LMFDB - Embedded newform 637.2.w.a.92.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(92,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("637.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.w (of order $7$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			92.16
Character	$\chi$	$=$	637.92
Dual form			637.2.w.a.547.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.251865 - 0.315829i) q^{2} +(-0.214027 - 0.103070i) q^{3} +(0.408730 + 1.79076i) q^{4} +(0.747465 + 0.359960i) q^{5} +(-0.0864582 + 0.0416361i) q^{6} +(1.94492 + 1.79368i) q^{7} +(1.39643 + 0.672485i) q^{8} +(-1.83529 - 2.30138i) q^{9} +O(q^{10})$	\(q+(0.251865 - 0.315829i) q^{2} +(-0.214027 - 0.103070i) q^{3} +(0.408730 + 1.79076i) q^{4} +(0.747465 + 0.359960i) q^{5} +(-0.0864582 + 0.0416361i) q^{6} +(1.94492 + 1.79368i) q^{7} +(1.39643 + 0.672485i) q^{8} +(-1.83529 - 2.30138i) q^{9} +(0.301946 - 0.145409i) q^{10} +(2.82531 - 3.54283i) q^{11} +(0.0970945 - 0.425399i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(1.05635 - 0.162494i) q^{14} +(-0.122876 - 0.154082i) q^{15} +(-2.74573 + 1.32227i) q^{16} +(-0.845215 + 3.70313i) q^{17} -1.18908 q^{18} +8.18558 q^{19} +(-0.339092 + 1.48566i) q^{20} +(-0.231389 - 0.584358i) q^{21} +(-0.407330 - 1.78463i) q^{22} +(1.45722 + 6.38449i) q^{23} +(-0.229560 - 0.287859i) q^{24} +(-2.68832 - 3.37104i) q^{25} +(0.0898895 + 0.393832i) q^{26} +(0.314178 + 1.37651i) q^{27} +(-2.41712 + 4.21602i) q^{28} +(-0.571622 + 2.50444i) q^{29} -0.0796118 q^{30} -4.58955 q^{31} +(-0.963720 + 4.22233i) q^{32} +(-0.969851 + 0.467055i) q^{33} +(0.956675 + 1.19963i) q^{34} +(0.808101 + 2.04081i) q^{35} +(3.37108 - 4.22720i) q^{36} +(-0.425107 + 1.86252i) q^{37} +(2.06166 - 2.58524i) q^{38} +(0.214027 - 0.103070i) q^{39} +(0.801714 + 1.00532i) q^{40} +(4.89287 + 2.35628i) q^{41} +(-0.242836 - 0.0741001i) q^{42} +(-6.40742 + 3.08565i) q^{43} +(7.49916 + 3.61141i) q^{44} +(-0.543408 - 2.38083i) q^{45} +(2.38343 + 1.14780i) q^{46} +(5.47093 - 6.86032i) q^{47} +0.723945 q^{48} +(0.565391 + 6.97713i) q^{49} -1.74176 q^{50} +(0.562580 - 0.705452i) q^{51} +(-1.65491 - 0.796965i) q^{52} +(-0.734570 - 3.21836i) q^{53} +(0.513870 + 0.247467i) q^{54} +(3.38710 - 1.63114i) q^{55} +(1.50971 + 3.81268i) q^{56} +(-1.75193 - 0.843686i) q^{57} +(0.647002 + 0.811314i) q^{58} +(11.5053 - 5.54068i) q^{59} +(0.225701 - 0.283020i) q^{60} +(2.96509 - 12.9909i) q^{61} +(-1.15595 + 1.44951i) q^{62} +(0.558467 - 7.76790i) q^{63} +(-2.70940 - 3.39748i) q^{64} +(-0.747465 + 0.359960i) q^{65} +(-0.0967619 + 0.423941i) q^{66} -7.01503 q^{67} -6.97690 q^{68} +(0.346165 - 1.51665i) q^{69} +(0.848078 + 0.258787i) q^{70} +(0.773429 + 3.38862i) q^{71} +(-1.01521 - 4.44791i) q^{72} +(-5.38171 - 6.74845i) q^{73} +(0.481166 + 0.603363i) q^{74} +(0.227919 + 0.998577i) q^{75} +(3.34569 + 14.6584i) q^{76} +(11.8497 - 1.82278i) q^{77} +(0.0213534 - 0.0935554i) q^{78} -8.55020 q^{79} -2.52830 q^{80} +(-1.89038 + 8.28231i) q^{81} +(1.97652 - 0.951844i) q^{82} +(-0.443517 - 0.556153i) q^{83} +(0.951872 - 0.653208i) q^{84} +(-1.96475 + 2.46372i) q^{85} +(-0.639268 + 2.80082i) q^{86} +(0.380474 - 0.477099i) q^{87} +(6.32785 - 3.04733i) q^{88} +(-3.15074 - 3.95091i) q^{89} +(-0.888798 - 0.428023i) q^{90} +(-2.61499 + 0.402252i) q^{91} +(-10.8375 + 5.21907i) q^{92} +(0.982286 + 0.473044i) q^{93} +(-0.788752 - 3.45575i) q^{94} +(6.11843 + 2.94648i) q^{95} +(0.641457 - 0.804361i) q^{96} -0.306464 q^{97} +(2.34598 + 1.57873i) q^{98} -13.3386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 3 q^{2} - 25 q^{4} - 4 q^{5} + 18 q^{6} - 15 q^{7} + 3 q^{8} - 5 q^{9}+O(q^{10}) $ 162 * q + 3 * q^2 - 25 * q^4 - 4 * q^5 + 18 * q^6 - 15 * q^7 + 3 * q^8 - 5 * q^9	\( 162 q + 3 q^{2} - 25 q^{4} - 4 q^{5} + 18 q^{6} - 15 q^{7} + 3 q^{8} - 5 q^{9} - 10 q^{10} + 15 q^{11} + 25 q^{12} + 27 q^{13} + 33 q^{14} + 18 q^{15} - 5 q^{16} + 3 q^{17} - 64 q^{18} + 24 q^{19} - 47 q^{20} + 24 q^{22} + 27 q^{23} - 8 q^{24} - 35 q^{25} - 3 q^{26} + 15 q^{27} + 2 q^{28} + 46 q^{29} - 30 q^{30} + 46 q^{31} + 16 q^{32} - 18 q^{33} - 62 q^{34} - 51 q^{35} + 39 q^{36} + 16 q^{37} - 54 q^{38} + 74 q^{40} - 2 q^{41} + 88 q^{42} + 14 q^{43} - 95 q^{44} + 83 q^{45} + 56 q^{46} - 4 q^{47} - 20 q^{48} - 3 q^{49} - 216 q^{50} - 56 q^{51} + 25 q^{52} + 38 q^{53} - 6 q^{54} + 73 q^{55} - 35 q^{56} + 41 q^{57} + 72 q^{58} - 44 q^{59} + 24 q^{60} - 6 q^{61} - 36 q^{62} - q^{63} - 11 q^{64} + 4 q^{65} + 95 q^{66} - 126 q^{67} - 382 q^{68} - 108 q^{69} - 47 q^{70} + 51 q^{71} + 130 q^{72} + 14 q^{73} - 26 q^{74} + 3 q^{75} + 75 q^{76} - 6 q^{77} + 31 q^{78} - 58 q^{79} + 110 q^{80} - 5 q^{81} - 90 q^{82} - 35 q^{83} + 21 q^{84} + 18 q^{85} + 76 q^{86} - 100 q^{87} + 6 q^{88} + 32 q^{89} + 13 q^{90} + q^{91} + 46 q^{92} + 19 q^{93} + 72 q^{94} + 38 q^{95} + 95 q^{96} + 6 q^{97} - 299 q^{98} - 334 q^{99}+O(q^{100}) \) 162 * q + 3 * q^2 - 25 * q^4 - 4 * q^5 + 18 * q^6 - 15 * q^7 + 3 * q^8 - 5 * q^9 - 10 * q^10 + 15 * q^11 + 25 * q^12 + 27 * q^13 + 33 * q^14 + 18 * q^15 - 5 * q^16 + 3 * q^17 - 64 * q^18 + 24 * q^19 - 47 * q^20 + 24 * q^22 + 27 * q^23 - 8 * q^24 - 35 * q^25 - 3 * q^26 + 15 * q^27 + 2 * q^28 + 46 * q^29 - 30 * q^30 + 46 * q^31 + 16 * q^32 - 18 * q^33 - 62 * q^34 - 51 * q^35 + 39 * q^36 + 16 * q^37 - 54 * q^38 + 74 * q^40 - 2 * q^41 + 88 * q^42 + 14 * q^43 - 95 * q^44 + 83 * q^45 + 56 * q^46 - 4 * q^47 - 20 * q^48 - 3 * q^49 - 216 * q^50 - 56 * q^51 + 25 * q^52 + 38 * q^53 - 6 * q^54 + 73 * q^55 - 35 * q^56 + 41 * q^57 + 72 * q^58 - 44 * q^59 + 24 * q^60 - 6 * q^61 - 36 * q^62 - q^63 - 11 * q^64 + 4 * q^65 + 95 * q^66 - 126 * q^67 - 382 * q^68 - 108 * q^69 - 47 * q^70 + 51 * q^71 + 130 * q^72 + 14 * q^73 - 26 * q^74 + 3 * q^75 + 75 * q^76 - 6 * q^77 + 31 * q^78 - 58 * q^79 + 110 * q^80 - 5 * q^81 - 90 * q^82 - 35 * q^83 + 21 * q^84 + 18 * q^85 + 76 * q^86 - 100 * q^87 + 6 * q^88 + 32 * q^89 + 13 * q^90 + q^91 + 46 * q^92 + 19 * q^93 + 72 * q^94 + 38 * q^95 + 95 * q^96 + 6 * q^97 - 299 * q^98 - 334 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{7}\right)$

Coefficient data

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

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

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

$2$	0.251865	−	0.315829i	0.178095	−	0.223325i	−0.684769	−	0.728760i	$-0.740097\pi$
$2$	0.251865	−	0.315829i	0.178095	−	0.223325i	0.862864	+	0.505436i	$0.168668\pi$
$3$	−0.214027	−	0.103070i	−0.123568	−	0.0595074i	0.371078	−	0.928602i	$-0.378988\pi$
$3$	−0.214027	−	0.103070i	−0.123568	−	0.0595074i	−0.494647	+	0.869094i	$0.664702\pi$
$4$	0.408730	+	1.79076i	0.204365	+	0.895382i
$5$	0.747465	+	0.359960i	0.334276	+	0.160979i	0.593491	−	0.804841i	$-0.297749\pi$
$5$	0.747465	+	0.359960i	0.334276	+	0.160979i	−0.259214	+	0.965820i	$0.583464\pi$
$6$	−0.0864582	+	0.0416361i	−0.0352964	+	0.0169979i
$7$	1.94492	+	1.79368i	0.735109	+	0.677949i
$7$	1.94492	+	1.79368i	0.735109	+	0.677949i
$8$	1.39643	+	0.672485i	0.493712	+	0.237759i
$9$	−1.83529	−	2.30138i	−0.611762	−	0.767125i
$10$	0.301946	−	0.145409i	0.0954836	−	0.0459825i
$11$	2.82531	−	3.54283i	0.851864	−	1.06820i	−0.145029	−	0.989427i	$-0.546327\pi$
$11$	2.82531	−	3.54283i	0.851864	−	1.06820i	0.996892	−	0.0787759i	$-0.0251011\pi$
$12$	0.0970945	−	0.425399i	0.0280288	−	0.122802i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$14$	1.05635	−	0.162494i	0.282322	−	0.0434283i
$15$	−0.122876	−	0.154082i	−0.0317265	−	0.0397838i
$16$	−2.74573	+	1.32227i	−0.686432	+	0.330568i
$17$	−0.845215	+	3.70313i	−0.204995	+	0.898141i	0.762846	+	0.646580i	$0.223801\pi$
$17$	−0.845215	+	3.70313i	−0.204995	+	0.898141i	−0.967841	+	0.251561i	$0.919056\pi$
$18$	−1.18908			−0.280270
$19$	8.18558			1.87790			0.938951	−	0.344052i	$-0.111800\pi$
$19$	8.18558			1.87790			0.938951	+	0.344052i	$0.111800\pi$
$20$	−0.339092	+	1.48566i	−0.0758233	+	0.332203i
$21$	−0.231389	−	0.584358i	−0.0504932	−	0.127517i
$22$	−0.407330	−	1.78463i	−0.0868430	−	0.380484i
$23$	1.45722	+	6.38449i	0.303851	+	1.33126i	0.864261	+	0.503043i	$0.167786\pi$
$23$	1.45722	+	6.38449i	0.303851	+	1.33126i	−0.560410	+	0.828215i	$0.689356\pi$
$24$	−0.229560	−	0.287859i	−0.0468588	−	0.0587591i
$25$	−2.68832	−	3.37104i	−0.537663	−	0.674209i
$26$	0.0898895	+	0.393832i	0.0176288	+	0.0772368i
$27$	0.314178	+	1.37651i	0.0604636	+	0.264909i
$28$	−2.41712	+	4.21602i	−0.456793	+	0.796752i
$29$	−0.571622	+	2.50444i	−0.106147	+	0.465062i	0.893718	+	0.448630i	$0.148088\pi$
$29$	−0.571622	+	2.50444i	−0.106147	+	0.465062i	−0.999865	+	0.0164323i	$0.994769\pi$
$30$	−0.0796118			−0.0145351
$31$	−4.58955			−0.824308			−0.412154	−	0.911114i	$-0.635223\pi$
$31$	−4.58955			−0.824308			−0.412154	+	0.911114i	$0.635223\pi$
$32$	−0.963720	+	4.22233i	−0.170363	+	0.746410i
$33$	−0.969851	+	0.467055i	−0.168829	+	0.0813039i
$34$	0.956675	+	1.19963i	0.164068	+	0.205735i
$35$	0.808101	+	2.04081i	0.136594	+	0.344959i
$36$	3.37108	−	4.22720i	0.561847	−	0.704534i
$37$	−0.425107	+	1.86252i	−0.0698872	+	0.306196i	−0.997776	−	0.0666623i	$-0.978765\pi$
$37$	−0.425107	+	1.86252i	−0.0698872	+	0.306196i	0.927888	+	0.372858i	$0.121622\pi$
$38$	2.06166	−	2.58524i	0.334446	−	0.419381i
$39$	0.214027	−	0.103070i	0.0342717	−	0.0165044i
$40$	0.801714	+	1.00532i	0.126762	+	0.158955i
$41$	4.89287	+	2.35628i	0.764138	+	0.367989i	0.775008	−	0.631952i	$-0.217746\pi$
$41$	4.89287	+	2.35628i	0.764138	+	0.367989i	−0.0108700	+	0.999941i	$0.503460\pi$
$42$	−0.242836	−	0.0741001i	−0.0374704	−	0.0114339i
$43$	−6.40742	+	3.08565i	−0.977123	+	0.470558i	−0.853115	−	0.521724i	$-0.825289\pi$
$43$	−6.40742	+	3.08565i	−0.977123	+	0.470558i	−0.124008	+	0.992281i	$0.539575\pi$
$44$	7.49916	+	3.61141i	1.13054	+	0.544440i
$45$	−0.543408	−	2.38083i	−0.0810065	−	0.354913i
