LMFDB - Embedded newform 744.2.o.e.557.16

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			557.16
Character	$\chi$	$=$	744.557
Dual form			744.2.o.e.557.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30178 + 0.552593i) q^{2} +(1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} -2.01938 q^{5} +(-1.49334 + 1.94163i) q^{6} -0.359027 q^{7} +(-1.01352 + 2.64060i) q^{8} +(1.55095 - 2.56798i) q^{9} +O(q^{10})$	\(q+(-1.30178 + 0.552593i) q^{2} +(1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} -2.01938 q^{5} +(-1.49334 + 1.94163i) 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} +(0.871072 - 3.35279i) 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} +(-0.599958 + 4.20001i) 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} +(0.718783 + 4.84596i) 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} +(3.01562 - 3.92090i) 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} +(-1.53988 - 5.79903i) 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} +(0.536150 - 0.697100i) 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} +(-3.61355 - 5.91120i) 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} +(2.66998 + 6.84625i) 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} +(-1.75903 + 6.77057i) q^{60} +6.24528 q^{61} +(6.72358 + 4.09798i) q^{62} +(-0.556835 + 0.921977i) q^{63} +(-5.94554 - 5.35262i) q^{64} +9.90562 q^{65} +(2.43751 + 1.87472i) 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} +(5.20909 + 6.69816i) 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} +(7.32524 - 9.52424i) 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} +(-0.312739 + 1.20375i) 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} +(1.21155 - 8.48142i) 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} +(7.97054 + 5.69829i) 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	$-0.649128\pi$
$5$	−2.01938			−0.903095			−0.451548	+	0.892247i	$0.649128\pi$
$6$	−1.49334	+	1.94163i	−0.609653	+	0.792668i
$7$	−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	$-0.0606080\pi$
$12$	0.871072	−	3.35279i	0.251457	−	0.967869i
$13$	−4.90527			−1.36048			−0.680239	−	0.732990i	$-0.738124\pi$
$13$	−4.90527			−1.36048			−0.680239	+	0.732990i	$0.738124\pi$
$14$	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	$0.520476\pi$
$18$	−0.599958	+	4.20001i	−0.141412	+	0.989951i
$19$		−	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	$0.512301\pi$
$24$	0.718783	+	4.84596i	0.146721	+	0.989178i
$25$	−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	$-0.121409\pi$
$30$	3.01562	−	3.92090i	0.550575	−	0.715855i
$31$	−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
$36$	−1.53988	−	5.79903i	−0.256646	−	0.966505i
$37$	−6.16631			−1.01373			−0.506867	−	0.862024i	$-0.669197\pi$
$37$	−6.16631			−1.01373			−0.506867	+	0.862024i	$0.669197\pi$
$38$	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	$-0.917709\pi$
$41$		−	3.27399i		−	0.511311i	0.966768	−	0.255655i	$-0.0822912\pi$
$42$	0.536150	−	0.697100i	0.0827297	−	0.107565i
$43$	4.57537			0.697738			0.348869	−	0.937172i	$-0.386566\pi$
$43$	4.57537			0.697738			0.348869	+	0.937172i	$0.386566\pi$
$44$	−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	$0.165451\pi$
$47$			6.81027i			0.993381i	−0.867928	+	0.496690i	$0.834549\pi$
$48$	−3.61355	−	5.91120i	−0.521570	−	0.853208i
$49$	−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	$0.987053\pi$
$54$	2.66998	+	6.84625i	0.363338	+	0.931657i
$55$			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	$-0.802777\pi$
$59$	−12.5066			−1.62823			−0.814114	+	0.580706i	$0.802777\pi$
$60$	−1.75903	+	6.77057i	−0.227089	+	0.874077i
$61$	6.24528			0.799626			0.399813	−	0.916597i	$-0.369075\pi$
$61$	6.24528			0.799626			0.399813	+	0.916597i	$0.369075\pi$
$62$	6.72358	+	4.09798i	0.853896	+	0.520444i
$63$	−0.556835	+	0.921977i	−0.0701547	+	0.116158i
$64$	−5.94554	−	5.35262i	−0.743193	−	0.669077i
$65$	9.90562			1.22864
$66$	2.43751	+	1.87472i	0.300036	+	0.230762i
$67$			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	$-0.954996\pi$
$71$		−	2.37470i		−	0.281826i	0.990022	−	0.140913i	$-0.0450037\pi$
