LMFDB - Embedded newform 378.2.u.b.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.2
Root			$0.500000 + 1.27297i$ of defining polynomial
Character	$\chi$	$=$	378.85
Dual form			378.2.u.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(1.71872 - 0.214444i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.701272 + 3.97711i) q^{5} +(-1.68842 - 0.386327i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.90803 - 0.737141i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(1.71872 - 0.214444i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.701272 + 3.97711i) q^{5} +(-1.68842 - 0.386327i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.90803 - 0.737141i) q^{9} +(2.01923 - 3.49741i) q^{10} +(-0.324801 - 1.84204i) q^{11} +(1.45446 + 0.940501i) q^{12} +(0.134587 - 0.0489857i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.352425 + 6.98595i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.90612 + 5.03355i) q^{17} +(-2.98477 - 0.301918i) q^{18} +(2.89839 + 5.02016i) q^{19} +(-3.09365 + 2.59588i) q^{20} +(1.17878 - 1.26905i) q^{21} +(-0.324801 + 1.84204i) q^{22} +(3.84135 + 3.22328i) q^{23} +(-1.04508 - 1.38124i) q^{24} +(-10.6272 - 3.86798i) q^{25} -0.143225 q^{26} +(4.84002 - 1.89055i) q^{27} +1.00000 q^{28} +(0.917198 + 0.333833i) q^{29} +(2.72051 - 6.44411i) q^{30} +(0.339014 + 0.284467i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-0.953258 - 3.09631i) q^{33} +(4.45244 - 3.73604i) q^{34} +(2.01923 + 3.49741i) q^{35} +(2.70150 + 1.30456i) q^{36} +(5.61042 - 9.71753i) q^{37} +(-1.00660 - 5.70871i) q^{38} +(0.220814 - 0.113054i) q^{39} +(3.79492 - 1.38124i) q^{40} +(-5.19951 + 1.89247i) q^{41} +(-1.54173 + 0.789350i) q^{42} +(-1.36463 - 7.73918i) q^{43} +(0.935228 - 1.61986i) q^{44} +(0.892373 + 12.0825i) q^{45} +(-2.50726 - 4.34271i) q^{46} +(0.648941 - 0.544526i) q^{47} +(0.509640 + 1.65538i) q^{48} +(0.173648 - 0.984808i) q^{49} +(8.66336 + 7.26942i) q^{50} +(-3.91541 + 9.27449i) q^{51} +(0.134587 + 0.0489857i) q^{52} +1.33744 q^{53} +(-5.19474 + 0.121152i) q^{54} +7.55377 q^{55} +(-0.939693 - 0.342020i) q^{56} +(6.05807 + 8.00672i) q^{57} +(-0.747706 - 0.627400i) q^{58} +(1.11071 - 6.29914i) q^{59} +(-4.76045 + 5.12501i) q^{60} +(-3.40242 + 2.85497i) q^{61} +(-0.221276 - 0.383261i) q^{62} +(1.75385 - 2.43393i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.100439 + 0.569621i) q^{65} +(-0.163229 + 3.23561i) q^{66} +(-10.4707 + 3.81104i) q^{67} +(-5.46173 + 1.98791i) q^{68} +(7.29344 + 4.71617i) q^{69} +(-0.701272 - 3.97711i) q^{70} +(8.19790 - 14.1992i) q^{71} +(-2.09240 - 2.14986i) q^{72} +(-2.37122 - 4.10707i) q^{73} +(-8.59566 + 7.21261i) q^{74} +(-19.0947 - 4.36905i) q^{75} +(-1.00660 + 5.70871i) q^{76} +(-1.43285 - 1.20231i) q^{77} +(-0.246164 + 0.0307137i) q^{78} +(13.0798 + 4.76064i) q^{79} -4.03847 q^{80} +(7.91325 - 4.28725i) q^{81} +5.53320 q^{82} +(-5.71616 - 2.08051i) q^{83} +(1.71872 - 0.214444i) q^{84} +(-17.9810 - 15.0879i) q^{85} +(-1.36463 + 7.73918i) q^{86} +(1.64800 + 0.377079i) q^{87} +(-1.43285 + 1.20231i) q^{88} +(-7.33655 - 12.7073i) q^{89} +(3.29390 - 11.6590i) q^{90} +(0.0716123 - 0.124036i) q^{91} +(0.870764 + 4.93835i) q^{92} +(0.643675 + 0.416220i) q^{93} +(-0.796044 + 0.289736i) q^{94} +(-21.9983 + 8.00672i) q^{95} +(0.0872671 - 1.72985i) q^{96} +(1.20884 + 6.85567i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(-2.30237 - 5.11728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	1.71872	−	0.214444i	0.992306	−	0.123809i
$3$	1.71872	−	0.214444i	0.992306	−	0.123809i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.701272	+	3.97711i	−0.313619	+	1.77862i	0.266245	+	0.963905i	$0.414217\pi$
$5$	−0.701272	+	3.97711i	−0.313619	+	1.77862i	−0.579863	+	0.814714i	$0.696894\pi$
$6$	−1.68842	−	0.386327i	−0.689293	−	0.157717i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.90803	−	0.737141i	0.969342	−	0.245714i
$10$	2.01923	−	3.49741i	0.638538	−	1.10598i
$11$	−0.324801	−	1.84204i	−0.0979313	−	0.555396i	−0.993810	−	0.111096i	$-0.964564\pi$
$11$	−0.324801	−	1.84204i	−0.0979313	−	0.555396i	0.895878	−	0.444299i	$-0.146547\pi$
$12$	1.45446	+	0.940501i	0.419867	+	0.271499i
$13$	0.134587	−	0.0489857i	0.0373278	−	0.0135862i	−0.323289	−	0.946300i	$-0.604789\pi$
$13$	0.134587	−	0.0489857i	0.0373278	−	0.0135862i	0.360617	+	0.932714i	$0.382566\pi$
$14$	−0.939693	+	0.342020i	−0.251143	+	0.0914087i
$15$	−0.352425	+	6.98595i	−0.0909959	+	1.80376i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.90612	+	5.03355i	−0.704838	+	1.22082i	0.261911	+	0.965092i	$0.415647\pi$
$17$	−2.90612	+	5.03355i	−0.704838	+	1.22082i	−0.966750	+	0.255724i	$0.917686\pi$
$18$	−2.98477	−	0.301918i	−0.703517	−	0.0711628i
$19$	2.89839	+	5.02016i	0.664936	+	1.15170i	0.979303	+	0.202401i	$0.0648744\pi$
$19$	2.89839	+	5.02016i	0.664936	+	1.15170i	−0.314367	+	0.949302i	$0.601792\pi$
$20$	−3.09365	+	2.59588i	−0.691760	+	0.580456i
$21$	1.17878	−	1.26905i	0.257230	−	0.276929i
$22$	−0.324801	+	1.84204i	−0.0692479	+	0.392724i
$23$	3.84135	+	3.22328i	0.800977	+	0.672100i	0.948436	−	0.316969i	$-0.102665\pi$
$23$	3.84135	+	3.22328i	0.800977	+	0.672100i	−0.147459	+	0.989068i	$0.547109\pi$
$24$	−1.04508	−	1.38124i	−0.213325	−	0.281944i
$25$	−10.6272	−	3.86798i	−2.12544	−	0.773596i
$26$	−0.143225			−0.0280887
$27$	4.84002	−	1.89055i	0.931463	−	0.363837i
$28$	1.00000			0.188982
$29$	0.917198	+	0.333833i	0.170319	+	0.0619912i	0.425772	−	0.904830i	$-0.360002\pi$
$29$	0.917198	+	0.333833i	0.170319	+	0.0619912i	−0.255453	+	0.966821i	$0.582225\pi$
$30$	2.72051	−	6.44411i	0.496694	−	1.17653i
$31$	0.339014	+	0.284467i	0.0608888	+	0.0510918i	0.672724	−	0.739893i	$-0.265124\pi$
$31$	0.339014	+	0.284467i	0.0608888	+	0.0510918i	−0.611835	+	0.790985i	$0.709569\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−0.953258	−	3.09631i	−0.165941	−	0.538998i
$34$	4.45244	−	3.73604i	0.763587	−	0.640726i
$35$	2.01923	+	3.49741i	0.341313	+	0.591171i
$36$	2.70150	+	1.30456i	0.450251	+	0.217427i
$37$	5.61042	−	9.71753i	0.922347	−	1.59755i	0.126573	−	0.991957i	$-0.459602\pi$
$37$	5.61042	−	9.71753i	0.922347	−	1.59755i	0.795774	−	0.605594i	$-0.207065\pi$
$38$	−1.00660	−	5.70871i	−0.163292	−	0.926075i
$39$	0.220814	−	0.113054i	0.0353585	−	0.0181032i
$40$	3.79492	−	1.38124i	0.600029	−	0.218393i
$41$	−5.19951	+	1.89247i	−0.812027	+	0.295554i	−0.714461	−	0.699676i	$-0.753328\pi$
$41$	−5.19951	+	1.89247i	−0.812027	+	0.295554i	−0.0975659	+	0.995229i	$0.531106\pi$
$42$	−1.54173	+	0.789350i	−0.237894	+	0.121799i
$43$	−1.36463	−	7.73918i	−0.208103	−	1.18021i	−0.892481	−	0.451085i	$-0.851037\pi$
$43$	−1.36463	−	7.73918i	−0.208103	−	1.18021i	0.684377	−	0.729128i	$-0.260074\pi$
$44$	0.935228	−	1.61986i	0.140991	−	0.244203i
$45$	0.892373	+	12.0825i	0.133027	+	1.80115i
$46$	−2.50726	−	4.34271i	−0.369676	−	0.640297i
$47$	0.648941	−	0.544526i	0.0946578	−	0.0794273i	−0.594231	−	0.804295i	$-0.702543\pi$
$47$	0.648941	−	0.544526i	0.0946578	−	0.0794273i	0.688889	+	0.724867i	$0.258099\pi$
$48$	0.509640	+	1.65538i	0.0735601	+	0.238933i
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$	8.66336	+	7.26942i	1.22518	+	1.02805i
$51$	−3.91541	+	9.27449i	−0.548267	+	1.29869i
$52$	0.134587	+	0.0489857i	0.0186639	+	0.00679310i
$53$	1.33744			0.183712			0.0918559	−	0.995772i	$-0.470720\pi$
$53$	1.33744			0.183712			0.0918559	+	0.995772i	$0.470720\pi$
$54$	−5.19474	+	0.121152i	−0.706915	+	0.0164867i
$55$	7.55377			1.01855
$56$	−0.939693	−	0.342020i	−0.125572	−	0.0457044i
$57$	6.05807	+	8.00672i	0.802411	+	1.06052i
$58$	−0.747706	−	0.627400i	−0.0981786	−	0.0823817i
$59$	1.11071	−	6.29914i	0.144602	−	0.820078i	−0.823084	−	0.567919i	$-0.807749\pi$
$59$	1.11071	−	6.29914i	0.144602	−	0.820078i	0.967686	−	0.252158i	$-0.0811404\pi$
$60$	−4.76045	+	5.12501i	−0.614572	+	0.661636i
$61$	−3.40242	+	2.85497i	−0.435635	+	0.365542i	−0.834073	−	0.551654i	$-0.813997\pi$
$61$	−3.40242	+	2.85497i	−0.435635	+	0.365542i	0.398438	+	0.917195i	$0.369553\pi$
$62$	−0.221276	−	0.383261i	−0.0281021	−	0.0486742i
$63$	1.75385	−	2.43393i	0.220965	−	0.306646i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.100439	+	0.569621i	0.0124580	+	0.0706527i
$66$	−0.163229	+	3.23561i	−0.0200921	+	0.398276i
$67$	−10.4707	+	3.81104i	−1.27920	+	0.465592i	−0.890169	−	0.455630i	$-0.849414\pi$
$67$	−10.4707	+	3.81104i	−1.27920	+	0.465592i	−0.389036	+	0.921223i	$0.627192\pi$
$68$	−5.46173	+	1.98791i	−0.662331	+	0.241069i
$69$	7.29344	+	4.71617i	0.878027	+	0.567760i
$70$	−0.701272	−	3.97711i	−0.0838181	−	0.475356i
$71$	8.19790	−	14.1992i	0.972912	−	1.68513i	0.286252	−	0.958154i	$-0.407591\pi$
$71$	8.19790	−	14.1992i	0.972912	−	1.68513i	0.686660	−	0.726978i	$-0.259076\pi$
$72$	−2.09240	−	2.14986i	−0.246591	−	0.253363i
$73$	−2.37122	−	4.10707i	−0.277530	−	0.480696i	0.693240	−	0.720706i	$-0.256182\pi$
$73$	−2.37122	−	4.10707i	−0.277530	−	0.480696i	−0.970770	+	0.240011i	$0.922849\pi$
$74$	−8.59566	+	7.21261i	−0.999225	+	0.838449i
$75$	−19.0947	−	4.36905i	−2.20486	−	0.504495i
$76$	−1.00660	+	5.70871i	−0.115465	+	0.654834i
$77$	−1.43285	−	1.20231i	−0.163289	−	0.137015i
$78$	−0.246164	+	0.0307137i	−0.0278726	+	0.00347764i
