LMFDB - Embedded newform 380.3.h.a.39.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(39,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("380.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.h (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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$108$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.15
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75001 - 0.968228i) q^{2} -4.24708 q^{3} +(2.12507 + 3.38882i) q^{4} +(4.77157 + 1.49403i) q^{5} +(7.43242 + 4.11214i) q^{6} +7.86306 q^{7} +(-0.437742 - 7.98801i) q^{8} +9.03765 q^{9} +O(q^{10})$	\(q+(-1.75001 - 0.968228i) q^{2} -4.24708 q^{3} +(2.12507 + 3.38882i) q^{4} +(4.77157 + 1.49403i) q^{5} +(7.43242 + 4.11214i) q^{6} +7.86306 q^{7} +(-0.437742 - 7.98801i) q^{8} +9.03765 q^{9} +(-6.90374 - 7.23453i) q^{10} +2.63701i q^{11} +(-9.02533 - 14.3926i) q^{12} -5.11257i q^{13} +(-13.7604 - 7.61323i) q^{14} +(-20.2652 - 6.34524i) q^{15} +(-6.96817 + 14.4029i) q^{16} +12.2680i q^{17} +(-15.8160 - 8.75051i) q^{18} +4.35890i q^{19} +(5.07693 + 19.3449i) q^{20} -33.3950 q^{21} +(2.55323 - 4.61480i) q^{22} -17.2507 q^{23} +(1.85912 + 33.9257i) q^{24} +(20.5358 + 14.2577i) q^{25} +(-4.95014 + 8.94705i) q^{26} -0.159903 q^{27} +(16.7095 + 26.6465i) q^{28} +4.95966 q^{29} +(29.3207 + 30.7256i) q^{30} -59.4651i q^{31} +(26.1397 - 18.4585i) q^{32} -11.1996i q^{33} +(11.8783 - 21.4692i) q^{34} +(37.5191 + 11.7476i) q^{35} +(19.2056 + 30.6269i) q^{36} +47.8677i q^{37} +(4.22041 - 7.62812i) q^{38} +21.7135i q^{39} +(9.84558 - 38.7694i) q^{40} -4.38513 q^{41} +(58.4416 + 32.3340i) q^{42} +51.2362 q^{43} +(-8.93636 + 5.60383i) q^{44} +(43.1238 + 13.5025i) q^{45} +(30.1889 + 16.7026i) q^{46} +41.3609 q^{47} +(29.5943 - 61.1704i) q^{48} +12.8277 q^{49} +(-22.1331 - 44.8344i) q^{50} -52.1032i q^{51} +(17.3256 - 10.8646i) q^{52} +42.9820i q^{53} +(0.279832 + 0.154823i) q^{54} +(-3.93976 + 12.5827i) q^{55} +(-3.44199 - 62.8102i) q^{56} -18.5126i q^{57} +(-8.67945 - 4.80208i) q^{58} +103.336i q^{59} +(-21.5621 - 82.1592i) q^{60} +68.7279 q^{61} +(-57.5757 + 104.064i) q^{62} +71.0636 q^{63} +(-63.6168 + 6.99338i) q^{64} +(7.63831 - 24.3950i) q^{65} +(-10.8438 + 19.5994i) q^{66} +69.7930 q^{67} +(-41.5741 + 26.0704i) q^{68} +73.2652 q^{69} +(-54.2845 - 56.8855i) q^{70} +55.1475i q^{71} +(-3.95616 - 72.1929i) q^{72} -45.6447i q^{73} +(46.3468 - 83.7689i) q^{74} +(-87.2170 - 60.5535i) q^{75} +(-14.7715 + 9.26296i) q^{76} +20.7350i q^{77} +(21.0236 - 37.9988i) q^{78} +84.1513i q^{79} +(-54.7675 + 58.3140i) q^{80} -80.6597 q^{81} +(7.67402 + 4.24580i) q^{82} -2.16220 q^{83} +(-70.9667 - 113.170i) q^{84} +(-18.3287 + 58.5378i) q^{85} +(-89.6639 - 49.6084i) q^{86} -21.0640 q^{87} +(21.0645 - 1.15433i) q^{88} +89.6522 q^{89} +(-62.3936 - 65.3831i) q^{90} -40.2004i q^{91} +(-36.6590 - 58.4596i) q^{92} +252.553i q^{93} +(-72.3821 - 40.0468i) q^{94} +(-6.51231 + 20.7988i) q^{95} +(-111.017 + 78.3947i) q^{96} +36.5447i q^{97} +(-22.4485 - 12.4201i) q^{98} +23.8324i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) $ 108 * q + 4 * q^5 + 324 * q^9	$ 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) $ 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.75001	−	0.968228i	−0.875005	−	0.484114i
$2$	−1.75001	−	0.968228i	−0.875005	−	0.484114i
$3$	−4.24708			−1.41569			−0.707846	−	0.706367i	$-0.750333\pi$
$3$	−4.24708			−1.41569			−0.707846	+	0.706367i	$0.750333\pi$
$4$	2.12507	+	3.38882i	0.531267	+	0.847204i
$5$	4.77157	+	1.49403i	0.954314	+	0.298805i
$5$	4.77157	+	1.49403i	0.954314	+	0.298805i
$6$	7.43242	+	4.11214i	1.23874	+	0.685356i
$7$	7.86306			1.12329			0.561647	−	0.827377i	$-0.310168\pi$
$7$	7.86306			1.12329			0.561647	+	0.827377i	$0.310168\pi$
$8$	−0.437742	−	7.98801i	−0.0547178	−	0.998502i
$9$	9.03765			1.00418
$10$	−6.90374	−	7.23453i	−0.690374	−	0.723453i
$11$			2.63701i			0.239728i	0.992790	+	0.119864i	$0.0382459\pi$
$11$			2.63701i			0.239728i	−0.992790	+	0.119864i	$0.961754\pi$
$12$	−9.02533	−	14.3926i	−0.752111	−	1.19938i
$13$		−	5.11257i		−	0.393275i	−0.980476	−	0.196637i	$-0.936998\pi$
$13$		−	5.11257i		−	0.393275i	0.980476	−	0.196637i	$-0.0630022\pi$
$14$	−13.7604	−	7.61323i	−0.982888	−	0.543802i
$15$	−20.2652	−	6.34524i	−1.35101	−	0.423016i
$16$	−6.96817	+	14.4029i	−0.435511	+	0.900184i
$17$			12.2680i			0.721649i	0.932634	+	0.360824i	$0.117505\pi$
$17$			12.2680i			0.721649i	−0.932634	+	0.360824i	$0.882495\pi$
$18$	−15.8160	−	8.75051i	−0.878665	−	0.486139i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	5.07693	+	19.3449i	0.253847	+	0.967244i
$21$	−33.3950			−1.59024
$22$	2.55323	−	4.61480i	0.116056	−	0.209764i
$23$	−17.2507			−0.750032			−0.375016	−	0.927018i	$-0.622363\pi$
$23$	−17.2507			−0.750032			−0.375016	+	0.927018i	$0.622363\pi$
$24$	1.85912	+	33.9257i	0.0774635	+	1.41357i
$25$	20.5358	+	14.2577i	0.821431	+	0.570308i
$26$	−4.95014	+	8.94705i	−0.190390	+	0.344117i
$27$	−0.159903			−0.00592234
$28$	16.7095	+	26.6465i	0.596769	+	0.951659i
$29$	4.95966			0.171023			0.0855114	−	0.996337i	$-0.472748\pi$
$29$	4.95966			0.171023			0.0855114	+	0.996337i	$0.472748\pi$
$30$	29.3207	+	30.7256i	0.977357	+	1.02419i
$31$		−	59.4651i		−	1.91823i	−0.283020	−	0.959114i	$-0.591336\pi$
$31$		−	59.4651i		−	1.91823i	0.283020	−	0.959114i	$-0.408664\pi$
$32$	26.1397	−	18.4585i	0.816865	−	0.576828i
$33$		−	11.1996i		−	0.339382i
$34$	11.8783	−	21.4692i	0.349360	−	0.631446i
$35$	37.5191	+	11.7476i	1.07198	+	0.335646i
$36$	19.2056	+	30.6269i	0.533490	+	0.850749i
$37$			47.8677i			1.29372i	0.762609	+	0.646860i	$0.223918\pi$
$37$			47.8677i			1.29372i	−0.762609	+	0.646860i	$0.776082\pi$
$38$	4.22041	−	7.62812i	0.111063	−	0.200740i
$39$			21.7135i			0.556756i
$40$	9.84558	−	38.7694i	0.246140	−	0.969234i
$41$	−4.38513			−0.106954			−0.0534772	−	0.998569i	$-0.517030\pi$
$41$	−4.38513			−0.106954			−0.0534772	+	0.998569i	$0.517030\pi$
$42$	58.4416	+	32.3340i	1.39147	+	0.769857i
$43$	51.2362			1.19154			0.595770	−	0.803155i	$-0.296847\pi$
$43$	51.2362			1.19154			0.595770	+	0.803155i	$0.296847\pi$
$44$	−8.93636	+	5.60383i	−0.203099	+	0.127360i
$45$	43.1238	+	13.5025i	0.958306	+	0.300055i
$46$	30.1889	+	16.7026i	0.656281	+	0.363101i
$47$	41.3609			0.880020			0.440010	−	0.897993i	$-0.354975\pi$
$47$	41.3609			0.880020			0.440010	+	0.897993i	$0.354975\pi$
$48$	29.5943	−	61.1704i	0.616549	−	1.27438i
$49$	12.8277			0.261789
$50$	−22.1331	−	44.8344i	−0.442662	−	0.896689i
$51$		−	52.1032i		−	1.02163i
$52$	17.3256	−	10.8646i	0.333184	−	0.208934i
$53$			42.9820i			0.810982i	0.914099	+	0.405491i	$0.132899\pi$
$53$			42.9820i			0.810982i	−0.914099	+	0.405491i	$0.867101\pi$
$54$	0.279832	+	0.154823i	0.00518208	+	0.00286709i
$55$	−3.93976	+	12.5827i	−0.0716321	+	0.228776i
$56$	−3.44199	−	62.8102i	−0.0614641	−	1.12161i
$57$		−	18.5126i		−	0.324782i
$58$	−8.67945	−	4.80208i	−0.149646	−	0.0827945i
$59$			103.336i			1.75146i	0.482800	+	0.875731i	$0.339620\pi$
$59$			103.336i			1.75146i	−0.482800	+	0.875731i	$0.660380\pi$
$60$	−21.5621	−	82.1592i	−0.359369	−	1.36932i
$61$	68.7279			1.12669			0.563343	−	0.826223i	$-0.309515\pi$
$61$	68.7279			1.12669			0.563343	+	0.826223i	$0.309515\pi$
$62$	−57.5757	+	104.064i	−0.928641	+	1.67846i
$63$	71.0636			1.12799
$64$	−63.6168	+	6.99338i	−0.994012	+	0.109272i
$65$	7.63831	−	24.3950i	0.117513	−	0.375308i
$66$	−10.8438	+	19.5994i	−0.164299	+	0.296961i
$67$	69.7930			1.04169			0.520843	−	0.853652i	$-0.325618\pi$
$67$	69.7930			1.04169			0.520843	+	0.853652i	$0.325618\pi$
$68$	−41.5741	+	26.0704i	−0.611384	+	0.383388i
$69$	73.2652			1.06181
$70$	−54.2845	−	56.8855i	−0.775493	−	0.812650i
$71$			55.1475i			0.776725i	0.921507	+	0.388362i	$0.126959\pi$
$71$			55.1475i			0.776725i	−0.921507	+	0.388362i	$0.873041\pi$
$72$	−3.95616	−	72.1929i	−0.0549467	−	1.00268i
$73$		−	45.6447i		−	0.625270i	−0.949873	−	0.312635i	$-0.898788\pi$
$73$		−	45.6447i		−	0.625270i	0.949873	−	0.312635i	$-0.101212\pi$