$72$	5.20909	+	6.69816i	0.613897	+	0.789386i
$73$		−	6.69918i		−	0.784079i	−0.919948	−	0.392040i	$-0.871770\pi$
$73$		−	6.69918i		−	0.784079i	0.919948	−	0.392040i	$-0.128230\pi$
$74$	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
$78$	7.32524	−	9.52424i	0.829420	−	1.07841i
$79$		−	9.72903i		−	1.09460i	−0.836936	−	0.547301i	$-0.815655\pi$
$79$		−	9.72903i		−	1.09460i	0.836936	−	0.547301i	$-0.184345\pi$
$80$	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	$-0.129754\pi$
$84$	−0.312739	+	1.20375i	−0.0341226	+	0.131339i
$85$	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	$0.375252\pi$
$90$	1.21155	−	8.48142i	0.127708	−	0.894020i
$91$	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
$96$	7.97054	+	5.69829i	0.813490	+	0.581579i
$97$	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	$-0.599635\pi$
$101$	−6.18926			−0.615854			−0.307927	+	0.951410i	$0.599635\pi$
$102$	0.791586	−	1.02922i	0.0783787	−	0.101908i
$103$	−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	$-0.493290\pi$
$107$	0.436108			0.0421602			0.0210801	+	0.999778i	$0.493290\pi$
$108$	−7.25893	−	7.43693i	−0.698491	−	0.715619i
$109$			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	$-0.819047\pi$
$113$		−	11.4455i		−	1.07670i	0.842721	−	0.538351i	$-0.180953\pi$
$114$	2.94184	+	2.26262i	0.275529	+	0.211913i
$115$	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
$120$	−1.45150	−	9.78585i	−0.132503	−	0.893322i
$121$	9.42400			0.856727
$122$	−8.13001	+	3.45110i	−0.736056	+	0.312448i
$123$	−2.78678	−	4.93870i	−0.251275	−	0.445308i
$124$	−11.0172	−	1.61928i	−0.989371	−	0.145416i
$125$	11.9590			1.06964
$126$	0.215402	−	1.50792i	0.0191895	−	0.134336i
$127$		−	18.8970i		−	1.67684i	−0.545028	−	0.838418i	$-0.683481\pi$
$127$		−	18.8970i		−	1.67684i	0.545028	−	0.838418i	$-0.316519\pi$
$128$	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	$-0.576724\pi$
$131$	−5.46430			−0.477418			−0.238709	+	0.971091i	$0.576724\pi$
$132$	−4.20906	−	1.09353i	−0.366352	−	0.0951800i
$133$			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	$0.302948\pi$
$138$	0.553413	−	0.719545i	0.0471096	−	0.0612518i
$139$	0.453491			0.0384646			0.0192323	−	0.999815i	$-0.493878\pi$
$139$	0.453491			0.0384646			0.0192323	+	0.999815i	$0.493878\pi$
$140$	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
$144$	−10.4825	−	5.84105i	−0.873539	−	0.486754i
$145$			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	$-0.202692\pi$
$149$	19.6286			1.60804			0.804018	+	0.594605i	$0.202692\pi$
$150$	1.37700	−	1.79037i	0.112432	−	0.146183i
$151$		−	2.86421i		−	0.233086i	−0.993186	−	0.116543i	$-0.962819\pi$
$151$		−	2.86421i		−	0.233086i	0.993186	−	0.116543i	$-0.0371813\pi$
$152$	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
$156$	−4.27285	+	16.4464i	−0.342101	+	1.31676i
$157$			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
$162$	9.85504	+	8.05470i	0.774285	+	0.632837i
$163$			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	$0.602473\pi$
$168$	−0.258063	−	1.73983i	−0.0199100	−	0.134231i
$169$	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	$-0.302474\pi$
$173$	15.2964			1.16296			0.581480	+	0.813560i	$0.302474\pi$
$174$	7.78420	+	5.98695i	0.590119	+	0.453869i
$175$	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	$0.748026\pi$
$180$	3.10960	+	11.7105i	0.231776	+	0.872846i
$181$	4.49019			0.333753			0.166877	−	0.985978i	$-0.446632\pi$
$181$	4.49019			0.333753			0.166877	+	0.985978i	$0.446632\pi$
$182$	−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
$186$	13.6305	+	0.458641i	0.999434	+	0.0336292i
$187$			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	$0.192173\pi$
$191$			15.6920i			1.13543i	−0.823224	+	0.567716i	$0.807827\pi$
$192$	−13.5248	−	3.01347i	−0.976065	−	0.217479i
$193$	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	$-0.0993627\pi$
$198$	5.27265	+	0.753182i	0.374711	+	0.0535263i
$199$		−	12.2556i		−	0.868779i	−0.900725	−	0.434389i	$-0.856964\pi$
$199$		−	12.2556i		−	0.868779i	0.900725	−	0.434389i	$-0.143036\pi$
$200$	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
$204$	−0.461736	+	1.77724i	−0.0323280	+	0.124432i
