LMFDB - Embedded newform 804.2.e.b.535.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.1
Character	$\chi$	$=$	804.535
Dual form			804.2.e.b.535.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40514 - 0.159923i) q^{2} +1.00000 q^{3} +(1.94885 + 0.449428i) q^{4} +0.947080i q^{5} +(-1.40514 - 0.159923i) q^{6} -0.0251164 q^{7} +(-2.66654 - 0.943176i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.40514 - 0.159923i) q^{2} +1.00000 q^{3} +(1.94885 + 0.449428i) q^{4} +0.947080i q^{5} +(-1.40514 - 0.159923i) q^{6} -0.0251164 q^{7} +(-2.66654 - 0.943176i) q^{8} +1.00000 q^{9} +(0.151460 - 1.33078i) q^{10} -1.77930 q^{11} +(1.94885 + 0.449428i) q^{12} -5.89167i q^{13} +(0.0352920 + 0.00401668i) q^{14} +0.947080i q^{15} +(3.59603 + 1.75174i) q^{16} +2.08504 q^{17} +(-1.40514 - 0.159923i) q^{18} -4.96753i q^{19} +(-0.425645 + 1.84572i) q^{20} -0.0251164 q^{21} +(2.50017 + 0.284551i) q^{22} -4.05820i q^{23} +(-2.66654 - 0.943176i) q^{24} +4.10304 q^{25} +(-0.942211 + 8.27863i) q^{26} +1.00000 q^{27} +(-0.0489480 - 0.0112880i) q^{28} +5.86732 q^{29} +(0.151460 - 1.33078i) q^{30} +3.69465 q^{31} +(-4.77279 - 3.03653i) q^{32} -1.77930 q^{33} +(-2.92978 - 0.333446i) q^{34} -0.0237872i q^{35} +(1.94885 + 0.449428i) q^{36} +5.82584 q^{37} +(-0.794421 + 6.98009i) q^{38} -5.89167i q^{39} +(0.893263 - 2.52542i) q^{40} +6.60505i q^{41} +(0.0352920 + 0.00401668i) q^{42} +2.25768 q^{43} +(-3.46759 - 0.799669i) q^{44} +0.947080i q^{45} +(-0.648998 + 5.70235i) q^{46} +11.4405i q^{47} +(3.59603 + 1.75174i) q^{48} -6.99937 q^{49} +(-5.76535 - 0.656169i) q^{50} +2.08504 q^{51} +(2.64788 - 11.4820i) q^{52} -7.44096i q^{53} +(-1.40514 - 0.159923i) q^{54} -1.68514i q^{55} +(0.0669737 + 0.0236891i) q^{56} -4.96753i q^{57} +(-8.24442 - 0.938318i) q^{58} +2.53323i q^{59} +(-0.425645 + 1.84572i) q^{60} +2.42545i q^{61} +(-5.19151 - 0.590858i) q^{62} -0.0251164 q^{63} +(6.22084 + 5.03003i) q^{64} +5.57988 q^{65} +(2.50017 + 0.284551i) q^{66} +(7.47363 + 3.33840i) q^{67} +(4.06344 + 0.937077i) q^{68} -4.05820i q^{69} +(-0.00380411 + 0.0334244i) q^{70} -1.82520i q^{71} +(-2.66654 - 0.943176i) q^{72} -9.08258 q^{73} +(-8.18613 - 0.931684i) q^{74} +4.10304 q^{75} +(2.23255 - 9.68097i) q^{76} +0.0446896 q^{77} +(-0.942211 + 8.27863i) q^{78} +12.9024 q^{79} +(-1.65903 + 3.40573i) q^{80} +1.00000 q^{81} +(1.05630 - 9.28104i) q^{82} -14.6510i q^{83} +(-0.0489480 - 0.0112880i) q^{84} +1.97470i q^{85} +(-3.17237 - 0.361055i) q^{86} +5.86732 q^{87} +(4.74458 + 1.67820i) q^{88} -9.99659 q^{89} +(0.151460 - 1.33078i) q^{90} +0.147977i q^{91} +(1.82387 - 7.90882i) q^{92} +3.69465 q^{93} +(1.82959 - 16.0755i) q^{94} +4.70465 q^{95} +(-4.77279 - 3.03653i) q^{96} -3.04196i q^{97} +(9.83511 + 1.11936i) q^{98} -1.77930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40514	−	0.159923i	−0.993586	−	0.113082i
$2$	−1.40514	−	0.159923i	−0.993586	−	0.113082i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.94885	+	0.449428i	0.974425	+	0.224714i
$5$			0.947080i			0.423547i	0.977319	+	0.211774i	$0.0679239\pi$
$5$			0.947080i			0.423547i	−0.977319	+	0.211774i	$0.932076\pi$
$6$	−1.40514	−	0.159923i	−0.573647	−	0.0652882i
$7$	−0.0251164			−0.00949309			−0.00474654	−	0.999989i	$-0.501511\pi$
$7$	−0.0251164			−0.00949309			−0.00474654	+	0.999989i	$0.501511\pi$
$8$	−2.66654	−	0.943176i	−0.942763	−	0.333463i
$9$	1.00000			0.333333
$10$	0.151460	−	1.33078i	0.0478957	−	0.420830i
$11$	−1.77930			−0.536480			−0.268240	−	0.963352i	$-0.586442\pi$
$11$	−1.77930			−0.536480			−0.268240	+	0.963352i	$0.586442\pi$
$12$	1.94885	+	0.449428i	0.562584	+	0.129739i
$13$		−	5.89167i		−	1.63405i	−0.576599	−	0.817027i	$-0.695620\pi$
$13$		−	5.89167i		−	1.63405i	0.576599	−	0.817027i	$-0.304380\pi$
$14$	0.0352920	+	0.00401668i	0.00943220	+	0.00107350i
$15$			0.947080i			0.244535i
$16$	3.59603	+	1.75174i	0.899007	+	0.437934i
$17$	2.08504			0.505697			0.252849	−	0.967506i	$-0.418633\pi$
$17$	2.08504			0.505697			0.252849	+	0.967506i	$0.418633\pi$
$18$	−1.40514	−	0.159923i	−0.331195	−	0.0376941i
$19$		−	4.96753i		−	1.13963i	−0.821773	−	0.569815i	$-0.807015\pi$
$19$		−	4.96753i		−	1.13963i	0.821773	−	0.569815i	$-0.192985\pi$
$20$	−0.425645	+	1.84572i	−0.0951771	+	0.412715i
$21$	−0.0251164			−0.00548084
$22$	2.50017	+	0.284551i	0.533039	+	0.0606664i
$23$		−	4.05820i		−	0.846193i	−0.906085	−	0.423097i	$-0.860943\pi$
$23$		−	4.05820i		−	0.846193i	0.906085	−	0.423097i	$-0.139057\pi$
$24$	−2.66654	−	0.943176i	−0.544305	−	0.192525i
$25$	4.10304			0.820608
$26$	−0.942211	+	8.27863i	−0.184783	+	1.62357i
$27$	1.00000			0.192450
$28$	−0.0489480	−	0.0112880i	−0.00925030	−	0.00213323i
$29$	5.86732			1.08953			0.544767	−	0.838587i	$-0.316618\pi$
$29$	5.86732			1.08953			0.544767	+	0.838587i	$0.316618\pi$
$30$	0.151460	−	1.33078i	0.0276526	−	0.242967i
$31$	3.69465			0.663579			0.331789	−	0.943354i	$-0.392348\pi$
$31$	3.69465			0.663579			0.331789	+	0.943354i	$0.392348\pi$
$32$	−4.77279	−	3.03653i	−0.843718	−	0.536787i
$33$	−1.77930			−0.309737
$34$	−2.92978	−	0.333446i	−0.502454	−	0.0571855i
$35$		−	0.0237872i		−	0.00402077i
$36$	1.94885	+	0.449428i	0.324808	+	0.0749047i
$37$	5.82584			0.957762			0.478881	−	0.877880i	$-0.341043\pi$
$37$	5.82584			0.957762			0.478881	+	0.877880i	$0.341043\pi$
$38$	−0.794421	+	6.98009i	−0.128872	+	1.13232i
$39$		−	5.89167i		−	0.943422i
$40$	0.893263	−	2.52542i	0.141237	−	0.399305i
$41$			6.60505i			1.03154i	0.856728	+	0.515768i	$0.172493\pi$
$41$			6.60505i			1.03154i	−0.856728	+	0.515768i	$0.827507\pi$
$42$	0.0352920	+	0.00401668i	0.00544568	+	0.000619786i
$43$	2.25768			0.344294			0.172147	−	0.985071i	$-0.444930\pi$
$43$	2.25768			0.344294			0.172147	+	0.985071i	$0.444930\pi$
$44$	−3.46759	−	0.799669i	−0.522759	−	0.120555i
$45$			0.947080i			0.141182i
$46$	−0.648998	+	5.70235i	−0.0956896	+	0.840765i
$47$			11.4405i			1.66877i	0.551185	+	0.834383i	$0.314176\pi$
$47$			11.4405i			1.66877i	−0.551185	+	0.834383i	$0.685824\pi$
$48$	3.59603	+	1.75174i	0.519042	+	0.252841i
$49$	−6.99937			−0.999910
$50$	−5.76535	−	0.656169i	−0.815344	−	0.0927963i
$51$	2.08504			0.291964
$52$	2.64788	−	11.4820i	0.367195	−	1.59226i
$53$		−	7.44096i		−	1.02209i	−0.859553	−	0.511047i	$-0.829258\pi$
$53$		−	7.44096i		−	1.02209i	0.859553	−	0.511047i	$-0.170742\pi$
$54$	−1.40514	−	0.159923i	−0.191216	−	0.0217627i
$55$		−	1.68514i		−	0.227225i
$56$	0.0669737	+	0.0236891i	0.00894973	+	0.00316559i
$57$		−	4.96753i		−	0.657966i
$58$	−8.24442	−	0.938318i	−1.08255	−	0.123207i
$59$			2.53323i			0.329798i	0.986310	+	0.164899i	$0.0527298\pi$
$59$			2.53323i			0.329798i	−0.986310	+	0.164899i	$0.947270\pi$
$60$	−0.425645	+	1.84572i	−0.0549505	+	0.238281i
$61$			2.42545i			0.310547i	0.987872	+	0.155273i	$0.0496258\pi$
$61$			2.42545i			0.310547i	−0.987872	+	0.155273i	$0.950374\pi$
$62$	−5.19151	−	0.590858i	−0.659322	−	0.0750391i
$63$	−0.0251164			−0.00316436
$64$	6.22084	+	5.03003i	0.777605	+	0.628753i
$65$	5.57988			0.692099
$66$	2.50017	+	0.284551i	0.307750	+	0.0350258i
$67$	7.47363	+	3.33840i	0.913049	+	0.407850i
$67$	7.47363	+	3.33840i	0.913049	+	0.407850i
$68$	4.06344	+	0.937077i	0.492764	+	0.113637i
$69$		−	4.05820i		−	0.488550i
$70$	−0.00380411	+	0.0334244i	−0.000454679	+	0.00399498i
$71$		−	1.82520i		−	0.216611i	−0.994118	−	0.108306i	$-0.965458\pi$
$71$		−	1.82520i		−	0.216611i	0.994118	−	0.108306i	$-0.0345425\pi$
$72$	−2.66654	−	0.943176i	−0.314254	−	0.111154i
$73$	−9.08258			−1.06304			−0.531518	−	0.847047i	$-0.678378\pi$
$73$	−9.08258			−1.06304			−0.531518	+	0.847047i	$0.678378\pi$
$74$	−8.18613	−	0.931684i	−0.951618	−	0.108306i
$75$	4.10304			0.473778
$76$	2.23255	−	9.68097i	0.256091	−	1.11048i
$77$	0.0446896			0.00509285
$78$	−0.942211	+	8.27863i	−0.106684	+	0.937370i
