LMFDB - Embedded newform 350.5.d.a.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,5,Mod(349,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("350.349");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	350.d (of order $2$, degree $1$, 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:	$36.1794870793$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.6850489614336.26
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 60x^{6} + 1800x^{4} + 38340x^{2} + 408321 $ x^8 - 60x^6 + 1800x^4 + 38340*x^2 + 408321
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.2
Root			$-6.80249 - 2.81768i$ of defining polynomial
Character	$\chi$	$=$	350.349
Dual form			350.5.d.a.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -11.2707 q^{3} -8.00000 q^{4} +31.8784i q^{6} +(20.6077 + 44.4558i) q^{7} +22.6274i q^{8} +46.0294 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -11.2707 q^{3} -8.00000 q^{4} +31.8784i q^{6} +(20.6077 + 44.4558i) q^{7} +22.6274i q^{8} +46.0294 q^{9} -11.8234 q^{11} +90.1659 q^{12} +20.6077 q^{13} +(125.740 - 58.2874i) q^{14} +64.0000 q^{16} +289.172 q^{17} -130.191i q^{18} -104.641i q^{19} +(-232.264 - 501.050i) q^{21} +33.4416i q^{22} +73.5290i q^{23} -255.028i q^{24} -58.2874i q^{26} +394.144 q^{27} +(-164.862 - 355.647i) q^{28} -950.881 q^{29} -1385.30i q^{31} -181.019i q^{32} +133.258 q^{33} -817.901i q^{34} -368.235 q^{36} +1279.47i q^{37} -295.968 q^{38} -232.264 q^{39} -1303.54i q^{41} +(-1417.18 + 656.942i) q^{42} -96.2338i q^{43} +94.5870 q^{44} +207.971 q^{46} -186.190 q^{47} -721.327 q^{48} +(-1551.64 + 1832.27i) q^{49} -3259.18 q^{51} -164.862 q^{52} +4376.94i q^{53} -1114.81i q^{54} +(-1005.92 + 466.299i) q^{56} +1179.38i q^{57} +2689.50i q^{58} +1650.28i q^{59} +5200.50i q^{61} -3918.23 q^{62} +(948.562 + 2046.28i) q^{63} -512.000 q^{64} -376.911i q^{66} -552.587i q^{67} -2313.37 q^{68} -828.726i q^{69} -8487.61 q^{71} +1041.53i q^{72} +317.344 q^{73} +3618.89 q^{74} +837.124i q^{76} +(-243.653 - 525.618i) q^{77} +656.942i q^{78} +624.377 q^{79} -8170.68 q^{81} -3686.96 q^{82} -7662.33 q^{83} +(1858.11 + 4008.40i) q^{84} -272.190 q^{86} +10717.1 q^{87} -267.532i q^{88} -4190.72i q^{89} +(424.678 + 916.133i) q^{91} -588.232i q^{92} +15613.4i q^{93} +526.625i q^{94} +2040.22i q^{96} -12994.4 q^{97} +(5182.43 + 4388.71i) q^{98} -544.223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 64 q^{4} + 504 q^{9}+O(q^{10}) $ 8 * q - 64 * q^4 + 504 * q^9	$ 8 q - 64 q^{4} + 504 q^{9} + 720 q^{11} + 576 q^{14} + 512 q^{16} + 1536 q^{21} - 2448 q^{29} - 4032 q^{36} + 1536 q^{39} - 5760 q^{44} + 6144 q^{46} + 3064 q^{49} - 22272 q^{51} - 4608 q^{56} - 4096 q^{64} - 43056 q^{71} + 6912 q^{74} - 25552 q^{79} - 59256 q^{81} - 12288 q^{84} - 23040 q^{86} + 11136 q^{91} + 59184 q^{99}+O(q^{100}) $ 8 * q - 64 * q^4 + 504 * q^9 + 720 * q^11 + 576 * q^14 + 512 * q^16 + 1536 * q^21 - 2448 * q^29 - 4032 * q^36 + 1536 * q^39 - 5760 * q^44 + 6144 * q^46 + 3064 * q^49 - 22272 * q^51 - 4608 * q^56 - 4096 * q^64 - 43056 * q^71 + 6912 * q^74 - 25552 * q^79 - 59256 * q^81 - 12288 * q^84 - 23040 * q^86 + 11136 * q^91 + 59184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−11.2707			−1.25230			−0.626152	−	0.779701i	$-0.715371\pi$
$3$	−11.2707			−1.25230			−0.626152	+	0.779701i	$0.715371\pi$
$4$	−8.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			31.8784i			0.885512i
$7$	20.6077	+	44.4558i	0.420566	+	0.907262i
$7$	20.6077	+	44.4558i	0.420566	+	0.907262i
$8$			22.6274i			0.353553i
$9$	46.0294			0.568265
$10$		0			0
$11$	−11.8234			−0.0977139			−0.0488569	−	0.998806i	$-0.515558\pi$
$11$	−11.8234			−0.0977139			−0.0488569	+	0.998806i	$0.515558\pi$
$12$	90.1659			0.626152
$13$	20.6077			0.121939			0.0609696	−	0.998140i	$-0.480581\pi$
$13$	20.6077			0.121939			0.0609696	+	0.998140i	$0.480581\pi$
$14$	125.740	−	58.2874i	0.641531	−	0.297385i
$15$		0			0
$16$	64.0000			0.250000
$17$	289.172			1.00059			0.500297	−	0.865854i	$-0.333224\pi$
$17$	289.172			1.00059			0.500297	+	0.865854i	$0.333224\pi$
$18$		−	130.191i		−	0.401824i
$19$		−	104.641i		−	0.289863i	−0.989442	−	0.144932i	$-0.953704\pi$
$19$		−	104.641i		−	0.289863i	0.989442	−	0.144932i	$-0.0462962\pi$
$20$		0			0
$21$	−232.264	−	501.050i	−0.526676	−	1.13617i
$22$			33.4416i			0.0690941i
$23$			73.5290i			0.138996i	0.997582	+	0.0694981i	$0.0221398\pi$
$23$			73.5290i			0.138996i	−0.997582	+	0.0694981i	$0.977860\pi$
$24$		−	255.028i		−	0.442756i
$25$		0			0
$26$		−	58.2874i		−	0.0862240i
$27$	394.144			0.540664
$28$	−164.862	−	355.647i	−0.210283	−	0.453631i
$29$	−950.881			−1.13066			−0.565328	−	0.824866i	$-0.691250\pi$
$29$	−950.881			−1.13066			−0.565328	+	0.824866i	$0.691250\pi$
$30$		0			0
$31$		−	1385.30i		−	1.44152i	−0.693182	−	0.720762i	$-0.743792\pi$
$31$		−	1385.30i		−	1.44152i	0.693182	−	0.720762i	$-0.256208\pi$
$32$		−	181.019i		−	0.176777i
$33$	133.258			0.122367
$34$		−	817.901i		−	0.707527i
$35$		0			0
$36$	−368.235			−0.284132
$37$			1279.47i			0.934602i	0.884098	+	0.467301i	$0.154774\pi$
$37$			1279.47i			0.934602i	−0.884098	+	0.467301i	$0.845226\pi$
$38$	−295.968			−0.204964
$39$	−232.264			−0.152705
$40$		0			0
$41$		−	1303.54i		−	0.775454i	−0.921774	−	0.387727i	$-0.873260\pi$
$41$		−	1303.54i		−	0.775454i	0.921774	−	0.387727i	$-0.126740\pi$
$42$	−1417.18	+	656.942i	−0.803392	+	0.372416i
$43$		−	96.2338i		−	0.0520464i	−0.999661	−	0.0260232i	$-0.991716\pi$
$43$		−	96.2338i		−	0.0520464i	0.999661	−	0.0260232i	$-0.00828437\pi$
$44$	94.5870			0.0488569
$45$		0			0
$46$	207.971			0.0982852
$47$	−186.190			−0.0842870			−0.0421435	−	0.999112i	$-0.513419\pi$
$47$	−186.190			−0.0842870			−0.0421435	+	0.999112i	$0.513419\pi$
$48$	−721.327			−0.313076
$49$	−1551.64	+	1832.27i	−0.646249	+	0.763127i
$50$		0			0
$51$	−3259.18			−1.25305
$52$	−164.862			−0.0609696
$53$			4376.94i			1.55818i	0.626910	+	0.779092i	$0.284319\pi$
$53$			4376.94i			1.55818i	−0.626910	+	0.779092i	$0.715681\pi$
$54$		−	1114.81i		−	0.382307i
$55$		0			0
$56$	−1005.92	+	466.299i	−0.320766	+	0.148692i
$57$			1179.38i			0.362997i
$58$			2689.50i			0.799494i
$59$			1650.28i			0.474081i	0.971500	+	0.237041i	$0.0761774\pi$
$59$			1650.28i			0.474081i	−0.971500	+	0.237041i	$0.923823\pi$
$60$		0			0
$61$			5200.50i			1.39761i	0.715313	+	0.698804i	$0.246284\pi$
$61$			5200.50i			1.39761i	−0.715313	+	0.698804i	$0.753716\pi$
$62$	−3918.23			−1.01931
$63$	948.562	+	2046.28i	0.238993	+	0.515565i
$64$	−512.000			−0.125000
$65$		0			0
$66$		−	376.911i		−	0.0865268i
