LMFDB - Embedded newform 403.2.bk.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(9,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 2]))

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

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

chi := DirichletCharacter("403.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bk (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	403.9
Dual form			403.2.bk.a.224.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59232 - 1.76846i) q^{2} +(-1.58986 + 1.76572i) q^{3} +(-0.382880 + 3.64286i) q^{4} +(1.32032 + 2.28686i) q^{5} +5.65416 q^{6} +(2.08439 + 1.51440i) q^{7} +(3.20149 - 2.32602i) q^{8} +(-0.276520 - 2.63091i) q^{9} +O(q^{10})$	\(q+(-1.59232 - 1.76846i) q^{2} +(-1.58986 + 1.76572i) q^{3} +(-0.382880 + 3.64286i) q^{4} +(1.32032 + 2.28686i) q^{5} +5.65416 q^{6} +(2.08439 + 1.51440i) q^{7} +(3.20149 - 2.32602i) q^{8} +(-0.276520 - 2.63091i) q^{9} +(1.94183 - 5.97634i) q^{10} +(0.430421 + 0.312719i) q^{11} +(-5.82354 - 6.46770i) q^{12} +(-3.04415 + 1.93214i) q^{13} +(-0.640880 - 6.09757i) q^{14} +(-6.13706 - 1.30447i) q^{15} +(-2.04549 - 0.434783i) q^{16} +(0.927769 - 0.674064i) q^{17} +(-4.21234 + 4.67828i) q^{18} +(-0.517416 + 1.59244i) q^{19} +(-8.83623 + 3.93414i) q^{20} +(-5.98789 + 1.27277i) q^{21} +(-0.132340 - 1.25913i) q^{22} +(-0.164049 - 1.56082i) q^{23} +(-0.982826 + 9.35096i) q^{24} +(-0.986478 + 1.70863i) q^{25} +(8.26417 + 2.30686i) q^{26} +(-0.681610 - 0.495219i) q^{27} +(-6.31482 + 7.01332i) q^{28} +(3.12549 + 3.47121i) q^{29} +(7.46529 + 12.9303i) q^{30} +(-2.94868 + 4.72285i) q^{31} +(-1.46906 - 2.54449i) q^{32} +(-1.23648 + 0.262822i) q^{33} +(-2.66936 - 0.567390i) q^{34} +(-0.711156 + 6.76620i) q^{35} +9.68994 q^{36} +(0.790993 + 1.37004i) q^{37} +(3.64005 - 1.62066i) q^{38} +(1.42817 - 8.44693i) q^{39} +(9.54625 + 4.25027i) q^{40} +(2.70886 - 8.33700i) q^{41} +(11.7855 + 8.56266i) q^{42} +(-3.67638 + 11.3147i) q^{43} +(-1.30399 + 1.44823i) q^{44} +(5.65143 - 4.10601i) q^{45} +(-2.49903 + 2.77545i) q^{46} +(0.0452766 + 0.139347i) q^{47} +(4.01975 - 2.92052i) q^{48} +(-0.111834 - 0.344189i) q^{49} +(4.59243 - 0.976151i) q^{50} +(-0.284816 + 2.70984i) q^{51} +(-5.87296 - 11.8292i) q^{52} +(-8.75266 - 3.89694i) q^{53} +(0.209572 + 1.99395i) q^{54} +(-0.146852 + 1.39720i) q^{55} +10.1957 q^{56} +(-1.98918 - 3.44537i) q^{57} +(1.16188 - 11.0546i) q^{58} +(-2.93187 - 9.02337i) q^{59} +(7.10178 - 21.8570i) q^{60} +(6.22875 + 10.7885i) q^{61} +(13.0474 - 2.30569i) q^{62} +(3.40788 - 5.90262i) q^{63} +(-3.45302 + 10.6273i) q^{64} +(-8.43776 - 4.41051i) q^{65} +(2.43367 + 1.76817i) q^{66} -8.39468 q^{67} +(2.10030 + 3.63782i) q^{68} +(3.01679 + 2.19182i) q^{69} +(13.0981 - 9.51633i) q^{70} +(1.05717 + 10.0583i) q^{71} +(-7.00483 - 7.77965i) q^{72} +(-0.271657 + 2.58464i) q^{73} +(1.16334 - 3.58038i) q^{74} +(-1.44860 - 4.45832i) q^{75} +(-5.60294 - 2.49459i) q^{76} +(0.423585 + 1.30366i) q^{77} +(-17.2121 + 10.9246i) q^{78} +(0.00374488 + 0.0356301i) q^{79} +(-1.70641 - 5.25180i) q^{80} +(9.72087 - 2.06624i) q^{81} +(-19.0570 + 8.48472i) q^{82} +(-13.4053 + 2.84938i) q^{83} +(-2.34386 - 22.3004i) q^{84} +(2.76644 + 1.23170i) q^{85} +(25.8636 - 11.5152i) q^{86} -11.0983 q^{87} +2.10538 q^{88} +(9.08786 - 4.04618i) q^{89} +(-16.2602 - 3.45621i) q^{90} +(-9.27123 - 0.582733i) q^{91} +5.74868 q^{92} +(-3.65122 - 12.7152i) q^{93} +(0.174334 - 0.301955i) q^{94} +(-4.32484 + 0.919273i) q^{95} +(6.82845 + 1.45143i) q^{96} +(0.297215 - 2.82782i) q^{97} +(-0.430607 + 0.745834i) q^{98} +(0.703718 - 1.21887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−1.59232	−	1.76846i	−1.12594	−	1.25049i	−0.964637	−	0.263582i	$-0.915096\pi$
$2$	−1.59232	−	1.76846i	−1.12594	−	1.25049i	−0.161306	−	0.986904i	$-0.551571\pi$
$3$	−1.58986	+	1.76572i	−0.917905	+	1.01944i	0.0818349	+	0.996646i	$0.473922\pi$
$3$	−1.58986	+	1.76572i	−0.917905	+	1.01944i	−0.999740	+	0.0227912i	$0.992745\pi$
$4$	−0.382880	+	3.64286i	−0.191440	+	1.82143i
$5$	1.32032	+	2.28686i	0.590464	+	1.02271i	0.994170	+	0.107825i	$0.0343886\pi$
$5$	1.32032	+	2.28686i	0.590464	+	1.02271i	−0.403706	+	0.914889i	$0.632278\pi$
$6$	5.65416			2.30830
$7$	2.08439	+	1.51440i	0.787826	+	0.572389i	0.907318	−	0.420446i	$-0.138126\pi$
$7$	2.08439	+	1.51440i	0.787826	+	0.572389i	−0.119491	+	0.992835i	$0.538126\pi$
$8$	3.20149	−	2.32602i	1.13190	−	0.822371i
$9$	−0.276520	−	2.63091i	−0.0921734	−	0.876972i
$10$	1.94183	−	5.97634i	0.614061	−	1.88988i
$11$	0.430421	+	0.312719i	0.129777	+	0.0942884i	0.650780	−	0.759266i	$-0.274442\pi$
$11$	0.430421	+	0.312719i	0.129777	+	0.0942884i	−0.521003	+	0.853555i	$0.674442\pi$
$12$	−5.82354	−	6.46770i	−1.68111	−	1.86706i
$13$	−3.04415	+	1.93214i	−0.844295	+	0.535878i
$13$	−3.04415	+	1.93214i	−0.844295	+	0.535878i
$14$	−0.640880	−	6.09757i	−0.171282	−	1.62964i
$15$	−6.13706	−	1.30447i	−1.58458	−	0.336813i
$16$	−2.04549	−	0.434783i	−0.511373	−	0.108696i
$17$	0.927769	−	0.674064i	0.225017	−	0.163484i	−0.469565	−	0.882898i	$-0.655589\pi$
$17$	0.927769	−	0.674064i	0.225017	−	0.163484i	0.694582	+	0.719413i	$0.255589\pi$
$18$	−4.21234	+	4.67828i	−0.992859	+	1.10268i
$19$	−0.517416	+	1.59244i	−0.118703	+	0.365331i	−0.992701	−	0.120598i	$-0.961519\pi$
$19$	−0.517416	+	1.59244i	−0.118703	+	0.365331i	0.873998	+	0.485929i	$0.161519\pi$
$20$	−8.83623	+	3.93414i	−1.97584	+	0.879701i
$21$	−5.98789	+	1.27277i	−1.30666	+	0.277740i
$22$	−0.132340	−	1.25913i	−0.0282150	−	0.268448i
$23$	−0.164049	−	1.56082i	−0.0342066	−	0.325454i	−0.998222	−	0.0596074i	$-0.981015\pi$
$23$	−0.164049	−	1.56082i	−0.0342066	−	0.325454i	0.964015	−	0.265847i	$-0.0856515\pi$
$24$	−0.982826	+	9.35096i	−0.200618	+	1.90876i
$25$	−0.986478	+	1.70863i	−0.197296	+	0.341726i
$26$	8.26417	+	2.30686i	1.62074	+	0.452412i
$27$	−0.681610	−	0.495219i	−0.131176	−	0.0953049i
$28$	−6.31482	+	7.01332i	−1.19339	+	1.32539i
$29$	3.12549	+	3.47121i	0.580389	+	0.644587i	0.959815	−	0.280635i	$-0.0905451\pi$
$29$	3.12549	+	3.47121i	0.580389	+	0.644587i	−0.379426	+	0.925222i	$0.623878\pi$
$30$	7.46529	+	12.9303i	1.36297	+	2.36073i
$31$	−2.94868	+	4.72285i	−0.529599	+	0.848248i
$31$	−2.94868	+	4.72285i	−0.529599	+	0.848248i
$32$	−1.46906	−	2.54449i	−0.259696	−	0.449807i
$33$	−1.23648	+	0.262822i	−0.215244	+	0.0457515i
$34$	−2.66936	−	0.567390i	−0.457791	−	0.0973066i
$35$	−0.711156	+	6.76620i	−0.120207	+	1.14370i
$36$	9.68994			1.61499
$37$	0.790993	+	1.37004i	0.130038	+	0.225233i	0.923691	−	0.383138i	$-0.125157\pi$
$37$	0.790993	+	1.37004i	0.130038	+	0.225233i	−0.793653	+	0.608371i	$0.791823\pi$
$38$	3.64005	−	1.62066i	0.590495	−	0.262905i
$39$	1.42817	−	8.44693i	0.228690	−	1.35259i
$40$	9.54625	+	4.25027i	1.50939	+	0.672026i
$41$	2.70886	−	8.33700i	0.423052	−	1.30202i	−0.481795	−	0.876284i	$-0.660015\pi$
$41$	2.70886	−	8.33700i	0.423052	−	1.30202i	0.904847	−	0.425737i	$-0.139985\pi$
$42$	11.7855	+	8.56266i	1.81854	+	1.32125i
$43$	−3.67638	+	11.3147i	−0.560643	+	1.72548i	0.119913	+	0.992784i	$0.461738\pi$
$43$	−3.67638	+	11.3147i	−0.560643	+	1.72548i	−0.680556	+	0.732696i	$0.738262\pi$
$44$	−1.30399	+	1.44823i	−0.196584	+	0.218329i
$45$	5.65143	−	4.10601i	0.842466	−	0.612087i
$46$	−2.49903	+	2.77545i	−0.368461	+	0.409218i
$47$	0.0452766	+	0.139347i	0.00660427	+	0.0203258i	0.954304	−	0.298836i	$-0.0965985\pi$
$47$	0.0452766	+	0.139347i	0.00660427	+	0.0203258i	−0.947700	+	0.319162i	$0.896598\pi$
$48$	4.01975	−	2.92052i	0.580201	−	0.421541i
$49$	−0.111834	−	0.344189i	−0.0159763	−	0.0491699i
$50$	4.59243	−	0.976151i	0.649467	−	0.138049i
$51$	−0.284816	+	2.70984i	−0.0398822	+	0.379454i
$52$	−5.87296	−	11.8292i	−0.814433	−	1.64042i
$53$	−8.75266	−	3.89694i	−1.20227	−	0.535285i	−0.294864	−	0.955539i	$-0.595274\pi$
$53$	−8.75266	−	3.89694i	−1.20227	−	0.535285i	−0.907407	+	0.420254i	$0.861941\pi$
$54$	0.209572	+	1.99395i	0.0285191	+	0.271342i
$55$	−0.146852	+	1.39720i	−0.0198015	+	0.188399i
$56$	10.1957			1.36245
$57$	−1.98918	−	3.44537i	−0.263474	−	0.456350i
$58$	1.16188	−	11.0546i	0.152563	−	1.45154i
$59$	−2.93187	−	9.02337i	−0.381697	−	1.17474i	−0.938848	−	0.344331i	$-0.888106\pi$
$59$	−2.93187	−	9.02337i	−0.381697	−	1.17474i	0.557151	−	0.830411i	$-0.311894\pi$
$60$	7.10178	−	21.8570i	0.916835	−	2.82173i
$61$	6.22875	+	10.7885i	0.797510	+	1.38133i	0.921233	+	0.389011i	$0.127183\pi$
$61$	6.22875	+	10.7885i	0.797510	+	1.38133i	−0.123723	+	0.992317i	$0.539484\pi$
$62$	13.0474	−	2.30569i	1.65702	−	0.292823i
$63$	3.40788	−	5.90262i	0.429352	−	0.743660i
$64$	−3.45302	+	10.6273i	−0.431628	+	1.32841i
$65$	−8.43776	−	4.41051i	−1.04658	−	0.547056i
$66$	2.43367	+	1.76817i	0.299564	+	0.217646i
$67$	−8.39468			−1.02557			−0.512787	−	0.858516i	$-0.671387\pi$
$67$	−8.39468			−1.02557			−0.512787	+	0.858516i	$0.671387\pi$
$68$	2.10030	+	3.63782i	0.254698	+	0.441151i
$69$	3.01679	+	2.19182i	0.363179	+	0.263865i
$70$	13.0981	−	9.51633i	1.56552	−	1.13742i
$71$	1.05717	+	10.0583i	0.125463	+	1.19370i	0.858246	+	0.513239i	$0.171555\pi$
$71$	1.05717	+	10.0583i	0.125463	+	1.19370i	−0.732783	+	0.680463i	$0.761779\pi$
$72$	−7.00483	−	7.77965i	−0.825527	−	0.916841i
$73$	−0.271657	+	2.58464i	−0.0317950	+	0.302509i	0.967055	+	0.254567i	$0.0819330\pi$
