LMFDB - Embedded newform 744.2.o.e.557.81

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [744,2,Mod(557,744)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(744, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("744.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 744 = 2^{3} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	744.o (of order $2$, degree $1$, 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:	$5.94086991038$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			557.81
Character	$\chi$	$=$	744.557
Dual form			744.2.o.e.557.83

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30178 - 0.552593i) q^{2} +(-1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} +2.01938 q^{5} +(-2.43406 - 0.274495i) q^{6} -0.359027 q^{7} +(1.01352 - 2.64060i) q^{8} +(1.55095 + 2.56798i) q^{9} +O(q^{10})$	\(q+(1.30178 - 0.552593i) q^{2} +(-1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} +2.01938 q^{5} +(-2.43406 - 0.274495i) q^{6} -0.359027 q^{7} +(1.01352 - 2.64060i) q^{8} +(1.55095 + 2.56798i) q^{9} +(2.62880 - 1.11590i) q^{10} -1.25539i q^{11} +(-3.32031 + 0.987712i) q^{12} +4.90527 q^{13} +(-0.467376 + 0.198396i) q^{14} +(-3.04617 - 1.71888i) q^{15} +(-0.139790 - 3.99756i) q^{16} -0.530078 q^{17} +(3.43806 + 2.48591i) q^{18} -1.51514i q^{19} +(2.80549 - 2.90531i) q^{20} +(0.541582 + 0.305600i) q^{21} +(-0.693720 - 1.63425i) q^{22} -0.370588 q^{23} +(-3.77652 + 3.12056i) q^{24} -0.922095 q^{25} +(6.38561 - 2.71062i) q^{26} +(-0.153728 - 5.19388i) q^{27} +(-0.498790 + 0.516538i) q^{28} -4.00910i q^{29} +(-4.91530 - 0.554310i) q^{30} +(-3.24407 + 4.52505i) q^{31} +(-2.39100 - 5.12671i) q^{32} +(-1.06857 + 1.89372i) q^{33} +(-0.690047 + 0.292917i) q^{34} -0.725014 q^{35} +(5.84931 + 1.33627i) q^{36} +6.16631 q^{37} +(-0.837255 - 1.97238i) q^{38} +(-7.39945 - 4.17531i) q^{39} +(2.04669 - 5.33238i) q^{40} +3.27399i q^{41} +(0.873895 + 0.0985512i) q^{42} -4.57537 q^{43} +(-1.80615 - 1.74409i) q^{44} +(3.13197 + 5.18574i) q^{45} +(-0.482425 + 0.204784i) q^{46} -6.81027i q^{47} +(-3.19181 + 6.14918i) q^{48} -6.87110 q^{49} +(-1.20037 + 0.509543i) q^{50} +(0.799606 + 0.451196i) q^{51} +(6.81481 - 7.05728i) q^{52} +0.592046i q^{53} +(-3.07022 - 6.67636i) q^{54} -2.53511i q^{55} +(-0.363882 + 0.948048i) q^{56} +(-1.28967 + 2.28554i) q^{57} +(-2.21540 - 5.21898i) q^{58} +12.5066 q^{59} +(-6.70496 + 1.99457i) q^{60} -6.24528 q^{61} +(-1.72256 + 7.68328i) q^{62} +(-0.556835 - 0.921977i) q^{63} +(-5.94554 - 5.35262i) q^{64} +9.90562 q^{65} +(-0.344598 + 3.05570i) q^{66} +9.87091i q^{67} +(-0.736428 + 0.762630i) q^{68} +(0.559020 + 0.315440i) q^{69} +(-0.943811 + 0.400637i) q^{70} +2.37470i q^{71} +(8.35295 - 1.49274i) q^{72} +6.69918i q^{73} +(8.02720 - 3.40746i) q^{74} +(1.39095 + 0.784877i) q^{75} +(-2.17985 - 2.10496i) q^{76} +0.450719i q^{77} +(-11.9397 - 1.34647i) q^{78} +9.72903i q^{79} +(-0.282290 - 8.07259i) q^{80} +(-4.18908 + 7.96565i) q^{81} +(1.80918 + 4.26202i) q^{82} -7.22344i q^{83} +(1.19208 - 0.354616i) q^{84} -1.07043 q^{85} +(-5.95615 + 2.52832i) q^{86} +(-3.41250 + 6.04760i) q^{87} +(-3.31498 - 1.27237i) q^{88} +7.20666 q^{89} +(6.94275 + 5.02001i) q^{90} -1.76113 q^{91} +(-0.514851 + 0.533169i) q^{92} +(8.74524 - 4.06458i) q^{93} +(-3.76331 - 8.86550i) q^{94} -3.05965i q^{95} +(-0.757051 + 9.76867i) q^{96} +4.22348 q^{97} +(-8.94469 + 3.79692i) q^{98} +(3.22382 - 1.94705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/744\mathbb{Z}\right)^\times$.

$n$	$313$	$373$	$497$	$559$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.30178	−	0.552593i	0.920500	−	0.390742i
$2$	1.30178	−	0.552593i	0.920500	−	0.390742i
$3$	−1.50847	−	0.851189i	−0.870915	−	0.491434i
$3$	−1.50847	−	0.851189i	−0.870915	−	0.491434i
$4$	1.38928	−	1.43871i	0.694641	−	0.719357i
$5$	2.01938			0.903095			0.451548	−	0.892247i	$-0.350872\pi$
$5$	2.01938			0.903095			0.451548	+	0.892247i	$0.350872\pi$
$6$	−2.43406	−	0.274495i	−0.993701	−	0.112062i
$7$	−0.359027			−0.135700			−0.0678498	−	0.997696i	$-0.521614\pi$
$7$	−0.359027			−0.135700			−0.0678498	+	0.997696i	$0.521614\pi$
$8$	1.01352	−	2.64060i	0.358334	−	0.933593i
$9$	1.55095	+	2.56798i	0.516985	+	0.855994i
$10$	2.62880	−	1.11590i	0.831299	−	0.352877i
$11$		−	1.25539i		−	0.378514i	−0.981928	−	0.189257i	$-0.939392\pi$
$11$		−	1.25539i		−	0.378514i	0.981928	−	0.189257i	$-0.0606080\pi$
$12$	−3.32031	+	0.987712i	−0.958489	+	0.285128i
$13$	4.90527			1.36048			0.680239	−	0.732990i	$-0.261876\pi$
$13$	4.90527			1.36048			0.680239	+	0.732990i	$0.261876\pi$
$14$	−0.467376	+	0.198396i	−0.124912	+	0.0530236i
$15$	−3.04617	−	1.71888i	−0.786519	−	0.443812i
$16$	−0.139790	−	3.99756i	−0.0349476	−	0.999389i
$17$	−0.530078			−0.128563			−0.0642814	−	0.997932i	$-0.520476\pi$
$17$	−0.530078			−0.128563			−0.0642814	+	0.997932i	$0.520476\pi$
$18$	3.43806	+	2.48591i	0.810358	+	0.585935i
$19$		−	1.51514i		−	0.347597i	−0.984781	−	0.173798i	$-0.944396\pi$
$19$		−	1.51514i		−	0.347597i	0.984781	−	0.173798i	$-0.0556041\pi$
$20$	2.80549	−	2.90531i	0.627327	−	0.649647i
$21$	0.541582	+	0.305600i	0.118183	+	0.0666874i
$22$	−0.693720	−	1.63425i	−0.147902	−	0.348422i
$23$	−0.370588			−0.0772729			−0.0386364	−	0.999253i	$-0.512301\pi$
$23$	−0.370588			−0.0772729			−0.0386364	+	0.999253i	$0.512301\pi$
$24$	−3.77652	+	3.12056i	−0.770878	+	0.636983i
$25$	−0.922095			−0.184419
$26$	6.38561	−	2.71062i	1.25232	−	0.531596i
$27$	−0.153728	−	5.19388i	−0.0295849	−	0.999562i
$28$	−0.498790	+	0.516538i	−0.0942625	+	0.0976164i
$29$		−	4.00910i		−	0.744471i	−0.928138	−	0.372236i	$-0.878591\pi$
$29$		−	4.00910i		−	0.744471i	0.928138	−	0.372236i	$-0.121409\pi$
$30$	−4.91530	−	0.554310i	−0.897407	−	0.101203i
$31$	−3.24407	+	4.52505i	−0.582651	+	0.812722i
$31$	−3.24407	+	4.52505i	−0.582651	+	0.812722i
$32$	−2.39100	−	5.12671i	−0.422673	−	0.906282i
$33$	−1.06857	+	1.89372i	−0.186015	+	0.329654i
$34$	−0.690047	+	0.292917i	−0.118342	+	0.0502349i
$35$	−0.725014			−0.122550
$36$	5.84931	+	1.33627i	0.974884	+	0.222712i
$37$	6.16631			1.01373			0.506867	−	0.862024i	$-0.330803\pi$
$37$	6.16631			1.01373			0.506867	+	0.862024i	$0.330803\pi$
$38$	−0.837255	−	1.97238i	−0.135821	−	0.319963i
$39$	−7.39945	−	4.17531i	−1.18486	−	0.668585i
$40$	2.04669	−	5.33238i	0.323610	−	0.843124i
$41$			3.27399i			0.511311i	0.966768	+	0.255655i	$0.0822912\pi$
$41$			3.27399i			0.511311i	−0.966768	+	0.255655i	$0.917709\pi$
$42$	0.873895	+	0.0985512i	0.134845	+	0.0152068i
$43$	−4.57537			−0.697738			−0.348869	−	0.937172i	$-0.613434\pi$
$43$	−4.57537			−0.697738			−0.348869	+	0.937172i	$0.613434\pi$
$44$	−1.80615	−	1.74409i	−0.272287	−	0.262932i
$45$	3.13197	+	5.18574i	0.466887	+	0.773044i
$46$	−0.482425	+	0.204784i	−0.0711297	+	0.0301938i
$47$		−	6.81027i		−	0.993381i	−0.867928	−	0.496690i	$-0.834549\pi$
$47$		−	6.81027i		−	0.993381i	0.867928	−	0.496690i	$-0.165451\pi$
$48$	−3.19181	+	6.14918i	−0.460698	+	0.887557i
$49$	−6.87110			−0.981586
$50$	−1.20037	+	0.509543i	−0.169758	+	0.0720603i
$51$	0.799606	+	0.451196i	0.111967	+	0.0631801i
$52$	6.81481	−	7.05728i	0.945044	−	0.978669i
$53$			0.592046i			0.0813238i	0.999173	+	0.0406619i	$0.0129467\pi$
$53$			0.592046i			0.0813238i	−0.999173	+	0.0406619i	$0.987053\pi$
$54$	−3.07022	−	6.67636i	−0.417804	−	0.908537i
$55$		−	2.53511i		−	0.341834i
$56$	−0.363882	+	0.948048i	−0.0486258	+	0.126688i
$57$	−1.28967	+	2.28554i	−0.170821	+	0.302727i
$58$	−2.21540	−	5.21898i	−0.290896	−	0.685286i
$59$	12.5066			1.62823			0.814114	−	0.580706i	$-0.197223\pi$
$59$	12.5066			1.62823			0.814114	+	0.580706i	$0.197223\pi$
$60$	−6.70496	+	1.99457i	−0.865607	+	0.257498i
$61$	−6.24528			−0.799626			−0.399813	−	0.916597i	$-0.630925\pi$
$61$	−6.24528			−0.799626			−0.399813	+	0.916597i	$0.630925\pi$
$62$	−1.72256	+	7.68328i	−0.218766	+	0.975777i
$63$	−0.556835	−	0.921977i	−0.0701547	−	0.116158i
$64$	−5.94554	−	5.35262i	−0.743193	−	0.669077i
$65$	9.90562			1.22864
$66$	−0.344598	+	3.05570i	−0.0424171	+	0.376130i
$67$			9.87091i			1.20592i	0.797770	+	0.602962i	$0.206013\pi$
$67$			9.87091i			1.20592i	−0.797770	+	0.602962i	$0.793987\pi$
$68$	−0.736428	+	0.762630i	−0.0893050	+	0.0924825i
$69$	0.559020	+	0.315440i	0.0672981	+	0.0379745i
$70$	−0.943811	+	0.400637i	−0.112807	+	0.0478853i
$71$			2.37470i			0.281826i	0.990022	+	0.140913i	$0.0450037\pi$
