LMFDB - Embedded newform 162.7.b.c.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(161,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.161");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.b (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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{42} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.4
Root			$-11.8022i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.c.161.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -32.0000 q^{4} +10.8441i q^{5} -644.082 q^{7} +181.019i q^{8} +O(q^{10})$	\(q-5.65685i q^{2} -32.0000 q^{4} +10.8441i q^{5} -644.082 q^{7} +181.019i q^{8} +61.3435 q^{10} -1222.35i q^{11} -2326.78 q^{13} +3643.48i q^{14} +1024.00 q^{16} -3382.18i q^{17} +6234.31 q^{19} -347.011i q^{20} -6914.66 q^{22} +14369.4i q^{23} +15507.4 q^{25} +13162.2i q^{26} +20610.6 q^{28} +13576.7i q^{29} +8786.32 q^{31} -5792.62i q^{32} -19132.5 q^{34} -6984.49i q^{35} -27898.6 q^{37} -35266.6i q^{38} -1962.99 q^{40} +55389.1i q^{41} +53918.0 q^{43} +39115.2i q^{44} +81285.7 q^{46} +176005. i q^{47} +297193. q^{49} -87723.1i q^{50} +74456.8 q^{52} +83918.6i q^{53} +13255.3 q^{55} -116591. i q^{56} +76801.7 q^{58} -353158. i q^{59} +166629. q^{61} -49702.9i q^{62} -32768.0 q^{64} -25231.8i q^{65} -90498.8 q^{67} +108230. i q^{68} -39510.3 q^{70} -429740. i q^{71} +274010. q^{73} +157818. i q^{74} -199498. q^{76} +787294. i q^{77} +326294. q^{79} +11104.4i q^{80} +313328. q^{82} -991699. i q^{83} +36676.7 q^{85} -305006. i q^{86} +221269. q^{88} +538101. i q^{89} +1.49863e6 q^{91} -459821. i q^{92} +995634. q^{94} +67605.5i q^{95} -85949.5 q^{97} -1.68118e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 384 q^{4} - 480 q^{7}+O(q^{10}) $ 12 * q - 384 * q^4 - 480 * q^7	$ 12 q - 384 q^{4} - 480 q^{7} - 3360 q^{13} + 12288 q^{16} - 2820 q^{19} + 7200 q^{22} - 16188 q^{25} + 15360 q^{28} - 42960 q^{31} + 54720 q^{34} - 25536 q^{37} - 142860 q^{43} - 135072 q^{46} + 271908 q^{49} + 107520 q^{52} + 580392 q^{55} - 318528 q^{58} - 271488 q^{61} - 393216 q^{64} + 579876 q^{67} - 311904 q^{70} - 977700 q^{73} + 90240 q^{76} + 1529592 q^{79} + 1073088 q^{82} - 3239136 q^{85} - 230400 q^{88} + 355584 q^{91} + 1473696 q^{94} + 77748 q^{97}+O(q^{100}) $ 12 * q - 384 * q^4 - 480 * q^7 - 3360 * q^13 + 12288 * q^16 - 2820 * q^19 + 7200 * q^22 - 16188 * q^25 + 15360 * q^28 - 42960 * q^31 + 54720 * q^34 - 25536 * q^37 - 142860 * q^43 - 135072 * q^46 + 271908 * q^49 + 107520 * q^52 + 580392 * q^55 - 318528 * q^58 - 271488 * q^61 - 393216 * q^64 + 579876 * q^67 - 311904 * q^70 - 977700 * q^73 + 90240 * q^76 + 1529592 * q^79 + 1073088 * q^82 - 3239136 * q^85 - 230400 * q^88 + 355584 * q^91 + 1473696 * q^94 + 77748 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$-1$

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 $

$2$	− 5.65685i	− 0.707107i
$2$	− 5.65685i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−32.0000	−0.500000
$5$	10.8441i	0.0867528i	0.999059	+	0.0433764i	$0.0138115\pi$
$5$	10.8441i	0.0867528i	−0.999059	+	0.0433764i	$0.986189\pi$
$6$	0	0
$7$	−644.082	−1.87779	−0.938896	−	0.344202i	$-0.888150\pi$
$7$	−644.082	−1.87779	−0.938896	+	0.344202i	$0.888150\pi$
$8$	181.019i	0.353553i
$9$	0	0
$10$	61.3435	0.0613435
$11$	− 1222.35i	− 0.918370i	−0.888341	−	0.459185i	$-0.848142\pi$
$11$	− 1222.35i	− 0.918370i	0.888341	−	0.459185i	$-0.151858\pi$
$12$	0	0
$13$	−2326.78	−1.05907	−0.529535	−	0.848288i	$-0.677633\pi$
$13$	−2326.78	−1.05907	−0.529535	+	0.848288i	$0.677633\pi$
$14$	3643.48i	1.32780i
$15$	0	0
$16$	1024.00	0.250000
$17$	− 3382.18i	− 0.688415i	−0.938894	−	0.344207i	$-0.888148\pi$
$17$	− 3382.18i	− 0.688415i	0.938894	−	0.344207i	$-0.111852\pi$
$18$	0	0
$19$	6234.31	0.908924	0.454462	−	0.890766i	$-0.349831\pi$
$19$	6234.31	0.908924	0.454462	+	0.890766i	$0.349831\pi$
$20$	− 347.011i	− 0.0433764i
$21$	0	0
$22$	−6914.66	−0.649385
$23$	14369.4i	1.18102i	0.807032	+	0.590508i	$0.201072\pi$
$23$	14369.4i	1.18102i	−0.807032	+	0.590508i	$0.798928\pi$
$24$	0	0
$25$	15507.4	0.992474
$26$	13162.2i	0.748875i
$27$	0	0
$28$	20610.6	0.938896
$29$	13576.7i	0.556675i	0.960483	+	0.278338i	$0.0897834\pi$
$29$	13576.7i	0.556675i	−0.960483	+	0.278338i	$0.910217\pi$
$30$	0	0
$31$	8786.32	0.294932	0.147466	−	0.989067i	$-0.452888\pi$
$31$	8786.32	0.294932	0.147466	+	0.989067i	$0.452888\pi$
$32$	− 5792.62i	− 0.176777i
$33$	0	0
$34$	−19132.5	−0.486783
$35$	− 6984.49i	− 0.162904i
$36$	0	0
$37$	−27898.6	−0.550779	−0.275389	−	0.961333i	$-0.588807\pi$
$37$	−27898.6	−0.550779	−0.275389	+	0.961333i	$0.588807\pi$
$38$	− 35266.6i	− 0.642707i
$39$	0	0
$40$	−1962.99	−0.0306717
$41$	55389.1i	0.803661i	0.915714	+	0.401831i	$0.131626\pi$
$41$	55389.1i	0.803661i	−0.915714	+	0.401831i	$0.868374\pi$
$42$	0	0
$43$	53918.0	0.678154	0.339077	−	0.940759i	$-0.389885\pi$
$43$	53918.0	0.678154	0.339077	+	0.940759i	$0.389885\pi$
$44$	39115.2i	0.459185i
$45$	0	0
$46$	81285.7	0.835104
$47$	176005.i	1.69524i	0.530604	+	0.847620i	$0.321965\pi$
$47$	176005.i	1.69524i	−0.530604	+	0.847620i	$0.678035\pi$
$48$	0	0
$49$	297193.	2.52610
$50$	− 87723.1i	− 0.701785i
$51$	0	0
$52$	74456.8	0.529535
$53$	83918.6i	0.563678i	0.959462	+	0.281839i	$0.0909443\pi$
$53$	83918.6i	0.563678i	−0.959462	+	0.281839i	$0.909056\pi$
$54$	0	0
$55$	13255.3	0.0796711
$56$	− 116591.i	− 0.663900i
$57$	0	0
$58$	76801.7	0.393629
$59$	− 353158.i	− 1.71954i	−0.510681	−	0.859770i	$-0.670607\pi$
$59$	− 353158.i	− 1.71954i	0.510681	−	0.859770i	$-0.329393\pi$
$60$	0	0