$67$		−	552.587i		−	0.123098i	−0.998104	−	0.0615490i	$-0.980396\pi$
$67$		−	552.587i		−	0.123098i	0.998104	−	0.0615490i	$-0.0196040\pi$
$68$	−2313.37			−0.500297
$69$		−	828.726i		−	0.174065i
$70$		0			0
$71$	−8487.61			−1.68372			−0.841858	−	0.539699i	$-0.818538\pi$
$71$	−8487.61			−1.68372			−0.841858	+	0.539699i	$0.818538\pi$
$72$			1041.53i			0.200912i
$73$	317.344			0.0595503			0.0297751	−	0.999557i	$-0.490521\pi$
$73$	317.344			0.0595503			0.0297751	+	0.999557i	$0.490521\pi$
$74$	3618.89			0.660863
$75$		0			0
$76$			837.124i			0.144932i
$77$	−243.653	−	525.618i	−0.0410951	−	0.0886521i
$78$			656.942i			0.107979i
$79$	624.377			0.100044			0.0500222	−	0.998748i	$-0.484071\pi$
$79$	624.377			0.100044			0.0500222	+	0.998748i	$0.484071\pi$
$80$		0			0
$81$	−8170.68			−1.24534
$82$	−3686.96			−0.548329
$83$	−7662.33			−1.11226			−0.556128	−	0.831097i	$-0.687713\pi$
$83$	−7662.33			−1.11226			−0.556128	+	0.831097i	$0.687713\pi$
$84$	1858.11	+	4008.40i	0.263338	+	0.568084i
$85$		0			0
$86$	−272.190			−0.0368024
$87$	10717.1			1.41592
$88$		−	267.532i		−	0.0345471i
$89$		−	4190.72i		−	0.529065i	−0.964377	−	0.264532i	$-0.914782\pi$
$89$		−	4190.72i		−	0.529065i	0.964377	−	0.264532i	$-0.0852176\pi$
$90$		0			0
$91$	424.678	+	916.133i	0.0512834	+	0.110631i
$92$		−	588.232i		−	0.0694981i
$93$			15613.4i			1.80523i
$94$			526.625i			0.0595999i
$95$		0			0
$96$			2040.22i			0.221378i
$97$	−12994.4			−1.38106			−0.690529	−	0.723305i	$-0.742622\pi$
$97$	−12994.4			−1.38106			−0.690529	+	0.723305i	$0.742622\pi$
$98$	5182.43	+	4388.71i	0.539612	+	0.456967i
$99$	−544.223			−0.0555273
$100$		0			0
$101$		−	13694.8i		−	1.34249i	−0.741234	−	0.671246i	$-0.765759\pi$
$101$		−	13694.8i		−	1.34249i	0.741234	−	0.671246i	$-0.234241\pi$
$102$			9218.34i			0.886038i
$103$	−15146.7			−1.42773			−0.713863	−	0.700285i	$-0.753056\pi$
$103$	−15146.7			−1.42773			−0.713863	+	0.700285i	$0.753056\pi$
$104$			466.299i			0.0431120i
$105$		0			0
$106$	12379.8			1.10180
$107$		−	7137.28i		−	0.623398i	−0.950181	−	0.311699i	$-0.899102\pi$
$107$		−	7137.28i		−	0.623398i	0.950181	−	0.311699i	$-0.100898\pi$
$108$	−3153.15			−0.270332
$109$	13556.3			1.14101			0.570505	−	0.821294i	$-0.306748\pi$
$109$	13556.3			1.14101			0.570505	+	0.821294i	$0.306748\pi$
$110$		0			0
$111$		−	14420.6i		−	1.17041i
$112$	1318.89	+	2845.17i	0.105141	+	0.226816i
$113$			768.202i			0.0601615i	0.999547	+	0.0300807i	$0.00957644\pi$
$113$			768.202i			0.0601615i	−0.999547	+	0.0300807i	$0.990424\pi$
$114$	3335.78			0.256677
$115$		0			0
$116$	7607.05			0.565328
$117$	948.562			0.0692937
$118$	4667.69			0.335226
$119$	5959.17	+	12855.4i	0.420815	+	0.907801i
$120$		0			0
$121$	−14501.2			−0.990452
$122$	14709.2			0.988258
$123$			14691.8i			0.971104i
$124$			11082.4i			0.720762i
$125$		0			0
$126$	5787.75	−	2682.94i	0.364560	−	0.168993i
$127$		−	948.919i		−	0.0588331i	−0.999567	−	0.0294166i	$-0.990635\pi$
$127$		−	948.919i		−	0.0588331i	0.999567	−	0.0294166i	$-0.00936493\pi$
$128$			1448.15i			0.0883883i
$129$			1084.63i			0.0651779i
$130$		0			0
$131$		−	5443.08i		−	0.317177i	−0.987345	−	0.158589i	$-0.949306\pi$
$131$		−	5443.08i		−	0.317177i	0.987345	−	0.158589i	$-0.0506944\pi$
$132$	−1066.07			−0.0611837
$133$	4651.88	−	2156.40i	0.262982	−	0.121906i
$134$	−1562.95			−0.0870434
$135$		0			0
$136$			6543.21i			0.353763i
$137$		−	453.997i		−	0.0241886i	−0.999927	−	0.0120943i	$-0.996150\pi$
$137$		−	453.997i		−	0.0241886i	0.999927	−	0.0120943i	$-0.00384984\pi$
$138$	−2343.99			−0.123083
$139$		−	18530.3i		−	0.959074i	−0.877522	−	0.479537i	$-0.840805\pi$
$139$		−	18530.3i		−	0.959074i	0.877522	−	0.479537i	$-0.159195\pi$
$140$		0			0
$141$	2098.50			0.105553
$142$			24006.6i			1.19057i
$143$	−243.653			−0.0119151
$144$	2945.88			0.142066
$145$		0			0
$146$		−	897.583i		−	0.0421084i
$147$	17488.2	−	20651.0i	0.809300	−	0.955666i
$148$		−	10235.8i		−	0.467301i
$149$	−18132.6			−0.816746			−0.408373	−	0.912815i	$-0.633904\pi$
$149$	−18132.6			−0.816746			−0.408373	+	0.912815i	$0.633904\pi$
$150$		0			0
$151$	8838.45			0.387634			0.193817	−	0.981038i	$-0.437913\pi$
$151$	8838.45			0.387634			0.193817	+	0.981038i	$0.437913\pi$
$152$	2367.75			0.102482
$153$	13310.4			0.568602
$154$	−1486.67	+	689.154i	−0.0626865	+	0.0290586i
$155$		0			0
$156$	1858.11			0.0763524
$157$	20618.3			0.836475			0.418238	−	0.908338i	$-0.362648\pi$
$157$	20618.3			0.836475			0.418238	+	0.908338i	$0.362648\pi$
$158$		−	1766.00i		−	0.0707420i
$159$		−	49331.3i		−	1.95132i
$160$		0			0
$161$	−3268.79	+	1515.26i	−0.126106	+	0.0584570i
$162$			23110.2i			0.880588i
$163$		−	30626.0i		−	1.15270i	−0.817204	−	0.576348i	$-0.804477\pi$
$163$		−	30626.0i		−	1.15270i	0.817204	−	0.576348i	$-0.195523\pi$
$164$			10428.3i			0.387727i
$165$		0			0
$166$			21672.3i			0.786483i
$167$	−52757.1			−1.89168			−0.945841	−	0.324629i	$-0.894760\pi$
$167$	−52757.1			−1.89168			−0.945841	+	0.324629i	$0.894760\pi$
$168$	11337.5	−	5255.54i	0.401696	−	0.186208i
$169$	−28136.3			−0.985131
$170$		0			0
$171$		−	4816.55i		−	0.164719i
$172$			769.870i			0.0260232i
$173$	17169.1			0.573663			0.286831	−	0.957981i	$-0.407398\pi$
$173$	17169.1			0.573663			0.286831	+	0.957981i	$0.407398\pi$
$174$		−	30312.6i		−	1.00121i
$175$		0			0
$176$	−756.696			−0.0244285
$177$		−	18599.8i		−	0.593693i
$178$	−11853.2			−0.374105
$179$	−30421.3			−0.949451			−0.474725	−	0.880134i	$-0.657453\pi$
$179$	−30421.3			−0.949451			−0.474725	+	0.880134i	$0.657453\pi$
$180$		0			0
$181$			41530.0i			1.26766i	0.773471	+	0.633832i	$0.218519\pi$
$181$			41530.0i			1.26766i	−0.773471	+	0.633832i	$0.781481\pi$
$182$	2591.22	−	1201.17i	0.0782278	−	0.0362628i
$183$		−	58613.5i		−	1.75023i
$184$	−1663.77			−0.0491426
$185$		0			0
$186$	44161.4			1.27649
$187$	−3418.98			−0.0977719
$188$	1489.52			0.0421435
$189$	8122.41	+	17522.0i	0.227385	+	0.490524i
$190$		0			0
$191$	−51530.4			−1.41253			−0.706263	−	0.707949i	$-0.749621\pi$
$191$	−51530.4			−1.41253			−0.706263	+	0.707949i	$0.749621\pi$
$192$	5770.62			0.156538
$193$		−	23547.7i		−	0.632169i	−0.948731	−	0.316084i	$-0.897632\pi$
$193$		−	23547.7i		−	0.632169i	0.948731	−	0.316084i	$-0.102368\pi$
$194$			36753.6i			0.976555i
$195$		0			0
$196$	12413.2	−	14658.1i	0.323125	−	0.381563i
$197$		−	53661.4i		−	1.38270i	−0.722518	−	0.691352i	$-0.757015\pi$
$197$		−	53661.4i		−	1.38270i	0.722518	−	0.691352i	$-0.242985\pi$
$198$			1539.30i			0.0392638i
$199$			48660.6i			1.22877i	0.789006	+	0.614386i	$0.210596\pi$
