LMFDB - Embedded newform 231.2.y.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	231.4
Dual form			231.2.y.a.58.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133110 + 1.26646i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(0.370096 + 0.0786664i) q^{4} +(-3.47779 - 1.54841i) q^{5} +(1.03023 - 0.748506i) q^{6} +(-1.94739 - 1.79100i) q^{7} +(-0.935917 + 2.88046i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.133110 + 1.26646i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(0.370096 + 0.0786664i) q^{4} +(-3.47779 - 1.54841i) q^{5} +(1.03023 - 0.748506i) q^{6} +(-1.94739 - 1.79100i) q^{7} +(-0.935917 + 2.88046i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(2.42393 - 4.19837i) q^{10} +(-2.89776 - 1.61338i) q^{11} +(-0.189182 - 0.327673i) q^{12} +(-2.88004 - 2.09247i) q^{13} +(2.52744 - 2.22789i) q^{14} +(1.17640 + 3.62060i) q^{15} +(-2.83209 - 1.26093i) q^{16} +(0.0636660 + 0.605742i) q^{17} +(-1.24561 - 0.264762i) q^{18} +(1.49034 - 0.316781i) q^{19} +(-1.16531 - 0.846648i) q^{20} +(-0.0279140 + 2.64560i) q^{21} +(2.42899 - 3.45514i) q^{22} +(2.06152 + 3.57065i) q^{23} +(2.76685 - 1.23188i) q^{24} +(6.35182 + 7.05441i) q^{25} +(3.03339 - 3.36893i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.579830 - 0.816036i) q^{28} +(-3.27695 - 10.0854i) q^{29} +(-4.74193 + 1.00793i) q^{30} +(5.22208 - 2.32502i) q^{31} +(-1.05480 + 1.82696i) q^{32} +(0.740009 + 3.23302i) q^{33} -0.775621 q^{34} +(3.99941 + 9.24409i) q^{35} +(-0.116921 + 0.359846i) q^{36} +(-1.76193 + 1.95682i) q^{37} +(0.202811 + 1.92962i) q^{38} +(0.372114 + 3.54043i) q^{39} +(7.71507 - 8.56845i) q^{40} +(-0.843831 + 2.59705i) q^{41} +(-3.34683 - 0.387509i) q^{42} -4.52771 q^{43} +(-0.945532 - 0.825061i) q^{44} +(1.90346 - 3.29689i) q^{45} +(-4.79649 + 2.13554i) q^{46} +(-9.50390 + 2.02012i) q^{47} +(0.957987 + 2.94838i) q^{48} +(0.584647 + 6.97554i) q^{49} +(-9.77961 + 7.10530i) q^{50} +(0.407553 - 0.452633i) q^{51} +(-0.901286 - 1.00098i) q^{52} +(8.23278 - 3.66547i) q^{53} +(0.636717 + 1.10283i) q^{54} +(7.57965 + 10.0979i) q^{55} +(6.98149 - 3.93314i) q^{56} +(-1.23264 - 0.895569i) q^{57} +(13.2090 - 2.80765i) q^{58} +(1.33807 + 0.284417i) q^{59} +(0.150563 + 1.43251i) q^{60} +(-5.70294 - 2.53911i) q^{61} +(2.24943 + 6.92304i) q^{62} +(1.98475 - 1.74951i) q^{63} +(-7.18945 - 5.22344i) q^{64} +(6.77618 + 11.7367i) q^{65} +(-4.19298 + 0.506844i) q^{66} +(-3.02094 + 5.23243i) q^{67} +(-0.0240889 + 0.229191i) q^{68} +(1.27409 - 3.92124i) q^{69} +(-12.2396 + 3.83461i) q^{70} +(7.45523 - 5.41654i) q^{71} +(-2.76685 - 1.23188i) q^{72} +(-11.0706 - 2.35313i) q^{73} +(-2.24370 - 2.49188i) q^{74} +(0.992251 - 9.44064i) q^{75} +0.576488 q^{76} +(2.75351 + 8.33176i) q^{77} -4.53334 q^{78} +(0.181027 - 1.72236i) q^{79} +(7.89700 + 8.77050i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.17673 - 1.41437i) q^{82} +(-3.23967 + 2.35376i) q^{83} +(-0.218451 + 0.976932i) q^{84} +(0.716521 - 2.20523i) q^{85} +(0.602684 - 5.73416i) q^{86} +(-5.30222 + 9.18372i) q^{87} +(7.35932 - 6.83689i) q^{88} +(-2.84444 - 4.92671i) q^{89} +(3.92200 + 2.84950i) q^{90} +(1.86095 + 9.23301i) q^{91} +(0.482069 + 1.48366i) q^{92} +(-5.22208 - 2.32502i) q^{93} +(-1.29333 - 12.3052i) q^{94} +(-5.67360 - 1.20596i) q^{95} +(2.06349 - 0.438609i) q^{96} +(-8.18062 - 5.94357i) q^{97} +(-8.91206 - 0.188085i) q^{98} +(1.90744 - 2.71324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.133110	+	1.26646i	−0.0941231	+	0.895521i	0.840961	+	0.541096i	$0.181990\pi$
$2$	−0.133110	+	1.26646i	−0.0941231	+	0.895521i	−0.935084	+	0.354426i	$0.884676\pi$
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	0.370096	+	0.0786664i	0.185048	+	0.0393332i
$5$	−3.47779	−	1.54841i	−1.55532	−	0.692472i	−0.564221	−	0.825624i	$-0.690824\pi$
$5$	−3.47779	−	1.54841i	−1.55532	−	0.692472i	−0.991096	+	0.133152i	$0.957490\pi$
$6$	1.03023	−	0.748506i	0.420590	−	0.305576i
$7$	−1.94739	−	1.79100i	−0.736044	−	0.676934i
$7$	−1.94739	−	1.79100i	−0.736044	−	0.676934i
$8$	−0.935917	+	2.88046i	−0.330897	+	1.01840i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	2.42393	−	4.19837i	0.766515	−	1.32764i
$11$	−2.89776	−	1.61338i	−0.873708	−	0.486451i
$11$	−2.89776	−	1.61338i	−0.873708	−	0.486451i
$12$	−0.189182	−	0.327673i	−0.0546122	−	0.0945911i
$13$	−2.88004	−	2.09247i	−0.798780	−	0.580348i	0.111776	−	0.993733i	$-0.464346\pi$
$13$	−2.88004	−	2.09247i	−0.798780	−	0.580348i	−0.910556	+	0.413386i	$0.864346\pi$
$14$	2.52744	−	2.22789i	0.675488	−	0.595428i
$15$	1.17640	+	3.62060i	0.303746	+	0.934834i
$16$	−2.83209	−	1.26093i	−0.708023	−	0.315232i
$17$	0.0636660	+	0.605742i	0.0154413	+	0.146914i	0.999526	−	0.0307860i	$-0.00980103\pi$
$17$	0.0636660	+	0.605742i	0.0154413	+	0.146914i	−0.984085	+	0.177700i	$0.943134\pi$
$18$	−1.24561	−	0.264762i	−0.293592	−	0.0624050i
$19$	1.49034	−	0.316781i	0.341907	−	0.0726746i	−0.0337582	−	0.999430i	$-0.510748\pi$
$19$	1.49034	−	0.316781i	0.341907	−	0.0726746i	0.375665	+	0.926755i	$0.377414\pi$
$20$	−1.16531	−	0.846648i	−0.260571	−	0.189316i
$21$	−0.0279140	+	2.64560i	−0.00609133	+	0.577318i
$22$	2.42899	−	3.45514i	0.517863	−	0.736638i
$23$	2.06152	+	3.57065i	0.429856	+	0.744532i	0.996860	−	0.0791825i	$-0.0252310\pi$
$23$	2.06152	+	3.57065i	0.429856	+	0.744532i	−0.567004	+	0.823715i	$0.691898\pi$
$24$	2.76685	−	1.23188i	0.564780	−	0.251456i
$25$	6.35182	+	7.05441i	1.27036	+	1.41088i
$26$	3.03339	−	3.36893i	0.594898	−	0.660701i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−0.579830	−	0.816036i	−0.109578	−	0.154216i
$29$	−3.27695	−	10.0854i	−0.608515	−	1.87282i	−0.470535	−	0.882381i	$-0.655939\pi$
$29$	−3.27695	−	10.0854i	−0.608515	−	1.87282i	−0.137980	−	0.990435i	$-0.544061\pi$
$30$	−4.74193	+	1.00793i	−0.865753	+	0.184022i
$31$	5.22208	−	2.32502i	0.937914	−	0.417586i	0.119901	−	0.992786i	$-0.461742\pi$
$31$	5.22208	−	2.32502i	0.937914	−	0.417586i	0.818013	+	0.575200i	$0.195076\pi$
$32$	−1.05480	+	1.82696i	−0.186463	+	0.322964i
$33$	0.740009	+	3.23302i	0.128819	+	0.562796i
$34$	−0.775621			−0.133018
$35$	3.99941	+	9.24409i	0.676024	+	1.56254i
$36$	−0.116921	+	0.359846i	−0.0194868	+	0.0599743i
$37$	−1.76193	+	1.95682i	−0.289659	+	0.321699i	−0.870358	−	0.492419i	$-0.836113\pi$
$37$	−1.76193	+	1.95682i	−0.289659	+	0.321699i	0.580699	+	0.814118i	$0.302779\pi$
$38$	0.202811	+	1.92962i	0.0329003	+	0.313025i
$39$	0.372114	+	3.54043i	0.0595859	+	0.566922i
$40$	7.71507	−	8.56845i	1.21986	−	1.35479i
$41$	−0.843831	+	2.59705i	−0.131784	+	0.405590i	−0.995076	−	0.0991149i	$-0.968399\pi$
$41$	−0.843831	+	2.59705i	−0.131784	+	0.405590i	0.863292	+	0.504705i	$0.168399\pi$
$42$	−3.34683	−	0.387509i	−0.516427	−	0.0597939i
$43$	−4.52771			−0.690469			−0.345235	−	0.938516i	$-0.612201\pi$
$43$	−4.52771			−0.690469			−0.345235	+	0.938516i	$0.612201\pi$
$44$	−0.945532	−	0.825061i	−0.142544	−	0.124383i
$45$	1.90346	−	3.29689i	0.283751	−	0.491471i
$46$	−4.79649	+	2.13554i	−0.707204	+	0.314868i
$47$	−9.50390	+	2.02012i	−1.38629	+	0.294664i	−0.839842	−	0.542831i	$-0.817352\pi$
$47$	−9.50390	+	2.02012i	−1.38629	+	0.294664i	−0.546445	+	0.837495i	$0.684019\pi$
$48$	0.957987	+	2.94838i	0.138274	+	0.425562i
$49$	0.584647	+	6.97554i	0.0835210	+	0.996506i
$50$	−9.77961	+	7.10530i	−1.38305	+	1.00484i
$51$	0.407553	−	0.452633i	0.0570688	−	0.0633813i
$52$	−0.901286	−	1.00098i	−0.124986	−	0.138811i
$53$	8.23278	−	3.66547i	1.13086	−	0.503491i	0.245963	−	0.969279i	$-0.420896\pi$
$53$	8.23278	−	3.66547i	1.13086	−	0.503491i	0.884896	+	0.465788i	$0.154229\pi$
$54$	0.636717	+	1.10283i	0.0866462	+	0.150076i
$55$	7.57965	+	10.0979i	1.02204	+	1.36160i
$56$	6.98149	−	3.93314i	0.932941	−	0.525588i
$57$	−1.23264	−	0.895569i	−0.163268	−	0.118621i
$58$	13.2090	−	2.80765i	1.73442	−	0.368663i
$59$	1.33807	+	0.284417i	0.174203	+	0.0370279i	0.294187	−	0.955748i	$-0.404951\pi$
$59$	1.33807	+	0.284417i	0.174203	+	0.0370279i	−0.119984	+	0.992776i	$0.538284\pi$
$60$	0.150563	+	1.43251i	0.0194376	+	0.184937i
$61$	−5.70294	−	2.53911i	−0.730187	−	0.325100i	0.00774976	−	0.999970i	$-0.497533\pi$
$61$	−5.70294	−	2.53911i	−0.730187	−	0.325100i	−0.737937	+	0.674870i	$0.764200\pi$
$62$	2.24943	+	6.92304i	0.285678	+	0.879226i
$63$	1.98475	−	1.74951i	0.250054	−	0.220418i
$64$	−7.18945	−	5.22344i	−0.898682	−	0.652930i
$65$	6.77618	+	11.7367i	0.840482	+	1.45576i
$66$	−4.19298	+	0.506844i	−0.516120	+	0.0623882i
$67$	−3.02094	+	5.23243i	−0.369067	+	0.639243i	−0.989420	−	0.145080i	$-0.953656\pi$
$67$	−3.02094	+	5.23243i	−0.369067	+	0.639243i	0.620353	+	0.784323i	$0.286989\pi$
$68$	−0.0240889	+	0.229191i	−0.00292121	+	0.0277935i
$69$	1.27409	−	3.92124i	0.153382	−	0.472062i
$70$	−12.2396	+	3.83461i	−1.46291	+	0.458323i
$71$	7.45523	−	5.41654i	0.884773	−	0.642825i	−0.0497367	−	0.998762i	$-0.515838\pi$
$71$	7.45523	−	5.41654i	0.884773	−	0.642825i	0.934510	+	0.355937i	$0.115838\pi$
$72$	−2.76685	−	1.23188i	−0.326076	−	0.145178i
$73$	−11.0706	−	2.35313i	−1.29571	−	0.275413i	−0.492087	−	0.870546i	$-0.663766\pi$
$73$	−11.0706	−	2.35313i	−1.29571	−	0.275413i	−0.803627	+	0.595133i	$0.797099\pi$
$74$	−2.24370	−	2.49188i	−0.260825	−	0.289675i
$75$	0.992251	−	9.44064i	0.114575	−	1.09011i
$76$	0.576488			0.0661278
$77$	2.75351	+	8.33176i	0.313792	+	0.949492i
$78$	−4.53334			−0.513299
