LMFDB - Embedded newform 725.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, 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("725.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.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:	$5.78915414654$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.240881.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 9x^{2} + 5x - 7 $ x^5 - 2x^4 - 5x^3 + 9x^2 + 5x - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.06634$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06634 q^{2} -3.37897 q^{3} -0.862915 q^{4} -3.60314 q^{6} +2.91576 q^{7} -3.05285 q^{8} +8.41742 q^{9} +O(q^{10})$	\(q+1.06634 q^{2} -3.37897 q^{3} -0.862915 q^{4} -3.60314 q^{6} +2.91576 q^{7} -3.05285 q^{8} +8.41742 q^{9} +2.52330 q^{11} +2.91576 q^{12} +0.109198 q^{13} +3.10920 q^{14} -1.52955 q^{16} -6.38621 q^{17} +8.97585 q^{18} -6.56175 q^{19} -9.85226 q^{21} +2.69070 q^{22} -3.08708 q^{23} +10.3155 q^{24} +0.116443 q^{26} -18.3053 q^{27} -2.51605 q^{28} +1.00000 q^{29} +1.18904 q^{31} +4.47467 q^{32} -8.52614 q^{33} -6.80989 q^{34} -7.26352 q^{36} -4.65949 q^{37} -6.99707 q^{38} -0.368978 q^{39} +2.26977 q^{41} -10.5059 q^{42} -10.1183 q^{43} -2.17739 q^{44} -3.29189 q^{46} -4.78582 q^{47} +5.16830 q^{48} +1.50166 q^{49} +21.5788 q^{51} -0.0942289 q^{52} +10.3020 q^{53} -19.5197 q^{54} -8.90137 q^{56} +22.1720 q^{57} +1.06634 q^{58} -7.38896 q^{59} -10.2542 q^{61} +1.26792 q^{62} +24.5432 q^{63} +7.83063 q^{64} -9.09178 q^{66} -4.55891 q^{67} +5.51076 q^{68} +10.4312 q^{69} -1.42485 q^{71} -25.6971 q^{72} +3.96771 q^{73} -4.96861 q^{74} +5.66223 q^{76} +7.35733 q^{77} -0.393457 q^{78} -1.47907 q^{79} +36.6007 q^{81} +2.42035 q^{82} +2.72280 q^{83} +8.50166 q^{84} -10.7896 q^{86} -3.37897 q^{87} -7.70324 q^{88} -0.228569 q^{89} +0.318396 q^{91} +2.66389 q^{92} -4.01771 q^{93} -5.10332 q^{94} -15.1198 q^{96} +8.49736 q^{97} +1.60129 q^{98} +21.2397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9	$ 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26} - 27 q^{27} - 10 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} + 7 q^{33} + 3 q^{34} - 13 q^{36} - 14 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{41} - 24 q^{42} - 28 q^{43} + 7 q^{44} - 20 q^{46} - 15 q^{47} + 26 q^{48} - 3 q^{49} + 5 q^{51} - 6 q^{52} + 8 q^{53} + 10 q^{54} - 16 q^{56} + 6 q^{57} - 2 q^{58} - 11 q^{59} - 5 q^{61} + 6 q^{62} + 5 q^{63} - 5 q^{64} - 27 q^{66} - 23 q^{67} - q^{68} - 26 q^{69} - 5 q^{71} - 3 q^{72} - 16 q^{73} + 8 q^{74} + 16 q^{76} + 30 q^{77} + 33 q^{78} - 10 q^{79} + 49 q^{81} + 19 q^{82} - 9 q^{83} + 32 q^{84} - 13 q^{86} - 6 q^{87} - 35 q^{88} - 18 q^{89} + q^{91} + 27 q^{92} - 7 q^{93} - 13 q^{94} - 38 q^{96} - 23 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * 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 $

$2$	1.06634	0.754018	0.377009	−	0.926210i	$-0.376953\pi$
$2$	1.06634	0.754018	0.377009	+	0.926210i	$0.376953\pi$
$3$	−3.37897	−1.95085	−0.975424	−	0.220336i	$-0.929285\pi$
$3$	−3.37897	−1.95085	−0.975424	+	0.220336i	$0.929285\pi$
$4$	−0.862915	−0.431457
$5$	0	0
$5$	0	0
$6$	−3.60314	−1.47097
$7$	2.91576	1.10205	0.551027	−	0.834487i	$-0.314236\pi$
$7$	2.91576	1.10205	0.551027	+	0.834487i	$0.314236\pi$
$8$	−3.05285	−1.07934
$9$	8.41742	2.80581
$10$	0	0
$11$	2.52330	0.760803	0.380401	−	0.924821i	$-0.375786\pi$
$11$	2.52330	0.760803	0.380401	+	0.924821i	$0.375786\pi$
$12$	2.91576	0.841708
$13$	0.109198	0.0302862	0.0151431	−	0.999885i	$-0.495180\pi$
$13$	0.109198	0.0302862	0.0151431	+	0.999885i	$0.495180\pi$
$14$	3.10920	0.830968
$15$	0	0
$16$	−1.52955	−0.382387
$17$	−6.38621	−1.54888	−0.774442	−	0.632645i	$-0.781969\pi$
$17$	−6.38621	−1.54888	−0.774442	+	0.632645i	$0.781969\pi$
$18$	8.97585	2.11563
$19$	−6.56175	−1.50537	−0.752685	−	0.658381i	$-0.771241\pi$
$19$	−6.56175	−1.50537	−0.752685	+	0.658381i	$0.771241\pi$
$20$	0	0
$21$	−9.85226	−2.14994
$22$	2.69070	0.573659
$23$	−3.08708	−0.643701	−0.321851	−	0.946790i	$-0.604305\pi$
$23$	−3.08708	−0.643701	−0.321851	+	0.946790i	$0.604305\pi$
$24$	10.3155	2.10564
$25$	0	0
$26$	0.116443	0.0228363
$27$	−18.3053	−3.52286
$28$	−2.51605	−0.475489
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	1.18904	0.213557	0.106779	−	0.994283i	$-0.465946\pi$
$31$	1.18904	0.213557	0.106779	+	0.994283i	$0.465946\pi$
$32$	4.47467	0.791017
$33$	−8.52614	−1.48421
$34$	−6.80989	−1.16789
$35$	0	0
$36$	−7.26352	−1.21059
$37$	−4.65949	−0.766015	−0.383008	−	0.923745i	$-0.625112\pi$
$37$	−4.65949	−0.766015	−0.383008	+	0.923745i	$0.625112\pi$
$38$	−6.99707	−1.13508
$39$	−0.368978	−0.0590837
$40$	0	0
$41$	2.26977	0.354478	0.177239	−	0.984168i	$-0.443283\pi$
$41$	2.26977	0.354478	0.177239	+	0.984168i	$0.443283\pi$
$42$	−10.5059	−1.62109
$43$	−10.1183	−1.54303	−0.771513	−	0.636214i	$-0.780500\pi$
$43$	−10.1183	−1.54303	−0.771513	+	0.636214i	$0.780500\pi$
$44$	−2.17739	−0.328254
$45$	0	0
$46$	−3.29189	−0.485362
$47$	−4.78582	−0.698084	−0.349042	−	0.937107i	$-0.613493\pi$
$47$	−4.78582	−0.698084	−0.349042	+	0.937107i	$0.613493\pi$
$48$	5.16830	0.745979
$49$	1.50166	0.214523
$50$	0	0
$51$	21.5788	3.02164
$52$	−0.0942289	−0.0130672
$53$	10.3020	1.41508	0.707542	−	0.706671i	$-0.249804\pi$
$53$	10.3020	1.41508	0.707542	+	0.706671i	$0.249804\pi$
$54$	−19.5197	−2.65630
$55$	0	0
$56$	−8.90137	−1.18950
$57$	22.1720	2.93675
$58$	1.06634	0.140018
