LMFDB - Embedded newform 175.4.k.b.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(74,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("175.74");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	175.149
Dual form			175.4.k.b.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59808 - 1.50000i) q^{2} +(1.73205 - 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} -6.00000 q^{6} +(-12.1244 - 14.0000i) q^{7} +21.0000i q^{8} +(-11.5000 + 19.9186i) q^{9} +(22.5000 + 38.9711i) q^{11} +(1.73205 + 1.00000i) q^{12} -59.0000i q^{13} +(10.5000 + 54.5596i) q^{14} +(35.5000 - 61.4878i) q^{16} +(-46.7654 + 27.0000i) q^{17} +(59.7558 - 34.5000i) q^{18} +(-60.5000 + 104.789i) q^{19} +(-35.0000 - 12.1244i) q^{21} -135.000i q^{22} +(59.7558 + 34.5000i) q^{23} +(21.0000 + 36.3731i) q^{24} +(-88.5000 + 153.286i) q^{26} +100.000i q^{27} +(6.06218 - 17.5000i) q^{28} +162.000 q^{29} +(44.0000 + 76.2102i) q^{31} +(-38.9711 + 22.5000i) q^{32} +(77.9423 + 45.0000i) q^{33} +162.000 q^{34} -23.0000 q^{36} +(224.301 + 129.500i) q^{37} +(314.367 - 181.500i) q^{38} +(-59.0000 - 102.191i) q^{39} +195.000 q^{41} +(72.7461 + 84.0000i) q^{42} +286.000i q^{43} +(-22.5000 + 38.9711i) q^{44} +(-103.500 - 179.267i) q^{46} +(-38.9711 - 22.5000i) q^{47} -142.000i q^{48} +(-49.0000 + 339.482i) q^{49} +(-54.0000 + 93.5307i) q^{51} +(51.0955 - 29.5000i) q^{52} +(-517.017 + 298.500i) q^{53} +(150.000 - 259.808i) q^{54} +(294.000 - 254.611i) q^{56} +242.000i q^{57} +(-420.888 - 243.000i) q^{58} +(-180.000 - 311.769i) q^{59} +(-196.000 + 339.482i) q^{61} -264.000i q^{62} +(418.290 - 80.5000i) q^{63} -433.000 q^{64} +(-135.000 - 233.827i) q^{66} +(-242.487 + 140.000i) q^{67} +(-46.7654 - 27.0000i) q^{68} +138.000 q^{69} +48.0000 q^{71} +(-418.290 - 241.500i) q^{72} +(-578.505 + 334.000i) q^{73} +(-388.500 - 672.902i) q^{74} -121.000 q^{76} +(272.798 - 787.500i) q^{77} +354.000i q^{78} +(391.000 - 677.232i) q^{79} +(-210.500 - 364.597i) q^{81} +(-506.625 - 292.500i) q^{82} -768.000i q^{83} +(-7.00000 - 36.3731i) q^{84} +(429.000 - 743.050i) q^{86} +(280.592 - 162.000i) q^{87} +(-818.394 + 472.500i) q^{88} +(-597.000 + 1034.03i) q^{89} +(-826.000 + 715.337i) q^{91} +69.0000i q^{92} +(152.420 + 88.0000i) q^{93} +(67.5000 + 116.913i) q^{94} +(-45.0000 + 77.9423i) q^{96} +902.000i q^{97} +(636.529 - 808.500i) q^{98} -1035.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 24 q^{6} - 46 q^{9} + 90 q^{11} + 42 q^{14} + 142 q^{16} - 242 q^{19} - 140 q^{21} + 84 q^{24} - 354 q^{26} + 648 q^{29} + 176 q^{31} + 648 q^{34} - 92 q^{36} - 236 q^{39} + 780 q^{41} - 90 q^{44}+ \cdots - 4140 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 24 * q^6 - 46 * q^9 + 90 * q^11 + 42 * q^14 + 142 * q^16 - 242 * q^19 - 140 * q^21 + 84 * q^24 - 354 * q^26 + 648 * q^29 + 176 * q^31 + 648 * q^34 - 92 * q^36 - 236 * q^39 + 780 * q^41 - 90 * q^44 - 414 * q^46 - 196 * q^49 - 216 * q^51 + 600 * q^54 + 1176 * q^56 - 720 * q^59 - 784 * q^61 - 1732 * q^64 - 540 * q^66 + 552 * q^69 + 192 * q^71 - 1554 * q^74 - 484 * q^76 + 1564 * q^79 - 842 * q^81 - 28 * q^84 + 1716 * q^86 - 2388 * q^89 - 3304 * q^91 + 270 * q^94 - 180 * q^96 - 4140 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.59808	−	1.50000i	−0.918559	−	0.530330i	−0.0353837	−	0.999374i	$-0.511265\pi$
$2$	−2.59808	−	1.50000i	−0.918559	−	0.530330i	−0.883175	+	0.469044i	$0.844599\pi$
$3$	1.73205	−	1.00000i	0.333333	−	0.192450i	−0.323987	−	0.946062i	$-0.605023\pi$
$3$	1.73205	−	1.00000i	0.333333	−	0.192450i	0.657320	+	0.753612i	$0.271690\pi$
$4$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$5$		0			0
$5$		0			0
$6$	−6.00000			−0.408248
$7$	−12.1244	−	14.0000i	−0.654654	−	0.755929i
$7$	−12.1244	−	14.0000i	−0.654654	−	0.755929i
$8$			21.0000i			0.928078i
$9$	−11.5000	+	19.9186i	−0.425926	+	0.737725i
$10$		0			0
$11$	22.5000	+	38.9711i	0.616728	+	1.06820i	0.990079	+	0.140514i	$0.0448754\pi$
$11$	22.5000	+	38.9711i	0.616728	+	1.06820i	−0.373351	+	0.927690i	$0.621791\pi$
$12$	1.73205	+	1.00000i	0.0416667	+	0.0240563i
$13$		−	59.0000i		−	1.25874i	−0.777105	−	0.629371i	$-0.783312\pi$
$13$		−	59.0000i		−	1.25874i	0.777105	−	0.629371i	$-0.216688\pi$
$14$	10.5000	+	54.5596i	0.200446	+	1.04155i
$15$		0			0
$16$	35.5000	−	61.4878i	0.554688	−	0.960747i
$17$	−46.7654	+	27.0000i	−0.667192	+	0.385204i	−0.795012	−	0.606594i	$-0.792535\pi$
$17$	−46.7654	+	27.0000i	−0.667192	+	0.385204i	0.127820	+	0.991797i	$0.459202\pi$
$18$	59.7558	−	34.5000i	0.782476	−	0.451763i
$19$	−60.5000	+	104.789i	−0.730508	+	1.26528i	0.226158	+	0.974091i	$0.427383\pi$
$19$	−60.5000	+	104.789i	−0.730508	+	1.26528i	−0.956666	+	0.291186i	$0.905950\pi$
$20$		0			0
$21$	−35.0000	−	12.1244i	−0.363696	−	0.125988i
$22$		−	135.000i		−	1.30828i
$23$	59.7558	+	34.5000i	0.541736	+	0.312772i	0.745782	−	0.666190i	$-0.232076\pi$
$23$	59.7558	+	34.5000i	0.541736	+	0.312772i	−0.204046	+	0.978961i	$0.565409\pi$
$24$	21.0000	+	36.3731i	0.178609	+	0.309359i
$25$		0			0
$26$	−88.5000	+	153.286i	−0.667549	+	1.15623i
$27$			100.000i			0.712778i
$28$	6.06218	−	17.5000i	0.0409159	−	0.118114i
$29$	162.000			1.03733			0.518666	−	0.854977i	$-0.326429\pi$
$29$	162.000			1.03733			0.518666	+	0.854977i	$0.326429\pi$
$30$		0			0
$31$	44.0000	+	76.2102i	0.254924	+	0.441541i	0.964875	−	0.262710i	$-0.0846163\pi$
$31$	44.0000	+	76.2102i	0.254924	+	0.441541i	−0.709951	+	0.704251i	$0.751283\pi$
$32$	−38.9711	+	22.5000i	−0.215287	+	0.124296i
$33$	77.9423	+	45.0000i	0.411152	+	0.237379i
$34$	162.000			0.817140
$35$		0			0
$36$	−23.0000			−0.106481
$37$	224.301	+	129.500i	0.996616	+	0.575396i	0.907245	−	0.420602i	$-0.138181\pi$
$37$	224.301	+	129.500i	0.996616	+	0.575396i	0.0893706	+	0.995998i	$0.471514\pi$
$38$	314.367	−	181.500i	1.34203	−	0.774821i
$39$	−59.0000	−	102.191i	−0.242245	−	0.419581i
$40$		0			0
$41$	195.000			0.742778			0.371389	−	0.928477i	$-0.378882\pi$
$41$	195.000			0.742778			0.371389	+	0.928477i	$0.378882\pi$
$42$	72.7461	+	84.0000i	0.267261	+	0.308607i
$43$			286.000i			1.01429i	0.861860	+	0.507146i	$0.169300\pi$
$43$			286.000i			1.01429i	−0.861860	+	0.507146i	$0.830700\pi$
$44$	−22.5000	+	38.9711i	−0.0770910	+	0.133525i
$45$		0			0
$46$	−103.500	−	179.267i	−0.331744	−	0.574598i
$47$	−38.9711	−	22.5000i	−0.120947	−	0.0698290i	0.438306	−	0.898826i	$-0.355579\pi$
$47$	−38.9711	−	22.5000i	−0.120947	−	0.0698290i	−0.559253	+	0.828997i	$0.688912\pi$
$48$		−	142.000i		−	0.426999i
$49$	−49.0000	+	339.482i	−0.142857	+	0.989743i
$50$		0			0
$51$	−54.0000	+	93.5307i	−0.148265	+	0.256802i
$52$	51.0955	−	29.5000i	0.136263	−	0.0786714i
$53$	−517.017	+	298.500i	−1.33996	+	0.773625i	−0.986801	−	0.161939i	$-0.948225\pi$
$53$	−517.017	+	298.500i	−1.33996	+	0.773625i	−0.353157	+	0.935564i	$0.614892\pi$
$54$	150.000	−	259.808i	0.378008	−	0.654729i
$55$		0			0
$56$	294.000	−	254.611i	0.701561	−	0.607569i
$57$			242.000i			0.562345i
$58$	−420.888	−	243.000i	−0.952851	−	0.550129i
$59$	−180.000	−	311.769i	−0.397187	−	0.687947i	0.596191	−	0.802843i	$-0.296680\pi$
$59$	−180.000	−	311.769i	−0.397187	−	0.687947i	−0.993378	+	0.114895i	$0.963347\pi$
$60$		0			0
$61$	−196.000	+	339.482i	−0.411397	+	0.712561i	−0.995043	−	0.0994477i	$-0.968292\pi$
$61$	−196.000	+	339.482i	−0.411397	+	0.712561i	0.583646	+	0.812009i	$0.301626\pi$
$62$		−	264.000i		−	0.540775i
$63$	418.290	−	80.5000i	0.836502	−	0.160985i
$64$	−433.000			−0.845703
$65$		0			0
$66$	−135.000	−	233.827i	−0.251778	−	0.436092i
$67$	−242.487	+	140.000i	−0.442157	+	0.255279i	−0.704512	−	0.709692i	$-0.748834\pi$
$67$	−242.487	+	140.000i	−0.442157	+	0.255279i	0.262355	+	0.964971i	$0.415501\pi$
$68$	−46.7654	−	27.0000i	−0.0833990	−	0.0481505i
$69$	138.000			0.240772
$70$		0			0
$71$	48.0000			0.0802331			0.0401166	−	0.999195i	$-0.487227\pi$
$71$	48.0000			0.0802331			0.0401166	+	0.999195i	$0.487227\pi$
$72$	−418.290	−	241.500i	−0.684666	−	0.395292i