$199$			48660.6i			1.22877i	−0.789006	+	0.614386i	$0.789404\pi$
$200$		0			0
$201$			6228.06i			0.154156i
$202$	−38734.6			−0.949286
$203$	−19595.5	−	42272.2i	−0.475515	−	1.02580i
$204$	26073.4			0.626524
$205$		0			0
$206$			42841.5i			1.00955i
$207$			3384.50i			0.0789866i
$208$	1318.89			0.0304848
$209$			1237.20i			0.0283236i
$210$		0			0
$211$	56724.4			1.27410			0.637052	−	0.770821i	$-0.280154\pi$
$211$	56724.4			1.27410			0.637052	+	0.770821i	$0.280154\pi$
$212$		−	35015.5i		−	0.779092i
$213$	95661.6			2.10852
$214$	−20187.3			−0.440809
$215$		0			0
$216$			8918.46i			0.191154i
$217$	61584.9	−	28548.0i	1.30784	−	0.606256i
$218$		−	38343.1i		−	0.806816i
$219$	−3576.69			−0.0745751
$220$		0			0
$221$	5959.17			0.122012
$222$	−40787.5			−0.827602
$223$	−63263.2			−1.27216			−0.636080	−	0.771623i	$-0.719445\pi$
$223$	−63263.2			−1.27216			−0.636080	+	0.771623i	$0.719445\pi$
$224$	8047.37	−	3730.39i	0.160383	−	0.0743462i
$225$		0			0
$226$	2172.80			0.0425406
$227$	−17.6038			−0.000341630			−0.000170815	−	1.00000i	$-0.500054\pi$
$227$	−17.6038			−0.000341630			−0.000170815		1.00000i	$0.500054\pi$
$228$		−	9435.01i		−	0.181498i
$229$		−	31463.8i		−	0.599984i	−0.953942	−	0.299992i	$-0.903016\pi$
$229$		−	31463.8i		−	0.599984i	0.953942	−	0.299992i	$-0.0969841\pi$
$230$		0			0
$231$	2746.15	+	5924.10i	0.0514635	+	0.111019i
$232$		−	21516.0i		−	0.399747i
$233$			58746.9i			1.08211i	0.840986	+	0.541057i	$0.181976\pi$
$233$			58746.9i			1.08211i	−0.840986	+	0.541057i	$0.818024\pi$
$234$		−	2682.94i		−	0.0489980i
$235$		0			0
$236$		−	13202.2i		−	0.237041i
$237$	−7037.18			−0.125286
$238$	36360.5	−	16855.1i	0.641912	−	0.297561i
$239$	−48468.5			−0.848524			−0.424262	−	0.905539i	$-0.639466\pi$
$239$	−48468.5			−0.848524			−0.424262	+	0.905539i	$0.639466\pi$
$240$		0			0
$241$			35732.8i			0.615223i	0.951512	+	0.307612i	$0.0995297\pi$
$241$			35732.8i			0.615223i	−0.951512	+	0.307612i	$0.900470\pi$
$242$			41015.6i			0.700355i
$243$	60163.8			1.01888
$244$		−	41604.0i		−	0.698804i
$245$		0			0
$246$	41554.8			0.686674
$247$		−	2156.40i		−	0.0353456i
$248$	31345.9			0.509656
$249$	86360.0			1.39288
$250$		0			0
$251$		−	15060.5i		−	0.239052i	−0.992831	−	0.119526i	$-0.961863\pi$
$251$		−	15060.5i		−	0.239052i	0.992831	−	0.119526i	$-0.0381375\pi$
$252$	−7588.49	−	16370.2i	−0.119496	−	0.257783i
$253$		−	869.361i		−	0.0135819i
$254$	−2683.95			−0.0416013
$255$		0			0
$256$	4096.00			0.0625000
$257$	75600.7			1.14461			0.572307	−	0.820039i	$-0.306048\pi$
$257$	75600.7			1.14461			0.572307	+	0.820039i	$0.306048\pi$
$258$	3067.78			0.0460877
$259$	−56879.9	+	26367.0i	−0.847929	+	0.393061i
$260$		0			0
$261$	−43768.5			−0.642512
$262$	−15395.4			−0.224278
$263$		−	37721.9i		−	0.545358i	−0.962105	−	0.272679i	$-0.912090\pi$
$263$		−	37721.9i		−	0.545358i	0.962105	−	0.272679i	$-0.0879097\pi$
$264$			3015.29i			0.0432634i
$265$		0			0
$266$	−6099.23	−	13157.5i	−0.0862009	−	0.185956i
$267$			47232.5i			0.662550i
$268$			4420.70i			0.0615490i
$269$			53660.8i			0.741571i	0.928719	+	0.370785i	$0.120911\pi$
$269$			53660.8i			0.741571i	−0.928719	+	0.370785i	$0.879089\pi$
$270$		0			0
$271$		−	90791.9i		−	1.23626i	−0.786077	−	0.618128i	$-0.787891\pi$
$271$		−	90791.9i		−	1.23626i	0.786077	−	0.618128i	$-0.212109\pi$
$272$	18507.0			0.250148
$273$	−4786.43	−	10325.5i	−0.0642224	−	0.138543i
$274$	−1284.10			−0.0171039
$275$		0			0
$276$			6629.81i			0.0870327i
$277$			112687.i			1.46863i	0.678806	+	0.734317i	$0.262498\pi$
$277$			112687.i			1.46863i	−0.678806	+	0.734317i	$0.737502\pi$
$278$	−52411.5			−0.678168
$279$		−	63764.8i		−	0.819167i
$280$		0			0
$281$	48637.8			0.615972			0.307986	−	0.951391i	$-0.400345\pi$
$281$	48637.8			0.615972			0.307986	+	0.951391i	$0.400345\pi$
$282$		−	5935.45i		−	0.0746372i
$283$	−8280.01			−0.103385			−0.0516925	−	0.998663i	$-0.516462\pi$
$283$	−8280.01			−0.103385			−0.0516925	+	0.998663i	$0.516462\pi$
$284$	67900.9			0.841858
$285$		0			0
$286$			689.154i			0.00842528i
$287$	57949.9	−	26862.9i	0.703540	−	0.326129i
$288$		−	8332.22i		−	0.100456i
$289$	99.1974			0.00118769
$290$		0			0
$291$	146456.			1.72950
$292$	−2538.75			−0.0297751
$293$	−109853.			−1.27961			−0.639805	−	0.768538i	$-0.720985\pi$
$293$	−109853.			−1.27961			−0.639805	+	0.768538i	$0.720985\pi$
$294$	−58409.8	−	49464.0i	−0.675758	−	0.572262i
$295$		0			0
$296$	−28951.1			−0.330432
$297$	−4660.11			−0.0528303
$298$			51286.7i			0.577526i
$299$			1515.26i			0.0169491i
$300$		0			0
$301$	4278.15	−	1983.16i	0.0472197	−	0.0218889i
$302$		−	24998.9i		−	0.274099i
$303$			154350.i			1.68121i
$304$		−	6697.00i		−	0.0724658i
$305$		0			0
$306$		−	37647.5i		−	0.402062i
$307$	76154.3			0.808011			0.404006	−	0.914756i	$-0.367618\pi$
$307$	76154.3			0.808011			0.404006	+	0.914756i	$0.367618\pi$
$308$	1949.22	+	4204.95i	0.0205475	+	0.0443260i
$309$	170715.			1.78795
$310$		0			0
$311$		−	81972.5i		−	0.847515i	−0.905776	−	0.423758i	$-0.860711\pi$
$311$		−	81972.5i		−	0.847515i	0.905776	−	0.423758i	$-0.139289\pi$
$312$		−	5255.54i		−	0.0539893i
$313$	31765.5			0.324240			0.162120	−	0.986771i	$-0.448167\pi$
$313$	31765.5			0.324240			0.162120	+	0.986771i	$0.448167\pi$
$314$		−	58317.3i		−	0.591477i
$315$		0			0
$316$	−4995.01			−0.0500222
$317$			1127.92i			0.0112243i	0.999984	+	0.00561214i	$0.00178641\pi$
$317$			1127.92i			0.0112243i	−0.999984	+	0.00561214i	$0.998214\pi$
$318$	−139530.			−1.37979
$319$	11242.6			0.110481
$320$		0			0
$321$			80442.4i			0.780683i
$322$	4285.82	+	9245.55i	0.0413354	+	0.0891704i
$323$		−	30259.1i		−	0.290035i
$324$	65365.4			0.622670
$325$		0			0
$326$	−86623.4			−0.815080
$327$	−152790.			−1.42889
$328$	29495.7			0.274164
$329$	−3836.95	−	8277.23i	−0.0354482	−	0.0764704i
$330$		0			0
$331$	−136973.			−1.25019			−0.625097	−	0.780547i	$-0.714941\pi$
$331$	−136973.			−1.25019			−0.625097	+	0.780547i	$0.714941\pi$
$332$	61298.6			0.556128
$333$			58893.3i			0.531101i
$334$			149220.i			1.33762i
$335$		0			0
$336$	−14864.9	−	32067.2i	−0.131669	−	0.284042i
$337$			150838.i			1.32816i	0.747660	+	0.664082i	$0.231177\pi$
$337$			150838.i			1.32816i	−0.747660	+	0.664082i	$0.768823\pi$
$338$			79581.5i			0.696593i
$339$		−	8658.20i		−	0.0753404i
$340$		0			0
$341$			16379.0i			0.140857i
$342$	−13623.2			−0.116474
$343$	−113431.	−	31220.8i	−0.964146	−	0.265373i
$344$	2177.52			0.0184012
$345$		0			0
$346$		−	48561.7i		−	0.405641i
$347$		−	12987.5i		−	0.107861i	−0.998545	−	0.0539306i	$-0.982825\pi$
