LMFDB - Embedded newform 294.2.m.b.205.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			205.2
Character	$\chi$	$=$	294.205
Dual form			294.2.m.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.380567 + 0.969668i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-2.32432 - 1.26394i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})$	\(q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.380567 + 0.969668i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-2.32432 - 1.26394i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +(0.380567 - 0.969668i) q^{10} +(3.82664 - 1.18036i) q^{11} +(0.0747301 - 0.997204i) q^{12} +(1.16255 - 5.09345i) q^{13} +(0.844147 + 2.50747i) q^{14} +(-0.231794 - 1.01556i) q^{15} +(-0.988831 + 0.149042i) q^{16} +(0.102235 + 0.0697023i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.12711 - 5.41631i) q^{19} +(-0.938517 + 0.451966i) q^{20} +(2.10998 + 1.59625i) q^{21} +(-3.60798 - 1.73751i) q^{22} +(-5.78156 + 3.94180i) q^{23} +(-0.733052 + 0.680173i) q^{24} +(2.86983 - 2.66282i) q^{25} +(-4.31663 + 2.94303i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(1.08671 - 2.41227i) q^{28} +(6.18133 - 2.97677i) q^{29} +(-0.520837 + 0.902117i) q^{30} +(-4.13026 - 7.15382i) q^{31} +(0.826239 + 0.563320i) q^{32} +(-3.95983 + 0.596848i) q^{33} +(-0.0275336 - 0.120633i) q^{34} +(0.341046 - 2.73483i) q^{35} +(-0.222521 + 0.974928i) q^{36} +(-0.584347 + 7.79757i) q^{37} +(-5.97636 + 1.84346i) q^{38} +(-1.90870 + 4.86329i) q^{39} +(0.995396 + 0.307039i) q^{40} +(4.34914 - 5.45365i) q^{41} +(-0.460999 - 2.60528i) q^{42} +(-6.67448 - 8.36953i) q^{43} +(1.46303 + 3.72774i) q^{44} +(0.0778445 + 1.03876i) q^{45} +(6.91929 + 1.04292i) q^{46} +(2.55942 + 2.37480i) q^{47} +1.00000 q^{48} +(3.80490 + 5.87560i) q^{49} -3.91491 q^{50} +(-0.0907041 - 0.0841611i) q^{51} +(5.16608 + 0.778661i) q^{52} +(0.604876 + 8.07151i) q^{53} +(0.365341 + 0.930874i) q^{54} +(2.60085 + 3.26137i) q^{55} +(-2.43738 + 1.02917i) q^{56} +(-3.89944 + 4.88975i) q^{57} +(-6.55596 - 2.02225i) q^{58} +(-2.15452 + 5.48962i) q^{59} +(0.995396 - 0.307039i) q^{60} +(-0.683516 + 9.12089i) q^{61} +(-1.83814 + 8.05341i) q^{62} +(-1.84850 - 1.89289i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(5.38138 - 0.811112i) q^{65} +(3.30872 + 2.25585i) q^{66} +(4.48626 + 7.77044i) q^{67} +(-0.0618674 + 0.107158i) q^{68} +(6.30448 - 3.03608i) q^{69} +(-2.11016 + 1.77280i) q^{70} +(7.56226 + 3.64179i) q^{71} +(0.826239 - 0.563320i) q^{72} +(0.906718 - 0.841311i) q^{73} +(5.73205 - 5.31856i) q^{74} +(-3.23465 + 2.20535i) q^{75} +(5.63486 + 2.71361i) q^{76} +(-10.3862 - 2.09312i) q^{77} +(4.70705 - 2.26680i) q^{78} +(4.69788 - 8.13696i) q^{79} +(-0.520837 - 0.902117i) q^{80} +(0.826239 + 0.563320i) q^{81} +(-6.89757 + 1.03964i) q^{82} +(-2.84057 - 12.4453i) q^{83} +(-1.43410 + 2.22336i) q^{84} +(-0.0286811 + 0.125660i) q^{85} +(-0.799988 + 10.6751i) q^{86} +(-6.55596 + 2.02225i) q^{87} +(1.46303 - 3.72774i) q^{88} +(-6.25916 - 1.93069i) q^{89} +(0.649474 - 0.814414i) q^{90} +(-9.13994 + 10.3694i) q^{91} +(-4.36284 - 5.47082i) q^{92} +(3.01791 + 7.68950i) q^{93} +(-0.260917 - 3.48170i) q^{94} +(6.44210 + 0.970990i) q^{95} +(-0.733052 - 0.680173i) q^{96} +6.13103 q^{97} +(1.20723 - 6.89511i) q^{98} +4.00456 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−0.733052	−	0.680173i	−0.518346	−	0.480955i
$2$	−0.733052	−	0.680173i	−0.518346	−	0.480955i
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$4$	0.0747301	+	0.997204i	0.0373650	+	0.498602i
$5$	0.380567	+	0.969668i	0.170195	+	0.433649i	0.990367	−	0.138468i	$-0.0442178\pi$
$5$	0.380567	+	0.969668i	0.170195	+	0.433649i	−0.820172	+	0.572116i	$0.806123\pi$
$6$	0.623490	+	0.781831i	0.254539	+	0.319181i
$7$	−2.32432	−	1.26394i	−0.878509	−	0.477725i
$7$	−2.32432	−	1.26394i	−0.878509	−	0.477725i
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	0.955573	+	0.294755i	0.318524	+	0.0982517i
$10$	0.380567	−	0.969668i	0.120346	−	0.306636i
$11$	3.82664	−	1.18036i	1.15378	−	0.355893i	0.341908	−	0.939733i	$-0.388927\pi$
$11$	3.82664	−	1.18036i	1.15378	−	0.355893i	0.811869	+	0.583840i	$0.198451\pi$
$12$	0.0747301	−	0.997204i	0.0215727	−	0.287868i
$13$	1.16255	−	5.09345i	0.322432	−	1.41267i	−0.510779	−	0.859712i	$-0.670643\pi$
$13$	1.16255	−	5.09345i	0.322432	−	1.41267i	0.833211	−	0.552956i	$-0.186500\pi$
$14$	0.844147	+	2.50747i	0.225608	+	0.670150i
$15$	−0.231794	−	1.01556i	−0.0598491	−	0.262216i
$16$	−0.988831	+	0.149042i	−0.247208	+	0.0372606i
$17$	0.102235	+	0.0697023i	0.0247955	+	0.0169053i	0.575654	−	0.817693i	$-0.304747\pi$
$17$	0.102235	+	0.0697023i	0.0247955	+	0.0169053i	−0.550859	+	0.834598i	$0.685700\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.12711	−	5.41631i	0.717408	−	1.24259i	−0.244615	−	0.969620i	$-0.578662\pi$
$19$	3.12711	−	5.41631i	0.717408	−	1.24259i	0.962023	−	0.272967i	$-0.0880051\pi$
$20$	−0.938517	+	0.451966i	−0.209859	+	0.101063i
$21$	2.10998	+	1.59625i	0.460435	+	0.348329i
$22$	−3.60798	−	1.73751i	−0.769224	−	0.370439i
$23$	−5.78156	+	3.94180i	−1.20554	+	0.821922i	−0.988049	−	0.154140i	$-0.950739\pi$
$23$	−5.78156	+	3.94180i	−1.20554	+	0.821922i	−0.217490	+	0.976063i	$0.569787\pi$
$24$	−0.733052	+	0.680173i	−0.149634	+	0.138840i
$25$	2.86983	−	2.66282i	0.573967	−	0.532563i
$26$	−4.31663	+	2.94303i	−0.846561	+	0.577175i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	1.08671	−	2.41227i	0.205369	−	0.455877i
$29$	6.18133	−	2.97677i	1.14785	−	0.552773i	0.239459	−	0.970906i	$-0.423030\pi$
$29$	6.18133	−	2.97677i	1.14785	−	0.552773i	0.908386	+	0.418133i	$0.137316\pi$
$30$	−0.520837	+	0.902117i	−0.0950915	+	0.164703i
$31$	−4.13026	−	7.15382i	−0.741816	−	1.28486i	−0.951668	−	0.307130i	$-0.900631\pi$
$31$	−4.13026	−	7.15382i	−0.741816	−	1.28486i	0.209851	−	0.977733i	$-0.432702\pi$
$32$	0.826239	+	0.563320i	0.146060	+	0.0995819i
$33$	−3.95983	+	0.596848i	−0.689318	+	0.103898i
$34$	−0.0275336	−	0.120633i	−0.00472197	−	0.0206883i
$35$	0.341046	−	2.73483i	0.0576473	−	0.462271i
$36$	−0.222521	+	0.974928i	−0.0370868	+	0.162488i
$37$	−0.584347	+	7.79757i	−0.0960660	+	1.28191i	0.715898	+	0.698205i	$0.246018\pi$
$37$	−0.584347	+	7.79757i	−0.0960660	+	1.28191i	−0.811964	+	0.583707i	$0.801602\pi$
$38$	−5.97636	+	1.84346i	−0.969494	+	0.299049i
$39$	−1.90870	+	4.86329i	−0.305637	+	0.778749i
$40$	0.995396	+	0.307039i	0.157386	+	0.0485471i
$41$	4.34914	−	5.45365i	0.679221	−	0.851717i	−0.316061	−	0.948739i	$-0.602360\pi$
$41$	4.34914	−	5.45365i	0.679221	−	0.851717i	0.995282	+	0.0970223i	$0.0309318\pi$
$42$	−0.460999	−	2.60528i	−0.0711337	−	0.402003i
$43$	−6.67448	−	8.36953i	−1.01785	−	1.27634i	−0.960586	−	0.277982i	$-0.910334\pi$
$43$	−6.67448	−	8.36953i	−1.01785	−	1.27634i	−0.0572619	−	0.998359i	$-0.518237\pi$
$44$	1.46303	+	3.72774i	0.220560	+	0.561977i
$45$	0.0778445	+	1.03876i	0.0116044	+	0.154850i
$46$	6.91929	+	1.04292i	1.02019	+	0.153769i
$47$	2.55942	+	2.37480i	0.373330	+	0.346400i	0.844416	−	0.535688i	$-0.179947\pi$
$47$	2.55942	+	2.37480i	0.373330	+	0.346400i	−0.471086	+	0.882087i	$0.656138\pi$
$48$	1.00000			0.144338
$49$	3.80490	+	5.87560i	0.543558	+	0.839372i
$50$	−3.91491			−0.553652
$51$	−0.0907041	−	0.0841611i	−0.0127011	−	0.0117849i
$52$	5.16608	+	0.778661i	0.716407	+	0.107981i
$53$	0.604876	+	8.07151i	0.0830861	+	1.10871i	0.870463	+	0.492235i	$0.163820\pi$
$53$	0.604876	+	8.07151i	0.0830861	+	1.10871i	−0.787376	+	0.616473i	$0.788561\pi$
$54$	0.365341	+	0.930874i	0.0497166	+	0.126676i
$55$	2.60085	+	3.26137i	0.350699	+	0.439763i
$56$	−2.43738	+	1.02917i	−0.325708	+	0.137529i
$57$	−3.89944	+	4.88975i	−0.516494	+	0.647663i
$58$	−6.55596	−	2.02225i	−0.860840	−	0.265534i
$59$	−2.15452	+	5.48962i	−0.280494	+	0.714688i	0.719306	+	0.694694i	$0.244460\pi$
$59$	−2.15452	+	5.48962i	−0.280494	+	0.714688i	−0.999800	+	0.0199943i	$0.993635\pi$
$60$	0.995396	−	0.307039i	0.128505	−	0.0396386i
$61$	−0.683516	+	9.12089i	−0.0875153	+	1.16781i	0.764618	+	0.644484i	$0.222928\pi$
$61$	−0.683516	+	9.12089i	−0.0875153	+	1.16781i	−0.852133	+	0.523326i	$0.824691\pi$
$62$	−1.83814	+	8.05341i	−0.233444	+	1.02278i
$63$	−1.84850	−	1.89289i	−0.232889	−	0.238482i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	5.38138	−	0.811112i	0.667478	−	0.100606i
$66$	3.30872	+	2.25585i	0.407275	+	0.277676i
$67$	4.48626	+	7.77044i	0.548084	+	0.949310i	0.998406	+	0.0564434i	$0.0179761\pi$
$67$	4.48626	+	7.77044i	0.548084	+	0.949310i	−0.450321	+	0.892867i	$0.648691\pi$
$68$	−0.0618674	+	0.107158i	−0.00750253	+	0.0129948i
$69$	6.30448	−	3.03608i	0.758970	−	0.365501i
$70$	−2.11016	+	1.77280i	−0.252212	+	0.211890i
$71$	7.56226	+	3.64179i	0.897475	+	0.432201i	0.824976	−	0.565167i	$-0.191188\pi$
$71$	7.56226	+	3.64179i	0.897475	+	0.432201i	0.0724989	+	0.997368i	$0.476903\pi$
$72$	0.826239	−	0.563320i	0.0973732	−	0.0663879i
$73$	0.906718	−	0.841311i	0.106123	−	0.0984680i	−0.625327	−	0.780363i	$-0.715034\pi$
$73$	0.906718	−	0.841311i	0.106123	−	0.0984680i	0.731450	+	0.681895i	$0.238844\pi$
$74$	5.73205	−	5.31856i	0.666337	−	0.618271i
$75$	−3.23465	+	2.20535i	−0.373506	+	0.254652i
$76$	5.63486	+	2.71361i	0.646363	+	0.311272i
$77$	−10.3862	−	2.09312i	−1.18362	−	0.238533i
$78$	4.70705	−	2.26680i	0.532969	−	0.256664i
$79$	4.69788	−	8.13696i	0.528553	−	0.915480i	−0.470893	−	0.882190i	$-0.656068\pi$
