LMFDB - Embedded newform 1050.5.h.a.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,5,Mod(349,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1050.349");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	1050.h (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:	$108.538461238$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1050.349
Dual form			1050.5.h.a.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +14.6969i q^{6} +(29.7420 - 38.9411i) q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +14.6969i q^{6} +(29.7420 - 38.9411i) q^{7} +22.6274i q^{8} +27.0000 q^{9} +16.7939 q^{11} +41.5692 q^{12} +54.5254 q^{13} +(-110.142 - 84.1232i) q^{14} +64.0000 q^{16} -187.554 q^{17} -76.3675i q^{18} +417.866i q^{19} +(-154.544 + 202.344i) q^{21} -47.5004i q^{22} -455.470i q^{23} -117.576i q^{24} -154.221i q^{26} -140.296 q^{27} +(-237.936 + 311.529i) q^{28} +1022.03 q^{29} -1547.79i q^{31} -181.019i q^{32} -87.2639 q^{33} +530.482i q^{34} -216.000 q^{36} -1551.12i q^{37} +1181.90 q^{38} -283.322 q^{39} +2542.74i q^{41} +(572.315 + 437.117i) q^{42} +1409.82i q^{43} -134.352 q^{44} -1288.26 q^{46} +2633.39 q^{47} -332.554 q^{48} +(-631.823 - 2316.38i) q^{49} +974.558 q^{51} -436.203 q^{52} +1117.09i q^{53} +396.817i q^{54} +(881.137 + 672.985i) q^{56} -2171.29i q^{57} -2890.73i q^{58} +5838.80i q^{59} +3746.84i q^{61} -4377.81 q^{62} +(803.035 - 1051.41i) q^{63} -512.000 q^{64} +246.819i q^{66} +6948.23i q^{67} +1500.43 q^{68} +2366.69i q^{69} -4513.18 q^{71} +610.940i q^{72} +6461.29 q^{73} -4387.22 q^{74} -3342.93i q^{76} +(499.486 - 653.975i) q^{77} +801.356i q^{78} +7443.29 q^{79} +729.000 q^{81} +7191.94 q^{82} +7335.80 q^{83} +(1236.35 - 1618.75i) q^{84} +3987.58 q^{86} -5310.62 q^{87} +380.003i q^{88} -10369.3i q^{89} +(1621.70 - 2123.28i) q^{91} +3643.76i q^{92} +8042.55i q^{93} -7448.36i q^{94} +940.604i q^{96} +7930.48 q^{97} +(-6551.70 + 1787.06i) q^{98} +453.436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 64 q^{4} + 216 q^{9}+O(q^{10}) $ 8 * q - 64 * q^4 + 216 * q^9	$ 8 q - 64 q^{4} + 216 q^{9} - 816 q^{11} - 768 q^{14} + 512 q^{16} - 1440 q^{21} + 3696 q^{29} - 1728 q^{36} + 5472 q^{39} + 6528 q^{44} - 6912 q^{46} + 376 q^{49} + 5760 q^{51} + 6144 q^{56} - 4096 q^{64} - 32304 q^{71} - 11520 q^{74} + 28592 q^{79} + 5832 q^{81} + 11520 q^{84} + 28416 q^{86} - 43776 q^{91} - 22032 q^{99}+O(q^{100}) $ 8 * q - 64 * q^4 + 216 * q^9 - 816 * q^11 - 768 * q^14 + 512 * q^16 - 1440 * q^21 + 3696 * q^29 - 1728 * q^36 + 5472 * q^39 + 6528 * q^44 - 6912 * q^46 + 376 * q^49 + 5760 * q^51 + 6144 * q^56 - 4096 * q^64 - 32304 * q^71 - 11520 * q^74 + 28592 * q^79 + 5832 * q^81 + 11520 * q^84 + 28416 * q^86 - 43776 * q^91 - 22032 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	−8.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			14.6969i			0.408248i
$7$	29.7420	−	38.9411i	0.606980	−	0.794717i
$7$	29.7420	−	38.9411i	0.606980	−	0.794717i
$8$			22.6274i			0.353553i
$9$	27.0000			0.333333
$10$		0			0
$11$	16.7939			0.138793			0.0693964	−	0.997589i	$-0.477893\pi$
$11$	16.7939			0.138793			0.0693964	+	0.997589i	$0.477893\pi$
$12$	41.5692			0.288675
$13$	54.5254			0.322635			0.161318	−	0.986903i	$-0.448426\pi$
$13$	54.5254			0.322635			0.161318	+	0.986903i	$0.448426\pi$
$14$	−110.142	−	84.1232i	−0.561950	−	0.429200i
$15$		0			0
$16$	64.0000			0.250000
$17$	−187.554			−0.648975			−0.324488	−	0.945890i	$-0.605192\pi$
$17$	−187.554			−0.648975			−0.324488	+	0.945890i	$0.605192\pi$
$18$		−	76.3675i		−	0.235702i
$19$			417.866i			1.15752i	0.815497	+	0.578761i	$0.196464\pi$
$19$			417.866i			1.15752i	−0.815497	+	0.578761i	$0.803536\pi$
$20$		0			0
$21$	−154.544	+	202.344i	−0.350440	+	0.458830i
$22$		−	47.5004i		−	0.0981414i
$23$		−	455.470i		−	0.861002i	−0.902590	−	0.430501i	$-0.858337\pi$
$23$		−	455.470i		−	0.861002i	0.902590	−	0.430501i	$-0.141663\pi$
$24$		−	117.576i		−	0.204124i
$25$		0			0
$26$		−	154.221i		−	0.228138i
$27$	−140.296			−0.192450
$28$	−237.936	+	311.529i	−0.303490	+	0.397358i
$29$	1022.03			1.21525			0.607627	−	0.794223i	$-0.292122\pi$
$29$	1022.03			1.21525			0.607627	+	0.794223i	$0.292122\pi$
$30$		0			0
$31$		−	1547.79i		−	1.61060i	−0.592866	−	0.805301i	$-0.702004\pi$
$31$		−	1547.79i		−	1.61060i	0.592866	−	0.805301i	$-0.297996\pi$
$32$		−	181.019i		−	0.176777i
$33$	−87.2639			−0.0801321
$34$			530.482i			0.458895i
$35$		0			0
$36$	−216.000			−0.166667
$37$		−	1551.12i		−	1.13303i	−0.824052	−	0.566515i	$-0.808291\pi$
$37$		−	1551.12i		−	1.13303i	0.824052	−	0.566515i	$-0.191709\pi$
$38$	1181.90			0.818492
$39$	−283.322			−0.186274
$40$		0			0
$41$			2542.74i			1.51263i	0.654206	+	0.756316i	$0.273003\pi$
$41$			2542.74i			1.51263i	−0.654206	+	0.756316i	$0.726997\pi$
$42$	572.315	+	437.117i	0.324442	+	0.247799i
$43$			1409.82i			0.762478i	0.924477	+	0.381239i	$0.124502\pi$
$43$			1409.82i			0.762478i	−0.924477	+	0.381239i	$0.875498\pi$
$44$	−134.352			−0.0693964
$45$		0			0
$46$	−1288.26			−0.608820
$47$	2633.39			1.19212			0.596060	−	0.802940i	$-0.296732\pi$
$47$	2633.39			1.19212			0.596060	+	0.802940i	$0.296732\pi$
$48$	−332.554			−0.144338
$49$	−631.823	−	2316.38i	−0.263150	−	0.964755i
$50$		0			0
$51$	974.558			0.374686
$52$	−436.203			−0.161318
$53$			1117.09i			0.397682i	0.980032	+	0.198841i	$0.0637178\pi$
$53$			1117.09i			0.397682i	−0.980032	+	0.198841i	$0.936282\pi$
$54$			396.817i			0.136083i
$55$		0			0
$56$	881.137	+	672.985i	0.280975	+	0.214600i
$57$		−	2171.29i		−	0.668296i
$58$		−	2890.73i		−	0.859314i
$59$			5838.80i			1.67733i	0.544644	+	0.838667i	$0.316665\pi$
$59$			5838.80i			1.67733i	−0.544644	+	0.838667i	$0.683335\pi$
$60$		0			0
$61$			3746.84i			1.00695i	0.864011	+	0.503473i	$0.167945\pi$
$61$			3746.84i			1.00695i	−0.864011	+	0.503473i	$0.832055\pi$
$62$	−4377.81			−1.13887
$63$	803.035	−	1051.41i	0.202327	−	0.264906i
$64$	−512.000			−0.125000
$65$		0			0
$66$			246.819i			0.0566620i
$67$			6948.23i			1.54783i	0.633287	+	0.773917i	$0.281705\pi$
$67$			6948.23i			1.54783i	−0.633287	+	0.773917i	$0.718295\pi$
$68$	1500.43			0.324488
$69$			2366.69i			0.497100i
$70$		0			0
$71$	−4513.18			−0.895294			−0.447647	−	0.894210i	$-0.647738\pi$
$71$	−4513.18			−0.895294			−0.447647	+	0.894210i	$0.647738\pi$
$72$			610.940i			0.117851i
$73$	6461.29			1.21248			0.606239	−	0.795283i	$-0.292678\pi$
