LMFDB - Embedded newform 400.2.be.a.381.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(21,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 12]))

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

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

chi := DirichletCharacter("400.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.be (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$58$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			381.11
Character	$\chi$	$=$	400.381
Dual form			400.2.be.a.21.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12780 + 0.853266i) q^{2} +(-1.06205 - 0.168212i) q^{3} +(0.543875 - 1.92463i) q^{4} +(-2.22886 + 0.179410i) q^{5} +(1.34131 - 0.716502i) q^{6} +0.652480i q^{7} +(1.02884 + 2.63467i) q^{8} +(-1.75351 - 0.569750i) q^{9} +O(q^{10})$	\(q+(-1.12780 + 0.853266i) q^{2} +(-1.06205 - 0.168212i) q^{3} +(0.543875 - 1.92463i) q^{4} +(-2.22886 + 0.179410i) q^{5} +(1.34131 - 0.716502i) q^{6} +0.652480i q^{7} +(1.02884 + 2.63467i) q^{8} +(-1.75351 - 0.569750i) q^{9} +(2.36063 - 2.10415i) q^{10} +(-0.0916387 - 0.0466923i) q^{11} +(-0.901370 + 1.95257i) q^{12} +(1.93430 - 0.985577i) q^{13} +(-0.556739 - 0.735868i) q^{14} +(2.39734 + 0.184379i) q^{15} +(-3.40840 - 2.09352i) q^{16} +(5.59874 + 4.06773i) q^{17} +(2.46376 - 0.853645i) q^{18} +(-0.711791 - 4.49407i) q^{19} +(-0.866923 + 4.38730i) q^{20} +(0.109755 - 0.692967i) q^{21} +(0.143191 - 0.0255325i) q^{22} +(4.10250 - 1.33298i) q^{23} +(-0.649493 - 2.97122i) q^{24} +(4.93562 - 0.799761i) q^{25} +(-1.34055 + 2.76201i) q^{26} +(4.64075 + 2.36458i) q^{27} +(1.25578 + 0.354868i) q^{28} +(4.07069 + 0.644733i) q^{29} +(-2.86105 + 1.83763i) q^{30} +(-0.494887 - 0.359556i) q^{31} +(5.63033 - 0.547196i) q^{32} +(0.0894708 + 0.0650044i) q^{33} +(-9.78513 + 0.189626i) q^{34} +(-0.117062 - 1.45429i) q^{35} +(-2.05025 + 3.06499i) q^{36} +(-0.284100 - 0.557578i) q^{37} +(4.63739 + 4.46107i) q^{38} +(-2.22012 + 0.721359i) q^{39} +(-2.76582 - 5.68773i) q^{40} +(9.57611 + 3.11147i) q^{41} +(0.467503 + 0.875180i) q^{42} +(1.67889 - 1.67889i) q^{43} +(-0.139705 + 0.150976i) q^{44} +(4.01055 + 0.955295i) q^{45} +(-3.48942 + 5.00386i) q^{46} +(-9.46218 + 6.87468i) q^{47} +(3.26774 + 2.79676i) q^{48} +6.57427 q^{49} +(-4.88400 + 5.11337i) q^{50} +(-5.26191 - 5.26191i) q^{51} +(-0.844850 - 4.25885i) q^{52} +(-0.984078 + 6.21322i) q^{53} +(-7.25147 + 1.29301i) q^{54} +(0.212627 + 0.0876295i) q^{55} +(-1.71907 + 0.671295i) q^{56} +4.89267i q^{57} +(-5.14106 + 2.74624i) q^{58} +(-4.79171 - 9.40426i) q^{59} +(1.65872 - 4.51372i) q^{60} +(2.34097 - 4.59440i) q^{61} +(0.864931 - 0.0167615i) q^{62} +(0.371751 - 1.14413i) q^{63} +(-5.88299 + 5.42129i) q^{64} +(-4.13447 + 2.54375i) q^{65} +(-0.156371 + 0.00303033i) q^{66} +(0.323177 + 2.04046i) q^{67} +(10.8739 - 8.56317i) q^{68} +(-4.58129 + 0.725604i) q^{69} +(1.37291 + 1.54026i) q^{70} +(1.38615 + 1.90787i) q^{71} +(-0.302972 - 5.20611i) q^{72} +(5.51294 - 1.79126i) q^{73} +(0.796171 + 0.386425i) q^{74} +(-5.37642 + 0.0191542i) q^{75} +(-9.03655 - 1.07428i) q^{76} +(0.0304658 - 0.0597924i) q^{77} +(1.88834 - 2.70790i) q^{78} +(8.71761 - 6.33371i) q^{79} +(7.97244 + 4.05465i) q^{80} +(-0.0560878 - 0.0407502i) q^{81} +(-13.4549 + 4.66185i) q^{82} +(-2.77551 - 17.5239i) q^{83} +(-1.27401 - 0.588126i) q^{84} +(-13.2086 - 8.06191i) q^{85} +(-0.460916 + 3.32599i) q^{86} +(-4.21483 - 1.36948i) q^{87} +(0.0287375 - 0.289477i) q^{88} +(2.66709 - 0.866592i) q^{89} +(-5.33823 + 2.34468i) q^{90} +(0.643069 + 1.26209i) q^{91} +(-0.334250 - 8.62076i) q^{92} +(0.465113 + 0.465113i) q^{93} +(4.80554 - 15.8270i) q^{94} +(2.39276 + 9.88894i) q^{95} +(-6.07174 - 0.365940i) q^{96} +(3.71648 - 2.70018i) q^{97} +(-7.41448 + 5.60960i) q^{98} +(0.134087 + 0.134087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) $ 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8	$ 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99}+O(q^{100}) $ 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8 - 14 * q^10 - 6 * q^11 + 10 * q^12 - 6 * q^13 + 6 * q^14 - 16 * q^15 - 6 * q^16 - 12 * q^17 - 24 * q^18 - 6 * q^19 - 22 * q^20 + 12 * q^21 + 10 * q^22 - 16 * q^24 + 4 * q^26 - 18 * q^27 + 18 * q^28 - 6 * q^29 - 6 * q^30 + 12 * q^31 - 36 * q^32 - 12 * q^33 - 30 * q^34 + 44 * q^35 - 82 * q^36 - 6 * q^37 - 76 * q^38 - 52 * q^40 - 10 * q^42 - 48 * q^43 + 36 * q^44 - 12 * q^45 - 14 * q^46 - 12 * q^47 - 116 * q^48 - 400 * q^49 + 10 * q^50 - 4 * q^51 + 32 * q^52 - 6 * q^53 - 30 * q^54 + 36 * q^56 + 26 * q^58 - 6 * q^59 + 48 * q^60 - 6 * q^61 - 34 * q^62 + 72 * q^63 - 24 * q^64 + 16 * q^65 + 92 * q^66 + 30 * q^67 + 28 * q^68 - 18 * q^69 + 60 * q^70 + 22 * q^72 + 28 * q^74 - 26 * q^75 - 76 * q^76 + 36 * q^77 + 14 * q^78 - 52 * q^79 - 34 * q^80 + 72 * q^81 + 56 * q^82 - 46 * q^83 + 112 * q^84 + 2 * q^85 - 46 * q^86 - 136 * q^88 - 42 * q^90 + 36 * q^91 - 4 * q^93 + 50 * q^94 - 40 * q^95 - 66 * q^96 - 12 * q^97 - 8 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−1.12780	+	0.853266i	−0.797477	+	0.603350i
$2$	−1.12780	+	0.853266i	−0.797477	+	0.603350i
$3$	−1.06205	−	0.168212i	−0.613176	−	0.0971175i	−0.157881	−	0.987458i	$-0.550466\pi$
$3$	−1.06205	−	0.168212i	−0.613176	−	0.0971175i	−0.455295	+	0.890341i	$0.650466\pi$
$4$	0.543875	−	1.92463i	0.271938	−	0.962315i
$5$	−2.22886	+	0.179410i	−0.996776	+	0.0802348i
$5$	−2.22886	+	0.179410i	−0.996776	+	0.0802348i
$6$	1.34131	−	0.716502i	0.547589	−	0.292511i
$7$			0.652480i			0.246614i	0.992369	+	0.123307i	$0.0393500\pi$
$7$			0.652480i			0.246614i	−0.992369	+	0.123307i	$0.960650\pi$
$8$	1.02884	+	2.63467i	0.363749	+	0.931497i
$9$	−1.75351	−	0.569750i	−0.584504	−	0.189917i
$10$	2.36063	−	2.10415i	0.746496	−	0.665390i
$11$	−0.0916387	−	0.0466923i	−0.0276301	−	0.0140782i	0.440121	−	0.897939i	$-0.354936\pi$
$11$	−0.0916387	−	0.0466923i	−0.0276301	−	0.0140782i	−0.467751	+	0.883860i	$0.654936\pi$
$12$	−0.901370	+	1.95257i	−0.260203	+	0.563658i
$13$	1.93430	−	0.985577i	0.536479	−	0.273350i	−0.164689	−	0.986346i	$-0.552662\pi$
$13$	1.93430	−	0.985577i	0.536479	−	0.273350i	0.701168	+	0.712996i	$0.252662\pi$
$14$	−0.556739	−	0.735868i	−0.148795	−	0.196669i
$15$	2.39734	+	0.184379i	0.618991	+	0.0476064i
$16$	−3.40840	−	2.09352i	−0.852100	−	0.523379i
$17$	5.59874	+	4.06773i	1.35789	+	0.986568i	0.998576	+	0.0533537i	$0.0169911\pi$
$17$	5.59874	+	4.06773i	1.35789	+	0.986568i	0.359319	+	0.933215i	$0.383009\pi$
$18$	2.46376	−	0.853645i	0.580714	−	0.201206i
$19$	−0.711791	−	4.49407i	−0.163296	−	1.03101i	−0.924134	−	0.382068i	$-0.875212\pi$
$19$	−0.711791	−	4.49407i	−0.163296	−	1.03101i	0.760838	−	0.648942i	$-0.224788\pi$
$20$	−0.866923	+	4.38730i	−0.193850	+	0.981031i
$21$	0.109755	−	0.692967i	0.0239506	−	0.151218i
$22$	0.143191	−	0.0255325i	0.0305285	−	0.00544356i
$23$	4.10250	−	1.33298i	0.855429	−	0.277946i	0.151711	−	0.988425i	$-0.451522\pi$
$23$	4.10250	−	1.33298i	0.855429	−	0.277946i	0.703718	+	0.710479i	$0.251522\pi$
$24$	−0.649493	−	2.97122i	−0.132577	−	0.606498i
$25$	4.93562	−	0.799761i	0.987125	−	0.159952i
$26$	−1.34055	+	2.76201i	−0.262904	+	0.541675i
$27$	4.64075	+	2.36458i	0.893113	+	0.455064i
$28$	1.25578	+	0.354868i	0.237321	+	0.0670637i
$29$	4.07069	+	0.644733i	0.755907	+	0.119724i	0.522481	−	0.852651i	$-0.325006\pi$
$29$	4.07069	+	0.644733i	0.755907	+	0.119724i	0.233426	+	0.972375i	$0.425006\pi$
$30$	−2.86105	+	1.83763i	−0.522354	+	0.335503i
$31$	−0.494887	−	0.359556i	−0.0888843	−	0.0645782i	0.542456	−	0.840084i	$-0.317495\pi$
$31$	−0.494887	−	0.359556i	−0.0888843	−	0.0645782i	−0.631340	+	0.775506i	$0.717495\pi$
$32$	5.63033	−	0.547196i	0.995311	−	0.0967316i
$33$	0.0894708	+	0.0650044i	0.0155749	+	0.0113158i
$34$	−9.78513	+	0.189626i	−1.67814	+	0.0325206i
$35$	−0.117062	−	1.45429i	−0.0197870	−	0.245819i
$36$	−2.05025	+	3.06499i	−0.341708	+	0.510831i
$37$	−0.284100	−	0.557578i	−0.0467058	−	0.0916653i	0.866474	−	0.499222i	$-0.166381\pi$
$37$	−0.284100	−	0.557578i	−0.0467058	−	0.0916653i	−0.913180	+	0.407557i	$0.866381\pi$
$38$	4.63739	+	4.46107i	0.752285	+	0.723682i
$39$	−2.22012	+	0.721359i	−0.355503	+	0.115510i
$40$	−2.76582	−	5.68773i	−0.437314	−	0.899309i
$41$	9.57611	+	3.11147i	1.49554	+	0.485929i	0.938713	−	0.344701i	$-0.112020\pi$
$41$	9.57611	+	3.11147i	1.49554	+	0.485929i	0.556824	+	0.830630i	$0.312020\pi$
$42$	0.467503	+	0.875180i	0.0721373	+	0.135043i
$43$	1.67889	−	1.67889i	0.256028	−	0.256028i	−0.567408	−	0.823437i	$-0.692054\pi$
$43$	1.67889	−	1.67889i	0.256028	−	0.256028i	0.823437	+	0.567408i	$0.192054\pi$
$44$	−0.139705	+	0.150976i	−0.0210614	+	0.0227605i
$45$	4.01055	+	0.955295i	0.597857	+	0.142407i
$46$	−3.48942	+	5.00386i	−0.514486	+	0.737779i
$47$	−9.46218	+	6.87468i	−1.38020	+	1.00277i	−0.383340	+	0.923607i	$0.625226\pi$
$47$	−9.46218	+	6.87468i	−1.38020	+	1.00277i	−0.996861	+	0.0791672i	$0.974774\pi$
$48$	3.26774	+	2.79676i	0.471658	+	0.403677i
$49$	6.57427			0.939181
$50$	−4.88400	+	5.11337i	−0.690702	+	0.723140i
$51$	−5.26191	−	5.26191i	−0.736815	−	0.736815i
$52$	−0.844850	−	4.25885i	−0.117160	−	0.590596i
$53$	−0.984078	+	6.21322i	−0.135173	+	0.853452i	0.823162	+	0.567807i	$0.192208\pi$
$53$	−0.984078	+	6.21322i	−0.135173	+	0.853452i	−0.958335	+	0.285645i	$0.907792\pi$
$54$	−7.25147	+	1.29301i	−0.986800	+	0.175957i
$55$	0.212627	+	0.0876295i	0.0286706	+	0.0118160i
$56$	−1.71907	+	0.671295i	−0.229720	+	0.0897056i
$57$			4.89267i			0.648049i
$58$	−5.14106	+	2.74624i	−0.675054	+	0.360600i
$59$	−4.79171	−	9.40426i	−0.623828	−	1.22433i	−0.959329	−	0.282291i	$-0.908906\pi$
$59$	−4.79171	−	9.40426i	−0.623828	−	1.22433i	0.335501	−	0.942040i	$-0.391094\pi$
$60$	1.65872	−	4.51372i	0.214139	−	0.582718i
