319i
$697$	−10.5226	−	12.1438i	−0.398573	−	0.459978i
$698$	−1.34643	−	9.36463i	−0.0509631	−	0.354456i
$699$	−21.1708	−	6.21629i	−0.800751	−	0.235122i
$700$	2.25922	−	2.60728i	0.0853904	−	0.0985458i
$701$	4.59536	+	2.95326i	0.173564	+	0.111543i	0.624539	−	0.780994i	$-0.285287\pi$
$701$	4.59536	+	2.95326i	0.173564	+	0.111543i	−0.450974	+	0.892537i	$0.648923\pi$
$702$	2.45398	+	1.57708i	0.0926196	+	0.0595230i
$703$	−1.61515	+	1.86399i	−0.0609167	+	0.0703016i
$704$	−3.42798	−	1.00654i	−0.129197	−	0.0379356i
$705$	0.948203	+	6.59490i	0.0357114	+	0.248378i
$706$	22.8475	+	26.3675i	0.859878	+	0.992352i
$707$	−21.1464	−	46.3042i	−0.795293	−	1.74145i
$708$	2.19510	−	0.644538i	0.0824968	−	0.0242232i
$709$	13.7314	−	30.0676i	0.515694	−	1.12921i	−0.455351	−	0.890312i	$-0.650486\pi$
$709$	13.7314	−	30.0676i	0.515694	−	1.12921i	0.971044	−	0.238899i	$-0.0767866\pi$
$710$	0.653113	−	4.54250i	0.0245109	−	0.170477i
$711$	4.72329	−	3.03548i	0.177137	−	0.113839i
$712$	−10.9400			−0.409996
$713$	−1.46323	+	8.43774i	−0.0547985	+	0.315996i
$714$	6.90817			0.258532
$715$	8.76733	−	5.63442i	0.327880	−	0.210715i
$716$	−0.142747	+	0.992830i	−0.00533472	+	0.0371038i
$717$	−2.60056	+	5.69444i	−0.0971198	+	0.212663i
$718$	18.4440	−	5.41566i	0.688325	−	0.202110i
$719$	−11.8243	−	25.8916i	−0.440971	−	0.965593i	−0.991419	−	0.130723i	$-0.958270\pi$
$719$	−11.8243	−	25.8916i	−0.440971	−	0.965593i	0.550447	−	0.834870i	$-0.314457\pi$
$720$	0.654861	+	0.755750i	0.0244052	+	0.0281651i
$721$	7.66180	+	53.2890i	0.285340	+	1.98459i
$722$	17.4816	+	5.13306i	0.650598	+	0.191033i
$723$	0.210652	−	0.243105i	0.00783421	−	0.00904117i
$724$	−10.0803	−	6.47824i	−0.374633	−	0.240762i
$725$	−3.71638	−	2.38837i	−0.138023	−	0.0887019i
$726$	1.15528	−	1.33326i	0.0428763	−	0.0494819i
$727$	39.9797	+	11.7391i	1.48276	+	0.435379i	0.920224	−	0.391392i	$-0.128006\pi$
$727$	39.9797	+	11.7391i	1.48276	+	0.435379i	0.562539	+	0.826771i	$0.309824\pi$
$728$	−1.43220	−	9.96118i	−0.0530809	−	0.369186i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	0.637855	+	1.39671i	0.0236081	+	0.0516945i
$731$	6.40541	−	1.88080i	0.236913	−	0.0695638i
$732$	−0.179236	+	0.392473i	−0.00662476	+	0.0145062i
$733$	4.12562	−	28.6943i	0.152383	−	1.05985i	−0.759827	−	0.650126i	$-0.774716\pi$
$733$	4.12562	−	28.6943i	0.152383	−	1.05985i	0.912210	−	0.409723i	$-0.134375\pi$
$734$	19.3040	−	12.4059i	0.712524	−	0.457911i
$735$	4.90196			0.180811
$736$	3.95788	+	2.70835i	0.145889	+	0.0998312i
$737$	−19.9274			−0.734035
$738$	6.75069	−	4.33840i	0.248496	−	0.159699i
$739$	−2.14188	+	14.8971i	−0.0787905	+	0.548000i	0.911746	+	0.410753i	$0.134734\pi$
$739$	−2.14188	+	14.8971i	−0.0787905	+	0.548000i	−0.990537	+	0.137246i	$0.956175\pi$
$740$	1.15984	−	2.53969i	0.0426364	−	0.0933608i
$741$	2.47250	−	0.725992i	0.0908296	−	0.0266700i