$79$	0.181027	−	1.72236i	0.0203671	−	0.193780i	−0.979607	−	0.200921i	$-0.935606\pi$
$79$	0.181027	−	1.72236i	0.0203671	−	0.193780i	0.999975	+	0.00714110i	$0.00227310\pi$
$80$	7.89700	+	8.77050i	0.882911	+	0.980572i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−3.17673	−	1.41437i	−0.350811	−	0.156191i
$83$	−3.23967	+	2.35376i	−0.355600	+	0.258359i	−0.751215	−	0.660058i	$-0.770532\pi$
$83$	−3.23967	+	2.35376i	−0.355600	+	0.258359i	0.395614	+	0.918417i	$0.370532\pi$
$84$	−0.218451	+	0.976932i	−0.0238350	+	0.106592i
$85$	0.716521	−	2.20523i	0.0777177	−	0.239190i
$86$	0.602684	−	5.73416i	0.0649891	−	0.618330i
$87$	−5.30222	+	9.18372i	−0.568458	+	0.984598i
$88$	7.35932	−	6.83689i	0.784506	−	0.728815i
$89$	−2.84444	−	4.92671i	−0.301510	−	0.522230i	0.674968	−	0.737847i	$-0.264157\pi$
$89$	−2.84444	−	4.92671i	−0.301510	−	0.522230i	−0.976478	+	0.215616i	$0.930824\pi$
$90$	3.92200	+	2.84950i	0.413416	+	0.300364i
$91$	1.86095	+	9.23301i	0.195080	+	0.967883i
$92$	0.482069	+	1.48366i	0.0502592	+	0.154682i
$93$	−5.22208	−	2.32502i	−0.541505	−	0.241093i
$94$	−1.29333	−	12.3052i	−0.133397	−	1.26918i
$95$	−5.67360	−	1.20596i	−0.582099	−	0.123729i
$96$	2.06349	−	0.438609i	0.210604	−	0.0447654i
$97$	−8.18062	−	5.94357i	−0.830617	−	0.603478i	0.0891171	−	0.996021i	$-0.471595\pi$
$97$	−8.18062	−	5.94357i	−0.830617	−	0.603478i	−0.919734	+	0.392543i	$0.871595\pi$
$98$	−8.91206	−	0.188085i	−0.900254	−	0.0189994i
$99$	1.90744	−	2.71324i	0.191704	−	0.272691i
$100$	1.79584	+	3.11048i	0.179584	+	0.311048i
$101$	10.4576	−	4.65602i	1.04057	−	0.463291i	0.185957	−	0.982558i	$-0.440461\pi$
$101$	10.4576	−	4.65602i	1.04057	−	0.463291i	0.854612	+	0.519266i	$0.173795\pi$
$102$	0.518992	+	0.576399i	0.0513878	+	0.0570720i
$103$	6.08058	−	6.75316i	0.599137	−	0.665409i	−0.364940	−	0.931031i	$-0.618911\pi$
$103$	6.08058	−	6.75316i	0.599137	−	0.665409i	0.964077	+	0.265622i	$0.0855773\pi$
$104$	8.72276	−	6.33746i	0.855337	−	0.621439i
$105$	4.19357	−	9.15765i	0.409250	−	0.893695i
$106$	3.54630	+	10.9144i	0.344447	+	1.06010i
$107$	−1.24901	+	0.265484i	−0.120746	+	0.0256653i	−0.267888	−	0.963450i	$-0.586326\pi$
$107$	−1.24901	+	0.265484i	−0.120746	+	0.0256653i	0.147142	+	0.989115i	$0.452992\pi$
$108$	0.345653	−	0.153895i	0.0332605	−	0.0148085i
$109$	7.89365	−	13.6722i	0.756074	−	1.30956i	−0.188764	−	0.982022i	$-0.560448\pi$
$109$	7.89365	−	13.6722i	0.756074	−	1.30956i	0.944838	−	0.327537i	$-0.106219\pi$
$110$	−13.7975	+	8.25517i	−1.31554	+	0.787100i
$111$	2.63316			0.249929
$112$	3.25686	+	7.52779i	0.307745	+	0.711310i
$113$	6.05225	−	18.6269i	0.569348	−	1.75227i	−0.0853182	−	0.996354i	$-0.527191\pi$
$113$	6.05225	−	18.6269i	0.569348	−	1.75227i	0.654666	−	0.755918i	$-0.272809\pi$
$114$	1.29828	−	1.44188i	0.121595	−	0.135045i
$115$	−1.64069	−	15.6101i	−0.152995	−	1.45565i
$116$	−0.419404	−	3.99036i	−0.0389407	−	0.370496i
$117$	2.38206	−	2.64554i	0.220221	−	0.244581i
$118$	−0.538313	+	1.65676i	−0.0495557	+	0.152517i
$119$	0.960900	−	1.29364i	0.0880855	−	0.118588i
$120$	−11.5300			−1.05254
$121$	5.79404	+	9.35035i	0.526731	+	0.850032i
$122$	3.97480	−	6.88456i	0.359862	−	0.623299i
$123$	2.49461	−	1.11067i	0.224932	−	0.100146i
$124$	2.11557	−	0.449679i	0.189984	−	0.0403824i
$125$	−5.28516	−	16.2660i	−0.472719	−	1.45488i
$126$	1.95149	+	2.74648i	0.173853	+	0.244675i
$127$	−7.93743	+	5.76688i	−0.704333	+	0.511728i	−0.881340	−	0.472482i	$-0.843358\pi$
$127$	−7.93743	+	5.76688i	−0.704333	+	0.511728i	0.177008	+	0.984209i	$0.443358\pi$
$128$	4.74908	−	5.27438i	0.419763	−	0.466194i
$129$	3.02963	+	3.36474i	0.266744	+	0.296249i
$130$	−15.7660	+	7.01948i	−1.38277	+	0.615649i
$131$	3.45688	+	5.98749i	0.302029	+	0.523130i	0.976595	−	0.215084i	$-0.0690027\pi$
$131$	3.45688	+	5.98749i	0.302029	+	0.523130i	−0.674566	+	0.738214i	$0.735669\pi$
$132$	0.0195450	+	1.25474i	0.00170117	+	0.109211i
$133$	−3.46962	−	2.05230i	−0.300854	−	0.177957i
$134$	−6.22453	−	4.52239i	−0.537718	−	0.390675i
$135$	−3.72373	+	0.791503i	−0.320488	+	0.0681218i
$136$	−1.80440	−	0.383537i	−0.154726	−	0.0328880i
$137$	−1.47827	−	14.0648i	−0.126297	−	1.20163i	−0.855671	−	0.517520i	$-0.826855\pi$
$137$	−1.47827	−	14.0648i	−0.126297	−	1.20163i	0.729374	−	0.684115i	$-0.239811\pi$
$138$	4.79649	+	2.13554i	0.408304	+	0.181789i
$139$	3.85300	+	11.8583i	0.326807	+	1.00581i	0.970618	+	0.240624i	$0.0773522\pi$
$139$	3.85300	+	11.8583i	0.326807	+	1.00581i	−0.643811	+	0.765184i	$0.722648\pi$
$140$	0.752968	+	3.73582i	0.0636374	+	0.315735i
$141$	7.86059	+	5.71105i	0.661981	+	0.480958i
$142$	5.86746	+	10.1627i	0.492386	+	0.852838i
$143$	4.96973	+	10.7101i	0.415590	+	0.895622i
$144$	1.55006	−	2.68478i	0.129171	−	0.223731i
$145$	−4.21984	+	40.1491i	−0.350439	+	3.33420i
$146$	4.45375	−	13.7072i	0.368595	−	1.13442i
$147$	4.79263	−	5.10203i	0.395290	−	0.420808i
$148$	−0.806019	+	0.585607i	−0.0662544	+	0.0481366i
$149$	−20.7483	−	9.23774i	−1.69977	−	0.756785i	−0.999061	−	0.0433364i	$-0.986201\pi$
$149$	−20.7483	−	9.23774i	−1.69977	−	0.756785i	−0.700707	−	0.713449i	$-0.747132\pi$
$150$	11.8241	+	2.51329i	0.965434	+	0.205209i
$151$	2.62876	+	2.91953i	0.213925	+	0.237588i	0.840551	−	0.541732i	$-0.182231\pi$
$151$	2.62876	+	2.91953i	0.213925	+	0.237588i	−0.626626	+	0.779320i	$0.715565\pi$
$152$	−0.482358	+	4.58933i	−0.0391244	+	0.372244i
$153$	−0.609078			−0.0492410
$154$	−10.9183	+	2.37817i	−0.879825	+	0.191638i
$155$	−21.7614			−1.74792
$156$	−0.140795	+	1.33957i	−0.0112726	+	0.107252i
$157$	−1.23867	−	1.37568i	−0.0988567	−	0.109792i	0.691686	−	0.722198i	$-0.256868\pi$
$157$	−1.23867	−	1.37568i	−0.0988567	−	0.109792i	−0.790543	+	0.612407i	$0.790202\pi$
$158$	2.15720	+	0.458526i	0.171617	+	0.0364784i
$159$	−8.23278	−	3.66547i	−0.652902	−	0.290691i
$160$	6.49726	−	4.72054i	0.513653	−	0.373191i
$161$	2.38046	−	10.6456i	0.187606	−	0.838993i
$162$	0.393513	−	1.21111i	0.0309173	−	0.0951537i
$163$	−0.965919	+	9.19011i	−0.0756566	+	0.719825i	0.889284	+	0.457356i	$0.151203\pi$
$163$	−0.965919	+	9.19011i	−0.0756566	+	0.719825i	−0.964940	+	0.262469i	$0.915463\pi$
$164$	−0.516599	+	0.894776i	−0.0403396	+	0.0698702i
$165$	2.43245	−	12.3896i	0.189366	−	0.964529i
$166$	−2.54970	−	4.41622i	−0.197895	−	0.342765i
$167$	0.938252	+	0.681680i	0.0726041	+	0.0527500i	0.623495	−	0.781827i	$-0.285712\pi$
$167$	0.938252	+	0.681680i	0.0726041	+	0.0527500i	−0.550891	+	0.834577i	$0.685712\pi$
$168$	−7.59442	−	2.55647i	−0.585922	−	0.197236i
$169$	−0.101019	−	0.310906i	−0.00777072	−	0.0239158i
$170$	2.69745	+	1.20098i	0.206885	+	0.0921112i
$171$	0.159263	+	1.51529i	0.0121791	+	0.115877i
$172$	−1.67569	−	0.356179i	−0.127770	−	0.0271584i
$173$	2.37107	−	0.503986i	0.180269	−	0.0383173i	−0.116893	−	0.993145i	$-0.537293\pi$
$173$	2.37107	−	0.503986i	0.180269	−	0.0383173i	0.297161	+	0.954827i	$0.403960\pi$
$174$	−10.9250	−	7.93749i	−0.828223	−	0.601740i
$175$	0.264977	−	25.1138i	0.0200304	−	1.89842i
$176$	6.17238	+	8.22310i	0.465260	+	0.619839i
$177$	−0.683984	−	1.18470i	−0.0514114	−	0.0890472i
$178$	6.61810	−	2.94657i	0.496048	−	0.220855i
$179$	11.6729	+	12.9641i	0.872473	+	0.968979i	0.999738	−	0.0228895i	$-0.00728658\pi$
$179$	11.6729	+	12.9641i	0.872473	+	0.968979i	−0.127265	+	0.991869i	$0.540620\pi$
$180$	0.963818	−	1.07043i	0.0718387	−	0.0797850i
$181$	−8.58001	+	6.23374i	−0.637747	+	0.463350i	−0.859075	−	0.511849i	$-0.828961\pi$
$181$	−8.58001	+	6.23374i	−0.637747	+	0.463350i	0.221328	+	0.975199i	$0.428961\pi$
$182$	−11.9409	+	1.12780i	−0.885121	+	0.0835983i
$183$	1.92908	+	5.93711i	0.142602	+	0.438884i
$184$	−12.2145	+	2.59628i	−0.900466	+	0.191400i
$185$	9.15759	−	4.07722i	0.673280	−	0.299763i
$186$	3.63966	−	6.30407i	0.266872	−	0.462237i
$187$	0.792800	−	1.85801i	0.0579752	−	0.135871i
$188$	−3.67627			−0.268120
$189$	−2.62819	−	0.304302i	−0.191173	−	0.0221347i
$190$	2.28251	−	7.02485i	0.165591	−	0.509636i
$191$	−12.5337	+	13.9200i	−0.906904	+	1.00722i	0.0930297	+	0.995663i	$0.470345\pi$
$191$	−12.5337	+	13.9200i	−0.906904	+	1.00722i	−0.999933	+	0.0115551i	$0.996322\pi$
$192$	0.928908	+	8.83797i	0.0670382	+	0.637826i
$193$	0.157883	+	1.50215i	0.0113646	+	0.108127i	0.998734	−	0.0503102i	$-0.0160210\pi$
$193$	0.157883	+	1.50215i	0.0113646	+	0.108127i	−0.987369	+	0.158438i	$0.949354\pi$
$194$	8.61621	−	9.56927i	0.618608	−	0.687034i
$195$	4.18791	−	12.8891i	0.299903	−	0.923005i
$196$	−0.332365	+	2.62761i	−0.0237404	+	0.187687i
$197$	−5.24342			−0.373578			−0.186789	−	0.982400i	$-0.559808\pi$
$197$	−5.24342			−0.373578			−0.186789	+	0.982400i	$0.559808\pi$
$198$	3.18231	+	2.77685i	0.226157	+	0.197342i
$199$	−2.68510	+	4.65073i	−0.190342	+	0.329681i	−0.945363	−	0.326018i	$-0.894293\pi$
$199$	−2.68510	+	4.65073i	−0.190342	+	0.329681i	0.755022	+	0.655700i	$0.227626\pi$
$200$	−26.2647	+	11.6938i	−1.85719	+	0.826876i
$201$	5.90986	−	1.25618i	0.416849	−	0.0886040i
$202$	4.50465	+	13.8639i	0.316946	+	0.975459i
$203$	−11.6815	+	25.5093i	−0.819879	+	1.79040i
$204$	0.186441	−	0.135457i	0.0130535	−	0.00948390i
$205$	6.95597	−	7.72539i	0.485826	−	0.539565i
$206$	7.74321	+	8.59971i	0.539495	+	0.599170i
$207$	−3.76658	+	1.67699i	−0.261795	+	0.116559i
$208$	5.51809	+	9.55761i	0.382611	+	0.662701i
$209$	−4.82973	−	1.48652i	−0.334079	−	0.102825i
$210$	11.0396	+	6.52996i	0.761803	+	0.450610i
$211$	−6.68740	−	4.85868i	−0.460379	−	0.334485i	0.333301	−	0.942821i	$-0.391838\pi$
