LMFDB - Embedded newform 6025.2.a.o.1.10

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:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.38463 q^{2} -1.64656 q^{3} -0.0828005 q^{4} +2.27988 q^{6} -2.06195 q^{7} +2.88391 q^{8} -0.288826 q^{9} +O(q^{10})$	\(q-1.38463 q^{2} -1.64656 q^{3} -0.0828005 q^{4} +2.27988 q^{6} -2.06195 q^{7} +2.88391 q^{8} -0.288826 q^{9} -1.34137 q^{11} +0.136336 q^{12} +0.417965 q^{13} +2.85504 q^{14} -3.82754 q^{16} -7.21876 q^{17} +0.399918 q^{18} -4.92447 q^{19} +3.39514 q^{21} +1.85730 q^{22} +7.81577 q^{23} -4.74854 q^{24} -0.578727 q^{26} +5.41526 q^{27} +0.170731 q^{28} -5.56380 q^{29} -6.74787 q^{31} -0.468085 q^{32} +2.20865 q^{33} +9.99531 q^{34} +0.0239150 q^{36} +8.08306 q^{37} +6.81856 q^{38} -0.688206 q^{39} -11.3454 q^{41} -4.70101 q^{42} -8.61222 q^{43} +0.111066 q^{44} -10.8219 q^{46} -9.63705 q^{47} +6.30230 q^{48} -2.74835 q^{49} +11.8862 q^{51} -0.0346077 q^{52} +6.10247 q^{53} -7.49814 q^{54} -5.94648 q^{56} +8.10845 q^{57} +7.70381 q^{58} +5.97172 q^{59} +4.14705 q^{61} +9.34330 q^{62} +0.595546 q^{63} +8.30321 q^{64} -3.05816 q^{66} -6.95749 q^{67} +0.597717 q^{68} -12.8692 q^{69} -7.17068 q^{71} -0.832948 q^{72} -7.06759 q^{73} -11.1920 q^{74} +0.407748 q^{76} +2.76583 q^{77} +0.952911 q^{78} -3.70548 q^{79} -8.05010 q^{81} +15.7091 q^{82} +1.93561 q^{83} -0.281119 q^{84} +11.9247 q^{86} +9.16116 q^{87} -3.86838 q^{88} -4.50996 q^{89} -0.861824 q^{91} -0.647149 q^{92} +11.1108 q^{93} +13.3438 q^{94} +0.770732 q^{96} -6.92472 q^{97} +3.80545 q^{98} +0.387422 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9	$ 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9} + q^{11} + 14 q^{12} + 9 q^{13} - q^{14} + 43 q^{16} + 12 q^{17} + 42 q^{18} + 2 q^{21} + 5 q^{22} + 77 q^{23} - 2 q^{24} + 2 q^{26} + 38 q^{27} + 42 q^{28} + 2 q^{29} + q^{31} + 72 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 28 q^{37} + 23 q^{38} - 2 q^{39} - 2 q^{41} + 37 q^{42} + 31 q^{43} + 3 q^{44} + 14 q^{46} + 96 q^{47} + 13 q^{48} + 40 q^{49} - 10 q^{51} + 42 q^{52} + 54 q^{53} + 4 q^{54} - 15 q^{56} + 37 q^{57} + 27 q^{58} + q^{59} + 5 q^{61} + 39 q^{62} + 70 q^{63} + 65 q^{64} - 52 q^{66} + 34 q^{67} + 52 q^{68} + 21 q^{69} - 9 q^{71} + 70 q^{72} + 25 q^{73} + 22 q^{74} - 47 q^{76} + 54 q^{77} + 58 q^{78} + 13 q^{79} + 12 q^{81} - 5 q^{82} + 63 q^{83} + 95 q^{84} - 18 q^{86} + 47 q^{87} + 13 q^{88} + 19 q^{89} - 31 q^{91} + 137 q^{92} + 52 q^{93} + 120 q^{94} - 49 q^{96} + 36 q^{97} + 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9 + q^11 + 14 * q^12 + 9 * q^13 - q^14 + 43 * q^16 + 12 * q^17 + 42 * q^18 + 2 * q^21 + 5 * q^22 + 77 * q^23 - 2 * q^24 + 2 * q^26 + 38 * q^27 + 42 * q^28 + 2 * q^29 + q^31 + 72 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 28 * q^37 + 23 * q^38 - 2 * q^39 - 2 * q^41 + 37 * q^42 + 31 * q^43 + 3 * q^44 + 14 * q^46 + 96 * q^47 + 13 * q^48 + 40 * q^49 - 10 * q^51 + 42 * q^52 + 54 * q^53 + 4 * q^54 - 15 * q^56 + 37 * q^57 + 27 * q^58 + q^59 + 5 * q^61 + 39 * q^62 + 70 * q^63 + 65 * q^64 - 52 * q^66 + 34 * q^67 + 52 * q^68 + 21 * q^69 - 9 * q^71 + 70 * q^72 + 25 * q^73 + 22 * q^74 - 47 * q^76 + 54 * q^77 + 58 * q^78 + 13 * q^79 + 12 * q^81 - 5 * q^82 + 63 * q^83 + 95 * q^84 - 18 * q^86 + 47 * q^87 + 13 * q^88 + 19 * q^89 - 31 * q^91 + 137 * q^92 + 52 * q^93 + 120 * q^94 - 49 * q^96 + 36 * q^97 + 64 * q^98 + 16 * 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 $

$2$	−1.38463	−0.979081	−0.489541	−	0.871981i	$-0.662835\pi$
$2$	−1.38463	−0.979081	−0.489541	+	0.871981i	$0.662835\pi$
$3$	−1.64656	−0.950644	−0.475322	−	0.879812i	$-0.657668\pi$
$3$	−1.64656	−0.950644	−0.475322	+	0.879812i	$0.657668\pi$
$4$	−0.0828005	−0.0414002
$5$	0	0
$5$	0	0
$6$	2.27988	0.930758
$7$	−2.06195	−0.779345	−0.389672	−	0.920954i	$-0.627412\pi$
$7$	−2.06195	−0.779345	−0.389672	+	0.920954i	$0.627412\pi$
$8$	2.88391	1.01962
$9$	−0.288826	−0.0962754
$10$	0	0
$11$	−1.34137	−0.404437	−0.202219	−	0.979340i	$-0.564815\pi$
$11$	−1.34137	−0.404437	−0.202219	+	0.979340i	$0.564815\pi$
$12$	0.136336	0.0393569
$13$	0.417965	0.115923	0.0579613	−	0.998319i	$-0.481540\pi$
$13$	0.417965	0.115923	0.0579613	+	0.998319i	$0.481540\pi$
$14$	2.85504	0.763042
$15$	0	0
$16$	−3.82754	−0.956886
$17$	−7.21876	−1.75081	−0.875403	−	0.483393i	$-0.839404\pi$
$17$	−7.21876	−1.75081	−0.875403	+	0.483393i	$0.839404\pi$
$18$	0.399918	0.0942615
$19$	−4.92447	−1.12975	−0.564875	−	0.825176i	$-0.691076\pi$
$19$	−4.92447	−1.12975	−0.564875	+	0.825176i	$0.691076\pi$
$20$	0	0
$21$	3.39514	0.740880
$22$	1.85730	0.395977
$23$	7.81577	1.62970	0.814850	−	0.579671i	$-0.196819\pi$
$23$	7.81577	1.62970	0.814850	+	0.579671i	$0.196819\pi$
$24$	−4.74854	−0.969291
$25$	0	0
$26$	−0.578727	−0.113498
$27$	5.41526	1.04217
$28$	0.170731	0.0322651
$29$	−5.56380	−1.03317	−0.516586	−	0.856235i	$-0.672797\pi$
$29$	−5.56380	−1.03317	−0.516586	+	0.856235i	$0.672797\pi$
$30$	0	0
$31$	−6.74787	−1.21195	−0.605977	−	0.795483i	$-0.707217\pi$
$31$	−6.74787	−1.21195	−0.605977	+	0.795483i	$0.707217\pi$
$32$	−0.468085	−0.0827465
$33$	2.20865	0.384476
$34$	9.99531	1.71418
$35$	0	0
$36$	0.0239150	0.00398583
$37$	8.08306	1.32885	0.664424	−	0.747356i	$-0.268677\pi$
$37$	8.08306	1.32885	0.664424	+	0.747356i	$0.268677\pi$
$38$	6.81856	1.10612
$39$	−0.688206	−0.110201
$40$	0	0
$41$	−11.3454	−1.77185	−0.885925	−	0.463829i	$-0.846475\pi$
$41$	−11.3454	−1.77185	−0.885925	+	0.463829i	$0.846475\pi$
$42$	−4.70101	−0.725381
$43$	−8.61222	−1.31335	−0.656675	−	0.754173i	$-0.728038\pi$
$43$	−8.61222	−1.31335	−0.656675	+	0.754173i	$0.728038\pi$