$61$	2.34097	−	4.59440i	0.299730	−	0.588253i	−0.691195	−	0.722668i	$-0.742915\pi$
$61$	2.34097	−	4.59440i	0.299730	−	0.588253i	0.990925	+	0.134415i	$0.0429155\pi$
$62$	0.864931	−	0.0167615i	0.109846	−	0.00212872i
$63$	0.371751	−	1.14413i	0.0468362	−	0.144147i
$64$	−5.88299	+	5.42129i	−0.735374	+	0.677662i
$65$	−4.13447	+	2.54375i	−0.512817	+	0.315513i
$66$	−0.156371	+	0.00303033i	−0.0192480	+	0.000373008i
$67$	0.323177	+	2.04046i	0.0394824	+	0.249282i	0.999533	−	0.0305429i	$-0.00972363\pi$
$67$	0.323177	+	2.04046i	0.0394824	+	0.249282i	−0.960051	+	0.279825i	$0.909724\pi$
$68$	10.8739	−	8.56317i	1.31865	−	1.03844i
$69$	−4.58129	+	0.725604i	−0.551522	+	0.0873525i
$70$	1.37291	+	1.54026i	0.164095	+	0.184096i
$71$	1.38615	+	1.90787i	0.164505	+	0.226422i	0.883309	−	0.468791i	$-0.155310\pi$
$71$	1.38615	+	1.90787i	0.164505	+	0.226422i	−0.718804	+	0.695213i	$0.755310\pi$
$72$	−0.302972	−	5.20611i	−0.0357055	−	0.613546i
$73$	5.51294	−	1.79126i	0.645241	−	0.209652i	0.0319264	−	0.999490i	$-0.489836\pi$
$73$	5.51294	−	1.79126i	0.645241	−	0.209652i	0.613315	+	0.789839i	$0.289836\pi$
$74$	0.796171	+	0.386425i	0.0925530	+	0.0449210i
$75$	−5.37642	+	0.0191542i	−0.620815	+	0.00221174i
$76$	−9.03655	−	1.07428i	−1.03656	−	0.123228i
$77$	0.0304658	−	0.0597924i	0.00347190	−	0.00681398i
$78$	1.88834	−	2.70790i	0.213812	−	0.306609i
$79$	8.71761	−	6.33371i	0.980807	−	0.712598i	0.0229183	−	0.999737i	$-0.492704\pi$
$79$	8.71761	−	6.33371i	0.980807	−	0.712598i	0.957889	+	0.287139i	$0.0927042\pi$
$80$	7.97244	+	4.05465i	0.891346	+	0.453324i
$81$	−0.0560878	−	0.0407502i	−0.00623198	−	0.00452780i
$82$	−13.4549	+	4.66185i	−1.48584	+	0.514815i
$83$	−2.77551	−	17.5239i	−0.304652	−	1.92350i	−0.377197	−	0.926133i	$-0.623112\pi$
$83$	−2.77551	−	17.5239i	−0.304652	−	1.92350i	0.0725447	−	0.997365i	$-0.476888\pi$
$84$	−1.27401	−	0.588126i	−0.139006	−	0.0641698i
$85$	−13.2086	−	8.06191i	−1.43267	−	0.874437i
$86$	−0.460916	+	3.32599i	−0.0497019	+	0.358651i
$87$	−4.21483	−	1.36948i	−0.451877	−	0.146824i
$88$	0.0287375	−	0.289477i	0.00306343	−	0.0308583i
$89$	2.66709	−	0.866592i	0.282711	−	0.0918585i	−0.164229	−	0.986422i	$-0.552514\pi$
$89$	2.66709	−	0.866592i	0.282711	−	0.0918585i	0.446940	+	0.894564i	$0.352514\pi$
$90$	−5.33823	+	2.34468i	−0.562698	+	0.247151i
$91$	0.643069	+	1.26209i	0.0674119	+	0.132303i
$92$	−0.334250	−	8.62076i	−0.0348479	−	0.898776i
$93$	0.465113	+	0.465113i	0.0482300	+	0.0482300i
$94$	4.80554	−	15.8270i	0.495654	−	1.63243i
$95$	2.39276	+	9.88894i	0.245492	+	1.01458i
$96$	−6.07174	−	0.365940i	−0.619695	−	0.0373486i
$97$	3.71648	−	2.70018i	0.377352	−	0.274162i	−0.382901	−	0.923789i	$-0.625075\pi$
$97$	3.71648	−	2.70018i	0.377352	−	0.274162i	0.760253	+	0.649627i	$0.225075\pi$
$98$	−7.41448	+	5.60960i	−0.748975	+	0.566655i
$99$	0.134087	+	0.134087i	0.0134762	+	0.0134762i
$100$	1.14512	−	9.93422i	0.114512	−	0.993422i
$101$	−8.91969	+	8.91969i	−0.887542	+	0.887542i	−0.994287	−	0.106744i	$-0.965957\pi$
$101$	−8.91969	+	8.91969i	−0.887542	+	0.887542i	0.106744	+	0.994287i	$0.465957\pi$
$102$	10.4242	+	1.44459i	1.03215	+	0.143035i
$103$	−7.11610	−	9.79446i	−0.701170	−	0.965077i	−0.999942	−	0.0107529i	$-0.996577\pi$
$103$	−7.11610	−	9.79446i	−0.701170	−	0.965077i	0.298772	−	0.954324i	$-0.403423\pi$
$104$	4.58675	+	4.08226i	0.449768	+	0.400298i
$105$	−0.120303	+	1.56422i	−0.0117404	+	0.152652i
$106$	−4.19168	−	7.84697i	−0.407132	−	0.762165i
$107$	−2.13231	+	2.13231i	−0.206138	+	0.206138i	−0.802624	−	0.596486i	$-0.796563\pi$
$107$	−2.13231	+	2.13231i	−0.206138	+	0.206138i	0.596486	+	0.802624i	$0.296563\pi$
$108$	7.07493	−	7.64569i	0.680786	−	0.735707i
$109$	−1.92627	+	0.981484i	−0.184503	+	0.0940091i	−0.543802	−	0.839213i	$-0.683016\pi$
$109$	−1.92627	+	0.981484i	−0.184503	+	0.0940091i	0.359299	+	0.933222i	$0.383016\pi$
$110$	−0.314572	+	0.0825985i	−0.0299933	+	0.00787545i
$111$	0.207938	+	0.639966i	0.0197366	+	0.0607429i
$112$	1.36598	−	2.22391i	0.129073	−	0.210140i
$113$	−1.16422	+	3.58311i	−0.109521	+	0.337071i	−0.990765	−	0.135591i	$-0.956707\pi$
$113$	−1.16422	+	3.58311i	−0.109521	+	0.337071i	0.881244	+	0.472662i	$0.156707\pi$
$114$	−4.17474	−	5.51796i	−0.391001	−	0.516804i
$115$	−8.90473	+	3.70706i	−0.830371	+	0.345685i
$116$	3.45482	−	7.48391i	0.320772	−	0.694863i
$117$	−3.95336	+	0.626150i	−0.365488	+	0.0578876i
$118$	13.4284	+	6.51755i	1.23619	+	0.599989i
$119$	−2.65411	+	3.65307i	−0.243302	+	0.334876i
$120$	1.98070	+	6.50590i	0.180812	+	0.593905i
$121$	−6.45942	−	8.89063i	−0.587220	−	0.808239i
$122$	1.28010	+	7.17905i	0.115895	+	0.649960i
$123$	−9.64693	−	4.91536i	−0.869835	−	0.443203i
$124$	−0.961169	+	0.756920i	−0.0863155	+	0.0679734i
$125$	−10.8573	+	2.66806i	−0.971109	+	0.238638i
$126$	0.556986	+	1.60756i	0.0496203	+	0.143212i
$127$	5.45447	+	16.7871i	0.484006	+	1.48962i	0.833415	+	0.552647i	$0.186382\pi$
$127$	5.45447	+	16.7871i	0.484006	+	1.48962i	−0.349409	+	0.936970i	$0.613618\pi$
$128$	2.00905	−	11.1339i	0.177576	−	0.984107i
$129$	−2.06548	+	1.50066i	−0.181855	+	0.132125i
$130$	2.49237	−	6.39664i	0.218595	−	0.561022i
$131$	0.485546	+	3.06561i	0.0424223	+	0.267844i	0.999778	−	0.0210678i	$-0.00670657\pi$
$131$	0.485546	+	3.06561i	0.0424223	+	0.267844i	−0.957356	+	0.288912i	$0.906707\pi$
$132$	0.173770	−	0.136844i	0.0151248	−	0.0119107i
$133$	2.93229	−	0.464429i	0.254262	−	0.0402711i
$134$	−2.10553	−	2.02548i	−0.181890	−	0.174975i
$135$	−10.7678	−	4.43772i	−0.926746	−	0.381938i
$136$	−4.95693	+	18.9359i	−0.425053	+	1.62374i
$137$	3.03020	+	0.984572i	0.258888	+	0.0841177i	0.435585	−	0.900148i	$-0.356541\pi$
$137$	3.03020	+	0.984572i	0.258888	+	0.0841177i	−0.176698	+	0.984265i	$0.556541\pi$
$138$	4.54765	−	4.72739i	0.387122	−	0.402422i
$139$	13.9102	+	7.08759i	1.17985	+	0.601161i	0.930156	−	0.367164i	$-0.119671\pi$
$139$	13.9102	+	7.08759i	1.17985	+	0.601161i	0.249690	+	0.968326i	$0.419671\pi$
$140$	−2.86263	−	0.565650i	−0.241936	−	0.0478061i
$141$	11.2057	−	5.70960i	0.943693	−	0.480835i
$142$	−3.19122	−	0.968946i	−0.267801	−	0.0813121i
$143$	−0.223276			−0.0186713
$144$	4.78388	+	5.61294i	0.398657	+	0.467745i
$145$	−9.18865	−	0.706696i	−0.763076	−	0.0586879i
$146$	−4.68908	+	6.72419i	−0.388071	+	0.556498i
$147$	−6.98221	−	1.10587i	−0.575883	−	0.0912109i
$148$	−1.22765	+	0.243535i	−0.100912	+	0.0200184i
$149$	11.9059	−	11.9059i	0.975371	−	0.975371i	−0.0243331	−	0.999704i	$-0.507746\pi$
$149$	11.9059	−	11.9059i	0.975371	−	0.975371i	0.999704	+	0.0243331i	$0.00774624\pi$
$150$	6.04719	−	4.60911i	0.493751	−	0.376333i
$151$		−	3.09090i		−	0.251534i	−0.992060	−	0.125767i	$-0.959861\pi$
$151$		−	3.09090i		−	0.251534i	0.992060	−	0.125767i	$-0.0401391\pi$
$152$	11.1081	−	6.49900i	0.900984	−	0.527138i
$153$	−7.49987	−	10.3227i	−0.606329	−	0.834540i
$154$	0.0166595	+	0.0934294i	0.00134246	+	0.00752876i
$155$	1.16754	+	0.712612i	0.0937791	+	0.0572384i
$156$	0.180883	+	4.66523i	0.0144823	+	0.373517i
$157$	11.8964	+	11.8964i	0.949438	+	0.949438i	0.998782	−	0.0493436i	$-0.0157129\pi$
$157$	11.8964	+	11.8964i	0.949438	+	0.949438i	−0.0493436	+	0.998782i	$0.515713\pi$
$158$	−4.42740	+	14.5816i	−0.352225	+	1.16005i
$159$	2.09028	−	6.43323i	0.165770	−	0.510188i
$160$	−12.4510	+	2.22976i	−0.984340	+	0.176278i
$161$	0.869744	+	2.67680i	0.0685454	+	0.210961i
$162$	0.0980267	−	0.00189966i	0.00770170	−	0.000149252i
$163$	9.22936	−	4.70259i	0.722899	−	0.368336i	−0.0535078	−	0.998567i	$-0.517040\pi$
$163$	9.22936	−	4.70259i	0.722899	−	0.368336i	0.776407	+	0.630232i	$0.217040\pi$
$164$	11.1966	−	16.7382i	0.874310	−	1.30704i
$165$	−0.211080	−	0.128834i	−0.0164326	−	0.0100297i
$166$	18.0828	+	17.3952i	1.40350	+	1.35013i
$167$	−3.20629	+	4.41308i	−0.248110	+	0.341495i	−0.914848	−	0.403798i	$-0.867690\pi$
$167$	−3.20629	+	4.41308i	−0.248110	+	0.341495i	0.666738	+	0.745292i	$0.267690\pi$
$168$	1.93866	−	0.423781i	0.149571	−	0.0326954i
$169$	−4.87104	+	6.70441i	−0.374695	+	0.515724i
$170$	21.7756	−	2.17820i	1.67012	−	0.167061i
$171$	−1.31236	+	8.28595i	−0.100359	+	0.633642i
$172$	−2.31813	−	4.14434i	−0.176756	−	0.316003i
$173$	−8.84947	+	17.3681i	−0.672813	+	1.32047i	0.261910	+	0.965092i	$0.415648\pi$
$173$	−8.84947	+	17.3681i	−0.672813	+	1.32047i	−0.934723	+	0.355378i	$0.884352\pi$
$174$	5.92202	−	2.05186i	0.448947	−	0.155551i
$175$	0.521828	+	3.22040i	0.0394465	+	0.243439i
$176$	0.214590	+	0.350993i	0.0161754	+	0.0264571i
$177$	3.50713	+	10.7938i	0.263612	+	0.811314i
$178$	−2.26852	+	3.25308i	−0.170033	+	0.243829i
$179$	20.8704	+	3.30554i	1.55992	+	0.247068i	0.875937	−	0.482426i	$-0.160244\pi$
$179$	20.8704	+	3.30554i	1.55992	+	0.247068i	0.683987	+	0.729494i	$0.260244\pi$
$180$	4.01983	−	7.19926i	0.299620	−	0.536601i
$181$	−7.82619	+	1.23955i	−0.581716	+	0.0921348i	−0.440356	−	0.897823i	$-0.645148\pi$
$181$	−7.82619	+	1.23955i	−0.581716	+	0.0921348i	−0.141361	+	0.989958i	$0.545148\pi$
$182$	−1.80216	−	0.874684i	−0.133585	−	0.0648359i
$183$	−3.25906	+	4.48571i	−0.240917	+	0.331594i
$184$	7.73277	+	9.43731i	0.570067	+	0.695728i
$185$	0.733255	+	1.19179i	0.0539100	+	0.0876223i
$186$	−0.921421	−	0.127691i	−0.0675619	−	0.00936273i
$187$	−0.323131	−	0.634179i	−0.0236296	−	0.0463758i
$188$	8.08496	+	21.9502i	0.589656	+	1.60088i
$189$	−1.54284	+	3.02800i	−0.112225	+	0.220254i
$190$	−11.1365	−	9.11111i	−0.807924	−	0.660989i
$191$	3.16158	−	9.73033i	0.228764	−	0.704062i	−0.769124	−	0.639100i	$-0.779307\pi$
$191$	3.16158	−	9.73033i	0.228764	−	0.704062i	0.997888	−	0.0649627i	$-0.0206928\pi$
$192$	7.15997	−	4.76810i	0.516726	−	0.344108i
$193$	5.96531			0.429392			0.214696	−	0.976681i	$-0.431124\pi$
$193$	5.96531			0.429392			0.214696	+	0.976681i	$0.431124\pi$
$194$	−1.88748	+	6.21642i	−0.135513	+	0.446313i
$195$	4.81891	−	2.00612i	0.345089	−	0.143661i