$74$	46.3468	−	83.7689i	0.626308	−	1.13201i
$75$	−87.2170	−	60.5535i	−1.16289	−	0.807380i
$76$	−14.7715	+	9.26296i	−0.194362	+	0.121881i
$77$			20.7350i			0.269285i
$78$	21.0236	−	37.9988i	0.269533	−	0.487164i
$79$			84.1513i			1.06521i	0.846365	+	0.532603i	$0.178786\pi$
$79$			84.1513i			1.06521i	−0.846365	+	0.532603i	$0.821214\pi$
$80$	−54.7675	+	58.3140i	−0.684593	+	0.728925i
$81$	−80.6597			−0.995799
$82$	7.67402	+	4.24580i	0.0935856	+	0.0517781i
$83$	−2.16220			−0.0260506			−0.0130253	−	0.999915i	$-0.504146\pi$
$83$	−2.16220			−0.0260506			−0.0130253	+	0.999915i	$0.504146\pi$
$84$	−70.9667	−	113.170i	−0.844841	−	1.34726i
$85$	−18.3287	+	58.5378i	−0.215632	+	0.688680i
$86$	−89.6639	−	49.6084i	−1.04260	−	0.576842i
$87$	−21.0640			−0.242115
$88$	21.0645	−	1.15433i	0.239369	−	0.0131174i
$89$	89.6522			1.00733			0.503664	−	0.863900i	$-0.331985\pi$
$89$	89.6522			1.00733			0.503664	+	0.863900i	$0.331985\pi$
$90$	−62.3936	−	65.3831i	−0.693262	−	0.726479i
$91$		−	40.2004i		−	0.441763i
$92$	−36.6590	−	58.4596i	−0.398467	−	0.635430i
$93$			252.553i			2.71562i
$94$	−72.3821	−	40.0468i	−0.770022	−	0.426030i
$95$	−6.51231	+	20.7988i	−0.0685506	+	0.218935i
$96$	−111.017	+	78.3947i	−1.15643	+	0.816611i
$97$			36.5447i			0.376750i	0.982097	+	0.188375i	$0.0603220\pi$
$97$			36.5447i			0.376750i	−0.982097	+	0.188375i	$0.939678\pi$
$98$	−22.4485	−	12.4201i	−0.229067	−	0.126736i
$99$			23.8324i			0.240731i
$100$	−4.67681	+	99.8906i	−0.0467681	+	0.998906i
$101$	−105.739			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$101$	−105.739			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$102$	−50.4478	+	91.1812i	−0.494587	+	0.893933i
$103$	187.570			1.82106			0.910532	−	0.413438i	$-0.135672\pi$
$103$	187.570			1.82106			0.910532	+	0.413438i	$0.135672\pi$
$104$	−40.8393	+	2.23799i	−0.392686	+	0.0215191i
$105$	−159.347	−	49.8930i	−1.51759	−	0.475171i
$106$	41.6164	−	75.2190i	0.392608	−	0.709613i
$107$	−111.693			−1.04386			−0.521932	−	0.852987i	$-0.674788\pi$
$107$	−111.693			−1.04386			−0.521932	+	0.852987i	$0.674788\pi$
$108$	−0.339805	−	0.541883i	−0.00314635	−	0.00501744i
$109$	88.2072			0.809241			0.404620	−	0.914485i	$-0.367404\pi$
$109$	88.2072			0.809241			0.404620	+	0.914485i	$0.367404\pi$
$110$	19.0775	−	18.2052i	0.173432	−	0.165502i
$111$		−	203.298i		−	1.83151i
$112$	−54.7911	+	113.251i	−0.489206	+	1.01117i
$113$		−	108.161i		−	0.957175i	−0.878040	−	0.478587i	$-0.841149\pi$
$113$		−	108.161i		−	0.957175i	0.878040	−	0.478587i	$-0.158851\pi$
$114$	−17.9244	+	32.3972i	−0.157232	+	0.284186i
$115$	−82.3131	−	25.7730i	−0.715766	−	0.224113i
$116$	10.5396	+	16.8074i	0.0908587	+	0.144891i
$117$		−	46.2056i		−	0.394920i
$118$	100.053	−	180.839i	0.847907	−	1.53254i
$119$			96.4642i			0.810624i
$120$	−41.8149	+	164.656i	−0.348458	+	1.37214i
$121$	114.046			0.942530
$122$	−120.274	−	66.5443i	−0.985857	−	0.545445i
$123$	18.6240			0.151414
$124$	201.516	−	126.367i	1.62513	−	1.01909i
$125$	76.6865	+	98.7126i	0.613492	+	0.789701i
$126$	−124.362	−	68.8057i	−0.986999	−	0.546077i
$127$	−61.2479			−0.482267			−0.241133	−	0.970492i	$-0.577519\pi$
$127$	−61.2479			−0.482267			−0.241133	+	0.970492i	$0.577519\pi$
$128$	118.101	+	49.3571i	0.922665	+	0.385602i
$129$	−217.604			−1.68685
$130$	−36.9871	+	35.2959i	−0.284516	+	0.271507i
$131$			66.5870i			0.508297i	0.967165	+	0.254149i	$0.0817953\pi$
$131$			66.5870i			0.508297i	−0.967165	+	0.254149i	$0.918205\pi$
$132$	37.9534	−	23.7999i	0.287526	−	0.180302i
$133$			34.2743i			0.257701i
$134$	−122.138	−	67.5756i	−0.911481	−	0.504295i
$135$	−0.762990	−	0.238900i	−0.00565178	−	0.00176963i
$136$	97.9972	−	5.37023i	0.720568	−	0.0394870i
$137$		−	94.0958i		−	0.686831i	−0.939184	−	0.343415i	$-0.888416\pi$
$137$		−	94.0958i		−	0.686831i	0.939184	−	0.343415i	$-0.111584\pi$
$138$	−128.215	−	70.9374i	−0.929092	−	0.514039i
$139$			13.5798i			0.0976963i	0.998806	+	0.0488481i	$0.0155550\pi$
$139$			13.5798i			0.0976963i	−0.998806	+	0.0488481i	$0.984445\pi$
$140$	39.9202	+	152.110i	0.285144	+	1.08650i
$141$	−175.663			−1.24584
$142$	53.3953	−	96.5086i	0.376023	−	0.679638i
$143$	13.4819			0.0942792
$144$	−62.9759	+	130.169i	−0.437332	+	0.903949i
$145$	23.6654	+	7.40986i	0.163209	+	0.0511025i
$146$	−44.1945	+	79.8787i	−0.302702	+	0.547114i
$147$	−54.4801			−0.370613
$148$	−162.215	+	101.722i	−1.09605	+	0.687311i
$149$	60.1634			0.403781			0.201890	−	0.979408i	$-0.435291\pi$
$149$	60.1634			0.403781			0.201890	+	0.979408i	$0.435291\pi$
$150$	94.0010	+	190.415i	0.626673	+	1.26943i
$151$		−	121.691i		−	0.805903i	−0.915221	−	0.402951i	$-0.867984\pi$
$151$		−	121.691i		−	0.805903i	0.915221	−	0.402951i	$-0.132016\pi$
$152$	34.8189	−	1.90807i	0.229072	−	0.0125531i
$153$			110.874i			0.724668i
$154$	20.0762	−	36.2864i	0.130365	−	0.235626i
$155$	88.8423	−	283.742i	0.573176	−	1.83059i
$156$	−73.5830	+	46.1426i	−0.471686	+	0.295786i
$157$			156.552i			0.997149i	0.866847	+	0.498574i	$0.166143\pi$
$157$			156.552i			0.997149i	−0.866847	+	0.498574i	$0.833857\pi$
$158$	81.4777	−	147.266i	0.515682	−	0.932061i
$159$		−	182.548i		−	1.14810i
$160$	152.305	−	49.0227i	0.951905	−	0.306392i
$161$	−135.643			−0.842506
$162$	141.155	+	78.0970i	0.871329	+	0.482080i
$163$	−12.1590			−0.0745948			−0.0372974	−	0.999304i	$-0.511875\pi$
$163$	−12.1590			−0.0745948			−0.0372974	+	0.999304i	$0.511875\pi$
$164$	−9.31870	−	14.8604i	−0.0568213	−	0.0906122i
$165$	16.7325	−	53.4397i	0.101409	−	0.323877i
$166$	3.78387	+	2.09350i	0.0227944	+	0.0126115i
$167$	−153.497			−0.919144			−0.459572	−	0.888140i	$-0.651997\pi$
$167$	−153.497			−0.919144			−0.459572	+	0.888140i	$0.651997\pi$
$168$	14.6184	+	266.760i	0.0870142	+	1.58786i
$169$	142.862			0.845335
$170$	88.7534	−	84.6953i	0.522079	−	0.498207i
$171$			39.3942i			0.230375i
$172$	108.881	+	173.630i	0.633026	+	1.00948i
$173$			310.676i			1.79581i	0.440184	+	0.897907i	$0.354913\pi$
$173$			310.676i			1.79581i	−0.440184	+	0.897907i	$0.645087\pi$
$174$	36.8623	+	20.3948i	0.211852	+	0.117211i
$175$	161.474	+	112.109i	0.922708	+	0.640623i
$176$	−37.9807	−	18.3751i	−0.215800	−	0.104404i
$177$		−	438.877i		−	2.47953i
$178$	−156.892	−	86.8038i	−0.881417	−	0.487662i
$179$		−	104.826i		−	0.585622i	−0.956170	−	0.292811i	$-0.905409\pi$
$179$		−	104.826i		−	0.585622i	0.956170	−	0.292811i	$-0.0945907\pi$
$180$	45.8836	+	174.832i	0.254909	+	0.971291i
$181$	−212.521			−1.17415			−0.587075	−	0.809532i	$-0.699721\pi$
$181$	−212.521			−1.17415			−0.587075	+	0.809532i	$0.699721\pi$
$182$	−38.9232	+	70.3512i	−0.213864	+	0.386545i
$183$	−291.893			−1.59504
$184$	7.55137	+	137.799i	0.0410401	+	0.748908i
$185$	−71.5155	+	228.404i	−0.386570	+	1.23462i
$186$	244.529	−	441.970i	1.31467	−	2.37618i
$187$	−32.3510			−0.173000
$188$	87.8948	+	140.165i	0.467526	+	0.745557i
$189$	−1.25733			−0.00665253
$190$	31.5346	−	30.0927i	0.165971	−	0.158383i
$191$		−	90.5900i		−	0.474293i	−0.971474	−	0.237147i	$-0.923788\pi$
$191$		−	90.5900i		−	0.474293i	0.971474	−	0.237147i	$-0.0762122\pi$
$192$	270.185	−	29.7014i	1.40721	−	0.154695i
$193$		−	326.222i		−	1.69027i	−0.534553	−	0.845135i	$-0.679520\pi$
$193$		−	326.222i		−	1.69027i	0.534553	−	0.845135i	$-0.320480\pi$
$194$	35.3836	−	63.9537i	0.182390	−	0.329658i
$195$	−32.4405	+	103.607i	−0.166362	+	0.531320i
$196$	27.2597	+	43.4706i	0.139080	+	0.221789i
$197$		−	310.516i		−	1.57622i	−0.615531	−	0.788112i	$-0.711059\pi$
$197$		−	310.516i		−	1.57622i	0.615531	−	0.788112i	$-0.288941\pi$
$198$	23.0752	−	41.7069i	0.116541	−	0.210641i
$199$		−	113.446i		−	0.570079i	−0.958516	−	0.285039i	$-0.907993\pi$
$199$		−	113.446i		−	0.570079i	0.958516	−	0.285039i	$-0.0920067\pi$
$200$	104.901	−	170.281i	0.524507	−	0.851406i
$201$	−296.416			−1.47471
$202$	185.044	+	102.379i	0.916057	+	0.506827i
$203$	38.9981			0.192109
$204$	176.568	−	110.723i	0.865531	−	0.542760i
$205$	−20.9239	−	6.55149i	−0.102068	−	0.0319585i
