LMFDB - Embedded newform 6025.2.a.g.1.8

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:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 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			1.8
Root			$0.745266$ 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)

$f(q)$	$=$	$q+1.59654 q^{2} +1.29420 q^{3} +0.548929 q^{4} +2.06623 q^{6} +2.14214 q^{7} -2.31669 q^{8} -1.32506 q^{9} +O(q^{10})$	\(q+1.59654 q^{2} +1.29420 q^{3} +0.548929 q^{4} +2.06623 q^{6} +2.14214 q^{7} -2.31669 q^{8} -1.32506 q^{9} +1.42476 q^{11} +0.710421 q^{12} +0.111301 q^{13} +3.42000 q^{14} -4.79653 q^{16} +0.0188326 q^{17} -2.11551 q^{18} +5.78509 q^{19} +2.77235 q^{21} +2.27468 q^{22} +6.68839 q^{23} -2.99825 q^{24} +0.177695 q^{26} -5.59747 q^{27} +1.17588 q^{28} -2.60024 q^{29} +7.75666 q^{31} -3.02447 q^{32} +1.84392 q^{33} +0.0300670 q^{34} -0.727363 q^{36} +6.16382 q^{37} +9.23610 q^{38} +0.144045 q^{39} +4.60331 q^{41} +4.42615 q^{42} -5.99336 q^{43} +0.782091 q^{44} +10.6783 q^{46} +7.28654 q^{47} -6.20765 q^{48} -2.41124 q^{49} +0.0243731 q^{51} +0.0610961 q^{52} -13.1223 q^{53} -8.93657 q^{54} -4.96267 q^{56} +7.48703 q^{57} -4.15139 q^{58} -5.37653 q^{59} +1.14718 q^{61} +12.3838 q^{62} -2.83846 q^{63} +4.76440 q^{64} +2.94388 q^{66} +8.04527 q^{67} +0.0103378 q^{68} +8.65608 q^{69} +0.347891 q^{71} +3.06975 q^{72} +8.73948 q^{73} +9.84077 q^{74} +3.17560 q^{76} +3.05203 q^{77} +0.229972 q^{78} -16.1513 q^{79} -3.26904 q^{81} +7.34935 q^{82} +9.99707 q^{83} +1.52182 q^{84} -9.56861 q^{86} -3.36522 q^{87} -3.30072 q^{88} +14.5153 q^{89} +0.238421 q^{91} +3.67145 q^{92} +10.0386 q^{93} +11.6332 q^{94} -3.91425 q^{96} +8.41148 q^{97} -3.84963 q^{98} -1.88789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * 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 $

$2$	1.59654	1.12892	0.564461	−	0.825460i	$-0.309084\pi$
$2$	1.59654	1.12892	0.564461	+	0.825460i	$0.309084\pi$
$3$	1.29420	0.747204	0.373602	−	0.927589i	$-0.378123\pi$
$3$	1.29420	0.747204	0.373602	+	0.927589i	$0.378123\pi$
$4$	0.548929	0.274464
$5$	0	0
$5$	0	0
$6$	2.06623	0.843535
$7$	2.14214	0.809653	0.404826	−	0.914394i	$-0.367332\pi$
$7$	2.14214	0.809653	0.404826	+	0.914394i	$0.367332\pi$
$8$	−2.31669	−0.819073
$9$	−1.32506	−0.441686
$10$	0	0
$11$	1.42476	0.429581	0.214790	−	0.976660i	$-0.431093\pi$
$11$	1.42476	0.429581	0.214790	+	0.976660i	$0.431093\pi$
$12$	0.710421	0.205081
$13$	0.111301	0.0308692	0.0154346	−	0.999881i	$-0.495087\pi$
$13$	0.111301	0.0308692	0.0154346	+	0.999881i	$0.495087\pi$
$14$	3.42000	0.914035
$15$	0	0
$16$	−4.79653	−1.19913
$17$	0.0188326	0.00456758	0.00228379	−	0.999997i	$-0.499273\pi$
$17$	0.0188326	0.00456758	0.00228379	+	0.999997i	$0.499273\pi$
$18$	−2.11551	−0.498629
$19$	5.78509	1.32719	0.663595	−	0.748092i	$-0.269030\pi$
$19$	5.78509	1.32719	0.663595	+	0.748092i	$0.269030\pi$
$20$	0	0
$21$	2.77235	0.604976
$22$	2.27468	0.484963
$23$	6.68839	1.39463	0.697313	−	0.716767i	$-0.254379\pi$
$23$	6.68839	1.39463	0.697313	+	0.716767i	$0.254379\pi$
$24$	−2.99825	−0.612014
$25$	0	0
$26$	0.177695	0.0348489
$27$	−5.59747	−1.07723
$28$	1.17588	0.222221
$29$	−2.60024	−0.482853	−0.241427	−	0.970419i	$-0.577615\pi$
$29$	−2.60024	−0.482853	−0.241427	+	0.970419i	$0.577615\pi$
$30$	0	0
$31$	7.75666	1.39314	0.696568	−	0.717490i	$-0.254709\pi$
$31$	7.75666	1.39314	0.696568	+	0.717490i	$0.254709\pi$
$32$	−3.02447	−0.534655
$33$	1.84392	0.320984
$34$	0.0300670	0.00515644
$35$	0	0
$36$	−0.727363	−0.121227
$37$	6.16382	1.01333	0.506663	−	0.862144i	$-0.330879\pi$
$37$	6.16382	1.01333	0.506663	+	0.862144i	$0.330879\pi$
$38$	9.23610	1.49829
$39$	0.144045	0.0230656
$40$	0	0
$41$	4.60331	0.718916	0.359458	−	0.933161i	$-0.382962\pi$
$41$	4.60331	0.718916	0.359458	+	0.933161i	$0.382962\pi$
$42$	4.42615	0.682970
$43$	−5.99336	−0.913978	−0.456989	−	0.889472i	$-0.651072\pi$
$43$	−5.99336	−0.913978	−0.456989	+	0.889472i	$0.651072\pi$
$44$	0.782091	0.117905
$45$	0	0
$46$	10.6783	1.57442
$47$	7.28654	1.06285	0.531425	−	0.847105i	$-0.321657\pi$
$47$	7.28654	1.06285	0.531425	+	0.847105i	$0.321657\pi$
$48$	−6.20765	−0.895997
$49$	−2.41124	−0.344462
$50$	0	0
$51$	0.0243731	0.00341291
$52$	0.0610961	0.00847250
$53$	−13.1223	−1.80248	−0.901241	−	0.433318i	$-0.857343\pi$
$53$	−13.1223	−1.80248	−0.901241	+	0.433318i	$0.857343\pi$
$54$	−8.93657	−1.21611
$55$	0	0
$56$	−4.96267	−0.663165
$57$	7.48703	0.991682
$58$	−4.15139	−0.545104
$59$	−5.37653	−0.699965	−0.349982	−	0.936756i	$-0.613812\pi$
$59$	−5.37653	−0.699965	−0.349982	+	0.936756i	$0.613812\pi$
$60$	0	0
$61$	1.14718	0.146881	0.0734406	−	0.997300i	$-0.476602\pi$
$61$	1.14718	0.146881	0.0734406	+	0.997300i	$0.476602\pi$
$62$	12.3838	1.57274
$63$	−2.83846	−0.357613
$64$	4.76440	0.595550
$65$	0	0
$66$	2.94388	0.362366
$67$	8.04527	0.982886	0.491443	−	0.870910i	$-0.336470\pi$
$67$	8.04527	0.982886	0.491443	+	0.870910i	$0.336470\pi$
$68$	0.0103378	0.00125364
$69$	8.65608	1.04207
$70$	0	0
$71$	0.347891	0.0412871	0.0206435	−	0.999787i	$-0.493428\pi$
$71$	0.347891	0.0412871	0.0206435	+	0.999787i	$0.493428\pi$
$72$	3.06975	0.361773
$73$	8.73948	1.02288	0.511439	−	0.859319i	$-0.329112\pi$
