LMFDB - Embedded newform 690.2.w.b.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	690.37
Dual form			690.2.w.b.373.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.18586 - 0.471182i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33355 + 3.57540i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.18586 - 0.471182i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33355 + 3.57540i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-2.14430 - 0.634025i) q^{10} +(0.274213 - 0.933883i) q^{11} +(0.479249 + 0.877679i) q^{12} +(-0.363351 - 0.135523i) q^{13} +(0.543073 - 3.77716i) q^{14} +(2.21391 - 0.314044i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(6.16390 - 1.34087i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-4.73875 + 3.04541i) q^{19} +(1.57815 + 1.58412i) q^{20} +(1.07509 + 3.66142i) q^{21} +(-0.688234 + 0.688234i) q^{22} +(-3.01793 + 3.72721i) q^{23} -1.00000i q^{24} +(4.55597 - 2.05988i) q^{25} +(0.253957 + 0.293081i) q^{26} +(0.977147 + 0.212565i) q^{27} +(-2.28684 + 3.05486i) q^{28} +(-1.75012 + 2.72324i) q^{29} +(-2.09360 - 0.785382i) q^{30} +(0.0490589 - 0.0566169i) q^{31} +(0.800541 - 0.599278i) q^{32} +(0.340137 - 0.911942i) q^{33} +(-6.05253 - 1.77718i) q^{34} +(4.59963 + 7.18698i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-5.11516 - 6.83305i) q^{37} +(5.61861 - 0.401851i) q^{38} +(-0.352757 - 0.161099i) q^{39} +(-0.625919 - 2.14668i) q^{40} +(0.842836 + 5.86205i) q^{41} +(0.811149 - 3.72879i) q^{42} +(0.138451 - 1.93580i) q^{43} +(0.933883 - 0.274213i) q^{44} +(2.23067 - 0.155306i) q^{45} +(4.43504 - 1.82495i) q^{46} +(-7.27937 - 7.27937i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(-5.71486 + 4.95196i) q^{49} +(-4.98588 - 0.375535i) q^{50} +(6.24385 - 0.897730i) q^{51} +(-0.0824333 - 0.378940i) q^{52} +(11.9363 - 4.45203i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(0.159362 - 2.17054i) q^{55} +(3.47115 - 1.58522i) q^{56} +(-4.94393 + 2.69959i) q^{57} +(2.84115 - 1.55139i) q^{58} +(11.1289 - 5.08238i) q^{59} +(1.46112 + 1.69267i) q^{60} +(5.42228 + 4.69843i) q^{61} +(-0.0701916 + 0.0261801i) q^{62} +(0.811149 + 3.72879i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-0.858092 - 0.125030i) q^{65} +(-0.735578 + 0.637382i) q^{66} +(-2.25028 + 4.12107i) q^{67} +(4.46047 + 4.46047i) q^{68} +(-3.27614 + 3.50242i) q^{69} +(-0.592647 - 8.51223i) q^{70} +(-3.89999 + 1.14514i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(0.475950 - 2.18791i) q^{73} +(1.21473 + 8.44866i) q^{74} +(4.69132 - 1.72961i) q^{75} +(-5.12392 - 2.34002i) q^{76} +(3.70468 - 0.264964i) q^{77} +(0.232401 + 0.310452i) q^{78} +(2.42651 + 5.31332i) q^{79} +(-0.479437 + 2.18407i) q^{80} +(0.959493 + 0.281733i) q^{81} +(2.06964 - 5.54893i) q^{82} +(2.85816 - 2.13959i) q^{83} +(-2.49895 + 2.88394i) q^{84} +(12.8416 - 5.83528i) q^{85} +(-1.04925 + 1.63266i) q^{86} +(-1.93993 + 2.59145i) q^{87} +(-0.951066 - 0.206892i) q^{88} +(0.830562 + 0.958520i) q^{89} +(-2.03224 - 0.932737i) q^{90} -1.47985i q^{91} +(-4.76715 - 0.523762i) q^{92} +(0.0529729 - 0.0529729i) q^{93} +(2.90032 + 9.87758i) q^{94} +(-8.92330 + 8.88965i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-10.6558 - 7.97683i) q^{97} +(7.38904 - 1.60739i) q^{98} +(0.404327 - 0.885353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$3$	0.997452	+	0.0713392i	0.575879	+	0.0411877i
$3$	0.997452	+	0.0713392i	0.575879	+	0.0411877i
$4$	0.540641	+	0.841254i	0.270320	+	0.420627i
$5$	2.18586	−	0.471182i	0.977547	−	0.210719i
$5$	2.18586	−	0.471182i	0.977547	−	0.210719i
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	1.33355	+	3.57540i	0.504036	+	1.35137i	0.901111	+	0.433588i	$0.142753\pi$
$7$	1.33355	+	3.57540i	0.504036	+	1.35137i	−0.397075	+	0.917786i	$0.629975\pi$
$8$	−0.0713392	−	0.997452i	−0.0252222	−	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	−2.14430	−	0.634025i	−0.678086	−	0.200496i
$11$	0.274213	−	0.933883i	0.0826783	−	0.281576i	−0.907769	−	0.419471i	$-0.862215\pi$
$11$	0.274213	−	0.933883i	0.0826783	−	0.281576i	0.990447	+	0.137895i	$0.0440336\pi$
$12$	0.479249	+	0.877679i	0.138347	+	0.253364i
$13$	−0.363351	−	0.135523i	−0.100776	−	0.0375873i	0.298571	−	0.954388i	$-0.403490\pi$
$13$	−0.363351	−	0.135523i	−0.100776	−	0.0375873i	−0.399346	+	0.916800i	$0.630763\pi$
$14$	0.543073	−	3.77716i	0.145142	−	1.00949i
$15$	2.21391	−	0.314044i	0.571628	−	0.0810859i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	6.16390	−	1.34087i	1.49496	−	0.325210i	0.610574	−	0.791959i	$-0.290939\pi$
$17$	6.16390	−	1.34087i	1.49496	−	0.325210i	0.884390	+	0.466749i	$0.154575\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	−4.73875	+	3.04541i	−1.08714	+	0.698665i	−0.956197	−	0.292725i	$-0.905438\pi$
$19$	−4.73875	+	3.04541i	−1.08714	+	0.698665i	−0.130947	+	0.991389i	$0.541802\pi$
$20$	1.57815	+	1.58412i	0.352885	+	0.354221i
$21$	1.07509	+	3.66142i	0.234604	+	0.798988i
$22$	−0.688234	+	0.688234i	−0.146732	+	0.146732i
$23$	−3.01793	+	3.72721i	−0.629282	+	0.777177i
$23$	−3.01793	+	3.72721i	−0.629282	+	0.777177i
$24$		−	1.00000i		−	0.204124i
$25$	4.55597	−	2.05988i	0.911195	−	0.411976i
$26$	0.253957	+	0.293081i	0.0498050	+	0.0574780i
$27$	0.977147	+	0.212565i	0.188052	+	0.0409082i
$28$	−2.28684	+	3.05486i	−0.432173	+	0.577315i
$29$	−1.75012	+	2.72324i	−0.324989	+	0.505692i	−0.964851	−	0.262797i	$-0.915355\pi$
$29$	−1.75012	+	2.72324i	−0.324989	+	0.505692i	0.639862	+	0.768490i	$0.278991\pi$
$30$	−2.09360	−	0.785382i	−0.382238	−	0.143390i
$31$	0.0490589	−	0.0566169i	0.00881123	−	0.0101687i	−0.751327	−	0.659930i	$-0.770586\pi$
$31$	0.0490589	−	0.0566169i	0.00881123	−	0.0101687i	0.760138	+	0.649762i	$0.225131\pi$
$32$	0.800541	−	0.599278i	0.141517	−	0.105938i
$33$	0.340137	−	0.911942i	0.0592102	−	0.158749i
$34$	−6.05253	−	1.77718i	−1.03800	−	0.304785i
$35$	4.59963	+	7.18698i	0.777479	+	1.21482i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−5.11516	−	6.83305i	−0.840927	−	1.12335i	−0.990892	−	0.134656i	$-0.957007\pi$
$37$	−5.11516	−	6.83305i	−0.840927	−	1.12335i	0.149965	−	0.988691i	$-0.452084\pi$
$38$	5.61861	−	0.401851i	0.911459	−	0.0651888i
$39$	−0.352757	−	0.161099i	−0.0564864	−	0.0257965i
$40$	−0.625919	−	2.14668i	−0.0989665	−	0.339420i
$41$	0.842836	+	5.86205i	0.131629	+	0.915499i	0.943432	+	0.331567i	$0.107577\pi$
$41$	0.842836	+	5.86205i	0.131629	+	0.915499i	−0.811803	+	0.583932i	$0.801514\pi$
$42$	0.811149	−	3.72879i	0.125163	−	0.575365i
$43$	0.138451	−	1.93580i	0.0211136	−	0.295207i	−0.975914	−	0.218157i	$-0.929995\pi$
$43$	0.138451	−	1.93580i	0.0211136	−	0.295207i	0.997027	−	0.0770499i	$-0.0245501\pi$
$44$	0.933883	−	0.274213i	0.140788	−	0.0413392i
$45$	2.23067	−	0.155306i	0.332528	−	0.0231516i
$46$	4.43504	−	1.82495i	0.653910	−	0.269075i
$47$	−7.27937	−	7.27937i	−1.06181	−	1.06181i	−0.997960	−	0.0638453i	$-0.979664\pi$
$47$	−7.27937	−	7.27937i	−1.06181	−	1.06181i	−0.0638453	−	0.997960i	$-0.520336\pi$
$48$	−0.479249	+	0.877679i	−0.0691736	+	0.126682i
$49$	−5.71486	+	4.95196i	−0.816409	+	0.707422i
$50$	−4.98588	−	0.375535i	−0.705110	−	0.0531086i
$51$	6.24385	−	0.897730i	0.874313	−	0.125707i
$52$	−0.0824333	−	0.378940i	−0.0114314	−	0.0525495i
$53$	11.9363	−	4.45203i	1.63958	−	0.611533i	0.650582	−	0.759436i	$-0.274525\pi$
$53$	11.9363	−	4.45203i	1.63958	−	0.611533i	0.989002	+	0.147903i	$0.0472525\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	0.159362	−	2.17054i	0.0214884	−	0.292676i
$56$	3.47115	−	1.58522i	0.463853	−	0.211834i
$57$	−4.94393	+	2.69959i	−0.654840	+	0.357569i
$58$	2.84115	−	1.55139i	0.373061	−	0.203707i
$59$	11.1289	−	5.08238i	1.44886	−	0.661670i	0.473195	−	0.880958i	$-0.343101\pi$
$59$	11.1289	−	5.08238i	1.44886	−	0.661670i	0.975660	+	0.219288i	$0.0703733\pi$
$60$	1.46112	+	1.69267i	0.188630	+	0.218523i
$61$	5.42228	+	4.69843i	0.694251	+	0.601572i	0.928822	−	0.370527i	$-0.120823\pi$
$61$	5.42228	+	4.69843i	0.694251	+	0.601572i	−0.234570	+	0.972099i	$0.575368\pi$
$62$	−0.0701916	+	0.0261801i	−0.00891434	+	0.00332488i
$63$	0.811149	+	3.72879i	0.102195	+	0.469784i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	−0.858092	−	0.125030i	−0.106433	−	0.0155080i
$66$	−0.735578	+	0.637382i	−0.0905434	+	0.0784563i
$67$	−2.25028	+	4.12107i	−0.274915	+	0.503469i	−0.978261	−	0.207379i	$-0.933507\pi$
$67$	−2.25028	+	4.12107i	−0.274915	+	0.503469i	0.703346	+	0.710848i	$0.251689\pi$
$68$	4.46047	+	4.46047i	0.540911	+	0.540911i
$69$	−3.27614	+	3.50242i	−0.394401	+	0.421642i
$70$	−0.592647	−	8.51223i	−0.0708349	−	1.01741i
$71$	−3.89999	+	1.14514i	−0.462844	+	0.135903i	−0.504837	−	0.863215i	$-0.668447\pi$
$71$	−3.89999	+	1.14514i	−0.462844	+	0.135903i	0.0419930	+	0.999118i	$0.486629\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	0.475950	−	2.18791i	0.0557058	−	0.256075i	−0.940869	−	0.338770i	$-0.889989\pi$
$73$	0.475950	−	2.18791i	0.0557058	−	0.256075i	0.996575	+	0.0826949i	$0.0263527\pi$
$74$	1.21473	+	8.44866i	0.141210	+	0.982137i
$75$	4.69132	−	1.72961i	0.541707	−	0.199718i
$76$	−5.12392	−	2.34002i	−0.587754	−	0.268418i
$77$	3.70468	−	0.264964i	0.422188	−	0.0301955i
$78$	0.232401	+	0.310452i	0.0263143	+	0.0351517i
$79$	2.42651	+	5.31332i	0.273004	+	0.597795i	0.995624	−	0.0934502i	$-0.0297896\pi$
$79$	2.42651	+	5.31332i	0.273004	+	0.597795i	−0.722620	+	0.691246i	$0.757062\pi$
