LMFDB - Embedded newform 775.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.144209.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 6x^{3} - x^{2} + 6x - 1 $ x^5 - 6x^3 - x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.43848$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70816 q^{2} -0.930775 q^{3} +0.917797 q^{4} -1.58991 q^{6} -1.50771 q^{7} -1.84857 q^{8} -2.13366 q^{9} +O(q^{10})$	\(q+1.70816 q^{2} -0.930775 q^{3} +0.917797 q^{4} -1.58991 q^{6} -1.50771 q^{7} -1.84857 q^{8} -2.13366 q^{9} +1.68949 q^{11} -0.854262 q^{12} -4.04706 q^{13} -2.57540 q^{14} -4.99324 q^{16} +0.146636 q^{17} -3.64462 q^{18} -3.59081 q^{19} +1.40333 q^{21} +2.88591 q^{22} -4.77169 q^{23} +1.72060 q^{24} -6.91300 q^{26} +4.77828 q^{27} -1.38377 q^{28} +6.52727 q^{29} -1.00000 q^{31} -4.83209 q^{32} -1.57253 q^{33} +0.250477 q^{34} -1.95827 q^{36} -5.06769 q^{37} -6.13366 q^{38} +3.76690 q^{39} +0.252300 q^{41} +2.39711 q^{42} -0.0635347 q^{43} +1.55061 q^{44} -8.15079 q^{46} +0.392322 q^{47} +4.64758 q^{48} -4.72682 q^{49} -0.136485 q^{51} -3.71438 q^{52} -8.47346 q^{53} +8.16205 q^{54} +2.78710 q^{56} +3.34223 q^{57} +11.1496 q^{58} +7.08400 q^{59} -0.825505 q^{61} -1.70816 q^{62} +3.21693 q^{63} +1.73251 q^{64} -2.68613 q^{66} -13.4370 q^{67} +0.134582 q^{68} +4.44137 q^{69} +14.1291 q^{71} +3.94422 q^{72} +8.86670 q^{73} -8.65641 q^{74} -3.29563 q^{76} -2.54725 q^{77} +6.43445 q^{78} +4.74952 q^{79} +1.95347 q^{81} +0.430967 q^{82} +4.20538 q^{83} +1.28798 q^{84} -0.108527 q^{86} -6.07542 q^{87} -3.12314 q^{88} -7.58991 q^{89} +6.10177 q^{91} -4.37944 q^{92} +0.930775 q^{93} +0.670146 q^{94} +4.49759 q^{96} +2.57936 q^{97} -8.07415 q^{98} -3.60479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

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 $

$2$	1.70816	1.20785	0.603924	−	0.797042i	$-0.293603\pi$
$2$	1.70816	1.20785	0.603924	+	0.797042i	$0.293603\pi$
$3$	−0.930775	−0.537383	−0.268692	−	0.963226i	$-0.586591\pi$
$3$	−0.930775	−0.537383	−0.268692	+	0.963226i	$0.586591\pi$
$4$	0.917797	0.458898
$5$	0	0
$5$	0	0
$6$	−1.58991	−0.649077
$7$	−1.50771	−0.569859	−0.284930	−	0.958548i	$-0.591970\pi$
$7$	−1.50771	−0.569859	−0.284930	+	0.958548i	$0.591970\pi$
$8$	−1.84857	−0.653569
$9$	−2.13366	−0.711219
$10$	0	0
$11$	1.68949	0.509400	0.254700	−	0.967020i	$-0.418023\pi$
$11$	1.68949	0.509400	0.254700	+	0.967020i	$0.418023\pi$
$12$	−0.854262	−0.246604
$13$	−4.04706	−1.12245	−0.561226	−	0.827663i	$-0.689670\pi$
$13$	−4.04706	−1.12245	−0.561226	+	0.827663i	$0.689670\pi$
$14$	−2.57540	−0.688304
$15$	0	0
$16$	−4.99324	−1.24831
$17$	0.146636	0.0355645	0.0177822	−	0.999842i	$-0.494339\pi$
$17$	0.146636	0.0355645	0.0177822	+	0.999842i	$0.494339\pi$
$18$	−3.64462	−0.859045
$19$	−3.59081	−0.823788	−0.411894	−	0.911232i	$-0.635133\pi$
$19$	−3.59081	−0.823788	−0.411894	+	0.911232i	$0.635133\pi$
$20$	0	0
$21$	1.40333	0.306233
$22$	2.88591	0.615278
$23$	−4.77169	−0.994966	−0.497483	−	0.867474i	$-0.665742\pi$
$23$	−4.77169	−0.994966	−0.497483	+	0.867474i	$0.665742\pi$
$24$	1.72060	0.351217
$25$	0	0
$26$	−6.91300	−1.35575
$27$	4.77828	0.919580
$28$	−1.38377	−0.261507
$29$	6.52727	1.21208	0.606042	−	0.795433i	$-0.292756\pi$
$29$	6.52727	1.21208	0.606042	+	0.795433i	$0.292756\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−4.83209	−0.854202
$33$	−1.57253	−0.273743
$34$	0.250477	0.0429565
$35$	0	0
$36$	−1.95827	−0.326378
$37$	−5.06769	−0.833123	−0.416562	−	0.909107i	$-0.636765\pi$
$37$	−5.06769	−0.833123	−0.416562	+	0.909107i	$0.636765\pi$
$38$	−6.13366	−0.995011
$39$	3.76690	0.603187
$40$	0	0
$41$	0.252300	0.0394026	0.0197013	−	0.999806i	$-0.493728\pi$
$41$	0.252300	0.0394026	0.0197013	+	0.999806i	$0.493728\pi$
$42$	2.39711	0.369883
$43$	−0.0635347	−0.00968895	−0.00484448	−	0.999988i	$-0.501542\pi$
$43$	−0.0635347	−0.00968895	−0.00484448	+	0.999988i	$0.501542\pi$
$44$	1.55061	0.233763
$45$	0	0
$46$	−8.15079	−1.20177
$47$	0.392322	0.0572260	0.0286130	−	0.999591i	$-0.490891\pi$
$47$	0.392322	0.0572260	0.0286130	+	0.999591i	$0.490891\pi$
$48$	4.64758	0.670821
$49$	−4.72682	−0.675261
$50$	0	0
$51$	−0.136485	−0.0191118
$52$	−3.71438	−0.515091
$53$	−8.47346	−1.16392	−0.581959	−	0.813218i	$-0.697714\pi$
$53$	−8.47346	−1.16392	−0.581959	+	0.813218i	$0.697714\pi$
$54$	8.16205	1.11071
$55$	0	0
$56$	2.78710	0.372442
$57$	3.34223	0.442690
$58$	11.1496	1.46401
$59$	7.08400	0.922258	0.461129	−	0.887333i	$-0.347444\pi$
$59$	7.08400	0.922258	0.461129	+	0.887333i	$0.347444\pi$
$60$	0	0
$61$	−0.825505	−0.105695	−0.0528475	−	0.998603i	$-0.516830\pi$
$61$	−0.825505	−0.105695	−0.0528475	+	0.998603i	$0.516830\pi$
$62$	−1.70816	−0.216936
$63$	3.21693	0.405295
$64$	1.73251	0.216564
$65$	0	0
$66$	−2.68613	−0.330640
$67$	−13.4370	−1.64159	−0.820797	−	0.571221i	$-0.806470\pi$
$67$	−13.4370	−1.64159	−0.820797	+	0.571221i	$0.806470\pi$
$68$	0.134582	0.0163205
$69$	4.44137	0.534678
$70$	0	0
$71$	14.1291	1.67681	0.838407	−	0.545044i	$-0.183487\pi$
$71$	14.1291	1.67681	0.838407	+	0.545044i	$0.183487\pi$
$72$	3.94422	0.464831
$73$	8.86670	1.03777	0.518885	−	0.854844i	$-0.326347\pi$
$73$	8.86670	1.03777	0.518885	+	0.854844i	$0.326347\pi$