$196$	3.57558	−	12.6530i	0.255399	−	0.903788i
$197$	1.71490	−	10.8275i	0.122182	−	0.771425i	−0.848169	−	0.529725i	$-0.822295\pi$
$197$	1.71490	−	10.8275i	0.122182	−	0.771425i	0.970351	−	0.241700i	$-0.0777049\pi$
$198$	−0.265635	−	0.0368117i	−0.0188778	−	0.00261609i
$199$			18.0887i			1.28227i	0.767427	+	0.641136i	$0.221537\pi$
$199$			18.0887i			1.28227i	−0.767427	+	0.641136i	$0.778463\pi$
$200$	7.18506	+	12.1809i	0.508060	+	0.861321i
$201$		−	2.22144i		−	0.156688i
$202$	2.44878	−	17.6705i	0.172296	−	1.24329i
$203$	−0.420675	+	2.65604i	−0.0295256	+	0.186417i
$204$	−12.9891	+	7.26541i	−0.909416	+	0.508680i
$205$	−21.9020	−	5.21697i	−1.52970	−	0.364369i
$206$	16.3828	+	4.97430i	1.14145	+	0.346576i
$207$	−7.95324			−0.552788
$208$	−8.65620	−	0.690259i	−0.600199	−	0.0478608i
$209$	−0.144611	+	0.445066i	−0.0100029	+	0.0307859i
$210$	−1.19901	−	1.86678i	−0.0827399	−	0.128820i
$211$	−4.35339	+	8.54401i	−0.299700	+	0.588194i	−0.990920	−	0.134450i	$-0.957073\pi$
$211$	−4.35339	+	8.54401i	−0.299700	+	0.588194i	0.691221	+	0.722644i	$0.257073\pi$
$212$	11.4229	+	5.27320i	0.784531	+	0.362165i
$213$	−1.15123	−	2.25942i	−0.0788812	−	0.154813i
$214$	0.585396	−	4.22425i	0.0400169	−	0.288764i
$215$	−3.44080	+	4.04322i	−0.234660	+	0.275745i
$216$	−1.45532	+	14.6596i	−0.0990220	+	0.997461i
$217$	0.234603	−	0.322904i	0.0159259	−	0.0219201i
$218$	1.33499	−	2.75054i	0.0904166	−	0.186290i
$219$	−6.15634	+	0.975069i	−0.416007	+	0.0658890i
$220$	0.284297	−	0.361569i	0.0191673	−	0.0243769i
$221$	14.8387	+	2.35022i	0.998161	+	0.158093i
$222$	−0.780573	−	0.544329i	−0.0523886	−	0.0365330i
$223$	6.01964	+	18.5265i	0.403105	+	1.24063i	0.922468	+	0.386075i	$0.126169\pi$
$223$	6.01964	+	18.5265i	0.403105	+	1.24063i	−0.519363	+	0.854554i	$0.673831\pi$
$224$	0.357035	+	3.67367i	0.0238554	+	0.245458i
$225$	−9.11034	−	1.40968i	−0.607356	−	0.0939789i
$226$	−1.74433	−	5.03444i	−0.116031	−	0.334886i
$227$	5.50737	−	10.8088i	0.365537	−	0.717407i	−0.632845	−	0.774279i	$-0.718113\pi$
$227$	5.50737	−	10.8088i	0.365537	−	0.717407i	0.998381	+	0.0568723i	$0.0181128\pi$
$228$	9.41657	+	2.66100i	0.623628	+	0.176229i
$229$	−0.529703	+	3.34441i	−0.0350038	+	0.221005i	−0.998989	−	0.0449498i	$-0.985687\pi$
$229$	−0.529703	+	3.34441i	−0.0350038	+	0.221005i	0.963985	+	0.265955i	$0.0856872\pi$
$230$	6.87967	−	11.7789i	0.453632	−	0.776680i
$231$	−0.0424140	+	0.0583779i	−0.00279064	+	0.00384099i
$232$	2.48941	+	11.3882i	0.163438	+	0.747675i
$233$	8.42590	−	11.5973i	0.551999	−	0.759761i	−0.438283	−	0.898837i	$-0.644413\pi$
$233$	8.42590	−	11.5973i	0.551999	−	0.759761i	0.990282	+	0.139076i	$0.0444132\pi$
$234$	3.92433	−	4.07944i	0.256542	−	0.266681i
$235$	19.8565	−	17.0203i	1.29529	−	1.11028i
$236$	−20.7058	+	4.10752i	−1.34783	+	0.267377i
$237$	−10.3240	+	5.26032i	−0.670613	+	0.341694i
$238$	−0.123727	−	6.38460i	−0.00802005	−	0.413852i
$239$	−3.49834	−	10.7668i	−0.226289	−	0.696445i	−0.998158	−	0.0606639i	$-0.980678\pi$
$239$	−3.49834	−	10.7668i	−0.226289	−	0.696445i	0.771870	−	0.635781i	$-0.219322\pi$
$240$	−7.78510	−	5.64731i	−0.502526	−	0.364533i
$241$	7.70351	−	23.7090i	0.496227	−	1.52723i	−0.318810	−	0.947819i	$-0.603283\pi$
$241$	7.70351	−	23.7090i	0.496227	−	1.52723i	0.815036	−	0.579410i	$-0.196717\pi$
$242$	14.8710	+	4.51527i	0.955945	+	0.290253i
$243$	−10.9961	−	10.9961i	−0.705397	−	0.705397i
$244$	−7.56933	−	7.00428i	−0.484577	−	0.448403i
$245$	−14.6531	+	1.17949i	−0.936153	+	0.0753550i
$246$	15.0739	−	2.68785i	0.961079	−	0.171371i
$247$	−5.80607	−	7.99137i	−0.369431	−	0.508479i
$248$	0.438155	−	1.67379i	0.0278229	−	0.106286i
$249$			19.0782i			1.20903i
$250$	9.96835	−	12.2732i	0.630454	−	0.776227i
$251$	−11.0428	+	11.0428i	−0.697016	+	0.697016i	−0.963766	−	0.266750i	$-0.914050\pi$
$251$	−11.0428	+	11.0428i	−0.697016	+	0.697016i	0.266750	+	0.963766i	$0.414050\pi$
$252$	−1.99984	−	1.33775i	−0.125978	−	0.0842702i
$253$	−0.438187	−	0.0694021i	−0.0275486	−	0.00436327i
$254$	−20.4754	−	14.2785i	−1.28474	−	0.895910i
$255$	12.6721	+	10.7840i	0.793558	+	0.675321i
$256$	7.23437	+	14.2711i	0.452148	+	0.891943i
$257$	22.9546			1.43187			0.715934	−	0.698168i	$-0.246001\pi$
$257$	22.9546			1.43187			0.715934	+	0.698168i	$0.246001\pi$
$258$	1.04899	−	3.45484i	0.0653073	−	0.215089i
$259$	0.363809	−	0.185370i	0.0226060	−	0.0115183i
$260$	2.64713	+	9.34080i	0.164168	+	0.579292i
$261$	−6.77066	−	3.44982i	−0.419093	−	0.213539i
$262$	−3.16338	−	3.04311i	−0.195434	−	0.188004i
$263$	−9.33065	−	3.03171i	−0.575352	−	0.186943i	0.00686511	−	0.999976i	$-0.497815\pi$
$263$	−9.33065	−	3.03171i	−0.575352	−	0.186943i	−0.582217	+	0.813033i	$0.697815\pi$
$264$	−0.0792143	+	0.302605i	−0.00487530	+	0.0186241i
$265$	1.07865	−	14.0249i	0.0662612	−	0.861546i
$266$	−2.91076	+	3.02581i	−0.178470	+	0.185524i
$267$	−2.97836	+	0.471726i	−0.182273	+	0.0288692i
$268$	4.10290	+	0.487760i	0.250624	+	0.0297947i
$269$	−1.20756	−	7.62424i	−0.0736263	−	0.464858i	−0.996764	−	0.0803879i	$-0.974384\pi$
$269$	−1.20756	−	7.62424i	−0.0736263	−	0.464858i	0.923137	−	0.384470i	$-0.125616\pi$
$270$	15.9305	−	4.18294i	0.969500	−	0.254565i
$271$	7.56407	−	5.49562i	0.459485	−	0.333835i	−0.333844	−	0.942628i	$-0.608346\pi$
$271$	7.56407	−	5.49562i	0.459485	−	0.333835i	0.793329	+	0.608793i	$0.208346\pi$
$272$	−10.5669	−	25.5855i	−0.640712	−	1.55135i
$273$	−0.470672	−	1.44858i	−0.0284864	−	0.0876721i
$274$	−4.25757	+	1.47516i	−0.257209	+	0.0891179i
$275$	−0.489637	−	0.157166i	−0.0295262	−	0.00947749i
$276$	−1.09513	+	9.21192i	−0.0659190	+	0.554492i
$277$	6.69047	+	3.40897i	0.401992	+	0.204825i	0.643284	−	0.765627i	$-0.277571\pi$
$277$	6.69047	+	3.40897i	0.401992	+	0.204825i	−0.241293	+	0.970452i	$0.577571\pi$
$278$	−21.7355	+	3.87568i	−1.30361	+	0.232448i
$279$	0.662932	+	0.912448i	0.0396887	+	0.0546268i
$280$	3.71113	−	1.80464i	0.221782	−	0.107848i
$281$	8.97459	−	12.3525i	0.535379	−	0.736886i	−0.452559	−	0.891734i	$-0.649489\pi$
$281$	8.97459	−	12.3525i	0.535379	−	0.736886i	0.987938	+	0.154848i	$0.0494888\pi$
$282$	−7.76604	+	16.0008i	−0.462461	+	0.952832i
$283$	−18.9297	+	2.99816i	−1.12525	+	0.178222i	−0.691198	−	0.722665i	$-0.742917\pi$
$283$	−18.9297	+	2.99816i	−1.12525	+	0.178222i	−0.434053	+	0.900887i	$0.642917\pi$
$284$	4.42583	−	1.63018i	0.262625	−	0.0967333i
$285$	−0.877795	−	10.9051i	−0.0519961	−	0.645960i
$286$	0.251811	−	0.190514i	0.0148899	−	0.0112653i
$287$	−2.03017	+	6.24822i	−0.119837	+	0.368821i
$288$	−10.1846	−	2.24837i	−0.600134	−	0.132486i
$289$	9.54626	+	29.3804i	0.561544	+	1.72826i
$290$	10.9660	−	7.04335i	0.643945	−	0.413600i
$291$	−4.40130	+	2.24258i	−0.258009	+	0.131462i
$292$	−0.449165	−	11.5846i	−0.0262854	−	0.677937i
$293$	−15.5671	+	15.5671i	−0.909442	+	0.909442i	−0.996227	−	0.0867849i	$-0.972341\pi$
$293$	−15.5671	+	15.5671i	−0.909442	+	0.909442i	0.0867849	+	0.996227i	$0.472341\pi$
$294$	8.81816	−	4.71048i	0.514286	−	0.274721i
$295$	12.3673	+	20.1011i	0.720050	+	1.17033i
$296$	1.17674	−	1.32217i	0.0683968	−	0.0768494i
$297$	−0.314865	−	0.433375i	−0.0182703	−	0.0251469i
$298$	−3.26861	+	23.5864i	−0.189345	+	1.36633i
$299$	6.62171	−	6.62171i	0.382944	−	0.382944i
$300$	−2.88724	+	10.3580i	−0.166695	+	0.598021i
$301$	1.09544	+	1.09544i	0.0631402	+	0.0631402i
$302$	2.63736	+	3.48592i	0.151763	+	0.200592i
$303$	10.9736	−	7.97277i	0.630415	−	0.458024i
$304$	−6.98235	+	16.8077i	−0.400465	+	0.963989i
$305$	−4.39340	+	10.6603i	−0.251565	+	0.610405i
$306$	17.2664	+	5.24257i	0.987053	+	0.299698i
$307$	12.9872	+	12.9872i	0.741217	+	0.741217i	0.972812	−	0.231595i	$-0.0743945\pi$
$307$	12.9872	+	12.9872i	0.741217	+	0.741217i	−0.231595	+	0.972812i	$0.574395\pi$
$308$	−0.0985087	−	0.0911550i	−0.00561306	−	0.00519404i
$309$	5.91011	+	11.5992i	0.336214	+	0.659858i
$310$	−1.92480	+	0.192537i	−0.109321	+	0.0109354i
$311$	−17.0590	+	5.54279i	−0.967325	+	0.314303i	−0.749736	−	0.661737i	$-0.769819\pi$
$311$	−17.0590	+	5.54279i	−0.967325	+	0.314303i	−0.217590	+	0.976040i	$0.569819\pi$
$312$	−4.18468	−	5.10712i	−0.236911	−	0.289133i
$313$	−13.0790	−	4.24962i	−0.739267	−	0.240203i	−0.0849108	−	0.996389i	$-0.527061\pi$
$313$	−13.0790	−	4.24962i	−0.739267	−	0.240203i	−0.654357	+	0.756186i	$0.727061\pi$
$314$	−23.5676	−	3.26600i	−1.33000	−	0.184311i
$315$	−0.623311	+	2.61680i	−0.0351196	+	0.147440i
$316$	−7.44876	−	20.2229i	−0.419025	−	1.13763i
$317$	−0.530806	−	3.35137i	−0.0298130	−	0.188232i	0.968287	−	0.249839i	$-0.0803776\pi$
$317$	−0.530806	−	3.35137i	−0.0298130	−	0.188232i	−0.998101	+	0.0616067i	$0.980378\pi$
$318$	3.13183	+	9.03898i	0.175624	+	0.506881i
$319$	−0.342928	−	0.249152i	−0.0192003	−	0.0139498i
$320$	12.1397	−	13.1388i	0.678631	−	0.734479i
$321$	2.62330	−	1.90594i	0.146418	−	0.106379i
$322$	−3.26492	−	2.27677i	−0.181947	−	0.126880i
$323$	14.2955	−	28.0565i	0.795423	−	1.56111i
$324$	−0.108934	+	0.0857852i	−0.00605188	+	0.00476585i
$325$	8.75877	−	6.41142i	0.485849	−	0.355641i
$326$	−6.39633	+	13.1787i	−0.354260	+	0.729900i
$327$	2.21090	−	0.718364i	0.122263	−	0.0397256i
$328$	1.65456	+	28.4311i	0.0913577	+	1.56984i
$329$	−4.48559	−	6.17388i	−0.247298	−	0.340377i
$330$	0.347986	−	0.0348088i	0.0191560	−	0.00191616i
$331$	25.7208	−	4.07377i	1.41374	−	0.223915i	0.597613	−	0.801785i	$-0.296116\pi$
$331$	25.7208	−	4.07377i	1.41374	−	0.223915i	0.816129	+	0.577870i	$0.196116\pi$
$332$	−35.2366	−	4.18898i	−1.93386	−	0.229900i
$333$	0.180493	+	1.13959i	0.00989094	+	0.0624489i
$334$	−0.149469	−	7.71290i	−0.00817856	−	0.422031i
$335$	−1.08640	−	4.48992i	−0.0593562	−	0.245310i
$336$	−1.82483	+	2.13213i	−0.0995526	+	0.116317i
$337$	9.05842	−	27.8790i	0.493444	−	1.51866i	−0.325924	−	0.945396i	$-0.605675\pi$
$337$	9.05842	−	27.8790i	0.493444	−	1.51866i	0.819368	−	0.573268i	$-0.194325\pi$
$338$	−0.227075	−	11.7175i	−0.0123512	−	0.637350i
