LMFDB - Embedded newform 92.2.h.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(7,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 19]))

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

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

chi := DirichletCharacter("92.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.h (of order $22$, 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	92.11
Dual form			92.2.h.a.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04738 - 0.950264i) q^{2} +(1.65123 + 0.237411i) q^{3} +(0.193997 + 1.99057i) q^{4} +(0.934364 + 3.18215i) q^{5} +(-1.50386 - 1.81776i) q^{6} +(-0.148303 - 0.171151i) q^{7} +(1.68838 - 2.26922i) q^{8} +(-0.208284 - 0.0611576i) q^{9} +O(q^{10})$	\(q+(-1.04738 - 0.950264i) q^{2} +(1.65123 + 0.237411i) q^{3} +(0.193997 + 1.99057i) q^{4} +(0.934364 + 3.18215i) q^{5} +(-1.50386 - 1.81776i) q^{6} +(-0.148303 - 0.171151i) q^{7} +(1.68838 - 2.26922i) q^{8} +(-0.208284 - 0.0611576i) q^{9} +(2.04525 - 4.22080i) q^{10} +(-3.48603 - 2.24034i) q^{11} +(-0.152250 + 3.33294i) q^{12} +(3.81497 - 4.40271i) q^{13} +(-0.00730929 + 0.320186i) q^{14} +(0.787372 + 5.47629i) q^{15} +(-3.92473 + 0.772328i) q^{16} +(-0.449525 + 0.205291i) q^{17} +(0.160036 + 0.261980i) q^{18} +(0.608905 - 1.33332i) q^{19} +(-6.15303 + 2.47724i) q^{20} +(-0.204249 - 0.317818i) q^{21} +(1.52228 + 5.65913i) q^{22} +(-4.22490 + 2.26941i) q^{23} +(3.32664 - 3.34617i) q^{24} +(-5.04678 + 3.24337i) q^{25} +(-8.17944 + 0.986067i) q^{26} +(-4.88178 - 2.22943i) q^{27} +(0.311917 - 0.328410i) q^{28} +(-0.299010 - 0.654741i) q^{29} +(4.37925 - 6.48395i) q^{30} +(9.23576 - 1.32790i) q^{31} +(4.84459 + 2.92061i) q^{32} +(-5.22436 - 4.52693i) q^{33} +(0.665903 + 0.212150i) q^{34} +(0.406059 - 0.631840i) q^{35} +(0.0813321 - 0.426468i) q^{36} +(-1.33496 + 4.54647i) q^{37} +(-1.90476 + 0.817864i) q^{38} +(7.34464 - 6.36416i) q^{39} +(8.79858 + 3.25239i) q^{40} +(-2.79241 + 0.819926i) q^{41} +(-0.0880851 + 0.526966i) q^{42} +(-0.508752 + 3.53845i) q^{43} +(3.78327 - 7.37380i) q^{44} -0.719934i q^{45} +(6.58160 + 1.63784i) q^{46} +6.02195i q^{47} +(-6.66399 + 0.343516i) q^{48} +(0.988905 - 6.87799i) q^{49} +(8.36794 + 1.39875i) q^{50} +(-0.791007 + 0.232261i) q^{51} +(9.50398 + 6.73984i) q^{52} +(4.56115 - 3.95226i) q^{53} +(2.99451 + 6.97403i) q^{54} +(3.87187 - 13.1864i) q^{55} +(-0.638771 + 0.0475654i) q^{56} +(1.32199 - 2.05705i) q^{57} +(-0.309000 + 0.969899i) q^{58} +(-4.34794 - 3.76751i) q^{59} +(-10.7482 + 2.62970i) q^{60} +(-9.72972 + 1.39892i) q^{61} +(-10.9352 - 7.38560i) q^{62} +(0.0204219 + 0.0447178i) q^{63} +(-2.29876 - 7.66262i) q^{64} +(17.5746 + 8.02607i) q^{65} +(1.17009 + 9.70592i) q^{66} +(-10.2383 + 6.57976i) q^{67} +(-0.495852 - 0.854984i) q^{68} +(-7.51506 + 2.74429i) q^{69} +(-1.02571 + 0.275911i) q^{70} +(2.54626 + 3.96206i) q^{71} +(-0.490442 + 0.369385i) q^{72} +(-2.85291 + 6.24699i) q^{73} +(5.71855 - 3.49330i) q^{74} +(-9.10341 + 4.15739i) q^{75} +(2.77218 + 0.953409i) q^{76} +(0.133554 + 0.928886i) q^{77} +(-13.7402 - 0.313665i) q^{78} +(-1.34769 + 1.55532i) q^{79} +(-6.12479 - 11.7675i) q^{80} +(-6.98379 - 4.48821i) q^{81} +(3.70385 + 1.79476i) q^{82} +(6.97591 + 2.04831i) q^{83} +(0.593015 - 0.468228i) q^{84} +(-1.07329 - 1.23864i) q^{85} +(3.89531 - 3.22264i) q^{86} +(-0.338292 - 1.15212i) q^{87} +(-10.9696 + 4.12805i) q^{88} +(14.1914 + 2.04041i) q^{89} +(-0.684127 + 0.754042i) q^{90} -1.31930 q^{91} +(-5.33704 - 7.96969i) q^{92} +15.5656 q^{93} +(5.72245 - 6.30725i) q^{94} +(4.81175 + 0.691826i) q^{95} +(7.30614 + 5.97276i) q^{96} +(-0.265360 - 0.903735i) q^{97} +(-7.57166 + 6.26412i) q^{98} +(0.589070 + 0.679823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) $ 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9	$ 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25} + 12 q^{26} - 11 q^{28} - 42 q^{29} - 11 q^{30} - 27 q^{32} - 22 q^{33} + 11 q^{34} + 77 q^{36} - 22 q^{37} + 44 q^{38} + 77 q^{40} - 10 q^{41} + 99 q^{42} + 66 q^{44} + 65 q^{46} + 38 q^{48} - 8 q^{49} + 30 q^{50} + 96 q^{52} - 22 q^{53} + 48 q^{54} + 44 q^{56} - 22 q^{57} + 79 q^{58} + 11 q^{60} - 22 q^{61} - 36 q^{62} + 10 q^{64} - 22 q^{65} - 44 q^{66} - 10 q^{69} + 34 q^{70} - 21 q^{72} - 18 q^{73} - 22 q^{74} - 66 q^{76} + 122 q^{77} - 66 q^{78} - 110 q^{80} + 8 q^{81} - 122 q^{82} - 165 q^{84} + 54 q^{85} - 121 q^{86} - 99 q^{88} + 22 q^{89} - 198 q^{90} - 86 q^{92} + 212 q^{93} - 61 q^{94} - 147 q^{96} + 22 q^{97} - 71 q^{98}+O(q^{100}) $ 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9 - 11 * q^10 - 18 * q^12 - 18 * q^13 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 24 * q^18 - 11 * q^20 - 22 * q^21 - 30 * q^24 - 16 * q^25 + 12 * q^26 - 11 * q^28 - 42 * q^29 - 11 * q^30 - 27 * q^32 - 22 * q^33 + 11 * q^34 + 77 * q^36 - 22 * q^37 + 44 * q^38 + 77 * q^40 - 10 * q^41 + 99 * q^42 + 66 * q^44 + 65 * q^46 + 38 * q^48 - 8 * q^49 + 30 * q^50 + 96 * q^52 - 22 * q^53 + 48 * q^54 + 44 * q^56 - 22 * q^57 + 79 * q^58 + 11 * q^60 - 22 * q^61 - 36 * q^62 + 10 * q^64 - 22 * q^65 - 44 * q^66 - 10 * q^69 + 34 * q^70 - 21 * q^72 - 18 * q^73 - 22 * q^74 - 66 * q^76 + 122 * q^77 - 66 * q^78 - 110 * q^80 + 8 * q^81 - 122 * q^82 - 165 * q^84 + 54 * q^85 - 121 * q^86 - 99 * q^88 + 22 * q^89 - 198 * q^90 - 86 * q^92 + 212 * q^93 - 61 * q^94 - 147 * q^96 + 22 * q^97 - 71 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$-1$

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 $

$2$	−1.04738	−	0.950264i	−0.740607	−	0.671938i
$2$	−1.04738	−	0.950264i	−0.740607	−	0.671938i
$3$	1.65123	+	0.237411i	0.953338	+	0.137069i	0.601395	−	0.798952i	$-0.294612\pi$
$3$	1.65123	+	0.237411i	0.953338	+	0.137069i	0.351943	+	0.936021i	$0.385521\pi$
$4$	0.193997	+	1.99057i	0.0969984	+	0.995285i
$5$	0.934364	+	3.18215i	0.417860	+	1.42310i	0.852609	+	0.522550i	$0.175019\pi$
$5$	0.934364	+	3.18215i	0.417860	+	1.42310i	−0.434749	+	0.900552i	$0.643163\pi$
$6$	−1.50386	−	1.81776i	−0.613947	−	0.742099i
$7$	−0.148303	−	0.171151i	−0.0560533	−	0.0646889i	0.727030	−	0.686605i	$-0.240900\pi$
$7$	−0.148303	−	0.171151i	−0.0560533	−	0.0646889i	−0.783084	+	0.621916i	$0.786354\pi$
$8$	1.68838	−	2.26922i	0.596932	−	0.802292i
$9$	−0.208284	−	0.0611576i	−0.0694279	−	0.0203859i
$10$	2.04525	−	4.22080i	0.646766	−	1.33474i
$11$	−3.48603	−	2.24034i	−1.05108	−	0.675487i	−0.103376	−	0.994642i	$-0.532964\pi$
$11$	−3.48603	−	2.24034i	−1.05108	−	0.675487i	−0.947702	+	0.319156i	$0.896601\pi$
$12$	−0.152250	+	3.33294i	−0.0439507	+	0.962138i
$13$	3.81497	−	4.40271i	1.05808	−	1.22109i	0.0836287	−	0.996497i	$-0.473349\pi$
$13$	3.81497	−	4.40271i	1.05808	−	1.22109i	0.974452	−	0.224594i	$-0.0721055\pi$
$14$	−0.00730929	+	0.320186i	−0.00195349	+	0.0855734i
$15$	0.787372	+	5.47629i	0.203299	+	1.41397i
$16$	−3.92473	+	0.772328i	−0.981183	+	0.193082i
$17$	−0.449525	+	0.205291i	−0.109026	+	0.0497904i	−0.469181	−	0.883102i	$-0.655451\pi$
$17$	−0.449525	+	0.205291i	−0.109026	+	0.0497904i	0.360155	+	0.932892i	$0.382724\pi$
$18$	0.160036	+	0.261980i	0.0377208	+	0.0617492i
$19$	0.608905	−	1.33332i	0.139692	−	0.305884i	−0.826836	−	0.562443i	$-0.809862\pi$
$19$	0.608905	−	1.33332i	0.139692	−	0.305884i	0.966529	+	0.256559i	$0.0825889\pi$
$20$	−6.15303	+	2.47724i	−1.37586	+	0.553928i
$21$	−0.204249	−	0.317818i	−0.0445708	−	0.0693536i
$22$	1.52228	+	5.65913i	0.324551	+	1.20653i
$23$	−4.22490	+	2.26941i	−0.880952	+	0.473206i
$23$	−4.22490	+	2.26941i	−0.880952	+	0.473206i
$24$	3.32664	−	3.34617i	0.679047	−	0.683034i
$25$	−5.04678	+	3.24337i	−1.00936	+	0.648674i
$26$	−8.17944	+	0.986067i	−1.60412	+	0.193384i
$27$	−4.88178	−	2.22943i	−0.939498	−	0.429054i
$28$	0.311917	−	0.328410i	0.0589468	−	0.0620637i
$29$	−0.299010	−	0.654741i	−0.0555248	−	0.121582i	0.879836	−	0.475277i	$-0.157652\pi$
$29$	−0.299010	−	0.654741i	−0.0555248	−	0.121582i	−0.935361	+	0.353695i	$0.884925\pi$
$30$	4.37925	−	6.48395i	0.799537	−	1.18380i
$31$	9.23576	−	1.32790i	1.65879	−	0.238498i	0.751723	−	0.659479i	$-0.229223\pi$
$31$	9.23576	−	1.32790i	1.65879	−	0.238498i	0.907069	+	0.420981i	$0.138314\pi$
$32$	4.84459	+	2.92061i	0.856410	+	0.516296i
$33$	−5.22436	−	4.52693i	−0.909444	−	0.788038i
$34$	0.665903	+	0.212150i	0.114201	+	0.0363834i
$35$	0.406059	−	0.631840i	0.0686364	−	0.106800i
$36$	0.0813321	−	0.426468i	0.0135554	−	0.0710779i
$37$	−1.33496	+	4.54647i	−0.219467	+	0.747435i	0.773987	+	0.633201i	$0.218259\pi$
$37$	−1.33496	+	4.54647i	−0.219467	+	0.747435i	−0.993454	+	0.114233i	$0.963559\pi$
$38$	−1.90476	+	0.817864i	−0.308992	+	0.132675i
$39$	7.34464	−	6.36416i	1.17608	−	1.01908i
$40$	8.79858	+	3.25239i	1.39118	+	0.514249i
$41$	−2.79241	+	0.819926i	−0.436101	+	0.128051i	−0.492412	−	0.870362i	$-0.663885\pi$
$41$	−2.79241	+	0.819926i	−0.436101	+	0.128051i	0.0563103	+	0.998413i	$0.482066\pi$
$42$	−0.0880851	+	0.526966i	−0.0135918	+	0.0813126i
$43$	−0.508752	+	3.53845i	−0.0775839	+	0.539608i	0.913548	+	0.406730i	$0.133331\pi$
$43$	−0.508752	+	3.53845i	−0.0775839	+	0.539608i	−0.991132	+	0.132878i	$0.957578\pi$
$44$	3.78327	−	7.37380i	0.570349	−	1.11164i
$45$		−	0.719934i		−	0.107321i
$46$	6.58160	+	1.63784i	0.970404	+	0.241486i
$47$			6.02195i			0.878392i	0.898391	+	0.439196i	$0.144737\pi$
$47$			6.02195i			0.878392i	−0.898391	+	0.439196i	$0.855263\pi$
$48$	−6.66399	+	0.343516i	−0.961864	+	0.0495823i
$49$	0.988905	−	6.87799i	0.141272	−	0.982569i
$50$	8.36794	+	1.39875i	1.18341	+	0.197812i
$51$	−0.791007	+	0.232261i	−0.110763	+	0.0325230i
$52$	9.50398	+	6.73984i	1.31796	+	0.934648i
$53$	4.56115	−	3.95226i	0.626522	−	0.542885i	−0.282693	−	0.959210i	$-0.591228\pi$
$53$	4.56115	−	3.95226i	0.626522	−	0.542885i	0.909216	+	0.416326i	$0.136682\pi$
$54$	2.99451	+	6.97403i	0.407501	+	0.949045i
$55$	3.87187	−	13.1864i	0.522083	−	1.77805i
$56$	−0.638771	+	0.0475654i	−0.0853594	+	0.00635620i