$74$	−8.65641	−1.00629
$75$	0	0
$76$	−3.29563	−0.378035
$77$	−2.54725	−0.290286
$78$	6.43445	0.728558
$79$	4.74952	0.534363	0.267182	−	0.963646i	$-0.413908\pi$
$79$	4.74952	0.534363	0.267182	+	0.963646i	$0.413908\pi$
$80$	0	0
$81$	1.95347	0.217053
$82$	0.430967	0.0475924
$83$	4.20538	0.461600	0.230800	−	0.973001i	$-0.425866\pi$
$83$	4.20538	0.461600	0.230800	+	0.973001i	$0.425866\pi$
$84$	1.28798	0.140530
$85$	0	0
$86$	−0.108527	−0.0117028
$87$	−6.07542	−0.651353
$88$	−3.12314	−0.332928
$89$	−7.58991	−0.804529	−0.402264	−	0.915524i	$-0.631777\pi$
$89$	−7.58991	−0.804529	−0.402264	+	0.915524i	$0.631777\pi$
$90$	0	0
$91$	6.10177	0.639639
$92$	−4.37944	−0.456588
$93$	0.930775	0.0965168
$94$	0.670146	0.0691203
$95$	0	0
$96$	4.49759	0.459033
$97$	2.57936	0.261895	0.130947	−	0.991389i	$-0.458198\pi$
$97$	2.57936	0.261895	0.130947	+	0.991389i	$0.458198\pi$
$98$	−8.07415	−0.815613
$99$	−3.60479	−0.362295
$100$	0	0
$101$	5.01677	0.499187	0.249593	−	0.968351i	$-0.419703\pi$
$101$	5.01677	0.499187	0.249593	+	0.968351i	$0.419703\pi$
$102$	−0.233138	−0.0230841
$103$	−3.20953	−0.316245	−0.158122	−	0.987420i	$-0.550544\pi$
$103$	−3.20953	−0.316245	−0.158122	+	0.987420i	$0.550544\pi$
$104$	7.48128	0.733599
$105$	0	0
$106$	−14.4740	−1.40584
$107$	−11.5370	−1.11532	−0.557662	−	0.830068i	$-0.688301\pi$
$107$	−11.5370	−1.11532	−0.557662	+	0.830068i	$0.688301\pi$
$108$	4.38549	0.421994
$109$	11.7744	1.12778	0.563891	−	0.825849i	$-0.309304\pi$
$109$	11.7744	1.12778	0.563891	+	0.825849i	$0.309304\pi$
$110$	0	0
$111$	4.71688	0.447706
$112$	7.52834	0.711361
$113$	−14.7365	−1.38630	−0.693149	−	0.720795i	$-0.743777\pi$
$113$	−14.7365	−1.38630	−0.693149	+	0.720795i	$0.743777\pi$
$114$	5.70905	0.534702
$115$	0	0
$116$	5.99071	0.556223
$117$	8.63504	0.798309
$118$	12.1006	1.11395
$119$	−0.221084	−0.0202668
$120$	0	0
$121$	−8.14563	−0.740512
$122$	−1.41009	−0.127664
$123$	−0.234834	−0.0211743
$124$	−0.917797	−0.0824206
$125$	0	0
$126$	5.49502	0.489535
$127$	1.86026	0.165071	0.0825356	−	0.996588i	$-0.473698\pi$
$127$	1.86026	0.165071	0.0825356	+	0.996588i	$0.473698\pi$
$128$	12.6236	1.11578
$129$	0.0591365	0.00520668
$130$	0	0
$131$	5.96735	0.521370	0.260685	−	0.965424i	$-0.416052\pi$
$131$	5.96735	0.521370	0.260685	+	0.965424i	$0.416052\pi$
$132$	−1.44327	−0.125620
$133$	5.41388	0.469443
$134$	−22.9525	−1.98280
$135$	0	0
$136$	−0.271067	−0.0232438
$137$	−5.44434	−0.465141	−0.232571	−	0.972580i	$-0.574714\pi$
$137$	−5.44434	−0.465141	−0.232571	+	0.972580i	$0.574714\pi$
$138$	7.58655	0.645810
$139$	−16.0083	−1.35780	−0.678901	−	0.734229i	$-0.737544\pi$
$139$	−16.0083	−1.35780	−0.678901	+	0.734229i	$0.737544\pi$
$140$	0	0
$141$	−0.365163	−0.0307523
$142$	24.1347	2.02534
$143$	−6.83745	−0.571777
$144$	10.6539	0.887823
$145$	0	0
$146$	15.1457	1.25347
$147$	4.39961	0.362874
$148$	−4.65111	−0.382319
$149$	−7.04333	−0.577012	−0.288506	−	0.957478i	$-0.593159\pi$
$149$	−7.04333	−0.577012	−0.288506	+	0.957478i	$0.593159\pi$
$150$	0	0
$151$	4.90355	0.399045	0.199523	−	0.979893i	$-0.436061\pi$
$151$	4.90355	0.399045	0.199523	+	0.979893i	$0.436061\pi$
$152$	6.63786	0.538402
$153$	−0.312872	−0.0252942
$154$	−4.35110	−0.350622
$155$	0	0
$156$	3.45725	0.276801
$157$	−1.45325	−0.115982	−0.0579912	−	0.998317i	$-0.518470\pi$
$157$	−1.45325	−0.115982	−0.0579912	+	0.998317i	$0.518470\pi$
$158$	8.11293	0.645430
$159$	7.88688	0.625470
$160$	0	0
$161$	7.19430	0.566991
$162$	3.33684	0.262167
$163$	24.2080	1.89612	0.948060	−	0.318092i	$-0.103042\pi$
$163$	24.2080	1.89612	0.948060	+	0.318092i	$0.103042\pi$
$164$	0.231560	0.0180818
$165$	0	0
$166$	7.18344	0.557543
$167$	16.3393	1.26437	0.632187	−	0.774815i	$-0.282157\pi$
$167$	16.3393	1.26437	0.632187	+	0.774815i	$0.282157\pi$
$168$	−2.59416	−0.200144
$169$	3.37867	0.259898
$170$	0	0
$171$	7.66156	0.585894
$172$	−0.0583120	−0.00444625
$173$	4.14414	0.315073	0.157537	−	0.987513i	$-0.449645\pi$
$173$	4.14414	0.315073	0.157537	+	0.987513i	$0.449645\pi$
$174$	−10.3778	−0.786736
$175$	0	0
$176$	−8.43602	−0.635889
$177$	−6.59361	−0.495606
$178$	−12.9647	−0.971749
$179$	−23.3747	−1.74711	−0.873553	−	0.486728i	$-0.838190\pi$
$179$	−23.3747	−1.74711	−0.873553	+	0.486728i	$0.838190\pi$
$180$	0	0
$181$	−24.8415	−1.84645	−0.923226	−	0.384256i	$-0.874458\pi$
$181$	−24.8415	−1.84645	−0.923226	+	0.384256i	$0.874458\pi$
$182$	10.4228	0.772587
$183$	0.768359	0.0567988
$184$	8.82081	0.650279
$185$	0	0
$186$	1.58991	0.116578
$187$	0.247740	0.0181165
$188$	0.360071	0.0262609
$189$	−7.20424	−0.524031
$190$	0	0
$191$	2.32373	0.168139	0.0840697	−	0.996460i	$-0.473208\pi$
$191$	2.32373	0.168139	0.0840697	+	0.996460i	$0.473208\pi$
$192$	−1.61258	−0.116378
$193$	−4.74287	−0.341399	−0.170700	−	0.985323i	$-0.554603\pi$
$193$	−4.74287	−0.341399	−0.170700	+	0.985323i	$0.554603\pi$
$194$	4.40596	0.316329
$195$	0	0
$196$	−4.33826	−0.309876
$197$	−14.6528	−1.04397	−0.521985	−	0.852955i	$-0.674808\pi$
$197$	−14.6528	−1.04397	−0.521985	+	0.852955i	$0.674808\pi$
$198$	−6.15754	−0.437597
$199$	−10.0654	−0.713517	−0.356758	−	0.934197i	$-0.616118\pi$
$199$	−10.0654	−0.713517	−0.356758	+	0.934197i	$0.616118\pi$
$200$	0	0
$201$	12.5068	0.882164
$202$	8.56942	0.602942