$59$	−7.38896	−0.961960	−0.480980	−	0.876731i	$-0.659719\pi$
$59$	−7.38896	−0.961960	−0.480980	+	0.876731i	$0.659719\pi$
$60$	0	0
$61$	−10.2542	−1.31292	−0.656461	−	0.754360i	$-0.727947\pi$
$61$	−10.2542	−1.31292	−0.656461	+	0.754360i	$0.727947\pi$
$62$	1.26792	0.161026
$63$	24.5432	3.09215
$64$	7.83063	0.978828
$65$	0	0
$66$	−9.09178	−1.11912
$67$	−4.55891	−0.556959	−0.278480	−	0.960442i	$-0.589831\pi$
$67$	−4.55891	−0.556959	−0.278480	+	0.960442i	$0.589831\pi$
$68$	5.51076	0.668277
$69$	10.4312	1.25576
$70$	0	0
$71$	−1.42485	−0.169099	−0.0845493	−	0.996419i	$-0.526945\pi$
$71$	−1.42485	−0.169099	−0.0845493	+	0.996419i	$0.526945\pi$
$72$	−25.6971	−3.02843
$73$	3.96771	0.464386	0.232193	−	0.972670i	$-0.425410\pi$
$73$	3.96771	0.464386	0.232193	+	0.972670i	$0.425410\pi$
$74$	−4.96861	−0.577589
$75$	0	0
$76$	5.66223	0.649503
$77$	7.35733	0.838446
$78$	−0.393457	−0.0445502
$79$	−1.47907	−0.166409	−0.0832043	−	0.996533i	$-0.526515\pi$
$79$	−1.47907	−0.166409	−0.0832043	+	0.996533i	$0.526515\pi$
$80$	0	0
$81$	36.6007	4.06675
$82$	2.42035	0.267283
$83$	2.72280	0.298867	0.149433	−	0.988772i	$-0.452255\pi$
$83$	2.72280	0.298867	0.149433	+	0.988772i	$0.452255\pi$
$84$	8.50166	0.927607
$85$	0	0
$86$	−10.7896	−1.16347
$87$	−3.37897	−0.362263
$88$	−7.70324	−0.821168
$89$	−0.228569	−0.0242282	−0.0121141	−	0.999927i	$-0.503856\pi$
$89$	−0.228569	−0.0242282	−0.0121141	+	0.999927i	$0.503856\pi$
$90$	0	0
$91$	0.318396	0.0333770
$92$	2.66389	0.277730
$93$	−4.01771	−0.416618
$94$	−5.10332	−0.526368
$95$	0	0
$96$	−15.1198	−1.54315
$97$	8.49736	0.862776	0.431388	−	0.902166i	$-0.358024\pi$
$97$	8.49736	0.862776	0.431388	+	0.902166i	$0.358024\pi$
$98$	1.60129	0.161754
$99$	21.2397	2.13467
$100$	0	0
$101$	−10.7862	−1.07327	−0.536634	−	0.843815i	$-0.680305\pi$
$101$	−10.7862	−1.07327	−0.536634	+	0.843815i	$0.680305\pi$
$102$	23.0104	2.27837
$103$	−18.2205	−1.79532	−0.897659	−	0.440692i	$-0.854733\pi$
$103$	−18.2205	−1.79532	−0.897659	+	0.440692i	$0.854733\pi$
$104$	−0.333366	−0.0326892
$105$	0	0
$106$	10.9854	1.06700
$107$	−12.1902	−1.17847	−0.589237	−	0.807960i	$-0.700571\pi$
$107$	−12.1902	−1.17847	−0.589237	+	0.807960i	$0.700571\pi$
$108$	15.7959	1.51996
$109$	−11.8279	−1.13291	−0.566453	−	0.824094i	$-0.691685\pi$
$109$	−11.8279	−1.13291	−0.566453	+	0.824094i	$0.691685\pi$
$110$	0	0
$111$	15.7443	1.49438
$112$	−4.45980	−0.421411
$113$	6.13756	0.577373	0.288687	−	0.957424i	$-0.406781\pi$
$113$	6.13756	0.577373	0.288687	+	0.957424i	$0.406781\pi$
$114$	23.6429	2.21436
$115$	0	0
$116$	−0.862915	−0.0801196
$117$	0.919169	0.0849772
$118$	−7.87916	−0.725335
$119$	−18.6207	−1.70695
$120$	0	0
$121$	−4.63297	−0.421179
$122$	−10.9345	−0.989966
$123$	−7.66948	−0.691533
$124$	−1.02604	−0.0921408
$125$	0	0
$126$	26.1714	2.33154
$127$	7.33593	0.650958	0.325479	−	0.945549i	$-0.394474\pi$
$127$	7.33593	0.650958	0.325479	+	0.945549i	$0.394474\pi$
$128$	−0.599215	−0.0529636
$129$	34.1894	3.01021
$130$	0	0
$131$	−4.39700	−0.384168	−0.192084	−	0.981379i	$-0.561525\pi$
$131$	−4.39700	−0.384168	−0.192084	+	0.981379i	$0.561525\pi$
$132$	7.35733	0.640374
$133$	−19.1325	−1.65900
$134$	−4.86136	−0.419957
$135$	0	0
$136$	19.4961	1.67178
$137$	10.7122	0.915208	0.457604	−	0.889156i	$-0.348708\pi$
$137$	10.7122	0.915208	0.457604	+	0.889156i	$0.348708\pi$
$138$	11.1232	0.946868
$139$	−0.565817	−0.0479920	−0.0239960	−	0.999712i	$-0.507639\pi$
$139$	−0.565817	−0.0479920	−0.0239960	+	0.999712i	$0.507639\pi$
$140$	0	0
$141$	16.1711	1.36186
$142$	−1.51938	−0.127503
$143$	0.275540	0.0230418
$144$	−12.8749	−1.07290
$145$	0	0
$146$	4.23094	0.350155
$147$	−5.07407	−0.418502
$148$	4.02074	0.330503
$149$	5.00058	0.409663	0.204832	−	0.978797i	$-0.434335\pi$
$149$	5.00058	0.409663	0.204832	+	0.978797i	$0.434335\pi$
$150$	0	0
$151$	−15.3330	−1.24778	−0.623891	−	0.781511i	$-0.714449\pi$
$151$	−15.3330	−1.24778	−0.623891	+	0.781511i	$0.714449\pi$
$152$	20.0320	1.62481
$153$	−53.7554	−4.34587
$154$	7.84543	0.632203
$155$	0	0
$156$	0.318396	0.0254921
$157$	15.2493	1.21702	0.608512	−	0.793545i	$-0.291767\pi$
$157$	15.2493	1.21702	0.608512	+	0.793545i	$0.291767\pi$
$158$	−1.57720	−0.125475
$159$	−34.8100	−2.76062
$160$	0	0
$161$	−9.00119	−0.709393
$162$	39.0289	3.06640
$163$	−3.25655	−0.255073	−0.127536	−	0.991834i	$-0.540707\pi$
$163$	−3.25655	−0.255073	−0.127536	+	0.991834i	$0.540707\pi$
$164$	−1.95862	−0.152942
$165$	0	0
$166$	2.90344	0.225351
$167$	21.7348	1.68189	0.840946	−	0.541119i	$-0.181999\pi$
$167$	21.7348	1.68189	0.840946	+	0.541119i	$0.181999\pi$
$168$	30.0774	2.32052
$169$	−12.9881	−0.999083
$170$	0	0
$171$	−55.2330	−4.22378
$172$	8.73122	0.665750
$173$	3.90440	0.296846	0.148423	−	0.988924i	$-0.452580\pi$
$173$	3.90440	0.296846	0.148423	+	0.988924i	$0.452580\pi$
$174$	−3.60314	−0.273153
$175$	0	0
$176$	−3.85951	−0.290921
$177$	24.9670	1.87664
$178$	−0.243733	−0.0182685
$179$	23.3527	1.74546	0.872730	−	0.488204i	$-0.162348\pi$
$179$	23.3527	1.74546	0.872730	+	0.488204i	$0.162348\pi$
$180$	0	0
$181$	24.1086	1.79198	0.895990	−	0.444074i	$-0.146467\pi$
$181$	24.1086	1.79198	0.895990	+	0.444074i	$0.146467\pi$
$182$	0.339519	0.0251669
$183$	34.6488	2.56131
$184$	9.42439	0.694775
$185$	0	0
$186$	−4.28426	−0.314137
$187$	−16.1143	−1.17840
$188$	4.12976	0.301193
$189$	−53.3739	−3.88238
$190$	0	0
$191$	−10.3422	−0.748337	−0.374168	−	0.927361i	$-0.622072\pi$