$61$	166629.	0.734108	0.367054	−	0.930200i	$-0.380366\pi$
$61$	166629.	0.734108	0.367054	+	0.930200i	$0.380366\pi$
$62$	− 49702.9i	− 0.208548i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	− 25231.8i	− 0.0918772i
$66$	0	0
$67$	−90498.8	−0.300897	−0.150449	−	0.988618i	$-0.548072\pi$
$67$	−90498.8	−0.300897	−0.150449	+	0.988618i	$0.548072\pi$
$68$	108230.i	0.344207i
$69$	0	0
$70$	−39510.3	−0.115190
$71$	− 429740.i	− 1.20069i	−0.799741	−	0.600345i	$-0.795030\pi$
$71$	− 429740.i	− 1.20069i	0.799741	−	0.600345i	$-0.204970\pi$
$72$	0	0
$73$	274010.	0.704366	0.352183	−	0.935931i	$-0.385440\pi$
$73$	274010.	0.704366	0.352183	+	0.935931i	$0.385440\pi$
$74$	157818.i	0.389459i
$75$	0	0
$76$	−199498.	−0.454462
$77$	787294.i	1.72451i
$78$	0	0
$79$	326294.	0.661802	0.330901	−	0.943665i	$-0.392647\pi$
$79$	326294.	0.661802	0.330901	+	0.943665i	$0.392647\pi$
$80$	11104.4i	0.0216882i
$81$	0	0
$82$	313328.	0.568274
$83$	− 991699.i	− 1.73438i	−0.497973	−	0.867192i	$-0.665922\pi$
$83$	− 991699.i	− 1.73438i	0.497973	−	0.867192i	$-0.334078\pi$
$84$	0	0
$85$	36676.7	0.0597219
$86$	− 305006.i	− 0.479527i
$87$	0	0
$88$	221269.	0.324693
$89$	538101.i	0.763298i	0.924307	+	0.381649i	$0.124644\pi$
$89$	538101.i	0.763298i	−0.924307	+	0.381649i	$0.875356\pi$
$90$	0	0
$91$	1.49863e6	1.98871
$92$	− 459821.i	− 0.590508i
$93$	0	0
$94$	995634.	1.19872
$95$	67605.5i	0.0788517i
$96$	0	0
$97$	−85949.5	−0.0941733	−0.0470867	−	0.998891i	$-0.514994\pi$
$97$	−85949.5	−0.0941733	−0.0470867	+	0.998891i	$0.514994\pi$
$98$	− 1.68118e6i	− 1.78622i
$99$	0	0
$100$	−496237.	−0.496237
$101$	1.20187e6i	1.16652i	0.812284	+	0.583262i	$0.198224\pi$
$101$	1.20187e6i	1.16652i	−0.812284	+	0.583262i	$0.801776\pi$
$102$	0	0
$103$	−333474.	−0.305176	−0.152588	−	0.988290i	$-0.548761\pi$
$103$	−333474.	−0.305176	−0.152588	+	0.988290i	$0.548761\pi$
$104$	− 421191.i	− 0.374438i
$105$	0	0
$106$	474715.	0.398580
$107$	2.15926e6i	1.76260i	0.472558	+	0.881299i	$0.343331\pi$
$107$	2.15926e6i	1.76260i	−0.472558	+	0.881299i	$0.656669\pi$
$108$	0	0
$109$	−651642.	−0.503187	−0.251594	−	0.967833i	$-0.580955\pi$
$109$	−651642.	−0.503187	−0.251594	+	0.967833i	$0.580955\pi$
$110$	− 74983.2i	− 0.0563360i
$111$	0	0
$112$	−659540.	−0.469448
$113$	445563.i	0.308798i	0.988009	+	0.154399i	$0.0493441\pi$
$113$	445563.i	0.308798i	−0.988009	+	0.154399i	$0.950656\pi$
$114$	0	0
$115$	−155823.	−0.102456
$116$	− 434456.i	− 0.278338i
$117$	0	0
$118$	−1.99776e6	−1.21590
$119$	2.17840e6i	1.29270i
$120$	0	0
$121$	277421.	0.156597
$122$	− 942593.i	− 0.519093i
$123$	0	0
$124$	−281162.	−0.147466
$125$	337603.i	0.172853i
$126$	0	0
$127$	−3.14533e6	−1.53552	−0.767760	−	0.640737i	$-0.778629\pi$
$127$	−3.14533e6	−1.53552	−0.767760	+	0.640737i	$0.778629\pi$
$128$	185364.i	0.0883883i
$129$	0	0
$130$	−142732.	−0.0649670
$131$	− 1.04628e6i	− 0.465410i	−0.972547	−	0.232705i	$-0.925242\pi$
$131$	− 1.04628e6i	− 0.465410i	0.972547	−	0.232705i	$-0.0747576\pi$
$132$	0	0
$133$	−4.01541e6	−1.70677
$134$	511939.i	0.212767i
$135$	0	0
$136$	612240.	0.243391
$137$	− 46654.8i	− 0.0181441i	−0.999959	−	0.00907203i	$-0.997112\pi$
$137$	− 46654.8i	− 0.0181441i	0.999959	−	0.00907203i	$-0.00288776\pi$
$138$	0	0
$139$	−1.38860e6	−0.517051	−0.258526	−	0.966004i	$-0.583237\pi$
$139$	−1.38860e6	−0.517051	−0.258526	+	0.966004i	$0.583237\pi$
$140$	223504.i	0.0814518i
$141$	0	0
$142$	−2.43098e6	−0.849017
$143$	2.84413e6i	0.972617i
$144$	0	0
$145$	−147228.	−0.0482931
$146$	− 1.55004e6i	− 0.498062i
$147$	0	0
$148$	892755.	0.275389
$149$	3.77877e6i	1.14233i	0.820835	+	0.571165i	$0.193508\pi$
$149$	3.77877e6i	1.14233i	−0.820835	+	0.571165i	$0.806492\pi$
$150$	0	0
$151$	2.54065e6	0.737927	0.368964	−	0.929444i	$-0.379713\pi$
$151$	2.54065e6	0.737927	0.368964	+	0.929444i	$0.379713\pi$
$152$	1.12853e6i	0.321353i
$153$	0	0
$154$	4.45361e6	1.21941
$155$	95279.7i	0.0255862i
$156$	0	0
$157$	624064.	0.161261	0.0806307	−	0.996744i	$-0.474307\pi$
$157$	624064.	0.161261	0.0806307	+	0.996744i	$0.474307\pi$
$158$	− 1.84580e6i	− 0.467965i
$159$	0	0
$160$	62815.7	0.0153359
$161$	− 9.25509e6i	− 2.21770i
$162$	0	0
$163$	−2.16727e6	−0.500438	−0.250219	−	0.968189i	$-0.580503\pi$
$163$	−2.16727e6	−0.500438	−0.250219	+	0.968189i	$0.580503\pi$
$164$	− 1.77245e6i	− 0.401831i
$165$	0	0
$166$	−5.60990e6	−1.22640
$167$	3.32006e6i	0.712847i	0.934325	+	0.356423i	$0.116004\pi$
$167$	3.32006e6i	0.712847i	−0.934325	+	0.356423i	$0.883996\pi$
$168$	0	0
$169$	587073.	0.121628
$170$	− 207475.i	− 0.0422298i
$171$	0	0
$172$	−1.72538e6	−0.339077
$173$	914421.i	0.176607i	0.996094	+	0.0883035i	$0.0281445\pi$
$173$	914421.i	0.176607i	−0.996094	+	0.0883035i	$0.971855\pi$
$174$	0	0
$175$	−9.98805e6	−1.86366
$176$	− 1.25169e6i	− 0.229592i
$177$	0	0
$178$	3.04396e6	0.539733
$179$	3.42647e6i	0.597431i	0.954342	+	0.298716i	$0.0965582\pi$
$179$	3.42647e6i	0.597431i	−0.954342	+	0.298716i	$0.903442\pi$
$180$	0	0
$181$	−5.16532e6	−0.871087	−0.435543	−	0.900168i	$-0.643444\pi$
$181$	−5.16532e6	−0.871087	−0.435543	+	0.900168i	$0.643444\pi$
$182$	− 8.47756e6i	− 1.40623i
$183$	0	0
$184$	−2.60114e6	−0.417552
$185$	− 302535.i	− 0.0477816i
$186$	0	0
$187$	−4.13421e6	−0.632219
$188$	− 5.63216e6i	− 0.847620i
$189$	0	0
$190$	382434.	0.0557566
$191$	5.38224e6i	0.772437i	0.922407	+	0.386218i	$0.126219\pi$
$191$	5.38224e6i	0.772437i	−0.922407	+	0.386218i	$0.873781\pi$
$192$	0	0
$193$	7.46389e6	1.03823	0.519115	−	0.854704i	$-0.326262\pi$
$193$	7.46389e6	1.03823	0.519115	+	0.854704i	$0.326262\pi$
$194$	486204.i	0.0665906i
$195$	0	0
$196$	−9.51018e6	−1.26305
