LMFDB - Embedded newform 520.2.ca.a.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24568 - 0.669541i) q^{2} +(-2.59349 + 1.49735i) q^{3} +(1.10343 + 1.66806i) q^{4} -1.00000 q^{5} +(4.23319 - 0.128773i) q^{6} +(-0.668489 - 0.385952i) q^{7} +(-0.257683 - 2.81666i) q^{8} +(2.98412 - 5.16865i) q^{9} +O(q^{10})$	\(q+(-1.24568 - 0.669541i) q^{2} +(-2.59349 + 1.49735i) q^{3} +(1.10343 + 1.66806i) q^{4} -1.00000 q^{5} +(4.23319 - 0.128773i) q^{6} +(-0.668489 - 0.385952i) q^{7} +(-0.257683 - 2.81666i) q^{8} +(2.98412 - 5.16865i) q^{9} +(1.24568 + 0.669541i) q^{10} +(0.183144 + 0.317214i) q^{11} +(-5.35941 - 2.67388i) q^{12} +(-2.71812 - 2.36893i) q^{13} +(0.574312 + 0.928353i) q^{14} +(2.59349 - 1.49735i) q^{15} +(-1.56488 + 3.68119i) q^{16} +(1.37075 - 2.37421i) q^{17} +(-7.17788 + 4.44049i) q^{18} +(-0.199573 + 0.345670i) q^{19} +(-1.10343 - 1.66806i) q^{20} +2.31162 q^{21} +(-0.0157504 - 0.517769i) q^{22} +(-0.390725 - 0.676756i) q^{23} +(4.88583 + 6.91914i) q^{24} +1.00000 q^{25} +(1.79981 + 4.77082i) q^{26} +8.88900i q^{27} +(-0.0938379 - 1.54095i) q^{28} +(1.82591 - 1.05419i) q^{29} +(-4.23319 + 0.128773i) q^{30} +9.83751i q^{31} +(4.41404 - 3.53783i) q^{32} +(-0.949962 - 0.548461i) q^{33} +(-3.29715 + 2.03973i) q^{34} +(0.668489 + 0.385952i) q^{35} +(11.9144 - 0.725539i) q^{36} +(4.55194 + 7.88418i) q^{37} +(0.480044 - 0.296972i) q^{38} +(10.5965 + 2.07382i) q^{39} +(0.257683 + 2.81666i) q^{40} +(6.57018 - 3.79330i) q^{41} +(-2.87954 - 1.54773i) q^{42} +(5.38510 + 3.10909i) q^{43} +(-0.327048 + 0.655520i) q^{44} +(-2.98412 + 5.16865i) q^{45} +(0.0336025 + 1.10463i) q^{46} +8.57446i q^{47} +(-1.45353 - 11.8903i) q^{48} +(-3.20208 - 5.54617i) q^{49} +(-1.24568 - 0.669541i) q^{50} +8.20999i q^{51} +(0.952275 - 7.14795i) q^{52} -4.85612i q^{53} +(5.95155 - 11.0728i) q^{54} +(-0.183144 - 0.317214i) q^{55} +(-0.914840 + 1.98236i) q^{56} -1.19532i q^{57} +(-2.98032 + 0.0906607i) q^{58} +(6.27654 - 10.8713i) q^{59} +(5.35941 + 2.67388i) q^{60} +(1.23481 + 0.712917i) q^{61} +(6.58661 - 12.2544i) q^{62} +(-3.98970 + 2.30346i) q^{63} +(-7.86720 + 1.45161i) q^{64} +(2.71812 + 2.36893i) q^{65} +(0.816131 + 1.31924i) q^{66} +(2.10071 + 3.63853i) q^{67} +(5.47287 - 0.333275i) q^{68} +(2.02668 + 1.17011i) q^{69} +(-0.574312 - 0.928353i) q^{70} +(1.22610 + 0.707891i) q^{71} +(-15.3273 - 7.07340i) q^{72} +16.3452i q^{73} +(-0.391468 - 12.8689i) q^{74} +(-2.59349 + 1.49735i) q^{75} +(-0.796816 + 0.0485228i) q^{76} -0.282739i q^{77} +(-11.8114 - 9.67812i) q^{78} -4.89500 q^{79} +(1.56488 - 3.68119i) q^{80} +(-4.35760 - 7.54758i) q^{81} +(-10.7241 + 0.326225i) q^{82} +2.70803 q^{83} +(2.55072 + 3.85594i) q^{84} +(-1.37075 + 2.37421i) q^{85} +(-4.62645 - 7.47847i) q^{86} +(-3.15698 + 5.46806i) q^{87} +(0.846293 - 0.597595i) q^{88} +(-10.0848 + 5.82248i) q^{89} +(7.17788 - 4.44049i) q^{90} +(0.902738 + 2.63267i) q^{91} +(0.697734 - 1.39851i) q^{92} +(-14.7302 - 25.5135i) q^{93} +(5.74095 - 10.6810i) q^{94} +(0.199573 - 0.345670i) q^{95} +(-6.15040 + 15.7847i) q^{96} +(11.2409 + 6.48992i) q^{97} +(0.275380 + 9.05267i) q^{98} +2.18609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

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 $

$2$	−1.24568	−	0.669541i	−0.880828	−	0.473437i
$2$	−1.24568	−	0.669541i	−0.880828	−	0.473437i
$3$	−2.59349	+	1.49735i	−1.49735	+	0.864496i	−0.999995	−	0.00305049i	$-0.999029\pi$
$3$	−2.59349	+	1.49735i	−1.49735	+	0.864496i	−0.497356	+	0.867547i	$0.665696\pi$
$4$	1.10343	+	1.66806i	0.551715	+	0.834032i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	4.23319	−	0.128773i	1.72819	−	0.0525713i
$7$	−0.668489	−	0.385952i	−0.252665	−	0.145876i	0.368319	−	0.929700i	$-0.379933\pi$
$7$	−0.668489	−	0.385952i	−0.252665	−	0.145876i	−0.620984	+	0.783823i	$0.713267\pi$
$8$	−0.257683	−	2.81666i	−0.0911047	−	0.995841i
$9$	2.98412	−	5.16865i	0.994707	−	1.72288i
$10$	1.24568	+	0.669541i	0.393918	+	0.211727i
$11$	0.183144	+	0.317214i	0.0552199	+	0.0956437i	0.892314	−	0.451415i	$-0.149081\pi$
$11$	0.183144	+	0.317214i	0.0552199	+	0.0956437i	−0.837094	+	0.547059i	$0.815747\pi$
$12$	−5.35941	−	2.67388i	−1.54713	−	0.771884i
$13$	−2.71812	−	2.36893i	−0.753870	−	0.657023i
$13$	−2.71812	−	2.36893i	−0.753870	−	0.657023i
$14$	0.574312	+	0.928353i	0.153491	+	0.248113i
$15$	2.59349	−	1.49735i	0.669636	−	0.386614i
$16$	−1.56488	+	3.68119i	−0.391220	+	0.920297i
$17$	1.37075	−	2.37421i	0.332456	−	0.575831i	−0.650537	−	0.759475i	$-0.725456\pi$
$17$	1.37075	−	2.37421i	0.332456	−	0.575831i	0.982993	+	0.183644i	$0.0587893\pi$
$18$	−7.17788	+	4.44049i	−1.69184	+	1.04663i
$19$	−0.199573	+	0.345670i	−0.0457852	+	0.0793022i	−0.888010	−	0.459825i	$-0.847912\pi$
$19$	−0.199573	+	0.345670i	−0.0457852	+	0.0793022i	0.842225	+	0.539127i	$0.181246\pi$
$20$	−1.10343	−	1.66806i	−0.246735	−	0.372991i
$21$	2.31162			0.504438
$22$	−0.0157504	−	0.517769i	−0.00335800	−	0.110389i
$23$	−0.390725	−	0.676756i	−0.0814718	−	0.141113i	0.822411	−	0.568894i	$-0.192629\pi$
$23$	−0.390725	−	0.676756i	−0.0814718	−	0.141113i	−0.903882	+	0.427781i	$0.859295\pi$
$24$	4.88583	+	6.91914i	0.997317	+	1.41236i
$25$	1.00000			0.200000
$26$	1.79981	+	4.77082i	0.352971	+	0.935634i
$27$			8.88900i			1.71069i
$28$	−0.0938379	−	1.54095i	−0.0177337	−	0.291213i
$29$	1.82591	−	1.05419i	0.339063	−	0.195758i	−0.320795	−	0.947149i	$-0.603950\pi$
$29$	1.82591	−	1.05419i	0.339063	−	0.195758i	0.659858	+	0.751391i	$0.270617\pi$
$30$	−4.23319	+	0.128773i	−0.772871	+	0.0235106i
$31$			9.83751i			1.76687i	0.468555	+	0.883435i	$0.344775\pi$
$31$			9.83751i			1.76687i	−0.468555	+	0.883435i	$0.655225\pi$
$32$	4.41404	−	3.53783i	0.780300	−	0.625405i
$33$	−0.949962	−	0.548461i	−0.165367	−	0.0954748i
$34$	−3.29715	+	2.03973i	−0.565456	+	0.349811i
$35$	0.668489	+	0.385952i	0.112995	+	0.0652378i
$36$	11.9144	−	0.725539i	1.98574	−	0.120923i
$37$	4.55194	+	7.88418i	0.748334	+	1.29615i	0.948621	+	0.316415i	$0.102479\pi$
$37$	4.55194	+	7.88418i	0.748334	+	1.29615i	−0.200287	+	0.979737i	$0.564188\pi$
$38$	0.480044	−	0.296972i	0.0778734	−	0.0481752i
$39$	10.5965	+	2.07382i	1.69680	+	0.332076i
$40$	0.257683	+	2.81666i	0.0407433	+	0.445354i
$41$	6.57018	−	3.79330i	1.02609	−	0.592413i	0.110228	−	0.993906i	$-0.464842\pi$
$41$	6.57018	−	3.79330i	1.02609	−	0.592413i	0.915862	+	0.401493i	$0.131509\pi$
$42$	−2.87954	−	1.54773i	−0.444323	−	0.238819i
$43$	5.38510	+	3.10909i	0.821221	+	0.474132i	0.850837	−	0.525429i	$-0.176095\pi$
$43$	5.38510	+	3.10909i	0.821221	+	0.474132i	−0.0296165	+	0.999561i	$0.509429\pi$
$44$	−0.327048	+	0.655520i	−0.0493043	+	0.0988233i
$45$	−2.98412	+	5.16865i	−0.444847	+	0.770497i
$46$	0.0336025	+	1.10463i	0.00495442	+	0.162868i
$47$			8.57446i			1.25071i	0.780339	+	0.625357i	$0.215046\pi$
$47$			8.57446i			1.25071i	−0.780339	+	0.625357i	$0.784954\pi$
$48$	−1.45353	−	11.8903i	−0.209799	−	1.71622i
$49$	−3.20208	−	5.54617i	−0.457440	−	0.792310i
$50$	−1.24568	−	0.669541i	−0.176166	−	0.0946873i
$51$			8.20999i			1.14963i
$52$	0.952275	−	7.14795i	0.132057	−	0.991242i
