LMFDB - Embedded newform 731.2.bd.a.7.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(7,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([33, 40]))

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

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

chi := DirichletCharacter("731.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.bd (of order $48$, degree $16$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.13
Character	$\chi$	$=$	731.7
Dual form			731.2.bd.a.209.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74510 - 0.722845i) q^{2} +(-0.119895 + 1.82924i) q^{3} +(1.10866 + 1.10866i) q^{4} +(0.813236 + 0.927317i) q^{5} +(1.53149 - 3.10555i) q^{6} +(-2.47493 + 2.82212i) q^{7} +(0.312353 + 0.754087i) q^{8} +(-0.357413 - 0.0470543i) q^{9} +O(q^{10})$	\(q+(-1.74510 - 0.722845i) q^{2} +(-0.119895 + 1.82924i) q^{3} +(1.10866 + 1.10866i) q^{4} +(0.813236 + 0.927317i) q^{5} +(1.53149 - 3.10555i) q^{6} +(-2.47493 + 2.82212i) q^{7} +(0.312353 + 0.754087i) q^{8} +(-0.357413 - 0.0470543i) q^{9} +(-0.748872 - 2.20611i) q^{10} +(1.64746 - 1.10080i) q^{11} +(-2.16093 + 1.89509i) q^{12} +(0.371553 + 1.38665i) q^{13} +(6.35895 - 3.13589i) q^{14} +(-1.79379 + 1.37642i) q^{15} -4.67751i q^{16} +(3.76392 + 1.68312i) q^{17} +(0.589708 + 0.340468i) q^{18} +(1.09851 + 8.34403i) q^{19} +(-0.126478 + 1.92968i) q^{20} +(-4.86560 - 4.86560i) q^{21} +(-3.67070 + 0.730147i) q^{22} +(-0.573720 + 1.16339i) q^{23} +(-1.41686 + 0.480958i) q^{24} +(0.454065 - 3.44897i) q^{25} +(0.353938 - 2.68843i) q^{26} +(-0.943973 + 4.74567i) q^{27} +(-5.87263 + 0.384912i) q^{28} +(-1.18881 - 0.403548i) q^{29} +(4.12529 - 1.10537i) q^{30} +(0.177565 - 2.70911i) q^{31} +(-2.75641 + 6.65455i) q^{32} +(1.81611 + 3.14559i) q^{33} +(-5.35179 - 5.65795i) q^{34} -4.62970 q^{35} +(-0.344082 - 0.448417i) q^{36} +(0.430686 - 6.57100i) q^{37} +(4.11442 - 15.3552i) q^{38} +(-2.58107 + 0.513407i) q^{39} +(-0.445261 + 0.902901i) q^{40} +(-0.00691467 + 0.0347624i) q^{41} +(4.97389 + 12.0080i) q^{42} +(3.10469 - 5.77589i) q^{43} +(3.04689 + 0.606064i) q^{44} +(-0.247026 - 0.369701i) q^{45} +(1.84215 - 1.61552i) q^{46} +(-7.63631 + 7.63631i) q^{47} +(8.55629 + 0.560809i) q^{48} +(-0.925379 - 7.02895i) q^{49} +(-3.28546 + 5.69058i) q^{50} +(-3.53011 + 6.68332i) q^{51} +(-1.12540 + 1.94926i) q^{52} +(-7.05380 + 0.928651i) q^{53} +(5.07771 - 7.59934i) q^{54} +(2.36057 + 0.632512i) q^{55} +(-2.90117 - 0.984815i) q^{56} +(-15.3949 + 1.00904i) q^{57} +(1.78290 + 1.56356i) q^{58} +(5.00514 - 2.07320i) q^{59} +(-3.51469 - 0.462718i) q^{60} +(1.63818 + 1.43664i) q^{61} +(-2.26814 + 4.59933i) q^{62} +(1.01736 - 0.892204i) q^{63} +(3.00542 - 3.00542i) q^{64} +(-0.983709 + 1.47222i) q^{65} +(-0.895517 - 6.80213i) q^{66} +(-11.2648 + 6.50374i) q^{67} +(2.30690 + 6.03893i) q^{68} +(-2.05933 - 1.18896i) q^{69} +(8.07929 + 3.34655i) q^{70} +(-3.68034 + 1.81494i) q^{71} +(-0.0761559 - 0.284218i) q^{72} +(-3.68428 + 10.8535i) q^{73} +(-5.50140 + 11.1557i) q^{74} +(6.25456 + 1.24411i) q^{75} +(-8.03282 + 10.4686i) q^{76} +(-0.970770 + 7.37373i) q^{77} +(4.87535 + 0.969767i) q^{78} +(-0.768349 - 11.7227i) q^{79} +(4.33754 - 3.80392i) q^{80} +(-9.61244 - 2.57565i) q^{81} +(0.0371946 - 0.0556657i) q^{82} +(1.28748 + 9.77936i) q^{83} -10.7886i q^{84} +(1.50016 + 4.85912i) q^{85} +(-9.59307 + 7.83531i) q^{86} +(0.880719 - 2.12624i) q^{87} +(1.34469 + 0.898492i) q^{88} +(-11.0340 - 2.95656i) q^{89} +(0.163850 + 0.823728i) q^{90} +(-4.83287 - 2.38331i) q^{91} +(-1.92586 + 0.653743i) q^{92} +(4.93433 + 0.649617i) q^{93} +(18.8460 - 7.80627i) q^{94} +(-6.84421 + 7.80433i) q^{95} +(-11.8423 - 5.83998i) q^{96} +(12.2493 - 2.43655i) q^{97} +(-3.46596 + 12.9351i) q^{98} +(-0.640621 + 0.315920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 24 q^{3} - 32 q^{4} - 24 q^{5} - 8 q^{6} - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 1024 * q - 24 * q^3 - 32 * q^4 - 24 * q^5 - 8 * q^6 - 24 * q^7 - 8 * q^9	$ 1024 q - 24 q^{3} - 32 q^{4} - 24 q^{5} - 8 q^{6} - 24 q^{7} - 8 q^{9} - 8 q^{10} - 48 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{17} - 48 q^{18} - 24 q^{19} - 24 q^{20} - 32 q^{21} + 40 q^{24} - 24 q^{25} - 24 q^{26} - 24 q^{28} - 24 q^{29} - 24 q^{30} + 24 q^{31} - 24 q^{34} - 192 q^{35} + 8 q^{36} - 24 q^{37} - 16 q^{38} - 8 q^{40} - 32 q^{41} + 24 q^{43} + 32 q^{44} + 72 q^{46} + 48 q^{47} + 48 q^{48} - 8 q^{49} - 144 q^{52} - 8 q^{53} + 144 q^{54} + 72 q^{55} - 8 q^{56} - 24 q^{57} - 128 q^{58} + 96 q^{59} - 112 q^{60} + 24 q^{61} - 192 q^{62} - 24 q^{63} + 192 q^{64} - 136 q^{66} - 8 q^{68} - 96 q^{69} - 24 q^{71} - 432 q^{72} - 24 q^{73} + 88 q^{74} + 144 q^{76} - 24 q^{77} - 496 q^{78} - 40 q^{79} + 264 q^{80} - 120 q^{81} - 16 q^{83} - 48 q^{86} - 32 q^{87} - 24 q^{89} - 112 q^{90} - 24 q^{91} + 184 q^{92} + 168 q^{93} + 72 q^{95} + 40 q^{96} - 160 q^{97} - 432 q^{98} + 8 q^{99}+O(q^{100}) $ 1024 * q - 24 * q^3 - 32 * q^4 - 24 * q^5 - 8 * q^6 - 24 * q^7 - 8 * q^9 - 8 * q^10 - 48 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^17 - 48 * q^18 - 24 * q^19 - 24 * q^20 - 32 * q^21 + 40 * q^24 - 24 * q^25 - 24 * q^26 - 24 * q^28 - 24 * q^29 - 24 * q^30 + 24 * q^31 - 24 * q^34 - 192 * q^35 + 8 * q^36 - 24 * q^37 - 16 * q^38 - 8 * q^40 - 32 * q^41 + 24 * q^43 + 32 * q^44 + 72 * q^46 + 48 * q^47 + 48 * q^48 - 8 * q^49 - 144 * q^52 - 8 * q^53 + 144 * q^54 + 72 * q^55 - 8 * q^56 - 24 * q^57 - 128 * q^58 + 96 * q^59 - 112 * q^60 + 24 * q^61 - 192 * q^62 - 24 * q^63 + 192 * q^64 - 136 * q^66 - 8 * q^68 - 96 * q^69 - 24 * q^71 - 432 * q^72 - 24 * q^73 + 88 * q^74 + 144 * q^76 - 24 * q^77 - 496 * q^78 - 40 * q^79 + 264 * q^80 - 120 * q^81 - 16 * q^83 - 48 * q^86 - 32 * q^87 - 24 * q^89 - 112 * q^90 - 24 * q^91 + 184 * q^92 + 168 * q^93 + 72 * q^95 + 40 * q^96 - 160 * q^97 - 432 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.74510	−	0.722845i	−1.23397	−	0.511128i	−0.332147	−	0.943228i	$-0.607773\pi$
$2$	−1.74510	−	0.722845i	−1.23397	−	0.511128i	−0.901826	+	0.432099i	$0.857773\pi$
$3$	−0.119895	+	1.82924i	−0.0692213	+	1.05611i	0.812076	+	0.583551i	$0.198337\pi$
$3$	−0.119895	+	1.82924i	−0.0692213	+	1.05611i	−0.881298	+	0.472562i	$0.843329\pi$
$4$	1.10866	+	1.10866i	0.554331	+	0.554331i
$5$	0.813236	+	0.927317i	0.363690	+	0.414709i	0.904526	−	0.426419i	$-0.140225\pi$
$5$	0.813236	+	0.927317i	0.363690	+	0.414709i	−0.540836	+	0.841128i	$0.681892\pi$
$6$	1.53149	−	3.10555i	0.625226	−	1.26783i
$7$	−2.47493	+	2.82212i	−0.935435	+	1.06666i	0.0622094	+	0.998063i	$0.480185\pi$
$7$	−2.47493	+	2.82212i	−0.935435	+	1.06666i	−0.997645	+	0.0685962i	$0.978148\pi$
$8$	0.312353	+	0.754087i	0.110433	+	0.266610i
$9$	−0.357413	−	0.0470543i	−0.119138	−	0.0156848i
$10$	−0.748872	−	2.20611i	−0.236814	−	0.697632i
$11$	1.64746	−	1.10080i	0.496729	−	0.331904i	−0.281841	−	0.959461i	$-0.590945\pi$
$11$	1.64746	−	1.10080i	0.496729	−	0.331904i	0.778570	+	0.627557i	$0.215945\pi$
$12$	−2.16093	+	1.89509i	−0.623807	+	0.547064i
$13$	0.371553	+	1.38665i	0.103050	+	0.384589i	0.998117	−	0.0613440i	$-0.0195387\pi$
$13$	0.371553	+	1.38665i	0.103050	+	0.384589i	−0.895066	+	0.445933i	$0.852872\pi$
$14$	6.35895	−	3.13589i	1.69950	−	0.838101i
$15$	−1.79379	+	1.37642i	−0.463155	+	0.355391i
$16$		−	4.67751i		−	1.16938i
$17$	3.76392	+	1.68312i	0.912885	+	0.408217i
$17$	3.76392	+	1.68312i	0.912885	+	0.408217i
$18$	0.589708	+	0.340468i	0.138996	+	0.0802491i
$19$	1.09851	+	8.34403i	0.252016	+	1.91425i	0.384608	+	0.923080i	$0.374337\pi$
$19$	1.09851	+	8.34403i	0.252016	+	1.91425i	−0.132592	+	0.991171i	$0.542330\pi$
$20$	−0.126478	+	1.92968i	−0.0282814	+	0.431490i
$21$	−4.86560	−	4.86560i	−1.06176	−	1.06176i
$22$	−3.67070	+	0.730147i	−0.782595	+	0.155668i
$23$	−0.573720	+	1.16339i	−0.119629	+	0.242583i	−0.948448	−	0.316934i	$-0.897347\pi$
$23$	−0.573720	+	1.16339i	−0.119629	+	0.242583i	0.828819	+	0.559517i	$0.189013\pi$
$24$	−1.41686	+	0.480958i	−0.289215	+	0.0981751i
$25$	0.454065	−	3.44897i	0.0908131	−	0.689794i
$26$	0.353938	−	2.68843i	0.0694130	−	0.527244i
$27$	−0.943973	+	4.74567i	−0.181668	+	0.913305i
$28$	−5.87263	+	0.384912i	−1.10982	+	0.0727416i
$29$	−1.18881	−	0.403548i	−0.220757	−	0.0749370i	0.208870	−	0.977943i	$-0.433022\pi$
$29$	−1.18881	−	0.403548i	−0.220757	−	0.0749370i	−0.429627	+	0.903007i	$0.641355\pi$
$30$	4.12529	−	1.10537i	0.753171	−	0.201811i
$31$	0.177565	−	2.70911i	0.0318916	−	0.486571i	−0.951801	−	0.306715i	$-0.900770\pi$
$31$	0.177565	−	2.70911i	0.0318916	−	0.486571i	0.983693	−	0.179856i	$-0.0575632\pi$
$32$	−2.75641	+	6.65455i	−0.487268	+	1.17637i
$33$	1.81611	+	3.14559i	0.316143	+	0.547576i
$34$	−5.35179	−	5.65795i	−0.917824	−	0.970330i
$35$	−4.62970			−0.782562
$36$	−0.344082	−	0.448417i	−0.0573470	−	0.0747361i
$37$	0.430686	−	6.57100i	0.0708044	−	1.08027i	−0.803632	−	0.595126i	$-0.797102\pi$
$37$	0.430686	−	6.57100i	0.0708044	−	1.08027i	0.874437	−	0.485140i	$-0.161231\pi$
$38$	4.11442	−	15.3552i	0.667447	−	2.49095i
$39$	−2.58107	+	0.513407i	−0.413302	+	0.0822110i
$40$	−0.445261	+	0.902901i	−0.0704020	+	0.142761i
$41$	−0.00691467	+	0.0347624i	−0.00107989	+	0.00542898i	−0.981321	−	0.192375i	$-0.938381\pi$
$41$	−0.00691467	+	0.0347624i	−0.00107989	+	0.00542898i	0.980242	+	0.197804i	$0.0633810\pi$
$42$	4.97389	+	12.0080i	0.767488	+	1.85288i
$43$	3.10469	−	5.77589i	0.473461	−	0.880815i
$43$	3.10469	−	5.77589i	0.473461	−	0.880815i
$44$	3.04689	+	0.606064i	0.459336	+	0.0913677i
$45$	−0.247026	−	0.369701i	−0.0368245	−	0.0551118i
$46$	1.84215	−	1.61552i	0.271610	−	0.238196i
$47$	−7.63631	+	7.63631i	−1.11387	+	1.11387i	−0.121248	+	0.992622i	$0.538690\pi$
$47$	−7.63631	+	7.63631i	−1.11387	+	1.11387i	−0.992622	+	0.121248i	$0.961310\pi$
$48$	8.55629	+	0.560809i	1.23499	+	0.0809458i
$49$	−0.925379	−	7.02895i	−0.132197	−	1.00414i
$50$	−3.28546	+	5.69058i	−0.464634	+	0.804770i
$51$	−3.53011	+	6.68332i	−0.494315	+	0.935852i
$52$	−1.12540	+	1.94926i	−0.156065	+	0.270313i