$73$	8.73948	1.02288	0.511439	+	0.859319i	$0.329112\pi$
$74$	9.84077	1.14397
$75$	0	0
$76$	3.17560	0.364267
$77$	3.05203	0.347811
$78$	0.229972	0.0260393
$79$	−16.1513	−1.81717	−0.908584	−	0.417702i	$-0.862836\pi$
$79$	−16.1513	−1.81717	−0.908584	+	0.417702i	$0.862836\pi$
$80$	0	0
$81$	−3.26904	−0.363227
$82$	7.34935	0.811599
$83$	9.99707	1.09732	0.548661	−	0.836045i	$-0.315138\pi$
$83$	9.99707	1.09732	0.548661	+	0.836045i	$0.315138\pi$
$84$	1.52182	0.166044
$85$	0	0
$86$	−9.56861	−1.03181
$87$	−3.36522	−0.360790
$88$	−3.30072	−0.351858
$89$	14.5153	1.53862	0.769311	−	0.638875i	$-0.220600\pi$
$89$	14.5153	1.53862	0.769311	+	0.638875i	$0.220600\pi$
$90$	0	0
$91$	0.238421	0.0249933
$92$	3.67145	0.382775
$93$	10.0386	1.04096
$94$	11.6332	1.19988
$95$	0	0
$96$	−3.91425	−0.399497
$97$	8.41148	0.854056	0.427028	−	0.904238i	$-0.359561\pi$
$97$	8.41148	0.854056	0.427028	+	0.904238i	$0.359561\pi$
$98$	−3.84963	−0.388871
$99$	−1.88789	−0.189740
$100$	0	0
$101$	−0.127620	−0.0126987	−0.00634934	−	0.999980i	$-0.502021\pi$
$101$	−0.127620	−0.0126987	−0.00634934	+	0.999980i	$0.502021\pi$
$102$	0.0389125	0.00385291
$103$	10.7340	1.05766	0.528829	−	0.848729i	$-0.322631\pi$
$103$	10.7340	1.05766	0.528829	+	0.848729i	$0.322631\pi$
$104$	−0.257849	−0.0252841
$105$	0	0
$106$	−20.9502	−2.03486
$107$	19.9601	1.92961	0.964807	−	0.262959i	$-0.0846985\pi$
$107$	19.9601	1.92961	0.964807	+	0.262959i	$0.0846985\pi$
$108$	−3.07261	−0.295662
$109$	−1.37900	−0.132084	−0.0660422	−	0.997817i	$-0.521037\pi$
$109$	−1.37900	−0.132084	−0.0660422	+	0.997817i	$0.521037\pi$
$110$	0	0
$111$	7.97719	0.757161
$112$	−10.2748	−0.970882
$113$	10.2805	0.967106	0.483553	−	0.875315i	$-0.339346\pi$
$113$	10.2805	0.967106	0.483553	+	0.875315i	$0.339346\pi$
$114$	11.9533	1.11953
$115$	0	0
$116$	−1.42735	−0.132526
$117$	−0.147480	−0.0136345
$118$	−8.58383	−0.790206
$119$	0.0403421	0.00369815
$120$	0	0
$121$	−8.97006	−0.815460
$122$	1.83151	0.165817
$123$	5.95758	0.537176
$124$	4.25785	0.382367
$125$	0	0
$126$	−4.53171	−0.403717
$127$	18.6746	1.65710	0.828550	−	0.559915i	$-0.189166\pi$
$127$	18.6746	1.65710	0.828550	+	0.559915i	$0.189166\pi$
$128$	13.6555	1.20698
$129$	−7.75657	−0.682928
$130$	0	0
$131$	3.33201	0.291119	0.145560	−	0.989349i	$-0.453502\pi$
$131$	3.33201	0.291119	0.145560	+	0.989349i	$0.453502\pi$
$132$	1.01218	0.0880988
$133$	12.3925	1.07456
$134$	12.8446	1.10960
$135$	0	0
$136$	−0.0436293	−0.00374118
$137$	−3.69822	−0.315960	−0.157980	−	0.987442i	$-0.550498\pi$
$137$	−3.69822	−0.315960	−0.157980	+	0.987442i	$0.550498\pi$
$138$	13.8197	1.17641
$139$	−18.8705	−1.60057	−0.800287	−	0.599617i	$-0.795320\pi$
$139$	−18.8705	−1.60057	−0.800287	+	0.599617i	$0.795320\pi$
$140$	0	0
$141$	9.43020	0.794166
$142$	0.555421	0.0466099
$143$	0.158576	0.0132608
$144$	6.35569	0.529641
$145$	0	0
$146$	13.9529	1.15475
$147$	−3.12061	−0.257384
$148$	3.38350	0.278122
$149$	22.5225	1.84512	0.922558	−	0.385860i	$-0.126095\pi$
$149$	22.5225	1.84512	0.922558	+	0.385860i	$0.126095\pi$
$150$	0	0
$151$	−12.2564	−0.997410	−0.498705	−	0.866772i	$-0.666191\pi$
$151$	−12.2564	−0.997410	−0.498705	+	0.866772i	$0.666191\pi$
$152$	−13.4022	−1.08707
$153$	−0.0249543	−0.00201744
$154$	4.87268	0.392652
$155$	0	0
$156$	0.0790703	0.00633069
$157$	−3.23759	−0.258388	−0.129194	−	0.991619i	$-0.541239\pi$
$157$	−3.23759	−0.258388	−0.129194	+	0.991619i	$0.541239\pi$
$158$	−25.7862	−2.05144
$159$	−16.9828	−1.34682
$160$	0	0
$161$	14.3275	1.12916
$162$	−5.21914	−0.410055
$163$	−13.9358	−1.09154	−0.545770	−	0.837935i	$-0.683763\pi$
$163$	−13.9358	−1.09154	−0.545770	+	0.837935i	$0.683763\pi$
$164$	2.52689	0.197317
$165$	0	0
$166$	15.9607	1.23879
$167$	23.9794	1.85558	0.927790	−	0.373103i	$-0.121706\pi$
$167$	23.9794	1.85558	0.927790	+	0.373103i	$0.121706\pi$
$168$	−6.42266	−0.495519
$169$	−12.9876	−0.999047
$170$	0	0
$171$	−7.66558	−0.586202
$172$	−3.28993	−0.250855
$173$	−23.3451	−1.77490	−0.887449	−	0.460906i	$-0.847524\pi$
$173$	−23.3451	−1.77490	−0.887449	+	0.460906i	$0.847524\pi$
$174$	−5.37270	−0.407304
$175$	0	0
$176$	−6.83390	−0.515125
$177$	−6.95828	−0.523016
$178$	23.1742	1.73698
$179$	−16.8957	−1.26284	−0.631421	−	0.775440i	$-0.717528\pi$
$179$	−16.8957	−1.26284	−0.631421	+	0.775440i	$0.717528\pi$
$180$	0	0
$181$	17.4111	1.29415	0.647077	−	0.762425i	$-0.275991\pi$
$181$	17.4111	1.29415	0.647077	+	0.762425i	$0.275991\pi$
$182$	0.380648	0.0282155
$183$	1.48467	0.109750
$184$	−15.4949	−1.14230
$185$	0	0
$186$	16.0270	1.17516
$187$	0.0268319	0.00196215
$188$	3.99979	0.291715
$189$	−11.9906	−0.872185
$190$	0	0
$191$	−10.8329	−0.783840	−0.391920	−	0.919999i	$-0.628189\pi$
$191$	−10.8329	−0.783840	−0.391920	+	0.919999i	$0.628189\pi$
$192$	6.16606	0.444997
$193$	22.5203	1.62105	0.810523	−	0.585706i	$-0.199183\pi$
$193$	22.5203	1.62105	0.810523	+	0.585706i	$0.199183\pi$
$194$	13.4292	0.964163
$195$	0	0
$196$	−1.32360	−0.0945427
$197$	−14.5353	−1.03560	−0.517800	−	0.855502i	$-0.673249\pi$
$197$	−14.5353	−1.03560	−0.517800	+	0.855502i	$0.673249\pi$
$198$	−3.01408	−0.214202
$199$	18.7813	1.33137	0.665684	−	0.746234i	$-0.268140\pi$
$199$	18.7813	1.33137	0.665684	+	0.746234i	$0.268140\pi$
$200$	0	0
