LMFDB - Embedded newform 1050.3.f.e.601.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(601,1050)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1050.601");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2744 x^{12} - 10640 x^{11} + 39126 x^{10} - 108488 x^{9} + \cdots + 33124 $ x^16 - 8x^15 + 88x^14 - 476x^13 + 2744x^12 - 10640x^11 + 39126x^10 - 108488x^9 + 259514x^8 - 486436x^7 + 690168x^6 - 725188x^5 + 619745x^4 - 430504x^3 + 108130x^2 + 42224*x + 33124
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			601.8
Root			$-0.207107 - 1.12945i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.e.601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.73333 + 1.91369i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.73333 + 1.91369i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +17.5116 q^{11} +3.46410i q^{12} +4.83531i q^{13} +(-9.52237 - 2.70636i) q^{14} +4.00000 q^{16} +18.0284i q^{17} +4.24264 q^{18} +9.13350i q^{19} +(-3.31461 + 11.6625i) q^{21} -24.7651 q^{22} -3.72515 q^{23} -4.89898i q^{24} -6.83816i q^{26} -5.19615i q^{27} +(13.4667 + 3.82738i) q^{28} -1.12582 q^{29} -57.0859i q^{31} -5.65685 q^{32} +30.3310i q^{33} -25.4960i q^{34} -6.00000 q^{36} +41.3624 q^{37} -12.9167i q^{38} -8.37500 q^{39} -11.7156i q^{41} +(4.68756 - 16.4932i) q^{42} +64.4171 q^{43} +35.0232 q^{44} +5.26816 q^{46} +77.6614i q^{47} +6.92820i q^{48} +(41.6756 + 25.7710i) q^{49} -31.2261 q^{51} +9.67062i q^{52} -77.5383 q^{53} +7.34847i q^{54} +(-19.0447 - 5.41273i) q^{56} -15.8197 q^{57} +1.59215 q^{58} -87.0651i q^{59} -5.36957i q^{61} +80.7317i q^{62} +(-20.2000 - 5.74106i) q^{63} +8.00000 q^{64} -42.8945i q^{66} +47.1879 q^{67} +36.0568i q^{68} -6.45216i q^{69} -58.3047 q^{71} +8.48528 q^{72} +53.4082i q^{73} -58.4953 q^{74} +18.2670i q^{76} +(117.911 + 33.5117i) q^{77} +11.8440 q^{78} +74.9637 q^{79} +9.00000 q^{81} +16.5683i q^{82} -28.7890i q^{83} +(-6.62921 + 23.3250i) q^{84} -91.0996 q^{86} -1.94997i q^{87} -49.5303 q^{88} +101.499i q^{89} +(-9.25327 + 32.5578i) q^{91} -7.45031 q^{92} +98.8757 q^{93} -109.830i q^{94} -9.79796i q^{96} +107.830i q^{97} +(-58.9382 - 36.4457i) q^{98} -52.5348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 48 * q^9	$ 16 q + 32 q^{4} - 48 q^{9} + 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{21} - 64 q^{29} - 96 q^{36} + 144 q^{39} + 192 q^{44} - 176 q^{46} - 224 q^{49} - 48 q^{51} - 32 q^{56} + 128 q^{64} - 384 q^{71} - 224 q^{74} + 608 q^{79} + 144 q^{81} + 48 q^{84} + 416 q^{86} + 224 q^{91} - 288 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 - 48 * q^9 + 96 * q^11 - 16 * q^14 + 64 * q^16 + 24 * q^21 - 64 * q^29 - 96 * q^36 + 144 * q^39 + 192 * q^44 - 176 * q^46 - 224 * q^49 - 48 * q^51 - 32 * q^56 + 128 * q^64 - 384 * q^71 - 224 * q^74 + 608 * q^79 + 144 * q^81 + 48 * q^84 + 416 * q^86 + 224 * q^91 - 288 * 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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	6.73333	+	1.91369i	0.961905	+	0.273384i
$7$	6.73333	+	1.91369i	0.961905	+	0.273384i
$8$	−2.82843			−0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	17.5116			1.59196			0.795982	−	0.605321i	$-0.206955\pi$
$11$	17.5116			1.59196			0.795982	+	0.605321i	$0.206955\pi$
$12$			3.46410i			0.288675i
$13$			4.83531i			0.371947i	0.982555	+	0.185973i	$0.0595438\pi$
$13$			4.83531i			0.371947i	−0.982555	+	0.185973i	$0.940456\pi$
$14$	−9.52237	−	2.70636i	−0.680170	−	0.193312i
$15$		0			0
$16$	4.00000			0.250000
$17$			18.0284i			1.06049i	0.847843	+	0.530247i	$0.177901\pi$
$17$			18.0284i			1.06049i	−0.847843	+	0.530247i	$0.822099\pi$
$18$	4.24264			0.235702
$19$			9.13350i			0.480711i	0.970685	+	0.240355i	$0.0772640\pi$
$19$			9.13350i			0.480711i	−0.970685	+	0.240355i	$0.922736\pi$
$20$		0			0
$21$	−3.31461	+	11.6625i	−0.157838	+	0.555356i
$22$	−24.7651			−1.12569
$23$	−3.72515			−0.161963			−0.0809816	−	0.996716i	$-0.525806\pi$
$23$	−3.72515			−0.161963			−0.0809816	+	0.996716i	$0.525806\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$		−	6.83816i		−	0.263006i
$27$		−	5.19615i		−	0.192450i
$28$	13.4667	+	3.82738i	0.480952	+	0.136692i
$29$	−1.12582			−0.0388213			−0.0194107	−	0.999812i	$-0.506179\pi$
$29$	−1.12582			−0.0388213			−0.0194107	+	0.999812i	$0.506179\pi$
$30$		0			0
$31$		−	57.0859i		−	1.84148i	−0.390175	−	0.920741i	$-0.627585\pi$
$31$		−	57.0859i		−	1.84148i	0.390175	−	0.920741i	$-0.372415\pi$
$32$	−5.65685			−0.176777
$33$			30.3310i			0.919120i
$34$		−	25.4960i		−	0.749882i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	41.3624			1.11790			0.558952	−	0.829200i	$-0.311204\pi$
$37$	41.3624			1.11790			0.558952	+	0.829200i	$0.311204\pi$
$38$		−	12.9167i		−	0.339914i
$39$	−8.37500			−0.214744
$40$		0			0
$41$		−	11.7156i		−	0.285745i	−0.989741	−	0.142873i	$-0.954366\pi$
$41$		−	11.7156i		−	0.285745i	0.989741	−	0.142873i	$-0.0456340\pi$
$42$	4.68756	−	16.4932i	0.111609	−	0.392696i
$43$	64.4171			1.49807			0.749036	−	0.662529i	$-0.230517\pi$
$43$	64.4171			1.49807			0.749036	+	0.662529i	$0.230517\pi$
$44$	35.0232			0.795982
$45$		0			0
$46$	5.26816			0.114525
$47$			77.6614i			1.65237i	0.563399	+	0.826185i	$0.309493\pi$
$47$			77.6614i			1.65237i	−0.563399	+	0.826185i	$0.690507\pi$
$48$			6.92820i			0.144338i
$49$	41.6756	+	25.7710i	0.850522	+	0.525939i
$50$		0			0
$51$	−31.2261			−0.612276
$52$			9.67062i			0.185973i
$53$	−77.5383			−1.46299			−0.731493	−	0.681849i	$-0.761176\pi$
$53$	−77.5383			−1.46299			−0.731493	+	0.681849i	$0.761176\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	−19.0447	−	5.41273i	−0.340085	−	0.0966559i
$57$	−15.8197			−0.277539
$58$	1.59215			0.0274508
$59$		−	87.0651i		−	1.47568i	−0.674976	−	0.737839i	$-0.735846\pi$
$59$		−	87.0651i		−	1.47568i	0.674976	−	0.737839i	$-0.264154\pi$
$60$		0			0
$61$		−	5.36957i		−	0.0880258i	−0.999031	−	0.0440129i	$-0.985986\pi$
$61$		−	5.36957i		−	0.0880258i	0.999031	−	0.0440129i	$-0.0140143\pi$
$62$			80.7317i			1.30212i
$63$	−20.2000	−	5.74106i	−0.320635	−	0.0911280i
$64$	8.00000			0.125000
$65$		0			0
$66$		−	42.8945i		−	0.649916i
$67$	47.1879			0.704297			0.352149	−	0.935944i	$-0.385451\pi$
$67$	47.1879			0.704297			0.352149	+	0.935944i	$0.385451\pi$
$68$			36.0568i			0.530247i
$69$		−	6.45216i		−	0.0935095i
$70$		0			0
$71$	−58.3047			−0.821193			−0.410597	−	0.911817i	$-0.634680\pi$