$53$	−7.05380	+	0.928651i	−0.968914	+	0.127560i	−0.598340	−	0.801243i	$-0.704173\pi$
$53$	−7.05380	+	0.928651i	−0.968914	+	0.127560i	−0.370575	+	0.928803i	$0.620839\pi$
$54$	5.07771	−	7.59934i	0.690989	−	1.03414i
$55$	2.36057	+	0.632512i	0.318299	+	0.0852879i
$56$	−2.90117	−	0.984815i	−0.387685	−	0.131601i
$57$	−15.3949	+	1.00904i	−2.03911	+	0.133650i
$58$	1.78290	+	1.56356i	0.234106	+	0.205305i
$59$	5.00514	−	2.07320i	0.651614	−	0.269907i	−0.0322911	−	0.999479i	$-0.510280\pi$
$59$	5.00514	−	2.07320i	0.651614	−	0.269907i	0.683905	+	0.729571i	$0.260280\pi$
$60$	−3.51469	−	0.462718i	−0.453745	−	0.0597366i
$61$	1.63818	+	1.43664i	0.209747	+	0.183943i	0.757773	−	0.652518i	$-0.226287\pi$
$61$	1.63818	+	1.43664i	0.209747	+	0.183943i	−0.548026	+	0.836461i	$0.684621\pi$
$62$	−2.26814	+	4.59933i	−0.288054	+	0.584115i
$63$	1.01736	−	0.892204i	0.128176	−	0.112407i
$64$	3.00542	−	3.00542i	0.375678	−	0.375678i
$65$	−0.983709	+	1.47222i	−0.122014	+	0.182607i
$66$	−0.895517	−	6.80213i	−0.110231	−	0.837284i
$67$	−11.2648	+	6.50374i	−1.37622	+	0.794558i	−0.991702	−	0.128561i	$-0.958964\pi$
$67$	−11.2648	+	6.50374i	−1.37622	+	0.794558i	−0.384514	+	0.923119i	$0.625631\pi$
$68$	2.30690	+	6.03893i	0.279753	+	0.732327i
$69$	−2.05933	−	1.18896i	−0.247914	−	0.143133i
$70$	8.07929	+	3.34655i	0.965660	+	0.399989i
$71$	−3.68034	+	1.81494i	−0.436775	+	0.215394i	−0.647364	−	0.762181i	$-0.724129\pi$
$71$	−3.68034	+	1.81494i	−0.436775	+	0.215394i	0.210589	+	0.977575i	$0.432462\pi$
$72$	−0.0761559	−	0.284218i	−0.00897506	−	0.0334954i
$73$	−3.68428	+	10.8535i	−0.431212	+	1.27031i	0.486715	+	0.873561i	$0.338195\pi$
$73$	−3.68428	+	10.8535i	−0.431212	+	1.27031i	−0.917927	+	0.396749i	$0.870138\pi$
$74$	−5.50140	+	11.1557i	−0.639525	+	1.29683i
$75$	6.25456	+	1.24411i	0.722214	+	0.143657i
$76$	−8.03282	+	10.4686i	−0.921428	+	1.20083i
$77$	−0.970770	+	7.37373i	−0.110630	+	0.840315i
$78$	4.87535	+	0.969767i	0.552024	+	0.109804i
$79$	−0.768349	−	11.7227i	−0.0864460	−	1.31891i	−0.792116	−	0.610371i	$-0.791021\pi$
$79$	−0.768349	−	11.7227i	−0.0864460	−	1.31891i	0.705670	−	0.708541i	$-0.250646\pi$
$80$	4.33754	−	3.80392i	0.484951	−	0.425291i
$81$	−9.61244	−	2.57565i	−1.06805	−	0.286183i
$82$	0.0371946	−	0.0556657i	0.00410746	−	0.00614725i
$83$	1.28748	+	9.77936i	0.141319	+	1.07342i	0.904268	+	0.426966i	$0.140417\pi$
$83$	1.28748	+	9.77936i	0.141319	+	1.07342i	−0.762949	+	0.646459i	$0.776249\pi$
$84$		−	10.7886i		−	1.17713i
$85$	1.50016	+	4.85912i	0.162716	+	0.527046i
$86$	−9.59307	+	7.83531i	−1.03445	+	0.844903i
$87$	0.880719	−	2.12624i	0.0944230	−	0.227957i
$88$	1.34469	+	0.898492i	0.143344	+	0.0957796i
$89$	−11.0340	−	2.95656i	−1.16960	−	0.313394i	−0.378808	−	0.925475i	$-0.623666\pi$
$89$	−11.0340	−	2.95656i	−1.16960	−	0.313394i	−0.790795	+	0.612081i	$0.790333\pi$
$90$	0.163850	+	0.823728i	0.0172713	+	0.0868285i
$91$	−4.83287	−	2.38331i	−0.506622	−	0.249838i
$92$	−1.92586	+	0.653743i	−0.200785	+	0.0681574i
$93$	4.93433	+	0.649617i	0.511667	+	0.0673622i
$94$	18.8460	−	7.80627i	1.94382	−	0.805155i
$95$	−6.84421	+	7.80433i	−0.702201	+	0.800707i
$96$	−11.8423	−	5.83998i	−1.20865	−	0.596040i
$97$	12.2493	−	2.43655i	1.24373	−	0.247394i	0.471004	−	0.882131i	$-0.343892\pi$
$97$	12.2493	−	2.43655i	1.24373	−	0.247394i	0.772728	+	0.634737i	$0.218892\pi$
$98$	−3.46596	+	12.9351i	−0.350115	+	1.30665i
$99$	−0.640621	+	0.315920i	−0.0643849	+	0.0317511i
$100$	4.32714	−	3.32033i	0.432714	−	0.332033i
$101$	−6.15658	−	3.55450i	−0.612602	−	0.353686i	0.161381	−	0.986892i	$-0.448405\pi$
$101$	−6.15658	−	3.55450i	−0.612602	−	0.353686i	−0.773983	+	0.633206i	$0.781739\pi$
$102$	10.9914	−	9.11135i	1.08831	−	0.902158i
$103$	4.86116	−	8.41977i	0.478984	−	0.829625i	−0.520725	−	0.853724i	$-0.674338\pi$
$103$	4.86116	−	8.41977i	0.478984	−	0.829625i	0.999710	+	0.0240993i	$0.00767177\pi$
$104$	−0.929603	+	0.713309i	−0.0911550	+	0.0699457i
$105$	0.555076	−	8.46883i	0.0541699	−	0.826473i
$106$	12.9809	+	3.47821i	1.26081	+	0.337834i
$107$	1.19341	+	5.99966i	0.115371	+	0.580009i	0.994615	+	0.103637i	$0.0330482\pi$
$107$	1.19341	+	5.99966i	0.115371	+	0.580009i	−0.879244	+	0.476371i	$0.841952\pi$
$108$	−6.30789	+	4.21480i	−0.606977	+	0.405569i
$109$	3.59527	−	1.22043i	0.344365	−	0.116896i	−0.143898	−	0.989592i	$-0.545964\pi$
$109$	3.59527	−	1.22043i	0.344365	−	0.116896i	0.488263	+	0.872696i	$0.337631\pi$
$110$	−3.66222	−	2.81012i	−0.349179	−	0.267934i
$111$	11.9683	+	1.57566i	1.13598	+	0.149555i
$112$	13.2005	+	11.5765i	1.24733	+	1.09388i
$113$	5.40388	+	8.08747i	0.508354	+	0.760805i	0.993525	−	0.113614i	$-0.0362427\pi$
$113$	5.40388	+	8.08747i	0.508354	+	0.760805i	−0.485171	+	0.874419i	$0.661243\pi$
$114$	27.5951	+	9.36728i	2.58452	+	0.877326i
$115$	−1.54540	+	0.414089i	−0.144109	+	0.0386140i
$116$	−0.870594	−	1.76539i	−0.0808326	−	0.163912i
$117$	−0.0675497	−	0.513091i	−0.00624497	−	0.0474353i
$118$	−10.2331			−0.942031
$119$	−14.0654	+	6.45661i	−1.28937	+	0.591876i
$120$	−1.59824	−	0.922743i	−0.145899	−	0.0842346i
$121$	−2.70714	+	6.53562i	−0.246104	+	0.594147i
$122$	−1.82031	−	3.69123i	−0.164804	−	0.334189i
$123$	−0.0627598	−	0.0168164i	−0.00565886	−	0.00151629i
$124$	3.20035	−	2.80663i	0.287400	−	0.252043i
$125$	8.69521	−	5.80996i	0.777724	−	0.519658i
$126$	−2.42033	+	0.821590i	−0.215620	+	0.0731931i
$127$	4.70597	−	1.94928i	0.417587	−	0.172970i	−0.163989	−	0.986462i	$-0.552436\pi$
$127$	4.70597	−	1.94928i	0.417587	−	0.172970i	0.581576	+	0.813492i	$0.302436\pi$
$128$	5.89189	−	2.44050i	0.520774	−	0.215712i
$129$	10.1933	+	6.37172i	0.897466	+	0.560999i
$130$	2.78086	−	1.85811i	0.243898	−	0.162967i
$131$	−0.650491	−	3.27024i	−0.0568336	−	0.285722i	0.941908	−	0.335871i	$-0.109030\pi$
$131$	−0.650491	−	3.27024i	−0.0568336	−	0.285722i	−0.998742	+	0.0501486i	$0.984030\pi$
$132$	−1.47394	+	5.50084i	−0.128290	+	0.478786i
$133$	−26.2665	−	17.5507i	−2.27760	−	1.52184i
$134$	24.3594	−	3.20698i	2.10433	−	0.277041i
$135$	−5.16842	+	2.98399i	−0.444827	+	0.256821i
$136$	−0.0935491	+	3.36405i	−0.00802177	+	0.288465i
$137$			8.91732i			0.761858i	0.924604	+	0.380929i	$0.124396\pi$
$137$			8.91732i			0.761858i	−0.924604	+	0.380929i	$0.875604\pi$
$138$	2.73431	+	3.56343i	0.232760	+	0.303339i
$139$	1.26276	+	0.0827656i	0.107106	+	0.00702009i	0.118862	−	0.992911i	$-0.462075\pi$
$139$	1.26276	+	0.0827656i	0.107106	+	0.00702009i	−0.0117560	+	0.999931i	$0.503742\pi$
$140$	−5.13277	−	5.13277i	−0.433798	−	0.433798i
$141$	−13.0531	−	14.8842i	−1.09927	−	1.25348i
$142$	7.73448	−	0.506944i	0.649063	−	0.0425418i
$143$	2.13855	+	1.87546i	0.178834	+	0.156834i
$144$	−0.220097	+	1.67180i	−0.0183414	+	0.139317i
$145$	−0.592569	−	1.43059i	−0.0492102	−	0.118804i
$146$	14.2749	−	16.2774i	1.18140	−	1.34712i
$147$	12.9686	−	0.850007i	1.06963	−	0.0701074i
$148$	7.76250	−	6.80753i	0.638073	−	0.559575i
$149$	1.22116	−	4.55744i	0.100041	−	0.373360i	−0.897694	−	0.440619i	$-0.854759\pi$
$149$	1.22116	−	4.55744i	0.100041	−	0.373360i	0.997736	+	0.0672596i	$0.0214256\pi$
$150$	−10.0155	−	6.69217i	−0.817765	−	0.546413i
$151$	6.81173	−	16.4450i	0.554331	−	1.33827i	−0.359867	−	0.933004i	$-0.617178\pi$
$151$	6.81173	−	16.4450i	0.554331	−	1.33827i	0.914198	−	0.405269i	$-0.132822\pi$
$152$	−5.94900	+	3.43466i	−0.482527	+	0.278587i
$153$	−1.26607	−	0.778678i	−0.102356	−	0.0629524i
$154$	7.02416	−	12.1662i	0.566023	−	0.980380i
$155$	2.65661	−	2.03849i	0.213384	−	0.163735i
$156$	−3.43073	−	2.29234i	−0.274678	−	0.183534i
$157$	−4.03604	−	15.0627i	−0.322111	−	1.20214i	−0.917184	−	0.398464i	$-0.869543\pi$
$157$	−4.03604	−	15.0627i	−0.322111	−	1.20214i	0.595073	−	0.803672i	$-0.297123\pi$
$158$	−7.13287	+	21.0128i	−0.567461	+	1.67169i
$159$	−0.853012	−	13.0144i	−0.0676482	−	1.03211i
$160$	−8.41249	+	2.85566i	−0.665066	+	0.225759i
$161$	−1.86330	−	4.49841i	−0.146849	−	0.354524i
$162$	14.9129	+	11.4431i	1.17167	+	0.899052i
$163$	−0.703079	−	0.616584i	−0.0550694	−	0.0482946i	0.631369	−	0.775483i	$-0.282493\pi$
$163$	−0.703079	−	0.616584i	−0.0550694	−	0.0482946i	−0.686438	+	0.727188i	$0.740827\pi$
$164$	−0.0462058	+	0.0308737i	−0.00360806	+	0.00241083i
$165$	−1.44004	+	4.24221i	−0.112107	+	0.330256i
$166$	4.82218	−	17.9966i	0.374274	−	1.39681i
$167$	−0.569888	+	8.69481i	−0.0440992	+	0.672824i	0.917391	+	0.397986i	$0.130291\pi$
$167$	−0.569888	+	8.69481i	−0.0440992	+	0.672824i	−0.961491	+	0.274838i	$0.911376\pi$
$168$	2.14930	−	5.18887i	0.165822	−	0.400330i
$169$	9.47357	−	5.46957i	0.728736	−	0.420736i
$170$	0.894453	−	9.56405i	0.0686014	−	0.733529i
$171$		−	3.03395i		−	0.232012i
$172$	9.84555	−	2.96146i	0.750716	−	0.225809i
$173$	13.7628	−	20.5975i	1.04637	−	1.56600i	0.243444	−	0.969915i	$-0.421723\pi$
$173$	13.7628	−	20.5975i	1.04637	−	1.56600i	0.802923	−	0.596083i	$-0.203277\pi$
$174$	−3.07389	+	3.07389i	−0.233031	+	0.233031i
$175$	8.60961	+	9.81738i	0.650825	+	0.742124i
$176$	−5.14900	−	7.70602i	−0.388120	−	0.580863i
$177$	3.19229	+	9.40417i	0.239947	+	0.706861i
$178$	17.1183	+	13.1354i	1.28307	+	0.984537i
$179$	−3.30464	+	25.1013i	−0.247001	+	1.87616i	0.197393	+	0.980324i	$0.436753\pi$
$179$	−3.30464	+	25.1013i	−0.247001	+	1.87616i	−0.444393	+	0.895832i	$0.646581\pi$
$180$	0.136005	−	0.683742i	0.0101372	−	0.0509631i
$181$	−0.242387	−	3.69811i	−0.0180165	−	0.274878i	−0.997357	−	0.0726593i	$-0.976851\pi$
$181$	−0.242387	−	3.69811i	−0.0180165	−	0.274878i	0.979340	−	0.202219i	$-0.0648152\pi$
$182$	6.71108	+	7.65252i	0.497459	+	0.567243i
$183$	−2.82437	+	2.82437i	−0.208784	+	0.208784i
$184$	−1.05650	−	0.0692466i	−0.0778862	−	0.00510493i
$185$	6.44365	−	4.94439i	0.473747	−	0.363519i
$186$	−8.14134	−	4.70041i	−0.596952	−	0.344650i
$187$	8.05370	−	1.37044i	0.588945	−	0.100216i
$188$	−16.9322			−1.23491
$189$	−11.0566	−	14.4092i	−0.804247	−	1.04812i
$190$	17.5852	−	8.67204i	1.27576	−	0.629136i
$191$	−2.67950	−	0.717971i	−0.193882	−	0.0519506i	0.160571	−	0.987024i	$-0.448666\pi$