$53$		−	4.85612i		−	0.667039i	−0.942743	−	0.333520i	$-0.891764\pi$
$53$		−	4.85612i		−	0.667039i	0.942743	−	0.333520i	$-0.108236\pi$
$54$	5.95155	−	11.0728i	0.809903	−	1.50682i
$55$	−0.183144	−	0.317214i	−0.0246951	−	0.0427732i
$56$	−0.914840	+	1.98236i	−0.122251	+	0.264904i
$57$		−	1.19532i		−	0.158324i
$58$	−2.98032	+	0.0906607i	−0.391335	+	0.0119043i
$59$	6.27654	−	10.8713i	0.817135	−	1.41532i	−0.0906489	−	0.995883i	$-0.528894\pi$
$59$	6.27654	−	10.8713i	0.817135	−	1.41532i	0.907784	−	0.419437i	$-0.137773\pi$
$60$	5.35941	+	2.67388i	0.691897	+	0.345197i
$61$	1.23481	+	0.712917i	0.158101	+	0.0912797i	0.576963	−	0.816770i	$-0.304238\pi$
$61$	1.23481	+	0.712917i	0.158101	+	0.0912797i	−0.418862	+	0.908050i	$0.637571\pi$
$62$	6.58661	−	12.2544i	0.836501	−	1.55631i
$63$	−3.98970	+	2.30346i	−0.502656	+	0.290208i
$64$	−7.86720	+	1.45161i	−0.983400	+	0.181452i
$65$	2.71812	+	2.36893i	0.337141	+	0.293830i
$66$	0.816131	+	1.31924i	0.100459	+	0.162388i
$67$	2.10071	+	3.63853i	0.256642	+	0.444518i	0.965340	−	0.260994i	$-0.0840504\pi$
$67$	2.10071	+	3.63853i	0.256642	+	0.444518i	−0.708698	+	0.705512i	$0.750717\pi$
$68$	5.47287	−	0.333275i	0.663683	−	0.0404156i
$69$	2.02668	+	1.17011i	0.243984	+	0.140864i
$70$	−0.574312	−	0.928353i	−0.0686434	−	0.110959i
$71$	1.22610	+	0.707891i	0.145512	+	0.0840112i	0.570988	−	0.820958i	$-0.306560\pi$
$71$	1.22610	+	0.707891i	0.145512	+	0.0840112i	−0.425477	+	0.904969i	$0.639894\pi$
$72$	−15.3273	−	7.07340i	−1.80634	−	0.833608i
$73$			16.3452i			1.91306i	0.291627	+	0.956532i	$0.405803\pi$
$73$			16.3452i			1.91306i	−0.291627	+	0.956532i	$0.594197\pi$
$74$	−0.391468	−	12.8689i	−0.0455073	−	1.49598i
$75$	−2.59349	+	1.49735i	−0.299470	+	0.172899i
$76$	−0.796816	+	0.0485228i	−0.0914010	+	0.00556595i
$77$		−	0.282739i		−	0.0322211i
$78$	−11.8114	−	9.67812i	−1.33737	−	1.09583i
$79$	−4.89500			−0.550730			−0.275365	−	0.961340i	$-0.588799\pi$
$79$	−4.89500			−0.550730			−0.275365	+	0.961340i	$0.588799\pi$
$80$	1.56488	−	3.68119i	0.174959	−	0.411569i
$81$	−4.35760	−	7.54758i	−0.484177	−	0.838620i
$82$	−10.7241	+	0.326225i	−1.18428	+	0.0360255i
$83$	2.70803			0.297245			0.148622	−	0.988894i	$-0.452516\pi$
$83$	2.70803			0.297245			0.148622	+	0.988894i	$0.452516\pi$
$84$	2.55072	+	3.85594i	0.278306	+	0.420718i
$85$	−1.37075	+	2.37421i	−0.148679	+	0.257519i
$86$	−4.62645	−	7.47847i	−0.498883	−	0.806425i
$87$	−3.15698	+	5.46806i	−0.338464	+	0.586237i
$88$	0.846293	−	0.597595i	0.0902152	−	0.0637039i
$89$	−10.0848	+	5.82248i	−1.06899	+	0.617182i	−0.927905	−	0.372816i	$-0.878392\pi$
$89$	−10.0848	+	5.82248i	−1.06899	+	0.617182i	−0.141084	+	0.989998i	$0.545059\pi$
$90$	7.17788	−	4.44049i	0.756615	−	0.468068i
$91$	0.902738	+	2.63267i	0.0946326	+	0.275979i
$92$	0.697734	−	1.39851i	0.0727438	−	0.145804i
$93$	−14.7302	−	25.5135i	−1.52745	−	2.64562i
$94$	5.74095	−	10.6810i	0.592134	−	1.10166i
$95$	0.199573	−	0.345670i	0.0204758	−	0.0354650i
$96$	−6.15040	+	15.7847i	−0.627723	+	1.61102i
$97$	11.2409	+	6.48992i	1.14134	+	0.658952i	0.946762	−	0.321936i	$-0.104334\pi$
$97$	11.2409	+	6.48992i	1.14134	+	0.658952i	0.194576	+	0.980887i	$0.437667\pi$
$98$	0.275380	+	9.05267i	0.0278176	+	0.914457i
$99$	2.18609			0.219711
$100$	1.10343	+	1.66806i	0.110343	+	0.166806i
$101$	2.07252	−	1.19657i	0.206224	−	0.119063i	−0.393331	−	0.919397i	$-0.628678\pi$
$101$	2.07252	−	1.19657i	0.206224	−	0.119063i	0.599555	+	0.800333i	$0.295344\pi$
$102$	5.49692	−	10.2270i	0.544276	−	1.01262i
$103$	−6.21721			−0.612599			−0.306300	−	0.951935i	$-0.599091\pi$
$103$	−6.21721			−0.612599			−0.306300	+	0.951935i	$0.599091\pi$
$104$	−5.97207	+	8.26646i	−0.585610	+	0.810593i
$105$	−2.31162			−0.225591
$106$	−3.25137	+	6.04916i	−0.315801	+	0.587547i
$107$	5.79179	−	3.34389i	0.559913	−	0.323266i	−0.193197	−	0.981160i	$-0.561886\pi$
$107$	5.79179	−	3.34389i	0.559913	−	0.323266i	0.753111	+	0.657894i	$0.228552\pi$
$108$	−14.8274	+	9.80840i	−1.42677	+	0.943814i
$109$	16.3988			1.57072			0.785361	−	0.619039i	$-0.212478\pi$
$109$	16.3988			1.57072			0.785361	+	0.619039i	$0.212478\pi$
$110$	0.0157504	+	0.517769i	0.00150174	+	0.0493674i
$111$	−23.6108	−	13.6317i	−2.24104	−	1.29386i
$112$	2.46687	−	1.85686i	0.233097	−	0.175457i
$113$	8.42307	−	14.5892i	0.792375	−	1.37243i	−0.132117	−	0.991234i	$-0.542178\pi$
$113$	8.42307	−	14.5892i	0.792375	−	1.37243i	0.924493	−	0.381200i	$-0.124489\pi$
$114$	−0.800317	+	1.48899i	−0.0749566	+	0.139457i
$115$	0.390725	+	0.676756i	0.0364353	+	0.0631078i
$116$	3.77322	+	1.88251i	0.350335	+	0.174787i
$117$	−20.3554	+	6.97982i	−1.88185	+	0.645285i
$118$	−15.0973	+	9.33973i	−1.38982	+	0.859791i
$119$	−1.83266	+	1.05809i	−0.168000	+	0.0969949i
$120$	−4.88583	−	6.91914i	−0.446014	−	0.631629i
$121$	5.43292	−	9.41009i	0.493902	−	0.855463i
$122$	−1.06085	−	1.71482i	−0.0960447	−	0.155253i
$123$	−11.3598	+	19.6757i	−1.02428	+	1.77410i
$124$	−16.4096	+	10.8550i	−1.47363	+	0.974809i
$125$	−1.00000			−0.0894427
$126$	6.51215	−	0.198098i	0.580148	−	0.0176480i
$127$	−4.90403	−	8.49402i	−0.435162	−	0.753723i	0.562147	−	0.827037i	$-0.309976\pi$
$127$	−4.90403	−	8.49402i	−0.435162	−	0.753723i	−0.997309	+	0.0733147i	$0.976642\pi$
$128$	10.7719	+	3.45916i	0.952112	+	0.305750i
$129$	−18.6216			−1.63954
$130$	−1.79981	−	4.77082i	−0.157853	−	0.418428i
$131$			5.06554i			0.442578i	0.975208	+	0.221289i	$0.0710264\pi$
$131$			5.06554i			0.442578i	−0.975208	+	0.221289i	$0.928974\pi$
$132$	−0.133349	−	2.18979i	−0.0116066	−	0.190597i
$133$	0.266825	−	0.154051i	0.0231366	−	0.0133579i
$134$	−0.180662	−	5.93895i	−0.0156068	−	0.513047i
$135$		−	8.88900i		−	0.765044i
$136$	−7.04058	−	3.24915i	−0.603724	−	0.278613i
$137$	14.4204	+	8.32560i	1.23202	+	0.711304i	0.967450	−	0.253064i	$-0.0814382\pi$
$137$	14.4204	+	8.32560i	1.23202	+	0.711304i	0.264565	+	0.964368i	$0.414772\pi$
$138$	−1.74116	−	2.81452i	−0.148217	−	0.239588i
$139$	4.85477	+	2.80290i	0.411776	+	0.237739i	0.691553	−	0.722326i	$-0.256927\pi$
$139$	4.85477	+	2.80290i	0.411776	+	0.237739i	−0.279776	+	0.960065i	$0.590260\pi$
$140$	0.0938379	+	1.54095i	0.00793075	+	0.130234i
$141$	−12.8390	−	22.2378i	−1.08124	−	1.87276i
$142$	−1.05337	−	1.70273i	−0.0883967	−	0.142890i
$143$	0.253652	−	1.29608i	0.0212115	−	0.108384i
$144$	14.3570	+	19.0734i	1.19641	+	1.58945i
$145$	−1.82591	+	1.05419i	−0.151634	+	0.0875457i
$146$	10.9438	−	20.3609i	0.905715	−	1.68508i
$147$	16.6091	+	9.58928i	1.36990	+	0.790911i
$148$	−8.12858	+	16.2926i	−0.668166	+	1.33924i
$149$	−10.8116	+	18.7262i	−0.885720	+	1.53411i	−0.0408344	+	0.999166i	$0.513002\pi$
$149$	−10.8116	+	18.7262i	−0.885720	+	1.53411i	−0.844886	+	0.534947i	$0.820332\pi$
$150$	4.23319	−	0.128773i	0.345639	−	0.0105143i
$151$		−	16.9637i		−	1.38049i	−0.723577	−	0.690243i	$-0.757503\pi$
$151$		−	16.9637i		−	1.38049i	0.723577	−	0.690243i	$-0.242497\pi$
$152$	1.02506	+	0.473057i	0.0831437	+	0.0383700i
$153$	−8.18098	−	14.1699i	−0.661393	−	1.14557i
$154$	−0.189305	+	0.352202i	−0.0152546	+	0.0283812i
$155$		−	9.83751i		−	0.790168i
$156$	8.23328	+	19.9640i	0.659190	+	1.59840i
