LMFDB - Embedded newform 425.2.k.c.86.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.5
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52182 + 1.10567i) q^{2} +(0.721199 - 2.21962i) q^{3} +(0.475405 - 1.46315i) q^{4} +(-0.865877 + 2.06162i) q^{5} +(1.35663 + 4.17527i) q^{6} -1.25766 q^{7} +(-0.268296 - 0.825730i) q^{8} +(-1.97954 - 1.43822i) q^{9} +(-0.961753 - 4.09478i) q^{10} +(3.07888 - 2.23694i) q^{11} +(-2.90477 - 2.11044i) q^{12} +(-2.58569 - 1.87861i) q^{13} +(1.91393 - 1.39055i) q^{14} +(3.95154 + 3.40875i) q^{15} +(3.81053 + 2.76852i) q^{16} +(-0.309017 - 0.951057i) q^{17} +4.60270 q^{18} +(-0.771132 - 2.37330i) q^{19} +(2.60480 + 2.24701i) q^{20} +(-0.907021 + 2.79152i) q^{21} +(-2.21220 + 6.80844i) q^{22} +(0.986841 - 0.716982i) q^{23} -2.02630 q^{24} +(-3.50052 - 3.57021i) q^{25} +6.01207 q^{26} +(1.04442 - 0.758818i) q^{27} +(-0.597897 + 1.84014i) q^{28} +(0.781596 - 2.40550i) q^{29} +(-9.78248 - 0.818425i) q^{30} +(-3.01928 - 9.29239i) q^{31} -7.12356 q^{32} +(-2.74467 - 8.44722i) q^{33} +(1.52182 + 1.10567i) q^{34} +(1.08898 - 2.59281i) q^{35} +(-3.04541 + 2.21262i) q^{36} +(-8.89261 - 6.46086i) q^{37} +(3.79761 + 2.75912i) q^{38} +(-6.03460 + 4.38439i) q^{39} +(1.93465 + 0.161857i) q^{40} +(7.17360 + 5.21193i) q^{41} +(-1.70617 - 5.25107i) q^{42} +2.39610 q^{43} +(-1.80925 - 5.56830i) q^{44} +(4.67909 - 2.83573i) q^{45} +(-0.709052 + 2.18224i) q^{46} +(2.59675 - 7.99198i) q^{47} +(8.89321 - 6.46129i) q^{48} -5.41830 q^{49} +(9.27463 + 1.56281i) q^{50} -2.33385 q^{51} +(-3.97793 + 2.89014i) q^{52} +(-0.104146 + 0.320528i) q^{53} +(-0.750425 + 2.30957i) q^{54} +(1.94577 + 8.28438i) q^{55} +(0.337425 + 1.03849i) q^{56} -5.82397 q^{57} +(1.47024 + 4.52493i) q^{58} +(7.23078 + 5.25347i) q^{59} +(6.86608 - 4.16114i) q^{60} +(-2.77431 + 2.01565i) q^{61} +(14.8691 + 10.8030i) q^{62} +(2.48958 + 1.80879i) q^{63} +(3.21973 - 2.33927i) q^{64} +(6.11186 - 3.70405i) q^{65} +(13.5167 + 9.82047i) q^{66} +(-0.249057 - 0.766518i) q^{67} -1.53844 q^{68} +(-0.879720 - 2.70750i) q^{69} +(1.20956 + 5.14984i) q^{70} +(1.31814 - 4.05683i) q^{71} +(-0.656479 + 2.02043i) q^{72} +(7.15905 - 5.20135i) q^{73} +20.6765 q^{74} +(-10.4491 + 5.19499i) q^{75} -3.83909 q^{76} +(-3.87218 + 2.81330i) q^{77} +(4.33590 - 13.3445i) q^{78} +(-3.16823 + 9.75080i) q^{79} +(-9.00707 + 5.45866i) q^{80} +(-3.19940 - 9.84675i) q^{81} -16.6796 q^{82} +(1.74479 + 5.36992i) q^{83} +(3.65321 + 2.65421i) q^{84} +(2.22828 + 0.186423i) q^{85} +(-3.64644 + 2.64929i) q^{86} +(-4.77562 - 3.46969i) q^{87} +(-2.67316 - 1.94216i) q^{88} +(4.53797 - 3.29703i) q^{89} +(-3.98537 + 9.48900i) q^{90} +(3.25191 + 2.36265i) q^{91} +(-0.579900 - 1.78475i) q^{92} -22.8031 q^{93} +(4.88468 + 15.0335i) q^{94} +(5.56054 + 0.465208i) q^{95} +(-5.13751 + 15.8116i) q^{96} +(2.01172 - 6.19144i) q^{97} +(8.24568 - 5.99084i) q^{98} -9.31197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.52182	+	1.10567i	−1.07609	+	0.781825i	−0.976997	−	0.213253i	$-0.931594\pi$
$2$	−1.52182	+	1.10567i	−1.07609	+	0.781825i	−0.0990933	+	0.995078i	$0.531594\pi$
$3$	0.721199	−	2.21962i	0.416384	−	1.28150i	−0.494623	−	0.869108i	$-0.664694\pi$
$3$	0.721199	−	2.21962i	0.416384	−	1.28150i	0.911007	−	0.412391i	$-0.135306\pi$
$4$	0.475405	−	1.46315i	0.237702	−	0.731573i
$5$	−0.865877	+	2.06162i	−0.387232	+	0.921982i
$5$	−0.865877	+	2.06162i	−0.387232	+	0.921982i
$6$	1.35663	+	4.17527i	0.553841	+	1.70455i
$7$	−1.25766			−0.475350			−0.237675	−	0.971345i	$-0.576385\pi$
$7$	−1.25766			−0.475350			−0.237675	+	0.971345i	$0.576385\pi$
$8$	−0.268296	−	0.825730i	−0.0948569	−	0.291940i
$9$	−1.97954	−	1.43822i	−0.659847	−	0.479407i
$10$	−0.961753	−	4.09478i	−0.304133	−	1.29488i
$11$	3.07888	−	2.23694i	0.928317	−	0.674462i	−0.0172632	−	0.999851i	$-0.505495\pi$
$11$	3.07888	−	2.23694i	0.928317	−	0.674462i	0.945580	+	0.325389i	$0.105495\pi$
$12$	−2.90477	−	2.11044i	−0.838534	−	0.609231i
$13$	−2.58569	−	1.87861i	−0.717140	−	0.521033i	0.168329	−	0.985731i	$-0.446163\pi$
$13$	−2.58569	−	1.87861i	−0.717140	−	0.521033i	−0.885469	+	0.464698i	$0.846163\pi$
$14$	1.91393	−	1.39055i	0.511520	−	0.371641i
$15$	3.95154	+	3.40875i	1.02028	+	0.880136i
$16$	3.81053	+	2.76852i	0.952634	+	0.692129i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	4.60270			1.08487
$19$	−0.771132	−	2.37330i	−0.176910	−	0.544473i	0.822806	−	0.568323i	$-0.192408\pi$
$19$	−0.771132	−	2.37330i	−0.176910	−	0.544473i	−0.999716	+	0.0238502i	$0.992408\pi$
$20$	2.60480	+	2.24701i	0.582451	+	0.502446i
$21$	−0.907021	+	2.79152i	−0.197928	+	0.609161i
$22$	−2.21220	+	6.80844i	−0.471642	+	1.45156i
$23$	0.986841	−	0.716982i	0.205771	−	0.149501i	−0.480127	−	0.877199i	$-0.659410\pi$
$23$	0.986841	−	0.716982i	0.205771	−	0.149501i	0.685898	+	0.727698i	$0.259410\pi$
$24$	−2.02630			−0.413617
$25$	−3.50052	−	3.57021i	−0.700103	−	0.714042i
$26$	6.01207			1.17906
$27$	1.04442	−	0.758818i	0.200999	−	0.146035i
$28$	−0.597897	+	1.84014i	−0.112992	+	0.347753i
$29$	0.781596	−	2.40550i	0.145139	−	0.446691i	−0.851890	−	0.523721i	$-0.824544\pi$
$29$	0.781596	−	2.40550i	0.145139	−	0.446691i	0.997029	+	0.0770296i	$0.0245436\pi$
$30$	−9.78248	−	0.818425i	−1.78603	−	0.149423i
$31$	−3.01928	−	9.29239i	−0.542279	−	1.66896i	−0.727374	−	0.686242i	$-0.759259\pi$
$31$	−3.01928	−	9.29239i	−0.542279	−	1.66896i	0.185095	−	0.982721i	$-0.440741\pi$
$32$	−7.12356			−1.25928
$33$	−2.74467	−	8.44722i	−0.477785	−	1.47047i
$34$	1.52182	+	1.10567i	0.260990	+	0.189621i
$35$	1.08898	−	2.59281i	0.184071	−	0.438264i
$36$	−3.04541	+	2.21262i	−0.507568	+	0.368770i
$37$	−8.89261	−	6.46086i	−1.46194	−	1.06216i	−0.982853	−	0.184388i	$-0.940970\pi$
$37$	−8.89261	−	6.46086i	−1.46194	−	1.06216i	−0.479082	−	0.877770i	$-0.659030\pi$
$38$	3.79761	+	2.75912i	0.616054	+	0.447589i
$39$	−6.03460	+	4.38439i	−0.966309	+	0.702065i
$40$	1.93465	+	0.161857i	0.305895	+	0.0255919i
$41$	7.17360	+	5.21193i	1.12033	+	0.813966i	0.984259	−	0.176733i	$-0.0565529\pi$
$41$	7.17360	+	5.21193i	1.12033	+	0.813966i	0.136070	+	0.990699i	$0.456553\pi$
$42$	−1.70617	−	5.25107i	−0.263268	−	0.810257i
$43$	2.39610			0.365402			0.182701	−	0.983169i	$-0.441516\pi$
$43$	2.39610			0.365402			0.182701	+	0.983169i	$0.441516\pi$
$44$	−1.80925	−	5.56830i	−0.272755	−	0.839453i
$45$	4.67909	−	2.83573i	0.697518	−	0.422726i
$46$	−0.709052	+	2.18224i	−0.104544	+	0.321753i
$47$	2.59675	−	7.99198i	0.378775	−	1.16575i	−0.562121	−	0.827055i	$-0.690015\pi$
$47$	2.59675	−	7.99198i	0.378775	−	1.16575i	0.940896	−	0.338695i	$-0.109985\pi$
$48$	8.89321	−	6.46129i	1.28362	−	0.932607i
$49$	−5.41830			−0.774042
$50$	9.27463	+	1.56281i	1.31163	+	0.221015i
$51$	−2.33385			−0.326804
$52$	−3.97793	+	2.89014i	−0.551640	+	0.400790i
$53$	−0.104146	+	0.320528i	−0.0143055	+	0.0440279i	−0.957954	−	0.286920i	$-0.907369\pi$
$53$	−0.104146	+	0.320528i	−0.0143055	+	0.0440279i	0.943649	+	0.330948i	$0.107369\pi$
$54$	−0.750425	+	2.30957i	−0.102120	+	0.314293i
$55$	1.94577	+	8.28438i	0.262368	+	1.11706i