$191$	−2.67950	−	0.717971i	−0.193882	−	0.0519506i	−0.354453	+	0.935074i	$0.615333\pi$
$192$	5.13730	+	5.85797i	0.370753	+	0.422763i
$193$	−12.5593	−	18.7963i	−0.904036	−	1.35299i	−0.935443	−	0.353478i	$-0.884999\pi$
$193$	−12.5593	−	18.7963i	−0.904036	−	1.35299i	0.0314069	−	0.999507i	$-0.490001\pi$
$194$	−23.1376	−	4.60235i	−1.66118	−	0.330430i
$195$	−2.57511	−	1.97595i	−0.184408	−	0.141501i
$196$	6.76680	−	8.81866i	0.483343	−	0.629904i
$197$	2.20046	−	2.50915i	0.156777	−	0.178769i	−0.668119	−	0.744054i	$-0.732900\pi$
$197$	2.20046	−	2.50915i	0.156777	−	0.178769i	0.824896	+	0.565285i	$0.191234\pi$
$198$	1.34631	−	0.0882418i	0.0956781	−	0.00627107i
$199$	−5.46504	−	27.4746i	−0.387406	−	1.94762i	−0.310455	−	0.950588i	$-0.600481\pi$
$199$	−5.46504	−	27.4746i	−0.387406	−	1.94762i	−0.0769511	−	0.997035i	$-0.524519\pi$
$200$	2.74265	−	0.734891i	0.193935	−	0.0519647i
$201$	−10.5463	−	21.3858i	−0.743880	−	1.50844i
$202$	8.17450	+	10.6532i	0.575156	+	0.749558i
$203$	4.08109	−	2.35622i	0.286436	−	0.165374i
$204$	−11.3232	+	3.49584i	−0.792785	+	0.244758i
$205$	−0.0378591	+	0.0218579i	−0.00264419	+	0.00152662i
$206$	−14.5694	+	11.1795i	−1.01510	+	0.778912i
$207$	0.259797	−	0.388814i	0.0180571	−	0.0270244i
$208$	6.48609	−	1.73794i	0.449729	−	0.120505i
$209$	10.9949	+	12.5372i	0.760530	+	0.867219i
$210$	−7.09031	+	14.3777i	−0.489278	+	0.992158i
$211$	1.71836	+	0.341803i	0.118297	+	0.0235307i	0.253884	−	0.967235i	$-0.418292\pi$
$211$	1.71836	+	0.341803i	0.118297	+	0.0235307i	−0.135587	+	0.990765i	$0.543292\pi$
$212$	−8.84984	−	6.79072i	−0.607809	−	0.466388i
$213$	−2.87871	−	6.94982i	−0.197246	−	0.476194i
$214$	2.25421	−	11.3327i	0.154094	−	0.774685i
$215$	7.88093	−	1.81813i	0.537475	−	0.123995i
$216$	−3.87350	+	0.770488i	−0.263559	+	0.0524251i
$217$	7.20597	+	7.20597i	0.489173	+	0.489173i
$218$	−7.15630	−	0.469049i	−0.484686	−	0.0317680i
$219$	−19.4120	−	8.04072i	−1.31174	−	0.543341i
$220$	1.91583	+	3.31831i	0.129165	+	0.223720i
$221$	−0.935415	+	5.84463i	−0.0629228	+	0.393152i
$222$	−19.7470	−	11.4009i	−1.32533	−	0.765179i
$223$	19.2835	+	7.98748i	1.29132	+	0.534882i	0.919378	−	0.393375i	$-0.128693\pi$
$223$	19.2835	+	7.98748i	1.29132	+	0.534882i	0.371940	+	0.928257i	$0.378693\pi$
$224$	−11.9580	−	24.2484i	−0.798978	−	1.62017i
$225$	−0.324577	+	1.21134i	−0.0216385	+	0.0807560i
$226$	−3.58433	−	18.0196i	−0.238426	−	1.19865i
$227$	9.27375	+	4.57331i	0.615521	+	0.303541i	0.723194	−	0.690645i	$-0.242673\pi$
$227$	9.27375	+	4.57331i	0.615521	+	0.303541i	−0.107673	+	0.994186i	$0.534340\pi$
$228$	−18.1865	−	15.9491i	−1.20443	−	1.05625i
$229$	−3.88813	+	29.5332i	−0.256935	+	1.95161i	0.0469338	+	0.998898i	$0.485055\pi$
$229$	−3.88813	+	29.5332i	−0.256935	+	1.95161i	−0.303868	+	0.952714i	$0.598278\pi$
$230$	2.99620	+	0.394457i	0.197564	+	0.0260098i
$231$	−13.3719	−	2.65984i	−0.879809	−	0.175005i
$232$	−0.0670194	−	1.02252i	−0.00440004	−	0.0671316i
$233$	−10.3628	−	3.51770i	−0.678891	−	0.230453i	−0.0393685	−	0.999225i	$-0.512535\pi$
$233$	−10.3628	−	3.51770i	−0.678891	−	0.230453i	−0.639523	+	0.768772i	$0.720868\pi$
$234$	−0.253004	+	0.944224i	−0.0165394	+	0.0617259i
$235$	−13.2914	−	0.871165i	−0.867036	−	0.0568285i
$236$	7.84748	+	3.25053i	0.510827	+	0.211592i
$237$	21.5358			1.39890
$238$	29.2127	−	1.10033i	1.89358	−	0.0713241i
$239$	0.146134	+	0.253111i	0.00945262	+	0.0163724i	0.870713	−	0.491791i	$-0.163658\pi$
$239$	0.146134	+	0.253111i	0.00945262	+	0.0163724i	−0.861260	+	0.508164i	$0.830324\pi$
$240$	6.43823	+	8.39047i	0.415586	+	0.541602i
$241$	−1.37249	+	0.676838i	−0.0884099	+	0.0435990i	−0.485956	−	0.873983i	$-0.661529\pi$
$241$	−1.37249	+	0.676838i	−0.0884099	+	0.0435990i	0.397546	+	0.917582i	$0.369862\pi$
$242$	9.44848	−	9.44848i	0.607371	−	0.607371i
$243$	1.19796	−	3.52908i	0.0768493	−	0.226391i
$244$	0.223433	+	3.40893i	0.0143038	+	0.218235i
$245$	5.76552	−	6.57432i	0.368346	−	0.420018i
$246$	0.0973665	+	0.0747120i	0.00620786	+	0.00476346i
$247$	−11.1621	+	4.62351i	−0.710229	+	0.294187i
$248$	2.09837	−	0.712301i	0.133247	−	0.0452312i
$249$	−18.0432	+	1.18261i	−1.14344	+	0.0749450i
$250$	−19.3737	+	3.85367i	−1.22530	+	0.243728i
$251$	2.80623	+	10.4730i	0.177128	+	0.661050i	0.996179	+	0.0873301i	$0.0278335\pi$
$251$	2.80623	+	10.4730i	0.177128	+	0.661050i	−0.819052	+	0.573720i	$0.805500\pi$
$252$	2.11706	+	0.138760i	0.133362	+	0.00874103i
$253$	0.335476	+	2.54819i	0.0210912	+	0.160203i
$254$	−9.62141			−0.603701
$255$	−9.06837	+	2.16158i	−0.567883	+	0.135363i
$256$	−20.5467			−1.28417
$257$	9.60821	+	3.97985i	0.599344	+	0.248256i	0.661665	−	0.749800i	$-0.269850\pi$
$257$	9.60821	+	3.97985i	0.599344	+	0.248256i	−0.0623210	+	0.998056i	$0.519850\pi$
$258$	−13.1825	−	18.4874i	−0.820707	−	1.15098i
$259$	17.4782	+	17.4782i	1.08604	+	1.08604i
$260$	−2.72280	+	0.541598i	−0.168861	+	0.0335885i
$261$	0.405908	+	0.200172i	0.0251251	+	0.0123903i
$262$	−1.22870	+	6.17710i	−0.0759094	+	0.381623i
$263$	−6.79494	+	8.85534i	−0.418994	+	0.546044i	−0.954392	−	0.298556i	$-0.903495\pi$
$263$	−6.79494	+	8.85534i	−0.418994	+	0.546044i	0.535398	+	0.844600i	$0.320162\pi$
$264$	−1.80478	+	2.35204i	−0.111077	+	0.144758i
$265$	−6.59756	−	5.78590i	−0.405285	−	0.355425i
$266$	33.1513	+	49.6145i	2.03264	+	3.04206i
$267$	6.73117	−	19.8294i	0.411941	−	1.21354i
$268$	−19.6993	−	5.27841i	−1.20333	−	0.322430i
$269$	26.4737	+	17.6892i	1.61413	+	1.07853i	0.940679	+	0.339298i	$0.110190\pi$
$269$	26.4737	+	17.6892i	1.61413	+	1.07853i	0.673453	+	0.739230i	$0.264810\pi$
$270$	11.1764	−	1.47140i	0.680173	−	0.0895464i
$271$	16.1902	+	9.34743i	0.983486	+	0.567816i	0.903321	−	0.428966i	$-0.141122\pi$
$271$	16.1902	+	9.34743i	0.983486	+	0.567816i	0.0801653	+	0.996782i	$0.474455\pi$
$272$	7.87282	−	17.6058i	0.477360	−	1.06751i
$273$	4.93908	−	8.55473i	0.298927	−	0.517756i
$274$	6.44584	−	15.5616i	0.389407	−	0.940112i
$275$	−3.04857	−	6.18188i	−0.183836	−	0.372782i
$276$	−0.964952	−	3.60125i	−0.0580833	−	0.216770i
$277$	8.18840	+	9.33707i	0.491993	+	0.561010i	0.943549	−	0.331232i	$-0.107464\pi$
$277$	8.18840	+	9.33707i	0.491993	+	0.561010i	−0.451556	+	0.892243i	$0.649131\pi$
$278$	−2.14382	−	1.05721i	−0.128578	−	0.0634074i
$279$	−0.190939	+	0.959917i	−0.0114312	+	0.0574687i
$280$	−1.44610	−	3.49119i	−0.0864210	−	0.208639i
$281$	0.160701	−	0.209430i	0.00958663	−	0.0124935i	−0.788535	−	0.614989i	$-0.789160\pi$
$281$	0.160701	−	0.209430i	0.00958663	−	0.0124935i	0.798122	+	0.602496i	$0.205827\pi$
$282$	12.0200	+	35.4098i	0.715781	+	2.10862i
$283$	1.42653	+	21.7647i	0.0847986	+	1.29378i	0.802174	+	0.597090i	$0.203676\pi$
$283$	1.42653	+	21.7647i	0.0847986	+	1.29378i	−0.717376	+	0.696687i	$0.754657\pi$
$284$	−6.09240	−	2.06809i	−0.361517	−	0.122719i
$285$	−13.4554	−	13.4554i	−0.797030	−	0.797030i
$286$	−2.37632	−	4.81870i	−0.140515	−	0.284936i
$287$	−0.0809902	−	0.105549i	−0.00478070	−	0.00623033i
$288$	1.29830	−	2.24872i	0.0765030	−	0.132507i
$289$	11.3342	+	12.6703i	0.666717	+	0.745311i
$290$			2.92486i			0.171753i
$291$	2.98840	+	22.6991i	0.175183	+	1.33065i
$292$	−16.1175	+	7.94828i	−0.943206	+	0.465138i
$293$	3.58089	+	3.58089i	0.209198	+	0.209198i	0.803927	−	0.594729i	$-0.202740\pi$
$293$	3.58089	+	3.58089i	0.209198	+	0.209198i	−0.594729	+	0.803927i	$0.702740\pi$
$294$	−23.2459	−	7.89093i	−1.35573	−	0.460209i
$295$	5.99287	+	2.95536i	0.348918	+	0.172067i
$296$	5.08963	−	1.72770i	0.295829	−	0.100420i
$297$	3.66887	+	8.85745i	0.212890	+	0.513961i
$298$	−5.42537	+	7.07048i	−0.314283	+	0.409582i
$299$	−1.82639	−	0.363291i	−0.105623	−	0.0210096i
$300$	5.55489	+	8.31348i	0.320712	+	0.479979i
$301$	8.61635	+	23.0567i	0.496638	+	1.32897i
$302$	−23.7743	+	23.7743i	−1.36806	+	1.36806i
$303$	7.24018	−	10.8357i	0.415938	−	0.622495i
$304$	39.0292	−	5.13830i	2.23848	−	0.294702i
$305$			2.68744i			0.153882i
$306$	1.64657	+	2.27405i	0.0941279	+	0.129999i
$307$	−1.02119	−	1.76876i	−0.0582826	−	0.100948i	0.835412	−	0.549624i	$-0.185229\pi$
$307$	−1.02119	−	1.76876i	−0.0582826	−	0.100948i	−0.893695	+	0.448676i	$0.851896\pi$
$308$	−9.25122	+	7.09871i	−0.527137	+	0.404487i
$309$	14.8190	+	9.90172i	0.843022	+	0.563289i
$310$	−6.10957	+	1.63705i	−0.347000	+	0.0929784i
$311$	−6.89378	+	6.04568i	−0.390910	+	0.342819i	−0.832131	−	0.554580i	$-0.812879\pi$
$311$	−6.89378	+	6.04568i	−0.390910	+	0.342819i	0.441220	+	0.897399i	$0.354546\pi$
$312$	−1.19336	−	1.78599i	−0.0675607	−	0.101112i
$313$	−7.16374	−	21.1037i	−0.404919	−	1.19285i	−0.937954	−	0.346759i	$-0.887282\pi$
$313$	−7.16374	−	21.1037i	−0.404919	−	1.19285i	0.533035	−	0.846093i	$-0.321051\pi$
$314$	−3.84470	+	29.2034i	−0.216969	+	1.64804i
$315$	1.65471	+	0.217847i	0.0932325	+	0.0122743i
$316$	12.1447	−	13.8484i	0.683193	−	0.779032i
$317$	26.3475	−	17.6049i	1.47982	−	0.988787i	0.486470	−	0.873697i	$-0.338284\pi$
$317$	26.3475	−	17.6049i	1.47982	−	0.988787i	0.993355	−	0.115090i	$-0.0367156\pi$
$318$	−7.91883	+	23.3281i	−0.444066	+	1.30818i
$319$	−2.40275	+	0.643816i	−0.134528	+	0.0360468i
$320$	5.23109	+	0.342864i	0.292427	+	0.0191667i
$321$	−11.1179	+	1.46370i	−0.620541	+	0.0816957i
$322$			9.19706i			0.512532i
$323$	−9.90931	+	33.2552i	−0.551369	+	1.85037i
$324$	−7.80142	−	13.5125i	−0.433412	−	0.750692i
$325$	4.95124	−	0.651843i	0.274645	−	0.0361577i
$326$	0.781250	+	1.58422i	0.0432694	+	0.0877417i
$327$	1.80141	+	6.72295i	0.0996181	+	0.371780i
$328$	−0.0283737	+	0.00564388i	−0.00156668	+	0.000311631i
$329$	−2.65123	−	40.4499i	−0.146167	−	2.23007i
$330$	5.57947	−	6.36216i	0.307140	−	0.350226i
$331$	9.24042	+	1.21652i	0.507899	+	0.0668662i	0.380121	−	0.924937i	$-0.375882\pi$
$331$	9.24042	+	1.21652i	0.507899	+	0.0668662i	0.127778	+	0.991803i	$0.459216\pi$
$332$	−9.41462	+	12.2694i	−0.516695	+	0.673369i
$333$	−0.463126	+	2.32829i	−0.0253792	+	0.127590i
$334$	7.27951	−	14.7614i	0.398317	−	0.807707i
$335$	−15.1920	−	5.15698i	−0.830026	−	0.281756i
$336$	−22.7589	+	22.7589i	−1.24160	+	1.24160i
$337$	6.95715	−	3.43089i	0.378980	−	0.186892i	−0.242814	−	0.970073i	$-0.578071\pi$