$203$	−9.84120	−0.690717
$204$	−0.125266	−0.00877036
$205$	0	0
$206$	−5.48239	−0.381976
$207$	10.1812	0.707639
$208$	20.2079	1.40117
$209$	−6.06662	−0.419637
$210$	0	0
$211$	11.3609	0.782117	0.391058	−	0.920366i	$-0.372109\pi$
$211$	11.3609	0.782117	0.391058	+	0.920366i	$0.372109\pi$
$212$	−7.77691	−0.534121
$213$	−13.1510	−0.901092
$214$	−19.7070	−1.34714
$215$	0	0
$216$	−8.83299	−0.601009
$217$	1.50771	0.102350
$218$	20.1125	1.36219
$219$	−8.25290	−0.557680
$220$	0	0
$221$	−0.593445	−0.0399194
$222$	8.05716	0.540761
$223$	10.9582	0.733813	0.366906	−	0.930258i	$-0.380417\pi$
$223$	10.9582	0.733813	0.366906	+	0.930258i	$0.380417\pi$
$224$	7.28537	0.486775
$225$	0	0
$226$	−25.1723	−1.67444
$227$	23.2624	1.54398	0.771990	−	0.635634i	$-0.219261\pi$
$227$	23.2624	1.54398	0.771990	+	0.635634i	$0.219261\pi$
$228$	3.06749	0.203150
$229$	−28.9501	−1.91307	−0.956537	−	0.291611i	$-0.905809\pi$
$229$	−28.9501	−1.91307	−0.956537	+	0.291611i	$0.905809\pi$
$230$	0	0
$231$	2.37092	0.155995
$232$	−12.0661	−0.792180
$233$	17.7216	1.16098	0.580489	−	0.814268i	$-0.302861\pi$
$233$	17.7216	1.16098	0.580489	+	0.814268i	$0.302861\pi$
$234$	14.7500	0.964237
$235$	0	0
$236$	6.50167	0.423223
$237$	−4.42074	−0.287158
$238$	−0.377646	−0.0244792
$239$	−21.5484	−1.39385	−0.696926	−	0.717143i	$-0.745450\pi$
$239$	−21.5484	−1.39385	−0.696926	+	0.717143i	$0.745450\pi$
$240$	0	0
$241$	−17.0153	−1.09605	−0.548026	−	0.836461i	$-0.684621\pi$
$241$	−17.0153	−1.09605	−0.548026	+	0.836461i	$0.684621\pi$
$242$	−13.9140	−0.894426
$243$	−16.1531	−1.03622
$244$	−0.757646	−0.0485033
$245$	0	0
$246$	−0.401134	−0.0255753
$247$	14.5322	0.924662
$248$	1.84857	0.117384
$249$	−3.91426	−0.248056
$250$	0	0
$251$	−7.52627	−0.475054	−0.237527	−	0.971381i	$-0.576337\pi$
$251$	−7.52627	−0.475054	−0.237527	+	0.971381i	$0.576337\pi$
$252$	2.95249	0.185989
$253$	−8.06171	−0.506836
$254$	3.17761	0.199381
$255$	0	0
$256$	18.0980	1.13113
$257$	−21.4877	−1.34037	−0.670184	−	0.742195i	$-0.733785\pi$
$257$	−21.4877	−1.34037	−0.670184	+	0.742195i	$0.733785\pi$
$258$	0.101014	0.00628888
$259$	7.64058	0.474763
$260$	0	0
$261$	−13.9270	−0.862058
$262$	10.1932	0.629736
$263$	−7.79202	−0.480477	−0.240238	−	0.970714i	$-0.577226\pi$
$263$	−7.79202	−0.480477	−0.240238	+	0.970714i	$0.577226\pi$
$264$	2.90694	0.178910
$265$	0	0
$266$	9.24775	0.567016
$267$	7.06450	0.432340
$268$	−12.3325	−0.753325
$269$	27.1817	1.65730	0.828649	−	0.559768i	$-0.189110\pi$
$269$	27.1817	1.65730	0.828649	+	0.559768i	$0.189110\pi$
$270$	0	0
$271$	6.46754	0.392875	0.196438	−	0.980516i	$-0.437063\pi$
$271$	6.46754	0.392875	0.196438	+	0.980516i	$0.437063\pi$
$272$	−0.732190	−0.0443955
$273$	−5.67937	−0.343731
$274$	−9.29978	−0.561820
$275$	0	0
$276$	4.07628	0.245363
$277$	−18.3195	−1.10071	−0.550357	−	0.834930i	$-0.685508\pi$
$277$	−18.3195	−1.10071	−0.550357	+	0.834930i	$0.685508\pi$
$278$	−27.3446	−1.64002
$279$	2.13366	0.127739
$280$	0	0
$281$	−15.5765	−0.929217	−0.464609	−	0.885516i	$-0.653805\pi$
$281$	−15.5765	−0.929217	−0.464609	+	0.885516i	$0.653805\pi$
$282$	−0.623755	−0.0371441
$283$	29.7118	1.76619	0.883093	−	0.469199i	$-0.155457\pi$
$283$	29.7118	1.76619	0.883093	+	0.469199i	$0.155457\pi$
$284$	12.9676	0.769488
$285$	0	0
$286$	−11.6794	−0.690620
$287$	−0.380394	−0.0224539
$288$	10.3100	0.607525
$289$	−16.9785	−0.998735
$290$	0	0
$291$	−2.40081	−0.140738
$292$	8.13783	0.476231
$293$	−5.90735	−0.345111	−0.172556	−	0.985000i	$-0.555202\pi$
$293$	−5.90735	−0.345111	−0.172556	+	0.985000i	$0.555202\pi$
$294$	7.51522	0.438296
$295$	0	0
$296$	9.36799	0.544503
$297$	8.07284	0.468434
$298$	−12.0311	−0.696943
$299$	19.3113	1.11680
$300$	0	0
$301$	0.0957916	0.00552134
$302$	8.37603	0.481986
$303$	−4.66948	−0.268255
$304$	17.9298	1.02834
$305$	0	0
$306$	−0.534433	−0.0305515
$307$	−24.5783	−1.40276	−0.701379	−	0.712788i	$-0.747432\pi$
$307$	−24.5783	−1.40276	−0.701379	+	0.712788i	$0.747432\pi$
$308$	−2.33786	−0.133212
$309$	2.98735	0.169945
$310$	0	0
$311$	5.20092	0.294917	0.147459	−	0.989068i	$-0.452891\pi$
$311$	5.20092	0.294917	0.147459	+	0.989068i	$0.452891\pi$
$312$	−6.96338	−0.394224
$313$	−25.0015	−1.41317	−0.706584	−	0.707629i	$-0.749765\pi$
$313$	−25.0015	−1.41317	−0.706584	+	0.707629i	$0.749765\pi$
$314$	−2.48239	−0.140089
$315$	0	0
$316$	4.35910	0.245218
$317$	−26.4784	−1.48717	−0.743587	−	0.668640i	$-0.766877\pi$
$317$	−26.4784	−1.48717	−0.743587	+	0.668640i	$0.766877\pi$
$318$	13.4720	0.755474
$319$	11.0277	0.617435
$320$	0	0
$321$	10.7383	0.599356
$322$	12.2890	0.684839
$323$	−0.526542	−0.0292976
$324$	1.79289	0.0996051
$325$	0	0
$326$	41.3511	2.29023
$327$	−10.9593	−0.606051
$328$	−0.466394	−0.0257523
$329$	−0.591505	−0.0326107
$330$	0	0
$331$	−9.66552	−0.531265	−0.265633	−	0.964074i	$-0.585581\pi$
$331$	−9.66552	−0.531265	−0.265633	+	0.964074i	$0.585581\pi$
$332$	3.85968	0.211828
$333$	10.8127	0.592533
$334$	27.9101	1.52717
$335$	0	0
$336$	−7.00719	−0.382273
$337$	−21.2134	−1.15557	−0.577783	−	0.816190i	$-0.696082\pi$
$337$	−21.2134	−1.15557	−0.577783	+	0.816190i	$0.696082\pi$
$338$	5.77130	0.313917
$339$	13.7164	0.744973
$340$	0	0
$341$	−1.68949	−0.0914909
$342$	13.0871	0.707671