$71$			2.37470i			0.281826i	−0.990022	+	0.140913i	$0.954996\pi$
$72$	8.35295	−	1.49274i	0.984404	−	0.175922i
$73$			6.69918i			0.784079i	0.919948	+	0.392040i	$0.128230\pi$
$73$			6.69918i			0.784079i	−0.919948	+	0.392040i	$0.871770\pi$
$74$	8.02720	−	3.40746i	0.933143	−	0.396109i
$75$	1.39095	+	0.784877i	0.160613	+	0.0906298i
$76$	−2.17985	−	2.10496i	−0.250046	−	0.241455i
$77$			0.450719i			0.0513643i
$78$	−11.9397	−	1.34647i	−1.35191	−	0.152458i
$79$			9.72903i			1.09460i	0.836936	+	0.547301i	$0.184345\pi$
$79$			9.72903i			1.09460i	−0.836936	+	0.547301i	$0.815655\pi$
$80$	−0.282290	−	8.07259i	−0.0315610	−	0.902544i
$81$	−4.18908	+	7.96565i	−0.465453	+	0.885073i
$82$	1.80918	+	4.26202i	0.199791	+	0.470662i
$83$		−	7.22344i		−	0.792876i	−0.918062	−	0.396438i	$-0.870246\pi$
$83$		−	7.22344i		−	0.792876i	0.918062	−	0.396438i	$-0.129754\pi$
$84$	1.19208	−	0.354616i	0.130067	−	0.0386917i
$85$	−1.07043			−0.116104
$86$	−5.95615	+	2.52832i	−0.642268	+	0.272636i
$87$	−3.41250	+	6.04760i	−0.365859	+	0.648371i
$88$	−3.31498	−	1.27237i	−0.353378	−	0.135635i
$89$	7.20666			0.763904			0.381952	−	0.924182i	$-0.375252\pi$
$89$	7.20666			0.763904			0.381952	+	0.924182i	$0.375252\pi$
$90$	6.94275	+	5.02001i	0.731830	+	0.529155i
$91$	−1.76113			−0.184616
$92$	−0.514851	+	0.533169i	−0.0536769	+	0.0555867i
$93$	8.74524	−	4.06458i	0.906839	−	0.421477i
$94$	−3.76331	−	8.86550i	−0.388156	−	0.914407i
$95$		−	3.05965i		−	0.313913i
$96$	−0.757051	+	9.76867i	−0.0772662	+	0.997011i
$97$	4.22348			0.428829			0.214415	−	0.976743i	$-0.431216\pi$
$97$	4.22348			0.428829			0.214415	+	0.976743i	$0.431216\pi$
$98$	−8.94469	+	3.79692i	−0.903550	+	0.383547i
$99$	3.22382	−	1.94705i	0.324006	−	0.195686i
$100$	−1.28105	+	1.32663i	−0.128105	+	0.132663i
$101$	6.18926			0.615854			0.307927	−	0.951410i	$-0.400365\pi$
$101$	6.18926			0.615854			0.307927	+	0.951410i	$0.400365\pi$
$102$	1.29024	+	0.145504i	0.127753	+	0.0144070i
$103$	−2.20770			−0.217531			−0.108766	−	0.994067i	$-0.534690\pi$
$103$	−2.20770			−0.217531			−0.108766	+	0.994067i	$0.534690\pi$
$104$	4.97160	−	12.9529i	0.487506	−	1.27013i
$105$	1.09366	+	0.617124i	0.106730	+	0.0602251i
$106$	0.327161	+	0.770716i	0.0317766	+	0.0748586i
$107$	−0.436108			−0.0421602			−0.0210801	−	0.999778i	$-0.506710\pi$
$107$	−0.436108			−0.0421602			−0.0210801	+	0.999778i	$0.506710\pi$
$108$	−7.68607	−	6.99459i	−0.739593	−	0.673055i
$109$			3.38785i			0.324497i	0.986750	+	0.162249i	$0.0518746\pi$
$109$			3.38785i			0.324497i	−0.986750	+	0.162249i	$0.948125\pi$
$110$	−1.40088	−	3.30017i	−0.133569	−	0.314659i
$111$	−9.30168	−	5.24869i	−0.882876	−	0.498184i
$112$	0.0501886	+	1.43523i	0.00474237	+	0.135617i
$113$			11.4455i			1.07670i	0.842721	+	0.538351i	$0.180953\pi$
$113$			11.4455i			1.07670i	−0.842721	+	0.538351i	$0.819047\pi$
$114$	−0.415898	+	3.68794i	−0.0389524	+	0.345407i
$115$	−0.748358			−0.0697848
$116$	−5.76795	−	5.56977i	−0.535540	−	0.517140i
$117$	7.60786	+	12.5967i	0.703347	+	1.16456i
$118$	16.2810	−	6.91109i	1.49878	−	0.636217i
$119$	0.190313			0.0174459
$120$	−7.62623	+	6.30161i	−0.696176	+	0.575256i
$121$	9.42400			0.856727
$122$	−8.13001	+	3.45110i	−0.736056	+	0.312448i
$123$	2.78678	−	4.93870i	0.251275	−	0.445308i
$124$	2.00332	+	10.9538i	0.179903	+	0.983684i
$125$	−11.9590			−1.06964
$126$	−1.23436	−	0.892511i	−0.109965	−	0.0795112i
$127$			18.8970i			1.67684i	0.545028	+	0.838418i	$0.316519\pi$
$127$			18.8970i			1.67684i	−0.545028	+	0.838418i	$0.683481\pi$
$128$	−10.6976	−	3.68248i	−0.945546	−	0.325489i
$129$	6.90180	+	3.89451i	0.607670	+	0.342892i
$130$	12.8950	−	5.47378i	1.13096	−	0.480082i
$131$	5.46430			0.477418			0.238709	−	0.971091i	$-0.423276\pi$
$131$	5.46430			0.477418			0.238709	+	0.971091i	$0.423276\pi$
$132$	1.23996	+	4.16828i	0.107925	+	0.362802i
$133$			0.543977i			0.0471688i
$134$	5.45460	+	12.8498i	0.471205	+	1.11005i
$135$	−0.310435	−	10.4884i	−0.0267180	−	0.902700i
$136$	−0.537246	+	1.39972i	−0.0460685	+	0.120025i
$137$	13.5837			1.16054			0.580268	−	0.814425i	$-0.302948\pi$
$137$	13.5837			1.16054			0.580268	+	0.814425i	$0.302948\pi$
$138$	0.902033	+	0.101724i	0.0767862	+	0.00865936i
$139$	−0.453491			−0.0384646			−0.0192323	−	0.999815i	$-0.506122\pi$
$139$	−0.453491			−0.0384646			−0.0192323	+	0.999815i	$0.506122\pi$
$140$	−1.00725	+	1.04309i	−0.0851280	+	0.0881569i
$141$	−5.79683	+	10.2731i	−0.488181	+	0.865150i
$142$	1.31224	+	3.09135i	0.110121	+	0.259421i
$143$		−	6.15803i		−	0.514960i
$144$	10.0489	−	6.55901i	0.837404	−	0.546584i
$145$		−	8.09591i		−	0.672329i
$146$	3.70192	+	8.72088i	0.306373	+	0.721745i
$147$	10.3648	+	5.84860i	0.854877	+	0.482385i
$148$	8.56674	−	8.87154i	0.704182	−	0.729236i
$149$	−19.6286			−1.60804			−0.804018	−	0.594605i	$-0.797308\pi$
$149$	−19.6286			−1.60804			−0.804018	+	0.594605i	$0.797308\pi$
$150$	2.24444	+	0.253110i	0.183257	+	0.0206664i
$151$			2.86421i			0.233086i	0.993186	+	0.116543i	$0.0371813\pi$
$151$			2.86421i			0.233086i	−0.993186	+	0.116543i	$0.962819\pi$
$152$	−4.00088	−	1.53563i	−0.324514	−	0.124556i
$153$	−0.822127	−	1.36123i	−0.0664650	−	0.110049i
$154$	0.249064	+	0.586739i	0.0200702	+	0.0472808i
$155$	−6.55101	+	9.13780i	−0.526190	+	0.733965i
$156$	−16.2870	+	4.84500i	−1.30400	+	0.387910i
$157$			17.5419i			1.39999i	0.714146	+	0.699997i	$0.246815\pi$
$157$			17.5419i			1.39999i	−0.714146	+	0.699997i	$0.753185\pi$
$158$	5.37620	+	12.6651i	0.427707	+	1.00758i
$159$	0.503943	−	0.893083i	0.0399653	−	0.0708261i
$160$	−4.82834	−	10.3528i	−0.381714	−	0.818459i
$161$	0.133051			0.0104859
$162$	−1.05151	+	12.6844i	−0.0826145	+	0.996582i
$163$			20.5511i			1.60969i	0.593486	+	0.804845i	$0.297751\pi$
$163$			20.5511i			1.60969i	−0.593486	+	0.804845i	$0.702249\pi$
$164$	4.71033	+	4.54849i	0.367815	+	0.355177i
$165$	−2.15786	+	3.82414i	−0.167989	+	0.297709i
$166$	−3.99162	−	9.40336i	−0.309810	−	0.729842i
$167$	−8.17750			−0.632794			−0.316397	−	0.948627i	$-0.602473\pi$
$167$	−8.17750			−0.632794			−0.316397	+	0.948627i	$0.602473\pi$
$168$	1.35587	−	1.12037i	0.104608	−	0.0864383i
$169$	11.0617			0.850901
$170$	−1.39347	+	0.591512i	−0.106874	+	0.0453669i
$171$	3.89085	−	2.34991i	0.297541	−	0.179702i
$172$	−6.35648	+	6.58265i	−0.484677	+	0.501922i
$173$	−15.2964			−1.16296			−0.581480	−	0.813560i	$-0.697526\pi$
$173$	−15.2964			−1.16296			−0.581480	+	0.813560i	$0.697526\pi$
$174$	−1.10048	+	9.75840i	−0.0834270	+	0.739782i
$175$	0.331058			0.0250256
$176$	−5.01849	+	0.175491i	−0.378283	+	0.0132282i
$177$	−18.8659	−	10.6455i	−1.41805	−	0.800166i
$178$	9.38151	−	3.98235i	0.703174	−	0.298490i
$179$			19.0378i			1.42296i	0.702709	+	0.711478i	$0.251974\pi$
$179$			19.0378i			1.42296i	−0.702709	+	0.711478i	$0.748026\pi$
$180$	11.8120	+	2.69845i	0.880413	+	0.201131i
$181$	−4.49019			−0.333753			−0.166877	−	0.985978i	$-0.553368\pi$
$181$	−4.49019			−0.333753			−0.166877	+	0.985978i	$0.553368\pi$
$182$	−2.29261	+	0.973187i	−0.169939	+	0.0721374i
$183$	9.42081	+	5.31591i	0.696406	+	0.392964i
$184$	−0.375599	+	0.978574i	−0.0276895	+	0.0721414i
$185$	12.4521			0.915499
$186$	9.13836	−	10.1238i	0.670057	−	0.742310i
$187$			0.665455i			0.0486629i
$188$	−9.79803	−	9.46139i	−0.714595	−	0.690043i
$189$	0.0551925	+	1.86474i	0.00401466	+	0.135640i
$190$	−1.69074	−	3.98300i	−0.122659	−	0.288957i
$191$		−	15.6920i		−	1.13543i	−0.823224	−	0.567716i	$-0.807827\pi$
$191$		−	15.6920i		−	1.13543i	0.823224	−	0.567716i	$-0.192173\pi$
$192$	4.41258	+	13.1350i	0.318451	+	0.947939i
$193$	10.0352			0.722350			0.361175	−	0.932498i	$-0.382376\pi$
$193$	10.0352			0.722350			0.361175	+	0.932498i	$0.382376\pi$
$194$	5.49806	−	2.33386i	0.394737	−	0.167562i
$195$	−14.9423	−	8.43156i	−1.07004	−	0.603796i
$196$	−9.54590	+	9.88554i	−0.681850	+	0.706110i
$197$		−	8.62105i		−	0.614224i	−0.951673	−	0.307112i	$-0.900637\pi$
$197$		−	8.62105i		−	0.614224i	0.951673	−	0.307112i	$-0.0993627\pi$
$198$	3.12079	−	4.31610i	0.221785	−	0.306732i
$199$			12.2556i			0.868779i	0.900725	+	0.434389i	$0.143036\pi$
$199$			12.2556i			0.868779i	−0.900725	+	0.434389i	$0.856964\pi$
$200$	−0.934564	+	2.43489i	−0.0660837	+	0.172172i
$201$	8.40201	−	14.8900i	0.592632	−	1.05026i
$202$	8.05708	−	3.42014i	0.566894	−	0.240640i
$203$			1.43938i			0.101024i
$204$	1.76002	−	0.523564i	0.123226	−	0.0366568i