$206$	−328.249	−	181.610i	−1.59344	−	0.881603i
$207$	−155.906			−0.753169
$208$	73.6361	+	35.6253i	0.354020	+	0.171275i
$209$	−11.4945			−0.0549975
$210$	230.550	+	241.597i	1.09786	+	1.15046i
$211$			371.986i			1.76297i	0.472216	+	0.881483i	$0.343454\pi$
$211$			371.986i			1.76297i	−0.472216	+	0.881483i	$0.656546\pi$
$212$	−145.658	+	91.3398i	−0.687067	+	0.430848i
$213$		−	234.215i		−	1.09960i
$214$	195.464	+	108.145i	0.913385	+	0.505349i
$215$	244.477	+	76.5483i	1.13710	+	0.356038i
$216$	0.0699964	+	1.27731i	0.000324057	+	0.00591347i
$217$		−	467.577i		−	2.15473i
$218$	−154.364	−	85.4047i	−0.708090	−	0.391765i
$219$			193.856i			0.885189i
$220$	−51.0127	+	13.3879i	−0.231876	+	0.0608543i
$221$	62.7212			0.283806
$222$	−196.838	+	355.773i	−0.886660	+	1.60258i
$223$	−230.646			−1.03429			−0.517143	−	0.855899i	$-0.673005\pi$
$223$	−230.646			−1.03429			−0.517143	+	0.855899i	$0.673005\pi$
$224$	205.538	−	145.140i	0.917580	−	0.647948i
$225$	185.595	+	128.856i	0.824867	+	0.572694i
$226$	−104.724	+	189.282i	−0.463382	+	0.837532i
$227$	−158.053			−0.696270			−0.348135	−	0.937444i	$-0.613185\pi$
$227$	−158.053			−0.696270			−0.348135	+	0.937444i	$0.613185\pi$
$228$	62.7357	−	39.3405i	0.275157	−	0.172546i
$229$	391.514			1.70967			0.854834	−	0.518902i	$-0.173659\pi$
$229$	391.514			1.70967			0.854834	+	0.518902i	$0.173659\pi$
$230$	119.095	+	124.801i	0.517802	+	0.542613i
$231$		−	88.0630i		−	0.381225i
$232$	−2.17105	−	39.6178i	−0.00935798	−	0.170766i
$233$			66.5715i			0.285715i	0.989743	+	0.142857i	$0.0456290\pi$
$233$			66.5715i			0.285715i	−0.989743	+	0.142857i	$0.954371\pi$
$234$	−44.7376	+	80.8603i	−0.191186	+	0.345557i
$235$	197.357	+	61.7943i	0.839816	+	0.262955i
$236$	−350.188	+	219.597i	−1.48385	+	0.930494i
$237$		−	357.397i		−	1.50800i
$238$	93.3994	−	168.813i	0.392434	−	0.709300i
$239$			379.735i			1.58885i	0.607362	+	0.794425i	$0.292228\pi$
$239$			379.735i			1.58885i	−0.607362	+	0.794425i	$0.707772\pi$
$240$	232.602	−	247.664i	0.969173	−	1.03193i
$241$	133.100			0.552284			0.276142	−	0.961117i	$-0.410944\pi$
$241$	133.100			0.552284			0.276142	+	0.961117i	$0.410944\pi$
$242$	−199.582	−	110.423i	−0.824719	−	0.456292i
$243$	344.007			1.41567
$244$	146.051	+	232.906i	0.598572	+	0.954534i
$245$	61.2081	+	19.1649i	0.249829	+	0.0782239i
$246$	−32.5921	−	18.0323i	−0.132488	−	0.0733018i
$247$	22.2852			0.0902234
$248$	−475.008	+	26.0304i	−1.91535	+	0.104961i
$249$	9.18303			0.0368796
$250$	−38.6259	−	246.998i	−0.154504	−	0.987992i
$251$		−	316.008i		−	1.25900i	−0.777002	−	0.629498i	$-0.783261\pi$
$251$		−	316.008i		−	1.25900i	0.777002	−	0.629498i	$-0.216739\pi$
$252$	151.015	+	240.821i	0.599266	+	0.955641i
$253$		−	45.4904i		−	0.179804i
$254$	107.184	+	59.3019i	0.421986	+	0.233472i
$255$	77.8436	−	248.614i	0.305269	−	0.974958i
$256$	−158.889	−	200.724i	−0.620661	−	0.784079i
$257$			128.416i			0.499672i	0.968288	+	0.249836i	$0.0803766\pi$
$257$			128.416i			0.499672i	−0.968288	+	0.249836i	$0.919623\pi$
$258$	380.810	+	210.691i	1.47601	+	0.816630i
$259$			376.386i			1.45323i
$260$	98.9021	−	25.9562i	0.380393	−	0.0998315i
$261$	44.8237			0.171738
$262$	64.4714	−	116.528i	0.246074	−	0.444763i
$263$	−124.982			−0.475217			−0.237608	−	0.971361i	$-0.576363\pi$
$263$	−124.982			−0.475217			−0.237608	+	0.971361i	$0.576363\pi$
$264$	−89.4625	+	4.90253i	−0.338873	+	0.0185702i
$265$	−64.2163	+	205.092i	−0.242326	+	0.773932i
$266$	33.1853	−	59.9803i	0.124757	−	0.225490i
$267$	−380.760			−1.42607
$268$	148.315	+	236.516i	0.553414	+	0.882522i
$269$	9.37613			0.0348555			0.0174278	−	0.999848i	$-0.494452\pi$
$269$	9.37613			0.0348555			0.0174278	+	0.999848i	$0.494452\pi$
$270$	1.10393	+	1.15682i	0.00408863	+	0.00428454i
$271$			256.996i			0.948325i	0.880437	+	0.474163i	$0.157249\pi$
$271$			256.996i			0.948325i	−0.880437	+	0.474163i	$0.842751\pi$
$272$	−176.696	−	85.4857i	−0.649616	−	0.314286i
$273$			170.734i			0.625400i
$274$	−91.1062	+	164.669i	−0.332504	+	0.600980i
$275$	−37.5977	+	54.1531i	−0.136719	+	0.196920i
$276$	155.693	+	248.282i	0.564107	+	0.899573i
$277$			188.140i			0.679205i	0.940569	+	0.339602i	$0.110292\pi$
$277$			188.140i			0.679205i	−0.940569	+	0.339602i	$0.889708\pi$
$278$	13.1483	−	23.7647i	0.0472961	−	0.0854847i
$279$		−	537.424i		−	1.92625i
$280$	77.4164	−	304.846i	0.276487	−	1.08874i
$281$	−296.580			−1.05544			−0.527722	−	0.849417i	$-0.676954\pi$
$281$	−296.580			−1.05544			−0.527722	+	0.849417i	$0.676954\pi$
$282$	307.412	+	170.082i	1.09011	+	0.603127i
$283$	−75.8785			−0.268122			−0.134061	−	0.990973i	$-0.542802\pi$
$283$	−75.8785			−0.268122			−0.134061	+	0.990973i	$0.542802\pi$
$284$	−186.885	+	117.192i	−0.658045	+	0.412648i
$285$	27.6583	−	88.3341i	0.0970465	−	0.309944i
$286$	−23.5935	−	13.0536i	−0.0824947	−	0.0456419i
$287$	−34.4805			−0.120141
$288$	236.241	−	166.822i	0.820283	−	0.579241i
$289$	138.495			0.479223
$290$	−34.2402	−	35.8808i	−0.118070	−	0.123727i
$291$		−	155.208i		−	0.533362i
$292$	154.682	−	96.9981i	0.529731	−	0.332185i
$293$		−	517.511i		−	1.76625i	−0.469140	−	0.883124i	$-0.655436\pi$
$293$		−	517.511i		−	1.76625i	0.469140	−	0.883124i	$-0.344564\pi$
$294$	95.3406	+	52.7491i	0.324288	+	0.179419i
$295$	−154.387	+	493.076i	−0.523346	+	1.67144i
$296$	382.368	−	20.9537i	1.29178	−	0.0707895i
$297$		−	0.421667i		−	0.00141975i
$298$	−105.286	−	58.2519i	−0.353310	−	0.195476i
$299$			88.1956i			0.294969i
$300$	19.8628	−	424.243i	0.0662092	−	1.41414i
$301$	402.874			1.33845
$302$	−117.825	+	212.961i	−0.390149	+	0.705169i
$303$	449.080			1.48211
$304$	−62.7810	−	30.3735i	−0.206516	−	0.0999130i
$305$	327.940	+	102.681i	1.07521	+	0.336660i
$306$	107.351	−	194.031i	0.350822	−	0.634088i
$307$	389.782			1.26965			0.634825	−	0.772656i	$-0.281072\pi$
$307$	389.782			1.26965			0.634825	+	0.772656i	$0.281072\pi$
$308$	−70.2671	+	44.0633i	−0.228140	+	0.143063i
$309$	−796.622			−2.57807
$310$	−430.202	+	410.531i	−1.38775	+	1.32429i
$311$			98.8294i			0.317779i	0.987296	+	0.158890i	$0.0507914\pi$
$311$			98.8294i			0.317779i	−0.987296	+	0.158890i	$0.949209\pi$
$312$	173.448	−	9.50490i	0.555922	−	0.0304644i
$313$		−	334.942i		−	1.07010i	−0.844820	−	0.535051i	$-0.820292\pi$
$313$		−	334.942i		−	1.07010i	0.844820	−	0.535051i	$-0.179708\pi$
$314$	151.578	−	273.968i	0.482734	−	0.872510i
$315$	339.085	+	106.171i	1.07646	+	0.337050i
$316$	−285.174	+	178.827i	−0.902448	+	0.565909i
$317$			409.880i			1.29300i	0.762916	+	0.646498i	$0.223767\pi$
$317$			409.880i			1.29300i	−0.762916	+	0.646498i	$0.776233\pi$
$318$	−176.748	+	319.461i	−0.555812	+	1.00459i
$319$			13.0787i			0.0409990i
$320$	−314.000	−	61.6757i	−0.981251	−	0.192736i
$321$	474.370			1.47779
$322$	237.377	+	131.334i	0.737197	+	0.407869i
$323$	−53.4751			−0.165558
$324$	−171.407	−	273.341i	−0.529035	−	0.843645i
$325$	72.8935	−	104.991i	0.224288	−	0.323048i
$326$	21.2783	+	11.7726i	0.0652708	+	0.0361124i
$327$	−374.623			−1.14564
$328$	1.91955	+	35.0285i	0.00585230	+	0.106794i
$329$	325.223			0.988521
$330$	−81.0238	+	77.3191i	−0.245527	+	0.234300i
$331$			89.0283i			0.268968i	0.990916	+	0.134484i	$0.0429377\pi$
$331$			89.0283i			0.268968i	−0.990916	+	0.134484i	$0.957062\pi$
$332$	−4.59482	−	7.32730i	−0.0138398	−	0.0220702i
$333$			432.611i			1.29913i
$334$	268.621	+	148.620i	0.804256	+	0.444971i
$335$	333.022	+	104.273i	0.994097	+	0.311261i
$336$	232.702	−	480.986i	0.692565	−	1.43151i
$337$		−	634.325i		−	1.88227i	−0.338030	−	0.941135i	$-0.609761\pi$
$337$		−	634.325i		−	1.88227i	0.338030	−	0.941135i	$-0.390239\pi$
$338$	−250.009	−	138.323i	−0.739672	−	0.409239i
$339$			459.367i			1.35506i
$340$	−237.324	+	62.2840i	−0.698011	+	0.183188i
$341$	156.810			0.459854
$342$	38.1426	−	68.9402i	0.111528	−	0.201580i
$343$	−284.425			−0.829228
$344$	−22.4283	−	409.276i	−0.0651984	−	1.18976i
$345$	349.590	+	109.460i	1.01330	+	0.317275i
$346$	300.805	−	543.686i	0.869379	−	1.57135i
$347$	−71.6174			−0.206390			−0.103195	−	0.994661i	$-0.532907\pi$