$56$	0.337425	+	1.03849i	0.0450902	+	0.138774i
$57$	−5.82397			−0.771404
$58$	1.47024	+	4.52493i	0.193052	+	0.594153i
$59$	7.23078	+	5.25347i	0.941367	+	0.683943i	0.948749	−	0.316030i	$-0.102350\pi$
$59$	7.23078	+	5.25347i	0.941367	+	0.683943i	−0.00738237	+	0.999973i	$0.502350\pi$
$60$	6.86608	−	4.16114i	0.886407	−	0.537200i
$61$	−2.77431	+	2.01565i	−0.355214	+	0.258078i	−0.751053	−	0.660242i	$-0.770454\pi$
$61$	−2.77431	+	2.01565i	−0.355214	+	0.258078i	0.395839	+	0.918320i	$0.370454\pi$
$62$	14.8691	+	10.8030i	1.88838	+	1.37199i
$63$	2.48958	+	1.80879i	0.313658	+	0.227886i
$64$	3.21973	−	2.33927i	0.402466	−	0.292408i
$65$	6.11186	−	3.70405i	0.758083	−	0.459430i
$66$	13.5167	+	9.82047i	1.66379	+	1.20882i
$67$	−0.249057	−	0.766518i	−0.0304271	−	0.0936450i	0.934690	−	0.355465i	$-0.115677\pi$
$67$	−0.249057	−	0.766518i	−0.0304271	−	0.0936450i	−0.965117	+	0.261820i	$0.915677\pi$
$68$	−1.53844			−0.186564
$69$	−0.879720	−	2.70750i	−0.105906	−	0.325945i
$70$	1.20956	+	5.14984i	0.144570	+	0.615523i
$71$	1.31814	−	4.05683i	0.156435	−	0.481457i	−0.841869	−	0.539683i	$-0.818544\pi$
$71$	1.31814	−	4.05683i	0.156435	−	0.481457i	0.998303	+	0.0582256i	$0.0185443\pi$
$72$	−0.656479	+	2.02043i	−0.0773668	+	0.238110i
$73$	7.15905	−	5.20135i	0.837903	−	0.608772i	−0.0838810	−	0.996476i	$-0.526732\pi$
$73$	7.15905	−	5.20135i	0.837903	−	0.608772i	0.921784	+	0.387704i	$0.126732\pi$
$74$	20.6765			2.40360
$75$	−10.4491	+	5.19499i	−1.20656	+	0.599866i
$76$	−3.83909			−0.440373
$77$	−3.87218	+	2.81330i	−0.441276	+	0.320605i
$78$	4.33590	−	13.3445i	0.490944	−	1.51097i
$79$	−3.16823	+	9.75080i	−0.356453	+	1.09705i	0.598709	+	0.800967i	$0.295681\pi$
$79$	−3.16823	+	9.75080i	−0.356453	+	1.09705i	−0.955162	+	0.296084i	$0.904319\pi$
$80$	−9.00707	+	5.45866i	−1.00702	+	0.610297i
$81$	−3.19940	−	9.84675i	−0.355489	−	1.09408i
$82$	−16.6796			−1.84195
$83$	1.74479	+	5.36992i	0.191516	+	0.589426i	1.00000		0.000906885i	$0.000288670\pi$
$83$	1.74479	+	5.36992i	0.191516	+	0.589426i	−0.808484	+	0.588519i	$0.799711\pi$
$84$	3.65321	+	2.65421i	0.398597	+	0.289598i
$85$	2.22828	+	0.186423i	0.241691	+	0.0202204i
$86$	−3.64644	+	2.64929i	−0.393206	+	0.285681i
$87$	−4.77562	−	3.46969i	−0.512001	−	0.371990i
$88$	−2.67316	−	1.94216i	−0.284959	−	0.207035i
$89$	4.53797	−	3.29703i	0.481024	−	0.349484i	−0.320698	−	0.947181i	$-0.603917\pi$
$89$	4.53797	−	3.29703i	0.481024	−	0.349484i	0.801722	+	0.597697i	$0.203917\pi$
$90$	−3.98537	+	9.48900i	−0.420095	+	1.00023i
$91$	3.25191	+	2.36265i	0.340893	+	0.247673i
$92$	−0.579900	−	1.78475i	−0.0604588	−	0.186073i
$93$	−22.8031			−2.36457
$94$	4.88468	+	15.0335i	0.503817	+	1.55059i
$95$	5.56054	+	0.465208i	0.570499	+	0.0477293i
$96$	−5.13751	+	15.8116i	−0.524344	+	1.61377i
$97$	2.01172	−	6.19144i	0.204259	−	0.628645i	−0.795484	−	0.605975i	$-0.792783\pi$
$97$	2.01172	−	6.19144i	0.204259	−	0.628645i	0.999743	−	0.0226703i	$-0.00721681\pi$
$98$	8.24568	−	5.99084i	0.832939	−	0.605166i
$99$	−9.31197			−0.935888
$100$	−6.88790	+	3.42447i	−0.688790	+	0.342447i
$101$	−14.4522			−1.43805			−0.719023	−	0.694987i	$-0.755410\pi$
$101$	−14.4522			−1.43805			−0.719023	+	0.694987i	$0.755410\pi$
$102$	3.55170	−	2.58046i	0.351671	−	0.255504i
$103$	−5.48923	+	16.8941i	−0.540870	+	1.66463i	0.189742	+	0.981834i	$0.439235\pi$
$103$	−5.48923	+	16.8941i	−0.540870	+	1.66463i	−0.730612	+	0.682793i	$0.760765\pi$
$104$	−0.857496	+	2.63910i	−0.0840844	+	0.258785i
$105$	−4.96968	−	4.28704i	−0.484991	−	0.418373i
$106$	−0.195906	−	0.602937i	−0.0190281	−	0.0585624i
$107$	−9.10441			−0.880156			−0.440078	−	0.897959i	$-0.645049\pi$
$107$	−9.10441			−0.880156			−0.440078	+	0.897959i	$0.645049\pi$
$108$	−0.613737	−	1.88889i	−0.0590569	−	0.181758i
$109$	14.1493	+	10.2801i	1.35526	+	0.984652i	0.998731	+	0.0503675i	$0.0160393\pi$
$109$	14.1493	+	10.2801i	1.35526	+	0.984652i	0.356527	+	0.934285i	$0.383961\pi$
$110$	−12.1209	−	10.4560i	−1.15568	−	0.996937i
$111$	−20.7540	+	15.0787i	−1.96988	+	1.43120i
$112$	−4.79235	−	3.48185i	−0.452834	−	0.329003i
$113$	0.665307	+	0.483374i	0.0625868	+	0.0454720i	0.618639	−	0.785676i	$-0.287684\pi$
$113$	0.665307	+	0.483374i	0.0625868	+	0.0454720i	−0.556052	+	0.831148i	$0.687684\pi$
$114$	8.86304	−	6.43938i	0.830100	−	0.603103i
$115$	0.623659	+	2.65531i	0.0581565	+	0.247608i
$116$	−3.14803	−	2.28718i	−0.292287	−	0.212359i
$117$	2.41661	+	7.43757i	0.223416	+	0.687604i
$118$	−16.8125			−1.54772
$119$	0.388638	+	1.19610i	0.0356264	+	0.109647i
$120$	1.75453	−	4.17746i	0.160166	−	0.381348i
$121$	1.07642	−	3.31289i	0.0978568	−	0.301172i
$122$	1.99336	−	6.13493i	0.180470	−	0.555431i
$123$	16.7421	−	12.1638i	1.50958	−	1.09678i
$124$	−15.0315			−1.34987
$125$	10.3914	−	4.12536i	0.929436	−	0.368983i
$126$	−5.78862			−0.515692
$127$	−2.98633	+	2.16969i	−0.264994	+	0.192529i	−0.712346	−	0.701829i	$-0.752367\pi$
$127$	−2.98633	+	2.16969i	−0.264994	+	0.192529i	0.447352	+	0.894358i	$0.352367\pi$
$128$	2.08921	−	6.42993i	0.184662	−	0.568331i
$129$	1.72807	−	5.31844i	0.152148	−	0.468263i
$130$	−5.20571	+	12.3946i	−0.456571	+	1.08708i
$131$	3.27681	+	10.0850i	0.286296	+	0.881130i	0.986007	+	0.166704i	$0.0533123\pi$
$131$	3.27681	+	10.0850i	0.286296	+	0.881130i	−0.699711	+	0.714426i	$0.746688\pi$
$132$	−13.6643			−1.18933
$133$	0.969821	+	2.98480i	0.0840941	+	0.258815i
$134$	1.22653	+	0.891129i	0.105956	+	0.0769818i
$135$	0.660049	+	2.81024i	0.0568080	+	0.241867i
$136$	−0.702408	+	0.510329i	−0.0602310	+	0.0437604i
$137$	13.8984	+	10.0978i	1.18742	+	0.862710i	0.992989	−	0.118207i	$-0.0377145\pi$
$137$	13.8984	+	10.0978i	1.18742	+	0.862710i	0.194429	+	0.980917i	$0.437714\pi$
$138$	4.33237	+	3.14765i	0.368796	+	0.267946i
$139$	2.83819	−	2.06207i	0.240732	−	0.174902i	−0.460877	−	0.887464i	$-0.652465\pi$
$139$	2.83819	−	2.06207i	0.240732	−	0.174902i	0.701609	+	0.712562i	$0.252465\pi$
$140$	−3.27595	−	2.82596i	−0.276868	−	0.238838i
$141$	−15.8664	−	11.5276i	−1.33619	−	0.970800i
$142$	2.47953	+	7.63120i	0.208077	+	0.640396i
$143$	−12.1634			−1.01715
$144$	−3.56137	−	10.9608i	−0.296781	−	0.913398i
$145$	4.28246	+	3.69422i	0.355639	+	0.306788i
$146$	−5.14382	+	15.8311i	−0.425706	+	1.31019i
$147$	−3.90767	+	12.0266i	−0.322299	+	0.991934i
$148$	−13.6808	+	9.93966i	−1.12455	+	0.817035i
$149$	−17.8349			−1.46109			−0.730544	−	0.682865i	$-0.760734\pi$
$149$	−17.8349			−1.46109			−0.730544	+	0.682865i	$0.760734\pi$
$150$	10.1577	−	19.4591i	0.829373	−	1.58883i
$151$	10.5233			0.856376			0.428188	−	0.903690i	$-0.359152\pi$
$151$	10.5233			0.856376			0.428188	+	0.903690i	$0.359152\pi$
$152$	−1.75281	+	1.27349i	−0.142172	+	0.103294i
$153$	−0.756117	+	2.32709i	−0.0611284	+	0.188134i
$154$	2.78219	−	8.56268i	0.224195	−	0.690001i
$155$	21.7717	+	1.82147i	1.74874	+	0.146304i
$156$	3.54613	+	10.9139i	0.283918	+	0.873808i
$157$	7.77722			0.620690			0.310345	−	0.950624i	$-0.399555\pi$
$157$	7.77722			0.620690			0.310345	+	0.950624i	$0.399555\pi$
$158$	−5.95967	−	18.3420i	−0.474126	−	1.45921i