$44$	0.111066	0.0167438
$45$	0	0
$46$	−10.8219	−1.59561
$47$	−9.63705	−1.40571	−0.702854	−	0.711334i	$-0.748091\pi$
$47$	−9.63705	−1.40571	−0.702854	+	0.711334i	$0.748091\pi$
$48$	6.30230	0.909658
$49$	−2.74835	−0.392622
$50$	0	0
$51$	11.8862	1.66439
$52$	−0.0346077	−0.00479922
$53$	6.10247	0.838239	0.419119	−	0.907931i	$-0.362339\pi$
$53$	6.10247	0.838239	0.419119	+	0.907931i	$0.362339\pi$
$54$	−7.49814	−1.02037
$55$	0	0
$56$	−5.94648	−0.794632
$57$	8.10845	1.07399
$58$	7.70381	1.01156
$59$	5.97172	0.777452	0.388726	−	0.921353i	$-0.372915\pi$
$59$	5.97172	0.777452	0.388726	+	0.921353i	$0.372915\pi$
$60$	0	0
$61$	4.14705	0.530975	0.265488	−	0.964114i	$-0.414467\pi$
$61$	4.14705	0.530975	0.265488	+	0.964114i	$0.414467\pi$
$62$	9.34330	1.18660
$63$	0.595546	0.0750318
$64$	8.30321	1.03790
$65$	0	0
$66$	−3.05816	−0.376433
$67$	−6.95749	−0.849992	−0.424996	−	0.905195i	$-0.639725\pi$
$67$	−6.95749	−0.849992	−0.424996	+	0.905195i	$0.639725\pi$
$68$	0.597717	0.0724838
$69$	−12.8692	−1.54927
$70$	0	0
$71$	−7.17068	−0.851003	−0.425502	−	0.904958i	$-0.639902\pi$
$71$	−7.17068	−0.851003	−0.425502	+	0.904958i	$0.639902\pi$
$72$	−0.832948	−0.0981639
$73$	−7.06759	−0.827199	−0.413599	−	0.910459i	$-0.635729\pi$
$73$	−7.06759	−0.827199	−0.413599	+	0.910459i	$0.635729\pi$
$74$	−11.1920	−1.30105
$75$	0	0
$76$	0.407748	0.0467719
$77$	2.76583	0.315196
$78$	0.952911	0.107896
$79$	−3.70548	−0.416900	−0.208450	−	0.978033i	$-0.566842\pi$
$79$	−3.70548	−0.416900	−0.208450	+	0.978033i	$0.566842\pi$
$80$	0	0
$81$	−8.05010	−0.894456
$82$	15.7091	1.73478
$83$	1.93561	0.212461	0.106231	−	0.994342i	$-0.466122\pi$
$83$	1.93561	0.212461	0.106231	+	0.994342i	$0.466122\pi$
$84$	−0.281119	−0.0306726
$85$	0	0
$86$	11.9247	1.28588
$87$	9.16116	0.982179
$88$	−3.86838	−0.412370
$89$	−4.50996	−0.478055	−0.239027	−	0.971013i	$-0.576829\pi$
$89$	−4.50996	−0.478055	−0.239027	+	0.971013i	$0.576829\pi$
$90$	0	0
$91$	−0.861824	−0.0903437
$92$	−0.647149	−0.0674700
$93$	11.1108	1.15214
$94$	13.3438	1.37630
$95$	0	0
$96$	0.770732	0.0786625
$97$	−6.92472	−0.703099	−0.351549	−	0.936169i	$-0.614345\pi$
$97$	−6.92472	−0.703099	−0.351549	+	0.936169i	$0.614345\pi$
$98$	3.80545	0.384408
$99$	0.387422	0.0389374
$100$	0	0
$101$	−11.0008	−1.09462	−0.547309	−	0.836931i	$-0.684348\pi$
$101$	−11.0008	−1.09462	−0.547309	+	0.836931i	$0.684348\pi$
$102$	−16.4579	−1.62958
$103$	−2.97168	−0.292809	−0.146404	−	0.989225i	$-0.546770\pi$
$103$	−2.97168	−0.292809	−0.146404	+	0.989225i	$0.546770\pi$
$104$	1.20537	0.118197
$105$	0	0
$106$	−8.44966	−0.820704
$107$	3.80672	0.368010	0.184005	−	0.982925i	$-0.441094\pi$
$107$	3.80672	0.368010	0.184005	+	0.982925i	$0.441094\pi$
$108$	−0.448386	−0.0431460
$109$	15.6457	1.49859	0.749293	−	0.662239i	$-0.230394\pi$
$109$	15.6457	1.49859	0.749293	+	0.662239i	$0.230394\pi$
$110$	0	0
$111$	−13.3093	−1.26326
$112$	7.89221	0.745744
$113$	−14.1342	−1.32963	−0.664816	−	0.747007i	$-0.731490\pi$
$113$	−14.1342	−1.32963	−0.664816	+	0.747007i	$0.731490\pi$
$114$	−11.2272	−1.05152
$115$	0	0
$116$	0.460685	0.0427736
$117$	−0.120719	−0.0111605
$118$	−8.26863	−0.761189
$119$	14.8847	1.36448
$120$	0	0
$121$	−9.20074	−0.836431
$122$	−5.74213	−0.519868
$123$	18.6809	1.68440
$124$	0.558727	0.0501751
$125$	0	0
$126$	−0.824611	−0.0734622
$127$	0.646721	0.0573872	0.0286936	−	0.999588i	$-0.490865\pi$
$127$	0.646721	0.0573872	0.0286936	+	0.999588i	$0.490865\pi$
$128$	−10.5607	−0.933443
$129$	14.1806	1.24853
$130$	0	0
$131$	2.60419	0.227529	0.113765	−	0.993508i	$-0.463709\pi$
$131$	2.60419	0.227529	0.113765	+	0.993508i	$0.463709\pi$
$132$	−0.182877	−0.0159174
$133$	10.1540	0.880465
$134$	9.63354	0.832211
$135$	0	0
$136$	−20.8182	−1.78515
$137$	−0.0226842	−0.00193805	−0.000969023	−	1.00000i	$-0.500308\pi$
$137$	−0.0226842	−0.00193805	−0.000969023		1.00000i	$0.500308\pi$
$138$	17.8190	1.51686
$139$	4.43007	0.375754	0.187877	−	0.982193i	$-0.439839\pi$
$139$	4.43007	0.375754	0.187877	+	0.982193i	$0.439839\pi$
$140$	0	0
$141$	15.8680	1.33633
$142$	9.92874	0.833201
$143$	−0.560644	−0.0468834
$144$	1.10550	0.0921246
$145$	0	0
$146$	9.78600	0.809895
$147$	4.52534	0.373243
$148$	−0.669281	−0.0550146
$149$	−14.8194	−1.21406	−0.607028	−	0.794680i	$-0.707638\pi$
$149$	−14.8194	−1.21406	−0.607028	+	0.794680i	$0.707638\pi$
$150$	0	0
$151$	−17.5886	−1.43134	−0.715671	−	0.698437i	$-0.753879\pi$
$151$	−17.5886	−1.43134	−0.715671	+	0.698437i	$0.753879\pi$
$152$	−14.2017	−1.15191
$153$	2.08497	0.168560
$154$	−3.82966	−0.308602
$155$	0	0
$156$	0.0569838	0.00456236
$157$	1.09676	0.0875309	0.0437655	−	0.999042i	$-0.486065\pi$
$157$	1.09676	0.0875309	0.0437655	+	0.999042i	$0.486065\pi$
$158$	5.13072	0.408178
$159$	−10.0481	−0.796867
$160$	0	0
$161$	−16.1157	−1.27010
$162$	11.1464	0.875745
$163$	−7.83810	−0.613927	−0.306964	−	0.951721i	$-0.599313\pi$
$163$	−7.83810	−0.613927	−0.306964	+	0.951721i	$0.599313\pi$
$164$	0.939402	0.0733550
$165$	0	0
$166$	−2.68011	−0.208017
$167$	−20.8848	−1.61611	−0.808057	−	0.589105i	$-0.799481\pi$
$167$	−20.8848	−1.61611	−0.808057	+	0.589105i	$0.799481\pi$
$168$	9.79126	0.755412
$169$	−12.8253	−0.986562
$170$	0	0
$171$	1.42232	0.108767
$172$	0.713096	0.0543730
$173$	8.57560	0.651991	0.325995	−	0.945371i	$-0.394301\pi$
$173$	8.57560	0.651991	0.325995	+	0.945371i	$0.394301\pi$
$174$	−12.6848	−0.961633
$175$	0	0
$176$	5.13414	0.387000
$177$	−9.83283	−0.739080
$178$	6.24462	0.468054
$179$	−15.1512	−1.13246	−0.566228	−	0.824248i	$-0.691598\pi$
$179$	−15.1512	−1.13246	−0.566228	+	0.824248i	$0.691598\pi$
$180$	0	0
