LMFDB - Embedded newform 4235.2.a.z.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.270017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 7x^{2} + 7x - 3 $ x^5 - 2x^4 - 5x^3 + 7x^2 + 7x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.343016$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.22536 q^{2} +0.343016 q^{3} +2.95221 q^{4} +1.00000 q^{5} +0.763334 q^{6} -1.00000 q^{7} +2.11901 q^{8} -2.88234 q^{9} +O(q^{10})$	\(q+2.22536 q^{2} +0.343016 q^{3} +2.95221 q^{4} +1.00000 q^{5} +0.763334 q^{6} -1.00000 q^{7} +2.11901 q^{8} -2.88234 q^{9} +2.22536 q^{10} +1.01266 q^{12} -4.67472 q^{13} -2.22536 q^{14} +0.343016 q^{15} -1.18888 q^{16} -7.08387 q^{17} -6.41423 q^{18} +2.89500 q^{19} +2.95221 q^{20} -0.343016 q^{21} -3.27883 q^{23} +0.726854 q^{24} +1.00000 q^{25} -10.4029 q^{26} -2.01774 q^{27} -2.95221 q^{28} -6.05856 q^{29} +0.763334 q^{30} +3.38892 q^{31} -6.88369 q^{32} -15.7641 q^{34} -1.00000 q^{35} -8.50927 q^{36} +5.57406 q^{37} +6.44240 q^{38} -1.60351 q^{39} +2.11901 q^{40} +4.72386 q^{41} -0.763334 q^{42} +0.350447 q^{43} -2.88234 q^{45} -7.29657 q^{46} -8.30165 q^{47} -0.407804 q^{48} +1.00000 q^{49} +2.22536 q^{50} -2.42988 q^{51} -13.8008 q^{52} +7.12469 q^{53} -4.49019 q^{54} -2.11901 q^{56} +0.993031 q^{57} -13.4825 q^{58} +4.82324 q^{59} +1.01266 q^{60} -12.5383 q^{61} +7.54155 q^{62} +2.88234 q^{63} -12.9409 q^{64} -4.67472 q^{65} -8.33739 q^{67} -20.9131 q^{68} -1.12469 q^{69} -2.22536 q^{70} -16.5209 q^{71} -6.10770 q^{72} +8.39161 q^{73} +12.4043 q^{74} +0.343016 q^{75} +8.54664 q^{76} -3.56837 q^{78} -2.08935 q^{79} -1.18888 q^{80} +7.95490 q^{81} +10.5123 q^{82} +3.95370 q^{83} -1.01266 q^{84} -7.08387 q^{85} +0.779869 q^{86} -2.07819 q^{87} +10.4043 q^{89} -6.41423 q^{90} +4.67472 q^{91} -9.67980 q^{92} +1.16245 q^{93} -18.4741 q^{94} +2.89500 q^{95} -2.36122 q^{96} +5.13849 q^{97} +2.22536 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9	$ 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9} - 2 q^{10} - 3 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 6 q^{17} - 11 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 3 q^{23} + 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} - 4 q^{28} - 17 q^{29} + q^{30} + 12 q^{31} + 3 q^{32} - 12 q^{34} - 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} - 14 q^{39} - 5 q^{41} - q^{42} - 4 q^{43} - q^{45} - 2 q^{46} - 12 q^{48} + 5 q^{49} - 2 q^{50} - 14 q^{51} - 2 q^{52} + 8 q^{53} - 22 q^{54} - 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} - 24 q^{61} - 9 q^{62} + q^{63} - 38 q^{64} - 8 q^{65} - 9 q^{67} - 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} - 4 q^{72} - 11 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 5 q^{78} - 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} - 10 q^{83} + 3 q^{84} - 6 q^{85} + 15 q^{86} + 2 q^{87} - 9 q^{89} - 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} - 34 q^{94} - 7 q^{95} + 18 q^{96} + 11 q^{97} - 2 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9 - 2 * q^10 - 3 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 6 * q^17 - 11 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 3 * q^23 + 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 - 4 * q^28 - 17 * q^29 + q^30 + 12 * q^31 + 3 * q^32 - 12 * q^34 - 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 - 14 * q^39 - 5 * q^41 - q^42 - 4 * q^43 - q^45 - 2 * q^46 - 12 * q^48 + 5 * q^49 - 2 * q^50 - 14 * q^51 - 2 * q^52 + 8 * q^53 - 22 * q^54 - 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 - 24 * q^61 - 9 * q^62 + q^63 - 38 * q^64 - 8 * q^65 - 9 * q^67 - 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 - 4 * q^72 - 11 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 5 * q^78 - 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 - 10 * q^83 + 3 * q^84 - 6 * q^85 + 15 * q^86 + 2 * q^87 - 9 * q^89 - 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 - 34 * q^94 - 7 * q^95 + 18 * q^96 + 11 * q^97 - 2 * q^98

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 $

$2$	2.22536	1.57356	0.786782	−	0.617231i	$-0.211745\pi$
$2$	2.22536	1.57356	0.786782	+	0.617231i	$0.211745\pi$
$3$	0.343016	0.198041	0.0990203	−	0.995085i	$-0.468429\pi$
$3$	0.343016	0.198041	0.0990203	+	0.995085i	$0.468429\pi$
$4$	2.95221	1.47610
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.763334	0.311630
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.11901	0.749182
$9$	−2.88234	−0.960780
$10$	2.22536	0.703719
$11$	0	0
$11$	0	0
$12$	1.01266	0.292329
$13$	−4.67472	−1.29653	−0.648267	−	0.761413i	$-0.724506\pi$
$13$	−4.67472	−1.29653	−0.648267	+	0.761413i	$0.724506\pi$
$14$	−2.22536	−0.594751
$15$	0.343016	0.0885664
$16$	−1.18888	−0.297219
$17$	−7.08387	−1.71809	−0.859046	−	0.511899i	$-0.828942\pi$
$17$	−7.08387	−1.71809	−0.859046	+	0.511899i	$0.828942\pi$
$18$	−6.41423	−1.51185
$19$	2.89500	0.664158	0.332079	−	0.943252i	$-0.392250\pi$
$19$	2.89500	0.664158	0.332079	+	0.943252i	$0.392250\pi$
$20$	2.95221	0.660134
$21$	−0.343016	−0.0748523
$22$	0	0
$23$	−3.27883	−0.683684	−0.341842	−	0.939757i	$-0.611051\pi$
$23$	−3.27883	−0.683684	−0.341842	+	0.939757i	$0.611051\pi$
$24$	0.726854	0.148368
$25$	1.00000	0.200000
$26$	−10.4029	−2.04018
$27$	−2.01774	−0.388314
$28$	−2.95221	−0.557915
$29$	−6.05856	−1.12505	−0.562523	−	0.826782i	$-0.690169\pi$
$29$	−6.05856	−1.12505	−0.562523	+	0.826782i	$0.690169\pi$
$30$	0.763334	0.139365
$31$	3.38892	0.608668	0.304334	−	0.952565i	$-0.401566\pi$
$31$	3.38892	0.608668	0.304334	+	0.952565i	$0.401566\pi$
$32$	−6.88369	−1.21688
$33$	0	0
$34$	−15.7641	−2.70353
$35$	−1.00000	−0.169031
$36$	−8.50927	−1.41821
$37$	5.57406	0.916370	0.458185	−	0.888857i	$-0.348500\pi$
$37$	5.57406	0.916370	0.458185	+	0.888857i	$0.348500\pi$
$38$	6.44240	1.04509
$39$	−1.60351	−0.256766
$40$	2.11901	0.335044
$41$	4.72386	0.737743	0.368871	−	0.929480i	$-0.379744\pi$
