LMFDB - Embedded newform 349.2.b.b.348.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(348,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("349.348");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.b (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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			348.12
Character	$\chi$	$=$	349.348
Dual form			349.2.b.b.348.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.788732i q^{2} -0.670838 q^{3} +1.37790 q^{4} -1.84585 q^{5} +0.529112i q^{6} -0.0300147i q^{7} -2.66426i q^{8} -2.54998 q^{9} +O(q^{10})$	\(q-0.788732i q^{2} -0.670838 q^{3} +1.37790 q^{4} -1.84585 q^{5} +0.529112i q^{6} -0.0300147i q^{7} -2.66426i q^{8} -2.54998 q^{9} +1.45588i q^{10} -3.59289i q^{11} -0.924348 q^{12} -6.25431i q^{13} -0.0236736 q^{14} +1.23826 q^{15} +0.654414 q^{16} +3.51955 q^{17} +2.01125i q^{18} +3.38809 q^{19} -2.54339 q^{20} +0.0201350i q^{21} -2.83383 q^{22} -1.78386 q^{23} +1.78729i q^{24} -1.59285 q^{25} -4.93297 q^{26} +3.72313 q^{27} -0.0413573i q^{28} -4.91079 q^{29} -0.976658i q^{30} -3.21062 q^{31} -5.84468i q^{32} +2.41025i q^{33} -2.77599i q^{34} +0.0554026i q^{35} -3.51362 q^{36} +11.3291 q^{37} -2.67230i q^{38} +4.19563i q^{39} +4.91781i q^{40} -8.41782 q^{41} +0.0158811 q^{42} +10.1802i q^{43} -4.95065i q^{44} +4.70686 q^{45} +1.40699i q^{46} -2.19423i q^{47} -0.439006 q^{48} +6.99910 q^{49} +1.25634i q^{50} -2.36105 q^{51} -8.61782i q^{52} +12.0535i q^{53} -2.93656i q^{54} +6.63193i q^{55} -0.0799671 q^{56} -2.27286 q^{57} +3.87330i q^{58} -9.14785i q^{59} +1.70620 q^{60} +0.831451i q^{61} +2.53232i q^{62} +0.0765369i q^{63} -3.30106 q^{64} +11.5445i q^{65} +1.90104 q^{66} -3.48029 q^{67} +4.84960 q^{68} +1.19668 q^{69} +0.0436978 q^{70} -7.63048i q^{71} +6.79380i q^{72} +8.96223 q^{73} -8.93563i q^{74} +1.06855 q^{75} +4.66846 q^{76} -0.107840 q^{77} +3.30923 q^{78} +9.94862i q^{79} -1.20795 q^{80} +5.15231 q^{81} +6.63941i q^{82} +16.1328 q^{83} +0.0277441i q^{84} -6.49655 q^{85} +8.02949 q^{86} +3.29435 q^{87} -9.57240 q^{88} +8.20545i q^{89} -3.71246i q^{90} -0.187721 q^{91} -2.45798 q^{92} +2.15381 q^{93} -1.73066 q^{94} -6.25390 q^{95} +3.92083i q^{96} +6.03521i q^{97} -5.52042i q^{98} +9.16179i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	0.788732i		−	0.557718i	−0.960332	−	0.278859i	$-0.910044\pi$
$2$		−	0.788732i		−	0.557718i	0.960332	−	0.278859i	$-0.0899562\pi$
$3$	−0.670838			−0.387308			−0.193654	−	0.981070i	$-0.562034\pi$
$3$	−0.670838			−0.387308			−0.193654	+	0.981070i	$0.562034\pi$
$4$	1.37790			0.688951
$5$	−1.84585			−0.825487			−0.412744	−	0.910847i	$-0.635429\pi$
$5$	−1.84585			−0.825487			−0.412744	+	0.910847i	$0.635429\pi$
$6$			0.529112i			0.216009i
$7$		−	0.0300147i		−	0.0113445i	−0.999984	−	0.00567225i	$-0.998194\pi$
$7$		−	0.0300147i		−	0.0113445i	0.999984	−	0.00567225i	$-0.00180554\pi$
$8$		−	2.66426i		−	0.941958i
$9$	−2.54998			−0.849992
$10$			1.45588i			0.460389i
$11$		−	3.59289i		−	1.08330i	−0.840605	−	0.541649i	$-0.817800\pi$
$11$		−	3.59289i		−	1.08330i	0.840605	−	0.541649i	$-0.182200\pi$
$12$	−0.924348			−0.266836
$13$		−	6.25431i		−	1.73463i	−0.497757	−	0.867316i	$-0.665843\pi$
$13$		−	6.25431i		−	1.73463i	0.497757	−	0.867316i	$-0.334157\pi$
$14$	−0.0236736			−0.00632703
$15$	1.23826			0.319718
$16$	0.654414			0.163604
$17$	3.51955			0.853617			0.426808	−	0.904342i	$-0.359638\pi$
$17$	3.51955			0.853617			0.426808	+	0.904342i	$0.359638\pi$
$18$			2.01125i			0.474056i
$19$	3.38809			0.777282			0.388641	−	0.921389i	$-0.372945\pi$
$19$	3.38809			0.777282			0.388641	+	0.921389i	$0.372945\pi$
$20$	−2.54339			−0.568720
$21$			0.0201350i			0.00439382i
$22$	−2.83383			−0.604175
$23$	−1.78386			−0.371960			−0.185980	−	0.982553i	$-0.559546\pi$
$23$	−1.78386			−0.371960			−0.185980	+	0.982553i	$0.559546\pi$
$24$			1.78729i			0.364828i
$25$	−1.59285			−0.318571
$26$	−4.93297			−0.967436
$27$	3.72313			0.716518
$28$		−	0.0413573i		−	0.00781580i
$29$	−4.91079			−0.911911			−0.455956	−	0.890002i	$-0.650702\pi$
$29$	−4.91079			−0.911911			−0.455956	+	0.890002i	$0.650702\pi$
$30$		−	0.976658i		−	0.178313i
$31$	−3.21062			−0.576645			−0.288322	−	0.957533i	$-0.593097\pi$
$31$	−3.21062			−0.576645			−0.288322	+	0.957533i	$0.593097\pi$
$32$		−	5.84468i		−	1.03320i
$33$			2.41025i			0.419570i
$34$		−	2.77599i		−	0.476078i
$35$			0.0554026i			0.00936474i
$36$	−3.51362			−0.585603
$37$	11.3291			1.86249			0.931246	−	0.364390i	$-0.118723\pi$
$37$	11.3291			1.86249			0.931246	+	0.364390i	$0.118723\pi$
$38$		−	2.67230i		−	0.433504i
$39$			4.19563i			0.671838i
$40$			4.91781i			0.777574i
$41$	−8.41782			−1.31464			−0.657321	−	0.753610i	$-0.728311\pi$
$41$	−8.41782			−1.31464			−0.657321	+	0.753610i	$0.728311\pi$
$42$	0.0158811			0.00245051
$43$			10.1802i			1.55247i	0.630442	+	0.776237i	$0.282874\pi$
$43$			10.1802i			1.55247i	−0.630442	+	0.776237i	$0.717126\pi$
$44$		−	4.95065i		−	0.746339i
$45$	4.70686			0.701658
$46$			1.40699i			0.207449i
$47$		−	2.19423i		−	0.320062i	−0.987112	−	0.160031i	$-0.948841\pi$
$47$		−	2.19423i		−	0.320062i	0.987112	−	0.160031i	$-0.0511594\pi$
$48$	−0.439006			−0.0633651
$49$	6.99910			0.999871
$50$			1.25634i			0.177673i
$51$	−2.36105			−0.330613
$52$		−	8.61782i		−	1.19508i
$53$			12.0535i			1.65567i	0.560971	+	0.827835i	$0.310428\pi$
$53$			12.0535i			1.65567i	−0.560971	+	0.827835i	$0.689572\pi$
$54$		−	2.93656i		−	0.399615i
$55$			6.63193i			0.894249i
$56$	−0.0799671			−0.0106860
$57$	−2.27286			−0.301048
$58$			3.87330i			0.508589i
$59$		−	9.14785i		−	1.19095i	−0.803374	−	0.595474i	$-0.796964\pi$
$59$		−	9.14785i		−	1.19095i	0.803374	−	0.595474i	$-0.203036\pi$
$60$	1.70620			0.220270
$61$			0.831451i			0.106456i	0.998582	+	0.0532282i	$0.0169511\pi$
$61$			0.831451i			0.106456i	−0.998582	+	0.0532282i	$0.983049\pi$
$62$			2.53232i			0.321605i
$63$			0.0765369i			0.00964274i
$64$	−3.30106			−0.412632
$65$			11.5445i			1.43192i
$66$	1.90104			0.234002
$67$	−3.48029			−0.425186			−0.212593	−	0.977141i	$-0.568191\pi$
$67$	−3.48029			−0.425186			−0.212593	+	0.977141i	$0.568191\pi$
$68$	4.84960			0.588100
$69$	1.19668			0.144063
$70$	0.0436978			0.00522289
$71$		−	7.63048i		−	0.905571i	−0.891619	−	0.452786i	$-0.850430\pi$
$71$		−	7.63048i		−	0.905571i	0.891619	−	0.452786i	$-0.149570\pi$