$181$	−5.61849	−0.417619	−0.208810	−	0.977956i	$-0.566959\pi$
$181$	−5.61849	−0.417619	−0.208810	+	0.977956i	$0.566959\pi$
$182$	1.19331	0.0884538
$183$	−6.82838	−0.504768
$184$	22.5400	1.66167
$185$	0	0
$186$	−15.3843	−1.12803
$187$	9.68300	0.708091
$188$	0.797953	0.0581967
$189$	−11.1660	−0.812208
$190$	0	0
$191$	−10.9250	−0.790508	−0.395254	−	0.918572i	$-0.629343\pi$
$191$	−10.9250	−0.790508	−0.395254	+	0.918572i	$0.629343\pi$
$192$	−13.6718	−0.986675
$193$	−2.21043	−0.159110	−0.0795550	−	0.996830i	$-0.525350\pi$
$193$	−2.21043	−0.159110	−0.0795550	+	0.996830i	$0.525350\pi$
$194$	9.58818	0.688391
$195$	0	0
$196$	0.227565	0.0162546
$197$	−14.5835	−1.03903	−0.519517	−	0.854460i	$-0.673888\pi$
$197$	−14.5835	−1.03903	−0.519517	+	0.854460i	$0.673888\pi$
$198$	−0.536436	−0.0381228
$199$	−18.2910	−1.29662	−0.648309	−	0.761378i	$-0.724523\pi$
$199$	−18.2910	−1.29662	−0.648309	+	0.761378i	$0.724523\pi$
$200$	0	0
$201$	11.4559	0.808040
$202$	15.2320	1.07172
$203$	11.4723	0.805197
$204$	−0.984179	−0.0689063
$205$	0	0
$206$	4.11468	0.286683
$207$	−2.25740	−0.156900
$208$	−1.59978	−0.110925
$209$	6.60551	0.456913
$210$	0	0
$211$	−11.2223	−0.772577	−0.386289	−	0.922378i	$-0.626243\pi$
$211$	−11.2223	−0.772577	−0.386289	+	0.922378i	$0.626243\pi$
$212$	−0.505287	−0.0347033
$213$	11.8070	0.809002
$214$	−5.27090	−0.360311
$215$	0	0
$216$	15.6171	1.06261
$217$	13.9138	0.944529
$218$	−21.6635	−1.46724
$219$	11.6372	0.786372
$220$	0	0
$221$	−3.01719	−0.202958
$222$	18.4284	1.23683
$223$	28.3422	1.89793	0.948967	−	0.315376i	$-0.102131\pi$
$223$	28.3422	1.89793	0.948967	+	0.315376i	$0.102131\pi$
$224$	0.965169	0.0644881
$225$	0	0
$226$	19.5706	1.30182
$227$	11.9976	0.796309	0.398154	−	0.917318i	$-0.369651\pi$
$227$	11.9976	0.796309	0.398154	+	0.917318i	$0.369651\pi$
$228$	−0.671383	−0.0444635
$229$	−29.0089	−1.91696	−0.958480	−	0.285161i	$-0.907953\pi$
$229$	−29.0089	−1.91696	−0.958480	+	0.285161i	$0.907953\pi$
$230$	0	0
$231$	−4.55412	−0.299639
$232$	−16.0455	−1.05344
$233$	−3.31885	−0.217425	−0.108712	−	0.994073i	$-0.534673\pi$
$233$	−3.31885	−0.217425	−0.108712	+	0.994073i	$0.534673\pi$
$234$	0.167152	0.0109270
$235$	0	0
$236$	−0.494461	−0.0321867
$237$	6.10132	0.396323
$238$	−20.6099	−1.33594
$239$	−19.0537	−1.23248	−0.616240	−	0.787559i	$-0.711345\pi$
$239$	−19.0537	−1.23248	−0.616240	+	0.787559i	$0.711345\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	12.7396	0.818933
$243$	−2.99078	−0.191859
$244$	−0.343377	−0.0219825
$245$	0	0
$246$	−25.8661	−1.64916
$247$	−2.05825	−0.130964
$248$	−19.4602	−1.23573
$249$	−3.18711	−0.201975
$250$	0	0
$251$	17.8825	1.12873	0.564367	−	0.825524i	$-0.309120\pi$
$251$	17.8825	1.12873	0.564367	+	0.825524i	$0.309120\pi$
$252$	−0.0493115	−0.00310633
$253$	−10.4838	−0.659112
$254$	−0.895470	−0.0561868
$255$	0	0
$256$	−1.98376	−0.123985
$257$	−14.3310	−0.893943	−0.446972	−	0.894548i	$-0.647498\pi$
$257$	−14.3310	−0.893943	−0.446972	+	0.894548i	$0.647498\pi$
$258$	−19.6348	−1.22241
$259$	−16.6669	−1.03563
$260$	0	0
$261$	1.60697	0.0994691
$262$	−3.60584	−0.222770
$263$	23.9082	1.47424	0.737121	−	0.675761i	$-0.236185\pi$
$263$	23.9082	1.47424	0.737121	+	0.675761i	$0.236185\pi$
$264$	6.36953	0.392018
$265$	0	0
$266$	−14.0596	−0.862047
$267$	7.42594	0.454460
$268$	0.576083	0.0351899
$269$	4.97851	0.303545	0.151773	−	0.988415i	$-0.451502\pi$
$269$	4.97851	0.303545	0.151773	+	0.988415i	$0.451502\pi$
$270$	0	0
$271$	22.1270	1.34412	0.672059	−	0.740498i	$-0.265410\pi$
$271$	22.1270	1.34412	0.672059	+	0.740498i	$0.265410\pi$
$272$	27.6301	1.67532
$273$	1.41905	0.0858847
$274$	0.0314093	0.00189750
$275$	0	0
$276$	1.06557	0.0641400
$277$	1.68536	0.101263	0.0506317	−	0.998717i	$-0.483877\pi$
$277$	1.68536	0.101263	0.0506317	+	0.998717i	$0.483877\pi$
$278$	−6.13401	−0.367894
$279$	1.94896	0.116681
$280$	0	0
$281$	9.53103	0.568574	0.284287	−	0.958739i	$-0.408243\pi$
$281$	9.53103	0.568574	0.284287	+	0.958739i	$0.408243\pi$
$282$	−21.9713	−1.30837
$283$	19.7041	1.17129	0.585644	−	0.810569i	$-0.300842\pi$
$283$	19.7041	1.17129	0.585644	+	0.810569i	$0.300842\pi$
$284$	0.593736	0.0352317
$285$	0	0
$286$	0.776285	0.0459027
$287$	23.3936	1.38088
$288$	0.135195	0.00796646
$289$	35.1105	2.06532
$290$	0	0
$291$	11.4020	0.668397
$292$	0.585200	0.0342462
$293$	−19.0690	−1.11403	−0.557013	−	0.830504i	$-0.688053\pi$
$293$	−19.0690	−1.11403	−0.557013	+	0.830504i	$0.688053\pi$
$294$	−6.26592	−0.365436
$295$	0	0
$296$	23.3108	1.35491
$297$	−7.26385	−0.421491
$298$	20.5194	1.18866
$299$	3.26672	0.188919
$300$	0	0
$301$	17.7580	1.02355
$302$	24.3537	1.40140
$303$	18.1135	1.04059
$304$	18.8486	1.08104
$305$	0	0
$306$	−2.88691	−0.165034
$307$	−20.3386	−1.16078	−0.580392	−	0.814337i	$-0.697101\pi$
$307$	−20.3386	−1.16078	−0.580392	+	0.814337i	$0.697101\pi$
$308$	−0.229012	−0.0130492
$309$	4.89306	0.278357
$310$	0	0
$311$	−22.5673	−1.27967	−0.639836	−	0.768511i	$-0.720998\pi$
$311$	−22.5673	−1.27967	−0.639836	+	0.768511i	$0.720998\pi$
$312$	−1.98472	−0.112363
$313$	24.7224	1.39739	0.698696	−	0.715419i	$-0.253764\pi$
$313$	24.7224	1.39739	0.698696	+	0.715419i	$0.253764\pi$
$314$	−1.51861	−0.0856999
$315$	0	0
$316$	0.306816	0.0172597
$317$	16.6940	0.937629	0.468815	−	0.883297i	$-0.344681\pi$
$317$	16.6940	0.937629	0.468815	+	0.883297i	$0.344681\pi$
$318$	13.9129	0.780197
$319$	7.46310	0.417853
$320$	0	0
$321$	−6.26801	−0.349846
$322$	22.3143	1.24353
$323$	35.5485	1.97797
$324$	0.666552	0.0370307
$325$	0	0
$326$	10.8529	0.601085
$327$	−25.7616	−1.42462
$328$	−32.7190	−1.80661
$329$	19.8711	1.09553
$330$	0	0
$331$	35.0604	1.92709	0.963547	−	0.267538i	$-0.0862099\pi$