$191$	−10.3422	−0.748337	−0.374168	+	0.927361i	$0.622072\pi$
$192$	−26.4594	−1.90955
$193$	19.0274	1.36962	0.684812	−	0.728720i	$-0.259884\pi$
$193$	19.0274	1.36962	0.684812	+	0.728720i	$0.259884\pi$
$194$	9.06109	0.650548
$195$	0	0
$196$	−1.29581	−0.0925576
$197$	−15.0204	−1.07016	−0.535079	−	0.844802i	$-0.679718\pi$
$197$	−15.0204	−1.07016	−0.535079	+	0.844802i	$0.679718\pi$
$198$	22.6487	1.60958
$199$	4.77877	0.338758	0.169379	−	0.985551i	$-0.445824\pi$
$199$	4.77877	0.338758	0.169379	+	0.985551i	$0.445824\pi$
$200$	0	0
$201$	15.4044	1.08654
$202$	−11.5018	−0.809264
$203$	2.91576	0.204646
$204$	−18.6207	−1.30371
$205$	0	0
$206$	−19.4293	−1.35370
$207$	−25.9853	−1.80610
$208$	−0.167024	−0.0115811
$209$	−16.5573	−1.14529
$210$	0	0
$211$	−9.03818	−0.622214	−0.311107	−	0.950375i	$-0.600700\pi$
$211$	−9.03818	−0.622214	−0.311107	+	0.950375i	$0.600700\pi$
$212$	−8.88972	−0.610549
$213$	4.81452	0.329885
$214$	−12.9989	−0.888590
$215$	0	0
$216$	55.8833	3.80237
$217$	3.46695	0.235352
$218$	−12.6126	−0.854231
$219$	−13.4068	−0.905946
$220$	0	0
$221$	−0.697364	−0.0469098
$222$	16.7888	1.12679
$223$	1.10167	0.0737736	0.0368868	−	0.999319i	$-0.488256\pi$
$223$	1.10167	0.0737736	0.0368868	+	0.999319i	$0.488256\pi$
$224$	13.0471	0.871744
$225$	0	0
$226$	6.54474	0.435349
$227$	−3.43954	−0.228290	−0.114145	−	0.993464i	$-0.536413\pi$
$227$	−3.43954	−0.228290	−0.114145	+	0.993464i	$0.536413\pi$
$228$	−19.1325	−1.26708
$229$	1.95557	0.129228	0.0646140	−	0.997910i	$-0.479418\pi$
$229$	1.95557	0.129228	0.0646140	+	0.997910i	$0.479418\pi$
$230$	0	0
$231$	−24.8602	−1.63568
$232$	−3.05285	−0.200429
$233$	19.0832	1.25018	0.625091	−	0.780552i	$-0.285062\pi$
$233$	19.0832	1.25018	0.625091	+	0.780552i	$0.285062\pi$
$234$	0.980149	0.0640743
$235$	0	0
$236$	6.37604	0.415045
$237$	4.99774	0.324638
$238$	−19.8560	−1.28707
$239$	−24.8573	−1.60788	−0.803941	−	0.594709i	$-0.797267\pi$
$239$	−24.8573	−1.60788	−0.803941	+	0.594709i	$0.797267\pi$
$240$	0	0
$241$	4.80969	0.309820	0.154910	−	0.987929i	$-0.450491\pi$
$241$	4.80969	0.309820	0.154910	+	0.987929i	$0.450491\pi$
$242$	−4.94033	−0.317576
$243$	−68.7568	−4.41075
$244$	8.84854	0.566469
$245$	0	0
$246$	−8.17829	−0.521428
$247$	−0.716533	−0.0455919
$248$	−3.62994	−0.230502
$249$	−9.20027	−0.583043
$250$	0	0
$251$	3.63263	0.229290	0.114645	−	0.993407i	$-0.463427\pi$
$251$	3.63263	0.229290	0.114645	+	0.993407i	$0.463427\pi$
$252$	−21.1787	−1.33413
$253$	−7.78963	−0.489730
$254$	7.82261	0.490834
$255$	0	0
$256$	−16.3002	−1.01876
$257$	−19.5977	−1.22247	−0.611234	−	0.791450i	$-0.709327\pi$
$257$	−19.5977	−1.22247	−0.611234	+	0.791450i	$0.709327\pi$
$258$	36.4576	2.26975
$259$	−13.5860	−0.844190
$260$	0	0
$261$	8.41742	0.521025
$262$	−4.68871	−0.289669
$263$	24.9746	1.54000	0.770000	−	0.638044i	$-0.220256\pi$
$263$	24.9746	1.54000	0.770000	+	0.638044i	$0.220256\pi$
$264$	26.0290	1.60197
$265$	0	0
$266$	−20.4018	−1.25091
$267$	0.772327	0.0472656
$268$	3.93395	0.240304
$269$	−6.41410	−0.391075	−0.195537	−	0.980696i	$-0.562645\pi$
$269$	−6.41410	−0.391075	−0.195537	+	0.980696i	$0.562645\pi$
$270$	0	0
$271$	30.0491	1.82535	0.912676	−	0.408685i	$-0.134012\pi$
$271$	30.0491	1.82535	0.912676	+	0.408685i	$0.134012\pi$
$272$	9.76802	0.592273
$273$	−1.07585	−0.0651135
$274$	11.4229	0.690083
$275$	0	0
$276$	−9.00119	−0.541808
$277$	12.9606	0.778727	0.389364	−	0.921084i	$-0.372695\pi$
$277$	12.9606	0.778727	0.389364	+	0.921084i	$0.372695\pi$
$278$	−0.603354	−0.0361868
$279$	10.0086	0.599200
$280$	0	0
$281$	7.71295	0.460116	0.230058	−	0.973177i	$-0.426108\pi$
$281$	7.71295	0.460116	0.230058	+	0.973177i	$0.426108\pi$
$282$	17.2440	1.02686
$283$	−11.1251	−0.661316	−0.330658	−	0.943751i	$-0.607271\pi$
$283$	−11.1251	−0.661316	−0.330658	+	0.943751i	$0.607271\pi$
$284$	1.22952	0.0729588
$285$	0	0
$286$	0.293820	0.0173739
$287$	6.61810	0.390654
$288$	37.6652	2.21944
$289$	23.7837	1.39904
$290$	0	0
$291$	−28.7123	−1.68314
$292$	−3.42380	−0.200363
$293$	−9.73819	−0.568911	−0.284456	−	0.958689i	$-0.591813\pi$
$293$	−9.73819	−0.568911	−0.284456	+	0.958689i	$0.591813\pi$
$294$	−5.41069	−0.315558
$295$	0	0
$296$	14.2247	0.826794
$297$	−46.1897	−2.68020
$298$	5.33233	0.308893
$299$	−0.337104	−0.0194953
$300$	0	0
$301$	−29.5025	−1.70050
$302$	−16.3502	−0.940850
$303$	36.4463	2.09378
$304$	10.0365	0.575634
$305$	0	0
$306$	−57.3217	−3.27686
$307$	−2.72543	−0.155549	−0.0777743	−	0.996971i	$-0.524781\pi$
$307$	−2.72543	−0.155549	−0.0777743	+	0.996971i	$0.524781\pi$
$308$	−6.34875	−0.361754
$309$	61.5664	3.50239
$310$	0	0
$311$	−13.8995	−0.788169	−0.394085	−	0.919074i	$-0.628938\pi$
$311$	−13.8995	−0.788169	−0.394085	+	0.919074i	$0.628938\pi$
$312$	1.12643	0.0637717
$313$	−23.1555	−1.30882	−0.654412	−	0.756138i	$-0.727084\pi$
$313$	−23.1555	−1.30882	−0.654412	+	0.756138i	$0.727084\pi$
$314$	16.2609	0.917657
$315$	0	0
$316$	1.27631	0.0717982
$317$	0.906946	0.0509392	0.0254696	−	0.999676i	$-0.491892\pi$
$317$	0.906946	0.0509392	0.0254696	+	0.999676i	$0.491892\pi$
$318$	−37.1194	−2.08155
$319$	2.52330	0.141278
$320$	0	0
$321$	41.1904	2.29902
$322$	−9.59835	−0.534895
$323$	41.9047	2.33164
$324$	−31.5833	−1.75463
$325$	0	0
$326$	−3.47260	−0.192330
$327$	39.9660	2.21013
$328$	−6.92926	−0.382604
$329$	−13.9543	−0.769326
$330$	0	0
$331$	2.78994	0.153349	0.0766746	−	0.997056i	$-0.475570\pi$
$331$	2.78994	0.153349	0.0766746	+	0.997056i	$0.475570\pi$