$57$	1.32199	−	2.05705i	0.175101	−	0.272463i
$58$	−0.309000	+	0.969899i	−0.0405737	+	0.127354i
$59$	−4.34794	−	3.76751i	−0.566053	−	0.490488i	0.324178	−	0.945996i	$-0.394912\pi$
$59$	−4.34794	−	3.76751i	−0.566053	−	0.490488i	−0.890232	+	0.455508i	$0.849458\pi$
$60$	−10.7482	+	2.62970i	−1.38759	+	0.339493i
$61$	−9.72972	+	1.39892i	−1.24576	+	0.179114i	−0.733485	−	0.679706i	$-0.762107\pi$
$61$	−9.72972	+	1.39892i	−1.24576	+	0.179114i	−0.512278	+	0.858820i	$0.671198\pi$
$62$	−10.9352	−	7.38560i	−1.38877	−	0.937972i
$63$	0.0204219	+	0.0447178i	0.00257292	+	0.00563391i
$64$	−2.29876	−	7.66262i	−0.287345	−	0.957827i
$65$	17.5746	+	8.02607i	2.17987	+	0.995511i
$66$	1.17009	+	9.70592i	0.144028	+	1.19472i
$67$	−10.2383	+	6.57976i	−1.25081	+	0.803846i	−0.986999	−	0.160729i	$-0.948615\pi$
$67$	−10.2383	+	6.57976i	−1.25081	+	0.803846i	−0.263810	+	0.964575i	$0.584979\pi$
$68$	−0.495852	−	0.854984i	−0.0601309	−	0.103682i
$69$	−7.51506	+	2.74429i	−0.904707	+	0.330373i
$70$	−1.02571	+	0.275911i	−0.122596	+	0.0329777i
$71$	2.54626	+	3.96206i	0.302186	+	0.470210i	0.958826	−	0.283993i	$-0.0916594\pi$
$71$	2.54626	+	3.96206i	0.302186	+	0.470210i	−0.656640	+	0.754204i	$0.728023\pi$
$72$	−0.490442	+	0.369385i	−0.0577992	+	0.0435325i
$73$	−2.85291	+	6.24699i	−0.333907	+	0.731155i	−0.999890	−	0.0148119i	$-0.995285\pi$
$73$	−2.85291	+	6.24699i	−0.333907	+	0.731155i	0.665983	+	0.745967i	$0.268012\pi$
$74$	5.71855	−	3.49330i	0.664768	−	0.406088i
$75$	−9.10341	+	4.15739i	−1.05117	+	0.480054i
$76$	2.77218	+	0.953409i	0.317991	+	0.109363i
$77$	0.133554	+	0.928886i	0.0152198	+	0.105856i
$78$	−13.7402	−	0.313665i	−1.55578	−	0.0355156i
$79$	−1.34769	+	1.55532i	−0.151627	+	0.174987i	−0.826482	−	0.562964i	$-0.809661\pi$
$79$	−1.34769	+	1.55532i	−0.151627	+	0.174987i	0.674854	+	0.737951i	$0.264206\pi$
$80$	−6.12479	−	11.7675i	−0.684772	−	1.31564i
$81$	−6.98379	−	4.48821i	−0.775977	−	0.498690i
$82$	3.70385	+	1.79476i	0.409022	+	0.198198i
$83$	6.97591	+	2.04831i	0.765706	+	0.224832i	0.641186	−	0.767386i	$-0.278443\pi$
$83$	6.97591	+	2.04831i	0.765706	+	0.224832i	0.124520	+	0.992217i	$0.460261\pi$
$84$	0.593015	−	0.468228i	0.0647032	−	0.0510878i
$85$	−1.07329	−	1.23864i	−0.116414	−	0.134349i
$86$	3.89531	−	3.22264i	0.420042	−	0.347506i
$87$	−0.338292	−	1.15212i	−0.0362687	−	0.123520i
$88$	−10.9696	+	4.12805i	−1.16936	+	0.440052i
$89$	14.1914	+	2.04041i	1.50428	+	0.216283i	0.844655	−	0.535311i	$-0.179806\pi$
$89$	14.1914	+	2.04041i	1.50428	+	0.216283i	0.659626	+	0.751594i	$0.270715\pi$
$90$	−0.684127	+	0.754042i	−0.0721133	+	0.0794830i
$91$	−1.31930			−0.138300
$92$	−5.33704	−	7.96969i	−0.556425	−	0.830898i
$93$	15.5656			1.61408
$94$	5.72245	−	6.30725i	0.590225	−	0.650544i
$95$	4.81175	+	0.691826i	0.493675	+	0.0709798i
$96$	7.30614	+	5.97276i	0.745680	+	0.609592i
$97$	−0.265360	−	0.903735i	−0.0269433	−	0.0917604i	0.944924	−	0.327290i	$-0.106136\pi$
$97$	−0.265360	−	0.903735i	−0.0269433	−	0.0917604i	−0.971867	+	0.235530i	$0.924317\pi$
$98$	−7.57166	+	6.26412i	−0.764853	+	0.632772i
$99$	0.589070	+	0.679823i	0.0592038	+	0.0683248i
$100$	−7.43521	−	9.41677i	−0.743521	−	0.941677i
$101$	−6.24015	−	1.83227i	−0.620918	−	0.182318i	−0.0438819	−	0.999037i	$-0.513973\pi$
$101$	−6.24015	−	1.83227i	−0.620918	−	0.182318i	−0.577036	+	0.816719i	$0.695791\pi$
$102$	1.04919	+	0.508401i	0.103885	+	0.0503392i
$103$	13.9976	+	8.99568i	1.37922	+	0.886371i	0.999254	−	0.0386294i	$-0.0122992\pi$
$103$	13.9976	+	8.99568i	1.37922	+	0.886371i	0.379966	+	0.925000i	$0.375936\pi$
$104$	−3.54962	−	16.0904i	−0.348069	−	1.57780i
$105$	0.820502	−	0.946910i	0.0800728	−	0.0924089i
$106$	−8.53294	−	0.194792i	−0.828792	−	0.0189199i
$107$	−0.239943	−	1.66884i	−0.0231962	−	0.161333i	0.974931	−	0.222508i	$-0.0714244\pi$
$107$	−0.239943	−	1.66884i	−0.0231962	−	0.161333i	−0.998127	+	0.0611749i	$0.980515\pi$
$108$	3.49079	−	10.1500i	0.335901	−	0.976685i
$109$	9.26235	−	4.22998i	0.887173	−	0.405158i	0.0809138	−	0.996721i	$-0.474216\pi$
$109$	9.26235	−	4.22998i	0.887173	−	0.405158i	0.806259	+	0.591563i	$0.201489\pi$
$110$	−16.5858	+	10.1318i	−1.58140	+	0.966030i
$111$	−3.28371	+	7.19033i	−0.311676	+	0.682475i
$112$	0.714234	+	0.557182i	0.0674887	+	0.0526488i
$113$	−0.769424	−	1.19725i	−0.0723813	−	0.112628i	0.803176	−	0.595742i	$-0.203142\pi$
$113$	−0.769424	−	1.19725i	−0.0723813	−	0.112628i	−0.875557	+	0.483114i	$0.839506\pi$
$114$	−3.33936	+	0.898271i	−0.312760	+	0.0841308i
$115$	−11.1692	−	11.3238i	−1.04153	−	1.05595i
$116$	1.24530	−	0.722218i	0.115623	−	0.0670562i
$117$	−1.06385	+	0.683698i	−0.0983534	+	0.0632079i
$118$	0.973801	+	8.07769i	0.0896457	+	0.743612i
$119$	0.101802	+	0.0464912i	0.00933214	+	0.00426184i
$120$	13.7563	+	7.45933i	1.25577	+	0.680940i
$121$	2.56374	+	5.61381i	0.233068	+	0.510347i
$122$	11.5200	+	7.78060i	1.04297	+	0.704423i
$123$	−4.80557	+	0.690937i	−0.433304	+	0.0622997i
$124$	4.43499	+	18.1268i	0.398274	+	1.62784i
$125$	−2.50424	−	2.16994i	−0.223986	−	0.194085i
$126$	0.0211042	−	0.0662426i	0.00188012	−	0.00590136i
$127$	−5.96025	+	9.27434i	−0.528887	+	0.822964i	−0.998194	−	0.0600708i	$-0.980867\pi$
$127$	−5.96025	+	9.27434i	−0.528887	+	0.822964i	0.469307	+	0.883035i	$0.344504\pi$
$128$	−4.87385	+	10.2101i	−0.430791	+	0.902452i
$129$	−1.68013	+	5.72200i	−0.147927	+	0.503794i
$130$	−10.7804	−	25.1069i	−0.945503	−	2.20202i
$131$	12.4602	−	10.7968i	1.08865	−	0.943319i	0.0900338	−	0.995939i	$-0.471302\pi$
$131$	12.4602	−	10.7968i	1.08865	−	0.943319i	0.998615	+	0.0526195i	$0.0167570\pi$
$132$	7.99766	−	11.2777i	0.696107	−	0.981594i
$133$	−0.318500	+	0.0935202i	−0.0276175	+	0.00810923i
$134$	16.9759	+	2.83761i	1.46649	+	0.245132i
$135$	2.53304	−	17.6176i	0.218009	−	1.51629i
$136$	−0.293116	+	1.36668i	−0.0251345	+	0.117192i
$137$			0.721415i			0.0616346i	0.999525	+	0.0308173i	$0.00981101\pi$
$137$			0.721415i			0.0616346i	−0.999525	+	0.0308173i	$0.990189\pi$
$138$	10.4789	+	4.26699i	0.892023	+	0.363230i
$139$		−	10.8579i		−	0.920954i	−0.887672	−	0.460477i	$-0.847678\pi$
$139$		−	10.8579i		−	0.920954i	0.887672	−	0.460477i	$-0.152322\pi$
$140$	1.33649	+	0.685713i	0.112954	+	0.0579533i
$141$	−1.42968	+	9.94363i	−0.120401	+	0.837404i
$142$	1.09811	−	6.56940i	0.0921512	−	0.551291i
$143$	−23.1626	+	6.80116i	−1.93696	+	0.568742i
$144$	0.864691	+	0.0791639i	0.0720576	+	0.00659699i
$145$	1.80410	−	1.56326i	0.149822	−	0.129822i
$146$	8.92436	−	3.83194i	0.738585	−	0.317134i
$147$	3.26582	−	11.1224i	0.269360	−	0.917357i
$148$	−9.30903	−	1.77534i	−0.765198	−	0.145932i
$149$	−11.8722	+	18.4735i	−0.972611	+	1.51341i	−0.118740	+	0.992925i	$0.537886\pi$
$149$	−11.8722	+	18.4735i	−0.972611	+	1.51341i	−0.853870	+	0.520486i	$0.825751\pi$
$150$	13.4853	+	4.29629i	1.10107	+	0.350791i
$151$	5.04526	+	4.37174i	0.410577	+	0.355767i	0.835527	−	0.549450i	$-0.185163\pi$
$151$	5.04526	+	4.37174i	0.410577	+	0.355767i	−0.424950	+	0.905217i	$0.639708\pi$
$152$	−1.99753	−	3.63288i	−0.162021	−	0.294666i
$153$	0.106184	−	0.0152669i	0.00858445	−	0.00123426i
$154$	0.742806	−	1.09980i	0.0598570	−	0.0886248i
$155$	12.8552	+	28.1489i	1.03255	+	2.26097i
$156$	14.0931	+	13.3854i	1.12835	+	1.07169i
$157$	−17.8415	−	8.14792i	−1.42390	−	0.650275i	−0.453388	−	0.891313i	$-0.649785\pi$
$157$	−17.8415	−	8.14792i	−1.42390	−	0.650275i	−0.970516	+	0.241039i	$0.922512\pi$
$158$	2.88951	−	0.348343i	0.229877	−	0.0277126i
$159$	8.46982	−	5.44322i	0.671700	−	0.431676i
$160$	−4.76722	+	18.1451i	−0.376882	+	1.43450i
$161$	1.01498	+	0.386533i	0.0799914	+	0.0304631i
$162$	3.04968	+	11.3373i	0.239605	+	0.890742i
$163$	1.56002	+	2.42744i	0.122190	+	0.190132i	0.896960	−	0.442112i	$-0.145771\pi$
$163$	1.56002	+	2.42744i	0.122190	+	0.190132i	−0.774770	+	0.632244i	$0.782134\pi$
$164$	−2.17384	−	5.39943i	−0.169748	−	0.421624i
$165$	9.52393	−	20.8545i	0.741437	−	1.62352i
$166$	−5.35997	−	8.77431i	−0.416014	−	0.681019i
$167$	9.48722	−	4.33267i	0.734143	−	0.335272i	−0.0130176	−	0.999915i	$-0.504144\pi$
$167$	9.48722	−	4.33267i	0.734143	−	0.335272i	0.747161	+	0.664643i	$0.231416\pi$
$168$	−1.06605	−	0.0731098i	−0.0822476	−	0.00564054i
$169$	−2.97976	−	20.7247i	−0.229212	−	1.59420i
$170$	−0.0528982	+	2.31723i	−0.00405711	+	0.177723i
$171$	−0.208367	+	0.240469i	−0.0159343	+	0.0183891i
$172$	−7.14222	−	0.326259i	−0.544589	−	0.0248770i
$173$	−0.735539	−	0.472702i	−0.0559220	−	0.0359389i	0.512381	−	0.858758i	$-0.328764\pi$
$173$	−0.735539	−	0.472702i	−0.0559220	−	0.0359389i	−0.568303	+	0.822819i	$0.692400\pi$
$174$	−0.740495	+	1.52817i	−0.0561368	+	0.115850i
$175$	1.30356	+	0.382759i	0.0985398	+	0.0289339i
$176$	15.4120	+	6.10036i	1.16172	+	0.459832i
$177$	−6.28500	−	7.25327i	−0.472409	−	0.545189i
$178$	−12.9248	−	15.6226i	−0.968752	−	1.17096i
$179$	−4.14534	−	14.1177i	−0.309838	−	1.05521i	−0.956330	−	0.292289i	$-0.905583\pi$
$179$	−4.14534	−	14.1177i	−0.309838	−	1.05521i	0.646492	−	0.762920i	$-0.276235\pi$
$180$	1.43308	−	0.139665i	0.106815	−	0.0104100i
$181$	−0.314564	−	0.0452275i	−0.0233814	−	0.00336173i	0.130614	−	0.991433i	$-0.458305\pi$
$181$	−0.314564	−	0.0452275i	−0.0233814	−	0.00336173i	−0.153996	+	0.988072i	$0.549214\pi$
$182$	1.38180	+	1.25368i	0.102426	+	0.0929290i
$183$	−16.3981			−1.21218
$184$	−1.98341	+	13.4189i	−0.146219	+	0.989252i
$185$	−15.7149			−1.15538
$186$	−16.3031	−	14.7915i	−1.19540	−	1.08456i
$187$	2.02698	+	0.291436i	0.148227	+	0.0213119i
$188$	−11.9871	+	1.16824i	−0.874250	+	0.0852026i
$189$	0.342413	+	1.16615i	0.0249069	+	0.0848250i
$190$	−4.38230	−	5.29704i	−0.317926	−	0.384287i
$191$	−8.85070	−	10.2143i	−0.640414	−	0.739077i	0.339034	−	0.940774i	$-0.389900\pi$
$191$	−8.85070	−	10.2143i	−0.640414	−	0.739077i	−0.979448	+	0.201697i	$0.935354\pi$
$192$	−1.97659	−	13.1985i	−0.142648	−	0.952519i
$193$	16.3630	+	4.80462i	1.17784	+	0.345844i	0.811340	−	0.584575i	$-0.198739\pi$
$193$	16.3630	+	4.80462i	1.17784	+	0.345844i	0.366498	+	0.930419i	$0.380557\pi$