$331$	35.0604	1.92709	0.963547	+	0.267538i	$0.0862099\pi$
$332$	−0.160270	−0.00879594
$333$	−2.33460	−0.127935
$334$	28.9177	1.58231
$335$	0	0
$336$	−12.9950	−0.708937
$337$	−5.64050	−0.307258	−0.153629	−	0.988129i	$-0.549096\pi$
$337$	−5.64050	−0.307258	−0.153629	+	0.988129i	$0.549096\pi$
$338$	17.7583	0.965924
$339$	23.2728	1.26401
$340$	0	0
$341$	9.05137	0.490159
$342$	−1.96938	−0.106492
$343$	20.1006	1.08533
$344$	−24.8368	−1.33911
$345$	0	0
$346$	−11.8740	−0.638352
$347$	−2.23421	−0.119939	−0.0599693	−	0.998200i	$-0.519100\pi$
$347$	−2.23421	−0.119939	−0.0599693	+	0.998200i	$0.519100\pi$
$348$	−0.758548	−0.0406624
$349$	12.8552	0.688122	0.344061	−	0.938947i	$-0.388197\pi$
$349$	12.8552	0.688122	0.344061	+	0.938947i	$0.388197\pi$
$350$	0	0
$351$	2.26339	0.120811
$352$	0.627873	0.0334658
$353$	−9.26644	−0.493203	−0.246601	−	0.969117i	$-0.579314\pi$
$353$	−9.26644	−0.493203	−0.246601	+	0.969117i	$0.579314\pi$
$354$	13.6148	0.723620
$355$	0	0
$356$	0.373427	0.0197916
$357$	−24.5087	−1.29714
$358$	20.9789	1.10877
$359$	32.9863	1.74095	0.870476	−	0.492210i	$-0.163811\pi$
$359$	32.9863	1.74095	0.870476	+	0.492210i	$0.163811\pi$
$360$	0	0
$361$	5.25037	0.276335
$362$	7.77953	0.408883
$363$	15.1496	0.795148
$364$	0.0713594	0.00374025
$365$	0	0
$366$	9.45478	0.494209
$367$	−29.2561	−1.52716	−0.763578	−	0.645716i	$-0.776559\pi$
$367$	−29.2561	−1.52716	−0.763578	+	0.645716i	$0.776559\pi$
$368$	−29.9152	−1.55944
$369$	3.27684	0.170586
$370$	0	0
$371$	−12.5830	−0.653277
$372$	−0.919979	−0.0476987
$373$	−0.209348	−0.0108396	−0.00541981	−	0.999985i	$-0.501725\pi$
$373$	−0.209348	−0.0108396	−0.00541981	+	0.999985i	$0.501725\pi$
$374$	−13.4074	−0.693279
$375$	0	0
$376$	−27.7924	−1.43328
$377$	−2.32548	−0.119768
$378$	15.4608	0.795218
$379$	26.3780	1.35495	0.677474	−	0.735546i	$-0.263074\pi$
$379$	26.3780	1.35495	0.677474	+	0.735546i	$0.263074\pi$
$380$	0	0
$381$	−1.06487	−0.0545549
$382$	15.1271	0.773971
$383$	−18.0656	−0.923109	−0.461554	−	0.887112i	$-0.652708\pi$
$383$	−18.0656	−0.923109	−0.461554	+	0.887112i	$0.652708\pi$
$384$	17.3889	0.887372
$385$	0	0
$386$	3.06062	0.155782
$387$	2.48744	0.126443
$388$	0.573370	0.0291085
$389$	3.97219	0.201398	0.100699	−	0.994917i	$-0.467892\pi$
$389$	3.97219	0.201398	0.100699	+	0.994917i	$0.467892\pi$
$390$	0	0
$391$	−56.4202	−2.85329
$392$	−7.92599	−0.400323
$393$	−4.28797	−0.216299
$394$	20.1928	1.01730
$395$	0	0
$396$	−0.0320787	−0.00161202
$397$	−30.1212	−1.51174	−0.755869	−	0.654723i	$-0.772785\pi$
$397$	−30.1212	−1.51174	−0.755869	+	0.654723i	$0.772785\pi$
$398$	25.3263	1.26949
$399$	−16.7192	−0.837009
$400$	0	0
$401$	27.5649	1.37653	0.688263	−	0.725461i	$-0.258373\pi$
$401$	27.5649	1.37653	0.688263	+	0.725461i	$0.258373\pi$
$402$	−15.8622	−0.791137
$403$	−2.82037	−0.140493
$404$	0.910869	0.0453174
$405$	0	0
$406$	−15.8849	−0.788354
$407$	−10.8423	−0.537435
$408$	34.2786	1.69704
$409$	−24.8656	−1.22952	−0.614762	−	0.788712i	$-0.710748\pi$
$409$	−24.8656	−1.22952	−0.614762	+	0.788712i	$0.710748\pi$
$410$	0	0
$411$	0.0373511	0.00184239
$412$	0.246057	0.0121223
$413$	−12.3134	−0.605903
$414$	3.12566	0.153618
$415$	0	0
$416$	−0.195643	−0.00959219
$417$	−7.29440	−0.357208
$418$	−9.14619	−0.447355
$419$	−18.1561	−0.886986	−0.443493	−	0.896278i	$-0.646261\pi$
$419$	−18.1561	−0.886986	−0.443493	+	0.896278i	$0.646261\pi$
$420$	0	0
$421$	23.2163	1.13149	0.565746	−	0.824579i	$-0.308588\pi$
$421$	23.2163	1.13149	0.565746	+	0.824579i	$0.308588\pi$
$422$	15.5388	0.756416
$423$	2.78344	0.135335
$424$	17.5990	0.854681
$425$	0	0
$426$	−16.3483	−0.792078
$427$	−8.55102	−0.413813
$428$	−0.315198	−0.0152357
$429$	0.923137	0.0445695
$430$	0	0
$431$	13.7520	0.662411	0.331206	−	0.943559i	$-0.392545\pi$
$431$	13.7520	0.662411	0.331206	+	0.943559i	$0.392545\pi$
$432$	−20.7272	−0.997236
$433$	−27.1426	−1.30439	−0.652196	−	0.758051i	$-0.726152\pi$
$433$	−27.1426	−1.30439	−0.652196	+	0.758051i	$0.726152\pi$
$434$	−19.2654	−0.924771
$435$	0	0
$436$	−1.29547	−0.0620418
$437$	−38.4885	−1.84115
$438$	−16.1133	−0.769922
$439$	−12.7912	−0.610492	−0.305246	−	0.952274i	$-0.598739\pi$
$439$	−12.7912	−0.610492	−0.305246	+	0.952274i	$0.598739\pi$
$440$	0	0
$441$	0.793796	0.0377998
$442$	4.17769	0.198713
$443$	23.7861	1.13011	0.565056	−	0.825053i	$-0.308855\pi$
$443$	23.7861	1.13011	0.565056	+	0.825053i	$0.308855\pi$
$444$	1.10201	0.0522993
$445$	0	0
$446$	−39.2434	−1.85823
$447$	24.4012	1.15414
$448$	−17.1208	−0.808883
$449$	24.5498	1.15858	0.579289	−	0.815122i	$-0.303330\pi$
$449$	24.5498	1.15858	0.579289	+	0.815122i	$0.303330\pi$
$450$	0	0
$451$	15.2183	0.716602
$452$	1.17032	0.0550470
$453$	28.9608	1.36070
$454$	−16.6122	−0.779651
$455$	0	0
$456$	23.3840	1.09506
$457$	13.4325	0.628346	0.314173	−	0.949366i	$-0.398273\pi$
$457$	13.4325	0.628346	0.314173	+	0.949366i	$0.398273\pi$
$458$	40.1665	1.87686
$459$	−39.0915	−1.82463
$460$	0	0
$461$	4.69879	0.218844	0.109422	−	0.993995i	$-0.465100\pi$
$461$	4.69879	0.218844	0.109422	+	0.993995i	$0.465100\pi$
$462$	6.30577	0.293371
$463$	14.7186	0.684032	0.342016	−	0.939694i	$-0.388890\pi$
$463$	14.7186	0.684032	0.342016	+	0.939694i	$0.388890\pi$
$464$	21.2957	0.988628
$465$	0	0
$466$	4.59537	0.212876
$467$	27.1988	1.25861	0.629306	−	0.777158i	$-0.283339\pi$
$467$	27.1988	1.25861	0.629306	+	0.777158i	$0.283339\pi$
$468$	0.00999562	0.000462048 0
$469$	14.3460	0.662437
$470$	0	0
$471$	−1.80588	−0.0832108
$472$	17.2219	0.792702
$473$	11.5521	0.531168
$474$	−8.44807	−0.388032
$475$	0	0
$476$	−1.23246	−0.0564899
$477$	−1.76255	−0.0807018