$159$	0.636340	+	0.462328i	0.0504651	+	0.0366650i
$160$	6.16813	−	14.6860i	0.487633	−	1.16103i
$161$	−1.24111	+	0.901718i	−0.0978131	+	0.0710654i
$162$	15.7562	+	11.4475i	1.23792	+	0.899402i
$163$	−4.59794	−	3.34060i	−0.360139	−	0.261656i	0.392971	−	0.919551i	$-0.371447\pi$
$163$	−4.59794	−	3.34060i	−0.360139	−	0.261656i	−0.753110	+	0.657895i	$0.771447\pi$
$164$	11.0362	−	8.01825i	0.861781	−	0.626120i
$165$	19.7915	+	1.65580i	1.54076	+	0.128904i
$166$	−8.59262	−	6.24290i	−0.666916	−	0.484543i
$167$	5.61375	+	17.2773i	0.434405	+	1.33696i	0.893695	+	0.448675i	$0.148104\pi$
$167$	5.61375	+	17.2773i	0.434405	+	1.33696i	−0.459290	+	0.888286i	$0.651896\pi$
$168$	2.54840			0.196613
$169$	−0.860626	−	2.64873i	−0.0662020	−	0.203749i
$170$	−3.59717	+	2.18004i	−0.275890	+	0.167201i
$171$	−1.88684	+	5.80710i	−0.144290	+	0.444080i
$172$	1.13912	−	3.50585i	0.0868570	−	0.267318i
$173$	0.208755	−	0.151670i	0.0158714	−	0.0115312i	−0.579821	−	0.814744i	$-0.696878\pi$
$173$	0.208755	−	0.151670i	0.0158714	−	0.0115312i	0.595693	+	0.803212i	$0.296878\pi$
$174$	11.1040			0.841790
$175$	4.40245	+	4.49010i	0.332794	+	0.339420i
$176$	17.9252			1.35116
$177$	16.8755	−	12.2608i	1.26844	−	0.921578i
$178$	−3.26056	+	10.0350i	−0.244389	+	0.752153i
$179$	3.11644	−	9.59141i	0.232934	−	0.716896i	−0.764455	−	0.644677i	$-0.776992\pi$
$179$	3.11644	−	9.59141i	0.232934	−	0.716896i	0.997389	−	0.0722190i	$-0.0230081\pi$
$180$	−1.92462	−	8.19432i	−0.143453	−	0.610768i
$181$	−0.0190451	−	0.0586146i	−0.00141561	−	0.00435679i	0.950346	−	0.311195i	$-0.100729\pi$
$181$	−0.0190451	−	0.0586146i	−0.00141561	−	0.00435679i	−0.951762	+	0.306838i	$0.900729\pi$
$182$	−7.56113			−0.560468
$183$	2.47316	+	7.61161i	0.182821	+	0.562666i
$184$	−0.856799	−	0.622501i	−0.0631641	−	0.0458914i
$185$	21.0197	−	12.7388i	1.54540	−	0.936578i
$186$	34.7022	−	25.2126i	2.54449	−	1.84868i
$187$	−3.07888	−	2.23694i	−0.225150	−	0.163581i
$188$	−10.4589	−	7.59885i	−0.762795	−	0.554203i
$189$	−1.31353	+	0.954333i	−0.0955450	+	0.0694175i
$190$	−8.97651	+	5.44015i	−0.651225	+	0.394670i
$191$	−9.17774	−	6.66802i	−0.664078	−	0.482481i	0.203959	−	0.978979i	$-0.434619\pi$
$191$	−9.17774	−	6.66802i	−0.664078	−	0.482481i	−0.868038	+	0.496498i	$0.834619\pi$
$192$	−2.87023	−	8.83365i	−0.207141	−	0.637514i
$193$	−4.25444			−0.306242			−0.153121	−	0.988207i	$-0.548932\pi$
$193$	−4.25444			−0.306242			−0.153121	+	0.988207i	$0.548932\pi$
$194$	3.78420	+	11.6466i	0.271689	+	0.836174i
$195$	−3.81371	−	16.2374i	−0.273106	−	1.16278i
$196$	−2.57588	+	7.92776i	−0.183992	+	0.566268i
$197$	−0.865331	+	2.66321i	−0.0616523	+	0.189746i	−0.977139	−	0.212603i	$-0.931806\pi$
$197$	−0.865331	+	2.66321i	−0.0616523	+	0.189746i	0.915486	+	0.402349i	$0.131806\pi$
$198$	14.1712	−	10.2959i	1.00710	−	0.731701i
$199$	−0.268017			−0.0189992			−0.00949960	−	0.999955i	$-0.503024\pi$
$199$	−0.268017			−0.0189992			−0.00949960	+	0.999955i	$0.503024\pi$
$200$	−2.00885	+	3.84835i	−0.142047	+	0.272120i
$201$	−1.88100			−0.132675
$202$	21.9936	−	15.9793i	1.54747	−	1.12430i
$203$	−0.982980	+	3.02530i	−0.0689917	+	0.212335i
$204$	−1.10952	+	3.41476i	−0.0776821	+	0.239081i
$205$	−16.9564	+	10.2763i	−1.18429	+	0.717730i
$206$	−10.3257	−	31.7791i	−0.719423	−	2.21416i
$207$	−2.98467			−0.207449
$208$	−4.65188	−	14.3170i	−0.322550	−	0.992707i
$209$	−7.68315	−	5.58213i	−0.531454	−	0.386124i
$210$	12.3030	+	1.02930i	0.848989	+	0.0710284i
$211$	9.59508	−	6.97124i	0.660553	−	0.479920i	−0.206297	−	0.978489i	$-0.566141\pi$
$211$	9.59508	−	6.97124i	0.660553	−	0.479920i	0.866850	+	0.498570i	$0.166141\pi$
$212$	0.419467	+	0.304761i	0.0288091	+	0.0209311i
$213$	−8.05398	−	5.85156i	−0.551850	−	0.400942i
$214$	13.8553	−	10.0665i	0.947128	−	0.688129i
$215$	−2.07473	+	4.93984i	−0.141495	+	0.336894i
$216$	−0.906793	−	0.658823i	−0.0616994	−	0.0448273i
$217$	3.79722	+	11.6866i	0.257772	+	0.793341i
$218$	−32.8991			−2.22821
$219$	−6.38194	−	19.6416i	−0.431251	−	1.32726i
$220$	13.0463	+	1.09148i	0.879580	+	0.0735877i
$221$	−0.987644	+	3.03966i	−0.0664362	+	0.204469i
$222$	14.9119	−	45.8941i	1.00082	−	3.08021i
$223$	12.7421	−	9.25765i	0.853272	−	0.619938i	−0.0727743	−	0.997348i	$-0.523185\pi$
$223$	12.7421	−	9.25765i	0.853272	−	0.619938i	0.926046	+	0.377410i	$0.123185\pi$
$224$	8.95901			0.598599
$225$	1.79467	+	12.1019i	0.119644	+	0.806792i
$226$	−1.54693			−0.102900
$227$	−5.03922	+	3.66121i	−0.334465	+	0.243003i	−0.742323	−	0.670042i	$-0.766276\pi$
$227$	−5.03922	+	3.66121i	−0.334465	+	0.243003i	0.407858	+	0.913045i	$0.366276\pi$
$228$	−2.76874	+	8.52132i	−0.183365	+	0.564338i
$229$	7.68958	−	23.6661i	0.508142	−	1.56390i	−0.287282	−	0.957846i	$-0.592752\pi$
$229$	7.68958	−	23.6661i	0.508142	−	1.56390i	0.795424	−	0.606054i	$-0.207248\pi$
$230$	−3.88498	−	3.35134i	−0.256168	−	0.220981i
$231$	3.45185	+	10.6237i	0.227115	+	0.698989i
$232$	−2.19600			−0.144174
$233$	3.65414	+	11.2463i	0.239391	+	0.736769i	0.996509	+	0.0834906i	$0.0266068\pi$
$233$	3.65414	+	11.2463i	0.239391	+	0.736769i	−0.757118	+	0.653278i	$0.773393\pi$
$234$	−11.9011	−	8.64669i	−0.778002	−	0.565251i
$235$	14.2279	+	12.2736i	0.928127	+	0.800639i
$236$	11.1241	−	8.08216i	0.724120	−	0.526104i
$237$	19.3582	+	14.0645i	1.25745	+	0.913589i
$238$	−1.91393	−	1.39055i	−0.124062	−	0.0901361i
$239$	3.88783	−	2.82468i	0.251483	−	0.182713i	−0.454901	−	0.890542i	$-0.650325\pi$
$239$	3.88783	−	2.82468i	0.251483	−	0.182713i	0.706384	+	0.707829i	$0.250325\pi$
$240$	5.62028	+	23.9291i	0.362788	+	1.54461i
$241$	−13.6683	−	9.93060i	−0.880453	−	0.639686i	0.0529184	−	0.998599i	$-0.483148\pi$
$241$	−13.6683	−	9.93060i	−0.880453	−	0.639686i	−0.933371	+	0.358912i	$0.883148\pi$
$242$	2.02484	+	6.23180i	0.130161	+	0.400595i
$243$	−20.2905			−1.30164
$244$	1.63028	+	5.01747i	0.104368	+	0.321211i
$245$	4.69158	−	11.1704i	0.299734	−	0.713653i
$246$	−12.0293	+	37.0224i	−0.766961	+	2.36046i
$247$	−2.46460	+	7.58527i	−0.156819	+	0.482639i
$248$	−6.86294	+	4.98622i	−0.435797	+	0.316625i
$249$	13.1775			0.835092
$250$	−11.2526	+	17.7675i	−0.711677	+	1.12372i
$251$	−9.53532			−0.601864			−0.300932	−	0.953646i	$-0.597298\pi$
$251$	−9.53532			−0.601864			−0.300932	+	0.953646i	$0.597298\pi$
$252$	3.83008	−	2.78272i	0.241273	−	0.175295i
$253$	1.43452	−	4.41500i	0.0901876	−	0.277569i
$254$	2.14570	−	6.60377i	0.134633	−	0.414357i
$255$	2.02082	−	4.81150i	0.126549	−	0.301308i
$256$	6.38961	+	19.6652i	0.399351	+	1.22908i
$257$	13.0526			0.814201			0.407101	−	0.913383i	$-0.366540\pi$
$257$	13.0526			0.814201			0.407101	+	0.913383i	$0.366540\pi$
$258$	3.25062	+	10.0044i	0.202375	+	0.622846i
$259$	11.1839	+	8.12555i	0.694931	+	0.504897i
$260$	−2.51395	−	10.7035i	−0.155909	−	0.663801i
$261$	−5.00685	+	3.63769i	−0.309916	+	0.225167i
$262$	−16.1374	−	11.7245i	−0.996971	−	0.724342i
$263$	−19.9159	−	14.4698i	−1.22807	−	0.892245i	−0.231326	−	0.972876i	$-0.574306\pi$
$263$	−19.9159	−	14.4698i	−1.22807	−	0.892245i	−0.996744	+	0.0806314i	$0.974306\pi$
$264$	−6.23874	+	4.53271i	−0.383968	+	0.278969i
