LMFDB - Embedded newform 531.8.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.a (trivial)

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:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-3.62331$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.62331 q^{2} -114.872 q^{4} -300.817 q^{5} +1353.78 q^{7} -880.000 q^{8} +O(q^{10})$	\(q+3.62331 q^{2} -114.872 q^{4} -300.817 q^{5} +1353.78 q^{7} -880.000 q^{8} -1089.96 q^{10} -8127.65 q^{11} +1822.67 q^{13} +4905.17 q^{14} +11515.0 q^{16} -1656.90 q^{17} +18541.4 q^{19} +34555.4 q^{20} -29449.0 q^{22} -15601.2 q^{23} +12366.0 q^{25} +6604.11 q^{26} -155511. q^{28} -150338. q^{29} -248513. q^{31} +154363. q^{32} -6003.46 q^{34} -407240. q^{35} -170725. q^{37} +67181.2 q^{38} +264719. q^{40} -283414. q^{41} +39428.6 q^{43} +933636. q^{44} -56528.0 q^{46} +77426.6 q^{47} +1.00917e6 q^{49} +44805.9 q^{50} -209373. q^{52} -1.98028e6 q^{53} +2.44494e6 q^{55} -1.19133e6 q^{56} -544721. q^{58} +205379. q^{59} -938894. q^{61} -900440. q^{62} -914622. q^{64} -548291. q^{65} +2.93505e6 q^{67} +190331. q^{68} -1.47556e6 q^{70} +5.87325e6 q^{71} -2.53313e6 q^{73} -618590. q^{74} -2.12988e6 q^{76} -1.10030e7 q^{77} -1.99924e6 q^{79} -3.46392e6 q^{80} -1.02690e6 q^{82} -5.33794e6 q^{83} +498424. q^{85} +142862. q^{86} +7.15233e6 q^{88} -2.14988e6 q^{89} +2.46749e6 q^{91} +1.79213e6 q^{92} +280541. q^{94} -5.57757e6 q^{95} -3.36902e6 q^{97} +3.65656e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) $ 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	3.62331	0.320259	0.160129	−	0.987096i	$-0.448809\pi$
$2$	3.62331	0.320259	0.160129	+	0.987096i	$0.448809\pi$
$3$	0	0
$3$	0	0
$4$	−114.872	−0.897434
$5$	−300.817	−1.07624	−0.538118	−	0.842869i	$-0.680865\pi$
$5$	−300.817	−1.07624	−0.538118	+	0.842869i	$0.680865\pi$
$6$	0	0
$7$	1353.78	1.49178	0.745890	−	0.666070i	$-0.232025\pi$
$7$	1353.78	1.49178	0.745890	+	0.666070i	$0.232025\pi$
$8$	−880.000	−0.607670
$9$	0	0
$10$	−1089.96	−0.344674
$11$	−8127.65	−1.84116	−0.920578	−	0.390558i	$-0.872282\pi$
$11$	−8127.65	−1.84116	−0.920578	+	0.390558i	$0.872282\pi$
$12$	0	0
$13$	1822.67	0.230095	0.115047	−	0.993360i	$-0.463298\pi$
$13$	1822.67	0.230095	0.115047	+	0.993360i	$0.463298\pi$
$14$	4905.17	0.477755
$15$	0	0
$16$	11515.0	0.702823
$17$	−1656.90	−0.0817946	−0.0408973	−	0.999163i	$-0.513022\pi$
$17$	−1656.90	−0.0817946	−0.0408973	+	0.999163i	$0.513022\pi$
$18$	0	0
$19$	18541.4	0.620161	0.310081	−	0.950710i	$-0.399644\pi$
$19$	18541.4	0.620161	0.310081	+	0.950710i	$0.399644\pi$
$20$	34555.4	0.965852
$21$	0	0
$22$	−29449.0	−0.589646
$23$	−15601.2	−0.267369	−0.133684	−	0.991024i	$-0.542681\pi$
$23$	−15601.2	−0.267369	−0.133684	+	0.991024i	$0.542681\pi$
$24$	0	0
$25$	12366.0	0.158285
$26$	6604.11	0.0736899
$27$	0	0
$28$	−155511.	−1.33877
$29$	−150338.	−1.14466	−0.572328	−	0.820025i	$-0.693960\pi$
$29$	−150338.	−1.14466	−0.572328	+	0.820025i	$0.693960\pi$
$30$	0	0
$31$	−248513.	−1.49825	−0.749123	−	0.662431i	$-0.769525\pi$
$31$	−248513.	−1.49825	−0.749123	+	0.662431i	$0.769525\pi$
$32$	154363.	0.832755
$33$	0	0
$34$	−6003.46	−0.0261954
$35$	−407240.	−1.60551
$36$	0	0
$37$	−170725.	−0.554104	−0.277052	−	0.960855i	$-0.589357\pi$
$37$	−170725.	−0.554104	−0.277052	+	0.960855i	$0.589357\pi$
$38$	67181.2	0.198612
$39$	0	0
$40$	264719.	0.653997
$41$	−283414.	−0.642210	−0.321105	−	0.947044i	$-0.604054\pi$
$41$	−283414.	−0.642210	−0.321105	+	0.947044i	$0.604054\pi$
$42$	0	0
$43$	39428.6	0.0756261	0.0378130	−	0.999285i	$-0.487961\pi$
$43$	39428.6	0.0756261	0.0378130	+	0.999285i	$0.487961\pi$
$44$	933636.	1.65232
$45$	0	0
$46$	−56528.0	−0.0856271
$47$	77426.6	0.108780	0.0543898	−	0.998520i	$-0.482679\pi$
$47$	77426.6	0.108780	0.0543898	+	0.998520i	$0.482679\pi$
$48$	0	0
$49$	1.00917e6	1.22541
$50$	44805.9	0.0506921
$51$	0	0
$52$	−209373.	−0.206495
$53$	−1.98028e6	−1.82709	−0.913546	−	0.406735i	$-0.866667\pi$
$53$	−1.98028e6	−1.82709	−0.913546	+	0.406735i	$0.866667\pi$
$54$	0	0
$55$	2.44494e6	1.98152
$56$	−1.19133e6	−0.906509
$57$	0	0
$58$	−544721.	−0.366586
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−938894.	−0.529617	−0.264808	−	0.964301i	$-0.585309\pi$
$61$	−938894.	−0.529617	−0.264808	+	0.964301i	$0.585309\pi$
$62$	−900440.	−0.479826
$63$	0	0
$64$	−914622.	−0.436126
$65$	−548291.	−0.247636
$66$	0	0
$67$	2.93505e6	1.19221	0.596107	−	0.802905i	$-0.296714\pi$
$67$	2.93505e6	1.19221	0.596107	+	0.802905i	$0.296714\pi$
$68$	190331.	0.0734053
$69$	0	0
$70$	−1.47556e6	−0.514178
$71$	5.87325e6	1.94749	0.973743	−	0.227650i	$-0.0731043\pi$
$71$	5.87325e6	1.94749	0.973743	+	0.227650i	$0.0731043\pi$
$72$	0	0
$73$	−2.53313e6	−0.762126	−0.381063	−	0.924549i	$-0.624442\pi$
$73$	−2.53313e6	−0.762126	−0.381063	+	0.924549i	$0.624442\pi$
$74$	−618590.	−0.177457
$75$	0	0
$76$	−2.12988e6	−0.556554
$77$	−1.10030e7	−2.74660
$78$	0	0
$79$	−1.99924e6	−0.456217	−0.228108	−	0.973636i	$-0.573254\pi$
$79$	−1.99924e6	−0.456217	−0.228108	+	0.973636i	$0.573254\pi$
$80$	−3.46392e6	−0.756403
$81$	0	0