$79$	4.69788	−	8.13696i	0.528553	−	0.915480i	0.999446	−	0.0332896i	$-0.0105984\pi$
$80$	−0.520837	−	0.902117i	−0.0582314	−	0.100860i
$81$	0.826239	+	0.563320i	0.0918043	+	0.0625911i
$82$	−6.89757	+	1.03964i	−0.761709	+	0.114809i
$83$	−2.84057	−	12.4453i	−0.311793	−	1.36605i	−0.851568	−	0.524244i	$-0.824348\pi$
$83$	−2.84057	−	12.4453i	−0.311793	−	1.36605i	0.539775	−	0.841809i	$-0.318509\pi$
$84$	−1.43410	+	2.22336i	−0.156474	+	0.242589i
$85$	−0.0286811	+	0.125660i	−0.00311090	+	0.0136297i
$86$	−0.799988	+	10.6751i	−0.0862649	+	1.15113i
$87$	−6.55596	+	2.02225i	−0.702873	+	0.216807i
$88$	1.46303	−	3.72774i	0.155959	−	0.397378i
$89$	−6.25916	−	1.93069i	−0.663469	−	0.204653i	−0.0553112	−	0.998469i	$-0.517615\pi$
$89$	−6.25916	−	1.93069i	−0.663469	−	0.204653i	−0.608158	+	0.793816i	$0.708091\pi$
$90$	0.649474	−	0.814414i	0.0684605	−	0.0858468i
$91$	−9.13994	+	10.3694i	−0.958126	+	1.08701i
$92$	−4.36284	−	5.47082i	−0.454857	−	0.570373i
$93$	3.01791	+	7.68950i	0.312942	+	0.797364i
$94$	−0.260917	−	3.48170i	−0.0269115	−	0.359110i
$95$	6.44210	+	0.970990i	0.660946	+	0.0996215i
$96$	−0.733052	−	0.680173i	−0.0748168	−	0.0694198i
$97$	6.13103			0.622512			0.311256	−	0.950326i	$-0.399250\pi$
$97$	6.13103			0.622512			0.311256	+	0.950326i	$0.399250\pi$
$98$	1.20723	−	6.89511i	0.121949	−	0.696512i
$99$	4.00456			0.402473
$100$	2.86983	+	2.66282i	0.286983	+	0.266282i
$101$	−15.7789	−	2.37828i	−1.57006	−	0.236648i	−0.694403	−	0.719586i	$-0.744332\pi$
$101$	−15.7789	−	2.37828i	−1.57006	−	0.236648i	−0.875655	+	0.482938i	$0.839570\pi$
$102$	0.00924672	+	0.123389i	0.000915562	+	0.0122173i
$103$	−0.395742	−	1.00833i	−0.0389936	−	0.0993541i	0.910050	−	0.414497i	$-0.136043\pi$
$103$	−0.395742	−	1.00833i	−0.0389936	−	0.0993541i	−0.949044	+	0.315143i	$0.897947\pi$
$104$	−3.25738	−	4.08463i	−0.319413	−	0.400531i
$105$	−0.744842	+	2.65345i	−0.0726891	+	0.258951i
$106$	5.04662	−	6.32826i	0.490171	−	0.614655i
$107$	4.32402	+	1.33378i	0.418019	+	0.128942i	0.496627	−	0.867964i	$-0.334572\pi$
$107$	4.32402	+	1.33378i	0.418019	+	0.128942i	−0.0786086	+	0.996906i	$0.525048\pi$
$108$	0.365341	−	0.930874i	0.0351550	−	0.0895734i
$109$	−11.2859	+	3.48124i	−1.08099	+	0.333442i	−0.783570	−	0.621304i	$-0.786603\pi$
$109$	−11.2859	+	3.48124i	−1.08099	+	0.333442i	−0.297423	+	0.954746i	$0.596127\pi$
$110$	0.311733	−	4.15978i	0.0297225	−	0.396620i
$111$	1.73999	−	7.62338i	0.165152	−	0.723579i
$112$	2.48674	+	0.903403i	0.234975	+	0.0853635i
$113$	0.463242	+	2.02959i	0.0435781	+	0.190928i	0.992032	−	0.125987i	$-0.0402099\pi$
$113$	0.463242	+	2.02959i	0.0435781	+	0.190928i	−0.948454	+	0.316916i	$0.897353\pi$
$114$	6.18437	−	0.932143i	0.579219	−	0.0873032i
$115$	−6.02251	−	4.10608i	−0.561602	−	0.382894i
$116$	3.43038	+	5.94160i	0.318503	+	0.551663i
$117$	2.61222	−	4.52449i	0.241500	−	0.418289i
$118$	5.31327	−	2.55873i	0.489126	−	0.235551i
$119$	−0.149526	−	0.291229i	−0.0137070	−	0.0266969i
$120$	−0.938517	−	0.451966i	−0.0856745	−	0.0412586i
$121$	4.16133	−	2.83714i	0.378302	−	0.257922i
$122$	6.70483	−	6.22117i	0.607027	−	0.563239i
$123$	−5.11339	+	4.74453i	−0.461058	+	0.427800i
$124$	6.82516	−	4.65331i	0.612917	−	0.417880i
$125$	8.36680	+	4.02924i	0.748349	+	0.360386i
$126$	0.0675534	+	2.64489i	0.00601814	+	0.235625i
$127$	−3.13188	+	1.50823i	−0.277909	+	0.133834i	−0.567647	−	0.823272i	$-0.692146\pi$
$127$	−3.13188	+	1.50823i	−0.277909	+	0.133834i	0.289738	+	0.957106i	$0.406432\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.35251	+	9.27083i	0.471263	+	0.816251i
$130$	−4.49653	−	3.06568i	−0.394371	−	0.268878i
$131$	−7.19353	+	1.08425i	−0.628501	+	0.0947313i	−0.455566	−	0.890202i	$-0.650563\pi$
$131$	−7.19353	+	1.08425i	−0.628501	+	0.0947313i	−0.172935	+	0.984933i	$0.555325\pi$
$132$	−0.891098	−	3.90415i	−0.0775601	−	0.339813i
$133$	−14.1143	+	8.63675i	−1.22387	+	0.748901i
$134$	1.99658	−	8.74757i	0.172478	−	0.755675i
$135$	0.0778445	−	1.03876i	0.00669979	−	0.0894024i
$136$	0.118238	−	0.0364715i	0.0101388	−	0.00312740i
$137$	1.90368	−	4.85050i	0.162642	−	0.414406i	−0.826199	−	0.563378i	$-0.809501\pi$
$137$	1.90368	−	4.85050i	0.162642	−	0.414406i	0.988841	+	0.148972i	$0.0475966\pi$
$138$	−6.68657	−	2.06253i	−0.569199	−	0.175574i
$139$	−5.86927	+	7.35984i	−0.497825	+	0.624253i	−0.965737	−	0.259522i	$-0.916435\pi$
$139$	−5.86927	+	7.35984i	−0.497825	+	0.624253i	0.467912	+	0.883775i	$0.345006\pi$
$140$	2.75267	+	0.135718i	0.232643	+	0.0114703i
$141$	−2.17689	−	2.72973i	−0.183327	−	0.229885i
$142$	−3.06648	−	7.81327i	−0.257333	−	0.655675i
$143$	−1.56347	−	20.8630i	−0.130744	−	1.74465i
$144$	−0.988831	−	0.149042i	−0.0824026	−	0.0124202i
$145$	5.23889	+	4.86098i	0.435066	+	0.403683i
$146$	−1.23691			−0.102367
$147$	−2.88669	−	6.37707i	−0.238090	−	0.525972i
$148$	−7.81943			−0.642753
$149$	1.73324	+	1.60821i	0.141992	+	0.131750i	0.747971	−	0.663731i	$-0.231028\pi$
$149$	1.73324	+	1.60821i	0.141992	+	0.131750i	−0.605979	+	0.795481i	$0.707218\pi$
$150$	3.87119	+	0.583488i	0.316081	+	0.0476416i
$151$	0.00352982	+	0.0471022i	0.000287253	+	0.00383312i	0.997346	−	0.0728134i	$-0.0231978\pi$
$151$	0.00352982	+	0.0471022i	0.000287253	+	0.00383312i	−0.997058	+	0.0766465i	$0.975579\pi$
$152$	−2.28492	−	5.82189i	−0.185332	−	0.472218i
$153$	0.0771474	+	0.0967398i	0.00623700	+	0.00782095i
$154$	6.18998	+	8.59880i	0.498803	+	0.692911i
$155$	5.36499	−	6.72748i	0.430926	−	0.540364i
$156$	−4.99233	−	1.53993i	−0.399706	−	0.123293i
$157$	6.94390	−	17.6928i	0.554184	−	1.41204i	−0.329591	−	0.944124i	$-0.606911\pi$
$157$	6.94390	−	17.6928i	0.554184	−	1.41204i	0.883775	−	0.467913i	$-0.154994\pi$
$158$	−8.97833	+	2.76945i	−0.714277	+	0.220325i
$159$	0.604876	−	8.07151i	0.0479698	−	0.640112i
$160$	−0.231794	+	1.01556i	−0.0183250	+	0.0802869i
$161$	18.4204	−	1.85444i	1.45173	−	0.146151i
$162$	−0.222521	−	0.974928i	−0.0174829	−	0.0765976i
$163$	1.76009	−	0.265291i	0.137861	−	0.0207792i	−0.0797493	−	0.996815i	$-0.525412\pi$
$163$	1.76009	−	0.265291i	0.137861	−	0.0207792i	0.217610	+	0.976036i	$0.430174\pi$
$164$	5.76341	+	3.92943i	0.450047	+	0.306837i
$165$	−2.08572	−	3.61258i	−0.162373	−	0.281239i
$166$	−6.38270	+	11.0552i	−0.495393	+	0.858046i
$167$	−4.99353	+	2.40476i	−0.386411	+	0.186086i	−0.616996	−	0.786967i	$-0.711650\pi$
$167$	−4.99353	+	2.40476i	−0.386411	+	0.186086i	0.230585	+	0.973052i	$0.425936\pi$
$168$	2.56354	−	0.654403i	0.197782	−	0.0504883i
$169$	−12.8791	−	6.20224i	−0.990699	−	0.477096i
$170$	0.106495	−	0.0726072i	0.00816781	−	0.00556872i
$171$	4.58467	−	4.25395i	0.350598	−	0.325308i
$172$	7.84734	−	7.28127i	0.598354	−	0.555192i
$173$	−2.02861	+	1.38308i	−0.154232	+	0.105154i	−0.637977	−	0.770055i	$-0.720229\pi$
$173$	−2.02861	+	1.38308i	−0.154232	+	0.105154i	0.483745	+	0.875209i	$0.339276\pi$
$174$	6.18133	+	2.97677i	0.468606	+	0.225669i
$175$	−10.0361	+	2.56193i	−0.758654	+	0.193664i
$176$	−3.60798	+	1.73751i	−0.271962	+	0.130970i
$177$	2.94864	−	5.10719i	0.221633	−	0.383880i
$178$	3.27508	+	5.67261i	0.245478	+	0.425180i
$179$	−8.72669	−	5.94975i	−0.652263	−	0.444706i	0.191448	−	0.981503i	$-0.438682\pi$
$179$	−8.72669	−	5.94975i	−0.652263	−	0.444706i	−0.843711	+	0.536797i	$0.819634\pi$
$180$	−1.03004	+	0.155254i	−0.0767747	+	0.0115719i
$181$	−0.313318	−	1.37273i	−0.0232887	−	0.102035i	0.961948	−	0.273233i	$-0.0880931\pi$
$181$	−0.313318	−	1.37273i	−0.0232887	−	0.102035i	−0.985237	+	0.171199i	$0.945236\pi$
$182$	13.7530	−	1.38457i	1.01944	−	0.102631i
$183$	2.03528	−	8.91714i	0.150452	−	0.659174i
$184$	−0.522920	+	6.97788i	−0.0385502	+	0.514416i
$185$	−7.78343	+	2.40087i	−0.572249	+	0.176516i
$186$	3.01791	−	7.68950i	0.221284	−	0.563821i
$187$	0.473489	+	0.146052i	0.0346250	+	0.0106804i
$188$	−2.17689	+	2.72973i	−0.158766	+	0.199086i
$189$	1.54573	+	2.14726i	0.112436	+	0.156190i
$190$	−4.06195	−	5.09353i	−0.294685	−	0.369523i
$191$	8.09273	+	20.6199i	0.585569	+	1.49201i	0.849566	+	0.527483i	$0.176864\pi$
$191$	8.09273	+	20.6199i	0.585569	+	1.49201i	−0.263996	+	0.964524i	$0.585041\pi$
$192$	0.0747301	+	0.997204i	0.00539318	+	0.0719670i
$193$	19.1863	+	2.89188i	1.38106	+	0.208162i	0.797212	−	0.603699i	$-0.206307\pi$
$193$	19.1863	+	2.89188i	1.38106	+	0.208162i	0.583851	+	0.811861i	$0.301545\pi$
$194$	−4.49437	−	4.17016i	−0.322677	−	0.299400i
$195$	−5.44216			−0.389721
$196$	−5.57483	+	4.23335i	−0.398202	+	0.302382i
$197$	6.97587			0.497010			0.248505	−	0.968631i	$-0.420061\pi$
$197$	6.97587			0.497010			0.248505	+	0.968631i	$0.420061\pi$
$198$	−2.93555	−	2.72379i	−0.208620	−	0.193571i
$199$	1.61100	+	0.242819i	0.114201	+	0.0172130i	0.205894	−	0.978574i	$-0.433990\pi$
$199$	1.61100	+	0.242819i	0.114201	+	0.0172130i	−0.0916932	+	0.995787i	$0.529228\pi$
$200$	−0.292562	−	3.90397i	−0.0206872	−	0.276052i
$201$	−3.27803	−	8.35229i	−0.231215	−	0.589125i
$202$	9.94910	+	12.4758i	0.700016	+	0.877792i
$203$	−18.1299	−	0.893877i	−1.27247	−	0.0627379i
$204$	0.0771474	−	0.0967398i	0.00540140	−	0.00677314i
$205$	6.94336	+	2.14174i	0.484946	+	0.149586i
$206$	−0.395742	+	1.00833i	−0.0275727	+	0.0702540i
$207$	−6.68657	+	2.06253i	−0.464749	+	0.143356i
$208$	−0.390422	+	5.20983i	−0.0270709	+	0.361236i
$209$	5.57312	−	24.4174i	0.385501	−	1.68899i
$210$	2.35081	−	1.43850i	0.162222	−	0.0992658i
$211$	4.30215	+	18.8490i	0.296172	+	1.29762i	0.875776	+	0.482718i	$0.160350\pi$
