LMFDB - Embedded newform 403.2.f.c.94.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.13
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.497248 + 0.861259i) q^{2} +(1.12055 + 1.94084i) q^{3} +(0.505488 - 0.875531i) q^{4} +0.441402 q^{5} +(-1.11438 + 1.93016i) q^{6} +(0.363263 - 0.629189i) q^{7} +2.99441 q^{8} +(-1.01125 + 1.75153i) q^{9} +O(q^{10})$	\(q+(0.497248 + 0.861259i) q^{2} +(1.12055 + 1.94084i) q^{3} +(0.505488 - 0.875531i) q^{4} +0.441402 q^{5} +(-1.11438 + 1.93016i) q^{6} +(0.363263 - 0.629189i) q^{7} +2.99441 q^{8} +(-1.01125 + 1.75153i) q^{9} +(0.219486 + 0.380161i) q^{10} +(-0.802559 - 1.39007i) q^{11} +2.26569 q^{12} +(3.59969 + 0.205478i) q^{13} +0.722527 q^{14} +(0.494611 + 0.856691i) q^{15} +(0.477986 + 0.827897i) q^{16} +(-2.47057 + 4.27915i) q^{17} -2.01137 q^{18} +(-3.58054 + 6.20168i) q^{19} +(0.223123 - 0.386461i) q^{20} +1.62821 q^{21} +(0.798142 - 1.38242i) q^{22} +(-4.10557 - 7.11106i) q^{23} +(3.35537 + 5.81167i) q^{24} -4.80516 q^{25} +(1.61297 + 3.20244i) q^{26} +2.19067 q^{27} +(-0.367250 - 0.636096i) q^{28} +(-2.94094 - 5.09386i) q^{29} +(-0.491889 + 0.851977i) q^{30} +1.00000 q^{31} +(2.51905 - 4.36312i) q^{32} +(1.79861 - 3.11528i) q^{33} -4.91395 q^{34} +(0.160345 - 0.277725i) q^{35} +(1.02235 + 1.77076i) q^{36} +(-3.23407 - 5.60157i) q^{37} -7.12167 q^{38} +(3.63482 + 7.21669i) q^{39} +1.32174 q^{40} +(-1.04745 - 1.81423i) q^{41} +(0.809625 + 1.40231i) q^{42} +(-5.25879 + 9.10849i) q^{43} -1.62274 q^{44} +(-0.446367 + 0.773130i) q^{45} +(4.08298 - 7.07193i) q^{46} +2.12604 q^{47} +(-1.07121 + 1.85539i) q^{48} +(3.23608 + 5.60506i) q^{49} +(-2.38936 - 4.13849i) q^{50} -11.0736 q^{51} +(1.99950 - 3.04778i) q^{52} +4.51848 q^{53} +(1.08931 + 1.88674i) q^{54} +(-0.354251 - 0.613580i) q^{55} +(1.08776 - 1.88405i) q^{56} -16.0487 q^{57} +(2.92475 - 5.06582i) q^{58} +(2.53649 - 4.39332i) q^{59} +1.00008 q^{60} +(-5.97766 + 10.3536i) q^{61} +(0.497248 + 0.861259i) q^{62} +(0.734698 + 1.27253i) q^{63} +6.92232 q^{64} +(1.58891 + 0.0906982i) q^{65} +3.57742 q^{66} +(-5.31933 - 9.21336i) q^{67} +(2.49769 + 4.32613i) q^{68} +(9.20097 - 15.9366i) q^{69} +0.318924 q^{70} +(4.27591 - 7.40609i) q^{71} +(-3.02809 + 5.24481i) q^{72} +11.6073 q^{73} +(3.21627 - 5.57074i) q^{74} +(-5.38441 - 9.32607i) q^{75} +(3.61985 + 6.26976i) q^{76} -1.16616 q^{77} +(-4.40803 + 6.71901i) q^{78} +1.20558 q^{79} +(0.210984 + 0.365435i) q^{80} +(5.48850 + 9.50636i) q^{81} +(1.04168 - 1.80425i) q^{82} -3.17604 q^{83} +(0.823041 - 1.42555i) q^{84} +(-1.09051 + 1.88883i) q^{85} -10.4597 q^{86} +(6.59092 - 11.4158i) q^{87} +(-2.40319 - 4.16244i) q^{88} +(6.93878 + 12.0183i) q^{89} -0.887821 q^{90} +(1.43692 - 2.19024i) q^{91} -8.30128 q^{92} +(1.12055 + 1.94084i) q^{93} +(1.05717 + 1.83107i) q^{94} +(-1.58046 + 2.73743i) q^{95} +11.2909 q^{96} +(3.48002 - 6.02757i) q^{97} +(-3.21827 + 5.57421i) q^{98} +3.24635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.497248	+	0.861259i	0.351608	+	0.609002i	0.986531	−	0.163573i	$-0.0523018\pi$
$2$	0.497248	+	0.861259i	0.351608	+	0.609002i	−0.634924	+	0.772575i	$0.718968\pi$
$3$	1.12055	+	1.94084i	0.646948	+	1.12055i	0.983848	+	0.179006i	$0.0572882\pi$
$3$	1.12055	+	1.94084i	0.646948	+	1.12055i	−0.336900	+	0.941540i	$0.609378\pi$
$4$	0.505488	−	0.875531i	0.252744	−	0.437766i
$5$	0.441402			0.197401			0.0987004	−	0.995117i	$-0.468531\pi$
$5$	0.441402			0.197401			0.0987004	+	0.995117i	$0.468531\pi$
$6$	−1.11438	+	1.93016i	−0.454944	+	0.787985i
$7$	0.363263	−	0.629189i	0.137300	−	0.237811i	−0.789174	−	0.614170i	$-0.789491\pi$
$7$	0.363263	−	0.629189i	0.137300	−	0.237811i	0.926474	+	0.376359i	$0.122824\pi$
$8$	2.99441			1.05868
$9$	−1.01125	+	1.75153i	−0.337083	+	0.583845i
$10$	0.219486	+	0.380161i	0.0694076	+	0.120218i
$11$	−0.802559	−	1.39007i	−0.241981	−	0.419123i	0.719298	−	0.694702i	$-0.244464\pi$
$11$	−0.802559	−	1.39007i	−0.241981	−	0.419123i	−0.961278	+	0.275579i	$0.911130\pi$
$12$	2.26569			0.654049
$13$	3.59969	+	0.205478i	0.998375	+	0.0569893i
$13$	3.59969	+	0.205478i	0.998375	+	0.0569893i
$14$	0.722527			0.193103
$15$	0.494611	+	0.856691i	0.127708	+	0.221197i
$16$	0.477986	+	0.827897i	0.119497	+	0.206974i
$17$	−2.47057	+	4.27915i	−0.599202	+	1.03785i	0.393738	+	0.919223i	$0.371182\pi$
$17$	−2.47057	+	4.27915i	−0.599202	+	1.03785i	−0.992939	+	0.118625i	$0.962151\pi$
$18$	−2.01137			−0.474084
$19$	−3.58054	+	6.20168i	−0.821433	+	1.42276i	0.0831824	+	0.996534i	$0.473492\pi$
$19$	−3.58054	+	6.20168i	−0.821433	+	1.42276i	−0.904615	+	0.426229i	$0.859842\pi$
$20$	0.223123	−	0.386461i	0.0498919	−	0.0864153i
$21$	1.62821			0.355305
$22$	0.798142	−	1.38242i	0.170164	−	0.294733i
$23$	−4.10557	−	7.11106i	−0.856071	−	1.48276i	−0.875648	−	0.482950i	$-0.839565\pi$
$23$	−4.10557	−	7.11106i	−0.856071	−	1.48276i	0.0195764	−	0.999808i	$-0.493768\pi$
$24$	3.35537	+	5.81167i	0.684912	+	1.18630i
$25$	−4.80516			−0.961033
$26$	1.61297	+	3.20244i	0.316330	+	0.628050i
$27$	2.19067			0.421595
$28$	−0.367250	−	0.636096i	−0.0694037	−	0.120211i
$29$	−2.94094	−	5.09386i	−0.546119	−	0.945905i	−0.998536	−	0.0540988i	$-0.982771\pi$
$29$	−2.94094	−	5.09386i	−0.546119	−	0.945905i	0.452417	−	0.891807i	$-0.350562\pi$
$30$	−0.491889	+	0.851977i	−0.0898062	+	0.155549i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	2.51905	−	4.36312i	0.445309	−	0.771298i
$33$	1.79861	−	3.11528i	0.313098	−	0.542301i
$34$	−4.91395			−0.842735
$35$	0.160345	−	0.277725i	0.0271032	−	0.0469441i
$36$	1.02235	+	1.77076i	0.170392	+	0.295127i
$37$	−3.23407	−	5.60157i	−0.531678	−	0.920893i	−0.999316	−	0.0369729i	$-0.988228\pi$
$37$	−3.23407	−	5.60157i	−0.531678	−	0.920893i	0.467639	−	0.883920i	$-0.345105\pi$
$38$	−7.12167			−1.15529
$39$	3.63482	+	7.21669i	0.582037	+	1.15559i
$40$	1.32174			0.208985
$41$	−1.04745	−	1.81423i	−0.163584	−	0.283336i	0.772568	−	0.634933i	$-0.218972\pi$
$41$	−1.04745	−	1.81423i	−0.163584	−	0.283336i	−0.936152	+	0.351597i	$0.885639\pi$
$42$	0.809625	+	1.40231i	0.124928	+	0.216381i
$43$	−5.25879	+	9.10849i	−0.801958	+	1.38903i	0.116368	+	0.993206i	$0.462875\pi$
$43$	−5.25879	+	9.10849i	−0.801958	+	1.38903i	−0.918326	+	0.395825i	$0.870459\pi$
$44$	−1.62274			−0.244637
$45$	−0.446367	+	0.773130i	−0.0665405	+	0.115251i
$46$	4.08298	−	7.07193i	0.602002	−	1.04270i
$47$	2.12604			0.310115			0.155057	−	0.987905i	$-0.450444\pi$
$47$	2.12604			0.310115			0.155057	+	0.987905i	$0.450444\pi$
$48$	−1.07121	+	1.85539i	−0.154616	+	0.267803i
$49$	3.23608	+	5.60506i	0.462297	+	0.800722i
$50$	−2.38936	−	4.13849i	−0.337906	−	0.585271i
$51$	−11.0736			−1.55061
$52$	1.99950	−	3.04778i	0.277281	−	0.422651i
$53$	4.51848			0.620660			0.310330	−	0.950629i	$-0.399560\pi$
$53$	4.51848			0.620660			0.310330	+	0.950629i	$0.399560\pi$
$54$	1.08931	+	1.88674i	0.148236	+	0.256752i
$55$	−0.354251	−	0.613580i	−0.0477672	−	0.0827352i
$56$	1.08776	−	1.88405i	0.145357	−	0.251766i
$57$	−16.0487			−2.12570
$58$	2.92475	−	5.06582i	0.384039	−	0.665175i
$59$	2.53649	−	4.39332i	0.330222	−	0.571962i	−0.652333	−	0.757932i	$-0.726210\pi$
$59$	2.53649	−	4.39332i	0.330222	−	0.571962i	0.982555	+	0.185971i	$0.0595430\pi$
$60$	1.00008			0.129110
$61$	−5.97766	+	10.3536i	−0.765361	+	1.32564i	0.174694	+	0.984623i	$0.444106\pi$
$61$	−5.97766	+	10.3536i	−0.765361	+	1.32564i	−0.940055	+	0.341022i	$0.889227\pi$
$62$	0.497248	+	0.861259i	0.0631506	+	0.109380i
$63$	0.734698	+	1.27253i	0.0925632	+	0.160324i
$64$	6.92232			0.865290
$65$	1.58891	+	0.0906982i	0.197080	+	0.0112497i
$66$	3.57742			0.440350
$67$	−5.31933	−	9.21336i	−0.649860	−	1.12559i	−0.983156	−	0.182768i	$-0.941494\pi$
$67$	−5.31933	−	9.21336i	−0.649860	−	1.12559i	0.333296	−	0.942822i	$-0.391839\pi$
$68$	2.49769	+	4.32613i	0.302889	+	0.524620i
$69$	9.20097	−	15.9366i	1.10767	−	1.91854i
$70$	0.318924			0.0381188
$71$	4.27591	−	7.40609i	0.507457	−	0.878941i	−0.492506	−	0.870309i	$-0.663919\pi$
$71$	4.27591	−	7.40609i	0.507457	−	0.878941i	0.999963	−	0.00863193i	$-0.00274766\pi$
$72$	−3.02809	+	5.24481i	−0.356864	+	0.618106i
$73$	11.6073			1.35853			0.679266	−	0.733892i	$-0.262298\pi$
$73$	11.6073			1.35853			0.679266	+	0.733892i	$0.262298\pi$
$74$	3.21627	−	5.57074i	0.373884	−	0.647586i
$75$	−5.38441	−	9.32607i	−0.621738	−	1.07688i
$76$	3.61985	+	6.26976i	0.415225	+	0.719190i
$77$	−1.16616			−0.132896
$78$	−4.40803	+	6.71901i	−0.499111	+	0.760778i
