LMFDB - Embedded newform 1050.3.f.e.601.15

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			601.15
Root			$1.20711 - 0.264184i$ of defining polynomial
Character	$\chi$	$=$	1050.601
Dual form			1050.3.f.e.601.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(0.853218 - 6.94781i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(0.853218 - 6.94781i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +2.88097 q^{11} +3.46410i q^{12} +13.8145i q^{13} +(1.20663 - 9.82568i) q^{14} +4.00000 q^{16} -24.1754i q^{17} -4.24264 q^{18} -6.53403i q^{19} +(12.0340 + 1.47782i) q^{21} +4.07430 q^{22} +28.8420 q^{23} +4.89898i q^{24} +19.5367i q^{26} -5.19615i q^{27} +(1.70644 - 13.8956i) q^{28} +32.9589 q^{29} -2.43276i q^{31} +5.65685 q^{32} +4.98998i q^{33} -34.1892i q^{34} -6.00000 q^{36} +50.9799 q^{37} -9.24052i q^{38} -23.9275 q^{39} -21.5225i q^{41} +(17.0186 + 2.08995i) q^{42} +13.5554 q^{43} +5.76193 q^{44} +40.7887 q^{46} +40.7305i q^{47} +6.92820i q^{48} +(-47.5440 - 11.8560i) q^{49} +41.8730 q^{51} +27.6291i q^{52} -17.2758 q^{53} -7.34847i q^{54} +(2.41326 - 19.6514i) q^{56} +11.3173 q^{57} +46.6109 q^{58} +1.47488i q^{59} -111.568i q^{61} -3.44045i q^{62} +(-2.55965 + 20.8434i) q^{63} +8.00000 q^{64} +7.05690i q^{66} +120.293 q^{67} -48.3508i q^{68} +49.9558i q^{69} -90.3855 q^{71} -8.48528 q^{72} -21.4890i q^{73} +72.0964 q^{74} -13.0681i q^{76} +(2.45809 - 20.0164i) q^{77} -33.8385 q^{78} +66.1324 q^{79} +9.00000 q^{81} -30.4375i q^{82} -78.5172i q^{83} +(24.0679 + 2.95563i) q^{84} +19.1703 q^{86} +57.0865i q^{87} +8.14861 q^{88} +90.9724i q^{89} +(95.9807 + 11.7868i) q^{91} +57.6840 q^{92} +4.21367 q^{93} +57.6016i q^{94} +9.79796i q^{96} +44.1972i q^{97} +(-67.2374 - 16.7669i) q^{98} -8.64290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	0.853218	−	6.94781i	0.121888	−	0.992544i
$7$	0.853218	−	6.94781i	0.121888	−	0.992544i
$8$	2.82843			0.353553
$9$	−3.00000			−0.333333
$10$		0			0
$11$	2.88097			0.261906			0.130953	−	0.991389i	$-0.458196\pi$
$11$	2.88097			0.261906			0.130953	+	0.991389i	$0.458196\pi$
$12$			3.46410i			0.288675i
$13$			13.8145i			1.06266i	0.847166	+	0.531328i	$0.178307\pi$
$13$			13.8145i			1.06266i	−0.847166	+	0.531328i	$0.821693\pi$
$14$	1.20663	−	9.82568i	0.0861880	−	0.701834i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	24.1754i		−	1.42208i	−0.703150	−	0.711041i	$-0.748224\pi$
$17$		−	24.1754i		−	1.42208i	0.703150	−	0.711041i	$-0.251776\pi$
$18$	−4.24264			−0.235702
$19$		−	6.53403i		−	0.343896i	−0.985106	−	0.171948i	$-0.944994\pi$
$19$		−	6.53403i		−	0.343896i	0.985106	−	0.171948i	$-0.0550062\pi$
$20$		0			0
$21$	12.0340	+	1.47782i	0.573045	+	0.0703722i
$22$	4.07430			0.185196
$23$	28.8420			1.25400			0.627000	−	0.779019i	$-0.284283\pi$
$23$	28.8420			1.25400			0.627000	+	0.779019i	$0.284283\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$			19.5367i			0.751411i
$27$		−	5.19615i		−	0.192450i
$28$	1.70644	−	13.8956i	0.0609441	−	0.496272i
$29$	32.9589			1.13651			0.568257	−	0.822851i	$-0.307618\pi$
$29$	32.9589			1.13651			0.568257	+	0.822851i	$0.307618\pi$
$30$		0			0
$31$		−	2.43276i		−	0.0784762i	−0.999230	−	0.0392381i	$-0.987507\pi$
$31$		−	2.43276i		−	0.0784762i	0.999230	−	0.0392381i	$-0.0124931\pi$
$32$	5.65685			0.176777
$33$			4.98998i			0.151212i
$34$		−	34.1892i		−	1.00556i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	50.9799			1.37783			0.688917	−	0.724840i	$-0.258086\pi$
$37$	50.9799			1.37783			0.688917	+	0.724840i	$0.258086\pi$
$38$		−	9.24052i		−	0.243171i
$39$	−23.9275			−0.613525
$40$		0			0
$41$		−	21.5225i		−	0.524940i	−0.964940	−	0.262470i	$-0.915463\pi$
$41$		−	21.5225i		−	0.524940i	0.964940	−	0.262470i	$-0.0845371\pi$
$42$	17.0186	+	2.08995i	0.405204	+	0.0497607i
$43$	13.5554			0.315243			0.157621	−	0.987500i	$-0.449617\pi$
$43$	13.5554			0.315243			0.157621	+	0.987500i	$0.449617\pi$
$44$	5.76193			0.130953
$45$		0			0
$46$	40.7887			0.886712
$47$			40.7305i			0.866605i	0.901248	+	0.433303i	$0.142652\pi$
$47$			40.7305i			0.866605i	−0.901248	+	0.433303i	$0.857348\pi$
$48$			6.92820i			0.144338i
$49$	−47.5440	−	11.8560i	−0.970287	−	0.241959i
$50$		0			0
$51$	41.8730			0.821040
$52$			27.6291i			0.531328i
$53$	−17.2758			−0.325959			−0.162979	−	0.986629i	$-0.552110\pi$
$53$	−17.2758			−0.325959			−0.162979	+	0.986629i	$0.552110\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	2.41326	−	19.6514i	0.0430940	−	0.350917i
$57$	11.3173			0.198549
$58$	46.6109			0.803636
$59$			1.47488i			0.0249980i	0.999922	+	0.0124990i	$0.00397867\pi$
$59$			1.47488i			0.0249980i	−0.999922	+	0.0124990i	$0.996021\pi$
$60$		0			0
$61$		−	111.568i		−	1.82898i	−0.404609	−	0.914490i	$-0.632592\pi$
$61$		−	111.568i		−	1.82898i	0.404609	−	0.914490i	$-0.367408\pi$
$62$		−	3.44045i		−	0.0554911i
$63$	−2.55965	+	20.8434i	−0.0406294	+	0.330848i
$64$	8.00000			0.125000
$65$		0			0
$66$			7.05690i			0.106923i
$67$	120.293			1.79542			0.897709	−	0.440590i	$-0.145231\pi$
$67$	120.293			1.79542			0.897709	+	0.440590i	$0.145231\pi$
$68$		−	48.3508i		−	0.711041i
$69$			49.9558i			0.723997i
$70$		0			0
$71$	−90.3855			−1.27304			−0.636518	−	0.771262i	$-0.719626\pi$
$71$	−90.3855			−1.27304			−0.636518	+	0.771262i	$0.719626\pi$
$72$	−8.48528			−0.117851
$73$		−	21.4890i		−	0.294370i	−0.989109	−	0.147185i	$-0.952979\pi$
$73$		−	21.4890i		−	0.294370i	0.989109	−	0.147185i	$-0.0470212\pi$
$74$	72.0964			0.974276
$75$		0			0
$76$		−	13.0681i		−	0.171948i
$77$	2.45809	−	20.0164i	0.0319233	−	0.259953i
$78$	−33.8385			−0.433827
$79$	66.1324			0.837119			0.418559	−	0.908189i	$-0.362535\pi$
$79$	66.1324			0.837119			0.418559	+	0.908189i	$0.362535\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	30.4375i		−	0.371189i
$83$		−	78.5172i		−	0.945990i	−0.881065	−	0.472995i	$-0.843173\pi$
$83$		−	78.5172i		−	0.945990i	0.881065	−	0.472995i	$-0.156827\pi$
$84$	24.0679	+	2.95563i	0.286523	+	0.0351861i
$85$		0			0
$86$	19.1703			0.222910
$87$			57.0865i			0.656166i
$88$	8.14861			0.0925978
$89$			90.9724i			1.02216i	0.859533	+	0.511081i	$0.170755\pi$
$89$			90.9724i			1.02216i	−0.859533	+	0.511081i	$0.829245\pi$
