LMFDB - Embedded newform 363.3.b.n.122.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(122,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 290 x^{8} + 580 x^{7} + 3656 x^{6} + 5424 x^{5} + \cdots + 48312 $ x^12 - 4x^11 + 10x^10 - 12x^9 + 290x^8 + 580x^7 + 3656x^6 + 5424x^5 + 6124x^4 + 6920x^3 - 32528x^2 - 23952*x + 48312
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.5
Root			$-1.59440 + 0.311973i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.n.122.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89788i q^{2} +(-2.98373 - 0.311973i) q^{3} +0.398042 q^{4} +8.25850i q^{5} +(-0.592088 + 5.66278i) q^{6} -3.60566 q^{7} -8.34697i q^{8} +(8.80535 + 1.86169i) q^{9} +O(q^{10})$	\(q-1.89788i q^{2} +(-2.98373 - 0.311973i) q^{3} +0.398042 q^{4} +8.25850i q^{5} +(-0.592088 + 5.66278i) q^{6} -3.60566 q^{7} -8.34697i q^{8} +(8.80535 + 1.86169i) q^{9} +15.6737 q^{10} +(-1.18765 - 0.124178i) q^{12} -13.1106 q^{13} +6.84311i q^{14} +(2.57643 - 24.6412i) q^{15} -14.2494 q^{16} -25.6297i q^{17} +(3.53327 - 16.7115i) q^{18} -12.5064 q^{19} +3.28723i q^{20} +(10.7583 + 1.12487i) q^{21} -27.7941i q^{23} +(-2.60403 + 24.9051i) q^{24} -43.2029 q^{25} +24.8824i q^{26} +(-25.6920 - 8.30182i) q^{27} -1.43520 q^{28} -9.48941i q^{29} +(-46.7661 - 4.88976i) q^{30} -5.08780 q^{31} -6.34419i q^{32} -48.6422 q^{34} -29.7773i q^{35} +(3.50490 + 0.741031i) q^{36} -34.6432 q^{37} +23.7357i q^{38} +(39.1187 + 4.09017i) q^{39} +68.9334 q^{40} +34.2402i q^{41} +(2.13487 - 20.4180i) q^{42} +39.5371 q^{43} +(-15.3748 + 72.7190i) q^{45} -52.7499 q^{46} -19.4547i q^{47} +(42.5164 + 4.44543i) q^{48} -35.9992 q^{49} +81.9940i q^{50} +(-7.99578 + 76.4722i) q^{51} -5.21858 q^{52} +17.2882i q^{53} +(-15.7559 + 48.7604i) q^{54} +30.0963i q^{56} +(37.3158 + 3.90167i) q^{57} -18.0098 q^{58} +27.1498i q^{59} +(1.02553 - 9.80822i) q^{60} -43.7397 q^{61} +9.65605i q^{62} +(-31.7490 - 6.71262i) q^{63} -69.0381 q^{64} -108.274i q^{65} +82.0860 q^{67} -10.2017i q^{68} +(-8.67101 + 82.9302i) q^{69} -56.5139 q^{70} -117.008i q^{71} +(15.5395 - 73.4979i) q^{72} -107.556 q^{73} +65.7488i q^{74} +(128.906 + 13.4781i) q^{75} -4.97808 q^{76} +(7.76265 - 74.2426i) q^{78} -62.8893 q^{79} -117.679i q^{80} +(74.0682 + 32.7857i) q^{81} +64.9839 q^{82} -49.1246i q^{83} +(4.28226 + 0.447744i) q^{84} +211.663 q^{85} -75.0368i q^{86} +(-2.96044 + 28.3139i) q^{87} -69.1475i q^{89} +(138.012 + 29.1795i) q^{90} +47.2724 q^{91} -11.0632i q^{92} +(15.1806 + 1.58726i) q^{93} -36.9228 q^{94} -103.284i q^{95} +(-1.97922 + 18.9294i) q^{96} -16.0182 q^{97} +68.3223i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9}+O(q^{10}) $ 12 * q - 4 * q^3 - 44 * q^4 - 12 * q^9	$ 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9} - 80 q^{12} + 68 q^{15} + 92 q^{16} - 88 q^{25} - 232 q^{27} - 8 q^{31} + 116 q^{34} + 164 q^{36} - 244 q^{37} + 404 q^{42} - 52 q^{45} + 540 q^{48} + 100 q^{49} - 460 q^{58} + 24 q^{60} - 1276 q^{64} - 128 q^{67} + 128 q^{69} - 784 q^{70} + 684 q^{75} + 528 q^{78} + 348 q^{81} - 380 q^{82} + 120 q^{91} + 196 q^{93} - 156 q^{97}+O(q^{100}) $ 12 * q - 4 * q^3 - 44 * q^4 - 12 * q^9 - 80 * q^12 + 68 * q^15 + 92 * q^16 - 88 * q^25 - 232 * q^27 - 8 * q^31 + 116 * q^34 + 164 * q^36 - 244 * q^37 + 404 * q^42 - 52 * q^45 + 540 * q^48 + 100 * q^49 - 460 * q^58 + 24 * q^60 - 1276 * q^64 - 128 * q^67 + 128 * q^69 - 784 * q^70 + 684 * q^75 + 528 * q^78 + 348 * q^81 - 380 * q^82 + 120 * q^91 + 196 * q^93 - 156 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.89788i		−	0.948941i	−0.880271	−	0.474471i	$-0.842640\pi$
$2$		−	1.89788i		−	0.948941i	0.880271	−	0.474471i	$-0.157360\pi$
$3$	−2.98373	−	0.311973i	−0.994578	−	0.103991i
$3$	−2.98373	−	0.311973i	−0.994578	−	0.103991i
$4$	0.398042			0.0995104
$5$			8.25850i			1.65170i	0.563890	+	0.825850i	$0.309304\pi$
$5$			8.25850i			1.65170i	−0.563890	+	0.825850i	$0.690696\pi$
$6$	−0.592088	+	5.66278i	−0.0986814	+	0.943796i
$7$	−3.60566			−0.515094			−0.257547	−	0.966266i	$-0.582914\pi$
$7$	−3.60566			−0.515094			−0.257547	+	0.966266i	$0.582914\pi$
$8$		−	8.34697i		−	1.04337i
$9$	8.80535	+	1.86169i	0.978372	+	0.206854i
$10$	15.6737			1.56737
$11$		0			0
$11$		0			0
$12$	−1.18765	−	0.124178i	−0.0989709	−	0.0103482i
$13$	−13.1106			−1.00851			−0.504255	−	0.863555i	$-0.668233\pi$
$13$	−13.1106			−1.00851			−0.504255	+	0.863555i	$0.668233\pi$
$14$			6.84311i			0.488794i
$15$	2.57643	−	24.6412i	0.171762	−	1.64275i
$16$	−14.2494			−0.890587
$17$		−	25.6297i		−	1.50763i	−0.657087	−	0.753815i	$-0.728212\pi$
$17$		−	25.6297i		−	1.50763i	0.657087	−	0.753815i	$-0.271788\pi$
$18$	3.53327	−	16.7115i	0.196293	−	0.928417i
$19$	−12.5064			−0.658232			−0.329116	−	0.944289i	$-0.606751\pi$
$19$	−12.5064			−0.658232			−0.329116	+	0.944289i	$0.606751\pi$
$20$			3.28723i			0.164361i
$21$	10.7583	+	1.12487i	0.512301	+	0.0535651i
$22$		0			0
$23$		−	27.7941i		−	1.20844i	−0.796818	−	0.604219i	$-0.793485\pi$
$23$		−	27.7941i		−	1.20844i	0.796818	−	0.604219i	$-0.206515\pi$
$24$	−2.60403	+	24.9051i	−0.108501	+	1.03771i
$25$	−43.2029			−1.72811
$26$			24.8824i			0.957017i
$27$	−25.6920	−	8.30182i	−0.951556	−	0.307475i
$28$	−1.43520			−0.0512572
$29$		−	9.48941i		−	0.327221i	−0.986525	−	0.163611i	$-0.947686\pi$
$29$		−	9.48941i		−	0.327221i	0.986525	−	0.163611i	$-0.0523140\pi$
$30$	−46.7661	−	4.88976i	−1.55887	−	0.162992i
$31$	−5.08780			−0.164123			−0.0820613	−	0.996627i	$-0.526150\pi$
$31$	−5.08780			−0.164123			−0.0820613	+	0.996627i	$0.526150\pi$
$32$		−	6.34419i		−	0.198256i
$33$		0			0
$34$	−48.6422			−1.43065
$35$		−	29.7773i		−	0.850781i
$36$	3.50490	+	0.741031i	0.0973582	+	0.0205842i
$37$	−34.6432			−0.936303			−0.468152	−	0.883648i	$-0.655080\pi$
$37$	−34.6432			−0.936303			−0.468152	+	0.883648i	$0.655080\pi$
$38$			23.7357i			0.624624i
$39$	39.1187	+	4.09017i	1.00304	+	0.104876i
$40$	68.9334			1.72334
$41$			34.2402i			0.835127i	0.908648	+	0.417563i	$0.137116\pi$
$41$			34.2402i			0.835127i	−0.908648	+	0.417563i	$0.862884\pi$
$42$	2.13487	−	20.4180i	0.0508302	−	0.486144i
$43$	39.5371			0.919467			0.459734	−	0.888057i	$-0.347945\pi$
$43$	39.5371			0.919467			0.459734	+	0.888057i	$0.347945\pi$
$44$		0			0
$45$	−15.3748	+	72.7190i	−0.341662	+	1.61598i
$46$	−52.7499			−1.14674
$47$		−	19.4547i		−	0.413930i	−0.978348	−	0.206965i	$-0.933641\pi$
$47$		−	19.4547i		−	0.413930i	0.978348	−	0.206965i	$-0.0663587\pi$
$48$	42.5164	+	4.44543i	0.885759	+	0.0926131i
$49$	−35.9992			−0.734678
$50$			81.9940i			1.63988i
$51$	−7.99578	+	76.4722i	−0.156780	+	1.49946i
$52$	−5.21858			−0.100357
$53$			17.2882i			0.326192i	0.986610	+	0.163096i	$0.0521480\pi$
$53$			17.2882i			0.326192i	−0.986610	+	0.163096i	$0.947852\pi$
$54$	−15.7559	+	48.7604i	−0.291776	+	0.902971i
$55$		0			0
$56$			30.0963i			0.537434i
$57$	37.3158	+	3.90167i	0.654664	+	0.0684503i
$58$	−18.0098			−0.310514
$59$			27.1498i			0.460167i	0.973171	+	0.230083i	$0.0738999\pi$
$59$			27.1498i			0.460167i	−0.973171	+	0.230083i	$0.926100\pi$
$60$	1.02553	−	9.80822i	0.0170921	−	0.163470i
$61$	−43.7397			−0.717044			−0.358522	−	0.933521i	$-0.616719\pi$
$61$	−43.7397			−0.717044			−0.358522	+	0.933521i	$0.616719\pi$
$62$			9.65605i			0.155743i
$63$	−31.7490	−	6.71262i	−0.503953	−	0.106549i