$194$	−0.580854	+	1.19871i	−0.0417029	+	0.0860626i
$195$	27.1143	+	17.4253i	1.94169	+	1.24785i
$196$	13.8830	+	0.634177i	0.991639	+	0.0452984i
$197$	3.20560	−	3.69946i	0.228390	−	0.263576i	−0.629975	−	0.776615i	$-0.716935\pi$
$197$	3.20560	−	3.69946i	0.228390	−	0.263576i	0.858365	+	0.513039i	$0.171481\pi$
$198$	0.0290330	−	1.27180i	0.00206329	−	0.0903831i
$199$	1.95487	+	13.5964i	0.138577	+	0.963824i	0.933873	+	0.357604i	$0.116406\pi$
$199$	1.95487	+	13.5964i	0.138577	+	0.963824i	−0.795296	+	0.606221i	$0.792685\pi$
$200$	−1.16095	+	16.9283i	−0.0820912	+	1.19701i
$201$	−18.4679	+	8.43401i	−1.30263	+	0.594889i
$202$	4.79464	+	7.84887i	0.337350	+	0.552244i
$203$	−0.0677153	+	0.148276i	−0.00475268	+	0.0104069i
$204$	−0.615784	−	1.52950i	−0.0431135	−	0.107086i
$205$	−5.21826	−	8.11977i	−0.364459	−	0.567109i
$206$	−6.11244	−	22.7232i	−0.425874	−	1.58320i
$207$	1.01877	−	0.214298i	0.0708094	−	0.0148947i
$208$	−11.5724	+	20.2258i	−0.802400	+	1.40241i
$209$	−5.10974	+	3.28383i	−0.353448	+	0.227147i
$210$	−1.75919	+	0.212078i	−0.121396	+	0.0146348i
$211$	−12.7533	−	5.82424i	−0.877974	−	0.400957i	−0.0751489	−	0.997172i	$-0.523943\pi$
$211$	−12.7533	−	5.82424i	−0.877974	−	0.400957i	−0.802825	+	0.596215i	$0.796670\pi$
$212$	8.75210	+	8.31256i	0.601096	+	0.570909i
$213$	3.26383	+	7.14679i	0.223634	+	0.489690i
$214$	−1.33453	+	1.97592i	−0.0912266	+	0.135071i
$215$	−11.7352	+	1.68727i	−0.800336	+	0.115071i
$216$	−13.3014	+	7.31372i	−0.905043	+	0.497635i
$217$	−1.59696	−	1.38378i	−0.108409	−	0.0939368i
$218$	−13.7208	−	4.37130i	−0.929288	−	0.296062i
$219$	−6.19391	+	9.63791i	−0.418545	+	0.651269i
$220$	26.9995	+	5.14911i	1.82031	+	0.347153i
$221$	−0.811086	+	2.76230i	−0.0545595	+	0.185813i
$222$	10.2720	−	4.41059i	0.689411	−	0.296019i
$223$	−6.13470	+	5.31575i	−0.410810	+	0.355969i	−0.835615	−	0.549316i	$-0.814888\pi$
$223$	−6.13470	+	5.31575i	−0.410810	+	0.355969i	0.424805	+	0.905285i	$0.360343\pi$
$224$	−0.218602	−	1.26229i	−0.0146059	−	0.0843403i
$225$	1.24952	−	0.366892i	0.0833013	−	0.0244595i
$226$	−0.331824	+	1.98512i	−0.0220726	+	0.132049i
$227$	2.87711	−	20.0108i	0.190961	−	1.32816i	−0.638511	−	0.769613i	$-0.720449\pi$
$227$	2.87711	−	20.0108i	0.190961	−	1.32816i	0.829472	−	0.558549i	$-0.188642\pi$
$228$	4.35116	+	2.23244i	0.288163	+	0.147847i
$229$			8.45120i			0.558471i	0.960223	+	0.279235i	$0.0900810\pi$
$229$			8.45120i			0.558471i	−0.960223	+	0.279235i	$0.909919\pi$
$230$	0.937773	+	22.4740i	0.0618349	+	1.48189i
$231$			1.56551i			0.103003i
$232$	−1.99060	−	0.426929i	−0.130689	−	0.0280293i
$233$	−0.00171763	+	0.0119464i	−0.000112525	+	0.000782632i	−0.989878	−	0.141924i	$-0.954671\pi$
$233$	−0.00171763	+	0.0119464i	−0.000112525	+	0.000782632i	0.989765	+	0.142706i	$0.0455804\pi$
$234$	1.76395	+	0.294853i	0.115313	+	0.0192752i
$235$	−19.1628	+	5.62670i	−1.25004	+	0.367045i
$236$	6.65600	−	9.38576i	0.433269	−	0.610961i
$237$	−2.59460	+	2.24823i	−0.168537	+	0.146038i
$238$	−0.0624457	−	0.145432i	−0.00404775	−	0.00942697i
$239$	1.03134	−	3.51242i	0.0667118	−	0.227200i	−0.919388	−	0.393351i	$-0.871316\pi$
$239$	1.03134	−	3.51242i	0.0667118	−	0.227200i	0.986100	+	0.166151i	$0.0531340\pi$
$240$	−7.31971	−	20.8849i	−0.472485	−	1.34811i
$241$	5.51958	−	8.58863i	0.355547	−	0.553242i	−0.616700	−	0.787198i	$-0.711531\pi$
$241$	5.51958	−	8.58863i	0.355547	−	0.553242i	0.972247	+	0.233956i	$0.0751672\pi$
$242$	2.64940	−	8.31601i	0.170310	−	0.534574i
$243$	1.70149	+	1.47435i	0.109150	+	0.0945793i
$244$	−4.67219	−	19.0963i	−0.299106	−	1.22251i
$245$	22.8108	−	3.27970i	1.45733	−	0.209532i
$246$	5.68982	+	3.84289i	0.362770	+	0.245014i
$247$	−3.54725	−	7.76738i	−0.225706	−	0.494227i
$248$	12.5802	−	23.2000i	0.798841	−	1.47320i
$249$	11.0325	+	5.03839i	0.699159	+	0.319295i
$250$	0.560871	+	4.65244i	0.0354726	+	0.294246i
$251$	−8.50515	+	5.46593i	−0.536840	+	0.345006i	−0.780802	−	0.624779i	$-0.785189\pi$
$251$	−8.50515	+	5.46593i	−0.536840	+	0.345006i	0.243962	+	0.969785i	$0.421553\pi$
$252$	−0.0850520	+	0.0493264i	−0.00535777	+	0.00310727i
$253$	19.8124	+	1.55394i	1.24559	+	0.0976954i
$254$	15.0557	−	4.04991i	0.944679	−	0.254114i
$255$	−1.47818	−	2.30009i	−0.0925670	−	0.144037i
$256$	14.8070	−	6.06236i	0.925439	−	0.378897i
$257$	−5.11757	+	11.2059i	−0.319225	+	0.699006i	−0.999421	−	0.0340247i	$-0.989168\pi$
$257$	−5.11757	+	11.2059i	−0.319225	+	0.699006i	0.680196	+	0.733031i	$0.261895\pi$
$258$	7.19714	−	4.39652i	0.448075	−	0.273716i
$259$	0.976110	−	0.445775i	0.0606525	−	0.0276991i
$260$	−12.5670	+	36.5406i	−0.779374	+	2.26615i
$261$	0.0222365	+	0.154659i	0.00137641	+	0.00957313i
$262$	−23.3103	−	0.532132i	−1.44011	−	0.0328753i
$263$	13.2929	−	15.3408i	0.819675	−	0.945955i	−0.179611	−	0.983738i	$-0.557484\pi$
$263$	13.2929	−	15.3408i	0.819675	−	0.945955i	0.999286	+	0.0377828i	$0.0120295\pi$
$264$	−19.0933	+	4.21206i	−1.17511	+	0.259235i
$265$	16.8385	+	10.8214i	1.03438	+	0.664755i
$266$	0.422459	+	0.204709i	0.0259026	+	0.0125515i
$267$	22.9488	+	6.73837i	1.40444	+	0.412381i
$268$	−15.0837	−	19.1036i	−0.921381	−	1.16694i
$269$	2.05592	+	2.37266i	0.125352	+	0.144664i	0.814956	−	0.579523i	$-0.196761\pi$
$269$	2.05592	+	2.37266i	0.125352	+	0.144664i	−0.689604	+	0.724186i	$0.742216\pi$
$270$	−19.3945	+	16.0453i	−1.18031	+	0.976484i
$271$	−0.293217	−	0.998607i	−0.0178117	−	0.0606610i	0.950108	−	0.311922i	$-0.100973\pi$
$271$	−0.293217	−	0.998607i	−0.0178117	−	0.0606610i	−0.967919	+	0.251261i	$0.919155\pi$
$272$	1.60571	−	1.15289i	0.0973606	−	0.0699044i
$273$	−2.17846	−	0.313216i	−0.131847	−	0.0189567i
$274$	0.685535	−	0.755593i	0.0414147	−	0.0456471i
$275$	24.8595			1.49908
$276$	−6.92059	−	14.4269i	−0.416571	−	0.868395i
$277$	−9.66266			−0.580573			−0.290287	−	0.956940i	$-0.593751\pi$
$277$	−9.66266			−0.580573			−0.290287	+	0.956940i	$0.593751\pi$
$278$	−10.3179	+	11.3723i	−0.618824	+	0.682065i
$279$	−2.00487	−	0.288257i	−0.120028	−	0.0172575i
$280$	−0.748205	−	1.98822i	−0.0447138	−	0.118819i
$281$	−6.70438	−	22.8330i	−0.399950	−	1.36210i	−0.875841	−	0.482600i	$-0.839692\pi$
$281$	−6.70438	−	22.8330i	−0.399950	−	1.36210i	0.475891	−	0.879504i	$-0.342126\pi$
$282$	10.9465	−	9.05615i	0.651854	−	0.539286i
$283$	12.0743	+	13.9345i	0.717741	+	0.828318i	0.991034	−	0.133614i	$-0.0426581\pi$
$283$	12.0743	+	13.9345i	0.717741	+	0.828318i	−0.273292	+	0.961931i	$0.588113\pi$
$284$	−7.39279	+	5.83714i	−0.438682	+	0.346371i
$285$	7.78106	+	2.28473i	0.460910	+	0.135335i
$286$	30.7229	+	14.8872i	1.81668	+	0.880301i
$287$	0.554454	+	0.356326i	0.0327284	+	0.0210333i
$288$	−0.830431	−	0.904599i	−0.0489336	−	0.0533040i
$289$	−10.9727	+	12.6632i	−0.645453	+	0.744893i
$290$	−3.37508	−	0.0770472i	−0.198192	−	0.00452437i
$291$	−0.223614	−	1.55527i	−0.0131085	−	0.0911717i
$292$	−12.9885	−	4.46701i	−0.760096	−	0.261412i
$293$	18.5780	−	8.48429i	1.08534	−	0.495658i	0.209277	−	0.977856i	$-0.432889\pi$
$293$	18.5780	−	8.48429i	1.08534	−	0.495658i	0.876062	+	0.482199i	$0.160162\pi$
$294$	−13.9897	+	8.54591i	−0.815897	+	0.498408i
$295$	7.92623	−	17.3560i	0.461483	−	1.01051i
$296$	8.06303	+	10.7055i	0.468654	+	0.622244i
$297$	12.0233	+	18.7087i	0.697665	+	1.08559i
$298$	29.9894	−	8.06701i	1.73724	−	0.467310i
$299$	−6.12627	+	27.2587i	−0.354292	+	1.57641i
$300$	−10.0416	−	17.3145i	−0.579752	−	0.999650i
$301$	0.681057	−	0.437689i	0.0392555	−	0.0252280i
$302$	−1.12998	−	9.37318i	−0.0650229	−	0.539366i
$303$	−9.86891	−	4.50698i	−0.566954	−	0.258919i
$304$	−1.36003	+	5.70318i	−0.0780031	+	0.327100i
$305$	−13.5427	−	29.6543i	−0.775452	−	1.69800i
$306$	−0.125722	−	0.0849124i	−0.00718705	−	0.00485412i
$307$	3.69491	−	0.531248i	0.210880	−	0.0303199i	−0.0360652	−	0.999349i	$-0.511482\pi$
$307$	3.69491	−	0.531248i	0.210880	−	0.0303199i	0.246945	+	0.969030i	$0.420573\pi$
$308$	−1.82310	+	0.446048i	−0.103881	+	0.0254160i
$309$	20.9775	+	18.1771i	1.19337	+	1.03406i
$310$	13.2847	−	41.6982i	0.754518	−	2.36830i
$311$	−9.86340	+	15.3477i	−0.559302	+	0.870291i	−0.999620	−	0.0275508i	$-0.991229\pi$
$311$	−9.86340	+	15.3477i	−0.559302	+	0.870291i	0.440318	+	0.897842i	$0.354866\pi$
$312$	−2.04119	−	27.4117i	−0.115560	−	1.55188i
$313$	−2.31132	+	7.87163i	−0.130644	+	0.444931i	−0.998668	−	0.0515898i	$-0.983571\pi$
$313$	−2.31132	+	7.87163i	−0.130644	+	0.444931i	0.868025	+	0.496521i	$0.165389\pi$
$314$	10.9441	+	25.4880i	0.617609	+	1.43837i
$315$	−0.123217	+	0.106768i	−0.00694250	+	0.00601571i
$316$	−3.35742	−	2.38095i	−0.188870	−	0.133939i
$317$	7.02989	−	2.06416i	0.394838	−	0.115935i	−0.0782855	−	0.996931i	$-0.524945\pi$
$317$	7.02989	−	2.06416i	0.394838	−	0.115935i	0.473124	+	0.880996i	$0.343126\pi$
$318$	−14.0436	−	2.34746i	−0.787525	−	0.131639i
$319$	−0.424481	+	2.95233i	−0.0237664	+	0.165299i
$320$	22.2357	−	14.4747i	1.24302	−	0.809158i
$321$		−	2.81261i		−	0.156985i
$322$	−0.695755	−	1.36934i	−0.0387729	−	0.0763105i
$323$			0.724361i			0.0403045i
$324$	7.57926	−	14.7724i	0.421070	−	0.820690i
$325$	−4.97370	+	34.5929i	−0.275891	+	1.91887i
$326$	0.672779	−	4.02488i	0.0372618	−	0.222917i
$327$	16.2985	−	4.78568i	0.901310	−	0.264648i
$328$	−2.85405	+	7.72095i	−0.157589	+	0.426318i
$329$	1.03066	−	0.893074i	0.0568222	−	0.0492367i
$330$	−29.7924	+	12.7923i	−1.64002	+	0.704191i
$331$	5.52944	−	18.8316i	0.303926	−	1.03508i	−0.655986	−	0.754773i	$-0.727747\pi$
$331$	5.52944	−	18.8316i	0.303926	−	1.03508i	0.959912	−	0.280303i	$-0.0904348\pi$
$332$	−2.72400	+	14.2834i	−0.149499	+	0.783904i
$333$	0.556102	−	0.865312i	0.0304742	−	0.0474188i
$334$	−14.0539	−	4.47743i	−0.768994	−	0.244994i
$335$	−30.5041	−	26.4320i	−1.66662	−	1.44413i
$336$	1.04708	+	1.08960i	0.0571230	+	0.0594427i
$337$	−7.17700	+	1.03190i	−0.390956	+	0.0562110i	−0.334990	−	0.942222i	$-0.608733\pi$
$337$	−7.17700	+	1.03190i	−0.390956	+	0.0562110i	−0.0559660	+	0.998433i	$0.517824\pi$
