LMFDB - Embedded newform 400.2.y.d.369.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$400 = 2^{4} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	400.y (of order $10$ , degree $4$ , not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			369.4
Character	$\chi$	$=$	400.369
Dual form			400.2.y.d.129.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0350089 - 0.0481856i) q^{3} +(-0.243712 - 2.22275i) q^{5} +1.71675i q^{7} +(0.925955 - 2.84980i) q^{9} +(-0.573356 - 1.76461i) q^{11} +(0.533844 + 0.173457i) q^{13} +(-0.0985723 + 0.0895593i) q^{15} +(2.29552 - 3.15952i) q^{17} +(-4.69249 - 3.40929i) q^{19} +(0.0827227 - 0.0601016i) q^{21} +(6.95461 - 2.25969i) q^{23} +(-4.88121 + 1.08342i) q^{25} +(-0.339673 + 0.110366i) q^{27} +(2.13709 - 1.55269i) q^{29} +(-1.56235 - 1.13511i) q^{31} +(-0.0649561 + 0.0894045i) q^{33} +(3.81590 - 0.418393i) q^{35} +(0.725506 + 0.235731i) q^{37} +(-0.0103312 - 0.0317961i) q^{39} +(-3.00636 + 9.25262i) q^{41} -9.68774i q^{43} +(-6.56004 - 1.36363i) q^{45} +(6.11994 + 8.42338i) q^{47} +4.05276 q^{49} -0.232607 q^{51} +(0.654009 + 0.900166i) q^{53} +(-3.78254 + 1.70448i) q^{55} +0.345466i q^{57} +(1.56343 - 4.81174i) q^{59} +(4.18521 + 12.8808i) q^{61} +(4.89239 + 1.58963i) q^{63} +(0.255446 - 1.22887i) q^{65} +(-0.733847 + 1.01005i) q^{67} +(-0.352358 - 0.256003i) q^{69} +(-10.8951 + 7.91578i) q^{71} +(-3.88964 + 1.26382i) q^{73} +(0.223091 + 0.197275i) q^{75} +(3.02939 - 0.984309i) q^{77} +(-5.25455 + 3.81765i) q^{79} +(-7.25533 - 5.27131i) q^{81} +(-0.536761 + 0.738788i) q^{83} +(-7.58225 - 4.33236i) q^{85} +(-0.149634 - 0.0486192i) q^{87} +(-1.61785 - 4.97923i) q^{89} +(-0.297782 + 0.916478i) q^{91} +0.115022i q^{93} +(-6.43438 + 11.2611i) q^{95} +(8.54098 + 11.7557i) q^{97} -5.55967 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53}+ \cdots - 92 q^{99}+O(q^{100})$ 32 * q + 2 * q^5 + 10 * q^9 - 6 * q^11 - 12 * q^15 + 6 * q^19 - 4 * q^21 + 30 * q^23 + 6 * q^25 - 2 * q^29 - 6 * q^31 - 8 * q^35 - 40 * q^37 + 12 * q^39 - 12 * q^45 + 20 * q^47 - 60 * q^49 + 60 * q^51 - 30 * q^53 + 28 * q^55 + 30 * q^59 + 14 * q^61 + 20 * q^63 - 26 * q^65 - 4 * q^69 - 12 * q^71 + 40 * q^73 - 16 * q^75 - 16 * q^79 - 52 * q^81 - 30 * q^83 + 60 * q^85 - 110 * q^87 + 24 * q^89 + 4 * q^91 - 68 * q^95 + 30 * q^97 - 92 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$ .

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−0.0350089	−	0.0481856i	−0.0202124	−	0.0278200i	0.798791	−	0.601608i	$-0.205473\pi$
$3$	−0.0350089	−	0.0481856i	−0.0202124	−	0.0278200i	−0.819004	+	0.573788i	$0.805473\pi$
$4$		0			0
$5$	−0.243712	−	2.22275i	−0.108991	−	0.994043i
$5$	−0.243712	−	2.22275i	−0.108991	−	0.994043i
$6$		0			0
$7$			1.71675i			0.648871i	0.945908	+	0.324436i	$0.105174\pi$
$7$			1.71675i			0.648871i	−0.945908	+	0.324436i	$0.894826\pi$
$8$		0			0
$9$	0.925955	−	2.84980i	0.308652	−	0.949932i
$10$		0			0
$11$	−0.573356	−	1.76461i	−0.172873	−	0.532049i	0.826657	−	0.562707i	$-0.190240\pi$
$11$	−0.573356	−	1.76461i	−0.172873	−	0.532049i	−0.999530	+	0.0306574i	$0.990240\pi$
$12$		0			0
$13$	0.533844	+	0.173457i	0.148062	+	0.0481082i	0.382110	−	0.924117i	$-0.375197\pi$
$13$	0.533844	+	0.173457i	0.148062	+	0.0481082i	−0.234048	+	0.972225i	$0.575197\pi$
$14$		0			0
$15$	−0.0985723	+	0.0895593i	−0.0254513	+	0.0231241i
$16$		0			0
$17$	2.29552	−	3.15952i	0.556746	−	0.766295i	−0.434162	−	0.900835i	$-0.642955\pi$
$17$	2.29552	−	3.15952i	0.556746	−	0.766295i	0.990908	+	0.134539i	$0.0429555\pi$
$18$		0			0
$19$	−4.69249	−	3.40929i	−1.07653	−	0.782145i	−0.0994556	−	0.995042i	$-0.531710\pi$
$19$	−4.69249	−	3.40929i	−1.07653	−	0.782145i	−0.977075	+	0.212897i	$0.931710\pi$
$20$		0			0
$21$	0.0827227	−	0.0601016i	0.0180516	−	0.0131152i
$22$		0			0
$23$	6.95461	−	2.25969i	1.45014	−	0.471178i	0.525094	−	0.851044i	$-0.324030\pi$
$23$	6.95461	−	2.25969i	1.45014	−	0.471178i	0.925041	+	0.379866i	$0.124030\pi$
$24$		0			0
$25$	−4.88121	+	1.08342i	−0.976242	+	0.216684i
$26$		0			0
$27$	−0.339673	+	0.110366i	−0.0653700	+	0.0212400i
$28$		0			0
$29$	2.13709	−	1.55269i	0.396848	−	0.288327i	−0.371408	−	0.928470i	$-0.621125\pi$
$29$	2.13709	−	1.55269i	0.396848	−	0.288327i	0.768256	+	0.640143i	$0.221125\pi$
$30$		0			0
$31$	−1.56235	−	1.13511i	−0.280607	−	0.203873i	0.438575	−	0.898694i	$-0.355483\pi$
$31$	−1.56235	−	1.13511i	−0.280607	−	0.203873i	−0.719182	+	0.694822i	$0.755483\pi$
$32$		0			0
$33$	−0.0649561	+	0.0894045i	−0.0113074	+	0.0155633i
$34$		0			0
$35$	3.81590	−	0.418393i	0.645006	−	0.0707213i
$36$		0			0
$37$	0.725506	+	0.235731i	0.119272	+	0.0387539i	0.368045	−	0.929808i	$-0.380027\pi$
$37$	0.725506	+	0.235731i	0.119272	+	0.0387539i	−0.248773	+	0.968562i	$0.580027\pi$
$38$		0			0
$39$	−0.0103312	−	0.0317961i	−0.00165431	−	0.00509146i
$40$		0			0
$41$	−3.00636	+	9.25262i	−0.469514	+	1.44502i	0.383701	+	0.923457i	$0.374649\pi$
$41$	−3.00636	+	9.25262i	−0.469514	+	1.44502i	−0.853215	+	0.521559i	$0.825351\pi$
$42$		0			0
$43$		−	9.68774i		−	1.47737i	−0.674053	−	0.738683i	$-0.735448\pi$
$43$		−	9.68774i		−	1.47737i	0.674053	−	0.738683i	$-0.264552\pi$
$44$		0			0
$45$	−6.56004	−	1.36363i	−0.977913	−	0.203278i
$46$		0			0
$47$	6.11994	+	8.42338i	0.892685	+	1.22868i	0.972743	+	0.231886i	$0.0744896\pi$
$47$	6.11994	+	8.42338i	0.892685	+	1.22868i	−0.0800577	+	0.996790i	$0.525510\pi$
$48$		0			0
$49$	4.05276			0.578966
$50$		0			0
$51$	−0.232607			−0.0325715
$52$		0			0
$53$	0.654009	+	0.900166i	0.0898351	+	0.123647i	0.851569	−	0.524243i	$-0.175652\pi$
$53$	0.654009	+	0.900166i	0.0898351	+	0.123647i	−0.761734	+	0.647890i	$0.775652\pi$
$54$		0			0
$55$	−3.78254	+	1.70448i	−0.510038	+	0.229832i
$56$		0			0
$57$			0.345466i			0.0457581i
$58$		0			0
$59$	1.56343	−	4.81174i	0.203541	−	0.626435i	−0.796229	−	0.604995i	$-0.793175\pi$
$59$	1.56343	−	4.81174i	0.203541	−	0.626435i	0.999770	−	0.0214397i	$-0.00682500\pi$
$60$		0			0
$61$	4.18521	+	12.8808i	0.535862	+	1.64921i	0.741780	+	0.670643i	$0.233982\pi$
$61$	4.18521	+	12.8808i	0.535862	+	1.64921i	−0.205918	+	0.978569i	$0.566018\pi$
$62$		0			0
$63$	4.89239	+	1.58963i	0.616383	+	0.200275i
$64$		0			0
$65$	0.255446	−	1.22887i	0.0316841	−	0.152423i
$66$		0			0
$67$	−0.733847	+	1.01005i	−0.0896537	+	0.123398i	−0.851488	−	0.524375i	$-0.824299\pi$
$67$	−0.733847	+	1.01005i	−0.0896537	+	0.123398i	0.761834	+	0.647772i	$0.224299\pi$
$68$		0			0
$69$	−0.352358	−	0.256003i	−0.0424189	−	0.0308191i
$70$		0			0
$71$	−10.8951	+	7.91578i	−1.29302	+	0.939430i	−0.999862	−	0.0166349i	$-0.994705\pi$
$71$	−10.8951	+	7.91578i	−1.29302	+	0.939430i	−0.293154	+	0.956065i	$0.594705\pi$