$742$	−4.52086	−	9.89930i	−0.165966	−	0.363415i
$743$	−11.8152	−	13.6355i	−0.433457	−	0.500237i	0.496432	−	0.868076i	$-0.334643\pi$
$743$	−11.8152	−	13.6355i	−0.433457	−	0.500237i	−0.929889	+	0.367839i	$0.880098\pi$
$744$	0.254124	+	1.76747i	0.00931665	+	0.0647987i
$745$	−18.9647	−	5.56854i	−0.694812	−	0.204015i
$746$	−11.7858	+	13.6015i	−0.431508	+	0.497987i
$747$	−14.0284	−	9.01550i	−0.513272	−	0.329860i
$748$	6.01834	+	3.86775i	0.220052	+	0.141419i
$749$	−19.8721	+	22.9336i	−0.726110	+	0.837976i
$750$	−0.959493	−	0.281733i	−0.0350357	−	0.0102874i
$751$	3.89754	+	27.1080i	0.142223	+	0.989184i	0.928506	+	0.371317i	$0.121094\pi$
$751$	3.89754	+	27.1080i	0.142223	+	0.989184i	−0.786283	+	0.617867i	$0.787997\pi$
$752$	4.36315	+	5.03534i	0.159108	+	0.183620i
$753$	−3.96072	−	8.67276i	−0.144337	−	0.316053i
$754$	−12.3646	+	3.63057i	−0.450291	+	0.132217i
$755$	3.98097	−	8.71711i	0.144882	−	0.317248i
$756$	−0.490975	+	3.41481i	−0.0178566	+	0.124195i
$757$	27.8301	−	17.8853i	1.01150	−	0.650054i	0.0737214	−	0.997279i	$-0.476512\pi$
$757$	27.8301	−	17.8853i	1.01150	−	0.650054i	0.937782	+	0.347225i	$0.112876\pi$
$758$	−31.8583			−1.15714
$759$	−14.6758	+	8.84287i	−0.532698	+	0.320976i
$760$	0.883386			0.0320438
$761$	−38.4969	+	24.7404i	−1.39551	+	0.896840i	−0.999768	−	0.0215211i	$-0.993149\pi$
$761$	−38.4969	+	24.7404i	−1.39551	+	0.896840i	−0.395743	+	0.918362i	$0.629513\pi$
$762$	2.86886	−	19.9533i	0.103928	−	0.722833i
$763$	−21.1153	+	46.2360i	−0.764424	+	1.67386i
$764$	−16.9158	+	4.96694i	−0.611994	+	0.179698i
$765$	−0.831833	−	1.82146i	−0.0300750	−	0.0658550i
$766$	6.10368	+	7.04402i	0.220535	+	0.254511i
$767$	0.949744	+	6.60561i	0.0342933	+	0.238515i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	−26.9000	+	31.0443i	−0.970040	+	1.11949i	0.0227642	+	0.999741i	$0.492753\pi$
$769$	−26.9000	+	31.0443i	−0.970040	+	1.11949i	−0.992805	+	0.119745i	$0.961792\pi$
$770$	10.3689	+	6.66368i	0.373669	+	0.240142i
$771$	−9.65316	−	6.20371i	−0.347650	−	0.223421i
$772$	−10.4183	+	12.0233i	−0.374962	+	0.432730i
$773$	28.6971	+	8.42622i	1.03216	+	0.303070i	0.753590	−	0.657345i	$-0.228321\pi$
$773$	28.6971	+	8.42622i	1.03216	+	0.303070i	0.278573	+	0.960415i	$0.410139\pi$
$774$	0.474462	+	3.29995i	0.0170542	+	0.118614i
$775$	−1.16935	−	1.34950i	−0.0420043	−	0.0484756i
$776$	1.36997	+	2.99981i	0.0491790	+	0.107687i
$777$	9.24199	−	2.71369i	0.331555	−	0.0973532i
$778$	9.58609	−	20.9906i	0.343678	−	0.752550i
$779$	1.00884	−	7.01663i	0.0361454	−	0.251397i
$780$	−2.45398	+	1.57708i	−0.0878667	+	0.0564685i
$781$	16.3959			0.586690
$782$	−6.07638	−	7.43638i	−0.217291	−	0.265925i
$783$	4.41767			0.157874
$784$	4.12379	−	2.65020i	0.147278	−	0.0946499i
$785$	−1.85610	+	12.9095i	−0.0662470	+	0.460758i
$786$	−5.07535	+	11.1135i	−0.181032	+	0.396404i