$72$			6.79380i			0.800657i
$73$	8.96223			1.04895			0.524475	−	0.851426i	$-0.324262\pi$
$73$	8.96223			1.04895			0.524475	+	0.851426i	$0.324262\pi$
$74$		−	8.93563i		−	1.03875i
$75$	1.06855			0.123385
$76$	4.66846			0.535509
$77$	−0.107840			−0.0122895
$78$	3.30923			0.374696
$79$			9.94862i			1.11931i	0.828727	+	0.559654i	$0.189066\pi$
$79$			9.94862i			1.11931i	−0.828727	+	0.559654i	$0.810934\pi$
$80$	−1.20795			−0.135053
$81$	5.15231			0.572479
$82$			6.63941i			0.733200i
$83$	16.1328			1.77081			0.885404	−	0.464822i	$-0.153882\pi$
$83$	16.1328			1.77081			0.885404	+	0.464822i	$0.153882\pi$
$84$			0.0277441i			0.00302713i
$85$	−6.49655			−0.704650
$86$	8.02949			0.865842
$87$	3.29435			0.353191
$88$	−9.57240			−1.02042
$89$			8.20545i			0.869776i	0.900485	+	0.434888i	$0.143212\pi$
$89$			8.20545i			0.869776i	−0.900485	+	0.434888i	$0.856788\pi$
$90$		−	3.71246i		−	0.391327i
$91$	−0.187721			−0.0196785
$92$	−2.45798			−0.256262
$93$	2.15381			0.223339
$94$	−1.73066			−0.178504
$95$	−6.25390			−0.641637
$96$			3.92083i			0.400168i
$97$			6.03521i			0.612783i	0.951906	+	0.306391i	$0.0991217\pi$
$97$			6.03521i			0.612783i	−0.951906	+	0.306391i	$0.900878\pi$
$98$		−	5.52042i		−	0.557646i
$99$			9.16179i			0.920795i
$100$	−2.19480			−0.219480
$101$		−	11.2989i		−	1.12428i	−0.827041	−	0.562142i	$-0.809977\pi$
$101$		−	11.2989i		−	1.12428i	0.827041	−	0.562142i	$-0.190023\pi$
$102$			1.86224i			0.184389i
$103$		−	12.5359i		−	1.23519i	−0.786495	−	0.617597i	$-0.788106\pi$
$103$		−	12.5359i		−	1.23519i	0.786495	−	0.617597i	$-0.211894\pi$
$104$	−16.6631			−1.63395
$105$		−	0.0371661i		−	0.00362704i
$106$	9.50696			0.923397
$107$			8.28857i			0.801286i	0.916234	+	0.400643i	$0.131213\pi$
$107$			8.28857i			0.801286i	−0.916234	+	0.400643i	$0.868787\pi$
$108$	5.13011			0.493645
$109$	8.95010			0.857264			0.428632	−	0.903479i	$-0.358996\pi$
$109$	8.95010			0.857264			0.428632	+	0.903479i	$0.358996\pi$
$110$	5.23081			0.498739
$111$	−7.59999			−0.721359
$112$		−	0.0196421i		−	0.00185600i
$113$			4.88103i			0.459168i	0.973289	+	0.229584i	$0.0737366\pi$
$113$			4.88103i			0.459168i	−0.973289	+	0.229584i	$0.926263\pi$
$114$			1.79268i			0.167900i
$115$	3.29273			0.307049
$116$	−6.76659			−0.628262
$117$			15.9483i			1.47442i
$118$	−7.21521			−0.664213
$119$		−	0.105638i		−	0.00968386i
$120$		−	3.29906i		−	0.301161i
$121$	−1.90888			−0.173534
$122$	0.655792			0.0593726
$123$	5.64699			0.509172
$124$	−4.42392			−0.397280
$125$	12.1694			1.08846
$126$	0.0603671			0.00537793
$127$		−	17.7772i		−	1.57747i	−0.614731	−	0.788737i	$-0.710736\pi$
$127$		−	17.7772i		−	1.57747i	0.614731	−	0.788737i	$-0.289264\pi$
$128$		−	9.08570i		−	0.803070i
$129$		−	6.82930i		−	0.601286i
$130$	9.10551			0.798606
$131$		−	6.23886i		−	0.545092i	−0.962143	−	0.272546i	$-0.912134\pi$
$131$		−	6.23886i		−	0.545092i	0.962143	−	0.272546i	$-0.0878656\pi$
$132$			3.32108i			0.289063i
$133$		−	0.101693i		−	0.00881788i
$134$			2.74502i			0.237134i
$135$	−6.87233			−0.591476
$136$		−	9.37700i		−	0.804071i
$137$		−	16.5477i		−	1.41377i	−0.707329	−	0.706885i	$-0.750100\pi$
$137$		−	16.5477i		−	1.41377i	0.707329	−	0.706885i	$-0.249900\pi$
$138$		−	0.943860i		−	0.0803467i
$139$	−0.969588			−0.0822393			−0.0411197	−	0.999154i	$-0.513092\pi$
$139$	−0.969588			−0.0822393			−0.0411197	+	0.999154i	$0.513092\pi$
$140$			0.0763393i			0.00645185i
$141$			1.47198i			0.123963i
$142$	−6.01841			−0.505053
$143$	−22.4711			−1.87912
$144$	−1.66874			−0.139062
$145$	9.06457			0.752771
$146$		−	7.06880i		−	0.585018i
$147$	−4.69526			−0.387259
$148$	15.6104			1.28317
$149$			12.3434i			1.01121i	0.862765	+	0.505604i	$0.168730\pi$
$149$			12.3434i			1.01121i	−0.862765	+	0.505604i	$0.831270\pi$
$150$		−	0.842797i		−	0.0688141i
$151$	−17.0086			−1.38414			−0.692069	−	0.721831i	$-0.743301\pi$
$151$	−17.0086			−1.38414			−0.692069	+	0.721831i	$0.743301\pi$
$152$		−	9.02677i		−	0.732167i
$153$	−8.97478			−0.725568
$154$			0.0850567i			0.00685406i
$155$	5.92631			0.476013
$156$			5.78116i			0.462863i
$157$	−9.12133			−0.727962			−0.363981	−	0.931406i	$-0.618583\pi$
$157$	−9.12133			−0.727962			−0.363981	+	0.931406i	$0.618583\pi$
$158$	7.84680			0.624258
$159$		−	8.08592i		−	0.641255i
$160$			10.7884i			0.852896i
$161$			0.0535421i			0.00421970i
$162$		−	4.06379i		−	0.319282i
$163$		−	10.5597i		−	0.827100i	−0.910481	−	0.413550i	$-0.864289\pi$
$163$		−	10.5597i		−	0.827100i	0.910481	−	0.413550i	$-0.135711\pi$
$164$	−11.5989			−0.905724
$165$		−	4.44895i		−	0.346350i
$166$		−	12.7245i		−	0.987612i
$167$		−	3.12053i		−	0.241474i	−0.992685	−	0.120737i	$-0.961474\pi$
$167$		−	3.12053i		−	0.241474i	0.992685	−	0.120737i	$-0.0385257\pi$
$168$	0.0536449			0.00413880
$169$	−26.1164			−2.00895
$170$			5.12404i			0.392996i
$171$	−8.63956			−0.660684
$172$			14.0274i			1.06958i
$173$			15.7397i			1.19666i	0.801248	+	0.598332i	$0.204170\pi$
$173$			15.7397i			1.19666i	−0.801248	+	0.598332i	$0.795830\pi$
$174$		−	2.59836i		−	0.196981i
$175$			0.0478091i			0.00361403i
$176$		−	2.35124i		−	0.177231i
$177$			6.13672i			0.461264i
$178$	6.47190			0.485090
$179$			5.46170i			0.408227i	0.978947	+	0.204113i	$0.0654311\pi$
$179$			5.46170i			0.408227i	−0.978947	+	0.204113i	$0.934569\pi$
$180$	6.48559			0.483408
$181$	8.46090			0.628894			0.314447	−	0.949275i	$-0.398181\pi$
$181$	8.46090			0.628894			0.314447	+	0.949275i	$0.398181\pi$
$182$			0.148062i			0.0109751i
$183$		−	0.557769i		−	0.0412314i
$184$			4.75266i			0.350371i
$185$	−20.9118			−1.53746
$186$		−	1.69878i		−	0.124560i
$187$		−	12.6454i		−	0.924721i
$188$		−	3.02344i		−	0.220507i
$189$		−	0.111749i		−	0.00812854i
$190$			4.93265i			0.357852i
$191$	6.62820			0.479599			0.239800	−	0.970822i	$-0.422918\pi$
$191$	6.62820			0.479599			0.239800	+	0.970822i	$0.422918\pi$
$192$	2.21447			0.159816
$193$			20.5955i			1.48250i	0.671229	+	0.741250i	$0.265767\pi$
$193$			20.5955i			1.48250i	−0.671229	+	0.741250i	$0.734233\pi$
$194$	4.76017			0.341760
$195$		−	7.74448i		−	0.554594i
$196$	9.64407			0.688862
$197$			16.9134i			1.20503i	0.798108	+	0.602515i	$0.205835\pi$
$197$			16.9134i			1.20503i	−0.798108	+	0.602515i	$0.794165\pi$
$198$	7.22620			0.513544
$199$		−	23.0973i		−	1.63732i	−0.574277	−	0.818661i	$-0.694717\pi$
$199$		−	23.0973i		−	1.63732i	0.574277	−	0.818661i	$-0.305283\pi$