$205$			6.61143i			0.461762i
$206$	−2.87395	+	1.21996i	−0.200238	+	0.0849987i
$207$	−0.574765	−	0.951663i	−0.0399489	−	0.0661452i
$208$	−0.685710	−	19.6091i	−0.0475454	−	1.35965i
$209$	−1.90209			−0.131570
$210$	1.76473	+	0.199013i	0.121778	+	0.0137332i
$211$		−	17.4011i		−	1.19794i	−0.800770	−	0.598972i	$-0.795576\pi$
$211$		−	17.4011i		−	1.19794i	0.800770	−	0.598972i	$-0.204424\pi$
$212$	0.851785	+	0.822519i	0.0585008	+	0.0564909i
$213$	2.02132	−	3.58217i	0.138499	−	0.245446i
$214$	−0.567719	+	0.240990i	−0.0388084	+	0.0164738i
$215$	−9.23942			−0.630124
$216$	−13.8708	−	4.85818i	−0.943786	−	0.330557i
$217$	1.16471	−	1.62462i	0.0790656	−	0.110286i
$218$	1.87210	+	4.41025i	0.126795	+	0.298700i
$219$	5.70226	−	10.1055i	0.385323	−	0.682866i
$220$	−3.64730	−	3.52199i	−0.245901	−	0.237452i
$221$	−2.60018			−0.174907
$222$	−15.0092	−	1.69262i	−1.00735	−	0.113601i
$223$		−	13.3927i		−	0.896840i	−0.893823	−	0.448420i	$-0.851987\pi$
$223$		−	13.3927i		−	0.896840i	0.893823	−	0.448420i	$-0.148013\pi$
$224$	0.858434	+	1.84063i	0.0573565	+	0.122982i
$225$	−1.43013	−	2.36793i	−0.0953419	−	0.157862i
$226$	6.32470	+	14.8996i	0.420713	+	0.991105i
$227$	14.6335			0.971260			0.485630	−	0.874164i	$-0.338590\pi$
$227$	14.6335			0.971260			0.485630	+	0.874164i	$0.338590\pi$
$228$	1.49652	+	5.03073i	0.0991095	+	0.333168i
$229$	−17.1847			−1.13560			−0.567799	−	0.823167i	$-0.692205\pi$
$229$	−17.1847			−1.13560			−0.567799	+	0.823167i	$0.692205\pi$
$230$	−0.974201	+	0.413537i	−0.0642369	+	0.0272679i
$231$	0.383647	−	0.679896i	0.0252421	−	0.0447339i
$232$	−10.5864	−	4.06331i	−0.695034	−	0.266770i
$233$			4.28624i			0.280801i	0.990095	+	0.140401i	$0.0448390\pi$
$233$			4.28624i			0.280801i	−0.990095	+	0.140401i	$0.955161\pi$
$234$	16.8646	+	12.1941i	1.10247	+	0.797152i
$235$		−	13.7525i		−	0.897117i
$236$	17.3753	−	17.9935i	1.13103	−	1.17128i
$237$	8.28125	−	14.6759i	0.537925	−	0.953305i
$238$	0.247746	−	0.105165i	0.0160590	−	0.00681686i
$239$	−26.9964			−1.74625			−0.873125	−	0.487497i	$-0.837910\pi$
$239$	−26.9964			−1.74625			−0.873125	+	0.487497i	$0.837910\pi$
$240$	−6.44548	+	12.4175i	−0.416054	+	0.801549i
$241$		−	22.0932i		−	1.42315i	−0.702610	−	0.711575i	$-0.747982\pi$
$241$		−	22.0932i		−	1.42315i	0.702610	−	0.711575i	$-0.252018\pi$
$242$	12.2680	−	5.20763i	0.788617	−	0.334759i
$243$	13.0994	−	8.45024i	0.840325	−	0.542083i
$244$	−8.67646	+	8.98517i	−0.555453	+	0.575216i
$245$	−13.8754			−0.886465
$246$	0.898692	−	7.96908i	0.0572985	−	0.508090i
$247$		−	7.43217i		−	0.472898i
$248$	8.66090	+	13.1525i	0.549968	+	0.835186i
$249$	−6.14851	+	10.8963i	−0.389646	+	0.690527i
$250$	−15.5680	+	6.60844i	−0.984607	+	0.417955i
$251$		−	15.4005i		−	0.972072i	−0.873939	−	0.486036i	$-0.838442\pi$
$251$		−	15.4005i		−	0.972072i	0.873939	−	0.486036i	$-0.161558\pi$
$252$	−2.10006	−	0.479759i	−0.132291	−	0.0302220i
$253$			0.465232i			0.0292489i
$254$	10.4423	+	24.5998i	0.655210	+	1.54353i
$255$	1.61471	+	0.911138i	0.101117	+	0.0570577i
$256$	−15.9609	+	1.11764i	−0.997557	+	0.0698525i
$257$			9.32155i			0.581462i	0.956805	+	0.290731i	$0.0938985\pi$
$257$			9.32155i			0.581462i	−0.956805	+	0.290731i	$0.906102\pi$
$258$	11.1367	+	1.25592i	0.693343	+	0.0781899i
$259$	−2.21387			−0.137563
$260$	13.7617	−	14.2513i	0.853465	−	0.883831i
$261$	10.2953	−	6.21793i	0.637263	−	0.384881i
$262$	7.11333	−	3.01953i	0.439463	−	0.186547i
$263$	24.2167			1.49327			0.746634	−	0.665235i	$-0.231669\pi$
$263$	24.2167			1.49327			0.746634	+	0.665235i	$0.231669\pi$
$264$	3.91752	+	4.74100i	0.241107	+	0.291788i
$265$			1.19557i			0.0734432i
$266$	0.300598	+	0.708140i	0.0184308	+	0.0434189i
$267$	−10.8710	−	6.13423i	−0.665295	−	0.375408i
$268$	14.2014	+	13.7135i	0.867489	+	0.837684i
$269$		−	32.2092i		−	1.96383i	−0.189326	−	0.981914i	$-0.560630\pi$
$269$		−	32.2092i		−	1.96383i	0.189326	−	0.981914i	$-0.439370\pi$
$270$	−6.19995	−	13.4821i	−0.377317	−	0.820496i
$271$		−	17.2940i		−	1.05054i	−0.850936	−	0.525269i	$-0.823965\pi$
$271$		−	17.2940i		−	1.05054i	0.850936	−	0.525269i	$-0.176035\pi$
$272$	0.0740998	+	2.11902i	0.00449296	+	0.128484i
$273$	2.65661	+	1.49905i	0.160785	+	0.0907268i
$274$	17.6831	−	7.50627i	1.06827	−	0.453471i
$275$			1.15759i			0.0698053i
$276$	1.23046	−	0.366034i	0.0740652	−	0.0220326i
$277$	−20.2977			−1.21957			−0.609786	−	0.792566i	$-0.708745\pi$
$277$	−20.2977			−1.21957			−0.609786	+	0.792566i	$0.708745\pi$
$278$	−0.590347	+	0.250596i	−0.0354066	+	0.0150297i
$279$	−16.6516	−	1.31257i	−0.996908	−	0.0785813i
$280$	−0.734818	+	1.91447i	−0.0439138	+	0.114412i
$281$		−	31.5946i		−	1.88477i	−0.334526	−	0.942386i	$-0.608576\pi$
$281$		−	31.5946i		−	1.88477i	0.334526	−	0.942386i	$-0.391424\pi$
$282$	−1.86939	+	16.5766i	−0.111320	+	0.987123i
$283$		−	10.2707i		−	0.610530i	−0.952267	−	0.305265i	$-0.901255\pi$
$283$		−	10.2707i		−	0.610530i	0.952267	−	0.305265i	$-0.0987451\pi$
$284$	3.41652	+	3.29913i	0.202733	+	0.195768i
$285$	−2.60434	+	4.61538i	−0.154268	+	0.273392i
$286$	−3.40288	−	8.01642i	−0.201217	−	0.474021i
$287$		−	1.17545i		−	0.0693847i
$288$	9.45697	−	14.0913i	0.557257	−	0.830340i
$289$	−16.7190			−0.983472
$290$	−4.47374	−	10.5391i	−0.262707	−	0.618879i
$291$	−6.37099	−	3.59498i	−0.373474	−	0.210741i
$292$	9.63819	+	9.30704i	0.564032	+	0.544654i
$293$	13.9548			0.815250			0.407625	−	0.913149i	$-0.366357\pi$
$293$	13.9548			0.815250			0.407625	+	0.913149i	$0.366357\pi$
$294$	16.7247	+	1.88608i	0.975403	+	0.109999i
$295$	25.2557			1.47044
$296$	6.24969	−	16.2828i	0.363256	−	0.946416i
$297$	−6.52034	+	0.192988i	−0.378349	+	0.0111983i
$298$	−25.5522	+	10.8466i	−1.48020	+	0.628327i
$299$	−1.81783			−0.105128
$300$	3.06164	−	0.910765i	0.176764	−	0.0525830i
$301$	1.64268			0.0946827
$302$	1.58274	+	3.72858i	0.0910765	+	0.214556i
$303$	−9.33630	−	5.26823i	−0.536357	−	0.302652i
$304$	−6.05686	+	0.211802i	−0.347385	+	0.0121477i
$305$	−12.6116			−0.722139
$306$	−1.82244	−	1.31773i	−0.104182	−	0.0753295i
$307$		−	6.39879i		−	0.365198i	−0.983187	−	0.182599i	$-0.941549\pi$
$307$		−	6.39879i		−	0.365198i	0.983187	−	0.182599i	$-0.0584510\pi$
$308$	0.648456	+	0.626177i	0.0369492	+	0.0356797i
$309$	3.33025	+	1.87917i	0.189451	+	0.106902i
$310$	−3.47852	+	15.5155i	−0.197566	+	0.881220i
$311$		−	4.40781i		−	0.249944i	−0.992160	−	0.124972i	$-0.960116\pi$
$311$		−	4.40781i		−	0.249944i	0.992160	−	0.124972i	$-0.0398841\pi$
$312$	−18.5248	+	15.3072i	−1.04876	+	0.866601i
$313$			16.7888i			0.948959i	0.880266	+	0.474480i	$0.157364\pi$
$313$			16.7888i			0.948959i	−0.880266	+	0.474480i	$0.842636\pi$
$314$	9.69352	+	22.8357i	0.547037	+	1.28869i
$315$	−1.12446	−	1.86182i	−0.0633563	−	0.104902i
$316$	13.9973	+	13.5164i	0.787409	+	0.760355i
$317$	11.3323			0.636484			0.318242	−	0.948009i	$-0.396908\pi$
$317$	11.3323			0.636484			0.318242	+	0.948009i	$0.396908\pi$
$318$	0.162514	−	1.44108i	0.00911332	−	0.0808116i
$319$	−5.03299			−0.281793
$320$	−12.0063	−	10.8090i	−0.671174	−	0.604240i
$321$	0.657856	+	0.371210i	0.0367179	+	0.0207189i
$322$	0.173204	−	0.0735231i	0.00965227	−	0.00409728i
$323$			0.803142i			0.0446880i
$324$	5.64048	+	17.0934i	0.313360	+	0.949634i
$325$	−4.52313			−0.250898
$326$	11.3564	+	26.7531i	0.628973	+	1.48172i
$327$	2.88370	−	5.11047i	0.159469	−	0.282609i
$328$	8.64529	+	3.31826i	0.477356	+	0.183220i
$329$			2.44508i			0.134801i
$330$	−0.695875	+	6.17062i	−0.0383067	+	0.339681i
$331$	−28.9555			−1.59154			−0.795769	−	0.605601i	$-0.792933\pi$
$331$	−28.9555			−1.59154			−0.795769	+	0.605601i	$0.792933\pi$
$332$	−10.3925	−	10.0354i	−0.570360	−	0.550764i
$333$	9.56366	+	15.8350i	0.524085	+	0.867751i
$334$	−10.6453	+	4.51883i	−0.582487	+	0.247259i
$335$			19.9331i			1.08906i
$336$	1.14595	−	2.20772i	0.0625165	−	0.120441i
$337$			31.5174i			1.71686i	0.512931	+	0.858430i	$0.328560\pi$
$337$			31.5174i			1.71686i	−0.512931	+	0.858430i	$0.671440\pi$
$338$	14.4000	−	6.11262i	0.783254	−	0.332483i
$339$	9.74228	−	17.2652i	0.529128	−	0.937716i
$340$	−1.48713	+	1.54004i	−0.0806509	+	0.0835205i
$341$	5.68070	+	4.07257i	0.307627	+	0.220542i
$342$	3.76650	−	5.20914i	0.203669	−	0.281678i
$343$	4.98011			0.268900
$344$	−4.63724	+	12.0817i	−0.250023	+	0.651403i
$345$	1.12887	+	0.636994i	0.0607766	+	0.0342946i
$346$	−19.9126	+	8.45266i	−1.07051	+	0.454418i
$347$			33.3853i			1.79222i	0.443833	+	0.896109i	$0.353618\pi$