$73$	−578.505	+	334.000i	−0.927519	+	0.535503i	−0.886026	−	0.463635i	$-0.846545\pi$
$73$	−578.505	+	334.000i	−0.927519	+	0.535503i	−0.0414929	+	0.999139i	$0.513211\pi$
$74$	−388.500	−	672.902i	−0.610300	−	1.05707i
$75$		0			0
$76$	−121.000			−0.182627
$77$	272.798	−	787.500i	0.403743	−	1.16551i
$78$			354.000i			0.513880i
$79$	391.000	−	677.232i	0.556847	−	0.964488i	−0.440910	−	0.897551i	$-0.645344\pi$
$79$	391.000	−	677.232i	0.556847	−	0.964488i	0.997757	−	0.0669365i	$-0.0213225\pi$
$80$		0			0
$81$	−210.500	−	364.597i	−0.288752	−	0.500133i
$82$	−506.625	−	292.500i	−0.682285	−	0.393917i
$83$		−	768.000i		−	1.01565i	−0.861460	−	0.507825i	$-0.830450\pi$
$83$		−	768.000i		−	1.01565i	0.861460	−	0.507825i	$-0.169550\pi$
$84$	−7.00000	−	36.3731i	−0.00909241	−	0.0472456i
$85$		0			0
$86$	429.000	−	743.050i	0.537910	−	0.931687i
$87$	280.592	−	162.000i	0.345778	−	0.199635i
$88$	−818.394	+	472.500i	−0.991376	+	0.572371i
$89$	−597.000	+	1034.03i	−0.711032	+	1.23154i	0.253438	+	0.967352i	$0.418439\pi$
$89$	−597.000	+	1034.03i	−0.711032	+	1.23154i	−0.964470	+	0.264192i	$0.914895\pi$
$90$		0			0
$91$	−826.000	+	715.337i	−0.951520	+	0.824041i
$92$			69.0000i			0.0781929i
$93$	152.420	+	88.0000i	0.169949	+	0.0981202i
$94$	67.5000	+	116.913i	0.0740648	+	0.128284i
$95$		0			0
$96$	−45.0000	+	77.9423i	−0.0478416	+	0.0828641i
$97$			902.000i			0.944167i	0.881554	+	0.472084i	$0.156498\pi$
$97$			902.000i			0.944167i	−0.881554	+	0.472084i	$0.843502\pi$
$98$	636.529	−	808.500i	0.656113	−	0.833376i
$99$	−1035.00			−1.05072
$100$		0			0
$101$	−342.000	−	592.361i	−0.336933	−	0.583586i	0.646921	−	0.762557i	$-0.276056\pi$
$101$	−342.000	−	592.361i	−0.336933	−	0.583586i	−0.983854	+	0.178971i	$0.942723\pi$
$102$	280.592	−	162.000i	0.272380	−	0.157259i
$103$	−1312.89	−	758.000i	−1.25595	−	0.725126i	−0.283669	−	0.958922i	$-0.591552\pi$
$103$	−1312.89	−	758.000i	−1.25595	−	0.725126i	−0.972286	+	0.233796i	$0.924885\pi$
$104$	1239.00			1.16821
$105$		0			0
$106$	1791.00			1.64111
$107$	633.931	+	366.000i	0.572751	+	0.330678i	0.758247	−	0.651967i	$-0.226056\pi$
$107$	633.931	+	366.000i	0.572751	+	0.330678i	−0.185496	+	0.982645i	$0.559389\pi$
$108$	−86.6025	+	50.0000i	−0.0771605	+	0.0445486i
$109$	−800.000	−	1385.64i	−0.702992	−	1.21762i	−0.967411	−	0.253210i	$-0.918514\pi$
$109$	−800.000	−	1385.64i	−0.702992	−	1.21762i	0.264420	−	0.964408i	$-0.414820\pi$
$110$		0			0
$111$	518.000			0.442940
$112$	−1291.24	+	248.500i	−1.08938	+	0.209652i
$113$			1392.00i			1.15883i	0.815031	+	0.579417i	$0.196720\pi$
$113$			1392.00i			1.15883i	−0.815031	+	0.579417i	$0.803280\pi$
$114$	363.000	−	628.734i	0.298229	−	0.516547i
$115$		0			0
$116$	81.0000	+	140.296i	0.0648333	+	0.112295i
$117$	1175.20	+	678.500i	0.928606	+	0.536131i
$118$			1080.00i			0.842560i
$119$	945.000	+	327.358i	0.727966	+	0.252175i
$120$		0			0
$121$	−347.000	+	601.022i	−0.260706	+	0.451556i
$122$	1018.45	−	588.000i	0.755785	−	0.436353i
$123$	337.750	−	195.000i	0.247593	−	0.142948i
$124$	−44.0000	+	76.2102i	−0.0318655	+	0.0551926i
$125$		0			0
$126$	−1207.50	−	418.290i	−0.853751	−	0.295748i
$127$			803.000i			0.561061i	0.959845	+	0.280530i	$0.0905104\pi$
$127$			803.000i			0.561061i	−0.959845	+	0.280530i	$0.909490\pi$
$128$	1436.74	+	829.500i	0.992115	+	0.572798i
$129$	286.000	+	495.367i	0.195201	+	0.338098i
$130$		0			0
$131$	−1009.50	+	1748.51i	−0.673286	+	1.16617i	0.303681	+	0.952774i	$0.401784\pi$
$131$	−1009.50	+	1748.51i	−0.673286	+	1.16617i	−0.976967	+	0.213391i	$0.931549\pi$
$132$			90.0000i			0.0593447i
$133$	2200.57	−	423.500i	1.43469	−	0.276106i
$134$	840.000			0.541529
$135$		0			0
$136$	−567.000	−	982.073i	−0.357499	−	0.619206i
$137$	51.9615	−	30.0000i	0.0324042	−	0.0187086i	−0.483710	−	0.875228i	$-0.660711\pi$
$137$	51.9615	−	30.0000i	0.0324042	−	0.0187086i	0.516115	+	0.856520i	$0.327378\pi$
$138$	−358.535	−	207.000i	−0.221163	−	0.127688i
$139$	1708.00			1.04224			0.521118	−	0.853485i	$-0.325515\pi$
$139$	1708.00			1.04224			0.521118	+	0.853485i	$0.325515\pi$
$140$		0			0
$141$	−90.0000			−0.0537544
$142$	−124.708	−	72.0000i	−0.0736988	−	0.0425500i
$143$	2299.30	−	1327.50i	1.34459	−	0.776302i
$144$	816.500	+	1414.22i	0.472512	+	0.818414i
$145$		0			0
$146$	2004.00			1.13597
$147$	254.611	+	637.000i	0.142857	+	0.357407i
$148$			259.000i			0.143849i
$149$	−543.000	+	940.504i	−0.298552	+	0.517108i	−0.975805	−	0.218643i	$-0.929837\pi$
$149$	−543.000	+	940.504i	−0.298552	+	0.517108i	0.677253	+	0.735751i	$0.263170\pi$
$150$		0			0
$151$	1433.00	+	2482.03i	0.772291	+	1.33765i	0.936305	+	0.351189i	$0.114222\pi$
$151$	1433.00	+	2482.03i	0.772291	+	1.33765i	−0.164014	+	0.986458i	$0.552444\pi$
$152$	−2200.57	−	1270.50i	−1.17428	−	0.677968i
$153$		−	1242.00i		−	0.656273i
$154$	−1890.00	+	1636.79i	−0.988965	+	0.856468i
$155$		0			0
$156$	59.0000	−	102.191i	0.0302806	−	0.0524476i
$157$	−198.320	+	114.500i	−0.100813	+	0.0582044i	−0.549559	−	0.835455i	$-0.685204\pi$
$157$	−198.320	+	114.500i	−0.100813	+	0.0582044i	0.448746	+	0.893659i	$0.351871\pi$
$158$	−2031.70	+	1173.00i	−1.02299	+	0.590626i
$159$	−597.000	+	1034.03i	−0.297768	+	0.515750i
$160$		0			0
$161$	−241.500	−	1254.87i	−0.118217	−	0.614271i
$162$			1263.00i			0.612535i
$163$	−1063.48	−	614.000i	−0.511031	−	0.295044i	0.222226	−	0.974995i	$-0.428668\pi$
$163$	−1063.48	−	614.000i	−0.511031	−	0.295044i	−0.733258	+	0.679951i	$0.762001\pi$
$164$	97.5000	+	168.875i	0.0464236	+	0.0804080i
$165$		0			0
$166$	−1152.00	+	1995.32i	−0.538630	+	0.932934i
$167$		−	1929.00i		−	0.893835i	−0.894575	−	0.446918i	$-0.852522\pi$
$167$		−	1929.00i		−	0.893835i	0.894575	−	0.446918i	$-0.147478\pi$
$168$	254.611	−	735.000i	0.116927	−	0.337539i
$169$	−1284.00			−0.584433
$170$		0			0
$171$	−1391.50	−	2410.15i	−0.622285	−	1.07783i
$172$	−247.683	+	143.000i	−0.109800	+	0.0633933i
$173$	−605.352	−	349.500i	−0.266035	−	0.153595i	0.361049	−	0.932547i	$-0.382419\pi$
$173$	−605.352	−	349.500i	−0.266035	−	0.153595i	−0.627084	+	0.778951i	$0.715752\pi$
$174$	−972.000			−0.423489
$175$		0			0
$176$	3195.00			1.36836
$177$	−623.538	−	360.000i	−0.264791	−	0.152877i
$178$	3102.10	−	1791.00i	1.30625	−	0.754164i
$179$	1558.50	+	2699.40i	0.650770	+	1.12717i	0.982936	+	0.183945i	$0.0588870\pi$
$179$	1558.50	+	2699.40i	0.650770	+	1.12717i	−0.332167	+	0.943221i	$0.607780\pi$
$180$		0			0
$181$	−1798.00			−0.738366			−0.369183	−	0.929357i	$-0.620362\pi$
$181$	−1798.00			−0.738366			−0.369183	+	0.929357i	$0.620362\pi$
$182$	3219.02	−	619.500i	1.31104	−	0.252310i
$183$			784.000i			0.316694i
$184$	−724.500	+	1254.87i	−0.290276	+	0.502773i
$185$		0			0
$186$	−264.000	−	457.261i	−0.104072	−	0.180258i
$187$	−2104.44	−	1215.00i	−0.822952	−	0.475132i
$188$		−	45.0000i		−	0.0174572i
$189$	1400.00	−	1212.44i	0.538810	−	0.466623i
$190$		0			0
$191$	1194.00	−	2068.07i	0.452329	−	0.783457i	−0.546201	−	0.837654i	$-0.683927\pi$
$191$	1194.00	−	2068.07i	0.452329	−	0.783457i	0.998530	+	0.0541974i	$0.0172600\pi$
$192$	−749.978	+	433.000i	−0.281901	+	0.162756i
$193$	−235.559	+	136.000i	−0.0878544	+	0.0507228i	−0.543284	−	0.839549i	$-0.682819\pi$
$193$	−235.559	+	136.000i	−0.0878544	+	0.0507228i	0.455429	+	0.890272i	$0.349486\pi$
$194$	1353.00	−	2343.46i	0.500720	−	0.867273i
$195$		0			0
$196$	−318.500	+	127.306i	−0.116071	+	0.0463942i
$197$		−	2109.00i		−	0.762741i	−0.924422	−	0.381371i	$-0.875452\pi$
$197$		−	2109.00i		−	0.762741i	0.924422	−	0.381371i	$-0.124548\pi$
$198$	2689.01	+	1552.50i	0.965149	+	0.557229i
$199$	712.000	+	1233.22i	0.253630	+	0.439300i	0.964522	−	0.264001i	$-0.0850422\pi$
$199$	712.000	+	1233.22i	0.253630	+	0.439300i	−0.710893	+	0.703301i	$0.751709\pi$
$200$		0			0
$201$	−280.000	+	484.974i	−0.0982571	+	0.170186i
$202$			2052.00i			0.714744i
$203$	−1964.15	−	2268.00i	−0.679094	−	0.784150i
$204$	−108.000			−0.0370662
$205$		0			0
$206$	2274.00	+	3938.68i	0.769112	+	1.33214i
$207$	−1374.38	+	793.500i	−0.461479	+	0.266435i