$343$	17.6806	0.954662
$344$	0.117448	0.00633240
$345$	0	0
$346$	7.07884	0.380561
$347$	−15.8255	−0.849560	−0.424780	−	0.905297i	$-0.639648\pi$
$347$	−15.8255	−0.849560	−0.424780	+	0.905297i	$0.639648\pi$
$348$	−5.57600	−0.298905
$349$	34.6360	1.85402	0.927011	−	0.375034i	$-0.122369\pi$
$349$	34.6360	1.85402	0.927011	+	0.375034i	$0.122369\pi$
$350$	0	0
$351$	−19.3380	−1.03218
$352$	−8.16376	−0.435130
$353$	−29.3051	−1.55975	−0.779875	−	0.625935i	$-0.784718\pi$
$353$	−29.3051	−1.55975	−0.779875	+	0.625935i	$0.784718\pi$
$354$	−11.2629	−0.598617
$355$	0	0
$356$	−6.96599	−0.369197
$357$	0.205780	0.0108910
$358$	−39.9276	−2.11024
$359$	−34.9463	−1.84439	−0.922197	−	0.386721i	$-0.873608\pi$
$359$	−34.9463	−1.84439	−0.922197	+	0.386721i	$0.873608\pi$
$360$	0	0
$361$	−6.10611	−0.321374
$362$	−42.4331	−2.23024
$363$	7.58175	0.397939
$364$	5.60019	0.293529
$365$	0	0
$366$	1.31248	0.0686043
$367$	11.7486	0.613272	0.306636	−	0.951827i	$-0.400797\pi$
$367$	11.7486	0.613272	0.306636	+	0.951827i	$0.400797\pi$
$368$	23.8262	1.24203
$369$	−0.538322	−0.0280239
$370$	0	0
$371$	12.7755	0.663270
$372$	0.854262	0.0442914
$373$	22.2888	1.15407	0.577034	−	0.816720i	$-0.304210\pi$
$373$	22.2888	1.15407	0.577034	+	0.816720i	$0.304210\pi$
$374$	0.423179	0.0218820
$375$	0	0
$376$	−0.725234	−0.0374011
$377$	−26.4162	−1.36051
$378$	−12.3060	−0.632950
$379$	28.1163	1.44424	0.722118	−	0.691770i	$-0.243169\pi$
$379$	28.1163	1.44424	0.722118	+	0.691770i	$0.243169\pi$
$380$	0	0
$381$	−1.73148	−0.0887064
$382$	3.96930	0.203087
$383$	24.5287	1.25336	0.626679	−	0.779277i	$-0.284414\pi$
$383$	24.5287	1.25336	0.626679	+	0.779277i	$0.284414\pi$
$384$	−11.7497	−0.599601
$385$	0	0
$386$	−8.10156	−0.412359
$387$	0.135561	0.00689097
$388$	2.36733	0.120183
$389$	29.6625	1.50395	0.751974	−	0.659193i	$-0.229102\pi$
$389$	29.6625	1.50395	0.751974	+	0.659193i	$0.229102\pi$
$390$	0	0
$391$	−0.699703	−0.0353855
$392$	8.73787	0.441329
$393$	−5.55426	−0.280175
$394$	−25.0293	−1.26096
$395$	0	0
$396$	−3.30846	−0.166257
$397$	32.9987	1.65616	0.828078	−	0.560613i	$-0.189435\pi$
$397$	32.9987	1.65616	0.828078	+	0.560613i	$0.189435\pi$
$398$	−17.1933	−0.861820
$399$	−5.03910	−0.252271
$400$	0	0
$401$	−18.3043	−0.914072	−0.457036	−	0.889448i	$-0.651089\pi$
$401$	−18.3043	−0.914072	−0.457036	+	0.889448i	$0.651089\pi$
$402$	21.3636	1.06552
$403$	4.04706	0.201598
$404$	4.60437	0.229076
$405$	0	0
$406$	−16.8103	−0.834282
$407$	−8.56180	−0.424393
$408$	0.252303	0.0124908
$409$	32.7463	1.61920	0.809601	−	0.586980i	$-0.199683\pi$
$409$	32.7463	1.61920	0.809601	+	0.586980i	$0.199683\pi$
$410$	0	0
$411$	5.06745	0.249959
$412$	−2.94570	−0.145124
$413$	−10.6806	−0.525557
$414$	17.3910	0.854721
$415$	0	0
$416$	19.5558	0.958800
$417$	14.9001	0.729660
$418$	−10.3627	−0.506858
$419$	−9.46641	−0.462465	−0.231232	−	0.972899i	$-0.574276\pi$
$419$	−9.46641	−0.462465	−0.231232	+	0.972899i	$0.574276\pi$
$420$	0	0
$421$	−26.2012	−1.27697	−0.638484	−	0.769635i	$-0.720438\pi$
$421$	−26.2012	−1.27697	−0.638484	+	0.769635i	$0.720438\pi$
$422$	19.4062	0.944679
$423$	−0.837080	−0.0407002
$424$	15.6638	0.760701
$425$	0	0
$426$	−22.4640	−1.08838
$427$	1.24462	0.0602313
$428$	−10.5886	−0.511820
$429$	6.36413	0.307263
$430$	0	0
$431$	−7.84987	−0.378115	−0.189058	−	0.981966i	$-0.560543\pi$
$431$	−7.84987	−0.378115	−0.189058	+	0.981966i	$0.560543\pi$
$432$	−23.8591	−1.14792
$433$	18.7559	0.901349	0.450674	−	0.892688i	$-0.351184\pi$
$433$	18.7559	0.901349	0.450674	+	0.892688i	$0.351184\pi$
$434$	2.57540	0.123623
$435$	0	0
$436$	10.8065	0.517537
$437$	17.1342	0.819641
$438$	−14.0972	−0.673593
$439$	2.29975	0.109761	0.0548806	−	0.998493i	$-0.482522\pi$
$439$	2.29975	0.109761	0.0548806	+	0.998493i	$0.482522\pi$
$440$	0	0
$441$	10.0854	0.480258
$442$	−1.01370	−0.0482166
$443$	16.1095	0.765385	0.382692	−	0.923876i	$-0.374997\pi$
$443$	16.1095	0.765385	0.382692	+	0.923876i	$0.374997\pi$
$444$	4.32914	0.205452
$445$	0	0
$446$	18.7182	0.886335
$447$	6.55576	0.310077
$448$	−2.61212	−0.123411
$449$	2.51235	0.118565	0.0592825	−	0.998241i	$-0.481119\pi$
$449$	2.51235	0.118565	0.0592825	+	0.998241i	$0.481119\pi$
$450$	0	0
$451$	0.426257	0.0200717
$452$	−13.5252	−0.636170
$453$	−4.56410	−0.214440
$454$	39.7358	1.86490
$455$	0	0
$456$	−6.17836	−0.289328
$457$	−8.32036	−0.389210	−0.194605	−	0.980882i	$-0.562342\pi$
$457$	−8.32036	−0.389210	−0.194605	+	0.980882i	$0.562342\pi$
$458$	−49.4512	−2.31070
$459$	0.700669	0.0327044
$460$	0	0
$461$	12.9178	0.601640	0.300820	−	0.953681i	$-0.402740\pi$
$461$	12.9178	0.601640	0.300820	+	0.953681i	$0.402740\pi$
$462$	4.04989	0.188418
$463$	−8.54868	−0.397291	−0.198645	−	0.980071i	$-0.563654\pi$
$463$	−8.54868	−0.397291	−0.198645	+	0.980071i	$0.563654\pi$
$464$	−32.5923	−1.51306
$465$	0	0
$466$	30.2712	1.40229
$467$	27.6109	1.27768	0.638840	−	0.769339i	$-0.279414\pi$
$467$	27.6109	1.27768	0.638840	+	0.769339i	$0.279414\pi$
$468$	7.92521	0.366343
$469$	20.2591	0.935477
$470$	0	0
$471$	1.35265	0.0623270
$472$	−13.0953	−0.602759
$473$	−0.107341	−0.00493555
$474$	−7.55131	−0.346843
$475$	0	0
$476$	−0.202910	−0.00930038
$477$	18.0795	0.827802
$478$	−36.8081	−1.68356