$79$	13.0798	+	4.76064i	1.47159	+	0.535614i	0.948531	−	0.316684i	$-0.102570\pi$
$79$	13.0798	+	4.76064i	1.47159	+	0.535614i	0.523056	+	0.852298i	$0.324792\pi$
$80$	−4.03847			−0.451514
$81$	7.91325	−	4.28725i	0.879250	−	0.476361i
$82$	5.53320			0.611040
$83$	−5.71616	−	2.08051i	−0.627430	−	0.228366i	0.00868210	−	0.999962i	$-0.497236\pi$
$83$	−5.71616	−	2.08051i	−0.627430	−	0.228366i	−0.636113	+	0.771596i	$0.719459\pi$
$84$	1.71872	−	0.214444i	0.187528	−	0.0233978i
$85$	−17.9810	−	15.0879i	−1.95032	−	1.63651i
$86$	−1.36463	+	7.73918i	−0.147151	+	0.834537i
$87$	1.64800	+	0.377079i	0.176684	+	0.0404271i
$88$	−1.43285	+	1.20231i	−0.152743	+	0.128166i
$89$	−7.33655	−	12.7073i	−0.777672	−	1.34697i	−0.933280	−	0.359149i	$-0.883067\pi$
$89$	−7.33655	−	12.7073i	−0.777672	−	1.34697i	0.155608	−	0.987819i	$-0.450266\pi$
$90$	3.29390	−	11.6590i	0.347207	−	1.22897i
$91$	0.0716123	−	0.124036i	0.00750701	−	0.0130025i
$92$	0.870764	+	4.93835i	0.0907834	+	0.514858i
$93$	0.643675	+	0.416220i	0.0667459	+	0.0431601i
$94$	−0.796044	+	0.289736i	−0.0821057	+	0.0298840i
$95$	−21.9983	+	8.00672i	−2.25698	+	0.821472i
$96$	0.0872671	−	1.72985i	0.00890667	−	0.176552i
$97$	1.20884	+	6.85567i	0.122739	+	0.696087i	0.982625	+	0.185601i	$0.0594233\pi$
$97$	1.20884	+	6.85567i	0.122739	+	0.696087i	−0.859886	+	0.510486i	$0.829466\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	−2.30237	−	5.11728i	−0.231397	−	0.514306i
$100$	−5.65461	−	9.79407i	−0.565461	−	0.979407i
$101$	3.99434	−	3.35165i	0.397452	−	0.333501i	−0.422056	−	0.906570i	$-0.638691\pi$
$101$	3.99434	−	3.35165i	0.397452	−	0.333501i	0.819508	+	0.573068i	$0.194247\pi$
$102$	6.85134	−	7.37602i	0.678384	−	0.730335i
$103$	0.871428	−	4.94211i	0.0858644	−	0.486961i	−0.911302	−	0.411738i	$-0.864922\pi$
$103$	0.871428	−	4.94211i	0.0858644	−	0.486961i	0.997167	−	0.0752232i	$-0.0239669\pi$
$104$	−0.109716	−	0.0920630i	−0.0107586	−	0.00902752i
$105$	4.22051	+	5.57808i	0.411879	+	0.544365i
$106$	−1.25678	−	0.457432i	−0.122070	−	0.0444297i
$107$	−14.2271			−1.37538			−0.687690	−	0.726004i	$-0.741375\pi$
$107$	−14.2271			−1.37538			−0.687690	+	0.726004i	$0.741375\pi$
$108$	4.92290	+	1.66286i	0.473706	+	0.160009i
$109$	1.65651			0.158665			0.0793324	−	0.996848i	$-0.474721\pi$
$109$	1.65651			0.158665			0.0793324	+	0.996848i	$0.474721\pi$
$110$	−7.09823	−	2.58354i	−0.676789	−	0.246331i
$111$	7.55889	−	17.9049i	0.717458	−	1.69946i
$112$	0.766044	+	0.642788i	0.0723844	+	0.0607377i
$113$	2.26304	−	12.8343i	0.212889	−	1.20735i	−0.671644	−	0.740874i	$-0.734411\pi$
$113$	2.26304	−	12.8343i	0.212889	−	1.20735i	0.884533	−	0.466478i	$-0.154477\pi$
$114$	−2.95427	−	9.59584i	−0.276692	−	0.898733i
$115$	−15.5132	+	13.0171i	−1.44661	+	1.21385i
$116$	0.488031	+	0.845294i	0.0453125	+	0.0784836i
$117$	0.355274	−	0.241661i	0.0328451	−	0.0223416i
$118$	−3.19816	+	5.53937i	−0.294414	+	0.509940i
$119$	1.00929	+	5.72395i	0.0925211	+	0.524713i
$120$	6.22622	−	3.18776i	0.568373	−	0.291002i
$121$	7.04901	−	2.56563i	0.640819	−	0.233239i
$122$	4.17369	−	1.51910i	0.377868	−	0.137533i
$123$	−8.53069	+	4.36763i	−0.769187	+	0.393816i
$124$	0.0768483	+	0.435828i	0.00690118	+	0.0391386i
$125$	12.7398	−	22.0659i	1.13948	−	1.97364i
$126$	−2.48053	+	1.68729i	−0.220984	+	0.150316i
$127$	8.54778	+	14.8052i	0.758492	+	1.31375i	0.943619	+	0.331033i	$0.107397\pi$
$127$	8.54778	+	14.8052i	0.758492	+	1.31375i	−0.185127	+	0.982715i	$0.559270\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−4.00504	−	13.0089i	−0.352624	−	1.14537i
$130$	0.100439	−	0.569621i	0.00880913	−	0.0499590i
$131$	1.67327	+	1.40404i	0.146194	+	0.122671i	0.712952	−	0.701213i	$-0.247358\pi$
$131$	1.67327	+	1.40404i	0.146194	+	0.122671i	−0.566757	+	0.823885i	$0.691802\pi$
$132$	1.26003	−	2.98465i	0.109671	−	0.259781i
$133$	5.44719	+	1.98261i	0.472331	+	0.171914i
$134$	11.1427			0.962585
$135$	4.12476	+	20.5751i	0.355003	+	1.77082i
$136$	5.81225			0.498396
$137$	5.13665	+	1.86959i	0.438854	+	0.159730i	0.551992	−	0.833850i	$-0.313868\pi$
$137$	5.13665	+	1.86959i	0.438854	+	0.159730i	−0.113138	+	0.993579i	$0.536090\pi$
$138$	−5.24056	−	6.92625i	−0.446106	−	0.589602i
$139$	−0.950055	−	0.797190i	−0.0805826	−	0.0676168i	0.601607	−	0.798793i	$-0.294528\pi$
$139$	−0.950055	−	0.797190i	−0.0805826	−	0.0676168i	−0.682189	+	0.731176i	$0.738972\pi$
$140$	−0.701272	+	3.97711i	−0.0592683	+	0.336127i
$141$	0.998581	−	1.07505i	0.0840957	−	0.0905357i
$142$	−12.5599	+	10.5390i	−1.05400	+	0.884415i
$143$	−0.133948	−	0.232004i	−0.0112013	−	0.0194012i
$144$	1.23092	+	2.73584i	0.102576	+	0.227987i
$145$	−1.97090	+	3.41369i	−0.163674	+	0.283492i
$146$	0.823515	+	4.67038i	0.0681546	+	0.386524i
$147$	0.0872671	−	1.72985i	0.00719767	−	0.142676i
$148$	10.5441	−	3.83775i	0.866723	−	0.315461i
$149$	−10.0097	+	3.64323i	−0.820026	+	0.298465i	−0.717759	−	0.696292i	$-0.754832\pi$
$149$	−10.0097	+	3.64323i	−0.820026	+	0.298465i	−0.102267	+	0.994757i	$0.532610\pi$
$150$	16.4488	+	10.6363i	1.34304	+	0.868453i
$151$	0.698196	+	3.95966i	0.0568184	+	0.322233i	0.999948	−	0.0101921i	$-0.00324429\pi$
$151$	0.698196	+	3.95966i	0.0568184	+	0.322233i	−0.943130	+	0.332425i	$0.892133\pi$
$152$	2.89839	−	5.02016i	0.235090	−	0.407188i
$153$	−4.74065	+	16.7799i	−0.383259	+	1.35658i
$154$	0.935228	+	1.61986i	0.0753628	+	0.130532i
$155$	−1.36910	+	1.14881i	−0.109969	+	0.0922746i
$156$	0.241823	+	0.0553315i	0.0193613	+	0.00443007i
$157$	3.04833	−	17.2879i	0.243283	−	1.37973i	−0.581163	−	0.813787i	$-0.697402\pi$
$157$	3.04833	−	17.2879i	0.243283	−	1.37973i	0.824446	−	0.565941i	$-0.191487\pi$
$158$	−10.6627	−	8.94708i	−0.848280	−	0.711791i
$159$	2.29869	−	0.286807i	0.182298	−	0.0227452i
$160$	3.79492	+	1.38124i	0.300015	+	0.109196i
$161$	5.01453			0.395200
$162$	−8.90235	+	1.32221i	−0.699434	+	0.103882i
$163$	−19.5981			−1.53504			−0.767520	−	0.641025i	$-0.778510\pi$
$163$	−19.5981			−1.53504			−0.767520	+	0.641025i	$0.778510\pi$
$164$	−5.19951	−	1.89247i	−0.406013	−	0.147777i
$165$	12.9829	−	1.61986i	1.01071	−	0.126106i
$166$	4.65986	+	3.91009i	0.361675	+	0.303482i
$167$	−1.89828	+	10.7657i	−0.146893	+	0.833072i	0.818935	+	0.573887i	$0.194565\pi$
$167$	−1.89828	+	10.7657i	−0.146893	+	0.833072i	−0.965828	+	0.259185i	$0.916546\pi$
$168$	−1.68842	−	0.386327i	−0.130264	−	0.0298058i
$169$	−9.94286	+	8.34305i	−0.764836	+	0.641773i
$170$	11.7363	+	20.3278i	0.900132	+	1.55907i
$171$	12.1292	+	12.4622i	0.927539	+	0.953010i
$172$	3.92928	−	6.80572i	0.299605	−	0.518931i
$173$	−0.350017	−	1.98504i	−0.0266113	−	0.150920i	0.968607	−	0.248598i	$-0.0799697\pi$
$173$	−0.350017	−	1.98504i	−0.0266113	−	0.150920i	−0.995218	+	0.0976776i	$0.968859\pi$
$174$	−1.41964	−	0.917987i	−0.107623	−	0.0695924i
$175$	−10.6272	+	3.86798i	−0.803340	+	0.292392i
$176$	1.75765	−	0.639734i	0.132488	−	0.0482217i
$177$	0.558188	−	11.0647i	0.0419560	−	0.831671i
$178$	2.54796	+	14.4502i	0.190977	+	1.08309i
$179$	5.26387	−	9.11729i	0.393440	−	0.681458i	−0.599461	−	0.800404i	$-0.704618\pi$
$179$	5.26387	−	9.11729i	0.393440	−	0.681458i	0.992901	+	0.118946i	$0.0379515\pi$
$180$	−7.08288	+	9.82933i	−0.527927	+	0.732635i
$181$	13.3805	+	23.1756i	0.994562	+	1.72263i	0.587476	+	0.809241i	$0.300122\pi$
$181$	13.3805	+	23.1756i	0.994562	+	1.72263i	0.407085	+	0.913390i	$0.366545\pi$
$182$	−0.109716	+	0.0920630i	−0.00813272	+	0.00682417i
$183$	−5.23559	+	5.63654i	−0.387026	+	0.416665i
$184$	0.870764	−	4.93835i	0.0641935	−	0.364060i
$185$	34.7133	+	29.1279i	2.55217	+	2.14153i
$186$	−0.462500	−	0.611269i	−0.0339122	−	0.0448204i
$187$	10.2159	+	3.71829i	0.747062	+	0.271908i
$188$	0.847133			0.0617835
$189$	2.49245	−	4.55935i	0.181299	−	0.331644i
$190$	23.4101			1.69835
$191$	0.349848	+	0.127334i	0.0253141	+	0.00921358i	0.354646	−	0.935001i	$-0.384601\pi$
$191$	0.349848	+	0.127334i	0.0253141	+	0.00921358i	−0.329332	+	0.944214i	$0.606824\pi$
$192$	−0.673648	+	1.59568i	−0.0486164	+	0.115158i
$193$	−20.4027	−	17.1199i	−1.46862	−	1.23232i	−0.917407	−	0.397950i	$-0.869722\pi$
$193$	−20.4027	−	17.1199i	−1.46862	−	1.23232i	−0.551210	−	0.834366i	$-0.685834\pi$
$194$	1.20884	−	6.85567i	0.0867896	−	0.492208i
$195$	0.294780	+	0.957482i	0.0211096	+	0.0685667i
$196$	0.766044	−	0.642788i	0.0547175	−	0.0459134i
$197$	−3.00912	−	5.21195i	−0.214391	−	0.371336i	0.738693	−	0.674042i	$-0.235443\pi$
$197$	−3.00912	−	5.21195i	−0.214391	−	0.371336i	−0.953084	+	0.302706i	$0.902110\pi$
$198$	0.413311	+	5.59613i	0.0293727	+	0.397699i
$199$	3.78279	−	6.55198i	0.268155	−	0.464458i	−0.700231	−	0.713917i	$-0.746919\pi$
$199$	3.78279	−	6.55198i	0.268155	−	0.464458i	0.968385	+	0.249459i	$0.0802528\pi$
$200$	1.96382	+	11.1374i	0.138863	+	0.787533i
$201$	−17.1791	+	8.79551i	−1.21172	+	0.620388i
$202$	−4.89978	+	1.78337i	−0.344747	+	0.125478i
$203$	0.917198	−	0.333833i	0.0643746	−	0.0234305i
$204$	−8.96091	+	4.58790i	−0.627389	+	0.321217i
$205$	−3.88028	−	22.0062i	−0.271011	−	1.53698i
$206$	−2.50918	+	4.34602i	−0.174823	+	0.302802i
$207$	13.5468	+	6.54176i	0.941565	+	0.454684i
$208$	0.0716123	+	0.124036i	0.00496542	+	0.00860036i
$209$	8.30592	−	6.96950i	0.574533	−	0.482090i
$210$	−2.05816	−	6.68518i	−0.142027	−	0.461321i
$211$	−3.25946	+	18.4853i	−0.224390	+	1.27258i	0.639457	+	0.768827i	$0.279159\pi$
