LMFDB - Embedded newform 6025.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.07739$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.07739 q^{2} -0.702822 q^{3} -0.839239 q^{4} +0.757210 q^{6} -0.460803 q^{7} +3.05896 q^{8} -2.50604 q^{9} +O(q^{10})$	\(q-1.07739 q^{2} -0.702822 q^{3} -0.839239 q^{4} +0.757210 q^{6} -0.460803 q^{7} +3.05896 q^{8} -2.50604 q^{9} +1.22210 q^{11} +0.589835 q^{12} -2.49700 q^{13} +0.496463 q^{14} -1.61720 q^{16} +0.555622 q^{17} +2.69997 q^{18} -5.42691 q^{19} +0.323862 q^{21} -1.31667 q^{22} +8.01126 q^{23} -2.14990 q^{24} +2.69024 q^{26} +3.86976 q^{27} +0.386724 q^{28} -2.96885 q^{29} -2.38677 q^{31} -4.37557 q^{32} -0.858918 q^{33} -0.598620 q^{34} +2.10317 q^{36} +1.61973 q^{37} +5.84687 q^{38} +1.75495 q^{39} +2.77902 q^{41} -0.348925 q^{42} +9.46271 q^{43} -1.02563 q^{44} -8.63122 q^{46} +9.51335 q^{47} +1.13660 q^{48} -6.78766 q^{49} -0.390503 q^{51} +2.09558 q^{52} -7.09445 q^{53} -4.16923 q^{54} -1.40958 q^{56} +3.81415 q^{57} +3.19860 q^{58} +5.37709 q^{59} -8.34813 q^{61} +2.57148 q^{62} +1.15479 q^{63} +7.94857 q^{64} +0.925386 q^{66} -7.64811 q^{67} -0.466300 q^{68} -5.63048 q^{69} +7.43280 q^{71} -7.66587 q^{72} -1.66440 q^{73} -1.74508 q^{74} +4.55447 q^{76} -0.563147 q^{77} -1.89076 q^{78} +0.470333 q^{79} +4.79837 q^{81} -2.99408 q^{82} -2.16643 q^{83} -0.271798 q^{84} -10.1950 q^{86} +2.08657 q^{87} +3.73835 q^{88} +1.07180 q^{89} +1.15063 q^{91} -6.72336 q^{92} +1.67748 q^{93} -10.2496 q^{94} +3.07524 q^{96} -5.67189 q^{97} +7.31293 q^{98} -3.06263 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * 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 $

$2$	−1.07739	−0.761827	−0.380914	−	0.924611i	$-0.624390\pi$
$2$	−1.07739	−0.761827	−0.380914	+	0.924611i	$0.624390\pi$
$3$	−0.702822	−0.405774	−0.202887	−	0.979202i	$-0.565032\pi$
$3$	−0.702822	−0.405774	−0.202887	+	0.979202i	$0.565032\pi$
$4$	−0.839239	−0.419620
$5$	0	0
$5$	0	0
$6$	0.757210	0.309130
$7$	−0.460803	−0.174167	−0.0870836	−	0.996201i	$-0.527755\pi$
$7$	−0.460803	−0.174167	−0.0870836	+	0.996201i	$0.527755\pi$
$8$	3.05896	1.08150
$9$	−2.50604	−0.835347
$10$	0	0
$11$	1.22210	0.368477	0.184238	−	0.982882i	$-0.441018\pi$
$11$	1.22210	0.368477	0.184238	+	0.982882i	$0.441018\pi$
$12$	0.589835	0.170271
$13$	−2.49700	−0.692545	−0.346272	−	0.938134i	$-0.612553\pi$
$13$	−2.49700	−0.692545	−0.346272	+	0.938134i	$0.612553\pi$
$14$	0.496463	0.132685
$15$	0	0
$16$	−1.61720	−0.404300
$17$	0.555622	0.134758	0.0673791	−	0.997727i	$-0.478536\pi$
$17$	0.555622	0.134758	0.0673791	+	0.997727i	$0.478536\pi$
$18$	2.69997	0.636390
$19$	−5.42691	−1.24502	−0.622509	−	0.782613i	$-0.713887\pi$
$19$	−5.42691	−1.24502	−0.622509	+	0.782613i	$0.713887\pi$
$20$	0	0
$21$	0.323862	0.0706726
$22$	−1.31667	−0.280716
$23$	8.01126	1.67046	0.835231	−	0.549899i	$-0.185334\pi$
$23$	8.01126	1.67046	0.835231	+	0.549899i	$0.185334\pi$
$24$	−2.14990	−0.438847
$25$	0	0
$26$	2.69024	0.527599
$27$	3.86976	0.744737
$28$	0.386724	0.0730840
$29$	−2.96885	−0.551302	−0.275651	−	0.961258i	$-0.588893\pi$
$29$	−2.96885	−0.551302	−0.275651	+	0.961258i	$0.588893\pi$
$30$	0	0
$31$	−2.38677	−0.428677	−0.214339	−	0.976759i	$-0.568760\pi$
$31$	−2.38677	−0.428677	−0.214339	+	0.976759i	$0.568760\pi$
$32$	−4.37557	−0.773498
$33$	−0.858918	−0.149518
$34$	−0.598620	−0.102662
$35$	0	0
$36$	2.10317	0.350528
$37$	1.61973	0.266282	0.133141	−	0.991097i	$-0.457494\pi$
$37$	1.61973	0.266282	0.133141	+	0.991097i	$0.457494\pi$
$38$	5.84687	0.948488
$39$	1.75495	0.281017
$40$	0	0
$41$	2.77902	0.434011	0.217005	−	0.976170i	$-0.430371\pi$
$41$	2.77902	0.434011	0.217005	+	0.976170i	$0.430371\pi$
$42$	−0.348925	−0.0538403
$43$	9.46271	1.44305	0.721525	−	0.692388i	$-0.243441\pi$
$43$	9.46271	1.44305	0.721525	+	0.692388i	$0.243441\pi$
$44$	−1.02563	−0.154620
$45$	0	0
$46$	−8.63122	−1.27260
$47$	9.51335	1.38767	0.693833	−	0.720136i	$-0.255921\pi$
$47$	9.51335	1.38767	0.693833	+	0.720136i	$0.255921\pi$
$48$	1.13660	0.164054
$49$	−6.78766	−0.969666
$50$	0	0
$51$	−0.390503	−0.0546814
$52$	2.09558	0.290605
$53$	−7.09445	−0.974497	−0.487249	−	0.873263i	$-0.661999\pi$
$53$	−7.09445	−0.974497	−0.487249	+	0.873263i	$0.661999\pi$
$54$	−4.16923	−0.567360
$55$	0	0
$56$	−1.40958	−0.188363
$57$	3.81415	0.505196
$58$	3.19860	0.419997
$59$	5.37709	0.700038	0.350019	−	0.936743i	$-0.386175\pi$
$59$	5.37709	0.700038	0.350019	+	0.936743i	$0.386175\pi$
$60$	0	0
$61$	−8.34813	−1.06887	−0.534434	−	0.845210i	$-0.679475\pi$
$61$	−8.34813	−1.06887	−0.534434	+	0.845210i	$0.679475\pi$
$62$	2.57148	0.326578
$63$	1.15479	0.145490
$64$	7.94857	0.993572
$65$	0	0
$66$	0.925386	0.113907
$67$	−7.64811	−0.934365	−0.467183	−	0.884161i	$-0.654731\pi$
$67$	−7.64811	−0.934365	−0.467183	+	0.884161i	$0.654731\pi$
$68$	−0.466300	−0.0565472
$69$	−5.63048	−0.677831
$70$	0	0
$71$	7.43280	0.882111	0.441055	−	0.897480i	$-0.354604\pi$
$71$	7.43280	0.882111	0.441055	+	0.897480i	$0.354604\pi$
$72$	−7.66587	−0.903432
$73$	−1.66440	−0.194803	−0.0974017	−	0.995245i	$-0.531053\pi$
$73$	−1.66440	−0.194803	−0.0974017	+	0.995245i	$0.531053\pi$
$74$	−1.74508	−0.202861
$75$	0	0
$76$	4.55447	0.522434