$200$			4.24378i			0.300080i
$201$	2.33471			0.164678
$202$	−8.91182			−0.627033
$203$			0.147396i			0.0103452i
$204$	−3.25329			−0.227776
$205$	15.5380			1.08522
$206$	−9.88743			−0.688890
$207$	4.54880			0.316163
$208$		−	4.09291i		−	0.283792i
$209$		−	12.1731i		−	0.842028i
$210$	−0.0293141			−0.00202287
$211$			2.51498i			0.173138i	0.996246	+	0.0865691i	$0.0275903\pi$
$211$			2.51498i			0.173138i	−0.996246	+	0.0865691i	$0.972410\pi$
$212$			16.6085i			1.14068i
$213$			5.11881i			0.350735i
$214$	6.53746			0.446892
$215$		−	18.7912i		−	1.28155i
$216$		−	9.91940i		−	0.674930i
$217$			0.0963659i			0.00654175i
$218$		−	7.05923i		−	0.478112i
$219$	−6.01220			−0.406267
$220$			9.13814i			0.616093i
$221$		−	22.0124i		−	1.48071i
$222$			5.99436i			0.402315i
$223$	24.1776			1.61905			0.809527	−	0.587083i	$-0.199724\pi$
$223$	24.1776			1.61905			0.809527	+	0.587083i	$0.199724\pi$
$224$	−0.175426			−0.0117212
$225$	4.06174			0.270783
$226$	3.84982			0.256087
$227$	−22.1023			−1.46698			−0.733490	−	0.679700i	$-0.762110\pi$
$227$	−22.1023			−1.46698			−0.733490	+	0.679700i	$0.762110\pi$
$228$	−3.13178			−0.207407
$229$		−	0.173530i		−	0.0114672i	−0.999984	−	0.00573359i	$-0.998175\pi$
$229$		−	0.173530i		−	0.0114672i	0.999984	−	0.00573359i	$-0.00182507\pi$
$230$		−	2.59708i		−	0.171246i
$231$	0.0723430			0.00475982
$232$			13.0836i			0.858982i
$233$	10.7789			0.706151			0.353076	−	0.935595i	$-0.385136\pi$
$233$	10.7789			0.706151			0.353076	+	0.935595i	$0.385136\pi$
$234$	12.5790			0.822313
$235$			4.05022i			0.264207i
$236$		−	12.6048i		−	0.820505i
$237$		−	6.67391i		−	0.433517i
$238$	−0.0833205			−0.00540086
$239$	−2.20687			−0.142750			−0.0713752	−	0.997450i	$-0.522739\pi$
$239$	−2.20687			−0.142750			−0.0713752	+	0.997450i	$0.522739\pi$
$240$	0.810337			0.0523071
$241$	1.01191			0.0651830			0.0325915	−	0.999469i	$-0.489624\pi$
$241$	1.01191			0.0651830			0.0325915	+	0.999469i	$0.489624\pi$
$242$			1.50559i			0.0967832i
$243$	−14.6258			−0.938243
$244$			1.14566i			0.0733432i
$245$	−12.9193			−0.825381
$246$		−	4.45397i		−	0.283974i
$247$		−	21.1902i		−	1.34830i
$248$			8.55393i			0.543175i
$249$	−10.8225			−0.685849
$250$		−	9.59839i		−	0.607056i
$251$		−	11.4660i		−	0.723725i	−0.932231	−	0.361863i	$-0.882141\pi$
$251$		−	11.4660i		−	0.723725i	0.932231	−	0.361863i	$-0.117859\pi$
$252$			0.105460i			0.00664337i
$253$			6.40921i			0.402944i
$254$	−14.0215			−0.879785
$255$	4.35813			0.272917
$256$	−13.7683			−0.860519
$257$	18.7115			1.16719			0.583595	−	0.812045i	$-0.301646\pi$
$257$	18.7115			1.16719			0.583595	+	0.812045i	$0.301646\pi$
$258$	−5.38649			−0.335348
$259$		−	0.340040i		−	0.0211291i
$260$			15.9072i			0.986520i
$261$	12.5224			0.775118
$262$	−4.92079			−0.304007
$263$	19.7949			1.22061			0.610303	−	0.792168i	$-0.291048\pi$
$263$	19.7949			1.22061			0.610303	+	0.792168i	$0.291048\pi$
$264$	6.42153			0.395218
$265$		−	22.2488i		−	1.36673i
$266$	−0.0802084			−0.00491789
$267$		−	5.50453i		−	0.336872i
$268$	−4.79550			−0.292932
$269$	−5.95983			−0.363377			−0.181689	−	0.983356i	$-0.558156\pi$
$269$	−5.95983			−0.363377			−0.181689	+	0.983356i	$0.558156\pi$
$270$			5.42043i			0.329877i
$271$	−27.7621			−1.68643			−0.843214	−	0.537578i	$-0.819339\pi$
$271$	−27.7621			−1.68643			−0.843214	+	0.537578i	$0.819339\pi$
$272$	2.30325			0.139655
$273$	0.125931			0.00762167
$274$	−13.0517			−0.788485
$275$			5.72295i			0.345107i
$276$	1.64891			0.0992526
$277$			25.2961i			1.51990i	0.649983	+	0.759949i	$0.274776\pi$
$277$			25.2961i			1.51990i	−0.649983	+	0.759949i	$0.725224\pi$
$278$			0.764745i			0.0458664i
$279$	8.18701			0.490143
$280$	0.147607			0.00882120
$281$	24.2563			1.44701			0.723505	−	0.690319i	$-0.242530\pi$
$281$	24.2563			1.44701			0.723505	+	0.690319i	$0.242530\pi$
$282$	1.16099			0.0691362
$283$	−6.47666			−0.384997			−0.192499	−	0.981297i	$-0.561659\pi$
$283$	−6.47666			−0.384997			−0.192499	+	0.981297i	$0.561659\pi$
$284$		−	10.5140i		−	0.623894i
$285$	4.19535			0.248511
$286$			17.7236i			1.04802i
$287$			0.252659i			0.0149140i
$288$			14.9038i			0.878214i
$289$	−4.61275			−0.271338
$290$		−	7.14952i		−	0.419834i
$291$		−	4.04865i		−	0.237336i
$292$	12.3491			0.722674
$293$	5.02181			0.293377			0.146689	−	0.989183i	$-0.453139\pi$
$293$	5.02181			0.293377			0.146689	+	0.989183i	$0.453139\pi$
$294$			3.70330i			0.215981i
$295$			16.8855i			0.983113i
$296$		−	30.1837i		−	1.75439i
$297$		−	13.3768i		−	0.776202i
$298$	9.73562			0.563969
$299$			11.1568i			0.645215i
$300$	1.47235			0.0850063
$301$	0.305557			0.0176120
$302$			13.4152i			0.771959i
$303$			7.57974i			0.435445i
$304$	2.21722			0.127166
$305$		−	1.53473i		−	0.0878784i
$306$			7.07870i			0.404662i
$307$	4.71979			0.269373			0.134686	−	0.990888i	$-0.456997\pi$
$307$	4.71979			0.269373			0.134686	+	0.990888i	$0.456997\pi$
$308$	−0.148592			−0.00846684
$309$			8.40953i			0.478401i
$310$		−	4.67427i		−	0.265481i
$311$		−	3.46578i		−	0.196526i	−0.995160	−	0.0982632i	$-0.968671\pi$
$311$		−	3.46578i		−	0.196526i	0.995160	−	0.0982632i	$-0.0313287\pi$
$312$	11.1782			0.632843
$313$	21.4195			1.21070			0.605351	−	0.795958i	$-0.293033\pi$
$313$	21.4195			1.21070			0.605351	+	0.795958i	$0.293033\pi$
$314$			7.19429i			0.405997i
$315$		−	0.141275i		−	0.00795996i
$316$			13.7082i			0.771148i
$317$		−	11.7243i		−	0.658502i	−0.944242	−	0.329251i	$-0.893204\pi$
$317$		−	11.7243i		−	0.658502i	0.944242	−	0.329251i	$-0.106796\pi$
$318$	−6.37763			−0.357640
$319$			17.6440i			0.987872i
$320$	6.09324			0.340623
$321$		−	5.56029i		−	0.310345i
$322$	0.0422303			0.00235341
$323$	11.9246			0.663501
$324$	7.09937			0.394410
$325$			9.96220i			0.552603i
$326$	−8.32878			−0.461288
$327$	−6.00407			−0.332026
$328$			22.4273i			1.23834i
$329$	−0.0658594			−0.00363094
$330$	−3.50903			−0.193166
$331$			23.5903i			1.29664i	0.761369	+	0.648319i	$0.224528\pi$
$331$			23.5903i			1.29664i	−0.761369	+	0.648319i	$0.775472\pi$
$332$	22.2294			1.22000
$333$	−28.8889			−1.58310
$334$	−2.46126			−0.134674
$335$	6.42409			0.350985
$336$			0.0131766i			0.000718845i
$337$	−8.37654			−0.456299			−0.228150	−	0.973626i	$-0.573268\pi$
$337$	−8.37654			−0.456299			−0.228150	+	0.973626i	$0.573268\pi$
$338$			20.5988i			1.12043i
$339$		−	3.27438i		−	0.177840i