$211$	−3.25946	+	18.4853i	−0.224390	+	1.27258i	−0.863847	+	0.503754i	$0.831952\pi$
$212$	1.02454	+	0.859691i	0.0703657	+	0.0590438i
$213$	11.0450	−	26.1625i	0.756791	−	1.79262i
$214$	13.3691	+	4.86594i	0.913890	+	0.332629i
$215$	31.7366			2.16442
$216$	−4.05728	−	3.24631i	−0.276063	−	0.220883i
$217$	0.442552			0.0300424
$218$	−1.55661	−	0.566560i	−0.105427	−	0.0383723i
$219$	−4.95620	−	6.55042i	−0.334909	−	0.442637i
$220$	5.78653	+	4.85547i	0.390128	+	0.327356i
$221$	−0.144555	+	0.819810i	−0.00972380	+	0.0551464i
$222$	−13.2269	+	14.2398i	−0.887729	+	0.955712i
$223$	2.99149	−	2.51016i	0.200325	−	0.168093i	−0.537107	−	0.843514i	$-0.680483\pi$
$223$	2.99149	−	2.51016i	0.200325	−	0.168093i	0.737432	+	0.675422i	$0.236038\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−33.7554	−	3.41446i	−2.25036	−	0.227631i
$226$	−6.51616	+	11.2863i	−0.433449	+	0.750755i
$227$	−2.37421	−	13.4648i	−0.157582	−	0.893690i	−0.956387	−	0.292101i	$-0.905646\pi$
$227$	−2.37421	−	13.4648i	−0.157582	−	0.893690i	0.798806	−	0.601589i	$-0.205465\pi$
$228$	−0.505868	+	10.0276i	−0.0335019	+	0.664091i
$229$	−4.27135	+	1.55464i	−0.282259	+	0.102734i	−0.479270	−	0.877667i	$-0.659099\pi$
$229$	−4.27135	+	1.55464i	−0.282259	+	0.102734i	0.197012	+	0.980401i	$0.436876\pi$
$230$	19.0297	−	6.92625i	1.25478	−	0.456703i
$231$	−2.72051	−	1.75917i	−0.178996	−	0.115745i
$232$	−0.169491	−	0.961233i	−0.0111276	−	0.0631080i
$233$	13.5384	−	23.4492i	0.886931	−	1.53621i	0.0434464	−	0.999056i	$-0.486166\pi$
$233$	13.5384	−	23.4492i	0.886931	−	1.53621i	0.843484	−	0.537154i	$-0.180500\pi$
$234$	−0.416501	+	0.105577i	−0.0272275	+	0.00690177i
$235$	1.71056	+	2.96277i	0.111585	+	0.193270i
$236$	4.89986	−	4.11147i	0.318954	−	0.267634i
$237$	23.5014	+	5.37735i	1.52658	+	0.349297i
$238$	1.00929	−	5.72395i	0.0654223	−	0.371028i
$239$	1.40909	+	1.18237i	0.0911467	+	0.0764812i	0.687222	−	0.726447i	$-0.258830\pi$
$239$	1.40909	+	1.18237i	0.0911467	+	0.0764812i	−0.596076	+	0.802928i	$0.703274\pi$
$240$	−6.94101	+	0.866025i	−0.448040	+	0.0559017i
$241$	13.9391	+	5.07340i	0.897893	+	0.326806i	0.749408	−	0.662108i	$-0.230338\pi$
$241$	13.9391	+	5.07340i	0.897893	+	0.326806i	0.148485	+	0.988915i	$0.452560\pi$
$242$	−7.50139			−0.482208
$243$	12.6813	−	9.06555i	0.813507	−	0.581555i
$244$	−4.44155			−0.284341
$245$	3.79492	+	1.38124i	0.242448	+	0.0882440i
$246$	9.51005	−	1.18656i	0.606338	−	0.0756524i
$247$	0.636002	+	0.533669i	0.0404678	+	0.0339565i
$248$	0.0768483	−	0.435828i	0.00487987	−	0.0276751i
$249$	−10.2707	−	2.35003i	−0.650877	−	0.148927i
$250$	−19.5185	+	16.3779i	−1.23446	+	1.03583i
$251$	8.95502	+	15.5106i	0.565236	+	0.979018i	0.997028	+	0.0770443i	$0.0245483\pi$
$251$	8.95502	+	15.5106i	0.565236	+	0.979018i	−0.431792	+	0.901973i	$0.642118\pi$
$252$	2.90803	−	0.737141i	0.183189	−	0.0464355i
$253$	4.68973	−	8.12284i	0.294841	−	0.510679i
$254$	−2.96861	−	16.8358i	−0.186267	−	1.05637i
$255$	−34.1399	−	22.0760i	−2.13793	−	1.38245i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	26.9143	−	9.79601i	1.67887	−	0.611058i	0.685715	−	0.727870i	$-0.259490\pi$
$257$	26.9143	−	9.79601i	1.67887	−	0.611058i	0.993154	+	0.116812i	$0.0372675\pi$
$258$	−0.685795	+	13.5941i	−0.0426957	+	0.846335i
$259$	−1.94848	−	11.0504i	−0.121072	−	0.686636i
$260$	−0.289204	+	0.500916i	−0.0179357	+	0.0310655i
$261$	2.91332	+	0.294691i	0.180330	+	0.0182409i
$262$	−1.09215	−	1.89166i	−0.0674732	−	0.116867i
$263$	−19.2683	+	16.1680i	−1.18813	+	0.996961i	−0.188242	+	0.982123i	$0.560279\pi$
$263$	−19.2683	+	16.1680i	−1.18813	+	0.996961i	−0.999890	+	0.0148386i	$0.995277\pi$
$264$	−2.20485	+	2.37370i	−0.135699	+	0.146091i
$265$	−0.937911	+	5.31916i	−0.0576154	+	0.326753i
$266$	−4.44059	−	3.72610i	−0.272270	−	0.228462i
$267$	−15.3345	−	20.2670i	−0.938456	−	1.24032i
$268$	−10.4707	−	3.81104i	−0.639602	−	0.232796i
$269$	−18.8481			−1.14919			−0.574595	−	0.818438i	$-0.694840\pi$
$269$	−18.8481			−1.14919			−0.574595	+	0.818438i	$0.694840\pi$
$270$	3.16109	−	20.7450i	0.192378	−	1.26250i
$271$	−8.29592			−0.503941			−0.251971	−	0.967735i	$-0.581079\pi$
$271$	−8.29592			−0.503941			−0.251971	+	0.967735i	$0.581079\pi$
$272$	−5.46173	−	1.98791i	−0.331166	−	0.120534i
$273$	0.0964830	−	0.228541i	0.00583942	−	0.0138319i
$274$	−4.18744	−	3.51368i	−0.252972	−	0.212269i
$275$	−3.67325	+	20.8320i	−0.221505	+	1.25622i
$276$	2.55560	+	8.30093i	0.153829	+	0.499657i
$277$	−12.7031	+	10.6592i	−0.763255	+	0.640447i	−0.938972	−	0.343994i	$-0.888220\pi$
$277$	−12.7031	+	10.6592i	−0.763255	+	0.640447i	0.175717	+	0.984441i	$0.443776\pi$
$278$	0.620104	+	1.07405i	0.0371914	+	0.0644173i
$279$	1.19556	+	0.577336i	0.0715760	+	0.0345642i
$280$	2.01923	−	3.49741i	0.120672	−	0.209011i
$281$	5.17006	+	29.3209i	0.308420	+	1.74914i	0.606954	+	0.794737i	$0.292391\pi$
$281$	5.17006	+	29.3209i	0.308420	+	1.74914i	−0.298534	+	0.954399i	$0.596498\pi$
$282$	−1.30605	+	0.668684i	−0.0777741	+	0.0398196i
$283$	15.4418	−	5.62035i	0.917919	−	0.334095i	0.160509	−	0.987034i	$-0.448687\pi$
$283$	15.4418	−	5.62035i	0.917919	−	0.334095i	0.757410	+	0.652939i	$0.226464\pi$
$284$	15.4070	−	5.60770i	0.914238	−	0.332755i
$285$	−36.0920	+	18.4787i	−2.13791	+	1.09459i
$286$	0.0465195	+	0.263825i	0.00275076	+	0.0156003i
$287$	−2.76660	+	4.79189i	−0.163307	+	0.282856i
$288$	−0.220968	−	2.99185i	−0.0130207	−	0.176297i
$289$	−8.39111	−	14.5338i	−0.493594	−	0.854931i
$290$	3.01959	−	2.53373i	0.177316	−	0.148786i
$291$	3.54782	+	11.5238i	0.207977	+	0.675535i
$292$	0.823515	−	4.67038i	0.0481926	−	0.273314i
$293$	−9.29473	−	7.79920i	−0.543004	−	0.455634i	0.329560	−	0.944135i	$-0.393100\pi$
$293$	−9.29473	−	7.79920i	−0.543004	−	0.455634i	−0.872564	+	0.488500i	$0.837544\pi$
$294$	−0.673648	+	1.59568i	−0.0392880	+	0.0930620i
$295$	24.2735	+	8.83482i	1.41326	+	0.514383i
$296$	−11.2208			−0.652198
$297$	−5.05451	−	8.30146i	−0.293293	−	0.481700i
$298$	10.6521			0.617059
$299$	0.674891	+	0.245640i	0.0390300	+	0.0142057i
$300$	−11.8190	−	15.6207i	−0.682370	−	0.901862i
$301$	−6.02001	−	5.05139i	−0.346988	−	0.291157i
$302$	0.698196	−	3.95966i	0.0401766	−	0.227853i
$303$	6.14643	−	6.61712i	0.353103	−	0.380144i
$304$	−4.44059	+	3.72610i	−0.254685	+	0.213706i
$305$	−8.96852	−	15.5339i	−0.513536	−	0.889470i
$306$	10.1938	−	14.1466i	0.582742	−	0.808706i
$307$	−11.6331	+	20.1491i	−0.663935	+	1.14997i	0.315637	+	0.948880i	$0.397782\pi$
$307$	−11.6331	+	20.1491i	−0.663935	+	1.14997i	−0.979573	+	0.201090i	$0.935552\pi$
$308$	−0.324801	−	1.84204i	−0.0185073	−	0.104960i
$309$	0.437937	−	8.68101i	0.0249134	−	0.493845i
$310$	1.67945	−	0.611269i	0.0953862	−	0.0347177i
$311$	−1.26459	+	0.460273i	−0.0717083	+	0.0260997i	−0.377625	−	0.925959i	$-0.623259\pi$
$311$	−1.26459	+	0.460273i	−0.0717083	+	0.0260997i	0.305917	+	0.952058i	$0.401037\pi$
$312$	−0.208315	−	0.134703i	−0.0117935	−	0.00762605i
$313$	3.31953	+	18.8260i	0.187631	+	1.06411i	0.922528	+	0.385930i	$0.126119\pi$
$313$	3.31953	+	18.8260i	0.187631	+	1.06411i	−0.734897	+	0.678179i	$0.762770\pi$
$314$	−8.77732	+	15.2028i	−0.495333	+	0.857942i
$315$	8.45007	+	8.68212i	0.476108	+	0.489182i
$316$	6.95959	+	12.0544i	0.391508	+	0.678111i
$317$	−8.44115	+	7.08296i	−0.474102	+	0.397819i	−0.848288	−	0.529535i	$-0.822367\pi$
$317$	−8.44115	+	7.08296i	−0.474102	+	0.397819i	0.374186	+	0.927354i	$0.377922\pi$
$318$	−2.25816	−	0.516690i	−0.126631	−	0.0289745i
$319$	0.317026	−	1.79794i	0.0177500	−	0.100665i
$320$	−3.09365	−	2.59588i	−0.172940	−	0.145114i
$321$	−24.4524	+	3.05091i	−1.36480	+	0.170285i
$322$	−4.71211	−	1.71507i	−0.262596	−	0.0955771i
$323$	−33.6923			−1.87469
$324$	8.81769	+	1.80231i	0.489872	+	0.100128i
$325$	−1.61976			−0.0898480
$326$	18.4162	+	6.70294i	1.01998	+	0.371242i
$327$	2.84708	−	0.355229i	0.157444	−	0.0196442i
$328$	4.23868	+	3.55667i	0.234042	+	0.196384i
$329$	0.147103	−	0.834263i	0.00811005	−	0.0459944i
$330$	−12.7539	−	2.91823i	−0.702080	−	0.160643i
$331$	7.80619	−	6.55017i	0.429067	−	0.360030i	−0.402533	−	0.915406i	$-0.631870\pi$
$331$	7.80619	−	6.55017i	0.429067	−	0.360030i	0.831600	+	0.555376i	$0.187426\pi$
$332$	−3.04151	−	5.26804i	−0.166924	−	0.289121i
$333$	9.15206	−	32.3945i	0.501530	−	1.77521i
$334$	5.46587	−	9.46716i	0.299079	−	0.518020i
$335$	−7.81409	−	44.3159i	−0.426929	−	2.42124i
$336$	1.45446	+	0.940501i	0.0793474	+	0.0513085i
$337$	−8.83173	+	3.21449i	−0.481095	+	0.175104i	−0.571172	−	0.820830i	$-0.693511\pi$
$337$	−8.83173	+	3.21449i	−0.481095	+	0.175104i	0.0900766	+	0.995935i	$0.471289\pi$
$338$	12.1967	−	4.43925i	0.663415	−	0.241463i
$339$	1.13729	−	22.5440i	0.0617693	−	1.22442i
$340$	−4.07597	−	23.1160i	−0.221050	−	1.25364i
$341$	0.413887	−	0.716873i	0.0224132	−	0.0388209i
$342$	−7.13534	−	15.8591i	−0.385835	−	0.857561i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	−6.02001	+	5.05139i	−0.324577	+	0.272353i
$345$	−23.8714	+	25.6995i	−1.28519	+	1.38361i
$346$	−0.350017	+	1.98504i	−0.0188170	+	0.106717i
$347$	−6.28929	−	5.27734i	−0.337627	−	0.283302i	0.458172	−	0.888863i	$-0.348504\pi$
$347$	−6.28929	−	5.27734i	−0.337627	−	0.283302i	−0.795799	+	0.605561i	$0.792949\pi$
$348$	1.02006	+	1.34817i	0.0546809	+	0.0722696i