$90$		0			0
$91$	95.9807	+	11.7868i	1.05473	+	0.129525i
$92$	57.6840			0.627000
$93$	4.21367			0.0453083
$94$			57.6016i			0.612783i
$95$		0			0
$96$			9.79796i			0.102062i
$97$			44.1972i			0.455642i	0.973703	+	0.227821i	$0.0731600\pi$
$97$			44.1972i			0.455642i	−0.973703	+	0.227821i	$0.926840\pi$
$98$	−67.2374	−	16.7669i	−0.686096	−	0.171091i
$99$	−8.64290			−0.0873020
$100$		0			0
$101$			180.052i			1.78269i	0.453326	+	0.891345i	$0.350237\pi$
$101$			180.052i			1.78269i	−0.453326	+	0.891345i	$0.649763\pi$
$102$	59.2174			0.580563
$103$			107.208i			1.04086i	0.853906	+	0.520428i	$0.174228\pi$
$103$			107.208i			1.04086i	−0.853906	+	0.520428i	$0.825772\pi$
$104$			39.0734i			0.375706i
$105$		0			0
$106$	−24.4317			−0.230488
$107$	33.1521			0.309833			0.154917	−	0.987928i	$-0.450489\pi$
$107$	33.1521			0.309833			0.154917	+	0.987928i	$0.450489\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−108.819			−0.998338			−0.499169	−	0.866505i	$-0.666361\pi$
$109$	−108.819			−0.998338			−0.499169	+	0.866505i	$0.666361\pi$
$110$		0			0
$111$			88.2997i			0.795493i
$112$	3.41287	−	27.7912i	0.0304721	−	0.248136i
$113$	157.658			1.39520			0.697600	−	0.716488i	$-0.254251\pi$
$113$	157.658			1.39520			0.697600	+	0.716488i	$0.254251\pi$
$114$	16.0050			0.140395
$115$		0			0
$116$	65.9178			0.568257
$117$		−	41.4436i		−	0.354219i
$118$			2.08580i			0.0176763i
$119$	−167.966	−	20.6269i	−1.41148	−	0.173335i
$120$		0			0
$121$	−112.700			−0.931405
$122$		−	157.781i		−	1.29328i
$123$	37.2781			0.303074
$124$		−	4.86553i		−	0.0392381i
$125$		0			0
$126$	−3.61990	+	29.4770i	−0.0287293	+	0.233945i
$127$	28.2047			0.222085			0.111042	−	0.993816i	$-0.464581\pi$
$127$	28.2047			0.222085			0.111042	+	0.993816i	$0.464581\pi$
$128$	11.3137			0.0883883
$129$			23.4787i			0.182006i
$130$		0			0
$131$			157.620i			1.20321i	0.798795	+	0.601604i	$0.205471\pi$
$131$			157.620i			1.20321i	−0.798795	+	0.601604i	$0.794529\pi$
$132$			9.97996i			0.0756058i
$133$	−45.3972	−	5.57495i	−0.341332	−	0.0419169i
$134$	170.120			1.26955
$135$		0			0
$136$		−	68.3784i		−	0.502782i
$137$	244.855			1.78726			0.893632	−	0.448800i	$-0.148148\pi$
$137$	244.855			1.78726			0.893632	+	0.448800i	$0.148148\pi$
$138$			70.6482i			0.511943i
$139$		−	238.245i		−	1.71399i	−0.515325	−	0.856995i	$-0.672329\pi$
$139$		−	238.245i		−	1.71399i	0.515325	−	0.856995i	$-0.327671\pi$
$140$		0			0
$141$	−70.5472			−0.500335
$142$	−127.824			−0.900172
$143$			39.7992i			0.278316i
$144$	−12.0000			−0.0833333
$145$		0			0
$146$		−	30.3900i		−	0.208151i
$147$	20.5352	−	82.3487i	0.139695	−	0.560195i
$148$	101.960			0.688917
$149$	−10.8398			−0.0727503			−0.0363751	−	0.999338i	$-0.511581\pi$
$149$	−10.8398			−0.0727503			−0.0363751	+	0.999338i	$0.511581\pi$
$150$		0			0
$151$	−112.999			−0.748340			−0.374170	−	0.927360i	$-0.622072\pi$
$151$	−112.999			−0.748340			−0.374170	+	0.927360i	$0.622072\pi$
$152$		−	18.4810i		−	0.121586i
$153$			72.5262i			0.474027i
$154$	3.47627	−	28.3075i	0.0225732	−	0.183815i
$155$		0			0
$156$	−47.8549			−0.306762
$157$		−	103.693i		−	0.660462i	−0.943900	−	0.330231i	$-0.892873\pi$
$157$		−	103.693i		−	0.660462i	0.943900	−	0.330231i	$-0.107127\pi$
$158$	93.5253			0.591932
$159$		−	29.9226i		−	0.188193i
$160$		0			0
$161$	24.6085	−	200.389i	0.152848	−	1.24465i
$162$	12.7279			0.0785674
$163$	−199.576			−1.22439			−0.612196	−	0.790706i	$-0.709713\pi$
$163$	−199.576			−1.22439			−0.612196	+	0.790706i	$0.709713\pi$
$164$		−	43.0451i		−	0.262470i
$165$		0			0
$166$		−	111.040i		−	0.668916i
$167$			87.0777i			0.521424i	0.965417	+	0.260712i	$0.0839572\pi$
$167$			87.0777i			0.521424i	−0.965417	+	0.260712i	$0.916043\pi$
$168$	34.0372	+	4.17990i	0.202602	+	0.0248803i
$169$	−21.8411			−0.129237
$170$		0			0
$171$			19.6021i			0.114632i
$172$	27.1109			0.157621
$173$		−	106.597i		−	0.616166i	−0.951359	−	0.308083i	$-0.900313\pi$
$173$		−	106.597i		−	0.616166i	0.951359	−	0.308083i	$-0.0996875\pi$
$174$			80.7325i			0.463980i
$175$		0			0
$176$	11.5239			0.0654765
$177$	−2.55458			−0.0144326
$178$			128.654i			0.722778i
$179$	−275.881			−1.54123			−0.770617	−	0.637298i	$-0.780052\pi$
$179$	−275.881			−1.54123			−0.770617	+	0.637298i	$0.780052\pi$
$180$		0			0
$181$		−	186.431i		−	1.03000i	−0.857189	−	0.515002i	$-0.827791\pi$
$181$		−	186.431i		−	1.03000i	0.857189	−	0.515002i	$-0.172209\pi$
$182$	135.737	+	16.6690i	0.745808	+	0.0915882i
$183$	193.241			1.05596
$184$	81.5775			0.443356
$185$		0			0
$186$	5.95903			0.0320378
$187$		−	69.6485i		−	0.372452i
$188$			81.4609i			0.433303i
$189$	−36.1019	−	4.43345i	−0.191015	−	0.0234574i
$190$		0			0
$191$	−177.076			−0.927102			−0.463551	−	0.886070i	$-0.653425\pi$
$191$	−177.076			−0.927102			−0.463551	+	0.886070i	$0.653425\pi$
$192$			13.8564i			0.0721688i
$193$	153.453			0.795092			0.397546	−	0.917582i	$-0.369862\pi$
$193$	153.453			0.795092			0.397546	+	0.917582i	$0.369862\pi$
$194$			62.5043i			0.322187i
$195$		0			0
$196$	−95.0881	−	23.7120i	−0.485143	−	0.120979i
$197$	−214.041			−1.08650			−0.543252	−	0.839570i	$-0.682807\pi$
$197$	−214.041			−1.08650			−0.543252	+	0.839570i	$0.682807\pi$
$198$	−12.2229			−0.0617319
$199$			178.176i			0.895359i	0.894194	+	0.447679i	$0.147749\pi$
$199$			178.176i			0.895359i	−0.894194	+	0.447679i	$0.852251\pi$
$200$		0			0
$201$			208.354i			1.03658i
$202$			254.631i			1.26055i
$203$	28.1211	−	228.992i	0.138528	−	1.12804i
$204$	83.7460			0.410520
$205$		0			0
$206$			151.615i			0.735996i
$207$	−86.5260			−0.418000
$208$			55.2581i			0.265664i
$209$		−	18.8243i		−	0.0900686i
$210$		0			0
$211$	−398.012			−1.88631			−0.943156	−	0.332350i	$-0.892158\pi$
$211$	−398.012			−1.88631			−0.943156	+	0.332350i	$0.892158\pi$
$212$	−34.5517			−0.162979
$213$		−	156.552i		−	0.734987i
$214$	46.8842			0.219085
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−16.9024	−	2.07568i	−0.0778911	−	0.00956533i
$218$	−153.893			−0.705932
$219$	37.2200			0.169954
$220$		0			0
$221$	333.972			1.51118
$222$			124.875i			0.562499i
$223$			6.96741i			0.0312440i	0.999878	+	0.0156220i	$0.00497284\pi$
