LMFDB - Embedded newform 833.4.a.g.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,4,Mod(1,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("833.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	833.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:	$49.1485910348$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 53x^{7} + 90x^{6} + 880x^{5} - 1087x^{4} - 4674x^{3} + 2515x^{2} + 1814x + 36 $ x^9 - 2x^8 - 53x^7 + 90x^6 + 880x^5 - 1087x^4 - 4674x^3 + 2515x^2 + 1814x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$4.42628$ of defining polynomial
Character	$\chi$	$=$	833.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.42628 q^{2} +5.22352 q^{3} +11.5919 q^{4} -16.9037 q^{5} +23.1207 q^{6} +15.8988 q^{8} +0.285172 q^{9} +O(q^{10})$	\(q+4.42628 q^{2} +5.22352 q^{3} +11.5919 q^{4} -16.9037 q^{5} +23.1207 q^{6} +15.8988 q^{8} +0.285172 q^{9} -74.8205 q^{10} +22.2449 q^{11} +60.5506 q^{12} -69.0502 q^{13} -88.2969 q^{15} -22.3627 q^{16} -17.0000 q^{17} +1.26225 q^{18} -6.54805 q^{19} -195.946 q^{20} +98.4621 q^{22} -202.353 q^{23} +83.0479 q^{24} +160.735 q^{25} -305.635 q^{26} -139.545 q^{27} -8.82223 q^{29} -390.826 q^{30} +297.162 q^{31} -226.174 q^{32} +116.197 q^{33} -75.2467 q^{34} +3.30569 q^{36} -343.891 q^{37} -28.9835 q^{38} -360.685 q^{39} -268.749 q^{40} +151.543 q^{41} +150.940 q^{43} +257.861 q^{44} -4.82046 q^{45} -895.670 q^{46} +308.563 q^{47} -116.812 q^{48} +711.459 q^{50} -88.7999 q^{51} -800.424 q^{52} +570.022 q^{53} -617.667 q^{54} -376.021 q^{55} -34.2039 q^{57} -39.0496 q^{58} -539.811 q^{59} -1023.53 q^{60} -27.4019 q^{61} +1315.32 q^{62} -822.208 q^{64} +1167.20 q^{65} +514.319 q^{66} +19.7566 q^{67} -197.063 q^{68} -1057.00 q^{69} -69.4533 q^{71} +4.53390 q^{72} -320.158 q^{73} -1522.16 q^{74} +839.605 q^{75} -75.9044 q^{76} -1596.49 q^{78} -372.464 q^{79} +378.013 q^{80} -736.618 q^{81} +670.772 q^{82} -312.615 q^{83} +287.363 q^{85} +668.101 q^{86} -46.0831 q^{87} +353.668 q^{88} +443.861 q^{89} -21.3367 q^{90} -2345.66 q^{92} +1552.23 q^{93} +1365.79 q^{94} +110.686 q^{95} -1181.43 q^{96} -1415.74 q^{97} +6.34361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9} - 134 q^{10} - 8 q^{11} - 56 q^{12} - 164 q^{13} + 34 q^{15} + 178 q^{16} - 153 q^{17} + 98 q^{18} - 244 q^{19} + 41 q^{20} - 80 q^{22} - 14 q^{23} - 298 q^{24} + 684 q^{25} - 326 q^{26} - 218 q^{27} - 234 q^{29} - 335 q^{30} - 555 q^{31} - 181 q^{32} - 458 q^{33} - 34 q^{34} - 1221 q^{36} - 364 q^{37} + 714 q^{38} - 52 q^{39} - 123 q^{40} + 45 q^{41} - 135 q^{43} - 748 q^{44} + 844 q^{45} - 1576 q^{46} + 172 q^{47} + 949 q^{48} - 2901 q^{50} + 187 q^{51} + 1596 q^{52} + 101 q^{53} + 1163 q^{54} - 1260 q^{55} - 602 q^{57} + 1062 q^{58} - 280 q^{59} - 1727 q^{60} - 639 q^{61} + 1708 q^{62} - 2390 q^{64} + 638 q^{65} + 2476 q^{66} + 35 q^{67} - 646 q^{68} - 1288 q^{69} - 1616 q^{71} + 1335 q^{72} - 1049 q^{73} - 370 q^{74} - 1260 q^{75} - 4964 q^{76} - 4714 q^{78} + 2304 q^{79} + 3996 q^{80} - 791 q^{81} + 215 q^{82} - 2508 q^{83} - 51 q^{85} + 623 q^{86} - 166 q^{87} - 416 q^{88} - 2762 q^{89} - 2935 q^{90} - 2392 q^{92} + 2784 q^{93} + 862 q^{94} - 3462 q^{95} - 2928 q^{96} - 3107 q^{97} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9 - 134 * q^10 - 8 * q^11 - 56 * q^12 - 164 * q^13 + 34 * q^15 + 178 * q^16 - 153 * q^17 + 98 * q^18 - 244 * q^19 + 41 * q^20 - 80 * q^22 - 14 * q^23 - 298 * q^24 + 684 * q^25 - 326 * q^26 - 218 * q^27 - 234 * q^29 - 335 * q^30 - 555 * q^31 - 181 * q^32 - 458 * q^33 - 34 * q^34 - 1221 * q^36 - 364 * q^37 + 714 * q^38 - 52 * q^39 - 123 * q^40 + 45 * q^41 - 135 * q^43 - 748 * q^44 + 844 * q^45 - 1576 * q^46 + 172 * q^47 + 949 * q^48 - 2901 * q^50 + 187 * q^51 + 1596 * q^52 + 101 * q^53 + 1163 * q^54 - 1260 * q^55 - 602 * q^57 + 1062 * q^58 - 280 * q^59 - 1727 * q^60 - 639 * q^61 + 1708 * q^62 - 2390 * q^64 + 638 * q^65 + 2476 * q^66 + 35 * q^67 - 646 * q^68 - 1288 * q^69 - 1616 * q^71 + 1335 * q^72 - 1049 * q^73 - 370 * q^74 - 1260 * q^75 - 4964 * q^76 - 4714 * q^78 + 2304 * q^79 + 3996 * q^80 - 791 * q^81 + 215 * q^82 - 2508 * q^83 - 51 * q^85 + 623 * q^86 - 166 * q^87 - 416 * q^88 - 2762 * q^89 - 2935 * q^90 - 2392 * q^92 + 2784 * q^93 + 862 * q^94 - 3462 * q^95 - 2928 * q^96 - 3107 * q^97 - 2396 * 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 $

$2$	4.42628	1.56492	0.782462	−	0.622698i	$-0.213963\pi$
$2$	4.42628	1.56492	0.782462	+	0.622698i	$0.213963\pi$
$3$	5.22352	1.00527	0.502634	−	0.864500i	$-0.332365\pi$
$3$	5.22352	1.00527	0.502634	+	0.864500i	$0.332365\pi$
$4$	11.5919	1.44899
$5$	−16.9037	−1.51191	−0.755957	−	0.654621i	$-0.772828\pi$
$5$	−16.9037	−1.51191	−0.755957	+	0.654621i	$0.772828\pi$
$6$	23.1207	1.57317
$7$	0	0
$7$	0	0
$8$	15.8988	0.702636
$9$	0.285172	0.0105619
$10$	−74.8205	−2.36603
$11$	22.2449	0.609735	0.304868	−	0.952395i	$-0.401388\pi$
$11$	22.2449	0.609735	0.304868	+	0.952395i	$0.401388\pi$
$12$	60.5506	1.45662
$13$	−69.0502	−1.47316	−0.736580	−	0.676350i	$-0.763561\pi$
$13$	−69.0502	−1.47316	−0.736580	+	0.676350i	$0.763561\pi$
$14$	0	0
$15$	−88.2969	−1.51988
$16$	−22.3627	−0.349418
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	1.26225	0.0165286
$19$	−6.54805	−0.0790645	−0.0395322	−	0.999218i	$-0.512587\pi$
$19$	−6.54805	−0.0790645	−0.0395322	+	0.999218i	$0.512587\pi$
$20$	−195.946	−2.19075
$21$	0	0
$22$	98.4621	0.954190
$23$	−202.353	−1.83450	−0.917251	−	0.398311i	$-0.869597\pi$
$23$	−202.353	−1.83450	−0.917251	+	0.398311i	$0.869597\pi$
$24$	83.0479	0.706337
$25$	160.735	1.28588
$26$	−305.635	−2.30538
$27$	−139.545	−0.994650
$28$	0	0
$29$	−8.82223	−0.0564913	−0.0282456	−	0.999601i	$-0.508992\pi$
$29$	−8.82223	−0.0564913	−0.0282456	+	0.999601i	$0.508992\pi$
$30$	−390.826	−2.37849
$31$	297.162	1.72168	0.860838	−	0.508879i	$-0.169940\pi$
$31$	297.162	1.72168	0.860838	+	0.508879i	$0.169940\pi$
