LMFDB - Embedded newform 637.2.bl.b.534.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			534.15
Character	$\chi$	$=$	637.534
Dual form			637.2.bl.b.235.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.157460 + 0.0237333i) q^{2} +(0.607692 + 0.414318i) q^{3} +(-1.88692 + 0.582036i) q^{4} +(0.234624 - 3.13084i) q^{5} +(-0.105520 - 0.0508159i) q^{6} +(1.73776 + 1.99504i) q^{7} +(0.570238 - 0.274612i) q^{8} +(-0.898392 - 2.28907i) q^{9} +O(q^{10})$	\(q+(-0.157460 + 0.0237333i) q^{2} +(0.607692 + 0.414318i) q^{3} +(-1.88692 + 0.582036i) q^{4} +(0.234624 - 3.13084i) q^{5} +(-0.105520 - 0.0508159i) q^{6} +(1.73776 + 1.99504i) q^{7} +(0.570238 - 0.274612i) q^{8} +(-0.898392 - 2.28907i) q^{9} +(0.0373612 + 0.498551i) q^{10} +(-1.99537 + 5.08411i) q^{11} +(-1.38781 - 0.428083i) q^{12} +(0.623490 + 0.781831i) q^{13} +(-0.320977 - 0.272896i) q^{14} +(1.43974 - 1.80538i) q^{15} +(3.17978 - 2.16794i) q^{16} +(5.63217 - 5.22589i) q^{17} +(0.195788 + 0.339115i) q^{18} +(3.85863 - 6.68334i) q^{19} +(1.37955 + 6.04420i) q^{20} +(0.229447 + 1.93236i) q^{21} +(0.193528 - 0.847900i) q^{22} +(-0.215435 - 0.199895i) q^{23} +(0.460306 + 0.0693800i) q^{24} +(-4.80298 - 0.723933i) q^{25} +(-0.116730 - 0.108310i) q^{26} +(0.893442 - 3.91442i) q^{27} +(-4.44020 - 2.75302i) q^{28} +(-0.882682 - 3.86728i) q^{29} +(-0.183854 + 0.318445i) q^{30} +(0.656712 + 1.13746i) q^{31} +(-1.37716 + 1.27782i) q^{32} +(-3.31900 + 2.26286i) q^{33} +(-0.762815 + 0.956539i) q^{34} +(6.65387 - 4.97259i) q^{35} +(3.02751 + 3.79638i) q^{36} +(-3.34704 - 1.03243i) q^{37} +(-0.448962 + 1.14394i) q^{38} +(0.0549634 + 0.733436i) q^{39} +(-0.725976 - 1.84976i) q^{40} +(1.95555 - 0.941744i) q^{41} +(-0.0819899 - 0.298823i) q^{42} +(-0.0234820 - 0.0113083i) q^{43} +(0.805950 - 10.7547i) q^{44} +(-7.37749 + 2.27566i) q^{45} +(0.0386666 + 0.0263625i) q^{46} +(11.2721 - 1.69899i) q^{47} +2.83054 q^{48} +(-0.960347 + 6.93381i) q^{49} +0.773459 q^{50} +(5.58781 - 0.842227i) q^{51} +(-1.63153 - 1.11236i) q^{52} +(7.87160 - 2.42807i) q^{53} +(-0.0477792 + 0.637570i) q^{54} +(15.4494 + 7.44003i) q^{55} +(1.53880 + 0.660435i) q^{56} +(5.11388 - 2.46272i) q^{57} +(0.230770 + 0.587993i) q^{58} +(-0.551154 - 7.35464i) q^{59} +(-1.66588 + 4.24458i) q^{60} +(-7.39462 - 2.28094i) q^{61} +(-0.130401 - 0.163518i) q^{62} +(3.00558 - 5.77018i) q^{63} +(-4.61248 + 5.78387i) q^{64} +(2.59408 - 1.76861i) q^{65} +(0.468905 - 0.435081i) q^{66} +(3.53890 + 6.12955i) q^{67} +(-7.58578 + 13.1389i) q^{68} +(-0.0480985 - 0.210733i) q^{69} +(-0.929703 + 0.940902i) q^{70} +(-1.33428 + 5.84586i) q^{71} +(-1.14090 - 1.05860i) q^{72} +(2.46782 + 0.371964i) q^{73} +(0.551528 + 0.0831295i) q^{74} +(-2.61880 - 2.42989i) q^{75} +(-3.39096 + 14.8568i) q^{76} +(-13.6105 + 4.85416i) q^{77} +(-0.0260614 - 0.114182i) q^{78} +(-6.32682 + 10.9584i) q^{79} +(-6.04142 - 10.4641i) q^{80} +(-3.24308 + 3.00914i) q^{81} +(-0.285570 + 0.194699i) q^{82} +(5.52296 - 6.92557i) q^{83} +(-1.55765 - 3.51264i) q^{84} +(-15.0400 - 18.8596i) q^{85} +(0.00396586 + 0.00122331i) q^{86} +(1.06588 - 2.71583i) q^{87} +(0.258325 + 3.44710i) q^{88} +(1.86201 + 4.74431i) q^{89} +(1.10765 - 0.533417i) q^{90} +(-0.476304 + 2.60252i) q^{91} +(0.522854 + 0.251793i) q^{92} +(-0.0721902 + 0.963312i) q^{93} +(-1.73458 + 0.535047i) q^{94} +(-20.0192 - 13.6488i) q^{95} +(-1.36631 + 0.205938i) q^{96} -9.35947 q^{97} +(-0.0133459 - 1.11459i) q^{98} +13.4305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

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 $

$2$	−0.157460	+	0.0237333i	−0.111341	+	0.0167820i	−0.204476	−	0.978871i	$-0.565549\pi$
$2$	−0.157460	+	0.0237333i	−0.111341	+	0.0167820i	0.0931354	+	0.995653i	$0.470311\pi$
$3$	0.607692	+	0.414318i	0.350851	+	0.239206i	0.725902	−	0.687798i	$-0.241422\pi$
$3$	0.607692	+	0.414318i	0.350851	+	0.239206i	−0.375051	+	0.927004i	$0.622375\pi$
$4$	−1.88692	+	0.582036i	−0.943458	+	0.291018i
$5$	0.234624	−	3.13084i	0.104927	−	1.40016i	−0.657681	−	0.753296i	$-0.728463\pi$
$5$	0.234624	−	3.13084i	0.104927	−	1.40016i	0.762609	−	0.646860i	$-0.223918\pi$
$6$	−0.105520	−	0.0508159i	−0.0430785	−	0.0207455i
$7$	1.73776	+	1.99504i	0.656813	+	0.754053i
$7$	1.73776	+	1.99504i	0.656813	+	0.754053i
$8$	0.570238	−	0.274612i	0.201610	−	0.0970901i
$9$	−0.898392	−	2.28907i	−0.299464	−	0.763022i
$10$	0.0373612	+	0.498551i	0.0118147	+	0.157656i
$11$	−1.99537	+	5.08411i	−0.601625	+	1.53292i	0.227456	+	0.973788i	$0.426959\pi$
$11$	−1.99537	+	5.08411i	−0.601625	+	1.53292i	−0.829081	+	0.559128i	$0.811136\pi$
$12$	−1.38781	−	0.428083i	−0.400627	−	0.123577i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$14$	−0.320977	−	0.272896i	−0.0857848	−	0.0729344i
$15$	1.43974	−	1.80538i	0.371740	−	0.466147i
$16$	3.17978	−	2.16794i	0.794945	−	0.541985i
$17$	5.63217	−	5.22589i	1.36600	−	1.26747i	0.435984	−	0.899955i	$-0.356401\pi$
$17$	5.63217	−	5.22589i	1.36600	−	1.26747i	0.930019	−	0.367511i	$-0.119790\pi$
$18$	0.195788	+	0.339115i	0.0461476	+	0.0799301i
$19$	3.85863	−	6.68334i	0.885230	−	1.53326i	0.0397798	−	0.999208i	$-0.487334\pi$
$19$	3.85863	−	6.68334i	0.885230	−	1.53326i	0.845450	−	0.534055i	$-0.179332\pi$
$20$	1.37955	+	6.04420i	0.308476	+	1.35152i
$21$	0.229447	+	1.93236i	0.0500695	+	0.421675i
$22$	0.193528	−	0.847900i	0.0412602	−	0.180773i
$23$	−0.215435	−	0.199895i	−0.0449214	−	0.0416810i	0.657393	−	0.753548i	$-0.271659\pi$
$23$	−0.215435	−	0.199895i	−0.0449214	−	0.0416810i	−0.702314	+	0.711867i	$0.747850\pi$
$24$	0.460306	+	0.0693800i	0.0939596	+	0.0141621i
$25$	−4.80298	−	0.723933i	−0.960597	−	0.144787i
$26$	−0.116730	−	0.108310i	−0.0228927	−	0.0212413i
$27$	0.893442	−	3.91442i	0.171943	−	0.753331i
$28$	−4.44020	−	2.75302i	−0.839119	−	0.520273i
$29$	−0.882682	−	3.86728i	−0.163910	−	0.718136i	−0.988351	−	0.152189i	$-0.951368\pi$
$29$	−0.882682	−	3.86728i	−0.163910	−	0.718136i	0.824442	−	0.565947i	$-0.191489\pi$
$30$	−0.183854	+	0.318445i	−0.0335671	+	0.0581399i
$31$	0.656712	+	1.13746i	0.117949	+	0.204293i	0.918955	−	0.394363i	$-0.129035\pi$
$31$	0.656712	+	1.13746i	0.117949	+	0.204293i	−0.801006	+	0.598657i	$0.795701\pi$
$32$	−1.37716	+	1.27782i	−0.243449	+	0.225888i
$33$	−3.31900	+	2.26286i	−0.577764	+	0.393913i
$34$	−0.762815	+	0.956539i	−0.130822	+	0.164045i
$35$	6.65387	−	4.97259i	1.12471	−	0.840521i
$36$	3.02751	+	3.79638i	0.504585	+	0.632729i
$37$	−3.34704	−	1.03243i	−0.550250	−	0.169730i	0.00714876	−	0.999974i	$-0.497724\pi$
$37$	−3.34704	−	1.03243i	−0.550250	−	0.169730i	−0.557399	+	0.830245i	$0.688201\pi$
$38$	−0.448962	+	1.14394i	−0.0728312	+	0.185571i
$39$	0.0549634	+	0.733436i	0.00880119	+	0.117444i
$40$	−0.725976	−	1.84976i	−0.114787	−	0.292472i
$41$	1.95555	−	0.941744i	0.305406	−	0.147076i	−0.274904	−	0.961472i	$-0.588646\pi$
$41$	1.95555	−	0.941744i	0.305406	−	0.147076i	0.580309	+	0.814396i	$0.302932\pi$
$42$	−0.0819899	−	0.298823i	−0.0126513	−	0.0461094i
$43$	−0.0234820	−	0.0113083i	−0.00358097	−	0.00172450i	0.432092	−	0.901829i	$-0.357775\pi$
$43$	−0.0234820	−	0.0113083i	−0.00358097	−	0.00172450i	−0.435673	+	0.900105i	$0.643490\pi$
$44$	0.805950	−	10.7547i	0.121502	−	1.62133i
$45$	−7.37749	+	2.27566i	−1.09977	+	0.339235i
$46$	0.0386666	+	0.0263625i	0.00570108	+	0.00388693i
$47$	11.2721	−	1.69899i	1.64420	−	0.247823i	0.739279	−	0.673400i	$-0.235167\pi$
$47$	11.2721	−	1.69899i	1.64420	−	0.247823i	0.904923	+	0.425576i	$0.139929\pi$
$48$	2.83054			0.408554
$49$	−0.960347	+	6.93381i	−0.137192	+	0.990544i
$50$	0.773459			0.109384
$51$	5.58781	−	0.842227i	0.782450	−	0.117935i
$52$	−1.63153	−	1.11236i	−0.226252	−	0.154256i
$53$	7.87160	−	2.42807i	1.08125	−	0.333521i	0.297577	−	0.954698i	$-0.403821\pi$
$53$	7.87160	−	2.42807i	1.08125	−	0.333521i	0.783670	+	0.621177i	$0.213345\pi$
$54$	−0.0477792	+	0.637570i	−0.00650193	+	0.0867622i
$55$	15.4494	+	7.44003i	2.08320	+	1.00321i
$56$	1.53880	+	0.660435i	0.205631	+	0.0882543i
$57$	5.11388	−	2.46272i	0.677350	−	0.326195i
$58$	0.230770	+	0.587993i	0.0303016	+	0.0772073i
$59$	−0.551154	−	7.35464i	−0.0717541	−	0.957492i	−0.910644	−	0.413191i	$-0.864414\pi$
$59$	−0.551154	−	7.35464i	−0.0717541	−	0.957492i	0.838890	−	0.544301i	$-0.183205\pi$
$60$	−1.66588	+	4.24458i	−0.215064	+	0.547974i
$61$	−7.39462	−	2.28094i	−0.946784	−	0.292044i	−0.217349	−	0.976094i	$-0.569741\pi$
$61$	−7.39462	−	2.28094i	−0.946784	−	0.292044i	−0.729435	+	0.684050i	$0.760217\pi$
$62$	−0.130401	−	0.163518i	−0.0165610	−	0.0207668i
$63$	3.00558	−	5.77018i	0.378667	−	0.726975i
$64$	−4.61248	+	5.78387i	−0.576560	+	0.722984i
$65$	2.59408	−	1.76861i	0.321756	−	0.219369i
$66$	0.468905	−	0.435081i	0.0577183	−	0.0535547i
$67$	3.53890	+	6.12955i	0.432345	+	0.748844i	0.997075	−	0.0764323i	$-0.0243529\pi$
$67$	3.53890	+	6.12955i	0.432345	+	0.748844i	−0.564730	+	0.825276i	$0.691020\pi$
$68$	−7.58578	+	13.1389i	−0.919910	+	1.59333i
$69$	−0.0480985	−	0.210733i	−0.00579038	−	0.0253693i
$70$	−0.929703	+	0.940902i	−0.111121	+	0.112459i
$71$	−1.33428	+	5.84586i	−0.158350	+	0.693776i	0.831953	+	0.554847i	$0.187223\pi$
$71$	−1.33428	+	5.84586i	−0.158350	+	0.693776i	−0.990302	+	0.138929i	$0.955634\pi$
$72$	−1.14090	−	1.05860i	−0.134457	−	0.124758i
$73$	2.46782	+	0.371964i	0.288836	+	0.0435351i	0.291862	−	0.956460i	$-0.405725\pi$
$73$	2.46782	+	0.371964i	0.288836	+	0.0435351i	−0.00302602	+	0.999995i	$0.500963\pi$
$74$	0.551528	+	0.0831295i	0.0641138	+	0.00966361i
