LMFDB - Embedded newform 425.4.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,4,Mod(1,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("425.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	425.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:	$25.0758117524$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.2636.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 14x - 4 $ x^3 - 14*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.87707$ of defining polynomial
Character	$\chi$	$=$	425.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} +4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} +O(q^{10})$	\(q-1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} +4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} +27.6161 q^{11} +19.3918 q^{12} -58.1117 q^{13} -10.8088 q^{14} +22.9632 q^{16} +17.0000 q^{17} +23.2065 q^{18} +89.1688 q^{19} -25.0493 q^{21} -37.5916 q^{22} +115.269 q^{23} -60.7497 q^{24} +79.1029 q^{26} +138.956 q^{27} -48.8108 q^{28} -128.558 q^{29} +273.460 q^{31} -185.316 q^{32} -87.1187 q^{33} -23.1408 q^{34} +104.797 q^{36} +132.351 q^{37} -121.379 q^{38} +183.321 q^{39} -470.559 q^{41} +34.0977 q^{42} -352.642 q^{43} -169.758 q^{44} -156.907 q^{46} -152.598 q^{47} -72.4403 q^{48} -279.949 q^{49} -53.6287 q^{51} +357.217 q^{52} -527.614 q^{53} -189.150 q^{54} +152.912 q^{56} -281.295 q^{57} +174.995 q^{58} -292.020 q^{59} -53.8962 q^{61} -372.239 q^{62} -135.372 q^{63} +68.5514 q^{64} +118.588 q^{66} -52.9572 q^{67} -104.500 q^{68} -363.632 q^{69} +788.400 q^{71} -328.304 q^{72} -295.780 q^{73} -180.159 q^{74} -548.127 q^{76} +219.285 q^{77} -249.541 q^{78} -720.325 q^{79} +21.9487 q^{81} +640.535 q^{82} +116.051 q^{83} +153.980 q^{84} +480.024 q^{86} +405.552 q^{87} +531.812 q^{88} -813.329 q^{89} -461.435 q^{91} -708.569 q^{92} -862.664 q^{93} +207.720 q^{94} +584.605 q^{96} -794.693 q^{97} +381.072 q^{98} -470.808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) $ 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} - 28 q^{11} - 22 q^{12} - 30 q^{13} + 92 q^{14} + 137 q^{16} + 51 q^{17} + 103 q^{18} + 80 q^{19} - 192 q^{21} - 286 q^{22} - 142 q^{23} - 666 q^{24} + 26 q^{26} + 20 q^{27} - 476 q^{28} - 456 q^{29} + 230 q^{31} + 71 q^{32} + 332 q^{33} - 17 q^{34} + 1313 q^{36} - 356 q^{37} - 724 q^{38} + 268 q^{39} - 294 q^{41} + 1128 q^{42} - 556 q^{43} - 1122 q^{44} - 704 q^{46} - 640 q^{47} - 774 q^{48} - 269 q^{49} - 68 q^{51} + 774 q^{52} - 302 q^{53} - 1100 q^{54} + 684 q^{56} + 720 q^{57} + 1304 q^{58} + 636 q^{59} - 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} + 2468 q^{66} - 1008 q^{67} + 425 q^{68} + 576 q^{69} - 402 q^{71} + 927 q^{72} - 838 q^{73} + 836 q^{74} - 908 q^{76} + 504 q^{77} - 1308 q^{78} - 594 q^{79} - 505 q^{81} - 358 q^{82} + 2396 q^{83} - 2040 q^{84} - 1264 q^{86} - 1428 q^{87} - 1838 q^{88} - 170 q^{89} - 1016 q^{91} - 4896 q^{92} - 632 q^{93} - 2016 q^{94} + 678 q^{96} + 270 q^{97} - 2857 q^{98} - 2920 q^{99}+O(q^{100}) \) 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 - 28 * q^11 - 22 * q^12 - 30 * q^13 + 92 * q^14 + 137 * q^16 + 51 * q^17 + 103 * q^18 + 80 * q^19 - 192 * q^21 - 286 * q^22 - 142 * q^23 - 666 * q^24 + 26 * q^26 + 20 * q^27 - 476 * q^28 - 456 * q^29 + 230 * q^31 + 71 * q^32 + 332 * q^33 - 17 * q^34 + 1313 * q^36 - 356 * q^37 - 724 * q^38 + 268 * q^39 - 294 * q^41 + 1128 * q^42 - 556 * q^43 - 1122 * q^44 - 704 * q^46 - 640 * q^47 - 774 * q^48 - 269 * q^49 - 68 * q^51 + 774 * q^52 - 302 * q^53 - 1100 * q^54 + 684 * q^56 + 720 * q^57 + 1304 * q^58 + 636 * q^59 - 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 + 2468 * q^66 - 1008 * q^67 + 425 * q^68 + 576 * q^69 - 402 * q^71 + 927 * q^72 - 838 * q^73 + 836 * q^74 - 908 * q^76 + 504 * q^77 - 1308 * q^78 - 594 * q^79 - 505 * q^81 - 358 * q^82 + 2396 * q^83 - 2040 * q^84 - 1264 * q^86 - 1428 * q^87 - 1838 * q^88 - 170 * q^89 - 1016 * q^91 - 4896 * q^92 - 632 * q^93 - 2016 * q^94 + 678 * q^96 + 270 * q^97 - 2857 * q^98 - 2920 * 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 $

$2$	−1.36122	−0.481264	−0.240632	−	0.970616i	$-0.577355\pi$
$2$	−1.36122	−0.481264	−0.240632	+	0.970616i	$0.577355\pi$
$3$	−3.15463	−0.607109	−0.303555	−	0.952814i	$-0.598173\pi$
$3$	−3.15463	−0.607109	−0.303555	+	0.952814i	$0.598173\pi$
$4$	−6.14708	−0.768385
$5$	0	0
$5$	0	0
$6$	4.29415	0.292180
$7$	7.94049	0.428746	0.214373	−	0.976752i	$-0.431229\pi$
$7$	7.94049	0.428746	0.214373	+	0.976752i	$0.431229\pi$
$8$	19.2573	0.851061
$9$	−17.0483	−0.631419
$10$	0	0
$11$	27.6161	0.756961	0.378481	−	0.925609i	$-0.376447\pi$
$11$	27.6161	0.756961	0.378481	+	0.925609i	$0.376447\pi$
$12$	19.3918	0.466493
$13$	−58.1117	−1.23979	−0.619896	−	0.784684i	$-0.712825\pi$
$13$	−58.1117	−1.23979	−0.619896	+	0.784684i	$0.712825\pi$
$14$	−10.8088	−0.206340
$15$	0	0
$16$	22.9632	0.358799
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	23.2065	0.303879
$19$	89.1688	1.07667	0.538335	−	0.842731i	$-0.319054\pi$
$19$	89.1688	1.07667	0.538335	+	0.842731i	$0.319054\pi$
$20$	0	0
$21$	−25.0493	−0.260296
$22$	−37.5916	−0.364298
$23$	115.269	1.04501	0.522507	−	0.852635i	$-0.324997\pi$
$23$	115.269	1.04501	0.522507	+	0.852635i	$0.324997\pi$
$24$	−60.7497	−0.516687
$25$	0	0
$26$	79.1029	0.596668
$27$	138.956	0.990449
$28$	−48.8108	−0.329442
$29$	−128.558	−0.823191	−0.411596	−	0.911367i	$-0.635028\pi$
$29$	−128.558	−0.823191	−0.411596	+	0.911367i	$0.635028\pi$
$30$	0	0
$31$	273.460	1.58435	0.792174	−	0.610295i	$-0.208949\pi$
$31$	273.460	1.58435	0.792174	+	0.610295i	$0.208949\pi$
$32$	−185.316	−1.02374
$33$	−87.1187	−0.459558
$34$	−23.1408	−0.116724
$35$	0	0
$36$	104.797	0.485172
$37$	132.351	0.588063	0.294031	−	0.955796i	$-0.405003\pi$
$37$	132.351	0.588063	0.294031	+	0.955796i	$0.405003\pi$