$478$	26.3823	1.20670
$479$	29.8189	1.36246	0.681230	−	0.732070i	$-0.261446\pi$
$479$	29.8189	1.36246	0.681230	+	0.732070i	$0.261446\pi$
$480$	0	0
$481$	3.37844	0.154043
$482$	1.38463	0.0630682
$483$	26.5356	1.20741
$484$	0.761825	0.0346284
$485$	0	0
$486$	4.14113	0.187845
$487$	−21.3770	−0.968684	−0.484342	−	0.874879i	$-0.660941\pi$
$487$	−21.3770	−0.968684	−0.484342	+	0.874879i	$0.660941\pi$
$488$	11.9597	0.541390
$489$	12.9059	0.583627
$490$	0	0
$491$	11.1552	0.503426	0.251713	−	0.967802i	$-0.419006\pi$
$491$	11.1552	0.503426	0.251713	+	0.967802i	$0.419006\pi$
$492$	−1.54679	−0.0697345
$493$	40.1638	1.80888
$494$	2.84992	0.128224
$495$	0	0
$496$	25.8278	1.15970
$497$	14.7856	0.663225
$498$	4.41297	0.197750
$499$	28.7179	1.28559	0.642794	−	0.766039i	$-0.277775\pi$
$499$	28.7179	1.28559	0.642794	+	0.766039i	$0.277775\pi$
$500$	0	0
$501$	34.3881	1.53635
$502$	−24.7606	−1.10512
$503$	−28.6595	−1.27786	−0.638932	−	0.769263i	$-0.720623\pi$
$503$	−28.6595	−1.27786	−0.638932	+	0.769263i	$0.720623\pi$
$504$	1.71750	0.0765035
$505$	0	0
$506$	14.5162	0.645324
$507$	21.1177	0.937869
$508$	−0.0535488	−0.00237585
$509$	−20.8136	−0.922548	−0.461274	−	0.887258i	$-0.652608\pi$
$509$	−20.8136	−0.922548	−0.461274	+	0.887258i	$0.652608\pi$
$510$	0	0
$511$	14.5730	0.644673
$512$	23.8682	1.05483
$513$	−26.6673	−1.17739
$514$	19.8431	0.875243
$515$	0	0
$516$	−1.17416	−0.0516894
$517$	12.9268	0.568521
$518$	23.0775	1.01397
$519$	−14.1203	−0.619811
$520$	0	0
$521$	4.41729	0.193525	0.0967624	−	0.995308i	$-0.469151\pi$
$521$	4.41729	0.193525	0.0967624	+	0.995308i	$0.469151\pi$
$522$	−2.22506	−0.0973883
$523$	−23.9978	−1.04935	−0.524676	−	0.851302i	$-0.675814\pi$
$523$	−23.9978	−1.04935	−0.524676	+	0.851302i	$0.675814\pi$
$524$	−0.215628	−0.00941977
$525$	0	0
$526$	−33.1040	−1.44340
$527$	48.7113	2.12190
$528$	−8.45369	−0.367900
$529$	38.0863	1.65592
$530$	0	0
$531$	−1.72479	−0.0748496
$532$	−0.840757	−0.0364514
$533$	−4.74197	−0.205398
$534$	−10.2822	−0.444953
$535$	0	0
$536$	−20.0647	−0.866665
$537$	24.9475	1.07656
$538$	−6.89339	−0.297195
$539$	3.68655	0.158791
$540$	0	0
$541$	−39.9056	−1.71567	−0.857837	−	0.513922i	$-0.828192\pi$
$541$	−39.9056	−1.71567	−0.857837	+	0.513922i	$0.828192\pi$
$542$	−30.6377	−1.31600
$543$	9.25121	0.397007
$544$	3.37899	0.144873
$545$	0	0
$546$	−1.96486	−0.0840881
$547$	−12.9840	−0.555156	−0.277578	−	0.960703i	$-0.589532\pi$
$547$	−12.9840	−0.555156	−0.277578	+	0.960703i	$0.589532\pi$
$548$	0.00187827	8.02355e−5 0
$549$	−1.19778	−0.0511199
$550$	0	0
$551$	27.3988	1.16723
$552$	−37.1135	−1.57965
$553$	7.64053	0.324908
$554$	−2.33360	−0.0991450
$555$	0	0
$556$	−0.366812	−0.0155563
$557$	29.8988	1.26685	0.633427	−	0.773802i	$-0.281648\pi$
$557$	29.8988	1.26685	0.633427	+	0.773802i	$0.281648\pi$
$558$	−2.69859	−0.114240
$559$	−3.59961	−0.152247
$560$	0	0
$561$	−15.9437	−0.673143
$562$	−13.1970	−0.556680
$563$	23.6076	0.994942	0.497471	−	0.867481i	$-0.334262\pi$
$563$	23.6076	0.994942	0.497471	+	0.867481i	$0.334262\pi$
$564$	−1.31388	−0.0553243
$565$	0	0
$566$	−27.2829	−1.14679
$567$	16.5989	0.697089
$568$	−20.6796	−0.867696
$569$	19.3970	0.813163	0.406581	−	0.913615i	$-0.366721\pi$
$569$	19.3970	0.813163	0.406581	+	0.913615i	$0.366721\pi$
$570$	0	0
$571$	10.6056	0.443831	0.221916	−	0.975066i	$-0.428769\pi$
$571$	10.6056	0.443831	0.221916	+	0.975066i	$0.428769\pi$
$572$	0.0464216	0.00194099
$573$	17.9888	0.751492
$574$	−32.3915	−1.35200
$575$	0	0
$576$	−2.39819	−0.0999244
$577$	23.2122	0.966336	0.483168	−	0.875528i	$-0.339486\pi$
$577$	23.2122	0.966336	0.483168	+	0.875528i	$0.339486\pi$
$578$	−48.6151	−2.02212
$579$	3.63961	0.151257
$580$	0	0
$581$	−3.99114	−0.165581
$582$	−15.7875	−0.654415
$583$	−8.18565	−0.339015
$584$	−20.3823	−0.843425
$585$	0	0
$586$	26.4036	1.09072
$587$	12.5563	0.518253	0.259127	−	0.965843i	$-0.416565\pi$
$587$	12.5563	0.518253	0.259127	+	0.965843i	$0.416565\pi$
$588$	−0.374700	−0.0154524
$589$	33.2297	1.36920
$590$	0	0
$591$	24.0127	0.987752
$592$	−30.9383	−1.27155
$593$	−7.29640	−0.299627	−0.149814	−	0.988714i	$-0.547867\pi$
$593$	−7.29640	−0.299627	−0.149814	+	0.988714i	$0.547867\pi$
$594$	10.0577	0.412674
$595$	0	0
$596$	1.22706	0.0502622
$597$	30.1174	1.23262
$598$	−4.52320	−0.184967
$599$	4.83080	0.197381	0.0986905	−	0.995118i	$-0.468535\pi$
$599$	4.83080	0.197381	0.0986905	+	0.995118i	$0.468535\pi$
$600$	0	0
$601$	−26.9173	−1.09798	−0.548989	−	0.835829i	$-0.684987\pi$
$601$	−26.9173	−1.09798	−0.548989	+	0.835829i	$0.684987\pi$
$602$	−24.5882	−1.00214
$603$	2.00951	0.0818334
$604$	1.45635	0.0592579
$605$	0	0
$606$	−25.0805	−1.01882
$607$	5.96717	0.242200	0.121100	−	0.992640i	$-0.461358\pi$
$607$	5.96717	0.242200	0.121100	+	0.992640i	$0.461358\pi$
$608$	2.30507	0.0934829
$609$	−18.8899	−0.765456
$610$	0	0
$611$	−4.02795	−0.162953
$612$	−0.172636	−0.00697841
$613$	−8.13615	−0.328616	−0.164308	−	0.986409i	$-0.552539\pi$
$613$	−8.13615	−0.328616	−0.164308	+	0.986409i	$0.552539\pi$
$614$	28.1614	1.13650
$615$	0	0
$616$	7.97641	0.321379
$617$	−43.5523	−1.75335	−0.876676	−	0.481082i	$-0.840244\pi$
$617$	−43.5523	−1.75335	−0.876676	+	0.481082i	$0.840244\pi$
$618$	−6.77508	−0.272534
$619$	−43.0430	−1.73004	−0.865022	−	0.501733i	$-0.832696\pi$
$619$	−43.0430	−1.73004	−0.865022	+	0.501733i	$0.832696\pi$
$620$	0	0
$621$	42.3245	1.69842
$622$	31.2473	1.25290
$623$	9.29932	0.372569
$624$	2.63414	0.105450
$625$	0	0
$626$	−34.2313	−1.36816
$627$	−10.8764	−0.434362
$628$	−0.0908122	−0.00362380
$629$	−58.3497	−2.32655
$630$	0	0
$631$	−13.4857	−0.536857	−0.268428	−	0.963300i	$-0.586504\pi$