$347$			33.3853i			1.79222i	−0.443833	+	0.896109i	$0.646382\pi$
$348$	3.95984	+	13.3114i	0.212270	+	0.713568i
$349$		−	2.59037i		−	0.138659i	−0.997594	−	0.0693296i	$-0.977914\pi$
$349$		−	2.59037i		−	0.138659i	0.997594	−	0.0693296i	$-0.0220860\pi$
$350$	0.430965	−	0.182940i	0.0230361	−	0.00977856i
$351$	−0.754076	−	25.4774i	−0.0402496	−	1.35988i
$352$	−6.43602	+	3.00164i	−0.343041	+	0.159988i
$353$	1.41331			0.0752228			0.0376114	−	0.999292i	$-0.488025\pi$
$353$	1.41331			0.0752228			0.0376114	+	0.999292i	$0.488025\pi$
$354$	−30.4419	−	3.43301i	−1.61797	−	0.182462i
$355$			4.79544i			0.254515i
$356$	10.0121	−	10.3683i	0.530639	−	0.549519i
$357$	−0.287080	−	0.161992i	−0.0151939	−	0.00857352i
$358$	10.5202	+	24.7832i	0.556009	+	1.30983i
$359$			17.6500i			0.931529i	0.884909	+	0.465765i	$0.154221\pi$
$359$			17.6500i			0.931529i	−0.884909	+	0.465765i	$0.845779\pi$
$360$	16.8678	−	3.01442i	0.889011	−	0.158874i
$361$	16.7044			0.879176
$362$	−5.84526	+	2.48125i	−0.307220	+	0.130412i
$363$	−14.2158	−	8.02160i	−0.746136	−	0.421025i
$364$	−2.44670	+	2.53376i	−0.128242	+	0.132805i
$365$			13.5282i			0.708098i
$366$	15.2014	+	1.71430i	0.794590	+	0.0896078i
$367$			13.3942i			0.699169i	0.936905	+	0.349585i	$0.113677\pi$
$367$			13.3942i			0.699169i	−0.936905	+	0.349585i	$0.886323\pi$
$368$	0.0518046	+	1.48145i	0.00270050	+	0.0772257i
$369$	−8.40754	+	5.07780i	−0.437679	+	0.264340i
$370$	16.2100	−	6.88096i	0.842717	−	0.357724i
$371$		−	0.212561i		−	0.0110356i
$372$	6.30185	−	18.2287i	0.326736	−	0.945116i
$373$		−	23.7437i		−	1.22940i	−0.788760	−	0.614702i	$-0.789276\pi$
$373$		−	23.7437i		−	1.22940i	0.788760	−	0.614702i	$-0.210724\pi$
$374$	0.367725	+	0.866278i	0.0190146	+	0.0447942i
$375$	18.0397	+	10.1793i	0.931568	+	0.525659i
$376$	−17.9832	−	6.90236i	−0.927413	−	0.355962i
$377$		−	19.6657i		−	1.01284i
$378$	1.10229	+	2.39700i	0.0566959	+	0.123288i
$379$		−	14.9481i		−	0.767833i	−0.923368	−	0.383916i	$-0.874575\pi$
$379$		−	14.9481i		−	0.767833i	0.923368	−	0.383916i	$-0.125425\pi$
$380$	−4.40195	−	4.25071i	−0.225815	−	0.218057i
$381$	16.0849	−	28.5055i	0.824054	−	1.46038i
$382$	−8.67129	−	20.4276i	−0.443662	−	1.04517i
$383$	−15.5799			−0.796094			−0.398047	−	0.917365i	$-0.630312\pi$
$383$	−15.5799			−0.796094			−0.398047	+	0.917365i	$0.630312\pi$
$384$	13.0026	+	14.6606i	0.663534	+	0.748146i
$385$			0.910175i			0.0463868i
$386$	13.0637	−	5.54538i	0.664923	−	0.282252i
$387$	−7.09620	−	11.7495i	−0.360720	−	0.597260i
$388$	5.86760	−	6.07637i	0.297882	−	0.308481i
$389$		−	1.11800i		−	0.0566850i	−0.999598	−	0.0283425i	$-0.990977\pi$
$389$		−	1.11800i		−	0.0566850i	0.999598	−	0.0283425i	$-0.00902291\pi$
$390$	−24.1109	−	2.71904i	−1.22090	−	0.137684i
$391$	0.196440			0.00993442
$392$	−6.96401	+	18.1438i	−0.351736	+	0.916402i
$393$	−8.24272	−	4.65115i	−0.415790	−	0.234619i
$394$	−4.76393	−	11.2227i	−0.240003	−	0.565394i
$395$			19.6466i			0.988530i
$396$	1.67755	−	7.34316i	0.0842998	−	0.369008i
$397$		−	1.26271i		−	0.0633738i	−0.999498	−	0.0316869i	$-0.989912\pi$
$397$		−	1.26271i		−	0.0633738i	0.999498	−	0.0316869i	$-0.0100879\pi$
$398$	6.77238	+	15.9542i	0.339469	+	0.799711i
$399$	0.463027	−	0.820572i	0.0231803	−	0.0410800i
$400$	0.128900	+	3.68613i	0.00644500	+	0.184306i
$401$	−22.4892			−1.12306			−0.561529	−	0.827457i	$-0.689787\pi$
$401$	−22.4892			−1.12306			−0.561529	+	0.827457i	$0.689787\pi$
$402$	2.70951	−	24.0264i	0.135138	−	1.19833i
$403$	−15.9130	+	22.1966i	−0.792685	+	1.10569i
$404$	8.59863	−	8.90457i	0.427798	−	0.443019i
$405$	−8.45935	+	16.0857i	−0.420348	+	0.799305i
$406$	0.795390	+	1.87376i	0.0394745	+	0.0929931i
$407$		−	7.74112i		−	0.383713i
$408$	2.00185	−	1.65414i	0.0991063	−	0.0818922i
$409$			22.8174i			1.12825i	0.825690	+	0.564125i	$0.190786\pi$
$409$			22.8174i			1.12825i	−0.825690	+	0.564125i	$0.809214\pi$
$410$	3.65343	+	8.60665i	0.180430	+	0.425052i
$411$	−20.4906	−	11.5623i	−1.01073	−	0.570327i
$412$	−3.06712	+	3.17625i	−0.151106	+	0.156483i
$413$	−4.49023			−0.220950
$414$	−1.27410	−	0.921249i	−0.0626187	−	0.0452769i
$415$		−	14.5869i		−	0.716042i
$416$	−11.7285	−	25.1479i	−0.575037	−	1.23298i
$417$	0.684076	+	0.386006i	0.0334994	+	0.0189028i
$418$	−2.47611	+	1.05108i	−0.121111	+	0.0514101i
$419$	17.7592			0.867596			0.433798	−	0.901010i	$-0.357173\pi$
$419$	17.7592			0.867596			0.433798	+	0.901010i	$0.357173\pi$
$420$	2.40727	−	0.716105i	0.117463	−	0.0349423i
$421$			2.99995i			0.146209i	0.997324	+	0.0731043i	$0.0232906\pi$
$421$			2.99995i			0.146209i	−0.997324	+	0.0731043i	$0.976709\pi$
$422$	−9.61575	−	22.6525i	−0.468087	−	1.10271i
$423$	17.4887	−	10.5624i	0.850328	−	0.513563i
$424$	1.56336	+	0.600052i	0.0759234	+	0.0291411i
$425$	0.488782			0.0237094
$426$	0.651844	−	5.78018i	0.0315820	−	0.280050i
$427$	2.24223			0.108509
$428$	−0.605877	+	0.627435i	−0.0292862	+	0.0303282i
$429$	−5.24165	+	9.28920i	−0.253069	+	0.448487i
$430$	−12.0277	+	5.10564i	−0.580029	+	0.246216i
$431$			14.5862i			0.702595i	0.936264	+	0.351297i	$0.114259\pi$
$431$			14.5862i			0.702595i	−0.936264	+	0.351297i	$0.885741\pi$
$432$	−20.7413	+	1.34059i	−0.997918	+	0.0644991i
$433$		−	40.3152i		−	1.93743i	−0.248182	−	0.968713i	$-0.579833\pi$
$433$		−	40.3152i		−	1.93743i	0.248182	−	0.968713i	$-0.420167\pi$
$434$	0.618448	−	2.75851i	0.0296865	−	0.132413i
$435$	−6.89115	+	12.2124i	−0.330405	+	0.585541i
$436$	4.87414	+	4.70668i	0.233429	+	0.225409i
$437$			0.561492i			0.0268598i
$438$	1.83889	−	16.3062i	0.0878655	−	0.779140i
$439$	−1.28668			−0.0614097			−0.0307049	−	0.999528i	$-0.509775\pi$
$439$	−1.28668			−0.0614097			−0.0307049	+	0.999528i	$0.509775\pi$
$440$	−6.69422	−	2.56939i	−0.319134	−	0.122491i
$441$	−10.6568	−	17.6449i	−0.507465	−	0.840232i
$442$	−3.38487	+	1.43684i	−0.161002	+	0.0683435i
$443$	−24.5573			−1.16675			−0.583375	−	0.812203i	$-0.698268\pi$
$443$	−24.5573			−1.16675			−0.583375	+	0.812203i	$0.698268\pi$
$444$	−20.4740	+	6.09053i	−0.971654	+	0.289044i
$445$	14.5530			0.689878
$446$	−7.40070	−	17.4344i	−0.350433	−	0.825541i
$447$	29.6091	+	16.7076i	1.40046	+	0.790244i
$448$	2.13461	+	1.92174i	0.100851	+	0.0907935i
$449$	−15.8486			−0.747944			−0.373972	−	0.927440i	$-0.622004\pi$
$449$	−15.8486			−0.747944			−0.373972	+	0.927440i	$0.622004\pi$
$450$	−3.17022	−	2.29225i	−0.149445	−	0.108058i
$451$	4.11013			0.193538
$452$	16.4668	+	15.9010i	0.774533	+	0.747922i
$453$	2.43798	−	4.32057i	0.114546	−	0.202998i
$454$	19.0497	−	8.08637i	0.894045	−	0.379512i
$455$	−3.55639			−0.166726
$456$	4.72809	+	5.72195i	0.221413	+	0.267955i
$457$			20.3442i			0.951661i	0.879537	+	0.475830i	$0.157852\pi$
$457$			20.3442i			0.951661i	−0.879537	+	0.475830i	$0.842148\pi$
$458$	−22.3708	+	9.49615i	−1.04532	+	0.443726i
$459$	0.0814877	+	2.75316i	0.00380352	+	0.128507i
$460$	−1.03968	+	1.07667i	−0.0484754	+	0.0502001i
$461$		−	24.3721i		−	1.13512i	−0.823332	−	0.567560i	$-0.807887\pi$
$461$		−	24.3721i		−	1.13512i	0.823332	−	0.567560i	$-0.192113\pi$
$462$	0.123720	−	1.09708i	0.00575598	−	0.0510407i
$463$		−	23.7526i		−	1.10388i	−0.833885	−	0.551939i	$-0.813888\pi$
$463$		−	23.7526i		−	1.10388i	0.833885	−	0.551939i	$-0.186112\pi$
$464$	−16.0266	+	0.560434i	−0.744017	+	0.0260175i
$465$	17.6600	−	8.20793i	0.818962	−	0.380634i
$466$	2.36855	+	5.57976i	0.109721	+	0.258477i
$467$	29.7836			1.37822			0.689110	−	0.724656i	$-0.258001\pi$
$467$	29.7836			1.37822			0.689110	+	0.724656i	$0.258001\pi$
$468$	28.6924	+	6.55479i	1.32631	+	0.302995i
$469$		−	3.54393i		−	0.163643i
$470$	−7.59956	−	17.9028i	−0.350542	−	0.825796i
$471$	14.9315	−	26.4614i	0.688005	−	1.21928i
$472$	12.6758	−	33.0251i	0.583450	−	1.52010i
$473$			5.74388i			0.264104i
$474$	2.67057	−	23.6811i	0.122663	−	1.08771i
$475$			1.39710i			0.0641035i
$476$	0.264398	−	0.273805i	0.0121187	−	0.0125498i
$477$	−1.52037	+	0.918237i	−0.0696127	+	0.0420432i
$478$	−35.1434	+	14.9180i	−1.60742	+	0.682333i
$479$			17.3877i			0.794466i	0.917718	+	0.397233i	$0.130030\pi$
$479$			17.3877i			0.794466i	−0.917718	+	0.397233i	$0.869970\pi$
$480$	−1.52877	+	19.7267i	−0.0697787	+	0.900395i
$481$	30.2474			1.37916
$482$	−12.2086	−	28.7606i	−0.556085	−	1.31001i
$483$	−0.200704	−	0.113252i	−0.00913233	−	0.00515313i
$484$	13.0926	−	13.5584i	0.595118	−	0.616292i
$485$	8.52882			0.387274