$72$		0			0
$73$	−3.88964	+	1.26382i	−0.455248	+	0.147919i	−0.527660	−	0.849456i	$-0.676930\pi$
$73$	−3.88964	+	1.26382i	−0.455248	+	0.147919i	0.0724119	+	0.997375i	$0.476930\pi$
$74$		0			0
$75$	0.223091	+	0.197275i	0.0257603	+	0.0227793i
$76$		0			0
$77$	3.02939	−	0.984309i	0.345231	−	0.112172i
$78$		0			0
$79$	−5.25455	+	3.81765i	−0.591183	+	0.429520i	−0.842738	−	0.538323i	$-0.819058\pi$
$79$	−5.25455	+	3.81765i	−0.591183	+	0.429520i	0.251555	+	0.967843i	$0.419058\pi$
$80$		0			0
$81$	−7.25533	−	5.27131i	−0.806148	−	0.585701i
$82$		0			0
$83$	−0.536761	+	0.738788i	−0.0589172	+	0.0810925i	−0.837459	−	0.546500i	$-0.815960\pi$
$83$	−0.536761	+	0.738788i	−0.0589172	+	0.0810925i	0.778542	+	0.627593i	$0.215960\pi$
$84$		0			0
$85$	−7.58225	−	4.33236i	−0.822411	−	0.469910i
$86$		0			0
$87$	−0.149634	−	0.0486192i	−0.0160425	−	0.00521252i
$88$		0			0
$89$	−1.61785	−	4.97923i	−0.171492	−	0.527797i	0.827964	−	0.560781i	$-0.189499\pi$
$89$	−1.61785	−	4.97923i	−0.171492	−	0.527797i	−0.999456	+	0.0329839i	$0.989499\pi$
$90$		0			0
$91$	−0.297782	+	0.916478i	−0.0312160	+	0.0960730i
$92$		0			0
$93$			0.115022i			0.0119272i
$94$		0			0
$95$	−6.43438	+	11.2611i	−0.660153	+	1.15536i
$96$		0			0
$97$	8.54098	+	11.7557i	0.867205	+	1.19361i	0.979803	+	0.199965i	$0.0640828\pi$
$97$	8.54098	+	11.7557i	0.867205	+	1.19361i	−0.112598	+	0.993641i	$0.535917\pi$
$98$		0			0
$99$	−5.55967			−0.558768
$100$		0			0
$101$	−1.84989			−0.184071			−0.0920354	−	0.995756i	$-0.529337\pi$
$101$	−1.84989			−0.184071			−0.0920354	+	0.995756i	$0.529337\pi$
$102$		0			0
$103$	6.06351	+	8.34571i	0.597456	+	0.822327i	0.995472	−	0.0950510i	$-0.0303014\pi$
$103$	6.06351	+	8.34571i	0.597456	+	0.822327i	−0.398017	+	0.917378i	$0.630301\pi$
$104$		0			0
$105$	−0.153751	−	0.169224i	−0.0150046	−	0.0165146i
$106$		0			0
$107$			15.1159i			1.46131i	0.682746	+	0.730656i	$0.260786\pi$
$107$			15.1159i			1.46131i	−0.682746	+	0.730656i	$0.739214\pi$
$108$		0			0
$109$	1.40146	−	4.31325i	0.134235	−	0.413134i	−0.861235	−	0.508207i	$-0.830308\pi$
$109$	1.40146	−	4.31325i	0.134235	−	0.413134i	0.995470	+	0.0950729i	$0.0303084\pi$
$110$		0			0
$111$	−0.0140403	−	0.0432116i	−0.00133265	−	0.00410146i
$112$		0			0
$113$	14.8637	+	4.82952i	1.39826	+	0.454323i	0.908628	−	0.417606i	$-0.137131\pi$
$113$	14.8637	+	4.82952i	1.39826	+	0.454323i	0.489633	+	0.871929i	$0.337131\pi$
$114$		0			0
$115$	−6.71764	−	14.9076i	−0.626423	−	1.39014i
$116$		0			0
$117$	0.988632	−	1.36073i	0.0913990	−	0.125800i
$118$		0			0
$119$	5.42411	+	3.94084i	0.497227	+	0.361257i
$120$		0			0
$121$	6.11408	−	4.44214i	0.555826	−	0.403831i
$122$		0			0
$123$	0.551092	−	0.179061i	0.0496903	−	0.0161454i
$124$		0			0
$125$	3.59778	+	10.5856i	0.321795	+	0.946809i
$126$		0			0
$127$	1.27621	−	0.414665i	0.113245	−	0.0367956i	−0.251846	−	0.967767i	$-0.581038\pi$
$127$	1.27621	−	0.414665i	0.113245	−	0.0367956i	0.365091	+	0.930972i	$0.381038\pi$
$128$		0			0
$129$	−0.466810	+	0.339157i	−0.0411003	+	0.0298611i
$130$		0			0
$131$	11.2000	+	8.13727i	0.978548	+	0.710957i	0.957384	−	0.288819i	$-0.0932626\pi$
$131$	11.2000	+	8.13727i	0.978548	+	0.710957i	0.0211645	+	0.999776i	$0.493263\pi$
$132$		0			0
$133$	5.85291	−	8.05583i	0.507511	−	0.698529i
$134$		0			0
$135$	0.328099	+	0.728109i	0.0282382	+	0.0626656i
$136$		0			0
$137$	−8.02147	−	2.60633i	−0.685320	−	0.222674i	−0.0543972	−	0.998519i	$-0.517324\pi$
$137$	−8.02147	−	2.60633i	−0.685320	−	0.222674i	−0.630923	+	0.775845i	$0.717324\pi$
$138$		0			0
$139$	−4.91470	−	15.1259i	−0.416860	−	1.28296i	−0.910577	−	0.413340i	$-0.864362\pi$
$139$	−4.91470	−	15.1259i	−0.416860	−	1.28296i	0.493717	−	0.869622i	$-0.335638\pi$
$140$		0			0
$141$	0.191633	−	0.589786i	0.0161384	−	0.0496690i
$142$		0			0
$143$		−	1.04148i		−	0.0870928i
$144$		0			0
$145$	−3.97207	−	4.37181i	−0.329862	−	0.363059i
$146$		0			0
$147$	−0.141883	−	0.195285i	−0.0117023	−	0.0161068i
$148$		0			0
$149$	−8.35969			−0.684852			−0.342426	−	0.939545i	$-0.611249\pi$
$149$	−8.35969			−0.684852			−0.342426	+	0.939545i	$0.611249\pi$
$150$		0			0
$151$	5.35624			0.435885			0.217942	−	0.975962i	$-0.430066\pi$
$151$	5.35624			0.435885			0.217942	+	0.975962i	$0.430066\pi$
$152$		0			0
$153$	−6.87843	−	9.46734i	−0.556088	−	0.765389i
$154$		0			0
$155$	−2.14231	+	3.74935i	−0.172074	+	0.301155i
$156$		0			0
$157$			13.3180i			1.06289i	0.847092	+	0.531446i	$0.178351\pi$
$157$			13.3180i			1.06289i	−0.847092	+	0.531446i	$0.821649\pi$
$158$		0			0
$159$	0.0204789	−	0.0630277i	0.00162408	−	0.00499842i
$160$		0			0
$161$	3.87932	+	11.9393i	0.305734	+	0.940951i
$162$		0			0
$163$	−13.4848	−	4.38148i	−1.05621	−	0.343184i	−0.271109	−	0.962549i	$-0.587390\pi$
$163$	−13.4848	−	4.38148i	−1.05621	−	0.343184i	−0.785104	+	0.619364i	$0.787390\pi$
$164$		0			0
$165$	0.214554	+	0.122592i	0.0167030	+	0.00954379i
$166$		0			0
$167$	13.3299	−	18.3470i	1.03150	−	1.41973i	0.127677	−	0.991816i	$-0.459248\pi$
$167$	13.3299	−	18.3470i	1.03150	−	1.41973i	0.903818	−	0.427916i	$-0.140752\pi$
$168$		0			0
$169$	−10.2623	−	7.45601i	−0.789409	−	0.573539i
$170$		0			0
$171$	−14.0608	+	10.2158i	−1.07526	+	0.781220i
$172$		0			0
$173$	6.43969	−	2.09238i	0.489601	−	0.159081i	−0.0538045	−	0.998551i	$-0.517135\pi$
$173$	6.43969	−	2.09238i	0.489601	−	0.159081i	0.543405	+	0.839471i	$0.317135\pi$
$174$		0			0
$175$	−1.85996	−	8.37982i	−0.140600	−	0.633455i
$176$		0			0
$177$	−0.286590	+	0.0931189i	−0.0215415	+	0.00699924i
$178$		0			0
$179$	20.3012	−	14.7497i	1.51739	−	1.10245i	0.554621	−	0.832103i	$-0.312863\pi$
$179$	20.3012	−	14.7497i	1.51739	−	1.10245i	0.962764	−	0.270342i	$-0.0871368\pi$
$180$		0			0
$181$	−20.3908	−	14.8148i	−1.51564	−	1.10117i	−0.963598	−	0.267356i	$-0.913850\pi$
$181$	−20.3908	−	14.8148i	−1.51564	−	1.10117i	−0.552039	−	0.833818i	$-0.686150\pi$
$182$		0			0
$183$	0.474148	−	0.652608i	0.0350500	−	0.0482422i
$184$		0			0
$185$	0.347156	−	1.67007i	0.0255234	−	0.122786i
$186$		0			0
$187$	−6.89146	−	2.23917i	−0.503953	−	0.163744i
$188$		0			0
$189$	−0.189472	−	0.583133i	−0.0137820	−	0.0424167i
$190$		0			0
$191$	6.14957	−	18.9264i	0.444967	−	1.36947i	−0.437552	−	0.899193i	$-0.644155\pi$
$191$	6.14957	−	18.9264i	0.444967	−	1.36947i	0.882520	−	0.470275i	$-0.155845\pi$
$192$		0			0
$193$			4.79198i			0.344934i	0.985015	+	0.172467i	$0.0551738\pi$
$193$			4.79198i			0.344934i	−0.985015	+	0.172467i	$0.944826\pi$
$194$		0			0
$195$	−0.0681569	+	0.0307127i	−0.00488082	+	0.00219938i
$196$		0			0
$197$	0.393872	+	0.542119i	0.0280622	+	0.0386244i	0.822818	−	0.568306i	$-0.192401\pi$