$79$	1.20558			0.135639			0.0678193	−	0.997698i	$-0.478396\pi$
$79$	1.20558			0.135639			0.0678193	+	0.997698i	$0.478396\pi$
$80$	0.210984	+	0.365435i	0.0235887	+	0.0408569i
$81$	5.48850	+	9.50636i	0.609833	+	1.05626i
$82$	1.04168	−	1.80425i	0.115035	−	0.199246i
$83$	−3.17604			−0.348615			−0.174308	−	0.984691i	$-0.555769\pi$
$83$	−3.17604			−0.348615			−0.174308	+	0.984691i	$0.555769\pi$
$84$	0.823041	−	1.42555i	0.0898012	−	0.155540i
$85$	−1.09051	+	1.88883i	−0.118283	+	0.204872i
$86$	−10.4597			−1.12790
$87$	6.59092	−	11.4158i	0.706621	−	1.22390i
$88$	−2.40319	−	4.16244i	−0.256181	−	0.443718i
$89$	6.93878	+	12.0183i	0.735509	+	1.27394i	0.954500	+	0.298212i	$0.0963902\pi$
$89$	6.93878	+	12.0183i	0.735509	+	1.27394i	−0.218991	+	0.975727i	$0.570276\pi$
$90$	−0.887821			−0.0935845
$91$	1.43692	−	2.19024i	0.150630	−	0.229600i
$92$	−8.30128			−0.865468
$93$	1.12055	+	1.94084i	0.116195	+	0.201256i
$94$	1.05717	+	1.83107i	0.109039	+	0.188861i
$95$	−1.58046	+	2.73743i	−0.162152	+	0.280855i
$96$	11.2909			1.15237
$97$	3.48002	−	6.02757i	0.353342	−	0.612007i	−0.633490	−	0.773751i	$-0.718378\pi$
$97$	3.48002	−	6.02757i	0.353342	−	0.612007i	0.986833	+	0.161743i	$0.0517117\pi$
$98$	−3.21827	+	5.57421i	−0.325094	+	0.563080i
$99$	3.24635			0.326270
$100$	−2.42895	+	4.20707i	−0.242895	+	0.420707i
$101$	−8.13712	−	14.0939i	−0.809674	−	1.40240i	−0.913090	−	0.407758i	$-0.866311\pi$
$101$	−8.13712	−	14.0939i	−0.809674	−	1.40240i	0.103416	−	0.994638i	$-0.467023\pi$
$102$	−5.50631	−	9.53721i	−0.545206	−	0.944324i
$103$	−19.9443			−1.96517			−0.982587	−	0.185802i	$-0.940512\pi$
$103$	−19.9443			−1.96517			−0.982587	+	0.185802i	$0.940512\pi$
$104$	10.7789	+	0.615284i	1.05696	+	0.0603335i
$105$	0.718695			0.0701374
$106$	2.24680	+	3.89158i	0.218229	+	0.377984i
$107$	−4.62910	−	8.01784i	−0.447512	−	0.775114i	0.550711	−	0.834696i	$-0.314357\pi$
$107$	−4.62910	−	8.01784i	−0.447512	−	0.775114i	−0.998223	+	0.0595822i	$0.981023\pi$
$108$	1.10736	−	1.91800i	0.106556	−	0.184560i
$109$	20.2557			1.94015			0.970074	−	0.242811i	$-0.0780693\pi$
$109$	20.2557			1.94015			0.970074	+	0.242811i	$0.0780693\pi$
$110$	0.352301	−	0.610203i	0.0335906	−	0.0581806i
$111$	7.24785	−	12.5536i	0.687935	−	1.19154i
$112$	0.694538			0.0656277
$113$	4.74308	−	8.21525i	0.446191	−	0.772826i	−0.551943	−	0.833882i	$-0.686113\pi$
$113$	4.74308	−	8.21525i	0.446191	−	0.772826i	0.998134	+	0.0610557i	$0.0194467\pi$
$114$	−7.98017	−	13.8221i	−0.747411	−	1.29455i
$115$	−1.81221	−	3.13883i	−0.168989	−	0.292698i
$116$	−5.94644			−0.552113
$117$	−4.00009	+	6.09720i	−0.369808	+	0.563686i
$118$	5.04505			0.464435
$119$	1.79493	+	3.10891i	0.164541	+	0.284994i
$120$	1.48107	+	2.56528i	0.135202	+	0.234177i
$121$	4.21180	−	7.29505i	0.382891	−	0.663186i
$122$	−11.8895			−1.07643
$123$	2.34743	−	4.06587i	0.211661	−	0.366607i
$124$	0.505488	−	0.875531i	0.0453942	−	0.0786250i
$125$	−4.32802			−0.387109
$126$	−0.730654	+	1.26553i	−0.0650919	+	0.112742i
$127$	7.13395	+	12.3564i	0.633036	+	1.09645i	0.986928	+	0.161164i	$0.0515248\pi$
$127$	7.13395	+	12.3564i	0.633036	+	1.09645i	−0.353892	+	0.935286i	$0.615142\pi$
$128$	−1.59599	−	2.76433i	−0.141067	−	0.244335i
$129$	−23.5709			−2.07530
$130$	0.711968	+	1.41356i	0.0624437	+	0.123978i
$131$	−12.0054			−1.04892			−0.524458	−	0.851436i	$-0.675732\pi$
$131$	−12.0054			−1.04892			−0.524458	+	0.851436i	$0.675732\pi$
$132$	−1.81835	−	3.14948i	−0.158267	−	0.274127i
$133$	2.60135	+	4.50568i	0.225566	+	0.390692i
$134$	5.29006	−	9.16265i	0.456991	−	0.791532i
$135$	0.966967			0.0832232
$136$	−7.39789	+	12.8135i	−0.634364	+	1.09875i
$137$	−9.09329	+	15.7500i	−0.776892	+	1.34562i	0.156833	+	0.987625i	$0.449872\pi$
$137$	−9.09329	+	15.7500i	−0.776892	+	1.34562i	−0.933725	+	0.357991i	$0.883462\pi$
$138$	18.3007			1.55786
$139$	−4.19933	+	7.27345i	−0.356183	+	0.616926i	−0.987320	−	0.158745i	$-0.949255\pi$
$139$	−4.19933	+	7.27345i	−0.356183	+	0.616926i	0.631137	+	0.775671i	$0.282589\pi$
$140$	−0.162105	−	0.280774i	−0.0137004	−	0.0237297i
$141$	2.38233	+	4.12631i	0.200628	+	0.347498i
$142$	8.50475			0.713703
$143$	−2.60334	−	5.16874i	−0.217702	−	0.432232i
$144$	−1.93345			−0.161121
$145$	−1.29814	−	2.24844i	−0.107804	−	0.186722i
$146$	5.77171	+	9.99690i	0.477670	+	0.827349i
$147$	−7.25236	+	12.5615i	−0.598164	+	1.03605i
$148$	−6.53914			−0.537514
$149$	−1.55221	+	2.68850i	−0.127162	+	0.220251i	−0.922576	−	0.385816i	$-0.873920\pi$
$149$	−1.55221	+	2.68850i	−0.127162	+	0.220251i	0.795414	+	0.606066i	$0.207253\pi$
$150$	5.35478	−	9.27475i	0.437216	−	0.757280i
$151$	−1.72507			−0.140384			−0.0701919	−	0.997534i	$-0.522361\pi$
$151$	−1.72507			−0.140384			−0.0701919	+	0.997534i	$0.522361\pi$
$152$	−10.7216	+	18.5704i	−0.869636	+	1.50625i
$153$	−4.99673	−	8.65458i	−0.403961	−	0.699681i
$154$	−0.579870	−	1.00436i	−0.0467273	−	0.0809340i
$155$	0.441402			0.0354542
$156$	8.15580	+	0.465550i	0.652986	+	0.0372738i
$157$	2.74711			0.219244			0.109622	−	0.993973i	$-0.465036\pi$
$157$	2.74711			0.219244			0.109622	+	0.993973i	$0.465036\pi$
$158$	0.599474	+	1.03832i	0.0476916	+	0.0826042i
$159$	5.06316	+	8.76966i	0.401535	+	0.695479i
$160$	1.11191	−	1.92589i	0.0879044	−	0.152255i
$161$	−5.96560			−0.470156
$162$	−5.45829	+	9.45404i	−0.428844	+	0.742779i
$163$	−1.26432	+	2.18986i	−0.0990289	+	0.171523i	−0.911283	−	0.411781i	$-0.864907\pi$
$163$	−1.26432	+	2.18986i	−0.0990289	+	0.171523i	0.812254	+	0.583304i	$0.198240\pi$
$164$	−2.11789			−0.165380
$165$	0.793909	−	1.37509i	0.0618057	−	0.107051i
$166$	−1.57928	−	2.73539i	−0.122576	−	0.212308i
$167$	3.36451	+	5.82750i	0.260354	+	0.450946i	0.966336	−	0.257284i	$-0.0828275\pi$
$167$	3.36451	+	5.82750i	0.260354	+	0.450946i	−0.705982	+	0.708230i	$0.749494\pi$
$168$	4.87552			0.376155
$169$	12.9156	+	1.47931i	0.993504	+	0.113793i
$170$	−2.16902			−0.166357
$171$	−7.24164	−	12.5429i	−0.553782	−	0.959179i
$172$	5.31651	+	9.20847i	0.405380	+	0.702139i
$173$	8.05498	−	13.9516i	0.612409	−	1.06072i	−0.378424	−	0.925632i	$-0.623534\pi$
$173$	8.05498	−	13.9516i	0.612409	−	1.06072i	0.990833	−	0.135091i	$-0.0431328\pi$
$174$	13.1093			0.993813
$175$	−1.74554	+	3.02336i	−0.131950	+	0.228544i
$176$	0.767224	−	1.32887i	0.0578317	−	0.100167i
$177$	11.3690			0.854546
$178$	−6.90059	+	11.9522i	−0.517221	+	0.895853i
$179$	2.51609	+	4.35799i	0.188061	+	0.325731i	0.944604	−	0.328213i	$-0.106446\pi$
$179$	2.51609	+	4.35799i	0.188061	+	0.325731i	−0.756543	+	0.653944i	$0.773113\pi$
$180$	0.451267	+	0.781617i	0.0336354	+	0.0582583i
$181$	−15.6864			−1.16596			−0.582979	−	0.812487i	$-0.698113\pi$
$181$	−15.6864			−1.16596			−0.582979	+	0.812487i	$0.698113\pi$
$182$	2.60087	+	0.148463i	0.192790	+	0.0110048i
$183$	−26.7930			−1.98060
$184$	−12.2938	−	21.2934i	−0.906307	−	1.56977i
$185$	−1.42752	−	2.47254i	−0.104954	−	0.181785i
$186$	−1.11438	+	1.93016i	−0.0817103	+	0.141526i
$187$	7.93111			0.579981
$188$	1.07469	−	1.86142i	0.0783797	−	0.135758i
$189$	0.795790	−	1.37835i	0.0578852	−	0.100260i
$190$	−3.14352			−0.228055
$191$	−4.18209	+	7.24360i	−0.302606	+	0.524128i	−0.976725	−	0.214494i	$-0.931190\pi$
$191$	−4.18209	+	7.24360i	−0.302606	+	0.524128i	0.674120	+	0.738622i	$0.264523\pi$
$192$	7.75678	+	13.4351i	0.559797	+	0.969597i
$193$	3.84809	+	6.66508i	0.276991	+	0.479763i	0.970636	−	0.240555i	$-0.0773293\pi$
$193$	3.84809	+	6.66508i	0.276991	+	0.479763i	−0.693644	+	0.720318i	$0.743996\pi$
$194$	6.92173			0.496952
$195$	1.60442	+	3.18546i	0.114895	+	0.228115i
$196$	6.54320			0.467372
$197$	4.82433	+	8.35598i	0.343719	+	0.595339i	0.985120	−	0.171867i	$-0.0549798\pi$
$197$	4.82433	+	8.35598i	0.343719	+	0.595339i	−0.641401	+	0.767206i	$0.721646\pi$
$198$	1.61424	+	2.79595i	0.114719	+	0.198699i
$199$	−3.76133	+	6.51482i	−0.266634	+	0.461823i	−0.967990	−	0.250987i	$-0.919245\pi$
$199$	−3.76133	+	6.51482i	−0.266634	+	0.461823i	0.701357	+	0.712811i	$0.252578\pi$
$200$	−14.3886			−1.01743
$201$	11.9211	−	20.6480i	0.840851	−	1.45640i
$202$	8.09234	−	14.0163i	0.569375	−	0.986186i
$203$	−4.27333			−0.299929
$204$	−5.59756	+	9.69525i	−0.391907	+	0.678803i
$205$	−0.462346	−	0.800806i	−0.0322916	−	0.0559307i
$206$	−9.91729	−	17.1772i	−0.690970	−	1.19680i
$207$	16.6070			1.15427
$208$	1.55049	+	3.07839i	0.107507	+	0.213448i
$209$	11.4944			0.795083
$210$	0.357370	+	0.618983i	0.0246609	+	0.0427139i