$347$		−	12987.5i		−	0.107861i	0.998545	−	0.0539306i	$-0.0171750\pi$
$348$	−85737.0			−0.707962
$349$			184152.i			1.51191i	0.654623	+	0.755955i	$0.272827\pi$
$349$			184152.i			1.51191i	−0.654623	+	0.755955i	$0.727173\pi$
$350$		0			0
$351$	8122.41			0.0659281
$352$			2140.26i			0.0172735i
$353$	−61196.5			−0.491108			−0.245554	−	0.969383i	$-0.578970\pi$
$353$	−61196.5			−0.491108			−0.245554	+	0.969383i	$0.578970\pi$
$354$	−52608.2			−0.419805
$355$		0			0
$356$			33525.8i			0.264532i
$357$	−67164.2	−	144889.i	−0.526989	−	1.13684i
$358$			86044.6i			0.671363i
$359$	6045.92			0.0469109			0.0234555	−	0.999725i	$-0.492533\pi$
$359$	6045.92			0.0469109			0.0234555	+	0.999725i	$0.492533\pi$
$360$		0			0
$361$	119371.			0.915979
$362$	117464.			0.896374
$363$	163439.			1.24035
$364$	−3397.42	−	7329.07i	−0.0256417	−	0.0553154i
$365$		0			0
$366$	−165784.			−1.23760
$367$	−214788.			−1.59470			−0.797349	−	0.603518i	$-0.793765\pi$
$367$	−214788.			−1.59470			−0.797349	+	0.603518i	$0.793765\pi$
$368$			4705.86i			0.0347491i
$369$		−	60001.1i		−	0.440663i
$370$		0			0
$371$	−194580.	+	90198.7i	−1.41368	+	0.655318i
$372$		−	124907.i		−	0.902613i
$373$			231029.i			1.66053i	0.557365	+	0.830267i	$0.311812\pi$
$373$			231029.i			1.66053i	−0.557365	+	0.830267i	$0.688188\pi$
$374$			9670.35i			0.0691351i
$375$		0			0
$376$		−	4213.00i		−	0.0297999i
$377$	−19595.5			−0.137871
$378$	49559.7	−	22973.6i	0.346853	−	0.160785i
$379$	−91543.4			−0.637307			−0.318654	−	0.947871i	$-0.603231\pi$
$379$	−91543.4			−0.637307			−0.318654	+	0.947871i	$0.603231\pi$
$380$		0			0
$381$			10695.0i			0.0736769i
$382$			145750.i			0.998807i
$383$	84780.4			0.577960			0.288980	−	0.957335i	$-0.406684\pi$
$383$	84780.4			0.577960			0.288980	+	0.957335i	$0.406684\pi$
$384$		−	16321.8i		−	0.110689i
$385$		0			0
$386$	−66602.8			−0.447011
$387$		−	4429.59i		−	0.0295761i
$388$	103955.			0.690529
$389$	55678.0			0.367946			0.183973	−	0.982931i	$-0.441104\pi$
$389$	55678.0			0.367946			0.183973	+	0.982931i	$0.441104\pi$
$390$		0			0
$391$			21262.5i			0.139079i
$392$	−41459.5	−	35109.7i	−0.269806	−	0.228484i
$393$			61347.5i			0.397202i
$394$	−151777.			−0.977719
$395$		0			0
$396$	4353.79			0.0277637
$397$	−194941.			−1.23687			−0.618434	−	0.785837i	$-0.712232\pi$
$397$	−194941.			−1.23687			−0.618434	+	0.785837i	$0.712232\pi$
$398$	137633.			0.868873
$399$	−52430.1	+	24304.2i	−0.329333	+	0.152664i
$400$		0			0
$401$	−198450.			−1.23413			−0.617066	−	0.786912i	$-0.711679\pi$
$401$	−198450.			−1.23413			−0.617066	+	0.786912i	$0.711679\pi$
$402$	17615.6			0.109005
$403$		−	28548.0i		−	0.175778i
$404$			109558.i			0.671246i
$405$		0			0
$406$	−119564.	+	55424.4i	−0.725351	+	0.336240i
$407$		−	15127.7i		−	0.0913236i
$408$		−	73746.7i		−	0.443019i
$409$		−	272739.i		−	1.63042i	−0.579163	−	0.815212i	$-0.696620\pi$
$409$		−	272739.i		−	1.63042i	0.579163	−	0.815212i	$-0.303380\pi$
$410$		0			0
$411$			5116.87i			0.0302915i
$412$	121174.			0.713863
$413$	−73364.4	+	34008.4i	−0.430116	+	0.199382i
$414$	9572.81			0.0558520
$415$		0			0
$416$		−	3730.39i		−	0.0215560i
$417$			208850.i			1.20105i
$418$	3499.34			0.0200278
$419$			187423.i			1.06756i	0.845622	+	0.533782i	$0.179230\pi$
$419$			187423.i			1.06756i	−0.845622	+	0.533782i	$0.820770\pi$
$420$		0			0
$421$	167675.			0.946030			0.473015	−	0.881054i	$-0.343166\pi$
$421$	167675.			0.946030			0.473015	+	0.881054i	$0.343166\pi$
$422$		−	160441.i		−	0.900927i
$423$	−8570.22			−0.0478973
$424$	−99038.8			−0.550901
$425$		0			0
$426$		−	270572.i		−	1.49095i
$427$	−231193.	+	107170.i	−1.26800	+	0.587786i
$428$			57098.2i			0.311699i
$429$	2746.15			0.0149214
$430$		0			0
$431$	49932.1			0.268798			0.134399	−	0.990927i	$-0.457090\pi$
$431$	49932.1			0.268798			0.134399	+	0.990927i	$0.457090\pi$
$432$	25225.2			0.135166
$433$	−209375.			−1.11673			−0.558365	−	0.829595i	$-0.688571\pi$
$433$	−209375.			−1.11673			−0.558365	+	0.829595i	$0.688571\pi$
$434$	−80745.8	−	174188.i	−0.428687	−	0.924783i
$435$		0			0
$436$	−108451.			−0.570505
$437$	7694.12			0.0402899
$438$			10116.4i			0.0527325i
$439$		−	146706.i		−	0.761233i	−0.924733	−	0.380617i	$-0.875712\pi$
$439$		−	146706.i		−	0.761233i	0.924733	−	0.380617i	$-0.124288\pi$
$440$		0			0
$441$	−71421.3	+	84338.2i	−0.367241	+	0.433658i
$442$		−	16855.1i		−	0.0862752i
$443$		−	295799.i		−	1.50726i	−0.657297	−	0.753632i	$-0.728300\pi$
$443$		−	295799.i		−	1.50726i	0.657297	−	0.753632i	$-0.271700\pi$
$444$			115365.i			0.585203i
$445$		0			0
$446$			178935.i			0.899553i
$447$	204367.			1.02281
$448$	−10551.2	−	22761.4i	−0.0525707	−	0.113408i
$449$	141239.			0.700585			0.350292	−	0.936640i	$-0.386082\pi$
$449$	141239.			0.700585			0.350292	+	0.936640i	$0.386082\pi$
$450$		0			0
$451$			15412.2i			0.0757726i
$452$		−	6145.61i		−	0.0300807i
$453$	−99615.8			−0.485436
$454$			49.7912i			0.000241569i
$455$		0			0
$456$	−26686.2			−0.128339
$457$			58499.5i			0.280104i	0.990144	+	0.140052i	$0.0447270\pi$
$457$			58499.5i			0.280104i	−0.990144	+	0.140052i	$0.955273\pi$
$458$	−88993.0			−0.424253
$459$	113975.			0.540985
$460$		0			0
$461$		−	203637.i		−	0.958195i	−0.877762	−	0.479098i	$-0.840964\pi$
$461$		−	203637.i		−	0.958195i	0.877762	−	0.479098i	$-0.159036\pi$
$462$	16755.9	−	7767.27i	0.0785025	−	0.0363902i
$463$			137727.i			0.642474i	0.946999	+	0.321237i	$0.104099\pi$
$463$			137727.i			0.642474i	−0.946999	+	0.321237i	$0.895901\pi$
$464$	−60856.4			−0.282664
$465$		0			0
$466$	166161.			0.765170
$467$	243217.			1.11522			0.557610	−	0.830103i	$-0.311718\pi$
$467$	243217.			1.11522			0.557610	+	0.830103i	$0.311718\pi$
$468$	−7588.49			−0.0346469
$469$	24565.7	−	11387.6i	0.111682	−	0.0517708i
$470$		0			0
$471$	−232383.			−1.04752
$472$	−37341.5			−0.167613
$473$			1137.81i			0.00508565i
$474$			19904.2i			0.0885905i
$475$		0			0
$476$	−47673.3	−	102843.i	−0.210408	−	0.453900i
$477$			201468.i			0.885460i
$478$			137090.i			0.599997i
$479$		−	363910.i		−	1.58607i	−0.609174	−	0.793036i	$-0.708499\pi$
$479$		−	363910.i		−	1.58607i	0.609174	−	0.793036i	$-0.291501\pi$
$480$		0			0
$481$			26367.0i			0.113965i
$482$	101068.			0.435028
$483$	36841.7	−	17078.1i	0.157923	−	0.0732060i
$484$	116010.			0.495226
$485$		0			0
$486$		−	170169.i		−	0.720457i
$487$			441526.i			1.86165i	0.365466	+	0.930825i	$0.380910\pi$
$487$			441526.i			1.86165i	−0.365466	+	0.930825i	$0.619090\pi$
$488$	−117674.			−0.494129
$489$			345178.i			1.44353i
$490$		0			0