$75$	−2.61880	−	2.42989i	−0.302393	−	0.280580i
$76$	−3.39096	+	14.8568i	−0.388969	+	1.70419i
$77$	−13.6105	+	4.85416i	−1.55106	+	0.553182i
$78$	−0.0260614	−	0.114182i	−0.00295087	−	0.0129286i
$79$	−6.32682	+	10.9584i	−0.711822	+	1.23291i	0.252350	+	0.967636i	$0.418797\pi$
$79$	−6.32682	+	10.9584i	−0.711822	+	1.23291i	−0.964172	+	0.265276i	$0.914537\pi$
$80$	−6.04142	−	10.4641i	−0.675452	−	1.16992i
$81$	−3.24308	+	3.00914i	−0.360343	+	0.334349i
$82$	−0.285570	+	0.194699i	−0.0315360	+	0.0215009i
$83$	5.52296	−	6.92557i	0.606224	−	0.760180i	−0.380110	−	0.924941i	$-0.624114\pi$
$83$	5.52296	−	6.92557i	0.606224	−	0.760180i	0.986334	+	0.164761i	$0.0526853\pi$
$84$	−1.55765	−	3.51264i	−0.169953	−	0.383261i
$85$	−15.0400	−	18.8596i	−1.63132	−	2.04561i
$86$	0.00396586	+	0.00122331i	0.000427650	+	0.000131912i
$87$	1.06588	−	2.71583i	0.114275	−	0.291167i
$88$	0.258325	+	3.44710i	0.0275375	+	0.367462i
$89$	1.86201	+	4.74431i	0.197372	+	0.502896i	0.994956	−	0.100312i	$-0.0319841\pi$
$89$	1.86201	+	4.74431i	0.197372	+	0.502896i	−0.797584	+	0.603208i	$0.793889\pi$
$90$	1.10765	−	0.533417i	0.116757	−	0.0562271i
$91$	−0.476304	+	2.60252i	−0.0499302	+	0.272819i
$92$	0.522854	+	0.251793i	0.0545113	+	0.0262513i
$93$	−0.0721902	+	0.963312i	−0.00748578	+	0.0998908i
$94$	−1.73458	+	0.535047i	−0.178908	+	0.0551858i
$95$	−20.0192	−	13.6488i	−2.05392	−	1.40034i
$96$	−1.36631	+	0.205938i	−0.139448	+	0.0210185i
$97$	−9.35947			−0.950311			−0.475155	−	0.879902i	$-0.657608\pi$
$97$	−9.35947			−0.950311			−0.475155	+	0.879902i	$0.657608\pi$
$98$	−0.0133459	−	1.11459i	−0.00134814	−	0.112591i
$99$	13.4305			1.34981
$100$	9.48418	−	1.42951i	0.948418	−	0.142951i
$101$	−3.29772	−	2.24835i	−0.328135	−	0.223719i	0.388035	−	0.921645i	$-0.373154\pi$
$101$	−3.29772	−	2.24835i	−0.328135	−	0.223719i	−0.716170	+	0.697926i	$0.754106\pi$
$102$	−0.859868	+	0.265234i	−0.0851396	+	0.0262621i
$103$	−0.199097	+	2.65677i	−0.0196176	+	0.261779i	0.978768	+	0.204973i	$0.0657107\pi$
$103$	−0.199097	+	2.65677i	−0.0196176	+	0.261779i	−0.998385	+	0.0568061i	$0.981908\pi$
$104$	0.570238	+	0.274612i	0.0559164	+	0.0269279i
$105$	6.10374	−	0.264986i	0.595664	−	0.0258600i
$106$	−1.18184	+	0.569142i	−0.114790	+	0.0552800i
$107$	5.99437	+	15.2734i	0.579498	+	1.47654i	0.856746	+	0.515738i	$0.172482\pi$
$107$	5.99437	+	15.2734i	0.579498	+	1.47654i	−0.277248	+	0.960798i	$0.589422\pi$
$108$	0.592488	+	7.90620i	0.0570122	+	0.760775i
$109$	−3.01834	+	7.69061i	−0.289105	+	0.736626i	0.710358	+	0.703841i	$0.248533\pi$
$109$	−3.01834	+	7.69061i	−0.289105	+	0.736626i	−0.999462	+	0.0327857i	$0.989562\pi$
$110$	−2.60924	−	0.804843i	−0.248781	−	0.0767388i
$111$	−1.60622	−	2.01414i	−0.152456	−	0.191173i
$112$	9.85083	+	2.57641i	0.930816	+	0.243448i
$113$	−3.14111	+	3.93883i	−0.295491	+	0.370534i	−0.907309	−	0.420465i	$-0.861867\pi$
$113$	−3.14111	+	3.93883i	−0.295491	+	0.370534i	0.611818	+	0.790999i	$0.290439\pi$
$114$	−0.746784	+	0.509149i	−0.0699427	+	0.0476861i
$115$	−0.676386	+	0.627595i	−0.0630733	+	0.0585235i
$116$	3.91644	+	6.78348i	0.363633	+	0.629830i
$117$	1.22953	−	2.12960i	0.113670	−	0.196882i
$118$	0.261334	+	1.14498i	0.0240578	+	0.105404i
$119$	20.2132	+	2.15502i	1.85295	+	0.197551i
$120$	0.325217	−	1.42487i	0.0296881	−	0.130072i
$121$	−13.8031	−	12.8074i	−1.25483	−	1.16431i
$122$	1.21849	+	0.183658i	0.110317	+	0.0166276i
$123$	1.57855	+	0.237929i	0.142333	+	0.0214533i
$124$	−1.90120	−	1.76406i	−0.170733	−	0.158417i
$125$	0.0997393	−	0.436987i	0.00892096	−	0.0390853i
$126$	−0.336313	+	0.979905i	−0.0299611	+	0.0872969i
$127$	−4.55906	−	19.9746i	−0.404551	−	1.77245i	−0.608583	−	0.793490i	$-0.708262\pi$
$127$	−4.55906	−	19.9746i	−0.404551	−	1.77245i	0.204032	−	0.978964i	$-0.434595\pi$
$128$	2.46767	−	4.27414i	0.218114	−	0.377784i
$129$	−0.00958459	−	0.0166010i	−0.000843876	−	0.00146164i
$130$	−0.366489	+	0.340052i	−0.0321432	+	0.0298245i
$131$	−18.2953	+	12.4735i	−1.59847	+	1.08982i	−0.656392	+	0.754420i	$0.727918\pi$
$131$	−18.2953	+	12.4735i	−1.59847	+	1.08982i	−0.942077	+	0.335397i	$0.891130\pi$
$132$	4.94561	−	6.20160i	0.430460	−	0.539780i
$133$	20.0389	−	3.91597i	1.73759	−	0.339557i
$134$	−0.702709	−	0.881169i	−0.0607048	−	0.0761214i
$135$	−12.0458	−	3.71565i	−1.03674	−	0.319792i
$136$	1.77659	−	4.52667i	0.152341	−	0.388159i
$137$	−0.496486	−	6.62514i	−0.0424176	−	0.566024i	−0.977409	−	0.211355i	$-0.932213\pi$
$137$	−0.496486	−	6.62514i	−0.0424176	−	0.566024i	0.934992	−	0.354669i	$-0.115407\pi$
$138$	0.0125750	+	0.0320405i	0.00107045	+	0.00272747i
$139$	−3.58067	+	1.72436i	−0.303709	+	0.146258i	−0.579531	−	0.814950i	$-0.696764\pi$
$139$	−3.58067	+	1.72436i	−0.303709	+	0.146258i	0.275822	+	0.961209i	$0.411050\pi$
$140$	−9.66107	+	13.2556i	−0.816509	+	1.12031i
$141$	7.55388	+	3.63776i	0.636151	+	0.306354i
$142$	0.0713542	−	0.952156i	0.00598791	−	0.0799031i
$143$	−5.21901	+	1.60985i	−0.436435	+	0.134622i
$144$	−7.81924	−	5.33107i	−0.651604	−	0.444256i
$145$	−12.3150	+	1.85618i	−1.02270	+	0.154147i
$146$	−0.397411			−0.0328899
$147$	−3.45640	+	3.81574i	−0.285079	+	0.314717i
$148$	6.91649			0.568532
$149$	−1.48087	+	0.223206i	−0.121318	+	0.0182857i	−0.209421	−	0.977826i	$-0.567158\pi$
$149$	−1.48087	+	0.223206i	−0.121318	+	0.0182857i	0.0881026	+	0.996111i	$0.471920\pi$
$150$	0.470025	+	0.320458i	0.0383774	+	0.0261653i
$151$	−14.4547	+	4.45870i	−1.17631	+	0.362844i	−0.820463	−	0.571700i	$-0.806284\pi$
$151$	−14.4547	+	4.45870i	−1.17631	+	0.362844i	−0.355848	+	0.934544i	$0.615808\pi$
$152$	0.365010	−	4.87072i	0.0296062	−	0.395068i
$153$	−17.0223	−	8.19752i	−1.37617	−	0.662730i
$154$	2.02790	−	1.08736i	0.163413	−	0.0876217i
$155$	3.71528	−	1.78919i	0.298419	−	0.143711i
$156$	−0.530598	−	1.35194i	−0.0424818	−	0.108242i
$157$	−0.786984	−	10.5016i	−0.0628081	−	0.838116i	−0.936283	−	0.351247i	$-0.885758\pi$
$157$	−0.786984	−	10.5016i	−0.0628081	−	0.838116i	0.873475	−	0.486870i	$-0.161861\pi$
$158$	0.736142	−	1.87566i	0.0585644	−	0.149220i
$159$	5.78950	+	1.78583i	0.459137	+	0.141625i
$160$	3.67753	+	4.61147i	0.290734	+	0.364569i
$161$	0.0244216	−	0.777172i	0.00192469	−	0.0612497i
$162$	0.439239	−	0.550788i	0.0345099	−	0.0432740i
$163$	5.24048	−	3.57290i	0.410466	−	0.279851i	−0.340432	−	0.940269i	$-0.610573\pi$
$163$	5.24048	−	3.57290i	0.410466	−	0.279851i	0.750898	+	0.660418i	$0.229621\pi$
$164$	−3.14183	+	2.91519i	−0.245336	+	0.227638i
$165$	6.30594	+	10.9222i	0.490917	+	0.850293i
$166$	−0.705279	+	1.22158i	−0.0547403	+	0.0948129i
$167$	1.22180	+	5.35307i	0.0945459	+	0.414233i	0.999947	−	0.0103252i	$-0.00328668\pi$
$167$	1.22180	+	5.35307i	0.0945459	+	0.414233i	−0.905401	+	0.424558i	$0.860430\pi$
$168$	0.661488	+	1.03889i	0.0510349	+	0.0801524i
$169$	−0.222521	+	0.974928i	−0.0171170	+	0.0749945i
$170$	2.81580	+	2.61268i	0.215962	+	0.200384i
$171$	−18.7652	−	2.82839i	−1.43501	−	0.216293i
$172$	0.0508904	+	0.00767049i	0.00388036	+	0.000584870i
$173$	15.4662	+	14.3505i	1.17587	+	1.09105i	0.994184	+	0.107693i	$0.0343463\pi$
$173$	15.4662	+	14.3505i	1.17587	+	1.09105i	0.181687	+	0.983356i	$0.441844\pi$
$174$	−0.103379	+	0.452931i	−0.00783711	+	0.0343366i
$175$	−6.90218	−	10.8402i	−0.521756	−	0.819439i
$176$	4.67721	+	20.4922i	0.352558	+	1.54466i
$177$	2.71222	−	4.69771i	0.203863	−	0.353102i
$178$	−0.405789	−	0.702848i	−0.0304152	−	0.0526807i
$179$	7.17996	−	6.66203i	0.536655	−	0.497943i	−0.364640	−	0.931149i	$-0.618808\pi$
$179$	7.17996	−	6.66203i	0.536655	−	0.497943i	0.901295	+	0.433205i	$0.142617\pi$
$180$	12.5962	−	8.58794i	0.938865	−	0.640107i
$181$	−11.1601	+	13.9943i	−0.829523	+	1.04019i	0.168986	+	0.985618i	$0.445951\pi$
$181$	−11.1601	+	13.9943i	−0.829523	+	1.04019i	−0.998510	+	0.0545712i	$0.982621\pi$
$182$	0.0132324	−	0.421098i	0.000980853	−	0.0312138i
$183$	−3.54862	−	4.44983i	−0.262322	−	0.328941i
$184$	−0.177743	−	0.0548265i	−0.0131034	−	0.00404186i
$185$	−4.01766	+	10.2368i	−0.295384	+	0.752627i
$186$	−0.0114955	−	0.153396i	−0.000842889	−	0.0112476i
$187$	15.3308	+	39.0622i	1.12110	+	2.85651i
$188$	−20.2806	+	9.76661i	−1.47911	+	0.712303i
$189$	9.36201	−	5.01990i	0.680986	−	0.365144i
$190$	3.47615	+	1.67403i	0.252186	+	0.121447i
$191$	−0.227945	+	3.04172i	−0.0164936	+	0.220091i	0.982866	+	0.184319i	$0.0590080\pi$
$191$	−0.227945	+	3.04172i	−0.0164936	+	0.220091i	−0.999360	+	0.0357719i	$0.988611\pi$
$192$	−5.19933	+	1.60378i	−0.375229	+	0.115743i
$193$	−7.40477	−	5.04849i	−0.533007	−	0.363398i	0.266708	−	0.963777i	$-0.414064\pi$
$193$	−7.40477	−	5.04849i	−0.533007	−	0.363398i	−0.799715	+	0.600379i	$0.795016\pi$
$194$	1.47374	−	0.222131i	0.105809	−	0.0159481i
$195$	2.30917			0.165363
$196$	−2.22364	−	13.6425i	−0.158831	−	0.974462i
$197$	14.8472			1.05782			0.528908	−	0.848679i	$-0.322602\pi$
$197$	14.8472			1.05782			0.528908	+	0.848679i	$0.322602\pi$
$198$	−2.11476	+	0.318749i	−0.150290	+	0.0226525i
$199$	14.2697	+	9.72891i	1.01155	+	0.689664i	0.951220	−	0.308514i	$-0.0998318\pi$
$199$	14.2697	+	9.72891i	1.01155	+	0.689664i	0.0603316	+	0.998178i	$0.480784\pi$
$200$	−2.93765	+	0.906144i	−0.207723	+	0.0640740i
$201$	−0.389020	+	5.19111i	−0.0274393	+	0.366153i
$202$	0.572620	+	0.275759i	0.0402894	+	0.0194023i
$203$	6.18148	−	8.48141i	0.433855	−	0.595278i
$204$	−10.0535	+	4.84152i	−0.703887	+	0.338974i
$205$	−2.48963	−	6.34348i	−0.173884	−	0.443048i
$206$	−0.0317040	−	0.423060i	−0.00220892	−	0.0294760i
$207$	−0.264027	+	0.672730i	−0.0183511	+	0.0467580i
$208$	3.67752	+	1.13437i	0.254990	+	0.0786541i