$201$	10.4121	0.734416
$202$	−0.203750	−0.0143358
$203$	−5.57009	−0.390943
$204$	0.0133791	0.000936724 0
$205$	0	0
$206$	17.1373	1.19401
$207$	−8.86251	−0.615987
$208$	−0.533857	−0.0370163
$209$	8.24235	0.570136
$210$	0	0
$211$	−17.9385	−1.23494	−0.617470	−	0.786594i	$-0.711842\pi$
$211$	−17.9385	−1.23494	−0.617470	+	0.786594i	$0.711842\pi$
$212$	−7.20319	−0.494717
$213$	0.450239	0.0308499
$214$	31.8670	2.17838
$215$	0	0
$216$	12.9676	0.882333
$217$	16.6158	1.12796
$218$	−2.20163	−0.149113
$219$	11.3106	0.764299
$220$	0	0
$221$	0.00209608	0.000140998 0
$222$	12.7359	0.854776
$223$	−11.1117	−0.744092	−0.372046	−	0.928214i	$-0.621344\pi$
$223$	−11.1117	−0.744092	−0.372046	+	0.928214i	$0.621344\pi$
$224$	−6.47883	−0.432885
$225$	0	0
$226$	16.4132	1.09179
$227$	−10.8474	−0.719966	−0.359983	−	0.932959i	$-0.617218\pi$
$227$	−10.8474	−0.719966	−0.359983	+	0.932959i	$0.617218\pi$
$228$	4.10985	0.272181
$229$	6.05485	0.400115	0.200058	−	0.979784i	$-0.435887\pi$
$229$	6.05485	0.400115	0.200058	+	0.979784i	$0.435887\pi$
$230$	0	0
$231$	3.94992	0.259886
$232$	6.02396	0.395492
$233$	−0.0414841	−0.00271771	−0.00135886	−	0.999999i	$-0.500433\pi$
$233$	−0.0414841	−0.00271771	−0.00135886	+	0.999999i	$0.500433\pi$
$234$	−0.235457	−0.0153923
$235$	0	0
$236$	−2.95133	−0.192115
$237$	−20.9030	−1.35779
$238$	0.0644076	0.00417493
$239$	−0.199868	−0.0129284	−0.00646421	−	0.999979i	$-0.502058\pi$
$239$	−0.199868	−0.0129284	−0.00646421	+	0.999979i	$0.502058\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−14.3210	−0.920591
$243$	12.5616	0.805829
$244$	0.629719	0.0403136
$245$	0	0
$246$	9.51149	0.606430
$247$	0.643883	0.0409693
$248$	−17.9698	−1.14108
$249$	12.9382	0.819922
$250$	0	0
$251$	9.05030	0.571250	0.285625	−	0.958342i	$-0.407799\pi$
$251$	9.05030	0.571250	0.285625	+	0.958342i	$0.407799\pi$
$252$	−1.55811	−0.0981520
$253$	9.52934	0.599104
$254$	29.8146	1.87074
$255$	0	0
$256$	12.2727	0.767041
$257$	1.14423	0.0713750	0.0356875	−	0.999363i	$-0.488638\pi$
$257$	1.14423	0.0713750	0.0356875	+	0.999363i	$0.488638\pi$
$258$	−12.3836	−0.770972
$259$	13.2038	0.820442
$260$	0	0
$261$	3.44548	0.213270
$262$	5.31968	0.328651
$263$	−25.4711	−1.57061	−0.785307	−	0.619106i	$-0.787495\pi$
$263$	−25.4711	−1.57061	−0.785307	+	0.619106i	$0.787495\pi$
$264$	−4.27178	−0.262910
$265$	0	0
$266$	19.7850	1.21310
$267$	18.7857	1.14966
$268$	4.41628	0.269767
$269$	1.04254	0.0635647	0.0317823	−	0.999495i	$-0.489882\pi$
$269$	1.04254	0.0635647	0.0317823	+	0.999495i	$0.489882\pi$
$270$	0	0
$271$	−26.7577	−1.62542	−0.812708	−	0.582671i	$-0.802007\pi$
$271$	−26.7577	−1.62542	−0.812708	+	0.582671i	$0.802007\pi$
$272$	−0.0903313	−0.00547714
$273$	0.308564	0.0186751
$274$	−5.90434	−0.356694
$275$	0	0
$276$	4.75157	0.286011
$277$	−12.3217	−0.740337	−0.370168	−	0.928965i	$-0.620700\pi$
$277$	−12.3217	−0.740337	−0.370168	+	0.928965i	$0.620700\pi$
$278$	−30.1274	−1.80692
$279$	−10.2780	−0.615330
$280$	0	0
$281$	−26.9203	−1.60593	−0.802966	−	0.596024i	$-0.796746\pi$
$281$	−26.9203	−1.60593	−0.802966	+	0.596024i	$0.796746\pi$
$282$	15.0557	0.896552
$283$	−26.0464	−1.54830	−0.774149	−	0.633004i	$-0.781822\pi$
$283$	−26.0464	−1.54830	−0.774149	+	0.633004i	$0.781822\pi$
$284$	0.190968	0.0113318
$285$	0	0
$286$	0.253173	0.0149704
$287$	9.86092	0.582072
$288$	4.00760	0.236150
$289$	−16.9996	−0.999979
$290$	0	0
$291$	10.8861	0.638154
$292$	4.79735	0.280744
$293$	1.70503	0.0996092	0.0498046	−	0.998759i	$-0.484140\pi$
$293$	1.70503	0.0996092	0.0498046	+	0.998759i	$0.484140\pi$
$294$	−4.98217	−0.290566
$295$	0	0
$296$	−14.2797	−0.829988
$297$	−7.97504	−0.462759
$298$	35.9580	2.08299
$299$	0.744421	0.0430510
$300$	0	0
$301$	−12.8386	−0.740005
$302$	−19.5677	−1.12600
$303$	−0.165165	−0.00948851
$304$	−27.7484	−1.59148
$305$	0	0
$306$	−0.0398405	−0.00227753
$307$	2.87893	0.164309	0.0821547	−	0.996620i	$-0.473820\pi$
$307$	2.87893	0.164309	0.0821547	+	0.996620i	$0.473820\pi$
$308$	1.67535	0.0954618
$309$	13.8920	0.790286
$310$	0	0
$311$	30.4572	1.72707	0.863533	−	0.504292i	$-0.168246\pi$
$311$	30.4572	1.72707	0.863533	+	0.504292i	$0.168246\pi$
$312$	−0.333706	−0.0188924
$313$	−3.87498	−0.219027	−0.109513	−	0.993985i	$-0.534929\pi$
$313$	−3.87498	−0.219027	−0.109513	+	0.993985i	$0.534929\pi$
$314$	−5.16893	−0.291699
$315$	0	0
$316$	−8.86594	−0.498748
$317$	3.54986	0.199380	0.0996900	−	0.995019i	$-0.468215\pi$
$317$	3.54986	0.199380	0.0996900	+	0.995019i	$0.468215\pi$
$318$	−27.1136	−1.52046
$319$	−3.70472	−0.207425
$320$	0	0
$321$	25.8322	1.44181
$322$	22.8743	1.27474
$323$	0.108948	0.00606205
$324$	−1.79447	−0.0996928
$325$	0	0
$326$	−22.2491	−1.23226
$327$	−1.78470	−0.0986940
$328$	−10.6644	−0.588844
$329$	15.6088	0.860540
$330$	0	0
$331$	−28.9142	−1.58927	−0.794633	−	0.607090i	$-0.792337\pi$
$331$	−28.9142	−1.58927	−0.794633	+	0.607090i	$0.792337\pi$
$332$	5.48768	0.301176
$333$	−8.16743	−0.447572
$334$	38.2840	2.09480
$335$	0	0
$336$	−13.2977	−0.725447
$337$	12.8081	0.697703	0.348851	−	0.937178i	$-0.386572\pi$
$337$	12.8081	0.697703	0.348851	+	0.937178i	$0.386572\pi$
$338$	−20.7352	−1.12785
$339$	13.3049	0.722626
$340$	0	0
$341$	11.0514	0.598465
$342$	−12.2384	−0.661776