$339$	1.83919	−	3.60961i	0.0998911	−	0.196047i
$340$	−22.7000	+	21.0370i	−1.23108	+	1.14089i
$341$	0.0285623	+	0.0560567i	0.00154673	+	0.00303564i
$342$	−5.59003	−	10.4647i	−0.302274	−	0.565866i
$343$			8.85694i			0.478230i
$344$	6.15062	+	2.69602i	0.331619	+	0.145360i
$345$	10.0809	−	2.43920i	0.542735	−	0.131322i
$346$	−4.83912	−	27.1387i	−0.260153	−	1.45899i
$347$	2.09837	−	13.2486i	0.112646	−	0.711221i	−0.865126	−	0.501554i	$-0.832762\pi$
$347$	2.09837	−	13.2486i	0.112646	−	0.711221i	0.977773	−	0.209667i	$-0.0672381\pi$
$348$	−4.92808	+	7.36715i	−0.264173	+	0.394921i
$349$	−16.1833	−	16.1833i	−0.866275	−	0.866275i	0.125783	−	0.992058i	$-0.459856\pi$
$349$	−16.1833	−	16.1833i	−0.866275	−	0.866275i	−0.992058	+	0.125783i	$0.959856\pi$
$350$	−3.33637	−	3.18671i	−0.178337	−	0.170337i
$351$	11.3071			0.603528
$352$	−0.541506	−	0.212748i	−0.0288624	−	0.0113395i
$353$	−18.3237	+	13.3129i	−0.975272	+	0.708576i	−0.956647	−	0.291250i	$-0.905929\pi$
$353$	−18.3237	+	13.3129i	−0.975272	+	0.708576i	−0.0186247	+	0.999827i	$0.505929\pi$
$354$	−13.1654	−	9.18080i	−0.699731	−	0.487954i
$355$	−3.43182	−	4.00368i	−0.182142	−	0.212493i
$356$	−0.217301	−	5.60449i	−0.0115169	−	0.297037i
$357$	3.43329	−	3.43329i	0.181709	−	0.181709i
$358$	−26.3581	+	14.0800i	−1.39307	+	0.744149i
$359$	16.4762	+	5.35343i	0.869578	+	0.282543i	0.709623	−	0.704581i	$-0.248865\pi$
$359$	16.4762	+	5.35343i	0.869578	+	0.282543i	0.159955	+	0.987124i	$0.448865\pi$
$360$	1.60931	+	11.5493i	0.0848181	+	0.608703i
$361$	−1.61994	+	0.526351i	−0.0852601	+	0.0277027i
$362$	7.76874	−	8.07579i	0.408316	−	0.424454i
$363$	5.36472	+	10.5289i	0.281575	+	0.552622i
$364$	2.77881	−	0.551248i	0.145649	−	0.0288932i
$365$	−11.9662	+	4.98155i	−0.626339	+	0.260746i
$366$	−0.151929	−	7.83985i	−0.00794144	−	0.409795i
$367$	−29.3729	−	21.3406i	−1.53325	−	1.11397i	−0.954397	−	0.298541i	$-0.903500\pi$
$367$	−29.3729	−	21.3406i	−1.53325	−	1.11397i	−0.578854	−	0.815431i	$-0.696500\pi$
$368$	−16.7736	−	4.04531i	−0.874382	−	0.210877i
$369$	−15.0191	−	10.9120i	−0.781861	−	0.568055i
$370$	−1.84388	−	0.718445i	−0.0958588	−	0.0373502i
$371$	−4.05400	−	0.642091i	−0.210473	−	0.0333357i
$372$	1.14813	−	0.642207i	0.0595280	−	0.0332969i
$373$	2.19907	+	1.12048i	0.113864	+	0.0580164i	0.509995	−	0.860178i	$-0.329647\pi$
$373$	2.19907	+	1.12048i	0.113864	+	0.0580164i	−0.396131	+	0.918194i	$0.629647\pi$
$374$	0.905551	+	0.439513i	0.0468249	+	0.0227267i
$375$	11.9798	−	1.00728i	0.618636	−	0.0520156i
$376$	−27.8476	−	17.8568i	−1.43613	−	0.920895i
$377$	8.50937	−	2.76486i	0.438255	−	0.142398i
$378$	−0.843666	−	4.73144i	−0.0433935	−	0.243359i
$379$	2.29563	−	14.4940i	0.117918	−	0.744507i	−0.855894	−	0.517152i	$-0.826992\pi$
$379$	2.29563	−	14.4940i	0.117918	−	0.744507i	0.973812	−	0.227355i	$-0.0730078\pi$
$380$	20.3339	+	0.773169i	1.04311	+	0.0396627i
$381$	−2.96912	−	18.7463i	−0.152113	−	0.960403i
$382$	4.73693	+	13.6716i	0.242362	+	0.699498i
$383$	−19.6467	−	14.2742i	−1.00390	−	0.729375i	−0.0409783	−	0.999160i	$-0.513047\pi$
$383$	−19.6467	−	14.2742i	−1.00390	−	0.729375i	−0.962921	+	0.269785i	$0.913047\pi$
$384$	−4.00657	+	11.4868i	−0.204459	+	0.586185i
$385$	−0.0571765	+	0.138735i	−0.00291398	+	0.00707058i
$386$	−6.72768	+	5.08999i	−0.342430	+	0.259074i
$387$	−3.90050	+	1.98740i	−0.198273	+	0.101025i
$388$	−3.17555	−	8.62142i	−0.161214	−	0.437686i
$389$	34.3543	+	17.5044i	1.74183	+	0.887509i	0.966779	+	0.255615i	$0.0822781\pi$
$389$	34.3543	+	17.5044i	1.74183	+	0.887509i	0.775055	+	0.631893i	$0.217722\pi$
$390$	−3.72302	+	6.37431i	−0.188522	+	0.322776i
$391$	28.3910	+	9.22480i	1.43580	+	0.466518i
$392$	6.76385	+	17.3210i	0.341626	+	0.874845i
$393$		−	3.33752i		−	0.168355i
$394$	7.30463	+	13.6745i	0.368002	+	0.688911i
$395$	−18.2940	+	15.6810i	−0.920470	+	0.788996i
$396$	0.330994	−	0.185141i	0.0166331	−	0.00930367i
$397$	−14.4899	−	2.29497i	−0.727226	−	0.115181i	−0.218165	−	0.975912i	$-0.570007\pi$
$397$	−14.4899	−	2.29497i	−0.727226	−	0.115181i	−0.509061	+	0.860730i	$0.670007\pi$
$398$	−15.4344	−	20.4004i	−0.773659	−	1.02258i
$399$	−3.19237			−0.159818
$400$	−18.4969	−	7.60691i	−0.924844	−	0.380345i
$401$	−15.8485			−0.791436			−0.395718	−	0.918372i	$-0.629504\pi$
$401$	−15.8485			−0.791436			−0.395718	+	0.918372i	$0.629504\pi$
$402$	1.89548	+	2.50534i	0.0945377	+	0.124955i
$403$	−1.31163	−	0.207742i	−0.0653370	−	0.0103484i
$404$	12.3159	+	22.0183i	0.612739	+	1.09545i
$405$	0.132323	+	0.0807636i	0.00657517	+	0.00401318i
$406$	−1.79187	−	3.35444i	−0.0889290	−	0.166478i
$407$			0.0643610i			0.00319026i
$408$	8.44976	−	19.2771i	0.418326	−	0.954357i
$409$	−22.1337	−	7.19167i	−1.09444	−	0.355605i	−0.294479	−	0.955658i	$-0.595146\pi$
$409$	−22.1337	−	7.19167i	−1.09444	−	0.355605i	−0.799960	+	0.600053i	$0.795146\pi$
$410$	29.1526	−	12.8045i	1.43974	−	0.632371i
$411$	−3.05261	−	1.55538i	−0.150574	−	0.0767214i
$412$	−22.7210	+	8.36888i	−1.11938	+	0.412305i
$413$	6.13609	−	3.12650i	0.301937	−	0.153845i
$414$	8.96968	−	6.78623i	0.440836	−	0.333525i
$415$	9.33020	+	38.5604i	0.458001	+	1.89285i
$416$	10.3515	−	6.60756i	0.507522	−	0.323962i
$417$	−13.5811	−	9.86725i	−0.665069	−	0.483201i
$418$	−0.216667	−	0.625338i	−0.0105975	−	0.0305863i
$419$	1.48347	+	9.36623i	0.0724720	+	0.457570i	0.997061	+	0.0766054i	$0.0244082\pi$
$419$	1.48347	+	9.36623i	0.0724720	+	0.457570i	−0.924589	+	0.380965i	$0.875592\pi$
$420$	2.94511	+	1.08228i	0.143707	+	0.0528098i
$421$	2.05317	−	12.9632i	0.100065	−	0.631788i	−0.885777	−	0.464112i	$-0.846374\pi$
$421$	2.05317	−	12.9632i	0.100065	−	0.631788i	0.985842	−	0.167676i	$-0.0536263\pi$
$422$	−2.38055	−	13.3506i	−0.115883	−	0.649895i
$423$	20.5089	−	6.66374i	0.997177	−	0.324002i
$424$	−17.3823	+	3.79967i	−0.844157	+	0.184528i
$425$	30.8865	+	15.5991i	1.49822	+	0.756668i
$426$	3.22625	+	1.56587i	0.156312	+	0.0758668i
$427$	2.99776	+	1.52743i	0.145072	+	0.0739177i
$428$	2.94419	+	5.26361i	0.142313	+	0.254426i
$429$	0.237131	+	0.0375578i	0.0114488	+	0.00181331i
$430$	0.430599	−	7.49586i	0.0207653	−	0.361482i
$431$	−2.99695	−	2.17741i	−0.144358	−	0.104882i	0.513262	−	0.858232i	$-0.328437\pi$
$431$	−2.99695	−	2.17741i	−0.144358	−	0.104882i	−0.657620	+	0.753350i	$0.728437\pi$
$432$	−10.8672	−	17.7749i	−0.522850	−	0.855197i
$433$	26.8755	+	19.5262i	1.29155	+	0.938367i	0.999836	−	0.0181375i	$-0.00577365\pi$
$433$	26.8755	+	19.5262i	1.29155	+	0.938367i	0.291716	+	0.956505i	$0.405774\pi$
$434$	0.0109366	+	0.564350i	0.000524972	+	0.0270897i
$435$	9.63995	+	2.29619i	0.462200	+	0.110094i
$436$	0.841342	+	4.24116i	0.0402930	+	0.203115i
$437$	−8.91063	−	17.4881i	−0.426253	−	0.836569i
$438$	6.11114	−	6.35268i	0.292002	−	0.303543i
$439$	−12.1543	+	3.94916i	−0.580092	+	0.188483i	−0.584342	−	0.811508i	$-0.698647\pi$
$439$	−12.1543	+	3.94916i	−0.580092	+	0.188483i	0.00424998	+	0.999991i	$0.498647\pi$
$440$	−0.0121167	+	0.650359i	−0.000577642	+	0.0310046i
$441$	−11.5281	−	3.74569i	−0.548955	−	0.178366i
$442$	−18.7405	+	10.0108i	−0.891395	+	0.476165i
$443$	−14.9935	+	14.9935i	−0.712365	+	0.712365i	−0.967029	−	0.254665i	$-0.918035\pi$
$443$	−14.9935	+	14.9935i	−0.712365	+	0.712365i	0.254665	+	0.967029i	$0.418035\pi$
$444$	1.34479	−	0.0521410i	0.0638209	−	0.00247450i
$445$	−5.78910	+	2.41002i	−0.274430	+	0.114246i
$446$	−22.5970	−	15.7579i	−1.07000	−	0.746159i
$447$	−14.6474	+	10.6420i	−0.692799	+	0.503348i
$448$	−3.53729	−	3.83853i	−0.167121	−	0.181354i
$449$	−39.3669			−1.85784			−0.928920	−	0.370279i	$-0.879262\pi$
$449$	−39.3669			−1.85784			−0.928920	+	0.370279i	$0.879262\pi$
$450$	11.4775	−	6.18369i	0.541054	−	0.291502i
$451$	−0.732261	−	0.732261i	−0.0344808	−	0.0344808i
$452$	6.26297	+	4.18947i	0.294586	+	0.197056i
$453$	−0.519928	+	3.28269i	−0.0244283	+	0.154234i
$454$	3.01157	+	16.8895i	0.141340	+	0.792662i
$455$	−1.65974	−	2.69766i	−0.0778099	−	0.126468i
$456$	−12.8906	+	5.03375i	−0.603656	+	0.235727i
$457$			32.7074i			1.52999i	0.644037	+	0.764994i	$0.277258\pi$
$457$			32.7074i			1.52999i	−0.644037	+	0.764994i	$0.722742\pi$
$458$	−2.25627	−	4.22381i	−0.105429	−	0.197366i
$459$	16.3639	+	32.1160i	0.763802	+	1.49905i
$460$	2.29165	+	19.1545i	0.106849	+	0.893083i
$461$	10.3999	−	20.4110i	0.484372	−	0.950633i	−0.511450	−	0.859313i	$-0.670891\pi$
$461$	10.3999	−	20.4110i	0.484372	−	0.950633i	0.995822	−	0.0913200i	$-0.0291086\pi$
$462$	−0.00197723	−	0.102029i	−9.19890e−5	−	0.00474683i
$463$	6.94292	−	21.3681i	0.322665	−	0.993060i	−0.649819	−	0.760089i	$-0.725155\pi$
$463$	6.94292	−	21.3681i	0.322665	−	0.993060i	0.972484	−	0.232971i	$-0.0748447\pi$
$464$	−12.5248	−	10.7196i	−0.581447	−	0.497643i
$465$	−1.12012	−	0.953226i	−0.0519442	−	0.0442048i
$466$	0.392792	+	20.2689i	0.0181958	+	0.938940i
$467$	3.75442	+	23.7045i	0.173734	+	1.09691i	0.908283	+	0.418357i	$0.137394\pi$
$467$	3.75442	+	23.7045i	0.173734	+	1.09691i	−0.734549	+	0.678556i	$0.762606\pi$
$468$	−0.945026	+	7.94929i	−0.0436838	+	0.367456i
$469$	−1.33136	+	0.210867i	−0.0614765	+	0.00973691i
$470$	−7.87134	+	36.1384i	−0.363078	+	1.66694i
$471$	−10.6335	−	14.6357i	−0.489965	−	0.674380i
$472$	19.8473	−	22.3000i	0.913544	−	1.02644i
$473$	−0.232242	+	0.0754601i	−0.0106785	+	0.00346966i
$474$	7.15493	−	14.7417i	0.328637	−	0.677108i
$475$	−7.10731	−	21.6118i	−0.326106	−	0.991616i
$476$	5.58730	+	7.09499i	0.256093	+	0.325198i
$477$	5.26558	−	10.3343i	0.241094	−	0.473174i
$478$	13.1323	+	9.15778i	0.600660	+	0.418867i
$479$	27.5250	−	19.9981i	1.25765	−	0.913737i	0.259011	−	0.965874i	$-0.416603\pi$
$479$	27.5250	−	19.9981i	1.25765	−	0.913737i	0.998640	+	0.0521374i	$0.0166034\pi$
$480$	13.5987	−	0.273705i	0.620693	−	0.0124929i
$481$	−1.09907	−	0.798522i	−0.0501134	−	0.0364095i
$482$	11.5420	+	33.3122i	0.525724	+	1.51733i