$73$	6461.29			1.21248			0.606239	+	0.795283i	$0.292678\pi$
$74$	−4387.22			−0.801173
$75$		0			0
$76$		−	3342.93i		−	0.578761i
$77$	499.486	−	653.975i	0.0842446	−	0.110301i
$78$			801.356i			0.131715i
$79$	7443.29			1.19264			0.596322	−	0.802746i	$-0.296628\pi$
$79$	7443.29			1.19264			0.596322	+	0.802746i	$0.296628\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	7191.94			1.06959
$83$	7335.80			1.06486			0.532429	−	0.846475i	$-0.321279\pi$
$83$	7335.80			1.06486			0.532429	+	0.846475i	$0.321279\pi$
$84$	1236.35	−	1618.75i	0.175220	−	0.229415i
$85$		0			0
$86$	3987.58			0.539153
$87$	−5310.62			−0.701627
$88$			380.003i			0.0490707i
$89$		−	10369.3i		−	1.30909i	−0.756022	−	0.654547i	$-0.772860\pi$
$89$		−	10369.3i		−	1.30909i	0.756022	−	0.654547i	$-0.227140\pi$
$90$		0			0
$91$	1621.70	−	2123.28i	0.195833	−	0.256404i
$92$			3643.76i			0.430501i
$93$			8042.55i			0.929882i
$94$		−	7448.36i		−	0.842956i
$95$		0			0
$96$			940.604i			0.102062i
$97$	7930.48			0.842861			0.421431	−	0.906861i	$-0.361528\pi$
$97$	7930.48			0.842861			0.421431	+	0.906861i	$0.361528\pi$
$98$	−6551.70	+	1787.06i	−0.682185	+	0.186075i
$99$	453.436			0.0462643
$100$		0			0
$101$		−	1245.39i		−	0.122085i	−0.998135	−	0.0610425i	$-0.980557\pi$
$101$		−	1245.39i		−	0.122085i	0.998135	−	0.0610425i	$-0.0194425\pi$
$102$		−	2756.47i		−	0.264943i
$103$	−3086.95			−0.290974			−0.145487	−	0.989360i	$-0.546475\pi$
$103$	−3086.95			−0.290974			−0.145487	+	0.989360i	$0.546475\pi$
$104$			1233.77i			0.114069i
$105$		0			0
$106$	3159.61			0.281204
$107$			1325.86i			0.115806i	0.998322	+	0.0579031i	$0.0184414\pi$
$107$			1325.86i			0.115806i	−0.998322	+	0.0579031i	$0.981559\pi$
$108$	1122.37			0.0962250
$109$	−5821.22			−0.489960			−0.244980	−	0.969528i	$-0.578781\pi$
$109$	−5821.22			−0.489960			−0.244980	+	0.969528i	$0.578781\pi$
$110$		0			0
$111$			8059.84i			0.654155i
$112$	1903.49	−	2492.23i	0.151745	−	0.198679i
$113$		−	17988.8i		−	1.40878i	−0.709812	−	0.704392i	$-0.751220\pi$
$113$		−	17988.8i		−	1.40878i	0.709812	−	0.704392i	$-0.248780\pi$
$114$	−6141.35			−0.472557
$115$		0			0
$116$	−8176.23			−0.607627
$117$	1472.18			0.107545
$118$	16514.6			1.18605
$119$	−5578.23	+	7303.56i	−0.393915	+	0.515752i
$120$		0			0
$121$	−14359.0			−0.980737
$122$	10597.7			0.712018
$123$		−	13212.4i		−	0.873319i
$124$			12382.3i			0.805301i
$125$		0			0
$126$	−2973.84	−	2271.33i	−0.187317	−	0.143067i
$127$		−	26203.4i		−	1.62461i	−0.583230	−	0.812307i	$-0.698211\pi$
$127$		−	26203.4i		−	1.62461i	0.583230	−	0.812307i	$-0.301789\pi$
$128$			1448.15i			0.0883883i
$129$		−	7325.65i		−	0.440217i
$130$		0			0
$131$		−	12906.7i		−	0.752097i	−0.926600	−	0.376048i	$-0.877283\pi$
$131$		−	12906.7i		−	0.752097i	0.926600	−	0.376048i	$-0.122717\pi$
$132$	698.111			0.0400661
$133$	16272.2	+	12428.2i	0.919903	+	0.702593i
$134$	19652.6			1.09448
$135$		0			0
$136$		−	4243.86i		−	0.229447i
$137$		−	14834.2i		−	0.790356i	−0.918605	−	0.395178i	$-0.870683\pi$
$137$		−	14834.2i		−	0.790356i	0.918605	−	0.395178i	$-0.129317\pi$
$138$	6694.02			0.351503
$139$		−	18122.2i		−	0.937954i	−0.883210	−	0.468977i	$-0.844623\pi$
$139$		−	18122.2i		−	0.937954i	0.883210	−	0.468977i	$-0.155377\pi$
$140$		0			0
$141$	−13683.5			−0.688271
$142$			12765.2i			0.633068i
$143$	915.696			0.0447795
$144$	1728.00			0.0833333
$145$		0			0
$146$		−	18275.3i		−	0.857351i
$147$	3283.05	+	12036.2i	0.151930	+	0.557002i
$148$			12408.9i			0.566515i
$149$	−4953.47			−0.223119			−0.111560	−	0.993758i	$-0.535585\pi$
$149$	−4953.47			−0.223119			−0.111560	+	0.993758i	$0.535585\pi$
$150$		0			0
$151$	−11436.9			−0.501597			−0.250798	−	0.968039i	$-0.580693\pi$
$151$	−11436.9			−0.501597			−0.250798	+	0.968039i	$0.580693\pi$
$152$	−9455.22			−0.409246
$153$	−5063.95			−0.216325
$154$	−1849.72	−	1412.76i	−0.0779946	−	0.0595699i
$155$		0			0
$156$	2266.58			0.0931368
$157$	11046.2			0.448141			0.224071	−	0.974573i	$-0.428065\pi$
$157$	11046.2			0.448141			0.224071	+	0.974573i	$0.428065\pi$
$158$		−	21052.8i		−	0.843326i
$159$		−	5804.57i		−	0.229602i
$160$		0			0
$161$	−17736.5	−	13546.6i	−0.684253	−	0.522611i
$162$		−	2061.92i		−	0.0785674i
$163$		−	31283.4i		−	1.17744i	−0.808338	−	0.588719i	$-0.799632\pi$
$163$		−	31283.4i		−	1.17744i	0.808338	−	0.588719i	$-0.200368\pi$
$164$		−	20341.9i		−	0.756316i
$165$		0			0
$166$		−	20748.8i		−	0.752968i
$167$	33873.7			1.21459			0.607294	−	0.794477i	$-0.292255\pi$
$167$	33873.7			1.21459			0.607294	+	0.794477i	$0.292255\pi$
$168$	−4578.52	−	3496.94i	−0.162221	−	0.123899i
$169$	−25588.0			−0.895906
$170$		0			0
$171$			11282.4i			0.385841i
$172$		−	11278.6i		−	0.381239i
$173$	45030.7			1.50458			0.752291	−	0.658831i	$-0.228949\pi$
$173$	45030.7			1.50458			0.752291	+	0.658831i	$0.228949\pi$
$174$			15020.7i			0.496125i
$175$		0			0
$176$	1074.81			0.0346982
$177$		−	30339.3i		−	0.968410i
$178$	−29328.9			−0.925669
$179$	−19531.6			−0.609582			−0.304791	−	0.952419i	$-0.598587\pi$
$179$	−19531.6			−0.609582			−0.304791	+	0.952419i	$0.598587\pi$
$180$		0			0
$181$			5722.58i			0.174677i	0.996179	+	0.0873383i	$0.0278361\pi$
$181$			5722.58i			0.174677i	−0.996179	+	0.0873383i	$0.972164\pi$
$182$	−6005.54	−	4586.85i	−0.181305	−	0.138475i
$183$		−	19469.2i		−	0.581360i
$184$	10306.1			0.304410
$185$		0			0
$186$	22747.8			0.657526
$187$	−3149.77			−0.0900732
$188$	−21067.1			−0.596060
$189$	−4172.69	+	5463.29i	−0.116813	+	0.152943i
$190$		0			0
$191$	69955.1			1.91758			0.958788	−	0.284123i	$-0.0917024\pi$
$191$	69955.1			1.91758			0.958788	+	0.284123i	$0.0917024\pi$
$192$	2660.43			0.0721688
$193$		−	38129.9i		−	1.02365i	−0.859090	−	0.511824i	$-0.828970\pi$
$193$		−	38129.9i		−	1.02365i	0.859090	−	0.511824i	$-0.171030\pi$
$194$		−	22430.8i		−	0.595993i
$195$		0			0
$196$	5054.58	+	18531.0i	0.131575	+	0.482378i
$197$			51728.6i			1.33290i	0.745549	+	0.666451i	$0.232187\pi$
$197$			51728.6i			1.33290i	−0.745549	+	0.666451i	$0.767813\pi$
$198$		−	1282.51i		−	0.0327138i
$199$		−	55949.9i		−	1.41284i	−0.707792	−	0.706421i	$-0.750309\pi$
$199$		−	55949.9i		−	1.41284i	0.707792	−	0.706421i	$-0.249691\pi$
$200$		0			0
$201$		−	36104.1i		−	0.893643i
$202$	−3522.49			−0.0863272
$203$	30397.2	−	39798.9i	0.737635	−	0.965783i
$204$	−7796.47			−0.187343
$205$		0			0
$206$			8731.20i			0.205750i
$207$		−	12297.7i		−	0.287001i
$208$	3489.62			0.0806588
$209$			7017.61i			0.160656i