$197$	2.66109e6i	0.348066i	0.984740	+	0.174033i	$0.0556799\pi$
$197$	2.66109e6i	0.348066i	−0.984740	+	0.174033i	$0.944320\pi$
$198$	0	0
$199$	1.13134e7	1.43560	0.717801	−	0.696248i	$-0.245149\pi$
$199$	1.13134e7	1.43560	0.717801	+	0.696248i	$0.245149\pi$
$200$	2.80714e6i	0.350893i
$201$	0	0
$202$	6.79881e6	0.824857
$203$	− 8.74454e6i	− 1.04532i
$204$	0	0
$205$	−600645.	−0.0697198
$206$	1.88641e6i	0.215792i
$207$	0	0
$208$	−2.38262e6	−0.264767
$209$	− 7.62051e6i	− 0.834729i
$210$	0	0
$211$	5.23669e6	0.557454	0.278727	−	0.960370i	$-0.410087\pi$
$211$	5.23669e6	0.557454	0.278727	+	0.960370i	$0.410087\pi$
$212$	− 2.68540e6i	− 0.281839i
$213$	0	0
$214$	1.22146e7	1.24635
$215$	584692.i	0.0588318i
$216$	0	0
$217$	−5.65912e6	−0.553821
$218$	3.68625e6i	0.355807i
$219$	0	0
$220$	−424169.	−0.0398356
$221$	7.86958e6i	0.729079i
$222$	0	0
$223$	8.92370e6	0.804693	0.402347	−	0.915487i	$-0.368195\pi$
$223$	8.92370e6	0.804693	0.402347	+	0.915487i	$0.368195\pi$
$224$	3.73092e6i	0.331950i
$225$	0	0
$226$	2.52049e6	0.218353
$227$	1.25992e6i	0.107712i	0.998549	+	0.0538562i	$0.0171513\pi$
$227$	1.25992e6i	0.107712i	−0.998549	+	0.0538562i	$0.982849\pi$
$228$	0	0
$229$	1.52511e7	1.26997	0.634986	−	0.772524i	$-0.281006\pi$
$229$	1.52511e7	1.26997	0.634986	+	0.772524i	$0.281006\pi$
$230$	881470.i	0.0724476i
$231$	0	0
$232$	−2.45765e6	−0.196814
$233$	988329.i	0.0781329i	0.999237	+	0.0390664i	$0.0124384\pi$
$233$	988329.i	0.0781329i	−0.999237	+	0.0390664i	$0.987562\pi$
$234$	0	0
$235$	−1.90861e6	−0.147067
$236$	1.13010e7i	0.859770i
$237$	0	0
$238$	1.23229e7	0.914077
$239$	− 1.82707e7i	− 1.33832i	−0.743118	−	0.669161i	$-0.766654\pi$
$239$	− 1.82707e7i	− 1.33832i	0.743118	−	0.669161i	$-0.233346\pi$
$240$	0	0
$241$	−646606.	−0.0461943	−0.0230972	−	0.999733i	$-0.507353\pi$
$241$	−646606.	−0.0461943	−0.0230972	+	0.999733i	$0.507353\pi$
$242$	− 1.56933e6i	− 0.110731i
$243$	0	0
$244$	−5.33211e6	−0.367054
$245$	3.22279e6i	0.219146i
$246$	0	0
$247$	−1.45058e7	−0.962614
$248$	1.59049e6i	0.104274i
$249$	0	0
$250$	1.90977e6	0.122225
$251$	1.02408e6i	0.0647606i	0.999476	+	0.0323803i	$0.0103088\pi$
$251$	1.02408e6i	0.0647606i	−0.999476	+	0.0323803i	$0.989691\pi$
$252$	0	0
$253$	1.75645e7	1.08461
$254$	1.77927e7i	1.08578i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	1.01335e7i	0.596981i	0.954413	+	0.298490i	$0.0964831\pi$
$257$	1.01335e7i	0.596981i	−0.954413	+	0.298490i	$0.903517\pi$
$258$	0	0
$259$	1.79690e7	1.03425
$260$	807417.i	0.0459386i
$261$	0	0
$262$	−5.91868e6	−0.329095
$263$	− 2.21278e7i	− 1.21638i	−0.793790	−	0.608192i	$-0.791895\pi$
$263$	− 2.21278e7i	− 1.21638i	0.793790	−	0.608192i	$-0.208105\pi$
$264$	0	0
$265$	−910022.	−0.0489006
$266$	2.27146e7i	1.20687i
$267$	0	0
$268$	2.89596e6	0.150449
$269$	1.79826e7i	0.923840i	0.886922	+	0.461920i	$0.152839\pi$
$269$	1.79826e7i	0.923840i	−0.886922	+	0.461920i	$0.847161\pi$
$270$	0	0
$271$	3.08379e7	1.54945	0.774724	−	0.632299i	$-0.217889\pi$
$271$	3.08379e7	1.54945	0.774724	+	0.632299i	$0.217889\pi$
$272$	− 3.46335e6i	− 0.172104i
$273$	0	0
$274$	−263919.	−0.0128298
$275$	− 1.89555e7i	− 0.911458i
$276$	0	0
$277$	−1.18521e7	−0.557644	−0.278822	−	0.960343i	$-0.589944\pi$
$277$	−1.18521e7	−0.557644	−0.278822	+	0.960343i	$0.589944\pi$
$278$	7.85512e6i	0.365610i
$279$	0	0
$280$	1.26433e6	0.0575951
$281$	5.65448e6i	0.254844i	0.991849	+	0.127422i	$0.0406702\pi$
$281$	5.65448e6i	0.254844i	−0.991849	+	0.127422i	$0.959330\pi$
$282$	0	0
$283$	2.20884e7	0.974553	0.487277	−	0.873248i	$-0.337990\pi$
$283$	2.20884e7	0.974553	0.487277	+	0.873248i	$0.337990\pi$
$284$	1.37517e7i	0.600345i
$285$	0	0
$286$	1.60889e7	0.687744
$287$	− 3.56752e7i	− 1.50911i
$288$	0	0
$289$	1.26984e7	0.526085
$290$	832845.i	0.0341484i
$291$	0	0
$292$	−8.76833e6	−0.352183
$293$	4.30878e7i	1.71298i	0.516167	+	0.856488i	$0.327358\pi$
$293$	4.30878e7i	1.71298i	−0.516167	+	0.856488i	$0.672642\pi$
$294$	0	0
$295$	3.82967e6	0.149175
$296$	− 5.05018e6i	− 0.194730i
$297$	0	0
$298$	2.13760e7	0.807750
$299$	− 3.34344e7i	− 1.25078i
$300$	0	0
$301$	−3.47276e7	−1.27343
$302$	− 1.43721e7i	− 0.521793i
$303$	0	0
$304$	6.38394e6	0.227231
$305$	1.80694e6i	0.0636859i
$306$	0	0
$307$	−7.12229e6	−0.246153	−0.123076	−	0.992397i	$-0.539276\pi$
$307$	−7.12229e6	−0.246153	−0.123076	+	0.992397i	$0.539276\pi$
$308$	− 2.51934e7i	− 0.862253i
$309$	0	0
$310$	538983.	0.0180922
$311$	2.23285e7i	0.742300i	0.928573	+	0.371150i	$0.121036\pi$
$311$	2.23285e7i	0.742300i	−0.928573	+	0.371150i	$0.878964\pi$
$312$	0	0
$313$	2.68066e7	0.874195	0.437097	−	0.899414i	$-0.356007\pi$
$313$	2.68066e7	0.874195	0.437097	+	0.899414i	$0.356007\pi$
$314$	− 3.53024e6i	− 0.114029i
$315$	0	0
$316$	−1.04414e7	−0.330901
$317$	2.84445e7i	0.892938i	0.894799	+	0.446469i	$0.147319\pi$
$317$	2.84445e7i	0.892938i	−0.894799	+	0.446469i	$0.852681\pi$
$318$	0	0
$319$	1.65955e7	0.511233
$320$	− 355339.i	− 0.0108441i
$321$	0	0
$322$	−5.23547e7	−1.56815
$323$	− 2.10856e7i	− 0.625717i
$324$	0	0
$325$	−3.60822e7	−1.05110
$326$	1.22599e7i	0.353863i
$327$	0	0
$328$	−1.00265e7	−0.284137
$329$	− 1.13362e8i	− 3.18331i
$330$	0	0
$331$	−6.55453e7	−1.80741	−0.903707	−	0.428151i	$-0.859165\pi$
$331$	−6.55453e7	−1.80741	−0.903707	+	0.428151i	$0.859165\pi$
$332$	3.17344e7i	0.867192i
$333$	0	0
$334$	1.87811e7	0.504059
$335$	− 981378.i	− 0.0261037i
$336$	0	0
$337$	−3.09965e6	−0.0809885	−0.0404943	−	0.999180i	$-0.512893\pi$
$337$	−3.09965e6	−0.0809885	−0.0404943	+	0.999180i	$0.512893\pi$
$338$	− 3.32099e6i	− 0.0860037i
$339$	0	0
$340$	−1.17365e6	−0.0298609