$631$	−13.4857	−0.536857	−0.268428	+	0.963300i	$0.586504\pi$
$632$	−10.6863	−0.425077
$633$	18.4783	0.734446
$634$	−23.1150	−0.918015
$635$	0	0
$636$	0.831988	0.0329905
$637$	−1.14871	−0.0455137
$638$	−10.3336	−0.409112
$639$	2.07108	0.0819307
$640$	0	0
$641$	20.9590	0.827831	0.413916	−	0.910315i	$-0.364161\pi$
$641$	20.9590	0.827831	0.413916	+	0.910315i	$0.364161\pi$
$642$	8.67887	0.342528
$643$	22.0635	0.870100	0.435050	−	0.900406i	$-0.356731\pi$
$643$	22.0635	0.870100	0.435050	+	0.900406i	$0.356731\pi$
$644$	1.33439	0.0525824
$645$	0	0
$646$	−49.2216	−1.93660
$647$	32.0792	1.26116	0.630581	−	0.776123i	$-0.282817\pi$
$647$	32.0792	1.26116	0.630581	+	0.776123i	$0.282817\pi$
$648$	−23.2157	−0.912001
$649$	−8.01027	−0.314431
$650$	0	0
$651$	−22.9099	−0.897912
$652$	0.648998	0.0254167
$653$	−2.80038	−0.109587	−0.0547936	−	0.998498i	$-0.517450\pi$
$653$	−2.80038	−0.109587	−0.0547936	+	0.998498i	$0.517450\pi$
$654$	35.6703	1.39482
$655$	0	0
$656$	43.4249	1.69546
$657$	2.04131	0.0796389
$658$	−27.5142	−1.07261
$659$	−18.4805	−0.719899	−0.359949	−	0.932972i	$-0.617206\pi$
$659$	−18.4805	−0.719899	−0.359949	+	0.932972i	$0.617206\pi$
$660$	0	0
$661$	34.8535	1.35564	0.677821	−	0.735227i	$-0.262924\pi$
$661$	34.8535	1.35564	0.677821	+	0.735227i	$0.262924\pi$
$662$	−48.5457	−1.88678
$663$	4.96800	0.192941
$664$	5.58213	0.216629
$665$	0	0
$666$	3.23256	0.125259
$667$	−43.4854	−1.68376
$668$	1.72927	0.0669075
$669$	−46.6672	−1.80426
$670$	0	0
$671$	−5.56271	−0.214746
$672$	−1.58921	−0.0613052
$673$	−19.2994	−0.743938	−0.371969	−	0.928245i	$-0.621317\pi$
$673$	−19.2994	−0.743938	−0.371969	+	0.928245i	$0.621317\pi$
$674$	7.81001	0.300830
$675$	0	0
$676$	1.06194	0.0408439
$677$	26.1860	1.00641	0.503206	−	0.864167i	$-0.332154\pi$
$677$	26.1860	1.00641	0.503206	+	0.864167i	$0.332154\pi$
$678$	−32.2242	−1.23756
$679$	14.2784	0.547957
$680$	0	0
$681$	−19.7548	−0.757006
$682$	−12.5328	−0.479905
$683$	4.14063	0.158437	0.0792183	−	0.996857i	$-0.474758\pi$
$683$	4.14063	0.158437	0.0792183	+	0.996857i	$0.474758\pi$
$684$	−0.117768	−0.00450299
$685$	0	0
$686$	−27.8319	−1.06263
$687$	47.7649	1.82235
$688$	32.9636	1.25673
$689$	2.55062	0.0971708
$690$	0	0
$691$	−20.6760	−0.786551	−0.393275	−	0.919421i	$-0.628658\pi$
$691$	−20.6760	−0.786551	−0.393275	+	0.919421i	$0.628658\pi$
$692$	−0.710063	−0.0269926
$693$	−0.798846	−0.0303456
$694$	3.09355	0.117430
$695$	0	0
$696$	26.4199	1.00144
$697$	81.8996	3.10217
$698$	−17.7997	−0.673727
$699$	5.46469	0.206694
$700$	0	0
$701$	−0.888108	−0.0335434	−0.0167717	−	0.999859i	$-0.505339\pi$
$701$	−0.888108	−0.0335434	−0.0167717	+	0.999859i	$0.505339\pi$
$702$	−3.13396	−0.118284
$703$	−39.8048	−1.50127
$704$	−11.1376	−0.419766
$705$	0	0
$706$	12.8306	0.482886
$707$	22.6831	0.853085
$708$	0.814163	0.0305981
$709$	−28.2488	−1.06091	−0.530454	−	0.847714i	$-0.677978\pi$
$709$	−28.2488	−1.06091	−0.530454	+	0.847714i	$0.677978\pi$
$710$	0	0
$711$	1.07024	0.0401372
$712$	−13.0063	−0.487432
$713$	−52.7398	−1.97512
$714$	33.9355	1.27000
$715$	0	0
$716$	1.25453	0.0468840
$717$	31.3731	1.17165
$718$	−45.6739	−1.70453
$719$	45.4534	1.69513	0.847563	−	0.530695i	$-0.178069\pi$
$719$	45.4534	1.69513	0.847563	+	0.530695i	$0.178069\pi$
$720$	0	0
$721$	6.12747	0.228199
$722$	−7.26981	−0.270554
$723$	1.64656	0.0612364
$724$	0.465214	0.0172895
$725$	0	0
$726$	−20.9766	−0.778514
$727$	21.5900	0.800728	0.400364	−	0.916356i	$-0.368884\pi$
$727$	21.5900	0.800728	0.400364	+	0.916356i	$0.368884\pi$
$728$	−2.48542	−0.0921158
$729$	29.0748	1.07685
$730$	0	0
$731$	62.1695	2.29942
$732$	0.565393	0.0208975
$733$	9.38267	0.346557	0.173278	−	0.984873i	$-0.444564\pi$
$733$	9.38267	0.346557	0.173278	+	0.984873i	$0.444564\pi$
$734$	40.5089	1.49521
$735$	0	0
$736$	−3.65844	−0.134852
$737$	9.33254	0.343768
$738$	−4.53721	−0.167017
$739$	22.1420	0.814508	0.407254	−	0.913315i	$-0.366486\pi$
$739$	22.1420	0.814508	0.407254	+	0.913315i	$0.366486\pi$
$740$	0	0
$741$	3.38905	0.124500
$742$	17.4228	0.639611
$743$	43.2942	1.58831	0.794156	−	0.607714i	$-0.207913\pi$
$743$	43.2942	1.58831	0.794156	+	0.607714i	$0.207913\pi$
$744$	32.0425	1.17474
$745$	0	0
$746$	0.289869	0.0106129
$747$	−0.559056	−0.0204548
$748$	−0.801757	−0.0293151
$749$	−7.84928	−0.286806
$750$	0	0
$751$	20.1177	0.734107	0.367053	−	0.930200i	$-0.380367\pi$
$751$	20.1177	0.734107	0.367053	+	0.930200i	$0.380367\pi$
$752$	36.8862	1.34510
$753$	−29.4447	−1.07302
$754$	3.21992	0.117263
$755$	0	0
$756$	0.924551	0.0336256
$757$	−49.8385	−1.81141	−0.905706	−	0.423907i	$-0.860659\pi$
$757$	−49.8385	−1.81141	−0.905706	+	0.423907i	$0.860659\pi$
$758$	−36.5238	−1.32660
$759$	17.2623	0.626581
$760$	0	0
$761$	1.78695	0.0647769	0.0323885	−	0.999475i	$-0.489689\pi$
$761$	1.78695	0.0647769	0.0323885	+	0.999475i	$0.489689\pi$
$762$	1.47445	0.0534136
$763$	−32.2607	−1.16791
$764$	0.904598	0.0327272
$765$	0	0
$766$	25.0142	0.903798
$767$	2.49597	0.0901243
$768$	3.26639	0.117866
$769$	−11.5324	−0.415869	−0.207934	−	0.978143i	$-0.566674\pi$
$769$	−11.5324	−0.415869	−0.207934	+	0.978143i	$0.566674\pi$
$770$	0	0
$771$	23.5969	0.849822
$772$	0.183024	0.00658719
$773$	35.2642	1.26836	0.634182	−	0.773184i	$-0.281337\pi$
$773$	35.2642	1.26836	0.634182	+	0.773184i	$0.281337\pi$
$774$	−3.44418	−0.123798
$775$	0	0
$776$	−19.9703	−0.716890
$777$	27.4431	0.984516
$778$	−5.50002	−0.197185
$779$	55.8699	2.00175
$780$	0	0
$781$	9.61851	0.344177
$782$	78.1211	2.79360
$783$	−30.1295	−1.07674
$784$	10.5194	0.375694
$785$	0	0
$786$	5.93725	0.211775
$787$	15.7447	0.561236	0.280618	−	0.959820i	$-0.409461\pi$