$343$	−20.1602	−1.08855
$344$	13.8847	0.748615
$345$	0	0
$346$	−37.2714	−2.00372
$347$	7.53133	0.404303	0.202151	−	0.979354i	$-0.435207\pi$
$347$	7.53133	0.404303	0.202151	+	0.979354i	$0.435207\pi$
$348$	−1.84727	−0.0990240
$349$	8.77815	0.469884	0.234942	−	0.972009i	$-0.424510\pi$
$349$	8.77815	0.469884	0.234942	+	0.972009i	$0.424510\pi$
$350$	0	0
$351$	−0.623001	−0.0332534
$352$	−4.30914	−0.229678
$353$	8.53462	0.454252	0.227126	−	0.973865i	$-0.427067\pi$
$353$	8.53462	0.454252	0.227126	+	0.973865i	$0.427067\pi$
$354$	−11.1092	−0.590445
$355$	0	0
$356$	7.96788	0.422297
$357$	0.0522105	0.00276327
$358$	−26.9746	−1.42565
$359$	−30.5054	−1.61001	−0.805007	−	0.593266i	$-0.797838\pi$
$359$	−30.5054	−1.61001	−0.805007	+	0.593266i	$0.797838\pi$
$360$	0	0
$361$	14.4672	0.761434
$362$	27.7974	1.46100
$363$	−11.6090	−0.609315
$364$	0.130876	0.00685978
$365$	0	0
$366$	2.37033	0.123899
$367$	−10.0384	−0.524001	−0.262001	−	0.965068i	$-0.584382\pi$
$367$	−10.0384	−0.524001	−0.262001	+	0.965068i	$0.584382\pi$
$368$	−32.0811	−1.67234
$369$	−6.09965	−0.317535
$370$	0	0
$371$	−28.1097	−1.45938
$372$	5.51049	0.285706
$373$	−29.7213	−1.53891	−0.769454	−	0.638702i	$-0.779472\pi$
$373$	−29.7213	−1.53891	−0.769454	+	0.638702i	$0.779472\pi$
$374$	0.0428382	0.00221511
$375$	0	0
$376$	−16.8806	−0.870552
$377$	−0.289409	−0.0149053
$378$	−19.1434	−0.984629
$379$	−0.374781	−0.0192512	−0.00962560	−	0.999954i	$-0.503064\pi$
$379$	−0.374781	−0.0192512	−0.00962560	+	0.999954i	$0.503064\pi$
$380$	0	0
$381$	24.1685	1.23819
$382$	−17.2951	−0.884894
$383$	7.70824	0.393872	0.196936	−	0.980416i	$-0.436901\pi$
$383$	7.70824	0.393872	0.196936	+	0.980416i	$0.436901\pi$
$384$	17.6728	0.901863
$385$	0	0
$386$	35.9545	1.83004
$387$	7.94155	0.403692
$388$	4.61730	0.234408
$389$	−19.2063	−0.973797	−0.486899	−	0.873459i	$-0.661872\pi$
$389$	−19.2063	−0.973797	−0.486899	+	0.873459i	$0.661872\pi$
$390$	0	0
$391$	0.125960	0.00637006
$392$	5.58608	0.282140
$393$	4.31227	0.217525
$394$	−23.2062	−1.16911
$395$	0	0
$396$	−1.03632	−0.0520769
$397$	19.1563	0.961429	0.480715	−	0.876877i	$-0.340377\pi$
$397$	19.1563	0.961429	0.480715	+	0.876877i	$0.340377\pi$
$398$	29.9850	1.50301
$399$	16.0383	0.802918
$400$	0	0
$401$	34.1394	1.70484	0.852419	−	0.522859i	$-0.175135\pi$
$401$	34.1394	1.70484	0.852419	+	0.522859i	$0.175135\pi$
$402$	16.6234	0.829098
$403$	0.863320	0.0430050
$404$	−0.0700544	−0.00348534
$405$	0	0
$406$	−8.89285	−0.441345
$407$	8.78196	0.435306
$408$	−0.0564648	−0.00279543
$409$	1.37498	0.0679886	0.0339943	−	0.999422i	$-0.489177\pi$
$409$	1.37498	0.0679886	0.0339943	+	0.999422i	$0.489177\pi$
$410$	0	0
$411$	−4.78622	−0.236087
$412$	5.89223	0.290289
$413$	−11.5173	−0.566728
$414$	−14.1493	−0.695401
$415$	0	0
$416$	−0.336625	−0.0165044
$417$	−24.4221	−1.19596
$418$	13.1592	0.643638
$419$	−8.79270	−0.429552	−0.214776	−	0.976663i	$-0.568902\pi$
$419$	−8.79270	−0.429552	−0.214776	+	0.976663i	$0.568902\pi$
$420$	0	0
$421$	−14.6064	−0.711871	−0.355935	−	0.934511i	$-0.615838\pi$
$421$	−14.6064	−0.711871	−0.355935	+	0.934511i	$0.615838\pi$
$422$	−28.6395	−1.39415
$423$	−9.65510	−0.469447
$424$	30.4002	1.47636
$425$	0	0
$426$	0.718823	0.0348271
$427$	2.45742	0.118923
$428$	10.9567	0.529610
$429$	0.205229	0.00990854
$430$	0	0
$431$	24.2730	1.16919	0.584594	−	0.811326i	$-0.301254\pi$
$431$	24.2730	1.16919	0.584594	+	0.811326i	$0.301254\pi$
$432$	26.8485	1.29175
$433$	22.1657	1.06522	0.532608	−	0.846362i	$-0.321212\pi$
$433$	22.1657	1.06522	0.532608	+	0.846362i	$0.321212\pi$
$434$	26.5278	1.27338
$435$	0	0
$436$	−0.756974	−0.0362525
$437$	38.6929	1.85093
$438$	18.0578	0.862834
$439$	16.5895	0.791775	0.395888	−	0.918299i	$-0.370437\pi$
$439$	16.5895	0.791775	0.395888	+	0.918299i	$0.370437\pi$
$440$	0	0
$441$	3.19503	0.152144
$442$	0.00334647	0.000159175 0
$443$	14.5572	0.691631	0.345816	−	0.938303i	$-0.387602\pi$
$443$	14.5572	0.691631	0.345816	+	0.938303i	$0.387602\pi$
$444$	4.37891	0.207814
$445$	0	0
$446$	−17.7402	−0.840022
$447$	29.1485	1.37868
$448$	10.2060	0.482188
$449$	−2.30946	−0.108990	−0.0544950	−	0.998514i	$-0.517355\pi$
$449$	−2.30946	−0.108990	−0.0544950	+	0.998514i	$0.517355\pi$
$450$	0	0
$451$	6.55860	0.308832
$452$	5.64325	0.265436
$453$	−15.8621	−0.745268
$454$	−17.3182	−0.812785
$455$	0	0
$456$	−17.3451	−0.812260
$457$	−2.31754	−0.108410	−0.0542049	−	0.998530i	$-0.517262\pi$
$457$	−2.31754	−0.108410	−0.0542049	+	0.998530i	$0.517262\pi$
$458$	9.66678	0.451699
$459$	−0.105415	−0.00492035
$460$	0	0
$461$	−5.68817	−0.264924	−0.132462	−	0.991188i	$-0.542288\pi$
$461$	−5.68817	−0.264924	−0.132462	+	0.991188i	$0.542288\pi$
$462$	6.30620	0.293391
$463$	12.6162	0.586326	0.293163	−	0.956063i	$-0.405292\pi$
$463$	12.6162	0.586326	0.293163	+	0.956063i	$0.405292\pi$
$464$	12.4722	0.579006
$465$	0	0
$466$	−0.0662309	−0.00306809
$467$	−21.9477	−1.01562	−0.507810	−	0.861469i	$-0.669545\pi$
$467$	−21.9477	−1.01562	−0.507810	+	0.861469i	$0.669545\pi$
$468$	−0.0809559	−0.00374219
$469$	17.2341	0.795796
$470$	0	0
$471$	−4.19007	−0.193068
$472$	12.4557	0.573322
$473$	−8.53909	−0.392628
$474$	−33.3724	−1.53284
$475$	0	0
$476$	0.0221449	0.00101501
$477$	17.3878	0.796132