$64$	−69.0381			−1.07872
$65$		−	108.274i		−	1.66576i
$66$		0			0
$67$	82.0860			1.22516			0.612582	−	0.790407i	$-0.290131\pi$
$67$	82.0860			1.22516			0.612582	+	0.790407i	$0.290131\pi$
$68$		−	10.2017i		−	0.150025i
$69$	−8.67101	+	82.9302i	−0.125667	+	1.20189i
$70$	−56.5139			−0.807341
$71$		−	117.008i		−	1.64800i	−0.566586	−	0.824002i	$-0.691736\pi$
$71$		−	117.008i		−	1.64800i	0.566586	−	0.824002i	$-0.308264\pi$
$72$	15.5395	−	73.4979i	0.215826	−	1.02080i
$73$	−107.556			−1.47337			−0.736683	−	0.676238i	$-0.763609\pi$
$73$	−107.556			−1.47337			−0.736683	+	0.676238i	$0.763609\pi$
$74$			65.7488i			0.888497i
$75$	128.906	+	13.4781i	1.71874	+	0.179708i
$76$	−4.97808			−0.0655010
$77$		0			0
$78$	7.76265	−	74.2426i	0.0995212	−	0.951828i
$79$	−62.8893			−0.796068			−0.398034	−	0.917371i	$-0.630307\pi$
$79$	−62.8893			−0.796068			−0.398034	+	0.917371i	$0.630307\pi$
$80$		−	117.679i		−	1.47098i
$81$	74.0682	+	32.7857i	0.914422	+	0.404761i
$82$	64.9839			0.792486
$83$		−	49.1246i		−	0.591862i	−0.955209	−	0.295931i	$-0.904370\pi$
$83$		−	49.1246i		−	0.591862i	0.955209	−	0.295931i	$-0.0956299\pi$
$84$	4.28226	+	0.447744i	0.0509793	+	0.00533029i
$85$	211.663			2.49015
$86$		−	75.0368i		−	0.872521i
$87$	−2.96044	+	28.3139i	−0.0340281	+	0.325447i
$88$		0			0
$89$		−	69.1475i		−	0.776938i	−0.921462	−	0.388469i	$-0.873004\pi$
$89$		−	69.1475i		−	0.776938i	0.921462	−	0.388469i	$-0.126996\pi$
$90$	138.012	+	29.1795i	1.53347	+	0.324217i
$91$	47.2724			0.519477
$92$		−	11.0632i		−	0.120252i
$93$	15.1806	+	1.58726i	0.163233	+	0.0170673i
$94$	−36.9228			−0.392795
$95$		−	103.284i		−	1.08720i
$96$	−1.97922	+	18.9294i	−0.0206168	+	0.197181i
$97$	−16.0182			−0.165136			−0.0825682	−	0.996585i	$-0.526312\pi$
$97$	−16.0182			−0.165136			−0.0825682	+	0.996585i	$0.526312\pi$
$98$			68.3223i			0.697167i
$99$		0			0
$100$	−17.1965			−0.171965
$101$			79.5876i			0.787996i	0.919111	+	0.393998i	$0.128908\pi$
$101$			79.5876i			0.787996i	−0.919111	+	0.393998i	$0.871092\pi$
$102$	145.135	+	15.1750i	1.42290	+	0.148775i
$103$	22.1291			0.214845			0.107423	−	0.994213i	$-0.465740\pi$
$103$	22.1291			0.214845			0.107423	+	0.994213i	$0.465740\pi$
$104$			109.434i			1.05225i
$105$	−9.28972	+	88.8476i	−0.0884736	+	0.846168i
$106$	32.8109			0.309537
$107$		−	200.970i		−	1.87823i	−0.343607	−	0.939114i	$-0.611649\pi$
$107$		−	200.970i		−	1.87823i	0.343607	−	0.939114i	$-0.388351\pi$
$108$	−10.2265	−	3.30447i	−0.0946898	−	0.0305970i
$109$	−31.8118			−0.291852			−0.145926	−	0.989296i	$-0.546616\pi$
$109$	−31.8118			−0.291852			−0.145926	+	0.989296i	$0.546616\pi$
$110$		0			0
$111$	103.366	+	10.8078i	0.931227	+	0.0973672i
$112$	51.3784			0.458736
$113$			95.2227i			0.842679i	0.906903	+	0.421339i	$0.138440\pi$
$113$			95.2227i			0.842679i	−0.906903	+	0.421339i	$0.861560\pi$
$114$	7.40490	−	70.8210i	0.0649553	−	0.621237i
$115$	229.537			1.99598
$116$		−	3.77718i		−	0.0325619i
$117$	−115.444	−	24.4079i	−0.986698	−	0.208615i
$118$	51.5272			0.436671
$119$			92.4119i			0.776571i
$120$	−205.679	−	21.5054i	−1.71399	−	0.179212i
$121$		0			0
$122$			83.0128i			0.680432i
$123$	10.6820	−	102.164i	0.0868457	−	0.830599i
$124$	−2.02516			−0.0163319
$125$		−	150.328i		−	1.20263i
$126$	−12.7398	+	60.2560i	−0.101109	+	0.478222i
$127$	−94.9399			−0.747558			−0.373779	−	0.927518i	$-0.621938\pi$
$127$	−94.9399			−0.747558			−0.373779	+	0.927518i	$0.621938\pi$
$128$			105.649i			0.825386i
$129$	−117.968	−	12.3345i	−0.914482	−	0.0956164i
$130$	−205.492			−1.58071
$131$			143.710i			1.09702i	0.836143	+	0.548511i	$0.184805\pi$
$131$			143.710i			1.09702i	−0.836143	+	0.548511i	$0.815195\pi$
$132$		0			0
$133$	45.0938			0.339051
$134$		−	155.790i		−	1.16261i
$135$	68.5606	−	212.178i	0.507856	−	1.57169i
$136$	−213.930			−1.57302
$137$			208.513i			1.52200i	0.648754	+	0.760998i	$0.275290\pi$
$137$			208.513i			1.52200i	−0.648754	+	0.760998i	$0.724710\pi$
$138$	157.392	+	16.4566i	1.14052	+	0.119250i
$139$	80.0972			0.576239			0.288119	−	0.957595i	$-0.406970\pi$
$139$	80.0972			0.576239			0.288119	+	0.957595i	$0.406970\pi$
$140$		−	11.8526i		−	0.0846616i
$141$	−6.06935	+	58.0477i	−0.0430450	+	0.411686i
$142$	−222.068			−1.56386
$143$		0			0
$144$	−125.471	−	26.5280i	−0.871325	−	0.184222i
$145$	78.3683			0.540471
$146$			204.128i			1.39814i
$147$	107.412	+	11.2308i	0.730695	+	0.0764000i
$148$	−13.7895			−0.0931720
$149$		−	94.4891i		−	0.634155i	−0.948400	−	0.317078i	$-0.897298\pi$
$149$		−	94.4891i		−	0.634155i	0.948400	−	0.317078i	$-0.102702\pi$
$150$	25.5799	−	244.648i	0.170533	−	1.63099i
$151$	182.072			1.20577			0.602887	−	0.797826i	$-0.294017\pi$
$151$	182.072			1.20577			0.602887	+	0.797826i	$0.294017\pi$
$152$			104.391i			0.686780i
$153$	47.7146	−	225.678i	0.311860	−	1.47502i
$154$		0			0
$155$		−	42.0176i		−	0.271081i
$156$	15.5709	+	1.62806i	0.0998132	+	0.0104363i
$157$	144.073			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$157$	144.073			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$158$			119.357i			0.755422i
$159$	5.39344	−	51.5833i	0.0339210	−	0.324423i
$160$	52.3935			0.327459
$161$			100.216i			0.622459i
$162$	62.2233	−	140.573i	0.384095	−	0.867733i
$163$	56.5652			0.347026			0.173513	−	0.984832i	$-0.444488\pi$
$163$	56.5652			0.347026			0.173513	+	0.984832i	$0.444488\pi$
$164$			13.6290i			0.0831038i
$165$		0			0
$166$	−93.2327			−0.561643
$167$			131.092i			0.784982i	0.919756	+	0.392491i	$0.128387\pi$
$167$			131.092i			0.784982i	−0.919756	+	0.392491i	$0.871613\pi$
$168$	9.38924	−	89.7994i	0.0558883	−	0.534520i
$169$	2.88870			0.0170929
$170$		−	401.711i		−	2.36301i
$171$	−110.123	−	23.2831i	−0.643996	−	0.136158i
$172$	15.7374			0.0914966
$173$			181.736i			1.05050i	0.850949	+	0.525248i	$0.176028\pi$
$173$			181.736i			1.05050i	−0.850949	+	0.525248i	$0.823972\pi$
$174$	53.7364	+	5.61857i	0.308830	+	0.0322906i
$175$	155.775			0.890141
$176$		0			0
$177$	8.47002	−	81.0079i	0.0478532	−	0.457672i
$178$	−131.234			−0.737269
$179$			11.9126i			0.0665507i	0.999446	+	0.0332754i	$0.0105938\pi$
$179$			11.9126i			0.0665507i	−0.999446	+	0.0332754i	$0.989406\pi$
$180$	−6.11980	+	28.9452i	−0.0339989	+	0.160807i
$181$	−84.7596			−0.468285			−0.234143	−	0.972202i	$-0.575228\pi$
$181$	−84.7596			−0.468285			−0.234143	+	0.972202i	$0.575228\pi$
$182$		−	89.7175i		−	0.492953i
$183$	130.508	+	13.6456i	0.713156	+	0.0745661i
$184$	−231.996			−1.26085
$185$		−	286.101i		−	1.54649i
$186$	3.01243	−	28.8111i	0.0161958	−	0.154898i
$187$		0			0
$188$		−	7.74379i		−	0.0411904i
$189$	92.6366	+	29.9335i	0.490141	+	0.158378i
$190$	−196.021			−1.03169
$191$		−	69.0031i		−	0.361273i	−0.983550	−	0.180636i	$-0.942184\pi$
$191$		−	69.0031i		−	0.361273i	0.983550	−	0.180636i	$-0.0578157\pi$
$192$	205.991	+	21.5380i	1.07287	+	0.112177i
$193$	−118.824			−0.615670			−0.307835	−	0.951440i	$-0.599604\pi$
$193$	−118.824			−0.615670			−0.307835	+	0.951440i	$0.599604\pi$
$194$			30.4007i			0.156705i
$195$	−33.7786	+	323.061i	−0.173224	+	1.65673i
$196$	−14.3292			−0.0731082
$197$			305.098i			1.54872i	0.632744	+	0.774361i	$0.281929\pi$
$197$			305.098i			1.54872i	−0.632744	+	0.774361i	$0.718071\pi$
$198$		0			0
$199$	125.117			0.628727			0.314364	−	0.949303i	$-0.398209\pi$
$199$	125.117			0.628727			0.314364	+	0.949303i	$0.398209\pi$