$332$	−2.34955	−0.128948
$333$	−39.2209	−2.14929
$334$	23.1768	1.26818
$335$	0	0
$336$	15.0695	0.822109
$337$	7.72445	0.420778	0.210389	−	0.977618i	$-0.432527\pi$
$337$	7.72445	0.420778	0.210389	+	0.977618i	$0.432527\pi$
$338$	−13.8497	−0.753326
$339$	−20.7386	−1.12637
$340$	0	0
$341$	3.00029	0.162475
$342$	−58.8973	−3.18480
$343$	−16.0318	−0.865638
$344$	30.8896	1.66546
$345$	0	0
$346$	4.16342	0.223827
$347$	21.7982	1.17019	0.585094	−	0.810965i	$-0.301058\pi$
$347$	21.7982	1.17019	0.585094	+	0.810965i	$0.301058\pi$
$348$	2.91576	0.156301
$349$	−14.3938	−0.770484	−0.385242	−	0.922816i	$-0.625882\pi$
$349$	−14.3938	−0.770484	−0.385242	+	0.922816i	$0.625882\pi$
$350$	0	0
$351$	−1.99891	−0.106694
$352$	11.2909	0.601808
$353$	18.4125	0.979999	0.489999	−	0.871723i	$-0.336997\pi$
$353$	18.4125	0.979999	0.489999	+	0.871723i	$0.336997\pi$
$354$	26.6234	1.41502
$355$	0	0
$356$	0.197235	0.0104535
$357$	62.9186	3.33001
$358$	24.9019	1.31611
$359$	14.0439	0.741211	0.370606	−	0.928790i	$-0.379150\pi$
$359$	14.0439	0.741211	0.370606	+	0.928790i	$0.379150\pi$
$360$	0	0
$361$	24.0566	1.26614
$362$	25.7080	1.35119
$363$	15.6547	0.821656
$364$	−0.274749	−0.0144008
$365$	0	0
$366$	36.9474	1.93127
$367$	−28.5738	−1.49154	−0.745770	−	0.666204i	$-0.767918\pi$
$367$	−28.5738	−1.49154	−0.745770	+	0.666204i	$0.767918\pi$
$368$	4.72184	0.246143
$369$	19.1056	0.994598
$370$	0	0
$371$	30.0381	1.55950
$372$	3.46695	0.179753
$373$	−0.792828	−0.0410511	−0.0205255	−	0.999789i	$-0.506534\pi$
$373$	−0.792828	−0.0410511	−0.0205255	+	0.999789i	$0.506534\pi$
$374$	−17.1834	−0.888531
$375$	0	0
$376$	14.6104	0.753473
$377$	0.109198	0.00562400
$378$	−56.9148	−2.92738
$379$	0.316228	0.0162435	0.00812177	−	0.999967i	$-0.497415\pi$
$379$	0.316228	0.0162435	0.00812177	+	0.999967i	$0.497415\pi$
$380$	0	0
$381$	−24.7879	−1.26992
$382$	−11.0283	−0.564259
$383$	10.5888	0.541061	0.270531	−	0.962711i	$-0.412801\pi$
$383$	10.5888	0.541061	0.270531	+	0.962711i	$0.412801\pi$
$384$	2.02473	0.103324
$385$	0	0
$386$	20.2897	1.03272
$387$	−85.1699	−4.32943
$388$	−7.33250	−0.372251
$389$	−5.63278	−0.285593	−0.142797	−	0.989752i	$-0.545610\pi$
$389$	−5.63278	−0.285593	−0.142797	+	0.989752i	$0.545610\pi$
$390$	0	0
$391$	19.7148	0.997018
$392$	−4.58434	−0.231544
$393$	14.8573	0.749453
$394$	−16.0169	−0.806918
$395$	0	0
$396$	−18.3280	−0.921017
$397$	−27.7780	−1.39414	−0.697070	−	0.717004i	$-0.745513\pi$
$397$	−27.7780	−1.39414	−0.697070	+	0.717004i	$0.745513\pi$
$398$	5.09581	0.255430
$399$	64.6481	3.23645
$400$	0	0
$401$	17.2875	0.863298	0.431649	−	0.902042i	$-0.357932\pi$
$401$	17.2875	0.863298	0.431649	+	0.902042i	$0.357932\pi$
$402$	16.4264	0.819273
$403$	0.129841	0.00646783
$404$	9.30759	0.463070
$405$	0	0
$406$	3.10920	0.154307
$407$	−11.7573	−0.582786
$408$	−65.8768	−3.26139
$409$	−11.4741	−0.567358	−0.283679	−	0.958919i	$-0.591555\pi$
$409$	−11.4741	−0.567358	−0.283679	+	0.958919i	$0.591555\pi$
$410$	0	0
$411$	−36.1963	−1.78543
$412$	15.7227	0.774603
$413$	−21.5444	−1.06013
$414$	−27.7092	−1.36183
$415$	0	0
$416$	0.488627	0.0239569
$417$	1.91188	0.0936250
$418$	−17.6557	−0.863568
$419$	−1.07767	−0.0526477	−0.0263238	−	0.999653i	$-0.508380\pi$
$419$	−1.07767	−0.0526477	−0.0263238	+	0.999653i	$0.508380\pi$
$420$	0	0
$421$	−40.6938	−1.98330	−0.991648	−	0.128974i	$-0.958832\pi$
$421$	−40.6938	−1.98330	−0.991648	+	0.128974i	$0.958832\pi$
$422$	−9.63779	−0.469160
$423$	−40.2843	−1.95869
$424$	−31.4503	−1.52736
$425$	0	0
$426$	5.13393	0.248739
$427$	−29.8989	−1.44691
$428$	10.5191	0.508461
$429$	−0.931041	−0.0449511
$430$	0	0
$431$	12.3570	0.595216	0.297608	−	0.954688i	$-0.403811\pi$
$431$	12.3570	0.595216	0.297608	+	0.954688i	$0.403811\pi$
$432$	27.9988	1.34710
$433$	15.5589	0.747711	0.373856	−	0.927487i	$-0.378036\pi$
$433$	15.5589	0.747711	0.373856	+	0.927487i	$0.378036\pi$
$434$	3.69695	0.177459
$435$	0	0
$436$	10.2065	0.488800
$437$	20.2567	0.969008
$438$	−14.2962	−0.683099
$439$	−10.8130	−0.516078	−0.258039	−	0.966135i	$-0.583076\pi$
$439$	−10.8130	−0.516078	−0.258039	+	0.966135i	$0.583076\pi$
$440$	0	0
$441$	12.6401	0.601911
$442$	−0.743629	−0.0353708
$443$	17.9608	0.853341	0.426671	−	0.904407i	$-0.359686\pi$
$443$	17.9608	0.853341	0.426671	+	0.904407i	$0.359686\pi$
$444$	−13.5860	−0.644761
$445$	0	0
$446$	1.17476	0.0556266
$447$	−16.8968	−0.799191
$448$	22.8322	1.07872
$449$	−3.42485	−0.161629	−0.0808143	−	0.996729i	$-0.525752\pi$
$449$	−3.42485	−0.161629	−0.0808143	+	0.996729i	$0.525752\pi$
$450$	0	0
$451$	5.72730	0.269688
$452$	−5.29619	−0.249112
$453$	51.8097	2.43423
$454$	−3.66772	−0.172135
$455$	0	0
$456$	−67.6876	−3.16976
$457$	−36.8181	−1.72228	−0.861138	−	0.508371i	$-0.830248\pi$
$457$	−36.8181	−1.72228	−0.861138	+	0.508371i	$0.830248\pi$
$458$	2.08531	0.0974401
$459$	116.902	5.45650
$460$	0	0
$461$	23.5705	1.09779	0.548893	−	0.835893i	$-0.315049\pi$
$461$	23.5705	1.09779	0.548893	+	0.835893i	$0.315049\pi$
$462$	−26.5095	−1.23333
$463$	6.75079	0.313736	0.156868	−	0.987620i	$-0.449860\pi$
$463$	6.75079	0.313736	0.156868	+	0.987620i	$0.449860\pi$
$464$	−1.52955	−0.0710075
$465$	0	0
$466$	20.3492	0.942660
$467$	−34.1819	−1.58175	−0.790876	−	0.611977i	$-0.790375\pi$
$467$	−34.1819	−1.58175	−0.790876	+	0.611977i	$0.790375\pi$
$468$	−0.793165	−0.0366640
$469$	−13.2927	−0.613799
$470$	0	0
$471$	−51.5268	−2.37423
$472$	22.5574	1.03829
$473$	−25.5315	−1.17394