$32$	−226.174	−1.24945
$33$	116.197	0.612947
$34$	−75.2467	−0.379550
$35$	0	0
$36$	3.30569	0.0153041
$37$	−343.891	−1.52798	−0.763992	−	0.645226i	$-0.776763\pi$
$37$	−343.891	−1.52798	−0.763992	+	0.645226i	$0.776763\pi$
$38$	−28.9835	−0.123730
$39$	−360.685	−1.48092
$40$	−268.749	−1.06232
$41$	151.543	0.577245	0.288623	−	0.957443i	$-0.406803\pi$
$41$	151.543	0.577245	0.288623	+	0.957443i	$0.406803\pi$
$42$	0	0
$43$	150.940	0.535305	0.267652	−	0.963516i	$-0.413752\pi$
$43$	150.940	0.535305	0.267652	+	0.963516i	$0.413752\pi$
$44$	257.861	0.883500
$45$	−4.82046	−0.0159687
$46$	−895.670	−2.87086
$47$	308.563	0.957629	0.478815	−	0.877916i	$-0.341067\pi$
$47$	308.563	0.957629	0.478815	+	0.877916i	$0.341067\pi$
$48$	−116.812	−0.351258
$49$	0	0
$50$	711.459	2.01231
$51$	−88.7999	−0.243813
$52$	−800.424	−2.13459
$53$	570.022	1.47733	0.738665	−	0.674073i	$-0.235457\pi$
$53$	570.022	1.47733	0.738665	+	0.674073i	$0.235457\pi$
$54$	−617.667	−1.55655
$55$	−376.021	−0.921867
$56$	0	0
$57$	−34.2039	−0.0794809
$58$	−39.0496	−0.0884046
$59$	−539.811	−1.19114	−0.595571	−	0.803302i	$-0.703074\pi$
$59$	−539.811	−1.19114	−0.595571	+	0.803302i	$0.703074\pi$
$60$	−1023.53	−2.20229
$61$	−27.4019	−0.0575157	−0.0287579	−	0.999586i	$-0.509155\pi$
$61$	−27.4019	−0.0575157	−0.0287579	+	0.999586i	$0.509155\pi$
$62$	1315.32	2.69429
$63$	0	0
$64$	−822.208	−1.60588
$65$	1167.20	2.22729
$66$	514.319	0.959216
$67$	19.7566	0.0360246	0.0180123	−	0.999838i	$-0.494266\pi$
$67$	19.7566	0.0360246	0.0180123	+	0.999838i	$0.494266\pi$
$68$	−197.063	−0.351432
$69$	−1057.00	−1.84416
$70$	0	0
$71$	−69.4533	−0.116093	−0.0580464	−	0.998314i	$-0.518487\pi$
$71$	−69.4533	−0.116093	−0.0580464	+	0.998314i	$0.518487\pi$
$72$	4.53390	0.00742118
$73$	−320.158	−0.513310	−0.256655	−	0.966503i	$-0.582620\pi$
$73$	−320.158	−0.513310	−0.256655	+	0.966503i	$0.582620\pi$
$74$	−1522.16	−2.39118
$75$	839.605	1.29266
$76$	−75.9044	−0.114564
$77$	0	0
$78$	−1596.49	−2.31753
$79$	−372.464	−0.530449	−0.265225	−	0.964187i	$-0.585446\pi$
$79$	−372.464	−0.530449	−0.265225	+	0.964187i	$0.585446\pi$
$80$	378.013	0.528290
$81$	−736.618	−1.01045
$82$	670.772	0.903346
$83$	−312.615	−0.413421	−0.206711	−	0.978402i	$-0.566276\pi$
$83$	−312.615	−0.413421	−0.206711	+	0.978402i	$0.566276\pi$
$84$	0	0
$85$	287.363	0.366693
$86$	668.101	0.837712
$87$	−46.0831	−0.0567888
$88$	353.668	0.428422
$89$	443.861	0.528642	0.264321	−	0.964435i	$-0.414852\pi$
$89$	443.861	0.528642	0.264321	+	0.964435i	$0.414852\pi$
$90$	−21.3367	−0.0249898
$91$	0	0
$92$	−2345.66	−2.65817
$93$	1552.23	1.73074
$94$	1365.79	1.49862
$95$	110.686	0.119539
$96$	−1181.43	−1.25603
$97$	−1415.74	−1.48193	−0.740964	−	0.671545i	$-0.765631\pi$
$97$	−1415.74	−1.48193	−0.740964	+	0.671545i	$0.765631\pi$
$98$	0	0
$99$	6.34361	0.00643997
$100$	1863.23	1.86323
$101$	−1119.77	−1.10318	−0.551592	−	0.834114i	$-0.685980\pi$
$101$	−1119.77	−1.10318	−0.551592	+	0.834114i	$0.685980\pi$
$102$	−393.053	−0.381549
$103$	930.310	0.889963	0.444981	−	0.895540i	$-0.353210\pi$
$103$	930.310	0.889963	0.444981	+	0.895540i	$0.353210\pi$
$104$	−1097.82	−1.03510
$105$	0	0
$106$	2523.07	2.31191
$107$	−939.841	−0.849139	−0.424569	−	0.905395i	$-0.639574\pi$
$107$	−939.841	−0.849139	−0.424569	+	0.905395i	$0.639574\pi$
$108$	−1617.60	−1.44124
$109$	250.597	0.220210	0.110105	−	0.993920i	$-0.464881\pi$
$109$	250.597	0.220210	0.110105	+	0.993920i	$0.464881\pi$
$110$	−1664.37	−1.44265
$111$	−1796.32	−1.53603
$112$	0	0
$113$	758.427	0.631387	0.315694	−	0.948861i	$-0.397763\pi$
$113$	758.427	0.631387	0.315694	+	0.948861i	$0.397763\pi$
$114$	−151.396	−0.124382
$115$	3420.52	2.77361
$116$	−102.267	−0.0818553
$117$	−19.6912	−0.0155594
$118$	−2389.35	−1.86405
$119$	0	0
$120$	−1403.82	−1.06792
$121$	−836.165	−0.628223
$122$	−121.289	−0.0900078
$123$	791.589	0.580286
$124$	3444.68	2.49469
$125$	−604.060	−0.432230
$126$	0	0
$127$	−794.380	−0.555038	−0.277519	−	0.960720i	$-0.589512\pi$
$127$	−794.380	−0.555038	−0.277519	+	0.960720i	$0.589512\pi$
$128$	−1829.93	−1.26363
$129$	788.437	0.538124
$130$	5166.37	3.48554
$131$	−1633.80	−1.08966	−0.544831	−	0.838546i	$-0.683406\pi$
$131$	−1633.80	−1.08966	−0.544831	+	0.838546i	$0.683406\pi$
$132$	1346.94	0.888154
$133$	0	0
$134$	87.4480	0.0563758
$135$	2358.84	1.50382
$136$	−270.280	−0.170414
$137$	−810.805	−0.505633	−0.252817	−	0.967514i	$-0.581357\pi$
$137$	−810.805	−0.505633	−0.252817	+	0.967514i	$0.581357\pi$
$138$	−4678.55	−2.88598
$139$	3035.90	1.85253	0.926266	−	0.376870i	$-0.123000\pi$
$139$	3035.90	1.85253	0.926266	+	0.376870i	$0.123000\pi$
$140$	0	0
$141$	1611.79	0.962673
$142$	−307.419	−0.181676
$143$	−1536.01	−0.898238
$144$	−6.37722	−0.00369052
$145$	149.128	0.0854099
$146$	−1417.11	−0.803291
$147$	0	0
$148$	−3986.36	−2.21403
$149$	2210.48	1.21537	0.607684	−	0.794179i	$-0.292099\pi$
$149$	2210.48	1.21537	0.607684	+	0.794179i	$0.292099\pi$
$150$	3716.32	2.02291
$151$	13.3482	0.00719378	0.00359689	−	0.999994i	$-0.498855\pi$
$151$	13.3482	0.00719378	0.00359689	+	0.999994i	$0.498855\pi$
$152$	−104.106	−0.0555535
$153$	−4.84792	−0.00256164
$154$	0	0
$155$	−5023.15	−2.60303
$156$	−4181.03	−2.14584
$157$	−1189.54	−0.604684	−0.302342	−	0.953200i	$-0.597768\pi$
$157$	−1189.54	−0.604684	−0.302342	+	0.953200i	$0.597768\pi$
$158$	−1648.63	−0.830113
$159$	2977.52	1.48511
$160$	3823.18	1.88906
$161$	0	0
$162$	−3260.48	−1.58128
$163$	3487.28	1.67574	0.837868	−	0.545873i	$-0.183802\pi$
$163$	3487.28	1.67574	0.837868	+	0.545873i	$0.183802\pi$
$164$	1756.68	0.836423
$165$	−1964.15	−0.926723
$166$	−1383.72	−0.646973
$167$	3091.88	1.43268	0.716338	−	0.697754i	$-0.245817\pi$
$167$	3091.88	1.43268	0.716338	+	0.697754i	$0.245817\pi$
$168$	0	0
$169$	2570.93	1.17020
$170$	1271.95	0.573847
$171$	−1.86732	−0.000835072 0
$172$	1749.68	0.775651
$173$	3139.53	1.37973	0.689867	−	0.723936i	$-0.257669\pi$