$205$			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
$210$	−1.08269	+	1.40771i	−0.0747128	+	0.0971413i
$211$		−	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
$216$	13.5592	+	5.67004i	0.922583	+	0.385798i
$217$	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
$222$	9.20838	−	11.9727i	0.618026	−	0.803555i
$223$			13.3927i			0.896840i	0.893823	+	0.448420i	$0.148013\pi$
$223$			13.3927i			0.896840i	−0.893823	+	0.448420i	$0.851987\pi$
$224$	−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	$-0.661410\pi$
$227$	−14.6335			−0.971260			−0.485630	+	0.874164i	$0.661410\pi$
$228$	−5.07995	−	1.31980i	−0.336428	−	0.0874056i
$229$	17.1847			1.13560			0.567799	−	0.823167i	$-0.307795\pi$
$229$	17.1847			1.13560			0.567799	+	0.823167i	$0.307795\pi$
$230$	−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	$-0.955161\pi$
$233$		−	4.28624i		−	0.280801i	0.990095	−	0.140401i	$-0.0448390\pi$
$234$	2.94296	−	20.6022i	0.192387	−	1.34681i
$235$		−	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	$0.837910\pi$
$240$	7.29713	+	11.9370i	0.471028	+	0.770528i
$241$			22.0932i			1.42315i	0.702610	+	0.711575i	$0.252018\pi$
$241$			22.0932i			1.42315i	−0.702610	+	0.711575i	$0.747982\pi$
$242$	−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
$246$	6.35688	+	4.88917i	0.405300	+	0.311722i
$247$			7.43217i			0.472898i
$248$	15.2368	−	3.98005i	0.967536	−	0.252733i
$249$	−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	$-0.161558\pi$
$252$	0.552858	+	2.08201i	0.0348268	+	0.131154i
$253$			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	$-0.906102\pi$
$257$		−	9.32155i		−	0.581462i	0.956805	−	0.290731i	$-0.0938985\pi$
$258$	−6.83258	+	8.88369i	−0.425378	+	0.553075i
$259$	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	$0.231669\pi$
$264$	6.08357	−	0.902354i	0.374418	−	0.0555360i
$265$		−	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	$-0.439370\pi$
$270$	−5.39171	−	13.8252i	−0.328129	−	0.841375i
$271$			17.2940i			1.05054i	0.850936	+	0.525269i	$0.176035\pi$
$271$			17.2940i			1.05054i	−0.850936	+	0.525269i	$0.823965\pi$
$272$	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
$276$	−0.322809	+	1.24250i	−0.0194308	+	0.0747900i
$277$	20.2977			1.21957			0.609786	−	0.792566i	$-0.291255\pi$
$277$	20.2977			1.21957			0.609786	+	0.792566i	$0.291255\pi$
$278$	−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	$0.391424\pi$
$281$			31.5946i			1.88477i	−0.334526	+	0.942386i	$0.608576\pi$
$282$	−13.2231	−	10.1700i	−0.787421	−	0.605617i
$283$		−	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
$288$	16.8736	+	1.81125i	0.994288	+	0.106729i
$289$	−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	$-0.633643\pi$
$293$	−13.9548			−0.815250			−0.407625	+	0.913149i	$0.633643\pi$
$294$	10.2609	−	13.3412i	0.598427	−	0.778072i
$295$	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
$300$	−0.803211	+	3.09160i	−0.0463734	+	0.178493i
$301$	−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
$306$	0.318025	−	2.22633i	0.0181803	−	0.127271i
$307$		−	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
$310$	−13.5775	−	8.27539i	−0.771149	−	0.470011i
$311$			4.40781i			0.249944i	0.992160	+	0.124972i	$0.0398841\pi$
$311$			4.40781i			0.249944i	−0.992160	+	0.124972i	$0.960116\pi$
$312$	−3.52583	−	23.7708i	−0.199611	−	1.34575i
$313$		−	16.7888i		−	0.948959i	−0.880266	−	0.474480i	$-0.842636\pi$
$313$		−	16.7888i		−	0.948959i	0.880266	−	0.474480i	$-0.157364\pi$
$314$	−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	$-0.603092\pi$
$317$	−11.3323			−0.636484			−0.318242	+	0.948009i	$0.603092\pi$
$318$	−1.14954	−	0.884126i	−0.0644628	−	0.0495793i
$319$	−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
$324$	−17.2801	−	5.03966i	−0.960006	−	0.279981i
$325$	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
$330$	−4.92226	−	3.78578i	−0.270961	−	0.208400i
$331$	28.9555			1.59154			0.795769	−	0.605601i	$-0.207067\pi$
$331$	28.9555			1.59154			0.795769	+	0.605601i	$0.207067\pi$
$332$	−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
$336$	1.29736	+	2.12228i	0.0707769	+	0.115780i