$209$	26.2794	+	32.9534i	1.81779	+	2.27943i
$210$	−0.954806	+	0.186586i	−0.0658879	+	0.0128757i
$211$	14.0023	−	17.5584i	0.963961	−	1.20877i	−0.0139828	−	0.999902i	$-0.504451\pi$
$211$	14.0023	−	17.5584i	0.963961	−	1.20877i	0.977944	−	0.208867i	$-0.0669776\pi$
$212$	−13.4398	+	9.16312i	−0.923051	+	0.629325i
$213$	−3.23287	+	2.99967i	−0.221513	+	0.205534i
$214$	−1.30636	−	2.26269i	−0.0893011	−	0.154674i
$215$	−0.0409141	+	0.0708653i	−0.00279032	+	0.00483297i
$216$	−0.565474	−	2.47750i	−0.0384756	−	0.168573i
$217$	−1.12806	+	3.28680i	−0.0765777	+	0.223122i
$218$	0.292745	−	1.28260i	0.0198272	−	0.0868685i
$219$	1.34556	+	1.24850i	0.0909247	+	0.0843658i
$220$	−33.4821	−	5.04661i	−2.25736	−	0.340242i
$221$	7.59737	+	1.14512i	0.511055	+	0.0770291i
$222$	0.300717	+	0.279025i	0.0201828	+	0.0187269i
$223$	−2.97140	+	13.0186i	−0.198980	+	0.871788i	0.772566	+	0.634935i	$0.218973\pi$
$223$	−2.97140	+	13.0186i	−0.198980	+	0.871788i	−0.971545	+	0.236853i	$0.923884\pi$
$224$	−4.94246	−	0.526938i	−0.330232	−	0.0352075i
$225$	2.65783	+	11.6447i	0.177189	+	0.776315i
$226$	0.401118	−	0.694757i	0.0266820	−	0.0462146i
$227$	−12.6141	−	21.8482i	−0.837225	−	1.45012i	−0.892206	−	0.451629i	$-0.850843\pi$
$227$	−12.6141	−	21.8482i	−0.837225	−	1.45012i	0.0549811	−	0.998487i	$-0.482490\pi$
$228$	−8.21607	+	7.62340i	−0.544123	+	0.504872i
$229$	3.45325	−	2.35439i	0.228197	−	0.155582i	−0.443824	−	0.896114i	$-0.646379\pi$
$229$	3.45325	−	2.35439i	0.228197	−	0.155582i	0.672022	+	0.740531i	$0.265426\pi$
$230$	0.0916089	−	0.114874i	0.00604051	−	0.00757456i
$231$	−10.2821	−	2.68922i	−0.676515	−	0.176938i
$232$	−1.56534	−	1.96288i	−0.102770	−	0.128869i
$233$	3.26874	+	1.00827i	0.214142	+	0.0660541i	0.399970	−	0.916528i	$-0.369021\pi$
$233$	3.26874	+	1.00827i	0.214142	+	0.0660541i	−0.185828	+	0.982582i	$0.559497\pi$
$234$	−0.143059	+	0.364508i	−0.00935204	+	0.0238286i
$235$	−2.67458	−	35.6897i	−0.174470	−	2.32814i
$236$	5.32065	+	13.5568i	0.346345	+	0.882472i
$237$	−8.38500	+	4.03800i	−0.544664	+	0.262297i
$238$	−3.23392	+	0.140397i	−0.209624	+	0.00910057i
$239$	20.4746	+	9.86002i	1.32439	+	0.637792i	0.956406	−	0.292041i	$-0.0943343\pi$
$239$	20.4746	+	9.86002i	1.32439	+	0.637792i	0.367983	+	0.929833i	$0.380049\pi$
$240$	0.664115	−	8.86199i	0.0428684	−	0.572039i
$241$	7.26671	−	2.24148i	0.468090	−	0.144387i	−0.0517326	−	0.998661i	$-0.516474\pi$
$241$	7.26671	−	2.24148i	0.468090	−	0.144387i	0.519822	+	0.854274i	$0.325998\pi$
$242$	2.47740	+	1.68906i	0.159253	+	0.108577i
$243$	−15.1283	+	2.28022i	−0.970479	+	0.146276i
$244$	15.2806			0.978241
$245$	21.4834	+	4.63354i	1.37252	+	0.296026i
$246$	−0.254206			−0.0162076
$247$	7.63106	−	1.15020i	0.485553	−	0.0731853i
$248$	0.686842	+	0.468281i	0.0436145	+	0.0297359i
$249$	6.22565	−	1.92036i	0.394534	−	0.121698i
$250$	−0.00533383	+	0.0711750i	−0.000337341	+	0.00450150i
$251$	−16.0767	−	7.74211i	−1.01475	−	0.488678i	−0.148831	−	0.988863i	$-0.547551\pi$
$251$	−16.0767	−	7.74211i	−1.01475	−	0.488678i	−0.865919	+	0.500185i	$0.833265\pi$
$252$	−2.31281	+	12.6372i	−0.145694	+	0.796069i
$253$	1.44616	−	0.696434i	0.0909193	−	0.0437844i
$254$	1.19193	+	3.03699i	0.0747884	+	0.190558i
$255$	−1.32584	−	17.6922i	−0.0830276	−	1.10793i
$256$	5.11835	−	13.0414i	0.319897	−	0.815085i
$257$	−15.9938	−	4.93344i	−0.997668	−	0.307740i	−0.247429	−	0.968906i	$-0.579586\pi$
$257$	−15.9938	−	4.93344i	−0.997668	−	0.307740i	−0.750239	+	0.661166i	$0.770062\pi$
$258$	0.00190318	+	0.00238652i	0.000118487	+	0.000148578i
$259$	−3.75664	−	8.47159i	−0.233427	−	0.526399i
$260$	−3.86541	+	4.84707i	−0.239723	+	0.300603i
$261$	−8.05947	+	5.49485i	−0.498868	+	0.340123i
$262$	2.58474	−	2.39829i	0.159686	−	0.148167i
$263$	1.71679	+	2.97357i	0.105862	+	0.183358i	0.914090	−	0.405511i	$-0.132907\pi$
$263$	1.71679	+	2.97357i	0.105862	+	0.183358i	−0.808228	+	0.588870i	$0.799573\pi$
$264$	−1.27121	+	2.20181i	−0.0782378	+	0.135512i
$265$	−5.75503	−	25.2144i	−0.353529	−	1.54891i
$266$	−3.06239	+	1.09220i	−0.187767	+	0.0669669i
$267$	−0.834126	+	3.65454i	−0.0510477	+	0.223654i
$268$	−10.2452	−	9.50617i	−0.625826	−	0.580682i
$269$	−3.42459	−	0.516174i	−0.208801	−	0.0314717i	0.0438087	−	0.999040i	$-0.486051\pi$
$269$	−3.42459	−	0.516174i	−0.208801	−	0.0314717i	−0.252610	+	0.967568i	$0.581289\pi$
$270$	1.98492	+	0.299179i	0.120798	+	0.0182074i
$271$	0.797975	+	0.740412i	0.0484735	+	0.0449768i	0.704038	−	0.710163i	$-0.251379\pi$
$271$	0.797975	+	0.740412i	0.0484735	+	0.0449768i	−0.655564	+	0.755140i	$0.727569\pi$
$272$	6.57967	−	28.8274i	0.398951	−	1.74792i
$273$	−1.36772	+	1.38419i	−0.0827781	+	0.0837752i
$274$	0.235413	+	1.03141i	0.0142218	+	0.0623098i
$275$	13.2643	−	22.9744i	0.799865	−	1.38541i
$276$	0.213412	+	0.369641i	0.0128459	+	0.0222498i
$277$	−4.30468	+	3.99416i	−0.258643	+	0.239986i	−0.798826	−	0.601562i	$-0.794545\pi$
$277$	−4.30468	+	3.99416i	−0.258643	+	0.239986i	0.540183	+	0.841547i	$0.318355\pi$
$278$	0.522888	−	0.356499i	0.0313607	−	0.0213814i
$279$	2.01373	−	2.52514i	0.120559	−	0.151176i
$280$	2.42876	−	4.66279i	0.145146	−	0.278655i
$281$	9.93881	+	12.4629i	0.592899	+	0.743472i	0.984253	−	0.176768i	$-0.0565643\pi$
$281$	9.93881	+	12.4629i	0.592899	+	0.743472i	−0.391353	+	0.920241i	$0.627993\pi$
$282$	−1.27577	−	0.393523i	−0.0759710	−	0.0234339i
$283$	−11.7085	+	29.8327i	−0.695998	+	1.77337i	−0.0646032	+	0.997911i	$0.520578\pi$
$283$	−11.7085	+	29.8327i	−0.695998	+	1.77337i	−0.631394	+	0.775462i	$0.717517\pi$
$284$	−0.884830	−	11.8072i	−0.0525050	−	0.700631i
$285$	−6.51054	−	16.5886i	−0.385651	−	0.982623i
$286$	0.783578	−	0.377351i	0.0463339	−	0.0223132i
$287$	5.27710	+	2.26487i	0.311497	+	0.133691i
$288$	4.16223	+	2.00442i	0.245262	+	0.118112i
$289$	3.14101	−	41.9138i	0.184765	−	2.46552i
$290$	1.89506	−	0.584548i	0.111282	−	0.0343259i
$291$	−5.68768	−	3.87780i	−0.333418	−	0.227320i
$292$	−4.87306	+	0.734496i	−0.285174	+	0.0429831i
$293$	18.6222			1.08792			0.543961	−	0.839110i	$-0.316924\pi$
$293$	18.6222			1.08792			0.543961	+	0.839110i	$0.316924\pi$
$294$	0.453684	−	0.682857i	0.0264594	−	0.0398250i
$295$	−23.1555			−1.34817
$296$	−2.19213	+	0.330410i	−0.127415	+	0.0192047i
$297$	18.1186	+	12.3531i	1.05135	+	0.716797i
$298$	0.227881	−	0.0702920i	0.0132008	−	0.00407190i
$299$	0.0219623	−	0.293067i	0.00127011	−	0.0169485i
$300$	6.35574	+	3.06076i	0.366949	+	0.176713i
$301$	−0.0182456	−	0.0664987i	−0.00105166	−	0.00383292i
$302$	2.17023	−	1.04513i	0.124882	−	0.0601402i
$303$	−1.07247	−	2.73261i	−0.0616118	−	0.156984i
$304$	−2.21947	−	29.6168i	−0.127296	−	1.69864i
$305$	−8.87622	+	22.6163i	−0.508251	+	1.29500i
$306$	2.87489	+	0.886786i	0.164346	+	0.0506942i
$307$	−7.28553	−	9.13576i	−0.415807	−	0.521405i	0.529182	−	0.848509i	$-0.322499\pi$
$307$	−7.28553	−	9.13576i	−0.415807	−	0.521405i	−0.944989	+	0.327103i	$0.893928\pi$
$308$	22.8565	−	17.0812i	1.30237	−	0.973290i
$309$	−1.22174	+	1.53201i	−0.0695022	+	0.0871530i
$310$	−0.542545	+	0.369901i	−0.0308145	+	0.0210090i
$311$	5.25570	−	4.87658i	0.298023	−	0.276525i	−0.516960	−	0.856010i	$-0.672936\pi$
$311$	5.25570	−	4.87658i	0.298023	−	0.276525i	0.814984	+	0.579484i	$0.196746\pi$
$312$	0.232753	+	0.403139i	0.0131770	+	0.0228233i
$313$	−3.65311	+	6.32738i	−0.206486	+	0.357645i	−0.950605	−	0.310402i	$-0.899536\pi$
$313$	−3.65311	+	6.32738i	−0.206486	+	0.357645i	0.744119	+	0.668047i	$0.232870\pi$
$314$	0.373155	+	1.63490i	0.0210584	+	0.0922627i
$315$	−17.3604	−	10.7638i	−0.978146	−	0.606473i
$316$	5.56000	−	24.3599i	0.312774	−	1.37035i
$317$	9.98408	+	9.26387i	0.560762	+	0.520311i	0.908835	−	0.417157i	$-0.136973\pi$
$317$	9.98408	+	9.26387i	0.560762	+	0.520311i	−0.348073	+	0.937467i	$0.613164\pi$
$318$	−0.953999	−	0.143792i	−0.0534976	−	0.00806346i
$319$	21.4229	+	3.22899i	1.19945	+	0.180789i
$320$	17.0262	+	15.7980i	0.951793	+	0.883135i
$321$	−2.68531	+	11.7651i	−0.149879	+	0.656664i
$322$	0.0145994	+	0.122953i	0.000813594	+	0.00685191i
$323$	−13.1940	−	57.8065i	−0.734131	−	3.21644i
$324$	4.36799	−	7.56559i	0.242666	−	0.420310i
$325$	−2.42862	−	4.20649i	−0.134715	−	0.233334i
$326$	−0.740369	+	0.686962i	−0.0410053	+	0.0380473i
$327$	−5.02058	+	3.42297i	−0.277639	+	0.189291i
$328$	0.856515	−	1.07404i	0.0472931	−	0.0593037i
$329$	22.9778	+	19.5358i	1.26681	+	1.07704i
$330$	−1.25215	−	1.57015i	−0.0689288	−	0.0864339i
$331$	5.77186	+	1.78038i	0.317250	+	0.0978587i	0.449291	−	0.893386i	$-0.351677\pi$
$331$	5.77186	+	1.78038i	0.317250	+	0.0978587i	−0.132041	+	0.991244i	$0.542153\pi$
$332$	−6.39042	+	16.2825i	−0.350720	+	0.893620i
$333$	0.643666	+	8.58912i	0.0352727	+	0.470681i
$334$	−0.319431	−	0.813896i	−0.0174785	−	0.0445344i
$335$	20.0210	−	9.64160i	1.09386	−	0.526777i
$336$	4.91882	+	5.64704i	0.268344	+	0.308071i
$337$	23.8434	+	11.4824i	1.29883	+	0.625486i	0.950161	−	0.311759i	$-0.100918\pi$
$337$	23.8434	+	11.4824i	1.29883	+	0.625486i	0.348673	+	0.937244i	$0.386632\pi$
$338$	0.0118999	−	0.158793i	0.000647270	−	0.00863722i
$339$	−3.54076	+	1.09218i	−0.192308	+	0.0593190i
$340$	39.3562	+	26.8326i	2.13439	+	1.45520i
$341$	−7.09334	+	1.06915i	−0.384126	+	0.0578976i
$342$	3.02189			0.163405
$343$	−15.5021	+	10.1334i	−0.837033	+	0.547152i
$344$	−0.0164957			−0.000889390
$345$	−0.671058	+	0.101146i	−0.0361286	+	0.00544550i
$346$	−2.77589	−	1.89257i	−0.149233	−	0.101745i
$347$	−24.0101	+	7.40614i	−1.28893	+	0.397583i	−0.862095	−	0.506747i	$-0.830848\pi$
