LMFDB - Embedded newform 5635.2.a.bb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5635,2,Mod(1,5635)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5635, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5635.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5635 = 5 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5635.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:	$44.9957015390$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 $ x^8 - x^7 - 11x^6 + 9x^5 + 36x^4 - 23x^3 - 30x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.18794$ of defining polynomial
Character	$\chi$	$=$	5635.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18794 q^{2} -1.57054 q^{3} -0.588791 q^{4} -1.00000 q^{5} -1.86571 q^{6} -3.07534 q^{8} -0.533418 q^{9} +O(q^{10})$	\(q+1.18794 q^{2} -1.57054 q^{3} -0.588791 q^{4} -1.00000 q^{5} -1.86571 q^{6} -3.07534 q^{8} -0.533418 q^{9} -1.18794 q^{10} +6.49072 q^{11} +0.924717 q^{12} -0.322236 q^{13} +1.57054 q^{15} -2.47574 q^{16} -5.08903 q^{17} -0.633671 q^{18} +0.234610 q^{19} +0.588791 q^{20} +7.71061 q^{22} +1.00000 q^{23} +4.82993 q^{24} +1.00000 q^{25} -0.382798 q^{26} +5.54936 q^{27} -4.41828 q^{29} +1.86571 q^{30} -3.11530 q^{31} +3.20963 q^{32} -10.1939 q^{33} -6.04547 q^{34} +0.314072 q^{36} +11.7161 q^{37} +0.278703 q^{38} +0.506083 q^{39} +3.07534 q^{40} +9.61105 q^{41} -4.63328 q^{43} -3.82168 q^{44} +0.533418 q^{45} +1.18794 q^{46} +10.4958 q^{47} +3.88824 q^{48} +1.18794 q^{50} +7.99250 q^{51} +0.189730 q^{52} -7.94284 q^{53} +6.59232 q^{54} -6.49072 q^{55} -0.368463 q^{57} -5.24866 q^{58} -3.68364 q^{59} -0.924717 q^{60} +0.967566 q^{61} -3.70080 q^{62} +8.76435 q^{64} +0.322236 q^{65} -12.1098 q^{66} -14.4218 q^{67} +2.99637 q^{68} -1.57054 q^{69} +0.213174 q^{71} +1.64044 q^{72} +6.15185 q^{73} +13.9181 q^{74} -1.57054 q^{75} -0.138136 q^{76} +0.601198 q^{78} -8.13690 q^{79} +2.47574 q^{80} -7.11521 q^{81} +11.4174 q^{82} -6.84749 q^{83} +5.08903 q^{85} -5.50408 q^{86} +6.93906 q^{87} -19.9612 q^{88} -4.38509 q^{89} +0.633671 q^{90} -0.588791 q^{92} +4.89268 q^{93} +12.4684 q^{94} -0.234610 q^{95} -5.04084 q^{96} -12.2380 q^{97} -3.46227 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 8 q^{5} - q^{6} + 3 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 8 * q^5 - q^6 + 3 * q^8 + 9 * q^9	$ 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 8 q^{5} - q^{6} + 3 q^{8} + 9 q^{9} - q^{10} + 6 q^{11} - 8 q^{12} - 8 q^{13} + 7 q^{15} + q^{16} - 4 q^{17} - 11 q^{18} - 7 q^{20} - 8 q^{22} + 8 q^{23} + 8 q^{24} + 8 q^{25} - 2 q^{26} - 28 q^{27} - 3 q^{29} + q^{30} + 16 q^{31} + 12 q^{32} - 5 q^{33} + 4 q^{34} - 14 q^{36} - 7 q^{37} - 11 q^{38} + 16 q^{39} - 3 q^{40} - 7 q^{41} - 10 q^{43} + 7 q^{44} - 9 q^{45} + q^{46} - 19 q^{47} + 6 q^{48} + q^{50} + 7 q^{51} - 18 q^{52} - q^{53} + 25 q^{54} - 6 q^{55} - 25 q^{57} - 9 q^{58} - 21 q^{59} + 8 q^{60} + 7 q^{61} - 18 q^{62} - 37 q^{64} + 8 q^{65} + 43 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 8 q^{71} + 4 q^{72} + 3 q^{73} + 12 q^{74} - 7 q^{75} - 8 q^{76} - 50 q^{78} - 15 q^{79} - q^{80} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 4 q^{85} - 12 q^{86} - 21 q^{87} - 29 q^{88} - q^{89} + 11 q^{90} + 7 q^{92} - 5 q^{93} + 36 q^{94} - 30 q^{96} - 10 q^{97} - 18 q^{99}+O(q^{100}) $ 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 8 * q^5 - q^6 + 3 * q^8 + 9 * q^9 - q^10 + 6 * q^11 - 8 * q^12 - 8 * q^13 + 7 * q^15 + q^16 - 4 * q^17 - 11 * q^18 - 7 * q^20 - 8 * q^22 + 8 * q^23 + 8 * q^24 + 8 * q^25 - 2 * q^26 - 28 * q^27 - 3 * q^29 + q^30 + 16 * q^31 + 12 * q^32 - 5 * q^33 + 4 * q^34 - 14 * q^36 - 7 * q^37 - 11 * q^38 + 16 * q^39 - 3 * q^40 - 7 * q^41 - 10 * q^43 + 7 * q^44 - 9 * q^45 + q^46 - 19 * q^47 + 6 * q^48 + q^50 + 7 * q^51 - 18 * q^52 - q^53 + 25 * q^54 - 6 * q^55 - 25 * q^57 - 9 * q^58 - 21 * q^59 + 8 * q^60 + 7 * q^61 - 18 * q^62 - 37 * q^64 + 8 * q^65 + 43 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 8 * q^71 + 4 * q^72 + 3 * q^73 + 12 * q^74 - 7 * q^75 - 8 * q^76 - 50 * q^78 - 15 * q^79 - q^80 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 4 * q^85 - 12 * q^86 - 21 * q^87 - 29 * q^88 - q^89 + 11 * q^90 + 7 * q^92 - 5 * q^93 + 36 * q^94 - 30 * q^96 - 10 * q^97 - 18 * 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 $

$2$	1.18794	0.840003	0.420001	−	0.907523i	$-0.362030\pi$
$2$	1.18794	0.840003	0.420001	+	0.907523i	$0.362030\pi$
$3$	−1.57054	−0.906749	−0.453375	−	0.891320i	$-0.649780\pi$
$3$	−1.57054	−0.906749	−0.453375	+	0.891320i	$0.649780\pi$
$4$	−0.588791	−0.294395
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.86571	−0.761672
$7$	0	0
$7$	0	0
$8$	−3.07534	−1.08730
$9$	−0.533418	−0.177806
$10$	−1.18794	−0.375661
$11$	6.49072	1.95703	0.978514	−	0.206182i	$-0.0661040\pi$
$11$	6.49072	1.95703	0.978514	+	0.206182i	$0.0661040\pi$
$12$	0.924717	0.266943
$13$	−0.322236	−0.0893722	−0.0446861	−	0.999001i	$-0.514229\pi$
$13$	−0.322236	−0.0893722	−0.0446861	+	0.999001i	$0.514229\pi$
$14$	0	0
$15$	1.57054	0.405511
$16$	−2.47574	−0.618936
$17$	−5.08903	−1.23427	−0.617135	−	0.786857i	$-0.711707\pi$
$17$	−5.08903	−1.23427	−0.617135	+	0.786857i	$0.711707\pi$
$18$	−0.633671	−0.149358
$19$	0.234610	0.0538231	0.0269116	−	0.999638i	$-0.491433\pi$
$19$	0.234610	0.0538231	0.0269116	+	0.999638i	$0.491433\pi$
$20$	0.588791	0.131658
$21$	0	0
$22$	7.71061	1.64391
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	4.82993	0.985904
$25$	1.00000	0.200000
$26$	−0.382798	−0.0750729
$27$	5.54936	1.06797
$28$	0	0
$29$	−4.41828	−0.820453	−0.410227	−	0.911984i	$-0.634550\pi$
$29$	−4.41828	−0.820453	−0.410227	+	0.911984i	$0.634550\pi$
$30$	1.86571	0.340630
$31$	−3.11530	−0.559524	−0.279762	−	0.960069i	$-0.590256\pi$
$31$	−3.11530	−0.559524	−0.279762	+	0.960069i	$0.590256\pi$
$32$	3.20963	0.567388
$33$	−10.1939	−1.77453