$337$		−	31.5174i		−	1.71686i	−0.512931	−	0.858430i	$-0.671440\pi$
$337$		−	31.5174i		−	1.71686i	0.512931	−	0.858430i	$-0.328560\pi$
$338$	−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
$342$	6.36360	+	0.909021i	0.344104	+	0.0491542i
$343$	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	$0.646382\pi$
$348$	−13.4417	−	3.49222i	−0.720550	−	0.187202i
$349$		−	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	$0.488025\pi$
$354$	18.6767	−	24.2833i	0.992654	−	1.29064i
$355$			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	$-0.845779\pi$
$359$		−	17.6500i		−	0.931529i	0.884909	−	0.465765i	$-0.154221\pi$
$360$	−10.5191	−	13.5261i	−0.554408	−	0.712891i
$361$	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
$366$	−9.32632	+	12.1260i	−0.487495	+	0.633838i
$367$		−	13.3942i		−	0.699169i	−0.936905	−	0.349585i	$-0.886323\pi$
$367$		−	13.3942i		−	0.699169i	0.936905	−	0.349585i	$-0.113677\pi$
$368$	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
$372$	−17.9974	+	6.93505i	−0.933120	+	0.359566i
$373$		−	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
$378$	−0.958596	−	2.45799i	−0.0493049	−	0.126426i
$379$		−	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	$0.630312\pi$
$384$	19.2715	−	3.55080i	0.983446	−	0.181201i
$385$		−	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	$-0.00902291\pi$
$390$	−14.7925	+	19.2331i	−0.749045	+	0.973905i
$391$	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
$396$	−7.28005	+	1.93315i	−0.365836	+	0.0971443i
$397$		−	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	$0.689787\pi$
$402$	−19.1657	−	14.7406i	−0.955898	−	0.735195i
$403$	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
$408$	−0.381011	−	2.56874i	−0.0188629	−	0.127171i
$409$		−	22.8174i		−	1.12825i	−0.825690	−	0.564125i	$-0.809214\pi$
$409$		−	22.8174i		−	1.12825i	0.825690	−	0.564125i	$-0.190786\pi$
$410$	−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
$414$	0.222337	−	1.55647i	0.0109273	−	0.0764964i
$415$			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	$-0.642827\pi$
$419$	−17.7592			−0.867596			−0.433798	+	0.901010i	$0.642827\pi$
$420$	0.631539	−	2.43082i	0.0308159	−	0.118612i
$421$			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
$426$	4.61080	+	3.54624i	0.223394	+	0.171816i
$427$	−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	$-0.885741\pi$
$431$		−	14.5862i		−	0.702595i	0.936264	−	0.351297i	$-0.114259\pi$
$432$	−20.7843	+	0.111519i	−0.999986	+	0.00536545i
$433$			40.3152i			1.93743i	0.248182	+	0.968713i	$0.420167\pi$
$433$			40.3152i			1.93743i	−0.248182	+	0.968713i	$0.579833\pi$
$434$	−2.41395	−	1.47129i	−0.115873	−	0.0706241i
$435$	6.89115	+	12.2124i	0.330405	+	0.585541i
$436$	4.87414	+	4.70668i	0.233429	+	0.225409i
$437$			0.561492i			0.0268598i
$438$	13.0073	+	10.0041i	0.621515	+	0.478016i
$439$	−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	$-0.301732\pi$
$443$	24.5573			1.16675			0.583375	+	0.812203i	$0.301732\pi$
$444$	−5.37130	+	20.6744i	−0.254910	+	0.981162i
$445$	−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	$0.622004\pi$
$450$	0.553219	−	3.87281i	0.0260790	−	0.182566i
$451$	−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
$456$	7.34231	−	1.08906i	0.343835	−	0.0509998i
$457$		−	20.3442i		−	0.951661i	−0.879537	−	0.475830i	$-0.842148\pi$
$457$		−	20.3442i		−	0.951661i	0.879537	−	0.475830i	$-0.157852\pi$
$458$	−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	$-0.192113\pi$
$462$	−0.875132	−	0.673077i	−0.0407148	−	0.0313144i
$463$			23.7526i			1.10388i	0.833885	+	0.551939i	$0.186112\pi$
$463$			23.7526i			1.10388i	−0.833885	+	0.551939i	$0.813888\pi$
$464$	−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	$-0.741999\pi$
$467$	−29.7836			−1.37822			−0.689110	+	0.724656i	$0.741999\pi$
$468$	7.55352	+	28.4458i	0.349162	+	1.31491i
$469$		−	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
$474$	18.8902	+	14.5287i	0.867656	+	0.667327i
$475$			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	$-0.869970\pi$
$479$		−	17.3877i		−	0.794466i	0.917718	−	0.397233i	$-0.130030\pi$
$480$	−16.0956	−	11.5070i	−0.734659	−	0.525221i