$77$	−0.563147	−0.0641766
$78$	−1.89076	−0.214086
$79$	0.470333	0.0529166	0.0264583	−	0.999650i	$-0.491577\pi$
$79$	0.470333	0.0529166	0.0264583	+	0.999650i	$0.491577\pi$
$80$	0	0
$81$	4.79837	0.533152
$82$	−2.99408	−0.330641
$83$	−2.16643	−0.237797	−0.118898	−	0.992906i	$-0.537936\pi$
$83$	−2.16643	−0.237797	−0.118898	+	0.992906i	$0.537936\pi$
$84$	−0.271798	−0.0296556
$85$	0	0
$86$	−10.1950	−1.09935
$87$	2.08657	0.223704
$88$	3.73835	0.398509
$89$	1.07180	0.113611	0.0568054	−	0.998385i	$-0.481909\pi$
$89$	1.07180	0.113611	0.0568054	+	0.998385i	$0.481909\pi$
$90$	0	0
$91$	1.15063	0.120619
$92$	−6.72336	−0.700959
$93$	1.67748	0.173946
$94$	−10.2496	−1.05716
$95$	0	0
$96$	3.07524	0.313866
$97$	−5.67189	−0.575894	−0.287947	−	0.957646i	$-0.592973\pi$
$97$	−5.67189	−0.575894	−0.287947	+	0.957646i	$0.592973\pi$
$98$	7.31293	0.738718
$99$	−3.06263	−0.307806
$100$	0	0
$101$	16.2441	1.61635	0.808174	−	0.588944i	$-0.200456\pi$
$101$	16.2441	1.61635	0.808174	+	0.588944i	$0.200456\pi$
$102$	0.420723	0.0416578
$103$	−5.20192	−0.512560	−0.256280	−	0.966603i	$-0.582497\pi$
$103$	−5.20192	−0.512560	−0.256280	+	0.966603i	$0.582497\pi$
$104$	−7.63823	−0.748990
$105$	0	0
$106$	7.64346	0.742398
$107$	2.43640	0.235536	0.117768	−	0.993041i	$-0.462426\pi$
$107$	2.43640	0.235536	0.117768	+	0.993041i	$0.462426\pi$
$108$	−3.24766	−0.312506
$109$	2.30059	0.220356	0.110178	−	0.993912i	$-0.464858\pi$
$109$	2.30059	0.220356	0.110178	+	0.993912i	$0.464858\pi$
$110$	0	0
$111$	−1.13838	−0.108051
$112$	0.745211	0.0704158
$113$	12.6359	1.18868	0.594341	−	0.804213i	$-0.297413\pi$
$113$	12.6359	1.18868	0.594341	+	0.804213i	$0.297413\pi$
$114$	−4.10931	−0.384872
$115$	0	0
$116$	2.49158	0.231337
$117$	6.25760	0.578515
$118$	−5.79320	−0.533308
$119$	−0.256033	−0.0234705
$120$	0	0
$121$	−9.50647	−0.864225
$122$	8.99416	0.814293
$123$	−1.95316	−0.176110
$124$	2.00307	0.179881
$125$	0	0
$126$	−1.24416	−0.110838
$127$	−7.41200	−0.657708	−0.328854	−	0.944381i	$-0.606662\pi$
$127$	−7.41200	−0.657708	−0.328854	+	0.944381i	$0.606662\pi$
$128$	0.187450	0.0165684
$129$	−6.65060	−0.585553
$130$	0	0
$131$	13.0428	1.13955	0.569775	−	0.821800i	$-0.307030\pi$
$131$	13.0428	1.13955	0.569775	+	0.821800i	$0.307030\pi$
$132$	0.720837	0.0627408
$133$	2.50074	0.216841
$134$	8.23996	0.711825
$135$	0	0
$136$	1.69962	0.145742
$137$	3.30574	0.282428	0.141214	−	0.989979i	$-0.454899\pi$
$137$	3.30574	0.282428	0.141214	+	0.989979i	$0.454899\pi$
$138$	6.06620	0.516390
$139$	2.81623	0.238869	0.119435	−	0.992842i	$-0.461892\pi$
$139$	2.81623	0.238869	0.119435	+	0.992842i	$0.461892\pi$
$140$	0	0
$141$	−6.68619	−0.563079
$142$	−8.00799	−0.672016
$143$	−3.05159	−0.255187
$144$	4.05277	0.337731
$145$	0	0
$146$	1.79320	0.148406
$147$	4.77051	0.393465
$148$	−1.35934	−0.111737
$149$	−5.45554	−0.446935	−0.223467	−	0.974711i	$-0.571738\pi$
$149$	−5.45554	−0.446935	−0.223467	+	0.974711i	$0.571738\pi$
$150$	0	0
$151$	−11.1500	−0.907370	−0.453685	−	0.891162i	$-0.649891\pi$
$151$	−11.1500	−0.907370	−0.453685	+	0.891162i	$0.649891\pi$
$152$	−16.6007	−1.34649
$153$	−1.39241	−0.112570
$154$	0.606727	0.0488915
$155$	0	0
$156$	−1.47282	−0.117920
$157$	8.49438	0.677925	0.338963	−	0.940800i	$-0.389924\pi$
$157$	8.49438	0.677925	0.338963	+	0.940800i	$0.389924\pi$
$158$	−0.506730	−0.0403133
$159$	4.98613	0.395426
$160$	0	0
$161$	−3.69161	−0.290940
$162$	−5.16970	−0.406170
$163$	17.7191	1.38787	0.693935	−	0.720038i	$-0.255876\pi$
$163$	17.7191	1.38787	0.693935	+	0.720038i	$0.255876\pi$
$164$	−2.33227	−0.182119
$165$	0	0
$166$	2.33408	0.181160
$167$	−0.625818	−0.0484272	−0.0242136	−	0.999707i	$-0.507708\pi$
$167$	−0.625818	−0.0484272	−0.0242136	+	0.999707i	$0.507708\pi$
$168$	0.990681	0.0764327
$169$	−6.76497	−0.520382
$170$	0	0
$171$	13.6001	1.04002
$172$	−7.94148	−0.605532
$173$	−16.8880	−1.28397	−0.641987	−	0.766716i	$-0.721890\pi$
$173$	−16.8880	−1.28397	−0.641987	+	0.766716i	$0.721890\pi$
$174$	−2.24805	−0.170424
$175$	0	0
$176$	−1.97638	−0.148975
$177$	−3.77913	−0.284057
$178$	−1.15475	−0.0865518
$179$	1.75907	0.131479	0.0657394	−	0.997837i	$-0.479059\pi$
$179$	1.75907	0.131479	0.0657394	+	0.997837i	$0.479059\pi$
$180$	0	0
$181$	−1.59607	−0.118635	−0.0593174	−	0.998239i	$-0.518892\pi$
$181$	−1.59607	−0.118635	−0.0593174	+	0.998239i	$0.518892\pi$
$182$	−1.23967	−0.0918905
$183$	5.86725	0.433719
$184$	24.5061	1.80661
$185$	0	0
$186$	−1.80729	−0.132517
$187$	0.679026	0.0496553
$188$	−7.98398	−0.582291
$189$	−1.78320	−0.129709
$190$	0	0
$191$	9.82176	0.710677	0.355339	−	0.934738i	$-0.384366\pi$
$191$	9.82176	0.710677	0.355339	+	0.934738i	$0.384366\pi$
$192$	−5.58643	−0.403166
$193$	−7.15693	−0.515167	−0.257583	−	0.966256i	$-0.582926\pi$
$193$	−7.15693	−0.515167	−0.257583	+	0.966256i	$0.582926\pi$
$194$	6.11082	0.438731
$195$	0	0
$196$	5.69647	0.406891
$197$	12.9954	0.925884	0.462942	−	0.886389i	$-0.346794\pi$
$197$	12.9954	0.925884	0.462942	+	0.886389i	$0.346794\pi$
$198$	3.29964	0.234495
$199$	10.8915	0.772080	0.386040	−	0.922482i	$-0.373843\pi$
$199$	10.8915	0.772080	0.386040	+	0.922482i	$0.373843\pi$
$200$	0	0
$201$	5.37525	0.379141
$202$	−17.5012	−1.23138
$203$	1.36806	0.0960188