$486$	12.3830	−	18.2390i	0.561704	−	0.827338i
$487$			14.3592i			0.650679i	0.945597	+	0.325339i	$0.105479\pi$
$487$			14.3592i			0.650679i	−0.945597	+	0.325339i	$0.894521\pi$
$488$	−6.32973	+	16.4913i	−0.286533	+	0.746526i
$489$	17.4929	−	31.0007i	0.791056	−	1.40190i
$490$	−18.0627	+	7.66743i	−0.815991	+	0.346379i
$491$			11.3456i			0.512019i	0.966674	+	0.256009i	$0.0824078\pi$
$491$			11.3456i			0.512019i	−0.966674	+	0.256009i	$0.917592\pi$
$492$	−3.23375	−	10.8706i	−0.145789	−	0.490086i
$493$			2.12514i			0.0957113i
$494$	−4.10697	−	9.67508i	−0.184781	−	0.435303i
$495$	6.51013	−	3.93184i	0.292608	−	0.176723i
$496$	18.5426	+	12.3358i	0.832588	+	0.553893i
$497$		−	0.852584i		−	0.0382436i
$498$	−1.98280	+	17.5823i	−0.0888513	+	0.787882i
$499$	34.9340			1.56386			0.781931	−	0.623365i	$-0.214235\pi$
$499$	34.9340			1.56386			0.781931	+	0.623365i	$0.214235\pi$
$500$	−16.6144	+	17.2055i	−0.743018	+	0.769455i
$501$	12.3355	+	6.96060i	0.551110	+	0.310977i
$502$	−8.51021	−	20.0481i	−0.379829	−	0.894792i
$503$			4.42949i			0.197501i	0.995112	+	0.0987506i	$0.0314846\pi$
$503$			4.42949i			0.197501i	−0.995112	+	0.0987506i	$0.968515\pi$
$504$	−2.99894	+	0.535936i	−0.133583	+	0.0238725i
$505$	12.4985			0.556175
$506$	0.257084	+	0.605632i	0.0114288	+	0.0269236i
$507$	−16.6862	−	9.41560i	−0.741062	−	0.418162i
$508$	27.1873	+	26.2532i	1.20624	+	1.16480i
$509$		−	22.3665i		−	0.991377i	−0.868500	−	0.495688i	$-0.834916\pi$
$509$		−	22.3665i		−	0.991377i	0.868500	−	0.495688i	$-0.165084\pi$
$510$	2.60549	+	0.293828i	0.115373	+	0.0130109i
$511$		−	2.40519i		−	0.106399i
$512$	−20.1601	+	10.2748i	−0.890957	+	0.454087i
$513$	−7.86945	+	0.232919i	−0.347445	+	0.0102836i
$514$	5.15102	+	12.1346i	0.227202	+	0.535236i
$515$	−4.45819			−0.196451
$516$	15.1916	−	4.51915i	0.668774	−	0.198944i
$517$	−8.54955			−0.376009
$518$	−2.88198	+	1.22337i	−0.126627	+	0.0537518i
$519$	23.0741	+	13.0201i	1.01284	+	0.571519i
$520$	10.0396	−	26.1568i	0.440264	−	1.14705i
$521$			0.310368i			0.0135975i	0.999977	+	0.00679874i	$0.00216412\pi$
$521$			0.310368i			0.0135975i	−0.999977	+	0.00679874i	$0.997836\pi$
$522$	9.96627	−	13.7835i	0.436212	−	0.603288i
$523$	−3.12326			−0.136570			−0.0682852	−	0.997666i	$-0.521753\pi$
$523$	−3.12326			−0.136570			−0.0682852	+	0.997666i	$0.521753\pi$
$524$	7.59145	−	7.86155i	0.331634	−	0.343434i
$525$	−0.499390	−	0.281793i	−0.0217952	−	0.0122984i
$526$	31.5250	−	13.3820i	1.37455	−	0.583483i
$527$	1.71961	−	2.39863i	0.0749073	−	0.104486i
$528$	7.71961	+	4.00696i	0.335953	+	0.174381i
$529$	−22.8627			−0.994029
$530$	0.660662	+	1.55637i	0.0286973	+	0.0676044i
$531$	19.3972	+	32.1169i	0.841769	+	1.39375i
$532$	0.782626	+	0.755737i	0.0339312	+	0.0327654i
$533$			16.0598i			0.695627i
$534$	−17.5414	−	1.97819i	−0.759092	−	0.0856047i
$535$	−0.880669			−0.0380747
$536$	26.0651	+	10.0044i	1.12584	+	0.432124i
$537$	16.2048	−	28.7180i	0.699289	−	1.23927i
$538$	−17.7986	−	41.9294i	−0.767351	−	1.80770i
$539$			8.62591i			0.371544i
$540$	−15.5211	−	14.1248i	−0.667922	−	0.607833i
$541$		−	37.9126i		−	1.62999i	−0.579467	−	0.814996i	$-0.696739\pi$
$541$		−	37.9126i		−	1.62999i	0.579467	−	0.814996i	$-0.303261\pi$
$542$	−9.55656	−	22.5131i	−0.410489	−	0.967020i
$543$	6.77331	+	3.82200i	0.290671	+	0.164018i
$544$	1.26742	+	2.71755i	0.0543400	+	0.116514i
$545$			6.84136i			0.293052i
$546$	4.28669	+	0.483421i	0.183454	+	0.0206885i
$547$			24.7663i			1.05893i	0.848331	+	0.529466i	$0.177608\pi$
$547$			24.7663i			1.05893i	−0.848331	+	0.529466i	$0.822392\pi$
$548$	18.8716	−	19.5431i	0.806156	−	0.834839i
$549$	−9.68615	−	16.0378i	−0.413395	−	0.684476i
$550$	0.639676	+	1.50693i	0.0272759	+	0.0642558i
$551$	−6.07435			−0.258776
$552$	1.39953	−	1.15644i	0.0595680	−	0.0492215i
$553$		−	3.49299i		−	0.148537i
$554$	−26.4232	+	11.2164i	−1.12262	+	0.476538i
$555$	−18.7836	−	10.5991i	−0.797321	−	0.449907i
$556$	−0.630026	+	0.652443i	−0.0267191	+	0.0276697i
$557$			25.0783i			1.06260i	0.847183	+	0.531302i	$0.178297\pi$
$557$			25.0783i			1.06260i	−0.847183	+	0.531302i	$0.821703\pi$
$558$	−22.4022	+	7.49290i	−0.948359	+	0.317200i
$559$	−22.4435			−0.949257
$560$	0.101350	+	2.89828i	0.00428282	+	0.122475i
$561$	0.566427	−	1.00382i	0.0239146	−	0.0423812i
$562$	−17.4589	−	41.1293i	−0.736460	−	1.73493i
$563$	22.1982			0.935541			0.467770	−	0.883850i	$-0.345057\pi$
$563$	22.1982			0.935541			0.467770	+	0.883850i	$0.345057\pi$
$564$	6.72659	+	22.6122i	0.283240	+	0.952145i
$565$			23.1128i			0.972365i
$566$	−5.67552	−	13.3702i	−0.238560	−	0.561993i
$567$	1.50399	−	2.85989i	0.0631618	−	0.120104i
$568$	6.27065	+	2.40682i	0.263111	+	0.100988i
$569$	−3.66233			−0.153533			−0.0767665	−	0.997049i	$-0.524460\pi$
$569$	−3.66233			−0.153533			−0.0767665	+	0.997049i	$0.524460\pi$
$570$	−0.839857	+	7.44736i	−0.0351777	+	0.311936i
$571$	−29.0424			−1.21539			−0.607693	−	0.794172i	$-0.707905\pi$
$571$	−29.0424			−1.21539			−0.607693	+	0.794172i	$0.707905\pi$
$572$	−8.85964	−	8.55524i	−0.370440	−	0.357713i
$573$	−13.3569	+	23.6709i	−0.557990	+	0.988865i
$574$	−0.649546	−	1.53018i	−0.0271115	−	0.0638686i
$575$	0.341717			0.0142506
$576$	4.52416	−	23.5697i	0.188507	−	0.982072i
$577$	−28.7589			−1.19725			−0.598624	−	0.801030i	$-0.704286\pi$
$577$	−28.7589			−1.19725			−0.598624	+	0.801030i	$0.704286\pi$
$578$	−21.7645	+	9.23881i	−0.905286	+	0.384284i
$579$	−15.1378	−	8.54185i	−0.629105	−	0.354987i
$580$	−11.6477	−	11.2475i	−0.483644	−	0.467027i
$581$			2.59341i			0.107593i
$582$	−10.2802	−	1.15932i	−0.426128	−	0.0480555i
$583$	0.743249			0.0307822
$584$	17.6898	+	6.78976i	0.732011	+	0.280962i
$585$	15.3632	+	25.4375i	0.635189	+	1.05171i
$586$	18.1662	−	7.71135i	0.750438	−	0.318553i
$587$		−	15.3051i		−	0.631710i	−0.948807	−	0.315855i	$-0.897709\pi$
$587$		−	15.3051i		−	0.631710i	0.948807	−	0.315855i	$-0.102291\pi$
$588$	22.8141	−	6.78667i	0.940839	−	0.279877i
$589$	6.85608	+	4.91521i	0.282500	+	0.202528i
$590$	32.8775	−	13.9561i	1.35354	−	0.574565i
$591$	−7.33814	+	13.0046i	−0.301851	+	0.534937i
$592$	−0.861990	−	24.6502i	−0.0354276	−	1.01312i
$593$		−	34.4043i		−	1.41282i	−0.707804	−	0.706409i	$-0.750314\pi$
$593$		−	34.4043i		−	1.41282i	0.707804	−	0.706409i	$-0.249686\pi$
$594$	−8.38143	+	3.85432i	−0.343894	+	0.158145i
$595$	0.384314			0.0157553
$596$	−27.2696	+	28.2399i	−1.11701	+	1.15675i
$597$	10.4319	−	18.4872i	0.426948	−	0.756632i
$598$	−2.36643	+	1.00452i	−0.0967704	+	0.0410780i
$599$			35.1757i			1.43724i	0.695402	+	0.718621i	$0.255226\pi$
$599$			35.1757i			1.43724i	−0.695402	+	0.718621i	$0.744774\pi$
$600$	3.48231	−	2.87746i	0.142165	−	0.117472i
$601$			12.1715i			0.496487i	0.968698	+	0.248244i	$0.0798533\pi$
$601$			12.1715i			0.496487i	−0.968698	+	0.248244i	$0.920147\pi$
$602$	2.13842	−	0.907736i	0.0871555	−	0.0369965i
$603$	−25.3483	+	15.3093i	−1.03226	+	0.623444i
$604$	4.12077	+	3.97919i	0.167672	+	0.161911i
$605$	19.0307			0.773706
$606$	−15.0650	−	1.69892i	−0.611975	−	0.0690139i
$607$	11.2629			0.457147			0.228573	−	0.973527i	$-0.426594\pi$
$607$	11.2629			0.457147			0.228573	+	0.973527i	$0.426594\pi$
$608$	−7.76768	+	3.62270i	−0.315021	+	0.146920i
$609$	1.22518	−	2.17126i	0.0496469	−	0.0879837i
$610$	−16.4176	+	6.96909i	−0.664729	+	0.282170i
$611$		−	33.4063i		−	1.35147i
$612$	−3.10059	−	0.708330i	−0.125334	−	0.0286325i
$613$	47.1446			1.90415			0.952076	−	0.305860i	$-0.0989440\pi$
$613$	47.1446			1.90415			0.952076	+	0.305860i	$0.0989440\pi$
$614$	−3.53592	−	8.32984i	−0.142698	−	0.336165i
$615$	5.62757	−	9.97313i	0.226926	−	0.402155i
$616$	1.19017	+	0.456814i	0.0479533	+	0.0184056i
$617$			0.713094i			0.0287081i	0.999897	+	0.0143540i	$0.00456919\pi$
$617$			0.713094i			0.0287081i	−0.999897	+	0.0143540i	$0.995431\pi$
$618$	5.37368	+	0.606003i	0.216161	+	0.0243770i
$619$	21.4057			0.860367			0.430184	−	0.902741i	$-0.358449\pi$
$619$	21.4057			0.860367			0.430184	+	0.902741i	$0.358449\pi$
$620$	4.04547	+	22.1200i	0.162470	+	0.888361i
$621$	0.0569696	+	1.92479i	0.00228611	+	0.0772391i
$622$	−2.43573	−	5.73802i	−0.0976637	−	0.230074i
$623$	−2.58739			−0.103661
$624$	−15.6567	+	30.1634i	−0.626769	+	1.20750i
$625$	−19.5393			−0.781571
$626$	9.27737	+	21.8554i	0.370798	+	0.873517i
$627$	2.86924	+	1.61904i	0.114587	+	0.0646582i
$628$	25.2377	+	24.3706i	1.00709	+	0.972494i
$629$	−3.26862			−0.130329