$210$		0			0
$211$	−25671.8			−0.576623			−0.288311	−	0.957537i	$-0.593094\pi$
$211$	−25671.8			−0.576623			−0.288311	+	0.957537i	$0.593094\pi$
$212$		−	8936.72i		−	0.198841i
$213$	23451.1			0.516898
$214$	3750.11			0.0818873
$215$		0			0
$216$		−	3174.54i		−	0.0680414i
$217$	−60272.6	−	46034.4i	−1.27997	−	0.977604i
$218$			16464.9i			0.346454i
$219$	−33573.9			−0.700024
$220$		0			0
$221$	−10226.4			−0.209382
$222$	22796.7			0.462557
$223$	22841.6			0.459321			0.229660	−	0.973271i	$-0.426238\pi$
$223$	22841.6			0.459321			0.229660	+	0.973271i	$0.426238\pi$
$224$	−7049.10	−	5383.88i	−0.140487	−	0.107300i
$225$		0			0
$226$	−50879.9			−0.996160
$227$	−66087.7			−1.28254			−0.641268	−	0.767317i	$-0.721591\pi$
$227$	−66087.7			−1.28254			−0.641268	+	0.767317i	$0.721591\pi$
$228$			17370.3i			0.334148i
$229$		−	1194.45i		−	0.0227770i	−0.999935	−	0.0113885i	$-0.996375\pi$
$229$		−	1194.45i		−	0.0227770i	0.999935	−	0.0113885i	$-0.00362516\pi$
$230$		0			0
$231$	−2595.41	+	3398.15i	−0.0486386	+	0.0636823i
$232$			23125.9i			0.429657i
$233$		−	69349.2i		−	1.27741i	−0.769453	−	0.638704i	$-0.779471\pi$
$233$		−	69349.2i		−	1.27741i	0.769453	−	0.638704i	$-0.220529\pi$
$234$		−	4163.97i		−	0.0760459i
$235$		0			0
$236$		−	46710.4i		−	0.838667i
$237$	−38676.5			−0.688573
$238$	20657.6	+	15777.6i	0.364691	+	0.278540i
$239$	−48621.3			−0.851199			−0.425599	−	0.904912i	$-0.639937\pi$
$239$	−48621.3			−0.851199			−0.425599	+	0.904912i	$0.639937\pi$
$240$		0			0
$241$		−	12082.4i		−	0.208026i	−0.994576	−	0.104013i	$-0.966832\pi$
$241$		−	12082.4i		−	0.208026i	0.994576	−	0.104013i	$-0.0331684\pi$
$242$			40613.3i			0.693485i
$243$	−3788.00			−0.0641500
$244$		−	29974.8i		−	0.503473i
$245$		0			0
$246$	−37370.4			−0.617530
$247$			22784.3i			0.373458i
$248$	35022.5			0.569434
$249$	−38117.9			−0.614796
$250$		0			0
$251$		−	24255.3i		−	0.384999i	−0.981297	−	0.192499i	$-0.938341\pi$
$251$		−	24255.3i		−	0.384999i	0.981297	−	0.192499i	$-0.0616594\pi$
$252$	−6424.28	+	8411.28i	−0.101163	+	0.132453i
$253$		−	7649.14i		−	0.119501i
$254$	−74114.4			−1.14878
$255$		0			0
$256$	4096.00			0.0625000
$257$	57301.0			0.867553			0.433777	−	0.901020i	$-0.357181\pi$
$257$	57301.0			0.867553			0.433777	+	0.901020i	$0.357181\pi$
$258$	−20720.1			−0.311280
$259$	−60402.2	−	46133.4i	−0.900437	−	0.687726i
$260$		0			0
$261$	27594.8			0.405085
$262$	−36505.8			−0.531813
$263$			88536.8i			1.28001i	0.768372	+	0.640003i	$0.221067\pi$
$263$			88536.8i			1.28001i	−0.768372	+	0.640003i	$0.778933\pi$
$264$		−	1974.56i		−	0.0283310i
$265$		0			0
$266$	35152.2	−	46024.6i	0.496809	−	0.650469i
$267$			53880.6i			0.755805i
$268$		−	55585.8i		−	0.773917i
$269$		−	126248.i		−	1.74470i	−0.488882	−	0.872350i	$-0.662595\pi$
$269$		−	126248.i		−	1.74470i	0.488882	−	0.872350i	$-0.337405\pi$
$270$		0			0
$271$			120538.i			1.64129i	0.571439	+	0.820644i	$0.306385\pi$
$271$			120538.i			1.64129i	−0.571439	+	0.820644i	$0.693615\pi$
$272$	−12003.4			−0.162244
$273$	−8426.58	+	11032.9i	−0.113064	+	0.148035i
$274$	−41957.4			−0.558866
$275$		0			0
$276$		−	18933.5i		−	0.248550i
$277$		−	65542.2i		−	0.854204i	−0.904204	−	0.427102i	$-0.859535\pi$
$277$		−	65542.2i		−	0.854204i	0.904204	−	0.427102i	$-0.140465\pi$
$278$	−51257.4			−0.663234
$279$		−	41790.3i		−	0.536868i
$280$		0			0
$281$	64221.6			0.813333			0.406667	−	0.913577i	$-0.366691\pi$
$281$	64221.6			0.813333			0.406667	+	0.913577i	$0.366691\pi$
$282$			38702.8i			0.486681i
$283$	102815.			1.28376			0.641882	−	0.766804i	$-0.278154\pi$
$283$	102815.			1.28376			0.641882	+	0.766804i	$0.278154\pi$
$284$	36105.4			0.447647
$285$		0			0
$286$		−	2589.98i		−	0.0316639i
$287$	99017.0	+	75626.1i	1.20211	+	0.918138i
$288$		−	4887.52i		−	0.0589256i
$289$	−48344.5			−0.578831
$290$		0			0
$291$	−41208.0			−0.486626
$292$	−51690.3			−0.606239
$293$	37735.8			0.439560			0.219780	−	0.975549i	$-0.429466\pi$
$293$	37735.8			0.439560			0.219780	+	0.975549i	$0.429466\pi$
$294$	34043.6	−	9285.86i	0.393860	−	0.107430i
$295$		0			0
$296$	35097.8			0.400586
$297$	−2356.12			−0.0267107
$298$			14010.5i			0.157769i
$299$		−	24834.7i		−	0.277790i
$300$		0			0
$301$	54900.0	+	41931.0i	0.605954	+	0.462809i
$302$			32348.5i			0.354683i
$303$			6471.23i			0.0704858i
$304$			26743.4i			0.289381i
$305$		0			0
$306$			14323.0i			0.152965i
$307$	−174430.			−1.85074			−0.925369	−	0.379067i	$-0.876245\pi$
$307$	−174430.			−1.85074			−0.925369	+	0.379067i	$0.876245\pi$
$308$	−3995.89	+	5231.80i	−0.0421223	+	0.0551505i
$309$	16040.2			0.167994
$310$		0			0
$311$		−	72315.8i		−	0.747674i	−0.927494	−	0.373837i	$-0.878042\pi$
$311$		−	72315.8i		−	0.747674i	0.927494	−	0.373837i	$-0.121958\pi$
$312$		−	6410.85i		−	0.0658576i
$313$	101560.			1.03666			0.518329	−	0.855181i	$-0.326554\pi$
$313$	101560.			1.03666			0.518329	+	0.855181i	$0.326554\pi$
$314$		−	31243.5i		−	0.316884i
$315$		0			0
$316$	−59546.3			−0.596322
$317$			66131.3i			0.658095i	0.944313	+	0.329047i	$0.106728\pi$
$317$			66131.3i			0.658095i	−0.944313	+	0.329047i	$0.893272\pi$
$318$	−16417.8			−0.162353
$319$	17163.9			0.168669
$320$		0			0
$321$		−	6889.39i		−	0.0668607i
$322$	−38315.6	+	50166.5i	−0.369542	+	0.483840i
$323$		−	78372.3i		−	0.751204i
$324$	−5832.00			−0.0555556
$325$		0			0
$326$	−88482.7			−0.832575
$327$	30247.9			0.282879
$328$	−57535.5			−0.534796
$329$	78322.5	−	102547.i	0.723593	−	0.947398i
$330$		0			0
$331$	−16051.8			−0.146511			−0.0732553	−	0.997313i	$-0.523339\pi$
$331$	−16051.8			−0.146511			−0.0732553	+	0.997313i	$0.523339\pi$
$332$	−58686.4			−0.532429
$333$		−	41880.2i		−	0.377676i
$334$		−	95809.2i		−	0.858844i
$335$		0			0
$336$	−9890.83	+	12950.0i	−0.0876101	+	0.114707i
$337$		−	43734.1i		−	0.385088i	−0.981288	−	0.192544i	$-0.938326\pi$
$337$		−	43734.1i		−	0.385088i	0.981288	−	0.192544i	$-0.0616738\pi$
$338$			72373.8i			0.633502i
$339$			93472.3i			0.813361i
$340$		0			0
$341$		−	25993.5i		−	0.223540i
$342$	31911.4			0.272831
$343$	−108994.	−	44289.9i	−0.926434	−	0.376458i
$344$	−31900.6			−0.269577
$345$		0			0
$346$		−	127366.i		−	1.06390i
$347$			45160.4i			0.375058i	0.982259	+	0.187529i	$0.0600479\pi$
$347$			45160.4i			0.375058i	−0.982259	+	0.187529i	$0.939952\pi$
$348$	42484.9			0.350814
$349$		−	15305.9i		−	0.125663i	−0.998024	−	0.0628317i	$-0.979987\pi$
$349$		−	15305.9i		−	0.125663i	0.998024	−	0.0628317i	$-0.0200131\pi$