$82$	−1.02690e6	−0.205673
$83$	−5.33794e6	−1.02471	−0.512354	−	0.858774i	$-0.671227\pi$
$83$	−5.33794e6	−1.02471	−0.512354	+	0.858774i	$0.671227\pi$
$84$	0	0
$85$	498424.	0.0880303
$86$	142862.	0.0242199
$87$	0	0
$88$	7.15233e6	1.11882
$89$	−2.14988e6	−0.323258	−0.161629	−	0.986852i	$-0.551675\pi$
$89$	−2.14988e6	−0.323258	−0.161629	+	0.986852i	$0.551675\pi$
$90$	0	0
$91$	2.46749e6	0.343251
$92$	1.79213e6	0.239946
$93$	0	0
$94$	280541.	0.0348376
$95$	−5.57757e6	−0.667440
$96$	0	0
$97$	−3.36902e6	−0.374802	−0.187401	−	0.982283i	$-0.560006\pi$
$97$	−3.36902e6	−0.374802	−0.187401	+	0.982283i	$0.560006\pi$
$98$	3.65656e6	0.392447
$99$	0	0
$100$	−1.42050e6	−0.142050
$101$	−1.18390e6	−0.114338	−0.0571688	−	0.998365i	$-0.518207\pi$
$101$	−1.18390e6	−0.114338	−0.0571688	+	0.998365i	$0.518207\pi$
$102$	0	0
$103$	−1.00671e7	−0.907764	−0.453882	−	0.891062i	$-0.649961\pi$
$103$	−1.00671e7	−0.907764	−0.453882	+	0.891062i	$0.649961\pi$
$104$	−1.60395e6	−0.139822
$105$	0	0
$106$	−7.17517e6	−0.585142
$107$	5.24702e6	0.414066	0.207033	−	0.978334i	$-0.433619\pi$
$107$	5.24702e6	0.414066	0.207033	+	0.978334i	$0.433619\pi$
$108$	0	0
$109$	1.31376e7	0.971681	0.485841	−	0.874047i	$-0.338514\pi$
$109$	1.31376e7	0.971681	0.485841	+	0.874047i	$0.338514\pi$
$110$	8.85878e6	0.634599
$111$	0	0
$112$	1.55888e7	1.04846
$113$	−9.32454e6	−0.607929	−0.303965	−	0.952683i	$-0.598310\pi$
$113$	−9.32454e6	−0.607929	−0.303965	+	0.952683i	$0.598310\pi$
$114$	0	0
$115$	4.69311e6	0.287752
$116$	1.72695e7	1.02725
$117$	0	0
$118$	744153.	0.0416941
$119$	−2.24307e6	−0.122020
$120$	0	0
$121$	4.65715e7	2.38986
$122$	−3.40191e6	−0.169614
$123$	0	0
$124$	2.85471e7	1.34458
$125$	1.97814e7	0.905884
$126$	0	0
$127$	1.14096e7	0.494263	0.247131	−	0.968982i	$-0.420512\pi$
$127$	1.14096e7	0.494263	0.247131	+	0.968982i	$0.420512\pi$
$128$	−2.30724e7	−0.972428
$129$	0	0
$130$	−1.98663e6	−0.0793077
$131$	−1.68449e7	−0.654666	−0.327333	−	0.944909i	$-0.606150\pi$
$131$	−1.68449e7	−0.654666	−0.327333	+	0.944909i	$0.606150\pi$
$132$	0	0
$133$	2.51009e7	0.925143
$134$	1.06346e7	0.381817
$135$	0	0
$136$	1.45807e6	0.0497041
$137$	5.53033e7	1.83751	0.918754	−	0.394830i	$-0.129196\pi$
$137$	5.53033e7	1.83751	0.918754	+	0.394830i	$0.129196\pi$
$138$	0	0
$139$	−392568.	−0.0123983	−0.00619916	−	0.999981i	$-0.501973\pi$
$139$	−392568.	−0.0123983	−0.00619916	+	0.999981i	$0.501973\pi$
$140$	4.67803e7	1.44084
$141$	0	0
$142$	2.12806e7	0.623699
$143$	−1.48140e7	−0.423640
$144$	0	0
$145$	4.52242e7	1.23192
$146$	−9.17831e6	−0.244078
$147$	0	0
$148$	1.96115e7	0.497272
$149$	3.39826e7	0.841598	0.420799	−	0.907154i	$-0.361750\pi$
$149$	3.39826e7	0.841598	0.420799	+	0.907154i	$0.361750\pi$
$150$	0	0
$151$	1.86602e7	0.441059	0.220530	−	0.975380i	$-0.429221\pi$
$151$	1.86602e7	0.441059	0.220530	+	0.975380i	$0.429221\pi$
$152$	−1.63164e7	−0.376853
$153$	0	0
$154$	−3.98675e7	−0.879622
$155$	7.47570e7	1.61247
$156$	0	0
$157$	3.31311e7	0.683262	0.341631	−	0.939834i	$-0.389021\pi$
$157$	3.31311e7	0.683262	0.341631	+	0.939834i	$0.389021\pi$
$158$	−7.24389e6	−0.146107
$159$	0	0
$160$	−4.64349e7	−0.896241
$161$	−2.11206e7	−0.398855
$162$	0	0
$163$	−7.04997e7	−1.27506	−0.637530	−	0.770426i	$-0.720044\pi$
$163$	−7.04997e7	−1.27506	−0.637530	+	0.770426i	$0.720044\pi$
$164$	3.25562e7	0.576342
$165$	0	0
$166$	−1.93410e7	−0.328172
$167$	5.02367e7	0.834667	0.417333	−	0.908753i	$-0.362965\pi$
$167$	5.02367e7	0.834667	0.417333	+	0.908753i	$0.362965\pi$
$168$	0	0
$169$	−5.94264e7	−0.947056
$170$	1.80595e6	0.0281925
$171$	0	0
$172$	−4.52922e6	−0.0678694
$173$	−3.60070e7	−0.528719	−0.264360	−	0.964424i	$-0.585161\pi$
$173$	−3.60070e7	−0.528719	−0.264360	+	0.964424i	$0.585161\pi$
$174$	0	0
$175$	1.67408e7	0.236126
$176$	−9.35903e7	−1.29401
$177$	0	0
$178$	−7.78968e6	−0.103526
$179$	6.95659e7	0.906589	0.453295	−	0.891361i	$-0.350249\pi$
$179$	6.95659e7	0.906589	0.453295	+	0.891361i	$0.350249\pi$
$180$	0	0
$181$	1.45844e8	1.82816	0.914079	−	0.405536i	$-0.132915\pi$
$181$	1.45844e8	1.82816	0.914079	+	0.405536i	$0.132915\pi$
$182$	8.94051e6	0.109929
$183$	0	0
$184$	1.37291e7	0.162472
$185$	5.13570e7	0.596347
$186$	0	0
$187$	1.34667e7	0.150597
$188$	−8.89412e6	−0.0976226
$189$	0	0
$190$	−2.02093e7	−0.213753
$191$	−3.79780e7	−0.394380	−0.197190	−	0.980365i	$-0.563182\pi$
$191$	−3.79780e7	−0.394380	−0.197190	+	0.980365i	$0.563182\pi$
$192$	0	0
$193$	−1.18553e8	−1.18704	−0.593518	−	0.804821i	$-0.702261\pi$
$193$	−1.18553e8	−1.18704	−0.593518	+	0.804821i	$0.702261\pi$
$194$	−1.22070e7	−0.120034
$195$	0	0
$196$	−1.15925e8	−1.09972
$197$	1.37665e8	1.28290	0.641450	−	0.767165i	$-0.278333\pi$
$197$	1.37665e8	1.28290	0.641450	+	0.767165i	$0.278333\pi$
$198$	0	0
$199$	−1.00525e8	−0.904248	−0.452124	−	0.891955i	$-0.649334\pi$
$199$	−1.00525e8	−0.904248	−0.452124	+	0.891955i	$0.649334\pi$
$200$	−1.08821e7	−0.0961850
$201$	0	0
$202$	−4.28963e6	−0.0366176
$203$	−2.03524e8	−1.70757
$204$	0	0
$205$	8.52557e7	0.691170
$206$	−3.64762e7	−0.290719
$207$	0	0
$208$	2.09882e7	0.161716