$223$			6.96741i			0.0312440i	−0.999878	+	0.0156220i	$0.995027\pi$
$224$	4.82653	−	39.3027i	0.0215470	−	0.175459i
$225$		0			0
$226$	222.961			0.986555
$227$		−	242.118i		−	1.06660i	−0.845927	−	0.533299i	$-0.820952\pi$
$227$		−	242.118i		−	1.06660i	0.845927	−	0.533299i	$-0.179048\pi$
$228$	22.6345			0.0992743
$229$			225.586i			0.985093i	0.870286	+	0.492547i	$0.163934\pi$
$229$			225.586i			0.985093i	−0.870286	+	0.492547i	$0.836066\pi$
$230$		0			0
$231$	34.6694	+	4.25754i	0.150084	+	0.0184309i
$232$	93.2218			0.401818
$233$	−435.850			−1.87060			−0.935300	−	0.353856i	$-0.884870\pi$
$233$	−435.850			−1.87060			−0.935300	+	0.353856i	$0.884870\pi$
$234$		−	58.6101i		−	0.250470i
$235$		0			0
$236$			2.94977i			0.0124990i
$237$			114.545i			0.483311i
$238$	−237.540	−	29.1708i	−0.998066	−	0.122566i
$239$	−194.711			−0.814690			−0.407345	−	0.913274i	$-0.633545\pi$
$239$	−194.711			−0.814690			−0.407345	+	0.913274i	$0.633545\pi$
$240$		0			0
$241$		−	245.810i		−	1.01996i	−0.860186	−	0.509980i	$-0.829653\pi$
$241$		−	245.810i		−	1.01996i	0.860186	−	0.509980i	$-0.170347\pi$
$242$	−159.382			−0.658603
$243$			15.5885i			0.0641500i
$244$		−	223.136i		−	0.914490i
$245$		0			0
$246$	52.7192			0.214306
$247$	90.2645			0.365443
$248$		−	6.88089i		−	0.0277455i
$249$	135.996			0.546168
$250$		0			0
$251$			147.023i			0.585749i	0.956151	+	0.292875i	$0.0946118\pi$
$251$			147.023i			0.585749i	−0.956151	+	0.292875i	$0.905388\pi$
$252$	−5.11931	+	41.6868i	−0.0203147	+	0.165424i
$253$	83.0928			0.328430
$254$	39.8875			0.157038
$255$		0			0
$256$	16.0000			0.0625000
$257$			421.734i			1.64099i	0.571654	+	0.820495i	$0.306302\pi$
$257$			421.734i			1.64099i	−0.571654	+	0.820495i	$0.693698\pi$
$258$			33.2039i			0.128697i
$259$	43.4969	−	354.198i	0.167942	−	1.36756i
$260$		0			0
$261$	−98.8767			−0.378838
$262$			222.909i			0.850796i
$263$	68.6354			0.260971			0.130486	−	0.991450i	$-0.458346\pi$
$263$	68.6354			0.260971			0.130486	+	0.991450i	$0.458346\pi$
$264$			14.1138i			0.0534614i
$265$		0			0
$266$	−64.2013	−	7.88417i	−0.241358	−	0.0296397i
$267$	−157.569			−0.590145
$268$	240.586			0.897709
$269$		−	93.2991i		−	0.346837i	−0.984848	−	0.173418i	$-0.944519\pi$
$269$		−	93.2991i		−	0.346837i	0.984848	−	0.173418i	$-0.0554813\pi$
$270$		0			0
$271$		−	288.317i		−	1.06390i	−0.846776	−	0.531949i	$-0.821460\pi$
$271$		−	288.317i		−	1.06390i	0.846776	−	0.531949i	$-0.178540\pi$
$272$		−	96.7016i		−	0.355521i
$273$	−20.4153	+	166.243i	−0.0747814	+	0.608950i
$274$	346.278			1.26379
$275$		0			0
$276$			99.9116i			0.361999i
$277$	−385.440			−1.39148			−0.695740	−	0.718294i	$-0.744923\pi$
$277$	−385.440			−1.39148			−0.695740	+	0.718294i	$0.744923\pi$
$278$		−	336.929i		−	1.21197i
$279$			7.29829i			0.0261587i
$280$		0			0
$281$	243.958			0.868179			0.434090	−	0.900870i	$-0.357070\pi$
$281$	243.958			0.868179			0.434090	+	0.900870i	$0.357070\pi$
$282$	−99.7688			−0.353790
$283$		−	501.435i		−	1.77185i	−0.463825	−	0.885927i	$-0.653523\pi$
$283$		−	501.435i		−	1.77185i	0.463825	−	0.885927i	$-0.346477\pi$
$284$	−180.771			−0.636518
$285$		0			0
$286$			56.2846i			0.196799i
$287$	−149.534	−	18.3634i	−0.521026	−	0.0639840i
$288$	−16.9706			−0.0589256
$289$	−295.450			−1.02232
$290$		0			0
$291$	−76.5519			−0.263065
$292$		−	42.9780i		−	0.147185i
$293$			337.308i			1.15122i	0.817724	+	0.575611i	$0.195236\pi$
$293$			337.308i			1.15122i	−0.817724	+	0.575611i	$0.804764\pi$
$294$	29.0411	−	116.459i	0.0987793	−	0.396118i
$295$		0			0
$296$	144.193			0.487138
$297$		−	14.9699i		−	0.0504039i
$298$	−15.3298			−0.0514422
$299$			398.438i			1.33257i
$300$		0			0
$301$	11.5657	−	94.1806i	0.0384244	−	0.312892i
$302$	−159.805			−0.529156
$303$	−311.859			−1.02924
$304$		−	26.1361i		−	0.0859741i
$305$		0			0
$306$			102.568i			0.335188i
$307$			112.285i			0.365751i	0.983136	+	0.182875i	$0.0585405\pi$
$307$			112.285i			0.365751i	−0.983136	+	0.182875i	$0.941460\pi$
$308$	4.91618	−	40.0328i	0.0159616	−	0.129977i
$309$	−185.690			−0.600938
$310$		0			0
$311$			146.478i			0.470990i	0.971876	+	0.235495i	$0.0756711\pi$
$311$			146.478i			0.470990i	−0.971876	+	0.235495i	$0.924329\pi$
$312$	−67.6771			−0.216914
$313$			139.927i			0.447052i	0.974698	+	0.223526i	$0.0717568\pi$
$313$			139.927i			0.447052i	−0.974698	+	0.223526i	$0.928243\pi$
$314$		−	146.643i		−	0.467017i
$315$		0			0
$316$	132.265			0.418559
$317$	39.7776			0.125481			0.0627407	−	0.998030i	$-0.480016\pi$
$317$	39.7776			0.125481			0.0627407	+	0.998030i	$0.480016\pi$
$318$		−	42.3170i		−	0.133072i
$319$	94.9535			0.297660
$320$		0			0
$321$			57.4212i			0.178882i
$322$	34.8017	−	283.392i	0.108080	−	0.880100i
$323$	−157.963			−0.489049
$324$	18.0000			0.0555556
$325$		0			0
$326$	−282.243			−0.865775
$327$		−	188.480i		−	0.576391i
$328$		−	60.8749i		−	0.185594i
$329$	282.987	+	34.7519i	0.860144	+	0.105629i
$330$		0			0
$331$	−13.6736			−0.0413101			−0.0206550	−	0.999787i	$-0.506575\pi$
$331$	−13.6736			−0.0413101			−0.0206550	+	0.999787i	$0.506575\pi$
$332$		−	157.034i		−	0.472995i
$333$	−152.940			−0.459278
$334$			123.147i			0.368702i
$335$		0			0
$336$	48.1358	+	5.91127i	0.143261	+	0.0175931i
$337$	−364.873			−1.08271			−0.541354	−	0.840795i	$-0.682088\pi$
$337$	−364.873			−1.08271			−0.541354	+	0.840795i	$0.682088\pi$
$338$	−30.8880			−0.0913846
$339$			273.071i			0.805519i
$340$		0			0
$341$		−	7.00871i		−	0.0205534i
$342$			27.7215i			0.0810572i
$343$	−122.938	+	320.211i	−0.358421	+	0.933560i
$344$	38.3406			0.111455
$345$		0			0
$346$		−	150.751i		−	0.435695i
$347$	−469.783			−1.35384			−0.676920	−	0.736056i	$-0.736686\pi$
$347$	−469.783			−1.35384			−0.676920	+	0.736056i	$0.736686\pi$
$348$			114.173i			0.328083i
$349$		−	26.7504i		−	0.0766487i	−0.999265	−	0.0383244i	$-0.987798\pi$
$349$		−	26.7504i		−	0.0766487i	0.999265	−	0.0383244i	$-0.0122020\pi$
$350$		0			0
$351$	71.7824			0.204508
$352$	16.2972			0.0462989
$353$			473.408i			1.34110i	0.741864	+	0.670550i	$0.233942\pi$
$353$			473.408i			1.34110i	−0.741864	+	0.670550i	$0.766058\pi$
$354$	−3.61272			−0.0102054
$355$		0			0
$356$			181.945i			0.511081i
$357$	35.7268	−	290.926i	0.100075	−	0.814918i