$338$	−16.5730	+	24.5381i	−0.901451	+	1.33470i
$339$	−0.986256	−	2.15960i	−0.0535661	−	0.117293i
$340$	2.25738	−	2.37674i	0.122424	−	0.128897i
$341$	−35.1711	−	16.0621i	−1.90462	−	0.869812i
$342$	0.446748	−	0.0538574i	0.0241574	−	0.00291228i
$343$	−2.65743	+	1.70783i	−0.143488	+	0.0922140i
$344$	7.17056	+	7.12871i	0.386611	+	0.384354i
$345$	−15.7545	−	21.3499i	−0.848196	−	1.14944i
$346$	0.321195	+	1.19405i	0.0172675	+	0.0641927i
$347$	11.1039	+	17.2780i	0.596089	+	0.927532i	0.999919	+	0.0126982i	$0.00404206\pi$
$347$	11.1039	+	17.2780i	0.596089	+	0.927532i	−0.403831	+	0.914834i	$0.632322\pi$
$348$	2.22774	−	0.896900i	0.119419	−	0.0480789i
$349$	7.29006	−	15.9630i	0.390228	−	0.854480i	−0.607940	−	0.793983i	$-0.708004\pi$
$349$	7.29006	−	15.9630i	0.390228	−	0.854480i	0.998168	−	0.0604973i	$-0.0192687\pi$
$350$	−1.00159	−	1.63962i	−0.0535375	−	0.0876413i
$351$	−28.4393	+	12.9878i	−1.51798	+	0.693238i
$352$	−10.3452	−	21.0349i	−0.551403	−	1.12116i
$353$	3.14653	+	21.8846i	0.167473	+	1.16480i	0.884084	+	0.467328i	$0.154783\pi$
$353$	3.14653	+	21.8846i	0.167473	+	1.16480i	−0.716611	+	0.697473i	$0.754308\pi$
$354$	−0.309764	+	13.5693i	−0.0164638	+	0.721201i
$355$	−10.2287	+	11.8046i	−0.542886	+	0.626523i
$356$	−1.30850	+	28.6447i	−0.0693503	+	1.51817i
$357$	0.157060	+	0.100937i	0.00831251	+	0.00534213i
$358$	−9.07385	+	18.7258i	−0.479568	+	0.989688i
$359$	−1.98261	−	0.582148i	−0.104638	−	0.0307246i	0.228994	−	0.973428i	$-0.426456\pi$
$359$	−1.98261	−	0.582148i	−0.104638	−	0.0307246i	−0.333633	+	0.942703i	$0.608274\pi$
$360$	−1.63369	−	1.21552i	−0.0861031	−	0.0640636i
$361$	11.0354	+	12.7355i	0.580810	+	0.670290i
$362$	0.286489	+	0.346289i	0.0150575	+	0.0182006i
$363$	2.90055	+	9.87836i	0.152239	+	0.518479i
$364$	−0.255939	−	2.62615i	−0.0134149	−	0.137648i
$365$	−22.5445	−	3.24141i	−1.18003	−	0.169663i
$366$	17.1750	+	15.5825i	0.897752	+	0.814513i
$367$	−11.7631			−0.614031			−0.307015	−	0.951705i	$-0.599330\pi$
$367$	−11.7631			−0.614031			−0.307015	+	0.951705i	$0.599330\pi$
$368$	14.8289	−	12.1698i	0.773007	−	0.634397i
$369$	0.631759			0.0328880
$370$	16.4594	+	14.9333i	0.855684	+	0.776345i
$371$	−1.35286	−	0.194513i	−0.0702372	−	0.0100986i
$372$	3.01968	+	30.9844i	0.156563	+	1.60647i
$373$	−10.6300	−	36.2024i	−0.550399	−	1.87449i	−0.480626	−	0.876926i	$-0.659591\pi$
$373$	−10.6300	−	36.2024i	−0.550399	−	1.87449i	−0.0697734	−	0.997563i	$-0.522228\pi$
$374$	−1.84607	−	2.23141i	−0.0954580	−	0.115383i
$375$	−3.61991	−	4.17760i	−0.186931	−	0.215730i
$376$	13.6652	+	10.1673i	0.704727	+	0.524340i
$377$	−4.02334	−	1.18136i	−0.207213	−	0.0608432i
$378$	0.749516	−	1.54678i	0.0385509	−	0.0795579i
$379$	−12.1796	−	7.82734i	−0.625623	−	0.402063i	0.189064	−	0.981965i	$-0.439455\pi$
$379$	−12.1796	−	7.82734i	−0.625623	−	0.402063i	−0.814687	+	0.579901i	$0.803091\pi$
$380$	−0.443662	+	9.71234i	−0.0227594	+	0.498232i
$381$	−12.0436	+	13.8990i	−0.617011	+	0.712069i
$382$	−0.436217	+	19.1087i	−0.0223188	+	0.977685i
$383$	1.64015	+	11.4075i	0.0838078	+	0.582896i	0.987845	+	0.155442i	$0.0496803\pi$
$383$	1.64015	+	11.4075i	0.0838078	+	0.582896i	−0.904037	+	0.427454i	$0.859411\pi$
$384$	−10.4718	+	15.7021i	−0.534388	+	0.801293i
$385$	−2.83107	+	1.29290i	−0.144285	+	0.0658925i
$386$	−12.5726	−	20.5815i	−0.639929	−	1.04757i
$387$	0.322368	−	0.705887i	0.0163869	−	0.0358822i
$388$	1.74747	−	0.703540i	0.0887142	−	0.0357168i
$389$	−17.1025	−	26.6120i	−0.867131	−	1.34928i	−0.936126	−	0.351664i	$-0.885616\pi$
$389$	−17.1025	−	26.6120i	−0.867131	−	1.34928i	0.0689956	−	0.997617i	$-0.478021\pi$
$390$	−11.8403	−	44.0166i	−0.599554	−	2.22887i
$391$	1.43331	−	1.88749i	0.0724854	−	0.0954546i
$392$	−13.9380	−	13.8567i	−0.703978	−	0.699869i
$393$	23.1378	−	14.8698i	1.16715	−	0.750082i
$394$	−6.87293	+	0.828562i	−0.346253	+	0.0417424i
$395$	−6.20850	−	2.83533i	−0.312383	−	0.142661i
$396$	−1.23896	+	1.30447i	−0.0622599	+	0.0655520i
$397$	6.67961	+	14.6263i	0.335240	+	0.734073i	0.999915	−	0.0130597i	$-0.00415716\pi$
$397$	6.67961	+	14.6263i	0.335240	+	0.734073i	−0.664675	+	0.747133i	$0.731430\pi$
$398$	10.8727	−	16.0982i	0.544999	−	0.806931i
$399$	−0.548120	+	0.0788078i	−0.0274403	+	0.00394532i
$400$	17.3023	−	16.6271i	0.865116	−	0.831357i
$401$	−0.720019	−	0.623900i	−0.0359560	−	0.0311561i	0.636697	−	0.771114i	$-0.280300\pi$
$401$	−0.720019	−	0.623900i	−0.0359560	−	0.0311561i	−0.672653	+	0.739958i	$0.734845\pi$
$402$	27.3574	+	8.71580i	1.36446	+	0.434704i
$403$	29.3878	−	45.7282i	1.46391	−	2.27789i
$404$	2.43670	−	12.7769i	0.121230	−	0.635674i
$405$	7.75676	−	26.4171i	0.385437	−	1.31268i
$406$	0.211825	−	0.0909532i	0.0105127	−	0.00451393i
$407$	14.8393	−	12.8584i	0.735559	−	0.637365i
$408$	−0.808468	+	2.18712i	−0.0400251	+	0.108278i
$409$	4.14518	−	1.21713i	0.204966	−	0.0601834i	−0.177638	−	0.984096i	$-0.556846\pi$
$409$	4.14518	−	1.21713i	0.204966	−	0.0601834i	0.382604	+	0.923912i	$0.375027\pi$
$410$	−2.25044	+	13.4632i	−0.111141	+	0.664899i
$411$	−0.171272	+	1.19122i	−0.00844821	+	0.0587586i
$412$	−15.1910	+	29.6082i	−0.748409	+	1.45869i
$413$			1.30289i			0.0641108i
$414$	−1.27067	−	0.743650i	−0.0624503	−	0.0365484i
$415$			24.1123i			1.18363i
$416$	31.3405	−	10.1873i	1.53660	−	0.499471i
$417$	2.57778	−	17.9289i	0.126235	−	0.877981i
$418$	8.47233	+	1.41619i	0.414395	+	0.0692683i
$419$	17.9501	−	5.27063i	0.876920	−	0.257487i	0.187864	−	0.982195i	$-0.439844\pi$
$419$	17.9501	−	5.27063i	0.876920	−	0.257487i	0.689056	+	0.724708i	$0.258025\pi$
$420$	2.04406	+	1.44957i	0.0997401	+	0.0707317i
$421$	−5.24002	+	4.54050i	−0.255383	+	0.221290i	−0.773137	−	0.634239i	$-0.781314\pi$
$421$	−5.24002	+	4.54050i	−0.255383	+	0.221290i	0.517754	+	0.855529i	$0.326768\pi$
$422$	7.82295	+	18.2192i	0.380815	+	0.886896i
$423$	0.368288	−	1.25427i	0.0179068	−	0.0609849i
$424$	−1.26761	−	17.0232i	−0.0615608	−	0.826719i
$425$	1.60282	−	2.49404i	0.0777482	−	0.120978i
$426$	3.37288	−	10.5869i	0.163416	−	0.512936i
$427$	1.68237	+	1.45778i	0.0814157	+	0.0705471i
$428$	3.27540	−	0.801374i	0.158322	−	0.0387359i
$429$	−39.8615	+	5.73122i	−1.92453	+	0.276706i
$430$	13.8946	+	9.38436i	0.670055	+	0.452554i
$431$	−1.44075	−	3.15481i	−0.0693987	−	0.151962i	0.871754	−	0.489944i	$-0.162983\pi$
$431$	−1.44075	−	3.15481i	−0.0693987	−	0.151962i	−0.941152	+	0.337982i	$0.890256\pi$
$432$	20.8815	+	4.97959i	1.00466	+	0.239581i
$433$	−1.08463	−	0.495333i	−0.0521239	−	0.0238042i	0.389183	−	0.921161i	$-0.372758\pi$
$433$	−1.08463	−	0.495333i	−0.0521239	−	0.0238042i	−0.441306	+	0.897356i	$0.645485\pi$
$434$	0.357669	+	2.96687i	0.0171687	+	0.142414i
$435$	3.35012	−	2.15299i	0.160626	−	0.103228i
$436$	10.2169	+	17.6168i	0.489302	+	0.843690i
$437$	0.453286	+	7.01498i	0.0216836	+	0.335572i
$438$	15.6459	−	4.20867i	0.747591	−	0.201098i
$439$	8.76184	+	13.6337i	0.418180	+	0.650701i	0.984883	−	0.173222i	$-0.0554177\pi$
$439$	8.76184	+	13.6337i	0.418180	+	0.650701i	−0.566703	+	0.823922i	$0.691781\pi$
$440$	−23.3857	−	31.0497i	−1.11487	−	1.48024i
$441$	−0.626614	+	1.37209i	−0.0298388	+	0.0653378i
$442$	3.47443	−	2.12243i	0.165262	−	0.100954i
$443$	24.8880	−	11.3660i	1.18246	−	0.540013i	0.275533	−	0.961292i	$-0.411146\pi$
$443$	24.8880	−	11.3660i	1.18246	−	0.540013i	0.906931	+	0.421278i	$0.138418\pi$
$444$	−14.9499	−	5.14156i	−0.709489	−	0.244007i
$445$	6.76700	+	47.0655i	0.320787	+	2.23112i
$446$	11.4767	+	0.261993i	0.543438	+	0.0124057i
$447$	−23.9896	+	27.6855i	−1.13467	+	1.30948i
$448$	−0.970551	+	1.52982i	−0.0458542	+	0.0722773i
$449$	−15.7819	−	10.1424i	−0.744793	−	0.478649i	0.112388	−	0.993664i	$-0.464150\pi$
$449$	−15.7819	−	10.1424i	−0.744793	−	0.478649i	−0.857181	+	0.515015i	$0.827786\pi$
$450$	−1.65736	−	0.803099i	−0.0781288	−	0.0378585i
$451$	11.5713	+	3.39765i	0.544873	+	0.159989i
$452$	2.23394	−	1.76385i	0.105076	−	0.0829647i
$453$	7.29298	+	8.41654i	0.342654	+	0.395444i
$454$	−22.0289	+	18.2248i	−1.03387	+	0.855332i
$455$	−1.23270	−	4.19820i	−0.0577900	−	0.196815i
$456$	−2.43590	−	6.47296i	−0.114071	−	0.303124i
$457$	−10.9084	−	1.56839i	−0.510275	−	0.0733664i	−0.117631	−	0.993057i	$-0.537530\pi$
$457$	−10.9084	−	1.56839i	−0.510275	−	0.0733664i	−0.392643	+	0.919691i	$0.628439\pi$
$458$	8.03087	−	8.85159i	0.375258	−	0.413608i
$459$	2.65216			0.123792
$460$	20.3740	−	24.4299i	0.949944	−	1.13905i
$461$	−8.45702			−0.393882			−0.196941	−	0.980415i	$-0.563101\pi$
$461$	−8.45702			−0.393882			−0.196941	+	0.980415i	$0.563101\pi$
$462$	1.48765	−	1.63968i	0.0692117	−	0.0762848i
$463$	34.9943	+	5.03142i	1.62632	+	0.233830i	0.894306	−	0.447455i	$-0.147670\pi$
$463$	34.9943	+	5.03142i	1.62632	+	0.233830i	0.732018	+	0.681285i	$0.238579\pi$
$464$	1.67921	+	2.33875i	0.0779553	+	0.108574i
$465$	14.5440	+	49.5322i	0.674460	+	2.29700i
$466$	0.0131512	−	0.0108801i	0.000609217	−	0.000504013i
$467$	−21.4802	−	24.7895i	−0.993985	−	1.14712i	−0.989117	−	0.147131i	$-0.952996\pi$
$467$	−21.4802	−	24.7895i	−0.993985	−	1.14712i	−0.00486789	−	0.999988i	$-0.501550\pi$
$468$	−1.56733	−	1.98504i	−0.0724499	−	0.0917585i
$469$	2.64450	+	0.776496i	0.122112	+	0.0358552i
$470$	25.4175	+	12.3164i	1.17242	+	0.568114i
$471$	−27.5259	−	17.6898i	−1.26833	−	0.815105i
$472$	−15.8903	+	3.50546i	−0.731410	+	0.161352i
$473$	9.70083	−	11.1954i	0.446045	−	0.514763i
$474$	4.85394	+	0.110807i	0.222949	+	0.00508953i
$475$	1.25143	+	8.70386i	0.0574194	+	0.399361i
$476$	−0.0727948	+	0.211662i	−0.00333655	+	0.00970152i
$477$	−1.19172	+	0.544242i	−0.0545653	+	0.0249191i
$478$	−4.41793	+	2.69878i	−0.202071	+	0.123439i
$479$	4.39145	−	9.61594i	0.200651	−	0.439364i	−0.782381	−	0.622800i	$-0.785995\pi$
$479$	4.39145	−	9.61594i	0.200651	−	0.439364i	0.983032	+	0.183437i	$0.0587222\pi$
$480$	−12.1796	+	28.8300i	−0.555921	+	1.31590i
$481$	14.9239	+	23.2221i	0.680472	+	1.05883i
$482$	−13.9425	+	3.75048i	−0.635065	+	0.170829i
$483$	1.58419	+	0.879222i	0.0720833	+	0.0400060i