$350$		0			0
$351$	−7649.70			−0.0620912
$352$		−	3040.03i		−	0.0245353i
$353$	25310.9			0.203123			0.101561	−	0.994829i	$-0.467616\pi$
$353$	25310.9			0.203123			0.101561	+	0.994829i	$0.467616\pi$
$354$	−85812.5			−0.684769
$355$		0			0
$356$			82954.6i			0.654547i
$357$	28985.4	−	37950.4i	0.227427	−	0.297769i
$358$			55243.8i			0.431040i
$359$	78217.5			0.606897			0.303448	−	0.952848i	$-0.401862\pi$
$359$	78217.5			0.606897			0.303448	+	0.952848i	$0.401862\pi$
$360$		0			0
$361$	−44290.7			−0.339858
$362$	16185.9			0.123515
$363$	74611.4			0.566229
$364$	−12973.6	+	16986.2i	−0.0979166	+	0.128202i
$365$		0			0
$366$	−55067.1			−0.411084
$367$	−87175.5			−0.647235			−0.323618	−	0.946188i	$-0.604899\pi$
$367$	−87175.5			−0.647235			−0.323618	+	0.946188i	$0.604899\pi$
$368$		−	29150.1i		−	0.215251i
$369$			68653.8i			0.504211i
$370$		0			0
$371$	43500.7	+	33224.5i	0.316045	+	0.241385i
$372$		−	64340.4i		−	0.464941i
$373$		−	30493.9i		−	0.219177i	−0.993977	−	0.109589i	$-0.965047\pi$
$373$		−	30493.9i		−	0.219177i	0.993977	−	0.109589i	$-0.0349534\pi$
$374$			8908.89i			0.0636913i
$375$		0			0
$376$			59586.9i			0.421478i
$377$	55726.5			0.392084
$378$	15452.5	+	11802.2i	0.108147	+	0.0825996i
$379$	180693.			1.25795			0.628974	−	0.777426i	$-0.283475\pi$
$379$	180693.			1.25795			0.628974	+	0.777426i	$0.283475\pi$
$380$		0			0
$381$			136157.i			0.937971i
$382$		−	197863.i		−	1.35593i
$383$	16491.7			0.112426			0.0562130	−	0.998419i	$-0.482097\pi$
$383$	16491.7			0.112426			0.0562130	+	0.998419i	$0.482097\pi$
$384$		−	7524.83i		−	0.0510310i
$385$		0			0
$386$	−107848.			−0.723828
$387$			38065.2i			0.254159i
$388$	−63443.8			−0.421431
$389$	−262564.			−1.73515			−0.867573	−	0.497310i	$-0.834321\pi$
$389$	−262564.			−1.73515			−0.867573	+	0.497310i	$0.834321\pi$
$390$		0			0
$391$			85425.2i			0.558769i
$392$	52413.6	−	14296.5i	0.341092	−	0.0930375i
$393$			67065.4i			0.434223i
$394$	146310.			0.942503
$395$		0			0
$396$	−3627.49			−0.0231321
$397$	42981.7			0.272711			0.136355	−	0.990660i	$-0.456461\pi$
$397$	42981.7			0.272711			0.136355	+	0.990660i	$0.456461\pi$
$398$	−158250.			−0.999030
$399$	−84552.6	−	64578.7i	−0.531106	−	0.405642i
$400$		0			0
$401$	24638.3			0.153222			0.0766110	−	0.997061i	$-0.475590\pi$
$401$	24638.3			0.153222			0.0766110	+	0.997061i	$0.475590\pi$
$402$	−102118.			−0.631901
$403$		−	84393.8i		−	0.519637i
$404$			9963.12i			0.0610425i
$405$		0			0
$406$	−112568.	−	85976.3i	−0.682912	−	0.521587i
$407$		−	26049.4i		−	0.157256i
$408$			22051.7i			0.132472i
$409$		−	317287.i		−	1.89673i	−0.317177	−	0.948366i	$-0.602735\pi$
$409$		−	317287.i		−	1.89673i	0.317177	−	0.948366i	$-0.397265\pi$
$410$		0			0
$411$			77080.7i			0.456312i
$412$	24695.6			0.145487
$413$	227370.	+	173658.i	1.33301	+	1.01811i
$414$	−34783.1			−0.202940
$415$		0			0
$416$		−	9870.14i		−	0.0570344i
$417$			94165.8i			0.541528i
$418$	19848.8			0.113601
$419$			104621.i			0.595924i	0.954578	+	0.297962i	$0.0963068\pi$
$419$			104621.i			0.595924i	−0.954578	+	0.297962i	$0.903693\pi$
$420$		0			0
$421$	−95579.9			−0.539265			−0.269633	−	0.962963i	$-0.586902\pi$
$421$	−95579.9			−0.539265			−0.269633	+	0.962963i	$0.586902\pi$
$422$			72610.9i			0.407734i
$423$	71101.6			0.397373
$424$	−25276.9			−0.140602
$425$		0			0
$426$		−	66329.9i		−	0.365502i
$427$	145906.	+	111439.i	0.800236	+	0.611196i
$428$		−	10606.9i		−	0.0579031i
$429$	−4758.09			−0.0258534
$430$		0			0
$431$	320809.			1.72700			0.863498	−	0.504352i	$-0.168268\pi$
$431$	320809.			1.72700			0.863498	+	0.504352i	$0.168268\pi$
$432$	−8978.95			−0.0481125
$433$	−65623.7			−0.350014			−0.175007	−	0.984567i	$-0.555995\pi$
$433$	−65623.7			−0.350014			−0.175007	+	0.984567i	$0.555995\pi$
$434$	−130205.	+	170477.i	−0.691270	+	0.905078i
$435$		0			0
$436$	46569.8			0.244980
$437$	190325.			0.996629
$438$			94961.2i			0.494992i
$439$		−	19965.4i		−	0.103597i	−0.998658	−	0.0517987i	$-0.983505\pi$
$439$		−	19965.4i		−	0.103597i	0.998658	−	0.0517987i	$-0.0164954\pi$
$440$		0			0
$441$	−17059.2	−	62542.2i	−0.0877166	−	0.321585i
$442$			28924.7i			0.148056i
$443$		−	128890.i		−	0.656769i	−0.944544	−	0.328385i	$-0.893496\pi$
$443$		−	128890.i		−	0.656769i	0.944544	−	0.328385i	$-0.106504\pi$
$444$		−	64478.7i		−	0.327077i
$445$		0			0
$446$		−	64605.7i		−	0.324789i
$447$	25739.0			0.128818
$448$	−15227.9	+	19937.9i	−0.0758725	+	0.0993396i
$449$	−7201.03			−0.0357192			−0.0178596	−	0.999841i	$-0.505685\pi$
$449$	−7201.03			−0.0357192			−0.0178596	+	0.999841i	$0.505685\pi$
$450$		0			0
$451$			42702.5i			0.209943i
$452$			143910.i			0.704392i
$453$	59427.9			0.289597
$454$			186924.i			0.906889i
$455$		0			0
$456$	49130.8			0.236278
$457$		−	318731.i		−	1.52613i	−0.646321	−	0.763066i	$-0.723693\pi$
$457$		−	318731.i		−	1.52613i	0.646321	−	0.763066i	$-0.276307\pi$
$458$	−3378.42			−0.0161058
$459$	26313.1			0.124895
$460$		0			0
$461$		−	50183.0i		−	0.236132i	−0.993006	−	0.118066i	$-0.962331\pi$
$461$		−	50183.0i		−	0.236132i	0.993006	−	0.118066i	$-0.0376694\pi$
$462$	9611.43	+	7340.91i	0.0450302	+	0.0343927i
$463$		−	249397.i		−	1.16340i	−0.813403	−	0.581700i	$-0.802388\pi$
$463$		−	249397.i		−	1.16340i	0.813403	−	0.581700i	$-0.197612\pi$
$464$	65409.8			0.303813
$465$		0			0
$466$	−196149.			−0.903264
$467$	71423.1			0.327495			0.163747	−	0.986502i	$-0.447642\pi$
$467$	71423.1			0.327495			0.163747	+	0.986502i	$0.447642\pi$
$468$	−11777.5			−0.0537725
$469$	270572.	+	206655.i	1.23009	+	0.939505i
$470$		0			0
$471$	−57397.9			−0.258734
$472$	−132117.			−0.593027
$473$			23676.5i			0.105827i
$474$			109394.i			0.486895i
$475$		0			0
$476$	44625.9	−	58428.5i	0.196958	−	0.257876i
$477$			30161.4i			0.132561i
$478$			137522.i			0.601888i
$479$		−	46641.2i		−	0.203282i	−0.994821	−	0.101641i	$-0.967591\pi$
$479$		−	46641.2i		−	0.203282i	0.994821	−	0.101641i	$-0.0324093\pi$
$480$		0			0
$481$		−	84575.2i		−	0.365555i
$482$	−34174.1			−0.147097
$483$	92161.7	+	70390.2i	0.395054	+	0.301730i
$484$	114872.			0.490368
$485$		0			0
$486$			10714.1i			0.0453609i
$487$		−	244060.i		−	1.02906i	−0.857473	−	0.514528i	$-0.827967\pi$
$487$		−	244060.i		−	1.02906i	0.857473	−	0.514528i	$-0.172033\pi$
$488$	−84781.4			−0.356009
$489$			162553.i			0.679794i
$490$		0			0
$491$	−79777.2			−0.330914			−0.165457	−	0.986217i	$-0.552910\pi$