$337$	6.95715	−	3.43089i	0.378980	−	0.186892i	0.621795	+	0.783180i	$0.286404\pi$
$338$	−20.4860	+	2.69703i	−1.11429	+	0.146699i
$339$	−15.4418	+	8.91534i	−0.838685	+	0.484215i
$340$	−3.72395	+	7.05030i	−0.201959	+	0.382356i
$341$	−2.68966	−	4.65863i	−0.145653	−	0.252279i
$342$	−2.19307	+	5.29455i	−0.118588	+	0.286296i
$343$	0.279665	+	0.186866i	0.0151005	+	0.0100898i
$344$	5.32528	+	0.537088i	0.287120	+	0.0289578i
$345$	−0.572183	−	2.87656i	−0.0308053	−	0.154869i
$346$	−38.9063	+	25.9963i	−2.09161	+	1.39757i
$347$	−7.65971	−	22.5648i	−0.411195	−	1.21134i	−0.933499	−	0.358581i	$-0.883261\pi$
$347$	−7.65971	−	22.5648i	−0.411195	−	1.21134i	0.522304	−	0.852760i	$-0.325073\pi$
$348$	3.33370	−	1.38086i	0.178705	−	0.0740221i
$349$	18.6811	+	14.3345i	0.999975	+	0.767308i	0.972640	−	0.232318i	$-0.0746311\pi$
$349$	18.6811	+	14.3345i	0.999975	+	0.767308i	0.0273355	+	0.999626i	$0.491298\pi$
$350$	−7.92820	−	23.3557i	−0.423780	−	1.24842i
$351$	−6.93135	+	0.454305i	−0.369968	+	0.0242490i
$352$	2.78425	+	13.9974i	0.148401	+	0.746063i
$353$	−3.41447	−	12.7430i	−0.181734	−	0.678240i	−0.995306	−	0.0967765i	$-0.969147\pi$
$353$	−3.41447	−	12.7430i	−0.181734	−	0.678240i	0.813572	−	0.581464i	$-0.197520\pi$
$354$	1.22689	−	18.7188i	0.0652086	−	0.994891i
$355$	−4.67601	−	1.93686i	−0.248177	−	0.102798i
$356$	−8.95516	−	15.5108i	−0.474623	−	0.822071i
$357$	−10.1243	−	26.5031i	−0.535836	−	1.40269i
$358$	23.9113	−	41.4155i	1.26375	−	2.18888i
$359$	3.37800	+	4.40229i	0.178284	+	0.232344i	0.873944	−	0.486027i	$-0.161554\pi$
$359$	3.37800	+	4.40229i	0.178284	+	0.232344i	−0.695660	+	0.718371i	$0.744888\pi$
$360$	0.201627	−	0.301757i	0.0106267	−	0.0159040i
$361$	−50.0634	+	13.4145i	−2.63492	+	0.706024i
$362$	−2.25017	+	6.62878i	−0.118266	+	0.348401i
$363$	−11.6307	−	5.73560i	−0.610451	−	0.301041i
$364$	−2.71573	−	8.00029i	−0.142343	−	0.419329i
$365$	−13.0609	+	5.40999i	−0.683637	+	0.283172i
$366$	6.97040	−	2.88723i	0.364349	−	0.150918i
$367$	3.88801	+	11.4537i	0.202953	+	0.597879i	0.999982	−	0.00606189i	$-0.00192957\pi$
$367$	3.88801	+	11.4537i	0.202953	+	0.597879i	−0.797029	+	0.603941i	$0.793596\pi$
$368$	5.44176	+	2.68358i	0.283671	+	0.139891i
$369$	0.00410711	−	0.0120992i	0.000213808	−	0.000629857i
$370$	−14.8189	+	3.97070i	−0.770396	+	0.206427i
$371$	14.8369	−	22.2050i	0.770293	−	1.15283i
$372$	4.75030	+	6.19071i	0.246292	+	0.320973i
$373$	17.7082	−	30.6715i	0.916897	−	1.58811i	0.112797	−	0.993618i	$-0.464019\pi$
$373$	17.7082	−	30.6715i	0.916897	−	1.58811i	0.804100	−	0.594494i	$-0.202648\pi$
$374$	−15.0451	−	3.43002i	−0.777966	−	0.177362i
$375$	9.58530	+	16.6022i	0.494983	+	0.857335i
$376$	−8.14367	−	3.37322i	−0.419978	−	0.173960i
$377$	0.117874	−	1.79841i	0.00607083	−	0.0926230i
$378$	8.87922	+	33.1377i	0.456698	+	1.70442i
$379$	2.53026	+	12.7205i	0.129971	+	0.653407i	0.989758	+	0.142755i	$0.0455960\pi$
$379$	2.53026	+	12.7205i	0.129971	+	0.653407i	−0.859787	+	0.510652i	$0.829404\pi$
$380$	−16.2403	+	1.06444i	−0.833108	+	0.0546048i
$381$	3.00147	+	8.84205i	0.153770	+	0.452992i
$382$	4.15703	+	3.18980i	0.212692	+	0.163204i
$383$	−20.5318	+	8.50454i	−1.04912	+	0.434562i	−0.839579	−	0.543237i	$-0.817198\pi$
$383$	−20.5318	+	8.50454i	−1.04912	+	0.434562i	−0.209545	+	0.977799i	$0.567198\pi$
$384$	3.75786	+	11.0703i	0.191767	+	0.564928i
$385$	−7.62725	+	5.09637i	−0.388721	+	0.259735i
$386$	8.33041	+	41.8798i	0.424007	+	2.13163i
$387$	−1.38144	+	1.91829i	−0.0702223	+	0.0975120i
$388$	16.2817	+	10.8791i	0.826577	+	0.552301i
$389$	−12.7243	+	30.7191i	−0.645147	+	1.55752i	0.174503	+	0.984657i	$0.444168\pi$
$389$	−12.7243	+	30.7191i	−0.645147	+	1.55752i	−0.819649	+	0.572865i	$0.805832\pi$
$390$	3.06552	+	5.30964i	0.155229	+	0.268864i
$391$	−4.11756	+	3.41326i	−0.208234	+	0.172616i
$392$	5.01140	−	2.89333i	0.253114	−	0.146135i
$393$	6.06004	−	0.797820i	0.305689	−	0.0402447i
$394$	−5.65376	+	2.78813i	−0.284832	+	0.140464i
$395$	10.2459	−	10.2459i	0.515525	−	0.515525i
$396$	−1.06048	−	0.359984i	−0.0532911	−	0.0180899i
$397$	−10.1804	+	20.6438i	−0.510939	+	1.03608i	0.476661	+	0.879087i	$0.341847\pi$
$397$	−10.1804	+	20.6438i	−0.510939	+	1.03608i	−0.987600	+	0.156994i	$0.949820\pi$
$398$	−10.3228	+	51.8963i	−0.517436	+	2.60133i
$399$	35.2538	−	45.9436i	1.76490	−	2.30006i
$400$	−16.1326	−	2.12389i	−0.806629	−	0.106195i
$401$	16.8394	−	19.2017i	0.840921	−	0.958886i	−0.158675	−	0.987331i	$-0.550722\pi$
$401$	16.8394	−	19.2017i	0.840921	−	0.958886i	0.999595	+	0.0284447i	$0.00905544\pi$
$402$	2.94577	+	44.9438i	0.146922	+	2.24159i
$403$	3.82258	−	0.760359i	0.190416	−	0.0378762i
$404$	−2.88482	−	10.7663i	−0.143525	−	0.535643i
$405$	−5.42874	−	11.0084i	−0.269756	−	0.547011i
$406$	−8.82509	+	1.16185i	−0.437982	+	0.0576614i
$407$	−6.52382	−	11.2996i	−0.323374	−	0.560099i
$408$	−6.14245	−	0.574456i	−0.304096	−	0.0284398i
$409$			16.0274i			0.792506i	0.918141	+	0.396253i	$0.129690\pi$
$409$			16.0274i			0.792506i	−0.918141	+	0.396253i	$0.870310\pi$
$410$	0.0818678	−	0.0107781i	0.00404316	−	0.000532292i
$411$	−16.3119	−	1.06914i	−0.804608	−	0.0527368i
$412$	14.7241	−	3.94530i	0.725402	−	0.194371i
$413$	−6.53656	+	19.2561i	−0.321643	+	0.947530i
$414$	−0.734424	+	0.490727i	−0.0360950	+	0.0241179i
$415$	−8.02155	+	9.14683i	−0.393762	+	0.449000i
$416$	−10.2517	−	1.34966i	−0.502632	−	0.0661727i
$417$	−0.302796	+	2.29997i	−0.0148280	+	0.112630i
$418$	−10.1247	−	29.8263i	−0.495214	−	1.45885i
$419$	13.0606	+	19.5465i	0.638050	+	0.954910i	0.999744	+	0.0226129i	$0.00719852\pi$
$419$	13.0606	+	19.5465i	0.638050	+	0.954910i	−0.361694	+	0.932297i	$0.617801\pi$
$420$	10.0045	−	8.77367i	0.488167	−	0.428111i
$421$	−31.3530	+	8.40101i	−1.52805	+	0.409440i	−0.922383	−	0.386277i	$-0.873761\pi$
$421$	−31.3530	+	8.40101i	−1.52805	+	0.409440i	−0.605669	+	0.795717i	$0.707094\pi$
$422$	−2.75164	−	1.83859i	−0.133948	−	0.0895011i
$423$	3.08864	−	2.36999i	0.150175	−	0.115233i
$424$	−2.90356	−	5.02911i	−0.141009	−	0.244235i
$425$	7.51411	−	12.2174i	0.364488	−	0.592631i
$426$			14.2090i			0.688428i
$427$	−8.10874	+	1.06754i	−0.392409	+	0.0516617i
$428$	−5.32850	+	7.97467i	−0.257563	+	0.385470i
$429$	−3.68706	+	3.68706i	−0.178013	+	0.178013i
$430$	−15.0672	−	2.52387i	−0.726607	−	0.121712i
$431$	−3.59416	−	5.37904i	−0.173125	−	0.259099i	0.734753	−	0.678335i	$-0.237298\pi$
$431$	−3.59416	−	5.37904i	−0.173125	−	0.259099i	−0.907878	+	0.419236i	$0.862298\pi$
$432$	22.1979	+	4.41544i	1.06800	+	0.212438i
$433$	−15.4905	+	20.1876i	−0.744427	+	0.970156i	0.255567	+	0.966791i	$0.417738\pi$
$433$	−15.4905	+	20.1876i	−0.744427	+	0.970156i	−0.999994	+	0.00336474i	$0.998929\pi$
$434$	−7.36636	−	17.7840i	−0.353596	−	0.853657i
$435$	2.68793	−	0.912431i	0.128877	−	0.0437477i
$436$	5.33899	+	2.63290i	0.255691	+	0.126093i
$437$	−10.3376	−	3.50914i	−0.494514	−	0.167865i
$438$	28.0637	+	28.0637i	1.34094	+	1.34094i
$439$	20.7071	−	10.2116i	0.988296	−	0.487374i	0.125046	−	0.992151i	$-0.460092\pi$
$439$	20.7071	−	10.2116i	0.988296	−	0.487374i	0.863250	+	0.504777i	$0.168425\pi$
$440$	0.260361	+	1.97764i	0.0124122	+	0.0942803i
$441$			2.55578i			0.121704i
$442$	5.85715	−	9.52331i	0.278596	−	0.452978i
$443$	−0.224264	+	0.388436i	−0.0106551	+	0.0184552i	−0.871304	−	0.490744i	$-0.836725\pi$
$443$	−0.224264	+	0.388436i	−0.0106551	+	0.0184552i	0.860649	+	0.509199i	$0.170058\pi$
$444$	11.5219	+	15.0157i	0.546806	+	0.712612i
$445$	−6.23159	−	12.6364i	−0.295406	−	0.599023i
$446$	−27.8779	−	27.8779i	−1.32006	−	1.32006i
$447$	8.19024	+	2.78021i	0.387385	+	0.131499i
$448$	1.04344	+	15.9198i	0.0492980	+	0.752142i
$449$	−3.19021	−	9.39805i	−0.150555	−	0.443521i	0.845319	−	0.534261i	$-0.179410\pi$
$449$	−3.19021	−	9.39805i	−0.150555	−	0.443521i	−0.995875	+	0.0907399i	$0.971077\pi$
$450$	1.44203	−	1.87929i	0.0679780	−	0.0885906i
$451$	0.0268748	+	0.0648815i	0.00126548	+	0.00305515i
$452$	−2.97520	+	14.9573i	−0.139942	+	0.703534i
$453$	29.2651	+	14.4320i	1.37499	+	0.678072i
$454$	−12.8778	−	14.6844i	−0.604387	−	0.689172i
$455$	−1.72018	−	6.41979i	−0.0806432	−	0.300964i
$456$	−5.56956	−	11.2939i	−0.260818	−	0.528888i
$457$	−3.12890	+	7.55382i	−0.146364	+	0.353353i	−0.980011	−	0.198944i	$-0.936249\pi$
$457$	−3.12890	+	7.55382i	−0.146364	+	0.353353i	0.833647	+	0.552297i	$0.186249\pi$
$458$	28.1331	−	48.7280i	1.31457	−	2.27691i
$459$	−11.5406	+	16.2735i	−0.538669	+	0.759583i
$460$	−2.17241	−	1.25424i	−0.101289	−	0.0584793i
$461$	−19.3647	+	2.54941i	−0.901905	+	0.118738i	−0.567195	−	0.823583i	$-0.691971\pi$
$461$	−19.3647	+	2.54941i	−0.901905	+	0.118738i	−0.334709	+	0.942321i	$0.608638\pi$
$462$	21.4127	+	14.3075i	0.996211	+	0.665647i
$463$	16.9143	+	4.53218i	0.786075	+	0.210628i	0.629461	−	0.777032i	$-0.283276\pi$
$463$	16.9143	+	4.53218i	0.786075	+	0.210628i	0.156613	+	0.987660i	$0.449942\pi$
$464$	−1.88760	+	5.56069i	−0.0876296	+	0.258148i
$465$	3.41037	+	5.10399i	0.158152	+	0.236692i
$466$	15.5414	+	13.6295i	0.719943	+	0.631373i
$467$	6.56107	−	8.55056i	0.303610	−	0.395673i	−0.616485	−	0.787366i	$-0.711444\pi$
$467$	6.56107	−	8.55056i	0.303610	−	0.395673i	0.920096	+	0.391694i	$0.128111\pi$
$468$	0.493954	−	0.643734i	0.0228330	−	0.0297566i
$469$	9.52529	−	47.8869i	0.439837	−	2.21121i
$470$	22.5651	+	11.1279i	1.04085	+	0.513291i
$471$	28.0372	−	5.57695i	1.29189	−	0.256972i
$472$	3.12674	+	3.12674i	0.143920	+	0.143920i
$473$	−1.24324	−	12.9332i	−0.0571642	−	0.594669i
$474$	−37.5822	−	15.5671i	−1.72621	−	0.715019i
$475$	29.2771			1.34332
$476$	−22.7520	−	8.43557i	−1.04283	−	0.386644i
$477$	2.56482			0.117435
$478$	−0.0720583	−	0.547337i	−0.00329587	−	0.0250346i
$479$	5.06591	+	0.332037i	0.231467	+	0.0151712i	0.180695	−	0.983539i	$-0.442165\pi$
$479$	5.06591	+	0.332037i	0.231467	+	0.0151712i	0.0507719	+	0.998710i	$0.483832\pi$
$480$	−4.21507	−	15.7308i	−0.192391	−	0.718012i
$481$	9.27173	−	1.84426i	0.422755	−	0.0840911i
$482$	2.88439	−	0.189053i	0.131380	−	0.00861111i