$474$	5.32930	0.244783
$475$	0	0
$476$	16.0680	0.736478
$477$	86.7161	3.97046
$478$	−26.5063	−1.21237
$479$	18.5011	0.845336	0.422668	−	0.906285i	$-0.361094\pi$
$479$	18.5011	0.845336	0.422668	+	0.906285i	$0.361094\pi$
$480$	0	0
$481$	−0.508809	−0.0231997
$482$	5.12878	0.233609
$483$	30.4147	1.38392
$484$	3.99786	0.181721
$485$	0	0
$486$	−73.3183	−3.32579
$487$	−23.6643	−1.07233	−0.536165	−	0.844113i	$-0.680128\pi$
$487$	−23.6643	−1.07233	−0.536165	+	0.844113i	$0.680128\pi$
$488$	31.3046	1.41709
$489$	11.0038	0.497609
$490$	0	0
$491$	32.9543	1.48721	0.743603	−	0.668622i	$-0.233115\pi$
$491$	32.9543	1.48721	0.743603	+	0.668622i	$0.233115\pi$
$492$	6.61810	0.298367
$493$	−6.38621	−0.287621
$494$	−0.764069	−0.0343771
$495$	0	0
$496$	−1.81869	−0.0816615
$497$	−4.15452	−0.186356
$498$	−9.81063	−0.439625
$499$	−18.7339	−0.838644	−0.419322	−	0.907838i	$-0.637732\pi$
$499$	−18.7339	−0.838644	−0.419322	+	0.907838i	$0.637732\pi$
$500$	0	0
$501$	−73.4413	−3.28112
$502$	3.87363	0.172888
$503$	−21.4417	−0.956036	−0.478018	−	0.878350i	$-0.658645\pi$
$503$	−21.4417	−0.956036	−0.478018	+	0.878350i	$0.658645\pi$
$504$	−74.9266	−3.33750
$505$	0	0
$506$	−8.30641	−0.369265
$507$	43.8863	1.94906
$508$	−6.33028	−0.280861
$509$	13.9863	0.619933	0.309966	−	0.950748i	$-0.399682\pi$
$509$	13.9863	0.619933	0.309966	+	0.950748i	$0.399682\pi$
$510$	0	0
$511$	11.5689	0.511778
$512$	−16.1832	−0.715202
$513$	120.115	5.30320
$514$	−20.8978	−0.921763
$515$	0	0
$516$	−29.5025	−1.29878
$517$	−12.0761	−0.531104
$518$	−14.4873	−0.636534
$519$	−13.1928	−0.579101
$520$	0	0
$521$	−14.2407	−0.623898	−0.311949	−	0.950099i	$-0.600982\pi$
$521$	−14.2407	−0.623898	−0.311949	+	0.950099i	$0.600982\pi$
$522$	8.97585	0.392862
$523$	8.40308	0.367441	0.183721	−	0.982979i	$-0.441186\pi$
$523$	8.40308	0.367441	0.183721	+	0.982979i	$0.441186\pi$
$524$	3.79424	0.165752
$525$	0	0
$526$	26.6315	1.16119
$527$	−7.59344	−0.330775
$528$	13.0411	0.567543
$529$	−13.4699	−0.585649
$530$	0	0
$531$	−62.1960	−2.69908
$532$	16.5097	0.715787
$533$	0.247855	0.0107358
$534$	0.823564	0.0356391
$535$	0	0
$536$	13.9176	0.601151
$537$	−78.9079	−3.40513
$538$	−6.83962	−0.294877
$539$	3.78914	0.163210
$540$	0	0
$541$	−25.7576	−1.10741	−0.553704	−	0.832714i	$-0.686786\pi$
$541$	−25.7576	−1.10741	−0.553704	+	0.832714i	$0.686786\pi$
$542$	32.0426	1.37635
$543$	−81.4623	−3.49588
$544$	−28.5762	−1.22519
$545$	0	0
$546$	−1.14723	−0.0490967
$547$	−28.7284	−1.22834	−0.614170	−	0.789174i	$-0.710509\pi$
$547$	−28.7284	−1.22834	−0.614170	+	0.789174i	$0.710509\pi$
$548$	−9.24375	−0.394873
$549$	−86.3143	−3.68380
$550$	0	0
$551$	−6.56175	−0.279540
$552$	−31.8447	−1.35540
$553$	−4.31262	−0.183391
$554$	13.8204	0.587174
$555$	0	0
$556$	0.488252	0.0207065
$557$	−14.4627	−0.612804	−0.306402	−	0.951902i	$-0.599125\pi$
$557$	−14.4627	−0.612804	−0.306402	+	0.951902i	$0.599125\pi$
$558$	10.6726	0.451808
$559$	−1.10490	−0.0467323
$560$	0	0
$561$	54.4497	2.29887
$562$	8.22464	0.346936
$563$	4.49606	0.189487	0.0947433	−	0.995502i	$-0.469797\pi$
$563$	4.49606	0.189487	0.0947433	+	0.995502i	$0.469797\pi$
$564$	−13.9543	−0.587583
$565$	0	0
$566$	−11.8631	−0.498644
$567$	106.719	4.48178
$568$	4.34985	0.182515
$569$	4.75833	0.199480	0.0997398	−	0.995014i	$-0.468199\pi$
$569$	4.75833	0.199480	0.0997398	+	0.995014i	$0.468199\pi$
$570$	0	0
$571$	−12.7603	−0.534002	−0.267001	−	0.963696i	$-0.586033\pi$
$571$	−12.7603	−0.534002	−0.267001	+	0.963696i	$0.586033\pi$
$572$	−0.237768	−0.00994156
$573$	34.9460	1.45989
$574$	7.05716	0.294560
$575$	0	0
$576$	65.9137	2.74640
$577$	10.0898	0.420044	0.210022	−	0.977697i	$-0.432646\pi$
$577$	10.0898	0.420044	0.210022	+	0.977697i	$0.432646\pi$
$578$	25.3616	1.05490
$579$	−64.2931	−2.67193
$580$	0	0
$581$	7.93905	0.329367
$582$	−30.6171	−1.26912
$583$	25.9949	1.07660
$584$	−12.1128	−0.501232
$585$	0	0
$586$	−10.3842	−0.428969
$587$	20.3709	0.840795	0.420398	−	0.907340i	$-0.361891\pi$
$587$	20.3709	0.840795	0.420398	+	0.907340i	$0.361891\pi$
$588$	4.37849	0.180566
$589$	−7.80216	−0.321482
$590$	0	0
$591$	50.7534	2.08771
$592$	7.12691	0.292914
$593$	−10.0591	−0.413076	−0.206538	−	0.978439i	$-0.566220\pi$
$593$	−10.0591	−0.413076	−0.206538	+	0.978439i	$0.566220\pi$
$594$	−49.2540	−2.02092
$595$	0	0
$596$	−4.31507	−0.176752
$597$	−16.1473	−0.660866
$598$	−0.359469	−0.0146998
$599$	34.0869	1.39275	0.696377	−	0.717676i	$-0.254794\pi$
$599$	34.0869	1.39275	0.696377	+	0.717676i	$0.254794\pi$
$600$	0	0
$601$	28.0304	1.14338	0.571692	−	0.820468i	$-0.306287\pi$
$601$	28.0304	1.14338	0.571692	+	0.820468i	$0.306287\pi$
$602$	−31.4598	−1.28220
$603$	−38.3743	−1.56272
$604$	13.2311	0.538365
$605$	0	0
$606$	38.8642	1.57875
$607$	17.7142	0.718997	0.359499	−	0.933146i	$-0.382948\pi$
$607$	17.7142	0.718997	0.359499	+	0.933146i	$0.382948\pi$
$608$	−29.3617	−1.19077
$609$	−9.85226	−0.399234
$610$	0	0
$611$	−0.522604	−0.0211423
$612$	46.3864	1.87506
$613$	16.9062	0.682835	0.341418	−	0.939912i	$-0.389093\pi$
$613$	16.9062	0.682835	0.341418	+	0.939912i	$0.389093\pi$
$614$	−2.90624	−0.117286
$615$	0	0
$616$	−22.4608	−0.904972
$617$	28.0075	1.12754	0.563770	−	0.825932i	$-0.309351\pi$
$617$	28.0075	1.12754	0.563770	+	0.825932i	$0.309351\pi$
$618$	65.6509	2.64086
$619$	10.8957	0.437933	0.218967	−	0.975732i	$-0.429731\pi$
$619$	10.8957	0.437933	0.218967	+	0.975732i	$0.429731\pi$
$620$	0	0
$621$	56.5100	2.26767