$478$	−0.319097	−0.0145952
$479$	−33.5604	−1.53341	−0.766707	−	0.641997i	$-0.778106\pi$
$479$	−33.5604	−1.53341	−0.766707	+	0.641997i	$0.778106\pi$
$480$	0	0
$481$	0.686037	0.0312806
$482$	1.59654	0.0727202
$483$	18.5425	0.843714
$484$	−4.92393	−0.223815
$485$	0	0
$486$	20.0551	0.909718
$487$	−29.2925	−1.32737	−0.663685	−	0.748012i	$-0.731009\pi$
$487$	−29.2925	−1.32737	−0.663685	+	0.748012i	$0.731009\pi$
$488$	−2.65765	−0.120306
$489$	−18.0357	−0.815603
$490$	0	0
$491$	14.2240	0.641918	0.320959	−	0.947093i	$-0.395995\pi$
$491$	14.2240	0.641918	0.320959	+	0.947093i	$0.395995\pi$
$492$	3.27029	0.147436
$493$	−0.0489694	−0.00220547
$494$	1.02798	0.0462512
$495$	0	0
$496$	−37.2051	−1.67056
$497$	0.745232	0.0334282
$498$	20.6562	0.925628
$499$	−23.3653	−1.04597	−0.522987	−	0.852341i	$-0.675182\pi$
$499$	−23.3653	−1.04597	−0.522987	+	0.852341i	$0.675182\pi$
$500$	0	0
$501$	31.0340	1.38650
$502$	14.4491	0.644896
$503$	−3.63393	−0.162029	−0.0810144	−	0.996713i	$-0.525816\pi$
$503$	−3.63393	−0.162029	−0.0810144	+	0.996713i	$0.525816\pi$
$504$	6.57583	0.292911
$505$	0	0
$506$	15.2139	0.676342
$507$	−16.8085	−0.746492
$508$	10.2510	0.454815
$509$	−35.3368	−1.56628	−0.783139	−	0.621847i	$-0.786383\pi$
$509$	−35.3368	−1.56628	−0.783139	+	0.621847i	$0.786383\pi$
$510$	0	0
$511$	18.7212	0.828177
$512$	−7.71719	−0.341055
$513$	−32.3819	−1.42969
$514$	1.82680	0.0805768
$515$	0	0
$516$	−4.25781	−0.187439
$517$	10.3816	0.456580
$518$	21.0803	0.926215
$519$	−30.2132	−1.32621
$520$	0	0
$521$	29.3267	1.28483	0.642413	−	0.766358i	$-0.277933\pi$
$521$	29.3267	1.28483	0.642413	+	0.766358i	$0.277933\pi$
$522$	5.50083	0.240765
$523$	−13.3970	−0.585810	−0.292905	−	0.956142i	$-0.594622\pi$
$523$	−13.3970	−0.585810	−0.292905	+	0.956142i	$0.594622\pi$
$524$	1.82904	0.0799019
$525$	0	0
$526$	−40.6655	−1.77310
$527$	0.146078	0.00636326
$528$	−8.84440	−0.384903
$529$	21.7345	0.944979
$530$	0	0
$531$	7.12422	0.309165
$532$	6.80258	0.294929
$533$	0.512350	0.0221924
$534$	29.9920	1.29788
$535$	0	0
$536$	−18.6384	−0.805055
$537$	−21.8663	−0.943600
$538$	1.66445	0.0717596
$539$	−3.43543	−0.147974
$540$	0	0
$541$	−20.4353	−0.878584	−0.439292	−	0.898344i	$-0.644771\pi$
$541$	−20.4353	−0.878584	−0.439292	+	0.898344i	$0.644771\pi$
$542$	−42.7197	−1.83497
$543$	22.5333	0.966997
$544$	−0.0569586	−0.00244208
$545$	0	0
$546$	0.492633	0.0210828
$547$	−2.84201	−0.121516	−0.0607578	−	0.998153i	$-0.519352\pi$
$547$	−2.84201	−0.121516	−0.0607578	+	0.998153i	$0.519352\pi$
$548$	−2.03006	−0.0867199
$549$	−1.52008	−0.0648754
$550$	0	0
$551$	−15.0426	−0.640838
$552$	−20.0534	−0.853531
$553$	−34.5984	−1.47128
$554$	−19.6720	−0.835782
$555$	0	0
$556$	−10.3586	−0.439301
$557$	−13.4318	−0.569123	−0.284562	−	0.958658i	$-0.591848\pi$
$557$	−13.4318	−0.569123	−0.284562	+	0.958658i	$0.591848\pi$
$558$	−16.4092	−0.694659
$559$	−0.667064	−0.0282138
$560$	0	0
$561$	0.0347258	0.00146612
$562$	−42.9793	−1.81297
$563$	8.77608	0.369868	0.184934	−	0.982751i	$-0.440793\pi$
$563$	8.77608	0.369868	0.184934	+	0.982751i	$0.440793\pi$
$564$	5.17651	0.217970
$565$	0	0
$566$	−41.5840	−1.74791
$567$	−7.00274	−0.294087
$568$	−0.805955	−0.0338171
$569$	8.36653	0.350743	0.175372	−	0.984502i	$-0.443887\pi$
$569$	8.36653	0.350743	0.175372	+	0.984502i	$0.443887\pi$
$570$	0	0
$571$	−22.6148	−0.946400	−0.473200	−	0.880955i	$-0.656901\pi$
$571$	−22.6148	−0.946400	−0.473200	+	0.880955i	$0.656901\pi$
$572$	0.0870472	0.00363963
$573$	−14.0199	−0.585689
$574$	15.7433	0.657114
$575$	0	0
$576$	−6.31311	−0.263046
$577$	2.73234	0.113749	0.0568744	−	0.998381i	$-0.481887\pi$
$577$	2.73234	0.113749	0.0568744	+	0.998381i	$0.481887\pi$
$578$	−27.1406	−1.12890
$579$	29.1457	1.21125
$580$	0	0
$581$	21.4151	0.888449
$582$	17.3800	0.720426
$583$	−18.6961	−0.774312
$584$	−20.2466	−0.837812
$585$	0	0
$586$	2.72215	0.112451
$587$	9.41141	0.388450	0.194225	−	0.980957i	$-0.437781\pi$
$587$	9.41141	0.388450	0.194225	+	0.980957i	$0.437781\pi$
$588$	−1.71299	−0.0706427
$589$	44.8729	1.84896
$590$	0	0
$591$	−18.8115	−0.773804
$592$	−29.5650	−1.21511
$593$	44.4743	1.82634	0.913171	−	0.407578i	$-0.133626\pi$
$593$	44.4743	1.82634	0.913171	+	0.407578i	$0.133626\pi$
$594$	−12.7324	−0.522419
$595$	0	0
$596$	12.3633	0.506419
$597$	24.3066	0.994804
$598$	1.18850	0.0486012
$599$	−22.3536	−0.913345	−0.456672	−	0.889635i	$-0.650959\pi$
$599$	−22.3536	−0.913345	−0.456672	+	0.889635i	$0.650959\pi$
$600$	0	0
$601$	2.57395	0.104994	0.0524968	−	0.998621i	$-0.483282\pi$
$601$	2.57395	0.104994	0.0524968	+	0.998621i	$0.483282\pi$
$602$	−20.4973	−0.835408
$603$	−10.6605	−0.434127
$604$	−6.72788	−0.273753
$605$	0	0
$606$	−0.263693	−0.0107118
$607$	4.05053	0.164406	0.0822030	−	0.996616i	$-0.473804\pi$
$607$	4.05053	0.164406	0.0822030	+	0.996616i	$0.473804\pi$
$608$	−17.4968	−0.709589
$609$	−7.20878	−0.292114
$610$	0	0
$611$	0.810996	0.0328094
$612$	−0.0136982	−0.000553715 0
$613$	18.3186	0.739883	0.369941	−	0.929055i	$-0.379378\pi$
$613$	18.3186	0.739883	0.369941	+	0.929055i	$0.379378\pi$
$614$	4.59632	0.185492
$615$	0	0
$616$	−7.07061	−0.284883
$617$	−6.61438	−0.266285	−0.133143	−	0.991097i	$-0.542507\pi$