$79$	12.9024			1.45163			0.725817	−	0.687888i	$-0.241462\pi$
$79$	12.9024			1.45163			0.725817	+	0.687888i	$0.241462\pi$
$80$	−1.65903	+	3.40573i	−0.185486	+	0.380772i
$81$	1.00000			0.111111
$82$	1.05630	−	9.28104i	0.116649	−	1.02492i
$83$		−	14.6510i		−	1.60815i	−0.594525	−	0.804077i	$-0.702660\pi$
$83$		−	14.6510i		−	1.60815i	0.594525	−	0.804077i	$-0.297340\pi$
$84$	−0.0489480	−	0.0112880i	−0.00534066	−	0.00123162i
$85$			1.97470i			0.214187i
$86$	−3.17237	−	0.361055i	−0.342085	−	0.0389335i
$87$	5.86732			0.629043
$88$	4.74458	+	1.67820i	0.505773	+	0.178896i
$89$	−9.99659			−1.05964			−0.529818	−	0.848111i	$-0.677740\pi$
$89$	−9.99659			−1.05964			−0.529818	+	0.848111i	$0.677740\pi$
$90$	0.151460	−	1.33078i	0.0159652	−	0.140277i
$91$			0.147977i			0.0155122i
$92$	1.82387	−	7.90882i	0.190152	−	0.824551i
$93$	3.69465			0.383117
$94$	1.82959	−	16.0755i	0.188708	−	1.65806i
$95$	4.70465			0.482687
$96$	−4.77279	−	3.03653i	−0.487121	−	0.309914i
$97$		−	3.04196i		−	0.308864i	−0.988003	−	0.154432i	$-0.950645\pi$
$97$		−	3.04196i		−	0.308864i	0.988003	−	0.154432i	$-0.0493547\pi$
$98$	9.83511	+	1.11936i	0.993496	+	0.113072i
$99$	−1.77930			−0.178827
$100$	7.99620	+	1.84402i	0.799620	+	0.184402i
$101$		−	12.2472i		−	1.21864i	−0.792923	−	0.609322i	$-0.791442\pi$
$101$		−	12.2472i		−	1.21864i	0.792923	−	0.609322i	$-0.208558\pi$
$102$	−2.92978	−	0.333446i	−0.290092	−	0.0330161i
$103$		−	5.90791i		−	0.582124i	−0.956704	−	0.291062i	$-0.905991\pi$
$103$		−	5.90791i		−	0.582124i	0.956704	−	0.291062i	$-0.0940086\pi$
$104$	−5.55688	+	15.7103i	−0.544897	+	1.54053i
$105$		−	0.0237872i		−	0.00232139i
$106$	−1.18998	+	10.4556i	−0.115581	+	1.01554i
$107$		−	3.36968i		−	0.325760i	−0.986646	−	0.162880i	$-0.947922\pi$
$107$		−	3.36968i		−	0.325760i	0.986646	−	0.162880i	$-0.0520783\pi$
$108$	1.94885	+	0.449428i	0.187528	+	0.0432463i
$109$			10.9353i			1.04741i	0.851898	+	0.523707i	$0.175451\pi$
$109$			10.9353i			1.04741i	−0.851898	+	0.523707i	$0.824549\pi$
$110$	−0.269493	+	2.36786i	−0.0256951	+	0.225767i
$111$	5.82584			0.552964
$112$	−0.0903191	−	0.0439972i	−0.00853435	−	0.00415735i
$113$			12.5428i			1.17993i	0.807428	+	0.589966i	$0.200859\pi$
$113$			12.5428i			1.17993i	−0.807428	+	0.589966i	$0.799141\pi$
$114$	−0.794421	+	6.98009i	−0.0744043	+	0.653745i
$115$	3.84344			0.358403
$116$	11.4345	+	2.63694i	1.06167	+	0.244834i
$117$		−	5.89167i		−	0.544685i
$118$	0.405120	−	3.55954i	0.0372944	−	0.327683i
$119$	−0.0523687			−0.00480063
$120$	0.893263	−	2.52542i	0.0815434	−	0.230539i
$121$	−7.83408			−0.712189
$122$	0.387884	−	3.40810i	0.0351174	−	0.308555i
$123$			6.60505i			0.595557i
$124$	7.20032	+	1.66048i	0.646607	+	0.149115i
$125$			8.62131i			0.771113i
$126$	0.0352920	+	0.00401668i	0.00314407	+	0.000357834i
$127$		−	18.3109i		−	1.62483i	−0.583082	−	0.812413i	$-0.698154\pi$
$127$		−	18.3109i		−	1.62483i	0.583082	−	0.812413i	$-0.301846\pi$
$128$	−7.93675	−	8.06276i	−0.701516	−	0.712654i
$129$	2.25768			0.198778
$130$	−7.84053	−	0.892350i	−0.687660	−	0.0782643i
$131$		−	0.858472i		−	0.0750051i	−0.999297	−	0.0375025i	$-0.988060\pi$
$131$		−	0.858472i		−	0.0750051i	0.999297	−	0.0375025i	$-0.0119402\pi$
$132$	−3.46759	−	0.799669i	−0.301815	−	0.0696022i
$133$			0.124766i			0.0108186i
$134$	−9.96762	−	5.88613i	−0.861072	−	0.508484i
$135$			0.947080i			0.0815117i
$136$	−5.55984	−	1.96656i	−0.476753	−	0.168631i
$137$		−	19.5425i		−	1.66963i	−0.550529	−	0.834816i	$-0.685574\pi$
$137$		−	19.5425i		−	1.66963i	0.550529	−	0.834816i	$-0.314426\pi$
$138$	−0.648998	+	5.70235i	−0.0552464	+	0.485416i
$139$	−3.18812			−0.270413			−0.135206	−	0.990817i	$-0.543170\pi$
$139$	−3.18812			−0.270413			−0.135206	+	0.990817i	$0.543170\pi$
$140$	0.0106906	−	0.0463577i	0.000903524	−	0.00391794i
$141$			11.4405i			0.963463i
$142$	−0.291891	+	2.56466i	−0.0244949	+	0.215222i
$143$			10.4831i			0.876637i
$144$	3.59603	+	1.75174i	0.299669	+	0.145978i
$145$			5.55683i			0.461469i
$146$	12.7623	+	1.45251i	1.05622	+	0.120211i
$147$	−6.99937			−0.577298
$148$	11.3537	+	2.61830i	0.933267	+	0.215223i
$149$	−3.18333			−0.260788			−0.130394	−	0.991462i	$-0.541624\pi$
$149$	−3.18333			−0.260788			−0.130394	+	0.991462i	$0.541624\pi$
$150$	−5.76535	−	0.656169i	−0.470739	−	0.0535760i
$151$		−	9.58369i		−	0.779910i	−0.920834	−	0.389955i	$-0.872491\pi$
$151$		−	9.58369i		−	0.779910i	0.920834	−	0.389955i	$-0.127509\pi$
$152$	−4.68526	+	13.2461i	−0.380024	+	1.07440i
$153$	2.08504			0.168566
$154$	−0.0627952	−	0.00714688i	−0.00506018	−	0.000575912i
$155$			3.49913i			0.281057i
$156$	2.64788	−	11.4820i	0.212000	−	0.919294i
$157$	−0.495196			−0.0395209			−0.0197605	−	0.999805i	$-0.506290\pi$
$157$	−0.495196			−0.0395209			−0.0197605	+	0.999805i	$0.506290\pi$
$158$	−18.1297	−	2.06339i	−1.44232	−	0.164154i
$159$		−	7.44096i		−	0.590106i
$160$	2.87583	−	4.52021i	0.227355	−	0.357354i
$161$			0.101927i			0.00803299i
$162$	−1.40514	−	0.159923i	−0.110398	−	0.0125647i
$163$			18.2942i			1.43292i	0.697630	+	0.716458i	$0.254238\pi$
$163$			18.2942i			1.43292i	−0.697630	+	0.716458i	$0.745762\pi$
$164$	−2.96850	+	12.8723i	−0.231801	+	1.00515i
$165$		−	1.68514i		−	0.131188i
$166$	−2.34302	+	20.5867i	−0.181854	+	1.59784i
$167$			9.79844i			0.758226i	0.925350	+	0.379113i	$0.123771\pi$
$167$			9.79844i			0.758226i	−0.925350	+	0.379113i	$0.876229\pi$
$168$	0.0669737	+	0.0236891i	0.00516713	+	0.00182766i
$169$	−21.7117			−1.67013
$170$	0.315800	−	2.77474i	0.0242207	−	0.212813i
$171$		−	4.96753i		−	0.379877i
$172$	4.39989	+	1.01467i	0.335488	+	0.0773676i
$173$	4.12328			0.313487			0.156744	−	0.987639i	$-0.449900\pi$
$173$	4.12328			0.313487			0.156744	+	0.987639i	$0.449900\pi$
$174$	−8.24442	−	0.938318i	−0.625008	−	0.0711337i
$175$	−0.103053			−0.00779010
$176$	−6.39842	−	3.11687i	−0.482299	−	0.234943i
$177$			2.53323i			0.190409i
$178$	14.0466	+	1.59868i	1.05284	+	0.119826i
$179$	−3.42794			−0.256216			−0.128108	−	0.991760i	$-0.540890\pi$
$179$	−3.42794			−0.256216			−0.128108	+	0.991760i	$0.540890\pi$
$180$	−0.425645	+	1.84572i	−0.0317257	+	0.137572i
$181$	−19.6517			−1.46070			−0.730351	−	0.683072i	$-0.760643\pi$
$181$	−19.6517			−1.46070			−0.730351	+	0.683072i	$0.760643\pi$
$182$	0.0236649	−	0.207929i	0.00175416	−	0.0154127i
$183$			2.42545i			0.179294i
$184$	−3.82760	+	10.8213i	−0.282174	+	0.797760i
$185$			5.51754i			0.405657i
$186$	−5.19151	−	0.590858i	−0.380660	−	0.0433238i
$187$	−3.70992			−0.271296
$188$	−5.14168	+	22.2958i	−0.374995	+	1.62609i
$189$	−0.0251164			−0.00182695
$190$	−6.61070	−	0.752381i	−0.479591	−	0.0545834i
$191$	−2.52854			−0.182959			−0.0914793	−	0.995807i	$-0.529160\pi$
$191$	−2.52854			−0.182959			−0.0914793	+	0.995807i	$0.529160\pi$
$192$	6.22084	+	5.03003i	0.448950	+	0.363011i
$193$	−10.4620			−0.753073			−0.376537	−	0.926402i	$-0.622885\pi$
$193$	−10.4620			−0.753073			−0.376537	+	0.926402i	$0.622885\pi$
$194$	−0.486478	+	4.27438i	−0.0349271	+	0.306883i
$195$	5.57988			0.399584
$196$	−13.6407	−	3.14571i	−0.974337	−	0.224694i
$197$			21.9353i			1.56282i	0.624016	+	0.781412i	$0.285500\pi$
$197$			21.9353i			1.56282i	−0.624016	+	0.781412i	$0.714500\pi$
$198$	2.50017	+	0.284551i	0.177680	+	0.0202221i
$199$			17.6608i			1.25194i	0.779846	+	0.625971i	$0.215297\pi$
$199$			17.6608i			1.25194i	−0.779846	+	0.625971i	$0.784703\pi$
$200$	−10.9409	−	3.86989i	−0.773639	−	0.273642i
$201$	7.47363	+	3.33840i	0.527149	+	0.235472i
$202$	−1.95861	+	17.2091i	−0.137807	+	1.21083i
$203$	−0.147366			−0.0103430
$204$	4.06344	+	0.937077i	0.284497	+	0.0656085i
$205$	−6.25551			−0.436904
$206$	−0.944809	+	8.30146i	−0.0658280	+	0.578390i
$207$		−	4.05820i		−	0.282064i
$208$	10.3206	−	21.1866i	0.715608	−	1.46903i
$209$			8.83874i			0.611388i
$210$	−0.00380411	+	0.0334244i	−0.000262509	+	0.00230650i