$73$	−0.271657	+	2.58464i	−0.0317950	+	0.302509i	−0.998850	+	0.0479421i	$0.984734\pi$
$74$	1.16334	−	3.58038i	0.135235	−	0.416211i
$75$	−1.44860	−	4.45832i	−0.167269	−	0.514803i
$76$	−5.60294	−	2.49459i	−0.642701	−	0.286149i
$77$	0.423585	+	1.30366i	0.0482720	+	0.148566i
$78$	−17.2121	+	10.9246i	−1.94889	+	1.23697i
$79$	0.00374488	+	0.0356301i	0.000421331	+	0.00400870i	0.994731	−	0.102524i	$-0.0326918\pi$
$79$	0.00374488	+	0.0356301i	0.000421331	+	0.00400870i	−0.994309	+	0.106533i	$0.966025\pi$
$80$	−1.70641	−	5.25180i	−0.190783	−	0.587169i
$81$	9.72087	−	2.06624i	1.08010	−	0.229582i
$82$	−19.0570	+	8.48472i	−2.10449	+	0.936980i
$83$	−13.4053	+	2.84938i	−1.47142	+	0.312760i	−0.872722	−	0.488217i	$-0.837648\pi$
$83$	−13.4053	+	2.84938i	−1.47142	+	0.312760i	−0.598696	+	0.800976i	$0.704314\pi$
$84$	−2.34386	−	22.3004i	−0.255737	−	2.43317i
$85$	2.76644	+	1.23170i	0.300062	+	0.133596i
$86$	25.8636	−	11.5152i	2.78894	−	1.24172i
$87$	−11.0983			−1.18986
$88$	2.10538			0.224434
$89$	9.08786	−	4.04618i	0.963311	−	0.428894i	0.136044	−	0.990703i	$-0.456561\pi$
$89$	9.08786	−	4.04618i	0.963311	−	0.428894i	0.827267	+	0.561809i	$0.189894\pi$
$90$	−16.2602	−	3.45621i	−1.71398	−	0.364317i
$91$	−9.27123	−	0.582733i	−0.971889	−	0.0610870i
$92$	5.74868			0.599341
$93$	−3.65122	−	12.7152i	−0.378614	−	1.31850i
$94$	0.174334	−	0.301955i	0.0179812	−	0.0311443i
$95$	−4.32484	+	0.919273i	−0.443719	+	0.0943154i
$96$	6.82845	+	1.45143i	0.696926	+	0.148136i
$97$	0.297215	−	2.82782i	0.0301776	−	0.287121i	−0.969017	−	0.246994i	$-0.920557\pi$
$97$	0.297215	−	2.82782i	0.0301776	−	0.287121i	0.999195	−	0.0401269i	$-0.0127762\pi$
$98$	−0.430607	+	0.745834i	−0.0434979	+	0.0753406i
$99$	0.703718	−	1.21887i	0.0707263	−	0.122502i
$100$	−5.84660	−	4.24780i	−0.584660	−	0.424780i
$101$	0.380878	+	3.62381i	0.0378987	+	0.360582i	0.996993	+	0.0774947i	$0.0246921\pi$
$101$	0.380878	+	3.62381i	0.0378987	+	0.360582i	−0.959094	+	0.283088i	$0.908641\pi$
$102$	5.24575	−	3.81126i	0.519407	−	0.377371i
$103$	1.42350	−	0.302574i	0.140262	−	0.0298135i	−0.137246	−	0.990537i	$-0.543825\pi$
$103$	1.42350	−	0.302574i	0.140262	−	0.0298135i	0.277507	+	0.960724i	$0.410492\pi$
$104$	−5.25163	+	13.2665i	−0.514965	+	1.30088i
$105$	−10.8166	−	12.0130i	−1.05559	−	1.17235i
$106$	7.04552	+	21.6839i	0.684321	+	2.10612i
$107$	0.825535	+	0.367552i	0.0798075	+	0.0355326i	0.446252	−	0.894907i	$-0.352758\pi$
$107$	0.825535	+	0.367552i	0.0798075	+	0.0355326i	−0.366445	+	0.930440i	$0.619425\pi$
$108$	2.06499	−	2.29340i	0.198704	−	0.220683i
$109$	−5.36273	−	16.5048i	−0.513656	−	1.58087i	−0.785714	−	0.618590i	$-0.787704\pi$
$109$	−5.36273	−	16.5048i	−0.513656	−	1.58087i	0.272058	−	0.962281i	$-0.412296\pi$
$110$	2.70472	−	1.96510i	0.257885	−	0.187365i
$111$	−3.67667	−	0.781500i	−0.348974	−	0.0741767i
$112$	−3.60518	−	4.00395i	−0.340657	−	0.378338i
$113$	8.46667	−	3.76961i	0.796478	−	0.354615i	0.0321831	−	0.999482i	$-0.489754\pi$
$113$	8.46667	−	3.76961i	0.796478	−	0.354615i	0.764295	+	0.644867i	$0.223087\pi$
$114$	−2.92555	+	9.00392i	−0.274003	+	0.843294i
$115$	3.35278	−	2.43594i	0.312649	−	0.227153i
$116$	−13.8418	+	10.0567i	−1.28518	+	0.933739i
$117$	5.92505	+	7.47463i	0.547771	+	0.691029i
$118$	−11.2889	+	19.5530i	−1.03923	+	1.80000i
$119$	2.95464			0.270851
$120$	−22.6820	+	10.0987i	−2.07057	+	0.921877i
$121$	−3.31172	−	10.1924i	−0.301065	−	0.926584i
$122$	9.16081	−	28.1941i	0.829381	−	2.55257i
$123$	10.4141	+	18.0377i	0.939007	+	1.62641i
$124$	−16.0757	−	12.5499i	−1.44364	−	1.12702i
$125$	7.99332			0.714944
$126$	−15.8650	+	3.37220i	−1.41336	+	0.300420i
$127$	−12.4905	+	13.8722i	−1.10836	+	1.23095i	−0.137702	+	0.990474i	$0.543972\pi$
$127$	−12.4905	+	13.8722i	−1.10836	+	1.23095i	−0.970654	+	0.240481i	$0.922695\pi$
$128$	18.9240	−	8.42552i	1.67266	−	0.744718i
$129$	−14.1337	−	24.4803i	−1.24440	−	2.15537i
$130$	5.63587	+	21.9448i	0.494299	+	1.92468i
$131$	7.56698	−	3.36904i	0.661130	−	0.294354i	−0.0486097	−	0.998818i	$-0.515479\pi$
$131$	7.56698	−	3.36904i	0.661130	−	0.294354i	0.709740	+	0.704464i	$0.248812\pi$
$132$	−0.484001	−	4.60497i	−0.0421269	−	0.400811i
$133$	−3.49009	+	2.53570i	−0.302629	+	0.219873i
$134$	13.3671	+	14.8456i	1.15474	+	1.28247i
$135$	0.232553	−	2.21259i	0.0200149	−	0.190429i
$136$	1.40236	−	4.31601i	0.120251	−	0.370095i
$137$	8.02134	+	1.70499i	0.685309	+	0.145667i	0.537392	−	0.843333i	$-0.319410\pi$
$137$	8.02134	+	1.70499i	0.685309	+	0.145667i	0.147918	+	0.989000i	$0.452743\pi$
$138$	−0.927561	−	8.82515i	−0.0789592	−	0.751247i
$139$	13.9521	−	15.4953i	1.18340	−	1.31430i	0.244684	−	0.969603i	$-0.421316\pi$
$139$	13.9521	−	15.4953i	1.18340	−	1.31430i	0.938715	−	0.344695i	$-0.112018\pi$
$140$	−24.3760	−	5.18129i	−2.06015	−	0.437899i
$141$	−0.318031	−	0.141596i	−0.0267830	−	0.0119246i
$142$	16.1043	−	17.8856i	1.35144	−	1.50093i
$143$	−1.91448	−	0.120333i	−0.160097	−	0.0100627i
$144$	−0.578257	+	5.50175i	−0.0481881	+	0.458479i
$145$	−3.81152	+	11.7306i	−0.316529	+	0.974177i
$146$	5.00338	−	3.63517i	0.414083	−	0.300849i
$147$	0.785541	+	0.349745i	0.0647903	+	0.0288465i
$148$	−5.29372	+	2.35692i	−0.435141	+	0.193737i
$149$	−6.51640			−0.533845			−0.266922	−	0.963718i	$-0.586007\pi$
$149$	−6.51640			−0.533845			−0.266922	+	0.963718i	$0.586007\pi$
$150$	−5.57771	+	9.66087i	−0.455418	+	0.788807i
$151$	7.12032	+	5.17322i	0.579444	+	0.420991i	0.838524	−	0.544865i	$-0.183419\pi$
$151$	7.12032	+	5.17322i	0.579444	+	0.420991i	−0.259080	+	0.965856i	$0.583419\pi$
$152$	2.04755	+	6.30170i	0.166078	+	0.511135i
$153$	−2.02995	−	2.25449i	−0.164112	−	0.182265i
$154$	1.63098	−	2.82494i	0.131428	−	0.227640i
$155$	−14.6937	−	0.507560i	−1.18022	−	0.0407682i
$156$	30.2242	+	8.43677i	2.41987	+	0.675483i
$157$	−1.08268	+	3.33215i	−0.0864073	+	0.265934i	−0.984919	−	0.173015i	$-0.944649\pi$
$157$	−1.08268	+	3.33215i	−0.0864073	+	0.265934i	0.898512	+	0.438949i	$0.144649\pi$
$158$	0.0570472	−	0.0633573i	0.00453843	−	0.00504044i
$159$	20.7964	−	9.25914i	1.64926	−	0.734298i
$160$	3.87926	−	6.71908i	0.306682	−	0.531190i
$161$	2.02177	−	3.50181i	0.159338	−	0.275981i
$162$	−19.1328	−	13.9008i	−1.50322	−	1.09215i
$163$	11.7590	+	5.23546i	0.921040	+	0.410073i	0.811796	−	0.583942i	$-0.198490\pi$
$163$	11.7590	+	5.23546i	0.921040	+	0.410073i	0.109244	+	0.994015i	$0.465157\pi$
$164$	29.3334	+	13.0601i	2.29055	+	1.01982i
$165$	−2.23359	−	2.48065i	−0.173885	−	0.193118i
$166$	26.3845	+	19.1695i	2.04783	+	1.48784i
$167$	9.92347	−	2.10930i	0.767901	−	0.163222i	0.192726	−	0.981253i	$-0.438267\pi$
$167$	9.92347	−	2.10930i	0.767901	−	0.163222i	0.575175	+	0.818030i	$0.304934\pi$
$168$	−16.2097	+	18.0027i	−1.25060	+	1.38894i
$169$	5.53371	−	11.7634i	0.425670	−	0.904879i
$170$	−2.22686	−	6.85358i	−0.170793	−	0.525646i
$171$	4.33265	+	0.920934i	0.331326	+	0.0704256i
$172$	−39.8104	−	17.7247i	−3.03552	−	1.35150i
$173$	20.2565	+	4.30565i	1.54007	+	0.327353i	0.898245	−	0.439495i	$-0.144843\pi$
$173$	20.2565	+	4.30565i	1.54007	+	0.327353i	0.641829	+	0.766848i	$0.278176\pi$
$174$	17.6720	+	19.6268i	1.33971	+	1.48790i
$175$	−4.64376	+	2.06753i	−0.351035	+	0.156291i
$176$	−0.744459	−	0.826805i	−0.0561157	−	0.0623228i
$177$	20.5940	+	9.16903i	1.54794	+	0.689186i
$178$	−21.6263	−	9.62865i	−1.62096	−	0.721698i
$179$	−1.74193	+	16.5734i	−0.130198	+	1.23875i	0.713006	+	0.701158i	$0.247333\pi$
$179$	−1.74193	+	16.5734i	−0.130198	+	1.23875i	−0.843204	+	0.537594i	$0.819333\pi$
$180$	12.7938	+	22.1595i	0.953593	+	1.65167i
$181$	6.61190	+	11.4521i	0.491458	+	0.851231i	0.999952	−	0.00983511i	$-0.00313066\pi$
$181$	6.61190	+	11.4521i	0.491458	+	0.851231i	−0.508493	+	0.861066i	$0.669797\pi$
$182$	13.7323	+	17.3237i	1.01790	+	1.28411i
$183$	−28.9523	−	6.15400i	−2.14022	−	0.454917i
$184$	−4.15570	−	4.61538i	−0.306363	−	0.340250i
$185$	−2.08872	+	3.61778i	−0.153566	+	0.265984i
$186$	−16.6723	+	26.7037i	−1.22247	+	1.95801i
$187$	0.610124			0.0446167
$188$	−0.524957	+	0.111583i	−0.0382865	+	0.00813804i
$189$	−0.670784	−	2.06446i	−0.0487923	−	0.150167i
$190$	8.51224	+	6.18450i	0.617543	+	0.448671i
$191$	−11.9561	+	20.7085i	−0.865110	+	1.49841i	0.00182773	+	0.999998i	$0.499418\pi$
$191$	−11.9561	+	20.7085i	−0.865110	+	1.49841i	−0.866938	+	0.498416i	$0.833915\pi$
$192$	−13.2750	−	22.9930i	−0.958041	−	1.65938i
$193$	−0.669535	+	6.37020i	−0.0481942	+	0.458537i	0.943637	+	0.330982i	$0.107380\pi$
$193$	−0.669535	+	6.37020i	−0.0481942	+	0.458537i	−0.991831	+	0.127556i	$0.959287\pi$
$194$	−5.47413	+	3.97719i	−0.393019	+	0.285545i
$195$	21.2026	−	7.88662i	1.51835	−	0.564773i
$196$	1.29665	−	0.275612i	0.0926181	−	0.0196866i
$197$	−16.2118	−	11.7786i	−1.15504	−	0.839189i	−0.165901	−	0.986142i	$-0.553053\pi$
$197$	−16.2118	−	11.7786i	−1.15504	−	0.839189i	−0.989143	+	0.146953i	$0.953053\pi$
$198$	−3.27607	+	0.696351i	−0.232820	+	0.0494875i
$199$	19.7934	+	4.20721i	1.40312	+	0.298241i	0.846438	−	0.532487i	$-0.178743\pi$
$199$	19.7934	+	4.20721i	1.40312	+	0.298241i	0.556678	+	0.830729i	$0.312076\pi$
$200$	0.816105	+	7.76472i	0.0577074	+	0.549049i
$201$	13.3464	−	14.8226i	0.941380	−	1.04551i
$202$	5.80206	−	6.44384i	0.408232	−	0.453387i
$203$	1.25795	+	11.9686i	0.0882908	+	0.840031i
$204$	−9.76254	−	2.07509i	−0.683514	−	0.145285i
$205$	22.6421	−	4.81272i	1.58139	−	0.336135i