$197$	0.393872	+	0.542119i	0.0280622	+	0.0386244i	−0.794755	+	0.606930i	$0.792401\pi$
$198$		0			0
$199$	9.41311			0.667278			0.333639	−	0.942701i	$-0.391723\pi$
$199$	9.41311			0.667278			0.333639	+	0.942701i	$0.391723\pi$
$200$		0			0
$201$	0.0743612			0.00524504
$202$		0			0
$203$	2.66558	+	3.66886i	0.187087	+	0.257503i
$204$		0			0
$205$	21.2989	+	4.42740i	1.48758	+	0.309223i
$206$		0			0
$207$		−	21.9116i		−	1.52296i
$208$		0			0
$209$	−3.32560	+	10.2351i	−0.230036	+	0.707979i
$210$		0			0
$211$	3.80217	+	11.7019i	0.261752	+	0.805589i	0.992424	+	0.122861i	$0.0392069\pi$
$211$	3.80217	+	11.7019i	0.261752	+	0.805589i	−0.730672	+	0.682729i	$0.760793\pi$
$212$		0			0
$213$	0.762854	+	0.247866i	0.0522699	+	0.0169835i
$214$		0			0
$215$	−21.5334	+	2.36102i	−1.46857	+	0.161020i
$216$		0			0
$217$	1.94871	−	2.68217i	0.132287	−	0.182078i
$218$		0			0
$219$	0.197070	+	0.143180i	0.0133168	+	0.00967519i
$220$		0			0
$221$	1.77349	−	1.28852i	0.119298	−	0.0866750i
$222$		0			0
$223$	13.4389	−	4.36656i	0.899934	−	0.292406i	0.177724	−	0.984080i	$-0.443127\pi$
$223$	13.4389	−	4.36656i	0.899934	−	0.292406i	0.722210	+	0.691674i	$0.243127\pi$
$224$		0			0
$225$	−1.43225	+	14.9136i	−0.0954834	+	0.994243i
$226$		0			0
$227$	3.72885	−	1.21158i	0.247492	−	0.0804151i	−0.182644	−	0.983179i	$-0.558466\pi$
$227$	3.72885	−	1.21158i	0.247492	−	0.0804151i	0.430136	+	0.902764i	$0.358466\pi$
$228$		0			0
$229$	2.16082	−	1.56993i	0.142791	−	0.103744i	−0.514096	−	0.857732i	$-0.671873\pi$
$229$	2.16082	−	1.56993i	0.142791	−	0.103744i	0.656887	+	0.753989i	$0.271873\pi$
$230$		0			0
$231$	−0.153485	−	0.111514i	−0.0100986	−	0.00733705i
$232$		0			0
$233$	13.1641	−	18.1188i	0.862409	−	1.18700i	−0.118581	−	0.992944i	$-0.537835\pi$
$233$	13.1641	−	18.1188i	0.862409	−	1.18700i	0.980990	−	0.194059i	$-0.0621654\pi$
$234$		0			0
$235$	17.2315	−	15.6560i	1.12406	−	1.02128i
$236$		0			0
$237$	0.367912	+	0.119542i	0.0238985	+	0.00776508i
$238$		0			0
$239$	6.69719	+	20.6118i	0.433205	+	1.33327i	0.894915	+	0.446237i	$0.147236\pi$
$239$	6.69719	+	20.6118i	0.433205	+	1.33327i	−0.461710	+	0.887031i	$0.652764\pi$
$240$		0			0
$241$	5.45316	−	16.7831i	0.351269	−	1.08109i	−0.606872	−	0.794799i	$-0.707576\pi$
$241$	5.45316	−	16.7831i	0.351269	−	1.08109i	0.958141	−	0.286296i	$-0.0924239\pi$
$242$		0			0
$243$			1.60560i			0.103000i
$244$		0			0
$245$	−0.987708	−	9.00827i	−0.0631023	−	0.575517i
$246$		0			0
$247$	−1.91369	−	2.63397i	−0.121765	−	0.167596i
$248$		0			0
$249$	0.0543904			0.00344685
$250$		0			0
$251$	16.2475			1.02553			0.512766	−	0.858528i	$-0.328621\pi$
$251$	16.2475			1.02553			0.512766	+	0.858528i	$0.328621\pi$
$252$		0			0
$253$	−7.97493	−	10.9765i	−0.501379	−	0.690090i
$254$		0			0
$255$	0.0566891	+	0.517027i	0.00355001	+	0.0323775i
$256$		0			0
$257$			9.12754i			0.569361i	0.958623	+	0.284680i	$0.0918874\pi$
$257$			9.12754i			0.569361i	−0.958623	+	0.284680i	$0.908113\pi$
$258$		0			0
$259$	−0.404692	+	1.24551i	−0.0251463	+	0.0773924i
$260$		0			0
$261$	−2.44599	−	7.52800i	−0.151403	−	0.465971i
$262$		0			0
$263$	−18.2735	−	5.93742i	−1.12679	−	0.366117i	−0.314436	−	0.949279i	$-0.601816\pi$
$263$	−18.2735	−	5.93742i	−1.12679	−	0.366117i	−0.812356	+	0.583161i	$0.801816\pi$
$264$		0			0
$265$	1.84145	−	1.67308i	0.113120	−	0.102776i
$266$		0			0
$267$	−0.183288	+	0.252274i	−0.0112170	+	0.0154389i
$268$		0			0
$269$	4.36357	+	3.17032i	0.266052	+	0.193298i	0.712811	−	0.701356i	$-0.247422\pi$
$269$	4.36357	+	3.17032i	0.266052	+	0.193298i	−0.446759	+	0.894654i	$0.647422\pi$
$270$		0			0
$271$	−17.3290	+	12.5902i	−1.05266	+	0.764803i	−0.972717	−	0.231996i	$-0.925474\pi$
$271$	−17.3290	+	12.5902i	−1.05266	+	0.764803i	−0.0799442	+	0.996799i	$0.525474\pi$
$272$		0			0
$273$	0.0545861	−	0.0177361i	0.00330370	−	0.00107344i
$274$		0			0
$275$	4.71048	+	7.99223i	0.284053	+	0.481950i
$276$		0			0
$277$	−13.7152	+	4.45635i	−0.824068	+	0.267756i	−0.690545	−	0.723290i	$-0.742629\pi$
$277$	−13.7152	+	4.45635i	−0.824068	+	0.267756i	−0.133524	+	0.991046i	$0.542629\pi$
$278$		0			0
$279$	−4.68151	+	3.40132i	−0.280275	+	0.203632i
$280$		0			0
$281$	−10.6166	−	7.71340i	−0.633332	−	0.460143i	0.224221	−	0.974538i	$-0.428016\pi$
$281$	−10.6166	−	7.71340i	−0.633332	−	0.460143i	−0.857553	+	0.514395i	$0.828016\pi$
$282$		0			0
$283$	−15.5938	+	21.4630i	−0.926953	+	1.27584i	0.0340827	+	0.999419i	$0.489149\pi$
$283$	−15.5938	+	21.4630i	−0.926953	+	1.27584i	−0.961036	+	0.276423i	$0.910851\pi$
$284$		0			0
$285$	0.767883	−	0.0841942i	0.0454855	−	0.00498723i
$286$		0			0
$287$	−15.8844	−	5.16117i	−0.937629	−	0.304654i
$288$		0			0
$289$	0.540169	+	1.66247i	0.0317747	+	0.0977923i
$290$		0			0
$291$	0.267443	−	0.823105i	0.0156778	−	0.0482513i
$292$		0			0
$293$			24.1828i			1.41277i	0.707827	+	0.706386i	$0.249676\pi$
$293$			24.1828i			1.41277i	−0.707827	+	0.706386i	$0.750324\pi$
$294$		0			0
$295$	−11.0763	−	2.30243i	−0.644887	−	0.134053i
$296$		0			0
$297$	0.389506	+	0.536110i	0.0226015	+	0.0311082i
$298$		0			0
$299$	4.10464			0.237377
$300$		0			0
$301$	16.6314			0.958621
$302$		0			0
$303$	0.0647625	+	0.0891380i	0.00372051	+	0.00512084i
$304$		0			0
$305$	27.6107	−	12.4419i	1.58098	−	0.712419i
$306$		0			0
$307$			19.1169i			1.09106i	0.838091	+	0.545530i	$0.183672\pi$
$307$			19.1169i			1.09106i	−0.838091	+	0.545530i	$0.816328\pi$
$308$		0			0
$309$	0.189866	−	0.584348i	0.0108011	−	0.0332424i
$310$		0			0
$311$	−7.01668	−	21.5951i	−0.397879	−	1.22455i	−0.926696	−	0.375811i	$-0.877364\pi$
$311$	−7.01668	−	21.5951i	−0.397879	−	1.22455i	0.528817	−	0.848736i	$-0.322636\pi$
$312$		0			0
$313$	−12.7661	−	4.14797i	−0.721585	−	0.234457i	−0.0748747	−	0.997193i	$-0.523856\pi$
$313$	−12.7661	−	4.14797i	−0.721585	−	0.234457i	−0.646710	+	0.762736i	$0.723856\pi$
$314$		0			0
$315$	2.34102	−	11.2620i	0.131902	−	0.634540i
$316$		0			0
$317$	15.9915	−	22.0105i	0.898174	−	1.23623i	−0.0728730	−	0.997341i	$-0.523217\pi$
$317$	15.9915	−	22.0105i	0.898174	−	1.23623i	0.971047	−	0.238889i	$-0.0767832\pi$
$318$		0			0
$319$	−3.96520	−	2.88089i	−0.222009	−	0.161299i
$320$		0			0
$321$	0.728370	−	0.529192i	0.0406537	−	0.0295366i
$322$		0			0
$323$	−21.5434	+	6.99988i	−1.19871	+	0.389484i
$324$		0			0
$325$	−2.79373	−	0.268300i	−0.154968	−	0.0148826i
$326$		0			0
$327$	−0.256900	+	0.0834719i	−0.0142066	+	0.00461601i
$328$		0			0
$329$	−14.4608	+	10.5064i	−0.797252	+	0.579238i
$330$		0			0
$331$	23.3469	+	16.9625i	1.28326	+	0.932344i	0.999646	−	0.0265941i	$-0.00846615\pi$
$331$	23.3469	+	16.9625i	1.28326	+	0.932344i	0.283615	+	0.958938i	$0.408466\pi$