$484$	−10.6773	+	6.19237i	−0.485333	+	0.281471i
$485$	2.62788	−	1.68883i	0.119326	−	0.0766860i
$486$	−0.381079	−	3.16106i	−0.0172861	−	0.143388i
$487$	−0.361362	−	0.165028i	−0.0163749	−	0.00747815i	0.407211	−	0.913334i	$-0.366501\pi$
$487$	−0.361362	−	0.165028i	−0.0163749	−	0.00747815i	−0.423586	+	0.905856i	$0.639229\pi$
$488$	−13.2530	+	24.4408i	−0.599934	+	1.10638i
$489$	1.99965	+	4.37863i	0.0904274	+	0.198008i
$490$	−27.0081	−	18.2412i	−1.22010	−	0.824053i
$491$	24.0344	−	3.45563i	1.08466	−	0.155950i	0.423278	−	0.906000i	$-0.360879\pi$
$491$	24.0344	−	3.45563i	1.08466	−	0.155950i	0.661382	+	0.750049i	$0.269970\pi$
$492$	−2.30762	−	9.43178i	−0.104036	−	0.425218i
$493$	0.268825	+	0.232938i	0.0121073	+	0.0104910i
$494$	−3.66576	+	11.5062i	−0.164930	+	0.517688i
$495$	−1.61289	+	2.50971i	−0.0724942	+	0.112803i
$496$	−35.2223	+	12.3447i	−1.58153	+	0.554293i
$497$	0.300492	−	1.02338i	0.0134789	−	0.0459049i
$498$	−6.76743	−	15.7609i	−0.303256	−	0.706264i
$499$	−17.2176	+	14.9191i	−0.770766	+	0.667873i	−0.948703	−	0.316169i	$-0.897603\pi$
$499$	−17.2176	+	14.9191i	−0.770766	+	0.667873i	0.177937	+	0.984042i	$0.443058\pi$
$500$	3.83360	−	5.40583i	0.171444	−	0.241756i
$501$	16.6942	−	4.90186i	0.745842	−	0.218999i
$502$	14.1022	+	2.35725i	0.629411	+	0.105209i
$503$	−1.84791	+	12.8525i	−0.0823944	+	0.573066i	0.906244	+	0.422754i	$0.138937\pi$
$503$	−1.84791	+	12.8525i	−0.0823944	+	0.573066i	−0.988639	+	0.150311i	$0.951972\pi$
$504$	0.135955	+	0.0291586i	0.00605590	+	0.00129883i
$505$		−	21.5691i		−	0.959812i
$506$	−19.2744	−	20.4545i	−0.856850	−	0.909316i
$507$		−	34.9286i		−	1.55123i
$508$	−19.6175	−	10.0651i	−0.870385	−	0.446567i
$509$	3.61245	−	25.1252i	0.160119	−	1.11365i	−0.738287	−	0.674487i	$-0.764365\pi$
$509$	3.61245	−	25.1252i	0.160119	−	1.11365i	0.898406	−	0.439166i	$-0.144726\pi$
$510$	−0.637483	+	3.81372i	−0.0282282	+	0.168874i
$511$	1.49227	−	0.438171i	0.0660142	−	0.0193835i
$512$	−21.2694	−	7.72101i	−0.939982	−	0.341223i
$513$	−5.94507	+	5.15144i	−0.262481	+	0.227441i
$514$	16.0086	−	6.87377i	0.706109	−	0.303189i
$515$	−15.5468	+	52.9476i	−0.685074	+	2.33315i
$516$	−11.7160	−	2.23437i	−0.515767	−	0.0983626i
$517$	13.4912	−	20.9927i	0.593342	−	0.923259i
$518$	−1.44596	−	0.460668i	−0.0635318	−	0.0202406i
$519$	−1.10232	−	0.955165i	−0.0483865	−	0.0419271i
$520$	47.8856	−	26.3298i	2.09992	−	1.15464i
$521$	29.0404	−	4.17538i	1.27228	−	0.182927i	0.527110	−	0.849797i	$-0.323275\pi$
$521$	29.0404	−	4.17538i	1.27228	−	0.182927i	0.745174	+	0.666870i	$0.232366\pi$
$522$	0.123676	−	0.183116i	0.00541317	−	0.00801479i
$523$	−14.2767	−	31.2616i	−0.624277	−	1.36698i	−0.912367	−	0.409372i	$-0.865748\pi$
$523$	−14.2767	−	31.2616i	−0.624277	−	1.36698i	0.288091	−	0.957603i	$-0.406980\pi$
$524$	23.9090	+	22.7083i	1.04447	+	0.992015i
$525$	2.06160	+	0.941503i	0.0899757	+	0.0410905i
$526$	−28.5005	+	3.43586i	−1.24268	+	0.149811i
$527$	−3.87910	+	2.49294i	−0.168976	+	0.108594i
$528$	24.0005	+	13.7321i	1.04449	+	0.597612i
$529$	12.6995	−	19.1761i	0.552153	−	0.833743i
$530$	−7.35301	−	27.3351i	−0.319394	−	1.18736i
$531$	0.675193	+	1.05062i	0.0293009	+	0.0455931i
$532$	−0.247946	−	0.615855i	−0.0107498	−	0.0267007i
$533$	−7.04306	+	15.4222i	−0.305069	+	0.668008i
$534$	−17.6328	−	28.8650i	−0.763045	−	1.24911i
$535$	5.08632	−	2.32284i	0.219901	−	0.100425i
$536$	−2.35519	+	34.3421i	−0.101729	+	1.48335i
$537$	−3.49321	−	24.2958i	−0.150743	−	1.04844i
$538$	0.101329	−	4.43874i	0.00436859	−	0.191368i
$539$	−18.8564	+	21.7614i	−0.812201	+	0.937330i
$540$	35.5605	+	1.62442i	1.53028	+	0.0699037i
$541$	12.2280	+	7.85844i	0.525721	+	0.337861i	0.776432	−	0.630202i	$-0.217028\pi$
$541$	12.2280	+	7.85844i	0.525721	+	0.337861i	−0.250710	+	0.968062i	$0.580664\pi$
$542$	−0.641831	+	1.32455i	−0.0275690	+	0.0568944i
$543$	−0.508680	−	0.149362i	−0.0218296	−	0.00640974i
$544$	−2.77734	−	0.318337i	−0.119077	−	0.0136486i
$545$	22.1148	+	25.5219i	0.947295	+	1.09324i
$546$	1.98403	+	2.39817i	0.0849088	+	0.102632i
$547$	8.99528	+	30.6351i	0.384611	+	1.30986i	0.893512	+	0.449039i	$0.148233\pi$
$547$	8.99528	+	30.6351i	0.384611	+	1.30986i	−0.508902	+	0.860825i	$0.669948\pi$
$548$	−1.43603	+	0.139952i	−0.0613440	+	0.00597846i
$549$	2.11210	+	0.303674i	0.0901421	+	0.0129605i
$550$	−26.0373	−	23.6231i	−1.11023	−	1.00729i
$551$	−1.05505			−0.0449464
$552$	−6.46086	+	21.6868i	−0.274992	+	0.923049i
$553$	0.466061			0.0198189
$554$	10.1204	+	9.18208i	0.429977	+	0.390109i
$555$	−25.9489	−	3.73089i	−1.10147	−	0.158367i
$556$	21.6134	−	2.10640i	0.916612	−	0.0893311i
$557$	4.57086	+	15.5669i	0.193674	+	0.659592i	0.997870	+	0.0652286i	$0.0207777\pi$
$557$	4.57086	+	15.5669i	0.193674	+	0.659592i	−0.804197	+	0.594363i	$0.797404\pi$
$558$	1.82593	+	2.20707i	0.0772980	+	0.0934327i
$559$	13.6379	+	15.7389i	0.576820	+	0.665686i
$560$	−1.10568	+	2.79341i	−0.0467237	+	0.118043i
$561$	3.27782	+	0.962454i	0.138390	+	0.0406348i
$562$	−14.6754	+	30.2857i	−0.619044	+	1.27753i
$563$	−29.5452	−	18.9876i	−1.24518	−	0.800230i	−0.258997	−	0.965878i	$-0.583392\pi$
$563$	−29.5452	−	18.9876i	−1.24518	−	0.800230i	−0.986185	+	0.165648i	$0.947028\pi$
$564$	−20.0708	−	0.916841i	−0.845134	−	0.0386060i
$565$	3.09090	−	3.56709i	0.130035	−	0.150068i
$566$	0.595095	−	26.0684i	0.0250137	−	1.09574i
$567$	0.267556	+	1.86090i	0.0112363	+	0.0781503i
$568$	13.2899	+	0.911420i	0.557630	+	0.0382423i
$569$	−31.5524	+	14.4095i	−1.32274	+	0.604077i	−0.946578	−	0.322475i	$-0.895485\pi$
$569$	−31.5524	+	14.4095i	−1.32274	+	0.604077i	−0.376166	+	0.926552i	$0.622758\pi$
$570$	−5.97861	−	9.78703i	−0.250416	−	0.409934i
$571$	−1.13150	+	2.47764i	−0.0473518	+	0.103686i	−0.931829	−	0.362897i	$-0.881788\pi$
$571$	−1.13150	+	2.47764i	−0.0473518	+	0.103686i	0.884478	+	0.466583i	$0.154515\pi$
$572$	−18.0317	−	44.7874i	−0.753942	−	1.87266i
$573$	−12.1896	−	18.9673i	−0.509226	−	0.792372i
$574$	−0.242119	−	0.900085i	−0.0101058	−	0.0375688i
$575$	13.9616	−	25.1562i	0.582239	−	1.04908i
$576$	0.0101661	+	1.73659i	0.000423587	+	0.0723577i
$577$	0.656067	−	0.421629i	0.0273124	−	0.0175526i	−0.526913	−	0.849919i	$-0.676651\pi$
$577$	0.656067	−	0.421629i	0.0273124	−	0.0175526i	0.554226	+	0.832366i	$0.313014\pi$
$578$	23.5259	−	2.83615i	0.978549	−	0.117968i
$579$	25.8785	+	11.8183i	1.07547	+	0.491152i
$580$	3.46177	+	3.28792i	0.143742	+	0.136523i
$581$	−0.683978	−	1.49770i	−0.0283762	−	0.0621352i
$582$	−1.24371	+	1.84145i	−0.0515535	+	0.0763305i
$583$	−24.7547	+	3.55919i	−1.02524	+	0.147407i
$584$	9.35904	+	17.0212i	0.387280	+	0.704341i
$585$	−3.16966	−	2.74652i	−0.131049	−	0.113555i
$586$	−27.5205	−	8.76776i	−1.13686	−	0.362193i
$587$	−10.9250	+	16.9996i	−0.450922	+	0.701648i	−0.990072	−	0.140562i	$-0.955109\pi$
$587$	−10.9250	+	16.9996i	−0.450922	+	0.701648i	0.539150	+	0.842210i	$0.318745\pi$
$588$	22.7734	+	4.34314i	0.939158	+	0.179108i
$589$	3.85319	−	13.1228i	0.158768	−	0.540714i
$590$	−24.7946	+	10.6463i	−1.02078	+	0.438301i
$591$	6.17147	−	5.34761i	0.253861	−	0.219971i
$592$	1.72801	−	18.8747i	0.0710207	−	0.775745i
$593$	−32.9444	+	9.67334i	−1.35286	+	0.397237i	−0.876242	−	0.481872i	$-0.839957\pi$
$593$	−32.9444	+	9.67334i	−1.35286	+	0.397237i	−0.476622	+	0.879108i	$0.658139\pi$
$594$	5.18522	−	31.0204i	0.212752	−	1.27278i
$595$	−0.0528224	+	0.367388i	−0.00216551	+	0.0150614i
$596$	−39.0760	−	20.0487i	−1.60062	−	0.821226i
$597$			22.9149i			0.937845i
$598$	32.3195	−	22.7286i	1.32164	−	0.929440i
$599$		−	0.463611i		−	0.0189426i	−0.999955	−	0.00947132i	$-0.996985\pi$
$599$		−	0.463611i		−	0.0189426i	0.999955	−	0.00947132i	$-0.00301486\pi$
$600$	−5.93596	+	27.6769i	−0.242334	+	1.12991i
$601$	0.181420	−	1.26180i	0.00740027	−	0.0514700i	−0.985787	−	0.168002i	$-0.946269\pi$
$601$	0.181420	−	1.26180i	0.00740027	−	0.0514700i	0.993187	+	0.116532i	$0.0371777\pi$
$602$	−1.12924	−	0.188759i	−0.0460245	−	0.00769324i
$603$	2.53488	−	0.744307i	0.103228	−	0.0303105i
$604$	−7.72349	+	10.8910i	−0.314264	+	0.443150i
$605$	−15.4685	+	13.4036i	−0.628886	+	0.544932i
$606$	6.05365	+	14.0986i	0.245913	+	0.572716i
$607$	2.29758	−	7.82486i	0.0932561	−	0.317601i	−0.899633	−	0.436648i	$-0.856166\pi$
$607$	2.29758	−	7.82486i	0.0932561	−	0.317601i	0.992889	+	0.119047i	$0.0379838\pi$
$608$	6.84399	−	4.68099i	0.277561	−	0.189839i
$609$	−0.147016	+	0.228761i	−0.00595738	+	0.00926987i
$610$	−13.9952	+	43.9284i	−0.566647	+	1.77861i
$611$	26.5129	+	22.9735i	1.07260	+	0.929410i
$612$	0.0509892	+	0.208404i	0.00206112	+	0.00842425i
$613$	31.4275	−	4.51859i	1.26934	−	0.182504i	0.525463	−	0.850816i	$-0.323892\pi$
$613$	31.4275	−	4.51859i	1.26934	−	0.182504i	0.743881	+	0.668312i	$0.232983\pi$
$614$	−4.37479	−	2.95472i	−0.176552	−	0.119243i
$615$	−6.68882	−	14.6465i	−0.269719	−	0.590603i
$616$	2.33334	+	1.26525i	0.0940129	+	0.0509783i
$617$	30.6896	+	14.0155i	1.23552	+	0.564242i	0.922680	−	0.385565i	$-0.125994\pi$
$617$	30.6896	+	14.0155i	1.23552	+	0.564242i	0.312836	+	0.949807i	$0.398721\pi$
$618$	−4.69830	−	38.9724i	−0.188993	−	1.56770i
$619$	−11.9212	+	7.66127i	−0.479152	+	0.307932i	−0.757830	−	0.652452i	$-0.773740\pi$
$619$	−11.9212	+	7.66127i	−0.479152	+	0.307932i	0.278678	+	0.960385i	$0.410104\pi$
$620$	−53.5384	+	31.0498i	−2.15015	+	1.24699i
$621$	25.6845	−	1.65965i	1.03068	−	0.0665995i
$622$	24.9151	−	6.70204i	0.999005	−	0.268727i
$623$	−1.75540	−	2.73146i	−0.0703287	−	0.109434i
$624$	−23.9105	+	30.6501i	−0.957186	+	1.22699i
$625$	−7.89543	+	17.2886i	−0.315817	+	0.691543i
$626$	9.90095	−	6.04820i	0.395722	−	0.241735i
$627$	−9.21697	+	4.20925i	−0.368090	+	0.168101i
$628$	12.7578	−	37.0953i	0.509092	−	1.48026i
$629$	−0.333250	−	2.31781i	−0.0132876	−	0.0924170i
$630$	0.230513	+	0.00526221i	0.00918386	+	0.000209651i
$631$	31.1382	−	35.9354i	1.23959	−	1.43056i	0.375810	−	0.926697i	$-0.377365\pi$
$631$	31.1382	−	35.9354i	1.23959	−	1.43056i	0.863781	−	0.503867i	$-0.168090\pi$