$211$			13.3556i			0.919441i	0.888064	+	0.459720i	$0.152050\pi$
$211$			13.3556i			0.919441i	−0.888064	+	0.459720i	$0.847950\pi$
$212$	3.34418	−	14.5013i	0.229679	−	0.995954i
$213$		−	1.82520i		−	0.125060i
$214$	−0.538889	+	4.73488i	−0.0368377	+	0.323670i
$215$			2.13821i			0.145825i
$216$	−2.66654	−	0.943176i	−0.181435	−	0.0641750i
$217$	−0.0927961			−0.00629941
$218$	1.74881	−	15.3657i	0.118444	−	1.04070i
$219$	−9.08258			−0.613744
$220$	0.757351	−	3.28409i	0.0510606	−	0.221413i
$221$		−	12.2844i		−	0.826337i
$222$	−8.18613	−	0.931684i	−0.549417	−	0.0625305i
$223$			5.28059i			0.353614i	0.984246	+	0.176807i	$0.0565769\pi$
$223$			5.28059i			0.353614i	−0.984246	+	0.176807i	$0.943423\pi$
$224$	0.119875	+	0.0762664i	0.00800949	+	0.00509577i
$225$	4.10304			0.273536
$226$	2.00589	−	17.6245i	0.133430	−	1.17236i
$227$			3.00443i			0.199411i	0.995017	+	0.0997054i	$0.0317900\pi$
$227$			3.00443i			0.199411i	−0.995017	+	0.0997054i	$0.968210\pi$
$228$	2.23255	−	9.68097i	0.147854	−	0.641138i
$229$			16.7641i			1.10780i	0.832583	+	0.553900i	$0.186861\pi$
$229$			16.7641i			1.10780i	−0.832583	+	0.553900i	$0.813139\pi$
$230$	−5.40058	−	0.614653i	−0.356104	−	0.0405291i
$231$	0.0446896			0.00294036
$232$	−15.6454	−	5.53392i	−1.02717	−	0.363320i
$233$		−	14.8547i		−	0.973164i	−0.873635	−	0.486582i	$-0.838243\pi$
$233$		−	14.8547i		−	0.973164i	0.873635	−	0.486582i	$-0.161757\pi$
$234$	−0.942211	+	8.27863i	−0.0615943	+	0.541191i
$235$	−10.8351			−0.706801
$236$	−1.13850	+	4.93688i	−0.0741103	+	0.321363i
$237$	12.9024			0.838102
$238$	0.0735855	+	0.00837494i	0.00476984	+	0.000542867i
$239$	−25.2628			−1.63411			−0.817057	−	0.576556i	$-0.804396\pi$
$239$	−25.2628			−1.63411			−0.817057	+	0.576556i	$0.804396\pi$
$240$	−1.65903	+	3.40573i	−0.107090	+	0.219839i
$241$	−21.3105			−1.37273			−0.686366	−	0.727257i	$-0.740795\pi$
$241$	−21.3105			−1.37273			−0.686366	+	0.727257i	$0.740795\pi$
$242$	11.0080	+	1.25285i	0.707621	+	0.0805361i
$243$	1.00000			0.0641500
$244$	−1.09006	+	4.72683i	−0.0697842	+	0.302604i
$245$		−	6.62897i		−	0.423509i
$246$	1.05630	−	9.28104i	0.0673471	−	0.591737i
$247$	−29.2670			−1.86222
$248$	−9.85192	−	3.48470i	−0.625597	−	0.221279i
$249$		−	14.6510i		−	0.928468i
$250$	1.37874	−	12.1142i	0.0871994	−	0.766167i
$251$	−4.16214			−0.262712			−0.131356	−	0.991335i	$-0.541933\pi$
$251$	−4.16214			−0.262712			−0.131356	+	0.991335i	$0.541933\pi$
$252$	−0.0489480	−	0.0112880i	−0.00308343	−	0.000711077i
$253$			7.22076i			0.453966i
$254$	−2.92832	+	25.7294i	−0.183739	+	1.61440i
$255$			1.97470i			0.123661i
$256$	9.86284	+	12.5986i	0.616428	+	0.787412i
$257$	5.06462			0.315923			0.157961	−	0.987445i	$-0.449508\pi$
$257$	5.06462			0.315923			0.157961	+	0.987445i	$0.449508\pi$
$258$	−3.17237	−	0.361055i	−0.197503	−	0.0224783i
$259$	−0.146324			−0.00909212
$260$	10.8744	+	2.50776i	0.674399	+	0.155524i
$261$	5.86732			0.363178
$262$	−0.137289	+	1.20628i	−0.00848176	+	0.0745240i
$263$		−	23.1973i		−	1.43040i	−0.698918	−	0.715202i	$-0.746335\pi$
$263$		−	23.1973i		−	1.43040i	0.698918	−	0.715202i	$-0.253665\pi$
$264$	4.74458	+	1.67820i	0.292008	+	0.103286i
$265$	7.04719			0.432905
$266$	0.0199530	−	0.175314i	0.00122339	−	0.0107492i
$267$	−9.99659			−0.611782
$268$	13.0646	+	9.86489i	0.798048	+	0.602594i
$269$	23.2052			1.41485			0.707424	−	0.706789i	$-0.249857\pi$
$269$	23.2052			1.41485			0.707424	+	0.706789i	$0.249857\pi$
$270$	0.151460	−	1.33078i	0.00921754	−	0.0809889i
$271$	30.7842			1.87000			0.935002	−	0.354642i	$-0.115397\pi$
$271$	30.7842			1.87000			0.935002	+	0.354642i	$0.115397\pi$
$272$	7.49787	+	3.65245i	0.454625	+	0.221462i
$273$			0.147977i			0.00895599i
$274$	−3.12530	+	27.4600i	−0.188806	+	1.65892i
$275$	−7.30055			−0.440240
$276$	1.82387	−	7.90882i	0.109784	−	0.476055i
$277$	16.3644			0.983244			0.491622	−	0.870809i	$-0.336404\pi$
$277$	16.3644			0.983244			0.491622	+	0.870809i	$0.336404\pi$
$278$	4.47976	+	0.509852i	0.268678	+	0.0305789i
$279$	3.69465			0.221193
$280$	−0.0224355	+	0.0634295i	−0.00134078	+	0.00379064i
$281$		−	4.90280i		−	0.292477i	−0.989249	−	0.146238i	$-0.953283\pi$
$281$		−	4.90280i		−	0.292477i	0.989249	−	0.146238i	$-0.0467166\pi$
$282$	1.82959	−	16.0755i	0.108951	−	0.957283i
$283$			4.94961i			0.294223i	0.989120	+	0.147112i	$0.0469977\pi$
$283$			4.94961i			0.294223i	−0.989120	+	0.147112i	$0.953002\pi$
$284$	0.820295	−	3.55704i	0.0486756	−	0.211071i
$285$	4.70465			0.278679
$286$	1.67648	−	14.7302i	0.0991323	−	0.871014i
$287$		−	0.165895i		−	0.00979246i
$288$	−4.77279	−	3.03653i	−0.281239	−	0.178929i
$289$	−12.6526			−0.744270
$290$	0.888663	−	7.80813i	0.0521841	−	0.458509i
$291$		−	3.04196i		−	0.178323i
$292$	−17.7006	−	4.08197i	−1.03585	−	0.238879i
$293$	11.7129			0.684274			0.342137	−	0.939650i	$-0.388849\pi$
$293$	11.7129			0.684274			0.342137	+	0.939650i	$0.388849\pi$
$294$	9.83511	+	1.11936i	0.573595	+	0.0652823i
$295$	−2.39917			−0.139685
$296$	−15.5348	−	5.49479i	−0.902943	−	0.319378i
$297$	−1.77930			−0.103246
$298$	4.47303	+	0.509087i	0.259116	+	0.0294906i
$299$	−23.9096			−1.38273
$300$	7.99620	+	1.84402i	0.461661	+	0.106465i
$301$	−0.0567048			−0.00326841
$302$	−1.53265	+	13.4665i	−0.0881941	+	0.774907i
$303$		−	12.2472i		−	0.703584i
$304$	8.70180	−	17.8634i	0.499083	−	1.02454i
$305$	−2.29709			−0.131531
$306$	−2.92978	−	0.333446i	−0.167485	−	0.0190618i
$307$			11.7010i			0.667813i	0.942606	+	0.333907i	$0.108367\pi$
$307$			11.7010i			0.667813i	−0.942606	+	0.333907i	$0.891633\pi$
$308$	0.0870933	+	0.0200848i	0.00496260	+	0.00114444i
$309$		−	5.90791i		−	0.336089i
$310$	0.559590	−	4.91677i	0.0317826	−	0.279254i
$311$	9.01428			0.511153			0.255577	−	0.966789i	$-0.417735\pi$
$311$	9.01428			0.511153			0.255577	+	0.966789i	$0.417735\pi$
$312$	−5.55688	+	15.7103i	−0.314596	+	0.889423i
$313$			14.3607i			0.811717i	0.913936	+	0.405859i	$0.133027\pi$
$313$			14.3607i			0.811717i	−0.913936	+	0.405859i	$0.866973\pi$
$314$	0.695821	+	0.0791931i	0.0392674	+	0.00446912i
$315$		−	0.0237872i		−	0.00134026i
$316$	25.1449	+	5.79871i	1.41451	+	0.326203i
$317$	28.4682			1.59893			0.799465	−	0.600712i	$-0.205116\pi$
$317$	28.4682			1.59893			0.799465	+	0.600712i	$0.205116\pi$
$318$	−1.18998	+	10.4556i	−0.0667307	+	0.586321i
$319$	−10.4397			−0.584513
$320$	−4.76384	+	5.89163i	−0.266307	+	0.329352i
$321$		−	3.36968i		−	0.188077i
$322$	0.0163005	−	0.143222i	0.000908390	−	0.00798146i
$323$		−	10.3575i		−	0.576308i
$324$	1.94885	+	0.449428i	0.108269	+	0.0249682i
$325$		−	24.1737i		−	1.34092i
$326$	2.92566	−	25.7060i	0.162038	−	1.42372i
$327$			10.9353i			0.604725i
$328$	6.22973	−	17.6126i	0.343979	−	0.972494i
$329$		−	0.287343i		−	0.0158417i
$330$	−0.269493	+	2.36786i	−0.0148351	+	0.130347i
$331$	12.1555			0.668126			0.334063	−	0.942551i	$-0.391580\pi$
$331$	12.1555			0.668126			0.334063	+	0.942551i	$0.391580\pi$
$332$	6.58457	−	28.5526i	0.361375	−	1.56703i
$333$	5.82584			0.319254
$334$	1.56699	−	13.7682i	0.0857420	−	0.753362i
$335$	−3.16173	+	7.07813i	−0.172744	+	0.386719i
$336$	−0.0903191	−	0.0439972i	−0.00492731	−	0.00240025i
$337$			24.8528i			1.35382i	0.736066	+	0.676910i	$0.236681\pi$
$337$			24.8528i			1.35382i	−0.736066	+	0.676910i	$0.763319\pi$
$338$	30.5081	+	3.47220i	1.65942	+	0.188863i
$339$			12.5428i			0.681234i
$340$	−0.887488	+	3.84840i	−0.0481308	+	0.208709i
$341$	−6.57390			−0.355997
$342$	−0.794421	+	6.98009i	−0.0429574	+	0.377440i
$343$	0.351613			0.0189853
$344$	−6.02020	−	2.12939i	−0.324587	−	0.114809i
$345$	3.84344			0.206924
$346$	−5.79379	−	0.659406i	−0.311476	−	0.0354499i
$347$	1.31925			0.0708212			0.0354106	−	0.999373i	$-0.488726\pi$
$347$	1.31925			0.0708212			0.0354106	+	0.999373i	$0.488726\pi$
$348$	11.4345	+	2.63694i	0.612955	+	0.141355i
$349$	8.84302			0.473356			0.236678	−	0.971588i	$-0.423941\pi$
