LMFDB - Embedded newform 435.4.a.j.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$25.6658308525$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 $ x^7 - x^6 - 35x^5 + 18x^4 + 329x^3 - 167x^2 - 767*x + 638
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-3.96612$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.96612 q^{2} +3.00000 q^{3} +7.73008 q^{4} -5.00000 q^{5} +11.8983 q^{6} -32.8717 q^{7} -1.07055 q^{8} +9.00000 q^{9} -19.8306 q^{10} +12.6426 q^{11} +23.1902 q^{12} -52.2979 q^{13} -130.373 q^{14} -15.0000 q^{15} -66.0865 q^{16} -17.2978 q^{17} +35.6950 q^{18} +48.0486 q^{19} -38.6504 q^{20} -98.6150 q^{21} +50.1421 q^{22} -130.535 q^{23} -3.21165 q^{24} +25.0000 q^{25} -207.420 q^{26} +27.0000 q^{27} -254.100 q^{28} -29.0000 q^{29} -59.4917 q^{30} +196.614 q^{31} -253.542 q^{32} +37.9278 q^{33} -68.6049 q^{34} +164.358 q^{35} +69.5707 q^{36} -119.645 q^{37} +190.566 q^{38} -156.894 q^{39} +5.35275 q^{40} -134.133 q^{41} -391.118 q^{42} -222.109 q^{43} +97.7283 q^{44} -45.0000 q^{45} -517.716 q^{46} -569.042 q^{47} -198.260 q^{48} +737.546 q^{49} +99.1529 q^{50} -51.8933 q^{51} -404.267 q^{52} +393.464 q^{53} +107.085 q^{54} -63.2131 q^{55} +35.1908 q^{56} +144.146 q^{57} -115.017 q^{58} +741.684 q^{59} -115.951 q^{60} +758.295 q^{61} +779.796 q^{62} -295.845 q^{63} -476.886 q^{64} +261.489 q^{65} +150.426 q^{66} -74.7083 q^{67} -133.713 q^{68} -391.604 q^{69} +651.864 q^{70} -118.322 q^{71} -9.63496 q^{72} -498.399 q^{73} -474.525 q^{74} +75.0000 q^{75} +371.419 q^{76} -415.584 q^{77} -622.259 q^{78} +106.032 q^{79} +330.433 q^{80} +81.0000 q^{81} -531.988 q^{82} +42.5010 q^{83} -762.301 q^{84} +86.4888 q^{85} -880.911 q^{86} -87.0000 q^{87} -13.5346 q^{88} -161.806 q^{89} -178.475 q^{90} +1719.12 q^{91} -1009.04 q^{92} +589.843 q^{93} -2256.88 q^{94} -240.243 q^{95} -760.627 q^{96} +128.506 q^{97} +2925.19 q^{98} +113.784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) $ 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * q^99

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 $

$2$	3.96612	1.40223	0.701117	−	0.713046i	$-0.252685\pi$
$2$	3.96612	1.40223	0.701117	+	0.713046i	$0.252685\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	7.73008	0.966259
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	11.8983	0.809580
$7$	−32.8717	−1.77490	−0.887451	−	0.460901i	$-0.847526\pi$
$7$	−32.8717	−1.77490	−0.887451	+	0.460901i	$0.847526\pi$
$8$	−1.07055	−0.0473121
$9$	9.00000	0.333333
$10$	−19.8306	−0.627098
$11$	12.6426	0.346536	0.173268	−	0.984875i	$-0.444567\pi$
$11$	12.6426	0.346536	0.173268	+	0.984875i	$0.444567\pi$
$12$	23.1902	0.557870
$13$	−52.2979	−1.11576	−0.557878	−	0.829923i	$-0.688384\pi$
$13$	−52.2979	−1.11576	−0.557878	+	0.829923i	$0.688384\pi$
$14$	−130.373	−2.48883
$15$	−15.0000	−0.258199
$16$	−66.0865	−1.03260
$17$	−17.2978	−0.246784	−0.123392	−	0.992358i	$-0.539377\pi$
$17$	−17.2978	−0.246784	−0.123392	+	0.992358i	$0.539377\pi$
$18$	35.6950	0.467411
$19$	48.0486	0.580163	0.290082	−	0.957002i	$-0.406318\pi$
$19$	48.0486	0.580163	0.290082	+	0.957002i	$0.406318\pi$
$20$	−38.6504	−0.432124
$21$	−98.6150	−1.02474
$22$	50.1421	0.485924