$341$	− 1.07400e7i	− 0.270857i
$342$	0	0
$343$	−1.15641e8	−2.86570
$344$	9.76020e6i	0.239764i
$345$	0	0
$346$	5.17275e6	0.124880
$347$	− 4.91739e6i	− 0.117692i	−0.998267	−	0.0588459i	$-0.981258\pi$
$347$	− 4.91739e6i	− 0.117692i	0.998267	−	0.0588459i	$-0.0187421\pi$
$348$	0	0
$349$	1.79878e7	0.423158	0.211579	−	0.977361i	$-0.432139\pi$
$349$	1.79878e7	0.423158	0.211579	+	0.977361i	$0.432139\pi$
$350$	5.65009e7i	1.31781i
$351$	0	0
$352$	−7.08061e6	−0.162346
$353$	2.29012e7i	0.520636i	0.965523	+	0.260318i	$0.0838274\pi$
$353$	2.29012e7i	0.520636i	−0.965523	+	0.260318i	$0.916173\pi$
$354$	0	0
$355$	4.66015e6	0.104163
$356$	− 1.72192e7i	− 0.381649i
$357$	0	0
$358$	1.93831e7	0.422448
$359$	− 4.37616e7i	− 0.945823i	−0.881110	−	0.472911i	$-0.843203\pi$
$359$	− 4.37616e7i	− 0.945823i	0.881110	−	0.472911i	$-0.156797\pi$
$360$	0	0
$361$	−8.17922e6	−0.173856
$362$	2.92195e7i	0.615951i
$363$	0	0
$364$	−4.79563e7	−0.994356
$365$	2.97139e6i	0.0611057i
$366$	0	0
$367$	1.53969e6	0.0311484	0.0155742	−	0.999879i	$-0.495042\pi$
$367$	1.53969e6	0.0311484	0.0155742	+	0.999879i	$0.495042\pi$
$368$	1.47143e7i	0.295254i
$369$	0	0
$370$	−1.71140e6	−0.0337867
$371$	− 5.40505e7i	− 1.05847i
$372$	0	0
$373$	6.56732e6	0.126550	0.0632749	−	0.997996i	$-0.479846\pi$
$373$	6.56732e6	0.126550	0.0632749	+	0.997996i	$0.479846\pi$
$374$	2.33866e7i	0.447047i
$375$	0	0
$376$	−3.18603e7	−0.599358
$377$	− 3.15900e7i	− 0.589557i
$378$	0	0
$379$	1.40337e7	0.257783	0.128892	−	0.991659i	$-0.458858\pi$
$379$	1.40337e7	0.257783	0.128892	+	0.991659i	$0.458858\pi$
$380$	− 2.16338e6i	− 0.0394259i
$381$	0	0
$382$	3.04465e7	0.546195
$383$	− 3.88724e7i	− 0.691902i	−0.938253	−	0.345951i	$-0.887556\pi$
$383$	− 3.88724e7i	− 0.691902i	0.938253	−	0.345951i	$-0.112444\pi$
$384$	0	0
$385$	−8.53749e6	−0.149606
$386$	− 4.22222e7i	− 0.734139i
$387$	0	0
$388$	2.75038e6	0.0470867
$389$	1.56134e7i	0.265246i	0.991167	+	0.132623i	$0.0423399\pi$
$389$	1.56134e7i	0.265246i	−0.991167	+	0.132623i	$0.957660\pi$
$390$	0	0
$391$	4.86000e7	0.813028
$392$	5.37977e7i	0.893111i
$393$	0	0
$394$	1.50534e7	0.246120
$395$	3.53836e6i	0.0574131i
$396$	0	0
$397$	1.02776e8	1.64255	0.821277	−	0.570530i	$-0.193262\pi$
$397$	1.02776e8	1.64255	0.821277	+	0.570530i	$0.193262\pi$
$398$	− 6.39983e7i	− 1.01512i
$399$	0	0
$400$	1.58796e7	0.248118
$401$	4.94668e7i	0.767151i	0.923509	+	0.383576i	$0.125307\pi$
$401$	4.94668e7i	0.767151i	−0.923509	+	0.383576i	$0.874693\pi$
$402$	0	0
$403$	−2.04438e7	−0.312353
$404$	− 3.84599e7i	− 0.583262i
$405$	0	0
$406$	−4.94666e7	−0.739153
$407$	3.41018e7i	0.505818i
$408$	0	0
$409$	−1.32640e8	−1.93868	−0.969338	−	0.245730i	$-0.920972\pi$
$409$	−1.32640e8	−1.93868	−0.969338	+	0.245730i	$0.920972\pi$
$410$	3.39776e6i	0.0492994i
$411$	0	0
$412$	1.06712e7	0.152588
$413$	2.27463e8i	3.22894i
$414$	0	0
$415$	1.07541e7	0.150463
$416$	1.34781e7i	0.187219i
$417$	0	0
$418$	−4.31081e7	−0.590242
$419$	1.10865e8i	1.50713i	0.657371	+	0.753567i	$0.271668\pi$
$419$	1.10865e8i	1.50713i	−0.657371	+	0.753567i	$0.728332\pi$
$420$	0	0
$421$	−9.23503e7	−1.23763	−0.618817	−	0.785535i	$-0.712388\pi$
$421$	−9.23503e7	−1.23763	−0.618817	+	0.785535i	$0.712388\pi$
$422$	− 2.96232e7i	− 0.394180i
$423$	0	0
$424$	−1.51909e7	−0.199290
$425$	− 5.24489e7i	− 0.683234i
$426$	0	0
$427$	−1.07323e8	−1.37850
$428$	− 6.90963e7i	− 0.881299i
$429$	0	0
$430$	3.30752e6	0.0416003
$431$	− 7.54869e7i	− 0.942844i	−0.881908	−	0.471422i	$-0.843741\pi$
$431$	− 7.54869e7i	− 0.942844i	0.881908	−	0.471422i	$-0.156259\pi$
$432$	0	0
$433$	−1.02871e8	−1.26716	−0.633578	−	0.773679i	$-0.718414\pi$
$433$	−1.02871e8	−1.26716	−0.633578	+	0.773679i	$0.718414\pi$
$434$	3.20128e7i	0.391611i
$435$	0	0
$436$	2.08526e7	0.251594
$437$	8.95834e7i	1.07345i
$438$	0	0
$439$	−4.53719e7	−0.536282	−0.268141	−	0.963380i	$-0.586409\pi$
$439$	−4.53719e7	−0.536282	−0.268141	+	0.963380i	$0.586409\pi$
$440$	2.39946e6i	0.0281680i
$441$	0	0
$442$	4.45171e7	0.515537
$443$	1.04394e8i	1.20079i	0.799705	+	0.600393i	$0.204989\pi$
$443$	1.04394e8i	1.20079i	−0.799705	+	0.600393i	$0.795011\pi$
$444$	0	0
$445$	−5.83522e6	−0.0662182
$446$	− 5.04801e7i	− 0.569004i
$447$	0	0
$448$	2.11053e7	0.234724
$449$	1.66601e7i	0.184051i	0.995757	+	0.0920257i	$0.0293342\pi$
$449$	1.66601e7i	0.184051i	−0.995757	+	0.0920257i	$0.970666\pi$
$450$	0	0
$451$	6.77049e7	0.738058
$452$	− 1.42580e7i	− 0.154399i
$453$	0	0
$454$	7.12719e6	0.0761642
$455$	1.62513e7i	0.172526i
$456$	0	0
$457$	1.77161e8	1.85618	0.928088	−	0.372360i	$-0.121451\pi$
$457$	1.77161e8	1.85618	0.928088	+	0.372360i	$0.121451\pi$
$458$	− 8.62732e7i	− 0.898006i
$459$	0	0
$460$	4.98634e6	0.0512282
$461$	− 1.80252e7i	− 0.183983i	−0.995760	−	0.0919915i	$-0.970677\pi$
$461$	− 1.80252e7i	− 0.183983i	0.995760	−	0.0919915i	$-0.0293233\pi$
$462$	0	0
$463$	4.74747e7	0.478320	0.239160	−	0.970980i	$-0.423128\pi$
$463$	4.74747e7	0.478320	0.239160	+	0.970980i	$0.423128\pi$
$464$	1.39026e7i	0.139169i
$465$	0	0
$466$	5.59083e6	0.0552483
$467$	1.97335e7i	0.193755i	0.995296	+	0.0968776i	$0.0308855\pi$
$467$	1.97335e7i	0.193755i	−0.995296	+	0.0968776i	$0.969114\pi$
$468$	0	0
$469$	5.82887e7	0.565023
$470$	1.07967e7i	0.103992i
$471$	0	0
$472$	6.39284e7	0.607950
$473$	− 6.59067e7i	− 0.622796i
$474$	0	0
$475$	9.66780e7	0.902084
$476$	− 6.97089e7i	− 0.646350i
$477$	0	0
$478$	−1.03354e8	−0.946336
$479$	− 1.90958e8i	− 1.73753i	−0.495229	−	0.868763i	$-0.664916\pi$
$479$	− 1.90958e8i	− 1.73753i	0.495229	−	0.868763i	$-0.335084\pi$
$480$	0	0
$481$	6.49137e7	0.583313
$482$	3.65776e6i	0.0326643i
$483$	0	0