$211$	−6.68740	−	4.85868i	−0.460379	−	0.334485i	−0.793680	+	0.608335i	$0.791838\pi$
$212$	3.33527	−	0.708933i	0.229067	−	0.0486897i
$213$	−9.01380	−	1.91594i	−0.617615	−	0.131278i
$214$	−0.169970	−	1.61715i	−0.0116189	−	0.110546i
$215$	15.7464	+	7.01077i	1.07390	+	0.478130i
$216$	0.935917	+	2.88046i	0.0636811	+	0.195990i
$217$	−14.3335	−	4.82502i	−0.973024	−	0.327544i
$218$	16.2645	+	11.8169i	1.10157	+	0.800341i
$219$	5.65896	+	9.80160i	0.382397	+	0.662331i
$220$	2.01083	+	4.33347i	0.135570	+	0.292162i
$221$	1.08414	−	1.87778i	0.0729270	−	0.126313i
$222$	−0.350500	+	3.33479i	−0.0235241	+	0.223816i
$223$	−2.20383	+	6.78270i	−0.147580	+	0.454203i	−0.997334	−	0.0729759i	$-0.976750\pi$
$223$	−2.20383	+	6.78270i	−0.147580	+	0.454203i	0.849754	+	0.527179i	$0.176750\pi$
$224$	5.32619	−	1.66866i	0.355871	−	0.111492i
$225$	−7.67971	+	5.57964i	−0.511981	+	0.371976i
$226$	22.7846	+	10.1444i	1.51561	+	0.674792i
$227$	−4.93471	−	1.04890i	−0.327528	−	0.0696183i	0.0412130	−	0.999150i	$-0.486878\pi$
$227$	−4.93471	−	1.04890i	−0.327528	−	0.0696183i	−0.368741	+	0.929532i	$0.620211\pi$
$228$	−0.385746	−	0.428414i	−0.0255467	−	0.0283724i
$229$	2.69801	−	25.6699i	0.178290	−	1.69631i	−0.430186	−	0.902740i	$-0.641552\pi$
$229$	2.69801	−	25.6699i	0.178290	−	1.69631i	0.608475	−	0.793573i	$-0.291781\pi$
$230$	19.9879			1.31796
$231$	4.34924	−	7.62129i	0.286159	−	0.501444i
$232$	32.1176			2.10862
$233$	1.37295	−	13.0628i	0.0899451	−	0.855770i	−0.852796	−	0.522244i	$-0.825095\pi$
$233$	1.37295	−	13.0628i	0.0899451	−	0.855770i	0.942741	−	0.333526i	$-0.108238\pi$
$234$	3.03339	+	3.36893i	0.198299	+	0.220234i
$235$	36.1806	+	7.69042i	2.36016	+	0.501668i
$236$	0.472842	+	0.210523i	0.0307794	+	0.0137039i
$237$	−1.40109	+	1.01795i	−0.0910106	+	0.0661231i
$238$	1.51044	+	1.38914i	0.0979070	+	0.0900443i
$239$	−3.55894	+	10.9533i	−0.230209	+	0.708510i	0.767512	+	0.641035i	$0.221494\pi$
$239$	−3.55894	+	10.9533i	−0.230209	+	0.708510i	−0.997721	+	0.0674756i	$0.978506\pi$
$240$	1.23363	−	11.7372i	0.0796306	−	0.757635i
$241$	−13.8923	+	24.0621i	−0.894879	+	1.54998i	−0.0609252	+	0.998142i	$0.519405\pi$
$241$	−13.8923	+	24.0621i	−0.894879	+	1.54998i	−0.833954	+	0.551834i	$0.813928\pi$
$242$	−12.6131	+	6.09328i	−0.810800	+	0.391691i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.91090	−	1.38835i	−0.122333	−	0.0888798i
$245$	8.76775	−	25.1648i	0.560151	−	1.60772i
$246$	1.07456	+	3.30717i	0.0685117	+	0.210857i
$247$	−4.95509	−	2.20615i	−0.315285	−	0.140374i
$248$	1.80969	+	17.2180i	0.114915	+	1.09334i
$249$	3.91695	+	0.832573i	0.248226	+	0.0527622i
$250$	21.3038	−	4.52826i	1.34737	−	0.286392i
$251$	22.4605	+	16.3185i	1.41770	+	1.03002i	0.992146	+	0.125082i	$0.0399196\pi$
$251$	22.4605	+	16.3185i	1.41770	+	1.03002i	0.425551	+	0.904935i	$0.360080\pi$
$252$	0.872174	−	0.491355i	0.0549418	−	0.0309524i
$253$	−0.212982	−	13.6729i	−0.0133900	−	0.859608i
$254$	−6.24696	−	10.8201i	−0.391969	−	0.678911i
$255$	−2.11825	+	0.943105i	−0.132650	+	0.0590595i
$256$	−5.84502	−	6.49156i	−0.365314	−	0.405722i
$257$	0.716825	−	0.796115i	0.0447143	−	0.0496603i	−0.720373	−	0.693587i	$-0.756029\pi$
$257$	0.716825	−	0.796115i	0.0447143	−	0.0496603i	0.765087	+	0.643927i	$0.222696\pi$
$258$	−4.66458	+	3.38902i	−0.290404	+	0.210991i
$259$	6.93582	−	0.655077i	0.430971	−	0.0407045i
$260$	1.58456	+	4.87676i	0.0982700	+	0.302444i
$261$	10.3727	−	2.20479i	0.642055	−	0.136473i
$262$	−8.04306	+	3.58100i	−0.496902	+	0.221235i
$263$	8.87850	−	15.3780i	0.547472	−	0.948249i	−0.450975	−	0.892536i	$-0.648924\pi$
$263$	8.87850	−	15.3780i	0.547472	−	0.948249i	0.998447	−	0.0557122i	$-0.0177429\pi$
$264$	−10.0051	−	0.894270i	−0.615774	−	0.0550385i
$265$	−34.3076			−2.10750
$266$	3.06099	−	4.12095i	0.187681	−	0.252672i
$267$	−1.75796	+	5.41044i	−0.107585	+	0.331114i
$268$	−1.52966	+	1.69885i	−0.0934386	+	0.103774i
$269$	0.916889	+	8.72361i	0.0559037	+	0.531888i	0.986256	+	0.165222i	$0.0528341\pi$
$269$	0.916889	+	8.72361i	0.0559037	+	0.531888i	−0.930353	+	0.366666i	$0.880499\pi$
$270$	−0.506740	−	4.82131i	−0.0308392	−	0.293415i
$271$	−1.90640	+	2.11727i	−0.115806	+	0.128615i	−0.798260	−	0.602313i	$-0.794246\pi$
$271$	−1.90640	+	2.11727i	−0.115806	+	0.128615i	0.682454	+	0.730928i	$0.260913\pi$
$272$	0.583489	−	1.79579i	0.0353792	−	0.108886i
$273$	5.61625	−	7.56104i	0.339911	−	0.457615i
$274$	18.0092			1.08798
$275$	−7.02464	−	30.6899i	−0.423602	−	1.85067i
$276$	0.780005	−	1.35101i	0.0469508	−	0.0813211i
$277$	−14.5710	+	6.48744i	−0.875489	+	0.389793i	−0.794746	−	0.606942i	$-0.792396\pi$
$277$	−14.5710	+	6.48744i	−0.875489	+	0.389793i	−0.0807428	+	0.996735i	$0.525729\pi$
$278$	−15.5309	+	3.30120i	−0.931483	+	0.197993i
$279$	1.76643	+	5.43651i	0.105753	+	0.325475i
$280$	−30.3703	+	2.86843i	−1.81497	+	0.171421i
$281$	6.21015	−	4.51194i	0.370466	−	0.269160i	−0.386938	−	0.922106i	$-0.626467\pi$
$281$	6.21015	−	4.51194i	0.370466	−	0.269160i	0.757404	+	0.652946i	$0.226467\pi$
$282$	−8.27914	+	9.19491i	−0.493015	+	0.547549i
$283$	−20.6611	−	22.9465i	−1.22818	−	1.36403i	−0.909252	−	0.416247i	$-0.863345\pi$
$283$	−20.6611	−	22.9465i	−1.22818	−	1.36403i	−0.318924	−	0.947780i	$-0.603321\pi$
$284$	3.18525	−	1.41817i	0.189010	−	0.0841527i
$285$	2.90017	+	5.02325i	0.171791	+	0.297552i
$286$	−14.2254	+	4.86834i	−0.841165	+	0.287871i
$287$	6.29457	−	3.54616i	0.371557	−	0.209323i
$288$	−1.70670	−	1.23999i	−0.100568	−	0.0730670i
$289$	16.2656	−	3.45737i	0.956802	−	0.203375i
$290$	−50.2855	−	10.6885i	−2.95287	−	0.627651i
$291$	1.05697	+	10.0564i	0.0619608	+	0.589517i
$292$	−3.91207	−	1.74177i	−0.228937	−	0.101929i
$293$	−1.58194	−	4.86872i	−0.0924181	−	0.284434i	0.894154	−	0.447759i	$-0.147778\pi$
$293$	−1.58194	−	4.86872i	−0.0924181	−	0.284434i	−0.986572	+	0.163326i	$0.947778\pi$
$294$	5.82356	+	6.74880i	0.339637	+	0.393598i
$295$	−4.21316	−	3.06104i	−0.245299	−	0.178220i
$296$	−3.98752	−	6.90658i	−0.231770	−	0.401437i
$297$	−3.29266	+	0.398013i	−0.191059	+	0.0230951i
$298$	14.4610	−	25.0472i	0.837705	−	1.45095i
$299$	1.53424	−	14.5973i	0.0887273	−	0.844184i
$300$	1.10989	−	3.41589i	0.0640795	−	0.197216i
$301$	8.81721	+	8.10912i	0.508216	+	0.467402i
$302$	−4.04738	+	2.94059i	−0.232900	+	0.169212i
$303$	−10.4576	−	4.65602i	−0.600773	−	0.267481i
$304$	−4.62021	−	0.982057i	−0.264987	−	0.0563248i
$305$	15.9021	+	17.6610i	0.910550	+	1.01127i
$306$	0.0810745	−	0.771372i	0.00463472	−	0.0440964i
$307$	6.19640			0.353647			0.176824	−	0.984243i	$-0.443418\pi$
$307$	6.19640			0.353647			0.176824	+	0.984243i	$0.443418\pi$
$308$	0.363636	+	3.30016i	0.0207201	+	0.188044i
$309$	−9.08728			−0.516957
$310$	2.89667	−	27.5599i	0.164520	−	1.56530i
$311$	−17.8618	−	19.8376i	−1.01285	−	1.12489i	−0.992144	−	0.125100i	$-0.960075\pi$
$311$	−17.8618	−	19.8376i	−1.01285	−	1.12489i	−0.0207069	−	0.999786i	$-0.506592\pi$
$312$	−10.5463	−	2.24169i	−0.597068	−	0.126911i
$313$	17.9014	+	7.97023i	1.01185	+	0.450504i	0.844593	−	0.535409i	$-0.179843\pi$
$313$	17.9014	+	7.97023i	1.01185	+	0.450504i	0.167256	+	0.985913i	$0.446509\pi$
$314$	1.90713	−	1.38561i	0.107625	−	0.0781944i
$315$	−9.61150	+	3.01123i	−0.541547	+	0.169664i
$316$	0.202489	−	0.623197i	0.0113909	−	0.0350576i
$317$	−2.07364	+	19.7294i	−0.116467	+	1.10811i	0.767657	+	0.640861i	$0.221423\pi$
$317$	−2.07364	+	19.7294i	−0.116467	+	1.10811i	−0.884124	+	0.467252i	$0.845244\pi$
$318$	5.73803	−	9.93856i	0.321773	−	0.557327i
$319$	−6.77575	+	34.5121i	−0.379369	+	1.93231i
$320$	16.9154	+	29.2983i	0.945599	+	1.63783i
$321$	1.03304	+	0.750548i	0.0576587	+	0.0418915i
$322$	13.1654	+	4.43179i	0.733678	+	0.246974i
$323$	0.286771	+	0.882591i	0.0159564	+	0.0491087i
$324$	−0.345653	−	0.153895i	−0.0192029	−	0.00854970i
$325$	−3.53234	−	33.6080i	−0.195939	−	1.86424i
$326$	−11.5103	−	2.44659i	−0.637498	−	0.135504i
$327$	−15.4423	+	3.28236i	−0.853961	+	0.181515i
$328$	−6.69092	−	4.86124i	−0.369444	−	0.268417i
$329$	22.1258	+	13.0875i	1.21984	+	0.721539i
$330$	15.3671	+	4.72977i	0.845933	+	0.260365i
$331$	−11.9127	−	20.6334i	−0.654781	−	1.13411i	−0.981949	−	0.189148i	$-0.939427\pi$
$331$	−11.9127	−	20.6334i	−0.654781	−	1.13411i	0.327167	−	0.944967i	$-0.393906\pi$
$332$	−1.38415	+	0.616264i	−0.0759652	+	0.0338219i
$333$	−1.76193	−	1.95682i	−0.0965531	−	0.107233i
$334$	−0.988211	+	1.09752i	−0.0540725	+	0.0600536i
$335$	18.6082	−	13.5196i	1.01667	−	0.738657i
$336$	3.41497	−	7.45740i	0.186302	−	0.406834i
$337$	7.40291	+	22.7838i	0.403262	+	1.24111i	0.922338	+	0.386385i	$0.126276\pi$
$337$	7.40291	+	22.7838i	0.403262	+	1.24111i	−0.519076	+	0.854728i	$0.673724\pi$
$338$	0.407196	−	0.0865522i	0.0221485	−	0.00470782i
$339$	−17.8922	+	7.96614i	−0.971773	+	0.432661i
$340$	0.438659	−	0.759780i	0.0237896	−	0.0412048i
$341$	−18.8835	−	1.68782i	−1.02260	−	0.0914008i
$342$	−1.94025			−0.104917
$343$	11.3547	−	14.6312i	0.613094	−	0.790010i
$344$	4.23756	−	13.0419i	0.228474	−	0.703171i
$345$	−10.5027	+	11.6644i	−0.565447	+	0.627993i
$346$	0.322664	+	3.06994i	0.0173465	+	0.165041i
$347$	−0.397191	−	3.77902i	−0.0213223	−	0.202868i	0.978674	−	0.205417i	$-0.0658552\pi$
$347$	−0.397191	−	3.77902i	−0.0213223	−	0.202868i	−0.999997	+	0.00254923i	$0.999189\pi$
$348$	−2.68478	+	2.98175i	−0.143919	+	0.159839i
$349$	6.31670	−	19.4408i	0.338125	−	1.04064i	−0.627037	−	0.778989i	$-0.715733\pi$