$157$		−	14.5213i		−	1.15893i	−0.814997	−	0.579465i	$-0.803262\pi$
$157$		−	14.5213i		−	1.15893i	0.814997	−	0.579465i	$-0.196738\pi$
$158$	6.09759	+	3.27740i	0.485098	+	0.260736i
$159$	7.27132	+	12.5943i	0.576653	+	0.998792i
$160$	−4.41404	+	3.53783i	−0.348961	+	0.279690i
$161$			0.603205i			0.0475392i
$162$	0.374755	+	12.3194i	0.0294435	+	0.967907i
$163$	6.31713	−	10.9416i	0.494796	−	0.857012i	−0.505186	−	0.863010i	$-0.668576\pi$
$163$	6.31713	−	10.9416i	0.494796	−	0.857012i	0.999982	+	0.00599866i	$0.00190944\pi$
$164$	13.5772	+	6.77385i	1.06020	+	0.528949i
$165$	0.949962	+	0.548461i	0.0739545	+	0.0426976i
$166$	−3.37334	−	1.81314i	−0.261822	−	0.140727i
$167$	12.8775	−	7.43485i	0.996494	−	0.575326i	0.0892849	−	0.996006i	$-0.471542\pi$
$167$	12.8775	−	7.43485i	0.996494	−	0.575326i	0.907209	+	0.420680i	$0.138208\pi$
$168$	−0.595667	−	6.51107i	−0.0459567	−	0.502340i
$169$	1.77633	+	12.8781i	0.136641	+	0.990621i
$170$	3.29715	−	2.03973i	0.252880	−	0.156440i
$171$	1.19110	+	2.06305i	0.0910857	+	0.157765i
$172$	0.755924	+	12.4134i	0.0576386	+	0.946511i
$173$	−8.47690	−	4.89414i	−0.644487	−	0.372095i	0.141854	−	0.989888i	$-0.454694\pi$
$173$	−8.47690	−	4.89414i	−0.644487	−	0.372095i	−0.786341	+	0.617793i	$0.788027\pi$
$174$	7.59367	−	4.69771i	0.575675	−	0.356133i
$175$	−0.668489	−	0.385952i	−0.0505330	−	0.0291753i
$176$	−1.45432	+	0.177784i	−0.109624	+	0.0134010i
$177$			37.5927i			2.82564i
$178$	16.4608	−	0.500735i	1.23379	−	0.0375317i
$179$	−6.67998	+	3.85669i	−0.499286	+	0.288263i	−0.728418	−	0.685133i	$-0.759744\pi$
$179$	−6.67998	+	3.85669i	−0.499286	+	0.288263i	0.229133	+	0.973395i	$0.426411\pi$
$180$	−11.9144	+	0.725539i	−0.888048	+	0.0540785i
$181$			12.1896i			0.906047i	0.891499	+	0.453023i	$0.149655\pi$
$181$			12.1896i			0.906047i	−0.891499	+	0.453023i	$0.850345\pi$
$182$	0.638157	−	3.88388i	0.0473033	−	0.287892i
$183$	−4.26995			−0.315644
$184$	−1.80551	+	1.27493i	−0.133104	+	0.0939891i
$185$	−4.55194	−	7.88418i	−0.334665	−	0.579657i
$186$	1.26680	+	41.6441i	0.0928865	+	3.05349i
$187$	1.00418			0.0734328
$188$	−14.3028	+	9.46132i	−1.04314	+	0.690038i
$189$	3.43073	−	5.94220i	0.249549	−	0.432232i
$190$	−0.480044	+	0.296972i	−0.0348261	+	0.0215446i
$191$	3.86844	−	6.70033i	0.279911	−	0.484819i	−0.691452	−	0.722423i	$-0.743029\pi$
$191$	3.86844	−	6.70033i	0.279911	−	0.484819i	0.971362	+	0.237603i	$0.0763619\pi$
$192$	18.2299	−	15.5447i	1.31563	−	1.12184i
$193$	13.9837	−	8.07351i	1.00657	−	0.581144i	0.0963852	−	0.995344i	$-0.469272\pi$
$193$	13.9837	−	8.07351i	1.00657	−	0.581144i	0.910186	+	0.414200i	$0.135939\pi$
$194$	−9.65725	−	15.6106i	−0.693350	−	1.12077i
$195$	−10.5965	−	2.07382i	−0.758833	−	0.148509i
$196$	5.71809	−	11.4611i	0.408435	−	0.818649i
$197$	0.485382	+	0.840706i	0.0345820	+	0.0598978i	0.882798	−	0.469752i	$-0.155657\pi$
$197$	0.485382	+	0.840706i	0.0345820	+	0.0598978i	−0.848216	+	0.529650i	$0.822323\pi$
$198$	−2.72317	−	1.46368i	−0.193527	−	0.104019i
$199$	−1.60816	+	2.78542i	−0.114000	+	0.197453i	−0.917379	−	0.398014i	$-0.869700\pi$
$199$	−1.60816	+	2.78542i	−0.114000	+	0.197453i	0.803380	+	0.595467i	$0.203033\pi$
$200$	−0.257683	−	2.81666i	−0.0182209	−	0.199168i
$201$	−10.8963	−	6.29100i	−0.768568	−	0.443733i
$202$	−3.38285	+	0.102906i	−0.238016	+	0.00724041i
$203$	−1.62747			−0.114226
$204$	−13.6948	+	9.05915i	−0.958827	+	0.634267i
$205$	−6.57018	+	3.79330i	−0.458882	+	0.264935i
$206$	7.74464	+	4.16267i	0.539595	+	0.290027i
$207$	−4.66388			−0.324162
$208$	12.9740	−	6.29881i	0.899586	−	0.436744i
$209$	−0.146202			−0.0101130
$210$	2.87954	+	1.54773i	0.198707	+	0.106803i
$211$	23.8237	−	13.7546i	1.64009	−	0.946906i	0.659290	−	0.751889i	$-0.270857\pi$
$211$	23.8237	−	13.7546i	1.64009	−	0.946906i	0.980800	−	0.195017i	$-0.0624764\pi$
$212$	8.10032	−	5.35839i	0.556332	−	0.368016i
$213$	−4.23984			−0.290509
$214$	−9.45358	+	0.287576i	−0.646233	+	0.0196583i
$215$	−5.38510	−	3.10909i	−0.367261	−	0.212038i
$216$	25.0373	−	2.29055i	1.70358	−	0.155852i
$217$	3.79681	−	6.57627i	0.257744	−	0.446426i
$218$	−20.4276	−	10.9797i	−1.38353	−	0.743637i
$219$	−24.4745	−	42.3912i	−1.65384	−	2.86453i
$220$	0.327048	−	0.655520i	0.0220495	−	0.0441951i
$221$	−9.35021	+	3.20617i	−0.628963	+	0.215670i
$222$	20.2845	+	32.7891i	1.36141	+	2.20066i
$223$	−10.0424	+	5.79797i	−0.672488	+	0.388261i	−0.797019	−	0.603955i	$-0.793591\pi$
$223$	−10.0424	+	5.79797i	−0.672488	+	0.388261i	0.124531	+	0.992216i	$0.460257\pi$
$224$	−4.31617	+	0.661388i	−0.288386	+	0.0441908i
$225$	2.98412	−	5.16865i	0.198941	−	0.344577i
$226$	−20.2605	+	12.5338i	−1.34771	+	0.833739i
$227$	6.20835	−	10.7532i	0.412063	−	0.713714i	−0.583052	−	0.812435i	$-0.698142\pi$
$227$	6.20835	−	10.7532i	0.412063	−	0.713714i	0.995115	+	0.0987210i	$0.0314751\pi$
$228$	1.99388	−	1.31896i	0.132048	−	0.0873500i
$229$	13.8237			0.913494			0.456747	−	0.889597i	$-0.349014\pi$
$229$	13.8237			0.913494			0.456747	+	0.889597i	$0.349014\pi$
$230$	−0.0336025	−	1.10463i	−0.00221568	−	0.0728369i
$231$	0.423360	+	0.733280i	0.0278550	+	0.0482463i
$232$	−3.43980	−	4.87133i	−0.225834	−	0.319818i
$233$	14.8667			0.973948			0.486974	−	0.873417i	$-0.338101\pi$
$233$	14.8667			0.973948			0.486974	+	0.873417i	$0.338101\pi$
$234$	30.0295	+	4.93413i	1.96309	+	0.322554i
$235$		−	8.57446i		−	0.559336i
$236$	25.0597	−	1.52604i	1.63125	−	0.0993364i
$237$	12.6951	−	7.32953i	0.824637	−	0.476104i
$238$	2.99135	−	0.0909961i	0.193900	−	0.00589840i
$239$		−	14.4448i		−	0.934357i	−0.884163	−	0.467178i	$-0.845271\pi$
$239$		−	14.4448i		−	0.934357i	0.884163	−	0.467178i	$-0.154729\pi$
$240$	1.45353	+	11.8903i	0.0938250	+	0.767515i
$241$	−10.2446	−	5.91471i	−0.659911	−	0.381000i	0.132332	−	0.991205i	$-0.457754\pi$
$241$	−10.2446	−	5.91471i	−0.659911	−	0.381000i	−0.792243	+	0.610205i	$0.791087\pi$
$242$	−13.0681	+	8.08439i	−0.840050	+	0.519684i
$243$	−0.491557	−	0.283801i	−0.0315334	−	0.0182058i
$244$	0.173334	+	2.84640i	0.0110966	+	0.182222i
$245$	3.20208	+	5.54617i	0.204573	+	0.354332i
$246$	27.3244	−	16.9038i	1.74214	−	1.07775i
$247$	1.36133	−	0.466799i	0.0866195	−	0.0297017i
$248$	27.7090	−	2.53496i	1.75952	−	0.160970i
$249$	−7.02325	+	4.05487i	−0.445080	+	0.256967i
$250$	1.24568	+	0.669541i	0.0787836	+	0.0423455i
$251$	18.9533	+	10.9427i	1.19632	+	0.690697i	0.959733	−	0.280913i	$-0.0906372\pi$
$251$	18.9533	+	10.9427i	1.19632	+	0.690697i	0.236589	+	0.971610i	$0.423971\pi$
$252$	−8.24468	−	4.11338i	−0.519366	−	0.259119i
$253$	0.143118	−	0.247887i	0.00899773	−	0.0155845i
$254$	0.421748	+	13.8643i	0.0264628	+	0.869922i
$255$		−	8.20999i		−	0.514129i
$256$	−11.1023	−	11.5212i	−0.693893	−	0.720078i
$257$	11.5238	+	19.9598i	0.718836	+	1.24506i	0.961461	+	0.274941i	$0.0886582\pi$
$257$	11.5238	+	19.9598i	0.718836	+	1.24506i	−0.242625	+	0.970120i	$0.578008\pi$
$258$	23.1965	+	12.4679i	1.44415	+	0.776219i
$259$		−	7.02732i		−	0.436656i
$260$	−0.952275	+	7.14795i	−0.0590576	+	0.443297i
$261$		−	12.5833i		−	0.778888i
$262$	3.39158	−	6.31003i	0.209533	−	0.389835i
$263$	13.9302	+	24.1278i	0.858972	+	1.48778i	0.872911	+	0.487880i	$0.162230\pi$