$491$	−79777.2			−0.330914			−0.165457	+	0.986217i	$0.552910\pi$
$492$			105700.i			0.436659i
$493$	−191685.			−0.788670
$494$	64443.7			0.264074
$495$		0			0
$496$		−	99058.5i		−	0.402651i
$497$	−134231.	+	175748.i	−0.543426	+	0.711505i
$498$			107814.i			0.434726i
$499$	−236475.			−0.949694			−0.474847	−	0.880068i	$-0.657497\pi$
$499$	−236475.			−0.949694			−0.474847	+	0.880068i	$0.657497\pi$
$500$		0			0
$501$	−176013.			−0.701243
$502$	−68604.4			−0.272235
$503$	−155469.			−0.614481			−0.307241	−	0.951632i	$-0.599406\pi$
$503$	−155469.			−0.614481			−0.307241	+	0.951632i	$0.599406\pi$
$504$	23790.7	+	18170.6i	0.0936583	+	0.0715333i
$505$		0			0
$506$	−21635.0			−0.0844999
$507$	132959.			0.517252
$508$			209627.i			0.812307i
$509$			337758.i			1.30368i	0.758357	+	0.651839i	$0.226002\pi$
$509$			337758.i			1.30368i	−0.758357	+	0.651839i	$0.773998\pi$
$510$		0			0
$511$	192172.	−	251610.i	0.735950	−	0.963576i
$512$		−	11585.2i		−	0.0441942i
$513$		−	58624.9i		−	0.222765i
$514$		−	162072.i		−	0.613453i
$515$		0			0
$516$			58605.2i			0.220108i
$517$	44225.0			0.165458
$518$	−130485.	+	170843.i	−0.486296	+	0.636705i
$519$	−233986.			−0.868671
$520$		0			0
$521$			358982.i			1.32251i	0.750163	+	0.661253i	$0.229975\pi$
$521$			358982.i			1.32251i	−0.750163	+	0.661253i	$0.770025\pi$
$522$		−	78049.8i		−	0.286438i
$523$	−64377.8			−0.235360			−0.117680	−	0.993052i	$-0.537546\pi$
$523$	−64377.8			−0.235360			−0.117680	+	0.993052i	$0.537546\pi$
$524$			103254.i			0.376048i
$525$		0			0
$526$	250420.			0.905102
$527$			290294.i			1.04524i
$528$	−5584.89			−0.0200330
$529$	72388.0			0.258675
$530$		0			0
$531$			157648.i			0.559112i
$532$	−130177.	−	99425.4i	−0.459951	−	0.351297i
$533$			138644.i			0.488029i
$534$	152397.			0.534435
$535$		0			0
$536$	−157221.			−0.547242
$537$	101489.			0.351943
$538$	−357084.			−1.23369
$539$	−10610.8	−	38901.1i	−0.0365233	−	0.133901i
$540$		0			0
$541$	580837.			1.98454			0.992270	−	0.124094i	$-0.0396024\pi$
$541$	580837.			1.98454			0.992270	+	0.124094i	$0.0396024\pi$
$542$	340933.			1.16057
$543$		−	29735.4i		−	0.100850i
$544$			33950.9i			0.114724i
$545$		0			0
$546$	31205.7	+	23834.0i	0.104676	+	0.0799486i
$547$		−	415198.i		−	1.38765i	−0.720142	−	0.693826i	$-0.755924\pi$
$547$		−	415198.i		−	1.38765i	0.720142	−	0.693826i	$-0.244076\pi$
$548$			118673.i			0.395178i
$549$			101165.i			0.335648i
$550$		0			0
$551$			427071.i			1.40668i
$552$	−53552.1			−0.175751
$553$	221379.	−	289850.i	0.723911	−	0.947814i
$554$	−185381.			−0.604013
$555$		0			0
$556$			144978.i			0.468977i
$557$		−	278665.i		−	0.898197i	−0.893482	−	0.449099i	$-0.851745\pi$
$557$		−	278665.i		−	0.898197i	0.893482	−	0.449099i	$-0.148255\pi$
$558$	−118201.			−0.379623
$559$			76871.0i			0.246002i
$560$		0			0
$561$	16366.7			0.0520038
$562$		−	181646.i		−	0.575113i
$563$	34015.6			0.107315			0.0536576	−	0.998559i	$-0.482912\pi$
$563$	34015.6			0.107315			0.0536576	+	0.998559i	$0.482912\pi$
$564$	109468.			0.344135
$565$		0			0
$566$		−	290806.i		−	0.907758i
$567$	21681.9	−	28388.1i	0.0674423	−	0.0883019i
$568$		−	102122.i		−	0.316534i
$569$	577774.			1.78457			0.892284	−	0.451474i	$-0.149101\pi$
$569$	577774.			1.78457			0.892284	+	0.451474i	$0.149101\pi$
$570$		0			0
$571$	−123577.			−0.379021			−0.189511	−	0.981879i	$-0.560690\pi$
$571$	−123577.			−0.379021			−0.189511	+	0.981879i	$0.560690\pi$
$572$	−7325.56			−0.0223897
$573$	−363497.			−1.10711
$574$	213903.	−	280062.i	0.649222	−	0.850023i
$575$		0			0
$576$	−13824.0			−0.0416667
$577$	−215637.			−0.647695			−0.323848	−	0.946109i	$-0.604977\pi$
$577$	−215637.			−0.647695			−0.323848	+	0.946109i	$0.604977\pi$
$578$			136739.i			0.409295i
$579$			198129.i			0.591003i
$580$		0			0
$581$	218182.	−	285664.i	0.646347	−	0.846260i
$582$			116554.i			0.344097i
$583$			18760.3i			0.0551955i
$584$			146202.i			0.428676i
$585$		0			0
$586$		−	106733.i		−	0.310816i
$587$	430625.			1.24975			0.624875	−	0.780724i	$-0.285150\pi$
$587$	430625.			1.24975			0.624875	+	0.780724i	$0.285150\pi$
$588$	−26264.4	−	96290.0i	−0.0759648	−	0.278501i
$589$	646768.			1.86431
$590$		0			0
$591$		−	268789.i		−	0.769551i
$592$		−	99271.5i		−	0.283257i
$593$	627147.			1.78345			0.891723	−	0.452582i	$-0.149497\pi$
$593$	627147.			1.78345			0.891723	+	0.452582i	$0.149497\pi$
$594$			6664.13i			0.0188873i
$595$		0			0
$596$	39627.7			0.111560
$597$			290724.i			0.815704i
$598$	−70243.1			−0.196427
$599$	227512.			0.634091			0.317045	−	0.948410i	$-0.397309\pi$
$599$	227512.			0.634091			0.317045	+	0.948410i	$0.397309\pi$
$600$		0			0
$601$			176657.i			0.489083i	0.969639	+	0.244541i	$0.0786374\pi$
$601$			176657.i			0.489083i	−0.969639	+	0.244541i	$0.921363\pi$
$602$	118599.	−	155281.i	0.327255	−	0.428474i
$603$			187602.i			0.515945i
$604$	91495.3			0.250798
$605$		0			0
$606$	18303.4			0.0498410
$607$	170698.			0.463288			0.231644	−	0.972801i	$-0.425589\pi$
$607$	170698.			0.463288			0.231644	+	0.972801i	$0.425589\pi$
$608$	75641.8			0.204623
$609$	−157949.	+	206801.i	−0.425874	+	0.557595i
$610$		0			0
$611$	143587.			0.384620
$612$	40511.6			0.108163
$613$		−	76723.2i		−	0.204177i	−0.994775	−	0.102088i	$-0.967448\pi$
$613$		−	76723.2i		−	0.204177i	0.994775	−	0.102088i	$-0.0325524\pi$
$614$			493363.i			1.30867i
$615$		0			0
$616$	14797.8	+	11302.1i	0.0389973	+	0.0297849i
$617$		−	169691.i		−	0.445746i	−0.974847	−	0.222873i	$-0.928456\pi$
$617$		−	169691.i		−	0.445746i	0.974847	−	0.222873i	$-0.0715436\pi$
$618$		−	45368.7i		−	0.118790i
$619$			521329.i			1.36060i	0.732934	+	0.680300i	$0.238150\pi$
$619$			521329.i			1.36060i	−0.732934	+	0.680300i	$0.761850\pi$
$620$		0			0
$621$			63900.7i			0.165700i
$622$	−204540.			−0.528685
$623$	−403793.	−	308405.i	−1.04036	−	0.794594i
$624$	−18132.6			−0.0465684
$625$		0			0
$626$		−	287256.i		−	0.733029i
$627$		−	36464.6i		−	0.0927547i
$628$	−88369.9			−0.224071
$629$			290918.i			0.735308i
$630$		0			0
$631$	−192751.			−0.484103			−0.242051	−	0.970263i	$-0.577820\pi$
$631$	−192751.			−0.484103			−0.242051	+	0.970263i	$0.577820\pi$
$632$			168422.i			0.421663i
$633$	133395.			0.332913
$634$	187047.			0.465343
$635$		0			0
$636$			46436.6i			0.114801i
$637$	−34450.3	−	126301.i	−0.0849014	−	0.311264i
$638$		−	48546.8i		−	0.119267i
$639$	−121856.			−0.298431
$640$		0			0
$641$	−302302.			−0.735741			−0.367871	−	0.929877i	$-0.619913\pi$