$347$	−71.6174			−0.206390			−0.103195	+	0.994661i	$0.532907\pi$
$348$	−44.7625	−	71.3822i	−0.128628	−	0.205121i
$349$	−334.791			−0.959287			−0.479644	−	0.877463i	$-0.659234\pi$
$349$	−334.791			−0.959287			−0.479644	+	0.877463i	$0.659234\pi$
$350$	−174.034	−	352.536i	−0.497240	−	1.00724i
$351$			0.817517i			0.00232911i
$352$	48.6753	+	68.9307i	0.138282	+	0.195826i
$353$			435.693i			1.23426i	0.786863	+	0.617128i	$0.211704\pi$
$353$			435.693i			1.23426i	−0.786863	+	0.617128i	$0.788296\pi$
$354$	−424.933	+	768.039i	−1.20038	+	2.16960i
$355$	−82.3917	+	263.140i	−0.232089	+	0.741240i
$356$	190.517	+	303.815i	0.535160	+	0.853413i
$357$		−	409.691i		−	1.14759i
$358$	−101.496	+	183.447i	−0.283508	+	0.512422i
$359$		−	637.864i		−	1.77678i	−0.459088	−	0.888391i	$-0.651824\pi$
$359$		−	637.864i		−	1.77678i	0.459088	−	0.888391i	$-0.348176\pi$
$360$	88.9809	−	350.384i	0.247169	−	0.973289i
$361$	−19.0000			−0.0526316
$362$	371.914	+	205.769i	1.02739	+	0.568423i
$363$	−484.363			−1.33433
$364$	136.232	−	85.4287i	0.374264	−	0.234694i
$365$	68.1943	−	217.797i	0.186834	−	0.596704i
$366$	510.815	+	282.619i	1.39567	+	0.772182i
$367$	85.8418			0.233901			0.116951	−	0.993138i	$-0.462688\pi$
$367$	85.8418			0.233901			0.116951	+	0.993138i	$0.462688\pi$
$368$	120.206	−	248.461i	0.326647	−	0.675166i
$369$	−39.6313			−0.107402
$370$	346.300	−	330.466i	0.935946	−	0.893151i
$371$			337.970i			0.910971i
$372$	−855.855	+	536.692i	−2.30068	+	1.44272i
$373$		−	286.992i		−	0.769414i	−0.923039	−	0.384707i	$-0.874302\pi$
$373$		−	286.992i		−	0.769414i	0.923039	−	0.384707i	$-0.125698\pi$
$374$	56.6145	+	31.3231i	0.151376	+	0.0837516i
$375$	−325.694	−	419.240i	−0.868516	−	1.11797i
$376$	−18.1054	−	330.392i	−0.0481527	−	0.878702i
$377$		−	25.3566i		−	0.0672589i
$378$	2.20034	+	1.21738i	0.00582100	+	0.00322058i
$379$			58.3444i			0.153943i	0.997033	+	0.0769715i	$0.0245250\pi$
$379$			58.3444i			0.153943i	−0.997033	+	0.0769715i	$0.975475\pi$
$380$	−84.3224	+	22.1298i	−0.221901	+	0.0582364i
$381$	260.124			0.682741
$382$	−87.7118	+	158.533i	−0.229612	+	0.415009i
$383$	−643.140			−1.67922			−0.839608	−	0.543192i	$-0.817215\pi$
$383$	−643.140			−1.67922			−0.839608	+	0.543192i	$0.817215\pi$
$384$	−501.584	−	209.623i	−1.30621	−	0.545894i
$385$	−30.9786	+	98.9384i	−0.0804639	+	0.256983i
$386$	−315.857	+	570.892i	−0.818283	+	1.47899i
$387$	463.055			1.19653
$388$	−123.843	+	77.6601i	−0.319184	+	0.200155i
$389$	−455.761			−1.17162			−0.585811	−	0.810448i	$-0.699224\pi$
$389$	−455.761			−1.17162			−0.585811	+	0.810448i	$0.699224\pi$
$390$	157.087	−	149.904i	0.402787	−	0.384370i
$391$		−	211.632i		−	0.541259i
$392$	−5.61521	−	102.468i	−0.0143245	−	0.261397i
$393$		−	282.800i		−	0.719593i
$394$	−300.651	+	543.406i	−0.763073	+	1.37920i
$395$	−125.724	+	401.534i	−0.318289	+	1.01654i
$396$	−80.7637	+	50.6455i	−0.203949	+	0.127893i
$397$		−	76.3626i		−	0.192349i	−0.995364	−	0.0961745i	$-0.969339\pi$
$397$		−	76.3626i		−	0.192349i	0.995364	−	0.0961745i	$-0.0306607\pi$
$398$	−109.841	+	198.531i	−0.275983	+	0.498822i
$399$		−	145.565i		−	0.364826i
$400$	−348.449	+	196.425i	−0.871124	+	0.491064i
$401$	−748.596			−1.86682			−0.933412	−	0.358806i	$-0.883184\pi$
$401$	−748.596			−1.86682			−0.933412	+	0.358806i	$0.883184\pi$
$402$	518.731	+	286.999i	1.29038	+	0.713927i
$403$	−304.019			−0.754391
$404$	−224.702	−	358.329i	−0.556192	−	0.886953i
$405$	−384.874	−	120.508i	−0.950305	−	0.297550i
$406$	−68.2470	−	37.7590i	−0.168096	−	0.0930026i
$407$	−126.228			−0.310142
$408$	−416.201	+	22.8078i	−1.02010	+	0.0559014i
$409$	−800.314			−1.95676			−0.978379	−	0.206820i	$-0.933689\pi$
$409$	−800.314			−1.95676			−0.978379	+	0.206820i	$0.933689\pi$
$410$	30.2738	+	31.7243i	0.0738385	+	0.0773764i
$411$			399.632i			0.972341i
$412$	398.598	+	635.639i	0.967471	+	1.54281i
$413$			812.539i			1.96741i
$414$	272.837	+	150.953i	0.659027	+	0.364620i
$415$	−10.3171	−	3.23038i	−0.0248605	−	0.00778405i
$416$	−94.3704	−	133.641i	−0.226852	−	0.321253i
$417$		−	57.6744i		−	0.138308i
$418$	20.1154	+	11.1293i	0.0481231	+	0.0266251i
$419$		−	570.553i		−	1.36170i	−0.732422	−	0.680851i	$-0.761610\pi$
$419$		−	570.553i		−	1.36170i	0.732422	−	0.680851i	$-0.238390\pi$
$420$	−169.544	−	646.022i	−0.403677	−	1.53815i
$421$	−324.604			−0.771031			−0.385515	−	0.922701i	$-0.625976\pi$
$421$	−324.604			−0.771031			−0.385515	+	0.922701i	$0.625976\pi$
$422$	360.167	−	650.979i	0.853477	−	1.54260i
$423$	373.806			0.883702
$424$	343.341	−	18.8150i	0.809767	−	0.0443751i
$425$	−174.914	+	251.933i	−0.411562	+	0.592785i
$426$	−226.774	+	409.879i	−0.532333	+	0.962158i
$427$	540.411			1.26560
$428$	−237.356	−	378.508i	−0.554570	−	0.884365i
$429$	−57.2587			−0.133470
$430$	−353.722	−	370.670i	−0.822608	−	0.862023i
$431$		−	536.510i		−	1.24480i	−0.782699	−	0.622401i	$-0.786157\pi$
$431$		−	536.510i		−	1.24480i	0.782699	−	0.622401i	$-0.213843\pi$
$432$	1.11423	−	2.30308i	0.00257924	−	0.00533120i
$433$			95.6563i			0.220915i	0.993881	+	0.110458i	$0.0352317\pi$
$433$			95.6563i			0.220915i	−0.993881	+	0.110458i	$0.964768\pi$
$434$	−452.721	+	818.265i	−1.04314	+	1.88540i
$435$	−100.509	−	31.4702i	−0.231054	−	0.0723453i
$436$	187.446	+	298.918i	0.429923	+	0.685592i
$437$		−	75.1942i		−	0.172069i
$438$	187.697	−	339.251i	0.428533	−	0.774545i
$439$		−	710.451i		−	1.61834i	−0.587575	−	0.809170i	$-0.699917\pi$
$439$		−	710.451i		−	1.61834i	0.587575	−	0.809170i	$-0.300083\pi$
$440$	102.235	+	25.9629i	0.232353	+	0.0590066i
$441$	115.932			0.262884
$442$	−109.763	−	60.7284i	−0.248332	−	0.137395i
$443$	651.816			1.47137			0.735684	−	0.677325i	$-0.236861\pi$
$443$	651.816			1.47137			0.735684	+	0.677325i	$0.236861\pi$
$444$	688.938	−	432.021i	1.55166	−	0.973021i
$445$	427.782	+	133.943i	0.961308	+	0.300995i
$446$	403.633	+	223.318i	0.905006	+	0.500713i
$447$	−255.518			−0.571629
$448$	−500.222	+	54.9893i	−1.11657	+	0.122744i
$449$	−327.873			−0.730229			−0.365114	−	0.930963i	$-0.618970\pi$
$449$	−327.873			−0.730229			−0.365114	+	0.930963i	$0.618970\pi$
$450$	−200.031	−	405.198i	−0.444514	−	0.900440i
$451$		−	11.5636i		−	0.0256400i
$452$	366.537	−	229.849i	0.810922	−	0.508515i
$453$			516.832i			1.14091i
$454$	276.595	+	153.032i	0.609240	+	0.337074i
$455$	60.0605	−	191.819i	0.132001	−	0.421581i
$456$	−147.879	+	8.10373i	−0.324295	+	0.0177713i
$457$		−	352.240i		−	0.770765i	−0.922757	−	0.385382i	$-0.874070\pi$
$457$		−	352.240i		−	0.770765i	0.922757	−	0.385382i	$-0.125930\pi$
$458$	−685.153	−	379.075i	−1.49597	−	0.827674i
$459$		−	1.96170i		−	0.00427385i
$460$	−87.5808	−	333.713i	−0.190393	−	0.725464i
$461$	−134.182			−0.291068			−0.145534	−	0.989353i	$-0.546490\pi$
$461$	−134.182			−0.291068			−0.145534	+	0.989353i	$0.546490\pi$
$462$	−85.2651	+	154.111i	−0.184557	+	0.333574i
$463$	−715.864			−1.54614			−0.773072	−	0.634319i	$-0.781281\pi$
$463$	−715.864			−1.54614			−0.773072	+	0.634319i	$0.781281\pi$
$464$	−34.5597	+	71.4337i	−0.0744822	+	0.153952i
$465$	−377.320	+	1205.07i	−0.811441	+	2.59155i
$466$	64.4564	−	116.501i	0.138319	−	0.250002i
$467$	351.403			0.752469			0.376235	−	0.926524i	$-0.377219\pi$
$467$	351.403			0.752469			0.376235	+	0.926524i	$0.377219\pi$
$468$	156.582	−	98.1901i	0.334578	−	0.209808i
$469$	548.787			1.17012
$470$	−285.545	−	299.227i	−0.607543	−	0.636653i
$471$		−	664.890i		−	1.41166i
$472$	825.451	−	45.2346i	1.74884	−	0.0958360i
$473$			135.111i			0.285646i
$474$	−346.042	+	625.448i	−0.730046	+	1.31951i
$475$	−62.1479	+	89.5134i	−0.130838	+	0.188449i
$476$	−326.900	+	204.993i	−0.686764	+	0.430658i
$477$			388.457i			0.814375i
$478$	367.670	−	664.540i	0.769185	−	1.39025i
$479$		−	566.321i		−	1.18230i	−0.806562	−	0.591149i	$-0.798675\pi$
$479$		−	566.321i		−	1.18230i	0.806562	−	0.591149i	$-0.201325\pi$
$480$	−646.850	+	208.203i	−1.34760	+	0.433756i
$481$	244.727			0.508788
$482$	−232.927	−	128.872i	−0.483251	−	0.267368i
$483$	576.088			1.19273
$484$	242.356	+	386.482i	0.500735	+	0.798516i