$206$	−2.80176	−	2.03560i	−0.195208	−	0.141827i
$207$	−4.06103	+	0.863199i	−0.282261	+	0.0599965i
$208$	7.06685	−	2.62862i	0.489998	−	0.182262i
$209$	−0.720694	+	0.523615i	−0.0498514	+	0.0362192i
$210$	−4.02099	+	38.2572i	−0.277475	+	2.64000i
$211$	8.68933	+	15.0504i	0.598198	+	1.03611i	0.993087	+	0.117381i	$0.0374497\pi$
$211$	8.68933	+	15.0504i	0.598198	+	1.03611i	−0.394889	+	0.918729i	$0.629217\pi$
$212$	17.5472	−	30.3927i	1.20515	−	2.08738i
$213$	−19.4409	−	14.1246i	−1.33207	−	0.967803i
$214$	−0.664521	−	2.04518i	−0.0454257	−	0.139806i
$215$	−30.7292	+	6.53169i	−2.09571	+	0.445457i
$216$	−3.33405			−0.226854
$217$	−13.2985	+	5.37878i	−0.902760	+	0.365135i
$218$	−20.6488	+	35.7647i	−1.39851	+	2.42229i
$219$	−4.13185	−	4.58888i	−0.279204	−	0.310088i
$220$	−5.03358	−	1.06992i	−0.339364	−	0.0721341i
$221$	−1.52189	+	3.84453i	−0.102373	+	0.258611i
$222$	4.47240	+	7.74643i	0.300168	+	0.519906i
$223$	−5.43794	−	9.41878i	−0.364151	−	0.630728i	0.624488	−	0.781034i	$-0.285308\pi$
$223$	−5.43794	−	9.41878i	−0.364151	−	0.630728i	−0.988640	+	0.150306i	$0.951974\pi$
$224$	0.791274	−	7.52847i	0.0528692	−	0.503017i
$225$	4.76804	+	2.12287i	0.317869	+	0.141525i
$226$	−20.1481	−	8.97050i	−1.34023	−	0.596709i
$227$	6.98845	+	7.76146i	0.463840	+	0.515146i	0.929000	−	0.370080i	$-0.120670\pi$
$227$	6.98845	+	7.76146i	0.463840	+	0.515146i	−0.465160	+	0.885227i	$0.654003\pi$
$228$	13.3126	−	5.92716i	0.881649	−	0.392536i
$229$	14.1486	+	15.7136i	0.934964	+	1.03838i	0.999182	+	0.0404471i	$0.0128782\pi$
$229$	14.1486	+	15.7136i	0.934964	+	1.03838i	−0.0642174	+	0.997936i	$0.520455\pi$
$230$	−9.64657	−	2.05044i	−0.636076	−	0.135202i
$231$	−2.97533	−	1.32470i	−0.195763	−	0.0871591i
$232$	18.0803	+	3.84309i	1.18703	+	0.252311i
$233$	7.09608	+	21.8395i	0.464879	+	1.43075i	0.859134	+	0.511750i	$0.171003\pi$
$233$	7.09608	+	21.8395i	0.464879	+	1.43075i	−0.394255	+	0.919001i	$0.628997\pi$
$234$	3.78394	−	22.3802i	0.247364	−	1.46304i
$235$	−0.258887	+	0.287523i	−0.0168879	+	0.0187560i
$236$	33.9934	−	7.22553i	2.21278	−	0.470342i
$237$	−0.0688665	−	0.0500345i	−0.00447336	−	0.00325009i
$238$	−4.70474	−	5.22514i	−0.304963	−	0.338696i
$239$	−2.60830	−	1.16129i	−0.168717	−	0.0751175i	0.320640	−	0.947201i	$-0.396102\pi$
$239$	−2.60830	−	1.16129i	−0.168717	−	0.0751175i	−0.489357	+	0.872083i	$0.662769\pi$
$240$	11.9862	+	5.33658i	0.773703	+	0.344475i
$241$	−6.88070	−	4.99912i	−0.443225	−	0.322022i	0.343690	−	0.939083i	$-0.388323\pi$
$241$	−6.88070	−	4.99912i	−0.443225	−	0.322022i	−0.786915	+	0.617061i	$0.788323\pi$
$242$	−12.7515	+	22.0863i	−0.819698	+	1.41976i
$243$	−10.5427	+	18.2604i	−0.676312	+	1.17141i
$244$	−41.6859	+	18.5598i	−2.66867	+	1.18817i
$245$	0.639455	−	0.710187i	0.0408533	−	0.0453722i
$246$	15.3163	−	47.1387i	0.976532	−	3.00546i
$247$	−1.50172	−	5.84735i	−0.0955522	−	0.372058i
$248$	1.54525	+	21.9788i	0.0981233	+	1.39566i
$249$	16.2813	−	28.2000i	1.03178	−	1.78710i
$250$	−12.7280	−	14.1358i	−0.804987	−	0.894028i
$251$	−3.31174	−	10.1925i	−0.209035	−	0.643344i	−0.999524	−	0.0308669i	$-0.990173\pi$
$251$	−3.31174	−	10.1925i	−0.209035	−	0.643344i	0.790488	−	0.612477i	$-0.209827\pi$
$252$	20.1976	+	14.6744i	1.27233	+	0.924403i
$253$	0.417489	−	0.723113i	0.0262473	−	0.0454617i
$254$	44.4213			2.78724
$255$	−6.57307	+	2.92652i	−0.411622	+	0.183266i
$256$	−24.6170	−	10.9602i	−1.53856	−	0.685013i
$257$	12.3674	−	8.98541i	0.771454	−	0.560494i	−0.130948	−	0.991389i	$-0.541802\pi$
$257$	12.3674	−	8.98541i	0.771454	−	0.560494i	0.902402	+	0.430895i	$0.141802\pi$
$258$	−20.7868	+	63.9753i	−1.29413	+	3.98293i
$259$	−0.426049	+	4.05358i	−0.0264734	+	0.251877i
$260$	19.2975	−	29.0489i	1.19678	−	1.80154i
$261$	8.26819	−	9.18276i	0.511788	−	0.568398i
$262$	−18.0071	−	8.01727i	−1.11248	−	0.495309i
$263$	−27.1230	−	5.76517i	−1.67248	−	0.355496i	−0.728382	−	0.685172i	$-0.759727\pi$
$263$	−27.1230	−	5.76517i	−1.67248	−	0.355496i	−0.944094	+	0.329676i	$0.893060\pi$
$264$	−3.34725	+	3.71750i	−0.206009	+	0.228797i
$265$	−2.64456	−	25.1613i	−0.162454	−	1.54565i
$266$	10.0416	+	2.13441i	0.615691	+	0.130869i
$267$	−7.30401	+	22.4794i	−0.446998	+	1.37572i
$268$	3.21416	−	30.5807i	0.196336	−	1.86801i
$269$	1.36047	+	1.51096i	0.0829495	+	0.0921248i	0.783191	−	0.621782i	$-0.213591\pi$
$269$	1.36047	+	1.51096i	0.0829495	+	0.0921248i	−0.700241	+	0.713906i	$0.746924\pi$
$270$	−4.28317	+	3.11190i	−0.260665	+	0.189384i
$271$	−1.73412	−	16.4990i	−0.105340	−	1.00224i	−0.911711	−	0.410833i	$-0.865238\pi$
$271$	−1.73412	−	16.4990i	−0.105340	−	1.00224i	0.806371	−	0.591410i	$-0.201429\pi$
$272$	−2.19082	+	0.975414i	−0.132838	+	0.0591432i
$273$	15.7689	−	15.4439i	0.954376	−	0.934708i
$274$	−9.75738	−	16.9003i	−0.589465	−	1.02098i
$275$	−0.958923	+	0.426940i	−0.0578252	+	0.0257454i
$276$	−9.13959	+	10.1505i	−0.550138	+	0.610991i
$277$	−19.7023	+	4.18786i	−1.18380	+	0.251624i	−0.757424	−	0.652923i	$-0.773543\pi$
$277$	−19.7023	+	4.18786i	−1.18380	+	0.251624i	−0.426374	+	0.904547i	$0.640209\pi$
$278$	−49.6190			−2.97595
$279$	13.2408	+	6.45177i	0.792704	+	0.386257i
$280$	13.4615	+	23.3161i	0.804481	+	1.39340i
$281$	1.39134	−	4.28211i	0.0830004	−	0.255449i	−0.900941	−	0.433942i	$-0.857122\pi$
$281$	1.39134	−	4.28211i	0.0830004	−	0.255449i	0.983941	+	0.178493i	$0.0571222\pi$
$282$	0.256001	+	0.787890i	0.0152446	+	0.0469182i
$283$	26.7669	−	11.9174i	1.59113	−	0.708416i	0.595635	−	0.803255i	$-0.296900\pi$
$283$	26.7669	−	11.9174i	1.59113	−	0.708416i	0.995493	+	0.0948391i	$0.0302337\pi$
$284$	−37.0458			−2.19826
$285$	5.25271	−	9.09796i	0.311144	−	0.538916i
$286$	2.83567	+	3.57729i	0.167677	+	0.211529i
$287$	18.2719	−	13.2753i	1.07855	−	0.783616i
$288$	−6.28812	+	4.56858i	−0.370531	+	0.269206i
$289$	−4.84690	+	14.9172i	−0.285111	+	0.877483i
$290$	26.8143	−	11.9385i	1.57459	−	0.701052i
$291$	4.52059	+	5.02062i	0.265002	+	0.294314i
$292$	−9.31147	−	1.97921i	−0.544913	−	0.115825i
$293$	−2.17067	+	1.57708i	−0.126812	+	0.0921342i	−0.649383	−	0.760461i	$-0.724973\pi$
$293$	−2.17067	+	1.57708i	−0.126812	+	0.0921342i	0.522571	+	0.852596i	$0.324973\pi$
$294$	−0.632326	−	1.94610i	−0.0368780	−	0.113499i
$295$	16.7642	−	18.6185i	0.976047	−	1.08401i
$296$	5.71909	+	2.54630i	0.332415	+	0.148001i
$297$	−0.138515	−	0.426305i	−0.00803745	−	0.0247367i
$298$	10.3762	+	11.5240i	0.601079	+	0.667566i
$299$	3.51511	+	4.43442i	0.203284	+	0.256449i
$300$	16.7957	−	3.57003i	0.969700	−	0.206116i
$301$	−24.7980	+	18.0168i	−1.42934	+	1.03847i
$302$	−2.18926	−	20.8294i	−0.125978	−	1.19860i
$303$	−7.00416	−	5.08882i	−0.402378	−	0.292345i
$304$	1.75074	−	3.03236i	0.100412	−	0.173918i
$305$	−16.4479	+	28.4885i	−0.941802	+	1.63125i
$306$	−0.754622	+	7.17975i	−0.0431389	+	0.410439i
$307$	−6.39574	−	1.35946i	−0.365024	−	0.0775883i	0.0217481	−	0.999763i	$-0.493077\pi$
$307$	−6.39574	−	1.35946i	−0.365024	−	0.0775883i	−0.386773	+	0.922175i	$0.626410\pi$
$308$	−4.91124	+	1.04392i	−0.279844	+	0.0594826i
$309$	−1.72890	+	2.99455i	−0.0983538	+	0.170354i
$310$	22.4995	+	26.7933i	1.27789	+	1.52176i
$311$	0.291983			0.0165568			0.00827842	−	0.999966i	$-0.497365\pi$
$311$	0.291983			0.0165568			0.00827842	+	0.999966i	$0.497365\pi$
$312$	−15.0755	−	30.3647i	−0.853479	−	1.71906i
$313$	25.6162	+	5.44489i	1.44791	+	0.307763i	0.863770	−	0.503887i	$-0.168097\pi$
$313$	25.6162	+	5.44489i	1.44791	+	0.307763i	0.584143	+	0.811650i	$0.301431\pi$
$314$	7.61673	−	3.39119i	0.429837	−	0.191376i
$315$	17.9979			1.01407
$316$	−0.131229			−0.00738223
$317$	2.51273	−	1.11874i	0.141129	−	0.0628346i	−0.334957	−	0.942233i	$-0.608722\pi$
$317$	2.51273	−	1.11874i	0.141129	−	0.0628346i	0.476086	+	0.879399i	$0.342055\pi$
$318$	−49.4890	−	22.0339i	−2.77520	−	1.23560i
$319$	0.259763	+	2.47148i	0.0145440	+	0.138376i
$320$	−28.8622	+	6.13486i	−1.61345	+	0.342949i
$321$	−1.96148	+	0.873306i	−0.109479	+	0.0487432i
$322$	−9.41210	+	2.00060i	−0.524516	+	0.111489i
$323$	0.593365	+	1.82619i	0.0330157	+	0.101612i
$324$	3.80508	+	36.2029i	0.211393	+	2.01127i
$325$	−0.298316	−	7.10734i	−0.0165476	−	0.394244i
$326$	−9.46553	−	29.1319i	−0.524247	−	1.61347i
$327$	37.6687	+	16.7712i	2.08309	+	0.927450i
$328$	−10.7196	−	32.9917i	−0.591893	−	1.82166i
$329$	−0.116653	+	0.359021i	−0.00643128	+	0.0197934i
$330$	−0.830323	+	7.90000i	−0.0457078	+	0.434881i
$331$	−1.84201	−	2.04576i	−0.101246	−	0.112445i	0.690392	−	0.723436i	$-0.257438\pi$
$331$	−1.84201	−	2.04576i	−0.101246	−	0.112445i	−0.791638	+	0.610990i	$0.790771\pi$
$332$	−5.24728	−	49.9245i	−0.287982	−	2.73996i
$333$	3.38573	−	2.45988i	0.185537	−	0.134801i
$334$	−19.5316	−	14.1905i	−1.06872	−	0.776471i
$335$	−11.0836	−	19.1974i	−0.605564	−	1.04887i
$336$	12.8016			0.698383
$337$	1.91719	+	1.39292i	0.104436	+	0.0758773i	0.638778	−	0.769391i	$-0.279440\pi$
$337$	1.91719	+	1.39292i	0.104436	+	0.0758773i	−0.534342	+	0.845269i	$0.679440\pi$
$338$	−29.6145	+	8.94507i	−1.61082	+	0.486547i
$339$	−6.80476	+	20.9429i	−0.369584	+	1.13746i
$340$	−5.54612	+	9.60616i	−0.300780	+	0.520967i
$341$	−2.74610	+	1.11070i	−0.148710	+	0.0601479i
$342$	−5.27036	−	9.12853i	−0.284988	−	0.493614i
$343$	5.86130	−	18.0392i	0.316481	−	0.974027i
$344$	14.5484	+	44.7753i	0.784396	+	2.41412i
$345$	−1.02927	+	9.79287i	−0.0554141	+	0.527230i
$346$	−24.6406	−	42.6787i	−1.32469	−	2.29442i