$483$	−0.473442	−	2.98920i	−0.0215424	−	0.136013i
$484$	−20.6243	+	7.59660i	−0.937468	+	0.345300i
$485$	−7.79908	+	6.68510i	−0.354138	+	0.303555i
$486$	21.7839	+	3.01882i	0.988139	+	0.136936i
$487$	13.2368	+	4.30091i	0.599819	+	0.194893i	0.593160	−	0.805085i	$-0.297880\pi$
$487$	13.2368	+	4.30091i	0.599819	+	0.194893i	0.00665905	+	0.999978i	$0.497880\pi$
$488$	14.5132	+	1.44079i	0.656983	+	0.0652213i
$489$	−10.5931	+	3.44190i	−0.479036	+	0.155648i
$490$	15.5194	−	13.8332i	0.701095	−	0.624922i
$491$	11.3239	+	22.2245i	0.511042	+	1.00298i	0.992001	+	0.126233i	$0.0402887\pi$
$491$	11.3239	+	22.2245i	0.511042	+	1.00298i	−0.480959	+	0.876743i	$0.659711\pi$
$492$	−14.7070	+	15.8934i	−0.663042	+	0.716531i
$493$	20.1681	+	20.1681i	0.908327	+	0.908327i
$494$	13.3669	+	4.05856i	0.601403	+	0.182603i
$495$	−0.322917	−	0.274804i	−0.0145140	−	0.0123515i
$496$	0.934034	+	2.26156i	0.0419394	+	0.101547i
$497$	−1.24485	+	0.904433i	−0.0558390	+	0.0405694i
$498$	−16.2787	−	21.5164i	−0.729468	−	0.964173i
$499$	14.4668	+	14.4668i	0.647625	+	0.647625i	0.952418	−	0.304794i	$-0.0985875\pi$
$499$	14.4668	+	14.4668i	0.647625	+	0.647625i	−0.304794	+	0.952418i	$0.598588\pi$
$500$	−0.770009	+	22.3474i	−0.0344359	+	0.999407i
$501$	4.14758	−	4.14758i	0.185300	−	0.185300i
$502$	3.03166	−	21.8766i	0.135309	−	0.976399i
$503$	15.9540	+	21.9588i	0.711354	+	0.979095i	0.999767	+	0.0215886i	$0.00687239\pi$
$503$	15.9540	+	21.9588i	0.711354	+	0.979095i	−0.288413	+	0.957506i	$0.593128\pi$
$504$	3.39688	−	0.197683i	0.151309	−	0.00880549i
$505$	18.2804	−	21.4810i	0.813469	−	0.955893i
$506$	0.553407	−	0.295619i	0.0246020	−	0.0131418i
$507$	6.30106	−	6.30106i	0.279840	−	0.279840i
$508$	35.2756	−	1.36773i	1.56510	−	0.0606831i
$509$	−0.0558894	+	0.0284771i	−0.00247725	+	0.00126222i	−0.455229	−	0.890375i	$-0.650442\pi$
$509$	−0.0558894	+	0.0284771i	−0.00247725	+	0.00126222i	0.452751	+	0.891637i	$0.350442\pi$
$510$	−23.4933	−	1.34957i	−1.04030	−	0.0597599i
$511$	1.16876	+	3.59708i	0.0517030	+	0.159126i
$512$	−20.3360	−	9.92212i	−0.898731	−	0.438500i
$513$	7.32335	−	22.5389i	0.323334	−	0.995119i
$514$	−25.8882	+	19.5864i	−1.14188	+	0.863918i
$515$	17.6180	+	20.5538i	0.776342	+	0.905708i
$516$	1.76485	+	4.79145i	0.0776930	+	0.210932i
$517$	1.18810	−	0.188176i	0.0522524	−	0.00827597i
$518$	−0.252134	+	0.519486i	−0.0110782	+	0.0228249i
$519$	12.3201	−	16.9572i	0.540793	−	0.744338i
$520$	−10.9556	−	8.27586i	−0.480436	−	0.362921i
$521$	−22.2089	−	30.5679i	−0.972989	−	1.33920i	−0.940522	−	0.339732i	$-0.889664\pi$
$521$	−22.2089	−	30.5679i	−0.972989	−	1.33920i	−0.0324666	−	0.999473i	$-0.510336\pi$
$522$	10.5796	−	1.88645i	0.463055	−	0.0825678i
$523$	4.75534	+	2.42297i	0.207936	+	0.105949i	0.554857	−	0.831945i	$-0.312773\pi$
$523$	4.75534	+	2.42297i	0.207936	+	0.105949i	−0.346921	+	0.937894i	$0.612773\pi$
$524$	6.16425	+	0.732817i	0.269286	+	0.0320133i
$525$	−0.0124977	−	3.50800i	−0.000545446	−	0.153102i
$526$	13.1100	−	4.54235i	0.571622	−	0.198056i
$527$	−1.30817	−	4.02613i	−0.0569847	−	0.175381i
$528$	−0.168865	−	0.408870i	−0.00734889	−	0.0177938i
$529$	−3.55376	+	2.58196i	−0.154511	+	0.112259i
$530$	10.7505	+	16.7377i	0.466972	+	0.727041i
$531$	3.04424	+	19.2206i	0.132109	+	0.834101i
$532$	0.700946	−	5.89616i	0.0303899	−	0.255631i
$533$	21.5897	−	3.41947i	0.935153	−	0.148114i
$534$	2.95650	−	3.07335i	0.127940	−	0.132997i
$535$	4.37006	−	5.13517i	0.188934	−	0.222013i
$536$	−5.04345	+	2.95077i	−0.217844	+	0.127454i
$537$	−21.6094	−	7.02131i	−0.932513	−	0.302992i
$538$	7.86739	+	7.56827i	0.339187	+	0.326291i
$539$	−0.602458	−	0.306968i	−0.0259497	−	0.0132220i
$540$	−14.3973	+	18.3105i	−0.619562	+	0.787958i
$541$	−0.247797	+	0.126259i	−0.0106536	+	0.00542829i	−0.459309	−	0.888276i	$-0.651903\pi$
$541$	−0.247797	+	0.126259i	−0.0106536	+	0.00542829i	0.448656	+	0.893705i	$0.351903\pi$
$542$	−3.84155	+	12.6521i	−0.165009	+	0.543456i
$543$	8.52033			0.365642
$544$	33.7486	+	19.8390i	1.44696	+	0.850591i
$545$	4.11730	−	2.53318i	0.176366	−	0.108510i
$546$	1.76685	+	1.23210i	0.0756142	+	0.0527292i
$547$	11.1579	+	1.76724i	0.477077	+	0.0755616i	0.390342	−	0.920670i	$-0.372357\pi$
$547$	11.1579	+	1.76724i	0.477077	+	0.0755616i	0.0867349	+	0.996231i	$0.472357\pi$
$548$	3.54299	−	5.29653i	0.151349	−	0.226257i
$549$	−6.72258	+	6.72258i	−0.286913	+	0.286913i
$550$	0.686318	−	0.240538i	0.0292647	−	0.0102566i
$551$		−	18.7529i		−	0.798899i
$552$	−6.62512	−	11.3237i	−0.281984	−	0.481967i
$553$	4.13262	+	5.68806i	0.175737	+	0.241881i
$554$	−10.4543	+	1.86411i	−0.444160	+	0.0791985i
$555$	−0.578280	−	1.38909i	−0.0245466	−	0.0589635i
$556$	21.2064	−	22.9172i	0.899351	−	0.971905i
$557$	−4.09916	−	4.09916i	−0.173687	−	0.173687i	0.614910	−	0.788597i	$-0.289192\pi$
$557$	−4.09916	−	4.09916i	−0.173687	−	0.173687i	−0.788597	+	0.614910i	$0.789192\pi$
$558$	−1.52622	−	0.463403i	−0.0646099	−	0.0196174i
$559$	1.59281	−	4.90215i	0.0673685	−	0.207339i
$560$	−2.64558	+	5.20186i	−0.111796	+	0.219819i
$561$	0.236504	+	0.727886i	0.00998522	+	0.0307314i
$562$	0.418371	+	21.5889i	0.0176479	+	0.910671i
$563$	−16.7133	+	8.51587i	−0.704383	+	0.358901i	−0.769211	−	0.638995i	$-0.779350\pi$
$563$	−16.7133	+	8.51587i	−0.704383	+	0.358901i	0.0648273	+	0.997896i	$0.479350\pi$
$564$	−4.89435	−	24.6722i	−0.206089	−	1.03889i
$565$	1.95204	−	8.19513i	0.0821231	−	0.344772i
$566$	18.7907	−	19.5334i	0.789831	−	0.821048i
$567$	0.0265887	−	0.0365962i	0.00111662	−	0.00153689i
$568$	−3.60049	+	5.61493i	−0.151073	+	0.235597i
$569$	−16.4333	+	22.6185i	−0.688919	+	0.948215i	−0.999998	−	0.00216902i	$-0.999310\pi$
$569$	−16.4333	+	22.6185i	−0.688919	+	0.948215i	0.311079	+	0.950384i	$0.399310\pi$
$570$	10.2949	+	11.5498i	0.431206	+	0.483766i
$571$	−1.08505	+	6.85077i	−0.0454081	+	0.286696i	−0.999935	−	0.0114303i	$-0.996362\pi$
$571$	−1.08505	+	6.85077i	−0.0454081	+	0.286696i	0.954527	+	0.298126i	$0.0963615\pi$
$572$	−0.121434	+	0.429723i	−0.00507742	+	0.0179676i
$573$	−4.99452	+	9.80230i	−0.208649	+	0.409497i
$574$	−3.04176	−	8.77903i	−0.126961	−	0.366430i
$575$	19.1823	−	9.86011i	0.799958	−	0.411195i
$576$	13.4047	−	6.15446i	0.558528	−	0.256436i
$577$	5.41920	+	16.6786i	0.225604	+	0.694339i	0.998230	+	0.0594767i	$0.0189432\pi$
$577$	5.41920	+	16.6786i	0.225604	+	0.694339i	−0.772625	+	0.634862i	$0.781057\pi$
$578$	−35.8355	−	24.9897i	−1.49056	−	1.03944i
$579$	−6.33546	−	1.00344i	−0.263293	−	0.0417015i
$580$	−6.35761	+	17.3004i	−0.263985	+	0.718360i
$581$	11.4340	−	1.81097i	0.474362	−	0.0751316i
$582$	3.05028	−	6.28466i	0.126438	−	0.260508i
$583$	0.380289	−	0.523423i	0.0157500	−	0.0216780i
$584$	10.3913	+	12.6819i	0.429995	+	0.524780i
$585$	8.69913	−	2.10487i	0.359665	−	0.0870258i
$586$	4.27375	−	30.8396i	0.176547	−	1.27397i
$587$	−19.5882	−	38.4440i	−0.808491	−	1.58675i	−0.809766	−	0.586753i	$-0.800406\pi$
$587$	−19.5882	−	38.4440i	−0.808491	−	1.58675i	0.00127536	−	0.999999i	$-0.499594\pi$
$588$	−5.92585	+	12.8367i	−0.244378	+	0.529377i
$589$	−1.26361	+	2.47998i	−0.0520663	+	0.102186i
$590$	−31.0994	−	12.1175i	−1.28034	−	0.498869i
$591$	−3.64263	+	11.2109i	−0.149838	+	0.461153i
$592$	−0.198973	+	2.49522i	−0.00817772	+	0.102553i
$593$	−20.1326			−0.826747			−0.413374	−	0.910561i	$-0.635650\pi$
$593$	−20.1326			−0.826747			−0.413374	+	0.910561i	$0.635650\pi$
$594$	0.724889	+	0.220097i	0.0297426	+	0.00903070i
$595$	5.26024	−	8.61835i	0.215649	−	0.353318i
$596$	−16.4391	−	29.3898i	−0.673374	−	1.20385i
$597$	3.04274	−	19.2111i	0.124531	−	0.786258i
$598$	−1.81790	+	13.1181i	−0.0743395	+	0.536438i
$599$		−	35.4964i		−	1.45034i	−0.688568	−	0.725172i	$-0.741760\pi$
$599$		−	35.4964i		−	1.45034i	0.688568	−	0.725172i	$-0.258240\pi$
$600$	−5.58192	−	14.1454i	−0.227881	−	0.577483i
$601$			10.7148i			0.437064i	0.975830	+	0.218532i	$0.0701269\pi$
$601$			10.7148i			0.437064i	−0.975830	+	0.218532i	$0.929873\pi$
$602$	−2.17014	−	0.300739i	−0.0884484	−	0.0122572i
$603$	0.595858	−	3.76210i	0.0242652	−	0.153205i
$604$	−5.94884	−	1.68106i	−0.242055	−	0.0684015i
$605$	15.9922	+	18.6571i	0.650176	+	0.758518i
$606$	−5.57313	+	18.3551i	−0.226393	+	0.745624i
$607$	−40.9846			−1.66351			−0.831756	−	0.555141i	$-0.812664\pi$
$607$	−40.9846			−1.66351			−0.831756	+	0.555141i	$0.812664\pi$
$608$	−6.46675	−	24.9136i	−0.262261	−	1.01038i
$609$	0.893558	−	2.75009i	0.0362088	−	0.111439i
$610$	−4.14116	−	15.7714i	−0.167671	−	0.638566i
$611$	−11.5272	+	22.6234i	−0.466341	+	0.915245i
$612$	−23.9464	+	8.82022i	−0.967974	+	0.356536i
$613$	−3.18792	−	6.25665i	−0.128759	−	0.252704i	0.817623	−	0.575754i	$-0.195292\pi$
$613$	−3.18792	−	6.25665i	−0.128759	−	0.252704i	−0.946382	+	0.323051i	$0.895292\pi$
$614$	−25.7285	−	3.56545i	−1.03832	−	0.143890i
$615$	22.3835	+	9.22488i	0.902591	+	0.371983i
$616$	0.188878	+	0.0187507i	0.00761010	+	0.000755485i
$617$	−11.7865	+	16.2227i	−0.474505	+	0.653100i	−0.977437	−	0.211226i	$-0.932254\pi$
$617$	−11.7865	+	16.2227i	−0.474505	+	0.653100i	0.502932	+	0.864326i	$0.332254\pi$
$618$	−16.5627	−	8.03876i	−0.666248	−	0.323366i
$619$	13.8264	−	2.18989i	0.555732	−	0.0880192i	0.127749	−	0.991806i	$-0.459225\pi$
$619$	13.8264	−	2.18989i	0.555732	−	0.0880192i	0.427982	+	0.903787i	$0.359225\pi$
$620$	2.00651	−	1.85951i	0.0805834	−	0.0746798i
$621$	22.1906	+	3.51465i	0.890478	+	0.141038i
$622$	14.5097	−	20.8070i	0.581784	−	0.834285i
$623$	0.565434	+	1.74023i	0.0226536	+	0.0697207i
$624$	9.07722	+	2.18917i	0.363380	+	0.0876370i
$625$	23.7208	−	7.89464i	0.948831	−	0.315786i
$626$	18.3766	−	6.36711i	0.734475	−	0.254481i
$627$	0.228450	−	0.448358i	0.00912340	−	0.0179057i
$628$	29.3664	−	16.4260i	1.17185	−	0.655471i
$629$	0.677470	−	4.27738i	0.0270125	−	0.170550i
$630$	−1.52986	−	3.48309i	−0.0609509	−	0.138769i