$34$	−6.04547	−1.03679
$35$	0	0
$36$	0.314072	0.0523453
$37$	11.7161	1.92612	0.963061	−	0.269285i	$-0.0867872\pi$
$37$	11.7161	1.92612	0.963061	+	0.269285i	$0.0867872\pi$
$38$	0.278703	0.0452116
$39$	0.506083	0.0810382
$40$	3.07534	0.486253
$41$	9.61105	1.50099	0.750497	−	0.660874i	$-0.229814\pi$
$41$	9.61105	1.50099	0.750497	+	0.660874i	$0.229814\pi$
$42$	0	0
$43$	−4.63328	−0.706569	−0.353285	−	0.935516i	$-0.614935\pi$
$43$	−4.63328	−0.706569	−0.353285	+	0.935516i	$0.614935\pi$
$44$	−3.82168	−0.576140
$45$	0.533418	0.0795173
$46$	1.18794	0.175153
$47$	10.4958	1.53097	0.765483	−	0.643456i	$-0.222500\pi$
$47$	10.4958	1.53097	0.765483	+	0.643456i	$0.222500\pi$
$48$	3.88824	0.561220
$49$	0	0
$50$	1.18794	0.168001
$51$	7.99250	1.11917
$52$	0.189730	0.0263108
$53$	−7.94284	−1.09103	−0.545516	−	0.838100i	$-0.683666\pi$
$53$	−7.94284	−1.09103	−0.545516	+	0.838100i	$0.683666\pi$
$54$	6.59232	0.897102
$55$	−6.49072	−0.875209
$56$	0	0
$57$	−0.368463	−0.0488041
$58$	−5.24866	−0.689183
$59$	−3.68364	−0.479569	−0.239785	−	0.970826i	$-0.577077\pi$
$59$	−3.68364	−0.479569	−0.239785	+	0.970826i	$0.577077\pi$
$60$	−0.924717	−0.119380
$61$	0.967566	0.123884	0.0619421	−	0.998080i	$-0.480271\pi$
$61$	0.967566	0.123884	0.0619421	+	0.998080i	$0.480271\pi$
$62$	−3.70080	−0.470002
$63$	0	0
$64$	8.76435	1.09554
$65$	0.322236	0.0399685
$66$	−12.1098	−1.49061
$67$	−14.4218	−1.76190	−0.880951	−	0.473208i	$-0.843096\pi$
$67$	−14.4218	−1.76190	−0.880951	+	0.473208i	$0.843096\pi$
$68$	2.99637	0.363363
$69$	−1.57054	−0.189070
$70$	0	0
$71$	0.213174	0.0252991	0.0126496	−	0.999920i	$-0.495973\pi$
$71$	0.213174	0.0252991	0.0126496	+	0.999920i	$0.495973\pi$
$72$	1.64044	0.193328
$73$	6.15185	0.720020	0.360010	−	0.932948i	$-0.382773\pi$
$73$	6.15185	0.720020	0.360010	+	0.932948i	$0.382773\pi$
$74$	13.9181	1.61795
$75$	−1.57054	−0.181350
$76$	−0.138136	−0.0158453
$77$	0	0
$78$	0.601198	0.0680723
$79$	−8.13690	−0.915472	−0.457736	−	0.889088i	$-0.651340\pi$
$79$	−8.13690	−0.915472	−0.457736	+	0.889088i	$0.651340\pi$
$80$	2.47574	0.276797
$81$	−7.11521	−0.790579
$82$	11.4174	1.26084
$83$	−6.84749	−0.751610	−0.375805	−	0.926699i	$-0.622634\pi$
$83$	−6.84749	−0.751610	−0.375805	+	0.926699i	$0.622634\pi$
$84$	0	0
$85$	5.08903	0.551982
$86$	−5.50408	−0.593520
$87$	6.93906	0.743945
$88$	−19.9612	−2.12787
$89$	−4.38509	−0.464818	−0.232409	−	0.972618i	$-0.574661\pi$
$89$	−4.38509	−0.464818	−0.232409	+	0.972618i	$0.574661\pi$
$90$	0.633671	0.0667947
$91$	0	0
$92$	−0.588791	−0.0613857
$93$	4.89268	0.507348
$94$	12.4684	1.28602
$95$	−0.234610	−0.0240704
$96$	−5.04084	−0.514478
$97$	−12.2380	−1.24258	−0.621291	−	0.783580i	$-0.713391\pi$
$97$	−12.2380	−1.24258	−0.621291	+	0.783580i	$0.713391\pi$
$98$	0	0
$99$	−3.46227	−0.347971
$100$	−0.588791	−0.0588791
$101$	7.42524	0.738839	0.369420	−	0.929263i	$-0.379557\pi$
$101$	7.42524	0.738839	0.369420	+	0.929263i	$0.379557\pi$
$102$	9.49463	0.940109
$103$	8.10089	0.798204	0.399102	−	0.916906i	$-0.369322\pi$
$103$	8.10089	0.798204	0.399102	+	0.916906i	$0.369322\pi$
$104$	0.990985	0.0971740
$105$	0	0
$106$	−9.43564	−0.916471
$107$	−0.911987	−0.0881651	−0.0440825	−	0.999028i	$-0.514036\pi$
$107$	−0.911987	−0.0881651	−0.0440825	+	0.999028i	$0.514036\pi$
$108$	−3.26741	−0.314407
$109$	2.31369	0.221612	0.110806	−	0.993842i	$-0.464657\pi$
$109$	2.31369	0.221612	0.110806	+	0.993842i	$0.464657\pi$
$110$	−7.71061	−0.735178
$111$	−18.4006	−1.74651
$112$	0	0
$113$	5.00788	0.471101	0.235551	−	0.971862i	$-0.424311\pi$
$113$	5.00788	0.471101	0.235551	+	0.971862i	$0.424311\pi$
$114$	−0.437713	−0.0409955
$115$	−1.00000	−0.0932505
$116$	2.60144	0.241538
$117$	0.171887	0.0158909
$118$	−4.37596	−0.402840
$119$	0	0
$120$	−4.82993	−0.440910
$121$	31.1295	2.82996
$122$	1.14941	0.104063
$123$	−15.0945	−1.36102
$124$	1.83426	0.164721
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−12.8730	−1.14229	−0.571147	−	0.820848i	$-0.693501\pi$
$127$	−12.8730	−1.14229	−0.571147	+	0.820848i	$0.693501\pi$
$128$	3.99229	0.352872
$129$	7.27674	0.640681
$130$	0.382798	0.0335736
$131$	5.00398	0.437200	0.218600	−	0.975815i	$-0.429851\pi$
$131$	5.00398	0.437200	0.218600	+	0.975815i	$0.429851\pi$
$132$	6.00208	0.522414
$133$	0	0
$134$	−17.1323	−1.48000
$135$	−5.54936	−0.477613
$136$	15.6505	1.34202
$137$	−12.6062	−1.07702	−0.538510	−	0.842619i	$-0.681013\pi$
$137$	−12.6062	−1.07702	−0.538510	+	0.842619i	$0.681013\pi$
$138$	−1.86571	−0.158820
$139$	−11.4166	−0.968346	−0.484173	−	0.874972i	$-0.660879\pi$
$139$	−11.4166	−0.968346	−0.484173	+	0.874972i	$0.660879\pi$
$140$	0	0
$141$	−16.4840	−1.38820
$142$	0.253239	0.0212513
$143$	−2.09155	−0.174904
$144$	1.32061	0.110051
$145$	4.41828	0.366918
$146$	7.30805	0.604819
$147$	0	0
$148$	−6.89835	−0.567041
$149$	−5.95844	−0.488134	−0.244067	−	0.969758i	$-0.578482\pi$
$149$	−5.95844	−0.488134	−0.244067	+	0.969758i	$0.578482\pi$
$150$	−1.86571	−0.152334
$151$	−11.6835	−0.950790	−0.475395	−	0.879772i	$-0.657695\pi$
$151$	−11.6835	−0.950790	−0.475395	+	0.879772i	$0.657695\pi$
$152$	−0.721503	−0.0585216
$153$	2.71458	0.219461
$154$	0	0
$155$	3.11530	0.250227
$156$	−0.297977	−0.0238573
$157$	3.90565	0.311705	0.155852	−	0.987780i	$-0.450188\pi$
$157$	3.90565	0.311705	0.155852	+	0.987780i	$0.450188\pi$
$158$	−9.66617	−0.768999
$159$	12.4745	0.989293
$160$	−3.20963	−0.253743
$161$	0	0
$162$	−8.45247	−0.664089
$163$	13.6246	1.06716	0.533580	−	0.845749i	$-0.320846\pi$
$163$	13.6246	1.06716	0.533580	+	0.845749i	$0.320846\pi$
$164$	−5.65890	−0.441886
$165$	10.1939	0.793595
$166$	−8.13443	−0.631354
$167$	−19.7970	−1.53194	−0.765970	−	0.642876i	$-0.777741\pi$
$167$	−19.7970	−1.53194	−0.765970	+	0.642876i	$0.777741\pi$
$168$	0	0
$169$	−12.8962	−0.992013
$170$	6.04547	0.463667
$171$	−0.125145	−0.00957008
$172$	2.72803	0.208011
$173$	−5.90781	−0.449162	−0.224581	−	0.974455i	$-0.572101\pi$