$80$	−0.479437	+	2.18407i	−0.0536027	+	0.244186i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	2.06964	−	5.54893i	0.228554	−	0.612777i
$83$	2.85816	−	2.13959i	0.313723	−	0.234850i	−0.430799	−	0.902448i	$-0.641768\pi$
$83$	2.85816	−	2.13959i	0.313723	−	0.234850i	0.744522	+	0.667598i	$0.232677\pi$
$84$	−2.49895	+	2.88394i	−0.272658	+	0.314664i
$85$	12.8416	−	5.83528i	1.39287	−	0.632925i
$86$	−1.04925	+	1.63266i	−0.113143	+	0.176054i
$87$	−1.93993	+	2.59145i	−0.207983	+	0.277832i
$88$	−0.951066	−	0.206892i	−0.101384	−	0.0220547i
$89$	0.830562	+	0.958520i	0.0880394	+	0.101603i	0.798060	−	0.602578i	$-0.205860\pi$
$89$	0.830562	+	0.958520i	0.0880394	+	0.101603i	−0.710021	+	0.704181i	$0.751314\pi$
$90$	−2.03224	−	0.932737i	−0.214217	−	0.0983191i
$91$		−	1.47985i		−	0.155131i
$92$	−4.76715	−	0.523762i	−0.497009	−	0.0546059i
$93$	0.0529729	−	0.0529729i	0.00549303	−	0.00549303i
$94$	2.90032	+	9.87758i	0.299145	+	1.01879i
$95$	−8.92330	+	8.88965i	−0.915511	+	0.912059i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	−10.6558	−	7.97683i	−1.08193	−	0.809925i	−0.0992207	−	0.995065i	$-0.531635\pi$
$97$	−10.6558	−	7.97683i	−1.08193	−	0.809925i	−0.982712	+	0.185141i	$0.940726\pi$
$98$	7.38904	−	1.60739i	0.746405	−	0.162371i
$99$	0.404327	−	0.885353i	0.0406364	−	0.0889814i
$100$	4.19603	+	2.71908i	0.419603	+	0.271908i
$101$	1.55156	−	10.7913i	0.154386	−	1.07378i	−0.754370	−	0.656450i	$-0.772057\pi$
$101$	1.55156	−	10.7913i	0.154386	−	1.07378i	0.908756	−	0.417328i	$-0.137033\pi$
$102$	−5.91033	−	2.20444i	−0.585210	−	0.218272i
$103$	−5.67500	−	10.3930i	−0.559174	−	1.02405i	−0.992434	−	0.122782i	$-0.960819\pi$
$103$	−5.67500	−	10.3930i	−0.559174	−	1.02405i	0.433260	−	0.901269i	$-0.357363\pi$
$104$	−0.109257	+	0.372094i	−0.0107135	+	0.0364868i
$105$	4.07520	+	7.49680i	0.397699	+	0.731613i
$106$	−12.6099	−	1.81303i	−1.22478	−	0.176097i
$107$	−1.22992	−	17.1965i	−0.118901	−	1.66245i	−0.610793	−	0.791791i	$-0.709149\pi$
$107$	−1.22992	−	17.1965i	−0.118901	−	1.66245i	0.491892	−	0.870656i	$-0.336305\pi$
$108$	0.349464	+	0.936950i	0.0336272	+	0.0901580i
$109$	−10.2548	−	6.59035i	−0.982231	−	0.631241i	−0.0521665	−	0.998638i	$-0.516613\pi$
$109$	−10.2548	−	6.59035i	−0.982231	−	0.631241i	−0.930064	+	0.367397i	$0.880249\pi$
$110$	−1.18010	+	1.82867i	−0.112518	+	0.174356i
$111$	−4.61466	−	7.18056i	−0.438004	−	0.681548i
$112$	−3.80628	−	0.272230i	−0.359659	−	0.0257233i
$113$	11.8013	+	6.44401i	1.11018	+	0.606202i	0.926315	−	0.376750i	$-0.122959\pi$
$113$	11.8013	+	6.44401i	1.11018	+	0.606202i	0.183861	+	0.982952i	$0.441140\pi$
$114$	5.63296			0.527575
$115$	−4.84058	+	9.56916i	−0.451386	+	0.892329i
$116$	−3.23712			−0.300559
$117$	−0.340366	−	0.185854i	−0.0314668	−	0.0171822i
$118$	−12.2033	−	0.872797i	−1.12341	−	0.0803475i
$119$	13.0140	+	20.2503i	1.19300	+	1.85634i
$120$	−0.471182	−	2.18586i	−0.0430129	−	0.199541i
$121$	8.45684	+	5.43488i	0.768804	+	0.494080i
$122$	−2.50730	−	6.72233i	−0.227000	−	0.608611i
$123$	0.422495	+	5.90725i	0.0380950	+	0.532638i
$124$	0.0741524	+	0.0106615i	0.00665909	+	0.000957432i
$125$	8.98815	−	6.64930i	0.803924	−	0.594731i
$126$	1.07509	−	3.66142i	0.0957767	−	0.326186i
$127$	−0.372763	−	0.682665i	−0.0330774	−	0.0605768i	0.860618	−	0.509252i	$-0.170078\pi$
$127$	−0.372763	−	0.682665i	−0.0330774	−	0.0605768i	−0.893695	+	0.448675i	$0.851896\pi$
$128$	0.936950	+	0.349464i	0.0828154	+	0.0308886i
$129$	0.276197	−	1.92099i	0.0243178	−	0.169134i
$130$	0.693208	+	0.520976i	0.0607984	+	0.0456926i
$131$	−2.71596	+	5.94713i	−0.237295	+	0.519603i	−0.990389	−	0.138310i	$-0.955833\pi$
$131$	−2.71596	+	5.94713i	−0.237295	+	0.519603i	0.753094	+	0.657913i	$0.228560\pi$
$132$	0.951066	−	0.206892i	0.0827797	−	0.0180076i
$133$	−17.2079	−	12.8817i	−1.49212	−	1.11698i
$134$	3.95004	−	2.53854i	0.341231	−	0.219296i
$135$	2.23606	+	0.00422385i	0.192450	+	0.000363532i
$136$	−1.77718	−	6.05253i	−0.152392	−	0.519000i
$137$	−4.37090	+	4.37090i	−0.373431	+	0.373431i	−0.868725	−	0.495294i	$-0.835060\pi$
$137$	−4.37090	+	4.37090i	−0.373431	+	0.373431i	0.495294	+	0.868725i	$0.335060\pi$
$138$	4.55393	−	1.50391i	0.387656	−	0.128022i
$139$			17.8821i			1.51674i	0.651824	+	0.758370i	$0.274004\pi$
$139$			17.8821i			1.51674i	−0.651824	+	0.758370i	$0.725996\pi$
$140$	−3.55932	+	7.75503i	−0.300818	+	0.655419i
$141$	−6.74152	−	7.78013i	−0.567738	−	0.655205i
$142$	3.97175	+	0.864002i	0.333302	+	0.0725054i
$143$	−0.226198	+	0.302166i	−0.0189157	+	0.0252684i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	−2.54237	+	6.77724i	−0.211133	+	0.562819i
$146$	−1.46628	+	1.69218i	−0.121351	+	0.140046i
$147$	−6.05357	+	4.53165i	−0.499290	+	0.373764i
$148$	2.98287	−	7.99738i	0.245190	−	0.657380i
$149$	−22.5527	−	6.62207i	−1.84759	−	0.542501i	−0.999928	−	0.0119646i	$-0.996191\pi$
$149$	−22.5527	−	6.62207i	−1.84759	−	0.542501i	−0.847662	−	0.530537i	$-0.821990\pi$
$150$	−4.94638	−	0.730266i	−0.403871	−	0.0596260i
$151$	−3.11780	−	6.82703i	−0.253723	−	0.555575i	0.739317	−	0.673358i	$-0.235149\pi$
$151$	−3.11780	−	6.82703i	−0.253723	−	0.555575i	−0.993039	+	0.117783i	$0.962421\pi$
$152$	3.37571	+	4.50942i	0.273806	+	0.365762i
$153$	6.29198	−	0.450011i	0.508677	−	0.0363813i
$154$	−3.37851	−	1.54291i	−0.272248	−	0.124331i
$155$	0.0805589	−	0.146872i	0.00647065	−	0.0117971i
$156$	−0.0551900	−	0.383855i	−0.00441874	−	0.0307330i
$157$	1.98589	−	9.12901i	0.158492	−	0.728574i	−0.827457	−	0.561528i	$-0.810214\pi$
$157$	1.98589	−	9.12901i	0.158492	−	0.728574i	0.985949	−	0.167046i	$-0.0534228\pi$
$158$	0.416705	−	5.82629i	0.0331513	−	0.463515i
$159$	12.2235	−	3.58915i	0.969390	−	0.284638i
$160$	1.46750	−	1.68714i	0.116016	−	0.133380i
$161$	−17.3508	−	5.81986i	−1.36744	−	0.458669i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−7.76393	+	14.2186i	−0.608118	+	1.11368i	0.374356	+	0.927285i	$0.377864\pi$
$163$	−7.76393	+	14.2186i	−0.608118	+	1.11368i	−0.982474	+	0.186400i	$0.940318\pi$
$164$	−4.47580	+	3.87830i	−0.349501	+	0.302845i
$165$	0.313801	−	2.15364i	0.0244294	−	0.167661i
$166$	−3.53394	+	0.508104i	−0.274287	+	0.0394365i
$167$	−2.78193	−	12.7883i	−0.215272	−	0.989590i	−0.950247	−	0.311496i	$-0.899170\pi$
$167$	−2.78193	−	12.7883i	−0.215272	−	0.989590i	0.734975	−	0.678094i	$-0.237194\pi$
$168$	3.57540	−	1.33355i	0.275848	−	0.102886i
$169$	−9.71109	−	8.41470i	−0.747007	−	0.647285i
$170$	−14.0674	−	1.03283i	−1.07892	−	0.0792145i
$171$	−5.12392	+	2.34002i	−0.391836	+	0.178946i
$172$	1.70335	−	0.930102i	0.129880	−	0.0709196i
$173$	−6.67813	+	3.64654i	−0.507729	+	0.277241i	−0.712628	−	0.701542i	$-0.752495\pi$
$173$	−6.67813	+	3.64654i	−0.507729	+	0.277241i	0.204899	+	0.978783i	$0.434313\pi$
$174$	2.94459	−	1.34475i	0.223228	−	0.101945i
$175$	13.4405	+	13.5425i	1.01601	+	1.02371i
$176$	0.735578	+	0.637382i	0.0554463	+	0.0480445i
$177$	11.4631	−	4.27551i	0.861618	−	0.321367i
$178$	−0.269597	−	1.23932i	−0.0202072	−	0.0928909i
$179$	−24.5473	+	3.52937i	−1.83475	+	0.263797i	−0.970819	−	0.239814i	$-0.922914\pi$
$179$	−24.5473	+	3.52937i	−1.83475	+	0.263797i	−0.863931	+	0.503611i	$0.832005\pi$
$180$	1.33664	+	1.79259i	0.0996274	+	0.133612i
$181$	−17.9599	+	15.5624i	−1.33495	+	1.15674i	−0.360345	+	0.932819i	$0.617341\pi$
$181$	−17.9599	+	15.5624i	−1.33495	+	1.15674i	−0.974607	+	0.223924i	$0.928113\pi$
$182$	−0.709218	+	1.29884i	−0.0525708	+	0.0962762i
$183$	5.07328	+	5.07328i	0.375028	+	0.375028i
$184$	3.93301	+	2.74434i	0.289945	+	0.202316i
$185$	−14.4006	−	12.5259i	−1.05876	−	0.920925i
$186$	−0.0718804	+	0.0211060i	−0.00527053	+	0.00154757i
$187$	0.438000	−	6.12404i	0.0320298	−	0.447834i
$188$	2.18827	−	10.0593i	0.159596	−	0.733651i
$189$	0.543073	+	3.77716i	0.0395028	+	0.274748i
$190$	12.0921	−	3.52578i	0.877257	−	0.255787i
$191$	−5.22626	−	2.38675i	−0.378159	−	0.172699i	0.217262	−	0.976113i	$-0.430287\pi$
$191$	−5.22626	−	2.38675i	−0.378159	−	0.172699i	−0.595421	+	0.803414i	$0.703015\pi$
$192$	−0.997452	+	0.0713392i	−0.0719849	+	0.00514846i
$193$	2.72149	+	3.63548i	0.195897	+	0.261688i	0.887725	−	0.460375i	$-0.152285\pi$
$193$	2.72149	+	3.63548i	0.195897	+	0.261688i	−0.691828	+	0.722063i	$0.743194\pi$
$194$	5.52948	+	12.1079i	0.396994	+	0.869295i
$195$	−0.846986	−	0.185927i	−0.0606539	−	0.0133145i
$196$	−7.25554	−	2.13042i	−0.518253	−	0.152173i
$197$	5.41721	−	14.5241i	0.385960	−	1.03480i	−0.588155	−	0.808748i	$-0.700146\pi$
$197$	5.41721	−	14.5241i	0.385960	−	1.03480i	0.974115	−	0.226051i	$-0.0725817\pi$
$198$	−0.779174	+	0.583283i	−0.0553735	+	0.0414521i
$199$	−2.24405	+	2.58977i	−0.159076	+	0.183584i	−0.829693	−	0.558221i	$-0.811484\pi$
$199$	−2.24405	+	2.58977i	−0.159076	+	0.183584i	0.670616	+	0.741804i	$0.266030\pi$
$200$	−2.37965	−	4.39742i	−0.168267	−	0.310944i
$201$	−2.53854	+	3.95004i	−0.179055	+	0.278614i
$202$	−6.53351	+	8.72774i	−0.459696	+	0.614082i
$203$	−12.0705	−	2.62578i	−0.847185	−	0.184294i
$204$	4.13090	+	4.76731i	0.289221	+	0.333778i
$205$	4.60442	+	12.4165i	0.321587	+	0.867206i
$206$			11.8414i			0.825032i
$207$	−3.51765	+	3.25978i	−0.244494	+	0.226570i
$208$	0.274218	−	0.274218i	0.0190136	−	0.0190136i
$209$	1.54463	+	5.26053i	0.106844	+	0.363878i
$210$	0.0161182	−	8.53282i	0.00111226	−	0.588820i
$211$	0.879820	−	0.565426i	0.0605693	−	0.0389255i	−0.510006	−	0.860171i	$-0.670357\pi$
$211$	0.879820	−	0.565426i	0.0605693	−	0.0389255i	0.570575	+	0.821245i	$0.306720\pi$
$212$	10.1986	+	7.63455i	0.700440	+	0.524343i