$208$	−3627.78	−	2094.50i	−1.20933	−	0.698209i
$209$	−5445.00			−1.80210
$210$		0			0
$211$	−3625.00			−1.18273			−0.591363	−	0.806405i	$-0.701410\pi$
$211$	−3625.00			−1.18273			−0.591363	+	0.806405i	$0.701410\pi$
$212$	−517.017	−	298.500i	−0.167495	−	0.0967031i
$213$	83.1384	−	48.0000i	0.0267444	−	0.0154409i
$214$	−1098.00	−	1901.79i	−0.350737	−	0.607494i
$215$		0			0
$216$	−2100.00			−0.661513
$217$	533.472	−	1540.00i	0.166887	−	0.481760i
$218$			4800.00i			1.49127i
$219$	−668.000	+	1157.01i	−0.206115	+	0.357002i
$220$		0			0
$221$	1593.00	+	2759.16i	0.484872	+	0.839823i
$222$	−1345.80	−	777.000i	−0.406867	−	0.234905i
$223$			4960.00i			1.48944i	0.667374	+	0.744722i	$0.267418\pi$
$223$			4960.00i			1.48944i	−0.667374	+	0.744722i	$0.732582\pi$
$224$	787.500	+	272.798i	0.234898	+	0.0813709i
$225$		0			0
$226$	2088.00	−	3616.52i	0.614565	−	1.06446i
$227$	−1299.04	+	750.000i	−0.379825	+	0.219292i	−0.677742	−	0.735300i	$-0.737041\pi$
$227$	−1299.04	+	750.000i	−0.379825	+	0.219292i	0.297917	+	0.954592i	$0.403708\pi$
$228$	−209.578	+	121.000i	−0.0608757	+	0.0351466i
$229$	3046.00	−	5275.83i	0.878975	−	1.52243i	0.0265085	−	0.999649i	$-0.491561\pi$
$229$	3046.00	−	5275.83i	0.878975	−	1.52243i	0.852467	−	0.522781i	$-0.175106\pi$
$230$		0			0
$231$	−315.000	−	1636.79i	−0.0897207	−	0.466202i
$232$			3402.00i			0.962725i
$233$	119.512	+	69.0000i	0.0336028	+	0.0194006i	0.516707	−	0.856162i	$-0.327158\pi$
$233$	119.512	+	69.0000i	0.0336028	+	0.0194006i	−0.483104	+	0.875563i	$0.660491\pi$
$234$	−2035.50	−	3525.59i	−0.568653	−	0.984936i
$235$		0			0
$236$	180.000	−	311.769i	0.0496483	−	0.0859934i
$237$		−	1564.00i		−	0.428661i
$238$	−1964.15	−	2268.00i	−0.534944	−	0.617700i
$239$	5502.00			1.48910			0.744550	−	0.667567i	$-0.232664\pi$
$239$	5502.00			1.48910			0.744550	+	0.667567i	$0.232664\pi$
$240$		0			0
$241$	−1775.50	−	3075.26i	−0.474564	−	0.821970i	0.525011	−	0.851095i	$-0.324061\pi$
$241$	−1775.50	−	3075.26i	−0.474564	−	0.821970i	−0.999576	+	0.0291256i	$0.990728\pi$
$242$	1803.06	−	1041.00i	0.478948	−	0.276521i
$243$	−3067.46	−	1771.00i	−0.809785	−	0.467530i
$244$	−392.000			−0.102849
$245$		0			0
$246$	−1170.00			−0.303238
$247$	6182.56	+	3569.50i	1.59266	+	0.919522i
$248$	−1600.41	+	924.000i	−0.409784	+	0.236589i
$249$	−768.000	−	1330.22i	−0.195462	−	0.338550i
$250$		0			0
$251$	7065.00			1.77665			0.888324	−	0.459216i	$-0.151870\pi$
$251$	7065.00			1.77665			0.888324	+	0.459216i	$0.151870\pi$
$252$	278.860	+	322.000i	0.0697085	+	0.0804924i
$253$			3105.00i			0.771580i
$254$	1204.50	−	2086.26i	0.297547	−	0.515367i
$255$		0			0
$256$	−756.500	−	1310.30i	−0.184692	−	0.319897i
$257$	3533.38	+	2040.00i	0.857613	+	0.495143i	0.863212	−	0.504842i	$-0.168449\pi$
$257$	3533.38	+	2040.00i	0.857613	+	0.495143i	−0.00559954	+	0.999984i	$0.501782\pi$
$258$		−	1716.00i		−	0.414083i
$259$	−906.500	−	4710.31i	−0.217479	−	1.13006i
$260$		0			0
$261$	−1863.00	+	3226.81i	−0.441827	+	0.765267i
$262$	5245.52	−	3028.50i	1.23690	−	0.714127i
$263$	2847.49	−	1644.00i	0.667619	−	0.385450i	−0.127555	−	0.991832i	$-0.540713\pi$
$263$	2847.49	−	1644.00i	0.667619	−	0.385450i	0.795174	+	0.606381i	$0.207380\pi$
$264$	−945.000	+	1636.79i	−0.220306	+	0.381581i
$265$		0			0
$266$	−6352.50	−	2200.57i	−1.46427	−	0.507239i
$267$			2388.00i			0.547353i
$268$	−242.487	−	140.000i	−0.0552696	−	0.0319099i
$269$	−1632.00	−	2826.71i	−0.369906	−	0.640697i	0.619644	−	0.784883i	$-0.287277\pi$
$269$	−1632.00	−	2826.71i	−0.369906	−	0.640697i	−0.989551	+	0.144186i	$0.953944\pi$
$270$		0			0
$271$	1376.00	−	2383.30i	0.308436	−	0.534226i	−0.669585	−	0.742736i	$-0.733528\pi$
$271$	1376.00	−	2383.30i	0.308436	−	0.534226i	0.978020	+	0.208510i	$0.0668612\pi$
$272$			3834.00i			0.854671i
$273$	−715.337	+	2065.00i	−0.158587	+	0.457800i
$274$	−180.000			−0.0396869
$275$		0			0
$276$	69.0000	+	119.512i	0.0150482	+	0.0260643i
$277$	−4061.66	+	2345.00i	−0.881016	+	0.508655i	−0.870993	−	0.491295i	$-0.836524\pi$
$277$	−4061.66	+	2345.00i	−0.881016	+	0.508655i	−0.0100228	+	0.999950i	$0.503190\pi$
$278$	−4437.51	−	2562.00i	−0.957354	−	0.552729i
$279$	−2024.00			−0.434314
$280$		0			0
$281$	7821.00			1.66036			0.830181	−	0.557494i	$-0.188237\pi$
$281$	7821.00			1.66036			0.830181	+	0.557494i	$0.188237\pi$
$282$	233.827	+	135.000i	0.0493765	+	0.0285076i
$283$	569.845	−	329.000i	0.119695	−	0.0691061i	−0.438957	−	0.898508i	$-0.644652\pi$
$283$	569.845	−	329.000i	0.119695	−	0.0691061i	0.558652	+	0.829402i	$0.311319\pi$
$284$	24.0000	+	41.5692i	0.00501457	+	0.00868549i
$285$		0			0
$286$	−7965.00			−1.64678
$287$	−2364.25	−	2730.00i	−0.486262	−	0.561487i
$288$		−	1035.00i		−	0.211764i
$289$	−998.500	+	1729.45i	−0.203236	+	0.352016i
$290$		0			0
$291$	902.000	+	1562.31i	0.181705	+	0.314722i
$292$	−578.505	−	334.000i	−0.115940	−	0.0669379i
$293$			5997.00i			1.19573i	0.801597	+	0.597864i	$0.203984\pi$
$293$			5997.00i			1.19573i	−0.801597	+	0.597864i	$0.796016\pi$
$294$	294.000	−	2036.89i	0.0583212	−	0.404061i
$295$		0			0
$296$	−2719.50	+	4710.31i	−0.534013	+	0.924937i
$297$	−3897.11	+	2250.00i	−0.761392	+	0.439590i
$298$	2821.51	−	1629.00i	0.548476	−	0.316663i
$299$	2035.50	−	3525.59i	0.393699	−	0.681907i
$300$		0			0
$301$	4004.00	−	3467.57i	0.766733	−	0.664011i
$302$		−	8598.00i		−	1.63828i
$303$	−1184.72	−	684.000i	−0.224622	−	0.129686i
$304$	4295.50	+	7440.02i	0.810407	+	1.40367i
$305$		0			0
$306$	−1863.00	+	3226.81i	−0.348041	+	0.602825i
$307$		−	6226.00i		−	1.15745i	−0.815523	−	0.578724i	$-0.803551\pi$
$307$		−	6226.00i		−	1.15745i	0.815523	−	0.578724i	$-0.196449\pi$
$308$	818.394	−	157.500i	0.151404	−	0.0291376i
$309$	−3032.00			−0.558202
$310$		0			0
$311$	−2340.00	−	4053.00i	−0.426653	−	0.738985i	0.569920	−	0.821700i	$-0.306974\pi$
$311$	−2340.00	−	4053.00i	−0.426653	−	0.738985i	−0.996573	+	0.0827149i	$0.973641\pi$
$312$	2146.01	−	1239.00i	0.389404	−	0.224822i
$313$	890.274	+	514.000i	0.160771	+	0.0928211i	0.578227	−	0.815876i	$-0.303745\pi$
$313$	890.274	+	514.000i	0.160771	+	0.0928211i	−0.417456	+	0.908697i	$0.637078\pi$
$314$	687.000			0.123470
$315$		0			0
$316$	782.000			0.139212
$317$	−7466.87	−	4311.00i	−1.32297	−	0.763817i	−0.338768	−	0.940870i	$-0.610010\pi$
$317$	−7466.87	−	4311.00i	−1.32297	−	0.763817i	−0.984201	+	0.177053i	$0.943344\pi$
$318$	3102.10	−	1791.00i	0.547036	−	0.315831i
$319$	3645.00	+	6313.33i	0.639752	+	1.10808i
$320$		0			0
$321$	1464.00			0.254556
$322$	−1254.87	+	3622.50i	−0.217178	+	0.626938i
$323$		−	6534.00i		−	1.12558i
$324$	210.500	−	364.597i	0.0360940	−	0.0625166i
$325$		0			0
$326$	1842.00	+	3190.44i	0.312942	+	0.542031i
$327$	−2771.28	−	1600.00i	−0.468661	−	0.270582i
$328$			4095.00i			0.689355i
$329$	157.500	+	818.394i	0.0263929	+	0.137141i
$330$		0			0
$331$	999.500	−	1731.18i	0.165974	−	0.287476i	−0.771027	−	0.636803i	$-0.780256\pi$
$331$	999.500	−	1731.18i	0.165974	−	0.287476i	0.937001	+	0.349327i	$0.113590\pi$
$332$	665.108	−	384.000i	0.109947	−	0.0634781i
$333$	−5158.91	+	2978.50i	−0.848969	+	0.490153i
$334$	−2893.50	+	5011.69i	−0.474028	+	0.821040i
$335$		0			0
$336$	−1988.00	+	1721.66i	−0.322781	+	0.279536i
$337$			5114.00i			0.826639i	0.910586	+	0.413319i	$0.135631\pi$
$337$			5114.00i			0.826639i	−0.910586	+	0.413319i	$0.864369\pi$
$338$	3335.93	+	1926.00i	0.536836	+	0.309943i
$339$	1392.00	+	2411.01i	0.223018	+	0.386278i
$340$		0			0
$341$	−1980.00	+	3429.46i	−0.314437	+	0.544621i
$342$			8349.00i			1.32006i
$343$	5346.84	−	3430.00i	0.841698	−	0.539949i
$344$	−6006.00			−0.941342
$345$		0			0
$346$	1048.50	+	1816.06i	0.162912	+	0.282173i
$347$	3741.23	−	2160.00i	0.578789	−	0.334164i	−0.181863	−	0.983324i	$-0.558213\pi$
$347$	3741.23	−	2160.00i	0.578789	−	0.334164i	0.760652	+	0.649160i	$0.224879\pi$
$348$	280.592	+	162.000i	0.0432222	+	0.0249543i
$349$	−7922.00			−1.21506			−0.607529	−	0.794298i	$-0.707839\pi$
$349$	−7922.00			−1.21506			−0.607529	+	0.794298i	$0.707839\pi$