$483$	8.45207	−	2.86909i	0.384583	−	0.130548i
$484$	−10.2471	+	4.24449i	−0.465777	+	0.192931i
$485$	12.2211	+	9.37754i	0.554929	+	0.425812i
$486$	−4.64154	+	5.29267i	−0.210545	+	0.240080i
$487$	−0.364520	−	5.56149i	−0.0165180	−	0.252015i	−0.998130	−	0.0611281i	$-0.980530\pi$
$487$	−0.364520	−	5.56149i	−0.0165180	−	0.252015i	0.981612	−	0.190887i	$-0.0611365\pi$
$488$	−0.571664	+	1.68407i	−0.0258780	+	0.0762341i
$489$	1.21218	−	1.21218i	0.0548165	−	0.0548165i
$490$	−14.8136	+	7.30527i	−0.669212	+	0.330019i
$491$	4.67633	+	6.09431i	0.211040	+	0.275033i	0.886864	−	0.462030i	$-0.152879\pi$
$491$	4.67633	+	6.09431i	0.211040	+	0.275033i	−0.675824	+	0.737063i	$0.736212\pi$
$492$	−0.0509356	−	0.0882231i	−0.00229635	−	0.00397740i
$493$	−3.79538	−	3.51984i	−0.170935	−	0.158526i
$494$	22.8211			1.02677
$495$	−0.813934	−	0.337142i	−0.0365836	−	0.0151534i
$496$	−12.6719	−	0.830561i	−0.568985	−	0.0372933i
$497$	3.98660	−	14.8782i	0.178823	−	0.667377i
$498$	32.3420	+	10.9786i	1.44928	+	0.491964i
$499$	−2.25141	−	34.3499i	−0.100787	−	1.53771i	−0.686461	−	0.727166i	$-0.740837\pi$
$499$	−2.25141	−	34.3499i	−0.100787	−	1.53771i	0.585674	−	0.810547i	$-0.300830\pi$
$500$	16.0813	+	3.19877i	0.719178	+	0.143053i
$501$	−15.8366	−	2.08492i	−0.707526	−	0.0931475i
$502$	2.67319	−	20.3049i	0.119310	−	0.906253i
$503$	20.6957	+	18.1497i	0.922777	+	0.809254i	0.981979	−	0.188992i	$-0.0605221\pi$
$503$	20.6957	+	18.1497i	0.922777	+	0.809254i	−0.0592014	+	0.998246i	$0.518855\pi$
$504$	0.990576	+	0.488498i	0.0441237	+	0.0217594i
$505$	−1.71060	−	8.59975i	−0.0761206	−	0.382684i
$506$	1.25651	−	4.68935i	0.0558586	−	0.208467i
$507$	8.86933	+	17.9852i	0.393901	+	0.798751i
$508$	7.37841	+	3.05624i	0.327364	+	0.135599i
$509$	−20.0795	−	11.5929i	−0.890008	−	0.513846i	−0.0160630	−	0.999871i	$-0.505113\pi$
$509$	−20.0795	−	11.5929i	−0.890008	−	0.513846i	−0.873945	+	0.486024i	$0.838447\pi$
$510$	17.3877	+	2.78285i	0.769941	+	0.123227i
$511$	−21.5116	−	37.2592i	−0.951617	−	1.64825i
$512$	24.0722	+	9.97104i	1.06385	+	0.440662i
$513$	−40.6350	−	2.66336i	−1.79408	−	0.117590i
$514$	−13.8905	−	13.8905i	−0.612683	−	0.612683i
$515$	11.7611	−	2.33942i	0.518255	−	0.103087i
$516$	4.23679	+	18.3649i	0.186514	+	0.808472i
$517$	−4.17449	+	20.9866i	−0.183594	+	0.922989i
$518$	−17.8672	−	43.1353i	−0.785040	−	1.89525i
$519$	36.0277	+	27.6450i	1.58144	+	1.21348i
$520$	−1.41745	−	0.281948i	−0.0621593	−	0.0123643i
$521$	−5.98440	+	12.1352i	−0.262181	+	0.531651i	−0.987664	−	0.156589i	$-0.949950\pi$
$521$	−5.98440	+	12.1352i	−0.262181	+	0.531651i	0.725482	+	0.688241i	$0.241617\pi$
$522$	−0.563658	−	0.642729i	−0.0246707	−	0.0281315i
$523$	−19.8736	+	5.32511i	−0.869011	+	0.232851i	−0.665660	−	0.746255i	$-0.731850\pi$
$523$	−19.8736	+	5.32511i	−0.869011	+	0.232851i	−0.203351	+	0.979106i	$0.565183\pi$
$524$	2.90441	−	4.34676i	0.126880	−	0.189889i
$525$	−18.9906	+	14.5720i	−0.828818	+	0.635974i
$526$	18.2589	−	10.5418i	0.796126	−	0.459644i
$527$	5.22811	−	9.89803i	0.227740	−	0.431165i
$528$	14.7135	−	8.49485i	0.640323	−	0.369691i
$529$	12.9772	+	16.9122i	0.564226	+	0.735313i
$530$	7.33110	+	14.8660i	0.318443	+	0.645738i
$531$	−1.88645	+	0.505473i	−0.0818651	+	0.0219357i
$532$	−9.66287	−	48.5785i	−0.418938	−	2.10615i
$533$	−0.0507726	+	0.00332781i	−0.00219921	+	0.000144144i
$534$	−26.0802	+	29.7387i	−1.12860	+	1.28692i
$535$	−4.59307	+	5.98580i	−0.198576	+	0.258789i
$536$	−8.42298	−	6.46318i	−0.363817	−	0.279167i
$537$	−45.5200	−	9.05450i	−1.96433	−	0.390730i
$538$	−33.4128	−	50.0058i	−1.44053	−	2.15590i
$539$	−9.26200	−	10.5613i	−0.398943	−	0.454907i
$540$	−9.03826	−	2.42179i	−0.388945	−	0.104217i
$541$	−6.59426	+	3.25193i	−0.283510	+	0.139811i	−0.578484	−	0.815694i	$-0.696356\pi$
$541$	−6.59426	+	3.25193i	−0.283510	+	0.139811i	0.294975	+	0.955505i	$0.404689\pi$
$542$	−21.4968	−	28.0152i	−0.923369	−	1.20336i
$543$	6.79379			0.291549
$544$	−21.5753	+	20.4078i	−0.925034	+	0.874979i
$545$	4.05553	+	2.34146i	0.173720	+	0.100297i
$546$	−14.8029	+	11.3587i	−0.633507	+	0.486107i
$547$	−0.303076	−	0.0198646i	−0.0129586	−	0.000849351i	0.0589225	−	0.998263i	$-0.481234\pi$
$547$	−0.303076	−	0.0198646i	−0.0129586	−	0.000849351i	−0.0718810	+	0.997413i	$0.522900\pi$
$548$	−9.88629	+	9.88629i	−0.422321	+	0.422321i
$549$	−0.517905	−	0.590557i	−0.0221036	−	0.0252044i
$550$	0.851518	+	12.9917i	0.0363089	+	0.553966i
$551$	2.06129	−	10.3628i	0.0878138	−	0.441470i
$552$	0.253338	−	1.92429i	0.0107828	−	0.0819032i
$553$	34.9845	+	26.8446i	1.48769	+	1.14155i
$554$	−7.54033	−	22.2131i	−0.320358	−	0.943743i
$555$	8.27192	+	12.3798i	0.351123	+	0.525493i
$556$	1.30821	+	1.49173i	0.0554806	+	0.0632635i
$557$	16.1787	−	16.1787i	0.685515	−	0.685515i	−0.275722	−	0.961237i	$-0.588917\pi$
$557$	16.1787	−	16.1787i	0.685515	−	0.685515i	0.961237	+	0.275722i	$0.0889169\pi$
$558$	1.02708	−	1.53713i	0.0434797	−	0.0650720i
$559$	9.16272	+	2.15908i	0.387542	+	0.0913194i
$560$			21.6554i			0.915110i
$561$	1.54127	+	14.8965i	0.0650723	+	0.628929i
$562$	−0.431825	+	0.249314i	−0.0182154	+	0.0105167i
$563$	−3.45046	+	8.33015i	−0.145420	+	0.351074i	−0.979760	−	0.200176i	$-0.935849\pi$
$563$	−3.45046	+	8.33015i	−0.145420	+	0.351074i	0.834341	+	0.551249i	$0.185849\pi$
$564$	2.03008	−	30.9730i	0.0854817	−	1.30420i
$565$	−3.10503	+	11.5881i	−0.130630	+	0.487516i
$566$	13.2430	−	39.0128i	0.556647	−	1.63983i
$567$	31.0589	−	20.7529i	1.30435	−	0.871539i
$568$	−2.51819	−	2.20839i	−0.105661	−	0.0926620i
$569$	26.6397	+	20.4414i	1.11679	+	0.856946i	0.990833	−	0.135089i	$-0.0431321\pi$
$569$	26.6397	+	20.4414i	1.11679	+	0.856946i	0.125961	+	0.992035i	$0.459799\pi$
$570$	13.7549	+	33.2072i	0.576129	+	1.39090i
$571$	18.3858	−	6.24114i	0.769423	−	0.261184i	0.0909952	−	0.995851i	$-0.470995\pi$
$571$	18.3858	−	6.24114i	0.769423	−	0.261184i	0.678427	+	0.734668i	$0.262662\pi$
$572$	0.291680	+	4.45017i	0.0121957	+	0.186071i
$573$	1.63460	−	4.81538i	0.0682864	−	0.201165i
$574$	0.0650410	+	0.242736i	0.00271476	+	0.0101316i
$575$	3.75199	+	2.50700i	0.156469	+	0.104549i
$576$	−1.21559	+	0.932757i	−0.0506497	+	0.0388649i
$577$	−6.46420	+	11.1963i	−0.269108	+	0.466109i	−0.968632	−	0.248501i	$-0.920062\pi$
$577$	−6.46420	+	11.1963i	−0.269108	+	0.466109i	0.699524	+	0.714609i	$0.253396\pi$
$578$	−10.6207	−	30.3038i	−0.441762	−	1.26047i
$579$	35.8887	−	20.7203i	1.49148	−	0.861108i
$580$	0.929079	−	2.24299i	0.0385779	−	0.0931353i
$581$	−30.7849	−	20.5698i	−1.27717	−	0.853380i
$582$	11.1929	−	41.7724i	0.463960	−	1.73152i
$583$	−10.5986	+	9.29474i	−0.438950	+	0.384949i
$584$	−9.33531	+	0.611868i	−0.386298	+	0.0253193i
$585$	0.420864	−	0.479904i	0.0174006	−	0.0198416i
$586$	−3.66059	−	8.83745i	−0.151218	−	0.365072i
$587$	1.19554	−	9.08105i	0.0493454	−	0.374815i	−0.948899	−	0.315581i	$-0.897801\pi$
$587$	1.19554	−	9.08105i	0.0493454	−	0.374815i	0.998244	−	0.0592345i	$-0.0188660\pi$
$588$	15.3202	+	13.4354i	0.631792	+	0.554067i
$589$	22.8000	−	1.49439i	0.939457	−	0.0615753i
$590$	−8.32190	−	9.48931i	−0.342607	−	0.390669i
$591$	4.32601	+	4.32601i	0.177948	+	0.177948i
$592$	−30.7359	−	2.01454i	−1.26324	−	0.0827970i
$593$	21.1186	+	27.5222i	0.867235	+	1.13020i	0.990457	+	0.137824i	$0.0440107\pi$
$593$	21.1186	+	27.5222i	0.867235	+	1.13020i	−0.123222	+	0.992379i	$0.539323\pi$
$594$		−	18.1092i		−	0.743028i
$595$	−17.4258	−	7.79235i	−0.714389	−	0.319455i
$596$	6.40651	−	3.69880i	0.262421	−	0.151509i
$597$	50.9129	−	6.70281i	2.08373	−	0.274328i
$598$	2.92463	+	1.95417i	0.119597	+	0.0799121i
$599$	−0.111573	+	0.416397i	−0.00455876	+	0.0170135i	−0.968168	−	0.250302i	$-0.919470\pi$
$599$	−0.111573	+	0.416397i	−0.00455876	+	0.0170135i	0.963609	+	0.267316i	$0.0861367\pi$
$600$	1.01546	+	5.10508i	0.0414561	+	0.208414i
$601$	7.92078	−	5.29250i	0.323095	−	0.215885i	−0.383435	−	0.923568i	$-0.625259\pi$
$601$	7.92078	−	5.29250i	0.323095	−	0.215885i	0.706531	+	0.707682i	$0.250259\pi$
$602$	1.63002	−	46.4646i	0.0664346	−	1.89375i
$603$	4.33221	−	1.79446i	0.176421	−	0.0730761i
$604$	25.7838	−	10.6800i	1.04913	−	0.434563i
$605$	−8.26214	+	2.80462i	−0.335904	+	0.114024i
$606$	−20.4674	+	13.6759i	−0.831430	+	0.555544i
$607$	−32.0230	+	28.0834i	−1.29977	+	1.13987i	−0.318359	+	0.947970i	$0.603132\pi$
$607$	−32.0230	+	28.0834i	−1.29977	+	1.13987i	−0.981414	+	0.191900i	$0.938535\pi$
$608$	−58.5537	−	15.6894i	−2.37467	−	0.636290i
$609$	3.82079	+	7.74779i	0.154826	+	0.313956i
$610$	1.94260	−	4.68985i	0.0786536	−	0.189887i
$611$	−13.4262	−	7.75163i	−0.543167	−	0.313598i
$612$	−0.540358	−	2.26694i	−0.0218427	−	0.0916355i
$613$	−12.4485			−0.502791			−0.251396	−	0.967884i	$-0.580890\pi$
$613$	−12.4485			−0.502791			−0.251396	+	0.967884i	$0.580890\pi$
$614$	0.503549	+	3.82483i	0.0203216	+	0.154358i
$615$	−0.0354443	−	0.0718740i	−0.00142925	−	0.00289824i
$616$	−5.86366	+	1.57116i	−0.236254	+	0.0633039i
$617$	5.29069	+	1.79595i	0.212995	+	0.0723022i	0.425898	−	0.904771i	$-0.359958\pi$
$617$	5.29069	+	1.79595i	0.212995	+	0.0723022i	−0.212902	+	0.977073i	$0.568292\pi$
$618$	−18.7032	−	27.9913i	−0.752353	−	1.12598i
$619$	−29.5917	−	25.9512i	−1.18939	−	1.04307i	−0.998105	−	0.0615319i	$-0.980401\pi$
$619$	−29.5917	−	25.9512i	−1.18939	−	1.04307i	−0.191284	−	0.981535i	$-0.561265\pi$
$620$	5.20528	+	0.685288i	0.209049	+	0.0275218i
$621$	−4.97949	−	3.82090i	−0.199820	−	0.153327i
$622$	16.4004	−	5.56720i	0.657598	−	0.223224i
$623$	35.6521	−	23.8220i	1.42837	−	0.954408i
$624$	2.40147	+	12.0730i	0.0961356	+	0.483306i
$625$	−4.34204	−	1.16345i	−0.173682	−	0.0465379i
$626$	−2.75324	+	42.0064i	−0.110042	+	1.67891i
$627$	−24.2518	+	18.6091i	−0.968525	+	0.743176i
$628$	12.2248	−	21.1741i	0.487824	−	0.844937i
$629$	12.6809	−	24.0078i	0.505619	−	0.957255i
$630$	−2.73017	−	1.57626i	−0.108773	−	0.0627999i
$631$	24.2005	−	18.5697i	0.963408	−	0.739249i	−0.00199870	−	0.999998i	$-0.500636\pi$
$631$	24.2005	−	18.5697i	0.963408	−	0.739249i	0.965407	+	0.260749i	$0.0839695\pi$
$632$	8.59997	−	4.24104i	0.342088	−	0.168699i