$211$	4.30215	+	18.8490i	0.296172	+	1.29762i	−0.579603	+	0.814899i	$0.696793\pi$
$212$	−8.00374	+	1.20637i	−0.549699	+	0.0828538i
$213$	−6.93502	−	4.72821i	−0.475180	−	0.323972i
$214$	−2.26253	−	3.91881i	−0.154663	−	0.267885i
$215$	5.57558	−	9.65719i	0.380251	−	0.658615i
$216$	−0.900969	+	0.433884i	−0.0613032	+	0.0295220i
$217$	0.558026	+	21.8481i	0.0378813	+	1.48315i
$218$	10.6410	+	5.12443i	0.720699	+	0.347070i
$219$	−1.02198	+	0.696775i	−0.0690591	+	0.0470837i
$220$	−3.05789	+	2.83730i	−0.206163	+	0.191291i
$221$	0.473877	−	0.439694i	0.0318764	−	0.0295770i
$222$	−6.46072	+	4.40484i	−0.433615	+	0.295634i
$223$	5.64145	+	2.71678i	0.377779	+	0.181929i	0.613131	−	0.789981i	$-0.289910\pi$
$223$	5.64145	+	2.71678i	0.377779	+	0.181929i	−0.235352	+	0.971910i	$0.575624\pi$
$224$	−1.20844	−	2.35365i	−0.0807421	−	0.157260i
$225$	3.52721	−	1.69862i	0.235148	−	0.113241i
$226$	1.04089	−	1.80288i	0.0692393	−	0.119926i
$227$	8.78765	+	15.2207i	0.583257	+	1.01023i	0.995090	+	0.0989712i	$0.0315552\pi$
$227$	8.78765	+	15.2207i	0.583257	+	1.01023i	−0.411834	+	0.911259i	$0.635111\pi$
$228$	−5.16748	−	3.52313i	−0.342225	−	0.233325i
$229$	7.34806	−	1.10754i	0.485574	−	0.0731885i	0.0983069	−	0.995156i	$-0.468657\pi$
$229$	7.34806	−	1.10754i	0.485574	−	0.0731885i	0.387267	+	0.921968i	$0.373419\pi$
$230$	1.62197	+	7.10631i	0.106949	+	0.468576i
$231$	9.95828	+	3.61773i	0.655207	+	0.238029i
$232$	1.52666	−	6.68875i	0.100230	−	0.439138i
$233$	0.902533	−	12.0435i	0.0591269	−	0.788994i	−0.886290	−	0.463131i	$-0.846726\pi$
$233$	0.902533	−	12.0435i	0.0591269	−	0.788994i	0.945417	−	0.325863i	$-0.105655\pi$
$234$	−4.99233	+	1.53993i	−0.326359	+	0.100668i
$235$	−1.32873	+	3.38556i	−0.0866770	+	0.220849i
$236$	−5.63528	−	1.73825i	−0.366825	−	0.113151i
$237$	−5.85816	+	7.34590i	−0.380528	+	0.477167i
$238$	−0.0884757	+	0.315189i	−0.00573503	+	0.0204307i
$239$	18.7288	+	23.4852i	1.21147	+	1.51913i	0.790993	+	0.611825i	$0.209564\pi$
$239$	18.7288	+	23.4852i	1.21147	+	1.51913i	0.420473	+	0.907305i	$0.361864\pi$
$240$	0.380567	+	0.969668i	0.0245655	+	0.0625918i
$241$	−0.0523629	−	0.698735i	−0.00337299	−	0.0450094i	0.995263	−	0.0972158i	$-0.0309937\pi$
$241$	−0.0523629	−	0.698735i	−0.00337299	−	0.0450094i	−0.998636	+	0.0522063i	$0.983375\pi$
$242$	−4.98022	−	0.750647i	−0.320140	−	0.0482534i
$243$	−0.733052	−	0.680173i	−0.0470253	−	0.0436331i
$244$	−9.14646			−0.585542
$245$	−4.24936	+	5.92555i	−0.271482	+	0.378570i
$246$	6.97548			0.444740
$247$	−23.9523	−	22.2245i	−1.52405	−	1.41411i
$248$	−8.16825	−	1.23117i	−0.518685	−	0.0781791i
$249$	0.953959	+	12.7297i	0.0604547	+	0.806712i
$250$	−3.39272	−	8.64451i	−0.214574	−	0.546727i
$251$	7.47926	+	9.37870i	0.472087	+	0.591978i	0.959681	−	0.281092i	$-0.0906967\pi$
$251$	7.47926	+	9.37870i	0.472087	+	0.591978i	−0.487594	+	0.873071i	$0.662125\pi$
$252$	1.74946	−	1.98479i	0.110206	−	0.125030i
$253$	−17.4712	+	21.9082i	−1.09841	+	1.37736i
$254$	3.32169	+	1.02460i	0.208421	+	0.0642894i
$255$	0.0470894	−	0.119982i	0.00294885	−	0.00751355i
$256$	0.955573	−	0.294755i	0.0597233	−	0.0184222i
$257$	−1.90843	+	25.4662i	−0.119044	+	1.58854i	0.543432	+	0.839453i	$0.317125\pi$
$257$	−1.90843	+	25.4662i	−0.119044	+	1.58854i	−0.662476	+	0.749083i	$0.730495\pi$
$258$	2.38209	−	10.4366i	0.148303	−	0.649756i
$259$	11.2139	−	17.3854i	0.696796	−	1.08028i
$260$	1.21100	+	5.30572i	0.0751027	+	0.329047i
$261$	6.78414	−	1.02254i	0.419927	−	0.0632939i
$262$	6.01070	+	4.09803i	0.371343	+	0.253177i
$263$	−14.0168	−	24.2778i	−0.864314	−	1.49704i	−0.867727	−	0.497041i	$-0.834420\pi$
$263$	−14.0168	−	24.2778i	−0.864314	−	1.49704i	0.00341329	−	0.999994i	$-0.498914\pi$
$264$	−2.00228	+	3.46805i	−0.123232	+	0.213444i
$265$	−7.59649	+	3.65828i	−0.466649	+	0.224726i
$266$	16.2210	+	3.26898i	0.994573	+	0.200434i
$267$	5.90149	+	2.84201i	0.361165	+	0.173928i
$268$	−7.41345	+	5.05440i	−0.452849	+	0.308747i
$269$	−13.3071	+	12.3472i	−0.811351	+	0.752824i	−0.972199	−	0.234155i	$-0.924768\pi$
$269$	−13.3071	+	12.3472i	−0.811351	+	0.752824i	0.160848	+	0.986979i	$0.448577\pi$
$270$	−0.763602	+	0.708519i	−0.0464713	+	0.0431191i
$271$	6.40463	−	4.36660i	0.389054	−	0.265252i	−0.352958	−	0.935639i	$-0.614824\pi$
$271$	6.40463	−	4.36660i	0.389054	−	0.265252i	0.742012	+	0.670387i	$0.233872\pi$
$272$	−0.111481	−	0.0536865i	−0.00675954	−	0.00325523i
$273$	10.5833	−	8.89134i	0.640533	−	0.538128i
$274$	−4.69467	+	2.26083i	−0.283615	+	0.136582i
$275$	7.83874	−	13.5771i	0.472694	−	0.818730i
$276$	3.49872	+	6.05997i	0.210598	+	0.364767i
$277$	19.1860	+	13.0808i	1.15278	+	0.785950i	0.979997	−	0.199010i	$-0.0637727\pi$
$277$	19.1860	+	13.0808i	1.15278	+	0.785950i	0.172780	+	0.984960i	$0.444725\pi$
$278$	9.30844	−	1.40302i	0.558283	−	0.0841477i
$279$	−1.83814	−	8.05341i	−0.110046	−	0.482145i
$280$	−1.92554	−	1.97178i	−0.115073	−	0.117836i
$281$	3.29770	−	14.4482i	0.196724	−	0.861905i	−0.776146	−	0.630553i	$-0.782828\pi$
$281$	3.29770	−	14.4482i	0.196724	−	0.861905i	0.972870	−	0.231351i	$-0.0743147\pi$
$282$	−0.260917	+	3.48170i	−0.0155374	+	0.207332i
$283$	9.62157	−	2.96786i	0.571943	−	0.176421i	0.00472501	−	0.999989i	$-0.498496\pi$
$283$	9.62157	−	2.96786i	0.571943	−	0.176421i	0.567218	+	0.823568i	$0.308020\pi$
$284$	−3.06648	+	7.81327i	−0.181962	+	0.463632i
$285$	−6.22543	−	1.92029i	−0.368763	−	0.113748i
$286$	−13.0444	+	16.3571i	−0.771330	+	0.967217i
$287$	−17.0019	+	7.17895i	−1.00359	+	0.423760i
$288$	0.623490	+	0.781831i	0.0367395	+	0.0460699i
$289$	−6.20520	−	15.8106i	−0.365012	−	0.930035i
$290$	−0.534073	−	7.12670i	−0.0313618	−	0.418494i
$291$	−6.06255	−	0.913783i	−0.355393	−	0.0535669i
$292$	0.906718	+	0.841311i	0.0530617	+	0.0492340i
$293$	−18.2463			−1.06596			−0.532979	−	0.846128i	$-0.678928\pi$
$293$	−18.2463			−1.06596			−0.532979	+	0.846128i	$0.678928\pi$
$294$	−2.22141	+	6.63817i	−0.129555	+	0.387146i
$295$	−6.14305			−0.357662
$296$	5.73205	+	5.31856i	0.333169	+	0.309135i
$297$	−3.95983	−	0.596848i	−0.229773	−	0.0346326i
$298$	−0.176693	−	2.35780i	−0.0102355	−	0.136584i
$299$	13.3560	+	34.0306i	0.772399	+	1.96804i
$300$	−2.44091	−	3.06080i	−0.140926	−	0.176716i
$301$	4.93501	+	27.8896i	0.284449	+	1.60753i
$302$	0.0294501	−	0.0369292i	0.00169466	−	0.00212504i
$303$	15.2482	+	4.70344i	0.875985	+	0.270206i
$304$	−2.28492	+	5.82189i	−0.131049	+	0.333908i
$305$	−9.10436	+	2.80832i	−0.521314	+	0.160804i
$306$	0.00924672	−	0.123389i	0.000528600	−	0.00705367i
$307$	−6.94577	+	30.4314i	−0.396416	+	1.73681i	0.244913	+	0.969545i	$0.421241\pi$
$307$	−6.94577	+	30.4314i	−0.396416	+	1.73681i	−0.641329	+	0.767266i	$0.721617\pi$
$308$	1.31110	−	10.5136i	0.0747067	−	0.599069i
$309$	0.241038	+	1.05605i	0.0137121	+	0.0600768i
$310$	−8.50866	+	1.28247i	−0.483260	+	0.0728397i
$311$	16.4657	+	11.2261i	0.933685	+	0.636576i	0.931624	−	0.363422i	$-0.118392\pi$
$311$	16.4657	+	11.2261i	0.933685	+	0.636576i	0.00206031	+	0.999998i	$0.499344\pi$
$312$	2.61222	+	4.52449i	0.147888	+	0.256149i
$313$	10.1355	−	17.5553i	0.572895	−	0.992283i	−0.423372	−	0.905956i	$-0.639154\pi$
$313$	10.1355	−	17.5553i	0.572895	−	0.992283i	0.996267	−	0.0863274i	$-0.0275131\pi$
$314$	−17.1244	+	8.24667i	−0.966385	+	0.465386i
$315$	1.13200	−	2.51280i	0.0637809	−	0.141580i
$316$	8.46528	+	4.07667i	0.476209	+	0.229330i
$317$	9.78489	−	6.67123i	0.549574	−	0.374694i	−0.256467	−	0.966553i	$-0.582558\pi$
$317$	9.78489	−	6.67123i	0.549574	−	0.374694i	0.806041	+	0.591860i	$0.201606\pi$
$318$	−5.93343	+	5.50542i	−0.332730	+	0.308728i
$319$	20.1401	−	18.6873i	1.12763	−	1.04629i
$320$	0.860672	−	0.586796i	0.0481130	−	0.0328029i
$321$	−4.07693	−	1.96335i	−0.227552	−	0.109583i
$322$	−14.7644	−	11.1696i	−0.822790	−	0.622460i
$323$	0.697229	−	0.335768i	0.0387948	−	0.0186826i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−10.2266	−	17.7130i	−0.567270	−	0.982540i
$326$	−1.47068	−	1.00269i	−0.0814535	−	0.0555340i
$327$	11.6787	−	1.76028i	0.645833	−	0.0973437i
$328$	−1.55219	−	6.80059i	−0.0857053	−	0.375500i
$329$	−2.94730	−	8.75474i	−0.162490	−	0.482664i
$330$	−0.928234	+	4.06686i	−0.0510976	+	0.223873i
$331$	0.0491980	−	0.656502i	0.00270417	−	0.0360846i	−0.995688	−	0.0927602i	$-0.970431\pi$
$331$	0.0491980	−	0.656502i	0.00270417	−	0.0360846i	0.998393	+	0.0566756i	$0.0180501\pi$
$332$	12.1983	−	3.76267i	0.669467	−	0.206503i
$333$	−2.85676	+	7.27890i	−0.156549	+	0.398882i
$334$	5.29616	+	1.63365i	0.289793	+	0.0893893i
$335$	−5.82742	+	7.30735i	−0.318386	+	0.399243i
$336$	−2.32432	−	1.26394i	−0.126802	−	0.0689537i
$337$	0.662034	+	0.830164i	0.0360633	+	0.0452219i	0.799536	−	0.600618i	$-0.205079\pi$
$337$	0.662034	+	0.830164i	0.0360633	+	0.0452219i	−0.763473	+	0.645840i	$0.776507\pi$
$338$	5.22244	+	13.3066i	0.284064	+	0.723782i
$339$	−0.155572	−	2.07597i	−0.00844953	−	0.112751i
$340$	−0.127452	−	0.0192103i	−0.00691205	−	0.00104182i
$341$	−24.2491	−	22.4999i	−1.31316	−	1.21844i
$342$	−6.25422			−0.338190
$343$	−1.41739	−	18.4659i	−0.0765318	−	0.997067i
$344$	−10.7050			−0.577177
$345$	5.34326	+	4.95782i	0.287672	+	0.266920i
$346$	2.42781	+	0.365934i	0.130520	+	0.0196727i
$347$	1.45081	+	19.3597i	0.0778833	+	1.03928i	0.890052	+	0.455858i	$0.150668\pi$
$347$	1.45081	+	19.3597i	0.0778833	+	1.03928i	−0.812169	+	0.583422i	$0.801713\pi$
$348$	−2.50652	−	6.38651i	−0.134364	−	0.342353i
$349$	4.08122	+	5.11768i	0.218462	+	0.273943i	0.878971	−	0.476875i	$-0.158231\pi$