$479$	−19.0396	−0.869943	−0.434971	−	0.900444i	$-0.643242\pi$
$479$	−19.0396	−0.869943	−0.434971	+	0.900444i	$0.643242\pi$
$480$	0	0
$481$	20.5092	0.935141
$482$	−29.0648	−1.32387
$483$	−6.69628	−0.304691
$484$	−7.47604	−0.339820
$485$	0	0
$486$	−27.5920	−1.25160
$487$	2.70816	0.122718	0.0613591	−	0.998116i	$-0.480457\pi$
$487$	2.70816	0.122718	0.0613591	+	0.998116i	$0.480457\pi$
$488$	1.52601	0.0690790
$489$	−22.5322	−1.01894
$490$	0	0
$491$	−17.3623	−0.783549	−0.391774	−	0.920061i	$-0.628139\pi$
$491$	−17.3623	−0.783549	−0.391774	+	0.920061i	$0.628139\pi$
$492$	−0.215530	−0.00971685
$493$	0.957134	0.0431072
$494$	24.8233	1.11685
$495$	0	0
$496$	4.99324	0.224203
$497$	−21.3025	−0.955548
$498$	−6.68617	−0.299614
$499$	−5.49072	−0.245799	−0.122899	−	0.992419i	$-0.539219\pi$
$499$	−5.49072	−0.245799	−0.122899	+	0.992419i	$0.539219\pi$
$500$	0	0
$501$	−15.2082	−0.679454
$502$	−12.8560	−0.573793
$503$	−0.0479977	−0.00214011	−0.00107006	−	0.999999i	$-0.500341\pi$
$503$	−0.0479977	−0.00214011	−0.00107006	+	0.999999i	$0.500341\pi$
$504$	−5.94672	−0.264888
$505$	0	0
$506$	−13.7707	−0.612181
$507$	−3.14478	−0.139665
$508$	1.70734	0.0757509
$509$	−27.5596	−1.22156	−0.610778	−	0.791802i	$-0.709143\pi$
$509$	−27.5596	−1.22156	−0.610778	+	0.791802i	$0.709143\pi$
$510$	0	0
$511$	−13.3684	−0.591382
$512$	5.66708	0.250452
$513$	−17.1579	−0.757539
$514$	−36.7044	−1.61896
$515$	0	0
$516$	0.0542753	0.00238934
$517$	0.662822	0.0291509
$518$	13.0513	0.573442
$519$	−3.85726	−0.169315
$520$	0	0
$521$	−25.3222	−1.10939	−0.554693	−	0.832055i	$-0.687164\pi$
$521$	−25.3222	−1.10939	−0.554693	+	0.832055i	$0.687164\pi$
$522$	−23.7894	−1.04124
$523$	−4.21023	−0.184100	−0.0920502	−	0.995754i	$-0.529342\pi$
$523$	−4.21023	−0.184100	−0.0920502	+	0.995754i	$0.529342\pi$
$524$	5.47681	0.239256
$525$	0	0
$526$	−13.3100	−0.580343
$527$	−0.146636	−0.00638757
$528$	7.85204	0.341716
$529$	−0.230968	−0.0100421
$530$	0	0
$531$	−15.1148	−0.655928
$532$	4.96884	0.215427
$533$	−1.02107	−0.0442275
$534$	12.0673	0.522201
$535$	0	0
$536$	24.8393	1.07289
$537$	21.7566	0.938866
$538$	46.4306	2.00177
$539$	−7.98591	−0.343978
$540$	0	0
$541$	7.18074	0.308724	0.154362	−	0.988014i	$-0.450668\pi$
$541$	7.18074	0.308724	0.154362	+	0.988014i	$0.450668\pi$
$542$	11.0476	0.474534
$543$	23.1218	0.992252
$544$	−0.708560	−0.0303793
$545$	0	0
$546$	−9.70126	−0.415175
$547$	−11.2805	−0.482321	−0.241160	−	0.970485i	$-0.577528\pi$
$547$	−11.2805	−0.482321	−0.241160	+	0.970485i	$0.577528\pi$
$548$	−4.99680	−0.213453
$549$	1.76135	0.0751724
$550$	0	0
$551$	−23.4382	−0.998500
$552$	−8.21019	−0.349449
$553$	−7.16088	−0.304512
$554$	−31.2926	−1.32950
$555$	0	0
$556$	−14.6923	−0.623094
$557$	4.29074	0.181805	0.0909023	−	0.995860i	$-0.471025\pi$
$557$	4.29074	0.181805	0.0909023	+	0.995860i	$0.471025\pi$
$558$	3.64462	0.154289
$559$	0.257129	0.0108754
$560$	0	0
$561$	−0.230590	−0.00973552
$562$	−26.6071	−1.12235
$563$	4.71566	0.198741	0.0993707	−	0.995050i	$-0.468317\pi$
$563$	4.71566	0.198741	0.0993707	+	0.995050i	$0.468317\pi$
$564$	−0.335145	−0.0141122
$565$	0	0
$566$	50.7525	2.13328
$567$	−2.94526	−0.123689
$568$	−26.1186	−1.09591
$569$	6.01377	0.252110	0.126055	−	0.992023i	$-0.459768\pi$
$569$	6.01377	0.252110	0.126055	+	0.992023i	$0.459768\pi$
$570$	0	0
$571$	−2.62131	−0.109699	−0.0548493	−	0.998495i	$-0.517468\pi$
$571$	−2.62131	−0.109699	−0.0548493	+	0.998495i	$0.517468\pi$
$572$	−6.27539	−0.262387
$573$	−2.16287	−0.0903553
$574$	−0.649772	−0.0271210
$575$	0	0
$576$	−3.69659	−0.154025
$577$	28.2940	1.17790	0.588948	−	0.808171i	$-0.299542\pi$
$577$	28.2940	1.17790	0.588948	+	0.808171i	$0.299542\pi$
$578$	−29.0019	−1.20632
$579$	4.41455	0.183462
$580$	0	0
$581$	−6.34047	−0.263047
$582$	−4.10095	−0.169990
$583$	−14.3158	−0.592900
$584$	−16.3907	−0.678254
$585$	0	0
$586$	−10.0907	−0.416842
$587$	−3.89919	−0.160937	−0.0804684	−	0.996757i	$-0.525642\pi$
$587$	−3.89919	−0.160937	−0.0804684	+	0.996757i	$0.525642\pi$
$588$	4.03795	0.166522
$589$	3.59081	0.147957
$590$	0	0
$591$	13.6385	0.561011
$592$	25.3042	1.04000
$593$	−13.1943	−0.541826	−0.270913	−	0.962604i	$-0.587326\pi$
$593$	−13.1943	−0.541826	−0.270913	+	0.962604i	$0.587326\pi$
$594$	13.7897	0.565797
$595$	0	0
$596$	−6.46435	−0.264790
$597$	9.36861	0.383432
$598$	32.9867	1.34893
$599$	−24.8218	−1.01419	−0.507095	−	0.861890i	$-0.669281\pi$
$599$	−24.8218	−1.01419	−0.507095	+	0.861890i	$0.669281\pi$
$600$	0	0
$601$	24.7518	1.00965	0.504824	−	0.863222i	$-0.331557\pi$
$601$	24.7518	1.00965	0.504824	+	0.863222i	$0.331557\pi$
$602$	0.163627	0.00666894
$603$	28.6700	1.16753
$604$	4.50047	0.183121
$605$	0	0
$606$	−7.97620	−0.324011
$607$	14.1035	0.572445	0.286222	−	0.958163i	$-0.407600\pi$
$607$	14.1035	0.572445	0.286222	+	0.958163i	$0.407600\pi$
$608$	17.3511	0.703681
$609$	9.15994	0.371180
$610$	0	0
$611$	−1.58775	−0.0642334
$612$	−0.287153	−0.0116075
$613$	−40.2582	−1.62602	−0.813008	−	0.582253i	$-0.802171\pi$
$613$	−40.2582	−1.62602	−0.813008	+	0.582253i	$0.802171\pi$
$614$	−41.9836	−1.69432
$615$	0	0
$616$	4.70877	0.189722
$617$	2.30815	0.0929225	0.0464612	−	0.998920i	$-0.485206\pi$
$617$	2.30815	0.0929225	0.0464612	+	0.998920i	$0.485206\pi$