$481$	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
$486$	21.7221	+	3.76177i	0.985334	+	0.170637i
$487$		−	14.3592i		−	0.650679i	−0.945597	−	0.325339i	$-0.894521\pi$
$487$		−	14.3592i		−	0.650679i	0.945597	−	0.325339i	$-0.105479\pi$
$488$	−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	$0.917592\pi$
$492$	−10.9770	−	2.85188i	−0.494881	−	0.128573i
$493$			2.12514i			0.0957113i
$494$	−4.10697	−	9.67508i	−0.184781	−	0.435303i
$495$	6.51013	+	3.93184i	0.292608	+	0.176723i
$496$	−17.6356	+	13.6009i	−0.791863	+	0.610698i
$497$			0.852584i			0.0382436i
$498$	14.0253	+	10.7870i	0.628488	+	0.483379i
$499$	−34.9340			−1.56386			−0.781931	−	0.623365i	$-0.785765\pi$
$499$	−34.9340			−1.56386			−0.781931	+	0.623365i	$0.785765\pi$
$500$	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	$-0.968515\pi$
$503$		−	4.42949i		−	0.197501i	0.995112	−	0.0987506i	$-0.0314846\pi$
$504$	−1.87021	−	2.40482i	−0.0833056	−	0.107119i
$505$	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	$-0.165084\pi$
$510$	−1.59851	+	2.07838i	−0.0707834	+	0.0920323i
$511$			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
$516$	3.98548	−	15.3403i	0.175451	−	0.675318i
$517$	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	$-0.997836\pi$
$521$		−	0.310368i		−	0.0135975i	0.999977	−	0.00679874i	$-0.00216412\pi$
$522$	16.8382	+	2.40529i	0.736990	+	0.105277i
$523$	3.12326			0.136570			0.0682852	−	0.997666i	$-0.478247\pi$
$523$	3.12326			0.136570			0.0682852	+	0.997666i	$0.478247\pi$
$524$	−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
$528$	−7.42086	+	4.53641i	−0.322952	+	0.197422i
$529$	−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
$534$	−10.7620	+	13.9927i	−0.465716	+	0.605523i
$535$	−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
$540$	14.6586	+	15.0180i	0.630804	+	0.646272i
$541$		−	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
$546$	−2.62996	+	3.41946i	−0.112552	+	0.146340i
$547$			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
$552$	−0.266372	−	1.79585i	−0.0113376	−	0.0764366i
$553$			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	$0.821703\pi$
$558$	20.9515	−	10.9103i	0.886949	−	0.461868i
$559$	−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	$-0.654943\pi$
$563$	−22.1982			−0.935541			−0.467770	+	0.883850i	$0.654943\pi$
$564$	22.8335	+	5.93224i	0.961462	+	0.249792i
$565$			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	$0.524460\pi$
$570$	−5.94071	−	4.56909i	−0.248829	−	0.191378i
$571$	29.0424			1.21539			0.607693	−	0.794172i	$-0.292095\pi$
$571$	29.0424			1.21539			0.607693	+	0.794172i	$0.292095\pi$
$572$	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
$576$	−22.9667	+	6.96640i	−0.956946	+	0.290266i
$577$	−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
$582$	−6.30709	+	8.20045i	−0.261437	+	0.339919i
$583$	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	$-0.102291\pi$
$588$	−5.98522	+	23.0374i	−0.246826	+	0.950046i
$589$	−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	$0.249686\pi$
$593$			34.4043i			1.41282i	−0.707804	+	0.706409i	$0.750314\pi$
$594$	8.59472	−	3.35187i	0.352646	−	0.137529i
$595$	−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	$-0.744774\pi$
$599$		−	35.1757i		−	1.43724i	0.695402	−	0.718621i	$-0.255226\pi$
$600$	−0.662787	−	4.46844i	−0.0270582	−	0.182423i
$601$		−	12.1715i		−	0.496487i	−0.968698	−	0.248244i	$-0.920147\pi$
$601$		−	12.1715i		−	0.496487i	0.968698	−	0.248244i	$-0.0798533\pi$
$602$	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
$606$	9.24266	−	12.0173i	0.375457	−	0.488168i
$607$	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
$612$	0.816255	+	3.07394i	0.0329952	+	0.124257i
$613$	−47.1446			−1.90415			−0.952076	−	0.305860i	$-0.901056\pi$
$613$	−47.1446			−1.90415			−0.952076	+	0.305860i	$0.901056\pi$
$614$	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	$-0.995431\pi$
$617$		−	0.713094i		−	0.0287081i	0.999897	−	0.0143540i	$-0.00456919\pi$
$618$	3.29685	−	4.28655i	0.132619	−	0.172430i
$619$	−21.4057			−0.860367			−0.430184	−	0.902741i	$-0.641551\pi$
$619$	−21.4057			−0.860367			−0.430184	+	0.902741i	$0.641551\pi$