$46$	2.38343	+	1.14780i	0.351417	+	0.169234i
$47$	5.47093	−	6.86032i	0.798016	−	1.00068i	−0.201758	−	0.979435i	$-0.564665\pi$
$47$	5.47093	−	6.86032i	0.798016	−	1.00068i	0.999774	−	0.0212456i	$-0.00676318\pi$
$48$	0.723945			0.104492
$49$	0.565391	+	6.97713i	0.0807701	+	0.996733i
$50$	−1.74176			−0.246323
$51$	0.562580	−	0.705452i	0.0787769	−	0.0987831i
$52$	−1.65491	−	0.796965i	−0.229495	−	0.110519i
$53$	−0.734570	−	3.21836i	−0.100901	−	0.442076i	−0.999991	−	0.00431163i	$-0.998628\pi$
$53$	−0.734570	−	3.21836i	−0.100901	−	0.442076i	0.899090	−	0.437764i	$-0.144230\pi$
$54$	0.513870	+	0.247467i	0.0699289	+	0.0336760i
$55$	3.38710	−	1.63114i	0.456716	−	0.219943i
$56$	1.50971	+	3.81268i	0.201744	+	0.509491i
$57$	−1.75193	−	0.843686i	−0.232049	−	0.111749i
$58$	0.647002	+	0.811314i	0.0849555	+	0.106531i
$59$	11.5053	−	5.54068i	1.49787	−	0.721335i	0.507741	−	0.861510i	$-0.330481\pi$
$59$	11.5053	−	5.54068i	1.49787	−	0.721335i	0.990127	+	0.140174i	$0.0447663\pi$
$60$	0.225701	−	0.283020i	0.0291379	−	0.0365378i
$61$	2.96509	−	12.9909i	0.379641	−	1.66332i	−0.318931	−	0.947778i	$-0.603324\pi$
$61$	2.96509	−	12.9909i	0.379641	−	1.66332i	0.698572	−	0.715540i	$-0.253819\pi$
$62$	−1.15595	+	1.44951i	−0.146805	+	0.184088i
$63$	0.558467	−	7.76790i	0.0703602	−	0.978664i
$64$	−2.70940	−	3.39748i	−0.338675	−	0.424685i
$65$	−0.747465	+	0.359960i	−0.0927116	+	0.0446475i
$66$	−0.0967619	+	0.423941i	−0.0119106	+	0.0521836i
$67$	−7.01503			−0.857022			−0.428511	−	0.903537i	$-0.640962\pi$
$67$	−7.01503			−0.857022			−0.428511	+	0.903537i	$0.640962\pi$
$68$	−6.97690			−0.846073
$69$	0.346165	−	1.51665i	0.0416733	−	0.182583i
$70$	0.848078	+	0.258787i	0.101365	+	0.0309309i
$71$	0.773429	+	3.38862i	0.0917892	+	0.402155i	0.999861	−	0.0166593i	$-0.00530308\pi$
$71$	0.773429	+	3.38862i	0.0917892	+	0.402155i	−0.908072	+	0.418814i	$0.862446\pi$
$72$	−1.01521	−	4.44791i	−0.119643	−	0.524191i
$73$	−5.38171	−	6.74845i	−0.629882	−	0.789847i	0.359815	−	0.933024i	$-0.382840\pi$
$73$	−5.38171	−	6.74845i	−0.629882	−	0.789847i	−0.989697	+	0.143177i	$0.954268\pi$
$74$	0.481166	+	0.603363i	0.0559344	+	0.0701396i
$75$	0.227919	+	0.998577i	0.0263178	+	0.115306i
$76$	3.34569	+	14.6584i	0.383777	+	1.68144i
$77$	11.8497	−	1.82278i	1.35040	−	0.207726i
$78$	0.0213534	−	0.0935554i	0.00241780	−	0.0105931i
$79$	−8.55020			−0.961972			−0.480986	−	0.876728i	$-0.659721\pi$
$79$	−8.55020			−0.961972			−0.480986	+	0.876728i	$0.659721\pi$
$80$	−2.52830			−0.282672
$81$	−1.89038	+	8.28231i	−0.210043	+	0.920257i
$82$	1.97652	−	0.951844i	0.218270	−	0.105114i
$83$	−0.443517	−	0.556153i	−0.0486824	−	0.0610458i	0.756894	−	0.653537i	$-0.226716\pi$
$83$	−0.443517	−	0.556153i	−0.0486824	−	0.0610458i	−0.805577	+	0.592492i	$0.798144\pi$
$84$	0.951872	−	0.653208i	0.103858	−	0.0712708i
$85$	−1.96475	+	2.46372i	−0.213107	+	0.267228i
$86$	−0.639268	+	2.80082i	−0.0689340	+	0.302020i
$87$	0.380474	−	0.477099i	0.0407911	−	0.0511504i
$88$	6.32785	−	3.04733i	0.674551	−	0.324847i
$89$	−3.15074	−	3.95091i	−0.333978	−	0.418795i	0.586279	−	0.810109i	$-0.300592\pi$
$89$	−3.15074	−	3.95091i	−0.333978	−	0.418795i	−0.920257	+	0.391314i	$0.872021\pi$
$90$	−0.888798	−	0.428023i	−0.0936876	−	0.0451176i
$91$	−2.61499	+	0.402252i	−0.274126	+	0.0421675i
$92$	−10.8375	+	5.21907i	−1.12989	+	0.544125i
$93$	0.982286	+	0.473044i	0.101858	+	0.0490524i
$94$	−0.788752	−	3.45575i	−0.0813536	−	0.356433i
$95$	6.11843	+	2.94648i	0.627738	+	0.302303i
$96$	0.641457	−	0.804361i	0.0654684	−	0.0820948i
$97$	−0.306464			−0.0311167			−0.0155583	−	0.999879i	$-0.504953\pi$
$97$	−0.306464			−0.0311167			−0.0155583	+	0.999879i	$0.504953\pi$
$98$	2.34598	+	1.57873i	0.236980	+	0.159476i
$99$	−13.3386			−1.34058
$100$	4.93794	−	6.19199i	0.493794	−	0.619199i
$101$	−6.78189	−	3.26599i	−0.674824	−	0.324978i	0.0648971	−	0.997892i	$-0.479328\pi$
$101$	−6.78189	−	3.26599i	−0.674824	−	0.324978i	−0.739721	+	0.672914i	$0.765042\pi$
$102$	−0.0811080	−	0.355357i	−0.00803089	−	0.0351856i
$103$	1.42831	+	0.687836i	0.140735	+	0.0677745i	0.502926	−	0.864329i	$-0.332257\pi$
$103$	1.42831	+	0.687836i	0.140735	+	0.0677745i	−0.362191	+	0.932104i	$0.617971\pi$
$104$	−1.39643	+	0.672485i	−0.136931	+	0.0659426i
$105$	0.0373906	−	0.520078i	0.00364894	−	0.0507544i
$106$	−1.20146	−	0.578594i	−0.116696	−	0.0561980i
$107$	−9.42550	−	11.8192i	−0.911198	−	1.14261i	−0.989334	−	0.145663i	$-0.953468\pi$
$107$	−9.42550	−	11.8192i	−0.911198	−	1.14261i	0.0781363	−	0.996943i	$-0.475103\pi$
$108$	−2.33658	+	1.12524i	−0.224838	+	0.108276i
$109$	8.77489	−	11.0034i	0.840482	−	1.05393i	−0.157313	−	0.987549i	$-0.550283\pi$
$109$	8.77489	−	11.0034i	0.840482	−	1.05393i	0.997794	−	0.0663818i	$-0.0211455\pi$
$110$	0.337930	−	1.48057i	0.0322204	−	0.141167i
$111$	0.282953	−	0.354812i	0.0268567	−	0.0336773i
$112$	−7.71195	−	2.35326i	−0.728710	−	0.222362i
$113$	12.0936	+	15.1649i	1.13767	+	1.42659i	0.888941	+	0.458021i	$0.151442\pi$
$113$	12.0936	+	15.1649i	1.13767	+	1.42659i	0.248729	+	0.968573i	$0.419987\pi$
$114$	−0.707710	+	0.340815i	−0.0662832	+	0.0319203i
$115$	−1.20894	+	5.29672i	−0.112734	+	0.493922i
$116$	−4.71849			−0.438101
$117$	2.94357			0.272133
$118$	1.14789	−	5.02922i	0.105672	−	0.462977i
$119$	−8.28612	+	5.68623i	−0.759588	+	0.521255i
$120$	−0.0679703	−	0.297797i	−0.00620481	−	0.0271850i
$121$	−2.12152	−	9.29499i	−0.192866	−	0.844999i
$122$	−3.35610	−	4.20842i	−0.303847	−	0.381012i
$123$	−0.804343	−	1.00861i	−0.0725252	−	0.0909437i
$124$	−1.87589	−	8.21880i	−0.168460	−	0.738070i
$125$	−1.71902	−	7.53154i	−0.153754	−	0.673641i
$126$	−2.31267	−	2.13284i	−0.206029	−	0.190009i
$127$	3.23769	−	14.1853i	0.287299	−	1.25874i	−0.600917	−	0.799311i	$-0.705198\pi$
$127$	3.23769	−	14.1853i	0.287299	−	1.25874i	0.888216	−	0.459426i	$-0.151945\pi$
$128$	−10.4173			−0.920764
$129$	1.68940			0.148743
$130$	−0.0745745	+	0.326732i	−0.00654061	+	0.0286563i
$131$	−5.57086	+	2.68278i	−0.486728	+	0.234396i	−0.661120	−	0.750281i	$-0.729918\pi$
$131$	−5.57086	+	2.68278i	−0.486728	+	0.234396i	0.174392	+	0.984676i	$0.444204\pi$
$132$	−1.23279	−	1.54587i	−0.107301	−	0.134551i
$133$	15.9203	+	14.6824i	1.38046	+	1.27312i
$134$	−1.76684	+	2.21555i	−0.152632	+	0.191394i
$135$	−0.260650	+	1.14198i	−0.0224331	+	0.0982860i
$136$	−3.67058	+	4.60277i	−0.314750	+	0.394684i
$137$	−8.55293	+	4.11887i	−0.730726	+	0.351899i	−0.761970	−	0.647613i	$-0.775767\pi$
$137$	−8.55293	+	4.11887i	−0.730726	+	0.351899i	0.0312438	+	0.999512i	$0.490053\pi$
$138$	−0.391814	−	0.491319i	−0.0333534	−	0.0418238i
$139$	−8.84665	−	4.26032i	−0.750363	−	0.361356i	0.0192934	−	0.999814i	$-0.493858\pi$
$139$	−8.84665	−	4.26032i	−0.750363	−	0.361356i	−0.769657	+	0.638458i	$0.779573\pi$
$140$	−3.32431	+	2.28126i	−0.280955	+	0.192801i
$141$	−1.87802	+	0.904405i	−0.158157	+	0.0761646i
$142$	1.26502	+	0.609202i	0.106158	+	0.0511231i
$143$	1.00834	+	4.41784i	0.0843218	+	0.369438i
$144$	8.08224	+	3.89220i	0.673520	+	0.324350i
$145$	−1.32876	+	1.66622i	−0.110348	+	0.138372i
$146$	−3.48682			−0.288571
$147$	0.598123	−	1.55157i	0.0493323	−	0.127971i
$148$	−3.50908			−0.288445
$149$	5.40960	−	6.78342i	0.443172	−	0.555720i	−0.509204	−	0.860646i	$-0.670060\pi$
$149$	5.40960	−	6.78342i	0.443172	−	0.555720i	0.952376	+	0.304926i	$0.0986317\pi$
$150$	0.372784	+	0.179523i	0.0304377	+	0.0146580i
$151$	−1.38414	−	6.06431i	−0.112640	−	0.493507i	−0.999504	−	0.0314776i	$-0.989979\pi$
$151$	−1.38414	−	6.06431i	−0.112640	−	0.493507i	0.886865	−	0.462029i	$-0.152878\pi$
$152$	11.4306	+	5.50468i	0.927143	+	0.446489i
$153$	10.0735	−	4.85114i	0.814395	−	0.392192i
$154$	2.40884	−	4.20157i	0.194110	−	0.338572i
$155$	−3.43053	−	1.65206i	−0.275547	−	0.132696i
$156$	0.272053	+	0.341143i	0.0217817	+	0.0273133i
$157$	15.3031	−	7.36958i	1.22132	−	0.588157i	0.291641	−	0.956528i	$-0.405799\pi$
$157$	15.3031	−	7.36958i	1.22132	−	0.588157i	0.929679	+	0.368371i	$0.120084\pi$
$158$	−2.15349	+	2.70040i	−0.171323	+	0.214832i
$159$	−0.174498	+	0.764527i	−0.0138386	+	0.0606309i
$160$	−2.24022	+	2.80914i	−0.177105	+	0.222082i
$161$	−8.61760	+	15.0311i	−0.679162	+	1.18462i
$162$	2.13967	+	2.68306i	0.168108	+	0.210801i
$163$	−13.8012	+	6.64633i	−1.08100	+	0.520581i	−0.887635	−	0.460547i	$-0.847653\pi$
$163$	−13.8012	+	6.64633i	−1.08100	+	0.520581i	−0.193362	+	0.981128i	$0.561939\pi$
$164$	−2.21968	+	9.72506i	−0.173328	+	0.759399i
$165$	−0.893050			−0.0695239
$166$	−0.287356			−0.0223031
$167$	−2.26233	+	9.91194i	−0.175065	+	0.767009i	0.808798	+	0.588086i	$0.200118\pi$
$167$	−2.26233	+	9.91194i	−0.175065	+	0.767009i	−0.983863	+	0.178923i	$0.942739\pi$
$168$	0.0698538	−	0.971621i	0.00538934	−	0.0749622i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	0.283261	+	1.24105i	0.0217251	+	0.0951840i
$171$	−15.0229	−	18.8381i	−1.14883	−	1.44058i
$172$	−8.14458	−	10.2130i	−0.621019	−	0.778733i
$173$	0.324715	+	1.42267i	0.0246877	+	0.108164i	0.985771	−	0.168096i	$-0.0537620\pi$
$173$	0.324715	+	1.42267i	0.0246877	+	0.108164i	−0.961083	+	0.276260i	$0.910905\pi$
$174$	−0.0548536	−	0.240329i	−0.00415844	−	0.0182193i
$175$	0.818039	−	11.3784i	0.0618379	−	0.860125i
$176$	−3.07295	+	13.4635i	−0.231632	+	1.01485i
$177$	−3.03353			−0.228014
$178$	−2.04137			−0.153007
$179$	3.48919	−	15.2871i	0.260794	−	1.14261i	−0.659599	−	0.751618i	$-0.729274\pi$
$179$	3.48919	−	15.2871i	0.260794	−	1.14261i	0.920393	−	0.390995i	$-0.127869\pi$
$180$	4.04139	−	1.94623i	0.301227	−	0.145063i
$181$	14.4955	+	18.1768i	1.07744	+	1.35107i	0.932310	+	0.361661i	$0.117790\pi$
$181$	14.4955	+	18.1768i	1.07744	+	1.35107i	0.145135	+	0.989412i	$0.453638\pi$
$182$	−0.531583	+	0.927203i	−0.0394035	+	0.0687289i
$183$	−1.97358	+	2.47479i	−0.145891	+	0.182942i
$184$	−2.25857	+	9.89545i	−0.166504	+	0.729502i
$185$	−0.988184	+	1.23914i	−0.0726527	+	0.0911036i