$622$	−14.8216	−0.594294
$623$	−0.666452	−0.0267008
$624$	0.564370	0.0225929
$625$	0	0
$626$	−24.6917	−0.986877
$627$	55.9464	2.23429
$628$	−13.1588	−0.525094
$629$	29.7565	1.18647
$630$	0	0
$631$	14.9507	0.595179	0.297589	−	0.954694i	$-0.403817\pi$
$631$	14.9507	0.595179	0.297589	+	0.954694i	$0.403817\pi$
$632$	4.51538	0.179612
$633$	30.5397	1.21384
$634$	0.967115	0.0384090
$635$	0	0
$636$	30.0381	1.19109
$637$	0.163979	0.00649709
$638$	2.69070	0.106526
$639$	−11.9936	−0.474458
$640$	0	0
$641$	−19.3764	−0.765323	−0.382661	−	0.923889i	$-0.624992\pi$
$641$	−19.3764	−0.765323	−0.382661	+	0.923889i	$0.624992\pi$
$642$	43.9230	1.73350
$643$	−39.9904	−1.57707	−0.788533	−	0.614993i	$-0.789159\pi$
$643$	−39.9904	−1.57707	−0.788533	+	0.614993i	$0.789159\pi$
$644$	7.76726	0.306073
$645$	0	0
$646$	44.6848	1.75810
$647$	8.45221	0.332291	0.166145	−	0.986101i	$-0.446868\pi$
$647$	8.45221	0.332291	0.166145	+	0.986101i	$0.446868\pi$
$648$	−111.736	−4.38942
$649$	−18.6445	−0.731862
$650$	0	0
$651$	−11.7147	−0.459135
$652$	2.81013	0.110053
$653$	0.165672	0.00648325	0.00324162	−	0.999995i	$-0.498968\pi$
$653$	0.165672	0.00648325	0.00324162	+	0.999995i	$0.498968\pi$
$654$	42.6175	1.66647
$655$	0	0
$656$	−3.47172	−0.135548
$657$	33.3979	1.30298
$658$	−14.8801	−0.580086
$659$	15.4273	0.600961	0.300481	−	0.953788i	$-0.402853\pi$
$659$	15.4273	0.600961	0.300481	+	0.953788i	$0.402853\pi$
$660$	0	0
$661$	6.18033	0.240387	0.120193	−	0.992750i	$-0.461649\pi$
$661$	6.18033	0.240387	0.120193	+	0.992750i	$0.461649\pi$
$662$	2.97503	0.115628
$663$	2.35637	0.0915139
$664$	−8.31230	−0.322580
$665$	0	0
$666$	−41.8229	−1.62060
$667$	−3.08708	−0.119532
$668$	−18.7553	−0.725665
$669$	−3.72252	−0.143921
$670$	0	0
$671$	−25.8745	−0.998874
$672$	−44.0856	−1.70064
$673$	43.6082	1.68097	0.840486	−	0.541833i	$-0.182270\pi$
$673$	43.6082	1.68097	0.840486	+	0.541833i	$0.182270\pi$
$674$	8.23691	0.317274
$675$	0	0
$676$	11.2076	0.431062
$677$	31.5489	1.21252	0.606261	−	0.795266i	$-0.292669\pi$
$677$	31.5489	1.21252	0.606261	+	0.795266i	$0.292669\pi$
$678$	−22.1145	−0.849301
$679$	24.7763	0.950826
$680$	0	0
$681$	11.6221	0.445360
$682$	3.19934	0.122509
$683$	9.95629	0.380967	0.190483	−	0.981690i	$-0.438994\pi$
$683$	9.95629	0.380967	0.190483	+	0.981690i	$0.438994\pi$
$684$	47.6614	1.82238
$685$	0	0
$686$	−17.0954	−0.652706
$687$	−6.60782	−0.252104
$688$	15.4764	0.590033
$689$	1.12496	0.0428575
$690$	0	0
$691$	0.632508	0.0240617	0.0120309	−	0.999928i	$-0.496170\pi$
$691$	0.632508	0.0240617	0.0120309	+	0.999928i	$0.496170\pi$
$692$	−3.36916	−0.128076
$693$	61.9298	2.35252
$694$	23.2443	0.882343
$695$	0	0
$696$	10.3155	0.391007
$697$	−14.4952	−0.549046
$698$	−15.3487	−0.580959
$699$	−64.4816	−2.43892
$700$	0	0
$701$	33.8462	1.27835	0.639177	−	0.769060i	$-0.279275\pi$
$701$	33.8462	1.27835	0.639177	+	0.769060i	$0.279275\pi$
$702$	−2.13152	−0.0804491
$703$	30.5744	1.15314
$704$	19.7590	0.744695
$705$	0	0
$706$	19.6340	0.738936
$707$	−31.4500	−1.18280
$708$	−21.5444	−0.809689
$709$	22.3699	0.840120	0.420060	−	0.907496i	$-0.362009\pi$
$709$	22.3699	0.840120	0.420060	+	0.907496i	$0.362009\pi$
$710$	0	0
$711$	−12.4500	−0.466910
$712$	0.697785	0.0261506
$713$	−3.67065	−0.137467
$714$	67.0928	2.51088
$715$	0	0
$716$	−20.1513	−0.753091
$717$	83.9919	3.13673
$718$	14.9756	0.558886
$719$	−13.8851	−0.517828	−0.258914	−	0.965900i	$-0.583365\pi$
$719$	−13.8851	−0.517828	−0.258914	+	0.965900i	$0.583365\pi$
$720$	0	0
$721$	−53.1266	−1.97854
$722$	25.6526	0.954689
$723$	−16.2518	−0.604411
$724$	−20.8037	−0.773163
$725$	0	0
$726$	16.6932	0.619543
$727$	−46.6331	−1.72953	−0.864763	−	0.502179i	$-0.832532\pi$
$727$	−46.6331	−1.72953	−0.864763	+	0.502179i	$0.832532\pi$
$728$	−0.972015	−0.0360253
$729$	122.525	4.53796
$730$	0	0
$731$	64.6176	2.38997
$732$	−29.8989	−1.10510
$733$	5.86275	0.216546	0.108273	−	0.994121i	$-0.465468\pi$
$733$	5.86275	0.216546	0.108273	+	0.994121i	$0.465468\pi$
$734$	−30.4694	−1.12465
$735$	0	0
$736$	−13.8137	−0.509179
$737$	−11.5035	−0.423736
$738$	20.3731	0.749945
$739$	16.8666	0.620448	0.310224	−	0.950663i	$-0.399596\pi$
$739$	16.8666	0.620448	0.310224	+	0.950663i	$0.399596\pi$
$740$	0	0
$741$	2.42114	0.0889429
$742$	32.0309	1.17589
$743$	−25.2538	−0.926472	−0.463236	−	0.886235i	$-0.653312\pi$
$743$	−25.2538	−0.926472	−0.463236	+	0.886235i	$0.653312\pi$
$744$	12.2655	0.449674
$745$	0	0
$746$	−0.845425	−0.0309532
$747$	22.9190	0.838562
$748$	13.9053	0.508427
$749$	−35.5438	−1.29874
$750$	0	0
$751$	−19.5611	−0.713796	−0.356898	−	0.934143i	$-0.616166\pi$
$751$	−19.5611	−0.713796	−0.356898	+	0.934143i	$0.616166\pi$
$752$	7.32015	0.266938
$753$	−12.2745	−0.447309
$754$	0.116443	0.00424060
$755$	0	0
$756$	46.0571	1.67508
$757$	−44.5295	−1.61845	−0.809226	−	0.587498i	$-0.800113\pi$
$757$	−44.5295	−1.61845	−0.809226	+	0.587498i	$0.800113\pi$
$758$	0.337207	0.0122479
$759$	26.3209	0.955388
$760$	0	0
$761$	0.420014	0.0152255	0.00761274	−	0.999971i	$-0.497577\pi$
$761$	0.420014	0.0152255	0.00761274	+	0.999971i	$0.497577\pi$
$762$	−26.4323	−0.957543
$763$	−34.4873	−1.24852
$764$	8.92445	0.322875
$765$	0	0
$766$	11.2913	0.407970
$767$	−0.806862	−0.0291341
$768$	55.0779	1.98745
$769$	37.3900	1.34832	0.674158	−	0.738587i	$-0.264507\pi$
$769$	37.3900	1.34832	0.674158	+	0.738587i	$0.264507\pi$
$770$	0	0
$771$	66.2198	2.38485
$772$	−16.4190	−0.590934