$633$	−0.831263	+	3.10231i	−0.0330397	+	0.123306i
$634$	−58.7047	+	11.6771i	−2.33146	+	0.463756i
$635$	5.63466	+	2.77870i	0.223605	+	0.110270i
$636$	13.4829	−	15.3743i	0.534632	−	0.609631i
$637$	9.40291	−	3.89481i	0.372557	−	0.154318i
$638$	4.65843	+	0.613293i	0.184429	+	0.0242805i
$639$	1.40080	−	0.475507i	0.0554147	−	0.0188108i
$640$	7.05461	+	3.47895i	0.278858	+	0.137518i
$641$	−6.46923	−	32.5230i	−0.255519	−	1.28458i	−0.868976	−	0.494854i	$-0.835222\pi$
$641$	−6.46923	−	32.5230i	−0.255519	−	1.28458i	0.613457	−	0.789728i	$-0.289778\pi$
$642$	20.4599	+	5.48221i	0.807488	+	0.216366i
$643$	−18.8627	−	12.6036i	−0.743872	−	0.497039i	0.124951	−	0.992163i	$-0.460123\pi$
$643$	−18.8627	−	12.6036i	−0.743872	−	0.497039i	−0.868823	+	0.495124i	$0.835123\pi$
$644$	2.92144	−	7.05298i	0.115121	−	0.277926i
$645$	2.38091	+	14.6341i	0.0937483	+	0.576217i
$646$	41.3311	−	50.8708i	1.62615	−	2.00148i
$647$			17.7889i			0.699353i	0.936871	+	0.349676i	$0.113708\pi$
$647$			17.7889i			0.699353i	−0.936871	+	0.349676i	$0.886292\pi$
$648$	−1.06021	−	8.05313i	−0.0416492	−	0.316357i
$649$	5.96361	−	8.92517i	0.234092	−	0.350344i
$650$	−9.11160	−	2.44144i	−0.357386	−	0.0957613i
$651$	−14.0454	+	12.3175i	−0.550483	+	0.482761i
$652$	−0.0958939	−	1.46306i	−0.00375550	−	0.0572978i
$653$	−4.63830	−	0.922616i	−0.181511	−	0.0361048i	0.103498	−	0.994630i	$-0.466997\pi$
$653$	−4.63830	−	0.922616i	−0.181511	−	0.0361048i	−0.285009	+	0.958525i	$0.591997\pi$
$654$	1.71601	−	13.0344i	0.0671012	−	0.509684i
$655$	2.50355	−	3.26269i	0.0978217	−	0.127484i
$656$	0.162601	+	0.0323434i	0.00634852	+	0.00126280i
$657$	1.82751	−	3.70583i	0.0712981	−	0.144578i
$658$	−24.6123	+	72.5056i	−0.959488	+	2.82656i
$659$	11.3164	+	42.2335i	0.440826	+	1.64519i	0.726727	+	0.686926i	$0.241040\pi$
$659$	11.3164	+	42.2335i	0.440826	+	1.64519i	−0.285901	+	0.958259i	$0.592293\pi$
$660$	−6.29968	+	3.10666i	−0.245215	+	0.120927i
$661$	26.5410	+	10.9936i	1.03232	+	0.427603i	0.833551	−	0.552442i	$-0.186304\pi$
$661$	26.5410	+	10.9936i	1.03232	+	0.427603i	0.198774	+	0.980045i	$0.436304\pi$
$662$	−15.2461	−	8.80235i	−0.592557	−	0.342113i
$663$	−10.5791	−	2.41184i	−0.410857	−	0.0936681i
$664$	−6.97234	+	4.02548i	−0.270579	+	0.156219i
$665$	−5.08578	−	38.6303i	−0.197218	−	1.49802i
$666$	2.49120	−	3.72834i	0.0965319	−	0.144470i
$667$	1.15153	−	1.15153i	0.0445874	−	0.0445874i
$668$	−10.2714	+	9.00778i	−0.397413	+	0.348522i
$669$	−16.9230	+	34.3165i	−0.654282	+	1.32675i
$670$	22.7838	+	19.9809i	0.880217	+	0.771929i
$671$	4.28029	+	0.563511i	0.165239	+	0.0217541i
$672$	45.7899	−	18.9668i	1.76639	−	0.731661i
$673$	9.33160	+	8.18359i	0.359707	+	0.315454i	0.820056	−	0.572284i	$-0.193942\pi$
$673$	9.33160	+	8.18359i	0.359707	+	0.315454i	−0.460349	+	0.887738i	$0.652276\pi$
$674$	−14.6209	+	0.958307i	−0.563178	+	0.0369126i
$675$	15.9391	+	5.41058i	0.613495	+	0.208253i
$676$	16.5669	+	4.43908i	0.637188	+	0.170734i
$677$	6.61790	−	9.90438i	0.254346	−	0.380656i	−0.682220	−	0.731147i	$-0.738985\pi$
$677$	6.61790	−	9.90438i	0.254346	−	0.380656i	0.936566	+	0.350491i	$0.113985\pi$
$678$	33.3920	−	4.39614i	1.28241	−	0.168833i
$679$	−23.4400	+	40.5993i	−0.899546	+	1.55806i
$680$	−3.19562	+	2.64902i	−0.122546	+	0.101585i
$681$	−9.47756	+	16.4156i	−0.363181	+	0.629048i
$682$	1.32627	+	10.0740i	0.0507853	+	0.385753i
$683$	19.1850	+	1.25745i	0.734093	+	0.0481150i	0.427864	−	0.903843i	$-0.359266\pi$
$683$	19.1850	+	1.25745i	0.734093	+	0.0481150i	0.306229	+	0.951958i	$0.400933\pi$
$684$	3.36362	−	3.36362i	0.128611	−	0.128611i
$685$	−8.26919	+	7.25188i	−0.315949	+	0.277080i
$686$	−0.352968	−	0.528254i	−0.0134764	−	0.0201688i
$687$	−53.5573	−	10.6532i	−2.04334	−	0.406445i
$688$	−27.0168	−	14.5222i	−1.03000	−	0.553654i
$689$	−3.90858	−	9.43615i	−0.148905	−	0.359489i
$690$	−1.08079	+	5.43348i	−0.0411448	+	0.206849i
$691$	8.16386	−	16.5547i	0.310568	−	0.629769i	−0.684495	−	0.729018i	$-0.739977\pi$
$691$	8.16386	−	16.5547i	0.310568	−	0.629769i	0.995063	+	0.0992486i	$0.0316439\pi$
$692$	38.0939	−	7.57735i	1.44811	−	0.288048i
$693$	0.693931	−	2.58979i	0.0263603	−	0.0983778i
$694$	−2.94386	+	44.9146i	−0.111747	+	1.70494i
$695$	0.950171	+	1.23829i	0.0360420	+	0.0469709i
$696$	1.87847			0.0712031
$697$	−0.0845357	+	0.119205i	−0.00320202	+	0.00451520i
$698$	−22.2388	−	38.5187i	−0.841750	−	1.45795i
$699$	7.67718	−	18.5343i	0.290378	−	0.701033i
$700$	−1.33901	+	20.4293i	−0.0506097	+	0.772154i
$701$	34.3795	−	9.21195i	1.29850	−	0.347931i	0.457614	−	0.889151i	$-0.348704\pi$
$701$	34.3795	−	9.21195i	1.29850	−	0.347931i	0.840881	+	0.541220i	$0.182037\pi$
$702$	12.4243	+	4.21748i	0.468925	+	0.159179i
$703$	55.3017	−	3.62467i	2.08574	−	0.136707i
$704$	1.64295	−	8.25968i	0.0619211	−	0.311299i
$705$	3.18714	−	24.2087i	0.120035	−	0.911754i
$706$	−3.25260	+	24.7059i	−0.122413	+	0.929820i
$707$	25.2683	−	8.57743i	0.950312	−	0.322588i
$708$	−6.88687	+	13.9652i	−0.258825	+	0.524844i
$709$	32.0881	−	6.38272i	1.20509	−	0.239708i	0.448614	−	0.893726i	$-0.351918\pi$
$709$	32.0881	−	6.38272i	1.20509	−	0.239708i	0.756479	+	0.654018i	$0.226918\pi$
$710$	6.76005	+	6.76005i	0.253700	+	0.253700i
$711$	−0.276987	+	4.22601i	−0.0103878	+	0.158488i
$712$	−1.21701	−	9.24410i	−0.0456093	−	0.346437i
$713$	3.04988	+	1.76085i	0.114219	+	0.0659443i
$714$	−1.48967	+	53.5689i	−0.0557495	+	2.00477i
$715$			3.50830i			0.131203i
$716$	−31.4925	+	24.1651i	−1.17693	+	0.903091i
$717$	−0.480522	+	0.236967i	−0.0179454	+	0.00884971i
$718$	−2.71277	−	10.1242i	−0.101240	−	0.377832i
$719$	−30.0642	+	26.3656i	−1.12120	+	0.983270i	−0.999956	−	0.00935233i	$-0.997023\pi$
$719$	−30.0642	+	26.3656i	−1.12120	+	0.983270i	−0.121248	+	0.992622i	$0.538690\pi$
$720$	−1.72928	+	1.15547i	−0.0644465	+	0.0430618i
$721$	11.7306	+	34.5571i	0.436869	+	1.28697i
$722$	97.0624	+	12.7785i	3.61229	+	0.475567i
$723$	−1.07354	−	2.59177i	−0.0399256	−	0.0963888i
$724$	3.83122	−	4.36867i	0.142386	−	0.162360i
$725$	−1.93162	+	3.91695i	−0.0717387	+	0.145472i
$726$	16.1507	+	18.4164i	0.599409	+	0.683495i
$727$	−8.21498	−	8.21498i	−0.304677	−	0.304677i	0.538164	−	0.842840i	$-0.319118\pi$
$727$	−8.21498	−	8.21498i	−0.304677	−	0.304677i	−0.842840	+	0.538164i	$0.819118\pi$
$728$	0.287659	−	4.38884i	0.0106614	−	0.162661i
$729$	−21.2701	−	8.81038i	−0.787783	−	0.326310i
$730$	26.7031			0.988326
$731$	21.4073	−	16.5144i	0.791779	−	0.610808i
$732$	−6.26255			−0.231470
$733$	3.05943	+	1.26726i	0.113002	+	0.0468072i	0.438468	−	0.898747i	$-0.355521\pi$
$733$	3.05943	+	1.26726i	0.113002	+	0.0468072i	−0.325466	+	0.945554i	$0.605521\pi$
$734$	1.49428	−	22.7983i	0.0551549	−	0.841502i
$735$	11.3348	+	11.3348i	0.418089	+	0.418089i
$736$	−6.16043	−	7.02462i	−0.227076	−	0.258931i
$737$	−11.3990	+	23.1150i	−0.419889	+	0.851451i
$738$	−0.0159131	+	0.0181455i	−0.000585771	+	0.000667944i
$739$	−5.09579	−	12.3023i	−0.187452	−	0.452548i	0.802016	−	0.597303i	$-0.203761\pi$
$739$	−5.09579	−	12.3023i	−0.187452	−	0.452548i	−0.989468	+	0.144754i	$0.953761\pi$
$740$	12.6255	+	1.66218i	0.464122	+	0.0611028i
$741$	−7.11922	−	20.9726i	−0.261531	−	0.770446i
$742$	−41.9427	+	28.0252i	−1.53976	+	1.02884i
$743$	−16.0744	+	14.0969i	−0.589712	+	0.517164i	−0.901381	−	0.433027i	$-0.857445\pi$
$743$	−16.0744	+	14.0969i	−0.589712	+	0.517164i	0.311669	+	0.950191i	$0.399112\pi$
$744$	1.05139	+	3.92383i	0.0385457	+	0.143854i
$745$	5.21928	−	2.57387i	0.191220	−	0.0942991i
$746$	−53.0734	+	40.7247i	−1.94316	+	1.49104i
$747$		−	3.55585i		−	0.130102i
$748$	10.4482	+	7.40947i	0.382023	+	0.270917i
$749$	−19.8853	−	11.4808i	−0.726594	−	0.419499i
$750$	−4.72649	−	35.9013i	−0.172587	−	1.31093i
$751$	−1.74514	+	26.6256i	−0.0636809	+	0.971583i	0.839784	+	0.542921i	$0.182682\pi$
$751$	−1.74514	+	26.6256i	−0.0636809	+	0.971583i	−0.903465	+	0.428662i	$0.858985\pi$
$752$	35.7189	+	35.7189i	1.30253	+	1.30253i
$753$	−19.4941	+	3.87762i	−0.710404	+	0.141308i
$754$	−1.50568	+	3.05321i	−0.0548335	+	0.111191i
$755$	20.7892	−	7.05700i	0.756598	−	0.256830i
$756$	3.71693	−	28.2329i	0.135184	−	1.02682i
$757$	2.07715	−	15.7775i	0.0754953	−	0.573444i	−0.911333	−	0.411671i	$-0.864945\pi$
$757$	2.07715	−	15.7775i	0.0754953	−	0.573444i	0.986828	−	0.161773i	$-0.0517213\pi$
$758$	4.77937	−	24.0275i	0.173594	−	0.872718i
$759$	−4.70148	+	0.308151i	−0.170653	+	0.0111852i
$760$	−8.02295	−	2.72343i	−0.291023	−	0.0987890i
$761$	−5.25821	+	1.40893i	−0.190610	+	0.0510738i	−0.352861	−	0.935676i	$-0.614791\pi$
$761$	−5.25821	+	1.40893i	−0.190610	+	0.0510738i	0.162251	+	0.986749i	$0.448125\pi$
$762$	1.15356	−	17.5999i	0.0417890	−	0.637576i
$763$	−5.45385	+	13.1668i	−0.197443	+	0.476669i
$764$	−2.17468	−	3.76665i	−0.0786770	−	0.136273i
$765$	−0.307535	−	1.80730i	−0.0111190	−	0.0653431i
$766$	41.9775			1.51671
$767$	4.73448	+	6.17010i	0.170952	+	0.222789i
$768$	2.46344	−	37.5848i	0.0888916	−	1.35622i
$769$	−5.20374	+	19.4206i	−0.187652	+	0.700325i	0.806396	+	0.591376i	$0.201415\pi$
$769$	−5.20374	+	19.4206i	−0.187652	+	0.700325i	−0.994047	+	0.108949i	$0.965252\pi$
$770$	16.9942	−	3.38036i	0.612429	−	0.121820i
$771$	−8.43208	+	17.0986i	−0.303674	+	0.615790i
$772$	6.91472	−	34.7627i	0.248866	−	1.25114i
$773$	13.6832	+	33.0343i	0.492152	+	1.18816i	0.953623	+	0.301004i	$0.0973219\pi$
$773$	13.6832	+	33.0343i	0.492152	+	1.18816i	−0.461471	+	0.887155i	$0.652678\pi$
$774$	3.79737	−	2.34904i	0.136494	−	0.0844346i
$775$	−9.26303	−	1.84253i	−0.332738	−	0.0661857i
$776$	5.66349	+	8.47601i	0.203307	+	0.304271i
$777$	−34.0674	+	29.8763i	−1.22216	+	1.07181i
$778$	44.4103	−	44.4103i	1.59219	−	1.59219i
$779$	−0.297654	−	0.0195093i	−0.0106646	−	0.000698993i
$780$	−0.664264	−	5.04559i	−0.0237845	−	0.180661i
$781$	−4.06533	+	7.04136i	−0.145469	+	0.251960i
$782$	9.65282	−	2.98013i	0.345184	−	0.106569i
$783$	3.03732	−	5.26078i	0.108545	−	0.188005i
$784$	−32.8780	+	4.32847i	−1.17421	+	0.154588i
$785$	10.6857	−	15.9922i	0.381388	−	0.570787i
$786$	−11.1521	−	2.98819i	−0.397782	−	0.106585i