$347$	−26.5481			−1.42518			−0.712588	−	0.701583i	$-0.752477\pi$
$347$	−26.5481			−1.42518			−0.712588	+	0.701583i	$0.752477\pi$
$348$	4.24930	−	40.4294i	0.227787	−	2.16725i
$349$	1.09134	+	10.3834i	0.0584181	+	0.555811i	0.984113	+	0.177541i	$0.0568142\pi$
$349$	1.09134	+	10.3834i	0.0584181	+	0.555811i	−0.925695	+	0.378270i	$0.876519\pi$
$350$	11.0507	+	4.92009i	0.590685	+	0.262990i
$351$	3.03175	+	0.190558i	0.161823	+	0.0101712i
$352$	0.163396	−	1.55461i	0.00870903	−	0.0828609i
$353$	12.9273	−	2.74778i	0.688050	−	0.146250i	0.149397	−	0.988777i	$-0.452267\pi$
$353$	12.9273	−	2.74778i	0.688050	−	0.146250i	0.538653	+	0.842528i	$0.318933\pi$
$354$	−16.5773	−	51.0196i	−0.881072	−	2.71166i
$355$	−21.6061	+	15.6978i	−1.14673	+	0.833151i
$356$	11.2601	+	34.6550i	0.596784	+	1.83671i
$357$	−4.69745	+	5.21705i	−0.248616	+	0.276116i
$358$	32.0830	−	23.3097i	1.69564	−	1.23195i
$359$	−15.2540	+	16.9413i	−0.805074	+	0.894126i	−0.996169	−	0.0874459i	$-0.972130\pi$
$359$	−15.2540	+	16.9413i	−0.805074	+	0.894126i	0.191095	+	0.981572i	$0.438796\pi$
$360$	8.54235	−	26.2907i	0.450222	−	1.38564i
$361$	13.1032	+	9.52001i	0.689641	+	0.501053i
$362$	9.72431	−	29.9284i	0.511099	−	1.57300i
$363$	23.2621	+	10.3570i	1.22094	+	0.543599i
$364$	5.67259	−	33.5507i	0.297324	−	1.75853i
$365$	−6.26937	+	2.79131i	−0.328154	+	0.146104i
$366$	35.2184	+	61.0000i	1.84089	+	3.18852i
$367$	10.7160			0.559372			0.279686	−	0.960092i	$-0.409770\pi$
$367$	10.7160			0.559372			0.279686	+	0.960092i	$0.409770\pi$
$368$	−0.343058	+	3.26398i	−0.0178831	+	0.170147i
$369$	−22.6830	−	4.82142i	−1.18083	−	0.250993i
$370$	9.72380	−	2.06686i	0.505516	−	0.107451i
$371$	−12.3425	−	21.3778i	−0.640789	−	1.10988i
$372$	47.7177	−	8.43249i	2.47405	−	0.437204i
$373$	8.22430	+	14.2449i	0.425838	+	0.737574i	0.996498	−	0.0836128i	$-0.0266459\pi$
$373$	8.22430	+	14.2449i	0.425838	+	0.737574i	−0.570660	+	0.821186i	$0.693313\pi$
$374$	−0.971515	−	1.07898i	−0.0502359	−	0.0557926i
$375$	−12.7082	+	14.1139i	−0.656251	+	0.728841i
$376$	0.469076	+	0.340804i	0.0241907	+	0.0175756i
$377$	−16.2213	−	4.52801i	−0.835440	−	0.233204i
$378$	−2.58280	+	4.47354i	−0.132845	+	0.230094i
$379$	−1.56895	+	14.9276i	−0.0805915	+	0.766777i	0.877357	+	0.479838i	$0.159304\pi$
$379$	−1.56895	+	14.9276i	−0.0805915	+	0.766777i	−0.957949	+	0.286939i	$0.907362\pi$
$380$	−1.69289	−	16.1068i	−0.0868434	−	0.826260i
$381$	−4.63610	−	44.1095i	−0.237514	−	2.25980i
$382$	55.6600	−	11.8309i	2.84781	−	0.605321i
$383$	−3.12035	+	1.38927i	−0.159443	+	0.0709884i	−0.484906	−	0.874566i	$-0.661146\pi$
$383$	−3.12035	+	1.38927i	−0.159443	+	0.0709884i	0.325464	+	0.945555i	$0.394480\pi$
$384$	−15.2094	+	46.8099i	−0.776154	+	2.38876i
$385$	−2.42202	+	2.68992i	−0.123437	+	0.137091i
$386$	12.3315	−	8.95938i	0.627659	−	0.456021i
$387$	30.7847	+	6.54349i	1.56487	+	0.332624i
$388$	10.1875	+	2.16543i	0.517194	+	0.109933i
$389$	2.94264	+	27.9973i	0.149198	+	1.41952i	0.771244	+	0.636540i	$0.219635\pi$
$389$	2.94264	+	27.9973i	0.149198	+	1.41952i	−0.622046	+	0.782980i	$0.713698\pi$
$390$	−47.7085	−	24.9377i	−2.41581	−	1.26277i
$391$	−1.20429	−	1.33750i	−0.0609038	−	0.0676405i
$392$	−1.15862	−	0.841790i	−0.0585194	−	0.0425168i
$393$	−6.08167	+	18.7174i	−0.306780	+	0.944170i
$394$	4.98459	+	47.4252i	0.251120	+	2.38925i
$395$	−0.0765366	+	0.0556071i	−0.00385097	+	0.00279790i
$396$	4.17075	+	3.03023i	0.209588	+	0.152275i
$397$	30.3187			1.52165			0.760825	−	0.648957i	$-0.224794\pi$
$397$	30.3187			1.52165			0.760825	+	0.648957i	$0.224794\pi$
$398$	−24.0772	−	41.7029i	−1.20688	−	2.09038i
$399$	1.07142	−	10.1939i	0.0536383	−	0.510334i
$400$	2.76072	−	3.06609i	0.138036	−	0.153304i
$401$	−13.5265	−	15.0227i	−0.675482	−	0.750199i	0.303792	−	0.952738i	$-0.401747\pi$
$401$	−13.5265	−	15.0227i	−0.675482	−	0.750199i	−0.979274	+	0.202539i	$0.935081\pi$
$402$	−47.4649			−2.36733
$403$	−0.148941	−	20.0743i	−0.00741929	−	0.999972i
$404$	−13.3469			−0.664031
$405$	17.5598	+	19.5022i	0.872555	+	0.969070i
$406$	19.1629	−	21.2825i	0.951037	−	1.05623i
$407$	−0.0879778	+	0.837053i	−0.00436090	+	0.0414912i
$408$	5.39131	+	9.33802i	0.266909	+	0.462301i
$409$	−2.71214			−0.134107			−0.0670533	−	0.997749i	$-0.521360\pi$
$409$	−2.71214			−0.134107			−0.0670533	+	0.997749i	$0.521360\pi$
$410$	−44.5646	−	32.3781i	−2.20089	−	1.59904i
$411$	−15.7633	+	11.4527i	−0.777547	+	0.564921i
$412$	0.557206	+	5.30146i	0.0274516	+	0.261184i
$413$	7.55382	−	23.2483i	0.371699	−	1.14397i
$414$	7.99301	+	5.80726i	0.392835	+	0.285411i
$415$	−24.2153	−	26.8938i	−1.18868	−	1.32017i
$416$	9.38835	+	4.90739i	0.460302	+	0.240605i
$417$	5.17857	+	49.2708i	0.253596	+	2.41280i
$418$	2.07357	+	0.440750i	0.101421	+	0.0215578i
$419$	17.2609	+	3.66892i	0.843251	+	0.179239i	0.609231	−	0.792993i	$-0.291478\pi$
$419$	17.2609	+	3.66892i	0.843251	+	0.179239i	0.234021	+	0.972232i	$0.424812\pi$
$420$	47.9031	−	34.8037i	2.33743	−	1.69825i
$421$	−3.68321	+	4.09062i	−0.179509	+	0.199364i	−0.826183	−	0.563401i	$-0.809492\pi$
$421$	−3.68321	+	4.09062i	−0.179509	+	0.199364i	0.646675	+	0.762766i	$0.276159\pi$
$422$	12.7797	−	39.3317i	0.622104	−	1.91464i
$423$	0.354090	−	0.157651i	0.0172164	−	0.00766526i
$424$	−37.0859	+	7.88285i	−1.80105	+	0.382825i
$425$	0.236502	+	2.25016i	0.0114720	+	0.109149i
$426$	5.97741	+	56.8713i	0.289607	+	2.75542i
$427$	−3.35496	+	31.9203i	−0.162358	+	1.54473i
$428$	−1.65502	+	2.86658i	−0.0799986	+	0.138562i
$429$	3.25623	−	3.18912i	0.157212	−	0.153972i
$430$	60.4818	+	43.9426i	2.91669	+	2.11910i
$431$	16.7496	−	18.6024i	0.806802	−	0.896044i	−0.189508	−	0.981879i	$-0.560689\pi$
$431$	16.7496	−	18.6024i	0.806802	−	0.896044i	0.996309	+	0.0858352i	$0.0273559\pi$
$432$	1.17892	+	1.30932i	0.0567206	+	0.0629946i
$433$	1.40934	+	2.44104i	0.0677284	+	0.117309i	0.897901	−	0.440197i	$-0.145092\pi$
$433$	1.40934	+	2.44104i	0.0677284	+	0.117309i	−0.830173	+	0.557506i	$0.811758\pi$
$434$	30.6876	+	14.9530i	1.47305	+	0.717768i
$435$	−14.6532	−	25.3801i	−0.702568	−	1.21688i
$436$	62.1779	−	13.2163i	2.97778	−	0.632947i
$437$	2.57040	+	0.546356i	0.122959	+	0.0261357i
$438$	−1.53599	+	14.6140i	−0.0733924	+	0.698282i
$439$	−12.8527			−0.613428			−0.306714	−	0.951802i	$-0.599229\pi$
$439$	−12.8527			−0.613428			−0.306714	+	0.951802i	$0.599229\pi$
$440$	2.77977	+	4.81470i	0.132520	+	0.229532i
$441$	−0.874608	+	0.389401i	−0.0416480	+	0.0185429i
$442$	9.22221	−	3.43034i	0.438656	−	0.163165i
$443$	21.3834	+	9.52050i	1.01596	+	0.452333i	0.846036	−	0.533125i	$-0.178983\pi$
$443$	21.3834	+	9.52050i	1.01596	+	0.452333i	0.169919	+	0.985458i	$0.445649\pi$
$444$	4.25462	−	13.0944i	0.201915	−	0.621432i
$445$	21.2519	+	15.4404i	1.00744	+	0.731945i
$446$	−7.99774	+	24.6145i	−0.378704	+	1.16553i
$447$	10.3602	−	11.5061i	0.490019	−	0.544221i
$448$	−23.2914	+	16.9222i	−1.10042	+	0.799500i
$449$	−20.0713	+	22.2914i	−0.947221	+	1.05200i	0.0513564	+	0.998680i	$0.483646\pi$
$449$	−20.0713	+	22.2914i	−0.947221	+	1.05200i	−0.998578	+	0.0533155i	$0.983021\pi$
$450$	−3.83807	−	11.8124i	−0.180928	−	0.556840i
$451$	3.77309	−	2.74131i	0.177668	−	0.129083i
$452$	10.4904	+	32.2862i	0.493429	+	1.51862i
$453$	−20.4547	+	4.34779i	−0.961048	+	0.204277i
$454$	2.59792	−	24.7175i	0.121926	−	1.16005i
$455$	−10.9083	−	21.9714i	−0.511391	−	1.03003i
$456$	−14.3823	−	6.40342i	−0.673514	−	0.299868i
$457$	−3.67726	−	34.9868i	−0.172015	−	1.63661i	−0.651205	−	0.758902i	$-0.725736\pi$
$457$	−3.67726	−	34.9868i	−0.172015	−	1.63661i	0.479190	−	0.877711i	$-0.340930\pi$
$458$	5.25965	−	50.0422i	0.245767	−	2.33832i
$459$	−0.966185			−0.0450977
$460$	7.59008	+	13.1464i	0.353889	+	0.612954i
$461$	0.467403	−	4.44705i	0.0217691	−	0.207120i	−0.978231	−	0.207520i	$-0.933461\pi$
$461$	0.467403	−	4.44705i	0.0217691	−	0.207120i	1.00000		0.000400428i	$0.000127460\pi$
$462$	2.39502	+	7.37110i	0.111426	+	0.342935i
$463$	4.62101	−	14.2220i	0.214756	−	0.660952i	−0.784414	−	0.620237i	$-0.787036\pi$
$463$	4.62101	−	14.2220i	0.214756	−	0.660952i	0.999171	−	0.0407152i	$-0.0129636\pi$
$464$	−4.88395	−	8.45924i	−0.226732	−	0.392710i
$465$	24.2571	−	25.1379i	1.12489	−	1.16574i
$466$	27.3229	−	47.3246i	1.26571	−	2.19227i
$467$	2.77579	−	8.54300i	0.128448	−	0.395323i	−0.866065	−	0.499931i	$-0.833359\pi$
$467$	2.77579	−	8.54300i	0.128448	−	0.395323i	0.994514	+	0.104608i	$0.0333587\pi$
$468$	−29.4976	+	18.7223i	−1.36353	+	0.865437i
$469$	−17.4978	−	12.7129i	−0.807974	−	0.587027i
$470$	0.920704			0.0424689
$471$	−4.16232	−	7.20935i	−0.191790	−	0.332189i
$472$	−30.3749	−	22.0686i	−1.39812	−	1.01579i
$473$	−5.12073	+	3.72043i	−0.235451	+	0.171065i
$474$	0.0211741	+	0.201458i	0.000972560	+	0.00925329i
$475$	−2.21047	−	2.45498i	−0.101423	−	0.112642i
$476$	−1.13127	+	10.7633i	−0.0518518	+	0.493337i
$477$	−7.83222	+	24.1051i	−0.358613	+	1.10370i
$478$	2.09957	+	6.46180i	0.0960320	+	0.295556i
$479$	−16.6174	−	7.39855i	−0.759269	−	0.338048i	−0.00968115	−	0.999953i	$-0.503082\pi$
$479$	−16.6174	−	7.39855i	−0.759269	−	0.338048i	−0.749588	+	0.661905i	$0.769748\pi$
$480$	5.69651	+	17.5321i	0.260009	+	0.800225i
$481$	−5.05500	−	2.64230i	−0.230488	−	0.120479i
$482$	2.11558	+	20.1284i	0.0963622	+	0.916825i
$483$	2.96887	+	9.13725i	0.135088	+	0.415759i
$484$	38.3976	−	8.16166i	1.74534	−	0.370984i