$209$	−1.50698e8	−1.14181
$210$	0	0
$211$	2.62670e8	1.92496	0.962480	−	0.271354i	$-0.0874714\pi$
$211$	2.62670e8	1.92496	0.962480	+	0.271354i	$0.0874714\pi$
$212$	2.27478e8	1.63970
$213$	0	0
$214$	1.90116e7	0.132608
$215$	−1.18608e7	−0.0813915
$216$	0	0
$217$	−3.36432e8	−2.23505
$218$	4.76017e7	0.311189
$219$	0	0
$220$	−2.80854e8	−1.77828
$221$	−3.01998e6	−0.0188205
$222$	0	0
$223$	2.67872e8	1.61756	0.808781	−	0.588110i	$-0.200128\pi$
$223$	2.67872e8	1.61756	0.808781	+	0.588110i	$0.200128\pi$
$224$	2.08973e8	1.24229
$225$	0	0
$226$	−3.37857e7	−0.194695
$227$	9.46663e7	0.537161	0.268581	−	0.963257i	$-0.413445\pi$
$227$	9.46663e7	0.537161	0.268581	+	0.963257i	$0.413445\pi$
$228$	0	0
$229$	2.26035e8	1.24380	0.621900	−	0.783096i	$-0.286361\pi$
$229$	2.26035e8	1.24380	0.621900	+	0.783096i	$0.286361\pi$
$230$	1.70046e7	0.0921550
$231$	0	0
$232$	1.32297e8	0.695573
$233$	6.28293e7	0.325399	0.162700	−	0.986676i	$-0.447980\pi$
$233$	6.28293e7	0.325399	0.162700	+	0.986676i	$0.447980\pi$
$234$	0	0
$235$	−2.32913e7	−0.117073
$236$	−2.35922e7	−0.116836
$237$	0	0
$238$	−8.12736e6	−0.0390778
$239$	1.86677e7	0.0884499	0.0442250	−	0.999022i	$-0.485918\pi$
$239$	1.86677e7	0.0884499	0.0442250	+	0.999022i	$0.485918\pi$
$240$	0	0
$241$	−2.43058e7	−0.111854	−0.0559268	−	0.998435i	$-0.517811\pi$
$241$	−2.43058e7	−0.111854	−0.0559268	+	0.998435i	$0.517811\pi$
$242$	1.68743e8	0.765372
$243$	0	0
$244$	1.07852e8	0.475296
$245$	−3.03577e8	−1.31883
$246$	0	0
$247$	3.37949e7	0.142696
$248$	2.18691e8	0.910439
$249$	0	0
$250$	7.16744e7	0.290117
$251$	1.85068e8	0.738708	0.369354	−	0.929289i	$-0.379579\pi$
$251$	1.85068e8	0.738708	0.369354	+	0.929289i	$0.379579\pi$
$252$	0	0
$253$	1.26801e8	0.492267
$254$	4.13406e7	0.158292
$255$	0	0
$256$	3.34731e7	0.124697
$257$	−7.99627e7	−0.293847	−0.146924	−	0.989148i	$-0.546937\pi$
$257$	−7.99627e7	−0.293847	−0.146924	+	0.989148i	$0.546937\pi$
$258$	0	0
$259$	−2.31124e8	−0.826601
$260$	6.29831e7	0.222237
$261$	0	0
$262$	−6.10345e7	−0.209663
$263$	4.27501e7	0.144908	0.0724539	−	0.997372i	$-0.476917\pi$
$263$	4.27501e7	0.144908	0.0724539	+	0.997372i	$0.476917\pi$
$264$	0	0
$265$	5.95702e8	1.96638
$266$	9.09486e7	0.296285
$267$	0	0
$268$	−3.37154e8	−1.06993
$269$	2.49600e8	0.781830	0.390915	−	0.920427i	$-0.372159\pi$
$269$	2.49600e8	0.781830	0.390915	+	0.920427i	$0.372159\pi$
$270$	0	0
$271$	−6.59051e7	−0.201153	−0.100577	−	0.994929i	$-0.532069\pi$
$271$	−6.59051e7	−0.201153	−0.100577	+	0.994929i	$0.532069\pi$
$272$	−1.90793e7	−0.0574871
$273$	0	0
$274$	2.00381e8	0.588478
$275$	−1.00507e8	−0.291427
$276$	0	0
$277$	9.39872e7	0.265699	0.132849	−	0.991136i	$-0.457587\pi$
$277$	9.39872e7	0.265699	0.132849	+	0.991136i	$0.457587\pi$
$278$	−1.42240e6	−0.00397067
$279$	0	0
$280$	3.58371e8	0.975619
$281$	−1.08507e8	−0.291733	−0.145867	−	0.989304i	$-0.546597\pi$
$281$	−1.08507e8	−0.291733	−0.145867	+	0.989304i	$0.546597\pi$
$282$	0	0
$283$	6.20243e8	1.62671	0.813353	−	0.581770i	$-0.197640\pi$
$283$	6.20243e8	1.62671	0.813353	+	0.581770i	$0.197640\pi$
$284$	−6.74670e8	−1.74774
$285$	0	0
$286$	−5.36759e7	−0.135675
$287$	−3.83679e8	−0.958036
$288$	0	0
$289$	−4.07593e8	−0.993310
$290$	1.63861e8	0.394533
$291$	0	0
$292$	2.90984e8	0.683958
$293$	−6.28432e8	−1.45956	−0.729779	−	0.683683i	$-0.760377\pi$
$293$	−6.28432e8	−1.45956	−0.729779	+	0.683683i	$0.760377\pi$
$294$	0	0
$295$	−6.17815e7	−0.140114
$296$	1.50238e8	0.336712
$297$	0	0
$298$	1.23130e8	0.269529
$299$	−2.84359e7	−0.0615201
$300$	0	0
$301$	5.33776e7	0.112817
$302$	6.76117e7	0.141253
$303$	0	0
$304$	2.13505e8	0.435863
$305$	2.82435e8	0.569993
$306$	0	0
$307$	7.45356e8	1.47021	0.735105	−	0.677953i	$-0.237133\pi$
$307$	7.45356e8	1.47021	0.735105	+	0.677953i	$0.237133\pi$
$308$	1.26394e9	2.46489
$309$	0	0
$310$	2.70868e8	0.516407
$311$	−7.31974e8	−1.37986	−0.689929	−	0.723877i	$-0.742358\pi$
$311$	−7.31974e8	−1.37986	−0.689929	+	0.723877i	$0.742358\pi$
$312$	0	0
$313$	3.03184e8	0.558857	0.279429	−	0.960166i	$-0.409855\pi$
$313$	3.03184e8	0.558857	0.279429	+	0.960166i	$0.409855\pi$
$314$	1.20044e8	0.218821
$315$	0	0
$316$	2.29656e8	0.409425
$317$	−2.79655e8	−0.493077	−0.246539	−	0.969133i	$-0.579293\pi$
$317$	−2.79655e8	−0.493077	−0.246539	+	0.969133i	$0.579293\pi$
$318$	0	0
$319$	1.22189e9	2.10749
$320$	2.75134e8	0.469374
$321$	0	0
$322$	−7.65264e7	−0.127737
$323$	−3.07212e7	−0.0507258
$324$	0	0
$325$	2.25392e7	0.0364205
$326$	−2.55443e8	−0.408349
$327$	0	0
$328$	2.49404e8	0.390252
$329$	1.04818e8	0.162275
$330$	0	0
$331$	1.20182e9	1.82156	0.910778	−	0.412897i	$-0.135483\pi$
$331$	1.20182e9	1.82156	0.910778	+	0.412897i	$0.135483\pi$
$332$	6.13178e8	0.919609
$333$	0	0
$334$	1.82023e8	0.267309
$335$	−8.82914e8	−1.28310
$336$	0	0
$337$	−1.16073e9	−1.65206	−0.826031	−	0.563624i	$-0.809407\pi$
$337$	−1.16073e9	−1.65206	−0.826031	+	0.563624i	$0.809407\pi$
$338$	−2.15320e8	−0.303303
$339$	0	0
$340$	−5.72547e7	−0.0790015
$341$	2.01983e9	2.75850
$342$	0	0
$343$	2.51304e8	0.336255
$344$	−3.46971e7	−0.0459557
$345$	0	0
$346$	−1.30465e8	−0.169327