$263$	13.9302	+	24.1278i	0.858972	+	1.48778i	−0.0139390	+	0.999903i	$0.504437\pi$
$264$	−1.30004	+	2.81705i	−0.0800120	+	0.173378i
$265$			4.85612i			0.298309i
$266$	−0.435521	+	0.0132485i	−0.0267035	+	0.000812316i
$267$	17.4366	−	30.2011i	1.06710	−	1.84827i
$268$	−3.75132	+	7.51899i	−0.229149	+	0.459295i
$269$	−22.5817	−	13.0375i	−1.37683	−	0.794912i	−0.385052	−	0.922895i	$-0.625816\pi$
$269$	−22.5817	−	13.0375i	−1.37683	−	0.794912i	−0.991776	+	0.127983i	$0.959150\pi$
$270$	−5.95155	+	11.0728i	−0.362200	+	0.673872i
$271$	7.33087	−	4.23248i	0.445319	−	0.257105i	−0.260532	−	0.965465i	$-0.583898\pi$
$271$	7.33087	−	4.23248i	0.445319	−	0.257105i	0.705851	+	0.708360i	$0.250565\pi$
$272$	6.59486	+	8.76135i	0.399872	+	0.531235i
$273$	−6.28327	−	5.47608i	−0.380281	−	0.331427i
$274$	−12.3888	−	20.0260i	−0.748436	−	1.20982i
$275$	0.183144	+	0.317214i	0.0110440	+	0.0191287i
$276$	0.284492	+	4.67177i	0.0171244	+	0.281207i
$277$	22.1387	+	12.7818i	1.33019	+	0.767983i	0.985328	−	0.170672i	$-0.0545938\pi$
$277$	22.1387	+	12.7818i	1.33019	+	0.767983i	0.344858	+	0.938655i	$0.387927\pi$
$278$	−4.17083	−	6.74198i	−0.250149	−	0.404357i
$279$	50.8466	+	29.3563i	3.04411	+	1.75752i
$280$	0.914840	−	1.98236i	0.0546721	−	0.118469i
$281$		−	8.03285i		−	0.479200i	−0.970872	−	0.239600i	$-0.922984\pi$
$281$		−	8.03285i		−	0.479200i	0.970872	−	0.239600i	$-0.0770162\pi$
$282$	1.10416	+	36.2973i	0.0657516	+	2.16147i
$283$	−26.1531	+	15.0995i	−1.55464	+	0.897573i	−0.556888	+	0.830588i	$0.688005\pi$
$283$	−26.1531	+	15.0995i	−1.55464	+	0.897573i	−0.997754	+	0.0669853i	$0.978662\pi$
$284$	0.172112	+	2.82633i	0.0102130	+	0.167712i
$285$			1.19532i			0.0708048i
$286$	−1.18375	+	1.44467i	−0.0699965	+	0.0854251i
$287$	−5.85613			−0.345676
$288$	−5.11374	−	33.3720i	−0.301330	−	1.96646i
$289$	4.74208	+	8.21352i	0.278946	+	0.483148i
$290$	2.98032	−	0.0906607i	0.175010	−	0.00532378i
$291$	−38.8708			−2.27864
$292$	−27.2649	+	18.0358i	−1.59556	+	1.05547i
$293$	0.595312	−	1.03111i	0.0347785	−	0.0602381i	−0.848112	−	0.529817i	$-0.822261\pi$
$293$	0.595312	−	1.03111i	0.0347785	−	0.0602381i	0.882891	+	0.469578i	$0.155594\pi$
$294$	−14.2692	−	23.0656i	−0.832198	−	1.34522i
$295$	−6.27654	+	10.8713i	−0.365434	+	0.632950i
$296$	21.0341	−	14.8529i	1.22258	−	0.863307i
$297$	−2.81972	+	1.62797i	−0.163617	+	0.0944641i
$298$	26.0057	−	16.0881i	1.50647	−	0.931957i
$299$	−0.541150	+	2.76510i	−0.0312955	+	0.159910i
$300$	−5.35941	−	2.67388i	−0.309426	−	0.154377i
$301$	−2.39992	−	4.15679i	−0.138329	−	0.239593i
$302$	−11.3579	+	21.1313i	−0.653573	+	1.21597i
$303$	−3.58338	+	6.20659i	−0.205860	+	0.356559i
$304$	−0.960170	−	1.27560i	−0.0550695	−	0.0731606i
$305$	−1.23481	−	0.712917i	−0.0707049	−	0.0408215i
$306$	0.703567	+	23.1286i	0.0402203	+	1.32217i
$307$	−16.6908			−0.952593			−0.476297	−	0.879285i	$-0.658021\pi$
$307$	−16.6908			−0.952593			−0.476297	+	0.879285i	$0.658021\pi$
$308$	0.471627	−	0.311983i	0.0268734	−	0.0177769i
$309$	16.1243	−	9.30934i	0.917277	−	0.529590i
$310$	−6.58661	+	12.2544i	−0.374094	+	0.696002i
$311$	−3.24826			−0.184192			−0.0920961	−	0.995750i	$-0.529357\pi$
$311$	−3.24826			−0.184192			−0.0920961	+	0.995750i	$0.529357\pi$
$312$	3.11070	−	30.3813i	0.176109	−	1.72000i
$313$	1.89125			0.106900			0.0534499	−	0.998571i	$-0.482978\pi$
$313$	1.89125			0.106900			0.0534499	+	0.998571i	$0.482978\pi$
$314$	−9.72263	+	18.0889i	−0.548680	+	1.02082i
$315$	3.98970	−	2.30346i	0.224794	−	0.129785i
$316$	−5.40129	−	8.16517i	−0.303846	−	0.459327i
$317$	−16.9803			−0.953707			−0.476854	−	0.878983i	$-0.658223\pi$
$317$	−16.9803			−0.953707			−0.476854	+	0.878983i	$0.658223\pi$
$318$	−0.625336	−	20.5569i	−0.0350671	−	1.15277i
$319$	0.668808	+	0.386136i	0.0374460	+	0.0216195i
$320$	7.86720	−	1.45161i	0.439790	−	0.0811477i
$321$	−10.0140	+	17.3447i	−0.558925	+	0.968086i
$322$	0.403870	−	0.751399i	0.0225068	−	0.0418739i
$323$	0.547130	+	0.947657i	0.0304431	+	0.0527290i
$324$	7.78154	−	15.5970i	0.432308	−	0.866499i
$325$	−2.71812	−	2.36893i	−0.150774	−	0.131405i
$326$	−15.1950	+	9.40013i	−0.841571	+	0.520625i
$327$	−42.5301	+	24.5548i	−2.35192	+	1.35788i
$328$	−12.3775	−	17.5285i	−0.683432	−	0.967851i
$329$	3.30933	−	5.73193i	0.182449	−	0.316012i
$330$	−0.816131	−	1.31924i	−0.0449265	−	0.0726220i
$331$	−10.0567	+	17.4187i	−0.552767	+	0.957420i	0.445307	+	0.895378i	$0.353095\pi$
$331$	−10.0567	+	17.4187i	−0.552767	+	0.957420i	−0.998074	+	0.0620419i	$0.980239\pi$
$332$	2.98812	+	4.51717i	0.163995	+	0.247912i
$333$	54.3341			2.97749
$334$	−21.0192	+	0.639400i	−1.15012	+	0.0349864i
$335$	−2.10071	−	3.63853i	−0.114774	−	0.198794i
$336$	−3.61742	+	8.50953i	−0.197346	+	0.464233i
$337$	−10.1602			−0.553460			−0.276730	−	0.960948i	$-0.589251\pi$
$337$	−10.1602			−0.553460			−0.276730	+	0.960948i	$0.589251\pi$
$338$	6.40965	−	17.2313i	0.348639	−	0.937257i
$339$			50.4491i			2.74002i
$340$	−5.47287	+	0.333275i	−0.296808	+	0.0180744i
$341$	−3.12060	+	1.80168i	−0.168990	+	0.0975664i
$342$	−0.102435	−	3.36738i	−0.00553905	−	0.182087i
$343$			10.3467i			0.558671i
$344$	7.36962	−	15.9692i	0.397343	−	0.861001i
$345$	−2.02668	−	1.17011i	−0.109113	−	0.0629963i
$346$	7.28267	+	11.7722i	0.391519	+	0.632875i
$347$	−13.3705	−	7.71947i	−0.717767	−	0.414403i	0.0961633	−	0.995366i	$-0.469343\pi$
$347$	−13.3705	−	7.71947i	−0.717767	−	0.414403i	−0.813930	+	0.580963i	$0.802676\pi$
$348$	−12.6046	+	0.767568i	−0.675677	+	0.0411460i
$349$	5.42931	+	9.40383i	0.290624	+	0.503376i	0.973957	−	0.226731i	$-0.0728038\pi$
$349$	5.42931	+	9.40383i	0.290624	+	0.503376i	−0.683333	+	0.730106i	$0.739470\pi$
$350$	0.574312	+	0.928353i	0.0306983	+	0.0496226i
$351$	21.0574	−	24.1614i	1.12396	−	1.28964i
$352$	1.93065	+	0.752267i	0.102904	+	0.0400960i
$353$	−17.3940	+	10.0424i	−0.925791	+	0.534505i	−0.885478	−	0.464682i	$-0.846169\pi$
$353$	−17.3940	+	10.0424i	−0.925791	+	0.534505i	−0.0403128	+	0.999187i	$0.512835\pi$
$354$	25.1699	−	46.8284i	1.33776	−	2.48890i
$355$	−1.22610	−	0.707891i	−0.0650748	−	0.0375709i
$356$	−20.8402	−	10.3974i	−1.10453	−	0.551064i
$357$	3.16866	−	5.48829i	0.167703	−	0.290471i
$358$	10.9033	−	0.331677i	0.576259	−	0.0175297i
$359$			19.0632i			1.00612i	0.864252	+	0.503060i	$0.167792\pi$
$359$			19.0632i			1.00612i	−0.864252	+	0.503060i	$0.832208\pi$
$360$	15.3273	+	7.07340i	0.807820	+	0.372801i
$361$	9.42034	+	16.3165i	0.495807	+	0.858764i
$362$	8.16144	−	15.1843i	0.428956	−	0.798071i
$363$			32.5399i			1.70790i
$364$	−3.39535	+	4.41079i	−0.177965	+	0.231188i
$365$		−	16.3452i		−	0.855548i
$366$	5.31898	+	2.85890i	0.278028	+	0.149437i
$367$	−4.48429	−	7.76702i	−0.234078	−	0.405435i	0.724926	−	0.688827i	$-0.241874\pi$
$367$	−4.48429	−	7.76702i	−0.234078	−	0.405435i	−0.959004	+	0.283391i	$0.908540\pi$
$368$	3.10270	−	0.379290i	0.161740	−	0.0197719i
$369$		−	45.2786i		−	2.35711i
$370$	0.391468	+	12.8689i	0.0203515	+	0.669020i
$371$	−1.87423	+	3.24626i	−0.0973052	+	0.168538i
$372$	26.3044	−	52.7233i	1.36382	−	2.73358i
$373$	22.0539	+	12.7328i	1.14191	+	0.659280i	0.946902	−	0.321522i	$-0.104194\pi$