$485$	−54.5988	+	174.376i	−0.112575	+	0.359538i
$486$	−602.016	−	333.077i	−1.23872	−	0.685344i
$487$	80.6170			0.165538			0.0827690	−	0.996569i	$-0.473624\pi$
$487$	80.6170			0.165538			0.0827690	+	0.996569i	$0.473624\pi$
$488$	−30.0851	−	548.999i	−0.0616498	−	1.12500i
$489$	51.6400			0.105603
$490$	−88.5588	−	92.8021i	−0.180732	−	0.189392i
$491$		−	103.774i		−	0.211352i	−0.994401	−	0.105676i	$-0.966299\pi$
$491$		−	103.774i		−	0.211352i	0.994401	−	0.105676i	$-0.0337006\pi$
$492$	39.5772	+	63.1132i	0.0804415	+	0.128279i
$493$			60.8452i			0.123418i
$494$	−38.9993	−	21.5771i	−0.0789459	−	0.0436784i
$495$	−35.6062	+	113.718i	−0.0719317	+	0.229733i
$496$	856.472	+	414.363i	1.72676	+	0.835408i
$497$			433.628i			0.872490i
$498$	−16.0704	−	8.89126i	−0.0322698	−	0.0178539i
$499$			67.8705i			0.136013i	0.997685	+	0.0680065i	$0.0216639\pi$
$499$			67.8705i			0.136013i	−0.997685	+	0.0680065i	$0.978336\pi$
$500$	−171.555	+	469.648i	−0.343110	+	0.939295i
$501$	651.914			1.30123
$502$	−305.968	+	553.017i	−0.609497	+	1.10163i
$503$	804.311			1.59903			0.799514	−	0.600648i	$-0.205091\pi$
$503$	804.311			1.59903			0.799514	+	0.600648i	$0.205091\pi$
$504$	−31.1075	−	567.657i	−0.0617212	−	1.12630i
$505$	−504.539	−	157.976i	−0.999088	−	0.312824i
$506$	−44.0451	+	79.6086i	−0.0870456	+	0.157329i
$507$	−606.744			−1.19673
$508$	−130.156	−	207.558i	−0.256212	−	0.408579i
$509$	187.425			0.368223			0.184111	−	0.982905i	$-0.441059\pi$
$509$	187.425			0.368223			0.184111	+	0.982905i	$0.441059\pi$
$510$	−376.942	+	359.707i	−0.739103	+	0.705308i
$511$		−	358.907i		−	0.702362i
$512$	83.7110	+	505.110i	0.163498	+	0.986544i
$513$		−	0.697002i		−	0.00135868i
$514$	124.336	−	224.729i	0.241898	−	0.437215i
$515$	895.002	+	280.234i	1.73787	+	0.544143i
$516$	−462.424	−	737.421i	−0.896170	−	1.42911i
$517$			109.069i			0.210966i
$518$	364.428	−	658.679i	0.703528	−	1.27158i
$519$		−	1319.46i		−	2.54232i
$520$	−198.211	−	50.3362i	−0.381175	−	0.0968005i
$521$	917.427			1.76090			0.880449	−	0.474142i	$-0.157242\pi$
$521$	917.427			1.76090			0.880449	+	0.474142i	$0.157242\pi$
$522$	−78.4418	−	43.3995i	−0.150272	−	0.0831409i
$523$	−377.064			−0.720964			−0.360482	−	0.932766i	$-0.617388\pi$
$523$	−377.064			−0.720964			−0.360482	+	0.932766i	$0.617388\pi$
$524$	−225.651	+	141.502i	−0.430632	+	0.270042i
$525$	−685.792	−	476.136i	−1.30627	−	0.906925i
$526$	218.720	+	121.011i	0.415817	+	0.230059i
$527$	729.519			1.38429
$528$	161.307	+	78.0406i	0.305506	+	0.147804i
$529$	−231.412			−0.437452
$530$	310.955	−	296.737i	0.586707	−	0.559881i
$531$			933.917i			1.75879i
$532$	−116.149	+	72.8352i	−0.218326	+	0.136908i
$533$			22.4193i			0.0420624i
$534$	666.333	+	368.662i	1.24782	+	0.690379i
$535$	−532.953	−	166.873i	−0.996173	−	0.311912i
$536$	−30.5513	−	557.508i	−0.0569988	−	1.04013i
$537$			445.206i			0.829061i
$538$	−16.4083	−	9.07824i	−0.0304987	−	0.0168740i
$539$			33.8267i			0.0627583i
$540$	−0.811819	−	3.09331i	−0.00150337	−	0.00572835i
$541$	−773.178			−1.42917			−0.714583	−	0.699551i	$-0.753383\pi$
$541$	−773.178			−1.42917			−0.714583	+	0.699551i	$0.753383\pi$
$542$	248.831	−	449.746i	0.459098	−	0.829789i
$543$	902.594			1.66224
$544$	226.449	+	320.683i	0.416267	+	0.589490i
$545$	420.887	+	131.784i	0.772270	+	0.241805i
$546$	165.310	−	298.787i	0.302765	−	0.547228i
$547$	−565.381			−1.03360			−0.516801	−	0.856105i	$-0.672877\pi$
$547$	−565.381			−1.03360			−0.516801	+	0.856105i	$0.672877\pi$
$548$	318.874	−	199.960i	0.581886	−	0.364891i
$549$	621.139			1.13140
$550$	118.229	−	58.3653i	0.214962	−	0.106119i
$551$			21.6186i			0.0392353i
$552$	−32.0712	−	585.243i	−0.0581001	−	1.06022i
$553$			661.687i			1.19654i
$554$	182.162	−	329.246i	0.328812	−	0.594307i
$555$	303.732	−	970.049i	0.547264	−	1.74784i
$556$	−46.0194	+	28.8580i	−0.0827687	+	0.0519028i
$557$			192.344i			0.345321i	0.984981	+	0.172660i	$0.0552363\pi$
$557$			192.344i			0.345321i	−0.984981	+	0.172660i	$0.944764\pi$
$558$	−520.349	+	940.498i	−0.932526	+	1.68548i
$559$		−	261.949i		−	0.468603i
$560$	−430.640	+	458.526i	−0.768999	+	0.818797i
$561$	137.397			0.244914
$562$	519.018	+	287.157i	0.923519	+	0.510956i
$563$	404.100			0.717762			0.358881	−	0.933383i	$-0.383158\pi$
$563$	404.100			0.717762			0.358881	+	0.933383i	$0.383158\pi$
$564$	−373.296	−	595.290i	−0.661872	−	1.05548i
$565$	161.595	−	516.097i	0.286009	−	0.913445i
$566$	132.788	+	73.4677i	0.234608	+	0.129802i
$567$	−634.232			−1.11858
$568$	440.519	−	24.1404i	0.775561	−	0.0425006i
$569$	896.493			1.57556			0.787780	−	0.615957i	$-0.211230\pi$
$569$	896.493			1.57556			0.787780	+	0.615957i	$0.211230\pi$
$570$	−133.930	+	127.806i	−0.234964	+	0.224221i
$571$			363.602i			0.636782i	0.947960	+	0.318391i	$0.103142\pi$
$571$			363.602i			0.636782i	−0.947960	+	0.318391i	$0.896858\pi$
$572$	28.6500	+	45.6878i	0.0500874	+	0.0798737i
$573$			384.743i			0.671453i
$574$	60.3412	+	33.3850i	0.105124	+	0.0581620i
$575$	−354.257	−	245.956i	−0.616099	−	0.427749i
$576$	−574.946	+	63.2037i	−0.998170	+	0.109729i
$577$		−	119.730i		−	0.207505i	−0.994603	−	0.103753i	$-0.966915\pi$
$577$		−	119.730i		−	0.207505i	0.994603	−	0.103753i	$-0.0330850\pi$
$578$	−242.368	−	134.095i	−0.419323	−	0.231999i
$579$			1385.49i			2.39290i
$580$	25.1799	+	95.9440i	0.0434136	+	0.165421i
$581$	−17.0015			−0.0292625
$582$	−150.277	+	271.616i	−0.258208	+	0.466694i
$583$	−113.344			−0.194415
$584$	−364.610	+	19.9806i	−0.624333	+	0.0342134i
$585$	69.0324	−	220.473i	0.118004	−	0.376878i
$586$	−501.068	+	905.648i	−0.855065	+	1.54548i
$587$	249.223			0.424571			0.212286	−	0.977208i	$-0.431909\pi$
$587$	249.223			0.424571			0.212286	+	0.977208i	$0.431909\pi$
$588$	−115.774	−	184.623i	−0.196894	−	0.313985i
$589$	259.202			0.440072
$590$	747.589	−	713.406i	1.26710	−	1.20916i
$591$			1318.79i			2.23145i
$592$	−689.435	−	333.550i	−1.16459	−	0.563429i
$593$			749.974i			1.26471i	0.774678	+	0.632356i	$0.217912\pi$
$593$			749.974i			1.26471i	−0.774678	+	0.632356i	$0.782088\pi$
$594$	−0.408270	+	0.737921i	−0.000687323	+	0.00124229i
$595$	−144.120	+	460.286i	−0.242218	+	0.773590i
$596$	127.851	+	203.883i	0.214516	+	0.342085i
$597$			481.812i			0.807056i
$598$	85.3935	−	154.343i	0.142798	−	0.258099i
$599$			442.294i			0.738387i	0.929352	+	0.369194i	$0.120366\pi$
$599$			442.294i			0.738387i	−0.929352	+	0.369194i	$0.879634\pi$
$600$	−445.524	+	723.197i	−0.742540	+	1.20533i
$601$	−153.350			−0.255158			−0.127579	−	0.991828i	$-0.540721\pi$
$601$	−153.350			−0.255158			−0.127579	+	0.991828i	$0.540721\pi$
$602$	−705.033	−	390.074i	−1.17115	−	0.647963i
$603$	630.765			1.04604
$604$	412.390	−	258.602i	0.682764	−	0.428150i
$605$	544.179	+	170.388i	0.899470	+	0.281633i
$606$	−785.894	−	434.812i	−1.29685	−	0.717511i
$607$	111.674			0.183977			0.0919887	−	0.995760i	$-0.470678\pi$
$607$	111.674			0.183977			0.0919887	+	0.995760i	$0.470678\pi$
$608$	80.4588	+	113.940i	0.132333	+	0.187402i
$609$	−165.628			−0.271967
$610$	−474.479	−	497.214i	−0.777835	−	0.815105i
$611$		−	211.461i		−	0.346090i
$612$	−375.732	+	235.615i	−0.613942	+	0.384992i
$613$		−	613.574i		−	1.00094i	−0.865755	−	0.500468i	$-0.833161\pi$
$613$		−	613.574i		−	1.00094i	0.865755	−	0.500468i	$-0.166839\pi$
$614$	−682.123	−	377.398i	−1.11095	−	0.614655i
$615$	88.8656	+	27.8247i	0.144497	+	0.0452434i
$616$	165.631	−	9.07657i	0.268882	−	0.0147347i
$617$		−	433.924i		−	0.703281i	−0.936135	−	0.351640i	$-0.885624\pi$
$617$		−	433.924i		−	0.703281i	0.936135	−	0.351640i	$-0.114376\pi$
$618$	1394.10	+	771.312i	2.25582	+	1.24808i
$619$			415.261i			0.670857i	0.942066	+	0.335429i	$0.108881\pi$
$619$			415.261i			0.670857i	−0.942066	+	0.335429i	$0.891119\pi$
$620$	1150.35	−	301.900i	1.85540	−	0.486936i
$621$	2.75845			0.00444195
$622$	95.6894	−	172.952i	0.153841	−	0.278059i
$623$	704.940			1.13153
$624$	−312.738	−	151.303i	−0.501183	−	0.242473i
$625$	218.436	+	585.586i	0.349498	+	0.936937i