$186$	0.396804	−	0.191091i	0.0290951	−	0.0140115i
$187$	10.7316	+	13.4570i	0.784770	+	0.984070i
$188$	14.5213	+	6.99311i	1.05908	+	0.510025i
$189$	−1.85797	+	3.24072i	−0.135147	+	0.235728i
$190$	2.47160	−	1.19026i	0.179309	−	0.0863506i
$191$	−11.8045	−	5.68475i	−0.854144	−	0.411334i	−0.0450298	−	0.998986i	$-0.514338\pi$
$191$	−11.8045	−	5.68475i	−0.854144	−	0.411334i	−0.809114	+	0.587652i	$0.800053\pi$
$192$	0.229706	+	1.00641i	0.0165776	+	0.0726312i
$193$	−20.1505	−	9.70395i	−1.45046	−	0.698505i	−0.467786	−	0.883842i	$-0.654948\pi$
$193$	−20.1505	−	9.70395i	−1.45046	−	0.698505i	−0.982675	+	0.185336i	$0.940663\pi$
$194$	−0.0771875	+	0.0967900i	−0.00554174	+	0.00694912i
$195$	0.197078			0.0141131
$196$	−12.2633	+	3.86424i	−0.875950	+	0.276017i
$197$	2.01402			0.143493			0.0717466	−	0.997423i	$-0.477143\pi$
$197$	2.01402			0.143493			0.0717466	+	0.997423i	$0.477143\pi$
$198$	−3.35953	+	4.21272i	−0.238752	+	0.299385i
$199$	−15.6186	−	7.52153i	−1.10717	−	0.533187i	−0.211267	−	0.977428i	$-0.567759\pi$
$199$	−15.6186	−	7.52153i	−1.10717	−	0.533187i	−0.895907	+	0.444241i	$0.853473\pi$
$200$	−1.48707	−	6.51528i	−0.105152	−	0.460700i
$201$	1.50140	+	0.723037i	0.105901	+	0.0509991i
$202$	−2.73961	+	1.31933i	−0.192759	+	0.0928276i
$203$	−5.60393	+	3.84561i	−0.393319	+	0.269909i
$204$	1.49324	+	0.719107i	0.104548	+	0.0503476i
$205$	2.80908	+	3.52248i	0.196195	+	0.246020i
$206$	0.576978	−	0.277858i	0.0402000	−	0.0193593i
$207$	12.0187	−	15.0710i	0.835357	−	1.04750i
$208$	0.678139	−	2.97112i	0.0470204	−	0.206010i
$209$	23.1268	−	29.0001i	1.59972	−	2.00598i
$210$	−0.154838	−	0.142798i	−0.0106848	−	0.00985402i
$211$	−8.61399	−	10.8016i	−0.593012	−	0.743613i	0.391259	−	0.920281i	$-0.372040\pi$
$211$	−8.61399	−	10.8016i	−0.593012	−	0.743613i	−0.984271	+	0.176667i	$0.943468\pi$
$212$	5.46308	−	2.63088i	0.375206	−	0.180690i
$213$	0.183729	−	0.804971i	0.0125889	−	0.0551557i
$214$	−6.10680			−0.417452
$215$	−5.90003			−0.402379
$216$	−0.486951	+	2.13347i	−0.0331328	+	0.145164i
$217$	−8.92629	−	8.23221i	−0.605956	−	0.558839i
$218$	−1.26509	−	5.54272i	−0.0856827	−	0.375400i
$219$	0.456268	+	1.99904i	0.0308317	+	0.135083i
$220$	4.30540	+	5.39880i	0.290270	+	0.363987i
$221$	−2.36824	−	2.96968i	−0.159305	−	0.199762i
$222$	−0.0407938	−	0.178729i	−0.00273790	−	0.0119955i
$223$	−0.229747	−	1.00659i	−0.0153850	−	0.0674059i	0.966653	−	0.256091i	$-0.0824346\pi$
$223$	−0.229747	−	1.00659i	−0.0153850	−	0.0674059i	−0.982038	+	0.188685i	$0.939578\pi$
$224$	−9.44789	+	6.48347i	−0.631264	+	0.433195i
$225$	−2.82420	+	12.3737i	−0.188280	+	0.824910i
$226$	7.83546			0.521207
$227$	21.9580			1.45740			0.728701	−	0.684832i	$-0.240124\pi$
$227$	21.9580			1.45740			0.728701	+	0.684832i	$0.240124\pi$
$228$	0.794775	−	3.48214i	0.0526352	−	0.230610i
$229$	2.87678	−	1.38538i	0.190103	−	0.0915486i	−0.336411	−	0.941715i	$-0.609213\pi$
$229$	2.87678	−	1.38538i	0.190103	−	0.0915486i	0.526514	+	0.850167i	$0.323499\pi$
$230$	1.36837	+	1.71588i	0.0902274	+	0.113142i
$231$	−2.72403	−	0.831223i	−0.179228	−	0.0546905i
$232$	−2.48243	+	3.11286i	−0.162979	+	0.204370i
$233$	−2.27516	+	9.96811i	−0.149050	+	0.653033i	0.844100	+	0.536186i	$0.180136\pi$
$233$	−2.27516	+	9.96811i	−0.149050	+	0.653033i	−0.993150	+	0.116846i	$0.962722\pi$
$234$	0.741382	−	0.929663i	0.0484656	−	0.0607740i
$235$	6.55877	−	3.15854i	0.427847	−	0.206040i
$236$	14.6246	+	18.3387i	0.951982	+	1.19375i
$237$	1.82997	+	0.881267i	0.118869	+	0.0572444i
$238$	−0.291110	+	4.04915i	−0.0188699	+	0.262468i
$239$	6.50361	−	3.13198i	0.420684	−	0.202591i	−0.211552	−	0.977367i	$-0.567852\pi$
$239$	6.50361	−	3.13198i	0.420684	−	0.202591i	0.632236	+	0.774776i	$0.282137\pi$
$240$	0.541123	+	0.260591i	0.0349294	+	0.0168211i
$241$	0.940177	+	4.11918i	0.0605621	+	0.265340i	0.996140	−	0.0877810i	$-0.0279776\pi$
$241$	0.940177	+	4.11918i	0.0605621	+	0.265340i	−0.935578	+	0.353121i	$0.885120\pi$
$242$	−3.46996	−	1.67105i	−0.223058	−	0.107419i
$243$	3.89917	−	4.88941i	0.250132	−	0.313656i
$244$	24.4756			1.56689
$245$	−2.08888	+	5.41868i	−0.133454	+	0.346187i
$246$	−0.521135			−0.0332263
$247$	−5.10363	+	6.39974i	−0.324736	+	0.407206i
$248$	−6.40899	−	3.08641i	−0.406971	−	0.195987i
$249$	0.0376019	+	0.164745i	0.00238293	+	0.0104403i
$250$	−2.81164	−	1.35401i	−0.177823	−	0.0856353i
$251$	4.70201	−	2.26437i	0.296788	−	0.142926i	−0.279564	−	0.960127i	$-0.590190\pi$
$251$	4.70201	−	2.26437i	0.296788	−	0.142926i	0.576352	+	0.817201i	$0.304476\pi$
$252$	14.1387	−	2.17489i	0.890657	−	0.137005i
$253$	26.7363	+	12.8755i	1.68089	+	0.809476i
$254$	−3.66465	−	4.59532i	−0.229940	−	0.288336i
$255$	0.674443	−	0.324795i	0.0422353	−	0.0203394i
$256$	2.79505	−	3.50489i	0.174691	−	0.219055i
$257$	1.43036	−	6.26682i	0.0892235	−	0.390914i	−0.910522	−	0.413460i	$-0.864320\pi$
$257$	1.43036	−	6.26682i	0.0892235	−	0.390914i	0.999746	+	0.0225463i	$0.00717732\pi$
$258$	0.425500	−	0.533560i	0.0264905	−	0.0332180i
$259$	−4.16756	+	2.85993i	−0.258960	+	0.177707i
$260$	−0.950115	−	1.19141i	−0.0589236	−	0.0738879i
$261$	6.81274	−	3.28084i	0.421698	−	0.203079i
$262$	−0.555803	+	2.43513i	−0.0343377	+	0.150443i
$263$	11.1841			0.689643			0.344821	−	0.938668i	$-0.387939\pi$
$263$	11.1841			0.689643			0.344821	+	0.938668i	$0.387939\pi$
$264$	−1.66842			−0.102684
$265$	0.609416	−	2.67003i	0.0374361	−	0.164018i
$266$	8.64686	−	1.33010i	0.530173	−	0.0815540i
$267$	0.267124	+	1.17035i	0.0163477	+	0.0716240i
$268$	−2.86725	−	12.5623i	−0.175145	−	0.767362i
$269$	−6.37586	−	7.99507i	−0.388743	−	0.487468i	0.548497	−	0.836152i	$-0.315200\pi$
$269$	−6.37586	−	7.99507i	−0.388743	−	0.487468i	−0.937240	+	0.348684i	$0.886629\pi$
$270$	0.295022	+	0.369945i	0.0179544	+	0.0225142i
$271$	2.12248	+	9.29919i	0.128931	+	0.564886i	0.997584	+	0.0694646i	$0.0221291\pi$
$271$	2.12248	+	9.29919i	0.128931	+	0.564886i	−0.868653	+	0.495421i	$0.835014\pi$
$272$	−2.57582	−	11.2854i	−0.156182	−	0.684277i
$273$	0.601138	+	0.183434i	0.0363825	+	0.0111019i
$274$	−0.853324	+	3.73866i	−0.0515512	+	0.225861i
$275$	−19.5384			−1.17821
$276$	2.85744			0.171998
$277$	3.25357	−	14.2548i	0.195488	−	0.856488i	−0.778094	−	0.628148i	$-0.783813\pi$
$277$	3.25357	−	14.2548i	0.195488	−	0.856488i	0.973581	−	0.228340i	$-0.0733297\pi$
$278$	−3.57369	+	1.72100i	−0.214336	+	0.103219i
$279$	8.42314	+	10.5623i	0.504280	+	0.632347i
$280$	−0.243957	+	3.39328i	−0.0145792	+	0.202787i
$281$	−10.4035	+	13.0456i	−0.620623	+	0.778236i	−0.988432	−	0.151665i	$-0.951537\pi$
$281$	−10.4035	+	13.0456i	−0.620623	+	0.778236i	0.367809	+	0.929901i	$0.380108\pi$
$282$	−0.187369	+	0.820919i	−0.0111577	+	0.0488850i
$283$	1.88046	−	2.35803i	0.111782	−	0.140170i	−0.722793	−	0.691065i	$-0.757142\pi$
$283$	1.88046	−	2.35803i	0.111782	−	0.140170i	0.834575	+	0.550895i	$0.185713\pi$
$284$	−5.75208	+	2.77006i	−0.341323	+	0.164373i
$285$	−1.00581	−	1.26125i	−0.0595793	−	0.0747101i
$286$	1.64925	+	0.794235i	0.0975219	+	0.0469641i
$287$	5.28979	+	13.3590i	0.312246	+	0.788559i
$288$	11.4859	−	5.53131i	0.676812	−	0.325935i
$289$	2.31768	+	1.11614i	0.136334	+	0.0656551i
$290$	0.191570	+	0.839324i	0.0112494	+	0.0492868i
$291$	0.0655914	+	0.0315871i	0.00384504	+	0.00185167i
$292$	9.88522	−	12.3957i	0.578489	−	0.725402i
$293$	17.4952			1.02208			0.511040	−	0.859557i	$-0.329261\pi$
$293$	17.4952			1.02208			0.511040	+	0.859557i	$0.329261\pi$
$294$	−0.339383	−	0.579689i	−0.0197932	−	0.0338082i
$295$	10.5943			0.616822
$296$	−1.84615	+	2.31499i	−0.107305	+	0.134556i
$297$	5.76437	+	2.77598i	0.334483	+	0.161078i
$298$	−0.779911	−	3.41701i	−0.0451790	−	0.197942i
$299$	−5.90016	−	2.84137i	−0.341215	−	0.164320i
$300$	−1.69506	+	0.816297i	−0.0978642	+	0.0471289i
$301$	−17.9966	−	5.49156i	−1.03731	−	0.316529i
$302$	−2.26390	−	1.09024i	−0.130273	−	0.0627361i
$303$	1.11488	+	1.39802i	0.0640482	+	0.0803140i
$304$	−22.4754	+	10.8236i	−1.28905	+	0.620774i
$305$	6.89252	−	8.64294i	0.394664	−	0.494894i
$306$	1.00503	−	4.40333i	0.0574539	−	0.251722i
$307$	−14.7752	+	18.5275i	−0.843266	+	1.05742i	0.154322	+	0.988021i	$0.450681\pi$
$307$	−14.7752	+	18.5275i	−0.843266	+	1.05742i	−0.997589	+	0.0694020i	$0.977891\pi$
$308$	8.10751	+	20.4750i	0.461968	+	1.16667i
$309$	−0.234800	−	0.294430i	−0.0133573	−	0.0167496i
$310$	−1.38580	+	0.667364i	−0.0787079	+	0.0379037i
$311$	−1.36425	+	5.97715i	−0.0773592	+	0.338933i	−0.998766	−	0.0496669i	$-0.984184\pi$
$311$	−1.36425	+	5.97715i	−0.0773592	+	0.338933i	0.921407	+	0.388600i	$0.127041\pi$
$312$	0.368186			0.0208444
$313$	−2.43583			−0.137682			−0.0688408	−	0.997628i	$-0.521930\pi$
$313$	−2.43583			−0.137682			−0.0688408	+	0.997628i	$0.521930\pi$
$314$	1.52679	−	6.68930i	0.0861616	−	0.377499i
$315$	3.21357	−	5.60521i	0.181064	−	0.315818i
$316$	−3.49472	−	15.3114i	−0.196593	−	0.861332i
$317$	−1.23989	−	5.43233i	−0.0696393	−	0.305110i	0.928099	−	0.372335i	$-0.121443\pi$
$317$	−1.23989	−	5.43233i	−0.0696393	−	0.305110i	−0.997738	+	0.0672248i	$0.978586\pi$
$318$	0.197509	+	0.247669i	0.0110758	+	0.0138886i
$319$	7.25779	+	9.10098i	0.406358	+	0.509557i
$320$	−0.802223	−	3.51477i	−0.0448456	−	0.196482i
$321$	0.799105	+	3.50111i	0.0446017	+	0.195413i
$322$	2.57678	+	6.50749i	0.143598	+	0.362648i
$323$	−6.91858	+	30.3123i	−0.384960	+	1.68662i
$324$	−15.6043			−0.866907
$325$	4.31173			0.239171
$326$	−1.37695	+	6.03281i	−0.0762621	+	0.334126i
$327$	−3.01217	+	1.45059i	−0.166574	+	0.0802176i
$328$	5.24798	+	6.58076i	0.289771	+	0.363362i
$329$	22.9457	−	3.52963i	1.26504	−	0.194595i
$330$	−0.224928	+	0.282051i	−0.0123819	+	0.0155264i
$331$	4.93099	−	21.6041i	0.271032	−	1.18747i	−0.637766	−	0.770230i	$-0.720141\pi$
$331$	4.93099	−	21.6041i	0.271032	−	1.18747i	0.908798	−	0.417237i	$-0.137002\pi$
$332$	0.814660	−	1.02155i	0.0447103	−	0.0560649i
$333$	5.06654	−	2.43992i	0.277645	−	0.133707i