$358$	−390.155			−1.08982
$359$	98.8174			0.275257			0.137629	−	0.990484i	$-0.456052\pi$
$359$	98.8174			0.275257			0.137629	+	0.990484i	$0.456052\pi$
$360$		0			0
$361$	318.306			0.881735
$362$		−	263.653i		−	0.728323i
$363$		−	195.202i		−	0.537747i
$364$	191.961	+	23.5736i	0.527366	+	0.0647626i
$365$		0			0
$366$	273.284			0.746678
$367$		−	331.526i		−	0.903341i	−0.892185	−	0.451671i	$-0.850828\pi$
$367$		−	331.526i		−	0.903341i	0.892185	−	0.451671i	$-0.149172\pi$
$368$	115.368			0.313500
$369$			64.5676i			0.174980i
$370$		0			0
$371$	−14.7400	+	120.029i	−0.0397306	+	0.323529i
$372$	8.42734			0.0226541
$373$	416.519			1.11667			0.558337	−	0.829614i	$-0.311440\pi$
$373$	416.519			1.11667			0.558337	+	0.829614i	$0.311440\pi$
$374$		−	98.4979i		−	0.263363i
$375$		0			0
$376$			115.203i			0.306391i
$377$			455.311i			1.20772i
$378$	−51.0557	−	6.26984i	−0.135068	−	0.0165869i
$379$	−560.942			−1.48006			−0.740028	−	0.672576i	$-0.765188\pi$
$379$	−560.942			−1.48006			−0.740028	+	0.672576i	$0.765188\pi$
$380$		0			0
$381$			48.8520i			0.128221i
$382$	−250.424			−0.655560
$383$			135.702i			0.354314i	0.984183	+	0.177157i	$0.0566900\pi$
$383$			135.702i			0.354314i	−0.984183	+	0.177157i	$0.943310\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	217.015			0.562215
$387$	−40.6663			−0.105081
$388$			88.3945i			0.227821i
$389$	703.375			1.80816			0.904081	−	0.427361i	$-0.140557\pi$
$389$	703.375			1.80816			0.904081	+	0.427361i	$0.140557\pi$
$390$		0			0
$391$		−	697.267i		−	1.78329i
$392$	−134.475	−	33.5338i	−0.343048	−	0.0855454i
$393$	−273.006			−0.694672
$394$	−302.700			−0.768274
$395$		0			0
$396$	−17.2858			−0.0436510
$397$		−	2.16495i		−	0.00545326i	−0.999996	−	0.00272663i	$-0.999132\pi$
$397$		−	2.16495i		−	0.00545326i	0.999996	−	0.00272663i	$-0.000867915\pi$
$398$			251.979i			0.633114i
$399$	9.65610	−	78.6302i	0.0242007	−	0.197068i
$400$		0			0
$401$	−227.907			−0.568347			−0.284174	−	0.958773i	$-0.591719\pi$
$401$	−227.907			−0.568347			−0.284174	+	0.958773i	$0.591719\pi$
$402$			294.656i			0.732976i
$403$	33.6075			0.0833932
$404$			360.103i			0.891345i
$405$		0			0
$406$	39.7693	−	323.844i	0.0979538	−	0.797644i
$407$	146.871			0.360863
$408$	118.435			0.290281
$409$		−	219.271i		−	0.536116i	−0.963403	−	0.268058i	$-0.913618\pi$
$409$		−	219.271i		−	0.536116i	0.963403	−	0.268058i	$-0.0863818\pi$
$410$		0			0
$411$			424.102i			1.03188i
$412$			214.416i			0.520428i
$413$	10.2472	+	1.25840i	0.0248117	+	0.00304697i
$414$	−122.366			−0.295571
$415$		0			0
$416$			78.1468i			0.187853i
$417$	412.652			0.989572
$418$		−	26.6216i		−	0.0636881i
$419$		−	636.723i		−	1.51963i	−0.650141	−	0.759813i	$-0.725290\pi$
$419$		−	636.723i		−	1.51963i	0.650141	−	0.759813i	$-0.274710\pi$
$420$		0			0
$421$	816.589			1.93964			0.969821	−	0.243819i	$-0.0784003\pi$
$421$	816.589			1.93964			0.969821	+	0.243819i	$0.0784003\pi$
$422$	−562.874			−1.33382
$423$		−	122.191i		−	0.288868i
$424$	−48.8634			−0.115244
$425$		0			0
$426$		−	221.398i		−	0.519714i
$427$	−775.151	−	95.1916i	−1.81534	−	0.222931i
$428$	66.3043			0.154917
$429$	−68.9342			−0.160686
$430$		0			0
$431$	−288.911			−0.670328			−0.335164	−	0.942160i	$-0.608792\pi$
$431$	−288.911			−0.670328			−0.335164	+	0.942160i	$0.608792\pi$
$432$		−	20.7846i		−	0.0481125i
$433$			114.744i			0.264997i	0.991183	+	0.132498i	$0.0423000\pi$
$433$			114.744i			0.264997i	−0.991183	+	0.132498i	$0.957700\pi$
$434$	−23.9036	−	2.93545i	−0.0550773	−	0.00676371i
$435$		0			0
$436$	−217.638			−0.499169
$437$		−	188.454i		−	0.431246i
$438$	52.6371			0.120176
$439$			637.443i			1.45203i	0.687677	+	0.726017i	$0.258631\pi$
$439$			637.443i			1.45203i	−0.687677	+	0.726017i	$0.741369\pi$
$440$		0			0
$441$	142.632	+	35.5679i	0.323429	+	0.0806529i
$442$	472.307			1.06857
$443$	184.901			0.417384			0.208692	−	0.977981i	$-0.433079\pi$
$443$	184.901			0.417384			0.208692	+	0.977981i	$0.433079\pi$
$444$			176.599i			0.397747i
$445$		0			0
$446$			9.85341i			0.0220928i
$447$		−	18.7751i		−	0.0420024i
$448$	6.82574	−	55.5825i	0.0152360	−	0.124068i
$449$	313.278			0.697723			0.348862	−	0.937174i	$-0.386568\pi$
$449$	313.278			0.697723			0.348862	+	0.937174i	$0.386568\pi$
$450$		0			0
$451$		−	62.0057i		−	0.137485i
$452$	315.315			0.697600
$453$		−	195.721i		−	0.432054i
$454$		−	342.406i		−	0.754198i
$455$		0			0
$456$	32.0101			0.0701976
$457$	−174.826			−0.382551			−0.191275	−	0.981536i	$-0.561262\pi$
$457$	−174.826			−0.382551			−0.191275	+	0.981536i	$0.561262\pi$
$458$			319.027i			0.696566i
$459$	−125.619			−0.273680
$460$		0			0
$461$			379.263i			0.822695i	0.911479	+	0.411348i	$0.134942\pi$
$461$			379.263i			0.822695i	−0.911479	+	0.411348i	$0.865058\pi$
$462$	49.0300	+	6.02107i	0.106125	+	0.0130326i
$463$	−403.499			−0.871489			−0.435744	−	0.900071i	$-0.643515\pi$
$463$	−403.499			−0.871489			−0.435744	+	0.900071i	$0.643515\pi$
$464$	131.836			0.284128
$465$		0			0
$466$	−616.385			−1.32271
$467$			807.901i			1.72998i	0.501788	+	0.864991i	$0.332676\pi$
$467$			807.901i			1.72998i	−0.501788	+	0.864991i	$0.667324\pi$
$468$		−	82.8872i		−	0.177109i
$469$	102.636	−	835.772i	0.218840	−	1.78203i
$470$		0			0
$471$	179.601			0.381318
$472$			4.17160i			0.00883815i
$473$	39.0528			0.0825640
$474$			161.991i			0.341752i
$475$		0			0
$476$	−335.932	−	41.2538i	−0.705740	−	0.0866675i
$477$	51.8275			0.108653
$478$	−275.363			−0.576073
$479$			439.564i			0.917671i	0.888521	+	0.458835i	$0.151733\pi$
$479$			439.564i			0.917671i	−0.888521	+	0.458835i	$0.848267\pi$
$480$		0			0
$481$			704.263i			1.46416i
$482$		−	347.628i		−	0.721220i
$483$	347.083	+	42.6232i	0.718599	+	0.0882467i
$484$	−225.400			−0.465703
$485$		0			0
$486$			22.0454i			0.0453609i
$487$	37.9665			0.0779599			0.0389799	−	0.999240i	$-0.487589\pi$
$487$	37.9665			0.0779599			0.0389799	+	0.999240i	$0.487589\pi$
$488$		−	315.561i		−	0.646642i
$489$		−	345.675i		−	0.706903i
$490$		0			0
$491$	−7.32753			−0.0149237			−0.00746184	−	0.999972i	$-0.502375\pi$
$491$	−7.32753			−0.0149237			−0.00746184	+	0.999972i	$0.502375\pi$
$492$	74.5563			0.151537
$493$		−	796.794i		−	1.61622i
