LMFDB - Embedded newform 637.2.bl.b.625.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.29
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.b.53.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.30234 - 1.56971i) q^{2} +(-0.652644 + 0.605565i) q^{3} +(2.10611 - 5.36627i) q^{4} +(-3.46195 - 1.06787i) q^{5} +(-0.552048 + 2.41868i) q^{6} +(-2.11683 + 1.58714i) q^{7} +(-2.33439 - 10.2276i) q^{8} +(-0.164955 + 2.20118i) q^{9} +O(q^{10})$	\(q+(2.30234 - 1.56971i) q^{2} +(-0.652644 + 0.605565i) q^{3} +(2.10611 - 5.36627i) q^{4} +(-3.46195 - 1.06787i) q^{5} +(-0.552048 + 2.41868i) q^{6} +(-2.11683 + 1.58714i) q^{7} +(-2.33439 - 10.2276i) q^{8} +(-0.164955 + 2.20118i) q^{9} +(-9.64684 + 2.97565i) q^{10} +(-0.296786 - 3.96033i) q^{11} +(1.87509 + 4.77765i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-2.38233 + 6.97695i) q^{14} +(2.90608 - 1.39950i) q^{15} +(-12.9772 - 12.0411i) q^{16} +(-0.592848 - 0.0893574i) q^{17} +(3.07542 + 5.32679i) q^{18} +(2.14944 - 3.72293i) q^{19} +(-13.0217 + 16.3287i) q^{20} +(0.420422 - 2.31772i) q^{21} +(-6.89988 - 8.65217i) q^{22} +(3.46323 - 0.521998i) q^{23} +(7.71701 + 5.26137i) q^{24} +(6.71355 + 4.57722i) q^{25} +(-2.75541 + 0.415311i) q^{26} +(-2.89060 - 3.62469i) q^{27} +(4.05875 + 14.7022i) q^{28} +(1.94642 - 2.44074i) q^{29} +(4.49400 - 7.78383i) q^{30} +(-0.354521 - 0.614048i) q^{31} +(-28.0321 - 4.22515i) q^{32} +(2.59193 + 2.40496i) q^{33} +(-1.50520 + 0.724867i) q^{34} +(9.02323 - 3.23410i) q^{35} +(11.4647 + 5.52110i) q^{36} +(-0.299117 - 0.762138i) q^{37} +(-0.895188 - 11.9455i) q^{38} +(0.850756 - 0.262424i) q^{39} +(-2.84024 + 37.9003i) q^{40} +(1.60713 + 7.04130i) q^{41} +(-2.67019 - 5.99612i) q^{42} +(-0.644964 + 2.82577i) q^{43} +(-21.8773 - 6.74825i) q^{44} +(2.92164 - 7.44421i) q^{45} +(7.15416 - 6.63809i) q^{46} +(7.11986 - 4.85424i) q^{47} +15.7612 q^{48} +(1.96197 - 6.71942i) q^{49} +22.6418 q^{50} +(0.441030 - 0.300689i) q^{51} +(-4.22587 + 3.92104i) q^{52} +(0.911887 - 2.32345i) q^{53} +(-12.3449 - 3.80788i) q^{54} +(-3.20166 + 14.0274i) q^{55} +(21.1742 + 17.9452i) q^{56} +(0.851661 + 3.73137i) q^{57} +(0.650082 - 8.67474i) q^{58} +(7.00113 - 2.15956i) q^{59} +(-1.38955 - 18.5423i) q^{60} +(-1.62455 - 4.13928i) q^{61} +(-1.78010 - 0.857253i) q^{62} +(-3.14439 - 4.92133i) q^{63} +(-39.2720 + 18.9124i) q^{64} +(2.65578 + 2.46420i) q^{65} +(9.74262 + 1.46846i) q^{66} +(-6.97165 - 12.0753i) q^{67} +(-1.72812 + 2.99318i) q^{68} +(-1.94415 + 2.43789i) q^{69} +(15.6980 - 21.6098i) q^{70} +(8.29122 + 10.3969i) q^{71} +(22.8979 - 3.45130i) q^{72} +(-9.49640 - 6.47453i) q^{73} +(-1.88500 - 1.28517i) q^{74} +(-7.15336 + 1.07820i) q^{75} +(-15.4513 - 19.3753i) q^{76} +(6.91385 + 7.91233i) q^{77} +(1.54680 - 1.93963i) q^{78} +(-8.59524 + 14.8874i) q^{79} +(32.0681 + 55.5437i) q^{80} +(-2.46656 - 0.371775i) q^{81} +(14.7530 + 13.6888i) q^{82} +(-4.85228 + 2.33673i) q^{83} +(-11.5520 - 7.13746i) q^{84} +(1.95699 + 0.942435i) q^{85} +(2.95072 + 7.51830i) q^{86} +(0.207704 + 2.77162i) q^{87} +(-39.8120 + 12.2804i) q^{88} +(1.00374 - 13.3939i) q^{89} +(-4.95864 - 21.7252i) q^{90} +(2.59584 - 0.511504i) q^{91} +(4.49275 - 19.6840i) q^{92} +(0.603221 + 0.186069i) q^{93} +(8.77260 - 22.3522i) q^{94} +(-11.4168 + 10.5933i) q^{95} +(20.8536 - 14.2177i) q^{96} +8.83567 q^{97} +(-6.03042 - 18.5501i) q^{98} +8.76634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	2.30234	−	1.56971i	1.62800	−	1.10995i	0.717405	−	0.696657i	$-0.245330\pi$
$2$	2.30234	−	1.56971i	1.62800	−	1.10995i	0.910597	−	0.413296i	$-0.135622\pi$
$3$	−0.652644	+	0.605565i	−0.376804	+	0.349623i	−0.845727	−	0.533616i	$-0.820833\pi$
$3$	−0.652644	+	0.605565i	−0.376804	+	0.349623i	0.468923	+	0.883239i	$0.344642\pi$
$4$	2.10611	−	5.36627i	1.05305	−	2.68313i
$5$	−3.46195	−	1.06787i	−1.54823	−	0.477566i	−0.601305	−	0.799019i	$-0.705352\pi$
$5$	−3.46195	−	1.06787i	−1.54823	−	0.477566i	−0.946925	+	0.321453i	$0.895829\pi$
$6$	−0.552048	+	2.41868i	−0.225373	+	0.987421i
$7$	−2.11683	+	1.58714i	−0.800088	+	0.599883i
$7$	−2.11683	+	1.58714i	−0.800088	+	0.599883i
$8$	−2.33439	−	10.2276i	−0.825331	−	3.61601i
$9$	−0.164955	+	2.20118i	−0.0549851	+	0.733725i
$10$	−9.64684	+	2.97565i	−3.05060	+	0.940985i
$11$	−0.296786	−	3.96033i	−0.0894843	−	1.19409i	−0.843463	−	0.537187i	$-0.819487\pi$
$11$	−0.296786	−	3.96033i	−0.0894843	−	1.19409i	0.753979	−	0.656899i	$-0.228132\pi$
$12$	1.87509	+	4.77765i	0.541291	+	1.37919i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$14$	−2.38233	+	6.97695i	−0.636703	+	1.86467i
$15$	2.90608	−	1.39950i	0.750348	−	0.361348i
$16$	−12.9772	−	12.0411i	−3.24430	−	3.01027i
$17$	−0.592848	−	0.0893574i	−0.143787	−	0.0216723i	0.0767545	−	0.997050i	$-0.475544\pi$
$17$	−0.592848	−	0.0893574i	−0.143787	−	0.0216723i	−0.220541	+	0.975378i	$0.570782\pi$
$18$	3.07542	+	5.32679i	0.724884	+	1.25554i
$19$	2.14944	−	3.72293i	0.493114	−	0.854099i	−0.506854	−	0.862032i	$-0.669192\pi$
$19$	2.14944	−	3.72293i	0.493114	−	0.854099i	0.999969	+	0.00793257i	$0.00252504\pi$
$20$	−13.0217	+	16.3287i	−2.91174	+	3.65121i
$21$	0.420422	−	2.31772i	0.0917436	−	0.505767i
$22$	−6.89988	−	8.65217i	−1.47106	−	1.84465i
$23$	3.46323	−	0.521998i	0.722134	−	0.108844i	0.222316	−	0.974975i	$-0.428638\pi$
$23$	3.46323	−	0.521998i	0.722134	−	0.108844i	0.499818	+	0.866131i	$0.333400\pi$
$24$	7.71701	+	5.26137i	1.57523	+	1.07397i
$25$	6.71355	+	4.57722i	1.34271	+	0.915445i
$26$	−2.75541	+	0.415311i	−0.540380	+	0.0814492i
$27$	−2.89060	−	3.62469i	−0.556295	−	0.697572i
$28$	4.05875	+	14.7022i	0.767031	+	2.77845i
$29$	1.94642	−	2.44074i	0.361442	−	0.453234i	−0.567547	−	0.823341i	$-0.692108\pi$
$29$	1.94642	−	2.44074i	0.361442	−	0.453234i	0.928989	+	0.370107i	$0.120679\pi$
$30$	4.49400	−	7.78383i	0.820488	−	1.42113i
$31$	−0.354521	−	0.614048i	−0.0636738	−	0.110286i	0.832431	−	0.554128i	$-0.186948\pi$
$31$	−0.354521	−	0.614048i	−0.0636738	−	0.110286i	−0.896105	+	0.443842i	$0.853615\pi$
$32$	−28.0321	−	4.22515i	−4.95542	−	0.746909i
$33$	2.59193	+	2.40496i	0.451198	+	0.418650i
$34$	−1.50520	+	0.724867i	−0.258140	+	0.124314i
$35$	9.02323	−	3.23410i	1.52520	−	0.546662i
$36$	11.4647	+	5.52110i	1.91078	+	0.920184i
$37$	−0.299117	−	0.762138i	−0.0491745	−	0.125295i	0.904176	−	0.427160i	$-0.140486\pi$
$37$	−0.299117	−	0.762138i	−0.0491745	−	0.125295i	−0.953351	+	0.301865i	$0.902391\pi$
$38$	−0.895188	−	11.9455i	−0.145219	−	1.93781i
$39$	0.850756	−	0.262424i	0.136230	−	0.0420214i
$40$	−2.84024	+	37.9003i	−0.449081	+	5.99257i
$41$	1.60713	+	7.04130i	0.250992	+	1.09967i	0.930585	+	0.366077i	$0.119299\pi$
$41$	1.60713	+	7.04130i	0.250992	+	1.09967i	−0.679593	+	0.733590i	$0.737844\pi$
$42$	−2.67019	−	5.99612i	−0.412019	−	0.925221i
$43$	−0.644964	+	2.82577i	−0.0983561	+	0.430926i	−0.999999	−	0.00155543i	$-0.999505\pi$
$43$	−0.644964	+	2.82577i	−0.0983561	+	0.430926i	0.901643	+	0.432482i	$0.142362\pi$
$44$	−21.8773	−	6.74825i	−3.29812	−	1.01734i
$45$	2.92164	−	7.44421i	0.435532	−	1.10972i
$46$	7.15416	−	6.63809i	1.05482	−	0.978733i
$47$	7.11986	−	4.85424i	1.03854	−	0.708063i	0.0811012	−	0.996706i	$-0.474156\pi$
$47$	7.11986	−	4.85424i	1.03854	−	0.708063i	0.957437	+	0.288643i	$0.0932039\pi$
$48$	15.7612			2.27493
$49$	1.96197	−	6.71942i	0.280282	−	0.959918i
$50$	22.6418			3.20204
$51$	0.441030	−	0.300689i	0.0617565	−	0.0421049i
$52$	−4.22587	+	3.92104i	−0.586023	+	0.543750i
$53$	0.911887	−	2.32345i	0.125257	−	0.319151i	−0.854465	−	0.519508i	$-0.826115\pi$
$53$	0.911887	−	2.32345i	0.125257	−	0.319151i	0.979723	+	0.200358i	$0.0642104\pi$
$54$	−12.3449	−	3.80788i	−1.67992	−	0.518187i
$55$	−3.20166	+	14.0274i	−0.431712	+	1.89145i
$56$	21.1742	+	17.9452i	2.82952	+	2.39803i
$57$	0.851661	+	3.73137i	0.112805	+	0.494232i
$58$	0.650082	−	8.67474i	0.0853599	−	1.13905i
$59$	7.00113	−	2.15956i	0.911469	−	0.281151i	0.196661	−	0.980472i	$-0.436990\pi$
$59$	7.00113	−	2.15956i	0.911469	−	0.281151i	0.714808	+	0.699320i	$0.246514\pi$
$60$	−1.38955	−	18.5423i	−0.179391	−	2.39380i
$61$	−1.62455	−	4.13928i	−0.208002	−	0.529980i	0.788359	−	0.615215i	$-0.210931\pi$
$61$	−1.62455	−	4.13928i	−0.208002	−	0.529980i	−0.996361	+	0.0852355i	$0.972836\pi$
$62$	−1.78010	−	0.857253i	−0.226073	−	0.108871i
$63$	−3.14439	−	4.92133i	−0.396156	−	0.620029i
$64$	−39.2720	+	18.9124i	−4.90900	+	2.36405i
$65$	2.65578	+	2.46420i	0.329409	+	0.305647i
$66$	9.74262	+	1.46846i	1.19923	+	0.180755i
$67$	−6.97165	−	12.0753i	−0.851723	−	1.47523i	−0.879652	−	0.475618i	$-0.842225\pi$
$67$	−6.97165	−	12.0753i	−0.851723	−	1.47523i	0.0279292	−	0.999610i	$-0.491109\pi$
$68$	−1.72812	+	2.99318i	−0.209565	+	0.362977i
$69$	−1.94415	+	2.43789i	−0.234048	+	0.293488i
$70$	15.6980	−	21.6098i	1.87627	−	2.58287i
$71$	8.29122	+	10.3969i	0.983987	+	1.23388i	0.972249	+	0.233950i	$0.0751651\pi$
$71$	8.29122	+	10.3969i	0.983987	+	1.23388i	0.0117383	+	0.999931i	$0.496264\pi$
$72$	22.8979	−	3.45130i	2.69854	−	0.406739i
$73$	−9.49640	−	6.47453i	−1.11147	−	0.757787i	−0.138878	−	0.990309i	$-0.544350\pi$
$73$	−9.49640	−	6.47453i	−1.11147	−	0.757787i	−0.972591	+	0.232523i	$0.925302\pi$
$74$	−1.88500	−	1.28517i	−0.219127	−	0.149398i
$75$	−7.15336	+	1.07820i	−0.825999	+	0.124499i
$76$	−15.4513	−	19.3753i	−1.77239	−	2.22250i