$340$	−8.95161			−0.485469
$341$			11.5354i			0.624678i
$342$			6.81430i			0.368475i
$343$		−	0.420179i		−	0.0226875i
$344$	27.1228			1.46236
$345$	−2.20889			−0.118922
$346$	12.4144			0.667401
$347$		−	15.3314i		−	0.823033i	−0.911402	−	0.411517i	$-0.864999\pi$
$347$		−	15.3314i		−	0.823033i	0.911402	−	0.411517i	$-0.135001\pi$
$348$	4.53928			0.243331
$349$	9.18130	−	16.2697i	0.491464	−	0.870898i
$349$	9.18130	−	16.2697i	0.491464	−	0.870898i
$350$	0.0377086			0.00201561
$351$		−	23.2856i		−	1.24289i
$352$	−20.9993			−1.11927
$353$	8.65387			0.460599			0.230300	−	0.973120i	$-0.426029\pi$
$353$	8.65387			0.460599			0.230300	+	0.973120i	$0.426029\pi$
$354$	4.84023			0.257255
$355$			14.0847i			0.747538i
$356$			11.3063i			0.599233i
$357$			0.0708663i			0.00375064i
$358$	4.30782			0.227675
$359$			30.4931i			1.60937i	0.593705	+	0.804683i	$0.297665\pi$
$359$			30.4931i			1.60937i	−0.593705	+	0.804683i	$0.702335\pi$
$360$		−	12.5403i		−	0.660932i
$361$	−7.52081			−0.395832
$362$		−	6.67338i		−	0.350745i
$363$	1.28055			0.0672113
$364$	−0.258661			−0.0135575
$365$	−16.5429			−0.865894
$366$	−0.439930			−0.0229955
$367$		−	13.2514i		−	0.691718i	−0.938286	−	0.345859i	$-0.887587\pi$
$367$		−	13.2514i		−	0.691718i	0.938286	−	0.345859i	$-0.112413\pi$
$368$	−1.16738			−0.0608541
$369$	21.4652			1.11744
$370$			16.4938i			0.857471i
$371$	0.361781			0.0187828
$372$	2.96773			0.153870
$373$		−	4.11705i		−	0.213173i	−0.994303	−	0.106586i	$-0.966008\pi$
$373$		−	4.11705i		−	0.213173i	0.994303	−	0.106586i	$-0.0339920\pi$
$374$	−9.97382			−0.515734
$375$	−8.16369			−0.421571
$376$	−5.84601			−0.301485
$377$			30.7136i			1.58183i
$378$	−0.0881400			−0.00453343
$379$			31.6652i			1.62653i	0.581891	+	0.813267i	$0.302313\pi$
$379$			31.6652i			1.62653i	−0.581891	+	0.813267i	$0.697687\pi$
$380$	−8.61726			−0.442056
$381$			11.9256i			0.610969i
$382$		−	5.22787i		−	0.267481i
$383$			13.3358i			0.681426i	0.940167	+	0.340713i	$0.110669\pi$
$383$			13.3358i			0.681426i	−0.940167	+	0.340713i	$0.889331\pi$
$384$			6.09504i			0.311036i
$385$	0.199055			0.0101448
$386$	16.2444			0.826817
$387$		−	25.9594i		−	1.31959i
$388$			8.31593i			0.422177i
$389$			2.48312i			0.125899i	0.998017	+	0.0629497i	$0.0200508\pi$
$389$			2.48312i			0.125899i	−0.998017	+	0.0629497i	$0.979949\pi$
$390$	−6.10832			−0.309307
$391$	−6.27839			−0.317512
$392$		−	18.6474i		−	0.941837i
$393$			4.18526i			0.211119i
$394$	13.3401			0.672067
$395$		−	18.3636i		−	0.923974i
$396$			12.6240i			0.634382i
$397$	2.36477			0.118684			0.0593421	−	0.998238i	$-0.481100\pi$
$397$	2.36477			0.118684			0.0593421	+	0.998238i	$0.481100\pi$
$398$	−18.2176			−0.913164
$399$			0.0682194i			0.00341524i
$400$	−1.04239			−0.0521193
$401$			22.6817i			1.13267i	0.824175	+	0.566335i	$0.191639\pi$
$401$			22.6817i			1.13267i	−0.824175	+	0.566335i	$0.808361\pi$
$402$		−	1.84146i		−	0.0918439i
$403$			20.0802i			1.00027i
$404$		−	15.5688i		−	0.774576i
$405$	−9.51037			−0.472574
$406$	0.116256			0.00576969
$407$		−	40.7042i		−	2.01763i
$408$			6.29045i			0.311424i
$409$	−4.44480			−0.219781			−0.109891	−	0.993944i	$-0.535050\pi$
$409$	−4.44480			−0.219781			−0.109891	+	0.993944i	$0.535050\pi$
$410$		−	12.2553i		−	0.605247i
$411$			11.1009i			0.547565i
$412$		−	17.2732i		−	0.850988i
$413$	−0.274570			−0.0135107
$414$		−	3.58778i		−	0.176330i
$415$	−29.7787			−1.46178
$416$	−36.5544			−1.79223
$417$	0.650436			0.0318520
$418$	−9.60129			−0.469614
$419$	−2.00191			−0.0977998			−0.0488999	−	0.998804i	$-0.515572\pi$
$419$	−2.00191			−0.0977998			−0.0488999	+	0.998804i	$0.515572\pi$
$420$		−	0.0512113i		−	0.00249885i
$421$		−	20.0437i		−	0.976868i	−0.872601	−	0.488434i	$-0.837568\pi$
$421$		−	20.0437i		−	0.976868i	0.872601	−	0.488434i	$-0.162432\pi$
$422$	1.98364			0.0965623
$423$			5.59525i			0.272050i
$424$	32.1136			1.55957
$425$	−5.60613			−0.271937
$426$	4.03737			0.195611
$427$	0.0249558			0.00120769
$428$			11.4208i			0.552047i
$429$	15.0744			0.727801
$430$	−14.8212			−0.714742
$431$		−	25.9316i		−	1.24908i	−0.780992	−	0.624542i	$-0.785286\pi$
$431$		−	25.9316i		−	1.24908i	0.780992	−	0.624542i	$-0.214714\pi$
$432$	2.43647			0.117225
$433$		−	15.7362i		−	0.756232i	−0.925758	−	0.378116i	$-0.876572\pi$
$433$		−	15.7362i		−	0.756232i	0.925758	−	0.378116i	$-0.123428\pi$
$434$	0.0760069			0.00364845
$435$	−6.08085			−0.291555
$436$	12.3324			0.590613
$437$	−6.04388			−0.289118
$438$			4.74202i			0.226582i
$439$		−	35.2908i		−	1.68434i	−0.539215	−	0.842168i	$-0.681279\pi$
$439$		−	35.2908i		−	1.68434i	0.539215	−	0.842168i	$-0.318721\pi$
$440$	17.6692			0.842345
$441$	−17.8475			−0.849883
$442$	−17.3619			−0.825820
$443$	28.9420			1.37508			0.687539	−	0.726148i	$-0.258691\pi$
$443$	28.9420			1.37508			0.687539	+	0.726148i	$0.258691\pi$
$444$	−10.4720			−0.496981
$445$		−	15.1460i		−	0.717989i
$446$		−	19.0697i		−	0.902976i
$447$		−	8.28040i		−	0.391650i
$448$			0.0990804i			0.00468111i
$449$	−26.0204			−1.22798			−0.613989	−	0.789315i	$-0.710436\pi$
$449$	−26.0204			−1.22798			−0.613989	+	0.789315i	$0.710436\pi$
$450$		−	3.20363i		−	0.151020i
$451$			30.2443i			1.42415i
$452$			6.72557i			0.316344i
$453$	11.4100			0.536088
$454$			17.4328i			0.818161i
$455$	0.346505			0.0162444
$456$			6.05550i			0.283575i
$457$	23.3619			1.09282			0.546411	−	0.837517i	$-0.315994\pi$
$457$	23.3619			1.09282			0.546411	+	0.837517i	$0.315994\pi$
$458$	−0.136869			−0.00639545
$459$	13.1038			0.611632
$460$	4.53705			0.211541
$461$		−	21.5259i		−	1.00256i	−0.865285	−	0.501280i	$-0.832863\pi$
$461$		−	21.5259i		−	1.00256i	0.865285	−	0.501280i	$-0.167137\pi$
$462$		−	0.0570592i		−	0.00265464i
$463$		−	38.7691i		−	1.80175i	−0.434075	−	0.900877i	$-0.642925\pi$
$463$		−	38.7691i		−	1.80175i	0.434075	−	0.900877i	$-0.357075\pi$
$464$	−3.21369			−0.149192
$465$	−3.97559			−0.184364
$466$		−	8.50169i		−	0.393833i
$467$	−7.07576			−0.327427			−0.163713	−	0.986508i	$-0.552347\pi$
$467$	−7.07576			−0.327427			−0.163713	+	0.986508i	$0.552347\pi$
$468$			21.9752i			1.01581i
$469$			0.104460i			0.00482352i
$470$	3.19454			0.147353
$471$	6.11894			0.281946
$472$	−24.3723			−1.12182
$473$	36.5765			1.68179
$474$	−5.26393			−0.241780
$475$	−5.39674			−0.247619
$476$		−	0.145559i		−	0.00667170i
$477$		−	30.7360i		−	1.40731i