$787$	49.9506	+	16.9559i	1.78055	+	0.604414i	0.999791	−	0.0204225i	$-0.00650115\pi$
$787$	49.9506	+	16.9559i	1.78055	+	0.604414i	0.780755	+	0.624837i	$0.214834\pi$
$788$	5.22137	−	0.342226i	0.186003	−	0.0121913i
$789$	−15.3839	−	13.4913i	−0.547681	−	0.480303i
$790$	−25.2862	+	10.4739i	−0.899643	+	0.372644i
$791$	−36.1980	−	4.76556i	−1.28705	−	0.169444i
$792$	−0.438331	−	0.384406i	−0.0155754	−	0.0136593i
$793$	−1.38346	+	2.80537i	−0.0491280	+	0.0996218i
$794$	32.6880	−	28.6666i	1.16006	−	1.01734i
$795$	11.3748	−	11.3748i	0.403423	−	0.403423i
$796$	24.4011	−	36.5189i	0.864876	−	1.29438i
$797$	−0.850599	−	6.46094i	−0.0301298	−	0.228858i	0.969754	−	0.244083i	$-0.0784870\pi$
$797$	−0.850599	−	6.46094i	−0.0301298	−	0.228858i	−0.999884	+	0.0152247i	$0.995154\pi$
$798$	−94.7315	+	54.6932i	−3.35346	+	1.93612i
$799$	−41.5953	+	15.8896i	−1.47154	+	0.562134i
$800$	21.6998	+	12.5284i	0.767202	+	0.442944i
$801$	3.80458	+	1.57591i	0.134428	+	0.0556820i
$802$	−43.2663	+	21.3366i	−1.52779	+	0.753421i
$803$	5.87786	+	21.9365i	0.207425	+	0.774121i
$804$	12.0173	−	35.4019i	0.423818	−	1.24853i
$805$	2.65615	−	5.38614i	0.0936170	−	0.189836i
$806$	−7.22041	−	1.43623i	−0.254328	−	0.0505890i
$807$	−35.5318	+	46.3060i	−1.25078	+	1.63005i
$808$	0.757378	−	5.75285i	0.0266445	−	0.202385i
$809$	10.0416	+	1.99739i	0.353043	+	0.0702246i	0.368426	−	0.929657i	$-0.379897\pi$
$809$	10.0416	+	1.99739i	0.353043	+	0.0702246i	−0.0153830	+	0.999882i	$0.504897\pi$
$810$	1.51634	+	23.1349i	0.0532788	+	0.812877i
$811$	14.7260	−	12.9143i	0.517099	−	0.453484i	−0.360583	−	0.932727i	$-0.617422\pi$
$811$	14.7260	−	12.9143i	0.517099	−	0.453484i	0.877682	+	0.479243i	$0.159089\pi$
$812$	7.13679	+	1.91230i	0.250452	+	0.0671085i
$813$	−19.0398	+	28.4951i	−0.667756	+	0.999367i
$814$	3.21688	+	24.4346i	0.112752	+	0.856433i
$815$		−	1.15341i		−	0.0404020i
$816$	31.2613	+	16.5121i	1.09436	+	0.578040i
$817$	51.6047	+	19.5607i	1.80542	+	0.684343i
$818$	11.5854	−	27.9695i	0.405072	−	0.977931i
$819$	1.61518	+	1.07923i	0.0564391	+	0.0377114i
$820$	−0.0662059	−	0.0177398i	−0.00231201	−	0.000619501i
$821$	−2.35553	−	11.8420i	−0.0822085	−	0.413290i	−0.999873	−	0.0159340i	$-0.994928\pi$
$821$	−2.35553	−	11.8420i	−0.0822085	−	0.413290i	0.917665	−	0.397356i	$-0.130072\pi$
$822$	27.6931	+	13.6567i	0.965909	+	0.476334i
$823$	−13.2310	+	4.49132i	−0.461203	+	0.156557i	−0.542364	−	0.840144i	$-0.682471\pi$
$823$	−13.2310	+	4.49132i	−0.461203	+	0.156557i	0.0811607	+	0.996701i	$0.474137\pi$
$824$	7.86764	+	1.03579i	0.274082	+	0.0360836i
$825$	11.6737	−	4.83539i	0.406425	−	0.168347i
$826$	25.3261	−	28.8789i	0.881209	−	1.00483i
$827$	18.0314	+	8.89209i	0.627012	+	0.309208i	0.727893	−	0.685690i	$-0.240500\pi$
$827$	18.0314	+	8.89209i	0.627012	+	0.309208i	−0.100881	+	0.994898i	$0.532166\pi$
$828$	0.719090	−	0.143036i	0.0249901	−	0.00497084i
$829$	9.25374	−	34.5354i	0.321396	−	1.19946i	−0.596490	−	0.802620i	$-0.703439\pi$
$829$	9.25374	−	34.5354i	0.321396	−	1.19946i	0.917886	−	0.396845i	$-0.129895\pi$
$830$	20.6102	−	10.1638i	0.715389	−	0.352791i
$831$	−18.0615	+	13.8591i	−0.626547	+	0.480766i
$832$	5.28415	+	3.05081i	0.183195	+	0.105768i
$833$	8.34754	−	28.0140i	0.289225	−	0.970626i
$834$	2.19093	−	3.79480i	0.0758657	−	0.131403i
$835$	−8.52630	+	6.54246i	−0.295065	+	0.226411i
$836$	−1.70997	+	26.0891i	−0.0591406	+	0.902311i
$837$	12.6890	+	3.40000i	0.438595	+	0.117521i
$838$	−8.66291	−	43.5514i	−0.299255	−	1.50446i
$839$	31.4548	−	21.0174i	1.08594	−	0.725602i	0.122216	−	0.992504i	$-0.461000\pi$
$839$	31.4548	−	21.0174i	1.08594	−	0.725602i	0.963724	+	0.266902i	$0.0859999\pi$
$840$	6.55961	−	2.22669i	0.226328	−	0.0768281i
$841$	−21.7568	−	16.6946i	−0.750235	−	0.575676i
$842$	60.7868	+	8.00273i	2.09485	+	0.275792i
$843$	0.363830	+	0.319071i	0.0125310	+	0.0109894i
$844$	1.52614	+	2.28402i	0.0525317	+	0.0786193i
$845$	12.7763	+	4.33696i	0.439517	+	0.149196i
$846$	−7.10312	+	1.90328i	−0.244210	+	0.0654359i
$847$	−11.7443	−	23.8151i	−0.403539	−	0.818295i
$848$	4.34377	+	32.9942i	0.149166	+	1.13303i
$849$	−39.9839			−1.37224
$850$	−21.9442	+	15.8891i	−0.752678	+	0.544991i
$851$	7.39754	+	4.27097i	0.253584	+	0.146407i
$852$	4.51348	−	10.8965i	0.154629	−	0.373308i
$853$	−7.15194	−	14.5027i	−0.244878	−	0.496563i	0.739383	−	0.673285i	$-0.235117\pi$
$853$	−7.15194	−	14.5027i	−0.244878	−	0.496563i	−0.984261	+	0.176722i	$0.943451\pi$
$854$	14.9222	+	3.99840i	0.510628	+	0.136822i
$855$	2.81343	−	2.46732i	0.0962174	−	0.0843804i
$856$	−4.15150	+	2.77394i	−0.141895	+	0.0948114i
$857$	−24.9454	+	8.46783i	−0.852120	+	0.289256i	−0.713125	−	0.701037i	$-0.752721\pi$
$857$	−24.9454	+	8.46783i	−0.852120	+	0.289256i	−0.138995	+	0.990293i	$0.544387\pi$
$858$	9.09947	−	3.76913i	0.310651	−	0.128676i
$859$	26.5998	−	11.0180i	0.907573	−	0.375929i	0.120446	−	0.992720i	$-0.461568\pi$
$859$	26.5998	−	11.0180i	0.907573	−	0.375929i	0.787127	+	0.616791i	$0.211568\pi$
$860$	10.7530	+	6.72159i	0.366673	+	0.229204i
$861$	0.202784	−	0.135496i	0.00691086	−	0.00461769i
$862$	2.38396	+	11.9850i	0.0811982	+	0.408211i
$863$	−5.37377	+	20.0552i	−0.182925	+	0.682687i	0.812140	+	0.583463i	$0.198303\pi$
$863$	−5.37377	+	20.0552i	−0.182925	+	0.682687i	−0.995065	+	0.0992237i	$0.968364\pi$
$864$	−28.9784	−	19.3627i	−0.985864	−	0.658733i
$865$	30.2928	−	3.98812i	1.02999	−	0.135600i
$866$	41.6251	−	24.0322i	1.41448	−	0.816649i
$867$	−24.5359	+	19.2139i	−0.833283	+	0.652537i
$868$			15.9780i			0.542328i
$869$	−14.1702	−	18.4670i	−0.480692	−	0.626449i
$870$	−5.35027	−	0.350675i	−0.181391	−	0.0118890i
$871$	−13.2039	−	13.2039i	−0.447398	−	0.447398i
$872$	2.04331	+	2.32994i	0.0691951	+	0.0789019i
$873$	−4.49272	+	0.294468i	−0.152055	+	0.00996624i
$874$	15.5036	+	13.5963i	0.524416	+	0.459901i
$875$	−5.12367	+	38.9181i	−0.173212	+	1.31567i
$876$	−12.6069	−	30.4358i	−0.425948	−	1.02833i
$877$	−18.9723	+	21.6338i	−0.640649	+	0.730520i	−0.977476	−	0.211046i	$-0.932313\pi$
$877$	−18.9723	+	21.6338i	−0.640649	+	0.730520i	0.336827	+	0.941567i	$0.390646\pi$
$878$	−43.5174	+	2.85228i	−1.46864	+	0.0962598i
$879$	−6.97964	+	6.12098i	−0.235418	+	0.206456i
$880$	2.95858	−	11.0416i	0.0997337	−	0.372211i
$881$	9.86745	+	6.59322i	0.332443	+	0.222131i	0.710577	−	0.703620i	$-0.248434\pi$
$881$	9.86745	+	6.59322i	0.332443	+	0.222131i	−0.378134	+	0.925751i	$0.623434\pi$
$882$	1.84743	−	4.46010i	0.0622063	−	0.150179i
$883$	−21.6994	+	12.5281i	−0.730242	+	0.421605i	−0.818511	−	0.574491i	$-0.805200\pi$
$883$	−21.6994	+	12.5281i	−0.730242	+	0.421605i	0.0882687	+	0.996097i	$0.471867\pi$
$884$	−7.51677	+	5.44265i	−0.252816	+	0.183056i
$885$	−6.12457	+	10.6081i	−0.205875	+	0.356586i
$886$	0.672142	−	0.515753i	0.0225811	−	0.0173271i
$887$	6.68675	+	4.46795i	0.224519	+	0.150019i	0.662743	−	0.748847i	$-0.269392\pi$
$887$	6.68675	+	4.46795i	0.224519	+	0.150019i	−0.438224	+	0.898866i	$0.644392\pi$
$888$	2.55015	+	9.51731i	0.0855776	+	0.319380i
$889$	−6.14585	+	18.1051i	−0.206125	+	0.607225i
$890$	1.74059	+	26.5563i	0.0583447	+	0.890169i
$891$	−18.6714	+	6.33809i	−0.625516	+	0.212334i
$892$	12.5234	+	30.2343i	0.419316	+	1.01232i
$893$	−72.1062	−	55.3290i	−2.41294	−	1.85151i
$894$	−12.2831	−	10.7720i	−0.410809	−	0.360270i
$895$	−25.9643	+	17.3488i	−0.867891	+	0.579906i
$896$	−7.69463	+	22.6677i	−0.257060	+	0.757273i
$897$	0.883520	−	3.29734i	0.0294999	−	0.110095i
$898$	−1.22609	+	18.7066i	−0.0409153	+	0.624246i
$899$	−1.30435	+	3.14898i	−0.0435025	+	0.105024i
$900$	−1.70281	+	0.983119i	−0.0567604	+	0.0327706i
$901$	−28.1130	−	8.37705i	−0.936579	−	0.279080i
$902$		−	0.132651i		−	0.00441680i
$903$	−43.2093	+	12.9970i	−1.43792	+	0.432513i
$904$	−4.41074	+	6.60114i	−0.146699	+	0.219551i
$905$	3.23220	−	3.23220i	0.107442	−	0.107442i
$906$	−40.6385	−	46.3394i	−1.35012	−	1.53952i
$907$	−18.5678	−	27.7886i	−0.616533	−	0.922707i	0.383467	−	0.923555i	$-0.374730\pi$
$907$	−18.5678	−	27.7886i	−0.616533	−	0.922707i	−1.00000		0.000848023i	$0.999730\pi$
$908$	5.21120	+	15.3517i	0.172940	+	0.509464i
$909$	2.03318	+	1.56012i	0.0674365	+	0.0517458i
$910$	−1.63863	+	12.4466i	−0.0543200	+	0.412601i
$911$	4.39029	−	22.0715i	0.145457	−	0.731260i	−0.837356	−	0.546657i	$-0.815900\pi$
$911$	4.39029	−	22.0715i	0.145457	−	0.731260i	0.982813	−	0.184603i	$-0.0590999\pi$
$912$	4.71978	+	72.0100i	0.156288	+	2.38449i
$913$	12.8862	+	14.6939i	0.426471	+	0.486297i
$914$	10.9205	−	10.9205i	0.361217	−	0.361217i
$915$	−4.91597	−	0.322210i	−0.162517	−	0.0106519i
$916$	−37.0530	+	28.4318i	−1.22426	+	0.939411i
$917$	10.8389	+	6.25785i	0.357932	+	0.206652i
$918$	31.9027	−	20.0569i	1.05295	−	0.661976i
$919$	−7.71121			−0.254369			−0.127185	−	0.991879i	$-0.540594\pi$
$919$	−7.71121			−0.254369			−0.127185	+	0.991879i	$0.540594\pi$
$920$	−0.794969	−	1.03602i	−0.0262094	−	0.0341567i
$921$	3.35792	−	1.65594i	0.110647	−	0.0545652i
$922$	35.6362	+	9.54870i	1.17362	+	0.314470i
$923$	−3.88414	−	4.42901i	−0.127848	−	0.145783i
$924$	−11.8761	−	17.7738i	−0.390694	−	0.584716i
$925$	−22.4676	−	4.46909i	−0.738731	−	0.146943i
$926$	−26.2411	−	20.1355i	−0.862337	−	0.661695i
$927$	−2.13363	+	2.78060i	−0.0700775	+	0.0913267i
$928$	5.96228	−	6.79868i	0.195722	−	0.223178i
$929$	−53.2179	+	3.48809i	−1.74602	+	0.114440i	−0.904689	−	0.426073i	$-0.859897\pi$
$929$	−53.2179	+	3.48809i	−1.74602	+	0.114440i	−0.841335	+	0.540514i	$0.818230\pi$
$930$	−2.26206	−	11.3721i	−0.0741759	−	0.372907i
$931$	57.6332	−	15.4428i	1.88885	−	0.506117i
$932$	−7.58892	−	15.3888i	−0.248583	−	0.504077i
$933$	−10.2325	−	13.3352i	−0.334996	−	0.436576i
$934$	−17.6305	+	10.1790i	−0.576886	+	0.333065i
$935$	7.82039	+	6.35385i	0.255754	+	0.207793i
$936$	0.365816	−	0.211204i	0.0119571	−	0.00690342i
$937$	23.3117	−	17.8877i	0.761561	−	0.584367i	−0.153279	−	0.988183i	$-0.548983\pi$
$937$	23.3117	−	17.8877i	0.761561	−	0.584367i	0.914840	+	0.403816i	$0.132317\pi$
$938$	−51.2374	+	76.6822i	−1.67296	+	2.50376i