$347$	−24.0101	+	7.40614i	−1.28893	+	0.397583i	−0.426836	+	0.904329i	$0.640372\pi$
$348$	−0.430522	+	5.74492i	−0.0230784	+	0.307960i
$349$	10.5405	+	5.07603i	0.564219	+	0.271714i	0.694175	−	0.719806i	$-0.255769\pi$
$349$	10.5405	+	5.07603i	0.564219	+	0.271714i	−0.129956	+	0.991520i	$0.541484\pi$
$350$	1.34409	+	1.54308i	0.0718447	+	0.0824811i
$351$	3.61747	−	1.74208i	0.193086	−	0.0929855i
$352$	−3.74862	−	9.55132i	−0.199802	−	0.509087i
$353$	1.78244	+	23.7850i	0.0948695	+	1.26595i	0.817993	+	0.575227i	$0.195086\pi$
$353$	1.78244	+	23.7850i	0.0948695	+	1.26595i	−0.723124	+	0.690718i	$0.757294\pi$
$354$	−0.315575	+	0.804071i	−0.0167726	+	0.0427359i
$355$	17.9894	+	5.54900i	0.954779	+	0.294510i
$356$	−6.27481	−	7.86836i	−0.332564	−	0.417022i
$357$	11.3906	+	9.68430i	0.602853	+	0.512547i
$358$	−0.972445	+	1.21941i	−0.0513953	+	0.0644477i
$359$	5.79251	−	3.94927i	0.305717	−	0.208434i	−0.400737	−	0.916193i	$-0.631246\pi$
$359$	5.79251	−	3.94927i	0.305717	−	0.208434i	0.706454	+	0.707759i	$0.250294\pi$
$360$	−3.58201	+	3.32362i	−0.188788	+	0.175170i
$361$	−20.2780	−	35.1225i	−1.06726	−	1.84855i
$362$	1.42514	−	2.46841i	0.0749036	−	0.129737i
$363$	−3.08171	−	13.5018i	−0.161748	−	0.708662i
$364$	−0.616018	−	5.18797i	−0.0322881	−	0.271923i
$365$	1.74357	−	7.63908i	0.0912627	−	0.399848i
$366$	0.664375	+	0.616450i	0.0347275	+	0.0322224i
$367$	22.9609	+	3.46081i	1.19855	+	0.180653i	0.717828	−	0.696220i	$-0.245136\pi$
$367$	22.9609	+	3.46081i	1.19855	+	0.180653i	0.480723	+	0.876873i	$0.340374\pi$
$368$	−1.11840	−	0.168571i	−0.0583005	−	0.00878738i
$369$	−3.91256	−	3.63033i	−0.203680	−	0.188987i
$370$	0.389667	−	1.70724i	0.0202578	−	0.0887554i
$371$	18.5231	+	11.4847i	0.961670	+	0.596257i
$372$	−0.424465	−	1.85970i	−0.0220075	−	0.0964212i
$373$	−4.70695	+	8.15267i	−0.243717	+	0.422129i	−0.961770	−	0.273859i	$-0.911700\pi$
$373$	−4.70695	+	8.15267i	−0.243717	+	0.422129i	0.718053	+	0.695988i	$0.245033\pi$
$374$	−3.34106	−	5.78688i	−0.172762	−	0.299232i
$375$	0.241662	−	0.224230i	0.0124794	−	0.0115792i
$376$	5.96120	−	4.06428i	0.307426	−	0.209599i
$377$	2.47322	−	3.10132i	0.127377	−	0.159726i
$378$	−1.35500	+	1.01262i	−0.0696939	+	0.0520838i
$379$	6.64679	+	8.33481i	0.341423	+	0.428130i	0.922666	−	0.385599i	$-0.126005\pi$
$379$	6.64679	+	8.33481i	0.341423	+	0.428130i	−0.581244	+	0.813729i	$0.697434\pi$
$380$	45.7186	+	14.1023i	2.34531	+	0.723434i
$381$	5.50530	−	14.0273i	0.282045	−	0.718639i
$382$	−0.0362977	−	0.484359i	−0.00185715	−	0.0247820i
$383$	−2.01841	−	5.14282i	−0.103136	−	0.262786i	0.869986	−	0.493076i	$-0.164128\pi$
$383$	−2.01841	−	5.14282i	−0.103136	−	0.262786i	−0.973122	+	0.230290i	$0.926032\pi$
$384$	3.27044	−	1.57496i	0.166894	−	0.0803718i
$385$	12.0043	+	43.7511i	0.611794	+	2.22976i
$386$	1.28577	+	0.619195i	0.0654441	+	0.0315162i
$387$	−0.00478948	+	0.0639111i	−0.000243463	+	0.00324879i
$388$	17.6605	−	5.44755i	0.896578	−	0.276558i
$389$	−18.5236	−	12.6292i	−0.939182	−	0.640324i	−0.00609814	−	0.999981i	$-0.501941\pi$
$389$	−18.5236	−	12.6292i	−0.939182	−	0.640324i	−0.933084	+	0.359658i	$0.882893\pi$
$390$	−0.363602	+	0.0548042i	−0.0184117	+	0.00277512i
$391$	−2.25800			−0.114192
$392$	1.35648	+	4.21765i	0.0685127	+	0.213023i
$393$	−16.2859			−0.821516
$394$	−2.33783	+	0.352372i	−0.117778	+	0.0177522i
$395$	32.8245	+	22.3794i	1.65158	+	1.12603i
$396$	−25.3422	+	7.81703i	−1.27349	+	0.392820i
$397$	0.281525	−	3.75668i	0.0141293	−	0.188543i	−0.985673	−	0.168667i	$-0.946054\pi$
$397$	0.281525	−	3.75668i	0.0141293	−	0.188543i	0.999802	−	0.0198759i	$-0.00632711\pi$
$398$	−2.47780	−	1.19325i	−0.124201	−	0.0598121i
$399$	13.7999	+	5.92277i	0.690861	+	0.296509i
$400$	−16.8419	+	8.11062i	−0.842094	+	0.405531i
$401$	11.4379	+	29.1432i	0.571179	+	1.45534i	0.866125	+	0.499827i	$0.166603\pi$
$401$	11.4379	+	29.1432i	0.571179	+	1.45534i	−0.294946	+	0.955514i	$0.595302\pi$
$402$	−0.0619470	−	0.826625i	−0.00308963	−	0.0412283i
$403$	−0.479847	+	1.22263i	−0.0239029	+	0.0609036i
$404$	7.53114	+	2.32305i	0.374688	+	0.115576i
$405$	8.66025	+	10.8596i	0.430331	+	0.539618i
$406$	−0.772044	+	1.48219i	−0.0383159	+	0.0735598i
$407$	11.9275	−	14.9567i	0.591226	−	0.741374i
$408$	2.95510	−	2.01475i	0.146299	−	0.0997450i
$409$	−3.82055	+	3.54495i	−0.188914	+	0.175287i	−0.768959	−	0.639298i	$-0.779225\pi$
$409$	−3.82055	+	3.54495i	−0.188914	+	0.175287i	0.580045	+	0.814584i	$0.303035\pi$
$410$	0.542569	+	0.939758i	0.0267956	+	0.0464113i
$411$	2.44320	−	4.23175i	0.120514	−	0.208737i
$412$	−1.17066	−	5.12898i	−0.0576741	−	0.252687i
$413$	13.7150	−	13.8802i	0.674871	−	0.683000i
$414$	0.0256076	−	0.112194i	0.00125855	−	0.00551405i
$415$	−20.3871	−	18.9164i	−1.00076	−	0.928571i
$416$	−1.85768	−	0.280000i	−0.0910802	−	0.0137281i
$417$	−2.89038	−	0.435655i	−0.141543	−	0.0213341i
$418$	−4.92005	−	4.56514i	−0.240648	−	0.223288i
$419$	0.566123	−	2.48035i	0.0276569	−	0.121173i	−0.959215	−	0.282677i	$-0.908777\pi$
$419$	0.566123	−	2.48035i	0.0276569	−	0.121173i	0.986872	+	0.161504i	$0.0516346\pi$
$420$	−11.3630	+	4.05260i	−0.554458	+	0.197747i
$421$	−2.85877	−	12.5251i	−0.139328	−	0.610435i	−0.995583	−	0.0938824i	$-0.970072\pi$
$421$	−2.85877	−	12.5251i	−0.139328	−	0.610435i	0.856256	−	0.516553i	$-0.172785\pi$
$422$	−1.78809	+	3.09707i	−0.0870429	+	0.150763i
$423$	−14.0158	−	24.2762i	−0.681474	−	1.18035i
$424$	3.82191	−	3.54621i	0.185608	−	0.172219i
$425$	−30.8344	+	21.0226i	−1.49569	+	1.01974i
$426$	0.437856	−	0.549055i	0.0212142	−	0.0266018i
$427$	−8.29956	−	18.7163i	−0.401644	−	0.905744i
$428$	−20.2006	−	25.3307i	−0.976431	−	1.22441i
$429$	−3.83854	−	1.18403i	−0.185326	−	0.0571656i
$430$	0.00476047	−	0.0121295i	0.000229570	−	0.000584935i
$431$	0.556776	+	7.42966i	0.0268190	+	0.357874i	0.994428	+	0.105420i	$0.0336187\pi$
$431$	0.556776	+	7.42966i	0.0268190	+	0.357874i	−0.967609	+	0.252454i	$0.918762\pi$
$432$	−5.64528	−	14.3839i	−0.271609	−	0.692048i
$433$	−2.82507	+	1.36048i	−0.135764	+	0.0653805i	−0.500533	−	0.865718i	$-0.666862\pi$
$433$	−2.82507	+	1.36048i	−0.135764	+	0.0653805i	0.364768	+	0.931098i	$0.381148\pi$
$434$	0.0996179	−	0.544312i	0.00478181	−	0.0261278i
$435$	−8.25275	−	3.97432i	−0.395689	−	0.190554i
$436$	1.21914	−	16.2683i	0.0583863	−	0.779111i
$437$	−2.16725	+	0.668508i	−0.103674	+	0.0319791i
$438$	−0.241503	−	0.164654i	−0.0115395	−	0.00786748i
$439$	−27.3550	+	4.12310i	−1.30558	+	0.196785i	−0.764740	−	0.644340i	$-0.777132\pi$
$439$	−27.3550	+	4.12310i	−1.30558	+	0.196785i	−0.540842	+	0.841124i	$0.681894\pi$
$440$	10.8530			0.517394
$441$	16.7347	−	4.03098i	0.796891	−	0.191952i
$442$	−1.22346			−0.0581940
$443$	−16.0666	+	2.42165i	−0.763346	+	0.115056i	−0.519166	−	0.854674i	$-0.673757\pi$
$443$	−16.0666	+	2.42165i	−0.763346	+	0.115056i	−0.244181	+	0.969730i	$0.578519\pi$
$444$	4.20310	+	2.86563i	0.199470	+	0.135997i
$445$	15.2906	−	4.71652i	0.724843	−	0.223584i
$446$	0.158904	−	2.12043i	0.00752432	−	0.100405i
$447$	−0.992394	−	0.477912i	−0.0469386	−	0.0226044i
$448$	−19.5544	+	0.848932i	−0.923861	+	0.0401083i
$449$	−10.4118	+	5.01404i	−0.491361	+	0.236627i	−0.663122	−	0.748512i	$-0.730769\pi$
$449$	−10.4118	+	5.01404i	−0.491361	+	0.236627i	0.171760	+	0.985139i	$0.445054\pi$
$450$	−0.694870	−	1.77050i	−0.0327565	−	0.0834621i
$451$	0.885888	+	11.8214i	0.0417148	+	0.556646i
$452$	3.63447	−	9.26048i	0.170951	−	0.435576i
$453$	−10.6314	−	3.27934i	−0.499505	−	0.154077i
$454$	2.50474	+	3.14084i	0.117553	+	0.147407i
$455$	8.03635	+	2.10185i	0.376750	+	0.0985363i
$456$	2.23984	−	2.80867i	0.104890	−	0.131528i
$457$	−18.6102	+	12.6882i	−0.870548	+	0.593529i	−0.914085	−	0.405522i	$-0.867090\pi$
$457$	−18.6102	+	12.6882i	−0.870548	+	0.593529i	0.0435373	+	0.999052i	$0.486137\pi$
$458$	−0.487872	+	0.452679i	−0.0227968	+	0.0211523i
$459$	−15.4243	−	26.7157i	−0.719947	−	1.24698i
$460$	0.911000	−	1.57790i	0.0424756	−	0.0735699i
$461$	−1.28463	−	5.62833i	−0.0598312	−	0.262138i	0.936162	−	0.351570i	$-0.114352\pi$
$461$	−1.28463	−	5.62833i	−0.0598312	−	0.262138i	−0.995993	+	0.0894321i	$0.971495\pi$
$462$	1.68285	+	0.179416i	0.0782932	+	0.00834718i
$463$	−1.45186	+	6.36103i	−0.0674739	+	0.295622i	−0.997395	−	0.0721374i	$-0.977018\pi$
$463$	−1.45186	+	6.36103i	−0.0674739	+	0.295622i	0.929921	+	0.367760i	$0.119875\pi$
$464$	−11.1908	−	10.3835i	−0.519518	−	0.482042i
$465$	2.99904	+	0.452033i	0.139077	+	0.0209625i
$466$	−0.538625	−	0.0811847i	−0.0249513	−	0.00376081i
$467$	9.40616	+	8.72764i	0.435265	+	0.403867i	0.867138	−	0.498067i	$-0.165957\pi$
$467$	9.40616	+	8.72764i	0.435265	+	0.403867i	−0.431873	+	0.901934i	$0.642147\pi$
$468$	−1.08051	+	4.73400i	−0.0499464	+	0.218829i
$469$	−6.07891	+	17.7119i	−0.280698	+	0.817862i
$470$	1.26817	+	5.55623i	0.0584965	+	0.256290i
$471$	3.87274	−	6.70779i	0.178447	−	0.309078i
$472$	−2.33396	−	4.04254i	−0.107429	−	0.186073i
$473$	0.104348	−	0.0968207i	0.00479792	−	0.00445182i
$474$	1.22447	−	0.834828i	0.0562417	−	0.0383449i
$475$	−23.3712	+	29.3066i	−1.07235	+	1.34468i
$476$	−39.3950	+	7.69850i	−1.80567	+	0.352860i
$477$	−12.6298	−	15.8373i	−0.578278	−	0.725138i
$478$	−3.45793	−	1.06663i	−0.158162	−	0.0487866i
$479$	−0.0200097	+	0.0509840i	−0.000914268	+	0.00232952i	−0.931330	−	0.364176i	$-0.881351\pi$
$479$	−0.0200097	+	0.0509840i	−0.000914268	+	0.00232952i	0.930416	+	0.366505i	$0.119446\pi$
$480$	0.324190	+	4.32602i	0.0147972	+	0.197455i
$481$	−1.27966	−	3.26053i	−0.0583476	−	0.148667i
$482$	−1.09102	+	0.525406i	−0.0496945	+	0.0239316i