$334$	2.56067	+	3.21098i	0.140114	+	0.175697i
$335$	−5.24348	−	2.52513i	−0.286482	−	0.137963i
$336$	1.40801	+	1.29853i	0.0768133	+	0.0708406i
$337$	4.22277	−	2.03358i	0.230029	−	0.110776i	−0.315319	−	0.948986i	$-0.602112\pi$
$337$	4.22277	−	2.03358i	0.230029	−	0.110776i	0.545348	+	0.838209i	$0.316397\pi$
$338$	−0.363955	−	0.175272i	−0.0197966	−	0.00953352i
$339$	−1.02531	−	4.49218i	−0.0556872	−	0.243982i
$340$	−5.21498	−	2.51140i	−0.282822	−	0.136200i
$341$	−12.9669	+	16.2600i	−0.702198	+	0.880528i
$342$	−9.73334			−0.526319
$343$	−11.4151	+	14.5841i	−0.616359	+	0.787465i
$344$	−11.0226			−0.594297
$345$	0.804678	−	1.00903i	0.0433224	−	0.0543246i
$346$	0.531105	+	0.255767i	0.0285524	+	0.0137501i
$347$	6.71691	+	29.4287i	0.360583	+	1.57982i	0.751719	+	0.659483i	$0.229225\pi$
$347$	6.71691	+	29.4287i	0.360583	+	1.57982i	−0.391137	+	0.920333i	$0.627918\pi$
$348$	1.00988	+	0.486334i	0.0541354	+	0.0260702i
$349$	−15.0454	+	7.24547i	−0.805360	+	0.387841i	−0.790817	−	0.612053i	$-0.790344\pi$
$349$	−15.0454	+	7.24547i	−0.805360	+	0.387841i	−0.0145435	+	0.999894i	$0.504630\pi$
$350$	−3.38758	−	3.12418i	−0.181074	−	0.166994i
$351$	−1.27208	−	0.612602i	−0.0678987	−	0.0326983i
$352$	12.2362	+	15.3437i	0.652192	+	0.817822i
$353$	−15.4051	+	7.41870i	−0.819930	+	0.394857i	−0.796329	−	0.604864i	$-0.793227\pi$
$353$	−15.4051	+	7.41870i	−0.819930	+	0.394857i	−0.0236010	+	0.999721i	$0.507513\pi$
$354$	−0.764039	+	0.958075i	−0.0406082	+	0.0509211i
$355$	−0.641655	+	2.81127i	−0.0340555	+	0.149207i
$356$	5.78734	−	7.25709i	0.306728	−	0.384625i
$357$	2.35953	−	0.362955i	0.124879	−	0.0192096i
$358$	−3.94931	−	4.95227i	−0.208727	−	0.261736i
$359$	−0.704025	+	0.339041i	−0.0371570	+	0.0178939i	−0.452370	−	0.891830i	$-0.649421\pi$
$359$	−0.704025	+	0.339041i	−0.0371570	+	0.0178939i	0.415213	+	0.909724i	$0.363707\pi$
$360$	0.842239	−	3.69009i	0.0443899	−	0.194485i
$361$	48.0037			2.52651
$362$	9.39168			0.493616
$363$	−0.503971	+	2.20804i	−0.0264516	+	0.115892i
$364$	−1.78916	−	4.51842i	−0.0937777	−	0.236830i
$365$	−1.59347	−	6.98143i	−0.0834058	−	0.365425i
$366$	0.284534	+	1.24663i	0.0148729	+	0.0651622i
$367$	−12.7219	−	15.9527i	−0.664077	−	0.832726i	0.329704	−	0.944084i	$-0.393051\pi$
$367$	−12.7219	−	15.9527i	−0.664077	−	0.832726i	−0.993780	+	0.111359i	$0.964480\pi$
$368$	−12.4432	−	15.6032i	−0.648645	−	0.813375i
$369$	−3.55712	−	15.5848i	−0.185176	−	0.811311i
$370$	0.142468	+	0.624193i	0.00740656	+	0.0324503i
$371$	4.34405	−	7.57703i	0.225532	−	0.393380i
$372$	−0.445620	+	1.95239i	−0.0231043	+	0.101227i
$373$	0.520676			0.0269596			0.0134798	−	0.999909i	$-0.495709\pi$
$373$	0.520676			0.0269596			0.0134798	+	0.999909i	$0.495709\pi$
$374$	6.95300			0.359531
$375$	−0.408357	+	1.78913i	−0.0210875	+	0.0923902i
$376$	12.2532	−	5.90084i	0.631912	−	0.304313i
$377$	−1.60165	−	2.00840i	−0.0824891	−	0.103438i
$378$	0.555556	+	1.40302i	0.0285747	+	0.0721637i
$379$	−14.6907	+	18.4216i	−0.754613	+	0.946255i	−0.999730	−	0.0232387i	$-0.992602\pi$
$379$	−14.6907	+	18.4216i	−0.754613	+	0.946255i	0.245117	+	0.969494i	$0.421174\pi$
$380$	−2.77566	+	12.1610i	−0.142389	+	0.623845i
$381$	−2.15502	+	2.70231i	−0.110405	+	0.138444i
$382$	−4.76855	+	2.29641i	−0.243980	+	0.117495i
$383$	4.15256	+	5.20715i	0.212186	+	0.266073i	0.876523	−	0.481361i	$-0.159857\pi$
$383$	4.15256	+	5.20715i	0.212186	+	0.266073i	−0.664337	+	0.747434i	$0.731286\pi$
$384$	2.22957	+	1.07370i	0.113777	+	0.0547923i
$385$	9.51337	+	2.90296i	0.484846	+	0.147948i
$386$	−8.13997	+	3.92001i	−0.414314	+	0.199523i
$387$	18.8607	+	9.08283i	0.958743	+	0.461706i
$388$	−0.125261	−	0.548804i	−0.00635916	−	0.0278613i
$389$	23.8686	+	11.4945i	1.21019	+	0.582795i	0.926563	−	0.376140i	$-0.122749\pi$
$389$	23.8686	+	11.4945i	1.21019	+	0.582795i	0.283624	+	0.958935i	$0.408463\pi$
$390$	0.0496371	−	0.0622430i	0.00251347	−	0.00315180i
$391$	−24.8743			−1.25795
$392$	−3.90249	+	10.1233i	−0.197105	+	0.511303i
$393$	1.46883			0.0740924
$394$	0.507262	−	0.636086i	0.0255555	−	0.0320456i
$395$	−6.39097	−	3.07773i	−0.321565	−	0.154857i
$396$	−5.45190	−	23.8863i	−0.273968	−	1.20033i
$397$	21.4802	+	10.3443i	1.07806	+	0.519166i	0.886696	−	0.462353i	$-0.152995\pi$
$397$	21.4802	+	10.3443i	1.07806	+	0.519166i	0.191364	+	0.981519i	$0.438709\pi$
$398$	−6.30930	+	3.03840i	−0.316256	+	0.152301i
$399$	−1.89405	−	4.78331i	−0.0948212	−	0.239465i
$400$	11.8388	+	5.70128i	0.591941	+	0.285064i
$401$	−21.0048	−	26.3391i	−1.04893	−	1.31531i	−0.947250	−	0.320496i	$-0.896150\pi$
$401$	−21.0048	−	26.3391i	−1.04893	−	1.31531i	−0.101677	−	0.994817i	$-0.532421\pi$
$402$	0.606506	−	0.292078i	0.0302498	−	0.0145675i
$403$	2.86154	−	3.58826i	0.142543	−	0.178744i
$404$	3.07665	−	13.4797i	0.153069	−	0.670639i
$405$	−4.39430	+	5.51027i	−0.218354	+	0.273808i
$406$	−0.196879	+	2.73845i	−0.00977093	+	0.135907i
$407$	5.39751	+	6.76827i	0.267545	+	0.335491i
$408$	1.26001	−	0.606788i	0.0623797	−	0.0300405i
$409$	4.66660	−	20.4457i	0.230748	−	1.01097i	−0.718273	−	0.695762i	$-0.755067\pi$
$409$	4.66660	−	20.4457i	0.230748	−	1.01097i	0.949021	−	0.315213i	$-0.102076\pi$
$410$	1.82001			0.0898837
$411$	2.25509			0.111235
$412$	−0.647960	+	2.83890i	−0.0319227	+	0.139862i
$413$	32.3152	+	9.86080i	1.59012	+	0.485218i
$414$	−1.73276	−	7.59170i	−0.0851603	−	0.373112i
$415$	−0.131321	−	0.575354i	−0.00644628	−	0.0282430i
$416$	−2.70028	−	3.38605i	−0.132392	−	0.166015i
$417$	1.45431	+	1.82365i	0.0712178	+	0.0893043i
$418$	−3.33423	−	14.6082i	−0.163083	−	0.714512i
$419$	6.95503	+	30.4720i	0.339776	+	1.48865i	0.799540	+	0.600613i	$0.205077\pi$
$419$	6.95503	+	30.4720i	0.339776	+	1.48865i	−0.459764	+	0.888041i	$0.652066\pi$
$420$	0.946619	−	0.145614i	0.0461903	−	0.00710523i
$421$	−2.45639	+	10.7621i	−0.119717	+	0.524515i	0.879133	+	0.476576i	$0.158122\pi$
$421$	−2.45639	+	10.7621i	−0.119717	+	0.524515i	−0.998850	+	0.0479387i	$0.984735\pi$
$422$	−5.58102			−0.271680
$423$	−25.8289			−1.25584
$424$	1.13852	−	4.98820i	0.0552917	−	0.242249i
$425$	14.7556	−	7.10593i	0.715753	−	0.344688i
$426$	−0.207958	−	0.260771i	−0.0100756	−	0.0126344i
$427$	29.0685	−	19.9478i	1.40672	−	0.965342i
$428$	17.3129	−	21.7097i	0.836852	−	1.04938i
$429$	0.239533	−	1.04946i	0.0115648	−	0.0506686i
$430$	−1.48601	+	1.86340i	−0.0716618	+	0.0898611i
$431$	−9.01207	+	4.33998i	−0.434096	+	0.209050i	−0.638153	−	0.769909i	$-0.720301\pi$
$431$	−9.01207	+	4.33998i	−0.434096	+	0.209050i	0.204057	+	0.978959i	$0.434587\pi$
$432$	−2.68276	−	3.36408i	−0.129074	−	0.161854i
$433$	1.24791	+	0.600961i	0.0599706	+	0.0288803i	0.463629	−	0.886030i	$-0.346547\pi$
$433$	1.24791	+	0.600961i	0.0599706	+	0.0288803i	−0.403658	+	0.914910i	$0.632261\pi$
$434$	−4.84819	+	0.745773i	−0.232720	+	0.0357983i
$435$	0.456128	−	0.219659i	0.0218696	−	0.0105319i
$436$	23.2910	+	11.2163i	1.11544	+	0.537165i
$437$	11.9282	+	52.2608i	0.570602	+	2.49997i
$438$	0.746272	+	0.359386i	0.0356583	+	0.0171721i
$439$	−3.42688	+	4.29718i	−0.163556	+	0.205093i	−0.856855	−	0.515557i	$-0.827585\pi$
$439$	−3.42688	+	4.29718i	−0.163556	+	0.205093i	0.693299	+	0.720650i	$0.256156\pi$
$440$	5.82676			0.277780
$441$	15.0193	−	14.1062i	0.715207	−	0.671724i
$442$	−1.53439			−0.0729833
$443$	−24.0750	+	30.1891i	−1.14384	+	1.43433i	−0.260572	+	0.965454i	$0.583911\pi$
$443$	−24.0750	+	30.1891i	−1.14384	+	1.43433i	−0.883266	+	0.468873i	$0.844660\pi$
$444$	0.751036	+	0.361680i	0.0356426	+	0.0171646i
$445$	−0.932901	−	4.08731i	−0.0442237	−	0.193757i
$446$	−0.375774	−	0.180963i	−0.0177934	−	0.00856885i
$447$	−1.85696	+	0.894267i	−0.0878314	+	0.0422974i
$448$	0.824454	−	11.4676i	0.0389518	−	0.541794i
$449$	−8.27942	−	3.98716i	−0.390730	−	0.188166i	0.228196	−	0.973615i	$-0.426717\pi$
$449$	−8.27942	−	3.98716i	−0.390730	−	0.188166i	−0.618926	+	0.785450i	$0.712432\pi$
$450$	3.19663	+	4.00845i	0.150691	+	0.188960i
$451$	22.1718	−	10.6774i	1.04403	−	0.502778i
$452$	−22.2137	+	27.8551i	−1.04485	+	1.31020i
$453$	−0.328805	+	1.44059i	−0.0154486	+	0.0676847i
$454$	5.53045	−	6.93496i	0.259557	−	0.325474i
$455$	−2.09941	−	0.640624i	−0.0984219	−	0.0300329i
$456$	−1.87908	−	2.35630i	−0.0879962	−	0.110344i
$457$	23.6011	−	11.3657i	1.10401	−	0.531665i	0.209096	−	0.977895i	$-0.432948\pi$
$457$	23.6011	−	11.3657i	1.10401	−	0.531665i	0.894918	+	0.446230i	$0.147234\pi$
$458$	0.287016	−	1.25750i	0.0134114	−	0.0587590i
$459$	−5.36293			−0.250320
$460$	−9.97931			−0.465288
$461$	−3.32709	+	14.5769i	−0.154958	+	0.678915i	0.836443	+	0.548054i	$0.184631\pi$
$461$	−3.32709	+	14.5769i	−0.154958	+	0.678915i	−0.991401	+	0.130861i	$0.958226\pi$
$462$	−0.948611	+	0.650970i	−0.0441334	+	0.0302859i
$463$	6.13853	+	26.8946i	0.285282	+	1.24990i	0.890920	+	0.454160i	$0.150061\pi$
$463$	6.13853	+	26.8946i	0.285282	+	1.24990i	−0.605638	+	0.795740i	$0.707082\pi$
$464$	−1.74203	−	7.63234i	−0.0808718	−	0.354323i
$465$	0.563947	+	0.707168i	0.0261524	+	0.0327941i
$466$	2.57518	+	3.22918i	0.119293	+	0.149589i
$467$	4.11911	+	18.0470i	0.190610	+	0.835116i	0.976287	+	0.216480i	$0.0694575\pi$
$467$	4.11911	+	18.0470i	0.190610	+	0.835116i	−0.785677	+	0.618637i	$0.787685\pi$
$468$	1.20313	+	5.27124i	0.0556145	+	0.243663i
$469$	−13.6436	−	12.5827i	−0.630004	−	0.581017i
$470$	0.654367	−	2.86697i	0.0301837	−	0.132243i
$471$	−4.03485			−0.185916
$472$	19.7924			0.911021
$473$	−7.17103	+	31.4183i	−0.329724	+	1.44462i
$474$	0.739234	−	0.355997i	0.0339542	−	0.0163515i
$475$	−22.0054	−	27.5939i	−1.00968	−	1.26610i
$476$	−13.5695	−	12.5144i	−0.621956	−	0.573594i
$477$	−6.05851	+	7.59713i	−0.277400	+	0.347849i
$478$	0.648865	−	2.84286i	0.0296784	−	0.130029i
$479$	19.3808	−	24.3028i	0.885533	−	1.11042i	−0.107689	−	0.994185i	$-0.534345\pi$
$479$	19.3808	−	24.3028i	0.885533	−	1.11042i	0.993221	−	0.116238i	$-0.0370836\pi$