$617$	−6.61438	−0.266285	−0.133143	+	0.991097i	$0.542507\pi$
$618$	22.1790	0.892171
$619$	−45.5456	−1.83063	−0.915317	−	0.402735i	$-0.868060\pi$
$619$	−45.5456	−1.83063	−0.915317	+	0.402735i	$0.868060\pi$
$620$	0	0
$621$	−37.4380	−1.50234
$622$	48.6260	1.94972
$623$	31.0938	1.24575
$624$	−0.690915	−0.0276587
$625$	0	0
$626$	−6.18655	−0.247264
$627$	10.6672	0.426007
$628$	−1.77721	−0.0709182
$629$	0.116081	0.00462845
$630$	0	0
$631$	−0.818123	−0.0325690	−0.0162845	−	0.999867i	$-0.505184\pi$
$631$	−0.818123	−0.0325690	−0.0162845	+	0.999867i	$0.505184\pi$
$632$	37.4176	1.48839
$633$	−23.2160	−0.922752
$634$	5.66748	0.225085
$635$	0	0
$636$	−9.32234	−0.369655
$637$	−0.268372	−0.0106333
$638$	−5.91472	−0.234166
$639$	−0.460977	−0.0182359
$640$	0	0
$641$	8.98911	0.355049	0.177524	−	0.984116i	$-0.443191\pi$
$641$	8.98911	0.355049	0.177524	+	0.984116i	$0.443191\pi$
$642$	41.2421	1.62770
$643$	28.2410	1.11371	0.556857	−	0.830608i	$-0.312007\pi$
$643$	28.2410	1.11371	0.556857	+	0.830608i	$0.312007\pi$
$644$	7.86476	0.309915
$645$	0	0
$646$	0.173940	0.00684358
$647$	1.24951	0.0491234	0.0245617	−	0.999698i	$-0.492181\pi$
$647$	1.24951	0.0491234	0.0245617	+	0.999698i	$0.492181\pi$
$648$	7.57335	0.297509
$649$	−7.66026	−0.300692
$650$	0	0
$651$	21.5041	0.842814
$652$	−7.64979	−0.299589
$653$	5.57752	0.218265	0.109133	−	0.994027i	$-0.465193\pi$
$653$	5.57752	0.218265	0.109133	+	0.994027i	$0.465193\pi$
$654$	−2.84933	−0.111418
$655$	0	0
$656$	−22.0799	−0.862076
$657$	−11.5803	−0.451792
$658$	24.9200	0.971482
$659$	37.8697	1.47519	0.737597	−	0.675241i	$-0.235961\pi$
$659$	37.8697	1.47519	0.737597	+	0.675241i	$0.235961\pi$
$660$	0	0
$661$	−9.64078	−0.374983	−0.187492	−	0.982266i	$-0.560036\pi$
$661$	−9.64078	−0.374983	−0.187492	+	0.982266i	$0.560036\pi$
$662$	−46.1625	−1.79416
$663$	0.00271274	0.000105354 0
$664$	−23.1601	−0.898786
$665$	0	0
$666$	−13.0396	−0.505274
$667$	−17.3914	−0.673399
$668$	13.1630	0.509291
$669$	−14.3807	−0.555988
$670$	0	0
$671$	1.63445	0.0630973
$672$	−8.38487	−0.323453
$673$	23.9023	0.921368	0.460684	−	0.887564i	$-0.347604\pi$
$673$	23.9023	0.921368	0.460684	+	0.887564i	$0.347604\pi$
$674$	20.4486	0.787652
$675$	0	0
$676$	−7.12928	−0.274203
$677$	−22.1937	−0.852973	−0.426486	−	0.904494i	$-0.640249\pi$
$677$	−22.1937	−0.852973	−0.426486	+	0.904494i	$0.640249\pi$
$678$	21.2418	0.815788
$679$	18.0186	0.691489
$680$	0	0
$681$	−14.0386	−0.537961
$682$	17.6439	0.675620
$683$	−35.7361	−1.36740	−0.683702	−	0.729761i	$-0.739631\pi$
$683$	−35.7361	−1.36740	−0.683702	+	0.729761i	$0.739631\pi$
$684$	−4.20786	−0.160892
$685$	0	0
$686$	−32.1865	−1.22889
$687$	7.83615	0.298968
$688$	28.7473	1.09598
$689$	−1.46052	−0.0556412
$690$	0	0
$691$	−7.22170	−0.274726	−0.137363	−	0.990521i	$-0.543863\pi$
$691$	−7.22170	−0.274726	−0.137363	+	0.990521i	$0.543863\pi$
$692$	−12.8148	−0.487146
$693$	−4.04412	−0.153624
$694$	12.0240	0.456426
$695$	0	0
$696$	7.79617	0.295513
$697$	0.0866923	0.00328370
$698$	14.0146	0.530462
$699$	−0.0536885	−0.00203069
$700$	0	0
$701$	20.3728	0.769471	0.384735	−	0.923027i	$-0.374293\pi$
$701$	20.3728	0.769471	0.384735	+	0.923027i	$0.374293\pi$
$702$	−0.994645	−0.0375404
$703$	35.6583	1.34488
$704$	6.78812	0.255837
$705$	0	0
$706$	13.6258	0.512815
$707$	−0.273380	−0.0102815
$708$	−3.81960	−0.143549
$709$	−46.0549	−1.72963	−0.864814	−	0.502092i	$-0.832564\pi$
$709$	−46.0549	−1.72963	−0.864814	+	0.502092i	$0.832564\pi$
$710$	0	0
$711$	21.4015	0.802618
$712$	−33.6275	−1.26024
$713$	51.8795	1.94290
$714$	0.0833560	0.00311952
$715$	0	0
$716$	−9.27452	−0.346605
$717$	−0.258669	−0.00966016
$718$	−48.7030	−1.81758
$719$	29.0016	1.08158	0.540788	−	0.841159i	$-0.318126\pi$
$719$	29.0016	1.08158	0.540788	+	0.841159i	$0.318126\pi$
$720$	0	0
$721$	22.9938	0.856335
$722$	23.0975	0.859599
$723$	1.29420	0.0481316
$724$	9.55744	0.355199
$725$	0	0
$726$	−18.5342	−0.687869
$727$	36.0390	1.33661	0.668307	−	0.743886i	$-0.267019\pi$
$727$	36.0390	1.33661	0.668307	+	0.743886i	$0.267019\pi$
$728$	−0.552348	−0.0204714
$729$	26.0643	0.965345
$730$	0	0
$731$	−0.112871	−0.00417467
$732$	0.814980	0.0301225
$733$	−5.08969	−0.187992	−0.0939960	−	0.995573i	$-0.529964\pi$
$733$	−5.08969	−0.187992	−0.0939960	+	0.995573i	$0.529964\pi$
$734$	−16.0267	−0.591556
$735$	0	0
$736$	−20.2288	−0.745644
$737$	11.4626	0.422229
$738$	−9.73832	−0.358472
$739$	28.1391	1.03511	0.517557	−	0.855649i	$-0.326841\pi$
$739$	28.1391	1.03511	0.517557	+	0.855649i	$0.326841\pi$
$740$	0	0
$741$	0.833311	0.0306124
$742$	−44.8782	−1.64753
$743$	−42.9523	−1.57577	−0.787884	−	0.615824i	$-0.788823\pi$
$743$	−42.9523	−1.57577	−0.787884	+	0.615824i	$0.788823\pi$
$744$	−23.2564	−0.852620
$745$	0	0
$746$	−47.4511	−1.73731
$747$	−13.2467	−0.484672
$748$	0.0147288	0.000538539 0
$749$	42.7573	1.56232
$750$	0	0
$751$	−12.6967	−0.463309	−0.231654	−	0.972798i	$-0.574414\pi$
$751$	−12.6967	−0.463309	−0.231654	+	0.972798i	$0.574414\pi$
$752$	−34.9501	−1.27450
$753$	11.7128	0.426840
$754$	−0.462051	−0.0168269
$755$	0	0
$756$	−6.58197	−0.239384
$757$	−41.2709	−1.50002	−0.750008	−	0.661429i	$-0.769950\pi$
$757$	−41.2709	−1.50002	−0.750008	+	0.661429i	$0.769950\pi$
$758$	−0.598352	−0.0217331