$347$	1.18359e8	0.152071	0.0760356	−	0.997105i	$-0.475774\pi$
$347$	1.18359e8	0.152071	0.0760356	+	0.997105i	$0.475774\pi$
$348$	0	0
$349$	2.87181e8	0.361632	0.180816	−	0.983517i	$-0.442126\pi$
$349$	2.87181e8	0.361632	0.180816	+	0.983517i	$0.442126\pi$
$350$	6.06573e7	0.0756215
$351$	0	0
$352$	−1.25461e9	−1.53323
$353$	4.86525e8	0.588700	0.294350	−	0.955698i	$-0.404897\pi$
$353$	4.86525e8	0.588700	0.294350	+	0.955698i	$0.404897\pi$
$354$	0	0
$355$	−1.76678e9	−2.09596
$356$	2.46960e8	0.290102
$357$	0	0
$358$	2.52059e8	0.290343
$359$	−1.52624e9	−1.74098	−0.870488	−	0.492189i	$-0.836197\pi$
$359$	−1.52624e9	−1.74098	−0.870488	+	0.492189i	$0.836197\pi$
$360$	0	0
$361$	−5.50089e8	−0.615400
$362$	5.28439e8	0.585484
$363$	0	0
$364$	−2.83445e8	−0.308045
$365$	7.62008e8	0.820228
$366$	0	0
$367$	−1.48262e8	−0.156566	−0.0782832	−	0.996931i	$-0.524944\pi$
$367$	−1.48262e8	−0.156566	−0.0782832	+	0.996931i	$0.524944\pi$
$368$	−1.79648e8	−0.187913
$369$	0	0
$370$	1.86083e8	0.190985
$371$	−2.68086e9	−2.72562
$372$	0	0
$373$	−1.55988e9	−1.55636	−0.778180	−	0.628041i	$-0.783857\pi$
$373$	−1.55988e9	−1.55636	−0.778180	+	0.628041i	$0.783857\pi$
$374$	4.87941e7	0.0482299
$375$	0	0
$376$	−6.81354e7	−0.0661021
$377$	−2.74016e8	−0.263379
$378$	0	0
$379$	1.77311e9	1.67301	0.836504	−	0.547961i	$-0.184596\pi$
$379$	1.77311e9	1.67301	0.836504	+	0.547961i	$0.184596\pi$
$380$	6.40704e8	0.598983
$381$	0	0
$382$	−1.37606e8	−0.126304
$383$	−1.71331e9	−1.55826	−0.779129	−	0.626863i	$-0.784338\pi$
$383$	−1.71331e9	−1.55826	−0.779129	+	0.626863i	$0.784338\pi$
$384$	0	0
$385$	3.30990e9	2.95599
$386$	−4.29557e8	−0.380159
$387$	0	0
$388$	3.87004e8	0.336360
$389$	9.34250e8	0.804711	0.402355	−	0.915484i	$-0.368192\pi$
$389$	9.34250e8	0.804711	0.402355	+	0.915484i	$0.368192\pi$
$390$	0	0
$391$	2.58496e7	0.0218693
$392$	−8.88073e8	−0.744642
$393$	0	0
$394$	4.98805e8	0.410860
$395$	6.01407e8	0.490997
$396$	0	0
$397$	7.43414e8	0.596299	0.298150	−	0.954519i	$-0.403631\pi$
$397$	7.43414e8	0.596299	0.298150	+	0.954519i	$0.403631\pi$
$398$	−3.64233e8	−0.289593
$399$	0	0
$400$	1.42395e8	0.111246
$401$	−2.43334e9	−1.88450	−0.942252	−	0.334905i	$-0.891296\pi$
$401$	−2.43334e9	−1.88450	−0.942252	+	0.334905i	$0.891296\pi$
$402$	0	0
$403$	−4.52957e8	−0.344739
$404$	1.35996e8	0.102611
$405$	0	0
$406$	−7.37432e8	−0.546866
$407$	1.38759e9	1.02019
$408$	0	0
$409$	−2.52851e9	−1.82740	−0.913701	−	0.406388i	$-0.866788\pi$
$409$	−2.52851e9	−1.82740	−0.913701	+	0.406388i	$0.866788\pi$
$410$	3.08908e8	0.221353
$411$	0	0
$412$	1.15642e9	0.814659
$413$	2.78038e8	0.194213
$414$	0	0
$415$	1.60574e9	1.10283
$416$	2.81352e8	0.191613
$417$	0	0
$418$	−5.46026e8	−0.365676
$419$	1.34539e9	0.893507	0.446753	−	0.894657i	$-0.352580\pi$
$419$	1.34539e9	0.893507	0.446753	+	0.894657i	$0.352580\pi$
$420$	0	0
$421$	1.01782e9	0.664790	0.332395	−	0.943140i	$-0.392143\pi$
$421$	1.01782e9	0.664790	0.332395	+	0.943140i	$0.392143\pi$
$422$	9.51735e8	0.616485
$423$	0	0
$424$	1.74264e9	1.11027
$425$	−2.04892e7	−0.0129469
$426$	0	0
$427$	−1.27105e9	−0.790072
$428$	−6.02734e8	−0.371597
$429$	0	0
$430$	−4.29754e7	−0.0260663
$431$	2.08550e9	1.25470	0.627349	−	0.778738i	$-0.284140\pi$
$431$	2.08550e9	1.25470	0.627349	+	0.778738i	$0.284140\pi$
$432$	0	0
$433$	−1.27758e9	−0.756277	−0.378139	−	0.925749i	$-0.623436\pi$
$433$	−1.27758e9	−0.756277	−0.378139	+	0.925749i	$0.623436\pi$
$434$	−1.21900e9	−0.715795
$435$	0	0
$436$	−1.50914e9	−0.872020
$437$	−2.89268e8	−0.165812
$438$	0	0
$439$	−3.72523e8	−0.210149	−0.105074	−	0.994464i	$-0.533508\pi$
$439$	−3.72523e8	−0.210149	−0.105074	+	0.994464i	$0.533508\pi$
$440$	−2.15155e9	−1.20411
$441$	0	0
$442$	−1.09423e7	−0.00602743
$443$	−2.51167e8	−0.137262	−0.0686309	−	0.997642i	$-0.521863\pi$
$443$	−2.51167e8	−0.137262	−0.0686309	+	0.997642i	$0.521863\pi$
$444$	0	0
$445$	6.46720e8	0.347902
$446$	9.70586e8	0.518038
$447$	0	0
$448$	−1.23820e9	−0.650603
$449$	7.22359e8	0.376609	0.188304	−	0.982111i	$-0.439701\pi$
$449$	7.22359e8	0.376609	0.188304	+	0.982111i	$0.439701\pi$
$450$	0	0
$451$	2.30349e9	1.18241
$452$	1.07113e9	0.545577
$453$	0	0
$454$	3.43006e8	0.172031
$455$	−7.42265e8	−0.369419
$456$	0	0
$457$	−3.81278e9	−1.86868	−0.934341	−	0.356380i	$-0.884011\pi$
$457$	−3.81278e9	−1.86868	−0.934341	+	0.356380i	$0.884011\pi$
$458$	8.18995e8	0.398338
$459$	0	0
$460$	−5.39105e8	−0.258238
$461$	2.43626e9	1.15817	0.579083	−	0.815269i	$-0.303411\pi$
$461$	2.43626e9	1.15817	0.579083	+	0.815269i	$0.303411\pi$
$462$	0	0
$463$	−2.87487e9	−1.34612	−0.673061	−	0.739587i	$-0.735021\pi$
$463$	−2.87487e9	−1.34612	−0.673061	+	0.739587i	$0.735021\pi$
$464$	−1.73115e9	−0.804490
$465$	0	0
$466$	2.27650e8	0.104212
$467$	1.80431e9	0.819787	0.409894	−	0.912133i	$-0.365566\pi$
$467$	1.80431e9	0.819787	0.409894	+	0.912133i	$0.365566\pi$
$468$	0	0
$469$	3.97341e9	1.77852
$470$	−8.43915e7	−0.0374935
$471$	0	0
$472$	−1.80734e8	−0.0791119
$473$	−3.20462e8	−0.139239
$474$	0	0
$475$	2.29283e8	0.0981621
$476$	2.57666e8	0.109504
$477$	0	0