$631$	7.51950	−	10.3497i	0.299346	−	0.412015i	−0.632675	−	0.774417i	$-0.718043\pi$
$631$	7.51950	−	10.3497i	0.299346	−	0.412015i	0.932022	+	0.362402i	$0.118043\pi$
$632$	25.6562	+	16.4517i	1.02055	+	0.654412i
$633$	6.06074	−	8.34189i	0.240893	−	0.331560i
$634$	3.45826	+	3.32677i	0.137345	+	0.132123i
$635$	−15.1690	−	36.4376i	−0.601965	−	1.44598i
$636$	−11.2447	−	7.52189i	−0.445883	−	0.298263i
$637$	12.7166	−	6.47945i	0.503851	−	0.256725i
$638$	0.599348	−	0.0116148i	0.0237284	−	0.000459834i
$639$	−1.34362	−	4.13523i	−0.0531527	−	0.163587i
$640$	−2.48034	+	25.1763i	−0.0980441	+	0.995182i
$641$	1.14317	−	3.51832i	0.0451525	−	0.138965i	−0.925939	−	0.377674i	$-0.876724\pi$
$641$	1.14317	−	3.51832i	0.0451525	−	0.138965i	0.971091	+	0.238709i	$0.0767241\pi$
$642$	−1.33229	+	4.38790i	−0.0525814	+	0.173176i
$643$	−4.11067	−	4.11067i	−0.162109	−	0.162109i	0.621391	−	0.783500i	$-0.286568\pi$
$643$	−4.11067	−	4.11067i	−0.162109	−	0.162109i	−0.783500	+	0.621391i	$0.786568\pi$
$644$	5.62487	−	0.218091i	0.221651	−	0.00859400i
$645$	4.33442	−	3.71532i	0.170668	−	0.146291i
$646$	7.81716	+	43.8401i	0.307562	+	1.72486i
$647$	−10.3952	−	14.3078i	−0.408677	−	0.562496i	0.554218	−	0.832372i	$-0.313017\pi$
$647$	−10.3952	−	14.3078i	−0.408677	−	0.562496i	−0.962895	+	0.269876i	$0.913017\pi$
$648$	0.0496581	−	0.189698i	0.00195076	−	0.00745205i
$649$			1.08553i			0.0426108i
$650$	−4.40751	+	14.7044i	−0.172877	+	0.576753i
$651$	−0.303477	+	0.303477i	−0.0118942	+	0.0118942i
$652$	−4.03113	−	20.3207i	−0.157871	−	0.795821i
$653$	−4.89200	−	0.774817i	−0.191439	−	0.0303209i	0.0599787	−	0.998200i	$-0.480897\pi$
$653$	−4.89200	−	0.774817i	−0.191439	−	0.0303209i	−0.251418	+	0.967879i	$0.580897\pi$
$654$	−1.88050	+	2.69665i	−0.0735333	+	0.105447i
$655$	−1.63222	−	6.74571i	−0.0637760	−	0.263577i
$656$	−26.1253	−	30.6529i	−1.02002	−	1.19679i
$657$	−10.6876			−0.416962
$658$	10.3268	+	3.13552i	0.402581	+	0.122235i
$659$	−28.2425	+	14.3903i	−1.10017	+	0.560565i	−0.907226	−	0.420644i	$-0.861804\pi$
$659$	−28.2425	+	14.3903i	−1.10017	+	0.560565i	−0.192946	+	0.981209i	$0.561804\pi$
$660$	−0.362758	+	0.336182i	−0.0141203	+	0.0130859i
$661$	16.7173	+	8.51789i	0.650228	+	0.331307i	0.747803	−	0.663921i	$-0.231109\pi$
$661$	16.7173	+	8.51789i	0.650228	+	0.331307i	−0.0975755	+	0.995228i	$0.531109\pi$
$662$	−25.5319	+	26.5411i	−0.992327	+	1.03155i
$663$	−15.3642	−	4.99212i	−0.596694	−	0.193878i
$664$	43.3142	−	25.3418i	1.68092	−	0.983453i
$665$	−6.45234	+	1.56123i	−0.250211	+	0.0605419i
$666$	−1.17593	−	1.13122i	−0.0455663	−	0.0438339i
$667$	17.5594	−	2.78113i	0.679902	−	0.107686i
$668$	6.74973	+	8.57109i	0.261155	+	0.331626i
$669$	−3.27677	−	20.6887i	−0.126687	−	0.799872i
$670$	5.05633	+	4.13675i	0.195343	+	0.159817i
$671$	−0.429046	+	0.311720i	−0.0165632	+	0.0120338i
$672$	0.238769	−	3.96169i	0.00921070	−	0.152825i
$673$	−3.99615	−	12.2989i	−0.154040	−	0.474087i	0.844022	−	0.536308i	$-0.180182\pi$
$673$	−3.99615	−	12.2989i	−0.154040	−	0.474087i	−0.998062	+	0.0622211i	$0.980182\pi$
$674$	13.5721	+	39.1712i	0.522776	+	1.50882i
$675$	24.7961	+	7.95919i	0.954403	+	0.306349i
$676$	10.2543	+	13.0213i	0.394395	+	0.500820i
$677$	38.2371	+	19.4828i	1.46957	+	0.748783i	0.991569	−	0.129577i	$-0.0413619\pi$
$677$	38.2371	+	19.4828i	1.46957	+	0.748783i	0.478000	+	0.878360i	$0.341362\pi$
$678$	1.00572	+	5.64025i	0.0386243	+	0.216612i
$679$	1.76182	+	2.42493i	0.0676123	+	0.0930603i
$680$	7.65100	−	43.0947i	0.293403	−	1.65261i
$681$	−7.66729	+	10.5531i	−0.293811	+	0.404396i
$682$	−0.0800438	−	0.0388496i	−0.00306504	−	0.00148763i
$683$	−42.4851	+	6.72898i	−1.62565	+	0.257477i	−0.901695	−	0.432373i	$-0.857676\pi$
$683$	−42.4851	+	6.72898i	−1.62565	+	0.257477i	−0.723952	+	0.689850i	$0.757676\pi$
$684$	15.2336	+	7.03234i	0.582472	+	0.268888i
$685$	−6.93053	−	1.65082i	−0.264802	−	0.0630747i
$686$	−7.55732	−	9.98887i	−0.288540	−	0.381377i
$687$	1.12514	−	3.46284i	0.0429269	−	0.132115i
$688$	−9.23710	+	2.20754i	−0.352161	+	0.0841617i
$689$	4.22010	+	12.9881i	0.160773	+	0.494809i
$690$	−9.28793	+	11.3526i	−0.353585	+	0.432186i
$691$	−42.0963	+	21.4492i	−1.60142	+	0.815964i	−0.601567	+	0.798822i	$0.705457\pi$
$691$	−42.0963	+	21.4492i	−1.60142	+	0.815964i	−0.999853	+	0.0171418i	$0.994543\pi$
$692$	28.6141	+	26.4780i	1.08774	+	1.00654i
$693$	−0.0874888	+	0.0874888i	−0.00332343	+	0.00332343i
$694$	8.93801	+	16.7322i	0.339282	+	0.635147i
$695$	−32.2754	−	13.3016i	−1.22428	−	0.504559i
$696$	−0.728237	−	12.5137i	−0.0276038	−	0.474329i
$697$	40.9576	+	56.3733i	1.55138	+	2.13529i
$698$	32.0603	+	4.44292i	1.21350	+	0.168167i
$699$	−10.8995	+	10.8995i	−0.412258	+	0.412258i
$700$	6.48188	+	0.747168i	0.244992	+	0.0282403i
$701$	30.6973	+	30.6973i	1.15942	+	1.15942i	0.984600	+	0.174820i	$0.0559344\pi$
$701$	30.6973	+	30.6973i	1.15942	+	1.15942i	0.174820	+	0.984600i	$0.444066\pi$
$702$	−12.7522	+	9.64796i	−0.481300	+	0.364139i
$703$	−2.30357	+	1.67365i	−0.0868810	+	0.0631227i
$704$	0.792242	−	0.222110i	0.0298588	−	0.00837110i
$705$	−23.9516	+	14.7363i	−0.902070	+	0.555002i
$706$	9.30602	−	30.6493i	0.350237	−	1.15350i
$707$	−5.81992	−	5.81992i	−0.218881	−	0.218881i
$708$	22.6816	−	0.879425i	0.852426	−	0.0330508i
$709$	−1.73267	−	3.40056i	−0.0650719	−	0.127711i	0.856179	−	0.516679i	$-0.172832\pi$
$709$	−1.73267	−	3.40056i	−0.0650719	−	0.127711i	−0.921251	+	0.388968i	$0.872832\pi$
$710$	7.28661	+	1.58711i	0.273462	+	0.0595630i
$711$	−18.8951	+	6.13938i	−0.708620	+	0.230245i
$712$	5.02719	+	6.13534i	0.188402	+	0.229932i
$713$	−2.50955	−	0.815403i	−0.0939834	−	0.0305371i
$714$	−0.942564	+	6.80159i	−0.0352746	+	0.254543i
$715$	0.497651	−	0.0400580i	0.0186111	−	0.00149809i
$716$	17.7128	−	38.3699i	0.661959	−	1.43395i
$717$	1.90431	+	12.0233i	0.0711177	+	0.449020i
$718$	−23.1497	+	8.02093i	−0.863941	+	0.299339i
$719$	−41.0052	−	29.7920i	−1.52924	−	1.11106i	−0.956661	−	0.291203i	$-0.905945\pi$
$719$	−41.0052	−	29.7920i	−1.52924	−	1.11106i	−0.572575	−	0.819853i	$-0.694055\pi$
$720$	−11.6696	−	11.6522i	−0.434901	−	0.434251i
$721$	6.39069	−	4.64311i	0.238002	−	0.172918i
$722$	1.37786	−	1.97586i	0.0512785	−	0.0735339i
$723$	−12.1697	+	23.8843i	−0.452595	+	0.888267i
$724$	−1.87080	+	15.7367i	−0.0695279	+	0.584849i
$725$	20.6070	−	0.0734152i	0.765325	−	0.00272657i
$726$	−15.0343	−	7.29694i	−0.557974	−	0.270815i
$727$	15.0483	−	4.88947i	0.558109	−	0.181341i	−0.0163612	−	0.999866i	$-0.505208\pi$
$727$	15.0483	−	4.88947i	0.558109	−	0.181341i	0.574470	+	0.818526i	$0.305208\pi$
$728$	−2.66359	+	2.99276i	−0.0987192	+	0.110919i
$729$	9.95095	+	13.6963i	0.368554	+	0.507271i
$730$	9.24492	−	15.8286i	0.342170	−	0.585841i
$731$	16.2289	−	2.57041i	0.600248	−	0.0950700i
$732$	6.86082	+	8.71216i	0.253583	+	0.322011i
$733$	3.90316	+	24.6436i	0.144166	+	0.910231i	0.948666	+	0.316278i	$0.102433\pi$
$733$	3.90316	+	24.6436i	0.144166	+	0.910231i	−0.804500	+	0.593953i	$0.797567\pi$
$734$	51.3360	−	0.994842i	1.89485	−	0.0367203i
$735$	15.7608	+	1.21216i	0.581345	+	0.0447110i
$736$	22.3690	−	9.74999i	0.824532	−	0.359389i
$737$	0.0656582	−	0.202075i	0.00241855	−	0.00744353i
$738$	26.2494	−	0.508687i	0.966252	−	0.0187250i
$739$	−13.8010	+	27.0861i	−0.507679	+	0.996377i	0.484876	+	0.874583i	$0.338865\pi$
$739$	−13.8010	+	27.0861i	−0.507679	+	0.996377i	−0.992555	+	0.121794i	$0.961135\pi$
$740$	2.69256	−	0.763057i	0.0989804	−	0.0280505i
$741$	4.82210	+	9.46390i	0.177144	+	0.347665i
$742$	5.11999	−	2.73499i	0.187961	−	0.100405i
$743$		−	35.3535i		−	1.29699i	−0.761218	−	0.648497i	$-0.775398\pi$
$743$		−	35.3535i		−	1.29699i	0.761218	−	0.648497i	$-0.224602\pi$
$744$	−0.746895	+	1.70395i	−0.0273825	+	0.0624697i
$745$	−24.4006	+	28.6727i	−0.893968	+	1.05048i
$746$	−3.43619	+	0.612709i	−0.125808	+	0.0224329i
$747$	−5.11736	+	32.3097i	−0.187234	+	1.18215i
$748$	−1.39630	+	0.276992i	−0.0510539	+	0.0101278i
$749$	−1.39129	−	1.39129i	−0.0508366	−	0.0508366i
$750$	−12.6514	+	11.3580i	−0.461964	+	0.414735i
$751$	21.8745			0.798211			0.399106	−	0.916905i	$-0.369321\pi$
$751$	21.8745			0.798211			0.399106	+	0.916905i	$0.369321\pi$
$752$	46.6431	−	3.62240i	1.70090	−	0.132095i
$753$	13.5856	−	9.87050i	0.495086	−	0.359701i
$754$	−7.23773	+	10.3790i	−0.263582	+	0.377980i
$755$	0.554539	+	6.88918i	0.0201818	+	0.250723i
$756$	4.98866	+	4.61625i	0.181436	+	0.167891i
$757$	7.09097	−	7.09097i	0.257726	−	0.257726i	−0.566403	−	0.824129i	$-0.691665\pi$
$757$	7.09097	−	7.09097i	0.257726	−	0.257726i	0.824129	+	0.566403i	$0.191665\pi$
$758$	9.77823	+	18.3052i	0.355161	+	0.664873i
$759$	0.453703	+	0.147417i	0.0164684	+	0.00535090i
$760$	−23.5924	+	16.4783i	−0.855785	+	0.597729i
$761$	−38.2050	+	12.4136i	−1.38493	+	0.449991i	−0.904287	−	0.426925i	$-0.859597\pi$
$761$	−38.2050	+	12.4136i	−1.38493	+	0.449991i	−0.480643	+	0.876916i	$0.659597\pi$
$762$	19.3442	+	18.6087i	0.700765	+	0.674121i
$763$	−0.640398	−	1.25685i	−0.0231840	−	0.0455011i
$764$	−17.0078	−	11.3770i	−0.615320	−	0.411604i
$765$	18.5682	+	21.6623i	0.671333	+	0.783201i
$766$	34.3372	−	0.665422i	1.24065	−	0.0240427i
$767$	−18.5372	−	13.4681i	−0.669341	−	0.486305i
$768$	−5.28270	−	16.3735i	−0.190623	−	0.590829i
$769$	−17.7971	−	12.9304i	−0.641781	−	0.466281i	0.218680	−	0.975797i	$-0.429825\pi$
$769$	−17.7971	−	12.9304i	−0.641781	−	0.466281i	−0.860462	+	0.509515i	$0.829825\pi$
$770$	−0.0538938	−	0.205252i	−0.00194220	−	0.00739677i
$771$	−24.3790	−	3.86125i	−0.877987	−	0.139059i
$772$	3.24438	−	11.4810i	0.116768	−	0.413210i
$773$	−21.8210	−	11.1183i	−0.784846	−	0.399899i	0.0151644	−	0.999885i	$-0.495173\pi$
$773$	−21.8210	−	11.1183i	−0.784846	−	0.399899i	−0.800011	+	0.599986i	$0.795173\pi$
$774$	2.70321	−	5.56956i	0.0971648	−	0.200194i
$775$	−2.73013	−	1.37884i	−0.0980693	−	0.0495295i