$349$	8.84302			0.473356			0.236678	+	0.971588i	$0.423941\pi$
$350$	0.144805	+	0.0164806i	0.00774013	+	0.000880924i
$351$		−	5.89167i		−	0.314474i
$352$	8.49224	+	5.40290i	0.452638	+	0.287975i
$353$		−	8.19013i		−	0.435917i	−0.975958	−	0.217958i	$-0.930060\pi$
$353$		−	8.19013i		−	0.435917i	0.975958	−	0.217958i	$-0.0699397\pi$
$354$	0.405120	−	3.55954i	0.0215319	−	0.189188i
$355$	1.72861			0.0917450
$356$	−19.4819	−	4.49275i	−1.03254	−	0.238115i
$357$	−0.0523687			−0.00277164
$358$	4.81674	+	0.548205i	0.254573	+	0.0289735i
$359$			23.4837i			1.23942i	0.784829	+	0.619712i	$0.212751\pi$
$359$			23.4837i			1.23942i	−0.784829	+	0.619712i	$0.787249\pi$
$360$	0.893263	−	2.52542i	0.0470791	−	0.133102i
$361$	−5.67637			−0.298756
$362$	27.6135	+	3.14276i	1.45133	+	0.165180i
$363$	−7.83408			−0.411183
$364$	−0.0665051	+	0.288385i	−0.00348582	+	0.0151155i
$365$		−	8.60193i		−	0.450246i
$366$	0.387884	−	3.40810i	0.0202750	−	0.178144i
$367$	−6.29768			−0.328736			−0.164368	−	0.986399i	$-0.552558\pi$
$367$	−6.29768			−0.328736			−0.164368	+	0.986399i	$0.552558\pi$
$368$	7.10889	−	14.5934i	0.370577	−	0.760734i
$369$			6.60505i			0.343845i
$370$	0.882379	−	7.75292i	0.0458727	−	0.403055i
$371$			0.186890i			0.00970283i
$372$	7.20032	+	1.66048i	0.373319	+	0.0860919i
$373$		−	16.1029i		−	0.833779i	−0.908957	−	0.416890i	$-0.863120\pi$
$373$		−	16.1029i		−	0.833779i	0.908957	−	0.416890i	$-0.136880\pi$
$374$	5.21297	+	0.593301i	0.269556	+	0.0306789i
$375$			8.62131i			0.445202i
$376$	10.7904	−	30.5065i	0.556472	−	1.57325i
$377$		−	34.5683i		−	1.78036i
$378$	0.0352920	+	0.00401668i	0.00181523	+	0.000206595i
$379$	−29.5997			−1.52044			−0.760218	−	0.649668i	$-0.774908\pi$
$379$	−29.5997			−1.52044			−0.760218	+	0.649668i	$0.774908\pi$
$380$	9.16866	+	2.11440i	0.470342	+	0.108467i
$381$		−	18.3109i		−	0.938094i
$382$	3.55296	+	0.404371i	0.181785	+	0.0206894i
$383$	29.7912			1.52226			0.761129	−	0.648601i	$-0.224645\pi$
$383$	29.7912			1.52226			0.761129	+	0.648601i	$0.224645\pi$
$384$	−7.93675	−	8.06276i	−0.405020	−	0.411451i
$385$			0.0423246i			0.00215706i
$386$	14.7006	+	1.67312i	0.748243	+	0.0851594i
$387$	2.25768			0.114765
$388$	1.36714	−	5.92831i	0.0694061	−	0.300965i
$389$	7.47432			0.378963			0.189481	−	0.981884i	$-0.439319\pi$
$389$	7.47432			0.378963			0.189481	+	0.981884i	$0.439319\pi$
$390$	−7.84053	−	0.892350i	−0.397021	−	0.0451859i
$391$		−	8.46152i		−	0.427918i
$392$	18.6641	+	6.60164i	0.942678	+	0.333433i
$393$		−	0.858472i		−	0.0433042i
$394$	3.50795	−	30.8222i	0.176728	−	1.55280i
$395$			12.2196i			0.614836i
$396$	−3.46759	−	0.799669i	−0.174253	−	0.0401849i
$397$	4.50959			0.226330			0.113165	−	0.993576i	$-0.463901\pi$
$397$	4.50959			0.226330			0.113165	+	0.993576i	$0.463901\pi$
$398$	2.82437	−	24.8160i	0.141573	−	1.24391i
$399$			0.124766i			0.00624613i
$400$	14.7546	+	7.18744i	0.737732	+	0.359372i
$401$			33.5008i			1.67295i	0.548004	+	0.836476i	$0.315388\pi$
$401$			33.5008i			1.67295i	−0.548004	+	0.836476i	$0.684612\pi$
$402$	−9.96762	−	5.88613i	−0.497140	−	0.293573i
$403$		−	21.7676i		−	1.08432i
$404$	5.50424	−	23.8680i	0.273846	−	1.18748i
$405$			0.947080i			0.0470608i
$406$	0.207070	+	0.0235671i	0.0102767	+	0.00116962i
$407$	−10.3659			−0.513820
$408$	−5.55984	−	1.96656i	−0.275253	−	0.0973594i
$409$			23.1180i			1.14311i	0.820564	+	0.571555i	$0.193659\pi$
$409$			23.1180i			1.14311i	−0.820564	+	0.571555i	$0.806341\pi$
$410$	8.78989	+	1.00040i	0.434102	+	0.0494062i
$411$		−	19.5425i		−	0.963962i
$412$	2.65518	−	11.5136i	0.130811	−	0.567236i
$413$		−	0.0636254i		−	0.00313080i
$414$	−0.648998	+	5.70235i	−0.0318965	+	0.280255i
$415$	13.8757			0.681129
$416$	−17.8902	+	28.1197i	−0.877139	+	1.37868i
$417$	−3.18812			−0.156123
$418$	1.41352	−	12.4197i	0.0691373	−	0.607467i
$419$		−	1.11408i		−	0.0544262i	−0.999630	−	0.0272131i	$-0.991337\pi$
$419$		−	1.11408i		−	0.0544262i	0.999630	−	0.0272131i	$-0.00866327\pi$
$420$	0.0106906	−	0.0463577i	0.000521650	−	0.00226202i
$421$	−8.22429			−0.400827			−0.200414	−	0.979711i	$-0.564229\pi$
$421$	−8.22429			−0.400827			−0.200414	+	0.979711i	$0.564229\pi$
$422$	2.13587	−	18.7666i	0.103973	−	0.913543i
$423$			11.4405i			0.556255i
$424$	−7.01813	+	19.8416i	−0.340831	+	0.963593i
$425$	8.55501			0.414979
$426$	−0.291891	+	2.56466i	−0.0141421	+	0.124258i
$427$		−	0.0609184i		−	0.00294805i
$428$	1.51443	−	6.56701i	0.0732028	−	0.317428i
$429$			10.4831i			0.506127i
$430$	0.341948	−	3.00449i	0.0164902	−	0.144889i
$431$		−	3.87687i		−	0.186742i	−0.995631	−	0.0933712i	$-0.970236\pi$
$431$		−	3.87687i		−	0.186742i	0.995631	−	0.0933712i	$-0.0297643\pi$
$432$	3.59603	+	1.75174i	0.173014	+	0.0842804i
$433$			19.7299i			0.948159i	0.880482	+	0.474080i	$0.157219\pi$
$433$			19.7299i			0.948159i	−0.880482	+	0.474080i	$0.842781\pi$
$434$	0.130392	+	0.0148402i	0.00625900	+	0.000712353i
$435$			5.55683i			0.266429i
$436$	−4.91465	+	21.3113i	−0.235369	+	1.02063i
$437$	−20.1592			−0.964347
$438$	12.7623	+	1.45251i	0.609807	+	0.0694036i
$439$			22.7099i			1.08388i	0.840416	+	0.541941i	$0.182310\pi$
$439$			22.7099i			1.08388i	−0.840416	+	0.541941i	$0.817690\pi$
$440$	−1.58939	+	4.49349i	−0.0757710	+	0.214219i
$441$	−6.99937			−0.333303
$442$	−1.96455	+	17.2613i	−0.0934442	+	0.821037i
$443$	30.8156			1.46409			0.732046	−	0.681255i	$-0.238565\pi$
$443$	30.8156			1.46409			0.732046	+	0.681255i	$0.238565\pi$
$444$	11.3537	+	2.61830i	0.538822	+	0.124259i
$445$		−	9.46758i		−	0.448806i
$446$	0.844486	−	7.41998i	0.0399876	−	0.351346i
$447$	−3.18333			−0.150566
$448$	−0.156245	−	0.126336i	−0.00738187	−	0.00596881i
$449$	−30.8425			−1.45555			−0.727774	−	0.685817i	$-0.759445\pi$
$449$	−30.8425			−1.45555			−0.727774	+	0.685817i	$0.759445\pi$
$450$	−5.76535	−	0.656169i	−0.271781	−	0.0309321i
$451$		−	11.7524i		−	0.553398i
$452$	−5.63711	+	24.4441i	−0.265147	+	1.14975i
$453$		−	9.58369i		−	0.450281i
$454$	0.480476	−	4.22164i	0.0225498	−	0.198132i
$455$	−0.140146			−0.00657016
$456$	−4.68526	+	13.2461i	−0.219407	+	0.620306i
$457$	13.6098			0.636641			0.318321	−	0.947983i	$-0.396881\pi$
$457$	13.6098			0.636641			0.318321	+	0.947983i	$0.396881\pi$
$458$	2.68095	−	23.5559i	0.125273	−	1.10069i
$459$	2.08504			0.0973215
$460$	7.49029	+	1.72735i	0.349236	+	0.0805382i
$461$	16.1508			0.752219			0.376110	−	0.926575i	$-0.377262\pi$
$461$	16.1508			0.752219			0.376110	+	0.926575i	$0.377262\pi$
$462$	−0.0627952	−	0.00714688i	−0.00292150	−	0.000332503i
$463$	−25.4577			−1.18312			−0.591560	−	0.806261i	$-0.701488\pi$
$463$	−25.4577			−1.18312			−0.591560	+	0.806261i	$0.701488\pi$
$464$	21.0991	+	10.2780i	0.979499	+	0.477144i
$465$			3.49913i			0.162268i
$466$	−2.37560	+	20.8730i	−0.110048	+	0.966922i
$467$		−	19.5912i		−	0.906574i	−0.891365	−	0.453287i	$-0.850251\pi$
$467$		−	19.5912i		−	0.906574i	0.891365	−	0.453287i	$-0.149749\pi$
$468$	2.64788	−	11.4820i	0.122398	−	0.530754i
$469$	−0.187710	−	0.0838484i	−0.00866765	−	0.00387176i
$470$	15.2248	+	1.73277i	0.702268	+	0.0799268i
$471$	−0.495196			−0.0228174
$472$	2.38928	−	6.75494i	0.109975	−	0.310921i
$473$	−4.01710			−0.184707
$474$	−18.1297	−	2.06339i	−0.832726	−	0.0947746i
$475$		−	20.3820i		−	0.935189i
$476$	−0.102059	−	0.0235360i	−0.00467785	−	0.00107877i
$477$		−	7.44096i		−	0.340698i
$478$	35.4978	+	4.04010i	1.62363	+	0.184790i
$479$		−	11.1131i		−	0.507772i	−0.967234	−	0.253886i	$-0.918291\pi$
$479$		−	11.1131i		−	0.507772i	0.967234	−	0.253886i	$-0.0817088\pi$
$480$	2.87583	−	4.52021i	0.131263	−	0.206319i
$481$		−	34.3239i		−	1.56503i
$482$	29.9443	+	3.40804i	1.36393	+	0.155232i
$483$			0.101927i			0.00463785i
$484$	−15.2674	−	3.52086i	−0.693975	−	0.160039i
$485$	2.88098			0.130818
$486$	−1.40514	−	0.159923i	−0.0637385	−	0.00725424i