$71$	−58.3047			−0.821193			−0.410597	+	0.911817i	$0.634680\pi$
$72$	8.48528			0.117851
$73$			53.4082i			0.731619i	0.930690	+	0.365810i	$0.119208\pi$
$73$			53.4082i			0.731619i	−0.930690	+	0.365810i	$0.880792\pi$
$74$	−58.4953			−0.790477
$75$		0			0
$76$			18.2670i			0.240355i
$77$	117.911	+	33.5117i	1.53132	+	0.435217i
$78$	11.8440			0.151847
$79$	74.9637			0.948907			0.474454	−	0.880280i	$-0.342646\pi$
$79$	74.9637			0.948907			0.474454	+	0.880280i	$0.342646\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			16.5683i			0.202053i
$83$		−	28.7890i		−	0.346855i	−0.984847	−	0.173428i	$-0.944516\pi$
$83$		−	28.7890i		−	0.346855i	0.984847	−	0.173428i	$-0.0554843\pi$
$84$	−6.62921	+	23.3250i	−0.0789192	+	0.277678i
$85$		0			0
$86$	−91.0996			−1.05930
$87$		−	1.94997i		−	0.0224135i
$88$	−49.5303			−0.562844
$89$			101.499i			1.14043i	0.821494	+	0.570217i	$0.193141\pi$
$89$			101.499i			1.14043i	−0.821494	+	0.570217i	$0.806859\pi$
$90$		0			0
$91$	−9.25327	+	32.5578i	−0.101684	+	0.357778i
$92$	−7.45031			−0.0809816
$93$	98.8757			1.06318
$94$		−	109.830i		−	1.16840i
$95$		0			0
$96$		−	9.79796i		−	0.102062i
$97$			107.830i			1.11165i	0.831298	+	0.555827i	$0.187598\pi$
$97$			107.830i			1.11165i	−0.831298	+	0.555827i	$0.812402\pi$
$98$	−58.9382	−	36.4457i	−0.601410	−	0.371895i
$99$	−52.5348			−0.530654
$100$		0			0
$101$			52.6151i			0.520941i	0.965482	+	0.260471i	$0.0838777\pi$
$101$			52.6151i			0.520941i	−0.965482	+	0.260471i	$0.916122\pi$
$102$	44.1604			0.432945
$103$		−	72.4002i		−	0.702915i	−0.936204	−	0.351457i	$-0.885686\pi$
$103$		−	72.4002i		−	0.702915i	0.936204	−	0.351457i	$-0.114314\pi$
$104$		−	13.6763i		−	0.131503i
$105$		0			0
$106$	109.656			1.03449
$107$	−173.562			−1.62207			−0.811037	−	0.584994i	$-0.801097\pi$
$107$	−173.562			−1.62207			−0.811037	+	0.584994i	$0.801097\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−49.9966			−0.458684			−0.229342	−	0.973346i	$-0.573658\pi$
$109$	−49.9966			−0.458684			−0.229342	+	0.973346i	$0.573658\pi$
$110$		0			0
$111$			71.6418i			0.645422i
$112$	26.9333	+	7.65475i	0.240476	+	0.0683460i
$113$	70.1536			0.620828			0.310414	−	0.950601i	$-0.399532\pi$
$113$	70.1536			0.620828			0.310414	+	0.950601i	$0.399532\pi$
$114$	22.3724			0.196249
$115$		0			0
$116$	−2.25164			−0.0194107
$117$		−	14.5059i		−	0.123982i
$118$			123.129i			1.04346i
$119$	−34.5007	+	121.391i	−0.289922	+	1.02009i
$120$		0			0
$121$	185.656			1.53435
$122$			7.59373i			0.0622436i
$123$	20.2919			0.164975
$124$		−	114.172i		−	0.920741i
$125$		0			0
$126$	28.5671	+	8.11909i	0.226723	+	0.0644372i
$127$	−197.945			−1.55863			−0.779313	−	0.626635i	$-0.784432\pi$
$127$	−197.945			−1.55863			−0.779313	+	0.626635i	$0.784432\pi$
$128$	−11.3137			−0.0883883
$129$			111.574i			0.864912i
$130$		0			0
$131$			114.901i			0.877105i	0.898706	+	0.438552i	$0.144509\pi$
$131$			114.901i			0.877105i	−0.898706	+	0.438552i	$0.855491\pi$
$132$			60.6619i			0.459560i
$133$	−17.4787	+	61.4989i	−0.131419	+	0.462398i
$134$	−66.7338			−0.498013
$135$		0			0
$136$		−	50.9920i		−	0.374941i
$137$	95.3358			0.695882			0.347941	−	0.937516i	$-0.386881\pi$
$137$	95.3358			0.695882			0.347941	+	0.937516i	$0.386881\pi$
$138$			9.12473i			0.0661212i
$139$			237.587i			1.70926i	0.519237	+	0.854630i	$0.326216\pi$
$139$			237.587i			1.70926i	−0.519237	+	0.854630i	$0.673784\pi$
$140$		0			0
$141$	−134.513			−0.953996
$142$	82.4553			0.580671
$143$			84.6740i			0.592126i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	75.5306i		−	0.517333i
$147$	−44.6367	+	72.1842i	−0.303651	+	0.491049i
$148$	82.7248			0.558952
$149$	−133.844			−0.898285			−0.449142	−	0.893460i	$-0.648270\pi$
$149$	−133.844			−0.898285			−0.449142	+	0.893460i	$0.648270\pi$
$150$		0			0
$151$	155.064			1.02691			0.513456	−	0.858116i	$-0.328365\pi$
$151$	155.064			1.02691			0.513456	+	0.858116i	$0.328365\pi$
$152$		−	25.8335i		−	0.169957i
$153$		−	54.0852i		−	0.353498i
$154$	−166.752	−	47.3928i	−1.08280	−	0.307745i
$155$		0			0
$156$	−16.7500			−0.107372
$157$			104.634i			0.666459i	0.942846	+	0.333230i	$0.108138\pi$
$157$			104.634i			0.666459i	−0.942846	+	0.333230i	$0.891862\pi$
$158$	−106.015			−0.670979
$159$		−	134.300i		−	0.844656i
$160$		0			0
$161$	−25.0827	−	7.12878i	−0.155793	−	0.0442782i
$162$	−12.7279			−0.0785674
$163$	130.909			0.803120			0.401560	−	0.915833i	$-0.368468\pi$
$163$	130.909			0.803120			0.401560	+	0.915833i	$0.368468\pi$
$164$		−	23.4311i		−	0.142873i
$165$		0			0
$166$			40.7138i			0.245264i
$167$			102.845i			0.615838i	0.951413	+	0.307919i	$0.0996325\pi$
$167$			102.845i			0.615838i	−0.951413	+	0.307919i	$0.900367\pi$
$168$	9.37512	−	32.9865i	0.0558043	−	0.196348i
$169$	145.620			0.861656
$170$		0			0
$171$		−	27.4005i		−	0.160237i
$172$	128.834			0.749036
$173$			197.432i			1.14122i	0.821220	+	0.570612i	$0.193294\pi$
$173$			197.432i			1.14122i	−0.821220	+	0.570612i	$0.806706\pi$
$174$			2.75768i			0.0158487i
$175$		0			0
$176$	70.0464			0.397991
$177$	150.801			0.851984
$178$		−	143.541i		−	0.806409i
$179$	118.822			0.663809			0.331904	−	0.943313i	$-0.392309\pi$
$179$	118.822			0.663809			0.331904	+	0.943313i	$0.392309\pi$
$180$		0			0
$181$		−	14.4148i		−	0.0796399i	−0.999207	−	0.0398199i	$-0.987322\pi$
$181$		−	14.4148i		−	0.0796399i	0.999207	−	0.0398199i	$-0.0126784\pi$
$182$	13.0861	−	46.0436i	0.0719017	−	0.252987i
$183$	9.30038			0.0508217
$184$	10.5363			0.0572626
$185$		0			0
$186$	−139.831			−0.751782
$187$			315.706i			1.68827i
$188$			155.323i			0.826185i
$189$	9.94382	−	34.9874i	0.0526128	−	0.185119i
$190$		0			0
$191$	59.9375			0.313809			0.156904	−	0.987614i	$-0.449849\pi$
$191$	59.9375			0.313809			0.156904	+	0.987614i	$0.449849\pi$
$192$			13.8564i			0.0721688i
$193$	−245.948			−1.27434			−0.637171	−	0.770723i	$-0.719895\pi$
$193$	−245.948			−1.27434			−0.637171	+	0.770723i	$0.719895\pi$
$194$		−	152.495i		−	0.786058i
$195$		0			0
$196$	83.3512	+	51.5420i	0.425261	+	0.262969i
$197$	82.0594			0.416545			0.208273	−	0.978071i	$-0.433216\pi$
$197$	82.0594			0.416545			0.208273	+	0.978071i	$0.433216\pi$
$198$	74.2954			0.375229
$199$			289.338i			1.45396i	0.686658	+	0.726981i	$0.259077\pi$
$199$			289.338i			1.45396i	−0.686658	+	0.726981i	$0.740923\pi$
$200$		0			0
$201$			81.7319i			0.406626i
$202$		−	74.4089i		−	0.368361i
$203$	−7.58051	−	2.15447i	−0.0373424	−	0.0106131i