$630$	−2.49264	−	1.80232i	−0.0993091	−	0.0718062i
$631$		−	24.5796i		−	0.978497i	−0.872144	−	0.489248i	$-0.837271\pi$
$631$		−	24.5796i		−	0.978497i	0.872144	−	0.489248i	$-0.162729\pi$
$632$	25.6905	+	9.86059i	1.02191	+	0.392233i
$633$	−14.8117	+	26.2491i	−0.588711	+	1.04331i
$634$	14.7522	−	6.26214i	0.585884	−	0.248701i
$635$			38.1602i			1.51434i
$636$	−0.584771	−	1.96577i	−0.0231877	−	0.0779480i
$637$	−33.7046			−1.33543
$638$	−6.55186	+	2.78119i	−0.259391	+	0.110108i
$639$	−6.09820	+	3.68306i	−0.241241	+	0.145700i
$640$	−21.6026	−	7.43634i	−0.853918	−	0.293947i
$641$	−28.8232			−1.13845			−0.569225	−	0.822182i	$-0.692757\pi$
$641$	−28.8232			−1.13845			−0.569225	+	0.822182i	$0.692757\pi$
$642$	1.06151	+	0.119709i	0.0418946	+	0.00472456i
$643$	45.5128			1.79485			0.897424	−	0.441169i	$-0.145436\pi$
$643$	45.5128			1.79485			0.897424	+	0.441169i	$0.145436\pi$
$644$	0.184846	−	0.191422i	0.00728394	−	0.00754310i
$645$	13.9374	+	7.86450i	0.548784	+	0.309664i
$646$	0.443811	+	1.04552i	0.0174615	+	0.0411353i
$647$	19.2950			0.758563			0.379281	−	0.925281i	$-0.376171\pi$
$647$	19.2950			0.758563			0.379281	+	0.925281i	$0.376171\pi$
$648$	16.7884	+	19.1350i	0.659510	+	0.751696i
$649$		−	15.7007i		−	0.616307i
$650$	−5.88814	+	2.49945i	−0.230952	+	0.0980365i
$651$	−3.13978	+	1.45929i	−0.123058	+	0.0571943i
$652$	29.5672	+	28.5513i	1.15794	+	1.11816i
$653$	−20.6505			−0.808116			−0.404058	−	0.914733i	$-0.632401\pi$
$653$	−20.6505			−0.808116			−0.404058	+	0.914733i	$0.632401\pi$
$654$	0.929948	−	8.24623i	0.0363638	−	0.322453i
$655$	11.0345			0.431154
$656$	13.0879	−	0.457671i	0.510998	−	0.0178691i
$657$	−17.2034	+	10.3901i	−0.671167	+	0.405357i
$658$	1.35113	+	3.18296i	0.0526726	+	0.124085i
$659$	−17.0833			−0.665470			−0.332735	−	0.943020i	$-0.607971\pi$
$659$	−17.0833			−0.665470			−0.332735	+	0.943020i	$0.607971\pi$
$660$	2.50396	+	8.41735i	0.0974665	+	0.327645i
$661$		−	34.9359i		−	1.35885i	−0.733745	−	0.679425i	$-0.762229\pi$
$661$		−	34.9359i		−	1.35885i	0.733745	−	0.679425i	$-0.237771\pi$
$662$	−37.6938	+	16.0006i	−1.46501	+	0.621881i
$663$	3.92229	+	2.21324i	0.152329	+	0.0859552i
$664$	−19.0742	−	7.32112i	−0.740224	−	0.284115i
$665$			1.09850i			0.0425979i
$666$	21.2001	+	15.3289i	0.821488	+	0.593983i
$667$			1.48572i			0.0575274i
$668$	−11.3609	+	11.7651i	−0.439565	+	0.455205i
$669$	−11.3997	+	20.2024i	−0.440738	+	0.781071i
$670$	11.0149	+	25.9486i	0.425543	+	1.00248i
$671$			7.84026i			0.302670i
$672$	0.271802	−	3.50722i	0.0104850	−	0.135294i
$673$			9.63430i			0.371375i	0.982609	+	0.185687i	$0.0594512\pi$
$673$			9.63430i			0.371375i	−0.982609	+	0.185687i	$0.940549\pi$
$674$	17.4163	+	41.0288i	0.670850	+	1.58037i
$675$	0.141752	+	4.78925i	0.00545602	+	0.184338i
$676$	15.3678	−	15.9146i	0.591071	−	0.612101i
$677$		−	8.42522i		−	0.323808i	−0.986807	−	0.161904i	$-0.948237\pi$
$677$		−	8.42522i		−	0.323808i	0.986807	−	0.161904i	$-0.0517634\pi$
$678$	3.14173	−	27.8590i	0.120657	−	1.06992i
$679$	−1.51635			−0.0581920
$680$	−1.08490	+	2.82658i	−0.0416042	+	0.108394i
$681$	−22.0742	−	12.4559i	−0.845885	−	0.477310i
$682$	9.64551	+	2.16249i	0.369346	+	0.0828060i
$683$	−35.2639			−1.34934			−0.674669	−	0.738121i	$-0.735713\pi$
$683$	−35.2639			−1.34934			−0.674669	+	0.738121i	$0.735713\pi$
$684$	2.02464	−	8.86251i	0.0774141	−	0.338867i
$685$	27.4307			1.04807
$686$	6.48302	−	2.75197i	0.247523	−	0.105071i
$687$	25.9226	+	14.6274i	0.989009	+	0.558072i
$688$	0.639593	+	18.2903i	0.0243842	+	0.697311i
$689$			2.90415i			0.110639i
$690$	1.82155	+	0.205421i	0.0693452	+	0.00782022i
$691$			32.6503i			1.24208i	0.783780	+	0.621038i	$0.213289\pi$
$691$			32.6503i			1.24208i	−0.783780	+	0.621038i	$0.786711\pi$
$692$	−21.2510	+	22.0071i	−0.807840	+	0.836583i
$693$	−1.15744	+	0.699046i	−0.0439675	+	0.0265545i
$694$	18.4485	+	43.4605i	0.700296	+	1.64974i
$695$	−0.915771			−0.0347372
$696$	12.5107	+	15.1404i	0.474215	+	0.573897i
$697$		−	1.73547i		−	0.0657355i
$698$	−1.43142	−	3.37210i	−0.0541800	−	0.127636i
$699$	3.64840	−	6.46566i	0.137995	−	0.244554i
$700$	0.459932	−	0.476297i	0.0173838	−	0.0180023i
$701$	−30.5160			−1.15257			−0.576287	−	0.817248i	$-0.695499\pi$
$701$	−30.5160			−1.15257			−0.576287	+	0.817248i	$0.695499\pi$
$702$	−15.0603	−	32.7494i	−0.568413	−	1.23604i
$703$		−	9.34281i		−	0.352371i
$704$	−6.71962	+	7.46398i	−0.253255	+	0.281309i
$705$	−11.7060	+	20.7453i	−0.440874	+	0.781313i
$706$	1.83982	−	0.780984i	0.0692426	−	0.0293927i
$707$	−2.22211			−0.0835712
$708$	−41.5259	+	12.3530i	−1.56064	+	0.464253i
$709$	12.8448			0.482396			0.241198	−	0.970476i	$-0.422460\pi$
$709$	12.8448			0.482396			0.241198	+	0.970476i	$0.422460\pi$
$710$	2.64992	+	6.24262i	0.0994499	+	0.234281i
$711$	−24.9840	+	15.0893i	−0.936973	+	0.565893i
$712$	7.30411	−	19.0299i	0.273733	−	0.713176i
$713$	1.20221	−	1.67693i	0.0450232	−	0.0628014i
$714$	−0.463232	−	0.0522398i	−0.0173360	−	0.00195503i
$715$		−	12.4354i		−	0.465058i
$716$	27.3900	+	26.4489i	1.02361	+	0.988443i
$717$	40.7232	+	22.9790i	1.52083	+	0.858167i
$718$	9.75324	+	22.9764i	0.363988	+	0.857473i
$719$	0.729364			0.0272007			0.0136003	−	0.999908i	$-0.495671\pi$
$719$	0.729364			0.0272007			0.0136003	+	0.999908i	$0.495671\pi$
$720$	20.2925	−	13.2451i	0.756256	−	0.493617i
$721$	0.792626			0.0295189
$722$	21.7455	−	9.23071i	0.809282	−	0.343531i
$723$	−18.8055	+	33.3269i	−0.699384	+	1.23944i
$724$	−6.23814	+	6.46010i	−0.231839	+	0.240088i
$725$			3.69677i			0.137295i
$726$	−22.9386	−	2.58684i	−0.851331	−	0.0960066i
$727$	−28.9918			−1.07525			−0.537624	−	0.843185i	$-0.680678\pi$
$727$	−28.9918			−1.07525			−0.537624	+	0.843185i	$0.680678\pi$
$728$	−1.78494	+	4.65044i	−0.0661544	+	0.172357i
$729$	−26.9527	+	1.59689i	−0.998249	+	0.0591439i
$730$	7.47559	+	17.6108i	0.276684	+	0.651804i
$731$	2.42530			0.0897031
$732$	20.7362	−	6.16854i	0.766433	−	0.227996i
$733$			9.05166i			0.334331i	0.985929	+	0.167165i	$0.0534614\pi$
$733$			9.05166i			0.334331i	−0.985929	+	0.167165i	$0.946539\pi$
$734$	7.40152	+	17.4363i	0.273195	+	0.643586i
$735$	20.9306	+	11.8106i	0.772036	+	0.435639i
$736$	0.886075	+	1.89989i	0.0326611	+	0.0700310i
$737$	12.3918			0.456459
$738$	−8.13884	+	11.2561i	−0.299595	+	0.414345i
$739$	45.0935			1.65879			0.829396	−	0.558661i	$-0.188685\pi$
$739$	45.0935			1.65879			0.829396	+	0.558661i	$0.188685\pi$
$740$	17.2995	−	17.9150i	0.635943	−	0.658570i
$741$	−6.32618	+	11.2112i	−0.232398	+	0.411854i
$742$	−0.117460	−	0.276708i	−0.00431208	−	0.0101583i
$743$	−40.4715			−1.48475			−0.742377	−	0.669983i	$-0.766302\pi$
$743$	−40.4715			−1.48475			−0.742377	+	0.669983i	$0.766302\pi$
$744$	−1.86942	−	27.2122i	−0.0685364	−	0.997649i
$745$	−39.6376			−1.45221
$746$	−13.1206	−	30.9092i	−0.480380	−	1.13167i
$747$	18.5497	−	11.2032i	0.678697	−	0.409905i
$748$	0.957398	+	0.924504i	0.0350059	+	0.0338032i
$749$	0.156575			0.00572112
$750$	29.1089	+	3.28268i	1.06291	+	0.119866i
$751$	27.5619			1.00575			0.502873	−	0.864360i	$-0.332276\pi$
$751$	27.5619			1.00575			0.502873	+	0.864360i	$0.332276\pi$
$752$	−27.2245	+	0.952010i	−0.992774	+	0.0347162i
$753$	−13.1087	+	23.2312i	−0.477709	+	0.846592i
$754$	−10.8671	−	25.6005i	−0.395758	−	0.932317i
$755$			5.78393i			0.210499i
$756$	2.75951	+	2.51125i	0.100362	+	0.0913333i
$757$	24.0859			0.875417			0.437708	−	0.899117i	$-0.355790\pi$
$757$	24.0859			0.875417			0.437708	+	0.899117i	$0.355790\pi$
$758$	−8.26022	−	19.4592i	−0.300025	−	0.706790i
$759$	0.396000	−	0.701788i	0.0143739	−	0.0254733i
$760$	−8.07930	−	3.10102i	−0.293067	−	0.112486i
$761$	−16.0015			−0.580056			−0.290028	−	0.957018i	$-0.593665\pi$
$761$	−16.0015			−0.580056			−0.290028	+	0.957018i	$0.593665\pi$
$762$	5.18712	−	45.9964i	0.187910	−	1.66627i
$763$		−	1.21633i		−	0.0440341i
$764$	−22.5763	−	21.8006i	−0.816781	−	0.788718i
$765$	−1.66019	−	2.74885i	−0.0600242	−	0.0993848i
$766$	−20.2816	+	8.60933i	−0.732805	+	0.311068i
$767$	61.3485			2.21517
$768$	25.0279	+	11.8998i	0.903115	+	0.429398i
$769$	0.443249			0.0159840			0.00799199	−	0.999968i	$-0.497456\pi$
$769$	0.443249			0.0159840			0.00799199	+	0.999968i	$0.497456\pi$
$770$	0.502956	+	1.18485i	0.0181253	+	0.0426991i
$771$	7.93440	−	14.0613i	0.285750	−	0.506404i
$772$	13.9417	−	14.4378i	0.501774	−	0.519627i
$773$		−	25.3696i		−	0.912482i	−0.889856	−	0.456241i	$-0.849195\pi$