$483$	0.336837	−	0.462163i	0.0153266	−	0.0210292i
$484$	33.4997	+	16.1326i	1.52271	+	0.733299i
$485$	−2.19596	+	29.3031i	−0.0997134	+	1.33058i
$486$	2.32798	−	0.718087i	0.105599	−	0.0325731i
$487$	23.4975	+	16.0203i	1.06477	+	0.725949i	0.963175	−	0.268877i	$-0.0866524\pi$
$487$	23.4975	+	16.0203i	1.06477	+	0.725949i	0.101597	+	0.994826i	$0.467605\pi$
$488$	−4.84307	+	0.729975i	−0.219235	+	0.0330444i
$489$	4.66491			0.210955
$490$	−3.49274	−	0.219726i	−0.157786	−	0.00992622i
$491$	−5.51047			−0.248684			−0.124342	−	0.992239i	$-0.539682\pi$
$491$	−5.51047			−0.248684			−0.124342	+	0.992239i	$0.539682\pi$
$492$	−3.11708	+	0.469824i	−0.140529	+	0.0211813i
$493$	−25.1814	−	17.1684i	−1.13411	−	0.773226i
$494$	−1.17429	+	0.362220i	−0.0528337	+	0.0162971i
$495$	3.15112	−	42.0487i	0.141632	−	1.88995i
$496$	4.55414	+	2.19316i	0.204487	+	0.0984756i
$497$	−13.9814	+	7.49679i	−0.627150	+	0.336277i
$498$	−0.934714	+	0.450135i	−0.0418855	+	0.0201710i
$499$	−0.167979	−	0.428003i	−0.00751976	−	0.0191600i	0.927065	−	0.374902i	$-0.122324\pi$
$499$	−0.167979	−	0.428003i	−0.00751976	−	0.0191600i	−0.934584	+	0.355742i	$0.884228\pi$
$500$	0.0661424	+	0.882608i	0.00295798	+	0.0394714i
$501$	−1.47539	+	3.75923i	−0.0659156	+	0.167950i
$502$	2.71518	+	0.837521i	0.121184	+	0.0373804i
$503$	9.73921	+	12.2126i	0.434250	+	0.544532i	0.950018	−	0.312196i	$-0.101065\pi$
$503$	9.73921	+	12.2126i	0.434250	+	0.544532i	−0.515768	+	0.856729i	$0.672493\pi$
$504$	0.129332	−	4.11575i	0.00576089	−	0.183330i
$505$	−7.81295	+	9.79713i	−0.347672	+	0.435967i
$506$	−0.211184	+	0.143983i	−0.00938826	+	0.00640080i
$507$	−0.539154	+	0.500262i	−0.0239447	+	0.0222174i
$508$	20.2285	+	35.0367i	0.897493	+	1.55450i
$509$	14.7954	−	25.6264i	0.655794	−	1.13587i	−0.325900	−	0.945404i	$-0.605667\pi$
$509$	14.7954	−	25.6264i	0.655794	−	1.13587i	0.981694	−	0.190464i	$-0.0609994\pi$
$510$	0.628661	+	2.75434i	0.0278376	+	0.121964i
$511$	3.54641	+	5.56977i	0.156884	+	0.246392i
$512$	−2.69286	+	11.7982i	−0.119009	+	0.521411i
$513$	−22.7140	−	21.0755i	−1.00285	−	0.930505i
$514$	2.63548	+	0.397234i	0.116246	+	0.0175212i
$515$	8.27122	+	1.24669i	0.364474	+	0.0549356i
$516$	0.0277477	+	0.0257461i	0.00122152	+	0.00113341i
$517$	−13.8541	+	60.6986i	−0.609300	+	2.66952i
$518$	0.792580	+	1.24478i	0.0348240	+	0.0546924i
$519$	3.45301	+	15.1286i	0.151570	+	0.664072i
$520$	0.993560	−	1.72090i	0.0435705	−	0.0754663i
$521$	−1.12124	−	1.94204i	−0.0491223	−	0.0850824i	0.840419	−	0.541938i	$-0.182309\pi$
$521$	−1.12124	−	1.94204i	−0.0491223	−	0.0850824i	−0.889541	+	0.456855i	$0.848976\pi$
$522$	1.13863	−	1.05650i	0.0498366	−	0.0462416i
$523$	11.5314	−	7.86199i	0.504234	−	0.343781i	−0.284337	−	0.958724i	$-0.591774\pi$
$523$	11.5314	−	7.86199i	0.504234	−	0.343781i	0.788571	+	0.614944i	$0.210821\pi$
$524$	27.2616	−	34.1850i	1.19093	−	1.49338i
$525$	0.296865	−	9.44718i	0.0129562	−	0.412309i
$526$	−0.340899	−	0.427473i	−0.0148639	−	0.0186387i
$527$	9.64295	+	2.97446i	0.420053	+	0.129569i
$528$	−5.64797	+	14.3908i	−0.245796	+	0.626279i
$529$	−1.71234	−	22.8496i	−0.0744495	−	0.993459i
$530$	1.50461	+	3.83368i	0.0653560	+	0.166524i
$531$	−16.3401	+	7.86898i	−0.709100	+	0.341485i
$532$	−35.5325	+	19.0525i	−1.54053	+	0.826029i
$533$	1.95555	+	0.941744i	0.0847043	+	0.0407914i
$534$	0.0446071	−	0.595241i	0.00193034	−	0.0257586i
$535$	49.2251	−	15.1839i	2.12819	−	0.656459i
$536$	3.70126	+	2.52348i	0.159870	+	0.108998i
$537$	7.12340	−	1.07368i	0.307397	−	0.0463327i
$538$	0.551487			0.0237763
$539$	−33.3360	−	18.7180i	−1.43588	−	0.806241i
$540$	24.8921			1.07119
$541$	−30.4132	+	4.58406i	−1.30757	+	0.197084i	−0.765601	−	0.643316i	$-0.777558\pi$
$541$	−30.4132	+	4.58406i	−1.30757	+	0.197084i	−0.541966	+	0.840400i	$0.682320\pi$
$542$	−0.143221	−	0.0976467i	−0.00615189	−	0.00419429i
$543$	−12.5800	+	3.88042i	−0.539859	+	0.166525i
$544$	−1.07866	+	14.3938i	−0.0462473	+	0.617127i
$545$	23.3699	+	11.2544i	1.00106	+	0.482084i
$546$	0.182509	−	0.250415i	0.00781069	−	0.0107168i
$547$	−34.4280	+	16.5796i	−1.47203	+	0.708894i	−0.986261	−	0.165192i	$-0.947176\pi$
$547$	−34.4280	+	16.5796i	−1.47203	+	0.708894i	−0.485772	+	0.874086i	$0.661461\pi$
$548$	4.79290	+	12.2121i	0.204742	+	0.521675i
$549$	1.42205	+	18.9760i	0.0606917	+	0.809874i
$550$	−1.54333	+	3.93235i	−0.0658080	+	0.167676i
$551$	−29.2523	−	9.02313i	−1.24619	−	0.384398i
$552$	−0.0852975	−	0.106960i	−0.00363050	−	0.00455251i
$553$	−32.8569	+	6.42083i	−1.39722	+	0.273042i
$554$	0.583020	−	0.731084i	0.0247702	−	0.0310608i
$555$	−6.68280	+	4.55626i	−0.283669	+	0.193402i
$556$	5.75279	−	5.33781i	0.243972	−	0.226373i
$557$	−13.3051	−	23.0452i	−0.563757	−	0.976455i	−0.997164	−	0.0752571i	$-0.976022\pi$
$557$	−13.3051	−	23.0452i	−0.563757	−	0.976455i	0.433407	−	0.901198i	$-0.357311\pi$
$558$	−0.257152	+	0.445401i	−0.0108861	+	0.0188553i
$559$	−0.00579957	−	0.0254096i	−0.000245296	−	0.00107471i
$560$	10.3776	−	30.2369i	0.438534	−	1.27774i
$561$	−6.86775	+	30.0896i	−0.289957	+	1.27038i
$562$	−1.86075	−	1.72652i	−0.0784910	−	0.0728290i
$563$	1.69802	+	0.255935i	0.0715630	+	0.0107864i	0.184726	−	0.982790i	$-0.440860\pi$
$563$	1.69802	+	0.255935i	0.0715630	+	0.0107864i	−0.113163	+	0.993576i	$0.536098\pi$
$564$	−16.3708	−	2.46751i	−0.689336	−	0.103901i
$565$	11.5949	+	10.7585i	0.487800	+	0.452613i
$566$	1.13559	−	4.97535i	0.0477324	−	0.209129i
$567$	−11.6391	−	1.24089i	−0.488795	−	0.0521125i
$568$	0.844487	+	3.69994i	0.0354339	+	0.155246i
$569$	5.85520	−	10.1415i	0.245463	−	0.425154i	−0.716799	−	0.697280i	$-0.754393\pi$
$569$	5.85520	−	10.1415i	0.245463	−	0.425154i	0.962262	+	0.272126i	$0.0877268\pi$
$570$	1.41885	+	2.45752i	0.0594291	+	0.102934i
$571$	−34.3735	+	31.8940i	−1.43849	+	1.33472i	−0.587847	+	0.808972i	$0.700024\pi$
$571$	−34.3735	+	31.8940i	−1.43849	+	1.33472i	−0.850640	+	0.525749i	$0.823785\pi$
$572$	8.91083	−	6.07530i	0.372581	−	0.254021i
$573$	−1.39876	+	1.75399i	−0.0584340	+	0.0732739i
$574$	−0.884685	−	0.231383i	−0.0369260	−	0.00965775i
$575$	0.890022	+	1.11605i	0.0371165	+	0.0465426i
$576$	17.3835	+	5.36209i	0.724312	+	0.223421i
$577$	−7.83164	+	19.9547i	−0.326035	+	0.830724i	0.670049	+	0.742317i	$0.266273\pi$
$577$	−7.83164	+	19.9547i	−0.326035	+	0.830724i	−0.996084	+	0.0884075i	$0.971822\pi$
$578$	0.500169	+	6.67430i	0.0208043	+	0.277614i
$579$	−2.40815	−	6.13585i	−0.100079	−	0.254997i
$580$	22.1569	−	10.6702i	0.920016	−	0.443056i
$581$	23.4144	−	1.01651i	0.971392	−	0.0421718i
$582$	0.987615	+	0.475610i	0.0409380	+	0.0197147i
$583$	−3.36216	+	44.8650i	−0.139247	+	1.85812i
$584$	1.50939	−	0.465585i	0.0624590	−	0.0192660i
$585$	−6.37897	−	4.34911i	−0.263738	−	0.179814i
$586$	−2.93226	+	0.441967i	−0.121130	+	0.0182575i
$587$	25.6892			1.06031			0.530153	−	0.847902i	$-0.322135\pi$
$587$	25.6892			1.06031			0.530153	+	0.847902i	$0.322135\pi$
$588$	4.30103	−	9.21172i	0.177371	−	0.379885i
$589$	10.1360			0.417647
$590$	3.64607	−	0.549557i	0.150106	−	0.0226249i
$591$	9.02251	+	6.15144i	0.371136	+	0.253037i
$592$	−12.8811	+	3.97329i	−0.529410	+	0.163301i
$593$	3.09277	−	41.2702i	0.127005	−	1.69476i	−0.462197	−	0.886777i	$-0.652939\pi$
$593$	3.09277	−	41.2702i	0.127005	−	1.69476i	0.589202	−	0.807986i	$-0.299442\pi$
$594$	−3.14614	−	1.51510i	−0.129087	−	0.0621653i
$595$	11.4896	−	62.7789i	0.471026	−	2.57368i
$596$	2.66437	−	1.28309i	0.109137	−	0.0525575i
$597$	4.64072	+	11.8244i	0.189932	+	0.483939i
$598$	0.00349725	+	0.0466675i	0.000143013	+	0.00190838i
$599$	2.16384	−	5.51337i	0.0884120	−	0.225270i	−0.879828	−	0.475292i	$-0.842343\pi$
$599$	2.16384	−	5.51337i	0.0884120	−	0.225270i	0.968240	+	0.250022i	$0.0804378\pi$
$600$	−2.16062	−	0.666462i	−0.0882068	−	0.0272082i
$601$	−1.27818	−	1.60278i	−0.0521379	−	0.0653789i	0.755079	−	0.655634i	$-0.227599\pi$
$601$	−1.27818	−	1.60278i	−0.0521379	−	0.0653789i	−0.807217	+	0.590255i	$0.799027\pi$
$602$	0.00445119	+	0.0100379i	0.000181417	+	0.000409112i
$603$	10.8516	−	13.6075i	0.441912	−	0.554141i
$604$	24.6798	−	16.8264i	1.00421	−	0.684656i
$605$	−43.3365	+	40.2104i	−1.76188	+	1.63479i
$606$	0.233725	+	0.404823i	0.00949442	+	0.0164448i
$607$	3.29487	−	5.70688i	0.133735	−	0.231635i	−0.791379	−	0.611326i	$-0.790636\pi$
$607$	3.29487	−	5.70688i	0.133735	−	0.231635i	0.925113	+	0.379691i	$0.123970\pi$
$608$	3.22614	+	14.1346i	0.130837	+	0.573235i
$609$	7.27043	−	2.59299i	0.294613	−	0.105073i
$610$	0.860893	−	3.77182i	0.0348565	−	0.152716i
$611$	8.35635	+	7.75356i	0.338062	+	0.313675i
$612$	36.8909	+	5.56041i	1.49123	+	0.224766i
$613$	−5.88046	−	0.886337i	−0.237510	−	0.0357988i	0.0292088	−	0.999573i	$-0.490701\pi$
$613$	−5.88046	−	0.886337i	−0.237510	−	0.0357988i	−0.266718	+	0.963775i	$0.585939\pi$
$614$	1.36400	+	1.26561i	0.0550466	+	0.0510758i
$615$	1.11529	−	4.88638i	0.0449726	−	0.197038i
$616$	−6.42819	+	6.50562i	−0.258999	+	0.262119i
$617$	−2.81097	−	12.3157i	−0.113165	−	0.495810i	−0.999465	−	0.0326982i	$-0.989590\pi$
$617$	−2.81097	−	12.3157i	−0.113165	−	0.495810i	0.886300	−	0.463112i	$-0.153267\pi$
$618$	0.156015	−	0.270226i	0.00627585	−	0.0108701i
$619$	−17.2712	−	29.9146i	−0.694187	−	1.20237i	−0.970454	−	0.241287i	$-0.922431\pi$
$619$	−17.2712	−	29.9146i	−0.694187	−	1.20237i	0.276267	−	0.961081i	$-0.410903\pi$
$620$	−5.96905	+	5.53847i	−0.239723	+	0.222430i
$621$	−0.974952	+	0.664711i	−0.0391235	+	0.0266739i
$622$	−0.711826	+	0.892601i	−0.0285416	+	0.0357900i