$204$	−62.4522			−0.306138
$205$		0			0
$206$			102.389i			0.497036i
$207$	11.1755			0.0539877
$208$			19.3412i			0.0929867i
$209$			159.942i			0.765274i
$210$		0			0
$211$	33.6995			0.159713			0.0798567	−	0.996806i	$-0.474554\pi$
$211$	33.6995			0.159713			0.0798567	+	0.996806i	$0.474554\pi$
$212$	−155.077			−0.731493
$213$		−	100.987i		−	0.474116i
$214$	245.454			1.14698
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	109.245	−	384.379i	0.503432	−	1.77133i
$218$	70.7059			0.324339
$219$	−92.5057			−0.422401
$220$		0			0
$221$	−87.1728			−0.394447
$222$		−	101.317i		−	0.456382i
$223$		−	10.7556i		−	0.0482313i	−0.999709	−	0.0241156i	$-0.992323\pi$
$223$		−	10.7556i		−	0.0482313i	0.999709	−	0.0241156i	$-0.00767699\pi$
$224$	−38.0895	−	10.8255i	−0.170042	−	0.0483279i
$225$		0			0
$226$	−99.2121			−0.438992
$227$		−	416.450i		−	1.83458i	−0.398219	−	0.917290i	$-0.630372\pi$
$227$		−	416.450i		−	1.83458i	0.398219	−	0.917290i	$-0.369628\pi$
$228$	−31.6394			−0.138769
$229$		−	388.469i		−	1.69637i	−0.529700	−	0.848185i	$-0.677695\pi$
$229$		−	388.469i		−	1.69637i	0.529700	−	0.848185i	$-0.322305\pi$
$230$		0			0
$231$	−58.0440	+	204.229i	−0.251273	+	0.884107i
$232$	3.18429			0.0137254
$233$	70.4036			0.302162			0.151081	−	0.988521i	$-0.451725\pi$
$233$	70.4036			0.302162			0.151081	+	0.988521i	$0.451725\pi$
$234$			20.5145i			0.0876687i
$235$		0			0
$236$		−	174.130i		−	0.737839i
$237$			129.841i			0.547852i
$238$	48.7914	−	171.673i	0.205006	−	0.721315i
$239$	313.133			1.31018			0.655091	−	0.755550i	$-0.272630\pi$
$239$	313.133			1.31018			0.655091	+	0.755550i	$0.272630\pi$
$240$		0			0
$241$		−	198.727i		−	0.824595i	−0.911049	−	0.412297i	$-0.864726\pi$
$241$		−	198.727i		−	0.824595i	0.911049	−	0.412297i	$-0.135274\pi$
$242$	−262.557			−1.08495
$243$			15.5885i			0.0641500i
$244$		−	10.7391i		−	0.0440129i
$245$		0			0
$246$	−28.6971			−0.116655
$247$	−44.1633			−0.178799
$248$			161.463i			0.651062i
$249$	49.8640			0.200257
$250$		0			0
$251$			300.878i			1.19872i	0.800480	+	0.599359i	$0.204578\pi$
$251$			300.878i			1.19872i	−0.800480	+	0.599359i	$0.795422\pi$
$252$	−40.4000	−	11.4821i	−0.160317	−	0.0455640i
$253$	−65.2334			−0.257839
$254$	279.937			1.10211
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	306.052i		−	1.19087i	−0.803405	−	0.595433i	$-0.796981\pi$
$257$		−	306.052i		−	1.19087i	0.803405	−	0.595433i	$-0.203019\pi$
$258$		−	157.789i		−	0.611585i
$259$	278.507	+	79.1548i	1.07532	+	0.305617i
$260$		0			0
$261$	3.37745			0.0129404
$262$		−	162.494i		−	0.620207i
$263$	−286.135			−1.08797			−0.543984	−	0.839096i	$-0.683085\pi$
$263$	−286.135			−1.08797			−0.543984	+	0.839096i	$0.683085\pi$
$264$		−	85.7889i		−	0.324958i
$265$		0			0
$266$	24.7186	−	86.9726i	0.0929270	−	0.326965i
$267$	−175.801			−0.658430
$268$	94.3758			0.352149
$269$		−	188.412i		−	0.700415i	−0.936672	−	0.350208i	$-0.886111\pi$
$269$		−	188.412i		−	0.700415i	0.936672	−	0.350208i	$-0.113889\pi$
$270$		0			0
$271$		−	9.59288i		−	0.0353981i	−0.999843	−	0.0176990i	$-0.994366\pi$
$271$		−	9.59288i		−	0.0353981i	0.999843	−	0.0176990i	$-0.00563408\pi$
$272$			72.1136i			0.265123i
$273$	−56.3917	−	16.0271i	−0.206563	−	0.0587075i
$274$	−134.825			−0.492063
$275$		0			0
$276$		−	12.9043i		−	0.0467548i
$277$	−161.066			−0.581464			−0.290732	−	0.956804i	$-0.593899\pi$
$277$	−161.066			−0.581464			−0.290732	+	0.956804i	$0.593899\pi$
$278$		−	335.999i		−	1.20863i
$279$			171.258i			0.613827i
$280$		0			0
$281$	−343.107			−1.22102			−0.610510	−	0.792008i	$-0.709036\pi$
$281$	−343.107			−1.22102			−0.610510	+	0.792008i	$0.709036\pi$
$282$	190.231			0.674577
$283$		−	324.748i		−	1.14752i	−0.819024	−	0.573759i	$-0.805484\pi$
$283$		−	324.748i		−	1.14752i	0.819024	−	0.573759i	$-0.194516\pi$
$284$	−116.609			−0.410597
$285$		0			0
$286$		−	119.747i		−	0.418696i
$287$	22.4199	−	78.8848i	0.0781182	−	0.274860i
$288$	16.9706			0.0589256
$289$	−36.0229			−0.124647
$290$		0			0
$291$	−186.768			−0.641813
$292$			106.816i			0.365810i
$293$			100.918i			0.344429i	0.985059	+	0.172215i	$0.0550923\pi$
$293$			100.918i			0.344429i	−0.985059	+	0.172215i	$0.944908\pi$
$294$	63.1258	−	102.084i	0.214714	−	0.347224i
$295$		0			0
$296$	−116.991			−0.395238
$297$		−	90.9929i		−	0.306373i
$298$	189.285			0.635183
$299$		−	18.0123i		−	0.0602417i
$300$		0			0
$301$	433.742	+	123.274i	1.44100	+	0.409549i
$302$	−219.293			−0.726136
$303$	−91.1320			−0.300766
$304$			36.5340i			0.120178i
$305$		0			0
$306$			76.4880i			0.249961i
$307$		−	41.3057i		−	0.134546i	−0.997735	−	0.0672732i	$-0.978570\pi$
$307$		−	41.3057i		−	0.134546i	0.997735	−	0.0672732i	$-0.0214299\pi$
$308$	235.823	+	67.0235i	0.765659	+	0.217609i
$309$	125.401			0.405828
$310$		0			0
$311$			470.341i			1.51235i	0.654369	+	0.756176i	$0.272934\pi$
$311$			470.341i			1.51235i	−0.654369	+	0.756176i	$0.727066\pi$
$312$	23.6881			0.0759233
$313$		−	160.220i		−	0.511884i	−0.966692	−	0.255942i	$-0.917614\pi$
$313$		−	160.220i		−	0.511884i	0.966692	−	0.255942i	$-0.0823855\pi$
$314$		−	147.975i		−	0.471258i
$315$		0			0
$316$	149.927			0.474454
$317$	268.766			0.847843			0.423922	−	0.905699i	$-0.360653\pi$
$317$	268.766			0.847843			0.423922	+	0.905699i	$0.360653\pi$
$318$			189.929i			0.597262i
$319$	−19.7149			−0.0618021
$320$		0			0
$321$		−	300.618i		−	0.936505i
$322$	35.4723	+	10.0816i	0.110162	+	0.0313094i
$323$	−164.662			−0.509791
$324$	18.0000			0.0555556
$325$		0			0
$326$	−185.133			−0.567891
$327$		−	86.5967i		−	0.264822i
$328$			33.1366i			0.101026i
$329$	−148.620	+	522.920i	−0.451732	+	1.58942i
$330$		0			0
$331$	555.018			1.67679			0.838395	−	0.545063i	$-0.183494\pi$
$331$	555.018			1.67679			0.838395	+	0.545063i	$0.183494\pi$
$332$		−	57.5780i		−	0.173428i
$333$	−124.087			−0.372634
$334$		−	145.445i		−	0.435463i
$335$		0			0
$336$	−13.2584	+	46.6499i	−0.0394596	+	0.138839i
$337$	47.7972			0.141831			0.0709157	−	0.997482i	$-0.477408\pi$
$337$	47.7972			0.141831			0.0709157	+	0.997482i	$0.477408\pi$
$338$	−205.937			−0.609282
$339$			121.510i			0.358435i
$340$		0			0
$341$		−	999.666i		−	2.93157i
$342$			38.7502i			0.113305i
$343$	231.298	+	253.279i	0.674338	+	0.738422i
$344$	−182.199			−0.529649
$345$		0			0
$346$		−	279.211i		−	0.806967i
$347$	−283.766			−0.817771			−0.408885	−	0.912586i	$-0.634082\pi$
$347$	−283.766			−0.817771			−0.408885	+	0.912586i	$0.634082\pi$