$173$	−5.90781	−0.449162	−0.224581	+	0.974455i	$0.572101\pi$
$174$	8.24321	0.624916
$175$	0	0
$176$	−16.0694	−1.21127
$177$	5.78529	0.434849
$178$	−5.20923	−0.390449
$179$	−3.85087	−0.287828	−0.143914	−	0.989590i	$-0.545969\pi$
$179$	−3.85087	−0.287828	−0.143914	+	0.989590i	$0.545969\pi$
$180$	−0.314072	−0.0234095
$181$	−6.44804	−0.479279	−0.239640	−	0.970862i	$-0.577029\pi$
$181$	−6.44804	−0.479279	−0.239640	+	0.970862i	$0.577029\pi$
$182$	0	0
$183$	−1.51960	−0.112332
$184$	−3.07534	−0.226717
$185$	−11.7161	−0.861388
$186$	5.81223	0.426174
$187$	−33.0315	−2.41550
$188$	−6.17981	−0.450709
$189$	0	0
$190$	−0.278703	−0.0202192
$191$	7.38632	0.534456	0.267228	−	0.963633i	$-0.413892\pi$
$191$	7.38632	0.534456	0.267228	+	0.963633i	$0.413892\pi$
$192$	−13.7647	−0.993383
$193$	−1.89576	−0.136460	−0.0682298	−	0.997670i	$-0.521735\pi$
$193$	−1.89576	−0.136460	−0.0682298	+	0.997670i	$0.521735\pi$
$194$	−14.5381	−1.04377
$195$	−0.506083	−0.0362414
$196$	0	0
$197$	−4.74737	−0.338236	−0.169118	−	0.985596i	$-0.554092\pi$
$197$	−4.74737	−0.338236	−0.169118	+	0.985596i	$0.554092\pi$
$198$	−4.11298	−0.292297
$199$	5.16675	0.366261	0.183131	−	0.983089i	$-0.441377\pi$
$199$	5.16675	0.366261	0.183131	+	0.983089i	$0.441377\pi$
$200$	−3.07534	−0.217459
$201$	22.6499	1.59760
$202$	8.82077	0.620627
$203$	0	0
$204$	−4.70591	−0.329479
$205$	−9.61105	−0.671265
$206$	9.62340	0.670494
$207$	−0.533418	−0.0370751
$208$	0.797774	0.0553157
$209$	1.52279	0.105333
$210$	0	0
$211$	0.790527	0.0544221	0.0272111	−	0.999630i	$-0.491337\pi$
$211$	0.790527	0.0544221	0.0272111	+	0.999630i	$0.491337\pi$
$212$	4.67667	0.321195
$213$	−0.334798	−0.0229400
$214$	−1.08339	−0.0740589
$215$	4.63328	0.315987
$216$	−17.0661	−1.16120
$217$	0	0
$218$	2.74854	0.186154
$219$	−9.66170	−0.652877
$220$	3.82168	0.257657
$221$	1.63987	0.110309
$222$	−21.8589	−1.46707
$223$	−20.5760	−1.37787	−0.688937	−	0.724821i	$-0.741922\pi$
$223$	−20.5760	−1.37787	−0.688937	+	0.724821i	$0.741922\pi$
$224$	0	0
$225$	−0.533418	−0.0355612
$226$	5.94907	0.395727
$227$	−21.8255	−1.44861	−0.724303	−	0.689482i	$-0.757838\pi$
$227$	−21.8255	−1.44861	−0.724303	+	0.689482i	$0.757838\pi$
$228$	0.216947	0.0143677
$229$	27.7545	1.83407	0.917034	−	0.398809i	$-0.130576\pi$
$229$	27.7545	1.83407	0.917034	+	0.398809i	$0.130576\pi$
$230$	−1.18794	−0.0783307
$231$	0	0
$232$	13.5877	0.892075
$233$	−28.7795	−1.88541	−0.942703	−	0.333632i	$-0.891726\pi$
$233$	−28.7795	−1.88541	−0.942703	+	0.333632i	$0.891726\pi$
$234$	0.204192	0.0133484
$235$	−10.4958	−0.684669
$236$	2.16889	0.141183
$237$	12.7793	0.830104
$238$	0	0
$239$	−9.32089	−0.602918	−0.301459	−	0.953479i	$-0.597474\pi$
$239$	−9.32089	−0.602918	−0.301459	+	0.953479i	$0.597474\pi$
$240$	−3.88824	−0.250985
$241$	−22.1174	−1.42471	−0.712355	−	0.701820i	$-0.752371\pi$
$241$	−22.1174	−1.42471	−0.712355	+	0.701820i	$0.752371\pi$
$242$	36.9801	2.37717
$243$	−5.47339	−0.351118
$244$	−0.569694	−0.0364709
$245$	0	0
$246$	−17.9314	−1.14326
$247$	−0.0755997	−0.00481029
$248$	9.58059	0.608368
$249$	10.7542	0.681521
$250$	−1.18794	−0.0751321
$251$	21.2221	1.33953	0.669765	−	0.742573i	$-0.266395\pi$
$251$	21.2221	1.33953	0.669765	+	0.742573i	$0.266395\pi$
$252$	0	0
$253$	6.49072	0.408068
$254$	−15.2924	−0.959530
$255$	−7.99250	−0.500510
$256$	−12.7861	−0.799130
$257$	−27.5172	−1.71648	−0.858238	−	0.513251i	$-0.828441\pi$
$257$	−27.5172	−1.71648	−0.858238	+	0.513251i	$0.828441\pi$
$258$	8.64435	0.538174
$259$	0	0
$260$	−0.189730	−0.0117665
$261$	2.35679	0.145882
$262$	5.94445	0.367249
$263$	−8.28509	−0.510880	−0.255440	−	0.966825i	$-0.582220\pi$
$263$	−8.28509	−0.510880	−0.255440	+	0.966825i	$0.582220\pi$
$264$	31.3497	1.92944
$265$	7.94284	0.487925
$266$	0	0
$267$	6.88693	0.421473
$268$	8.49141	0.518696
$269$	22.6695	1.38219	0.691093	−	0.722766i	$-0.257129\pi$
$269$	22.6695	1.38219	0.691093	+	0.722766i	$0.257129\pi$
$270$	−6.59232	−0.401196
$271$	−13.8971	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$271$	−13.8971	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$272$	12.5991	0.763934
$273$	0	0
$274$	−14.9755	−0.904701
$275$	6.49072	0.391405
$276$	0.924717	0.0556614
$277$	−23.0692	−1.38609	−0.693047	−	0.720893i	$-0.743732\pi$
$277$	−23.0692	−1.38609	−0.693047	+	0.720893i	$0.743732\pi$
$278$	−13.5623	−0.813413
$279$	1.66176	0.0994867
$280$	0	0
$281$	14.9705	0.893064	0.446532	−	0.894768i	$-0.352659\pi$
$281$	14.9705	0.893064	0.446532	+	0.894768i	$0.352659\pi$
$282$	−19.5820	−1.16609
$283$	−12.5950	−0.748698	−0.374349	−	0.927288i	$-0.622134\pi$
$283$	−12.5950	−0.748698	−0.374349	+	0.927288i	$0.622134\pi$
$284$	−0.125515	−0.00744795
$285$	0.368463	0.0218258
$286$	−2.48464	−0.146920
$287$	0	0
$288$	−1.71207	−0.100885
$289$	8.89819	0.523423
$290$	5.24866	0.308212
$291$	19.2202	1.12671
$292$	−3.62215	−0.211970
$293$	−21.5482	−1.25886	−0.629429	−	0.777058i	$-0.716711\pi$
$293$	−21.5482	−1.25886	−0.629429	+	0.777058i	$0.716711\pi$
$294$	0	0
$295$	3.68364	0.214470
$296$	−36.0311	−2.09426
$297$	36.0194	2.09006
$298$	−7.07829	−0.410034
$299$	−0.322236	−0.0186354
$300$	0.924717	0.0533885
$301$	0	0
$302$	−13.8793	−0.798666
$303$	−11.6616	−0.669942
$304$	−0.580833	−0.0333131
$305$	−0.967566	−0.0554027
$306$	3.22477	0.184348
$307$	15.8007	0.901793	0.450897	−	0.892576i	$-0.351104\pi$
$307$	15.8007	0.901793	0.450897	+	0.892576i	$0.351104\pi$
$308$	0	0
$309$	−12.7227	−0.723771
$310$	3.70080	0.210191
$311$	−22.4751	−1.27445	−0.637224	−	0.770679i	$-0.719917\pi$
$311$	−22.4751	−1.27445	−0.637224	+	0.770679i	$0.719917\pi$
$312$	−1.55638	−0.0881125
$313$	5.42703	0.306754	0.153377	−	0.988168i	$-0.450985\pi$
$313$	5.42703	0.306754	0.153377	+	0.988168i	$0.450985\pi$
$314$	4.63969	0.261833
$315$	0	0
$316$	4.79093	0.269511
$317$	5.53722	0.311002	0.155501	−	0.987836i	$-0.450301\pi$
$317$	5.53722	0.311002	0.155501	+	0.987836i	$0.450301\pi$