$350$		0			0
$351$	5900.00			0.897204
$352$	−1753.70	−	1012.50i	−0.265547	−	0.153314i
$353$	−717.069	+	414.000i	−0.108118	+	0.0624221i	−0.553084	−	0.833125i	$-0.686549\pi$
$353$	−717.069	+	414.000i	−0.108118	+	0.0624221i	0.444966	+	0.895548i	$0.353216\pi$
$354$	1080.00	+	1870.61i	0.162151	+	0.280853i
$355$		0			0
$356$	−1194.00			−0.177758
$357$	1964.15	−	378.000i	0.291187	−	0.0560389i
$358$		−	9351.00i		−	1.38049i
$359$	−675.000	+	1169.13i	−0.0992344	+	0.171879i	−0.911368	−	0.411593i	$-0.864973\pi$
$359$	−675.000	+	1169.13i	−0.0992344	+	0.171879i	0.812134	+	0.583472i	$0.198306\pi$
$360$		0			0
$361$	−3891.00	−	6739.41i	−0.567284	−	0.982564i
$362$	4671.34	+	2697.00i	0.678233	+	0.391578i
$363$			1388.00i			0.200692i
$364$	−1032.50	−	357.668i	−0.148675	−	0.0515025i
$365$		0			0
$366$	1176.00	−	2036.89i	0.167952	−	0.290902i
$367$	2425.74	−	1400.50i	0.345020	−	0.199198i	−0.317470	−	0.948268i	$-0.602833\pi$
$367$	2425.74	−	1400.50i	0.345020	−	0.199198i	0.662490	+	0.749071i	$0.269500\pi$
$368$	4242.66	−	2449.50i	0.600989	−	0.346981i
$369$	−2242.50	+	3884.12i	−0.316368	+	0.547966i
$370$		0			0
$371$	10447.5	+	3619.12i	1.46201	+	0.506456i
$372$			176.000i			0.0245300i
$373$	5717.50	+	3301.00i	0.793675	+	0.458229i	0.841255	−	0.540639i	$-0.181817\pi$
$373$	5717.50	+	3301.00i	0.793675	+	0.458229i	−0.0475795	+	0.998867i	$0.515151\pi$
$374$	3645.00	+	6313.33i	0.503953	+	0.872872i
$375$		0			0
$376$	472.500	−	818.394i	0.0648067	−	0.112249i
$377$		−	9558.00i		−	1.30573i
$378$	−5455.96	+	1050.00i	−0.742392	+	0.142873i
$379$	8305.00			1.12559			0.562796	−	0.826596i	$-0.309726\pi$
$379$	8305.00			1.12559			0.562796	+	0.826596i	$0.309726\pi$
$380$		0			0
$381$	803.000	+	1390.84i	0.107976	+	0.187020i
$382$	−6204.21	+	3582.00i	−0.830981	+	0.479767i
$383$	818.394	+	472.500i	0.109185	+	0.0630382i	0.553598	−	0.832784i	$-0.313254\pi$
$383$	818.394	+	472.500i	0.109185	+	0.0630382i	−0.444413	+	0.895822i	$0.646588\pi$
$384$	3318.00			0.440940
$385$		0			0
$386$	816.000			0.107599
$387$	−5696.72	−	3289.00i	−0.748270	−	0.432014i
$388$	−781.155	+	451.000i	−0.102209	+	0.0590105i
$389$	6018.00	+	10423.5i	0.784382	+	1.35859i	0.929367	+	0.369156i	$0.120353\pi$
$389$	6018.00	+	10423.5i	0.784382	+	1.35859i	−0.144985	+	0.989434i	$0.546313\pi$
$390$		0			0
$391$	−3726.00			−0.481923
$392$	−7129.12	−	1029.00i	−0.918559	−	0.132583i
$393$			4038.00i			0.518296i
$394$	−3163.50	+	5479.34i	−0.404505	+	0.700623i
$395$		0			0
$396$	−517.500	−	896.336i	−0.0656701	−	0.113744i
$397$	2336.54	+	1349.00i	0.295384	+	0.170540i	0.640367	−	0.768069i	$-0.278782\pi$
$397$	2336.54	+	1349.00i	0.295384	+	0.170540i	−0.344983	+	0.938609i	$0.612115\pi$
$398$		−	4272.00i		−	0.538030i
$399$	3388.00	−	2934.09i	0.425093	−	0.368141i
$400$		0			0
$401$	−3526.50	+	6108.08i	−0.439165	+	0.760655i	−0.997625	−	0.0688756i	$-0.978059\pi$
$401$	−3526.50	+	6108.08i	−0.439165	+	0.760655i	0.558461	+	0.829531i	$0.311392\pi$
$402$	1454.92	−	840.000i	0.180510	−	0.104217i
$403$	4496.40	−	2596.00i	0.555786	−	0.320883i
$404$	342.000	−	592.361i	0.0421167	−	0.0729482i
$405$		0			0
$406$	1701.00	+	8838.66i	0.207929	+	1.08043i
$407$			11655.0i			1.41945i
$408$	−1964.15	−	1134.00i	−0.238333	−	0.137601i
$409$	−5435.00	−	9413.70i	−0.657074	−	1.13809i	−0.981369	−	0.192130i	$-0.938460\pi$
$409$	−5435.00	−	9413.70i	−0.657074	−	1.13809i	0.324295	−	0.945956i	$-0.394873\pi$
$410$		0			0
$411$	60.0000	−	103.923i	0.00720093	−	0.0124724i
$412$		−	1516.00i		−	0.181281i
$413$	−2182.38	+	6300.00i	−0.260020	+	0.750612i
$414$	4761.00			0.565194
$415$		0			0
$416$	1327.50	+	2299.30i	0.156457	+	0.270991i
$417$	2958.34	−	1708.00i	0.347412	−	0.200578i
$418$	14146.5	+	8167.50i	1.65533	+	0.955707i
$419$	9729.00			1.13435			0.567175	−	0.823597i	$-0.308036\pi$
$419$	9729.00			1.13435			0.567175	+	0.823597i	$0.308036\pi$
$420$		0			0
$421$	−12550.0			−1.45285			−0.726425	−	0.687246i	$-0.758819\pi$
$421$	−12550.0			−1.45285			−0.726425	+	0.687246i	$0.758819\pi$
$422$	9418.03	+	5437.50i	1.08640	+	0.627235i
$423$	896.336	−	517.500i	0.103029	−	0.0594840i
$424$	−6268.50	−	10857.4i	−0.717984	−	1.24358i
$425$		0			0
$426$	−288.000			−0.0327550
$427$	7129.12	−	1372.00i	0.807968	−	0.155494i
$428$			732.000i			0.0826695i
$429$	2655.00	−	4598.59i	0.298799	−	0.517534i
$430$		0			0
$431$	−1494.00	−	2587.68i	−0.166969	−	0.289198i	0.770384	−	0.637580i	$-0.220065\pi$
$431$	−1494.00	−	2587.68i	−0.166969	−	0.289198i	−0.937353	+	0.348382i	$0.886731\pi$
$432$	6148.78	+	3550.00i	0.684799	+	0.395369i
$433$		−	16616.0i		−	1.84414i	−0.387019	−	0.922072i	$-0.626495\pi$
$433$		−	16616.0i		−	1.84414i	0.387019	−	0.922072i	$-0.373505\pi$
$434$	−3696.00	+	3200.83i	−0.408787	+	0.354020i
$435$		0			0
$436$	800.000	−	1385.64i	0.0878740	−	0.152202i
$437$	−7230.45	+	4174.50i	−0.791485	+	0.456964i
$438$	3471.03	−	2004.00i	0.378658	−	0.218618i
$439$	3673.00	−	6361.82i	0.399323	−	0.691647i	−0.594320	−	0.804229i	$-0.702579\pi$
$439$	3673.00	−	6361.82i	0.399323	−	0.691647i	0.993642	+	0.112581i	$0.0359119\pi$
$440$		0			0
$441$	−6198.50	−	4880.05i	−0.669312	−	0.526947i
$442$		−	9558.00i		−	1.02857i
$443$	10.3923	+	6.00000i	0.00111457	+	0.000643496i	0.500557	−	0.865703i	$-0.333129\pi$
$443$	10.3923	+	6.00000i	0.00111457	+	0.000643496i	−0.499443	+	0.866347i	$0.666462\pi$
$444$	259.000	+	448.601i	0.0276838	+	0.0479497i
$445$		0			0
$446$	7440.00	−	12886.5i	0.789897	−	1.36814i
$447$			2172.00i			0.229826i
$448$	5249.85	+	6062.00i	0.553643	+	0.639291i
$449$	−9669.00			−1.01628			−0.508138	−	0.861275i	$-0.669666\pi$
$449$	−9669.00			−1.01628			−0.508138	+	0.861275i	$0.669666\pi$
$450$		0			0
$451$	4387.50	+	7599.37i	0.458092	+	0.793438i
$452$	−1205.51	+	696.000i	−0.125448	+	0.0724272i
$453$	4964.06	+	2866.00i	0.514860	+	0.297255i
$454$	4500.00			0.465188
$455$		0			0
$456$	−5082.00			−0.521900
$457$	8343.29	+	4817.00i	0.854010	+	0.493063i	0.862002	−	0.506905i	$-0.169211\pi$
$457$	8343.29	+	4817.00i	0.854010	+	0.493063i	−0.00799181	+	0.999968i	$0.502544\pi$
$458$	−15827.5	+	9138.00i	−1.61478	+	0.932294i
$459$	−2700.00	−	4676.54i	−0.274565	−	0.475560i
$460$		0			0
$461$	−342.000			−0.0345521			−0.0172761	−	0.999851i	$-0.505499\pi$
$461$	−342.000			−0.0345521			−0.0172761	+	0.999851i	$0.505499\pi$
$462$	−1636.79	+	4725.00i	−0.164827	+	0.475816i
$463$		−	2411.00i		−	0.242006i	−0.992652	−	0.121003i	$-0.961389\pi$
$463$		−	2411.00i		−	0.242006i	0.992652	−	0.121003i	$-0.0386110\pi$
$464$	5751.00	−	9961.02i	0.575395	−	0.996614i
$465$		0			0
$466$	−207.000	−	358.535i	−0.0205774	−	0.0356412i
$467$	1044.43	+	603.000i	0.103491	+	0.0597506i	0.550852	−	0.834603i	$-0.314303\pi$
$467$	1044.43	+	603.000i	0.103491	+	0.0597506i	−0.447361	+	0.894353i	$0.647636\pi$
$468$			1357.00i			0.134033i
$469$	4900.00	+	1697.41i	0.482433	+	0.167120i
$470$		0			0
$471$	−229.000	+	396.640i	−0.0224029	+	0.0388030i
$472$	6547.15	−	3780.00i	0.638468	−	0.368620i
$473$	−11145.7	+	6435.00i	−1.08347	+	0.625543i
$474$	−2346.00	+	4063.39i	−0.227332	+	0.393751i
$475$		0			0
$476$	189.000	+	982.073i	0.0181992	+	0.0945656i
$477$		−	13731.0i		−	1.31803i
$478$	−14294.6	−	8253.00i	−1.36783	−	0.789714i
$479$	−216.000	−	374.123i	−0.0206039	−	0.0356871i	0.855540	−	0.517737i	$-0.173226\pi$
$479$	−216.000	−	374.123i	−0.0206039	−	0.0356871i	−0.876144	+	0.482050i	$0.839892\pi$
$480$		0			0
$481$	7640.50	−	13233.7i	0.724276	−	1.25448i
$482$			10653.0i			1.00670i
$483$	−1673.16	−	1932.00i	−0.157622	−	0.182006i
$484$	−694.000			−0.0651766
$485$		0			0
$486$	5313.00	+	9202.39i	0.495890	+	0.858907i
$487$	−10302.2	+	5948.00i	−0.958602	+	0.553449i	−0.895742	−	0.444574i	$-0.853355\pi$
$487$	−10302.2	+	5948.00i	−0.958602	+	0.553449i	−0.0628592	+	0.998022i	$0.520022\pi$
$488$	−7129.12	−	4116.00i	−0.661312	−	0.381809i
$489$	−2456.00			−0.227125
$490$		0			0
$491$	−12276.0			−1.12833			−0.564163	−	0.825663i	$-0.690801\pi$