$349$	4.08122	+	5.11768i	0.218462	+	0.273943i	−0.660508	+	0.750819i	$0.729659\pi$
$350$	9.09950	+	4.94822i	0.486389	+	0.264494i
$351$	−3.25738	+	4.08463i	−0.173866	+	0.218021i
$352$	3.82664	+	1.18036i	0.203961	+	0.0629136i
$353$	7.87014	−	20.0528i	0.418885	−	1.06730i	−0.553278	−	0.832997i	$-0.686623\pi$
$353$	7.87014	−	20.0528i	0.418885	−	1.06730i	0.972163	−	0.234306i	$-0.0752816\pi$
$354$	−5.63528	+	1.73825i	−0.299512	+	0.0923871i
$355$	−0.653386	+	8.71883i	−0.0346781	+	0.462747i
$356$	1.45755	−	6.38593i	0.0772499	−	0.338454i
$357$	0.104450	+	0.310262i	0.00552810	+	0.0164208i
$358$	2.35025	+	10.2971i	0.124215	+	0.544220i
$359$	−32.9252	+	4.96268i	−1.73773	+	0.261920i	−0.940019	−	0.341123i	$-0.889193\pi$
$359$	−32.9252	+	4.96268i	−1.73773	+	0.261920i	−0.797709	+	0.603043i	$0.793955\pi$
$360$	0.860672	+	0.586796i	0.0453614	+	0.0309269i
$361$	−10.0576	−	17.4203i	−0.529350	−	0.916861i
$362$	−0.704018	+	1.21940i	−0.0370024	+	0.0640900i
$363$	−4.53770	+	2.18524i	−0.238168	+	0.114695i
$364$	−11.0234	−	8.33948i	−0.577785	−	0.437108i
$365$	1.16086	+	0.559040i	0.0607621	+	0.0292615i
$366$	−7.55716	+	5.15239i	−0.395019	+	0.269320i
$367$	1.00173	−	0.929473i	0.0522901	−	0.0485181i	−0.653595	−	0.756845i	$-0.726740\pi$
$367$	1.00173	−	0.929473i	0.0522901	−	0.0485181i	0.705885	+	0.708326i	$0.250550\pi$
$368$	5.12949	−	4.75947i	0.267393	−	0.248105i
$369$	5.76341	−	3.92943i	0.300031	−	0.204558i
$370$	7.33867	+	3.53412i	0.381519	+	0.183730i
$371$	8.79599	−	19.5253i	0.456665	−	1.01370i
$372$	−7.44247	+	3.58410i	−0.385874	+	0.185827i
$373$	6.66317	−	11.5410i	0.345006	−	0.597568i	−0.640349	−	0.768084i	$-0.721210\pi$
$373$	6.66317	−	11.5410i	0.345006	−	0.597568i	0.985355	+	0.170516i	$0.0545436\pi$
$374$	−0.247752	−	0.429118i	−0.0128109	−	0.0221892i
$375$	−7.67282	−	5.23124i	−0.396223	−	0.270140i
$376$	3.45246	−	0.520375i	0.178047	−	0.0268363i
$377$	−7.97595	−	34.9449i	−0.410782	−	1.79976i
$378$	0.327401	−	2.62542i	0.0168397	−	0.135037i
$379$	4.84092	−	21.2095i	0.248662	−	1.08946i	−0.684220	−	0.729275i	$-0.739857\pi$
$379$	4.84092	−	21.2095i	0.248662	−	1.08946i	0.932882	−	0.360182i	$-0.117285\pi$
$380$	−0.486857	+	6.49665i	−0.0249752	+	0.333271i
$381$	3.32169	−	1.02460i	0.170175	−	0.0524921i
$382$	8.09273	−	20.6199i	0.414060	−	1.05501i
$383$	7.28996	+	2.24865i	0.372500	+	0.114901i	0.475352	−	0.879796i	$-0.342321\pi$
$383$	7.28996	+	2.24865i	0.372500	+	0.114901i	−0.102852	+	0.994697i	$0.532797\pi$
$384$	0.623490	−	0.781831i	0.0318173	−	0.0398977i
$385$	−1.92303	−	10.8678i	−0.0980068	−	0.553873i
$386$	−12.0976	−	15.1699i	−0.615752	−	0.772129i
$387$	−3.91099	−	9.96503i	−0.198807	−	0.506551i
$388$	0.458173	+	6.11389i	0.0232602	+	0.310386i
$389$	10.0632	+	1.51678i	0.510224	+	0.0769039i	0.399109	−	0.916904i	$-0.369320\pi$
$389$	10.0632	+	1.51678i	0.510224	+	0.0769039i	0.111115	+	0.993808i	$0.464558\pi$
$390$	3.98939	+	3.70161i	0.202010	+	0.187438i
$391$	−0.865828			−0.0437868
$392$	6.96605	+	0.688584i	0.351839	+	0.0347788i
$393$	7.27478			0.366964
$394$	−5.11367	−	4.74480i	−0.257623	−	0.239039i
$395$	9.67801	+	1.45872i	0.486953	+	0.0733964i
$396$	0.299261	+	3.99336i	0.0150384	+	0.200674i
$397$	1.79489	+	4.57330i	0.0900829	+	0.229527i	0.968814	−	0.247790i	$-0.0797044\pi$
$397$	1.79489	+	4.57330i	0.0900829	+	0.229527i	−0.878731	+	0.477318i	$0.841609\pi$
$398$	−1.01579	−	1.27376i	−0.0509168	−	0.0638476i
$399$	15.2439	−	6.43666i	0.763149	−	0.322236i
$400$	−2.44091	+	3.06080i	−0.122045	+	0.153040i
$401$	−11.1199	−	3.43003i	−0.555300	−	0.171287i	0.00438847	−	0.999990i	$-0.498603\pi$
$401$	−11.1199	−	3.43003i	−0.555300	−	0.171287i	−0.559689	+	0.828703i	$0.689079\pi$
$402$	−3.27803	+	8.35229i	−0.163493	+	0.416574i
$403$	−41.2392	+	12.7206i	−2.05427	+	0.633659i
$404$	1.19248	−	15.9125i	0.0593279	−	0.791676i
$405$	−0.231794	+	1.01556i	−0.0115180	+	0.0504635i
$406$	12.6821	+	12.9867i	0.629404	+	0.644519i
$407$	6.96788	+	30.5283i	0.345385	+	1.51323i
$408$	−0.122353	+	0.0184417i	−0.00605737	+	0.000913001i
$409$	10.2247	+	6.97106i	0.505577	+	0.344697i	0.789096	−	0.614270i	$-0.210549\pi$
$409$	10.2247	+	6.97106i	0.505577	+	0.344697i	−0.283519	+	0.958967i	$0.591502\pi$
$410$	−3.63309	−	6.29270i	−0.179426	−	0.310774i
$411$	−2.60535	+	4.51259i	−0.128512	+	0.222590i
$412$	0.975941	−	0.469988i	0.0480812	−	0.0231547i
$413$	11.9463	−	10.0364i	0.587841	−	0.493861i
$414$	6.30448	+	3.03608i	0.309848	+	0.149215i
$415$	10.9868	−	7.49069i	0.539322	−	0.367703i
$416$	3.82978	−	3.55352i	0.187770	−	0.174226i
$417$	6.90065	−	6.40286i	0.337926	−	0.313550i
$418$	−20.6935	+	14.1086i	−1.01215	+	0.690072i
$419$	23.1236	+	11.1357i	1.12966	+	0.544017i	0.902865	−	0.429925i	$-0.141460\pi$
$419$	23.1236	+	11.1357i	1.12966	+	0.544017i	0.226798	+	0.973942i	$0.427174\pi$
$420$	−2.70170	−	0.544466i	−0.131829	−	0.0265672i
$421$	7.90509	−	3.80689i	0.385270	−	0.185536i	−0.231215	−	0.972903i	$-0.574270\pi$
$421$	7.90509	−	3.80689i	0.385270	−	0.185536i	0.616486	+	0.787366i	$0.288556\pi$
$422$	9.66685	−	16.7435i	0.470575	−	0.815060i
$423$	1.74573	+	3.02369i	0.0848803	+	0.147017i
$424$	6.68769	+	4.55959i	0.324783	+	0.221433i
$425$	0.479001	−	0.0721978i	0.0232350	−	0.00350211i
$426$	1.86772	+	8.18304i	0.0904915	+	0.396469i
$427$	13.1170	−	20.3359i	0.634775	−	0.984124i
$428$	−1.00692	+	4.41160i	−0.0486713	+	0.213243i
$429$	−1.56347	+	20.8630i	−0.0754850	+	1.00728i
$430$	−10.6557	+	3.28686i	−0.513866	+	0.158507i
$431$	−4.57685	+	11.6616i	−0.220459	+	0.561721i	−0.997722	−	0.0674546i	$-0.978512\pi$
$431$	−4.57685	+	11.6616i	−0.220459	+	0.561721i	0.777263	+	0.629176i	$0.216607\pi$
$432$	0.955573	+	0.294755i	0.0459750	+	0.0141814i
$433$	0.402793	−	0.505087i	0.0193570	−	0.0242729i	−0.772059	−	0.635551i	$-0.780773\pi$
$433$	0.402793	−	0.505087i	0.0193570	−	0.0242729i	0.791416	+	0.611278i	$0.209344\pi$
$434$	14.4514	−	16.3954i	0.693692	−	0.787003i
$435$	−4.45589	−	5.58750i	−0.213643	−	0.267900i
$436$	−4.31490	−	10.9942i	−0.206646	−	0.526526i
$437$	3.27046	+	43.6412i	0.156447	+	2.08764i
$438$	1.22309	+	0.184352i	0.0584416	+	0.00880866i
$439$	22.6128	+	20.9816i	1.07925	+	1.00140i	0.999990	+	0.00454149i	$0.00144561\pi$
$439$	22.6128	+	20.9816i	1.07925	+	1.00140i	0.0792581	+	0.996854i	$0.474745\pi$
$440$	4.17145			0.198866
$441$	1.90400	+	6.73608i	0.0906666	+	0.320766i
$442$	−0.646445			−0.0307482
$443$	−20.1894	−	18.7330i	−0.959227	−	0.890033i	0.0347746	−	0.999395i	$-0.488929\pi$
$443$	−20.1894	−	18.7330i	−0.959227	−	0.890033i	−0.994002	+	0.109362i	$0.965119\pi$
$444$	7.73210	+	1.16543i	0.366949	+	0.0553087i
$445$	−0.509894	−	6.80406i	−0.0241713	−	0.322543i
$446$	−2.28759	−	5.82870i	−0.108321	−	0.275997i
$447$	−1.47419	−	1.84857i	−0.0697267	−	0.0874345i
$448$	−0.715042	+	2.54730i	−0.0337826	+	0.120348i
$449$	−17.6397	+	22.1195i	−0.832470	+	1.04388i	0.165862	+	0.986149i	$0.446959\pi$
$449$	−17.6397	+	22.1195i	−0.832470	+	1.04388i	−0.998332	+	0.0577356i	$0.981612\pi$
$450$	−3.74098	−	1.15394i	−0.176352	−	0.0543973i
$451$	10.2053	−	26.0027i	0.480550	−	1.22442i
$452$	−1.98930	+	0.613618i	−0.0935689	+	0.0288622i
$453$	0.00352982	−	0.0471022i	0.000165845	−	0.00221305i
$454$	3.91087	−	17.1346i	0.183546	−	0.804169i
$455$	−13.5332	−	4.91646i	−0.634448	−	0.230487i
$456$	1.39170	+	6.09742i	0.0651721	+	0.285538i
$457$	8.39407	−	1.26520i	0.392658	−	0.0591836i	0.0502539	−	0.998736i	$-0.483997\pi$
$457$	8.39407	−	1.26520i	0.392658	−	0.0591836i	0.342404	+	0.939553i	$0.388759\pi$
$458$	−6.13983	−	4.18607i	−0.286896	−	0.195602i
$459$	−0.0618674	−	0.107158i	−0.00288772	−	0.00500169i
$460$	3.64453	−	6.31251i	0.169927	−	0.294323i
$461$	−24.1087	+	11.6101i	−1.12285	+	0.540738i	−0.900773	−	0.434291i	$-0.856999\pi$
$461$	−24.1087	+	11.6101i	−1.12285	+	0.540738i	−0.222081	+	0.975028i	$0.571285\pi$
$462$	−4.83926	−	9.42533i	−0.225143	−	0.438506i
$463$	2.48977	+	1.19901i	0.115709	+	0.0557226i	0.490843	−	0.871248i	$-0.336689\pi$
$463$	2.48977	+	1.19901i	0.115709	+	0.0557226i	−0.375134	+	0.926971i	$0.622403\pi$
$464$	−5.66863	+	3.86481i	−0.263160	+	0.179419i
$465$	−6.30774	+	5.85273i	−0.292515	+	0.271414i
$466$	−8.85324	+	8.21461i	−0.410119	+	0.380534i
$467$	27.8286	−	18.9732i	1.28775	−	0.877976i	0.290863	−	0.956765i	$-0.406058\pi$
$467$	27.8286	−	18.9732i	1.28775	−	0.877976i	0.996891	+	0.0787886i	$0.0251052\pi$
$468$	4.70705	+	2.26680i	0.217584	+	0.104783i
$469$	−0.606125	−	23.7313i	−0.0279882	−	1.09581i
$470$	3.27679	−	1.57802i	0.151147	−	0.0727887i
$471$	−9.50331	+	16.4602i	−0.437890	+	0.758447i
$472$	2.94864	+	5.10719i	0.135722	+	0.235078i
$473$	−35.4199	−	24.1489i	−1.62861	−	1.11037i
$474$	9.29081	−	1.40036i	0.426741	−	0.0643209i
$475$	−5.44837	−	23.8709i	−0.249988	−	1.09527i
$476$	0.279240	−	0.170871i	0.0127990	−	0.00783188i
$477$	−1.80112	+	7.89121i	−0.0824674	+	0.361313i
$478$	2.24479	−	29.9547i	0.102674	−	1.37010i
$479$	−3.49299	+	1.07744i	−0.159599	+	0.0492297i	−0.373525	−	0.927620i	$-0.621851\pi$
$479$	−3.49299	+	1.07744i	−0.159599	+	0.0492297i	0.213926	+	0.976850i	$0.431375\pi$
$480$	0.380567	−	0.969668i	0.0173704	−	0.0442591i
$481$	39.0372	+	12.0414i	1.77994	+	0.549039i
$482$	−0.436875	+	0.547824i	−0.0198991	+	0.0249527i
$483$	−18.4910	−	0.911685i	−0.841371	−	0.0414831i
$484$	3.14019	+	3.93767i	0.142736	+	0.178985i
$485$	2.33327	+	5.94507i	0.105948	+	0.269952i
$486$	0.0747301	+	0.997204i	0.00338983	+	0.0452341i