$618$	5.10287	0.205267
$619$	−13.7118	−0.551126	−0.275563	−	0.961283i	$-0.588864\pi$
$619$	−13.7118	−0.551126	−0.275563	+	0.961283i	$0.588864\pi$
$620$	0	0
$621$	−22.8005	−0.914951
$622$	8.88398	0.356215
$623$	11.4433	0.458468
$624$	−18.8090	−0.752964
$625$	0	0
$626$	−42.7064	−1.70689
$627$	5.64666	0.225506
$628$	−1.33379	−0.0532241
$629$	−0.743107	−0.0296296
$630$	0	0
$631$	39.9282	1.58952	0.794759	−	0.606925i	$-0.207597\pi$
$631$	39.9282	1.58952	0.794759	+	0.606925i	$0.207597\pi$
$632$	−8.77983	−0.349243
$633$	−10.5744	−0.420296
$634$	−45.2292	−1.79628
$635$	0	0
$636$	7.23855	0.287027
$637$	19.1297	0.757947
$638$	18.8371	0.745768
$639$	−30.1467	−1.19258
$640$	0	0
$641$	26.8928	1.06220	0.531101	−	0.847309i	$-0.321779\pi$
$641$	26.8928	1.06220	0.531101	+	0.847309i	$0.321779\pi$
$642$	18.3428	0.723931
$643$	2.01612	0.0795079	0.0397539	−	0.999210i	$-0.487343\pi$
$643$	2.01612	0.0795079	0.0397539	+	0.999210i	$0.487343\pi$
$644$	6.60291	0.260191
$645$	0	0
$646$	−0.899416	−0.0353871
$647$	48.0278	1.88817	0.944084	−	0.329705i	$-0.106949\pi$
$647$	48.0278	1.88817	0.944084	+	0.329705i	$0.106949\pi$
$648$	−3.61113	−0.141859
$649$	11.9683	0.469798
$650$	0	0
$651$	−1.40333	−0.0550010
$652$	22.2181	0.870126
$653$	13.8241	0.540978	0.270489	−	0.962723i	$-0.412815\pi$
$653$	13.8241	0.540978	0.270489	+	0.962723i	$0.412815\pi$
$654$	−18.7202	−0.732018
$655$	0	0
$656$	−1.25979	−0.0491867
$657$	−18.9185	−0.738082
$658$	−1.01038	−0.0393888
$659$	46.1112	1.79624	0.898118	−	0.439754i	$-0.144934\pi$
$659$	46.1112	1.79624	0.898118	+	0.439754i	$0.144934\pi$
$660$	0	0
$661$	44.6278	1.73582	0.867910	−	0.496722i	$-0.165463\pi$
$661$	44.6278	1.73582	0.867910	+	0.496722i	$0.165463\pi$
$662$	−16.5102	−0.641688
$663$	0.552364	0.0214520
$664$	−7.77394	−0.301688
$665$	0	0
$666$	18.4698	0.715691
$667$	−31.1461	−1.20598
$668$	14.9962	0.580220
$669$	−10.1996	−0.394338
$670$	0	0
$671$	−1.39468	−0.0538410
$672$	−6.78104	−0.261584
$673$	38.3586	1.47861	0.739307	−	0.673368i	$-0.235153\pi$
$673$	38.3586	1.47861	0.739307	+	0.673368i	$0.235153\pi$
$674$	−36.2357	−1.39575
$675$	0	0
$676$	3.10093	0.119267
$677$	15.7801	0.606479	0.303239	−	0.952914i	$-0.401932\pi$
$677$	15.7801	0.606479	0.303239	+	0.952914i	$0.401932\pi$
$678$	23.4298	0.899814
$679$	−3.88892	−0.149243
$680$	0	0
$681$	−21.6521	−0.829709
$682$	−2.88591	−0.110507
$683$	12.3468	0.472436	0.236218	−	0.971700i	$-0.424092\pi$
$683$	12.3468	0.472436	0.236218	+	0.971700i	$0.424092\pi$
$684$	7.03175	0.268866
$685$	0	0
$686$	30.2012	1.15309
$687$	26.9460	1.02805
$688$	0.317244	0.0120948
$689$	34.2926	1.30644
$690$	0	0
$691$	45.3865	1.72658	0.863291	−	0.504706i	$-0.168399\pi$
$691$	45.3865	1.72658	0.863291	+	0.504706i	$0.168399\pi$
$692$	3.80348	0.144587
$693$	5.43496	0.206457
$694$	−27.0325	−1.02614
$695$	0	0
$696$	11.2308	0.425704
$697$	0.0369963	0.00140133
$698$	59.1637	2.23938
$699$	−16.4948	−0.623890
$700$	0	0
$701$	−39.8104	−1.50362	−0.751810	−	0.659380i	$-0.770819\pi$
$701$	−39.8104	−1.50362	−0.751810	+	0.659380i	$0.770819\pi$
$702$	−33.0323	−1.24672
$703$	18.1971	0.686317
$704$	2.92706	0.110318
$705$	0	0
$706$	−50.0576	−1.88394
$707$	−7.56380	−0.284466
$708$	−6.05159	−0.227433
$709$	17.0671	0.640967	0.320484	−	0.947254i	$-0.396155\pi$
$709$	17.0671	0.640967	0.320484	+	0.947254i	$0.396155\pi$
$710$	0	0
$711$	−10.1339	−0.380049
$712$	14.0305	0.525815
$713$	4.77169	0.178701
$714$	0.351504	0.0131547
$715$	0	0
$716$	−21.4532	−0.801745
$717$	20.0567	0.749033
$718$	−59.6937	−2.22775
$719$	26.0121	0.970089	0.485045	−	0.874489i	$-0.338803\pi$
$719$	26.0121	0.970089	0.485045	+	0.874489i	$0.338803\pi$
$720$	0	0
$721$	4.83903	0.180215
$722$	−10.4302	−0.388171
$723$	15.8374	0.589000
$724$	−22.7994	−0.847334
$725$	0	0
$726$	12.9508	0.480650
$727$	15.5941	0.578352	0.289176	−	0.957276i	$-0.406619\pi$
$727$	15.5941	0.578352	0.289176	+	0.957276i	$0.406619\pi$
$728$	−11.2796	−0.418048
$729$	9.17446	0.339795
$730$	0	0
$731$	−0.00931649	−0.000344583 0
$732$	0.705198	0.0260649
$733$	−15.8360	−0.584916	−0.292458	−	0.956278i	$-0.594473\pi$
$733$	−15.8360	−0.584916	−0.292458	+	0.956278i	$0.594473\pi$
$734$	20.0684	0.740740
$735$	0	0
$736$	23.0573	0.849902
$737$	−22.7017	−0.836227
$738$	−0.919537	−0.0338486
$739$	14.0347	0.516276	0.258138	−	0.966108i	$-0.416891\pi$
$739$	14.0347	0.516276	0.258138	+	0.966108i	$0.416891\pi$
$740$	0	0
$741$	−13.5262	−0.496898
$742$	21.8225	0.801130
$743$	−50.6986	−1.85995	−0.929976	−	0.367621i	$-0.880172\pi$
$743$	−50.6986	−1.85995	−0.929976	+	0.367621i	$0.880172\pi$
$744$	−1.72060	−0.0630804
$745$	0	0
$746$	38.0727	1.39394
$747$	−8.97284	−0.328299
$748$	0.227375	0.00831365
$749$	17.3944	0.635577
$750$	0	0
$751$	−1.89436	−0.0691260	−0.0345630	−	0.999403i	$-0.511004\pi$
$751$	−1.89436	−0.0691260	−0.0345630	+	0.999403i	$0.511004\pi$
$752$	−1.95896	−0.0714358
$753$	7.00526	0.255286
$754$	−45.1231	−1.64329
$755$	0	0
$756$	−6.61203	−0.240477
$757$	31.4194	1.14196	0.570979	−	0.820965i	$-0.306564\pi$
$757$	31.4194	1.14196	0.570979	+	0.820965i	$0.306564\pi$
$758$	48.0270	1.74442
$759$	7.50364	0.272365
$760$	0	0
$761$	22.0845	0.800562	0.400281	−	0.916392i	$-0.368913\pi$
$761$	22.0845	0.800562	0.400281	+	0.916392i	$0.368913\pi$