$318$	14.8190	0.831009
$319$	−28.6778	−1.60565
$320$	−8.76435	−0.489942
$321$	1.43231	0.0799436
$322$	0	0
$323$	−1.19393	−0.0664323
$324$	4.18937	0.232743
$325$	−0.322236	−0.0178744
$326$	16.1852	0.896418
$327$	−3.63374	−0.200946
$328$	−29.5572	−1.63202
$329$	0	0
$330$	12.1098	0.666622
$331$	−10.3994	−0.571602	−0.285801	−	0.958289i	$-0.592260\pi$
$331$	−10.3994	−0.571602	−0.285801	+	0.958289i	$0.592260\pi$
$332$	4.03174	0.221270
$333$	−6.24960	−0.342476
$334$	−23.5178	−1.28683
$335$	14.4218	0.787946
$336$	0	0
$337$	3.98225	0.216927	0.108463	−	0.994100i	$-0.465407\pi$
$337$	3.98225	0.216927	0.108463	+	0.994100i	$0.465407\pi$
$338$	−15.3199	−0.833293
$339$	−7.86505	−0.427171
$340$	−2.99637	−0.162501
$341$	−20.2205	−1.09500
$342$	−0.148665	−0.00803889
$343$	0	0
$344$	14.2489	0.768250
$345$	1.57054	0.0845548
$346$	−7.01814	−0.377298
$347$	1.65560	0.0888775	0.0444388	−	0.999012i	$-0.485850\pi$
$347$	1.65560	0.0888775	0.0444388	+	0.999012i	$0.485850\pi$
$348$	−4.08565	−0.219014
$349$	17.8257	0.954187	0.477093	−	0.878853i	$-0.341690\pi$
$349$	17.8257	0.954187	0.477093	+	0.878853i	$0.341690\pi$
$350$	0	0
$351$	−1.78820	−0.0954473
$352$	20.8328	1.11039
$353$	−28.4680	−1.51520	−0.757598	−	0.652721i	$-0.773627\pi$
$353$	−28.4680	−1.51520	−0.757598	+	0.652721i	$0.773627\pi$
$354$	6.87260	0.365275
$355$	−0.213174	−0.0113141
$356$	2.58190	0.136840
$357$	0	0
$358$	−4.57462	−0.241776
$359$	18.2427	0.962812	0.481406	−	0.876498i	$-0.340126\pi$
$359$	18.2427	0.962812	0.481406	+	0.876498i	$0.340126\pi$
$360$	−1.64044	−0.0864588
$361$	−18.9450	−0.997103
$362$	−7.65991	−0.402596
$363$	−48.8900	−2.56606
$364$	0	0
$365$	−6.15185	−0.322003
$366$	−1.80520	−0.0943591
$367$	5.76823	0.301099	0.150550	−	0.988602i	$-0.451896\pi$
$367$	5.76823	0.301099	0.150550	+	0.988602i	$0.451896\pi$
$368$	−2.47574	−0.129057
$369$	−5.12671	−0.266886
$370$	−13.9181	−0.723568
$371$	0	0
$372$	−2.88077	−0.149361
$373$	1.46028	0.0756105	0.0378053	−	0.999285i	$-0.487963\pi$
$373$	1.46028	0.0756105	0.0378053	+	0.999285i	$0.487963\pi$
$374$	−39.2395	−2.02903
$375$	1.57054	0.0811021
$376$	−32.2780	−1.66461
$377$	1.42373	0.0733257
$378$	0	0
$379$	−31.1522	−1.60018	−0.800089	−	0.599881i	$-0.795215\pi$
$379$	−31.1522	−1.60018	−0.800089	+	0.599881i	$0.795215\pi$
$380$	0.138136	0.00708622
$381$	20.2175	1.03577
$382$	8.77453	0.448944
$383$	−25.7399	−1.31525	−0.657624	−	0.753346i	$-0.728439\pi$
$383$	−25.7399	−1.31525	−0.657624	+	0.753346i	$0.728439\pi$
$384$	−6.27003	−0.319966
$385$	0	0
$386$	−2.25205	−0.114626
$387$	2.47148	0.125632
$388$	7.20562	0.365810
$389$	29.5386	1.49767	0.748833	−	0.662759i	$-0.230615\pi$
$389$	29.5386	1.49767	0.748833	+	0.662759i	$0.230615\pi$
$390$	−0.601198	−0.0304429
$391$	−5.08903	−0.257363
$392$	0	0
$393$	−7.85893	−0.396431
$394$	−5.63961	−0.284119
$395$	8.13690	0.409412
$396$	2.03855	0.102441
$397$	−4.42817	−0.222244	−0.111122	−	0.993807i	$-0.535444\pi$
$397$	−4.42817	−0.222244	−0.111122	+	0.993807i	$0.535444\pi$
$398$	6.13781	0.307660
$399$	0	0
$400$	−2.47574	−0.123787
$401$	18.0474	0.901245	0.450623	−	0.892715i	$-0.351202\pi$
$401$	18.0474	0.901245	0.450623	+	0.892715i	$0.351202\pi$
$402$	26.9068	1.34199
$403$	1.00386	0.0500059
$404$	−4.37191	−0.217511
$405$	7.11521	0.353558
$406$	0	0
$407$	76.0462	3.76947
$408$	−24.5796	−1.21687
$409$	−24.6796	−1.22033	−0.610163	−	0.792276i	$-0.708896\pi$
$409$	−24.6796	−1.22033	−0.610163	+	0.792276i	$0.708896\pi$
$410$	−11.4174	−0.563864
$411$	19.7985	0.976588
$412$	−4.76973	−0.234988
$413$	0	0
$414$	−0.633671	−0.0311432
$415$	6.84749	0.336130
$416$	−1.03426	−0.0507087
$417$	17.9302	0.878047
$418$	1.80898	0.0884803
$419$	−10.9927	−0.537026	−0.268513	−	0.963276i	$-0.586532\pi$
$419$	−10.9927	−0.537026	−0.268513	+	0.963276i	$0.586532\pi$
$420$	0	0
$421$	−29.6274	−1.44395	−0.721975	−	0.691919i	$-0.756765\pi$
$421$	−29.6274	−1.44395	−0.721975	+	0.691919i	$0.756765\pi$
$422$	0.939101	0.0457147
$423$	−5.59863	−0.272215
$424$	24.4269	1.18628
$425$	−5.08903	−0.246854
$426$	−0.397721	−0.0192696
$427$	0	0
$428$	0.536969	0.0259554
$429$	3.28485	0.158594
$430$	5.50408	0.265430
$431$	6.06408	0.292096	0.146048	−	0.989277i	$-0.453345\pi$
$431$	6.06408	0.292096	0.146048	+	0.989277i	$0.453345\pi$
$432$	−13.7388	−0.661008
$433$	1.64010	0.0788182	0.0394091	−	0.999223i	$-0.487452\pi$
$433$	1.64010	0.0788182	0.0394091	+	0.999223i	$0.487452\pi$
$434$	0	0
$435$	−6.93906	−0.332702
$436$	−1.36228	−0.0652414
$437$	0.234610	0.0112229
$438$	−11.4776	−0.548419
$439$	32.7745	1.56424	0.782121	−	0.623126i	$-0.214138\pi$
$439$	32.7745	1.56424	0.782121	+	0.623126i	$0.214138\pi$
$440$	19.9612	0.951611
$441$	0	0
$442$	1.94807	0.0926603
$443$	39.8692	1.89424	0.947122	−	0.320874i	$-0.103977\pi$
$443$	39.8692	1.89424	0.947122	+	0.320874i	$0.103977\pi$
$444$	10.8341	0.514164
$445$	4.38509	0.207873
$446$	−24.4432	−1.15742
$447$	9.35794	0.442616
$448$	0	0
$449$	12.1715	0.574408	0.287204	−	0.957870i	$-0.407274\pi$
$449$	12.1715	0.574408	0.287204	+	0.957870i	$0.407274\pi$
$450$	−0.633671	−0.0298715
$451$	62.3827	2.93749
$452$	−2.94859	−0.138690
$453$	18.3494	0.862128
$454$	−25.9274	−1.21683
$455$	0	0
$456$	1.13315	0.0530644
$457$	38.4552	1.79886	0.899430	−	0.437066i	$-0.143982\pi$
$457$	38.4552	1.79886	0.899430	+	0.437066i	$0.143982\pi$
$458$	32.9708	1.54062
$459$	−28.2408	−1.31817
$460$	0.588791	0.0274525
$461$	19.7613	0.920376	0.460188	−	0.887822i	$-0.347782\pi$
$461$	19.7613	0.920376	0.460188	+	0.887822i	$0.347782\pi$
$462$	0	0
$463$	39.4592	1.83382	0.916912	−	0.399089i	$-0.130673\pi$
$463$	39.4592	1.83382	0.916912	+	0.399089i	$0.130673\pi$
$464$	10.9385	0.507808
$465$	−4.89268	−0.226893
$466$	−34.1884	−1.58375
$467$	−6.92546	−0.320472	−0.160236	−	0.987079i	$-0.551226\pi$
$467$	−6.92546	−0.320472	−0.160236	+	0.987079i	$0.551226\pi$
$468$	−0.101205	−0.00467821
$469$	0	0
$470$	−12.4684	−0.575123
$471$	−6.13396	−0.282638