$348$		−	3.89995i		−	0.0112067i
$349$			20.0321i			0.0573987i	0.999588	+	0.0286993i	$0.00913653\pi$
$349$			20.0321i			0.0573987i	−0.999588	+	0.0286993i	$0.990863\pi$
$350$		0			0
$351$	25.1250			0.0715812
$352$	−99.0605			−0.281422
$353$		−	595.015i		−	1.68559i	−0.538231	−	0.842797i	$-0.680907\pi$
$353$		−	595.015i		−	1.68559i	0.538231	−	0.842797i	$-0.319093\pi$
$354$	−213.265			−0.602443
$355$		0			0
$356$			202.997i			0.570217i
$357$	−210.256	−	59.7570i	−0.588952	−	0.167387i
$358$	−168.039			−0.469384
$359$	−588.390			−1.63897			−0.819485	−	0.573101i	$-0.805740\pi$
$359$	−588.390			−1.63897			−0.819485	+	0.573101i	$0.805740\pi$
$360$		0			0
$361$	277.579			0.768917
$362$			20.3856i			0.0563139i
$363$			321.566i			0.885856i
$364$	−18.5065	+	65.1155i	−0.0508422	+	0.178889i
$365$		0			0
$366$	−13.1527			−0.0359364
$367$		−	662.601i		−	1.80545i	−0.430215	−	0.902726i	$-0.641562\pi$
$367$		−	662.601i		−	1.80545i	0.430215	−	0.902726i	$-0.358438\pi$
$368$	−14.9006			−0.0404908
$369$			35.1467i			0.0952485i
$370$		0			0
$371$	−522.091	−	148.384i	−1.40725	−	0.399957i
$372$	197.751			0.531590
$373$	−236.349			−0.633644			−0.316822	−	0.948485i	$-0.602616\pi$
$373$	−236.349			−0.633644			−0.316822	+	0.948485i	$0.602616\pi$
$374$		−	446.476i		−	1.19378i
$375$		0			0
$376$		−	219.660i		−	0.584201i
$377$		−	5.44368i		−	0.0144395i
$378$	−14.0627	+	49.4797i	−0.0372029	+	0.130899i
$379$	−344.235			−0.908272			−0.454136	−	0.890932i	$-0.650052\pi$
$379$	−344.235			−0.908272			−0.454136	+	0.890932i	$0.650052\pi$
$380$		0			0
$381$		−	342.852i		−	0.899873i
$382$	−84.7644			−0.221896
$383$		−	65.7097i		−	0.171566i	−0.996314	−	0.0857828i	$-0.972661\pi$
$383$		−	65.7097i		−	0.171566i	0.996314	−	0.0857828i	$-0.0273391\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	347.823			0.901095
$387$	−193.251			−0.499357
$388$			215.661i			0.555827i
$389$	−161.296			−0.414642			−0.207321	−	0.978273i	$-0.566474\pi$
$389$	−161.296			−0.414642			−0.207321	+	0.978273i	$0.566474\pi$
$390$		0			0
$391$		−	67.1585i		−	0.171761i
$392$	−117.876	−	72.8914i	−0.300705	−	0.185947i
$393$	−199.014			−0.506397
$394$	−116.050			−0.294542
$395$		0			0
$396$	−105.070			−0.265327
$397$		−	667.752i		−	1.68200i	−0.541039	−	0.840998i	$-0.681969\pi$
$397$		−	667.752i		−	1.68200i	0.541039	−	0.840998i	$-0.318031\pi$
$398$		−	409.186i		−	1.02811i
$399$	−106.519	−	30.2740i	−0.266966	−	0.0758746i
$400$		0			0
$401$	−593.826			−1.48086			−0.740431	−	0.672132i	$-0.765379\pi$
$401$	−593.826			−1.48086			−0.740431	+	0.672132i	$0.765379\pi$
$402$		−	115.586i		−	0.287528i
$403$	276.028			0.684933
$404$			105.230i			0.260471i
$405$		0			0
$406$	10.7205	+	3.04687i	0.0264051	+	0.00750461i
$407$	724.322			1.77966
$408$	88.3207			0.216472
$409$		−	569.625i		−	1.39273i	−0.717690	−	0.696363i	$-0.754800\pi$
$409$		−	569.625i		−	1.39273i	0.717690	−	0.696363i	$-0.245200\pi$
$410$		0			0
$411$			165.127i			0.401768i
$412$		−	144.800i		−	0.351457i
$413$	166.615	−	586.238i	0.403427	−	1.41946i
$414$	−15.8045			−0.0381751
$415$		0			0
$416$		−	27.3526i		−	0.0657515i
$417$	−411.513			−0.986842
$418$		−	226.192i		−	0.541130i
$419$			209.456i			0.499894i	0.968260	+	0.249947i	$0.0804132\pi$
$419$			209.456i			0.499894i	−0.968260	+	0.249947i	$0.919587\pi$
$420$		0			0
$421$	−169.713			−0.403119			−0.201560	−	0.979476i	$-0.564601\pi$
$421$	−169.713			−0.403119			−0.201560	+	0.979476i	$0.564601\pi$
$422$	−47.6583			−0.112934
$423$		−	232.984i		−	0.550790i
$424$	219.311			0.517244
$425$		0			0
$426$			142.817i			0.335251i
$427$	10.2757	−	36.1551i	0.0240649	−	0.0846725i
$428$	−347.124			−0.811037
$429$	−146.660			−0.341864
$430$		0			0
$431$	538.427			1.24925			0.624625	−	0.780925i	$-0.285252\pi$
$431$	538.427			1.24925			0.624625	+	0.780925i	$0.285252\pi$
$432$		−	20.7846i		−	0.0481125i
$433$			118.314i			0.273243i	0.990623	+	0.136622i	$0.0436244\pi$
$433$			118.314i			0.273243i	−0.990623	+	0.136622i	$0.956376\pi$
$434$	−154.495	+	543.593i	−0.355980	+	1.25252i
$435$		0			0
$436$	−99.9932			−0.229342
$437$		−	34.0237i		−	0.0778575i
$438$	130.823			0.298682
$439$		−	434.834i		−	0.990510i	−0.868748	−	0.495255i	$-0.835075\pi$
$439$		−	434.834i		−	0.990510i	0.868748	−	0.495255i	$-0.164925\pi$
$440$		0			0
$441$	−125.027	−	77.3130i	−0.283507	−	0.175313i
$442$	123.281			0.278916
$443$	555.005			1.25283			0.626417	−	0.779488i	$-0.284521\pi$
$443$	555.005			1.25283			0.626417	+	0.779488i	$0.284521\pi$
$444$			143.284i			0.322711i
$445$		0			0
$446$			15.2107i			0.0341047i
$447$		−	231.825i		−	0.518625i
$448$	53.8667	+	15.3095i	0.120238	+	0.0341730i
$449$	66.8926			0.148981			0.0744906	−	0.997222i	$-0.476267\pi$
$449$	66.8926			0.148981			0.0744906	+	0.997222i	$0.476267\pi$
$450$		0			0
$451$		−	205.158i		−	0.454896i
$452$	140.307			0.310414
$453$			268.578i			0.592888i
$454$			588.949i			1.29724i
$455$		0			0
$456$	44.7449			0.0981247
$457$	−750.939			−1.64319			−0.821596	−	0.570070i	$-0.806916\pi$
$457$	−750.939			−1.64319			−0.821596	+	0.570070i	$0.806916\pi$
$458$			549.378i			1.19951i
$459$	93.6783			0.204092
$460$		0			0
$461$			395.377i			0.857651i	0.903387	+	0.428826i	$0.141072\pi$
$461$			395.377i			0.857651i	−0.903387	+	0.428826i	$0.858928\pi$
$462$	82.0867	−	288.823i	0.177677	−	0.625158i
$463$	−423.981			−0.915726			−0.457863	−	0.889023i	$-0.651385\pi$
$463$	−423.981			−0.915726			−0.457863	+	0.889023i	$0.651385\pi$
$464$	−4.50327			−0.00970533
$465$		0			0
$466$	−99.5658			−0.213660
$467$			584.408i			1.25141i	0.780060	+	0.625705i	$0.215188\pi$
$467$			584.408i			1.25141i	−0.780060	+	0.625705i	$0.784812\pi$
$468$		−	29.0119i		−	0.0619911i
$469$	317.732	+	90.3030i	0.677467	+	0.192544i
$470$		0			0
$471$	−181.232			−0.384780
$472$			246.257i			0.521731i
$473$	1128.05			2.38488
$474$		−	183.623i		−	0.387390i
$475$		0			0
$476$	−69.0014	+	242.782i	−0.144961	+	0.510047i
$477$	232.615			0.487662
$478$	−442.837			−0.926438
$479$		−	734.511i		−	1.53343i	−0.641990	−	0.766713i	$-0.721891\pi$
$479$		−	734.511i		−	1.53343i	0.641990	−	0.766713i	$-0.278109\pi$
$480$		0			0
$481$			200.000i			0.415801i
$482$			281.043i			0.583077i
$483$	12.3474	−	43.4445i	0.0255640	−	0.0899473i
$484$	371.312			0.767174
$485$		0			0
$486$		−	22.0454i		−	0.0453609i
$487$	91.6643			0.188222			0.0941111	−	0.995562i	$-0.469999\pi$