$204$	0.327726	0.0229454
$205$	0	0
$206$	5.60448	0.390482
$207$	−20.0765	−1.39542
$208$	4.03815	0.279996
$209$	−6.63222	−0.458760
$210$	0	0
$211$	−7.91237	−0.544710	−0.272355	−	0.962197i	$-0.587802\pi$
$211$	−7.91237	−0.544710	−0.272355	+	0.962197i	$0.587802\pi$
$212$	5.95394	0.408918
$213$	−5.22393	−0.357938
$214$	−2.62495	−0.179438
$215$	0	0
$216$	11.8374	0.805436
$217$	1.09983	0.0746615
$218$	−2.47862	−0.167873
$219$	1.16978	0.0790462
$220$	0	0
$221$	−1.38739	−0.0933261
$222$	1.22648	0.0823158
$223$	7.78931	0.521611	0.260805	−	0.965391i	$-0.416012\pi$
$223$	7.78931	0.521611	0.260805	+	0.965391i	$0.416012\pi$
$224$	2.01628	0.134718
$225$	0	0
$226$	−13.6137	−0.905570
$227$	6.27195	0.416284	0.208142	−	0.978099i	$-0.433258\pi$
$227$	6.27195	0.416284	0.208142	+	0.978099i	$0.433258\pi$
$228$	−3.20098	−0.211990
$229$	−16.8653	−1.11449	−0.557245	−	0.830348i	$-0.688142\pi$
$229$	−16.8653	−1.11449	−0.557245	+	0.830348i	$0.688142\pi$
$230$	0	0
$231$	0.395792	0.0260412
$232$	−9.08160	−0.596236
$233$	−4.43705	−0.290681	−0.145341	−	0.989382i	$-0.546428\pi$
$233$	−4.43705	−0.290681	−0.145341	+	0.989382i	$0.546428\pi$
$234$	−6.74185	−0.440729
$235$	0	0
$236$	−4.51266	−0.293749
$237$	−0.330560	−0.0214722
$238$	0.275846	0.0178804
$239$	−10.8864	−0.704182	−0.352091	−	0.935966i	$-0.614529\pi$
$239$	−10.8864	−0.704182	−0.352091	+	0.935966i	$0.614529\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	10.2421	0.658390
$243$	−14.9817	−0.961076
$244$	7.00608	0.448518
$245$	0	0
$246$	2.10431	0.134166
$247$	13.5510	0.862230
$248$	−7.30104	−0.463616
$249$	1.52262	0.0964918
$250$	0	0
$251$	−6.15139	−0.388272	−0.194136	−	0.980975i	$-0.562190\pi$
$251$	−6.15139	−0.388272	−0.194136	+	0.980975i	$0.562190\pi$
$252$	−0.969147	−0.0610505
$253$	9.79055	0.615527
$254$	7.98558	0.501060
$255$	0	0
$256$	−16.0991	−1.00619
$257$	1.50994	0.0941875	0.0470938	−	0.998890i	$-0.485004\pi$
$257$	1.50994	0.0941875	0.0470938	+	0.998890i	$0.485004\pi$
$258$	7.16526	0.446090
$259$	−0.746378	−0.0463777
$260$	0	0
$261$	7.44007	0.460529
$262$	−14.0521	−0.868141
$263$	19.1100	1.17837	0.589187	−	0.807997i	$-0.299448\pi$
$263$	19.1100	1.17837	0.589187	+	0.807997i	$0.299448\pi$
$264$	−2.62739	−0.161705
$265$	0	0
$266$	−2.69426	−0.165196
$267$	−0.753286	−0.0461004
$268$	6.41859	0.392078
$269$	−4.15503	−0.253337	−0.126668	−	0.991945i	$-0.540428\pi$
$269$	−4.15503	−0.253337	−0.126668	+	0.991945i	$0.540428\pi$
$270$	0	0
$271$	−24.2827	−1.47507	−0.737534	−	0.675310i	$-0.764010\pi$
$271$	−24.2827	−1.47507	−0.737534	+	0.675310i	$0.764010\pi$
$272$	−0.898552	−0.0544827
$273$	−0.808686	−0.0489439
$274$	−3.56155	−0.215161
$275$	0	0
$276$	4.72532	0.284431
$277$	−25.8385	−1.55248	−0.776241	−	0.630436i	$-0.782876\pi$
$277$	−25.8385	−1.55248	−0.776241	+	0.630436i	$0.782876\pi$
$278$	−3.03416	−0.181977
$279$	5.98135	0.358094
$280$	0	0
$281$	11.4840	0.685076	0.342538	−	0.939504i	$-0.388713\pi$
$281$	11.4840	0.685076	0.342538	+	0.939504i	$0.388713\pi$
$282$	7.20361	0.428969
$283$	1.00215	0.0595714	0.0297857	−	0.999556i	$-0.490518\pi$
$283$	1.00215	0.0595714	0.0297857	+	0.999556i	$0.490518\pi$
$284$	−6.23790	−0.370151
$285$	0	0
$286$	3.28774	0.194408
$287$	−1.28058	−0.0755905
$288$	10.9654	0.646140
$289$	−16.6913	−0.981840
$290$	0	0
$291$	3.98633	0.233683
$292$	1.39683	0.0817433
$293$	15.0713	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$293$	15.0713	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$294$	−5.13969	−0.299753
$295$	0	0
$296$	4.95469	0.287986
$297$	4.72924	0.274418
$298$	5.87772	0.340487
$299$	−20.0041	−1.15687
$300$	0	0
$301$	−4.36045	−0.251332
$302$	12.0128	0.691259
$303$	−11.4167	−0.655872
$304$	8.77639	0.503360
$305$	0	0
$306$	1.50017	0.0857588
$307$	9.20980	0.525631	0.262816	−	0.964846i	$-0.415349\pi$
$307$	9.20980	0.525631	0.262816	+	0.964846i	$0.415349\pi$
$308$	0.472615	0.0269298
$309$	3.65602	0.207984
$310$	0	0
$311$	−7.46305	−0.423191	−0.211595	−	0.977357i	$-0.567866\pi$
$311$	−7.46305	−0.423191	−0.211595	+	0.977357i	$0.567866\pi$
$312$	5.36831	0.303921
$313$	−21.2995	−1.20392	−0.601960	−	0.798526i	$-0.705613\pi$
$313$	−21.2995	−1.20392	−0.601960	+	0.798526i	$0.705613\pi$
$314$	−9.15172	−0.516462
$315$	0	0
$316$	−0.394722	−0.0222048
$317$	−11.4035	−0.640482	−0.320241	−	0.947336i	$-0.603764\pi$
$317$	−11.4035	−0.640482	−0.320241	+	0.947336i	$0.603764\pi$
$318$	−5.37199	−0.301246
$319$	−3.62824	−0.203142
$320$	0	0
$321$	−1.71236	−0.0955745
$322$	3.97729	0.221646
$323$	−3.01531	−0.167776
$324$	−4.02698	−0.223721
$325$	0	0
$326$	−19.0903	−1.05732
$327$	−1.61690	−0.0894148
$328$	8.50092	0.469385
$329$	−4.38378	−0.241686
$330$	0	0
$331$	1.34559	0.0739602	0.0369801	−	0.999316i	$-0.488226\pi$
$331$	1.34559	0.0739602	0.0369801	+	0.999316i	$0.488226\pi$
$332$	1.81816	0.0997842
$333$	−4.05912	−0.222438
$334$	0.674247	0.0368932
$335$	0	0
$336$	−0.523750	−0.0285729
$337$	−27.4397	−1.49473	−0.747367	−	0.664412i	$-0.768682\pi$
$337$	−27.4397	−1.49473	−0.747367	+	0.664412i	$0.768682\pi$
$338$	7.28848	0.396441
$339$	−8.88076	−0.482336
$340$	0	0
$341$	−2.91687	−0.157958
$342$	−14.6525	−0.792317
$343$	6.35340	0.343051
$344$	28.9460	1.56067
$345$	0	0