$623$	−6.22935	+	11.9593i	−0.249574	+	0.479138i
$624$	1.76482	+	2.21301i	0.0706491	+	0.0885912i
$625$	−24.5519	−	7.57327i	−0.982078	−	0.302931i
$626$	0.425050	−	1.08301i	0.0169884	−	0.0432858i
$627$	2.31665	+	30.9136i	0.0925181	+	1.23457i
$628$	7.59727	+	19.3575i	0.303164	+	0.772449i
$629$	−24.2465	+	11.6765i	−0.966770	+	0.465572i
$630$	2.98902	+	1.28285i	0.119086	+	0.0511101i
$631$	18.2246	+	8.77649i	0.725509	+	0.349387i	0.759916	−	0.650021i	$-0.225240\pi$
$631$	18.2246	+	8.77649i	0.725509	+	0.349387i	−0.0344071	+	0.999408i	$0.510954\pi$
$632$	−0.598490	+	7.98630i	−0.0238067	+	0.317678i
$633$	15.7839	−	4.86868i	0.627352	−	0.193513i
$634$	−1.79195	−	1.22173i	−0.0711676	−	0.0485213i
$635$	−63.6069	+	9.58719i	−2.52416	+	0.380456i
$636$	−11.9637			−0.474392
$637$	−6.01984	+	3.57233i	−0.238515	+	0.141541i
$638$	−3.44989			−0.136583
$639$	14.5803	−	2.19762i	0.576786	−	0.0869366i
$640$	−12.8027	−	8.72872i	−0.506070	−	0.345033i
$641$	23.4719	−	7.24012i	0.927084	−	0.285968i	0.205790	−	0.978596i	$-0.434024\pi$
$641$	23.4719	−	7.24012i	0.927084	−	0.285968i	0.721294	+	0.692629i	$0.243547\pi$
$642$	0.143604	−	1.91627i	0.00566761	−	0.0756290i
$643$	−14.7615	−	7.10876i	−0.582136	−	0.280342i	0.119550	−	0.992828i	$-0.461855\pi$
$643$	−14.7615	−	7.10876i	−0.582136	−	0.280342i	−0.701686	+	0.712486i	$0.747569\pi$
$644$	0.406261	+	1.48067i	0.0160089	+	0.0583466i
$645$	−0.0542239	+	0.0261129i	−0.00213506	+	0.00102819i
$646$	3.44946	+	8.78908i	0.135717	+	0.345802i
$647$	−0.292091	−	3.89768i	−0.0114833	−	0.153234i	−0.999998	−	0.00210761i	$-0.999329\pi$
$647$	−0.292091	−	3.89768i	−0.0114833	−	0.153234i	0.988515	−	0.151126i	$-0.0482899\pi$
$648$	−1.02298	+	2.60652i	−0.0401865	+	0.102394i
$649$	38.4915	+	11.8731i	1.51092	+	0.466059i
$650$	0.482244	+	0.604715i	0.0189152	+	0.0237189i
$651$	−2.04729	+	1.52999i	−0.0802397	+	0.0599649i
$652$	−7.80878	+	9.79191i	−0.305816	+	0.383481i
$653$	3.00373	−	2.04791i	0.117545	−	0.0801409i	−0.503121	−	0.864216i	$-0.667815\pi$
$653$	3.00373	−	2.04791i	0.117545	−	0.0801409i	0.620666	+	0.784075i	$0.286862\pi$
$654$	0.709302	−	0.658136i	0.0277359	−	0.0257351i
$655$	34.7602	+	60.2064i	1.35819	+	2.35246i
$656$	4.17658	−	7.23405i	0.163068	−	0.282442i
$657$	−1.36562	−	5.98317i	−0.0532779	−	0.233426i
$658$	−4.08173	−	2.53076i	−0.159122	−	0.0986594i
$659$	0.326368	−	1.42991i	0.0127135	−	0.0557015i	−0.968173	−	0.250281i	$-0.919477\pi$
$659$	0.326368	−	1.42991i	0.0127135	−	0.0557015i	0.980887	+	0.194579i	$0.0623342\pi$
$660$	−18.2559	−	16.9390i	−0.710610	−	0.659349i
$661$	48.9475	+	7.37765i	1.90384	+	0.286958i	0.992261	−	0.124170i	$-0.0396269\pi$
$661$	48.9475	+	7.37765i	1.90384	+	0.286958i	0.911578	+	0.411128i	$0.134865\pi$
$662$	−0.951091	−	0.143354i	−0.0369652	−	0.00557161i
$663$	4.14242	+	3.84361i	0.160878	+	0.149273i
$664$	1.24756	−	5.46590i	0.0484145	−	0.212118i
$665$	−7.55867	−	63.6574i	−0.293113	−	2.46853i
$666$	−0.305200	−	1.33717i	−0.0118262	−	0.0518142i
$667$	−0.582889	+	1.00959i	−0.0225695	+	0.0390916i
$668$	−5.42112	−	9.38965i	−0.209749	−	0.363296i
$669$	−7.19952	+	6.68018i	−0.278350	+	0.258271i
$670$	−2.92368	+	1.99333i	−0.112951	+	0.0770090i
$671$	26.3515	−	33.0438i	1.01729	−	1.27564i
$672$	−2.78518	−	2.36797i	−0.107441	−	0.0913463i
$673$	0.897181	+	1.12503i	0.0345838	+	0.0433667i	0.798823	−	0.601567i	$-0.205457\pi$
$673$	0.897181	+	1.12503i	0.0345838	+	0.0433667i	−0.764239	+	0.644933i	$0.776885\pi$
$674$	−4.02690	−	1.24213i	−0.155110	−	0.0478452i
$675$	−7.12497	+	18.1541i	−0.274240	+	0.698753i
$676$	−0.147565	−	1.96912i	−0.00567559	−	0.0757354i
$677$	−10.8600	−	27.6707i	−0.417382	−	1.06347i	−0.972748	−	0.231866i	$-0.925517\pi$
$677$	−10.8600	−	27.6707i	−0.417382	−	1.06347i	0.555366	−	0.831606i	$-0.312578\pi$
$678$	0.531607	−	0.256008i	0.0204162	−	0.00983194i
$679$	−16.2646	−	18.6725i	−0.624177	−	0.716585i
$680$	−13.7555	−	6.62428i	−0.527498	−	0.254030i
$681$	1.38662	−	18.5032i	0.0531356	−	0.709045i
$682$	1.09154	−	0.336696i	0.0417973	−	0.0128928i
$683$	21.5254	+	14.6758i	0.823647	+	0.561553i	0.900182	−	0.435514i	$-0.143433\pi$
$683$	21.5254	+	14.6758i	0.823647	+	0.561553i	−0.0765351	+	0.997067i	$0.524386\pi$
$684$	37.0545	−	5.58507i	1.41681	−	0.213550i
$685$	−20.8588			−0.796973
$686$	2.20046	−	1.96352i	0.0840138	−	0.0749676i
$687$	3.07398			0.117280
$688$	−0.0991834	+	0.0149495i	−0.00378133	+	0.000569944i
$689$	6.80620	+	4.64039i	0.259296	+	0.176785i
$690$	0.103264	−	0.0318528i	0.00393120	−	0.00121262i
$691$	2.67736	−	35.7269i	0.101852	−	1.35911i	−0.678881	−	0.734248i	$-0.737535\pi$
$691$	2.67736	−	35.7269i	0.101852	−	1.35911i	0.780732	−	0.624866i	$-0.214846\pi$
$692$	−37.5359	−	18.0763i	−1.42690	−	0.687159i
$693$	23.3390	+	26.7943i	0.886576	+	1.01783i
$694$	3.60486	−	1.73601i	0.136839	−	0.0658980i
$695$	4.55859	+	11.6151i	0.172917	+	0.440586i
$696$	−0.137992	−	1.84137i	−0.00523057	−	0.0697971i
$697$	6.09255	−	15.5236i	0.230772	−	0.587997i
$698$	−1.78018	−	0.549111i	−0.0673806	−	0.0207842i
$699$	1.56864	+	1.96702i	0.0593315	+	0.0743994i
$700$	19.3332	+	16.4371i	0.730726	+	0.621266i
$701$	−23.2338	+	29.1343i	−0.877529	+	1.10039i	0.116706	+	0.993166i	$0.462766\pi$
$701$	−23.2338	+	29.1343i	−0.877529	+	1.10039i	−0.994235	+	0.107220i	$0.965805\pi$
$702$	−0.528262	+	0.360163i	−0.0199380	+	0.0135935i
$703$	−19.8150	+	18.3857i	−0.747338	+	0.693429i
$704$	−20.2022	−	34.9913i	−0.761400	−	1.31878i
$705$	13.1616	−	22.7965i	0.495693	−	0.858566i
$706$	−0.845158	−	3.70288i	−0.0318079	−	0.139360i
$707$	−1.24513	−	10.4862i	−0.0468278	−	0.394373i
$708$	−2.38350	+	10.4428i	−0.0895774	+	0.392464i
$709$	6.74254	+	6.25616i	0.253221	+	0.234955i	0.796561	−	0.604558i	$-0.206650\pi$
$709$	6.74254	+	6.25616i	0.253221	+	0.234955i	−0.543340	+	0.839513i	$0.682841\pi$
$710$	−2.96431	−	0.446798i	−0.111249	−	0.0167680i
$711$	30.7684	+	4.63759i	1.15390	+	0.173923i
$712$	2.36463	+	2.19406i	0.0886183	+	0.0822258i
$713$	0.0858930	−	0.376322i	0.00321672	−	0.0140934i
$714$	−2.02340	−	1.25455i	−0.0757238	−	0.0469505i
$715$	3.81568	+	16.7176i	0.142699	+	0.625203i
$716$	−9.67043	+	16.7497i	−0.361401	+	0.625965i
$717$	8.35705	+	14.4748i	0.312100	+	0.540572i
$718$	−0.818360	+	0.759327i	−0.0305409	+	0.0283378i
$719$	−25.6047	+	17.4570i	−0.954893	+	0.651035i	−0.937194	−	0.348808i	$-0.886586\pi$
$719$	−25.6047	+	17.4570i	−0.954893	+	0.651035i	−0.0176991	+	0.999843i	$0.505634\pi$
$720$	−18.5253	+	23.2300i	−0.690399	+	0.865732i
$721$	−5.64634	+	4.21964i	−0.210281	+	0.157147i
$722$	4.02655	+	5.04913i	0.149853	+	0.187909i
$723$	5.34461	+	1.64859i	0.198768	+	0.0613118i
$724$	12.9130	−	32.9017i	0.479906	−	1.22278i
$725$	1.43985	+	19.2135i	0.0534748	+	0.713571i
$726$	0.805688	+	2.05286i	0.0299019	+	0.0761888i
$727$	−5.06437	+	2.43887i	−0.187827	+	0.0904528i	−0.525434	−	0.850835i	$-0.676097\pi$
$727$	−5.06437	+	2.43887i	−0.187827	+	0.0904528i	0.337607	+	0.941287i	$0.390383\pi$
$728$	0.443078	+	1.61486i	0.0164216	+	0.0598506i
$729$	1.81981	+	0.876376i	0.0674005	+	0.0324584i
$730$	−0.0932422	+	1.24423i	−0.00345105	+	0.0460510i
$731$	−0.191351	+	0.0590239i	−0.00707737	+	0.00218308i
$732$	9.28591	+	6.33103i	0.343217	+	0.234002i
$733$	29.6608	−	4.47065i	1.09555	−	0.165127i	0.423690	−	0.905807i	$-0.360735\pi$
$733$	29.6608	−	4.47065i	1.09555	−	0.165127i	0.671858	+	0.740680i	$0.265497\pi$
$734$	−3.69757			−0.136480
$735$	11.1355	+	11.7167i	0.410740	+	0.432177i
$736$	0.552117			0.0203513
$737$	−38.2247	+	5.76144i	−1.40802	+	0.212226i
$738$	0.702232	+	0.478774i	0.0258495	+	0.0176239i
$739$	39.2750	−	12.1147i	1.44475	−	0.445647i	0.529425	−	0.848357i	$-0.322408\pi$
$739$	39.2750	−	12.1147i	1.44475	−	0.445647i	0.915328	+	0.402709i	$0.131931\pi$
$740$	1.62278	−	21.6545i	0.0596545	−	0.796034i
$741$	5.11388	+	2.46272i	0.187863	+	0.0904702i
$742$	−3.18921	−	1.36877i	−0.117080	−	0.0502492i
$743$	−15.1229	+	7.28281i	−0.554806	+	0.267180i	−0.690209	−	0.723610i	$-0.742481\pi$
$743$	−15.1229	+	7.28281i	−0.554806	+	0.267180i	0.135403	+	0.990791i	$0.456767\pi$
$744$	0.223371	+	0.569141i	0.00818920	+	0.0208657i
$745$	0.351374	+	4.68875i	0.0128733	+	0.171783i
$746$	0.547667	−	1.39543i	0.0200515	−	0.0510904i
$747$	−20.8149	−	6.42054i	−0.761577	−	0.234915i
$748$	−51.6634	−	64.7839i	−1.88900	−	2.36873i
$749$	−20.0542	+	38.5006i	−0.732765	+	1.40678i
$750$	−0.0327304	+	0.0410426i	−0.00119515	+	0.00149866i
$751$	−4.36473	+	2.97582i	−0.159271	+	0.108589i	−0.640333	−	0.768097i	$-0.721204\pi$
$751$	−4.36473	+	2.97582i	−0.159271	+	0.108589i	0.481062	+	0.876687i	$0.340251\pi$
$752$	32.1594	−	29.8396i	1.17273	−	1.08814i
$753$	−6.56197	−	11.3657i	−0.239132	−	0.414188i
$754$	−0.315829	+	0.547031i	−0.0115018	+	0.0199217i
$755$	10.5681	+	46.3017i	0.384611	+	1.68509i
$756$	−14.7436	+	14.9212i	−0.536218	+	0.542677i
$757$	−9.84229	+	43.1219i	−0.357724	+	1.56729i	0.401124	+	0.916024i	$0.368620\pi$
$757$	−9.84229	+	43.1219i	−0.357724	+	1.56729i	−0.758848	+	0.651268i	$0.774238\pi$
$758$	−1.24442	−	1.15465i	−0.0451992	−	0.0419387i
$759$	1.16736	+	0.175952i	0.0423727	+	0.00638665i
$760$	−15.1638	−	2.28558i	−0.550050	−	0.0829067i
$761$	35.4065	+	32.8524i	1.28348	+	1.19090i	0.970489	+	0.241144i	$0.0775225\pi$
$761$	35.4065	+	32.8524i	1.28348	+	1.19090i	0.312994	+	0.949755i	$0.398668\pi$
$762$	−0.533952	+	2.33939i	−0.0193430	+	0.0847473i
$763$	−20.5882	+	7.34276i	−0.745343	+	0.265826i
$764$	−1.34028	−	5.87214i	−0.0484895	−	0.212447i
$765$	−29.6590	+	51.3709i	−1.07232	+	1.85732i