$484$	−8.87748e6	−0.0782985
$485$	− 932044.i	− 0.00816980i
$486$	0	0
$487$	1.45899e8	1.26318	0.631592	−	0.775301i	$-0.282402\pi$
$487$	1.45899e8	1.26318	0.631592	+	0.775301i	$0.282402\pi$
$488$	3.01630e7i	0.259546i
$489$	0	0
$490$	1.82309e7	0.154960
$491$	− 9.52804e7i	− 0.804931i	−0.915435	−	0.402466i	$-0.868153\pi$
$491$	− 9.52804e7i	− 0.804931i	0.915435	−	0.402466i	$-0.131847\pi$
$492$	0	0
$493$	4.59190e7	0.383223
$494$	8.20574e7i	0.680671i
$495$	0	0
$496$	8.99719e6	0.0737330
$497$	2.76788e8i	2.25465i
$498$	0	0
$499$	2.18536e8	1.75882	0.879410	−	0.476066i	$-0.157938\pi$
$499$	2.18536e8	1.75882	0.879410	+	0.476066i	$0.157938\pi$
$500$	− 1.08033e7i	− 0.0864263i
$501$	0	0
$502$	5.79304e6	0.0457926
$503$	1.09519e8i	0.860569i	0.902693	+	0.430285i	$0.141587\pi$
$503$	1.09519e8i	0.860569i	−0.902693	+	0.430285i	$0.858413\pi$
$504$	0	0
$505$	−1.30332e7	−0.101199
$506$	− 9.93596e7i	− 0.766934i
$507$	0	0
$508$	1.00651e8	0.767760
$509$	− 3.26109e7i	− 0.247291i	−0.992326	−	0.123646i	$-0.960541\pi$
$509$	− 3.26109e7i	− 0.247291i	0.992326	−	0.123646i	$-0.0394586\pi$
$510$	0	0
$511$	−1.76485e8	−1.32265
$512$	− 5.93164e6i	− 0.0441942i
$513$	0	0
$514$	5.73238e7	0.422129
$515$	− 3.61622e6i	− 0.0264748i
$516$	0	0
$517$	2.15140e8	1.55686
$518$	− 1.01648e8i	− 0.731323i
$519$	0	0
$520$	4.56744e6	0.0324835
$521$	1.60218e8i	1.13292i	0.824090	+	0.566459i	$0.191687\pi$
$521$	1.60218e8i	1.13292i	−0.824090	+	0.566459i	$0.808313\pi$
$522$	0	0
$523$	−1.05186e8	−0.735277	−0.367638	−	0.929969i	$-0.619834\pi$
$523$	−1.05186e8	−0.735277	−0.367638	+	0.929969i	$0.619834\pi$
$524$	3.34811e7i	0.232705i
$525$	0	0
$526$	−1.25174e8	−0.860113
$527$	− 2.97169e7i	− 0.203036i
$528$	0	0
$529$	−5.84441e7	−0.394797
$530$	5.14786e6i	0.0345779i
$531$	0	0
$532$	1.28493e8	0.853385
$533$	− 1.28878e8i	− 0.851133i
$534$	0	0
$535$	−2.34152e7	−0.152910
$536$	− 1.63820e7i	− 0.106383i
$537$	0	0
$538$	1.01725e8	0.653253
$539$	− 3.63274e8i	− 2.31989i
$540$	0	0
$541$	5.75829e7	0.363665	0.181833	−	0.983329i	$-0.441797\pi$
$541$	5.75829e7	0.363665	0.181833	+	0.983329i	$0.441797\pi$
$542$	− 1.74446e8i	− 1.09563i
$543$	0	0
$544$	−1.95917e7	−0.121696
$545$	− 7.06647e6i	− 0.0436529i
$546$	0	0
$547$	2.97479e8	1.81759	0.908793	−	0.417247i	$-0.137005\pi$
$547$	2.97479e8	1.81759	0.908793	+	0.417247i	$0.137005\pi$
$548$	1.49295e6i	0.00907203i
$549$	0	0
$550$	−1.07228e8	−0.644498
$551$	8.46417e7i	0.505976i
$552$	0	0
$553$	−2.10160e8	−1.24273
$554$	6.70457e7i	0.394314i
$555$	0	0
$556$	4.44353e7	0.258526
$557$	− 1.72089e8i	− 0.995837i	−0.867224	−	0.497919i	$-0.834098\pi$
$557$	− 1.72089e8i	− 0.995837i	0.867224	−	0.497919i	$-0.165902\pi$
$558$	0	0
$559$	−1.25455e8	−0.718212
$560$	− 7.15212e6i	− 0.0407259i
$561$	0	0
$562$	3.19866e7	0.180202
$563$	− 1.10657e8i	− 0.620089i	−0.950722	−	0.310045i	$-0.899656\pi$
$563$	− 1.10657e8i	− 0.620089i	0.950722	−	0.310045i	$-0.100344\pi$
$564$	0	0
$565$	−4.83173e6	−0.0267891
$566$	− 1.24951e8i	− 0.689113i
$567$	0	0
$568$	7.77913e7	0.424508
$569$	3.10143e8i	1.68355i	0.539832	+	0.841773i	$0.318488\pi$
$569$	3.10143e8i	1.68355i	−0.539832	+	0.841773i	$0.681512\pi$
$570$	0	0
$571$	−8.86366e7	−0.476107	−0.238054	−	0.971252i	$-0.576509\pi$
$571$	−8.86366e7	−0.476107	−0.238054	+	0.971252i	$0.576509\pi$
$572$	− 9.10123e7i	− 0.486309i
$573$	0	0
$574$	−2.01809e8	−1.06710
$575$	2.22832e8i	1.17213i
$576$	0	0
$577$	2.56524e7	0.133537	0.0667683	−	0.997769i	$-0.478731\pi$
$577$	2.56524e7	0.133537	0.0667683	+	0.997769i	$0.478731\pi$
$578$	− 7.18331e7i	− 0.371998i
$579$	0	0
$580$	4.71128e6	0.0241465
$581$	6.38736e8i	3.25681i
$582$	0	0
$583$	1.02578e8	0.517665
$584$	4.96011e7i	0.249031i
$585$	0	0
$586$	2.43741e8	1.21126
$587$	− 1.48812e8i	− 0.735739i	−0.929877	−	0.367870i	$-0.880087\pi$
$587$	− 1.48812e8i	− 0.735739i	0.929877	−	0.367870i	$-0.119913\pi$
$588$	0	0
$589$	5.47767e7	0.268071
$590$	− 2.16639e7i	− 0.105483i
$591$	0	0
$592$	−2.85682e7	−0.137695
$593$	2.06413e8i	0.989858i	0.868933	+	0.494929i	$0.164806\pi$
$593$	2.06413e8i	0.989858i	−0.868933	+	0.494929i	$0.835194\pi$
$594$	0	0
$595$	−2.36228e7	−0.112145
$596$	− 1.20921e8i	− 0.571165i
$597$	0	0
$598$	−1.89133e8	−0.884433
$599$	− 2.21331e8i	− 1.02982i	−0.857244	−	0.514910i	$-0.827825\pi$
$599$	− 2.21331e8i	− 1.02982i	0.857244	−	0.514910i	$-0.172175\pi$
$600$	0	0
$601$	9.14352e7	0.421202	0.210601	−	0.977572i	$-0.432458\pi$
$601$	9.14352e7	0.421202	0.210601	+	0.977572i	$0.432458\pi$
$602$	1.96449e8i	0.900453i
$603$	0	0
$604$	−8.13007e7	−0.368964
$605$	3.00838e6i	0.0135852i
$606$	0	0
$607$	−5.02431e7	−0.224652	−0.112326	−	0.993671i	$-0.535830\pi$
$607$	−5.02431e7	−0.224652	−0.112326	+	0.993671i	$0.535830\pi$
$608$	− 3.61130e7i	− 0.160677i
$609$	0	0
$610$	1.02216e7	0.0450327
$611$	− 4.09524e8i	− 1.79538i
$612$	0	0
$613$	7.04589e7	0.305883	0.152941	−	0.988235i	$-0.451125\pi$
$613$	7.04589e7	0.305883	0.152941	+	0.988235i	$0.451125\pi$
$614$	4.02898e7i	0.174056i
$615$	0	0
$616$	−1.42515e8	−0.609705
$617$	4.03804e8i	1.71916i	0.511004	+	0.859578i	$0.329274\pi$
$617$	4.03804e8i	1.71916i	−0.511004	+	0.859578i	$0.670726\pi$
$618$	0	0
$619$	−1.00243e8	−0.422653	−0.211326	−	0.977416i	$-0.567778\pi$
$619$	−1.00243e8	−0.422653	−0.211326	+	0.977416i	$0.567778\pi$
$620$	− 3.04895e6i	− 0.0127931i
$621$	0	0
$622$	1.26309e8	0.524885
$623$	− 3.46582e8i	− 1.43331i
$624$	0	0
$625$	2.38642e8	0.977479
$626$	− 1.51641e8i	− 0.618149i
$627$	0	0
$628$	−1.99701e7	−0.0806307
$629$	9.43581e7i	0.379164i
$630$	0	0
$631$	1.87082e8	0.744635	0.372318	−	0.928105i	$-0.378563\pi$