$759$	12.3328	0.447653
$760$	0	0
$761$	−10.3286	−0.374412	−0.187206	−	0.982321i	$-0.559943\pi$
$761$	−10.3286	−0.374412	−0.187206	+	0.982321i	$0.559943\pi$
$762$	38.5860	1.39782
$763$	−2.95401	−0.106942
$764$	−5.94649	−0.215136
$765$	0	0
$766$	12.3065	0.444651
$767$	−0.598411	−0.0216074
$768$	15.8832	0.573136
$769$	3.19829	0.115333	0.0576667	−	0.998336i	$-0.481634\pi$
$769$	3.19829	0.115333	0.0576667	+	0.998336i	$0.481634\pi$
$770$	0	0
$771$	1.48086	0.0533317
$772$	12.3620	0.444920
$773$	16.5099	0.593821	0.296910	−	0.954905i	$-0.404044\pi$
$773$	16.5099	0.593821	0.296910	+	0.954905i	$0.404044\pi$
$774$	12.6790	0.455736
$775$	0	0
$776$	−19.4868	−0.699534
$777$	17.0883	0.613038
$778$	−30.6635	−1.09934
$779$	26.6305	0.954138
$780$	0	0
$781$	0.495661	0.0177361
$782$	0.201099	0.00719130
$783$	14.5548	0.520146
$784$	11.5656	0.413057
$785$	0	0
$786$	6.88470	0.245569
$787$	−25.9655	−0.925570	−0.462785	−	0.886471i	$-0.653150\pi$
$787$	−25.9655	−0.925570	−0.462785	+	0.886471i	$0.653150\pi$
$788$	−7.97886	−0.284235
$789$	−32.9646	−1.17357
$790$	0	0
$791$	22.0222	0.783020
$792$	4.37365	0.155411
$793$	0.127682	0.00453411
$794$	30.5838	1.08538
$795$	0	0
$796$	10.3096	0.365413
$797$	−14.6552	−0.519115	−0.259558	−	0.965728i	$-0.583577\pi$
$797$	−14.6552	−0.519115	−0.259558	+	0.965728i	$0.583577\pi$
$798$	25.6057	0.906431
$799$	0.137225	0.00485466
$800$	0	0
$801$	−19.2337	−0.679588
$802$	54.5047	1.92463
$803$	12.4516	0.439409
$804$	5.71553	0.201571
$805$	0	0
$806$	1.37832	0.0485493
$807$	1.34925	0.0474958
$808$	0.295656	0.0104012
$809$	−14.1302	−0.496792	−0.248396	−	0.968659i	$-0.579903\pi$
$809$	−14.1302	−0.496792	−0.248396	+	0.968659i	$0.579903\pi$
$810$	0	0
$811$	1.90222	0.0667961	0.0333981	−	0.999442i	$-0.489367\pi$
$811$	1.90222	0.0667961	0.0333981	+	0.999442i	$0.489367\pi$
$812$	−3.05758	−0.107300
$813$	−34.6297	−1.21452
$814$	14.0207	0.491426
$815$	0	0
$816$	−0.116906	−0.00409254
$817$	−34.6721	−1.21302
$818$	2.19521	0.0767538
$819$	−0.315922	−0.0110392
$820$	0	0
$821$	−39.2989	−1.37154	−0.685771	−	0.727817i	$-0.740535\pi$
$821$	−39.2989	−1.37154	−0.685771	+	0.727817i	$0.740535\pi$
$822$	−7.64137	−0.266523
$823$	50.0559	1.74484	0.872420	−	0.488758i	$-0.162550\pi$
$823$	50.0559	1.74484	0.872420	+	0.488758i	$0.162550\pi$
$824$	−24.8674	−0.866298
$825$	0	0
$826$	−18.3878	−0.639792
$827$	42.4676	1.47674	0.738372	−	0.674393i	$-0.235595\pi$
$827$	42.4676	1.47674	0.738372	+	0.674393i	$0.235595\pi$
$828$	−4.86489	−0.169067
$829$	−8.66486	−0.300943	−0.150472	−	0.988614i	$-0.548079\pi$
$829$	−8.66486	−0.300943	−0.150472	+	0.988614i	$0.548079\pi$
$830$	0	0
$831$	−15.9466	−0.553182
$832$	0.530280	0.0183842
$833$	−0.0454099	−0.00157336
$834$	−38.9908	−1.35014
$835$	0	0
$836$	4.52447	0.156482
$837$	−43.4177	−1.50073
$838$	−14.0379	−0.484930
$839$	45.4724	1.56988	0.784941	−	0.619571i	$-0.212693\pi$
$839$	45.4724	1.56988	0.784941	+	0.619571i	$0.212693\pi$
$840$	0	0
$841$	−22.2387	−0.766853
$842$	−23.3196	−0.803646
$843$	−34.8402	−1.19996
$844$	−9.84699	−0.338947
$845$	0	0
$846$	−15.4147	−0.529969
$847$	−19.2151	−0.660240
$848$	62.9414	2.16142
$849$	−33.7091	−1.15689
$850$	0	0
$851$	41.2260	1.41321
$852$	0.247149	0.00846719
$853$	−40.4543	−1.38513	−0.692565	−	0.721355i	$-0.743520\pi$
$853$	−40.4543	−1.38513	−0.692565	+	0.721355i	$0.743520\pi$
$854$	3.92335	0.134254
$855$	0	0
$856$	−46.2413	−1.58049
$857$	−40.0583	−1.36837	−0.684183	−	0.729310i	$-0.739841\pi$
$857$	−40.0583	−1.36837	−0.684183	+	0.729310i	$0.739841\pi$
$858$	0.327655	0.0111860
$859$	−37.5087	−1.27978	−0.639889	−	0.768467i	$-0.721020\pi$
$859$	−37.5087	−1.27978	−0.639889	+	0.768467i	$0.721020\pi$
$860$	0	0
$861$	12.7620	0.434926
$862$	38.7527	1.31992
$863$	−25.8329	−0.879362	−0.439681	−	0.898154i	$-0.644909\pi$
$863$	−25.8329	−0.879362	−0.439681	+	0.898154i	$0.644909\pi$
$864$	16.9294	0.575949
$865$	0	0
$866$	35.3884	1.20255
$867$	−22.0009	−0.747188
$868$	9.12092	0.309584
$869$	−23.0118	−0.780621
$870$	0	0
$871$	0.895443	0.0303409
$872$	3.19472	0.108187
$873$	−11.1457	−0.377225
$874$	61.7746	2.08956
$875$	0	0
$876$	6.20871	0.209773
$877$	54.5066	1.84056	0.920279	−	0.391263i	$-0.127962\pi$
$877$	54.5066	1.84056	0.920279	+	0.391263i	$0.127962\pi$
$878$	26.4858	0.893852
$879$	2.20665	0.0744284
$880$	0	0
$881$	−0.663049	−0.0223387	−0.0111693	−	0.999938i	$-0.503555\pi$
$881$	−0.663049	−0.0223387	−0.0111693	+	0.999938i	$0.503555\pi$
$882$	5.10099	0.171759
$883$	10.6974	0.359995	0.179998	−	0.983667i	$-0.442391\pi$
$883$	10.6974	0.359995	0.179998	+	0.983667i	$0.442391\pi$
$884$	0.00115060	3.86988e−5 0
$885$	0	0
$886$	23.2410	0.780797
$887$	−28.4360	−0.954786	−0.477393	−	0.878690i	$-0.658418\pi$
$887$	−28.4360	−0.954786	−0.477393	+	0.878690i	$0.658418\pi$
$888$	−18.4807	−0.620170
$889$	40.0035	1.34168
$890$	0	0
$891$	−4.65759	−0.156035
$892$	−6.09951	−0.204227
$893$	42.1533	1.41061
$894$	46.5367	1.55642
$895$	0	0
$896$	29.2519	0.977238
$897$	0.963426	0.0321679
$898$	−3.68713	−0.123041
$899$	−20.1692	−0.672681
$900$	0	0
$901$	−0.247127	−0.00823298
$902$	10.4710	0.348648
$903$	−16.6157	−0.552935
$904$	−23.8167	−0.792131
$905$	0	0
$906$	−25.3245	−0.841350