$641$	−302302.			−0.735741			−0.367871	+	0.929877i	$0.619913\pi$
$642$	−19486.1			−0.0472776
$643$	−589543.			−1.42591			−0.712957	−	0.701207i	$-0.752645\pi$
$643$	−589543.			−1.42591			−0.712957	+	0.701207i	$0.752645\pi$
$644$	141892.	+	108373.i	0.342126	+	0.261306i
$645$		0			0
$646$	−221670.			−0.531181
$647$	−409647.			−0.978591			−0.489296	−	0.872118i	$-0.662746\pi$
$647$	−409647.			−0.978591			−0.489296	+	0.872118i	$0.662746\pi$
$648$			16495.4i			0.0392837i
$649$			98056.5i			0.232802i
$650$		0			0
$651$	313186.	+	239202.i	0.738993	+	0.564420i
$652$			250267.i			0.588719i
$653$			398777.i			0.935199i	0.883940	+	0.467600i	$0.154881\pi$
$653$			398777.i			0.935199i	−0.883940	+	0.467600i	$0.845119\pi$
$654$		−	85554.1i		−	0.200025i
$655$		0			0
$656$			162735.i			0.378158i
$657$	174455.			0.404159
$658$	−290048.	−	221529.i	−0.669911	−	0.511658i
$659$	224690.			0.517385			0.258693	−	0.965960i	$-0.416708\pi$
$659$	224690.			0.517385			0.258693	+	0.965960i	$0.416708\pi$
$660$		0			0
$661$			317889.i			0.727567i	0.931484	+	0.363783i	$0.118515\pi$
$661$			317889.i			0.727567i	−0.931484	+	0.363783i	$0.881485\pi$
$662$			45401.5i			0.103599i
$663$	53138.1			0.120887
$664$			165990.i			0.376484i
$665$		0			0
$666$	−118455.			−0.267058
$667$		−	465503.i		−	1.04634i
$668$	−270989.			−0.607294
$669$	−118688.			−0.265189
$670$		0			0
$671$			62924.3i			0.139757i
$672$	36628.2	+	27975.5i	0.0811104	+	0.0619497i
$673$			3782.87i			0.00835201i	0.999991	+	0.00417601i	$0.00132927\pi$
$673$			3782.87i			0.00835201i	−0.999991	+	0.00417601i	$0.998671\pi$
$674$	−123699.			−0.272298
$675$		0			0
$676$	204704.			0.447953
$677$	361508.			0.788753			0.394377	−	0.918949i	$-0.370961\pi$
$677$	361508.			0.788753			0.394377	+	0.918949i	$0.370961\pi$
$678$	264380.			0.575133
$679$	235869.	−	308822.i	0.511600	−	0.669836i
$680$		0			0
$681$	343402.			0.740472
$682$	−73520.7			−0.158067
$683$			158993.i			0.340829i	0.985373	+	0.170414i	$0.0545106\pi$
$683$			158993.i			0.340829i	−0.985373	+	0.170414i	$0.945489\pi$
$684$		−	90259.0i		−	0.192920i
$685$		0			0
$686$	−125271.	+	308282.i	−0.266196	+	0.655088i
$687$			6206.55i			0.0131503i
$688$			90228.6i			0.190619i
$689$			60909.7i			0.128306i
$690$		0			0
$691$			790541.i			1.65565i	0.560988	+	0.827824i	$0.310422\pi$
$691$			790541.i			1.65565i	−0.560988	+	0.827824i	$0.689578\pi$
$692$	−360245.			−0.752291
$693$	13486.1	−	17657.3i	0.0280815	−	0.0367670i
$694$	127733.			0.265206
$695$		0			0
$696$		−	120166.i		−	0.248063i
$697$		−	476900.i		−	0.981661i
$698$	−43291.7			−0.0888575
$699$			360349.i			0.737512i
$700$		0			0
$701$	885170.			1.80132			0.900660	−	0.434525i	$-0.143084\pi$
$701$	885170.			1.80132			0.900660	+	0.434525i	$0.143084\pi$
$702$			21636.6i			0.0439051i
$703$	648158.			1.31151
$704$	−8598.50			−0.0173491
$705$		0			0
$706$		−	71590.1i		−	0.143629i
$707$	−48496.9	−	37040.4i	−0.0970230	−	0.0741032i
$708$			242714.i			0.484205i
$709$	874630.			1.73993			0.869965	−	0.493114i	$-0.164141\pi$
$709$	874630.			1.73993			0.869965	+	0.493114i	$0.164141\pi$
$710$		0			0
$711$	200969.			0.397548
$712$	234631.			0.462834
$713$	−704972.			−1.38673
$714$	−107340.	−	81983.0i	−0.210555	−	0.160815i
$715$		0			0
$716$	156253.			0.304791
$717$	252644.			0.491440
$718$		−	221232.i		−	0.429141i
$719$			16933.5i			0.0327559i	0.999866	+	0.0163779i	$0.00521349\pi$
$719$			16933.5i			0.0327559i	−0.999866	+	0.0163779i	$0.994787\pi$
$720$		0			0
$721$	−91812.1	+	120209.i	−0.176616	+	0.231242i
$722$			125273.i			0.240316i
$723$			62781.9i			0.120104i
$724$		−	45780.7i		−	0.0873383i
$725$		0			0
$726$		−	211033.i		−	0.400384i
$727$	−529962.			−1.00271			−0.501356	−	0.865241i	$-0.667165\pi$
$727$	−529962.			−1.00271			−0.501356	+	0.865241i	$0.667165\pi$
$728$	48044.3	+	36694.8i	0.0906524	+	0.0692375i
$729$	19683.0			0.0370370
$730$		0			0
$731$		−	264417.i		−	0.494829i
$732$			155753.i			0.290680i
$733$	−702103.			−1.30675			−0.653375	−	0.757034i	$-0.726648\pi$
$733$	−702103.			−1.30675			−0.653375	+	0.757034i	$0.726648\pi$
$734$			246570.i			0.457665i
$735$		0			0
$736$	−82448.9			−0.152205
$737$			116688.i			0.214828i
$738$	194182.			0.356531
$739$	147389.			0.269884			0.134942	−	0.990853i	$-0.456915\pi$
$739$	147389.			0.269884			0.134942	+	0.990853i	$0.456915\pi$
$740$		0			0
$741$		−	118391.i		−	0.215616i
$742$	93973.2	−	123039.i	0.170685	−	0.223478i
$743$			112546.i			0.203870i	0.994791	+	0.101935i	$0.0325034\pi$
$743$			112546.i			0.203870i	−0.994791	+	0.101935i	$0.967497\pi$
$744$	−181982.			−0.328763
$745$		0			0
$746$	−86249.9			−0.154982
$747$	198067.			0.354952
$748$	25198.1			0.0450366
$749$	51630.6	+	39433.9i	0.0920331	+	0.0702920i
$750$		0			0
$751$	−633477.			−1.12318			−0.561592	−	0.827414i	$-0.689811\pi$
$751$	−633477.			−1.12318			−0.561592	+	0.827414i	$0.689811\pi$
$752$	168537.			0.298030
$753$			126034.i			0.222279i
$754$		−	157618.i		−	0.277245i
$755$		0			0
$756$	33381.5	−	43706.3i	0.0584067	−	0.0764717i
$757$			68457.5i			0.119462i	0.998215	+	0.0597309i	$0.0190243\pi$
$757$			68457.5i			0.119462i	−0.998215	+	0.0597309i	$0.980976\pi$
$758$		−	511077.i		−	0.889503i
$759$			39746.1i			0.0689939i
$760$		0			0
$761$			338746.i			0.584932i	0.956276	+	0.292466i	$0.0944758\pi$
$761$			338746.i			0.584932i	−0.956276	+	0.292466i	$0.905524\pi$
$762$	385110.			0.663246
$763$	−173135.	+	226685.i	−0.297396	+	0.389380i
$764$	−559641.			−0.958788
$765$		0			0
$766$		−	46645.4i		−	0.0794972i
$767$			318363.i			0.541167i
$768$	−21283.4			−0.0360844
$769$			597401.i			1.01021i	0.863057	+	0.505107i	$0.168547\pi$
$769$			597401.i			1.01021i	−0.863057	+	0.505107i	$0.831453\pi$
$770$		0			0
$771$	−297745.			−0.500882
$772$			305039.i			0.511824i
$773$	872716.			1.46054			0.730271	−	0.683158i	$-0.239394\pi$
$773$	872716.			1.46054			0.730271	+	0.683158i	$0.239394\pi$
$774$	107665.			0.179718
$775$		0			0
$776$			179446.i			0.297996i
$777$	313859.	+	239716.i	0.519868	+	0.397059i
$778$			742643.i			1.22693i
$779$	−1.06252e6			−1.75091
$780$		0			0
$781$	−75794.0			−0.124260
$782$	241619.			0.395109
$783$	−143387.			−0.233876
$784$	−40436.6	−	148248.i	−0.0657874	−	0.241189i
$785$		0			0
$786$	189690.			0.307042
$787$	−756386.			−1.22122			−0.610610	−	0.791932i	$-0.709076\pi$
$787$	−756386.			−1.22122			−0.610610	+	0.791932i	$0.709076\pi$
$788$		−	413828.i		−	0.666451i