$632$	1.25395	+	5.68418i	0.0498796	+	0.226105i
$633$	−19.6759	−	12.6449i	−0.782046	−	0.502591i
$634$	−9.32445	−	4.51830i	−0.370321	−	0.179445i
$635$	−35.0814	−	10.3008i	−1.39216	−	0.408776i
$636$	12.4782	+	15.8038i	0.494794	+	0.626661i
$637$	−26.5091	−	30.5931i	−1.05033	−	1.21214i
$638$	3.25008	−	2.68883i	0.128672	−	0.106452i
$639$	−0.288035	−	0.980957i	−0.0113945	−	0.0388060i
$640$	−37.0440	−	5.96939i	−1.46429	−	0.235961i
$641$	13.2032	+	1.89834i	0.521496	+	0.0749798i	0.398036	−	0.917370i	$-0.369692\pi$
$641$	13.2032	+	1.89834i	0.521496	+	0.0749798i	0.123460	+	0.992350i	$0.460601\pi$
$642$	−2.67272	+	2.94586i	−0.105484	+	0.116264i
$643$	−11.2686			−0.444389			−0.222194	−	0.975002i	$-0.571322\pi$
$643$	−11.2686			−0.444389			−0.222194	+	0.975002i	$0.571322\pi$
$644$	−0.572519	+	2.09537i	−0.0225604	+	0.0825691i
$645$	−19.7781			−0.778763
$646$	0.688334	−	0.758679i	0.0270822	−	0.0298498i
$647$	6.89859	+	0.991868i	0.271212	+	0.0389944i	0.276579	−	0.960991i	$-0.410799\pi$
$647$	6.89859	+	0.991868i	0.271212	+	0.0389944i	−0.00536711	+	0.999986i	$0.501708\pi$
$648$	−21.9760	+	8.26999i	−0.863300	+	0.324876i
$649$	6.71656	+	22.8745i	0.263648	+	0.897903i
$650$	38.0817	−	31.5054i	1.49369	−	1.23574i
$651$	−2.30843	−	2.66407i	−0.0904744	−	0.104413i
$652$	−4.52935	+	3.57624i	−0.177383	+	0.140057i
$653$	33.8759	+	9.94686i	1.32567	+	0.389251i	0.866534	−	0.499117i	$-0.166342\pi$
$653$	33.8759	+	9.94686i	1.32567	+	0.389251i	0.459132	+	0.888368i	$0.348161\pi$
$654$	−21.6183	−	10.4755i	−0.845344	−	0.409624i
$655$	45.9993	+	29.5620i	1.79734	+	1.15508i
$656$	10.3262	−	5.37465i	0.403171	−	0.209845i
$657$	0.976265	−	1.12667i	0.0380877	−	0.0439556i
$658$	−1.92815	−	0.0440162i	−0.0751670	−	0.00171593i
$659$	−4.18500	−	29.1073i	−0.163024	−	1.13386i	−0.892892	−	0.450271i	$-0.851327\pi$
$659$	−4.18500	−	29.1073i	−0.163024	−	1.13386i	0.729867	−	0.683589i	$-0.239582\pi$
$660$	43.3599	+	14.9123i	1.68778	+	0.580462i
$661$	−21.9073	+	10.0047i	−0.852096	+	0.389139i	−0.793080	−	0.609118i	$-0.791524\pi$
$661$	−21.9073	+	10.0047i	−0.852096	+	0.389139i	−0.0590160	+	0.998257i	$0.518796\pi$
$662$	−23.6864	+	14.4693i	−0.920596	+	0.562365i
$663$	−1.99509	+	4.36864i	−0.0774829	+	0.169664i
$664$	16.4261	−	12.3716i	0.637455	−	0.480111i
$665$	−0.595191	−	0.926135i	−0.0230805	−	0.0359140i
$666$	−1.40472	+	0.377864i	−0.0544319	+	0.0146419i
$667$	2.74917	+	2.08763i	0.106448	+	0.0808335i
$668$	10.4650	+	18.0444i	0.404902	+	0.698161i
$669$	−11.3918	+	7.32107i	−0.440433	+	0.283049i
$670$	6.83196	+	56.6712i	0.263941	+	2.18940i
$671$	37.0522	+	16.9212i	1.43038	+	0.653234i
$672$	−0.0612802	−	2.13623i	−0.00236393	−	0.0824068i
$673$	−13.1225	−	28.7344i	−0.505837	−	1.10763i	−0.974528	−	0.224266i	$-0.928002\pi$
$673$	−13.1225	−	28.7344i	−0.505837	−	1.10763i	0.468691	−	0.883362i	$-0.344726\pi$
$674$	8.49759	+	5.73926i	0.327315	+	0.221068i
$675$	31.8681	−	4.58195i	1.22661	−	0.176359i
$676$	40.6758	−	9.95193i	1.56445	−	0.382766i
$677$	9.38954	+	8.13608i	0.360869	+	0.312695i	0.816358	−	0.577547i	$-0.195990\pi$
$677$	9.38954	+	8.13608i	0.360869	+	0.312695i	−0.455488	+	0.890242i	$0.650535\pi$
$678$	−1.01921	+	3.19912i	−0.0391424	+	0.122861i
$679$	−0.115321	+	0.179443i	−0.00442562	+	0.00688640i
$680$	−4.62287	+	0.344237i	−0.177279	+	0.0132009i
$681$	9.50155	−	32.3593i	0.364100	−	1.24001i
$682$	21.5742	+	50.2449i	0.826117	+	1.92398i
$683$	−17.9654	+	15.5671i	−0.687428	+	0.595659i	−0.926929	−	0.375237i	$-0.877561\pi$
$683$	−17.9654	+	15.5671i	−0.687428	+	0.595659i	0.239502	+	0.970896i	$0.423016\pi$
$684$	−0.519092	−	0.368120i	−0.0198480	−	0.0140754i
$685$	−2.29565	+	0.674064i	−0.0877123	+	0.0257547i
$686$	4.40622	+	0.736522i	0.168230	+	0.0281205i
$687$	−2.00641	+	13.9549i	−0.0765492	+	0.532411i
$688$	−0.736126	−	14.2804i	−0.0280646	−	0.544434i
$689$		−	35.1591i		−	1.33946i
$690$	−3.78709	+	37.3324i	−0.144172	+	1.42122i
$691$		−	5.58196i		−	0.212348i	−0.994348	−	0.106174i	$-0.966140\pi$
$691$		−	5.58196i		−	0.212348i	0.994348	−	0.106174i	$-0.0338600\pi$
$692$	0.798255	−	1.55584i	0.0303451	−	0.0591443i
$693$	0.0289914	−	0.201640i	0.00110129	−	0.00765965i
$694$	4.78870	−	28.6482i	0.181776	−	1.08747i
$695$	34.5515	−	10.1452i	1.31061	−	0.384830i
$696$	−3.18557	−	1.17755i	−0.120749	−	0.0446348i
$697$	1.08693	−	0.941834i	0.0411706	−	0.0356745i
$698$	−22.8045	+	9.79180i	−0.863163	+	0.370625i
$699$	−0.00567239	+	0.0193184i	−0.000214550	+	0.000730689i
$700$	−0.509023	+	2.66908i	−0.0192393	+	0.100882i
$701$	−3.08890	+	4.80642i	−0.116666	+	0.181536i	−0.894676	−	0.446717i	$-0.852593\pi$
$701$	−3.08890	+	4.80642i	−0.116666	+	0.181536i	0.778009	+	0.628253i	$0.216230\pi$
$702$	42.1286	+	13.4217i	1.59004	+	0.506571i
$703$	5.24901	+	4.54829i	0.197970	+	0.171542i
$704$	−9.15331	+	31.8621i	−0.344978	+	1.20085i
$705$	−32.9780	+	4.74152i	−1.24202	+	0.178576i
$706$	17.5006	−	25.9115i	0.658642	−	0.975191i
$707$	0.611838	+	1.33974i	0.0230105	+	0.0503860i
$708$	13.2189	−	13.9178i	0.496796	−	0.523064i
$709$	−3.66776	−	1.67501i	−0.137746	−	0.0629063i	0.345350	−	0.938474i	$-0.387760\pi$
$709$	−3.66776	−	1.67501i	−0.137746	−	0.0629063i	−0.483095	+	0.875568i	$0.660488\pi$
$710$	21.9308	−	2.64386i	0.823050	−	0.0992223i
$711$	0.375822	−	0.241526i	0.0140944	−	0.00905794i
$712$	28.5905	−	28.7584i	1.07148	−	1.07777i
$713$	−36.0066	+	26.5700i	−1.34846	+	0.995055i
$714$	−0.0685850	−	0.254967i	−0.00256673	−	0.00954191i
$715$	−43.2847	−	67.3522i	−1.61875	−	2.51883i
$716$	27.2982	−	10.9904i	1.02018	−	0.410730i
$717$	2.53687	−	5.55496i	0.0947410	−	0.207454i
$718$	1.52335	+	2.49374i	0.0568509	+	0.0930654i
$719$	14.2275	−	6.49749i	0.530597	−	0.242316i	−0.132056	−	0.991242i	$-0.542158\pi$
$719$	14.2275	−	6.49749i	0.530597	−	0.242316i	0.662653	+	0.748927i	$0.269431\pi$
$720$	0.556025	+	2.82555i	0.0207218	+	0.105302i
$721$	−0.536261	−	3.72978i	−0.0199714	−	0.138904i
$722$	0.543892	−	23.8254i	0.0202416	−	0.886690i
$723$	11.1531	−	12.8714i	0.414789	−	0.478692i
$724$	0.0290041	−	0.634936i	0.00107793	−	0.0235972i
$725$	3.63261	+	2.33453i	0.134912	+	0.0867024i
$726$	6.34908	−	13.1026i	0.235636	−	0.486285i
$727$	−19.3621	−	5.68523i	−0.718101	−	0.210853i	−0.0977873	−	0.995207i	$-0.531176\pi$
$727$	−19.3621	−	5.68523i	−0.718101	−	0.210853i	−0.620314	+	0.784354i	$0.712995\pi$
$728$	−2.22747	+	2.99378i	−0.0825556	+	0.110957i
$729$	18.7688	+	21.6603i	0.695140	+	0.802235i
$730$	20.5324	+	24.8182i	0.759939	+	0.918564i
$731$	−0.497715	−	1.69506i	−0.0184086	−	0.0626941i
$732$	−3.18118	−	32.6416i	−0.117580	−	1.20647i
$733$	−21.9322	−	3.15338i	−0.810085	−	0.116473i	−0.275189	−	0.961390i	$-0.588740\pi$
$733$	−21.9322	−	3.15338i	−0.810085	−	0.116473i	−0.534896	+	0.844918i	$0.679649\pi$
$734$	12.3204	+	11.1781i	0.454756	+	0.412591i
$735$	38.4445			1.41805
$736$	−27.0960	−	1.34491i	−0.998770	−	0.0495739i
$737$	50.4319			1.85768
$738$	−0.661689	−	0.600337i	−0.0243571	−	0.0220987i
$739$	−50.8417	−	7.30993i	−1.87024	−	0.268900i	−0.888466	−	0.458942i	$-0.848229\pi$
$739$	−50.8417	−	7.30993i	−1.87024	−	0.268900i	−0.981776	+	0.190042i	$0.939138\pi$
$740$	−3.04864	−	31.2816i	−0.112070	−	1.14993i
$741$	−4.01325	−	13.6679i	−0.147431	−	0.502102i
$742$	1.23212	+	1.48931i	0.0452326	+	0.0546742i
$743$	−12.4738	−	14.3955i	−0.457620	−	0.528121i	0.479307	−	0.877647i	$-0.340888\pi$
$743$	−12.4738	−	14.3955i	−0.457620	−	0.528121i	−0.936927	+	0.349526i	$0.886343\pi$
$744$	26.2807	−	35.3219i	0.963496	−	1.29496i
$745$	−69.8786	−	20.5182i	−2.56015	−	0.751729i
$746$	−23.2682	+	48.0188i	−0.851910	+	1.75809i
$747$	−1.32770	−	0.853260i	−0.0485780	−	0.0312192i
$748$	−0.186895	+	4.09138i	−0.00683357	+	0.149596i
$749$	−0.250040	+	0.288561i	−0.00913625	+	0.0105438i
$750$	−0.178412	+	7.81540i	−0.00651468	+	0.285378i
$751$	−2.94158	−	20.4591i	−0.107340	−	0.746564i	−0.970407	−	0.241475i	$-0.922369\pi$
$751$	−2.94158	−	20.4591i	−0.107340	−	0.746564i	0.863067	−	0.505089i	$-0.168540\pi$
$752$	−4.65092	−	23.6345i	−0.169602	−	0.861863i
$753$	−15.3416	+	7.00628i	−0.559080	+	0.255323i
$754$	3.09135	+	5.06057i	0.112580	+	0.184295i
$755$	−9.19743	+	20.1396i	−0.334729	+	0.732954i
$756$	−2.25488	+	0.907826i	−0.0820091	+	0.0330173i
$757$	7.54433	+	11.7392i	0.274203	+	0.426669i	0.950856	−	0.309634i	$-0.100206\pi$
$757$	7.54433	+	11.7392i	0.274203	+	0.426669i	−0.676653	+	0.736302i	$0.736570\pi$
$758$	5.31857	+	19.7720i	0.193179	+	0.718151i
$759$	32.3459	+	7.26959i	1.17408	+	0.263869i
$760$	9.69397	−	9.75088i	0.351637	−	0.353702i
$761$	7.36982	−	4.73630i	0.267156	−	0.171691i	−0.400204	−	0.916426i	$-0.631061\pi$
$761$	7.36982	−	4.73630i	0.267156	−	0.171691i	0.667360	+	0.744735i	$0.267424\pi$
$762$	25.8219	−	3.11294i	0.935429	−	0.112770i
$763$	−2.09760	−	0.957941i	−0.0759382	−	0.0346798i
$764$	18.6152	−	19.5995i	0.673473	−	0.709084i
$765$	0.147796	+	0.323628i	0.00534358	+	0.0117008i
$766$	9.12228	−	13.5065i	0.329602	−	0.488011i
$767$	−33.1745	+	4.76977i	−1.19786	+	0.172226i
$768$	25.8891	−	6.49499i	0.934191	−	0.234368i
$769$	−30.6072	−	26.5213i	−1.10372	−	0.956382i	−0.104452	−	0.994530i	$-0.533309\pi$
$769$	−30.6072	−	26.5213i	−1.10372	−	0.956382i	−0.999272	+	0.0381479i	$0.987854\pi$
$770$	4.19379	+	1.33610i	0.151134	+	0.0481498i
$771$	−11.1107	+	17.2886i	−0.400142	+	0.622633i
$772$	−6.38956	+	33.5038i	−0.229965	+	1.20583i
$773$	−10.1397	+	34.5325i	−0.364698	+	1.24205i	0.549058	+	0.835785i	$0.314987\pi$
$773$	−10.1397	+	34.5325i	−0.364698	+	1.24205i	−0.913756	+	0.406264i	$0.866831\pi$
$774$	−1.00842	+	0.432995i	−0.0362469	+	0.0155637i
$775$	−42.3040	+	36.6566i	−1.51961	+	1.31675i
$776$	−2.49881	−	0.923684i	−0.0897019	−	0.0331583i
$777$	1.71761	−	0.504337i	0.0616191	−	0.0180930i
$778$	−7.37567	+	44.1247i	−0.264430	+	1.58195i
$779$	−0.607093	+	4.22242i	−0.0217514	+	0.151284i
$780$	−29.4262	+	57.3533i	−1.05363	+	2.05358i
$781$		−	19.5164i		−	0.698350i
$782$	−3.29483	+	0.614897i	−0.117823	+	0.0219887i