$478$			1.74063i			0.0796144i
$479$	−24.3302			−1.11167			−0.555837	−	0.831291i	$-0.687602\pi$
$479$	−24.3302			−1.11167			−0.555837	+	0.831291i	$0.687602\pi$
$480$		−	7.23725i		−	0.330334i
$481$		−	70.8557i		−	3.23074i
$482$		−	0.798128i		−	0.0363537i
$483$		−	0.0359180i		−	0.00163433i
$484$	−2.63025			−0.119557
$485$		−	11.1401i		−	0.505845i
$486$			11.5358i			0.523275i
$487$		−	14.1656i		−	0.641903i	−0.947096	−	0.320952i	$-0.895997\pi$
$487$		−	14.1656i		−	0.641903i	0.947096	−	0.320952i	$-0.104003\pi$
$488$	2.21520			0.100277
$489$			7.08385i			0.320343i
$490$			10.1898i			0.460330i
$491$	−0.191185			−0.00862804			−0.00431402	−	0.999991i	$-0.501373\pi$
$491$	−0.191185			−0.00862804			−0.00431402	+	0.999991i	$0.501373\pi$
$492$	7.78100			0.350795
$493$	−17.2838			−0.778423
$494$	−16.7134			−0.751971
$495$		−	16.9113i		−	0.760104i
$496$	−2.10108			−0.0943411
$497$	−0.229027			−0.0102733
$498$			8.53607i			0.382510i
$499$			23.7243i			1.06205i	0.847357	+	0.531023i	$0.178192\pi$
$499$			23.7243i			1.06205i	−0.847357	+	0.531023i	$0.821808\pi$
$500$	16.7682			0.749898
$501$			2.09337i			0.0935247i
$502$	−9.04358			−0.403635
$503$			26.2049i			1.16842i	0.811603	+	0.584210i	$0.198595\pi$
$503$			26.2049i			1.16842i	−0.811603	+	0.584210i	$0.801405\pi$
$504$	0.203914			0.00908306
$505$			20.8560i			0.928082i
$506$	5.05515			0.224729
$507$	17.5198			0.778083
$508$		−	24.4953i		−	1.08680i
$509$			24.7149i			1.09547i	0.836652	+	0.547734i	$0.184509\pi$
$509$			24.7149i			1.09547i	−0.836652	+	0.547734i	$0.815491\pi$
$510$		−	3.43740i		−	0.152211i
$511$		−	0.268999i		−	0.0118998i
$512$		−	7.31190i		−	0.323143i
$513$	12.6143			0.556936
$514$		−	14.7583i		−	0.650963i
$515$			23.1393i			1.01964i
$516$		−	9.41010i		−	0.414256i
$517$	−7.88365			−0.346723
$518$	−0.268200			−0.0117841
$519$		−	10.5588i		−	0.463478i
$520$	30.7575			1.34881
$521$			40.4715i			1.77309i	0.462644	+	0.886544i	$0.346901\pi$
$521$			40.4715i			1.77309i	−0.462644	+	0.886544i	$0.653099\pi$
$522$		−	9.87683i		−	0.432297i
$523$			19.5402i			0.854432i	0.904150	+	0.427216i	$0.140506\pi$
$523$			19.5402i			0.854432i	−0.904150	+	0.427216i	$0.859494\pi$
$524$		−	8.59653i		−	0.375541i
$525$		−	0.0320721i		−	0.00139974i
$526$		−	15.6129i		−	0.680754i
$527$	−11.3000			−0.492234
$528$			1.57730i			0.0686432i
$529$	−19.8178			−0.861646
$530$	−17.5484			−0.762253
$531$			23.3268i			1.01230i
$532$		−	0.140123i		−	0.00607508i
$533$			52.6476i			2.28042i
$534$	−4.34160			−0.187879
$535$		−	15.2994i		−	0.661451i
$536$			9.27241i			0.400507i
$537$		−	3.66391i		−	0.158110i
$538$			4.70071i			0.202662i
$539$		−	25.1470i		−	1.08316i
$540$	−9.46939			−0.407498
$541$	27.3545			1.17606			0.588032	−	0.808838i	$-0.299903\pi$
$541$	27.3545			1.17606			0.588032	+	0.808838i	$0.299903\pi$
$542$			21.8969i			0.940551i
$543$	−5.67589			−0.243576
$544$		−	20.5707i		−	0.881960i
$545$	−16.5205			−0.707661
$546$		−	0.0993255i		−	0.00425074i
$547$	−11.3165			−0.483859			−0.241930	−	0.970294i	$-0.577780\pi$
$547$	−11.3165			−0.483859			−0.241930	+	0.970294i	$0.577780\pi$
$548$		−	22.8012i		−	0.974017i
$549$		−	2.12018i		−	0.0904871i
$550$	4.51388			0.192472
$551$	−16.6382			−0.708813
$552$		−	3.18827i		−	0.135702i
$553$	0.298605			0.0126980
$554$	19.9519			0.847674
$555$	14.0284			0.595473
$556$	−1.33600			−0.0566589
$557$			0.788448i			0.0334076i	0.999860	+	0.0167038i	$0.00531723\pi$
$557$			0.788448i			0.0334076i	−0.999860	+	0.0167038i	$0.994683\pi$
$558$		−	6.45736i		−	0.273362i
$559$	63.6704			2.69297
$560$			0.0362562i			0.00153211i
$561$			8.48300i			0.358152i
$562$		−	19.1317i		−	0.807024i
$563$	−17.9707			−0.757377			−0.378688	−	0.925524i	$-0.623625\pi$
$563$	−17.9707			−0.757377			−0.378688	+	0.925524i	$0.623625\pi$
$564$			2.02824i			0.0854042i
$565$		−	9.00962i		−	0.379038i
$566$			5.10835i			0.214720i
$567$		−	0.154645i		−	0.00649449i
$568$	−20.3296			−0.853010
$569$			10.5879i			0.443867i	0.975062	+	0.221933i	$0.0712367\pi$
$569$			10.5879i			0.443867i	−0.975062	+	0.221933i	$0.928763\pi$
$570$		−	3.30901i		−	0.138599i
$571$		−	9.65312i		−	0.403971i	−0.979389	−	0.201985i	$-0.935261\pi$
$571$		−	9.65312i		−	0.403971i	0.979389	−	0.201985i	$-0.0647393\pi$
$572$	−30.9629			−1.29462
$573$	−4.44644			−0.185753
$574$	0.199280			0.00831779
$575$	2.84143			0.118496
$576$	8.41762			0.350734
$577$	1.94051			0.0807846			0.0403923	−	0.999184i	$-0.487139\pi$
$577$	1.94051			0.0807846			0.0403923	+	0.999184i	$0.487139\pi$
$578$			3.63822i			0.151330i
$579$		−	13.8163i		−	0.574185i
$580$	12.4901			0.518622
$581$		−	0.484223i		−	0.0200889i
$582$	−3.19330			−0.132367
$583$	43.3068			1.79358
$584$		−	23.8777i		−	0.988066i
$585$		−	29.4382i		−	1.21712i
$586$		−	3.96086i		−	0.163622i
$587$	30.1175			1.24308			0.621542	−	0.783381i	$-0.286506\pi$
$587$	30.1175			1.24308			0.621542	+	0.783381i	$0.286506\pi$
$588$	−6.46961			−0.266802
$589$	−10.8779			−0.448216
$590$	13.3182			0.548300
$591$		−	11.3461i		−	0.466718i
$592$	7.41393			0.304711
$593$		−	10.6110i		−	0.435741i	−0.975978	−	0.217871i	$-0.930089\pi$
$593$		−	10.6110i		−	0.435741i	0.975978	−	0.217871i	$-0.0699111\pi$
$594$	−10.5507			−0.432902
$595$			0.194992i			0.00799390i
$596$			17.0080i			0.696673i
$597$			15.4945i			0.634149i
$598$	8.79973			0.359848
$599$			1.34186i			0.0548271i	0.999624	+	0.0274135i	$0.00872709\pi$
$599$			1.34186i			0.0548271i	−0.999624	+	0.0274135i	$0.991273\pi$
$600$		−	2.84689i		−	0.116224i
$601$		−	0.110017i		−	0.00448768i	−0.999997	−	0.00224384i	$-0.999286\pi$
$601$		−	0.110017i		−	0.00448768i	0.999997	−	0.00224384i	$-0.000714237\pi$
$602$		−	0.241003i		−	0.00982255i
$603$	8.87467			0.361404
$604$	−23.4361			−0.953603
$605$	3.52349			0.143250
$606$	5.97838			0.242855
$607$	−30.0254			−1.21869			−0.609346	−	0.792904i	$-0.708568\pi$
$607$	−30.0254			−1.21869			−0.609346	+	0.792904i	$0.708568\pi$
$608$		−	19.8023i		−	0.803090i
$609$		−	0.0988789i		−	0.00400678i
$610$	−1.21049			−0.0490113
$611$	−13.7234			−0.555190
$612$	−12.3664			−0.499880
$613$	−31.4913			−1.27192			−0.635961	−	0.771721i	$-0.719396\pi$
$613$	−31.4913			−1.27192			−0.635961	+	0.771721i	$0.719396\pi$
$614$		−	3.72265i		−	0.150234i
$615$	−10.4235			−0.420315
$616$			0.287313i			0.0115762i
$617$	11.1677			0.449596			0.224798	−	0.974405i	$-0.427828\pi$