$77$	6.91385	+	7.91233i	0.787906	+	0.901694i
$78$	1.54680	−	1.93963i	0.175141	−	0.219620i
$79$	−8.59524	+	14.8874i	−0.967040	+	1.67496i	−0.263007	+	0.964794i	$0.584714\pi$
$79$	−8.59524	+	14.8874i	−0.967040	+	1.67496i	−0.704033	+	0.710168i	$0.748619\pi$
$80$	32.0681	+	55.5437i	3.58533	+	6.20997i
$81$	−2.46656	−	0.371775i	−0.274063	−	0.0413083i
$82$	14.7530	+	13.6888i	1.62919	+	1.51167i
$83$	−4.85228	+	2.33673i	−0.532607	+	0.256490i	−0.680801	−	0.732468i	$-0.738368\pi$
$83$	−4.85228	+	2.33673i	−0.532607	+	0.256490i	0.148194	+	0.988958i	$0.452654\pi$
$84$	−11.5520	−	7.13746i	−1.26043	−	0.778760i
$85$	1.95699	+	0.942435i	0.212265	+	0.102221i
$86$	2.95072	+	7.51830i	0.318184	+	0.810719i
$87$	0.207704	+	2.77162i	0.0222682	+	0.297149i
$88$	−39.8120	+	12.2804i	−4.24397	+	1.30909i
$89$	1.00374	−	13.3939i	0.106396	−	1.41975i	−0.647152	−	0.762361i	$-0.724040\pi$
$89$	1.00374	−	13.3939i	0.106396	−	1.41975i	0.753548	−	0.657393i	$-0.228341\pi$
$90$	−4.95864	−	21.7252i	−0.522687	−	2.29004i
$91$	2.59584	−	0.511504i	0.272118	−	0.0536202i
$92$	4.49275	−	19.6840i	0.468401	−	2.05220i
$93$	0.603221	+	0.186069i	0.0625511	+	0.0192945i
$94$	8.77260	−	22.3522i	0.904825	−	2.30546i
$95$	−11.4168	+	10.5933i	−1.17134	+	1.08685i
$96$	20.8536	−	14.2177i	2.12836	−	1.45109i
$97$	8.83567			0.897126			0.448563	−	0.893751i	$-0.351936\pi$
$97$	8.83567			0.897126			0.448563	+	0.893751i	$0.351936\pi$
$98$	−6.03042	−	18.5501i	−0.609164	−	1.87385i
$99$	8.76634			0.881051
$100$	38.7021	−	26.3866i	3.87021	−	2.63866i
$101$	−0.677254	+	0.628400i	−0.0673893	+	0.0625281i	−0.713148	−	0.701013i	$-0.752731\pi$
$101$	−0.677254	+	0.628400i	−0.0673893	+	0.0625281i	0.645759	+	0.763541i	$0.276541\pi$
$102$	0.543407	−	1.38458i	0.0538053	−	0.137094i
$103$	2.78741	+	0.859803i	0.274652	+	0.0847189i	0.429021	−	0.903294i	$-0.358858\pi$
$103$	2.78741	+	0.859803i	0.274652	+	0.0847189i	−0.154370	+	0.988013i	$0.549335\pi$
$104$	−2.33439	+	10.2276i	−0.228906	+	1.00290i
$105$	−3.93050	+	7.57486i	−0.383578	+	0.739231i
$106$	−1.54767	−	6.78078i	−0.150323	−	0.658607i
$107$	0.889085	−	11.8640i	0.0859511	−	1.14694i	−0.772836	−	0.634605i	$-0.781163\pi$
$107$	0.889085	−	11.8640i	0.0859511	−	1.14694i	0.858787	−	0.512332i	$-0.171218\pi$
$108$	−25.5390	+	7.87773i	−2.45749	+	0.758035i
$109$	−0.0811924	−	1.08344i	−0.00777683	−	0.103775i	0.991965	−	0.126516i	$-0.0403795\pi$
$109$	−0.0811924	−	1.08344i	−0.00777683	−	0.103775i	−0.999741	+	0.0227416i	$0.992760\pi$
$110$	14.6476	+	37.3216i	1.39660	+	3.55847i
$111$	0.656741	+	0.316270i	0.0623351	+	0.0300190i
$112$	46.5815	+	4.89234i	4.40154	+	0.462283i
$113$	−3.65106	+	1.75826i	−0.343463	+	0.165403i	−0.597660	−	0.801749i	$-0.703903\pi$
$113$	−3.65106	+	1.75826i	−0.343463	+	0.165403i	0.254198	+	0.967152i	$0.418189\pi$
$114$	7.81799	+	7.25403i	0.732222	+	0.679402i
$115$	−12.5470	−	1.89115i	−1.17001	−	0.176351i
$116$	−8.99829	−	15.5855i	−0.835470	−	1.44708i
$117$	1.10367	−	1.91162i	0.102035	−	0.176729i
$118$	12.7291	−	15.9618i	1.17181	−	1.46940i
$119$	1.39678	−	0.751777i	0.128043	−	0.0689153i
$120$	−21.0975	−	26.4554i	−1.92593	−	2.41503i
$121$	−4.71902	+	0.711278i	−0.429002	+	0.0646617i
$122$	−10.2377	−	6.97996i	−0.926880	−	0.631936i
$123$	−5.31285	−	3.62224i	−0.479044	−	0.326606i
$124$	−4.04180	+	0.609204i	−0.362965	+	0.0547081i
$125$	−7.05988	−	8.85281i	−0.631455	−	0.791820i
$126$	−14.9645	−	6.39480i	−1.33315	−	0.569694i
$127$	−10.5019	+	13.1689i	−0.931890	+	1.16855i	0.0535557	+	0.998565i	$0.482945\pi$
$127$	−10.5019	+	13.1689i	−0.931890	+	1.16855i	−0.985446	+	0.169989i	$0.945627\pi$
$128$	−32.3818	+	56.0870i	−2.86218	+	4.95744i
$129$	−1.29026	−	2.23479i	−0.113601	−	0.196762i
$130$	9.98259	+	1.50463i	0.875531	+	0.131965i
$131$	12.3690	+	11.4768i	1.08069	+	1.00273i	0.999982	+	0.00599124i	$0.00190708\pi$
$131$	12.3690	+	11.4768i	1.08069	+	1.00273i	0.0807032	+	0.996738i	$0.474283\pi$
$132$	18.3646	−	8.84391i	1.59843	−	0.769764i
$133$	1.35882	+	11.2923i	0.117824	+	0.979165i
$134$	−35.0058	−	16.8579i	−3.02404	−	1.45630i
$135$	6.13640	+	15.6353i	0.528137	+	1.34567i
$136$	0.470023	+	6.27202i	0.0403041	+	0.537821i
$137$	18.2059	−	5.61577i	1.55543	−	0.479787i	0.606452	−	0.795120i	$-0.292592\pi$
$137$	18.2059	−	5.61577i	1.55543	−	0.479787i	0.948981	+	0.315333i	$0.102116\pi$
$138$	−0.649323	+	8.66461i	−0.0552740	+	0.737581i
$139$	1.47027	+	6.44168i	0.124707	+	0.546376i	0.998223	+	0.0595817i	$0.0189767\pi$
$139$	1.47027	+	6.44168i	0.124707	+	0.546376i	−0.873517	+	0.486794i	$0.838166\pi$
$140$	1.64885	−	55.2324i	0.139353	−	4.66799i
$141$	−1.70718	+	7.47962i	−0.143770	+	0.629898i
$142$	35.4093	+	10.9223i	2.97148	+	0.916581i
$143$	−1.45093	+	3.69691i	−0.121333	+	0.309151i
$144$	28.6452	−	26.5789i	2.38710	−	2.21491i
$145$	−9.34481	+	6.37119i	−0.776045	+	0.529098i
$146$	−32.0271			−2.65058
$147$	2.78858	+	5.57349i	0.229998	+	0.459694i
$148$	−4.71981			−0.387966
$149$	−3.22786	+	2.20072i	−0.264436	+	0.180290i	−0.688279	−	0.725446i	$-0.741633\pi$
$149$	−3.22786	+	2.20072i	−0.264436	+	0.180290i	0.423842	+	0.905736i	$0.360681\pi$
$150$	−14.7770	+	13.7111i	−1.20654	+	1.11951i
$151$	3.10681	−	7.91602i	0.252828	−	0.644196i	−0.746958	−	0.664871i	$-0.768486\pi$
$151$	3.10681	−	7.91602i	0.252828	−	0.644196i	0.999786	+	0.0206751i	$0.00658156\pi$
$152$	−43.0944	−	13.2929i	−3.49542	−	1.07819i
$153$	0.294485	−	1.29022i	0.0238077	−	0.104308i
$154$	28.3381	+	7.36414i	2.28355	+	0.593419i
$155$	0.571609	+	2.50438i	0.0459128	+	0.201157i
$156$	0.383547	−	5.11808i	0.0307083	−	0.409774i
$157$	3.82693	−	1.18045i	0.305422	−	0.0942103i	−0.138256	−	0.990397i	$-0.544150\pi$
$157$	3.82693	−	1.18045i	0.305422	−	0.0942103i	0.443678	+	0.896186i	$0.353673\pi$
$158$	3.57971	+	47.7679i	0.284786	+	3.80021i
$159$	0.811863	+	2.06859i	0.0643849	+	0.164050i
$160$	92.5337	+	44.5619i	7.31543	+	3.52293i
$161$	−6.50260	+	6.60162i	−0.512477	+	0.520280i
$162$	−6.26245	+	3.01584i	−0.492024	+	0.236946i
$163$	1.00821	+	0.935484i	0.0789693	+	0.0732728i	0.718670	−	0.695351i	$-0.244751\pi$
$163$	1.00821	+	0.935484i	0.0789693	+	0.0732728i	−0.639701	+	0.768624i	$0.720942\pi$
$164$	41.1703	+	6.20543i	3.21486	+	0.484562i
$165$	−6.40496	−	11.0937i	−0.498625	−	0.863644i
$166$	−7.50361	+	12.9966i	−0.582393	+	1.00873i
$167$	−7.67510	+	9.62428i	−0.593917	+	0.744749i	−0.984416	−	0.175855i	$-0.943731\pi$
$167$	−7.67510	+	9.62428i	−0.593917	+	0.744749i	0.390499	+	0.920603i	$0.372303\pi$
$168$	−24.6862	+	1.11053i	−1.90458	+	0.0856795i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	5.98500	−	0.902094i	0.459029	−	0.0691874i
$171$	7.84027	+	5.34540i	0.599560	+	0.408773i
$172$	13.8055	+	9.41243i	1.05266	+	0.717691i
$173$	−20.8466	+	3.14212i	−1.58494	+	0.238891i	−0.881611	−	0.471977i	$-0.843540\pi$
$173$	−20.8466	+	3.14212i	−1.58494	+	0.238891i	−0.703326	+	0.710868i	$0.748302\pi$
$174$	4.82884	+	6.05518i	0.366074	+	0.459042i
$175$	−21.4762	+	0.966128i	−1.62345	+	0.0730324i
$176$	−43.8353	+	54.9677i	−3.30421	+	4.14335i
$177$	−3.26149	+	5.64906i	−0.245148	+	0.424610i
$178$	−18.7136	−	32.4130i	−1.40265	−	2.42946i
$179$	16.5220	+	2.49030i	1.23491	+	0.186133i	0.733871	−	0.679289i	$-0.237712\pi$
$179$	16.5220	+	2.49030i	1.23491	+	0.186133i	0.501043	+	0.865422i	$0.332950\pi$
$180$	−33.7943	−	31.3566i	−2.51888	−	2.33718i
$181$	5.23025	−	2.51875i	0.388761	−	0.187218i	−0.229285	−	0.973359i	$-0.573639\pi$
$181$	5.23025	−	2.51875i	0.388761	−	0.187218i	0.618046	+	0.786142i	$0.287924\pi$
$182$	5.17359	−	5.25237i	0.383492	−	0.389331i
$183$	3.56685	+	1.71770i	0.263669	+	0.126976i
$184$	−13.4233	−	34.2021i	−0.989581	−	2.52141i
$185$	0.221664	+	2.95790i	0.0162971	+	0.217469i
$186$	1.68090	−	0.518488i	0.123249	−	0.0380174i
$187$	−0.177936	+	2.37439i	−0.0130120	+	0.173633i
$188$	−11.0540	−	48.4306i	−0.806194	−	3.53217i
$189$	11.8718	+	3.08509i	0.863547	+	0.224407i
$190$	−9.65710	+	42.3105i	−0.700599	+	3.06953i
$191$	12.0757	+	3.72486i	0.873767	+	0.269522i	0.699029	−	0.715093i	$-0.253616\pi$
$191$	12.0757	+	3.72486i	0.873767	+	0.269522i	0.174738	+	0.984615i	$0.444092\pi$
$192$	14.1779	−	36.1248i	1.02320	−	2.60708i
$193$	0.303765	−	0.281853i	0.0218655	−	0.0202882i	−0.669164	−	0.743114i	$-0.733348\pi$
$193$	0.303765	−	0.281853i	0.0218655	−	0.0202882i	0.691030	+	0.722826i	$0.257157\pi$
$194$	20.3427	−	13.8694i	1.46052	−	0.995767i
$195$	−3.22551			−0.230984
$196$	−31.9261	−	24.6803i	−2.28044	−	1.76288i
$197$	−3.23112			−0.230208			−0.115104	−	0.993353i	$-0.536720\pi$
$197$	−3.23112			−0.230208			−0.115104	+	0.993353i	$0.536720\pi$
$198$	20.1831	−	13.7606i	1.43435	−	0.977925i
$199$	0.407065	−	0.377701i	0.0288560	−	0.0267745i	−0.665613	−	0.746297i	$-0.731830\pi$
$199$	0.407065	−	0.377701i	0.0288560	−	0.0267745i	0.694469	+	0.719523i	$0.255639\pi$
$200$	31.1421	−	79.3487i	2.20208	−	5.61080i
$201$	11.8624	+	3.65905i	0.836706	+	0.258090i
$202$	−0.572864	+	2.50988i	−0.0403066	+	0.176595i
$203$	−0.246463	+	8.25589i	−0.0172983	+	0.579450i
$204$	−0.684723	−	2.99997i	−0.0479402	−	0.210040i
$205$	1.95539	−	26.0928i	0.136570	−	1.82240i
$206$	7.76721	−	2.39587i	0.541167	−	0.166928i
$207$	0.577731	+	7.70929i	0.0401551	+	0.535832i
$208$	6.46763	+	16.4793i	0.448450	+	1.14263i
$209$	−15.3820	−	7.40757i	−1.06399	−	0.512392i
$210$	2.84098	+	23.6097i	0.196046	+	1.62922i