$349$	14.4931	+	5.27506i	0.775798	+	0.282368i	0.699420	−	0.714711i	$-0.253442\pi$
$349$	14.4931	+	5.27506i	0.775798	+	0.282368i	0.0763789	+	0.997079i	$0.475664\pi$
$350$	11.3092			0.604503
$351$	0.558795	−	0.491536i	0.0298263	−	0.0262362i
$352$	−1.87046			−0.0996956
$353$	−11.7876	−	4.29033i	−0.627390	−	0.228351i	0.00870476	−	0.999962i	$-0.497229\pi$
$353$	−11.7876	−	4.29033i	−0.627390	−	0.228351i	−0.636095	+	0.771611i	$0.719451\pi$
$354$	−4.30886	+	10.2065i	−0.229013	+	0.542468i
$355$	50.7228	+	42.5615i	2.69209	+	2.25893i
$356$	2.54796	−	14.4502i	0.135041	−	0.765858i
$357$	2.96215	+	9.62145i	0.156774	+	0.509221i
$358$	−8.06472	+	6.76710i	−0.426234	+	0.357652i
$359$	13.2218	+	22.9009i	0.697821	+	1.20866i	0.969221	+	0.246194i	$0.0791801\pi$
$359$	13.2218	+	22.9009i	0.697821	+	1.20866i	−0.271400	+	0.962467i	$0.587487\pi$
$360$	10.0176	−	6.81406i	0.527972	−	0.359133i
$361$	−7.30130	+	12.6462i	−0.384279	+	0.665591i
$362$	−4.64698	−	26.3544i	−0.244240	−	1.38515i
$363$	11.5651	−	5.92123i	0.607011	−	0.310784i
$364$	0.134587	−	0.0489857i	0.00705428	−	0.00256755i
$365$	17.9971	−	6.55042i	0.942013	−	0.342865i
$366$	6.84766	−	3.50593i	0.357933	−	0.183258i
$367$	−1.86052	−	10.5515i	−0.0971182	−	0.550785i	−0.994078	−	0.108672i	$-0.965340\pi$
$367$	−1.86052	−	10.5515i	−0.0971182	−	0.550785i	0.896959	−	0.442113i	$-0.145771\pi$
$368$	−2.50726	+	4.34271i	−0.130700	+	0.226379i
$369$	−13.7253	+	9.33611i	−0.714510	+	0.486019i
$370$	−22.6575	−	39.2439i	−1.17791	−	2.04019i
$371$	1.02454	−	0.859691i	0.0531915	−	0.0446329i
$372$	0.225542	+	0.732589i	0.0116938	+	0.0379830i
$373$	−1.98986	+	11.2851i	−0.103031	+	0.584319i	0.888957	+	0.457990i	$0.151431\pi$
$373$	−1.98986	+	11.2851i	−0.103031	+	0.584319i	−0.991988	+	0.126329i	$0.959681\pi$
$374$	−8.32809	−	6.98810i	−0.430635	−	0.361346i
$375$	17.1643	−	40.6572i	0.886358	−	2.09953i
$376$	−0.796044	−	0.289736i	−0.0410528	−	0.0149420i
$377$	0.139796			0.00719986
$378$	−3.90153	+	3.43192i	−0.200673	+	0.176519i
$379$	25.7730			1.32387			0.661936	−	0.749560i	$-0.269735\pi$
$379$	25.7730			1.32387			0.661936	+	0.749560i	$0.269735\pi$
$380$	−21.9983	−	8.00672i	−1.12849	−	0.410736i
$381$	17.8662	+	23.6130i	0.915311	+	1.20973i
$382$	−0.285199	−	0.239310i	−0.0145920	−	0.0122442i
$383$	−0.142628	+	0.808881i	−0.00728793	+	0.0413319i	−0.988235	−	0.152944i	$-0.951125\pi$
$383$	−0.142628	+	0.808881i	−0.00728793	+	0.0413319i	0.980947	+	0.194276i	$0.0622357\pi$
$384$	1.17878	−	1.26905i	0.0601542	−	0.0647609i
$385$	5.78653	−	4.85547i	0.294909	−	0.247458i
$386$	13.3169	+	23.0656i	0.677813	+	1.17401i
$387$	−9.67323	−	21.4998i	−0.491718	−	1.09290i
$388$	−3.48071	+	6.02877i	−0.176706	+	0.306064i
$389$	2.03448	+	11.5381i	0.103152	+	0.585004i	0.991942	+	0.126690i	$0.0404354\pi$
$389$	2.03448	+	11.5381i	0.103152	+	0.585004i	−0.888790	+	0.458314i	$0.848453\pi$
$390$	0.0504760	−	1.00056i	0.00255595	−	0.0506653i
$391$	−27.3880	+	9.96841i	−1.38507	+	0.504124i
$392$	−0.939693	+	0.342020i	−0.0474616	+	0.0172746i
$393$	3.17698	+	2.05433i	0.160257	+	0.103627i
$394$	1.04506	+	5.92681i	0.0526492	+	0.298589i
$395$	−28.1061	+	48.6811i	−1.41417	+	2.44941i
$396$	1.52560	−	5.40000i	0.0766644	−	0.271360i
$397$	−8.56236	−	14.8304i	−0.429733	−	0.744319i	0.567117	−	0.823637i	$-0.308059\pi$
$397$	−8.56236	−	14.8304i	−0.429733	−	0.744319i	−0.996849	+	0.0793187i	$0.974726\pi$
$398$	−5.79557	+	4.86306i	−0.290506	+	0.243763i
$399$	9.78737	+	2.23945i	0.489982	+	0.112113i
$400$	1.96382	−	11.1374i	0.0981912	−	0.556870i
$401$	20.4643	+	17.1716i	1.02194	+	0.857509i	0.989870	−	0.141976i	$-0.0453457\pi$
$401$	20.4643	+	17.1716i	1.02194	+	0.857509i	0.0320697	+	0.999486i	$0.489790\pi$
$402$	19.1513	−	2.38949i	0.955179	−	0.119177i
$403$	0.0595618	+	0.0216787i	0.00296698	+	0.00107989i
$404$	5.21424			0.259418
$405$	11.5015	+	34.4784i	0.571516	+	1.71325i
$406$	−0.976061			−0.0484411
$407$	−19.7223	−	7.17834i	−0.977600	−	0.355817i
$408$	9.98965	−	1.24640i	0.494561	−	0.0617061i
$409$	−17.2699	−	14.4912i	−0.853941	−	0.716541i	0.106713	−	0.994290i	$-0.465967\pi$
$409$	−17.2699	−	14.4912i	−0.853941	−	0.716541i	−0.960654	+	0.277749i	$0.910412\pi$
$410$	−3.88028	+	22.0062i	−0.191633	+	1.08681i
$411$	9.22941	+	2.11178i	0.455253	+	0.104167i
$412$	3.84428	−	3.22574i	0.189394	−	0.158921i
$413$	−3.19816	−	5.53937i	−0.157371	−	0.272574i
$414$	−10.4924	−	10.7805i	−0.515672	−	0.529833i
$415$	12.2830	−	21.2748i	0.602950	−	1.04434i
$416$	−0.0248707	−	0.141049i	−0.00121939	−	0.00691548i
$417$	−1.80383	−	1.16642i	−0.0883342	−	0.0571197i
$418$	−10.1887	+	3.70839i	−0.498347	+	0.181383i
$419$	−9.21448	+	3.35379i	−0.450157	+	0.163844i	−0.557142	−	0.830417i	$-0.688102\pi$
$419$	−9.21448	+	3.35379i	−0.450157	+	0.163844i	0.106986	+	0.994261i	$0.465880\pi$
$420$	−0.352425	+	6.98595i	−0.0171966	+	0.340879i
$421$	2.01256	+	11.4138i	0.0980859	+	0.556273i	0.993758	+	0.111558i	$0.0355840\pi$
$421$	2.01256	+	11.4138i	0.0980859	+	0.556273i	−0.895672	+	0.444715i	$0.853305\pi$
$422$	9.38523	−	16.2557i	0.456866	−	0.791315i
$423$	1.48575	−	2.06186i	0.0722395	−	0.100251i
$424$	−0.668721	−	1.15826i	−0.0324760	−	0.0562500i
$425$	50.3536	−	42.2517i	2.44251	−	2.04951i
$426$	−19.3270	+	20.8071i	−0.936396	+	1.00811i
$427$	−0.771266	+	4.37407i	−0.0373242	+	0.211676i
$428$	−10.8986	−	9.14497i	−0.526801	−	0.442039i
$429$	−0.279971	−	0.370027i	−0.0135171	−	0.0178651i
$430$	−29.8226	−	10.8545i	−1.43817	−	0.523452i
$431$	26.2094			1.26246			0.631232	−	0.775594i	$-0.282549\pi$
$431$	26.2094			1.26246			0.631232	+	0.775594i	$0.282549\pi$
$432$	2.70229	+	4.43820i	0.130014	+	0.213533i
$433$	1.41235			0.0678730			0.0339365	−	0.999424i	$-0.489196\pi$
$433$	1.41235			0.0678730			0.0339365	+	0.999424i	$0.489196\pi$
$434$	−0.415863	−	0.151362i	−0.0199620	−	0.00726559i
$435$	−2.65538	+	6.28984i	−0.127316	+	0.301575i
$436$	1.26896	+	1.06478i	0.0607722	+	0.0509939i
$437$	−5.04762	+	28.6265i	−0.241460	+	1.36939i
$438$	2.41693	+	7.85051i	0.115485	+	0.375112i
$439$	11.4747	−	9.62846i	0.547660	−	0.459541i	−0.326488	−	0.945201i	$-0.605865\pi$
$439$	11.4747	−	9.62846i	0.547660	−	0.459541i	0.874148	+	0.485660i	$0.161421\pi$
$440$	−3.77689	−	6.54176i	−0.180056	−	0.311866i
$441$	−0.220968	−	2.99185i	−0.0105223	−	0.142469i
$442$	0.416228	−	0.720929i	0.0197980	−	0.0342911i
$443$	4.22405	+	23.9558i	0.200691	+	1.13817i	0.904079	+	0.427366i	$0.140559\pi$
$443$	4.22405	+	23.9558i	0.200691	+	1.13817i	−0.703388	+	0.710806i	$0.748330\pi$
$444$	17.2995	−	8.85716i	0.820997	−	0.420342i
$445$	55.6832	−	20.2670i	2.63964	−	0.960749i
$446$	−3.66960	+	1.33563i	−0.173761	+	0.0632438i
$447$	−16.4226	+	8.40822i	−0.776764	+	0.397695i
$448$	0.173648	+	0.984808i	0.00820411	+	0.0465278i
$449$	0.909705	−	1.57566i	0.0429316	−	0.0743598i	−0.843761	−	0.536719i	$-0.819664\pi$
$449$	0.909705	−	1.57566i	0.0429316	−	0.0743598i	0.886693	+	0.462359i	$0.152997\pi$
$450$	30.5519	+	14.7536i	1.44023	+	0.695490i
$451$	5.17480	+	8.96302i	0.243672	+	0.422052i
$452$	9.98334	−	8.37702i	0.469577	−	0.394022i
$453$	2.04913	+	6.65585i	0.0962766	+	0.312719i
$454$	−2.37421	+	13.4648i	−0.111427	+	0.631934i
$455$	0.443086	+	0.371793i	0.0207722	+	0.0174299i
$456$	3.90499	−	9.24981i	0.182868	−	0.433162i
$457$	−5.58503	−	2.03278i	−0.261257	−	0.0950896i	0.208071	−	0.978114i	$-0.433281\pi$
$457$	−5.58503	−	2.03278i	−0.261257	−	0.0950896i	−0.469328	+	0.883024i	$0.655504\pi$
$458$	4.54547			0.212396
$459$	−4.54951	+	29.8567i	−0.212353	+	1.39359i
$460$	−20.2510			−0.944208
$461$	−6.69058	−	2.43517i	−0.311611	−	0.113417i	0.181480	−	0.983395i	$-0.441911\pi$
$461$	−6.69058	−	2.43517i	−0.311611	−	0.113417i	−0.493092	+	0.869977i	$0.664133\pi$
$462$	1.95477	+	2.58354i	0.0909441	+	0.120197i
$463$	−13.4528	−	11.2883i	−0.625207	−	0.524611i	0.274229	−	0.961665i	$-0.411577\pi$
$463$	−13.4528	−	11.2883i	−0.625207	−	0.524611i	−0.899435	+	0.437054i	$0.856022\pi$
$464$	−0.169491	+	0.961233i	−0.00786843	+	0.0446241i
$465$	−2.10675	+	2.26808i	−0.0976981	+	0.105180i
$466$	−20.7421	+	17.4046i	−0.960857	+	0.806255i
$467$	10.8850	+	18.8534i	0.503700	+	0.872433i	0.999991	+	0.00427731i	$0.00136152\pi$
$467$	10.8850	+	18.8534i	0.503700	+	0.872433i	−0.496291	+	0.868156i	$0.665305\pi$
$468$	0.427492	+	0.0432421i	0.0197608	+	0.00199887i
$469$	−5.57136	+	9.64989i	−0.257262	+	0.445590i
$470$	−0.594071	−	3.36914i	−0.0274024	−	0.155407i
$471$	1.53194	−	30.3669i	0.0705882	−	1.39923i
$472$	−6.01057	+	2.18767i	−0.276659	+	0.100696i
$473$	−13.8126	+	5.02739i	−0.635106	+	0.231160i
$474$	−20.2449	−	13.0910i	−0.929880	−	0.601290i
$475$	−11.3838	−	64.5610i	−0.522327	−	2.96226i
$476$	−2.90612	+	5.03355i	−0.133202	+	0.230713i
$477$	3.88932	−	0.985883i	0.178080	−	0.0451405i
$478$	−0.919721	−	1.59300i	−0.0420671	−	0.0728623i
$479$	−20.4386	+	17.1500i	−0.933862	+	0.783603i	−0.976507	−	0.215487i	$-0.930866\pi$
$479$	−20.4386	+	17.1500i	−0.933862	+	0.783603i	0.0426446	+	0.999090i	$0.486422\pi$
$480$	6.81862	+	1.56017i	0.311226	+	0.0712116i
$481$	0.279070	−	1.58268i	0.0127245	−	0.0721642i
$482$	−11.3632	−	9.53487i	−0.517580	−	0.434302i
$483$	8.61859	−	1.07534i	0.392160	−	0.0489295i
$484$	7.04901	+	2.56563i	0.320409	+	0.116619i
$485$	−28.1135			−1.27657
$486$	−15.0171	+	4.18157i	−0.681191	+	0.189680i