$494$	127.653			0.258408
$495$		0			0
$496$		−	9.73105i		−	0.0196191i
$497$	−77.1185	+	627.981i	−0.155168	+	1.26354i
$498$	192.327			0.386199
$499$	397.886			0.797366			0.398683	−	0.917089i	$-0.369467\pi$
$499$	397.886			0.797366			0.398683	+	0.917089i	$0.369467\pi$
$500$		0			0
$501$	−150.823			−0.301044
$502$			207.922i			0.414187i
$503$			70.5081i			0.140175i	0.997541	+	0.0700876i	$0.0223279\pi$
$503$			70.5081i			0.140175i	−0.997541	+	0.0700876i	$0.977672\pi$
$504$	−7.23979	+	58.9541i	−0.0143647	+	0.116972i
$505$		0			0
$506$	117.511			0.232235
$507$		−	37.8299i		−	0.0746152i
$508$	56.4095			0.111042
$509$			505.073i			0.992285i	0.868241	+	0.496143i	$0.165251\pi$
$509$			505.073i			0.992285i	−0.868241	+	0.496143i	$0.834749\pi$
$510$		0			0
$511$	−149.301	−	18.3348i	−0.292175	−	0.0358802i
$512$	22.6274			0.0441942
$513$	−33.9518			−0.0661829
$514$			596.422i			1.16035i
$515$		0			0
$516$			46.9574i			0.0910028i
$517$			117.343i			0.226969i
$518$	61.5139	−	500.912i	0.118753	−	0.967012i
$519$	184.631			0.355744
$520$		0			0
$521$			214.185i			0.411104i	0.978646	+	0.205552i	$0.0658990\pi$
$521$			214.185i			0.411104i	−0.978646	+	0.205552i	$0.934101\pi$
$522$	−139.833			−0.267879
$523$			121.732i			0.232757i	0.993205	+	0.116379i	$0.0371286\pi$
$523$			121.732i			0.232757i	−0.993205	+	0.116379i	$0.962871\pi$
$524$			315.240i			0.601604i
$525$		0			0
$526$	97.0651			0.184534
$527$	−58.8130			−0.111600
$528$			19.9599i			0.0378029i
$529$	302.861			0.572515
$530$		0			0
$531$		−	4.42465i		−	0.00833268i
$532$	−90.7944	−	11.1499i	−0.170666	−	0.0209585i
$533$	297.324			0.557830
$534$	−222.836			−0.417296
$535$		0			0
$536$	340.240			0.634776
$537$		−	477.840i		−	0.889832i
$538$		−	131.945i		−	0.245251i
$539$	−136.973	−	34.1567i	−0.254124	−	0.0633705i
$540$		0			0
$541$	600.626			1.11021			0.555107	−	0.831779i	$-0.312677\pi$
$541$	600.626			1.11021			0.555107	+	0.831779i	$0.312677\pi$
$542$		−	407.741i		−	0.752290i
$543$	322.908			0.594674
$544$		−	136.757i		−	0.251391i
$545$		0			0
$546$	−28.8716	+	235.104i	−0.0528785	+	0.430593i
$547$	1045.16			1.91071			0.955356	−	0.295457i	$-0.0954719\pi$
$547$	1045.16			1.91071			0.955356	+	0.295457i	$0.0954719\pi$
$548$	489.711			0.893632
$549$			334.703i			0.609660i
$550$		0			0
$551$		−	215.354i		−	0.390843i
$552$			141.296i			0.255972i
$553$	56.4253	−	459.475i	0.102035	−	0.830877i
$554$	−545.094			−0.983924
$555$		0			0
$556$		−	476.489i		−	0.856995i
$557$	601.731			1.08031			0.540154	−	0.841566i	$-0.318366\pi$
$557$	601.731			1.08031			0.540154	+	0.841566i	$0.318366\pi$
$558$			10.3213i			0.0184970i
$559$			187.262i			0.334995i
$560$		0			0
$561$	120.635			0.215035
$562$	345.009			0.613896
$563$			363.871i			0.646308i	0.946346	+	0.323154i	$0.104743\pi$
$563$			363.871i			0.646308i	−0.946346	+	0.323154i	$0.895257\pi$
$564$	−141.094			−0.250167
$565$		0			0
$566$		−	709.136i		−	1.25289i
$567$	7.67896	−	62.5303i	0.0135431	−	0.110283i
$568$	−255.649			−0.450086
$569$	−902.900			−1.58682			−0.793410	−	0.608688i	$-0.791696\pi$
$569$	−902.900			−1.58682			−0.793410	+	0.608688i	$0.791696\pi$
$570$		0			0
$571$	−847.207			−1.48372			−0.741862	−	0.670552i	$-0.766057\pi$
$571$	−847.207			−1.48372			−0.741862	+	0.670552i	$0.766057\pi$
$572$			79.5984i			0.139158i
$573$		−	306.705i		−	0.535263i
$574$	−211.474	−	25.9698i	−0.368421	−	0.0452435i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$			306.535i			0.531256i	0.964076	+	0.265628i	$0.0855793\pi$
$577$			306.535i			0.531256i	−0.964076	+	0.265628i	$0.914421\pi$
$578$	−417.829			−0.722888
$579$			265.788i			0.459047i
$580$		0			0
$581$	−545.522	−	66.9923i	−0.938937	−	0.115305i
$582$	−108.261			−0.186015
$583$	−49.7711			−0.0853707
$584$		−	60.7801i		−	0.104075i
$585$		0			0
$586$			477.025i			0.814037i
$587$			467.524i			0.796463i	0.917285	+	0.398232i	$0.130376\pi$
$587$			467.524i			0.796463i	−0.917285	+	0.398232i	$0.869624\pi$
$588$	41.0703	−	164.697i	0.0698475	−	0.280098i
$589$	−15.8958			−0.0269877
$590$		0			0
$591$		−	370.730i		−	0.627293i
$592$	203.920			0.344459
$593$			744.542i			1.25555i	0.778395	+	0.627775i	$0.216034\pi$
$593$			744.542i			1.25555i	−0.778395	+	0.627775i	$0.783966\pi$
$594$		−	21.1707i		−	0.0356409i
$595$		0			0
$596$	−21.6796			−0.0363751
$597$	−308.611			−0.516936
$598$			563.477i			0.942269i
$599$	276.145			0.461011			0.230505	−	0.973071i	$-0.425962\pi$
$599$	276.145			0.461011			0.230505	+	0.973071i	$0.425962\pi$
$600$		0			0
$601$		−	779.606i		−	1.29718i	−0.761137	−	0.648591i	$-0.775359\pi$
$601$		−	779.606i		−	1.29718i	0.761137	−	0.648591i	$-0.224641\pi$
$602$	16.3564	−	133.191i	0.0271702	−	0.221248i
$603$	−360.879			−0.598472
$604$	−225.999			−0.374170
$605$		0			0
$606$	−441.035			−0.727780
$607$		−	567.539i		−	0.934990i	−0.883996	−	0.467495i	$-0.845157\pi$
$607$		−	567.539i		−	0.934990i	0.883996	−	0.467495i	$-0.154843\pi$
$608$		−	36.9621i		−	0.0607929i
$609$	396.626	+	48.7072i	0.651274	+	0.0799790i
$610$		0			0
$611$	−562.672			−0.920903
$612$			145.052i			0.237014i
$613$	−801.088			−1.30683			−0.653416	−	0.756999i	$-0.726665\pi$
$613$	−801.088			−1.30683			−0.653416	+	0.756999i	$0.726665\pi$
$614$			158.796i			0.258625i
$615$		0			0
$616$	6.95253	−	56.6149i	0.0112866	−	0.0919074i
$617$	71.2583			0.115492			0.0577458	−	0.998331i	$-0.481609\pi$
$617$	71.2583			0.115492			0.0577458	+	0.998331i	$0.481609\pi$
$618$	−262.605			−0.424928
$619$		−	821.793i		−	1.32761i	−0.747904	−	0.663807i	$-0.768940\pi$
$619$		−	821.793i		−	1.32761i	0.747904	−	0.663807i	$-0.231060\pi$
$620$		0			0
$621$		−	149.867i		−	0.241332i
$622$			207.151i			0.333040i
$623$	632.059	+	77.6193i	1.01454	+	0.124590i
$624$	−95.7098			−0.153381
$625$		0			0
$626$			197.887i			0.316114i
$627$	32.6047			0.0520011
$628$		−	207.385i		−	0.330231i
$629$		−	1232.46i		−	1.95939i
$630$		0			0
$631$	−916.907			−1.45310			−0.726551	−	0.687113i	$-0.758878\pi$
$631$	−916.907			−1.45310			−0.726551	+	0.687113i	$0.758878\pi$
$632$	187.051			0.295966
$633$		−	689.377i		−	1.08906i
$634$	56.2540			0.0887287
$635$		0			0
$636$		−	59.8452i		−	0.0940963i
$637$	163.785	−	656.798i	0.257119	−	1.03108i