$211$	−2.26389	−	3.92118i	−0.155853	−	0.269945i	0.777516	−	0.628863i	$-0.216479\pi$
$211$	−2.26389	−	3.92118i	−0.155853	−	0.269945i	−0.933369	+	0.358918i	$0.883146\pi$
$212$	2.28404	−	3.95607i	0.156868	−	0.271704i
$213$	19.1654			1.31319
$214$	4.60362	−	7.97371i	0.314697	−	0.545072i
$215$	−2.32124	+	4.02050i	−0.158307	+	0.274196i
$216$	6.55976			0.446335
$217$	0.363263	−	0.629189i	0.0246599	−	0.0427121i
$218$	10.0721	+	17.4454i	0.682171	+	1.18155i
$219$	13.0065	+	22.5280i	0.878899	+	1.52230i
$220$	−0.716279			−0.0482915
$221$	−9.77257	+	14.8960i	−0.657374	+	1.00201i
$222$	14.4159			0.967533
$223$	−4.07196	−	7.05284i	−0.272678	−	0.472293i	0.696868	−	0.717199i	$-0.254576\pi$
$223$	−4.07196	−	7.05284i	−0.272678	−	0.472293i	−0.969547	+	0.244906i	$0.921243\pi$
$224$	−1.83015	−	3.16992i	−0.122282	−	0.211799i
$225$	4.85922	−	8.41641i	0.323948	−	0.561094i
$226$	9.43395			0.627537
$227$	3.58384	−	6.20739i	0.237868	−	0.411999i	−0.722235	−	0.691648i	$-0.756885\pi$
$227$	3.58384	−	6.20739i	0.237868	−	0.411999i	0.960102	+	0.279649i	$0.0902182\pi$
$228$	−8.11241	+	14.0511i	−0.537257	+	0.930557i
$229$	27.6178			1.82504			0.912519	−	0.409035i	$-0.134134\pi$
$229$	27.6178			1.82504			0.912519	+	0.409035i	$0.134134\pi$
$230$	1.80223	−	3.12156i	0.118836	−	0.205830i
$231$	−1.30673	−	2.26333i	−0.0859768	−	0.148916i
$232$	−8.80637	−	15.2531i	−0.578166	−	1.00141i
$233$	−21.6019			−1.41519			−0.707594	−	0.706619i	$-0.750219\pi$
$233$	−21.6019			−1.41519			−0.707594	+	0.706619i	$0.750219\pi$
$234$	−7.24030	−	0.413291i	−0.473313	−	0.0270177i
$235$	0.938438			0.0612169
$236$	−2.56433	−	4.44155i	−0.166924	−	0.289120i
$237$	1.35091	+	2.33985i	0.0877511	+	0.151989i
$238$	−1.78505	+	3.09180i	−0.115708	+	0.200412i
$239$	0.0432516			0.00279772			0.00139886	−	0.999999i	$-0.499555\pi$
$239$	0.0432516			0.00279772			0.00139886	+	0.999999i	$0.499555\pi$
$240$	−0.472835	+	0.818974i	−0.0305213	+	0.0528645i
$241$	−5.99148	+	10.3776i	−0.385945	+	0.668477i	−0.991900	−	0.127022i	$-0.959458\pi$
$241$	−5.99148	+	10.3776i	−0.385945	+	0.668477i	0.605954	+	0.795499i	$0.292791\pi$
$242$	8.37724			0.538509
$243$	−9.01423	+	15.6131i	−0.578263	+	1.00158i
$244$	6.04328	+	10.4673i	0.386881	+	0.670098i
$245$	1.42841	+	2.47408i	0.0912578	+	0.158063i
$246$	4.66902			0.297686
$247$	−14.1632	+	21.5884i	−0.901180	+	1.37364i
$248$	2.99441			0.190145
$249$	−3.55890	−	6.16419i	−0.225536	−	0.390640i
$250$	−2.15210	−	3.72754i	−0.136111	−	0.235751i
$251$	0.235489	−	0.407879i	0.0148639	−	0.0257451i	−0.858498	−	0.512817i	$-0.828602\pi$
$251$	0.235489	−	0.407879i	0.0148639	−	0.0257451i	0.873362	+	0.487072i	$0.161935\pi$
$252$	1.48552			0.0935793
$253$	−6.58993	+	11.4141i	−0.414305	+	0.717598i
$254$	−7.09469	+	12.2884i	−0.445161	+	0.771041i
$255$	−4.88789			−0.306091
$256$	8.50952	−	14.7389i	0.531845	−	0.921183i
$257$	9.94392	+	17.2234i	0.620284	+	1.07436i	0.989433	+	0.144994i	$0.0463162\pi$
$257$	9.94392	+	17.2234i	0.620284	+	1.07436i	−0.369148	+	0.929371i	$0.620350\pi$
$258$	−11.7206	−	20.3006i	−0.729691	−	1.26386i
$259$	−4.69926			−0.291998
$260$	0.882584	−	1.34529i	0.0547356	−	0.0834316i
$261$	11.8961			0.736349
$262$	−5.96966	−	10.3398i	−0.368807	−	0.638793i
$263$	2.11743	+	3.66750i	0.130566	+	0.226148i	0.923895	−	0.382646i	$-0.124987\pi$
$263$	2.11743	+	3.66750i	0.130566	+	0.226148i	−0.793329	+	0.608794i	$0.791654\pi$
$264$	5.38577	−	9.32842i	0.331471	−	0.574124i
$265$	1.99446			0.122519
$266$	−2.58704	+	4.48088i	−0.158621	+	0.274740i
$267$	−15.5504	+	26.9342i	−0.951672	+	1.64834i
$268$	−10.7554			−0.656993
$269$	−9.43015	+	16.3335i	−0.574966	+	0.995871i	0.421079	+	0.907024i	$0.361651\pi$
$269$	−9.43015	+	16.3335i	−0.574966	+	0.995871i	−0.996045	+	0.0888467i	$0.971682\pi$
$270$	0.480822	+	0.832809i	0.0292619	+	0.0506831i
$271$	−3.23157	−	5.59724i	−0.196304	−	0.340008i	0.751023	−	0.660276i	$-0.229560\pi$
$271$	−3.23157	−	5.59724i	−0.196304	−	0.340008i	−0.947327	+	0.320268i	$0.896227\pi$
$272$	−4.72360			−0.286410
$273$	5.86106	+	0.334561i	0.354727	+	0.0202486i
$274$	−18.0865			−1.09264
$275$	3.85643	+	6.67953i	0.232551	+	0.402791i
$276$	−9.30197	−	16.1115i	−0.559913	−	0.969797i
$277$	−0.133618	+	0.231434i	−0.00802835	+	0.0139055i	−0.870012	−	0.493031i	$-0.835889\pi$
$277$	−0.133618	+	0.231434i	−0.00802835	+	0.0139055i	0.861983	+	0.506937i	$0.169222\pi$
$278$	−8.35244			−0.500946
$279$	−1.01125	+	1.75153i	−0.0605419	+	0.104862i
$280$	0.480137	−	0.831622i	0.0286937	−	0.0496989i
$281$	26.9831			1.60968			0.804838	−	0.593495i	$-0.202252\pi$
$281$	26.9831			1.60968			0.804838	+	0.593495i	$0.202252\pi$
$282$	−2.36922	+	4.10360i	−0.141085	+	0.244366i
$283$	16.2521	+	28.1495i	0.966088	+	1.67331i	0.706663	+	0.707551i	$0.250200\pi$
$283$	16.2521	+	28.1495i	0.966088	+	1.67331i	0.259425	+	0.965763i	$0.416467\pi$
$284$	−4.32284	−	7.48738i	−0.256514	−	0.444294i
$285$	−7.08390			−0.419614
$286$	3.15712	−	4.81229i	0.186685	−	0.284557i
$287$	−1.52200			−0.0898406
$288$	5.09477	+	8.82441i	0.300212	+	0.519983i
$289$	−3.70744	−	6.42148i	−0.218085	−	0.377734i
$290$	1.29099	−	2.23606i	0.0758096	−	0.131306i
$291$	15.5981			0.914377
$292$	5.86736	−	10.1626i	0.343361	−	0.594719i
$293$	0.874253	−	1.51425i	0.0510744	−	0.0884634i	−0.839358	−	0.543579i	$-0.817069\pi$
$293$	0.874253	−	1.51425i	0.0510744	−	0.0884634i	0.890432	+	0.455116i	$0.150402\pi$
$294$	−14.4249			−0.841277
$295$	1.11961	−	1.93922i	0.0651861	−	0.112906i
$296$	−9.68411	−	16.7734i	−0.562878	−	0.974933i
$297$	−1.75814	−	3.04519i	−0.102018	−	0.176700i
$298$	−3.08733			−0.178844
$299$	−13.3176	−	26.4412i	−0.770179	−	1.52914i
$300$	−10.8870			−0.628563
$301$	3.82064	+	6.61755i	0.220218	+	0.381429i
$302$	−0.857786	−	1.48573i	−0.0493600	−	0.0854941i
$303$	18.2360	−	31.5858i	1.04763	−	1.81455i
$304$	−6.84580			−0.392634
$305$	−2.63855	+	4.57010i	−0.151083	+	0.261683i
$306$	4.96923	−	8.60695i	0.284072	−	0.492027i
$307$	−15.0111			−0.856729			−0.428364	−	0.903606i	$-0.640910\pi$
$307$	−15.0111			−0.856729			−0.428364	+	0.903606i	$0.640910\pi$
$308$	−0.589479	+	1.02101i	−0.0335887	+	0.0581773i
$309$	−22.3486	−	38.7088i	−1.27137	−	2.20207i
$310$	0.219486	+	0.380161i	0.0124660	+	0.0215917i
$311$	6.54332			0.371038			0.185519	−	0.982641i	$-0.440603\pi$
$311$	6.54332			0.371038			0.185519	+	0.982641i	$0.440603\pi$
$312$	10.8841	+	21.6097i	0.616193	+	1.22341i
$313$	9.53783			0.539110			0.269555	−	0.962985i	$-0.413123\pi$
$313$	9.53783			0.539110			0.269555	+	0.962985i	$0.413123\pi$
$314$	1.36600	+	2.36598i	0.0770877	+	0.133520i
$315$	0.324297	+	0.561699i	0.0182721	+	0.0316481i
$316$	0.609408	−	1.05553i	0.0342819	−	0.0593779i
$317$	−8.21601			−0.461457			−0.230729	−	0.973018i	$-0.574111\pi$
$317$	−8.21601			−0.461457			−0.230729	+	0.973018i	$0.574111\pi$
$318$	−5.03530	+	8.72139i	−0.282365	+	0.489071i
$319$	−4.72055	+	8.17624i	−0.264300	+	0.457781i
$320$	3.05552			0.170809
$321$	10.3742	−	17.9687i	0.579034	−	1.00292i
$322$	−2.96639	−	5.13793i	−0.165310	−	0.286326i
$323$	−17.6920	−	30.6434i	−0.984408	−	1.70504i
$324$	11.0975			0.616527
$325$	−17.2971	−	0.987355i	−0.959471	−	0.0547686i
$326$	−2.51472			−0.139277
$327$	22.6975	+	39.3132i	1.25517	+	2.17403i
$328$	−3.13649	−	5.43256i	−0.173184	−	0.299963i
$329$	0.772311	−	1.33768i	0.0425789	−	0.0737488i
$330$	1.57908			0.0869255
$331$	6.02594	−	10.4372i	0.331216	−	0.573682i	−0.651535	−	0.758619i	$-0.725875\pi$
$331$	6.02594	−	10.4372i	0.331216	−	0.573682i	0.982750	+	0.184936i	$0.0592079\pi$
$332$	−1.60545	+	2.78072i	−0.0881105	+	0.152612i
$333$	13.0818			0.716878
$334$	−3.34599	+	5.79543i	−0.183085	+	0.317112i
$335$	−2.34796	−	4.06679i	−0.128283	−	0.222192i
$336$	0.778262	+	1.34799i	0.0424577	+	0.0735389i
$337$	5.45300			0.297044			0.148522	−	0.988909i	$-0.452548\pi$
$337$	5.45300			0.297044			0.148522	+	0.988909i	$0.452548\pi$
$338$	5.14817	+	11.8592i	0.280023	+	0.645057i
$339$	21.2594			1.15465
$340$	1.10248	+	1.90956i	0.0597906	+	0.103560i
$341$	−0.802559	−	1.39007i	−0.0434610	−	0.0752767i
$342$	7.20179	−	12.4739i	0.389428	−	0.674509i
$343$	9.78786			0.528495
$344$	−15.7469	+	27.2745i	−0.849018	+	1.47054i
$345$	4.06132	−	7.03442i	0.218654	−	0.378720i
$346$	16.0213			0.861311
$347$	−6.04784	+	10.4752i	−0.324665	+	0.562337i	−0.981445	−	0.191746i	$-0.938585\pi$
$347$	−6.04784	+	10.4752i	−0.324665	+	0.562337i	0.656779	+	0.754083i	$0.271918\pi$
$348$	−6.66327	−	11.5411i	−0.357189	−	0.618669i