$485$	6.85923	−	3.05393i	0.311462	−	0.138672i
$486$	49.0800	−	10.4323i	2.22632	−	0.473218i
$487$	3.96173	+	37.6933i	0.179523	+	1.70805i	0.599386	+	0.800460i	$0.295411\pi$
$487$	3.96173	+	37.6933i	0.179523	+	1.70805i	−0.419863	+	0.907587i	$0.637922\pi$
$488$	45.0355	+	20.0511i	2.03866	+	0.907671i
$489$	−27.9396	+	12.4395i	−1.26347	+	0.562534i
$490$	−2.27415			−0.102736
$491$	19.5395			0.881804			0.440902	−	0.897555i	$-0.354659\pi$
$491$	19.5395			0.881804			0.440902	+	0.897555i	$0.354659\pi$
$492$	−69.6963	+	31.0308i	−3.14215	+	1.39898i
$493$	5.23955	+	1.11370i	0.235977	+	0.0501585i
$494$	−7.94955	+	11.9666i	−0.357667	+	0.538403i
$495$	3.71652			0.167045
$496$	8.08492	−	8.37851i	0.363024	−	0.376206i
$497$	−13.0287	+	22.5664i	−0.584419	+	1.01224i
$498$	−75.7955	+	16.1108i	−3.39648	+	0.721943i
$499$	9.60665	+	2.04196i	0.430053	+	0.0914106i	0.417852	−	0.908515i	$-0.362783\pi$
$499$	9.60665	+	2.04196i	0.430053	+	0.0914106i	0.0122007	+	0.999926i	$0.496116\pi$
$500$	−3.06049	+	29.1186i	−0.136869	+	1.30222i
$501$	−12.0525	+	20.8755i	−0.538465	+	0.932649i
$502$	−12.7516	+	22.0864i	−0.569131	+	0.985764i
$503$	31.6016	+	22.9599i	1.40905	+	1.02373i	0.993460	+	0.114177i	$0.0364230\pi$
$503$	31.6016	+	22.9599i	1.40905	+	1.02373i	0.415585	+	0.909554i	$0.363577\pi$
$504$	−2.81931	−	26.8240i	−0.125582	−	1.19483i
$505$	−7.78425	+	5.65559i	−0.346395	+	0.251670i
$506$	−1.94357	+	0.413119i	−0.0864023	+	0.0183654i
$507$	11.9731	+	28.4731i	0.531742	+	1.26454i
$508$	−45.7520	−	50.8127i	−2.02992	−	2.25445i
$509$	−5.29816	−	16.3061i	−0.234837	−	0.722754i	−0.997143	−	0.0755371i	$-0.975933\pi$
$509$	−5.29816	−	16.3061i	−0.234837	−	0.722754i	0.762306	−	0.647217i	$-0.224067\pi$
$510$	15.6419	+	6.96421i	0.692634	+	0.308381i
$511$	−4.48042	+	4.97601i	−0.198202	+	0.220126i
$512$	7.01312	+	21.5842i	0.309939	+	0.953895i
$513$	1.14128	−	0.829190i	0.0503888	−	0.0366096i
$514$	−35.5831	−	7.56343i	−1.56950	−	0.333608i
$515$	2.57141	+	2.85585i	0.113310	+	0.125844i
$516$	94.5898	−	42.1141i	4.16408	−	1.85397i
$517$	−0.0240885	+	0.0741367i	−0.00105941	+	0.00326053i
$518$	7.84698	−	5.70117i	0.344777	−	0.250495i
$519$	−39.8076	+	28.9219i	−1.74736	+	1.26953i
$520$	−37.2723	+	5.50620i	−1.63450	+	0.241463i
$521$	−2.84884	+	4.93434i	−0.124810	+	0.216177i	−0.921659	−	0.388002i	$-0.873165\pi$
$521$	−2.84884	+	4.93434i	−0.124810	+	0.216177i	0.796849	+	0.604179i	$0.206499\pi$
$522$	−29.4049			−1.28702
$523$	24.8577	−	11.0674i	1.08695	−	0.483942i	0.216543	−	0.976273i	$-0.430522\pi$
$523$	24.8577	−	11.0674i	1.08695	−	0.483942i	0.870408	+	0.492331i	$0.163855\pi$
$524$	9.37570	+	28.8554i	0.409579	+	1.26056i
$525$	3.73224	−	11.4866i	0.162888	−	0.501318i
$526$	32.9932	+	57.1458i	1.43857	+	2.49168i
$527$	0.447802	+	6.36931i	0.0195066	+	0.277451i
$528$	2.64349			0.115043
$529$	20.0881	−	4.26987i	0.873397	−	0.185646i
$530$	−40.2856	+	44.7417i	−1.74989	+	1.94345i
$531$	−22.9290	+	10.2086i	−0.995033	+	0.443017i
$532$	−7.90092	−	13.6848i	−0.342548	−	0.593311i
$533$	7.86205	+	30.6130i	0.340543	+	1.32599i
$534$	51.3842	−	22.8777i	2.22361	−	0.990016i
$535$	0.249430	+	2.37317i	0.0107838	+	0.102601i
$536$	−26.8755	+	19.5262i	−1.16084	+	0.843402i
$537$	−26.4945	−	29.4251i	−1.14332	−	1.26979i
$538$	0.505748	−	4.81187i	0.0218043	−	0.207455i
$539$	0.0594989	−	0.183119i	0.00256280	−	0.00788749i
$540$	7.97113	+	1.69432i	0.343023	+	0.0729117i
$541$	−1.69144	−	16.0930i	−0.0727207	−	0.691891i	−0.968774	−	0.247945i	$-0.920245\pi$
$541$	−1.69144	−	16.0930i	−0.0727207	−	0.691891i	0.896053	−	0.443946i	$-0.146422\pi$
$542$	−26.4165	+	29.3385i	−1.13468	+	1.26020i
$543$	−30.7332	−	6.53255i	−1.31889	−	0.280338i
$544$	−3.07810	−	1.37046i	−0.131972	−	0.0587579i
$545$	30.6636	−	34.0553i	1.31348	−	1.45877i
$546$	−52.4210	−	3.29487i	−2.24341	−	0.141007i
$547$	3.49250	−	33.2289i	0.149329	−	1.42077i	−0.621346	−	0.783537i	$-0.713414\pi$
$547$	3.49250	−	33.2289i	0.149329	−	1.42077i	0.770674	−	0.637229i	$-0.219920\pi$
$548$	−9.28225	+	28.5678i	−0.396518	+	1.22036i
$549$	26.6613	−	19.3706i	1.13788	−	0.826715i
$550$	2.28194	+	1.01598i	0.0973022	+	0.0433217i
$551$	−7.14487	+	3.18110i	−0.304382	+	0.135519i
$552$	14.7564			0.628076
$553$	−0.0461524	+	0.0799384i	−0.00196260	+	0.00339933i
$554$	38.7785	+	28.1743i	1.64754	+	1.19701i
$555$	−3.06719	−	9.43985i	−0.130195	−	0.400699i
$556$	51.1054	+	56.7583i	2.16735	+	2.40709i
$557$	−5.55524	+	9.62196i	−0.235383	+	0.407696i	−0.959384	−	0.282104i	$-0.908968\pi$
$557$	−5.55524	+	9.62196i	−0.235383	+	0.407696i	0.724001	+	0.689799i	$0.242301\pi$
$558$	−9.67394	−	33.6890i	−0.409530	−	1.42617i
$559$	−10.6701	−	41.5470i	−0.451299	−	1.75725i
$560$	4.39649	−	13.5310i	0.185786	−	0.571790i
$561$	−0.970011	+	1.07731i	−0.0409539	+	0.0454839i
$562$	−9.78818	+	4.35798i	−0.412889	+	0.183830i
$563$	12.6317	−	21.8787i	0.532362	−	0.922077i	−0.466924	−	0.884297i	$-0.654638\pi$
$563$	12.6317	−	21.8787i	0.532362	−	0.922077i	0.999286	−	0.0377801i	$-0.0120287\pi$
$564$	0.637584	−	1.10433i	0.0268471	−	0.0465006i
$565$	19.7993	+	14.3850i	0.832961	+	0.605181i
$566$	−63.6970	−	28.3597i	−2.67738	−	1.19205i
$567$	23.3912	+	10.4144i	0.982339	+	0.437365i
$568$	26.7803	+	29.7426i	1.12368	+	1.24797i
$569$	4.61900	+	3.35590i	0.193639	+	0.140687i	0.680380	−	0.732859i	$-0.261815\pi$
$569$	4.61900	+	3.35590i	0.193639	+	0.140687i	−0.486742	+	0.873546i	$0.661815\pi$
$570$	−24.4533	+	5.19772i	−1.02424	+	0.217708i
$571$	−14.6466	+	16.2667i	−0.612940	+	0.680739i	−0.967086	−	0.254451i	$-0.918105\pi$
$571$	−14.6466	+	16.2667i	−0.612940	+	0.680739i	0.354145	+	0.935190i	$0.384772\pi$
$572$	1.17137	−	6.92813i	0.0489776	−	0.289680i
$573$	−17.5569	−	54.0346i	−0.733450	−	2.25733i
$574$	−52.5715	−	11.1744i	−2.19429	−	0.466411i
$575$	2.82870	+	1.25942i	0.117965	+	0.0525214i
$576$	28.9144	+	6.14594i	1.20477	+	0.256081i
$577$	−1.28048	−	1.42212i	−0.0533071	−	0.0592036i	0.715901	−	0.698201i	$-0.246016\pi$
$577$	−1.28048	−	1.42212i	−0.0533071	−	0.0592036i	−0.769209	+	0.638998i	$0.779349\pi$
$578$	34.0982	−	15.1815i	1.41830	−	0.631468i
$579$	−10.1835	−	11.3099i	−0.423212	−	0.470025i
$580$	−41.2738	−	18.3763i	−1.71380	−	0.763033i
$581$	−32.2569	−	14.3617i	−1.33824	−	0.595824i
$582$	1.68050	−	15.9889i	0.0696591	−	0.662762i
$583$	−2.54868	−	4.41445i	−0.105556	−	0.182828i
$584$	5.14221	+	8.90657i	0.212786	+	0.368556i
$585$	−9.27045	+	23.4186i	−0.383286	+	0.968241i
$586$	6.24541	+	1.32750i	0.257995	+	0.0548386i
$587$	−6.49567	−	7.21417i	−0.268105	−	0.297761i	0.594026	−	0.804446i	$-0.297537\pi$
$587$	−6.49567	−	7.21417i	−0.268105	−	0.297761i	−0.862131	+	0.506685i	$0.830871\pi$
$588$	−1.57484	+	2.72771i	−0.0649454	+	0.112489i
$589$	−5.99516	−	7.13928i	−0.247026	−	0.294169i
$590$	−59.6199			−2.45451
$591$	46.5721	−	9.89921i	1.91572	−	0.407199i
$592$	−1.02230	−	3.14632i	−0.0420163	−	0.129313i
$593$	−23.5410	−	17.1036i	−0.966714	−	0.702359i	−0.0120137	−	0.999928i	$-0.503824\pi$
$593$	−23.5410	−	17.1036i	−0.966714	−	0.702359i	−0.954700	+	0.297569i	$0.903824\pi$
$594$	−0.533341	+	0.923773i	−0.0218832	+	0.0379029i
$595$	3.90106	+	6.75683i	0.159928	+	0.277003i
$596$	2.49500	−	23.7384i	0.102199	−	0.972362i
$597$	−38.8974	+	28.2606i	−1.59197	+	1.15663i
$598$	2.24487	−	13.2773i	0.0917995	−	0.542951i
$599$	−22.1049	+	4.69855i	−0.903182	+	0.191977i	−0.636019	−	0.771674i	$-0.719420\pi$
$599$	−22.1049	+	4.69855i	−0.903182	+	0.191977i	−0.267164	+	0.963651i	$0.586087\pi$
$600$	−15.0078	−	10.9038i	−0.612691	−	0.445146i
$601$	−22.2981	+	4.73962i	−0.909560	+	0.193333i	−0.638853	−	0.769329i	$-0.720591\pi$
$601$	−22.2981	+	4.73962i	−0.909560	+	0.193333i	−0.270707	+	0.962662i	$0.587258\pi$
$602$	71.3485	+	15.1656i	2.90795	+	0.618103i
$603$	2.32130	+	22.0857i	0.0945306	+	0.899399i
$604$	−21.5716	+	23.9576i	−0.877734	+	0.974823i
$605$	18.9361	−	21.0307i	0.769862	−	0.855018i
$606$	2.15354	+	20.4896i	0.0874817	+	0.832333i
$607$	−9.17684	−	1.95060i	−0.372476	−	0.0791723i	0.0178701	−	0.999840i	$-0.494311\pi$
$607$	−9.17684	−	1.95060i	−0.372476	−	0.0791723i	−0.390347	+	0.920668i	$0.627645\pi$
$608$	4.81207	−	1.02284i	0.195155	−	0.0414815i
$609$	−23.1331	−	16.8072i	−0.937401	−	0.681062i
$610$	76.5710	−	16.2757i	3.10027	−	0.658983i
$611$	−0.407066	−	0.336713i	−0.0164681	−	0.0136219i
$612$	8.99002	−	6.53163i	0.363400	−	0.264026i
$613$	0.0594902	−	0.566012i	0.00240279	−	0.0228610i	−0.993255	−	0.115952i	$-0.963008\pi$
$613$	0.0594902	−	0.566012i	0.00240279	−	0.0228610i	0.995658	+	0.0930911i	$0.0296748\pi$
$614$	7.77996	+	13.4753i	0.313974	+	0.543818i
$615$	−27.4998	+	47.6311i	−1.10890	+	1.92067i
$616$	4.38844	+	3.18839i	0.176815	+	0.128464i
$617$	−12.5371	−	38.5851i	−0.504724	−	1.55338i	−0.801235	−	0.598350i	$-0.795823\pi$
$617$	−12.5371	−	38.5851i	−0.504724	−	1.55338i	0.296511	−	0.955029i	$-0.404177\pi$
$618$	8.04869	−	1.71080i	0.323766	−	0.0688186i
$619$	5.98976			0.240749			0.120374	−	0.992729i	$-0.461590\pi$
$619$	5.98976			0.240749			0.120374	+	0.992729i	$0.461590\pi$
$620$	7.47489	−	53.3327i	0.300199	−	2.14189i
$621$	−0.661131	+	1.14511i	−0.0265303	+	0.0459518i
$622$	−0.464932	−	0.516359i	−0.0186421	−	0.0207041i
$623$	25.0702	+	5.32884i	1.00442	+	0.213495i
$624$	−6.59389	+	16.6572i	−0.263967	+	0.666822i
$625$	15.4861	+	26.8227i	0.619444	+	1.07291i