$638$	134.285			0.210477
$639$	271.156			0.424345
$640$		0			0
$641$	737.240			1.15014			0.575070	−	0.818104i	$-0.304975\pi$
$641$	737.240			1.15014			0.575070	+	0.818104i	$0.304975\pi$
$642$			81.2058i			0.126489i
$643$			256.297i			0.398596i	0.979939	+	0.199298i	$0.0638661\pi$
$643$			256.297i			0.398596i	−0.979939	+	0.199298i	$0.936134\pi$
$644$	49.2170	−	400.777i	0.0764239	−	0.622325i
$645$		0			0
$646$	−223.393			−0.345810
$647$		−	689.147i		−	1.06514i	−0.846385	−	0.532571i	$-0.821226\pi$
$647$		−	689.147i		−	1.06514i	0.846385	−	0.532571i	$-0.178774\pi$
$648$	25.4558			0.0392837
$649$			4.24910i			0.00654714i
$650$		0			0
$651$	3.59518	−	29.2758i	0.00552255	−	0.0449705i
$652$	−399.152			−0.612196
$653$	−395.775			−0.606087			−0.303044	−	0.952977i	$-0.598003\pi$
$653$	−395.775			−0.606087			−0.303044	+	0.952977i	$0.598003\pi$
$654$		−	266.551i		−	0.407570i
$655$		0			0
$656$		−	86.0902i		−	0.131235i
$657$			64.4670i			0.0981233i
$658$	400.205	+	49.1467i	0.608214	+	0.0746910i
$659$	47.8147			0.0725565			0.0362782	−	0.999342i	$-0.488450\pi$
$659$	47.8147			0.0725565			0.0362782	+	0.999342i	$0.488450\pi$
$660$		0			0
$661$			89.9129i			0.136026i	0.997684	+	0.0680128i	$0.0216659\pi$
$661$			89.9129i			0.136026i	−0.997684	+	0.0680128i	$0.978334\pi$
$662$	−19.3374			−0.0292106
$663$			578.456i			0.872482i
$664$		−	222.080i		−	0.334458i
$665$		0			0
$666$	−216.289			−0.324759
$667$	950.600			1.42519
$668$			174.155i			0.260712i
$669$	−12.0679			−0.0180387
$670$		0			0
$671$		−	321.423i		−	0.479021i
$672$	68.0743	+	8.35979i	0.101301	+	0.0124402i
$673$	833.478			1.23845			0.619226	−	0.785213i	$-0.287447\pi$
$673$	833.478			1.23845			0.619226	+	0.785213i	$0.287447\pi$
$674$	−516.008			−0.765590
$675$		0			0
$676$	−43.6822			−0.0646187
$677$			44.1092i			0.0651540i	0.999469	+	0.0325770i	$0.0103714\pi$
$677$			44.1092i			0.0651540i	−0.999469	+	0.0325770i	$0.989629\pi$
$678$			386.181i			0.569588i
$679$	307.074	+	37.7099i	0.452244	+	0.0555373i
$680$		0			0
$681$	419.360			0.615800
$682$		−	9.91182i		−	0.0145335i
$683$	130.146			0.190550			0.0952750	−	0.995451i	$-0.469627\pi$
$683$	130.146			0.190550			0.0952750	+	0.995451i	$0.469627\pi$
$684$			39.2042i			0.0573161i
$685$		0			0
$686$	−173.861	+	452.847i	−0.253442	+	0.660127i
$687$	−390.727			−0.568744
$688$	54.2218			0.0788107
$689$		−	238.657i		−	0.346382i
$690$		0			0
$691$			714.724i			1.03433i	0.855885	+	0.517167i	$0.173013\pi$
$691$			714.724i			1.03433i	−0.855885	+	0.517167i	$0.826987\pi$
$692$		−	213.194i		−	0.308083i
$693$	−7.37428	+	60.0492i	−0.0106411	+	0.0866511i
$694$	−664.373			−0.957310
$695$		0			0
$696$			161.465i			0.231990i
$697$	−520.316			−0.746508
$698$		−	37.8308i		−	0.0541988i
$699$		−	754.914i		−	1.07999i
$700$		0			0
$701$	463.854			0.661704			0.330852	−	0.943683i	$-0.392664\pi$
$701$	463.854			0.661704			0.330852	+	0.943683i	$0.392664\pi$
$702$	101.516			0.144609
$703$		−	333.104i		−	0.473832i
$704$	23.0477			0.0327383
$705$		0			0
$706$			669.500i			0.948301i
$707$	1250.96	+	153.623i	1.76940	+	0.217289i
$708$	−5.10915			−0.00721632
$709$	970.049			1.36819			0.684097	−	0.729391i	$-0.260197\pi$
$709$	970.049			1.36819			0.684097	+	0.729391i	$0.260197\pi$
$710$		0			0
$711$	−198.397			−0.279040
$712$			257.309i			0.361389i
$713$		−	70.1657i		−	0.0984092i
$714$	50.5253	−	411.431i	0.0707638	−	0.576234i
$715$		0			0
$716$	−551.762			−0.770617
$717$		−	337.249i		−	0.470362i
$718$	139.749			0.194636
$719$			1369.36i			1.90453i	0.305266	+	0.952267i	$0.401255\pi$
$719$			1369.36i			1.90453i	−0.305266	+	0.952267i	$0.598745\pi$
$720$		0			0
$721$	744.861	+	91.4719i	1.03309	+	0.126868i
$722$	450.153			0.623481
$723$	425.756			0.588874
$724$		−	372.862i		−	0.515002i
$725$		0			0
$726$		−	276.058i		−	0.380245i
$727$		−	1106.85i		−	1.52249i	−0.648463	−	0.761246i	$-0.724588\pi$
$727$		−	1106.85i		−	1.52249i	0.648463	−	0.761246i	$-0.275412\pi$
$728$	271.474	+	33.3381i	0.372904	+	0.0457941i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	327.708i		−	0.448301i
$732$	386.482			0.527981
$733$			297.353i			0.405665i	0.979213	+	0.202833i	$0.0650147\pi$
$733$			297.353i			0.405665i	−0.979213	+	0.202833i	$0.934985\pi$
$734$		−	468.849i		−	0.638759i
$735$		0			0
$736$	163.155			0.221678
$737$	346.560			0.470231
$738$			91.3124i			0.123730i
$739$	−604.951			−0.818608			−0.409304	−	0.912398i	$-0.634228\pi$
$739$	−604.951			−0.818608			−0.409304	+	0.912398i	$0.634228\pi$
$740$		0			0
$741$			156.343i			0.210989i
$742$	−20.8456	+	169.747i	−0.0280938	+	0.228769i
$743$	−733.877			−0.987722			−0.493861	−	0.869541i	$-0.664415\pi$
$743$	−733.877			−0.987722			−0.493861	+	0.869541i	$0.664415\pi$
$744$	11.9181			0.0160189
$745$		0			0
$746$	589.047			0.789608
$747$			235.552i			0.315330i
$748$		−	139.297i		−	0.186226i
$749$	28.2860	−	230.335i	0.0377650	−	0.307523i
$750$		0			0
$751$	−71.0036			−0.0945455			−0.0472727	−	0.998882i	$-0.515053\pi$
$751$	−71.0036			−0.0945455			−0.0472727	+	0.998882i	$0.515053\pi$
$752$			162.922i			0.216651i
$753$	−254.651			−0.338182
$754$			643.908i			0.853989i
$755$		0			0
$756$	−72.2037	−	8.86690i	−0.0955076	−	0.0117287i
$757$	708.172			0.935497			0.467749	−	0.883861i	$-0.345065\pi$
$757$	708.172			0.935497			0.467749	+	0.883861i	$0.345065\pi$
$758$	−793.291			−1.04656
$759$			143.921i			0.189619i
$760$		0			0
$761$			797.652i			1.04816i	0.851668	+	0.524081i	$0.175591\pi$
$761$			797.652i			1.04816i	−0.851668	+	0.524081i	$0.824409\pi$
$762$			69.0872i			0.0906657i
$763$	−92.8462	+	756.052i	−0.121686	+	0.990894i
$764$	−354.153			−0.463551
$765$		0			0
$766$			191.912i			0.250538i
$767$	−20.3748			−0.0265643
$768$			27.7128i			0.0360844i
$769$			261.829i			0.340480i	0.985403	+	0.170240i	$0.0544543\pi$
$769$			261.829i			0.340480i	−0.985403	+	0.170240i	$0.945546\pi$
$770$		0			0
$771$	−730.465			−0.947426
$772$	306.906			0.397546
$773$		−	643.514i		−	0.832489i	−0.909253	−	0.416245i	$-0.863346\pi$
$773$		−	643.514i		−	0.832489i	0.909253	−	0.416245i	$-0.136654\pi$
$774$	−57.5109			−0.0743035
$775$		0			0
$776$			125.009i			0.161094i