$349$	0.646467	+	1.11971i	0.0346046	+	0.0599369i	0.882809	−	0.469732i	$-0.155649\pi$
$349$	0.646467	+	1.11971i	0.0346046	+	0.0599369i	−0.848204	+	0.529669i	$0.822316\pi$
$350$	−3.47186			−0.185579
$351$	7.88575	+	0.450135i	0.420910	+	0.0240264i
$352$	−8.08674			−0.431025
$353$	−14.3913	−	24.9265i	−0.765971	−	1.32670i	−0.939731	−	0.341913i	$-0.888925\pi$
$353$	−14.3913	−	24.9265i	−0.765971	−	1.32670i	0.173760	−	0.984788i	$-0.444408\pi$
$354$	5.65322	+	9.79166i	0.300465	+	0.520421i
$355$	1.88739	−	3.26906i	0.100172	−	0.173504i
$356$	14.0299			0.743582
$357$	−4.02261	+	6.96736i	−0.212899	+	0.368752i
$358$	−2.50224	+	4.33401i	−0.132247	+	0.229059i
$359$	21.3737			1.12806			0.564031	−	0.825754i	$-0.309250\pi$
$359$	21.3737			1.12806			0.564031	+	0.825754i	$0.309250\pi$
$360$	−1.33660	+	2.31507i	−0.0704452	+	0.122015i
$361$	−16.1406	−	27.9563i	−0.849504	−	1.47138i
$362$	−7.80002	−	13.5100i	−0.409960	−	0.710072i
$363$	18.8781			0.990841
$364$	−1.19128	−	2.36521i	−0.0624402	−	0.123971i
$365$	5.12348			0.268175
$366$	−13.3228	−	23.0757i	−0.696392	−	1.20619i
$367$	−4.21772	−	7.30531i	−0.220163	−	0.381334i	0.734694	−	0.678398i	$-0.237326\pi$
$367$	−4.21772	−	7.30531i	−0.220163	−	0.381334i	−0.954857	+	0.297065i	$0.903992\pi$
$368$	3.92482	−	6.79798i	0.204595	−	0.354369i
$369$	4.23693			0.220566
$370$	1.41967	−	2.45894i	0.0738050	−	0.127834i
$371$	1.64139	−	2.84298i	0.0852169	−	0.147600i
$372$	2.26569			0.117471
$373$	9.97172	−	17.2715i	0.516316	−	0.894286i	−0.483505	−	0.875342i	$-0.660636\pi$
$373$	9.97172	−	17.2715i	0.516316	−	0.894286i	0.999821	−	0.0189437i	$-0.00603033\pi$
$374$	3.94373	+	6.83075i	0.203926	+	0.353209i
$375$	−4.84974	−	8.40000i	−0.250440	−	0.433774i
$376$	6.36623			0.328313
$377$	−9.53980	−	18.9406i	−0.491325	−	0.975491i
$378$	1.58282			0.0814115
$379$	13.5195	+	23.4165i	0.694452	+	1.20283i	0.970365	+	0.241644i	$0.0776865\pi$
$379$	13.5195	+	23.4165i	0.694452	+	1.20283i	−0.275913	+	0.961183i	$0.588980\pi$
$380$	1.59781	+	2.76748i	0.0819657	+	0.141969i
$381$	−15.9879	+	27.6918i	−0.819083	+	1.41869i
$382$	−8.31815			−0.425594
$383$	−17.1580	+	29.7185i	−0.876732	+	1.51854i	−0.0218249	+	0.999762i	$0.506948\pi$
$383$	−17.1580	+	29.7185i	−0.876732	+	1.51854i	−0.854907	+	0.518782i	$0.826386\pi$
$384$	3.57676	−	6.19513i	0.182526	−	0.316144i
$385$	−0.514744			−0.0262338
$386$	−3.82691	+	6.62840i	−0.194785	+	0.337377i
$387$	−10.6359	−	18.4219i	−0.540653	−	0.936438i
$388$	−3.51822	−	6.09373i	−0.178610	−	0.309362i
$389$	13.8586			0.702657			0.351329	−	0.936252i	$-0.385730\pi$
$389$	13.8586			0.702657			0.351329	+	0.936252i	$0.385730\pi$
$390$	−1.94571	+	2.96578i	−0.0985249	+	0.150178i
$391$	40.5724			2.05184
$392$	9.69014	+	16.7838i	0.489426	+	0.847711i
$393$	−13.4526	−	23.3006i	−0.678594	−	1.17536i
$394$	−4.79778	+	8.31000i	−0.241709	+	0.418652i
$395$	0.532146			0.0267752
$396$	1.64099	−	2.84228i	0.0824629	−	0.142830i
$397$	−10.1006	+	17.4948i	−0.506937	+	0.878040i	0.493031	+	0.870012i	$0.335889\pi$
$397$	−10.1006	+	17.4948i	−0.506937	+	0.878040i	−0.999968	+	0.00802862i	$0.997444\pi$
$398$	−7.48126			−0.375002
$399$	−5.82988	+	10.0976i	−0.291859	+	0.505514i
$400$	−2.29680	−	3.97818i	−0.114840	−	0.198909i
$401$	−17.3680	−	30.0822i	−0.867315	−	1.50223i	−0.864730	−	0.502237i	$-0.832511\pi$
$401$	−17.3680	−	30.0822i	−0.867315	−	1.50223i	−0.00258477	−	0.999997i	$-0.500823\pi$
$402$	23.7110			1.18260
$403$	3.59969	+	0.205478i	0.179313	+	0.0102356i
$404$	−16.4529			−0.818561
$405$	2.42263	+	4.19612i	0.120382	+	0.208507i
$406$	−2.12491	−	3.68045i	−0.105457	−	0.182658i
$407$	−5.19106	+	8.99118i	−0.257311	+	0.445676i
$408$	−33.1587			−1.64160
$409$	11.9849	−	20.7584i	0.592614	−	1.02644i	−0.401265	−	0.915962i	$-0.631429\pi$
$409$	11.9849	−	20.7584i	0.592614	−	1.02644i	0.993879	−	0.110476i	$-0.0352374\pi$
$410$	0.459801	−	0.796399i	0.0227080	−	0.0393313i
$411$	−40.7578			−2.01043
$412$	−10.0816	+	17.4619i	−0.496686	+	0.860286i
$413$	−1.84282	−	3.19186i	−0.0906793	−	0.157061i
$414$	8.25782	+	14.3030i	0.405849	+	0.702952i
$415$	−1.40191			−0.0688170
$416$	9.96433	−	15.1883i	0.488541	−	0.744667i
$417$	−18.8222			−0.921726
$418$	5.71556	+	9.89964i	0.279557	+	0.484207i
$419$	−7.88219	−	13.6524i	−0.385070	−	0.666961i	0.606709	−	0.794924i	$-0.292489\pi$
$419$	−7.88219	−	13.6524i	−0.385070	−	0.666961i	−0.991779	+	0.127963i	$0.959156\pi$
$420$	0.363292	−	0.629240i	0.0177268	−	0.0307038i
$421$	27.5507			1.34274			0.671370	−	0.741123i	$-0.265706\pi$
$421$	27.5507			1.34274			0.671370	+	0.741123i	$0.265706\pi$
$422$	2.25143	−	3.89960i	0.109598	−	0.189830i
$423$	−2.14996	+	3.72383i	−0.104534	+	0.181059i
$424$	13.5302			0.657082
$425$	11.8715	−	20.5620i	0.575852	−	0.997406i
$426$	9.52997	+	16.5064i	0.461728	+	0.799737i
$427$	4.34292	+	7.52216i	0.210169	+	0.364023i
$428$	−9.35983			−0.452424
$429$	7.11456	−	10.8445i	0.343494	−	0.523576i
$430$	−4.61693			−0.222648
$431$	3.45636	+	5.98660i	0.166487	+	0.288364i	0.937182	−	0.348840i	$-0.113424\pi$
$431$	3.45636	+	5.98660i	0.166487	+	0.288364i	−0.770695	+	0.637204i	$0.780091\pi$
$432$	1.04711	+	1.81365i	0.0503792	+	0.0872593i
$433$	2.00535	−	3.47336i	0.0963709	−	0.166919i	−0.813809	−	0.581132i	$-0.802610\pi$
$433$	2.00535	−	3.47336i	0.0963709	−	0.166919i	0.910180	+	0.414213i	$0.135943\pi$
$434$	0.722527			0.0346824
$435$	2.90924	−	5.03896i	0.139487	−	0.241599i
$436$	10.2390	−	17.7345i	0.490361	−	0.849330i
$437$	58.8007			2.81282
$438$	−12.9349	+	22.4040i	−0.618055	+	1.07050i
$439$	9.49657	+	16.4485i	0.453246	+	0.785046i	0.998585	−	0.0531698i	$-0.0169325\pi$
$439$	9.49657	+	16.4485i	0.453246	+	0.785046i	−0.545339	+	0.838215i	$0.683599\pi$
$440$	−1.06077	−	1.83731i	−0.0505703	−	0.0875902i
$441$	−13.0899			−0.623330
$442$	−17.6887	−	1.00971i	−0.841366	−	0.0480269i
$443$	−16.2469			−0.771912			−0.385956	−	0.922517i	$-0.626128\pi$
$443$	−16.2469			−0.771912			−0.385956	+	0.922517i	$0.626128\pi$
$444$	−7.32741	−	12.6914i	−0.347743	−	0.602309i
$445$	3.06279	+	5.30490i	0.145190	+	0.251477i
$446$	4.04955	−	7.01402i	0.191752	−	0.332124i
$447$	−6.95728			−0.329068
$448$	2.51462	−	4.35545i	0.118805	−	0.205776i
$449$	6.57676	−	11.3913i	0.310377	−	0.537588i	−0.668067	−	0.744101i	$-0.732878\pi$
$449$	6.57676	−	11.3913i	0.310377	−	0.537588i	0.978444	+	0.206513i	$0.0662115\pi$
$450$	9.66495			0.455610
$451$	−1.68128	+	2.91206i	−0.0791683	+	0.137124i
$452$	−4.79514	−	8.30543i	−0.225545	−	0.390655i
$453$	−1.93302	−	3.34808i	−0.0908210	−	0.157307i
$454$	7.12823			0.334544
$455$	0.634258	−	0.966778i	0.0297345	−	0.0453232i
$456$	−48.0562			−2.25044
$457$	−7.91955	−	13.7171i	−0.370461	−	0.641657i	0.619175	−	0.785253i	$-0.287467\pi$
$457$	−7.91955	−	13.7171i	−0.370461	−	0.641657i	−0.989636	+	0.143595i	$0.954134\pi$
$458$	13.7329	+	23.7861i	0.641697	+	1.11145i
$459$	−5.41221	+	9.37423i	−0.252620	+	0.437552i
$460$	−3.66420			−0.170844
$461$	−5.27021	+	9.12827i	−0.245458	+	0.425146i	−0.962260	−	0.272131i	$-0.912272\pi$
$461$	−5.27021	+	9.12827i	−0.245458	+	0.425146i	0.716802	+	0.697277i	$0.245605\pi$
$462$	1.29954	−	2.25087i	0.0604602	−	0.104720i
$463$	4.75587			0.221024			0.110512	−	0.993875i	$-0.464751\pi$
$463$	4.75587			0.221024			0.110512	+	0.993875i	$0.464751\pi$
$464$	2.81146	−	4.86959i	0.130519	−	0.226065i
$465$	0.494611	+	0.856691i	0.0229370	+	0.0397281i
$466$	−10.7415	−	18.6048i	−0.497591	−	0.861853i
$467$	−27.9109			−1.29156			−0.645781	−	0.763523i	$-0.723468\pi$
$467$	−27.9109			−1.29156			−0.645781	+	0.763523i	$0.723468\pi$
$468$	3.31629	+	6.58426i	0.153296	+	0.304358i
$469$	−7.72926			−0.356904
$470$	0.466636	+	0.808238i	0.0215243	+	0.0372812i
$471$	3.07827	+	5.33172i	0.141839	+	0.245673i
$472$	7.59527	−	13.1554i	0.349600	−	0.605526i
$473$	16.8819			0.776233
$474$	−1.34348	+	2.32697i	−0.0617079	+	0.106881i
$475$	17.2051	−	29.8001i	0.789424	−	1.36732i
$476$	3.62927			0.166347
$477$	−4.56930	+	7.91427i	−0.209214	+	0.362369i
$478$	0.0215068	+	0.0372509i	0.000983698	+	0.00170382i
$479$	6.74022	+	11.6744i	0.307969	+	0.533417i	0.977918	−	0.208990i	$-0.0670175\pi$
$479$	6.74022	+	11.6744i	0.307969	+	0.533417i	−0.669949	+	0.742407i	$0.733684\pi$
$480$	4.98380			0.227478
$481$	−10.4907	−	20.8285i	−0.478333	−	0.949696i
$482$	−11.9170			−0.542805
$483$	−6.68474	−	11.5783i	−0.304166	−	0.526831i
$484$	−4.25803	−	7.37512i	−0.193547	−	0.335233i
$485$	1.53609	−	2.66058i	0.0697501	−	0.120811i