$491$	−12276.0			−1.12833			−0.564163	+	0.825663i	$0.690801\pi$
$492$	337.750	+	195.000i	0.0309491	+	0.0178685i
$493$	−7575.99	+	4374.00i	−0.692100	+	0.399584i
$494$	−10708.5	−	18547.7i	−0.975300	−	1.68927i
$495$		0			0
$496$	6248.00			0.565612
$497$	−581.969	−	672.000i	−0.0525249	−	0.0606505i
$498$			4608.00i			0.414637i
$499$	−5438.00	+	9418.89i	−0.487852	+	0.844985i	−0.999902	−	0.0139706i	$-0.995553\pi$
$499$	−5438.00	+	9418.89i	−0.487852	+	0.844985i	0.512050	+	0.858956i	$0.328886\pi$
$500$		0			0
$501$	−1929.00	−	3341.13i	−0.172019	−	0.297945i
$502$	−18355.4	−	10597.5i	−1.63196	−	0.942210i
$503$		−	12000.0i		−	1.06372i	−0.846831	−	0.531862i	$-0.821492\pi$
$503$		−	12000.0i		−	1.06372i	0.846831	−	0.531862i	$-0.178508\pi$
$504$	1690.50	+	8784.10i	0.149406	+	0.776339i
$505$		0			0
$506$	4657.50	−	8067.03i	0.409192	−	0.708741i
$507$	−2223.95	+	1284.00i	−0.194811	+	0.112474i
$508$	−695.418	+	401.500i	−0.0607366	+	0.0350663i
$509$	−5841.00	+	10116.9i	−0.508640	+	0.880990i	0.491310	+	0.870985i	$0.336518\pi$
$509$	−5841.00	+	10116.9i	−0.508640	+	0.880990i	−0.999950	+	0.0100055i	$0.996815\pi$
$510$		0			0
$511$	11690.0	+	4049.53i	1.01201	+	0.350569i
$512$		−	8733.00i		−	0.753804i
$513$	−10478.9	−	6050.00i	−0.901862	−	0.520690i
$514$	−6120.00	−	10600.2i	−0.525178	−	0.909635i
$515$		0			0
$516$	−286.000	+	495.367i	−0.0244001	+	0.0422622i
$517$		−	2025.00i		−	0.172262i
$518$	−4710.31	+	13597.5i	−0.399535	+	1.15336i
$519$	−1398.00			−0.118238
$520$		0			0
$521$	−4804.50	−	8321.64i	−0.404010	−	0.699765i	0.590196	−	0.807260i	$-0.299050\pi$
$521$	−4804.50	−	8321.64i	−0.404010	−	0.699765i	−0.994206	+	0.107495i	$0.965717\pi$
$522$	9680.43	−	5589.00i	0.811688	−	0.468628i
$523$	18349.3	+	10594.0i	1.53415	+	0.885742i	0.999164	+	0.0408820i	$0.0130168\pi$
$523$	18349.3	+	10594.0i	1.53415	+	0.885742i	0.534987	+	0.844860i	$0.320317\pi$
$524$	−2019.00			−0.168321
$525$		0			0
$526$	−9864.00			−0.817663
$527$	−4115.35	−	2376.00i	−0.340166	−	0.196395i
$528$	5533.90	−	3195.00i	0.456122	−	0.263342i
$529$	−3703.00	−	6413.78i	−0.304348	−	0.527146i
$530$		0			0
$531$	8280.00			0.676688
$532$	1467.05	+	1694.00i	0.119557	+	0.138053i
$533$		−	11505.0i		−	0.934966i
$534$	3582.00	−	6204.21i	0.290278	−	0.502776i
$535$		0			0
$536$	−2940.00	−	5092.23i	−0.236919	−	0.410356i
$537$	5398.80	+	3117.00i	0.433846	+	0.250481i
$538$			9792.00i			0.784690i
$539$	−14332.5	+	5728.76i	−1.14535	+	0.457802i
$540$		0			0
$541$	−4036.00	+	6990.56i	−0.320742	+	0.555541i	−0.980641	−	0.195813i	$-0.937265\pi$
$541$	−4036.00	+	6990.56i	−0.320742	+	0.555541i	0.659900	+	0.751354i	$0.270599\pi$
$542$	−7149.91	+	4128.00i	−0.566632	+	0.327145i
$543$	−3114.23	+	1798.00i	−0.246122	+	0.142099i
$544$	1215.00	−	2104.44i	0.0957586	−	0.165859i
$545$		0			0
$546$	4956.00	−	4292.02i	0.388456	−	0.336413i
$547$			344.000i			0.0268892i	0.999910	+	0.0134446i	$0.00427967\pi$
$547$			344.000i			0.0268892i	−0.999910	+	0.0134446i	$0.995720\pi$
$548$	51.9615	+	30.0000i	0.00405052	+	0.00233857i
$549$	−4508.00	−	7808.09i	−0.350449	−	0.606996i
$550$		0			0
$551$	−9801.00	+	16975.8i	−0.757780	+	1.31251i
$552$			2898.00i			0.223455i
$553$	−14221.9	+	2737.00i	−1.09363	+	0.210468i
$554$	14070.0			1.07902
$555$		0			0
$556$	854.000	+	1479.17i	0.0651397	+	0.112825i
$557$	15902.8	−	9181.50i	1.20974	−	0.698443i	0.247036	−	0.969006i	$-0.420543\pi$
$557$	15902.8	−	9181.50i	1.20974	−	0.698443i	0.962702	+	0.270563i	$0.0872100\pi$
$558$	5258.51	+	3036.00i	0.398943	+	0.230330i
$559$	16874.0			1.27673
$560$		0			0
$561$	−4860.00			−0.365756
$562$	−20319.6	−	11731.5i	−1.52514	−	0.880540i
$563$	5450.76	−	3147.00i	0.408033	−	0.235578i	−0.281912	−	0.959440i	$-0.590968\pi$
$563$	5450.76	−	3147.00i	0.408033	−	0.235578i	0.689944	+	0.723863i	$0.257635\pi$
$564$	−45.0000	−	77.9423i	−0.00335965	−	0.00581908i
$565$		0			0
$566$	−1974.00			−0.146596
$567$	−2552.18	+	7367.50i	−0.189032	+	0.545689i
$568$			1008.00i			0.0744626i
$569$	5866.50	−	10161.1i	0.432226	−	0.748637i	−0.564839	−	0.825201i	$-0.691062\pi$
$569$	5866.50	−	10161.1i	0.432226	−	0.748637i	0.997065	+	0.0765642i	$0.0243950\pi$
$570$		0			0
$571$	−526.000	−	911.059i	−0.0385506	−	0.0667717i	0.846106	−	0.533014i	$-0.178941\pi$
$571$	−526.000	−	911.059i	−0.0385506	−	0.0667717i	−0.884657	+	0.466242i	$0.845607\pi$
$572$	2299.30	+	1327.50i	0.168074	+	0.0970377i
$573$		−	4776.00i		−	0.348203i
$574$	2047.50	+	10639.1i	0.148887	+	0.773638i
$575$		0			0
$576$	4979.50	−	8624.75i	0.360207	−	0.623897i
$577$	−11393.4	+	6578.00i	−0.822036	+	0.474603i	−0.851118	−	0.524974i	$-0.824075\pi$
$577$	−11393.4	+	6578.00i	−0.822036	+	0.474603i	0.0290821	+	0.999577i	$0.490742\pi$
$578$	5188.36	−	2995.50i	0.373369	−	0.215565i
$579$	−272.000	+	471.118i	−0.0195232	+	0.0338152i
$580$		0			0
$581$	−10752.0	+	9311.51i	−0.767759	+	0.664899i
$582$		−	5412.00i		−	0.385455i
$583$	−23265.8	−	13432.5i	−1.65278	−	0.954232i
$584$	−7014.00	−	12148.6i	−0.496989	−	0.860810i
$585$		0			0
$586$	8995.50	−	15580.7i	0.634131	−	1.09835i
$587$		−	13368.0i		−	0.939960i	−0.882677	−	0.469980i	$-0.844261\pi$
$587$		−	13368.0i		−	0.939960i	0.882677	−	0.469980i	$-0.155739\pi$
$588$	−424.352	+	539.000i	−0.0297619	+	0.0378027i
$589$	−10648.0			−0.744895
$590$		0			0
$591$	−2109.00	−	3652.90i	−0.146790	−	0.254247i
$592$	15925.3	−	9194.50i	1.10562	−	0.638330i
$593$	23091.7	+	13332.0i	1.59909	+	0.923237i	0.991662	+	0.128865i	$0.0411334\pi$
$593$	23091.7	+	13332.0i	1.59909	+	0.923237i	0.607431	+	0.794372i	$0.292200\pi$
$594$	13500.0			0.932511
$595$		0			0
$596$	−1086.00			−0.0746381
$597$	2466.44	+	1424.00i	0.169087	+	0.0976222i
$598$	−10576.8	+	6106.50i	−0.723271	+	0.417581i
$599$	3807.00	+	6593.92i	0.259682	+	0.449783i	0.966157	−	0.257955i	$-0.0830488\pi$
$599$	3807.00	+	6593.92i	0.259682	+	0.449783i	−0.706474	+	0.707739i	$0.749715\pi$
$600$		0			0
$601$	6410.00			0.435057			0.217529	−	0.976054i	$-0.430200\pi$
$601$	6410.00			0.435057			0.217529	+	0.976054i	$0.430200\pi$
$602$	−15604.0	+	3003.00i	−1.05643	+	0.203311i
$603$		−	6440.00i		−	0.434921i
$604$	−1433.00	+	2482.03i	−0.0965363	+	0.167206i
$605$		0			0
$606$	2052.00	+	3554.17i	0.137552	+	0.238248i
$607$	18592.7	+	10734.5i	1.24325	+	0.717792i	0.969755	−	0.244080i	$-0.0784861\pi$
$607$	18592.7	+	10734.5i	1.24325	+	0.717792i	0.273498	+	0.961873i	$0.411819\pi$
$608$		−	5445.00i		−	0.363197i
$609$	−5670.00	−	1964.15i	−0.377274	−	0.130692i
$610$		0			0
$611$	−1327.50	+	2299.30i	−0.0878967	+	0.152242i
$612$	1075.60	−	621.000i	0.0710436	−	0.0410171i
$613$	−3236.34	+	1868.50i	−0.213237	+	0.123113i	−0.602815	−	0.797881i	$-0.705954\pi$
$613$	−3236.34	+	1868.50i	−0.213237	+	0.123113i	0.389578	+	0.920994i	$0.372621\pi$
$614$	−9339.00	+	16175.6i	−0.613830	+	1.06318i
$615$		0			0
$616$	16537.5	+	5728.76i	1.08168	+	0.374705i
$617$			18078.0i			1.17957i	0.807561	+	0.589784i	$0.200787\pi$
$617$			18078.0i			1.17957i	−0.807561	+	0.589784i	$0.799213\pi$
$618$	7877.37	+	4548.00i	0.512741	+	0.296031i
$619$	6143.50	+	10640.9i	0.398915	+	0.690940i	0.993592	−	0.113024i	$-0.0360537\pi$
$619$	6143.50	+	10640.9i	0.398915	+	0.690940i	−0.594678	+	0.803964i	$0.702720\pi$
$620$		0			0
$621$	−3450.00	+	5975.58i	−0.222937	+	0.386138i
$622$			14040.0i			0.905069i
$623$	21714.7	−	4179.00i	1.39644	−	0.268745i
$624$	−8378.00			−0.537481
$625$		0			0
$626$	−1542.00	−	2670.82i	−0.0984516	−	0.170523i
$627$	−9431.02	+	5445.00i	−0.600699	+	0.346814i
$628$	−198.320	−	114.500i	−0.0126016	−	0.00727555i
$629$	−13986.0			−0.886579
$630$		0			0
$631$	−9580.00			−0.604396			−0.302198	−	0.953245i	$-0.597720\pi$
$631$	−9580.00			−0.604396			−0.302198	+	0.953245i	$0.597720\pi$
$632$	14221.9	+	8211.00i	0.895120	+	0.516798i
$633$	−6278.68	+	3625.00i	−0.394242	+	0.227616i
$634$	12933.0	+	22400.6i	0.810150	+	1.40322i
$635$		0			0
$636$	−1194.00			−0.0744421
$637$	20029.4	+	2891.00i	1.24583	+	0.179820i
$638$		−	21870.0i		−	1.35712i