$787$	19.2252	−	5.64504i	0.685306	−	0.201224i	0.0794980	−	0.996835i	$-0.474668\pi$
$787$	19.2252	−	5.64504i	0.685306	−	0.201224i	0.605808	+	0.795611i	$0.292850\pi$
$788$	8.46909	+	18.5447i	0.301699	+	0.660628i
$789$	−10.9849	−	12.6773i	−0.391074	−	0.451323i
$790$	0.799040	+	5.55744i	0.0284286	+	0.197725i
$791$	−60.8731	−	17.8740i	−2.16440	−	0.635525i
$792$	−2.33962	+	2.70006i	−0.0831347	+	0.0959426i
$793$	−1.05880	−	0.680452i	−0.0375992	−	0.0241635i
$794$	15.7379	+	10.1141i	0.558515	+	0.358936i
$795$	−2.06575	+	2.38401i	−0.0732647	+	0.0845520i
$796$	3.95395	+	1.16099i	0.140144	+	0.0411500i
$797$	6.74111	+	46.8854i	0.238782	+	1.66077i	0.658102	+	0.752928i	$0.271359\pi$
$797$	6.74111	+	46.8854i	0.238782	+	1.66077i	−0.419320	+	0.907838i	$0.637731\pi$
$798$	1.99576	+	2.30323i	0.0706492	+	0.0815335i
$799$	−5.54226	−	12.1359i	−0.196071	−	0.429336i
$800$	−0.959493	+	0.281733i	−0.0339232	+	0.00996075i
$801$	−4.54466	+	9.95142i	−0.160578	+	0.351616i
$802$	−2.75760	+	19.1795i	−0.0973741	+	0.677252i
$803$	−4.61491	+	2.96582i	−0.162857	+	0.104662i
$804$	5.57769			0.196710
$805$	−10.4689	−	12.8120i	−0.368980	−	0.451564i
$806$	−5.20884			−0.183473
$807$	−6.97571	+	4.48301i	−0.245556	+	0.157810i
$808$	−2.09989	+	14.6050i	−0.0738738	+	0.513803i
$809$	17.1952	−	37.6522i	0.604550	−	1.32378i	−0.321690	−	0.946845i	$-0.604251\pi$
$809$	17.1952	−	37.6522i	0.604550	−	1.32378i	0.926240	−	0.376935i	$-0.123022\pi$
$810$	0.959493	−	0.281733i	0.0337131	−	0.00989907i
$811$	17.4372	+	38.1822i	0.612304	+	1.34076i	0.920987	+	0.389593i	$0.127384\pi$
$811$	17.4372	+	38.1822i	0.612304	+	1.34076i	−0.308683	+	0.951165i	$0.599888\pi$
$812$	−9.98047	−	11.5181i	−0.350246	−	0.404205i
$813$	1.56656	+	10.8956i	0.0549416	+	0.382127i
$814$	9.57089	+	2.81027i	0.335460	+	0.0984998i
$815$	−3.40640	+	3.93120i	−0.119321	+	0.137704i
$816$	−1.68454	−	1.08259i	−0.0589706	−	0.0378981i
$817$	2.47758	+	1.59225i	0.0866797	+	0.0557056i
$818$	10.2595	−	11.8401i	0.358714	−	0.413978i
$819$	−9.65596	−	2.83525i	−0.337407	−	0.0990715i
$820$	1.14201	+	7.94288i	0.0398809	+	0.277377i
$821$	5.09320	+	5.87787i	0.177754	+	0.205139i	0.837634	−	0.546232i	$-0.183938\pi$
$821$	5.09320	+	5.87787i	0.177754	+	0.205139i	−0.659880	+	0.751371i	$0.729393\pi$
$822$	6.09149	+	13.3385i	0.212465	+	0.465234i
$823$	−0.630761	+	0.185208i	−0.0219869	+	0.00645595i	−0.292708	−	0.956202i	$-0.594556\pi$
$823$	−0.630761	+	0.185208i	−0.0219869	+	0.00645595i	0.270721	+	0.962658i	$0.412738\pi$
$824$	6.48266	−	14.1951i	0.225834	−	0.494508i
$825$	0.508448	−	3.53633i	0.0177019	−	0.123119i
$826$	−6.63969	+	4.26707i	−0.231024	+	0.148470i
$827$	−19.6319			−0.682669			−0.341335	−	0.939942i	$-0.610879\pi$
$827$	−19.6319			−0.682669			−0.341335	+	0.939942i	$0.610879\pi$
$828$	4.10777	−	2.47513i	0.142755	−	0.0860166i