$776$	10.9378	+	7.01367i	0.392642	+	0.251776i
$777$	−0.417565	+	0.135675i	−0.0149801	+	0.00486732i
$778$	−53.6808	+	9.57187i	−1.92455	+	0.343168i
$779$	7.16696	−	45.2504i	0.256783	−	1.62126i
$780$	−1.24015	−	10.3657i	−0.0444046	−	0.371151i
$781$	−0.0379421	−	0.239557i	−0.00135768	−	0.00857202i
$782$	−39.8907	+	13.8213i	−1.42649	+	0.494250i
$783$	17.3665	+	12.6175i	0.620629	+	0.450913i
$784$	−22.4077	−	13.7633i	−0.800276	−	0.491548i
$785$	−28.6498	−	24.3811i	−1.02256	−	0.870199i
$786$	2.84779	+	3.76406i	0.101577	+	0.134259i
$787$	−0.492391	+	0.250886i	−0.0175518	+	0.00894311i	−0.462744	−	0.886492i	$-0.653135\pi$
$787$	−0.492391	+	0.250886i	−0.0175518	+	0.00894311i	0.445193	+	0.895435i	$0.353135\pi$
$788$	−19.9062	−	9.18934i	−0.709128	−	0.327357i
$789$	9.39966	+	4.78936i	0.334637	+	0.170506i
$790$	7.25195	−	33.2947i	0.258013	−	1.18457i
$791$	−2.33791	−	0.759633i	−0.0831265	−	0.0270094i
$792$	−0.215321	+	0.491228i	−0.00765110	+	0.0174550i
$793$		−	11.1942i		−	0.397517i
$794$	18.2999	−	9.77545i	0.649441	−	0.346918i
$795$	−3.50476	+	14.7138i	−0.124301	+	0.521844i
$796$	34.8140	+	9.83798i	1.23395	+	0.348698i
$797$	−50.1614	−	7.94479i	−1.77681	−	0.281419i	−0.820048	−	0.572295i	$-0.806053\pi$
$797$	−50.1614	−	7.94479i	−1.77681	−	0.281419i	−0.956761	+	0.290876i	$0.906053\pi$
$798$	3.60036	−	2.72394i	0.127451	−	0.0964263i
$799$	−80.9406			−2.86347
$800$	27.3515	−	7.20367i	0.967023	−	0.254688i
$801$	−5.17052			−0.182691
$802$	17.8740	−	13.5230i	0.631152	−	0.477513i
$803$	−0.588837	−	0.0932627i	−0.0207796	−	0.00329117i
$804$	−4.27544	−	1.20818i	−0.150783	−	0.0426094i
$805$	−2.41878	−	5.81016i	−0.0852508	−	0.204781i
$806$	1.65652	−	0.884878i	0.0583484	−	0.0311685i
$807$			8.30047i			0.292190i
$808$	−32.6774	−	14.3236i	−1.14959	−	0.503901i
$809$	−11.6297	−	3.77873i	−0.408880	−	0.132853i	0.0973530	−	0.995250i	$-0.468962\pi$
$809$	−11.6297	−	3.77873i	−0.408880	−	0.132853i	−0.506233	+	0.862397i	$0.668962\pi$
$810$	−0.218147	+	0.0218211i	−0.00766490	+	0.000766715i
$811$	10.1905	+	5.19234i	0.357838	+	0.182328i	0.623662	−	0.781694i	$-0.285644\pi$
$811$	10.1905	+	5.19234i	0.357838	+	0.182328i	−0.265824	+	0.964022i	$0.585644\pi$
$812$	4.88310	+	2.25420i	0.171363	+	0.0791069i
$813$	−8.95787	+	4.56426i	−0.314166	+	0.160076i
$814$	−0.0549171	−	0.0725865i	−0.00192484	−	0.00254416i
$815$	−19.7272	+	12.1373i	−0.691015	+	0.425150i
$816$	6.91879	+	28.9506i	0.242206	+	1.01347i
$817$	−8.74006	−	6.35002i	−0.305776	−	0.222159i
$818$	31.0988	−	10.7751i	1.08734	−	0.376743i
$819$	−0.408550	−	2.57948i	−0.0142759	−	0.0901345i
$820$	−21.9527	+	39.3159i	−0.766622	+	1.37297i
$821$	−5.50189	+	34.7376i	−0.192017	+	1.21235i	0.683787	+	0.729682i	$0.260332\pi$
$821$	−5.50189	+	34.7376i	−0.192017	+	1.21235i	−0.875804	+	0.482667i	$0.839668\pi$
$822$	4.76990	−	0.850524i	0.166369	−	0.0296654i
$823$	0.347055	−	0.112765i	0.0120976	−	0.00393074i	−0.302962	−	0.953003i	$-0.597976\pi$
$823$	0.347055	−	0.112765i	0.0120976	−	0.00393074i	0.315060	+	0.949072i	$0.397976\pi$
$824$	18.4839	−	28.8255i	0.643917	−	1.00418i
$825$	0.493582	+	0.249282i	0.0171843	+	0.00867888i
$826$	−4.25257	+	8.76179i	−0.147966	+	0.304861i
$827$	−1.35390	−	0.689848i	−0.0470798	−	0.0239883i	0.430292	−	0.902690i	$-0.358411\pi$
$827$	−1.35390	−	0.689848i	−0.0470798	−	0.0239883i	−0.477372	+	0.878701i	$0.658411\pi$
$828$	−4.32557	+	15.3070i	−0.150324	+	0.531956i
$829$	−31.6916	−	5.01946i	−1.10070	−	0.174333i	−0.420449	−	0.907316i	$-0.638127\pi$
$829$	−31.6916	−	5.01946i	−1.10070	−	0.174333i	−0.680247	+	0.732983i	$0.738127\pi$
$830$	−43.4248	−	35.5273i	−1.50730	−	1.23317i
$831$	−6.53220	−	4.74592i	−0.226599	−	0.164634i
$832$	−6.03639	+	16.2846i	−0.209274	+	0.564566i
$833$	36.8077	+	26.7423i	1.27531	+	0.926567i
$834$	23.7362	−	0.459984i	0.821917	−	0.0159280i
$835$	6.35462	−	10.4114i	0.219911	−	0.360301i
$836$	0.777937	+	0.520383i	0.0269055	+	0.0179978i
$837$	−1.44645	−	2.83881i	−0.0499965	−	0.0981236i
$838$	−9.66494	−	9.29747i	−0.333870	−	0.321176i
$839$	21.4437	−	6.96747i	0.740317	−	0.240544i	0.0855077	−	0.996338i	$-0.472749\pi$
$839$	21.4437	−	6.96747i	0.740317	−	0.240544i	0.654810	+	0.755794i	$0.272749\pi$
$840$	−4.24497	+	1.29236i	−0.146465	+	0.0445908i
$841$	−11.4258	−	3.71248i	−0.393995	−	0.128017i
$842$	8.74549	+	16.3718i	0.301389	+	0.564210i
$843$	−11.6093	+	11.6093i	−0.399846	+	0.399846i
$844$	14.0764	+	13.0255i	0.484528	+	0.448358i
$845$	9.65402	−	15.8171i	0.332108	−	0.544125i
$846$	−17.4440	+	25.0149i	−0.599738	+	0.860031i
$847$	5.80096	−	4.21464i	0.199323	−	0.144817i
$848$	16.3616	−	19.1170i	0.561860	−	0.656479i
$849$	20.6086			0.707285
$850$	−48.1440	+	8.76169i	−1.65133	+	0.300523i
$851$	−1.90876	−	1.90876i	−0.0654315	−	0.0654315i
$852$	−4.97468	+	0.986853i	−0.170430	+	0.0338090i
$853$	−4.85608	+	30.6601i	−0.166269	+	1.04978i	0.753536	+	0.657407i	$0.228347\pi$
$853$	−4.85608	+	30.6601i	−0.166269	+	1.04978i	−0.919805	+	0.392375i	$0.871653\pi$
$854$	−4.68418	+	0.835240i	−0.160289	+	0.0285813i
$855$	1.43849	−	18.7037i	0.0491954	−	0.639652i
$856$	−7.81173	−	3.42414i	−0.266999	−	0.117035i
$857$		−	24.1978i		−	0.826580i	−0.910600	−	0.413290i	$-0.864380\pi$
$857$		−	24.1978i		−	0.826580i	0.910600	−	0.413290i	$-0.135620\pi$
$858$	−0.299483	+	0.159978i	−0.0102242	+	0.00546154i
$859$	−2.68504	−	5.26969i	−0.0916125	−	0.179800i	0.840653	−	0.541574i	$-0.182171\pi$
$859$	−2.68504	−	5.26969i	−0.0916125	−	0.179800i	−0.932266	+	0.361774i	$0.882171\pi$
$860$	5.91033	+	8.82126i	0.201541	+	0.300803i
$861$	3.20717	−	6.29443i	0.109300	−	0.214514i
$862$	5.23788	−	0.101505i	0.178403	−	0.00345727i
$863$	−12.2610	+	37.7355i	−0.417369	+	1.28453i	0.492745	+	0.870174i	$0.335993\pi$
$863$	−12.2610	+	37.7355i	−0.417369	+	1.28453i	−0.910115	+	0.414357i	$0.864007\pi$
$864$	27.4228	+	10.7740i	0.932944	+	0.366538i
$865$	16.6082	−	40.2987i	0.564696	−	1.37020i
$866$	−46.9712	+	0.910257i	−1.59615	+	0.0309318i
$867$	−5.19647	−	32.8092i	−0.176482	−	1.11426i
$868$	−0.493875	−	0.627143i	−0.0167632	−	0.0212866i
$869$	−1.09461	+	0.173369i	−0.0371320	+	0.00588112i
$870$	−12.8312	+	5.63579i	−0.435019	+	0.191071i
$871$	2.63615	+	3.62835i	0.0893226	+	0.122942i
$872$	−4.56770	−	4.06530i	−0.154682	−	0.137669i
$873$	−8.05533	+	2.61733i	−0.272632	+	0.0885834i
$874$	24.9714	+	12.1200i	0.844671	+	0.409964i
$875$	−1.74085	−	7.08419i	−0.0588516	−	0.239489i
$876$	−1.47164	+	12.3790i	−0.0497220	+	0.418247i
$877$	13.5184	−	26.5314i	0.456484	−	0.895900i	−0.541974	−	0.840395i	$-0.682323\pi$
$877$	13.5184	−	26.5314i	0.456484	−	0.895900i	0.998458	−	0.0555053i	$-0.0176770\pi$
$878$	10.3379	−	14.8247i	0.348888	−	0.500309i
$879$	19.1517	−	13.9145i	0.645971	−	0.469325i
$880$	−0.541263	−	0.743815i	−0.0182460	−	0.0250740i
$881$	21.9213	+	15.9268i	0.738547	+	0.536586i	0.892256	−	0.451530i	$-0.149122\pi$
$881$	21.9213	+	15.9268i	0.738547	+	0.536586i	−0.153709	+	0.988116i	$0.549122\pi$
$882$	16.1974	−	5.61210i	0.545396	−	0.188969i
$883$	0.137805	+	0.870066i	0.00463750	+	0.0292801i	0.989899	−	0.141777i	$-0.0452817\pi$
$883$	0.137805	+	0.870066i	0.00463750	+	0.0292801i	−0.985261	+	0.171057i	$0.945282\pi$
$884$	12.5937	−	27.2808i	0.423573	−	0.917553i
$885$	−9.75343	−	23.4287i	−0.327858	−	0.787548i
$886$	4.11627	−	29.7032i	0.138289	−	0.997899i
$887$	−25.4625	−	8.27327i	−0.854947	−	0.277789i	−0.151430	−	0.988468i	$-0.548388\pi$
$887$	−25.4625	−	8.27327i	−0.854947	−	0.277789i	−0.703517	+	0.710679i	$0.748388\pi$
$888$	−1.47217	+	1.20627i	−0.0494027	+	0.0404797i
$889$	−10.9533	+	3.55893i	−0.367361	+	0.119363i
$890$	4.47258	−	7.65766i	0.149921	−	0.256685i
$891$	0.00323710	+	0.00635316i	0.000108447	+	0.000212839i
$892$	38.9306	−	1.50944i	1.30349	−	0.0505399i
$893$	37.6304	+	37.6304i	1.25925	+	1.25925i
$894$	7.43896	−	24.5002i	0.248796	−	0.819409i
$895$	−47.1101	−	3.62322i	−1.57472	−	0.121111i
$896$	7.26465	+	1.31086i	0.242695	+	0.0437928i
$897$	−8.14646	+	5.91875i	−0.272002	+	0.197621i
$898$	44.3981	−	33.5905i	1.48158	−	1.12093i
$899$	−1.78271	−	1.78271i	−0.0594567	−	0.0594567i
$900$	−7.66801	+	16.7673i	−0.255600	+	0.558911i
$901$	−30.7833	+	30.7833i	−1.02554	+	1.02554i
$902$	1.45066	+	0.201032i	0.0483017	+	0.00669365i
$903$	−0.979148	−	1.34768i	−0.0325840	−	0.0448480i
$904$	−10.6381	+	0.619090i	−0.353819	+	0.0205906i
$905$	17.2211	−	4.16688i	0.572449	−	0.138512i
$906$	−2.21463	−	4.14587i	−0.0735763	−	0.137737i
$907$	23.7115	−	23.7115i	0.787328	−	0.787328i	−0.193727	−	0.981055i	$-0.562058\pi$
$907$	23.7115	−	23.7115i	0.787328	−	0.787328i	0.981055	+	0.193727i	$0.0620578\pi$
$908$	−17.8077	−	16.4783i	−0.590968	−	0.546852i
$909$	20.7228	−	10.5588i	0.687331	−	0.350213i
$910$	4.17368	+	1.62622i	0.138356	+	0.0539087i
$911$	−8.76653	−	26.9806i	−0.290448	−	0.893907i	−0.984713	−	0.174187i	$-0.944270\pi$
$911$	−8.76653	−	26.9806i	−0.290448	−	0.893907i	0.694265	−	0.719720i	$-0.255730\pi$
$912$	10.2429	−	16.6762i	0.339176	−	0.552203i
$913$	−0.563886	+	1.73546i	−0.0186619	+	0.0574355i
$914$	−27.9081	−	36.8875i	−0.923119	−	1.22013i
$915$	6.45921	−	10.5827i	0.213535	−	0.349854i
$916$	6.14867	+	2.83843i	0.203158	+	0.0937843i
$917$	−2.00025	+	0.316809i	−0.0660541	+	0.0104619i
$918$	−45.8587	−	22.2577i	−1.51356	−	0.734614i
$919$	−26.9878	+	37.1455i	−0.890244	+	1.22532i	0.0832323	+	0.996530i	$0.473476\pi$
$919$	−26.9878	+	37.1455i	−0.890244	+	1.22532i	−0.973477	+	0.228786i	$0.926524\pi$
$920$	−18.9284	−	19.6471i	−0.624051	−	0.647745i
$921$	−11.6084	−	15.9776i	−0.382511	−	0.526481i
$922$	5.68694	+	31.8934i	0.187289	+	1.05035i
$923$	4.56158	+	2.32424i	0.150146	+	0.0765033i
$924$	0.0892879	+	0.113382i	0.00293736	+	0.00372998i
$925$	−1.84814	−	2.52478i	−0.0607665	−	0.0830144i
$926$	10.4024	+	30.0231i	0.341845	+	0.986622i
$927$	6.89775	+	21.2291i	0.226552	+	0.697255i