$265$	−0.570627	−	0.492246i	−0.0350534	−	0.0302384i
$266$	−4.77609	−	3.47003i	−0.292841	−	0.212761i
$267$	−4.04538	−	12.4504i	−0.247573	−	0.761951i
$268$	−1.23993			−0.0757408
$269$	7.31936	+	22.5267i	0.446269	+	1.37348i	0.881086	+	0.472956i	$0.156813\pi$
$269$	7.31936	+	22.5267i	0.446269	+	1.37348i	−0.434817	+	0.900519i	$0.643187\pi$
$270$	−4.11167	−	3.54689i	−0.250228	−	0.215857i
$271$	9.15919	−	28.1891i	0.556381	−	1.71237i	−0.135886	−	0.990724i	$-0.543388\pi$
$271$	9.15919	−	28.1891i	0.556381	−	1.71237i	0.692268	−	0.721641i	$-0.256612\pi$
$272$	1.45549	−	4.47955i	0.0882523	−	0.271613i
$273$	7.58946	−	5.51407i	0.459335	−	0.333727i
$274$	−32.3156			−1.95226
$275$	−18.7640	−	3.16181i	−1.13151	−	0.190664i
$276$	−4.37969			−0.263626
$277$	−24.3848	+	17.7166i	−1.46514	+	1.06449i	−0.483152	+	0.875537i	$0.660508\pi$
$277$	−24.3848	+	17.7166i	−1.46514	+	1.06449i	−0.981987	+	0.188949i	$0.939492\pi$
$278$	−2.03926	+	6.27619i	−0.122307	+	0.376421i
$279$	−7.38771	+	22.7370i	−0.442291	+	1.36123i
$280$	−2.43313	−	0.203561i	−0.145407	−	0.0121651i
$281$	−9.26092	−	28.5022i	−0.552460	−	1.70030i	−0.702558	−	0.711626i	$-0.747959\pi$
$281$	−9.26092	−	28.5022i	−0.552460	−	1.70030i	0.150098	−	0.988671i	$-0.452041\pi$
$282$	36.8915			2.19686
$283$	5.81432	+	17.8946i	0.345625	+	1.06372i	0.961248	+	0.275684i	$0.0889044\pi$
$283$	5.81432	+	17.8946i	0.345625	+	1.06372i	−0.615623	+	0.788041i	$0.711096\pi$
$284$	−5.30908	−	3.85727i	−0.315036	−	0.228887i
$285$	5.04284	−	12.0068i	0.298712	−	0.711221i
$286$	18.5105	−	13.4486i	1.09455	−	0.795234i
$287$	−9.02194	−	6.55482i	−0.532548	−	0.386919i
$288$	14.1014	+	10.2453i	0.830932	+	0.603707i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−10.6017	−	0.886964i	−0.622555	−	0.0520843i
$291$	−12.2918	−	8.93051i	−0.720558	−	0.523516i
$292$	−4.20689	−	12.9475i	−0.246190	−	0.757694i
$293$	32.4324			1.89472			0.947360	−	0.320169i	$-0.103740\pi$
$293$	32.4324			1.89472			0.947360	+	0.320169i	$0.103740\pi$
$294$	−7.35062	−	22.6229i	−0.428697	−	1.31939i
$295$	−17.0916	+	10.3582i	−0.995111	+	0.603079i
$296$	−2.94907	+	9.07631i	−0.171411	+	0.527550i
$297$	1.51822	−	4.67262i	0.0880963	−	0.271133i
$298$	27.1415	−	19.7194i	1.57226	−	1.14232i
$299$	−3.89859			−0.225461
$300$	2.63348	+	17.7582i	0.152044	+	1.02527i
$301$	−3.01348			−0.173694
$302$	−16.0146	+	11.6353i	−0.921538	+	0.669537i
$303$	−10.4229	+	32.0784i	−0.598779	+	1.84285i
$304$	3.63209	−	11.1784i	0.208315	−	0.641127i
$305$	−1.75329	−	7.46487i	−0.100393	−	0.427437i
$306$	−1.42231	−	4.37743i	−0.0813082	−	0.250241i
$307$	−7.67187			−0.437857			−0.218928	−	0.975741i	$-0.570256\pi$
$307$	−7.67187			−0.437857			−0.218928	+	0.975741i	$0.570256\pi$
$308$	2.27542	+	7.00302i	0.129654	+	0.399034i
$309$	33.5397	+	24.3680i	1.90801	+	1.38625i
$310$	−35.1465	+	21.3003i	−1.99619	+	1.20977i
$311$	16.3456	−	11.8758i	0.926875	−	0.673414i	−0.0183504	−	0.999832i	$-0.505841\pi$
$311$	16.3456	−	11.8758i	0.926875	−	0.673414i	0.945226	+	0.326417i	$0.105841\pi$
$312$	5.23938	+	3.80663i	0.296622	+	0.215508i
$313$	3.22002	+	2.33948i	0.182006	+	0.132235i	0.675058	−	0.737765i	$-0.264119\pi$
$313$	3.22002	+	2.33948i	0.182006	+	0.132235i	−0.493052	+	0.870000i	$0.664119\pi$
$314$	−11.8355	+	8.59903i	−0.667918	+	0.485271i
$315$	−5.88470	+	3.56638i	−0.331565	+	0.200943i
$316$	12.7606	+	9.27115i	0.717843	+	0.521543i
$317$	4.73927	+	14.5860i	0.266184	+	0.819229i	0.991418	+	0.130727i	$0.0417313\pi$
$317$	4.73927	+	14.5860i	0.266184	+	0.819229i	−0.725235	+	0.688502i	$0.758269\pi$
$318$	−1.47958			−0.0829706
$319$	−2.97452	−	9.15464i	−0.166541	−	0.512561i
$320$	2.03478	+	8.66335i	0.113748	+	0.484296i
$321$	−6.56609	+	20.2083i	−0.366483	+	1.12792i
$322$	0.891745	−	2.74451i	0.0496950	−	0.152945i
$323$	−2.01885	+	1.46678i	−0.112332	+	0.0816139i
$324$	−15.9282			−0.884902
$325$	2.34420	+	15.8075i	0.130033	+	0.876845i
$326$	10.6908			0.592111
$327$	33.0223	−	23.9921i	1.82614	−	1.32677i
$328$	2.37900	−	7.32180i	0.131358	−	0.404279i
$329$	−3.26582	+	10.0512i	−0.180051	+	0.554139i
$330$	−31.9498	+	19.3630i	−1.75878	+	1.06590i
$331$	−2.94251	−	9.05613i	−0.161735	−	0.497770i	0.837046	−	0.547133i	$-0.184281\pi$
$331$	−2.94251	−	9.05613i	−0.161735	−	0.497770i	−0.998781	+	0.0493633i	$0.984281\pi$
$332$	8.68646			0.476732
$333$	8.31114	+	25.5791i	0.455448	+	1.40172i
$334$	−27.6461	−	20.0861i	−1.51273	−	1.09906i
$335$	1.79592	+	0.150251i	0.0981214	+	0.00820906i
$336$	−11.1846	+	8.12610i	−0.610171	+	0.443315i
$337$	0.680272	+	0.494247i	0.0370568	+	0.0269233i	0.606159	−	0.795343i	$-0.292709\pi$
$337$	0.680272	+	0.494247i	0.0370568	+	0.0269233i	−0.569103	+	0.822266i	$0.692709\pi$
$338$	4.23834	+	3.07933i	0.230535	+	0.167494i
$339$	1.55273	−	1.12812i	0.0843325	−	0.0612712i
$340$	1.33210	−	3.17168i	0.0722433	−	0.172008i
$341$	−30.0825	−	21.8562i	−1.62906	−	1.18358i
$342$	−3.54929	−	10.9236i	−0.191924	−	0.590680i
$343$	15.6180			0.843291
$344$	−0.642864	−	1.97853i	−0.0346609	−	0.106675i
$345$	6.34355	+	0.530716i	0.341525	+	0.0285728i
$346$	−0.149992	+	0.461628i	−0.00806363	+	0.0248173i
$347$	5.55183	−	17.0868i	0.298038	−	0.917265i	−0.684147	−	0.729345i	$-0.739825\pi$
$347$	5.55183	−	17.0868i	0.298038	−	0.917265i	0.982184	−	0.187921i	$-0.0601749\pi$
$348$	−7.34702	+	5.33792i	−0.393842	+	0.286143i
$349$	−30.8024			−1.64881			−0.824407	−	0.565998i	$-0.808491\pi$
$349$	−30.8024			−1.64881			−0.824407	+	0.565998i	$0.808491\pi$
$350$	−11.6643	−	1.96548i	−0.623483	−	0.105059i
$351$	−4.12607			−0.220233
$352$	−21.9326	+	15.9350i	−1.16901	+	0.849336i
$353$	4.20439	−	12.9398i	0.223777	−	0.688715i	−0.774637	−	0.632407i	$-0.782067\pi$
$353$	4.20439	−	12.9398i	0.223777	−	0.688715i	0.998413	−	0.0563079i	$-0.0179328\pi$
$354$	−12.1252	+	37.3175i	−0.644446	+	1.98340i
$355$	7.22227	+	6.23022i	0.383318	+	0.330666i
$356$	−2.66666	−	8.20714i	−0.141333	−	0.434977i
$357$	2.93518			0.155346
$358$	5.86226	+	18.0422i	0.309830	+	0.953558i
$359$	4.91743	+	3.57272i	0.259532	+	0.188561i	0.709941	−	0.704262i	$-0.248722\pi$
$359$	4.91743	+	3.57272i	0.259532	+	0.188561i	−0.450409	+	0.892822i	$0.648722\pi$
$360$	−3.59693	−	3.10285i	−0.189575	−	0.163535i
$361$	10.3334	−	7.50766i	0.543864	−	0.395140i
$362$	0.0937915	+	0.0681435i	0.00492957	+	0.00358154i
$363$	−6.57705	−	4.77851i	−0.345206	−	0.250807i
$364$	5.00288	−	3.63480i	0.262222	−	0.190515i
$365$	4.52434	+	19.2629i	0.236815	+	1.00827i
$366$	−12.1796	−	8.84901i	−0.636639	−	0.462545i
$367$	4.50195	+	13.8556i	0.235000	+	0.723255i	0.997121	+	0.0758213i	$0.0241579\pi$
$367$	4.50195	+	13.8556i	0.235000	+	0.723255i	−0.762122	+	0.647434i	$0.775842\pi$
$368$	5.74537			0.299498
$369$	−6.70454	−	20.6344i	−0.349024	−	1.07419i
$370$	−17.9033	+	42.6270i	−0.930749	+	2.21607i
$371$	0.130980	−	0.403114i	0.00680013	−	0.0209286i
$372$	−10.8407	+	33.3642i	−0.562064	+	1.72986i
$373$	1.32815	−	0.964957i	0.0687690	−	0.0499636i	−0.552870	−	0.833268i	$-0.686467\pi$
$373$	1.32815	−	0.964957i	0.0687690	−	0.0499636i	0.621639	+	0.783304i	$0.286467\pi$