$639$	−552.000	+	956.092i	−0.0341734	+	0.0591900i
$640$		0			0
$641$	−5389.50	−	9334.89i	−0.332094	−	0.575204i	0.650828	−	0.759225i	$-0.274422\pi$
$641$	−5389.50	−	9334.89i	−0.332094	−	0.575204i	−0.982922	+	0.184021i	$0.941089\pi$
$642$	−3803.58	−	2196.00i	−0.233825	−	0.134999i
$643$		−	8882.00i		−	0.544746i	−0.962192	−	0.272373i	$-0.912191\pi$
$643$		−	8882.00i		−	0.544746i	0.962192	−	0.272373i	$-0.0878085\pi$
$644$	966.000	−	836.581i	0.0591083	−	0.0511893i
$645$		0			0
$646$	−9801.00	+	16975.8i	−0.596928	+	1.03391i
$647$	−9542.73	+	5509.50i	−0.579851	+	0.334777i	−0.761074	−	0.648665i	$-0.775328\pi$
$647$	−9542.73	+	5509.50i	−0.579851	+	0.334777i	0.181223	+	0.983442i	$0.441994\pi$
$648$	7656.53	−	4420.50i	0.464162	−	0.267984i
$649$	8100.00	−	14029.6i	0.489912	−	0.848552i
$650$		0			0
$651$	−616.000	−	3200.83i	−0.0370859	−	0.192704i
$652$		−	1228.00i		−	0.0737610i
$653$	19332.3	+	11161.5i	1.15855	+	0.668887i	0.950955	−	0.309329i	$-0.100104\pi$
$653$	19332.3	+	11161.5i	1.15855	+	0.668887i	0.207591	+	0.978216i	$0.433438\pi$
$654$	4800.00	+	8313.84i	0.286995	+	0.497090i
$655$		0			0
$656$	6922.50	−	11990.1i	0.412009	−	0.713621i
$657$		−	15364.0i		−	0.912339i
$658$	818.394	−	2362.50i	0.0484868	−	0.139969i
$659$	11856.0			0.700826			0.350413	−	0.936595i	$-0.386041\pi$
$659$	11856.0			0.700826			0.350413	+	0.936595i	$0.386041\pi$
$660$		0			0
$661$	16622.0	+	28790.1i	0.978095	+	1.69411i	0.669318	+	0.742976i	$0.266586\pi$
$661$	16622.0	+	28790.1i	0.978095	+	1.69411i	0.308777	+	0.951134i	$0.400080\pi$
$662$	−5193.55	+	2998.50i	−0.304914	+	0.176042i
$663$	5518.31	+	3186.00i	0.323248	+	0.186627i
$664$	16128.0			0.942602
$665$		0			0
$666$	17871.0			1.03977
$667$	9680.43	+	5589.00i	0.561961	+	0.324448i
$668$	1670.56	−	964.500i	0.0967605	−	0.0558647i
$669$	4960.00	+	8590.97i	0.286644	+	0.496482i
$670$		0			0
$671$	−17640.0			−1.01488
$672$	1636.79	−	315.000i	0.0939590	−	0.0180824i
$673$			12322.0i			0.705763i	0.935668	+	0.352881i	$0.114798\pi$
$673$			12322.0i			0.705763i	−0.935668	+	0.352881i	$0.885202\pi$
$674$	7671.00	−	13286.6i	0.438392	−	0.759316i
$675$		0			0
$676$	−642.000	−	1111.98i	−0.0365271	−	0.0632668i
$677$	10909.3	+	6298.50i	0.619320	+	0.357564i	0.776604	−	0.629989i	$-0.216941\pi$
$677$	10909.3	+	6298.50i	0.619320	+	0.357564i	−0.157285	+	0.987553i	$0.550274\pi$
$678$		−	8352.00i		−	0.473092i
$679$	12628.0	−	10936.2i	0.713723	−	0.618103i
$680$		0			0
$681$	−1500.00	+	2598.08i	−0.0844055	+	0.146195i
$682$	10288.4	−	5940.00i	0.577658	−	0.333511i
$683$	7222.65	−	4170.00i	0.404637	−	0.233617i	−0.283846	−	0.958870i	$-0.591610\pi$
$683$	7222.65	−	4170.00i	0.404637	−	0.233617i	0.688483	+	0.725253i	$0.258277\pi$
$684$	1391.50	−	2410.15i	0.0777856	−	0.134729i
$685$		0			0
$686$	−19036.5	+	891.140i	−1.05950	+	0.0495975i
$687$		−	12184.0i		−	0.676636i
$688$	17585.5	+	10153.0i	0.974479	+	0.562616i
$689$	17611.5	+	30504.0i	0.973795	+	1.68666i
$690$		0			0
$691$	10100.0	−	17493.7i	0.556038	−	0.963086i	−0.441784	−	0.897121i	$-0.645654\pi$
$691$	10100.0	−	17493.7i	0.556038	−	0.963086i	0.997822	−	0.0659643i	$-0.0210124\pi$
$692$		−	699.000i		−	0.0383988i
$693$	12548.7	+	14490.0i	0.687859	+	0.794271i
$694$	−12960.0			−0.708869
$695$		0			0
$696$	3402.00	+	5892.44i	0.185277	+	0.320908i
$697$	−9119.25	+	5265.00i	−0.495576	+	0.286121i
$698$	20582.0	+	11883.0i	1.11610	+	0.644381i
$699$	276.000			0.0149346
$700$		0			0
$701$	474.000			0.0255388			0.0127694	−	0.999918i	$-0.495935\pi$
$701$	474.000			0.0255388			0.0127694	+	0.999918i	$0.495935\pi$
$702$	−15328.6	−	8850.00i	−0.824135	−	0.475814i
$703$	−27140.4	+	15669.5i	−1.45607	+	0.840663i
$704$	−9742.50	−	16874.5i	−0.521569	−	0.903383i
$705$		0			0
$706$	2484.00			0.132417
$707$	−4146.53	+	11970.0i	−0.220575	+	0.636744i
$708$		−	720.000i		−	0.0382193i
$709$	−12563.0	+	21759.8i	−0.665463	+	1.15262i	0.313696	+	0.949523i	$0.398433\pi$
$709$	−12563.0	+	21759.8i	−0.665463	+	1.15262i	−0.979160	+	0.203093i	$0.934901\pi$
$710$		0			0
$711$	8993.00	+	15576.3i	0.474351	+	0.821601i
$712$	−21714.7	−	12537.0i	−1.14297	−	0.659893i
$713$			6072.00i			0.318932i
$714$	−5670.00	−	1964.15i	−0.297191	−	0.102950i
$715$		0			0
$716$	−1558.50	+	2699.40i	−0.0813462	+	0.140896i
$717$	9529.74	−	5502.00i	0.496367	−	0.286577i
$718$	3507.40	−	2025.00i	0.182305	−	0.105254i
$719$	−3648.00	+	6318.52i	−0.189218	+	0.327734i	−0.944990	−	0.327100i	$-0.893928\pi$
$719$	−3648.00	+	6318.52i	−0.189218	+	0.327734i	0.755772	+	0.654835i	$0.227262\pi$
$720$		0			0
$721$	5306.00	+	27570.8i	0.274072	+	1.42412i
$722$			23346.0i			1.20339i
$723$	−6150.51	−	3551.00i	−0.316376	−	0.182660i
$724$	−899.000	−	1557.11i	−0.0461479	−	0.0799305i
$725$		0			0
$726$	2082.00	−	3606.13i	0.106433	−	0.184347i
$727$		−	15421.0i		−	0.786703i	−0.919388	−	0.393352i	$-0.871316\pi$
$727$		−	15421.0i		−	0.786703i	0.919388	−	0.393352i	$-0.128684\pi$
$728$	−15022.1	−	17346.0i	−0.764774	−	0.883085i
$729$	4283.00			0.217599
$730$		0			0
$731$	−7722.00	−	13374.9i	−0.390709	−	0.676728i
$732$	−678.964	+	392.000i	−0.0342831	+	0.0197934i
$733$	−25259.4	−	14583.5i	−1.27282	−	0.734862i	−0.297301	−	0.954784i	$-0.596086\pi$
$733$	−25259.4	−	14583.5i	−1.27282	−	0.734862i	−0.975517	+	0.219922i	$0.929420\pi$
$734$	−8403.00			−0.422562
$735$		0			0
$736$	−3105.00			−0.155505
$737$	−10911.9	−	6300.00i	−0.545381	−	0.314876i
$738$	11652.4	−	6727.50i	0.581206	−	0.335559i
$739$	−6690.50	−	11588.3i	−0.333037	−	0.576836i	0.650069	−	0.759875i	$-0.274740\pi$
$739$	−6690.50	−	11588.3i	−0.333037	−	0.576836i	−0.983106	+	0.183039i	$0.941407\pi$
$740$		0			0
$741$	14278.0			0.707848
$742$	−21714.7	−	25074.0i	−1.07436	−	1.24056i
$743$		−	5487.00i		−	0.270927i	−0.990782	−	0.135463i	$-0.956748\pi$
$743$		−	5487.00i		−	0.270927i	0.990782	−	0.135463i	$-0.0432523\pi$
$744$	−1848.00	+	3200.83i	−0.0910631	+	0.157726i
$745$		0			0
$746$	−9903.00	−	17152.5i	−0.486025	−	0.841820i
$747$	15297.5	+	8832.00i	0.749271	+	0.432592i
$748$		−	2430.00i		−	0.118783i
$749$	−2562.00	−	13312.5i	−0.124985	−	0.649439i
$750$		0			0
$751$	−3319.00	+	5748.68i	−0.161268	+	0.279324i	−0.935324	−	0.353793i	$-0.884892\pi$
$751$	−3319.00	+	5748.68i	−0.161268	+	0.279324i	0.774056	+	0.633117i	$0.218225\pi$
$752$	−2766.95	+	1597.50i	−0.134176	+	0.0774665i
$753$	12236.9	−	7065.00i	0.592216	−	0.341916i
$754$	−14337.0	+	24832.4i	−0.692470	+	1.19939i
$755$		0			0
$756$	1750.00	+	606.218i	0.0841890	+	0.0291639i
$757$			14846.0i			0.712797i	0.934334	+	0.356398i	$0.115995\pi$
$757$			14846.0i			0.712797i	−0.934334	+	0.356398i	$0.884005\pi$
$758$	−21577.0	−	12457.5i	−1.03392	−	0.596935i
$759$	3105.00	+	5378.02i	0.148491	+	0.257193i
$760$		0			0
$761$	1825.50	−	3161.86i	0.0869571	−	0.150614i	−0.819266	−	0.573413i	$-0.805619\pi$
$761$	1825.50	−	3161.86i	0.0869571	−	0.150614i	0.906223	+	0.422799i	$0.138952\pi$
$762$		−	4818.00i		−	0.229052i
$763$	−9699.48	+	28000.0i	−0.460216	+	1.32853i
$764$	2388.00			0.113082
$765$		0			0
$766$	−1417.50	−	2455.18i	−0.0668621	−	0.115809i
$767$	−18394.4	+	10620.0i	−0.865949	+	0.499956i
$768$	−2620.59	−	1513.00i	−0.123128	−	0.0710881i
$769$	−29855.0			−1.40000			−0.699999	−	0.714144i	$-0.746816\pi$
$769$	−29855.0			−1.40000			−0.699999	+	0.714144i	$0.746816\pi$
$770$		0			0
$771$	8160.00			0.381161
$772$	−235.559	−	136.000i	−0.0109818	−	0.00634035i
$773$	5645.62	−	3259.50i	0.262689	−	0.151664i	−0.362871	−	0.931839i	$-0.618204\pi$
$773$	5645.62	−	3259.50i	0.262689	−	0.151664i	0.625561	+	0.780175i	$0.284870\pi$
$774$	9867.00	+	17090.1i	0.458220	+	0.793660i
$775$		0			0
$776$	−18942.0			−0.876261
$777$	−6280.42	−	7252.00i	−0.289973	−	0.334831i
$778$		−	36108.0i		−	1.66393i
$779$	−11797.5	+	20433.9i	−0.542605	+	0.939819i
$780$		0			0
$781$	1080.00	+	1870.61i	0.0494820	+	0.0857053i
$782$	9680.43	+	5589.00i	0.442675	+	0.255578i
$783$			16200.0i			0.739388i
$784$	19134.5	+	15064.5i	0.871652	+	0.686248i
$785$		0			0
$786$	6057.00	−	10491.0i	0.274868	−	0.476085i