$491$	219482.			0.910409			0.455204	−	0.890387i	$-0.349566\pi$
$491$	219482.			0.910409			0.455204	+	0.890387i	$0.349566\pi$
$492$		−	117535.i		−	0.485552i
$493$	−274968.			−1.13133
$494$	−6099.23			−0.0249931
$495$		0			0
$496$		−	88659.5i		−	0.360381i
$497$	−174910.	−	377324.i	−0.708113	−	1.52757i
$498$		−	244263.i		−	0.984916i
$499$	−322884.			−1.29672			−0.648360	−	0.761334i	$-0.724545\pi$
$499$	−322884.			−1.29672			−0.648360	+	0.761334i	$0.724545\pi$
$500$		0			0
$501$	594612.			2.36896
$502$	−42597.6			−0.169035
$503$	28222.0			0.111546			0.0557728	−	0.998443i	$-0.482238\pi$
$503$	28222.0			0.111546			0.0557728	+	0.998443i	$0.482238\pi$
$504$	−46302.0	+	21463.5i	−0.182280	+	0.0844966i
$505$		0			0
$506$	−2458.92			−0.00960382
$507$	317117.			1.23368
$508$			7591.36i			0.0294166i
$509$		−	47084.6i		−	0.181737i	−0.995863	−	0.0908685i	$-0.971036\pi$
$509$		−	47084.6i		−	0.181737i	0.995863	−	0.0908685i	$-0.0289643\pi$
$510$		0			0
$511$	6539.72	+	14107.8i	0.0250448	+	0.0540277i
$512$		−	11585.2i		−	0.0441942i
$513$		−	41243.4i		−	0.156718i
$514$		−	213831.i		−	0.809365i
$515$		0			0
$516$		−	8677.00i		−	0.0325889i
$517$	2201.39			0.00823600
$518$	74577.0	+	160881.i	0.277936	+	0.599576i
$519$	−193509.			−0.718400
$520$		0			0
$521$		−	146513.i		−	0.539760i	−0.962894	−	0.269880i	$-0.913016\pi$
$521$		−	146513.i		−	0.539760i	0.962894	−	0.269880i	$-0.0869840\pi$
$522$			123796.i			0.454324i
$523$	462892.			1.69229			0.846147	−	0.532949i	$-0.178916\pi$
$523$	462892.			1.69229			0.846147	+	0.532949i	$0.178916\pi$
$524$			43544.7i			0.158589i
$525$		0			0
$526$	−106694.			−0.385626
$527$		−	400591.i		−	1.44238i
$528$	8528.52			0.0305919
$529$	274434.			0.980680
$530$		0			0
$531$			75961.3i			0.269404i
$532$	−37215.1	+	17251.2i	−0.131491	+	0.0609532i
$533$		−	26862.9i		−	0.0945582i
$534$	133594.			0.468493
$535$		0			0
$536$	12503.6			0.0435217
$537$	342871.			1.18900
$538$	151776.			0.524370
$539$	18345.7	−	21663.6i	0.0631475	−	0.0745680i
$540$		0			0
$541$	272724.			0.931814			0.465907	−	0.884834i	$-0.345728\pi$
$541$	272724.			0.931814			0.465907	+	0.884834i	$0.345728\pi$
$542$	−256798.			−0.874166
$543$		−	468073.i		−	1.58750i
$544$		−	52345.6i		−	0.176882i
$545$		0			0
$546$	−29204.9	+	13538.1i	−0.0979649	+	0.0454121i
$547$			494466.i			1.65258i	0.563248	+	0.826288i	$0.309552\pi$
$547$			494466.i			1.65258i	−0.563248	+	0.826288i	$0.690448\pi$
$548$			3631.97i			0.0120943i
$549$			239376.i			0.794211i
$550$		0			0
$551$			99500.7i			0.327735i
$552$	18751.9			0.0615414
$553$	12867.0	+	27757.2i	0.0420752	+	0.0907664i
$554$	318727.			1.03848
$555$		0			0
$556$			148242.i			0.479537i
$557$			65156.0i			0.210012i	0.994472	+	0.105006i	$0.0334862\pi$
$557$			65156.0i			0.210012i	−0.994472	+	0.105006i	$0.966514\pi$
$558$	−180354.			−0.579239
$559$		−	1983.16i		−	0.00634649i
$560$		0			0
$561$	38534.5			0.122440
$562$		−	137568.i		−	0.435558i
$563$	478300.			1.50898			0.754491	−	0.656311i	$-0.227884\pi$
$563$	478300.			1.50898			0.754491	+	0.656311i	$0.227884\pi$
$564$	−16788.0			−0.0527764
$565$		0			0
$566$			23419.4i			0.0731043i
$567$	−168379.	−	363234.i	−0.523747	−	1.12985i
$568$		−	192053.i		−	0.595284i
$569$	132853.			0.410343			0.205172	−	0.978726i	$-0.434225\pi$
$569$	132853.			0.410343			0.205172	+	0.978726i	$0.434225\pi$
$570$		0			0
$571$	304216.			0.933060			0.466530	−	0.884505i	$-0.345504\pi$
$571$	304216.			0.933060			0.466530	+	0.884505i	$0.345504\pi$
$572$	1949.22			0.00595757
$573$	580785.			1.76891
$574$	−75979.8	−	163907.i	−0.230608	−	0.497478i
$575$		0			0
$576$	−23567.1			−0.0710331
$577$	−211529.			−0.635357			−0.317678	−	0.948199i	$-0.602903\pi$
$577$	−211529.			−0.635357			−0.317678	+	0.948199i	$0.602903\pi$
$578$		−	280.573i		−	0.000839826i
$579$			265399.i			0.791667i
$580$		0			0
$581$	−157903.	−	340635.i	−0.467776	−	1.00911i
$582$		−	414240.i		−	1.22294i
$583$		−	51750.2i		−	0.152256i
$584$			7180.66i			0.0210542i
$585$		0			0
$586$			310712.i			0.904820i
$587$	544796.			1.58109			0.790547	−	0.612401i	$-0.209796\pi$
$587$	544796.			1.58109			0.790547	+	0.612401i	$0.209796\pi$
$588$	−139905.	+	165208.i	−0.404650	+	0.477833i
$589$	−144959.			−0.417845
$590$		0			0
$591$			604803.i			1.73157i
$592$			81886.1i			0.233650i
$593$	−189340.			−0.538435			−0.269218	−	0.963079i	$-0.586765\pi$
$593$	−189340.			−0.538435			−0.269218	+	0.963079i	$0.586765\pi$
$594$			13180.8i			0.0373567i
$595$		0			0
$596$	145061.			0.408373
$597$		−	548440.i		−	1.53880i
$598$	4285.82			0.0119848
$599$	281405.			0.784292			0.392146	−	0.919903i	$-0.371733\pi$
$599$	281405.			0.784292			0.392146	+	0.919903i	$0.371733\pi$
$600$		0			0
$601$			261703.i			0.724534i	0.932074	+	0.362267i	$0.117997\pi$
$601$			261703.i			0.724534i	−0.932074	+	0.362267i	$0.882003\pi$
$602$	−5609.22	−	12100.4i	−0.0154778	−	0.0333894i
$603$		−	25435.3i		−	0.0699523i
$604$	−70707.6			−0.193817
$605$		0			0
$606$	436568.			1.18879
$607$	−49166.7			−0.133442			−0.0667212	−	0.997772i	$-0.521254\pi$
$607$	−49166.7			−0.133442			−0.0667212	+	0.997772i	$0.521254\pi$
$608$	−18942.0			−0.0512410
$609$	220856.	+	476439.i	0.595489	+	1.28461i
$610$		0			0
$611$	−3836.95			−0.0102779
$612$	−106483.			−0.284301
$613$			143767.i			0.382594i	0.981532	+	0.191297i	$0.0612693\pi$
$613$			143767.i			0.382594i	−0.981532	+	0.191297i	$0.938731\pi$
$614$		−	215397.i		−	0.571350i
$615$		0			0
$616$	11893.4	−	5513.23i	0.0313432	−	0.0145293i
$617$		−	270776.i		−	0.711280i	−0.934623	−	0.355640i	$-0.884263\pi$
$617$		−	270776.i		−	0.711280i	0.934623	−	0.355640i	$-0.115737\pi$
$618$		−	482855.i		−	1.26427i
$619$		−	94786.2i		−	0.247379i	−0.992321	−	0.123690i	$-0.960527\pi$
$619$		−	94786.2i		−	0.247379i	0.992321	−	0.123690i	$-0.0394728\pi$
$620$		0			0
$621$			28981.0i			0.0751502i
$622$	−231853.			−0.599284
$623$	186302.	−	86361.2i	0.480000	−	0.222506i
$624$	−14864.9			−0.0381762
$625$		0			0
$626$		−	89846.3i		−	0.229272i
$627$		−	13944.2i		−	0.0354698i
$628$	−164946.			−0.418238
$629$			369986.i			0.935157i
$630$		0			0
$631$	−71201.8			−0.178827			−0.0894133	−	0.995995i	$-0.528499\pi$
$631$	−71201.8			−0.178827			−0.0894133	+	0.995995i	$0.528499\pi$
$632$			14128.0i			0.0353710i
$633$	−639325.			−1.59557
$634$	3190.23			0.00793677
$635$		0			0
$636$			394650.i			0.975659i
$637$	−31975.8	+	37758.8i	−0.0788031	+	0.0930550i
$638$		−	31799.0i		−	0.0781217i
$639$	−390680.			−0.956796
$640$		0			0
$641$	471662.			1.14793			0.573964	−	0.818880i	$-0.305405\pi$
$641$	471662.			1.14793			0.573964	+	0.818880i	$0.305405\pi$