$373$	22.0539	+	12.7328i	1.14191	+	0.659280i	0.195005	+	0.980802i	$0.437528\pi$
$374$	−1.25088	−	0.672338i	−0.0646816	−	0.0347658i
$375$	2.59349	−	1.49735i	0.133927	−	0.0773229i
$376$	24.1514	−	2.20949i	1.24551	−	0.113946i
$377$	−7.46034	−	1.46004i	−0.384227	−	0.0751960i
$378$	−8.25213	+	5.10506i	−0.424444	+	0.262576i
$379$	−6.24679	−	10.8198i	−0.320876	−	0.555773i	0.659793	−	0.751447i	$-0.270644\pi$
$379$	−6.24679	−	10.8198i	−0.320876	−	0.555773i	−0.980669	+	0.195674i	$0.937311\pi$
$380$	0.796816	−	0.0485228i	0.0408758	−	0.00248917i
$381$	25.4371	+	14.6861i	1.30318	+	0.752392i
$382$	−9.30498	+	5.75639i	−0.476084	+	0.294522i
$383$	5.36702	+	3.09865i	0.274242	+	0.158334i	0.630814	−	0.775934i	$-0.282721\pi$
$383$	5.36702	+	3.09865i	0.274242	+	0.158334i	−0.356572	+	0.934268i	$0.616054\pi$
$384$	−33.1164	+	7.15804i	−1.68997	+	0.365282i
$385$			0.282739i			0.0144097i
$386$	−22.8248	+	0.694325i	−1.16175	+	0.0353402i
$387$	32.1396	−	18.5558i	1.63375	−	0.943245i
$388$	1.57792	+	25.9117i	0.0801065	+	1.31547i
$389$			34.3087i			1.73952i	0.493476	+	0.869759i	$0.335726\pi$
$389$			34.3087i			1.73952i	−0.493476	+	0.869759i	$0.664274\pi$
$390$	11.8114	+	9.67812i	0.598092	+	0.490070i
$391$	−2.14235			−0.108343
$392$	−14.7966	+	10.4483i	−0.747340	+	0.527721i
$393$	−7.58489	−	13.1374i	−0.382607	−	0.662695i
$394$	−0.0417430	−	1.37223i	−0.00210298	−	0.0691321i
$395$	4.89500			0.246294
$396$	2.41220	+	3.64654i	0.121218	+	0.183246i
$397$	−1.74941	+	3.03007i	−0.0878004	+	0.152075i	−0.906581	−	0.422032i	$-0.861317\pi$
$397$	−1.74941	+	3.03007i	−0.0878004	+	0.152075i	0.818781	+	0.574106i	$0.194650\pi$
$398$	3.86821	−	2.39301i	0.193896	−	0.119951i
$399$	−0.461338	+	0.799060i	−0.0230958	+	0.0400031i
$400$	−1.56488	+	3.68119i	−0.0782440	+	0.184059i
$401$	26.1071	−	15.0729i	1.30372	−	0.752706i	0.322683	−	0.946507i	$-0.395415\pi$
$401$	26.1071	−	15.0729i	1.30372	−	0.752706i	0.981041	+	0.193801i	$0.0620817\pi$
$402$	9.36124	+	15.1321i	0.466896	+	0.754720i
$403$	23.3044	−	26.7395i	1.16087	−	1.33199i
$404$	4.28284	+	2.13677i	0.213079	+	0.106308i
$405$	4.35760	+	7.54758i	0.216531	+	0.375042i
$406$	2.02730	+	1.08966i	0.100613	+	0.0540787i
$407$	−1.66732	+	2.88788i	−0.0826458	+	0.143147i
$408$	23.1248	−	2.11557i	1.14485	−	0.104737i
$409$	−11.4804	−	6.62824i	−0.567672	−	0.327745i	0.188547	−	0.982064i	$-0.439622\pi$
$409$	−11.4804	−	6.62824i	−0.567672	−	0.327745i	−0.756219	+	0.654319i	$0.772955\pi$
$410$	10.7241	−	0.326225i	0.529626	−	0.0161111i
$411$	−49.8654			−2.45968
$412$	−6.86026	−	10.3707i	−0.337981	−	0.510928i
$413$	−8.39159	+	4.84489i	−0.412923	+	0.238401i
$414$	5.80970	+	3.12266i	0.285531	+	0.153470i
$415$	−2.70803			−0.132932
$416$	−20.3788	−	0.840334i	−0.999151	−	0.0412007i
$417$	−16.7877			−0.822098
$418$	0.182121	+	0.0978883i	0.00890782	+	0.00478787i
$419$	−25.6127	+	14.7875i	−1.25126	+	0.722418i	−0.971361	−	0.237610i	$-0.923636\pi$
$419$	−25.6127	+	14.7875i	−1.25126	+	0.722418i	−0.279904	+	0.960028i	$0.590303\pi$
$420$	−2.55072	−	3.85594i	−0.124462	−	0.188151i
$421$	−5.81368			−0.283342			−0.141671	−	0.989914i	$-0.545247\pi$
$421$	−5.81368			−0.283342			−0.141671	+	0.989914i	$0.545247\pi$
$422$	−38.8859	+	1.18290i	−1.89294	+	0.0575827i
$423$	44.3184	+	25.5872i	2.15483	+	1.24409i
$424$	−13.6781	+	1.25134i	−0.664265	+	0.0607704i
$425$	1.37075	−	2.37421i	0.0664912	−	0.115166i
$426$	5.28148	+	2.83875i	0.255889	+	0.137538i
$427$	−0.550304	−	0.953155i	−0.0266311	−	0.0461264i
$428$	11.9687	+	5.97133i	0.578527	+	0.288635i
$429$	1.28284	+	3.74118i	0.0619363	+	0.180626i
$430$	4.62645	+	7.47847i	0.223107	+	0.360644i
$431$	−11.2754	+	6.50987i	−0.543118	+	0.313570i	−0.746342	−	0.665563i	$-0.768192\pi$
$431$	−11.2754	+	6.50987i	−0.543118	+	0.313570i	0.203223	+	0.979132i	$0.434858\pi$
$432$	−32.7221	−	13.9102i	−1.57434	−	0.669256i
$433$	−1.42803	+	2.47342i	−0.0686268	+	0.118865i	−0.898297	−	0.439389i	$-0.855195\pi$
$433$	−1.42803	+	2.47342i	−0.0686268	+	0.118865i	0.829670	+	0.558254i	$0.188528\pi$
$434$	−9.13268	+	5.64980i	−0.438383	+	0.271199i
$435$	3.15698	−	5.46806i	0.151366	−	0.262173i
$436$	18.0950	+	27.3543i	0.866591	+	1.31003i
$437$	0.311913			0.0149208
$438$	2.10482	+	69.1925i	0.100572	+	3.30614i
$439$	3.81841	+	6.61368i	0.182243	+	0.315654i	0.942644	−	0.333800i	$-0.108331\pi$
$439$	3.81841	+	6.61368i	0.182243	+	0.315654i	−0.760401	+	0.649454i	$0.774998\pi$
$440$	−0.846293	+	0.597595i	−0.0403454	+	0.0284892i
$441$	−38.2216			−1.82008
$442$	13.7940	+	2.26648i	0.656114	+	0.107806i
$443$		−	7.97304i		−	0.378810i	−0.981899	−	0.189405i	$-0.939344\pi$
$443$		−	7.97304i		−	0.378810i	0.981899	−	0.189405i	$-0.0606560\pi$
$444$	−3.31432	−	54.4260i	−0.157291	−	2.58294i
$445$	10.0848	−	5.82248i	0.478067	−	0.276012i
$446$	16.3916	−	0.498628i	0.776163	−	0.0236107i
$447$		−	64.7550i		−	3.06281i
$448$	5.81939	+	2.06598i	0.274940	+	0.0976082i
$449$	−19.1672	−	11.0662i	−0.904558	−	0.522247i	−0.0258815	−	0.999665i	$-0.508239\pi$
$449$	−19.1672	−	11.0662i	−0.904558	−	0.522247i	−0.878676	+	0.477418i	$0.841573\pi$
$450$	−7.17788	+	4.44049i	−0.338368	+	0.209327i
$451$	2.40658	+	1.38944i	0.113321	+	0.0654260i
$452$	33.6300	−	2.04793i	1.58182	−	0.0963264i
$453$	25.4006	+	43.9952i	1.19343	+	2.06707i
$454$	−14.9333	+	9.23826i	−0.700855	+	0.433573i
$455$	−0.902738	−	2.63267i	−0.0423210	−	0.123421i
$456$	−3.36682	+	0.308015i	−0.157666	+	0.0144241i
$457$	6.92974	−	4.00089i	0.324159	−	0.187154i	−0.329086	−	0.944300i	$-0.606740\pi$
$457$	6.92974	−	4.00089i	0.324159	−	0.187154i	0.653245	+	0.757147i	$0.273407\pi$
$458$	−17.2199	−	9.25551i	−0.804631	−	0.432482i
$459$	21.1044	+	12.1846i	0.985068	+	0.568729i
$460$	−0.697734	+	1.39851i	−0.0325320	+	0.0652058i
$461$	0.951302	−	1.64770i	0.0443066	−	0.0767412i	−0.843022	−	0.537880i	$-0.819225\pi$
$461$	0.951302	−	1.64770i	0.0443066	−	0.0767412i	0.887328	+	0.461138i	$0.152559\pi$
$462$	−0.0364091	−	1.19689i	−0.00169390	−	0.0556843i
$463$		−	37.9962i		−	1.76583i	−0.469529	−	0.882917i	$-0.655576\pi$
$463$		−	37.9962i		−	1.76583i	0.469529	−	0.882917i	$-0.344424\pi$
$464$	1.02334	+	8.37120i	0.0475073	+	0.388623i
$465$	14.7302	+	25.5135i	0.683097	+	1.18316i
$466$	−18.5191	−	9.95384i	−0.857880	−	0.461103i
$467$		−	24.0549i		−	1.11313i	−0.830805	−	0.556563i	$-0.812120\pi$
$467$		−	24.0549i		−	1.11313i	0.830805	−	0.556563i	$-0.187880\pi$
$468$	−34.1035	−	26.2523i	−1.57644	−	1.21351i
$469$		−	3.24309i		−	0.149752i
$470$	−5.74095	+	10.6810i	−0.264810	+	0.492679i
$471$	21.7435	+	37.6609i	1.00189	+	1.73532i
$472$	−32.2381	−	14.8776i	−1.48388	−	0.684795i
$473$			2.27764i			0.104726i
$474$	−20.7215	+	0.630342i	−0.951768	+	0.0289526i
$475$	−0.199573	+	0.345670i	−0.00915703	+	0.0158604i
$476$	−3.78718	−	1.88948i	−0.173585	−	0.0866039i
$477$	−25.0996	−	14.4912i	−1.14923	−	0.663509i
$478$	−9.67138	+	17.9936i	−0.442359	+	0.823008i
$479$	−19.8904	+	11.4838i	−0.908818	+	0.524706i	−0.880051	−	0.474880i	$-0.842491\pi$
$479$	−19.8904	+	11.4838i	−0.908818	+	0.524706i	−0.0287672	+	0.999586i	$0.509158\pi$
$480$	6.15040	−	15.7847i	0.280726	−	0.720469i