$38$	−121.379	−0.518163
$39$	183.321	0.752689
$40$	0	0
$41$	−470.559	−1.79241	−0.896207	−	0.443636i	$-0.853688\pi$
$41$	−470.559	−1.79241	−0.896207	+	0.443636i	$0.853688\pi$
$42$	34.0977	0.125271
$43$	−352.642	−1.25064	−0.625318	−	0.780370i	$-0.715031\pi$
$43$	−352.642	−1.25064	−0.625318	+	0.780370i	$0.715031\pi$
$44$	−169.758	−0.581637
$45$	0	0
$46$	−156.907	−0.502928
$47$	−152.598	−0.473589	−0.236795	−	0.971560i	$-0.576097\pi$
$47$	−152.598	−0.473589	−0.236795	+	0.971560i	$0.576097\pi$
$48$	−72.4403	−0.217830
$49$	−279.949	−0.816177
$50$	0	0
$51$	−53.6287	−0.147246
$52$	357.217	0.952637
$53$	−527.614	−1.36742	−0.683711	−	0.729753i	$-0.739635\pi$
$53$	−527.614	−1.36742	−0.683711	+	0.729753i	$0.739635\pi$
$54$	−189.150	−0.476668
$55$	0	0
$56$	152.912	0.364889
$57$	−281.295	−0.653656
$58$	174.995	0.396173
$59$	−292.020	−0.644368	−0.322184	−	0.946677i	$-0.604417\pi$
$59$	−292.020	−0.644368	−0.322184	+	0.946677i	$0.604417\pi$
$60$	0	0
$61$	−53.8962	−0.113126	−0.0565632	−	0.998399i	$-0.518014\pi$
$61$	−53.8962	−0.113126	−0.0565632	+	0.998399i	$0.518014\pi$
$62$	−372.239	−0.762490
$63$	−135.372	−0.270718
$64$	68.5514	0.133889
$65$	0	0
$66$	118.588	0.221169
$67$	−52.9572	−0.0965635	−0.0482817	−	0.998834i	$-0.515375\pi$
$67$	−52.9572	−0.0965635	−0.0482817	+	0.998834i	$0.515375\pi$
$68$	−104.500	−0.186361
$69$	−363.632	−0.634437
$70$	0	0
$71$	788.400	1.31783	0.658915	−	0.752218i	$-0.271016\pi$
$71$	788.400	1.31783	0.658915	+	0.752218i	$0.271016\pi$
$72$	−328.304	−0.537375
$73$	−295.780	−0.474224	−0.237112	−	0.971482i	$-0.576201\pi$
$73$	−295.780	−0.474224	−0.237112	+	0.971482i	$0.576201\pi$
$74$	−180.159	−0.283014
$75$	0	0
$76$	−548.127	−0.827296
$77$	219.285	0.324544
$78$	−249.541	−0.362242
$79$	−720.325	−1.02586	−0.512930	−	0.858430i	$-0.671440\pi$
$79$	−720.325	−1.02586	−0.512930	+	0.858430i	$0.671440\pi$
$80$	0	0
$81$	21.9487	0.0301079
$82$	640.535	0.862625
$83$	116.051	0.153473	0.0767363	−	0.997051i	$-0.475550\pi$
$83$	116.051	0.153473	0.0767363	+	0.997051i	$0.475550\pi$
$84$	153.980	0.200007
$85$	0	0
$86$	480.024	0.601887
$87$	405.552	0.499767
$88$	531.812	0.644220
$89$	−813.329	−0.968682	−0.484341	−	0.874879i	$-0.660941\pi$
$89$	−813.329	−0.968682	−0.484341	+	0.874879i	$0.660941\pi$
$90$	0	0
$91$	−461.435	−0.531556
$92$	−708.569	−0.802972
$93$	−862.664	−0.961872
$94$	207.720	0.227922
$95$	0	0
$96$	584.605	0.621521
$97$	−794.693	−0.831844	−0.415922	−	0.909400i	$-0.636541\pi$
$97$	−794.693	−0.831844	−0.415922	+	0.909400i	$0.636541\pi$
$98$	381.072	0.392797
$99$	−470.808	−0.477959
$100$	0	0
$101$	265.513	0.261579	0.130790	−	0.991410i	$-0.458249\pi$
$101$	265.513	0.261579	0.130790	+	0.991410i	$0.458249\pi$
$102$	73.0006	0.0708641
$103$	−523.107	−0.500420	−0.250210	−	0.968192i	$-0.580500\pi$
$103$	−523.107	−0.500420	−0.250210	+	0.968192i	$0.580500\pi$
$104$	−1119.07	−1.05514
$105$	0	0
$106$	718.199	0.658091
$107$	986.039	0.890878	0.445439	−	0.895312i	$-0.353048\pi$
$107$	986.039	0.890878	0.445439	+	0.895312i	$0.353048\pi$
$108$	−854.174	−0.761046
$109$	1814.39	1.59438	0.797188	−	0.603732i	$-0.206320\pi$
$109$	1814.39	1.59438	0.797188	+	0.603732i	$0.206320\pi$
$110$	0	0
$111$	−417.518	−0.357018
$112$	182.339	0.153834
$113$	707.339	0.588857	0.294429	−	0.955673i	$-0.404871\pi$
$113$	707.339	0.588857	0.294429	+	0.955673i	$0.404871\pi$
$114$	382.904	0.314581
$115$	0	0
$116$	790.253	0.632527
$117$	990.706	0.782827
$118$	397.503	0.310112
$119$	134.988	0.103986
$120$	0	0
$121$	−568.350	−0.427010
$122$	73.3647	0.0544437
$123$	1484.44	1.08819
$124$	−1680.98	−1.21739
$125$	0	0
$126$	184.271	0.130287
$127$	−2648.18	−1.85030	−0.925151	−	0.379600i	$-0.876062\pi$
$127$	−2648.18	−1.85030	−0.925151	+	0.379600i	$0.876062\pi$
$128$	1389.22	0.959302
$129$	1112.46	0.759273
$130$	0	0
$131$	−1979.08	−1.31995	−0.659974	−	0.751289i	$-0.729433\pi$
$131$	−1979.08	−1.31995	−0.659974	+	0.751289i	$0.729433\pi$
$132$	535.525	0.353117
$133$	708.044	0.461618
$134$	72.0865	0.0464726
$135$	0	0
$136$	327.374	0.206413
$137$	−3141.92	−1.95936	−0.979679	−	0.200570i	$-0.935721\pi$
$137$	−3141.92	−1.95936	−0.979679	+	0.200570i	$0.935721\pi$
$138$	494.984	0.305332
$139$	1468.07	0.895830	0.447915	−	0.894076i	$-0.352167\pi$
$139$	1468.07	0.895830	0.447915	+	0.894076i	$0.352167\pi$
$140$	0	0
$141$	481.390	0.287520
$142$	−1073.19	−0.634224
$143$	−1604.82	−0.938474
$144$	−391.483	−0.226553
$145$	0	0
$146$	402.621	0.228227
$147$	883.135	0.495508
$148$	−813.570	−0.451858
$149$	−286.027	−0.157263	−0.0786316	−	0.996904i	$-0.525055\pi$
$149$	−286.027	−0.157263	−0.0786316	+	0.996904i	$0.525055\pi$
$150$	0	0
$151$	−669.626	−0.360883	−0.180442	−	0.983586i	$-0.557753\pi$
$151$	−669.626	−0.360883	−0.180442	+	0.983586i	$0.557753\pi$
$152$	1717.15	0.916311
$153$	−289.821	−0.153141
$154$	−298.496	−0.156191
$155$	0	0
$156$	−1126.89	−0.578354
$157$	−720.809	−0.366413	−0.183206	−	0.983074i	$-0.558648\pi$
$157$	−720.809	−0.366413	−0.183206	+	0.983074i	$0.558648\pi$
$158$	980.522	0.493710
$159$	1664.43	0.830174
$160$	0	0
$161$	915.294	0.448045
$162$	−29.8770	−0.0144899
$163$	676.599	0.325125	0.162562	−	0.986698i	$-0.448024\pi$
$163$	676.599	0.325125	0.162562	+	0.986698i	$0.448024\pi$
$164$	2892.56	1.37726
$165$	0	0
$166$	−157.971	−0.0738609
$167$	2835.67	1.31396	0.656979	−	0.753909i	$-0.271834\pi$
$167$	2835.67	1.31396	0.656979	+	0.753909i	$0.271834\pi$
$168$	−482.382	−0.221527
$169$	1179.97	0.537083
$170$	0	0
$171$	−1520.18	−0.679829
$172$	2167.72	0.960970
$173$	177.314	0.0779243	0.0389621	−	0.999241i	$-0.487595\pi$
$173$	177.314	0.0779243	0.0389621	+	0.999241i	$0.487595\pi$
$174$	−552.046	−0.240520
$175$	0	0
$176$	634.153	0.271597
$177$	921.214	0.391202
$178$	1107.12	0.466192
$179$	−1023.76	−0.427483	−0.213741	−	0.976890i	$-0.568565\pi$