$487$	91.6643			0.188222			0.0941111	+	0.995562i	$0.469999\pi$
$488$			15.1875i			0.0311218i
$489$			226.740i			0.463681i
$490$		0			0
$491$	460.086			0.937038			0.468519	−	0.883453i	$-0.344788\pi$
$491$	460.086			0.937038			0.468519	+	0.883453i	$0.344788\pi$
$492$	40.5839			0.0824876
$493$		−	20.2967i		−	0.0411698i
$494$	62.4564			0.126430
$495$		0			0
$496$		−	228.344i		−	0.460370i
$497$	−392.585	−	111.577i	−0.789910	−	0.224501i
$498$	−70.5184			−0.141603
$499$	487.126			0.976204			0.488102	−	0.872786i	$-0.337689\pi$
$499$	487.126			0.976204			0.488102	+	0.872786i	$0.337689\pi$
$500$		0			0
$501$	−178.133			−0.355554
$502$		−	425.506i		−	0.847622i
$503$			305.145i			0.606650i	0.952887	+	0.303325i	$0.0980967\pi$
$503$			305.145i			0.606650i	−0.952887	+	0.303325i	$0.901903\pi$
$504$	57.1342	+	16.2382i	0.113362	+	0.0322186i
$505$		0			0
$506$	92.2539			0.182320
$507$			252.221i			0.497477i
$508$	−395.891			−0.779313
$509$		−	800.434i		−	1.57256i	−0.617869	−	0.786281i	$-0.712004\pi$
$509$		−	800.434i		−	1.57256i	0.617869	−	0.786281i	$-0.287996\pi$
$510$		0			0
$511$	−102.207	+	359.615i	−0.200013	+	0.703748i
$512$	−22.6274			−0.0441942
$513$	47.4591			0.0925128
$514$			432.824i			0.842069i
$515$		0			0
$516$			223.147i			0.432456i
$517$			1359.97i			2.63051i
$518$	−393.868	−	111.942i	−0.760364	−	0.216104i
$519$	−341.962			−0.658886
$520$		0			0
$521$		−	21.4194i		−	0.0411121i	−0.999789	−	0.0205560i	$-0.993456\pi$
$521$		−	21.4194i		−	0.0411121i	0.999789	−	0.0205560i	$-0.00654365\pi$
$522$	−4.77644			−0.00915027
$523$			842.290i			1.61050i	0.592937	+	0.805249i	$0.297968\pi$
$523$			842.290i			1.61050i	−0.592937	+	0.805249i	$0.702032\pi$
$524$			229.801i			0.438552i
$525$		0			0
$526$	404.657			0.769309
$527$	1029.17			1.95288
$528$			121.324i			0.229780i
$529$	−515.123			−0.973768
$530$		0			0
$531$			261.195i			0.491893i
$532$	−34.9574	+	122.998i	−0.0657093	+	0.231199i
$533$	56.6484			0.106282
$534$	248.620			0.465580
$535$		0			0
$536$	−133.468			−0.249007
$537$			205.805i			0.383250i
$538$			266.454i			0.495268i
$539$	729.806	+	451.291i	1.35400	+	0.837275i
$540$		0			0
$541$	−15.6795			−0.0289824			−0.0144912	−	0.999895i	$-0.504613\pi$
$541$	−15.6795			−0.0289824			−0.0144912	+	0.999895i	$0.504613\pi$
$542$			13.5664i			0.0250302i
$543$	24.9672			0.0459801
$544$		−	101.984i		−	0.187471i
$545$		0			0
$546$	79.7499	+	22.6658i	0.146062	+	0.0415125i
$547$	−315.792			−0.577317			−0.288659	−	0.957432i	$-0.593209\pi$
$547$	−315.792			−0.577317			−0.288659	+	0.957432i	$0.593209\pi$
$548$	190.672			0.347941
$549$			16.1087i			0.0293419i
$550$		0			0
$551$		−	10.2827i		−	0.0186618i
$552$			18.2495i			0.0330606i
$553$	504.756	+	143.457i	0.912759	+	0.259416i
$554$	227.781			0.411157
$555$		0			0
$556$			475.174i			0.854630i
$557$	358.421			0.643484			0.321742	−	0.946827i	$-0.395732\pi$
$557$	358.421			0.643484			0.321742	+	0.946827i	$0.395732\pi$
$558$		−	242.195i		−	0.434041i
$559$			311.477i			0.557203i
$560$		0			0
$561$	−546.819			−0.974721
$562$	485.226			0.863392
$563$		−	622.834i		−	1.10628i	−0.833089	−	0.553138i	$-0.813430\pi$
$563$		−	622.834i		−	1.10628i	0.833089	−	0.553138i	$-0.186570\pi$
$564$	−269.027			−0.476998
$565$		0			0
$566$			459.263i			0.811418i
$567$	60.6000	+	17.2232i	0.106878	+	0.0303760i
$568$	164.911			0.290336
$569$	185.789			0.326518			0.163259	−	0.986583i	$-0.447799\pi$
$569$	185.789			0.326518			0.163259	+	0.986583i	$0.447799\pi$
$570$		0			0
$571$	−486.258			−0.851589			−0.425795	−	0.904820i	$-0.640005\pi$
$571$	−486.258			−0.851589			−0.425795	+	0.904820i	$0.640005\pi$
$572$			169.348i			0.296063i
$573$			103.815i			0.181178i
$574$	−31.7066	+	111.560i	−0.0552379	+	0.194355i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$		−	270.057i		−	0.468037i	−0.972232	−	0.234018i	$-0.924812\pi$
$577$		−	270.057i		−	0.468037i	0.972232	−	0.234018i	$-0.0751876\pi$
$578$	50.9440			0.0881385
$579$		−	425.994i		−	0.735741i
$580$		0			0
$581$	55.0932	−	193.846i	0.0948247	−	0.333642i
$582$	264.129			0.453831
$583$	−1357.82			−2.32902
$584$		−	151.061i		−	0.258666i
$585$		0			0
$586$		−	142.719i		−	0.243548i
$587$		−	400.613i		−	0.682476i	−0.939977	−	0.341238i	$-0.889154\pi$
$587$		−	400.613i		−	0.682476i	0.939977	−	0.341238i	$-0.110846\pi$
$588$	−89.2734	+	144.368i	−0.151825	+	0.245525i
$589$	521.395			0.885220
$590$		0			0
$591$			142.131i			0.240493i
$592$	165.450			0.279476
$593$		−	157.686i		−	0.265912i	−0.991122	−	0.132956i	$-0.957553\pi$
$593$		−	157.686i		−	0.265912i	0.991122	−	0.132956i	$-0.0424469\pi$
$594$			128.683i			0.216639i
$595$		0			0
$596$	−267.689			−0.449142
$597$	−501.149			−0.839445
$598$			25.4732i			0.0425973i
$599$	468.940			0.782872			0.391436	−	0.920205i	$-0.371978\pi$
$599$	468.940			0.782872			0.391436	+	0.920205i	$0.371978\pi$
$600$		0			0
$601$			255.932i			0.425844i	0.977069	+	0.212922i	$0.0682980\pi$
$601$			255.932i			0.425844i	−0.977069	+	0.212922i	$0.931702\pi$
$602$	−613.404	−	174.336i	−1.01894	−	0.289595i
$603$	−141.564			−0.234766
$604$	310.127			0.513456
$605$		0			0
$606$	128.880			0.212673
$607$			773.553i			1.27439i	0.770704	+	0.637194i	$0.219905\pi$
$607$			773.553i			1.27439i	−0.770704	+	0.637194i	$0.780095\pi$
$608$		−	51.6669i		−	0.0849785i
$609$	3.73164	−	13.1298i	0.00612749	−	0.0215597i
$610$		0			0
$611$	−375.517			−0.614594
$612$		−	108.170i		−	0.176749i
$613$	443.208			0.723015			0.361507	−	0.932369i	$-0.382262\pi$
$613$	443.208			0.723015			0.361507	+	0.932369i	$0.382262\pi$
$614$			58.4151i			0.0951386i
$615$		0			0
$616$	−333.504	−	94.7855i	−0.541402	−	0.153873i
$617$	363.298			0.588813			0.294407	−	0.955680i	$-0.404878\pi$
$617$	363.298			0.588813			0.294407	+	0.955680i	$0.404878\pi$
$618$	−177.344			−0.286964
$619$			292.211i			0.472069i	0.971745	+	0.236035i	$0.0758479\pi$
$619$			292.211i			0.472069i	−0.971745	+	0.236035i	$0.924152\pi$
$620$		0			0
$621$			19.3565i			0.0311698i
$622$		−	665.163i		−	1.06939i
$623$	−194.237	+	683.425i	−0.311777	+	1.09699i
$624$	−33.5000			−0.0536859
$625$		0			0
$626$			226.585i			0.361956i
$627$	−277.028			−0.441831
$628$			209.268i			0.333230i
$629$			745.698i			1.18553i
$630$		0			0
$631$	189.221			0.299874			0.149937	−	0.988696i	$-0.452093\pi$
$631$	189.221			0.299874			0.149937	+	0.988696i	$0.452093\pi$
$632$	−212.029			−0.335489
$633$			58.3693i			0.0922106i
$634$	−380.093			−0.599516