$481$	6.30439	−	32.2134i	0.287455	−	1.46880i
$482$	8.80132	+	14.2270i	0.400889	+	0.648022i
$483$	−0.903210	−	1.56440i	−0.0410975	−	0.0711829i
$484$	21.6915	−	1.32092i	0.985977	−	0.0600420i
$485$	−11.2409	−	6.48992i	−0.510422	−	0.294692i
$486$	0.422306	+	0.682642i	0.0191562	+	0.0309653i
$487$	−22.7269	−	13.1214i	−1.02985	−	0.594586i	−0.112911	−	0.993605i	$-0.536017\pi$
$487$	−22.7269	−	13.1214i	−1.02985	−	0.594586i	−0.916943	+	0.399019i	$0.869351\pi$
$488$	1.68986	−	3.66175i	0.0764963	−	0.165760i
$489$			37.8359i			1.71100i
$490$	−0.275380	−	9.05267i	−0.0124404	−	0.408958i
$491$	15.1930	−	8.77168i	0.685650	−	0.395860i	−0.116330	−	0.993211i	$-0.537113\pi$
$491$	15.1930	−	8.77168i	0.685650	−	0.395860i	0.801980	+	0.597350i	$0.203780\pi$
$492$	−45.3552	+	2.76195i	−2.04477	+	0.124518i
$493$		−	5.78013i		−	0.260324i
$494$	−2.00832	−	0.329986i	−0.0903587	−	0.0148468i
$495$	−2.18609			−0.0982576
$496$	−36.2137	−	15.3945i	−1.62604	−	0.691235i
$497$	−0.546424	−	0.946434i	−0.0245105	−	0.0424534i
$498$	11.4636	−	0.348721i	0.513697	−	0.0156265i
$499$	−13.0252			−0.583089			−0.291544	−	0.956557i	$-0.594169\pi$
$499$	−13.0252			−0.583089			−0.291544	+	0.956557i	$0.594169\pi$
$500$	−1.10343	−	1.66806i	−0.0493469	−	0.0745981i
$501$	−22.2652	+	38.5644i	−0.994734	+	1.72293i
$502$	−16.2832	−	26.3211i	−0.726753	−	1.17477i
$503$	13.4851	−	23.3568i	0.601269	−	1.04143i	−0.391360	−	0.920237i	$-0.627995\pi$
$503$	13.4851	−	23.3568i	0.601269	−	1.04143i	0.992629	−	0.121191i	$-0.0386712\pi$
$504$	7.51615	+	10.6441i	0.334796	+	0.474126i
$505$	−2.07252	+	1.19657i	−0.0922260	+	0.0532467i
$506$	−0.344249	+	0.212965i	−0.0153037	+	0.00946743i
$507$	−23.8899	−	30.7393i	−1.06099	−	1.36518i
$508$	8.75733	−	17.5528i	0.388544	−	0.778780i
$509$	−5.29626	−	9.17339i	−0.234753	−	0.406603i	0.724448	−	0.689329i	$-0.242095\pi$
$509$	−5.29626	−	9.17339i	−0.234753	−	0.406603i	−0.959201	+	0.282726i	$0.908761\pi$
$510$	−5.49692	+	10.2270i	−0.243408	+	0.452859i
$511$	6.30848	−	10.9266i	0.279071	−	0.483364i
$512$	6.11595	+	21.7852i	0.270289	+	0.962779i
$513$	−3.07267	−	1.77400i	−0.135662	−	0.0783242i
$514$	−0.991053	−	32.5792i	−0.0437135	−	1.43701i
$515$	6.21721			0.273963
$516$	−20.5477	−	31.0621i	−0.904560	−	1.36743i
$517$	−2.71994	+	1.57036i	−0.119623	+	0.0690643i
$518$	−4.70508	+	8.75378i	−0.206729	+	0.384619i
$519$	29.3130			1.28670
$520$	5.97207	−	8.26646i	0.261893	−	0.362508i
$521$	12.4487			0.545386			0.272693	−	0.962101i	$-0.412086\pi$
$521$	12.4487			0.545386			0.272693	+	0.962101i	$0.412086\pi$
$522$	−8.42504	+	15.6748i	−0.368754	+	0.686066i
$523$	−0.832112	+	0.480420i	−0.0363857	+	0.0210073i	−0.518083	−	0.855331i	$-0.673354\pi$
$523$	−0.832112	+	0.480420i	−0.0363857	+	0.0210073i	0.481697	+	0.876338i	$0.340021\pi$
$524$	−8.44965	+	5.58947i	−0.369125	+	0.244177i
$525$	2.31162			0.100888
$526$	−1.19800	−	39.3823i	−0.0522353	−	1.71715i
$527$	23.3563	+	13.4848i	1.01742	+	0.587406i
$528$	3.50557	−	2.63871i	0.152560	−	0.114835i
$529$	11.1947	−	19.3897i	0.486725	−	0.843032i
$530$	3.25137	−	6.04916i	0.141230	−	0.262759i
$531$	−37.4599	−	64.8824i	−1.62562	−	2.81566i
$532$	0.551390	+	0.275096i	0.0239058	+	0.0119269i
$533$	−26.8446	−	5.25368i	−1.16277	−	0.227562i
$534$	−41.9412	+	25.9463i	−1.81497	+	1.12281i
$535$	−5.79179	+	3.34389i	−0.250401	+	0.144569i
$536$	9.70721	−	6.85458i	0.419288	−	0.296073i
$537$	11.5496	−	20.0046i	0.498404	−	0.863261i
$538$	19.4003	+	31.3599i	0.836408	+	1.35202i
$539$	1.17288	−	2.03149i	0.0505196	−	0.0875026i
$540$	14.8274	−	9.80840i	0.638071	−	0.422086i
$541$	7.60998			0.327179			0.163589	−	0.986529i	$-0.447693\pi$
$541$	7.60998			0.327179			0.163589	+	0.986529i	$0.447693\pi$
$542$	−11.9657	+	0.363995i	−0.513972	+	0.0156349i
$543$	−18.2521	−	31.6136i	−0.783274	−	1.35667i
$544$	−2.34899	−	15.3294i	−0.100712	−	0.657241i
$545$	−16.3988			−0.702448
$546$	4.16048	+	11.0283i	0.178052	+	0.471969i
$547$			27.5793i			1.17921i	0.807693	+	0.589603i	$0.200716\pi$
$547$			27.5793i			1.17921i	−0.807693	+	0.589603i	$0.799284\pi$
$548$	2.02423	+	33.2408i	0.0864709	+	1.41998i
$549$	7.36964	−	4.25486i	0.314528	−	0.181593i
$550$	−0.0157504	−	0.517769i	−0.000671601	−	0.0220778i
$551$			0.841551i			0.0358513i
$552$	2.77355	−	6.01000i	0.118050	−	0.255803i
$553$	3.27225	+	1.88924i	0.139150	+	0.0803385i
$554$	−19.0198	−	30.7448i	−0.808073	−	1.30622i
$555$	23.6108	+	13.6317i	1.00222	+	0.578633i
$556$	0.681479	+	11.1909i	0.0289011	+	0.474599i
$557$	17.3965	+	30.1316i	0.737112	+	1.27672i	0.953790	+	0.300473i	$0.0971446\pi$
$557$	17.3965	+	30.1316i	0.737112	+	1.27672i	−0.216678	+	0.976243i	$0.569522\pi$
$558$	−43.6833	−	70.6124i	−1.84926	−	2.98926i
$559$	−7.27213	−	21.2078i	−0.307578	−	0.896995i
$560$	−2.46687	+	1.85686i	−0.104244	+	0.0784668i
$561$	−2.60432	+	1.50361i	−0.109955	+	0.0634824i
$562$	−5.37832	+	10.0064i	−0.226871	+	0.422092i
$563$	−28.4103	−	16.4027i	−1.19735	−	0.691291i	−0.237388	−	0.971415i	$-0.576291\pi$
$563$	−28.4103	−	16.4027i	−1.19735	−	0.691291i	−0.959964	+	0.280124i	$0.909625\pi$
$564$	22.9271	−	45.9541i	0.965405	−	1.93502i
$565$	−8.42307	+	14.5892i	−0.354361	+	0.613771i
$566$	42.6881	−	1.29856i	1.79432	−	0.0545827i
$567$			6.72730i			0.282520i
$568$	1.67794	−	3.63593i	0.0704050	−	0.152560i
$569$	0.0298020	+	0.0516186i	0.00124937	+	0.00216397i	0.866649	−	0.498918i	$-0.166269\pi$
$569$	0.0298020	+	0.0516186i	0.00124937	+	0.00216397i	−0.865400	+	0.501082i	$0.832936\pi$
$570$	0.800317	−	1.48899i	0.0335216	−	0.0623669i
$571$			13.2683i			0.555261i	0.960688	+	0.277630i	$0.0895490\pi$
$571$			13.2683i			0.555261i	−0.960688	+	0.277630i	$0.910451\pi$
$572$	2.44183	−	1.00703i	0.102098	−	0.0421059i
$573$			23.1697i			0.967926i
$574$	7.29485	+	3.92091i	0.304481	+	0.163656i
$575$	−0.390725	−	0.676756i	−0.0162944	−	0.0282227i
$576$	−15.9738	+	44.9946i	−0.665575	+	1.87477i
$577$			38.2758i			1.59344i	0.604347	+	0.796722i	$0.293434\pi$
$577$			38.2758i			1.59344i	−0.604347	+	0.796722i	$0.706566\pi$
$578$	−0.407821	−	13.4064i	−0.0169631	−	0.557634i
$579$	−24.1778	+	41.8771i	−1.00479	+	1.74035i
$580$	−3.77322	−	1.88251i	−0.156674	−	0.0781670i
$581$	−1.81029	−	1.04517i	−0.0751034	−	0.0433610i
$582$	48.4205	+	26.0256i	2.00709	+	1.07879i
$583$	1.54043	−	0.889368i	0.0637981	−	0.0368338i
$584$	46.0390	−	4.21189i	1.90511	−	0.174289i
$585$	20.3554	−	6.97982i	0.841591	−	0.288580i
$586$	−1.43194	+	0.885847i	−0.0591528	+	0.0365940i
$587$	14.0435	+	24.3241i	0.579639	+	1.00396i	0.995521	+	0.0945454i	$0.0301398\pi$
$587$	14.0435	+	24.3241i	0.579639	+	1.00396i	−0.415882	+	0.909419i	$0.636527\pi$
$588$	2.33147	+	38.2862i	0.0961484	+	1.57890i
$589$	−3.40054	−	1.96330i	−0.140117	−	0.0808964i
$590$	15.0973	−	9.33973i	0.621546	−	0.384510i
$591$	−2.51767	−	1.45357i	−0.103563	−	0.0597921i
$592$	−36.1464	+	4.41872i	−1.48561	+	0.181608i
$593$			8.76776i			0.360049i	0.983662	+	0.180024i	$0.0576177\pi$
$593$			8.76776i			0.360049i	−0.983662	+	0.180024i	$0.942382\pi$
$594$	4.60245	−	0.140006i	0.188841	−	0.00574450i
$595$	1.83266	−	1.05809i	0.0751319	−	0.0433774i
$596$	−43.1664	+	2.62866i	−1.76817	+	0.107674i