$179$	−1023.76	−0.427483	−0.213741	+	0.976890i	$0.568565\pi$
$180$	0	0
$181$	−3450.21	−1.41686	−0.708432	−	0.705779i	$-0.750597\pi$
$181$	−3450.21	−1.41686	−0.708432	+	0.705779i	$0.750597\pi$
$182$	628.116	0.255819
$183$	170.023	0.0686800
$184$	2219.78	0.889370
$185$	0	0
$186$	1174.28	0.462915
$187$	469.474	0.183590
$188$	938.031	0.363899
$189$	1103.38	0.424651
$190$	0	0
$191$	−490.894	−0.185968	−0.0929839	−	0.995668i	$-0.529640\pi$
$191$	−490.894	−0.185968	−0.0929839	+	0.995668i	$0.529640\pi$
$192$	−216.254	−0.0812855
$193$	3548.80	1.32357	0.661783	−	0.749696i	$-0.269800\pi$
$193$	3548.80	1.32357	0.661783	+	0.749696i	$0.269800\pi$
$194$	1081.75	0.400337
$195$	0	0
$196$	1720.87	0.627138
$197$	−1363.15	−0.492996	−0.246498	−	0.969143i	$-0.579280\pi$
$197$	−1363.15	−0.492996	−0.246498	+	0.969143i	$0.579280\pi$
$198$	640.874	0.230025
$199$	3737.46	1.33137	0.665683	−	0.746235i	$-0.268140\pi$
$199$	3737.46	1.33137	0.665683	+	0.746235i	$0.268140\pi$
$200$	0	0
$201$	167.060	0.0586246
$202$	−361.422	−0.125889
$203$	−1020.81	−0.352940
$204$	329.660	0.113141
$205$	0	0
$206$	712.064	0.240834
$207$	−1965.15	−0.659841
$208$	−1334.43	−0.444836
$209$	2462.50	0.814997
$210$	0	0
$211$	−5266.12	−1.71817	−0.859087	−	0.511829i	$-0.828968\pi$
$211$	−5266.12	−1.71817	−0.859087	+	0.511829i	$0.828968\pi$
$212$	3243.28	1.05071
$213$	−2487.11	−0.800066
$214$	−1342.22	−0.428748
$215$	0	0
$216$	2675.92	0.842932
$217$	2171.40	0.679283
$218$	−2469.78	−0.767316
$219$	933.075	0.287906
$220$	0	0
$221$	−987.899	−0.300694
$222$	568.334	0.171820
$223$	−704.546	−0.211569	−0.105785	−	0.994389i	$-0.533735\pi$
$223$	−704.546	−0.211569	−0.105785	+	0.994389i	$0.533735\pi$
$224$	−1471.50	−0.438923
$225$	0	0
$226$	−962.845	−0.283396
$227$	2151.26	0.629006	0.314503	−	0.949256i	$-0.398162\pi$
$227$	2151.26	0.629006	0.314503	+	0.949256i	$0.398162\pi$
$228$	1729.14	0.502259
$229$	−3916.94	−1.13030	−0.565149	−	0.824989i	$-0.691181\pi$
$229$	−3916.94	−1.13030	−0.565149	+	0.824989i	$0.691181\pi$
$230$	0	0
$231$	−691.764	−0.197034
$232$	−2475.67	−0.700586
$233$	5192.74	1.46003	0.730017	−	0.683429i	$-0.239512\pi$
$233$	5192.74	1.46003	0.730017	+	0.683429i	$0.239512\pi$
$234$	−1348.57	−0.376747
$235$	0	0
$236$	1795.07	0.495123
$237$	2272.36	0.622809
$238$	−183.749	−0.0500448
$239$	334.305	0.0904786	0.0452393	−	0.998976i	$-0.485595\pi$
$239$	334.305	0.0904786	0.0452393	+	0.998976i	$0.485595\pi$
$240$	0	0
$241$	−1918.45	−0.512773	−0.256386	−	0.966574i	$-0.582532\pi$
$241$	−1918.45	−0.512773	−0.256386	+	0.966574i	$0.582532\pi$
$242$	773.651	0.205505
$243$	−3821.06	−1.00873
$244$	331.304	0.0869245
$245$	0	0
$246$	−2020.65	−0.523708
$247$	−5181.75	−1.33485
$248$	5266.09	1.34838
$249$	−366.097	−0.0931746
$250$	0	0
$251$	7695.71	1.93525	0.967627	−	0.252385i	$-0.0812148\pi$
$251$	7695.71	1.93525	0.967627	+	0.252385i	$0.0812148\pi$
$252$	832.141	0.208016
$253$	3183.29	0.791035
$254$	3604.76	0.890484
$255$	0	0
$256$	−2439.44	−0.595567
$257$	−5335.10	−1.29492	−0.647460	−	0.762099i	$-0.724169\pi$
$257$	−5335.10	−1.29492	−0.647460	+	0.762099i	$0.724169\pi$
$258$	−1514.30	−0.365411
$259$	1050.93	0.252130
$260$	0	0
$261$	2191.69	0.519778
$262$	2693.97	0.635244
$263$	−3934.15	−0.922396	−0.461198	−	0.887297i	$-0.652580\pi$
$263$	−3934.15	−0.922396	−0.461198	+	0.887297i	$0.652580\pi$
$264$	−1677.67	−0.391112
$265$	0	0
$266$	−963.804	−0.222160
$267$	2565.75	0.588095
$268$	325.532	0.0741979
$269$	3424.04	0.776088	0.388044	−	0.921641i	$-0.373151\pi$
$269$	3424.04	0.776088	0.388044	+	0.921641i	$0.373151\pi$
$270$	0	0
$271$	549.034	0.123068	0.0615340	−	0.998105i	$-0.480401\pi$
$271$	549.034	0.123068	0.0615340	+	0.998105i	$0.480401\pi$
$272$	390.374	0.0870216
$273$	1455.66	0.322712
$274$	4276.85	0.942970
$275$	0	0
$276$	2235.27	0.487492
$277$	−5203.65	−1.12873	−0.564363	−	0.825527i	$-0.690878\pi$
$277$	−5203.65	−1.12873	−0.564363	+	0.825527i	$0.690878\pi$
$278$	−1998.37	−0.431131
$279$	−4662.02	−1.00039
$280$	0	0
$281$	−1986.73	−0.421774	−0.210887	−	0.977510i	$-0.567635\pi$
$281$	−1986.73	−0.421774	−0.210887	+	0.977510i	$0.567635\pi$
$282$	−655.279	−0.138373
$283$	−753.696	−0.158313	−0.0791565	−	0.996862i	$-0.525223\pi$
$283$	−753.696	−0.158313	−0.0791565	+	0.996862i	$0.525223\pi$
$284$	−4846.36	−1.01260
$285$	0	0
$286$	2184.51	0.451654
$287$	−3736.47	−0.768490
$288$	3159.33	0.646407
$289$	289.000	0.0588235
$290$	0	0
$291$	2506.96	0.505020
$292$	1818.18	0.364387
$293$	7202.22	1.43603	0.718017	−	0.696025i	$-0.245050\pi$
$293$	7202.22	1.43603	0.718017	+	0.696025i	$0.245050\pi$
$294$	−1202.14	−0.238471
$295$	0	0
$296$	2548.72	0.500477
$297$	3837.43	0.749731
$298$	389.345	0.0756852
$299$	−6698.50	−1.29560
$300$	0	0
$301$	−2800.15	−0.536205
$302$	911.509	0.173680
$303$	−837.595	−0.158807
$304$	2047.60	0.386308
$305$	0	0
$306$	394.511	0.0737016
$307$	−2425.71	−0.450953	−0.225477	−	0.974249i	$-0.572394\pi$
$307$	−2425.71	−0.450953	−0.225477	+	0.974249i	$0.572394\pi$
$308$	−1347.96	−0.249375
$309$	1650.21	0.303809
$310$	0	0
$311$	−9544.94	−1.74033	−0.870167	−	0.492757i	$-0.835989\pi$
$311$	−9544.94	−1.74033	−0.870167	+	0.492757i	$0.835989\pi$
$312$	3530.27	0.640584
$313$	−588.379	−0.106253	−0.0531264	−	0.998588i	$-0.516919\pi$
$313$	−588.379	−0.106253	−0.0531264	+	0.998588i	$0.516919\pi$
$314$	981.180	0.176341
$315$	0	0
$316$	4427.89	0.788255
$317$	−7653.31	−1.35600	−0.678001	−	0.735061i	$-0.737154\pi$
$317$	−7653.31	−1.35600	−0.678001	+	0.735061i	$0.737154\pi$
$318$	−2265.65	−0.399533
$319$	−3550.26	−0.623124
$320$	0	0
$321$	−3110.59	−0.540860
$322$	−1245.92	−0.215628
$323$	1515.87	0.261131
$324$	−134.920	−0.0231345
$325$	0	0
$326$	−921.001	−0.156471
$327$	−5723.73	−0.967960
$328$	−9061.70	−1.52545
$329$	−1211.70	−0.203050
$330$	0	0
$331$	752.266	0.124919	0.0624597	−	0.998047i	$-0.480106\pi$