$626$	−324.300	+	586.151i	−0.518051	+	0.936344i
$627$	48.8179			0.0778595
$628$	−530.527	+	332.684i	−0.844789	+	0.529752i
$629$	−587.242			−0.933612
$630$	−490.604	−	514.111i	−0.778737	−	0.816050i
$631$			35.2728i			0.0558999i	0.999609	+	0.0279499i	$0.00889790\pi$
$631$			35.2728i			0.0558999i	−0.999609	+	0.0279499i	$0.991102\pi$
$632$	672.202	−	36.8366i	1.06361	−	0.0582857i
$633$		−	1579.85i		−	2.49582i
$634$	396.857	−	717.293i	0.625958	−	1.13138i
$635$	−292.249	−	91.5059i	−0.460234	−	0.144104i
$636$	618.622	−	387.927i	0.972676	−	0.609948i
$637$		−	65.5824i		−	0.102955i
$638$	12.6631	−	22.8878i	0.0198482	−	0.0358743i
$639$			498.404i			0.779974i
$640$	489.787	+	411.957i	0.765293	+	0.643683i
$641$	624.033			0.973531			0.486766	−	0.873533i	$-0.338177\pi$
$641$	624.033			0.973531			0.486766	+	0.873533i	$0.338177\pi$
$642$	−830.152	−	459.299i	−1.29307	−	0.715418i
$643$	10.7059			0.0166499			0.00832495	−	0.999965i	$-0.497350\pi$
$643$	10.7059			0.0166499			0.00832495	+	0.999965i	$0.497350\pi$
$644$	−288.252	−	459.671i	−0.447596	−	0.713775i
$645$	−1038.31	−	325.106i	−1.60979	−	0.504041i
$646$	93.5819	+	51.7761i	0.144864	+	0.0801488i
$647$	875.711			1.35349			0.676747	−	0.736215i	$-0.263389\pi$
$647$	875.711			1.35349			0.676747	+	0.736215i	$0.263389\pi$
$648$	35.3082	+	644.311i	0.0544879	+	0.994307i
$649$	−272.499			−0.419875
$650$	−229.219	+	113.157i	−0.352645	+	0.174088i
$651$			1985.84i			3.05044i
$652$	−25.8386	−	41.2045i	−0.0396298	−	0.0631971i
$653$		−	182.097i		−	0.278862i	−0.990232	−	0.139431i	$-0.955473\pi$
$653$		−	182.097i		−	0.278862i	0.990232	−	0.139431i	$-0.0445274\pi$
$654$	655.594	+	362.720i	1.00244	+	0.554618i
$655$	−99.4826	+	317.724i	−0.151882	+	0.485075i
$656$	30.5563	−	63.1587i	0.0465797	−	0.0962785i
$657$		−	412.521i		−	0.627886i
$658$	−569.144	−	314.891i	−0.864961	−	0.478557i
$659$		−	476.363i		−	0.722857i	−0.932400	−	0.361429i	$-0.882289\pi$
$659$		−	476.363i		−	0.722857i	0.932400	−	0.361429i	$-0.117711\pi$
$660$	216.655	−	56.8596i	0.328265	−	0.0861509i
$661$	856.895			1.29636			0.648181	−	0.761487i	$-0.275530\pi$
$661$	856.895			1.29636			0.648181	+	0.761487i	$0.275530\pi$
$662$	86.1998	−	155.800i	0.130211	−	0.235348i
$663$	−266.382			−0.401782
$664$	0.946486	+	17.2717i	0.00142543	+	0.0260116i
$665$	−51.2066	+	163.542i	−0.0770025	+	0.245928i
$666$	418.866	−	757.074i	0.628928	−	1.13675i
$667$	−85.5577			−0.128272
$668$	−326.192	−	520.174i	−0.488311	−	0.778703i
$669$	979.571			1.46423
$670$	−481.833	−	504.920i	−0.719153	−	0.753611i
$671$			181.236i			0.270099i
$672$	−872.935	+	616.422i	−1.29901	+	0.917294i
$673$			26.5352i			0.0394282i	0.999806	+	0.0197141i	$0.00627561\pi$
$673$			26.5352i			0.0394282i	−0.999806	+	0.0197141i	$0.993724\pi$
$674$	−614.171	+	1110.08i	−0.911234	+	1.64700i
$675$	−3.28374	−	2.27985i	−0.00486480	−	0.00337756i
$676$	303.591	+	484.132i	0.449099	+	0.716171i
$677$			273.013i			0.403269i	0.979461	+	0.201634i	$0.0646253\pi$
$677$			273.013i			0.403269i	−0.979461	+	0.201634i	$0.935375\pi$
$678$	444.772	−	803.896i	0.656006	−	1.18569i
$679$			287.353i			0.423201i
$680$	475.624	+	120.786i	0.699447	+	0.177626i
$681$	671.264			0.985704
$682$	−274.419	−	151.828i	−0.402374	−	0.222622i
$683$	−835.433			−1.22318			−0.611591	−	0.791174i	$-0.709470\pi$
$683$	−835.433			−1.22318			−0.611591	+	0.791174i	$0.709470\pi$
$684$	−133.500	+	83.7154i	−0.195175	+	0.122391i
$685$	140.582	−	448.985i	0.205229	−	0.655452i
$686$	497.747	+	275.388i	0.725578	+	0.401441i
$687$	−1662.79			−2.42036
$688$	−357.023	+	737.953i	−0.518928	+	1.07261i
$689$	219.749			0.318939
$690$	−505.803	−	530.039i	−0.733048	−	0.768172i
$691$		−	932.039i		−	1.34883i	−0.738354	−	0.674413i	$-0.764397\pi$
$691$		−	932.039i		−	1.34883i	0.738354	−	0.674413i	$-0.235603\pi$
$692$	−1052.82	+	660.208i	−1.52142	+	0.954057i
$693$			187.396i			0.270412i
$694$	125.331	+	69.3419i	0.180592	+	0.0999163i
$695$	−20.2885	+	64.7969i	−0.0291921	+	0.0932329i
$696$	9.22062	+	168.260i	0.0132480	+	0.241753i
$697$		−	53.7969i		−	0.0771835i
$698$	585.888	+	324.154i	0.839381	+	0.464404i
$699$		−	282.734i		−	0.404484i
$700$	−36.7740	+	785.445i	−0.0525343	+	1.12206i
$701$	124.960			0.178260			0.0891299	−	0.996020i	$-0.471591\pi$
$701$	124.960			0.178260			0.0891299	+	0.996020i	$0.471591\pi$
$702$	0.791543	−	1.43066i	0.00112755	−	0.00203798i
$703$	−208.650			−0.296800
$704$	−18.4416	−	167.758i	−0.0261955	−	0.238293i
$705$	−838.189	−	262.445i	−1.18892	−	0.372263i
$706$	421.850	−	762.466i	0.597521	−	1.07998i
$707$	−831.429			−1.17600
$708$	1487.27	−	932.643i	2.10067	−	1.31729i
$709$	−468.215			−0.660388			−0.330194	−	0.943913i	$-0.607114\pi$
$709$	−468.215			−0.660388			−0.330194	+	0.943913i	$0.607114\pi$
$710$	398.966	−	380.724i	0.561924	−	0.536231i
$711$			760.530i			1.06966i
$712$	−39.2445	−	716.143i	−0.0551187	−	1.00582i
$713$			1025.82i			1.43873i
$714$	−396.674	+	716.963i	−0.555566	+	1.00415i
$715$	64.3299	+	20.1423i	0.0899719	+	0.0281711i
$716$	355.238	−	222.763i	0.496142	−	0.311122i
$717$		−	1612.76i		−	2.24932i
$718$	−617.598	+	1116.27i	−0.860165	+	1.55469i
$719$			993.716i			1.38208i	0.722816	+	0.691040i	$0.242847\pi$
$719$			993.716i			1.38208i	−0.722816	+	0.691040i	$0.757153\pi$
$720$	−494.969	+	527.022i	−0.687457	+	0.731975i
$721$	1474.87			2.04559
$722$	33.2502	+	18.3963i	0.0460529	+	0.0254797i
$723$	−565.288			−0.781864
$724$	−451.622	−	720.196i	−0.623788	−	0.994746i
$725$	101.850	+	70.7133i	0.140483	+	0.0975356i
$726$	847.639	+	468.974i	1.16755	+	0.645969i
$727$	−1279.43			−1.75987			−0.879935	−	0.475094i	$-0.842414\pi$
$727$	−1279.43			−1.75987			−0.879935	+	0.475094i	$0.842414\pi$
$728$	−321.122	+	17.5974i	−0.441101	+	0.0241723i
$729$	−735.087			−1.00835
$730$	−330.218	+	315.119i	−0.452353	+	0.431670i
$731$			628.568i			0.859874i
$732$	−620.292	−	989.171i	−0.847393	−	1.35133i
$733$		−	665.369i		−	0.907734i	−0.891069	−	0.453867i	$-0.850044\pi$
$733$		−	665.369i		−	0.907734i	0.891069	−	0.453867i	$-0.149956\pi$
$734$	−150.224	−	83.1145i	−0.204665	−	0.113235i
$735$	−259.955	−	81.3946i	−0.353681	−	0.110741i
$736$	−450.929	+	318.423i	−0.612675	+	0.432640i
$737$			184.045i			0.249722i
$738$	69.3551	+	38.3721i	0.0939771	+	0.0519947i
$739$		−	1226.13i		−	1.65918i	−0.558376	−	0.829588i	$-0.688575\pi$
$739$		−	1226.13i		−	1.65918i	0.558376	−	0.829588i	$-0.311425\pi$
$740$	−925.995	+	243.021i	−1.25134	+	0.328407i
$741$	−94.6469			−0.127729
$742$	327.232	−	591.451i	0.441014	−	0.797104i
$743$	548.799			0.738625			0.369313	−	0.929305i	$-0.379593\pi$
$743$	548.799			0.738625			0.369313	+	0.929305i	$0.379593\pi$
$744$	2017.39	−	110.553i	2.71155	−	0.148593i
$745$	287.074	+	89.8856i	0.385334	+	0.120652i
$746$	−277.873	+	502.238i	−0.372484	+	0.673241i
$747$	−19.5412			−0.0261596
$748$	−68.7480	−	109.631i	−0.0919091	−	0.146566i
$749$	−878.251			−1.17257
$750$	164.047	+	1049.02i	0.218729	+	1.39869i
$751$		−	667.812i		−	0.889231i	−0.895722	−	0.444615i	$-0.853340\pi$
$751$		−	667.812i		−	0.889231i	0.895722	−	0.444615i	$-0.146660\pi$
$752$	−288.210	+	595.719i	−0.383258	+	0.792180i
$753$			1342.11i			1.78235i
$754$	−24.5510	+	44.3743i	−0.0325610	+	0.0588519i
$755$	181.810	−	580.659i	0.240808	−	0.769084i
$756$	−2.67191	−	4.26086i	−0.00353427	−	0.00563605i
$757$		−	102.907i		−	0.135941i	−0.997687	−	0.0679704i	$-0.978348\pi$
$757$		−	102.907i		−	0.135941i	0.997687	−	0.0679704i	$-0.0216524\pi$
$758$	56.4907	−	102.103i	0.0745260	−	0.134701i
$759$			193.201i			0.254547i
$760$	168.992	+	42.9159i	0.222358	+	0.0564683i
$761$	−667.712			−0.877414			−0.438707	−	0.898630i	$-0.644563\pi$
$761$	−667.712			−0.877414			−0.438707	+	0.898630i	$0.644563\pi$
$762$	−455.220	−	251.860i	−0.597402	−	0.330525i
$763$	693.579			0.909015
$764$	306.993	−	192.510i	0.401823	−	0.251976i
$765$	−165.649	+	529.044i	−0.216534	+	0.691561i
$766$	1125.50	+	622.706i	1.46932	+	0.812932i
$767$	528.314			0.688806
$768$	674.815	+	852.491i	0.878665	+	1.11001i