$173$	3139.53	1.37973	0.689867	+	0.723936i	$0.257669\pi$
$174$	−203.977	−0.0888702
$175$	0	0
$176$	−497.457	−0.213052
$177$	−2819.71	−1.19742
$178$	1964.65	0.827285
$179$	3822.18	1.59600	0.797998	−	0.602660i	$-0.205893\pi$
$179$	3822.18	1.59600	0.797998	+	0.602660i	$0.205893\pi$
$180$	−55.8784	−0.0231385
$181$	−2158.69	−0.886487	−0.443244	−	0.896401i	$-0.646172\pi$
$181$	−2158.69	−0.886487	−0.443244	+	0.896401i	$0.646172\pi$
$182$	0	0
$183$	−143.135	−0.0578187
$184$	−3217.18	−1.28899
$185$	5813.04	2.31018
$186$	6870.62	2.70848
$187$	−378.163	−0.147883
$188$	3576.84	1.38760
$189$	0	0
$190$	489.928	0.187069
$191$	−1055.33	−0.399797	−0.199899	−	0.979817i	$-0.564061\pi$
$191$	−1055.33	−0.399797	−0.199899	+	0.979817i	$0.564061\pi$
$192$	−4294.82	−1.61433
$193$	102.145	0.0380960	0.0190480	−	0.999819i	$-0.493936\pi$
$193$	102.145	0.0380960	0.0190480	+	0.999819i	$0.493936\pi$
$194$	−6266.47	−2.31911
$195$	6096.92	2.23902
$196$	0	0
$197$	−4360.12	−1.57688	−0.788440	−	0.615111i	$-0.789111\pi$
$197$	−4360.12	−1.57688	−0.788440	+	0.615111i	$0.789111\pi$
$198$	28.0786	0.0100781
$199$	−3775.79	−1.34502	−0.672510	−	0.740088i	$-0.734784\pi$
$199$	−3775.79	−1.34502	−0.672510	+	0.740088i	$0.734784\pi$
$200$	2555.50	0.903507
$201$	103.199	0.0362144
$202$	−4956.43	−1.72640
$203$	0	0
$204$	−1029.36	−0.353283
$205$	−2561.64	−0.872745
$206$	4117.81	1.39272
$207$	−57.7053	−0.0193758
$208$	1544.15	0.514748
$209$	−145.661	−0.0482084
$210$	0	0
$211$	5842.83	1.90634	0.953168	−	0.302443i	$-0.0978021\pi$
$211$	5842.83	1.90634	0.953168	+	0.302443i	$0.0978021\pi$
$212$	6607.65	2.14064
$213$	−362.791	−0.116704
$214$	−4159.99	−1.32884
$215$	−2551.44	−0.809334
$216$	−2218.61	−0.698876
$217$	0	0
$218$	1109.21	0.344612
$219$	−1672.35	−0.516013
$220$	−4358.81	−1.33578
$221$	1173.85	0.357294
$222$	−7951.03	−2.40377
$223$	−6090.44	−1.82891	−0.914454	−	0.404691i	$-0.867379\pi$
$223$	−6090.44	−1.82891	−0.914454	+	0.404691i	$0.867379\pi$
$224$	0	0
$225$	45.8372	0.0135814
$226$	3357.01	0.988074
$227$	5109.99	1.49410	0.747052	−	0.664765i	$-0.231468\pi$
$227$	5109.99	1.49410	0.747052	+	0.664765i	$0.231468\pi$
$228$	−396.488	−0.115167
$229$	−2493.77	−0.719619	−0.359809	−	0.933026i	$-0.617158\pi$
$229$	−2493.77	−0.719619	−0.359809	+	0.933026i	$0.617158\pi$
$230$	15140.2	4.34049
$231$	0	0
$232$	−140.263	−0.0396928
$233$	2113.26	0.594182	0.297091	−	0.954849i	$-0.403983\pi$
$233$	2113.26	0.594182	0.297091	+	0.954849i	$0.403983\pi$
$234$	−87.1585	−0.0243493
$235$	−5215.86	−1.44785
$236$	−6257.45	−1.72595
$237$	−1945.57	−0.533243
$238$	0	0
$239$	−4230.50	−1.14497	−0.572486	−	0.819915i	$-0.694021\pi$
$239$	−4230.50	−1.14497	−0.572486	+	0.819915i	$0.694021\pi$
$240$	1974.56	0.531072
$241$	−3922.05	−1.04830	−0.524152	−	0.851625i	$-0.675618\pi$
$241$	−3922.05	−1.04830	−0.524152	+	0.851625i	$0.675618\pi$
$242$	−3701.10	−0.983122
$243$	−80.0136	−0.0211229
$244$	−317.641	−0.0833397
$245$	0	0
$246$	3503.79	0.908104
$247$	452.144	0.116475
$248$	4724.54	1.20971
$249$	−1632.95	−0.415599
$250$	−2673.74	−0.676408
$251$	−0.674614	−0.000169646 0	−8.48232e−5	−	1.00000i	$-0.500027\pi$
$251$	−0.674614	−0.000169646 0	−8.48232e−5		1.00000i	$0.500027\pi$
$252$	0	0
$253$	−4501.32	−1.11856
$254$	−3516.15	−0.868593
$255$	1501.05	0.368624
$256$	−1522.09	−0.371604
$257$	−5160.55	−1.25255	−0.626277	−	0.779601i	$-0.715422\pi$
$257$	−5160.55	−1.25255	−0.626277	+	0.779601i	$0.715422\pi$
$258$	3489.84	0.842124
$259$	0	0
$260$	13530.1	3.22732
$261$	−2.51585	−0.000596656 0
$262$	−7231.64	−1.70524
$263$	−3100.41	−0.726918	−0.363459	−	0.931610i	$-0.618404\pi$
$263$	−3100.41	−0.726918	−0.363459	+	0.931610i	$0.618404\pi$
$264$	1847.39	0.430678
$265$	−9635.48	−2.23360
$266$	0	0
$267$	2318.52	0.531427
$268$	229.017	0.0521993
$269$	2982.89	0.676097	0.338048	−	0.941129i	$-0.390233\pi$
$269$	2982.89	0.676097	0.338048	+	0.941129i	$0.390233\pi$
$270$	10440.9	2.35337
$271$	630.039	0.141226	0.0706128	−	0.997504i	$-0.477505\pi$
$271$	630.039	0.141226	0.0706128	+	0.997504i	$0.477505\pi$
$272$	380.167	0.0847463
$273$	0	0
$274$	−3588.85	−0.791278
$275$	3575.54	0.784048
$276$	−12252.6	−2.67217
$277$	−6451.11	−1.39931	−0.699656	−	0.714480i	$-0.746664\pi$
$277$	−6451.11	−1.39931	−0.699656	+	0.714480i	$0.746664\pi$
$278$	13437.7	2.89907
$279$	84.7423	0.0181842
$280$	0	0
$281$	−6936.02	−1.47248	−0.736242	−	0.676718i	$-0.763402\pi$
$281$	−6936.02	−1.47248	−0.736242	+	0.676718i	$0.763402\pi$
$282$	7134.21	1.50651
$283$	3194.87	0.671078	0.335539	−	0.942026i	$-0.391082\pi$
$283$	3194.87	0.671078	0.335539	+	0.942026i	$0.391082\pi$
$284$	−805.097	−0.168217
$285$	578.172	0.120168
$286$	−6798.83	−1.40567
$287$	0	0
$288$	−64.4985	−0.0131966
$289$	289.000	0.0588235
$290$	660.083	0.133660
$291$	−7395.17	−1.48973
$292$	−3711.24	−0.743781
$293$	−9221.06	−1.83857	−0.919283	−	0.393597i	$-0.871230\pi$
$293$	−9221.06	−1.83857	−0.919283	+	0.393597i	$0.871230\pi$
$294$	0	0
$295$	9124.81	1.80090
$296$	−5467.47	−1.07362
$297$	−3104.17	−0.606473
$298$	9784.21	1.90196
$299$	13972.5	2.70251
$300$	9732.63	1.87305
$301$	0	0
$302$	59.0828	0.0112577
$303$	−5849.16	−1.10899
$304$	146.432	0.0276265
$305$	463.195	0.0869588
$306$	−21.4582	−0.00400877
$307$	−166.875	−0.0310230	−0.0155115	−	0.999880i	$-0.504938\pi$
$307$	−166.875	−0.0310230	−0.0155115	+	0.999880i	$0.504938\pi$
$308$	0	0
$309$	4859.49	0.894650
$310$	−22233.8	−4.07354
$311$	604.942	0.110299	0.0551497	−	0.998478i	$-0.482436\pi$
$311$	604.942	0.110299	0.0551497	+	0.998478i	$0.482436\pi$
$312$	−5734.47	−1.04055
$313$	6192.74	1.11832	0.559160	−	0.829060i	$-0.311124\pi$
$313$	6192.74	1.11832	0.559160	+	0.829060i	$0.311124\pi$
$314$	−5265.22	−0.946285
$315$	0	0
$316$	−4317.58	−0.768616
$317$	1803.66	0.319571	0.159785	−	0.987152i	$-0.448920\pi$
$317$	1803.66	0.319571	0.159785	+	0.987152i	$0.448920\pi$
$318$	13179.3	2.32409
$319$	−196.250	−0.0344447
$320$	13898.4	2.42794
$321$	−4909.28	−0.853611