$41$	4.72386	0.737743	0.368871	+	0.929480i	$0.379744\pi$
$42$	−0.763334	−0.117785
$43$	0.350447	0.0534427	0.0267213	−	0.999643i	$-0.491493\pi$
$43$	0.350447	0.0534427	0.0267213	+	0.999643i	$0.491493\pi$
$44$	0	0
$45$	−2.88234	−0.429674
$46$	−7.29657	−1.07582
$47$	−8.30165	−1.21092	−0.605460	−	0.795875i	$-0.707011\pi$
$47$	−8.30165	−1.21092	−0.605460	+	0.795875i	$0.707011\pi$
$48$	−0.407804	−0.0588614
$49$	1.00000	0.142857
$50$	2.22536	0.314713
$51$	−2.42988	−0.340252
$52$	−13.8008	−1.91382
$53$	7.12469	0.978652	0.489326	−	0.872101i	$-0.337243\pi$
$53$	7.12469	0.978652	0.489326	+	0.872101i	$0.337243\pi$
$54$	−4.49019	−0.611037
$55$	0	0
$56$	−2.11901	−0.283164
$57$	0.993031	0.131530
$58$	−13.4825	−1.77033
$59$	4.82324	0.627932	0.313966	−	0.949434i	$-0.398342\pi$
$59$	4.82324	0.627932	0.313966	+	0.949434i	$0.398342\pi$
$60$	1.01266	0.130733
$61$	−12.5383	−1.60537	−0.802684	−	0.596405i	$-0.796595\pi$
$61$	−12.5383	−1.60537	−0.802684	+	0.596405i	$0.796595\pi$
$62$	7.54155	0.957778
$63$	2.88234	0.363141
$64$	−12.9409	−1.61761
$65$	−4.67472	−0.579828
$66$	0	0
$67$	−8.33739	−1.01857	−0.509287	−	0.860597i	$-0.670091\pi$
$67$	−8.33739	−1.01857	−0.509287	+	0.860597i	$0.670091\pi$
$68$	−20.9131	−2.53608
$69$	−1.12469	−0.135397
$70$	−2.22536	−0.265981
$71$	−16.5209	−1.96067	−0.980337	−	0.197333i	$-0.936772\pi$
$71$	−16.5209	−1.96067	−0.980337	+	0.197333i	$0.936772\pi$
$72$	−6.10770	−0.719799
$73$	8.39161	0.982164	0.491082	−	0.871113i	$-0.336602\pi$
$73$	8.39161	0.982164	0.491082	+	0.871113i	$0.336602\pi$
$74$	12.4043	1.44197
$75$	0.343016	0.0396081
$76$	8.54664	0.980366
$77$	0	0
$78$	−3.56837	−0.404039
$79$	−2.08935	−0.235070	−0.117535	−	0.993069i	$-0.537499\pi$
$79$	−2.08935	−0.235070	−0.117535	+	0.993069i	$0.537499\pi$
$80$	−1.18888	−0.132920
$81$	7.95490	0.883878
$82$	10.5123	1.16089
$83$	3.95370	0.433975	0.216987	−	0.976174i	$-0.430377\pi$
$83$	3.95370	0.433975	0.216987	+	0.976174i	$0.430377\pi$
$84$	−1.01266	−0.110490
$85$	−7.08387	−0.768354
$86$	0.779869	0.0840955
$87$	−2.07819	−0.222805
$88$	0	0
$89$	10.4043	1.10285	0.551425	−	0.834224i	$-0.314084\pi$
$89$	10.4043	1.10285	0.551425	+	0.834224i	$0.314084\pi$
$90$	−6.41423	−0.676119
$91$	4.67472	0.490044
$92$	−9.67980	−1.00919
$93$	1.16245	0.120541
$94$	−18.4741	−1.90546
$95$	2.89500	0.297020
$96$	−2.36122	−0.240991
$97$	5.13849	0.521734	0.260867	−	0.965375i	$-0.415992\pi$
$97$	5.13849	0.521734	0.260867	+	0.965375i	$0.415992\pi$
$98$	2.22536	0.224795
$99$	0	0
$100$	2.95221	0.295221
$101$	−9.88045	−0.983142	−0.491571	−	0.870838i	$-0.663577\pi$
$101$	−9.88045	−0.983142	−0.491571	+	0.870838i	$0.663577\pi$
$102$	−5.40736	−0.535408
$103$	10.6264	1.04705	0.523525	−	0.852010i	$-0.324617\pi$
$103$	10.6264	1.04705	0.523525	+	0.852010i	$0.324617\pi$
$104$	−9.90577	−0.971340
$105$	−0.343016	−0.0334750
$106$	15.8550	1.53997
$107$	19.1128	1.84771	0.923854	−	0.382745i	$-0.125021\pi$
$107$	19.1128	1.84771	0.923854	+	0.382745i	$0.125021\pi$
$108$	−5.95679	−0.573192
$109$	−8.23413	−0.788687	−0.394343	−	0.918963i	$-0.629028\pi$
$109$	−8.23413	−0.788687	−0.394343	+	0.918963i	$0.629028\pi$
$110$	0	0
$111$	1.91199	0.181478
$112$	1.18888	0.112338
$113$	14.3879	1.35350	0.676749	−	0.736214i	$-0.263388\pi$
$113$	14.3879	1.35350	0.676749	+	0.736214i	$0.263388\pi$
$114$	2.20985	0.206971
$115$	−3.27883	−0.305753
$116$	−17.8861	−1.66069
$117$	13.4741	1.24568
$118$	10.7334	0.988092
$119$	7.08387	0.649378
$120$	0.726854	0.0663524
$121$	0	0
$122$	−27.9022	−2.52615
$123$	1.62036	0.146103
$124$	10.0048	0.898458
$125$	1.00000	0.0894427
$126$	6.41423	0.571425
$127$	−11.3400	−1.00626	−0.503132	−	0.864210i	$-0.667819\pi$
$127$	−11.3400	−1.00626	−0.503132	+	0.864210i	$0.667819\pi$
$128$	−15.0307	−1.32854
$129$	0.120209	0.0105838
$130$	−10.4029	−0.912397
$131$	−10.2588	−0.896319	−0.448160	−	0.893954i	$-0.647920\pi$
$131$	−10.2588	−0.896319	−0.448160	+	0.893954i	$0.647920\pi$
$132$	0	0
$133$	−2.89500	−0.251028
$134$	−18.5537	−1.60279
$135$	−2.01774	−0.173659
$136$	−15.0108	−1.28716
$137$	10.6898	0.913294	0.456647	−	0.889648i	$-0.349050\pi$
$137$	10.6898	0.913294	0.456647	+	0.889648i	$0.349050\pi$
$138$	−2.50284	−0.213056
$139$	−10.0383	−0.851436	−0.425718	−	0.904856i	$-0.639979\pi$
$139$	−10.0383	−0.851436	−0.425718	+	0.904856i	$0.639979\pi$
$140$	−2.95221	−0.249507
$141$	−2.84760	−0.239811
$142$	−36.7649	−3.08525
$143$	0	0
$144$	3.42675	0.285562
$145$	−6.05856	−0.503136
$146$	18.6743	1.54550
$147$	0.343016	0.0282915
$148$	16.4558	1.35266
$149$	14.6245	1.19809	0.599043	−	0.800717i	$-0.295548\pi$
$149$	14.6245	1.19809	0.599043	+	0.800717i	$0.295548\pi$
$150$	0.763334	0.0623259
$151$	−8.28591	−0.674298	−0.337149	−	0.941451i	$-0.609463\pi$
$151$	−8.28591	−0.674298	−0.337149	+	0.941451i	$0.609463\pi$
$152$	6.13451	0.497575
$153$	20.4181	1.65071
$154$	0	0
$155$	3.38892	0.272205
$156$	−4.73389	−0.379014
$157$	−8.74640	−0.698039	−0.349019	−	0.937116i	$-0.613485\pi$
$157$	−8.74640	−0.698039	−0.349019	+	0.937116i	$0.613485\pi$
$158$	−4.64955	−0.369899
$159$	2.44389	0.193813
$160$	−6.88369	−0.544203
$161$	3.27883	0.258408
$162$	17.7025	1.39084
$163$	−5.71280	−0.447461	−0.223730	−	0.974651i	$-0.571824\pi$
$163$	−5.71280	−0.447461	−0.223730	+	0.974651i	$0.571824\pi$
$164$	13.9458	1.08899
$165$	0	0
$166$	8.79839	0.682887
$167$	24.5499	1.89973	0.949864	−	0.312663i	$-0.101221\pi$
$167$	24.5499	1.89973	0.949864	+	0.312663i	$0.101221\pi$
$168$	−0.726854	−0.0560780
$169$	8.85303	0.681002
$170$	−15.7641	−1.20905
$171$	−8.34436	−0.638109
$172$	1.03459	0.0788870
$173$	9.47962	0.720722	0.360361	−	0.932813i	$-0.382654\pi$
$173$	9.47962	0.720722	0.360361	+	0.932813i	$0.382654\pi$
$174$	−4.62470	−0.350598
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	1.65445	0.124356
$178$	23.1532	1.73541
$179$	−8.27829	−0.618749	−0.309374	−	0.950940i	$-0.600120\pi$
$179$	−8.27829	−0.618749	−0.309374	+	0.950940i	$0.600120\pi$