$487$	−2.88454			−0.130711			−0.0653556	−	0.997862i	$-0.520818\pi$
$487$	−2.88454			−0.130711			−0.0653556	+	0.997862i	$0.520818\pi$
$488$	2.28762	−	6.46754i	0.103556	−	0.292772i
$489$			18.2942i			0.827294i
$490$	−1.06012	+	9.31464i	−0.0478914	+	0.420792i
$491$			16.4591i			0.742788i	0.928475	+	0.371394i	$0.121120\pi$
$491$			16.4591i			0.742788i	−0.928475	+	0.371394i	$0.878880\pi$
$492$	−2.96850	+	12.8723i	−0.133830	+	0.580326i
$493$	12.2336			0.550975
$494$	41.1244	+	4.68046i	1.85027	+	0.210584i
$495$		−	1.68514i		−	0.0757415i
$496$	13.2861	+	6.47205i	0.596562	+	0.290604i
$497$			0.0458423i			0.00205631i
$498$	−2.34302	+	20.5867i	−0.104993	+	0.922513i
$499$	−20.7269			−0.927864			−0.463932	−	0.885871i	$-0.653562\pi$
$499$	−20.7269			−0.927864			−0.463932	+	0.885871i	$0.653562\pi$
$500$	−3.87466	+	16.8016i	−0.173280	+	0.751392i
$501$			9.79844i			0.437762i
$502$	5.84840	+	0.665621i	0.261027	+	0.0297081i
$503$	−27.2712			−1.21596			−0.607982	−	0.793951i	$-0.708021\pi$
$503$	−27.2712			−1.21596			−0.607982	+	0.793951i	$0.708021\pi$
$504$	0.0669737	+	0.0236891i	0.00298324	+	0.00105520i
$505$	11.5991			0.516153
$506$	1.15476	−	10.1462i	0.0513355	−	0.451054i
$507$	−21.7117			−0.964253
$508$	8.22942	−	35.6851i	0.365121	−	1.58327i
$509$	−27.3306			−1.21141			−0.605704	−	0.795690i	$-0.707108\pi$
$509$	−27.3306			−1.21141			−0.605704	+	0.795690i	$0.707108\pi$
$510$	0.315800	−	2.77474i	0.0139839	−	0.122868i
$511$	0.228121			0.0100915
$512$	−11.8439	−	19.2801i	−0.523431	−	0.852068i
$513$		−	4.96753i		−	0.219322i
$514$	−7.11652	−	0.809948i	−0.313896	−	0.0357253i
$515$	5.59527			0.246557
$516$	4.39989	+	1.01467i	0.193694	+	0.0446682i
$517$		−	20.3561i		−	0.895259i
$518$	0.205606	+	0.0234005i	0.00903380	+	0.00102816i
$519$	4.12328			0.180992
$520$	−14.8790	−	5.26281i	−0.652486	−	0.230790i
$521$			37.7366i			1.65327i	0.562737	+	0.826636i	$0.309748\pi$
$521$			37.7366i			1.65327i	−0.562737	+	0.826636i	$0.690252\pi$
$522$	−8.24442	−	0.938318i	−0.360849	−	0.0410691i
$523$		−	0.772841i		−	0.0337940i	−0.999857	−	0.0168970i	$-0.994621\pi$
$523$		−	0.772841i		−	0.0337940i	0.999857	−	0.0168970i	$-0.00537873\pi$
$524$	0.385822	−	1.67303i	0.0168547	−	0.0730868i
$525$	−0.103053			−0.00449762
$526$	−3.70977	+	32.5954i	−0.161754	+	1.42123i
$527$	7.70350			0.335570
$528$	−6.39842	−	3.11687i	−0.278456	−	0.135644i
$529$	6.53102			0.283957
$530$	−9.90230	−	1.12701i	−0.430128	−	0.0489540i
$531$			2.53323i			0.109933i
$532$	−0.0560735	+	0.243151i	−0.00243109	+	0.0105419i
$533$	38.9148			1.68559
$534$	14.0466	+	1.59868i	0.607857	+	0.0691817i
$535$	3.19136			0.137975
$536$	−16.7800	−	15.9509i	−0.724786	−	0.688974i
$537$	−3.42794			−0.147926
$538$	−32.6067	−	3.71104i	−1.40577	−	0.159994i
$539$	12.4540			0.536432
$540$	−0.425645	+	1.84572i	−0.0183168	+	0.0794270i
$541$		−	37.0313i		−	1.59210i	−0.605230	−	0.796051i	$-0.706919\pi$
$541$		−	37.0313i		−	1.59210i	0.605230	−	0.796051i	$-0.293081\pi$
$542$	−43.2561	−	4.92309i	−1.85801	−	0.211465i
$543$	−19.6517			−0.843337
$544$	−9.95147	−	6.33129i	−0.426666	−	0.271452i
$545$	−10.3566			−0.443630
$546$	0.0236649	−	0.207929i	0.00101276	−	0.00889854i
$547$	−36.4076			−1.55667			−0.778337	−	0.627846i	$-0.783937\pi$
$547$	−36.4076			−1.55667			−0.778337	+	0.627846i	$0.783937\pi$
$548$	8.78297	−	38.0855i	0.375190	−	1.62693i
$549$			2.42545i			0.103516i
$550$	10.2583	+	1.16752i	0.437416	+	0.0497834i
$551$		−	29.1461i		−	1.24167i
$552$	−3.82760	+	10.8213i	−0.162913	+	0.460587i
$553$	−0.324061			−0.0137805
$554$	−22.9944	−	2.61704i	−0.976937	−	0.111188i
$555$			5.51754i			0.234206i
$556$	−6.21316	−	1.43283i	−0.263497	−	0.0607655i
$557$	−16.4941			−0.698875			−0.349438	−	0.936960i	$-0.613627\pi$
$557$	−16.4941			−0.698875			−0.349438	+	0.936960i	$0.613627\pi$
$558$	−5.19151	−	0.590858i	−0.219774	−	0.0250130i
$559$		−	13.3015i		−	0.562594i
$560$	0.0416689	−	0.0855395i	0.00176083	−	0.00361470i
$561$	−3.70992			−0.156633
$562$	−0.784069	+	6.88913i	−0.0330740	+	0.290601i
$563$	18.8664			0.795123			0.397561	−	0.917576i	$-0.369857\pi$
$563$	18.8664			0.795123			0.397561	+	0.917576i	$0.369857\pi$
$564$	−5.14168	+	22.2958i	−0.216504	+	0.938822i
$565$	−11.8791			−0.499757
$566$	0.791554	−	6.95490i	0.0332715	−	0.292336i
$567$	−0.0251164			−0.00105479
$568$	−1.72148	+	4.86696i	−0.0722318	+	0.204213i
$569$	30.7310			1.28831			0.644156	−	0.764894i	$-0.277209\pi$
$569$	30.7310			1.28831			0.644156	+	0.764894i	$0.277209\pi$
$570$	−6.61070	−	0.752381i	−0.276892	−	0.0315138i
$571$			40.3913i			1.69032i	0.534512	+	0.845161i	$0.320495\pi$
$571$			40.3913i			1.69032i	−0.534512	+	0.845161i	$0.679505\pi$
$572$	−4.71138	+	20.4299i	−0.196993	+	0.854217i
$573$	−2.52854			−0.105631
$574$	−0.0265303	+	0.233106i	−0.00110736	+	0.00972965i
$575$		−	16.6509i		−	0.694393i
$576$	6.22084	+	5.03003i	0.259202	+	0.209584i
$577$			27.5479i			1.14683i	0.819264	+	0.573416i	$0.194382\pi$
$577$			27.5479i			1.14683i	−0.819264	+	0.573416i	$0.805618\pi$
$578$	17.7787	+	2.02344i	0.739496	+	0.0841639i
$579$	−10.4620			−0.434787
$580$	−2.49740	+	10.8294i	−0.103699	+	0.449667i
$581$			0.367979i			0.0152664i
$582$	−0.486478	+	4.27438i	−0.0201652	+	0.177179i
$583$			13.2397i			0.548333i
$584$	24.2190	+	8.56647i	1.00219	+	0.354483i
$585$	5.57988			0.230700
$586$	−16.4583	−	1.87316i	−0.679885	−	0.0773794i
$587$	−0.747463			−0.0308511			−0.0154255	−	0.999881i	$-0.504910\pi$
$587$	−0.747463			−0.0308511			−0.0154255	+	0.999881i	$0.504910\pi$
$588$	−13.6407	−	3.14571i	−0.562534	−	0.129727i
$589$		−	18.3533i		−	0.756234i
$590$	3.37117	+	0.383682i	0.138789	+	0.0157959i
$591$			21.9353i			0.902297i
$592$	20.9499	+	10.2053i	0.861035	+	0.419436i
$593$		−	0.417184i		−	0.0171317i	−0.999963	−	0.00856585i	$-0.997273\pi$
$593$		−	0.417184i		−	0.0171317i	0.999963	−	0.00856585i	$-0.00272663\pi$
$594$	2.50017	+	0.284551i	0.102583	+	0.0116753i
$595$		−	0.0495974i		−	0.00203329i
$596$	−6.20383	−	1.43068i	−0.254119	−	0.0586029i
$597$			17.6608i			0.722809i
$598$	33.5963	+	3.82368i	1.37386	+	0.156362i
$599$	−32.1017			−1.31164			−0.655820	−	0.754917i	$-0.727677\pi$
$599$	−32.1017			−1.31164			−0.655820	+	0.754917i	$0.727677\pi$
$600$	−10.9409	−	3.86989i	−0.446661	−	0.157988i
$601$	−15.4178			−0.628904			−0.314452	−	0.949273i	$-0.601821\pi$
$601$	−15.4178			−0.628904			−0.314452	+	0.949273i	$0.601821\pi$
$602$	0.0796783	+	0.00906838i	0.00324744	+	0.000369600i
$603$	7.47363	+	3.33840i	0.304350	+	0.135950i
$604$	4.30718	−	18.6772i	0.175257	−	0.759964i
$605$		−	7.41951i		−	0.301646i
$606$	−1.95861	+	17.2091i	−0.0795630	+	0.699071i
$607$			20.1129i			0.816359i	0.912902	+	0.408179i	$0.133836\pi$
$607$			20.1129i			0.816359i	−0.912902	+	0.408179i	$0.866164\pi$
$608$	−15.0840	+	23.7090i	−0.611738	+	0.961526i
$609$	−0.147366			−0.00597156
$610$	3.22774	+	0.367357i	0.130687	+	0.0148739i
$611$	67.4035			2.72686
$612$	4.06344	+	0.937077i	0.164255	+	0.0378791i
$613$	24.5352			0.990969			0.495485	−	0.868617i	$-0.334991\pi$
$613$	24.5352			0.990969			0.495485	+	0.868617i	$0.334991\pi$
$614$	1.87126	−	16.4416i	0.0755180	−	0.663530i
$615$	−6.25551			−0.252247
$616$	−0.119166	−	0.0421501i	−0.00480135	−	0.00169828i
$617$	−33.2831			−1.33993			−0.669963	−	0.742394i	$-0.733690\pi$
$617$	−33.2831			−1.33993			−0.669963	+	0.742394i	$0.733690\pi$
$618$	−0.944809	+	8.30146i	−0.0380058	+	0.333934i
$619$			39.5688i			1.59040i	0.606346	+	0.795201i	$0.292635\pi$
$619$			39.5688i			1.59040i	−0.606346	+	0.795201i	$0.707365\pi$
$620$	−1.57261	+	6.81928i	−0.0631575	+	0.273869i
$621$		−	4.05820i		−	0.162850i
$622$	−12.6663	−	1.44159i	−0.507874	−	0.0578024i
$623$	0.251078			0.0100592
$624$	10.3206	−	21.1866i	0.413157	−	0.848143i
$625$	12.3501			0.494005
$626$	2.29661	−	20.1789i	0.0917909	−	0.806510i
$627$			8.83874i			0.352985i