$346$	18.1949	0.978166
$347$	−9.14923	−0.491157	−0.245578	−	0.969377i	$-0.578978\pi$
$347$	−9.14923	−0.491157	−0.245578	+	0.969377i	$0.578978\pi$
$348$	−1.75114	−0.0938707
$349$	26.7667	1.43279	0.716395	−	0.697695i	$-0.245791\pi$
$349$	26.7667	1.43279	0.716395	+	0.697695i	$0.245791\pi$
$350$	0	0
$351$	−9.66282	−0.515763
$352$	−5.34738	−0.285016
$353$	−1.78470	−0.0949898	−0.0474949	−	0.998871i	$-0.515124\pi$
$353$	−1.78470	−0.0949898	−0.0474949	+	0.998871i	$0.515124\pi$
$354$	4.07159	0.216402
$355$	0	0
$356$	−0.899499	−0.0476733
$357$	0.179945	0.00952371
$358$	−1.89519	−0.100164
$359$	−15.6688	−0.826970	−0.413485	−	0.910511i	$-0.635689\pi$
$359$	−15.6688	−0.826970	−0.413485	+	0.910511i	$0.635689\pi$
$360$	0	0
$361$	10.4513	0.550069
$362$	1.71958	0.0903791
$363$	6.68135	0.350680
$364$	−0.965652	−0.0506139
$365$	0	0
$366$	−6.32129	−0.330419
$367$	−29.2720	−1.52799	−0.763994	−	0.645224i	$-0.776764\pi$
$367$	−29.2720	−1.52799	−0.763994	+	0.645224i	$0.776764\pi$
$368$	−12.9558	−0.675368
$369$	−6.96435	−0.362550
$370$	0	0
$371$	3.26914	0.169726
$372$	−1.40780	−0.0729912
$373$	−1.67945	−0.0869587	−0.0434794	−	0.999054i	$-0.513844\pi$
$373$	−1.67945	−0.0869587	−0.0434794	+	0.999054i	$0.513844\pi$
$374$	−0.731573	−0.0378287
$375$	0	0
$376$	29.1009	1.50077
$377$	7.41324	0.381801
$378$	1.92120	0.0988156
$379$	−23.5112	−1.20769	−0.603845	−	0.797101i	$-0.706366\pi$
$379$	−23.5112	−1.20769	−0.603845	+	0.797101i	$0.706366\pi$
$380$	0	0
$381$	5.20931	0.266881
$382$	−10.5818	−0.541413
$383$	−14.7778	−0.755111	−0.377555	−	0.925987i	$-0.623235\pi$
$383$	−14.7778	−0.755111	−0.377555	+	0.925987i	$0.623235\pi$
$384$	−0.131744	−0.00672303
$385$	0	0
$386$	7.71077	0.392468
$387$	−23.7140	−1.20545
$388$	4.76008	0.241656
$389$	−13.2289	−0.670734	−0.335367	−	0.942087i	$-0.608860\pi$
$389$	−13.2289	−0.670734	−0.335367	+	0.942087i	$0.608860\pi$
$390$	0	0
$391$	4.45123	0.225109
$392$	−20.7632	−1.04870
$393$	−9.16673	−0.462400
$394$	−14.0011	−0.705364
$395$	0	0
$396$	2.57028	0.129161
$397$	15.8631	0.796146	0.398073	−	0.917354i	$-0.369679\pi$
$397$	15.8631	0.796146	0.398073	+	0.917354i	$0.369679\pi$
$398$	−11.7344	−0.588192
$399$	−1.75757	−0.0879886
$400$	0	0
$401$	−7.70559	−0.384799	−0.192399	−	0.981317i	$-0.561627\pi$
$401$	−7.70559	−0.384799	−0.192399	+	0.981317i	$0.561627\pi$
$402$	−5.79122	−0.288840
$403$	5.95978	0.296878
$404$	−13.6327	−0.678251
$405$	0	0
$406$	−1.47393	−0.0731497
$407$	1.97947	0.0981189
$408$	−1.19453	−0.0591382
$409$	−22.9252	−1.13358	−0.566789	−	0.823863i	$-0.691814\pi$
$409$	−22.9252	−1.13358	−0.566789	+	0.823863i	$0.691814\pi$
$410$	0	0
$411$	−2.32334	−0.114602
$412$	4.36566	0.215080
$413$	−2.47778	−0.121924
$414$	21.6302	1.06307
$415$	0	0
$416$	10.9258	0.535682
$417$	−1.97931	−0.0969270
$418$	7.14546	0.349496
$419$	−8.71804	−0.425904	−0.212952	−	0.977063i	$-0.568308\pi$
$419$	−8.71804	−0.425904	−0.212952	+	0.977063i	$0.568308\pi$
$420$	0	0
$421$	19.5851	0.954520	0.477260	−	0.878762i	$-0.341630\pi$
$421$	19.5851	0.954520	0.477260	+	0.878762i	$0.341630\pi$
$422$	8.52468	0.414975
$423$	−23.8409	−1.15918
$424$	−21.7016	−1.05392
$425$	0	0
$426$	5.62819	0.272687
$427$	3.84685	0.186162
$428$	−2.04473	−0.0988356
$429$	2.14472	0.103548
$430$	0	0
$431$	−14.7084	−0.708478	−0.354239	−	0.935155i	$-0.615260\pi$
$431$	−14.7084	−0.708478	−0.354239	+	0.935155i	$0.615260\pi$
$432$	−6.25818	−0.301097
$433$	17.0327	0.818541	0.409271	−	0.912413i	$-0.365783\pi$
$433$	17.0327	0.818541	0.409271	+	0.912413i	$0.365783\pi$
$434$	−1.18494	−0.0568792
$435$	0	0
$436$	−1.93074	−0.0924658
$437$	−43.4763	−2.07976
$438$	−1.26030	−0.0602195
$439$	−32.4141	−1.54704	−0.773519	−	0.633773i	$-0.781505\pi$
$439$	−32.4141	−1.54704	−0.773519	+	0.633773i	$0.781505\pi$
$440$	0	0
$441$	17.0102	0.810008
$442$	1.49476	0.0710983
$443$	−36.9779	−1.75687	−0.878437	−	0.477858i	$-0.841413\pi$
$443$	−36.9779	−1.75687	−0.878437	+	0.477858i	$0.841413\pi$
$444$	0.955376	0.0453401
$445$	0	0
$446$	−8.39209	−0.397377
$447$	3.83427	0.181355
$448$	−3.66273	−0.173048
$449$	−5.85114	−0.276132	−0.138066	−	0.990423i	$-0.544089\pi$
$449$	−5.85114	−0.276132	−0.138066	+	0.990423i	$0.544089\pi$
$450$	0	0
$451$	3.39624	0.159923
$452$	−10.6045	−0.498794
$453$	7.83643	0.368187
$454$	−6.75732	−0.317137
$455$	0	0
$456$	11.6673	0.546372
$457$	−6.95364	−0.325278	−0.162639	−	0.986686i	$-0.552001\pi$
$457$	−6.95364	−0.325278	−0.162639	+	0.986686i	$0.552001\pi$
$458$	18.1704	0.849048
$459$	2.15013	0.100359
$460$	0	0
$461$	−12.1418	−0.565499	−0.282749	−	0.959194i	$-0.591246\pi$
$461$	−12.1418	−0.565499	−0.282749	+	0.959194i	$0.591246\pi$
$462$	−0.426421	−0.0198389
$463$	−38.6639	−1.79686	−0.898432	−	0.439112i	$-0.855293\pi$
$463$	−38.6639	−1.79686	−0.898432	+	0.439112i	$0.855293\pi$
$464$	4.80123	0.222891
$465$	0	0
$466$	4.78042	0.221449
$467$	−25.5519	−1.18240	−0.591199	−	0.806525i	$-0.701345\pi$
$467$	−25.5519	−1.18240	−0.591199	+	0.806525i	$0.701345\pi$
$468$	−5.25162	−0.242756
$469$	3.52427	0.162736
$470$	0	0
$471$	−5.97003	−0.275084
$472$	16.4483	0.757094
$473$	11.5644	0.531731
$474$	0.356141	0.0163581
$475$	0	0
$476$	0.214873	0.00984867
$477$	17.7790	0.814044