$180$	−8.50927	−0.634244
$181$	−12.5712	−0.934408	−0.467204	−	0.884150i	$-0.654739\pi$
$181$	−12.5712	−0.934408	−0.467204	+	0.884150i	$0.654739\pi$
$182$	10.4029	0.771116
$183$	−4.30085	−0.317928
$184$	−6.94787	−0.512204
$185$	5.57406	0.409813
$186$	2.58688	0.189679
$187$	0	0
$188$	−24.5082	−1.78745
$189$	2.01774	0.146769
$190$	6.44240	0.467381
$191$	−22.4101	−1.62154	−0.810769	−	0.585366i	$-0.800951\pi$
$191$	−22.4101	−1.62154	−0.810769	+	0.585366i	$0.800951\pi$
$192$	−4.43894	−0.320353
$193$	−11.6129	−0.835914	−0.417957	−	0.908467i	$-0.637254\pi$
$193$	−11.6129	−0.835914	−0.417957	+	0.908467i	$0.637254\pi$
$194$	11.4350	0.820983
$195$	−1.60351	−0.114829
$196$	2.95221	0.210872
$197$	−5.77260	−0.411281	−0.205640	−	0.978628i	$-0.565928\pi$
$197$	−5.77260	−0.411281	−0.205640	+	0.978628i	$0.565928\pi$
$198$	0	0
$199$	4.42231	0.313489	0.156745	−	0.987639i	$-0.449900\pi$
$199$	4.42231	0.313489	0.156745	+	0.987639i	$0.449900\pi$
$200$	2.11901	0.149836
$201$	−2.85986	−0.201719
$202$	−21.9875	−1.54704
$203$	6.05856	0.425228
$204$	−7.17353	−0.502247
$205$	4.72386	0.329929
$206$	23.6475	1.64760
$207$	9.45071	0.656870
$208$	5.55767	0.385355
$209$	0	0
$210$	−0.763334	−0.0526750
$211$	−21.5956	−1.48670	−0.743351	−	0.668901i	$-0.766765\pi$
$211$	−21.5956	−1.48670	−0.743351	+	0.668901i	$0.766765\pi$
$212$	21.0336	1.44459
$213$	−5.66695	−0.388293
$214$	42.5329	2.90749
$215$	0.350447	0.0239003
$216$	−4.27560	−0.290918
$217$	−3.38892	−0.230055
$218$	−18.3239	−1.24105
$219$	2.87846	0.194508
$220$	0	0
$221$	33.1151	2.22757
$222$	4.25487	0.285568
$223$	0.213305	0.0142839	0.00714197	−	0.999974i	$-0.497727\pi$
$223$	0.213305	0.0142839	0.00714197	+	0.999974i	$0.497727\pi$
$224$	6.88369	0.459936
$225$	−2.88234	−0.192156
$226$	32.0181	2.12982
$227$	29.0440	1.92772	0.963858	−	0.266417i	$-0.0858399\pi$
$227$	29.0440	1.92772	0.963858	+	0.266417i	$0.0858399\pi$
$228$	2.93164	0.194152
$229$	−9.98634	−0.659916	−0.329958	−	0.943996i	$-0.607035\pi$
$229$	−9.98634	−0.659916	−0.329958	+	0.943996i	$0.607035\pi$
$230$	−7.29657	−0.481122
$231$	0	0
$232$	−12.8381	−0.842864
$233$	−20.0855	−1.31585	−0.657924	−	0.753085i	$-0.728565\pi$
$233$	−20.0855	−1.31585	−0.657924	+	0.753085i	$0.728565\pi$
$234$	29.9848	1.96016
$235$	−8.30165	−0.541540
$236$	14.2392	0.926894
$237$	−0.716682	−0.0465535
$238$	15.7641	1.02184
$239$	−4.56144	−0.295055	−0.147528	−	0.989058i	$-0.547131\pi$
$239$	−4.56144	−0.295055	−0.147528	+	0.989058i	$0.547131\pi$
$240$	−0.407804	−0.0263236
$241$	11.7927	0.759636	0.379818	−	0.925061i	$-0.375987\pi$
$241$	11.7927	0.759636	0.379818	+	0.925061i	$0.375987\pi$
$242$	0	0
$243$	8.78188	0.563358
$244$	−37.0158	−2.36969
$245$	1.00000	0.0638877
$246$	3.60588	0.229902
$247$	−13.5333	−0.861103
$248$	7.18114	0.456003
$249$	1.35618	0.0859446
$250$	2.22536	0.140744
$251$	11.6241	0.733704	0.366852	−	0.930279i	$-0.380436\pi$
$251$	11.6241	0.733704	0.366852	+	0.930279i	$0.380436\pi$
$252$	8.50927	0.536034
$253$	0	0
$254$	−25.2356	−1.58342
$255$	−2.42988	−0.152165
$256$	−7.56695	−0.472934
$257$	−27.5756	−1.72012	−0.860058	−	0.510196i	$-0.829573\pi$
$257$	−27.5756	−1.72012	−0.860058	+	0.510196i	$0.829573\pi$
$258$	0.267508	0.0166543
$259$	−5.57406	−0.346355
$260$	−13.8008	−0.855887
$261$	17.4628	1.08092
$262$	−22.8296	−1.41042
$263$	−16.6575	−1.02715	−0.513574	−	0.858046i	$-0.671679\pi$
$263$	−16.6575	−1.02715	−0.513574	+	0.858046i	$0.671679\pi$
$264$	0	0
$265$	7.12469	0.437666
$266$	−6.44240	−0.395009
$267$	3.56883	0.218409
$268$	−24.6137	−1.50352
$269$	−15.0492	−0.917568	−0.458784	−	0.888548i	$-0.651715\pi$
$269$	−15.0492	−0.917568	−0.458784	+	0.888548i	$0.651715\pi$
$270$	−4.49019	−0.273264
$271$	−20.6379	−1.25366	−0.626831	−	0.779155i	$-0.715649\pi$
$271$	−20.6379	−1.25366	−0.626831	+	0.779155i	$0.715649\pi$
$272$	8.42185	0.510650
$273$	1.60351	0.0970486
$274$	23.7887	1.43713
$275$	0	0
$276$	−3.32033	−0.199860
$277$	6.97787	0.419259	0.209630	−	0.977781i	$-0.432774\pi$
$277$	6.97787	0.419259	0.209630	+	0.977781i	$0.432774\pi$
$278$	−22.3388	−1.33979
$279$	−9.76802	−0.584796
$280$	−2.11901	−0.126635
$281$	−21.1690	−1.26284	−0.631419	−	0.775442i	$-0.717527\pi$
$281$	−21.1690	−1.26284	−0.631419	+	0.775442i	$0.717527\pi$
$282$	−6.33693	−0.377359
$283$	−15.5585	−0.924858	−0.462429	−	0.886656i	$-0.653022\pi$
$283$	−15.5585	−0.924858	−0.462429	+	0.886656i	$0.653022\pi$
$284$	−48.7732	−2.89416
$285$	0.993031	0.0588221
$286$	0	0
$287$	−4.72386	−0.278841
$288$	19.8411	1.16915
$289$	33.1812	1.95184
$290$	−13.4825	−0.791717
$291$	1.76259	0.103325
$292$	24.7738	1.44978
$293$	−0.202392	−0.0118239	−0.00591193	−	0.999983i	$-0.501882\pi$
$293$	−0.202392	−0.0118239	−0.00591193	+	0.999983i	$0.501882\pi$
$294$	0.763334	0.0445185
$295$	4.82324	0.280820
$296$	11.8115	0.686528
$297$	0	0
$298$	32.5447	1.88527
$299$	15.3276	0.886420
$300$	1.01266	0.0584657
$301$	−0.350447	−0.0201994
$302$	−18.4391	−1.06105
$303$	−3.38916	−0.194702
$304$	−3.44179	−0.197400
$305$	−12.5383	−0.717942
$306$	45.4376	2.59749
$307$	−2.32144	−0.132492	−0.0662458	−	0.997803i	$-0.521102\pi$
$307$	−2.32144	−0.132492	−0.0662458	+	0.997803i	$0.521102\pi$
$308$	0	0
$309$	3.64503	0.207358
$310$	7.54155	0.428331
$311$	−2.05882	−0.116745	−0.0583725	−	0.998295i	$-0.518591\pi$
$311$	−2.05882	−0.116745	−0.0583725	+	0.998295i	$0.518591\pi$
$312$	−3.39784	−0.192365
$313$	25.0103	1.41367	0.706834	−	0.707380i	$-0.250123\pi$
$313$	25.0103	1.41367	0.706834	+	0.707380i	$0.250123\pi$
$314$	−19.4639	−1.09841
$315$	2.88234	0.162401
$316$	−6.16821	−0.346989
$317$	−22.4778	−1.26248	−0.631239	−	0.775588i	$-0.717453\pi$
$317$	−22.4778	−1.26248	−0.631239	+	0.775588i	$0.717453\pi$
$318$	5.43852	0.304977
$319$	0	0
$320$	−12.9409	−0.723418
$321$	6.55602	0.365921
$322$	7.29657	0.406622
$323$	−20.5078	−1.14108
$324$	23.4845	1.30470
$325$	−4.67472	−0.259307
$326$	−12.7130	−0.704108
$327$	−2.82444	−0.156192
$328$	10.0099	0.552703