$200$			360.613i			1.80306i
$201$	−244.923	−	25.6086i	−1.21852	−	0.127406i
$202$	151.048			0.747762
$203$			34.2156i			0.168550i
$204$	−3.18265	+	30.4391i	−0.0156012	+	0.149211i
$205$	−282.773			−1.37938
$206$		−	41.9984i		−	0.203876i
$207$	51.7440	−	244.736i	0.249971	−	1.18230i
$208$	186.819			0.898166
$209$		0			0
$210$	168.622	+	17.6308i	0.802964	+	0.0839562i
$211$	−206.404			−0.978218			−0.489109	−	0.872223i	$-0.662678\pi$
$211$	−206.404			−0.978218			−0.489109	+	0.872223i	$0.662678\pi$
$212$			6.88141i			0.0324595i
$213$	−36.5035	+	349.122i	−0.171378	+	1.63907i
$214$	−381.418			−1.78233
$215$			326.517i			1.51868i
$216$	−69.2950	+	214.450i	−0.320810	+	0.992826i
$217$	18.3449			0.0845385
$218$			60.3751i			0.276950i
$219$	320.918	+	33.5545i	1.46538	+	0.153217i
$220$		0			0
$221$			336.022i			1.52046i
$222$	20.5119	−	196.177i	0.0923957	−	0.883680i
$223$	−69.1464			−0.310073			−0.155037	−	0.987909i	$-0.549550\pi$
$223$	−69.1464			−0.310073			−0.155037	+	0.987909i	$0.549550\pi$
$224$			22.8750i			0.102120i
$225$	−380.416	−	80.4303i	−1.69074	−	0.357468i
$226$	180.722			0.799653
$227$			99.6917i			0.439171i	0.975593	+	0.219585i	$0.0704704\pi$
$227$			99.6917i			0.439171i	−0.975593	+	0.219585i	$0.929530\pi$
$228$	14.8533	+	1.55303i	0.0651459	+	0.00681152i
$229$	248.362			1.08455			0.542276	−	0.840201i	$-0.317563\pi$
$229$	248.362			1.08455			0.542276	+	0.840201i	$0.317563\pi$
$230$		−	435.635i		−	1.89407i
$231$		0			0
$232$	−79.2078			−0.341413
$233$		−	290.908i		−	1.24853i	−0.781212	−	0.624265i	$-0.785398\pi$
$233$		−	290.908i		−	1.24853i	0.781212	−	0.624265i	$-0.214602\pi$
$234$	−46.3234	+	219.098i	−0.197963	+	0.936318i
$235$	160.667			0.683689
$236$			10.8068i			0.0457914i
$237$	187.645	+	19.6198i	0.791752	+	0.0827839i
$238$	175.387			0.736920
$239$		−	104.939i		−	0.439074i	−0.975604	−	0.219537i	$-0.929545\pi$
$239$		−	104.939i		−	0.439074i	0.975604	−	0.219537i	$-0.0704546\pi$
$240$	−36.7126	+	351.122i	−0.152969	+	1.46301i
$241$	88.3764			0.366707			0.183354	−	0.983047i	$-0.441305\pi$
$241$	88.3764			0.366707			0.183354	+	0.983047i	$0.441305\pi$
$242$		0			0
$243$	−210.772	−	120.931i	−0.867373	−	0.497658i
$244$	−17.4102			−0.0713534
$245$		−	297.300i		−	1.21347i
$246$	−193.895	−	20.2732i	−0.788190	−	0.0824115i
$247$	163.967			0.663834
$248$			42.4677i			0.171241i
$249$	−15.3255	+	146.575i	−0.0615484	+	0.588653i
$250$	−285.306			−1.14122
$251$		−	6.34574i		−	0.0252818i	−0.999920	−	0.0126409i	$-0.995976\pi$
$251$		−	6.34574i		−	0.0252818i	0.999920	−	0.0126409i	$-0.00402383\pi$
$252$	−12.6374	−	2.67190i	−0.0501486	−	0.0106028i
$253$		0			0
$254$			180.185i			0.709389i
$255$	−631.546	−	66.0332i	−2.47665	−	0.258954i
$256$	−75.6421			−0.295477
$257$		−	179.734i		−	0.699355i	−0.936870	−	0.349678i	$-0.886291\pi$
$257$		−	179.734i		−	0.699355i	0.936870	−	0.349678i	$-0.113709\pi$
$258$	−23.4095	+	223.890i	−0.0907343	+	0.867790i
$259$	124.912			0.482284
$260$		−	43.0977i		−	0.165760i
$261$	17.6663	−	83.5576i	0.0676872	−	0.320144i
$262$	272.745			1.04101
$263$		−	289.307i		−	1.10003i	−0.835156	−	0.550013i	$-0.814623\pi$
$263$		−	289.307i		−	1.10003i	0.835156	−	0.550013i	$-0.185377\pi$
$264$		0			0
$265$	−142.774			−0.538771
$266$		−	85.5828i		−	0.321740i
$267$	−21.5722	+	206.318i	−0.0807946	+	0.772726i
$268$	32.6737			0.121917
$269$			89.4021i			0.332350i	0.986096	+	0.166175i	$0.0531416\pi$
$269$			89.4021i			0.332350i	−0.986096	+	0.166175i	$0.946858\pi$
$270$	−402.688	−	130.120i	−1.49144	−	0.481926i
$271$	272.104			1.00407			0.502037	−	0.864846i	$-0.332584\pi$
$271$	272.104			1.00407			0.502037	+	0.864846i	$0.332584\pi$
$272$			365.208i			1.34268i
$273$	−141.048	−	14.7477i	−0.516661	−	0.0540210i
$274$	395.734			1.44428
$275$		0			0
$276$	−3.45142	+	33.0097i	−0.0125052	+	0.119600i
$277$	457.600			1.65199			0.825994	−	0.563679i	$-0.190615\pi$
$277$	457.600			1.65199			0.825994	+	0.563679i	$0.190615\pi$
$278$		−	152.015i		−	0.546817i
$279$	−44.7998	−	9.47191i	−0.160573	−	0.0339495i
$280$	−248.550			−0.887680
$281$			20.0841i			0.0714737i	0.999361	+	0.0357368i	$0.0113778\pi$
$281$			20.0841i			0.0714737i	−0.999361	+	0.0357368i	$0.988622\pi$
$282$	110.168	+	11.5189i	0.390666	+	0.0408472i
$283$	−511.601			−1.80778			−0.903888	−	0.427769i	$-0.859300\pi$
$283$	−511.601			−1.80778			−0.903888	+	0.427769i	$0.859300\pi$
$284$		−	46.5742i		−	0.163994i
$285$	−32.2219	+	308.173i	−0.113059	+	1.08131i
$286$		0			0
$287$		−	123.458i		−	0.430169i
$288$	11.8109	−	55.8628i	0.0410101	−	0.193968i
$289$	−367.882			−1.27295
$290$		−	148.734i		−	0.512876i
$291$	47.7941	+	4.99726i	0.164241	+	0.0171727i
$292$	−42.8117			−0.146615
$293$		−	493.954i		−	1.68585i	−0.538031	−	0.842925i	$-0.680832\pi$
$293$		−	493.954i		−	1.68585i	0.538031	−	0.842925i	$-0.319168\pi$
$294$	21.3147	−	203.856i	0.0724991	−	0.693387i
$295$	−224.217			−0.760058
$296$			289.166i			0.976912i
$297$		0			0
$298$	−179.329			−0.601776
$299$			364.398i			1.21872i
$300$	51.3099	+	5.36486i	0.171033	+	0.0178829i
$301$	−142.557			−0.473612
$302$		−	345.551i		−	1.14421i
$303$	24.8292	−	237.468i	0.0819445	−	0.783724i
$304$	178.209			0.586213
$305$		−	361.224i		−	1.18434i
$306$	−428.311	−	90.5566i	−1.39971	−	0.295937i
$307$	−560.423			−1.82548			−0.912741	−	0.408540i	$-0.866038\pi$
$307$	−560.423			−1.82548			−0.912741	+	0.408540i	$0.866038\pi$
$308$		0			0
$309$	−66.0273	−	6.90367i	−0.213680	−	0.0223420i
$310$	−79.7445			−0.257240
$311$			432.081i			1.38933i	0.719334	+	0.694665i	$0.244447\pi$
$311$			432.081i			1.38933i	−0.719334	+	0.694665i	$0.755553\pi$
$312$	34.1405	−	326.522i	0.109425	−	1.04655i
$313$	−156.126			−0.498805			−0.249403	−	0.968400i	$-0.580234\pi$
$313$	−156.126			−0.498805			−0.249403	+	0.968400i	$0.580234\pi$
$314$		−	273.434i		−	0.870808i
$315$	55.4361	−	262.200i	0.175988	−	0.832380i
$316$	−25.0326			−0.0792171
$317$			338.492i			1.06780i	0.845549	+	0.533898i	$0.179273\pi$
$317$			338.492i			1.06780i	−0.845549	+	0.533898i	$0.820727\pi$
$318$	−97.8990	−	10.2361i	−0.307858	−	0.0321890i
$319$		0			0
$320$		−	570.151i		−	1.78172i
$321$	−62.6973	+	599.642i	−0.195319	+	1.86804i
$322$	190.198			0.590677
$323$			320.536i			0.992370i
$324$	29.4822	+	13.0501i	0.0909946	+	0.0402780i
$325$	566.417			1.74282
$326$		−	107.354i		−	0.329307i
$327$	94.9181	+	9.92444i	0.290269	+	0.0303500i
$328$	285.802			0.871347
$329$			70.1470i			0.213213i
$330$		0			0
$331$	26.2867			0.0794161			0.0397081	−	0.999211i	$-0.487357\pi$
$331$	26.2867			0.0794161			0.0397081	+	0.999211i	$0.487357\pi$
$332$		−	19.5536i		−	0.0588965i
$333$	−305.046	−	64.4949i	−0.916053	−	0.193679i
$334$	248.797			0.744902
$335$			677.907i			2.02360i
$336$	−153.300	−	16.0287i	−0.456249	−	0.0477044i
$337$	−309.314			−0.917847			−0.458923	−	0.888476i	$-0.651765\pi$
$337$	−309.314			−0.917847			−0.458923	+	0.888476i	$0.651765\pi$
$338$		−	5.48242i		−	0.0162202i
$339$	29.7069	−	284.119i	0.0876311	−	0.838110i
$340$	84.2507			0.247796
$341$		0			0
$342$	−44.1885	+	209.001i	−0.129206	+	0.611114i
$343$	306.478			0.893522
$344$		−	330.015i		−	0.959346i
$345$	−684.879	−	71.6095i	−1.98516	−	0.207564i
$346$	344.914			0.996860
$347$		−	27.1134i		−	0.0781367i	−0.999237	−	0.0390683i	$-0.987561\pi$