$480$	0.769004	−	0.370333i	0.0351001	−	0.0169033i
$481$	−1.19112	−	1.49362i	−0.0543106	−	0.0681033i
$482$	1.53775	+	0.740543i	0.0700428	+	0.0337308i
$483$	3.39365	−	2.32884i	0.154416	−	0.105966i
$484$	15.7780	−	7.59829i	0.717182	−	0.345377i
$485$	−0.229071	−	0.110315i	−0.0104016	−	0.00500913i
$486$	−0.562150	−	2.46294i	−0.0254996	−	0.111721i
$487$	−12.2638	−	5.90592i	−0.555725	−	0.267623i	0.134872	−	0.990863i	$-0.456938\pi$
$487$	−12.2638	−	5.90592i	−0.555725	−	0.267623i	−0.690597	+	0.723240i	$0.742652\pi$
$488$	12.8768	−	16.1469i	0.582903	−	0.730937i
$489$	3.63887			0.164555
$490$	1.18526	+	2.02450i	0.0535445	+	0.0914577i
$491$	−18.7484			−0.846101			−0.423051	−	0.906106i	$-0.639041\pi$
$491$	−18.7484			−0.846101			−0.423051	+	0.906106i	$0.639041\pi$
$492$	1.47743	−	1.85264i	0.0666077	−	0.0835234i
$493$	−8.79112	−	4.23358i	−0.395932	−	0.190671i
$494$	0.735798	+	3.22374i	0.0331051	+	0.145043i
$495$	−9.97016	−	4.80138i	−0.448125	−	0.215806i
$496$	12.6017	−	6.06864i	0.565831	−	0.272490i
$497$	−4.57385	+	7.97786i	−0.205165	+	0.357856i
$498$	0.0615018	+	0.0296177i	0.00275596	+	0.00132720i
$499$	−1.58964	−	1.99334i	−0.0711620	−	0.0892343i	0.744976	−	0.667091i	$-0.232461\pi$
$499$	−1.58964	−	1.99334i	−0.0711620	−	0.0892343i	−0.816138	+	0.577857i	$0.803889\pi$
$500$	12.7846	−	6.15673i	0.571744	−	0.275337i
$501$	1.50582	−	1.88824i	0.0672751	−	0.0843603i
$502$	0.469119	−	2.05534i	0.0209378	−	0.0917345i
$503$	10.8058	−	13.5500i	0.481807	−	0.604167i	−0.480211	−	0.877153i	$-0.659440\pi$
$503$	10.8058	−	13.5500i	0.481807	−	0.604167i	0.962018	+	0.272986i	$0.0880113\pi$
$504$	6.00366	−	10.4718i	0.267424	−	0.466450i
$505$	−3.89360	−	4.88242i	−0.173263	−	0.217265i
$506$	10.8004	−	5.20119i	0.480135	−	0.231221i
$507$	−0.0528602	+	0.231596i	−0.00234760	+	0.0102855i
$508$	26.7258			1.18576
$509$	−38.3997			−1.70204			−0.851019	−	0.525134i	$-0.824015\pi$
$509$	−38.3997			−1.70204			−0.851019	+	0.525134i	$0.824015\pi$
$510$	0.0672891	−	0.294813i	0.00297961	−	0.0130545i
$511$	1.63762	−	22.7783i	0.0724442	−	1.00765i
$512$	−5.03908	−	22.0777i	−0.222698	−	0.975704i
$513$	2.57173	+	11.2675i	0.113545	+	0.497472i
$514$	−1.61898	−	2.03014i	−0.0714103	−	0.0895457i
$515$	0.820015	+	1.02827i	0.0361342	+	0.0453108i
$516$	0.690507	+	3.02531i	0.0303979	+	0.133182i
$517$	−8.84788	−	38.7651i	−0.389129	−	1.70489i
$518$	−0.146416	+	2.03655i	−0.00643315	+	0.0894809i
$519$	0.0771367	−	0.337958i	0.00338592	−	0.0148347i
$520$	−1.28585			−0.0563882
$521$	−12.7647			−0.559233			−0.279617	−	0.960112i	$-0.590207\pi$
$521$	−12.7647			−0.559233			−0.279617	+	0.960112i	$0.590207\pi$
$522$	0.679706	−	2.97799i	0.0297499	−	0.130343i
$523$	−38.9269	+	18.7462i	−1.70215	+	0.819714i	−0.708696	+	0.705514i	$0.750716\pi$
$523$	−38.9269	+	18.7462i	−1.70215	+	0.819714i	−0.993458	+	0.114199i	$0.963570\pi$
$524$	−7.08121	−	8.87955i	−0.309344	−	0.387905i
$525$	−1.34785	+	2.35096i	−0.0588250	+	0.102604i
$526$	2.81689	−	3.53227i	0.122822	−	0.154014i
$527$	3.87916	−	16.9957i	0.168979	−	0.740345i
$528$	2.04537	−	2.56481i	0.0890133	−	0.111619i
$529$	−17.9160	+	8.62788i	−0.778955	+	0.375125i
$530$	−0.689780	−	0.864957i	−0.0299621	−	0.0375713i
$531$	−33.8668	−	16.3094i	−1.46969	−	0.707767i
$532$	−19.7855	+	34.5105i	−0.857811	+	1.49622i
$533$	−4.89287	+	2.35628i	−0.211934	+	0.102062i
$534$	0.436908	+	0.210404i	0.0189069	+	0.00910506i
$535$	−2.79079	−	12.2272i	−0.120656	−	0.528630i
$536$	−9.79599	−	4.71750i	−0.423122	−	0.203765i
$537$	−2.32242	+	2.91222i	−0.100220	+	0.125672i
$538$	−4.13093			−0.178097
$539$	26.3162	+	17.7095i	1.13352	+	0.762802i
$540$	−2.15155			−0.0925881
$541$	−13.4106	+	16.8164i	−0.576568	+	0.722994i	−0.981523	−	0.191343i	$-0.938716\pi$
$541$	−13.4106	+	16.8164i	−0.576568	+	0.722994i	0.404955	+	0.914337i	$0.367287\pi$
$542$	3.47153	+	1.67180i	0.149115	+	0.0718100i
$543$	−1.22895	−	5.38438i	−0.0527392	−	0.231066i
$544$	−14.8213	−	7.13756i	−0.635458	−	0.306021i
$545$	10.5197	−	5.06601i	0.450614	−	0.217004i
$546$	0.209339	−	0.143656i	0.00895890	−	0.00614791i
$547$	−9.49837	−	4.57417i	−0.406121	−	0.195577i	0.219660	−	0.975577i	$-0.429505\pi$
$547$	−9.49837	−	4.57417i	−0.406121	−	0.195577i	−0.625781	+	0.779999i	$0.715220\pi$
$548$	−10.8718	−	13.6328i	−0.464419	−	0.582363i
$549$	−35.3388	+	17.0183i	−1.50822	+	0.726322i
$550$	−4.92103	+	6.17077i	−0.209833	+	0.263123i
$551$	−4.67905	+	20.5003i	−0.199334	+	0.873341i
$552$	1.50332	−	1.88510i	0.0639854	−	0.0802352i
$553$	−16.6294	−	15.3364i	−0.707154	−	0.652168i
$554$	−3.68262	−	4.61785i	−0.156459	−	0.196194i
$555$	0.339216	−	0.163358i	0.0143989	−	0.00693415i
$556$	4.01334	−	17.5836i	0.170203	−	0.745710i
$557$	−3.67833			−0.155856			−0.0779278	−	0.996959i	$-0.524830\pi$
$557$	−3.67833			−0.155856			−0.0779278	+	0.996959i	$0.524830\pi$
$558$	5.45736			0.231029
$559$	1.58250	−	6.93340i	0.0669327	−	0.293252i
$560$	−4.91733	−	4.53497i	−0.207795	−	0.191638i
$561$	−0.909835	−	3.98625i	−0.0384133	−	0.168299i
$562$	1.49989	+	6.57147i	0.0632692	+	0.277201i
$563$	17.1066	+	21.4510i	0.720959	+	0.904053i	0.998392	−	0.0566915i	$-0.0180552\pi$
$563$	17.1066	+	21.4510i	0.720959	+	0.904053i	−0.277433	+	0.960745i	$0.589484\pi$
$564$	−2.38718	−	2.99342i	−0.100518	−	0.126046i
$565$	3.58078	+	15.6884i	0.150645	+	0.660018i
$566$	−0.271109	−	1.18781i	−0.0113956	−	0.0499273i
$567$	−18.5325	+	12.7176i	−0.778292	+	0.534091i
$568$	−1.19875	+	5.25208i	−0.0502986	+	0.220373i
$569$	−19.1886			−0.804428			−0.402214	−	0.915546i	$-0.631759\pi$
$569$	−19.1886			−0.804428			−0.402214	+	0.915546i	$0.631759\pi$
$570$	−0.651668			−0.0272954
$571$	−6.54968	+	28.6960i	−0.274096	+	1.20089i	0.631034	+	0.775755i	$0.282631\pi$
$571$	−6.54968	+	28.6960i	−0.274096	+	1.20089i	−0.905129	+	0.425136i	$0.860226\pi$
$572$	−7.49916	+	3.61141i	−0.313556	+	0.151000i
$573$	1.94055	+	2.43337i	0.0810677	+	0.101656i
$574$	5.55148	+	1.69400i	0.231714	+	0.0707064i
$575$	17.6049	−	22.0759i	0.734176	−	0.920628i
$576$	−2.84635	+	12.4707i	−0.118598	+	0.519612i
$577$	21.9171	−	27.4831i	0.912419	−	1.14414i	−0.0767049	−	0.997054i	$-0.524440\pi$
$577$	21.9171	−	27.4831i	0.912419	−	1.14414i	0.989124	−	0.147084i	$-0.0469886\pi$
$578$	0.936250	−	0.450874i	0.0389429	−	0.0187539i
$579$	3.31255	+	4.15381i	0.137665	+	0.172626i
$580$	−3.52691	−	1.69847i	−0.146447	−	0.0705251i
$581$	0.134960	−	1.87720i	0.00559908	−	0.0778794i
$582$	0.0264963	−	0.0127599i	0.00109831	−	0.000528917i
$583$	−13.4775	−	6.49042i	−0.558181	−	0.268806i
$584$	−2.97695	−	13.0429i	−0.123187	−	0.539717i
$585$	2.20021	+	1.05957i	0.0909677	+	0.0438077i
$586$	4.40642	−	5.52548i	0.182028	−	0.228255i
$587$	10.3088			0.425491			0.212745	−	0.977108i	$-0.431760\pi$
$587$	10.3088			0.425491			0.212745	+	0.977108i	$0.431760\pi$
$588$	3.02296	+	0.436924i	0.124665	+	0.0180185i
$589$	−37.5682			−1.54797
$590$	2.66832	−	3.34597i	0.109853	−	0.137751i
$591$	−0.431055	−	0.207585i	−0.0177312	−	0.00853890i
$592$	−1.29553	−	5.67607i	−0.0532458	−	0.233285i
$593$	10.9344	+	5.26571i	0.449020	+	0.216237i	0.644707	−	0.764430i	$-0.276979\pi$
$593$	10.9344	+	5.26571i	0.449020	+	0.216237i	−0.195687	+	0.980666i	$0.562694\pi$
$594$	2.32858	−	1.12138i	0.0955427	−	0.0460109i
$595$	−8.24040	+	1.26758i	−0.337823	+	0.0519657i
$596$	14.3586	+	6.91473i	0.588150	+	0.283238i
$597$	2.56756	+	3.21962i	0.105083	+	0.131770i
$598$	−2.38343	+	1.14780i	−0.0974656	+	0.0469370i
$599$	18.0034	−	22.5755i	0.735598	−	0.922411i	−0.263509	−	0.964657i	$-0.584880\pi$
$599$	18.0034	−	22.5755i	0.735598	−	0.922411i	0.999107	+	0.0422460i	$0.0134513\pi$
$600$	−0.353256	+	1.54771i	−0.0144216	+	0.0631852i
$601$	−21.1112	+	26.4727i	−0.861146	+	1.07984i	0.134888	+	0.990861i	$0.456933\pi$
$601$	−21.1112	+	26.4727i	−0.861146	+	1.07984i	−0.996033	+	0.0889815i	$0.971639\pi$
$602$	−6.26710	+	4.30070i	−0.255428	+	0.175284i
$603$	12.8746	+	16.1442i	0.524293	+	0.657443i
$604$	10.2940	−	4.95733i	0.418857	−	0.201711i
$605$	1.76006	−	7.71134i	0.0715568	−	0.313511i
$606$	0.722333			0.0293428
$607$	−23.2326			−0.942982			−0.471491	−	0.881871i	$-0.656284\pi$
$607$	−23.2326			−0.942982			−0.471491	+	0.881871i	$0.656284\pi$
$608$	−7.88861	+	34.5623i	−0.319925	+	1.40168i
$609$	1.59576	−	0.245467i	0.0646633	−	0.00994684i
$610$	−0.993706	−	4.35371i	−0.0402340	−	0.176276i
$611$	1.95255	+	8.55468i	0.0789917	+	0.346085i
$612$	12.8046	+	16.0565i	0.517595	+	0.649044i
$613$	29.0766	+	36.4610i	1.17439	+	1.47264i	0.850047	+	0.526707i	$0.176573\pi$
$613$	29.0766	+	36.4610i	1.17439	+	1.47264i	0.324348	+	0.945938i	$0.394855\pi$
$614$	2.13017	+	9.33287i	0.0859666	+	0.376644i
$615$	−0.238157	−	1.04343i	−0.00960342	−	0.0420753i
$616$	17.7731	+	5.42337i	0.716098	+	0.218514i
$617$	8.70906	−	38.1569i	0.350614	−	1.53614i	−0.425154	−	0.905121i	$-0.639780\pi$
$617$	8.70906	−	38.1569i	0.350614	−	1.53614i	0.775768	−	0.631018i	$-0.217363\pi$
$618$	−0.152128			−0.00611947
$619$	−4.13350			−0.166139			−0.0830697	−	0.996544i	$-0.526472\pi$
$619$	−4.13350			−0.166139			−0.0830697	+	0.996544i	$0.526472\pi$
$620$	1.55628	−	6.81851i	0.0625017	−	0.273838i
$621$	−8.33046	+	4.01174i	−0.334290	+	0.160985i
$622$	1.54415	+	1.93630i	0.0619147	+	0.0776386i
$623$	0.958753	−	13.3356i	0.0384116	−	0.534280i
$624$	−0.451372	+	0.566003i	−0.0180694	+	0.0226583i
$625$	−3.37110	+	14.7698i	−0.134844	+	0.590791i
$626$	−0.613501	+	0.769306i	−0.0245204	+	0.0307477i
$627$	−7.93879	+	3.82312i	−0.317045	+	0.152681i
$628$	19.4520	+	24.3921i	0.776220	+	0.973349i
$629$	−6.53783	−	3.14845i	−0.260680	−	0.125537i
$630$	−0.960900	−	2.42669i	−0.0382832	−	0.0966817i
$631$	30.7761	−	14.8210i	1.22518	−	0.590014i	0.294428	−	0.955674i	$-0.404871\pi$
$631$	30.7761	−	14.8210i	1.22518	−	0.590014i	0.930748	+	0.365660i	$0.119157\pi$
$632$	−11.9397	−	5.74988i	−0.474938	−	0.228718i
$633$	0.730305	+	3.19967i	0.0290270	+	0.127176i