$329$	8.30165	0.457685
$330$	0	0
$331$	18.9616	1.04222	0.521112	−	0.853488i	$-0.325517\pi$
$331$	18.9616	1.04222	0.521112	+	0.853488i	$0.325517\pi$
$332$	11.6721	0.640592
$333$	−16.0663	−0.880430
$334$	54.6323	2.98934
$335$	−8.33739	−0.455520
$336$	0.407804	0.0222475
$337$	−8.91734	−0.485758	−0.242879	−	0.970057i	$-0.578092\pi$
$337$	−8.91734	−0.485758	−0.242879	+	0.970057i	$0.578092\pi$
$338$	19.7011	1.07160
$339$	4.93528	0.268047
$340$	−20.9131	−1.13417
$341$	0	0
$342$	−18.5692	−1.00411
$343$	−1.00000	−0.0539949
$344$	0.742599	0.0400383
$345$	−1.12469	−0.0605515
$346$	21.0955	1.13410
$347$	11.5209	0.618476	0.309238	−	0.950985i	$-0.399926\pi$
$347$	11.5209	0.618476	0.309238	+	0.950985i	$0.399926\pi$
$348$	−6.13524	−0.328883
$349$	16.3090	0.873002	0.436501	−	0.899704i	$-0.356217\pi$
$349$	16.3090	0.873002	0.436501	+	0.899704i	$0.356217\pi$
$350$	−2.22536	−0.118950
$351$	9.43237	0.503463
$352$	0	0
$353$	26.6161	1.41663	0.708316	−	0.705895i	$-0.249455\pi$
$353$	26.6161	1.41663	0.708316	+	0.705895i	$0.249455\pi$
$354$	3.68174	0.195682
$355$	−16.5209	−0.876840
$356$	30.7156	1.62792
$357$	2.42988	0.128603
$358$	−18.4222	−0.973641
$359$	−25.2990	−1.33523	−0.667614	−	0.744507i	$-0.732684\pi$
$359$	−25.2990	−1.33523	−0.667614	+	0.744507i	$0.732684\pi$
$360$	−6.10770	−0.321904
$361$	−10.6190	−0.558895
$362$	−27.9753	−1.47035
$363$	0	0
$364$	13.8008	0.723356
$365$	8.39161	0.439237
$366$	−9.57092	−0.500280
$367$	15.7228	0.820725	0.410362	−	0.911923i	$-0.365402\pi$
$367$	15.7228	0.820725	0.410362	+	0.911923i	$0.365402\pi$
$368$	3.89813	0.203204
$369$	−13.6158	−0.708808
$370$	12.4043	0.644867
$371$	−7.12469	−0.369896
$372$	3.43181	0.177931
$373$	−15.6308	−0.809333	−0.404666	−	0.914464i	$-0.632612\pi$
$373$	−15.6308	−0.809333	−0.404666	+	0.914464i	$0.632612\pi$
$374$	0	0
$375$	0.343016	0.0177133
$376$	−17.5913	−0.907200
$377$	28.3221	1.45866
$378$	4.49019	0.230950
$379$	−2.03204	−0.104379	−0.0521896	−	0.998637i	$-0.516620\pi$
$379$	−2.03204	−0.104379	−0.0521896	+	0.998637i	$0.516620\pi$
$380$	8.54664	0.438433
$381$	−3.88981	−0.199281
$382$	−49.8705	−2.55159
$383$	7.00858	0.358122	0.179061	−	0.983838i	$-0.442694\pi$
$383$	7.00858	0.358122	0.179061	+	0.983838i	$0.442694\pi$
$384$	−5.15579	−0.263105
$385$	0	0
$386$	−25.8428	−1.31536
$387$	−1.01011	−0.0513466
$388$	15.1699	0.770135
$389$	34.4454	1.74645	0.873226	−	0.487315i	$-0.162024\pi$
$389$	34.4454	1.74645	0.873226	+	0.487315i	$0.162024\pi$
$390$	−3.56837	−0.180692
$391$	23.2268	1.17463
$392$	2.11901	0.107026
$393$	−3.51895	−0.177508
$394$	−12.8461	−0.647176
$395$	−2.08935	−0.105127
$396$	0	0
$397$	−0.743894	−0.0373350	−0.0186675	−	0.999826i	$-0.505942\pi$
$397$	−0.743894	−0.0373350	−0.0186675	+	0.999826i	$0.505942\pi$
$398$	9.84122	0.493296
$399$	−0.993031	−0.0497137
$400$	−1.18888	−0.0594438
$401$	−4.47718	−0.223579	−0.111790	−	0.993732i	$-0.535658\pi$
$401$	−4.47718	−0.223579	−0.111790	+	0.993732i	$0.535658\pi$
$402$	−6.36421	−0.317418
$403$	−15.8423	−0.789159
$404$	−29.1692	−1.45122
$405$	7.95490	0.395282
$406$	13.4825	0.669123
$407$	0	0
$408$	−5.14894	−0.254910
$409$	6.50220	0.321513	0.160757	−	0.986994i	$-0.448607\pi$
$409$	6.50220	0.321513	0.160757	+	0.986994i	$0.448607\pi$
$410$	10.5123	0.519164
$411$	3.66679	0.180869
$412$	31.3713	1.54555
$413$	−4.82324	−0.237336
$414$	21.0312	1.03363
$415$	3.95370	0.194079
$416$	32.1793	1.57772
$417$	−3.44330	−0.168619
$418$	0	0
$419$	−5.44734	−0.266120	−0.133060	−	0.991108i	$-0.542480\pi$
$419$	−5.44734	−0.266120	−0.133060	+	0.991108i	$0.542480\pi$
$420$	−1.01266	−0.0494126
$421$	23.6598	1.15311	0.576555	−	0.817059i	$-0.304397\pi$
$421$	23.6598	1.15311	0.576555	+	0.817059i	$0.304397\pi$
$422$	−48.0579	−2.33942
$423$	23.9282	1.16343
$424$	15.0973	0.733188
$425$	−7.08387	−0.343618
$426$	−12.6110	−0.611004
$427$	12.5383	0.606772
$428$	56.4251	2.72741
$429$	0	0
$430$	0.779869	0.0376086
$431$	−27.7275	−1.33559	−0.667793	−	0.744347i	$-0.732761\pi$
$431$	−27.7275	−1.33559	−0.667793	+	0.744347i	$0.732761\pi$
$432$	2.39884	0.115414
$433$	31.9098	1.53348	0.766742	−	0.641955i	$-0.221876\pi$
$433$	31.9098	1.53348	0.766742	+	0.641955i	$0.221876\pi$
$434$	−7.54155	−0.362006
$435$	−2.07819	−0.0996414
$436$	−24.3089	−1.16418
$437$	−9.49221	−0.454074
$438$	6.40560	0.306071
$439$	−18.0174	−0.859923	−0.429961	−	0.902847i	$-0.641473\pi$
$439$	−18.0174	−0.859923	−0.429961	+	0.902847i	$0.641473\pi$
$440$	0	0
$441$	−2.88234	−0.137254
$442$	73.6930	3.50522
$443$	30.1953	1.43462	0.717312	−	0.696752i	$-0.245372\pi$
$443$	30.1953	1.43462	0.717312	+	0.696752i	$0.245372\pi$
$444$	5.64461	0.267881
$445$	10.4043	0.493210
$446$	0.474679	0.0224767
$447$	5.01644	0.237270
$448$	12.9409	0.611400
$449$	−19.0360	−0.898363	−0.449182	−	0.893440i	$-0.648284\pi$
$449$	−19.0360	−0.898363	−0.449182	+	0.893440i	$0.648284\pi$
$450$	−6.41423	−0.302370
$451$	0	0
$452$	42.4760	1.99790
$453$	−2.84220	−0.133538
$454$	64.6332	3.03338
$455$	4.67472	0.219154
$456$	2.10424	0.0985400
$457$	−20.5945	−0.963372	−0.481686	−	0.876344i	$-0.659975\pi$
$457$	−20.5945	−0.963372	−0.481686	+	0.876344i	$0.659975\pi$
$458$	−22.2232	−1.03842
$459$	14.2934	0.667159
$460$	−9.67980	−0.451323
$461$	−20.5195	−0.955689	−0.477844	−	0.878444i	$-0.658582\pi$
$461$	−20.5195	−0.955689	−0.477844	+	0.878444i	$0.658582\pi$
$462$	0	0
$463$	10.8626	0.504829	0.252415	−	0.967619i	$-0.418775\pi$
$463$	10.8626	0.504829	0.252415	+	0.967619i	$0.418775\pi$
$464$	7.20288	0.334385
$465$	1.16245	0.0539076
$466$	−44.6975	−2.07057
$467$	−18.4575	−0.854113	−0.427057	−	0.904225i	$-0.640449\pi$
$467$	−18.4575	−0.854113	−0.427057	+	0.904225i	$0.640449\pi$
$468$	39.7785	1.83876
$469$	8.33739	0.384985
$470$	−18.4741	−0.852148
$471$	−3.00016	−0.138240
$472$	10.2205	0.470435
$473$	0	0
$474$	−1.59487	−0.0732549
$475$	2.89500	0.132832
$476$	20.9131	0.958549
$477$	−20.5358	−0.940269
$478$	−10.1508	−0.464288