$331$	752.266	0.124919	0.0624597	+	0.998047i	$0.480106\pi$
$332$	−713.373	−0.117926
$333$	−2256.36	−0.371314
$334$	−3859.98	−0.632361
$335$	0	0
$336$	−575.211	−0.0933939
$337$	1968.57	0.318204	0.159102	−	0.987262i	$-0.449140\pi$
$337$	1968.57	0.318204	0.159102	+	0.987262i	$0.449140\pi$
$338$	−1606.20	−0.258479
$339$	−2231.39	−0.357501
$340$	0	0
$341$	7551.89	1.19929
$342$	2069.30	0.327178
$343$	−4946.52	−0.778678
$344$	−6790.93	−1.06437
$345$	0	0
$346$	−241.363	−0.0375022
$347$	−3983.10	−0.616207	−0.308104	−	0.951353i	$-0.599694\pi$
$347$	−3983.10	−0.616207	−0.308104	+	0.951353i	$0.599694\pi$
$348$	−2492.96	−0.384013
$349$	1495.61	0.229393	0.114697	−	0.993401i	$-0.463410\pi$
$349$	1495.61	0.229393	0.114697	+	0.993401i	$0.463410\pi$
$350$	0	0
$351$	−8074.98	−1.22795
$352$	−5117.72	−0.774930
$353$	−6482.49	−0.977417	−0.488708	−	0.872447i	$-0.662532\pi$
$353$	−6482.49	−0.977417	−0.488708	+	0.872447i	$0.662532\pi$
$354$	−1253.98	−0.188272
$355$	0	0
$356$	4999.59	0.744320
$357$	−425.838	−0.0631309
$358$	1393.56	0.205732
$359$	−4943.42	−0.726751	−0.363376	−	0.931643i	$-0.618376\pi$
$359$	−4943.42	−0.726751	−0.363376	+	0.931643i	$0.618376\pi$
$360$	0	0
$361$	1092.08	0.159218
$362$	4696.50	0.681886
$363$	1792.94	0.259242
$364$	2836.48	0.408439
$365$	0	0
$366$	−231.439	−0.0330533
$367$	14.8871	0.00211743	0.00105872	−	0.999999i	$-0.499663\pi$
$367$	14.8871	0.00211743	0.00105872	+	0.999999i	$0.499663\pi$
$368$	2646.95	0.374950
$369$	8022.23	1.13176
$370$	0	0
$371$	−4189.51	−0.586276
$372$	5302.86	0.739088
$373$	−1923.18	−0.266966	−0.133483	−	0.991051i	$-0.542616\pi$
$373$	−1923.18	−0.266966	−0.133483	+	0.991051i	$0.542616\pi$
$374$	−639.058	−0.0883554
$375$	0	0
$376$	−2938.63	−0.403053
$377$	7470.70	1.02059
$378$	−1501.94	−0.204369
$379$	−9592.87	−1.30014	−0.650069	−	0.759875i	$-0.725260\pi$
$379$	−9592.87	−1.30014	−0.650069	+	0.759875i	$0.725260\pi$
$380$	0	0
$381$	8354.04	1.12333
$382$	668.215	0.0894996
$383$	9083.77	1.21190	0.605951	−	0.795502i	$-0.292793\pi$
$383$	9083.77	1.21190	0.605951	+	0.795502i	$0.292793\pi$
$384$	−4382.47	−0.582401
$385$	0	0
$386$	−4830.70	−0.636985
$387$	6011.95	0.789675
$388$	4885.04	0.639176
$389$	−1143.78	−0.149079	−0.0745396	−	0.997218i	$-0.523749\pi$
$389$	−1143.78	−0.149079	−0.0745396	+	0.997218i	$0.523749\pi$
$390$	0	0
$391$	1959.58	0.253453
$392$	−5391.06	−0.694616
$393$	6243.27	0.801352
$394$	1855.55	0.237262
$395$	0	0
$396$	2894.09	0.367256
$397$	−10604.5	−1.34061	−0.670307	−	0.742084i	$-0.733838\pi$
$397$	−10604.5	−1.34061	−0.670307	+	0.742084i	$0.733838\pi$
$398$	−5087.51	−0.640739
$399$	−2233.62	−0.280252
$400$	0	0
$401$	13785.4	1.71674	0.858368	−	0.513035i	$-0.171479\pi$
$401$	13785.4	1.71674	0.858368	+	0.513035i	$0.171479\pi$
$402$	−227.406	−0.0282139
$403$	−15891.2	−1.96426
$404$	−1632.13	−0.200993
$405$	0	0
$406$	1389.55	0.169857
$407$	3655.01	0.445141
$408$	−1032.74	−0.125315
$409$	−9505.94	−1.14924	−0.574619	−	0.818421i	$-0.694850\pi$
$409$	−9505.94	−1.14924	−0.574619	+	0.818421i	$0.694850\pi$
$410$	0	0
$411$	9911.59	1.18954
$412$	3215.58	0.384515
$413$	−2318.78	−0.276270
$414$	2675.00	0.317558
$415$	0	0
$416$	10769.1	1.26922
$417$	−4631.23	−0.543866
$418$	−3352.00	−0.392229
$419$	9680.86	1.12874	0.564369	−	0.825523i	$-0.309120\pi$
$419$	9680.86	1.12874	0.564369	+	0.825523i	$0.309120\pi$
$420$	0	0
$421$	−12360.3	−1.43089	−0.715444	−	0.698671i	$-0.753775\pi$
$421$	−12360.3	−1.43089	−0.715444	+	0.698671i	$0.753775\pi$
$422$	7168.36	0.826897
$423$	2601.54	0.299033
$424$	−10160.4	−1.16376
$425$	0	0
$426$	3385.51	0.385043
$427$	−427.962	−0.0485025
$428$	−6061.25	−0.684537
$429$	5062.61	0.569756
$430$	0	0
$431$	2970.58	0.331990	0.165995	−	0.986127i	$-0.446916\pi$
$431$	2970.58	0.331990	0.165995	+	0.986127i	$0.446916\pi$
$432$	3190.87	0.355372
$433$	−6131.50	−0.680510	−0.340255	−	0.940333i	$-0.610513\pi$
$433$	−6131.50	−0.680510	−0.340255	+	0.940333i	$0.610513\pi$
$434$	−2955.76	−0.326915
$435$	0	0
$436$	−11153.2	−1.22509
$437$	10278.4	1.12513
$438$	−1270.12	−0.138559
$439$	−2544.91	−0.276679	−0.138339	−	0.990385i	$-0.544176\pi$
$439$	−2544.91	−0.276679	−0.138339	+	0.990385i	$0.544176\pi$
$440$	0	0
$441$	4772.65	0.515349
$442$	1344.75	0.144713
$443$	−8529.82	−0.914817	−0.457408	−	0.889257i	$-0.651222\pi$
$443$	−8529.82	−0.914817	−0.457408	+	0.889257i	$0.651222\pi$
$444$	2566.51	0.274327
$445$	0	0
$446$	959.043	0.101821
$447$	902.308	0.0954759
$448$	544.331	0.0574046
$449$	8855.74	0.930798	0.465399	−	0.885101i	$-0.345911\pi$
$449$	8855.74	0.930798	0.465399	+	0.885101i	$0.345911\pi$
$450$	0	0
$451$	−12995.0	−1.35679
$452$	−4348.07	−0.452469
$453$	2112.42	0.219095
$454$	−2928.35	−0.302718
$455$	0	0
$456$	−5416.98	−0.556301
$457$	7154.78	0.732356	0.366178	−	0.930545i	$-0.380666\pi$
$457$	7154.78	0.732356	0.366178	+	0.930545i	$0.380666\pi$
$458$	5331.82	0.543973
$459$	2362.25	0.240219
$460$	0	0
$461$	−7263.06	−0.733784	−0.366892	−	0.930264i	$-0.619578\pi$
$461$	−7263.06	−0.733784	−0.366892	+	0.930264i	$0.619578\pi$
$462$	941.645	0.0948253
$463$	−352.898	−0.0354224	−0.0177112	−	0.999843i	$-0.505638\pi$
$463$	−352.898	−0.0354224	−0.0177112	+	0.999843i	$0.505638\pi$
$464$	−2952.09	−0.295360
$465$	0	0
$466$	−7068.47	−0.702662
$467$	−1483.02	−0.146951	−0.0734753	−	0.997297i	$-0.523409\pi$
$467$	−1483.02	−0.146951	−0.0734753	+	0.997297i	$0.523409\pi$
$468$	−6089.94	−0.601512
$469$	−420.506	−0.0414012
$470$	0	0
$471$	2273.89	0.222452
$472$	−5623.51	−0.548396
$473$	−9738.60	−0.946683
$474$	−3093.19	−0.299736
$475$	0	0
$476$	−829.783	−0.0799014
$477$	8994.92	0.863415
$478$	−455.063	−0.0435441
$479$	−9990.10	−0.952942	−0.476471	−	0.879190i	$-0.658084\pi$
$479$	−9990.10	−0.952942	−0.476471	+	0.879190i	$0.658084\pi$
$480$	0	0
$481$	−7691.13	−0.729075
$482$	2611.44	0.246779