$487$	−0.474106			−0.0214838			−0.0107419	−	0.999942i	$-0.503419\pi$
$487$	−0.474106			−0.0214838			−0.0107419	+	0.999942i	$0.503419\pi$
$488$	4.17369	+	1.51910i	0.188934	+	0.0687664i
$489$	−33.6837	+	4.20269i	−1.52323	+	0.190052i
$490$	−3.09365	−	2.59588i	−0.139757	−	0.117270i
$491$	4.44602	−	25.2146i	0.200646	−	1.13792i	−0.703499	−	0.710696i	$-0.748380\pi$
$491$	4.44602	−	25.2146i	0.200646	−	1.13792i	0.904145	−	0.427225i	$-0.140509\pi$
$492$	−9.34235	−	2.13762i	−0.421186	−	0.0963715i
$493$	−4.34585	+	3.64660i	−0.195727	+	0.164235i
$494$	−0.415121	−	0.719010i	−0.0186772	−	0.0323498i
$495$	21.9666	−	5.56819i	0.987324	−	0.250272i
$496$	−0.221276	+	0.383261i	−0.00993558	+	0.0172089i
$497$	−2.84710	−	16.1467i	−0.127710	−	0.724279i
$498$	8.84751	+	5.72108i	0.396466	+	0.256368i
$499$	−30.4203	+	11.0721i	−1.36180	+	0.495655i	−0.916611	−	0.399781i	$-0.869086\pi$
$499$	−30.4203	+	11.0721i	−1.36180	+	0.495655i	−0.445190	+	0.895436i	$0.646864\pi$
$500$	23.9429	−	8.71452i	1.07076	−	0.389725i
$501$	−0.953982	+	18.9103i	−0.0426208	+	0.844849i
$502$	−3.11005	−	17.6380i	−0.138808	−	0.787220i
$503$	10.4516	−	18.1026i	0.466012	−	0.807157i	−0.533234	−	0.845968i	$-0.679024\pi$
$503$	10.4516	−	18.1026i	0.466012	−	0.807157i	0.999247	+	0.0388107i	$0.0123569\pi$
$504$	−2.98477	−	0.301918i	−0.132952	−	0.0134485i
$505$	10.5288	+	18.2364i	0.468524	+	0.811507i
$506$	−7.18508	+	6.02900i	−0.319416	+	0.268022i
$507$	−15.2999	+	16.4716i	−0.679493	+	0.731529i
$508$	−2.96861	+	16.8358i	−0.131711	+	0.746969i
$509$	−29.7747	−	24.9839i	−1.31974	−	1.10739i	−0.986361	−	0.164599i	$-0.947367\pi$
$509$	−29.7747	−	24.9839i	−1.31974	−	1.10739i	−0.333378	−	0.942793i	$-0.608189\pi$
$510$	24.5306	+	32.4212i	1.08623	+	1.43563i
$511$	−4.45643	−	1.62201i	−0.197141	−	0.0717534i
$512$	1.00000			0.0441942
$513$	23.5191	+	18.8181i	1.03839	+	0.830840i
$514$	−28.6416			−1.26333
$515$	19.0442	+	6.93154i	0.839189	+	0.305440i
$516$	5.29391	−	12.5398i	0.233051	−	0.552032i
$517$	−1.21382	−	1.01851i	−0.0533836	−	0.0447941i
$518$	−1.94848	+	11.0504i	−0.0856112	+	0.485525i
$519$	−1.02726	−	3.33668i	−0.0450918	−	0.146464i
$520$	0.443086	−	0.371793i	0.0194306	−	0.0163042i
$521$	−1.86798	−	3.23544i	−0.0818377	−	0.141747i	0.822202	−	0.569196i	$-0.192746\pi$
$521$	−1.86798	−	3.23544i	−0.0818377	−	0.141747i	−0.904039	+	0.427449i	$0.859412\pi$
$522$	−2.63683	−	1.27333i	−0.115411	−	0.0557322i
$523$	−0.558685	+	0.967670i	−0.0244296	+	0.0423133i	−0.877982	−	0.478694i	$-0.841110\pi$
$523$	−0.558685	+	0.967670i	−0.0244296	+	0.0423133i	0.853552	+	0.521007i	$0.174444\pi$
$524$	0.379299	+	2.15111i	0.0165698	+	0.0939718i
$525$	−17.4357	+	8.92693i	−0.760958	+	0.389603i
$526$	23.6360	−	8.60281i	1.03058	−	0.375100i
$527$	−2.41710	+	0.879751i	−0.105290	+	0.0383226i
$528$	2.88374	−	1.47644i	0.125498	−	0.0642540i
$529$	0.372561	+	2.11290i	0.0161983	+	0.0918650i
$530$	2.70061	−	4.67759i	0.117307	−	0.203182i
$531$	−1.41338	−	19.1368i	−0.0613355	−	0.830467i
$532$	2.89839	+	5.02016i	0.125661	+	0.217651i
$533$	−0.607083	+	0.509403i	−0.0262957	+	0.0220647i
$534$	7.47799	+	24.2895i	0.323604	+	1.05111i
$535$	9.97704	−	56.5826i	0.431345	−	2.44628i
$536$	8.53583	+	7.16241i	0.368692	+	0.309369i
$537$	7.09199	−	16.7989i	0.306042	−	0.724927i
$538$	17.7114	+	6.44643i	0.763594	+	0.277925i
$539$	−1.87046			−0.0805662
$540$	−10.0657	+	18.4128i	−0.433158	+	0.792360i
$541$	−15.5472			−0.668426			−0.334213	−	0.942498i	$-0.608471\pi$
$541$	−15.5472			−0.668426			−0.334213	+	0.942498i	$0.608471\pi$
$542$	7.79561	+	2.83737i	0.334850	+	0.121876i
$543$	27.9672	+	36.9632i	1.20019	+	1.58624i
$544$	4.45244	+	3.73604i	0.190897	+	0.160181i
$545$	−1.16166	+	6.58813i	−0.0497603	+	0.282204i
$546$	−0.168830	+	0.181759i	−0.00722526	+	0.00777857i
$547$	13.8868	−	11.6524i	0.593756	−	0.498220i	−0.295676	−	0.955288i	$-0.595545\pi$
$547$	13.8868	−	11.6524i	0.593756	−	0.498220i	0.889432	+	0.457068i	$0.151100\pi$
$548$	2.73316	+	4.73396i	0.116755	+	0.202225i
$549$	−7.78982	+	10.8104i	−0.332461	+	0.461377i
$550$	10.5767	−	18.3194i	0.450992	−	0.781141i
$551$	0.982503	+	5.57205i	0.0418560	+	0.237377i
$552$	0.437604	−	8.67439i	0.0186256	−	0.369206i
$553$	13.0798	−	4.76064i	0.556208	−	0.202443i
$554$	15.5827	−	5.67162i	0.662044	−	0.240964i
$555$	65.9089	+	42.6188i	2.79768	+	1.80907i
$556$	−0.215360	−	1.22137i	−0.00913329	−	0.0517975i
$557$	−5.21004	+	9.02405i	−0.220756	+	0.382361i	−0.955038	−	0.296484i	$-0.904186\pi$
$557$	−5.21004	+	9.02405i	−0.220756	+	0.382361i	0.734281	+	0.678845i	$0.237519\pi$
$558$	−0.925994	−	0.951422i	−0.0392004	−	0.0402769i
$559$	−0.562770	−	0.974746i	−0.0238026	−	0.0412274i
$560$	−3.09365	+	2.59588i	−0.130730	+	0.109696i
$561$	18.3557	+	4.19997i	0.774979	+	0.177323i
$562$	5.17006	−	29.3209i	0.218086	−	1.23683i
$563$	−27.6486	−	23.2000i	−1.16525	−	0.977762i	−0.165287	−	0.986245i	$-0.552855\pi$
$563$	−27.6486	−	23.2000i	−1.16525	−	0.977762i	−0.999964	+	0.00848362i	$0.997300\pi$
$564$	1.45599	−	0.181663i	0.0613081	−	0.00764938i
$565$	49.4566	+	18.0007i	2.08065	+	0.757296i
$566$	−16.4328			−0.690722
$567$	3.30611	−	8.37076i	0.138843	−	0.351539i
$568$	−16.3958			−0.687953
$569$	34.7927	+	12.6635i	1.45859	+	0.530882i	0.944975	−	0.327142i	$-0.106085\pi$
$569$	34.7927	+	12.6635i	1.45859	+	0.530882i	0.513610	+	0.858024i	$0.328308\pi$
$570$	40.2355	−	5.02016i	1.68528	−	0.210271i
$571$	9.18757	+	7.70929i	0.384488	+	0.322624i	0.814461	−	0.580218i	$-0.197033\pi$
$571$	9.18757	+	7.70929i	0.384488	+	0.322624i	−0.429973	+	0.902842i	$0.641477\pi$
$572$	0.0465195	−	0.263825i	0.00194508	−	0.0110311i
$573$	0.628598	+	0.143830i	0.0262601	+	0.00600857i
$574$	4.23868	−	3.55667i	0.176919	−	0.148453i
$575$	−28.3552	−	49.1126i	−1.18249	−	2.04814i
$576$	−0.815631	+	2.88700i	−0.0339846	+	0.120291i
$577$	−9.97108	+	17.2704i	−0.415101	+	0.718977i	−0.995439	−	0.0953992i	$-0.969587\pi$
$577$	−9.97108	+	17.2704i	−0.415101	+	0.718977i	0.580338	+	0.814376i	$0.302921\pi$
$578$	2.91420	+	16.5273i	0.121215	+	0.687443i
$579$	−38.7379	−	25.0491i	−1.60989	−	1.04101i
$580$	−3.70407	+	1.34817i	−0.153803	+	0.0559798i
$581$	−5.71616	+	2.08051i	−0.237146	+	0.0863142i
$582$	0.607504	−	12.0422i	0.0251818	−	0.499166i
$583$	−0.434403	−	2.46362i	−0.0179911	−	0.102033i
$584$	−2.37122	+	4.10707i	−0.0981216	+	0.169952i
$585$	0.711971	+	1.58243i	0.0294364	+	0.0654256i
$586$	6.06670	+	10.5078i	0.250613	+	0.434075i
$587$	−10.5311	+	8.83668i	−0.434667	+	0.364729i	−0.833709	−	0.552204i	$-0.813787\pi$
$587$	−10.5311	+	8.83668i	−0.434667	+	0.364729i	0.399042	+	0.916933i	$0.369343\pi$
$588$	1.17878	−	1.26905i	0.0486120	−	0.0523347i
$589$	−0.445472	+	2.52640i	−0.0183554	+	0.104098i
$590$	−19.7879	−	16.6040i	−0.814656	−	0.683577i
$591$	−6.28952	−	8.31262i	−0.258716	−	0.341936i
$592$	10.5441	+	3.83775i	0.433361	+	0.157731i
$593$	−1.92182			−0.0789196			−0.0394598	−	0.999221i	$-0.512564\pi$
$593$	−1.92182			−0.0789196			−0.0394598	+	0.999221i	$0.512564\pi$
$594$	1.91042	+	9.52957i	0.0783857	+	0.391003i
$595$	−23.4726			−0.962281
$596$	−10.0097	−	3.64323i	−0.410013	−	0.149232i
$597$	5.09654	−	12.0723i	0.208587	−	0.494084i
$598$	−0.550176	−	0.461653i	−0.0224984	−	0.0188784i
$599$	−0.352388	+	1.99849i	−0.0143982	+	0.0816561i	−0.991160	−	0.132671i	$-0.957645\pi$
$599$	−0.352388	+	1.99849i	−0.0143982	+	0.0816561i	0.976762	+	0.214327i	$0.0687558\pi$
$600$	5.76362	+	18.7210i	0.235299	+	0.764281i
$601$	−18.9142	+	15.8709i	−0.771526	+	0.647387i	−0.941099	−	0.338131i	$-0.890205\pi$
$601$	−18.9142	+	15.8709i	−0.771526	+	0.647387i	0.169573	+	0.985518i	$0.445761\pi$
$602$	3.92928	+	6.80572i	0.160146	+	0.277380i
$603$	−27.6399	+	18.8010i	−1.12558	+	0.765636i
$604$	−2.01037	+	3.48207i	−0.0818010	+	0.141683i
$605$	5.26052	+	29.8339i	0.213871	+	1.21292i
$606$	−8.03894	+	4.11586i	−0.326560	+	0.167195i
$607$	−6.95920	+	2.53294i	−0.282465	+	0.102809i	−0.479368	−	0.877614i	$-0.659134\pi$
$607$	−6.95920	+	2.53294i	−0.282465	+	0.102809i	0.196902	+	0.980423i	$0.436912\pi$
$608$	5.44719	−	1.98261i	0.220913	−	0.0804056i
$609$	1.50482	−	0.770454i	0.0609784	−	0.0312204i
$610$	3.11473	+	17.6645i	0.126112	+	0.715216i
$611$	0.0606651	−	0.105075i	0.00245425	−	0.00425088i
$612$	−14.4175	+	9.80694i	−0.582792	+	0.396422i
$613$	−14.4883	−	25.0946i	−0.585179	−	1.01356i	−0.994853	−	0.101328i	$-0.967691\pi$
$613$	−14.4883	−	25.0946i	−0.585179	−	1.01356i	0.409674	−	0.912232i	$-0.365642\pi$
$614$	17.8229	−	14.9552i	0.719275	−	0.603543i
$615$	−11.3882	−	36.9904i	−0.459218	−	1.49160i
$616$	−0.324801	+	1.84204i	−0.0130866	+	0.0742179i
$617$	−9.20524	−	7.72411i	−0.370589	−	0.310961i	0.438406	−	0.898777i	$-0.355543\pi$
$617$	−9.20524	−	7.72411i	−0.370589	−	0.310961i	−0.808994	+	0.587816i	$0.799988\pi$
$618$	−3.38061	+	8.00769i	−0.135988	+	0.322117i
$619$	15.6287	+	5.68838i	0.628170	+	0.228635i	0.636435	−	0.771331i	$-0.280409\pi$
$619$	15.6287	+	5.68838i	0.628170	+	0.228635i	−0.00826470	+	0.999966i	$0.502631\pi$
$620$	−1.78723			−0.0717769
$621$	24.6860	+	8.33846i	0.990615	+	0.334611i
$622$	1.34575			0.0539596
$623$	−13.7882	−	5.01849i	−0.552412	−	0.201062i
$624$	0.149681	+	0.197827i	0.00599202	+	0.00791943i
$625$	35.5079	+	29.7946i	1.42032	+	1.19179i
$626$	3.31953	−	18.8260i	0.132675	−	0.752438i