$478$	11.7288	0.536465
$479$	−28.3413	−1.29495	−0.647473	−	0.762088i	$-0.724174\pi$
$479$	−28.3413	−1.29495	−0.647473	+	0.762088i	$0.724174\pi$
$480$	0	0
$481$	−4.04448	−0.184412
$482$	1.07739	0.0490736
$483$	2.59455	0.118056
$484$	7.97820	0.362646
$485$	0	0
$486$	16.1411	0.732174
$487$	29.6524	1.34368	0.671840	−	0.740697i	$-0.265504\pi$
$487$	29.6524	1.34368	0.671840	+	0.740697i	$0.265504\pi$
$488$	−25.5366	−1.15599
$489$	−12.4534	−0.563161
$490$	0	0
$491$	1.38809	0.0626437	0.0313219	−	0.999509i	$-0.490028\pi$
$491$	1.38809	0.0626437	0.0313219	+	0.999509i	$0.490028\pi$
$492$	1.63917	0.0738993
$493$	−1.64956	−0.0742925
$494$	−14.5997	−0.656870
$495$	0	0
$496$	3.85989	0.173314
$497$	−3.42506	−0.153635
$498$	−1.64044	−0.0735101
$499$	−18.0071	−0.806108	−0.403054	−	0.915176i	$-0.632051\pi$
$499$	−18.0071	−0.806108	−0.403054	+	0.915176i	$0.632051\pi$
$500$	0	0
$501$	0.439838	0.0196505
$502$	6.62742	0.295796
$503$	5.96142	0.265806	0.132903	−	0.991129i	$-0.457570\pi$
$503$	5.96142	0.265806	0.132903	+	0.991129i	$0.457570\pi$
$504$	3.53246	0.157348
$505$	0	0
$506$	−10.5482	−0.468925
$507$	4.75456	0.211158
$508$	6.22044	0.275987
$509$	27.9980	1.24099	0.620494	−	0.784211i	$-0.286932\pi$
$509$	27.9980	1.24099	0.620494	+	0.784211i	$0.286932\pi$
$510$	0	0
$511$	0.766961	0.0339284
$512$	16.9700	0.749977
$513$	−21.0009	−0.927210
$514$	−1.62679	−0.0717546
$515$	0	0
$516$	5.58144	0.245709
$517$	11.6263	0.511322
$518$	0.804137	0.0353318
$519$	11.8693	0.521003
$520$	0	0
$521$	−27.0688	−1.18590	−0.592952	−	0.805238i	$-0.702038\pi$
$521$	−27.0688	−1.18590	−0.592952	+	0.805238i	$0.702038\pi$
$522$	−8.01583	−0.350843
$523$	44.4641	1.94428	0.972141	−	0.234399i	$-0.0753121\pi$
$523$	44.4641	1.94428	0.972141	+	0.234399i	$0.0753121\pi$
$524$	−10.9460	−0.478178
$525$	0	0
$526$	−20.5889	−0.897717
$527$	−1.32614	−0.0577678
$528$	1.38904	0.0604503
$529$	41.1802	1.79044
$530$	0	0
$531$	−13.4752	−0.584774
$532$	−2.09872	−0.0909909
$533$	−6.93924	−0.300572
$534$	0.811580	0.0351205
$535$	0	0
$536$	−23.3952	−1.01052
$537$	−1.23631	−0.0533507
$538$	4.47658	0.192999
$539$	−8.29520	−0.357299
$540$	0	0
$541$	−8.99658	−0.386793	−0.193397	−	0.981121i	$-0.561950\pi$
$541$	−8.99658	−0.386793	−0.193397	+	0.981121i	$0.561950\pi$
$542$	26.1618	1.12375
$543$	1.12175	0.0481389
$544$	−2.43116	−0.104235
$545$	0	0
$546$	0.871267	0.0372868
$547$	15.0833	0.644914	0.322457	−	0.946584i	$-0.395491\pi$
$547$	15.0833	0.644914	0.322457	+	0.946584i	$0.395491\pi$
$548$	−2.77430	−0.118512
$549$	20.9208	0.892876
$550$	0	0
$551$	16.1117	0.686381
$552$	−17.2234	−0.733077
$553$	−0.216731	−0.00921633
$554$	27.8380	1.18272
$555$	0	0
$556$	−2.36349	−0.100234
$557$	−5.22927	−0.221571	−0.110786	−	0.993844i	$-0.535337\pi$
$557$	−5.22927	−0.221571	−0.110786	+	0.993844i	$0.535337\pi$
$558$	−6.44423	−0.272806
$559$	−23.6284	−0.999377
$560$	0	0
$561$	−0.477234	−0.0201488
$562$	−12.3727	−0.521910
$563$	14.5860	0.614727	0.307363	−	0.951592i	$-0.400553\pi$
$563$	14.5860	0.614727	0.307363	+	0.951592i	$0.400553\pi$
$564$	5.61131	0.236279
$565$	0	0
$566$	−1.07970	−0.0453831
$567$	−2.21111	−0.0928577
$568$	22.7366	0.954007
$569$	35.7167	1.49732	0.748662	−	0.662952i	$-0.230697\pi$
$569$	35.7167	1.49732	0.748662	+	0.662952i	$0.230697\pi$
$570$	0	0
$571$	−36.3781	−1.52238	−0.761189	−	0.648531i	$-0.775384\pi$
$571$	−36.3781	−1.52238	−0.761189	+	0.648531i	$0.775384\pi$
$572$	2.56101	0.107081
$573$	−6.90294	−0.288375
$574$	1.37968	0.0575869
$575$	0	0
$576$	−19.9195	−0.829977
$577$	−16.3163	−0.679258	−0.339629	−	0.940559i	$-0.610302\pi$
$577$	−16.3163	−0.679258	−0.339629	+	0.940559i	$0.610302\pi$
$578$	17.9830	0.747992
$579$	5.03004	0.209041
$580$	0	0
$581$	0.998299	0.0414164
$582$	−4.29482	−0.178026
$583$	−8.67012	−0.359080
$584$	−5.09133	−0.210681
$585$	0	0
$586$	−16.2376	−0.670770
$587$	3.05068	0.125915	0.0629576	−	0.998016i	$-0.479947\pi$
$587$	3.05068	0.125915	0.0629576	+	0.998016i	$0.479947\pi$
$588$	−4.00360	−0.165106
$589$	12.9528	0.533711
$590$	0	0
$591$	−9.13345	−0.375700
$592$	−2.61943	−0.107658
$593$	11.7951	0.484366	0.242183	−	0.970231i	$-0.422137\pi$
$593$	11.7951	0.484366	0.242183	+	0.970231i	$0.422137\pi$
$594$	−5.09521	−0.209059
$595$	0	0
$596$	4.57850	0.187543
$597$	−7.65480	−0.313290
$598$	21.5522	0.881335
$599$	−6.92638	−0.283004	−0.141502	−	0.989938i	$-0.545193\pi$
$599$	−6.92638	−0.283004	−0.141502	+	0.989938i	$0.545193\pi$
$600$	0	0
$601$	11.7577	0.479606	0.239803	−	0.970822i	$-0.422917\pi$
$601$	11.7577	0.479606	0.239803	+	0.970822i	$0.422917\pi$
$602$	4.69789	0.191472
$603$	19.1665	0.780519
$604$	9.35748	0.380750
$605$	0	0
$606$	12.3002	0.499661
$607$	44.9454	1.82428	0.912140	−	0.409880i	$-0.134429\pi$
$607$	44.9454	1.82428	0.912140	+	0.409880i	$0.134429\pi$
$608$	23.7458	0.963019
$609$	−0.961501	−0.0389620
$610$	0	0
$611$	−23.7549	−0.961020
$612$	1.16857	0.0472365
$613$	21.4977	0.868285	0.434143	−	0.900844i	$-0.357051\pi$
$613$	21.4977	0.868285	0.434143	+	0.900844i	$0.357051\pi$
$614$	−9.92251	−0.400440
$615$	0	0
$616$	−1.72264	−0.0694073
$617$	−27.0065	−1.08724	−0.543619	−	0.839332i	$-0.682947\pi$
$617$	−27.0065	−1.08724	−0.543619	+	0.839332i	$0.682947\pi$