$597$		−	9.63194i		−	0.394209i
$598$	2.52545	−	3.08211i	0.103273	−	0.126037i
$599$	−44.0675			−1.80055			−0.900275	−	0.435321i	$-0.856635\pi$
$599$	−44.0675			−1.80055			−0.900275	+	0.435321i	$0.856635\pi$
$600$	4.88583	+	6.91914i	0.199463	+	0.282473i
$601$	3.41495	+	5.91487i	0.139299	+	0.241273i	0.927231	−	0.374489i	$-0.122182\pi$
$601$	3.41495	+	5.91487i	0.139299	+	0.241273i	−0.787933	+	0.615762i	$0.788848\pi$
$602$	0.206394	+	6.78487i	0.00841200	+	0.276530i
$603$	25.0751			1.02114
$604$	28.2966	−	18.7183i	1.15137	−	0.761636i
$605$	−5.43292	+	9.41009i	−0.220879	+	0.382574i
$606$	8.61930	−	5.33220i	0.350135	−	0.216606i
$607$	20.7623	−	35.9613i	0.842715	−	1.45962i	−0.0448766	−	0.998993i	$-0.514289\pi$
$607$	20.7623	−	35.9613i	0.842715	−	1.45962i	0.887591	−	0.460632i	$-0.152377\pi$
$608$	0.341998	+	2.23186i	0.0138699	+	0.0905138i
$609$	4.22082	−	2.43689i	0.171036	−	0.0987478i
$610$	1.06085	+	1.71482i	0.0429525	+	0.0694310i
$611$	20.3123	−	23.3064i	0.821748	−	0.942876i
$612$	14.6091	−	29.2819i	0.590539	−	1.18365i
$613$	−6.61499	−	11.4575i	−0.267177	−	0.462764i	0.700955	−	0.713206i	$-0.252758\pi$
$613$	−6.61499	−	11.4575i	−0.267177	−	0.462764i	−0.968132	+	0.250442i	$0.919424\pi$
$614$	20.7914	+	11.1752i	0.839071	+	0.450993i
$615$	11.3598	−	19.6757i	0.458071	−	0.793403i
$616$	−0.796381	+	0.0728571i	−0.0320871	+	0.00293549i
$617$	−17.8931	−	10.3306i	−0.720350	−	0.415894i	0.0945313	−	0.995522i	$-0.469865\pi$
$617$	−17.8931	−	10.3306i	−0.720350	−	0.415894i	−0.814882	+	0.579627i	$0.803198\pi$
$618$	−26.3186	+	0.800607i	−1.05869	+	0.0322051i
$619$	40.2474			1.61768			0.808840	−	0.588029i	$-0.200096\pi$
$619$	40.2474			1.61768			0.808840	+	0.588029i	$0.200096\pi$
$620$	16.4096	−	10.8550i	0.659026	−	0.435948i
$621$	6.01568	−	3.47316i	0.241401	−	0.139373i
$622$	4.04629	+	2.17484i	0.162242	+	0.0872033i
$623$	8.98880			0.360129
$624$	−24.2164	+	35.7625i	−0.969433	+	1.43165i
$625$	1.00000			0.0400000
$626$	−2.35589	−	1.26627i	−0.0941603	−	0.0506103i
$627$	0.379174	−	0.218916i	0.0151427	−	0.00874266i
$628$	24.2225	−	16.0233i	0.966585	−	0.639399i
$629$	24.9583			0.995152
$630$	−6.51215	+	0.198098i	−0.259450	+	0.00789242i
$631$	26.3130	+	15.1918i	1.04751	+	0.604778i	0.921950	−	0.387309i	$-0.126595\pi$
$631$	26.3130	+	15.1918i	1.04751	+	0.604778i	0.125556	+	0.992087i	$0.459929\pi$
$632$	1.26136	+	13.7876i	0.0501741	+	0.548440i
$633$	−41.1910	+	71.3448i	−1.63719	+	2.83570i
$634$	21.1520	+	11.3690i	0.840052	+	0.451520i
$635$	4.90403	+	8.49402i	0.194610	+	0.337075i
$636$	−12.9847	+	26.0259i	−0.514877	+	1.03200i
$637$	−4.43485	+	22.6607i	−0.175715	+	0.897848i
$638$	−0.574586	−	0.928796i	−0.0227481	−	0.0367714i
$639$	7.31768	−	4.22486i	0.289483	−	0.167133i
$640$	−10.7719	−	3.45916i	−0.425797	−	0.136735i
$641$	12.4586	−	21.5790i	0.492086	−	0.852317i	−0.507873	−	0.861432i	$-0.669568\pi$
$641$	12.4586	−	21.5790i	0.492086	−	0.852317i	0.999958	+	0.00911474i	$0.00290135\pi$
$642$	24.0871	−	14.9012i	0.950644	−	0.588102i
$643$	−5.62459	+	9.74208i	−0.221812	+	0.384190i	−0.955358	−	0.295450i	$-0.904531\pi$
$643$	−5.62459	+	9.74208i	−0.221812	+	0.384190i	0.733546	+	0.679640i	$0.237864\pi$
$644$	−1.00618	+	0.665595i	−0.0396492	+	0.0262281i
$645$	18.6216			0.733225
$646$	−0.0470534	−	1.54680i	−0.00185129	−	0.0608581i
$647$	−11.5954	−	20.0837i	−0.455860	−	0.789573i	0.542877	−	0.839812i	$-0.317335\pi$
$647$	−11.5954	−	20.0837i	−0.455860	−	0.789573i	−0.998737	+	0.0502389i	$0.984002\pi$
$648$	−20.1361	+	14.2188i	−0.791021	+	0.558566i
$649$	4.59803			0.180489
$650$	1.79981	+	4.77082i	0.0705942	+	0.187127i
$651$			22.7406i			0.891276i
$652$	25.2218	−	1.53591i	0.987762	−	0.0601507i
$653$	−21.8184	+	12.5969i	−0.853820	+	0.492953i	−0.861938	−	0.507014i	$-0.830749\pi$
$653$	−21.8184	+	12.5969i	−0.853820	+	0.492953i	0.00811809	+	0.999967i	$0.497416\pi$
$654$	69.4193	−	2.11172i	2.71451	−	0.0825748i
$655$		−	5.06554i		−	0.197927i
$656$	3.68229	+	30.1221i	0.143769	+	1.17607i
$657$	84.4827	+	48.7761i	3.29599	+	1.90294i
$658$	−7.96012	+	4.92441i	−0.310318	+	0.191974i
$659$	29.7310	+	17.1652i	1.15816	+	0.668662i	0.950861	−	0.309617i	$-0.100201\pi$
$659$	29.7310	+	17.1652i	1.15816	+	0.668662i	0.207294	+	0.978279i	$0.433534\pi$
$660$	0.133349	+	2.18979i	0.00519061	+	0.0852374i
$661$	−0.537260	−	0.930562i	−0.0208970	−	0.0361946i	0.855388	−	0.517988i	$-0.173319\pi$
$661$	−0.537260	−	0.930562i	−0.0208970	−	0.0361946i	−0.876285	+	0.481793i	$0.839986\pi$
$662$	24.1900	−	14.9648i	0.940170	−	0.581622i
$663$	19.4489	−	22.3157i	0.755332	−	0.866670i
$664$	−0.697814	−	7.62761i	−0.0270804	−	0.296009i
$665$	−0.266825	+	0.154051i	−0.0103470	+	0.00597385i
$666$	−67.6828	−	36.3789i	−2.62266	−	1.40965i
$667$	−1.42686	−	0.823796i	−0.0552481	−	0.0318975i
$668$	26.6113	+	13.2767i	1.02962	+	0.513692i
$669$	17.3632	−	30.0740i	0.671300	−	1.16273i
$670$	0.180662	+	5.93895i	0.00697957	+	0.229442i
$671$			0.522265i			0.0201618i
$672$	10.2036	−	8.17813i	0.393613	−	0.315478i
$673$	−6.50789	−	11.2720i	−0.250861	−	0.434503i	0.712902	−	0.701263i	$-0.247380\pi$
$673$	−6.50789	−	11.2720i	−0.250861	−	0.434503i	−0.963763	+	0.266760i	$0.914047\pi$
$674$	12.6563	+	6.80265i	0.487503	+	0.262028i
$675$			8.88900i			0.342138i
$676$	−19.5214	+	17.1731i	−0.750823	+	0.660504i
$677$			8.50951i			0.327047i	0.986539	+	0.163524i	$0.0522860\pi$
$677$			8.50951i			0.327047i	−0.986539	+	0.163524i	$0.947714\pi$
$678$	33.7778	−	62.8434i	1.29723	−	2.41349i
$679$	−5.00960	−	8.67688i	−0.192251	−	0.332988i
$680$	7.04058	+	3.24915i	0.269994	+	0.124599i
$681$			37.1843i			1.42491i
$682$	5.09356	−	0.154945i	0.195043	−	0.00593315i
$683$	18.6230	−	32.2559i	0.712588	−	1.23424i	−0.251295	−	0.967911i	$-0.580856\pi$
$683$	18.6230	−	32.2559i	0.712588	−	1.23424i	0.963883	−	0.266327i	$-0.0858102\pi$
$684$	−2.12700	+	4.26326i	−0.0813278	+	0.163010i
$685$	−14.4204	−	8.32560i	−0.550974	−	0.318105i
$686$	6.92756	−	12.8887i	0.264495	−	0.492093i
$687$	−35.8515	+	20.6989i	−1.36782	+	0.789712i
$688$	−19.8722	+	14.9582i	−0.757620	+	0.570277i
$689$	−11.5038	+	13.1995i	−0.438260	+	0.502861i
$690$	1.74116	+	2.81452i	0.0662849	+	0.107147i
$691$	13.5936	+	23.5448i	0.517125	+	0.895686i	0.999802	+	0.0198882i	$0.00633103\pi$
$691$	13.5936	+	23.5448i	0.517125	+	0.895686i	−0.482677	+	0.875798i	$0.660336\pi$
$692$	−1.18993	−	19.5404i	−0.0452343	−	0.742814i
$693$	−1.46138	−	0.843727i	−0.0555132	−	0.0320506i
$694$	11.4869	+	18.5681i	0.436036	+	0.704835i
$695$	−4.85477	−	2.80290i	−0.184152	−	0.106320i
$696$	16.2152	+	7.48314i	0.614635	+	0.283648i
$697$		−	20.7987i		−	0.787806i
$698$	−0.466922	−	15.3493i	−0.0176733	−	0.580979i
$699$	−38.5565	+	22.2606i	−1.45834	+	0.841974i
$700$	−0.0938379	−	1.54095i	−0.00354674	−	0.0582426i
$701$			0.970524i			0.0366562i	0.999832	+	0.0183281i	$0.00583434\pi$
$701$			0.970524i			0.0366562i	−0.999832	+	0.0183281i	$0.994166\pi$
$702$	−42.4078	+	15.9985i	−1.60058	+	0.603824i
$703$	−3.63377			−0.137050
$704$	−1.90130	−	2.22973i	−0.0716580	−	0.0840363i
$705$	12.8390	+	22.2378i	0.483544	+	0.837522i
$706$	28.3912	−	0.863654i	1.06852	−	0.0325041i