$628$	−0.965062	−	0.222555i	−0.0385102	−	0.00888091i
$629$	12.1471			0.484338
$630$	−0.00380411	+	0.0334244i	−0.000151560	+	0.00133166i
$631$	28.0832			1.11797			0.558987	−	0.829176i	$-0.311190\pi$
$631$	28.0832			1.11797			0.558987	+	0.829176i	$0.311190\pi$
$632$	−34.4048	−	12.1692i	−1.36855	−	0.484066i
$633$			13.3556i			0.530839i
$634$	−40.0018	−	4.55270i	−1.58867	−	0.180811i
$635$	17.3419			0.688191
$636$	3.34418	−	14.5013i	0.132605	−	0.575014i
$637$			41.2380i			1.63391i
$638$	14.6693	+	1.66955i	0.580764	+	0.0660982i
$639$		−	1.82520i		−	0.0722037i
$640$	7.63608	−	7.51674i	0.301843	−	0.297125i
$641$			20.4561i			0.807969i	0.914766	+	0.403985i	$0.132375\pi$
$641$			20.4561i			0.807969i	−0.914766	+	0.403985i	$0.867625\pi$
$642$	−0.538889	+	4.73488i	−0.0212682	+	0.186871i
$643$		−	1.91129i		−	0.0753740i	−0.999290	−	0.0376870i	$-0.988001\pi$
$643$		−	1.91129i		−	0.0753740i	0.999290	−	0.0376870i	$-0.0119990\pi$
$644$	−0.0458090	+	0.198641i	−0.00180513	+	0.00782754i
$645$			2.13821i			0.0841919i
$646$	−1.65640	+	14.5538i	−0.0651703	+	0.572611i
$647$	−12.7036			−0.499429			−0.249714	−	0.968320i	$-0.580337\pi$
$647$	−12.7036			−0.499429			−0.249714	+	0.968320i	$0.580337\pi$
$648$	−2.66654	−	0.943176i	−0.104751	−	0.0370515i
$649$		−	4.50738i		−	0.176930i
$650$	−3.86593	+	33.9675i	−0.151634	+	1.33232i
$651$	−0.0927961			−0.00363697
$652$	−8.22195	+	35.6527i	−0.321996	+	1.39627i
$653$		−	42.9720i		−	1.68162i	−0.541327	−	0.840812i	$-0.682078\pi$
$653$		−	42.9720i		−	1.68162i	0.541327	−	0.840812i	$-0.317922\pi$
$654$	1.74881	−	15.3657i	0.0683838	−	0.600846i
$655$	0.813042			0.0317682
$656$	−11.5703	+	23.7520i	−0.451745	+	0.927358i
$657$	−9.08258			−0.354345
$658$	−0.0459527	+	0.403758i	−0.00179142	+	0.0157401i
$659$		−	13.7403i		−	0.535245i	−0.963524	−	0.267623i	$-0.913762\pi$
$659$		−	13.7403i		−	0.535245i	0.963524	−	0.267623i	$-0.0862381\pi$
$660$	0.757351	−	3.28409i	0.0294798	−	0.127833i
$661$			13.7809i			0.536015i	0.963417	+	0.268008i	$0.0863653\pi$
$661$			13.7809i			0.536015i	−0.963417	+	0.268008i	$0.913635\pi$
$662$	−17.0802	−	1.94394i	−0.663841	−	0.0755533i
$663$		−	12.2844i		−	0.477086i
$664$	−13.8185	+	39.0674i	−0.536260	+	1.51611i
$665$	−0.118164			−0.00458219
$666$	−8.18613	−	0.931684i	−0.317206	−	0.0361020i
$667$		−	23.8108i		−	0.921957i
$668$	−4.40370	+	19.0957i	−0.170384	+	0.738834i
$669$			5.28059i			0.204159i
$670$	5.57463	−	9.44014i	0.215367	−	0.364704i
$671$		−	4.31560i		−	0.166602i
$672$	0.119875	+	0.0762664i	0.00462428	+	0.00294204i
$673$		−	12.7527i		−	0.491581i	−0.969323	−	0.245791i	$-0.920952\pi$
$673$		−	12.7527i		−	0.491581i	0.969323	−	0.245791i	$-0.0790476\pi$
$674$	3.97453	−	34.9217i	0.153093	−	1.34514i
$675$	4.10304			0.157926
$676$	−42.3129	−	9.75787i	−1.62742	−	0.375303i
$677$			4.49207i			0.172644i	0.996267	+	0.0863220i	$0.0275114\pi$
$677$			4.49207i			0.172644i	−0.996267	+	0.0863220i	$0.972489\pi$
$678$	2.00589	−	17.6245i	0.0770356	−	0.676864i
$679$			0.0764028i			0.00293207i
$680$	1.86249	−	5.26562i	0.0714233	−	0.201927i
$681$			3.00443i			0.115130i
$682$	9.23726	+	1.05132i	0.353713	+	0.0402570i
$683$	12.7534			0.487996			0.243998	−	0.969776i	$-0.421541\pi$
$683$	12.7534			0.487996			0.243998	+	0.969776i	$0.421541\pi$
$684$	2.23255	−	9.68097i	0.0853636	−	0.370161i
$685$	18.5084			0.707168
$686$	−0.494066	−	0.0562309i	−0.0188635	−	0.00214691i
$687$			16.7641i			0.639589i
$688$	8.11869	+	3.95487i	0.309522	+	0.150778i
$689$	−43.8397			−1.67016
$690$	−5.40058	−	0.614653i	−0.205597	−	0.0233995i
$691$		−	14.3784i		−	0.546982i	−0.961875	−	0.273491i	$-0.911822\pi$
$691$		−	14.3784i		−	0.546982i	0.961875	−	0.273491i	$-0.0881784\pi$
$692$	8.03565	+	1.85312i	0.305470	+	0.0704450i
$693$	0.0446896			0.00169762
$694$	−1.85374	−	0.210978i	−0.0703669	−	0.00800863i
$695$		−	3.01940i		−	0.114533i
$696$	−15.6454	−	5.53392i	−0.593039	−	0.209763i
$697$			13.7718i			0.521645i
$698$	−12.4257	−	1.41420i	−0.470320	−	0.0535283i
$699$		−	14.8547i		−	0.561857i
$700$	−0.200836	−	0.0463151i	−0.00759087	−	0.00175055i
$701$			18.2445i			0.689084i	0.938771	+	0.344542i	$0.111966\pi$
$701$			18.2445i			0.689084i	−0.938771	+	0.344542i	$0.888034\pi$
$702$	−0.942211	+	8.27863i	−0.0355615	+	0.312457i
$703$		−	28.9400i		−	1.09149i
$704$	−11.0688	−	8.94994i	−0.417169	−	0.337314i
$705$	−10.8351			−0.408072
$706$	−1.30979	+	11.5083i	−0.0492945	+	0.433120i
$707$			0.307605i			0.0115687i
$708$	−1.13850	+	4.93688i	−0.0427876	+	0.185539i
$709$	9.58820			0.360092			0.180046	−	0.983658i	$-0.442375\pi$
$709$	9.58820			0.360092			0.180046	+	0.983658i	$0.442375\pi$
$710$	−2.42894	−	0.276444i	−0.0911565	−	0.0103748i
$711$	12.9024			0.483878
$712$	26.6563	+	9.42855i	0.998987	+	0.353350i
$713$		−	14.9936i		−	0.561516i
$714$	0.0735855	+	0.00837494i	0.00275387	+	0.000313424i
$715$	−9.92830			−0.371297
$716$	−6.68054	−	1.54061i	−0.249663	−	0.0575754i
$717$	−25.2628			−0.943457
$718$	3.75558	−	32.9980i	0.140157	−	1.23147i
$719$			25.6628i			0.957063i	0.878070	+	0.478531i	$0.158831\pi$
$719$			25.6628i			0.957063i	−0.878070	+	0.478531i	$0.841169\pi$
$720$	−1.65903	+	3.40573i	−0.0618286	+	0.126924i
$721$			0.148385i			0.00552615i
$722$	7.97610	+	0.907780i	0.296840	+	0.0337841i
$723$	−21.3105			−0.792547
$724$	−38.2983	−	8.83205i	−1.42334	−	0.328240i
$725$	24.0739			0.894081
$726$	11.0080	+	1.25285i	0.408545	+	0.0464975i
$727$	−2.96124			−0.109826			−0.0549131	−	0.998491i	$-0.517488\pi$
$727$	−2.96124			−0.109826			−0.0549131	+	0.998491i	$0.517488\pi$
$728$	0.139569	−	0.394587i	0.00517275	−	0.0146244i
$729$	1.00000			0.0370370
$730$	−1.37564	+	12.0869i	−0.0509149	+	0.447358i
$731$	4.70737			0.174108
$732$	−1.09006	+	4.72683i	−0.0402899	+	0.174709i
$733$			12.9440i			0.478097i	0.971008	+	0.239049i	$0.0768355\pi$
$733$			12.9440i			0.478097i	−0.971008	+	0.239049i	$0.923164\pi$
$734$	8.84913	+	1.00714i	0.326627	+	0.0371743i
$735$		−	6.62897i		−	0.244513i
$736$	−12.3228	+	19.3689i	−0.454225	+	0.713948i
$737$	−13.2978	−	5.94002i	−0.489832	−	0.218803i
$738$	1.05630	−	9.28104i	0.0388829	−	0.341640i
$739$	29.5210			1.08595			0.542974	−	0.839749i	$-0.317298\pi$
$739$	29.5210			1.08595			0.542974	+	0.839749i	$0.317298\pi$
$740$	−2.47974	+	10.7528i	−0.0911569	+	0.395283i
$741$	−29.2670			−1.07515
$742$	0.0298879	−	0.262607i	0.00109722	−	0.00964060i
$743$			43.6088i			1.59985i	0.600099	+	0.799926i	$0.295128\pi$
$743$			43.6088i			1.59985i	−0.600099	+	0.799926i	$0.704872\pi$
$744$	−9.85192	−	3.48470i	−0.361189	−	0.127755i
$745$		−	3.01487i		−	0.110456i
$746$	−2.57523	+	22.6269i	−0.0942858	+	0.828431i
$747$		−	14.6510i		−	0.536051i
$748$	−7.23008	−	1.66734i	−0.264358	−	0.0609641i
$749$			0.0846342i			0.00309246i
$750$	1.37874	−	12.1142i	0.0503446	−	0.442347i
$751$		−	47.3689i		−	1.72852i	−0.503049	−	0.864258i	$-0.667788\pi$
$751$		−	47.3689i		−	1.72852i	0.503049	−	0.864258i	$-0.332212\pi$
$752$	−20.0407	+	41.1403i	−0.730810	+	1.50023i
$753$	−4.16214			−0.151677
$754$	−5.52826	+	48.5734i	−0.201327	+	1.76894i
$755$	9.07653			0.330329
$756$	−0.0489480	−	0.0112880i	−0.00178022	−	0.000410541i
$757$		−	12.6050i		−	0.458135i	−0.973411	−	0.229067i	$-0.926432\pi$
$757$		−	12.6050i		−	0.458135i	0.973411	−	0.229067i	$-0.0735676\pi$
$758$	41.5918	+	4.73367i	1.51068	+	0.171935i
$759$			7.22076i			0.262097i
$760$	−12.5451	−	4.43731i	−0.455060	−	0.160958i
$761$	−37.0014			−1.34130			−0.670649	−	0.741774i	$-0.733984\pi$
$761$	−37.0014			−1.34130			−0.670649	+	0.741774i	$0.733984\pi$
$762$	−2.92832	+	25.7294i	−0.106082	+	0.932076i
$763$		−	0.274656i		−	0.00994320i
$764$	−4.92774	−	1.13640i	−0.178279	−	0.0411134i
$765$			1.97470i			0.0713956i
$766$	−41.8608	−	4.76428i	−1.51249	−	0.172141i
$767$	14.9249			0.538908
$768$	9.86284	+	12.5986i	0.355895	+	0.454612i