$617$	11.1677			0.449596			0.224798	+	0.974405i	$0.427828\pi$
$618$	6.63287			0.266813
$619$		−	3.30375i		−	0.132789i	−0.997793	−	0.0663944i	$-0.978850\pi$
$619$		−	3.30375i		−	0.132789i	0.997793	−	0.0663944i	$-0.0211495\pi$
$620$	8.16587			0.327949
$621$	−6.64155			−0.266516
$622$	−2.73357			−0.109606
$623$	0.246284			0.00986718
$624$			2.74568i			0.109915i
$625$	−14.4985			−0.579942
$626$		−	16.8943i		−	0.675231i
$627$			8.16615i			0.326125i
$628$	−12.5683			−0.501530
$629$	39.8734			1.58986
$630$	−0.111428			−0.00443941
$631$	−37.0493			−1.47491			−0.737454	−	0.675398i	$-0.763972\pi$
$631$	−37.0493			−1.47491			−0.737454	+	0.675398i	$0.763972\pi$
$632$	26.5057			1.05434
$633$		−	1.68714i		−	0.0670579i
$634$	−9.24733			−0.367258
$635$			32.8140i			1.30218i
$636$		−	11.1416i		−	0.441793i
$637$		−	43.7745i		−	1.73441i
$638$	13.9164			0.550954
$639$			19.4575i			0.769729i
$640$			16.7708i			0.662924i
$641$	6.32318			0.249750			0.124875	−	0.992172i	$-0.460147\pi$
$641$	6.32318			0.249750			0.124875	+	0.992172i	$0.460147\pi$
$642$	−4.38558			−0.173085
$643$			44.1450i			1.74091i	0.492250	+	0.870454i	$0.336175\pi$
$643$			44.1450i			1.74091i	−0.492250	+	0.870454i	$0.663825\pi$
$644$			0.0737757i			0.00290717i
$645$			12.6058i			0.496354i
$646$		−	9.40530i		−	0.370047i
$647$	−13.1623			−0.517462			−0.258731	−	0.965949i	$-0.583304\pi$
$647$	−13.1623			−0.517462			−0.258731	+	0.965949i	$0.583304\pi$
$648$		−	13.7271i		−	0.539251i
$649$	−32.8672			−1.29015
$650$	7.85751			0.308197
$651$		−	0.0646459i		−	0.00253367i
$652$		−	14.5502i		−	0.569831i
$653$	−43.2419			−1.69218			−0.846092	−	0.533036i	$-0.821051\pi$
$653$	−43.2419			−1.69218			−0.846092	+	0.533036i	$0.821051\pi$
$654$			4.73560i			0.185177i
$655$			11.5160i			0.449966i
$656$	−5.50874			−0.215080
$657$	−22.8535			−0.891599
$658$			0.0519454i			0.00202504i
$659$			8.64846i			0.336896i	0.985711	+	0.168448i	$0.0538755\pi$
$659$			8.64846i			0.336896i	−0.985711	+	0.168448i	$0.946124\pi$
$660$		−	6.13021i		−	0.238618i
$661$	9.46928			0.368312			0.184156	−	0.982897i	$-0.441045\pi$
$661$	9.46928			0.368312			0.184156	+	0.982897i	$0.441045\pi$
$662$	18.6064			0.723159
$663$			14.7667i			0.573492i
$664$		−	42.9821i		−	1.66803i
$665$			0.187709i			0.00727905i
$666$			22.7856i			0.882926i
$667$	8.76016			0.339195
$668$		−	4.29978i		−	0.166363i
$669$	−16.2193			−0.627073
$670$		−	5.06688i		−	0.195751i
$671$	2.98731			0.115324
$672$	0.117683			0.00453971
$673$	−31.4948			−1.21403			−0.607017	−	0.794689i	$-0.707634\pi$
$673$	−31.4948			−1.21403			−0.607017	+	0.794689i	$0.707634\pi$
$674$			6.60685i			0.254486i
$675$	−5.93041			−0.228262
$676$	−35.9858			−1.38407
$677$			34.9692i			1.34397i	0.740563	+	0.671987i	$0.234559\pi$
$677$			34.9692i			1.34397i	−0.740563	+	0.671987i	$0.765441\pi$
$678$	−2.58261			−0.0991845
$679$	0.181145			0.00695172
$680$			17.3085i			0.663751i
$681$	14.8270			0.568174
$682$	9.09836			0.348394
$683$	42.7528			1.63589			0.817946	−	0.575295i	$-0.195113\pi$
$683$	42.7528			1.63589			0.817946	+	0.575295i	$0.195113\pi$
$684$	−11.9045			−0.455179
$685$			30.5446i			1.16705i
$686$	−0.331409			−0.0126533
$687$			0.116410i			0.00444133i
$688$			6.66210i			0.253990i
$689$	75.3861			2.87198
$690$			1.74222i			0.0663252i
$691$		−	15.2626i		−	0.580617i	−0.956933	−	0.290308i	$-0.906242\pi$
$691$		−	15.2626i		−	0.580617i	0.956933	−	0.290308i	$-0.0937579\pi$
$692$			21.6877i			0.824442i
$693$	0.274989			0.0104460
$694$	−12.0924			−0.459020
$695$	1.78971			0.0678875
$696$		−	8.77699i		−	0.332691i
$697$	−29.6270			−1.12220
$698$	−12.8325	−	7.24159i	−0.485715	−	0.274098i
$699$	−7.23092			−0.273498
$700$			0.0658762i			0.00248989i
$701$	−0.0712011			−0.00268923			−0.00134461	−	0.999999i	$-0.500428\pi$
$701$	−0.0712011			−0.00268923			−0.00134461	+	0.999999i	$0.500428\pi$
$702$	−18.3661			−0.693185
$703$	38.3841			1.44768
$704$			11.8603i			0.447004i
$705$		−	2.71704i		−	0.102330i
$706$		−	6.82559i		−	0.256884i
$707$	−0.339134			−0.0127544
$708$			8.45580i			0.317788i
$709$			15.2554i			0.572929i	0.958091	+	0.286465i	$0.0924801\pi$
$709$			15.2554i			0.572929i	−0.958091	+	0.286465i	$0.907520\pi$
$710$	11.1090			0.416915
$711$		−	25.3688i		−	0.951403i
$712$	21.8615			0.819293
$713$	5.72730			0.214489
$714$	0.0558945			0.00209180
$715$	41.4781			1.55119
$716$			7.52568i			0.281248i
$717$	1.48045			0.0552884
$718$	24.0509			0.897572
$719$			35.1960i			1.31259i	0.754505	+	0.656294i	$0.227877\pi$
$719$			35.1960i			1.31259i	−0.754505	+	0.656294i	$0.772123\pi$
$720$	3.08024			0.114794
$721$	−0.376260			−0.0140127
$722$			5.93191i			0.220763i
$723$	−0.678829			−0.0252459
$724$	11.6583			0.433277
$725$	7.82218			0.290508
$726$		−	1.01001i		−	0.0374850i
$727$	16.3492			0.606359			0.303180	−	0.952933i	$-0.401952\pi$
$727$	16.3492			0.606359			0.303180	+	0.952933i	$0.401952\pi$
$728$			0.500139i			0.0185364i
$729$	−5.64541			−0.209089
$730$			13.0479i			0.482925i
$731$			35.8299i			1.32522i
$732$		−	0.768550i		−	0.0284064i
$733$		−	18.8715i		−	0.697033i	−0.937303	−	0.348517i	$-0.886685\pi$
$733$		−	18.8715i		−	0.697033i	0.937303	−	0.348517i	$-0.113315\pi$
$734$	−10.4518			−0.385784
$735$	8.66673			0.319677
$736$			10.4261i			0.384310i
$737$			12.5043i			0.460603i
$738$		−	16.9303i		−	0.623214i
$739$	36.2309			1.33278			0.666388	−	0.745605i	$-0.267839\pi$
$739$	36.2309			1.33278			0.666388	+	0.745605i	$0.267839\pi$
$740$	−28.8144			−1.05924
$741$			14.2152i			0.522208i
$742$		−	0.285349i		−	0.0104755i
$743$	−27.2404			−0.999353			−0.499676	−	0.866212i	$-0.666548\pi$
$743$	−27.2404			−0.999353			−0.499676	+	0.866212i	$0.666548\pi$
$744$		−	5.73830i		−	0.210376i
$745$		−	22.7840i		−	0.834740i
$746$	−3.24725			−0.118890
$747$	−41.1383			−1.50517
$748$		−	17.4241i		−	0.637087i
$749$	0.248779			0.00909019
$750$			6.43897i			0.235118i
$751$			6.87645i			0.250925i	0.992098	+	0.125463i	$0.0400415\pi$
$751$			6.87645i			0.250925i	−0.992098	+	0.125463i	$0.959958\pi$
$752$		−	1.43594i		−	0.0523633i
$753$			7.69180i			0.280305i
$754$	24.2248			0.882216
$755$	31.3952			1.14259
$756$		−	0.153979i		−	0.00560016i
$757$		−	12.8488i		−	0.466996i	−0.972357	−	0.233498i	$-0.924983\pi$
$757$		−	12.8488i		−	0.466996i	0.972357	−	0.233498i	$-0.0750172\pi$
$758$	24.9754			0.907147