$829$	−9.62079			−0.334144			−0.167072	−	0.985945i	$-0.553431\pi$
$829$	−9.62079			−0.334144			−0.167072	+	0.985945i	$0.553431\pi$
$830$	14.0284	−	9.01550i	0.486932	−	0.312932i
$831$	2.44394	−	16.9980i	0.0847793	−	0.589653i
$832$	−1.21179	+	2.65345i	−0.0420112	+	0.0919917i
$833$	−9.41814	+	2.76542i	−0.326319	+	0.0958160i
$834$	−3.43090	−	7.51262i	−0.118802	−	0.260141i
$835$	−0.0958148	−	0.110576i	−0.00331581	−	0.00382665i
$836$	0.449155	+	3.12394i	0.0155344	+	0.108044i
$837$	1.71332	+	0.503076i	0.0592209	+	0.0173888i
$838$	−0.176870	+	0.204118i	−0.00610986	+	0.00705115i
$839$	29.1487	+	18.7327i	1.00632	+	0.646726i	0.936439	−	0.350829i	$-0.114100\pi$
$839$	29.1487	+	18.7327i	1.00632	+	0.646726i	0.0698854	+	0.997555i	$0.477737\pi$
$840$	−2.90226	−	1.86517i	−0.100137	−	0.0643544i
$841$	6.21085	−	7.16770i	0.214167	−	0.247162i
$842$	−17.2847	−	5.07526i	−0.595671	−	0.174905i
$843$	−1.20076	−	8.35146i	−0.0413563	−	0.287639i
$844$	−7.51369	−	8.67126i	−0.258632	−	0.298477i
$845$	1.86554	+	4.08497i	0.0641766	+	0.140527i
$846$	6.39283	−	1.87710i	0.219790	−	0.0645361i
$847$	−2.52830	+	5.53620i	−0.0868733	+	0.190226i
$848$	−0.448931	+	3.12239i	−0.0154164	+	0.107223i
$849$	−18.7289	+	12.0364i	−0.642775	+	0.413087i
$850$	2.00241			0.0686822
$851$	−11.0504	−	7.56171i	−0.378802	−	0.259212i
$852$	−4.58921			−0.157224
$853$	41.6679	−	26.7783i	1.42668	−	0.916873i	0.426761	−	0.904365i	$-0.359655\pi$
$853$	41.6679	−	26.7783i	1.42668	−	0.916873i	0.999922	−	0.0125087i	$-0.00398175\pi$
$854$	0.211838	−	1.47336i	0.00724894	−	0.0504175i
$855$	0.366972	−	0.803556i	0.0125502	−	0.0274810i
$856$	8.43970	−	2.47812i	0.288463	−	0.0847004i
$857$	2.16699	+	4.74504i	0.0740228	+	0.162087i	0.943026	−	0.332719i	$-0.107966\pi$
$857$	2.16699	+	4.74504i	0.0740228	+	0.162087i	−0.869003	+	0.494807i	$0.835239\pi$
$858$	−6.82480	−	7.87623i	−0.232995	−	0.268890i
$859$	−3.21486	−	22.3598i	−0.109690	−	0.762908i	−0.968212	−	0.250131i	$-0.919526\pi$
$859$	−3.21486	−	22.3598i	−0.109690	−	0.762908i	0.858522	−	0.512776i	$-0.171383\pi$
$860$	−3.19884	−	0.939265i	−0.109080	−	0.0320287i
$861$	−18.1292	+	20.9222i	−0.617843	+	0.713028i
$862$	−19.1943	−	12.3354i	−0.653760	−	0.420146i
$863$	5.02987	+	3.23250i	0.171219	+	0.110036i	0.623443	−	0.781868i	$-0.285733\pi$
$863$	5.02987	+	3.23250i	0.171219	+	0.110036i	−0.452225	+	0.891904i	$0.649370\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	17.4062	+	5.11093i	0.591829	+	0.173777i
$866$	−2.75618	−	19.1697i	−0.0936588	−	0.651411i
$867$	−8.50686	−	9.81744i	−0.288908	−	0.333418i
$868$	−2.55910	−	5.60365i	−0.0868616	−	0.190200i
$869$	−19.2467	+	5.65134i	−0.652899	+	0.191708i
$870$	−1.83516	+	4.01845i	−0.0622179	+	0.136238i
$871$	−2.31553	+	16.1048i	−0.0784586	+	0.545691i
$872$	12.3946	−	7.96552i	0.419734	−	0.269747i
$873$	3.29783			0.111615