$787$	15.7447	0.561236	0.280618	+	0.959820i	$0.409461\pi$
$788$	1.20752	0.0430163
$789$	−39.3664	−1.40148
$790$	0	0
$791$	29.1440	1.03624
$792$	1.11729	0.0397011
$793$	1.73332	0.0615520
$794$	41.7067	1.48011
$795$	0	0
$796$	1.51451	0.0536802
$797$	−12.3339	−0.436889	−0.218444	−	0.975849i	$-0.570098\pi$
$797$	−12.3339	−0.436889	−0.218444	+	0.975849i	$0.570098\pi$
$798$	23.1500	0.819500
$799$	69.5676	2.46112
$800$	0	0
$801$	1.30259	0.0460249
$802$	−38.1672	−1.34773
$803$	9.48023	0.334550
$804$	−0.948558	−0.0334530
$805$	0	0
$806$	3.90517	0.137554
$807$	−8.19744	−0.288563
$808$	−31.7252	−1.11609
$809$	−27.4905	−0.966515	−0.483257	−	0.875478i	$-0.660546\pi$
$809$	−27.4905	−0.966515	−0.483257	+	0.875478i	$0.660546\pi$
$810$	0	0
$811$	13.5069	0.474293	0.237147	−	0.971474i	$-0.423788\pi$
$811$	13.5069	0.474293	0.237147	+	0.971474i	$0.423788\pi$
$812$	−0.949912	−0.0333354
$813$	−36.4335	−1.27778
$814$	15.0126	0.526193
$815$	0	0
$816$	−45.4948	−1.59264
$817$	42.4106	1.48376
$818$	34.4297	1.20380
$819$	0.248918	0.00869788
$820$	0	0
$821$	−31.8399	−1.11122	−0.555610	−	0.831443i	$-0.687515\pi$
$821$	−31.8399	−1.11122	−0.555610	+	0.831443i	$0.687515\pi$
$822$	−0.0517174	−0.00180385
$823$	−31.2861	−1.09056	−0.545282	−	0.838253i	$-0.683577\pi$
$823$	−31.2861	−1.09056	−0.545282	+	0.838253i	$0.683577\pi$
$824$	−8.57006	−0.298552
$825$	0	0
$826$	17.0495	0.593229
$827$	−47.5627	−1.65392	−0.826958	−	0.562263i	$-0.809931\pi$
$827$	−47.5627	−1.65392	−0.826958	+	0.562263i	$0.809931\pi$
$828$	0.186914	0.00649570
$829$	−23.1699	−0.804724	−0.402362	−	0.915481i	$-0.631811\pi$
$829$	−23.1699	−0.804724	−0.402362	+	0.915481i	$0.631811\pi$
$830$	0	0
$831$	−2.77505	−0.0962654
$832$	3.47045	0.120316
$833$	19.8397	0.687405
$834$	10.1000	0.349736
$835$	0	0
$836$	−0.546940	−0.0189163
$837$	−36.5415	−1.26306
$838$	25.1395	0.868431
$839$	−42.5783	−1.46996	−0.734982	−	0.678086i	$-0.762810\pi$
$839$	−42.5783	−1.46996	−0.734982	+	0.678086i	$0.762810\pi$
$840$	0	0
$841$	1.95590	0.0674447
$842$	−32.1460	−1.10782
$843$	−15.6935	−0.540511
$844$	0.929214	0.0319849
$845$	0	0
$846$	−3.85403	−0.132504
$847$	18.9715	0.651868
$848$	−23.3575	−0.802099
$849$	−32.4441	−1.11348
$850$	0	0
$851$	63.1753	2.16562
$852$	−0.977624	−0.0334929
$853$	−21.3763	−0.731910	−0.365955	−	0.930633i	$-0.619258\pi$
$853$	−21.3763	−0.731910	−0.365955	+	0.930633i	$0.619258\pi$
$854$	11.8400	0.405156
$855$	0	0
$856$	10.9782	0.375228
$857$	38.3558	1.31021	0.655105	−	0.755538i	$-0.272624\pi$
$857$	38.3558	1.31021	0.655105	+	0.755538i	$0.272624\pi$
$858$	−1.27820	−0.0436371
$859$	−26.8547	−0.916271	−0.458136	−	0.888882i	$-0.651483\pi$
$859$	−26.8547	−0.916271	−0.458136	+	0.888882i	$0.651483\pi$
$860$	0	0
$861$	−38.5191	−1.31273
$862$	−19.0414	−0.648554
$863$	47.7585	1.62572	0.812859	−	0.582461i	$-0.197910\pi$
$863$	47.7585	1.62572	0.812859	+	0.582461i	$0.197910\pi$
$864$	−2.53480	−0.0862357
$865$	0	0
$866$	37.5825	1.27711
$867$	−57.8117	−1.96339
$868$	−1.15207	−0.0391037
$869$	4.97041	0.168610
$870$	0	0
$871$	−2.90799	−0.0985333
$872$	45.1207	1.52798
$873$	2.00004	0.0676912
$874$	53.2923	1.80264
$875$	0	0
$876$	−0.963569	−0.0325560
$877$	−22.2769	−0.752238	−0.376119	−	0.926571i	$-0.622742\pi$
$877$	−22.2769	−0.752238	−0.376119	+	0.926571i	$0.622742\pi$
$878$	17.7111	0.597721
$879$	31.3984	1.05904
$880$	0	0
$881$	−23.5240	−0.792544	−0.396272	−	0.918133i	$-0.629696\pi$
$881$	−23.5240	−0.792544	−0.396272	+	0.918133i	$0.629696\pi$
$882$	−1.09911	−0.0370091
$883$	−20.7165	−0.697165	−0.348582	−	0.937278i	$-0.613337\pi$
$883$	−20.7165	−0.697165	−0.348582	+	0.937278i	$0.613337\pi$
$884$	0.249825	0.00840252
$885$	0	0
$886$	−32.9349	−1.10647
$887$	−18.9138	−0.635065	−0.317532	−	0.948247i	$-0.602854\pi$
$887$	−18.9138	−0.635065	−0.317532	+	0.948247i	$0.602854\pi$
$888$	−38.3827	−1.28804
$889$	−1.33351	−0.0447245
$890$	0	0
$891$	10.7981	0.361751
$892$	−2.34675	−0.0785749
$893$	47.4573	1.58810
$894$	−33.7866	−1.12999
$895$	0	0
$896$	21.7757	0.727474
$897$	−5.37886	−0.179595
$898$	−33.9924	−1.13434
$899$	37.5438	1.25216
$900$	0	0
$901$	−44.0523	−1.46759
$902$	−21.0717	−0.701611
$903$	−29.2397	−0.973035
$904$	−40.7617	−1.35571
$905$	0	0
$906$	−40.1000	−1.33223
$907$	36.5086	1.21225	0.606124	−	0.795370i	$-0.292723\pi$
$907$	36.5086	1.21225	0.606124	+	0.795370i	$0.292723\pi$
$908$	−0.993407	−0.0329674
$909$	3.17731	0.105385
$910$	0	0
$911$	1.01796	0.0337265	0.0168632	−	0.999858i	$-0.494632\pi$
$911$	1.01796	0.0337265	0.0168632	+	0.999858i	$0.494632\pi$
$912$	−31.0354	−1.02769
$913$	−2.59637	−0.0859272
$914$	−18.5990	−0.615201
$915$	0	0
$916$	2.40195	0.0793626
$917$	−5.36972	−0.177324
$918$	54.1272	1.78647
$919$	9.80619	0.323476	0.161738	−	0.986834i	$-0.448290\pi$
$919$	9.80619	0.323476	0.161738	+	0.986834i	$0.448290\pi$
$920$	0	0
$921$	33.4888	1.10349
$922$	−6.50608	−0.214266
$923$	−2.99709	−0.0986506
$924$	0.377084	0.0124051
$925$	0	0
$926$	−20.3798	−0.669723
$927$	0.858300	0.0281903
$928$	2.60433	0.0854914
$929$	−16.5984	−0.544577	−0.272288	−	0.962216i	$-0.587781\pi$
$929$	−16.5984	−0.544577	−0.272288	+	0.962216i	$0.587781\pi$
$930$	0	0
$931$	13.5342	0.443564
$932$	0.274802	0.00900144
$933$	37.1585	1.21651
$934$	−37.6603	−1.23228
$935$	0	0
$936$	−0.348143	−0.0113794
$937$	−24.1653	−0.789446	−0.394723	−	0.918800i	$-0.629160\pi$
$937$	−24.1653	−0.789446	−0.394723	+	0.918800i	$0.629160\pi$
$938$	−19.8639	−0.648580
$939$	−40.7070	−1.32842
$940$	0	0
$941$	−41.4131	−1.35003	−0.675014	−	0.737804i	$-0.735863\pi$
$941$	−41.4131	−1.35003	−0.675014	+	0.737804i	$0.735863\pi$
$942$	2.50048	0.0814701