$769$	231.391			0.300899			0.150450	−	0.988618i	$-0.451928\pi$
$769$	231.391			0.300899			0.150450	+	0.988618i	$0.451928\pi$
$770$	150.008	−	143.149i	0.194815	−	0.185908i
$771$		−	545.391i		−	0.707381i
$772$	1105.51	−	693.244i	1.43200	−	0.897985i
$773$		−	1435.62i		−	1.85720i	−0.371081	−	0.928600i	$-0.621013\pi$
$773$		−	1435.62i		−	1.85720i	0.371081	−	0.928600i	$-0.378987\pi$
$774$	−810.351	−	448.343i	−1.04697	−	0.579255i
$775$	847.835	−	1221.16i	1.09398	−	1.57569i
$776$	291.920	−	15.9972i	0.376186	−	0.0206149i
$777$		−	1598.54i		−	2.05732i
$778$	797.586	+	441.281i	1.02517	+	0.567199i
$779$		−	19.1143i		−	0.0245370i
$780$	−420.045	+	110.238i	−0.538519	+	0.141331i
$781$	−145.425			−0.186203
$782$	−204.909	+	370.359i	−0.262031	+	0.473605i
$783$	−0.793066			−0.00101286
$784$	−89.3853	+	184.756i	−0.114012	+	0.235658i
$785$	−233.893	+	747.000i	−0.297953	+	0.951593i
$786$	−273.815	+	494.903i	−0.348365	+	0.629647i
$787$	1038.73			1.31986			0.659932	−	0.751325i	$-0.270585\pi$
$787$	1038.73			1.31986			0.659932	+	0.751325i	$0.270585\pi$
$788$	1052.28	−	659.868i	1.33538	−	0.837396i
$789$	530.808			0.672760
$790$	608.795	−	580.959i	0.770627	−	0.735391i
$791$		−	850.474i		−	1.07519i
$792$	190.374	−	10.4324i	0.240371	−	0.0131723i
$793$		−	351.376i		−	0.443098i
$794$	−73.9364	+	133.635i	−0.0931189	+	0.168306i
$795$	272.731	−	871.041i	0.343058	−	1.09565i
$796$	384.447	−	241.080i	0.482973	−	0.302864i
$797$			1320.40i			1.65671i	0.560202	+	0.828356i	$0.310724\pi$
$797$			1320.40i			1.65671i	−0.560202	+	0.828356i	$0.689276\pi$
$798$	−140.941	+	254.741i	−0.176617	+	0.319224i
$799$			507.417i			0.635065i
$800$	799.975	−	6.36790i	0.999968	−	0.00795987i
$801$	810.245			1.01154
$802$	1310.05	+	724.812i	1.63348	+	0.903756i
$803$	120.366			0.149895
$804$	−629.905	−	1004.50i	−0.783464	−	1.24938i
$805$	−647.232	−	202.655i	−0.804015	−	0.251745i
$806$	532.037	+	294.360i	0.660096	+	0.365211i
$807$	−39.8211			−0.0493447
$808$	46.2862	+	844.642i	0.0572849	+	1.04535i
$809$	50.1331			0.0619692			0.0309846	−	0.999520i	$-0.490136\pi$
$809$	50.1331			0.0619692			0.0309846	+	0.999520i	$0.490136\pi$
$810$	556.854	+	583.535i	0.687474	+	0.720414i
$811$			561.349i			0.692169i	0.938203	+	0.346084i	$0.112489\pi$
$811$			561.349i			0.692169i	−0.938203	+	0.346084i	$0.887511\pi$
$812$	82.8736	+	132.157i	0.102061	+	0.162755i
$813$		−	1091.48i		−	1.34254i
$814$	220.900	+	122.217i	0.271375	+	0.150144i
$815$	−58.0173	−	18.1658i	−0.0711869	−	0.0222893i
$816$	750.440	+	363.064i	0.919657	+	0.444932i
$817$			223.334i			0.273358i
$818$	1400.56	+	774.887i	1.71217	+	0.947294i
$819$		−	363.318i		−	0.443611i
$820$	−22.2630	−	84.8298i	−0.0271500	−	0.103451i
$821$	−782.961			−0.953667			−0.476834	−	0.878994i	$-0.658216\pi$
$821$	−782.961			−0.953667			−0.476834	+	0.878994i	$0.658216\pi$
$822$	386.935	−	699.360i	0.470724	−	0.850803i
$823$	758.379			0.921481			0.460740	−	0.887535i	$-0.347584\pi$
$823$	758.379			0.921481			0.460740	+	0.887535i	$0.347584\pi$
$824$	−82.1071	−	1498.31i	−0.0996445	−	1.81834i
$825$	159.680	−	229.992i	0.193552	−	0.278779i
$826$	786.723	−	1421.95i	0.952449	−	1.72149i
$827$	−778.360			−0.941186			−0.470593	−	0.882351i	$-0.655960\pi$
$827$	−778.360			−0.941186			−0.470593	+	0.882351i	$0.655960\pi$
$828$	−331.311	−	528.337i	−0.400134	−	0.638088i
$829$	−28.6575			−0.0345687			−0.0172844	−	0.999851i	$-0.505502\pi$
$829$	−28.6575			−0.0345687			−0.0172844	+	0.999851i	$0.505502\pi$
$830$	14.9273	+	15.6425i	0.0179846	+	0.0188464i
$831$		−	799.043i		−	0.961544i
$832$	35.7542	+	325.245i	0.0429738	+	0.390920i
$833$			157.370i			0.188920i
$834$	−55.8419	+	100.931i	−0.0669568	+	0.121020i
$835$	−732.422	−	229.329i	−0.877153	−	0.274645i
$836$	−24.4265	−	38.9527i	−0.0292184	−	0.0465941i
$837$			9.50866i			0.0113604i
$838$	−552.426	+	998.474i	−0.659219	+	1.19150i
$839$			862.524i			1.02804i	0.857779	+	0.514019i	$0.171844\pi$
$839$			862.524i			1.02804i	−0.857779	+	0.514019i	$0.828156\pi$
$840$	−328.793	+	1294.70i	−0.391420	+	1.54131i
$841$	−816.402			−0.970751
$842$	568.060	+	314.291i	0.674655	+	0.373267i
$843$	1259.60			1.49418
$844$	−1260.59	+	790.495i	−1.49359	+	0.936606i
$845$	681.674	+	213.439i	0.806715	+	0.252590i
$846$	−654.164	−	361.929i	−0.773243	−	0.427812i
$847$	896.751			1.05874
$848$	−619.068	−	299.506i	−0.730033	−	0.353191i
$849$	322.262			0.379578
$850$	550.030	−	271.530i	0.647094	−	0.319447i
$851$		−	825.752i		−	0.970332i
$852$	793.714	−	497.724i	0.931589	−	0.584183i
$853$		−	558.280i		−	0.654490i	−0.944940	−	0.327245i	$-0.893880\pi$
$853$		−	558.280i		−	0.654490i	0.944940	−	0.327245i	$-0.106120\pi$
$854$	−945.725	−	523.242i	−1.10741	−	0.612695i
$855$	−58.8559	+	187.972i	−0.0688374	+	0.219851i
$856$	48.8929	+	892.208i	0.0571179	+	1.04230i
$857$		−	576.203i		−	0.672349i	−0.941800	−	0.336175i	$-0.890867\pi$
$857$		−	576.203i		−	0.672349i	0.941800	−	0.336175i	$-0.109133\pi$
$858$	100.203	+	55.4395i	0.116787	+	0.0646148i
$859$			331.074i			0.385418i	0.981256	+	0.192709i	$0.0617273\pi$
$859$			331.074i			0.385418i	−0.981256	+	0.192709i	$0.938273\pi$
$860$	260.123	+	991.160i	0.302469	+	1.15251i
$861$	146.441			0.170083
$862$	−519.464	+	938.897i	−0.602626	+	1.08921i
$863$	−456.968			−0.529511			−0.264755	−	0.964316i	$-0.585291\pi$
$863$	−456.968			−0.529511			−0.264755	+	0.964316i	$0.585291\pi$
$864$	−4.17982	+	2.95158i	−0.00483776	+	0.00341618i
$865$	−464.158	+	1482.41i	−0.536599	+	1.71377i
$866$	92.6172	−	167.400i	0.106948	−	0.193302i
$867$	−588.201			−0.678432
$868$	1584.53	−	993.633i	1.82550	−	1.14474i
$869$	−221.908			−0.255360
$870$	145.421	+	152.388i	0.167150	+	0.175159i
$871$		−	356.822i		−	0.409669i
$872$	−38.6120	−	704.601i	−0.0442798	−	0.808028i
$873$			330.279i			0.378326i
$874$	−72.8051	+	131.591i	−0.0833011	+	0.150561i
$875$	602.991	+	776.183i	0.689132	+	0.887066i
$876$	−656.944	+	411.958i	−0.749936	+	0.470272i
$877$			478.389i			0.545484i	0.962087	+	0.272742i	$0.0879305\pi$
$877$			478.389i			0.545484i	−0.962087	+	0.272742i	$0.912070\pi$
$878$	−687.879	+	1243.30i	−0.783461	+	1.41605i
$879$			2197.91i			2.50046i
$880$	−153.775	−	144.423i	−0.174744	−	0.164116i
$881$	513.210			0.582531			0.291266	−	0.956642i	$-0.405924\pi$
$881$	513.210			0.582531			0.291266	+	0.956642i	$0.405924\pi$
$882$	−202.882	−	112.249i	−0.230025	−	0.127266i
$883$	−1246.82			−1.41203			−0.706013	−	0.708199i	$-0.749508\pi$
$883$	−1246.82			−1.41203			−0.706013	+	0.708199i	$0.749508\pi$
$884$	133.287	+	212.551i	0.150777	+	0.240442i
$885$	655.693	−	2094.13i	0.740896	−	2.36625i
$886$	−1140.68	−	631.107i	−1.28745	−	0.712310i
$887$	−41.0678			−0.0462997			−0.0231499	−	0.999732i	$-0.507369\pi$
$887$	−41.0678			−0.0462997			−0.0231499	+	0.999732i	$0.507369\pi$
$888$	−1623.94	+	88.9919i	−1.82877	+	0.100216i
$889$	−481.596			−0.541727
$890$	−618.935	−	648.592i	−0.695433	−	0.728755i
$891$		−	212.701i		−	0.238721i
$892$	−490.139	−	781.617i	−0.549483	−	0.876252i
$893$			180.288i			0.201890i
$894$	447.160	+	247.400i	0.500178	+	0.276734i
$895$	156.613	−	500.187i	0.174987	−	0.558868i
$896$	928.636	+	388.097i	1.03642	+	0.433144i
$897$		−	374.573i		−	0.417585i
$898$	573.780	+	317.456i	0.638954	+	0.353514i
$899$		−	294.926i		−	0.328061i
$900$	−42.2673	+	902.776i	−0.0469637	+	1.00308i
$901$	−527.305			−0.585244
$902$	−11.1962	+	20.2365i	−0.0124127	+	0.0224351i
$903$	−1711.03			−1.89483
$904$	−863.989	+	47.3465i	−0.955741	+	0.0523744i
$905$	−1014.06	−	317.512i	−1.12051	−	0.350842i
$906$	500.411	−	904.461i	0.552330	−	0.998302i
$907$	1246.98			1.37484			0.687420	−	0.726260i	$-0.258743\pi$
$907$	1246.98			1.37484			0.687420	+	0.726260i	$0.258743\pi$
$908$	−335.874	−	535.614i	−0.369905	−	0.589883i
$909$	−955.628			−1.05130
$910$	−290.831	+	277.533i	−0.319595	+	0.304982i
$911$		−	1127.03i		−	1.23714i	−0.785730	−	0.618570i	$-0.787712\pi$
$911$		−	1127.03i		−	1.23714i	0.785730	−	0.618570i	$-0.212288\pi$
$912$	266.635	+	128.999i	0.292363	+	0.141446i
$913$		−	5.70175i		−	0.00624507i