$479$	13.8959	0.634922	0.317461	−	0.948271i	$-0.397170\pi$
$479$	13.8959	0.634922	0.317461	+	0.948271i	$0.397170\pi$
$480$	−2.36122	−0.107774
$481$	−26.0572	−1.18811
$482$	26.2430	1.19534
$483$	1.12469	0.0511753
$484$	0	0
$485$	5.13849	0.233327
$486$	19.5428	0.886480
$487$	−34.4185	−1.55965	−0.779826	−	0.625997i	$-0.784692\pi$
$487$	−34.4185	−1.55965	−0.779826	+	0.625997i	$0.784692\pi$
$488$	−26.5688	−1.20271
$489$	−1.95958	−0.0886154
$490$	2.22536	0.100531
$491$	−41.2920	−1.86348	−0.931741	−	0.363124i	$-0.881710\pi$
$491$	−41.2920	−1.86348	−0.931741	+	0.363124i	$0.881710\pi$
$492$	4.78365	0.215663
$493$	42.9181	1.93293
$494$	−30.1164	−1.35500
$495$	0	0
$496$	−4.02901	−0.180908
$497$	16.5209	0.741065
$498$	3.01799	0.135239
$499$	19.6951	0.881674	0.440837	−	0.897587i	$-0.354682\pi$
$499$	19.6951	0.881674	0.440837	+	0.897587i	$0.354682\pi$
$500$	2.95221	0.132027
$501$	8.42102	0.376223
$502$	25.8677	1.15453
$503$	25.6703	1.14458	0.572291	−	0.820051i	$-0.306055\pi$
$503$	25.6703	1.14458	0.572291	+	0.820051i	$0.306055\pi$
$504$	6.10770	0.272058
$505$	−9.88045	−0.439674
$506$	0	0
$507$	3.03673	0.134866
$508$	−33.4781	−1.48535
$509$	−3.26675	−0.144796	−0.0723980	−	0.997376i	$-0.523065\pi$
$509$	−3.26675	−0.144796	−0.0723980	+	0.997376i	$0.523065\pi$
$510$	−5.40736	−0.239442
$511$	−8.39161	−0.371223
$512$	13.2223	0.584350
$513$	−5.84135	−0.257902
$514$	−61.3655	−2.70671
$515$	10.6264	0.468255
$516$	0.354882	0.0156228
$517$	0	0
$518$	−12.4043	−0.545012
$519$	3.25166	0.142732
$520$	−9.90577	−0.434397
$521$	−22.4225	−0.982350	−0.491175	−	0.871061i	$-0.663432\pi$
$521$	−22.4225	−0.982350	−0.491175	+	0.871061i	$0.663432\pi$
$522$	38.8610	1.70090
$523$	−4.22476	−0.184736	−0.0923680	−	0.995725i	$-0.529444\pi$
$523$	−4.22476	−0.184736	−0.0923680	+	0.995725i	$0.529444\pi$
$524$	−30.2863	−1.32306
$525$	−0.343016	−0.0149705
$526$	−37.0689	−1.61628
$527$	−24.0067	−1.04575
$528$	0	0
$529$	−12.2493	−0.532576
$530$	15.8550	0.688696
$531$	−13.9022	−0.603305
$532$	−8.54664	−0.370544
$533$	−22.0827	−0.956509
$534$	7.94193	0.343681
$535$	19.1128	0.826320
$536$	−17.6670	−0.763098
$537$	−2.83959	−0.122537
$538$	−33.4899	−1.44385
$539$	0	0
$540$	−5.95679	−0.256339
$541$	1.54043	0.0662281	0.0331140	−	0.999452i	$-0.489458\pi$
$541$	1.54043	0.0662281	0.0331140	+	0.999452i	$0.489458\pi$
$542$	−45.9267	−1.97272
$543$	−4.31212	−0.185051
$544$	48.7632	2.09070
$545$	−8.23413	−0.352711
$546$	3.56837	0.152712
$547$	10.0938	0.431579	0.215790	−	0.976440i	$-0.430767\pi$
$547$	10.0938	0.431579	0.215790	+	0.976440i	$0.430767\pi$
$548$	31.5586	1.34812
$549$	36.1397	1.54240
$550$	0	0
$551$	−17.5395	−0.747208
$552$	−2.38323	−0.101437
$553$	2.08935	0.0888483
$554$	15.5282	0.659732
$555$	1.91199	0.0811596
$556$	−29.6351	−1.25681
$557$	−32.7105	−1.38599	−0.692994	−	0.720943i	$-0.743709\pi$
$557$	−32.7105	−1.38599	−0.692994	+	0.720943i	$0.743709\pi$
$558$	−21.7373	−0.920214
$559$	−1.63824	−0.0692903
$560$	1.18888	0.0502392
$561$	0	0
$562$	−47.1086	−1.98716
$563$	38.3254	1.61522	0.807611	−	0.589716i	$-0.200760\pi$
$563$	38.3254	1.61522	0.807611	+	0.589716i	$0.200760\pi$
$564$	−8.40672	−0.353987
$565$	14.3879	0.605302
$566$	−34.6232	−1.45532
$567$	−7.95490	−0.334074
$568$	−35.0079	−1.46890
$569$	−3.74899	−0.157166	−0.0785829	−	0.996908i	$-0.525040\pi$
$569$	−3.74899	−0.157166	−0.0785829	+	0.996908i	$0.525040\pi$
$570$	2.20985	0.0925603
$571$	−22.1237	−0.925850	−0.462925	−	0.886397i	$-0.653200\pi$
$571$	−22.1237	−0.925850	−0.462925	+	0.886397i	$0.653200\pi$
$572$	0	0
$573$	−7.68703	−0.321130
$574$	−10.5123	−0.438774
$575$	−3.27883	−0.136737
$576$	37.3001	1.55417
$577$	−43.2498	−1.80051	−0.900256	−	0.435361i	$-0.856621\pi$
$577$	−43.2498	−1.80051	−0.900256	+	0.435361i	$0.856621\pi$
$578$	73.8401	3.07134
$579$	−3.98341	−0.165545
$580$	−17.8861	−0.742682
$581$	−3.95370	−0.164027
$582$	3.92238	0.162588
$583$	0	0
$584$	17.7819	0.735819
$585$	13.4741	0.557087
$586$	−0.450394	−0.0186056
$587$	−11.6480	−0.480765	−0.240382	−	0.970678i	$-0.577273\pi$
$587$	−11.6480	−0.480765	−0.240382	+	0.970678i	$0.577273\pi$
$588$	1.01266	0.0417612
$589$	9.81091	0.404251
$590$	10.7334	0.441888
$591$	−1.98010	−0.0814502
$592$	−6.62687	−0.272363
$593$	−8.92605	−0.366549	−0.183275	−	0.983062i	$-0.558670\pi$
$593$	−8.92605	−0.366549	−0.183275	+	0.983062i	$0.558670\pi$
$594$	0	0
$595$	7.08387	0.290410
$596$	43.1746	1.76850
$597$	1.51692	0.0620836
$598$	34.1095	1.39484
$599$	−9.17453	−0.374861	−0.187431	−	0.982278i	$-0.560016\pi$
$599$	−9.17453	−0.374861	−0.187431	+	0.982278i	$0.560016\pi$
$600$	0.726854	0.0296737
$601$	−17.3900	−0.709353	−0.354677	−	0.934989i	$-0.615409\pi$
$601$	−17.3900	−0.709353	−0.354677	+	0.934989i	$0.615409\pi$
$602$	−0.779869	−0.0317851
$603$	24.0312	0.978626
$604$	−24.4617	−0.995334
$605$	0	0
$606$	−7.54208	−0.306376
$607$	−9.62872	−0.390818	−0.195409	−	0.980722i	$-0.562603\pi$
$607$	−9.62872	−0.390818	−0.195409	+	0.980722i	$0.562603\pi$
$608$	−19.9282	−0.808197
$609$	2.07819	0.0842123
$610$	−27.9022	−1.12973
$611$	38.8079	1.57000
$612$	60.2786	2.43662
$613$	−1.36086	−0.0549647	−0.0274823	−	0.999622i	$-0.508749\pi$
$613$	−1.36086	−0.0549647	−0.0274823	+	0.999622i	$0.508749\pi$
$614$	−5.16603	−0.208484
$615$	1.62036	0.0653393
$616$	0	0
$617$	13.2656	0.534052	0.267026	−	0.963689i	$-0.413959\pi$
$617$	13.2656	0.534052	0.267026	+	0.963689i	$0.413959\pi$
$618$	8.11148	0.326292
$619$	42.7524	1.71836	0.859182	−	0.511671i	$-0.170973\pi$
$619$	42.7524	1.71836	0.859182	+	0.511671i	$0.170973\pi$
$620$	10.0048	0.401803
$621$	6.61583	0.265484
$622$	−4.58161	−0.183706
$623$	−10.4043	−0.416838
$624$	1.90637	0.0763159
$625$	1.00000	0.0400000
$626$	55.6569	2.22450
$627$	0	0
$628$	−25.8212	−1.03038
$629$	−39.4859	−1.57441
$630$	6.41423	0.255549
$631$	28.8198	1.14730	0.573649	−	0.819101i	$-0.305527\pi$
$631$	28.8198	1.14730	0.573649	+	0.819101i	$0.305527\pi$
$632$	−4.42735	−0.176111
$633$	−7.40764	−0.294427