$332$		0			0
$333$	1.34357	−	1.84927i	0.0736272	−	0.101339i
$334$		0			0
$335$	2.42394	+	1.38499i	0.132434	+	0.0756703i
$336$		0			0
$337$	−19.9562	−	6.48418i	−1.08709	−	0.353216i	−0.289966	−	0.957037i	$-0.593644\pi$
$337$	−19.9562	−	6.48418i	−1.08709	−	0.353216i	−0.797120	+	0.603821i	$0.793644\pi$
$338$		0			0
$339$	−0.287649	−	0.885294i	−0.0156230	−	0.0480825i
$340$		0			0
$341$	−1.10725	+	3.40776i	−0.0599609	+	0.184541i
$342$		0			0
$343$			18.9748i			1.02455i
$344$		0			0
$345$	−0.483156	+	0.845593i	−0.0260122	+	0.0455252i
$346$		0			0
$347$	10.3583	+	14.2570i	0.556063	+	0.765355i	0.990819	−	0.135193i	$-0.0431655\pi$
$347$	10.3583	+	14.2570i	0.556063	+	0.765355i	−0.434756	+	0.900548i	$0.643165\pi$
$348$		0			0
$349$	−13.6103			−0.728544			−0.364272	−	0.931293i	$-0.618682\pi$
$349$	−13.6103			−0.728544			−0.364272	+	0.931293i	$0.618682\pi$
$350$		0			0
$351$	−0.200476			−0.0107006
$352$		0			0
$353$	7.66202	+	10.5459i	0.407808	+	0.561299i	0.962682	−	0.270635i	$-0.0872336\pi$
$353$	7.66202	+	10.5459i	0.407808	+	0.561299i	−0.554874	+	0.831934i	$0.687234\pi$
$354$		0			0
$355$	20.2501	+	22.2880i	1.07476	+	1.18292i
$356$		0			0
$357$		−	0.399328i		−	0.0211347i
$358$		0			0
$359$	−4.59073	+	14.1288i	−0.242289	+	0.745690i	0.753781	+	0.657126i	$0.228228\pi$
$359$	−4.59073	+	14.1288i	−0.242289	+	0.745690i	−0.996070	+	0.0885643i	$0.971772\pi$
$360$		0			0
$361$	4.52484	+	13.9260i	0.238150	+	0.732949i
$362$		0			0
$363$	−0.428095	−	0.139096i	−0.0224691	−	0.00730067i
$364$		0			0
$365$	3.75711	+	8.33768i	0.196656	+	0.436414i
$366$		0			0
$367$	15.5525	−	21.4062i	0.811836	−	1.11740i	−0.179202	−	0.983812i	$-0.557351\pi$
$367$	15.5525	−	21.4062i	0.811836	−	1.11740i	0.991038	−	0.133584i	$-0.0426485\pi$
$368$		0			0
$369$	23.5843	+	17.1350i	1.22775	+	0.892013i
$370$		0			0
$371$	−1.54536	+	1.12277i	−0.0802312	+	0.0582914i
$372$		0			0
$373$	−31.8132	+	10.3367i	−1.64722	+	0.535215i	−0.978136	−	0.207968i	$-0.933315\pi$
$373$	−31.8132	+	10.3367i	−1.64722	+	0.535215i	−0.669088	+	0.743183i	$0.733315\pi$
$374$		0			0
$375$	0.384122	−	0.543953i	0.0198360	−	0.0280896i
$376$		0			0
$377$	1.41020	−	0.458201i	0.0726289	−	0.0235986i
$378$		0			0
$379$	−19.6075	+	14.2457i	−1.00717	+	0.731753i	−0.963614	−	0.267298i	$-0.913869\pi$
$379$	−19.6075	+	14.2457i	−1.00717	+	0.731753i	−0.0435574	+	0.999051i	$0.513869\pi$
$380$		0			0
$381$	−0.0646596	−	0.0469779i	−0.00331261	−	0.00240675i
$382$		0			0
$383$	1.50232	−	2.06777i	0.0767650	−	0.105658i	−0.768908	−	0.639360i	$-0.779200\pi$
$383$	1.50232	−	2.06777i	0.0767650	−	0.105658i	0.845673	+	0.533702i	$0.179200\pi$
$384$		0			0
$385$	−2.92617	−	6.49369i	−0.149131	−	0.330949i
$386$		0			0
$387$	−27.6081	−	8.97041i	−1.40340	−	0.455992i
$388$		0			0
$389$	3.92452	+	12.0784i	0.198981	+	0.612400i	0.999907	+	0.0136371i	$0.00434096\pi$
$389$	3.92452	+	12.0784i	0.198981	+	0.612400i	−0.800926	+	0.598763i	$0.795659\pi$
$390$		0			0
$391$	8.82494	−	27.1604i	0.446296	−	1.37356i
$392$		0			0
$393$		−	0.824556i		−	0.0415933i
$394$		0			0
$395$	9.76628	+	10.7491i	0.491395	+	0.540847i
$396$		0			0
$397$	11.7770	+	16.2097i	0.591072	+	0.813541i	0.994855	−	0.101314i	$-0.0323046\pi$
$397$	11.7770	+	16.2097i	0.591072	+	0.813541i	−0.403782	+	0.914855i	$0.632305\pi$
$398$		0			0
$399$	−0.593079			−0.0296911
$400$		0			0
$401$	0.685119			0.0342132			0.0171066	−	0.999854i	$-0.494555\pi$
$401$	0.685119			0.0342132			0.0171066	+	0.999854i	$0.494555\pi$
$402$		0			0
$403$	−0.637160	−	0.876975i	−0.0317392	−	0.0436852i
$404$		0			0
$405$	−9.94857	+	17.4115i	−0.494349	+	0.865182i
$406$		0			0
$407$		−	1.41539i		−	0.0701583i
$408$		0			0
$409$	0.120676	−	0.371402i	0.00596704	−	0.0183647i	−0.948029	−	0.318185i	$-0.896927\pi$
$409$	0.120676	−	0.371402i	0.00596704	−	0.0183647i	0.953996	+	0.299820i	$0.0969267\pi$
$410$		0			0
$411$	0.155235	+	0.477764i	0.00765718	+	0.0235664i
$412$		0			0
$413$	8.26056	+	2.68402i	0.406476	+	0.132072i
$414$		0			0
$415$	1.77295	+	1.01303i	0.0870309	+	0.0497278i
$416$		0			0
$417$	−0.556792	+	0.766359i	−0.0272662	+	0.0375288i
$418$		0			0
$419$	13.9723	+	10.1515i	0.682591	+	0.495931i	0.874216	−	0.485537i	$-0.161376\pi$
$419$	13.9723	+	10.1515i	0.682591	+	0.495931i	−0.191625	+	0.981468i	$0.561376\pi$
$420$		0			0
$421$	14.0506	−	10.2083i	0.684784	−	0.497524i	−0.190158	−	0.981754i	$-0.560900\pi$
$421$	14.0506	−	10.2083i	0.684784	−	0.497524i	0.874941	+	0.484229i	$0.160900\pi$
$422$		0			0
$423$	29.6717	−	9.64092i	1.44269	−	0.468758i
$424$		0			0
$425$	−7.78184	+	17.9093i	−0.377475	+	0.868728i
$426$		0			0
$427$	−22.1131	+	7.18497i	−1.07013	+	0.347705i
$428$		0			0
$429$	−0.0501843	+	0.0364610i	−0.00242292	+	0.00176035i
$430$		0			0
$431$	−27.9780	−	20.3272i	−1.34765	−	0.979126i	−0.999125	−	0.0418269i	$-0.986682\pi$
$431$	−27.9780	−	20.3272i	−1.34765	−	0.979126i	−0.348526	−	0.937299i	$-0.613318\pi$
$432$		0			0
$433$	−22.3305	+	30.7353i	−1.07314	+	1.47704i	−0.206275	+	0.978494i	$0.566134\pi$
$433$	−22.3305	+	30.7353i	−1.07314	+	1.47704i	−0.866861	+	0.498550i	$0.833866\pi$
$434$		0			0
$435$	−0.0716004	+	0.344449i	−0.00343298	+	0.0165151i
$436$		0			0
$437$	−40.3383	−	13.1067i	−1.92964	−	0.626979i
$438$		0			0
$439$	1.45680	+	4.48356i	0.0695291	+	0.213989i	0.979783	−	0.200061i	$-0.0641140\pi$
$439$	1.45680	+	4.48356i	0.0695291	+	0.213989i	−0.910254	+	0.414050i	$0.864114\pi$
$440$		0			0
$441$	3.75268	−	11.5495i	0.178699	−	0.549979i
$442$		0			0
$443$		−	30.4179i		−	1.44520i	−0.691267	−	0.722600i	$-0.742947\pi$
$443$		−	30.4179i		−	1.44520i	0.691267	−	0.722600i	$-0.257053\pi$
$444$		0			0
$445$	−10.6733	+	4.80957i	−0.505962	+	0.227995i
$446$		0			0
$447$	0.292663	+	0.402817i	0.0138425	+	0.0190526i
$448$		0			0
$449$	13.7761			0.650133			0.325067	−	0.945691i	$-0.394613\pi$
$449$	13.7761			0.650133			0.325067	+	0.945691i	$0.394613\pi$
$450$		0			0
$451$	18.0510			0.849986
$452$		0			0
$453$	−0.187516	−	0.258094i	−0.00881027	−	0.0121263i
$454$		0			0
$455$	2.10967	+	0.438537i	0.0989030	+	0.0205589i
$456$		0			0
$457$		−	14.6462i		−	0.685122i	−0.939496	−	0.342561i	$-0.888706\pi$
$457$		−	14.6462i		−	0.685122i	0.939496	−	0.342561i	$-0.111294\pi$
$458$		0			0
$459$	−0.431022	+	1.32655i	−0.0201184	+	0.0619180i
$460$		0			0
$461$	6.89410	+	21.2179i	0.321090	+	0.988215i	0.973175	+	0.230068i	$0.0738949\pi$
$461$	6.89410	+	21.2179i	0.321090	+	0.988215i	−0.652084	+	0.758147i	$0.726105\pi$
$462$		0			0
$463$	15.2144	+	4.94346i	0.707073	+	0.229742i	0.640410	−	0.768033i	$-0.278765\pi$
$463$	15.2144	+	4.94346i	0.707073	+	0.229742i	0.0666636	+	0.997776i	$0.478765\pi$
$464$		0			0