$322$	0	0
$323$	111.317	0.0191760
$324$	−8538.82	−1.46413
$325$	−11098.8	−1.89431
$326$	15435.7	2.62240
$327$	1309.00	0.221370
$328$	2409.36	0.405593
$329$	0	0
$330$	−8693.89	−1.45025
$331$	5111.31	0.848771	0.424385	−	0.905482i	$-0.360490\pi$
$331$	5111.31	0.848771	0.424385	+	0.905482i	$0.360490\pi$
$332$	−3623.81	−0.599043
$333$	−98.0681	−0.0161384
$334$	13685.5	2.24203
$335$	−333.959	−0.0544661
$336$	0	0
$337$	3865.00	0.624748	0.312374	−	0.949959i	$-0.398876\pi$
$337$	3865.00	0.624748	0.312374	+	0.949959i	$0.398876\pi$
$338$	11379.6	1.83128
$339$	3961.66	0.634713
$340$	3331.09	0.531334
$341$	6610.35	1.04977
$342$	−8.26526	−0.00130683
$343$	0	0
$344$	2399.77	0.376124
$345$	17867.1	2.78822
$346$	13896.4	2.15918
$347$	27.8871	0.00431428	0.00215714	−	0.999998i	$-0.499313\pi$
$347$	27.8871	0.00431428	0.00215714	+	0.999998i	$0.499313\pi$
$348$	−534.192	−0.0822864
$349$	−4895.68	−0.750888	−0.375444	−	0.926845i	$-0.622510\pi$
$349$	−4895.68	−0.750888	−0.375444	+	0.926845i	$0.622510\pi$
$350$	0	0
$351$	9635.64	1.46528
$352$	−5031.22	−0.761833
$353$	−3996.67	−0.602609	−0.301305	−	0.953528i	$-0.597422\pi$
$353$	−3996.67	−0.602609	−0.301305	+	0.953528i	$0.597422\pi$
$354$	−12480.8	−1.87387
$355$	1174.02	0.175522
$356$	5145.20	0.765997
$357$	0	0
$358$	16918.0	2.49761
$359$	482.472	0.0709300	0.0354650	−	0.999371i	$-0.488709\pi$
$359$	482.472	0.0709300	0.0354650	+	0.999371i	$0.488709\pi$
$360$	−76.6397	−0.0112202
$361$	−6816.12	−0.993749
$362$	−9554.96	−1.38729
$363$	−4367.72	−0.631532
$364$	0	0
$365$	5411.85	0.776080
$366$	−633.553	−0.0904819
$367$	−5495.14	−0.781592	−0.390796	−	0.920477i	$-0.627800\pi$
$367$	−5495.14	−0.781592	−0.390796	+	0.920477i	$0.627800\pi$
$368$	4525.17	0.641007
$369$	43.2158	0.00609681
$370$	25730.1	3.61526
$371$	0	0
$372$	17993.4	2.50783
$373$	−3038.90	−0.421845	−0.210922	−	0.977503i	$-0.567647\pi$
$373$	−3038.90	−0.421845	−0.210922	+	0.977503i	$0.567647\pi$
$374$	−1673.85	−0.231425
$375$	−3155.32	−0.434507
$376$	4905.80	0.672865
$377$	609.177	0.0832207
$378$	0	0
$379$	13910.5	1.88531	0.942654	−	0.333770i	$-0.108321\pi$
$379$	13910.5	1.88531	0.942654	+	0.333770i	$0.108321\pi$
$380$	1283.07	0.173210
$381$	−4149.46	−0.557962
$382$	−4671.20	−0.625653
$383$	−4187.26	−0.558640	−0.279320	−	0.960198i	$-0.590109\pi$
$383$	−4187.26	−0.558640	−0.279320	+	0.960198i	$0.590109\pi$
$384$	−9558.65	−1.27028
$385$	0	0
$386$	452.120	0.0596174
$387$	43.0437	0.00565384
$388$	−16411.2	−2.14730
$389$	−7416.22	−0.966626	−0.483313	−	0.875448i	$-0.660567\pi$
$389$	−7416.22	−0.966626	−0.483313	+	0.875448i	$0.660567\pi$
$390$	26986.6	3.50390
$391$	3440.00	0.444932
$392$	0	0
$393$	−8534.18	−1.09540
$394$	−19299.1	−2.46770
$395$	6296.03	0.801993
$396$	73.5347	0.00933145
$397$	−11937.9	−1.50918	−0.754590	−	0.656197i	$-0.772164\pi$
$397$	−11937.9	−1.50918	−0.754590	+	0.656197i	$0.772164\pi$
$398$	−16712.7	−2.10485
$399$	0	0
$400$	−3594.48	−0.449310
$401$	−15219.6	−1.89533	−0.947667	−	0.319260i	$-0.896566\pi$
$401$	−15219.6	−1.89533	−0.947667	+	0.319260i	$0.896566\pi$
$402$	456.787	0.0566728
$403$	−20519.1	−2.53630
$404$	−12980.3	−1.59850
$405$	12451.6	1.52771
$406$	0	0
$407$	−7649.83	−0.931666
$408$	−1411.81	−0.171312
$409$	−7534.85	−0.910940	−0.455470	−	0.890251i	$-0.650529\pi$
$409$	−7534.85	−0.910940	−0.455470	+	0.890251i	$0.650529\pi$
$410$	−11338.5	−1.36578
$411$	−4235.26	−0.508296
$412$	10784.1	1.28955
$413$	0	0
$414$	−255.420	−0.0303217
$415$	5284.35	0.625057
$416$	15617.4	1.84064
$417$	15858.1	1.86229
$418$	−644.734	−0.0754425
$419$	−3895.36	−0.454179	−0.227089	−	0.973874i	$-0.572921\pi$
$419$	−3895.36	−0.454179	−0.227089	+	0.973874i	$0.572921\pi$
$420$	0	0
$421$	−8636.29	−0.999779	−0.499889	−	0.866089i	$-0.666626\pi$
$421$	−8636.29	−0.999779	−0.499889	+	0.866089i	$0.666626\pi$
$422$	25862.0	2.98327
$423$	87.9935	0.0101144
$424$	9062.68	1.03803
$425$	−2732.50	−0.311872
$426$	−1605.81	−0.182633
$427$	0	0
$428$	−10894.6	−1.23039
$429$	−8023.40	−0.902969
$430$	−11293.4	−1.26655
$431$	9927.45	1.10949	0.554743	−	0.832022i	$-0.312817\pi$
$431$	9927.45	1.10949	0.554743	+	0.832022i	$0.312817\pi$
$432$	3120.62	0.347548
$433$	6576.00	0.729844	0.364922	−	0.931038i	$-0.381096\pi$
$433$	6576.00	0.729844	0.364922	+	0.931038i	$0.381096\pi$
$434$	0	0
$435$	778.975	0.0858598
$436$	2904.90	0.319082
$437$	1325.02	0.145044
$438$	−7402.28	−0.807522
$439$	−9719.62	−1.05670	−0.528351	−	0.849026i	$-0.677189\pi$
$439$	−9719.62	−1.05670	−0.528351	+	0.849026i	$0.677189\pi$
$440$	−5978.30	−0.647737
$441$	0	0
$442$	5195.80	0.559138
$443$	−11347.5	−1.21702	−0.608508	−	0.793548i	$-0.708232\pi$
$443$	−11347.5	−1.21702	−0.608508	+	0.793548i	$0.708232\pi$
$444$	−20822.8	−2.22570
$445$	−7502.90	−0.799261
$446$	−26958.0	−2.86210
$447$	11546.5	1.22177
$448$	0	0
$449$	16453.2	1.72934	0.864672	−	0.502338i	$-0.167527\pi$
$449$	16453.2	1.72934	0.864672	+	0.502338i	$0.167527\pi$
$450$	202.888	0.0212538
$451$	3371.06	0.351967
$452$	8791.62	0.914874
$453$	69.7246	0.00723167
$454$	22618.2	2.33816
$455$	0	0
$456$	−543.802	−0.0558461
$457$	−2402.41	−0.245908	−0.122954	−	0.992412i	$-0.539237\pi$
$457$	−2402.41	−0.245908	−0.122954	+	0.992412i	$0.539237\pi$
$458$	−11038.1	−1.12615
$459$	2372.27	0.241238
$460$	39650.4	4.01893
$461$	−12582.2	−1.27117	−0.635586	−	0.772030i	$-0.719241\pi$
$461$	−12582.2	−1.27117	−0.635586	+	0.772030i	$0.719241\pi$
$462$	0	0
$463$	−4320.33	−0.433656	−0.216828	−	0.976210i	$-0.569571\pi$
$463$	−4320.33	−0.433656	−0.216828	+	0.976210i	$0.569571\pi$
$464$	197.289	0.0197391
$465$	−26238.5	−2.61674
$466$	9353.88	0.929851
$467$	453.197	0.0449068	0.0224534	−	0.999748i	$-0.492852\pi$
$467$	453.197	0.0449068	0.0224534	+	0.999748i	$0.492852\pi$
$468$	−228.258	−0.0225454
$469$	0	0
$470$	−23086.9	−2.26578
$471$	−6213.57	−0.607869
$472$	−8582.37	−0.836939
$473$	3357.64	0.326394
$474$	−8611.65	−0.834486