$634$	−50.0211	−1.98659
$635$	−11.3400	−0.450015
$636$	7.21487	0.286088
$637$	−4.67472	−0.185219
$638$	0	0
$639$	47.6189	1.88378
$640$	−15.0307	−0.594142
$641$	−26.6223	−1.05152	−0.525759	−	0.850634i	$-0.676218\pi$
$641$	−26.6223	−1.05152	−0.525759	+	0.850634i	$0.676218\pi$
$642$	14.5895	0.575801
$643$	−21.8058	−0.859935	−0.429968	−	0.902844i	$-0.641475\pi$
$643$	−21.8058	−0.859935	−0.429968	+	0.902844i	$0.641475\pi$
$644$	9.67980	0.381438
$645$	0.120209	0.00473323
$646$	−45.6371	−1.79557
$647$	30.1523	1.18541	0.592704	−	0.805420i	$-0.298060\pi$
$647$	30.1523	1.18541	0.592704	+	0.805420i	$0.298060\pi$
$648$	16.8565	0.662185
$649$	0	0
$650$	−10.4029	−0.408036
$651$	−1.16245	−0.0455602
$652$	−16.8654	−0.660499
$653$	1.69077	0.0661650	0.0330825	−	0.999453i	$-0.489468\pi$
$653$	1.69077	0.0661650	0.0330825	+	0.999453i	$0.489468\pi$
$654$	−6.28539	−0.245778
$655$	−10.2588	−0.400846
$656$	−5.61608	−0.219271
$657$	−24.1875	−0.943643
$658$	18.4741	0.720197
$659$	29.8330	1.16213	0.581064	−	0.813858i	$-0.302636\pi$
$659$	29.8330	1.16213	0.581064	+	0.813858i	$0.302636\pi$
$660$	0	0
$661$	8.26957	0.321649	0.160824	−	0.986983i	$-0.448585\pi$
$661$	8.26957	0.321649	0.160824	+	0.986983i	$0.448585\pi$
$662$	42.1963	1.64001
$663$	11.3590	0.441148
$664$	8.37791	0.325126
$665$	−2.89500	−0.112263
$666$	−35.7533	−1.38541
$667$	19.8650	0.769176
$668$	72.4764	2.80420
$669$	0.0731670	0.00282880
$670$	−18.5537	−0.716791
$671$	0	0
$672$	2.36122	0.0910859
$673$	−4.53111	−0.174661	−0.0873307	−	0.996179i	$-0.527834\pi$
$673$	−4.53111	−0.174661	−0.0873307	+	0.996179i	$0.527834\pi$
$674$	−19.8443	−0.764372
$675$	−2.01774	−0.0776628
$676$	26.1360	1.00523
$677$	10.4967	0.403423	0.201711	−	0.979445i	$-0.435350\pi$
$677$	10.4967	0.403423	0.201711	+	0.979445i	$0.435350\pi$
$678$	10.9827	0.421790
$679$	−5.13849	−0.197197
$680$	−15.0108	−0.575637
$681$	9.96255	0.381766
$682$	0	0
$683$	49.5449	1.89578	0.947892	−	0.318592i	$-0.103210\pi$
$683$	49.5449	1.89578	0.947892	+	0.318592i	$0.103210\pi$
$684$	−24.6343	−0.941916
$685$	10.6898	0.408438
$686$	−2.22536	−0.0849645
$687$	−3.42548	−0.130690
$688$	−0.416638	−0.0158842
$689$	−33.3060	−1.26886
$690$	−2.50284	−0.0952816
$691$	21.1526	0.804683	0.402342	−	0.915490i	$-0.368196\pi$
$691$	21.1526	0.804683	0.402342	+	0.915490i	$0.368196\pi$
$692$	27.9858	1.06386
$693$	0	0
$694$	25.6382	0.973211
$695$	−10.0383	−0.380774
$696$	−4.40369	−0.166921
$697$	−33.4632	−1.26751
$698$	36.2934	1.37373
$699$	−6.88967	−0.260591
$700$	−2.95221	−0.111583
$701$	52.7531	1.99246	0.996228	−	0.0867731i	$-0.0276555\pi$
$701$	52.7531	1.99246	0.996228	+	0.0867731i	$0.0276555\pi$
$702$	20.9904	0.792231
$703$	16.1369	0.608614
$704$	0	0
$705$	−2.84760	−0.107247
$706$	59.2303	2.22916
$707$	9.88045	0.371593
$708$	4.88428	0.183563
$709$	−41.4107	−1.55521	−0.777606	−	0.628752i	$-0.783566\pi$
$709$	−41.4107	−1.55521	−0.777606	+	0.628752i	$0.783566\pi$
$710$	−36.7649	−1.37976
$711$	6.02222	0.225851
$712$	22.0467	0.826235
$713$	−11.1117	−0.416137
$714$	5.40736	0.202365
$715$	0	0
$716$	−24.4393	−0.913338
$717$	−1.56465	−0.0584329
$718$	−56.2992	−2.10107
$719$	23.5436	0.878030	0.439015	−	0.898480i	$-0.355328\pi$
$719$	23.5436	0.878030	0.439015	+	0.898480i	$0.355328\pi$
$720$	3.42675	0.127707
$721$	−10.6264	−0.395748
$722$	−23.6311	−0.879457
$723$	4.04510	0.150439
$724$	−37.1127	−1.37928
$725$	−6.05856	−0.225009
$726$	0	0
$727$	28.0763	1.04129	0.520647	−	0.853772i	$-0.325691\pi$
$727$	28.0763	1.04129	0.520647	+	0.853772i	$0.325691\pi$
$728$	9.90577	0.367132
$729$	−20.8524	−0.772310
$730$	18.6743	0.691168
$731$	−2.48252	−0.0918194
$732$	−12.6970	−0.469295
$733$	12.4455	0.459685	0.229843	−	0.973228i	$-0.426179\pi$
$733$	12.4455	0.459685	0.229843	+	0.973228i	$0.426179\pi$
$734$	34.9889	1.29146
$735$	0.343016	0.0126523
$736$	22.5705	0.831958
$737$	0	0
$738$	−30.2999	−1.11536
$739$	−36.8483	−1.35548	−0.677742	−	0.735299i	$-0.737042\pi$
$739$	−36.8483	−1.35548	−0.677742	+	0.735299i	$0.737042\pi$
$740$	16.4558	0.604927
$741$	−4.64214	−0.170533
$742$	−15.8550	−0.582055
$743$	−25.1359	−0.922147	−0.461073	−	0.887362i	$-0.652536\pi$
$743$	−25.1359	−0.922147	−0.461073	+	0.887362i	$0.652536\pi$
$744$	2.46325	0.0903071
$745$	14.6245	0.535800
$746$	−34.7841	−1.27354
$747$	−11.3959	−0.416954
$748$	0	0
$749$	−19.1128	−0.698368
$750$	0.763334	0.0278730
$751$	−14.2181	−0.518827	−0.259413	−	0.965766i	$-0.583529\pi$
$751$	−14.2181	−0.518827	−0.259413	+	0.965766i	$0.583529\pi$
$752$	9.86964	0.359909
$753$	3.98724	0.145303
$754$	63.0267	2.29530
$755$	−8.28591	−0.301555
$756$	5.95679	0.216646
$757$	−2.12627	−0.0772805	−0.0386402	−	0.999253i	$-0.512303\pi$
$757$	−2.12627	−0.0772805	−0.0386402	+	0.999253i	$0.512303\pi$
$758$	−4.52202	−0.164247
$759$	0	0
$760$	6.13451	0.222522
$761$	−3.34850	−0.121383	−0.0606914	−	0.998157i	$-0.519331\pi$
$761$	−3.34850	−0.121383	−0.0606914	+	0.998157i	$0.519331\pi$
$762$	−8.65622	−0.313582
$763$	8.23413	0.298096
$764$	−66.1593	−2.39356
$765$	20.4181	0.738219
$766$	15.5966	0.563527
$767$	−22.5473	−0.814136
$768$	−2.59559	−0.0936602
$769$	9.70926	0.350125	0.175062	−	0.984557i	$-0.443987\pi$
$769$	9.70926	0.350125	0.175062	+	0.984557i	$0.443987\pi$
$770$	0	0
$771$	−9.45887	−0.340653
$772$	−34.2837	−1.23390
$773$	18.3721	0.660798	0.330399	−	0.943841i	$-0.392817\pi$
$773$	18.3721	0.660798	0.330399	+	0.943841i	$0.392817\pi$
$774$	−2.24785	−0.0807973
$775$	3.38892	0.121734
$776$	10.8885	0.390874
$777$	−1.91199	−0.0685924
$778$	76.6534	2.74816
$779$	13.6756	0.489977
$780$	−4.73389	−0.169500
$781$	0	0
$782$	51.6880	1.84836
$783$	12.2246	0.436871
$784$	−1.18888	−0.0424599
$785$	−8.74640	−0.312172
$786$	−7.83092	−0.279320
$787$	−53.3957	−1.90335	−0.951675	−	0.307107i	$-0.900639\pi$
$787$	−53.3957	−1.90335	−0.951675	+	0.307107i	$0.900639\pi$
$788$	−17.0419	−0.607093
$789$	−5.71380	−0.203417
$790$	−4.64955	−0.165424
$791$	−14.3879	−0.511574
$792$	0	0