$642$	227525.			0.552026
$643$	−279296.			−0.675526			−0.337763	−	0.941231i	$-0.609670\pi$
$643$	−279296.			−0.675526			−0.337763	+	0.941231i	$0.609670\pi$
$644$	26150.4	−	12122.1i	0.0630530	−	0.0292285i
$645$		0			0
$646$	−85585.6			−0.205086
$647$	−652466.			−1.55865			−0.779326	−	0.626618i	$-0.784439\pi$
$647$	−652466.			−1.55865			−0.779326	+	0.626618i	$0.784439\pi$
$648$		−	184881.i		−	0.440294i
$649$		−	19511.8i		−	0.0463243i
$650$		0			0
$651$	−694107.	+	321757.i	−1.63781	+	0.759216i
$652$			245008.i			0.576348i
$653$		−	329674.i		−	0.773141i	−0.922260	−	0.386570i	$-0.873660\pi$
$653$		−	329674.i		−	0.773141i	0.922260	−	0.386570i	$-0.126340\pi$
$654$			432155.i			1.01038i
$655$		0			0
$656$		−	83426.4i		−	0.193863i
$657$	14607.1			0.0338403
$658$	−23411.5	+	10852.5i	−0.0540727	+	0.0250657i
$659$	−714693.			−1.64569			−0.822847	−	0.568264i	$-0.807615\pi$
$659$	−714693.			−1.64569			−0.822847	+	0.568264i	$0.807615\pi$
$660$		0			0
$661$			6632.86i			0.0151809i	0.999971	+	0.00759046i	$0.00241614\pi$
$661$			6632.86i			0.0151809i	−0.999971	+	0.00759046i	$0.997584\pi$
$662$			387417.i			0.884021i
$663$	−67164.2			−0.152796
$664$		−	173379.i		−	0.393242i
$665$		0			0
$666$	166575.			0.375545
$667$		−	69917.4i		−	0.157157i
$668$	422057.			0.945841
$669$	713023.			1.59313
$670$		0			0
$671$		−	61487.5i		−	0.136566i
$672$	−90699.7	+	42044.3i	−0.200848	+	0.0931040i
$673$			324015.i			0.715377i	0.933841	+	0.357688i	$0.116435\pi$
$673$			324015.i			0.715377i	−0.933841	+	0.357688i	$0.883565\pi$
$674$	426635.			0.939154
$675$		0			0
$676$	225091.			0.492565
$677$	−129070.			−0.281609			−0.140805	−	0.990037i	$-0.544969\pi$
$677$	−129070.			−0.281609			−0.140805	+	0.990037i	$0.544969\pi$
$678$	−24489.1			−0.0532737
$679$	−267784.	−	577676.i	−0.580825	−	1.25298i
$680$		0			0
$681$	198.408			0.000427824
$682$	46326.8			0.0996009
$683$		−	63841.7i		−	0.136856i	−0.997656	−	0.0684279i	$-0.978202\pi$
$683$		−	63841.7i		−	0.136856i	0.997656	−	0.0684279i	$-0.0217983\pi$
$684$			38532.4i			0.0823595i
$685$		0			0
$686$	−88305.8	+	320831.i	−0.187647	+	0.681754i
$687$			354620.i			0.751363i
$688$		−	6158.96i		−	0.0130116i
$689$			90198.7i			0.190004i
$690$		0			0
$691$		−	411380.i		−	0.861563i	−0.902456	−	0.430781i	$-0.858238\pi$
$691$		−	411380.i		−	0.861563i	0.902456	−	0.430781i	$-0.141762\pi$
$692$	−137353.			−0.286831
$693$	−11215.2	−	24193.9i	−0.0233529	−	0.0503778i
$694$	−36734.1			−0.0762693
$695$		0			0
$696$			242501.i			0.500605i
$697$		−	376946.i		−	0.775914i
$698$	520861.			1.06908
$699$		−	662120.i		−	1.35513i
$700$		0			0
$701$	−203545.			−0.414213			−0.207106	−	0.978318i	$-0.566405\pi$
$701$	−203545.			−0.414213			−0.207106	+	0.978318i	$0.566405\pi$
$702$		−	22973.6i		−	0.0466182i
$703$	133884.			0.270907
$704$	6053.57			0.0122142
$705$		0			0
$706$			173090.i			0.347266i
$707$	608812.	−	282218.i	1.21799	−	0.564606i
$708$			148799.i			0.296847i
$709$	−271184.			−0.539475			−0.269738	−	0.962934i	$-0.586937\pi$
$709$	−271184.			−0.539475			−0.269738	+	0.962934i	$0.586937\pi$
$710$		0			0
$711$	28739.7			0.0568517
$712$	94825.2			0.187053
$713$	101860.			0.200366
$714$	−409809.	+	189969.i	−0.803869	+	0.372637i
$715$		0			0
$716$	243371.			0.474725
$717$	546276.			1.06261
$718$		−	17100.5i		−	0.0331710i
$719$		−	457951.i		−	0.885853i	−0.896558	−	0.442927i	$-0.853940\pi$
$719$		−	457951.i		−	0.885853i	0.896558	−	0.442927i	$-0.146060\pi$
$720$		0			0
$721$	−312140.	−	673361.i	−0.600453	−	1.29532i
$722$		−	337633.i		−	0.647695i
$723$		−	402735.i		−	0.770446i
$724$		−	332240.i		−	0.633832i
$725$		0			0
$726$		−	462276.i		−	0.877058i
$727$	−331283.			−0.626802			−0.313401	−	0.949621i	$-0.601468\pi$
$727$	−331283.			−0.626802			−0.313401	+	0.949621i	$0.601468\pi$
$728$	−20729.7	+	9609.36i	−0.0391139	+	0.0181314i
$729$	−16266.0			−0.0306074
$730$		0			0
$731$		−	27828.1i		−	0.0520773i
$732$			468908.i			0.875115i
$733$	−179732.			−0.334516			−0.167258	−	0.985913i	$-0.553491\pi$
$733$	−179732.			−0.334516			−0.167258	+	0.985913i	$0.553491\pi$
$734$			607513.i			1.12762i
$735$		0			0
$736$	13310.2			0.0245713
$737$			6533.44i			0.0120284i
$738$	−169709.			−0.311596
$739$	−735946.			−1.34759			−0.673794	−	0.738920i	$-0.735336\pi$
$739$	−735946.			−1.34759			−0.673794	+	0.738920i	$0.735336\pi$
$740$		0			0
$741$			24304.2i			0.0442635i
$742$	255120.	+	550357.i	0.463380	+	0.999623i
$743$		−	705656.i		−	1.27825i	−0.769103	−	0.639125i	$-0.779297\pi$
$743$		−	705656.i		−	1.27825i	0.769103	−	0.639125i	$-0.220703\pi$
$744$	−353291.			−0.638244
$745$		0			0
$746$	653447.			1.17418
$747$	−352693.			−0.632055
$748$	27351.9			0.0488859
$749$	317294.	−	147083.i	0.565585	−	0.262180i
$750$		0			0
$751$	−662604.			−1.17483			−0.587414	−	0.809287i	$-0.699854\pi$
$751$	−662604.			−1.17483			−0.587414	+	0.809287i	$0.699854\pi$
$752$	−11916.2			−0.0210717
$753$			169743.i			0.299366i
$754$			55424.4i			0.0974896i
$755$		0			0
$756$	−64979.2	−	140176.i	−0.113692	−	0.245262i
$757$			628368.i			1.09653i	0.836303	+	0.548267i	$0.184712\pi$
$757$			628368.i			1.09653i	−0.836303	+	0.548267i	$0.815288\pi$
$758$			258924.i			0.450644i
$759$			9798.34i			0.0170086i
$760$		0			0
$761$			118942.i			0.205384i	0.994713	+	0.102692i	$0.0327456\pi$
$761$			118942.i			0.205384i	−0.994713	+	0.102692i	$0.967254\pi$
$762$	30250.1			0.0520975
$763$	279365.	+	602658.i	0.479869	+	1.03519i
$764$	412243.			0.706263
$765$		0			0
$766$		−	239795.i		−	0.408680i
$767$			34008.4i			0.0578090i
$768$	−46164.9			−0.0782690
$769$		−	814229.i		−	1.37687i	−0.725297	−	0.688436i	$-0.758297\pi$
$769$		−	814229.i		−	1.37687i	0.725297	−	0.688436i	$-0.241703\pi$
$770$		0			0
$771$	−852075.			−1.43341
$772$			188381.i			0.316084i
$773$	547344.			0.916012			0.458006	−	0.888949i	$-0.348564\pi$
$773$	547344.			0.916012			0.458006	+	0.888949i	$0.348564\pi$
$774$	−12528.8			−0.0209135
$775$		0			0
$776$		−	294029.i		−	0.488278i
$777$	641078.	−	297175.i	1.06186	−	0.492232i
$778$		−	157481.i		−	0.260177i
$779$	−136403.			−0.224775
$780$		0			0
$781$	100352.			0.164522
$782$	60139.4			0.0983435
$783$	−374784.			−0.611305
$784$	−99305.2	+	117265.i	−0.161562	+	0.190782i
$785$		0			0
$786$	173517.			0.280865
$787$	493397.			0.796612			0.398306	−	0.917253i	$-0.369598\pi$
$787$	493397.			0.796612			0.398306	+	0.917253i	$0.369598\pi$
$788$			429291.i			0.691352i
$789$			425153.i			0.682954i
$790$		0			0
$791$	−34151.1	+	15830.9i	−0.0545822	+	0.0253018i