$213$	−3.97175	+	0.864002i	−0.272140	+	0.0592004i
$214$	−7.16192	+	15.6824i	−0.489579	+	1.07203i
$215$	−0.609481	−	4.29663i	−0.0415663	−	0.293028i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	0.267851	+	0.0999032i	0.0181829	+	0.00678187i
$218$	5.84199	+	10.6988i	0.395670	+	0.724615i
$219$	0.630821	−	2.14838i	0.0426270	−	0.145174i
$220$	1.91213	−	1.03942i	0.128916	−	0.0700777i
$221$	−2.42138	−	0.348142i	−0.162880	−	0.0234185i
$222$	0.608919	+	8.51380i	0.0408679	+	0.571409i
$223$	5.08542	+	13.6345i	0.340545	+	0.913036i	0.988481	+	0.151342i	$0.0483594\pi$
$223$	5.08542	+	13.6345i	0.340545	+	0.913036i	−0.647937	+	0.761694i	$0.724368\pi$
$224$	3.21022	+	2.06308i	0.214492	+	0.137846i
$225$	4.80275	−	1.39053i	0.320183	−	0.0927019i
$226$	−7.26949	−	11.3116i	−0.483559	−	0.752433i
$227$	9.44228	+	0.675326i	0.626706	+	0.0448229i	0.381081	−	0.924542i	$-0.375552\pi$
$227$	9.44228	+	0.675326i	0.626706	+	0.0448229i	0.245626	+	0.969365i	$0.421007\pi$
$228$	−4.94393	−	2.69959i	−0.327420	−	0.178785i
$229$	3.31839			0.219285			0.109643	−	0.993971i	$-0.465029\pi$
$229$	3.31839			0.219285			0.109643	+	0.993971i	$0.465029\pi$
$230$	8.83448	−	6.07881i	0.582529	−	0.400825i
$231$	3.71415			0.244373
$232$	2.84115	+	1.55139i	0.186531	+	0.101853i
$233$	−6.38529	−	0.456685i	−0.418314	−	0.0299184i	−0.139404	−	0.990236i	$-0.544519\pi$
$233$	−6.38529	−	0.456685i	−0.418314	−	0.0299184i	−0.278910	+	0.960317i	$0.589973\pi$
$234$	0.209662	+	0.326240i	0.0137060	+	0.0213270i
$235$	−19.3416	−	12.4818i	−1.26171	−	0.814221i
$236$	10.2923	+	6.61446i	0.669971	+	0.430564i
$237$	2.04128	+	5.47289i	0.132596	+	0.355502i
$238$	−1.71724	−	24.0102i	−0.111312	−	1.55635i
$239$	6.07333	+	0.873213i	0.392851	+	0.0564834i	0.335910	−	0.941894i	$-0.390956\pi$
$239$	6.07333	+	0.873213i	0.392851	+	0.0564834i	0.0569410	+	0.998378i	$0.481865\pi$
$240$	−0.634025	+	2.14430i	−0.0409261	+	0.138414i
$241$	1.27095	−	4.32846i	0.0818690	−	0.278820i	−0.908377	−	0.418153i	$-0.862678\pi$
$241$	1.27095	−	4.32846i	0.0818690	−	0.278820i	0.990246	+	0.139333i	$0.0444957\pi$
$242$	−4.81773	−	8.82302i	−0.309696	−	0.567165i
$243$	0.936950	+	0.349464i	0.0601054	+	0.0224181i
$244$	−1.02107	+	7.10167i	−0.0653671	+	0.454638i
$245$	−10.1586	+	13.5170i	−0.649010	+	0.863571i
$246$	2.46023	−	5.38715i	0.156858	−	0.343472i
$247$	2.13455	−	0.464344i	0.135818	−	0.0295455i
$248$	−0.0599725	−	0.0448949i	−0.00380826	−	0.00285083i
$249$	3.00351	−	1.93024i	0.190340	−	0.122324i
$250$	−11.0754	+	1.52839i	−0.700468	+	0.0966639i
$251$	−4.74550	−	16.1617i	−0.299533	−	1.02012i	−0.962458	−	0.271431i	$-0.912503\pi$
$251$	−4.74550	−	16.1617i	−0.299533	−	1.02012i	0.662925	−	0.748686i	$-0.269315\pi$
$252$	−2.69832	+	2.69832i	−0.169978	+	0.169978i
$253$	2.65323	+	3.84044i	0.166807	+	0.241447i
$254$			0.777808i			0.0488040i
$255$	13.2252	−	4.90430i	0.828193	−	0.307119i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−5.84972	−	1.27253i	−0.364895	−	0.0793781i	0.0263796	−	0.999652i	$-0.491602\pi$
$257$	−5.84972	−	1.27253i	−0.364895	−	0.0793781i	−0.391275	+	0.920274i	$0.627966\pi$
$258$	−1.16305	+	1.55365i	−0.0724082	+	0.0967260i
$259$	17.6095	−	27.4010i	1.09420	−	1.70261i
$260$	−0.358738	−	0.789469i	−0.0222480	−	0.0489608i
$261$	−2.11986	+	2.44645i	−0.131216	+	0.151431i
$262$	5.23390	−	3.91805i	0.323351	−	0.242058i
$263$	−2.43648	+	6.53247i	−0.150240	+	0.402809i	−0.990167	−	0.139890i	$-0.955325\pi$
$263$	−2.43648	+	6.53247i	−0.150240	+	0.402809i	0.839927	+	0.542700i	$0.182598\pi$
$264$	−0.933883	−	0.274213i	−0.0574766	−	0.0168766i
$265$	23.9935	−	15.3557i	1.47391	−	0.943294i
$266$	8.92950	+	19.5529i	0.547503	+	1.19886i
$267$	0.760066	+	1.01533i	0.0465153	+	0.0621371i
$268$	−4.68346	+	0.334967i	−0.286088	+	0.0204614i
$269$	−9.83916	−	4.49339i	−0.599904	−	0.273967i	0.0922279	−	0.995738i	$-0.470601\pi$
$269$	−9.83916	−	4.49339i	−0.599904	−	0.273967i	−0.692132	+	0.721771i	$0.743328\pi$
$270$	−1.96052	−	1.07534i	−0.119314	−	0.0654430i
$271$	2.52104	+	17.5342i	0.153142	+	1.06513i	0.910910	+	0.412605i	$0.135381\pi$
$271$	2.52104	+	17.5342i	0.153142	+	1.06513i	−0.757768	+	0.652524i	$0.773710\pi$
$272$	−1.34087	+	6.16390i	−0.0813024	+	0.373741i
$273$	0.105572	−	1.47608i	0.00638948	−	0.0893366i
$274$	5.93100	−	1.74150i	0.358305	−	0.105208i
$275$	−0.674379	−	4.81959i	−0.0406666	−	0.290632i
$276$	−4.71763	−	0.862512i	−0.283968	−	0.0519171i
$277$	4.91405	+	4.91405i	0.295257	+	0.295257i	0.839153	−	0.543896i	$-0.183051\pi$
$277$	4.91405	+	4.91405i	0.295257	+	0.295257i	−0.543896	+	0.839153i	$0.683051\pi$
$278$	8.56998	−	15.6947i	0.513993	−	0.941308i
$279$	0.0566169	−	0.0490589i	0.00338957	−	0.00293708i
$280$	6.84053	−	5.10062i	0.408800	−	0.304821i
$281$	1.68557	−	0.242348i	0.100553	−	0.0144573i	−0.0918548	−	0.995772i	$-0.529280\pi$
$281$	1.68557	−	0.242348i	0.100553	−	0.0144573i	0.192407	+	0.981315i	$0.438370\pi$
$282$	2.18827	+	10.0593i	0.130310	+	0.599024i
$283$	24.7516	−	9.23186i	1.47133	−	0.548777i	0.519248	−	0.854624i	$-0.326212\pi$
$283$	24.7516	−	9.23186i	1.47133	−	0.548777i	0.952081	+	0.305846i	$0.0989393\pi$
$284$	−3.07185	−	2.66177i	−0.182281	−	0.157947i
$285$	−9.53474	+	8.23042i	−0.564790	+	0.487528i
$286$	0.343342	−	0.156799i	0.0203022	−	0.00927172i
$287$	−19.8352	+	10.8308i	−1.17084	+	0.639325i
$288$	0.877679	−	0.479249i	0.0517177	−	0.0282400i
$289$	20.7319	−	9.46795i	1.21952	−	0.556938i
$290$	5.47937	−	4.72981i	0.321760	−	0.277744i
$291$	−10.0596	−	8.71669i	−0.589704	−	0.510981i
$292$	2.09790	−	0.782478i	0.122771	−	0.0457911i
$293$	−2.82785	−	12.9994i	−0.165205	−	0.759434i	−0.982953	−	0.183858i	$-0.941141\pi$
$293$	−2.82785	−	12.9994i	−0.165205	−	0.759434i	0.817748	−	0.575576i	$-0.195222\pi$
$294$	7.48488	−	1.07616i	0.436527	−	0.0627631i
$295$	21.9314	−	16.3531i	1.27690	−	0.952115i
$296$	−6.45073	+	5.58959i	−0.374941	+	0.324888i
$297$	0.466457	−	0.854253i	0.0270666	−	0.0495688i
$298$	16.6204	+	16.6204i	0.962795	+	0.962795i
$299$	1.60169	−	0.945288i	0.0926282	−	0.0546674i
$300$	3.99136	+	3.01149i	0.230441	+	0.173868i
$301$	7.10590	−	2.08648i	0.409577	−	0.120263i
$302$	−0.535419	+	7.48614i	−0.0308099	+	0.430779i
$303$	2.31745	−	10.6532i	0.133134	−	0.612008i
$304$	−0.801654	−	5.57562i	−0.0459780	−	0.319784i
$305$	14.0662	+	7.71523i	0.805426	+	0.441773i
$306$	−5.73801	−	2.62046i	−0.328020	−	0.149802i
$307$	0.410966	−	0.0293928i	0.0234551	−	0.00167754i	−0.0596067	−	0.998222i	$-0.518985\pi$
$307$	0.410966	−	0.0293928i	0.0234551	−	0.00167754i	0.0830618	+	0.996544i	$0.473530\pi$
$308$	2.22581	+	2.97333i	0.126827	+	0.169421i
$309$	−4.91911	−	10.7713i	−0.279838	−	0.612761i
$310$	−0.141093	+	0.0902991i	−0.00801356	+	0.00512864i
$311$	17.0529	+	5.00719i	0.966982	+	0.283932i	0.726840	−	0.686806i	$-0.240988\pi$
$311$	17.0529	+	5.00719i	0.966982	+	0.283932i	0.240142	+	0.970738i	$0.422806\pi$
$312$	−0.135523	+	0.363351i	−0.00767248	+	0.0205707i
$313$	−13.3095	+	9.96338i	−0.752299	+	0.563164i	−0.905153	−	0.425085i	$-0.860244\pi$
$313$	−13.3095	+	9.96338i	−0.752299	+	0.563164i	0.152855	+	0.988249i	$0.451153\pi$
$314$	−6.11805	+	7.06060i	−0.345261	+	0.398453i
$315$	3.53000	+	7.76842i	0.198893	+	0.437701i
$316$	−3.15798	+	4.91391i	−0.177650	+	0.276429i
$317$	15.7961	−	21.1012i	0.887200	−	1.18516i	−0.0946521	−	0.995510i	$-0.530174\pi$
$317$	15.7961	−	21.1012i	0.887200	−	1.18516i	0.981852	−	0.189650i	$-0.0607352\pi$
$318$	−12.4484	−	2.70799i	−0.698074	−	0.151857i
$319$	2.06328	+	2.38115i	0.115522	+	0.133319i
$320$	−2.09656	+	0.777467i	−0.117201	+	0.0434617i
$321$		−	17.2404i		−	0.962266i
$322$	12.4393	+	13.4233i	0.693215	+	0.748054i
$323$	−25.1256	+	25.1256i	−1.39803	+	1.39803i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	−1.93458	+	0.131020i	−0.107311	+	0.00726767i
$326$	13.6285	−	8.75849i	0.754812	−	0.485088i
$327$	−9.75851	−	7.30513i	−0.539647	−	0.403975i
$328$	5.78699	−	1.25888i	0.319533	−	0.0695102i
$329$	16.3192	−	35.7341i	0.899707	−	1.97008i
$330$	−1.30755	+	1.73982i	−0.0719782	+	0.0957739i
$331$	4.05028	−	28.1703i	0.222624	−	1.54838i	−0.505434	−	0.862865i	$-0.668667\pi$
$331$	4.05028	−	28.1703i	0.222624	−	1.54838i	0.728057	−	0.685516i	$-0.240423\pi$
$332$	3.34517	+	1.24768i	0.183590	+	0.0684756i
$333$	−4.09065	−	7.49147i	−0.224166	−	0.410530i
$334$	−3.68715	+	12.5573i	−0.201752	+	0.687103i
$335$	−2.97701	+	10.0684i	−0.162652	+	0.550094i
$336$	−3.77716	−	0.543073i	−0.206061	−	0.0296271i
$337$	1.98422	+	27.7431i	0.108088	+	1.51126i	0.705145	+	0.709063i	$0.250882\pi$
$337$	1.98422	+	27.7431i	0.108088	+	1.51126i	−0.597058	+	0.802198i	$0.703664\pi$
$338$	4.49048	+	12.0394i	0.244250	+	0.654859i
$339$	11.3116	+	7.26949i	0.614359	+	0.394825i
$340$	11.8517	+	7.64827i	0.642746	+	0.414786i
$341$	−0.0394211	−	0.0613404i	−0.00213477	−	0.00332177i
$342$	5.61861	+	0.401851i	0.303820	+	0.0217296i
$343$	−1.88175	−	1.02751i	−0.101605	−	0.0554805i
$344$	−1.94075			−0.104638
$345$	−5.51090	+	9.19945i	−0.296697	+	0.495282i
$346$	7.60886			0.409055
$347$	1.98019	+	1.08127i	0.106302	+	0.0580454i	0.531520	−	0.847045i	$-0.321621\pi$
$347$	1.98019	+	1.08127i	0.106302	+	0.0580454i	−0.425218	+	0.905091i	$0.639803\pi$
$348$	−3.22887	−	0.230933i	−0.173086	−	0.0123793i
$349$	−3.55257	−	5.52791i	−0.190165	−	0.295902i	0.733059	−	0.680165i	$-0.238092\pi$
$349$	−3.55257	−	5.52791i	−0.190165	−	0.295902i	−0.923224	+	0.384263i	$0.874456\pi$