$762$	−2.95764	−0.107144
$763$	−17.7523	−0.642677
$764$	2.13271	0.0771589
$765$	0	0
$766$	41.8988	1.51387
$767$	−28.6694	−1.03519
$768$	−16.8452	−0.607849
$769$	46.3915	1.67292	0.836459	−	0.548029i	$-0.184622\pi$
$769$	46.3915	1.67292	0.836459	+	0.548029i	$0.184622\pi$
$770$	0	0
$771$	20.0002	0.720291
$772$	−4.35299	−0.156668
$773$	−31.6637	−1.13886	−0.569431	−	0.822039i	$-0.692837\pi$
$773$	−31.6637	−1.13886	−0.569431	+	0.822039i	$0.692837\pi$
$774$	0.231560	0.00832325
$775$	0	0
$776$	−4.76814	−0.171166
$777$	−7.11166	−0.255130
$778$	50.6681	1.81654
$779$	−0.905960	−0.0324594
$780$	0	0
$781$	23.8709	0.854169
$782$	−1.19520	−0.0427403
$783$	31.1891	1.11461
$784$	23.6022	0.842935
$785$	0	0
$786$	−9.48754	−0.338409
$787$	39.0199	1.39091	0.695455	−	0.718570i	$-0.255203\pi$
$787$	39.0199	1.39091	0.695455	+	0.718570i	$0.255203\pi$
$788$	−13.4483	−0.479076
$789$	7.25262	0.258200
$790$	0	0
$791$	22.2184	0.789994
$792$	6.66371	0.236785
$793$	3.34087	0.118638
$794$	56.3669	2.00038
$795$	0	0
$796$	−9.23799	−0.327432
$797$	36.1603	1.28087	0.640433	−	0.768014i	$-0.278755\pi$
$797$	36.1603	1.28087	0.640433	+	0.768014i	$0.278755\pi$
$798$	−8.60757	−0.304705
$799$	0.0575285	0.00203521
$800$	0	0
$801$	16.1943	0.572196
$802$	−31.2666	−1.10406
$803$	14.9802	0.528639
$804$	11.4787	0.404824
$805$	0	0
$806$	6.91300	0.243500
$807$	−25.3001	−0.890604
$808$	−9.27385	−0.326253
$809$	−44.8762	−1.57776	−0.788881	−	0.614546i	$-0.789339\pi$
$809$	−44.8762	−1.57776	−0.788881	+	0.614546i	$0.789339\pi$
$810$	0	0
$811$	−23.1881	−0.814243	−0.407121	−	0.913374i	$-0.633467\pi$
$811$	−23.1881	−0.814243	−0.407121	+	0.913374i	$0.633467\pi$
$812$	−9.03223	−0.316969
$813$	−6.01982	−0.211124
$814$	−14.6249	−0.512602
$815$	0	0
$816$	0.681504	0.0238574
$817$	0.228141	0.00798164
$818$	55.9359	1.95575
$819$	−13.0191	−0.454924
$820$	0	0
$821$	−45.2209	−1.57822	−0.789110	−	0.614252i	$-0.789458\pi$
$821$	−45.2209	−1.57822	−0.789110	+	0.614252i	$0.789458\pi$
$822$	8.65600	0.301913
$823$	15.9408	0.555661	0.277830	−	0.960630i	$-0.410385\pi$
$823$	15.9408	0.555661	0.277830	+	0.960630i	$0.410385\pi$
$824$	5.93305	0.206688
$825$	0	0
$826$	−18.2441	−0.634794
$827$	24.1361	0.839296	0.419648	−	0.907687i	$-0.362154\pi$
$827$	24.1361	0.839296	0.419648	+	0.907687i	$0.362154\pi$
$828$	9.34424	0.324735
$829$	9.01909	0.313246	0.156623	−	0.987658i	$-0.449939\pi$
$829$	9.01909	0.313246	0.156623	+	0.987658i	$0.449939\pi$
$830$	0	0
$831$	17.0514	0.591505
$832$	−7.01159	−0.243083
$833$	−0.693123	−0.0240153
$834$	25.4517	0.881319
$835$	0	0
$836$	−5.56793	−0.192571
$837$	−4.77828	−0.165162
$838$	−16.1701	−0.558587
$839$	37.8252	1.30587	0.652936	−	0.757413i	$-0.273537\pi$
$839$	37.8252	1.30587	0.652936	+	0.757413i	$0.273537\pi$
$840$	0	0
$841$	13.6053	0.469148
$842$	−44.7557	−1.54238
$843$	14.4982	0.499346
$844$	10.4270	0.358912
$845$	0	0
$846$	−1.42986	−0.0491597
$847$	12.2812	0.421987
$848$	42.3100	1.45293
$849$	−27.6550	−0.949118
$850$	0	0
$851$	24.1815	0.828930
$852$	−12.0699	−0.413510
$853$	26.8684	0.919955	0.459978	−	0.887931i	$-0.347857\pi$
$853$	26.8684	0.919955	0.459978	+	0.887931i	$0.347857\pi$
$854$	2.12600	0.0727503
$855$	0	0
$856$	21.3270	0.728940
$857$	−55.0595	−1.88080	−0.940398	−	0.340077i	$-0.889547\pi$
$857$	−55.0595	−1.88080	−0.940398	+	0.340077i	$0.889547\pi$
$858$	10.8709	0.371127
$859$	−34.7493	−1.18563	−0.592816	−	0.805338i	$-0.701984\pi$
$859$	−34.7493	−1.18563	−0.592816	+	0.805338i	$0.701984\pi$
$860$	0	0
$861$	0.354061	0.0120664
$862$	−13.4088	−0.456706
$863$	−23.6439	−0.804848	−0.402424	−	0.915453i	$-0.631832\pi$
$863$	−23.6439	−0.804848	−0.402424	+	0.915453i	$0.631832\pi$
$864$	−23.0891	−0.785507
$865$	0	0
$866$	32.0379	1.08869
$867$	15.8032	0.536703
$868$	1.38377	0.0469681
$869$	8.02426	0.272204
$870$	0	0
$871$	54.3804	1.84261
$872$	−21.7658	−0.737083
$873$	−5.50348	−0.186265
$874$	29.2679	0.990002
$875$	0	0
$876$	−7.57449	−0.255918
$877$	17.2533	0.582604	0.291302	−	0.956631i	$-0.405912\pi$
$877$	17.2533	0.582604	0.291302	+	0.956631i	$0.405912\pi$
$878$	3.92833	0.132575
$879$	5.49841	0.185457
$880$	0	0
$881$	−57.9997	−1.95406	−0.977031	−	0.213099i	$-0.931644\pi$
$881$	−57.9997	−1.95406	−0.977031	+	0.213099i	$0.931644\pi$
$882$	17.2275	0.580080
$883$	51.3264	1.72727	0.863636	−	0.504116i	$-0.168182\pi$
$883$	51.3264	1.72727	0.863636	+	0.504116i	$0.168182\pi$
$884$	−0.544662	−0.0183190
$885$	0	0
$886$	27.5175	0.924469
$887$	−10.4756	−0.351736	−0.175868	−	0.984414i	$-0.556273\pi$
$887$	−10.4756	−0.351736	−0.175868	+	0.984414i	$0.556273\pi$
$888$	−8.71949	−0.292607
$889$	−2.80472	−0.0940673
$890$	0	0
$891$	3.30037	0.110566
$892$	10.0574	0.336745
$893$	−1.40875	−0.0471420
$894$	11.1983	0.374526
$895$	0	0
$896$	−19.0327	−0.635837
$897$	−17.9745	−0.600150
$898$	4.29148	0.143208
$899$	−6.52727	−0.217697
$900$	0	0
$901$	−1.24252	−0.0413942
$902$	0.728114	0.0242435
$903$	−0.0891604	−0.00296707
$904$	27.2416	0.906041
$905$	0	0
$906$	−7.79620	−0.259011
$907$	−17.6369	−0.585625	−0.292813	−	0.956170i	$-0.594591\pi$
$907$	−17.6369	−0.585625	−0.292813	+	0.956170i	$0.594591\pi$
$908$	21.3502	0.708530
$909$	−10.7041	−0.355031
$910$	0	0