$874$	0.723882	−	4.17427i	0.0244857	−	0.141197i
$875$	3.44992			0.116629
$876$	1.29172	−	0.830135i	0.0436430	−	0.0280477i
$877$	−0.0560459	+	0.389808i	−0.00189254	+	0.0131629i	−0.990746	−	0.135730i	$-0.956662\pi$
$877$	−0.0560459	+	0.389808i	−0.00189254	+	0.0131629i	0.988853	+	0.148893i	$0.0475710\pi$
$878$	15.3038	−	33.5107i	0.516479	−	1.13093i
$879$	11.1615	−	3.27732i	0.376469	−	0.110541i
$880$	−1.48415	−	3.24984i	−0.0500307	−	0.109552i
$881$	−11.8955	−	13.7281i	−0.400768	−	0.462511i	0.519114	−	0.854705i	$-0.326262\pi$
$881$	−11.8955	−	13.7281i	−0.400768	−	0.462511i	−0.919883	+	0.392193i	$0.871716\pi$
$882$	−0.697621	−	4.85206i	−0.0234901	−	0.163377i
$883$	−4.49392	−	1.31953i	−0.151232	−	0.0444058i	0.205240	−	0.978712i	$-0.434202\pi$
$883$	−4.49392	−	1.31953i	−0.151232	−	0.0444058i	−0.356472	+	0.934306i	$0.616021\pi$
$884$	3.82514	−	4.41445i	0.128653	−	0.148474i
$885$	1.92459	+	1.23686i	0.0646944	+	0.0415766i
$886$	28.9056	+	18.5765i	0.971103	+	0.624090i
$887$	35.8713	−	41.3977i	1.20444	−	1.39000i	0.305345	−	0.952242i	$-0.401228\pi$
$887$	35.8713	−	41.3977i	1.20444	−	1.39000i	0.899094	−	0.437755i	$-0.144226\pi$
$888$	−2.67890	−	0.786596i	−0.0898980	−	0.0263964i
$889$	9.89732	+	68.8374i	0.331946	+	2.30873i
$890$	−7.16421	−	8.26794i	−0.240145	−	0.277142i
$891$	1.48415	+	3.24984i	0.0497209	+	0.108874i
$892$	4.01891	−	1.18006i	0.134563	−	0.0395113i
$893$	2.44503	−	5.35386i	0.0818197	−	0.179160i
$894$	−2.81290	+	19.5641i	−0.0940774	+	0.654323i
$895$	−0.843810	+	0.542284i	−0.0282055	+	0.0181266i
$896$	−3.44992			−0.115254
$897$	5.44129	+	12.8881i	0.181679	+	0.430323i
$898$	−26.9014			−0.897713
$899$	−6.63615	+	4.26479i	−0.221328	+	0.142239i
$900$	−0.142315	+	0.989821i	−0.00474383	+	0.0329940i
$901$	2.62401	−	5.74578i	0.0874185	−	0.191420i
$902$	−27.5080	+	8.07708i	−0.915916	+	0.268937i
$903$	−4.77796	−	10.4623i	−0.159001	−	0.348163i
$904$	12.0427	+	13.8980i	0.400534	+	0.462241i
$905$	−1.70529	−	11.8606i	−0.0566858	−	0.394258i
$906$	−9.19493	−	2.69988i	−0.305481	−	0.0896974i
$907$	23.3050	−	26.8954i	0.773829	−	0.893046i	−0.222819	−	0.974860i	$-0.571526\pi$
$907$	23.3050	−	26.8954i	0.773829	−	0.893046i	0.996648	+	0.0818140i	$0.0260713\pi$
$908$	13.6747	+	8.78822i	0.453812	+	0.291647i
$909$	12.4129	+	7.97728i	0.411709	+	0.264590i
$910$	6.59026	−	7.60557i	0.218465	−	0.252122i
$911$	−23.4130	−	6.87467i	−0.775707	−	0.227768i	−0.130164	−	0.991492i	$-0.541550\pi$
$911$	−23.4130	−	6.87467i	−0.775707	−	0.227768i	−0.645542	+	0.763724i	$0.723369\pi$
$912$	−0.125719	−	0.874394i	−0.00416297	−	0.0289541i
$913$	39.0145	+	45.0251i	1.29119	+	1.49011i
$914$	−11.5624	−	25.3182i	−0.382451	−	0.837450i
$915$	−0.413986	+	0.121557i	−0.0136860	+	0.00401856i
$916$	2.43703	−	5.33634i	0.0805216	−	0.176318i
$917$	5.99850	−	41.7205i	0.198088	−	1.37773i