$773$	−24.2503	−0.872222	−0.436111	−	0.899893i	$-0.643644\pi$
$773$	−24.2503	−0.872222	−0.436111	+	0.899893i	$0.643644\pi$
$774$	−90.8203	−3.26447
$775$	0	0
$776$	−25.9411	−0.931232
$777$	45.9065	1.64689
$778$	−6.00647	−0.215342
$779$	−14.8937	−0.533621
$780$	0	0
$781$	−3.59532	−0.128651
$782$	21.0227	0.751769
$783$	−18.3053	−0.654178
$784$	−2.29687	−0.0820309
$785$	0	0
$786$	15.8430	0.565101
$787$	54.9484	1.95870	0.979350	−	0.202173i	$-0.0648002\pi$
$787$	54.9484	1.95870	0.979350	+	0.202173i	$0.0648002\pi$
$788$	12.9613	0.461727
$789$	−84.3883	−3.00430
$790$	0	0
$791$	17.8957	0.636296
$792$	−64.8414	−2.30404
$793$	−1.11975	−0.0397634
$794$	−29.6209	−1.05121
$795$	0	0
$796$	−4.12367	−0.146160
$797$	4.01220	0.142119	0.0710596	−	0.997472i	$-0.477362\pi$
$797$	4.01220	0.142119	0.0710596	+	0.997472i	$0.477362\pi$
$798$	68.9370	2.44034
$799$	30.5633	1.08125
$800$	0	0
$801$	−1.92396	−0.0679798
$802$	18.4344	0.650942
$803$	10.0117	0.353306
$804$	−13.2927	−0.468797
$805$	0	0
$806$	0.138455	0.00487686
$807$	21.6730	0.762927
$808$	32.9287	1.15843
$809$	−30.6363	−1.07711	−0.538557	−	0.842589i	$-0.681030\pi$
$809$	−30.6363	−1.07711	−0.538557	+	0.842589i	$0.681030\pi$
$810$	0	0
$811$	44.3984	1.55904	0.779519	−	0.626378i	$-0.215463\pi$
$811$	44.3984	1.55904	0.779519	+	0.626378i	$0.215463\pi$
$812$	−2.51605	−0.0882962
$813$	−101.535	−3.56098
$814$	−12.5373	−0.439431
$815$	0	0
$816$	−33.0058	−1.15544
$817$	66.3937	2.32282
$818$	−12.2353	−0.427798
$819$	2.68008	0.0936495
$820$	0	0
$821$	−10.6489	−0.371649	−0.185825	−	0.982583i	$-0.559496\pi$
$821$	−10.6489	−0.371649	−0.185825	+	0.982583i	$0.559496\pi$
$822$	−38.5976	−1.34625
$823$	−33.4300	−1.16530	−0.582649	−	0.812724i	$-0.697984\pi$
$823$	−33.4300	−1.16530	−0.582649	+	0.812724i	$0.697984\pi$
$824$	55.6243	1.93777
$825$	0	0
$826$	−22.9737	−0.799358
$827$	11.6325	0.404502	0.202251	−	0.979334i	$-0.435174\pi$
$827$	11.6325	0.404502	0.202251	+	0.979334i	$0.435174\pi$
$828$	22.4231	0.779256
$829$	−27.7972	−0.965437	−0.482718	−	0.875776i	$-0.660351\pi$
$829$	−27.7972	−0.965437	−0.482718	+	0.875776i	$0.660351\pi$
$830$	0	0
$831$	−43.7935	−1.51918
$832$	0.855092	0.0296450
$833$	−9.58993	−0.332271
$834$	2.03872	0.0705949
$835$	0	0
$836$	14.2875	0.494143
$837$	−21.7657	−0.752331
$838$	−1.14917	−0.0396973
$839$	37.0871	1.28039	0.640195	−	0.768213i	$-0.278854\pi$
$839$	37.0871	1.28039	0.640195	+	0.768213i	$0.278854\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−43.3935	−1.49544
$843$	−26.0618	−0.897616
$844$	7.79917	0.268459
$845$	0	0
$846$	−42.9568	−1.47689
$847$	−13.5086	−0.464162
$848$	−15.7574	−0.541110
$849$	37.5912	1.29013
$850$	0	0
$851$	14.3842	0.493085
$852$	−4.15452	−0.142332
$853$	−28.7685	−0.985014	−0.492507	−	0.870308i	$-0.663919\pi$
$853$	−28.7685	−0.985014	−0.492507	+	0.870308i	$0.663919\pi$
$854$	−31.8825	−1.09100
$855$	0	0
$856$	37.2149	1.27198
$857$	−26.8534	−0.917295	−0.458648	−	0.888618i	$-0.651666\pi$
$857$	−26.8534	−0.917295	−0.458648	+	0.888618i	$0.651666\pi$
$858$	−0.992808	−0.0338939
$859$	−3.56800	−0.121739	−0.0608694	−	0.998146i	$-0.519387\pi$
$859$	−3.56800	−0.121739	−0.0608694	+	0.998146i	$0.519387\pi$
$860$	0	0
$861$	−22.3624	−0.762107
$862$	13.1768	0.448803
$863$	21.7423	0.740117	0.370058	−	0.929008i	$-0.379338\pi$
$863$	21.7423	0.740117	0.370058	+	0.929008i	$0.379338\pi$
$864$	−81.9102	−2.78664
$865$	0	0
$866$	16.5911	0.563787
$867$	−80.3644	−2.72932
$868$	−2.99168	−0.101544
$869$	−3.73214	−0.126604
$870$	0	0
$871$	−0.497826	−0.0168682
$872$	36.1087	1.22279
$873$	71.5259	2.42078
$874$	21.6005	0.730649
$875$	0	0
$876$	11.5689	0.390877
$877$	−9.54159	−0.322197	−0.161098	−	0.986938i	$-0.551504\pi$
$877$	−9.54159	−0.322197	−0.161098	+	0.986938i	$0.551504\pi$
$878$	−11.5304	−0.389132
$879$	32.9050	1.10986
$880$	0	0
$881$	−29.0815	−0.979779	−0.489890	−	0.871784i	$-0.662963\pi$
$881$	−29.0815	−0.979779	−0.489890	+	0.871784i	$0.662963\pi$
$882$	13.4787	0.453851
$883$	6.35083	0.213723	0.106861	−	0.994274i	$-0.465920\pi$
$883$	6.35083	0.213723	0.106861	+	0.994274i	$0.465920\pi$
$884$	0.601766	0.0202396
$885$	0	0
$886$	19.1523	0.643435
$887$	26.1572	0.878273	0.439136	−	0.898420i	$-0.355284\pi$
$887$	26.1572	0.878273	0.439136	+	0.898420i	$0.355284\pi$
$888$	−48.0648	−1.61295
$889$	21.3898	0.717391
$890$	0	0
$891$	92.3546	3.09399
$892$	−0.950651	−0.0318301
$893$	31.4034	1.05087
$894$	−18.0178	−0.602604
$895$	0	0
$896$	−1.74717	−0.0583687
$897$	1.13907	0.0380323
$898$	−3.65206	−0.121871
$899$	1.18904	0.0396566
$900$	0	0
$901$	−65.7906	−2.19180
$902$	6.10726	0.203350
$903$	99.6881	3.31741
$904$	−18.7370	−0.623184
$905$	0	0
$906$	55.2469	1.83545
$907$	23.4205	0.777664	0.388832	−	0.921309i	$-0.372879\pi$
$907$	23.4205	0.777664	0.388832	+	0.921309i	$0.372879\pi$
$908$	2.96803	0.0984975
$909$	−90.7922	−3.01139
$910$	0	0
$911$	−43.1582	−1.42989	−0.714947	−	0.699179i	$-0.753549\pi$
$911$	−43.1582	−1.42989	−0.714947	+	0.699179i	$0.753549\pi$
$912$	−33.9131	−1.12297
$913$	6.87044	0.227379
$914$	−39.2606	−1.29863
$915$	0	0
$916$	−1.68749	−0.0557563
$917$	−12.8206	−0.423373
$918$	124.657	4.11429
$919$	−9.56978	−0.315678	−0.157839	−	0.987465i	$-0.550453\pi$
$919$	−9.56978	−0.315678	−0.157839	+	0.987465i	$0.550453\pi$
$920$	0	0
$921$	9.20915	0.303452
$922$	25.1342	0.827750
$923$	−0.155591	−0.00512135
$924$	21.4522	0.705726
$925$	0	0
$926$	7.19865	0.236562
$927$	−153.369	−5.03731