$928$	23.2721	+	1.40259i	0.763944	+	0.0460424i
$929$	20.9041	−	15.1877i	0.685841	−	0.498292i	−0.189450	−	0.981890i	$-0.560670\pi$
$929$	20.9041	−	15.1877i	0.685841	−	0.498292i	0.875290	+	0.483598i	$0.160670\pi$
$930$	2.07663	+	0.119292i	0.0680952	+	0.00391173i
$931$	−4.67950	−	29.5452i	−0.153365	−	0.968306i
$932$	−17.7378	−	22.5242i	−0.581020	−	0.737804i
$933$	19.0499	−	3.01720i	0.623665	−	0.0987788i
$934$	−24.4605	−	23.5304i	−0.800371	−	0.769939i
$935$	0.833991	+	1.35552i	0.0272744	+	0.0443304i
$936$	−5.71706	−	9.77159i	−0.186868	−	0.319394i
$937$	34.3053	+	11.1465i	1.12071	+	0.364139i	0.810037	−	0.586379i	$-0.199447\pi$
$937$	34.3053	+	11.1465i	1.12071	+	0.364139i	0.310669	+	0.950518i	$0.399447\pi$
$938$	1.32158	−	1.37382i	0.0431513	−	0.0448568i
$939$	13.1757	+	6.71336i	0.429973	+	0.219082i
$940$	−21.9583	−	47.4733i	−0.716202	−	1.54841i
$941$	−45.4624	+	23.1643i	−1.48203	+	0.755133i	−0.993109	−	0.117193i	$-0.962610\pi$
$941$	−45.4624	+	23.1643i	−1.48203	+	0.755133i	−0.488923	+	0.872327i	$0.662610\pi$
$942$	24.4807	+	7.43303i	0.797623	+	0.242181i
$943$	43.4335			1.41439
$944$	−3.35592	+	42.0850i	−0.109226	+	1.36975i
$945$	2.89552	−	7.02578i	0.0941913	−	0.228549i
$946$	0.197536	−	0.283268i	0.00642245	−	0.00920985i
$947$	−48.1343	−	7.62372i	−1.56415	−	0.247738i	−0.686535	−	0.727097i	$-0.740869\pi$
$947$	−48.1343	−	7.62372i	−1.56415	−	0.247738i	−0.877619	+	0.479360i	$0.840869\pi$
$948$	4.50922	+	22.7307i	0.146453	+	0.738260i
$949$	8.89827	−	8.89827i	0.288850	−	0.288850i
$950$	26.4562	+	18.3094i	0.858353	+	0.594035i
$951$			3.64862i			0.118315i
$952$	−12.3553	−	3.23430i	−0.400437	−	0.104824i
$953$	13.6765	+	18.8240i	0.443024	+	0.609770i	0.970881	−	0.239563i	$-0.0770043\pi$
$953$	13.6765	+	18.8240i	0.443024	+	0.609770i	−0.527857	+	0.849333i	$0.677004\pi$
$954$	2.87935	+	16.1480i	0.0932226	+	0.522809i
$955$	−5.30099	+	22.2548i	−0.171536	+	0.720147i
$956$	−22.6247	+	0.877220i	−0.731735	+	0.0283713i
$957$	0.322297	+	0.322297i	0.0104184	+	0.0104184i
$958$	−13.9791	+	46.0401i	−0.451644	+	1.48749i
$959$	−0.642413	+	1.97715i	−0.0207446	+	0.0638453i
$960$	−15.1031	+	11.9120i	−0.487451	+	0.384458i
$961$	−9.46389	−	29.1269i	−0.305287	−	0.939577i
$962$	1.92089	−	0.0372250i	0.0619319	−	0.00120018i
$963$	4.95391	−	2.52414i	0.159638	−	0.0813394i
$964$	−41.4412	−	27.7211i	−1.33473	−	0.892837i
$965$	−13.2958	+	1.07024i	−0.428008	+	0.0344522i
$966$	3.08453	+	2.96725i	0.0992431	+	0.0954697i
$967$	17.4576	−	24.0283i	0.561399	−	0.772699i	−0.430105	−	0.902779i	$-0.641523\pi$
$967$	17.4576	−	24.0283i	0.561399	−	0.772699i	0.991504	+	0.130080i	$0.0415234\pi$
$968$	16.7782	−	26.1655i	0.539272	−	0.840990i
$969$	−19.9020	+	27.3928i	−0.639345	+	0.879983i
$970$	3.09165	−	14.1942i	0.0992668	−	0.455747i
$971$	−7.71387	+	48.7034i	−0.247550	+	1.56297i	0.480221	+	0.877147i	$0.340556\pi$
$971$	−7.71387	+	48.7034i	−0.247550	+	1.56297i	−0.727771	+	0.685820i	$0.759444\pi$
$972$	−27.1438	+	15.1828i	−0.870638	+	0.486990i
$973$	−4.62451	+	9.07611i	−0.148255	+	0.290967i
$974$	−18.5984	+	6.44397i	−0.595930	+	0.206478i
$975$	−10.3807	+	5.33592i	−0.332450	+	0.170886i
$976$	−17.5974	+	10.7587i	−0.563279	+	0.344378i
$977$	−7.15639	−	22.0251i	−0.228953	−	0.704646i	−0.997866	−	0.0652921i	$-0.979202\pi$
$977$	−7.15639	−	22.0251i	−0.228953	−	0.704646i	0.768913	−	0.639353i	$-0.220798\pi$
$978$	9.01005	−	12.9205i	0.288110	−	0.413152i
$979$	−0.284872	−	0.0451193i	−0.00910456	−	0.00144202i
$980$	−5.69938	+	28.8433i	−0.182060	+	0.921366i
$981$	3.93694	−	0.623550i	0.125697	−	0.0199084i
$982$	−31.7345	−	15.4025i	−1.01269	−	0.491513i
$983$	−20.3291	+	27.9807i	−0.648399	+	0.892444i	−0.999028	−	0.0440697i	$-0.985968\pi$
$983$	−20.3291	+	27.9807i	−0.648399	+	0.892444i	0.350630	+	0.936514i	$0.385968\pi$
$984$	3.02524	−	30.4736i	0.0964410	−	0.971463i
$985$	−1.87971	+	24.4406i	−0.0598927	+	0.778741i
$986$	−39.9544	−	5.53689i	−1.27241	−	0.176330i
$987$	3.72540	+	7.31151i	0.118581	+	0.232728i
$988$	−18.5382	+	6.82822i	−0.589779	+	0.217235i
$989$	4.64970	−	9.12556i	0.147852	−	0.290176i
$990$	0.598667	+	0.0343904i	0.0190269	+	0.00109300i
$991$	−1.22918	+	3.78303i	−0.0390462	+	0.120172i	−0.968680	−	0.248314i	$-0.920124\pi$
$991$	−1.22918	+	3.78303i	−0.0390462	+	0.120172i	0.929633	+	0.368486i	$0.120124\pi$
$992$	−2.98312	−	1.75362i	−0.0947142	−	0.0556774i
$993$	−28.0020			−0.888618
$994$	0.632218	−	2.08221i	0.0200527	−	0.0660436i
$995$	−3.24530	−	40.3171i	−0.102883	−	1.27814i
$996$	36.7184	+	10.3761i	1.16347	+	0.328781i
$997$	3.15560	−	19.9237i	0.0999388	−	0.630988i	−0.885975	−	0.463733i	$-0.846510\pi$
$997$	3.15560	−	19.9237i	0.0999388	−	0.630988i	0.985914	−	0.167255i	$-0.0534904\pi$
$998$	−28.6598	−	3.97168i	−0.907210	−	0.125721i
$999$		−	3.25936i		−	0.103122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.be.a.381.11	yes	464
16.5	even	4	inner	400.2.be.a.181.58	yes	464
25.21	even	5	inner	400.2.be.a.221.58	yes	464
400.21	even	20	inner	400.2.be.a.21.11	✓	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.be.a.21.11	✓	464	400.21	even	20	inner
400.2.be.a.181.58	yes	464	16.5	even	4	inner
400.2.be.a.221.58	yes	464	25.21	even	5	inner
400.2.be.a.381.11	yes	464	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.be (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12780 + 0.853266i) q^{2} +(-1.06205 - 0.168212i) q^{3} +(0.543875 - 1.92463i) q^{4} +(-2.22886 + 0.179410i) q^{5} +(1.34131 - 0.716502i) q^{6} +0.652480i q^{7} +(1.02884 + 2.63467i) q^{8} +(-1.75351 - 0.569750i) q^{9} +O(q^{10})\)	\(q+(-1.12780 + 0.853266i) q^{2} +(-1.06205 - 0.168212i) q^{3} +(0.543875 - 1.92463i) q^{4} +(-2.22886 + 0.179410i) q^{5} +(1.34131 - 0.716502i) q^{6} +0.652480i q^{7} +(1.02884 + 2.63467i) q^{8} +(-1.75351 - 0.569750i) q^{9} +(2.36063 - 2.10415i) q^{10} +(-0.0916387 - 0.0466923i) q^{11} +(-0.901370 + 1.95257i) q^{12} +(1.93430 - 0.985577i) q^{13} +(-0.556739 - 0.735868i) q^{14} +(2.39734 + 0.184379i) q^{15} +(-3.40840 - 2.09352i) q^{16} +(5.59874 + 4.06773i) q^{17} +(2.46376 - 0.853645i) q^{18} +(-0.711791 - 4.49407i) q^{19} +(-0.866923 + 4.38730i) q^{20} +(0.109755 - 0.692967i) q^{21} +(0.143191 - 0.0255325i) q^{22} +(4.10250 - 1.33298i) q^{23} +(-0.649493 - 2.97122i) q^{24} +(4.93562 - 0.799761i) q^{25} +(-1.34055 + 2.76201i) q^{26} +(4.64075 + 2.36458i) q^{27} +(1.25578 + 0.354868i) q^{28} +(4.07069 + 0.644733i) q^{29} +(-2.86105 + 1.83763i) q^{30} +(-0.494887 - 0.359556i) q^{31} +(5.63033 - 0.547196i) q^{32} +(0.0894708 + 0.0650044i) q^{33} +(-9.78513 + 0.189626i) q^{34} +(-0.117062 - 1.45429i) q^{35} +(-2.05025 + 3.06499i) q^{36} +(-0.284100 - 0.557578i) q^{37} +(4.63739 + 4.46107i) q^{38} +(-2.22012 + 0.721359i) q^{39} +(-2.76582 - 5.68773i) q^{40} +(9.57611 + 3.11147i) q^{41} +(0.467503 + 0.875180i) q^{42} +(1.67889 - 1.67889i) q^{43} +(-0.139705 + 0.150976i) q^{44} +(4.01055 + 0.955295i) q^{45} +(-3.48942 + 5.00386i) q^{46} +(-9.46218 + 6.87468i) q^{47} +(3.26774 + 2.79676i) q^{48} +6.57427 q^{49} +(-4.88400 + 5.11337i) q^{50} +(-5.26191 - 5.26191i) q^{51} +(-0.844850 - 4.25885i) q^{52} +(-0.984078 + 6.21322i) q^{53} +(-7.25147 + 1.29301i) q^{54} +(0.212627 + 0.0876295i) q^{55} +(-1.71907 + 0.671295i) q^{56} +4.89267i q^{57} +(-5.14106 + 2.74624i) q^{58} +(-4.79171 - 9.40426i) q^{59} +(1.65872 - 4.51372i) q^{60} +(2.34097 - 4.59440i) q^{61} +(0.864931 - 0.0167615i) q^{62} +(0.371751 - 1.14413i) q^{63} +(-5.88299 + 5.42129i) q^{64} +(-4.13447 + 2.54375i) q^{65} +(-0.156371 + 0.00303033i) q^{66} +(0.323177 + 2.04046i) q^{67} +(10.8739 - 8.56317i) q^{68} +(-4.58129 + 0.725604i) q^{69} +(1.37291 + 1.54026i) q^{70} +(1.38615 + 1.90787i) q^{71} +(-0.302972 - 5.20611i) q^{72} +(5.51294 - 1.79126i) q^{73} +(0.796171 + 0.386425i) q^{74} +(-5.37642 + 0.0191542i) q^{75} +(-9.03655 - 1.07428i) q^{76} +(0.0304658 - 0.0597924i) q^{77} +(1.88834 - 2.70790i) q^{78} +(8.71761 - 6.33371i) q^{79} +(7.97244 + 4.05465i) q^{80} +(-0.0560878 - 0.0407502i) q^{81} +(-13.4549 + 4.66185i) q^{82} +(-2.77551 - 17.5239i) q^{83} +(-1.27401 - 0.588126i) q^{84} +(-13.2086 - 8.06191i) q^{85} +(-0.460916 + 3.32599i) q^{86} +(-4.21483 - 1.36948i) q^{87} +(0.0287375 - 0.289477i) q^{88} +(2.66709 - 0.866592i) q^{89} +(-5.33823 + 2.34468i) q^{90} +(0.643069 + 1.26209i) q^{91} +(-0.334250 - 8.62076i) q^{92} +(0.465113 + 0.465113i) q^{93} +(4.80554 - 15.8270i) q^{94} +(2.39276 + 9.88894i) q^{95} +(-6.07174 - 0.365940i) q^{96} +(3.71648 - 2.70018i) q^{97} +(-7.41448 + 5.60960i) q^{98} +(0.134087 + 0.134087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) \) 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8	\( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99}+O(q^{100}) \) 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8 - 14 * q^10 - 6 * q^11 + 10 * q^12 - 6 * q^13 + 6 * q^14 - 16 * q^15 - 6 * q^16 - 12 * q^17 - 24 * q^18 - 6 * q^19 - 22 * q^20 + 12 * q^21 + 10 * q^22 - 16 * q^24 + 4 * q^26 - 18 * q^27 + 18 * q^28 - 6 * q^29 - 6 * q^30 + 12 * q^31 - 36 * q^32 - 12 * q^33 - 30 * q^34 + 44 * q^35 - 82 * q^36 - 6 * q^37 - 76 * q^38 - 52 * q^40 - 10 * q^42 - 48 * q^43 + 36 * q^44 - 12 * q^45 - 14 * q^46 - 12 * q^47 - 116 * q^48 - 400 * q^49 + 10 * q^50 - 4 * q^51 + 32 * q^52 - 6 * q^53 - 30 * q^54 + 36 * q^56 + 26 * q^58 - 6 * q^59 + 48 * q^60 - 6 * q^61 - 34 * q^62 + 72 * q^63 - 24 * q^64 + 16 * q^65 + 92 * q^66 + 30 * q^67 + 28 * q^68 - 18 * q^69 + 60 * q^70 + 22 * q^72 + 28 * q^74 - 26 * q^75 - 76 * q^76 + 36 * q^77 + 14 * q^78 - 52 * q^79 - 34 * q^80 + 72 * q^81 + 56 * q^82 - 46 * q^83 + 112 * q^84 + 2 * q^85 - 46 * q^86 - 136 * q^88 - 42 * q^90 + 36 * q^91 - 4 * q^93 + 50 * q^94 - 40 * q^95 - 66 * q^96 - 12 * q^97 - 8 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more