$483$	−2887.42	−0.272012
$484$	3493.69	0.328108
$485$	0	0
$486$	5201.30	0.485465
$487$	1129.88	0.105133	0.0525663	−	0.998617i	$-0.483260\pi$
$487$	1129.88	0.105133	0.0525663	+	0.998617i	$0.483260\pi$
$488$	−1037.90	−0.0962774
$489$	−2134.42	−0.197386
$490$	0	0
$491$	18774.9	1.72566	0.862832	−	0.505491i	$-0.168689\pi$
$491$	18774.9	1.72566	0.862832	+	0.505491i	$0.168689\pi$
$492$	−9124.97	−0.836149
$493$	−2185.48	−0.199653
$494$	7053.51	0.642414
$495$	0	0
$496$	6279.49	0.568463
$497$	6260.28	0.565014
$498$	498.339	0.0448416
$499$	17329.1	1.55462	0.777310	−	0.629118i	$-0.216584\pi$
$499$	17329.1	1.55462	0.777310	+	0.629118i	$0.216584\pi$
$500$	0	0
$501$	−8945.50	−0.797716
$502$	−10475.6	−0.931369
$503$	20837.0	1.84707	0.923533	−	0.383518i	$-0.125288\pi$
$503$	20837.0	1.84707	0.923533	+	0.383518i	$0.125288\pi$
$504$	−2606.90	−0.230398
$505$	0	0
$506$	−4333.16	−0.380697
$507$	−3722.37	−0.326068
$508$	16278.6	1.42174
$509$	11835.0	1.03060	0.515301	−	0.857009i	$-0.327680\pi$
$509$	11835.0	1.03060	0.515301	+	0.857009i	$0.327680\pi$
$510$	0	0
$511$	−2348.63	−0.203322
$512$	−7793.12	−0.672676
$513$	12390.6	1.06639
$514$	7262.26	0.623199
$515$	0	0
$516$	−6838.35	−0.583414
$517$	−4214.16	−0.358489
$518$	−1430.55	−0.121341
$519$	−559.359	−0.0473086
$520$	0	0
$521$	7686.37	0.646346	0.323173	−	0.946340i	$-0.395250\pi$
$521$	7686.37	0.646346	0.323173	+	0.946340i	$0.395250\pi$
$522$	−2983.37	−0.250151
$523$	−11476.4	−0.959518	−0.479759	−	0.877400i	$-0.659276\pi$
$523$	−11476.4	−0.959518	−0.479759	+	0.877400i	$0.659276\pi$
$524$	12165.6	1.01423
$525$	0	0
$526$	5355.25	0.443916
$527$	4648.81	0.384261
$528$	−2000.52	−0.164889
$529$	1120.01	0.0920535
$530$	0	0
$531$	4978.44	0.406866
$532$	−4352.40	−0.354700
$533$	27345.0	2.22222
$534$	−3492.56	−0.283029
$535$	0	0
$536$	−1019.81	−0.0821814
$537$	3229.59	0.259529
$538$	−4660.88	−0.373504
$539$	−7731.09	−0.617814
$540$	0	0
$541$	−546.481	−0.0434289	−0.0217145	−	0.999764i	$-0.506912\pi$
$541$	−546.481	−0.0434289	−0.0217145	+	0.999764i	$0.506912\pi$
$542$	−747.357	−0.0592283
$543$	10884.1	0.860191
$544$	−3150.38	−0.248293
$545$	0	0
$546$	−1981.47	−0.155310
$547$	−8397.33	−0.656388	−0.328194	−	0.944610i	$-0.606440\pi$
$547$	−8397.33	−0.656388	−0.328194	+	0.944610i	$0.606440\pi$
$548$	19313.6	1.50554
$549$	918.839	0.0714301
$550$	0	0
$551$	−11463.3	−0.886305
$552$	−7002.58	−0.539945
$553$	−5719.73	−0.439833
$554$	7083.32	0.543215
$555$	0	0
$556$	−9024.36	−0.688342
$557$	4881.65	0.371350	0.185675	−	0.982611i	$-0.440553\pi$
$557$	4881.65	0.371350	0.185675	+	0.982611i	$0.440553\pi$
$558$	6346.04	0.481451
$559$	20492.6	1.55053
$560$	0	0
$561$	−1481.02	−0.111459
$562$	2704.38	0.202985
$563$	−7198.57	−0.538870	−0.269435	−	0.963019i	$-0.586837\pi$
$563$	−7198.57	−0.538870	−0.269435	+	0.963019i	$0.586837\pi$
$564$	−2959.14	−0.220926
$565$	0	0
$566$	1025.95	0.0761904
$567$	174.283	0.0129087
$568$	15182.5	1.12155
$569$	−23946.9	−1.76433	−0.882167	−	0.470937i	$-0.843916\pi$
$569$	−23946.9	−1.76433	−0.882167	+	0.470937i	$0.843916\pi$
$570$	0	0
$571$	1593.15	0.116763	0.0583813	−	0.998294i	$-0.481406\pi$
$571$	1593.15	0.116763	0.0583813	+	0.998294i	$0.481406\pi$
$572$	9864.95	0.721109
$573$	1548.59	0.112903
$574$	5086.16	0.369847
$575$	0	0
$576$	−1168.69	−0.0845403
$577$	−12937.4	−0.933435	−0.466717	−	0.884406i	$-0.654564\pi$
$577$	−12937.4	−0.933435	−0.466717	+	0.884406i	$0.654564\pi$
$578$	−393.393	−0.0283097
$579$	−11195.2	−0.803549
$580$	0	0
$581$	921.499	0.0658007
$582$	−3412.53	−0.243048
$583$	−14570.6	−1.03508
$584$	−5695.92	−0.403594
$585$	0	0
$586$	−9803.82	−0.691112
$587$	12899.2	0.906998	0.453499	−	0.891257i	$-0.350176\pi$
$587$	12899.2	0.906998	0.453499	+	0.891257i	$0.350176\pi$
$588$	−5428.70	−0.380741
$589$	24384.1	1.70582
$590$	0	0
$591$	4300.23	0.299302
$592$	3039.19	0.210997
$593$	−4357.13	−0.301730	−0.150865	−	0.988554i	$-0.548206\pi$
$593$	−4357.13	−0.301730	−0.150865	+	0.988554i	$0.548206\pi$
$594$	−5223.59	−0.360819
$595$	0	0
$596$	1758.23	0.120839
$597$	−11790.3	−0.808284
$598$	9118.14	0.623526
$599$	13726.8	0.936328	0.468164	−	0.883642i	$-0.344916\pi$
$599$	13726.8	0.936328	0.468164	+	0.883642i	$0.344916\pi$
$600$	0	0
$601$	2531.41	0.171811	0.0859056	−	0.996303i	$-0.472622\pi$
$601$	2531.41	0.171811	0.0859056	+	0.996303i	$0.472622\pi$
$602$	3811.62	0.258057
$603$	902.830	0.0609720
$604$	4116.24	0.277297
$605$	0	0
$606$	1140.15	0.0764283
$607$	−185.004	−0.0123708	−0.00618540	−	0.999981i	$-0.501969\pi$
$607$	−185.004	−0.0123708	−0.00618540	+	0.999981i	$0.501969\pi$
$608$	−16524.4	−1.10223
$609$	3220.28	0.214273
$610$	0	0
$611$	8867.73	0.587152
$612$	1781.55	0.117672
$613$	17706.9	1.16668	0.583339	−	0.812228i	$-0.301746\pi$
$613$	17706.9	1.16668	0.583339	+	0.812228i	$0.301746\pi$
$614$	3301.93	0.217028
$615$	0	0
$616$	4222.84	0.276207
$617$	6183.89	0.403491	0.201746	−	0.979438i	$-0.435339\pi$
$617$	6183.89	0.403491	0.201746	+	0.979438i	$0.435339\pi$
$618$	−2246.30	−0.146213
$619$	−1247.51	−0.0810046	−0.0405023	−	0.999179i	$-0.512896\pi$
$619$	−1247.51	−0.0810046	−0.0405023	+	0.999179i	$0.512896\pi$
$620$	0	0
$621$	16017.4	1.03503
$622$	12992.8	0.837561
$623$	−6458.23	−0.415318
$624$	4209.63	0.270064
$625$	0	0
$626$	800.914	0.0511357
$627$	−7768.27	−0.494792
$628$	4430.87	0.281546
$629$	2249.96	0.142626
$630$	0	0
$631$	24053.3	1.51750	0.758752	−	0.651379i	$-0.225809\pi$
$631$	24053.3	1.51750	0.758752	+	0.651379i	$0.225809\pi$
$632$	−13871.5	−0.873069
$633$	16612.7	1.04312
$634$	10417.8	0.652596
$635$	0	0
$636$	−10231.4	−0.637893
$637$	16268.3	1.01189
$638$	4832.69	0.299887
$639$	−13440.9	−0.832102
$640$	0	0
$641$	−21286.8	−1.31167	−0.655834	−	0.754905i	$-0.727683\pi$
$641$	−21286.8	−1.31167	−0.655834	+	0.754905i	$0.727683\pi$
$642$	4234.20	0.260297