$347$		−	27.1134i		−	0.0781367i	0.999237	−	0.0390683i	$-0.0124390\pi$
$348$	−1.17838	+	11.2701i	−0.00338615	+	0.0323854i
$349$	−3.94875			−0.0113145			−0.00565723	−	0.999984i	$-0.501801\pi$
$349$	−3.94875			−0.0113145			−0.00565723	+	0.999984i	$0.501801\pi$
$350$		−	295.642i		−	0.844691i
$351$	336.839	+	108.842i	0.959654	+	0.310092i
$352$		0			0
$353$		−	580.275i		−	1.64384i	−0.569603	−	0.821920i	$-0.692903\pi$
$353$		−	580.275i		−	1.64384i	0.569603	−	0.821920i	$-0.307097\pi$
$354$	−153.744	−	16.0751i	−0.434304	−	0.0454099i
$355$	966.314			2.72201
$356$		−	27.5236i		−	0.0773135i
$357$	28.8300	−	275.733i	0.0807564	−	0.772360i
$358$	22.6087			0.0631527
$359$		−	73.2374i		−	0.204004i	−0.994784	−	0.102002i	$-0.967475\pi$
$359$		−	73.2374i		−	0.204004i	0.994784	−	0.102002i	$-0.0325248\pi$
$360$	606.983	+	128.333i	1.68606	+	0.356480i
$361$	−204.590			−0.566730
$362$			160.864i			0.444375i
$363$		0			0
$364$	18.8164			0.0516934
$365$		−	888.249i		−	2.43356i
$366$	25.8978	−	247.688i	0.0707589	−	0.676743i
$367$	326.075			0.888489			0.444244	−	0.895906i	$-0.353472\pi$
$367$	326.075			0.888489			0.444244	+	0.895906i	$0.353472\pi$
$368$			396.049i			1.07622i
$369$	−63.7446	+	301.497i	−0.172750	+	0.817064i
$370$	−542.986			−1.46753
$371$		−	62.3351i		−	0.168019i
$372$	6.04253	+	0.631795i	0.0162434	+	0.00169837i
$373$	−599.517			−1.60728			−0.803642	−	0.595113i	$-0.797107\pi$
$373$	−599.517			−1.60728			−0.803642	+	0.595113i	$0.797107\pi$
$374$		0			0
$375$	−46.8984	+	448.540i	−0.125062	+	1.19611i
$376$	−162.388			−0.431883
$377$			124.412i			0.330006i
$378$	56.8103	−	175.813i	0.150292	−	0.465115i
$379$	14.8149			0.0390895			0.0195447	−	0.999809i	$-0.493778\pi$
$379$	14.8149			0.0390895			0.0195447	+	0.999809i	$0.493778\pi$
$380$		−	41.1114i		−	0.108188i
$381$	283.275	+	29.6187i	0.743505	+	0.0777393i
$382$	−130.960			−0.342827
$383$			457.401i			1.19426i	0.802145	+	0.597129i	$0.203692\pi$
$383$			457.401i			1.19426i	−0.802145	+	0.597129i	$0.796308\pi$
$384$	32.9598	−	315.230i	0.0858328	−	0.820911i
$385$		0			0
$386$			225.515i			0.584235i
$387$	348.138	+	73.6058i	0.899581	+	0.190196i
$388$	−6.37592			−0.0164328
$389$			275.688i			0.708710i	0.935111	+	0.354355i	$0.115300\pi$
$389$			275.688i			0.708710i	−0.935111	+	0.354355i	$0.884700\pi$
$390$	613.133	+	64.1079i	1.57214	+	0.164379i
$391$	−712.354			−1.82188
$392$			300.484i			0.766542i
$393$	44.8337	−	428.793i	0.114081	−	1.09108i
$394$	579.041			1.46965
$395$		−	519.372i		−	1.31487i
$396$		0			0
$397$	582.127			1.46632			0.733158	−	0.680059i	$-0.238046\pi$
$397$	582.127			1.46632			0.733158	+	0.680059i	$0.238046\pi$
$398$		−	237.457i		−	0.596625i
$399$	−134.548	−	14.0681i	−0.337213	−	0.0352583i
$400$	615.615			1.53904
$401$		−	436.175i		−	1.08772i	−0.839177	−	0.543859i	$-0.816963\pi$
$401$		−	436.175i		−	1.08772i	0.839177	−	0.543859i	$-0.183037\pi$
$402$	−48.6022	+	464.835i	−0.120901	+	1.15631i
$403$	66.7043			0.165519
$404$			31.6792i			0.0784138i
$405$	−270.760	+	611.693i	−0.668544	+	1.51035i
$406$	64.9371			0.159944
$407$		0			0
$408$	638.311	+	66.7405i	1.56449	+	0.163580i
$409$	293.978			0.718773			0.359386	−	0.933189i	$-0.382986\pi$
$409$	293.978			0.718773			0.359386	+	0.933189i	$0.382986\pi$
$410$			536.669i			1.30895i
$411$	65.0506	−	622.149i	0.158274	−	1.51374i
$412$	8.80829			0.0213794
$413$		−	97.8930i		−	0.237029i
$414$	−464.481	−	98.2040i	−1.12194	−	0.237208i
$415$	405.695			0.977579
$416$			83.1763i			0.199943i
$417$	−238.989	−	24.9882i	−0.573114	−	0.0599237i
$418$		0			0
$419$			484.652i			1.15669i	0.815793	+	0.578344i	$0.196301\pi$
$419$			484.652i			1.15669i	−0.815793	+	0.578344i	$0.803699\pi$
$420$	−3.69770	+	35.3651i	−0.00880404	+	0.0842025i
$421$	−52.2706			−0.124158			−0.0620791	−	0.998071i	$-0.519773\pi$
$421$	−52.2706			−0.124158			−0.0620791	+	0.998071i	$0.519773\pi$
$422$			391.731i			0.928271i
$423$	36.2187	−	171.306i	0.0856233	−	0.404978i
$424$	144.304			0.340339
$425$			1107.28i			2.60536i
$426$	662.592	+	69.2793i	1.55538	+	0.162627i
$427$	157.710			0.369345
$428$		−	79.9946i		−	0.186903i
$429$		0			0
$430$	619.691			1.44114
$431$			209.726i			0.486603i	0.969951	+	0.243302i	$0.0782305\pi$
$431$			209.726i			0.486603i	−0.969951	+	0.243302i	$0.921770\pi$
$432$	366.096	+	118.296i	0.847444	+	0.273833i
$433$	−362.262			−0.836634			−0.418317	−	0.908301i	$-0.637380\pi$
$433$	−362.262			−0.836634			−0.418317	+	0.908301i	$0.637380\pi$
$434$		−	34.8164i		−	0.0802221i
$435$	−233.830	−	24.4488i	−0.537541	−	0.0562042i
$436$	−12.6624			−0.0290423
$437$			347.604i			0.795433i
$438$	63.6825	−	609.064i	0.145394	−	1.39056i
$439$	−414.518			−0.944233			−0.472116	−	0.881536i	$-0.656510\pi$
$439$	−414.518			−0.944233			−0.472116	+	0.881536i	$0.656510\pi$
$440$		0			0
$441$	−316.986	−	67.0194i	−0.718789	−	0.151972i
$442$	637.730			1.44283
$443$		−	772.276i		−	1.74329i	−0.490142	−	0.871643i	$-0.663055\pi$
$443$		−	772.276i		−	1.74329i	0.490142	−	0.871643i	$-0.336945\pi$
$444$	41.1441	+	4.30194i	0.0926668	+	0.00968905i
$445$	571.055			1.28327
$446$			131.232i			0.294241i
$447$	−29.4781	+	281.930i	−0.0659465	+	0.630717i
$448$	248.928			0.555642
$449$		−	674.192i		−	1.50154i	−0.660563	−	0.750771i	$-0.729682\pi$
$449$		−	674.192i		−	1.50154i	0.660563	−	0.750771i	$-0.270318\pi$
$450$	−152.647	+	721.985i	−0.339216	+	1.60441i
$451$		0			0
$452$			37.9026i			0.0838553i
$453$	−543.254	−	56.8016i	−1.19924	−	0.125390i
$454$	189.203			0.416747
$455$			390.400i			0.858021i
$456$	32.5671	−	311.474i	0.0714190	−	0.683057i
$457$	844.966			1.84894			0.924470	−	0.381255i	$-0.124508\pi$
$457$	844.966			1.84894			0.924470	+	0.381255i	$0.124508\pi$
$458$		−	471.363i		−	1.02918i
$459$	−212.773	+	658.479i	−0.463558	+	1.43459i
$460$	91.3655			0.198621
$461$			282.181i			0.612107i	0.952014	+	0.306054i	$0.0990087\pi$
$461$			282.181i			0.612107i	−0.952014	+	0.306054i	$0.900991\pi$
$462$		0			0
$463$	−732.770			−1.58266			−0.791329	−	0.611391i	$-0.790610\pi$
$463$	−732.770			−1.58266			−0.791329	+	0.611391i	$0.790610\pi$
$464$			135.218i			0.291419i
$465$	−13.1084	+	125.369i	−0.0281900	+	0.269612i
$466$	−552.109			−1.18478
$467$		−	459.059i		−	0.982996i	−0.870879	−	0.491498i	$-0.836449\pi$
$467$		−	459.059i		−	0.982996i	0.870879	−	0.491498i	$-0.163551\pi$
$468$	−45.9514	−	9.71538i	−0.0981868	−	0.0207594i
$469$	−295.974			−0.631074
$470$		−	304.927i		−	0.648780i
$471$	−429.876	−	44.9469i	−0.912687	−	0.0954287i
$472$	226.619			0.480125
$473$		0			0
$474$	37.2361	−	356.128i	0.0785571	−	0.751326i
$475$	540.313			1.13750
$476$			36.7838i			0.0772769i
$477$	−32.1852	+	152.228i	−0.0674742	+	0.319137i
$478$	−199.161			−0.416655
$479$		−	285.861i		−	0.596787i	−0.954443	−	0.298393i	$-0.903549\pi$
$479$		−	285.861i		−	0.596787i	0.954443	−	0.298393i	$-0.0964507\pi$
$480$	−156.328	−	16.3454i	−0.325684	−	0.0340528i
$481$	454.195			0.944271
$482$		−	167.728i		−	0.347983i
$483$	31.2647	−	299.018i	0.0647302	−	0.619084i
$484$		0			0
$485$		−	132.287i		−	0.272756i
$486$	−229.513	+	400.020i	−0.472249	+	0.823086i
$487$	724.781			1.48826			0.744128	−	0.668037i	$-0.232865\pi$
$487$	724.781			1.48826			0.744128	+	0.668037i	$0.232865\pi$
$488$			365.094i			0.748143i
$489$	−168.776	−	17.6468i	−0.345144	−	0.0360876i
$490$	−564.240			−1.15151