$759$		−	4.29954i		−	0.156064i
$760$			16.6620i			0.604395i
$761$			12.9989i			0.471209i	0.971849	+	0.235605i	$0.0757070\pi$
$761$			12.9989i			0.471209i	−0.971849	+	0.235605i	$0.924293\pi$
$762$	9.40613			0.340748
$763$		−	0.268635i		−	0.00972524i
$764$	9.13300			0.330420
$765$	16.5661			0.598947
$766$	10.5184			0.380044
$767$	−57.2135			−2.06586
$768$	9.23630			0.333286
$769$			31.4215i			1.13309i	0.824032	+	0.566543i	$0.191720\pi$
$769$			31.4215i			1.13309i	−0.824032	+	0.566543i	$0.808280\pi$
$770$		−	0.157001i		−	0.00565794i
$771$	−12.5524			−0.452062
$772$			28.3786i			1.02137i
$773$	15.9768			0.574645			0.287323	−	0.957834i	$-0.407235\pi$
$773$	15.9768			0.574645			0.287323	+	0.957834i	$0.407235\pi$
$774$	−20.4750			−0.735959
$775$	5.11405			0.183702
$776$	16.0794			0.577216
$777$			0.228112i			0.00818346i
$778$	1.95852			0.0702164
$779$	−28.5204			−1.02185
$780$		−	10.6711i		−	0.382088i
$781$	−27.4155			−0.981004
$782$			4.95197i			0.177082i
$783$	−18.2835			−0.653401
$784$	4.58031			0.163583
$785$	16.8366			0.600923
$786$	3.30105			0.117745
$787$			7.75438i			0.276414i	0.990403	+	0.138207i	$0.0441339\pi$
$787$			7.75438i			0.276414i	−0.990403	+	0.138207i	$0.955866\pi$
$788$			23.3050i			0.830206i
$789$	−13.2792			−0.472751
$790$	−14.4840			−0.515317
$791$	0.146503			0.00520904
$792$	24.4094			0.867350
$793$	5.20015			0.184663
$794$		−	1.86517i		−	0.0661923i
$795$			14.9254i			0.529348i
$796$		−	31.8258i		−	1.12803i
$797$			17.9182i			0.634694i	0.948309	+	0.317347i	$0.102792\pi$
$797$			17.9182i			0.634694i	−0.948309	+	0.317347i	$0.897208\pi$
$798$	0.0538068			0.00190474
$799$		−	7.72273i		−	0.273210i
$800$			9.30972i			0.329148i
$801$		−	20.9237i		−	0.739303i
$802$	17.8898			0.631711
$803$		−	32.2003i		−	1.13632i
$804$	3.21700			0.113455
$805$		−	0.0988304i		−	0.00348331i
$806$	15.8379			0.557867
$807$	3.99808			0.140739
$808$	−30.1032			−1.05903
$809$	18.1301			0.637421			0.318710	−	0.947852i	$-0.396750\pi$
$809$	18.1301			0.637421			0.318710	+	0.947852i	$0.396750\pi$
$810$			7.50114i			0.263563i
$811$			31.4742i			1.10521i	0.833443	+	0.552605i	$0.186366\pi$
$811$			31.4742i			1.10521i	−0.833443	+	0.552605i	$0.813634\pi$
$812$			0.203097i			0.00712732i
$813$	18.6239			0.653168
$814$	−32.1048			−1.12527
$815$			19.4916i			0.682760i
$816$	−1.54511			−0.0540895
$817$			34.4916i			1.20671i
$818$			3.50576i			0.122576i
$819$	0.478685			0.0167266
$820$	21.4098			0.747664
$821$	18.0058			0.628406			0.314203	−	0.949356i	$-0.398263\pi$
$821$	18.0058			0.628406			0.314203	+	0.949356i	$0.398263\pi$
$822$	8.75560			0.305387
$823$	−6.88450			−0.239979			−0.119989	−	0.992775i	$-0.538286\pi$
$823$	−6.88450			−0.239979			−0.119989	+	0.992775i	$0.538286\pi$
$824$	−33.3988			−1.16350
$825$		−	3.83917i		−	0.133663i
$826$			0.216562i			0.00753517i
$827$		−	17.1072i		−	0.594877i	−0.954741	−	0.297438i	$-0.903868\pi$
$827$		−	17.1072i		−	0.594877i	0.954741	−	0.297438i	$-0.0961323\pi$
$828$	6.26780			0.217821
$829$		−	36.3407i		−	1.26217i	−0.775715	−	0.631083i	$-0.782611\pi$
$829$		−	36.3407i		−	1.26217i	0.775715	−	0.631083i	$-0.217389\pi$
$830$			23.4874i			0.815261i
$831$		−	16.9696i		−	0.588669i
$832$			20.6458i			0.715765i
$833$	24.6337			0.853507
$834$		−	0.513020i		−	0.0177644i
$835$			5.76001i			0.199333i
$836$		−	16.7733i		−	0.580116i
$837$	−11.9536			−0.413176
$838$			1.57897i			0.0545447i
$839$		−	10.6808i		−	0.368741i	−0.982857	−	0.184371i	$-0.940975\pi$
$839$		−	10.6808i		−	0.368741i	0.982857	−	0.184371i	$-0.0590247\pi$
$840$	−0.0990203			−0.00341652
$841$	−4.88411			−0.168418
$842$	−15.8091			−0.544817
$843$	−16.2721			−0.560439
$844$			3.46539i			0.119284i
$845$	48.2068			1.65836
$846$	4.41315			0.151727
$847$			0.0572945i			0.00196866i
$848$			7.88796i			0.270874i
$849$	4.34479			0.149113
$850$			4.42174i			0.151664i
$851$	−20.2095			−0.692773
$852$			7.05322i			0.241639i
$853$	19.5072			0.667913			0.333957	−	0.942588i	$-0.391616\pi$
$853$	19.5072			0.667913			0.333957	+	0.942588i	$0.391616\pi$
$854$		−	0.0196834i		−	0.000673553i
$855$	15.9473			0.545386
$856$	22.0829			0.754778
$857$		−	6.14343i		−	0.209856i	−0.994480	−	0.104928i	$-0.966539\pi$
$857$		−	6.14343i		−	0.209856i	0.994480	−	0.104928i	$-0.0334612\pi$
$858$		−	11.8897i		−	0.405907i
$859$			6.42209i			0.219119i	0.993980	+	0.109560i	$0.0349440\pi$
$859$			6.42209i			0.219119i	−0.993980	+	0.109560i	$0.965056\pi$
$860$		−	25.8924i		−	0.882923i
$861$		−	0.169493i		−	0.00577631i
$862$	−20.4531			−0.696636
$863$			26.5905i			0.905150i	0.891726	+	0.452575i	$0.149494\pi$
$863$			26.5905i			0.905150i	−0.891726	+	0.452575i	$0.850506\pi$
$864$		−	21.7605i		−	0.740308i
$865$		−	29.0530i		−	0.987831i
$866$	−12.4116			−0.421764
$867$	3.09441			0.105092
$868$			0.132783i			0.00450694i
$869$	35.7443			1.21254
$870$			4.79617i			0.162605i
$871$			21.7668i			0.737541i
$872$		−	23.8454i		−	0.807507i
$873$		−	15.3897i		−	0.520861i
$874$			4.76701i			0.161246i
$875$		−	0.365261i		−	0.0123481i
$876$	−8.28422			−0.279898
$877$		−	27.1110i		−	0.915475i	−0.889087	−	0.457737i	$-0.848660\pi$
$877$		−	27.1110i		−	0.915475i	0.889087	−	0.457737i	$-0.151340\pi$
$878$	−27.8350			−0.939385
$879$	−3.36882			−0.113627
$880$			4.34003i			0.146302i
$881$			24.9494i			0.840567i	0.907393	+	0.420283i	$0.138069\pi$
$881$			24.9494i			0.840567i	−0.907393	+	0.420283i	$0.861931\pi$
$882$			14.0769i			0.473995i
$883$	30.3400			1.02102			0.510510	−	0.859872i	$-0.329456\pi$
$883$	30.3400			1.02102			0.510510	+	0.859872i	$0.329456\pi$
$884$		−	30.3309i		−	1.02014i
$885$		−	11.3274i		−	0.380768i
$886$		−	22.8275i		−	0.766905i
$887$		−	19.3671i		−	0.650282i	−0.945666	−	0.325141i	$-0.894588\pi$
$887$		−	19.3671i		−	0.650282i	0.945666	−	0.325141i	$-0.105412\pi$
$888$			20.2483i			0.679490i
$889$	−0.533579			−0.0178957
$890$	−11.9461			−0.400435
$891$		−	18.5117i		−	0.620165i
$892$	33.3144			1.11545
$893$		−	7.43428i		−	0.248779i
$894$	−6.53102			−0.218430
$895$		−	10.0815i		−	0.336986i
$896$	−0.272705			−0.00911044
$897$		−	7.48441i		−	0.249897i
$898$			20.5231i			0.684865i
$899$	15.7667			0.525849
$900$	5.59668			0.186556
$901$			42.4228i			1.41331i
$902$	23.8547			0.794274
$903$	−0.204979			−0.00682129
$904$	13.0043			0.432518
$905$	−15.6175			−0.519144
$906$		−	8.99943i		−	0.298986i