$465$	0.255665	−	0.0280322i	0.0118562	−	0.00129996i
$466$		0			0
$467$	−5.04792	+	6.94787i	−0.233590	+	0.321509i	−0.909680	−	0.415310i	$-0.863673\pi$
$467$	−5.04792	+	6.94787i	−0.233590	+	0.321509i	0.676090	+	0.736819i	$0.263673\pi$
$468$		0			0
$469$	−1.73401	−	1.25983i	−0.0800692	−	0.0581737i
$470$		0			0
$471$	0.641736	−	0.466248i	0.0295696	−	0.0214836i
$472$		0			0
$473$	−17.0951	+	5.55452i	−0.786032	+	0.255397i
$474$		0			0
$475$	26.5987	+	11.5575i	1.22043	+	0.530296i
$476$		0			0
$477$	3.17087	−	1.03028i	0.145184	−	0.0471732i
$478$		0			0
$479$	−3.64835	+	2.65068i	−0.166697	+	0.121113i	−0.668006	−	0.744156i	$-0.732852\pi$
$479$	−3.64835	+	2.65068i	−0.166697	+	0.121113i	0.501309	+	0.865268i	$0.332852\pi$
$480$		0			0
$481$	0.346418	+	0.251687i	0.0157953	+	0.0114760i
$482$		0			0
$483$	0.439493	−	0.604910i	0.0199976	−	0.0275244i
$484$		0			0
$485$	24.0483	−	21.8494i	1.09198	−	0.992132i
$486$		0			0
$487$	−6.69405	−	2.17503i	−0.303336	−	0.0985599i	0.153394	−	0.988165i	$-0.450980\pi$
$487$	−6.69405	−	2.17503i	−0.303336	−	0.0985599i	−0.456730	+	0.889605i	$0.650980\pi$
$488$		0			0
$489$	0.260964	+	0.803165i	0.0118012	+	0.0363204i
$490$		0			0
$491$	7.80243	−	24.0134i	0.352119	−	1.08371i	−0.605543	−	0.795813i	$-0.707044\pi$
$491$	7.80243	−	24.0134i	0.352119	−	1.08371i	0.957661	−	0.287897i	$-0.0929561\pi$
$492$		0			0
$493$		−	10.3164i		−	0.464628i
$494$		0			0
$495$	1.35496	+	12.3577i	0.0609009	+	0.555439i
$496$		0			0
$497$	−13.5894	−	18.7042i	−0.609569	−	0.839000i
$498$		0			0
$499$	−22.8665			−1.02364			−0.511822	−	0.859092i	$-0.671029\pi$
$499$	−22.8665			−1.02364			−0.511822	+	0.859092i	$0.671029\pi$
$500$		0			0
$501$	−1.35072			−0.0603459
$502$		0			0
$503$	−5.18231	−	7.13284i	−0.231068	−	0.318038i	0.677701	−	0.735338i	$-0.262976\pi$
$503$	−5.18231	−	7.13284i	−0.231068	−	0.318038i	−0.908769	+	0.417300i	$0.862976\pi$
$504$		0			0
$505$	0.450840	+	4.11183i	0.0200621	+	0.182974i
$506$		0			0
$507$			0.755523i			0.0335539i
$508$		0			0
$509$	−6.02799	+	18.5522i	−0.267186	+	0.822314i	0.723996	+	0.689804i	$0.242303\pi$
$509$	−6.02799	+	18.5522i	−0.267186	+	0.822314i	−0.991182	+	0.132509i	$0.957697\pi$
$510$		0			0
$511$	−2.16967	−	6.67755i	−0.0959804	−	0.295397i
$512$		0			0
$513$	1.97018	+	0.640150i	0.0869856	+	0.0282633i
$514$		0			0
$515$	17.0727	−	15.5116i	0.752311	−	0.683523i
$516$		0			0
$517$	11.3551	−	15.6289i	0.499395	−	0.687358i
$518$		0			0
$519$	−0.326269	−	0.237048i	−0.0143216	−	0.0104053i
$520$		0			0
$521$	−10.7036	+	7.77662i	−0.468933	+	0.340700i	−0.797025	−	0.603946i	$-0.793594\pi$
$521$	−10.7036	+	7.77662i	−0.468933	+	0.340700i	0.328092	+	0.944646i	$0.393594\pi$
$522$		0			0
$523$	−40.6072	+	13.1941i	−1.77563	+	0.576937i	−0.998618	−	0.0525482i	$-0.983266\pi$
$523$	−40.6072	+	13.1941i	−1.77563	+	0.576937i	−0.777012	+	0.629486i	$0.783266\pi$
$524$		0			0
$525$	−0.338672	+	0.382992i	−0.0147808	+	0.0167151i
$526$		0			0
$527$	−7.17283	+	2.33059i	−0.312453	+	0.101522i
$528$		0			0
$529$	24.6530	−	17.9114i	1.07187	−	0.778758i
$530$		0			0
$531$	−12.2648	−	8.91090i	−0.532247	−	0.386700i
$532$		0			0
$533$	−3.20985	+	4.41799i	−0.139034	+	0.191364i
$534$		0			0
$535$	33.5989	−	3.68393i	1.45261	−	0.159270i
$536$		0			0
$537$	−1.42145	−	0.461856i	−0.0613400	−	0.0199306i
$538$		0			0
$539$	−2.32368	−	7.15154i	−0.100088	−	0.308039i
$540$		0			0
$541$	2.59118	−	7.97483i	0.111404	−	0.342865i	−0.879776	−	0.475388i	$-0.842308\pi$
$541$	2.59118	−	7.97483i	0.111404	−	0.342865i	0.991180	+	0.132523i	$0.0423078\pi$
$542$		0			0
$543$			1.50119i			0.0644224i
$544$		0			0
$545$	−9.92881	−	2.06390i	−0.425304	−	0.0884077i
$546$		0			0
$547$	8.49189	+	11.6881i	0.363087	+	0.499747i	0.951006	−	0.309174i	$-0.100052\pi$
$547$	8.49189	+	11.6881i	0.363087	+	0.499747i	−0.587918	+	0.808920i	$0.700052\pi$
$548$		0			0
$549$	40.5829			1.73203
$550$		0			0
$551$	−15.3218			−0.652732
$552$		0			0
$553$	−6.55396	−	9.02076i	−0.278703	−	0.383602i
$554$		0			0
$555$	−0.0926267	+	0.0417392i	−0.00393178	+	0.00177173i
$556$		0			0
$557$		−	17.2330i		−	0.730187i	−0.930971	−	0.365093i	$-0.881037\pi$
$557$		−	17.2330i		−	0.730187i	0.930971	−	0.365093i	$-0.118963\pi$
$558$		0			0
$559$	1.68040	−	5.17175i	0.0710734	−	0.218742i
$560$		0			0
$561$	0.133367	+	0.410460i	0.00563074	+	0.0173296i
$562$		0			0
$563$	6.78168	+	2.20350i	0.285814	+	0.0928665i	0.448415	−	0.893825i	$-0.351989\pi$
$563$	6.78168	+	2.20350i	0.285814	+	0.0928665i	−0.162602	+	0.986692i	$0.551989\pi$
$564$		0			0
$565$	7.11232	−	34.2153i	0.299218	−	1.43945i
$566$		0			0
$567$	9.04953	−	12.4556i	0.380044	−	0.523086i
$568$		0			0
$569$	−11.5916	−	8.42179i	−0.485945	−	0.353060i	0.317678	−	0.948199i	$-0.397097\pi$
$569$	−11.5916	−	8.42179i	−0.485945	−	0.353060i	−0.803623	+	0.595139i	$0.797097\pi$
$570$		0			0
$571$	8.30283	−	6.03236i	0.347462	−	0.252446i	−0.400341	−	0.916366i	$-0.631108\pi$
$571$	8.30283	−	6.03236i	0.347462	−	0.252446i	0.747804	+	0.663920i	$0.231108\pi$
$572$		0			0
$573$	−1.12727	+	0.366273i	−0.0470924	+	0.0153013i
$574$		0			0
$575$	−31.4987	+	18.5648i	−1.31359	+	0.774205i
$576$		0			0
$577$	9.12639	−	2.96534i	0.379937	−	0.123449i	−0.112821	−	0.993615i	$-0.535989\pi$
$577$	9.12639	−	2.96534i	0.379937	−	0.123449i	0.492758	+	0.870166i	$0.335989\pi$
$578$		0			0
$579$	0.230904	−	0.167762i	0.00959606	−	0.00697194i
$580$		0			0
$581$	−1.26832	−	0.921485i	−0.0526186	−	0.0382296i
$582$		0			0
$583$	1.21346	−	1.67019i	0.0502564	−	0.0691720i
$584$		0			0
$585$	−3.26551	−	1.86585i	−0.135012	−	0.0771434i
$586$		0			0
$587$	−5.03134	−	1.63478i	−0.207666	−	0.0674747i	0.203337	−	0.979109i	$-0.434821\pi$
$587$	−5.03134	−	1.63478i	−0.207666	−	0.0674747i	−0.411003	+	0.911634i	$0.634821\pi$
$588$		0			0
$589$	3.46138	+	10.6530i	0.142624	+	0.438950i
$590$		0			0
$591$	0.0123333	−	0.0379580i	0.000507324	−	0.00156138i
$592$		0			0
$593$			2.21453i			0.0909397i	0.998966	+	0.0454699i	$0.0144785\pi$
$593$			2.21453i			0.0909397i	−0.998966	+	0.0454699i	$0.985522\pi$
$594$		0			0
$595$	7.43758	−	13.0168i	0.304911	−	0.533639i
$596$		0			0
$597$	−0.329543	−	0.453577i	−0.0134873	−	0.0185637i
$598$		0			0
$599$	1.85018			0.0755964			0.0377982	−	0.999285i	$-0.487966\pi$
$599$	1.85018			0.0755964			0.0377982	+	0.999285i	$0.487966\pi$
$600$		0			0
$601$	32.8477			1.33988			0.669942	−	0.742413i	$-0.266319\pi$
$601$	32.8477			1.33988			0.669942	+	0.742413i	$0.266319\pi$
$602$		0			0
$603$	2.19894	+	3.02658i	0.0895477	+	0.123252i
$604$		0			0
$605$	−11.3638	−	12.5075i	−0.462006	−	0.508500i
$606$		0			0
$607$			29.1371i			1.18264i	0.806438	+	0.591319i	$0.201392\pi$