$491$		−	615.334i		−	1.25323i	−0.779330	−	0.626613i	$-0.784441\pi$
$491$		−	615.334i		−	1.25323i	0.779330	−	0.626613i	$-0.215559\pi$
$492$	4.25189	−	40.6654i	0.00864206	−	0.0826533i
$493$	−243.211			−0.493328
$494$		−	311.190i		−	0.629940i
$495$		0			0
$496$	72.4981			0.146165
$497$			421.892i			0.848877i
$498$	278.182	+	29.0861i	0.558597	+	0.0584058i
$499$	737.017			1.47699			0.738494	−	0.674260i	$-0.235537\pi$
$499$	737.017			1.47699			0.738494	+	0.674260i	$0.235537\pi$
$500$		−	59.8370i		−	0.119674i
$501$	40.8972	−	391.144i	0.0816311	−	0.780726i
$502$	−12.0435			−0.0239910
$503$			800.853i			1.59215i	0.605196	+	0.796076i	$0.293095\pi$
$503$			800.853i			1.59215i	−0.605196	+	0.796076i	$0.706905\pi$
$504$	−56.0300	+	265.008i	−0.111171	+	0.525810i
$505$	−657.274			−1.30153
$506$		0			0
$507$	−8.61912	−	0.901198i	−0.0170002	−	0.00177751i
$508$	−37.7900			−0.0743898
$509$		−	372.727i		−	0.732273i	−0.930561	−	0.366137i	$-0.880680\pi$
$509$		−	372.727i		−	0.732273i	0.930561	−	0.366137i	$-0.119320\pi$
$510$	−125.323	+	1198.60i	−0.245732	+	2.35020i
$511$	387.809			0.758922
$512$			566.158i			1.10578i
$513$	321.315	+	103.826i	0.626345	+	0.202390i
$514$	−341.115			−0.663647
$515$			182.753i			0.354860i
$516$	−46.9563	−	4.90965i	−0.0910005	−	0.00951483i
$517$		0			0
$518$		−	237.067i		−	0.457659i
$519$	56.6967	−	542.252i	0.109242	−	1.04480i
$520$	−903.761			−1.73800
$521$		−	758.547i		−	1.45595i	−0.685606	−	0.727973i	$-0.740463\pi$
$521$		−	758.547i		−	1.45595i	0.685606	−	0.727973i	$-0.259537\pi$
$522$	−158.582	−	33.5287i	−0.303798	−	0.0642311i
$523$	−129.733			−0.248055			−0.124028	−	0.992279i	$-0.539581\pi$
$523$	−129.733			−0.248055			−0.124028	+	0.992279i	$0.539581\pi$
$524$			57.2026i			0.109165i
$525$	−464.790	−	48.5975i	−0.885315	−	0.0925667i
$526$	−549.071			−1.04386
$527$			130.399i			0.247436i
$528$		0			0
$529$	−243.511			−0.460323
$530$			270.969i			0.511262i
$531$	−50.5446	+	239.064i	−0.0951875	+	0.450214i
$532$	17.9492			0.0337392
$533$		−	448.911i		−	0.842234i
$534$	391.567	+	40.9414i	0.733271	+	0.0766693i
$535$	1659.71			3.10227
$536$		−	685.169i		−	1.27830i
$537$	3.71641	−	35.5440i	0.00692068	−	0.0661899i
$538$	169.675			0.315380
$539$		0			0
$540$	27.2900	−	84.4555i	0.0505370	−	0.156399i
$541$	−787.477			−1.45560			−0.727798	−	0.685792i	$-0.759456\pi$
$541$	−787.477			−1.45560			−0.727798	+	0.685792i	$0.759456\pi$
$542$		−	516.421i		−	0.952807i
$543$	252.900	+	26.4427i	0.465746	+	0.0486975i
$544$	−162.600			−0.298896
$545$		−	262.718i		−	0.482052i
$546$	−27.9895	+	267.693i	−0.0512628	+	0.490281i
$547$	−721.547			−1.31910			−0.659549	−	0.751661i	$-0.729253\pi$
$547$	−721.547			−1.31910			−0.659549	+	0.751661i	$0.729253\pi$
$548$			82.9971i			0.151455i
$549$	−385.143	−	81.4297i	−0.701535	−	0.148324i
$550$		0			0
$551$			118.679i			0.215388i
$552$	692.215	+	72.3766i	1.25401	+	0.131117i
$553$	226.757			0.410050
$554$		−	868.472i		−	1.56764i
$555$	−89.2559	+	853.650i	−0.160821	+	1.53811i
$556$	31.8820			0.0573418
$557$		−	546.419i		−	0.981003i	−0.871440	−	0.490501i	$-0.836814\pi$
$557$		−	546.419i		−	0.981003i	0.871440	−	0.490501i	$-0.163186\pi$
$558$	−17.9766	+	85.0248i	−0.0322161	+	0.152374i
$559$	−518.356			−0.927292
$560$			424.309i			0.757694i
$561$		0			0
$562$	38.1173			0.0678243
$563$		−	509.933i		−	0.905742i	−0.891576	−	0.452871i	$-0.850400\pi$
$563$		−	509.933i		−	0.905742i	0.891576	−	0.452871i	$-0.149600\pi$
$564$	−2.41586	+	23.1054i	−0.00428343	+	0.0409671i
$565$	−786.397			−1.39185
$566$			970.958i			1.71547i
$567$	−267.065	−	118.214i	−0.471013	−	0.208490i
$568$	−976.665			−1.71948
$569$		−	86.6541i		−	0.152292i	−0.997097	−	0.0761459i	$-0.975739\pi$
$569$		−	86.6541i		−	0.152292i	0.997097	−	0.0761459i	$-0.0242615\pi$
$570$	584.876	+	61.1534i	1.02610	+	0.107287i
$571$	773.591			1.35480			0.677400	−	0.735615i	$-0.263107\pi$
$571$	773.591			1.35480			0.677400	+	0.735615i	$0.263107\pi$
$572$		0			0
$573$	−21.5271	+	205.887i	−0.0375691	+	0.359314i
$574$	−234.310			−0.408205
$575$			1200.78i			2.08832i
$576$	−607.904	−	128.528i	−1.05539	−	0.223138i
$577$	−307.315			−0.532609			−0.266304	−	0.963889i	$-0.585803\pi$
$577$	−307.315			−0.532609			−0.266304	+	0.963889i	$0.585803\pi$
$578$			698.196i			1.20795i
$579$	354.540	+	37.0700i	0.612332	+	0.0640242i
$580$	31.1939			0.0537825
$581$			177.126i			0.304865i
$582$	9.48420	−	90.7076i	0.0162959	−	0.155855i
$583$		0			0
$584$			897.764i			1.53727i
$585$	201.573	−	953.392i	0.344569	−	1.62973i
$586$	−937.467			−1.59977
$587$		−	1025.95i		−	1.74779i	−0.486113	−	0.873896i	$-0.661586\pi$
$587$		−	1025.95i		−	1.74779i	0.486113	−	0.873896i	$-0.338414\pi$
$588$	42.7545	+	4.47033i	0.0727118	+	0.00760260i
$589$	63.6301			0.108031
$590$			425.538i			0.721250i
$591$	95.1825	−	910.332i	0.161053	−	1.54033i
$592$	493.645			0.833860
$593$		−	570.008i		−	0.961227i	−0.876933	−	0.480613i	$-0.840414\pi$
$593$		−	570.008i		−	0.961227i	0.876933	−	0.480613i	$-0.159586\pi$
$594$		0			0
$595$	−763.184			−1.28266
$596$		−	37.6106i		−	0.0631051i
$597$	−373.315	−	39.0331i	−0.625318	−	0.0653820i
$598$	691.585			1.15650
$599$		−	539.056i		−	0.899927i	−0.893047	−	0.449963i	$-0.851437\pi$
$599$		−	539.056i		−	0.899927i	0.893047	−	0.449963i	$-0.148563\pi$
$600$	112.502	−	1075.97i	0.187503	−	1.79329i
$601$	−597.502			−0.994179			−0.497090	−	0.867699i	$-0.665598\pi$
$601$	−597.502			−0.994179			−0.497090	+	0.867699i	$0.665598\pi$
$602$			270.557i			0.449430i
$603$	722.795	+	152.819i	1.19867	+	0.253431i
$604$	72.4722			0.119987
$605$		0			0
$606$	−450.687	−	47.1229i	−0.743708	−	0.0777605i
$607$	−626.939			−1.03285			−0.516424	−	0.856333i	$-0.672737\pi$
$607$	−626.939			−1.03285			−0.516424	+	0.856333i	$0.672737\pi$
$608$			79.3430i			0.130498i
$609$	10.6743	−	102.090i	0.0175276	−	0.167636i
$610$	−685.561			−1.12387
$611$			255.064i			0.417453i
$612$	18.9924	−	89.8294i	0.0310333	−	0.146780i
$613$	−180.077			−0.293763			−0.146881	−	0.989154i	$-0.546924\pi$
$613$	−180.077			−0.293763			−0.146881	+	0.989154i	$0.546924\pi$
$614$			1063.62i			1.73227i
$615$	843.719	+	88.2175i	1.37190	+	0.143443i
$616$		0			0
$617$			466.729i			0.756449i	0.925714	+	0.378225i	$0.123465\pi$
$617$			466.729i			0.756449i	−0.925714	+	0.378225i	$0.876535\pi$
$618$	−13.1024	+	125.312i	−0.0212012	+	0.202770i
$619$	350.279			0.565878			0.282939	−	0.959138i	$-0.408691\pi$
$619$	350.279			0.565878			0.282939	+	0.959138i	$0.408691\pi$
$620$		−	16.7248i		−	0.0269754i
$621$	−230.741	+	714.086i	−0.371564	+	1.14990i
$622$	820.040			1.31839
$623$			249.322i			0.400196i
$624$	−557.417	−	58.2824i	−0.893297	−	0.0934013i
$625$	161.415			0.258265
$626$			296.309i			0.473337i
$627$		0			0
$628$	57.3471			0.0913170
$629$			887.895i			1.41160i
$630$	−497.624	−	105.211i	−0.789879	−	0.167002i
$631$	−1043.41			−1.65358			−0.826790	−	0.562511i	$-0.809836\pi$
$631$	−1043.41			−1.65358			−0.826790	+	0.562511i	$0.809836\pi$
$632$			524.935i			0.830594i
$633$	615.855	+	64.3925i	0.972914	+	0.101726i
$634$	642.417			1.01328
$635$		−	784.061i		−	1.23474i
$636$	2.14681	−	20.5323i	0.00337549	−	0.0322835i
$637$	471.973			0.740931
$638$		0			0
$639$	217.833	−	1030.30i	0.340897	−	1.61236i
$640$	−872.506			−1.36329
$641$			84.2580i			0.131448i	0.997838	+	0.0657239i	$0.0209356\pi$