$627$	12.7810	−	13.7598i	0.510425	−	0.549514i
$628$	13.4476	−	11.2839i	0.536619	−	0.450277i
$629$	32.6091	+	56.4807i	1.30021	+	2.25203i
$630$	−4.97101	−	11.0486i	−0.198050	−	0.440187i
$631$	−8.79981	+	15.2417i	−0.350315	+	0.606763i	−0.986305	−	0.164935i	$-0.947259\pi$
$631$	−8.79981	+	15.2417i	−0.350315	+	0.606763i	0.635990	+	0.771697i	$0.280592\pi$
$632$	−2.41704	−	13.7077i	−0.0961447	−	0.545264i
$633$	−1.63804	+	32.4701i	−0.0651064	+	1.29057i
$634$	10.3546	−	3.76877i	0.411234	−	0.149677i
$635$	−64.8762	+	23.6130i	−2.57453	+	0.937054i
$636$	1.94526	+	1.25787i	0.0771345	+	0.0498776i
$637$	−0.0248707	−	0.141049i	−0.000985413	−	0.00558855i
$638$	−0.912840	+	1.58108i	−0.0361397	+	0.0625957i
$639$	13.3729	−	47.3346i	0.529025	−	1.87253i
$640$	2.01923	+	3.49741i	0.0798172	+	0.138247i
$641$	−1.08960	+	0.914286i	−0.0430368	+	0.0361121i	−0.664052	−	0.747686i	$-0.731165\pi$
$641$	−1.08960	+	0.914286i	−0.0430368	+	0.0361121i	0.621016	+	0.783798i	$0.286720\pi$
$642$	24.0212	+	5.49629i	0.948041	+	0.216921i
$643$	0.665454	−	3.77398i	0.0262429	−	0.148831i	−0.968871	−	0.247567i	$-0.920369\pi$
$643$	0.665454	−	3.77398i	0.0262429	−	0.148831i	0.995114	+	0.0987362i	$0.0314800\pi$
$644$	3.84135	+	3.22328i	0.151370	+	0.127015i
$645$	54.5464	−	6.80572i	2.14776	−	0.267975i
$646$	31.6604	+	11.5234i	1.24566	+	0.453384i
$647$	19.5538			0.768740			0.384370	−	0.923179i	$-0.374419\pi$
$647$	19.5538			0.768740			0.384370	+	0.923179i	$0.374419\pi$
$648$	−7.66949	−	4.70945i	−0.301286	−	0.185005i
$649$	−11.9640			−0.469629
$650$	1.52207	+	0.553990i	0.0597007	+	0.0217293i
$651$	0.760625	−	0.0949026i	0.0298112	−	0.00371953i
$652$	−15.0130	−	12.5974i	−0.587955	−	0.493353i
$653$	0.916996	−	5.20054i	0.0358848	−	0.203513i	−0.961594	−	0.274475i	$-0.911496\pi$
$653$	0.916996	−	5.20054i	0.0358848	−	0.203513i	0.997479	+	0.0709622i	$0.0226070\pi$
$654$	−2.79688	−	0.639954i	−0.109367	−	0.0250242i
$655$	−6.75744	+	5.67016i	−0.264035	+	0.221552i
$656$	−2.76660	−	4.79189i	−0.108018	−	0.187092i
$657$	−9.92305	−	10.1955i	−0.387135	−	0.397766i
$658$	−0.423566	+	0.733638i	−0.0165123	+	0.0286002i
$659$	3.22042	+	18.2639i	0.125450	+	0.711461i	0.981040	+	0.193807i	$0.0620836\pi$
$659$	3.22042	+	18.2639i	0.125450	+	0.711461i	−0.855590	+	0.517654i	$0.826805\pi$
$660$	10.9867	+	7.10433i	0.427656	+	0.276536i
$661$	−24.4686	+	8.90583i	−0.951717	+	0.346397i	−0.770783	−	0.637098i	$-0.780135\pi$
$661$	−24.4686	+	8.90583i	−0.951717	+	0.346397i	−0.180935	+	0.983495i	$0.557912\pi$
$662$	−9.57571	+	3.48527i	−0.372170	+	0.135459i
$663$	−0.0726461	+	1.44003i	−0.00282134	+	0.0559260i
$664$	1.05630	+	5.99060i	0.0409926	+	0.232480i
$665$	−11.7050	+	20.2737i	−0.453902	+	0.786181i
$666$	−19.6797	+	27.3107i	−0.762573	+	1.05827i
$667$	2.44724	+	4.23875i	0.0947576	+	0.164125i
$668$	−8.37420	+	7.02679i	−0.324007	+	0.271875i
$669$	4.60326	−	4.95578i	0.177972	−	0.191601i
$670$	−7.81409	+	44.3159i	−0.301885	+	1.71207i
$671$	6.36408	+	5.34010i	0.245683	+	0.206152i
$672$	−1.04508	−	1.38124i	−0.0403147	−	0.0532824i
$673$	−25.0848	−	9.13012i	−0.966948	−	0.351940i	−0.190195	−	0.981746i	$-0.560912\pi$
$673$	−25.0848	−	9.13012i	−0.966948	−	0.351940i	−0.776752	+	0.629806i	$0.783134\pi$
$674$	9.39854			0.362018
$675$	−58.7484	+	1.37013i	−2.26123	+	0.0527363i
$676$	−12.9795			−0.499211
$677$	0.413421	+	0.150473i	0.0158891	+	0.00578315i	0.349952	−	0.936767i	$-0.386198\pi$
$677$	0.413421	+	0.150473i	0.0158891	+	0.00578315i	−0.334063	+	0.942551i	$0.608420\pi$
$678$	−8.77920	+	20.7954i	−0.337163	+	0.798644i
$679$	5.33276	+	4.47472i	0.204653	+	0.171724i
$680$	−4.07597	+	23.1160i	−0.156306	+	0.886457i
$681$	−6.96806	−	22.6331i	−0.267016	−	0.867304i
$682$	−0.634111	+	0.532083i	−0.0242814	+	0.0203745i
$683$	−14.8735	−	25.7617i	−0.569120	−	0.985745i	−0.996653	−	0.0817455i	$-0.973951\pi$
$683$	−14.8735	−	25.7617i	−0.569120	−	0.985745i	0.427533	−	0.904000i	$-0.359383\pi$
$684$	1.28090	+	17.3431i	0.0489765	+	0.663130i
$685$	−11.0378	+	19.1180i	−0.421731	+	0.730460i
$686$	0.173648	+	0.984808i	0.00662992	+	0.0376001i
$687$	−7.00789	+	3.58797i	−0.267368	+	0.136890i
$688$	7.38464	−	2.68779i	0.281537	−	0.102471i
$689$	0.180003	−	0.0655156i	0.00685755	−	0.00249594i
$690$	31.2216	−	15.9851i	1.18858	−	0.608543i
$691$	−1.06268	−	6.02675i	−0.0404262	−	0.229268i	0.957900	−	0.287102i	$-0.0926919\pi$
$691$	−1.06268	−	6.02675i	−0.0404262	−	0.229268i	−0.998326	+	0.0578335i	$0.981581\pi$
$692$	1.00783	−	1.74562i	0.0383121	−	0.0663584i
$693$	−5.05304	−	2.44012i	−0.191949	−	0.0926927i
$694$	4.10504	+	7.11014i	0.155825	+	0.269897i
$695$	3.83676	−	3.21943i	0.145537	−	0.122120i
$696$	−0.497439	−	1.61575i	−0.0188554	−	0.0612448i
$697$	5.58458	−	31.6717i	0.211531	−	1.19965i
$698$	−11.8149	−	9.91387i	−0.447200	−	0.375246i
$699$	18.2403	−	43.2060i	0.689910	−	1.63420i
$700$	−10.6272	−	3.86798i	−0.401670	−	0.146196i
$701$	−36.3028			−1.37114			−0.685569	−	0.728007i	$-0.740447\pi$
$701$	−36.3028			−1.37114			−0.685569	+	0.728007i	$0.740447\pi$
$702$	−0.693210	+	0.270774i	−0.0261635	+	0.0102197i
$703$	65.0447			2.45321
$704$	1.75765	+	0.639734i	0.0662441	+	0.0241109i
$705$	3.57533	+	4.72537i	0.134655	+	0.177968i
$706$	9.60933	+	8.06319i	0.361652	+	0.303462i
$707$	0.905443	−	5.13502i	0.0340527	−	0.193122i
$708$	7.53983	−	8.11723i	0.283364	−	0.305064i
$709$	22.4981	−	18.8782i	0.844935	−	0.708985i	−0.113733	−	0.993511i	$-0.536281\pi$
$709$	22.4981	−	18.8782i	0.844935	−	0.708985i	0.958668	+	0.284526i	$0.0918364\pi$
$710$	−33.1070	−	57.3429i	−1.24248	−	2.15204i
$711$	41.5455	+	4.20246i	1.55808	+	0.157604i
$712$	−7.33655	+	12.7073i	−0.274949	+	0.476225i
$713$	0.385358	+	2.18547i	0.0144318	+	0.0818466i
$714$	0.507218	−	10.0543i	0.0189822	−	0.376273i
$715$	1.01664	−	0.370027i	0.0380202	−	0.0138382i
$716$	9.89284	−	3.60070i	0.369713	−	0.134564i
$717$	2.67540	+	1.73000i	0.0999145	+	0.0646079i
$718$	−4.59189	−	26.0419i	−0.171368	−	0.971875i
$719$	−23.7741	+	41.1779i	−0.886624	+	1.53568i	−0.0427831	+	0.999084i	$0.513622\pi$
$719$	−23.7741	+	41.1779i	−0.886624	+	1.53568i	−0.843841	+	0.536593i	$0.819711\pi$
$720$	−11.7440	+	2.97692i	−0.437672	+	0.110943i
$721$	−2.50918	−	4.34602i	−0.0934466	−	0.161854i
$722$	11.1862	−	9.38638i	0.416309	−	0.349325i
$723$	25.0454	+	5.73063i	0.931447	+	0.213124i
$724$	−4.64698	+	26.3544i	−0.172704	+	0.979452i
$725$	−8.45597	−	7.09540i	−0.314047	−	0.263517i
$726$	−12.8928	+	1.60863i	−0.478498	+	0.0597019i
$727$	21.2214	+	7.72397i	0.787060	+	0.286466i	0.704113	−	0.710088i	$-0.251345\pi$
$727$	21.2214	+	7.72397i	0.787060	+	0.286466i	0.0829464	+	0.996554i	$0.473567\pi$
$728$	−0.143225			−0.00530826
$729$	19.8516	−	18.3006i	0.735246	−	0.677801i
$730$	−19.1522			−0.708853
$731$	42.9213	+	15.6221i	1.58750	+	0.577804i
$732$	−7.63379	+	0.952463i	−0.282153	+	0.0352041i
$733$	−3.43760	−	2.88449i	−0.126971	−	0.106541i	0.577091	−	0.816680i	$-0.304188\pi$
$733$	−3.43760	−	2.88449i	−0.126971	−	0.106541i	−0.704062	+	0.710139i	$0.748632\pi$
$734$	−1.86052	+	10.5515i	−0.0686730	+	0.389464i
$735$	6.81862	+	1.56017i	0.251508	+	0.0575477i
$736$	3.84135	−	3.22328i	0.141594	−	0.118812i
$737$	10.4210	+	18.0497i	0.383862	+	0.664869i
$738$	16.0907	−	4.07875i	0.592307	−	0.150141i
$739$	10.5005	−	18.1875i	0.386269	−	0.669037i	−0.605676	−	0.795712i	$-0.707097\pi$
$739$	10.5005	−	18.1875i	0.386269	−	0.669037i	0.991944	+	0.126675i	$0.0404304\pi$
$740$	7.86886	+	44.6265i	0.289265	+	1.64050i
$741$	1.20755	+	0.780843i	0.0443606	+	0.0286850i
$742$	−1.25678	+	0.457432i	−0.0461380	+	0.0167929i
$743$	40.4804	−	14.7337i	1.48508	−	0.540526i	0.532934	−	0.846157i	$-0.321090\pi$
$743$	40.4804	−	14.7337i	1.48508	−	0.540526i	0.952150	+	0.305631i	$0.0988673\pi$
$744$	0.0386202	−	0.765549i	0.00141589	−	0.0280664i
$745$	−7.47001	−	42.3646i	−0.273680	−	1.55212i
$746$	5.72958	−	9.92393i	0.209775	−	0.363341i
$747$	−18.1564	−	1.83657i	−0.664308	−	0.0671967i
$748$	5.43578	+	9.41504i	0.198752	+	0.344248i
$749$	−10.8986	+	9.14497i	−0.398224	+	0.334150i
$750$	−30.0347	+	32.3348i	−1.09671	+	1.18070i
$751$	0.403440	−	2.28802i	0.0147217	−	0.0834912i	−0.976562	−	0.215238i	$-0.930947\pi$
$751$	0.403440	−	2.28802i	0.0147217	−	0.0834912i	0.991283	+	0.131747i	$0.0420585\pi$
$752$	0.648941	+	0.544526i	0.0236645	+	0.0198568i
$753$	18.7174	+	24.7380i	0.682099	+	0.901504i
$754$	−0.131365	−	0.0478131i	−0.00478404	−	0.00174125i
$755$	−16.2377			−0.590949
$756$	4.84002	−	1.89055i	0.176030	−	0.0687587i
$757$	−43.3714			−1.57636			−0.788181	−	0.615444i	$-0.788977\pi$
$757$	−43.3714			−1.57636			−0.788181	+	0.615444i	$0.788977\pi$
$758$	−24.2187	−	8.81490i	−0.879664	−	0.320172i
$759$	6.31845	−	14.9666i	0.229345	−	0.543254i
$760$	17.9332	+	15.0477i	0.650504	+	0.545838i
$761$	3.90808	−	22.1638i	0.141668	−	0.803438i	−0.828315	−	0.560263i	$-0.810700\pi$
$761$	3.90808	−	22.1638i	0.141668	−	0.803438i	0.969982	−	0.243175i	$-0.0781889\pi$
$762$	−8.71257	−	28.2996i	−0.315623	−	1.02518i
$763$	1.26896	−	1.06478i	0.0459394	−	0.0385478i
$764$	0.186150	+	0.322422i	0.00673468	+	0.0116648i
$765$	−63.4112	−	30.6214i	−2.29264	−	1.10712i
$766$	0.410680	−	0.711318i	0.0148385	−	0.0257010i
$767$	−0.159081	−	0.902192i	−0.00574407	−	0.0325762i
$768$	−1.54173	+	0.789350i	−0.0556323	+	0.0284832i