$607$			29.1371i			1.18264i	−0.806438	+	0.591319i	$0.798608\pi$
$608$		0			0
$609$	0.0834671	−	0.256885i	0.00338226	−	0.0104095i
$610$		0			0
$611$	1.80601	+	5.55832i	0.0730632	+	0.224865i
$612$		0			0
$613$	−3.61632	−	1.17501i	−0.146062	−	0.0474584i	0.235074	−	0.971978i	$-0.424467\pi$
$613$	−3.61632	−	1.17501i	−0.146062	−	0.0474584i	−0.381136	+	0.924519i	$0.624467\pi$
$614$		0			0
$615$	−0.532315	−	1.18130i	−0.0214650	−	0.0476346i
$616$		0			0
$617$	28.9502	−	39.8466i	1.16549	−	1.60416i	0.477035	−	0.878884i	$-0.341711\pi$
$617$	28.9502	−	39.8466i	1.16549	−	1.60416i	0.688456	−	0.725278i	$-0.258289\pi$
$618$		0			0
$619$	−5.13396	−	3.73004i	−0.206351	−	0.149923i	0.479810	−	0.877372i	$-0.340706\pi$
$619$	−5.13396	−	3.73004i	−0.206351	−	0.149923i	−0.686161	+	0.727449i	$0.740706\pi$
$620$		0			0
$621$	−2.11290	+	1.53511i	−0.0847876	+	0.0616018i
$622$		0			0
$623$	8.54810	−	2.77745i	0.342472	−	0.111276i
$624$		0			0
$625$	22.6524	−	10.5768i	0.906096	−	0.423072i
$626$		0			0
$627$	0.609612	−	0.198075i	0.0243455	−	0.00791035i
$628$		0			0
$629$	2.41021	−	1.75112i	0.0961014	−	0.0698218i
$630$		0			0
$631$	−4.48099	−	3.25563i	−0.178385	−	0.129604i	0.495010	−	0.868888i	$-0.335165\pi$
$631$	−4.48099	−	3.25563i	−0.178385	−	0.129604i	−0.673395	+	0.739283i	$0.735165\pi$
$632$		0			0
$633$	0.430752	−	0.592879i	0.0171208	−	0.0235648i
$634$		0			0
$635$	−1.23272	−	2.73563i	−0.0489191	−	0.108560i
$636$		0			0
$637$	2.16355	+	0.702979i	0.0857228	+	0.0278530i
$638$		0			0
$639$	12.4700	+	38.3786i	0.493304	+	1.51823i
$640$		0			0
$641$	3.16032	−	9.72646i	0.124825	−	0.384172i	−0.869044	−	0.494735i	$-0.835265\pi$
$641$	3.16032	−	9.72646i	0.124825	−	0.384172i	0.993869	+	0.110563i	$0.0352653\pi$
$642$		0			0
$643$		−	20.5779i		−	0.811515i	−0.913981	−	0.405757i	$-0.867008\pi$
$643$		−	20.5779i		−	0.811515i	0.913981	−	0.405757i	$-0.132992\pi$
$644$		0			0
$645$	0.867628	+	0.954943i	0.0341628	+	0.0376009i
$646$		0			0
$647$	−4.06226	−	5.59123i	−0.159704	−	0.219814i	0.721665	−	0.692243i	$-0.243377\pi$
$647$	−4.06226	−	5.59123i	−0.159704	−	0.219814i	−0.881369	+	0.472429i	$0.843377\pi$
$648$		0			0
$649$	−9.38723			−0.368481
$650$		0			0
$651$	−0.197464			−0.00773923
$652$		0			0
$653$	0.974775	+	1.34166i	0.0381459	+	0.0525033i	0.827664	−	0.561224i	$-0.189669\pi$
$653$	0.974775	+	1.34166i	0.0381459	+	0.0525033i	−0.789518	+	0.613727i	$0.789669\pi$
$654$		0			0
$655$	15.3575	−	26.8779i	0.600068	−	1.05021i
$656$		0			0
$657$			12.2549i			0.478110i
$658$		0			0
$659$	−0.956983	+	2.94529i	−0.0372788	+	0.114732i	−0.967964	−	0.251088i	$-0.919212\pi$
$659$	−0.956983	+	2.94529i	−0.0372788	+	0.114732i	0.930685	+	0.365820i	$0.119212\pi$
$660$		0			0
$661$	−4.38102	−	13.4834i	−0.170402	−	0.524443i	0.828992	−	0.559261i	$-0.188915\pi$
$661$	−4.38102	−	13.4834i	−0.170402	−	0.524443i	−0.999394	+	0.0348175i	$0.988915\pi$
$662$		0			0
$663$	−0.124176	−	0.0403472i	−0.00482259	−	0.00156696i
$664$		0			0
$665$	−19.3325	−	11.0462i	−0.749682	−	0.428354i
$666$		0			0
$667$	11.3540	−	15.6275i	0.439630	−	0.605099i
$668$		0			0
$669$	−0.680886	−	0.494692i	−0.0263246	−	0.0191259i
$670$		0			0
$671$	20.3299	−	14.7705i	0.784826	−	0.570210i
$672$		0			0
$673$	4.87403	−	1.58367i	0.187880	−	0.0610460i	−0.213566	−	0.976929i	$-0.568508\pi$
$673$	4.87403	−	1.58367i	0.187880	−	0.0610460i	0.401446	+	0.915883i	$0.368508\pi$
$674$		0			0
$675$	1.53844	−	0.906729i	0.0592146	−	0.0349000i
$676$		0			0
$677$	−25.7566	+	8.36884i	−0.989908	+	0.321641i	−0.758826	−	0.651294i	$-0.774227\pi$
$677$	−25.7566	+	8.36884i	−0.989908	+	0.321641i	−0.231082	+	0.972934i	$0.574227\pi$
$678$		0			0
$679$	−20.1815	+	14.6627i	−0.774496	+	0.562704i
$680$		0			0
$681$	−0.188923	−	0.137261i	−0.00723956	−	0.00525985i
$682$		0			0
$683$	8.64040	−	11.8925i	0.330616	−	0.455053i	−0.611056	−	0.791588i	$-0.709255\pi$
$683$	8.64040	−	11.8925i	0.330616	−	0.455053i	0.941671	+	0.336534i	$0.109255\pi$
$684$		0			0
$685$	−3.83829	+	18.4649i	−0.146654	+	0.705507i
$686$		0			0
$687$	−0.151296	−	0.0491590i	−0.00577229	−	0.00187553i
$688$		0			0
$689$	0.192999	+	0.593991i	0.00735269	+	0.0226293i
$690$		0			0
$691$	−4.25630	+	13.0995i	−0.161917	+	0.498330i	−0.998796	−	0.0490586i	$-0.984378\pi$
$691$	−4.25630	+	13.0995i	−0.161917	+	0.498330i	0.836879	+	0.547388i	$0.184378\pi$
$692$		0			0
$693$		−	9.54458i		−	0.362569i
$694$		0			0
$695$	−32.4233	+	14.6105i	−1.22988	+	0.554208i
$696$		0			0
$697$	22.3326	+	30.7382i	0.845909	+	1.16429i
$698$		0			0
$699$	−1.33393			−0.0504538
$700$		0			0
$701$	3.95616			0.149422			0.0747111	−	0.997205i	$-0.476197\pi$
$701$	3.95616			0.149422			0.0747111	+	0.997205i	$0.476197\pi$
$702$		0			0
$703$	−2.60075	−	3.57962i	−0.0980891	−	0.135008i
$704$		0			0
$705$	−1.35765	−	0.282214i	−0.0511320	−	0.0106288i
$706$		0			0
$707$		−	3.17580i		−	0.119438i
$708$		0			0
$709$	10.5384	−	32.4338i	0.395777	−	1.21808i	−0.532577	−	0.846381i	$-0.678776\pi$
$709$	10.5384	−	32.4338i	0.395777	−	1.21808i	0.928355	−	0.371696i	$-0.121224\pi$
$710$		0			0
$711$	6.01406	+	18.5094i	0.225545	+	0.694156i
$712$		0			0
$713$	−13.4305	−	4.36385i	−0.502978	−	0.163427i
$714$		0			0
$715$	−2.31494	+	0.253821i	−0.0865739	+	0.00949236i
$716$		0			0
$717$	0.758732	−	1.04431i	0.0283354	−	0.0390003i
$718$		0			0
$719$	−18.8977	−	13.7300i	−0.704766	−	0.512043i	0.176715	−	0.984262i	$-0.443453\pi$
$719$	−18.8977	−	13.7300i	−0.704766	−	0.512043i	−0.881481	+	0.472220i	$0.843453\pi$
$720$		0			0
$721$	−14.3275	+	10.4095i	−0.533584	+	0.387672i
$722$		0			0
$723$	−0.999614	+	0.324794i	−0.0371760	+	0.0120792i
$724$		0			0
$725$	−8.74938	+	9.89437i	−0.324944	+	0.367468i
$726$		0			0
$727$	12.1847	−	3.95904i	0.451904	−	0.146833i	−0.0742170	−	0.997242i	$-0.523646\pi$
$727$	12.1847	−	3.95904i	0.451904	−	0.146833i	0.526121	+	0.850409i	$0.323646\pi$
$728$		0			0
$729$	−21.6886	+	15.7577i	−0.803283	+	0.583619i
$730$		0			0
$731$	−30.6086	−	22.2384i	−1.13210	−	0.822518i
$732$		0			0
$733$	−15.7602	+	21.6920i	−0.582115	+	0.801213i	−0.993925	−	0.110057i	$-0.964897\pi$
$733$	−15.7602	+	21.6920i	−0.582115	+	0.801213i	0.411810	+	0.911270i	$0.364897\pi$
$734$		0			0
$735$	−0.399490	+	0.362963i	−0.0147354	+	0.0133881i
$736$		0			0
$737$	2.20310	+	0.715832i	0.0811524	+	0.0263680i
$738$		0			0
$739$	−15.7123	−	48.3574i	−0.577986	−	1.77886i	−0.625780	−	0.780000i	$-0.715219\pi$
$739$	−15.7123	−	48.3574i	−0.577986	−	1.77886i	0.0477941	−	0.998857i	$-0.484781\pi$
$740$		0			0
$741$	−0.0599233	+	0.184425i	−0.00220134	+	0.00677502i
$742$		0			0
$743$			25.4540i			0.933816i	0.884306	+	0.466908i	$0.154632\pi$