$943$	−88.6728	−2.88758
$944$	−22.8570	−0.743933
$945$	0	0
$946$	−15.9954	−0.520056
$947$	35.5992	1.15682	0.578409	−	0.815747i	$-0.303674\pi$
$947$	35.5992	1.15682	0.578409	+	0.815747i	$0.303674\pi$
$948$	−0.505192	−0.0164079
$949$	−2.95401	−0.0958911
$950$	0	0
$951$	−27.4878	−0.891352
$952$	42.9262	1.39125
$953$	60.4241	1.95733	0.978664	−	0.205465i	$-0.0658708\pi$
$953$	60.4241	1.95733	0.978664	+	0.205465i	$0.0658708\pi$
$954$	2.44048	0.0790136
$955$	0	0
$956$	1.57765	0.0510249
$957$	−12.2885	−0.397230
$958$	−41.2881	−1.33396
$959$	0.0467738	0.00151041
$960$	0	0
$961$	14.5337	0.468830
$962$	−4.67789	−0.150821
$963$	−1.09948	−0.0354303
$964$	0.0828005	0.00266682
$965$	0	0
$966$	−36.7420	−1.18215
$967$	16.7194	0.537661	0.268831	−	0.963187i	$-0.413363\pi$
$967$	16.7194	0.537661	0.268831	+	0.963187i	$0.413363\pi$
$968$	−26.5341	−0.852837
$969$	−58.5330	−1.88035
$970$	0	0
$971$	61.7506	1.98167	0.990835	−	0.135075i	$-0.0431274\pi$
$971$	61.7506	1.98167	0.990835	+	0.135075i	$0.0431274\pi$
$972$	0.247638	0.00794300
$973$	−9.13460	−0.292842
$974$	29.5992	0.948421
$975$	0	0
$976$	−15.8730	−0.508082
$977$	50.6020	1.61890	0.809450	−	0.587189i	$-0.199765\pi$
$977$	50.6020	1.61890	0.809450	+	0.587189i	$0.199765\pi$
$978$	−17.8699	−0.571418
$979$	6.04951	0.193343
$980$	0	0
$981$	−4.51889	−0.144277
$982$	−15.4458	−0.492895
$983$	15.8077	0.504187	0.252093	−	0.967703i	$-0.418881\pi$
$983$	15.8077	0.504187	0.252093	+	0.967703i	$0.418881\pi$
$984$	53.8740	1.71744
$985$	0	0
$986$	−55.6119	−1.77104
$987$	−32.7191	−1.04146
$988$	0.170424	0.00542192
$989$	−67.3111	−2.14037
$990$	0	0
$991$	23.8907	0.758912	0.379456	−	0.925210i	$-0.376111\pi$
$991$	23.8907	0.758912	0.379456	+	0.925210i	$0.376111\pi$
$992$	3.15858	0.100285
$993$	−57.7292	−1.83198
$994$	−20.4726	−0.649351
$995$	0	0
$996$	0.263894	0.00836181
$997$	−30.2576	−0.958268	−0.479134	−	0.877742i	$-0.659049\pi$
$997$	−30.2576	−0.958268	−0.479134	+	0.877742i	$0.659049\pi$
$998$	−39.7636	−1.25870
$999$	43.7719	1.38488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.o.1.10	yes	40
5.4	even	2		6025.2.a.l.1.31	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.31	✓	40	5.4	even	2
6025.2.a.o.1.10	yes	40	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)

\(f(q)\)	\(=\)	\(q-1.38463 q^{2} -1.64656 q^{3} -0.0828005 q^{4} +2.27988 q^{6} -2.06195 q^{7} +2.88391 q^{8} -0.288826 q^{9} +O(q^{10})\)	\(q-1.38463 q^{2} -1.64656 q^{3} -0.0828005 q^{4} +2.27988 q^{6} -2.06195 q^{7} +2.88391 q^{8} -0.288826 q^{9} -1.34137 q^{11} +0.136336 q^{12} +0.417965 q^{13} +2.85504 q^{14} -3.82754 q^{16} -7.21876 q^{17} +0.399918 q^{18} -4.92447 q^{19} +3.39514 q^{21} +1.85730 q^{22} +7.81577 q^{23} -4.74854 q^{24} -0.578727 q^{26} +5.41526 q^{27} +0.170731 q^{28} -5.56380 q^{29} -6.74787 q^{31} -0.468085 q^{32} +2.20865 q^{33} +9.99531 q^{34} +0.0239150 q^{36} +8.08306 q^{37} +6.81856 q^{38} -0.688206 q^{39} -11.3454 q^{41} -4.70101 q^{42} -8.61222 q^{43} +0.111066 q^{44} -10.8219 q^{46} -9.63705 q^{47} +6.30230 q^{48} -2.74835 q^{49} +11.8862 q^{51} -0.0346077 q^{52} +6.10247 q^{53} -7.49814 q^{54} -5.94648 q^{56} +8.10845 q^{57} +7.70381 q^{58} +5.97172 q^{59} +4.14705 q^{61} +9.34330 q^{62} +0.595546 q^{63} +8.30321 q^{64} -3.05816 q^{66} -6.95749 q^{67} +0.597717 q^{68} -12.8692 q^{69} -7.17068 q^{71} -0.832948 q^{72} -7.06759 q^{73} -11.1920 q^{74} +0.407748 q^{76} +2.76583 q^{77} +0.952911 q^{78} -3.70548 q^{79} -8.05010 q^{81} +15.7091 q^{82} +1.93561 q^{83} -0.281119 q^{84} +11.9247 q^{86} +9.16116 q^{87} -3.86838 q^{88} -4.50996 q^{89} -0.861824 q^{91} -0.647149 q^{92} +11.1108 q^{93} +13.3438 q^{94} +0.770732 q^{96} -6.92472 q^{97} +3.80545 q^{98} +0.387422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9	\( 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9} + q^{11} + 14 q^{12} + 9 q^{13} - q^{14} + 43 q^{16} + 12 q^{17} + 42 q^{18} + 2 q^{21} + 5 q^{22} + 77 q^{23} - 2 q^{24} + 2 q^{26} + 38 q^{27} + 42 q^{28} + 2 q^{29} + q^{31} + 72 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 28 q^{37} + 23 q^{38} - 2 q^{39} - 2 q^{41} + 37 q^{42} + 31 q^{43} + 3 q^{44} + 14 q^{46} + 96 q^{47} + 13 q^{48} + 40 q^{49} - 10 q^{51} + 42 q^{52} + 54 q^{53} + 4 q^{54} - 15 q^{56} + 37 q^{57} + 27 q^{58} + q^{59} + 5 q^{61} + 39 q^{62} + 70 q^{63} + 65 q^{64} - 52 q^{66} + 34 q^{67} + 52 q^{68} + 21 q^{69} - 9 q^{71} + 70 q^{72} + 25 q^{73} + 22 q^{74} - 47 q^{76} + 54 q^{77} + 58 q^{78} + 13 q^{79} + 12 q^{81} - 5 q^{82} + 63 q^{83} + 95 q^{84} - 18 q^{86} + 47 q^{87} + 13 q^{88} + 19 q^{89} - 31 q^{91} + 137 q^{92} + 52 q^{93} + 120 q^{94} - 49 q^{96} + 36 q^{97} + 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9 + q^11 + 14 * q^12 + 9 * q^13 - q^14 + 43 * q^16 + 12 * q^17 + 42 * q^18 + 2 * q^21 + 5 * q^22 + 77 * q^23 - 2 * q^24 + 2 * q^26 + 38 * q^27 + 42 * q^28 + 2 * q^29 + q^31 + 72 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 28 * q^37 + 23 * q^38 - 2 * q^39 - 2 * q^41 + 37 * q^42 + 31 * q^43 + 3 * q^44 + 14 * q^46 + 96 * q^47 + 13 * q^48 + 40 * q^49 - 10 * q^51 + 42 * q^52 + 54 * q^53 + 4 * q^54 - 15 * q^56 + 37 * q^57 + 27 * q^58 + q^59 + 5 * q^61 + 39 * q^62 + 70 * q^63 + 65 * q^64 - 52 * q^66 + 34 * q^67 + 52 * q^68 + 21 * q^69 - 9 * q^71 + 70 * q^72 + 25 * q^73 + 22 * q^74 - 47 * q^76 + 54 * q^77 + 58 * q^78 + 13 * q^79 + 12 * q^81 - 5 * q^82 + 63 * q^83 + 95 * q^84 - 18 * q^86 + 47 * q^87 + 13 * q^88 + 19 * q^89 - 31 * q^91 + 137 * q^92 + 52 * q^93 + 120 * q^94 - 49 * q^96 + 36 * q^97 + 64 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more