$918$	−1.68454	+	1.08259i	−0.0555980	+	0.0357307i
$919$	51.0608			1.68434			0.842170	−	0.539212i	$-0.181278\pi$
$919$	51.0608			1.68434			0.842170	+	0.539212i	$0.181278\pi$
$920$	0.545025	+	4.76476i	0.0179690	+	0.157090i
$921$	23.2130			0.764895
$922$	11.6381	−	7.47938i	0.383282	−	0.246320i
$923$	1.90517	−	13.2507i	0.0627093	−	0.436153i
$924$	5.12021	−	11.2117i	0.168442	−	0.368837i
$925$	2.67890	−	0.786596i	0.0880817	−	0.0258631i
$926$	−10.5321	−	23.0621i	−0.346107	−	0.757868i
$927$	−10.2193	−	11.7937i	−0.335645	−	0.387355i
$928$	0.628699	+	4.37270i	0.0206381	+	0.143541i
$929$	54.0027	+	15.8566i	1.77177	+	0.520239i	0.994103	−	0.108437i	$-0.0345846\pi$
$929$	54.0027	+	15.8566i	1.77177	+	0.520239i	0.777667	+	0.628676i	$0.216403\pi$
$930$	−1.16935	+	1.34950i	−0.0383445	+	0.0442520i
$931$	−3.64289	−	2.34115i	−0.119391	−	0.0767280i
$932$	−18.5619	−	11.9290i	−0.608014	−	0.390747i
$933$	9.05227	−	10.4469i	0.296358	−	0.342015i
$934$	−17.2641	−	5.06918i	−0.564897	−	0.165869i
$935$	1.01812	+	7.08120i	0.0332962	+	0.231580i
$936$	1.91026	+	2.20456i	0.0624390	+	0.0720584i
$937$	−4.83808	−	10.5939i	−0.158053	−	0.346088i	0.813994	−	0.580873i	$-0.197289\pi$
$937$	−4.83808	−	10.5939i	−0.158053	−	0.346088i	−0.972047	+	0.234785i	$0.924561\pi$
$938$	−18.4631	+	5.42127i	−0.602843	+	0.177011i
$939$	−11.8597	+	25.9690i	−0.387025	+	0.847467i
$940$	−0.948203	+	6.59490i	−0.0309270	+	0.215102i
$941$	14.3111	−	9.19717i	0.466528	−	0.299819i	−0.286178	−	0.958177i	$-0.592385\pi$
$941$	14.3111	−	9.19717i	0.466528	−	0.299819i	0.752705	+	0.658357i	$0.228748\pi$
$942$	13.0422			0.424938
$943$	38.4684	+	1.11235i	1.25270	+	0.0362232i
$944$	2.28777			0.0744605
$945$	−2.90226	+	1.86517i	−0.0944105	+	0.0606739i
$946$	1.69511	−	11.7897i	0.0551127	−	0.383317i
$947$	6.58188	−	14.4123i	0.213882	−	0.468337i	−0.772033	−	0.635583i	$-0.780760\pi$
$947$	6.58188	−	14.4123i	0.213882	−	0.468337i	0.985915	+	0.167245i	$0.0534872\pi$
$948$	5.38716	−	1.58181i	0.174967	−	0.0513749i
$949$	1.86066	+	4.07428i	0.0603996	+	0.132257i
$950$	0.578494	+	0.667618i	0.0187688	+	0.0216604i
$951$	0.506165	+	3.52046i	0.0164135	+	0.114159i
$952$	6.62834	+	1.94626i	0.214826	+	0.0630785i
$953$	39.3764	−	45.4428i	1.27553	−	1.47204i	0.466199	−	0.884680i	$-0.345623\pi$
$953$	39.3764	−	45.4428i	1.27553	−	1.47204i	0.809328	−	0.587357i	$-0.199832\pi$
$954$	2.65373	+	1.70545i	0.0859176	+	0.0552159i
$955$	−14.8313	−	9.53149i	−0.479929	−	0.308432i
$956$	−4.09953	+	4.73111i	−0.132588	+	0.153015i
$957$	−15.1437	−	4.44658i	−0.489525	−	0.143737i
$958$	−2.40721	−	16.7425i	−0.0777736	−	0.540927i
$959$	−33.1283	−	38.2321i	−1.06977	−	1.23458i
$960$	0.415415	+	0.909632i	0.0134075	+	0.0293582i
$961$	26.6849	−	7.83539i	0.860803	−	0.252755i
$962$	3.38331	−	7.40841i	0.109082	−	0.238857i
$963$	1.25180	−	8.70647i	0.0403387	−	0.280562i