$626$	−31.1602	−	53.9711i	−1.24541	−	2.15712i
$627$	0.221246	−	2.10501i	0.00883571	−	0.0840662i
$628$	−11.7240	−	5.21987i	−0.467839	−	0.208296i
$629$	1.65735	+	0.737901i	0.0660830	+	0.0294220i
$630$	−28.6585	−	31.8285i	−1.14178	−	1.26808i
$631$	16.2645	−	7.24143i	0.647480	−	0.288277i	−0.0566002	−	0.998397i	$-0.518026\pi$
$631$	16.2645	−	7.24143i	0.647480	−	0.288277i	0.704081	+	0.710120i	$0.251359\pi$
$632$	0.0948654	+	0.105359i	0.00377354	+	0.00419095i
$633$	−40.3895	−	8.58505i	−1.60534	−	0.341225i
$634$	−5.97952	−	2.66225i	−0.237477	−	0.105732i
$635$	−48.2151	−	10.2484i	−1.91336	−	0.406697i
$636$	25.7673	+	79.3035i	1.02174	+	3.14459i
$637$	1.00546	+	0.831685i	0.0398377	+	0.0329526i
$638$	3.95708	−	4.39478i	0.156662	−	0.173991i
$639$	26.1702	−	5.56265i	1.03528	−	0.220055i
$640$	44.2537	+	32.1522i	1.74928	+	1.27093i
$641$	−0.958004	−	1.06397i	−0.0378389	−	0.0420243i	0.723928	−	0.689875i	$-0.242335\pi$
$641$	−0.958004	−	1.06397i	−0.0378389	−	0.0420243i	−0.761767	+	0.647851i	$0.775668\pi$
$642$	4.66771	+	2.07820i	0.184220	+	0.0820200i
$643$	11.9553	+	5.32286i	0.471472	+	0.209913i	0.628698	−	0.777650i	$-0.283588\pi$
$643$	11.9553	+	5.32286i	0.471472	+	0.209913i	−0.157225	+	0.987563i	$0.550255\pi$
$644$	11.9825	+	8.70580i	0.472177	+	0.343056i
$645$	37.3219	−	64.6435i	1.46955	−	2.54533i
$646$	2.28470	−	3.95722i	0.0898905	−	0.155695i
$647$	−6.57625	+	2.92794i	−0.258539	+	0.115109i	−0.531914	−	0.846799i	$-0.678527\pi$
$647$	−6.57625	+	2.92794i	−0.258539	+	0.115109i	0.273374	+	0.961908i	$0.411860\pi$
$648$	26.3152	−	29.2259i	1.03376	−	1.14810i
$649$	1.55984	−	4.80070i	0.0612292	−	0.188444i
$650$	−12.0940	+	11.8447i	−0.474365	+	0.464589i
$651$	11.6453	−	32.0329i	0.456416	−	1.25547i
$652$	−23.5744	+	40.8320i	−0.923244	+	1.59911i
$653$	−22.8580	−	25.3864i	−0.894504	−	0.993447i	0.105496	−	0.994420i	$-0.466357\pi$
$653$	−22.8580	−	25.3864i	−0.894504	−	0.993447i	−1.00000		0.000972644i	$0.999690\pi$
$654$	−30.3217	−	93.3206i	−1.18567	−	3.64913i
$655$	17.6953	+	12.8564i	0.691414	+	0.502342i
$656$	−9.16573	+	15.8755i	−0.357862	+	0.619835i
$657$	6.87508			0.268223
$658$	0.820661	−	0.365382i	0.0319927	−	0.0142441i
$659$	−24.3962	−	10.8619i	−0.950341	−	0.423119i	−0.127784	−	0.991802i	$-0.540786\pi$
$659$	−24.3962	−	10.8619i	−0.950341	−	0.423119i	−0.822557	+	0.568683i	$0.807453\pi$
$660$	9.89187	−	7.18686i	0.385040	−	0.279748i
$661$	−11.3641	+	34.9750i	−0.442011	+	1.36037i	0.443717	+	0.896167i	$0.353659\pi$
$661$	−11.3641	+	34.9750i	−0.442011	+	1.36037i	−0.885728	+	0.464204i	$0.846341\pi$
$662$	−0.684758	+	6.51504i	−0.0266139	+	0.253214i
$663$	−4.36876	−	8.79947i	−0.169669	−	0.341743i
$664$	−36.2891	+	40.3031i	−1.40829	+	1.56406i
$665$	−10.4068	−	4.63341i	−0.403559	−	0.179676i
$666$	−9.74137	−	2.07059i	−0.377470	−	0.0802338i
$667$	4.90521	−	5.44779i	0.189930	−	0.210939i
$668$	3.88438	+	36.9574i	0.150291	+	1.42993i
$669$	25.2765	+	5.37268i	0.977244	+	0.207720i
$670$	−16.3011	+	50.1695i	−0.629765	+	1.93822i
$671$	−0.692790	+	6.59146i	−0.0267449	+	0.254460i
$672$	12.0351	+	13.3664i	0.464265	+	0.515619i
$673$	0.0330841	−	0.0240370i	0.00127530	−	0.000926559i	−0.587147	−	0.809480i	$-0.699749\pi$
$673$	0.0330841	−	0.0240370i	0.00127530	−	0.000926559i	0.588423	+	0.808553i	$0.299749\pi$
$674$	−0.589472	−	5.60845i	−0.0227056	−	0.216030i
$675$	1.51854	−	0.676097i	0.0584486	−	0.0260230i
$676$	40.7338	+	24.6625i	1.56668	+	0.948558i
$677$	10.3606	+	17.9451i	0.398190	+	0.689686i	0.993503	−	0.113809i	$-0.0363051\pi$
$677$	10.3606	+	17.9451i	0.398190	+	0.689686i	−0.595312	+	0.803494i	$0.702972\pi$
$678$	47.8719	−	21.3140i	1.83851	−	0.818558i
$679$	4.90196	−	5.44417i	0.188120	−	0.208928i
$680$	11.7217	−	2.49152i	0.449505	−	0.0955453i
$681$	−24.8152			−0.950920
$682$	6.33691	+	3.08776i	0.242653	+	0.118236i
$683$	18.5295	+	32.0941i	0.709014	+	1.22805i	0.965223	+	0.261426i	$0.0841928\pi$
$683$	18.5295	+	32.0941i	0.709014	+	1.22805i	−0.256210	+	0.966621i	$0.582474\pi$
$684$	−5.01372	+	15.4307i	−0.191705	+	0.590006i
$685$	6.69165	+	20.5948i	0.255675	+	0.786886i
$686$	−41.2347	+	18.3589i	−1.57435	+	0.700945i
$687$	−50.2400			−1.91677
$688$	12.4395	−	21.5458i	0.474250	−	0.821425i
$689$	34.1738	−	5.04846i	1.30192	−	0.192331i
$690$	18.9572	−	13.7732i	0.721688	−	0.524337i
$691$	−26.1303	+	18.9848i	−0.994043	+	0.722214i	−0.960803	−	0.277233i	$-0.910583\pi$
$691$	−26.1303	+	18.9848i	−0.994043	+	0.722214i	−0.0332402	+	0.999447i	$0.510583\pi$
$692$	−23.4407	+	72.1432i	−0.891083	+	2.74247i
$693$	3.31269	−	1.47490i	0.125839	−	0.0560269i
$694$	42.2732	+	46.9491i	1.60467	+	1.78216i
$695$	53.8568	+	11.4476i	2.04290	+	0.434233i
$696$	−35.5309	+	25.8147i	−1.34680	+	0.978505i
$697$	−3.10648	−	9.56075i	−0.117666	−	0.362139i
$698$	16.6248	−	18.4637i	0.629258	−	0.698862i
$699$	−49.8441	−	22.1920i	−1.88528	−	0.839379i
$700$	−5.75374	−	17.7082i	−0.217471	−	0.669306i
$701$	8.59033	+	9.54052i	0.324452	+	0.360341i	0.883200	−	0.468997i	$-0.155385\pi$
$701$	8.59033	+	9.54052i	0.324452	+	0.360341i	−0.558747	+	0.829338i	$0.688718\pi$
$702$	−4.49054	−	5.66495i	−0.169485	−	0.213810i
$703$	−2.59098	+	0.550730i	−0.0977207	+	0.0207712i
$704$	−4.80962	+	3.49439i	−0.181269	+	0.131700i
$705$	−0.0960908	−	0.914243i	−0.00361899	−	0.0344324i
$706$	−25.4438	−	18.4860i	−0.957589	−	0.695729i
$707$	−4.69400	+	8.13024i	−0.176536	+	0.305769i
$708$	−41.2865	+	71.5104i	−1.55164	+	2.68752i
$709$	5.09193	−	48.4464i	0.191231	−	1.81944i	−0.306229	−	0.951958i	$-0.599067\pi$
$709$	5.09193	−	48.4464i	0.191231	−	1.81944i	0.497460	−	0.867487i	$-0.334266\pi$
$710$	62.1647	+	13.2135i	2.33300	+	0.495895i
$711$	0.0927043	−	0.0197049i	0.00347668	−	0.000738991i
$712$	19.6832	−	34.0923i	0.737659	−	1.27766i
$713$	7.85526	+	3.82760i	0.294182	+	0.143345i
$714$	16.7060			0.625206
$715$	−2.25254	−	4.53703i	−0.0842403	−	0.169675i
$716$	−59.7076	−	12.6912i	−2.23138	−	0.474294i
$717$	6.19733	−	2.75923i	0.231444	−	0.103045i
$718$	54.2491			2.02456
$719$	39.2822			1.46498			0.732489	−	0.680779i	$-0.238358\pi$
$719$	39.2822			1.46498			0.732489	+	0.680779i	$0.238358\pi$
$720$	−13.3452	+	5.94166i	−0.497346	+	0.221433i
$721$	3.42535	+	1.52506i	0.127567	+	0.0567963i
$722$	−4.02878	−	38.3313i	−0.149936	−	1.42654i
$723$	19.7664	−	4.20147i	0.735120	−	0.156254i
$724$	−44.2501	+	19.7014i	−1.64454	+	0.732198i
$725$	−9.01424	+	1.91604i	−0.334780	+	0.0711598i
$726$	−18.7250	−	57.6296i	−0.694949	−	2.13883i
$727$	3.30199	+	31.4163i	0.122464	+	1.16517i	0.867253	+	0.497867i	$0.165883\pi$
$727$	3.30199	+	31.4163i	0.122464	+	1.16517i	−0.744790	+	0.667299i	$0.767450\pi$
$728$	−31.0372	+	19.6994i	−1.15031	+	0.730109i
$729$	−6.26832	−	19.2919i	−0.232160	−	0.714514i
$730$	14.9192	+	6.64244i	0.552183	+	0.245848i
$731$	4.21602	+	12.9756i	0.155935	+	0.479919i
$732$	33.5034	−	103.113i	1.23832	−	3.81117i
$733$	−3.56544	+	33.9229i	−0.131693	+	1.25297i	0.706546	+	0.707667i	$0.250252\pi$
$733$	−3.56544	+	33.9229i	−0.131693	+	1.25297i	−0.838239	+	0.545304i	$0.816414\pi$
$734$	−17.0634	−	18.9508i	−0.629821	−	0.699487i
$735$	0.237346	+	2.25819i	0.00875463	+	0.0832947i
$736$	−3.73050	+	2.71037i	−0.137508	+	0.0999056i
$737$	−3.61325	−	2.62518i	−0.133096	−	0.0966997i
$738$	27.5922	+	47.7911i	1.01568	+	1.75922i
$739$	38.8300			1.42838			0.714192	−	0.699950i	$-0.246794\pi$
$739$	38.8300			1.42838			0.714192	+	0.699950i	$0.246794\pi$
$740$	−12.3793	−	8.99411i	−0.455073	−	0.330630i
$741$	12.7123	+	6.64484i	0.466997	+	0.244104i
$742$	−18.1524	+	55.8674i	−0.666397	+	2.05096i
$743$	14.3253	−	24.8121i	0.525544	−	0.910269i	−0.474013	−	0.880518i	$-0.657195\pi$
$743$	14.3253	−	24.8121i	0.525544	−	0.910269i	0.999557	−	0.0297513i	$-0.00947153\pi$
$744$	−41.2651	−	32.2148i	−1.51285	−	1.18105i
$745$	−8.60372	−	14.9021i	−0.315216	−	0.545970i
$746$	12.0957	−	37.2268i	0.442856	−	1.36297i
$747$	11.2033	+	34.4802i	0.409907	+	1.26156i
$748$	−0.233605	+	2.22260i	−0.00854143	+	0.0812663i
$749$	1.16412	+	2.01631i	0.0425360	+	0.0736745i
$750$	45.1955			1.65031
$751$	5.71253	−	54.3511i	0.208453	−	1.98330i	0.0287004	−	0.999588i	$-0.490863\pi$
$751$	5.71253	−	54.3511i	0.208453	−	1.98330i	0.179753	−	0.983712i	$-0.442470\pi$
$752$	−0.0320272	−	0.304719i	−0.00116791	−	0.0111119i
$753$	23.2622	+	10.3570i	0.847723	+	0.377431i
$754$	17.8220	+	35.8967i	0.649039	+	1.30728i
$755$	−2.42932	+	23.1135i	−0.0884121	+	0.841185i
$756$	7.77737	−	1.65313i	0.282860	−	0.0601238i
$757$	9.15273	+	28.1692i	0.332662	+	1.02383i	0.967862	+	0.251480i	$0.0809173\pi$
$757$	9.15273	+	28.1692i	0.332662	+	1.02383i	−0.635201	+	0.772347i	$0.719083\pi$
$758$	28.8970	−	20.9949i	1.04959	−	0.762568i
$759$	0.613064	+	1.88682i	0.0222528	+	0.0684871i
$760$	−11.7077	+	13.0027i	−0.424682	+	0.471657i
$761$	−35.4170	+	25.7320i	−1.28387	+	0.932783i	−0.999662	−	0.0259805i	$-0.991729\pi$
$761$	−35.4170	+	25.7320i	−1.28387	+	0.932783i	−0.284204	+	0.958764i	$0.591729\pi$
$762$	−70.6235	+	78.4354i	−2.55842	+	2.84141i
$763$	13.8168	−	42.5237i	0.500202	−	1.53946i
$764$	−70.8605	−	51.4832i	−2.56364	−	1.86260i
$765$	2.47551	−	7.61885i	0.0895024	−	0.275460i
$766$	7.42548	+	3.30603i	0.268293	+	0.119452i
$767$	26.3594	+	21.8037i	0.951783	+	0.787287i
$768$	58.4902	−	26.0415i	2.11058	−	0.939692i
$769$	−19.4573	−	33.7011i	−0.701650	−	1.21529i	−0.967887	−	0.251386i	$-0.919114\pi$