$475$	−1052.50	−0.101668
$476$	0	0
$477$	162.554	0.0156034
$478$	−18725.4	−1.79180
$479$	7262.14	0.692726	0.346363	−	0.938101i	$-0.387417\pi$
$479$	7262.14	0.692726	0.346363	+	0.938101i	$0.387417\pi$
$480$	19970.5	1.89901
$481$	23745.8	2.25096
$482$	−17360.1	−1.64052
$483$	0	0
$484$	−9692.75	−0.910289
$485$	23931.3	2.24055
$486$	−354.162	−0.0330558
$487$	−10655.0	−0.991425	−0.495712	−	0.868487i	$-0.665093\pi$
$487$	−10655.0	−0.991425	−0.495712	+	0.868487i	$0.665093\pi$
$488$	−435.659	−0.0404126
$489$	18215.9	1.68456
$490$	0	0
$491$	21324.2	1.95998	0.979990	−	0.199048i	$-0.0637851\pi$
$491$	21324.2	1.95998	0.979990	+	0.199048i	$0.0637851\pi$
$492$	9176.03	0.840828
$493$	149.978	0.0137011
$494$	2001.31	0.182274
$495$	−107.231	−0.00973668
$496$	−6645.37	−0.601584
$497$	0	0
$498$	−7227.89	−0.650381
$499$	−6043.52	−0.542175	−0.271087	−	0.962555i	$-0.587383\pi$
$499$	−6043.52	−0.542175	−0.271087	+	0.962555i	$0.587383\pi$
$500$	−7002.22	−0.626297
$501$	16150.5	1.44022
$502$	−2.98603	−0.000265484 0
$503$	1741.30	0.154355	0.0771775	−	0.997017i	$-0.475409\pi$
$503$	1741.30	0.154355	0.0771775	+	0.997017i	$0.475409\pi$
$504$	0	0
$505$	18928.3	1.66792
$506$	−19924.1	−1.75046
$507$	13429.3	1.17636
$508$	−9208.39	−0.804245
$509$	7405.78	0.644902	0.322451	−	0.946586i	$-0.395493\pi$
$509$	7405.78	0.644902	0.322451	+	0.946586i	$0.395493\pi$
$510$	6644.05	0.576869
$511$	0	0
$512$	7902.21	0.682093
$513$	913.750	0.0786414
$514$	−22842.0	−1.96015
$515$	−15725.7	−1.34555
$516$	9139.50	0.779737
$517$	6863.96	0.583900
$518$	0	0
$519$	16399.4	1.38700
$520$	18557.2	1.56497
$521$	19487.0	1.63866	0.819331	−	0.573321i	$-0.194345\pi$
$521$	19487.0	1.63866	0.819331	+	0.573321i	$0.194345\pi$
$522$	−11.1358	−0.000933722 0
$523$	−4971.34	−0.415643	−0.207822	−	0.978167i	$-0.566637\pi$
$523$	−4971.34	−0.415643	−0.207822	+	0.978167i	$0.566637\pi$
$524$	−18938.9	−1.57891
$525$	0	0
$526$	−13723.3	−1.13757
$527$	−5051.76	−0.417568
$528$	−2598.48	−0.214175
$529$	28779.8	2.36539
$530$	−42649.3	−3.49541
$531$	−153.939	−0.0125807
$532$	0	0
$533$	−10464.1	−0.850375
$534$	10262.4	0.831643
$535$	15886.8	1.28382
$536$	314.106	0.0253122
$537$	19965.2	1.60440
$538$	13203.1	1.05804
$539$	0	0
$540$	27343.4	2.17903
$541$	−3403.45	−0.270472	−0.135236	−	0.990813i	$-0.543179\pi$
$541$	−3403.45	−0.270472	−0.135236	+	0.990813i	$0.543179\pi$
$542$	2788.73	0.221008
$543$	−11276.0	−0.891157
$544$	3844.96	0.303036
$545$	−4236.02	−0.332938
$546$	0	0
$547$	−9897.33	−0.773637	−0.386818	−	0.922156i	$-0.626426\pi$
$547$	−9897.33	−0.773637	−0.386818	+	0.922156i	$0.626426\pi$
$548$	−9398.79	−0.732658
$549$	−7.81426	−0.000607476 0
$550$	15826.3	1.22698
$551$	57.7684	0.00446645
$552$	−16805.0	−1.29578
$553$	0	0
$554$	−28554.4	−2.18982
$555$	30364.5	2.32235
$556$	35192.0	2.68430
$557$	−13722.2	−1.04386	−0.521930	−	0.852988i	$-0.674788\pi$
$557$	−13722.2	−1.04386	−0.521930	+	0.852988i	$0.674788\pi$
$558$	375.093	0.0284569
$559$	−10422.4	−0.788589
$560$	0	0
$561$	−1975.34	−0.148661
$562$	−30700.7	−2.30433
$563$	6833.01	0.511504	0.255752	−	0.966742i	$-0.417677\pi$
$563$	6833.01	0.511504	0.255752	+	0.966742i	$0.417677\pi$
$564$	18683.7	1.39490
$565$	−12820.2	−0.954603
$566$	14141.4	1.05019
$567$	0	0
$568$	−1104.23	−0.0815709
$569$	8285.15	0.610425	0.305212	−	0.952284i	$-0.401273\pi$
$569$	8285.15	0.610425	0.305212	+	0.952284i	$0.401273\pi$
$570$	2559.15	0.188054
$571$	12246.2	0.897526	0.448763	−	0.893651i	$-0.351865\pi$
$571$	12246.2	0.897526	0.448763	+	0.893651i	$0.351865\pi$
$572$	−17805.4	−1.30154
$573$	−5512.56	−0.401903
$574$	0	0
$575$	−32525.3	−2.35895
$576$	−234.470	−0.0169611
$577$	−552.177	−0.0398396	−0.0199198	−	0.999802i	$-0.506341\pi$
$577$	−552.177	−0.0398396	−0.0199198	+	0.999802i	$0.506341\pi$
$578$	1279.19	0.0920544
$579$	533.554	0.0382966
$580$	1728.68	0.123758
$581$	0	0
$582$	−32733.1	−2.33132
$583$	12680.1	0.900780
$584$	−5090.13	−0.360670
$585$	332.854	0.0235244
$586$	−40814.9	−2.87722
$587$	16616.0	1.16834	0.584170	−	0.811631i	$-0.301420\pi$
$587$	16616.0	1.16834	0.584170	+	0.811631i	$0.301420\pi$
$588$	0	0
$589$	−1945.83	−0.136123
$590$	40388.9	2.81828
$591$	−22775.2	−1.58519
$592$	7690.35	0.533905
$593$	−8807.53	−0.609919	−0.304959	−	0.952365i	$-0.598643\pi$
$593$	−8807.53	−0.609919	−0.304959	+	0.952365i	$0.598643\pi$
$594$	−13739.9	−0.949085
$595$	0	0
$596$	25623.7	1.76106
$597$	−19722.9	−1.35210
$598$	61846.2	4.22923
$599$	1706.32	0.116391	0.0581957	−	0.998305i	$-0.481465\pi$
$599$	1706.32	0.116391	0.0581957	+	0.998305i	$0.481465\pi$
$600$	13348.7	0.908266
$601$	−7869.44	−0.534111	−0.267056	−	0.963681i	$-0.586051\pi$
$601$	−7869.44	−0.534111	−0.267056	+	0.963681i	$0.586051\pi$
$602$	0	0
$603$	5.63401	0.000380489 0
$604$	154.731	0.0104237
$605$	14134.3	0.949819
$606$	−25890.0	−1.73549
$607$	−9589.90	−0.641256	−0.320628	−	0.947205i	$-0.603894\pi$
$607$	−9589.90	−0.641256	−0.320628	+	0.947205i	$0.603894\pi$
$608$	1481.00	0.0987870
$609$	0	0
$610$	2050.23	0.136084
$611$	−21306.4	−1.41074
$612$	−56.1967	−0.00371179
$613$	−19106.4	−1.25889	−0.629446	−	0.777045i	$-0.716718\pi$
$613$	−19106.4	−1.25889	−0.629446	+	0.777045i	$0.716718\pi$
$614$	−738.636	−0.0485487
$615$	−13380.8	−0.877342
$616$	0	0
$617$	−20503.2	−1.33781	−0.668905	−	0.743348i	$-0.733237\pi$
$617$	−20503.2	−1.33781	−0.668905	+	0.743348i	$0.733237\pi$
$618$	21509.5	1.40006
$619$	−2652.77	−0.172252	−0.0861258	−	0.996284i	$-0.527449\pi$
$619$	−2652.77	−0.172252	−0.0861258	+	0.996284i	$0.527449\pi$
$620$	−58227.9	−3.77176
$621$	28237.4	1.82469
$622$	2677.64	0.172610
$623$	0	0
$624$	8065.91	0.517460
$625$	−9881.06	−0.632388
$626$	27410.8	1.75009
$627$	−760.861	−0.0484623
$628$	−13789.0	−0.876181
$629$	5846.15	0.370591
$630$	0	0
$631$	15223.5	0.960440	0.480220	−	0.877148i	$-0.340557\pi$
$631$	15223.5	0.960440	0.480220	+	0.877148i	$0.340557\pi$
$632$	−5921.75	−0.372713
$633$	30520.1	1.91638