$349$	6.31670	−	19.4408i	0.338125	−	1.04064i	0.965162	−	0.261653i	$-0.0842675\pi$
$350$	31.7703	+	3.67848i	1.69819	+	0.196623i
$351$	−3.55993			−0.190015
$352$	6.00412	−	3.59232i	0.320021	−	0.191471i
$353$	−10.3919	+	17.9994i	−0.553107	+	0.958010i	0.444941	+	0.895560i	$0.353225\pi$
$353$	−10.3919	+	17.9994i	−0.553107	+	0.958010i	−0.998048	+	0.0624500i	$0.980109\pi$
$354$	1.59141	−	0.708543i	0.0845826	−	0.0376586i
$355$	−34.3148	+	7.29384i	−1.82124	+	0.387117i
$356$	−0.665149	−	2.04712i	−0.0352528	−	0.108497i
$357$	−1.60433	+	0.151526i	−0.0849101	+	0.00801963i
$358$	−17.9722	+	13.0576i	−0.949862	+	0.690115i
$359$	1.22894	−	1.36488i	0.0648610	−	0.0720355i	−0.709841	−	0.704362i	$-0.751233\pi$
$359$	1.22894	−	1.36488i	0.0648610	−	0.0720355i	0.774702	+	0.632327i	$0.217900\pi$
$360$	7.71507	+	8.56845i	0.406620	+	0.451597i
$361$	−15.2366	+	6.78377i	−0.801927	+	0.357041i
$362$	−6.75269	−	11.6960i	−0.354913	−	0.614728i
$363$	3.07170	−	10.5624i	0.161222	−	0.554383i
$364$	−0.0375988	+	3.56350i	−0.00197071	+	0.186778i
$365$	34.8576	+	25.3255i	1.82453	+	1.32560i
$366$	−7.77589	+	1.65282i	−0.406452	+	0.0863941i
$367$	25.0221	+	5.31861i	1.30614	+	0.277629i	0.807855	−	0.589382i	$-0.200629\pi$
$367$	25.0221	+	5.31861i	1.30614	+	0.277629i	0.498289	+	0.867011i	$0.333962\pi$
$368$	−1.33607	−	12.7118i	−0.0696474	−	0.662651i
$369$	−2.49461	−	1.11067i	−0.129864	−	0.0578194i
$370$	3.94467	+	12.1404i	0.205073	+	0.631151i
$371$	−22.5973	−	7.60680i	−1.17319	−	0.394926i
$372$	−1.74977	−	1.27128i	−0.0907215	−	0.0659130i
$373$	1.51467	+	2.62349i	0.0784268	+	0.135839i	0.902571	−	0.430540i	$-0.141677\pi$
$373$	1.51467	+	2.62349i	0.0784268	+	0.135839i	−0.824145	+	0.566380i	$0.808344\pi$
$374$	2.24756	+	1.25137i	0.116219	+	0.0647067i
$375$	−8.55157	+	14.8117i	−0.441601	+	0.764875i
$376$	3.07601	−	29.2662i	0.158633	−	1.50929i
$377$	−11.6657	+	35.9034i	−0.600815	+	1.84912i
$378$	0.735225	−	3.28799i	0.0378159	−	0.169116i
$379$	26.0592	−	18.9331i	1.33857	−	0.972529i	0.339076	−	0.940759i	$-0.389886\pi$
$379$	26.0592	−	18.9331i	1.33857	−	0.972529i	0.999495	−	0.0317697i	$-0.0101143\pi$
$380$	−2.00491	−	0.892643i	−0.102850	−	0.0457916i
$381$	9.59680	+	2.03986i	0.491659	+	0.104505i
$382$	−15.9608	−	17.7263i	−0.816625	−	0.906954i
$383$	−0.862387	+	8.20506i	−0.0440659	+	0.419259i	0.950145	+	0.311810i	$0.100935\pi$
$383$	−0.862387	+	8.20506i	−0.0440659	+	0.419259i	−0.994211	+	0.107450i	$0.965732\pi$
$384$	−7.09738			−0.362187
$385$	3.32485	−	33.2397i	0.169450	−	1.69405i
$386$	−1.92343			−0.0979000
$387$	0.473275	−	4.50291i	0.0240579	−	0.228896i
$388$	−2.56006	−	2.84323i	−0.129967	−	0.144343i
$389$	20.5578	+	4.36970i	1.04232	+	0.221552i	0.697104	−	0.716970i	$-0.254472\pi$
$389$	20.5578	+	4.36970i	1.04232	+	0.221552i	0.345218	+	0.938522i	$0.387805\pi$
$390$	15.7660	+	7.01948i	0.798343	+	0.355445i
$391$	−2.03164	+	1.47608i	−0.102745	+	0.0746483i
$392$	−20.6399	−	4.84448i	−1.04247	−	0.244683i
$393$	2.13647	−	6.57538i	0.107771	−	0.331684i
$394$	0.697953	−	6.64057i	0.0351623	−	0.334547i
$395$	−3.29650	+	5.70970i	−0.165865	+	0.287286i
$396$	0.919376	−	0.854110i	0.0462004	−	0.0429206i
$397$	7.68112	+	13.3041i	0.385504	+	0.667713i	0.991839	−	0.127496i	$-0.0406941\pi$
$397$	7.68112	+	13.3041i	0.385504	+	0.667713i	−0.606335	+	0.795210i	$0.707361\pi$
$398$	−5.53254	−	4.01963i	−0.277321	−	0.201486i
$399$	0.796476	+	3.95169i	0.0398737	+	0.197832i
$400$	−9.09383	−	27.9879i	−0.454691	−	1.39940i
$401$	−14.4064	−	6.41416i	−0.719423	−	0.320308i	0.0141675	−	0.999900i	$-0.495490\pi$
$401$	−14.4064	−	6.41416i	−0.719423	−	0.320308i	−0.733590	+	0.679592i	$0.762157\pi$
$402$	0.804236	+	7.65180i	0.0401117	+	0.381637i
$403$	−19.9049	−	4.23091i	−0.991532	−	0.210757i
$404$	4.23659	−	0.900515i	0.210778	−	0.0448023i
$405$	3.07986	+	2.23765i	0.153040	+	0.111190i
$406$	−30.7515	−	18.1897i	−1.52617	−	0.902737i
$407$	8.26273	−	2.82774i	0.409568	−	0.140166i
$408$	0.922355	+	1.59757i	0.0456634	+	0.0790913i
$409$	12.9698	−	5.77453i	0.641316	−	0.285532i	−0.0601996	−	0.998186i	$-0.519174\pi$
$409$	12.9698	−	5.77453i	0.641316	−	0.285532i	0.701516	+	0.712654i	$0.252507\pi$
$410$	8.85798	+	9.83778i	0.437464	+	0.485853i
$411$	−9.46301	+	10.5097i	−0.466776	+	0.518407i
$412$	2.78164	−	2.02098i	0.137042	−	0.0995667i
$413$	−2.09636	−	2.95036i	−0.103155	−	0.145178i
$414$	−1.62247	−	4.99344i	−0.0797399	−	0.245414i
$415$	14.9115	−	3.16954i	0.731977	−	0.155587i
$416$	6.86073	−	3.05459i	0.336375	−	0.149764i
$417$	6.23428	−	10.7981i	0.305294	−	0.528785i
$418$	2.52550	−	5.91878i	0.123526	−	0.289497i
$419$	−29.8307			−1.45733			−0.728663	−	0.684872i	$-0.759858\pi$
$419$	−29.8307			−1.45733			−0.728663	+	0.684872i	$0.759858\pi$
$420$	2.27242	−	3.05932i	0.110883	−	0.149279i
$421$	−0.610329	+	1.87840i	−0.0297456	+	0.0915476i	−0.964827	−	0.262885i	$-0.915326\pi$
$421$	−0.610329	+	1.87840i	−0.0297456	+	0.0915476i	0.935082	+	0.354433i	$0.115326\pi$
$422$	7.04348	−	7.82257i	0.342871	−	0.380797i
$423$	−1.01562	−	9.66300i	−0.0493812	−	0.469831i
$424$	2.85303	+	27.1447i	0.138555	+	1.31827i
$425$	−3.86875	+	4.29669i	−0.187662	+	0.208420i
$426$	3.62629	−	11.1606i	0.175694	−	0.540731i
$427$	6.55830	+	15.1586i	0.317378	+	0.733576i
$428$	−0.483137			−0.0233533
$429$	4.63374	−	10.8597i	0.223719	−	0.524310i
$430$	−10.9749	+	19.0090i	−0.529255	+	0.916696i
$431$	−3.55384	+	1.58227i	−0.171183	+	0.0762154i	−0.490539	−	0.871419i	$-0.663200\pi$
$431$	−3.55384	+	1.58227i	−0.171183	+	0.0762154i	0.319356	+	0.947635i	$0.396533\pi$
$432$	−3.03237	+	0.644549i	−0.145895	+	0.0310109i
$433$	−6.54499	−	20.1434i	−0.314532	−	0.968031i	−0.975947	−	0.218010i	$-0.930043\pi$
$433$	−6.54499	−	20.1434i	−0.314532	−	0.968031i	0.661414	−	0.750021i	$-0.269957\pi$
$434$	8.01863	−	17.5106i	0.384907	−	0.840534i
$435$	32.6602	−	23.7291i	1.56594	−	1.13772i
$436$	3.99695	−	4.43906i	0.191419	−	0.212593i
$437$	4.20347	+	4.66843i	0.201079	+	0.223321i
$438$	−13.1666	+	5.86214i	−0.629124	+	0.280104i
$439$	−4.77336	−	8.26770i	−0.227820	−	0.394596i	0.729342	−	0.684150i	$-0.239826\pi$
$439$	−4.77336	−	8.26770i	−0.227820	−	0.394596i	−0.957162	+	0.289554i	$0.906493\pi$
$440$	−36.1805	+	12.3820i	−1.72484	+	0.590290i
$441$	−6.99844	−	0.147699i	−0.333259	−	0.00703327i
$442$	2.23382	+	1.62297i	0.106252	+	0.0771967i
$443$	−8.99089	+	1.91107i	−0.427170	+	0.0907978i	−0.416480	−	0.909145i	$-0.636736\pi$
$443$	−8.99089	+	1.91107i	−0.427170	+	0.0907978i	−0.0106905	+	0.999943i	$0.503403\pi$
$444$	0.974523	+	0.207141i	0.0462488	+	0.00983049i
$445$	2.26378	+	21.5385i	0.107314	+	1.02102i
$446$	−8.29666	−	3.69391i	−0.392858	−	0.174912i
$447$	7.01835	+	21.6003i	0.331956	+	1.02166i
$448$	4.64548	+	23.0484i	0.219478	+	1.08893i
$449$	13.1413	+	9.54769i	0.620175	+	0.450584i	0.852983	−	0.521939i	$-0.174791\pi$
$449$	13.1413	+	9.54769i	0.620175	+	0.450584i	−0.232808	+	0.972523i	$0.574791\pi$
$450$	−6.04413	−	10.4687i	−0.284923	−	0.493501i
$451$	6.63523	−	6.16420i	0.312441	−	0.290261i
$452$	3.70523	−	6.41764i	0.174279	−	0.301860i
$453$	0.410652	−	3.90709i	0.0192941	−	0.183571i
$454$	1.98525	−	6.10999i	0.0931726	−	0.286756i
$455$	7.82454	−	34.9920i	0.366820	−	1.64045i
$456$	3.73330	−	2.71240i	0.174828	−	0.127020i
$457$	21.7448	+	9.68142i	1.01718	+	0.452878i	0.846466	−	0.532443i	$-0.178726\pi$
$457$	21.7448	+	9.68142i	1.01718	+	0.452878i	0.170714	+	0.985321i	$0.445392\pi$
$458$	32.1507	+	6.83384i	1.50230	+	0.319325i
$459$	0.407553	+	0.452633i	0.0190229	+	0.0211271i
$460$	0.620777	−	5.90630i	0.0289439	−	0.275383i
$461$	−10.2845			−0.478997			−0.239498	−	0.970897i	$-0.576983\pi$
$461$	−10.2845			−0.478997			−0.239498	+	0.970897i	$0.576983\pi$
$462$	9.07312	+	6.52260i	0.422120	+	0.303459i
$463$	32.4195			1.50666			0.753330	−	0.657643i	$-0.228446\pi$
$463$	32.4195			1.50666			0.753330	+	0.657643i	$0.228446\pi$
$464$	−3.43637	+	32.6949i	−0.159529	+	1.51782i
$465$	14.5612	+	16.1719i	0.675261	+	0.749954i
$466$	16.3607	+	3.47757i	0.757895	+	0.161095i
$467$	23.6059	+	10.5100i	1.09235	+	0.486346i	0.872215	−	0.489123i	$-0.162683\pi$
$467$	23.6059	+	10.5100i	1.09235	+	0.486346i	0.220136	+	0.975469i	$0.429350\pi$
$468$	1.08971	−	0.791718i	0.0503717	−	0.0365972i
$469$	15.2542	−	4.77906i	0.704374	−	0.220677i
$470$	−14.5556	+	44.7976i	−0.671400	+	2.06636i
$471$	−0.193499	+	1.84102i	−0.00891598	+	0.0848299i
$472$	−2.07158	+	3.58808i	−0.0953521	+	0.165155i
$473$	13.1202	+	7.30489i	0.603268	+	0.335879i
$474$	−1.10269	−	1.90992i	−0.0506484	−	0.0877257i
$475$	11.7011	+	8.50131i	0.536881	+	0.390067i
$476$	0.457391	−	0.403181i	0.0209645	−	0.0184798i
$477$	2.78483	+	8.57082i	0.127509	+	0.392431i
$478$	−13.3982	−	5.96525i	−0.612818	−	0.272844i
$479$	3.85778	+	36.7043i	0.176266	+	1.67706i	0.622867	+	0.782328i	$0.285968\pi$
$479$	3.85778	+	36.7043i	0.176266	+	1.67706i	−0.446600	+	0.894734i	$0.647365\pi$
$480$	−7.85556	−	1.66975i	−0.358555	−	0.0762133i
$481$	9.16902	−	1.94894i	0.418072	−	0.0888638i
$482$	−28.6245	−	20.7969i	−1.30381	−	0.947272i
$483$	−9.50408	+	5.35429i	−0.432450	+	0.243628i
$484$	1.40879	+	3.91633i	0.0640361	+	0.178015i
$485$	19.2474	+	33.3375i	0.873980	+	1.51378i
$486$	−1.16334	+	0.517953i	−0.0527702	+	0.0234948i
$487$	−4.73367	−	5.25727i	−0.214503	−	0.238230i	0.626285	−	0.779594i	$-0.284575\pi$
$487$	−4.73367	−	5.25727i	−0.214503	−	0.238230i	−0.840788	+	0.541364i	$0.817908\pi$
$488$	12.6513	−	14.0507i	0.572697	−	0.636045i