$374$	7.15881			0.370173
$375$	−1.66246	−	26.0402i	−0.0858490	−	1.34471i
$376$	−7.29591			−0.376258
$377$	−6.53997	+	4.75157i	−0.336826	+	0.244718i
$378$	0.943778	−	2.90465i	0.0485427	−	0.149399i
$379$	−0.907832	+	2.79402i	−0.0466322	+	0.143519i	−0.971662	−	0.236377i	$-0.924040\pi$
$379$	−0.907832	+	2.79402i	−0.0466322	+	0.143519i	0.925029	+	0.379896i	$0.124040\pi$
$380$	3.32417	−	7.91472i	0.170527	−	0.406016i
$381$	2.66216	+	8.19329i	0.136387	+	0.419755i
$382$	21.3395			1.09182
$383$	1.78135	+	5.48243i	0.0910226	+	0.280139i	0.986197	−	0.165578i	$-0.0529489\pi$
$383$	1.78135	+	5.48243i	0.0910226	+	0.280139i	−0.895174	+	0.445717i	$0.852949\pi$
$384$	−12.7653	−	9.27451i	−0.651425	−	0.473288i
$385$	−2.44712	−	10.4189i	−0.124717	−	0.530997i
$386$	6.47451	−	4.70400i	0.329544	−	0.239427i
$387$	−4.74318	−	3.44612i	−0.241109	−	0.175176i
$388$	−8.10259	−	5.88688i	−0.411347	−	0.298861i
$389$	14.3494	−	10.4254i	0.727543	−	0.528591i	−0.161242	−	0.986915i	$-0.551550\pi$
$389$	14.3494	−	10.4254i	0.727543	−	0.528591i	0.888785	+	0.458324i	$0.151550\pi$
$390$	23.7569	+	20.4937i	1.20298	+	1.03774i
$391$	−0.986841	−	0.716982i	−0.0499067	−	0.0362593i
$392$	1.45371	+	4.47405i	0.0734233	+	0.225974i
$393$	24.7481			1.24838
$394$	−1.62775	−	5.00971i	−0.0820050	−	0.252385i
$395$	−17.3591	−	14.9746i	−0.873431	−	0.753456i
$396$	−4.42696	+	13.6248i	−0.222463	+	0.684671i
$397$	9.72913	−	29.9432i	0.488291	−	1.50281i	−0.338866	−	0.940835i	$-0.610043\pi$
$397$	9.72913	−	29.9432i	0.488291	−	1.50281i	0.827157	−	0.561971i	$-0.189957\pi$
$398$	0.407874	−	0.296338i	0.0204449	−	0.0148541i
$399$	7.32456			0.366687
$400$	−3.45466	−	23.2956i	−0.172733	−	1.16478i
$401$	−8.31242			−0.415102			−0.207551	−	0.978224i	$-0.566549\pi$
$401$	−8.31242			−0.415102			−0.207551	+	0.978224i	$0.566549\pi$
$402$	2.86254	−	2.07976i	0.142771	−	0.103729i
$403$	−9.64988	+	29.6993i	−0.480695	+	1.47943i
$404$	−6.87064	+	21.1456i	−0.341827	+	1.05204i
$405$	23.0705	+	1.93013i	1.14638	+	0.0959090i
$406$	−1.84906	−	5.69082i	−0.0917673	−	0.282431i
$407$	−41.8318			−2.07353
$408$	0.626162	+	1.92713i	0.0309996	+	0.0954071i
$409$	21.9643	+	15.9580i	1.08606	+	0.789072i	0.978730	−	0.205152i	$-0.0657687\pi$
$409$	21.9643	+	15.9580i	1.08606	+	0.789072i	0.107334	+	0.994223i	$0.465769\pi$
$410$	14.4425	−	34.3869i	0.713263	−	1.69825i
$411$	32.4367	−	23.5666i	1.59998	−	1.16246i
$412$	22.1090	+	16.0631i	1.08923	+	0.791372i
$413$	−9.09384	−	6.60706i	−0.447479	−	0.325112i
$414$	4.54213	−	3.30005i	0.223234	−	0.162189i
$415$	−12.5815	−	1.05260i	−0.617601	−	0.0516699i
$416$	18.4193	+	13.3824i	0.903081	+	0.656127i
$417$	−2.53011	−	7.78686i	−0.123900	−	0.381324i
$418$	17.8644			0.873775
$419$	−10.2919	−	31.6752i	−0.502792	−	1.54744i	−0.804451	−	0.594019i	$-0.797540\pi$
$419$	−10.2919	−	31.6752i	−0.502792	−	1.54744i	0.301659	−	0.953416i	$-0.402460\pi$
$420$	−8.63518	+	5.23329i	−0.421354	+	0.255358i
$421$	7.65480	−	23.5591i	0.373072	−	1.14820i	−0.571698	−	0.820464i	$-0.693715\pi$
$421$	7.65480	−	23.5591i	0.373072	−	1.14820i	0.944770	−	0.327734i	$-0.106285\pi$
$422$	−6.89413	+	21.2180i	−0.335601	+	1.03287i
$423$	−16.6346	+	12.0857i	−0.808802	+	0.587629i
$424$	0.292611			0.0142105
$425$	−2.31375	+	4.43244i	−0.112233	+	0.215005i
$426$	18.7266			0.907307
$427$	3.48913	−	2.53500i	0.168851	−	0.122677i
$428$	−4.32828	+	13.3211i	−0.209215	+	0.643899i
$429$	−8.77219	+	26.9980i	−0.423525	+	1.30348i
$430$	−2.30446	−	9.81152i	−0.111131	−	0.473153i
$431$	9.93861	+	30.5879i	0.478726	+	1.47337i	0.840866	+	0.541244i	$0.182046\pi$
$431$	9.93861	+	30.5879i	0.478726	+	1.47337i	−0.362140	+	0.932124i	$0.617954\pi$
$432$	6.08061			0.292553
$433$	−7.29675	−	22.4571i	−0.350660	−	1.07922i	−0.958484	−	0.285147i	$-0.907957\pi$
$433$	−7.29675	−	22.4571i	−0.350660	−	1.07922i	0.607824	−	0.794072i	$-0.292043\pi$
$434$	−18.7002	−	13.5865i	−0.897641	−	0.652174i
$435$	11.2883	−	6.84117i	0.541231	−	0.328009i
$436$	21.7679	−	15.8153i	1.04249	−	0.757416i
$437$	−2.46260	−	1.78918i	−0.117802	−	0.0855882i
$438$	31.4292	+	22.8347i	1.50175	+	1.09108i
$439$	−8.21454	+	5.96822i	−0.392059	+	0.284847i	−0.766299	−	0.642485i	$-0.777904\pi$
$439$	−8.21454	+	5.96822i	−0.392059	+	0.284847i	0.374240	+	0.927332i	$0.377904\pi$
$440$	6.31861	−	3.82935i	0.301228	−	0.182557i
$441$	10.7257	+	7.79270i	0.510749	+	0.371081i
$442$	−1.85783	−	5.71782i	−0.0883681	−	0.271969i
$443$	−9.96234			−0.473325			−0.236663	−	0.971592i	$-0.576054\pi$
$443$	−9.96234			−0.473325			−0.236663	+	0.971592i	$0.576054\pi$
$444$	12.1957	+	37.5346i	0.578784	+	1.78131i
$445$	2.86788	+	12.2104i	0.135951	+	0.578827i
$446$	−9.15526	+	28.1770i	−0.433514	+	1.33422i
$447$	−12.8625	+	39.5866i	−0.608374	+	1.87238i
$448$	−4.04931	+	2.94200i	−0.191312	+	0.138996i
$449$	34.6202			1.63383			0.816913	−	0.576761i	$-0.195683\pi$
$449$	34.6202			1.63383			0.816913	+	0.576761i	$0.195683\pi$
$450$	−16.1118	−	16.4326i	−0.759519	−	0.774640i
$451$	33.7454			1.58901
$452$	1.02354	−	0.743643i	0.0481431	−	0.0349780i
$453$	7.58941	−	23.3578i	0.356582	−	1.09745i
$454$	3.62071	−	11.1434i	0.169929	−	0.522986i
$455$	−7.68663	+	4.65842i	−0.360355	+	0.218390i
$456$	1.56255	+	4.80903i	0.0731730	+	0.225203i
$457$	−11.2014			−0.523979			−0.261990	−	0.965071i	$-0.584379\pi$
$457$	−11.2014			−0.523979			−0.261990	+	0.965071i	$0.584379\pi$
$458$	14.4647	+	44.5177i	0.675890	+	2.08018i
$459$	−1.04442	−	0.758818i	−0.0487495	−	0.0354186i
$460$	4.18159	+	0.349841i	0.194968	+	0.0163114i
$461$	−0.438802	+	0.318808i	−0.0204370	+	0.0148484i	−0.597957	−	0.801528i	$-0.704021\pi$
$461$	−0.438802	+	0.318808i	−0.0204370	+	0.0148484i	0.577520	+	0.816377i	$0.304021\pi$
$462$	−16.9994	−	12.3508i	−0.790884	−	0.574611i
$463$	31.8061	+	23.1085i	1.47816	+	1.07394i	0.978145	+	0.207923i	$0.0666704\pi$
$463$	31.8061	+	23.1085i	1.47816	+	1.07394i	0.500010	+	0.866020i	$0.333330\pi$
$464$	9.63797	−	7.00240i	0.447432	−	0.325078i
$465$	19.7447	−	47.0112i	0.915637	−	2.18009i
$466$	−17.9956	−	13.0746i	−0.833631	−	0.605668i
$467$	9.03487	+	27.8065i	0.418084	+	1.28673i	0.909463	+	0.415784i	$0.136493\pi$
$467$	9.03487	+	27.8065i	0.418084	+	1.28673i	−0.491379	+	0.870946i	$0.663507\pi$
$468$	12.0311			0.556139
$469$	0.313228	+	0.964017i	0.0144635	+	0.0445142i
$470$	−35.2228	−	2.94682i	−1.62471	−	0.135927i
$471$	5.60892	−	17.2625i	0.258445	−	0.795413i
$472$	2.39796	−	7.38015i	0.110375	−	0.339699i
$473$	7.37731	−	5.35993i	0.339209	−	0.246450i
$474$	−45.0104			−2.06739
$475$	−5.77382	+	11.0609i	−0.264921	+	0.507508i
$476$	1.93483			0.0886830
$477$	0.667150	−	0.484713i	0.0305467	−	0.0221935i
$478$	−2.79344	+	8.59731i	−0.127769	+	0.393232i
$479$	−10.5192	+	32.3747i	−0.480633	+	1.47924i	0.357574	+	0.933885i	$0.383604\pi$
$479$	−10.5192	+	32.3747i	−0.480633	+	1.47924i	−0.838207	+	0.545352i	$0.816396\pi$
$480$	−28.1490	−	24.2825i	−1.28482	−	1.10834i
$481$	10.8561	+	33.4115i	0.494994	+	1.52343i
$482$	31.7807			1.44757
$483$	1.10639	+	3.40511i	0.0503424	+	0.154938i