$620$	22.2479	+	3.26995i	0.893496	+	0.131325i
$621$	−0.0569696	+	1.92479i	−0.00228611	+	0.0772391i
$622$	−2.43573	−	5.73802i	−0.0976637	−	0.230074i
$623$	−2.58739			−0.103661
$624$	17.7254	+	28.9961i	0.709585	+	1.16077i
$625$	−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
$630$	−0.434978	+	3.04506i	−0.0173299	+	0.121318i
$631$			24.5796i			0.978497i	0.872144	+	0.489248i	$0.162729\pi$
$631$			24.5796i			0.978497i	−0.872144	+	0.489248i	$0.837271\pi$
$632$	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
$636$	1.98501	+	0.515715i	0.0787108	+	0.0204494i
$637$	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	$0.692757\pi$
$642$	−0.651257	+	0.846762i	−0.0257031	+	0.0334190i
$643$	−45.5128			−1.79485			−0.897424	−	0.441169i	$-0.854564\pi$
$643$	−45.5128			−1.79485			−0.897424	+	0.441169i	$0.854564\pi$
$644$	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	$0.376171\pi$
$648$	25.2798	−	2.98832i	0.993086	−	0.117392i
$649$			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	$-0.367599\pi$
$653$	20.6505			0.808116			0.404058	+	0.914733i	$0.367599\pi$
$654$	−6.57796	−	5.05921i	−0.257219	−	0.197831i
$655$	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	$-0.392029\pi$
$659$	17.0833			0.665470			0.332735	+	0.943020i	$0.392029\pi$
$660$	8.49971	+	2.20826i	0.330851	+	0.0859566i
$661$		−	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
$666$	3.69953	−	25.8985i	0.143354	−	1.00355i
$667$			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
$672$	−2.86164	−	2.04584i	−0.110390	−	0.0789200i
$673$		−	9.63430i		−	0.371375i	−0.982609	−	0.185687i	$-0.940549\pi$
$673$		−	9.63430i		−	0.371375i	0.982609	−	0.185687i	$-0.0594512\pi$
$674$	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	$-0.0517634\pi$
$678$	22.2230	+	17.0920i	0.853468	+	0.656415i
$679$	−1.51635			−0.0581920
$680$	−1.08490	+	2.82658i	−0.0416042	+	0.108394i
$681$	−22.0742	+	12.4559i	−0.845885	+	0.477310i
$682$	5.14457	−	8.44072i	0.196996	−	0.323212i
$683$	35.2639			1.34934			0.674669	−	0.738121i	$-0.264287\pi$
$683$	35.2639			1.34934			0.674669	+	0.738121i	$0.264287\pi$
$684$	−8.78634	+	2.33313i	−0.335954	+	0.0892094i
$685$	−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
$690$	−1.11755	+	1.45304i	−0.0425445	+	0.0553162i
$691$			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
$696$	19.4280	−	2.88168i	0.736415	−	0.109230i
$697$			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	$-0.304501\pi$
$701$	30.5160			1.15257			0.576287	+	0.817248i	$0.304501\pi$
$702$	−13.0970	−	33.5828i	−0.494314	−	1.26750i
$703$			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
$708$	−10.8942	+	41.9322i	−0.409429	+	1.57591i
$709$	−12.8448			−0.482396			−0.241198	−	0.970476i	$-0.577540\pi$
$709$	−12.8448			−0.482396			−0.241198	+	0.970476i	$0.577540\pi$
$710$	−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
$714$	−0.284201	+	0.369517i	−0.0106360	+	0.0138288i
$715$		−	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	$0.495671\pi$
$720$	21.1681	+	11.7953i	0.788889	+	0.439585i
$721$	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
$726$	−14.0732	+	18.2979i	−0.522306	+	0.679100i
$727$	−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
$732$	5.44009	−	20.9391i	0.201071	−	0.773933i
$733$			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
$738$	13.7508	+	1.96426i	0.506172	+	0.0723052i
$739$	−45.0935			−1.65879			−0.829396	−	0.558661i	$-0.811315\pi$
$739$	−45.0935			−1.65879			−0.829396	+	0.558661i	$0.811315\pi$
$740$	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	$0.766302\pi$
$744$	19.5964	−	18.9732i	0.718440	−	0.695589i
$745$	−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
$750$	−17.8588	+	23.2199i	−0.652111	+	0.847872i
$751$	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
$756$	2.60615	+	2.67006i	0.0947849	+	0.0971092i
$757$	−24.0859			−0.875417			−0.437708	−	0.899117i	$-0.644210\pi$
$757$	−24.0859			−0.875417			−0.437708	+	0.899117i	$0.644210\pi$
$758$	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	$0.593665\pi$
$762$	36.6910	+	28.2196i	1.32917	+	1.02229i