$773$		−	25.3696i		−	0.912482i	0.889856	−	0.456241i	$-0.150805\pi$
$774$	−15.7304	−	11.3740i	−0.565417	−	0.408829i
$775$	2.99134	−	4.17252i	0.107452	−	0.149881i
$776$	4.28059	−	11.1525i	0.153664	−	0.400352i
$777$	3.33956	+	1.88442i	0.119806	+	0.0676033i
$778$	−0.617801	−	1.45540i	−0.0221492	−	0.0521786i
$779$	4.96054			0.177730
$780$	−32.8897	+	9.78390i	−1.17764	+	0.350320i
$781$	2.98118			0.106675
$782$	0.255723	−	0.108552i	0.00914463	−	0.00388180i
$783$	−20.8228	+	0.616310i	−0.744146	+	0.0220251i
$784$	0.960513	+	27.4676i	0.0343040	+	0.980986i
$785$			35.4238i			1.26433i
$786$	−13.3004	−	1.49992i	−0.474411	−	0.0535004i
$787$	−16.6822			−0.594656			−0.297328	−	0.954775i	$-0.596096\pi$
$787$	−16.6822			−0.594656			−0.297328	+	0.954775i	$0.596096\pi$
$788$	−12.4032	−	11.9771i	−0.441846	−	0.426665i
$789$	−36.5302	−	20.6130i	−1.30051	−	0.733843i
$790$	10.8566	+	25.5757i	0.386260	+	0.909942i
$791$		−	4.10925i		−	0.146108i
$792$	−1.87398	−	10.4862i	−0.0665888	−	0.372611i
$793$	−30.6348			−1.08787
$794$	−0.697767	−	1.64378i	−0.0247628	−	0.0583356i
$795$	1.01765	−	1.80348i	0.0360925	−	0.0639627i
$796$	17.6323	+	17.0265i	0.624962	+	0.603490i
$797$		−	48.0774i		−	1.70299i	−0.524364	−	0.851494i	$-0.675697\pi$
$797$		−	48.0774i		−	1.70299i	0.524364	−	0.851494i	$-0.324303\pi$
$798$	0.149319	−	1.32407i	0.00528583	−	0.0468717i
$799$			3.60998i			0.127712i
$800$	2.20473	+	4.72731i	0.0779489	+	0.167136i
$801$	11.1772	+	18.5066i	0.394927	+	0.653898i
$802$	−29.2761	+	12.4274i	−1.03377	+	0.438826i
$803$	8.41008			0.296785
$804$	−9.74962	−	32.7744i	−0.343842	−	1.15587i
$805$	0.268681			0.00946977
$806$	−8.44965	+	37.6886i	−0.297626	+	1.32752i
$807$	−27.4161	+	48.5865i	−0.965092	+	1.71033i
$808$	6.27295	−	16.3434i	0.220682	−	0.574958i
$809$	37.0743			1.30346			0.651732	−	0.758449i	$-0.274043\pi$
$809$	37.0743			1.30346			0.651732	+	0.758449i	$0.274043\pi$
$810$	−2.12340	+	25.6147i	−0.0746087	+	0.900008i
$811$		−	38.5331i		−	1.35308i	−0.736407	−	0.676539i	$-0.763479\pi$
$811$		−	38.5331i		−	1.35308i	0.736407	−	0.676539i	$-0.236521\pi$
$812$	2.07085	+	1.99970i	0.0726726	+	0.0701758i
$813$	−14.7205	+	26.0875i	−0.516270	+	0.914928i
$814$	−4.27769	−	10.0773i	−0.149933	−	0.353208i
$815$			41.5006i			1.45370i
$816$	1.69191	−	3.25954i	0.0592286	−	0.114107i
$817$			6.93233i			0.242531i
$818$	12.6087	+	29.7034i	0.440855	+	1.03855i
$819$	−2.73143	−	4.52255i	−0.0954439	−	0.158031i
$820$	9.51195	+	9.18514i	0.332172	+	0.320759i
$821$		−	3.00235i		−	0.104783i	−0.998627	−	0.0523914i	$-0.983316\pi$
$821$		−	3.00235i		−	0.104783i	0.998627	−	0.0523914i	$-0.0166843\pi$
$822$	−33.0636	−	3.72866i	−1.15323	−	0.130052i
$823$		−	5.26380i		−	0.183485i	−0.995783	−	0.0917423i	$-0.970756\pi$
$823$		−	5.26380i		−	0.183485i	0.995783	−	0.0917423i	$-0.0292436\pi$
$824$	−2.23756	+	5.82966i	−0.0779489	+	0.203086i
$825$	0.985327	−	1.74619i	0.0343047	−	0.0607944i
$826$	−5.84531	+	2.48127i	−0.203384	+	0.0863344i
$827$			30.2469i			1.05179i	0.850550	+	0.525894i	$0.176269\pi$
$827$			30.2469i			1.05179i	−0.850550	+	0.525894i	$0.823731\pi$
$828$	−2.16768	−	0.495207i	−0.0753321	−	0.0172096i
$829$	1.09771			0.0381251			0.0190625	−	0.999818i	$-0.493932\pi$
$829$	1.09771			0.0381251			0.0190625	+	0.999818i	$0.493932\pi$
$830$	−8.06061	−	18.9890i	−0.279788	−	0.659117i
$831$	30.6185	+	17.2772i	1.06214	+	0.599339i
$832$	−29.1645	−	26.2560i	−1.01110	−	0.910265i
$833$	3.64222			0.126195
$834$	1.10382	+	0.124481i	0.0382223	+	0.00431042i
$835$	−16.5135			−0.571473
$836$	−2.64254	+	2.73656i	−0.0913942	+	0.0946460i
$837$	24.0012	+	16.1537i	0.829604	+	0.558352i
$838$	23.1187	−	9.81363i	0.798622	−	0.339006i
$839$		−	8.04282i		−	0.277669i	−0.990316	−	0.138834i	$-0.955664\pi$
$839$		−	8.04282i		−	0.277669i	0.990316	−	0.138834i	$-0.0443356\pi$
$840$	2.73803	−	2.26245i	0.0944709	−	0.0780620i
$841$	12.9271			0.445762
$842$	1.65775	+	3.90529i	0.0571299	+	0.134585i
$843$	−26.8929	+	47.6594i	−0.926242	+	1.64148i
$844$	−25.0353	−	24.1751i	−0.861749	−	0.832141i
$845$	22.3378			0.768444
$846$	16.9297	−	23.4141i	0.582057	−	0.804994i
$847$	−3.38347			−0.116258
$848$	2.36674	−	0.0827624i	0.0812741	−	0.00284207i
$849$	−8.74232	+	15.4930i	−0.300036	+	0.531720i
$850$	0.636289	−	0.270098i	0.0218245	−	0.00926427i
$851$	−2.28516			−0.0783342
$852$	−2.34552	−	7.88474i	−0.0803563	−	0.270127i
$853$			17.1359i			0.586723i	0.956002	+	0.293362i	$0.0947740\pi$
$853$			17.1359i			0.586723i	−0.956002	+	0.293362i	$0.905226\pi$
$854$	2.91890	−	1.23904i	0.0998825	−	0.0423990i
$855$	7.85712	−	4.74537i	0.268708	−	0.162288i
$856$	−0.442005	+	1.15159i	−0.0151074	+	0.0393605i
$857$		−	31.4277i		−	1.07355i	−0.843725	−	0.536775i	$-0.819642\pi$
$857$		−	31.4277i		−	1.07355i	0.843725	−	0.536775i	$-0.180358\pi$
$858$	−1.69035	+	14.9890i	−0.0577075	+	0.511717i
$859$	0.472050			0.0161061			0.00805306	−	0.999968i	$-0.497437\pi$
$859$	0.472050			0.0161061			0.00805306	+	0.999968i	$0.497437\pi$
$860$	−12.8362	+	13.2929i	−0.437710	+	0.453283i
$861$	−1.00053	+	1.77313i	−0.0340980	+	0.0604281i
$862$	8.06026	+	18.9881i	0.274533	+	0.646739i
$863$	57.8887			1.97055			0.985276	−	0.170969i	$-0.0546897\pi$
$863$	57.8887			1.97055			0.985276	+	0.170969i	$0.0546897\pi$
$864$	−26.2599	+	13.2067i	−0.893381	+	0.449300i
$865$	−30.8892			−1.05026
$866$	−22.2779	−	52.4817i	−0.757034	−	1.78340i
$867$	25.2201	+	14.2310i	0.856520	+	0.483312i
$868$	−0.719246	−	3.93273i	−0.0244128	−	0.133486i
$869$	12.2137			0.414322
$870$	−2.22229	+	19.7059i	−0.0753425	+	0.668094i
$871$			48.4195i			1.64063i
$872$	8.94596	+	3.43366i	0.302948	+	0.116278i
$873$	6.55043	+	10.8458i	0.221698	+	0.367076i
$874$	0.310277	+	0.730941i	0.0104953	+	0.0247245i
$875$	4.29360			0.145150
$876$	−6.61685	−	22.2433i	−0.223563	−	0.751532i
$877$			23.6764i			0.799494i	0.916626	+	0.399747i	$0.130902\pi$
$877$			23.6764i			0.799494i	−0.916626	+	0.399747i	$0.869098\pi$
$878$	−1.67497	+	0.711008i	−0.0565277	+	0.0239954i
$879$	−21.0504	−	11.8782i	−0.710014	−	0.400642i
$880$	−10.1343	+	0.354384i	−0.341626	+	0.0119463i
$881$	18.1245			0.610631			0.305316	−	0.952251i	$-0.401238\pi$
$881$	18.1245			0.610631			0.305316	+	0.952251i	$0.401238\pi$
$882$	−23.6232	−	17.0810i	−0.795436	−	0.575146i
$883$	26.1465			0.879900			0.439950	−	0.898022i	$-0.354996\pi$
$883$	26.1465			0.879900			0.439950	+	0.898022i	$0.354996\pi$
$884$	−3.61238	+	3.74091i	−0.121497	+	0.125820i
$885$	−38.0974	−	21.4974i	−1.28063	−	0.722626i
$886$	−31.9682	+	13.5702i	−1.07399	+	0.455899i
$887$			24.0982i			0.809140i	0.914507	+	0.404570i	$0.132579\pi$
$887$			24.0982i			0.809140i	−0.914507	+	0.404570i	$0.867421\pi$
$888$	−23.2872	+	19.2424i	−0.781466	+	0.645731i
$889$		−	6.78453i		−	0.227546i
$890$	18.9448	−	8.04188i	0.635033	−	0.269564i
$891$	10.0000	+	5.25893i	0.335013	+	0.176181i
$892$	−19.2682	−	18.6062i	−0.645147	−	0.622982i
$893$	−10.3185			−0.345296
$894$	47.7772	+	5.38794i	1.59791	+	0.180200i
$895$			38.4447i			1.28506i
$896$	3.84074	+	1.32211i	0.128310	+	0.0441687i
$897$	2.74215	+	1.54732i	0.0915576	+	0.0516635i
$898$	−20.6315	+	8.75785i	−0.688483	+	0.292253i
$899$	18.1414	+	13.0058i	0.605048	+	0.433767i
$900$	−5.39362	−	1.23217i	−0.179787	−	0.0410724i
$901$		−	0.313831i		−	0.0104552i
$902$	5.35050	−	2.27123i	0.178152	−	0.0756236i
$903$	−2.47794	−	1.39823i	−0.0824606	−	0.0465303i
$904$	30.2230	+	11.6003i	1.00520	+	0.385819i
$905$	−9.06741			−0.301411
$906$	0.786210	−	6.97166i	0.0261201	−	0.231618i
$907$			15.9864i			0.530820i	0.964136	+	0.265410i	$0.0855074\pi$
$907$			15.9864i			0.530820i	−0.964136	+	0.265410i	$0.914493\pi$
$908$	20.3301	−	21.0534i	0.674677	−	0.698682i
$909$	9.59926	+	15.8939i	0.318387	+	0.527168i
$910$	−4.62965	+	1.96524i	−0.153471	+	0.0651469i
$911$	−25.8041			−0.854927			−0.427464	−	0.904033i	$-0.640593\pi$
$911$	−25.8041			−0.854927			−0.427464	+	0.904033i	$0.640593\pi$
$912$	9.31686	+	4.83603i	0.308512	+	0.160137i
$913$	−9.06824			−0.300115
$914$	11.2421	+	26.4837i	0.371854	+	0.876004i
$915$	19.0242	+	10.7349i	0.628921	+	0.354884i
$916$	−23.8744	+	24.7239i	−0.788833	+	0.816900i
$917$	−1.96183			−0.0647854
$918$	1.62746	+	3.53899i	0.0537141	+	0.116804i
$919$	−14.2523			−0.470139			−0.235070	−	0.971979i	$-0.575532\pi$
$919$	−14.2523			−0.470139			−0.235070	+	0.971979i	$0.575532\pi$
$920$	−0.758478	+	1.97612i	−0.0250063	+	0.0651506i