$484$	−4.33551	−	3.14993i	−0.197069	−	0.143179i
$485$	11.0225	+	9.50841i	0.500504	+	0.431755i
$486$	30.8786	−	22.4346i	1.40068	−	1.01765i
$487$	−22.4076	−	16.2800i	−1.01538	−	0.737719i	−0.0500518	−	0.998747i	$-0.515939\pi$
$487$	−22.4076	−	16.2800i	−1.01538	−	0.737719i	−0.965331	+	0.261028i	$0.915939\pi$
$488$	2.40872	+	1.75004i	0.109038	+	0.0792206i
$489$	−10.7309	+	7.79646i	−0.485268	+	0.352568i
$490$	5.21106	+	22.1867i	0.235412	+	1.00230i
$491$	−16.7870	−	12.1964i	−0.757585	−	0.550418i	0.140584	−	0.990069i	$-0.455102\pi$
$491$	−16.7870	−	12.1964i	−0.757585	−	0.550418i	−0.898169	+	0.439651i	$0.855102\pi$
$492$	−9.83821	−	30.2789i	−0.443541	−	1.36508i
$493$	−2.52930			−0.113914
$494$	−4.63610	−	14.2685i	−0.208588	−	0.641968i
$495$	8.06302	−	19.1977i	0.362406	−	0.862873i
$496$	14.2211	−	43.7679i	0.638544	−	1.96524i
$497$	−1.65777	+	5.10210i	−0.0743613	+	0.228861i
$498$	−20.0539	+	14.5700i	−0.898635	+	0.652897i
$499$	−6.57507			−0.294340			−0.147170	−	0.989111i	$-0.547017\pi$
$499$	−6.57507			−0.294340			−0.147170	+	0.989111i	$0.547017\pi$
$500$	−1.09587	−	17.1654i	−0.0490089	−	0.767659i
$501$	42.3978			1.89419
$502$	14.5111	−	10.5429i	0.647660	−	0.470553i
$503$	−7.73102	+	23.7936i	−0.344709	+	1.06091i	0.617030	+	0.786939i	$0.288336\pi$
$503$	−7.73102	+	23.7936i	−0.344709	+	1.06091i	−0.961739	+	0.273966i	$0.911664\pi$
$504$	0.825626	−	2.54101i	0.0367763	−	0.113186i
$505$	12.5138	−	29.7948i	0.556857	−	1.32585i
$506$	2.69844	+	8.30495i	0.119960	+	0.369200i
$507$	−6.49987			−0.288669
$508$	1.75486	+	5.40091i	0.0778595	+	0.239627i
$509$	27.9060	+	20.2749i	1.23691	+	0.898671i	0.997389	−	0.0722197i	$-0.0230083\pi$
$509$	27.9060	+	20.2749i	1.23691	+	0.898671i	0.239525	+	0.970890i	$0.423008\pi$
$510$	2.24458	+	9.55660i	0.0993919	+	0.423173i
$511$	−9.00363	+	6.54152i	−0.398297	+	0.289380i
$512$	−20.5278	−	14.9143i	−0.907209	−	0.659126i
$513$	−2.60629	−	1.89358i	−0.115071	−	0.0836036i
$514$	−19.8638	+	14.4319i	−0.876154	+	0.636563i
$515$	−30.0762	−	25.9449i	−1.32531	−	1.14327i
$516$	−6.96012	−	5.05682i	−0.306402	−	0.222614i
$517$	−9.88246	−	30.4151i	−0.434630	−	1.33765i
$518$	−26.0040			−1.14255
$519$	−0.186095	−	0.572742i	−0.00816867	−	0.0251406i
$520$	−4.69833	−	4.05296i	−0.206035	−	0.177734i
$521$	−10.1269	+	31.1674i	−0.443668	+	1.36547i	0.440271	+	0.897865i	$0.354882\pi$
$521$	−10.1269	+	31.1674i	−0.443668	+	1.36547i	−0.883938	+	0.467603i	$0.845118\pi$
$522$	3.59745	−	11.0718i	0.157456	−	0.484600i
$523$	16.7191	−	12.1471i	0.731076	−	0.531158i	−0.158828	−	0.987306i	$-0.550771\pi$
$523$	16.7191	−	12.1471i	0.731076	−	0.531158i	0.889904	+	0.456149i	$0.150771\pi$
$524$	16.3136			0.712664
$525$	13.1414	−	6.53352i	0.573536	−	0.285146i
$526$	46.3073			2.01909
$527$	−7.90458	+	5.74301i	−0.344329	+	0.250170i
$528$	12.9276	−	39.7871i	0.562602	−	1.73151i
$529$	−6.64760	+	20.4592i	−0.289026	+	0.889531i
$530$	1.41265	+	0.118186i	0.0613618	+	0.00513367i
$531$	−6.75797	−	20.7989i	−0.293271	−	0.902595i
$532$	4.82826			0.209331
$533$	−8.75750	−	26.9528i	−0.379330	−	1.16746i
$534$	19.9223	+	14.4744i	0.862124	+	0.626370i
$535$	7.88329	−	18.7698i	0.340825	−	0.811489i
$536$	−0.566116	+	0.411307i	−0.0244525	+	0.0177658i
$537$	−19.0417	−	13.8346i	−0.821711	−	0.597008i
$538$	−36.0458	−	26.1888i	−1.55404	−	1.12908i
$539$	−16.6823	+	12.1204i	−0.718557	+	0.522062i
$540$	4.42558	+	0.370254i	0.190447	+	0.0159332i
$541$	−15.2631	−	11.0893i	−0.656211	−	0.476765i	0.209170	−	0.977879i	$-0.432924\pi$
$541$	−15.2631	−	11.0893i	−0.656211	−	0.476765i	−0.865381	+	0.501114i	$0.832924\pi$
$542$	17.2291	+	53.0258i	0.740054	+	2.27765i
$543$	−0.143838			−0.00617266
$544$	2.20130	+	6.77491i	0.0943801	+	0.290472i
$545$	−33.4451	+	20.2692i	−1.43263	+	0.868235i
$546$	−5.45308	+	16.7829i	−0.233370	+	0.718240i
$547$	−5.62332	+	17.3068i	−0.240436	+	0.739985i	0.755918	+	0.654666i	$0.227191\pi$
$547$	−5.62332	+	17.3068i	−0.240436	+	0.739985i	−0.996354	+	0.0853188i	$0.972809\pi$
$548$	21.3819	−	15.5348i	0.913388	−	0.663615i
$549$	8.39081			0.358111
$550$	32.0514	−	15.9350i	1.36667	−	0.679472i
$551$	−6.31170			−0.268887
$552$	−1.99964	+	1.45282i	−0.0851103	+	0.0618362i
$553$	3.98454	−	12.2632i	0.169440	−	0.521483i
$554$	17.5206	−	53.9229i	0.744380	−	2.29096i
$555$	−13.1160	−	55.8430i	−0.556743	−	2.37040i
$556$	−1.66781	−	5.13300i	−0.0707310	−	0.217688i
$557$	−11.0068			−0.466372			−0.233186	−	0.972432i	$-0.574915\pi$
$557$	−11.0068			−0.466372			−0.233186	+	0.972432i	$0.574915\pi$
$558$	−13.8968	−	42.7701i	−0.588300	−	1.81060i
$559$	−6.19557	−	4.50135i	−0.262045	−	0.190387i
$560$	11.3278	−	6.86513i	0.478687	−	0.290105i
$561$	−7.18564	+	5.22067i	−0.303378	+	0.220417i
$562$	45.6074	+	33.1357i	1.92383	+	1.39775i
$563$	15.1774	+	11.0270i	0.639649	+	0.464732i	0.859730	−	0.510749i	$-0.170632\pi$
$563$	15.1774	+	11.0270i	0.639649	+	0.464732i	−0.220081	+	0.975482i	$0.570632\pi$
$564$	−24.4095	+	17.7346i	−1.02783	+	0.746760i
$565$	−1.57261	+	0.953066i	−0.0661600	+	0.0400958i
$566$	−28.6339	−	20.8037i	−1.20357	−	0.874446i
$567$	4.02375	+	12.3838i	0.168982	+	0.520072i
$568$	−3.70350			−0.155395
$569$	2.06764	+	6.36355i	0.0866800	+	0.266774i	0.984996	−	0.172576i	$-0.0552090\pi$
$569$	2.06764	+	6.36355i	0.0866800	+	0.266774i	−0.898316	+	0.439349i	$0.855209\pi$
$570$	5.60122	+	23.8479i	0.234609	+	0.998878i
$571$	−6.83824	+	21.0459i	−0.286172	+	0.880746i	0.699873	+	0.714267i	$0.253240\pi$
$571$	−6.83824	+	21.0459i	−0.286172	+	0.880746i	−0.986045	+	0.166479i	$0.946760\pi$
$572$	−5.78252	+	17.7968i	−0.241779	+	0.744120i
$573$	−21.4195	+	15.5621i	−0.894811	+	0.650118i
$574$	20.9772			0.875573
$575$	−6.01423	−	1.01342i	−0.250811	−	0.0422626i
$576$	−9.73796			−0.405748
$577$	−36.9245	+	26.8272i	−1.53719	+	1.11683i	−0.585118	+	0.810948i	$0.698952\pi$
$577$	−36.9245	+	26.8272i	−1.53719	+	1.11683i	−0.952069	+	0.305884i	$0.901048\pi$
$578$	0.581284	−	1.78901i	0.0241782	−	0.0744129i
$579$	−3.06830	+	9.44326i	−0.127514	+	0.392448i
$580$	7.44109	−	4.50961i	0.308974	−	0.187252i
$581$	−2.19435	−	6.75353i	−0.0910371	−	0.280183i
$582$	28.5801			1.18468
$583$	0.396348	+	1.21983i	0.0164151	+	0.0505203i
$584$	−6.21566	−	4.51594i	−0.257206	−	0.186871i
$585$	−17.4259	−	1.45789i	−0.720472	−	0.0602764i
$586$	−49.3563	+	35.8595i	−2.03889	+	1.48134i
$587$	7.50343	+	5.45156i	0.309700	+	0.225010i	0.731768	−	0.681554i	$-0.238696\pi$
$587$	7.50343	+	5.45156i	0.309700	+	0.225010i	−0.422068	+	0.906564i	$0.638696\pi$
$588$	15.7389	+	11.4350i	0.649061	+	0.471571i
$589$	−19.7254	+	14.3313i	−0.812770	+	0.590512i
$590$	14.5576	−	34.6610i	0.599326	−	1.42697i
$591$	5.28725	+	3.84141i	0.217489	+	0.158015i
$592$	−15.9986	−	49.2386i	−0.657539	−	2.02370i
$593$	22.3007			0.915779			0.457890	−	0.889009i	$-0.348606\pi$
$593$	22.3007			0.915779			0.457890	+	0.889009i	$0.348606\pi$
$594$	2.85589	+	8.78954i	0.117179	+	0.360639i
$595$	−2.80242	−	0.234457i	−0.114888	−	0.00961179i
$596$	−8.47878	+	26.0950i	−0.347304	+	1.06889i
$597$	−0.193293	+	0.594896i	−0.00791097	+	0.0243475i