$787$	30409.6	−	17557.0i	1.37736	−	0.795222i	0.385523	−	0.922698i	$-0.374021\pi$
$787$	30409.6	−	17557.0i	1.37736	−	0.795222i	0.991842	+	0.127477i	$0.0406878\pi$
$788$	1826.45	−	1054.50i	0.0825692	−	0.0476713i
$789$	3288.00	−	5694.98i	0.148360	−	0.256967i
$790$		0			0
$791$	19488.0	−	16877.1i	0.875997	−	0.758636i
$792$		−	21735.0i		−	0.975151i
$793$	20029.4	+	11564.0i	0.896931	+	0.517843i
$794$	−4047.00	−	7009.61i	−0.180885	−	0.313302i
$795$		0			0
$796$	−712.000	+	1233.22i	−0.0317037	+	0.0549125i
$797$			20910.0i			0.929323i	0.885488	+	0.464661i	$0.153824\pi$
$797$			20910.0i			0.929323i	−0.885488	+	0.464661i	$0.846176\pi$
$798$	−13203.4	+	2541.00i	−0.585709	+	0.112720i
$799$	2430.00			0.107594
$800$		0			0
$801$	−13731.0	−	23782.8i	−0.605694	−	1.04909i
$802$	18324.2	−	10579.5i	0.806797	−	0.465804i
$803$	−26032.7	−	15030.0i	−1.14405	−	0.660520i
$804$	−560.000			−0.0245643
$805$		0			0
$806$	−15576.0			−0.680696
$807$	−5653.41	−	3264.00i	−0.246604	−	0.142377i
$808$	12439.6	−	7182.00i	0.541613	−	0.312700i
$809$	2215.50	+	3837.36i	0.0962829	+	0.166767i	0.910143	−	0.414294i	$-0.135971\pi$
$809$	2215.50	+	3837.36i	0.0962829	+	0.166767i	−0.813860	+	0.581060i	$0.802638\pi$
$810$		0			0
$811$	−9577.00			−0.414666			−0.207333	−	0.978270i	$-0.566478\pi$
$811$	−9577.00			−0.414666			−0.207333	+	0.978270i	$0.566478\pi$
$812$	982.073	−	2835.00i	0.0424433	−	0.122523i
$813$		−	5504.00i		−	0.237434i
$814$	17482.5	−	30280.6i	0.752778	−	1.30385i
$815$		0			0
$816$	3834.00	+	6640.68i	0.164481	+	0.284890i
$817$	−29969.7	−	17303.0i	−1.28336	−	0.740949i
$818$			32610.0i			1.39387i
$819$	−4749.50	−	24679.1i	−0.202639	−	1.05294i
$820$		0			0
$821$	5469.00	−	9472.59i	0.232484	−	0.402674i	−0.726054	−	0.687637i	$-0.758648\pi$
$821$	5469.00	−	9472.59i	0.232484	−	0.402674i	0.958539	+	0.284963i	$0.0919813\pi$
$822$	−311.769	+	180.000i	−0.0132290	+	0.00763774i
$823$	−9993.93	+	5770.00i	−0.423289	+	0.244386i	−0.696483	−	0.717573i	$-0.745253\pi$
$823$	−9993.93	+	5770.00i	−0.423289	+	0.244386i	0.273195	+	0.961959i	$0.411920\pi$
$824$	15918.0	−	27570.8i	0.672973	−	1.16562i
$825$		0			0
$826$	15120.0	−	13094.3i	0.636915	−	0.551585i
$827$		−	18762.0i		−	0.788898i	−0.918918	−	0.394449i	$-0.870935\pi$
$827$		−	18762.0i		−	0.788898i	0.918918	−	0.394449i	$-0.129065\pi$
$828$	−1374.38	−	793.500i	−0.0576849	−	0.0333044i
$829$	−19805.0	−	34303.3i	−0.829742	−	1.43716i	−0.898241	−	0.439504i	$-0.855154\pi$
$829$	−19805.0	−	34303.3i	−0.829742	−	1.43716i	0.0684987	−	0.997651i	$-0.478179\pi$
$830$		0			0
$831$	−4690.00	+	8123.32i	−0.195781	+	0.339103i
$832$			25547.0i			1.06452i
$833$	−6874.51	−	17199.0i	−0.285940	−	0.715378i
$834$	−10248.0			−0.425491
$835$		0			0
$836$	−2722.50	−	4715.51i	−0.112631	−	0.195083i
$837$	−7621.02	+	4400.00i	−0.314721	+	0.181704i
$838$	−25276.7	−	14593.5i	−1.04197	−	0.601580i
$839$	−39162.0			−1.61147			−0.805734	−	0.592277i	$-0.798229\pi$
$839$	−39162.0			−1.61147			−0.805734	+	0.592277i	$0.798229\pi$
$840$		0			0
$841$	1855.00			0.0760589
$842$	32605.9	+	18825.0i	1.33453	+	0.770490i
$843$	13546.4	−	7821.00i	0.553454	−	0.319537i
$844$	−1812.50	−	3139.34i	−0.0739204	−	0.128034i
$845$		0			0
$846$	−3105.00			−0.126185
$847$	12621.5	−	2429.00i	0.512017	−	0.0985377i
$848$			42387.0i			1.71648i
$849$	658.000	−	1139.69i	0.0265989	−	0.0460707i
$850$		0			0
$851$	8935.50	+	15476.7i	0.359935	+	0.623426i
$852$	83.1384	+	48.0000i	0.00334305	+	0.00193011i
$853$			11527.0i			0.462693i	0.972871	+	0.231346i	$0.0743131\pi$
$853$			11527.0i			0.462693i	−0.972871	+	0.231346i	$0.925687\pi$
$854$	−20580.0	−	7129.12i	−0.824629	−	0.285660i
$855$		0			0
$856$	−7686.00	+	13312.5i	−0.306895	+	0.531558i
$857$	−36222.4	+	20913.0i	−1.44380	+	0.833576i	−0.998100	−	0.0616089i	$-0.980377\pi$
$857$	−36222.4	+	20913.0i	−1.44380	+	0.833576i	−0.445695	+	0.895185i	$0.647044\pi$
$858$	−13795.8	+	7965.00i	−0.548928	+	0.316924i
$859$	17596.0	−	30477.2i	0.698915	−	1.21056i	−0.269928	−	0.962880i	$-0.587000\pi$
$859$	17596.0	−	30477.2i	0.698915	−	1.21056i	0.968843	−	0.247675i	$-0.0796667\pi$
$860$		0			0
$861$	−6825.00	−	2364.25i	−0.270146	−	0.0935812i
$862$			8964.00i			0.354194i
$863$	−7848.79	−	4531.50i	−0.309590	−	0.178742i	0.337153	−	0.941450i	$-0.390536\pi$
$863$	−7848.79	−	4531.50i	−0.309590	−	0.178742i	−0.646743	+	0.762708i	$0.723869\pi$
$864$	−2250.00	−	3897.11i	−0.0885955	−	0.153452i
$865$		0			0
$866$	−24924.0	+	43169.6i	−0.978005	+	1.69395i
$867$			3994.00i			0.156451i
$868$	1600.41	−	308.000i	0.0625825	−	0.0120440i
$869$	35190.0			1.37369
$870$		0			0
$871$	8260.00	+	14306.7i	0.321331	+	0.556562i
$872$	29098.5	−	16800.0i	1.13004	−	0.652431i
$873$	−17966.6	−	10373.0i	−0.696536	−	0.402145i
$874$	25047.0			0.969368
$875$		0			0
$876$	−1336.00			−0.0515288
$877$	−24628.9	−	14219.5i	−0.948300	−	0.547501i	−0.0557473	−	0.998445i	$-0.517754\pi$
$877$	−24628.9	−	14219.5i	−0.948300	−	0.547501i	−0.892552	+	0.450944i	$0.851087\pi$
$878$	−19085.5	+	11019.0i	−0.733603	+	0.423546i
$879$	5997.00	+	10387.1i	0.230118	+	0.398576i
$880$		0			0
$881$	−9303.00			−0.355762			−0.177881	−	0.984052i	$-0.556924\pi$
$881$	−9303.00			−0.355762			−0.177881	+	0.984052i	$0.556924\pi$
$882$	8784.10	+	21976.5i	0.335347	+	0.838988i
$883$			14728.0i			0.561310i	0.959809	+	0.280655i	$0.0905517\pi$
$883$			14728.0i			0.561310i	−0.959809	+	0.280655i	$0.909448\pi$
$884$	−1593.00	+	2759.16i	−0.0606090	+	0.104978i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.000682530	−	0.00118218i
$887$	14736.3	+	8508.00i	0.557831	+	0.322064i	0.752274	−	0.658850i	$-0.228957\pi$
$887$	14736.3	+	8508.00i	0.557831	+	0.322064i	−0.194443	+	0.980914i	$0.562290\pi$
$888$			10878.0i			0.411083i
$889$	11242.0	−	9735.86i	0.424122	−	0.367301i
$890$		0			0
$891$	9472.50	−	16406.9i	0.356162	−	0.616891i
$892$	−4295.49	+	2480.00i	−0.161237	+	0.0930903i
$893$	4715.51	−	2722.50i	0.176706	−	0.102021i
$894$	3258.00	−	5643.02i	0.121883	−	0.211108i
$895$		0			0
$896$	−5806.50	−	30171.5i	−0.216497	−	1.12495i
$897$		−	8142.00i		−	0.303070i
$898$	25120.8	+	14503.5i	0.933510	+	0.538962i
$899$	7128.00	+	12346.1i	0.264441	+	0.458025i
$900$		0			0
$901$	16119.0	−	27918.9i	0.596006	−	1.03231i
$902$		−	26325.0i		−	0.971759i
$903$	3467.57	−	10010.0i	0.127789	−	0.368895i
$904$	−29232.0			−1.07549
$905$		0			0
$906$	−8598.00	−	14892.2i	−0.315286	−	0.546092i
$907$	−21583.1	+	12461.0i	−0.790137	+	0.456186i	−0.840011	−	0.542570i	$-0.817452\pi$
$907$	−21583.1	+	12461.0i	−0.790137	+	0.456186i	0.0498735	+	0.998756i	$0.484118\pi$
$908$	−1299.04	−	750.000i	−0.0474781	−	0.0274115i
$909$	15732.0			0.574035
$910$		0			0
$911$	30714.0			1.11701			0.558507	−	0.829500i	$-0.311374\pi$
$911$	30714.0			1.11701			0.558507	+	0.829500i	$0.311374\pi$
$912$	14880.0	+	8591.00i	0.540272	+	0.311926i
$913$	29929.8	−	17280.0i	1.08492	−	0.626380i
$914$	−14451.0	−	25029.9i	−0.522972	−	0.905814i
$915$		0			0
$916$	6092.00			0.219744
$917$	36718.6	−	7066.50i	1.32231	−	0.254478i
$918$			16200.0i			0.582440i
$919$	8713.00	−	15091.4i	0.312748	−	0.541695i	−0.666208	−	0.745766i	$-0.732084\pi$
$919$	8713.00	−	15091.4i	0.312748	−	0.541695i	0.978956	+	0.204070i	$0.0654172\pi$
$920$		0			0
$921$	−6226.00	−	10783.7i	−0.222751	−	0.385816i
$922$	888.542	+	513.000i	0.0317382	+	0.0183240i
$923$		−	2832.00i		−	0.100993i
$924$	1260.00	−	1091.19i	0.0448603	−	0.0388502i
$925$		0			0
$926$	−3616.50	+	6263.96i	−0.128343	+	0.222296i
$927$	30196.6	−	17434.0i	1.06989	−	0.617700i
$928$	−6313.33	+	3645.00i	−0.223324	+	0.128936i
$929$	13324.5	−	23078.7i	0.470573	−	0.815057i	−0.528860	−	0.848709i	$-0.677380\pi$
$929$	13324.5	−	23078.7i	0.470573	−	0.815057i	0.999434	+	0.0336519i	$0.0107138\pi$
$930$		0			0
$931$	−32609.5	−	25673.3i	−1.14794	−	0.903769i
$932$			138.000i			0.00485015i
$933$	−8106.00	−	4680.00i	−0.284436	−	0.164219i
$934$	−1809.00	−	3133.28i	−0.0633750	−	0.109769i
$935$		0			0