$769$		−	43.1762i		−	1.55697i	−0.627660	−	0.778487i	$-0.715987\pi$
$769$		−	43.1762i		−	1.55697i	0.627660	−	0.778487i	$-0.284013\pi$
$770$	0.00676867	−	0.0594721i	0.000243926	−	0.00214323i
$771$	5.06462			0.182398
$772$	−20.3889	−	4.70193i	−0.733813	−	0.169226i
$773$	−41.9089			−1.50736			−0.753679	−	0.657243i	$-0.771723\pi$
$773$	−41.9089			−1.50736			−0.753679	+	0.657243i	$0.771723\pi$
$774$	−3.17237	−	0.361055i	−0.114028	−	0.0129778i
$775$	15.1593			0.544538
$776$	−2.86910	+	8.11149i	−0.102995	+	0.291185i
$777$	−0.146324			−0.00524934
$778$	−10.5025	−	1.19531i	−0.376532	−	0.0428540i
$779$	32.8108			1.17557
$780$	10.8744	+	2.50776i	0.389364	+	0.0897921i
$781$			3.24758i			0.116208i
$782$	−1.35319	+	11.8896i	−0.0483900	+	0.425173i
$783$	5.86732			0.209681
$784$	−25.1699	−	12.2610i	−0.898926	−	0.437895i
$785$		−	0.468990i		−	0.0167390i
$786$	−0.137289	+	1.20628i	−0.00489694	+	0.0430264i
$787$	−10.3965			−0.370597			−0.185298	−	0.982682i	$-0.559325\pi$
$787$	−10.3965			−0.370597			−0.185298	+	0.982682i	$0.559325\pi$
$788$	−9.85833	+	42.7486i	−0.351189	+	1.52285i
$789$		−	23.1973i		−	0.825844i
$790$	1.95419	−	17.1703i	0.0695271	−	0.610892i
$791$		−	0.315030i		−	0.0112012i
$792$	4.74458	+	1.67820i	0.168591	+	0.0596321i
$793$	14.2899			0.507450
$794$	−6.33662	−	0.721186i	−0.224878	−	0.0255939i
$795$	7.04719			0.249938
$796$	−7.93727	+	34.4183i	−0.281329	+	1.21992i
$797$	6.97775			0.247165			0.123582	−	0.992334i	$-0.460562\pi$
$797$	6.97775			0.247165			0.123582	+	0.992334i	$0.460562\pi$
$798$	0.0199530	−	0.175314i	0.000706327	−	0.00620606i
$799$			23.8539i			0.843891i
$800$	−19.5829	−	12.4590i	−0.692361	−	0.440491i
$801$	−9.99659			−0.353212
$802$	5.35754	−	47.0734i	0.189181	−	1.66222i
$803$	16.1607			0.570297
$804$	13.0646	+	9.86489i	0.460753	+	0.347908i
$805$	−0.0965332			−0.00340235
$806$	−3.48114	+	30.5866i	−0.122618	+	1.07737i
$807$	23.2052			0.816863
$808$	−11.5513	+	32.6576i	−0.406372	+	1.14889i
$809$			44.2272i			1.55495i	0.628916	+	0.777473i	$0.283499\pi$
$809$			44.2272i			1.55495i	−0.628916	+	0.777473i	$0.716501\pi$
$810$	0.151460	−	1.33078i	0.00532175	−	0.0467589i
$811$	29.7001			1.04291			0.521457	−	0.853278i	$-0.325389\pi$
$811$	29.7001			1.04291			0.521457	+	0.853278i	$0.325389\pi$
$812$	−0.287194	−	0.0662304i	−0.0100785	−	0.00232423i
$813$	30.7842			1.07965
$814$	14.5656	+	1.65775i	0.510524	+	0.0581040i
$815$	−17.3261			−0.606907
$816$	7.49787	+	3.65245i	0.262478	+	0.127861i
$817$		−	11.2151i		−	0.392367i
$818$	3.69709	−	32.4840i	0.129266	−	1.13578i
$819$			0.147977i			0.00517074i
$820$	−12.1911	−	2.81141i	−0.425730	−	0.0981785i
$821$	−22.7228			−0.793029			−0.396515	−	0.918028i	$-0.629780\pi$
$821$	−22.7228			−0.793029			−0.396515	+	0.918028i	$0.629780\pi$
$822$	−3.12530	+	27.4600i	−0.109007	+	0.957779i
$823$		−	1.00825i		−	0.0351453i	−0.999846	−	0.0175727i	$-0.994406\pi$
$823$		−	1.00825i		−	0.0351453i	0.999846	−	0.0175727i	$-0.00559384\pi$
$824$	−5.57220	+	15.7537i	−0.194117	+	0.548805i
$825$	−7.30055			−0.254172
$826$	−0.0101751	+	0.0894028i	−0.000354039	+	0.00311072i
$827$		−	0.134446i		−	0.00467514i	−0.999997	−	0.00233757i	$-0.999256\pi$
$827$		−	0.134446i		−	0.00467514i	0.999997	−	0.00233757i	$-0.000744073\pi$
$828$	1.82387	−	7.90882i	0.0633839	−	0.274850i
$829$	9.43973			0.327855			0.163928	−	0.986472i	$-0.447584\pi$
$829$	9.43973			0.327855			0.163928	+	0.986472i	$0.447584\pi$
$830$	−19.4973	−	2.21903i	−0.676760	−	0.0770238i
$831$	16.3644			0.567676
$832$	29.6352	−	36.6511i	1.02742	−	1.27065i
$833$	−14.5940			−0.505652
$834$	4.47976	+	0.509852i	0.155121	+	0.0176547i
$835$	−9.27991			−0.321144
$836$	−3.97238	+	17.2254i	−0.137388	+	0.595752i
$837$	3.69465			0.127706
$838$	−0.178166	+	1.56544i	−0.00615465	+	0.0540771i
$839$		−	11.1921i		−	0.386395i	−0.981160	−	0.193198i	$-0.938114\pi$
$839$		−	11.1921i		−	0.386395i	0.981160	−	0.193198i	$-0.0618858\pi$
$840$	−0.0224355	+	0.0634295i	−0.000774099	+	0.00218852i
$841$	5.42549			0.187086
$842$	11.5563	+	1.31525i	0.398256	+	0.0453265i
$843$		−	4.90280i		−	0.168861i
$844$	−6.00241	+	26.0281i	−0.206611	+	0.895926i
$845$		−	20.5628i		−	0.707381i
$846$	1.82959	−	16.0755i	0.0629027	−	0.552687i
$847$	0.196764			0.00676088
$848$	13.0346	−	26.7579i	0.447610	−	0.918870i
$849$			4.94961i			0.169870i
$850$	−12.0210	−	1.36814i	−0.412317	−	0.0469268i
$851$		−	23.6424i		−	0.810451i
$852$	0.820295	−	3.55704i	0.0281029	−	0.121862i
$853$	27.9647			0.957492			0.478746	−	0.877953i	$-0.341091\pi$
$853$	27.9647			0.957492			0.478746	+	0.877953i	$0.341091\pi$
$854$	−0.00974223	+	0.0855990i	−0.000333372	+	0.00292914i
$855$	4.70465			0.160896
$856$	−3.17820	+	8.98538i	−0.108629	+	0.307114i
$857$			21.0349i			0.718537i	0.933234	+	0.359269i	$0.116974\pi$
$857$			21.0349i			0.718537i	−0.933234	+	0.359269i	$0.883026\pi$
$858$	1.67648	−	14.7302i	0.0572341	−	0.502880i
$859$		−	23.6839i		−	0.808084i	−0.914740	−	0.404042i	$-0.867605\pi$
$859$		−	23.6839i		−	0.808084i	0.914740	−	0.404042i	$-0.132395\pi$
$860$	−0.960971	+	4.16705i	−0.0327688	+	0.142095i
$861$		−	0.165895i		−	0.00565368i
$862$	−0.620000	+	5.44756i	−0.0211173	+	0.185545i
$863$		−	25.2929i		−	0.860980i	−0.902595	−	0.430490i	$-0.858341\pi$
$863$		−	25.2929i		−	0.860980i	0.902595	−	0.430490i	$-0.141659\pi$
$864$	−4.77279	−	3.03653i	−0.162374	−	0.103305i
$865$			3.90508i			0.132777i
$866$	3.15526	−	27.7233i	0.107220	−	0.942078i
$867$	−12.6526			−0.429705
$868$	−0.180846	−	0.0417052i	−0.00613830	−	0.00141557i
$869$	−22.9573			−0.778773
$870$	0.888663	−	7.80813i	0.0301285	−	0.264720i
$871$	19.6687	−	44.0321i	0.666449	−	1.49197i
$872$	10.3139	−	29.1595i	0.349274	−	0.987464i
$873$		−	3.04196i		−	0.102955i
$874$	28.3266	+	3.22392i	0.958161	+	0.109051i
$875$		−	0.216536i		−	0.00732025i
$876$	−17.7006	−	4.08197i	−0.598047	−	0.137917i
$877$	18.0196			0.608479			0.304240	−	0.952596i	$-0.401598\pi$
$877$	18.0196			0.608479			0.304240	+	0.952596i	$0.401598\pi$
$878$	3.63182	−	31.9106i	0.122568	−	1.07693i
$879$	11.7129			0.395066
$880$	2.95192	−	6.05982i	0.0995094	−	0.204276i
$881$	−2.54610			−0.0857803			−0.0428901	−	0.999080i	$-0.513657\pi$
$881$	−2.54610			−0.0857803			−0.0428901	+	0.999080i	$0.513657\pi$
$882$	9.83511	+	1.11936i	0.331165	+	0.0376907i
$883$	53.6049			1.80395			0.901974	−	0.431791i	$-0.142118\pi$
$883$	53.6049			1.80395			0.901974	+	0.431791i	$0.142118\pi$
$884$	5.52095	−	23.9404i	0.185690	−	0.805203i
$885$	−2.39917			−0.0806472
$886$	−43.3003	−	4.92811i	−1.45470	−	0.165563i
$887$		−	9.18543i		−	0.308417i	−0.988038	−	0.154208i	$-0.950717\pi$
$887$		−	9.18543i		−	0.308417i	0.988038	−	0.154208i	$-0.0492827\pi$
$888$	−15.5348	−	5.49479i	−0.521314	−	0.184393i
$889$			0.459902i			0.0154246i
$890$	−1.51408	+	13.3033i	−0.0507521	+	0.445927i
$891$	−1.77930			−0.0596089
$892$	−2.37325	+	10.2911i	−0.0794621	+	0.344570i
$893$	56.8310			1.90178
$894$	4.47303	+	0.509087i	0.149601	+	0.0170264i
$895$		−	3.24653i		−	0.108520i
$896$	0.199342	+	0.202507i	0.00665955	+	0.00676529i
$897$	−23.9096			−0.798317
$898$	43.3381	+	4.93242i	1.44621	+	0.164597i
$899$	21.6777			0.722992
$900$	7.99620	+	1.84402i	0.266540	+	0.0614674i
$901$		−	15.5147i		−	0.516870i
$902$	−1.87947	+	16.5138i	−0.0625796	+	0.549848i
$903$	−0.0567048			−0.00188702
$904$	11.8301	−	33.4460i	0.393464	−	1.11240i
$905$		−	18.6118i		−	0.618676i
$906$	−1.53265	+	13.4665i	−0.0509189	+	0.447393i
$907$			11.9712i			0.397496i	0.980051	+	0.198748i	$0.0636875\pi$
$907$			11.9712i			0.397496i	−0.980051	+	0.198748i	$0.936312\pi$
$908$	−1.35027	+	5.85517i	−0.0448104	+	0.194311i
$909$		−	12.2472i		−	0.406214i
$910$	0.196925	+	0.0224126i	0.00652802	+	0.000742970i
$911$			47.7871i			1.58326i	0.611002	+	0.791629i	$0.290767\pi$
$911$			47.7871i			1.58326i	−0.611002	+	0.791629i	$0.709233\pi$
$912$	8.70180	−	17.8634i	0.288146	−	0.591516i