$743$			25.4540i			0.933816i	−0.884306	+	0.466908i	$0.845368\pi$
$744$		0			0
$745$	2.03736	+	18.5815i	0.0746430	+	0.680772i
$746$		0			0
$747$	1.60838	+	2.21374i	0.0588475	+	0.0809966i
$748$		0			0
$749$	−25.9503			−0.948203
$750$		0			0
$751$	21.1719			0.772574			0.386287	−	0.922379i	$-0.373757\pi$
$751$	21.1719			0.772574			0.386287	+	0.922379i	$0.373757\pi$
$752$		0			0
$753$	−0.568806	−	0.782895i	−0.0207285	−	0.0285303i
$754$		0			0
$755$	−1.30538	−	11.9056i	−0.0475077	−	0.433288i
$756$		0			0
$757$			34.8326i			1.26601i	0.774147	+	0.633006i	$0.218179\pi$
$757$			34.8326i			1.26601i	−0.774147	+	0.633006i	$0.781821\pi$
$758$		0			0
$759$	−0.249718	+	0.768554i	−0.00906420	+	0.0278967i
$760$		0			0
$761$	−2.49606	−	7.68209i	−0.0904822	−	0.278476i	0.895568	−	0.444925i	$-0.146770\pi$
$761$	−2.49606	−	7.68209i	−0.0904822	−	0.278476i	−0.986050	+	0.166450i	$0.946770\pi$
$762$		0			0
$763$	7.40478	+	2.40596i	0.268071	+	0.0871015i
$764$		0			0
$765$	−19.3672	+	17.5963i	−0.700221	+	0.636196i
$766$		0			0
$767$	1.66926	−	2.29753i	0.0602733	−	0.0829591i
$768$		0			0
$769$	−10.2491	−	7.44644i	−0.369593	−	0.268525i	0.387449	−	0.921891i	$-0.373356\pi$
$769$	−10.2491	−	7.44644i	−0.369593	−	0.268525i	−0.757042	+	0.653366i	$0.773356\pi$
$770$		0			0
$771$	0.439816	−	0.319545i	0.0158396	−	0.0115081i
$772$		0			0
$773$	38.9161	−	12.6446i	1.39971	−	0.454795i	0.490615	−	0.871376i	$-0.336772\pi$
$773$	38.9161	−	12.6446i	1.39971	−	0.454795i	0.909098	+	0.416582i	$0.136772\pi$
$774$		0			0
$775$	8.85597	+	3.84805i	0.318116	+	0.138226i
$776$		0			0
$777$	0.0741836	−	0.0241037i	0.00266132	−	0.000864716i
$778$		0			0
$779$	45.6522	−	33.1682i	1.63566	−	1.18838i
$780$		0			0
$781$	20.2150	+	14.6871i	0.723351	+	0.525545i
$782$		0			0
$783$	−0.554547	+	0.763269i	−0.0198179	+	0.0272770i
$784$		0			0
$785$	29.6025	−	3.24576i	1.05656	−	0.115846i
$786$		0			0
$787$	2.46599	+	0.801249i	0.0879031	+	0.0285615i	0.352638	−	0.935760i	$-0.385285\pi$
$787$	2.46599	+	0.801249i	0.0879031	+	0.0285615i	−0.264735	+	0.964321i	$0.585285\pi$
$788$		0			0
$789$	0.353637	+	1.08838i	0.0125898	+	0.0387474i
$790$		0			0
$791$	−8.29108	+	25.5173i	−0.294797	+	0.907291i
$792$		0			0
$793$			7.60228i			0.269965i
$794$		0			0
$795$	−0.145086	−	0.0301589i	−0.00514565	−	0.00106963i
$796$		0			0
$797$	−12.6487	−	17.4095i	−0.448041	−	0.616676i	0.523934	−	0.851759i	$-0.324464\pi$
$797$	−12.6487	−	17.4095i	−0.448041	−	0.616676i	−0.971975	+	0.235083i	$0.924464\pi$
$798$		0			0
$799$	40.6623			1.43853
$800$		0			0
$801$	−15.6878			−0.554302
$802$		0			0
$803$	4.46029	+	6.13907i	0.157400	+	0.216643i
$804$		0			0
$805$	25.5927	−	11.5325i	0.902023	−	0.406468i
$806$		0			0
$807$		−	0.321251i		−	0.0113086i
$808$		0			0
$809$	1.07271	−	3.30147i	0.0377146	−	0.116074i	−0.930427	−	0.366478i	$-0.880564\pi$
$809$	1.07271	−	3.30147i	0.0377146	−	0.116074i	0.968141	+	0.250404i	$0.0805636\pi$
$810$		0			0
$811$	11.3665	+	34.9826i	0.399133	+	1.22841i	0.925696	+	0.378269i	$0.123481\pi$
$811$	11.3665	+	34.9826i	0.399133	+	1.22841i	−0.526563	+	0.850136i	$0.676519\pi$
$812$		0			0
$813$	1.21334	+	0.394237i	0.0425536	+	0.0138265i
$814$		0			0
$815$	−6.45252	+	31.0412i	−0.226022	+	1.08732i
$816$		0			0
$817$	−33.0283	+	45.4596i	−1.15552	+	1.59043i
$818$		0			0
$819$	2.33604	+	1.69723i	0.0816280	+	0.0593062i
$820$		0			0
$821$	−38.2615	+	27.7986i	−1.33534	+	0.970179i	−0.335735	+	0.941957i	$0.608985\pi$
$821$	−38.2615	+	27.7986i	−1.33534	+	0.970179i	−0.999602	+	0.0282220i	$0.991015\pi$
$822$		0			0
$823$	9.96867	−	3.23902i	0.347486	−	0.112905i	−0.130074	−	0.991504i	$-0.541521\pi$
$823$	9.96867	−	3.23902i	0.347486	−	0.112905i	0.477560	+	0.878599i	$0.341521\pi$
$824$		0			0
$825$	0.220202	−	0.506777i	0.00766645	−	0.0176437i
$826$		0			0
$827$	−5.48824	+	1.78324i	−0.190845	+	0.0620093i	−0.402880	−	0.915253i	$-0.631991\pi$
$827$	−5.48824	+	1.78324i	−0.190845	+	0.0620093i	0.212035	+	0.977262i	$0.431991\pi$
$828$		0			0
$829$	−23.6650	+	17.1936i	−0.821919	+	0.597159i	−0.917261	−	0.398286i	$-0.869605\pi$
$829$	−23.6650	+	17.1936i	−0.821919	+	0.597159i	0.0953427	+	0.995445i	$0.469605\pi$
$830$		0			0
$831$	0.694887	+	0.504865i	0.0241054	+	0.0175136i
$832$		0			0
$833$	9.30322	−	12.8048i	0.322337	−	0.443659i
$834$		0			0
$835$	−44.0294	−	25.1575i	−1.52370	−	0.870612i
$836$		0			0
$837$	0.655966	+	0.213136i	0.0226735	+	0.00736707i
$838$		0			0
$839$	4.96033	+	15.2663i	0.171250	+	0.527052i	0.999442	−	0.0333911i	$-0.0106307\pi$
$839$	4.96033	+	15.2663i	0.171250	+	0.527052i	−0.828193	+	0.560444i	$0.810631\pi$
$840$		0			0
$841$	−6.80517	+	20.9442i	−0.234661	+	0.722212i
$842$		0			0
$843$			0.781604i			0.0269199i
$844$		0			0
$845$	−14.0718	+	24.6277i	−0.484084	+	0.847217i
$846$		0			0
$847$	7.62605	+	10.4964i	0.262034	+	0.360659i
$848$		0			0
$849$	1.58013			0.0542298
$850$		0			0
$851$	5.57828			0.191221
$852$		0			0
$853$	19.7934	+	27.2433i	0.677713	+	0.932792i	0.999904	−	0.0138826i	$-0.00441911\pi$
$853$	19.7934	+	27.2433i	0.677713	+	0.932792i	−0.322190	+	0.946675i	$0.604419\pi$
$854$		0			0
$855$	26.1339	+	28.7639i	0.893760	+	0.983705i
$856$		0			0
$857$			18.5384i			0.633260i	0.948549	+	0.316630i	$0.102551\pi$
$857$			18.5384i			0.633260i	−0.948549	+	0.316630i	$0.897449\pi$
$858$		0			0
$859$	−0.00514740	+	0.0158421i	−0.000175627	+	0.000540524i	−0.951144	−	0.308747i	$-0.900090\pi$
$859$	−0.00514740	+	0.0158421i	−0.000175627	+	0.000540524i	0.950969	+	0.309287i	$0.100090\pi$
$860$		0			0
$861$	0.307403	+	0.946089i	0.0104763	+	0.0322426i
$862$		0			0
$863$	−31.6593	−	10.2867i	−1.07769	−	0.350164i	−0.284214	−	0.958761i	$-0.591733\pi$
$863$	−31.6593	−	10.2867i	−1.07769	−	0.350164i	−0.793480	+	0.608597i	$0.791733\pi$
$864$		0			0
$865$	−6.22027	−	13.8039i	−0.211495	−	0.469345i
$866$		0			0
$867$	0.0611964	−	0.0842296i	0.00207834	−	0.00286059i
$868$		0			0
$869$	9.74939	+	7.08335i	0.330725	+	0.240286i
$870$		0			0
$871$	−0.566961	+	0.411921i	−0.0192107	+	0.0139574i
$872$		0			0
$873$	41.4098	−	13.4548i	1.40151	−	0.455378i
$874$		0			0
$875$	−18.1729	+	6.17649i	−0.614357	+	0.208804i
$876$		0			0
$877$	38.7660	−	12.5958i	1.30903	−	0.425331i	0.430319	−	0.902677i	$-0.358401\pi$
$877$	38.7660	−	12.5958i	1.30903	−	0.425331i	0.878715	+	0.477346i	$0.158401\pi$
$878$		0			0
$879$	1.16526	−	0.846612i	0.0393033	−	0.0285555i
$880$		0			0
$881$	−20.0854	−	14.5929i	−0.676694	−	0.491647i	0.195565	−	0.980691i	$-0.437346\pi$
$881$	−20.0854	−	14.5929i	−0.676694	−	0.491647i	−0.872259	+	0.489044i	$0.837346\pi$
$882$		0			0
$883$	−0.996201	+	1.37115i	−0.0335248	+	0.0461430i	−0.825450	−	0.564475i	$-0.809079\pi$