$211$	6.51633	−	3.13810i	0.448603	−	0.216036i	−0.195922	−	0.980620i	$-0.562770\pi$
$211$	6.51633	−	3.13810i	0.448603	−	0.216036i	0.644524	+	0.764584i	$0.277055\pi$
$212$	−10.5477	−	9.78687i	−0.724421	−	0.672165i
$213$	−11.7072	−	1.76457i	−0.802163	−	0.120907i
$214$	−16.5761	−	28.7106i	−1.13312	−	1.96262i
$215$	5.25039	−	9.09395i	0.358074	−	0.620202i
$216$	−30.3242	+	38.0254i	−2.06330	+	2.58730i
$217$	1.72504	+	0.737163i	0.117103	+	0.0500419i
$218$	−1.88762	−	2.36700i	−0.127845	−	0.160313i
$219$	10.1185	−	1.52512i	0.683746	−	0.103058i
$220$	68.5318	+	46.7242i	4.62041	+	3.15014i
$221$	0.495366	+	0.337735i	0.0333220	+	0.0227185i
$222$	2.00849	−	0.302732i	0.134801	−	0.0203180i
$223$	−5.62961	−	7.05931i	−0.376987	−	0.472726i	0.556754	−	0.830678i	$-0.312047\pi$
$223$	−5.62961	−	7.05931i	−0.376987	−	0.472726i	−0.933740	+	0.357951i	$0.883475\pi$
$224$	66.0452	−	35.5469i	4.41283	−	2.37508i
$225$	−11.1827	+	14.0227i	−0.745514	+	0.934845i
$226$	−5.64603	+	9.77922i	−0.375569	+	0.650504i
$227$	−8.55609	−	14.8196i	−0.567887	−	0.983610i	−0.996775	−	0.0802518i	$-0.974428\pi$
$227$	−8.55609	−	14.8196i	−0.567887	−	0.983610i	0.428887	−	0.903358i	$-0.358906\pi$
$228$	21.8172	+	3.28842i	1.44488	+	0.217781i
$229$	−10.6885	−	9.91745i	−0.706314	−	0.655364i	0.242880	−	0.970056i	$-0.421908\pi$
$229$	−10.6885	−	9.91745i	−0.706314	−	0.655364i	−0.949194	+	0.314693i	$0.898098\pi$
$230$	−31.8559	+	15.3410i	−2.10052	+	1.01156i
$231$	−9.30371	−	0.977146i	−0.612139	−	0.0642915i
$232$	−29.5067	−	14.2097i	−1.93721	−	0.932910i
$233$	−4.15976	−	10.5989i	−0.272515	−	0.694357i	−0.999966	−	0.00819759i	$-0.997391\pi$
$233$	−4.15976	−	10.5989i	−0.272515	−	0.694357i	0.727451	−	0.686159i	$-0.240705\pi$
$234$	−0.459653	−	6.13365i	−0.0300485	−	0.400969i
$235$	−29.8323	+	9.20204i	−1.94604	+	0.600275i
$236$	3.15632	−	42.1182i	0.205459	−	2.74166i
$237$	−3.40565	−	14.9211i	−0.221221	−	0.969232i
$238$	2.03580	−	3.92339i	0.131961	−	0.254316i
$239$	−0.666439	+	2.91986i	−0.0431083	+	0.188870i	−0.991898	−	0.127040i	$-0.959452\pi$
$239$	−0.666439	+	2.91986i	−0.0431083	+	0.188870i	0.948789	+	0.315910i	$0.102310\pi$
$240$	−54.5644	−	16.8309i	−3.52211	−	1.08643i
$241$	6.70198	−	17.0764i	0.431712	−	1.09998i	−0.535166	−	0.844747i	$-0.679751\pi$
$241$	6.70198	−	17.0764i	0.431712	−	1.09998i	0.966878	−	0.255238i	$-0.0821538\pi$
$242$	−9.74830	+	9.04510i	−0.626645	+	0.581441i
$243$	13.3266	−	9.08595i	0.854904	−	0.582864i
$244$	−25.6339			−1.64104
$245$	−13.9677	+	21.1672i	−0.892365	+	1.35232i
$246$	−17.9179			−1.14240
$247$	−3.55189	+	2.42164i	−0.226002	+	0.154085i
$248$	−5.45266	+	5.05933i	−0.346244	+	0.321268i
$249$	1.75177	−	4.46343i	0.111014	−	0.282858i
$250$	−30.1506	−	9.30023i	−1.90689	−	0.588198i
$251$	−0.166453	+	0.729278i	−0.0105064	+	0.0460316i	−0.979909	−	0.199443i	$-0.936087\pi$
$251$	−0.166453	+	0.729278i	−0.0105064	+	0.0460316i	0.969403	+	0.245475i	$0.0789438\pi$
$252$	−33.0316	+	6.50881i	−2.08080	+	0.410016i
$253$	−3.09513	−	13.5606i	−0.194589	−	0.852550i
$254$	−3.50749	+	46.8043i	−0.220080	+	2.93676i
$255$	−1.84792	+	0.570008i	−0.115721	+	0.0356953i
$256$	6.97149	+	93.0280i	0.435718	+	5.81425i
$257$	−5.18305	−	13.2062i	−0.323310	−	0.823780i	−0.996444	−	0.0842593i	$-0.973148\pi$
$257$	−5.18305	−	13.2062i	−0.323310	−	0.823780i	0.673134	−	0.739520i	$-0.264948\pi$
$258$	−6.47859	−	3.11992i	−0.403339	−	0.194238i
$259$	1.84280	+	1.13858i	0.114506	+	0.0707478i
$260$	18.8169	−	9.06175i	1.16698	−	0.561986i
$261$	5.05142	+	4.68703i	0.312675	+	0.290120i
$262$	46.4929	+	7.00767i	2.87234	+	0.432935i
$263$	−8.90535	−	15.4245i	−0.549127	−	0.951117i	−0.998335	−	0.0576889i	$-0.981627\pi$
$263$	−8.90535	−	15.4245i	−0.549127	−	0.951117i	0.449207	−	0.893428i	$-0.351706\pi$
$264$	18.5465	−	32.1235i	1.14146	−	1.97706i
$265$	−5.63805	+	7.06989i	−0.346343	+	0.434300i
$266$	20.8541	+	23.8658i	1.27865	+	1.46330i
$267$	7.45581	+	9.34929i	0.456288	+	0.572167i
$268$	−79.4821	+	11.9800i	−4.85514	+	0.731795i
$269$	12.9297	+	8.81529i	0.788335	+	0.537478i	0.889252	−	0.457417i	$-0.151225\pi$
$269$	12.9297	+	8.81529i	0.788335	+	0.537478i	−0.100917	+	0.994895i	$0.532178\pi$
$270$	38.6709	+	26.3654i	2.35344	+	1.60455i
$271$	14.2607	−	2.14945i	0.866274	−	0.130570i	0.299154	−	0.954205i	$-0.403296\pi$
$271$	14.2607	−	2.14945i	0.866274	−	0.130570i	0.567120	+	0.823635i	$0.308058\pi$
$272$	6.61755	+	8.29815i	0.401248	+	0.503149i
$273$	−1.38441	+	1.90578i	−0.0837881	+	0.115343i
$274$	33.1010	−	41.5074i	1.99971	−	2.50755i
$275$	16.1348	−	27.9464i	0.972968	−	1.68523i
$276$	8.98779	+	15.5673i	0.541001	+	0.937042i
$277$	−13.5068	−	2.03582i	−0.811545	−	0.122321i	−0.269857	−	0.962900i	$-0.586976\pi$
$277$	−13.5068	−	2.03582i	−0.811545	−	0.122321i	−0.541688	+	0.840580i	$0.682215\pi$
$278$	13.4966	+	12.5230i	0.809474	+	0.751082i
$279$	1.41011	−	0.679071i	0.0844209	−	0.0406549i
$280$	−54.1408	−	84.7366i	−3.23553	−	5.06398i
$281$	27.2301	+	13.1133i	1.62441	+	0.782276i	0.999999	+	0.00118109i	$0.000375954\pi$
$281$	27.2301	+	13.1133i	1.62441	+	0.782276i	0.624413	+	0.781095i	$0.285338\pi$
$282$	7.81034	+	19.9004i	0.465099	+	1.18505i
$283$	1.41278	+	18.8523i	0.0839812	+	1.12065i	0.866885	+	0.498508i	$0.166119\pi$
$283$	1.41278	+	18.8523i	0.0839812	+	1.12065i	−0.782904	+	0.622143i	$0.786262\pi$
$284$	73.2546	−	22.5960i	4.34686	−	1.34083i
$285$	1.03621	−	13.8273i	0.0613799	−	0.819058i
$286$	2.46254	+	10.7891i	0.145613	+	0.637972i
$287$	−14.5776	−	12.3545i	−0.860486	−	0.729265i
$288$	13.9243	−	61.0065i	0.820500	−	3.59484i
$289$	−15.9013	−	4.90489i	−0.935368	−	0.288523i
$290$	−11.5140	+	29.3373i	−0.676128	+	1.72275i
$291$	−5.76654	+	5.35057i	−0.338041	+	0.313656i
$292$	−54.7445	+	37.3242i	−3.20368	+	2.18423i
$293$	−9.23444			−0.539481			−0.269741	−	0.962933i	$-0.586938\pi$
$293$	−9.23444			−0.539481			−0.269741	+	0.962933i	$0.586938\pi$
$294$	15.1690	+	8.45482i	0.884676	+	0.493095i
$295$	−26.5437			−1.54543
$296$	−7.09660	+	4.83838i	−0.412482	+	0.281225i
$297$	−13.4971	+	12.5235i	−0.783181	+	0.726686i
$298$	−3.97715	+	10.1336i	−0.230390	+	0.587024i
$299$	−3.34675	−	1.03234i	−0.193548	−	0.0597015i
$300$	−9.27985	+	40.6577i	−0.535772	+	2.34737i
$301$	−3.11962	−	7.00534i	−0.179812	−	0.403781i
$302$	−5.27292	−	23.1022i	−0.303422	−	1.32938i
$303$	0.0614687	−	0.820242i	0.00353128	−	0.0471217i
$304$	−72.7219	+	22.4317i	−4.17089	+	1.28655i
$305$	1.20389	+	16.0648i	0.0689344	+	0.919866i
$306$	−1.34727	−	3.43279i	−0.0770182	−	0.196239i
$307$	21.7924	+	10.4947i	1.24376	+	0.598964i	0.935832	−	0.352446i	$-0.114650\pi$
$307$	21.7924	+	10.4947i	1.24376	+	0.598964i	0.307928	+	0.951410i	$0.400364\pi$
$308$	57.0210	−	20.4374i	3.24907	−	1.16453i
$309$	−2.33985	+	1.12681i	−0.133110	+	0.0641022i
$310$	5.24720	+	4.86869i	0.298021	+	0.276523i
$311$	10.2635	+	1.54697i	0.581989	+	0.0877207i	0.433437	−	0.901184i	$-0.357301\pi$
$311$	10.2635	+	1.54697i	0.581989	+	0.0877207i	0.148552	+	0.988905i	$0.452539\pi$
$312$	−4.66997	−	8.08862i	−0.264385	−	0.457928i
$313$	4.04084	−	6.99894i	0.228402	−	0.395603i	−0.728933	−	0.684585i	$-0.759983\pi$
$313$	4.04084	−	6.99894i	0.228402	−	0.395603i	0.957335	+	0.288982i	$0.0933167\pi$
$314$	6.95793	−	8.72497i	0.392659	−	0.492379i
$315$	5.63038	+	20.3952i	0.317236	+	1.14914i
$316$	61.7872	+	77.4788i	3.47580	+	4.35852i
$317$	8.44336	−	1.27263i	0.474227	−	0.0714781i	0.0924194	−	0.995720i	$-0.470540\pi$
$317$	8.44336	−	1.27263i	0.474227	−	0.0714781i	0.381807	+	0.924242i	$0.375302\pi$
$318$	5.11628	+	3.48822i	0.286907	+	0.195610i
$319$	−10.2438	−	6.98411i	−0.573543	−	0.391035i
$320$	156.154	−	23.5364i	8.72925	−	1.31572i
$321$	6.60417	+	8.28137i	0.368609	+	0.462221i
$322$	−4.60859	+	25.4064i	−0.256827	+	1.41584i
$323$	−1.60696	+	2.01506i	−0.0894136	+	0.112121i
$324$	−7.18989	+	12.4532i	−0.399438	+	0.691847i
$325$	−4.06272	−	7.03684i	−0.225359	−	0.390334i
$326$	3.78969	+	0.571203i	0.209891	+	0.0316360i
$327$	0.709082	+	0.657932i	0.0392123	+	0.0363837i
$328$	68.2641	−	32.8743i	3.76926	−	1.81518i
$329$	−7.36720	+	21.5758i	−0.406167	+	1.18951i
$330$	−32.1603	−	15.4876i	−1.77037	−	0.852564i
$331$	3.02675	+	7.71203i	0.166365	+	0.423892i	0.989607	−	0.143800i	$-0.0459320\pi$
$331$	3.02675	+	7.71203i	0.166365	+	0.423892i	−0.823242	+	0.567691i	$0.807837\pi$
$332$	2.32014	+	30.9601i	0.127334	+	1.69915i
$333$	1.72694	−	0.532690i	0.0946357	−	0.0291912i
$334$	−2.56339	+	34.2061i	−0.140262	+	1.87167i
$335$	11.2407	+	49.2487i	0.614145	+	2.69075i
$336$	−33.3638	+	25.0152i	−1.82014	+	1.36469i
$337$	−0.720109	+	3.15500i	−0.0392268	+	0.171864i	−0.990747	−	0.135723i	$-0.956664\pi$
$337$	−0.720109	+	3.15500i	−0.0392268	+	0.171864i	0.951520	+	0.307587i	$0.0995215\pi$
$338$	2.66274	+	0.821345i	0.144834	+	0.0446753i
$339$	1.31810	−	3.35847i	0.0715895	−	0.182407i
$340$	9.17898	−	8.51685i	0.497800	−	0.461891i
$341$	−2.32662	+	1.58626i	−0.125993	+	0.0859008i
$342$	26.4417			1.42980
$343$	6.51150	+	17.3378i	0.351588	+	0.936155i
$344$	30.4065			1.63941
$345$	9.33391	−	6.36375i	0.502521	−	0.342613i
$346$	−43.0637	+	39.9573i	−2.31512	+	2.14812i
$347$	−9.53287	+	24.2894i	−0.511751	+	1.30392i	0.408559	+	0.912732i	$0.366031\pi$
$347$	−9.53287	+	24.2894i	−0.511751	+	1.30392i	−0.920310	+	0.391189i	$0.872064\pi$
$348$	15.3107	+	4.72273i	0.820740	+	0.253165i