$769$	−19.4573	−	33.7011i	−0.701650	−	1.21529i	0.266237	−	0.963908i	$-0.414220\pi$
$770$	8.61364			0.310414
$771$	−3.79666	+	36.1228i	−0.136733	+	1.30093i
$772$	−22.9494	−	4.87805i	−0.825968	−	0.175565i
$773$	46.7030	−	9.92704i	1.67979	−	0.357051i	0.733331	−	0.679872i	$-0.237965\pi$
$773$	46.7030	−	9.92704i	1.67979	−	0.357051i	0.946460	+	0.322821i	$0.104631\pi$
$774$	−37.4473	−	64.8607i	−1.34602	−	2.33137i
$775$	−5.16078	−	9.69719i	−0.185381	−	0.348333i
$776$	−5.62602	−	9.74454i	−0.201962	−	0.349809i
$777$	−6.48012	−	7.19690i	−0.232473	−	0.258187i
$778$	44.8264	−	49.7847i	1.60710	−	1.78487i
$779$	11.8746	+	8.62739i	0.425451	+	0.309108i
$780$	20.6118	+	80.2576i	0.738022	+	2.87368i
$781$	−2.69040	+	4.65991i	−0.0962700	+	0.166745i
$782$	−0.447689	+	4.25948i	−0.0160093	+	0.152319i
$783$	−0.411358	−	3.91381i	−0.0147007	−	0.139868i
$784$	0.0791078	+	0.752660i	0.00282528	+	0.0268807i
$785$	−9.04963	+	1.92356i	−0.322995	+	0.0686547i
$786$	42.7849	−	19.0491i	1.52609	−	0.679458i
$787$	−9.46444	+	29.1286i	−0.337371	+	1.03832i	0.628171	+	0.778075i	$0.283804\pi$
$787$	−9.46444	+	29.1286i	−0.337371	+	1.03832i	−0.965542	+	0.260246i	$0.916196\pi$
$788$	49.1149	−	54.5477i	1.74965	−	1.94318i
$789$	53.3014	−	38.7257i	1.89758	−	1.37867i
$790$	0.220210	+	0.0468070i	0.00783471	+	0.00166532i
$791$	23.3566	+	4.96459i	0.830464	+	0.176521i
$792$	−0.582180	−	5.53907i	−0.0206869	−	0.196822i
$793$	−39.8061	−	20.8071i	−1.41356	−	0.738881i
$794$	−48.2772	−	53.6172i	−1.71329	−	1.90280i
$795$	48.6322	+	35.3333i	1.72481	+	1.25314i
$796$	−22.9048	+	70.4937i	−0.811839	+	2.49858i
$797$	−3.19976	−	30.4437i	−0.113341	−	1.07837i	−0.892346	−	0.451352i	$-0.850942\pi$
$797$	−3.19976	−	30.4437i	−0.113341	−	1.07837i	0.779004	−	0.627018i	$-0.215725\pi$
$798$	−19.7335	+	14.3372i	−0.698559	+	0.507533i
$799$	0.135935	+	0.0987625i	0.00480903	+	0.00349397i
$800$	5.79679			0.204948
$801$	−13.1581	−	22.7905i	−0.464919	−	0.805264i
$802$	−5.02841	+	47.8421i	−0.177559	+	1.68936i
$803$	−0.925193	+	1.02753i	−0.0326494	+	0.0362608i
$804$	48.8868	+	54.2943i	1.72410	+	1.91481i
$805$	10.6775			0.376333
$806$	−35.2633	+	32.2282i	−1.24210	+	1.13519i
$807$	−4.83089			−0.170055
$808$	9.64841	+	10.7157i	0.339430	+	0.376975i
$809$	−12.8148	+	14.2323i	−0.450546	+	0.500382i	−0.925036	−	0.379879i	$-0.875966\pi$
$809$	−12.8148	+	14.2323i	−0.450546	+	0.500382i	0.474491	+	0.880261i	$0.342632\pi$
$810$	6.52776	−	62.1075i	0.229362	−	2.18224i
$811$	7.69496	+	13.3281i	0.270207	+	0.468011i	0.968915	−	0.247395i	$-0.0795747\pi$
$811$	7.69496	+	13.3281i	0.270207	+	0.468011i	−0.698708	+	0.715407i	$0.746241\pi$
$812$	−44.0816			−1.54696
$813$	31.8896	+	23.1691i	1.11842	+	0.812577i
$814$	1.62038	−	1.17727i	0.0567943	−	0.0412635i
$815$	3.55292	+	33.8037i	0.124453	+	1.18409i
$816$	1.76078	−	5.41913i	0.0616397	−	0.189708i
$817$	−16.1158	−	11.7088i	−0.563822	−	0.409640i
$818$	4.31860	+	4.79629i	0.150996	+	0.167698i
$819$	1.03056	+	24.5530i	0.0360108	+	0.857950i
$820$	8.86288	+	84.3247i	0.309505	+	2.94475i
$821$	−2.82275	−	0.599995i	−0.0985148	−	0.0209400i	0.158391	−	0.987377i	$-0.449370\pi$
$821$	−2.82275	−	0.599995i	−0.0985148	−	0.0209400i	−0.256905	+	0.966437i	$0.582703\pi$
$822$	45.3540	+	9.64028i	1.58190	+	0.336243i
$823$	13.2337	−	9.61488i	0.461299	−	0.335154i	−0.332741	−	0.943018i	$-0.607974\pi$
$823$	13.2337	−	9.61488i	0.461299	−	0.335154i	0.794041	+	0.607865i	$0.207974\pi$
$824$	3.85352	−	4.27977i	0.134244	−	0.149093i
$825$	0.770696	−	2.37196i	0.0268322	−	0.0825810i
$826$	−53.1416	+	23.6602i	−1.84903	+	0.823243i
$827$	−0.438290	+	0.0931613i	−0.0152408	+	0.00323954i	−0.215526	−	0.976498i	$-0.569147\pi$
$827$	−0.438290	+	0.0931613i	−0.0152408	+	0.00323954i	0.200285	+	0.979738i	$0.435813\pi$
$828$	−1.58963	−	15.1243i	−0.0552433	−	0.525605i
$829$	3.04058	+	28.9291i	0.105604	+	1.00475i	0.911110	+	0.412164i	$0.135227\pi$
$829$	3.04058	+	28.9291i	0.105604	+	1.00475i	−0.805506	+	0.592587i	$0.798107\pi$
$830$	−9.00190	+	85.6474i	−0.312461	+	2.97286i
$831$	23.9293	−	41.4468i	0.830100	−	1.43778i
$832$	−10.0219	−	39.0228i	−0.347446	−	1.35287i
$833$	−0.335761	−	0.243945i	−0.0116334	−	0.00845219i
$834$	78.8872	−	87.6131i	2.73164	−	3.03380i
$835$	17.9258	+	19.9086i	0.620348	+	0.688966i
$836$	−1.63152	−	2.82587i	−0.0564272	−	0.0977348i
$837$	4.34869	−	1.75890i	0.150313	−	0.0607963i
$838$	−20.9967	−	36.3673i	−0.725318	−	1.25629i
$839$	17.2112	−	3.65836i	0.594197	−	0.126301i	0.0990096	−	0.995086i	$-0.468433\pi$
$839$	17.2112	−	3.65836i	0.594197	−	0.126301i	0.495188	+	0.868786i	$0.335099\pi$
$840$	−62.5715	−	13.3000i	−2.15892	−	0.458893i
$841$	0.750726	−	7.14268i	0.0258871	−	0.246299i
$842$	13.0989			0.451419
$843$	5.34895	+	9.26466i	0.184228	+	0.319092i
$844$	−58.1534	+	25.8915i	−2.00172	+	0.891224i
$845$	34.2075	−	2.87665i	1.17677	−	0.0989599i
$846$	−0.842625	−	0.375161i	−0.0289700	−	0.0128983i
$847$	8.53248	−	26.2603i	0.293179	−	0.902313i
$848$	16.2092	+	11.7767i	0.556626	+	0.404412i
$849$	−21.5129	+	66.2098i	−0.738319	+	2.27231i
$850$	3.60272	−	4.00123i	0.123572	−	0.137241i
$851$	2.00863	−	1.45935i	0.0688549	−	0.0500260i
$852$	58.8976	−	65.4124i	2.01780	−	2.24099i
$853$	−0.388530	−	1.19577i	−0.0133030	−	0.0409424i	0.944185	−	0.329417i	$-0.106852\pi$
$853$	−0.388530	−	1.19577i	−0.0133030	−	0.0409424i	−0.957488	+	0.288474i	$0.906852\pi$
$854$	61.7918	−	44.8944i	2.11447	−	1.53625i
$855$	3.61443	+	11.1241i	0.123611	+	0.380436i
$856$	3.49787	−	0.743496i	0.119555	−	0.0254122i
$857$	−3.78572	+	36.0187i	−0.129318	+	1.23037i	0.716762	+	0.697318i	$0.245623\pi$
$857$	−3.78572	+	36.0187i	−0.129318	+	1.23037i	−0.846079	+	0.533057i	$0.821043\pi$
$858$	−10.8248	−	0.680381i	−0.369552	−	0.0232278i
$859$	−37.7907	−	16.8255i	−1.28940	−	0.574079i	−0.356530	−	0.934284i	$-0.616040\pi$
$859$	−37.7907	−	16.8255i	−1.28940	−	0.574079i	−0.932873	+	0.360204i	$0.882707\pi$
$860$	−12.0284	−	114.443i	−0.410167	−	3.90248i
$861$	−5.60929	+	53.3688i	−0.191164	+	1.81880i
$862$	−59.5683			−2.02890
$863$	3.01782	+	5.22701i	0.102728	+	0.177930i	0.912808	−	0.408390i	$-0.133910\pi$
$863$	3.01782	+	5.22701i	0.102728	+	0.177930i	−0.810080	+	0.586320i	$0.800576\pi$
$864$	−0.258752	+	2.46186i	−0.00880291	+	0.0837541i
$865$	16.8986	+	52.0086i	0.574570	+	1.76835i
$866$	2.07275	−	6.37928i	0.0704351	−	0.216777i
$867$	−18.6337	−	32.2745i	−0.632833	−	1.09610i
$868$	−14.5024	−	50.5040i	−0.492244	−	1.71422i
$869$	−0.00953035	+	0.0165071i	−0.000323295	+	0.000559963i
$870$	−21.5509	+	66.3270i	−0.730645	+	2.24869i
$871$	25.5547	−	16.2197i	0.865887	−	0.549582i
$872$	−55.5591	−	40.3660i	−1.88147	−	1.36697i
$873$	−7.52193			−0.254579
$874$	−3.12671	−	5.41562i	−0.105762	−	0.183186i
$875$	16.6612	+	12.1051i	0.563252	+	0.409226i
$876$	18.2987	−	13.2948i	0.618254	−	0.449188i
$877$	−4.58547	−	43.6278i	−0.154840	−	1.47321i	−0.745619	−	0.666373i	$-0.767846\pi$
$877$	−4.58547	−	43.6278i	−0.154840	−	1.47321i	0.590779	−	0.806834i	$-0.298821\pi$
$878$	20.4657	+	22.7295i	0.690685	+	0.767083i
$879$	0.666374	−	6.34013i	0.0224762	−	0.213847i
$880$	0.907863	−	2.79412i	0.0306041	−	0.0941896i
$881$	4.97631	+	15.3155i	0.167656	+	0.515993i	0.999222	−	0.0394333i	$-0.0125553\pi$
$881$	4.97631	+	15.3155i	0.167656	+	0.515993i	−0.831566	+	0.555426i	$0.812555\pi$
$882$	2.08130	+	0.926653i	0.0700809	+	0.0312020i
$883$	−11.2103	−	34.5017i	−0.377256	−	1.16107i	−0.941944	−	0.335770i	$-0.891004\pi$
$883$	−11.2103	−	34.5017i	−0.377256	−	1.16107i	0.564688	−	0.825304i	$-0.308996\pi$
$884$	−13.4224	−	7.01602i	−0.451444	−	0.235974i
$885$	6.22233	+	59.2015i	0.209161	+	1.99004i
$886$	−17.2127	−	52.9753i	−0.578272	−	1.77974i
$887$	0.949772	−	0.201880i	0.0318902	−	0.00677847i	−0.191939	−	0.981407i	$-0.561478\pi$
$887$	0.949772	−	0.201880i	0.0318902	−	0.00677847i	0.223829	+	0.974628i	$0.428144\pi$
$888$	−13.5886	+	6.05003i	−0.456004	+	0.203026i
$889$	−47.0432	+	9.99933i	−1.57778	+	0.335367i
$890$	−6.53424	−	62.1691i	−0.219028	−	2.08391i
$891$	4.83022	+	2.15055i	0.161819	+	0.0720462i
$892$	36.3934	−	16.2034i	1.21854	−	0.542530i
$893$	−0.245329			−0.00820961
$894$	−36.8448			−1.23227
$895$	−40.2009	+	17.8986i	−1.34377	+	0.598283i
$896$	52.2047	+	11.0965i	1.74404	+	0.370706i
$897$	−13.4185	−	0.843403i	−0.448029	−	0.0281604i
$898$	71.3813			2.38202
$899$	−25.6101	+	4.52571i	−0.854143	+	0.150941i
$900$	−9.55891	+	16.5565i	−0.318630	+	0.551884i
$901$	−10.7472	+	2.28439i	−0.358042	+	0.0761042i
$902$	−10.8559	−	2.30749i	−0.361461	−	0.0768309i
$903$	7.61276	−	72.4306i	0.253337	−	2.41034i
$904$	18.3378	−	31.7620i	0.609906	−	1.05639i
$905$	−17.4596	+	30.2409i	−0.580377	+	1.00524i
$906$	40.2595	+	29.2502i	1.33753	+	0.971773i
$907$	−4.33375	−	41.2328i	−0.143900	−	1.36911i	−0.793376	−	0.608732i	$-0.791678\pi$
$907$	−4.33375	−	41.2328i	−0.143900	−	1.36911i	0.649476	−	0.760382i	$-0.274988\pi$
$908$	−30.9497	+	22.4863i	−1.02710	+	0.746232i
$909$	9.42861	−	2.00411i	0.312727	−	0.0664722i
$910$	−21.4858	+	54.2765i	−0.712246	+	1.79925i
$911$	−2.95315	−	3.27980i	−0.0978421	−	0.108665i	0.692235	−	0.721672i	$-0.256626\pi$
$911$	−2.95315	−	3.27980i	−0.0978421	−	0.108665i	−0.790077	+	0.613008i	$0.789960\pi$
$912$	2.57087	+	7.91234i	0.0851301	+	0.262004i
$913$	−6.66096	−	2.96565i	−0.220446	−	0.0981487i