$631$	1.87082e8	0.744635	0.372318	+	0.928105i	$0.378563\pi$
$632$	5.90656e7i	0.233982i
$633$	0	0
$634$	1.60907e8	0.631402
$635$	− 3.41083e7i	− 0.133211i
$636$	0	0
$637$	−6.91502e8	−2.67532
$638$	− 9.38785e7i	− 0.361497i
$639$	0	0
$640$	−2.01010e6	−0.00766793
$641$	4.34030e8i	1.64795i	0.566623	+	0.823977i	$0.308250\pi$
$641$	4.34030e8i	1.64795i	−0.566623	+	0.823977i	$0.691750\pi$
$642$	0	0
$643$	−4.12837e8	−1.55291	−0.776453	−	0.630175i	$-0.782983\pi$
$643$	−4.12837e8	−1.55291	−0.776453	+	0.630175i	$0.782983\pi$
$644$	2.96163e8i	1.10885i
$645$	0	0
$646$	−1.19278e8	−0.442449
$647$	2.07934e8i	0.767736i	0.923388	+	0.383868i	$0.125408\pi$
$647$	2.07934e8i	0.767736i	−0.923388	+	0.383868i	$0.874592\pi$
$648$	0	0
$649$	−4.31682e8	−1.57917
$650$	2.04112e8i	0.743239i
$651$	0	0
$652$	6.93527e7	0.250219
$653$	− 4.08763e8i	− 1.46802i	−0.679139	−	0.734010i	$-0.737647\pi$
$653$	− 4.08763e8i	− 1.46802i	0.679139	−	0.734010i	$-0.262353\pi$
$654$	0	0
$655$	1.13460e7	0.0403756
$656$	5.67185e7i	0.200915i
$657$	0	0
$658$	−6.41270e8	−2.25094
$659$	− 9.35713e7i	− 0.326954i	−0.986547	−	0.163477i	$-0.947729\pi$
$659$	− 9.35713e7i	− 0.326954i	0.986547	−	0.163477i	$-0.0522709\pi$
$660$	0	0
$661$	−2.91881e8	−1.01065	−0.505326	−	0.862929i	$-0.668628\pi$
$661$	−2.91881e8	−1.01065	−0.505326	+	0.862929i	$0.668628\pi$
$662$	3.70780e8i	1.27804i
$663$	0	0
$664$	1.79517e8	0.613198
$665$	− 4.35435e7i	− 0.148067i
$666$	0	0
$667$	−1.95090e8	−0.657442
$668$	− 1.06242e8i	− 0.356423i
$669$	0	0
$670$	−5.55151e6	−0.0184581
$671$	− 2.03678e8i	− 0.674182i
$672$	0	0
$673$	4.27303e8	1.40182	0.700908	−	0.713252i	$-0.252778\pi$
$673$	4.27303e8	1.40182	0.700908	+	0.713252i	$0.252778\pi$
$674$	1.75343e7i	0.0572675i
$675$	0	0
$676$	−1.87863e7	−0.0608138
$677$	− 1.90064e8i	− 0.612539i	−0.951945	−	0.306270i	$-0.900919\pi$
$677$	− 1.90064e8i	− 0.612539i	0.951945	−	0.306270i	$-0.0990809\pi$
$678$	0	0
$679$	5.53585e7	0.176838
$680$	6.63919e6i	0.0211149i
$681$	0	0
$682$	−6.07544e7	−0.191525
$683$	4.43458e8i	1.39184i	0.718118	+	0.695921i	$0.245004\pi$
$683$	4.43458e8i	1.39184i	−0.718118	+	0.695921i	$0.754996\pi$
$684$	0	0
$685$	505929.	0.00157405
$686$	6.54166e8i	2.02635i
$687$	0	0
$688$	5.52120e7	0.169539
$689$	− 1.95260e8i	− 0.596974i
$690$	0	0
$691$	−4.23647e8	−1.28402	−0.642008	−	0.766698i	$-0.721898\pi$
$691$	−4.23647e8	−1.28402	−0.642008	+	0.766698i	$0.721898\pi$
$692$	− 2.92615e7i	− 0.0883035i
$693$	0	0
$694$	−2.78170e7	−0.0832207
$695$	− 1.50581e7i	− 0.0448556i
$696$	0	0
$697$	1.87336e8	0.553252
$698$	− 1.01755e8i	− 0.299218i
$699$	0	0
$700$	3.19618e8	0.931830
$701$	− 3.61142e8i	− 1.04839i	−0.851598	−	0.524196i	$-0.824366\pi$
$701$	− 3.61142e8i	− 1.04839i	0.851598	−	0.524196i	$-0.175634\pi$
$702$	0	0
$703$	−1.73929e8	−0.500616
$704$	4.00540e7i	0.114796i
$705$	0	0
$706$	1.29549e8	0.368145
$707$	− 7.74104e8i	− 2.19049i
$708$	0	0
$709$	−1.78710e8	−0.501431	−0.250715	−	0.968061i	$-0.580666\pi$
$709$	−1.78710e8	−0.501431	−0.250715	+	0.968061i	$0.580666\pi$
$710$	− 2.63618e7i	− 0.0736545i
$711$	0	0
$712$	−9.74068e7	−0.269867
$713$	1.26254e8i	0.348319i
$714$	0	0
$715$	−3.08421e7	−0.0843772
$716$	− 1.09647e8i	− 0.298716i
$717$	0	0
$718$	−2.47553e8	−0.668798
$719$	− 3.00407e8i	− 0.808209i	−0.914713	−	0.404105i	$-0.867583\pi$
$719$	− 3.00407e8i	− 0.808209i	0.914713	−	0.404105i	$-0.132417\pi$
$720$	0	0
$721$	2.14785e8	0.573056
$722$	4.62687e7i	0.122935i
$723$	0	0
$724$	1.65290e8	0.435543
$725$	2.10540e8i	0.552485i
$726$	0	0
$727$	5.89387e7	0.153390	0.0766950	−	0.997055i	$-0.475563\pi$
$727$	5.89387e7	0.153390	0.0766950	+	0.997055i	$0.475563\pi$
$728$	2.71282e8i	0.703116i
$729$	0	0
$730$	1.68087e7	0.0432082
$731$	− 1.82361e8i	− 0.466851i
$732$	0	0
$733$	4.49676e8	1.14180	0.570898	−	0.821021i	$-0.306595\pi$
$733$	4.49676e8	1.14180	0.570898	+	0.821021i	$0.306595\pi$
$734$	− 8.70980e6i	− 0.0220252i
$735$	0	0
$736$	8.32365e7	0.208776
$737$	1.10621e8i	0.276335i
$738$	0	0
$739$	5.27583e8	1.30725	0.653623	−	0.756820i	$-0.273248\pi$
$739$	5.27583e8	1.30725	0.653623	+	0.756820i	$0.273248\pi$
$740$	9.68112e6i	0.0238908i
$741$	0	0
$742$	−3.05756e8	−0.748451
$743$	2.46571e8i	0.601140i	0.953760	+	0.300570i	$0.0971770\pi$
$743$	2.46571e8i	0.601140i	−0.953760	+	0.300570i	$0.902823\pi$
$744$	0	0
$745$	−4.09774e7	−0.0991003
$746$	− 3.71504e7i	− 0.0894842i
$747$	0	0
$748$	1.32295e8	0.316110
$749$	− 1.39074e9i	− 3.30979i
$750$	0	0
$751$	−6.15412e8	−1.45294	−0.726468	−	0.687201i	$-0.758839\pi$
$751$	−6.15412e8	−1.45294	−0.726468	+	0.687201i	$0.758839\pi$
$752$	1.80229e8i	0.423810i
$753$	0	0
$754$	−1.78700e8	−0.416880
$755$	2.75510e7i	0.0640172i
$756$	0	0
$757$	−3.11945e8	−0.719102	−0.359551	−	0.933125i	$-0.617070\pi$
$757$	−3.11945e8	−0.719102	−0.359551	+	0.933125i	$0.617070\pi$
$758$	− 7.93867e7i	− 0.182280i
$759$	0	0
$760$	−1.22379e7	−0.0278783
$761$	2.30759e8i	0.523607i	0.965121	+	0.261804i	$0.0843172\pi$
$761$	2.30759e8i	0.523607i	−0.965121	+	0.261804i	$0.915683\pi$
$762$	0	0
$763$	4.19711e8	0.944881
$764$	− 1.72232e8i	− 0.386218i
$765$	0	0
$766$	−2.19895e8	−0.489249
$767$	8.21718e8i	1.82111i
$768$	0	0
$769$	−3.15506e8	−0.693791	−0.346895	−	0.937904i	$-0.612764\pi$
$769$	−3.15506e8	−0.693791	−0.346895	+	0.937904i	$0.612764\pi$
$770$	4.82954e7i	0.105787i
$771$	0	0
$772$	−2.38845e8	−0.519115
$773$	− 1.28960e8i	− 0.279200i	−0.990208	−	0.139600i	$-0.955418\pi$
$773$	− 1.28960e8i	− 0.279200i	0.990208	−	0.139600i	$-0.0445817\pi$
$774$	0	0
$775$	1.36253e8	0.292712
$776$	− 1.55585e7i	− 0.0332953i
$777$	0	0
$778$	8.83227e7	0.187557
$779$	3.45313e8i	0.730467i
$780$	0	0