$641$			84.2580i			0.131448i	−0.997838	+	0.0657239i	$0.979064\pi$
$642$	1138.05	+	118.992i	1.77266	+	0.185346i
$643$	−398.321			−0.619473			−0.309737	−	0.950822i	$-0.600241\pi$
$643$	−398.321			−0.619473			−0.309737	+	0.950822i	$0.600241\pi$
$644$			39.8901i			0.0619412i
$645$	101.865	−	974.241i	0.157930	−	1.51045i
$646$	608.339			0.941701
$647$		−	429.581i		−	0.663959i	−0.943287	−	0.331979i	$-0.892284\pi$
$647$		−	429.581i		−	0.663959i	0.943287	−	0.331979i	$-0.107716\pi$
$648$	273.661	−	618.245i	0.422316	−	0.954082i
$649$		0			0
$650$		−	1074.99i		−	1.65383i
$651$	−54.7362	−	5.72310i	−0.0840802	−	0.00879125i
$652$	22.5153			0.0345327
$653$			541.731i			0.829604i	0.909912	+	0.414802i	$0.136149\pi$
$653$			541.731i			0.829604i	−0.909912	+	0.414802i	$0.863851\pi$
$654$	18.8354	−	180.143i	0.0288003	−	0.275449i
$655$	−1186.83			−1.81195
$656$		−	487.902i		−	0.743753i
$657$	−947.065	−	200.235i	−1.44150	−	0.304772i
$658$	133.131			0.202326
$659$			742.491i			1.12669i	0.826221	+	0.563347i	$0.190486\pi$
$659$			742.491i			1.12669i	−0.826221	+	0.563347i	$0.809514\pi$
$660$		0			0
$661$	1145.01			1.73224			0.866118	−	0.499839i	$-0.166607\pi$
$661$	1145.01			1.73224			0.866118	+	0.499839i	$0.166607\pi$
$662$		−	49.8892i		−	0.0753613i
$663$	104.830	−	1002.60i	0.158114	−	1.51222i
$664$	−410.041			−0.617532
$665$			372.408i			0.560011i
$666$	−122.404	+	578.941i	−0.183790	+	0.869280i
$667$	−263.750			−0.395427
$668$			52.1801i			0.0781139i
$669$	206.314	+	21.5718i	0.308392	+	0.0322449i
$670$	1286.59			1.92028
$671$		0			0
$672$	7.13637	−	68.2528i	0.0106196	−	0.101567i
$673$	252.175			0.374702			0.187351	−	0.982293i	$-0.440010\pi$
$673$	252.175			0.374702			0.187351	+	0.982293i	$0.440010\pi$
$674$			587.042i			0.870983i
$675$	1109.97	+	358.662i	1.64440	+	0.531352i
$676$	1.14982			0.00170092
$677$		−	631.491i		−	0.932779i	−0.884580	−	0.466389i	$-0.845555\pi$
$677$		−	631.491i		−	0.932779i	0.884580	−	0.466389i	$-0.154445\pi$
$678$	−539.225	−	56.3803i	−0.795317	−	0.0831567i
$679$	57.7562			0.0850607
$680$		−	1766.74i		−	2.59815i
$681$	31.1011	−	297.454i	0.0456698	−	0.436789i
$682$		0			0
$683$		−	465.998i		−	0.682281i	−0.940012	−	0.341141i	$-0.889187\pi$
$683$		−	465.998i		−	0.682281i	0.940012	−	0.341141i	$-0.110813\pi$
$684$	−43.8337	−	9.26764i	−0.0640843	−	0.0135492i
$685$	−1722.01			−2.51388
$686$		−	581.659i		−	0.847900i
$687$	−741.047	−	77.4824i	−1.07867	−	0.112784i
$688$	−563.380			−0.818866
$689$		−	226.659i		−	0.328967i
$690$	−135.906	+	1299.82i	−0.196966	+	1.88380i
$691$	−610.944			−0.884144			−0.442072	−	0.896980i	$-0.645756\pi$
$691$	−610.944			−0.884144			−0.442072	+	0.896980i	$0.645756\pi$
$692$			72.3385i			0.104535i
$693$		0			0
$694$	−51.4581			−0.0741471
$695$			661.483i			0.951774i
$696$	236.335	+	24.7107i	0.339562	+	0.0355039i
$697$	877.566			1.25906
$698$			7.49426i			0.0107368i
$699$	−90.7554	+	867.991i	−0.129836	+	1.24176i
$700$	62.0048			0.0885783
$701$			681.303i			0.971901i	0.873986	+	0.485951i	$0.161526\pi$
$701$			681.303i			0.971901i	−0.873986	+	0.485951i	$0.838474\pi$
$702$	206.570	−	639.280i	0.294259	−	0.910655i
$703$	433.262			0.616305
$704$		0			0
$705$	−479.387	−	50.1237i	−0.679982	−	0.0710975i
$706$	−1101.29			−1.55991
$707$		−	286.965i		−	0.405892i
$708$	3.37142	−	32.2445i	0.00476190	−	0.0455431i
$709$	91.6430			0.129257			0.0646284	−	0.997909i	$-0.479414\pi$
$709$	91.6430			0.129257			0.0646284	+	0.997909i	$0.479414\pi$
$710$		−	1833.95i		−	2.58303i
$711$	−553.762	−	117.080i	−0.778850	−	0.164670i
$712$	−577.172			−0.810634
$713$			141.411i			0.198332i
$714$	−523.308	−	54.7160i	−0.732924	−	0.0766331i
$715$		0			0
$716$			4.74171i			0.00662249i
$717$	−32.7380	+	313.109i	−0.0456597	+	0.436693i
$718$	−138.996			−0.193588
$719$			659.916i			0.917824i	0.888482	+	0.458912i	$0.151761\pi$
$719$			659.916i			0.917824i	−0.888482	+	0.458912i	$0.848239\pi$
$720$	219.081	−	1036.20i	0.304279	−	1.43917i
$721$	−79.7898			−0.110665
$722$			388.287i			0.537794i
$723$	−263.692	−	27.5711i	−0.364719	−	0.0381343i
$724$	−33.7379			−0.0465993
$725$			409.970i			0.565476i
$726$		0			0
$727$	−718.942			−0.988915			−0.494458	−	0.869202i	$-0.664633\pi$
$727$	−718.942			−0.988915			−0.494458	+	0.869202i	$0.664633\pi$
$728$		−	394.581i		−	0.542007i
$729$	591.160	+	426.581i	0.810918	+	0.585159i
$730$	−1685.79			−2.30931
$731$		−	1013.32i		−	1.38622i
$732$	51.9475	+	5.43152i	0.0709665	+	0.00742011i
$733$	727.430			0.992400			0.496200	−	0.868208i	$-0.334728\pi$
$733$	727.430			0.992400			0.496200	+	0.868208i	$0.334728\pi$
$734$		−	618.853i		−	0.843123i
$735$	−92.7496	+	887.064i	−0.126190	+	1.20689i
$736$	−176.331			−0.239580
$737$		0			0
$738$	572.205	+	120.980i	0.775346	+	0.163929i
$739$	603.503			0.816648			0.408324	−	0.912837i	$-0.366113\pi$
$739$	603.503			0.816648			0.408324	+	0.912837i	$0.366113\pi$
$740$		−	113.880i		−	0.153892i
$741$	−489.234	−	51.1533i	−0.660235	−	0.0690328i
$742$	−118.305			−0.159440
$743$			434.637i			0.584976i	0.956269	+	0.292488i	$0.0944831\pi$
$743$			434.637i			0.584976i	−0.956269	+	0.292488i	$0.905517\pi$
$744$	13.2488	−	126.712i	0.0178075	−	0.170312i
$745$	780.339			1.04743
$746$			1137.81i			1.52522i
$747$	91.4547	−	432.559i	0.122429	−	0.579061i
$748$		0			0
$749$			724.630i			0.967463i
$750$	851.276	+	89.0077i	1.13503	+	0.118677i
$751$	−319.705			−0.425705			−0.212853	−	0.977084i	$-0.568275\pi$
$751$	−319.705			−0.425705			−0.212853	+	0.977084i	$0.568275\pi$
$752$			277.218i			0.368641i
$753$	−1.97970	+	18.9340i	−0.00262908	+	0.0251448i
$754$	236.120			0.313156
$755$			1503.64i			1.99158i
$756$	36.8732	+	11.9148i	0.0487741	+	0.0157603i
$757$	910.980			1.20341			0.601704	−	0.798719i	$-0.294489\pi$
$757$	910.980			1.20341			0.601704	+	0.798719i	$0.294489\pi$
$758$		−	28.1170i		−	0.0370936i
$759$		0			0
$760$	−862.110			−1.13436
$761$			645.430i			0.848134i	0.905631	+	0.424067i	$0.139398\pi$
$761$			645.430i			0.848134i	−0.905631	+	0.424067i	$0.860602\pi$
$762$	56.2128	−	537.623i	0.0737701	−	0.705542i
$763$	114.703			0.150331
$764$		−	27.4661i		−	0.0359504i
$765$	1863.77	+	394.051i	2.43629	+	0.515099i
$766$	868.093			1.13328
$767$		−	355.952i		−	0.464083i
$768$	225.696	+	23.5983i	0.293875	+	0.0307270i
$769$	−212.256			−0.276016			−0.138008	−	0.990431i	$-0.544070\pi$
$769$	−212.256			−0.276016			−0.138008	+	0.990431i	$0.544070\pi$
$770$		0			0
$771$	−56.0723	+	536.280i	−0.0727267	+	0.695564i
$772$	−47.2970			−0.0612656
$773$			1123.99i			1.45406i	0.686605	+	0.727030i	$0.259100\pi$
$773$			1123.99i			1.45406i	−0.686605	+	0.727030i	$0.740900\pi$
$774$	139.695	−	660.725i	0.180485	−	0.853650i
$775$	219.808			0.283623
$776$			133.704i			0.172298i
$777$	−372.703	−	38.9691i	−0.479669	−	0.0501532i
$778$	523.224			0.672524
$779$		−	428.222i		−	0.549707i
$780$	−13.4453	+	128.592i	−0.0172376	+	0.164861i
$781$		0			0
$782$			1351.96i			1.72885i
$783$	−78.7794	+	243.802i	−0.100612	+	0.311369i
$784$	512.967			0.654295
$785$			1189.83i			1.51570i
$786$	−813.798	−	85.0890i	−1.03537	−	0.108256i
$787$	−240.124			−0.305113			−0.152556	−	0.988295i	$-0.548751\pi$
$787$	−240.124			−0.305113			−0.152556	+	0.988295i	$0.548751\pi$
$788$			121.442i			0.154114i
$789$	−90.2560	+	863.215i	−0.114393	+	1.09406i