$486$	−17.9292			−0.813286
$487$	8.82357	−	15.2829i	0.399834	−	0.692533i	−0.593871	−	0.804560i	$-0.702401\pi$
$487$	8.82357	−	15.2829i	0.399834	−	0.692533i	0.993705	+	0.112027i	$0.0357344\pi$
$488$	−17.8995	+	31.0029i	−0.810274	+	1.40344i
$489$	−5.66690			−0.256266
$490$	−1.42055	+	2.46046i	−0.0641739	+	0.111152i
$491$	−0.112094	−	0.194153i	−0.00505873	−	0.00876198i	0.863485	−	0.504375i	$-0.168277\pi$
$491$	−0.112094	−	0.194153i	−0.00505873	−	0.00876198i	−0.868544	+	0.495613i	$0.834944\pi$
$492$	−2.37320	−	4.11050i	−0.106992	−	0.185316i
$493$	29.0632			1.30894
$494$	−25.6358	−	1.46335i	−1.15341	−	0.0658390i
$495$	1.43294			0.0644060
$496$	0.477986	+	0.827897i	0.0214622	+	0.0371737i
$497$	−3.10655	−	5.38071i	−0.139348	−	0.241358i
$498$	3.53931	−	6.13027i	0.158600	−	0.274704i
$499$	−29.2728			−1.31043			−0.655215	−	0.755443i	$-0.727422\pi$
$499$	−29.2728			−1.31043			−0.655215	+	0.755443i	$0.727422\pi$
$500$	−2.18776	+	3.78931i	−0.0978397	+	0.169463i
$501$	−7.54018	+	13.0600i	−0.336870	+	0.583477i
$502$	0.468386			0.0209051
$503$	11.1031	−	19.2311i	0.495062	−	0.857472i	−0.504922	−	0.863165i	$-0.668479\pi$
$503$	11.1031	−	19.2311i	0.495062	−	0.857472i	0.999984	+	0.00569299i	$0.00181214\pi$
$504$	2.19998	+	3.81048i	0.0979951	+	0.169732i
$505$	−3.59174	−	6.22107i	−0.159830	−	0.276834i
$506$	−13.1073			−0.582691
$507$	11.6014	+	26.7247i	0.515235	+	1.18689i
$508$	14.4245			0.639985
$509$	7.17416	+	12.4260i	0.317989	+	0.550773i	0.980068	−	0.198661i	$-0.0636592\pi$
$509$	7.17416	+	12.4260i	0.317989	+	0.550773i	−0.662079	+	0.749434i	$0.730326\pi$
$510$	−2.43049	−	4.20974i	−0.107624	−	0.186410i
$511$	4.21650	−	7.30319i	0.186527	−	0.323074i
$512$	10.5414			0.465870
$513$	−7.84380	+	13.5859i	−0.346312	+	0.599830i
$514$	−9.88919	+	17.1286i	−0.436193	+	0.755509i
$515$	−8.80347			−0.387927
$516$	−11.9148	+	20.6370i	−0.524520	+	0.908495i
$517$	−1.70627	−	2.95535i	−0.0750418	−	0.129976i
$518$	−2.33670	−	4.04729i	−0.102669	−	0.177828i
$519$	36.1039			1.58479
$520$	4.75784	+	0.271587i	0.208645	+	0.0119099i
$521$	34.9549			1.53140			0.765700	−	0.643197i	$-0.222392\pi$
$521$	34.9549			1.53140			0.765700	+	0.643197i	$0.222392\pi$
$522$	5.91531	+	10.2456i	0.258906	+	0.448438i
$523$	−1.90876	−	3.30607i	−0.0834642	−	0.144564i	0.821272	−	0.570538i	$-0.193265\pi$
$523$	−1.90876	−	3.30607i	−0.0834642	−	0.144564i	−0.904736	+	0.425973i	$0.859932\pi$
$524$	−6.06859	+	10.5111i	−0.265108	+	0.459180i
$525$	−7.82382			−0.341459
$526$	−2.10578	+	3.64731i	−0.0918163	+	0.159030i
$527$	−2.47057	+	4.27915i	−0.107620	+	0.186403i
$528$	3.43884			0.149656
$529$	−22.2115	+	38.4714i	−0.965716	+	1.67267i
$530$	0.991743	+	1.71775i	0.0430786	+	0.0746143i
$531$	5.13004	+	8.88548i	0.222625	+	0.385597i
$532$	5.25982			0.228042
$533$	−3.39771	−	6.74591i	−0.147171	−	0.292198i
$534$	−30.9297			−1.33846
$535$	−2.04329	−	3.53909i	−0.0883392	−	0.153008i
$536$	−15.9282	−	27.5885i	−0.687995	−	1.19164i
$537$	−5.63878	+	9.76666i	−0.243332	+	0.421463i
$538$	−18.7565			−0.808650
$539$	5.19429	−	8.99677i	0.223734	−	0.387518i
$540$	0.488790	−	0.846610i	0.0210342	−	0.0364323i
$541$	−18.6149			−0.800316			−0.400158	−	0.916446i	$-0.631045\pi$
$541$	−18.6149			−0.800316			−0.400158	+	0.916446i	$0.631045\pi$
$542$	3.21378	−	5.56643i	0.138044	−	0.239099i
$543$	−17.5773	−	30.4448i	−0.754315	−	1.30651i
$544$	12.4470	+	21.5588i	0.533660	+	0.924326i
$545$	8.94091			0.382987
$546$	2.62626	+	5.21425i	0.112393	+	0.223149i
$547$	25.4883			1.08980			0.544901	−	0.838500i	$-0.316567\pi$
$547$	25.4883			1.08980			0.544901	+	0.838500i	$0.316567\pi$
$548$	9.19310	+	15.9229i	0.392710	+	0.680193i
$549$	−12.0898	−	20.9402i	−0.515981	−	0.893704i
$550$	−3.83520	+	6.64277i	−0.163534	+	0.283249i
$551$	42.1206			1.79440
$552$	27.5514	−	47.7205i	1.17267	−	2.03112i
$553$	0.437943	−	0.758539i	0.0186232	−	0.0322564i
$554$	−0.265766			−0.0112913
$555$	3.19921	−	5.54120i	0.135799	−	0.235211i
$556$	4.24543	+	7.35329i	0.180046	+	0.311849i
$557$	9.01801	+	15.6196i	0.382105	+	0.661826i	0.991363	−	0.131147i	$-0.0418659\pi$
$557$	9.01801	+	15.6196i	0.382105	+	0.661826i	−0.609258	+	0.792972i	$0.708533\pi$
$558$	−2.01137			−0.0851480
$559$	−20.8016	+	31.7072i	−0.879814	+	1.34107i
$560$	0.306570			0.0129550
$561$	8.88718	+	15.3931i	0.375217	+	0.649895i
$562$	13.4173	+	23.2394i	0.565974	+	0.980296i
$563$	−8.56330	+	14.8321i	−0.360900	+	0.625097i	−0.988109	−	0.153754i	$-0.950864\pi$
$563$	−8.56330	+	14.8321i	−0.360900	+	0.625097i	0.627209	+	0.778851i	$0.284197\pi$
$564$	4.81695			0.202830
$565$	2.09360	−	3.62623i	0.0880785	−	0.152557i
$566$	−16.1627	+	27.9946i	−0.679368	+	1.17670i
$567$	7.97506			0.334921
$568$	12.8038	−	22.1768i	0.537236	−	0.930519i
$569$	12.3389	+	21.3715i	0.517272	+	0.895942i	0.999799	+	0.0200603i	$0.00638581\pi$
$569$	12.3389	+	21.3715i	0.517272	+	0.895942i	−0.482527	+	0.875881i	$0.660281\pi$
$570$	−3.52246	−	6.10108i	−0.147540	−	0.255546i
$571$	−27.7670			−1.16201			−0.581007	−	0.813898i	$-0.697341\pi$
$571$	−27.7670			−1.16201			−0.581007	+	0.813898i	$0.697341\pi$
$572$	−5.84135	−	0.333436i	−0.244239	−	0.0139417i
$573$	−18.7449			−0.783080
$574$	−0.756810	−	1.31083i	−0.0315886	−	0.0547131i
$575$	19.7280	+	34.1698i	0.822713	+	1.42498i
$576$	−7.00019	+	12.1247i	−0.291674	+	0.505195i
$577$	4.89174			0.203646			0.101823	−	0.994803i	$-0.467532\pi$
$577$	4.89174			0.203646			0.101823	+	0.994803i	$0.467532\pi$
$578$	3.68704	−	6.38614i	0.153361	−	0.265628i
$579$	−8.62392	+	14.9371i	−0.358398	+	0.620764i
$580$	−2.62477			−0.108988
$581$	−1.15374	+	1.99833i	−0.0478650	+	0.0829046i
$582$	7.75613	+	13.4340i	0.321502	+	0.556857i
$583$	−3.62634	−	6.28101i	−0.150188	−	0.260133i
$584$	34.7570			1.43825
$585$	−1.76564	+	2.69131i	−0.0730004	+	0.111272i
$586$	1.73888			0.0718326
$587$	4.14026	+	7.17114i	0.170887	+	0.295985i	0.938730	−	0.344653i	$-0.112003\pi$
$587$	4.14026	+	7.17114i	0.170887	+	0.295985i	−0.767843	+	0.640638i	$0.778670\pi$
$588$	7.33196	+	12.6993i	0.302365	+	0.523712i
$589$	−3.58054	+	6.20168i	−0.147534	+	0.255536i
$590$	2.22689			0.0916798
$591$	−10.8118	+	18.7265i	−0.444737	+	0.770307i
$592$	3.09168	−	5.35495i	0.127067	−	0.220087i
$593$	−11.1692			−0.458662			−0.229331	−	0.973348i	$-0.573654\pi$
$593$	−11.1692			−0.458662			−0.229331	+	0.973348i	$0.573654\pi$
$594$	1.74847	−	3.02844i	0.0717405	−	0.124258i
$595$	0.792286	+	1.37228i	0.0324806	+	0.0562580i
$596$	1.56925	+	2.71801i	0.0642788	+	0.111334i
$597$	−16.8590			−0.689993
$598$	16.1506	−	24.6178i	0.660447	−	1.00670i
$599$	−14.8970			−0.608675			−0.304338	−	0.952564i	$-0.598435\pi$
$599$	−14.8970			−0.608675			−0.304338	+	0.952564i	$0.598435\pi$
$600$	−16.1231	−	27.9260i	−0.658223	−	1.14008i
$601$	4.36491	+	7.56025i	0.178049	+	0.308389i	0.941212	−	0.337816i	$-0.109688\pi$
$601$	4.36491	+	7.56025i	0.178049	+	0.308389i	−0.763163	+	0.646205i	$0.776355\pi$
$602$	−3.79962	+	6.58113i	−0.154861	+	0.268227i
$603$	21.5167			0.876227
$604$	−0.872001	+	1.51035i	−0.0354812	+	0.0614553i
$605$	1.85909	−	3.22005i	0.0755830	−	0.130914i
$606$	36.2714			1.47342
$607$	7.67008	−	13.2850i	0.311319	−	0.539220i	−0.667329	−	0.744763i	$-0.732563\pi$
$607$	7.67008	−	13.2850i	0.311319	−	0.539220i	0.978648	+	0.205543i	$0.0658959\pi$
$608$	18.0391	+	31.2447i	0.731583	+	1.26714i
$609$	−4.78847	−	8.29387i	−0.194039	−	0.336085i
$610$	−5.24806			−0.212488
$611$	7.65309	+	0.436854i	0.309611	+	0.0176732i
$612$	−10.1031			−0.408395
$613$	2.10441	+	3.64495i	0.0849964	+	0.147218i	0.905390	−	0.424582i	$-0.139579\pi$
$613$	2.10441	+	3.64495i	0.0849964	+	0.147218i	−0.820393	+	0.571800i	$0.806245\pi$
$614$	−7.46424	−	12.9284i	−0.301232	−	0.521750i
$615$	1.03616	−	1.79468i	0.0417820	−	0.0723685i
$616$	−3.49195			−0.140695
$617$	12.6898	−	21.9793i	0.510871	−	0.884855i	−0.489050	−	0.872256i	$-0.662656\pi$
$617$	12.6898	−	21.9793i	0.510871	−	0.884855i	0.999921	−	0.0125987i	$-0.00401038\pi$
$618$	22.2256	−	38.4958i	0.894043	−	1.54853i
$619$	−33.6097			−1.35089			−0.675444	−	0.737412i	$-0.736048\pi$
$619$	−33.6097			−1.35089			−0.675444	+	0.737412i	$0.736048\pi$
$620$	0.223123	−	0.386461i	0.00896085	−	0.0155206i
$621$	−8.99397	−	15.5780i	−0.360916	−	0.625124i
$622$	3.25365	+	5.63549i	0.130460	+	0.225963i
$623$	10.0824			0.403943
$624$	−4.23727	+	6.45873i	−0.169627	+	0.258556i
$625$	22.1154			0.884617
$626$	4.74267	+	8.21455i	0.189555	+	0.328319i