$763$		−	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
$768$	−23.1252	+	15.2717i	−0.834459	+	0.551069i
$769$	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	$-0.150805\pi$
$774$	−2.74503	+	19.2166i	−0.0986682	+	0.690726i
$775$	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
$780$	8.62851	−	33.2115i	0.308950	−	1.18916i
$781$	−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
$786$	8.16005	−	10.6097i	0.291059	−	0.378434i
$787$	16.6822			0.594656			0.297328	−	0.954775i	$-0.403904\pi$
$787$	16.6822			0.594656			0.297328	+	0.954775i	$0.403904\pi$
$788$	−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
$792$	8.40880	−	6.53944i	0.298794	−	0.232369i
$793$	−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	$-0.324303\pi$
$798$	−1.05620	−	0.812342i	−0.0373892	−	0.0287566i
$799$		−	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
$804$	33.0951	+	8.59827i	1.16718	+	0.303238i
$805$	−0.268681			−0.00946977
$806$	−32.9810	−	20.1017i	−1.16171	−	0.708053i
$807$	−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	$0.274043\pi$
$810$	−19.9011	−	16.2655i	−0.699253	−	0.571512i
$811$		−	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
$816$	1.91546	+	3.13340i	0.0670545	+	0.109691i
$817$		−	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	$-0.0166843\pi$
$822$	−20.2851	+	26.3746i	−0.707525	+	0.919920i
$823$			5.26380i			0.183485i	0.995783	+	0.0917423i	$0.0292436\pi$
$823$			5.26380i			0.183485i	−0.995783	+	0.0917423i	$0.970756\pi$
$824$	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	$0.823731\pi$
$828$	0.570660	+	2.14905i	0.0198318	+	0.0746847i
$829$	−1.09771			−0.0381251			−0.0190625	−	0.999818i	$-0.506068\pi$
$829$	−1.09771			−0.0381251			−0.0190625	+	0.999818i	$0.506068\pi$
$830$	−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
$834$	−0.677215	+	0.880512i	−0.0234500	+	0.0304896i
$835$	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	$0.0443356\pi$
$839$			8.04282i			0.277669i	−0.990316	+	0.138834i	$0.955664\pi$
$840$	0.521128	+	3.51339i	0.0179806	+	0.121223i
$841$	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
$846$	−28.6032	−	4.08588i	−0.983398	−	0.140475i
$847$	−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
$852$	−7.96190	−	2.06854i	−0.272770	−	0.0708670i
$853$			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	$0.180358\pi$
$857$			31.4277i			1.07355i	−0.843725	+	0.536775i	$0.819642\pi$
$858$	−11.9566	−	9.19603i	−0.408193	−	0.313947i
$859$	−0.472050			−0.0161061			−0.00805306	−	0.999968i	$-0.502563\pi$
$859$	−0.472050			−0.0161061			−0.00805306	+	0.999968i	$0.502563\pi$
$860$	−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	$0.0546897\pi$
$864$	26.9951	−	11.6304i	0.918390	−	0.395675i
$865$	−30.8892			−1.05026
$866$	−22.2779	−	52.4817i	−0.757034	−	1.78340i
$867$	−25.2201	+	14.2310i	−0.856520	+	0.483312i
$868$	3.95546	+	0.581368i	0.134257	+	0.0197329i
$869$	−12.2137			−0.414322
$870$	−15.7193	−	12.0899i	−0.532934	−	0.409887i
$871$		−	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
$876$	−22.4610	−	5.83546i	−0.758886	−	0.197162i
$877$			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	$0.401238\pi$
$882$	4.12237	−	28.8587i	0.138808	−	0.971722i
$883$	−26.1465			−0.879900			−0.439950	−	0.898022i	$-0.645004\pi$
$883$	−26.1465			−0.879900			−0.439950	+	0.898022i	$0.645004\pi$
$884$	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	$-0.867421\pi$
$887$		−	24.0982i		−	0.809140i	0.914507	−	0.404570i	$-0.132579\pi$
$888$	−4.43224	−	29.8817i	−0.148736	−	1.00276i
$889$			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
$894$	−29.3121	+	38.1115i	−0.980344	+	1.27464i
$895$		−	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
$900$	1.41991	+	5.34726i	0.0473305	+	0.178242i
$901$		−	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
$906$	5.56124	+	4.27723i	0.184760	+	0.142102i
$907$			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	$0.640593\pi$
$912$	−8.95629	+	5.47503i	−0.296573	+	0.181296i
$913$	−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
$918$	−1.41530	−	3.62905i	−0.0467118	−	0.119776i
$919$	−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