$634$	−2.02797	−	0.976619i	−0.0805410	−	0.0387865i
$635$	7.52618	−	9.43754i	0.298667	−	0.374517i
$636$	−1.44041			−0.0571160
$637$	−5.80745	−	3.90813i	−0.230100	−	0.154846i
$638$	4.70233			0.186167
$639$	6.37901	−	7.99903i	0.252350	−	0.316437i
$640$	−7.78653	−	3.74980i	−0.307790	−	0.148224i
$641$	−0.629394	−	2.75755i	−0.0248596	−	0.108917i	0.960976	−	0.276632i	$-0.0892183\pi$
$641$	−0.629394	−	2.75755i	−0.0248596	−	0.108917i	−0.985836	+	0.167715i	$0.946361\pi$
$642$	1.30702	+	0.629426i	0.0515839	+	0.0248415i
$643$	1.68781	−	0.812805i	0.0665606	−	0.0320539i	−0.400307	−	0.916381i	$-0.631097\pi$
$643$	1.68781	−	0.812805i	0.0665606	−	0.0320539i	0.466868	+	0.884327i	$0.345382\pi$
$644$	−30.4394	−	9.28842i	−1.19948	−	0.366015i
$645$	1.26276	+	0.608115i	0.0497213	+	0.0239445i
$646$	7.83094	+	9.81968i	0.308104	+	0.386350i
$647$	16.3793	−	7.88784i	0.643936	−	0.310103i	−0.0832657	−	0.996527i	$-0.526535\pi$
$647$	16.3793	−	7.88784i	0.643936	−	0.310103i	0.727201	+	0.686424i	$0.240821\pi$
$648$	−8.20952	+	10.2944i	−0.322500	+	0.404403i
$649$	12.8765	−	56.4156i	0.505447	−	2.21451i
$650$	1.08597	−	1.36177i	0.0425953	−	0.0534129i
$651$	1.06197	+	2.68194i	0.0416219	+	0.105114i
$652$	−17.5430	−	21.9982i	−0.687037	−	0.861517i
$653$	21.3315	−	10.2727i	0.834766	−	0.402002i	0.0328656	−	0.999460i	$-0.489537\pi$
$653$	21.3315	−	10.2727i	0.834766	−	0.402002i	0.801900	+	0.597458i	$0.203822\pi$
$654$	−0.300524	+	1.31668i	−0.0117514	+	0.0514863i
$655$	−5.12971			−0.200434
$656$	−16.5501			−0.646174
$657$	−5.65374	+	24.7707i	−0.220574	+	0.966396i
$658$	4.66447	−	8.13591i	0.181840	−	0.317171i
$659$	−8.26644	−	36.2176i	−0.322015	−	1.41084i	−0.833962	−	0.551822i	$-0.813933\pi$
$659$	−8.26644	−	36.2176i	−0.322015	−	1.41084i	0.511947	−	0.859017i	$-0.328924\pi$
$660$	−0.365017	−	1.59924i	−0.0142083	−	0.0622504i
$661$	12.3631	+	15.5029i	0.480870	+	0.602992i	0.961795	−	0.273770i	$-0.0882707\pi$
$661$	12.3631	+	15.5029i	0.480870	+	0.602992i	−0.480925	+	0.876761i	$0.659699\pi$
$662$	−5.58124	−	6.99866i	−0.216921	−	0.272010i
$663$	0.200782	+	0.879685i	0.00779774	+	0.0341641i
$664$	−0.245336	−	1.07489i	−0.00952089	−	0.0417137i
$665$	6.61477	+	16.7052i	0.256510	+	0.647800i
$666$	0.505488	−	2.21469i	0.0195873	−	0.0858174i
$667$	−16.8225			−0.651371
$668$	−18.6746			−0.722543
$669$	−0.0545767	+	0.239116i	−0.00211006	+	0.00924476i
$670$	−2.11816	+	1.02005i	−0.0818316	+	0.0394080i
$671$	−37.6473	−	47.2082i	−1.45336	−	1.82245i
$672$	2.69035	−	0.413844i	0.103782	−	0.0159644i
$673$	−21.5172	+	26.9818i	−0.829429	+	1.04007i	0.169087	+	0.985601i	$0.445918\pi$
$673$	−21.5172	+	26.9818i	−0.829429	+	1.04007i	−0.998515	+	0.0544697i	$0.982653\pi$
$674$	0.421305	−	1.84586i	0.0162281	−	0.0710999i
$675$	3.79565	−	4.75959i	0.146094	−	0.183197i
$676$	1.65491	−	0.796965i	0.0636506	−	0.0306525i
$677$	2.82706	+	3.54502i	0.108653	+	0.136246i	0.833184	−	0.552995i	$-0.186515\pi$
$677$	2.82706	+	3.54502i	0.108653	+	0.136246i	−0.724532	+	0.689242i	$0.757944\pi$
$678$	−1.67700	−	0.807600i	−0.0644047	−	0.0310157i
$679$	−0.596046	−	0.549699i	−0.0228741	−	0.0210955i
$680$	−4.40044	+	2.11914i	−0.168749	+	0.0812654i
$681$	−4.69959	−	2.26320i	−0.180089	−	0.0867262i
$682$	1.86946	+	8.19065i	0.0715854	+	0.313636i
$683$	−41.7910	−	20.1255i	−1.59909	−	0.770080i	−0.599545	−	0.800341i	$-0.704652\pi$
$683$	−41.7910	−	20.1255i	−1.59909	−	0.770080i	−0.999542	+	0.0302617i	$0.990366\pi$
$684$	27.5943	−	34.6021i	1.05509	−	1.32304i
$685$	−7.87564			−0.300913
$686$	1.73099	+	7.27844i	0.0660896	+	0.277892i
$687$	−0.758498			−0.0289385
$688$	13.5130	−	16.9447i	0.515177	−	0.646011i
$689$	2.97421	+	1.43231i	0.113309	+	0.0545665i
$690$	−0.116012	−	0.508281i	−0.00441649	−	0.0193499i
$691$	−19.2452	−	9.26801i	−0.732123	−	0.352572i	0.0303959	−	0.999538i	$-0.490323\pi$
$691$	−19.2452	−	9.26801i	−0.732123	−	0.352572i	−0.762519	+	0.646966i	$0.776037\pi$
$692$	−2.41495	+	1.16298i	−0.0918025	+	0.0442098i
$693$	−25.9425	−	23.9253i	−0.985475	−	0.908847i
$694$	10.9862	+	5.29067i	0.417030	+	0.200831i
$695$	−5.07901	−	6.36888i	−0.192658	−	0.241585i
$696$	0.852148	−	0.410373i	0.0323006	−	0.0155551i
$697$	−12.8611	+	16.1274i	−0.487151	+	0.610868i
$698$	−1.50107	+	6.57664i	−0.0568165	+	0.248929i
$699$	1.51435	−	1.89894i	0.0572782	−	0.0718245i
$700$	20.7104	−	3.18577i	0.782778	−	0.120411i
$701$	29.6670	+	37.2012i	1.12051	+	1.40507i	0.903334	+	0.428938i	$0.141112\pi$
$701$	29.6670	+	37.2012i	1.12051	+	1.40507i	0.217173	+	0.976133i	$0.430317\pi$
$702$	−0.513870	+	0.247467i	−0.0193948	+	0.00934003i
$703$	−3.47975	+	15.2458i	−0.131241	+	0.575005i
$704$	−19.6916			−0.742154
$705$	−1.72930			−0.0651292
$706$	−1.53696	+	6.73387i	−0.0578444	+	0.253433i
$707$	−7.33206	−	18.5166i	−0.275750	−	0.696390i
$708$	−1.23989	−	5.43233i	−0.0465981	−	0.204159i
$709$	4.71246	+	20.6466i	0.176980	+	0.775401i	0.983014	+	0.183531i	$0.0587529\pi$
$709$	4.71246	+	20.6466i	0.176980	+	0.775401i	−0.806034	+	0.591870i	$0.798390\pi$
$710$	0.726270	+	0.910714i	0.0272564	+	0.0341785i
$711$	15.6920	+	19.6772i	0.588498	+	0.737953i
$712$	−1.74287	−	7.63599i	−0.0653167	−	0.286171i
$713$	−6.68798	−	29.3020i	−0.250467	−	1.09737i
$714$	0.479651	−	0.836622i	0.0179505	−	0.0313098i
$715$	−0.836544	+	3.66514i	−0.0312850	+	0.137068i
$716$	28.8018			1.07637
$717$	−1.71476			−0.0640388
$718$	−0.0702405	+	0.307744i	−0.00262135	+	0.0114849i
$719$	43.8485	−	21.1163i	1.63527	−	0.787506i	0.635389	−	0.772192i	$-0.280840\pi$
$719$	43.8485	−	21.1163i	1.63527	−	0.787506i	0.999883	−	0.0153137i	$-0.00487470\pi$
$720$	4.64015	+	5.81856i	0.172928	+	0.216845i
$721$	1.54417	+	3.89971i	0.0575080	+	0.145233i
$722$	12.0905	−	15.1610i	0.449960	−	0.564232i
$723$	0.223341	−	0.978519i	0.00830612	−	0.0363915i
$724$	−26.6256	+	33.3875i	−0.989534	+	1.24084i
$725$	9.97927	−	4.80576i	0.370621	−	0.178481i
$726$	0.570430	+	0.715296i	0.0211706	+	0.0265471i
$727$	−16.3821	−	7.88922i	−0.607580	−	0.292595i	0.104685	−	0.994505i	$-0.466616\pi$
$727$	−16.3821	−	7.88922i	−0.607580	−	0.292595i	−0.712265	+	0.701910i	$0.752331\pi$
$728$	−3.92216	−	1.19683i	−0.145365	−	0.0443574i
$729$	21.6235	−	10.4134i	0.800872	−	0.385680i
$730$	−2.60627	−	1.25512i	−0.0964625	−	0.0464539i
$731$	−6.01092	−	26.3356i	−0.222322	−	0.974056i
$732$	−5.23843	−	2.52269i	−0.193618	−	0.0932415i
$733$	−0.445383	+	0.558493i	−0.0164506	+	0.0206284i	−0.789989	−	0.613121i	$-0.789914\pi$
$733$	−0.445383	+	0.558493i	−0.0164506	+	0.0206284i	0.773538	+	0.633750i	$0.218485\pi$
$734$	−8.24252			−0.304237
$735$	1.00558	−	0.944441i	0.0370913	−	0.0348362i
$736$	−28.3618			−1.04543
$737$	−19.8196	+	24.8530i	−0.730066	+	0.915473i
$738$	−5.81803	−	2.80182i	−0.214165	−	0.103136i
$739$	−1.17105	−	5.13073i	−0.0430779	−	0.188737i	0.948811	−	0.315844i	$-0.102288\pi$
$739$	−1.17105	−	5.13073i	−0.0430779	−	0.188737i	−0.991889	+	0.127108i	$0.959431\pi$
$740$	−2.62291	−	1.26313i	−0.0964202	−	0.0464335i
$741$	1.75193	−	0.843686i	0.0643588	−	0.0309936i
$742$	−1.29893	−	3.28036i	−0.0476852	−	0.120426i
$743$	9.12936	+	4.39647i	0.334924	+	0.161291i	0.593785	−	0.804624i	$-0.297633\pi$
$743$	9.12936	+	4.39647i	0.334924	+	0.161291i	−0.258861	+	0.965914i	$0.583347\pi$
$744$	1.05358	+	1.32115i	0.0386261	+	0.0484356i
$745$	6.48525	−	3.12313i	0.237601	−	0.114423i
$746$	0.131140	−	0.164444i	0.00480138	−	0.00602074i
$747$	−0.465936	+	2.04140i	−0.0170477	+	0.0746909i
$748$	−19.7119	+	24.7180i	−0.720739	+	0.903778i
$749$	2.86813	−	39.8937i	0.104799	−	1.45769i
$750$	0.462207	+	0.579589i	0.0168774	+	0.0211636i
$751$	19.6048	−	9.44117i	0.715389	−	0.344513i	−0.0405300	−	0.999178i	$-0.512905\pi$
$751$	19.6048	−	9.44117i	0.715389	−	0.344513i	0.755919	+	0.654665i	$0.227190\pi$
$752$	−5.95045	+	26.0706i	−0.216991	+	0.950698i
$753$	−1.23974			−0.0451788
$754$	−1.03771			−0.0377912
$755$	1.14831	−	5.03109i	0.0417914	−	0.183100i
$756$	−6.56277	−	2.00260i	−0.238686	−	0.0728337i
$757$	−2.71583	−	11.8988i	−0.0987087	−	0.432471i	0.901291	−	0.433214i	$-0.142621\pi$
$757$	−2.71583	−	11.8988i	−0.0987087	−	0.432471i	−1.00000		0.000743157i	$0.999763\pi$
$758$	2.11799	+	9.27952i	0.0769288	+	0.337047i
$759$	−4.39520	−	5.51140i	−0.159536	−	0.200051i
$760$	6.56250	+	8.22911i	0.238047	+	0.298501i
$761$	5.11967	+	22.4307i	0.185588	+	0.813114i	0.978907	+	0.204307i	$0.0654942\pi$
$761$	5.11967	+	22.4307i	0.185588	+	0.813114i	−0.793319	+	0.608806i	$0.791649\pi$
$762$	0.310693	+	1.36124i	0.0112552	+	0.0493124i
$763$	36.8030	−	5.66122i	1.33236	−	0.204950i
$764$	5.35519	−	23.4626i	0.193744	−	0.848847i
$765$	9.27581			0.335368
$766$	2.69045			0.0972100
$767$	−2.84159	+	12.4498i	−0.102604	+	0.449536i
$768$	−0.959463	+	0.462053i	−0.0346217	+	0.0166729i
$769$	−3.97396	−	4.98319i	−0.143305	−	0.179698i	0.704999	−	0.709208i	$-0.250947\pi$
$769$	−3.97396	−	4.98319i	−0.143305	−	0.179698i	−0.848304	+	0.529510i	$0.822376\pi$
$770$	3.31292	−	2.27344i	0.119389	−	0.0819292i
$771$	−0.952055	+	1.19384i	−0.0342874	+	0.0429951i
$772$	9.14138	−	40.0510i	0.329005	−	1.44147i
$773$	−17.4395	+	21.8684i	−0.627255	+	0.786552i	−0.989345	−	0.145591i	$-0.953492\pi$
$773$	−17.4395	+	21.8684i	−0.627255	+	0.786552i	0.362090	+	0.932143i	$0.382063\pi$
$774$	7.61897	−	3.66910i	0.273858	−	0.131883i
$775$	12.3382	+	15.4716i	0.443200	+	0.555755i
$776$	−0.427955	−	0.206092i	−0.0153627	−	0.00739828i
$777$	1.18674	−	0.182551i	0.0425741	−	0.00654897i
$778$	9.64197	−	4.64333i	0.345681	−	0.166471i
$779$	40.0510	+	19.2875i	1.43498	+	0.691048i
$780$	0.0805518	+	0.352921i	0.00288422	+	0.0126366i
$781$	14.1905	+	6.83377i	0.507775	+	0.244531i
$782$	−6.26496	+	7.85601i	−0.224034	+	0.280930i
$783$	−3.62696			−0.129617
$784$	−10.7781	−	18.4097i	−0.384931	−	0.657489i
$785$	14.0913			0.502939
$786$	0.369945	−	0.463897i	0.0131955	−	0.0165467i