$634$	7983.51	0.500104
$635$	13428.0	0.839170
$636$	34515.2	2.15191
$637$	0	0
$638$	−868.655	−0.0539034
$639$	−19.8061	−0.00122616
$640$	30932.5	1.91049
$641$	8978.54	0.553247	0.276623	−	0.960978i	$-0.410785\pi$
$641$	8978.54	0.553247	0.276623	+	0.960978i	$0.410785\pi$
$642$	−21729.8	−1.33584
$643$	13807.1	0.846810	0.423405	−	0.905940i	$-0.360835\pi$
$643$	13807.1	0.846810	0.423405	+	0.905940i	$0.360835\pi$
$644$	0	0
$645$	−13327.5	−0.813597
$646$	492.719	0.0300089
$647$	−5033.05	−0.305826	−0.152913	−	0.988240i	$-0.548865\pi$
$647$	−5033.05	−0.305826	−0.152913	+	0.988240i	$0.548865\pi$
$648$	−11711.4	−0.709979
$649$	−12008.0	−0.726282
$650$	−49126.4	−2.96446
$651$	0	0
$652$	40424.3	2.42812
$653$	10208.1	0.611754	0.305877	−	0.952071i	$-0.401050\pi$
$653$	10208.1	0.611754	0.305877	+	0.952071i	$0.401050\pi$
$654$	5794.00	0.346427
$655$	27617.2	1.64747
$656$	−3388.92	−0.201700
$657$	−91.2999	−0.00542153
$658$	0	0
$659$	15428.3	0.911990	0.455995	−	0.889982i	$-0.349284\pi$
$659$	15428.3	0.911990	0.455995	+	0.889982i	$0.349284\pi$
$660$	−22768.3	−1.34281
$661$	−22651.9	−1.33291	−0.666457	−	0.745544i	$-0.732190\pi$
$661$	−22651.9	−1.33291	−0.666457	+	0.745544i	$0.732190\pi$
$662$	22624.1	1.32826
$663$	6131.65	0.359176
$664$	−4970.21	−0.290484
$665$	0	0
$666$	−434.076	−0.0252554
$667$	1785.20	0.103633
$668$	35840.8	2.07593
$669$	−31813.6	−1.83854
$670$	−1478.20	−0.0852354
$671$	−609.553	−0.0350694
$672$	0	0
$673$	−17291.4	−0.990393	−0.495196	−	0.868781i	$-0.664904\pi$
$673$	−17291.4	−0.990393	−0.495196	+	0.868781i	$0.664904\pi$
$674$	17107.6	0.977684
$675$	−22429.9	−1.27900
$676$	29802.0	1.69561
$677$	8539.36	0.484777	0.242389	−	0.970179i	$-0.422069\pi$
$677$	8539.36	0.484777	0.242389	+	0.970179i	$0.422069\pi$
$678$	17535.4	0.993278
$679$	0	0
$680$	4568.74	0.257652
$681$	26692.1	1.50197
$682$	29259.2	1.64281
$683$	1930.75	0.108167	0.0540835	−	0.998536i	$-0.482776\pi$
$683$	1930.75	0.108167	0.0540835	+	0.998536i	$0.482776\pi$
$684$	−21.6458	−0.00121001
$685$	13705.6	0.764474
$686$	0	0
$687$	−13026.2	−0.723409
$688$	−3375.43	−0.187045
$689$	−39360.1	−2.17634
$690$	79084.9	4.36335
$691$	−32951.2	−1.81407	−0.907036	−	0.421054i	$-0.861660\pi$
$691$	−32951.2	−1.81407	−0.907036	+	0.421054i	$0.861660\pi$
$692$	36393.2	1.99922
$693$	0	0
$694$	123.436	0.00675153
$695$	−51318.0	−2.80087
$696$	−732.668	−0.0399019
$697$	−2576.23	−0.140003
$698$	−21669.6	−1.17508
$699$	11038.7	0.597312
$700$	0	0
$701$	−21147.5	−1.13941	−0.569707	−	0.821848i	$-0.692943\pi$
$701$	−21147.5	−1.13941	−0.569707	+	0.821848i	$0.692943\pi$
$702$	42650.0	2.29305
$703$	2251.82	0.120809
$704$	−18289.9	−0.979159
$705$	−27245.2	−1.45548
$706$	−17690.3	−0.943038
$707$	0	0
$708$	−32685.9	−1.73504
$709$	−14069.8	−0.745279	−0.372639	−	0.927976i	$-0.621547\pi$
$709$	−14069.8	−0.745279	−0.372639	+	0.927976i	$0.621547\pi$
$710$	5196.53	0.274679
$711$	−106.216	−0.00560256
$712$	7056.87	0.371443
$713$	−60131.7	−3.15842
$714$	0	0
$715$	25964.3	1.35806
$716$	44306.4	2.31258
$717$	−22098.1	−1.15100
$718$	2135.55	0.111000
$719$	10892.1	0.564959	0.282479	−	0.959273i	$-0.408843\pi$
$719$	10892.1	0.564959	0.282479	+	0.959273i	$0.408843\pi$
$720$	107.799	0.00557975
$721$	0	0
$722$	−30170.0	−1.55514
$723$	−20486.9	−1.05383
$724$	−25023.4	−1.28451
$725$	−1418.04	−0.0726412
$726$	−19332.7	−0.988300
$727$	4947.43	0.252394	0.126197	−	0.992005i	$-0.459723\pi$
$727$	4947.43	0.252394	0.126197	+	0.992005i	$0.459723\pi$
$728$	0	0
$729$	19470.7	0.989216
$730$	23954.3	1.21451
$731$	−2565.98	−0.129830
$732$	−1659.21	−0.0837787
$733$	3023.86	0.152372	0.0761861	−	0.997094i	$-0.475726\pi$
$733$	3023.86	0.152372	0.0761861	+	0.997094i	$0.475726\pi$
$734$	−24323.0	−1.22313
$735$	0	0
$736$	45767.1	2.29211
$737$	439.483	0.0219655
$738$	191.285	0.00954106
$739$	22602.2	1.12508	0.562541	−	0.826769i	$-0.309824\pi$
$739$	22602.2	1.12508	0.562541	+	0.826769i	$0.309824\pi$
$740$	67384.3	3.34743
$741$	2361.78	0.117088
$742$	0	0
$743$	−4371.41	−0.215843	−0.107922	−	0.994159i	$-0.534420\pi$
$743$	−4371.41	−0.215843	−0.107922	+	0.994159i	$0.534420\pi$
$744$	24678.7	1.21608
$745$	−37365.4	−1.83753
$746$	−13451.0	−0.660155
$747$	−89.1489	−0.00436652
$748$	−4383.64	−0.214280
$749$	0	0
$750$	−13966.3	−0.679971
$751$	−9415.34	−0.457484	−0.228742	−	0.973487i	$-0.573461\pi$
$751$	−9415.34	−0.457484	−0.228742	+	0.973487i	$0.573461\pi$
$752$	−6900.32	−0.334613
$753$	−3.52386	−0.000170540 0
$754$	2696.38	0.130234
$755$	−225.634	−0.0108764
$756$	0	0
$757$	−20071.8	−0.963704	−0.481852	−	0.876253i	$-0.660036\pi$
$757$	−20071.8	−0.963704	−0.481852	+	0.876253i	$0.660036\pi$
$758$	61571.5	2.95037
$759$	−23512.8	−1.12445
$760$	1759.78	0.0839921
$761$	−420.505	−0.0200306	−0.0100153	−	0.999950i	$-0.503188\pi$
$761$	−420.505	−0.0200306	−0.0100153	+	0.999950i	$0.503188\pi$
$762$	−18366.7	−0.873168
$763$	0	0
$764$	−12233.4	−0.579303
$765$	81.9478	0.00387298
$766$	−18534.0	−0.874229
$767$	37274.1	1.75474
$768$	−7950.68	−0.373562
$769$	21370.8	1.00215	0.501074	−	0.865405i	$-0.332939\pi$
$769$	21370.8	1.00215	0.501074	+	0.865405i	$0.332939\pi$
$770$	0	0
$771$	−26956.2	−1.25915
$772$	1184.05	0.0552007
$773$	34813.4	1.61986	0.809929	−	0.586527i	$-0.199505\pi$
$773$	34813.4	1.61986	0.809929	+	0.586527i	$0.199505\pi$
$774$	190.523	0.00884784
$775$	47764.5	2.21387
$776$	−22508.7	−1.04126
$777$	0	0
$778$	−32826.3	−1.51270
$779$	−992.312	−0.0456396
$780$	70675.0	3.24432
$781$	−1544.98	−0.0707859
$782$	15226.4	0.696285
$783$	1231.10	0.0561890
$784$	0	0
$785$	20107.6	0.914230
$786$	−37774.6	−1.71422
$787$	23937.8	1.08423	0.542115	−	0.840304i	$-0.317624\pi$
$787$	23937.8	1.08423	0.542115	+	0.840304i	$0.317624\pi$
$788$	−50542.1	−2.28488
$789$	−16195.1	−0.730747
$790$	27867.9	1.25506
$791$	0	0
$792$	100.856	0.00452495
$793$	1892.11	0.0847299
$794$	−52840.3	−2.36175
$795$	−50331.1	−2.24536
$796$	−43768.7	−1.94892