$349$	1.73350	−	7.59496i	0.0927922	−	0.406549i	−0.907105	−	0.420905i	$-0.861713\pi$
$349$	1.73350	−	7.59496i	0.0927922	−	0.406549i	0.999897	+	0.0143558i	$0.00456975\pi$
$350$	−47.9289	+	35.9357i	−2.56191	+	1.92085i
$351$	1.03164	+	4.51992i	0.0550650	+	0.241255i
$352$	−8.41350	+	112.270i	−0.448441	+	5.98403i
$353$	28.9051	−	8.91604i	1.53846	−	0.474553i	0.594359	−	0.804200i	$-0.297406\pi$
$353$	28.9051	−	8.91604i	1.53846	−	0.474553i	0.944104	+	0.329647i	$0.106930\pi$
$354$	1.35833	+	18.1257i	0.0721945	+	0.963368i
$355$	−17.6013	−	44.8474i	−0.934180	−	2.38025i
$356$	−69.7615	−	33.5954i	−3.69735	−	1.78055i
$357$	−0.456351	+	1.33649i	−0.0241527	+	0.0707343i
$358$	41.9484	−	20.2013i	2.21704	−	1.06767i
$359$	−4.49811	−	4.17364i	−0.237401	−	0.220276i	0.552496	−	0.833516i	$-0.313676\pi$
$359$	−4.49811	−	4.17364i	−0.237401	−	0.220276i	−0.789897	+	0.613240i	$0.789866\pi$
$360$	−82.9568	−	12.5037i	−4.37221	−	0.659004i
$361$	0.259849	+	0.450072i	0.0136763	+	0.0236880i
$362$	8.08810	−	14.0090i	0.425101	−	0.736297i
$363$	2.64912	−	3.32189i	0.139043	−	0.174354i
$364$	2.72224	−	15.0072i	0.142684	−	0.786593i
$365$	25.9621	+	32.5554i	1.35892	+	1.70403i
$366$	10.9084	−	1.64418i	0.570191	−	0.0859425i
$367$	4.62298	+	3.15190i	0.241318	+	0.164528i	0.677940	−	0.735117i	$-0.262873\pi$
$367$	4.62298	+	3.15190i	0.241318	+	0.164528i	−0.436622	+	0.899645i	$0.643825\pi$
$368$	−51.2285	−	34.9270i	−2.67047	−	1.82070i
$369$	−15.7642	+	2.37608i	−0.820654	+	0.123694i
$370$	5.15339	+	6.46215i	0.267912	+	0.335951i
$371$	1.75733	+	6.36565i	0.0912359	+	0.330488i
$372$	2.26895	−	2.84517i	0.117639	−	0.147515i
$373$	−16.3013	+	28.2348i	−0.844052	+	1.46194i	0.0423904	+	0.999101i	$0.486503\pi$
$373$	−16.3013	+	28.2348i	−0.844052	+	1.46194i	−0.886442	+	0.462839i	$0.846831\pi$
$374$	3.31744	+	5.74597i	0.171541	+	0.297117i
$375$	9.96854	+	1.50252i	0.514773	+	0.0775896i
$376$	−66.2678	−	61.4876i	−3.41750	−	3.17098i
$377$	−2.81266	+	1.35451i	−0.144860	+	0.0697607i
$378$	32.1757	−	11.5324i	1.65494	−	0.593160i
$379$	−5.28211	−	2.54373i	−0.271324	−	0.130663i	0.293275	−	0.956028i	$-0.405255\pi$
$379$	−5.28211	−	2.54373i	−0.271324	−	0.130663i	−0.564599	+	0.825366i	$0.690969\pi$
$380$	32.8013	+	83.5765i	1.68267	+	4.28738i
$381$	−1.12066	−	14.9542i	−0.0574132	−	0.766126i
$382$	33.6494	−	10.3795i	1.72165	−	0.531059i
$383$	−0.0631402	+	0.842548i	−0.00322631	+	0.0430522i	−0.998585	−	0.0531866i	$-0.983062\pi$
$383$	−0.0631402	+	0.842548i	−0.00322631	+	0.0430522i	0.995358	+	0.0962388i	$0.0306812\pi$
$384$	−12.8305	−	56.2141i	−0.654754	−	2.86866i
$385$	−15.4861	−	34.7752i	−0.789243	−	1.77231i
$386$	0.256944	−	1.12574i	0.0130781	−	0.0572988i
$387$	−6.11363	−	1.88581i	−0.310773	−	0.0958609i
$388$	18.6088	−	47.4146i	0.944721	−	2.40711i
$389$	0.381782	−	0.354242i	0.0193571	−	0.0179608i	−0.670435	−	0.741968i	$-0.733892\pi$
$389$	0.381782	−	0.354242i	0.0193571	−	0.0179608i	0.689792	+	0.724008i	$0.257702\pi$
$390$	−7.42623	+	5.06312i	−0.376042	+	0.256381i
$391$	−2.09981			−0.106192
$392$	−73.3038	−	4.38057i	−3.70240	−	0.221252i
$393$	−15.0225			−0.757784
$394$	−7.43914	+	5.07192i	−0.374779	+	0.255520i
$395$	45.6541	−	42.3608i	2.29711	−	2.13140i
$396$	18.4628	−	47.0426i	0.927793	−	2.36398i
$397$	−20.2322	−	6.24082i	−1.01543	−	0.313218i	−0.258005	−	0.966144i	$-0.583065\pi$
$397$	−20.2322	−	6.24082i	−1.01543	−	0.313218i	−0.757422	+	0.652926i	$0.773541\pi$
$398$	0.344321	−	1.50857i	0.0172593	−	0.0756178i
$399$	−7.72504	−	6.54699i	−0.386735	−	0.327759i
$400$	−32.0084	−	140.238i	−1.60042	−	7.01191i
$401$	1.62531	−	21.6882i	0.0811639	−	1.08306i	−0.796772	−	0.604279i	$-0.793461\pi$
$401$	1.62531	−	21.6882i	0.0811639	−	1.08306i	0.877936	−	0.478777i	$-0.158920\pi$
$402$	33.0549	−	10.1961i	1.64863	−	0.508534i
$403$	0.0529867	+	0.707059i	0.00263946	+	0.0352211i
$404$	1.94579	+	4.95780i	0.0968069	+	0.246660i
$405$	8.14211	+	3.92103i	0.404585	+	0.194838i
$406$	12.3919	+	19.3947i	0.615000	+	0.962545i
$407$	−2.92955	+	1.41079i	−0.145212	+	0.0699305i
$408$	−4.10487	−	3.80876i	−0.203221	−	0.188562i
$409$	−21.3946	−	3.22471i	−1.05789	−	0.159452i	−0.403020	−	0.915191i	$-0.632040\pi$
$409$	−21.3946	−	3.22471i	−1.05789	−	0.159452i	−0.654873	+	0.755739i	$0.727278\pi$
$410$	−36.4562	−	63.1440i	−1.80044	−	3.11846i
$411$	−8.48124	+	14.6899i	−0.418349	+	0.724601i
$412$	10.4845	−	13.1472i	0.516535	−	0.647714i
$413$	−11.3927	+	15.6832i	−0.560598	+	0.771720i
$414$	13.4315	+	16.8425i	0.660121	+	0.827766i
$415$	19.2937	−	2.90805i	0.947089	−	0.142751i
$416$	23.4228	+	15.9694i	1.14840	+	0.782964i
$417$	−4.86042	−	3.31378i	−0.238016	−	0.162276i
$418$	−47.0423	+	7.09049i	−2.30091	+	0.346807i
$419$	−15.8230	−	19.8414i	−0.773004	−	0.969316i	0.226985	−	0.973898i	$-0.427113\pi$
$419$	−15.8230	−	19.8414i	−0.773004	−	0.969316i	−0.999990	+	0.00458170i	$0.998542\pi$
$420$	32.3707	+	37.0456i	1.57953	+	1.80764i
$421$	6.16401	−	7.72942i	0.300415	−	0.376709i	−0.608596	−	0.793480i	$-0.708267\pi$
$421$	6.16401	−	7.72942i	0.300415	−	0.376709i	0.909011	+	0.416771i	$0.136838\pi$
$422$	10.0769	−	17.4537i	0.490536	−	0.849634i
$423$	9.51057	+	16.4728i	0.462420	+	0.800934i
$424$	−25.8921	−	3.90260i	−1.25743	−	0.189527i
$425$	−3.57110	−	3.31350i	−0.173224	−	0.160728i
$426$	−29.7238	+	14.3142i	−1.44012	+	0.693527i
$427$	10.0085	+	6.18378i	0.484345	+	0.299254i
$428$	−61.7930	−	29.7579i	−2.98688	−	1.43840i
$429$	−1.29178	−	3.29140i	−0.0623676	−	0.158910i
$430$	−2.18666	−	29.1790i	−0.105450	−	1.40713i
$431$	−22.5478	+	6.95508i	−1.08609	+	0.335015i	−0.785578	−	0.618763i	$-0.787634\pi$
$431$	−22.5478	+	6.95508i	−1.08609	+	0.335015i	−0.300513	+	0.953778i	$0.597158\pi$
$432$	−6.13339	+	81.8444i	−0.295093	+	3.93774i
$433$	−3.70965	−	16.2530i	−0.178274	−	0.781070i	−0.982427	−	0.186648i	$-0.940238\pi$
$433$	−3.70965	−	16.2530i	−0.178274	−	0.781070i	0.804153	−	0.594423i	$-0.202619\pi$
$434$	5.12877	−	1.01061i	0.246189	−	0.0485109i
$435$	2.24067	−	9.81701i	0.107432	−	0.470689i
$436$	−5.98502	−	1.84613i	−0.286630	−	0.0884138i
$437$	5.50063	−	14.0154i	0.263131	−	0.670447i
$438$	20.9023	−	19.3945i	0.998750	−	0.926704i
$439$	15.2149	−	10.3733i	0.726167	−	0.495092i	−0.142931	−	0.989733i	$-0.545653\pi$
$439$	15.2149	−	10.3733i	0.726167	−	0.495092i	0.869098	+	0.494640i	$0.164700\pi$
$440$	150.941			7.19583
$441$	14.4670	+	5.42705i	0.688904	+	0.258431i
$442$	1.67065			0.0794647
$443$	21.9161	−	14.9422i	1.04127	−	0.709924i	0.0832187	−	0.996531i	$-0.473480\pi$
$443$	21.9161	−	14.9422i	1.04127	−	0.709924i	0.958048	+	0.286608i	$0.0925276\pi$
$444$	3.08035	−	2.85815i	0.146187	−	0.135642i
$445$	−17.7779	+	45.2973i	−0.842751	+	2.14730i
$446$	−24.0424	−	7.41608i	−1.13844	−	0.351162i
$447$	0.773965	−	3.39096i	0.0366073	−	0.160387i
$448$	53.1156	−	102.364i	2.50948	−	4.83627i
$449$	−0.495476	−	2.17082i	−0.0233830	−	0.102447i	0.961890	−	0.273437i	$-0.0881606\pi$
$449$	−0.495476	−	2.17082i	−0.0233830	−	0.102447i	−0.985273	+	0.170990i	$0.945303\pi$
$450$	−3.73489	+	49.8386i	−0.176064	+	2.34941i
$451$	27.4089	−	8.45454i	1.29064	−	0.398109i
$452$	1.74577	+	23.2957i	0.0821140	+	1.09574i
$453$	2.76602	+	7.04771i	0.129959	+	0.331130i
$454$	−42.9615	−	20.6892i	−2.01628	−	0.970990i
$455$	−9.53287	−	1.00121i	−0.446908	−	0.0469377i
$456$	36.1750	−	17.4209i	1.69405	−	0.815810i
$457$	26.6001	+	24.6813i	1.24430	+	1.15454i	0.981863	+	0.189594i	$0.0607172\pi$
$457$	26.6001	+	24.6813i	1.24430	+	1.15454i	0.262439	+	0.964949i	$0.415473\pi$
$458$	−40.1760	−	6.05556i	−1.87730	−	0.282958i
$459$	1.38979	+	2.40719i	0.0648698	+	0.112358i
$460$	−36.5736	+	63.3474i	−1.70525	+	2.95359i
$461$	−14.9761	+	18.7795i	−0.697508	+	0.874647i	−0.996835	−	0.0795036i	$-0.974666\pi$
$461$	−14.9761	+	18.7795i	−0.697508	+	0.874647i	0.299327	+	0.954151i	$0.403238\pi$
$462$	−22.9542	+	12.3544i	−1.06792	+	0.574779i
$463$	−5.74256	−	7.20094i	−0.266879	−	0.334656i	0.630276	−	0.776371i	$-0.282942\pi$
$463$	−5.74256	−	7.20094i	−0.266879	−	0.334656i	−0.897155	+	0.441715i	$0.854370\pi$
$464$	−54.6483	+	8.23691i	−2.53699	+	0.382389i
$465$	−1.88962	−	1.28832i	−0.0876292	−	0.0597446i
$466$	−26.2144	−	17.8727i	−1.21436	−	0.827935i
$467$	26.1368	−	3.93948i	1.20947	−	0.182298i	0.486811	−	0.873507i	$-0.338160\pi$
$467$	26.1368	−	3.93948i	1.20947	−	0.182298i	0.722654	+	0.691210i	$0.242922\pi$
$468$	−7.93381	−	9.94868i	−0.366740	−	0.459878i
$469$	33.9230	+	14.4963i	1.56642	+	0.669378i
$470$	−54.2396	+	68.0143i	−2.50189	+	3.13726i
$471$	−1.78278	+	3.08787i	−0.0821462	+	0.142281i
$472$	−38.4305	−	66.5637i	−1.76891	−	3.06384i
$473$	11.3824	+	1.71562i	0.523364	+	0.0788845i
$474$	−31.2628	−	29.0077i	−1.43595	−	1.33237i
$475$	31.4710	−	15.1557i	1.44399	−	0.695389i
$476$	−1.09247	−	9.07883i	−0.0500732	−	0.416128i
$477$	4.96390	+	2.39049i	0.227281	+	0.109453i
$478$	3.04896	+	7.76863i	0.139456	+	0.355329i
$479$	0.691855	+	9.23216i	0.0316117	+	0.421828i	0.990450	+	0.137875i	$0.0440271\pi$
$479$	0.691855	+	9.23216i	0.0316117	+	0.421828i	−0.958838	+	0.283954i	$0.908354\pi$
$480$	−87.3767	+	26.9521i	−3.98818	+	1.23019i
$481$	−0.0611840	+	0.816444i	−0.00278975	+	0.0372267i
$482$	−11.3747	−	49.8358i	−0.518103	−	2.26996i
$483$	0.246175	−	8.24625i	0.0112014	−	0.375217i
$484$	−6.12185	+	26.8216i	−0.278266	+	1.21916i