$769$	28.8724	−	10.5087i	1.04117	−	0.378954i	0.235845	−	0.971791i	$-0.424214\pi$
$769$	28.8724	−	10.5087i	1.04117	−	0.378954i	0.805323	+	0.592837i	$0.201992\pi$
$770$	−7.09823	+	2.58354i	−0.255802	+	0.0931044i
$771$	44.1576	−	22.6083i	1.59030	−	0.814217i
$772$	−4.62491	−	26.2292i	−0.166454	−	0.944009i
$773$	−1.62773	+	2.81931i	−0.0585454	+	0.101404i	−0.893813	−	0.448441i	$-0.851980\pi$
$773$	−1.62773	+	2.81931i	−0.0585454	+	0.101404i	0.835267	+	0.549844i	$0.185313\pi$
$774$	1.73649	+	23.5117i	0.0624169	+	0.845109i
$775$	−2.50246	−	4.33438i	−0.0898909	−	0.155696i
$776$	5.33276	−	4.47472i	0.191435	−	0.160633i
$777$	−5.71858	−	18.5747i	−0.205153	−	0.666363i
$778$	2.03448	−	11.5381i	0.0729395	−	0.413660i
$779$	−24.5707	−	20.6172i	−0.880335	−	0.738689i
$780$	−0.389643	+	0.922955i	−0.0139515	+	0.0330471i
$781$	−28.8181	−	10.4889i	−1.03119	−	0.375324i
$782$	29.1457			1.04225
$783$	5.07038	−	0.118251i	0.181201	−	0.00422596i
$784$	1.00000			0.0357143
$785$	66.6184	+	24.2471i	2.37771	+	0.865417i
$786$	−2.28276	−	3.01703i	−0.0814232	−	0.107614i
$787$	−21.4591	−	18.0063i	−0.764933	−	0.641855i	0.174473	−	0.984662i	$-0.444178\pi$
$787$	−21.4591	−	18.0063i	−0.764933	−	0.641855i	−0.939406	+	0.342807i	$0.888622\pi$
$788$	1.04506	−	5.92681i	0.0372286	−	0.211134i
$789$	−29.6497	+	31.9203i	−1.05556	+	1.13639i
$790$	43.0610	−	36.1325i	1.53204	−	1.28554i
$791$	−6.51616	−	11.2863i	−0.231688	−	0.401295i
$792$	−3.28051	+	4.55255i	−0.116568	+	0.161768i
$793$	−0.318069	+	0.550912i	−0.0112950	+	0.0195635i
$794$	2.97368	+	16.8646i	0.105532	+	0.598501i
$795$	−0.471349	+	9.34330i	−0.0167170	+	0.331373i
$796$	7.10932	−	2.58758i	0.251983	−	0.0917144i
$797$	−35.2074	+	12.8144i	−1.24711	+	0.453910i	−0.879424	−	0.476040i	$-0.842072\pi$
$797$	−35.2074	+	12.8144i	−1.24711	+	0.453910i	−0.367685	+	0.929950i	$0.619849\pi$
$798$	−8.43119	−	5.45187i	−0.298461	−	0.192994i
$799$	0.854999	+	4.84894i	0.0302477	+	0.171543i
$800$	−5.65461	+	9.79407i	−0.199921	+	0.346273i
$801$	−30.7019	−	31.5450i	−1.08480	−	1.11459i
$802$	−13.3571	−	23.1352i	−0.471657	−	0.816934i
$803$	−6.79521	+	5.70185i	−0.239798	+	0.201214i
$804$	−18.8136	−	4.30474i	−0.663504	−	0.151816i
$805$	−3.51655	+	19.9433i	−0.123942	+	0.702911i
$806$	−0.0485552	−	0.0407427i	−0.00171028	−	0.00143510i
$807$	−32.3947	+	4.04186i	−1.14035	+	0.142280i
$808$	−4.89978	−	1.78337i	−0.172374	−	0.0627389i
$809$	−0.163456			−0.00574679			−0.00287340	−	0.999996i	$-0.500915\pi$
$809$	−0.163456			−0.00574679			−0.00287340	+	0.999996i	$0.500915\pi$
$810$	0.984399	−	36.3329i	0.0345883	−	1.27661i
$811$	−8.72251			−0.306289			−0.153144	−	0.988204i	$-0.548940\pi$
$811$	−8.72251			−0.306289			−0.153144	+	0.988204i	$0.548940\pi$
$812$	0.917198	+	0.333833i	0.0321873	+	0.0117152i
$813$	−14.2584	+	1.77901i	−0.500064	+	0.0623926i
$814$	16.0778	+	13.4909i	0.563527	+	0.472855i
$815$	13.7436	−	77.9438i	0.481417	−	2.73025i
$816$	−9.81350	−	2.24543i	−0.343541	−	0.0786057i
$817$	34.8967	−	29.2818i	1.22088	−	1.02444i
$818$	11.2721	+	19.5239i	0.394120	+	0.682636i
$819$	0.116818	−	0.413489i	0.00408197	−	0.0144485i
$820$	11.1728	−	19.3519i	0.390172	−	0.675798i
$821$	−1.29006	−	7.31627i	−0.0450232	−	0.255339i	0.953986	−	0.299853i	$-0.0969375\pi$
$821$	−1.29006	−	7.31627i	−0.0450232	−	0.255339i	−0.999009	+	0.0445130i	$0.985826\pi$
$822$	−7.95054	−	5.14107i	−0.277307	−	0.179315i
$823$	12.1850	−	4.43499i	0.424744	−	0.154594i	−0.120799	−	0.992677i	$-0.538546\pi$
$823$	12.1850	−	4.43499i	0.424744	−	0.154594i	0.545543	+	0.838083i	$0.316323\pi$
$824$	−4.71571	+	1.71638i	−0.164280	+	0.0597929i
$825$	−1.84600	+	36.5922i	−0.0642693	+	1.27398i
$826$	1.11071	+	6.29914i	0.0386465	+	0.219175i
$827$	4.47828	−	7.75661i	0.155725	−	0.269724i	−0.777598	−	0.628762i	$-0.783562\pi$
$827$	4.47828	−	7.75661i	0.155725	−	0.269724i	0.933323	+	0.359038i	$0.116895\pi$
$828$	6.17246	+	13.7190i	0.214508	+	0.476767i
$829$	−12.8355	−	22.2317i	−0.445794	−	0.772139i	0.552313	−	0.833637i	$-0.313745\pi$
$829$	−12.8355	−	22.2317i	−0.445794	−	0.772139i	−0.998107	+	0.0614984i	$0.980412\pi$
$830$	−18.8187	+	15.7908i	−0.653206	+	0.548105i
$831$	−19.5473	+	21.0443i	−0.678089	+	0.730018i
$832$	−0.0248707	+	0.141049i	−0.000862236	+	0.00488999i
$833$	4.45244	+	3.73604i	0.154268	+	0.129446i
$834$	1.29611	+	1.71302i	0.0448807	+	0.0593171i
$835$	−41.4850	−	15.0993i	−1.43565	−	0.522534i
$836$	10.8426			0.375000
$837$	2.17864	+	0.735902i	0.0753047	+	0.0254365i
$838$	9.80584			0.338737
$839$	−1.10443	−	0.401981i	−0.0381293	−	0.0138779i	0.322885	−	0.946438i	$-0.395347\pi$
$839$	−1.10443	−	0.401981i	−0.0381293	−	0.0138779i	−0.361014	+	0.932560i	$0.617569\pi$
$840$	2.72051	−	6.44411i	0.0938664	−	0.222343i
$841$	−21.4855	−	18.0285i	−0.740879	−	0.621671i
$842$	2.01256	−	11.4138i	0.0693572	−	0.393344i
$843$	15.1736	+	49.2858i	0.522606	+	1.69749i
$844$	−14.3790	+	12.0654i	−0.494946	+	0.415309i
$845$	−26.2086	−	45.3946i	−0.901604	−	1.56162i
$846$	−2.10134	+	1.42936i	−0.0722456	+	0.0491423i
$847$	3.75070	−	6.49640i	0.128875	−	0.223219i
$848$	0.232244	+	1.31712i	0.00797531	+	0.0452302i
$849$	25.3349	−	12.9712i	0.869492	−	0.445172i
$850$	−61.7678	+	22.4816i	−2.11862	+	0.771114i
$851$	52.8739	−	19.2445i	1.81249	−	0.659693i
$852$	25.2779	−	12.9420i	0.866006	−	0.443387i
$853$	−7.30021	−	41.4015i	−0.249954	−	1.41756i	−0.808699	−	0.588222i	$-0.799828\pi$
$853$	−7.30021	−	41.4015i	−0.249954	−	1.41756i	0.558745	−	0.829340i	$-0.311283\pi$
$854$	2.22077	−	3.84649i	0.0759933	−	0.131624i
$855$	−58.0695	+	39.4996i	−1.98594	+	1.35086i
$856$	7.11353	+	12.3210i	0.243135	+	0.421123i
$857$	−27.8299	+	23.3521i	−0.950652	+	0.797692i	−0.979407	−	0.201895i	$-0.935290\pi$
$857$	−27.8299	+	23.3521i	−0.950652	+	0.797692i	0.0287551	+	0.999586i	$0.490846\pi$
$858$	0.136530	+	0.443467i	0.00466106	+	0.0151397i
$859$	−4.10982	+	23.3080i	−0.140225	+	0.795257i	0.830852	+	0.556493i	$0.187853\pi$
$859$	−4.10982	+	23.3080i	−0.140225	+	0.795257i	−0.971078	+	0.238764i	$0.923258\pi$
$860$	24.3116	+	20.3999i	0.829019	+	0.695630i
$861$	−3.72743	+	8.82922i	−0.127030	+	0.300899i
$862$	−24.6288	−	8.96416i	−0.838861	−	0.305320i
$863$	−2.73750			−0.0931856			−0.0465928	−	0.998914i	$-0.514836\pi$
$863$	−2.73750			−0.0931856			−0.0465928	+	0.998914i	$0.514836\pi$
$864$	−1.02137	−	5.09478i	−0.0347477	−	0.173328i
$865$	8.14020			0.276775
$866$	−1.32717	−	0.483051i	−0.0450991	−	0.0164147i
$867$	−17.5387	−	23.1802i	−0.595645	−	0.787241i
$868$	0.339014	+	0.284467i	0.0115069	+	0.00965543i
$869$	4.52097	−	25.6397i	0.153363	−	0.869767i
$870$	4.64649	−	5.00232i	0.157531	−	0.169595i
$871$	−1.22254	+	1.02583i	−0.0414242	+	0.0347590i
$872$	−0.828255	−	1.43458i	−0.0280483	−	0.0485810i
$873$	8.56893	+	19.0454i	0.290014	+	0.644588i
$874$	14.5340	−	25.1737i	0.491621	−	0.851513i
$875$	−4.42448	−	25.0925i	−0.149575	−	0.848280i
$876$	0.413859	−	8.20370i	0.0139830	−	0.277177i
$877$	−17.4075	+	6.33580i	−0.587808	+	0.213945i	−0.618765	−	0.785576i	$-0.712367\pi$
$877$	−17.4075	+	6.33580i	−0.587808	+	0.213945i	0.0309570	+	0.999521i	$0.490145\pi$
$878$	−14.0759	+	5.12319i	−0.475037	+	0.172899i
$879$	−17.6476	−	11.4115i	−0.595238	−	0.384900i
$880$	1.31170	+	7.43902i	0.0442174	+	0.250769i
$881$	−6.37779	+	11.0467i	−0.214873	+	0.372171i	−0.953233	−	0.302235i	$-0.902267\pi$
$881$	−6.37779	+	11.0467i	−0.214873	+	0.372171i	0.738360	+	0.674407i	$0.235600\pi$
$882$	−0.815631	+	2.88700i	−0.0274637	+	0.0972102i
$883$	3.07944	+	5.33374i	0.103631	+	0.179495i	0.913178	−	0.407561i	$-0.133620\pi$
$883$	3.07944	+	5.33374i	0.103631	+	0.179495i	−0.809547	+	0.587055i	$0.800287\pi$
$884$	−0.637699	+	0.535093i	−0.0214481	+	0.0179971i
$885$	43.6140	+	9.97932i	1.46607	+	0.335451i
$886$	4.22405	−	23.9558i	0.141910	−	0.804809i
$887$	38.1604	+	32.0204i	1.28130	+	1.07514i	0.993063	+	0.117580i	$0.0375136\pi$
$887$	38.1604	+	32.0204i	1.28130	+	1.07514i	0.288237	+	0.957559i	$0.406931\pi$
$888$	−19.2855	+	2.40624i	−0.647180	+	0.0807482i
$889$	16.0646	+	5.84702i	0.538788	+	0.196103i
$890$	−59.2568			−1.98629
$891$	−10.4675	−	13.1840i	−0.350675	−	0.441681i
$892$	3.90511			0.130753
$893$	4.61449	+	1.67954i	0.154418	+	0.0562036i
$894$	18.3080	−	2.28428i	0.612311	−	0.0763977i
$895$	32.5691	+	27.3287i	1.08866	+	0.913498i
$896$	0.173648	−	0.984808i	0.00580118	−	0.0329001i
$897$	1.21263	+	0.277461i	0.0404885	+	0.00926417i
$898$	−1.39375	+	1.16949i	−0.0465100	+	0.0390265i
$899$	0.215979	+	0.374086i	0.00720330	+	0.0124765i
$900$	−23.6634	−	24.3132i	−0.788779	−	0.810439i
$901$	−3.88677	+	6.73209i	−0.129487	+	0.224278i
$902$	−1.79719	−	10.1924i	−0.0598399	−	0.339369i
$903$	−11.4300	−	7.39099i	−0.380366	−	0.245957i
$904$	−12.2464	+	4.45732i	−0.407309	+	0.148248i
$905$	−101.555	+	36.9632i	−3.37582	+	1.22870i
$906$	0.350879	−	6.95530i	0.0116572	−	0.231074i
$907$	6.41155	+	36.3617i	0.212892	+	1.20737i	0.884527	+	0.466488i	$0.154481\pi$
$907$	6.41155	+	36.3617i	0.212892	+	1.20737i	−0.671635	+	0.740882i	$0.734408\pi$
$908$	6.83626	−	11.8407i	0.226869	−	0.392949i
$909$	9.14501	−	12.6911i	0.303321	−	0.420936i
$910$	−0.289204	−	0.500916i	−0.00958702	−	0.0166052i
$911$	6.37149	−	5.34631i	0.211097	−	0.177131i	−0.531109	−	0.847304i	$-0.678224\pi$