$478$	6.76388e7	0.0283269
$479$	2.36338e9	0.982558	0.491279	−	0.871002i	$-0.336529\pi$
$479$	2.36338e9	0.982558	0.491279	+	0.871002i	$0.336529\pi$
$480$	0	0
$481$	−3.11176e8	−0.127496
$482$	−8.80674e7	−0.0358221
$483$	0	0
$484$	−5.34975e9	−2.14474
$485$	1.01346e9	0.403376
$486$	0	0
$487$	3.50576e9	1.37541	0.687703	−	0.725993i	$-0.258619\pi$
$487$	3.50576e9	1.37541	0.687703	+	0.725993i	$0.258619\pi$
$488$	8.26226e8	0.321832
$489$	0	0
$490$	−1.09995e9	−0.422366
$491$	3.92494e9	1.49640	0.748199	−	0.663474i	$-0.230919\pi$
$491$	3.92494e9	1.49640	0.748199	+	0.663474i	$0.230919\pi$
$492$	0	0
$493$	2.49094e8	0.0936267
$494$	1.22449e8	0.0456996
$495$	0	0
$496$	−2.86164e9	−1.05300
$497$	7.95108e9	2.90522
$498$	0	0
$499$	−3.58721e9	−1.29242	−0.646212	−	0.763158i	$-0.723648\pi$
$499$	−3.58721e9	−1.29242	−0.646212	+	0.763158i	$0.723648\pi$
$500$	−2.27233e9	−0.812972
$501$	0	0
$502$	6.70559e8	0.236578
$503$	−2.48168e9	−0.869475	−0.434737	−	0.900557i	$-0.643159\pi$
$503$	−2.48168e9	−0.869475	−0.434737	+	0.900557i	$0.643159\pi$
$504$	0	0
$505$	3.56137e8	0.123054
$506$	4.59440e8	0.157653
$507$	0	0
$508$	−1.31064e9	−0.443568
$509$	−3.73752e9	−1.25624	−0.628118	−	0.778118i	$-0.716174\pi$
$509$	−3.73752e9	−1.25624	−0.628118	+	0.778118i	$0.716174\pi$
$510$	0	0
$511$	−3.42929e9	−1.13692
$512$	3.07455e9	1.01236
$513$	0	0
$514$	−2.89730e8	−0.0941071
$515$	3.02835e9	0.976969
$516$	0	0
$517$	−6.29296e8	−0.200280
$518$	−8.37435e8	−0.264726
$519$	0	0
$520$	4.82496e8	0.150481
$521$	3.12643e9	0.968539	0.484270	−	0.874919i	$-0.339085\pi$
$521$	3.12643e9	0.968539	0.484270	+	0.874919i	$0.339085\pi$
$522$	0	0
$523$	3.47385e9	1.06183	0.530915	−	0.847425i	$-0.321848\pi$
$523$	3.47385e9	1.06183	0.530915	+	0.847425i	$0.321848\pi$
$524$	1.93501e9	0.587520
$525$	0	0
$526$	1.54897e8	0.0464080
$527$	4.11761e8	0.122548
$528$	0	0
$529$	−3.16143e9	−0.928514
$530$	2.15841e9	0.629752
$531$	0	0
$532$	−2.88338e9	−0.830255
$533$	−5.16570e8	−0.147769
$534$	0	0
$535$	−1.57839e9	−0.445633
$536$	−2.58285e9	−0.724472
$537$	0	0
$538$	9.04381e8	0.250388
$539$	−8.20222e9	−2.25616
$540$	0	0
$541$	6.14788e8	0.166930	0.0834651	−	0.996511i	$-0.473401\pi$
$541$	6.14788e8	0.166930	0.0834651	+	0.996511i	$0.473401\pi$
$542$	−2.38795e8	−0.0644210
$543$	0	0
$544$	−2.55763e8	−0.0681149
$545$	−3.95202e9	−1.04576
$546$	0	0
$547$	−3.36033e9	−0.877863	−0.438931	−	0.898521i	$-0.644643\pi$
$547$	−3.36033e9	−0.877863	−0.438931	+	0.898521i	$0.644643\pi$
$548$	−6.35278e9	−1.64904
$549$	0	0
$550$	−3.64167e8	−0.0933321
$551$	−2.78747e9	−0.709871
$552$	0	0
$553$	−2.70654e9	−0.680575
$554$	3.40545e8	0.0850923
$555$	0	0
$556$	4.50949e7	0.0111267
$557$	2.92483e8	0.0717145	0.0358572	−	0.999357i	$-0.488584\pi$
$557$	2.92483e8	0.0717145	0.0358572	+	0.999357i	$0.488584\pi$
$558$	0	0
$559$	7.18654e7	0.0174012
$560$	−4.68939e9	−1.12839
$561$	0	0
$562$	−3.93156e8	−0.0934302
$563$	−5.83190e9	−1.37731	−0.688653	−	0.725091i	$-0.741798\pi$
$563$	−5.83190e9	−1.37731	−0.688653	+	0.725091i	$0.741798\pi$
$564$	0	0
$565$	2.80498e9	0.654276
$566$	2.24733e9	0.520967
$567$	0	0
$568$	−5.16846e9	−1.18343
$569$	1.28209e9	0.291760	0.145880	−	0.989302i	$-0.453399\pi$
$569$	1.28209e9	0.291760	0.145880	+	0.989302i	$0.453399\pi$
$570$	0	0
$571$	2.52700e9	0.568041	0.284020	−	0.958818i	$-0.408332\pi$
$571$	2.52700e9	0.568041	0.284020	+	0.958818i	$0.408332\pi$
$572$	1.70171e9	0.380189
$573$	0	0
$574$	−1.39019e9	−0.306819
$575$	−1.92925e8	−0.0423204
$576$	0	0
$577$	−3.17996e9	−0.689139	−0.344570	−	0.938761i	$-0.611975\pi$
$577$	−3.17996e9	−0.689139	−0.344570	+	0.938761i	$0.611975\pi$
$578$	−1.47684e9	−0.318116
$579$	0	0
$580$	−5.19497e9	−1.10557
$581$	−7.22639e9	−1.52864
$582$	0	0
$583$	1.60950e10	3.36396
$584$	2.22915e9	0.463121
$585$	0	0
$586$	−2.27701e9	−0.467437
$587$	−3.74135e9	−0.763474	−0.381737	−	0.924271i	$-0.624674\pi$
$587$	−3.74135e9	−0.763474	−0.381737	+	0.924271i	$0.624674\pi$
$588$	0	0
$589$	−4.60777e9	−0.929154
$590$	−2.23854e8	−0.0448728
$591$	0	0
$592$	−1.96591e9	−0.389437
$593$	1.49511e8	0.0294430	0.0147215	−	0.999892i	$-0.495314\pi$
$593$	1.49511e8	0.0294430	0.0147215	+	0.999892i	$0.495314\pi$
$594$	0	0
$595$	6.74755e8	0.131322
$596$	−3.90364e9	−0.755279
$597$	0	0
$598$	−1.03032e8	−0.0197024
$599$	4.90943e9	0.933335	0.466668	−	0.884433i	$-0.345454\pi$
$599$	4.90943e9	0.933335	0.466668	+	0.884433i	$0.345454\pi$
$600$	0	0
$601$	9.51517e9	1.78795	0.893976	−	0.448114i	$-0.147904\pi$
$601$	9.51517e9	1.78795	0.893976	+	0.448114i	$0.147904\pi$
$602$	1.93404e8	0.0361308
$603$	0	0
$604$	−2.14353e9	−0.395822
$605$	−1.40095e10	−2.57205
$606$	0	0
$607$	6.23277e9	1.13115	0.565576	−	0.824696i	$-0.308654\pi$
$607$	6.23277e9	1.13115	0.565576	+	0.824696i	$0.308654\pi$
$608$	2.86210e9	0.516442
$609$	0	0
$610$	1.02335e9	0.182545
$611$	1.41123e8	0.0250296
$612$	0	0
$613$	−2.97929e9	−0.522397	−0.261198	−	0.965285i	$-0.584118\pi$
$613$	−2.97929e9	−0.522397	−0.261198	+	0.965285i	$0.584118\pi$
$614$	2.70066e9	0.470848
$615$	0	0
$616$	9.68268e9	1.66903
$617$	−3.18056e9	−0.545137	−0.272569	−	0.962136i	$-0.587873\pi$