$777$	613.490	+	75.3389i	0.789562	+	0.0969613i
$778$	994.722			1.27856
$779$	−140.629			−0.180525
$780$		0			0
$781$	−260.398			−0.333416
$782$		−	986.084i		−	1.26098i
$783$		−	171.259i		−	0.218722i
$784$	−190.176	−	47.4239i	−0.242572	−	0.0604897i
$785$		0			0
$786$	−386.089			−0.491207
$787$			919.663i			1.16857i	0.811549	+	0.584284i	$0.198625\pi$
$787$			919.663i			1.16857i	−0.811549	+	0.584284i	$0.801375\pi$
$788$	−428.082			−0.543252
$789$			118.880i			0.150672i
$790$		0			0
$791$	134.516	−	1095.37i	0.170058	−	1.38480i
$792$	−24.4458			−0.0308659
$793$	1541.26			1.94358
$794$		−	3.06170i		−	0.00385604i
$795$		0			0
$796$			356.353i			0.447679i
$797$		−	246.244i		−	0.308964i	−0.987996	−	0.154482i	$-0.950629\pi$
$797$		−	246.244i		−	0.308964i	0.987996	−	0.154482i	$-0.0493708\pi$
$798$	13.6558	−	111.200i	0.0171125	−	0.139348i
$799$	984.675			1.23238
$800$		0			0
$801$		−	272.917i		−	0.340721i
$802$	−322.309			−0.401882
$803$		−	61.9091i		−	0.0770973i
$804$			416.707i			0.518292i
$805$		0			0
$806$	47.5281			0.0589679
$807$	161.599			0.200246
$808$			509.263i			0.630276i
$809$	609.838			0.753817			0.376908	−	0.926251i	$-0.376987\pi$
$809$	609.838			0.753817			0.376908	+	0.926251i	$0.376987\pi$
$810$		0			0
$811$			605.726i			0.746888i	0.927653	+	0.373444i	$0.121823\pi$
$811$			605.726i			0.746888i	−0.927653	+	0.373444i	$0.878177\pi$
$812$	56.2422	−	457.984i	0.0692638	−	0.564020i
$813$	499.379			0.614242
$814$	207.707			0.255169
$815$		0			0
$816$	167.492			0.205260
$817$		−	88.5717i		−	0.108411i
$818$		−	310.097i		−	0.379091i
$819$	−287.942	−	35.3604i	−0.351577	−	0.0431751i
$820$		0			0
$821$	890.751			1.08496			0.542480	−	0.840069i	$-0.317486\pi$
$821$	890.751			1.08496			0.542480	+	0.840069i	$0.317486\pi$
$822$			599.770i			0.729648i
$823$	317.029			0.385211			0.192606	−	0.981276i	$-0.438306\pi$
$823$	317.029			0.385211			0.192606	+	0.981276i	$0.438306\pi$
$824$			303.230i			0.367998i
$825$		0			0
$826$	14.4918	+	1.77964i	0.0175445	+	0.00215453i
$827$	90.7251			0.109704			0.0548520	−	0.998494i	$-0.482531\pi$
$827$	90.7251			0.109704			0.0548520	+	0.998494i	$0.482531\pi$
$828$	−173.052			−0.209000
$829$			1366.86i			1.64880i	0.566007	+	0.824400i	$0.308487\pi$
$829$			1366.86i			1.64880i	−0.566007	+	0.824400i	$0.691513\pi$
$830$		0			0
$831$		−	667.601i		−	0.803371i
$832$			110.516i			0.132832i
$833$	−286.623	+	1149.40i	−0.344085	+	1.37983i
$834$	583.578			0.699733
$835$		0			0
$836$		−	37.6487i		−	0.0450343i
$837$	−12.6410			−0.0151028
$838$		−	900.463i		−	1.07454i
$839$		−	73.5993i		−	0.0877227i	−0.999038	−	0.0438613i	$-0.986034\pi$
$839$		−	73.5993i		−	0.0877227i	0.999038	−	0.0438613i	$-0.0139660\pi$
$840$		0			0
$841$	245.289			0.291663
$842$	1154.83			1.37153
$843$			422.548i			0.501244i
$844$	−796.024			−0.943156
$845$		0			0
$846$		−	172.805i		−	0.204261i
$847$	−96.1576	+	783.018i	−0.113527	+	0.924460i
$848$	−69.1033			−0.0814897
$849$	868.510			1.02298
$850$		0			0
$851$	1470.36			1.72780
$852$		−	313.105i		−	0.367494i
$853$		−	822.046i		−	0.963711i	−0.876251	−	0.481856i	$-0.839963\pi$
$853$		−	822.046i		−	0.963711i	0.876251	−	0.481856i	$-0.160037\pi$
$854$	−1096.23	−	134.621i	−1.28364	−	0.157636i
$855$		0			0
$856$	93.7684			0.109543
$857$			625.685i			0.730087i	0.930990	+	0.365044i	$0.118946\pi$
$857$			625.685i			0.730087i	−0.930990	+	0.365044i	$0.881054\pi$
$858$	−97.4877			−0.113622
$859$			1396.65i			1.62590i	0.582332	+	0.812951i	$0.302140\pi$
$859$			1396.65i			1.62590i	−0.582332	+	0.812951i	$0.697860\pi$
$860$		0			0
$861$	31.8064	−	259.001i	0.0369412	−	0.300814i
$862$	−408.582			−0.473993
$863$	601.569			0.697068			0.348534	−	0.937296i	$-0.386680\pi$
$863$	601.569			0.697068			0.348534	+	0.937296i	$0.386680\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$			162.272i			0.187381i
$867$		−	511.734i		−	0.590236i
$868$	−33.8047	−	4.15135i	−0.0389456	−	0.00478267i
$869$	190.525			0.219246
$870$		0			0
$871$			1661.79i			1.90791i
$872$	−307.786			−0.352966
$873$		−	132.592i		−	0.151881i
$874$		−	266.515i		−	0.304937i
$875$		0			0
$876$	74.4401			0.0849772
$877$	570.762			0.650812			0.325406	−	0.945574i	$-0.394499\pi$
$877$	570.762			0.650812			0.325406	+	0.945574i	$0.394499\pi$
$878$			901.480i			1.02674i
$879$	−584.234			−0.664658
$880$		0			0
$881$		−	1095.44i		−	1.24341i	−0.783253	−	0.621703i	$-0.786441\pi$
$881$		−	1095.44i		−	1.24341i	0.783253	−	0.621703i	$-0.213559\pi$
$882$	201.712	+	50.3007i	0.228699	+	0.0570302i
$883$	−305.870			−0.346399			−0.173199	−	0.984887i	$-0.555410\pi$
$883$	−305.870			−0.346399			−0.173199	+	0.984887i	$0.555410\pi$
$884$	667.943			0.755592
$885$		0			0
$886$	261.490			0.295135
$887$			637.527i			0.718745i	0.933194	+	0.359372i	$0.117009\pi$
$887$			637.527i			0.718745i	−0.933194	+	0.359372i	$0.882991\pi$
$888$			249.749i			0.281249i
$889$	24.0648	−	195.961i	0.0270695	−	0.220429i
$890$		0			0
$891$	25.9287			0.0291007
$892$			13.9348i			0.0156220i
$893$	266.134			0.298022
$894$		−	26.5520i		−	0.0297002i
$895$		0			0
$896$	9.65306	−	78.6055i	0.0107735	−	0.0877293i
$897$	−690.116			−0.769360
$898$	443.042			0.493365
$899$		−	80.1812i		−	0.0891893i
$900$		0			0
$901$			417.650i			0.463541i
$902$		−	87.6893i		−	0.0972166i
$903$	163.126	+	20.0325i	0.180649	+	0.0221843i
$904$	445.923			0.493278
$905$		0			0
$906$		−	276.791i		−	0.305509i
$907$	−785.727			−0.866292			−0.433146	−	0.901324i	$-0.642597\pi$
$907$	−785.727			−0.866292			−0.433146	+	0.901324i	$0.642597\pi$
$908$		−	484.235i		−	0.533299i
$909$		−	540.155i		−	0.594230i
$910$		0			0
$911$	−909.376			−0.998217			−0.499109	−	0.866539i	$-0.666339\pi$
$911$	−909.376			−0.998217			−0.499109	+	0.866539i	$0.666339\pi$
$912$	45.2691			0.0496372
$913$		−	226.205i		−	0.247761i
$914$	−247.241			−0.270504
$915$		0			0
$916$			451.173i			0.492547i
$917$	1095.11	+	134.484i	1.19424	+	0.146657i
$918$	−177.652			−0.193521
$919$	270.279			0.294101			0.147050	−	0.989129i	$-0.453022\pi$
$919$	270.279			0.294101			0.147050	+	0.989129i	$0.453022\pi$
$920$		0			0
$921$	−194.484			−0.211166
$922$			536.358i			0.581733i
$923$		−	1248.63i		−	1.35280i
$924$	69.3389	+	8.51508i	0.0750421	+	0.00921546i