$487$	26.1124	+	3.93581i	1.18327	+	0.178349i	0.711055	−	0.703137i	$-0.248218\pi$
$487$	26.1124	+	3.93581i	1.18327	+	0.178349i	0.472211	+	0.881485i	$0.343456\pi$
$488$	6.70483	+	6.22117i	0.303513	+	0.281619i
$489$	−1.77997			−0.0804930
$490$	7.14540	−	1.45344i	0.322796	−	0.0656595i
$491$	−5.12742			−0.231397			−0.115699	−	0.993284i	$-0.536911\pi$
$491$	−5.12742			−0.231397			−0.115699	+	0.993284i	$0.536911\pi$
$492$	−5.11339	−	4.74453i	−0.230529	−	0.213900i
$493$	0.839434	+	0.126524i	0.0378062	+	0.00569837i
$494$	2.44179	+	32.5834i	0.109861	+	1.46600i
$495$	1.52400	+	3.88309i	0.0684987	+	0.174532i
$496$	5.15035	+	6.45833i	0.231257	+	0.289988i
$497$	−12.9741	−	18.0229i	−0.581967	−	0.808439i
$498$	7.95909	−	9.98039i	0.356655	−	0.447232i
$499$	−21.0178	−	6.48313i	−0.940885	−	0.290225i	−0.213883	−	0.976859i	$-0.568611\pi$
$499$	−21.0178	−	6.48313i	−0.940885	−	0.290225i	−0.727003	+	0.686635i	$0.759087\pi$
$500$	−3.39272	+	8.64451i	−0.151727	+	0.386594i
$501$	5.29616	−	1.63365i	0.236615	−	0.0729861i
$502$	0.896448	−	11.9623i	0.0400104	−	0.533902i
$503$	−0.782166	+	3.42689i	−0.0348750	+	0.152798i	−0.989367	−	0.145438i	$-0.953541\pi$
$503$	−0.782166	+	3.42689i	−0.0348750	+	0.152798i	0.954492	+	0.298235i	$0.0963980\pi$
$504$	−2.63244	+	0.265017i	−0.117258	+	0.0118048i
$505$	−3.69877	−	16.2054i	−0.164593	−	0.721130i
$506$	27.7087	−	4.17641i	1.23180	−	0.185664i
$507$	11.8108	+	8.05250i	0.524538	+	0.357624i
$508$	−1.73806	−	3.01041i	−0.0771140	−	0.133565i
$509$	−15.4857	+	26.8220i	−0.686391	+	1.18886i	0.286606	+	0.958048i	$0.407473\pi$
$509$	−15.4857	+	26.8220i	−0.686391	+	1.18886i	−0.972997	+	0.230816i	$0.925860\pi$
$510$	−0.116127	+	0.0559239i	−0.00514220	+	0.00247635i
$511$	−3.17087	+	0.809436i	−0.140271	+	0.0358074i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	−5.16748	+	3.52313i	−0.228150	+	0.155550i
$514$	18.7204	−	17.3700i	0.825720	−	0.766156i
$515$	0.827143	−	0.767477i	0.0364483	−	0.0338191i
$516$	−8.84491	+	6.03036i	−0.389375	+	0.265472i
$517$	12.5971	+	6.06645i	0.554021	+	0.266802i
$518$	−20.0455	+	5.11706i	−0.880747	+	0.224831i
$519$	2.21209	−	1.06529i	0.0971000	−	0.0467609i
$520$	2.72108	−	4.71305i	0.119327	−	0.206681i
$521$	12.9229	+	22.3832i	0.566164	+	0.980625i	0.996940	+	0.0781662i	$0.0249065\pi$
$521$	12.9229	+	22.3832i	0.566164	+	0.980625i	−0.430776	+	0.902459i	$0.641760\pi$
$522$	−5.66863	−	3.86481i	−0.248109	−	0.169158i
$523$	−0.441893	+	0.0666046i	−0.0193226	+	0.00291242i	−0.158696	−	0.987327i	$-0.550729\pi$
$523$	−0.441893	+	0.0666046i	−0.0193226	+	0.00291242i	0.139374	+	0.990240i	$0.455491\pi$
$524$	−1.61879	−	7.09239i	−0.0707172	−	0.309832i
$525$	10.3058	−	1.03752i	0.449782	−	0.0452811i
$526$	−6.23807	+	27.3308i	−0.271993	+	1.19168i
$527$	0.0763827	−	1.01926i	0.00332728	−	0.0443995i
$528$	3.82664	−	1.18036i	0.166533	−	0.0513687i
$529$	9.48580	−	24.1694i	0.412426	−	1.05084i
$530$	8.05688	+	2.48522i	0.349969	+	0.107951i
$531$	−3.67689	+	4.61068i	−0.159564	+	0.200086i
$532$	−9.66736	−	13.4294i	−0.419133	−	0.582239i
$533$	−22.7218	−	28.4922i	−0.984190	−	1.23413i
$534$	−2.39304	−	6.09737i	−0.103557	−	0.263859i
$535$	0.352251	+	4.70046i	0.0152291	+	0.203218i
$536$	8.87231	+	1.33729i	0.383225	+	0.0577620i
$537$	7.74245	+	7.18395i	0.334112	+	0.310010i
$538$	18.1531			0.782635
$539$	21.4954	+	17.9927i	0.925871	+	0.774999i
$540$	1.04167			0.0448266
$541$	−11.8286	−	10.9753i	−0.508549	−	0.471865i	0.383668	−	0.923471i	$-0.374661\pi$
$541$	−11.8286	−	10.9753i	−0.508549	−	0.471865i	−0.892217	+	0.451606i	$0.850851\pi$
$542$	−7.66497	−	1.15531i	−0.329239	−	0.0496248i
$543$	0.105223	+	1.40410i	0.00451554	+	0.0602557i
$544$	0.0452054	+	0.115182i	0.00193817	+	0.00493837i
$545$	−7.67068	−	9.61873i	−0.328576	−	0.412021i
$546$	−13.8058	−	0.680682i	−0.590833	−	0.0291305i
$547$	−12.9021	+	16.1787i	−0.551653	+	0.691751i	−0.976990	−	0.213284i	$-0.931584\pi$
$547$	−12.9021	+	16.1787i	−0.551653	+	0.691751i	0.425337	+	0.905035i	$0.360156\pi$
$548$	4.97920	+	1.53588i	0.212701	+	0.0656095i
$549$	−3.34158	+	8.51420i	−0.142615	+	0.363377i
$550$	−14.9810	+	4.62102i	−0.638791	+	0.197041i
$551$	3.20657	−	42.7888i	0.136605	−	1.82286i
$552$	1.55708	−	6.82200i	0.0662736	−	0.290364i
$553$	−21.2040	+	12.9750i	−0.901686	+	0.551755i
$554$	−5.16714	−	22.6387i	−0.219531	−	0.961828i
$555$	8.05433	−	1.21400i	0.341887	−	0.0515312i
$556$	−7.77787	−	5.30286i	−0.329855	−	0.224891i
$557$	5.23695	+	9.07067i	0.221897	+	0.384337i	0.955384	−	0.295367i	$-0.0954418\pi$
$557$	5.23695	+	9.07067i	0.221897	+	0.384337i	−0.733487	+	0.679703i	$0.762109\pi$
$558$	−4.13026	+	7.15382i	−0.174848	+	0.302845i
$559$	−50.3891	+	24.2661i	−2.13123	+	1.02635i
$560$	0.0703687	+	2.75511i	0.00297362	+	0.116425i
$561$	−0.446433	−	0.214991i	−0.0188484	−	0.00907692i
$562$	−12.2446	+	8.34824i	−0.516508	+	0.352149i
$563$	0.772308	−	0.716597i	0.0325489	−	0.0302010i	−0.663731	−	0.747972i	$-0.731028\pi$
$563$	0.772308	−	0.716597i	0.0325489	−	0.0302010i	0.696280	+	0.717771i	$0.254837\pi$
$564$	2.55942	−	2.37480i	0.107771	−	0.0999969i
$565$	−1.79174	+	1.22159i	−0.0753790	+	0.0513925i
$566$	−9.07177	−	4.36873i	−0.381315	−	0.183631i
$567$	−1.20844	−	2.35365i	−0.0507496	−	0.0988441i
$568$	7.56226	−	3.64179i	0.317305	−	0.152806i
$569$	4.02337	−	6.96868i	0.168668	−	0.292142i	−0.769284	−	0.638908i	$-0.779387\pi$
$569$	4.02337	−	6.96868i	0.168668	−	0.292142i	0.937952	+	0.346765i	$0.112720\pi$
$570$	3.25743	+	5.64204i	0.136439	+	0.236319i
$571$	3.15549	+	2.15138i	0.132053	+	0.0900323i	0.627545	−	0.778580i	$-0.284060\pi$
$571$	3.15549	+	2.15138i	0.132053	+	0.0900323i	−0.495492	+	0.868613i	$0.665012\pi$
$572$	20.6879	−	3.11819i	0.865003	−	0.130378i
$573$	−4.92910	−	21.5958i	−0.205916	−	0.902177i
$574$	17.3462	+	6.30166i	0.724016	+	0.263026i
$575$	−6.09583	+	26.7076i	−0.254213	+	1.11378i
$576$	0.0747301	−	0.997204i	0.00311375	−	0.0415502i
$577$	−35.9371	+	11.0851i	−1.49608	+	0.461480i	−0.931452	−	0.363863i	$-0.881457\pi$
$577$	−35.9371	+	11.0851i	−1.49608	+	0.461480i	−0.564630	+	0.825344i	$0.690981\pi$
$578$	−6.20520	+	15.8106i	−0.258102	+	0.657634i
$579$	−18.5410	−	5.71915i	−0.770539	−	0.237680i
$580$	−4.45589	+	5.58750i	−0.185021	+	0.232008i
$581$	−9.12780	+	32.5172i	−0.378685	+	1.34904i
$582$	3.82264	+	4.79343i	0.158453	+	0.198694i
$583$	11.8420	+	30.1728i	0.490444	+	1.24963i
$584$	−0.0924343	−	1.23345i	−0.00382496	−	0.0510405i
$585$	5.38138	+	0.811112i	0.222493	+	0.0335354i
$586$	13.3755	+	12.4106i	0.552535	+	0.512678i
$587$	33.3703			1.37734			0.688669	−	0.725076i	$-0.258195\pi$
$587$	33.3703			1.37734			0.688669	+	0.725076i	$0.258195\pi$
$588$	6.14351	−	3.35518i	0.253354	−	0.138365i
$589$	−51.6631			−2.12874
$590$	4.50317	+	4.17833i	0.185393	+	0.172019i
$591$	−6.89795	−	1.03970i	−0.283744	−	0.0427675i
$592$	−0.584347	−	7.79757i	−0.0240165	−	0.320478i
$593$	0.807652	+	2.05786i	0.0331663	+	0.0845063i	0.946497	−	0.322711i	$-0.104594\pi$
$593$	0.807652	+	2.05786i	0.0331663	+	0.0845063i	−0.913331	+	0.407218i	$0.866499\pi$
$594$	2.49680	+	3.13089i	0.102445	+	0.128462i
$595$	0.225491	−	0.255822i	0.00924422	−	0.0104877i
$596$	−1.47419	+	1.84857i	−0.0603851	+	0.0757205i
$597$	−1.55681	−	0.480214i	−0.0637162	−	0.0196538i
$598$	13.3560	−	34.0306i	0.546168	−	1.39161i
$599$	−41.4872	+	12.7971i	−1.69512	+	0.522876i	−0.983689	−	0.179878i	$-0.942430\pi$
$599$	−41.4872	+	12.7971i	−1.69512	+	0.522876i	−0.711433	+	0.702754i	$0.751954\pi$
$600$	−0.292562	+	3.90397i	−0.0119438	+	0.159379i
$601$	7.06672	−	30.9613i	0.288258	−	1.26294i	−0.598657	−	0.801006i	$-0.704299\pi$
$601$	7.06672	−	30.9613i	0.288258	−	1.26294i	0.886914	−	0.461934i	$-0.152844\pi$
$602$	15.3521	−	23.8012i	0.625706	−	0.970064i
$603$	1.99658	+	8.74757i	0.0813068	+	0.356228i
$604$	−0.0467067	+	0.00703990i	−0.00190047	+	0.000286449i
$605$	4.33475	+	2.95538i	0.176233	+	0.120153i
$606$	−7.97856	−	13.8193i	−0.324107	−	0.561369i
$607$	18.1833	−	31.4944i	0.738037	−	1.27832i	−0.215342	−	0.976539i	$-0.569087\pi$
$607$	18.1833	−	31.4944i	0.738037	−	1.27832i	0.953378	−	0.301778i	$-0.0975802\pi$
$608$	5.63486	−	2.71361i	0.228524	−	0.110051i
$609$	17.7941	+	3.58601i	0.721055	+	0.145312i
$610$	8.58411	+	4.13389i	0.347560	+	0.167376i
$611$	15.0713	−	10.2755i	0.609721	−	0.415701i
$612$	−0.0907041	+	0.0841611i	−0.00366650	+	0.00340201i
$613$	−24.6945	+	22.9132i	−0.997403	+	0.925455i	−0.997218	−	0.0745454i	$-0.976249\pi$
$613$	−24.6945	+	22.9132i	−0.997403	+	0.925455i	−0.000185235		1.00000i	$0.500059\pi$
$614$	25.7902	−	17.5835i	1.04081	−	0.709611i
$615$	−6.54660	−	3.15268i	−0.263984	−	0.127128i
$616$	−8.11218	+	6.81526i	−0.326849	+	0.274595i
$617$	19.1730	−	9.23323i	0.771875	−	0.371716i	−0.00612344	−	0.999981i	$-0.501949\pi$
$617$	19.1730	−	9.23323i	0.771875	−	0.371716i	0.777999	+	0.628266i	$0.216235\pi$
$618$	0.541606	−	0.938090i	0.0217866	−	0.0377355i
$619$	13.2988	+	23.0343i	0.534525	+	0.925825i	0.999186	+	0.0403361i	$0.0128429\pi$
$619$	13.2988	+	23.0343i	0.534525	+	0.925825i	−0.464661	+	0.885489i	$0.653824\pi$
$620$	7.10960	+	4.84724i	0.285528	+	0.194670i
$621$	6.91929	−	1.04292i	0.277662	−	0.0418507i
$622$	−4.43451	−	19.4289i	−0.177808	−	0.779026i
$623$	12.1080	+	12.3988i	0.485096	+	0.496746i
$624$	1.16255	−	5.09345i	0.0465391	−	0.203901i
$625$	0.739911	−	9.87343i	0.0295964	−	0.394937i
$626$	−19.3705	+	5.97501i	−0.774201	+	0.238809i