$598$	5.93296	−	4.31055i	0.242617	−	0.176271i
$599$	7.87283			0.321675			0.160838	−	0.986981i	$-0.448580\pi$
$599$	7.87283			0.321675			0.160838	+	0.986981i	$0.448580\pi$
$600$	7.09310	+	7.23432i	0.289575	+	0.295340i
$601$	48.1275			1.96316			0.981581	−	0.191045i	$-0.0611877\pi$
$601$	48.1275			1.96316			0.981581	+	0.191045i	$0.0611877\pi$
$602$	4.58597	−	3.33191i	0.186910	−	0.135798i
$603$	−0.609403	+	1.87555i	−0.0248168	+	0.0763783i
$604$	5.00284	−	15.3972i	0.203563	−	0.626502i
$605$	5.89786	+	5.08773i	0.239782	+	0.206846i
$606$	−19.6062	−	60.3418i	−0.796449	−	2.45122i
$607$	−10.5450			−0.428010			−0.214005	−	0.976833i	$-0.568651\pi$
$607$	−10.5450			−0.428010			−0.214005	+	0.976833i	$0.568651\pi$
$608$	5.49321	+	16.9064i	0.222779	+	0.685644i
$609$	6.00610	+	4.36369i	0.243379	+	0.176826i
$610$	10.9219	+	9.42164i	0.442213	+	0.381471i
$611$	−21.7282	+	15.7865i	−0.879029	+	0.638652i
$612$	3.04541	+	2.21262i	0.123103	+	0.0894398i
$613$	1.93381	+	1.40500i	0.0781059	+	0.0567473i	0.626153	−	0.779700i	$-0.284629\pi$
$613$	1.93381	+	1.40500i	0.0781059	+	0.0567473i	−0.548047	+	0.836447i	$0.684629\pi$
$614$	11.6752	−	8.48254i	0.471173	−	0.342327i
$615$	10.5806	+	45.0482i	0.426650	+	1.81652i
$616$	3.36192	+	2.44258i	0.135455	+	0.0984142i
$617$	8.58521	+	26.4225i	0.345627	+	1.06373i	0.961247	+	0.275688i	$0.0889057\pi$
$617$	8.58521	+	26.4225i	0.345627	+	1.06373i	−0.615620	+	0.788043i	$0.711094\pi$
$618$	−77.9844			−3.13699
$619$	−3.70623	−	11.4066i	−0.148966	−	0.458470i	0.848534	−	0.529141i	$-0.177486\pi$
$619$	−3.70623	−	11.4066i	−0.148966	−	0.458470i	−0.997500	+	0.0706711i	$0.977486\pi$
$620$	13.0154	−	30.9892i	0.522712	−	1.24456i
$621$	0.486621	−	1.49766i	0.0195274	−	0.0600992i
$622$	−11.7444	+	36.1457i	−0.470909	+	1.44931i
$623$	−5.70721	+	4.14653i	−0.228655	+	0.166127i
$624$	−35.1333			−1.40646
$625$	−0.492779	+	24.9951i	−0.0197112	+	0.999806i
$626$	−7.48698			−0.299240
$627$	−17.9313	+	13.0279i	−0.716107	+	0.520282i
$628$	3.69733	−	11.3792i	0.147540	−	0.454080i
$629$	−3.39667	+	10.4539i	−0.135434	+	0.416824i
$630$	5.01223	−	11.9339i	0.199692	−	0.475459i
$631$	−2.11457	−	6.50797i	−0.0841796	−	0.259078i	0.900103	−	0.435676i	$-0.143491\pi$
$631$	−2.11457	−	6.50797i	−0.0841796	−	0.259078i	−0.984283	+	0.176598i	$0.943491\pi$
$632$	8.90155			0.354085
$633$	−8.55354	−	26.3251i	−0.339973	−	1.04633i
$634$	−23.3396	−	16.9572i	−0.926932	−	0.673455i
$635$	−1.88728	−	8.03534i	−0.0748945	−	0.318873i
$636$	0.978973	−	0.711266i	0.0388188	−	0.0282035i
$637$	14.0100	+	10.1789i	0.555097	+	0.403302i
$638$	14.6487	+	10.6429i	0.579947	+	0.421356i
$639$	−8.44393	+	6.13487i	−0.334037	+	0.242692i
$640$	11.4470	+	9.87467i	0.452484	+	0.390331i
$641$	−0.723341	−	0.525538i	−0.0285703	−	0.0207575i	0.573408	−	0.819270i	$-0.305621\pi$
$641$	−0.723341	−	0.525538i	−0.0285703	−	0.0207575i	−0.601979	+	0.798512i	$0.705621\pi$
$642$	−12.3513	−	38.0134i	−0.487467	−	1.50027i
$643$	−18.5678			−0.732243			−0.366122	−	0.930567i	$-0.619315\pi$
$643$	−18.5678			−0.732243			−0.366122	+	0.930567i	$0.619315\pi$
$644$	0.729316	+	2.24460i	0.0287391	+	0.0884498i
$645$	9.46829	+	8.16772i	0.372813	+	0.321604i
$646$	1.45056	−	4.46436i	0.0570714	−	0.175648i
$647$	13.0690	−	40.2224i	0.513797	−	1.58131i	−0.271662	−	0.962393i	$-0.587573\pi$
$647$	13.0690	−	40.2224i	0.513797	−	1.58131i	0.785460	−	0.618913i	$-0.212427\pi$
$648$	−7.27237	+	5.28368i	−0.285686	+	0.207563i
$649$	34.0144			1.33518
$650$	−21.0454	−	21.4644i	−0.825467	−	0.841901i
$651$	28.6785			1.12400
$652$	−7.07367	+	5.13933i	−0.277026	+	0.201272i
$653$	−7.15866	+	22.0321i	−0.280140	+	0.862182i	0.707674	+	0.706540i	$0.249745\pi$
$653$	−7.15866	+	22.0321i	−0.280140	+	0.862182i	−0.987813	+	0.155642i	$0.950255\pi$
$654$	−23.7268	+	73.0235i	−0.927790	+	2.85544i
$655$	−23.6287	−	1.97683i	−0.923249	−	0.0772412i
$656$	12.9060	+	39.7205i	0.503893	+	1.55082i
$657$	−21.6523			−0.844737
$658$	−6.14326	−	18.9070i	−0.239489	−	0.737072i
$659$	4.17841	+	3.03579i	0.162768	+	0.118258i	0.666187	−	0.745784i	$-0.267925\pi$
$659$	4.17841	+	3.03579i	0.162768	+	0.118258i	−0.503420	+	0.864042i	$0.667925\pi$
$660$	11.8316	−	28.1706i	0.460546	−	1.09654i
$661$	0.690050	−	0.501351i	0.0268398	−	0.0195003i	−0.574284	−	0.818656i	$-0.694720\pi$
$661$	0.690050	−	0.501351i	0.0268398	−	0.0195003i	0.601124	+	0.799156i	$0.294720\pi$
$662$	14.4910	+	10.5284i	0.563211	+	0.409196i
$663$	6.03460	+	4.38439i	0.234364	+	0.170276i
$664$	3.96598	−	2.88146i	0.153910	−	0.111822i
$665$	−6.99326	−	0.585072i	−0.271187	−	0.0226881i
$666$	−40.9300	−	29.7374i	−1.58601	−	1.15230i
$667$	−0.953393	−	2.93424i	−0.0369155	−	0.113614i
$668$	27.9481			1.08134
$669$	−11.3589	−	34.9592i	−0.439161	−	1.35160i
$670$	−2.89919	+	1.75703i	−0.112006	+	0.0678801i
$671$	−4.03288	+	12.4119i	−0.155687	+	0.479157i
$672$	6.46122	−	19.8856i	0.249247	−	0.767104i
$673$	41.3500	−	30.0425i	1.59393	−	1.15805i	0.695874	−	0.718164i	$-0.255017\pi$
$673$	41.3500	−	30.0425i	1.59393	−	1.15805i	0.898051	−	0.439891i	$-0.144983\pi$
$674$	−1.58173			−0.0609258
$675$	−6.36516	−	1.07255i	−0.244995	−	0.0412826i
$676$	−4.28463			−0.164793
$677$	24.6931	−	17.9406i	0.949034	−	0.689514i	−0.00154425	−	0.999999i	$-0.500492\pi$
$677$	24.6931	−	17.9406i	0.949034	−	0.689514i	0.950578	+	0.310485i	$0.100492\pi$
$678$	−1.11564	+	3.43360i	−0.0428461	+	0.131867i
$679$	−2.53006	+	7.78671i	−0.0970946	+	0.298827i
$680$	−0.443904	−	1.88998i	−0.0170229	−	0.0724773i
$681$	4.49222	+	13.8256i	0.172142	+	0.529799i
$682$	69.9459			2.67837
$683$	−2.90073	−	8.92754i	−0.110993	−	0.341603i	0.880097	−	0.474794i	$-0.157478\pi$
$683$	−2.90073	−	8.92754i	−0.110993	−	0.341603i	−0.991090	+	0.133191i	$0.957478\pi$
$684$	7.59962	+	5.52145i	0.290579	+	0.211118i
$685$	−32.8520	+	19.9097i	−1.25521	+	0.760710i
$686$	−23.7678	+	17.2683i	−0.907457	+	0.659306i
$687$	−46.9841	−	34.1359i	−1.79255	−	1.30237i
$688$	9.13043	+	6.63365i	0.348094	+	0.252905i
$689$	0.871435	−	0.633135i	0.0331990	−	0.0241205i
$690$	−10.2406	+	6.20621i	−0.389851	+	0.236266i
$691$	35.7646	+	25.9845i	1.36055	+	0.988497i	0.998410	+	0.0563735i	$0.0179538\pi$
$691$	35.7646	+	25.9845i	1.36055	+	0.988497i	0.362140	+	0.932124i	$0.382046\pi$
$692$	−0.122671	−	0.377544i	−0.00466327	−	0.0143521i
$693$	11.7113			0.444875
$694$	10.4434	+	32.1415i	0.396426	+	1.22007i
$695$	1.79366	+	7.63675i	0.0680376	+	0.289678i
$696$	−1.58375	+	4.87428i	−0.0600319	+	0.184759i
$697$	2.74007	−	8.43308i	0.103788	−	0.319426i
$698$	46.8757	−	34.0572i	1.77427	−	1.28908i
$699$	27.5979			1.04385
$700$	8.66262	−	4.30681i	0.327416	−	0.162782i
$701$	−52.0182			−1.96470			−0.982351	−	0.187049i	$-0.940108\pi$
$701$	−52.0182			−1.96470			−0.982351	+	0.187049i	$0.940108\pi$
$702$	6.27915	−	4.56207i	0.236991	−	0.172184i
$703$	−8.47618	+	26.0870i	−0.319685	+	0.983890i
$704$	4.68035	−	14.4046i	0.176397	−	0.542895i
$705$	37.5038	−	22.7289i	1.41248	−	0.856020i
$706$	7.90877	+	24.3407i	0.297650	+	0.916074i
$707$	18.1759			0.683575
$708$	−9.91662	−	30.5202i	−0.372689	−	1.14702i