$911$	−23.6680	−0.784156	−0.392078	−	0.919932i	$-0.628244\pi$
$911$	−23.6680	−0.784156	−0.392078	+	0.919932i	$0.628244\pi$
$912$	−16.6886	−0.552614
$913$	7.10494	0.235139
$914$	−14.2125	−0.470107
$915$	0	0
$916$	−26.5703	−0.877907
$917$	−8.99700	−0.297107
$918$	1.19685	0.0395020
$919$	18.1214	0.597769	0.298884	−	0.954289i	$-0.403385\pi$
$919$	18.1214	0.597769	0.298884	+	0.954289i	$0.403385\pi$
$920$	0	0
$921$	22.8769	0.753819
$922$	22.0656	0.726690
$923$	−57.1812	−1.88214
$924$	2.17602	0.0715858
$925$	0	0
$926$	−14.6025	−0.479867
$927$	6.84805	0.224919
$928$	−31.5404	−1.03536
$929$	−18.6456	−0.611741	−0.305870	−	0.952073i	$-0.598947\pi$
$929$	−18.6456	−0.611741	−0.305870	+	0.952073i	$0.598947\pi$
$930$	0	0
$931$	16.9731	0.556271
$932$	16.2648	0.532771
$933$	−4.84088	−0.158483
$934$	47.1638	1.54325
$935$	0	0
$936$	−15.9625	−0.521750
$937$	6.88877	0.225046	0.112523	−	0.993649i	$-0.464107\pi$
$937$	6.88877	0.225046	0.112523	+	0.993649i	$0.464107\pi$
$938$	34.6056	1.12991
$939$	23.2708	0.759412
$940$	0	0
$941$	−12.6410	−0.412085	−0.206043	−	0.978543i	$-0.566059\pi$
$941$	−12.6410	−0.412085	−0.206043	+	0.978543i	$0.566059\pi$
$942$	2.31054	0.0752815
$943$	−1.20390	−0.0392043
$944$	−35.3721	−1.15126
$945$	0	0
$946$	−0.183355	−0.00596140
$947$	25.5531	0.830365	0.415182	−	0.909738i	$-0.363718\pi$
$947$	25.5531	0.830365	0.415182	+	0.909738i	$0.363718\pi$
$948$	−4.05734	−0.131776
$949$	−35.8841	−1.16485
$950$	0	0
$951$	24.6454	0.799182
$952$	0.408690	0.0132457
$953$	−35.7180	−1.15702	−0.578510	−	0.815675i	$-0.696366\pi$
$953$	−35.7180	−1.15702	−0.578510	+	0.815675i	$0.696366\pi$
$954$	30.8825	0.999859
$955$	0	0
$956$	−19.7771	−0.639637
$957$	−10.2643	−0.331799
$958$	−32.5227	−1.05076
$959$	8.20846	0.265065
$960$	0	0
$961$	1.00000	0.0322581
$962$	35.0330	1.12951
$963$	24.6160	0.793240
$964$	−15.6166	−0.502977
$965$	0	0
$966$	−11.4383	−0.368021
$967$	−28.8255	−0.926964	−0.463482	−	0.886106i	$-0.653400\pi$
$967$	−28.8255	−0.926964	−0.463482	+	0.886106i	$0.653400\pi$
$968$	15.0578	0.483976
$969$	0.490092	0.0157440
$970$	0	0
$971$	−22.0561	−0.707815	−0.353907	−	0.935280i	$-0.615147\pi$
$971$	−22.0561	−0.707815	−0.353907	+	0.935280i	$0.615147\pi$
$972$	−14.8252	−0.475520
$973$	24.1357	0.773756
$974$	4.62595	0.148225
$975$	0	0
$976$	4.12195	0.131940
$977$	1.18894	0.0380375	0.0190187	−	0.999819i	$-0.493946\pi$
$977$	1.18894	0.0380375	0.0190187	+	0.999819i	$0.493946\pi$
$978$	−38.4886	−1.23073
$979$	−12.8231	−0.409827
$980$	0	0
$981$	−25.1225	−0.802100
$982$	−29.6575	−0.946408
$983$	20.1277	0.641973	0.320987	−	0.947084i	$-0.395986\pi$
$983$	20.1277	0.641973	0.320987	+	0.947084i	$0.395986\pi$
$984$	0.434108	0.0138389
$985$	0	0
$986$	1.63493	0.0520669
$987$	0.550558	0.0175245
$988$	13.3376	0.424326
$989$	0.303168	0.00964018
$990$	0	0
$991$	−9.37058	−0.297666	−0.148833	−	0.988862i	$-0.547552\pi$
$991$	−9.37058	−0.297666	−0.148833	+	0.988862i	$0.547552\pi$
$992$	4.83209	0.153419
$993$	8.99642	0.285493
$994$	−36.3880	−1.15416
$995$	0	0
$996$	−3.59250	−0.113833
$997$	2.96440	0.0938836	0.0469418	−	0.998898i	$-0.485052\pi$
$997$	2.96440	0.0938836	0.0469418	+	0.998898i	$0.485052\pi$
$998$	−9.37901	−0.296887
$999$	−24.2148	−0.766124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.h.1.5	✓	5
3.2	odd	2		6975.2.a.by.1.1		5
5.2	odd	4		775.2.b.g.249.8		10
5.3	odd	4		775.2.b.g.249.3		10
5.4	even	2		775.2.a.k.1.1	yes	5
15.14	odd	2		6975.2.a.bp.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.a.h.1.5	✓	5	1.1	even	1	trivial
775.2.a.k.1.1	yes	5	5.4	even	2
775.2.b.g.249.3		10	5.3	odd	4
775.2.b.g.249.8		10	5.2	odd	4
6975.2.a.bp.1.5		5	15.14	odd	2
6975.2.a.by.1.1		5	3.2	odd	2

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q+1.70816 q^{2} -0.930775 q^{3} +0.917797 q^{4} -1.58991 q^{6} -1.50771 q^{7} -1.84857 q^{8} -2.13366 q^{9} +O(q^{10})\)	\(q+1.70816 q^{2} -0.930775 q^{3} +0.917797 q^{4} -1.58991 q^{6} -1.50771 q^{7} -1.84857 q^{8} -2.13366 q^{9} +1.68949 q^{11} -0.854262 q^{12} -4.04706 q^{13} -2.57540 q^{14} -4.99324 q^{16} +0.146636 q^{17} -3.64462 q^{18} -3.59081 q^{19} +1.40333 q^{21} +2.88591 q^{22} -4.77169 q^{23} +1.72060 q^{24} -6.91300 q^{26} +4.77828 q^{27} -1.38377 q^{28} +6.52727 q^{29} -1.00000 q^{31} -4.83209 q^{32} -1.57253 q^{33} +0.250477 q^{34} -1.95827 q^{36} -5.06769 q^{37} -6.13366 q^{38} +3.76690 q^{39} +0.252300 q^{41} +2.39711 q^{42} -0.0635347 q^{43} +1.55061 q^{44} -8.15079 q^{46} +0.392322 q^{47} +4.64758 q^{48} -4.72682 q^{49} -0.136485 q^{51} -3.71438 q^{52} -8.47346 q^{53} +8.16205 q^{54} +2.78710 q^{56} +3.34223 q^{57} +11.1496 q^{58} +7.08400 q^{59} -0.825505 q^{61} -1.70816 q^{62} +3.21693 q^{63} +1.73251 q^{64} -2.68613 q^{66} -13.4370 q^{67} +0.134582 q^{68} +4.44137 q^{69} +14.1291 q^{71} +3.94422 q^{72} +8.86670 q^{73} -8.65641 q^{74} -3.29563 q^{76} -2.54725 q^{77} +6.43445 q^{78} +4.74952 q^{79} +1.95347 q^{81} +0.430967 q^{82} +4.20538 q^{83} +1.28798 q^{84} -0.108527 q^{86} -6.07542 q^{87} -3.12314 q^{88} -7.58991 q^{89} +6.10177 q^{91} -4.37944 q^{92} +0.930775 q^{93} +0.670146 q^{94} +4.49759 q^{96} +2.57936 q^{97} -8.07415 q^{98} -3.60479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more