$913$			26.0685i			0.862742i
$914$	−19.1238	−	2.17652i	−0.632558	−	0.0719930i
$915$	−2.29709			−0.0759396
$916$	−7.53425	+	32.6706i	−0.248938	+	1.07947i
$917$			0.0215617i			0.000712030i
$918$	−2.92978	−	0.333446i	−0.0966972	−	0.0110054i
$919$	45.7619			1.50955			0.754773	−	0.655986i	$-0.227747\pi$
$919$	45.7619			1.50955			0.754773	+	0.655986i	$0.227747\pi$
$920$	−10.2487	−	3.62504i	−0.337889	−	0.119514i
$921$			11.7010i			0.385562i
$922$	−22.6942	−	2.58288i	−0.747394	−	0.0850628i
$923$	−10.7535			−0.353954
$924$	0.0870933	+	0.0200848i	0.00286516	+	0.000660740i
$925$	23.9036			0.785947
$926$	35.7717	+	4.07127i	1.17553	+	0.133790i
$927$		−	5.90791i		−	0.194041i
$928$	−28.0035	−	17.8163i	−0.919260	−	0.584848i
$929$		−	29.2121i		−	0.958417i	−0.877701	−	0.479209i	$-0.840924\pi$
$929$		−	29.2121i		−	0.958417i	0.877701	−	0.479209i	$-0.159076\pi$
$930$	0.559590	−	4.91677i	0.0183497	−	0.161227i
$931$			34.7696i			1.13953i
$932$	6.67613	−	28.9496i	0.218684	−	0.948275i
$933$	9.01428			0.295114
$934$	−3.13308	+	27.5285i	−0.102518	+	0.900759i
$935$		−	3.51359i		−	0.114907i
$936$	−5.55688	+	15.7103i	−0.181632	+	0.513509i
$937$		−	48.6220i		−	1.58841i	−0.607649	−	0.794205i	$-0.707887\pi$
$937$		−	48.6220i		−	1.58841i	0.607649	−	0.794205i	$-0.292113\pi$
$938$	0.250350	+	0.147838i	0.00817423	+	0.00482708i
$939$			14.3607i			0.468645i
$940$	−21.1159	−	4.86958i	−0.688725	−	0.158828i
$941$		−	7.50585i		−	0.244684i	−0.992488	−	0.122342i	$-0.960960\pi$
$941$		−	7.50585i		−	0.244684i	0.992488	−	0.122342i	$-0.0390404\pi$
$942$	0.695821	+	0.0791931i	0.0226711	+	0.00258025i
$943$	26.8046			0.872878
$944$	−4.43754	+	9.10956i	−0.144430	+	0.296491i
$945$		−	0.0237872i		−	0.000773798i
$946$	5.64460	+	0.642426i	0.183522	+	0.0208871i
$947$		−	9.56210i		−	0.310726i	−0.987857	−	0.155363i	$-0.950345\pi$
$947$		−	9.56210i		−	0.310726i	0.987857	−	0.155363i	$-0.0496548\pi$
$948$	25.1449	+	5.79871i	0.816667	+	0.188333i
$949$			53.5115i			1.73706i
$950$	−3.25954	+	28.6396i	−0.105753	+	0.929190i
$951$	28.4682			0.923143
$952$	0.139643	+	0.0493929i	0.00452586	+	0.00160083i
$953$	17.3531			0.562121			0.281061	−	0.959690i	$-0.409314\pi$
$953$	17.3531			0.562121			0.281061	+	0.959690i	$0.409314\pi$
$954$	−1.18998	+	10.4556i	−0.0385270	+	0.338513i
$955$		−	2.39473i		−	0.0774916i
$956$	−49.2334	−	11.3538i	−1.59232	−	0.367209i
$957$	−10.4397			−0.337469
$958$	−1.77724	+	15.6155i	−0.0574201	+	0.504515i
$959$			0.490837i			0.0158500i
$960$	−4.76384	+	5.89163i	−0.153752	+	0.190152i
$961$	−17.3496			−0.559663
$962$	−5.48917	+	48.2300i	−0.176978	+	1.55500i
$963$		−	3.36968i		−	0.108587i
$964$	−41.5310	−	9.57755i	−1.33762	−	0.308472i
$965$		−	9.90838i		−	0.318962i
$966$	0.0163005	−	0.143222i	0.000524459	−	0.00460810i
$967$			7.98086i			0.256647i	0.991732	+	0.128324i	$0.0409596\pi$
$967$			7.98086i			0.256647i	−0.991732	+	0.128324i	$0.959040\pi$
$968$	20.8899	+	7.38892i	0.671426	+	0.237489i
$969$		−	10.3575i		−	0.332731i
$970$	−4.04818	−	0.460734i	−0.129979	−	0.0147933i
$971$		−	41.9664i		−	1.34677i	−0.739294	−	0.673383i	$-0.764841\pi$
$971$		−	41.9664i		−	1.34677i	0.739294	−	0.673383i	$-0.235159\pi$
$972$	1.94885	+	0.449428i	0.0625094	+	0.0144154i
$973$	0.0800739			0.00256705
$974$	4.05319	+	0.461304i	0.129873	+	0.0147811i
$975$		−	24.1737i		−	0.774179i
$976$	−4.24874	+	8.72198i	−0.135999	+	0.279184i
$977$	−17.3280			−0.554373			−0.277187	−	0.960816i	$-0.589402\pi$
$977$	−17.3280			−0.554373			−0.277187	+	0.960816i	$0.589402\pi$
$978$	2.92566	−	25.7060i	0.0935524	−	0.821988i
$979$	17.7870			0.568474
$980$	2.97924	−	12.9189i	0.0951685	−	0.412678i
$981$			10.9353i			0.349138i
$982$	2.63218	−	23.1274i	0.0839963	−	0.738024i
$983$	−29.5082			−0.941166			−0.470583	−	0.882356i	$-0.655956\pi$
$983$	−29.5082			−0.941166			−0.470583	+	0.882356i	$0.655956\pi$
$984$	6.22973	−	17.6126i	0.198596	−	0.561470i
$985$	−20.7745			−0.661930
$986$	−17.1900	−	1.95643i	−0.547441	−	0.0623056i
$987$		−	0.287343i		−	0.00914624i
$988$	−57.0371	−	13.1534i	−1.81459	−	0.418467i
$989$		−	9.16213i		−	0.291339i
$990$	−0.269493	+	2.36786i	−0.00856503	+	0.0752557i
$991$	18.7533			0.595719			0.297859	−	0.954610i	$-0.403727\pi$
$991$	18.7533			0.595719			0.297859	+	0.954610i	$0.403727\pi$
$992$	−17.6338	−	11.2189i	−0.559873	−	0.356200i
$993$	12.1555			0.385743
$994$	0.00733123	−	0.0644150i	0.000232532	−	0.00204312i
$995$	−16.7262			−0.530257
$996$	6.58457	−	28.5526i	0.208640	−	0.904723i
$997$	26.1704			0.828824			0.414412	−	0.910089i	$-0.363987\pi$
$997$	26.1704			0.828824			0.414412	+	0.910089i	$0.363987\pi$
$998$	29.1242	+	3.31470i	0.921912	+	0.104925i
$999$	5.82584			0.184321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.b.535.1	yes	34
4.3	odd	2		804.2.e.a.535.33	✓	34
67.66	odd	2		804.2.e.a.535.34	yes	34
268.267	even	2	inner	804.2.e.b.535.2	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.33	✓	34	4.3	odd	2
804.2.e.a.535.34	yes	34	67.66	odd	2
804.2.e.b.535.1	yes	34	1.1	even	1	trivial
804.2.e.b.535.2	yes	34	268.267	even	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40514 - 0.159923i) q^{2} +1.00000 q^{3} +(1.94885 + 0.449428i) q^{4} +0.947080i q^{5} +(-1.40514 - 0.159923i) q^{6} -0.0251164 q^{7} +(-2.66654 - 0.943176i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.40514 - 0.159923i) q^{2} +1.00000 q^{3} +(1.94885 + 0.449428i) q^{4} +0.947080i q^{5} +(-1.40514 - 0.159923i) q^{6} -0.0251164 q^{7} +(-2.66654 - 0.943176i) q^{8} +1.00000 q^{9} +(0.151460 - 1.33078i) q^{10} -1.77930 q^{11} +(1.94885 + 0.449428i) q^{12} -5.89167i q^{13} +(0.0352920 + 0.00401668i) q^{14} +0.947080i q^{15} +(3.59603 + 1.75174i) q^{16} +2.08504 q^{17} +(-1.40514 - 0.159923i) q^{18} -4.96753i q^{19} +(-0.425645 + 1.84572i) q^{20} -0.0251164 q^{21} +(2.50017 + 0.284551i) q^{22} -4.05820i q^{23} +(-2.66654 - 0.943176i) q^{24} +4.10304 q^{25} +(-0.942211 + 8.27863i) q^{26} +1.00000 q^{27} +(-0.0489480 - 0.0112880i) q^{28} +5.86732 q^{29} +(0.151460 - 1.33078i) q^{30} +3.69465 q^{31} +(-4.77279 - 3.03653i) q^{32} -1.77930 q^{33} +(-2.92978 - 0.333446i) q^{34} -0.0237872i q^{35} +(1.94885 + 0.449428i) q^{36} +5.82584 q^{37} +(-0.794421 + 6.98009i) q^{38} -5.89167i q^{39} +(0.893263 - 2.52542i) q^{40} +6.60505i q^{41} +(0.0352920 + 0.00401668i) q^{42} +2.25768 q^{43} +(-3.46759 - 0.799669i) q^{44} +0.947080i q^{45} +(-0.648998 + 5.70235i) q^{46} +11.4405i q^{47} +(3.59603 + 1.75174i) q^{48} -6.99937 q^{49} +(-5.76535 - 0.656169i) q^{50} +2.08504 q^{51} +(2.64788 - 11.4820i) q^{52} -7.44096i q^{53} +(-1.40514 - 0.159923i) q^{54} -1.68514i q^{55} +(0.0669737 + 0.0236891i) q^{56} -4.96753i q^{57} +(-8.24442 - 0.938318i) q^{58} +2.53323i q^{59} +(-0.425645 + 1.84572i) q^{60} +2.42545i q^{61} +(-5.19151 - 0.590858i) q^{62} -0.0251164 q^{63} +(6.22084 + 5.03003i) q^{64} +5.57988 q^{65} +(2.50017 + 0.284551i) q^{66} +(7.47363 + 3.33840i) q^{67} +(4.06344 + 0.937077i) q^{68} -4.05820i q^{69} +(-0.00380411 + 0.0334244i) q^{70} -1.82520i q^{71} +(-2.66654 - 0.943176i) q^{72} -9.08258 q^{73} +(-8.18613 - 0.931684i) q^{74} +4.10304 q^{75} +(2.23255 - 9.68097i) q^{76} +0.0446896 q^{77} +(-0.942211 + 8.27863i) q^{78} +12.9024 q^{79} +(-1.65903 + 3.40573i) q^{80} +1.00000 q^{81} +(1.05630 - 9.28104i) q^{82} -14.6510i q^{83} +(-0.0489480 - 0.0112880i) q^{84} +1.97470i q^{85} +(-3.17237 - 0.361055i) q^{86} +5.86732 q^{87} +(4.74458 + 1.67820i) q^{88} -9.99659 q^{89} +(0.151460 - 1.33078i) q^{90} +0.147977i q^{91} +(1.82387 - 7.90882i) q^{92} +3.69465 q^{93} +(1.82959 - 16.0755i) q^{94} +4.70465 q^{95} +(-4.77279 - 3.03653i) q^{96} -3.04196i q^{97} +(9.83511 + 1.11936i) q^{98} -1.77930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Introduction

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