$709$	−26.6543	−	19.3655i	−1.00102	−	0.727286i	−0.0387157	−	0.999250i	$-0.512327\pi$
$709$	−26.6543	−	19.3655i	−1.00102	−	0.727286i	−0.962307	+	0.271965i	$0.912327\pi$
$710$	−17.8796	−	1.49585i	−0.671008	−	0.0561381i
$711$	20.2954	−	14.7455i	0.761138	−	0.552999i
$712$	−3.93997	−	2.86256i	−0.147657	−	0.107279i
$713$	−9.64203	−	7.00534i	−0.361097	−	0.262352i
$714$	−4.46682	+	3.24534i	−0.167167	+	0.121454i
$715$	10.5320	−	25.0762i	0.393873	−	0.937795i
$716$	−12.5521	−	9.11961i	−0.469093	−	0.340816i
$717$	−3.46581	−	10.6667i	−0.129433	−	0.398354i
$718$	−11.4337			−0.426701
$719$	−1.28160	−	3.94437i	−0.0477957	−	0.147100i	0.924310	−	0.381642i	$-0.124641\pi$
$719$	−1.28160	−	3.94437i	−0.0477957	−	0.147100i	−0.972106	+	0.234541i	$0.924641\pi$
$720$	25.6806	+	2.14850i	0.957060	+	0.0800698i
$721$	6.90358	−	21.2470i	0.257103	−	0.791281i
$722$	−7.42462	+	22.8506i	−0.276316	+	0.850413i
$723$	−31.8997	+	23.1765i	−1.18636	+	0.861944i
$724$	−0.0948159			−0.00352380
$725$	−11.3241	+	5.63005i	−0.420568	+	0.209095i
$726$	15.2925			0.567560
$727$	24.8812	−	18.0772i	0.922792	−	0.670448i	−0.0214253	−	0.999770i	$-0.506820\pi$
$727$	24.8812	−	18.0772i	0.922792	−	0.670448i	0.944217	+	0.329323i	$0.106820\pi$
$728$	1.07844	−	3.31909i	0.0399695	−	0.123014i
$729$	−5.03529	+	15.4970i	−0.186492	+	0.573964i
$730$	−28.1836	−	24.3123i	−1.04312	−	0.899840i
$731$	−0.740436	−	2.27883i	−0.0273860	−	0.0842855i
$732$	12.3126			0.455088
$733$	−4.58975	−	14.1258i	−0.169526	−	0.521748i	0.829815	−	0.558039i	$-0.188446\pi$
$733$	−4.58975	−	14.1258i	−0.169526	−	0.521748i	−0.999341	+	0.0362904i	$0.988446\pi$
$734$	−22.1708	−	16.1081i	−0.818340	−	0.594559i
$735$	−21.4106	−	18.4696i	−0.789742	−	0.681263i
$736$	−7.02983	+	5.10747i	−0.259123	+	0.188264i
$737$	−2.48147	−	1.80289i	−0.0914060	−	0.0664103i
$738$	33.0179	+	23.9889i	1.21541	+	0.883045i
$739$	17.7594	−	12.9029i	0.653289	−	0.474642i	−0.211101	−	0.977464i	$-0.567705\pi$
$739$	17.7594	−	12.9029i	0.653289	−	0.474642i	0.864390	+	0.502822i	$0.167705\pi$
$740$	−8.64590	−	36.8110i	−0.317830	−	1.35320i
$741$	15.0590	+	10.9410i	0.553205	+	0.401927i
$742$	0.246383	+	0.758288i	0.00904499	+	0.0278376i
$743$	29.9173			1.09756			0.548781	−	0.835966i	$-0.315092\pi$
$743$	29.9173			1.09756			0.548781	+	0.835966i	$0.315092\pi$
$744$	6.11798	+	18.8292i	0.224296	+	0.690312i
$745$	15.4428	−	36.7686i	0.565780	−	1.34710i
$746$	−0.954284	+	2.93698i	−0.0349388	+	0.107531i
$747$	4.26924	−	13.1394i	0.156203	−	0.480745i
$748$	−4.73668	+	3.44140i	−0.173190	+	0.125830i
$749$	11.4502			0.418382
$750$	31.3218	+	37.7904i	1.14371	+	1.37991i
$751$	45.5070			1.66058			0.830288	−	0.557335i	$-0.188176\pi$
$751$	45.5070			1.66058			0.830288	+	0.557335i	$0.188176\pi$
$752$	32.0209	−	23.2646i	1.16768	−	0.848371i
$753$	−6.87686	+	21.1648i	−0.250607	+	0.771288i
$754$	4.69901	−	14.4621i	0.171128	−	0.526678i
$755$	−9.11190	+	21.6951i	−0.331616	+	0.789564i
$756$	0.771871	+	2.37558i	0.0280727	+	0.0863989i
$757$	0.187351			0.00680939			0.00340469	−	0.999994i	$-0.498916\pi$
$757$	0.187351			0.00680939			0.00340469	+	0.999994i	$0.498916\pi$
$758$	−1.70770	−	5.25576i	−0.0620265	−	0.190898i
$759$	−8.76506	−	6.36819i	−0.318151	−	0.231151i
$760$	−1.10773	−	4.71632i	−0.0401817	−	0.171079i
$761$	−20.4900	+	14.8868i	−0.742761	+	0.539647i	−0.893575	−	0.448915i	$-0.851811\pi$
$761$	−20.4900	+	14.8868i	−0.742761	+	0.539647i	0.150814	+	0.988562i	$0.451811\pi$
$762$	−13.1104	−	9.52526i	−0.474940	−	0.345064i
$763$	−17.7950	−	12.9288i	−0.644222	−	0.468055i
$764$	−14.1194	+	10.2584i	−0.510823	+	0.371135i
$765$	−4.14286	−	3.57379i	−0.149785	−	0.129211i
$766$	−8.77264	−	6.37369i	−0.316968	−	0.230291i
$767$	−8.82730	−	27.1676i	−0.318735	−	0.980967i
$768$	48.2575			1.74134
$769$	10.2787	+	31.6346i	0.370659	+	1.14077i	0.946361	+	0.323112i	$0.104729\pi$
$769$	10.2787	+	31.6346i	0.370659	+	1.14077i	−0.575701	+	0.817660i	$0.695271\pi$
$770$	15.2439	+	13.1500i	0.549353	+	0.473894i
$771$	9.41355	−	28.9719i	0.339021	−	1.04340i
$772$

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52182 + 1.10567i) q^{2} +(0.721199 - 2.21962i) q^{3} +(0.475405 - 1.46315i) q^{4} +(-0.865877 + 2.06162i) q^{5} +(1.35663 + 4.17527i) q^{6} -1.25766 q^{7} +(-0.268296 - 0.825730i) q^{8} +(-1.97954 - 1.43822i) q^{9} +(-0.961753 - 4.09478i) q^{10} +(3.07888 - 2.23694i) q^{11} +(-2.90477 - 2.11044i) q^{12} +(-2.58569 - 1.87861i) q^{13} +(1.91393 - 1.39055i) q^{14} +(3.95154 + 3.40875i) q^{15} +(3.81053 + 2.76852i) q^{16} +(-0.309017 - 0.951057i) q^{17} +4.60270 q^{18} +(-0.771132 - 2.37330i) q^{19} +(2.60480 + 2.24701i) q^{20} +(-0.907021 + 2.79152i) q^{21} +(-2.21220 + 6.80844i) q^{22} +(0.986841 - 0.716982i) q^{23} -2.02630 q^{24} +(-3.50052 - 3.57021i) q^{25} +6.01207 q^{26} +(1.04442 - 0.758818i) q^{27} +(-0.597897 + 1.84014i) q^{28} +(0.781596 - 2.40550i) q^{29} +(-9.78248 - 0.818425i) q^{30} +(-3.01928 - 9.29239i) q^{31} -7.12356 q^{32} +(-2.74467 - 8.44722i) q^{33} +(1.52182 + 1.10567i) q^{34} +(1.08898 - 2.59281i) q^{35} +(-3.04541 + 2.21262i) q^{36} +(-8.89261 - 6.46086i) q^{37} +(3.79761 + 2.75912i) q^{38} +(-6.03460 + 4.38439i) q^{39} +(1.93465 + 0.161857i) q^{40} +(7.17360 + 5.21193i) q^{41} +(-1.70617 - 5.25107i) q^{42} +2.39610 q^{43} +(-1.80925 - 5.56830i) q^{44} +(4.67909 - 2.83573i) q^{45} +(-0.709052 + 2.18224i) q^{46} +(2.59675 - 7.99198i) q^{47} +(8.89321 - 6.46129i) q^{48} -5.41830 q^{49} +(9.27463 + 1.56281i) q^{50} -2.33385 q^{51} +(-3.97793 + 2.89014i) q^{52} +(-0.104146 + 0.320528i) q^{53} +(-0.750425 + 2.30957i) q^{54} +(1.94577 + 8.28438i) q^{55} +(0.337425 + 1.03849i) q^{56} -5.82397 q^{57} +(1.47024 + 4.52493i) q^{58} +(7.23078 + 5.25347i) q^{59} +(6.86608 - 4.16114i) q^{60} +(-2.77431 + 2.01565i) q^{61} +(14.8691 + 10.8030i) q^{62} +(2.48958 + 1.80879i) q^{63} +(3.21973 - 2.33927i) q^{64} +(6.11186 - 3.70405i) q^{65} +(13.5167 + 9.82047i) q^{66} +(-0.249057 - 0.766518i) q^{67} -1.53844 q^{68} +(-0.879720 - 2.70750i) q^{69} +(1.20956 + 5.14984i) q^{70} +(1.31814 - 4.05683i) q^{71} +(-0.656479 + 2.02043i) q^{72} +(7.15905 - 5.20135i) q^{73} +20.6765 q^{74} +(-10.4491 + 5.19499i) q^{75} -3.83909 q^{76} +(-3.87218 + 2.81330i) q^{77} +(4.33590 - 13.3445i) q^{78} +(-3.16823 + 9.75080i) q^{79} +(-9.00707 + 5.45866i) q^{80} +(-3.19940 - 9.84675i) q^{81} -16.6796 q^{82} +(1.74479 + 5.36992i) q^{83} +(3.65321 + 2.65421i) q^{84} +(2.22828 + 0.186423i) q^{85} +(-3.64644 + 2.64929i) q^{86} +(-4.77562 - 3.46969i) q^{87} +(-2.67316 - 1.94216i) q^{88} +(4.53797 - 3.29703i) q^{89} +(-3.98537 + 9.48900i) q^{90} +(3.25191 + 2.36265i) q^{91} +(-0.579900 - 1.78475i) q^{92} -22.8031 q^{93} +(4.88468 + 15.0335i) q^{94} +(5.56054 + 0.465208i) q^{95} +(-5.13751 + 15.8116i) q^{96} +(2.01172 - 6.19144i) q^{97} +(8.24568 - 5.99084i) q^{98} -9.31197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

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Database

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