$797$	14091.2	0.626267	0.313134	−	0.949709i	$-0.398621\pi$
$797$	14091.2	0.626267	0.313134	+	0.949709i	$0.398621\pi$
$798$	0	0
$799$	−5245.58	−0.232259
$800$	−36354.2	−1.60664
$801$	126.577	0.00558347
$802$	−67366.0	−2.96606
$803$	−7121.87	−0.312983
$804$	1196.27	0.0524743
$805$	0	0
$806$	−90823.3	−3.96913
$807$	15581.2	0.679658
$808$	−17803.1	−0.775137
$809$	−35107.7	−1.52574	−0.762868	−	0.646554i	$-0.776210\pi$
$809$	−35107.7	−1.52574	−0.762868	+	0.646554i	$0.776210\pi$
$810$	55114.1	2.39076
$811$	7397.43	0.320295	0.160147	−	0.987093i	$-0.448803\pi$
$811$	7397.43	0.320295	0.160147	+	0.987093i	$0.448803\pi$
$812$	0	0
$813$	3291.02	0.141969
$814$	−33860.3	−1.45799
$815$	−58948.0	−2.53357
$816$	1985.81	0.0851926
$817$	−988.361	−0.0423236
$818$	−33351.3	−1.42555
$819$	0	0
$820$	−29694.3	−1.26460
$821$	−19148.5	−0.813993	−0.406997	−	0.913430i	$-0.633424\pi$
$821$	−19148.5	−0.813993	−0.406997	+	0.913430i	$0.633424\pi$
$822$	−18746.4	−0.795446
$823$	6580.95	0.278733	0.139367	−	0.990241i	$-0.455493\pi$
$823$	6580.95	0.278733	0.139367	+	0.990241i	$0.455493\pi$
$824$	14790.8	0.625320
$825$	18676.9	0.788178
$826$	0	0
$827$	−5487.32	−0.230729	−0.115364	−	0.993323i	$-0.536804\pi$
$827$	−5487.32	−0.230729	−0.115364	+	0.993323i	$0.536804\pi$
$828$	−668.916	−0.0280754
$829$	21781.2	0.912537	0.456269	−	0.889842i	$-0.349186\pi$
$829$	21781.2	0.912537	0.456269	+	0.889842i	$0.349186\pi$
$830$	23390.0	0.978167
$831$	−33697.5	−1.40668
$832$	56773.6	2.36571
$833$	0	0
$834$	70192.4	2.91434
$835$	−52264.2	−2.16608
$836$	−1688.49	−0.0698535
$837$	−41467.7	−1.71246
$838$	−17242.0	−0.710756
$839$	−9781.70	−0.402505	−0.201252	−	0.979539i	$-0.564501\pi$
$839$	−9781.70	−0.402505	−0.201252	+	0.979539i	$0.564501\pi$
$840$	0	0
$841$	−24311.2	−0.996809
$842$	−38226.6	−1.56458
$843$	−36230.4	−1.48024
$844$	67729.6	2.76226
$845$	−43458.3	−1.76924
$846$	389.484	0.0158283
$847$	0	0
$848$	−12747.2	−0.516205
$849$	16688.5	0.674613
$850$	−12094.8	−0.488057
$851$	69587.5	2.80309
$852$	−4205.44	−0.169103
$853$	−42400.6	−1.70196	−0.850978	−	0.525202i	$-0.823990\pi$
$853$	−42400.6	−1.70196	−0.850978	+	0.525202i	$0.823990\pi$
$854$	0	0
$855$	31.5646	0.00126256
$856$	−14942.4	−0.596635
$857$	−33492.7	−1.33499	−0.667497	−	0.744612i	$-0.732634\pi$
$857$	−33492.7	−1.33499	−0.667497	+	0.744612i	$0.732634\pi$
$858$	−35513.8	−1.41308
$859$	−17039.5	−0.676810	−0.338405	−	0.941001i	$-0.609887\pi$
$859$	−17039.5	−0.676810	−0.338405	+	0.941001i	$0.609887\pi$
$860$	−29576.1	−1.17272
$861$	0	0
$862$	43941.7	1.73626
$863$	13005.4	0.512988	0.256494	−	0.966546i	$-0.417433\pi$
$863$	13005.4	0.512988	0.256494	+	0.966546i	$0.417433\pi$
$864$	31561.6	1.24276
$865$	−53069.7	−2.08604
$866$	29107.2	1.14215
$867$	1509.60	0.0591334
$868$	0	0
$869$	−8285.43	−0.323434
$870$	3447.96	0.134364
$871$	−1364.20	−0.0530700
$872$	3984.21	0.154727
$873$	−403.730	−0.0156520
$874$	5864.89	0.226983
$875$	0	0
$876$	−19385.8	−0.747698
$877$	−24871.7	−0.957647	−0.478824	−	0.877911i	$-0.658937\pi$
$877$	−24871.7	−0.957647	−0.478824	+	0.877911i	$0.658937\pi$
$878$	−43021.7	−1.65366
$879$	−48166.4	−1.84825
$880$	8408.86	0.322117
$881$	5392.80	0.206229	0.103115	−	0.994669i	$-0.467119\pi$
$881$	5392.80	0.206229	0.103115	+	0.994669i	$0.467119\pi$
$882$	0	0
$883$	−24850.0	−0.947077	−0.473539	−	0.880773i	$-0.657024\pi$
$883$	−24850.0	−0.947077	−0.473539	+	0.880773i	$0.657024\pi$
$884$	13607.2	0.517715
$885$	47663.6	1.81039
$886$	−50227.4	−1.90454
$887$	23725.5	0.898111	0.449056	−	0.893504i	$-0.351761\pi$
$887$	23725.5	0.898111	0.449056	+	0.893504i	$0.351761\pi$
$888$	−28559.5	−1.07927
$889$	0	0
$890$	−33209.9	−1.25078
$891$	−16386.0	−0.616107
$892$	−70599.9	−2.65007
$893$	−2020.49	−0.0757145
$894$	51108.0	1.91198
$895$	−64609.0	−2.41301
$896$	0	0
$897$	72985.7	2.71675
$898$	72826.5	2.70629
$899$	−2621.64	−0.0972597
$900$	531.341	0.0196793
$901$	−9690.37	−0.358305
$902$	14921.2	0.550802
$903$	0	0
$904$	12058.1	0.443635
$905$	36489.9	1.34029
$906$	308.620	0.0113170
$907$	47638.2	1.74399	0.871996	−	0.489513i	$-0.162825\pi$
$907$	47638.2	1.74399	0.871996	+	0.489513i	$0.162825\pi$
$908$	59234.6	2.16494
$909$	−319.328	−0.0116517
$910$	0	0
$911$	−20622.7	−0.750013	−0.375007	−	0.927022i	$-0.622360\pi$
$911$	−20622.7	−0.750013	−0.375007	+	0.927022i	$0.622360\pi$
$912$	764.892	0.0277720
$913$	−6954.09	−0.252077
$914$	−10633.7	−0.384827
$915$	2419.51	0.0874168
$916$	−28907.5	−1.04272
$917$	0	0
$918$	10500.3	0.377519
$919$	−4491.12	−0.161206	−0.0806030	−	0.996746i	$-0.525685\pi$
$919$	−4491.12	−0.161206	−0.0806030	+	0.996746i	$0.525685\pi$
$920$	54382.2	1.94884
$921$	−871.676	−0.0311864
$922$	−55692.1	−1.98929
$923$	4795.76	0.171023
$924$	0	0
$925$	−55275.5	−1.96481
$926$	−19123.0	−0.678639
$927$	265.298	0.00939971
$928$	1995.36	0.0705829
$929$	19354.9	0.683544	0.341772	−	0.939783i	$-0.388973\pi$
$929$	19354.9	0.683544	0.341772	+	0.939783i	$0.388973\pi$
$930$	−116139.	−4.09500
$931$	0	0
$932$	24496.8	0.860964
$933$	3159.93	0.110880
$934$	2005.98	0.0702757
$935$	6392.36	0.223586
$936$	−313.066	−0.0109326
$937$	18723.3	0.652788	0.326394	−	0.945234i	$-0.394166\pi$
$937$	18723.3	0.652788	0.326394	+	0.945234i	$0.394166\pi$
$938$	0	0
$939$	32347.9	1.12421
$940$	−60461.9	−2.09792
$941$	28104.8	0.973634	0.486817	−	0.873504i	$-0.338158\pi$
$941$	28104.8	0.973634	0.486817	+	0.873504i	$0.338158\pi$
$942$	−27503.0	−0.951269
$943$	−30665.2	−1.05896
$944$	12071.7	0.416206
$945$	0	0
$946$	14861.8	0.510782
$947$	−47298.0	−1.62300	−0.811498	−	0.584355i	$-0.801348\pi$
$947$	−47298.0	−1.62300	−0.811498	+	0.584355i	$0.801348\pi$
$948$	−22552.9	−0.772664
$949$	22107.0	0.756188
$950$	−4658.67	−0.159102
$951$	9421.48	0.321254
$952$	0	0
$953$	−31810.9	−1.08128	−0.540639	−	0.841255i	$-0.681817\pi$
$953$	−31810.9	−1.08128	−0.540639	+	0.841255i	$0.681817\pi$
$954$	719.509	0.0244182
$955$	17839.1	0.604459
$956$	−49039.6	−1.65905