$787$	−7.06891	−	3.40421i	−0.251979	−	0.121347i	0.303631	−	0.952790i	$-0.401801\pi$
$787$	−7.06891	−	3.40421i	−0.251979	−	0.121347i	−0.555610	+	0.831443i	$0.687515\pi$
$788$	0.823192	+	3.60664i	0.0293250	+	0.128481i
$789$	−2.39370	−	1.15275i	−0.0852180	−	0.0410388i
$790$	−2.58170	+	1.24328i	−0.0918526	+	0.0442339i
$791$	−3.68001	+	51.1866i	−0.130846	+	1.81998i
$792$	−18.6265	−	8.97003i	−0.661863	−	0.318736i
$793$	8.30801	+	10.4179i	0.295026	+	0.369951i
$794$	8.67714	−	4.17869i	0.307940	−	0.148296i
$795$	−0.405630	+	0.508645i	−0.0143862	+	0.0180398i
$796$	7.08548	−	31.0435i	0.251138	−	1.10031i
$797$	−4.29138	+	5.38122i	−0.152009	+	0.190613i	−0.852005	−	0.523534i	$-0.824613\pi$
$797$	−4.29138	+	5.38122i	−0.152009	+	0.190613i	0.699996	+	0.714146i	$0.253185\pi$
$798$	−1.98775	−	0.606552i	−0.0703657	−	0.0214717i
$799$	20.7806	+	26.0580i	0.735164	+	0.921866i
$800$	16.8245	−	8.10223i	0.594834	−	0.286457i
$801$	−3.31001	+	14.5021i	−0.116953	+	0.512406i
$802$	−13.6090			−0.480551
$803$	−39.1136			−1.38029
$804$	−0.681120	+	2.98418i	−0.0240213	+	0.105244i
$805$	−11.8519	+	8.13322i	−0.417726	+	0.286658i
$806$	−0.412553	−	1.80751i	−0.0145316	−	0.0636669i
$807$	0.540553	+	2.36832i	0.0190284	+	0.0833687i
$808$	−7.27411	−	9.12145i	−0.255902	−	0.320891i
$809$	−9.52880	−	11.9487i	−0.335015	−	0.420095i	0.585580	−	0.810615i	$-0.300867\pi$
$809$	−9.52880	−	11.9487i	−0.335015	−	0.420095i	−0.920595	+	0.390520i	$0.872295\pi$
$810$	0.633533	+	2.77569i	0.0222601	+	0.0975278i
$811$	12.1926	+	53.4194i	0.428141	+	1.87581i	0.480190	+	0.877165i	$0.340568\pi$
$811$	12.1926	+	53.4194i	0.428141	+	1.87581i	−0.0520486	+	0.998645i	$0.516575\pi$
$812$	−9.17707	−	8.46349i	−0.322052	−	0.297010i
$813$	0.504199	−	2.20904i	0.0176830	−	0.0774743i
$814$	3.49706			0.122572
$815$	−12.7084			−0.445154
$816$	−0.611889	+	2.68086i	−0.0214204	+	0.0938490i
$817$	−52.4485	+	25.2579i	−1.83494	+	0.883661i
$818$	−5.28198	−	6.62340i	−0.184680	−	0.231582i
$819$	5.72499	+	5.27983i	0.200047	+	0.184492i
$820$	−5.15976	+	6.47014i	−0.180187	+	0.225947i
$821$	−5.88862	+	25.7997i	−0.205514	+	0.900417i	0.761995	+	0.647583i	$0.224220\pi$
$821$	−5.88862	+	25.7997i	−0.205514	+	0.900417i	−0.967510	+	0.252834i	$0.918637\pi$
$822$	0.567977	−	0.712220i	0.0198105	−	0.0248415i
$823$	−22.5528	+	10.8608i	−0.786140	+	0.378585i	−0.783485	−	0.621411i	$-0.786560\pi$
$823$	−22.5528	+	10.8608i	−0.786140	+	0.378585i	−0.00265585	+	0.999996i	$0.500845\pi$
$824$	1.53197	+	1.92103i	0.0533687	+	0.0669222i
$825$	4.18173	+	2.01381i	0.145589	+	0.0701120i
$826$	11.2534	−	7.72246i	0.391555	−	0.268699i
$827$	36.9976	−	17.8171i	1.28653	−	0.619561i	0.339472	−	0.940616i	$-0.389752\pi$
$827$	36.9976	−	17.8171i	1.28653	−	0.619561i	0.947061	+	0.321055i	$0.104037\pi$
$828$	31.9010	+	15.3627i	1.10863	+	0.533890i
$829$	−4.59091	−	20.1141i	−0.159449	−	0.698591i	−0.989932	−	0.141547i	$-0.954793\pi$
$829$	−4.59091	−	20.1141i	−0.159449	−	0.698591i	0.830483	−	0.557044i	$-0.188065\pi$
$830$	−0.214788	−	0.103437i	−0.00745541	−	0.00359033i
$831$	−2.16559	+	2.71556i	−0.0751235	+	0.0942018i
$832$	4.34554			0.150654
$833$	−26.3151	−	3.80346i	−0.911764	−	0.131782i
$834$	0.942249			0.0326274
$835$	−5.25892	+	6.59447i	−0.181992	+	0.228211i
$836$	61.3850	+	29.5614i	2.12304	+	1.02240i
$837$	−1.44194	−	6.31754i	−0.0498407	−	0.218366i
$838$	11.3757	+	5.47823i	0.392965	+	0.189242i
$839$	15.0689	−	7.25679i	0.520236	−	0.250532i	−0.155290	−	0.987869i	$-0.549631\pi$
$839$	15.0689	−	7.25679i	0.520236	−	0.250532i	0.675526	+	0.737337i	$0.263917\pi$
$840$	0.401958	−	0.701108i	0.0138689	−	0.0241905i
$841$	20.1826	+	9.71945i	0.695953	+	0.335153i
$842$	2.78031	+	3.48640i	0.0958160	+	0.120149i
$843$	3.57124	−	1.71982i	0.123000	−	0.0592337i
$844$	15.8223	−	19.8406i	0.544627	−	0.682940i
$845$	0.184609	−	0.808823i	0.00635073	−	0.0278244i
$846$	−6.50539	+	8.15750i	−0.223660	+	0.280461i
$847$	12.5461	−	21.8833i	0.431089	−	0.751920i
$848$	6.27248	+	7.86544i	0.215398	+	0.270100i
$849$	−0.645510	+	0.310861i	−0.0221539	+	0.0106687i
$850$	1.47217	−	6.44998i	0.0504949	−	0.221233i
$851$	−12.5107			−0.428861
$852$	1.51661			0.0519582
$853$	6.39226	−	28.0063i	0.218867	−	0.958919i	−0.739450	−	0.673212i	$-0.764914\pi$
$853$	6.39226	−	28.0063i	0.218867	−	0.958919i	0.958317	−	0.285707i	$-0.0922285\pi$
$854$	1.02124	−	14.2048i	0.0349462	−	0.486079i
$855$	−4.44811	−	19.4884i	−0.152122	−	0.666491i
$856$	−5.21381	−	22.8432i	−0.178204	−	0.780765i
$857$	27.2053	+	34.1143i	0.929315	+	1.16532i	0.985969	+	0.166930i	$0.0533854\pi$
$857$	27.2053	+	34.1143i	0.929315	+	1.16532i	−0.0566540	+	0.998394i	$0.518043\pi$
$858$	−0.271121	−	0.339975i	−0.00925591	−	0.0116065i
$859$	−1.12729	−	4.93896i	−0.0384625	−	0.168515i	0.952049	−	0.305946i	$-0.0989727\pi$
$859$	−1.12729	−	4.93896i	−0.0384625	−	0.168515i	−0.990511	+	0.137431i	$0.956116\pi$
$860$	−2.41152	−	10.5656i	−0.0822322	−	0.360283i
$861$	0.244757	−	3.40441i	0.00834129	−	0.116022i
$862$	−0.899133	+	3.93936i	−0.0306246	+	0.134175i
$863$	−27.7621			−0.945032			−0.472516	−	0.881322i	$-0.656654\pi$
$863$	−27.7621			−0.945032			−0.472516	+	0.881322i	$0.656654\pi$
$864$	−6.11484			−0.208031
$865$	−0.269391	+	1.18028i	−0.00915958	+	0.0401308i
$866$	0.504105	−	0.242764i	0.0171302	−	0.00824946i
$867$	−0.381005	−	0.477766i	−0.0129396	−	0.0162258i
$868$	11.0935	−	19.3496i	0.376538	−	0.656769i
$869$	−24.1570	+	30.2919i	−0.819469	+	1.02758i
$870$	0.0455078	−	0.199383i	0.00154286	−	0.00675971i
$871$	4.37380	−	5.48457i	0.148200	−	0.185837i
$872$	19.6531	−	9.46444i	0.665538	−	0.320506i
$873$	0.562448	+	0.705288i	0.0190360	+	0.0238704i
$874$	19.5097	+	9.39539i	0.659927	+	0.317804i
$875$	10.1658	−	17.7316i	0.343668	−	0.599437i
$876$	−3.39332	+	1.63414i	−0.114650	+	0.0552123i
$877$	−3.18203	−	1.53238i	−0.107450	−	0.0517450i	0.379387	−	0.925238i	$-0.376135\pi$
$877$	−3.18203	−	1.53238i	−0.107450	−	0.0517450i	−0.486836	+	0.873493i	$0.661849\pi$
$878$	0.494059	+	2.16462i	0.0166737	+	0.0730522i
$879$	−3.74443	−	1.80322i	−0.126297	−	0.0608212i
$880$	−7.14324	+	8.95733i	−0.240798	+	0.301952i
$881$	54.1797			1.82536			0.912680	−	0.408676i	$-0.134009\pi$
$881$	54.1797			1.82536			0.912680	+	0.408676i	$0.134009\pi$
$882$	−0.672297	−	8.29639i	−0.0226374	−	0.279354i
$883$	−21.7112			−0.730641			−0.365321	−	0.930882i	$-0.619041\pi$
$883$	−21.7112			−0.730641			−0.365321	+	0.930882i	$0.619041\pi$
$884$	4.35002	−	5.45476i	0.146307	−	0.183463i
$885$	−2.26745	−	1.09195i	−0.0762196	−	0.0367054i
$886$	3.47093	+	15.2071i	0.116608	+	0.510894i
$887$	−6.93182	−	3.33819i	−0.232748	−	0.112085i	0.313875	−	0.949464i	$-0.398373\pi$
$887$	−6.93182	−	3.33819i	−0.232748	−	0.112085i	−0.546623	+	0.837379i	$0.684087\pi$
$888$	0.633730	−	0.305188i	0.0212666	−	0.0102415i
$889$	31.7409	−	21.7817i	1.06456	−	0.730535i
$890$	−1.52585	−	0.734812i	−0.0511467	−	0.0246310i
$891$	24.0019	+	30.0974i	0.804094	+	1.00830i
$892$	1.70865	−	0.822843i	0.0572099	−	0.0275508i
$893$	44.7827	−	56.1557i	1.49860	−	1.87918i
$894$	−0.185269	+	0.811717i	−0.00619633	+	0.0271479i
$895$	8.11079	−	10.1706i	0.271114	−	0.339966i
$896$	−20.2607	−	18.6853i	−0.676862	−	0.624231i
$897$	0.969932	+	1.21626i	0.0323851	+	0.0406096i
$898$	−3.34455	+	1.61065i	−0.111609	+	0.0537482i
$899$	2.62349	−	11.4942i	0.0874982	−	0.383355i
$900$	−23.3126			−0.777087
$901$	12.5389			0.417731
$902$	2.21208	−	9.69174i	0.0736541	−	0.322700i
$903$	3.28573	+	3.03025i	0.109342	+	0.100840i
$904$	6.68970	+	29.3095i	0.222496	+	0.974819i
$905$	4.29197	+	18.8044i	0.142670	+	0.625078i
$906$	0.372164	+	0.466679i	0.0123643	+	0.0155044i
$907$	19.8131	+	24.8449i	0.657884	+	0.824960i	0.993111	−	0.117177i	$-0.0373846\pi$
$907$	19.8131	+	24.8449i	0.657884	+	0.824960i	−0.335227	+	0.942137i	$0.608813\pi$
$908$	8.97489	+	39.3216i	0.297842	+	1.30493i
$909$	4.93045	+	21.6017i	0.163533	+	0.716483i
$910$	−0.731095	+	0.501703i	−0.0242356	+	0.0166313i
$911$	−3.11322	+	13.6399i	−0.103146	+	0.451911i	0.896809	+	0.442418i	$0.145879\pi$
$911$	−3.11322	+	13.6399i	−0.103146	+	0.451911i	−0.999955	+	0.00949349i	$0.996978\pi$
$912$	5.92591			0.196226
$913$	−3.22343			−0.106680
$914$	2.35468	−	10.3165i	0.0778859	−	0.341241i
$915$	−2.36601	+	1.13941i	−0.0782178	+	0.0376677i
$916$	3.65672	+	4.58538i	0.120821	+	0.151505i
$917$	−15.6469	−	4.77457i	−0.516706	−	0.157670i
$918$	−1.35073	+	1.69377i	−0.0445808	+	0.0559026i
$919$	7.44528	−	32.6199i	0.245597	−	1.07603i	−0.690235	−	0.723585i	$-0.742493\pi$
$919$	7.44528	−	32.6199i	0.245597	−	1.07603i	0.935832	−	0.352446i	$-0.114650\pi$
$920$	−5.25017	+	6.58351i	−0.173093	+	0.217052i
$921$	5.07192	−	2.44251i	0.167125	−	0.0804834i
$922$	3.76583	+	4.72220i	0.124021	+	0.155517i
$923$	−3.13155	−	1.50808i	−0.103076	−	0.0496389i
$924$	0.375132	−	5.21784i	0.0123409	−	0.171654i
$925$	7.42144	−	3.57398i	0.244015	−	0.117512i
$926$	10.0402	+	4.83509i	0.329941	+	0.158891i
$927$	−1.03838	−	4.54944i	−0.0341049	−	0.149423i
$928$	−10.0237	−	4.82715i	−0.329044	−	0.158459i
$929$	−20.4332	+	25.6224i	−0.670392	+	0.840644i	−0.994430	−	0.105400i	$-0.966388\pi$
$929$	−20.4332	+	25.6224i	−0.670392	+	0.840644i	0.324038	+	0.946044i	$0.394959\pi$
$930$	0.365382			0.0119814
$931$	4.62805	+	57.1119i	0.151678	+	1.87177i
$932$	−18.7805			−0.615174
$933$	0.908048	−	1.13866i	0.0297282	−	0.0372779i
$934$	6.73722	+	3.24448i	0.220449	+	0.106163i
$935$	3.17750	+	13.9215i	0.103915	+	0.455283i
$936$	4.11049	+	1.97951i	0.134355	+	0.0647022i
$937$	5.79404	−	2.79026i	0.189283	−	0.0911539i	−0.336842	−	0.941561i	$-0.609359\pi$
$937$	5.79404	−	2.79026i	0.189283	−	0.0911539i	0.526125	+	0.850407i	$0.323644\pi$
$938$	−7.41034	+	1.13990i	−0.241956	+	0.0372190i
$939$	0.521333	+	0.251061i	0.0170131	+	0.00819306i
$940$	8.33695	+	10.4542i	0.271921	+	0.340979i
$941$	39.6665	−	19.1024i	1.29309	−	0.622720i	0.344371	−	0.938834i	$-0.388092\pi$