$789$		−	460051.i		−	0.739012i
$790$		0			0
$791$	−700502.	−	535022.i	−1.11958	−	0.855104i
$792$			10260.1i			0.0163569i
$793$			204298.i			0.324876i
$794$		−	121570.i		−	0.192836i
$795$		0			0
$796$			447599.i			0.706421i
$797$	−266473.			−0.419504			−0.209752	−	0.977755i	$-0.567266\pi$
$797$	−266473.			−0.419504			−0.209752	+	0.977755i	$0.567266\pi$
$798$	−182656.	+	239151.i	−0.286833	+	0.375549i
$799$	−493903.			−0.773656
$800$		0			0
$801$		−	279972.i		−	0.436364i
$802$		−	69687.5i		−	0.108344i
$803$	108511.			0.168283
$804$			288833.i			0.446821i
$805$		0			0
$806$	−238702.			−0.367439
$807$			656005.i			1.00730i
$808$	28179.9			0.0431636
$809$	104174.			0.159171			0.0795855	−	0.996828i	$-0.474640\pi$
$809$	104174.			0.159171			0.0795855	+	0.996828i	$0.474640\pi$
$810$		0			0
$811$			18794.0i			0.0285744i	0.999898	+	0.0142872i	$0.00454792\pi$
$811$			18794.0i			0.0285744i	−0.999898	+	0.0142872i	$0.995452\pi$
$812$	−243178.	+	318392.i	−0.368818	+	0.482891i
$813$		−	626333.i		−	0.947599i
$814$	−73678.7			−0.111197
$815$		0			0
$816$	62371.7			0.0936715
$817$	−589116.			−0.882585
$818$	−897424.			−1.34119
$819$	43785.8	−	57328.5i	0.0652778	−	0.0854679i
$820$		0			0
$821$	101967.			0.151277			0.0756387	−	0.997135i	$-0.475900\pi$
$821$	101967.			0.151277			0.0756387	+	0.997135i	$0.475900\pi$
$822$	218017.			0.322661
$823$		−	47876.1i		−	0.0706836i	−0.999375	−	0.0353418i	$-0.988748\pi$
$823$		−	47876.1i		−	0.0706836i	0.999375	−	0.0353418i	$-0.0112520\pi$
$824$		−	69849.6i		−	0.102875i
$825$		0			0
$826$	491179.	−	643098.i	0.719912	−	0.942578i
$827$		−	37354.4i		−	0.0546173i	−0.999627	−	0.0273087i	$-0.991306\pi$
$827$		−	37354.4i		−	0.0546173i	0.999627	−	0.0273087i	$-0.00869370\pi$
$828$			98381.5i			0.143500i
$829$		−	830067.i		−	1.20783i	−0.797051	−	0.603913i	$-0.793608\pi$
$829$		−	830067.i		−	1.20783i	0.797051	−	0.603913i	$-0.206392\pi$
$830$		0			0
$831$			340567.i			0.493175i
$832$	−27917.0			−0.0403294
$833$	118501.	+	434445.i	0.170778	+	0.626102i
$834$	266341.			0.382918
$835$		0			0
$836$		−	56140.9i		−	0.0803279i
$837$			217149.i			0.309961i
$838$	295913.			0.421382
$839$			1.08122e6i			1.53600i	0.640452	+	0.767998i	$0.278747\pi$
$839$			1.08122e6i			1.53600i	−0.640452	+	0.767998i	$0.721253\pi$
$840$		0			0
$841$	337261.			0.476842
$842$			270341.i			0.381318i
$843$	−333705.			−0.469578
$844$	205375.			0.288311
$845$		0			0
$846$		−	201106.i		−	0.280985i
$847$	−427065.	+	559154.i	−0.595288	+	0.779408i
$848$			71493.8i			0.0994206i
$849$	−534244.			−0.741181
$850$		0			0
$851$	−706487.			−0.975541
$852$	−187609.			−0.258449
$853$	−235909.			−0.324225			−0.162113	−	0.986772i	$-0.551831\pi$
$853$	−235909.			−0.324225			−0.162113	+	0.986772i	$0.551831\pi$
$854$	315196.	−	412685.i	0.432181	−	0.565853i
$855$		0			0
$856$	−30000.9			−0.0409436
$857$	945097.			1.28681			0.643405	−	0.765526i	$-0.277521\pi$
$857$	945097.			1.28681			0.643405	+	0.765526i	$0.277521\pi$
$858$			13457.9i			0.0182811i
$859$		−	221849.i		−	0.300657i	−0.988636	−	0.150329i	$-0.951967\pi$
$859$		−	221849.i		−	0.300657i	0.988636	−	0.150329i	$-0.0480331\pi$
$860$		0			0
$861$	−514507.	−	392965.i	−0.694041	−	0.530087i
$862$		−	907384.i		−	1.22117i
$863$			1.14010e6i			1.53081i	0.643550	+	0.765404i	$0.277461\pi$
$863$			1.14010e6i			1.53081i	−0.643550	+	0.765404i	$0.722539\pi$
$864$			25396.3i			0.0340207i
$865$		0			0
$866$			185612.i			0.247497i
$867$	251206.			0.334188
$868$	482181.	+	368275.i	0.639987	+	0.488802i
$869$	125002.			0.165530
$870$		0			0
$871$			378855.i			0.499386i
$872$		−	131719.i		−	0.173227i
$873$	214123.			0.280954
$874$		−	538321.i		−	0.704723i
$875$		0			0
$876$	268591.			0.350012
$877$		−	388071.i		−	0.504559i	−0.967654	−	0.252279i	$-0.918820\pi$
$877$		−	388071.i		−	0.504559i	0.967654	−	0.252279i	$-0.0811802\pi$
$878$	−56470.7			−0.0732544
$879$	−196081.			−0.253780
$880$		0			0
$881$			338162.i			0.435685i	0.975984	+	0.217843i	$0.0699019\pi$
$881$			338162.i			0.435685i	−0.975984	+	0.217843i	$0.930098\pi$
$882$	−176896.	+	48250.7i	−0.227395	+	0.0620250i
$883$		−	69674.1i		−	0.0893614i	−0.999001	−	0.0446807i	$-0.985773\pi$
$883$		−	69674.1i		−	0.0893614i	0.999001	−	0.0446807i	$-0.0142270\pi$
$884$	81811.5			0.104691
$885$		0			0
$886$	−364557.			−0.464406
$887$	−408998.			−0.519846			−0.259923	−	0.965629i	$-0.583697\pi$
$887$	−408998.			−0.519846			−0.259923	+	0.965629i	$0.583697\pi$
$888$	−182373.			−0.231279
$889$	−1.02039e6	−	779342.i	−1.29111	−	0.986109i
$890$		0			0
$891$	12242.8			0.0154214
$892$	−182732.			−0.229660
$893$			1.10040e6i			1.37991i
$894$		−	72800.8i		−	0.0910880i
$895$		0			0
$896$	56392.8	+	43071.1i	0.0702437	+	0.0536500i
$897$			129045.i			0.160382i
$898$			20367.6i			0.0252573i
$899$		−	1.58188e6i		−	1.95729i
$900$		0			0
$901$		−	209515.i		−	0.258086i
$902$	120781.			0.148452
$903$	−285269.	−	217880.i	−0.349848	−	0.267203i
$904$	407039.			0.498080
$905$		0			0
$906$		−	168088.i		−	0.204776i
$907$			129375.i			0.157266i	0.996904	+	0.0786330i	$0.0250555\pi$
$907$			129375.i			0.157266i	−0.996904	+	0.0786330i	$0.974944\pi$
$908$	528702.			0.641268
$909$		−	33625.5i		−	0.0406950i
$910$		0			0
$911$	−668863.			−0.805935			−0.402968	−	0.915214i	$-0.632021\pi$
$911$	−668863.			−0.805935			−0.402968	+	0.915214i	$0.632021\pi$
$912$		−	138963.i		−	0.167074i
$913$	123197.			0.147795
$914$	−901508.			−1.07914
$915$		0			0
$916$			9555.61i			0.0113885i
$917$	−502603.	−	383873.i	−0.597704	−	0.456508i
$918$		−	74424.6i		−	0.0883144i
$919$	817573.			0.968045			0.484022	−	0.875056i	$-0.339175\pi$
$919$	817573.			0.968045			0.484022	+	0.875056i	$0.339175\pi$
$920$		0			0
$921$	906366.			1.06852
$922$	−141939.			−0.166970
$923$	−246083.			−0.288853
$924$	20763.2	−	27185.2i	0.0243193	−	0.0318412i
$925$		0			0
$926$	−705401.			−0.822648
$927$	−83347.5			−0.0969914
$928$		−	185007.i		−	0.214829i
$929$			259860.i			0.301098i	0.988603	+	0.150549i	$0.0481041\pi$
$929$			259860.i			0.301098i	−0.988603	+	0.150549i	$0.951896\pi$
$930$		0			0
$931$	967934.	−	264017.i	1.11673	−	0.304602i
$932$			554794.i			0.638704i
$933$			375764.i			0.431670i
$934$		−	202015.i		−	0.231574i
$935$		0			0
$936$			33311.7i			0.0380229i
$937$	82136.8			0.0935532			0.0467766	−	0.998905i	$-0.485105\pi$
$937$	82136.8			0.0935532			0.0467766	+	0.998905i	$0.485105\pi$
$938$	584507.	−	765293.i	0.664331	−	0.869805i