$957$	−1025.11	−0.0346261
$958$	32144.2	1.08406
$959$	0	0
$960$	72598.4	2.44073
$961$	58514.5	1.96417
$962$	105105.	3.52259
$963$	−268.016	−0.00896853
$964$	−45464.1	−1.51898
$965$	−1726.62	−0.0575978
$966$	0	0
$967$	5938.61	0.197490	0.0987450	−	0.995113i	$-0.468517\pi$
$967$	5938.61	0.197490	0.0987450	+	0.995113i	$0.468517\pi$
$968$	−13294.0	−0.441412
$969$	581.466	0.0192770
$970$	105927.	3.50629
$971$	−16153.1	−0.533860	−0.266930	−	0.963716i	$-0.586009\pi$
$971$	−16153.1	−0.533860	−0.266930	+	0.963716i	$0.586009\pi$
$972$	−927.511	−0.0306069
$973$	0	0
$974$	−47161.9	−1.55151
$975$	−57974.9	−1.90429
$976$	612.783	0.0200970
$977$	−49414.9	−1.61814	−0.809070	−	0.587713i	$-0.800029\pi$
$977$	−49414.9	−1.61814	−0.809070	+	0.587713i	$0.800029\pi$
$978$	80628.5	2.63621
$979$	9873.64	0.322332
$980$	0	0
$981$	71.4632	0.00232584
$982$	94387.0	3.06722
$983$	43923.2	1.42516	0.712581	−	0.701590i	$-0.247526\pi$
$983$	43923.2	1.42516	0.712581	+	0.701590i	$0.247526\pi$
$984$	12585.3	0.407730
$985$	73702.1	2.38411
$986$	663.844	0.0214413
$987$	0	0
$988$	5241.22	0.168771
$989$	−30543.1	−0.982017
$990$	−474.632	−0.0152372
$991$	24956.2	0.799961	0.399980	−	0.916524i	$-0.369017\pi$
$991$	24956.2	0.799961	0.399980	+	0.916524i	$0.369017\pi$
$992$	−67210.5	−2.15115
$993$	26699.0	0.853241
$994$	0	0
$995$	63824.9	2.03355
$996$	−18929.0	−0.602198
$997$	−51762.8	−1.64428	−0.822138	−	0.569288i	$-0.807219\pi$
$997$	−51762.8	−1.64428	−0.822138	+	0.569288i	$0.807219\pi$
$998$	−26750.3	−0.848463
$999$	47988.5	1.51981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.4.a.g.1.8		9
7.6	odd	2		119.4.a.e.1.8	✓	9
21.20	even	2		1071.4.a.r.1.2		9
28.27	even	2		1904.4.a.s.1.8		9
119.118	odd	2		2023.4.a.h.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.e.1.8	✓	9	7.6	odd	2
833.4.a.g.1.8		9	1.1	even	1	trivial
1071.4.a.r.1.2		9	21.20	even	2
1904.4.a.s.1.8		9	28.27	even	2
2023.4.a.h.1.8		9	119.118	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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	833.a (trivial)

\(f(q)\)	\(=\)	\(q+4.42628 q^{2} +5.22352 q^{3} +11.5919 q^{4} -16.9037 q^{5} +23.1207 q^{6} +15.8988 q^{8} +0.285172 q^{9} +O(q^{10})\)	\(q+4.42628 q^{2} +5.22352 q^{3} +11.5919 q^{4} -16.9037 q^{5} +23.1207 q^{6} +15.8988 q^{8} +0.285172 q^{9} -74.8205 q^{10} +22.2449 q^{11} +60.5506 q^{12} -69.0502 q^{13} -88.2969 q^{15} -22.3627 q^{16} -17.0000 q^{17} +1.26225 q^{18} -6.54805 q^{19} -195.946 q^{20} +98.4621 q^{22} -202.353 q^{23} +83.0479 q^{24} +160.735 q^{25} -305.635 q^{26} -139.545 q^{27} -8.82223 q^{29} -390.826 q^{30} +297.162 q^{31} -226.174 q^{32} +116.197 q^{33} -75.2467 q^{34} +3.30569 q^{36} -343.891 q^{37} -28.9835 q^{38} -360.685 q^{39} -268.749 q^{40} +151.543 q^{41} +150.940 q^{43} +257.861 q^{44} -4.82046 q^{45} -895.670 q^{46} +308.563 q^{47} -116.812 q^{48} +711.459 q^{50} -88.7999 q^{51} -800.424 q^{52} +570.022 q^{53} -617.667 q^{54} -376.021 q^{55} -34.2039 q^{57} -39.0496 q^{58} -539.811 q^{59} -1023.53 q^{60} -27.4019 q^{61} +1315.32 q^{62} -822.208 q^{64} +1167.20 q^{65} +514.319 q^{66} +19.7566 q^{67} -197.063 q^{68} -1057.00 q^{69} -69.4533 q^{71} +4.53390 q^{72} -320.158 q^{73} -1522.16 q^{74} +839.605 q^{75} -75.9044 q^{76} -1596.49 q^{78} -372.464 q^{79} +378.013 q^{80} -736.618 q^{81} +670.772 q^{82} -312.615 q^{83} +287.363 q^{85} +668.101 q^{86} -46.0831 q^{87} +353.668 q^{88} +443.861 q^{89} -21.3367 q^{90} -2345.66 q^{92} +1552.23 q^{93} +1365.79 q^{94} +110.686 q^{95} -1181.43 q^{96} -1415.74 q^{97} +6.34361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9} - 134 q^{10} - 8 q^{11} - 56 q^{12} - 164 q^{13} + 34 q^{15} + 178 q^{16} - 153 q^{17} + 98 q^{18} - 244 q^{19} + 41 q^{20} - 80 q^{22} - 14 q^{23} - 298 q^{24} + 684 q^{25} - 326 q^{26} - 218 q^{27} - 234 q^{29} - 335 q^{30} - 555 q^{31} - 181 q^{32} - 458 q^{33} - 34 q^{34} - 1221 q^{36} - 364 q^{37} + 714 q^{38} - 52 q^{39} - 123 q^{40} + 45 q^{41} - 135 q^{43} - 748 q^{44} + 844 q^{45} - 1576 q^{46} + 172 q^{47} + 949 q^{48} - 2901 q^{50} + 187 q^{51} + 1596 q^{52} + 101 q^{53} + 1163 q^{54} - 1260 q^{55} - 602 q^{57} + 1062 q^{58} - 280 q^{59} - 1727 q^{60} - 639 q^{61} + 1708 q^{62} - 2390 q^{64} + 638 q^{65} + 2476 q^{66} + 35 q^{67} - 646 q^{68} - 1288 q^{69} - 1616 q^{71} + 1335 q^{72} - 1049 q^{73} - 370 q^{74} - 1260 q^{75} - 4964 q^{76} - 4714 q^{78} + 2304 q^{79} + 3996 q^{80} - 791 q^{81} + 215 q^{82} - 2508 q^{83} - 51 q^{85} + 623 q^{86} - 166 q^{87} - 416 q^{88} - 2762 q^{89} - 2935 q^{90} - 2392 q^{92} + 2784 q^{93} + 862 q^{94} - 3462 q^{95} - 2928 q^{96} - 3107 q^{97} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9 - 134 * q^10 - 8 * q^11 - 56 * q^12 - 164 * q^13 + 34 * q^15 + 178 * q^16 - 153 * q^17 + 98 * q^18 - 244 * q^19 + 41 * q^20 - 80 * q^22 - 14 * q^23 - 298 * q^24 + 684 * q^25 - 326 * q^26 - 218 * q^27 - 234 * q^29 - 335 * q^30 - 555 * q^31 - 181 * q^32 - 458 * q^33 - 34 * q^34 - 1221 * q^36 - 364 * q^37 + 714 * q^38 - 52 * q^39 - 123 * q^40 + 45 * q^41 - 135 * q^43 - 748 * q^44 + 844 * q^45 - 1576 * q^46 + 172 * q^47 + 949 * q^48 - 2901 * q^50 + 187 * q^51 + 1596 * q^52 + 101 * q^53 + 1163 * q^54 - 1260 * q^55 - 602 * q^57 + 1062 * q^58 - 280 * q^59 - 1727 * q^60 - 639 * q^61 + 1708 * q^62 - 2390 * q^64 + 638 * q^65 + 2476 * q^66 + 35 * q^67 - 646 * q^68 - 1288 * q^69 - 1616 * q^71 + 1335 * q^72 - 1049 * q^73 - 370 * q^74 - 1260 * q^75 - 4964 * q^76 - 4714 * q^78 + 2304 * q^79 + 3996 * q^80 - 791 * q^81 + 215 * q^82 - 2508 * q^83 - 51 * q^85 + 623 * q^86 - 166 * q^87 - 416 * q^88 - 2762 * q^89 - 2935 * q^90 - 2392 * q^92 + 2784 * q^93 + 862 * q^94 - 3462 * q^95 - 2928 * q^96 - 3107 * q^97 - 2396 * q^99

Introduction

L-functions

Modular forms

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Database

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