$790$	−985.707			−1.24773
$791$		−	343.340i		−	0.434059i
$792$		0			0
$793$	573.455			0.723146
$794$		−	1104.81i		−	1.39145i
$795$	426.000	+	44.5417i	0.535850	+	0.0560273i
$796$	49.8017			0.0625649
$797$			591.993i			0.742777i	0.928478	+	0.371388i	$0.121118\pi$
$797$			591.993i			0.742777i	−0.928478	+	0.371388i	$0.878882\pi$
$798$	−26.6995	+	255.356i	−0.0334581	+	0.319995i
$799$	−498.619			−0.624053
$800$			274.087i			0.342609i
$801$	128.731	−	608.867i	0.160713	−	0.760134i
$802$	−827.808			−1.03218
$803$		0			0
$804$	−97.4895	−	10.1933i	−0.121256	−	0.0126782i
$805$	−827.633			−1.02812
$806$		−	126.597i		−	0.157068i
$807$	27.8910	−	266.752i	0.0345614	−	0.330548i
$808$	664.315			0.822172
$809$			891.236i			1.10165i	0.834620	+	0.550826i	$0.185687\pi$
$809$			891.236i			1.10165i	−0.834620	+	0.550826i	$0.814313\pi$
$810$	1160.92	+	513.871i	1.43324	+	0.634409i
$811$	968.274			1.19393			0.596963	−	0.802269i	$-0.296374\pi$
$811$	968.274			1.19393			0.596963	+	0.802269i	$0.296374\pi$
$812$			13.6192i			0.0167724i
$813$	−811.886	−	84.8891i	−0.998629	−	0.104415i
$814$		0			0
$815$			467.144i			0.573183i
$816$	113.935	−	1089.68i	0.139626	−	1.33540i
$817$	−494.467			−0.605223
$818$		−	557.936i		−	0.682073i
$819$	416.250	+	88.0066i	0.508242	+	0.107456i
$820$	−112.555			−0.137263
$821$			905.042i			1.10237i	0.834385	+	0.551183i	$0.185823\pi$
$821$			905.042i			1.10237i	−0.834385	+	0.551183i	$0.814177\pi$
$822$	−1180.77	−	123.458i	−1.43645	−	0.150193i
$823$	−1343.44			−1.63237			−0.816186	−	0.577789i	$-0.803915\pi$
$823$	−1343.44			−1.63237			−0.816186	+	0.577789i	$0.803915\pi$
$824$		−	184.711i		−	0.224163i
$825$		0			0
$826$	−185.789			−0.224927
$827$		−	1178.20i		−	1.42467i	−0.701840	−	0.712334i	$-0.747638\pi$
$827$		−	1178.20i		−	1.42467i	0.701840	−	0.712334i	$-0.252362\pi$
$828$	20.5963	−	97.4154i	0.0248747	−	0.117651i
$829$	−424.381			−0.511919			−0.255959	−	0.966688i	$-0.582391\pi$
$829$	−424.381			−0.511919			−0.255959	+	0.966688i	$0.582391\pi$
$830$		−	769.962i		−	0.927665i
$831$	−1365.36	−	142.759i	−1.64303	−	0.171792i
$832$	905.133			1.08790
$833$			922.650i			1.10762i
$834$	−47.4246	+	453.572i	−0.0568640	+	0.543852i
$835$	−1082.62			−1.29655
$836$		0			0
$837$	130.716	+	42.2380i	0.156172	+	0.0504636i
$838$	919.813			1.09763
$839$		−	1582.29i		−	1.88593i	−0.332899	−	0.942963i	$-0.608027\pi$
$839$		−	1582.29i		−	1.88593i	0.332899	−	0.942963i	$-0.391973\pi$
$840$	741.608	+	77.5410i	0.882867	+	0.0923107i
$841$	750.951			0.892926
$842$			99.2035i			0.117819i
$843$	6.26570	−	59.9256i	0.00743262	−	0.0710862i
$844$	−82.1574			−0.0973429
$845$			23.8564i			0.0282324i
$846$	−325.118	−	68.7388i	−0.384300	−	0.0812515i
$847$		0			0
$848$		−	246.346i		−	0.290502i
$849$	1526.48	+	159.606i	1.79797	+	0.187993i
$850$	2101.48			2.47233
$851$			962.877i			1.13146i
$852$	−14.5299	+	138.965i	−0.0170539	+	0.163105i
$853$	500.571			0.586836			0.293418	−	0.955984i	$-0.405207\pi$
$853$	500.571			0.586836			0.293418	+	0.955984i	$0.405207\pi$
$854$		−	299.315i		−	0.350487i
$855$	192.283	−	909.454i	0.224893	−	1.06369i
$856$	−1677.49			−1.95969
$857$		−	432.247i		−	0.504373i	−0.967679	−	0.252186i	$-0.918850\pi$
$857$		−	432.247i		−	0.504373i	0.967679	−	0.252186i	$-0.0811496\pi$
$858$		0			0
$859$	383.432			0.446370			0.223185	−	0.974776i	$-0.428355\pi$
$859$	383.432			0.446370			0.223185	+	0.974776i	$0.428355\pi$
$860$			129.968i			0.151125i
$861$	−38.5157	+	368.367i	−0.0447337	+	0.427836i
$862$	398.035			0.461758
$863$			395.738i			0.458561i	0.973360	+	0.229280i	$0.0736373\pi$
$863$			395.738i			0.458561i	−0.973360	+	0.229280i	$0.926363\pi$
$864$	−52.6683	+	162.995i	−0.0609587	+	0.188652i
$865$	−1500.87			−1.73511
$866$			687.532i			0.793916i
$867$	1097.66	+	114.769i	1.26605	+	0.132375i
$868$	7.30202			0.00841247
$869$		0			0
$870$	−46.4010	+	443.782i	−0.0533345	+	0.510095i
$871$	−1076.20			−1.23559
$872$			265.532i			0.304510i
$873$	−141.046	−	29.8210i	−0.161565	−	0.0341592i
$874$	659.712			0.754819
$875$			542.032i			0.619466i
$876$	127.739	+	13.3561i	0.145820	+	0.0152467i
$877$	−246.001			−0.280503			−0.140251	−	0.990116i	$-0.544791\pi$
$877$	−246.001			−0.280503			−0.140251	+	0.990116i	$0.544791\pi$
$878$			786.707i			0.896021i
$879$	−154.100	+	1473.83i	−0.175313	+	1.67671i
$880$		0			0
$881$		−	1110.60i		−	1.26061i	−0.776346	−	0.630307i	$-0.782929\pi$
$881$		−	1110.60i		−	1.26061i	0.776346	−	0.630307i	$-0.217071\pi$
$882$	−127.195	+	601.602i	−0.144212	+	0.682088i
$883$	−114.392			−0.129549			−0.0647744	−	0.997900i	$-0.520633\pi$
$883$	−114.392			−0.129549			−0.0647744	+	0.997900i	$0.520633\pi$
$884$			133.751i			0.151302i
$885$	669.004	+	69.9497i	0.755937	+	0.0790392i
$886$	−1465.69			−1.65428
$887$		−	985.799i		−	1.11139i	−0.831388	−	0.555693i	$-0.812453\pi$
$887$		−	985.799i		−	1.11139i	0.831388	−	0.555693i	$-0.187547\pi$
$888$	90.2120	−	862.794i	0.101590	−	0.971615i
$889$	342.320			0.385062
$890$		−	1083.79i		−	1.21775i
$891$		0			0
$892$	−27.5231			−0.0308555
$893$			243.309i			0.272462i
$894$	535.071	+	55.9459i	0.598513	+	0.0625793i
$895$	−98.3801			−0.109922
$896$		−	380.936i		−	0.425151i
$897$	113.682	−	1087.27i	0.126736	−	1.21211i
$898$	−1279.54			−1.42488
$899$			48.2802i			0.0537044i
$900$	−151.422	−	32.0146i	−0.168246	−	0.0355718i
$901$	443.090			0.491776
$902$		0			0
$903$	425.353	+	44.4740i	0.471044	+	0.0492514i
$904$	794.821			0.879227
$905$		−	699.988i		−	0.773467i
$906$	−107.803	+	1031.03i	−0.118988	+	1.13801i
$907$	−485.815			−0.535628			−0.267814	−	0.963471i	$-0.586301\pi$
$907$	−485.815			−0.535628			−0.267814	+	0.963471i	$0.586301\pi$
$908$			39.6815i			0.0437021i
$909$	−148.167	+	700.796i	−0.163000	+	0.770953i
$910$	740.932			0.814211
$911$		−	1063.16i		−	1.16703i	−0.812103	−	0.583515i	$-0.801677\pi$
$911$		−	1063.16i		−	1.16703i	0.812103	−	0.583515i	$-0.198323\pi$
$912$	−531.728	−	55.5964i	−0.583035	−	0.0609609i
$913$		0			0
$914$		−	1603.65i		−	1.75454i
$915$	−112.692	+	1077.80i	−0.123161	+	1.17792i
$916$	98.8586			0.107924
$917$		−	518.169i		−	0.565070i
$918$	1249.72	+	403.819i	1.36135	+	0.439889i
$919$	1366.68			1.48714			0.743571	−	0.668657i	$-0.233130\pi$
$919$	1366.68			1.48714			0.743571	+	0.668657i	$0.233130\pi$
$920$		−	1915.94i		−	2.08255i
$921$	1672.15	+	174.837i	1.81558	+	0.189834i
$922$	535.547			0.580854
$923$			1534.05i			1.66203i
$924$		0			0
$925$	1496.69			1.61804
$926$			1390.71i			1.50185i
$927$	194.854	+	41.1975i	0.210199	+	0.0444417i
$928$	−60.2026			−0.0648735
$929$			659.675i			0.710092i	0.934849	+	0.355046i	$0.115535\pi$
$929$			659.675i			0.710092i	−0.934849	+	0.355046i	$0.884465\pi$
$930$	237.936	+	24.8781i	0.255846	+	0.0267507i
$931$	450.221			0.483589
$932$		−	115.793i		−	0.124242i
$933$	134.798	−	1289.22i	0.144478	−	1.38180i
$934$	−871.241			−0.932806
$935$		0			0
$936$	−203.732	+	963.604i	−0.217663	+	1.02949i
$937$	1122.73			1.19821			0.599107	−	0.800669i	$-0.295523\pi$
$937$	1122.73			1.19821			0.599107	+	0.800669i	$0.295523\pi$
$938$			561.724i			0.598852i
$939$	465.839	+	48.7071i	0.496101	+	0.0518713i
$940$	63.9521			0.0680342
$941$			552.721i			0.587376i	0.955901	+	0.293688i	$0.0948827\pi$
$941$			552.721i			0.587376i	−0.955901	+	0.293688i	$0.905117\pi$
$942$	−85.3040	+	815.854i	−0.0905562	+	0.866087i