$941$	39.6665	−	19.1024i	1.29309	−	0.622720i	0.948721	+	0.316114i	$0.102378\pi$
$942$	−1.01624	+	1.27432i	−0.0331108	+	0.0415196i
$943$	−7.91368	+	34.6721i	−0.257705	+	1.12908i
$944$	−24.2642	+	30.4264i	−0.789734	+	0.990295i
$945$	−2.55529	+	1.75353i	−0.0831237	+	0.0570424i
$946$	8.11668	+	10.1780i	0.263896	+	0.330915i
$947$	17.6966	−	8.52225i	0.575063	−	0.276936i	−0.123664	−	0.992324i	$-0.539464\pi$
$947$	17.6966	−	8.52225i	0.575063	−	0.276936i	0.698727	+	0.715388i	$0.253750\pi$
$948$	−0.830177	+	3.63724i	−0.0269629	+	0.118132i
$949$	8.63160			0.280193
$950$	−14.2574			−0.462570
$951$	−0.294539	+	1.29046i	−0.00955107	+	0.0418460i
$952$	−15.3949	+	2.36812i	−0.498951	+	0.0767513i
$953$	7.52884	+	32.9860i	0.243883	+	1.06852i	0.937448	+	0.348126i	$0.113182\pi$
$953$	7.52884	+	32.9860i	0.243883	+	1.06852i	−0.693565	+	0.720394i	$0.743961\pi$
$954$	0.873466	+	3.82690i	0.0282795	+	0.123901i
$955$	−6.77717	−	8.49830i	−0.219304	−	0.274998i
$956$	8.26685	+	10.3663i	0.267369	+	0.335270i
$957$	−0.615324	−	2.69591i	−0.0198906	−	0.0871464i
$958$	−2.79417	−	12.2420i	−0.0902754	−	0.395522i
$959$	−24.0227	−	7.33040i	−0.775733	−	0.236711i
$960$	−0.190569	+	0.834939i	−0.00615060	+	0.0269475i
$961$	−9.93601			−0.320516
$962$	−0.771731			−0.0248816
$963$	−9.90194	+	43.3832i	−0.319086	+	1.39801i
$964$	−6.99221	+	3.36727i	−0.225204	+	0.108452i
$965$	−11.5687	−	14.5067i	−0.372410	−	0.466988i
$966$	0.119227	−	1.65836i	0.00383605	−	0.0533570i
$967$	26.9875	−	33.8412i	0.867858	−	1.08826i	−0.127482	−	0.991841i	$-0.540690\pi$
$967$	26.9875	−	33.8412i	0.867858	−	1.08826i	0.995341	−	0.0964193i	$-0.0307390\pi$
$968$	3.28819	−	14.4065i	0.105686	−	0.463042i
$969$	4.60504	−	5.77454i	0.147935	−	0.185505i
$970$	−0.0925354	+	0.0445627i	−0.00297113	+	0.00143082i
$971$	5.21804	+	6.54322i	0.167455	+	0.209982i	0.858477	−	0.512851i	$-0.171411\pi$
$971$	5.21804	+	6.54322i	0.167455	+	0.209982i	−0.691022	+	0.722833i	$0.742839\pi$
$972$	10.3495	+	4.98405i	0.331960	+	0.159863i
$973$	−9.56431	−	24.1541i	−0.306618	−	0.774344i
$974$	−4.95407	+	2.38576i	−0.158739	+	0.0764446i
$975$	−0.922824	−	0.444409i	−0.0295540	−	0.0142325i
$976$	9.03620	+	39.5902i	0.289242	+	1.26725i
$977$	49.0292	+	23.6112i	1.56858	+	0.755390i	0.997837	−	0.0657361i	$-0.0209395\pi$
$977$	49.0292	+	23.6112i	1.56858	+	0.755390i	0.570747	+	0.821126i	$0.306654\pi$
$978$	0.916504	−	1.14926i	0.0293066	−	0.0367493i
$979$	−22.8992			−0.731863
$980$	−10.5574	−	1.52591i	−0.337242	−	0.0487434i
$981$	−41.4273			−1.32267
$982$	−4.72205	+	5.92127i	−0.150687	+	0.188955i
$983$	46.1495	+	22.2244i	1.47194	+	0.708848i	0.986246	−	0.165281i	$-0.0528532\pi$
$983$	46.1495	+	22.2244i	1.47194	+	0.708848i	0.485693	+	0.874130i	$0.338567\pi$
$984$	−0.444930	−	1.94937i	−0.0141839	−	0.0621436i
$985$	1.50541	+	0.724968i	0.0479664	+	0.0230994i
$986$	−3.55126	+	1.71020i	−0.113095	+	0.0544637i
$987$	−5.27480	−	1.60958i	−0.167899	−	0.0512334i
$988$	−13.5464	−	6.52362i	−0.430970	−	0.207544i
$989$	−29.0373	−	36.4117i	−0.923334	−	1.15782i
$990$	−4.02754	+	1.93956i	−0.128004	+	0.0616434i
$991$	−35.5585	+	44.5890i	−1.12955	+	1.41642i	−0.233563	+	0.972342i	$0.575039\pi$
$991$	−35.5585	+	44.5890i	−1.12955	+	1.41642i	−0.895990	+	0.444074i	$0.853533\pi$
$992$	4.42304	−	19.3786i	0.140432	−	0.615272i
$993$	−3.28209	+	4.11561i	−0.104154	+	0.130605i
$994$	1.36764	+	3.45390i	0.0433790	+	0.109551i
$995$	−8.96692	−	11.2442i	−0.284270	−	0.356464i
$996$	−0.279650	+	0.134672i	−0.00886105	+	0.00426726i
$997$	4.02133	−	17.6186i	0.127357	−	0.557986i	−0.870478	−	0.492208i	$-0.836190\pi$
$997$	4.02133	−	17.6186i	0.127357	−	0.557986i	0.997834	−	0.0657781i	$-0.0209530\pi$
$998$	−1.02993			−0.0326018
$999$	−2.69732			−0.0853395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.w.a.92.16	✓	162
49.8	even	7	inner	637.2.w.a.547.16	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.w.a.92.16	✓	162	1.1	even	1	trivial
637.2.w.a.547.16	yes	162	49.8	even	7	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.w (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.251865 - 0.315829i) q^{2} +(-0.214027 - 0.103070i) q^{3} +(0.408730 + 1.79076i) q^{4} +(0.747465 + 0.359960i) q^{5} +(-0.0864582 + 0.0416361i) q^{6} +(1.94492 + 1.79368i) q^{7} +(1.39643 + 0.672485i) q^{8} +(-1.83529 - 2.30138i) q^{9} +O(q^{10})\)	\(q+(0.251865 - 0.315829i) q^{2} +(-0.214027 - 0.103070i) q^{3} +(0.408730 + 1.79076i) q^{4} +(0.747465 + 0.359960i) q^{5} +(-0.0864582 + 0.0416361i) q^{6} +(1.94492 + 1.79368i) q^{7} +(1.39643 + 0.672485i) q^{8} +(-1.83529 - 2.30138i) q^{9} +(0.301946 - 0.145409i) q^{10} +(2.82531 - 3.54283i) q^{11} +(0.0970945 - 0.425399i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(1.05635 - 0.162494i) q^{14} +(-0.122876 - 0.154082i) q^{15} +(-2.74573 + 1.32227i) q^{16} +(-0.845215 + 3.70313i) q^{17} -1.18908 q^{18} +8.18558 q^{19} +(-0.339092 + 1.48566i) q^{20} +(-0.231389 - 0.584358i) q^{21} +(-0.407330 - 1.78463i) q^{22} +(1.45722 + 6.38449i) q^{23} +(-0.229560 - 0.287859i) q^{24} +(-2.68832 - 3.37104i) q^{25} +(0.0898895 + 0.393832i) q^{26} +(0.314178 + 1.37651i) q^{27} +(-2.41712 + 4.21602i) q^{28} +(-0.571622 + 2.50444i) q^{29} -0.0796118 q^{30} -4.58955 q^{31} +(-0.963720 + 4.22233i) q^{32} +(-0.969851 + 0.467055i) q^{33} +(0.956675 + 1.19963i) q^{34} +(0.808101 + 2.04081i) q^{35} +(3.37108 - 4.22720i) q^{36} +(-0.425107 + 1.86252i) q^{37} +(2.06166 - 2.58524i) q^{38} +(0.214027 - 0.103070i) q^{39} +(0.801714 + 1.00532i) q^{40} +(4.89287 + 2.35628i) q^{41} +(-0.242836 - 0.0741001i) q^{42} +(-6.40742 + 3.08565i) q^{43} +(7.49916 + 3.61141i) q^{44} +(-0.543408 - 2.38083i) q^{45} +(2.38343 + 1.14780i) q^{46} +(5.47093 - 6.86032i) q^{47} +0.723945 q^{48} +(0.565391 + 6.97713i) q^{49} -1.74176 q^{50} +(0.562580 - 0.705452i) q^{51} +(-1.65491 - 0.796965i) q^{52} +(-0.734570 - 3.21836i) q^{53} +(0.513870 + 0.247467i) q^{54} +(3.38710 - 1.63114i) q^{55} +(1.50971 + 3.81268i) q^{56} +(-1.75193 - 0.843686i) q^{57} +(0.647002 + 0.811314i) q^{58} +(11.5053 - 5.54068i) q^{59} +(0.225701 - 0.283020i) q^{60} +(2.96509 - 12.9909i) q^{61} +(-1.15595 + 1.44951i) q^{62} +(0.558467 - 7.76790i) q^{63} +(-2.70940 - 3.39748i) q^{64} +(-0.747465 + 0.359960i) q^{65} +(-0.0967619 + 0.423941i) q^{66} -7.01503 q^{67} -6.97690 q^{68} +(0.346165 - 1.51665i) q^{69} +(0.848078 + 0.258787i) q^{70} +(0.773429 + 3.38862i) q^{71} +(-1.01521 - 4.44791i) q^{72} +(-5.38171 - 6.74845i) q^{73} +(0.481166 + 0.603363i) q^{74} +(0.227919 + 0.998577i) q^{75} +(3.34569 + 14.6584i) q^{76} +(11.8497 - 1.82278i) q^{77} +(0.0213534 - 0.0935554i) q^{78} -8.55020 q^{79} -2.52830 q^{80} +(-1.89038 + 8.28231i) q^{81} +(1.97652 - 0.951844i) q^{82} +(-0.443517 - 0.556153i) q^{83} +(0.951872 - 0.653208i) q^{84} +(-1.96475 + 2.46372i) q^{85} +(-0.639268 + 2.80082i) q^{86} +(0.380474 - 0.477099i) q^{87} +(6.32785 - 3.04733i) q^{88} +(-3.15074 - 3.95091i) q^{89} +(-0.888798 - 0.428023i) q^{90} +(-2.61499 + 0.402252i) q^{91} +(-10.8375 + 5.21907i) q^{92} +(0.982286 + 0.473044i) q^{93} +(-0.788752 - 3.45575i) q^{94} +(6.11843 + 2.94648i) q^{95} +(0.641457 - 0.804361i) q^{96} -0.306464 q^{97} +(2.34598 + 1.57873i) q^{98} -13.3386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 3 q^{2} - 25 q^{4} - 4 q^{5} + 18 q^{6} - 15 q^{7} + 3 q^{8} - 5 q^{9}+O(q^{10}) \) 162 * q + 3 * q^2 - 25 * q^4 - 4 * q^5 + 18 * q^6 - 15 * q^7 + 3 * q^8 - 5 * q^9	\( 162 q + 3 q^{2} - 25 q^{4} - 4 q^{5} + 18 q^{6} - 15 q^{7} + 3 q^{8} - 5 q^{9} - 10 q^{10} + 15 q^{11} + 25 q^{12} + 27 q^{13} + 33 q^{14} + 18 q^{15} - 5 q^{16} + 3 q^{17} - 64 q^{18} + 24 q^{19} - 47 q^{20} + 24 q^{22} + 27 q^{23} - 8 q^{24} - 35 q^{25} - 3 q^{26} + 15 q^{27} + 2 q^{28} + 46 q^{29} - 30 q^{30} + 46 q^{31} + 16 q^{32} - 18 q^{33} - 62 q^{34} - 51 q^{35} + 39 q^{36} + 16 q^{37} - 54 q^{38} + 74 q^{40} - 2 q^{41} + 88 q^{42} + 14 q^{43} - 95 q^{44} + 83 q^{45} + 56 q^{46} - 4 q^{47} - 20 q^{48} - 3 q^{49} - 216 q^{50} - 56 q^{51} + 25 q^{52} + 38 q^{53} - 6 q^{54} + 73 q^{55} - 35 q^{56} + 41 q^{57} + 72 q^{58} - 44 q^{59} + 24 q^{60} - 6 q^{61} - 36 q^{62} - q^{63} - 11 q^{64} + 4 q^{65} + 95 q^{66} - 126 q^{67} - 382 q^{68} - 108 q^{69} - 47 q^{70} + 51 q^{71} + 130 q^{72} + 14 q^{73} - 26 q^{74} + 3 q^{75} + 75 q^{76} - 6 q^{77} + 31 q^{78} - 58 q^{79} + 110 q^{80} - 5 q^{81} - 90 q^{82} - 35 q^{83} + 21 q^{84} + 18 q^{85} + 76 q^{86} - 100 q^{87} + 6 q^{88} + 32 q^{89} + 13 q^{90} + q^{91} + 46 q^{92} + 19 q^{93} + 72 q^{94} + 38 q^{95} + 95 q^{96} + 6 q^{97} - 299 q^{98} - 334 q^{99}+O(q^{100}) \) 162 * q + 3 * q^2 - 25 * q^4 - 4 * q^5 + 18 * q^6 - 15 * q^7 + 3 * q^8 - 5 * q^9 - 10 * q^10 + 15 * q^11 + 25 * q^12 + 27 * q^13 + 33 * q^14 + 18 * q^15 - 5 * q^16 + 3 * q^17 - 64 * q^18 + 24 * q^19 - 47 * q^20 + 24 * q^22 + 27 * q^23 - 8 * q^24 - 35 * q^25 - 3 * q^26 + 15 * q^27 + 2 * q^28 + 46 * q^29 - 30 * q^30 + 46 * q^31 + 16 * q^32 - 18 * q^33 - 62 * q^34 - 51 * q^35 + 39 * q^36 + 16 * q^37 - 54 * q^38 + 74 * q^40 - 2 * q^41 + 88 * q^42 + 14 * q^43 - 95 * q^44 + 83 * q^45 + 56 * q^46 - 4 * q^47 - 20 * q^48 - 3 * q^49 - 216 * q^50 - 56 * q^51 + 25 * q^52 + 38 * q^53 - 6 * q^54 + 73 * q^55 - 35 * q^56 + 41 * q^57 + 72 * q^58 - 44 * q^59 + 24 * q^60 - 6 * q^61 - 36 * q^62 - q^63 - 11 * q^64 + 4 * q^65 + 95 * q^66 - 126 * q^67 - 382 * q^68 - 108 * q^69 - 47 * q^70 + 51 * q^71 + 130 * q^72 + 14 * q^73 - 26 * q^74 + 3 * q^75 + 75 * q^76 - 6 * q^77 + 31 * q^78 - 58 * q^79 + 110 * q^80 - 5 * q^81 - 90 * q^82 - 35 * q^83 + 21 * q^84 + 18 * q^85 + 76 * q^86 - 100 * q^87 + 6 * q^88 + 32 * q^89 + 13 * q^90 + q^91 + 46 * q^92 + 19 * q^93 + 72 * q^94 + 38 * q^95 + 95 * q^96 + 6 * q^97 - 299 * q^98 - 334 * q^99

Introduction

L-functions

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