$627$	−9.15011	+	23.3141i	−0.365420	+	0.931075i
$628$	18.1622	+	5.60230i	0.724751	+	0.223556i
$629$	−0.603249	+	0.756450i	−0.0240531	+	0.0301617i
$630$	−2.53896	+	1.07206i	−0.101154	+	0.0427119i
$631$	8.83151	+	11.0744i	0.351577	+	0.440864i	0.925902	−	0.377764i	$-0.123307\pi$
$631$	8.83151	+	11.0744i	0.351577	+	0.440864i	−0.574325	+	0.818627i	$0.694735\pi$
$632$	−3.43266	−	8.74626i	−0.136544	−	0.347908i
$633$	−1.44481	−	19.2796i	−0.0574260	−	0.766297i
$634$	−11.7104	−	1.76506i	−0.465080	−	0.0700996i
$635$	−2.65437	−	2.46290i	−0.105336	−	0.0977371i
$636$	8.09414			0.320954
$637$	34.3504	−	12.5494i	1.36101	−	0.497226i
$638$	−27.4743			−1.08772
$639$	6.15285	+	5.70901i	0.243403	+	0.225845i
$640$	−1.03004	−	0.155254i	−0.0407159	−	0.00613694i
$641$	−0.528040	−	7.04620i	−0.0208563	−	0.278308i	−0.997875	−	0.0651552i	$-0.979246\pi$
$641$	−0.528040	−	7.04620i	−0.0208563	−	0.278308i	0.977019	−	0.213153i	$-0.0683733\pi$
$642$	1.65319	+	4.21225i	0.0652461	+	0.166244i
$643$	22.3903	+	28.0765i	0.882985	+	1.10723i	0.993554	+	0.113360i	$0.0361613\pi$
$643$	22.3903	+	28.0765i	0.882985	+	1.10723i	−0.110569	+	0.993868i	$0.535267\pi$
$644$	3.22582	+	18.2303i	0.127115	+	0.718374i
$645$	−6.95264	+	8.71833i	−0.273760	+	0.343284i
$646$	−0.739485	−	0.228101i	−0.0290946	−	0.00897451i
$647$	−11.6446	+	29.6699i	−0.457796	+	1.16645i	0.496620	+	0.867968i	$0.334574\pi$
$647$	−11.6446	+	29.6699i	−0.457796	+	1.16645i	−0.954417	+	0.298478i	$0.903521\pi$
$648$	0.955573	−	0.294755i	0.0375384	−	0.0115791i
$649$	−1.76482	+	23.5500i	−0.0692754	+	0.924416i
$650$	−4.55127	+	19.9404i	−0.178515	+	0.782127i
$651$	2.70450	−	21.6873i	0.105998	−	0.849992i
$652$	0.396081	+	1.73534i	0.0155117	+	0.0679613i
$653$	−23.7994	+	3.58719i	−0.931344	+	0.140378i	−0.597153	−	0.802128i	$-0.703701\pi$
$653$	−23.7994	+	3.58719i	−0.931344	+	0.140378i	−0.334192	+	0.942505i	$0.608463\pi$
$654$	−9.75838	−	6.65315i	−0.381583	−	0.260159i
$655$	−3.78898	−	6.56270i	−0.148048	−	0.256426i
$656$	−3.48774	+	6.04094i	−0.136173	+	0.235859i
$657$	1.11442	−	0.536674i	0.0434775	−	0.0209377i
$658$	−3.79421	+	8.42235i	−0.147914	+	0.328338i
$659$	25.3217	+	12.1943i	0.986394	+	0.475022i	0.856300	−	0.516479i	$-0.172758\pi$
$659$	25.3217	+	12.1943i	0.986394	+	0.475022i	0.130094	+	0.991502i	$0.458472\pi$
$660$	3.44661	−	2.34986i	0.134159	−	0.0914681i
$661$	−17.4347	+	16.1770i	−0.678131	+	0.629213i	−0.942106	−	0.335316i	$-0.891157\pi$
$661$	−17.4347	+	16.1770i	−0.678131	+	0.629213i	0.263975	+	0.964530i	$0.414966\pi$
$662$	−0.482600	+	0.447787i	−0.0187568	+	0.0174037i
$663$	−0.534118	+	0.364155i	−0.0207434	+	0.0141426i
$664$	−11.5012	−	5.53870i	−0.446334	−	0.214943i
$665$	−13.7462	−	10.3993i	−0.533055	−	0.403269i
$666$	7.04507	−	3.39272i	0.272991	−	0.131465i
$667$	−24.0039	+	41.5760i	−0.929435	+	1.60983i
$668$	−2.77120	−	4.79986i	−0.107221	−	0.185712i
$669$	−5.17352	−	3.52725i	−0.200020	−	0.136371i
$670$	9.24207	−	1.39302i	0.357052	−	0.0538169i
$671$	8.15039	+	35.7092i	0.314642	+	1.37854i
$672$	0.844147	+	2.50747i	0.0325637	+	0.0967278i
$673$	2.62667	−	11.5082i	0.101251	−	0.443608i	−0.898736	−	0.438490i	$-0.855514\pi$
$673$	2.62667	−	11.5082i	0.101251	−	0.443608i	0.999987	−	0.00511846i	$-0.00162926\pi$
$674$	0.0793499	−	1.05885i	0.00305644	−	0.0407854i
$675$	−3.74098	+	1.15394i	−0.143991	+	0.0444152i
$676$	5.22244	−	13.3066i	0.200863	−	0.511791i
$677$	−36.6546	−	11.3064i	−1.40875	−	0.434542i	−0.505192	−	0.863007i	$-0.668578\pi$
$677$	−36.6546	−	11.3064i	−1.40875	−	0.434542i	−0.903558	+	0.428465i	$0.859054\pi$
$678$	−1.29797	+	1.62761i	−0.0498484	+	0.0625079i
$679$	−14.2505	−	7.74927i	−0.546883	−	0.297390i
$680$	0.0803625	+	0.100771i	0.00308176	+	0.00386441i
$681$	−6.42098	−	16.3604i	−0.246052	−	0.626931i
$682$	2.47205	+	32.9872i	0.0946596	+	1.26315i
$683$	19.5260	+	2.94307i	0.747141	+	0.112613i	0.511568	−	0.859243i	$-0.329065\pi$
$683$	19.5260	+	2.94307i	0.747141	+	0.112613i	0.235574	+	0.971856i	$0.424303\pi$
$684$	4.58467	+	4.25395i	0.175299	+	0.162654i
$685$	5.42785			0.207387
$686$	−11.5210	+	14.5006i	−0.439874	+	0.553634i
$687$	−7.43106			−0.283513
$688$	7.84734	+	7.28127i	0.299177	+	0.277596i
$689$	41.8150	+	6.30260i	1.59302	+	0.240110i
$690$	−0.544712	−	7.26868i	−0.0207368	−	0.276714i
$691$	−13.1636	−	33.5404i	−0.500768	−	1.27594i	−0.928265	−	0.371920i	$-0.878700\pi$
$691$	−13.1636	−	33.5404i	−0.500768	−	1.27594i	0.427496	−	0.904017i	$-0.359396\pi$
$692$	−1.53081	−	1.91958i	−0.0581928	−	0.0729715i
$693$	−9.30786	−	5.06152i	−0.353576	−	0.192271i
$694$	12.1044	−	15.1784i	0.459477	−	0.576165i
$695$	−9.37025	−	2.89034i	−0.355434	−	0.109637i
$696$	−2.50652	+	6.38651i	−0.0950093	+	0.242080i
$697$	0.824764	−	0.254406i	0.0312402	−	0.00963632i
$698$	0.489165	−	6.52746i	0.0185152	−	0.247068i
$699$	−2.68744	+	11.7744i	−0.101648	+	0.445350i
$700$	−3.30476	−	9.81654i	−0.124908	−	0.371030i
$701$	−4.83368	−	21.1778i	−0.182566	−	0.799873i	−0.980403	−	0.197000i	$-0.936880\pi$
$701$	−4.83368	−	21.1778i	−0.182566	−	0.799873i	0.797838	−	0.602872i	$-0.205977\pi$
$702$	5.16608	−	0.778661i	0.194981	−	0.0293887i
$703$	40.4068	+	27.5489i	1.52397	+	1.03903i
$704$	−2.00228	−	3.46805i	−0.0754637	−	0.130707i
$705$	1.81848	−	3.14971i	0.0684880	−	0.118625i
$706$	−19.4086	+	9.34668i	−0.730452	+	0.351767i
$707$	33.6691	+	25.4715i	1.26626	+	0.957953i
$708$	5.31327	+	2.55873i	0.199685	+	0.0961631i
$709$	−28.9252	+	19.7209i	−1.08631	+	0.740634i	−0.967649	−	0.252301i	$-0.918813\pi$
$709$	−28.9252	+	19.7209i	−1.08631	+	0.740634i	−0.118662	+	0.992935i	$0.537860\pi$
$710$	6.40927	−	5.94694i	0.240536	−	0.223185i
$711$	6.88758	−	6.39074i	0.258304	−	0.239671i
$712$	−5.41200	+	3.68984i	−0.202823	+	0.138282i
$713$	52.0783	+	25.0796i	1.95035	+	0.939237i
$714$	0.134464	−	0.298482i	0.00503219	−	0.0111704i
$715$	19.6352	−	9.45582i	0.734315	−	0.353628i
$716$	5.28097	−	9.14691i	0.197359	−	0.341836i
$717$	−15.0193	−	26.0143i	−0.560907	−	0.971520i
$718$	27.5114	+	18.7569i	1.02672	+	0.700003i
$719$	−19.4637	+	2.93368i	−0.725874	+	0.109408i	−0.501577	−	0.865113i	$-0.667247\pi$
$719$	−19.4637	+	2.93368i	−0.725874	+	0.109408i	−0.224297	+	0.974521i	$0.572009\pi$
$720$	−0.231794	−	1.01556i	−0.00863847	−	0.0378476i
$721$	−0.354645	+	2.84388i	−0.0132077	+	0.105912i
$722$	−4.47607	+	19.6110i	−0.166582	+	0.729844i
$723$	−0.0523629	+	0.698735i	−0.00194740	+	0.0259862i
$724$	1.34548	−	0.415026i	0.0500044	−	0.0154243i
$725$	9.81280	−	25.0026i	0.364438	−	0.928574i
$726$	4.81271	+	1.48453i	0.178617	+	0.0550959i
$727$	−3.69973	+	4.63932i	−0.137216	+	0.172063i	−0.845691	−	0.533672i	$-0.820812\pi$
$727$	−3.69973	+	4.63932i	−0.137216	+	0.172063i	0.708476	+	0.705735i	$0.249383\pi$
$728$	2.40846	+	13.6111i	0.0892634	+	0.504461i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	−0.470726	−	1.19939i	−0.0174224	−	0.0443914i
$731$	−0.0989864	−	1.32088i	−0.00366114	−	0.0488546i
$732$	9.04430	+	1.36321i	0.334287	+	0.0503857i
$733$	−3.64314	−	3.38034i	−0.134562	−	0.124856i	0.610021	−	0.792386i	$-0.291161\pi$
$733$	−3.64314	−	3.38034i	−0.134562	−	0.124856i	−0.744583	+	0.667530i	$0.767352\pi$
$734$	−1.36652			−0.0504394
$735$	5.08506	−	5.22603i	0.187565	−	0.192765i
$736$	−6.99745			−0.257929
$737$	26.3393	+	24.4393i	0.970220	+	0.900232i
$738$	−6.89757	−	1.03964i	−0.253903	−	0.0382697i
$739$	−0.607439	−	8.10571i	−0.0223450	−	0.298173i	−0.997169	−	0.0751964i	$-0.976042\pi$
$739$	−0.607439	−	8.10571i	−0.0223450	−	0.298173i	0.974824	−	0.222977i	$-0.0715774\pi$
$740$	−2.97581	−	7.58225i	−0.109393	−	0.278729i
$741$	20.3724	+	25.5462i	0.748398	+	0.938462i
$742$	−19.7285	+	8.33025i	−0.724255	+	0.305813i
$743$	−6.03819	+	7.57165i	−0.221520	+	0.277777i	−0.880156	−	0.474685i	$-0.842562\pi$
$743$	−6.03819	+	7.57165i	−0.221520	+	0.277777i	0.658636	+	0.752461i	$0.271134\pi$
$744$	7.89352	+	2.43483i	0.289391	+	0.0892652i
$745$	−0.899817	+	2.29270i	−0.0329667	+	0.0839979i
$746$	−12.7343	+	3.92801i	−0.466235	+	0.143815i
$747$	0.953959	−	12.7297i	0.0349035	−	0.465755i
$748$	−0.110260	+	0.483080i	−0.00403150	+	0.0176632i
$749$	−8.36457	−	8.56544i	−0.305635	−	0.312974i
$750$	2.06643	+	9.05361i	0.0754553	+	0.330591i
$751$	8.24201	−	1.24228i	0.300755	−	0.0453315i	0.00306883	−	0.999995i	$-0.499023\pi$
$751$	8.24201	−	1.24228i	0.300755	−	0.0453315i	0.297686	+	0.954664i	$0.403785\pi$
$752$	−2.88478	−	1.96681i	−0.105197	−	0.0717222i
$753$	−5.99790	−	10.3887i	−0.218576	−	0.378584i
$754$	−17.9218	+	31.0415i	−0.652674	+	1.13046i
$755$	−0.0443301	+	0.0213483i	−0.00161334	+	0.000776943i
$756$	−2.02574	+	1.70188i	−0.0736754	+	0.0618967i
$757$	−18.6128	−	8.96347i	−0.676495	−	0.325783i	0.0638986	−	0.997956i	$-0.479647\pi$
$757$	−18.6128	−	8.96347i	−0.676495	−	0.325783i	−0.740394	+	0.672174i	$0.765361\pi$
$758$	−17.9748	+	12.2550i	−0.652872	+	0.445121i
$759$	20.5413	−	19.0596i	0.745603	−	0.691819i
$760$	4.77573	−	4.43123i	0.173234	−	0.160738i
$761$	−30.0534	+	20.4900i	−1.08943	+	0.742764i	−0.968279	−	0.249870i	$-0.919612\pi$
$761$	−30.0534	+	20.4900i	−1.08943	+	0.742764i	−0.121155	+	0.992634i	$0.538660\pi$
$762$	−3.13188	−	1.50823i	−0.113456	−	0.0546375i
$763$	30.6321	+	6.17321i	1.10896	+	0.223485i
$764$	−19.9575	+	9.61103i	−0.722037	+	0.347715i
$765$	−0.0644458	+	0.111623i	−0.00233004	+	0.00403575i
$766$	−3.81444	−	6.60681i	−0.137821	−	0.238714i
$767$	25.4564	+	17.3559i	0.919176	+	0.626684i