$485$	−30.5886	−	9.43534i	−1.38896	−	0.428437i
$486$	16.4202	−	41.8379i	0.744834	−	1.89781i
$487$	21.2044	−	19.6748i	0.960865	−	0.891552i	−0.0332979	−	0.999445i	$-0.510601\pi$
$487$	21.2044	−	19.6748i	0.960865	−	0.891552i	0.994162	+	0.107893i	$0.0344105\pi$
$488$	−38.5426	+	26.2779i	−1.74474	+	1.18955i
$489$	−1.22450			−0.0553738
$490$	1.06786	+	70.6593i	0.0482410	+	3.19206i
$491$	41.3087			1.86424			0.932119	−	0.362152i	$-0.117958\pi$
$491$	41.3087			1.86424			0.932119	+	0.362152i	$0.117958\pi$
$492$	−30.6273	+	20.8814i	−1.38079	+	0.941405i
$493$	−1.37203	+	1.27306i	−0.0617932	+	0.0573357i
$494$	−4.37640	+	11.1509i	−0.196904	+	0.501702i
$495$	−30.3486	−	9.36132i	−1.36407	−	0.420760i
$496$	−2.79312	+	12.2374i	−0.125415	+	0.549478i
$497$	−34.0524	−	8.84910i	−1.52746	−	0.396937i
$498$	−2.97312	−	13.0261i	−0.133229	−	0.583713i
$499$	0.563719	−	7.52231i	0.0252355	−	0.336745i	−0.970269	−	0.242030i	$-0.922187\pi$
$499$	0.563719	−	7.52231i	0.0252355	−	0.336745i	0.995504	−	0.0947152i	$-0.0301941\pi$
$500$	−62.3754	+	19.2403i	−2.78951	+	0.860451i
$501$	−0.819015	−	10.9290i	−0.0365909	−	0.488272i
$502$	0.761524	+	1.94033i	0.0339885	+	0.0866012i
$503$	33.6488	+	16.2044i	1.50033	+	0.722520i	0.990469	−	0.137738i	$-0.0439833\pi$
$503$	33.6488	+	16.2044i	1.50033	+	0.722520i	0.509859	+	0.860258i	$0.329698\pi$
$504$	−42.9933	+	43.6479i	−1.91507	+	1.94423i
$505$	3.01567	−	1.45227i	0.134195	−	0.0646251i
$506$	−28.4123	−	26.3628i	−1.26308	−	1.17197i
$507$	−0.880366	−	0.132694i	−0.0390984	−	0.00589314i
$508$	48.5500	+	84.0910i	2.15406	+	3.73094i
$509$	−12.0975	+	20.9535i	−0.536213	+	0.928748i	0.462891	+	0.886415i	$0.346812\pi$
$509$	−12.0975	+	20.9535i	−0.536213	+	0.928748i	−0.999104	+	0.0423324i	$0.986521\pi$
$510$	−3.35980	+	4.21305i	−0.148774	+	0.186557i
$511$	30.3783	−	1.36660i	1.34386	−	0.0604548i
$512$	81.3188	+	101.971i	3.59382	+	4.50651i
$513$	−19.7076	+	2.97045i	−0.870113	+	0.131148i
$514$	−32.6630	−	22.2693i	−1.44071	−	0.982256i
$515$	−8.73172	−	5.95319i	−0.384766	−	0.262329i
$516$	−14.7099	+	2.21716i	−0.647568	+	0.0976051i
$517$	−21.3375	−	26.7563i	−0.938421	−	1.17674i
$518$	6.02999	−	0.271266i	0.264943	−	0.0119187i
$519$	11.7026	−	14.6746i	0.513689	−	0.644145i
$520$	19.0033	−	32.9147i	0.833350	−	1.44340i
$521$	−4.81172	−	8.33415i	−0.210805	−	0.365126i	0.741161	−	0.671327i	$-0.234275\pi$
$521$	−4.81172	−	8.33415i	−0.210805	−	0.365126i	−0.951967	+	0.306201i	$0.900942\pi$
$522$	18.9874	+	2.86189i	0.831055	+	0.125261i
$523$	−1.50275	−	1.39435i	−0.0657107	−	0.0609706i	0.646634	−	0.762801i	$-0.276176\pi$
$523$	−1.50275	−	1.39435i	−0.0657107	−	0.0609706i	−0.712345	+	0.701830i	$0.752367\pi$
$524$	87.6378	−	42.2042i	3.82848	−	1.84370i
$525$	13.4312	−	13.6358i	0.586187	−	0.595113i
$526$	−44.7152	−	21.5337i	−1.94967	−	0.938914i
$527$	0.155307	+	0.395716i	0.00676528	+	0.0172376i
$528$	−4.67769	−	62.4195i	−0.203570	−	2.71646i
$529$	−10.2567	+	3.16377i	−0.445943	+	0.137555i
$530$	−1.88304	+	25.1274i	−0.0817940	+	1.09147i
$531$	3.59870	+	15.7669i	0.156170	+	0.684227i
$532$	63.4593	+	16.4910i	2.75131	+	0.714974i
$533$	1.60713	−	7.04130i	0.0696126	−	0.304993i
$534$	31.8415	+	9.82180i	1.37792	+	0.425031i
$535$	−15.7472	+	40.1232i	−0.680810	+	1.73468i
$536$	−107.227	+	99.4918i	−4.63149	+	4.29739i
$537$	−12.2910	+	8.37989i	−0.530397	+	0.361619i
$538$	43.6059			1.87999
$539$	−27.1934	−	5.77584i	−1.17130	−	0.248783i
$540$	96.8270			4.16677
$541$	29.5422	−	20.1415i	1.27012	−	0.865953i	0.274697	−	0.961531i	$-0.411422\pi$
$541$	29.5422	−	20.1415i	1.27012	−	0.865953i	0.995422	+	0.0955781i	$0.0304700\pi$
$542$	29.4589	−	27.3339i	1.26537	−	1.17409i
$543$	−1.88822	+	4.81110i	−0.0810312	+	0.206464i
$544$	16.2412	+	5.00975i	0.696335	+	0.214791i
$545$	−0.875887	+	3.83751i	−0.0375189	+	0.164381i
$546$	−0.195861	+	6.56087i	−0.00838209	+	0.280779i
$547$	−0.850347	−	3.72561i	−0.0363582	−	0.159296i	0.953490	−	0.301425i	$-0.0974623\pi$
$547$	−0.850347	−	3.72561i	−0.0363582	−	0.159296i	−0.989848	+	0.142129i	$0.954605\pi$
$548$	8.20777	−	109.525i	0.350618	−	4.67868i
$549$	9.37925	−	2.89311i	0.400296	−	0.123475i
$550$	−6.71977	−	89.6691i	−0.286532	−	3.82350i
$551$	−4.90299	−	12.4926i	−0.208874	−	0.532203i
$552$	29.4722	+	14.1931i	1.25442	+	0.604098i
$553$	−5.43368	−	45.1560i	−0.231063	−	1.92023i
$554$	−34.2929	+	16.5146i	−1.45697	+	0.701638i
$555$	−1.93587	−	1.79622i	−0.0821730	−	0.0762454i
$556$	37.6643	+	5.67698i	1.59732	+	0.240758i
$557$	−10.5353	−	18.2477i	−0.446396	−	0.773181i	0.551752	−	0.834008i	$-0.313959\pi$
$557$	−10.5353	−	18.2477i	−0.446396	−	0.773181i	−0.998148	+	0.0608274i	$0.980626\pi$
$558$	2.18060	−	3.77691i	0.0923122	−	0.159889i
$559$	1.80715	−	2.26609i	0.0764343	−	0.0958456i
$560$	−156.038	−	66.6801i	−6.59383	−	2.81775i
$561$	−1.32172	−	1.65739i	−0.0558031	−	0.0699749i
$562$	83.2771	−	12.5520i	3.51283	−	0.529475i
$563$	14.2883	+	9.74158i	0.602179	+	0.410559i	0.825675	−	0.564146i	$-0.190795\pi$
$563$	14.2883	+	9.74158i	0.602179	+	0.410559i	−0.223496	+	0.974705i	$0.571747\pi$
$564$	36.5422	+	24.9140i	1.53870	+	1.04907i
$565$	14.5174	−	2.18814i	0.610751	−	0.0920558i
$566$	32.8453	+	41.1867i	1.38059	+	1.73121i
$567$	5.81136	−	3.12780i	0.244054	−	0.131355i
$568$	86.9803	−	109.070i	3.64961	−	4.57647i
$569$	23.8274	−	41.2703i	0.998897	−	1.73014i	0.458785	−	0.888547i	$-0.348285\pi$
$569$	23.8274	−	41.2703i	0.998897	−	1.73014i	0.540112	−	0.841593i	$-0.318382\pi$
$570$	−19.3191	−	33.4617i	−0.809189	−	1.40156i
$571$	10.5254	+	1.58645i	0.440475	+	0.0663909i	0.365536	−	0.930797i	$-0.380886\pi$
$571$	10.5254	+	1.58645i	0.440475	+	0.0663909i	0.0749391	+	0.997188i	$0.476124\pi$
$572$	16.7828	+	15.5722i	0.701724	+	0.651105i
$573$	−10.1368	+	4.88162i	−0.423470	+	0.203932i
$574$	−52.9556	−	5.56179i	−2.21032	−	0.232145i
$575$	25.6399	+	12.3475i	1.06926	+	0.514927i
$576$	−35.1513	−	89.5642i	−1.46464	−	3.73184i
$577$	−0.173747	−	2.31850i	−0.00723320	−	0.0965203i	0.992419	−	0.122903i	$-0.0392203\pi$
$577$	−0.173747	−	2.31850i	−0.00723320	−	0.0965203i	−0.999652	+	0.0263824i	$0.991601\pi$
$578$	−44.3094	+	13.6676i	−1.84303	+	0.568498i
$579$	−0.0275702	+	0.367899i	−0.00114578	+	0.0152893i
$580$	14.5083	+	63.5652i	0.602426	+	2.63940i
$581$	6.56275	−	12.6477i	0.272269	−	0.524716i
$582$	−4.87771	+	21.3706i	−0.202188	+	0.885842i
$583$	−9.47228	−	2.92181i	−0.392302	−	0.121009i
$584$	−44.0508	+	112.240i	−1.82284	+	4.64451i
$585$	−5.86222	+	5.43935i	−0.242373	+	0.224889i
$586$	−21.2608	+	14.4954i	−0.878277	+	0.598799i
$587$	13.7602			0.567943			0.283972	−	0.958833i	$-0.408348\pi$
$587$	13.7602			0.567943			0.283972	+	0.958833i	$0.408348\pi$
$588$	35.7819	−	3.22590i	1.47562	−	0.133034i
$589$	−3.04808			−0.125594
$590$	−61.1126	+	41.6659i	−2.51597	+	1.71536i
$591$	2.10877	−	1.95665i	0.0867432	−	0.0804860i
$592$	−5.29527	+	13.4921i	−0.217634	+	0.554523i
$593$	−22.6192	−	6.97711i	−0.928861	−	0.286516i	−0.206830	−	0.978377i	$-0.566315\pi$
$593$	−22.6192	−	6.97711i	−0.928861	−	0.286516i	−0.722030	+	0.691861i	$0.756791\pi$
$594$	−11.4167	+	50.0199i	−0.468433	+	2.05234i
$595$	−5.63839	+	1.11103i	−0.231151	+	0.0455479i
$596$	5.01143	+	21.9565i	0.205276	+	0.899373i
$597$	−0.0369459	+	0.493008i	−0.00151209	+	0.0201775i
$598$	−9.32583	+	2.87664i	−0.381362	+	0.117634i
$599$	1.24144	+	16.5658i	0.0507237	+	0.676861i	0.963381	+	0.268136i	$0.0864075\pi$
$599$	1.24144	+	16.5658i	0.0507237	+	0.676861i	−0.912657	+	0.408725i	$0.865973\pi$
$600$	27.7261	+	70.6450i	1.13191	+	2.88407i
$601$	−10.1721	−	4.89863i	−0.414929	−	0.199819i	0.214760	−	0.976667i	$-0.431103\pi$
$601$	−10.1721	−	4.89863i	−0.414929	−	0.199819i	−0.629688	+	0.776848i	$0.716817\pi$
$602$	−18.1788	−	11.2318i	−0.740912	−	0.457774i
$603$	27.7298	−	13.3540i	1.12924	−	0.543815i
$604$	−35.9362	−	33.3439i	−1.46222	−	1.35675i
$605$	17.0966	+	2.57689i	0.695074	+	0.104766i
$606$	−1.14602	−	1.98497i	−0.0465539	−	0.0806337i
$607$	−22.3672	+	38.7411i	−0.907857	+	1.57245i	−0.0908217	+	0.995867i	$0.528949\pi$
$607$	−22.3672	+	38.7411i	−0.907857	+	1.57245i	−0.817035	+	0.576587i	$0.804384\pi$
$608$	−75.9831	+	95.2798i	−3.08152	+	3.86411i
$609$	−4.83862	−	5.53740i	−0.196071	−	0.224387i
$610$	27.9888	+	35.0968i	1.13323	+	1.42103i
$611$	−8.52095	+	1.28433i	−0.344721	+	0.0519583i
$612$	−6.30346	−	4.29763i	−0.254802	−	0.173721i
$613$	−20.3331	−	13.8629i	−0.821245	−	0.559915i	0.0782058	−	0.996937i	$-0.475081\pi$
$613$	−20.3331	−	13.8629i	−0.821245	−	0.559915i	−0.899451	+	0.437022i	$0.856033\pi$
$614$	66.6473	−	10.0455i	2.68967	−	0.405402i
$615$	14.5247	+	18.2134i	0.585694	+	0.734437i
$616$	64.7847	−	89.1827i	2.61025	−	3.59327i
$617$	−10.7192	+	13.4414i	−0.431539	+	0.541132i	−0.949291	−	0.314398i	$-0.898197\pi$
$617$	−10.7192	+	13.4414i	−0.431539	+	0.541132i	0.517753	+	0.855530i	$0.326769\pi$
$618$	−3.61837	+	6.26720i	−0.145552	+	0.252104i
$619$	−7.89190	−	13.6692i	−0.317202	−	0.549410i	0.662701	−	0.748884i	$-0.269410\pi$
$619$	−7.89190	−	13.6692i	−0.317202	−	0.549410i	−0.979903	+	0.199474i	$0.936077\pi$
$620$	14.6431	+	2.20709i	0.588080	+	0.0886388i
$621$	−11.9029	−	11.0443i	−0.477646	−	0.443191i
$622$	26.0584	−	12.5490i	1.04484	−	0.503171i
$623$	19.1333	+	29.9458i	0.766560	+	1.19975i
$624$	−14.2003	−	6.83851i	−0.568468	−	0.273760i