$489$	7.47591	−	5.43156i	0.338072	−	0.245624i
$490$	30.7031	+	14.4537i	1.38702	+	0.652950i
$491$	−5.08729	−	15.6571i	−0.229586	−	0.706594i	−0.997794	−	0.0663928i	$-0.978851\pi$
$491$	−5.08729	−	15.6571i	−0.229586	−	0.706594i	0.768207	−	0.640201i	$-0.221149\pi$
$492$	1.01062	−	0.214814i	0.0455623	−	0.00968456i
$493$	5.90053	−	2.62709i	0.265747	−	0.118318i
$494$	3.45357	−	5.98176i	0.155383	−	0.269132i
$495$	−10.8349	+	6.48260i	−0.486992	+	0.291371i
$496$	−17.7211			−0.795701
$497$	−24.2193	−	2.80420i	−1.08638	−	0.125785i
$498$	−1.57580	+	4.84983i	−0.0706135	+	0.217326i
$499$	−0.994543	+	1.10455i	−0.0445219	+	0.0494465i	−0.764994	−	0.644037i	$-0.777258\pi$
$499$	−0.994543	+	1.10455i	−0.0445219	+	0.0494465i	0.720473	+	0.693483i	$0.243925\pi$
$500$	−0.676426	−	6.43577i	−0.0302507	−	0.287816i
$501$	−0.121226	−	1.15339i	−0.00541599	−	0.0515297i
$502$	−23.6565	+	26.2732i	−1.05584	+	1.17263i
$503$	13.5944	−	41.8392i	0.606143	−	1.86552i	0.117411	−	0.993083i	$-0.462541\pi$
$503$	13.5944	−	41.8392i	0.606143	−	1.86552i	0.488732	−	0.872434i	$-0.337459\pi$
$504$	3.18183	+	7.35437i	0.141730	+	0.327590i
$505$	−43.5788			−1.93923
$506$	17.3445	+	1.55027i	0.771057	+	0.0689179i
$507$	−0.163453	+	0.283109i	−0.00725919	+	0.0125733i
$508$	−3.39127	+	1.50989i	−0.150463	+	0.0669906i
$509$	−4.06868	+	0.864826i	−0.180341	+	0.0383327i	−0.297197	−	0.954816i	$-0.596052\pi$
$509$	−4.06868	+	0.864826i	−0.180341	+	0.0383327i	0.116856	+	0.993149i	$0.462718\pi$
$510$	−0.912443	−	2.80821i	−0.0404037	−	0.124350i
$511$	17.3443	+	24.4099i	0.767267	+	1.07983i
$512$	20.4831	−	14.8819i	0.905235	−	0.657692i
$513$	1.01951	−	1.13228i	0.0450124	−	0.0499914i
$514$	0.912830	+	1.01380i	0.0402632	+	0.0447168i
$515$	−31.6037	+	14.0709i	−1.39262	+	0.620036i
$516$	0.856562	+	1.48361i	0.0377080	+	0.0653122i
$517$	30.7992	+	9.47955i	1.35455	+	0.416910i
$518$	−0.0936000	+	8.87113i	−0.00411255	+	0.389775i
$519$	−1.96109	−	1.42481i	−0.0860822	−	0.0625424i
$520$	−40.1490	+	8.53393i	−1.76065	+	0.374238i
$521$	−13.5489	−	2.87991i	−0.593588	−	0.126171i	−0.0986840	−	0.995119i	$-0.531463\pi$
$521$	−13.5489	−	2.87991i	−0.593588	−	0.126171i	−0.494904	+	0.868948i	$0.664797\pi$
$522$	1.41156	+	13.4301i	0.0617823	+	0.587819i
$523$	−3.60700	−	1.60594i	−0.157723	−	0.0702228i	0.326357	−	0.945247i	$-0.394179\pi$
$523$	−3.60700	−	1.60594i	−0.157723	−	0.0702228i	−0.484080	+	0.875024i	$0.660846\pi$
$524$	0.808364	+	2.48789i	0.0353136	+	0.108684i
$525$	−18.8405	+	16.6075i	−0.822266	+	0.724810i
$526$	18.2938	+	13.2912i	0.797647	+	0.579525i
$527$	1.74083	+	3.01521i	0.0758318	+	0.131345i
$528$	1.98083	−	10.0893i	0.0862045	−	0.439080i
$529$	3.00030	−	5.19667i	0.130448	−	0.225942i
$530$	4.56669	−	43.4491i	0.198364	−	1.88731i
$531$	−0.422725	+	1.30102i	−0.0183447	+	0.0564592i
$532$	−1.12265	−	1.03249i	−0.0486729	−	0.0447641i
$533$	7.86452	−	5.71391i	0.340650	−	0.247497i
$534$	−6.61810	−	2.94657i	−0.286393	−	0.127510i
$535$	4.75486	+	1.01068i	0.205571	+	0.0436954i
$536$	−12.2444	−	13.5988i	−0.528879	−	0.587379i
$537$	1.82348	−	17.3493i	0.0786892	−	0.748677i
$538$	−11.1701			−0.481579
$539$	9.56000	−	21.1567i	0.411778	−	0.911284i
$540$	−1.44040			−0.0619851
$541$	1.03370	−	9.83497i	0.0444421	−	0.422839i	−0.949569	−	0.313559i	$-0.898479\pi$
$541$	1.03370	−	9.83497i	0.0444421	−	0.422839i	0.994011	−	0.109280i	$-0.0348545\pi$
$542$	−2.42768	−	2.69621i	−0.104278	−	0.115812i
$543$	10.3737	+	2.20500i	0.445179	+	0.0946257i
$544$	−1.17382	−	0.522619i	−0.0503272	−	0.0224071i
$545$	−48.6227	+	35.3265i	−2.08277	+	1.51322i
$546$	8.82817	+	8.11920i	0.377811	+	0.347470i
$547$	4.95252	−	15.2423i	0.211755	−	0.651714i	−0.787614	−	0.616170i	$-0.788684\pi$
$547$	4.95252	−	15.2423i	0.211755	−	0.651714i	0.999368	−	0.0355440i	$-0.0113164\pi$
$548$	0.559324	−	5.32161i	0.0238931	−	0.227328i
$549$	3.12132	−	5.40629i	0.133215	−	0.230735i
$550$	39.8025	−	4.81129i	1.69718	−	0.205154i
$551$	−8.07864	−	13.9926i	−0.344162	−	0.596105i
$552$	10.1025	+	7.33991i	0.429992	+	0.312407i
$553$	−3.43727	+	3.02988i	−0.146168	+	0.128844i
$554$	−6.27653	−	19.3172i	−0.266664	−	0.820707i
$555$	−9.15759	−	4.07722i	−0.388718	−	0.173068i
$556$	0.493130	+	4.69182i	0.0209134	+	0.198977i
$557$	−22.1224	−	4.70225i	−0.937354	−	0.199241i	−0.286186	−	0.958174i	$-0.592388\pi$
$557$	−22.1224	−	4.70225i	−0.937354	−	0.199241i	−0.651168	+	0.758933i	$0.725721\pi$
$558$	−7.12024	+	1.51345i	−0.301424	+	0.0640696i
$559$	13.0400	+	9.47411i	0.551533	+	0.400712i
$560$	0.329437	−	31.2231i	0.0139213	−	1.31942i
$561$	−1.91126	+	0.654087i	−0.0806934	+	0.0276156i
$562$	4.88755	+	8.46548i	0.206169	+	0.357095i
$563$	3.16693	−	1.41001i	0.133470	−	0.0594248i	−0.338915	−	0.940817i	$-0.610060\pi$
$563$	3.16693	−	1.41001i	0.133470	−	0.0594248i	0.472385	+	0.881392i	$0.343393\pi$
$564$	2.45991	+	2.73200i	0.103581	+	0.115038i
$565$	−49.8906	+	55.4092i	−2.09892	+	2.33108i
$566$	31.8110	−	23.1120i	1.33712	−	0.971471i
$567$	1.53246	+	2.15675i	0.0643574	+	0.0905748i
$568$	8.62464	+	26.5439i	0.361882	+	1.11376i
$569$	−10.5391	+	2.24016i	−0.441823	+	0.0939124i	−0.423451	−	0.905919i	$-0.639182\pi$
$569$	−10.5391	+	2.24016i	−0.441823	+	0.0939124i	−0.0183716	+	0.999831i	$0.505848\pi$
$570$	−6.74778	+	3.00430i	−0.282633	+	0.125836i
$571$	−11.2494	+	19.4846i	−0.470775	+	0.815405i	−0.999441	−	0.0334240i	$-0.989359\pi$
$571$	−11.2494	+	19.4846i	−0.470775	+	0.815405i	0.528667	+	0.848830i	$0.322692\pi$
$572$	0.996756	+	4.35471i	0.0416764	+	0.182080i
$573$	18.7313			0.782509
$574$	3.65319	+	8.44385i	0.152481	+	0.352439i
$575$	−12.0945	+	37.2229i	−0.504374	+	1.55230i
$576$	5.94633	−	6.60407i	0.247764	−	0.275170i
$577$	−0.0887090	−	0.844010i	−0.00369300	−	0.0351366i	0.992520	−	0.122080i	$-0.0389566\pi$
$577$	−0.0887090	−	0.844010i	−0.00369300	−	0.0351366i	−0.996213	+	0.0869439i	$0.972290\pi$
$578$	2.21349	+	21.0600i	0.0920691	+	0.875979i
$579$	1.01067	−	1.12247i	0.0420022	−	0.0466481i
$580$	−4.72013	+	14.5271i	−0.195993	+	0.603204i
$581$	10.5245	+	1.21856i	0.436629	+	0.0505545i
$582$	−12.8767			−0.533757
$583$	−29.7704	−	2.66091i	−1.23296	−	0.110204i
$584$	17.1392	−	29.6860i	0.709227	−	1.22842i
$585$	−12.3807	+	5.51224i	−0.511879	+	0.227903i
$586$	6.37660	−	1.35539i	0.263415	−	0.0559906i
$587$	9.23505	+	28.4226i	0.381171	+	1.17312i	0.939220	+	0.343316i	$0.111550\pi$
$587$	9.23505	+	28.4226i	0.381171	+	1.17312i	−0.558049	+	0.829808i	$0.688450\pi$
$588$	2.17509	−	1.51122i	0.0896993	−	0.0623217i
$589$	7.04614	−	5.11932i	0.290331	−	0.210938i
$590$	4.43749	−	4.92833i	0.182689	−	0.202896i
$591$	3.50853	+	3.89662i	0.144322	+	0.160286i
$592$	7.45736	−	3.32023i	0.306495	−	0.136461i
$593$	3.63206	+	6.29090i	0.149151	+	0.258336i	0.930914	−	0.365239i	$-0.119013\pi$
$593$	3.63206	+	6.29090i	0.149151	+	0.258336i	−0.781763	+	0.623575i	$0.785679\pi$
$594$	−0.0657812	−	4.22299i	−0.00269904	−	0.173271i
$595$	−5.34490	+	3.01114i	−0.219120	+	0.123445i
$596$	−6.95217	−	5.05105i	−0.284772	−	0.206899i
$597$	5.25285	−	1.11653i	0.214985	−	0.0456964i
$598$	18.2827	+	3.88610i	0.747633	+	0.158914i
$599$	−0.0600007	−	0.570868i	−0.00245156	−	0.0233250i	0.993228	−	0.116184i	$-0.0370662\pi$
$599$	−0.0600007	−	0.570868i	−0.00245156	−	0.0233250i	−0.995679	+	0.0928588i	$0.970399\pi$
$600$	26.2647	+	11.6938i	1.07225	+	0.477397i
$601$	−8.02297	−	24.6922i	−0.327264	−	1.00721i	−0.970408	−	0.241469i	$-0.922371\pi$
$601$	−8.02297	−	24.6922i	−0.327264	−	1.00721i	0.643145	−	0.765745i	$-0.277629\pi$
$602$	−11.4435	+	10.0872i	−0.466403	+	0.411125i
$603$	−4.88799	−	3.55133i	−0.199054	−	0.144621i
$604$	0.743224	+	1.28730i	0.0302414	+	0.0523796i
$605$	−5.67226	−	41.4902i	−0.230610	−	1.68682i
$606$	7.28867	−	12.6243i	0.296082	−	0.512829i
$607$	−0.188235	+	1.79094i	−0.00764024	+	0.0726921i	−0.997678	−	0.0681126i	$-0.978302\pi$
$607$	−0.188235	+	1.79094i	−0.00764024	+	0.0726921i	0.990037	+	0.140805i	$0.0449690\pi$
$608$	−0.993257	+	3.05693i	−0.0402819	+	0.123975i
$609$	26.7735	−	8.38800i	1.08492	−	0.339899i
$610$	−24.4837	+	17.7884i	−0.991316	+	0.720233i
$611$	31.5987	+	14.0686i	1.27835	+	0.569156i
$612$	−0.225418	−	0.0479140i	−0.00911196	−	0.00193681i
$613$	−19.6894	−	21.8672i	−0.795246	−	0.883210i	0.200081	−	0.979779i	$-0.435880\pi$
$613$	−19.6894	−	21.8672i	−0.795246	−	0.883210i	−0.995326	+	0.0965697i	$0.969213\pi$
$614$	−0.824804	+	7.84749i	−0.0332864	+	0.316699i
$615$	−10.3955			−0.419189
$616$	−26.5763	+	0.133546i	−1.07079	+	0.00538074i
$617$	−7.13654			−0.287306			−0.143653	−	0.989628i	$-0.545885\pi$
$617$	−7.13654			−0.287306			−0.143653	+	0.989628i	$0.545885\pi$
$618$	1.20961	−	11.5087i	0.0486576	−	0.462946i
$619$	−13.1277	−	14.5798i	−0.527649	−	0.586013i	0.419119	−	0.907931i	$-0.362339\pi$
$619$	−13.1277	−	14.5798i	−0.527649	−	0.586013i	−0.946767	+	0.321918i	$0.895672\pi$
$620$	−8.05382	−	1.71189i	−0.323449	−	0.0687513i
$621$	3.76658	+	1.67699i	0.151148	+	0.0672952i
$622$	27.5010	−	19.9807i	1.10269	−	0.801152i
$623$	−3.28451	+	14.6886i	−0.131591	+	0.588487i
$624$	3.41037	−	10.4960i	0.136524	−	0.420177i
$625$	−1.84462	+	17.5504i	−0.0737847	+	0.702015i
$626$	−12.4768	+	21.6105i	−0.498675	+	0.863730i
$627$	2.12702	+	4.58386i	0.0849451	+	0.183062i
$628$	−0.350207	−	0.606577i	−0.0139748	−	0.0242051i
$629$	−1.29750	−	0.942690i	−0.0517348	−	0.0375875i
$630$	−2.53421	−	12.5734i	−0.100965	−	0.500936i