$617$	−3.18056e9	−0.545137	−0.272569	+	0.962136i	$0.587873\pi$
$618$	0	0
$619$	1.21436e8	0.0205793	0.0102896	−	0.999947i	$-0.496725\pi$
$619$	1.21436e8	0.0205793	0.0102896	+	0.999947i	$0.496725\pi$
$620$	−8.58745e9	−1.44708
$621$	0	0
$622$	−2.65217e9	−0.441912
$623$	−2.91046e9	−0.482229
$624$	0	0
$625$	−6.91669e9	−1.13323
$626$	1.09853e9	0.178979
$627$	0	0
$628$	−3.80583e9	−0.613183
$629$	2.82874e8	0.0453227
$630$	0	0
$631$	−5.92643e9	−0.939053	−0.469527	−	0.882918i	$-0.655575\pi$
$631$	−5.92643e9	−0.939053	−0.469527	+	0.882918i	$0.655575\pi$
$632$	1.75934e9	0.277229
$633$	0	0
$634$	−1.01328e9	−0.157912
$635$	−3.43221e9	−0.531943
$636$	0	0
$637$	1.83939e9	0.281959
$638$	4.42730e9	0.674942
$639$	0	0
$640$	6.94057e9	1.04656
$641$	7.39788e8	0.110944	0.0554721	−	0.998460i	$-0.482334\pi$
$641$	7.39788e8	0.110944	0.0554721	+	0.998460i	$0.482334\pi$
$642$	0	0
$643$	5.85977e9	0.869245	0.434622	−	0.900613i	$-0.356882\pi$
$643$	5.85977e9	0.869245	0.434622	+	0.900613i	$0.356882\pi$
$644$	2.42615e9	0.357946
$645$	0	0
$646$	−1.11313e8	−0.0162454
$647$	7.09749e9	1.03024	0.515122	−	0.857117i	$-0.327747\pi$
$647$	7.09749e9	1.03024	0.515122	+	0.857117i	$0.327747\pi$
$648$	0	0
$649$	−1.66925e9	−0.239698
$650$	8.16665e7	0.0116640
$651$	0	0
$652$	8.09841e9	1.14428
$653$	−3.83880e9	−0.539510	−0.269755	−	0.962929i	$-0.586943\pi$
$653$	−3.83880e9	−0.539510	−0.269755	+	0.962929i	$0.586943\pi$
$654$	0	0
$655$	5.06725e9	0.704576
$656$	−3.26352e9	−0.451360
$657$	0	0
$658$	3.79790e8	0.0519701
$659$	4.88094e9	0.664361	0.332181	−	0.943216i	$-0.392216\pi$
$659$	4.88094e9	0.664361	0.332181	+	0.943216i	$0.392216\pi$
$660$	0	0
$661$	−5.63851e9	−0.759381	−0.379690	−	0.925114i	$-0.623969\pi$
$661$	−5.63851e9	−0.759381	−0.379690	+	0.925114i	$0.623969\pi$
$662$	4.35458e9	0.583369
$663$	0	0
$664$	4.69739e9	0.622685
$665$	−7.55079e9	−0.995673
$666$	0	0
$667$	2.34545e9	0.306045
$668$	−5.77076e9	−0.749059
$669$	0	0
$670$	−3.19907e9	−0.410925
$671$	7.63100e9	0.975108
$672$	0	0
$673$	1.34178e10	1.69680	0.848399	−	0.529358i	$-0.177567\pi$
$673$	1.34178e10	1.69680	0.848399	+	0.529358i	$0.177567\pi$
$674$	−4.20569e9	−0.529088
$675$	0	0
$676$	6.82640e9	0.849921
$677$	1.49956e10	1.85740	0.928699	−	0.370835i	$-0.120928\pi$
$677$	1.49956e10	1.85740	0.928699	+	0.370835i	$0.120928\pi$
$678$	0	0
$679$	−4.56090e9	−0.559122
$680$	−4.38613e8	−0.0534934
$681$	0	0
$682$	7.31846e9	0.883435
$683$	6.32321e9	0.759391	0.379695	−	0.925112i	$-0.376029\pi$
$683$	6.32321e9	0.759391	0.379695	+	0.925112i	$0.376029\pi$
$684$	0	0
$685$	−1.66362e10	−1.97759
$686$	9.10552e8	0.107689
$687$	0	0
$688$	4.54022e8	0.0531517
$689$	−3.60940e9	−0.420404
$690$	0	0
$691$	−1.51402e10	−1.74565	−0.872826	−	0.488031i	$-0.837715\pi$
$691$	−1.51402e10	−1.74565	−0.872826	+	0.488031i	$0.837715\pi$
$692$	4.13618e9	0.474491
$693$	0	0
$694$	4.28850e8	0.0487021
$695$	1.18091e8	0.0133435
$696$	0	0
$697$	4.69588e8	0.0525293
$698$	1.04055e9	0.115816
$699$	0	0
$700$	−1.92305e9	−0.211908
$701$	−1.32383e10	−1.45151	−0.725755	−	0.687953i	$-0.758509\pi$
$701$	−1.32383e10	−1.45151	−0.725755	+	0.687953i	$0.758509\pi$
$702$	0	0
$703$	−3.16548e9	−0.343634
$704$	7.43373e9	0.802975
$705$	0	0
$706$	1.76283e9	0.188536
$707$	−1.60274e9	−0.170567
$708$	0	0
$709$	−6.66730e9	−0.702568	−0.351284	−	0.936269i	$-0.614255\pi$
$709$	−6.66730e9	−0.702568	−0.351284	+	0.936269i	$0.614255\pi$
$710$	−6.40158e9	−0.671248
$711$	0	0
$712$	1.89189e9	0.196434
$713$	3.87710e9	0.400584
$714$	0	0
$715$	4.45632e9	0.455937
$716$	−7.99114e9	−0.813604
$717$	0	0
$718$	−5.53005e9	−0.557563
$719$	5.24566e9	0.526319	0.263159	−	0.964752i	$-0.415235\pi$
$719$	5.24566e9	0.526319	0.263159	+	0.964752i	$0.415235\pi$
$720$	0	0
$721$	−1.36286e10	−1.35418
$722$	−1.99315e9	−0.197087
$723$	0	0
$724$	−1.67533e10	−1.64065
$725$	−1.85908e9	−0.181182
$726$	0	0
$727$	4.33721e9	0.418639	0.209320	−	0.977847i	$-0.432875\pi$
$727$	4.33721e9	0.418639	0.209320	+	0.977847i	$0.432875\pi$
$728$	−2.17140e9	−0.208583
$729$	0	0
$730$	2.76099e9	0.262685
$731$	−6.53291e7	−0.00618580
$732$	0	0
$733$	−1.14178e10	−1.07083	−0.535413	−	0.844590i	$-0.679844\pi$
$733$	−1.14178e10	−1.07083	−0.535413	+	0.844590i	$0.679844\pi$
$734$	−5.37200e8	−0.0501417
$735$	0	0
$736$	−2.40824e9	−0.222653
$737$	−2.38551e10	−2.19505
$738$	0	0
$739$	−1.87923e9	−0.171287	−0.0856433	−	0.996326i	$-0.527295\pi$
$739$	−1.87923e9	−0.171287	−0.0856433	+	0.996326i	$0.527295\pi$
$740$	−5.89946e9	−0.535182
$741$	0	0
$742$	−9.71359e9	−0.872903
$743$	9.66780e9	0.864703	0.432351	−	0.901705i	$-0.357684\pi$
$743$	9.66780e9	0.864703	0.432351	+	0.901705i	$0.357684\pi$
$744$	0	0
$745$	−1.02226e10	−0.905759
$746$	−5.65193e9	−0.498438
$747$	0	0
$748$	−1.54694e9	−0.135151
$749$	7.10331e9	0.617695
$750$	0	0
$751$	−1.07300e10	−0.924403	−0.462202	−	0.886775i	$-0.652940\pi$
$751$	−1.07300e10	−0.924403	−0.462202	+	0.886775i	$0.652940\pi$
$752$	8.91571e8	0.0764528
$753$	0	0
$754$	−9.92847e8	−0.0843496
$755$	−5.61331e9	−0.474684
$756$	0	0