$907$	−31.3320	−1.04036	−0.520181	−	0.854056i	$-0.674136\pi$
$907$	−31.3320	−1.04036	−0.520181	+	0.854056i	$0.674136\pi$
$908$	−5.95444	−0.197605
$909$	0.169104	0.00560884
$910$	0	0
$911$	21.8171	0.722832	0.361416	−	0.932405i	$-0.382293\pi$
$911$	21.8171	0.722832	0.361416	+	0.932405i	$0.382293\pi$
$912$	−35.9118	−1.18916
$913$	14.2434	0.471388
$914$	−3.70003	−0.122386
$915$	0	0
$916$	3.32368	0.109817
$917$	7.13764	0.235706
$918$	−0.168299	−0.00555469
$919$	42.1024	1.38883	0.694416	−	0.719574i	$-0.255663\pi$
$919$	42.1024	1.38883	0.694416	+	0.719574i	$0.255663\pi$
$920$	0	0
$921$	3.72590	0.122773
$922$	−9.08137	−0.299079
$923$	0.0387205	0.00127450
$924$	2.16823	0.0713295
$925$	0	0
$926$	20.1423	0.661916
$927$	−14.2233	−0.467153
$928$	7.86435	0.258160
$929$	−1.29743	−0.0425672	−0.0212836	−	0.999773i	$-0.506775\pi$
$929$	−1.29743	−0.0425672	−0.0212836	+	0.999773i	$0.506775\pi$
$930$	0	0
$931$	−13.9492	−0.457167
$932$	−0.0227718	−0.000745916 0
$933$	39.4175	1.29047
$934$	−35.0403	−1.14655
$935$	0	0
$936$	0.341665	0.0111677
$937$	−29.3997	−0.960447	−0.480223	−	0.877146i	$-0.659444\pi$
$937$	−29.3997	−0.960447	−0.480223	+	0.877146i	$0.659444\pi$
$938$	27.5148	0.898392
$939$	−5.01498	−0.163658
$940$	0	0
$941$	25.1675	0.820436	0.410218	−	0.911987i	$-0.365453\pi$
$941$	25.1675	0.820436	0.410218	+	0.911987i	$0.365453\pi$
$942$	−6.68960	−0.217959
$943$	30.7887	1.00262
$944$	25.7887	0.839351
$945$	0	0
$946$	−13.6330	−0.443246
$947$	−35.7219	−1.16081	−0.580404	−	0.814329i	$-0.697105\pi$
$947$	−35.7219	−1.16081	−0.580404	+	0.814329i	$0.697105\pi$
$948$	−11.4743	−0.372666
$949$	0.972709	0.0315755
$950$	0	0
$951$	4.59421	0.148978
$952$	−0.0934600	−0.00302906
$953$	−1.17285	−0.0379923	−0.0189962	−	0.999820i	$-0.506047\pi$
$953$	−1.17285	−0.0379923	−0.0189962	+	0.999820i	$0.506047\pi$
$954$	27.7602	0.898771
$955$	0	0
$956$	−0.109714	−0.00354839
$957$	−4.79463	−0.154988
$958$	−53.5804	−1.73110
$959$	−7.92210	−0.255818
$960$	0	0
$961$	29.1657	0.940830
$962$	1.09528	0.0353133
$963$	−26.4483	−0.852284
$964$	0.548929	0.0176798
$965$	0	0
$966$	29.6038	0.952487
$967$	−52.3784	−1.68437	−0.842187	−	0.539185i	$-0.818732\pi$
$967$	−52.3784	−1.68437	−0.842187	+	0.539185i	$0.818732\pi$
$968$	20.7808	0.667921
$969$	0.141000	0.00452959
$970$	0	0
$971$	−10.2076	−0.327576	−0.163788	−	0.986496i	$-0.552371\pi$
$971$	−10.2076	−0.327576	−0.163788	+	0.986496i	$0.552371\pi$
$972$	6.89544	0.221171
$973$	−40.4232	−1.29591
$974$	−46.7666	−1.49850
$975$	0	0
$976$	−5.50248	−0.176130
$977$	−10.1515	−0.324776	−0.162388	−	0.986727i	$-0.551920\pi$
$977$	−10.1515	−0.324776	−0.162388	+	0.986727i	$0.551920\pi$
$978$	−28.7947	−0.920752
$979$	20.6808	0.660962
$980$	0	0
$981$	1.82726	0.0583399
$982$	22.7091	0.724675
$983$	−25.9771	−0.828541	−0.414271	−	0.910154i	$-0.635963\pi$
$983$	−25.9771	−0.828541	−0.414271	+	0.910154i	$0.635963\pi$
$984$	−13.8018	−0.439987
$985$	0	0
$986$	−0.0781814	−0.00248980
$987$	20.2008	0.642999
$988$	0.353446	0.0112446
$989$	−40.0859	−1.27466
$990$	0	0
$991$	−5.22857	−0.166091	−0.0830454	−	0.996546i	$-0.526465\pi$
$991$	−5.22857	−0.166091	−0.0830454	+	0.996546i	$0.526465\pi$
$992$	−23.4598	−0.744848
$993$	−37.4206	−1.18751
$994$	1.18979	0.0377378
$995$	0	0
$996$	7.10213	0.225040
$997$	5.27997	0.167218	0.0836091	−	0.996499i	$-0.473355\pi$
$997$	5.27997	0.167218	0.0836091	+	0.996499i	$0.473355\pi$
$998$	−37.3035	−1.18082
$999$	−34.5018	−1.09159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.8		11
5.4	even	2		1205.2.a.b.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.4	✓	11	5.4	even	2
6025.2.a.g.1.8		11	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)

\(f(q)\)	\(=\)	\(q+1.59654 q^{2} +1.29420 q^{3} +0.548929 q^{4} +2.06623 q^{6} +2.14214 q^{7} -2.31669 q^{8} -1.32506 q^{9} +O(q^{10})\)	\(q+1.59654 q^{2} +1.29420 q^{3} +0.548929 q^{4} +2.06623 q^{6} +2.14214 q^{7} -2.31669 q^{8} -1.32506 q^{9} +1.42476 q^{11} +0.710421 q^{12} +0.111301 q^{13} +3.42000 q^{14} -4.79653 q^{16} +0.0188326 q^{17} -2.11551 q^{18} +5.78509 q^{19} +2.77235 q^{21} +2.27468 q^{22} +6.68839 q^{23} -2.99825 q^{24} +0.177695 q^{26} -5.59747 q^{27} +1.17588 q^{28} -2.60024 q^{29} +7.75666 q^{31} -3.02447 q^{32} +1.84392 q^{33} +0.0300670 q^{34} -0.727363 q^{36} +6.16382 q^{37} +9.23610 q^{38} +0.144045 q^{39} +4.60331 q^{41} +4.42615 q^{42} -5.99336 q^{43} +0.782091 q^{44} +10.6783 q^{46} +7.28654 q^{47} -6.20765 q^{48} -2.41124 q^{49} +0.0243731 q^{51} +0.0610961 q^{52} -13.1223 q^{53} -8.93657 q^{54} -4.96267 q^{56} +7.48703 q^{57} -4.15139 q^{58} -5.37653 q^{59} +1.14718 q^{61} +12.3838 q^{62} -2.83846 q^{63} +4.76440 q^{64} +2.94388 q^{66} +8.04527 q^{67} +0.0103378 q^{68} +8.65608 q^{69} +0.347891 q^{71} +3.06975 q^{72} +8.73948 q^{73} +9.84077 q^{74} +3.17560 q^{76} +3.05203 q^{77} +0.229972 q^{78} -16.1513 q^{79} -3.26904 q^{81} +7.34935 q^{82} +9.99707 q^{83} +1.52182 q^{84} -9.56861 q^{86} -3.36522 q^{87} -3.30072 q^{88} +14.5153 q^{89} +0.238421 q^{91} +3.67145 q^{92} +10.0386 q^{93} +11.6332 q^{94} -3.91425 q^{96} +8.41148 q^{97} -3.84963 q^{98} -1.88789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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