$625$	0.144519	+	0.368230i	0.00578078	+	0.0147292i
$626$	−1.68291	−	22.4569i	−0.0672626	−	0.897558i
$627$	14.5247	−	4.48028i	0.580061	−	0.178925i
$628$	1.72530	−	23.0225i	0.0688468	−	0.918697i
$629$	0.109228	+	0.478560i	0.00435521	+	0.0190814i
$630$	44.9776	+	38.1186i	1.79195	+	1.51868i
$631$	1.24315	−	5.44658i	0.0494889	−	0.216825i	−0.944137	−	0.329553i	$-0.893102\pi$
$631$	1.24315	−	5.44658i	0.0494889	−	0.216825i	0.993626	+	0.112728i	$0.0359590\pi$
$632$	172.327	+	53.1559i	6.85481	+	2.11443i
$633$	−2.35252	+	5.99412i	−0.0935043	+	0.238245i
$634$	17.4418	−	16.1837i	0.692704	−	0.642735i
$635$	50.4196	−	34.3755i	2.00084	−	1.36415i
$636$	12.8105			0.507969
$637$	−4.68313	+	5.20272i	−0.185552	+	0.206139i
$638$	−34.5478			−1.36776
$639$	−24.2530	+	16.5354i	−0.959434	+	0.654131i
$640$	171.998	−	159.591i	6.79881	−	6.30838i
$641$	8.03350	−	20.4690i	0.317304	−	0.808478i	−0.679869	−	0.733334i	$-0.737963\pi$
$641$	8.03350	−	20.4690i	0.317304	−	0.808478i	0.997173	−	0.0751439i	$-0.0239416\pi$
$642$	28.2044	+	8.69991i	1.11314	+	0.343358i
$643$	−8.99751	+	39.4207i	−0.354827	+	1.55460i	0.411050	+	0.911613i	$0.365162\pi$
$643$	−8.99751	+	39.4207i	−0.354827	+	1.55460i	−0.765877	+	0.642987i	$0.777695\pi$
$644$	21.7309	+	48.7984i	0.856317	+	1.92293i
$645$	2.08034	+	9.11456i	0.0819133	+	0.358885i
$646$	−0.536705	+	7.16182i	−0.0211164	+	0.281778i
$647$	37.6158	−	11.6029i	1.47883	−	0.456158i	0.552704	−	0.833378i	$-0.313596\pi$
$647$	37.6158	−	11.6029i	1.47883	−	0.456158i	0.926124	+	0.377219i	$0.123120\pi$
$648$	1.95555	+	26.0949i	0.0768211	+	1.02511i
$649$	−10.6304	−	27.0859i	−0.417281	−	1.06321i
$650$	−20.3996	−	9.82391i	−0.800137	−	0.385326i
$651$	−1.57224	+	0.563519i	−0.0616208	+	0.0220861i
$652$	7.14346	−	3.44011i	0.279760	−	0.134725i
$653$	−16.3252	−	15.1476i	−0.638854	−	0.592770i	0.292775	−	0.956181i	$-0.405421\pi$
$653$	−16.3252	−	15.1476i	−0.638854	−	0.592770i	−0.931629	+	0.363411i	$0.881612\pi$
$654$	2.66531	+	0.401731i	0.104222	+	0.0157089i
$655$	−30.5652	−	52.9405i	−1.19428	−	2.06856i
$656$	63.9289	−	110.728i	2.49600	−	4.32321i
$657$	15.8181	−	19.8352i	0.617121	−	0.773846i
$658$	16.9060	+	61.2393i	0.659063	+	2.38736i
$659$	−28.6509	−	35.9270i	−1.11608	−	1.39952i	−0.906747	−	0.421674i	$-0.861443\pi$
$659$	−28.6509	−	35.9270i	−1.11608	−	1.39952i	−0.209331	−	0.977845i	$-0.567129\pi$
$660$	−73.0214	+	11.0062i	−2.84235	+	0.428416i
$661$	11.8619	+	8.08729i	0.461373	+	0.314559i	0.771605	−	0.636102i	$-0.219454\pi$
$661$	11.8619	+	8.08729i	0.461373	+	0.314559i	−0.310232	+	0.950661i	$0.600407\pi$
$662$	19.0743	+	13.0046i	0.741342	+	0.505439i
$663$	−0.527818	+	0.0795558i	−0.0204988	+	0.00308969i
$664$	35.2264	+	44.1724i	1.36705	+	1.71422i
$665$	7.35454	−	40.5444i	0.285197	−	1.57224i
$666$	3.13984	−	3.93723i	0.121666	−	0.152565i
$667$	5.46686	−	9.46887i	0.211678	−	0.366636i
$668$	35.4819	+	61.4564i	1.37284	+	2.37782i
$669$	7.94900	+	1.19812i	0.307326	+	0.0463219i
$670$	103.186	+	95.7428i	3.98643	+	3.69887i
$671$	−15.9108	+	7.66222i	−0.614228	+	0.295797i
$672$	−21.5780	+	63.1941i	−0.832390	+	2.43776i
$673$	14.6520	+	7.05601i	0.564791	+	0.271989i	0.694416	−	0.719574i	$-0.255663\pi$
$673$	14.6520	+	7.05601i	0.564791	+	0.271989i	−0.129624	+	0.991563i	$0.541377\pi$
$674$	3.29450	+	8.39425i	0.126899	+	0.323335i
$675$	−2.81514	−	37.5655i	−0.108355	−	1.44590i
$676$	5.50865	−	1.69919i	0.211871	−	0.0653536i
$677$	−2.05525	+	27.4255i	−0.0789898	+	1.05405i	0.807064	+	0.590464i	$0.201055\pi$
$677$	−2.05525	+	27.4255i	−0.0789898	+	1.05405i	−0.886054	+	0.463582i	$0.846564\pi$
$678$	−2.23710	−	9.80138i	−0.0859154	−	0.376420i
$679$	−18.7036	+	14.0234i	−0.717780	+	0.538170i
$680$	5.07050	−	22.2153i	0.194445	−	0.851919i
$681$	14.5583	+	4.49064i	0.557875	+	0.172082i
$682$	−2.86670	+	7.30423i	−0.109772	+	0.279693i
$683$	−0.801439	+	0.743627i	−0.0306662	+	0.0284541i	−0.695357	−	0.718664i	$-0.744754\pi$
$683$	−0.801439	+	0.743627i	−0.0306662	+	0.0284541i	0.664691	+	0.747119i	$0.268563\pi$
$684$	45.1973	−	30.8150i	1.72816	−	1.17824i
$685$	−69.0247			−2.63730
$686$	42.2071	+	29.6964i	1.61147	+	1.13382i
$687$	12.9814			0.495272
$688$	42.3953	−	28.9046i	1.61630	−	1.10198i
$689$	−1.82969	+	1.69770i	−0.0697056	+	0.0646774i
$690$	11.5006	−	29.3031i	0.437820	−	1.11555i
$691$	−4.99224	−	1.53990i	−0.189914	−	0.0585806i	0.198339	−	0.980133i	$-0.436445\pi$
$691$	−4.99224	−	1.53990i	−0.189914	−	0.0585806i	−0.388253	+	0.921553i	$0.626921\pi$
$692$	−27.0437	+	118.486i	−1.02805	+	4.50416i
$693$	−18.5569	+	13.9134i	−0.704918	+	0.528527i
$694$	16.1793	+	70.8862i	0.614159	+	2.69080i
$695$	1.78887	−	23.8708i	0.0678557	−	0.905472i
$696$	27.8622	−	8.59436i	1.05611	−	0.325768i
$697$	−0.323591	−	4.31803i	−0.0122569	−	0.163557i
$698$	−7.93078	−	20.2073i	−0.300184	−	0.764857i
$699$	9.13316	+	4.39830i	0.345448	+	0.166359i
$700$	−40.0466	+	117.282i	−1.51362	+	4.43283i
$701$	6.70955	−	3.23115i	0.253416	−	0.122039i	−0.302864	−	0.953034i	$-0.597943\pi$
$701$	6.70955	−	3.23115i	0.253416	−	0.122039i	0.556280	+	0.830995i	$0.312228\pi$
$702$	9.47015	+	8.78702i	0.357428	+	0.331645i
$703$	−3.48032	−	0.524574i	−0.131263	−	0.0197847i
$704$	86.5547	+	149.917i	3.26215	+	5.65022i
$705$	13.8974	−	24.0710i	0.523407	−	0.906568i
$706$	52.5538	−	65.9004i	1.97789	−	2.48019i
$707$	0.436276	−	2.40511i	0.0164078	−	0.0904536i
$708$	23.4454	+	29.3995i	0.881130	+	1.10490i
$709$	−11.9656	+	1.80352i	−0.449377	+	0.0677326i	−0.369832	−	0.929099i	$-0.620585\pi$
$709$	−11.9656	+	1.80352i	−0.449377	+	0.0677326i	−0.0795447	+	0.996831i	$0.525347\pi$
$710$	−110.922	−	75.6250i	−4.16281	−	2.83816i
$711$	−31.3519	−	21.3754i	−1.17579	−	0.801639i
$712$	−139.331	+	21.0008i	−5.22166	+	0.787038i
$713$	−1.54832	−	1.94153i	−0.0579850	−	0.0727109i
$714$	1.04722	+	3.79338i	0.0391911	+	0.141964i
$715$	8.97086	−	11.2491i	0.335491	−	0.420693i
$716$	48.1607	−	83.4168i	1.79985	−	3.11743i
$717$	−1.33322	−	2.30920i	−0.0497899	−	0.0862386i
$718$	−16.9076	−	2.54841i	−0.630986	−	0.0951058i
$719$	27.6490	+	25.6545i	1.03113	+	0.956751i	0.999086	−	0.0427356i	$-0.0136073\pi$
$719$	27.6490	+	25.6545i	1.03113	+	0.956751i	0.0320457	+	0.999486i	$0.489798\pi$
$720$	−127.551	+	61.4254i	−4.75355	+	2.28919i
$721$	−7.26511	+	2.60395i	−0.270567	+	0.0969763i
$722$	1.30474	+	0.628331i	0.0485575	+	0.0233841i
$723$	5.96684	+	15.2033i	0.221909	+	0.565415i
$724$	−2.50086	−	33.3717i	−0.0929438	−	1.24025i
$725$	24.2392	−	7.47681i	0.900222	−	0.277682i
$726$	0.884772	−	11.8065i	0.0328370	−	0.438179i
$727$	−2.50035	−	10.9547i	−0.0927328	−	0.406289i	0.907162	−	0.420781i	$-0.138244\pi$
$727$	−2.50035	−	10.9547i	−0.0927328	−	0.406289i	−0.999895	+	0.0144923i	$0.995387\pi$
$728$	−11.2912	−	25.3552i	−0.418478	−	0.939726i
$729$	−1.53023	+	6.70438i	−0.0566752	+	0.248310i
$730$	110.876	+	34.2008i	4.10371	+	1.26583i
$731$	0.634869	−	1.61762i	0.0234815	−	0.0598299i
$732$	16.7298	−	15.5230i	0.618352	−	0.573747i
$733$	9.39954	−	6.40849i	0.347180	−	0.236703i	−0.377157	−	0.926149i	$-0.623098\pi$
$733$	9.39954	−	6.40849i	0.347180	−	0.236703i	0.724337	+	0.689446i	$0.242146\pi$
$734$	15.5913			0.575484
$735$	−3.70215	−	22.2730i	−0.136556	−	0.821551i
$736$	−99.2871			−3.65977
$737$	−45.7530	+	31.1938i	−1.68533	+	1.14904i
$738$	−32.5649	+	30.2158i	−1.19873	+	1.11226i
$739$	−6.08484	+	15.5039i	−0.223834	+	0.570321i	−0.998038	−	0.0626163i	$-0.980056\pi$
$739$	−6.08484	+	15.5039i	−0.223834	+	0.570321i	0.774203	+	0.632937i	$0.218151\pi$
$740$	16.3397	+	5.04014i	0.600661	+	0.185279i
$741$	0.851661	−	3.73137i	0.0312866	−	0.137075i
$742$	14.0382	+	11.8974i	0.515359	+	0.436768i
$743$	−4.61545	−	20.2216i	−0.169325	−	0.741859i	−0.986270	−	0.165144i	$-0.947191\pi$
$743$	−4.61545	−	20.2216i	−0.169325	−	0.741859i	0.816945	−	0.576716i	$-0.195666\pi$
$744$	0.494892	−	6.60388i	0.0181436	−	0.242110i
$745$	13.5248	−	4.17184i	0.495509	−	0.152844i
$746$	6.78912	+	90.5945i	0.248567	+	3.31690i
$747$	−4.34315	−	11.0662i	−0.158908	−	0.404890i
$748$	12.3669	+	5.95558i	0.452178	+	0.217758i
$749$	16.9478	+	26.5252i	0.619259	+	0.969211i
$750$	25.3095	−	12.1884i	0.924172	−	0.445058i
$751$	−11.5701	−	10.7355i	−0.422200	−	0.391745i	0.440259	−	0.897871i	$-0.354887\pi$
$751$	−11.5701	−	10.7355i	−0.422200	−	0.391745i	−0.862460	+	0.506126i	$0.831077\pi$
$752$	−150.846	−	22.7364i	−5.50080	−	0.829112i
$753$	−0.332991	−	0.576757i	−0.0121349	−	0.0210182i
$754$	−4.34953	+	7.53361i	−0.158401	+	0.274358i
$755$	−19.2089	+	24.0872i	−0.699083	+	0.876622i
$756$	41.5587	−	57.2098i	1.51148	−	2.08070i
$757$	6.11423	+	7.66701i	0.222226	+	0.278662i	0.880429	−	0.474178i	$-0.157255\pi$
$757$	6.11423	+	7.66701i	0.222226	+	0.278662i	−0.658203	+	0.752840i	$0.728683\pi$
$758$	−16.1541	+	2.43484i	−0.586744	+	0.0884375i
$759$	10.2319	+	6.97596i	0.371393	+	0.253211i
$760$	134.996	+	92.0384i	4.89680	+	3.33858i
$761$	−44.7757	+	6.74885i	−1.62312	+	0.244645i	−0.896710	−	0.442619i	$-0.854049\pi$
$761$	−44.7757	+	6.74885i	−1.62312	+	0.244645i	−0.726407	+	0.687265i	$0.758811\pi$
$762$	−26.0539	−	32.6705i	−0.943832	−	1.18353i
$763$	1.89144	+	2.16459i	0.0684747	+	0.0783636i
$764$	45.4213	−	56.9565i	1.64329	−	2.06062i
$765$	−2.39728	+	4.15221i	−0.0866738	+	0.150123i
$766$	1.17718	+	2.03894i	0.0425334	+	0.0736700i
$767$	−7.24480	−	1.09198i	−0.261594	−	0.0394290i