$907$		−	34.8244i		−	1.15633i	−0.815921	−	0.578163i	$-0.803770\pi$
$907$		−	34.8244i		−	1.15633i	0.815921	−	0.578163i	$-0.196230\pi$
$908$	−30.4548			−1.01068
$909$			28.8120i			0.955632i
$910$		−	0.273299i		−	0.00905979i
$911$			25.5123i			0.845259i	0.906302	+	0.422630i	$0.138893\pi$
$911$			25.5123i			0.845259i	−0.906302	+	0.422630i	$0.861107\pi$
$912$	−1.48739			−0.0492525
$913$		−	57.9635i		−	1.91831i
$914$		−	18.4262i		−	0.609486i
$915$			1.02955i			0.0340360i
$916$		−	0.239107i		−	0.00790032i
$917$	−0.187258			−0.00618379
$918$		−	10.3354i		−	0.341118i
$919$			30.1469i			0.994454i	0.867621	+	0.497227i	$0.165648\pi$
$919$			30.1469i			0.994454i	−0.867621	+	0.497227i	$0.834352\pi$
$920$		−	8.77268i		−	0.289227i
$921$	−3.16621			−0.104330
$922$	−16.9782			−0.559146
$923$	−47.7234			−1.57083
$924$	0.0996815			0.00327928
$925$	−18.0456			−0.593336
$926$	−30.5785			−1.00487
$927$			31.9661i			1.04991i
$928$			28.7020i			0.942189i
$929$	12.7788			0.419259			0.209629	−	0.977781i	$-0.432774\pi$
$929$	12.7788			0.419259			0.209629	+	0.977781i	$0.432774\pi$
$930$			3.13568i			0.102823i
$931$	23.7136			0.777182
$932$	14.8523			0.486503
$933$			2.32498i			0.0761164i
$934$			5.58088i			0.182612i
$935$			23.3414i			0.763346i
$936$	42.4905			1.38885
$937$	14.7173			0.480792			0.240396	−	0.970675i	$-0.422723\pi$
$937$	14.7173			0.480792			0.240396	+	0.970675i	$0.422723\pi$
$938$	0.0823911			0.00269016
$939$	−14.3690			−0.468915
$940$			5.58080i			0.182026i
$941$	−29.4957			−0.961534			−0.480767	−	0.876848i	$-0.659642\pi$
$941$	−29.4957			−0.961534			−0.480767	+	0.876848i	$0.659642\pi$
$942$		−	4.82620i		−	0.157246i
$943$	15.0162			0.488995
$944$		−	5.98649i		−	0.194844i
$945$			0.206271i			0.00671000i
$946$		−	28.8491i		−	0.937965i
$947$	45.9209			1.49223			0.746114	−	0.665819i	$-0.231918\pi$
$947$	45.9209			1.49223			0.746114	+	0.665819i	$0.231918\pi$
$948$		−	9.19599i		−	0.298672i
$949$		−	56.0525i		−	1.81954i
$950$			4.25658i			0.138102i
$951$			7.86510i			0.255043i
$952$	−0.281448			−0.00912179
$953$	−34.9964			−1.13364			−0.566822	−	0.823840i	$-0.691827\pi$
$953$	−34.9964			−1.13364			−0.566822	+	0.823840i	$0.691827\pi$
$954$	−24.2425			−0.784880
$955$	−12.2346			−0.395903
$956$	−3.04084			−0.0983479
$957$		−	11.8362i		−	0.382611i
$958$			19.1900i			0.620001i
$959$	−0.496676			−0.0160385
$960$	−4.08758			−0.131926
$961$	−20.6919			−0.667481
$962$	−55.8862			−1.80184
$963$		−	21.1357i		−	0.681087i
$964$	1.39432			0.0449079
$965$		−	38.0162i		−	1.22378i
$966$	−0.0283297			−0.000911494
$967$	2.95008			0.0948681			0.0474340	−	0.998874i	$-0.484896\pi$
$967$	2.95008			0.0948681			0.0474340	+	0.998874i	$0.484896\pi$
$968$			5.08575i			0.163462i
$969$	−7.99946			−0.256980
$970$	−8.78653			−0.282119
$971$	42.0530			1.34955			0.674773	−	0.738025i	$-0.264241\pi$
$971$	42.0530			1.34955			0.674773	+	0.738025i	$0.264241\pi$
$972$	−20.1529			−0.646403
$973$			0.0291019i			0.000932965i
$974$	−11.1728			−0.358001
$975$		−	6.68302i		−	0.214028i
$976$			0.544113i			0.0174166i
$977$	−23.3586			−0.747308			−0.373654	−	0.927568i	$-0.621895\pi$
$977$	−23.3586			−0.747308			−0.373654	+	0.927568i	$0.621895\pi$
$978$	5.58726			0.178661
$979$	29.4813			0.942227
$980$	−17.8015			−0.568647
$981$	−22.8225			−0.728668
$982$			0.150793i			0.00481201i
$983$	6.65682			0.212320			0.106160	−	0.994349i	$-0.466144\pi$
$983$	6.65682			0.212320			0.106160	+	0.994349i	$0.466144\pi$
$984$		−	15.0451i		−	0.479619i
$985$		−	31.2195i		−	0.994737i
$986$			13.6323i			0.434141i
$987$	0.0441810			0.00140630
$988$		−	29.1980i		−	0.928912i
$989$		−	18.1601i		−	0.577458i
$990$	−13.3385			−0.423924
$991$	−51.8478			−1.64700			−0.823500	−	0.567317i	$-0.807982\pi$
$991$	−51.8478			−1.64700			−0.823500	+	0.567317i	$0.807982\pi$
$992$			18.7650i			0.595791i
$993$		−	15.8252i		−	0.502199i
$994$			0.180641i			0.00572958i
$995$			42.6340i			1.35159i
$996$	−14.9124			−0.472516
$997$			8.35969i			0.264754i	0.991199	+	0.132377i	$0.0422609\pi$
$997$			8.35969i			0.264754i	−0.991199	+	0.132377i	$0.957739\pi$
$998$	18.7121			0.592323
$999$	42.1798			1.33451

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.b.b.348.12	✓	26
349.348	even	2	inner	349.2.b.b.348.15	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.b.b.348.12	✓	26	1.1	even	1	trivial
349.2.b.b.348.15	yes	26	349.348	even	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.788732i q^{2} -0.670838 q^{3} +1.37790 q^{4} -1.84585 q^{5} +0.529112i q^{6} -0.0300147i q^{7} -2.66426i q^{8} -2.54998 q^{9} +O(q^{10})\)	\(q-0.788732i q^{2} -0.670838 q^{3} +1.37790 q^{4} -1.84585 q^{5} +0.529112i q^{6} -0.0300147i q^{7} -2.66426i q^{8} -2.54998 q^{9} +1.45588i q^{10} -3.59289i q^{11} -0.924348 q^{12} -6.25431i q^{13} -0.0236736 q^{14} +1.23826 q^{15} +0.654414 q^{16} +3.51955 q^{17} +2.01125i q^{18} +3.38809 q^{19} -2.54339 q^{20} +0.0201350i q^{21} -2.83383 q^{22} -1.78386 q^{23} +1.78729i q^{24} -1.59285 q^{25} -4.93297 q^{26} +3.72313 q^{27} -0.0413573i q^{28} -4.91079 q^{29} -0.976658i q^{30} -3.21062 q^{31} -5.84468i q^{32} +2.41025i q^{33} -2.77599i q^{34} +0.0554026i q^{35} -3.51362 q^{36} +11.3291 q^{37} -2.67230i q^{38} +4.19563i q^{39} +4.91781i q^{40} -8.41782 q^{41} +0.0158811 q^{42} +10.1802i q^{43} -4.95065i q^{44} +4.70686 q^{45} +1.40699i q^{46} -2.19423i q^{47} -0.439006 q^{48} +6.99910 q^{49} +1.25634i q^{50} -2.36105 q^{51} -8.61782i q^{52} +12.0535i q^{53} -2.93656i q^{54} +6.63193i q^{55} -0.0799671 q^{56} -2.27286 q^{57} +3.87330i q^{58} -9.14785i q^{59} +1.70620 q^{60} +0.831451i q^{61} +2.53232i q^{62} +0.0765369i q^{63} -3.30106 q^{64} +11.5445i q^{65} +1.90104 q^{66} -3.48029 q^{67} +4.84960 q^{68} +1.19668 q^{69} +0.0436978 q^{70} -7.63048i q^{71} +6.79380i q^{72} +8.96223 q^{73} -8.93563i q^{74} +1.06855 q^{75} +4.66846 q^{76} -0.107840 q^{77} +3.30923 q^{78} +9.94862i q^{79} -1.20795 q^{80} +5.15231 q^{81} +6.63941i q^{82} +16.1328 q^{83} +0.0277441i q^{84} -6.49655 q^{85} +8.02949 q^{86} +3.29435 q^{87} -9.57240 q^{88} +8.20545i q^{89} -3.71246i q^{90} -0.187721 q^{91} -2.45798 q^{92} +2.15381 q^{93} -1.73066 q^{94} -6.25390 q^{95} +3.92083i q^{96} +6.03521i q^{97} -5.52042i q^{98} +9.16179i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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