$635$		0			0
$636$		−	268.600i		−	0.422328i
$637$	−124.611	+	201.514i	−0.195621	+	0.316349i
$638$	27.8810			0.0437007
$639$	174.914			0.273731
$640$		0			0
$641$	1162.94			1.81425			0.907127	−	0.420857i	$-0.138271\pi$
$641$	1162.94			1.81425			0.907127	+	0.420857i	$0.138271\pi$
$642$			425.138i			0.662209i
$643$		−	1096.08i		−	1.70464i	−0.523021	−	0.852320i	$-0.675195\pi$
$643$		−	1096.08i		−	1.70464i	0.523021	−	0.852320i	$-0.324805\pi$
$644$	−50.1654	−	14.2576i	−0.0778966	−	0.0221391i
$645$		0			0
$646$	232.868			0.360476
$647$		−	262.877i		−	0.406302i	−0.979147	−	0.203151i	$-0.934882\pi$
$647$		−	262.877i		−	0.406302i	0.979147	−	0.203151i	$-0.0651182\pi$
$648$	−25.4558			−0.0392837
$649$		−	1524.65i		−	2.34923i
$650$		0			0
$651$	665.763	+	189.217i	1.02268	+	0.290656i
$652$	261.817			0.401560
$653$	242.905			0.371983			0.185992	−	0.982551i	$-0.440450\pi$
$653$	242.905			0.371983			0.185992	+	0.982551i	$0.440450\pi$
$654$			122.466i			0.187257i
$655$		0			0
$656$		−	46.8622i		−	0.0714364i
$657$		−	160.225i		−	0.243873i
$658$	210.180	−	739.521i	0.319422	−	1.12389i
$659$	−1176.49			−1.78527			−0.892634	−	0.450783i	$-0.851145\pi$
$659$	−1176.49			−1.78527			−0.892634	+	0.450783i	$0.851145\pi$
$660$		0			0
$661$		−	246.444i		−	0.372835i	−0.982471	−	0.186418i	$-0.940312\pi$
$661$		−	246.444i		−	0.372835i	0.982471	−	0.186418i	$-0.0596877\pi$
$662$	−784.914			−1.18567
$663$		−	150.988i		−	0.227734i
$664$			81.4276i			0.122632i
$665$		0			0
$666$	175.486			0.263492
$667$	4.19385			0.00628763
$668$			205.690i			0.307919i
$669$	18.6292			0.0278464
$670$		0			0
$671$		−	94.0298i		−	0.140134i
$672$	18.7502	−	65.9729i	0.0279021	−	0.0981740i
$673$	−76.3328			−0.113422			−0.0567109	−	0.998391i	$-0.518061\pi$
$673$	−76.3328			−0.113422			−0.0567109	+	0.998391i	$0.518061\pi$
$674$	−67.5954			−0.100290
$675$		0			0
$676$	291.240			0.430828
$677$			310.277i			0.458312i	0.973390	+	0.229156i	$0.0735965\pi$
$677$			310.277i			0.458312i	−0.973390	+	0.229156i	$0.926403\pi$
$678$		−	171.840i		−	0.253452i
$679$	−206.354	+	726.058i	−0.303908	+	1.06930i
$680$		0			0
$681$	721.312			1.05920
$682$			1413.74i			2.07293i
$683$	157.333			0.230356			0.115178	−	0.993345i	$-0.463256\pi$
$683$	157.333			0.230356			0.115178	+	0.993345i	$0.463256\pi$
$684$		−	54.8010i		−	0.0801185i
$685$		0			0
$686$	−327.105	−	358.190i	−0.476829	−	0.522144i
$687$	672.848			0.979400
$688$	257.668			0.374518
$689$		−	374.921i		−	0.544153i
$690$		0			0
$691$		−	683.565i		−	0.989240i	−0.869109	−	0.494620i	$-0.835307\pi$
$691$		−	683.565i		−	0.989240i	0.869109	−	0.494620i	$-0.164693\pi$
$692$			394.863i			0.570612i
$693$	−353.734	−	100.535i	−0.510439	−	0.145072i
$694$	401.306			0.578251
$695$		0			0
$696$			5.51536i			0.00792437i
$697$	211.213			0.303031
$698$		−	28.3297i		−	0.0405870i
$699$			121.943i			0.174453i
$700$		0			0
$701$	−306.153			−0.436738			−0.218369	−	0.975866i	$-0.570074\pi$
$701$	−306.153			−0.436738			−0.218369	+	0.975866i	$0.570074\pi$
$702$	−35.5321			−0.0506156
$703$			377.784i			0.537388i
$704$	140.093			0.198995
$705$		0			0
$706$			841.478i			1.19190i
$707$	−100.689	+	354.275i	−0.142417	+	0.501096i
$708$	301.602			0.425992
$709$	−444.082			−0.626350			−0.313175	−	0.949695i	$-0.601393\pi$
$709$	−444.082			−0.626350			−0.313175	+	0.949695i	$0.601393\pi$
$710$		0			0
$711$	−224.891			−0.316302
$712$		−	287.082i		−	0.403205i
$713$			212.654i			0.298252i
$714$	297.346	+	84.5092i	0.416452	+	0.118360i
$715$		0			0
$716$	237.643			0.331904
$717$			542.363i			0.756434i
$718$	832.109			1.15893
$719$		−	672.926i		−	0.935919i	−0.883750	−	0.467960i	$-0.844989\pi$
$719$		−	672.926i		−	0.935919i	0.883750	−	0.467960i	$-0.155011\pi$
$720$		0			0
$721$	138.551	−	487.495i	0.192166	−	0.676137i
$722$	−392.556			−0.543707
$723$	344.206			0.476080
$724$		−	28.8296i		−	0.0398199i
$725$		0			0
$726$		−	454.762i		−	0.626395i
$727$			675.927i			0.929748i	0.885377	+	0.464874i	$0.153900\pi$
$727$			675.927i			0.929748i	−0.885377	+	0.464874i	$0.846100\pi$
$728$	26.1722	−	92.0872i	0.0359508	−	0.126493i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			1161.34i			1.58870i
$732$	18.6008			0.0254109
$733$			387.908i			0.529206i	0.964357	+	0.264603i	$0.0852409\pi$
$733$			387.908i			0.529206i	−0.964357	+	0.264603i	$0.914759\pi$
$734$			937.059i			1.27665i
$735$		0			0
$736$	21.0727			0.0286313
$737$	826.336			1.12122
$738$		−	49.7049i		−	0.0673508i
$739$	394.643			0.534024			0.267012	−	0.963693i	$-0.413964\pi$
$739$	394.643			0.534024			0.267012	+	0.963693i	$0.413964\pi$
$740$		0			0
$741$		−	76.4931i		−	0.103230i
$742$	738.348	+	209.847i	0.995079	+	0.282812i
$743$	147.027			0.197883			0.0989414	−	0.995093i	$-0.468454\pi$
$743$	147.027			0.197883			0.0989414	+	0.995093i	$0.468454\pi$
$744$	−279.663			−0.375891
$745$		0			0
$746$	334.248			0.448054
$747$			86.3670i			0.115618i
$748$			631.412i			0.844133i
$749$	−1168.65	−	332.144i	−1.56028	−	0.443449i
$750$		0			0
$751$	103.003			0.137154			0.0685771	−	0.997646i	$-0.478154\pi$
$751$	103.003			0.137154			0.0685771	+	0.997646i	$0.478154\pi$
$752$			310.646i			0.413092i
$753$	−521.136			−0.692080
$754$			7.69852i			0.0102102i
$755$		0			0
$756$	19.8876	−	69.9749i	0.0263064	−	0.0925593i
$757$	−547.747			−0.723575			−0.361788	−	0.932261i	$-0.617833\pi$
$757$	−547.747			−0.723575			−0.361788	+	0.932261i	$0.617833\pi$
$758$	486.822			0.642246
$759$		−	112.988i		−	0.148864i
$760$		0			0
$761$		−	1223.78i		−	1.60813i	−0.594544	−	0.804063i	$-0.702668\pi$
$761$		−	1223.78i		−	1.60813i	0.594544	−	0.804063i	$-0.297332\pi$
$762$			484.865i			0.636306i
$763$	−336.644	−	95.6779i	−0.441211	−	0.125397i
$764$	119.875			0.156904
$765$		0			0
$766$			92.9275i			0.121315i
$767$	420.986			0.548874
$768$			27.7128i			0.0360844i
$769$		−	194.874i		−	0.253413i	−0.991940	−	0.126706i	$-0.959559\pi$
$769$		−	194.874i		−	0.253413i	0.991940	−	0.126706i	$-0.0404406\pi$
$770$		0			0
$771$	530.098			0.687547
$772$	−491.896			−0.637171
$773$			1017.59i			1.31642i	0.752835	+	0.658209i	$0.228686\pi$
$773$			1017.59i			1.31642i	−0.752835	+	0.658209i	$0.771314\pi$
$774$	273.299			0.353099
$775$		0			0
$776$		−	304.990i		−	0.393029i
$777$	−137.100	+	482.388i	−0.176448	+	0.620834i
$778$	228.107			0.293196
$779$	107.004			0.137361
$780$		0			0
$781$	−1021.01			−1.30731
$782$			94.9765i			0.121453i