$793$	58.6132	2.08141
$794$	−1.65543	−0.0587490
$795$	2.44389	0.0866757
$796$	13.0556	0.462743
$797$	−17.0237	−0.603011	−0.301505	−	0.953465i	$-0.597489\pi$
$797$	−17.0237	−0.603011	−0.301505	+	0.953465i	$0.597489\pi$
$798$	−2.20985	−0.0782278
$799$	58.8079	2.08047
$800$	−6.88369	−0.243375
$801$	−29.9886	−1.05960
$802$	−9.96331	−0.351817
$803$	0	0
$804$	−8.44291	−0.297759
$805$	3.27883	0.115564
$806$	−35.2547	−1.24179
$807$	−5.16213	−0.181716
$808$	−20.9367	−0.736552
$809$	−54.4599	−1.91471	−0.957353	−	0.288920i	$-0.906704\pi$
$809$	−54.4599	−1.91471	−0.957353	+	0.288920i	$0.906704\pi$
$810$	17.7025	0.622002
$811$	29.7781	1.04565	0.522825	−	0.852440i	$-0.324878\pi$
$811$	29.7781	1.04565	0.522825	+	0.852440i	$0.324878\pi$
$812$	17.8861	0.627680
$813$	−7.07914	−0.248276
$814$	0	0
$815$	−5.71280	−0.200111
$816$	2.88883	0.101129
$817$	1.01454	0.0354944
$818$	14.4697	0.505922
$819$	−13.4741	−0.470824
$820$	13.9458	0.487009
$821$	40.3897	1.40961	0.704805	−	0.709401i	$-0.251035\pi$
$821$	40.3897	1.40961	0.704805	+	0.709401i	$0.251035\pi$
$822$	8.15991	0.284609
$823$	−16.6754	−0.581270	−0.290635	−	0.956834i	$-0.593866\pi$
$823$	−16.6754	−0.581270	−0.290635	+	0.956834i	$0.593866\pi$
$824$	22.5174	0.784430
$825$	0	0
$826$	−10.7334	−0.373464
$827$	−8.58324	−0.298469	−0.149234	−	0.988802i	$-0.547681\pi$
$827$	−8.58324	−0.298469	−0.149234	+	0.988802i	$0.547681\pi$
$828$	27.9005	0.969609
$829$	−8.89758	−0.309026	−0.154513	−	0.987991i	$-0.549381\pi$
$829$	−8.89758	−0.309026	−0.154513	+	0.987991i	$0.549381\pi$
$830$	8.79839	0.305397
$831$	2.39352	0.0830304
$832$	60.4951	2.09729
$833$	−7.08387	−0.245442
$834$	−7.66256	−0.265333
$835$	24.5499	0.849584
$836$	0	0
$837$	−6.83796	−0.236354
$838$	−12.1223	−0.418757
$839$	31.7481	1.09607	0.548033	−	0.836457i	$-0.315377\pi$
$839$	31.7481	1.09607	0.548033	+	0.836457i	$0.315377\pi$
$840$	−0.726854	−0.0250788
$841$	7.70615	0.265729
$842$	52.6515	1.81449
$843$	−7.26132	−0.250093
$844$	−63.7547	−2.19453
$845$	8.85303	0.304553
$846$	53.2487	1.83073
$847$	0	0
$848$	−8.47038	−0.290874
$849$	−5.33683	−0.183159
$850$	−15.7641	−0.540706
$851$	−18.2764	−0.626507
$852$	−16.7300	−0.573161
$853$	29.4095	1.00696	0.503481	−	0.864006i	$-0.332052\pi$
$853$	29.4095	1.00696	0.503481	+	0.864006i	$0.332052\pi$
$854$	27.9022	0.954795
$855$	−8.34436	−0.285371
$856$	40.5002	1.38427
$857$	−6.44703	−0.220226	−0.110113	−	0.993919i	$-0.535121\pi$
$857$	−6.44703	−0.220226	−0.110113	+	0.993919i	$0.535121\pi$
$858$	0	0
$859$	39.9961	1.36465	0.682325	−	0.731049i	$-0.260969\pi$
$859$	39.9961	1.36465	0.682325	+	0.731049i	$0.260969\pi$
$860$	1.03459	0.0352793
$861$	−1.62036	−0.0552217
$862$	−61.7035	−2.10163
$863$	56.5285	1.92425	0.962127	−	0.272602i	$-0.0878844\pi$
$863$	56.5285	1.92425	0.962127	+	0.272602i	$0.0878844\pi$
$864$	13.8895	0.472530
$865$	9.47962	0.322317
$866$	71.0106	2.41304
$867$	11.3817	0.386543
$868$	−10.0048	−0.339585
$869$	0	0
$870$	−4.62470	−0.156792
$871$	38.9750	1.32062
$872$	−17.4482	−0.590870
$873$	−14.8109	−0.501272
$874$	−21.1235	−0.714515
$875$	−1.00000	−0.0338062
$876$	8.49782	0.287115
$877$	−55.0680	−1.85952	−0.929758	−	0.368172i	$-0.879984\pi$
$877$	−55.0680	−1.85952	−0.929758	+	0.368172i	$0.879984\pi$
$878$	−40.0951	−1.35314
$879$	−0.0694237	−0.00234160
$880$	0	0
$881$	−20.5673	−0.692929	−0.346465	−	0.938063i	$-0.612618\pi$
$881$	−20.5673	−0.692929	−0.346465	+	0.938063i	$0.612618\pi$
$882$	−6.41423	−0.215978
$883$	−55.3641	−1.86315	−0.931576	−	0.363547i	$-0.881566\pi$
$883$	−55.3641	−1.86315	−0.931576	+	0.363547i	$0.881566\pi$
$884$	97.7628	3.28812
$885$	1.65445	0.0556137
$886$	67.1954	2.25747
$887$	19.5602	0.656766	0.328383	−	0.944545i	$-0.393496\pi$
$887$	19.5602	0.656766	0.328383	+	0.944545i	$0.393496\pi$
$888$	4.05153	0.135960
$889$	11.3400	0.380332
$890$	23.1532	0.776097
$891$	0	0
$892$	0.629720	0.0210846
$893$	−24.0333	−0.804242
$894$	11.1634	0.373359
$895$	−8.27829	−0.276713
$896$	15.0307	0.502142
$897$	5.25763	0.175547
$898$	−42.3618	−1.41363
$899$	−20.5320	−0.684780
$900$	−8.50927	−0.283642
$901$	−50.4704	−1.68141
$902$	0	0
$903$	−0.120209	−0.00400031
$904$	30.4880	1.01402
$905$	−12.5712	−0.417880
$906$	−6.32491	−0.210131
$907$	6.54055	0.217175	0.108588	−	0.994087i	$-0.465367\pi$
$907$	6.54055	0.217175	0.108588	+	0.994087i	$0.465367\pi$
$908$	85.7439	2.84551
$909$	28.4788	0.944583
$910$	10.4029	0.344854
$911$	37.8827	1.25511	0.627555	−	0.778573i	$-0.284056\pi$
$911$	37.8827	1.25511	0.627555	+	0.778573i	$0.284056\pi$
$912$	−1.18059	−0.0390933
$913$	0	0
$914$	−45.8302	−1.51593
$915$	−4.30085	−0.142182
$916$	−29.4818	−0.974105
$917$	10.2588	0.338777
$918$	31.8079	1.04982
$919$	5.62821	0.185658	0.0928288	−	0.995682i	$-0.470409\pi$
$919$	5.62821	0.185658	0.0928288	+	0.995682i	$0.470409\pi$
$920$	−6.94787	−0.229064
$921$	−0.796292	−0.0262387
$922$	−45.6632	−1.50384
$923$	77.2307	2.54208
$924$	0	0
$925$	5.57406	0.183274
$926$	24.1732	0.794382
$927$	−30.6289	−1.00598
$928$	41.7052	1.36904
$929$	−26.3192	−0.863505	−0.431752	−	0.901992i	$-0.642105\pi$
$929$	−26.3192	−0.863505	−0.431752	+	0.901992i	$0.642105\pi$
$930$	2.58688	0.0848270
$931$	2.89500	0.0948797
$932$	−59.2967	−1.94233
$933$	−0.706209	−0.0231203
$934$	−41.0746	−1.34400
$935$	0	0
$936$	28.5518	0.933244
$937$	3.13245	0.102333	0.0511663	−	0.998690i	$-0.483706\pi$
$937$	3.13245	0.102333	0.0511663	+	0.998690i	$0.483706\pi$
$938$	18.5537	0.605799
$939$	8.57895	0.279963
$940$	−24.5082	−0.799370
$941$	52.4425	1.70958	0.854788	−	0.518978i	$-0.173687\pi$
$941$	52.4425	1.70958	0.854788	+	0.518978i	$0.173687\pi$
$942$	−6.67642	−0.217530
$943$	−15.4887	−0.504383
$944$	−5.73424	−0.186633
$945$	2.01774	0.0656370
$946$	0	0
$947$	−49.9305	−1.62252	−0.811262	−	0.584683i	$-0.801219\pi$
$947$	−49.9305	−1.62252	−0.811262	+	0.584683i	$0.801219\pi$
$948$	−2.11580	−0.0687179
$949$	−39.2285	−1.27341
$950$	6.44240	0.209019
$951$	−7.71025	−0.250022