$964$	0.270609	−	0.173910i	0.00871574	−	0.00560126i
$965$	−15.9092			−0.512134
$966$	−11.1917	+	12.1857i	−0.360088	+	0.392067i
$967$	−28.5518			−0.918163			−0.459081	−	0.888394i	$-0.651821\pi$
$967$	−28.5518			−0.918163			−0.459081	+	0.888394i	$0.651821\pi$
$968$	1.48410	−	0.953774i	0.0477008	−	0.0306555i
$969$	−0.251741	+	1.75090i	−0.00808709	+	0.0562470i
$970$	−1.36997	+	2.99981i	−0.0439870	+	0.0963182i
$971$	10.9578	−	3.21749i	0.351651	−	0.103254i	−0.101136	−	0.994873i	$-0.532248\pi$
$971$	10.9578	−	3.21749i	0.351651	−	0.103254i	0.452788	+	0.891618i	$0.350430\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	18.6588	+	21.5334i	0.598174	+	0.690330i
$974$	4.53618	+	31.5498i	0.145349	+	1.01092i
$975$	−2.79889	−	0.821829i	−0.0896363	−	0.0263196i
$976$	−0.282548	+	0.326078i	−0.00904415	+	0.0104375i
$977$	3.64415	+	2.34195i	0.116587	+	0.0749257i	0.597635	−	0.801769i	$-0.296107\pi$
$977$	3.64415	+	2.34195i	0.116587	+	0.0749257i	−0.481048	+	0.876694i	$0.659744\pi$
$978$	4.37597	+	2.81226i	0.139928	+	0.0899263i
$979$	25.5955	−	29.5388i	0.818037	−	0.944065i
$980$	4.70339	+	1.38104i	0.150244	+	0.0441157i
$981$	−2.09679	−	14.5835i	−0.0669455	−	0.465616i
$982$	−14.2633	−	16.4607i	−0.455160	−	0.525283i
$983$	11.0955	+	24.2958i	0.353892	+	0.774914i	0.999933	+	0.0116117i	$0.00369619\pi$
$983$	11.0955	+	24.2958i	0.353892	+	0.774914i	−0.646041	+	0.763303i	$0.723577\pi$
$984$	7.69951	−	2.26078i	0.245451	−	0.0720710i
$985$	−8.46909	+	18.5447i	−0.269848	+	0.590884i
$986$	1.25892	−	8.75596i	0.0400921	−	0.278846i
$987$	−19.3369	+	12.4271i	−0.615501	+	0.395558i
$988$	2.57688			0.0819816
$989$	−7.05958	+	14.3458i	−0.224481	+	0.456171i
$990$	−3.57270			−0.113548
$991$	−10.8142	+	6.94989i	−0.343526	+	0.220770i	−0.701015	−	0.713147i	$-0.747269\pi$
$991$	−10.8142	+	6.94989i	−0.343526	+	0.220770i	0.357489	+	0.933917i	$0.383633\pi$
$992$	−0.254124	+	1.76747i	−0.00806846	+	0.0561174i
$993$	−4.94373	+	10.8253i	−0.156885	+	0.343529i
$994$	15.1911	−	4.46051i	0.481832	−	0.141479i
$995$	1.71187	+	3.74848i	0.0542701	+	0.118835i
$996$	−10.9202	−	12.6026i	−0.346019	−	0.399327i
$997$	6.11770	+	42.5496i	0.193750	+	1.34756i	0.821974	+	0.569525i	$0.192873\pi$
$997$	6.11770	+	42.5496i	0.193750	+	1.34756i	−0.628224	+	0.778032i	$0.716218\pi$
$998$	−7.82955	−	2.29896i	−0.247840	−	0.0727724i
$999$	−1.82837	+	2.11005i	−0.0578470	+	0.0667590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.541.2	yes	20
23.2	even	11	inner	690.2.m.d.301.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.301.2	✓	20	23.2	even	11	inner