$643$	1789.41	0.109747	0.0548736	−	0.998493i	$-0.482524\pi$
$643$	1789.41	0.109747	0.0548736	+	0.998493i	$0.482524\pi$
$644$	−5626.38	−0.344271
$645$	0	0
$646$	−2063.43	−0.125673
$647$	4378.61	0.266060	0.133030	−	0.991112i	$-0.457529\pi$
$647$	4378.61	0.266060	0.133030	+	0.991112i	$0.457529\pi$
$648$	422.672	0.0256237
$649$	−8064.45	−0.487762
$650$	0	0
$651$	−6849.97	−0.412399
$652$	−4159.11	−0.249821
$653$	7665.15	0.459358	0.229679	−	0.973266i	$-0.426232\pi$
$653$	7665.15	0.459358	0.229679	+	0.973266i	$0.426232\pi$
$654$	7791.26	0.465845
$655$	0	0
$656$	−10805.5	−0.643117
$657$	5042.54	0.299434
$658$	1649.39	0.0977205
$659$	−4710.22	−0.278428	−0.139214	−	0.990262i	$-0.544458\pi$
$659$	−4710.22	−0.278428	−0.139214	+	0.990262i	$0.544458\pi$
$660$	0	0
$661$	−31266.6	−1.83983	−0.919916	−	0.392116i	$-0.871743\pi$
$661$	−31266.6	−1.83983	−0.919916	+	0.392116i	$0.871743\pi$
$662$	−1024.00	−0.0601192
$663$	3116.46	0.182554
$664$	2234.82	0.130614
$665$	0	0
$666$	3071.40	0.178700
$667$	−14818.7	−0.860246
$668$	−17431.1	−1.00962
$669$	2222.58	0.128446
$670$	0	0
$671$	−1488.40	−0.0856322
$672$	4642.05	0.266474
$673$	−11723.0	−0.671454	−0.335727	−	0.941959i	$-0.608982\pi$
$673$	−11723.0	−0.671454	−0.335727	+	0.941959i	$0.608982\pi$
$674$	−2679.65	−0.153140
$675$	0	0
$676$	−7253.37	−0.412686
$677$	289.531	0.0164366	0.00821829	−	0.999966i	$-0.497384\pi$
$677$	289.531	0.0164366	0.00821829	+	0.999966i	$0.497384\pi$
$678$	3037.42	0.172052
$679$	−6310.25	−0.356650
$680$	0	0
$681$	−6786.45	−0.381875
$682$	−10279.8	−0.577175
$683$	−1720.10	−0.0963660	−0.0481830	−	0.998839i	$-0.515343\pi$
$683$	−1720.10	−0.0963660	−0.0481830	+	0.998839i	$0.515343\pi$
$684$	9344.64	0.522370
$685$	0	0
$686$	6733.30	0.374750
$687$	12356.5	0.686215
$688$	−8097.77	−0.448728
$689$	30660.5	1.69532
$690$	0	0
$691$	−16777.7	−0.923665	−0.461832	−	0.886967i	$-0.652808\pi$
$691$	−16777.7	−0.923665	−0.461832	+	0.886967i	$0.652808\pi$
$692$	−1089.96	−0.0598758
$693$	−3738.44	−0.204923
$694$	5421.88	0.296559
$695$	0	0
$696$	7809.84	0.425332
$697$	−7999.50	−0.434724
$698$	−2035.86	−0.110399
$699$	−16381.2	−0.886400
$700$	0	0
$701$	23981.1	1.29209	0.646043	−	0.763301i	$-0.276423\pi$
$701$	23981.1	1.29209	0.646043	+	0.763301i	$0.276423\pi$
$702$	10991.8	0.590969
$703$	11801.6	0.633150
$704$	1893.12	0.101349
$705$	0	0
$706$	8824.10	0.470396
$707$	2108.30	0.112151
$708$	−5662.78	−0.300593
$709$	−7709.28	−0.408361	−0.204181	−	0.978933i	$-0.565453\pi$
$709$	−7709.28	−0.408361	−0.204181	+	0.978933i	$0.565453\pi$
$710$	0	0
$711$	12280.3	0.647747
$712$	−15662.5	−0.824407
$713$	31521.5	1.65567
$714$	579.660	0.0303827
$715$	0	0
$716$	6293.13	0.328471
$717$	−1054.61	−0.0549304
$718$	6729.09	0.349760
$719$	−11976.5	−0.621209	−0.310605	−	0.950539i	$-0.600532\pi$
$719$	−11976.5	−0.621209	−0.310605	+	0.950539i	$0.600532\pi$
$720$	0	0
$721$	−4153.72	−0.214553
$722$	−1486.56	−0.0766260
$723$	6052.00	0.311309
$724$	21208.7	1.08870
$725$	0	0
$726$	−2440.58	−0.124764
$727$	18597.3	0.948745	0.474372	−	0.880324i	$-0.342675\pi$
$727$	18597.3	0.948745	0.474372	+	0.880324i	$0.342675\pi$
$728$	−8886.00	−0.452386
$729$	11461.4	0.582300
$730$	0	0
$731$	−5994.91	−0.303324
$732$	−1045.14	−0.0527727
$733$	23569.5	1.18767	0.593833	−	0.804588i	$-0.297614\pi$
$733$	23569.5	1.18767	0.593833	+	0.804588i	$0.297614\pi$
$734$	−20.2646	−0.00101905
$735$	0	0
$736$	−21361.3	−1.06982
$737$	−1462.47	−0.0730948
$738$	−10920.0	−0.544678
$739$	10149.1	0.505199	0.252599	−	0.967571i	$-0.418715\pi$
$739$	10149.1	0.505199	0.252599	+	0.967571i	$0.418715\pi$
$740$	0	0
$741$	16346.5	0.810397
$742$	5702.85	0.282154
$743$	−27758.0	−1.37058	−0.685291	−	0.728269i	$-0.740325\pi$
$743$	−27758.0	−1.37058	−0.685291	+	0.728269i	$0.740325\pi$
$744$	−16612.6	−0.818611
$745$	0	0
$746$	2617.87	0.128481
$747$	−1978.47	−0.0969054
$748$	−2885.89	−0.141068
$749$	7829.63	0.381960
$750$	0	0
$751$	−815.225	−0.0396112	−0.0198056	−	0.999804i	$-0.506305\pi$
$751$	−815.225	−0.0396112	−0.0198056	+	0.999804i	$0.506305\pi$
$752$	−3504.13	−0.169924
$753$	−24277.1	−1.17491
$754$	−10169.3	−0.491172
$755$	0	0
$756$	−6782.56	−0.326295
$757$	13239.4	0.635659	0.317829	−	0.948148i	$-0.397046\pi$
$757$	13239.4	0.635659	0.317829	+	0.948148i	$0.397046\pi$
$758$	13058.0	0.625710
$759$	−10042.1	−0.480244
$760$	0	0
$761$	−11028.2	−0.525324	−0.262662	−	0.964888i	$-0.584600\pi$
$761$	−11028.2	−0.525324	−0.262662	+	0.964888i	$0.584600\pi$
$762$	−11371.7	−0.540621
$763$	14407.1	0.683582
$764$	3017.56	0.142895
$765$	0	0
$766$	−12365.0	−0.583246
$767$	16969.8	0.798882
$768$	7695.55	0.361574
$769$	−18921.2	−0.887277	−0.443639	−	0.896206i	$-0.646313\pi$
$769$	−18921.2	−0.887277	−0.443639	+	0.896206i	$0.646313\pi$
$770$	0	0
$771$	16830.3	0.786158
$772$	−21814.7	−1.01701
$773$	−38728.6	−1.80203	−0.901016	−	0.433786i	$-0.857177\pi$
$773$	−38728.6	−1.80203	−0.901016	+	0.433786i	$0.857177\pi$
$774$	−8183.59	−0.380043
$775$	0	0
$776$	−15303.6	−0.707949
$777$	−3315.29	−0.153070
$778$	1556.93	0.0717465
$779$	−41959.2	−1.92984
$780$	0	0
$781$	21772.5	0.997545
$782$	−2667.42	−0.121978
$783$	−17863.9	−0.815329
$784$	−6428.50	−0.292844
$785$	0	0
$786$	−8498.47	−0.385662
$787$	20587.3	0.932477	0.466239	−	0.884659i	$-0.345609\pi$
$787$	20587.3	0.932477	0.466239	+	0.884659i	$0.345609\pi$
$788$	8379.37	0.378811
$789$	12410.8	0.559995
$790$	0	0
$791$	5616.62	0.252470
$792$	−9066.49	−0.406772
$793$	3132.00	0.140253
$794$	14435.0	0.645190
$795$	0	0
$796$	−22974.5	−1.02300
$797$	15871.4	0.705385	0.352693	−	0.935739i	$-0.385266\pi$
$797$	15871.4	0.705385	0.352693	+	0.935739i	$0.385266\pi$
$798$	3040.45	0.134876
$799$	−2594.17	−0.114862
$800$	0	0
$801$	13865.9	0.611644
$802$	−18765.0	−0.826204
$803$	−8168.28	−0.358969
$804$	−1026.93	−0.0450462
$805$	0	0
$806$	21631.4	0.945329