$783$			5.84992i			0.00747117i
$784$	166.702	+	103.084i	0.212631	+	0.131485i
$785$		0			0
$786$	281.448			0.358076
$787$		−	222.094i		−	0.282203i	−0.989995	−	0.141101i	$-0.954936\pi$
$787$		−	222.094i		−	0.282203i	0.989995	−	0.141101i	$-0.0450644\pi$
$788$	164.119			0.208273
$789$		−	495.601i		−	0.628138i
$790$		0			0
$791$	472.367	+	134.252i	0.597178	+	0.169724i
$792$	148.591			0.187615
$793$	25.9636			0.0327409
$794$			944.344i			1.18935i
$795$		0			0
$796$			578.677i			0.726981i
$797$		−	340.349i		−	0.427038i	−0.976939	−	0.213519i	$-0.931507\pi$
$797$		−	340.349i		−	0.427038i	0.976939	−	0.213519i	$-0.0684926\pi$
$798$	150.641	+	42.8139i	0.188773	+	0.0536514i
$799$	−1400.11			−1.75233
$800$		0			0
$801$		−	304.496i		−	0.380145i
$802$	839.796			1.04713
$803$			935.263i			1.16471i
$804$			163.464i			0.203313i
$805$		0			0
$806$	−390.363			−0.484321
$807$	326.339			0.404385
$808$		−	148.818i		−	0.184181i
$809$	462.403			0.571573			0.285787	−	0.958293i	$-0.407745\pi$
$809$	462.403			0.571573			0.285787	+	0.958293i	$0.407745\pi$
$810$		0			0
$811$			1420.09i			1.75103i	0.483190	+	0.875516i	$0.339478\pi$
$811$			1420.09i			1.75103i	−0.483190	+	0.875516i	$0.660522\pi$
$812$	−15.1610	−	4.30893i	−0.0186712	−	0.00530656i
$813$	16.6154			0.0204371
$814$	−1024.35			−1.25841
$815$		0			0
$816$	−124.904			−0.153069
$817$			588.354i			0.720140i
$818$			805.571i			0.984806i
$819$	27.7598	−	97.6733i	0.0338948	−	0.119259i
$820$		0			0
$821$	−651.695			−0.793782			−0.396891	−	0.917866i	$-0.629911\pi$
$821$	−651.695			−0.793782			−0.396891	+	0.917866i	$0.629911\pi$
$822$		−	233.524i		−	0.284093i
$823$	−604.705			−0.734756			−0.367378	−	0.930072i	$-0.619745\pi$
$823$	−604.705			−0.734756			−0.367378	+	0.930072i	$0.619745\pi$
$824$			204.779i			0.248518i
$825$		0			0
$826$	−235.630	+	829.066i	−0.285266	+	1.00371i
$827$	−504.280			−0.609771			−0.304885	−	0.952389i	$-0.598618\pi$
$827$	−504.280			−0.609771			−0.304885	+	0.952389i	$0.598618\pi$
$828$	22.3509			0.0269939
$829$			814.575i			0.982599i	0.870991	+	0.491300i	$0.163478\pi$
$829$			814.575i			0.982599i	−0.870991	+	0.491300i	$0.836522\pi$
$830$		0			0
$831$		−	278.974i		−	0.335709i
$832$			38.6825i			0.0464934i
$833$	−464.610	+	751.344i	−0.557755	+	0.901973i
$834$	581.967			0.697802
$835$		0			0
$836$			319.884i			0.382637i
$837$	−296.627			−0.354393
$838$		−	296.215i		−	0.353478i
$839$		−	128.459i		−	0.153109i	−0.997065	−	0.0765547i	$-0.975608\pi$
$839$		−	128.459i		−	0.153109i	0.997065	−	0.0765547i	$-0.0243920\pi$
$840$		0			0
$841$	−839.733			−0.998493
$842$	240.011			0.285048
$843$		−	594.278i		−	0.704956i
$844$	67.3991			0.0798567
$845$		0			0
$846$			329.489i			0.389467i
$847$	1250.08	+	355.288i	1.47590	+	0.419466i
$848$	−310.153			−0.365747
$849$	562.480			0.662520
$850$		0			0
$851$	−154.081			−0.181059
$852$		−	201.973i		−	0.237058i
$853$		−	636.175i		−	0.745808i	−0.927870	−	0.372904i	$-0.878362\pi$
$853$		−	636.175i		−	0.745808i	0.927870	−	0.372904i	$-0.121638\pi$
$854$	−14.5320	+	51.1311i	−0.0170164	+	0.0598725i
$855$		0			0
$856$	490.907			0.573490
$857$			494.679i			0.577221i	0.957447	+	0.288611i	$0.0931933\pi$
$857$			494.679i			0.577221i	−0.957447	+	0.288611i	$0.906807\pi$
$858$	207.408			0.241734
$859$		−	745.414i		−	0.867770i	−0.900968	−	0.433885i	$-0.857142\pi$
$859$		−	745.414i		−	0.867770i	0.900968	−	0.433885i	$-0.142858\pi$
$860$		0			0
$861$	136.632	+	38.8325i	0.158690	+	0.0451016i
$862$	−761.450			−0.883353
$863$	−593.451			−0.687661			−0.343830	−	0.939032i	$-0.611725\pi$
$863$	−593.451			−0.687661			−0.343830	+	0.939032i	$0.611725\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$		−	167.322i		−	0.193212i
$867$		−	62.3935i		−	0.0719648i
$868$	218.489	−	768.757i	0.251716	−	0.885665i
$869$	1312.73			1.51063
$870$		0			0
$871$			228.168i			0.261961i
$872$	141.412			0.162169
$873$		−	323.491i		−	0.370551i
$874$			48.1168i			0.0550535i
$875$		0			0
$876$	−185.011			−0.211200
$877$	−291.879			−0.332815			−0.166407	−	0.986057i	$-0.553217\pi$
$877$	−291.879			−0.332815			−0.166407	+	0.986057i	$0.553217\pi$
$878$			614.948i			0.700396i
$879$	−174.795			−0.198856
$880$		0			0
$881$		−	1226.42i		−	1.39208i	−0.718004	−	0.696039i	$-0.754944\pi$
$881$		−	1226.42i		−	1.39208i	0.718004	−	0.696039i	$-0.245056\pi$
$882$	176.815	+	109.337i	0.200470	+	0.123965i
$883$	1132.03			1.28202			0.641012	−	0.767531i	$-0.278515\pi$
$883$	1132.03			1.28202			0.641012	+	0.767531i	$0.278515\pi$
$884$	−174.346			−0.197224
$885$		0			0
$886$	−784.896			−0.885887
$887$		−	959.088i		−	1.08127i	−0.841257	−	0.540636i	$-0.818184\pi$
$887$		−	959.088i		−	1.08127i	0.841257	−	0.540636i	$-0.181816\pi$
$888$		−	202.634i		−	0.228191i
$889$	−1332.83	−	378.806i	−1.49925	−	0.426103i
$890$		0			0
$891$	157.604			0.176885
$892$		−	21.5112i		−	0.0241156i
$893$	−709.321			−0.794312
$894$			327.850i			0.366723i
$895$		0			0
$896$	−76.1790	−	21.6509i	−0.0850212	−	0.0241640i
$897$	31.1982			0.0347806
$898$	−94.6004			−0.105346
$899$			64.2684i			0.0714887i
$900$		0			0
$901$		−	1397.89i		−	1.55149i
$902$			290.137i			0.321660i
$903$	−213.517	+	751.263i	−0.236453	+	0.831964i
$904$	−198.424			−0.219496
$905$		0			0
$906$		−	379.827i		−	0.419235i
$907$	989.799			1.09129			0.545644	−	0.838017i	$-0.316285\pi$
$907$	989.799			1.09129			0.545644	+	0.838017i	$0.316285\pi$
$908$		−	832.900i		−	0.917290i
$909$		−	157.845i		−	0.173647i
$910$		0			0
$911$	994.781			1.09197			0.545983	−	0.837796i	$-0.316156\pi$
$911$	994.781			1.09197			0.545983	+	0.837796i	$0.316156\pi$
$912$	−63.2788			−0.0693846
$913$		−	504.141i		−	0.552181i
$914$	1061.99			1.16191
$915$		0			0
$916$		−	776.938i		−	0.848185i
$917$	−219.884	+	773.665i	−0.239786	+	0.843691i
$918$	−132.481			−0.144315
$919$	887.212			0.965410			0.482705	−	0.875783i	$-0.339654\pi$
$919$	887.212			0.965410			0.482705	+	0.875783i	$0.339654\pi$
$920$		0			0
$921$	71.5436			0.0776804
$922$		−	559.148i		−	0.606451i
$923$		−	281.921i		−	0.305440i
$924$	−116.088	+	408.457i	−0.125636	+	0.442053i
$925$		0			0
$926$	599.600			0.647516
$927$			217.201i			0.234305i
$928$	6.36859			0.00686270
$929$		−	1224.49i		−	1.31808i	−0.752109	−	0.659039i	$-0.770963\pi$
$929$		−	1224.49i		−	1.31808i	0.752109	−	0.659039i	$-0.229037\pi$
$930$		0			0
$931$	−235.380	+	380.644i	−0.252825	+	0.408855i
$932$	140.807			0.151081
$933$	−814.655			−0.873156