$618$	−3.93895	−0.158448
$619$	−2.32781	−0.0935626	−0.0467813	−	0.998905i	$-0.514896\pi$
$619$	−2.32781	−0.0935626	−0.0467813	+	0.998905i	$0.514896\pi$
$620$	0	0
$621$	31.0017	1.24405
$622$	8.04059	0.322398
$623$	−0.493890	−0.0197873
$624$	−2.83810	−0.113615
$625$	0	0
$626$	22.9478	0.917179
$627$	4.66127	0.186153
$628$	−7.12881	−0.284471
$629$	0.899960	0.0358837
$630$	0	0
$631$	−28.0612	−1.11710	−0.558549	−	0.829471i	$-0.688642\pi$
$631$	−28.0612	−1.11710	−0.558549	+	0.829471i	$0.688642\pi$
$632$	1.43873	0.0572295
$633$	5.56098	0.221029
$634$	12.2859	0.487936
$635$	0	0
$636$	−4.18455	−0.165928
$637$	16.9488	0.671537
$638$	3.90901	0.154759
$639$	−18.6269	−0.736869
$640$	0	0
$641$	−42.9372	−1.69592	−0.847958	−	0.530063i	$-0.822168\pi$
$641$	−42.9372	−1.69592	−0.847958	+	0.530063i	$0.822168\pi$
$642$	1.84487	0.0728112
$643$	28.7393	1.13337	0.566684	−	0.823935i	$-0.308226\pi$
$643$	28.7393	1.13337	0.566684	+	0.823935i	$0.308226\pi$
$644$	3.09815	0.122084
$645$	0	0
$646$	3.24865	0.127817
$647$	−47.4130	−1.86400	−0.931998	−	0.362464i	$-0.881936\pi$
$647$	−47.4130	−1.86400	−0.931998	+	0.362464i	$0.881936\pi$
$648$	14.6780	0.576607
$649$	6.57134	0.257948
$650$	0	0
$651$	−0.772986	−0.0302957
$652$	−14.8706	−0.582377
$653$	−28.4101	−1.11177	−0.555887	−	0.831258i	$-0.687621\pi$
$653$	−28.4101	−1.11177	−0.555887	+	0.831258i	$0.687621\pi$
$654$	1.74203	0.0681186
$655$	0	0
$656$	−4.49424	−0.175470
$657$	4.17106	0.162728
$658$	4.72303	0.184123
$659$	−19.9591	−0.777495	−0.388747	−	0.921344i	$-0.627092\pi$
$659$	−19.9591	−0.777495	−0.388747	+	0.921344i	$0.627092\pi$
$660$	0	0
$661$	−36.9264	−1.43627	−0.718135	−	0.695904i	$-0.755004\pi$
$661$	−36.9264	−1.43627	−0.718135	+	0.695904i	$0.755004\pi$
$662$	−1.44972	−0.0563449
$663$	0.975089	0.0378693
$664$	−6.62702	−0.257178
$665$	0	0
$666$	4.37324	0.169459
$667$	−23.7843	−0.920930
$668$	0.525211	0.0203210
$669$	−5.47449	−0.211656
$670$	0	0
$671$	−10.2022	−0.393853
$672$	−1.41708	−0.0546651
$673$	−25.8122	−0.994989	−0.497494	−	0.867467i	$-0.665746\pi$
$673$	−25.8122	−0.994989	−0.497494	+	0.867467i	$0.665746\pi$
$674$	29.5631	1.13873
$675$	0	0
$676$	5.67743	0.218363
$677$	38.8794	1.49426	0.747128	−	0.664680i	$-0.231432\pi$
$677$	38.8794	1.49426	0.747128	+	0.664680i	$0.231432\pi$
$678$	9.56800	0.367457
$679$	2.61363	0.100302
$680$	0	0
$681$	−4.40806	−0.168917
$682$	3.14260	0.120336
$683$	−27.1846	−1.04019	−0.520096	−	0.854108i	$-0.674104\pi$
$683$	−27.1846	−1.04019	−0.520096	+	0.854108i	$0.674104\pi$
$684$	−11.4137	−0.436414
$685$	0	0
$686$	−6.84506	−0.261346
$687$	11.8533	0.452231
$688$	−15.3031	−0.583425
$689$	17.7149	0.674883
$690$	0	0
$691$	−4.88363	−0.185782	−0.0928911	−	0.995676i	$-0.529611\pi$
$691$	−4.88363	−0.185782	−0.0928911	+	0.995676i	$0.529611\pi$
$692$	14.1731	0.538780
$693$	1.41127	0.0536098
$694$	9.85726	0.374176
$695$	0	0
$696$	6.38274	0.241937
$697$	1.54409	0.0584865
$698$	−28.8381	−1.09154
$699$	3.11846	0.117951
$700$	0	0
$701$	24.2926	0.917519	0.458759	−	0.888561i	$-0.348294\pi$
$701$	24.2926	0.917519	0.458759	+	0.888561i	$0.348294\pi$
$702$	10.4106	0.392922
$703$	−8.79014	−0.331526
$704$	9.71395	0.366108
$705$	0	0
$706$	1.92281	0.0723658
$707$	−7.48533	−0.281515
$708$	3.17160	0.119196
$709$	−10.4894	−0.393939	−0.196969	−	0.980410i	$-0.563110\pi$
$709$	−10.4894	−0.393939	−0.196969	+	0.980410i	$0.563110\pi$
$710$	0	0
$711$	−1.17867	−0.0442037
$712$	3.27860	0.122871
$713$	−19.1211	−0.716089
$714$	−0.193870	−0.00725542
$715$	0	0
$716$	−1.47628	−0.0551711
$717$	7.65119	0.285739
$718$	16.8814	0.630008
$719$	45.9629	1.71413	0.857064	−	0.515210i	$-0.172286\pi$
$719$	45.9629	1.71413	0.857064	+	0.515210i	$0.172286\pi$
$720$	0	0
$721$	2.39706	0.0892713
$722$	−11.2601	−0.419058
$723$	0.702822	0.0261382
$724$	1.33948	0.0497815
$725$	0	0
$726$	−7.19840	−0.267158
$727$	−7.14023	−0.264817	−0.132408	−	0.991195i	$-0.542271\pi$
$727$	−7.14023	−0.264817	−0.132408	+	0.991195i	$0.542271\pi$
$728$	3.51972	0.130450
$729$	−3.86566	−0.143173
$730$	0	0
$731$	5.25769	0.194463
$732$	−4.92402	−0.181997
$733$	−43.2857	−1.59879	−0.799397	−	0.600803i	$-0.794848\pi$
$733$	−43.2857	−1.59879	−0.799397	+	0.600803i	$0.794848\pi$
$734$	31.5373	1.16406
$735$	0	0
$736$	−35.0538	−1.29210
$737$	−9.34675	−0.344292
$738$	7.50330	0.276200
$739$	8.39072	0.308658	0.154329	−	0.988020i	$-0.450678\pi$
$739$	8.39072	0.308658	0.154329	+	0.988020i	$0.450678\pi$
$740$	0	0
$741$	−9.52394	−0.349871
$742$	−3.52213	−0.129301
$743$	−34.4270	−1.26300	−0.631501	−	0.775375i	$-0.717561\pi$
$743$	−34.4270	−1.26300	−0.631501	+	0.775375i	$0.717561\pi$
$744$	5.13133	0.188124
$745$	0	0
$746$	1.80942	0.0662475
$747$	5.42917	0.198643
$748$	−0.569865	−0.0208363
$749$	−1.12270	−0.0410227
$750$	0	0
$751$	−26.8127	−0.978411	−0.489205	−	0.872169i	$-0.662713\pi$
$751$	−26.8127	−0.978411	−0.489205	+	0.872169i	$0.662713\pi$
$752$	−15.3850	−0.561033
$753$	4.32333	0.157551
$754$	−7.98693	−0.290867
$755$	0	0
$756$	1.49653	0.0544283
$757$	12.5597	0.456491	0.228246	−	0.973604i	$-0.426701\pi$
$757$	12.5597	0.456491	0.228246	+	0.973604i	$0.426701\pi$
$758$	25.3307	0.920052
$759$	−6.88101	−0.249765
$760$	0	0