$952$	15.0108	0.486502
$953$	48.0291	1.55582	0.777908	−	0.628378i	$-0.216281\pi$
$953$	48.0291	1.55582	0.777908	+	0.628378i	$0.216281\pi$
$954$	−45.6994	−1.47957
$955$	−22.4101	−0.725174
$956$	−13.4663	−0.435532
$957$	0	0
$958$	30.9234	0.999091
$959$	−10.6898	−0.345193
$960$	−4.43894	−0.143266
$961$	−19.5152	−0.629523
$962$	−57.9865	−1.86956
$963$	−55.0897	−1.77524
$964$	34.8146	1.12130
$965$	−11.6129	−0.373832
$966$	2.50284	0.0805277
$967$	28.2899	0.909741	0.454871	−	0.890558i	$-0.349686\pi$
$967$	28.2899	0.909741	0.454871	+	0.890558i	$0.349686\pi$
$968$	0	0
$969$	−7.03451	−0.225981
$970$	11.4350	0.367155
$971$	−2.83731	−0.0910537	−0.0455269	−	0.998963i	$-0.514497\pi$
$971$	−2.83731	−0.0910537	−0.0455269	+	0.998963i	$0.514497\pi$
$972$	25.9259	0.831575
$973$	10.0383	0.321813
$974$	−76.5934	−2.45421
$975$	−1.60351	−0.0513533
$976$	14.9065	0.477146
$977$	12.2408	0.391619	0.195810	−	0.980642i	$-0.437267\pi$
$977$	12.2408	0.391619	0.195810	+	0.980642i	$0.437267\pi$
$978$	−4.36077	−0.139442
$979$	0	0
$980$	2.95221	0.0943049
$981$	23.7336	0.757755
$982$	−91.8894	−2.93231
$983$	−16.8083	−0.536103	−0.268052	−	0.963405i	$-0.586380\pi$
$983$	−16.8083	−0.536103	−0.268052	+	0.963405i	$0.586380\pi$
$984$	3.43355	0.109458
$985$	−5.77260	−0.183930
$986$	95.5080	3.04159
$987$	2.84760	0.0906402
$988$	−39.9532	−1.27108
$989$	−1.14906	−0.0365379
$990$	0	0
$991$	−1.49851	−0.0476019	−0.0238009	−	0.999717i	$-0.507577\pi$
$991$	−1.49851	−0.0476019	−0.0238009	+	0.999717i	$0.507577\pi$
$992$	−23.3283	−0.740673
$993$	6.50414	0.206403
$994$	36.7649	1.16611
$995$	4.42231	0.140197
$996$	4.00374	0.126863
$997$	−49.6075	−1.57108	−0.785542	−	0.618808i	$-0.787616\pi$
$997$	−49.6075	−1.57108	−0.785542	+	0.618808i	$0.787616\pi$
$998$	43.8286	1.38737
$999$	−11.2470	−0.355839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.z.1.5	✓	5
11.10	odd	2		4235.2.a.bf.1.1	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.z.1.5	✓	5	1.1	even	1	trivial
4235.2.a.bf.1.1	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+2.22536 q^{2} +0.343016 q^{3} +2.95221 q^{4} +1.00000 q^{5} +0.763334 q^{6} -1.00000 q^{7} +2.11901 q^{8} -2.88234 q^{9} +O(q^{10})\)	\(q+2.22536 q^{2} +0.343016 q^{3} +2.95221 q^{4} +1.00000 q^{5} +0.763334 q^{6} -1.00000 q^{7} +2.11901 q^{8} -2.88234 q^{9} +2.22536 q^{10} +1.01266 q^{12} -4.67472 q^{13} -2.22536 q^{14} +0.343016 q^{15} -1.18888 q^{16} -7.08387 q^{17} -6.41423 q^{18} +2.89500 q^{19} +2.95221 q^{20} -0.343016 q^{21} -3.27883 q^{23} +0.726854 q^{24} +1.00000 q^{25} -10.4029 q^{26} -2.01774 q^{27} -2.95221 q^{28} -6.05856 q^{29} +0.763334 q^{30} +3.38892 q^{31} -6.88369 q^{32} -15.7641 q^{34} -1.00000 q^{35} -8.50927 q^{36} +5.57406 q^{37} +6.44240 q^{38} -1.60351 q^{39} +2.11901 q^{40} +4.72386 q^{41} -0.763334 q^{42} +0.350447 q^{43} -2.88234 q^{45} -7.29657 q^{46} -8.30165 q^{47} -0.407804 q^{48} +1.00000 q^{49} +2.22536 q^{50} -2.42988 q^{51} -13.8008 q^{52} +7.12469 q^{53} -4.49019 q^{54} -2.11901 q^{56} +0.993031 q^{57} -13.4825 q^{58} +4.82324 q^{59} +1.01266 q^{60} -12.5383 q^{61} +7.54155 q^{62} +2.88234 q^{63} -12.9409 q^{64} -4.67472 q^{65} -8.33739 q^{67} -20.9131 q^{68} -1.12469 q^{69} -2.22536 q^{70} -16.5209 q^{71} -6.10770 q^{72} +8.39161 q^{73} +12.4043 q^{74} +0.343016 q^{75} +8.54664 q^{76} -3.56837 q^{78} -2.08935 q^{79} -1.18888 q^{80} +7.95490 q^{81} +10.5123 q^{82} +3.95370 q^{83} -1.01266 q^{84} -7.08387 q^{85} +0.779869 q^{86} -2.07819 q^{87} +10.4043 q^{89} -6.41423 q^{90} +4.67472 q^{91} -9.67980 q^{92} +1.16245 q^{93} -18.4741 q^{94} +2.89500 q^{95} -2.36122 q^{96} +5.13849 q^{97} +2.22536 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9	\( 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9} - 2 q^{10} - 3 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 6 q^{17} - 11 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 3 q^{23} + 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} - 4 q^{28} - 17 q^{29} + q^{30} + 12 q^{31} + 3 q^{32} - 12 q^{34} - 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} - 14 q^{39} - 5 q^{41} - q^{42} - 4 q^{43} - q^{45} - 2 q^{46} - 12 q^{48} + 5 q^{49} - 2 q^{50} - 14 q^{51} - 2 q^{52} + 8 q^{53} - 22 q^{54} - 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} - 24 q^{61} - 9 q^{62} + q^{63} - 38 q^{64} - 8 q^{65} - 9 q^{67} - 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} - 4 q^{72} - 11 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 5 q^{78} - 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} - 10 q^{83} + 3 q^{84} - 6 q^{85} + 15 q^{86} + 2 q^{87} - 9 q^{89} - 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} - 34 q^{94} - 7 q^{95} + 18 q^{96} + 11 q^{97} - 2 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9 - 2 * q^10 - 3 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 6 * q^17 - 11 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 3 * q^23 + 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 - 4 * q^28 - 17 * q^29 + q^30 + 12 * q^31 + 3 * q^32 - 12 * q^34 - 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 - 14 * q^39 - 5 * q^41 - q^42 - 4 * q^43 - q^45 - 2 * q^46 - 12 * q^48 + 5 * q^49 - 2 * q^50 - 14 * q^51 - 2 * q^52 + 8 * q^53 - 22 * q^54 - 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 - 24 * q^61 - 9 * q^62 + q^63 - 38 * q^64 - 8 * q^65 - 9 * q^67 - 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 - 4 * q^72 - 11 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 5 * q^78 - 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 - 10 * q^83 + 3 * q^84 - 6 * q^85 + 15 * q^86 + 2 * q^87 - 9 * q^89 - 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 - 34 * q^94 - 7 * q^95 + 18 * q^96 + 11 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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Database

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