$766$	0.439875	+	0.761885i	0.0158933	+	0.0275280i
$767$	5.40645	−	5.01645i	0.195216	−	0.181134i
$768$	8.51365	−	5.80451i	0.307210	−	0.209452i
$769$	−9.71502	+	12.1823i	−0.350333	+	0.439303i	−0.925509	−	0.378726i	$-0.876362\pi$
$769$	−9.71502	+	12.1823i	−0.350333	+	0.439303i	0.575176	+	0.818030i	$0.304934\pi$
$770$	−2.92855	−	6.60415i	−0.105538	−	0.237997i
$771$	−7.67532	−	9.62455i	−0.276420	−	0.346620i
$772$	16.9106	+	5.21622i	0.608625	+	0.187736i
$773$	−1.82645	+	4.65373i	−0.0656930	+	0.167383i	−0.959950	−	0.280170i	$-0.909609\pi$
$773$	−1.82645	+	4.65373i	−0.0656930	+	0.167383i	0.894257	+	0.447553i	$0.147704\pi$
$774$	−0.000762670	−	0.0101771i	−2.74136e−5	−	0.000365809i
$775$	−2.33073	−	5.93861i	−0.0837224	−	0.213321i
$776$	−5.33713	+	2.57023i	−0.191592	+	0.0922657i
$777$	1.22704	−	6.70456i	0.0440199	−	0.240525i
$778$	3.21645	+	1.54896i	0.115315	+	0.0555330i
$779$	1.25175	−	16.7034i	0.0448486	−	0.598463i
$780$	−4.35721	+	1.34402i	−0.156013	+	0.0481236i
$781$	−27.0586	−	18.4482i	−0.968233	−	0.660130i
$782$	0.355545	−	0.0535897i	0.0127142	−	0.00191636i
$783$	−15.9268			−0.569177
$784$	11.9784	+	24.1300i	0.427799	+	0.861785i
$785$	−33.0634			−1.18008
$786$	2.56438	−	0.386518i	0.0914685	−	0.0137867i
$787$	−7.15505	−	4.87823i	−0.255050	−	0.173890i	0.429045	−	0.903283i	$-0.358850\pi$
$787$	−7.15505	−	4.87823i	−0.255050	−	0.173890i	−0.684095	+	0.729393i	$0.739803\pi$
$788$	−28.0153	+	8.64159i	−0.998005	+	0.307844i
$789$	−0.188721	+	2.51831i	−0.00671866	+	0.0896543i
$790$	−5.69968	−	2.74482i	−0.202786	−	0.0976564i
$791$	−13.3166	+	0.578125i	−0.473485	+	0.0205558i
$792$	7.65857	−	3.68817i	0.272135	−	0.131054i
$793$	−2.82716	−	7.20349i	−0.100395	−	0.255803i
$794$	0.0448296	+	0.598209i	0.00159094	+	0.0212296i
$795$	6.94950	−	17.7070i	0.246473	−	0.628004i
$796$	−32.5883	−	10.0521i	−1.15506	−	0.356289i
$797$	−16.3657	−	20.5219i	−0.579701	−	0.726922i	0.402361	−	0.915481i	$-0.368190\pi$
$797$	−16.3657	−	20.5219i	−0.579701	−	0.726922i	−0.982062	+	0.188559i	$0.939618\pi$
$798$	−2.31351	−	0.605081i	−0.0818972	−	0.0214196i
$799$	54.6075	−	68.4757i	1.93188	−	2.42250i
$800$	7.53952	−	5.14036i	0.266562	−	0.181739i
$801$	9.18723	−	8.52451i	0.324615	−	0.301199i
$802$	−2.49267	−	4.31743i	−0.0880192	−	0.152454i
$803$	−6.81530	+	11.8044i	−0.240507	+	0.416570i
$804$	−2.28737	−	10.0216i	−0.0806692	−	0.353435i
$805$	−2.42747	−	0.258804i	−0.0855572	−	0.00912163i
$806$	0.0465397	−	0.203904i	0.00163929	−	0.00718221i
$807$	−1.86724	−	1.73254i	−0.0657299	−	0.0609884i
$808$	−2.49791	−	0.376499i	−0.0878761	−	0.0132452i
$809$	47.4321	+	7.14924i	1.66762	+	0.251354i	0.913930	−	0.405872i	$-0.133032\pi$
$809$	47.4321	+	7.14924i	1.66762	+	0.251354i	0.753694	+	0.657226i	$0.228270\pi$
$810$	−1.62138	−	1.50442i	−0.0569694	−	0.0528598i
$811$	5.31889	−	23.3036i	0.186771	−	0.818299i	−0.791533	−	0.611126i	$-0.790717\pi$
$811$	5.31889	−	23.3036i	0.186771	−	0.818299i	0.978304	−	0.207172i	$-0.0664261\pi$
$812$	−6.72743	+	19.6015i	−0.236087	+	0.687879i
$813$	0.178157	+	0.780558i	0.00624825	+	0.0273754i
$814$	−1.52314	+	2.63815i	−0.0533860	+	0.0924673i
$815$	−9.95665	−	17.2454i	−0.348766	−	0.604081i
$816$	15.9421	−	14.7921i	0.558086	−	0.517828i
$817$	−0.166186	+	0.113303i	−0.00581410	+	0.00396399i
$818$	0.517450	−	0.648862i	0.0180922	−	0.0226869i
$819$	6.38526	−	1.24780i	0.223119	−	0.0436015i
$820$	8.38986	+	10.5206i	0.292987	+	0.367394i
$821$	35.1988	+	10.8574i	1.22845	+	0.378926i	0.840021	−	0.542554i	$-0.182543\pi$
$821$	35.1988	+	10.8574i	1.22845	+	0.378926i	0.388426	+	0.921480i	$0.373019\pi$
$822$	−0.284273	+	0.724316i	−0.00991517	+	0.0252634i
$823$	1.39296	+	18.5878i	0.0485556	+	0.647930i	0.967391	+	0.253288i	$0.0815121\pi$
$823$	1.39296	+	18.5878i	0.0485556	+	0.647930i	−0.918835	+	0.394641i	$0.870869\pi$
$824$	0.616049	+	1.56967i	0.0214611	+	0.0546819i
$825$	17.5793	−	8.46574i	0.612032	−	0.294739i
$826$	−1.83014	+	2.51108i	−0.0636788	+	0.0873716i
$827$	−33.1314	−	15.9553i	−1.15209	−	0.554819i	−0.242431	−	0.970169i	$-0.577945\pi$
$827$	−33.1314	−	15.9553i	−1.15209	−	0.554819i	−0.909662	+	0.415350i	$0.863659\pi$
$828$	0.106643	−	1.42306i	0.00370611	−	0.0494547i
$829$	−29.8826	+	9.21755i	−1.03786	+	0.320139i	−0.766437	−	0.642320i	$-0.777972\pi$
$829$	−29.8826	+	9.21755i	−1.03786	+	0.320139i	−0.271428	+	0.962459i	$0.587496\pi$
$830$	3.65910	+	2.49473i	0.127009	+	0.0865934i
$831$	−4.27077	+	0.643715i	−0.148151	+	0.0223302i
$832$	−7.39785			−0.256474
$833$	30.8265	+	44.0711i	1.06808	+	1.52697i
$834$	0.465459			0.0161175
$835$	17.0463	−	2.56931i	0.589911	−	0.0889148i
$836$	−68.7671	−	46.8846i	−2.37836	−	1.62154i
$837$	5.03923	−	1.55440i	0.174181	−	0.0537278i
$838$	−0.0302750	+	0.403992i	−0.00104583	+	0.0139557i
$839$	−22.1437	−	10.6638i	−0.764484	−	0.368156i	0.0106580	−	0.999943i	$-0.496607\pi$
$839$	−22.1437	−	10.6638i	−0.764484	−	0.368156i	−0.775142	+	0.631787i	$0.782322\pi$
$840$	3.40782	−	1.82727i	0.117581	−	0.0630467i
$841$	11.9514	−	5.75547i	0.412116	−	0.198465i
$842$	0.747403	+	1.90435i	0.0257572	+	0.0656283i
$843$	0.876150	+	11.6914i	0.0301762	+	0.402674i
$844$	−16.2016	+	41.2811i	−0.557683	+	1.42095i
$845$	3.00014	+	0.925420i	0.103208	+	0.0318354i
$846$	2.78309	+	3.48988i	0.0956846	+	0.119985i
$847$	1.56471	−	49.7940i	0.0537640	−	1.71094i
$848$	19.7661	−	24.7859i	0.678770	−	0.851150i
$849$	−19.4754	+	13.2781i	−0.668394	+	0.455703i
$850$	4.35626	−	4.04202i	0.149418	−	0.138640i
$851$	0.514695	+	0.891478i	0.0176435	+	0.0305595i
$852$	4.35424	−	7.54177i	0.149174	−	0.258377i
$853$	3.76855	+	16.5111i	0.129033	+	0.565329i	0.997568	+	0.0697017i	$0.0222047\pi$
$853$	3.76855	+	16.5111i	0.129033	+	0.565329i	−0.868535	+	0.495628i	$0.834938\pi$
$854$	1.75105	+	2.75009i	0.0599196	+	0.0941062i
$855$	−13.2580	+	58.0872i	−0.453415	+	1.98654i
$856$	7.61248	+	7.06335i	0.260189	+	0.241420i
$857$	−19.2887	−	2.90731i	−0.658890	−	0.0993117i	−0.188918	−	0.981993i	$-0.560498\pi$
$857$	−19.2887	−	2.90731i	−0.658890	−	0.0993117i	−0.469972	+	0.882681i	$0.655736\pi$
$858$	0.632517	+	0.0953367i	0.0215938	+	0.00325474i
$859$	−0.0765562	−	0.0710337i	−0.00261206	−	0.00242364i	0.678866	−	0.734263i	$-0.262472\pi$
$859$	−0.0765562	−	0.0710337i	−0.00261206	−	0.00242364i	−0.681478	+	0.731839i	$0.738662\pi$
$860$	0.0359552	−	0.157530i	0.00122606	−	0.00537174i
$861$	2.26848	+	3.56274i	0.0773096	+	0.121418i
$862$	−0.264000	−	1.15666i	−0.00899188	−	0.0393960i
$863$	−22.0882	+	38.2579i	−0.751891	+	1.30231i	0.195014	+	0.980800i	$0.437525\pi$
$863$	−22.0882	+	38.2579i	−0.751891	+	1.30231i	−0.946905	+	0.321513i	$0.895809\pi$
$864$	3.77150	+	6.53243i	0.128309	+	0.222238i
$865$	48.5580	−	45.0552i	1.65102	−	1.53192i
$866$	0.412546	−	0.281269i	0.0140189	−	0.00955792i
$867$	19.2744	−	24.1693i	0.654593	−	0.820834i
$868$	0.215518	−	6.85848i	0.00731517	−	0.232792i
$869$	−43.0892	−	54.0322i	−1.46170	−	1.83292i
$870$	1.39380	+	0.429931i	0.0472543	+	0.0145760i
$871$	−2.58581	+	6.58853i	−0.0876168	+	0.223244i
$872$	0.390761	+	5.21435i	0.0132329	+	0.176580i
$873$	8.40848	+	21.4245i	0.284584	+	0.725108i
$874$	0.325389	−	0.156699i	0.0110065	−	0.00530043i
$875$	1.04513	−	0.560396i	0.0353318	−	0.0189448i
$876$	−3.26564	−	1.57265i	−0.110336	−	0.0531348i
$877$	−2.34621	+	31.3080i	−0.0792259	+	1.05720i	0.805963	+	0.591965i	$0.201648\pi$
$877$	−2.34621	+	31.3080i	−0.0792259	+	1.05720i	−0.885189	+	0.465231i	$0.845971\pi$
$878$	4.20946	−	1.29845i	0.142062	−	0.0438204i
$879$	11.3166	+	7.71552i	0.381699	+	0.260238i
$880$	65.2552	−	9.83564i	2.19975	−	0.331559i
$881$	−14.3520			−0.483530			−0.241765	−	0.970335i	$-0.577726\pi$
$881$	−14.3520			−0.483530			−0.241765	+	0.970335i	$0.577726\pi$
$882$	−2.53938	+	1.03189i	−0.0855054	+	0.0347455i
$883$	11.4019			0.383703			0.191852	−	0.981424i	$-0.438551\pi$
$883$	11.4019			0.383703			0.191852	+	0.981424i	$0.438551\pi$
$884$	−15.0021	+	2.26120i	−0.504575	+	0.0760525i
$885$	−14.0714	−	9.59375i	−0.473007	−	0.322490i
$886$	2.47237	−	0.762625i	0.0830609	−	0.0256209i
$887$	−4.12684	+	55.0689i	−0.138566	+	1.84903i	0.304461	+	0.952525i	$0.401524\pi$
$887$	−4.12684	+	55.0689i	−0.138566	+	1.84903i	−0.443027	+	0.896508i	$0.646095\pi$
$888$	−1.46903	−	0.707449i	−0.0492975	−	0.0237404i
$889$	31.9274	−	43.8066i	1.07081	−	1.46923i
$890$	−2.29572	+	1.10556i	−0.0769526	+	0.0370584i
$891$	−8.82766	−	22.4925i	−0.295738	−	0.753528i
$892$	−1.97049	−	26.2944i	−0.0659770	−	0.880402i
$893$	32.1398	−	81.8909i	1.07552	−	2.74037i
$894$	0.167605	+	0.0516992i	0.00560554	+	0.00172908i
$895$	−19.1732	−	24.0424i	−0.640889	−	0.803649i
$896$	12.8153	−	2.50434i	0.428129	−	0.0836642i
$897$	0.134769	−	0.168995i	0.00449981	−	0.00564258i
$898$	1.52044	−	1.03662i	0.0507376	−	0.0345923i
$899$	3.81920	−	3.54370i	0.127377	−	0.118189i
$900$	−11.7928	−	20.4257i	−0.393092	−	0.680855i
$901$	31.6454	−	54.8115i	1.05426	−	1.82603i
$902$	−0.420051	−	1.84037i	−0.0139862	−	0.0612775i
$903$	0.0164638	−	0.0479702i	0.000547882	−	0.00159635i
$904$	−0.709531	+	3.10866i	−0.0235986	+	0.103392i
$905$	41.1956	+	38.2239i	1.36939	+	1.27061i
$906$	1.75184	+	0.264048i	0.0582011	+	0.00877240i
$907$	32.4006	+	4.88361i	1.07585	+	0.162158i	0.662982	−	0.748635i	$-0.269291\pi$
$907$	32.4006	+	4.88361i	1.07585	+	0.162158i	0.412863	+	0.910793i	$0.364529\pi$
$908$	36.5181	+	33.8839i	1.21190	+	1.12448i
$909$	−2.18397	+	9.56860i	−0.0724377	+	0.317370i
$910$	−1.31529	−	0.140228i	−0.0436013	−	0.00464853i
$911$	11.0333	+	48.3399i	0.365548	+	1.60157i	0.738855	+	0.673864i	$0.235367\pi$