$934$		−	826.478i		−	0.884880i
$935$		0			0
$936$			41.0290i			0.0438344i
$937$		−	807.001i		−	0.861260i	−0.902529	−	0.430630i	$-0.858291\pi$
$937$		−	807.001i		−	0.861260i	0.902529	−	0.430630i	$-0.141709\pi$
$938$	−449.341	−	127.708i	−0.479042	−	0.136149i
$939$	277.508			0.295536
$940$		0			0
$941$		−	1246.48i		−	1.32464i	−0.749223	−	0.662318i	$-0.769573\pi$
$941$		−	1246.48i		−	1.32464i	0.749223	−	0.662318i	$-0.230427\pi$
$942$	256.300			0.272081
$943$			43.6423i			0.0462802i
$944$		−	348.260i		−	0.368920i
$945$		0			0
$946$	−1595.30			−1.68636
$947$	−675.978			−0.713810			−0.356905	−	0.934141i	$-0.616168\pi$
$947$	−675.978			−0.713810			−0.356905	+	0.934141i	$0.616168\pi$
$948$			259.682i			0.273926i
$949$	−258.245			−0.272123
$950$		0			0
$951$			465.517i			0.489502i
$952$	97.5828	−	343.346i	0.102503	−	0.360658i
$953$	1098.24			1.15240			0.576201	−	0.817308i	$-0.304534\pi$
$953$	1098.24			1.15240			0.576201	+	0.817308i	$0.304534\pi$
$954$	−328.967			−0.344829
$955$		0			0
$956$	626.267			0.655091
$957$		−	34.1472i		−	0.0356815i
$958$			1038.76i			1.08430i
$959$	641.928	+	182.443i	0.669372	+	0.190243i
$960$		0			0
$961$	−2297.80			−2.39105
$962$		−	282.843i		−	0.294015i
$963$	520.686			0.540692
$964$		−	397.455i		−	0.412297i
$965$		0			0
$966$	−17.4619	+	61.4398i	−0.0180765	+	0.0636023i
$967$	−1345.41			−1.39132			−0.695661	−	0.718370i	$-0.744889\pi$
$967$	−1345.41			−1.39132			−0.695661	+	0.718370i	$0.744889\pi$
$968$	−525.114			−0.542474
$969$		−	285.204i		−	0.294328i
$970$		0			0
$971$			1230.36i			1.26710i	0.773701	+	0.633551i	$0.218403\pi$
$971$			1230.36i			1.26710i	−0.773701	+	0.633551i	$0.781597\pi$
$972$			31.1769i			0.0320750i
$973$	−454.668	+	1599.75i	−0.467284	+	1.64415i
$974$	−129.633			−0.133093
$975$		0			0
$976$		−	21.4783i		−	0.0220065i
$977$	228.116			0.233487			0.116743	−	0.993162i	$-0.462755\pi$
$977$	228.116			0.233487			0.116743	+	0.993162i	$0.462755\pi$
$978$		−	320.659i		−	0.327872i
$979$			1777.40i			1.81553i
$980$		0			0
$981$	149.990			0.152895
$982$	−650.659			−0.662586
$983$		−	1721.09i		−	1.75085i	−0.483354	−	0.875425i	$-0.660582\pi$
$983$		−	1721.09i		−	1.75085i	0.483354	−	0.875425i	$-0.339418\pi$
$984$	−57.3943			−0.0583275
$985$		0			0
$986$			28.7039i			0.0291114i
$987$	−905.724	−	257.417i	−0.917654	−	0.260807i
$988$	−88.3266			−0.0893994
$989$	−239.964			−0.242633
$990$		0			0
$991$	−1911.05			−1.92841			−0.964205	−	0.265159i	$-0.914576\pi$
$991$	−1911.05			−1.92841			−0.964205	+	0.265159i	$0.914576\pi$
$992$			322.927i			0.325531i
$993$			961.319i			0.968095i
$994$	555.199	+	157.794i	0.558550	+	0.158746i
$995$		0			0
$996$	99.7280			0.100129
$997$			31.3627i			0.0314571i	0.999876	+	0.0157285i	$0.00500676\pi$
$997$			31.3627i			0.0314571i	−0.999876	+	0.0157285i	$0.994993\pi$
$998$	−688.900			−0.690281
$999$		−	214.925i		−	0.215141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.e.601.8		16
5.2	odd	4		210.3.h.a.139.8	yes	16
5.3	odd	4		210.3.h.a.139.9	yes	16
5.4	even	2	inner	1050.3.f.e.601.9		16
7.6	odd	2	inner	1050.3.f.e.601.4		16
15.2	even	4		630.3.h.e.559.9		16
15.8	even	4		630.3.h.e.559.8		16
20.3	even	4		1680.3.bd.a.769.10		16
20.7	even	4		1680.3.bd.a.769.8		16
35.13	even	4		210.3.h.a.139.16	yes	16
35.27	even	4		210.3.h.a.139.1	✓	16
35.34	odd	2	inner	1050.3.f.e.601.13		16
105.62	odd	4		630.3.h.e.559.16		16
105.83	odd	4		630.3.h.e.559.1		16
140.27	odd	4		1680.3.bd.a.769.9		16
140.83	odd	4		1680.3.bd.a.769.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.1	✓	16	35.27	even	4
210.3.h.a.139.8	yes	16	5.2	odd	4
210.3.h.a.139.9	yes	16	5.3	odd	4
210.3.h.a.139.16	yes	16	35.13	even	4
630.3.h.e.559.1		16	105.83	odd	4
630.3.h.e.559.8		16	15.8	even	4
630.3.h.e.559.9		16	15.2	even	4
630.3.h.e.559.16		16	105.62	odd	4
1050.3.f.e.601.4		16	7.6	odd	2	inner
1050.3.f.e.601.8		16	1.1	even	1	trivial
1050.3.f.e.601.9		16	5.4	even	2	inner
1050.3.f.e.601.13		16	35.34	odd	2	inner
1680.3.bd.a.769.7		16	140.83	odd	4
1680.3.bd.a.769.8		16	20.7	even	4
1680.3.bd.a.769.9		16	140.27	odd	4
1680.3.bd.a.769.10		16	20.3	even	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.73333 + 1.91369i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.73333 + 1.91369i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +17.5116 q^{11} +3.46410i q^{12} +4.83531i q^{13} +(-9.52237 - 2.70636i) q^{14} +4.00000 q^{16} +18.0284i q^{17} +4.24264 q^{18} +9.13350i q^{19} +(-3.31461 + 11.6625i) q^{21} -24.7651 q^{22} -3.72515 q^{23} -4.89898i q^{24} -6.83816i q^{26} -5.19615i q^{27} +(13.4667 + 3.82738i) q^{28} -1.12582 q^{29} -57.0859i q^{31} -5.65685 q^{32} +30.3310i q^{33} -25.4960i q^{34} -6.00000 q^{36} +41.3624 q^{37} -12.9167i q^{38} -8.37500 q^{39} -11.7156i q^{41} +(4.68756 - 16.4932i) q^{42} +64.4171 q^{43} +35.0232 q^{44} +5.26816 q^{46} +77.6614i q^{47} +6.92820i q^{48} +(41.6756 + 25.7710i) q^{49} -31.2261 q^{51} +9.67062i q^{52} -77.5383 q^{53} +7.34847i q^{54} +(-19.0447 - 5.41273i) q^{56} -15.8197 q^{57} +1.59215 q^{58} -87.0651i q^{59} -5.36957i q^{61} +80.7317i q^{62} +(-20.2000 - 5.74106i) q^{63} +8.00000 q^{64} -42.8945i q^{66} +47.1879 q^{67} +36.0568i q^{68} -6.45216i q^{69} -58.3047 q^{71} +8.48528 q^{72} +53.4082i q^{73} -58.4953 q^{74} +18.2670i q^{76} +(117.911 + 33.5117i) q^{77} +11.8440 q^{78} +74.9637 q^{79} +9.00000 q^{81} +16.5683i q^{82} -28.7890i q^{83} +(-6.62921 + 23.3250i) q^{84} -91.0996 q^{86} -1.94997i q^{87} -49.5303 q^{88} +101.499i q^{89} +(-9.25327 + 32.5578i) q^{91} -7.45031 q^{92} +98.8757 q^{93} -109.830i q^{94} -9.79796i q^{96} +107.830i q^{97} +(-58.9382 - 36.4457i) q^{98} -52.5348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 48 * q^9	\( 16 q + 32 q^{4} - 48 q^{9} + 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{21} - 64 q^{29} - 96 q^{36} + 144 q^{39} + 192 q^{44} - 176 q^{46} - 224 q^{49} - 48 q^{51} - 32 q^{56} + 128 q^{64} - 384 q^{71} - 224 q^{74} + 608 q^{79} + 144 q^{81} + 48 q^{84} + 416 q^{86} + 224 q^{91} - 288 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 - 48 * q^9 + 96 * q^11 - 16 * q^14 + 64 * q^16 + 24 * q^21 - 64 * q^29 - 96 * q^36 + 144 * q^39 + 192 * q^44 - 176 * q^46 - 224 * q^49 - 48 * q^51 - 32 * q^56 + 128 * q^64 - 384 * q^71 - 224 * q^74 + 608 * q^79 + 144 * q^81 + 48 * q^84 + 416 * q^86 + 224 * q^91 - 288 * q^99

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