$883$	−0.996201	+	1.37115i	−0.0335248	+	0.0461430i	0.791926	+	0.610618i	$0.209079\pi$
$884$		0			0
$885$	0.276825	+	0.614324i	0.00930538	+	0.0206503i
$886$		0			0
$887$	−11.5402	−	3.74964i	−0.387482	−	0.125901i	0.108796	−	0.994064i	$-0.465300\pi$
$887$	−11.5402	−	3.74964i	−0.387482	−	0.125901i	−0.496278	+	0.868164i	$0.665300\pi$
$888$		0			0
$889$	0.711877	+	2.19093i	0.0238756	+	0.0734816i
$890$		0			0
$891$	−5.14190	+	15.8252i	−0.172260	+	0.530163i
$892$		0			0
$893$		−	60.3913i		−	2.02092i
$894$		0			0
$895$	−37.7325	−	41.5298i	−1.26126	−	1.38819i
$896$		0			0
$897$	−0.143699	−	0.197784i	−0.00479796	−	0.00660383i
$898$		0			0
$899$	−5.10137			−0.170140
$900$		0			0
$901$	4.34538			0.144766
$902$		0			0
$903$	−0.582249	−	0.801396i	−0.0193760	−	0.0266688i
$904$		0			0
$905$	−27.9600	+	48.9341i	−0.929423	+	1.62663i
$906$		0			0
$907$		−	14.9224i		−	0.495491i	−0.968825	−	0.247746i	$-0.920310\pi$
$907$		−	14.9224i		−	0.495491i	0.968825	−	0.247746i	$-0.0796898\pi$
$908$		0			0
$909$	−1.71291	+	5.27180i	−0.0568137	+	0.174855i
$910$		0			0
$911$	14.2166	+	43.7543i	0.471018	+	1.44964i	0.851254	+	0.524754i	$0.175843\pi$
$911$	14.2166	+	43.7543i	0.471018	+	1.44964i	−0.380236	+	0.924890i	$0.624157\pi$
$912$		0			0
$913$	1.61143	+	0.523584i	0.0533304	+	0.0173281i
$914$		0			0
$915$	−1.56614	−	0.894862i	−0.0517750	−	0.0295832i
$916$		0			0
$917$	−13.9697	+	19.2276i	−0.461319	+	0.634952i
$918$		0			0
$919$	4.67512	+	3.39667i	0.154218	+	0.112046i	0.662218	−	0.749311i	$-0.269615\pi$
$919$	4.67512	+	3.39667i	0.154218	+	0.112046i	−0.508000	+	0.861357i	$0.669615\pi$
$920$		0			0
$921$	0.921160	−	0.669262i	0.0303532	−	0.0220529i
$922$		0			0
$923$	−7.18935	+	2.33596i	−0.236640	+	0.0768891i
$924$		0			0
$925$	−3.79674	−	0.364625i	−0.124836	−	0.0119888i
$926$		0			0
$927$	29.3981	−	9.55202i	0.965560	−	0.313730i
$928$		0			0
$929$	11.1761	−	8.11994i	0.366677	−	0.266406i	−0.389155	−	0.921172i	$-0.627233\pi$
$929$	11.1761	−	8.11994i	0.366677	−	0.266406i	0.755832	+	0.654766i	$0.227233\pi$
$930$		0			0
$931$	−19.0175	−	13.8171i	−0.623275	−	0.452836i
$932$		0			0
$933$	−0.794928	+	1.09412i	−0.0260248	+	0.0358200i
$934$		0			0
$935$	−3.29758	+	15.8637i	−0.107842	+	0.518798i
$936$		0			0
$937$	−2.29684	−	0.746290i	−0.0750346	−	0.0243802i	0.271259	−	0.962506i	$-0.412560\pi$
$937$	−2.29684	−	0.746290i	−0.0750346	−	0.0243802i	−0.346294	+	0.938126i	$0.612560\pi$
$938$		0			0
$939$	0.247056	+	0.760360i	0.00806237	+	0.0248134i
$940$		0			0
$941$	9.18367	−	28.2644i	0.299379	−	0.921394i	−0.682336	−	0.731039i	$-0.739036\pi$
$941$	9.18367	−	28.2644i	0.299379	−	0.921394i	0.981715	−	0.190356i	$-0.0609641\pi$
$942$		0			0
$943$			71.1417i			2.31669i
$944$		0			0
$945$	−1.24998	+	0.563264i	−0.0406619	+	0.0183230i
$946$		0			0
$947$	5.37375	+	7.39633i	0.174623	+	0.240348i	0.887353	−	0.461090i	$-0.152542\pi$
$947$	5.37375	+	7.39633i	0.174623	+	0.240348i	−0.712730	+	0.701438i	$0.752542\pi$
$948$		0			0
$949$	−2.29568			−0.0745209
$950$		0			0
$951$	−1.62043			−0.0525461
$952$		0			0
$953$	17.2277	+	23.7118i	0.558059	+	0.768102i	0.991078	−	0.133283i	$-0.0425518\pi$
$953$	17.2277	+	23.7118i	0.558059	+	0.768102i	−0.433019	+	0.901385i	$0.642552\pi$
$954$		0			0
$955$	−43.5674	−	9.05634i	−1.40981	−	0.293056i
$956$		0			0
$957$			0.291922i			0.00943651i
$958$		0			0
$959$	4.47443	−	13.7709i	0.144487	−	0.444685i
$960$		0			0
$961$	−8.42707	−	25.9359i	−0.271841	−	0.836640i
$962$		0			0
$963$	43.0773	+	13.9967i	1.38815	+	0.451036i
$964$		0			0
$965$	10.6514	−	1.16786i	0.342879	−	0.0375948i
$966$		0			0
$967$	−20.3443	+	28.0016i	−0.654230	+	0.900470i	−0.999273	−	0.0381168i	$-0.987864\pi$
$967$	−20.3443	+	28.0016i	−0.654230	+	0.900470i	0.345044	+	0.938587i	$0.387864\pi$
$968$		0			0
$969$	1.09151	+	0.793025i	0.0350642	+	0.0254756i
$970$		0			0
$971$	−24.0628	+	17.4826i	−0.772211	+	0.561044i	−0.902631	−	0.430415i	$-0.858367\pi$
$971$	−24.0628	+	17.4826i	−0.772211	+	0.561044i	0.130420	+	0.991459i	$0.458367\pi$
$972$		0			0
$973$	25.9674	−	8.43732i	0.832477	−	0.270488i
$974$		0			0
$975$	0.0848773	+	0.144011i	0.00271825	+	0.00461203i
$976$		0			0
$977$	−40.1184	+	13.0352i	−1.28350	+	0.417035i	−0.869812	−	0.493384i	$-0.835760\pi$
$977$	−40.1184	+	13.0352i	−1.28350	+	0.417035i	−0.413689	+	0.910418i	$0.635760\pi$
$978$		0			0
$979$	−7.85878	+	5.70974i	−0.251168	+	0.182484i
$980$		0			0
$981$	−10.9942	−	7.98775i	−0.351017	−	0.255029i
$982$		0			0
$983$	13.6846	−	18.8353i	0.436472	−	0.600752i	−0.532952	−	0.846146i	$-0.678917\pi$
$983$	13.6846	−	18.8353i	0.436472	−	0.600752i	0.969424	+	0.245394i	$0.0789172\pi$
$984$		0			0
$985$	1.10900	−	1.00760i	0.0353357	−	0.0321048i
$986$		0			0
$987$	1.01252	+	0.328987i	0.0322288	+	0.0104718i
$988$		0			0
$989$	−21.8913	−	67.3744i	−0.696102	−	2.14238i
$990$		0			0
$991$	−16.3062	+	50.1854i	−0.517984	+	1.59419i	0.259802	+	0.965662i	$0.416343\pi$
$991$	−16.3062	+	50.1854i	−0.517984	+	1.59419i	−0.777786	+	0.628529i	$0.783657\pi$
$992$		0			0
$993$		−	1.71882i		−	0.0545452i
$994$		0			0
$995$	−2.29409	−	20.9230i	−0.0727275	−	0.663303i
$996$		0			0
$997$	34.7408	+	47.8165i	1.10025	+	1.51437i	0.835052	+	0.550171i	$0.185438\pi$
$997$	34.7408	+	47.8165i	1.10025	+	1.51437i	0.265199	+	0.964194i	$0.414562\pi$
$998$		0			0
$999$	−0.272451			−0.00861997

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.d.369.4		32
4.3	odd	2		200.2.q.a.169.5	yes	32
20.3	even	4		1000.2.m.e.401.4		32
20.7	even	4		1000.2.m.d.401.5		32
20.19	odd	2		1000.2.q.c.849.4		32
25.2	odd	20		10000.2.a.bq.1.9		16
25.4	even	10	inner	400.2.y.d.129.4		32
25.23	odd	20		10000.2.a.br.1.8		16
100.3	even	20		1000.2.m.e.601.4		32
100.23	even	20		5000.2.a.q.1.9		16
100.27	even	20		5000.2.a.r.1.8		16
100.47	even	20		1000.2.m.d.601.5		32
100.71	odd	10		1000.2.q.c.649.4		32
100.79	odd	10		200.2.q.a.129.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.129.5	✓	32	100.79	odd	10
200.2.q.a.169.5	yes	32	4.3	odd	2
400.2.y.d.129.4		32	25.4	even	10	inner
400.2.y.d.369.4		32	1.1	even	1	trivial
1000.2.m.d.401.5		32	20.7	even	4
1000.2.m.d.601.5		32	100.47	even	20
1000.2.m.e.401.4		32	20.3	even	4
1000.2.m.e.601.4		32	100.3	even	20
1000.2.q.c.649.4		32	100.71	odd	10
1000.2.q.c.849.4		32	20.19	odd	2
5000.2.a.q.1.9		16	100.23	even	20
5000.2.a.r.1.8		16	100.27	even	20
10000.2.a.bq.1.9		16	25.2	odd	20
10000.2.a.br.1.8		16	25.23	odd	20

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	400.2.y.d.369.4

Level	$400$
Weight	$2$
Character	400.369
Analytic conductor	$3.194$
Analytic rank	$0$
Dimension	$32$
Inner twists	$2$