$350$	−5.30625	−	18.3273i	−0.283631	−	0.979635i
$351$	−0.326240	−	0.209662i	−0.0174134	−	0.0111909i
$352$	−0.340137	−	0.911942i	−0.0181293	−	0.0486067i
$353$	−2.28504	−	31.9490i	−0.121620	−	1.70047i	−0.582355	−	0.812935i	$-0.697869\pi$
$353$	−2.28504	−	31.9490i	−0.121620	−	1.70047i	0.460735	−	0.887538i	$-0.347586\pi$
$354$	−12.1099	−	1.74115i	−0.643636	−	0.0925409i
$355$	−7.98528	+	4.34073i	−0.423814	+	0.230382i
$356$	−0.357322	+	1.21693i	−0.0189380	+	0.0644971i
$357$	11.5363	+	21.1271i	0.610563	+	1.11816i
$358$	23.2361	+	8.66661i	1.22806	+	0.458044i
$359$	−3.31404	+	23.0497i	−0.174908	+	1.21652i	0.693423	+	0.720531i	$0.256102\pi$
$359$	−3.31404	+	23.0497i	−0.174908	+	1.21652i	−0.868331	+	0.495984i	$0.834807\pi$
$360$	−0.314044	−	2.21391i	−0.0165516	−	0.116683i
$361$	5.28833	−	11.5798i	0.278333	−	0.609465i
$362$	23.2213	−	5.05149i	1.22049	−	0.265500i
$363$	8.04758	+	6.02434i	0.422388	+	0.316196i
$364$	1.24493	−	0.800069i	0.0652522	−	0.0419350i
$365$	0.00945754	−	5.00672i	0.000495030	−	0.262064i
$366$	−2.02135	−	6.88407i	−0.105657	−	0.359836i
$367$	−18.2764	+	18.2764i	−0.954020	+	0.954020i	−0.998988	−	0.0449685i	$-0.985681\pi$
$367$	−18.2764	+	18.2764i	−0.954020	+	0.954020i	0.0449685	+	0.998988i	$0.485681\pi$
$368$	−2.13670	−	4.29354i	−0.111383	−	0.223816i
$369$			5.92233i			0.308304i
$370$	6.63610	+	17.8952i	0.344994	+	0.930329i
$371$	31.8355	+	36.7402i	1.65282	+	1.90746i
$372$	0.0732029	+	0.0159243i	0.00379539	+	0.000825638i
$373$	6.57802	−	8.78721i	0.340597	−	0.454984i	−0.597239	−	0.802063i	$-0.703736\pi$
$373$	6.57802	−	8.78721i	0.340597	−	0.454984i	0.937836	+	0.347079i	$0.112826\pi$
$374$	−3.31937	+	5.16503i	−0.171640	+	0.267078i
$375$	9.43960	−	5.99115i	0.487459	−	0.309382i
$376$	−6.74152	+	7.78013i	−0.347667	+	0.401229i
$377$	1.00497	−	0.752310i	0.0517585	−	0.0387460i
$378$	1.33355	−	3.57540i	0.0685907	−	0.183899i
$379$	4.88542	+	1.43449i	0.250947	+	0.0736848i	0.404787	−	0.914411i	$-0.367346\pi$
$379$	4.88542	+	1.43449i	0.250947	+	0.0736848i	−0.153840	+	0.988096i	$0.549164\pi$
$380$	−12.3028	−	2.70065i	−0.631118	−	0.138540i
$381$	−0.323113	−	0.707519i	−0.0165536	−	0.0362473i
$382$	3.44313	+	4.59948i	0.176166	+	0.235330i
$383$	−2.24872	+	0.160832i	−0.114904	+	0.00821813i	−0.128673	−	0.991687i	$-0.541072\pi$
$383$	−2.24872	+	0.160832i	−0.114904	+	0.00821813i	0.0137685	+	0.999905i	$0.495617\pi$
$384$	0.909632	+	0.415415i	0.0464195	+	0.0211991i
$385$	7.97308	−	2.32476i	0.406346	−	0.118481i
$386$	−0.646292	−	4.49506i	−0.0328954	−	0.228792i
$387$	0.412536	−	1.89640i	0.0209704	−	0.0963993i
$388$	0.949578	−	13.2768i	0.0482075	−	0.674029i
$389$	−26.2514	+	7.70811i	−1.33100	+	0.390816i	−0.868450	−	0.495777i	$-0.834883\pi$
$389$	−26.2514	+	7.70811i	−1.33100	+	0.390816i	−0.462549	+	0.886594i	$0.653065\pi$
$390$	0.654276	+	0.569101i	0.0331306	+	0.0288176i
$391$	−13.6045	+	27.0208i	−0.688008	+	1.36650i
$392$	5.34703	+	5.34703i	0.270066	+	0.270066i
$393$	−3.13331	+	5.73822i	−0.158054	+	0.289455i
$394$	−11.7152	+	10.1513i	−0.590205	+	0.511416i
$395$	7.80756	+	10.4709i	0.392841	+	0.526846i
$396$	0.963402	−	0.138516i	0.0484128	−	0.00696071i
$397$	−0.505823	−	2.32523i	−0.0253865	−	0.116700i	0.962710	−	0.270536i	$-0.0872009\pi$
$397$	−0.505823	−	2.32523i	−0.0253865	−	0.116700i	−0.988096	+	0.153836i	$0.950837\pi$
$398$	3.21070	−	1.19753i	0.160938	−	0.0600267i
$399$	−16.2451	−	14.0765i	−0.813273	−	0.704705i
$400$	−0.0188896	+	4.99996i	−0.000944481	+	0.249998i
$401$	−20.0093	+	9.13794i	−0.999217	+	0.456327i	−0.846755	−	0.531983i	$-0.821447\pi$
$401$	−20.0093	+	9.13794i	−0.999217	+	0.456327i	−0.152461	+	0.988309i	$0.548720\pi$
$402$	4.12107	−	2.25028i	0.205540	−	0.112234i
$403$	−0.0254985	+	0.0139232i	−0.00127017	+	0.000693566i
$404$	9.91708	−	4.52898i	0.493393	−	0.225325i
$405$	2.23007	+	0.163732i	0.110813	+	0.00813591i
$406$	9.33565	+	8.08939i	0.463321	+	0.401470i
$407$	−7.78392	+	2.90325i	−0.385835	+	0.143909i
$408$	−1.34087	−	6.16390i	−0.0663831	−	0.305158i
$409$	27.9282	−	4.01547i	1.38096	−	0.198552i	0.588512	−	0.808488i	$-0.299714\pi$
$409$	27.9282	−	4.01547i	1.38096	−	0.198552i	0.792451	+	0.609936i	$0.208805\pi$
$410$	1.90940	−	13.1044i	0.0942983	−	0.647179i
$411$	−4.67158	+	4.04795i	−0.230432	+	0.199671i
$412$	5.67500	−	10.3930i	0.279587	−	0.512025i
$413$	33.0125	+	33.0125i	1.62444	+	1.62444i
$414$	4.64961	−	1.17521i	0.228516	−	0.0577583i
$415$	5.23940	−	6.02356i	0.257192	−	0.295685i
$416$	−0.372094	+	0.109257i	−0.0182434	+	0.00535674i
$417$	−1.27569	+	17.8365i	−0.0624710	+	0.873459i
$418$	1.16541	−	5.35732i	0.0570022	−	0.262035i
$419$	2.07037	+	14.3998i	0.101144	+	0.703475i	0.975790	+	0.218711i	$0.0701853\pi$
$419$	2.07037	+	14.3998i	0.101144	+	0.703475i	−0.874645	+	0.484764i	$0.838906\pi$
$420$	−4.10349	+	7.48135i	−0.200230	+	0.365053i
$421$	13.0428	+	5.95647i	0.635670	+	0.290301i	0.707066	−	0.707147i	$-0.250018\pi$
$421$	13.0428	+	5.95647i	0.635670	+	0.290301i	−0.0713966	+	0.997448i	$0.522746\pi$
$422$	−1.04318	+	0.0746097i	−0.0507812	+	0.00363194i
$423$	−6.16931	−	8.24124i	−0.299962	−	0.400703i
$424$	−5.29221	−	11.5883i	−0.257013	−	0.562779i
$425$	25.3205	−	18.8059i	1.22823	−	0.912218i
$426$	3.89999	+	1.14514i	0.188955	+	0.0554823i
$427$	−9.56786	+	25.6524i	−0.463021	+	1.24141i
$428$	13.8017	−	10.3318i	0.667128	−	0.499406i
$429$	−0.247178	+	0.285259i	−0.0119339	+	0.0137724i
$430$	−1.52423	+	4.06316i	−0.0735048	+	0.195943i
$431$	−4.06779	+	6.32960i	−0.195938	+	0.304886i	−0.925295	−	0.379247i	$-0.876183\pi$
$431$	−4.06779	+	6.32960i	−0.195938	+	0.304886i	0.729357	+	0.684133i	$0.239819\pi$
$432$	−0.599278	+	0.800541i	−0.0288328	+	0.0385161i
$433$	−4.84668	−	1.05433i	−0.232917	−	0.0506679i	0.0945918	−	0.995516i	$-0.469845\pi$
$433$	−4.84668	−	1.05433i	−0.232917	−	0.0506679i	−0.327509	+	0.944848i	$0.606209\pi$
$434$	−0.187209	−	0.216050i	−0.00898630	−	0.0103707i
$435$	−3.01938	+	6.57860i	−0.144768	+	0.315420i
$436$		−	12.1899i		−	0.583790i
$437$	2.95033	−	26.8531i	0.141133	−	1.28456i
$438$	−1.58327	+	1.58327i	−0.0756515	+	0.0756515i
$439$	−5.84276	−	19.8986i	−0.278860	−	0.949709i	−0.973180	−	0.230043i	$-0.926113\pi$
$439$	−5.84276	−	19.8986i	−0.278860	−	0.949709i	0.694321	−	0.719666i	$-0.255705\pi$
$440$	−2.17638	−	0.00411112i	−0.103755	−	0.000195990i
$441$	−6.36143	+	4.08824i	−0.302925	+	0.194678i
$442$	1.95835	+	1.46600i	0.0931491	+	0.0697305i
$443$	24.6639	−	5.36531i	1.17182	−	0.254914i	0.415795	−	0.909458i	$-0.363503\pi$
$443$	24.6639	−	5.36531i	1.17182	−	0.254914i	0.756023	+	0.654545i	$0.227140\pi$
$444$	3.54579	−	7.76420i	0.168276	−	0.368473i
$445$	2.26713	+	1.70384i	0.107472	+	0.0807700i
$446$	2.07097	−	14.4039i	0.0980634	−	0.682046i
$447$	−22.0228	−	8.21409i	−1.04164	−	0.388513i
$448$	−1.82881	−	3.34922i	−0.0864033	−	0.158236i
$449$	5.27726	−	17.9727i	0.249050	−	0.848185i	−0.736157	−	0.676811i	$-0.763361\pi$
$449$	5.27726	−	17.9727i	0.249050	−	0.848185i	0.985206	−	0.171374i	$-0.0548205\pi$
$450$	−4.88168	−	1.08128i	−0.230125	−	0.0509719i
$451$	5.70559	+	0.820340i	0.268666	+	0.0386283i
$452$	0.959231	+	13.4118i	0.0451184	+	0.630838i
$453$	−2.62282	−	7.03205i	−0.123231	−	0.330395i
$454$	−7.96365	−	5.11792i	−0.373752	−	0.240196i
$455$	−0.697281	−	3.23475i	−0.0326890	−	0.151648i
$456$	3.04541	+	4.73875i	0.142614	+	0.221912i
$457$	29.5147	+	2.11093i	1.38064	+	0.0987452i	0.741813	−	0.670607i	$-0.233966\pi$
$457$	29.5147	+	2.11093i	1.38064	+	0.0987452i	0.638825	+	0.769352i	$0.279421\pi$
$458$	−2.91248	−	1.59033i	−0.136091	−	0.0743114i
$459$	6.30805			0.294435
$460$	−10.6671	+	1.10132i	−0.497356	+	0.0513495i
$461$	40.7854			1.89956			0.949782	−	0.312911i	$-0.101304\pi$
$461$	40.7854			1.89956			0.949782	+	0.312911i	$0.101304\pi$
$462$	−3.25983	−	1.78000i	−0.151661	−	0.0828132i
$463$	−20.5689	−	1.47112i	−0.955918	−	0.0683686i	−0.415343	−	0.909665i	$-0.636339\pi$
$463$	−20.5689	−	1.47112i	−0.955918	−	0.0683686i	−0.540574	+	0.841296i	$0.681793\pi$
$464$	−1.75012	−	2.72324i	−0.0812472	−	0.126423i
$465$	0.0908315	−	0.140751i	0.00421221	−	0.00652718i
$466$	5.38537	+	3.46097i	0.249472	+	0.160326i
$467$	−10.4118	−	27.9151i	−0.481801	−	1.29176i	−0.919660	−	0.392715i	$-0.871536\pi$
$467$	−10.4118	−	27.9151i	−0.481801	−	1.29176i	0.437859	−	0.899044i	$-0.355737\pi$
$468$	−0.0276655	−	0.386814i	−0.00127884	−	0.0178805i
$469$	−17.7353	−	2.54996i	−0.818942	−	0.117746i
$470$	10.9938	+	20.2244i	0.507108	+	0.932884i
$471$	2.63209	−	8.96408i	0.121280	−	0.413043i
$472$	−5.86336	−	10.7379i	−0.269883	−	0.494254i
$473$	−1.76985	−	0.660120i	−0.0813778	−	0.0303523i
$474$	0.831286	−	5.78172i	0.0381822	−	0.265563i
$475$	−15.3164	+	23.6360i	−0.702767	+	1.08450i
$476$	−9.99967	+	21.8962i	−0.458334	+	1.00361i
$477$	12.4484	−	2.70799i	0.569975	−	0.123990i
$478$	−4.91195	−	3.67704i	−0.224667	−	0.168184i
$479$	−15.8082	+	10.1593i	−0.722296	+	0.464192i	−0.849435	−	0.527693i	$-0.823057\pi$
$479$	−15.8082	+	10.1593i	−0.722296	+	0.464192i	0.127139	+	0.991885i	$0.459421\pi$
$480$	1.58412	−	1.57815i	0.0723050	−	0.0720323i
$481$	0.932564	+	3.17602i	0.0425213	+	0.144814i
$482$	−3.18989	+	3.18989i	−0.145296	+	0.145296i
$483$	−16.8914	−	7.04283i	−0.768588	−	0.320460i
$484$			10.0527i			0.456940i
$485$	−27.0506	−	12.4154i	−1.22831	−	0.563755i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	−25.6323	−	5.57596i	−1.16151	−	0.252671i	−0.409806	−	0.912173i	$-0.634404\pi$