$768$	−0.988831	+	0.149042i	−0.0356814	+	0.00537810i
$769$	1.11200	+	4.87199i	0.0400998	+	0.175689i	0.991012	−	0.133772i	$-0.0427088\pi$
$769$	1.11200	+	4.87199i	0.0400998	+	0.175689i	−0.950912	+	0.309460i	$0.899852\pi$
$770$	−5.98229	+	9.27464i	−0.215587	+	0.334235i
$771$	5.68264	−	24.8973i	0.204655	−	0.896654i
$772$	−1.44999	+	19.3488i	−0.0521864	+	0.696379i
$773$	11.1281	−	3.43258i	0.400252	−	0.123461i	−0.0880927	−	0.996112i	$-0.528077\pi$
$773$	11.1281	−	3.43258i	0.400252	−	0.123461i	0.488344	+	0.872651i	$0.337601\pi$
$774$	−3.91099	+	9.96503i	−0.140578	+	0.358186i
$775$	−30.9025	−	9.53215i	−1.11005	−	0.342405i
$776$	3.82264	−	4.79343i	0.137225	−	0.172074i
$777$	−13.6798	+	15.5199i	−0.490760	+	0.556774i
$778$	−6.34517	−	7.95659i	−0.227485	−	0.285258i
$779$	−15.9384	−	40.6105i	−0.571054	−	1.45502i
$780$	−0.406693	−	5.42694i	−0.0145620	−	0.194316i
$781$	33.2367	+	5.00963i	1.18930	+	0.179259i
$782$	0.634697	+	0.588913i	0.0226967	+	0.0210595i
$783$	−6.86076			−0.245184
$784$	−4.63812	−	5.24289i	−0.165647	−	0.187246i
$785$	19.7987			0.706647
$786$	−5.33279	−	4.94811i	−0.190214	−	0.176493i
$787$	−33.9858	−	5.12254i	−1.21146	−	0.182599i	−0.487927	−	0.872885i	$-0.662247\pi$
$787$	−33.9858	−	5.12254i	−1.21146	−	0.182599i	−0.723537	+	0.690286i	$0.757485\pi$
$788$	0.521307	+	6.95636i	0.0185708	+	0.247810i
$789$	10.2418	+	26.0958i	0.364619	+	0.929034i
$790$	−6.10230	−	7.65204i	−0.217110	−	0.272247i
$791$	1.48857	−	5.30293i	0.0529274	−	0.188551i
$792$	2.49680	−	3.13089i	0.0887199	−	0.111251i
$793$	45.6621	+	14.0849i	1.62151	+	0.500170i
$794$	1.79489	−	4.57330i	0.0636982	−	0.162300i
$795$	8.05688	−	2.48522i	0.285748	−	0.0881416i
$796$	−0.121750	+	1.62464i	−0.00431531	+	0.0575838i
$797$	11.4785	−	50.2906i	0.406590	−	1.78139i	−0.193128	−	0.981174i	$-0.561863\pi$
$797$	11.4785	−	50.2906i	0.406590	−	1.78139i	0.599718	−	0.800212i	$-0.295280\pi$
$798$	−15.5526	−	5.65008i	−0.550556	−	0.200011i
$799$	0.0961325	+	0.421184i	0.00340092	+	0.0149004i
$800$	3.87119	−	0.583488i	0.136867	−	0.0206294i
$801$	−5.41200	−	3.68984i	−0.191224	−	0.130374i
$802$	5.81844	+	10.0778i	0.205456	+	0.355860i
$803$	2.47663	−	4.28966i	0.0873985	−	0.151379i
$804$	8.08397	−	3.89303i	0.285100	−	0.137297i
$805$	8.80838	+	17.1559i	0.310455	+	0.604667i
$806$	38.8827	+	18.7249i	1.36958	+	0.659557i
$807$	14.9988	−	10.2260i	0.527982	−	0.359972i
$808$	−11.6974	+	10.8536i	−0.411513	+	0.381828i
$809$	29.4748	−	27.3486i	1.03628	−	0.961525i	0.0369920	−	0.999316i	$-0.488222\pi$
$809$	29.4748	−	27.3486i	1.03628	−	0.961525i	0.999286	+	0.0377904i	$0.0120319\pi$
$810$	0.860672	−	0.586796i	0.0302409	−	0.0206179i
$811$	2.18301	+	1.05128i	0.0766559	+	0.0369155i	0.471819	−	0.881695i	$-0.343598\pi$
$811$	2.18301	+	1.05128i	0.0766559	+	0.0369155i	−0.395163	+	0.918611i	$0.629312\pi$
$812$	−0.463468	−	18.1460i	−0.0162645	−	0.636798i
$813$	−6.98391	+	3.36327i	−0.244936	+	0.117955i
$814$	15.6567	−	27.1182i	0.548766	−	0.950491i
$815$	0.927075	+	1.60574i	0.0324740	+	0.0562467i
$816$	0.102235	+	0.0697023i	0.00357893	+	0.00244007i
$817$	−66.2038	+	9.97862i	−2.31618	+	0.349108i
$818$	−2.75369	−	12.0647i	−0.0962804	−	0.421832i
$819$	−11.7903	+	7.21467i	−0.411987	+	0.252101i
$820$	−1.61688	+	7.08400i	−0.0564638	+	0.247384i
$821$	2.82370	−	37.6797i	0.0985479	−	1.31503i	−0.700452	−	0.713699i	$-0.747018\pi$
$821$	2.82370	−	37.6797i	0.0985479	−	1.31503i	0.799000	−	0.601331i	$-0.205363\pi$
$822$	4.97920	−	1.53588i	0.173669	−	0.0535699i
$823$	−1.02058	+	2.60039i	−0.0355752	+	0.0906441i	−0.947557	−	0.319586i	$-0.896456\pi$
$823$	−1.02058	+	2.60039i	−0.0355752	+	0.0906441i	0.911982	+	0.410230i	$0.134551\pi$
$824$	−1.03509	−	0.319283i	−0.0360590	−	0.0111227i
$825$	−9.77475	+	12.2572i	−0.340313	+	0.426739i
$826$	−15.5838	−	0.768346i	−0.542230	−	0.0267342i
$827$	−20.9068	−	26.2162i	−0.726999	−	0.911628i	0.271712	−	0.962379i	$-0.412410\pi$
$827$	−20.9068	−	26.2162i	−0.726999	−	0.911628i	−0.998711	+	0.0507506i	$0.983839\pi$
$828$	−2.55645	−	6.51374i	−0.0888429	−	0.226368i
$829$	−1.38388	−	18.4665i	−0.0480640	−	0.641369i	−0.968265	−	0.249924i	$-0.919594\pi$
$829$	−1.38388	−	18.4665i	−0.0480640	−	0.641369i	0.920201	−	0.391445i	$-0.128025\pi$
$830$	−13.1489	−	1.98187i	−0.456404	−	0.0687918i
$831$	−17.0222	−	15.7942i	−0.590492	−	0.547896i
$832$	−5.22443			−0.181125
$833$	−0.0205505	+	0.865900i	−0.000712034	+	0.0300017i
$834$	−9.41359			−0.325966
$835$	−4.23218	−	3.92689i	−0.146461	−	0.135896i
$836$	24.7656	+	3.73282i	0.856538	+	0.129102i
$837$	0.617309	+	8.23742i	0.0213373	+	0.284727i
$838$	−9.37658	−	23.8911i	−0.323908	−	0.825305i
$839$	−28.0579	−	35.1834i	−0.968665	−	1.21467i	−0.976680	−	0.214700i	$-0.931123\pi$
$839$	−28.0579	−	35.1834i	−0.968665	−	1.21467i	0.00801521	−	0.999968i	$-0.497449\pi$
$840$	1.61015	+	2.23674i	0.0555555	+	0.0771749i
$841$	11.2665	−	14.1278i	0.388500	−	0.487164i
$842$	−8.38418	−	2.58618i	−0.288938	−	0.0891256i
$843$	−5.41425	+	13.7953i	−0.186477	+	0.475135i
$844$	−18.4748	+	5.69871i	−0.635928	+	0.196158i
$845$	1.11276	−	14.8488i	0.0382802	−	0.510814i
$846$	0.776923	−	3.40392i	0.0267112	−	0.117029i
$847$	−13.2582	+	1.33475i	−0.455558	+	0.0458626i
$848$	−1.80112	−	7.89121i	−0.0618506	−	0.270985i
$849$	−9.95644	+	1.50069i	−0.341704	+	0.0515036i
$850$	−0.400239	−	0.272879i	−0.0137281	−	0.00935966i
$851$	−27.3580	−	47.3855i	−0.937821	−	1.62435i
$852$	4.19674	−	7.26896i	0.143778	−	0.249031i
$853$	−15.2387	+	7.33857i	−0.521763	+	0.251268i	−0.676178	−	0.736738i	$-0.736365\pi$
$853$	−15.2387	+	7.33857i	−0.521763	+	0.251268i	0.154415	+	0.988006i	$0.450651\pi$
$854$	−23.4474	+	5.98547i	−0.802352	+	0.204819i
$855$	5.86969	+	2.82669i	0.200739	+	0.0966709i
$856$	3.73878	−	2.54905i	0.127789	−	0.0871249i
$857$	−9.56297	+	8.87314i	−0.326665	+	0.303101i	−0.826407	−	0.563074i	$-0.809619\pi$
$857$	−9.56297	+	8.87314i	−0.326665	+	0.303101i	0.499742	+	0.866174i	$0.333428\pi$
$858$	15.3366	−	14.2303i	0.523582	−	0.485813i
$859$	37.3508	−	25.4653i	1.27439	−	0.868866i	0.278592	−	0.960410i	$-0.410132\pi$
$859$	37.3508	−	25.4653i	1.27439	−	0.868866i	0.995801	+	0.0915431i	$0.0291799\pi$
$860$	10.0468	+	4.83831i	0.342595	+	0.164985i
$861$	17.8819	−	4.56477i	0.609415	−	0.155567i
$862$	11.2870	−	5.43553i	0.384437	−	0.185135i
$863$	4.72546	−	8.18473i	0.160856	−	0.278611i	−0.774320	−	0.632795i	$-0.781908\pi$
$863$	4.72546	−	8.18473i	0.160856	−	0.278611i	0.935176	+	0.354183i	$0.115241\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−2.11315	−	1.44072i	−0.0718493	−	0.0489860i
$866$	−0.638815	+	0.0962858i	−0.0217078	+	0.00327192i
$867$	3.77945	+	16.5588i	0.128357	+	0.562368i
$868$	−21.7454	+	2.18918i	−0.738085	+	0.0743056i
$869$	8.37253	−	36.6825i	0.284019	−	1.24437i
$870$	−0.534073	+	7.12670i	−0.0181068	+	0.241618i
$871$	44.7938	−	13.8171i	1.51778	−	0.468173i
$872$	−4.31490	+	10.9942i	−0.146121	+	0.372310i
$873$	5.85865	+	1.80715i	0.198285	+	0.0611629i
$874$	27.2861	−	34.2157i	0.922968	−	1.15736i
$875$	−14.3544	−	19.9404i	−0.485266	−	0.674107i
$876$	−0.771200	−	0.967054i	−0.0260564	−	0.0326737i
$877$	16.3955	+	41.7751i	0.553638	+	1.41065i	0.884310	+	0.466901i	$0.154629\pi$
$877$	16.3955	+	41.7751i	0.553638	+	1.41065i	−0.330672	+	0.943746i	$0.607275\pi$
$878$	−2.30523	−	30.7612i	−0.0777977	−	1.03814i
$879$	18.0425	+	2.71946i	0.608557	+	0.0917253i
$880$	−3.05789	−	2.83730i	−0.103081	−	0.0956455i
$881$	−12.3309			−0.415439			−0.207720	−	0.978188i	$-0.566604\pi$
$881$	−12.3309			−0.415439			−0.207720	+	0.978188i	$0.566604\pi$
$882$	3.18597	−	6.23294i	0.107277	−	0.209874i
$883$	14.2161			0.478410			0.239205	−	0.970969i	$-0.423113\pi$
$883$	14.2161			0.478410			0.239205	+	0.970969i	$0.423113\pi$
$884$	0.473877	+	0.439694i	0.0159382	+	0.0147885i
$885$	6.07444	+	0.915574i	0.204190	+	0.0307767i
$886$	2.05818	+	27.4646i	0.0691460	+	0.922690i
$887$	3.43379	+	8.74914i	0.115295	+	0.293767i	0.976860	−	0.213880i	$-0.0686103\pi$
$887$	3.43379	+	8.74914i	0.115295	+	0.293767i	−0.861565	+	0.507648i	$0.830515\pi$
$888$	−4.87534	−	6.11348i	−0.163606	−	0.205155i
$889$	9.18579	+	0.452898i	0.308082	+	0.0151897i
$890$	−4.25416	+	5.33454i	−0.142600	+	0.178814i
$891$	3.82664	+	1.18036i	0.128197	+	0.0395437i
$892$	−2.28759	+	5.82870i	−0.0765943	+	0.195159i
$893$	20.8662	−	6.43638i	0.698262	−	0.215385i
$894$	−0.176693	+	2.35780i	−0.00590949	+	0.0788567i
$895$	2.44820	−	10.7263i	0.0818343	−	0.358540i
$896$	2.25676	−	1.38095i	0.0753932	−	0.0461342i
$897$	−8.13485	−	35.6411i	−0.271615	−	1.19002i
$898$	27.9759	−	4.21669i	0.933569	−	0.140713i
$899$	−46.8258	−	31.9253i	−1.56173	−	1.06477i
$900$	1.95746	+	3.39041i	0.0652486	+	0.113014i
$901$	−0.500764	+	0.867348i	−0.0166829	+	0.0288956i
$902$	−25.1674	+	12.1200i	−0.837982	+	0.403551i
$903$	−0.723161	−	28.3136i	−0.0240653	−	0.942218i
$904$	1.87563	+	0.903255i	0.0623824	+	0.0300418i
$905$	1.21186	−	0.826231i	0.0402835	−	0.0274648i
$906$	−0.0346251	+	0.0321274i	−0.00115034	+	0.00106736i
$907$	−37.7537	+	35.0303i	−1.25359	+	1.16316i	−0.274095	+	0.961703i	$0.588378\pi$
$907$	−37.7537	+	35.0303i	−1.25359	+	1.16316i	−0.979497	+	0.201461i	$0.935431\pi$
$908$	−14.5214	+	9.90052i	−0.481909	+	0.328560i
$909$	−14.3769	−	6.92353i	−0.476850	−	0.229639i
$910$	6.57651	+	12.8090i	0.218009	+	0.424613i
$911$	47.8416	−	23.0393i	1.58506	−	0.763326i	0.586161	−	0.810194i	$-0.300638\pi$