$627$	12.8800	+	22.3088i	0.514377	+	0.890928i
$628$	1.38863	−	2.40519i	0.0554126	−	0.0959774i
$629$	31.9600			1.27433
$630$	−0.322512	+	0.558607i	−0.0128492	+	0.0222554i
$631$	−10.0861	+	17.4697i	−0.401522	+	0.695457i	−0.993910	−	0.110196i	$-0.964852\pi$
$631$	−10.0861	+	17.4697i	−0.401522	+	0.695457i	0.592387	+	0.805653i	$0.298185\pi$
$632$	3.61000			0.143598
$633$	5.07360	−	8.78773i	0.201657	−	0.349281i
$634$	−4.08540	−	7.07612i	−0.162252	−	0.281028i
$635$	3.14894	+	5.45412i	0.124962	+	0.216440i
$636$	10.2375			0.405942
$637$	10.4972	+	20.8414i	0.415913	+	0.825767i
$638$	−9.38915			−0.371720
$639$	8.64801	+	14.9788i	0.342110	+	0.592552i
$640$	−0.704472	−	1.22018i	−0.0278467	−	0.0482319i
$641$	14.7183	−	25.4929i	0.581338	−	1.00691i	−0.413983	−	0.910285i	$-0.635863\pi$
$641$	14.7183	−	25.4929i	0.581338	−	1.00691i	0.995321	−	0.0966230i	$-0.0308041\pi$
$642$	20.6343			0.814371
$643$	0.342951	−	0.594008i	0.0135247	−	0.0234254i	−0.859184	−	0.511667i	$-0.829028\pi$
$643$	0.342951	−	0.594008i	0.0135247	−	0.0234254i	0.872709	+	0.488242i	$0.162362\pi$
$644$	−3.01554	+	5.22307i	−0.118829	+	0.205818i
$645$	−10.4042			−0.409666
$646$	17.5946	−	30.4747i	0.692250	−	1.19901i
$647$	−10.0924	−	17.4806i	−0.396774	−	0.687233i	0.596552	−	0.802575i	$-0.296537\pi$
$647$	−10.0924	−	17.4806i	−0.396774	−	0.687233i	−0.993326	+	0.115341i	$0.963204\pi$
$648$	16.4348	+	28.4659i	0.645620	+	1.11825i
$649$	−8.14271			−0.319630
$650$	−7.75059	−	15.3883i	−0.304003	−	0.603577i
$651$	1.62821			0.0638146
$652$	1.27819	+	2.21390i	0.0500580	+	0.0867030i
$653$	14.7167	+	25.4902i	0.575911	+	0.997507i	0.995942	+	0.0899970i	$0.0286858\pi$
$653$	14.7167	+	25.4902i	0.575911	+	0.997507i	−0.420031	+	0.907510i	$0.637981\pi$
$654$	−22.5726	+	39.0969i	−0.882658	+	1.52881i
$655$	−5.29920			−0.207057
$656$	1.00133	−	1.73436i	0.0390955	−	0.0677153i
$657$	−11.7379	+	20.3306i	−0.457938	+	0.793172i
$658$	1.53612			0.0598842
$659$	3.63418	−	6.29458i	0.141567	−	0.245202i	−0.786520	−	0.617565i	$-0.788119\pi$
$659$	3.63418	−	6.29458i	0.141567	−	0.245202i	0.928087	+	0.372363i	$0.121452\pi$
$660$	−0.802623	−	1.39018i	−0.0312421	−	0.0541129i
$661$	−10.7043	−	18.5405i	−0.416351	−	0.721140i	0.579219	−	0.815172i	$-0.303358\pi$
$661$	−10.7043	−	18.5405i	−0.416351	−	0.721140i	−0.995569	+	0.0940319i	$0.970024\pi$
$662$	11.9855			0.465832
$663$	−39.8614	−	2.27537i	−1.54809	−	0.0883681i
$664$	−9.51035			−0.369073
$665$	1.14824	+	1.98881i	0.0445269	+	0.0771229i
$666$	6.50490	+	11.2668i	0.252060	+	0.436580i
$667$	−24.1485	+	41.8264i	−0.935033	+	1.61952i
$668$	6.80288			0.263211
$669$	9.12563	−	15.8061i	0.352817	−	0.611098i
$670$	2.33504	−	4.04441i	0.0902105	−	0.156249i
$671$	19.1897			0.740810
$672$	4.10154	−	7.10408i	0.158220	−	0.274046i
$673$	0.631402	+	1.09362i	0.0243388	+	0.0421560i	0.877938	−	0.478774i	$-0.158919\pi$
$673$	0.631402	+	1.09362i	0.0243388	+	0.0421560i	−0.853599	+	0.520930i	$0.825585\pi$
$674$	2.71149	+	4.69644i	0.104443	+	0.180900i
$675$	−10.5265			−0.405167
$676$	7.82385	−	10.5602i	0.300917	−	0.406162i
$677$	44.3444			1.70429			0.852147	−	0.523302i	$-0.175300\pi$
$677$	44.3444			1.70429			0.852147	+	0.523302i	$0.175300\pi$
$678$	10.5712	+	18.3098i	0.405984	+	0.703185i
$679$	−2.52832	−	4.37918i	−0.0970281	−	0.168058i
$680$	−3.26544	+	5.65591i	−0.125224	+	0.216894i
$681$	16.0634			0.615552
$682$	0.798142	−	1.38242i	0.0305624	−	0.0529357i
$683$	8.28658	−	14.3528i	0.317077	−	0.549194i	−0.662800	−	0.748797i	$-0.730632\pi$
$683$	8.28658	−	14.3528i	0.317077	−	0.549194i	0.979877	+	0.199603i	$0.0639652\pi$
$684$	−14.6423			−0.559861
$685$	−4.01379	+	6.95209i	−0.153359	+	0.265626i
$686$	4.86700	+	8.42989i	0.185823	+	0.321855i
$687$	30.9471	+	53.6019i	1.18070	+	2.04504i
$688$	−10.0545			−0.383325
$689$	16.2651	+	0.928447i	0.619652	+	0.0353710i
$690$	8.07794			0.307522
$691$	−1.64590	−	2.85078i	−0.0626129	−	0.108449i	0.833020	−	0.553243i	$-0.186610\pi$
$691$	−1.64590	−	2.85078i	−0.0626129	−	0.108449i	−0.895633	+	0.444795i	$0.853277\pi$
$692$	−8.14340	−	14.1048i	−0.309566	−	0.536183i
$693$	1.17928	−	2.04257i	0.0447970	−	0.0775907i
$694$	−12.0291			−0.456619
$695$	−1.85359	+	3.21051i	−0.0703107	+	0.121782i
$696$	19.7359	−	34.1836i	0.748087	−	1.29572i
$697$	10.3512			0.392079
$698$	−0.642909	+	1.11355i	−0.0243345	+	0.0421486i
$699$	−24.2059	−	41.9259i	−0.915553	−	1.58578i
$700$	1.76470	+	3.05654i	0.0666993	+	0.115527i
$701$	−24.5099			−0.925726			−0.462863	−	0.886430i	$-0.653178\pi$
$701$	−24.5099			−0.925726			−0.462863	+	0.886430i	$0.653178\pi$
$702$	3.53349	+	7.01550i	0.133363	+	0.264783i
$703$	46.3189			1.74695
$704$	−5.55557	−	9.62253i	−0.209383	−	0.362663i
$705$	1.05156	+	1.82136i	0.0396042	+	0.0685964i
$706$	14.3121	−	24.7893i	0.538643	−	0.932957i
$707$	−11.8236			−0.444674
$708$	5.74690	−	9.95392i	0.215982	−	0.374091i
$709$	−13.7853	+	23.8769i	−0.517719	+	0.896716i	0.482069	+	0.876133i	$0.339885\pi$
$709$	−13.7853	+	23.8769i	−0.517719	+	0.896716i	−0.999788	+	0.0205824i	$0.993448\pi$
$710$	3.75401			0.140886
$711$	−1.21914	+	2.11162i	−0.0457215	+	0.0791919i
$712$	20.7775	+	35.9877i	0.778670	+	1.34870i
$713$	−4.10557	−	7.11106i	−0.153755	−	0.266311i
$714$	−8.00094			−0.299428
$715$	−1.14912	−	2.28149i	−0.0429745	−	0.0853229i
$716$	5.08741			0.190125
$717$	0.0484655	+	0.0839446i	0.00180998	+	0.00313497i
$718$	10.6280	+	18.4083i	0.396635	+	0.686992i
$719$	21.8774	−	37.8928i	0.815889	−	1.41316i	−0.0927982	−	0.995685i	$-0.529581\pi$
$719$	21.8774	−	37.8928i	0.815889	−	1.41316i	0.908688	−	0.417477i	$-0.137086\pi$
$720$	−0.853429			−0.0318054
$721$	−7.24503	+	12.5488i	−0.269819	+	0.467340i
$722$	16.0517	−	27.8024i	0.597384	−	1.03470i
$723$	−26.8549			−0.998746
$724$	−7.92928	+	13.7339i	−0.294689	+	0.510417i
$725$	14.1317	+	24.4768i	0.524838	+	0.909046i
$726$	9.38709	+	16.2589i	0.348387	+	0.603425i
$727$	−14.2078			−0.526939			−0.263470	−	0.964668i	$-0.584867\pi$
$727$	−14.2078			−0.526939			−0.263470	+	0.964668i	$0.584867\pi$
$728$	4.30271	−	6.55848i	0.159469	−	0.243074i
$729$	−7.47245			−0.276757
$730$	2.54764	+	4.41265i	0.0942925	+	0.163319i
$731$	−25.9844	−	45.0063i	−0.961069	−	1.66462i
$732$	−13.5435	+	23.4581i	−0.500584	+	0.867037i
$733$	−40.2802			−1.48778			−0.743891	−	0.668301i	$-0.767022\pi$
$733$	−40.2802			−1.48778			−0.743891	+	0.668301i	$0.767022\pi$
$734$	4.19451	−	7.26510i	0.154822	−	0.268160i
$735$	−3.20120	+	5.54465i	−0.118078	+	0.204517i
$736$	−41.3686			−1.52487
$737$	−8.53816	+	14.7885i	−0.314507	+	0.544742i
$738$	2.10680	+	3.64909i	0.0775525	+	0.134325i
$739$	6.80663	+	11.7894i	0.250386	+	0.433681i	0.963632	−	0.267233i	$-0.0861092\pi$
$739$	6.80663	+	11.7894i	0.250386	+	0.433681i	−0.713246	+	0.700914i	$0.752776\pi$
$740$	−2.88639			−0.106106
$741$	−57.7702	−	3.29764i	−2.12224	−	0.121142i
$742$	3.26472			0.119852
$743$	5.34544	+	9.25858i	0.196105	+	0.339664i	0.947262	−	0.320459i	$-0.103837\pi$
$743$	5.34544	+	9.25858i	0.196105	+	0.339664i	−0.751157	+	0.660124i	$0.770504\pi$
$744$	3.35537	+	5.81167i	0.123014	+	0.213066i
$745$	−0.685147	+	1.18671i	−0.0251018	+	0.0434777i
$746$	19.8337			0.726163
$747$	3.21176	−	5.56294i	0.117512	−	0.203537i
$748$	4.00909	−	6.94394i	0.146587	−	0.253896i
$749$	−6.72632			−0.245774
$750$	4.82305	−	8.35377i	0.176113	−	0.305037i
$751$	−10.8172	−	18.7360i	−0.394727	−	0.683687i	0.598339	−	0.801243i	$-0.295827\pi$
$751$	−10.8172	−	18.7360i	−0.394727	−	0.683687i	−0.993066	+	0.117556i	$0.962494\pi$
$752$	1.01622	+	1.76014i	0.0370577	+	0.0641858i
$753$	1.05551			0.0384648
$754$	11.5691	−	17.6344i	0.421323	−	0.642208i
$755$	−0.761447			−0.0277119
$756$	−0.804525	−	1.39348i	−0.0292603	−	0.0506803i
$757$	4.28881	+	7.42844i	0.155879	+	0.269991i	0.933379	−	0.358892i	$-0.116846\pi$
$757$	4.28881	+	7.42844i	0.155879	+	0.269991i	−0.777499	+	0.628884i	$0.783512\pi$
$758$	−13.4451	+	23.2877i	−0.488349	+	0.845846i
$759$	−29.5373			−1.07214
$760$	−4.73253	+	8.19698i	−0.171667	+	0.297336i
$761$	−5.76149	+	9.97920i	−0.208854	+	0.361746i	−0.951354	−	0.308101i	$-0.900307\pi$
$761$	−5.76149	+	9.97920i	−0.208854	+	0.361746i	0.742500	+	0.669846i	$0.233640\pi$
$762$	−31.7997			−1.15198
$763$	7.35815	−	12.7447i	0.266383	−	0.461389i
$764$	4.22800	+	7.32311i	0.152964	+	0.264941i
$765$	−2.20556	−	3.82015i	−0.0797423	−	0.138118i
$766$	−34.1271			−1.23306
$767$	10.0333	−	15.2934i	0.362281	−	0.552213i