$487$	−25.6323	−	5.57596i	−1.16151	−	0.252671i	−0.751703	+	0.659502i	$0.770767\pi$
$488$	4.29964	−	5.74364i	0.194635	−	0.260003i
$489$	−8.75849	+	13.6285i	−0.396073	+	0.616301i
$490$	15.3940	−	6.99510i	0.695431	−	0.316007i
$491$	16.5050	−	19.0478i	0.744861	−	0.859615i	−0.249199	−	0.968452i	$-0.580167\pi$
$491$	16.5050	−	19.0478i	0.744861	−	0.859615i	0.994060	+	0.108837i	$0.0347127\pi$
$492$	−4.74107	+	3.54912i	−0.213744	+	0.160007i
$493$	−7.13603	+	19.1324i	−0.321390	+	0.861681i
$494$	−2.09599	−	0.615438i	−0.0943030	−	0.0276899i
$495$	0.466640	−	2.12577i	0.0209739	−	0.0955463i
$496$	0.0311208	+	0.0681450i	0.00139737	+	0.00305980i
$497$	−9.29520	−	12.4169i	−0.416947	−	0.556975i
$498$	−3.56118	+	0.254701i	−0.159580	+	0.0114134i
$499$	26.0877	+	11.9138i	1.16784	+	0.533336i	0.902446	−	0.430803i	$-0.141769\pi$
$499$	26.0877	+	11.9138i	1.16784	+	0.533336i	0.265398	+	0.964139i	$0.414497\pi$
$500$	10.4531	+	3.96643i	0.467477	+	0.177384i
$501$	−1.86253	−	12.9542i	−0.0832118	−	0.578751i
$502$	−3.58045	+	16.4590i	−0.159803	+	0.734603i
$503$	−3.02376	+	42.2777i	−0.134823	+	1.88507i	0.258991	+	0.965880i	$0.416610\pi$
$503$	−3.02376	+	42.2777i	−0.134823	+	1.88507i	−0.393814	+	0.919190i	$0.628845\pi$
$504$	3.66142	−	1.07509i	0.163093	−	0.0478884i
$505$	−1.69319	−	24.3194i	−0.0753460	−	1.08220i
$506$	−0.488151	−	4.64223i	−0.0217010	−	0.206372i
$507$	−9.08605	−	9.08605i	−0.403525	−	0.403525i
$508$	0.372763	−	0.682665i	0.0165387	−	0.0302884i
$509$	−8.01055	+	6.94118i	−0.355061	+	0.307662i	−0.814067	−	0.580771i	$-0.802751\pi$
$509$	−8.01055	+	6.94118i	−0.355061	+	0.307662i	0.459006	+	0.888433i	$0.348206\pi$
$510$	−13.9578	−	2.03375i	−0.618064	−	0.0900561i
$511$	8.45735	−	1.21598i	0.374131	−	0.0537920i
$512$	0.212565	+	0.977147i	0.00939415	+	0.0431842i
$513$	−5.27780	+	1.96852i	−0.233021	+	0.0869122i
$514$	4.52431	+	3.92034i	0.199559	+	0.172919i
$515$	−17.3017	−	20.0436i	−0.762406	−	0.883229i
$516$	1.76537	−	0.806216i	0.0777160	−	0.0354917i
$517$	−8.79418	+	4.80199i	−0.386768	+	0.211191i
$518$	−28.5874	+	15.6099i	−1.25606	+	0.685860i
$519$	−6.92126	+	3.16083i	−0.303810	+	0.138745i
$520$	−0.0634957	+	0.864825i	−0.00278447	+	0.0379251i
$521$	−19.8959	−	17.2399i	−0.871654	−	0.755292i	0.0991738	−	0.995070i	$-0.468380\pi$
$521$	−19.8959	−	17.2399i	−0.871654	−	0.755292i	−0.970828	+	0.239778i	$0.922925\pi$
$522$	3.03302	−	1.13126i	0.132752	−	0.0495138i
$523$	1.92103	+	8.83084i	0.0840008	+	0.386146i	0.999883	−	0.0153018i	$-0.00487091\pi$
$523$	1.92103	+	8.83084i	0.0840008	+	0.386146i	−0.915882	+	0.401447i	$0.868507\pi$
$524$	−6.47140	+	0.930447i	−0.282704	+	0.0406468i
$525$	12.4402	+	14.4668i	0.542934	+	0.631383i
$526$	5.26913	−	4.56573i	0.229745	−	0.199075i
$527$	0.226478	−	0.414763i	0.00986552	−	0.0180673i
$528$	0.688234	+	0.688234i	0.0299515	+	0.0299515i
$529$	−4.78420	−	22.4969i	−0.208009	−	0.978127i
$530$	−28.4178	+	1.97853i	−1.23439	+	0.0859419i
$531$	11.7389	−	3.44685i	0.509425	−	0.149581i
$532$	1.53346	−	21.4406i	0.0664840	−	0.929568i
$533$	0.488198	−	2.24421i	0.0211462	−	0.0972075i
$534$	−0.180498	−	1.25539i	−0.00781093	−	0.0543262i
$535$	−10.7911	−	37.0096i	−0.466540	−	1.60006i
$536$	4.27111	+	1.95055i	0.184484	+	0.0842509i
$537$	−24.7365	+	1.76919i	−1.06746	+	0.0763462i
$538$	6.48217	+	8.65917i	0.279466	+	0.373323i
$539$	3.05746	+	6.69491i	0.131694	+	0.288370i
$540$	1.20535	+	1.88338i	0.0518702	+	0.0810478i
$541$	−20.1977	−	5.93057i	−0.868366	−	0.254975i	−0.182946	−	0.983123i	$-0.558563\pi$
$541$	−20.1977	−	5.93057i	−0.868366	−	0.254975i	−0.685420	+	0.728148i	$0.740381\pi$
$542$	6.19060	−	16.5976i	0.265909	−	0.712929i
$543$	−19.0244	+	14.2415i	−0.816415	+	0.611160i
$544$	4.13090	−	4.76731i	0.177111	−	0.204397i
$545$	−25.5208	−	9.57372i	−1.09319	−	0.410093i
$546$	−0.800069	+	1.24493i	−0.0342398	+	0.0532782i
$547$	−0.812063	+	1.08479i	−0.0347213	+	0.0463822i	−0.817566	−	0.575835i	$-0.804677\pi$
$547$	−0.812063	+	1.08479i	−0.0347213	+	0.0463822i	0.782845	+	0.622217i	$0.213768\pi$
$548$	−6.04013	−	1.31395i	−0.258021	−	0.0561291i
$549$	4.69843	+	5.42228i	0.200524	+	0.231417i
$550$	−1.71790	+	4.55325i	−0.0732514	+	0.194151i
$551$		−	18.2346i		−	0.776818i
$552$	3.72721	+	3.01793i	0.158641	+	0.128452i
$553$	−15.7614	+	15.7614i	−0.670241	+	0.670241i
$554$	−1.95791	−	6.66801i	−0.0831834	−	0.283297i
$555$	−13.4704	−	13.5213i	−0.571785	−	0.573949i
$556$	−15.0434	+	9.66779i	−0.637981	+	0.410006i
$557$	−25.8650	−	19.3623i	−1.09593	−	0.820406i	−0.111084	−	0.993811i	$-0.535432\pi$
$557$	−25.8650	−	19.3623i	−1.09593	−	0.820406i	−0.984851	+	0.173405i	$0.944523\pi$
$558$	−0.0732029	+	0.0159243i	−0.00309893	+	0.000674130i
$559$	−0.312653	+	0.684614i	−0.0132238	+	0.0289561i
$560$	−8.44826	+	1.19839i	−0.357004	+	0.0506413i
$561$	0.873769	−	6.07719i	0.0368905	−	0.256579i
$562$	−1.59553	−	0.595103i	−0.0673035	−	0.0251029i
$563$	−14.5654	−	26.6745i	−0.613857	−	1.12420i	−0.980996	−	0.194029i	$-0.937844\pi$
$563$	−14.5654	−	26.6745i	−0.613857	−	1.12420i	0.367139	−	0.930166i	$-0.380337\pi$
$564$	2.90032	−	9.87758i	0.122125	−	0.415921i
$565$	28.8324	+	8.52514i	1.21299	+	0.358655i
$566$	−26.1483	−	3.75956i	−1.09910	−	0.158026i
$567$	0.272230	+	3.80628i	0.0114326	+	0.159849i
$568$	1.42045	+	3.80836i	0.0596006	+	0.159795i
$569$	23.9467	+	15.3896i	1.00390	+	0.645167i	0.935807	−	0.352512i	$-0.114673\pi$
$569$	23.9467	+	15.3896i	1.00390	+	0.645167i	0.0680917	+	0.997679i	$0.478309\pi$
$570$	12.3129	−	2.65415i	0.515729	−	0.111170i
$571$	3.09902	+	4.82216i	0.129690	+	0.201801i	0.900025	−	0.435837i	$-0.143548\pi$
$571$	3.09902	+	4.82216i	0.129690	+	0.201801i	−0.770336	+	0.637639i	$0.779911\pi$
$572$	−0.376490	−	0.0269271i	−0.0157418	−	0.00112588i
$573$	−5.04267	−	2.75351i	−0.210661	−	0.115029i
$574$	22.5996			0.943290
$575$	−6.07201	+	23.1976i	−0.253220	+	0.967409i
$576$	−1.00000			−0.0416667
$577$	9.65305	+	5.27096i	0.401862	+	0.219433i	0.667452	−	0.744653i	$-0.267385\pi$
$577$	9.65305	+	5.27096i	0.401862	+	0.219433i	−0.265590	+	0.964086i	$0.585567\pi$
$578$	−22.7335	−	1.62593i	−0.945588	−	0.0676298i
$579$	2.45520	+	3.82037i	0.102035	+	0.158769i
$580$	−7.07589	+	1.52527i	−0.293810	+	0.0633335i
$581$	11.4614	+	7.36579i	0.475499	+	0.305584i
$582$	4.65163	+	12.4715i	0.192816	+	0.516960i
$583$	−0.884574	−	12.3680i	−0.0366353	−	0.512229i
$584$	−2.21629	−	0.318654i	−0.0917107	−	0.0131860i
$585$	−0.831564	−	0.245876i	−0.0343809	−	0.0101657i
$586$	−3.74801	+	12.7646i	−0.154829	+	0.527299i
$587$	23.0673	+	42.2446i	0.952090	+	1.74362i	0.577361	+	0.816489i	$0.304082\pi$
$587$	23.0673	+	42.2446i	0.952090	+	1.74362i	0.374729	+	0.927134i	$0.377736\pi$
$588$	−7.08507	−	2.64259i	−0.292183	−	0.108979i
$589$	−0.0600559	+	0.417698i	−0.00247456	+	0.0172109i
$590$	−27.0860	+	3.84217i	−1.11511	+	0.158179i
$591$	6.43955	−	14.1006i	0.264888	−	0.580023i
$592$	8.34048	−	1.81436i	0.342792	−	0.0745697i
$593$	17.5347	+	13.1263i	0.720062	+	0.539032i	0.895283	−	0.445497i	$-0.146973\pi$
$593$	17.5347	+	13.1263i	0.720062	+	0.539032i	−0.175221	+	0.984529i	$0.556064\pi$
$594$	−0.818800	+	0.526211i	−0.0335958	+	0.0215907i
$595$	37.9885	+	38.1323i	1.55738	+	1.56327i
$596$	−6.62207	−	22.5527i	−0.271251	−	0.923795i
$597$	−2.42308	+	2.42308i	−0.0991702	+	0.0991702i
$598$	−1.85880	+	0.0620502i	−0.0760120	+	0.00253742i
$599$			3.34715i			0.136761i	0.997659	+	0.0683805i	$0.0217832\pi$
$599$			3.34715i			0.136761i	−0.997659	+	0.0683805i	$0.978217\pi$
$600$	−2.05988	−	4.55597i	−0.0840942	−	0.185997i
$601$	12.4486	+	14.3665i	0.507790	+	0.586021i	0.950531	−	0.310628i	$-0.100539\pi$
$601$	12.4486	+	14.3665i	0.507790	+	0.586021i	−0.442741	+	0.896649i	$0.645994\pi$
$602$	−7.23665	−	1.57424i	−0.294944	−	0.0641611i
$603$	−2.81386	+	3.75888i	−0.114589	+	0.153073i
$604$	4.05765	−	6.31383i	0.165103	−	0.256906i
$605$	21.0463	+	7.89518i	0.855654	+	0.320985i
$606$	−7.13949	+	8.23941i	−0.290022	+	0.334703i
$607$	17.6523	−	13.2144i	0.716486	−	0.536354i	−0.177681	−	0.984088i	$-0.556860\pi$
$607$	17.6523	−	13.2144i	0.716486	−	0.536354i	0.894167	+	0.447734i	$0.147769\pi$
$608$	−1.96852	+	5.27780i	−0.0798339	+	0.214043i
$609$	−11.8525	−	3.48020i	−0.480286	−	0.141025i
$610$	−8.64805	−	13.5127i	−0.350149	−	0.547113i
$611$	1.65845	+	3.63149i	0.0670936	+	0.146914i
$612$	3.78028	+	5.04986i	0.152809	+	0.204128i
$613$	−45.3100	+	3.24063i	−1.83005	+	0.130888i	−0.943423	−	0.331591i	$-0.892415\pi$
$613$	−45.3100	+	3.24063i	−1.83005	+	0.130888i	−0.886630	+	0.462479i	$0.846960\pi$
$614$	−0.374782	−	0.171157i	−0.0151250	−	0.00690735i
$615$	3.70690	+	12.7133i	0.149477	+	0.512651i
$616$	−0.528578	−	3.67634i	−0.0212970	−	0.148124i
$617$	−0.646927	+	2.97387i	−0.0260443	+	0.119724i	−0.988334	−	0.152304i	$-0.951331\pi$
$617$	−0.646927	+	2.97387i	−0.0260443	+	0.119724i	0.962289	+	0.272028i	$0.0876943\pi$
$618$	−0.844758	+	11.8113i	−0.0339812	+	0.475119i
$619$	44.5335	−	13.0762i	1.78995	−	0.525577i	0.793410	−	0.608687i	$-0.208304\pi$
$619$	44.5335	−	13.0762i	1.78995	−	0.525577i	0.996540	+	0.0831103i	$0.0264854\pi$
$620$	0.167110	−	0.0116347i	0.00671132	−	0.000467262i
$621$	−3.74124	+	3.00053i	−0.150131	+	0.120407i
$622$	−12.5673	−	12.5673i	−0.503903	−	0.503903i
$623$	−2.31949	+	4.24783i	−0.0929284	+	0.170186i
$624$	0.293081	−	0.253957i	0.0117326	−	0.0101664i
$625$	16.5138	−	18.7695i	0.660552	−	0.750780i
$626$	16.4564	−	2.36608i	0.657731	−	0.0945675i
$627$	1.16541	+	5.35732i	0.0465421	+	0.213951i