$914$	−56.0172	+	62.2134i	−1.85288	+	2.05784i
$915$	−24.1529	−	74.3350i	−0.798470	−	2.45744i
$916$	−62.6597	+	45.5249i	−2.07033	+	1.50419i
$917$	20.8746	+	4.43704i	0.689341	+	0.146524i
$918$	1.53848	+	1.70866i	0.0507774	+	0.0563940i
$919$	−30.8691	+	13.7438i	−1.01828	+	0.453367i	−0.846851	−	0.531830i	$-0.821505\pi$
$919$	−30.8691	+	13.7438i	−1.01828	+	0.453367i	−0.171427	+	0.985197i	$0.554838\pi$
$920$	5.06786	−	15.5973i	0.167082	−	0.514227i
$921$	12.5687	−	9.13173i	0.414154	−	0.300901i
$922$	−8.60866	+	6.25456i	−0.283511	+	0.205983i
$923$	−22.6522	−	28.5764i	−0.745606	−	0.940604i
$924$	5.96491	−	10.3315i	0.196231	−	0.339882i
$925$	−3.12119			−0.102624
$926$	−32.5091	+	14.4740i	−1.06832	+	0.475645i
$927$	−1.18967	−	3.66144i	−0.0390740	−	0.120257i
$928$	4.24092	−	13.0522i	0.139215	−	0.428460i
$929$	−9.27137	−	16.0585i	−0.304184	−	0.526862i	0.672895	−	0.739738i	$-0.265050\pi$
$929$	−9.27137	−	16.0585i	−0.304184	−	0.526862i	−0.977079	+	0.212876i	$0.931717\pi$
$930$	−83.0804	−	2.86983i	−2.72431	−	0.0941054i
$931$	0.605966			0.0198597
$932$	−82.2752	+	17.4881i	−2.69501	+	0.572843i
$933$	−0.464212	+	0.515560i	−0.0151976	+	0.0168787i
$934$	−19.5279	+	8.69437i	−0.638971	+	0.284488i
$935$	0.805558	+	1.39527i	0.0263446	+	0.0456301i
$936$	36.3551	+	10.1482i	1.18830	+	0.331703i
$937$	−10.4456	+	4.65067i	−0.341242	+	0.151931i	−0.570201	−	0.821505i	$-0.693135\pi$
$937$	−10.4456	+	4.65067i	−0.341242	+	0.151931i	0.228959	+	0.973436i	$0.426468\pi$
$938$	5.37999	+	51.1872i	0.175663	+	1.67132i
$939$	−50.3403	+	36.5743i	−1.64279	+	1.19356i
$940$	−0.948285	−	1.05318i	−0.0309297	−	0.0343509i
$941$	3.31123	−	31.5043i	0.107943	−	1.02701i	−0.797724	−	0.603022i	$-0.793963\pi$
$941$	3.31123	−	31.5043i	0.107943	−	1.02701i	0.905668	−	0.423988i	$-0.139370\pi$
$942$	−6.12165	+	18.8405i	−0.199454	+	0.613857i
$943$	−13.4570	−	2.86037i	−0.438219	−	0.0931464i
$944$	2.07391	+	19.7320i	0.0675001	+	0.642221i
$945$	3.83548	−	4.25973i	0.124768	−	0.138569i
$946$	14.7333	+	3.13165i	0.479020	+	0.101819i
$947$	−10.3207	−	4.59508i	−0.335378	−	0.149320i	0.232137	−	0.972683i	$-0.425428\pi$
$947$	−10.3207	−	4.59508i	−0.335378	−	0.149320i	−0.567515	+	0.823363i	$0.692095\pi$
$948$	0.208636	−	0.231714i	0.00677619	−	0.00752572i
$949$	−4.16691	−	8.39291i	−0.135264	−	0.272445i
$950$	−0.821731	+	7.81825i	−0.0266605	+	0.253657i
$951$	−2.01951	+	6.21540i	−0.0654870	+	0.201548i
$952$	9.45923	−	6.87253i	0.306575	−	0.222740i
$953$	−38.7946	−	17.2725i	−1.25668	−	0.559510i	−0.333092	−	0.942894i	$-0.608092\pi$
$953$	−38.7946	−	17.2725i	−1.25668	−	0.559510i	−0.923589	+	0.383384i	$0.874759\pi$
$954$	55.1002	−	24.5322i	1.78393	−	0.794259i
$955$	−63.1432			−2.04327
$956$	5.22908	−	9.05703i	0.169121	−	0.292925i
$957$	−4.77693	−	3.47064i	−0.154416	−	0.112190i
$958$	13.3763	+	41.1680i	0.432169	+	1.33008i
$959$	14.1376	+	15.7014i	0.456527	+	0.507024i
$960$	35.0544	−	60.7161i	1.13138	−	1.95960i
$961$	−13.6105	−	27.8523i	−0.439050	−	0.898463i
$962$	3.37641	+	13.1470i	0.108860	+	0.423875i
$963$	0.738721	−	2.27355i	0.0238049	−	0.0732641i
$964$	20.8456	−	23.1514i	0.671392	−	0.745656i
$965$	−15.4517	+	6.87956i	−0.497409	+	0.221461i
$966$	11.4314	−	19.7998i	0.367799	−	0.637047i
$967$	−3.87802	+	6.71692i	−0.124709	+	0.216002i	−0.921619	−	0.388096i	$-0.873133\pi$
$967$	−3.87802	+	6.71692i	−0.124709	+	0.216002i	0.796910	+	0.604098i	$0.206466\pi$
$968$	−34.3102	−	24.9278i	−1.10277	−	0.801210i
$969$	−4.16790	−	1.85567i	−0.133892	−	0.0596126i
$970$	−16.3228	−	7.26740i	−0.524095	−	0.233342i
$971$	−22.9203	−	25.4555i	−0.735547	−	0.816907i	0.253057	−	0.967451i	$-0.418564\pi$
$971$	−22.9203	−	25.4555i	−0.735547	−	0.816907i	−0.988603	+	0.150544i	$0.951897\pi$
$972$	−62.4836	−	45.3970i	−2.00416	−	1.45611i
$973$	52.5477	−	11.1694i	1.68460	−	0.358073i
$974$	60.3506	−	67.0261i	1.93376	−	2.14766i
$975$	13.0238	+	10.7729i	0.417096	+	0.345009i
$976$	−8.05021	−	24.7760i	−0.257681	−	0.793060i
$977$	52.1028	+	11.0748i	1.66692	+	0.354314i	0.942282	−	0.334821i	$-0.108676\pi$
$977$	52.1028	+	11.0748i	1.66692	+	0.354314i	0.724633	+	0.689135i	$0.242009\pi$
$978$	66.4875	+	29.6022i	2.12604	+	0.946573i
$979$	5.17693	+	1.10039i	0.165455	+	0.0351686i
$980$	2.34228	+	2.60136i	0.0748214	+	0.0830975i
$981$	−41.9398	+	18.6728i	−1.33903	+	0.596176i
$982$	−31.1132	−	34.5547i	−0.992862	−	1.10268i
$983$	−15.5692	−	6.93186i	−0.496581	−	0.221092i	0.143135	−	0.989703i	$-0.454282\pi$
$983$	−15.5692	−	6.93186i	−0.496581	−	0.221092i	−0.639716	+	0.768611i	$0.720948\pi$
$984$	75.2966	+	33.5242i	2.40037	+	1.06871i
$985$	5.53117	−	52.6256i	0.176238	−	1.67679i
$986$	−6.37353	−	11.0393i	−0.202974	−	0.351562i
$987$	−0.448467	−	0.776768i	−0.0142749	−	0.0247248i
$988$	21.8761	−	3.23173i	0.695970	−	0.102815i
$989$	18.2634	+	3.88201i	0.580743	+	0.123441i
$990$	−5.91791	−	6.57250i	−0.188084	−	0.208888i
$991$	20.1119	−	34.8349i	0.638876	−	1.10657i	−0.346804	−	0.937938i	$-0.612733\pi$
$991$	20.1119	−	34.8349i	0.638876	−	1.10657i	0.985680	−	0.168628i	$-0.0539337\pi$
$992$	16.3490	+	0.564741i	0.519083	+	0.0179306i
$993$	6.54078			0.207565
$994$	60.6537	−	12.8923i	1.92382	−	0.408920i
$995$	16.5123	+	50.8195i	0.523474	+	1.61109i
$996$	96.4949	+	70.1077i	3.05756	+	2.22145i
$997$	−15.1429	+	26.2282i	−0.479579	+	0.830656i	−0.999726	−	0.0234214i	$-0.992544\pi$
$997$	−15.1429	+	26.2282i	−0.479579	+	0.830656i	0.520146	+	0.854077i	$0.325877\pi$
$998$	−11.6858	−	20.2404i	−0.369907	−	0.640698i
$999$	0.139321	−	1.32555i	0.00440791	−	0.0419385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bk.a.9.3	yes	280
13.3	even	3		403.2.bj.a.133.33	yes	280
31.7	even	15		403.2.bj.a.100.33	✓	280
403.224	even	15	inner	403.2.bk.a.224.3	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bj.a.100.33	✓	280	31.7	even	15
403.2.bj.a.133.33	yes	280	13.3	even	3
403.2.bk.a.9.3	yes	280	1.1	even	1	trivial
403.2.bk.a.224.3	yes	280	403.224	even	15	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bk (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59232 - 1.76846i) q^{2} +(-1.58986 + 1.76572i) q^{3} +(-0.382880 + 3.64286i) q^{4} +(1.32032 + 2.28686i) q^{5} +5.65416 q^{6} +(2.08439 + 1.51440i) q^{7} +(3.20149 - 2.32602i) q^{8} +(-0.276520 - 2.63091i) q^{9} +O(q^{10})\)	\(q+(-1.59232 - 1.76846i) q^{2} +(-1.58986 + 1.76572i) q^{3} +(-0.382880 + 3.64286i) q^{4} +(1.32032 + 2.28686i) q^{5} +5.65416 q^{6} +(2.08439 + 1.51440i) q^{7} +(3.20149 - 2.32602i) q^{8} +(-0.276520 - 2.63091i) q^{9} +(1.94183 - 5.97634i) q^{10} +(0.430421 + 0.312719i) q^{11} +(-5.82354 - 6.46770i) q^{12} +(-3.04415 + 1.93214i) q^{13} +(-0.640880 - 6.09757i) q^{14} +(-6.13706 - 1.30447i) q^{15} +(-2.04549 - 0.434783i) q^{16} +(0.927769 - 0.674064i) q^{17} +(-4.21234 + 4.67828i) q^{18} +(-0.517416 + 1.59244i) q^{19} +(-8.83623 + 3.93414i) q^{20} +(-5.98789 + 1.27277i) q^{21} +(-0.132340 - 1.25913i) q^{22} +(-0.164049 - 1.56082i) q^{23} +(-0.982826 + 9.35096i) q^{24} +(-0.986478 + 1.70863i) q^{25} +(8.26417 + 2.30686i) q^{26} +(-0.681610 - 0.495219i) q^{27} +(-6.31482 + 7.01332i) q^{28} +(3.12549 + 3.47121i) q^{29} +(7.46529 + 12.9303i) q^{30} +(-2.94868 + 4.72285i) q^{31} +(-1.46906 - 2.54449i) q^{32} +(-1.23648 + 0.262822i) q^{33} +(-2.66936 - 0.567390i) q^{34} +(-0.711156 + 6.76620i) q^{35} +9.68994 q^{36} +(0.790993 + 1.37004i) q^{37} +(3.64005 - 1.62066i) q^{38} +(1.42817 - 8.44693i) q^{39} +(9.54625 + 4.25027i) q^{40} +(2.70886 - 8.33700i) q^{41} +(11.7855 + 8.56266i) q^{42} +(-3.67638 + 11.3147i) q^{43} +(-1.30399 + 1.44823i) q^{44} +(5.65143 - 4.10601i) q^{45} +(-2.49903 + 2.77545i) q^{46} +(0.0452766 + 0.139347i) q^{47} +(4.01975 - 2.92052i) q^{48} +(-0.111834 - 0.344189i) q^{49} +(4.59243 - 0.976151i) q^{50} +(-0.284816 + 2.70984i) q^{51} +(-5.87296 - 11.8292i) q^{52} +(-8.75266 - 3.89694i) q^{53} +(0.209572 + 1.99395i) q^{54} +(-0.146852 + 1.39720i) q^{55} +10.1957 q^{56} +(-1.98918 - 3.44537i) q^{57} +(1.16188 - 11.0546i) q^{58} +(-2.93187 - 9.02337i) q^{59} +(7.10178 - 21.8570i) q^{60} +(6.22875 + 10.7885i) q^{61} +(13.0474 - 2.30569i) q^{62} +(3.40788 - 5.90262i) q^{63} +(-3.45302 + 10.6273i) q^{64} +(-8.43776 - 4.41051i) q^{65} +(2.43367 + 1.76817i) q^{66} -8.39468 q^{67} +(2.10030 + 3.63782i) q^{68} +(3.01679 + 2.19182i) q^{69} +(13.0981 - 9.51633i) q^{70} +(1.05717 + 10.0583i) q^{71} +(-7.00483 - 7.77965i) q^{72} +(-0.271657 + 2.58464i) q^{73} +(1.16334 - 3.58038i) q^{74} +(-1.44860 - 4.45832i) q^{75} +(-5.60294 - 2.49459i) q^{76} +(0.423585 + 1.30366i) q^{77} +(-17.2121 + 10.9246i) q^{78} +(0.00374488 + 0.0356301i) q^{79} +(-1.70641 - 5.25180i) q^{80} +(9.72087 - 2.06624i) q^{81} +(-19.0570 + 8.48472i) q^{82} +(-13.4053 + 2.84938i) q^{83} +(-2.34386 - 22.3004i) q^{84} +(2.76644 + 1.23170i) q^{85} +(25.8636 - 11.5152i) q^{86} -11.0983 q^{87} +2.10538 q^{88} +(9.08786 - 4.04618i) q^{89} +(-16.2602 - 3.45621i) q^{90} +(-9.27123 - 0.582733i) q^{91} +5.74868 q^{92} +(-3.65122 - 12.7152i) q^{93} +(0.174334 - 0.301955i) q^{94} +(-4.32484 + 0.919273i) q^{95} +(6.82845 + 1.45143i) q^{96} +(0.297215 - 2.82782i) q^{97} +(-0.430607 + 0.745834i) q^{98} +(0.703718 - 1.21887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Introduction

L-functions

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