$925$		0			0
$926$	−570.634			−0.616235
$927$		−	321.624i		−	0.346952i
$928$	186.444			0.200909
$929$			1053.28i			1.13378i	0.823795	+	0.566889i	$0.191853\pi$
$929$			1053.28i			1.13378i	−0.823795	+	0.566889i	$0.808147\pi$
$930$		0			0
$931$	−77.4674	+	310.654i	−0.0832088	+	0.333678i
$932$	−871.699			−0.935300
$933$	−253.707			−0.271926
$934$			1142.55i			1.22328i
$935$		0			0
$936$		−	117.220i		−	0.125235i
$937$		−	1012.18i		−	1.08024i	−0.841589	−	0.540119i	$-0.818379\pi$
$937$		−	1012.18i		−	1.08024i	0.841589	−	0.540119i	$-0.181621\pi$
$938$	145.149	−	1181.96i	0.154743	−	1.26009i
$939$	−242.361			−0.258106
$940$		0			0
$941$		−	1384.55i		−	1.47136i	−0.677331	−	0.735679i	$-0.736863\pi$
$941$		−	1384.55i		−	1.47136i	0.677331	−	0.735679i	$-0.263137\pi$
$942$	253.994			0.269633
$943$		−	620.753i		−	0.658275i
$944$			5.89954i			0.00624951i
$945$		0			0
$946$	55.2290			0.0583816
$947$	−1216.79			−1.28489			−0.642444	−	0.766332i	$-0.722080\pi$
$947$	−1216.79			−1.28489			−0.642444	+	0.766332i	$0.722080\pi$
$948$			229.089i			0.241655i
$949$	296.860			0.312814
$950$		0			0
$951$			68.8968i			0.0724467i
$952$	−475.080	−	58.3416i	−0.499033	−	0.0612832i
$953$	−30.5870			−0.0320955			−0.0160478	−	0.999871i	$-0.505108\pi$
$953$	−30.5870			−0.0320955			−0.0160478	+	0.999871i	$0.505108\pi$
$954$	73.2951			0.0768293
$955$		0			0
$956$	−389.422			−0.407345
$957$			164.464i			0.171854i
$958$			621.638i			0.648891i
$959$	208.915	−	1701.21i	0.217847	−	1.77394i
$960$		0			0
$961$	955.082			0.993841
$962$			995.978i			1.03532i
$963$	−99.4564			−0.103278
$964$		−	491.620i		−	0.509980i
$965$		0			0
$966$	490.850	+	60.2783i	0.508126	+	0.0623999i
$967$	1878.59			1.94270			0.971351	−	0.237650i	$-0.0763772\pi$
$967$	1878.59			1.94270			0.971351	+	0.237650i	$0.0763772\pi$
$968$	−318.764			−0.329301
$969$		−	273.600i		−	0.282353i
$970$		0			0
$971$			712.009i			0.733274i	0.930364	+	0.366637i	$0.119491\pi$
$971$			712.009i			0.733274i	−0.930364	+	0.366637i	$0.880509\pi$
$972$			31.1769i			0.0320750i
$973$	−1655.28	−	203.274i	−1.70121	−	0.208915i
$974$	53.6927			0.0551260
$975$		0			0
$976$		−	446.271i		−	0.457245i
$977$	750.938			0.768616			0.384308	−	0.923205i	$-0.374440\pi$
$977$	750.938			0.768616			0.384308	+	0.923205i	$0.374440\pi$
$978$		−	488.859i		−	0.499856i
$979$			262.089i			0.267710i
$980$		0			0
$981$	326.457			0.332779
$982$	−10.3627			−0.0105526
$983$		−	1525.09i		−	1.55147i	−0.631059	−	0.775735i	$-0.717379\pi$
$983$		−	1525.09i		−	1.55147i	0.631059	−	0.775735i	$-0.282621\pi$
$984$	105.438			0.107153
$985$		0			0
$986$		−	1126.84i		−	1.14284i
$987$	−60.1921	+	490.148i	−0.0609849	+	0.496604i
$988$	180.529			0.182722
$989$	390.966			0.395314
$990$		0			0
$991$	1259.84			1.27128			0.635641	−	0.771985i	$-0.280736\pi$
$991$	1259.84			1.27128			0.635641	+	0.771985i	$0.280736\pi$
$992$		−	13.7618i		−	0.0138728i
$993$		−	23.6834i		−	0.0238504i
$994$	−109.062	+	888.099i	−0.109720	+	0.893460i
$995$		0			0
$996$	271.992			0.273084
$997$		−	1406.62i		−	1.41086i	−0.708781	−	0.705428i	$-0.750755\pi$
$997$		−	1406.62i		−	1.41086i	0.708781	−	0.705428i	$-0.249245\pi$
$998$	562.695			0.563823
$999$		−	264.899i		−	0.265164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.f.e.601.15		16
5.2	odd	4		210.3.h.a.139.14	yes	16
5.3	odd	4		210.3.h.a.139.3	✓	16
5.4	even	2	inner	1050.3.f.e.601.2		16
7.6	odd	2	inner	1050.3.f.e.601.11		16
15.2	even	4		630.3.h.e.559.6		16
15.8	even	4		630.3.h.e.559.11		16
20.3	even	4		1680.3.bd.a.769.13		16
20.7	even	4		1680.3.bd.a.769.3		16
35.13	even	4		210.3.h.a.139.6	yes	16
35.27	even	4		210.3.h.a.139.11	yes	16
35.34	odd	2	inner	1050.3.f.e.601.6		16
105.62	odd	4		630.3.h.e.559.3		16
105.83	odd	4		630.3.h.e.559.14		16
140.27	odd	4		1680.3.bd.a.769.14		16
140.83	odd	4		1680.3.bd.a.769.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.3	✓	16	5.3	odd	4
210.3.h.a.139.6	yes	16	35.13	even	4
210.3.h.a.139.11	yes	16	35.27	even	4
210.3.h.a.139.14	yes	16	5.2	odd	4
630.3.h.e.559.3		16	105.62	odd	4
630.3.h.e.559.6		16	15.2	even	4
630.3.h.e.559.11		16	15.8	even	4
630.3.h.e.559.14		16	105.83	odd	4
1050.3.f.e.601.2		16	5.4	even	2	inner
1050.3.f.e.601.6		16	35.34	odd	2	inner
1050.3.f.e.601.11		16	7.6	odd	2	inner
1050.3.f.e.601.15		16	1.1	even	1	trivial
1680.3.bd.a.769.3		16	20.7	even	4
1680.3.bd.a.769.4		16	140.83	odd	4
1680.3.bd.a.769.13		16	20.3	even	4
1680.3.bd.a.769.14		16	140.27	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(0.853218 - 6.94781i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(0.853218 - 6.94781i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +2.88097 q^{11} +3.46410i q^{12} +13.8145i q^{13} +(1.20663 - 9.82568i) q^{14} +4.00000 q^{16} -24.1754i q^{17} -4.24264 q^{18} -6.53403i q^{19} +(12.0340 + 1.47782i) q^{21} +4.07430 q^{22} +28.8420 q^{23} +4.89898i q^{24} +19.5367i q^{26} -5.19615i q^{27} +(1.70644 - 13.8956i) q^{28} +32.9589 q^{29} -2.43276i q^{31} +5.65685 q^{32} +4.98998i q^{33} -34.1892i q^{34} -6.00000 q^{36} +50.9799 q^{37} -9.24052i q^{38} -23.9275 q^{39} -21.5225i q^{41} +(17.0186 + 2.08995i) q^{42} +13.5554 q^{43} +5.76193 q^{44} +40.7887 q^{46} +40.7305i q^{47} +6.92820i q^{48} +(-47.5440 - 11.8560i) q^{49} +41.8730 q^{51} +27.6291i q^{52} -17.2758 q^{53} -7.34847i q^{54} +(2.41326 - 19.6514i) q^{56} +11.3173 q^{57} +46.6109 q^{58} +1.47488i q^{59} -111.568i q^{61} -3.44045i q^{62} +(-2.55965 + 20.8434i) q^{63} +8.00000 q^{64} +7.05690i q^{66} +120.293 q^{67} -48.3508i q^{68} +49.9558i q^{69} -90.3855 q^{71} -8.48528 q^{72} -21.4890i q^{73} +72.0964 q^{74} -13.0681i q^{76} +(2.45809 - 20.0164i) q^{77} -33.8385 q^{78} +66.1324 q^{79} +9.00000 q^{81} -30.4375i q^{82} -78.5172i q^{83} +(24.0679 + 2.95563i) q^{84} +19.1703 q^{86} +57.0865i q^{87} +8.14861 q^{88} +90.9724i q^{89} +(95.9807 + 11.7868i) q^{91} +57.6840 q^{92} +4.21367 q^{93} +57.6016i q^{94} +9.79796i q^{96} +44.1972i q^{97} +(-67.2374 - 16.7669i) q^{98} -8.64290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 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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