$631$	−10.4946	−	32.2991i	−0.417784	−	1.28581i	−0.909737	−	0.415185i	$-0.863717\pi$
$631$	−10.4946	−	32.2991i	−0.417784	−	1.28581i	0.491953	−	0.870622i	$-0.336283\pi$
$632$	4.79175	+	2.13342i	0.190605	+	0.0848630i
$633$	0.864040	+	8.22080i	0.0343425	+	0.326747i
$634$	−24.7105	−	5.25237i	−0.981377	−	0.208598i
$635$	36.5343	−	7.76560i	1.44982	−	0.308168i
$636$	−2.75857	−	2.00422i	−0.109384	−	0.0794725i
$637$	12.9123	−	21.3132i	0.511605	−	0.844461i
$638$	−42.8062	−	13.1751i	−1.69472	−	0.521608i
$639$	4.60759	+	7.98057i	0.182273	+	0.315707i
$640$	−24.6832	+	10.9897i	−0.975691	+	0.434406i
$641$	6.03576	+	6.70339i	0.238398	+	0.264768i	0.850457	−	0.526044i	$-0.176325\pi$
$641$	6.03576	+	6.70339i	0.238398	+	0.264768i	−0.612059	+	0.790812i	$0.709659\pi$
$642$	−1.08805	+	1.20840i	−0.0429418	+	0.0476917i
$643$	19.0558	−	13.8449i	0.751488	−	0.545988i	−0.144800	−	0.989461i	$-0.546254\pi$
$643$	19.0558	−	13.8449i	0.751488	−	0.545988i	0.896288	+	0.443473i	$0.146254\pi$
$644$	1.71845	−	3.75264i	0.0677165	−	0.147875i
$645$	−5.32641	−	16.3930i	−0.209727	−	0.645474i
$646$	−1.15594	+	0.245702i	−0.0454797	+	0.00966702i
$647$	−13.7619	+	6.12721i	−0.541037	+	0.240885i	−0.659014	−	0.752131i	$-0.729026\pi$
$647$	−13.7619	+	6.12721i	−0.541037	+	0.240885i	0.117976	+	0.993016i	$0.462359\pi$
$648$	1.51435	−	2.62292i	0.0594891	−	0.103038i
$649$	−3.41855	−	2.98299i	−0.134190	−	0.117093i
$650$	43.0333			1.68791
$651$	6.00532	+	13.8805i	0.235367	+	0.544018i
$652$	−1.08044	+	3.32524i	−0.0423131	+	0.130226i
$653$	−1.32289	+	1.46922i	−0.0517687	+	0.0574950i	−0.768473	−	0.639882i	$-0.778983\pi$
$653$	−1.32289	+	1.46922i	−0.0517687	+	0.0574950i	0.716704	+	0.697377i	$0.245650\pi$
$654$	−2.10145	−	19.9940i	−0.0821732	−	0.781826i
$655$	−2.75120	−	26.1760i	−0.107498	−	1.02278i
$656$	5.66450	−	6.29106i	0.221162	−	0.245625i
$657$	3.49743	−	10.7640i	0.136448	−	0.419943i
$658$	−19.5200	+	26.2794i	−0.760968	+	1.02448i
$659$	−15.2486			−0.594000			−0.297000	−	0.954877i	$-0.595986\pi$
$659$	−15.2486			−0.594000			−0.297000	+	0.954877i	$0.595986\pi$
$660$	1.87488	−	4.39399i	0.0729798	−	0.171036i
$661$	−9.68373	+	16.7727i	−0.376654	+	0.652383i	−0.990573	−	0.136986i	$-0.956259\pi$
$661$	−9.68373	+	16.7727i	−0.376654	+	0.652383i	0.613919	+	0.789369i	$0.289592\pi$
$662$	27.7171	−	12.3404i	1.07725	−	0.479624i
$663$	−2.12089	+	0.450810i	−0.0823687	+	0.0175080i
$664$	−3.74784	−	11.5347i	−0.145444	−	0.447631i
$665$	8.88883	+	12.5099i	0.344694	+	0.485112i
$666$	2.71276	−	1.97094i	0.105117	−	0.0763723i
$667$	29.2560	−	32.4921i	1.13280	−	1.25810i
$668$	0.293618	+	0.326096i	0.0113604	+	0.0126170i
$669$	6.51518	−	2.90075i	0.251892	−	0.112149i
$670$	14.6451	+	25.3661i	0.565790	+	0.979978i
$671$	12.4292	+	16.5587i	0.479825	+	0.639243i
$672$	−4.80397	−	2.84157i	−0.185317	−	0.109616i
$673$	7.29912	+	5.30312i	0.281360	+	0.204420i	0.719511	−	0.694481i	$-0.244366\pi$
$673$	7.29912	+	5.30312i	0.281360	+	0.204420i	−0.438150	+	0.898902i	$0.644366\pi$
$674$	−29.8401	+	6.34272i	−1.14940	+	0.244312i
$675$	9.28521	+	1.97363i	0.357388	+	0.0759651i
$676$	−0.0129291	−	0.123012i	−0.000497272	−	0.00473122i
$677$	−31.9609	−	14.2299i	−1.22836	−	0.546900i	−0.313081	−	0.949726i	$-0.601361\pi$
$677$	−31.9609	−	14.2299i	−1.22836	−	0.546900i	−0.915276	+	0.402826i	$0.868028\pi$
$678$	−7.70714	−	23.7201i	−0.295991	−	0.910967i
$679$	5.28593	+	26.2259i	0.202855	+	1.00646i
$680$	5.68145	+	4.12782i	0.217874	+	0.158295i
$681$	2.52248	+	4.36906i	0.0966615	+	0.167423i
$682$	4.65114	−	23.6905i	0.178101	−	0.907155i
$683$	2.83896	−	4.91722i	0.108630	−	0.188152i	−0.806586	−	0.591117i	$-0.798687\pi$
$683$	2.83896	−	4.91722i	0.108630	−	0.188152i	0.915215	+	0.402965i	$0.132020\pi$
$684$	−0.0602594	+	0.573330i	−0.00230408	+	0.0219218i
$685$	−16.6370	+	51.2034i	−0.635667	+	1.95638i
$686$	17.0184	+	16.3278i	0.649765	+	0.623397i
$687$	−20.8818	+	15.1715i	−0.796689	+	0.578828i
$688$	12.8229	+	5.70912i	0.488868	+	0.217658i
$689$	−31.3807	−	6.67016i	−1.19551	−	0.254113i
$690$	−13.3745	−	14.8539i	−0.509159	−	0.565479i
$691$	1.48498	−	14.1286i	0.0564912	−	0.537478i	−0.929279	−	0.369379i	$-0.879571\pi$
$691$	1.48498	−	14.1286i	0.0564912	−	0.537478i	0.985770	−	0.168099i	$-0.0537628\pi$
$692$	0.917169			0.0348655
$693$	−8.57393	+	1.86752i	−0.325697	+	0.0709414i
$694$	4.83884			0.183680
$695$	4.96164	−	47.2068i	0.188206	−	1.79066i
$696$	−21.4909	−	23.8680i	−0.814609	−	0.904715i
$697$	−1.62686	−	0.345800i	−0.0616218	−	0.0130981i
$698$	23.7801	+	10.5876i	0.900092	+	0.400747i
$699$	−10.6262	+	7.72039i	−0.401920	+	0.292012i
$700$	2.07368	−	9.27367i	0.0783776	−	0.350512i
$701$	−3.67754	+	11.3183i	−0.138899	+	0.427487i	−0.996176	−	0.0873683i	$-0.972154\pi$
$701$	−3.67754	+	11.3183i	−0.138899	+	0.427487i	0.857277	+	0.514855i	$0.172154\pi$
$702$	0.473863	−	4.50850i	0.0178848	−	0.170162i
$703$	−2.00599	+	3.47447i	−0.0756572	+	0.131042i
$704$	12.4059	+	26.7356i	0.467567	+	1.00764i
$705$	−18.4944	−	32.0333i	−0.696541	−	1.20644i
$706$	−21.4122	−	15.5569i	−0.805858	−	0.585490i
$707$	−28.7039	−	9.66246i	−1.07952	−	0.363394i
$708$	−0.159944	−	0.492258i	−0.00601107	−	0.0185002i
$709$	−13.2739	−	5.90993i	−0.498512	−	0.221952i	0.142048	−	0.989860i	$-0.454631\pi$
$709$	−13.2739	−	5.90993i	−0.498512	−	0.221952i	−0.640560	+	0.767908i	$0.721298\pi$
$710$	−4.66969	−	44.4292i	−0.175251	−	1.66740i
$711$	1.69400	+	0.360071i	0.0635299	+	0.0135037i
$712$	16.8533	−	3.58229i	0.631606	−	0.134252i
$713$	19.0673	+	13.8532i	0.714074	+	0.518805i
$714$	0.0216507	−	2.05199i	0.000810256	−	0.0767937i
$715$	−0.700068	−	44.9427i	−0.0261811	−	1.68076i
$716$	3.30026	+	5.71621i	0.123336	+	0.213625i
$717$	10.5213	−	4.68438i	0.392925	−	0.174941i
$718$	1.56498	+	1.73808i	0.0584044	+	0.0648646i
$719$	−7.97384	+	8.85584i	−0.297374	+	0.330267i	−0.873252	−	0.487268i	$-0.837993\pi$
$719$	−7.97384	+	8.85584i	−0.297374	+	0.330267i	0.575878	+	0.817535i	$0.304660\pi$
$720$	−9.54792	+	6.93697i	−0.355830	+	0.258526i
$721$	−23.9362	+	2.26073i	−0.891429	+	0.0841940i
$722$	−6.56322	−	20.1995i	−0.244258	−	0.751748i
$723$	27.1774	−	5.77673i	1.01074	−	0.214839i
$724$	−3.66581	+	1.63213i	−0.136239	+	0.0606575i
$725$	50.3321	−	87.1777i	1.86929	−	3.23770i
$726$	12.9680	+	5.29614i	0.481287	+	0.196558i
$727$	39.9778			1.48270			0.741348	−	0.671121i	$-0.234187\pi$
$727$	39.9778			1.48270			0.741348	+	0.671121i	$0.234187\pi$
$728$	−28.3370	−	3.28096i	−1.05024	−	0.121601i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−36.7137	+	40.7747i	−1.35883	+	1.50914i
$731$	−0.288261	−	2.74262i	−0.0106617	−	0.101440i
$732$	0.246896	+	2.34906i	0.00912553	+	0.0868236i
$733$	15.6679	−	17.4010i	0.578707	−	0.642719i	−0.380715	−	0.924692i	$-0.624322\pi$
$733$	15.6679	−	17.4010i	0.578707	−	0.642719i	0.959422	+	0.281973i	$0.0909888\pi$
$734$	−10.0665	+	30.9815i	−0.371561	+	1.14355i
$735$	−24.5678	+	10.3228i	−0.906199	+	0.380763i
$736$	−8.69793			−0.320610
$737$	17.1958	−	10.2884i	0.633417	−	0.378978i
$738$	1.73868	−	3.01148i	0.0640017	−	0.110854i
$739$	27.2551	−	12.1347i	1.00259	−	0.446383i	0.161267	−	0.986911i	$-0.448442\pi$
$739$	27.2551	−	12.1347i	1.00259	−	0.446383i	0.841326	+	0.540527i	$0.181775\pi$
$740$	3.70993	−	0.788570i	0.136380	−	0.0289884i
$741$	1.67612	+	5.15855i	0.0615736	+	0.189504i
$742$	12.6416	−	27.6060i	0.464089	−	1.01345i
$743$	3.65248	−	2.65368i	0.133996	−	0.0973541i	−0.518768	−	0.854915i	$-0.673609\pi$
$743$	3.65248	−	2.65368i	0.133996	−	0.0973541i	0.652764	+	0.757561i	$0.273609\pi$
$744$	11.5846	−	12.8660i	0.424711	−	0.471689i
$745$	57.8545	+	64.2539i	2.11963	+	2.35408i
$746$	−3.52416	+	1.56906i	−0.129029	+	0.0574473i
$747$	−2.00223	−	3.46796i	−0.0732577	−	0.126886i
$748$	0.439575	−	0.625276i	0.0160725	−	0.0228624i
$749$	2.90778	+	1.71997i	0.106248	+	0.0628462i
$750$	−17.6202	−	12.8018i	−0.643397	−	0.467456i
$751$	−28.7562	+	6.11232i	−1.04933	+	0.223042i	−0.700136	−	0.714009i	$-0.746878\pi$
$751$	−28.7562	+	6.11232i	−1.04933	+	0.223042i	−0.349193	+	0.937051i	$0.613544\pi$
$752$	29.4632	+	6.26259i	1.07441	+	0.228373i
$753$	−2.90200	−	27.6107i	−0.105755	−	1.00619i
$754$	−43.9173	−	19.5533i	−1.59938	−	0.712088i
$755$	−4.62164	−	14.2239i	−0.168199	−	0.517662i
$756$	−0.948746	−	0.319371i	−0.0345056	−	0.0116154i
$757$	−30.8181	−	22.3906i	−1.12010	−	0.813801i	−0.135877	−	0.990726i	$-0.543385\pi$
$757$	−30.8181	−	22.3906i	−1.12010	−	0.813801i	−0.984224	+	0.176925i	$0.943385\pi$
$758$	20.5093	+	35.5231i	0.744930	+	1.29026i
$759$	−10.0184	+	9.30723i	−0.363646	+	0.337831i
$760$	8.78373	−	15.2139i	0.318619	−	0.551865i
$761$	4.22275	−	40.1767i	0.153074	−	1.45641i	−0.600806	−	0.799395i	$-0.705154\pi$
$761$	4.22275	−	40.1767i	0.153074	−	1.45641i	0.753881	−	0.657011i	$-0.228180\pi$
$762$	−3.86083	+	11.8824i	−0.139863	+	0.430455i
$763$	−39.8589	+	12.4876i	−1.44299	+	0.452081i
$764$	−5.73370	+	4.16578i	−0.207438	+	0.150712i
$765$	2.11825	+	0.943105i	0.0765854	+	0.0340980i
$766$	−10.2766	−	2.18435i	−0.371308	−	0.0789239i
$767$	−3.25858	−	3.61902i	−0.117660	−	0.130675i
$768$	−0.913082	+	8.68740i	−0.0329480	+	0.313480i
$769$	22.1699			0.799467			0.399734	−	0.916631i	$-0.369103\pi$
$769$	22.1699			0.799467			0.399734	+	0.916631i	$0.369103\pi$
$770$	41.6542	+	8.63533i	1.50111	+	0.311196i
$771$	−1.07128			−0.0385812
$772$	−0.0597372	+	0.568361i	−0.00214999	+	0.0204558i
$773$	2.89402	+	3.21413i	0.104091	+	0.115604i	0.792939	−	0.609301i	$-0.208550\pi$