$911$	11.0333	+	48.3399i	0.365548	+	1.60157i	−0.373307	+	0.927708i	$0.621776\pi$
$912$	10.9220	−	18.9175i	0.361664	−	0.626420i
$913$	24.1900	+	41.8984i	0.800573	+	1.38663i
$914$	2.62923	−	2.43957i	0.0869671	−	0.0806937i
$915$	−14.7643	+	10.0661i	−0.488094	+	0.332777i
$916$	−5.14566	+	6.45245i	−0.170017	+	0.213195i
$917$	−56.6781	−	14.8238i	−1.87168	−	0.489524i
$918$	3.06277	+	3.84059i	0.101086	+	0.126758i
$919$	14.0984	+	4.34879i	0.465064	+	0.143453i	0.518427	−	0.855122i	$-0.326518\pi$
$919$	14.0984	+	4.34879i	0.465064	+	0.143453i	−0.0533627	+	0.998575i	$0.516994\pi$
$920$	−0.213356	+	0.543622i	−0.00703414	+	0.0179227i
$921$	−0.642252	−	8.57025i	−0.0211629	−	0.282399i
$922$	0.335857	+	0.855749i	0.0110609	+	0.0281826i
$923$	−5.40239	+	2.60165i	−0.177822	+	0.0856344i
$924$	20.9667	−	0.910245i	0.689755	−	0.0299449i
$925$	15.3284	+	7.38176i	0.503994	+	0.242711i
$926$	0.0776424	−	1.03607i	0.00255149	−	0.0340472i
$927$	6.26039	−	1.93107i	0.205618	−	0.0634248i
$928$	6.15726	+	4.19795i	0.202122	+	0.137804i
$929$	−34.9216	+	5.26358i	−1.14574	+	0.172692i	−0.694352	−	0.719636i	$-0.744309\pi$
$929$	−34.9216	+	5.26358i	−1.14574	+	0.172692i	−0.451387	+	0.892328i	$0.649071\pi$
$930$	−0.482957			−0.0158368
$931$	42.6354	+	33.1733i	1.39732	+	1.08721i
$932$	−6.75468			−0.221257
$933$	5.21430	−	0.785930i	0.170709	−	0.0257302i
$934$	−1.68823	−	1.15102i	−0.0552406	−	0.0376624i
$935$	125.894	−	38.8333i	4.11719	−	1.26998i
$936$	0.116308	−	1.55202i	0.00380164	−	0.0507294i
$937$	25.2385	+	12.1542i	0.824506	+	0.397061i	0.798052	−	0.602589i	$-0.205864\pi$
$937$	25.2385	+	12.1542i	0.824506	+	0.397061i	0.0264544	+	0.999650i	$0.491578\pi$
$938$	0.536822	−	2.93320i	0.0175279	−	0.0957722i
$939$	−4.84151	+	2.33155i	−0.157997	+	0.0760873i
$940$	25.8194	+	65.7868i	0.842137	+	2.14573i
$941$	0.542208	+	7.23526i	0.0176755	+	0.235863i	0.999044	+	0.0437258i	$0.0139228\pi$
$941$	0.542208	+	7.23526i	0.0176755	+	0.235863i	−0.981368	+	0.192137i	$0.938458\pi$
$942$	−0.450604	+	1.14812i	−0.0146815	+	0.0374078i
$943$	−0.609545	−	0.188020i	−0.0198495	−	0.00612276i
$944$	−17.6969	−	22.1913i	−0.575987	−	0.722264i
$945$	−13.5200	−	30.4888i	−0.439805	−	0.991801i
$946$	−0.0141328	+	0.0177219i	−0.000459495	+	0.000576189i
$947$	8.06065	−	5.49566i	0.261936	−	0.178585i	−0.425230	−	0.905085i	$-0.639807\pi$
$947$	8.06065	−	5.49566i	0.261936	−	0.178585i	0.687166	+	0.726500i	$0.258854\pi$
$948$	13.4715	−	12.4997i	0.437535	−	0.405973i
$949$	1.24785	+	2.16133i	0.0405068	+	0.0701598i
$950$	2.98449	−	5.16929i	0.0968297	−	0.167714i
$951$	2.22906	+	9.76616i	0.0722823	+	0.316690i
$952$	12.1182	−	4.32193i	0.392752	−	0.140074i
$953$	−6.52396	+	28.5833i	−0.211332	+	0.925905i	0.752331	+	0.658785i	$0.228929\pi$
$953$	−6.52396	+	28.5833i	−0.211332	+	0.925905i	−0.963663	+	0.267120i	$0.913928\pi$
$954$	2.36456	+	2.19399i	0.0765554	+	0.0710330i
$955$	9.46967	+	1.42732i	0.306431	+	0.0461871i
$956$	−44.3726	−	6.68810i	−1.43511	−	0.216309i
$957$	11.6807	+	10.8381i	0.377584	+	0.350347i
$958$	0.00194072	−	0.00850283i	6.27017e−5	−	0.000274714i
$959$	12.3546	−	12.5034i	0.398952	−	0.403757i
$960$	3.80130	+	16.6546i	0.122686	+	0.537524i
$961$	14.6375	−	25.3528i	0.472176	−	0.817833i
$962$	0.278879	+	0.483032i	0.00899142	+	0.0155736i
$963$	29.5766	−	27.4430i	0.953091	−	0.884339i
$964$	−12.4070	+	8.45897i	−0.399604	+	0.272445i
$965$	−17.5434	+	21.9987i	−0.564741	+	0.708163i
$966$	−0.0420697	+	0.0807665i	−0.00135357	+	0.00259862i
$967$	−20.3653	−	25.5373i	−0.654905	−	0.821225i	0.337873	−	0.941192i	$-0.390293\pi$
$967$	−20.3653	−	25.5373i	−0.654905	−	0.821225i	−0.992778	+	0.119967i	$0.961721\pi$
$968$	−11.3881	−	3.51277i	−0.366028	−	0.112905i
$969$	15.9324	−	40.5951i	0.511822	−	1.30410i
$970$	−0.349682	−	4.66618i	−0.0112276	−	0.149822i
$971$	10.9736	+	27.9603i	0.352160	+	0.897289i	0.991705	+	0.128535i	$0.0410275\pi$
$971$	10.9736	+	27.9603i	0.352160	+	0.897289i	−0.639545	+	0.768754i	$0.720877\pi$
$972$	27.2186	−	13.1078i	0.873037	−	0.420432i
$973$	−9.66253	−	4.14704i	−0.309767	−	0.132948i
$974$	−4.08012	−	1.96488i	−0.130736	−	0.0629590i
$975$	0.266970	−	3.56247i	0.00854989	−	0.114090i
$976$	−28.4582	+	8.77820i	−0.910925	+	0.280983i
$977$	−3.09866	−	2.11263i	−0.0991348	−	0.0675890i	0.512738	−	0.858545i	$-0.328631\pi$
$977$	−3.09866	−	2.11263i	−0.0991348	−	0.0675890i	−0.611873	+	0.790956i	$0.709584\pi$
$978$	−0.734537	+	0.110714i	−0.0234879	+	0.00354023i
$979$	−27.8360			−0.889642
$980$	−43.2342	+	3.76100i	−1.38106	+	0.120141i
$981$	20.3160			0.648639
$982$	0.867678	−	0.130781i	0.0276887	−	0.00417340i
$983$	21.0417	+	14.3460i	0.671127	+	0.457567i	0.850333	−	0.526245i	$-0.176400\pi$
$983$	21.0417	+	14.3460i	0.671127	+	0.457567i	−0.179206	+	0.983812i	$0.557353\pi$
$984$	0.965490	−	0.297814i	0.0307787	−	0.00949397i
$985$	3.48351	−	46.4842i	0.110994	−	1.48111i
$986$	4.37253	+	2.10570i	0.139250	+	0.0670591i
$987$	5.86940	+	21.3918i	0.186825	+	0.680909i
$988$	−13.7297	+	6.61188i	−0.436800	+	0.210352i
$989$	0.00279838	+	0.00713014i	8.89832e−5	+	0.000226725i
$990$	0.501779	+	6.69578i	0.0159476	+	0.212806i
$991$	−21.7284	+	55.3630i	−0.690225	+	1.75866i	−0.0396605	+	0.999213i	$0.512628\pi$
$991$	−21.7284	+	55.3630i	−0.690225	+	1.75866i	−0.650564	+	0.759451i	$0.725468\pi$
$992$	−2.35786	−	0.727302i	−0.0748620	−	0.0230919i
$993$	2.76987	+	3.47331i	0.0878992	+	0.110222i
$994$	2.02358	−	1.51227i	0.0641842	−	0.0479663i
$995$	33.8077	−	42.3935i	1.07178	−	1.34397i
$996$	−10.6296	+	7.24711i	−0.336810	+	0.229633i
$997$	−29.4780	+	27.3516i	−0.933576	+	0.866232i	−0.991236	−	0.132104i	$-0.957827\pi$
$997$	−29.4780	+	27.3516i	−0.933576	+	0.866232i	0.0576594	+	0.998336i	$0.481636\pi$
$998$	0.0366078	+	0.0634066i	0.00115880	+	0.00200710i
$999$	−7.03174	+	12.1793i	−0.222474	+	0.385337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.534.15	yes	348
49.39	even	21	inner	637.2.bl.b.235.15	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.235.15	✓	348	49.39	even	21	inner
637.2.bl.b.534.15	yes	348	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.157460 + 0.0237333i) q^{2} +(0.607692 + 0.414318i) q^{3} +(-1.88692 + 0.582036i) q^{4} +(0.234624 - 3.13084i) q^{5} +(-0.105520 - 0.0508159i) q^{6} +(1.73776 + 1.99504i) q^{7} +(0.570238 - 0.274612i) q^{8} +(-0.898392 - 2.28907i) q^{9} +O(q^{10})\)	\(q+(-0.157460 + 0.0237333i) q^{2} +(0.607692 + 0.414318i) q^{3} +(-1.88692 + 0.582036i) q^{4} +(0.234624 - 3.13084i) q^{5} +(-0.105520 - 0.0508159i) q^{6} +(1.73776 + 1.99504i) q^{7} +(0.570238 - 0.274612i) q^{8} +(-0.898392 - 2.28907i) q^{9} +(0.0373612 + 0.498551i) q^{10} +(-1.99537 + 5.08411i) q^{11} +(-1.38781 - 0.428083i) q^{12} +(0.623490 + 0.781831i) q^{13} +(-0.320977 - 0.272896i) q^{14} +(1.43974 - 1.80538i) q^{15} +(3.17978 - 2.16794i) q^{16} +(5.63217 - 5.22589i) q^{17} +(0.195788 + 0.339115i) q^{18} +(3.85863 - 6.68334i) q^{19} +(1.37955 + 6.04420i) q^{20} +(0.229447 + 1.93236i) q^{21} +(0.193528 - 0.847900i) q^{22} +(-0.215435 - 0.199895i) q^{23} +(0.460306 + 0.0693800i) q^{24} +(-4.80298 - 0.723933i) q^{25} +(-0.116730 - 0.108310i) q^{26} +(0.893442 - 3.91442i) q^{27} +(-4.44020 - 2.75302i) q^{28} +(-0.882682 - 3.86728i) q^{29} +(-0.183854 + 0.318445i) q^{30} +(0.656712 + 1.13746i) q^{31} +(-1.37716 + 1.27782i) q^{32} +(-3.31900 + 2.26286i) q^{33} +(-0.762815 + 0.956539i) q^{34} +(6.65387 - 4.97259i) q^{35} +(3.02751 + 3.79638i) q^{36} +(-3.34704 - 1.03243i) q^{37} +(-0.448962 + 1.14394i) q^{38} +(0.0549634 + 0.733436i) q^{39} +(-0.725976 - 1.84976i) q^{40} +(1.95555 - 0.941744i) q^{41} +(-0.0819899 - 0.298823i) q^{42} +(-0.0234820 - 0.0113083i) q^{43} +(0.805950 - 10.7547i) q^{44} +(-7.37749 + 2.27566i) q^{45} +(0.0386666 + 0.0263625i) q^{46} +(11.2721 - 1.69899i) q^{47} +2.83054 q^{48} +(-0.960347 + 6.93381i) q^{49} +0.773459 q^{50} +(5.58781 - 0.842227i) q^{51} +(-1.63153 - 1.11236i) q^{52} +(7.87160 - 2.42807i) q^{53} +(-0.0477792 + 0.637570i) q^{54} +(15.4494 + 7.44003i) q^{55} +(1.53880 + 0.660435i) q^{56} +(5.11388 - 2.46272i) q^{57} +(0.230770 + 0.587993i) q^{58} +(-0.551154 - 7.35464i) q^{59} +(-1.66588 + 4.24458i) q^{60} +(-7.39462 - 2.28094i) q^{61} +(-0.130401 - 0.163518i) q^{62} +(3.00558 - 5.77018i) q^{63} +(-4.61248 + 5.78387i) q^{64} +(2.59408 - 1.76861i) q^{65} +(0.468905 - 0.435081i) q^{66} +(3.53890 + 6.12955i) q^{67} +(-7.58578 + 13.1389i) q^{68} +(-0.0480985 - 0.210733i) q^{69} +(-0.929703 + 0.940902i) q^{70} +(-1.33428 + 5.84586i) q^{71} +(-1.14090 - 1.05860i) q^{72} +(2.46782 + 0.371964i) q^{73} +(0.551528 + 0.0831295i) q^{74} +(-2.61880 - 2.42989i) q^{75} +(-3.39096 + 14.8568i) q^{76} +(-13.6105 + 4.85416i) q^{77} +(-0.0260614 - 0.114182i) q^{78} +(-6.32682 + 10.9584i) q^{79} +(-6.04142 - 10.4641i) q^{80} +(-3.24308 + 3.00914i) q^{81} +(-0.285570 + 0.194699i) q^{82} +(5.52296 - 6.92557i) q^{83} +(-1.55765 - 3.51264i) q^{84} +(-15.0400 - 18.8596i) q^{85} +(0.00396586 + 0.00122331i) q^{86} +(1.06588 - 2.71583i) q^{87} +(0.258325 + 3.44710i) q^{88} +(1.86201 + 4.74431i) q^{89} +(1.10765 - 0.533417i) q^{90} +(-0.476304 + 2.60252i) q^{91} +(0.522854 + 0.251793i) q^{92} +(-0.0721902 + 0.963312i) q^{93} +(-1.73458 + 0.535047i) q^{94} +(-20.0192 - 13.6488i) q^{95} +(-1.36631 + 0.205938i) q^{96} -9.35947 q^{97} +(-0.0133459 - 1.11459i) q^{98} +13.4305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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