$472$	11.3284	0.521434
$473$	−30.0734	−1.38278
$474$	15.1811	0.697289
$475$	0.234610	0.0107646
$476$	0	0
$477$	4.23685	0.193992
$478$	−11.0727	−0.506453
$479$	−14.1135	−0.644864	−0.322432	−	0.946593i	$-0.604500\pi$
$479$	−14.1135	−0.644864	−0.322432	+	0.946593i	$0.604500\pi$
$480$	5.04084	0.230082
$481$	−3.77536	−0.172142
$482$	−26.2743	−1.19676
$483$	0	0
$484$	−18.3288	−0.833126
$485$	12.2380	0.555699
$486$	−6.50207	−0.294940
$487$	13.1395	0.595408	0.297704	−	0.954658i	$-0.403779\pi$
$487$	13.1395	0.595408	0.297704	+	0.954658i	$0.403779\pi$
$488$	−2.97559	−0.134699
$489$	−21.3979	−0.967647
$490$	0	0
$491$	35.5088	1.60249	0.801245	−	0.598336i	$-0.204171\pi$
$491$	35.5088	1.60249	0.801245	+	0.598336i	$0.204171\pi$
$492$	8.88750	0.400679
$493$	22.4847	1.01266
$494$	−0.0898081	−0.00404066
$495$	3.46227	0.155617
$496$	7.71268	0.346310
$497$	0	0
$498$	12.7754	0.572480
$499$	32.7127	1.46442	0.732210	−	0.681079i	$-0.238489\pi$
$499$	32.7127	1.46442	0.732210	+	0.681079i	$0.238489\pi$
$500$	0.588791	0.0263315
$501$	31.0919	1.38909
$502$	25.2107	1.12521
$503$	14.2151	0.633820	0.316910	−	0.948456i	$-0.397355\pi$
$503$	14.2151	0.633820	0.316910	+	0.948456i	$0.397355\pi$
$504$	0	0
$505$	−7.42524	−0.330419
$506$	7.71061	0.342779
$507$	20.2539	0.899507
$508$	7.57950	0.336286
$509$	−6.10592	−0.270640	−0.135320	−	0.990802i	$-0.543206\pi$
$509$	−6.10592	−0.270640	−0.135320	+	0.990802i	$0.543206\pi$
$510$	−9.49463	−0.420429
$511$	0	0
$512$	−23.1737	−1.02414
$513$	1.30193	0.0574817
$514$	−32.6889	−1.44185
$515$	−8.10089	−0.356968
$516$	−4.28448	−0.188613
$517$	68.1252	2.99614
$518$	0	0
$519$	9.27843	0.407278
$520$	−0.990985	−0.0434575
$521$	24.3773	1.06799	0.533996	−	0.845487i	$-0.320690\pi$
$521$	24.3773	1.06799	0.533996	+	0.845487i	$0.320690\pi$
$522$	2.79973	0.122541
$523$	−22.5812	−0.987409	−0.493704	−	0.869630i	$-0.664358\pi$
$523$	−22.5812	−0.987409	−0.493704	+	0.869630i	$0.664358\pi$
$524$	−2.94630	−0.128710
$525$	0	0
$526$	−9.84221	−0.429141
$527$	15.8538	0.690604
$528$	25.2375	1.09832
$529$	1.00000	0.0434783
$530$	9.43564	0.409858
$531$	1.96492	0.0852704
$532$	0	0
$533$	−3.09703	−0.134147
$534$	8.18129	0.354039
$535$	0.911987	0.0394286
$536$	44.3519	1.91571
$537$	6.04793	0.260987
$538$	26.9301	1.16104
$539$	0	0
$540$	3.26741	0.140607
$541$	−41.7443	−1.79473	−0.897364	−	0.441291i	$-0.854520\pi$
$541$	−41.7443	−1.79473	−0.897364	+	0.441291i	$0.854520\pi$
$542$	−16.5090	−0.709122
$543$	10.1269	0.434586
$544$	−16.3339	−0.700310
$545$	−2.31369	−0.0991077
$546$	0	0
$547$	−4.12228	−0.176256	−0.0881280	−	0.996109i	$-0.528088\pi$
$547$	−4.12228	−0.176256	−0.0881280	+	0.996109i	$0.528088\pi$
$548$	7.42242	0.317070
$549$	−0.516118	−0.0220274
$550$	7.71061	0.328782
$551$	−1.03657	−0.0441594
$552$	4.82993	0.205575
$553$	0	0
$554$	−27.4049	−1.16432
$555$	18.4006	0.781062
$556$	6.72200	0.285076
$557$	5.43214	0.230167	0.115083	−	0.993356i	$-0.463286\pi$
$557$	5.43214	0.230167	0.115083	+	0.993356i	$0.463286\pi$
$558$	1.97407	0.0835691
$559$	1.49301	0.0631477
$560$	0	0
$561$	51.8771	2.19025
$562$	17.7841	0.750176
$563$	19.0027	0.800867	0.400434	−	0.916326i	$-0.368859\pi$
$563$	19.0027	0.800867	0.400434	+	0.916326i	$0.368859\pi$
$564$	9.70561	0.408680
$565$	−5.00788	−0.210683
$566$	−14.9622	−0.628908
$567$	0	0
$568$	−0.655583	−0.0275076
$569$	−21.6585	−0.907972	−0.453986	−	0.891009i	$-0.649998\pi$
$569$	−21.6585	−0.907972	−0.453986	+	0.891009i	$0.649998\pi$
$570$	0.437713	0.0183338
$571$	−5.77047	−0.241486	−0.120743	−	0.992684i	$-0.538528\pi$
$571$	−5.77047	−0.241486	−0.120743	+	0.992684i	$0.538528\pi$
$572$	1.23148	0.0514909
$573$	−11.6005	−0.484617
$574$	0	0
$575$	1.00000	0.0417029
$576$	−4.67506	−0.194794
$577$	−7.06648	−0.294181	−0.147091	−	0.989123i	$-0.546991\pi$
$577$	−7.06648	−0.294181	−0.147091	+	0.989123i	$0.546991\pi$
$578$	10.5705	0.439677
$579$	2.97735	0.123735
$580$	−2.60144	−0.108019
$581$	0	0
$582$	22.8325	0.946439
$583$	−51.5548	−2.13518
$584$	−18.9190	−0.782874
$585$	−0.171887	−0.00710664
$586$	−25.5980	−1.05744
$587$	−18.9545	−0.782336	−0.391168	−	0.920319i	$-0.627929\pi$
$587$	−18.9545	−0.782336	−0.391168	+	0.920319i	$0.627929\pi$
$588$	0	0
$589$	−0.730878	−0.0301153
$590$	4.37596	0.180155
$591$	7.45591	0.306695
$592$	−29.0062	−1.19215
$593$	10.8359	0.444978	0.222489	−	0.974935i	$-0.428582\pi$
$593$	10.8359	0.444978	0.222489	+	0.974935i	$0.428582\pi$
$594$	42.7890	1.75565
$595$	0	0
$596$	3.50827	0.143705
$597$	−8.11456	−0.332107
$598$	−0.382798	−0.0156538
$599$	−2.78649	−0.113853	−0.0569264	−	0.998378i	$-0.518130\pi$
$599$	−2.78649	−0.113853	−0.0569264	+	0.998378i	$0.518130\pi$
$600$	4.82993	0.197181
$601$	32.2497	1.31549	0.657746	−	0.753240i	$-0.271510\pi$
$601$	32.2497	1.31549	0.657746	+	0.753240i	$0.271510\pi$
$602$	0	0
$603$	7.69284	0.313277
$604$	6.87914	0.279908
$605$	−31.1295	−1.26559
$606$	−13.8533	−0.562753
$607$	−22.4131	−0.909720	−0.454860	−	0.890563i	$-0.650311\pi$
$607$	−22.4131	−0.909720	−0.454860	+	0.890563i	$0.650311\pi$
$608$	0.753010	0.0305386
$609$	0	0
$610$	−1.14941	−0.0465384
$611$	−3.38212	−0.136826
$612$	−1.59832	−0.0646082
$613$	39.0811	1.57847	0.789235	−	0.614092i	$-0.210478\pi$
$613$	39.0811	1.57847	0.789235	+	0.614092i	$0.210478\pi$
$614$	18.7703	0.757509
$615$	15.0945	0.608669
$616$	0	0
$617$	−22.9012	−0.921969	−0.460984	−	0.887408i	$-0.652504\pi$
$617$	−22.9012	−0.921969	−0.460984	+	0.887408i	$0.652504\pi$
$618$	−15.1139	−0.607970
$619$	−11.3924	−0.457898	−0.228949	−	0.973438i	$-0.573529\pi$
$619$	−11.3924	−0.457898	−0.228949	+	0.973438i	$0.573529\pi$
$620$	−1.83426	−0.0736656
$621$	5.54936	0.222688
$622$	−26.6992	−1.07054
$623$	0	0
$624$	−1.25293	−0.0501575
$625$	1.00000	0.0400000
$626$	6.44700	0.257674
$627$	−2.39159	−0.0955109
$628$	−2.29961	−0.0917644
$629$	−59.6237	−2.37735
$630$	0	0
$631$	−46.3802	−1.84637	−0.923184	−	0.384359i	$-0.874423\pi$