$928$	4.47467	0.146888
$929$	−22.7262	−0.745623	−0.372811	−	0.927907i	$-0.621606\pi$
$929$	−22.7262	−0.745623	−0.372811	+	0.927907i	$0.621606\pi$
$930$	0	0
$931$	−9.85353	−0.322937
$932$	−16.4672	−0.539401
$933$	46.9660	1.53760
$934$	−36.4496	−1.19267
$935$	0	0
$936$	−2.80608	−0.0917197
$937$	2.99351	0.0977939	0.0488969	−	0.998804i	$-0.484429\pi$
$937$	2.99351	0.0977939	0.0488969	+	0.998804i	$0.484429\pi$
$938$	−14.1746	−0.462816
$939$	78.2416	2.55332
$940$	0	0
$941$	−46.4903	−1.51554	−0.757770	−	0.652522i	$-0.773711\pi$
$941$	−46.4903	−1.51554	−0.757770	+	0.652522i	$0.773711\pi$
$942$	−54.9452	−1.79021
$943$	−7.00696	−0.228178
$944$	11.3018	0.367841
$945$	0	0
$946$	−27.2253	−0.885170
$947$	40.3365	1.31076	0.655380	−	0.755300i	$-0.272509\pi$
$947$	40.3365	1.31076	0.655380	+	0.755300i	$0.272509\pi$
$948$	−4.31262	−0.140067
$949$	0.433268	0.0140645
$950$	0	0
$951$	−3.06454	−0.0993746
$952$	56.8460	1.84239
$953$	−23.2300	−0.752494	−0.376247	−	0.926519i	$-0.622786\pi$
$953$	−23.2300	−0.752494	−0.376247	+	0.926519i	$0.622786\pi$
$954$	92.4690	2.99379
$955$	0	0
$956$	21.4497	0.693733
$957$	−8.52614	−0.275611
$958$	19.7285	0.637398
$959$	31.2343	1.00861
$960$	0	0
$961$	−29.5862	−0.954393
$962$	−0.542564	−0.0174930
$963$	−102.610	−3.30657
$964$	−4.15035	−0.133674
$965$	0	0
$966$	32.4325	1.04350
$967$	6.87033	0.220935	0.110467	−	0.993880i	$-0.464765\pi$
$967$	6.87033	0.220935	0.110467	+	0.993880i	$0.464765\pi$
$968$	14.1437	0.454597
$969$	−141.595	−4.54868
$970$	0	0
$971$	8.03875	0.257976	0.128988	−	0.991646i	$-0.458827\pi$
$971$	8.03875	0.257976	0.128988	+	0.991646i	$0.458827\pi$
$972$	59.3313	1.90305
$973$	−1.64979	−0.0528897
$974$	−25.2342	−0.808556
$975$	0	0
$976$	15.6844	0.502044
$977$	−39.3490	−1.25888	−0.629442	−	0.777047i	$-0.716717\pi$
$977$	−39.3490	−1.25888	−0.629442	+	0.777047i	$0.716717\pi$
$978$	11.7338	0.375206
$979$	−0.576747	−0.0184329
$980$	0	0
$981$	−99.5603	−3.17872
$982$	35.1405	1.12138
$983$	−22.0597	−0.703596	−0.351798	−	0.936076i	$-0.614430\pi$
$983$	−22.0597	−0.703596	−0.351798	+	0.936076i	$0.614430\pi$
$984$	23.4137	0.746403
$985$	0	0
$986$	−6.80989	−0.216871
$987$	47.1512	1.50084
$988$	0.618307	0.0196710
$989$	31.2360	0.993247
$990$	0	0
$991$	−8.70393	−0.276490	−0.138245	−	0.990398i	$-0.544146\pi$
$991$	−8.70393	−0.276490	−0.138245	+	0.990398i	$0.544146\pi$
$992$	5.32054	0.168927
$993$	−9.42713	−0.299161
$994$	−4.43014	−0.140515
$995$	0	0
$996$	7.93905	0.251558
$997$	−13.8218	−0.437741	−0.218870	−	0.975754i	$-0.570237\pi$
$997$	−13.8218	−0.437741	−0.218870	+	0.975754i	$0.570237\pi$
$998$	−19.9767	−0.632352
$999$	85.2933	2.69856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.a.h.1.4	✓	5
3.2	odd	2		6525.2.a.bq.1.2		5
5.2	odd	4		725.2.b.f.349.7		10
5.3	odd	4		725.2.b.f.349.4		10
5.4	even	2		725.2.a.k.1.2	yes	5
15.14	odd	2		6525.2.a.bm.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.a.h.1.4	✓	5	1.1	even	1	trivial
725.2.a.k.1.2	yes	5	5.4	even	2
725.2.b.f.349.4		10	5.3	odd	4
725.2.b.f.349.7		10	5.2	odd	4
6525.2.a.bm.1.4		5	15.14	odd	2
6525.2.a.bq.1.2		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q+1.06634 q^{2} -3.37897 q^{3} -0.862915 q^{4} -3.60314 q^{6} +2.91576 q^{7} -3.05285 q^{8} +8.41742 q^{9} +O(q^{10})\)	\(q+1.06634 q^{2} -3.37897 q^{3} -0.862915 q^{4} -3.60314 q^{6} +2.91576 q^{7} -3.05285 q^{8} +8.41742 q^{9} +2.52330 q^{11} +2.91576 q^{12} +0.109198 q^{13} +3.10920 q^{14} -1.52955 q^{16} -6.38621 q^{17} +8.97585 q^{18} -6.56175 q^{19} -9.85226 q^{21} +2.69070 q^{22} -3.08708 q^{23} +10.3155 q^{24} +0.116443 q^{26} -18.3053 q^{27} -2.51605 q^{28} +1.00000 q^{29} +1.18904 q^{31} +4.47467 q^{32} -8.52614 q^{33} -6.80989 q^{34} -7.26352 q^{36} -4.65949 q^{37} -6.99707 q^{38} -0.368978 q^{39} +2.26977 q^{41} -10.5059 q^{42} -10.1183 q^{43} -2.17739 q^{44} -3.29189 q^{46} -4.78582 q^{47} +5.16830 q^{48} +1.50166 q^{49} +21.5788 q^{51} -0.0942289 q^{52} +10.3020 q^{53} -19.5197 q^{54} -8.90137 q^{56} +22.1720 q^{57} +1.06634 q^{58} -7.38896 q^{59} -10.2542 q^{61} +1.26792 q^{62} +24.5432 q^{63} +7.83063 q^{64} -9.09178 q^{66} -4.55891 q^{67} +5.51076 q^{68} +10.4312 q^{69} -1.42485 q^{71} -25.6971 q^{72} +3.96771 q^{73} -4.96861 q^{74} +5.66223 q^{76} +7.35733 q^{77} -0.393457 q^{78} -1.47907 q^{79} +36.6007 q^{81} +2.42035 q^{82} +2.72280 q^{83} +8.50166 q^{84} -10.7896 q^{86} -3.37897 q^{87} -7.70324 q^{88} -0.228569 q^{89} +0.318396 q^{91} +2.66389 q^{92} -4.01771 q^{93} -5.10332 q^{94} -15.1198 q^{96} +8.49736 q^{97} +1.60129 q^{98} +21.2397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9	\( 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26} - 27 q^{27} - 10 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} + 7 q^{33} + 3 q^{34} - 13 q^{36} - 14 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{41} - 24 q^{42} - 28 q^{43} + 7 q^{44} - 20 q^{46} - 15 q^{47} + 26 q^{48} - 3 q^{49} + 5 q^{51} - 6 q^{52} + 8 q^{53} + 10 q^{54} - 16 q^{56} + 6 q^{57} - 2 q^{58} - 11 q^{59} - 5 q^{61} + 6 q^{62} + 5 q^{63} - 5 q^{64} - 27 q^{66} - 23 q^{67} - q^{68} - 26 q^{69} - 5 q^{71} - 3 q^{72} - 16 q^{73} + 8 q^{74} + 16 q^{76} + 30 q^{77} + 33 q^{78} - 10 q^{79} + 49 q^{81} + 19 q^{82} - 9 q^{83} + 32 q^{84} - 13 q^{86} - 6 q^{87} - 35 q^{88} - 18 q^{89} + q^{91} + 27 q^{92} - 7 q^{93} - 13 q^{94} - 38 q^{96} - 23 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more