$921$	−5.44658	+	9.65237i	−0.179471	+	0.318056i
$922$	−13.4678	−	31.7272i	−0.443539	−	1.04488i
$923$			11.6486i			0.383418i
$924$	−0.445181	−	1.49653i	−0.0146454	−	0.0492321i
$925$	−5.68592			−0.186952
$926$	−13.1255	−	30.9208i	−0.431332	−	1.01612i
$927$	−3.42405	−	5.66934i	−0.112460	−	0.186206i
$928$	−20.5535	+	9.58575i	−0.674701	+	0.314668i
$929$	30.2498			0.992464			0.496232	−	0.868190i	$-0.334717\pi$
$929$	30.2498			0.992464			0.496232	+	0.868190i	$0.334717\pi$
$930$	18.4538	−	20.4437i	0.605125	−	0.670376i
$931$			10.4107i			0.341196i
$932$	6.16667	+	5.95480i	0.201996	+	0.195056i
$933$	−3.75188	+	6.64904i	−0.122831	+	0.217680i
$934$	38.7718	−	16.4582i	1.26865	−	0.538529i
$935$			1.34381i			0.0439472i
$936$	40.9735	−	7.32232i	1.33926	−	0.239337i
$937$	−19.8096			−0.647152			−0.323576	−	0.946202i	$-0.604885\pi$
$937$	−19.8096			−0.647152			−0.323576	+	0.946202i	$0.604885\pi$
$938$	−1.95835	−	4.61343i	−0.0639424	−	0.150634i
$939$	14.2904	−	25.3254i	0.466351	−	0.826463i
$940$	−19.7860	−	19.1062i	−0.645347	−	0.623174i
$941$		−	42.9009i		−	1.39853i	−0.714862	−	0.699265i	$-0.753511\pi$
$941$		−	42.9009i		−	1.39853i	0.714862	−	0.699265i	$-0.246489\pi$
$942$	4.81516	−	42.6980i	0.156886	−	1.39118i
$943$		−	1.21330i		−	0.0395104i
$944$	−1.74831	−	49.9960i	−0.0569026	−	1.62723i
$945$	0.111455	+	3.76563i	0.00362562	+	0.122496i
$946$	3.17403	+	7.47728i	0.103196	+	0.243107i
$947$		−	38.1906i		−	1.24103i	−0.784196	−	0.620514i	$-0.786924\pi$
$947$		−	38.1906i		−	1.24103i	0.784196	−	0.620514i	$-0.213076\pi$
$948$	−9.60948	−	32.3034i	−0.312101	−	1.04916i
$949$			32.8613i			1.06672i
$950$	0.772029	+	1.81873i	0.0250479	+	0.0590073i
$951$	−17.0944	−	9.64591i	−0.554323	−	0.312790i
$952$	0.192886	−	0.502539i	0.00625147	−	0.0162874i
$953$	18.7141			0.606208			0.303104	−	0.952957i	$-0.401977\pi$
$953$	18.7141			0.606208			0.303104	+	0.952957i	$0.401977\pi$
$954$	−1.47178	+	2.03549i	−0.0476505	+	0.0659014i
$955$		−	31.6881i		−	1.02540i
$956$	−37.5056	+	38.8400i	−1.21302	+	1.25618i
$957$	7.59210	+	4.28402i	0.245418	+	0.138483i
$958$	9.60834	+	22.6351i	0.310431	+	0.731306i
$959$	−4.87693			−0.157484
$960$	8.91069	+	26.5247i	0.287591	+	0.856080i
$961$	−9.95207	−	29.3591i	−0.321034	−	0.947068i
$962$	39.3756	−	16.7145i	1.26952	−	0.538897i
$963$	−0.676384	−	1.11992i	−0.0217962	−	0.0360889i
$964$	−31.7858	−	30.6937i	−1.02375	−	0.988578i
$965$	20.2649			0.652350
$966$	−0.323855	−	0.0365219i	−0.0104199	−	0.00117507i
$967$		−	41.4972i		−	1.33446i	−0.744852	−	0.667229i	$-0.767480\pi$
$967$		−	41.4972i		−	1.33446i	0.744852	−	0.667229i	$-0.232520\pi$
$968$	9.55143	−	24.8850i	0.306995	−	0.799835i
$969$	0.683626	−	1.21151i	0.0219612	−	0.0389195i
$970$	11.1027	−	4.71296i	0.356486	−	0.151324i
$971$	−19.0234			−0.610490			−0.305245	−	0.952274i	$-0.598738\pi$
$971$	−19.0234			−0.610490			−0.305245	+	0.952274i	$0.598738\pi$
$972$	6.04125	−	30.5860i	0.193773	−	0.981046i
$973$	0.162816			0.00521963
$974$	7.93481	+	18.6926i	0.254248	+	0.598950i
$975$	6.82300	+	3.85004i	0.218511	+	0.123300i
$976$	0.873030	+	24.9659i	0.0279450	+	0.799138i
$977$		−	47.2319i		−	1.51108i	−0.655100	−	0.755542i	$-0.727374\pi$
$977$		−	47.2319i		−	1.51108i	0.655100	−	0.755542i	$-0.272626\pi$
$978$	5.64118	−	50.0227i	0.180385	−	1.59955i
$979$		−	9.04716i		−	0.289149i
$980$	−19.2768	+	19.9627i	−0.615775	+	0.637685i
$981$	−8.69994	+	5.25440i	−0.277768	+	0.167760i
$982$	6.26949	+	14.7695i	0.200067	+	0.471314i
$983$	17.4021			0.555040			0.277520	−	0.960720i	$-0.410488\pi$
$983$	17.4021			0.555040			0.277520	+	0.960720i	$0.410488\pi$
$984$	−10.2167	−	12.3643i	−0.325696	−	0.394158i
$985$		−	17.4092i		−	0.554703i
$986$	1.17434	+	2.76647i	0.0373985	+	0.0881023i
$987$	2.08122	−	3.68832i	0.0662460	−	0.117400i
$988$	−10.6928	−	10.3254i	−0.340182	−	0.328494i
$989$	1.69558			0.0539162
$990$	6.30207	−	8.71586i	0.200293	−	0.277008i
$991$		−	8.19232i		−	0.260238i	−0.991498	−	0.130119i	$-0.958464\pi$
$991$		−	8.19232i		−	0.260238i	0.991498	−	0.130119i	$-0.0415359\pi$
$992$	30.9551	+	5.81200i	0.982827	+	0.184531i
$993$	43.6784	+	24.6466i	1.38609	+	0.782136i
$994$	−0.471132	−	1.10988i	−0.0149434	−	0.0352033i
$995$			24.7488i			0.784590i
$996$	7.13468	+	23.9840i	0.226071	+	0.759963i
$997$			35.0130i			1.10887i	0.832226	+	0.554437i	$0.187066\pi$
$997$			35.0130i			1.10887i	−0.832226	+	0.554437i	$0.812934\pi$
$998$	45.4765	−	19.3043i	1.43953	−	0.611067i
$999$	−0.947932	−	32.0270i	−0.0299912	−	1.01329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	744.2.o.e.557.81	yes	96
3.2	odd	2	inner	744.2.o.e.557.15	yes	96
8.5	even	2	inner	744.2.o.e.557.14	yes	96
24.5	odd	2	inner	744.2.o.e.557.84	yes	96
31.30	odd	2	inner	744.2.o.e.557.82	yes	96
93.92	even	2	inner	744.2.o.e.557.16	yes	96
248.61	odd	2	inner	744.2.o.e.557.13	✓	96
744.557	even	2	inner	744.2.o.e.557.83	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.o.e.557.13	✓	96	248.61	odd	2	inner
744.2.o.e.557.14	yes	96	8.5	even	2	inner
744.2.o.e.557.15	yes	96	3.2	odd	2	inner
744.2.o.e.557.16	yes	96	93.92	even	2	inner
744.2.o.e.557.81	yes	96	1.1	even	1	trivial
744.2.o.e.557.82	yes	96	31.30	odd	2	inner
744.2.o.e.557.83	yes	96	744.557	even	2	inner
744.2.o.e.557.84	yes	96	24.5	odd	2	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:	\( N \)	\(=\)	\( 744 = 2^{3} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	744.o (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30178 - 0.552593i) q^{2} +(-1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} +2.01938 q^{5} +(-2.43406 - 0.274495i) q^{6} -0.359027 q^{7} +(1.01352 - 2.64060i) q^{8} +(1.55095 + 2.56798i) q^{9} +O(q^{10})\)	\(q+(1.30178 - 0.552593i) q^{2} +(-1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} +2.01938 q^{5} +(-2.43406 - 0.274495i) q^{6} -0.359027 q^{7} +(1.01352 - 2.64060i) q^{8} +(1.55095 + 2.56798i) q^{9} +(2.62880 - 1.11590i) q^{10} -1.25539i q^{11} +(-3.32031 + 0.987712i) q^{12} +4.90527 q^{13} +(-0.467376 + 0.198396i) q^{14} +(-3.04617 - 1.71888i) q^{15} +(-0.139790 - 3.99756i) q^{16} -0.530078 q^{17} +(3.43806 + 2.48591i) q^{18} -1.51514i q^{19} +(2.80549 - 2.90531i) q^{20} +(0.541582 + 0.305600i) q^{21} +(-0.693720 - 1.63425i) q^{22} -0.370588 q^{23} +(-3.77652 + 3.12056i) q^{24} -0.922095 q^{25} +(6.38561 - 2.71062i) q^{26} +(-0.153728 - 5.19388i) q^{27} +(-0.498790 + 0.516538i) q^{28} -4.00910i q^{29} +(-4.91530 - 0.554310i) q^{30} +(-3.24407 + 4.52505i) q^{31} +(-2.39100 - 5.12671i) q^{32} +(-1.06857 + 1.89372i) q^{33} +(-0.690047 + 0.292917i) q^{34} -0.725014 q^{35} +(5.84931 + 1.33627i) q^{36} +6.16631 q^{37} +(-0.837255 - 1.97238i) q^{38} +(-7.39945 - 4.17531i) q^{39} +(2.04669 - 5.33238i) q^{40} +3.27399i q^{41} +(0.873895 + 0.0985512i) q^{42} -4.57537 q^{43} +(-1.80615 - 1.74409i) q^{44} +(3.13197 + 5.18574i) q^{45} +(-0.482425 + 0.204784i) q^{46} -6.81027i q^{47} +(-3.19181 + 6.14918i) q^{48} -6.87110 q^{49} +(-1.20037 + 0.509543i) q^{50} +(0.799606 + 0.451196i) q^{51} +(6.81481 - 7.05728i) q^{52} +0.592046i q^{53} +(-3.07022 - 6.67636i) q^{54} -2.53511i q^{55} +(-0.363882 + 0.948048i) q^{56} +(-1.28967 + 2.28554i) q^{57} +(-2.21540 - 5.21898i) q^{58} +12.5066 q^{59} +(-6.70496 + 1.99457i) q^{60} -6.24528 q^{61} +(-1.72256 + 7.68328i) q^{62} +(-0.556835 - 0.921977i) q^{63} +(-5.94554 - 5.35262i) q^{64} +9.90562 q^{65} +(-0.344598 + 3.05570i) q^{66} +9.87091i q^{67} +(-0.736428 + 0.762630i) q^{68} +(0.559020 + 0.315440i) q^{69} +(-0.943811 + 0.400637i) q^{70} +2.37470i q^{71} +(8.35295 - 1.49274i) q^{72} +6.69918i q^{73} +(8.02720 - 3.40746i) q^{74} +(1.39095 + 0.784877i) q^{75} +(-2.17985 - 2.10496i) q^{76} +0.450719i q^{77} +(-11.9397 - 1.34647i) q^{78} +9.72903i q^{79} +(-0.282290 - 8.07259i) q^{80} +(-4.18908 + 7.96565i) q^{81} +(1.80918 + 4.26202i) q^{82} -7.22344i q^{83} +(1.19208 - 0.354616i) q^{84} -1.07043 q^{85} +(-5.95615 + 2.52832i) q^{86} +(-3.41250 + 6.04760i) q^{87} +(-3.31498 - 1.27237i) q^{88} +7.20666 q^{89} +(6.94275 + 5.02001i) q^{90} -1.76113 q^{91} +(-0.514851 + 0.533169i) q^{92} +(8.74524 - 4.06458i) q^{93} +(-3.76331 - 8.86550i) q^{94} -3.05965i q^{95} +(-0.757051 + 9.76867i) q^{96} +4.22348 q^{97} +(-8.94469 + 3.79692i) q^{98} +(3.22382 - 1.94705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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