$783$			3.86292i			0.138049i
$784$	1.43087	+	27.7580i	0.0511026	+	0.991357i
$785$	9.25750	−	64.3873i	0.330414	−	2.29808i
$786$	−38.3643	−	6.41279i	−1.36841	−	0.228737i
$787$	−28.5686	+	8.38848i	−1.01836	+	0.299017i	−0.747969	−	0.663734i	$-0.768971\pi$
$787$	−28.5686	+	8.38848i	−1.01836	+	0.299017i	−0.270390	+	0.962751i	$0.587153\pi$
$788$	7.98591	+	5.66329i	0.284486	+	0.201746i
$789$	25.5917	−	22.1753i	0.911088	−	0.789462i
$790$	3.80833	+	8.86937i	0.135494	+	0.315558i
$791$	−0.0908019	+	0.309243i	−0.00322854	+	0.0109954i
$792$	2.53724	−	0.188933i	0.0901570	−	0.00671345i
$793$	−30.9595	+	48.1739i	−1.09940	+	1.71071i
$794$	6.90278	−	21.6666i	0.244971	−	0.768920i
$795$	25.2350	+	21.8663i	0.894995	+	0.775518i
$796$	−26.6854	+	6.52896i	−0.945838	+	0.231413i
$797$	12.5901	−	1.81019i	0.445966	−	0.0641202i	0.0843264	−	0.996438i	$-0.473126\pi$
$797$	12.5901	−	1.81019i	0.445966	−	0.0641202i	0.361640	+	0.932318i	$0.382217\pi$
$798$	0.648977	+	0.438317i	0.0229735	+	0.0155163i
$799$	−1.23625	−	2.70702i	−0.0437355	−	0.0957674i
$800$	−33.9222	+	0.973097i	−1.19933	+	0.0344042i
$801$	−2.83104	−	1.29289i	−0.100030	−	0.0456821i
$802$	0.161262	+	1.33767i	0.00569434	+	0.0472346i
$803$	23.9407	−	15.3857i	0.844848	−	0.542951i
$804$	−20.3712	−	35.1255i	−0.718436	−	1.23878i
$805$	−0.281650	+	3.59097i	−0.00992686	+	0.126565i
$806$	−74.2340	+	19.9686i	−2.61478	+	0.703363i
$807$	2.83151	+	4.40591i	0.0996737	+	0.155095i
$808$	−14.6936	+	11.0667i	−0.516918	+	0.389326i
$809$	−13.6199	+	29.8234i	−0.478850	+	1.04853i	0.503929	+	0.863745i	$0.331887\pi$
$809$	−13.6199	+	29.8234i	−0.478850	+	1.04853i	−0.982778	+	0.184789i	$0.940840\pi$
$810$	−33.2275	+	20.2977i	−1.16749	+	0.713188i
$811$	33.4165	−	15.2608i	1.17341	−	0.535880i	0.269251	−	0.963070i	$-0.413224\pi$
$811$	33.4165	−	15.2608i	1.17341	−	0.535880i	0.904162	+	0.427190i	$0.140496\pi$
$812$	−0.308290	−	0.106027i	−0.0108189	−	0.00372082i
$813$	−0.247089	−	1.71854i	−0.00866579	−	0.0602719i
$814$	−27.7612	−	0.633740i	−0.973030	−	0.0222126i
$815$	−6.26685	+	7.23233i	−0.219518	+	0.253338i
$816$	2.92511	−	1.52248i	0.102399	−	0.0532974i
$817$	4.40808	+	2.83290i	0.154219	+	0.0991108i
$818$	−5.49816	−	2.66422i	−0.192239	−	0.0931521i
$819$	0.274788	+	0.0806851i	0.00960187	+	0.00281936i
$820$	15.1506	−	11.9625i	0.529083	−	0.417749i
$821$	7.29501	+	8.41889i	0.254597	+	0.293821i	0.868632	−	0.495458i	$-0.165000\pi$
$821$	7.29501	+	8.41889i	0.254597	+	0.293821i	−0.614034	+	0.789279i	$0.710454\pi$
$822$	1.31136	−	1.08490i	0.0457390	−	0.0378404i
$823$	5.42382	+	18.4718i	0.189062	+	0.643887i	0.998400	+	0.0565438i	$0.0180080\pi$
$823$	5.42382	+	18.4718i	0.189062	+	0.643887i	−0.809338	+	0.587344i	$0.800174\pi$
$824$	44.0464	−	16.5755i	1.53443	−	0.577434i
$825$	41.0487	+	5.90192i	1.42913	+	0.205478i
$826$	1.23809	−	1.36461i	0.0430785	−	0.0474810i
$827$	10.8862			0.378552			0.189276	−	0.981924i	$-0.439386\pi$
$827$	10.8862			0.378552			0.189276	+	0.981924i	$0.439386\pi$
$828$	0.624212	+	1.98636i	0.0216929	+	0.0690307i
$829$	27.3003			0.948177			0.474089	−	0.880477i	$-0.342778\pi$
$829$	27.3003			0.948177			0.474089	+	0.880477i	$0.342778\pi$
$830$	22.9130	−	25.2546i	0.795323	−	0.876602i
$831$	−15.9553	−	2.29402i	−0.553482	−	0.0795787i
$832$	−42.5059	−	19.1119i	−1.47363	−	0.662585i
$833$	0.967452	+	3.29484i	0.0335202	+	0.114159i
$834$	−19.7371	+	16.3287i	−0.683439	+	0.565417i
$835$	22.6517	+	26.1415i	0.783895	+	0.904663i
$836$	−7.52796	−	9.53424i	−0.260360	−	0.329748i
$837$	−48.0474	−	14.1080i	−1.66076	−	0.487643i
$838$	−23.8090	−	11.5370i	−0.822469	−	0.398539i
$839$	−10.9536	−	7.03945i	−0.378160	−	0.243029i	0.337728	−	0.941244i	$-0.390342\pi$
$839$	−10.9536	−	7.03945i	−0.378160	−	0.243029i	−0.715888	+	0.698215i	$0.753978\pi$
$840$	−0.763432	−	3.46064i	−0.0263409	−	0.119404i
$841$	18.6517	−	21.5252i	0.643161	−	0.742248i
$842$	9.80294	+	0.223784i	0.337832	+	0.00771210i
$843$	−5.64966	−	39.2943i	−0.194585	−	1.35337i
$844$	9.11945	−	26.5162i	0.313904	−	0.912726i
$845$	63.1648	−	28.8464i	2.17294	−	0.992347i
$846$	−1.57763	+	0.963727i	−0.0542400	+	0.0331336i
$847$	0.580598	−	1.27133i	0.0199496	−	0.0436835i
$848$	−14.8489	+	19.0343i	−0.509912	+	0.653639i
$849$	16.6292	+	25.8756i	0.570713	+	0.888047i
$850$	−4.04875	+	1.08909i	−0.138871	+	0.0373556i
$851$	−4.67774	−	22.2379i	−0.160351	−	0.762307i
$852$	−13.5930	+	7.88333i	−0.465689	+	0.270078i
$853$	−3.55643	+	2.28558i	−0.121770	+	0.0782567i	−0.600108	−	0.799919i	$-0.704876\pi$
$853$	−3.55643	+	2.28558i	−0.121770	+	0.0782567i	0.478338	+	0.878176i	$0.341239\pi$
$854$	−0.376799	−	3.12555i	−0.0128938	−	0.106954i
$855$	−0.959899	−	0.438371i	−0.0328279	−	0.0149920i
$856$	−4.19210	−	2.27315i	−0.143283	−	0.0776948i
$857$	5.27755	+	11.5562i	0.180278	+	0.394753i	0.978099	−	0.208141i	$-0.0667414\pi$
$857$	5.27755	+	11.5562i	0.180278	+	0.394753i	−0.797821	+	0.602894i	$0.794014\pi$
$858$	47.1962	+	31.8762i	1.61125	+	1.08824i
$859$	−50.8716	+	7.31424i	−1.73572	+	0.249559i	−0.936296	−	0.351212i	$-0.885770\pi$
$859$	−50.8716	+	7.31424i	−1.73572	+	0.249559i	−0.799422	+	0.600770i	$0.794861\pi$
$860$	−5.63523	−	23.0325i	−0.192160	−	0.785400i
$861$	0.830935	+	0.720009i	0.0283182	+	0.0245379i
$862$	−1.48889	+	4.67337i	−0.0507118	+	0.159176i
$863$	6.32054	−	9.83496i	0.215154	−	0.334786i	−0.716854	−	0.697223i	$-0.754419\pi$
$863$	6.32054	−	9.83496i	0.215154	−	0.334786i	0.932008	+	0.362437i	$0.118055\pi$
$864$	−17.1389	−	25.0584i	−0.583077	−	0.852506i
$865$	0.816949	−	2.78227i	0.0277771	−	0.0946001i
$866$	0.665317	+	1.54948i	0.0226084	+	0.0526536i
$867$	−21.1248	+	18.3048i	−0.717437	+	0.621663i
$868$	2.44470	−	3.44731i	0.0829784	−	0.117009i
$869$	8.18254	−	2.40261i	0.277574	−	0.0815030i
$870$	−5.55475	−	0.928505i	−0.188324	−	0.0314793i
$871$	−10.0900	+	70.1778i	−0.341888	+	2.37788i
$872$	6.03960	−	28.1602i	0.204527	−	0.953623i
$873$			0.204462i			0.00691999i
$874$	6.19132	−	7.77807i	0.209425	−	0.263097i
$875$			0.750411i			0.0253685i
$876$	−20.3865	−	10.4597i	−0.688797	−	0.353400i
$877$	−5.09080	+	35.4073i	−0.171904	+	1.19562i	0.702952	+	0.711237i	$0.251865\pi$
$877$	−5.09080	+	35.4073i	−0.171904	+	1.19562i	−0.874856	+	0.484382i	$0.839044\pi$
$878$	3.77866	−	22.6057i	0.127523	−	0.762905i
$879$	32.6908	−	9.59889i	1.10263	−	0.323763i
$880$	−5.01184	+	54.7433i	−0.168949	+	1.84540i
$881$	−18.0081	+	15.6041i	−0.606708	+	0.525716i	−0.903144	−	0.429337i	$-0.858747\pi$
$881$	−18.0081	+	15.6041i	−0.606708	+	0.525716i	0.296436	+	0.955053i	$0.404202\pi$
$882$	1.96015	−	0.841650i	0.0660018	−	0.0283398i
$883$	−10.7479	+	36.6040i	−0.361695	+	1.23182i	0.554870	+	0.831937i	$0.312768\pi$
$883$	−10.7479	+	36.6040i	−0.361695	+	1.23182i	−0.916566	+	0.399884i	$0.869050\pi$
$884$	−5.65590	−	1.07864i	−0.190229	−	0.0362787i
$885$	17.2085	−	26.7770i	0.578459	−	0.900099i
$886$	−36.8678	−	11.7457i	−1.23860	−	0.394605i
$887$	22.8778	+	19.8237i	0.768160	+	0.665614i	0.948067	−	0.318069i	$-0.103034\pi$
$887$	22.8778	+	19.8237i	0.768160	+	0.665614i	−0.179908	+	0.983683i	$0.557580\pi$
$888$	10.7723	+	19.5915i	0.361495	+	0.657447i
$889$	2.47123	−	0.355310i	0.0828825	−	0.0119167i
$890$	37.6371	−	55.7258i	1.26160	−	1.86793i
$891$	14.2906	+	31.2921i	0.478754	+	1.04832i
$892$	−11.7715	−	11.1803i	−0.394138	−	0.374344i
$893$	8.02917	+	3.66680i	0.268686	+	0.122705i
$894$	51.4346	−	6.20067i	1.72023	−	0.207381i
$895$	41.0515	−	26.3822i	1.37220	−	0.881860i
$896$	2.47027	−	0.680022i	0.0825259	−	0.0227179i
$897$	−16.5874	+	43.5560i	−0.553837	+	1.45429i
$898$	6.89162	+	25.6199i	0.229976	+	0.854946i
$899$	−3.63102	−	5.64997i	−0.121101	−	0.188437i
$900$	0.972727	+	2.41608i	0.0324242	+	0.0805360i
$901$	−1.23899	+	2.71300i	−0.0412766	+	0.0903832i
$902$	−8.89089	−	14.5545i	−0.296034	−	0.484610i
$903$	1.22849	−	0.561034i	0.0408817	−	0.0186701i
$904$	−4.01590	−	0.275411i	−0.133567	−	0.00916002i
$905$	−0.149997	−	1.04325i	−0.00498606	−	0.0346788i
$906$	0.359443	−	15.7455i	0.0119417	−	0.523111i
$907$	35.7471	−	41.2544i	1.18696	−	1.36983i	0.274031	−	0.961721i	$-0.411643\pi$
$907$	35.7471	−	41.2544i	1.18696	−	1.36983i	0.912933	−	0.408109i	$-0.133812\pi$
$908$	40.3910	+	1.84507i	1.34042	+	0.0612308i
$909$	1.18766	+	0.763265i	0.0393923	+	0.0253159i
$910$	−2.69830	+	5.56850i	−0.0894476	+	0.184594i
$911$	−46.1314	−	13.5454i	−1.52840	−	0.448779i	−0.593840	−	0.804583i	$-0.702389\pi$
$911$	−46.1314	−	13.5454i	−1.52840	−	0.448779i	−0.934561	+	0.355804i	$0.884207\pi$
$912$	−3.59972	+	9.09437i	−0.119199	+	0.301145i
$913$	−19.7293	−	22.7689i	−0.652946	−	0.753540i
$914$	9.93484	+	12.0086i	0.328615	+	0.397209i
$915$	−15.3218	−	52.1813i	−0.506524	−	1.72506i
$916$	−16.8227	+	1.63950i	−0.555837	+	0.0541708i
$917$	−3.69576	−	0.531369i	−0.122045	−	0.0175474i
$918$	−2.77781	−	2.52025i	−0.0916815	−	0.0831808i
$919$	−5.18549			−0.171053			−0.0855267	−	0.996336i	$-0.527257\pi$
$919$	−5.18549			−0.171053			−0.0855267	+	0.996336i	$0.527257\pi$
$920$	−44.5541	+	6.22658i	−1.46891	+	0.205284i
$921$	6.22727			0.205196
$922$	8.85768	+	8.03640i	0.291712	+	0.264665i
$923$	27.1577	+	3.90469i	0.893907	+	0.128524i
$924$	−3.11626	+	0.303704i	−0.102517	+	0.00999112i
$925$	−8.00861	−	27.2748i	−0.263321	−	0.896790i
$926$	−31.8711	−	38.5236i	−1.04735	−	1.26597i
$927$	−2.36531	−	2.72971i	−0.0776869	−	0.0896555i
$928$	0.463663	−	4.04524i	0.0152205	−	0.132792i
$929$	−5.81700	−	1.70802i	−0.190849	−	0.0560384i	0.184911	−	0.982755i	$-0.440800\pi$
$929$	−5.81700	−	1.70802i	−0.190849	−	0.0560384i	−0.375761	+	0.926717i	$0.622618\pi$
$930$	31.8356	−	65.6995i	1.04393	−	2.15437i
$931$	−8.56838	−	5.50656i	−0.280817	−	0.180470i
$932$	−0.0241133	−	0.00110150i	−0.000789856	−	3.60809e-5i
$933$	−19.9305	+	23.0010i	−0.652494	+	0.753018i
$934$	−1.05868	+	46.3758i	−0.0346410	+	1.51746i
$935$	0.966544	+	6.72246i	0.0316094	+	0.219848i
$936$	−0.244725	+	3.56846i	−0.00799910	+	0.116639i