$792$		−	12314.4i		−	0.0196319i
$793$			107170.i			0.170423i
$794$			551378.i			0.874597i
$795$		0			0
$796$		−	389285.i		−	0.614386i
$797$	−1.12201e6			−1.76637			−0.883183	−	0.469028i	$-0.844604\pi$
$797$	−1.12201e6			−1.76637			−0.883183	+	0.469028i	$0.844604\pi$
$798$	68742.8	+	148295.i	0.107950	+	0.232874i
$799$	−53840.8			−0.0843370
$800$		0			0
$801$		−	192897.i		−	0.300649i
$802$			561300.i			0.872663i
$803$	−3752.07			−0.00581889
$804$		−	49824.5i		−	0.0770781i
$805$		0			0
$806$	−80745.8			−0.124294
$807$		−	604797.i		−	0.928672i
$808$	309877.			0.474643
$809$	417208.			0.637464			0.318732	−	0.947845i	$-0.396743\pi$
$809$	417208.			0.637464			0.318732	+	0.947845i	$0.396743\pi$
$810$		0			0
$811$		−	919516.i		−	1.39803i	−0.715105	−	0.699017i	$-0.753621\pi$
$811$		−	919516.i		−	1.39803i	0.715105	−	0.699017i	$-0.246379\pi$
$812$	156764.	+	338178.i	0.237757	+	0.512901i
$813$			1.02329e6i			1.54817i
$814$	−42787.5			−0.0645755
$815$		0			0
$816$	−208587.			−0.313262
$817$	−10070.0			−0.0150863
$818$	−771422.			−1.15288
$819$	19547.7	+	42169.1i	0.0291425	+	0.0628676i
$820$		0			0
$821$	−339844.			−0.504189			−0.252095	−	0.967703i	$-0.581119\pi$
$821$	−339844.			−0.504189			−0.252095	+	0.967703i	$0.581119\pi$
$822$	14472.7			0.0214193
$823$		−	428314.i		−	0.632357i	−0.948700	−	0.316179i	$-0.897600\pi$
$823$		−	428314.i		−	0.632357i	0.948700	−	0.316179i	$-0.102400\pi$
$824$		−	342732.i		−	0.504777i
$825$		0			0
$826$	96190.3	+	207506.i	0.140984	+	0.304138i
$827$			641009.i			0.937245i	0.883398	+	0.468623i	$0.155250\pi$
$827$			641009.i			0.937245i	−0.883398	+	0.468623i	$0.844750\pi$
$828$		−	27076.0i		−	0.0394933i
$829$			109753.i			0.159701i	0.996807	+	0.0798504i	$0.0254443\pi$
$829$			109753.i			0.159701i	−0.996807	+	0.0798504i	$0.974556\pi$
$830$		0			0
$831$		−	1.27006e6i		−	1.83918i
$832$	−10551.2			−0.0152424
$833$	−448691.	+	529839.i	−0.646633	+	0.763580i
$834$	590716.			0.849272
$835$		0			0
$836$		−	9897.64i		−	0.0141618i
$837$		−	546009.i		−	0.779380i
$838$	530111.			0.754882
$839$		−	882140.i		−	1.25318i	−0.779349	−	0.626591i	$-0.784450\pi$
$839$		−	882140.i		−	1.25318i	0.779349	−	0.626591i	$-0.215550\pi$
$840$		0			0
$841$	196894.			0.278382
$842$		−	474257.i		−	0.668944i
$843$	−548184.			−0.771385
$844$	−453795.			−0.637052
$845$		0			0
$846$			24240.2i			0.0338685i
$847$	−298837.	−	644663.i	−0.416550	−	0.898600i
$848$			280124.i			0.389546i
$849$	93321.8			0.129470
$850$		0			0
$851$	−94078.2			−0.129906
$852$	−765293.			−1.05426
$853$	−699021.			−0.960709			−0.480355	−	0.877074i	$-0.659492\pi$
$853$	−699021.			−0.960709			−0.480355	+	0.877074i	$0.659492\pi$
$854$	303124.	+	653912.i	0.415627	+	0.896609i
$855$		0			0
$856$	161498.			0.220404
$857$	776746.			1.05759			0.528795	−	0.848750i	$-0.322644\pi$
$857$	776746.			1.05759			0.528795	+	0.848750i	$0.322644\pi$
$858$		−	7767.27i		−	0.0105510i
$859$			1.10160e6i			1.49292i	0.665429	+	0.746461i	$0.268249\pi$
$859$			1.10160e6i			1.49292i	−0.665429	+	0.746461i	$0.731751\pi$
$860$		0			0
$861$	−653137.	+	302765.i	−0.881045	+	0.408413i
$862$		−	141229.i		−	0.190069i
$863$		−	27628.8i		−	0.0370971i	−0.999828	−	0.0185486i	$-0.994095\pi$
$863$		−	27628.8i		−	0.0370971i	0.999828	−	0.0185486i	$-0.00590453\pi$
$864$		−	71347.7i		−	0.0955768i
$865$		0			0
$866$			592201.i			0.789648i
$867$	−1118.03			−0.00148735
$868$	−492679.	+	228384.i	−0.653920	+	0.303128i
$869$	−7382.24			−0.00977572
$870$		0			0
$871$		−	11387.6i		−	0.0150105i
$872$			306745.i			0.403408i
$873$	−598123.			−0.784806
$874$		−	21762.2i		−	0.0284892i
$875$		0			0
$876$	28613.6			0.0372875
$877$			546244.i			0.710211i	0.934826	+	0.355105i	$0.115555\pi$
$877$			546244.i			0.710211i	−0.934826	+	0.355105i	$0.884445\pi$
$878$	−414946.			−0.538273
$879$	1.23813e6			1.60246
$880$		0			0
$881$			516904.i			0.665975i	0.942931	+	0.332988i	$0.108057\pi$
$881$			516904.i			0.665975i	−0.942931	+	0.332988i	$0.891943\pi$
$882$	238544.	+	202010.i	0.306642	+	0.259678i
$883$			1.24811e6i			1.60078i	0.599482	+	0.800388i	$0.295373\pi$
$883$			1.24811e6i			1.60078i	−0.599482	+	0.800388i	$0.704627\pi$
$884$	−47673.3			−0.0610058
$885$		0			0
$886$	−836646.			−1.06580
$887$	−229954.			−0.292276			−0.146138	−	0.989264i	$-0.546684\pi$
$887$	−229954.			−0.292276			−0.146138	+	0.989264i	$0.546684\pi$
$888$	326300.			0.413801
$889$	42185.0	−	19555.1i	0.0533771	−	0.0247432i
$890$		0			0
$891$	96605.0			0.121687
$892$	506106.			0.636080
$893$			19483.0i			0.0244317i
$894$		−	578038.i		−	0.723238i
$895$		0			0
$896$	−64378.9	+	29843.2i	−0.0801914	+	0.0371731i
$897$		−	17078.1i		−	0.0212254i
$898$		−	399483.i		−	0.495388i
$899$			1.31726e6i			1.62987i
$900$		0			0
$901$			1.26569e6i			1.55911i
$902$	43592.3			0.0535793
$903$	−48217.9	+	22351.6i	−0.0591334	+	0.0274116i
$904$	−17382.4			−0.0212703
$905$		0			0
$906$			281756.i			0.343255i
$907$			66711.4i			0.0810933i	0.999178	+	0.0405467i	$0.0129099\pi$
$907$			66711.4i			0.0810933i	−0.999178	+	0.0405467i	$0.987090\pi$
$908$	140.831			0.000170815
$909$		−	630362.i		−	0.762891i
$910$		0			0
$911$	−681437.			−0.821086			−0.410543	−	0.911841i	$-0.634661\pi$
$911$	−681437.			−0.821086			−0.410543	+	0.911841i	$0.634661\pi$
$912$			75480.0i			0.0907491i
$913$	90594.6			0.108683
$914$	165462.			0.198064
$915$		0			0
$916$			251710.i			0.299992i
$917$	241977.	−	112169.i	0.287763	−	0.133394i
$918$		−	322371.i		−	0.382534i
$919$	−659165.			−0.780483			−0.390241	−	0.920713i	$-0.627608\pi$
$919$	−659165.			−0.780483			−0.390241	+	0.920713i	$0.627608\pi$
$920$		0			0
$921$	−858314.			−1.01188
$922$	−575971.			−0.677546
$923$	−174910.			−0.205311
$924$	−21969.2	−	47392.8i	−0.0257318	−	0.0555097i
$925$		0			0
$926$	389549.			0.454298
$927$	−697196.			−0.811326
$928$			172128.i			0.199874i
$929$			146974.i			0.170298i	0.996368	+	0.0851491i	$0.0271367\pi$
$929$			146974.i			0.170298i	−0.996368	+	0.0851491i	$0.972863\pi$
$930$		0			0
$931$	191729.	+	162365.i	0.221202	+	0.187324i
$932$		−	469975.i		−	0.541057i
$933$			923891.i			1.06135i
$934$		−	687922.i		−	0.788580i
$935$		0			0
$936$			21463.5i			0.0244990i
$937$	−1.11634e6			−1.27150			−0.635751	−	0.771894i	$-0.719309\pi$
$937$	−1.11634e6			−1.27150			−0.635751	+	0.771894i	$0.719309\pi$
$938$	−32208.9	−	69482.4i	−0.0366075	−	0.0789712i
$939$	−358020.			−0.406047
$940$		0			0
$941$		−	569425.i		−	0.643068i	−0.946898	−	0.321534i	$-0.895801\pi$
$941$		−	569425.i		−	0.643068i	0.946898	−	0.321534i	$-0.104199\pi$