$757$	1.90038e10	1.59223	0.796115	−	0.605145i	$-0.206885\pi$
$757$	1.90038e10	1.59223	0.796115	+	0.605145i	$0.206885\pi$
$758$	6.42453e9	0.535796
$759$	0	0
$760$	4.90826e9	0.405583
$761$	−8.07062e9	−0.663836	−0.331918	−	0.943308i	$-0.607696\pi$
$761$	−8.07062e9	−0.663836	−0.331918	+	0.943308i	$0.607696\pi$
$762$	0	0
$763$	1.77854e10	1.44953
$764$	4.36259e9	0.353930
$765$	0	0
$766$	−6.20785e9	−0.499046
$767$	3.74339e8	0.0299558
$768$	0	0
$769$	−4.19821e9	−0.332906	−0.166453	−	0.986049i	$-0.553231\pi$
$769$	−4.19821e9	−0.332906	−0.166453	+	0.986049i	$0.553231\pi$
$770$	1.19928e10	0.946682
$771$	0	0
$772$	1.36184e10	1.06529
$773$	1.26866e10	0.987910	0.493955	−	0.869487i	$-0.335551\pi$
$773$	1.26866e10	0.987910	0.493955	+	0.869487i	$0.335551\pi$
$774$	0	0
$775$	−3.07311e9	−0.237150
$776$	2.96473e9	0.227756
$777$	0	0
$778$	3.38508e9	0.257716
$779$	−5.25488e9	−0.398274
$780$	0	0
$781$	−4.77357e10	−3.58563
$782$	9.36612e7	0.00700384
$783$	0	0
$784$	1.16207e10	0.861243
$785$	−9.96642e9	−0.735352
$786$	0	0
$787$	1.93383e10	1.41419	0.707093	−	0.707121i	$-0.250006\pi$
$787$	1.93383e10	1.41419	0.707093	+	0.707121i	$0.250006\pi$
$788$	−1.58138e10	−1.15132
$789$	0	0
$790$	2.17909e9	0.157246
$791$	−1.26234e10	−0.906896
$792$	0	0
$793$	−1.71129e9	−0.121862
$794$	2.69362e9	0.190970
$795$	0	0
$796$	1.15474e10	0.811503
$797$	2.47116e10	1.72901	0.864505	−	0.502624i	$-0.167632\pi$
$797$	2.47116e10	1.72901	0.864505	+	0.502624i	$0.167632\pi$
$798$	0	0
$799$	−1.28288e8	−0.00889759
$800$	1.90885e9	0.131813
$801$	0	0
$802$	−8.81675e9	−0.603529
$803$	2.05884e10	1.40319
$804$	0	0
$805$	6.35343e9	0.429262
$806$	−1.64121e9	−0.110406
$807$	0	0
$808$	1.04183e9	0.0694796
$809$	−2.28215e10	−1.51539	−0.757695	−	0.652609i	$-0.773674\pi$
$809$	−2.28215e10	−1.51539	−0.757695	+	0.652609i	$0.773674\pi$
$810$	0	0
$811$	−2.67364e10	−1.76007	−0.880037	−	0.474906i	$-0.842482\pi$
$811$	−2.67364e10	−1.76007	−0.880037	+	0.474906i	$0.842482\pi$
$812$	2.33791e10	1.53244
$813$	0	0
$814$	5.02769e9	0.326725
$815$	2.12075e10	1.37227
$816$	0	0
$817$	7.31060e8	0.0469003
$818$	−9.16160e9	−0.585241
$819$	0	0
$820$	−9.79346e9	−0.620280
$821$	−1.71127e10	−1.07924	−0.539618	−	0.841910i	$-0.681431\pi$
$821$	−1.71127e10	−1.07924	−0.539618	+	0.841910i	$0.681431\pi$
$822$	0	0
$823$	−2.37659e10	−1.48612	−0.743061	−	0.669224i	$-0.766627\pi$
$823$	−2.37659e10	−1.48612	−0.743061	+	0.669224i	$0.766627\pi$
$824$	8.85903e9	0.551621
$825$	0	0
$826$	1.00742e9	0.0621985
$827$	6.09517e9	0.374728	0.187364	−	0.982291i	$-0.440006\pi$
$827$	6.09517e9	0.374728	0.187364	+	0.982291i	$0.440006\pi$
$828$	0	0
$829$	−5.59971e9	−0.341370	−0.170685	−	0.985326i	$-0.554598\pi$
$829$	−5.59971e9	−0.341370	−0.170685	+	0.985326i	$0.554598\pi$
$830$	5.81812e9	0.353191
$831$	0	0
$832$	−1.66706e9	−0.100350
$833$	−1.67210e9	−0.100232
$834$	0	0
$835$	−1.51121e10	−0.898299
$836$	1.73109e10	1.02470
$837$	0	0
$838$	4.87476e9	0.286153
$839$	1.48782e10	0.869730	0.434865	−	0.900496i	$-0.356796\pi$
$839$	1.48782e10	0.869730	0.434865	+	0.900496i	$0.356796\pi$
$840$	0	0
$841$	5.35156e9	0.310237
$842$	3.68789e9	0.212905
$843$	0	0
$844$	−3.01733e10	−1.72752
$845$	1.78765e10	1.01926
$846$	0	0
$847$	6.30476e10	3.56514
$848$	−2.28030e10	−1.28412
$849$	0	0
$850$	−7.42389e7	−0.00414634
$851$	2.66351e9	0.148150
$852$	0	0
$853$	3.87811e9	0.213943	0.106972	−	0.994262i	$-0.465885\pi$
$853$	3.87811e9	0.213943	0.106972	+	0.994262i	$0.465885\pi$
$854$	−4.60543e9	−0.253027
$855$	0	0
$856$	−4.61738e9	−0.251616
$857$	1.92983e10	1.04733	0.523667	−	0.851923i	$-0.324564\pi$
$857$	1.92983e10	1.04733	0.523667	+	0.851923i	$0.324564\pi$
$858$	0	0
$859$	2.34053e10	1.25990	0.629952	−	0.776634i	$-0.283074\pi$
$859$	2.34053e10	1.25990	0.629952	+	0.776634i	$0.283074\pi$
$860$	1.36247e9	0.0730435
$861$	0	0
$862$	7.55642e9	0.401828
$863$	−2.15437e10	−1.14099	−0.570495	−	0.821301i	$-0.693249\pi$
$863$	−2.15437e10	−1.14099	−0.570495	+	0.821301i	$0.693249\pi$
$864$	0	0
$865$	1.08315e10	0.569027
$866$	−4.62908e9	−0.242204
$867$	0	0
$868$	3.86464e10	2.00581
$869$	1.62492e10	0.839966
$870$	0	0
$871$	5.34964e9	0.274322
$872$	−1.15611e10	−0.590462
$873$	0	0
$874$	−1.04811e9	−0.0531026
$875$	2.67797e10	1.35138
$876$	0	0
$877$	−1.77005e10	−0.886108	−0.443054	−	0.896495i	$-0.646105\pi$
$877$	−1.77005e10	−0.886108	−0.443054	+	0.896495i	$0.646105\pi$
$878$	−1.34977e9	−0.0673021
$879$	0	0
$880$	2.81536e10	1.39266
$881$	2.35041e10	1.15805	0.579027	−	0.815308i	$-0.303433\pi$
$881$	2.35041e10	1.15805	0.579027	+	0.815308i	$0.303433\pi$
$882$	0	0
$883$	6.99377e9	0.341860	0.170930	−	0.985283i	$-0.445323\pi$
$883$	6.99377e9	0.341860	0.170930	+	0.985283i	$0.445323\pi$
$884$	3.46910e8	0.0168902
$885$	0	0
$886$	−9.10057e8	−0.0439593
$887$	1.04556e10	0.503056	0.251528	−	0.967850i	$-0.419067\pi$
$887$	1.04556e10	0.503056	0.251528	+	0.967850i	$0.419067\pi$
$888$	0	0
$889$	1.54461e10	0.737331
$890$	2.34327e9	0.111419
$891$	0	0
$892$	−3.07709e10	−1.45166
$893$	1.43560e9	0.0674609
$894$	0	0
$895$	−2.09266e10	−0.975704
$896$	−3.12349e10	−1.45065