$943$	951.675			1.00920
$944$		−	386.869i		−	0.409819i
$945$	−247.206	+	765.039i	−0.261594	+	0.809566i
$946$		0			0
$947$		−	903.931i		−	0.954520i	−0.878762	−	0.477260i	$-0.841630\pi$
$947$		−	903.931i		−	0.954520i	0.878762	−	0.477260i	$-0.158370\pi$
$948$	74.6906	+	7.80950i	0.0787876	+	0.00823786i
$949$	1410.12			1.48590
$950$		−	1025.45i		−	1.07942i
$951$	105.600	−	1009.97i	0.111041	−	1.06201i
$952$	771.359			0.810251
$953$		−	904.813i		−	0.949437i	−0.880138	−	0.474719i	$-0.842550\pi$
$953$		−	904.813i		−	0.949437i	0.880138	−	0.474719i	$-0.157450\pi$
$954$	288.911	+	61.0837i	0.302842	+	0.0640290i
$955$	569.862			0.596714
$956$		−	41.7700i		−	0.0436924i
$957$		0			0
$958$	−542.530			−0.566316
$959$		−	751.828i		−	0.783971i
$960$	−177.872	+	1701.18i	−0.185283	+	1.77206i
$961$	−935.114			−0.973064
$962$		−	862.008i		−	0.896058i
$963$	374.144	−	1769.61i	0.388520	−	1.83760i
$964$	35.1775			0.0364912
$965$		−	981.311i		−	1.01690i
$966$	−567.500	−	59.3367i	−0.587475	−	0.0614251i
$967$	1145.53			1.18462			0.592310	−	0.805710i	$-0.298216\pi$
$967$	1145.53			1.18462			0.592310	+	0.805710i	$0.298216\pi$
$968$		0			0
$969$	99.9985	−	956.393i	0.103198	−	0.986990i
$970$	−251.064			−0.258829
$971$		−	1108.03i		−	1.14112i	−0.821256	−	0.570560i	$-0.806726\pi$
$971$		−	1108.03i		−	1.14112i	0.821256	−	0.570560i	$-0.193274\pi$
$972$	−83.8959	−	48.1356i	−0.0863127	−	0.0495222i
$973$	−288.803			−0.296817
$974$		−	1375.55i		−	1.41227i
$975$	−1690.04	−	176.707i	−1.73337	−	0.181238i
$976$	623.264			0.638590
$977$			766.291i			0.784330i	0.919895	+	0.392165i	$0.128274\pi$
$977$			766.291i			0.784330i	−0.919895	+	0.392165i	$0.871726\pi$
$978$	−33.4916	+	320.316i	−0.0342450	+	0.327522i
$979$		0			0
$980$		−	118.338i		−	0.120753i
$981$	−280.114	−	59.2238i	−0.285539	−	0.0603708i
$982$	−1167.83			−1.18924
$983$		−	1747.89i		−	1.77812i	−0.457791	−	0.889060i	$-0.651359\pi$
$983$		−	1747.89i		−	1.77812i	0.457791	−	0.889060i	$-0.348641\pi$
$984$	−852.757	−	89.1625i	−0.866623	−	0.0906123i
$985$	−2519.66			−2.55803
$986$			461.586i			0.468140i
$987$	21.8840	−	209.300i	0.0221722	−	0.212057i
$988$	65.2657			0.0660584
$989$		−	1098.90i		−	1.11112i
$990$		0			0
$991$	616.298			0.621895			0.310948	−	0.950427i	$-0.399354\pi$
$991$	616.298			0.621895			0.310948	+	0.950427i	$0.399354\pi$
$992$			32.2780i			0.0325383i
$993$	−78.4327	−	8.20076i	−0.0789856	−	0.00825857i
$994$	800.701			0.805534
$995$			1033.28i			1.03847i
$996$	−6.10021	+	58.3429i	−0.00612471	+	0.0585772i
$997$	−744.618			−0.746859			−0.373429	−	0.927659i	$-0.621818\pi$
$997$	−744.618			−0.746859			−0.373429	+	0.927659i	$0.621818\pi$
$998$		−	1398.77i		−	1.40158i
$999$	890.054	+	287.602i	0.890945	+	0.287890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.n.122.5	✓	12
3.2	odd	2	inner	363.3.b.n.122.8	yes	12
11.2	odd	10		363.3.h.r.323.7		48
11.3	even	5		363.3.h.r.251.6		48
11.4	even	5		363.3.h.r.269.7		48
11.5	even	5		363.3.h.r.245.8		48
11.6	odd	10		363.3.h.r.245.6		48
11.7	odd	10		363.3.h.r.269.5		48
11.8	odd	10		363.3.h.r.251.8		48
11.9	even	5		363.3.h.r.323.5		48
11.10	odd	2	inner	363.3.b.n.122.7	yes	12
33.2	even	10		363.3.h.r.323.6		48
33.5	odd	10		363.3.h.r.245.5		48
33.8	even	10		363.3.h.r.251.5		48
33.14	odd	10		363.3.h.r.251.7		48
33.17	even	10		363.3.h.r.245.7		48
33.20	odd	10		363.3.h.r.323.8		48
33.26	odd	10		363.3.h.r.269.6		48
33.29	even	10		363.3.h.r.269.8		48
33.32	even	2	inner	363.3.b.n.122.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.n.122.5	✓	12	1.1	even	1	trivial
363.3.b.n.122.6	yes	12	33.32	even	2	inner
363.3.b.n.122.7	yes	12	11.10	odd	2	inner
363.3.b.n.122.8	yes	12	3.2	odd	2	inner
363.3.h.r.245.5		48	33.5	odd	10
363.3.h.r.245.6		48	11.6	odd	10
363.3.h.r.245.7		48	33.17	even	10
363.3.h.r.245.8		48	11.5	even	5
363.3.h.r.251.5		48	33.8	even	10
363.3.h.r.251.6		48	11.3	even	5
363.3.h.r.251.7		48	33.14	odd	10
363.3.h.r.251.8		48	11.8	odd	10
363.3.h.r.269.5		48	11.7	odd	10
363.3.h.r.269.6		48	33.26	odd	10
363.3.h.r.269.7		48	11.4	even	5
363.3.h.r.269.8		48	33.29	even	10
363.3.h.r.323.5		48	11.9	even	5
363.3.h.r.323.6		48	33.2	even	10
363.3.h.r.323.7		48	11.2	odd	10
363.3.h.r.323.8		48	33.20	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.89788i q^{2} +(-2.98373 - 0.311973i) q^{3} +0.398042 q^{4} +8.25850i q^{5} +(-0.592088 + 5.66278i) q^{6} -3.60566 q^{7} -8.34697i q^{8} +(8.80535 + 1.86169i) q^{9} +O(q^{10})\)	\(q-1.89788i q^{2} +(-2.98373 - 0.311973i) q^{3} +0.398042 q^{4} +8.25850i q^{5} +(-0.592088 + 5.66278i) q^{6} -3.60566 q^{7} -8.34697i q^{8} +(8.80535 + 1.86169i) q^{9} +15.6737 q^{10} +(-1.18765 - 0.124178i) q^{12} -13.1106 q^{13} +6.84311i q^{14} +(2.57643 - 24.6412i) q^{15} -14.2494 q^{16} -25.6297i q^{17} +(3.53327 - 16.7115i) q^{18} -12.5064 q^{19} +3.28723i q^{20} +(10.7583 + 1.12487i) q^{21} -27.7941i q^{23} +(-2.60403 + 24.9051i) q^{24} -43.2029 q^{25} +24.8824i q^{26} +(-25.6920 - 8.30182i) q^{27} -1.43520 q^{28} -9.48941i q^{29} +(-46.7661 - 4.88976i) q^{30} -5.08780 q^{31} -6.34419i q^{32} -48.6422 q^{34} -29.7773i q^{35} +(3.50490 + 0.741031i) q^{36} -34.6432 q^{37} +23.7357i q^{38} +(39.1187 + 4.09017i) q^{39} +68.9334 q^{40} +34.2402i q^{41} +(2.13487 - 20.4180i) q^{42} +39.5371 q^{43} +(-15.3748 + 72.7190i) q^{45} -52.7499 q^{46} -19.4547i q^{47} +(42.5164 + 4.44543i) q^{48} -35.9992 q^{49} +81.9940i q^{50} +(-7.99578 + 76.4722i) q^{51} -5.21858 q^{52} +17.2882i q^{53} +(-15.7559 + 48.7604i) q^{54} +30.0963i q^{56} +(37.3158 + 3.90167i) q^{57} -18.0098 q^{58} +27.1498i q^{59} +(1.02553 - 9.80822i) q^{60} -43.7397 q^{61} +9.65605i q^{62} +(-31.7490 - 6.71262i) q^{63} -69.0381 q^{64} -108.274i q^{65} +82.0860 q^{67} -10.2017i q^{68} +(-8.67101 + 82.9302i) q^{69} -56.5139 q^{70} -117.008i q^{71} +(15.5395 - 73.4979i) q^{72} -107.556 q^{73} +65.7488i q^{74} +(128.906 + 13.4781i) q^{75} -4.97808 q^{76} +(7.76265 - 74.2426i) q^{78} -62.8893 q^{79} -117.679i q^{80} +(74.0682 + 32.7857i) q^{81} +64.9839 q^{82} -49.1246i q^{83} +(4.28226 + 0.447744i) q^{84} +211.663 q^{85} -75.0368i q^{86} +(-2.96044 + 28.3139i) q^{87} -69.1475i q^{89} +(138.012 + 29.1795i) q^{90} +47.2724 q^{91} -11.0632i q^{92} +(15.1806 + 1.58726i) q^{93} -36.9228 q^{94} -103.284i q^{95} +(-1.97922 + 18.9294i) q^{96} -16.0182 q^{97} +68.3223i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9}+O(q^{10}) \) 12 * q - 4 * q^3 - 44 * q^4 - 12 * q^9	\( 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9} - 80 q^{12} + 68 q^{15} + 92 q^{16} - 88 q^{25} - 232 q^{27} - 8 q^{31} + 116 q^{34} + 164 q^{36} - 244 q^{37} + 404 q^{42} - 52 q^{45} + 540 q^{48} + 100 q^{49} - 460 q^{58} + 24 q^{60} - 1276 q^{64} - 128 q^{67} + 128 q^{69} - 784 q^{70} + 684 q^{75} + 528 q^{78} + 348 q^{81} - 380 q^{82} + 120 q^{91} + 196 q^{93} - 156 q^{97}+O(q^{100}) \) 12 * q - 4 * q^3 - 44 * q^4 - 12 * q^9 - 80 * q^12 + 68 * q^15 + 92 * q^16 - 88 * q^25 - 232 * q^27 - 8 * q^31 + 116 * q^34 + 164 * q^36 - 244 * q^37 + 404 * q^42 - 52 * q^45 + 540 * q^48 + 100 * q^49 - 460 * q^58 + 24 * q^60 - 1276 * q^64 - 128 * q^67 + 128 * q^69 - 784 * q^70 + 684 * q^75 + 528 * q^78 + 348 * q^81 - 380 * q^82 + 120 * q^91 + 196 * q^93 - 156 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more