$807$	−10801.6	−0.471170
$808$	5113.06	0.222620
$809$	39667.1	1.72388	0.861942	−	0.507007i	$-0.169248\pi$
$809$	39667.1	1.72388	0.861942	+	0.507007i	$0.169248\pi$
$810$	0	0
$811$	8003.87	0.346552	0.173276	−	0.984873i	$-0.444565\pi$
$811$	8003.87	0.346552	0.173276	+	0.984873i	$0.444565\pi$
$812$	6275.00	0.271194
$813$	−1732.00	−0.0747157
$814$	−4975.28	−0.214230
$815$	0	0
$816$	−1231.48	−0.0528316
$817$	−31444.7	−1.34652
$818$	12939.7	0.553088
$819$	7866.69	0.335634
$820$	0	0
$821$	−13279.1	−0.564489	−0.282244	−	0.959343i	$-0.591079\pi$
$821$	−13279.1	−0.564489	−0.282244	+	0.959343i	$0.591079\pi$
$822$	−13491.9	−0.572486
$823$	−28934.0	−1.22549	−0.612745	−	0.790281i	$-0.709935\pi$
$823$	−28934.0	−1.22549	−0.612745	+	0.790281i	$0.709935\pi$
$824$	−10073.6	−0.425887
$825$	0	0
$826$	3156.37	0.132959
$827$	13679.6	0.575193	0.287597	−	0.957752i	$-0.407144\pi$
$827$	13679.6	0.575193	0.287597	+	0.957752i	$0.407144\pi$
$828$	12079.9	0.507012
$829$	16514.5	0.691886	0.345943	−	0.938256i	$-0.387559\pi$
$829$	16514.5	0.691886	0.345943	+	0.938256i	$0.387559\pi$
$830$	0	0
$831$	16415.6	0.685260
$832$	−3983.64	−0.165995
$833$	−4759.13	−0.197952
$834$	6304.13	0.261744
$835$	0	0
$836$	−15137.1	−0.626231
$837$	37998.9	1.56922
$838$	−13177.8	−0.543221
$839$	−87.9839	−0.00362043	−0.00181022	−	0.999998i	$-0.500576\pi$
$839$	−87.9839	−0.00362043	−0.00181022	+	0.999998i	$0.500576\pi$
$840$	0	0
$841$	−7861.94	−0.322356
$842$	16825.1	0.688635
$843$	6267.41	0.256063
$844$	32371.3	1.32022
$845$	0	0
$846$	−3541.27	−0.143914
$847$	−4512.98	−0.183079
$848$	−12115.7	−0.490630
$849$	2377.63	0.0961133
$850$	0	0
$851$	15256.0	0.614534
$852$	15288.5	0.614758
$853$	−8162.96	−0.327660	−0.163830	−	0.986489i	$-0.552385\pi$
$853$	−8162.96	−0.327660	−0.163830	+	0.986489i	$0.552385\pi$
$854$	582.551	0.0233425
$855$	0	0
$856$	18988.4	0.758191
$857$	−18724.9	−0.746361	−0.373181	−	0.927759i	$-0.621733\pi$
$857$	−18724.9	−0.746361	−0.373181	+	0.927759i	$0.621733\pi$
$858$	−6891.34	−0.274203
$859$	−46422.5	−1.84391	−0.921953	−	0.387301i	$-0.873407\pi$
$859$	−46422.5	−1.84391	−0.921953	+	0.387301i	$0.873407\pi$
$860$	0	0
$861$	11787.2	0.466557
$862$	−4043.61	−0.159775
$863$	−29112.3	−1.14831	−0.574157	−	0.818746i	$-0.694670\pi$
$863$	−29112.3	−1.14831	−0.574157	+	0.818746i	$0.694670\pi$
$864$	−25750.8	−1.01396
$865$	0	0
$866$	8346.33	0.327505
$867$	−911.688	−0.0357123
$868$	−13347.8	−0.521950
$869$	−19892.6	−0.776536
$870$	0	0
$871$	3077.43	0.119719
$872$	34940.2	1.35691
$873$	13548.2	0.525241
$874$	−13991.2	−0.541487
$875$	0	0
$876$	−5735.69	−0.221222
$877$	−39163.0	−1.50791	−0.753957	−	0.656924i	$-0.771857\pi$
$877$	−39163.0	−1.50791	−0.753957	+	0.656924i	$0.771857\pi$
$878$	3464.19	0.133156
$879$	−22720.3	−0.871830
$880$	0	0
$881$	−35073.2	−1.34125	−0.670627	−	0.741795i	$-0.733975\pi$
$881$	−35073.2	−1.34125	−0.670627	+	0.741795i	$0.733975\pi$
$882$	−6496.63	−0.248019
$883$	48775.7	1.85893	0.929463	−	0.368915i	$-0.120271\pi$
$883$	48775.7	1.85893	0.929463	+	0.368915i	$0.120271\pi$
$884$	6072.69	0.231048
$885$	0	0
$886$	11611.0	0.440269
$887$	−13296.0	−0.503309	−0.251654	−	0.967817i	$-0.580975\pi$
$887$	−13296.0	−0.503309	−0.251654	+	0.967817i	$0.580975\pi$
$888$	−8040.27	−0.303844
$889$	−21027.9	−0.793309
$890$	0	0
$891$	606.137	0.0227905
$892$	4330.90	0.162566
$893$	−13607.0	−0.509899
$894$	−1228.24	−0.0459492
$895$	0	0
$896$	11031.1	0.411297
$897$	21131.3	0.786570
$898$	−12054.6	−0.447960
$899$	−35155.3	−1.30422
$900$	0	0
$901$	−8969.43	−0.331648
$902$	17689.1	0.652974
$903$	8833.44	0.325535
$904$	13621.4	0.501153
$905$	0	0
$906$	−2875.47	−0.105443
$907$	11675.0	0.427410	0.213705	−	0.976898i	$-0.431447\pi$
$907$	11675.0	0.427410	0.213705	+	0.976898i	$0.431447\pi$
$908$	−13224.0	−0.483319
$909$	−4526.54	−0.165166
$910$	0	0
$911$	18552.9	0.674738	0.337369	−	0.941372i	$-0.390463\pi$
$911$	18552.9	0.674738	0.337369	+	0.941372i	$0.390463\pi$
$912$	−6459.41	−0.234531
$913$	3204.87	0.116173
$914$	−9739.24	−0.352457
$915$	0	0
$916$	24077.7	0.868504
$917$	−15714.9	−0.565922
$918$	−3215.55	−0.115609
$919$	33956.8	1.21886	0.609429	−	0.792841i	$-0.291399\pi$
$919$	33956.8	1.21886	0.609429	+	0.792841i	$0.291399\pi$
$920$	0	0
$921$	7652.23	0.273778
$922$	9886.63	0.353144
$923$	−45815.3	−1.63383
$924$	4252.33	0.151398
$925$	0	0
$926$	480.372	0.0170475
$927$	8918.08	0.315974
$928$	23823.8	0.842732
$929$	−23695.3	−0.836832	−0.418416	−	0.908256i	$-0.637415\pi$
$929$	−23695.3	−0.836832	−0.418416	+	0.908256i	$0.637415\pi$
$930$	0	0
$931$	−24962.7	−0.878753
$932$	−31920.2	−1.12187
$933$	30110.8	1.05657
$934$	2018.72	0.0707221
$935$	0	0
$936$	19078.3	0.666234
$937$	−7990.62	−0.278593	−0.139297	−	0.990251i	$-0.544484\pi$
$937$	−7990.62	−0.278593	−0.139297	+	0.990251i	$0.544484\pi$
$938$	572.402	0.0199249
$939$	1856.12	0.0645071
$940$	0	0
$941$	24385.9	0.844799	0.422400	−	0.906410i	$-0.361188\pi$
$941$	24385.9	0.844799	0.422400	+	0.906410i	$0.361188\pi$
$942$	−3095.26	−0.107058
$943$	−54241.0	−1.87310
$944$	−6705.69	−0.231199
$945$	0	0
$946$	13256.4	0.455605
$947$	1174.62	0.0403064	0.0201532	−	0.999797i	$-0.493585\pi$
$947$	1174.62	0.0403064	0.0201532	+	0.999797i	$0.493585\pi$
$948$	−13968.4	−0.478557
$949$	17188.3	0.587939
$950$	0	0
$951$	24143.4	0.823241
$952$	2599.51	0.0884985
$953$	33546.9	1.14029	0.570143	−	0.821546i	$-0.306888\pi$
$953$	33546.9	1.14029	0.570143	+	0.821546i	$0.306888\pi$
$954$	−12244.1	−0.415531
$955$	0	0
$956$	−2055.00	−0.0695224
$957$	11199.8	0.378304
$958$	13598.7	0.458617
$959$	−24948.4	−0.840067
$960$	0	0
$961$	44989.1	1.51016
$962$	10469.3	0.350878
$963$	−16810.3	−0.562517
$964$	11792.9	0.394007
$965$	0	0
$966$	3930.41	0.130910
$967$	−24766.8	−0.823625	−0.411813	−	0.911269i	$-0.635104\pi$
$967$	−24766.8	−0.823625	−0.411813	+	0.911269i	$0.635104\pi$