$631$	−46.3802	−1.84637	−0.923184	+	0.384359i	$0.874423\pi$
$632$	25.0237	0.995389
$633$	−1.24155	−0.0493472
$634$	6.57791	0.261242
$635$	12.8730	0.510849
$636$	−7.34488	−0.291243
$637$	0	0
$638$	−34.0676	−1.34875
$639$	−0.113711	−0.00449834
$640$	−3.99229	−0.157809
$641$	−20.0389	−0.791489	−0.395744	−	0.918361i	$-0.629513\pi$
$641$	−20.0389	−0.791489	−0.395744	+	0.918361i	$0.629513\pi$
$642$	1.70150	0.0671529
$643$	−32.8897	−1.29704	−0.648522	−	0.761196i	$-0.724613\pi$
$643$	−32.8897	−1.29704	−0.648522	+	0.761196i	$0.724613\pi$
$644$	0	0
$645$	−7.27674	−0.286521
$646$	−1.41833	−0.0558033
$647$	40.2806	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$647$	40.2806	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$648$	21.8817	0.859593
$649$	−23.9095	−0.938531
$650$	−0.382798	−0.0150146
$651$	0	0
$652$	−8.02203	−0.314167
$653$	−19.2200	−0.752135	−0.376068	−	0.926592i	$-0.622724\pi$
$653$	−19.2200	−0.752135	−0.376068	+	0.926592i	$0.622724\pi$
$654$	−4.31667	−0.168795
$655$	−5.00398	−0.195522
$656$	−23.7945	−0.929019
$657$	−3.28151	−0.128024
$658$	0	0
$659$	19.3672	0.754441	0.377220	−	0.926123i	$-0.376880\pi$
$659$	19.3672	0.754441	0.377220	+	0.926123i	$0.376880\pi$
$660$	−6.00208	−0.233631
$661$	43.2914	1.68384	0.841920	−	0.539603i	$-0.181426\pi$
$661$	43.2914	1.68384	0.841920	+	0.539603i	$0.181426\pi$
$662$	−12.3539	−0.480148
$663$	−2.57547	−0.100023
$664$	21.0583	0.817222
$665$	0	0
$666$	−7.42417	−0.287681
$667$	−4.41828	−0.171076
$668$	11.6563	0.450996
$669$	32.3154	1.24939
$670$	17.1323	0.661877
$671$	6.28021	0.242445
$672$	0	0
$673$	31.5669	1.21681	0.608407	−	0.793625i	$-0.291809\pi$
$673$	31.5669	1.21681	0.608407	+	0.793625i	$0.291809\pi$
$674$	4.73069	0.182219
$675$	5.54936	0.213595
$676$	7.59314	0.292044
$677$	5.12575	0.196998	0.0984992	−	0.995137i	$-0.468596\pi$
$677$	5.12575	0.196998	0.0984992	+	0.995137i	$0.468596\pi$
$678$	−9.34323	−0.358825
$679$	0	0
$680$	−15.6505	−0.600168
$681$	34.2776	1.31352
$682$	−24.0209	−0.919806
$683$	−38.8355	−1.48600	−0.742999	−	0.669292i	$-0.766597\pi$
$683$	−38.8355	−1.48600	−0.742999	+	0.669292i	$0.766597\pi$
$684$	0.0736842	0.00281739
$685$	12.6062	0.481658
$686$	0	0
$687$	−43.5894	−1.66304
$688$	11.4708	0.437321
$689$	2.55947	0.0975080
$690$	1.86571	0.0710263
$691$	2.46496	0.0937714	0.0468857	−	0.998900i	$-0.485070\pi$
$691$	2.46496	0.0937714	0.0468857	+	0.998900i	$0.485070\pi$
$692$	3.47846	0.132231
$693$	0	0
$694$	1.96676	0.0746574
$695$	11.4166	0.433057
$696$	−21.3399	−0.808889
$697$	−48.9109	−1.85263
$698$	21.1759	0.801520
$699$	45.1992	1.70959
$700$	0	0
$701$	−10.7452	−0.405839	−0.202919	−	0.979195i	$-0.565043\pi$
$701$	−10.7452	−0.405839	−0.202919	+	0.979195i	$0.565043\pi$
$702$	−2.12428	−0.0801760
$703$	2.74872	0.103670
$704$	56.8870	2.14401
$705$	16.4840	0.620823
$706$	−33.8183	−1.27277
$707$	0	0
$708$	−3.40633	−0.128018
$709$	−28.5004	−1.07035	−0.535177	−	0.844740i	$-0.679755\pi$
$709$	−28.5004	−1.07035	−0.535177	+	0.844740i	$0.679755\pi$
$710$	−0.253239	−0.00950389
$711$	4.34037	0.162777
$712$	13.4856	0.505395
$713$	−3.11530	−0.116669
$714$	0	0
$715$	2.09155	0.0782194
$716$	2.26736	0.0847351
$717$	14.6388	0.546695
$718$	21.6713	0.808765
$719$	−30.6191	−1.14190	−0.570949	−	0.820985i	$-0.693425\pi$
$719$	−30.6191	−1.14190	−0.570949	+	0.820985i	$0.693425\pi$
$720$	−1.32061	−0.0492161
$721$	0	0
$722$	−22.5055	−0.837569
$723$	34.7362	1.29185
$724$	3.79655	0.141098
$725$	−4.41828	−0.164091
$726$	−58.0785	−2.15550
$727$	14.0422	0.520797	0.260399	−	0.965501i	$-0.416146\pi$
$727$	14.0422	0.520797	0.260399	+	0.965501i	$0.416146\pi$
$728$	0	0
$729$	29.9418	1.10895
$730$	−7.30805	−0.270483
$731$	23.5789	0.872097
$732$	0.894725	0.0330700
$733$	−50.8361	−1.87767	−0.938837	−	0.344361i	$-0.888096\pi$
$733$	−50.8361	−1.87767	−0.938837	+	0.344361i	$0.888096\pi$
$734$	6.85234	0.252924
$735$	0	0
$736$	3.20963	0.118309
$737$	−93.6079	−3.44809
$738$	−6.09024	−0.224185
$739$	−16.7962	−0.617860	−0.308930	−	0.951085i	$-0.599971\pi$
$739$	−16.7962	−0.617860	−0.308930	+	0.951085i	$0.599971\pi$
$740$	6.89835	0.253589
$741$	0.118732	0.00436173
$742$	0	0
$743$	−13.4517	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$743$	−13.4517	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$744$	−15.0467	−0.551637
$745$	5.95844	0.218300
$746$	1.73473	0.0635131
$747$	3.65258	0.133641
$748$	19.4486	0.711112
$749$	0	0
$750$	1.86571	0.0681260
$751$	−14.4354	−0.526753	−0.263377	−	0.964693i	$-0.584836\pi$
$751$	−14.4354	−0.526753	−0.263377	+	0.964693i	$0.584836\pi$
$752$	−25.9848	−0.947570
$753$	−33.3301	−1.21462
$754$	1.69131	0.0615938
$755$	11.6835	0.425206
$756$	0	0
$757$	−38.5386	−1.40071	−0.700355	−	0.713795i	$-0.746975\pi$
$757$	−38.5386	−1.40071	−0.700355	+	0.713795i	$0.746975\pi$
$758$	−37.0070	−1.34415
$759$	−10.1939	−0.370016
$760$	0.721503	0.0261717
$761$	−7.98562	−0.289479	−0.144739	−	0.989470i	$-0.546234\pi$
$761$	−7.98562	−0.289479	−0.144739	+	0.989470i	$0.546234\pi$
$762$	24.0172	0.870053
$763$	0	0
$764$	−4.34900	−0.157341
$765$	−2.71458	−0.0981458
$766$	−30.5776	−1.10481
$767$	1.18700	0.0428602
$768$	20.0810	0.724610
$769$	−0.310783	−0.0112071	−0.00560355	−	0.999984i	$-0.501784\pi$
$769$	−0.310783	−0.0112071	−0.00560355	+	0.999984i	$0.501784\pi$
$770$	0	0
$771$	43.2168	1.55641
$772$	1.11620	0.0401731
$773$	−32.9111	−1.18373	−0.591864	−	0.806038i	$-0.701608\pi$
$773$	−32.9111	−1.18373	−0.591864	+	0.806038i	$0.701608\pi$
$774$	2.93598	0.105531
$775$	−3.11530	−0.111905
$776$	37.6360	1.35105
$777$	0	0
$778$	35.0902	1.25804
$779$	2.25484	0.0807882
$780$	0.297977	0.0106693
$781$	1.38366	0.0495111
$782$	−6.04547	−0.216186
$783$	−24.5186	−0.876223
$784$	0	0
$785$	−3.90565	−0.139399
$786$	−9.33596	−0.333003
$787$	37.0170	1.31951	0.659757	−	0.751479i	$-0.270659\pi$
$787$	37.0170	1.31951	0.659757	+	0.751479i	$0.270659\pi$
$788$	2.79521	0.0995751