$914$	−341.048	+	616.423i	−0.373138	+	0.674423i
$915$	−1392.79	−	436.095i	−1.52217	−	0.476607i
$916$	831.994	+	1326.77i	0.908290	+	1.44844i
$917$			523.577i			0.570967i
$918$	−1.89937	+	3.43299i	−0.00206903	+	0.00373964i
$919$		−	619.556i		−	0.674163i	−0.941475	−	0.337082i	$-0.890560\pi$
$919$		−	619.556i		−	0.674163i	0.941475	−	0.337082i	$-0.109440\pi$
$920$	−169.843	+	668.800i	−0.184612	+	0.726957i
$921$	−1655.44			−1.79743
$922$	234.821	+	129.919i	0.254686	+	0.140910i
$923$	281.945			0.305466
$924$	298.430	−	187.140i	0.322976	−	0.202532i
$925$	−682.483	+	983.000i	−0.737819	+	1.06270i
$926$	1252.77	+	693.120i	1.35288	+	0.748510i
$927$	1695.19			1.82868
$928$	129.644	−	91.5479i	0.139703	−	0.0986507i
$929$	591.938			0.637177			0.318589	−	0.947893i	$-0.396791\pi$
$929$	591.938			0.637177			0.318589	+	0.947893i	$0.396791\pi$
$930$	1827.10	−	1743.56i	1.96462	−	1.87479i
$931$			55.9145i			0.0600585i
$932$	−225.599	+	141.469i	−0.242059	+	0.151791i
$933$		−	419.736i		−	0.449878i
$934$	−614.959	−	340.239i	−0.658414	−	0.364281i
$935$	−154.365	−	48.3331i	−0.165096	−	0.0516932i
$936$	−369.091	+	20.2262i	−0.394328	+	0.0216091i
$937$			1740.89i			1.85794i	0.370158	+	0.928969i	$0.379304\pi$
$937$			1740.89i			1.85794i	−0.370158	+	0.928969i	$0.620696\pi$
$938$	−960.382	−	531.351i	−1.02386	−	0.566472i
$939$			1422.52i			1.51493i
$940$	209.987	+	800.123i	0.223390	+	0.851195i
$941$	879.263			0.934392			0.467196	−	0.884154i	$-0.345264\pi$
$941$	879.263			0.934392			0.467196	+	0.884154i	$0.345264\pi$
$942$	−643.765	+	1163.56i	−0.683402	+	1.23521i
$943$	75.6467			0.0802192
$944$	−1488.35	−	720.064i	−1.57664	−	0.762780i
$945$	−5.99943	−	1.87848i	−0.00634861	−	0.00198781i
$946$	130.818	−	236.445i	0.138285	−	0.249942i
$947$	−468.695			−0.494926			−0.247463	−	0.968897i	$-0.579597\pi$
$947$	−468.695			−0.494926			−0.247463	+	0.968897i	$0.579597\pi$
$948$	1211.15	−	759.493i	1.27759	−	0.801153i
$949$	−233.362			−0.245903
$950$	195.429	−	96.4760i	0.205714	−	0.101554i
$951$		−	1740.79i		−	1.83048i
$952$	770.558	−	42.2264i	0.809409	−	0.0443555i
$953$			231.717i			0.243145i	0.992583	+	0.121572i	$0.0387936\pi$
$953$			231.717i			0.243145i	−0.992583	+	0.121572i	$0.961206\pi$
$954$	376.115	−	679.803i	0.394250	−	0.712582i
$955$	135.344	−	432.257i	0.141721	−	0.452625i
$956$	−1286.85	+	806.963i	−1.34608	+	0.844104i
$957$		−	55.5462i		−	0.0580420i
$958$	−548.328	+	991.067i	−0.572367	+	1.03452i
$959$		−	739.881i		−	0.771513i
$960$	1333.58	+	261.941i	1.38915	+	0.272855i
$961$	−2575.09			−2.67960
$962$	−428.274	−	236.951i	−0.445192	−	0.246311i
$963$	−1009.45			−1.04823
$964$	282.847	+	451.053i	0.293410	+	0.467897i
$965$	487.384	−	1556.59i	0.505061	−	1.61305i
$966$	−1008.16	−	557.785i	−1.04364	−	0.577417i
$967$	−451.226			−0.466624			−0.233312	−	0.972402i	$-0.574956\pi$
$967$	−451.226			−0.466624			−0.233312	+	0.972402i	$0.574956\pi$
$968$	−49.9228	−	911.002i	−0.0515731	−	0.941118i
$969$	227.113			0.234379
$970$	264.384	−	252.295i	0.272561	−	0.260098i
$971$			536.770i			0.552801i	0.961043	+	0.276400i	$0.0891416\pi$
$971$			536.770i			0.552801i	−0.961043	+	0.276400i	$0.910858\pi$
$972$	731.039	+	1165.78i	0.752097	+	1.19936i
$973$			106.779i			0.109742i
$974$	−141.080	−	78.0556i	−0.144846	−	0.0801392i
$975$	−309.584	+	445.903i	−0.317522	+	0.457337i
$976$	−478.908	+	989.884i	−0.490684	+	1.01423i
$977$			589.656i			0.603538i	0.953381	+	0.301769i	$0.0975771\pi$
$977$			589.656i			0.603538i	−0.953381	+	0.301769i	$0.902423\pi$
$978$	−90.3705	−	49.9993i	−0.0924034	−	0.0511240i
$979$			236.414i			0.241485i
$980$	65.1252	+	248.150i	0.0664543	+	0.253214i
$981$	797.186			0.812626
$982$	−100.477	+	181.605i	−0.102318	+	0.184934i
$983$	−958.328			−0.974902			−0.487451	−	0.873150i	$-0.662073\pi$
$983$	−958.328			−0.974902			−0.487451	+	0.873150i	$0.662073\pi$
$984$	−8.15249	−	148.769i	−0.00828505	−	0.151188i
$985$	463.919	−	1481.65i	0.470984	−	1.50421i
$986$	58.9121	−	106.480i	0.0597485	−	0.107992i
$987$	−1381.25			−1.39944
$988$	47.3575	+	75.5204i	0.0479327	+	0.0764377i
$989$	−883.863			−0.893693
$990$	172.416	−	164.533i	0.174158	−	0.166195i
$991$		−	1894.25i		−	1.91145i	−0.294262	−	0.955725i	$-0.595074\pi$
$991$		−	1894.25i		−	1.91145i	0.294262	−	0.955725i	$-0.404926\pi$
$992$	−1097.64	−	1554.40i	−1.10649	−	1.56693i
$993$		−	378.110i		−	0.380776i
$994$	419.851	−	758.853i	0.422385	−	0.763433i
$995$	169.491	−	541.314i	0.170342	−	0.544034i
$996$	19.5146	+	31.1196i	0.0195929	+	0.0312446i
$997$			263.250i			0.264042i	0.991247	+	0.132021i	$0.0421466\pi$
$997$			263.250i			0.264042i	−0.991247	+	0.132021i	$0.957853\pi$
$998$	65.7142	−	118.774i	0.0658458	−	0.119012i
$999$		−	7.65420i		−	0.00766186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.15	✓	108
4.3	odd	2	inner	380.3.h.a.39.93	yes	108
5.4	even	2	inner	380.3.h.a.39.94	yes	108
20.19	odd	2	inner	380.3.h.a.39.16	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.15	✓	108	1.1	even	1	trivial
380.3.h.a.39.16	yes	108	20.19	odd	2	inner
380.3.h.a.39.93	yes	108	4.3	odd	2	inner
380.3.h.a.39.94	yes	108	5.4	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75001 - 0.968228i) q^{2} -4.24708 q^{3} +(2.12507 + 3.38882i) q^{4} +(4.77157 + 1.49403i) q^{5} +(7.43242 + 4.11214i) q^{6} +7.86306 q^{7} +(-0.437742 - 7.98801i) q^{8} +9.03765 q^{9} +O(q^{10})\)	\(q+(-1.75001 - 0.968228i) q^{2} -4.24708 q^{3} +(2.12507 + 3.38882i) q^{4} +(4.77157 + 1.49403i) q^{5} +(7.43242 + 4.11214i) q^{6} +7.86306 q^{7} +(-0.437742 - 7.98801i) q^{8} +9.03765 q^{9} +(-6.90374 - 7.23453i) q^{10} +2.63701i q^{11} +(-9.02533 - 14.3926i) q^{12} -5.11257i q^{13} +(-13.7604 - 7.61323i) q^{14} +(-20.2652 - 6.34524i) q^{15} +(-6.96817 + 14.4029i) q^{16} +12.2680i q^{17} +(-15.8160 - 8.75051i) q^{18} +4.35890i q^{19} +(5.07693 + 19.3449i) q^{20} -33.3950 q^{21} +(2.55323 - 4.61480i) q^{22} -17.2507 q^{23} +(1.85912 + 33.9257i) q^{24} +(20.5358 + 14.2577i) q^{25} +(-4.95014 + 8.94705i) q^{26} -0.159903 q^{27} +(16.7095 + 26.6465i) q^{28} +4.95966 q^{29} +(29.3207 + 30.7256i) q^{30} -59.4651i q^{31} +(26.1397 - 18.4585i) q^{32} -11.1996i q^{33} +(11.8783 - 21.4692i) q^{34} +(37.5191 + 11.7476i) q^{35} +(19.2056 + 30.6269i) q^{36} +47.8677i q^{37} +(4.22041 - 7.62812i) q^{38} +21.7135i q^{39} +(9.84558 - 38.7694i) q^{40} -4.38513 q^{41} +(58.4416 + 32.3340i) q^{42} +51.2362 q^{43} +(-8.93636 + 5.60383i) q^{44} +(43.1238 + 13.5025i) q^{45} +(30.1889 + 16.7026i) q^{46} +41.3609 q^{47} +(29.5943 - 61.1704i) q^{48} +12.8277 q^{49} +(-22.1331 - 44.8344i) q^{50} -52.1032i q^{51} +(17.3256 - 10.8646i) q^{52} +42.9820i q^{53} +(0.279832 + 0.154823i) q^{54} +(-3.93976 + 12.5827i) q^{55} +(-3.44199 - 62.8102i) q^{56} -18.5126i q^{57} +(-8.67945 - 4.80208i) q^{58} +103.336i q^{59} +(-21.5621 - 82.1592i) q^{60} +68.7279 q^{61} +(-57.5757 + 104.064i) q^{62} +71.0636 q^{63} +(-63.6168 + 6.99338i) q^{64} +(7.63831 - 24.3950i) q^{65} +(-10.8438 + 19.5994i) q^{66} +69.7930 q^{67} +(-41.5741 + 26.0704i) q^{68} +73.2652 q^{69} +(-54.2845 - 56.8855i) q^{70} +55.1475i q^{71} +(-3.95616 - 72.1929i) q^{72} -45.6447i q^{73} +(46.3468 - 83.7689i) q^{74} +(-87.2170 - 60.5535i) q^{75} +(-14.7715 + 9.26296i) q^{76} +20.7350i q^{77} +(21.0236 - 37.9988i) q^{78} +84.1513i q^{79} +(-54.7675 + 58.3140i) q^{80} -80.6597 q^{81} +(7.67402 + 4.24580i) q^{82} -2.16220 q^{83} +(-70.9667 - 113.170i) q^{84} +(-18.3287 + 58.5378i) q^{85} +(-89.6639 - 49.6084i) q^{86} -21.0640 q^{87} +(21.0645 - 1.15433i) q^{88} +89.6522 q^{89} +(-62.3936 - 65.3831i) q^{90} -40.2004i q^{91} +(-36.6590 - 58.4596i) q^{92} +252.553i q^{93} +(-72.3821 - 40.0468i) q^{94} +(-6.51231 + 20.7988i) q^{95} +(-111.017 + 78.3947i) q^{96} +36.5447i q^{97} +(-22.4485 - 12.4201i) q^{98} +23.8324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) 108 * q + 4 * q^5 + 324 * q^9	\( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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