$628$	8.75347	−	3.26488i	0.349301	−	0.130283i
$629$	−40.6916	−	35.2594i	−1.62248	−	1.40589i
$630$	0.624801	−	8.50993i	0.0248927	−	0.339044i
$631$	−38.8330	+	17.7344i	−1.54592	+	0.705996i	−0.991960	−	0.126550i	$-0.959610\pi$
$631$	−38.8330	+	17.7344i	−1.54592	+	0.705996i	−0.553956	+	0.832546i	$0.686882\pi$
$632$	5.12668	−	2.79938i	0.203928	−	0.111353i
$633$	0.917916	−	0.501220i	0.0364839	−	0.0199217i
$634$	−23.9767	+	10.9498i	−0.952235	+	0.434871i
$635$	−1.13647	−	1.31657i	−0.0450994	−	0.0522466i
$636$	9.62793	+	8.34265i	0.381772	+	0.330808i
$637$	2.74761	−	1.02480i	0.108864	−	0.0406042i
$638$	−0.669733	−	3.07871i	−0.0265150	−	0.121887i
$639$	−4.02327	+	0.578459i	−0.159158	+	0.0228835i
$640$	2.21270	+	0.322406i	0.0874648	+	0.0127442i
$641$	−20.4667	+	17.7345i	−0.808385	+	0.700470i	−0.957526	−	0.288346i	$-0.906895\pi$
$641$	−20.4667	+	17.7345i	−0.808385	+	0.700470i	0.149141	+	0.988816i	$0.452349\pi$
$642$	−8.26245	+	15.1315i	−0.326093	+	0.597194i
$643$	−32.8220	−	32.8220i	−1.29437	−	1.29437i	−0.932055	−	0.362316i	$-0.881986\pi$
$643$	−32.8220	−	32.8220i	−1.29437	−	1.29437i	−0.362316	−	0.932055i	$-0.618014\pi$
$644$	−4.48459	−	17.7429i	−0.176718	−	0.699169i
$645$	−0.301410	−	4.32917i	−0.0118680	−	0.170461i
$646$	34.0937	−	10.0108i	1.34140	−	0.393870i
$647$	−0.0598213	+	0.836411i	−0.00235182	+	0.0328827i	−0.998493	−	0.0548881i	$-0.982520\pi$
$647$	−0.0598213	+	0.836411i	−0.00235182	+	0.0328827i	0.996141	+	0.0877708i	$0.0279743\pi$
$648$	0.212565	−	0.977147i	0.00835035	−	0.0383860i
$649$	−1.69467	−	11.7867i	−0.0665218	−	0.462669i
$650$	1.76073	+	0.812152i	0.0690616	+	0.0318552i
$651$	0.260041	+	0.118757i	0.0101918	+	0.00465445i
$652$	−16.1589	+	1.15571i	−0.632832	+	0.0452611i
$653$	17.9671	+	24.0012i	0.703106	+	0.939239i	0.999877	−	0.0157094i	$-0.00500066\pi$
$653$	17.9671	+	24.0012i	0.703106	+	0.939239i	−0.296771	+	0.954949i	$0.595910\pi$
$654$	5.06386	+	11.0883i	0.198013	+	0.433587i
$655$	−3.13453	+	14.2793i	−0.122476	+	0.557939i
$656$	−5.68244	−	1.66851i	−0.221862	−	0.0651445i
$657$	0.782478	−	2.09790i	0.0305274	−	0.0818470i
$658$	−31.4486	+	23.5421i	−1.22599	+	0.917766i
$659$	−12.5771	+	14.5147i	−0.489934	+	0.565414i	−0.945848	−	0.324610i	$-0.894767\pi$
$659$	−12.5771	+	14.5147i	−0.489934	+	0.565414i	0.455914	+	0.890024i	$0.349312\pi$
$660$	1.98141	−	0.900362i	0.0771265	−	0.0350465i
$661$	−0.970932	+	1.51080i	−0.0377649	+	0.0587633i	−0.859623	−	0.510929i	$-0.829301\pi$
$661$	−0.970932	+	1.51080i	−0.0377649	+	0.0587633i	0.821858	+	0.569693i	$0.192938\pi$
$662$	−17.0555	+	22.7834i	−0.662879	+	0.885503i
$663$	−2.39037	−	0.519994i	−0.0928344	−	0.0201949i
$664$	−2.33804	−	2.69824i	−0.0907334	−	0.104712i
$665$	−43.6838	−	20.0495i	−1.69398	−	0.777487i
$666$			8.53554i			0.330746i
$667$	−4.86834	−	14.7416i	−0.188503	−	0.570797i
$668$	9.25419	−	9.25419i	0.358056	−	0.358056i
$669$	4.09979	+	13.9626i	0.158507	+	0.539825i
$670$	7.43812	−	7.41008i	0.287360	−	0.286276i
$671$	5.87464	−	3.77540i	0.226788	−	0.145748i
$672$	3.05486	+	2.28684i	0.117844	+	0.0882169i
$673$	−0.167349	+	0.0364046i	−0.00645083	+	0.00140329i	−0.215790	−	0.976440i	$-0.569233\pi$
$673$	−0.167349	+	0.0364046i	−0.00645083	+	0.00140329i	0.209339	+	0.977843i	$0.432869\pi$
$674$	11.5543	−	25.3004i	0.445056	−	0.974537i
$675$	4.88971	−	1.04436i	0.188205	−	0.0401975i
$676$	1.82869	−	12.7188i	0.0703342	−	0.489185i
$677$	47.6441	+	17.7703i	1.83111	+	0.682969i	0.989809	+	0.142403i	$0.0454830\pi$
$677$	47.6441	+	17.7703i	1.83111	+	0.682969i	0.841302	+	0.540566i	$0.181790\pi$
$678$	−6.44401	−	11.8013i	−0.247481	−	0.453227i
$679$	14.3103	−	48.7363i	0.549178	−	1.87033i
$680$	−6.73652	−	12.3926i	−0.258334	−	0.475235i
$681$	9.37005	+	1.34721i	0.359061	+	0.0516252i
$682$	0.00520173	+	0.0727296i	0.000199184	+	0.00278496i
$683$	6.01902	+	16.1376i	0.230311	+	0.617488i	0.999775	−	0.0212019i	$-0.00674929\pi$
$683$	6.01902	+	16.1376i	0.230311	+	0.617488i	−0.769464	+	0.638690i	$0.779477\pi$
$684$	−4.73875	−	3.04541i	−0.181191	−	0.116444i
$685$	−7.49469	+	11.6137i	−0.286358	+	0.443736i
$686$	1.15914	+	1.80365i	0.0442561	+	0.0688638i
$687$	3.30993	+	0.236731i	0.126282	+	0.00903185i
$688$	1.70335	+	0.930102i	0.0649398	+	0.0354598i
$689$	−4.94044			−0.188216
$690$	9.24563	−	5.43307i	0.351975	−	0.206834i
$691$	11.7454			0.446816			0.223408	−	0.974725i	$-0.428282\pi$
$691$	11.7454			0.446816			0.223408	+	0.974725i	$0.428282\pi$
$692$	−6.67813	−	3.64654i	−0.253865	−	0.138621i
$693$	3.70468	+	0.264964i	0.140729	+	0.0100652i
$694$	−1.21978	−	1.89801i	−0.0463021	−	0.0720474i
$695$	8.42573	+	39.0878i	0.319606	+	1.48268i
$696$	2.72324	+	1.75012i	0.103224	+	0.0663380i
$697$	13.0554	+	35.0029i	0.494509	+	1.32583i
$698$	0.468772	+	6.55430i	0.0177433	+	0.248084i
$699$	−6.33644	−	0.911043i	−0.239666	−	0.0344588i
$700$	−4.12615	+	18.6285i	−0.155954	+	0.704091i
$701$	−1.57999	+	5.38096i	−0.0596755	+	0.203236i	−0.983934	−	0.178530i	$-0.942866\pi$
$701$	−1.57999	+	5.38096i	−0.0596755	+	0.203236i	0.924259	+	0.381766i	$0.124684\pi$
$702$	0.185854	+	0.340366i	0.00701460	+	0.0128463i
$703$	45.0489	+	16.8024i	1.69905	+	0.633713i
$704$	−0.138516	+	0.963402i	−0.00522053	+	0.0363096i
$705$	−18.4019	−	13.8298i	−0.693055	−	0.520860i
$706$	−13.3060	+	29.1361i	−0.500778	+	1.09655i
$707$	40.6524	−	8.84339i	1.52889	−	0.332590i
$708$	9.79420	+	7.33185i	0.368089	+	0.275548i
$709$	−14.9460	+	9.60521i	−0.561309	+	0.360731i	−0.790322	−	0.612692i	$-0.790087\pi$
$709$	−14.9460	+	9.60521i	−0.561309	+	0.360731i	0.229013	+	0.973423i	$0.426450\pi$
$710$	9.08880	+	0.0171685i	0.341097	+	0.000644321i
$711$	1.64565	+	5.60457i	0.0617167	+	0.210188i
$712$	0.896826	−	0.896826i	0.0336100	−	0.0336100i
$713$	0.0629671	+	0.353719i	0.00235814	+	0.0132469i
$714$		−	24.0715i		−	0.900854i
$715$	−0.352063	+	0.767073i	−0.0131664	+	0.0286869i
$716$	−16.2403	−	18.7424i	−0.606930	−	0.700435i
$717$	5.99556	+	1.30425i	0.223908	+	0.0487083i
$718$	13.9552	−	18.6420i	0.520803	−	0.695712i
$719$	5.39152	−	8.38937i	0.201070	−	0.312871i	−0.726046	−	0.687646i	$-0.758644\pi$
$719$	5.39152	−	8.38937i	0.201070	−	0.312871i	0.927115	+	0.374776i	$0.122280\pi$
$720$	−0.785382	+	2.09360i	−0.0292695	+	0.0780240i
$721$	29.5911	−	34.1500i	1.10203	−	1.27181i
$722$	−10.1911	+	7.62895i	−0.379273	+	0.283920i
$723$	1.57650	−	4.22676i	0.0586307	−	0.157195i
$724$	−22.8018	−	6.69521i	−0.847422	−	0.248825i
$725$	−2.36396	+	16.0120i	−0.0877952	+	0.594672i
$726$	−4.17603	−	9.14423i	−0.154987	−	0.339374i
$727$	6.63141	+	8.85852i	0.245945	+	0.328544i	0.906478	−	0.422253i	$-0.138761\pi$
$727$	6.63141	+	8.85852i	0.245945	+	0.328544i	−0.660533	+	0.750797i	$0.729670\pi$
$728$	−1.47608	+	0.105572i	−0.0547073	+	0.00391274i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	−2.40777	+	4.38976i	−0.0891155	+	0.162472i
$731$	−1.74227	−	12.1177i	−0.0644401	−	0.448191i
$732$	−1.52509	+	7.01074i	−0.0563690	+	0.259124i
$733$	−3.71338	+	51.9199i	−0.137157	+	1.91770i	0.206219	+	0.978506i	$0.433884\pi$
$733$	−3.71338	+	51.9199i	−0.137157	+	1.91770i	−0.343376	+	0.939198i	$0.611570\pi$
$734$	24.7997	−	7.28186i	0.915375	−	0.268778i
$735$	−11.0970	+	12.7579i	−0.409320	+	0.470582i
$736$	−0.182343	+	4.79236i	−0.00672126	+	0.176649i
$737$	3.23155	+	3.23155i	0.119036	+	0.119036i
$738$	2.83827	−	5.19791i	0.104478	−	0.191338i
$739$	15.7237	−	13.6247i	0.578407	−	0.501193i	−0.315812	−	0.948822i	$-0.602277\pi$
$739$	15.7237	−	13.6247i	0.578407	−	0.501193i	0.894219	+	0.447629i	$0.147731\pi$
$740$	2.75191	−	18.8866i	0.101162	−	0.694286i
$741$	2.16224	−	0.310883i	0.0794319	−	0.0114206i
$742$	−10.3337	−	47.5032i	−0.379362	−	1.74390i
$743$	22.4603	−	8.37725i	0.823987	−	0.307331i	0.0981273	−	0.995174i	$-0.468715\pi$
$743$	22.4603	−	8.37725i	0.823987	−	0.307331i	0.725860	+	0.687842i	$0.241442\pi$
$744$	−0.0566169	−	0.0490589i	−0.00207568	−	0.00179859i
$745$	−52.4173	−	3.84849i	−1.92042	−	0.140998i
$746$	−9.98465	+	4.55984i	−0.365564	+	0.166948i
$747$	3.13356	−	1.71105i	0.114651	−	0.0626042i
$748$	5.38867	−	2.94244i	0.197029	−	0.107586i
$749$	59.8441	−	27.3299i	2.18666	−	0.998613i
$750$	−11.1562	+	0.734387i	−0.407367	+	0.0268160i
$751$	−9.27102	−	8.03339i	−0.338304	−	0.293142i	0.469095	−	0.883148i	$-0.344580\pi$
$751$	−9.27102	−	8.03339i	−0.338304	−	0.293142i	−0.807399	+	0.590005i	$0.799126\pi$
$752$	9.64551	−	3.59759i	0.351735	−	0.131191i
$753$	−3.58045	−	16.4590i	−0.130479	−	0.599801i
$754$	−1.24258	+	0.178657i	−0.0452522	+	0.00650629i
$755$	−10.0318	−	13.4539i	−0.365096	−	0.489637i
$756$	−2.88394	+	2.49895i	−0.104888	+	0.0908859i
$757$	−15.5440	+	28.4667i	−0.564955	+	1.03464i	0.426537	+	0.904470i	$0.359734\pi$
$757$	−15.5440	+	28.4667i	−0.564955	+	1.03464i	−0.991492	+	0.130168i	$0.958448\pi$
$758$	−3.60036	−	3.60036i	−0.130771	−	0.130771i
$759$	2.37249	+	4.01994i	0.0861160	+	0.145914i
$760$	9.50358	+	8.26638i	0.344731	+	0.299853i
$761$	14.7640	−	4.33509i	0.535193	−	0.157147i	−0.00295758	−	0.999996i	$-0.500941\pi$
$761$	14.7640	−	4.33509i	0.535193	−	0.157147i	0.538150	+	0.842849i	$0.319123\pi$
$762$	−0.0554882	+	0.775826i	−0.00201012	+	0.0281052i
$763$	9.88782	−	45.4536i	0.357963	−	1.64553i
$764$	−0.817665	−	5.68698i	−0.0295821	−	0.205748i
$765$	13.5414	−	3.94833i	0.489589	−	0.142752i
$766$	2.05074	+	0.936540i	0.0740961	+	0.0338386i
$767$	−4.73247	+	0.338473i	−0.170880	+	0.0122215i
$768$	−0.599278	−	0.800541i	−0.0216246	−	0.0288870i