$789$	13.0120	0.463240
$790$	9.66617	0.343907
$791$	0	0
$792$	10.6476	0.378348
$793$	−0.311785	−0.0110718
$794$	−5.26042	−0.186685
$795$	−12.4745	−0.442425
$796$	−3.04213	−0.107826
$797$	6.86702	0.243242	0.121621	−	0.992577i	$-0.461191\pi$
$797$	6.86702	0.243242	0.121621	+	0.992577i	$0.461191\pi$
$798$	0	0
$799$	−53.4133	−1.88962
$800$	3.20963	0.113478
$801$	2.33908	0.0826475
$802$	21.4393	0.757048
$803$	39.9300	1.40910
$804$	−13.3361	−0.470327
$805$	0	0
$806$	1.19253	0.0420051
$807$	−35.6033	−1.25330
$808$	−22.8351	−0.803337
$809$	−12.7631	−0.448726	−0.224363	−	0.974506i	$-0.572030\pi$
$809$	−12.7631	−0.448726	−0.224363	+	0.974506i	$0.572030\pi$
$810$	8.45247	0.296989
$811$	−30.2242	−1.06131	−0.530657	−	0.847587i	$-0.678055\pi$
$811$	−30.2242	−1.06131	−0.530657	+	0.847587i	$0.678055\pi$
$812$	0	0
$813$	21.8259	0.765468
$814$	90.3386	3.16637
$815$	−13.6246	−0.477249
$816$	−19.7874	−0.692697
$817$	−1.08701	−0.0380298
$818$	−29.3179	−1.02508
$819$	0	0
$820$	5.65890	0.197617
$821$	18.7140	0.653122	0.326561	−	0.945176i	$-0.394110\pi$
$821$	18.7140	0.653122	0.326561	+	0.945176i	$0.394110\pi$
$822$	23.5195	0.820336
$823$	8.30474	0.289485	0.144742	−	0.989469i	$-0.453765\pi$
$823$	8.30474	0.289485	0.144742	+	0.989469i	$0.453765\pi$
$824$	−24.9130	−0.867884
$825$	−10.1939	−0.354907
$826$	0	0
$827$	21.0285	0.731232	0.365616	−	0.930766i	$-0.380858\pi$
$827$	21.0285	0.731232	0.365616	+	0.930766i	$0.380858\pi$
$828$	0.314072	0.0109147
$829$	3.98272	0.138326	0.0691628	−	0.997605i	$-0.477967\pi$
$829$	3.98272	0.138326	0.0691628	+	0.997605i	$0.477967\pi$
$830$	8.13443	0.282350
$831$	36.2310	1.25684
$832$	−2.82419	−0.0979111
$833$	0	0
$834$	21.3001	0.737562
$835$	19.7970	0.685105
$836$	−0.896602	−0.0310096
$837$	−17.2879	−0.597557
$838$	−13.0586	−0.451104
$839$	−40.5667	−1.40052	−0.700258	−	0.713890i	$-0.746932\pi$
$839$	−40.5667	−1.40052	−0.700258	+	0.713890i	$0.746932\pi$
$840$	0	0
$841$	−9.47883	−0.326856
$842$	−35.1956	−1.21292
$843$	−23.5117	−0.809785
$844$	−0.465455	−0.0160216
$845$	12.8962	0.443642
$846$	−6.65086	−0.228661
$847$	0	0
$848$	19.6644	0.675280
$849$	19.7810	0.678881
$850$	−6.04547	−0.207358
$851$	11.7161	0.401624
$852$	0.197126	0.00675342
$853$	54.4100	1.86296	0.931482	−	0.363788i	$-0.118517\pi$
$853$	54.4100	1.86296	0.931482	+	0.363788i	$0.118517\pi$
$854$	0	0
$855$	0.125145	0.00427987
$856$	2.80467	0.0958615
$857$	−19.3399	−0.660640	−0.330320	−	0.943869i	$-0.607157\pi$
$857$	−19.3399	−0.660640	−0.330320	+	0.943869i	$0.607157\pi$
$858$	3.90221	0.133219
$859$	45.6294	1.55686	0.778428	−	0.627733i	$-0.216017\pi$
$859$	45.6294	1.55686	0.778428	+	0.627733i	$0.216017\pi$
$860$	−2.72803	−0.0930252
$861$	0	0
$862$	7.20378	0.245362
$863$	−8.78286	−0.298972	−0.149486	−	0.988764i	$-0.547762\pi$
$863$	−8.78286	−0.298972	−0.149486	+	0.988764i	$0.547762\pi$
$864$	17.8114	0.605956
$865$	5.90781	0.200872
$866$	1.94835	0.0662075
$867$	−13.9749	−0.474613
$868$	0	0
$869$	−52.8144	−1.79160
$870$	−8.24321	−0.279471
$871$	4.64722	0.157465
$872$	−7.11538	−0.240957
$873$	6.52798	0.220938
$874$	0.278703	0.00942726
$875$	0	0
$876$	5.68872	0.192204
$877$	−27.1931	−0.918246	−0.459123	−	0.888373i	$-0.651836\pi$
$877$	−27.1931	−0.918246	−0.459123	+	0.888373i	$0.651836\pi$
$878$	38.9343	1.31397
$879$	33.8422	1.14147
$880$	16.0694	0.541698
$881$	42.1577	1.42033	0.710164	−	0.704036i	$-0.248621\pi$
$881$	42.1577	1.42033	0.710164	+	0.704036i	$0.248621\pi$
$882$	0	0
$883$	7.95632	0.267752	0.133876	−	0.990998i	$-0.457258\pi$
$883$	7.95632	0.267752	0.133876	+	0.990998i	$0.457258\pi$
$884$	−0.965539	−0.0324746
$885$	−5.78529	−0.194470
$886$	47.3624	1.59117
$887$	45.8531	1.53960	0.769799	−	0.638287i	$-0.220357\pi$
$887$	45.8531	1.53960	0.769799	+	0.638287i	$0.220357\pi$
$888$	56.5881	1.89897
$889$	0	0
$890$	5.20923	0.174614
$891$	−46.1829	−1.54718
$892$	12.1150	0.405640
$893$	2.46241	0.0824013
$894$	11.1167	0.371798
$895$	3.85087	0.128720
$896$	0	0
$897$	0.506083	0.0168976
$898$	14.4590	0.482504
$899$	13.7642	0.459063
$900$	0.314072	0.0104691
$901$	40.4213	1.34663
$902$	74.1071	2.46750
$903$	0	0
$904$	−15.4009	−0.512227
$905$	6.44804	0.214340
$906$	21.7980	0.724190
$907$	15.2510	0.506403	0.253201	−	0.967414i	$-0.418516\pi$
$907$	15.2510	0.506403	0.253201	+	0.967414i	$0.418516\pi$
$908$	12.8506	0.426463
$909$	−3.96076	−0.131370
$910$	0	0
$911$	11.1170	0.368323	0.184162	−	0.982896i	$-0.441043\pi$
$911$	11.1170	0.368323	0.184162	+	0.982896i	$0.441043\pi$
$912$	0.912219	0.0302066
$913$	−44.4452	−1.47092
$914$	45.6826	1.51105
$915$	1.51960	0.0502363
$916$	−16.3416	−0.539941
$917$	0	0
$918$	−33.5485	−1.10727
$919$	21.0359	0.693911	0.346956	−	0.937882i	$-0.387215\pi$
$919$	21.0359	0.693911	0.346956	+	0.937882i	$0.387215\pi$
$920$	3.07534	0.101391
$921$	−24.8155	−0.817700
$922$	23.4753	0.773118
$923$	−0.0686925	−0.00226104
$924$	0	0
$925$	11.7161	0.385224
$926$	46.8753	1.54042
$927$	−4.32116	−0.141926
$928$	−14.1810	−0.465515
$929$	48.3609	1.58667	0.793335	−	0.608786i	$-0.208343\pi$
$929$	48.3609	1.58667	0.793335	+	0.608786i	$0.208343\pi$
$930$	−5.81223	−0.190591
$931$	0	0
$932$	16.9451	0.555055
$933$	35.2980	1.15560
$934$	−8.22705	−0.269197
$935$	33.0315	1.08024
$936$	−0.528609	−0.0172781
$937$	48.2934	1.57768	0.788838	−	0.614601i	$-0.210683\pi$
$937$	48.2934	1.57768	0.788838	+	0.614601i	$0.210683\pi$
$938$	0	0
$939$	−8.52334	−0.278149
$940$	6.17981	0.201563
$941$	−55.0945	−1.79603	−0.898015	−	0.439964i	$-0.854991\pi$
$941$	−55.0945	−1.79603	−0.898015	+	0.439964i	$0.854991\pi$
$942$	−7.28680	−0.237417
$943$	9.61105	0.312979
$944$	9.11976	0.296823
$945$	0	0
$946$	−35.7255	−1.16153
$947$	9.46192	0.307471	0.153736	−	0.988112i	$-0.450870\pi$
$947$	9.46192	0.307471	0.153736	+	0.988112i	$0.450870\pi$
$948$	−7.52432	−0.244379
$949$	−1.98235	−0.0643498
$950$	0.278703	0.00904231
$951$	−8.69641	−0.282000
$952$	0	0