$768$	38.1413			1.37630
$769$	−23.3783	−	40.4925i	−0.843044	−	1.46020i	−0.887309	−	0.461176i	$-0.847428\pi$
$769$	−23.3783	−	40.4925i	−0.843044	−	1.46020i	0.0442647	−	0.999020i	$-0.485905\pi$
$770$	−0.255956	−	0.443328i	−0.00922400	−	0.0159764i
$771$	−22.2852	+	38.5992i	−0.802583	+	1.39012i
$772$	7.78066			0.280032
$773$	24.1360	−	41.8048i	0.868112	−	1.50361i	0.00418917	−	0.999991i	$-0.498667\pi$
$773$	24.1360	−	41.8048i	0.868112	−	1.50361i	0.863923	−	0.503624i	$-0.168000\pi$
$774$	10.5774	−	18.3205i	0.380195	−	0.658517i
$775$	−4.80516			−0.172607
$776$	10.4206	−	18.0490i	0.374077	−	0.647921i
$777$	−5.26574	−	9.12054i	−0.188908	−	0.327197i
$778$	6.89115	+	11.9358i	0.247060	+	0.427920i
$779$	15.0017			0.537493
$780$	3.59998	+	0.205494i	0.128900	+	0.00735788i
$781$	−13.7267			−0.491179
$782$	20.1746	+	34.9434i	0.721441	+	1.24957i
$783$	−6.44264	−	11.1590i	−0.230241	−	0.398789i
$784$	−3.09360	+	5.35828i	−0.110486	+	0.191367i
$785$	1.21258			0.0432789
$786$	13.3786	−	23.1724i	0.477198	−	0.826531i
$787$	16.3762	−	28.3643i	0.583747	−	1.01108i	−0.411284	−	0.911507i	$-0.634919\pi$
$787$	16.3762	−	28.3643i	0.583747	−	1.01108i	0.995030	−	0.0995717i	$-0.0317472\pi$
$788$	9.75457			0.347492
$789$	−4.74536	+	8.21920i	−0.168939	+	0.292611i
$790$	0.264609	+	0.458316i	0.00941435	+	0.0163061i
$791$	−3.44597	−	5.96859i	−0.122524	−	0.212219i
$792$	9.72088			0.345416
$793$	−23.6452	+	36.0415i	−0.839665	+	1.27987i
$794$	−20.0901			−0.712971
$795$	2.23489	+	3.87094i	0.0792633	+	0.137288i
$796$	3.80262	+	6.58633i	0.134780	+	0.233446i
$797$	−7.51523	+	13.0168i	−0.266203	+	0.461077i	−0.967878	−	0.251420i	$-0.919103\pi$
$797$	−7.51523	+	13.0168i	−0.266203	+	0.461077i	0.701675	+	0.712497i	$0.252436\pi$
$798$	−11.5956			−0.410479
$799$	−5.25253	+	9.09765i	−0.185821	+	0.321852i
$800$	−12.1044	+	20.9655i	−0.427957	+	0.741243i
$801$	−28.0673			−0.991710
$802$	17.2724	−	29.9166i	0.609909	−	1.05639i
$803$	−9.31554	−	16.1350i	−0.328738	−	0.569392i
$804$	−12.0520	−	20.8746i	−0.425040	−	0.736192i
$805$	−2.63323			−0.0928091
$806$	1.61297	+	3.20244i	0.0568145	+	0.112801i
$807$	−42.2677			−1.48789
$808$	−24.3658	−	42.2029i	−0.857187	−	1.48469i
$809$	−15.0157	−	26.0080i	−0.527925	−	0.914393i	−0.999470	−	0.0325508i	$-0.989637\pi$
$809$	−15.0157	−	26.0080i	−0.527925	−	0.914393i	0.471545	−	0.881842i	$-0.343696\pi$
$810$	−2.40930	+	4.17303i	−0.0846541	+	0.146625i
$811$	−13.0456			−0.458093			−0.229046	−	0.973416i	$-0.573561\pi$
$811$	−13.0456			−0.458093			−0.229046	+	0.973416i	$0.573561\pi$
$812$	−2.16012	+	3.74144i	−0.0758054	+	0.131299i
$813$	7.24224	−	12.5439i	0.253996	−	0.439935i
$814$	−10.3250			−0.361890
$815$	−0.558072	+	0.966608i	−0.0195484	+	0.0338588i
$816$	−5.29301	−	9.16776i	−0.185292	−	0.320936i
$817$	−37.6586	−	65.2267i	−1.31751	−	2.28199i
$818$	23.8378			0.833471
$819$	2.38321	+	4.73169i	0.0832760	+	0.165339i
$820$	−0.934841			−0.0326461
$821$	−17.8408	−	30.9012i	−0.622649	−	1.07846i	−0.988990	−	0.147980i	$-0.952723\pi$
$821$	−17.8408	−	30.9012i	−0.622649	−	1.07846i	0.366341	−	0.930481i	$-0.380610\pi$
$822$	−20.2667	−	35.1030i	−0.706884	−	1.22436i
$823$	1.64006	−	2.84067i	0.0571689	−	0.0990194i	−0.836025	−	0.548692i	$-0.815126\pi$
$823$	1.64006	−	2.84067i	0.0571689	−	0.0990194i	0.893193	+	0.449673i	$0.148459\pi$
$824$	−59.7215			−2.08050
$825$	−8.64261	+	14.9694i	−0.300897	+	0.521169i
$826$	1.83268	−	3.17429i	0.0637670	−	0.110448i
$827$	−23.9423			−0.832554			−0.416277	−	0.909238i	$-0.636665\pi$
$827$	−23.9423			−0.832554			−0.416277	+	0.909238i	$0.636665\pi$
$828$	8.39466	−	14.5400i	0.291735	−	0.505299i
$829$	13.5532	+	23.4749i	0.470724	+	0.815317i	0.999439	−	0.0334817i	$-0.0106596\pi$
$829$	13.5532	+	23.4749i	0.470724	+	0.815317i	−0.528716	+	0.848799i	$0.677326\pi$
$830$	−0.697096	−	1.20741i	−0.0241966	−	0.0419097i
$831$	−0.598902			−0.0207757
$832$	24.9182	+	1.42238i	0.863884	+	0.0493122i
$833$	−31.9799			−1.10804
$834$	−9.35930	−	16.2108i	−0.324086	−	0.561333i
$835$	1.48510	+	2.57227i	0.0513940	+	0.0890170i
$836$	5.81028	−	10.0637i	0.200953	−	0.348060i
$837$	2.19067			0.0757207
$838$	7.83881	−	13.5772i	0.270787	−	0.469017i
$839$	15.8601	−	27.4704i	0.547550	−	0.948385i	−0.450891	−	0.892579i	$-0.648894\pi$
$839$	15.8601	−	27.4704i	0.547550	−	0.948385i	0.998442	−	0.0558061i	$-0.0177729\pi$
$840$	2.15206			0.0742533
$841$	−2.79825	+	4.84671i	−0.0964914	+	0.167128i
$842$	13.6995	+	23.7283i	0.472117	+	0.817731i
$843$	30.2358	+	52.3699i	1.04138	+	1.80372i
$844$	−4.57749			−0.157564
$845$	5.70095	+	0.652971i	0.196119	+	0.0224629i
$846$	−4.27625			−0.147020
$847$	−3.05998	−	5.30004i	−0.105142	−	0.182111i
$848$	2.15977	+	3.74083i	0.0741668	+	0.128461i
$849$	−36.4225	+	63.0856i	−1.25002	+	2.16509i
$850$	23.6123			0.809896
$851$	−26.5554	+	45.9953i	−0.910308	+	1.57670i
$852$	9.68789	−	16.7799i	0.331902	−	0.574871i
$853$	−15.5095			−0.531036			−0.265518	−	0.964106i	$-0.585543\pi$
$853$	−15.5095			−0.531036			−0.265518	+	0.964106i	$0.585543\pi$
$854$	−4.31902	+	7.48076i	−0.147794	+	0.255986i
$855$	−3.19647	−	5.53645i	−0.109317	−	0.189343i
$856$	−13.8614	−	24.0087i	−0.473773	−	0.820599i
$857$	34.9054			1.19235			0.596173	−	0.802856i	$-0.296687\pi$
$857$	34.9054			1.19235			0.596173	+	0.802856i	$0.296687\pi$
$858$	12.8776	+	0.735080i	0.439634	+	0.0250952i
$859$	−26.8366			−0.915654			−0.457827	−	0.889041i	$-0.651372\pi$
$859$	−26.8366			−0.915654			−0.457827	+	0.889041i	$0.651372\pi$
$860$	2.34672	+	4.06463i	0.0800224	+	0.138603i
$861$	−1.70547	−	2.95396i	−0.0581222	−	0.100671i
$862$	−3.43734	+	5.95365i	−0.117076	+	0.202782i
$863$	−23.4884			−0.799555			−0.399778	−	0.916612i	$-0.630913\pi$
$863$	−23.4884			−0.799555			−0.399778	+	0.916612i	$0.630913\pi$
$864$	5.51841	−	9.55817i	0.187740	−	0.325176i
$865$	3.55548	−	6.15828i	0.120890	−	0.209388i
$866$	3.98862			0.135539
$867$	8.30873	−	14.3911i	0.282179	−	0.488749i
$868$	−0.367250	−	0.636096i	−0.0124653	−	0.0215905i
$869$	−0.967550	−	1.67585i	−0.0328219	−	0.0568492i
$870$	5.78646			0.196179
$871$	−17.2548	−	34.2582i	−0.584657	−	1.16080i
$872$	60.6539			2.05400
$873$	7.03833	+	12.1907i	0.238211	+	0.412594i
$874$	29.2386	+	50.6427i	0.989009	+	1.71301i
$875$	−1.57221	+	2.72314i	−0.0531503	+	0.0920590i
$876$	26.2986			0.888547
$877$	0.471524	−	0.816704i	0.0159222	−	0.0275781i	−0.857954	−	0.513726i	$-0.828265\pi$
$877$	0.471524	−	0.816704i	0.0159222	−	0.0275781i	0.873877	+	0.486148i	$0.161598\pi$
$878$	−9.44430	+	16.3580i	−0.318730	+	0.552056i
$879$	3.91856			0.132170
$880$	0.338654	−	0.586566i	0.0114160	−	0.0197731i
$881$	12.6681	+	21.9418i	0.426800	+	0.739239i	0.996587	−	0.0825536i	$-0.0263076\pi$
$881$	12.6681	+	21.9418i	0.426800	+	0.739239i	−0.569787	+	0.821793i	$0.692974\pi$
$882$	−6.50895	−	11.2738i	−0.219168	−	0.379609i
$883$	−19.4070			−0.653098			−0.326549	−	0.945180i	$-0.605886\pi$
$883$	−19.4070			−0.653098			−0.326549	+	0.945180i	$0.605886\pi$
$884$	8.10199	+	16.0859i	0.272499	+	0.541029i
$885$	5.01829			0.168688
$886$	−8.07873	−	13.9928i	−0.271410	−	0.470096i
$887$	−7.69137	−	13.3218i	−0.258251	−	0.447304i	0.707522	−	0.706691i	$-0.249813\pi$
$887$	−7.69137	−	13.3218i	−0.258251	−	0.447304i	−0.965773	+	0.259387i	$0.916479\pi$
$888$	21.7030	−	37.5907i	0.728305	−	1.26146i
$889$	10.3660			0.347664
$890$	−3.04593	+	5.27571i	−0.102100	+	0.176842i
$891$	8.80968	−	15.2588i	0.295136	−	0.511190i
$892$	−8.23331			−0.275672
$893$	−7.61238	+	13.1850i	−0.254738	+	0.441220i
$894$	−3.45950	−	5.99203i	−0.115703	−	0.200403i
$895$	1.11060	+	1.92362i	0.0371234	+	0.0642997i
$896$	−2.31905			−0.0774741
$897$	36.3953	−	55.4761i	1.21520	−	1.85229i
$898$	13.0811			0.436523
$899$	−2.94094	−	5.09386i	−0.0980858	−	0.169890i
$900$	−4.91256	−	8.50880i	−0.163752	−	0.283627i
$901$	−11.1632	+	19.3353i	−0.371901	+	0.644151i
$902$	−3.34405			−0.111345
$903$	−8.56241	+	14.8305i	−0.284939	+	0.493529i
$904$	14.2027	−	24.5998i	0.472375	−	0.818177i
$905$	−6.92399			−0.230161
$906$	1.92238	−	3.32966i	0.0638667	−	0.110620i
$907$	8.28050	+	14.3422i	0.274949	+	0.476226i	0.970122	−	0.242616i	$-0.0780055\pi$
$907$	8.28050	+	14.3422i	0.274949	+	0.476226i	−0.695173	+	0.718843i	$0.744672\pi$
$908$	−3.62318	−	6.27552i	−0.120239	−	0.208261i
$909$	32.9146			1.09171
$910$	1.14803	+	0.0655319i	0.0380568	+	0.00217236i
$911$	−7.67015			−0.254123			−0.127062	−	0.991895i	$-0.540555\pi$
$911$	−7.67015			−0.254123			−0.127062	+	0.991895i	$0.540555\pi$