$768$	−60.8844	−	56.4925i	−2.19698	−	2.03850i
$769$	2.02056	−	0.973050i	0.0728632	−	0.0350891i	−0.397097	−	0.917777i	$-0.629982\pi$
$769$	2.02056	−	0.973050i	0.0728632	−	0.0350891i	0.469960	+	0.882687i	$0.344268\pi$
$770$	−90.2412	−	55.7557i	−3.25207	−	2.00930i
$771$	11.3799	+	5.48027i	0.409837	+	0.197367i
$772$	−0.872736	−	2.22370i	−0.0314105	−	0.0800326i
$773$	3.08172	+	41.1227i	0.110842	+	1.47908i	0.724372	+	0.689409i	$0.242130\pi$
$773$	3.08172	+	41.1227i	0.110842	+	1.47908i	−0.613531	+	0.789671i	$0.710251\pi$
$774$	−17.0358	+	5.25486i	−0.612341	+	0.188882i
$775$	0.430540	−	5.74516i	0.0154655	−	0.206372i
$776$	−20.6259	−	90.3679i	−0.740426	−	3.24402i
$777$	−1.89218	+	0.372849i	−0.0678814	+	0.0133759i
$778$	0.322936	−	1.41487i	0.0115778	−	0.0507257i
$779$	29.6687	+	9.15159i	1.06299	+	0.327890i
$780$	−6.79327	+	17.3090i	−0.243238	+	0.619760i
$781$	38.7143	−	35.9217i	1.38531	−	1.28538i
$782$	−4.83449	+	3.29610i	−0.172881	+	0.117868i
$783$	−14.4733			−0.517232
$784$	−106.370	+	63.5751i	−3.79894	+	2.27054i
$785$	−14.5092			−0.517856
$786$	−34.5869	+	23.5809i	−1.23367	+	0.841104i
$787$	0.337037	−	0.312724i	0.0120141	−	0.0111474i	−0.674143	−	0.738601i	$-0.735487\pi$
$787$	0.337037	−	0.312724i	0.0120141	−	0.0111474i	0.686157	+	0.727454i	$0.259296\pi$
$788$	−6.80508	+	17.3391i	−0.242421	+	0.617679i
$789$	15.1526	+	4.67395i	0.539446	+	0.166397i
$790$	38.6171	−	169.193i	1.37394	−	6.01960i
$791$	4.93809	−	9.51668i	0.175578	−	0.338374i
$792$	−20.4641	−	89.6589i	−0.727158	−	3.18589i
$793$	−0.332299	+	4.43422i	−0.0118003	+	0.157464i
$794$	−56.3778	+	17.3902i	−2.00077	+	0.617157i
$795$	−0.601640	−	8.02833i	−0.0213380	−	0.284735i
$796$	−1.16952	−	2.97990i	−0.0414527	−	0.105620i
$797$	−30.1514	−	14.5201i	−1.06802	−	0.514329i	−0.184549	−	0.982823i	$-0.559082\pi$
$797$	−30.1514	−	14.5201i	−1.06802	−	0.514329i	−0.883467	+	0.468494i	$0.844797\pi$
$798$	−28.0625	−	2.94734i	−0.993403	−	0.104335i
$799$	−4.65475	+	2.24161i	−0.164673	+	0.0793025i
$800$	−168.855	−	156.675i	−5.96994	−	5.53929i
$801$	29.3168	+	4.41880i	1.03586	+	0.156131i
$802$	−30.3022	−	52.4849i	−1.07001	−	1.85331i
$803$	−22.8229	+	39.5304i	−0.805403	+	1.39500i
$804$	44.6188	−	55.9503i	1.57359	−	1.97321i
$805$	29.5613	−	15.9105i	1.04190	−	0.560773i
$806$	1.23187	+	1.54472i	0.0433908	+	0.0544103i
$807$	−13.7767	+	2.07650i	−0.484963	+	0.0730963i
$808$	8.00801	+	5.45977i	0.281721	+	0.192074i
$809$	16.4026	+	11.1831i	0.576683	+	0.393176i	0.816246	−	0.577705i	$-0.196052\pi$
$809$	16.4026	+	11.1831i	0.576683	+	0.393176i	−0.239562	+	0.970881i	$0.577004\pi$
$810$	24.9008	−	3.75319i	0.874925	−	0.131874i
$811$	27.6379	+	34.6569i	0.970499	+	1.21697i	0.976175	+	0.216983i	$0.0696216\pi$
$811$	27.6379	+	34.6569i	0.970499	+	1.21697i	−0.00567679	+	0.999984i	$0.501807\pi$
$812$	43.7842	+	18.7104i	1.53653	+	0.656605i
$813$	−8.00550	+	10.0386i	−0.280765	+	0.352068i
$814$	−4.53028	+	7.84667i	−0.158786	+	0.275026i
$815$	−2.49140	−	4.31524i	−0.0872701	−	0.151156i
$816$	−9.34397	−	1.40838i	−0.327104	−	0.0493030i
$817$	9.13385	+	8.47498i	0.319553	+	0.296502i
$818$	−54.3194	+	26.1589i	−1.89923	+	0.914623i
$819$	0.697713	+	5.79826i	0.0243801	+	0.202608i
$820$	−135.903	−	65.4474i	−4.74594	−	2.28552i
$821$	4.35139	+	11.0871i	0.151864	+	0.386944i	0.986478	−	0.163891i	$-0.0524045\pi$
$821$	4.35139	+	11.0871i	0.151864	+	0.386944i	−0.834614	+	0.550835i	$0.814309\pi$
$822$	3.53223	+	47.1343i	0.123201	+	1.64400i
$823$	−37.5855	+	11.5936i	−1.31015	+	0.404128i	−0.869669	−	0.493635i	$-0.835668\pi$
$823$	−37.5855	+	11.5936i	−1.31015	+	0.404128i	−0.440480	+	0.897762i	$0.645192\pi$
$824$	2.28684	−	30.5157i	0.0796657	−	1.06307i
$825$	6.39304	+	28.0097i	0.222577	+	0.975173i
$826$	−1.61180	+	53.9913i	−0.0560817	+	1.87860i
$827$	4.71478	−	20.6568i	0.163949	−	0.718307i	−0.824388	−	0.566025i	$-0.808481\pi$
$827$	4.71478	−	20.6568i	0.163949	−	0.718307i	0.988337	−	0.152282i	$-0.0486623\pi$
$828$	42.5869	+	13.1363i	1.48000	+	0.456518i
$829$	14.3450	−	36.5504i	0.498222	−	1.26945i	−0.431808	−	0.901966i	$-0.642124\pi$
$829$	14.3450	−	36.5504i	0.498222	−	1.26945i	0.930030	−	0.367483i	$-0.119781\pi$
$830$	39.8558	−	36.9808i	1.38342	−	1.28362i
$831$	10.0480	−	6.85058i	0.348560	−	0.237644i
$832$	43.5886			1.51116
$833$	−1.76358	+	3.80828i	−0.0611045	+	0.131949i
$834$	−16.3920			−0.567609
$835$	36.8483	−	25.1227i	1.27519	−	0.869408i
$836$	−72.1471	+	66.9427i	−2.49526	+	2.31526i
$837$	−1.20096	+	3.05999i	−0.0415112	+	0.105769i
$838$	−67.5752	−	20.8442i	−2.33435	−	0.720051i
$839$	−6.29994	+	27.6018i	−0.217498	+	0.952921i	0.741821	+	0.670598i	$0.233962\pi$
$839$	−6.29994	+	27.6018i	−0.217498	+	0.952921i	−0.959319	+	0.282323i	$0.908895\pi$
$840$	86.6482	+	22.5170i	2.98965	+	0.776911i
$841$	4.28447	+	18.7715i	0.147740	+	0.647293i
$842$	2.05870	−	27.4715i	0.0709476	−	0.946730i
$843$	−25.7125	+	7.93127i	−0.885587	+	0.273167i
$844$	−3.11581	−	41.5776i	−0.107251	−	1.43116i
$845$	−1.32360	−	3.37247i	−0.0455331	−	0.116016i
$846$	47.7541	+	22.9972i	1.64182	+	0.790658i
$847$	8.86049	−	8.99541i	0.304450	−	0.309086i
$848$	−39.8107	+	19.1718i	−1.36710	+	0.658363i
$849$	−12.3383	−	11.4483i	−0.423450	−	0.392904i
$850$	−13.4231	−	2.02321i	−0.460410	−	0.0693956i
$851$	−1.43375	−	2.48332i	−0.0491482	−	0.0851271i
$852$	−34.1258	+	59.1076i	−1.16913	+	2.02499i
$853$	23.0472	−	28.9003i	0.789121	−	0.989527i	−0.210807	−	0.977528i	$-0.567609\pi$
$853$	23.0472	−	28.9003i	0.789121	−	0.989527i	0.999928	−	0.0119992i	$-0.00381956\pi$
$854$	32.7497	−	1.47328i	1.12067	−	0.0504146i
$855$	−21.4344	−	26.8779i	−0.733041	−	0.919205i
$856$	−123.416	+	18.6020i	−4.21828	+	0.635803i
$857$	0.326042	+	0.222292i	0.0111374	+	0.00759335i	0.568876	−	0.822423i	$-0.307378\pi$
$857$	0.326042	+	0.222292i	0.0111374	+	0.00759335i	−0.557739	+	0.830017i	$0.688331\pi$
$858$	−8.14065	−	5.55020i	−0.277917	−	0.189481i
$859$	6.48359	−	0.977243i	0.221217	−	0.0333431i	−0.0374983	−	0.999297i	$-0.511939\pi$
$859$	6.48359	−	0.977243i	0.221217	−	0.0333431i	0.258715	+	0.965954i	$0.416701\pi$
$860$	−37.7427	−	47.3278i	−1.28702	−	1.61387i
$861$	16.9954	−	0.764557i	0.579202	−	0.0260560i
$862$	−40.9953	+	51.4065i	−1.39631	+	1.75091i
$863$	−15.7957	+	27.3589i	−0.537690	+	0.931307i	0.461338	+	0.887225i	$0.347370\pi$
$863$	−15.7957	+	27.3589i	−0.537690	+	0.931307i	−0.999028	+	0.0440823i	$0.985964\pi$
$864$	65.7145	+	113.821i	2.23565	+	3.87226i
$865$	75.5252	+	11.3836i	2.56793	+	0.387054i
$866$	−34.0534	−	31.5969i	−1.15718	−	1.07371i
$867$	13.3481	−	6.42810i	0.453325	−	0.218310i
$868$	7.58893	−	7.70449i	0.257585	−	0.261507i
$869$	61.5100	+	29.6216i	2.08658	+	1.00485i
$870$	−10.2511	−	26.1193i	−0.347544	−	0.885527i
$871$	1.04198	+	13.9043i	0.0353063	+	0.471130i
$872$	−10.8915	+	3.35957i	−0.368831	+	0.113769i
$873$	−1.45749	+	19.4488i	−0.0493286	+	0.658244i
$874$	−9.33575	−	40.9026i	−0.315786	−	1.38355i
$875$	28.9953	+	7.53491i	0.980218	+	0.254727i
$876$	13.1265	−	57.5107i	0.443502	−	1.94311i
$877$	−4.12995	−	1.27392i	−0.139458	−	0.0430172i	0.224240	−	0.974534i	$-0.428010\pi$
$877$	−4.12995	−	1.27392i	−0.139458	−	0.0430172i	−0.363699	+	0.931517i	$0.618486\pi$
$878$	18.7467	−	47.7659i	0.632672	−	1.61202i
$879$	6.02680	−	5.59205i	0.203279	−	0.188615i
$880$	210.454	−	143.485i	7.09440	−	4.83688i
$881$	−10.0036			−0.337031			−0.168515	−	0.985699i	$-0.553897\pi$
$881$	−10.0036			−0.337031			−0.168515	+	0.985699i	$0.553897\pi$
$882$	41.8269	−	10.2141i	1.40838	−	0.343925i
$883$	1.52201			0.0512198			0.0256099	−	0.999672i	$-0.491847\pi$
$883$	1.52201			0.0512198			0.0256099	+	0.999672i	$0.491847\pi$
$884$	2.85567	−	1.94696i	0.0960466	−	0.0654835i
$885$	17.3236	−	16.0739i	0.582325	−	0.540319i
$886$	27.0036	−	68.8039i	0.907202	−	2.31151i
$887$	−9.43465	−	2.91020i	−0.316784	−	0.0977151i	0.132286	−	0.991212i	$-0.457768\pi$
$887$	−9.43465	−	2.91020i	−0.316784	−	0.0977151i	−0.449070	+	0.893497i	$0.648245\pi$
$888$	1.70160	−	7.45519i	0.0571019	−	0.250180i
$889$	1.32978	−	44.5444i	0.0445994	−	1.49397i
$890$	30.1728	+	132.196i	1.01140	+	4.43121i
$891$	−0.740310	+	9.87875i	−0.0248013	+	0.330951i
$892$	−49.7387	+	15.3424i	−1.66537	+	0.513700i
$893$	−2.76832	−	36.9406i	−0.0926382	−	1.23617i
$894$	−3.54089	−	9.02205i	−0.118425	−	0.301743i
$895$	−54.5391	−	26.2647i	−1.82304	−	0.877931i
$896$	−20.4709	−	170.121i	−0.683886	−	5.68335i
$897$	2.80938	−	1.35293i	0.0938025	−	0.0451729i
$898$	−4.54832	−	4.22022i	−0.151779	−	0.140831i
$899$	−2.18878	−	0.329905i	−0.0729998	−	0.0110030i
$900$	51.6975	+	89.5426i	1.72325	+	2.98475i
$901$	−0.748228	+	1.29597i	−0.0249271	+	0.0431750i
$902$	49.8336	−	62.4893i	1.65928	−	2.08067i
$903$	6.27819	+	2.68286i	0.208925	+	0.0892801i
$904$	26.5058	+	33.2372i	0.881570	+	1.10545i
$905$	−20.7966	+	3.13458i	−0.691301	+	0.104197i
$906$	17.4312	+	11.8844i	0.579113	+	0.394832i
$907$	−3.34810	−	2.28270i	−0.111172	−	0.0757957i	0.506458	−	0.862265i	$-0.330955\pi$
$907$	−3.34810	−	2.28270i	−0.111172	−	0.0757957i	−0.617630	+	0.786469i	$0.711907\pi$
$908$	−97.5459	+	14.7027i	−3.23717	+	0.487925i
$909$	−1.27150	−	1.59441i	−0.0421730	−	0.0528833i
$910$	−23.5195	+	12.6587i	−0.779665	+	0.419632i
$911$	5.51330	−	6.91345i	0.182664	−	0.229053i	−0.682066	−	0.731291i	$-0.738918\pi$