$773$	2.89402	+	3.21413i	0.104091	+	0.115604i	−0.688848	+	0.724906i	$0.741883\pi$
$774$	5.63975	+	1.19877i	0.202716	+	0.0430887i
$775$	49.5714	+	22.0706i	1.78066	+	0.792799i
$776$	24.7766	−	18.0012i	0.889428	−	0.646207i
$777$	−5.12779	−	4.71599i	−0.183958	−	0.169185i
$778$	−8.27049	+	25.4540i	−0.296511	+	0.912568i
$779$	−0.434899	+	4.13778i	−0.0155819	+	0.148252i
$780$	2.56387	−	4.44075i	0.0918011	−	0.159004i
$781$	−30.3424	+	3.66776i	−1.08574	+	0.131243i
$782$	−1.59896	−	2.76947i	−0.0571785	−	0.0990362i
$783$	−8.57918	−	6.23314i	−0.306595	−	0.222754i
$784$	7.13989	−	20.4926i	0.254996	−	0.731878i
$785$	2.17772	+	6.70232i	0.0777260	+	0.239216i
$786$	8.04306	+	3.58100i	0.286886	+	0.127730i
$787$	1.04197	+	9.91371i	0.0371423	+	0.353385i	0.997271	+	0.0738272i	$0.0235213\pi$
$787$	1.04197	+	9.91371i	0.0371423	+	0.353385i	−0.960129	+	0.279558i	$0.909812\pi$
$788$	−1.94057	−	0.412481i	−0.0691299	−	0.0146940i
$789$	−17.3690	+	3.69189i	−0.618351	+	0.131435i
$790$	−6.79230	−	4.93489i	−0.241659	−	0.175576i
$791$	−45.1469	+	25.4343i	−1.60524	+	0.904338i
$792$	6.03018	+	8.03366i	0.214273	+	0.285464i
$793$	11.1117	+	19.2460i	0.394588	+	0.683446i
$794$	−17.8715	+	7.95691i	−0.634236	+	0.282380i
$795$	22.9563	+	25.4955i	0.814174	+	0.904232i
$796$	−1.35960	+	1.50999i	−0.0481898	+	0.0535202i
$797$	−14.1107	+	10.2520i	−0.499826	+	0.363145i	−0.808951	−	0.587877i	$-0.799964\pi$
$797$	−14.1107	+	10.2520i	−0.499826	+	0.363145i	0.309125	+	0.951022i	$0.399964\pi$
$798$	−5.11067	+	0.482694i	−0.180916	+	0.0170872i
$799$	−1.82874	−	5.62830i	−0.0646963	−	0.199115i
$800$	−19.5880	+	4.16356i	−0.692541	+	0.147204i
$801$	5.19705	−	2.31388i	0.183629	−	0.0817568i
$802$	10.0409	−	17.3914i	0.354557	−	0.614110i
$803$	28.2834	+	24.6798i	0.998101	+	0.870932i
$804$	2.28603			0.0806222
$805$	−24.7626	+	33.3374i	−0.872766	+	1.17499i
$806$	8.00781	−	24.6455i	0.282063	−	0.868101i
$807$	5.86939	−	6.51862i	0.206612	−	0.229466i
$808$	3.62403	+	34.4803i	0.127493	+	1.21301i
$809$	1.21286	+	11.5396i	0.0426419	+	0.405710i	0.994935	+	0.100524i	$0.0320520\pi$
$809$	1.21286	+	11.5396i	0.0426419	+	0.405710i	−0.952293	+	0.305186i	$0.901281\pi$
$810$	−3.24385	+	3.60267i	−0.113977	+	0.126585i
$811$	−9.99201	+	30.7523i	−0.350867	+	1.07986i	0.607500	+	0.794320i	$0.292172\pi$
$811$	−9.99201	+	30.7523i	−0.350867	+	1.07986i	−0.958367	+	0.285538i	$0.907828\pi$
$812$	−6.32999	+	8.52194i	−0.222139	+	0.299062i
$813$	2.84907			0.0999212
$814$	2.48137	+	10.8408i	0.0869719	+	0.379970i
$815$	17.5894	−	30.4657i	0.616128	−	1.06717i
$816$	−1.72497	+	0.768004i	−0.0603859	+	0.0268855i
$817$	−6.74782	+	1.43429i	−0.236076	+	0.0501795i
$818$	5.58679	+	17.1944i	0.195338	+	0.601187i
$819$	−9.37696	+	0.885639i	−0.327657	+	0.0309467i
$820$	3.18211	−	2.31194i	0.111124	−	0.0807363i
$821$	−5.45141	+	6.05441i	−0.190256	+	0.211300i	−0.830724	−	0.556684i	$-0.812073\pi$
$821$	−5.45141	+	6.05441i	−0.190256	+	0.211300i	0.640469	+	0.767984i	$0.278740\pi$
$822$	−12.0505	−	13.3835i	−0.420310	−	0.466802i
$823$	15.6663	−	6.97507i	0.546092	−	0.243136i	−0.115098	−	0.993354i	$-0.536718\pi$
$823$	15.6663	−	6.97507i	0.546092	−	0.243136i	0.661190	+	0.750218i	$0.270052\pi$
$824$	13.7613	+	23.8352i	0.479397	+	0.830340i
$825$	−18.1066	+	25.7558i	−0.630391	+	0.896704i
$826$	4.01556	−	2.26223i	0.139719	−	0.0787132i
$827$	28.8748	+	20.9788i	1.00408	+	0.729504i	0.962958	−	0.269650i	$-0.0869081\pi$
$827$	28.8748	+	20.9788i	1.00408	+	0.729504i	0.0411178	+	0.999154i	$0.486908\pi$
$828$	−1.52592	+	0.324344i	−0.0530294	+	0.0112717i
$829$	−0.335705	−	0.0713563i	−0.0116595	−	0.00247831i	0.202078	−	0.979369i	$-0.435230\pi$
$829$	−0.335705	−	0.0713563i	−0.0116595	−	0.00247831i	−0.213738	+	0.976891i	$0.568564\pi$
$830$	2.02922	+	19.3067i	0.0704351	+	0.670145i
$831$	14.5710	+	6.48744i	0.505464	+	0.225047i
$832$	9.77602	+	30.0875i	0.338922	+	1.04310i
$833$	−4.18815	+	0.798250i	−0.145111	+	0.0276577i
$834$	12.8455	+	9.33280i	0.444803	+	0.323168i
$835$	−2.20753	−	3.82355i	−0.0763946	−	0.132319i
$836$	−1.67053	−	0.930092i	−0.0577763	−	0.0321679i
$837$	2.85814	−	4.95044i	0.0987918	−	0.171112i
$838$	3.97077	−	37.7794i	0.137168	−	1.30507i
$839$	17.7012	−	54.4786i	0.611112	−	1.88081i	0.163615	−	0.986524i	$-0.447684\pi$
$839$	17.7012	−	54.4786i	0.611112	−	1.88081i	0.447497	−	0.894285i	$-0.352316\pi$
$840$	22.4534	+	20.6502i	0.774715	+	0.712499i
$841$	−67.5159	+	49.0532i	−2.32813	+	1.69149i
$842$	−2.29767	−	1.02299i	−0.0791831	−	0.0352546i
$843$	−7.50842	−	1.59596i	−0.258604	−	0.0549679i
$844$	−2.09277	−	2.32425i	−0.0720360	−	0.0800040i
$845$	−0.130086	+	1.23769i	−0.00447510	+	0.0425777i
$846$	12.3730			0.425392
$847$	5.46322	−	28.5859i	0.187719	−	0.982223i
$848$	−27.9379			−0.959391
$849$	−3.22758	+	30.7084i	−0.110770	+	1.05391i
$850$	−4.92660	−	5.47155i	−0.168981	−	0.187673i
$851$	−10.6194	−	2.25722i	−0.364027	−	0.0773764i
$852$	−3.18525	−	1.41817i	−0.109125	−	0.0485856i
$853$	38.3617	−	27.8714i	1.31348	−	0.954299i	0.313492	−	0.949591i	$-0.398501\pi$
$853$	38.3617	−	27.8714i	1.31348	−	0.954299i	0.999989	−	0.00470844i	$-0.00149875\pi$
$854$	−20.0707	+	6.28805i	−0.686806	+	0.215173i
$855$	1.79241	−	5.51646i	0.0612990	−	0.188659i
$856$	0.404249	−	3.84618i	0.0138170	−	0.131460i
$857$	13.8895	−	24.0573i	0.474455	−	0.821780i	−0.525117	−	0.851030i	$-0.675978\pi$
$857$	13.8895	−	24.0573i	0.474455	−	0.821780i	0.999572	+	0.0292498i	$0.00931183\pi$
$858$	13.1365	+	7.31397i	0.448474	+	0.249695i
$859$	3.56421	+	6.17340i	0.121609	+	0.210634i	0.920402	−	0.390972i	$-0.127861\pi$
$859$	3.56421	+	6.17340i	0.121609	+	0.210634i	−0.798793	+	0.601606i	$0.794528\pi$
$860$	5.27619	+	3.83337i	0.179917	+	0.130717i
$861$	−6.84720	−	2.30494i	−0.233352	−	0.0785521i
$862$	−1.53083	−	4.71141i	−0.0521403	−	0.160471i
$863$	−23.9996	−	10.6853i	−0.816957	−	0.363733i	−0.0446663	−	0.999002i	$-0.514222\pi$
$863$	−23.9996	−	10.6853i	−0.816957	−	0.363733i	−0.772291	+	0.635269i	$0.780889\pi$
$864$	0.220513	+	2.09804i	0.00750199	+	0.0713767i
$865$	−9.02646	−	1.91863i	−0.306909	−	0.0652355i
$866$	26.3820	−	5.60767i	0.896497	−	0.190556i
$867$	−13.4532	−	9.77429i	−0.456893	−	0.331952i
$868$	−4.92522	−	2.91329i	−0.167173	−	0.0988835i
$869$	−3.30338	+	4.69891i	−0.112059	+	0.159400i
$870$	25.7045	+	44.5214i	0.871462	+	1.50942i
$871$	19.6492	−	8.74837i	0.665786	−	0.296427i
$872$	31.9944	+	35.5334i	1.08347	+	1.20331i
$873$	6.76612	−	7.51454i	0.228998	−	0.254329i
$874$	−6.47189	+	4.70211i	−0.218915	+	0.159051i
$875$	−18.8402	+	41.1420i	−0.636915	+	1.39085i
$876$	1.32330	+	4.07271i	0.0447102	+	0.137604i
$877$	0.117404	−	0.0249549i	0.00396444	−	0.000842667i	−0.205929	−	0.978567i	$-0.566022\pi$
$877$	0.117404	−	0.0249549i	0.00396444	−	0.000842667i	0.209893	+	0.977724i	$0.432688\pi$
$878$	11.1061	−	4.94475i	0.374812	−	0.166877i
$879$	−2.55964	+	4.43342i	−0.0863344	+	0.149536i
$880$	−8.73350	−	38.1556i	−0.294406	−	1.28623i
$881$	30.1851			1.01696			0.508481	−	0.861073i	$-0.330207\pi$
$881$	30.1851			1.01696			0.508481	+	0.861073i	$0.330207\pi$
$882$	1.11862	−	8.84358i	0.0376658	−	0.297779i
$883$	−4.25930	+	13.1088i	−0.143337	+	0.441146i	−0.996793	−	0.0800184i	$-0.974502\pi$
$883$	−4.25930	+	13.1088i	−0.143337	+	0.441146i	0.853456	+	0.521164i	$0.174502\pi$
$884$	0.548953	−	0.609675i	0.0184633	−	0.0205056i
$885$	0.544358	+	5.17922i	0.0182984	+	0.174098i
$886$	−1.22352	−	11.6410i	−0.0411048	−	0.391086i
$887$	−10.0779	+	11.1926i	−0.338381	+	0.375811i	−0.888187	−	0.459482i	$-0.848035\pi$
$887$	−10.0779	+	11.1926i	−0.338381	+	0.375811i	0.549806	+	0.835293i	$0.314702\pi$
$888$	−2.46442	+	7.58471i	−0.0827005	+	0.254526i
$889$	25.7857	+	2.98557i	0.864826	+	0.100133i
$890$	−27.5789			−0.924447
$891$	2.49900	+	2.18060i	0.0837196	+	0.0730528i
$892$	−1.34920	+	2.33689i	−0.0451746	+	0.0782447i
$893$	−13.5241	+	6.02131i	−0.452566	+	0.201496i
$894$	−28.2900	+	6.01323i	−0.946161	+	0.201113i
$895$	−20.5222	−	63.1608i	−0.685981	−	2.11123i
$896$	−18.6947	+	1.76569i	−0.624547	+	0.0589874i
$897$	−11.8745	+	8.62734i	−0.396478	+	0.288058i
$898$	−13.8410	+	15.3720i	−0.461880	+	0.512970i
$899$	−40.5613	−	45.0479i	−1.35280	−	1.50243i
$900$	−3.28116	+	1.46087i	−0.109372	+	0.0486956i
$901$	2.74448	+	4.75357i	0.0914317	+	0.158364i
$902$	6.92349	+	9.22376i	0.230527	+	0.307118i
$903$	0.126386	−	11.9785i	0.00420588	−	0.398620i
$904$	47.9896	+	34.8665i	1.59611	+	1.15964i
$905$	39.4919	−	8.39427i	1.31276	−	0.279035i
$906$	4.89351	+	1.04015i	0.162576	+	0.0345566i
$907$	−3.23304	−	30.7603i	−0.107351	−	1.02138i	−0.907063	−	0.420995i	$-0.861681\pi$
$907$	−3.23304	−	30.7603i	−0.107351	−	1.02138i	0.799711	−	0.600385i	$-0.204986\pi$
$908$	−1.74380	−	0.776391i	−0.0578702	−	0.0257655i
$909$	3.53740	+	10.8870i	0.117328	+	0.361099i
$910$	43.2744	+	14.5673i	1.43453	+	0.482900i
$911$	−13.6502	−	9.91745i	−0.452251	−	0.328580i	0.338233	−	0.941063i	$-0.390171\pi$
$911$	−13.6502	−	9.91745i	−0.452251	−	0.328580i	−0.790484	+	0.612483i	$0.790171\pi$
$912$	2.36172	+	4.09061i	0.0782042	+	0.135454i
$913$	13.1853	−	1.59383i	0.436369	−	0.0527479i
$914$	−15.1556	+	26.2502i	−0.501302	+	0.868280i
$915$	2.48415	−	23.6351i	0.0821234	−	0.781352i
$916$	3.01788	−	9.28808i	0.0997136	−	0.306887i
$917$	3.99170	−	17.8512i	0.131818	−	0.589500i
$918$	−0.627491	+	0.455899i	−0.0207103	+	0.0150469i