$912$	−7.67104	−	13.2866i	−0.254014	−	0.439964i
$913$	2.54896	+	4.41492i	0.0843582	+	0.146113i
$914$	7.87597	−	13.6416i	0.260514	−	0.451223i
$915$	−11.8265			−0.390971
$916$	13.9605	−	24.1803i	0.461268	−	0.798939i
$917$	−4.36111	+	7.55367i	−0.144017	+	0.249444i
$918$	−10.7649			−0.355293
$919$	15.4325	−	26.7299i	0.509072	−	0.881739i	−0.490872	−	0.871232i	$-0.663322\pi$
$919$	15.4325	−	26.7299i	0.509072	−	0.881739i	0.999945	−	0.0105079i	$-0.00334483\pi$
$920$	−5.42648	−	9.39894i	−0.178906	−	0.309874i
$921$	−16.8206	−	29.1342i	−0.554259	−	0.960004i
$922$	−10.4824			−0.345220
$923$	16.9137	−	25.7810i	0.556722	−	0.848593i
$924$	−2.64216			−0.0869206
$925$	15.5402	+	26.9165i	0.510960	+	0.885008i
$926$	2.36485	+	4.09604i	0.0777138	+	0.134604i
$927$	20.1687	−	34.9332i	0.662427	−	1.14736i
$928$	−29.6335			−0.972767
$929$	−19.7570	+	34.2202i	−0.648207	+	1.12273i	0.335344	+	0.942096i	$0.391147\pi$
$929$	−19.7570	+	34.2202i	−0.648207	+	1.12273i	−0.983551	+	0.180631i	$0.942186\pi$
$930$	−0.491889	+	0.851977i	−0.0161297	+	0.0279374i
$931$	−46.3477			−1.51898
$932$	−10.9195	+	18.9132i	−0.357681	+	0.619521i
$933$	7.33209	+	12.6996i	0.240042	+	0.415765i
$934$	−13.8786	−	24.0385i	−0.454123	−	0.786564i
$935$	3.50081			0.114489
$936$	−11.9779	+	18.2575i	−0.391509	+	0.596764i
$937$	9.43191			0.308127			0.154064	−	0.988061i	$-0.450764\pi$
$937$	9.43191			0.308127			0.154064	+	0.988061i	$0.450764\pi$
$938$	−3.84336	−	6.65690i	−0.125490	−	0.217355i
$939$	10.6876	+	18.5114i	0.348776	+	0.604098i
$940$	0.474369	−	0.821632i	0.0154722	−	0.0267987i
$941$	6.27062			0.204416			0.102208	−	0.994763i	$-0.467409\pi$
$941$	6.27062			0.204416			0.102208	+	0.994763i	$0.467409\pi$
$942$	−3.06133	+	5.30238i	−0.0997435	+	0.172761i
$943$	−8.60076	+	14.8969i	−0.280079	+	0.485111i
$944$	4.84962			0.157842
$945$	0.351263	−	0.608405i	0.0114266	−	0.0197914i
$946$	8.39452	+	14.5397i	0.272929	+	0.472727i
$947$	16.6047	+	28.7602i	0.539580	+	0.934580i	0.998927	+	0.0463227i	$0.0147503\pi$
$947$	16.6047	+	28.7602i	0.539580	+	0.934580i	−0.459347	+	0.888257i	$0.651916\pi$
$948$	2.73148			0.0887143
$949$	41.7827	+	2.38504i	1.35632	+	0.0774218i
$950$	34.2208			1.11027
$951$	−9.20642	−	15.9460i	−0.298539	−	0.517084i
$952$	5.37476	+	9.30935i	0.174197	+	0.301718i
$953$	12.8452	−	22.2486i	0.416098	−	0.720703i	−0.579445	−	0.815011i	$-0.696731\pi$
$953$	12.8452	−	22.2486i	0.416098	−	0.720703i	0.995543	+	0.0943082i	$0.0300639\pi$
$954$	−9.08832			−0.294245
$955$	−1.84598	+	3.19733i	−0.0597346	+	0.103463i
$956$	0.0218632	−	0.0378682i	0.000707106	−	0.00122474i
$957$	−21.1584			−0.683954
$958$	−6.70313	+	11.6102i	−0.216568	+	0.375107i
$959$	6.60650	+	11.4428i	0.213335	+	0.369507i
$960$	3.42386	+	5.93029i	0.110504	+	0.191399i
$961$	1.00000			0.0322581
$962$	12.7222	−	19.3921i	0.410182	−	0.625226i
$963$	18.7247			0.603395
$964$	6.05725	+	10.4915i	0.195091	+	0.337907i
$965$	1.69855	+	2.94198i	0.0546783	+	0.0947057i
$966$	6.64795	−	11.5146i	0.213894	−	0.370476i
$967$	47.4508			1.52592			0.762958	−	0.646448i	$-0.223746\pi$
$967$	47.4508			1.52592			0.762958	+	0.646448i	$0.223746\pi$
$968$	12.6118	−	21.8443i	0.405360	−	0.702104i
$969$	39.6494	−	68.6747i	1.27372	−	2.20615i
$970$	3.05526			0.0980986
$971$	17.6284	−	30.5334i	0.565724	−	0.979862i	−0.431258	−	0.902229i	$-0.641930\pi$
$971$	17.6284	−	30.5334i	0.565724	−	0.979862i	0.996982	−	0.0776338i	$-0.0247365\pi$
$972$	9.11317	+	15.7845i	0.292305	+	0.506287i
$973$	3.05092	+	5.28435i	0.0978080	+	0.169408i
$974$	17.5500			0.562339
$975$	−17.4659	−	34.6774i	−0.559357	−	1.11056i
$976$	−11.4290			−0.365832
$977$	−24.5795	−	42.5729i	−0.786367	−	1.36203i	−0.928179	−	0.372134i	$-0.878626\pi$
$977$	−24.5795	−	42.5729i	−0.786367	−	1.36203i	0.141812	−	0.989894i	$-0.454707\pi$
$978$	−2.81786	−	4.88067i	−0.0901052	−	0.156067i
$979$	11.1376	−	19.2908i	0.355958	−	0.616537i
$980$	2.88818			0.0922596
$981$	−20.4836	+	35.4786i	−0.653991	+	1.13275i
$982$	0.111477	−	0.193084i	0.00355738	−	0.00616156i
$983$	−36.3980			−1.16092			−0.580458	−	0.814290i	$-0.697126\pi$
$983$	−36.3980			−1.16092			−0.580458	+	0.814290i	$0.697126\pi$
$984$	7.02916	−	12.1749i	0.224081	−	0.388120i
$985$	2.12947	+	3.68834i	0.0678505	+	0.117520i
$986$	14.4516	+	25.0310i	0.460234	+	0.797148i
$987$	3.46164			0.110185
$988$	11.7420	+	23.3130i	0.373564	+	0.741685i
$989$	86.3614			2.74613
$990$	0.712528	+	1.23414i	0.0226456	+	0.0392234i
$991$	0.310538	+	0.537868i	0.00986458	+	0.0170859i	0.870916	−	0.491433i	$-0.163527\pi$
$991$	0.310538	+	0.537868i	0.00986458	+	0.0170859i	−0.861051	+	0.508519i	$0.830193\pi$
$992$	2.51905	−	4.36312i	0.0799799	−	0.138529i
$993$	27.0094			0.857117
$994$	3.08946	−	5.35110i	0.0979916	−	0.169727i
$995$	−1.66026	+	2.87565i	−0.0526337	+	0.0911643i
$996$	−7.19593			−0.228012
$997$	−1.78223	+	3.08691i	−0.0564437	+	0.0977634i	−0.892867	−	0.450321i	$-0.851309\pi$
$997$	−1.78223	+	3.08691i	−0.0564437	+	0.0977634i	0.836423	+	0.548085i	$0.184643\pi$
$998$	−14.5558	−	25.2114i	−0.460757	−	0.798054i
$999$	−7.08479	−	12.2712i	−0.224153	−	0.388244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.13	✓	36
13.3	even	3		5239.2.a.p.1.6		18
13.9	even	3	inner	403.2.f.c.373.13	yes	36
13.10	even	6		5239.2.a.o.1.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.13	✓	36	1.1	even	1	trivial
403.2.f.c.373.13	yes	36	13.9	even	3	inner
5239.2.a.o.1.13		18	13.10	even	6
5239.2.a.p.1.6		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.497248 + 0.861259i) q^{2} +(1.12055 + 1.94084i) q^{3} +(0.505488 - 0.875531i) q^{4} +0.441402 q^{5} +(-1.11438 + 1.93016i) q^{6} +(0.363263 - 0.629189i) q^{7} +2.99441 q^{8} +(-1.01125 + 1.75153i) q^{9} +O(q^{10})\)	\(q+(0.497248 + 0.861259i) q^{2} +(1.12055 + 1.94084i) q^{3} +(0.505488 - 0.875531i) q^{4} +0.441402 q^{5} +(-1.11438 + 1.93016i) q^{6} +(0.363263 - 0.629189i) q^{7} +2.99441 q^{8} +(-1.01125 + 1.75153i) q^{9} +(0.219486 + 0.380161i) q^{10} +(-0.802559 - 1.39007i) q^{11} +2.26569 q^{12} +(3.59969 + 0.205478i) q^{13} +0.722527 q^{14} +(0.494611 + 0.856691i) q^{15} +(0.477986 + 0.827897i) q^{16} +(-2.47057 + 4.27915i) q^{17} -2.01137 q^{18} +(-3.58054 + 6.20168i) q^{19} +(0.223123 - 0.386461i) q^{20} +1.62821 q^{21} +(0.798142 - 1.38242i) q^{22} +(-4.10557 - 7.11106i) q^{23} +(3.35537 + 5.81167i) q^{24} -4.80516 q^{25} +(1.61297 + 3.20244i) q^{26} +2.19067 q^{27} +(-0.367250 - 0.636096i) q^{28} +(-2.94094 - 5.09386i) q^{29} +(-0.491889 + 0.851977i) q^{30} +1.00000 q^{31} +(2.51905 - 4.36312i) q^{32} +(1.79861 - 3.11528i) q^{33} -4.91395 q^{34} +(0.160345 - 0.277725i) q^{35} +(1.02235 + 1.77076i) q^{36} +(-3.23407 - 5.60157i) q^{37} -7.12167 q^{38} +(3.63482 + 7.21669i) q^{39} +1.32174 q^{40} +(-1.04745 - 1.81423i) q^{41} +(0.809625 + 1.40231i) q^{42} +(-5.25879 + 9.10849i) q^{43} -1.62274 q^{44} +(-0.446367 + 0.773130i) q^{45} +(4.08298 - 7.07193i) q^{46} +2.12604 q^{47} +(-1.07121 + 1.85539i) q^{48} +(3.23608 + 5.60506i) q^{49} +(-2.38936 - 4.13849i) q^{50} -11.0736 q^{51} +(1.99950 - 3.04778i) q^{52} +4.51848 q^{53} +(1.08931 + 1.88674i) q^{54} +(-0.354251 - 0.613580i) q^{55} +(1.08776 - 1.88405i) q^{56} -16.0487 q^{57} +(2.92475 - 5.06582i) q^{58} +(2.53649 - 4.39332i) q^{59} +1.00008 q^{60} +(-5.97766 + 10.3536i) q^{61} +(0.497248 + 0.861259i) q^{62} +(0.734698 + 1.27253i) q^{63} +6.92232 q^{64} +(1.58891 + 0.0906982i) q^{65} +3.57742 q^{66} +(-5.31933 - 9.21336i) q^{67} +(2.49769 + 4.32613i) q^{68} +(9.20097 - 15.9366i) q^{69} +0.318924 q^{70} +(4.27591 - 7.40609i) q^{71} +(-3.02809 + 5.24481i) q^{72} +11.6073 q^{73} +(3.21627 - 5.57074i) q^{74} +(-5.38441 - 9.32607i) q^{75} +(3.61985 + 6.26976i) q^{76} -1.16616 q^{77} +(-4.40803 + 6.71901i) q^{78} +1.20558 q^{79} +(0.210984 + 0.365435i) q^{80} +(5.48850 + 9.50636i) q^{81} +(1.04168 - 1.80425i) q^{82} -3.17604 q^{83} +(0.823041 - 1.42555i) q^{84} +(-1.09051 + 1.88883i) q^{85} -10.4597 q^{86} +(6.59092 - 11.4158i) q^{87} +(-2.40319 - 4.16244i) q^{88} +(6.93878 + 12.0183i) q^{89} -0.887821 q^{90} +(1.43692 - 2.19024i) q^{91} -8.30128 q^{92} +(1.12055 + 1.94084i) q^{93} +(1.05717 + 1.83107i) q^{94} +(-1.58046 + 2.73743i) q^{95} +11.2909 q^{96} +(3.48002 - 6.02757i) q^{97} +(-3.21827 + 5.57421i) q^{98} +3.24635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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