$953$	−25.3971	−0.822692	−0.411346	−	0.911479i	$-0.634941\pi$
$953$	−25.3971	−0.822692	−0.411346	+	0.911479i	$0.634941\pi$
$954$	5.03314	0.162954
$955$	−7.38632	−0.239016
$956$	5.48805	0.177496
$957$	45.0395	1.45592
$958$	−16.7661	−0.541687
$959$	0	0
$960$	13.7647	0.444254
$961$	−21.2949	−0.686933
$962$	−4.48492	−0.144600
$963$	0.486470	0.0156763
$964$	13.0225	0.419428
$965$	1.89576	0.0610266
$966$	0	0
$967$	25.8614	0.831645	0.415823	−	0.909446i	$-0.363494\pi$
$967$	25.8614	0.831645	0.415823	+	0.909446i	$0.363494\pi$
$968$	−95.7337	−3.07700
$969$	1.87512	0.0602374
$970$	14.5381	0.466789
$971$	−24.7034	−0.792770	−0.396385	−	0.918084i	$-0.629735\pi$
$971$	−24.7034	−0.792770	−0.396385	+	0.918084i	$0.629735\pi$
$972$	3.22268	0.103367
$973$	0	0
$974$	15.6090	0.500145
$975$	0.506083	0.0162076
$976$	−2.39545	−0.0766764
$977$	45.2188	1.44668	0.723339	−	0.690493i	$-0.242606\pi$
$977$	45.2188	1.44668	0.723339	+	0.690493i	$0.242606\pi$
$978$	−25.4195	−0.812826
$979$	−28.4624	−0.909662
$980$	0	0
$981$	−1.23417	−0.0394039
$982$	42.1825	1.34610
$983$	−25.5998	−0.816506	−0.408253	−	0.912869i	$-0.633862\pi$
$983$	−25.5998	−0.816506	−0.408253	+	0.912869i	$0.633862\pi$
$984$	46.4207	1.47984
$985$	4.74737	0.151264
$986$	26.7106	0.850638
$987$	0	0
$988$	0.0445124	0.00141613
$989$	−4.63328	−0.147330
$990$	4.11298	0.130719
$991$	32.5499	1.03398	0.516991	−	0.855991i	$-0.327052\pi$
$991$	32.5499	1.03398	0.516991	+	0.855991i	$0.327052\pi$
$992$	−9.99895	−0.317467
$993$	16.3326	0.518300
$994$	0	0
$995$	−5.16675	−0.163797
$996$	−6.33199	−0.200637
$997$	−13.0752	−0.414095	−0.207047	−	0.978331i	$-0.566385\pi$
$997$	−13.0752	−0.414095	−0.207047	+	0.978331i	$0.566385\pi$
$998$	38.8608	1.23012
$999$	65.0171	2.05705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5635.2.a.bb.1.6		8
7.6	odd	2		805.2.a.m.1.6	✓	8
21.20	even	2		7245.2.a.bp.1.3		8
35.34	odd	2		4025.2.a.t.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.6	✓	8	7.6	odd	2
4025.2.a.t.1.3		8	35.34	odd	2
5635.2.a.bb.1.6		8	1.1	even	1	trivial
7245.2.a.bp.1.3		8	21.20	even	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:	\( N \)	\(=\)	\( 5635 = 5 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5635.a (trivial)

\(f(q)\)	\(=\)	\(q+1.18794 q^{2} -1.57054 q^{3} -0.588791 q^{4} -1.00000 q^{5} -1.86571 q^{6} -3.07534 q^{8} -0.533418 q^{9} +O(q^{10})\)	\(q+1.18794 q^{2} -1.57054 q^{3} -0.588791 q^{4} -1.00000 q^{5} -1.86571 q^{6} -3.07534 q^{8} -0.533418 q^{9} -1.18794 q^{10} +6.49072 q^{11} +0.924717 q^{12} -0.322236 q^{13} +1.57054 q^{15} -2.47574 q^{16} -5.08903 q^{17} -0.633671 q^{18} +0.234610 q^{19} +0.588791 q^{20} +7.71061 q^{22} +1.00000 q^{23} +4.82993 q^{24} +1.00000 q^{25} -0.382798 q^{26} +5.54936 q^{27} -4.41828 q^{29} +1.86571 q^{30} -3.11530 q^{31} +3.20963 q^{32} -10.1939 q^{33} -6.04547 q^{34} +0.314072 q^{36} +11.7161 q^{37} +0.278703 q^{38} +0.506083 q^{39} +3.07534 q^{40} +9.61105 q^{41} -4.63328 q^{43} -3.82168 q^{44} +0.533418 q^{45} +1.18794 q^{46} +10.4958 q^{47} +3.88824 q^{48} +1.18794 q^{50} +7.99250 q^{51} +0.189730 q^{52} -7.94284 q^{53} +6.59232 q^{54} -6.49072 q^{55} -0.368463 q^{57} -5.24866 q^{58} -3.68364 q^{59} -0.924717 q^{60} +0.967566 q^{61} -3.70080 q^{62} +8.76435 q^{64} +0.322236 q^{65} -12.1098 q^{66} -14.4218 q^{67} +2.99637 q^{68} -1.57054 q^{69} +0.213174 q^{71} +1.64044 q^{72} +6.15185 q^{73} +13.9181 q^{74} -1.57054 q^{75} -0.138136 q^{76} +0.601198 q^{78} -8.13690 q^{79} +2.47574 q^{80} -7.11521 q^{81} +11.4174 q^{82} -6.84749 q^{83} +5.08903 q^{85} -5.50408 q^{86} +6.93906 q^{87} -19.9612 q^{88} -4.38509 q^{89} +0.633671 q^{90} -0.588791 q^{92} +4.89268 q^{93} +12.4684 q^{94} -0.234610 q^{95} -5.04084 q^{96} -12.2380 q^{97} -3.46227 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 8 q^{5} - q^{6} + 3 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 8 * q^5 - q^6 + 3 * q^8 + 9 * q^9	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 8 q^{5} - q^{6} + 3 q^{8} + 9 q^{9} - q^{10} + 6 q^{11} - 8 q^{12} - 8 q^{13} + 7 q^{15} + q^{16} - 4 q^{17} - 11 q^{18} - 7 q^{20} - 8 q^{22} + 8 q^{23} + 8 q^{24} + 8 q^{25} - 2 q^{26} - 28 q^{27} - 3 q^{29} + q^{30} + 16 q^{31} + 12 q^{32} - 5 q^{33} + 4 q^{34} - 14 q^{36} - 7 q^{37} - 11 q^{38} + 16 q^{39} - 3 q^{40} - 7 q^{41} - 10 q^{43} + 7 q^{44} - 9 q^{45} + q^{46} - 19 q^{47} + 6 q^{48} + q^{50} + 7 q^{51} - 18 q^{52} - q^{53} + 25 q^{54} - 6 q^{55} - 25 q^{57} - 9 q^{58} - 21 q^{59} + 8 q^{60} + 7 q^{61} - 18 q^{62} - 37 q^{64} + 8 q^{65} + 43 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 8 q^{71} + 4 q^{72} + 3 q^{73} + 12 q^{74} - 7 q^{75} - 8 q^{76} - 50 q^{78} - 15 q^{79} - q^{80} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 4 q^{85} - 12 q^{86} - 21 q^{87} - 29 q^{88} - q^{89} + 11 q^{90} + 7 q^{92} - 5 q^{93} + 36 q^{94} - 30 q^{96} - 10 q^{97} - 18 q^{99}+O(q^{100}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 8 * q^5 - q^6 + 3 * q^8 + 9 * q^9 - q^10 + 6 * q^11 - 8 * q^12 - 8 * q^13 + 7 * q^15 + q^16 - 4 * q^17 - 11 * q^18 - 7 * q^20 - 8 * q^22 + 8 * q^23 + 8 * q^24 + 8 * q^25 - 2 * q^26 - 28 * q^27 - 3 * q^29 + q^30 + 16 * q^31 + 12 * q^32 - 5 * q^33 + 4 * q^34 - 14 * q^36 - 7 * q^37 - 11 * q^38 + 16 * q^39 - 3 * q^40 - 7 * q^41 - 10 * q^43 + 7 * q^44 - 9 * q^45 + q^46 - 19 * q^47 + 6 * q^48 + q^50 + 7 * q^51 - 18 * q^52 - q^53 + 25 * q^54 - 6 * q^55 - 25 * q^57 - 9 * q^58 - 21 * q^59 + 8 * q^60 + 7 * q^61 - 18 * q^62 - 37 * q^64 + 8 * q^65 + 43 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 8 * q^71 + 4 * q^72 + 3 * q^73 + 12 * q^74 - 7 * q^75 - 8 * q^76 - 50 * q^78 - 15 * q^79 - q^80 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 4 * q^85 - 12 * q^86 - 21 * q^87 - 29 * q^88 - q^89 + 11 * q^90 + 7 * q^92 - 5 * q^93 + 36 * q^94 - 30 * q^96 - 10 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more