690.2.m.d.541.2	yes	20	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(2.25922 + 2.60728i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(2.25922 + 2.60728i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.654861 - 0.755750i) q^{10} +(3.00554 + 1.93155i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(1.91026 - 2.20456i) q^{13} +(3.31018 + 0.971955i) q^{14} +(-0.142315 - 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.831833 + 1.82146i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(-0.366972 + 0.803556i) q^{19} +(0.142315 - 0.989821i) q^{20} +(2.90226 - 1.86517i) q^{21} +3.57270 q^{22} +(-4.56059 - 1.48358i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.415140 - 2.88736i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(3.31018 - 0.971955i) q^{28} +(-1.83516 - 4.01845i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(-0.254124 - 1.76747i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(2.33962 - 2.70006i) q^{33} +(1.68454 + 1.08259i) q^{34} +(2.90226 + 1.86517i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(2.67890 + 0.786596i) q^{37} +(0.125719 + 0.874394i) q^{38} +(-1.91026 - 2.20456i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(-7.69951 + 2.26078i) q^{41} +(1.43315 - 3.13816i) q^{42} +(0.474462 - 3.29995i) q^{43} +(3.00554 - 1.93155i) q^{44} -1.00000 q^{45} +(-4.63870 + 1.21757i) q^{46} -6.66271 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.697621 + 4.85206i) q^{49} +(0.415415 - 0.909632i) q^{50} +(1.92130 - 0.564145i) q^{51} +(-1.21179 - 2.65345i) q^{52} +(-2.06575 - 2.38401i) q^{53} +(0.142315 + 0.989821i) q^{54} +(3.42798 + 1.00654i) q^{55} +(2.25922 - 2.60728i) q^{56} +(0.743151 + 0.477594i) q^{57} +(-3.71638 - 2.38837i) q^{58} +(-1.49817 + 1.72898i) q^{59} +(-0.959493 - 0.281733i) q^{60} +(-0.0614036 - 0.427072i) q^{61} +(-1.16935 - 1.34950i) q^{62} +(-1.43315 - 3.13816i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(1.21179 - 2.65345i) q^{65} +(0.508448 - 3.53633i) q^{66} +(-4.69226 + 3.01553i) q^{67} +2.00241 q^{68} +(-2.11752 + 4.30303i) q^{69} +3.44992 q^{70} +(3.86069 - 2.48112i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-0.637855 + 1.39671i) q^{73} +(2.67890 - 0.786596i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(0.578494 + 0.667618i) q^{76} +(1.75410 + 12.2001i) q^{77} +(-2.79889 - 0.821829i) q^{78} +(-3.67678 + 4.24323i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-5.25497 + 6.06456i) q^{82} +(16.0001 + 4.69805i) q^{83} +(-0.490975 - 3.41481i) q^{84} +(1.31130 + 1.51332i) q^{85} +(-1.38495 - 3.03261i) q^{86} +(-4.23872 + 1.24460i) q^{87} +(1.48415 - 3.24984i) q^{88} +(1.55693 - 10.8287i) q^{89} +(-0.841254 + 0.540641i) q^{90} +10.0636 q^{91} +(-3.24405 + 3.53216i) q^{92} -1.78565 q^{93} +(-5.60503 + 3.60214i) q^{94} +(-0.125719 + 0.874394i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-3.16425 + 0.929106i) q^{97} +(2.03635 + 4.45898i) q^{98} +(-2.33962 - 2.70006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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