$769$	17.8823	+	39.1569i	0.644854	+	1.41203i	0.895987	+	0.444081i	$0.146470\pi$
$769$	17.8823	+	39.1569i	0.644854	+	1.41203i	−0.251133	+	0.967953i	$0.580803\pi$
$770$	−8.11194	−	1.78070i	−0.292334	−	0.0641719i
$771$	−5.74403	−	1.68660i	−0.206866	−	0.0607414i
$772$	−1.58701	+	4.25495i	−0.0571179	+	0.153139i
$773$	23.3442	−	17.4752i	0.839632	−	0.628541i	−0.0904464	−	0.995901i	$-0.528829\pi$
$773$	23.3442	−	17.4752i	0.839632	−	0.628541i	0.930079	+	0.367361i	$0.119738\pi$
$774$	−1.27092	+	1.46672i	−0.0456823	+	0.0527202i
$775$	0.106887	−	0.359001i	0.00383949	−	0.0128957i
$776$	−7.19633	+	11.1977i	−0.258333	+	0.401974i
$777$	19.5194	−	26.0749i	0.700256	−	0.935433i
$778$	26.7344	+	5.81571i	0.958475	+	0.208503i
$779$	−21.8463	−	25.2120i	−0.782726	−	0.903314i
$780$	−0.301503	−	0.813049i	−0.0107956	−	0.0291118i
$781$			3.95615i			0.141562i
$782$	24.8901	−	17.1957i	0.890067	−	0.614915i
$783$	−2.28899	+	2.28899i	−0.0818017	+	0.0818017i
$784$	−2.13042	−	7.25554i	−0.0760864	−	0.259126i
$785$	0.0394614	−	20.8905i	0.00140844	−	0.745613i
$786$	5.50007	−	3.53468i	0.196181	−	0.126078i
$787$	3.37974	+	2.53004i	0.120475	+	0.0901863i	0.657816	−	0.753179i	$-0.271480\pi$
$787$	3.37974	+	2.53004i	0.120475	+	0.0901863i	−0.537341	+	0.843365i	$0.680571\pi$
$788$	15.1472	−	3.29508i	0.539597	−	0.117382i
$789$	−2.89630	+	6.34201i	−0.103111	+	0.225781i
$790$	−1.83439	−	12.9318i	−0.0652646	−	0.460093i
$791$	−7.30220	+	50.7879i	−0.259636	+	1.80581i
$792$	−0.911942	−	0.340137i	−0.0324044	−	0.0120862i
$793$	−1.33345	−	2.44202i	−0.0473521	−	0.0867188i
$794$	−0.670414	+	2.28322i	−0.0237921	+	0.0810284i
$795$	25.0278	−	13.6049i	0.887645	−	0.482516i
$796$	−3.39188	−	0.487678i	−0.120222	−	0.0172853i
$797$	−1.49961	−	20.9673i	−0.0531189	−	0.742699i	−0.952308	−	0.305139i	$-0.901297\pi$
$797$	−1.49961	−	20.9673i	−0.0531189	−	0.742699i	0.899189	−	0.437561i	$-0.144157\pi$
$798$	7.51186	+	20.1401i	0.265917	+	0.712951i
$799$	−54.6300	−	35.1086i	−1.93267	−	1.24205i
$800$	2.41281	−	4.37931i	0.0853056	−	0.154832i
$801$	0.685697	+	1.06696i	0.0242279	+	0.0376993i
$802$	21.9411	+	1.56926i	0.774767	+	0.0554124i
$803$	−1.91274	−	1.04444i	−0.0674991	−	0.0368573i
$804$	−4.69542			−0.165595
$805$	−40.6687	−	4.54600i	−1.43338	−	0.160226i
$806$	0.0290522			0.00102332
$807$	−9.49354	−	5.18386i	−0.334188	−	0.182481i
$808$	−10.8745	−	0.777761i	−0.382564	−	0.0273615i
$809$	−1.68679	−	2.62469i	−0.0593043	−	0.0922792i	0.810335	−	0.585967i	$-0.199285\pi$
$809$	−1.68679	−	2.62469i	−0.0593043	−	0.0922792i	−0.869639	+	0.493687i	$0.835649\pi$
$810$	−1.87881	−	1.21246i	−0.0660148	−	0.0426015i
$811$	−6.91986	−	4.44713i	−0.242989	−	0.156160i	0.413478	−	0.910514i	$-0.364314\pi$
$811$	−6.91986	−	4.44713i	−0.242989	−	0.156160i	−0.656468	+	0.754354i	$0.727950\pi$
$812$	−4.31687	−	11.5740i	−0.151493	−	0.406167i
$813$	1.26374	+	17.6694i	0.0443213	+	0.619693i
$814$	8.22316	+	1.18231i	0.288222	+	0.0414400i
$815$	−10.2713	+	34.7381i	−0.359789	+	1.21682i
$816$	−1.77718	+	6.05253i	−0.0622139	+	0.211881i
$817$	5.23923	+	9.59493i	0.183297	+	0.335684i
$818$	−26.4364	−	9.86028i	−0.924329	−	0.344757i
$819$	0.210605	−	1.46479i	0.00735914	−	0.0511839i
$820$	−7.95609	+	10.5864i	−0.277839	+	0.369691i
$821$	−5.88133	+	12.8783i	−0.205260	+	0.449457i	−0.984065	−	0.177810i	$-0.943099\pi$
$821$	−5.88133	+	12.8783i	−0.205260	+	0.449457i	0.778805	+	0.627266i	$0.215826\pi$
$822$	6.04013	−	1.31395i	0.210674	−	0.0458292i
$823$	−7.55612	−	5.65644i	−0.263390	−	0.197171i	0.459418	−	0.888220i	$-0.348058\pi$
$823$	−7.55612	−	5.65644i	−0.263390	−	0.197171i	−0.722808	+	0.691049i	$0.757149\pi$
$824$	−9.96165	+	6.40196i	−0.347031	+	0.223023i
$825$	−0.328834	−	4.85542i	−0.0114485	−	0.169044i
$826$	−13.1532	−	44.7956i	−0.457657	−	1.55864i
$827$	7.55843	−	7.55843i	0.262832	−	0.262832i	−0.563371	−	0.826204i	$-0.690496\pi$
$827$	7.55843	−	7.55843i	0.262832	−	0.262832i	0.826204	+	0.563371i	$0.190496\pi$
$828$	−4.64408	−	1.19687i	−0.161393	−	0.0415940i
$829$		−	6.96694i		−	0.241972i	−0.992654	−	0.120986i	$-0.961394\pi$
$829$		−	6.96694i		−	0.241972i	0.992654	−	0.120986i	$-0.0386056\pi$
$830$	−7.48529	+	2.77577i	−0.259818	+	0.0963485i
$831$	4.55097	+	5.25210i	0.157871	+	0.182193i
$832$	0.378940	+	0.0824333i	0.0131374	+	0.00285786i
$833$	−28.5859	+	38.1862i	−0.990442	+	1.32308i
$834$	9.66779	−	15.0434i	0.334768	−	0.520910i
$835$	−12.1065	−	26.6427i	−0.418964	−	0.922008i
$836$	−3.59035	+	4.14348i	−0.124175	+	0.143305i
$837$	0.0599725	−	0.0448949i	0.00207295	−	0.00155179i
$838$	5.08395	−	13.6306i	0.175622	−	0.470861i
$839$	−15.2990	−	4.49220i	−0.528181	−	0.155088i	0.00676027	−	0.999977i	$-0.497848\pi$
$839$	−15.2990	−	4.49220i	−0.528181	−	0.155088i	−0.534941	+	0.844889i	$0.679666\pi$
$840$	7.18698	−	4.59963i	0.247974	−	0.158702i
$841$	7.69393	+	16.8474i	0.265308	+	0.580943i
$842$	−8.59280	−	11.4786i	−0.296128	−	0.395580i
$843$	1.69856	−	0.121484i	0.0585016	−	0.00418412i
$844$	0.951334	+	0.434460i	0.0327463	+	0.0149547i
$845$	−25.1919	−	13.8177i	−0.866629	−	0.475343i
$846$	1.46507	+	10.1898i	0.0503702	+	0.350332i
$847$	−8.15421	+	37.4843i	−0.280182	+	1.28798i
$848$	−0.908831	+	12.7071i	−0.0312094	+	0.436364i
$849$	25.3471	−	7.44258i	0.869911	−	0.255429i
$850$	−31.2360	+	4.37067i	−1.07138	+	0.149913i
$851$	40.9054	+	1.55640i	1.40222	+	0.0533526i
$852$	−2.87414	−	2.87414i	−0.0984663	−	0.0984663i
$853$	−24.0316	+	44.0105i	−0.822825	+	1.50689i	0.0387424	+	0.999249i	$0.487665\pi$
$853$	−24.0316	+	44.0105i	−0.822825	+	1.50689i	−0.861568	+	0.507643i	$0.830517\pi$
$854$	20.6914	−	17.9292i	0.708045	−	0.613525i
$855$	−10.0976	+	7.52925i	−0.345331	+	0.257495i
$856$	−17.0649	+	2.45357i	−0.583267	+	0.0838612i
$857$	−2.98149	−	13.7057i	−0.101846	−	0.468177i	−0.999616	−	0.0277129i	$-0.991178\pi$
$857$	−2.98149	−	13.7057i	−0.101846	−	0.468177i	0.897770	−	0.440464i	$-0.145186\pi$
$858$	0.353653	−	0.131906i	0.0120735	−	0.00450319i
$859$	43.1394	+	37.3805i	1.47190	+	1.27541i	0.884867	+	0.465844i	$0.154249\pi$
$859$	43.1394	+	37.3805i	1.47190	+	1.27541i	0.587032	+	0.809564i	$0.300296\pi$
$860$	3.28505	−	2.83566i	0.112019	−	0.0966953i
$861$	−20.5573	+	9.38822i	−0.700592	+	0.319950i
$862$	6.60367	−	3.60588i	0.224922	−	0.122817i
$863$	11.6782	−	6.37680i	0.397532	−	0.217069i	−0.268032	−	0.963410i	$-0.586373\pi$
$863$	11.6782	−	6.37680i	0.397532	−	0.217069i	0.665563	+	0.746341i	$0.268191\pi$
$864$	0.909632	−	0.415415i	0.0309463	−	0.0141327i
$865$	−12.8793	+	11.1174i	−0.437909	+	0.378004i
$866$	3.74855	+	3.24813i	0.127381	+	0.110376i
$867$	21.3545	−	7.96483i	0.725238	−	0.270500i
$868$	0.0607672	+	0.279342i	0.00206257	+	0.00948149i
$869$	5.62740	−	0.809099i	0.190897	−	0.0274468i
$870$	5.80283	−	4.32687i	0.196734	−	0.146695i
$871$	1.37614	−	1.19243i	0.0466288	−	0.0404040i
$872$	−5.84199	+	10.6988i	−0.197835	+	0.362307i
$873$	−9.41212	−	9.41212i	−0.318552	−	0.318552i
$874$	−15.4588	+	22.1545i	−0.522901	+	0.749387i
$875$	35.7601	+	23.2690i	1.20891	+	0.786636i
$876$	2.14838	−	0.630821i	0.0725871	−	0.0213135i
$877$	−2.27384	+	31.7925i	−0.0767823	+	1.07356i	0.802311	+	0.596907i	$0.203604\pi$
$877$	−2.27384	+	31.7925i	−0.0767823	+	1.07356i	−0.879093	+	0.476650i	$0.841851\pi$
$878$	−4.40832	+	20.2647i	−0.148774	+	0.683901i
$879$	−1.89328	−	13.1680i	−0.0638587	−	0.444147i
$880$	1.90819	+	1.04664i	0.0643252	+	0.0352821i
$881$	−5.17683	−	2.36418i	−0.174412	−	0.0796513i	0.326296	−	0.945268i	$-0.394200\pi$
$881$	−5.17683	−	2.36418i	−0.174412	−	0.0796513i	−0.500708	+	0.865617i	$0.666927\pi$
$882$	7.54258	−	0.539456i	0.253972	−	0.0181644i
$883$	−6.35988	−	8.49580i	−0.214027	−	0.285907i	0.680661	−	0.732599i	$-0.261693\pi$
$883$	−6.35988	−	8.49580i	−0.214027	−	0.285907i	−0.894688	+	0.446692i	$0.852602\pi$
$884$	−1.01622	−	2.22521i	−0.0341792	−	0.0748420i
$885$	23.0422	−	14.7469i	0.774554	−	0.495711i
$886$	−24.2183	−	7.11114i	−0.813631	−	0.238904i
$887$	−12.7143	+	34.0884i	−0.426905	+	1.14458i	0.528410	+	0.848989i	$0.322788\pi$
$887$	−12.7143	+	34.0884i	−0.426905	+	1.14458i	−0.955315	+	0.295588i	$0.904484\pi$
$888$	−6.83305	+	5.11516i	−0.229302	+	0.171654i
$889$	1.94370	−	2.24315i	0.0651896	−	0.0752328i
$890$	−1.17325	−	2.58195i	−0.0393273	−	0.0865471i
$891$	0.526211	−	0.818800i	0.0176287	−	0.0274308i
$892$	−8.72072	+	11.6495i	−0.291991	+	0.390055i
$893$	56.6637	+	12.3264i	1.89618	+	0.412489i
$894$	15.3924	+	17.7638i	0.514798	+	0.594109i
$895$	−51.9939	+	19.2809i	−1.73797	+	0.644491i
$896$			3.81600i			0.127484i
$897$	1.66505	−	0.828616i	0.0555943	−	0.0276667i
$898$	−13.2451	+	13.2451i	−0.441996	+	0.441996i
$899$	0.0683225	+	0.232685i	0.00227868	+	0.00776049i
$900$	3.76635	+	3.28856i	0.125545	+	0.109619i
$901$	67.6048	−	43.4470i	2.25224	−	1.44743i
$902$	−4.61453	−	3.45439i	−0.153647	−	0.115019i
$903$	7.23665	−	1.57424i	0.240821	−	0.0523873i
$904$	5.58570	−	12.2310i	0.185778	−	0.406796i
$905$	−31.9252	+	42.4796i	−1.06123	+	1.41207i
$906$	−1.06811	+	7.42887i	−0.0354856	+	0.246808i
$907$	43.9215	+	16.3819i	1.45839	+	0.543951i	0.948636	−	0.316370i	$-0.102464\pi$
$907$	43.9215	+	16.3819i	1.45839	+	0.543951i	0.509753	+	0.860321i	$0.329737\pi$
$908$	4.53676	+	8.30846i	0.150558	+	0.275726i
$909$	3.07153	−	10.4607i	0.101876	−	0.346959i
$910$	−0.938264	+	3.17325i	−0.0311031	+	0.105192i
$911$	32.6492	+	4.69424i	1.08172	+	0.155527i	0.660048	−	0.751223i	$-0.270536\pi$