$968$	−10944.9	−0.363411
$969$	−4782.01	−0.158535
$970$	0	0
$971$	42324.3	1.39882	0.699409	−	0.714721i	$-0.253447\pi$
$971$	42324.3	1.39882	0.699409	+	0.714721i	$0.253447\pi$
$972$	23488.3	0.775091
$973$	11657.2	0.384083
$974$	−1538.01	−0.0505966
$975$	0	0
$976$	−1237.63	−0.0405896
$977$	11320.4	0.370698	0.185349	−	0.982673i	$-0.440658\pi$
$977$	11320.4	0.370698	0.185349	+	0.982673i	$0.440658\pi$
$978$	2905.42	0.0949949
$979$	−22461.0	−0.733254
$980$	0	0
$981$	−30932.2	−1.00672
$982$	−25556.8	−0.830500
$983$	11311.9	0.367032	0.183516	−	0.983017i	$-0.441252\pi$
$983$	11311.9	0.367032	0.183516	+	0.983017i	$0.441252\pi$
$984$	28586.3	0.926116
$985$	0	0
$986$	2974.92	0.0960860
$987$	3822.47	0.123273
$988$	31852.6	1.02568
$989$	−40648.8	−1.30693
$990$	0	0
$991$	−29405.5	−0.942580	−0.471290	−	0.881978i	$-0.656212\pi$
$991$	−29405.5	−0.942580	−0.471290	+	0.881978i	$0.656212\pi$
$992$	−50676.5	−1.62196
$993$	−2373.12	−0.0758397
$994$	−8521.63	−0.271921
$995$	0	0
$996$	2250.43	0.0715939
$997$	54905.9	1.74412	0.872060	−	0.489398i	$-0.162784\pi$
$997$	54905.9	1.74412	0.872060	+	0.489398i	$0.162784\pi$
$998$	−23588.7	−0.748183
$999$	18390.9	0.582446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.a.g.1.2		3
5.2	odd	4		425.4.b.f.324.3		6
5.3	odd	4		425.4.b.f.324.4		6
5.4	even	2		17.4.a.b.1.2	✓	3
15.14	odd	2		153.4.a.g.1.2		3
20.19	odd	2		272.4.a.h.1.2		3
35.34	odd	2		833.4.a.d.1.2		3
40.19	odd	2		1088.4.a.x.1.2		3
40.29	even	2		1088.4.a.v.1.2		3
55.54	odd	2		2057.4.a.e.1.2		3
60.59	even	2		2448.4.a.bi.1.1		3
85.4	even	4		289.4.b.b.288.3		6
85.64	even	4		289.4.b.b.288.4		6
85.84	even	2		289.4.a.b.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.2	✓	3	5.4	even	2
153.4.a.g.1.2		3	15.14	odd	2
272.4.a.h.1.2		3	20.19	odd	2
289.4.a.b.1.2		3	85.84	even	2
289.4.b.b.288.3		6	85.4	even	4
289.4.b.b.288.4		6	85.64	even	4
425.4.a.g.1.2		3	1.1	even	1	trivial
425.4.b.f.324.3		6	5.2	odd	4
425.4.b.f.324.4		6	5.3	odd	4
833.4.a.d.1.2		3	35.34	odd	2
1088.4.a.v.1.2		3	40.29	even	2
1088.4.a.x.1.2		3	40.19	odd	2
2057.4.a.e.1.2		3	55.54	odd	2
2448.4.a.bi.1.1		3	60.59	even	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} +4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} +O(q^{10})\)	\(q-1.36122 q^{2} -3.15463 q^{3} -6.14708 q^{4} +4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} +27.6161 q^{11} +19.3918 q^{12} -58.1117 q^{13} -10.8088 q^{14} +22.9632 q^{16} +17.0000 q^{17} +23.2065 q^{18} +89.1688 q^{19} -25.0493 q^{21} -37.5916 q^{22} +115.269 q^{23} -60.7497 q^{24} +79.1029 q^{26} +138.956 q^{27} -48.8108 q^{28} -128.558 q^{29} +273.460 q^{31} -185.316 q^{32} -87.1187 q^{33} -23.1408 q^{34} +104.797 q^{36} +132.351 q^{37} -121.379 q^{38} +183.321 q^{39} -470.559 q^{41} +34.0977 q^{42} -352.642 q^{43} -169.758 q^{44} -156.907 q^{46} -152.598 q^{47} -72.4403 q^{48} -279.949 q^{49} -53.6287 q^{51} +357.217 q^{52} -527.614 q^{53} -189.150 q^{54} +152.912 q^{56} -281.295 q^{57} +174.995 q^{58} -292.020 q^{59} -53.8962 q^{61} -372.239 q^{62} -135.372 q^{63} +68.5514 q^{64} +118.588 q^{66} -52.9572 q^{67} -104.500 q^{68} -363.632 q^{69} +788.400 q^{71} -328.304 q^{72} -295.780 q^{73} -180.159 q^{74} -548.127 q^{76} +219.285 q^{77} -249.541 q^{78} -720.325 q^{79} +21.9487 q^{81} +640.535 q^{82} +116.051 q^{83} +153.980 q^{84} +480.024 q^{86} +405.552 q^{87} +531.812 q^{88} -813.329 q^{89} -461.435 q^{91} -708.569 q^{92} -862.664 q^{93} +207.720 q^{94} +584.605 q^{96} -794.693 q^{97} +381.072 q^{98} -470.808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) \) 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} - 4 q^{3} + 25 q^{4} - 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} - 28 q^{11} - 22 q^{12} - 30 q^{13} + 92 q^{14} + 137 q^{16} + 51 q^{17} + 103 q^{18} + 80 q^{19} - 192 q^{21} - 286 q^{22} - 142 q^{23} - 666 q^{24} + 26 q^{26} + 20 q^{27} - 476 q^{28} - 456 q^{29} + 230 q^{31} + 71 q^{32} + 332 q^{33} - 17 q^{34} + 1313 q^{36} - 356 q^{37} - 724 q^{38} + 268 q^{39} - 294 q^{41} + 1128 q^{42} - 556 q^{43} - 1122 q^{44} - 704 q^{46} - 640 q^{47} - 774 q^{48} - 269 q^{49} - 68 q^{51} + 774 q^{52} - 302 q^{53} - 1100 q^{54} + 684 q^{56} + 720 q^{57} + 1304 q^{58} + 636 q^{59} - 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} + 2468 q^{66} - 1008 q^{67} + 425 q^{68} + 576 q^{69} - 402 q^{71} + 927 q^{72} - 838 q^{73} + 836 q^{74} - 908 q^{76} + 504 q^{77} - 1308 q^{78} - 594 q^{79} - 505 q^{81} - 358 q^{82} + 2396 q^{83} - 2040 q^{84} - 1264 q^{86} - 1428 q^{87} - 1838 q^{88} - 170 q^{89} - 1016 q^{91} - 4896 q^{92} - 632 q^{93} - 2016 q^{94} + 678 q^{96} + 270 q^{97} - 2857 q^{98} - 2920 q^{99}+O(q^{100}) \) 3 * q - q^2 - 4 * q^3 + 25 * q^4 - 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 - 28 * q^11 - 22 * q^12 - 30 * q^13 + 92 * q^14 + 137 * q^16 + 51 * q^17 + 103 * q^18 + 80 * q^19 - 192 * q^21 - 286 * q^22 - 142 * q^23 - 666 * q^24 + 26 * q^26 + 20 * q^27 - 476 * q^28 - 456 * q^29 + 230 * q^31 + 71 * q^32 + 332 * q^33 - 17 * q^34 + 1313 * q^36 - 356 * q^37 - 724 * q^38 + 268 * q^39 - 294 * q^41 + 1128 * q^42 - 556 * q^43 - 1122 * q^44 - 704 * q^46 - 640 * q^47 - 774 * q^48 - 269 * q^49 - 68 * q^51 + 774 * q^52 - 302 * q^53 - 1100 * q^54 + 684 * q^56 + 720 * q^57 + 1304 * q^58 + 636 * q^59 - 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 + 2468 * q^66 - 1008 * q^67 + 425 * q^68 + 576 * q^69 - 402 * q^71 + 927 * q^72 - 838 * q^73 + 836 * q^74 - 908 * q^76 + 504 * q^77 - 1308 * q^78 - 594 * q^79 - 505 * q^81 - 358 * q^82 + 2396 * q^83 - 2040 * q^84 - 1264 * q^86 - 1428 * q^87 - 1838 * q^88 - 170 * q^89 - 1016 * q^91 - 4896 * q^92 - 632 * q^93 - 2016 * q^94 + 678 * q^96 + 270 * q^97 - 2857 * q^98 - 2920 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more