$911$	5.51330	−	6.91345i	0.182664	−	0.229053i	0.864730	+	0.502238i	$0.167490\pi$
$912$	33.8776	−	58.6778i	1.12180	−	1.94301i
$913$	10.6943	+	18.5231i	0.353931	+	0.613026i
$914$	99.9851	+	15.0703i	3.30721	+	0.498482i
$915$	−10.5140	−	9.75554i	−0.347581	−	0.322508i
$916$	−75.7308	+	36.4700i	−2.50221	+	1.20500i
$917$	−44.3984	−	4.66305i	−1.46616	−	0.153988i
$918$	6.97835	+	3.36060i	0.230320	+	0.110916i
$919$	9.33588	+	23.7874i	0.307962	+	0.784675i	0.998136	+	0.0610310i	$0.0194388\pi$
$919$	9.33588	+	23.7874i	0.307962	+	0.784675i	−0.690174	+	0.723644i	$0.742466\pi$
$920$	9.94751	+	132.740i	0.327960	+	4.37632i
$921$	−20.5779	+	6.34745i	−0.678065	+	0.209156i
$922$	−5.00184	+	66.7449i	−0.164727	+	2.19813i
$923$	−2.95910	−	12.9647i	−0.0974001	−	0.426738i
$924$	−24.8382	+	47.8682i	−0.817118	+	1.57475i
$925$	1.48034	−	6.48578i	0.0486732	−	0.213251i
$926$	−24.5247	−	7.56487i	−0.805932	−	0.248597i
$927$	−2.35237	+	5.99375i	−0.0772621	+	0.196861i
$928$	−64.8748	+	60.1950i	−2.12962	+	1.97600i
$929$	8.90837	−	6.07362i	0.292274	−	0.199269i	−0.408302	−	0.912847i	$-0.633879\pi$
$929$	8.90837	−	6.07362i	0.292274	−	0.199269i	0.700576	+	0.713578i	$0.252927\pi$
$930$	−6.37286			−0.208974
$931$	−20.7988	−	21.7473i	−0.681654	−	0.712738i
$932$	−65.6374			−2.15003
$933$	−7.63519	+	5.20559i	−0.249965	+	0.170423i
$934$	53.9919	−	50.0972i	1.76667	−	1.63923i
$935$	3.15155	−	8.03002i	0.103067	−	0.262610i
$936$	−22.1277	−	6.82550i	−0.723267	−	0.223098i
$937$	−6.88932	+	30.1841i	−0.225064	+	0.986071i	0.728539	+	0.685004i	$0.240200\pi$
$937$	−6.88932	+	30.1841i	−0.225064	+	0.986071i	−0.953603	+	0.301067i	$0.902657\pi$
$938$	100.857	−	19.8737i	3.29311	−	0.648900i
$939$	1.60108	+	7.01480i	0.0522494	+	0.228919i
$940$	−13.4493	+	179.469i	−0.438668	+	5.85362i
$941$	52.2745	−	16.1245i	1.70410	−	0.525645i	0.718615	−	0.695408i	$-0.244777\pi$
$941$	52.2745	−	16.1245i	1.70410	−	0.525645i	0.985485	+	0.169763i	$0.0543003\pi$
$942$	0.742485	+	9.90778i	0.0241915	+	0.322813i
$943$	9.24141	+	23.5467i	0.300942	+	0.766787i
$944$	−116.859	−	56.2762i	−3.80343	−	1.83163i
$945$	−37.8051	−	23.3580i	−1.22980	−	0.759835i
$946$	28.8993	−	13.9171i	0.939596	−	0.452486i
$947$	17.3936	+	16.1389i	0.565215	+	0.524443i	0.910202	−	0.414165i	$-0.135926\pi$
$947$	17.3936	+	16.1389i	0.565215	+	0.524443i	−0.344987	+	0.938607i	$0.612117\pi$
$948$	−87.2435	−	13.1498i	−2.83354	−	0.427087i
$949$	5.74676	+	9.95368i	0.186548	+	0.323110i
$950$	48.6671	−	84.2939i	1.57897	−	2.73486i
$951$	−4.73985	+	5.94358i	−0.153700	+	0.192734i
$952$	−10.9495	−	12.5308i	−0.354876	−	0.406126i
$953$	12.6254	+	15.8318i	0.408977	+	0.512841i	0.943074	−	0.332582i	$-0.107920\pi$
$953$	12.6254	+	15.8318i	0.408977	+	0.512841i	−0.534097	+	0.845423i	$0.679348\pi$
$954$	15.1810	−	2.28816i	0.491502	−	0.0740820i
$955$	−37.8278	−	25.7906i	−1.22408	−	0.834563i
$956$	14.2652	+	9.72582i	0.461368	+	0.314556i
$957$	10.9149	−	1.64516i	0.352828	−	0.0531803i
$958$	16.0847	+	20.1696i	0.519673	+	0.651650i
$959$	−29.6258	+	40.7829i	−0.956667	+	1.31695i
$960$	−87.6598	+	109.922i	−2.82921	+	3.54772i
$961$	15.2486	−	26.4114i	0.491891	−	0.851981i
$962$	1.14071	+	1.97577i	0.0367781	+	0.0637015i
$963$	25.9681	+	3.91406i	0.836811	+	0.126129i
$964$	−77.5213	−	71.9292i	−2.49679	−	2.31668i
$965$	−1.35260	+	0.651378i	−0.0435418	+	0.0209686i
$966$	−12.3774	−	19.3721i	−0.398238	−	0.623288i
$967$	2.17001	+	1.04502i	0.0697828	+	0.0336056i	0.468450	−	0.883490i	$-0.344813\pi$
$967$	2.17001	+	1.04502i	0.0697828	+	0.0336056i	−0.398667	+	0.917096i	$0.630527\pi$
$968$	18.2907	+	46.6040i	0.587886	+	1.49791i
$969$	−0.171480	−	2.28824i	−0.00550872	−	0.0735088i
$970$	−85.2362	+	26.2919i	−2.73677	+	0.844182i
$971$	−3.30412	+	44.0904i	−0.106034	+	1.41493i	0.649769	+	0.760131i	$0.274865\pi$
$971$	−3.30412	+	44.0904i	−0.106034	+	1.41493i	−0.755804	+	0.654798i	$0.772754\pi$
$972$	−20.6903	−	90.6503i	−0.663643	−	2.90761i
$973$	−13.3362	−	11.3024i	−0.427538	−	0.362339i
$974$	17.9361	−	78.5830i	0.574708	−	2.51796i
$975$	6.91277	+	2.13231i	0.221386	+	0.0682885i
$976$	−28.7593	+	73.2776i	−0.920564	+	2.34556i
$977$	−17.2589	+	16.0139i	−0.552160	+	0.512330i	−0.906171	−	0.422911i	$-0.861008\pi$
$977$	−17.2589	+	16.0139i	−0.552160	+	0.512330i	0.354011	+	0.935241i	$0.384818\pi$
$978$	−2.81922	+	1.92211i	−0.0901486	+	0.0614623i
$979$	−53.3423			−1.70483
$980$	84.1713	+	119.535i	2.68875	+	3.81840i
$981$	2.39823			0.0765696
$982$	95.1069	−	64.8428i	3.03498	−	2.06922i
$983$	15.5296	−	14.4094i	0.495317	−	0.459587i	−0.392521	−	0.919743i	$-0.628397\pi$
$983$	15.5296	−	14.4094i	0.495317	−	0.459587i	0.887838	+	0.460156i	$0.152206\pi$
$984$	−24.6446	+	62.7935i	−0.785643	+	2.00179i
$985$	11.1860	+	3.45042i	0.356415	+	0.109939i
$986$	−1.16055	+	5.08471i	−0.0369595	+	0.161930i
$987$	−8.25741	−	18.5427i	−0.262836	−	0.590219i
$988$	5.51451	+	24.1607i	0.175440	+	0.768653i
$989$	−0.758612	+	10.1230i	−0.0241225	+	0.321892i
$990$	−84.5675	+	26.0856i	−2.68773	+	0.829055i
$991$	2.17988	+	29.0885i	0.0692463	+	0.924028i	0.918342	+	0.395788i	$0.129529\pi$
$991$	2.17988	+	29.0885i	0.0692463	+	0.924028i	−0.849095	+	0.528239i	$0.822852\pi$
$992$	7.34350	+	18.7109i	0.233156	+	0.594073i
$993$	−6.64552	−	3.20032i	−0.210889	−	0.101559i
$994$	−92.2908	+	33.0788i	−2.92729	+	1.04919i
$995$	−1.81257	+	0.872889i	−0.0574624	+	0.0276724i
$996$	−20.2625	−	18.8009i	−0.642043	−	0.595729i
$997$	32.5408	+	4.90474i	1.03058	+	0.155335i	0.642495	−	0.766290i	$-0.277899\pi$
$997$	32.5408	+	4.90474i	1.03058	+	0.155335i	0.388083	+	0.921624i	$0.373137\pi$
$998$	−10.5100	−	18.2038i	−0.332687	−	0.576231i
$999$	−1.89789	+	3.28724i	−0.0600465	+	0.104004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.625.29	yes	348
49.4	even	21	inner	637.2.bl.b.53.29	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.29	✓	348	49.4	even	21	inner
637.2.bl.b.625.29	yes	348	1.1	even	1	trivial

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.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.30234 - 1.56971i) q^{2} +(-0.652644 + 0.605565i) q^{3} +(2.10611 - 5.36627i) q^{4} +(-3.46195 - 1.06787i) q^{5} +(-0.552048 + 2.41868i) q^{6} +(-2.11683 + 1.58714i) q^{7} +(-2.33439 - 10.2276i) q^{8} +(-0.164955 + 2.20118i) q^{9} +O(q^{10})\)	\(q+(2.30234 - 1.56971i) q^{2} +(-0.652644 + 0.605565i) q^{3} +(2.10611 - 5.36627i) q^{4} +(-3.46195 - 1.06787i) q^{5} +(-0.552048 + 2.41868i) q^{6} +(-2.11683 + 1.58714i) q^{7} +(-2.33439 - 10.2276i) q^{8} +(-0.164955 + 2.20118i) q^{9} +(-9.64684 + 2.97565i) q^{10} +(-0.296786 - 3.96033i) q^{11} +(1.87509 + 4.77765i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-2.38233 + 6.97695i) q^{14} +(2.90608 - 1.39950i) q^{15} +(-12.9772 - 12.0411i) q^{16} +(-0.592848 - 0.0893574i) q^{17} +(3.07542 + 5.32679i) q^{18} +(2.14944 - 3.72293i) q^{19} +(-13.0217 + 16.3287i) q^{20} +(0.420422 - 2.31772i) q^{21} +(-6.89988 - 8.65217i) q^{22} +(3.46323 - 0.521998i) q^{23} +(7.71701 + 5.26137i) q^{24} +(6.71355 + 4.57722i) q^{25} +(-2.75541 + 0.415311i) q^{26} +(-2.89060 - 3.62469i) q^{27} +(4.05875 + 14.7022i) q^{28} +(1.94642 - 2.44074i) q^{29} +(4.49400 - 7.78383i) q^{30} +(-0.354521 - 0.614048i) q^{31} +(-28.0321 - 4.22515i) q^{32} +(2.59193 + 2.40496i) q^{33} +(-1.50520 + 0.724867i) q^{34} +(9.02323 - 3.23410i) q^{35} +(11.4647 + 5.52110i) q^{36} +(-0.299117 - 0.762138i) q^{37} +(-0.895188 - 11.9455i) q^{38} +(0.850756 - 0.262424i) q^{39} +(-2.84024 + 37.9003i) q^{40} +(1.60713 + 7.04130i) q^{41} +(-2.67019 - 5.99612i) q^{42} +(-0.644964 + 2.82577i) q^{43} +(-21.8773 - 6.74825i) q^{44} +(2.92164 - 7.44421i) q^{45} +(7.15416 - 6.63809i) q^{46} +(7.11986 - 4.85424i) q^{47} +15.7612 q^{48} +(1.96197 - 6.71942i) q^{49} +22.6418 q^{50} +(0.441030 - 0.300689i) q^{51} +(-4.22587 + 3.92104i) q^{52} +(0.911887 - 2.32345i) q^{53} +(-12.3449 - 3.80788i) q^{54} +(-3.20166 + 14.0274i) q^{55} +(21.1742 + 17.9452i) q^{56} +(0.851661 + 3.73137i) q^{57} +(0.650082 - 8.67474i) q^{58} +(7.00113 - 2.15956i) q^{59} +(-1.38955 - 18.5423i) q^{60} +(-1.62455 - 4.13928i) q^{61} +(-1.78010 - 0.857253i) q^{62} +(-3.14439 - 4.92133i) q^{63} +(-39.2720 + 18.9124i) q^{64} +(2.65578 + 2.46420i) q^{65} +(9.74262 + 1.46846i) q^{66} +(-6.97165 - 12.0753i) q^{67} +(-1.72812 + 2.99318i) q^{68} +(-1.94415 + 2.43789i) q^{69} +(15.6980 - 21.6098i) q^{70} +(8.29122 + 10.3969i) q^{71} +(22.8979 - 3.45130i) q^{72} +(-9.49640 - 6.47453i) q^{73} +(-1.88500 - 1.28517i) q^{74} +(-7.15336 + 1.07820i) q^{75} +(-15.4513 - 19.3753i) q^{76} +(6.91385 + 7.91233i) q^{77} +(1.54680 - 1.93963i) q^{78} +(-8.59524 + 14.8874i) q^{79} +(32.0681 + 55.5437i) q^{80} +(-2.46656 - 0.371775i) q^{81} +(14.7530 + 13.6888i) q^{82} +(-4.85228 + 2.33673i) q^{83} +(-11.5520 - 7.13746i) q^{84} +(1.95699 + 0.942435i) q^{85} +(2.95072 + 7.51830i) q^{86} +(0.207704 + 2.77162i) q^{87} +(-39.8120 + 12.2804i) q^{88} +(1.00374 - 13.3939i) q^{89} +(-4.95864 - 21.7252i) q^{90} +(2.59584 - 0.511504i) q^{91} +(4.49275 - 19.6840i) q^{92} +(0.603221 + 0.186069i) q^{93} +(8.77260 - 22.3522i) q^{94} +(-11.4168 + 10.5933i) q^{95} +(20.8536 - 14.2177i) q^{96} +8.83567 q^{97} +(-6.03042 - 18.5501i) q^{98} +8.76634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

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