$919$	−12.4001	−	5.52088i	−0.409042	−	0.182117i	0.191892	−	0.981416i	$-0.438538\pi$
$919$	−12.4001	−	5.52088i	−0.409042	−	0.182117i	−0.600934	+	0.799299i	$0.705204\pi$
$920$	46.4997	+	9.88381i	1.53305	+	0.325860i
$921$	−4.14620	−	4.60482i	−0.136622	−	0.151734i
$922$	1.36897	−	13.0249i	0.0450846	−	0.428952i
$923$	−32.8054			−1.07980
$924$	2.20918	−	2.47847i	0.0726766	−	0.0815358i
$925$	−24.9957			−0.821852
$926$	−4.31536	+	41.0579i	−0.141811	+	1.34925i
$927$	6.08058	+	6.75316i	0.199712	+	0.221803i
$928$	21.8822	+	4.65121i	0.718319	+	0.152683i
$929$	−25.4030	−	11.3102i	−0.833446	−	0.371074i	−0.0547692	−	0.998499i	$-0.517442\pi$
$929$	−25.4030	−	11.3102i	−0.833446	−	0.371074i	−0.778677	+	0.627425i	$0.784109\pi$
$930$	−22.4193	+	16.2886i	−0.735157	+	0.534123i
$931$	3.08104	+	10.2107i	0.100977	+	0.334642i
$932$	1.53572	−	4.72647i	0.0503043	−	0.154821i
$933$	−2.79029	+	26.5478i	−0.0913500	+	0.869137i
$934$	−16.4527	+	28.4969i	−0.538349	+	0.932447i
$935$	−5.63417	+	5.23420i	−0.184257	+	0.171177i
$936$	5.39096	+	9.33742i	0.176209	+	0.305203i
$937$	−32.9978	−	23.9743i	−1.07799	−	0.783207i	−0.100660	−	0.994921i	$-0.532095\pi$
$937$	−32.9978	−	23.9743i	−1.07799	−	0.783207i	−0.977332	+	0.211714i	$0.932095\pi$
$938$	4.02200	+	19.9550i	0.131323	+	0.651553i
$939$	−6.05536	−	18.6365i	−0.197609	−	0.608179i
$940$	12.7853	+	5.69239i	0.417011	+	0.185665i
$941$	3.88703	+	36.9826i	0.126713	+	1.20560i	0.854373	+	0.519660i	$0.173941\pi$
$941$	3.88703	+	36.9826i	0.126713	+	1.20560i	−0.727660	+	0.685938i	$0.759392\pi$
$942$	−2.30582	−	0.490118i	−0.0751278	−	0.0159689i
$943$	−11.0127	+	2.34083i	−0.358623	+	0.0762278i
$944$	−3.43092	−	2.49271i	−0.111667	−	0.0811309i
$945$	8.66913	+	5.12783i	0.282007	+	0.166808i
$946$	−10.9978	+	15.6439i	−0.357569	+	0.508626i
$947$	−16.4708	−	28.5283i	−0.535230	−	0.927046i	−0.999152	−	0.0411697i	$-0.986892\pi$
$947$	−16.4708	−	28.5283i	−0.535230	−	0.927046i	0.463922	−	0.885876i	$-0.346442\pi$
$948$	−0.598617	+	0.266521i	−0.0194422	+	0.00865622i
$949$	26.9599	+	29.9420i	0.875156	+	0.971959i
$950$	−12.3241	+	13.6873i	−0.399846	+	0.444074i
$951$	16.0493	−	11.6605i	0.520436	−	0.378119i
$952$	2.82695	+	3.97857i	0.0916220	+	0.128946i
$953$	−0.828546	−	2.55000i	−0.0268392	−	0.0826027i	0.936740	−	0.350027i	$-0.113828\pi$
$953$	−0.828546	−	2.55000i	−0.0268392	−	0.0826027i	−0.963579	+	0.267424i	$0.913828\pi$
$954$	−11.2253	+	2.38601i	−0.363432	+	0.0772499i
$955$	65.1435	−	29.0037i	2.10799	−	0.938539i
$956$	−2.17881	+	3.77381i	−0.0704677	+	0.122054i
$957$	30.1814	−	18.0577i	0.975625	−	0.583724i
$958$	−46.9980			−1.51844
$959$	−22.3112	+	30.0372i	−0.720467	+	0.969951i
$960$	10.4543	−	32.1750i	0.337411	−	1.03844i
$961$	1.12138	−	1.24542i	0.0361735	−	0.0401747i
$962$	1.24776	+	11.8716i	0.0402293	+	0.382756i
$963$	−0.133473	−	1.26991i	−0.00430112	−	0.0409224i
$964$	−7.03435	+	7.81244i	−0.226561	+	0.251622i
$965$	1.77687	−	5.46865i	0.0571995	−	0.176042i
$966$	−5.51589	−	12.7492i	−0.177471	−	0.410200i
$967$	−24.8306			−0.798499			−0.399250	−	0.916842i	$-0.630729\pi$
$967$	−24.8306			−0.798499			−0.399250	+	0.916842i	$0.630729\pi$
$968$	−32.3560	+	7.93833i	−1.03996	+	0.255147i
$969$	0.464006	−	0.803681i	0.0149060	−	0.0258180i
$970$	−44.7826	+	19.9385i	−1.43788	+	0.640187i
$971$	−18.2669	+	3.88274i	−0.586212	+	0.124603i	−0.491464	−	0.870898i	$-0.663538\pi$
$971$	−18.2669	+	3.88274i	−0.586212	+	0.124603i	−0.0947482	+	0.995501i	$0.530205\pi$
$972$	0.116921	+	0.359846i	0.00375024	+	0.0115421i
$973$	13.7349	−	29.9935i	0.440322	−	0.961546i
$974$	7.28822	−	5.29520i	0.233530	−	0.169669i
$975$	−22.6120	+	25.1132i	−0.724164	+	0.804266i
$976$	12.9496	+	14.3820i	0.414507	+	0.460357i
$977$	−44.5176	+	19.8205i	−1.42424	+	0.634114i	−0.966895	−	0.255173i	$-0.917868\pi$
$977$	−44.5176	+	19.8205i	−1.42424	+	0.634114i	−0.457349	+	0.889287i	$0.651201\pi$
$978$	5.88373	+	10.1909i	0.188141	+	0.325870i
$979$	0.293868	+	18.8656i	0.00939205	+	0.602947i
$980$	5.22453	−	8.62366i	0.166892	−	0.275473i
$981$	12.7722	+	9.27954i	0.407785	+	0.296273i
$982$	20.5062	−	4.35873i	0.654380	−	0.139093i
$983$	23.2287	+	4.93742i	0.740881	+	0.157479i	0.562865	−	0.826549i	$-0.309699\pi$
$983$	23.2287	+	4.93742i	0.740881	+	0.157479i	0.178016	+	0.984028i	$0.443032\pi$
$984$	0.864496	+	8.22513i	0.0275591	+	0.262207i
$985$	18.2355	+	8.11899i	0.581033	+	0.258692i
$986$	2.54167	+	7.82247i	0.0809434	+	0.249118i
$987$	−5.07914	−	25.2000i	−0.161671	−	0.802123i
$988$	−1.66031	−	1.20629i	−0.0528215	−	0.0383771i
$989$	−9.33395	−	16.1669i	−0.296802	−	0.514077i
$990$	−6.76771	−	14.5848i	−0.215092	−	0.463537i
$991$	−7.16698	+	12.4136i	−0.227667	+	0.394330i	−0.957116	−	0.289705i	$-0.906443\pi$
$991$	−7.16698	+	12.4136i	−0.227667	+	0.394330i	0.729450	+	0.684035i	$0.239776\pi$
$992$	−1.26051	+	11.9930i	−0.0400213	+	0.380777i
$993$	−7.36246	+	22.6593i	−0.233641	+	0.719072i
$994$	6.77523	−	30.2994i	0.214897	−	0.961039i
$995$	16.5395	−	12.0166i	0.524337	−	0.380953i
$996$	1.38415	+	0.616264i	0.0438585	+	0.0195271i
$997$	58.4778	+	12.4298i	1.85201	+	0.393657i	0.992981	−	0.118272i	$-0.0377355\pi$
$997$	58.4778	+	12.4298i	1.85201	+	0.393657i	0.859028	+	0.511929i	$0.171069\pi$
$998$	−1.26649	−	1.40657i	−0.0400899	−	0.0445244i
$999$	−0.275240	+	2.61874i	−0.00870822	+	0.0828531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.4.3	✓	64
3.2	odd	2		693.2.by.d.235.6		64
7.2	even	3	inner	231.2.y.a.37.6	yes	64
11.3	even	5	inner	231.2.y.a.25.6	yes	64
21.2	odd	6		693.2.by.d.37.3		64
33.14	odd	10		693.2.by.d.487.3		64
77.58	even	15	inner	231.2.y.a.58.3	yes	64
231.212	odd	30		693.2.by.d.289.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.4.3	✓	64	1.1	even	1	trivial
231.2.y.a.25.6	yes	64	11.3	even	5	inner
231.2.y.a.37.6	yes	64	7.2	even	3	inner
231.2.y.a.58.3	yes	64	77.58	even	15	inner
693.2.by.d.37.3		64	21.2	odd	6
693.2.by.d.235.6		64	3.2	odd	2
693.2.by.d.289.6		64	231.212	odd	30
693.2.by.d.487.3		64	33.14	odd	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.133110 + 1.26646i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(0.370096 + 0.0786664i) q^{4} +(-3.47779 - 1.54841i) q^{5} +(1.03023 - 0.748506i) q^{6} +(-1.94739 - 1.79100i) q^{7} +(-0.935917 + 2.88046i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.133110 + 1.26646i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(0.370096 + 0.0786664i) q^{4} +(-3.47779 - 1.54841i) q^{5} +(1.03023 - 0.748506i) q^{6} +(-1.94739 - 1.79100i) q^{7} +(-0.935917 + 2.88046i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(2.42393 - 4.19837i) q^{10} +(-2.89776 - 1.61338i) q^{11} +(-0.189182 - 0.327673i) q^{12} +(-2.88004 - 2.09247i) q^{13} +(2.52744 - 2.22789i) q^{14} +(1.17640 + 3.62060i) q^{15} +(-2.83209 - 1.26093i) q^{16} +(0.0636660 + 0.605742i) q^{17} +(-1.24561 - 0.264762i) q^{18} +(1.49034 - 0.316781i) q^{19} +(-1.16531 - 0.846648i) q^{20} +(-0.0279140 + 2.64560i) q^{21} +(2.42899 - 3.45514i) q^{22} +(2.06152 + 3.57065i) q^{23} +(2.76685 - 1.23188i) q^{24} +(6.35182 + 7.05441i) q^{25} +(3.03339 - 3.36893i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.579830 - 0.816036i) q^{28} +(-3.27695 - 10.0854i) q^{29} +(-4.74193 + 1.00793i) q^{30} +(5.22208 - 2.32502i) q^{31} +(-1.05480 + 1.82696i) q^{32} +(0.740009 + 3.23302i) q^{33} -0.775621 q^{34} +(3.99941 + 9.24409i) q^{35} +(-0.116921 + 0.359846i) q^{36} +(-1.76193 + 1.95682i) q^{37} +(0.202811 + 1.92962i) q^{38} +(0.372114 + 3.54043i) q^{39} +(7.71507 - 8.56845i) q^{40} +(-0.843831 + 2.59705i) q^{41} +(-3.34683 - 0.387509i) q^{42} -4.52771 q^{43} +(-0.945532 - 0.825061i) q^{44} +(1.90346 - 3.29689i) q^{45} +(-4.79649 + 2.13554i) q^{46} +(-9.50390 + 2.02012i) q^{47} +(0.957987 + 2.94838i) q^{48} +(0.584647 + 6.97554i) q^{49} +(-9.77961 + 7.10530i) q^{50} +(0.407553 - 0.452633i) q^{51} +(-0.901286 - 1.00098i) q^{52} +(8.23278 - 3.66547i) q^{53} +(0.636717 + 1.10283i) q^{54} +(7.57965 + 10.0979i) q^{55} +(6.98149 - 3.93314i) q^{56} +(-1.23264 - 0.895569i) q^{57} +(13.2090 - 2.80765i) q^{58} +(1.33807 + 0.284417i) q^{59} +(0.150563 + 1.43251i) q^{60} +(-5.70294 - 2.53911i) q^{61} +(2.24943 + 6.92304i) q^{62} +(1.98475 - 1.74951i) q^{63} +(-7.18945 - 5.22344i) q^{64} +(6.77618 + 11.7367i) q^{65} +(-4.19298 + 0.506844i) q^{66} +(-3.02094 + 5.23243i) q^{67} +(-0.0240889 + 0.229191i) q^{68} +(1.27409 - 3.92124i) q^{69} +(-12.2396 + 3.83461i) q^{70} +(7.45523 - 5.41654i) q^{71} +(-2.76685 - 1.23188i) q^{72} +(-11.0706 - 2.35313i) q^{73} +(-2.24370 - 2.49188i) q^{74} +(0.992251 - 9.44064i) q^{75} +0.576488 q^{76} +(2.75351 + 8.33176i) q^{77} -4.53334 q^{78} +(0.181027 - 1.72236i) q^{79} +(7.89700 + 8.77050i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.17673 - 1.41437i) q^{82} +(-3.23967 + 2.35376i) q^{83} +(-0.218451 + 0.976932i) q^{84} +(0.716521 - 2.20523i) q^{85} +(0.602684 - 5.73416i) q^{86} +(-5.30222 + 9.18372i) q^{87} +(7.35932 - 6.83689i) q^{88} +(-2.84444 - 4.92671i) q^{89} +(3.92200 + 2.84950i) q^{90} +(1.86095 + 9.23301i) q^{91} +(0.482069 + 1.48366i) q^{92} +(-5.22208 - 2.32502i) q^{93} +(-1.29333 - 12.3052i) q^{94} +(-5.67360 - 1.20596i) q^{95} +(2.06349 - 0.438609i) q^{96} +(-8.18062 - 5.94357i) q^{97} +(-8.91206 - 0.188085i) q^{98} +(1.90744 - 2.71324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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