$937$	23.3197	−	10.6498i	0.761822	−	0.347912i	0.00367246	−	0.999993i	$-0.498831\pi$
$937$	23.3197	−	10.6498i	0.761822	−	0.347912i	0.758149	+	0.652081i	$0.226104\pi$
$938$	−2.03191	−	3.32626i	−0.0663444	−	0.108606i
$939$	−5.68533	+	12.4491i	−0.185534	+	0.406262i
$940$	−14.9178	−	37.0533i	−0.486566	−	1.20854i
$941$	17.8794	+	27.8210i	0.582853	+	0.906937i	0.999998	−	0.00190261i	$-0.000605621\pi$
$941$	17.8794	+	27.8210i	0.582853	+	0.906937i	−0.417145	+	0.908840i	$0.636969\pi$
$942$	12.0200	+	44.6848i	0.391633	+	1.45591i
$943$	9.93690	−	9.80124i	0.323590	−	0.319172i
$944$	19.9742	+	11.4284i	0.650106	+	0.371964i
$945$	−3.39093	+	2.17922i	−0.110307	+	0.0708900i
$946$	−20.7990	+	2.50741i	−0.676233	+	0.0815228i
$947$	−7.00174	−	3.19759i	−0.227526	−	0.103908i	0.298390	−	0.954444i	$-0.403550\pi$
$947$	−7.00174	−	3.19759i	−0.227526	−	0.103908i	−0.525916	+	0.850536i	$0.676278\pi$
$948$	−4.97861	−	4.72858i	−0.161698	−	0.153577i
$949$	16.6199	+	36.3926i	0.539506	+	1.18135i
$950$	6.96025	−	10.3054i	0.225820	−	0.334352i
$951$	12.0980	−	1.73943i	0.392305	−	0.0564050i
$952$	0.277379	−	0.152516i	0.00898989	−	0.00494307i
$953$	31.2472	+	27.0759i	1.01220	+	0.877073i	0.992440	−	0.122732i	$-0.0391654\pi$
$953$	31.2472	+	27.0759i	1.01220	+	0.877073i	0.0197566	+	0.999805i	$0.493711\pi$
$954$	1.76536	+	0.562426i	0.0571556	+	0.0182092i
$955$	24.2335	−	37.7081i	0.784178	−	1.22021i
$956$	7.19179	+	1.37155i	0.232599	+	0.0443593i
$957$	−1.40183	+	4.77420i	−0.0453148	+	0.154328i
$958$	−13.7372	+	5.89848i	−0.443829	+	0.190571i
$959$	0.123471	−	0.106988i	0.00398708	−	0.00345482i
$960$	40.1528	−	18.6220i	1.29592	−	0.601022i
$961$	53.7917	−	15.7947i	1.73522	−	0.509506i
$962$	6.43613	−	38.5039i	0.207509	−	1.24142i
$963$	−0.0520862	+	0.362267i	−0.00167845	+	0.0116739i
$964$	18.1670	+	9.32093i	0.585121	+	0.300207i
$965$			56.5589i			1.82070i
$966$	−0.823754	−	2.42628i	−0.0265038	−	0.0780642i
$967$		−	4.17765i		−	0.134344i	−0.997741	−	0.0671721i	$-0.978602\pi$
$967$		−	4.17765i		−	0.134344i	0.997741	−	0.0671721i	$-0.0213976\pi$
$968$	17.0676	+	3.66054i	0.548573	+	0.117654i
$969$	−0.171971	+	1.19609i	−0.00552452	+	0.0384238i
$970$	−4.35722	−	0.728331i	−0.139902	−	0.0233853i
$971$	22.7195	−	6.67106i	0.729104	−	0.214084i	0.103947	−	0.994583i	$-0.466853\pi$
$971$	22.7195	−	6.67106i	0.729104	−	0.214084i	0.625158	+	0.780498i	$0.285035\pi$
$972$	−2.60470	+	3.67294i	−0.0835459	+	0.117810i
$973$	−1.85834	+	1.61026i	−0.0595755	+	0.0516225i
$974$	0.221661	+	0.516236i	0.00710249	+	0.0165413i
$975$	−16.4254	+	55.9399i	−0.526035	+	1.79151i
$976$	37.1061	−	13.0049i	1.18774	−	0.416278i
$977$	15.4331	−	24.0144i	0.493749	−	0.768289i	−0.501551	−	0.865128i	$-0.667237\pi$
$977$	15.4331	−	24.0144i	0.493749	−	0.768289i	0.995300	+	0.0968393i	$0.0308733\pi$
$978$	2.06646	−	6.48627i	0.0660782	−	0.207408i
$979$	−44.9003	−	38.9063i	−1.43502	−	1.24345i
$980$	10.9537	+	44.7702i	0.349902	+	1.43013i
$981$	−2.18789	+	0.314572i	−0.0698540	+	0.0100435i
$982$	−28.4569	−	19.2197i	−0.908096	−	0.613326i
$983$	18.0583	+	39.5422i	0.575971	+	1.26120i	0.943557	+	0.331210i	$0.107457\pi$
$983$	18.0583	+	39.5422i	0.575971	+	1.26120i	−0.367586	+	0.929989i	$0.619816\pi$
$984$	−6.54573	+	12.0715i	−0.208670	+	0.384825i
$985$	14.7674	+	6.74406i	0.470530	+	0.214884i
$986$	−0.0602083	−	0.499429i	−0.00191742	−	0.0159050i
$987$	1.91388	−	1.22998i	0.0609196	−	0.0391507i
$988$	14.7734	−	8.56788i	0.470003	−	0.272581i
$989$	−5.88078	−	16.1041i	−0.186998	−	0.512082i
$990$	4.07420	−	1.09594i	0.129486	−	0.0348312i
$991$	−5.81282	−	9.04493i	−0.184650	−	0.287322i	0.736571	−	0.676360i	$-0.236444\pi$
$991$	−5.81282	−	9.04493i	−0.184650	−	0.287322i	−0.921222	+	0.389038i	$0.872807\pi$
$992$	48.6217	+	20.5409i	1.54374	+	0.652176i
$993$	13.6012	−	29.7825i	0.431621	−	0.945118i
$994$	−1.28721	+	0.786319i	−0.0408278	+	0.0249405i
$995$	−41.4393	+	18.9247i	−1.31371	+	0.599953i
$996$	−7.88899	+	22.9385i	−0.249972	+	0.726833i
$997$	−8.06259	−	56.0766i	−0.255345	−	1.77596i	−0.564978	−	0.825106i	$-0.691115\pi$
$997$	−8.06259	−	56.0766i	−0.255345	−	1.77596i	0.309633	−	0.950856i	$-0.399794\pi$
$998$	32.2105	+	0.735308i	1.01960	+	0.0232758i
$999$	16.6530	−	19.2186i	0.526878	−	0.608050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.h.a.11.3	✓	100
3.2	odd	2		828.2.u.a.379.8		100
4.3	odd	2	inner	92.2.h.a.11.7	yes	100
12.11	even	2		828.2.u.a.379.4		100
23.21	odd	22	inner	92.2.h.a.67.7	yes	100
69.44	even	22		828.2.u.a.343.4		100
92.67	even	22	inner	92.2.h.a.67.3	yes	100
276.251	odd	22		828.2.u.a.343.8		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.h.a.11.3	✓	100	1.1	even	1	trivial
92.2.h.a.11.7	yes	100	4.3	odd	2	inner
92.2.h.a.67.3	yes	100	92.67	even	22	inner
92.2.h.a.67.7	yes	100	23.21	odd	22	inner
828.2.u.a.343.4		100	69.44	even	22
828.2.u.a.343.8		100	276.251	odd	22
828.2.u.a.379.4		100	12.11	even	2
828.2.u.a.379.8		100	3.2	odd	2

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04738 - 0.950264i) q^{2} +(1.65123 + 0.237411i) q^{3} +(0.193997 + 1.99057i) q^{4} +(0.934364 + 3.18215i) q^{5} +(-1.50386 - 1.81776i) q^{6} +(-0.148303 - 0.171151i) q^{7} +(1.68838 - 2.26922i) q^{8} +(-0.208284 - 0.0611576i) q^{9} +O(q^{10})\)	\(q+(-1.04738 - 0.950264i) q^{2} +(1.65123 + 0.237411i) q^{3} +(0.193997 + 1.99057i) q^{4} +(0.934364 + 3.18215i) q^{5} +(-1.50386 - 1.81776i) q^{6} +(-0.148303 - 0.171151i) q^{7} +(1.68838 - 2.26922i) q^{8} +(-0.208284 - 0.0611576i) q^{9} +(2.04525 - 4.22080i) q^{10} +(-3.48603 - 2.24034i) q^{11} +(-0.152250 + 3.33294i) q^{12} +(3.81497 - 4.40271i) q^{13} +(-0.00730929 + 0.320186i) q^{14} +(0.787372 + 5.47629i) q^{15} +(-3.92473 + 0.772328i) q^{16} +(-0.449525 + 0.205291i) q^{17} +(0.160036 + 0.261980i) q^{18} +(0.608905 - 1.33332i) q^{19} +(-6.15303 + 2.47724i) q^{20} +(-0.204249 - 0.317818i) q^{21} +(1.52228 + 5.65913i) q^{22} +(-4.22490 + 2.26941i) q^{23} +(3.32664 - 3.34617i) q^{24} +(-5.04678 + 3.24337i) q^{25} +(-8.17944 + 0.986067i) q^{26} +(-4.88178 - 2.22943i) q^{27} +(0.311917 - 0.328410i) q^{28} +(-0.299010 - 0.654741i) q^{29} +(4.37925 - 6.48395i) q^{30} +(9.23576 - 1.32790i) q^{31} +(4.84459 + 2.92061i) q^{32} +(-5.22436 - 4.52693i) q^{33} +(0.665903 + 0.212150i) q^{34} +(0.406059 - 0.631840i) q^{35} +(0.0813321 - 0.426468i) q^{36} +(-1.33496 + 4.54647i) q^{37} +(-1.90476 + 0.817864i) q^{38} +(7.34464 - 6.36416i) q^{39} +(8.79858 + 3.25239i) q^{40} +(-2.79241 + 0.819926i) q^{41} +(-0.0880851 + 0.526966i) q^{42} +(-0.508752 + 3.53845i) q^{43} +(3.78327 - 7.37380i) q^{44} -0.719934i q^{45} +(6.58160 + 1.63784i) q^{46} +6.02195i q^{47} +(-6.66399 + 0.343516i) q^{48} +(0.988905 - 6.87799i) q^{49} +(8.36794 + 1.39875i) q^{50} +(-0.791007 + 0.232261i) q^{51} +(9.50398 + 6.73984i) q^{52} +(4.56115 - 3.95226i) q^{53} +(2.99451 + 6.97403i) q^{54} +(3.87187 - 13.1864i) q^{55} +(-0.638771 + 0.0475654i) q^{56} +(1.32199 - 2.05705i) q^{57} +(-0.309000 + 0.969899i) q^{58} +(-4.34794 - 3.76751i) q^{59} +(-10.7482 + 2.62970i) q^{60} +(-9.72972 + 1.39892i) q^{61} +(-10.9352 - 7.38560i) q^{62} +(0.0204219 + 0.0447178i) q^{63} +(-2.29876 - 7.66262i) q^{64} +(17.5746 + 8.02607i) q^{65} +(1.17009 + 9.70592i) q^{66} +(-10.2383 + 6.57976i) q^{67} +(-0.495852 - 0.854984i) q^{68} +(-7.51506 + 2.74429i) q^{69} +(-1.02571 + 0.275911i) q^{70} +(2.54626 + 3.96206i) q^{71} +(-0.490442 + 0.369385i) q^{72} +(-2.85291 + 6.24699i) q^{73} +(5.71855 - 3.49330i) q^{74} +(-9.10341 + 4.15739i) q^{75} +(2.77218 + 0.953409i) q^{76} +(0.133554 + 0.928886i) q^{77} +(-13.7402 - 0.313665i) q^{78} +(-1.34769 + 1.55532i) q^{79} +(-6.12479 - 11.7675i) q^{80} +(-6.98379 - 4.48821i) q^{81} +(3.70385 + 1.79476i) q^{82} +(6.97591 + 2.04831i) q^{83} +(0.593015 - 0.468228i) q^{84} +(-1.07329 - 1.23864i) q^{85} +(3.89531 - 3.22264i) q^{86} +(-0.338292 - 1.15212i) q^{87} +(-10.9696 + 4.12805i) q^{88} +(14.1914 + 2.04041i) q^{89} +(-0.684127 + 0.754042i) q^{90} -1.31930 q^{91} +(-5.33704 - 7.96969i) q^{92} +15.5656 q^{93} +(5.72245 - 6.30725i) q^{94} +(4.81175 + 0.691826i) q^{95} +(7.30614 + 5.97276i) q^{96} +(-0.265360 - 0.903735i) q^{97} +(-7.57166 + 6.26412i) q^{98} +(0.589070 + 0.679823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) \) 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9	\( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25} + 12 q^{26} - 11 q^{28} - 42 q^{29} - 11 q^{30} - 27 q^{32} - 22 q^{33} + 11 q^{34} + 77 q^{36} - 22 q^{37} + 44 q^{38} + 77 q^{40} - 10 q^{41} + 99 q^{42} + 66 q^{44} + 65 q^{46} + 38 q^{48} - 8 q^{49} + 30 q^{50} + 96 q^{52} - 22 q^{53} + 48 q^{54} + 44 q^{56} - 22 q^{57} + 79 q^{58} + 11 q^{60} - 22 q^{61} - 36 q^{62} + 10 q^{64} - 22 q^{65} - 44 q^{66} - 10 q^{69} + 34 q^{70} - 21 q^{72} - 18 q^{73} - 22 q^{74} - 66 q^{76} + 122 q^{77} - 66 q^{78} - 110 q^{80} + 8 q^{81} - 122 q^{82} - 165 q^{84} + 54 q^{85} - 121 q^{86} - 99 q^{88} + 22 q^{89} - 198 q^{90} - 86 q^{92} + 212 q^{93} - 61 q^{94} - 147 q^{96} + 22 q^{97} - 71 q^{98}+O(q^{100}) \) 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9 - 11 * q^10 - 18 * q^12 - 18 * q^13 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 24 * q^18 - 11 * q^20 - 22 * q^21 - 30 * q^24 - 16 * q^25 + 12 * q^26 - 11 * q^28 - 42 * q^29 - 11 * q^30 - 27 * q^32 - 22 * q^33 + 11 * q^34 + 77 * q^36 - 22 * q^37 + 44 * q^38 + 77 * q^40 - 10 * q^41 + 99 * q^42 + 66 * q^44 + 65 * q^46 + 38 * q^48 - 8 * q^49 + 30 * q^50 + 96 * q^52 - 22 * q^53 + 48 * q^54 + 44 * q^56 - 22 * q^57 + 79 * q^58 + 11 * q^60 - 22 * q^61 - 36 * q^62 + 10 * q^64 - 22 * q^65 - 44 * q^66 - 10 * q^69 + 34 * q^70 - 21 * q^72 - 18 * q^73 - 22 * q^74 - 66 * q^76 + 122 * q^77 - 66 * q^78 - 110 * q^80 + 8 * q^81 - 122 * q^82 - 165 * q^84 + 54 * q^85 - 121 * q^86 - 99 * q^88 + 22 * q^89 - 198 * q^90 - 86 * q^92 + 212 * q^93 - 61 * q^94 - 147 * q^96 + 22 * q^97 - 71 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more