$939$	−527723.			−0.598515
$940$		0			0
$941$			872150.i			0.984945i	0.870328	+	0.492473i	$0.163907\pi$
$941$			872150.i			0.984945i	−0.870328	+	0.492473i	$0.836093\pi$
$942$			162346.i			0.182953i
$943$	1.15814e6			1.30238
$944$			373683.i			0.419334i
$945$		0			0
$946$	66967.1			0.0748306
$947$		−	1.02079e6i		−	1.13825i	−0.822250	−	0.569126i	$-0.807282\pi$
$947$		−	1.02079e6i		−	1.13825i	0.822250	−	0.569126i	$-0.192718\pi$
$948$	309412.			0.344287
$949$	352304.			0.391188
$950$		0			0
$951$		−	343628.i		−	0.379951i
$952$	−165261.	−	126221.i	−0.182346	−	0.139270i
$953$		−	771233.i		−	0.849180i	−0.905386	−	0.424590i	$-0.860418\pi$
$953$		−	771233.i		−	0.849180i	0.905386	−	0.424590i	$-0.139582\pi$
$954$	85309.4			0.0937347
$955$		0			0
$956$	388970.			0.425599
$957$	−89186.2			−0.0973809
$958$	−131921.			−0.143742
$959$	−577660.	−	441199.i	−0.628109	−	0.479730i
$960$		0			0
$961$	−1.47213e6			−1.59404
$962$	−239215.			−0.258487
$963$			35798.3i			0.0386020i
$964$			96659.1i			0.104013i
$965$		0			0
$966$	199094.	−	260673.i	0.213355	−	0.279345i
$967$		−	675992.i		−	0.722917i	−0.932388	−	0.361459i	$-0.882279\pi$
$967$		−	675992.i		−	0.722917i	0.932388	−	0.361459i	$-0.117721\pi$
$968$		−	324906.i		−	0.346743i
$969$			407234.i			0.433708i
$970$		0			0
$971$		−	1.12382e6i		−	1.19195i	−0.803003	−	0.595975i	$-0.796766\pi$
$971$		−	1.12382e6i		−	1.19195i	0.803003	−	0.595975i	$-0.203234\pi$
$972$	30304.0			0.0320750
$973$	−705699.	−	538992.i	−0.745408	−	0.569320i
$974$	−690307.			−0.727653
$975$		0			0
$976$			239798.i			0.251736i
$977$			1.83352e6i			1.92087i	0.278507	+	0.960434i	$0.410160\pi$
$977$			1.83352e6i			1.92087i	−0.278507	+	0.960434i	$0.589840\pi$
$978$	459770.			0.480687
$979$		−	174142.i		−	0.181693i
$980$		0			0
$981$	−157173.			−0.163320
$982$			225644.i			0.233992i
$983$	62328.3			0.0645028			0.0322514	−	0.999480i	$-0.489732\pi$
$983$	62328.3			0.0645028			0.0322514	+	0.999480i	$0.489732\pi$
$984$	298963.			0.308765
$985$		0			0
$986$			542168.i			0.557674i
$987$	−406976.	+	532851.i	−0.417767	+	0.546980i
$988$		−	182274.i		−	0.186729i
$989$	642132.			0.656495
$990$		0			0
$991$	−1.16225e6			−1.18346			−0.591730	−	0.806136i	$-0.701555\pi$
$991$	−1.16225e6			−1.18346			−0.591730	+	0.806136i	$0.701555\pi$
$992$	−280180.			−0.284717
$993$	83407.8			0.0845879
$994$	497091.	+	379663.i	0.503110	+	0.384260i
$995$		0			0
$996$	304944.			0.307398
$997$	472590.			0.475438			0.237719	−	0.971334i	$-0.423600\pi$
$997$	472590.			0.475438			0.237719	+	0.971334i	$0.423600\pi$
$998$			668852.i			0.671535i
$999$			217616.i			0.218052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.5.h.a.349.1		8
5.2	odd	4		42.5.c.a.13.4	yes	4
5.3	odd	4		1050.5.f.a.601.1		4
5.4	even	2	inner	1050.5.h.a.349.8		8
7.6	odd	2	inner	1050.5.h.a.349.4		8
15.2	even	4		126.5.c.b.55.1		4
20.7	even	4		336.5.f.a.97.2		4
35.2	odd	12		294.5.g.a.31.1		4
35.12	even	12		294.5.g.b.31.1		4
35.13	even	4		1050.5.f.a.601.2		4
35.17	even	12		294.5.g.a.19.1		4
35.27	even	4		42.5.c.a.13.3	✓	4
35.32	odd	12		294.5.g.b.19.1		4
35.34	odd	2	inner	1050.5.h.a.349.5		8
60.47	odd	4		1008.5.f.f.433.1		4
105.62	odd	4		126.5.c.b.55.2		4
140.27	odd	4		336.5.f.a.97.3		4
420.167	even	4		1008.5.f.f.433.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.c.a.13.3	✓	4	35.27	even	4
42.5.c.a.13.4	yes	4	5.2	odd	4
126.5.c.b.55.1		4	15.2	even	4
126.5.c.b.55.2		4	105.62	odd	4
294.5.g.a.19.1		4	35.17	even	12
294.5.g.a.31.1		4	35.2	odd	12
294.5.g.b.19.1		4	35.32	odd	12
294.5.g.b.31.1		4	35.12	even	12
336.5.f.a.97.2		4	20.7	even	4
336.5.f.a.97.3		4	140.27	odd	4
1008.5.f.f.433.1		4	60.47	odd	4
1008.5.f.f.433.4		4	420.167	even	4
1050.5.f.a.601.1		4	5.3	odd	4
1050.5.f.a.601.2		4	35.13	even	4
1050.5.h.a.349.1		8	1.1	even	1	trivial
1050.5.h.a.349.4		8	7.6	odd	2	inner
1050.5.h.a.349.5		8	35.34	odd	2	inner
1050.5.h.a.349.8		8	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	1050.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +14.6969i q^{6} +(29.7420 - 38.9411i) q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +14.6969i q^{6} +(29.7420 - 38.9411i) q^{7} +22.6274i q^{8} +27.0000 q^{9} +16.7939 q^{11} +41.5692 q^{12} +54.5254 q^{13} +(-110.142 - 84.1232i) q^{14} +64.0000 q^{16} -187.554 q^{17} -76.3675i q^{18} +417.866i q^{19} +(-154.544 + 202.344i) q^{21} -47.5004i q^{22} -455.470i q^{23} -117.576i q^{24} -154.221i q^{26} -140.296 q^{27} +(-237.936 + 311.529i) q^{28} +1022.03 q^{29} -1547.79i q^{31} -181.019i q^{32} -87.2639 q^{33} +530.482i q^{34} -216.000 q^{36} -1551.12i q^{37} +1181.90 q^{38} -283.322 q^{39} +2542.74i q^{41} +(572.315 + 437.117i) q^{42} +1409.82i q^{43} -134.352 q^{44} -1288.26 q^{46} +2633.39 q^{47} -332.554 q^{48} +(-631.823 - 2316.38i) q^{49} +974.558 q^{51} -436.203 q^{52} +1117.09i q^{53} +396.817i q^{54} +(881.137 + 672.985i) q^{56} -2171.29i q^{57} -2890.73i q^{58} +5838.80i q^{59} +3746.84i q^{61} -4377.81 q^{62} +(803.035 - 1051.41i) q^{63} -512.000 q^{64} +246.819i q^{66} +6948.23i q^{67} +1500.43 q^{68} +2366.69i q^{69} -4513.18 q^{71} +610.940i q^{72} +6461.29 q^{73} -4387.22 q^{74} -3342.93i q^{76} +(499.486 - 653.975i) q^{77} +801.356i q^{78} +7443.29 q^{79} +729.000 q^{81} +7191.94 q^{82} +7335.80 q^{83} +(1236.35 - 1618.75i) q^{84} +3987.58 q^{86} -5310.62 q^{87} +380.003i q^{88} -10369.3i q^{89} +(1621.70 - 2123.28i) q^{91} +3643.76i q^{92} +8042.55i q^{93} -7448.36i q^{94} +940.604i q^{96} +7930.48 q^{97} +(-6551.70 + 1787.06i) q^{98} +453.436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 64 q^{4} + 216 q^{9}+O(q^{10}) \) 8 * q - 64 * q^4 + 216 * q^9	\( 8 q - 64 q^{4} + 216 q^{9} - 816 q^{11} - 768 q^{14} + 512 q^{16} - 1440 q^{21} + 3696 q^{29} - 1728 q^{36} + 5472 q^{39} + 6528 q^{44} - 6912 q^{46} + 376 q^{49} + 5760 q^{51} + 6144 q^{56} - 4096 q^{64} - 32304 q^{71} - 11520 q^{74} + 28592 q^{79} + 5832 q^{81} + 11520 q^{84} + 28416 q^{86} - 43776 q^{91} - 22032 q^{99}+O(q^{100}) \) 8 * q - 64 * q^4 + 216 * q^9 - 816 * q^11 - 768 * q^14 + 512 * q^16 - 1440 * q^21 + 3696 * q^29 - 1728 * q^36 + 5472 * q^39 + 6528 * q^44 - 6912 * q^46 + 376 * q^49 + 5760 * q^51 + 6144 * q^56 - 4096 * q^64 - 32304 * q^71 - 11520 * q^74 + 28592 * q^79 + 5832 * q^81 + 11520 * q^84 + 28416 * q^86 - 43776 * q^91 - 22032 * q^99

Introduction

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