$936$	−14248.5	+	24679.1i	−0.497571	+	0.861819i
$937$			27686.0i			0.965274i	0.875820	+	0.482637i	$0.160321\pi$
$937$			27686.0i			0.965274i	−0.875820	+	0.482637i	$0.839679\pi$
$938$	−10184.5	−	11760.0i	−0.354514	−	0.409358i
$939$	2056.00			0.0714537
$940$		0			0
$941$	8904.00	+	15422.2i	0.308461	+	0.534271i	0.978026	−	0.208483i	$-0.0668526\pi$
$941$	8904.00	+	15422.2i	0.308461	+	0.534271i	−0.669565	+	0.742754i	$0.733519\pi$
$942$	1189.92	−	687.000i	0.0411567	−	0.0237619i
$943$	11652.4	+	6727.50i	0.402390	+	0.232320i
$944$	−25560.0			−0.881258
$945$		0			0
$946$	38610.0			1.32698
$947$	5980.77	+	3453.00i	0.205226	+	0.118487i	0.599091	−	0.800681i	$-0.295529\pi$
$947$	5980.77	+	3453.00i	0.205226	+	0.118487i	−0.393865	+	0.919168i	$0.628862\pi$
$948$	1354.46	−	782.000i	0.0464039	−	0.0267913i
$949$	19706.0	+	34131.8i	0.674061	+	1.16751i
$950$		0			0
$951$	−17244.0			−0.587986
$952$	−6874.51	+	19845.0i	−0.234038	+	0.675609i
$953$			20940.0i			0.711766i	0.934530	+	0.355883i	$0.115820\pi$
$953$			20940.0i			0.711766i	−0.934530	+	0.355883i	$0.884180\pi$
$954$	−20596.5	+	35674.2i	−0.698990	+	1.21069i
$955$		0			0
$956$	2751.00	+	4764.87i	0.0930687	+	0.161200i
$957$	12626.7	+	7290.00i	0.426501	+	0.246241i
$958$			1296.00i			0.0437076i
$959$	−1050.00	−	363.731i	−0.0353559	−	0.0122476i
$960$		0			0
$961$	11023.5	−	19093.3i	0.370028	−	0.640907i
$962$	−39701.2	+	22921.5i	−1.33058	+	0.768211i
$963$	−14580.4	+	8418.00i	−0.487899	+	0.281689i
$964$	1775.50	−	3075.26i	0.0593205	−	0.102746i
$965$		0			0
$966$	1449.00	+	7529.22i	0.0482617	+	0.250775i
$967$			9176.00i			0.305150i	0.988292	+	0.152575i	$0.0487566\pi$
$967$			9176.00i			0.305150i	−0.988292	+	0.152575i	$0.951243\pi$
$968$	−12621.5	−	7287.00i	−0.419079	−	0.241956i
$969$	−6534.00	−	11317.2i	−0.216617	−	0.375192i
$970$		0			0
$971$	−14881.5	+	25775.5i	−0.491833	+	0.851880i	−0.999956	−	0.00940465i	$-0.997006\pi$
$971$	−14881.5	+	25775.5i	−0.491833	+	0.851880i	0.508123	+	0.861285i	$0.330340\pi$
$972$		−	3542.00i		−	0.116882i
$973$	−20708.4	−	23912.0i	−0.682303	−	0.787856i
$974$	35688.0			1.17404
$975$		0			0
$976$	13916.0	+	24103.2i	0.456394	+	0.790497i
$977$	−33333.3	+	19245.0i	−1.09153	+	0.630197i	−0.933984	−	0.357315i	$-0.883692\pi$
$977$	−33333.3	+	19245.0i	−1.09153	+	0.630197i	−0.157548	+	0.987511i	$0.550359\pi$
$978$	6380.88	+	3684.00i	0.208628	+	0.120451i
$979$	−53730.0			−1.75405
$980$		0			0
$981$	36800.0			1.19769
$982$	31894.0	+	18414.0i	1.03643	+	0.598385i
$983$	10919.7	−	6304.50i	0.354308	−	0.204560i	−0.312273	−	0.949992i	$-0.601090\pi$
$983$	10919.7	−	6304.50i	0.354308	−	0.204560i	0.666581	+	0.745433i	$0.267757\pi$
$984$	4095.00	+	7092.75i	0.132666	+	0.229785i
$985$		0			0
$986$	26244.0			0.847646
$987$	1091.19	+	1260.00i	0.0351905	+	0.0406345i
$988$			7139.00i			0.229880i
$989$	−9867.00	+	17090.1i	−0.317242	+	0.549479i
$990$		0			0
$991$	−9910.00	−	17164.6i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−9910.00	−	17164.6i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	−3429.46	−	1980.00i	−0.109764	−	0.0633720i
$993$		−	3998.00i		−	0.127767i
$994$	504.000	+	2618.86i	0.0160824	+	0.0835666i
$995$		0			0
$996$	768.000	−	1330.22i	0.0244327	−	0.0423188i
$997$	39866.6	−	23017.0i	1.26639	−	0.731149i	0.292085	−	0.956392i	$-0.405651\pi$
$997$	39866.6	−	23017.0i	1.26639	−	0.731149i	0.974303	+	0.225243i	$0.0723177\pi$
$998$	28256.7	−	16314.0i	0.896242	−	0.517446i
$999$	−12950.0	+	22430.1i	−0.410130	+	0.710366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.k.b.149.1		4
5.2	odd	4		175.4.e.b.51.1		2
5.3	odd	4		35.4.e.a.16.1	yes	2
5.4	even	2	inner	175.4.k.b.149.2		4
7.4	even	3	inner	175.4.k.b.74.2		4
15.8	even	4		315.4.j.b.226.1		2
20.3	even	4		560.4.q.b.401.1		2
35.2	odd	12		1225.4.a.b.1.1		1
35.3	even	12		245.4.e.a.116.1		2
35.4	even	6	inner	175.4.k.b.74.1		4
35.12	even	12		1225.4.a.a.1.1		1
35.13	even	4		245.4.e.a.226.1		2
35.18	odd	12		35.4.e.a.11.1	✓	2
35.23	odd	12		245.4.a.e.1.1		1
35.32	odd	12		175.4.e.b.151.1		2
35.33	even	12		245.4.a.f.1.1		1
105.23	even	12		2205.4.a.e.1.1		1
105.53	even	12		315.4.j.b.46.1		2
105.68	odd	12		2205.4.a.g.1.1		1
140.123	even	12		560.4.q.b.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.a.11.1	✓	2	35.18	odd	12
35.4.e.a.16.1	yes	2	5.3	odd	4
175.4.e.b.51.1		2	5.2	odd	4
175.4.e.b.151.1		2	35.32	odd	12
175.4.k.b.74.1		4	35.4	even	6	inner
175.4.k.b.74.2		4	7.4	even	3	inner
175.4.k.b.149.1		4	1.1	even	1	trivial
175.4.k.b.149.2		4	5.4	even	2	inner
245.4.a.e.1.1		1	35.23	odd	12
245.4.a.f.1.1		1	35.33	even	12
245.4.e.a.116.1		2	35.3	even	12
245.4.e.a.226.1		2	35.13	even	4
315.4.j.b.46.1		2	105.53	even	12
315.4.j.b.226.1		2	15.8	even	4
560.4.q.b.81.1		2	140.123	even	12
560.4.q.b.401.1		2	20.3	even	4
1225.4.a.a.1.1		1	35.12	even	12
1225.4.a.b.1.1		1	35.2	odd	12
2205.4.a.e.1.1		1	105.23	even	12
2205.4.a.g.1.1		1	105.68	odd	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 - 1.50000i) q^{2} +(1.73205 - 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} -6.00000 q^{6} +(-12.1244 - 14.0000i) q^{7} +21.0000i q^{8} +(-11.5000 + 19.9186i) q^{9} +(22.5000 + 38.9711i) q^{11} +(1.73205 + 1.00000i) q^{12} -59.0000i q^{13} +(10.5000 + 54.5596i) q^{14} +(35.5000 - 61.4878i) q^{16} +(-46.7654 + 27.0000i) q^{17} +(59.7558 - 34.5000i) q^{18} +(-60.5000 + 104.789i) q^{19} +(-35.0000 - 12.1244i) q^{21} -135.000i q^{22} +(59.7558 + 34.5000i) q^{23} +(21.0000 + 36.3731i) q^{24} +(-88.5000 + 153.286i) q^{26} +100.000i q^{27} +(6.06218 - 17.5000i) q^{28} +162.000 q^{29} +(44.0000 + 76.2102i) q^{31} +(-38.9711 + 22.5000i) q^{32} +(77.9423 + 45.0000i) q^{33} +162.000 q^{34} -23.0000 q^{36} +(224.301 + 129.500i) q^{37} +(314.367 - 181.500i) q^{38} +(-59.0000 - 102.191i) q^{39} +195.000 q^{41} +(72.7461 + 84.0000i) q^{42} +286.000i q^{43} +(-22.5000 + 38.9711i) q^{44} +(-103.500 - 179.267i) q^{46} +(-38.9711 - 22.5000i) q^{47} -142.000i q^{48} +(-49.0000 + 339.482i) q^{49} +(-54.0000 + 93.5307i) q^{51} +(51.0955 - 29.5000i) q^{52} +(-517.017 + 298.500i) q^{53} +(150.000 - 259.808i) q^{54} +(294.000 - 254.611i) q^{56} +242.000i q^{57} +(-420.888 - 243.000i) q^{58} +(-180.000 - 311.769i) q^{59} +(-196.000 + 339.482i) q^{61} -264.000i q^{62} +(418.290 - 80.5000i) q^{63} -433.000 q^{64} +(-135.000 - 233.827i) q^{66} +(-242.487 + 140.000i) q^{67} +(-46.7654 - 27.0000i) q^{68} +138.000 q^{69} +48.0000 q^{71} +(-418.290 - 241.500i) q^{72} +(-578.505 + 334.000i) q^{73} +(-388.500 - 672.902i) q^{74} -121.000 q^{76} +(272.798 - 787.500i) q^{77} +354.000i q^{78} +(391.000 - 677.232i) q^{79} +(-210.500 - 364.597i) q^{81} +(-506.625 - 292.500i) q^{82} -768.000i q^{83} +(-7.00000 - 36.3731i) q^{84} +(429.000 - 743.050i) q^{86} +(280.592 - 162.000i) q^{87} +(-818.394 + 472.500i) q^{88} +(-597.000 + 1034.03i) q^{89} +(-826.000 + 715.337i) q^{91} +69.0000i q^{92} +(152.420 + 88.0000i) q^{93} +(67.5000 + 116.913i) q^{94} +(-45.0000 + 77.9423i) q^{96} +902.000i q^{97} +(636.529 - 808.500i) q^{98} -1035.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 24 q^{6} - 46 q^{9} + 90 q^{11} + 42 q^{14} + 142 q^{16} - 242 q^{19} - 140 q^{21} + 84 q^{24} - 354 q^{26} + 648 q^{29} + 176 q^{31} + 648 q^{34} - 92 q^{36} - 236 q^{39} + 780 q^{41} - 90 q^{44}+ \cdots - 4140 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 24 * q^6 - 46 * q^9 + 90 * q^11 + 42 * q^14 + 142 * q^16 - 242 * q^19 - 140 * q^21 + 84 * q^24 - 354 * q^26 + 648 * q^29 + 176 * q^31 + 648 * q^34 - 92 * q^36 - 236 * q^39 + 780 * q^41 - 90 * q^44 - 414 * q^46 - 196 * q^49 - 216 * q^51 + 600 * q^54 + 1176 * q^56 - 720 * q^59 - 784 * q^61 - 1732 * q^64 - 540 * q^66 + 552 * q^69 + 192 * q^71 - 1554 * q^74 - 484 * q^76 + 1564 * q^79 - 842 * q^81 - 28 * q^84 + 1716 * q^86 - 2388 * q^89 - 3304 * q^91 + 270 * q^94 - 180 * q^96 - 4140 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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