$911$	32.6492	+	4.69424i	1.08172	+	0.155527i	0.421667	+	0.906751i	$0.361445\pi$
$912$	−0.401851	−	5.61861i	−0.0133066	−	0.186051i
$913$	−1.21438	−	3.25589i	−0.0401902	−	0.107754i
$914$	−24.8927	−	15.9976i	−0.823379	−	0.529153i
$915$	13.4799	+	8.69904i	0.445632	+	0.287581i
$916$	1.79406	+	2.79161i	0.0592773	+	0.0922372i
$917$	−24.8852	−	1.77983i	−0.821783	−	0.0587751i
$918$	−5.53645	−	3.02313i	−0.182730	−	0.0997781i
$919$	25.1454			0.829469			0.414735	−	0.909942i	$-0.363874\pi$
$919$	25.1454			0.829469			0.414735	+	0.909942i	$0.363874\pi$
$920$	9.89010	+	4.14559i	0.326067	+	0.136676i
$921$	0.412015			0.0135764
$922$	−35.7965	−	19.5464i	−1.17889	−	0.643725i
$923$	1.57226	+	0.112450i	0.0517516	+	0.00370135i
$924$	2.00802	+	3.12454i	0.0660590	+	0.102790i
$925$	−37.3798	−	20.5946i	−1.22904	−	0.677147i
$926$	17.3479	+	11.1488i	0.570086	+	0.366372i
$927$	−4.13816	−	11.0948i	−0.135915	−	0.364402i
$928$	0.230933	+	3.22887i	0.00758076	+	0.105993i
$929$	−25.5589	−	3.67481i	−0.838560	−	0.120567i	−0.290363	−	0.956916i	$-0.593776\pi$
$929$	−25.5589	−	3.67481i	−0.838560	−	0.120567i	−0.548196	+	0.836350i	$0.684685\pi$
$930$	−0.147176	+	0.0800035i	−0.00482608	+	0.00262342i
$931$	12.0006	−	40.8702i	0.393303	−	1.33947i
$932$	−3.06796	−	5.61855i	−0.100494	−	0.184042i
$933$	16.6523	+	6.21097i	0.545170	+	0.203338i
$934$	−4.24008	+	29.4904i	−0.138740	+	0.964955i
$935$	−1.92813	−	13.5927i	−0.0630567	−	0.444528i
$936$	−0.161099	+	0.352757i	−0.00526568	+	0.0115302i
$937$	−48.3044	+	10.5080i	−1.57804	+	0.343281i	−0.914412	−	0.404784i	$-0.867347\pi$
$937$	−48.3044	+	10.5080i	−1.57804	+	0.343281i	−0.663625	+	0.748065i	$0.730983\pi$
$938$	14.3439	+	10.7377i	0.468344	+	0.350598i
$939$	−13.9864	+	8.98851i	−0.456429	+	0.293329i
$940$	0.0434828	−	23.0193i	0.00141825	−	0.750808i
$941$	1.70148	+	5.79470i	0.0554666	+	0.188902i	0.982566	−	0.185913i	$-0.0595244\pi$
$941$	1.70148	+	5.79470i	0.0554666	+	0.188902i	−0.927100	+	0.374815i	$0.877706\pi$
$942$	−6.60616	+	6.60616i	−0.215240	+	0.215240i
$943$	−24.3927	−	14.5498i	−0.794337	−	0.473808i
$944$			12.2345i			0.398198i
$945$	2.96681	+	8.00045i	0.0965104	+	0.260255i
$946$	1.23700	+	1.42757i	0.0402183	+	0.0464144i
$947$	−6.72134	−	1.46214i	−0.218414	−	0.0475131i	0.102026	−	0.994782i	$-0.467467\pi$
$947$	−6.72134	−	1.46214i	−0.218414	−	0.0475131i	−0.320441	+	0.947269i	$0.603831\pi$
$948$	−3.50049	+	4.67610i	−0.113691	+	0.151873i
$949$	−0.469449	+	0.730477i	−0.0152390	+	0.0237123i
$950$	24.7705	−	13.4045i	0.803660	−	0.434898i
$951$	17.2612	−	19.9205i	0.559734	−	0.645967i
$952$	19.2702	−	14.4255i	0.624552	−	0.467534i
$953$	−4.74384	+	12.7187i	−0.153668	+	0.412000i	−0.990857	−	0.134913i	$-0.956925\pi$
$953$	−4.74384	+	12.7187i	−0.153668	+	0.412000i	0.837189	+	0.546913i	$0.184197\pi$
$954$	−12.2235	−	3.58915i	−0.395752	−	0.116203i
$955$	−12.5485	−	2.75459i	−0.406059	−	0.0891363i
$956$	2.54890	+	5.58130i	0.0824372	+	0.180512i
$957$	1.88815	+	2.52228i	0.0610353	+	0.0815337i
$958$	18.7434	−	1.34055i	0.605572	−	0.0433113i
$959$	−21.4566	−	9.79888i	−0.692869	−	0.316422i
$960$	−2.14668	+	0.625919i	−0.0692837	+	0.0202015i
$961$	4.41096	+	30.6789i	0.142289	+	0.989642i
$962$	0.703613	−	3.23446i	0.0226854	−	0.104283i
$963$	1.22992	−	17.1965i	0.0396335	−	0.554149i
$964$	4.32846	−	1.27095i	0.139410	−	0.0409345i
$965$	7.66177	+	6.66434i	0.246641	+	0.214533i
$966$	11.4500	+	14.2766i	0.368398	+	0.459341i
$967$	−19.4225	−	19.4225i	−0.624585	−	0.624585i	0.322115	−	0.946701i	$-0.395606\pi$
$967$	−19.4225	−	19.4225i	−0.624585	−	0.624585i	−0.946701	+	0.322115i	$0.895606\pi$
$968$	4.81773	−	8.82302i	0.154848	−	0.283582i
$969$	−26.8541	+	23.2692i	−0.862677	+	0.747514i
$970$	17.7917	+	23.8607i	0.571257	+	0.766122i
$971$	31.7495	−	4.56488i	1.01889	−	0.146494i	0.387426	−	0.921901i	$-0.373364\pi$
$971$	31.7495	−	4.56488i	1.01889	−	0.146494i	0.631462	+	0.775407i	$0.282455\pi$
$972$	0.212565	+	0.977147i	0.00681803	+	0.0313420i
$973$	−63.9356	+	23.8468i	−2.04968	+	0.764492i
$974$	19.8246	+	17.1782i	0.635223	+	0.550423i
$975$	−1.93900	−	0.00732544i	−0.0620976	−	0.000234602i
$976$	−6.52634	+	2.98048i	−0.208903	+	0.0954028i
$977$	20.7390	−	11.3243i	0.663499	−	0.362298i	−0.111945	−	0.993714i	$-0.535708\pi$
$977$	20.7390	−	11.3243i	0.663499	−	0.362298i	0.775444	+	0.631417i	$0.217526\pi$
$978$	14.2186	−	7.76393i	0.454660	−	0.248263i
$979$	1.12290	−	0.512810i	0.0358879	−	0.0163895i
$980$	−16.8634	−	1.23812i	−0.538682	−	0.0395502i
$981$	−9.21251	−	7.98268i	−0.294133	−	0.254867i
$982$	−23.6147	+	8.80784i	−0.753577	+	0.281070i
$983$	−7.47253	−	34.3507i	−0.238337	−	1.09562i	−0.928318	−	0.371788i	$-0.878745\pi$
$983$	−7.47253	−	34.3507i	−0.238337	−	1.09562i	0.689981	−	0.723828i	$-0.257619\pi$
$984$	5.86205	−	0.842836i	0.186875	−	0.0268686i
$985$	4.99777	−	34.3002i	0.159242	−	1.09289i
$986$	15.4323	−	13.3722i	0.491466	−	0.425857i
$987$	18.8269	−	34.4788i	0.599266	−	1.09747i
$988$	1.54466	+	1.54466i	0.0491421	+	0.0491421i
$989$	6.79731	+	6.35816i	0.216142	+	0.202178i
$990$	−1.42833	+	1.64211i	−0.0453954	+	0.0521896i
$991$	11.0720	−	3.25103i	0.351714	−	0.103272i	−0.101103	−	0.994876i	$-0.532237\pi$
$991$	11.0720	−	3.25103i	0.351714	−	0.103272i	0.452817	+	0.891603i	$0.350419\pi$
$992$	0.00534437	−	0.0747241i	0.000169684	−	0.00237249i
$993$	6.04961	−	27.8096i	0.191979	−	0.882512i
$994$	2.20740	+	15.3528i	0.0700144	+	0.486961i
$995$	−3.68492	+	6.71823i	−0.116820	+	0.212982i
$996$	3.24764	+	1.48315i	0.102905	+	0.0469953i
$997$	41.0218	−	2.93394i	1.29917	−	0.0929187i	0.595449	−	0.803393i	$-0.296974\pi$
$997$	41.0218	−	2.93394i	1.29917	−	0.0929187i	0.703723	+	0.710474i	$0.251519\pi$
$998$	−17.1869	−	22.9590i	−0.544042	−	0.726755i
$999$	−3.54579	−	7.76420i	−0.112184	−	0.245649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.37.6	✓	240
5.3	odd	4	inner	690.2.w.b.313.6	yes	240
23.5	odd	22	inner	690.2.w.b.97.6	yes	240
115.28	even	44	inner	690.2.w.b.373.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.6	✓	240	1.1	even	1	trivial
690.2.w.b.97.6	yes	240	23.5	odd	22	inner
690.2.w.b.313.6	yes	240	5.3	odd	4	inner
690.2.w.b.373.6	yes	240	115.28	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.18586 - 0.471182i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33355 + 3.57540i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.18586 - 0.471182i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33355 + 3.57540i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-2.14430 - 0.634025i) q^{10} +(0.274213 - 0.933883i) q^{11} +(0.479249 + 0.877679i) q^{12} +(-0.363351 - 0.135523i) q^{13} +(0.543073 - 3.77716i) q^{14} +(2.21391 - 0.314044i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(6.16390 - 1.34087i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-4.73875 + 3.04541i) q^{19} +(1.57815 + 1.58412i) q^{20} +(1.07509 + 3.66142i) q^{21} +(-0.688234 + 0.688234i) q^{22} +(-3.01793 + 3.72721i) q^{23} -1.00000i q^{24} +(4.55597 - 2.05988i) q^{25} +(0.253957 + 0.293081i) q^{26} +(0.977147 + 0.212565i) q^{27} +(-2.28684 + 3.05486i) q^{28} +(-1.75012 + 2.72324i) q^{29} +(-2.09360 - 0.785382i) q^{30} +(0.0490589 - 0.0566169i) q^{31} +(0.800541 - 0.599278i) q^{32} +(0.340137 - 0.911942i) q^{33} +(-6.05253 - 1.77718i) q^{34} +(4.59963 + 7.18698i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-5.11516 - 6.83305i) q^{37} +(5.61861 - 0.401851i) q^{38} +(-0.352757 - 0.161099i) q^{39} +(-0.625919 - 2.14668i) q^{40} +(0.842836 + 5.86205i) q^{41} +(0.811149 - 3.72879i) q^{42} +(0.138451 - 1.93580i) q^{43} +(0.933883 - 0.274213i) q^{44} +(2.23067 - 0.155306i) q^{45} +(4.43504 - 1.82495i) q^{46} +(-7.27937 - 7.27937i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(-5.71486 + 4.95196i) q^{49} +(-4.98588 - 0.375535i) q^{50} +(6.24385 - 0.897730i) q^{51} +(-0.0824333 - 0.378940i) q^{52} +(11.9363 - 4.45203i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(0.159362 - 2.17054i) q^{55} +(3.47115 - 1.58522i) q^{56} +(-4.94393 + 2.69959i) q^{57} +(2.84115 - 1.55139i) q^{58} +(11.1289 - 5.08238i) q^{59} +(1.46112 + 1.69267i) q^{60} +(5.42228 + 4.69843i) q^{61} +(-0.0701916 + 0.0261801i) q^{62} +(0.811149 + 3.72879i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-0.858092 - 0.125030i) q^{65} +(-0.735578 + 0.637382i) q^{66} +(-2.25028 + 4.12107i) q^{67} +(4.46047 + 4.46047i) q^{68} +(-3.27614 + 3.50242i) q^{69} +(-0.592647 - 8.51223i) q^{70} +(-3.89999 + 1.14514i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(0.475950 - 2.18791i) q^{73} +(1.21473 + 8.44866i) q^{74} +(4.69132 - 1.72961i) q^{75} +(-5.12392 - 2.34002i) q^{76} +(3.70468 - 0.264964i) q^{77} +(0.232401 + 0.310452i) q^{78} +(2.42651 + 5.31332i) q^{79} +(-0.479437 + 2.18407i) q^{80} +(0.959493 + 0.281733i) q^{81} +(2.06964 - 5.54893i) q^{82} +(2.85816 - 2.13959i) q^{83} +(-2.49895 + 2.88394i) q^{84} +(12.8416 - 5.83528i) q^{85} +(-1.04925 + 1.63266i) q^{86} +(-1.93993 + 2.59145i) q^{87} +(-0.951066 - 0.206892i) q^{88} +(0.830562 + 0.958520i) q^{89} +(-2.03224 - 0.932737i) q^{90} -1.47985i q^{91} +(-4.76715 - 0.523762i) q^{92} +(0.0529729 - 0.0529729i) q^{93} +(2.90032 + 9.87758i) q^{94} +(-8.92330 + 8.88965i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-10.6558 - 7.97683i) q^{97} +(7.38904 - 1.60739i) q^{98} +(0.404327 - 0.885353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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