$911$	6.37149	−	5.34631i	0.211097	−	0.177131i	0.742205	+	0.670173i	$0.233780\pi$
$912$	−6.83311	+	7.35639i	−0.226267	+	0.243594i
$913$	−1.97577	+	11.2052i	−0.0653885	+	0.370836i
$914$	4.55296	+	3.82038i	0.150598	+	0.126367i
$915$	−18.7456	−	24.7753i	−0.619710	−	0.819046i
$916$	−4.27135	−	1.55464i	−0.141129	−	0.0513669i
$917$	2.18430			0.0721318
$918$	14.4867	−	26.5001i	0.478133	−	0.874633i
$919$	48.0324			1.58444			0.792222	−	0.610233i	$-0.208924\pi$
$919$	48.0324			1.58444			0.792222	+	0.610233i	$0.208924\pi$
$920$	19.0297	+	6.92625i	0.627391	+	0.228352i
$921$	−15.6732	+	37.1254i	−0.516450	+	1.22332i
$922$	5.45421	+	4.57663i	0.179625	+	0.150723i
$923$	0.407775	−	2.31261i	0.0134221	−	0.0761204i
$924$	−0.953258	−	3.09631i	−0.0313599	−	0.101861i
$925$	−97.2101	+	81.5690i	−3.19625	+	2.68197i
$926$	8.78072	+	15.2087i	0.288552	+	0.499787i
$927$	−1.10890	−	15.0142i	−0.0364209	−	0.493130i
$928$	0.488031	−	0.845294i	0.0160204	−	0.0277481i
$929$	−1.19808	−	6.79464i	−0.0393077	−	0.222925i	0.958826	−	0.283995i	$-0.0916599\pi$
$929$	−1.19808	−	6.79464i	−0.0393077	−	0.222925i	−0.998133	+	0.0610698i	$0.980549\pi$
$930$	2.75542	−	1.41075i	0.0903539	−	0.0462603i
$931$	5.44719	−	1.98261i	0.178524	−	0.0649776i
$932$	25.4439	−	9.26082i	0.833442	−	0.303348i
$933$	−2.07478	+	1.06227i	−0.0679252	+	0.0347770i
$934$	−3.78034	−	21.4393i	−0.123696	−	0.701517i
$935$	−21.9522	+	38.0223i	−0.717914	+	1.24346i
$936$	−0.386922	−	0.186845i	−0.0126469	−	0.00610723i
$937$	−19.9847	−	34.6145i	−0.652872	−	1.13081i	−0.982423	−	0.186670i	$-0.940231\pi$
$937$	−19.9847	−	34.6145i	−0.652872	−	1.13081i	0.329551	−	0.944138i	$-0.393103\pi$
$938$	8.53583	−	7.16241i	0.278705	−	0.233861i
$939$	9.74248	+	31.6448i	0.317934	+	1.03269i
$940$	−0.594071	+	3.36914i	−0.0193765	+	0.109889i
$941$	26.6225	+	22.3389i	0.867868	+	0.728228i	0.963648	−	0.267175i	$-0.0860901\pi$
$941$	26.6225	+	22.3389i	0.867868	+	0.728228i	−0.0957799	+	0.995403i	$0.530534\pi$
$942$	−11.8257	+	28.0116i	−0.385301	+	0.912667i
$943$	−26.0731	−	9.48982i	−0.849056	−	0.309031i
$944$	6.39631			0.208182
$945$	16.3852	+	13.1101i	0.533010	+	0.426472i
$946$	14.6991			0.477909
$947$	44.9320	+	16.3539i	1.46009	+	0.531430i	0.945391	−	0.325939i	$-0.105680\pi$
$947$	44.9320	+	16.3539i	1.46009	+	0.531430i	0.514702	+	0.857369i	$0.327903\pi$
$948$	14.5466	+	19.2257i	0.472452	+	0.624421i
$949$	−0.520323	−	0.436603i	−0.0168904	−	0.0141727i
$950$	−11.3838	+	64.5610i	−0.369341	+	2.09464i
$951$	−12.9891	+	13.9838i	−0.421201	+	0.453456i
$952$	4.45244	−	3.73604i	0.144304	−	0.121086i
$953$	6.17451	+	10.6946i	0.200012	+	0.346431i	0.948532	−	0.316681i	$-0.102569\pi$
$953$	6.17451	+	10.6946i	0.200012	+	0.346431i	−0.748520	+	0.663112i	$0.769235\pi$
$954$	−3.99196	−	0.403798i	−0.129244	−	0.0130735i
$955$	−0.751761	+	1.30209i	−0.0243264	+	0.0421346i
$956$	0.319416	+	1.81150i	0.0103306	+	0.0585880i
$957$	0.159322	−	3.15815i	0.00515014	−	0.102089i
$958$	25.0716	−	9.12532i	0.810027	−	0.294826i
$959$	5.13665	−	1.86959i	0.165871	−	0.0603722i
$960$	−5.87379	−	3.79818i	−0.189576	−	0.122586i
$961$	−5.34908	−	30.3362i	−0.172551	−	0.978586i
$962$	−0.803550	+	1.39179i	−0.0259075	+	0.0448731i
$963$	−41.3727	+	10.4873i	−1.33322	+	0.337950i
$964$	7.41681	+	12.8463i	0.238880	+	0.413751i
$965$	82.3956	−	69.1381i	2.65241	−	2.22563i
$966$	−8.46661	−	1.93725i	−0.272409	−	0.0623299i
$967$	−1.29585	+	7.34915i	−0.0416718	+	0.236333i	−0.998529	−	0.0542272i	$-0.982730\pi$
$967$	−1.29585	+	7.34915i	−0.0416718	+	0.236333i	0.956857	+	0.290560i	$0.0938416\pi$
$968$	−5.74640	−	4.82180i	−0.184696	−	0.154979i
$969$	−57.9078	+	7.22511i	−1.86027	+	0.232104i
$970$	26.4180	+	9.61538i	0.848232	+	0.308731i
$971$	15.8911			0.509971			0.254986	−	0.966945i	$-0.417929\pi$
$971$	15.8911			0.509971			0.254986	+	0.966945i	$0.417929\pi$
$972$	15.5417	+	1.20678i	0.498499	+	0.0387074i
$973$	−1.24021			−0.0397592
$974$	0.445514	+	0.162154i	0.0142752	+	0.00519574i
$975$	−2.78392	+	0.347348i	−0.0891567	+	0.0111240i
$976$	−3.40242	−	2.85497i	−0.108909	−	0.0913854i
$977$	2.64785	−	15.0167i	0.0847121	−	0.480426i	−0.912706	−	0.408616i	$-0.866011\pi$
$977$	2.64785	−	15.0167i	0.0847121	−	0.480426i	0.997418	−	0.0718100i	$-0.0228775\pi$
$978$	33.0897	+	7.57127i	1.05809	+	0.242102i
$979$	−21.0244	+	17.6415i	−0.671942	+	0.563826i
$980$	2.01923	+	3.49741i	0.0645020	+	0.111721i
$981$	4.81718	−	1.22108i	0.153801	−	0.0389861i
$982$	−12.8018	+	22.1734i	−0.408522	+	0.707581i
$983$	−0.491206	−	2.78577i	−0.0156670	−	0.0888522i	0.975972	−	0.217897i	$-0.0699198\pi$
$983$	−0.491206	−	2.78577i	−0.0156670	−	0.0888522i	−0.991639	+	0.129045i	$0.958809\pi$
$984$	8.04783	+	5.20398i	0.256555	+	0.165897i
$985$	22.8387	−	8.31262i	0.727703	−	0.264862i
$986$	5.33098	−	1.94032i	0.169773	−	0.0617923i
$987$	0.0739268	−	1.46541i	0.00235312	−	0.0466446i
$988$	0.144170	+	0.817628i	0.00458665	+	0.0260122i
$989$	19.7035	−	34.1275i	0.626535	−	1.08519i
$990$	−22.5463	−	2.28062i	−0.716567	−	0.0724829i
$991$	3.04645	+	5.27661i	0.0967737	+	0.167617i	0.910347	−	0.413845i	$-0.135814\pi$
$991$	3.04645	+	5.27661i	0.0967737	+	0.167617i	−0.813574	+	0.581462i	$0.802481\pi$
$992$	0.339014	−	0.284467i	0.0107637	−	0.00903183i
$993$	12.0120	−	12.9319i	0.381191	−	0.410382i
$994$	−2.84710	+	16.1467i	−0.0903046	+	0.512143i
$995$	23.4052	+	19.6393i	0.741995	+	0.622608i
$996$	−6.35721	−	8.40208i	−0.201436	−	0.266230i
$997$	47.9253	+	17.4434i	1.51781	+	0.552438i	0.960600	−	0.277934i	$-0.0896496\pi$
$997$	47.9253	+	17.4434i	1.51781	+	0.552438i	0.557210	+	0.830372i	$0.311872\pi$
$998$	32.3726			1.02474
$999$	8.78306	−	57.6398i	0.277884	−	1.82364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.b.85.2	✓	12
27.7	even	9	inner	378.2.u.b.169.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.b.85.2	✓	12	1.1	even	1	trivial
378.2.u.b.169.2	yes	12	27.7	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(1.71872 - 0.214444i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.701272 + 3.97711i) q^{5} +(-1.68842 - 0.386327i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.90803 - 0.737141i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(1.71872 - 0.214444i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.701272 + 3.97711i) q^{5} +(-1.68842 - 0.386327i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.90803 - 0.737141i) q^{9} +(2.01923 - 3.49741i) q^{10} +(-0.324801 - 1.84204i) q^{11} +(1.45446 + 0.940501i) q^{12} +(0.134587 - 0.0489857i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.352425 + 6.98595i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.90612 + 5.03355i) q^{17} +(-2.98477 - 0.301918i) q^{18} +(2.89839 + 5.02016i) q^{19} +(-3.09365 + 2.59588i) q^{20} +(1.17878 - 1.26905i) q^{21} +(-0.324801 + 1.84204i) q^{22} +(3.84135 + 3.22328i) q^{23} +(-1.04508 - 1.38124i) q^{24} +(-10.6272 - 3.86798i) q^{25} -0.143225 q^{26} +(4.84002 - 1.89055i) q^{27} +1.00000 q^{28} +(0.917198 + 0.333833i) q^{29} +(2.72051 - 6.44411i) q^{30} +(0.339014 + 0.284467i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-0.953258 - 3.09631i) q^{33} +(4.45244 - 3.73604i) q^{34} +(2.01923 + 3.49741i) q^{35} +(2.70150 + 1.30456i) q^{36} +(5.61042 - 9.71753i) q^{37} +(-1.00660 - 5.70871i) q^{38} +(0.220814 - 0.113054i) q^{39} +(3.79492 - 1.38124i) q^{40} +(-5.19951 + 1.89247i) q^{41} +(-1.54173 + 0.789350i) q^{42} +(-1.36463 - 7.73918i) q^{43} +(0.935228 - 1.61986i) q^{44} +(0.892373 + 12.0825i) q^{45} +(-2.50726 - 4.34271i) q^{46} +(0.648941 - 0.544526i) q^{47} +(0.509640 + 1.65538i) q^{48} +(0.173648 - 0.984808i) q^{49} +(8.66336 + 7.26942i) q^{50} +(-3.91541 + 9.27449i) q^{51} +(0.134587 + 0.0489857i) q^{52} +1.33744 q^{53} +(-5.19474 + 0.121152i) q^{54} +7.55377 q^{55} +(-0.939693 - 0.342020i) q^{56} +(6.05807 + 8.00672i) q^{57} +(-0.747706 - 0.627400i) q^{58} +(1.11071 - 6.29914i) q^{59} +(-4.76045 + 5.12501i) q^{60} +(-3.40242 + 2.85497i) q^{61} +(-0.221276 - 0.383261i) q^{62} +(1.75385 - 2.43393i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.100439 + 0.569621i) q^{65} +(-0.163229 + 3.23561i) q^{66} +(-10.4707 + 3.81104i) q^{67} +(-5.46173 + 1.98791i) q^{68} +(7.29344 + 4.71617i) q^{69} +(-0.701272 - 3.97711i) q^{70} +(8.19790 - 14.1992i) q^{71} +(-2.09240 - 2.14986i) q^{72} +(-2.37122 - 4.10707i) q^{73} +(-8.59566 + 7.21261i) q^{74} +(-19.0947 - 4.36905i) q^{75} +(-1.00660 + 5.70871i) q^{76} +(-1.43285 - 1.20231i) q^{77} +(-0.246164 + 0.0307137i) q^{78} +(13.0798 + 4.76064i) q^{79} -4.03847 q^{80} +(7.91325 - 4.28725i) q^{81} +5.53320 q^{82} +(-5.71616 - 2.08051i) q^{83} +(1.71872 - 0.214444i) q^{84} +(-17.9810 - 15.0879i) q^{85} +(-1.36463 + 7.73918i) q^{86} +(1.64800 + 0.377079i) q^{87} +(-1.43285 + 1.20231i) q^{88} +(-7.33655 - 12.7073i) q^{89} +(3.29390 - 11.6590i) q^{90} +(0.0716123 - 0.124036i) q^{91} +(0.870764 + 4.93835i) q^{92} +(0.643675 + 0.416220i) q^{93} +(-0.796044 + 0.289736i) q^{94} +(-21.9983 + 8.00672i) q^{95} +(0.0872671 - 1.72985i) q^{96} +(1.20884 + 6.85567i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(-2.30237 - 5.11728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Introduction

L-functions

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