$924$	1.51117	+	0.392609i	0.0497138	+	0.0129159i
$925$	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	$0.334717\pi$
$930$	−27.5251	−	0.926171i	−0.902584	−	0.0303703i
$931$			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
$936$	−25.5520	−	32.8563i	−0.835194	−	1.07394i
$937$	−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	$-0.246489\pi$
$942$	−34.0599	−	26.1960i	−1.10973	−	0.853511i
$943$			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	$-0.213076\pi$
$948$	−32.6195	−	8.47469i	−1.05943	−	0.275245i
$949$			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	$0.401977\pi$
$954$	−2.48660	−	0.355203i	−0.0805066	−	0.0115001i
$955$		−	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
$960$	27.3116	+	6.08535i	0.881480	+	0.196404i
$961$	−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
$966$	−0.198690	+	0.258337i	−0.00639276	+	0.00831184i
$967$			41.4972i			1.33446i	0.744852	+	0.667229i	$0.232520\pi$
$967$			41.4972i			1.33446i	−0.744852	+	0.667229i	$0.767480\pi$
$968$	−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	$-0.401262\pi$
$971$	19.0234			0.610490			0.305245	+	0.952274i	$0.401262\pi$
$972$	−30.3562	+	7.10646i	−0.973675	+	0.227940i
$973$	−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	$0.272626\pi$
$977$			47.2319i			1.51108i	−0.655100	+	0.755542i	$0.727374\pi$
$978$	−39.9028	−	30.6898i	−1.27595	−	0.981352i
$979$		−	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	$0.410488\pi$
$984$	15.8656	−	2.35329i	0.505777	−	0.0750200i
$985$			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
$990$	−10.6475	−	1.52096i	−0.338399	−	0.0483393i
$991$			8.19232i			0.260238i	0.991498	+	0.130119i	$0.0415359\pi$
$991$			8.19232i			0.260238i	−0.991498	+	0.130119i	$0.958464\pi$
$992$	15.4420	−	27.4508i	0.490285	−	0.871562i
$993$	43.6784	−	24.6466i	1.38609	−	0.782136i
$994$	−0.471132	−	1.10988i	−0.0149434	−	0.0352033i
$995$			24.7488i			0.784590i
$996$	−24.2187	−	6.29214i	−0.767400	−	0.199374i
$997$			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.557.16	yes	96
3.2	odd	2	inner	744.2.o.e.557.82	yes	96
8.5	even	2	inner	744.2.o.e.557.83	yes	96
24.5	odd	2	inner	744.2.o.e.557.13	✓	96
31.30	odd	2	inner	744.2.o.e.557.15	yes	96
93.92	even	2	inner	744.2.o.e.557.81	yes	96
248.61	odd	2	inner	744.2.o.e.557.84	yes	96
744.557	even	2	inner	744.2.o.e.557.14	yes	96

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

\(f(q)\)	\(=\)	\(q+(-1.30178 + 0.552593i) q^{2} +(1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} -2.01938 q^{5} +(-1.49334 + 1.94163i) q^{6} -0.359027 q^{7} +(-1.01352 + 2.64060i) q^{8} +(1.55095 - 2.56798i) q^{9} +O(q^{10})\)	\(q+(-1.30178 + 0.552593i) q^{2} +(1.50847 - 0.851189i) q^{3} +(1.38928 - 1.43871i) q^{4} -2.01938 q^{5} +(-1.49334 + 1.94163i) 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} +(0.871072 - 3.35279i) 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} +(-0.599958 + 4.20001i) 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} +(0.718783 + 4.84596i) 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} +(3.01562 - 3.92090i) 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} +(-1.53988 - 5.79903i) 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} +(0.536150 - 0.697100i) 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} +(-3.61355 - 5.91120i) 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} +(2.66998 + 6.84625i) 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} +(-1.75903 + 6.77057i) q^{60} +6.24528 q^{61} +(6.72358 + 4.09798i) q^{62} +(-0.556835 + 0.921977i) q^{63} +(-5.94554 - 5.35262i) q^{64} +9.90562 q^{65} +(2.43751 + 1.87472i) 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} +(5.20909 + 6.69816i) 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} +(7.32524 - 9.52424i) 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} +(-0.312739 + 1.20375i) 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} +(1.21155 - 8.48142i) 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} +(7.97054 + 5.69829i) 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

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