$781$	−5.25293e8	−1.10268
$782$	− 2.74923e8i	− 0.574898i
$783$	0	0
$784$	3.04326e8	0.631525
$785$	6.76741e6i	0.0139899i
$786$	0	0
$787$	−4.21592e8	−0.864904	−0.432452	−	0.901657i	$-0.642352\pi$
$787$	−4.21592e8	−0.864904	−0.432452	+	0.901657i	$0.642352\pi$
$788$	− 8.51550e7i	− 0.174033i
$789$	0	0
$790$	2.00160e7	0.0405972
$791$	− 2.86980e8i	− 0.579858i
$792$	0	0
$793$	−3.87707e8	−0.777471
$794$	− 5.81388e8i	− 1.16146i
$795$	0	0
$796$	−3.62029e8	−0.717801
$797$	3.75685e8i	0.742076i	0.928618	+	0.371038i	$0.120998\pi$
$797$	3.75685e8i	0.742076i	−0.928618	+	0.371038i	$0.879002\pi$
$798$	0	0
$799$	5.95281e8	1.16703
$800$	− 8.98285e7i	− 0.175446i
$801$	0	0
$802$	2.79827e8	0.542458
$803$	− 3.34936e8i	− 0.646868i
$804$	0	0
$805$	1.00363e8	0.192392
$806$	1.15648e8i	0.220867i
$807$	0	0
$808$	−2.17562e8	−0.412429
$809$	− 8.24005e8i	− 1.55627i	−0.628099	−	0.778134i	$-0.716167\pi$
$809$	− 8.24005e8i	− 1.55627i	0.628099	−	0.778134i	$-0.283833\pi$
$810$	0	0
$811$	4.93886e8	0.925900	0.462950	−	0.886385i	$-0.346791\pi$
$811$	4.93886e8	0.925900	0.462950	+	0.886385i	$0.346791\pi$
$812$	2.79825e8i	0.522660i
$813$	0	0
$814$	1.92909e8	0.357668
$815$	− 2.35021e7i	− 0.0434144i
$816$	0	0
$817$	3.36142e8	0.616391
$818$	7.50326e8i	1.37085i
$819$	0	0
$820$	1.92206e7	0.0348599
$821$	− 2.82967e8i	− 0.511335i	−0.966765	−	0.255668i	$-0.917705\pi$
$821$	− 2.82967e8i	− 0.511335i	0.966765	−	0.255668i	$-0.0822952\pi$
$822$	0	0
$823$	9.03257e8	1.62036	0.810181	−	0.586180i	$-0.199369\pi$
$823$	9.03257e8	1.62036	0.810181	+	0.586180i	$0.199369\pi$
$824$	− 6.03652e7i	− 0.107896i
$825$	0	0
$826$	1.28672e9	2.28320
$827$	6.02362e8i	1.06498i	0.846437	+	0.532489i	$0.178743\pi$
$827$	6.02362e8i	1.06498i	−0.846437	+	0.532489i	$0.821257\pi$
$828$	0	0
$829$	7.35623e8	1.29120	0.645598	−	0.763678i	$-0.276608\pi$
$829$	7.35623e8	1.29120	0.645598	+	0.763678i	$0.276608\pi$
$830$	− 6.08342e7i	− 0.106393i
$831$	0	0
$832$	7.62438e7	0.132384
$833$	− 1.00516e9i	− 1.73901i
$834$	0	0
$835$	−3.60030e7	−0.0618414
$836$	2.43856e8i	0.417364i
$837$	0	0
$838$	6.27146e8	1.06570
$839$	6.85512e8i	1.16072i	0.814358	+	0.580362i	$0.197089\pi$
$839$	6.85512e8i	1.16072i	−0.814358	+	0.580362i	$0.802911\pi$
$840$	0	0
$841$	4.10495e8	0.690113
$842$	5.22412e8i	0.875139i
$843$	0	0
$844$	−1.67574e8	−0.278727
$845$	6.36628e6i	0.0105515i
$846$	0	0
$847$	−1.78682e8	−0.294056
$848$	8.59327e7i	0.140919i
$849$	0	0
$850$	−2.96696e8	−0.483119
$851$	− 4.00886e8i	− 0.650478i
$852$	0	0
$853$	1.06641e7	0.0171821	0.00859107	−	0.999963i	$-0.497265\pi$
$853$	1.06641e7	0.0171821	0.00859107	+	0.999963i	$0.497265\pi$
$854$	6.07108e8i	0.974748i
$855$	0	0
$856$	−3.90868e8	−0.623173
$857$	6.40409e8i	1.01745i	0.860928	+	0.508727i	$0.169884\pi$
$857$	6.40409e8i	1.01745i	−0.860928	+	0.508727i	$0.830116\pi$
$858$	0	0
$859$	9.34479e8	1.47431	0.737157	−	0.675721i	$-0.236168\pi$
$859$	9.34479e8	1.47431	0.737157	+	0.675721i	$0.236168\pi$
$860$	− 1.87101e7i	− 0.0294159i
$861$	0	0
$862$	−4.27018e8	−0.666691
$863$	− 9.15183e8i	− 1.42389i	−0.702236	−	0.711944i	$-0.747815\pi$
$863$	− 9.15183e8i	− 1.42389i	0.702236	−	0.711944i	$-0.252185\pi$
$864$	0	0
$865$	−9.91607e6	−0.0153211
$866$	5.81927e8i	0.896014i
$867$	0	0
$868$	1.81092e8	0.276910
$869$	− 3.98846e8i	− 0.607779i
$870$	0	0
$871$	2.10570e8	0.318671
$872$	− 1.17960e8i	− 0.177904i
$873$	0	0
$874$	5.06760e8	0.759046
$875$	− 2.17444e8i	− 0.324581i
$876$	0	0
$877$	5.31704e8	0.788263	0.394131	−	0.919054i	$-0.371045\pi$
$877$	5.31704e8	0.788263	0.394131	+	0.919054i	$0.371045\pi$
$878$	2.56662e8i	0.379209i
$879$	0	0
$880$	1.35734e7	0.0199178
$881$	8.42150e8i	1.23158i	0.787911	+	0.615789i	$0.211162\pi$
$881$	8.42150e8i	1.23158i	−0.787911	+	0.615789i	$0.788838\pi$
$882$	0	0
$883$	−8.92713e8	−1.29667	−0.648335	−	0.761355i	$-0.724534\pi$
$883$	−8.92713e8	−1.29667	−0.648335	+	0.761355i	$0.724534\pi$
$884$	− 2.51826e8i	− 0.364539i
$885$	0	0
$886$	5.90544e8	0.849084
$887$	5.85422e8i	0.838876i	0.907784	+	0.419438i	$0.137773\pi$
$887$	5.85422e8i	0.838876i	−0.907784	+	0.419438i	$0.862227\pi$
$888$	0	0
$889$	2.02585e9	2.88339
$890$	3.30090e7i	0.0468233i
$891$	0	0
$892$	−2.85558e8	−0.402347
$893$	1.09727e9i	1.54085i
$894$	0	0
$895$	−3.71570e7	−0.0518288
$896$	− 1.19390e8i	− 0.165975i
$897$	0	0
$898$	9.42439e7	0.130144
$899$	1.19290e8i	0.164181i
$900$	0	0
$901$	2.83828e8	0.388044
$902$	− 3.82997e8i	− 0.521886i
$903$	0	0
$904$	−8.06556e7	−0.109177
$905$	− 5.60132e7i	− 0.0755692i
$906$	0	0
$907$	−1.20054e9	−1.60900	−0.804500	−	0.593953i	$-0.797567\pi$
$907$	−1.20054e9	−1.60900	−0.804500	+	0.593953i	$0.797567\pi$
$908$	− 4.03175e7i	− 0.0538562i
$909$	0	0
$910$	9.19315e7	0.121994
$911$	− 1.19991e9i	− 1.58706i	−0.608529	−	0.793532i	$-0.708240\pi$
$911$	− 1.19991e9i	− 1.58706i	0.608529	−	0.793532i	$-0.291760\pi$
$912$	0	0
$913$	−1.21220e9	−1.59281
$914$	− 1.00217e9i	− 1.31252i
$915$	0	0
$916$	−4.88035e8	−0.634986
$917$	6.73893e8i	0.873943i
$918$	0	0
$919$	−2.76379e8	−0.356089	−0.178045	−	0.984022i	$-0.556977\pi$
$919$	−2.76379e8	−0.356089	−0.178045	+	0.984022i	$0.556977\pi$
$920$	− 2.82070e7i	− 0.0362238i
$921$	0	0
$922$	−1.01966e8	−0.130096
$923$	9.99909e8i	1.27161i
$924$	0	0
$925$	−4.32635e8	−0.546633
$926$	− 2.68557e8i	− 0.338224i
$927$	0	0
$928$	7.86449e7	0.0984072
$929$	1.14847e9i	1.43243i	0.697879	+	0.716216i	$0.254127\pi$
$929$	1.14847e9i	1.43243i	−0.697879	+	0.716216i	$0.745873\pi$
$930$	0	0
$931$	1.85280e9	2.29603
$932$	− 3.16265e7i	− 0.0390664i
$933$	0	0
$934$	1.11630e8	0.137006
$935$	− 4.48318e7i	− 0.0548468i
$936$	0	0