$939$	39.4627	−	10.5740i	1.28782	−	0.345069i
$940$	−13.7698	−	15.7015i	−0.449123	−	0.512126i
$941$	14.0921	−	28.5760i	0.459390	−	0.931550i	−0.536748	−	0.843743i	$-0.680347\pi$
$941$	14.0921	−	28.5760i	0.459390	−	0.931550i	0.996137	−	0.0878075i	$-0.0279860\pi$
$942$	−52.9591	−	10.5342i	−1.72550	−	0.343223i
$943$	−0.0364751	−	0.0279883i	−0.00118779	−	0.000911426i
$944$	−9.69739	−	23.4116i	−0.315623	−	0.761982i
$945$	4.37031	−	21.9710i	0.142166	−	0.714718i
$946$	−7.17912	+	23.4684i	−0.233413	+	0.763024i
$947$	−25.7584	+	5.12366i	−0.837035	+	0.166497i	−0.594954	−	0.803760i	$-0.702830\pi$
$947$	−25.7584	+	5.12366i	−0.837035	+	0.166497i	−0.242081	+	0.970256i	$0.577830\pi$
$948$	23.8759	+	23.8759i	0.775455	+	0.775455i
$949$	−16.4190	−	1.07616i	−0.532984	−	0.0349336i
$950$	−51.0915	−	21.1628i	−1.65763	−	0.686611i
$951$	29.0446	+	50.3067i	0.941835	+	1.63131i
$952$	−9.26222	−	8.58980i	−0.300190	−	0.278397i
$953$	−20.0728	−	11.5890i	−0.650222	−	0.375406i	0.138319	−	0.990388i	$-0.455830\pi$
$953$	−20.0728	−	11.5890i	−0.650222	−	0.375406i	−0.788541	+	0.614982i	$0.789163\pi$
$954$	−4.47586	−	1.85396i	−0.144911	−	0.0600243i
$955$	−1.51328	−	3.06863i	−0.0489686	−	0.0992986i
$956$	−0.118602	+	0.442628i	−0.00383586	+	0.0143156i
$957$	−0.889616	−	4.47240i	−0.0287572	−	0.144572i
$958$	−8.60051	−	4.24130i	−0.277870	−	0.137030i
$959$	−25.1657	−	22.0697i	−0.812643	−	0.712669i
$960$	−1.25436	+	9.52782i	−0.0404843	+	0.307509i
$961$	23.4270	+	3.08423i	0.755710	+	0.0994911i
$962$	−17.5132	−	3.48360i	−0.564649	−	0.112316i
$963$	−0.144229	−	2.20051i	−0.00464771	−	0.0709104i
$964$	−2.27201	−	0.771244i	−0.0731766	−	0.0248401i
$965$	7.21647	−	26.9322i	0.232306	−	0.866979i
$966$	−16.8236	−	1.10268i	−0.541291	−	0.0354781i
$967$	2.68689	+	1.11295i	0.0864047	+	0.0357900i	0.425467	−	0.904974i	$-0.360110\pi$
$967$	2.68689	+	1.11295i	0.0864047	+	0.0357900i	−0.339062	+	0.940764i	$0.610110\pi$
$968$	−5.77401			−0.185584
$969$	−59.6437	−	22.1136i	−1.91603	−	0.710392i
$970$	−14.5485	−	25.1987i	−0.467123	−	0.809081i
$971$	−31.7071	−	41.3215i	−1.01753	−	1.32607i	−0.944418	−	0.328746i	$-0.893374\pi$
$971$	−31.7071	−	41.3215i	−1.01753	−	1.32607i	−0.0731109	−	0.997324i	$-0.523293\pi$
$972$	5.24069	−	2.58442i	0.168095	−	0.0828954i
$973$	−3.35881	+	3.35881i	−0.107679	+	0.107679i
$974$	−3.38397	+	9.96886i	−0.108429	+	0.319423i
$975$	0.598750	+	9.13516i	0.0191754	+	0.292559i
$976$	6.71991	−	7.66258i	0.215099	−	0.245273i
$977$	−20.0930	−	15.4179i	−0.642831	−	0.493262i	0.235148	−	0.971959i	$-0.424442\pi$
$977$	−20.0930	−	15.4179i	−0.642831	−	0.493262i	−0.877980	+	0.478698i	$0.841109\pi$
$978$	−2.99158	+	1.23915i	−0.0956603	+	0.0396238i
$979$	−21.4327	+	7.27542i	−0.684992	+	0.232524i
$980$	13.6807	−	0.896680i	0.437014	−	0.0286434i
$981$	−1.34242	+	0.267025i	−0.0428603	+	0.00852544i
$982$	−3.75543	−	14.0155i	−0.119841	−	0.447251i
$983$	−25.3408	−	1.66092i	−0.808246	−	0.0529752i	−0.344323	−	0.938851i	$-0.611892\pi$
$983$	−25.3408	−	1.66092i	−0.808246	−	0.0529752i	−0.463922	+	0.885876i	$0.653558\pi$
$984$	−0.00692216	−	0.0525790i	−0.000220670	−	0.00167616i
$985$	4.11627			0.131155
$986$	4.07902	+	8.88595i	0.129903	+	0.282986i
$987$	74.3104			2.36533
$988$	−17.5009	−	7.24912i	−0.556778	−	0.230625i
$989$	4.93838	+	6.92570i	0.157032	+	0.220225i
$990$	1.17670	+	1.17670i	0.0373978	+	0.0373978i
$991$	3.21734	−	0.639969i	0.102202	−	0.0203293i	−0.143724	−	0.989618i	$-0.545908\pi$
$991$	3.21734	−	0.639969i	0.102202	−	0.0203293i	0.245926	+	0.969288i	$0.420908\pi$
$992$	17.5385	+	8.64903i	0.556848	+	0.274607i
$993$	−3.33319	+	16.7571i	−0.105776	+	0.531770i
$994$	−17.7116	+	23.0822i	−0.561779	+	0.732124i
$995$	21.0333	−	27.4111i	0.666801	−	0.868992i
$996$	−21.3149	−	18.6926i	−0.675388	−	0.592299i
$997$	−31.8763	−	47.7062i	−1.00953	−	1.51087i	−0.852126	−	0.523337i	$-0.824687\pi$
$997$	−31.8763	−	47.7062i	−1.00953	−	1.51087i	−0.157406	−	0.987534i	$-0.550313\pi$
$998$	−20.9007	+	61.5715i	−0.661600	+	1.94901i
$999$	30.7773	+	8.24674i	0.973750	+	0.260915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.bd.a.7.13	✓	1024
17.5	odd	16	inner	731.2.bd.a.566.52	yes	1024
43.37	odd	6	inner	731.2.bd.a.381.52	yes	1024
731.209	even	48	inner	731.2.bd.a.209.13	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.bd.a.7.13	✓	1024	1.1	even	1	trivial
731.2.bd.a.209.13	yes	1024	731.209	even	48	inner
731.2.bd.a.381.52	yes	1024	43.37	odd	6	inner
731.2.bd.a.566.52	yes	1024	17.5	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.bd (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74510 - 0.722845i) q^{2} +(-0.119895 + 1.82924i) q^{3} +(1.10866 + 1.10866i) q^{4} +(0.813236 + 0.927317i) q^{5} +(1.53149 - 3.10555i) q^{6} +(-2.47493 + 2.82212i) q^{7} +(0.312353 + 0.754087i) q^{8} +(-0.357413 - 0.0470543i) q^{9} +O(q^{10})\)	\(q+(-1.74510 - 0.722845i) q^{2} +(-0.119895 + 1.82924i) q^{3} +(1.10866 + 1.10866i) q^{4} +(0.813236 + 0.927317i) q^{5} +(1.53149 - 3.10555i) q^{6} +(-2.47493 + 2.82212i) q^{7} +(0.312353 + 0.754087i) q^{8} +(-0.357413 - 0.0470543i) q^{9} +(-0.748872 - 2.20611i) q^{10} +(1.64746 - 1.10080i) q^{11} +(-2.16093 + 1.89509i) q^{12} +(0.371553 + 1.38665i) q^{13} +(6.35895 - 3.13589i) q^{14} +(-1.79379 + 1.37642i) q^{15} -4.67751i q^{16} +(3.76392 + 1.68312i) q^{17} +(0.589708 + 0.340468i) q^{18} +(1.09851 + 8.34403i) q^{19} +(-0.126478 + 1.92968i) q^{20} +(-4.86560 - 4.86560i) q^{21} +(-3.67070 + 0.730147i) q^{22} +(-0.573720 + 1.16339i) q^{23} +(-1.41686 + 0.480958i) q^{24} +(0.454065 - 3.44897i) q^{25} +(0.353938 - 2.68843i) q^{26} +(-0.943973 + 4.74567i) q^{27} +(-5.87263 + 0.384912i) q^{28} +(-1.18881 - 0.403548i) q^{29} +(4.12529 - 1.10537i) q^{30} +(0.177565 - 2.70911i) q^{31} +(-2.75641 + 6.65455i) q^{32} +(1.81611 + 3.14559i) q^{33} +(-5.35179 - 5.65795i) q^{34} -4.62970 q^{35} +(-0.344082 - 0.448417i) q^{36} +(0.430686 - 6.57100i) q^{37} +(4.11442 - 15.3552i) q^{38} +(-2.58107 + 0.513407i) q^{39} +(-0.445261 + 0.902901i) q^{40} +(-0.00691467 + 0.0347624i) q^{41} +(4.97389 + 12.0080i) q^{42} +(3.10469 - 5.77589i) q^{43} +(3.04689 + 0.606064i) q^{44} +(-0.247026 - 0.369701i) q^{45} +(1.84215 - 1.61552i) q^{46} +(-7.63631 + 7.63631i) q^{47} +(8.55629 + 0.560809i) q^{48} +(-0.925379 - 7.02895i) q^{49} +(-3.28546 + 5.69058i) q^{50} +(-3.53011 + 6.68332i) q^{51} +(-1.12540 + 1.94926i) q^{52} +(-7.05380 + 0.928651i) q^{53} +(5.07771 - 7.59934i) q^{54} +(2.36057 + 0.632512i) q^{55} +(-2.90117 - 0.984815i) q^{56} +(-15.3949 + 1.00904i) q^{57} +(1.78290 + 1.56356i) q^{58} +(5.00514 - 2.07320i) q^{59} +(-3.51469 - 0.462718i) q^{60} +(1.63818 + 1.43664i) q^{61} +(-2.26814 + 4.59933i) q^{62} +(1.01736 - 0.892204i) q^{63} +(3.00542 - 3.00542i) q^{64} +(-0.983709 + 1.47222i) q^{65} +(-0.895517 - 6.80213i) q^{66} +(-11.2648 + 6.50374i) q^{67} +(2.30690 + 6.03893i) q^{68} +(-2.05933 - 1.18896i) q^{69} +(8.07929 + 3.34655i) q^{70} +(-3.68034 + 1.81494i) q^{71} +(-0.0761559 - 0.284218i) q^{72} +(-3.68428 + 10.8535i) q^{73} +(-5.50140 + 11.1557i) q^{74} +(6.25456 + 1.24411i) q^{75} +(-8.03282 + 10.4686i) q^{76} +(-0.970770 + 7.37373i) q^{77} +(4.87535 + 0.969767i) q^{78} +(-0.768349 - 11.7227i) q^{79} +(4.33754 - 3.80392i) q^{80} +(-9.61244 - 2.57565i) q^{81} +(0.0371946 - 0.0556657i) q^{82} +(1.28748 + 9.77936i) q^{83} -10.7886i q^{84} +(1.50016 + 4.85912i) q^{85} +(-9.59307 + 7.83531i) q^{86} +(0.880719 - 2.12624i) q^{87} +(1.34469 + 0.898492i) q^{88} +(-11.0340 - 2.95656i) q^{89} +(0.163850 + 0.823728i) q^{90} +(-4.83287 - 2.38331i) q^{91} +(-1.92586 + 0.653743i) q^{92} +(4.93433 + 0.649617i) q^{93} +(18.8460 - 7.80627i) q^{94} +(-6.84421 + 7.80433i) q^{95} +(-11.8423 - 5.83998i) q^{96} +(12.2493 - 2.43655i) q^{97} +(-3.46596 + 12.9351i) q^{98} +(-0.640621 + 0.315920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 24 q^{3} - 32 q^{4} - 24 q^{5} - 8 q^{6} - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 1024 * q - 24 * q^3 - 32 * q^4 - 24 * q^5 - 8 * q^6 - 24 * q^7 - 8 * q^9	\( 1024 q - 24 q^{3} - 32 q^{4} - 24 q^{5} - 8 q^{6} - 24 q^{7} - 8 q^{9} - 8 q^{10} - 48 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{17} - 48 q^{18} - 24 q^{19} - 24 q^{20} - 32 q^{21} + 40 q^{24} - 24 q^{25} - 24 q^{26} - 24 q^{28} - 24 q^{29} - 24 q^{30} + 24 q^{31} - 24 q^{34} - 192 q^{35} + 8 q^{36} - 24 q^{37} - 16 q^{38} - 8 q^{40} - 32 q^{41} + 24 q^{43} + 32 q^{44} + 72 q^{46} + 48 q^{47} + 48 q^{48} - 8 q^{49} - 144 q^{52} - 8 q^{53} + 144 q^{54} + 72 q^{55} - 8 q^{56} - 24 q^{57} - 128 q^{58} + 96 q^{59} - 112 q^{60} + 24 q^{61} - 192 q^{62} - 24 q^{63} + 192 q^{64} - 136 q^{66} - 8 q^{68} - 96 q^{69} - 24 q^{71} - 432 q^{72} - 24 q^{73} + 88 q^{74} + 144 q^{76} - 24 q^{77} - 496 q^{78} - 40 q^{79} + 264 q^{80} - 120 q^{81} - 16 q^{83} - 48 q^{86} - 32 q^{87} - 24 q^{89} - 112 q^{90} - 24 q^{91} + 184 q^{92} + 168 q^{93} + 72 q^{95} + 40 q^{96} - 160 q^{97} - 432 q^{98} + 8 q^{99}+O(q^{100}) \) 1024 * q - 24 * q^3 - 32 * q^4 - 24 * q^5 - 8 * q^6 - 24 * q^7 - 8 * q^9 - 8 * q^10 - 48 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^17 - 48 * q^18 - 24 * q^19 - 24 * q^20 - 32 * q^21 + 40 * q^24 - 24 * q^25 - 24 * q^26 - 24 * q^28 - 24 * q^29 - 24 * q^30 + 24 * q^31 - 24 * q^34 - 192 * q^35 + 8 * q^36 - 24 * q^37 - 16 * q^38 - 8 * q^40 - 32 * q^41 + 24 * q^43 + 32 * q^44 + 72 * q^46 + 48 * q^47 + 48 * q^48 - 8 * q^49 - 144 * q^52 - 8 * q^53 + 144 * q^54 + 72 * q^55 - 8 * q^56 - 24 * q^57 - 128 * q^58 + 96 * q^59 - 112 * q^60 + 24 * q^61 - 192 * q^62 - 24 * q^63 + 192 * q^64 - 136 * q^66 - 8 * q^68 - 96 * q^69 - 24 * q^71 - 432 * q^72 - 24 * q^73 + 88 * q^74 + 144 * q^76 - 24 * q^77 - 496 * q^78 - 40 * q^79 + 264 * q^80 - 120 * q^81 - 16 * q^83 - 48 * q^86 - 32 * q^87 - 24 * q^89 - 112 * q^90 - 24 * q^91 + 184 * q^92 + 168 * q^93 + 72 * q^95 + 40 * q^96 - 160 * q^97 - 432 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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