$707$	−1.84728			−0.0694740
$708$	−62.7071	+	41.4810i	−2.35668	+	1.55895i
$709$	23.9119	−	41.4166i	0.898030	−	1.55543i	0.0680217	−	0.997684i	$-0.478331\pi$
$709$	23.9119	−	41.4166i	0.898030	−	1.55543i	0.830009	−	0.557750i	$-0.188335\pi$
$710$	1.05337	+	1.70273i	0.0395322	+	0.0639023i
$711$	−14.6073	+	25.3005i	−0.547815	+	0.948844i
$712$	18.9987	+	26.9052i	0.712005	+	1.00832i
$713$	6.65759	−	3.84376i	0.249329	−	0.143950i
$714$	−7.62177	+	4.71509i	−0.285237	+	0.176458i
$715$	−0.253652	+	1.29608i	−0.00948606	+	0.0484707i
$716$	−13.8041	−	6.88706i	−0.515884	−	0.257381i
$717$	21.6289	+	37.4624i	0.807748	+	1.39906i
$718$	12.7636	−	23.7467i	0.476334	−	0.886218i
$719$	−2.67744	+	4.63746i	−0.0998516	+	0.172948i	−0.911623	−	0.411027i	$-0.865170\pi$
$719$	−2.67744	+	4.63746i	−0.0998516	+	0.172948i	0.811772	+	0.583975i	$0.198503\pi$
$720$	−14.3570	−	19.0734i	−0.535053	−	0.710825i
$721$	4.15613	+	2.39954i	0.154782	+	0.0893637i
$722$	−0.810153	−	26.6324i	−0.0301508	−	0.991156i
$723$	35.4256			1.31749
$724$	−20.3331	+	13.4504i	−0.755672	+	0.499880i
$725$	1.82591	−	1.05419i	0.0678126	−	0.0391516i
$726$	21.7868	−	40.5343i	0.808584	−	1.50437i
$727$	34.2028			1.26851			0.634256	−	0.773123i	$-0.281307\pi$
$727$	34.2028			1.26851			0.634256	+	0.773123i	$0.281307\pi$
$728$	7.18272	−	3.22110i	0.266209	−	0.119382i
$729$	27.8454			1.03131
$730$	−10.9438	+	20.3609i	−0.405048	+	0.753591i
$731$	14.7633	−	8.52358i	0.546040	−	0.315256i
$732$	−4.71159	−	7.12255i	−0.174146	−	0.263257i
$733$	18.3791			0.678848			0.339424	−	0.940634i	$-0.389768\pi$
$733$	18.3791			0.678848			0.339424	+	0.940634i	$0.389768\pi$
$734$	0.385651	+	12.6776i	0.0142346	+	0.467940i
$735$	−16.6091	−	9.58928i	−0.612637	−	0.353706i
$736$	−4.11892	−	1.60491i	−0.151825	−	0.0591578i
$737$	−0.769463	+	1.33275i	−0.0283435	+	0.0490925i
$738$	−30.3159	+	56.4026i	−1.11594	+	2.07621i
$739$	−0.350031	−	0.606272i	−0.0128761	−	0.0223021i	0.859516	−	0.511110i	$-0.170765\pi$
$739$	−0.350031	−	0.606272i	−0.0128761	−	0.0223021i	−0.872392	+	0.488808i	$0.837432\pi$
$740$	8.12858	−	16.2926i	0.298813	−	0.598927i
$741$	−2.83164	+	3.24903i	−0.104023	+	0.119356i
$742$	4.50819	−	2.78893i	0.165501	−	0.102385i
$743$	0.177140	−	0.102272i	0.00649865	−	0.00375200i	−0.496747	−	0.867895i	$-0.665472\pi$
$743$	0.177140	−	0.102272i	0.00649865	−	0.00375200i	0.503246	+	0.864143i	$0.332139\pi$
$744$	−68.0672	+	48.0644i	−2.49546	+	1.76213i
$745$	10.8116	−	18.7262i	0.396106	−	0.686076i
$746$	−18.9469	−	30.6270i	−0.693696	−	1.12133i
$747$	8.08109	−	13.9969i	0.295672	−	0.512118i
$748$	1.10804	+	1.67503i	0.0405140	+	0.0612453i
$749$	−5.16233			−0.188627
$750$	−4.23319	+	0.128773i	−0.154574	+	0.00470212i
$751$	−8.18415	−	14.1754i	−0.298644	−	0.517266i	0.677182	−	0.735815i	$-0.263201\pi$
$751$	−8.18415	−	14.1754i	−0.298644	−	0.517266i	−0.975826	+	0.218549i	$0.929868\pi$
$752$	−31.5642	−	13.4180i	−1.15103	−	0.489304i
$753$	−65.5402			−2.38842
$754$	8.31563	+	6.81374i	0.302837	+	0.248142i
$755$			16.9637i			0.617373i
$756$	13.6976	−	0.834125i	0.498175	−	0.0303368i
$757$	0.227301	−	0.131232i	0.00826140	−	0.00476972i	−0.495864	−	0.868400i	$-0.665148\pi$
$757$	0.227301	−	0.131232i	0.00826140	−	0.00476972i	0.504125	+	0.863631i	$0.331815\pi$
$758$	0.537226	+	17.6604i	0.0195129	+	0.641455i
$759$			0.857190i			0.0311140i
$760$	−1.02506	−	0.473057i	−0.0371830	−	0.0171596i
$761$	−31.7560	−	18.3343i	−1.15115	−	0.664618i	−0.201985	−	0.979389i	$-0.564739\pi$
$761$	−31.7560	−	18.3343i	−1.15115	−	0.664618i	−0.949168	+	0.314770i	$0.898073\pi$
$762$	−21.8535	−	35.3253i	−0.791668	−	1.27970i
$763$	−10.9624	−	6.32916i	−0.396866	−	0.229131i
$764$	15.4451	−	0.940547i	0.558786	−	0.0340278i
$765$	8.18098	+	14.1699i	0.295784	+	0.512313i
$766$	−4.61091	−	7.45336i	−0.166599	−	0.269301i
$767$	−42.8137	+	14.6807i	−1.54591	+	0.530091i
$768$	46.0450	+	13.2562i	1.66151	+	0.478341i
$769$	7.11636	−	4.10863i

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24568 - 0.669541i) q^{2} +(-2.59349 + 1.49735i) q^{3} +(1.10343 + 1.66806i) q^{4} -1.00000 q^{5} +(4.23319 - 0.128773i) q^{6} +(-0.668489 - 0.385952i) q^{7} +(-0.257683 - 2.81666i) q^{8} +(2.98412 - 5.16865i) q^{9} +O(q^{10})\)	\(q+(-1.24568 - 0.669541i) q^{2} +(-2.59349 + 1.49735i) q^{3} +(1.10343 + 1.66806i) q^{4} -1.00000 q^{5} +(4.23319 - 0.128773i) q^{6} +(-0.668489 - 0.385952i) q^{7} +(-0.257683 - 2.81666i) q^{8} +(2.98412 - 5.16865i) q^{9} +(1.24568 + 0.669541i) q^{10} +(0.183144 + 0.317214i) q^{11} +(-5.35941 - 2.67388i) q^{12} +(-2.71812 - 2.36893i) q^{13} +(0.574312 + 0.928353i) q^{14} +(2.59349 - 1.49735i) q^{15} +(-1.56488 + 3.68119i) q^{16} +(1.37075 - 2.37421i) q^{17} +(-7.17788 + 4.44049i) q^{18} +(-0.199573 + 0.345670i) q^{19} +(-1.10343 - 1.66806i) q^{20} +2.31162 q^{21} +(-0.0157504 - 0.517769i) q^{22} +(-0.390725 - 0.676756i) q^{23} +(4.88583 + 6.91914i) q^{24} +1.00000 q^{25} +(1.79981 + 4.77082i) q^{26} +8.88900i q^{27} +(-0.0938379 - 1.54095i) q^{28} +(1.82591 - 1.05419i) q^{29} +(-4.23319 + 0.128773i) q^{30} +9.83751i q^{31} +(4.41404 - 3.53783i) q^{32} +(-0.949962 - 0.548461i) q^{33} +(-3.29715 + 2.03973i) q^{34} +(0.668489 + 0.385952i) q^{35} +(11.9144 - 0.725539i) q^{36} +(4.55194 + 7.88418i) q^{37} +(0.480044 - 0.296972i) q^{38} +(10.5965 + 2.07382i) q^{39} +(0.257683 + 2.81666i) q^{40} +(6.57018 - 3.79330i) q^{41} +(-2.87954 - 1.54773i) q^{42} +(5.38510 + 3.10909i) q^{43} +(-0.327048 + 0.655520i) q^{44} +(-2.98412 + 5.16865i) q^{45} +(0.0336025 + 1.10463i) q^{46} +8.57446i q^{47} +(-1.45353 - 11.8903i) q^{48} +(-3.20208 - 5.54617i) q^{49} +(-1.24568 - 0.669541i) q^{50} +8.20999i q^{51} +(0.952275 - 7.14795i) q^{52} -4.85612i q^{53} +(5.95155 - 11.0728i) q^{54} +(-0.183144 - 0.317214i) q^{55} +(-0.914840 + 1.98236i) q^{56} -1.19532i q^{57} +(-2.98032 + 0.0906607i) q^{58} +(6.27654 - 10.8713i) q^{59} +(5.35941 + 2.67388i) q^{60} +(1.23481 + 0.712917i) q^{61} +(6.58661 - 12.2544i) q^{62} +(-3.98970 + 2.30346i) q^{63} +(-7.86720 + 1.45161i) q^{64} +(2.71812 + 2.36893i) q^{65} +(0.816131 + 1.31924i) q^{66} +(2.10071 + 3.63853i) q^{67} +(5.47287 - 0.333275i) q^{68} +(2.02668 + 1.17011i) q^{69} +(-0.574312 - 0.928353i) q^{70} +(1.22610 + 0.707891i) q^{71} +(-15.3273 - 7.07340i) q^{72} +16.3452i q^{73} +(-0.391468 - 12.8689i) q^{74} +(-2.59349 + 1.49735i) q^{75} +(-0.796816 + 0.0485228i) q^{76} -0.282739i q^{77} +(-11.8114 - 9.67812i) q^{78} -4.89500 q^{79} +(1.56488 - 3.68119i) q^{80} +(-4.35760 - 7.54758i) q^{81} +(-10.7241 + 0.326225i) q^{82} +2.70803 q^{83} +(2.55072 + 3.85594i) q^{84} +(-1.37075 + 2.37421i) q^{85} +(-4.62645 - 7.47847i) q^{86} +(-3.15698 + 5.46806i) q^{87} +(0.846293 - 0.597595i) q^{88} +(-10.0848 + 5.82248i) q^{89} +(7.17788 - 4.44049i) q^{90} +(0.902738 + 2.63267i) q^{91} +(0.697734 - 1.39851i) q^{92} +(-14.7302 - 25.5135i) q^{93} +(5.74095 - 10.6810i) q^{94} +(0.199573 - 0.345670i) q^{95} +(-6.15040 + 15.7847i) q^{96} +(11.2409 + 6.48992i) q^{97} +(0.275380 + 9.05267i) q^{98} +2.18609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more