$761$	−32.6735	−1.18441	−0.592207	−	0.805786i	$-0.701743\pi$
$761$	−32.6735	−1.18441	−0.592207	+	0.805786i	$0.701743\pi$
$762$	−5.61244	−0.203317
$763$	−1.06012	−0.0383788
$764$	−8.24280	−0.298214
$765$	0	0
$766$	15.9214	0.575264
$767$	−13.4266	−0.484807
$768$	11.3148	0.408287
$769$	−31.2178	−1.12574	−0.562871	−	0.826545i	$-0.690303\pi$
$769$	−31.2178	−1.12574	−0.562871	+	0.826545i	$0.690303\pi$
$770$	0	0
$771$	−1.06122	−0.0382189
$772$	6.00637	0.216174
$773$	−46.5905	−1.67574	−0.837872	−	0.545867i	$-0.816200\pi$
$773$	−46.5905	−1.67574	−0.837872	+	0.545867i	$0.816200\pi$
$774$	25.5491	0.918343
$775$	0	0
$776$	−17.3501	−0.622832
$777$	0.524571	0.0188189
$778$	14.2527	0.510984
$779$	−15.0815	−0.540351
$780$	0	0
$781$	9.08362	0.325037
$782$	−4.79570	−0.171494
$783$	−11.4888	−0.410575
$784$	10.9770	0.392036
$785$	0	0
$786$	9.87611	0.352269
$787$	29.5132	1.05203	0.526015	−	0.850475i	$-0.323685\pi$
$787$	29.5132	1.05203	0.526015	+	0.850475i	$0.323685\pi$
$788$	−10.9063	−0.388519
$789$	−13.4309	−0.478154
$790$	0	0
$791$	−5.82265	−0.207029
$792$	−9.36846	−0.332894
$793$	20.8453	0.740239
$794$	−17.0907	−0.606525
$795$	0	0
$796$	−9.14060	−0.323980
$797$	14.8791	0.527045	0.263522	−	0.964653i	$-0.415116\pi$
$797$	14.8791	0.527045	0.263522	+	0.964653i	$0.415116\pi$
$798$	1.89358	0.0670321
$799$	5.28583	0.186999
$800$	0	0
$801$	−2.68598	−0.0949045
$802$	8.30190	0.293150
$803$	−2.03406	−0.0717805
$804$	−4.51112	−0.159095
$805$	0	0
$806$	−6.42099	−0.226170
$807$	2.92025	0.102798
$808$	49.6900	1.74809
$809$	−35.7499	−1.25690	−0.628450	−	0.777850i	$-0.716310\pi$
$809$	−35.7499	−1.25690	−0.628450	+	0.777850i	$0.716310\pi$
$810$	0	0
$811$	−16.5503	−0.581160	−0.290580	−	0.956851i	$-0.593848\pi$
$811$	−16.5503	−0.581160	−0.290580	+	0.956851i	$0.593848\pi$
$812$	−1.14813	−0.0402914
$813$	17.0664	0.598545
$814$	−2.13266	−0.0747496
$815$	0	0
$816$	0.631522	0.0221077
$817$	−51.3533	−1.79662
$818$	24.6993	0.863590
$819$	−2.88352	−0.100758
$820$	0	0
$821$	42.7887	1.49334	0.746668	−	0.665197i	$-0.231653\pi$
$821$	42.7887	1.49334	0.746668	+	0.665197i	$0.231653\pi$
$822$	2.50314	0.0873069
$823$	50.4003	1.75684	0.878422	−	0.477887i	$-0.158597\pi$
$823$	50.4003	1.75684	0.878422	+	0.477887i	$0.158597\pi$
$824$	−15.9125	−0.554336
$825$	0	0
$826$	2.66953	0.0928847
$827$	−32.9351	−1.14527	−0.572633	−	0.819812i	$-0.694078\pi$
$827$	−32.9351	−1.14527	−0.572633	+	0.819812i	$0.694078\pi$
$828$	16.8490	0.585544
$829$	2.52667	0.0877549	0.0438775	−	0.999037i	$-0.486029\pi$
$829$	2.52667	0.0877549	0.0438775	+	0.999037i	$0.486029\pi$
$830$	0	0
$831$	18.1598	0.629957
$832$	−19.8476	−0.688093
$833$	−3.77138	−0.130670
$834$	2.13248	0.0738416
$835$	0	0
$836$	5.56602	0.192505
$837$	−9.23625	−0.319252
$838$	9.39269	0.324465
$839$	13.5937	0.469308	0.234654	−	0.972079i	$-0.424604\pi$
$839$	13.5937	0.469308	0.234654	+	0.972079i	$0.424604\pi$
$840$	0	0
$841$	−20.1859	−0.696066
$842$	−21.1007	−0.727179
$843$	−8.07118	−0.277986
$844$	6.64037	0.228571
$845$	0	0
$846$	25.6858	0.883096
$847$	4.38061	0.150520
$848$	11.4731	0.393989
$849$	−0.704329	−0.0241725
$850$	0	0
$851$	12.9761	0.444815
$852$	4.38413	0.150198
$853$	−0.947807	−0.0324523	−0.0162261	−	0.999868i	$-0.505165\pi$
$853$	−0.947807	−0.0324523	−0.0162261	+	0.999868i	$0.505165\pi$
$854$	−4.14454	−0.141823
$855$	0	0
$856$	7.45286	0.254733
$857$	57.8199	1.97509	0.987545	−	0.157337i	$-0.0502908\pi$
$857$	57.8199	1.97509	0.987545	+	0.157337i	$0.0502908\pi$
$858$	−2.31069	−0.0788858
$859$	49.7282	1.69671	0.848353	−	0.529432i	$-0.177595\pi$
$859$	49.7282	1.69671	0.848353	+	0.529432i	$0.177595\pi$
$860$	0	0
$861$	0.900022	0.0306727
$862$	15.8466	0.539737
$863$	−5.20181	−0.177072	−0.0885358	−	0.996073i	$-0.528219\pi$
$863$	−5.20181	−0.177072	−0.0885358	+	0.996073i	$0.528219\pi$
$864$	−16.9324	−0.576052
$865$	0	0
$866$	−18.3508	−0.623587
$867$	11.7310	0.398405
$868$	−0.923023	−0.0313294
$869$	0.574793	0.0194985
$870$	0	0
$871$	19.0974	0.647089
$872$	7.03739	0.238316
$873$	14.2140	0.481071
$874$	46.8408	1.58441
$875$	0	0
$876$	−0.981722	−0.0331693
$877$	23.9152	0.807559	0.403779	−	0.914856i	$-0.367696\pi$
$877$	23.9152	0.807559	0.403779	+	0.914856i	$0.367696\pi$
$878$	34.9224	1.17858
$879$	−10.5924	−0.357274
$880$	0	0
$881$	−19.3879	−0.653196	−0.326598	−	0.945163i	$-0.605902\pi$
$881$	−19.3879	−0.653196	−0.326598	+	0.945163i	$0.605902\pi$
$882$	−18.3265	−0.617086
$883$	22.7998	0.767274	0.383637	−	0.923484i	$-0.374671\pi$
$883$	22.7998	0.767274	0.383637	+	0.923484i	$0.374671\pi$
$884$	1.16435	0.0391614
$885$	0	0
$886$	39.8395	1.33843
$887$	4.87448	0.163669	0.0818346	−	0.996646i	$-0.473922\pi$
$887$	4.87448	0.163669	0.0818346	+	0.996646i	$0.473922\pi$
$888$	−3.48226	−0.116857
$889$	3.41547	0.114551
$890$	0	0
$891$	5.86409	0.196454
$892$	−6.53709	−0.218878
$893$	−51.6281	−1.72767
$894$	−4.13099	−0.138161
$895$	0	0
$896$	−0.0863776	−0.00288567
$897$	14.0593	0.469428
$898$	6.30394	0.210365
$899$	7.08598	0.236331
$900$	0	0
$901$	−3.94183	−0.131321
$902$	−3.65907	−0.121834
$903$	3.06462	0.101984
$904$	38.6526	1.28556
$905$	0	0
$906$	−8.44286	−0.280495
$907$	29.8282	0.990428	0.495214	−	0.868771i	$-0.335090\pi$