$911$	47.8416	−	23.0393i	1.58506	−	0.763326i	0.998901	+	0.0468684i	$0.0149241\pi$
$912$	3.12711	−	5.41631i	0.103549	−	0.179352i
$913$	−25.5599	−	44.2710i	−0.845908	−	1.46516i
$914$	−7.01384	−	4.78196i	−0.231997	−	0.158173i
$915$	9.42123	−	1.42002i	0.311456	−	0.0469445i
$916$	1.65357	+	7.24475i	0.0546354	+	0.239373i
$917$	18.0905	+	6.57205i	0.597400	+	0.217028i
$918$	−0.0275336	+	0.120633i	−0.000908744	+	0.00398147i
$919$	−1.10521	+	14.7480i	−0.0364574	+	0.486491i	0.948853	+	0.315718i	$0.102245\pi$
$919$	−1.10521	+	14.7480i	−0.0364574	+	0.486491i	−0.985310	+	0.170773i	$0.945374\pi$
$920$	−6.96523	+	2.14849i	−0.229637	+	0.0708336i
$921$	11.4038	−	29.0563i	0.375766	−	0.957437i
$922$	25.5698	+	7.88724i	0.842097	+	0.259753i
$923$	27.3408	−	34.2842i	0.899932	−	1.12848i
$924$	−2.86343	+	10.2008i	−0.0941999	+	0.335581i
$925$	19.0865	+	23.9337i	0.627561	+	0.786936i
$926$	−1.00959	−	2.57241i	−0.0331773	−	0.0845345i
$927$	−0.0809486	−	1.08018i	−0.00265870	−	0.0354779i
$928$	6.78414	+	1.02254i	0.222700	+	0.0335666i
$929$	−1.45450	−	1.34958i	−0.0477206	−	0.0442782i	0.655952	−	0.754803i	$-0.272267\pi$
$929$	−1.45450	−	1.34958i	−0.0477206	−	0.0442782i	−0.703673	+	0.710524i	$0.748458\pi$
$930$	8.60477			0.282162
$931$	43.7225	−	2.23490i	1.43295	−	0.0732459i
$932$	12.0772			0.395603
$933$	−14.6086	−	13.5548i	−0.478265	−	0.443765i
$934$	−33.3049	−	5.01990i	−1.08977	−	0.164256i
$935$	0.0385722	+	0.514710i	0.00126145	+	0.0168328i
$936$	−1.90870	−	4.86329i	−0.0623878	−	0.158962i
$937$	−3.76338	−	4.71913i	−0.122944	−	0.154167i	0.716550	−	0.697536i	$-0.245720\pi$
$937$	−3.76338	−	4.71913i	−0.122944	−	0.154167i	−0.839494	+	0.543368i	$0.817149\pi$
$938$	−15.6971	+	17.8086i	−0.512528	+	0.581470i
$939$	−12.6388	+	15.8486i	−0.412452	+	0.517199i
$940$	−3.47539	−	1.07201i	−0.113355	−	0.0349653i
$941$	4.10533	−	10.4602i	0.133830	−	0.340993i	−0.848212	−	0.529657i	$-0.822321\pi$
$941$	4.10533	−	10.4602i	0.133830	−	0.340993i	0.982042	+	0.188664i	$0.0604157\pi$
$942$	18.1622	−	5.60230i	0.591757	−	0.182533i
$943$	−3.64761	+	48.6740i	−0.118783	+	1.58504i
$944$	1.31227	−	5.74942i	0.0427107	−	0.187128i
$945$	−1.49387	+	2.31602i	−0.0485956	+	0.0753402i
$946$	9.53923	+	41.7941i	0.310147	+	1.35884i
$947$	−45.3354	+	6.83321i	−1.47320	+	0.222049i	−0.836035	−	0.548676i	$-0.815132\pi$
$947$	−45.3354	+	6.83321i	−1.47320	+	0.222049i	−0.637167	+	0.770726i	$0.719894\pi$
$948$	−7.76314	−	5.29282i	−0.252135	−	0.171903i
$949$	−3.23107	−	5.59638i	−0.104885	−	0.181666i
$950$	−12.2424	+	21.2044i	−0.397195	+	0.687962i
$951$	−10.6699	+	5.13835i	−0.345995	+	0.166623i
$952$	−0.320920	−	0.0646742i	−0.0104011	−	0.00209610i
$953$	−29.9398	−	14.4183i	−0.969846	−	0.467053i	−0.119245	−	0.992865i	$-0.538047\pi$
$953$	−29.9398	−	14.4183i	−0.969846	−	0.467053i	−0.850601	+	0.525811i	$0.823762\pi$
$954$	6.68769	−	4.55959i	0.216522	−	0.147622i
$955$	−16.9147	+	15.6945i	−0.547346	+	0.507863i
$956$	−22.0199	+	20.4315i	−0.712175	+	0.660802i
$957$	−22.7003	+	15.4768i	−0.733798	+	0.500295i
$958$	3.29339	+	1.58601i	0.106405	+	0.0512417i
$959$	−10.5555	+	8.86795i	−0.340855	+	0.286361i
$960$	−0.938517	+	0.451966i	−0.0302905	+	0.0145871i
$961$	−18.6181	+	32.2474i	−0.600582	+	1.04024i
$962$	−20.4261	−	35.3790i	−0.658562	−	1.14066i
$963$	3.73878	+	2.54905i	0.120480	+	0.0821421i
$964$	0.692868	−	0.104433i	0.0223158	−	0.00336356i
$965$	4.49752	+	19.7049i	0.144780	+	0.634324i
$966$	12.9348	+	13.2454i	0.416170	+	0.426164i
$967$	10.9149	−	47.8214i	0.351000	−	1.53783i	−0.423877	−	0.905720i	$-0.639331\pi$
$967$	10.9149	−	47.8214i	0.351000	−	1.53783i	0.774877	−	0.632112i	$-0.217812\pi$
$968$	0.376376	−	5.02239i	0.0120972	−	0.161426i
$969$	−0.739485	+	0.228101i	−0.0237557	+	0.00732765i
$970$	2.33327	−	5.94507i	0.0749167	−	0.190885i
$971$	−2.68362	−	0.827786i	−0.0861214	−	0.0265649i	0.251395	−	0.967885i	$-0.419111\pi$
$971$	−2.68362	−	0.827786i	−0.0861214	−	0.0265649i	−0.337516	+	0.941320i	$0.609587\pi$
$972$	0.623490	−	0.781831i	0.0199984	−	0.0250773i
$973$	22.9445	−	9.68818i	0.735566	−	0.310589i
$974$	−16.4647	−	20.6461i	−0.527563	−	0.661544i
$975$	7.47239	+	19.0394i	0.239308	+	0.609747i
$976$	−0.683516	−	9.12089i	−0.0218788	−	0.291952i
$977$	48.1162	+	7.25235i	1.53937	+	0.232023i	0.863254	−	0.504769i	$-0.168422\pi$
$977$	48.1162	+	7.25235i	1.53937	+	0.232023i	0.676119	+	0.736792i	$0.263660\pi$
$978$	1.30481	+	1.21069i	0.0417232	+	0.0387135i
$979$	−26.2305			−0.838330
$980$	−6.22654	−	3.79466i	−0.198899	−	0.121216i
$981$	−11.8106			−0.377084
$982$	3.75866	+	3.48753i	0.119944	+	0.111292i
$983$	13.4187	+	2.02254i	0.427989	+	0.0645090i	0.359505	−	0.933143i	$-0.382946\pi$
$983$	13.4187	+	2.02254i	0.427989	+	0.0645090i	0.0684844	+	0.997652i	$0.478184\pi$
$984$	0.521278	+	6.95597i	0.0166177	+	0.221748i
$985$	2.65478	+	6.76428i	0.0845884	+	0.215528i
$986$	−0.529290	−	0.663709i	−0.0168560	−	0.0211368i
$987$	1.60956	+	9.09623i	0.0512329	+	0.289536i
$988$	20.3724	−	25.5462i	0.648132	−	0.812732i
$989$	71.5799	+	22.0795i	2.27611	+	0.702087i
$990$	1.52400	−	3.88309i	0.0484359	−	0.123413i
$991$	−26.7744	+	8.25881i	−0.850517	+	0.262350i	−0.689216	−	0.724556i	$-0.742045\pi$
$991$	−26.7744	+	8.25881i	−0.850517	+	0.262350i	−0.161301	+	0.986905i	$0.551569\pi$
$992$	0.617309	−	8.23742i	0.0195996	−	0.261538i
$993$	−0.146495	+	0.641837i	−0.00464888	+	0.0203681i
$994$	−2.74804	+	22.0364i	−0.0871624	+	0.698951i
$995$	0.377638	+	1.65454i	0.0119719	+	0.0524525i
$996$	−12.6228	+	1.90258i	−0.399969	+	0.0602857i
$997$	−4.84617	−	3.30406i	−0.153480	−	0.104641i	0.484145	−	0.874988i	$-0.339131\pi$
$997$	−4.84617	−	3.30406i	−0.153480	−	0.104641i	−0.637625	+	0.770347i	$0.720083\pi$
$998$	10.9975	+	19.0482i	0.348119	+	0.602960i
$999$	3.90972	−	6.77183i	0.123698	−	0.214251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.205.2	yes	24
3.2	odd	2		882.2.z.a.793.1		24
49.11	even	21	inner	294.2.m.b.109.2	✓	24
147.11	odd	42		882.2.z.a.109.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.109.2	✓	24	49.11	even	21	inner
294.2.m.b.205.2	yes	24	1.1	even	1	trivial
882.2.z.a.109.1		24	147.11	odd	42
882.2.z.a.793.1		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.380567 + 0.969668i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-2.32432 - 1.26394i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})\)	\(q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.380567 + 0.969668i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-2.32432 - 1.26394i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +(0.380567 - 0.969668i) q^{10} +(3.82664 - 1.18036i) q^{11} +(0.0747301 - 0.997204i) q^{12} +(1.16255 - 5.09345i) q^{13} +(0.844147 + 2.50747i) q^{14} +(-0.231794 - 1.01556i) q^{15} +(-0.988831 + 0.149042i) q^{16} +(0.102235 + 0.0697023i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.12711 - 5.41631i) q^{19} +(-0.938517 + 0.451966i) q^{20} +(2.10998 + 1.59625i) q^{21} +(-3.60798 - 1.73751i) q^{22} +(-5.78156 + 3.94180i) q^{23} +(-0.733052 + 0.680173i) q^{24} +(2.86983 - 2.66282i) q^{25} +(-4.31663 + 2.94303i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(1.08671 - 2.41227i) q^{28} +(6.18133 - 2.97677i) q^{29} +(-0.520837 + 0.902117i) q^{30} +(-4.13026 - 7.15382i) q^{31} +(0.826239 + 0.563320i) q^{32} +(-3.95983 + 0.596848i) q^{33} +(-0.0275336 - 0.120633i) q^{34} +(0.341046 - 2.73483i) q^{35} +(-0.222521 + 0.974928i) q^{36} +(-0.584347 + 7.79757i) q^{37} +(-5.97636 + 1.84346i) q^{38} +(-1.90870 + 4.86329i) q^{39} +(0.995396 + 0.307039i) q^{40} +(4.34914 - 5.45365i) q^{41} +(-0.460999 - 2.60528i) q^{42} +(-6.67448 - 8.36953i) q^{43} +(1.46303 + 3.72774i) q^{44} +(0.0778445 + 1.03876i) q^{45} +(6.91929 + 1.04292i) q^{46} +(2.55942 + 2.37480i) q^{47} +1.00000 q^{48} +(3.80490 + 5.87560i) q^{49} -3.91491 q^{50} +(-0.0907041 - 0.0841611i) q^{51} +(5.16608 + 0.778661i) q^{52} +(0.604876 + 8.07151i) q^{53} +(0.365341 + 0.930874i) q^{54} +(2.60085 + 3.26137i) q^{55} +(-2.43738 + 1.02917i) q^{56} +(-3.89944 + 4.88975i) q^{57} +(-6.55596 - 2.02225i) q^{58} +(-2.15452 + 5.48962i) q^{59} +(0.995396 - 0.307039i) q^{60} +(-0.683516 + 9.12089i) q^{61} +(-1.83814 + 8.05341i) q^{62} +(-1.84850 - 1.89289i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(5.38138 - 0.811112i) q^{65} +(3.30872 + 2.25585i) q^{66} +(4.48626 + 7.77044i) q^{67} +(-0.0618674 + 0.107158i) q^{68} +(6.30448 - 3.03608i) q^{69} +(-2.11016 + 1.77280i) q^{70} +(7.56226 + 3.64179i) q^{71} +(0.826239 - 0.563320i) q^{72} +(0.906718 - 0.841311i) q^{73} +(5.73205 - 5.31856i) q^{74} +(-3.23465 + 2.20535i) q^{75} +(5.63486 + 2.71361i) q^{76} +(-10.3862 - 2.09312i) q^{77} +(4.70705 - 2.26680i) q^{78} +(4.69788 - 8.13696i) q^{79} +(-0.520837 - 0.902117i) q^{80} +(0.826239 + 0.563320i) q^{81} +(-6.89757 + 1.03964i) q^{82} +(-2.84057 - 12.4453i) q^{83} +(-1.43410 + 2.22336i) q^{84} +(-0.0286811 + 0.125660i) q^{85} +(-0.799988 + 10.6751i) q^{86} +(-6.55596 + 2.02225i) q^{87} +(1.46303 - 3.72774i) q^{88} +(-6.25916 - 1.93069i) q^{89} +(0.649474 - 0.814414i) q^{90} +(-9.13994 + 10.3694i) q^{91} +(-4.36284 - 5.47082i) q^{92} +(3.01791 + 7.68950i) q^{93} +(-0.260917 - 3.48170i) q^{94} +(6.44210 + 0.970990i) q^{95} +(-0.733052 - 0.680173i) q^{96} +6.13103 q^{97} +(1.20723 - 6.89511i) q^{98} +4.00456 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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