$937$	−3.65044e8	−0.443738	−0.221869	−	0.975077i	$-0.571216\pi$
$937$	−3.65044e8	−0.443738	−0.221869	+	0.975077i	$0.571216\pi$
$938$	− 3.29731e8i	− 0.399531i
$939$	0	0
$940$	6.10756e7	0.0735334
$941$	6.63786e8i	0.796635i	0.917248	+	0.398317i	$0.130406\pi$
$941$	6.63786e8i	0.796635i	−0.917248	+	0.398317i	$0.869594\pi$
$942$	0	0
$943$	−7.95909e8	−0.949136
$944$	− 3.61633e8i	− 0.429885i
$945$	0	0
$946$	−3.72825e8	−0.440384
$947$	− 5.84917e7i	− 0.0688723i	−0.999407	−	0.0344361i	$-0.989036\pi$
$947$	− 5.84917e7i	− 0.0688723i	0.999407	−	0.0344361i	$-0.0109635\pi$
$948$	0	0
$949$	−6.37560e8	−0.745972
$950$	− 5.46893e8i	− 0.637870i
$951$	0	0
$952$	−3.94333e8	−0.457038
$953$	− 1.97385e8i	− 0.228053i	−0.993478	−	0.114026i	$-0.963625\pi$
$953$	− 1.97385e8i	− 0.228053i	0.993478	−	0.114026i	$-0.0363748\pi$
$954$	0	0
$955$	−5.83655e7	−0.0670110
$956$	5.84661e8i	0.669161i
$957$	0	0
$958$	−1.08022e9	−1.22862
$959$	3.00495e7i	0.0340708i
$960$	0	0
$961$	−8.10304e8	−0.913015
$962$	− 3.67208e8i	− 0.412464i
$963$	0	0
$964$	2.06914e7	0.0230972
$965$	8.09392e7i	0.0900693i
$966$	0	0
$967$	−1.39670e9	−1.54463	−0.772316	−	0.635239i	$-0.780902\pi$
$967$	−1.39670e9	−1.54463	−0.772316	+	0.635239i	$0.780902\pi$
$968$	5.02186e7i	0.0553654i
$969$	0	0
$970$	−5.27244e6	−0.00577692
$971$	3.57183e8i	0.390152i	0.980788	+	0.195076i	$0.0624953\pi$
$971$	3.57183e8i	0.390152i	−0.980788	+	0.195076i	$0.937505\pi$
$972$	0	0
$973$	8.94375e8	0.970914
$974$	− 8.25331e8i	− 0.893206i
$975$	0	0
$976$	1.70628e8	0.183527
$977$	− 7.70243e8i	− 0.825932i	−0.910747	−	0.412966i	$-0.864493\pi$
$977$	− 7.70243e8i	− 0.825932i	0.910747	−	0.412966i	$-0.135507\pi$
$978$	0	0
$979$	6.57748e8	0.700990
$980$	− 1.03129e8i	− 0.109573i
$981$	0	0
$982$	−5.38987e8	−0.569172
$983$	− 4.60312e8i	− 0.484609i	−0.970200	−	0.242305i	$-0.922097\pi$
$983$	− 4.60312e8i	− 0.484609i	0.970200	−	0.242305i	$-0.0779033\pi$
$984$	0	0
$985$	−2.88572e7	−0.0301957
$986$	− 2.59757e8i	− 0.270980i
$987$	0	0
$988$	4.64187e8	0.481307
$989$	7.74770e8i	0.800911i
$990$	0	0
$991$	1.55561e8	0.159837	0.0799187	−	0.996801i	$-0.474534\pi$
$991$	1.55561e8	0.159837	0.0799187	+	0.996801i	$0.474534\pi$
$992$	− 5.08958e7i	− 0.0521371i
$993$	0	0
$994$	1.56575e9	1.59428
$995$	1.22684e8i	0.124542i
$996$	0	0
$997$	1.29503e9	1.30675	0.653376	−	0.757034i	$-0.273352\pi$
$997$	1.29503e9	1.30675	0.653376	+	0.757034i	$0.273352\pi$
$998$	− 1.23623e9i	− 1.24367i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.c.161.4		12
3.2	odd	2	inner	162.7.b.c.161.9		12
9.2	odd	6		54.7.d.a.17.5		12
9.4	even	3		54.7.d.a.35.5		12
9.5	odd	6		18.7.d.a.11.3	yes	12
9.7	even	3		18.7.d.a.5.3	✓	12
36.7	odd	6		144.7.q.c.113.1		12
36.11	even	6		432.7.q.b.17.4		12
36.23	even	6		144.7.q.c.65.1		12
36.31	odd	6		432.7.q.b.305.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.3	✓	12	9.7	even	3
18.7.d.a.11.3	yes	12	9.5	odd	6
54.7.d.a.17.5		12	9.2	odd	6
54.7.d.a.35.5		12	9.4	even	3
144.7.q.c.65.1		12	36.23	even	6
144.7.q.c.113.1		12	36.7	odd	6
162.7.b.c.161.4		12	1.1	even	1	trivial
162.7.b.c.161.9		12	3.2	odd	2	inner
432.7.q.b.17.4		12	36.11	even	6
432.7.q.b.305.4		12	36.31	odd	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -32.0000 q^{4} +10.8441i q^{5} -644.082 q^{7} +181.019i q^{8} +O(q^{10})\)	\(q-5.65685i q^{2} -32.0000 q^{4} +10.8441i q^{5} -644.082 q^{7} +181.019i q^{8} +61.3435 q^{10} -1222.35i q^{11} -2326.78 q^{13} +3643.48i q^{14} +1024.00 q^{16} -3382.18i q^{17} +6234.31 q^{19} -347.011i q^{20} -6914.66 q^{22} +14369.4i q^{23} +15507.4 q^{25} +13162.2i q^{26} +20610.6 q^{28} +13576.7i q^{29} +8786.32 q^{31} -5792.62i q^{32} -19132.5 q^{34} -6984.49i q^{35} -27898.6 q^{37} -35266.6i q^{38} -1962.99 q^{40} +55389.1i q^{41} +53918.0 q^{43} +39115.2i q^{44} +81285.7 q^{46} +176005. i q^{47} +297193. q^{49} -87723.1i q^{50} +74456.8 q^{52} +83918.6i q^{53} +13255.3 q^{55} -116591. i q^{56} +76801.7 q^{58} -353158. i q^{59} +166629. q^{61} -49702.9i q^{62} -32768.0 q^{64} -25231.8i q^{65} -90498.8 q^{67} +108230. i q^{68} -39510.3 q^{70} -429740. i q^{71} +274010. q^{73} +157818. i q^{74} -199498. q^{76} +787294. i q^{77} +326294. q^{79} +11104.4i q^{80} +313328. q^{82} -991699. i q^{83} +36676.7 q^{85} -305006. i q^{86} +221269. q^{88} +538101. i q^{89} +1.49863e6 q^{91} -459821. i q^{92} +995634. q^{94} +67605.5i q^{95} -85949.5 q^{97} -1.68118e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 384 q^{4} - 480 q^{7}+O(q^{10}) \) 12 * q - 384 * q^4 - 480 * q^7	\( 12 q - 384 q^{4} - 480 q^{7} - 3360 q^{13} + 12288 q^{16} - 2820 q^{19} + 7200 q^{22} - 16188 q^{25} + 15360 q^{28} - 42960 q^{31} + 54720 q^{34} - 25536 q^{37} - 142860 q^{43} - 135072 q^{46} + 271908 q^{49} + 107520 q^{52} + 580392 q^{55} - 318528 q^{58} - 271488 q^{61} - 393216 q^{64} + 579876 q^{67} - 311904 q^{70} - 977700 q^{73} + 90240 q^{76} + 1529592 q^{79} + 1073088 q^{82} - 3239136 q^{85} - 230400 q^{88} + 355584 q^{91} + 1473696 q^{94} + 77748 q^{97}+O(q^{100}) \) 12 * q - 384 * q^4 - 480 * q^7 - 3360 * q^13 + 12288 * q^16 - 2820 * q^19 + 7200 * q^22 - 16188 * q^25 + 15360 * q^28 - 42960 * q^31 + 54720 * q^34 - 25536 * q^37 - 142860 * q^43 - 135072 * q^46 + 271908 * q^49 + 107520 * q^52 + 580392 * q^55 - 318528 * q^58 - 271488 * q^61 - 393216 * q^64 + 579876 * q^67 - 311904 * q^70 - 977700 * q^73 + 90240 * q^76 + 1529592 * q^79 + 1073088 * q^82 - 3239136 * q^85 - 230400 * q^88 + 355584 * q^91 + 1473696 * q^94 + 77748 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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