$907$	29.8282	0.990428	0.495214	+	0.868771i	$0.335090\pi$
$908$	−5.26367	−0.174681
$909$	−40.7084	−1.35021
$910$	0	0
$911$	−7.78416	−0.257901	−0.128950	−	0.991651i	$-0.541161\pi$
$911$	−7.78416	−0.257901	−0.128950	+	0.991651i	$0.541161\pi$
$912$	−6.16824	−0.204251
$913$	−2.64760	−0.0876227
$914$	7.49176	0.247805
$915$	0	0
$916$	14.1540	0.467662
$917$	−6.01014	−0.198472
$918$	−2.31652	−0.0764565
$919$	45.9452	1.51559	0.757796	−	0.652492i	$-0.226276\pi$
$919$	45.9452	1.51559	0.757796	+	0.652492i	$0.226276\pi$
$920$	0	0
$921$	−6.47285	−0.213288
$922$	13.0814	0.430812
$923$	−18.5597	−0.610901
$924$	−0.332164	−0.0109274
$925$	0	0
$926$	41.6560	1.36890
$927$	13.0362	0.428166
$928$	12.9904	0.426431
$929$	22.5013	0.738245	0.369122	−	0.929381i	$-0.379658\pi$
$929$	22.5013	0.738245	0.369122	+	0.929381i	$0.379658\pi$
$930$	0	0
$931$	36.8360	1.20725
$932$	3.72375	0.121975
$933$	5.24519	0.171720
$934$	27.5292	0.900783
$935$	0	0
$936$	19.1417	0.625667
$937$	−23.7197	−0.774888	−0.387444	−	0.921893i	$-0.626642\pi$
$937$	−23.7197	−0.774888	−0.387444	+	0.921893i	$0.626642\pi$
$938$	−3.79700	−0.123977
$939$	14.9698	0.488520
$940$	0	0
$941$	26.8871	0.876495	0.438248	−	0.898854i	$-0.355599\pi$
$941$	26.8871	0.876495	0.438248	+	0.898854i	$0.355599\pi$
$942$	6.43203	0.209567
$943$	22.2635	0.724999
$944$	−8.69583	−0.283025
$945$	0	0
$946$	−12.4593	−0.405087
$947$	6.59383	0.214271	0.107135	−	0.994244i	$-0.465832\pi$
$947$	6.59383	0.214271	0.107135	+	0.994244i	$0.465832\pi$
$948$	0.277419	0.00901014
$949$	4.15602	0.134910
$950$	0	0
$951$	8.01459	0.259891
$952$	−0.783193	−0.0253834
$953$	−9.53300	−0.308804	−0.154402	−	0.988008i	$-0.549345\pi$
$953$	−9.53300	−0.308804	−0.154402	+	0.988008i	$0.549345\pi$
$954$	−19.1548	−0.620160
$955$	0	0
$956$	9.13629	0.295489
$957$	2.55000	0.0824298
$958$	30.5345	0.986525
$959$	−1.52329	−0.0491897
$960$	0	0
$961$	−25.3033	−0.816236
$962$	4.35747	0.140490
$963$	−6.10573	−0.196754
$964$	0.839239	0.0270301
$965$	0	0
$966$	−2.79533	−0.0899382
$967$	−2.15538	−0.0693122	−0.0346561	−	0.999399i	$-0.511034\pi$
$967$	−2.15538	−0.0693122	−0.0346561	+	0.999399i	$0.511034\pi$
$968$	−29.0799	−0.934663
$969$	2.11923	0.0680793
$970$	0	0
$971$	−28.8291	−0.925170	−0.462585	−	0.886575i	$-0.653078\pi$
$971$	−28.8291	−0.925170	−0.462585	+	0.886575i	$0.653078\pi$
$972$	12.5732	0.403286
$973$	−1.29773	−0.0416032
$974$	−31.9471	−1.02365
$975$	0	0
$976$	13.5006	0.432143
$977$	14.6389	0.468340	0.234170	−	0.972196i	$-0.424763\pi$
$977$	14.6389	0.468340	0.234170	+	0.972196i	$0.424763\pi$
$978$	13.4171	0.429032
$979$	1.30985	0.0418630
$980$	0	0
$981$	−5.76536	−0.184074
$982$	−1.49551	−0.0477237
$983$	−34.7287	−1.10767	−0.553837	−	0.832625i	$-0.686837\pi$
$983$	−34.7287	−1.10767	−0.553837	+	0.832625i	$0.686837\pi$
$984$	−5.97463	−0.190464
$985$	0	0
$986$	1.77722	0.0565981
$987$	3.08102	0.0980699
$988$	−11.3725	−0.361809
$989$	75.8082	2.41056
$990$	0	0
$991$	−4.52756	−0.143823	−0.0719114	−	0.997411i	$-0.522910\pi$
$991$	−4.52756	−0.143823	−0.0719114	+	0.997411i	$0.522910\pi$
$992$	10.4435	0.331581
$993$	−0.945709	−0.0300112
$994$	3.69011	0.117043
$995$	0	0
$996$	−1.27784	−0.0404899
$997$	47.4762	1.50359	0.751793	−	0.659399i	$-0.229189\pi$
$997$	47.4762	1.50359	0.751793	+	0.659399i	$0.229189\pi$
$998$	19.4006	0.614115
$999$	6.26798	0.198310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.i.1.6		15
5.4	even	2		1205.2.a.c.1.10	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.10	✓	15	5.4	even	2
6025.2.a.i.1.6		15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.07739 q^{2} -0.702822 q^{3} -0.839239 q^{4} +0.757210 q^{6} -0.460803 q^{7} +3.05896 q^{8} -2.50604 q^{9} +O(q^{10})\)	\(q-1.07739 q^{2} -0.702822 q^{3} -0.839239 q^{4} +0.757210 q^{6} -0.460803 q^{7} +3.05896 q^{8} -2.50604 q^{9} +1.22210 q^{11} +0.589835 q^{12} -2.49700 q^{13} +0.496463 q^{14} -1.61720 q^{16} +0.555622 q^{17} +2.69997 q^{18} -5.42691 q^{19} +0.323862 q^{21} -1.31667 q^{22} +8.01126 q^{23} -2.14990 q^{24} +2.69024 q^{26} +3.86976 q^{27} +0.386724 q^{28} -2.96885 q^{29} -2.38677 q^{31} -4.37557 q^{32} -0.858918 q^{33} -0.598620 q^{34} +2.10317 q^{36} +1.61973 q^{37} +5.84687 q^{38} +1.75495 q^{39} +2.77902 q^{41} -0.348925 q^{42} +9.46271 q^{43} -1.02563 q^{44} -8.63122 q^{46} +9.51335 q^{47} +1.13660 q^{48} -6.78766 q^{49} -0.390503 q^{51} +2.09558 q^{52} -7.09445 q^{53} -4.16923 q^{54} -1.40958 q^{56} +3.81415 q^{57} +3.19860 q^{58} +5.37709 q^{59} -8.34813 q^{61} +2.57148 q^{62} +1.15479 q^{63} +7.94857 q^{64} +0.925386 q^{66} -7.64811 q^{67} -0.466300 q^{68} -5.63048 q^{69} +7.43280 q^{71} -7.66587 q^{72} -1.66440 q^{73} -1.74508 q^{74} +4.55447 q^{76} -0.563147 q^{77} -1.89076 q^{78} +0.470333 q^{79} +4.79837 q^{81} -2.99408 q^{82} -2.16643 q^{83} -0.271798 q^{84} -10.1950 q^{86} +2.08657 q^{87} +3.73835 q^{88} +1.07180 q^{89} +1.15063 q^{91} -6.72336 q^{92} +1.67748 q^{93} -10.2496 q^{94} +3.07524 q^{96} -5.67189 q^{97} +7.31293 q^{98} -3.06263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Introduction

L-functions

Modular forms

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Database

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