$942$			657279.i			0.740709i
$943$	95847.8			0.107785
$944$			105618.i			0.118520i
$945$		0			0
$946$	3218.21			0.00359610
$947$			165748.i			0.184820i	0.995721	+	0.0924099i	$0.0294570\pi$
$947$			165748.i			0.184820i	−0.995721	+	0.0924099i	$0.970543\pi$
$948$	56297.5			0.0626429
$949$	6539.72			0.00726151
$950$		0			0
$951$		−	12712.5i		−	0.0140562i
$952$	−290884.	+	134841.i	−0.320956	+	0.148781i
$953$			1.21791e6i			1.34100i	0.741909	+	0.670501i	$0.233921\pi$
$953$			1.21791e6i			1.34100i	−0.741909	+	0.670501i	$0.766079\pi$
$954$	569837.			0.626115
$955$		0			0
$956$	387748.			0.424262
$957$	−126713.			−0.138355
$958$	−1.02929e6			−1.12152
$959$	20182.8	−	9355.83i	0.0219454	−	0.0101729i
$960$		0			0
$961$	−995549.			−1.07799
$962$	74577.0			0.0805851
$963$		−	328525.i		−	0.354255i
$964$		−	285862.i		−	0.307612i
$965$		0			0
$966$	−48304.3	−	104204.i	−0.0517644	−	0.111668i
$967$			473000.i			0.505834i	0.967488	+	0.252917i	$0.0813900\pi$
$967$			473000.i			0.505834i	−0.967488	+	0.252917i	$0.918610\pi$
$968$		−	328125.i		−	0.350178i
$969$			341042.i			0.363212i
$970$		0			0
$971$			823487.i			0.873410i	0.899605	+	0.436705i	$0.143855\pi$
$971$			823487.i			0.873410i	−0.899605	+	0.436705i	$0.856145\pi$
$972$	−481311.			−0.509440
$973$	823779.	−	381867.i	0.870132	−	0.403354i
$974$	1.24882e6			1.31639
$975$		0			0
$976$			332832.i			0.349402i
$977$			513003.i			0.537441i	0.963218	+	0.268721i	$0.0866008\pi$
$977$			513003.i			0.537441i	−0.963218	+	0.268721i	$0.913399\pi$
$978$	976310.			1.02073
$979$			49548.5i			0.0516970i
$980$		0			0
$981$	623991.			0.648396
$982$		−	620790.i		−	0.643756i
$983$	672941.			0.696418			0.348209	−	0.937417i	$-0.386790\pi$
$983$	672941.			0.696418			0.348209	+	0.937417i	$0.386790\pi$
$984$	−332438.			−0.343337
$985$		0			0
$986$			777727.i			0.799969i
$987$	43245.2	+	93290.5i	0.0443919	+	0.0957641i
$988$			17251.2i			0.0176728i
$989$	7075.97			0.00723425
$990$		0			0
$991$	496654.			0.505716			0.252858	−	0.967503i	$-0.418629\pi$
$991$	496654.			0.505716			0.252858	+	0.967503i	$0.418629\pi$
$992$	−250767.			−0.254828
$993$	1.54378e6			1.56562
$994$	−1.06723e6	+	494721.i	−1.08016	+	0.500712i
$995$		0			0
$996$	−690880.			−0.696441
$997$	972300.			0.978160			0.489080	−	0.872239i	$-0.337333\pi$
$997$	972300.			0.978160			0.489080	+	0.872239i	$0.337333\pi$
$998$			913255.i			0.916919i
$999$			504295.i			0.505305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.5.d.a.349.2		8
5.2	odd	4		14.5.b.a.13.4	yes	4
5.3	odd	4		350.5.b.a.251.1		4
5.4	even	2	inner	350.5.d.a.349.7		8
7.6	odd	2	inner	350.5.d.a.349.3		8
15.2	even	4		126.5.c.a.55.2		4
20.7	even	4		112.5.c.c.97.2		4
35.2	odd	12		98.5.d.d.31.1		8
35.12	even	12		98.5.d.d.31.2		8
35.13	even	4		350.5.b.a.251.2		4
35.17	even	12		98.5.d.d.19.1		8
35.27	even	4		14.5.b.a.13.3	✓	4
35.32	odd	12		98.5.d.d.19.2		8
35.34	odd	2	inner	350.5.d.a.349.6		8
40.27	even	4		448.5.c.f.321.3		4
40.37	odd	4		448.5.c.e.321.2		4
60.47	odd	4		1008.5.f.h.433.4		4
105.62	odd	4		126.5.c.a.55.1		4
140.27	odd	4		112.5.c.c.97.3		4
280.27	odd	4		448.5.c.f.321.2		4
280.237	even	4		448.5.c.e.321.3		4
420.167	even	4		1008.5.f.h.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.b.a.13.3	✓	4	35.27	even	4
14.5.b.a.13.4	yes	4	5.2	odd	4
98.5.d.d.19.1		8	35.17	even	12
98.5.d.d.19.2		8	35.32	odd	12
98.5.d.d.31.1		8	35.2	odd	12
98.5.d.d.31.2		8	35.12	even	12
112.5.c.c.97.2		4	20.7	even	4
112.5.c.c.97.3		4	140.27	odd	4
126.5.c.a.55.1		4	105.62	odd	4
126.5.c.a.55.2		4	15.2	even	4
350.5.b.a.251.1		4	5.3	odd	4
350.5.b.a.251.2		4	35.13	even	4
350.5.d.a.349.2		8	1.1	even	1	trivial
350.5.d.a.349.3		8	7.6	odd	2	inner
350.5.d.a.349.6		8	35.34	odd	2	inner
350.5.d.a.349.7		8	5.4	even	2	inner
448.5.c.e.321.2		4	40.37	odd	4
448.5.c.e.321.3		4	280.237	even	4
448.5.c.f.321.2		4	280.27	odd	4
448.5.c.f.321.3		4	40.27	even	4
1008.5.f.h.433.1		4	420.167	even	4
1008.5.f.h.433.4		4	60.47	odd	4

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	350.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -11.2707 q^{3} -8.00000 q^{4} +31.8784i q^{6} +(20.6077 + 44.4558i) q^{7} +22.6274i q^{8} +46.0294 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -11.2707 q^{3} -8.00000 q^{4} +31.8784i q^{6} +(20.6077 + 44.4558i) q^{7} +22.6274i q^{8} +46.0294 q^{9} -11.8234 q^{11} +90.1659 q^{12} +20.6077 q^{13} +(125.740 - 58.2874i) q^{14} +64.0000 q^{16} +289.172 q^{17} -130.191i q^{18} -104.641i q^{19} +(-232.264 - 501.050i) q^{21} +33.4416i q^{22} +73.5290i q^{23} -255.028i q^{24} -58.2874i q^{26} +394.144 q^{27} +(-164.862 - 355.647i) q^{28} -950.881 q^{29} -1385.30i q^{31} -181.019i q^{32} +133.258 q^{33} -817.901i q^{34} -368.235 q^{36} +1279.47i q^{37} -295.968 q^{38} -232.264 q^{39} -1303.54i q^{41} +(-1417.18 + 656.942i) q^{42} -96.2338i q^{43} +94.5870 q^{44} +207.971 q^{46} -186.190 q^{47} -721.327 q^{48} +(-1551.64 + 1832.27i) q^{49} -3259.18 q^{51} -164.862 q^{52} +4376.94i q^{53} -1114.81i q^{54} +(-1005.92 + 466.299i) q^{56} +1179.38i q^{57} +2689.50i q^{58} +1650.28i q^{59} +5200.50i q^{61} -3918.23 q^{62} +(948.562 + 2046.28i) q^{63} -512.000 q^{64} -376.911i q^{66} -552.587i q^{67} -2313.37 q^{68} -828.726i q^{69} -8487.61 q^{71} +1041.53i q^{72} +317.344 q^{73} +3618.89 q^{74} +837.124i q^{76} +(-243.653 - 525.618i) q^{77} +656.942i q^{78} +624.377 q^{79} -8170.68 q^{81} -3686.96 q^{82} -7662.33 q^{83} +(1858.11 + 4008.40i) q^{84} -272.190 q^{86} +10717.1 q^{87} -267.532i q^{88} -4190.72i q^{89} +(424.678 + 916.133i) q^{91} -588.232i q^{92} +15613.4i q^{93} +526.625i q^{94} +2040.22i q^{96} -12994.4 q^{97} +(5182.43 + 4388.71i) q^{98} -544.223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 64 q^{4} + 504 q^{9}+O(q^{10}) \) 8 * q - 64 * q^4 + 504 * q^9	\( 8 q - 64 q^{4} + 504 q^{9} + 720 q^{11} + 576 q^{14} + 512 q^{16} + 1536 q^{21} - 2448 q^{29} - 4032 q^{36} + 1536 q^{39} - 5760 q^{44} + 6144 q^{46} + 3064 q^{49} - 22272 q^{51} - 4608 q^{56} - 4096 q^{64} - 43056 q^{71} + 6912 q^{74} - 25552 q^{79} - 59256 q^{81} - 12288 q^{84} - 23040 q^{86} + 11136 q^{91} + 59184 q^{99}+O(q^{100}) \) 8 * q - 64 * q^4 + 504 * q^9 + 720 * q^11 + 576 * q^14 + 512 * q^16 + 1536 * q^21 - 2448 * q^29 - 4032 * q^36 + 1536 * q^39 - 5760 * q^44 + 6144 * q^46 + 3064 * q^49 - 22272 * q^51 - 4608 * q^56 - 4096 * q^64 - 43056 * q^71 + 6912 * q^74 - 25552 * q^79 - 59256 * q^81 - 12288 * q^84 - 23040 * q^86 + 11136 * q^91 + 59184 * q^99

Introduction

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