$897$	0	0
$898$	2.61733e9	0.120612
$899$	3.73609e10	1.71498
$900$	0	0
$901$	3.28112e9	0.149446
$902$	8.34626e9	0.378677
$903$	0	0
$904$	8.20560e9	0.369420
$905$	−4.38724e10	−1.96753
$906$	0	0
$907$	2.84631e10	1.26665	0.633325	−	0.773886i	$-0.281690\pi$
$907$	2.84631e10	1.26665	0.633325	+	0.773886i	$0.281690\pi$
$908$	−1.08745e10	−0.482067
$909$	0	0
$910$	−2.68946e9	−0.118310
$911$	8.69725e9	0.381125	0.190562	−	0.981675i	$-0.438969\pi$
$911$	8.69725e9	0.381125	0.190562	+	0.981675i	$0.438969\pi$
$912$	0	0
$913$	4.33849e10	1.88665
$914$	−1.38149e10	−0.598462
$915$	0	0
$916$	−2.59650e10	−1.11623
$917$	−2.28043e10	−0.976618
$918$	0	0
$919$	1.81679e10	0.772148	0.386074	−	0.922468i	$-0.373831\pi$
$919$	1.81679e10	0.772148	0.386074	+	0.922468i	$0.373831\pi$
$920$	−4.12993e9	−0.174858
$921$	0	0
$922$	8.82735e9	0.370913
$923$	1.07050e10	0.448106
$924$	0	0
$925$	−2.11119e9	−0.0877063
$926$	−1.04166e10	−0.431107
$927$	0	0
$928$	−2.32065e10	−0.953218
$929$	−2.23626e10	−0.915098	−0.457549	−	0.889184i	$-0.651273\pi$
$929$	−2.23626e10	−0.915098	−0.457549	+	0.889184i	$0.651273\pi$
$930$	0	0
$931$	1.87115e10	0.759949
$932$	−7.21731e9	−0.292025
$933$	0	0
$934$	6.53757e9	0.262544
$935$	−4.05101e9	−0.162078
$936$	0	0
$937$	−4.79626e8	−0.0190465	−0.00952323	−	0.999955i	$-0.503031\pi$
$937$	−4.79626e8	−0.0190465	−0.00952323	+	0.999955i	$0.503031\pi$
$938$	1.43969e10	0.569586
$939$	0	0
$940$	2.67550e9	0.105065
$941$	3.41566e10	1.33632	0.668161	−	0.744017i	$-0.267082\pi$
$941$	3.41566e10	1.33632	0.668161	+	0.744017i	$0.267082\pi$
$942$	0	0
$943$	4.42159e9	0.171707
$944$	2.36495e9	0.0914997
$945$	0	0
$946$	−1.16113e9	−0.0445926
$947$	1.00641e10	0.385079	0.192539	−	0.981289i	$-0.438328\pi$
$947$	1.00641e10	0.385079	0.192539	+	0.981289i	$0.438328\pi$
$948$	0	0
$949$	−4.61706e9	−0.175361
$950$	8.30764e8	0.0314373
$951$	0	0
$952$	1.97391e9	0.0741476
$953$	2.94200e10	1.10108	0.550539	−	0.834810i	$-0.314422\pi$
$953$	2.94200e10	1.10108	0.550539	+	0.834810i	$0.314422\pi$
$954$	0	0
$955$	1.14244e10	0.424446
$956$	−2.14438e9	−0.0793780
$957$	0	0
$958$	8.56325e9	0.314673
$959$	7.48685e10	2.74116
$960$	0	0
$961$	3.42460e10	1.24474
$962$	−1.12749e9	−0.0408318
$963$	0	0
$964$	2.79204e9	0.100381
$965$	3.56629e10	1.27753
$966$	0	0
$967$	9.18664e9	0.326711	0.163356	−	0.986567i	$-0.447768\pi$
$967$	9.18664e9	0.326711	0.163356	+	0.986567i	$0.447768\pi$
$968$	−4.09830e10	−1.45224
$969$	0	0
$970$	3.67208e9	0.129185
$971$	−2.46294e10	−0.863348	−0.431674	−	0.902030i	$-0.642077\pi$
$971$	−2.46294e10	−0.863348	−0.431674	+	0.902030i	$0.642077\pi$
$972$	0	0
$973$	−5.31450e8	−0.0184956
$974$	1.27025e10	0.440486
$975$	0	0
$976$	−1.08114e10	−0.372227
$977$	−3.26473e10	−1.12000	−0.559998	−	0.828494i	$-0.689198\pi$
$977$	−3.26473e10	−1.12000	−0.559998	+	0.828494i	$0.689198\pi$
$978$	0	0
$979$	1.74735e10	0.595168
$980$	3.48724e10	1.18356
$981$	0	0
$982$	1.42213e10	0.479235
$983$	−4.98914e9	−0.167528	−0.0837641	−	0.996486i	$-0.526694\pi$
$983$	−4.98914e9	−0.167528	−0.0837641	+	0.996486i	$0.526694\pi$
$984$	0	0
$985$	−4.14121e10	−1.38070
$986$	9.02547e8	0.0299848
$987$	0	0
$988$	−3.88207e9	−0.128060
$989$	−6.15133e8	−0.0202200
$990$	0	0
$991$	−1.15183e10	−0.375950	−0.187975	−	0.982174i	$-0.560192\pi$
$991$	−1.15183e10	−0.375950	−0.187975	+	0.982174i	$0.560192\pi$
$992$	−3.83611e10	−1.24767
$993$	0	0
$994$	2.88093e10	0.930422
$995$	3.02396e10	0.973185
$996$	0	0
$997$	2.00277e10	0.640026	0.320013	−	0.947413i	$-0.396313\pi$
$997$	2.00277e10	0.640026	0.320013	+	0.947413i	$0.396313\pi$
$998$	−1.29976e10	−0.413910
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.9		17
3.2	odd	2		177.8.a.c.1.9	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.9	✓	17	3.2	odd	2
531.8.a.c.1.9		17	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q+3.62331 q^{2} -114.872 q^{4} -300.817 q^{5} +1353.78 q^{7} -880.000 q^{8} +O(q^{10})\)	\(q+3.62331 q^{2} -114.872 q^{4} -300.817 q^{5} +1353.78 q^{7} -880.000 q^{8} -1089.96 q^{10} -8127.65 q^{11} +1822.67 q^{13} +4905.17 q^{14} +11515.0 q^{16} -1656.90 q^{17} +18541.4 q^{19} +34555.4 q^{20} -29449.0 q^{22} -15601.2 q^{23} +12366.0 q^{25} +6604.11 q^{26} -155511. q^{28} -150338. q^{29} -248513. q^{31} +154363. q^{32} -6003.46 q^{34} -407240. q^{35} -170725. q^{37} +67181.2 q^{38} +264719. q^{40} -283414. q^{41} +39428.6 q^{43} +933636. q^{44} -56528.0 q^{46} +77426.6 q^{47} +1.00917e6 q^{49} +44805.9 q^{50} -209373. q^{52} -1.98028e6 q^{53} +2.44494e6 q^{55} -1.19133e6 q^{56} -544721. q^{58} +205379. q^{59} -938894. q^{61} -900440. q^{62} -914622. q^{64} -548291. q^{65} +2.93505e6 q^{67} +190331. q^{68} -1.47556e6 q^{70} +5.87325e6 q^{71} -2.53313e6 q^{73} -618590. q^{74} -2.12988e6 q^{76} -1.10030e7 q^{77} -1.99924e6 q^{79} -3.46392e6 q^{80} -1.02690e6 q^{82} -5.33794e6 q^{83} +498424. q^{85} +142862. q^{86} +7.15233e6 q^{88} -2.14988e6 q^{89} +2.46749e6 q^{91} +1.79213e6 q^{92} +280541. q^{94} -5.57757e6 q^{95} -3.36902e6 q^{97} +3.65656e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more