$23$	−130.535	−1.18341	−0.591704	−	0.806156i	$-0.701544\pi$
$23$	−130.535	−1.18341	−0.591704	+	0.806156i	$0.701544\pi$
$24$	−3.21165	−0.0273157
$25$	25.0000	0.200000
$26$	−207.420	−1.56455
$27$	27.0000	0.192450
$28$	−254.100	−1.71502
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−59.4917	−0.362055
$31$	196.614	1.13913	0.569564	−	0.821947i	$-0.307112\pi$
$31$	196.614	1.13913	0.569564	+	0.821947i	$0.307112\pi$
$32$	−253.542	−1.40064
$33$	37.9278	0.200072
$34$	−68.6049	−0.346048
$35$	164.358	0.793761
$36$	69.5707	0.322086
$37$	−119.645	−0.531608	−0.265804	−	0.964027i	$-0.585637\pi$
$37$	−119.645	−0.531608	−0.265804	+	0.964027i	$0.585637\pi$
$38$	190.566	0.813525
$39$	−156.894	−0.644182
$40$	5.35275	0.0211586
$41$	−134.133	−0.510929	−0.255465	−	0.966818i	$-0.582228\pi$
$41$	−134.133	−0.510929	−0.255465	+	0.966818i	$0.582228\pi$
$42$	−391.118	−1.43693
$43$	−222.109	−0.787705	−0.393853	−	0.919174i	$-0.628858\pi$
$43$	−222.109	−0.787705	−0.393853	+	0.919174i	$0.628858\pi$
$44$	97.7283	0.334843
$45$	−45.0000	−0.149071
$46$	−517.716	−1.65941
$47$	−569.042	−1.76603	−0.883013	−	0.469348i	$-0.844489\pi$
$47$	−569.042	−1.76603	−0.883013	+	0.469348i	$0.844489\pi$
$48$	−198.260	−0.596173
$49$	737.546	2.15028
$50$	99.1529	0.280447
$51$	−51.8933	−0.142481
$52$	−404.267	−1.07811
$53$	393.464	1.01974	0.509872	−	0.860250i	$-0.329693\pi$
$53$	393.464	1.01974	0.509872	+	0.860250i	$0.329693\pi$
$54$	107.085	0.269860
$55$	−63.2131	−0.154975
$56$	35.1908	0.0839744
$57$	144.146	0.334957
$58$	−115.017	−0.260388
$59$	741.684	1.63659	0.818297	−	0.574795i	$-0.194918\pi$
$59$	741.684	1.63659	0.818297	+	0.574795i	$0.194918\pi$
$60$	−115.951	−0.249487
$61$	758.295	1.59163	0.795817	−	0.605537i	$-0.207042\pi$
$61$	758.295	1.59163	0.795817	+	0.605537i	$0.207042\pi$
$62$	779.796	1.59732
$63$	−295.845	−0.591634
$64$	−476.886	−0.931419
$65$	261.489	0.498981
$66$	150.426	0.280548
$67$	−74.7083	−0.136225	−0.0681125	−	0.997678i	$-0.521698\pi$
$67$	−74.7083	−0.136225	−0.0681125	+	0.997678i	$0.521698\pi$
$68$	−133.713	−0.238457
$69$	−391.604	−0.683240
$70$	651.864	1.11304
$71$	−118.322	−0.197779	−0.0988893	−	0.995098i	$-0.531529\pi$
$71$	−118.322	−0.197779	−0.0988893	+	0.995098i	$0.531529\pi$
$72$	−9.63496	−0.0157707
$73$	−498.399	−0.799084	−0.399542	−	0.916715i	$-0.630831\pi$
$73$	−498.399	−0.799084	−0.399542	+	0.916715i	$0.630831\pi$
$74$	−474.525	−0.745438
$75$	75.0000	0.115470
$76$	371.419	0.560588
$77$	−415.584	−0.615067
$78$	−622.259	−0.903294
$79$	106.032	0.151007	0.0755037	−	0.997146i	$-0.475944\pi$
$79$	106.032	0.151007	0.0755037	+	0.997146i	$0.475944\pi$
$80$	330.433	0.461794
$81$	81.0000	0.111111
$82$	−531.988	−0.716442
$83$	42.5010	0.0562059	0.0281030	−	0.999605i	$-0.491053\pi$
$83$	42.5010	0.0562059	0.0281030	+	0.999605i	$0.491053\pi$
$84$	−762.301	−0.990165
$85$	86.4888	0.110365
$86$	−880.911	−1.10455
$87$	−87.0000	−0.107211
$88$	−13.5346	−0.0163953
$89$	−161.806	−0.192713	−0.0963564	−	0.995347i	$-0.530719\pi$
$89$	−161.806	−0.192713	−0.0963564	+	0.995347i	$0.530719\pi$
$90$	−178.475	−0.209033
$91$	1719.12	1.98036
$92$	−1009.04	−1.14348
$93$	589.843	0.657676
$94$	−2256.88	−2.47638
$95$	−240.243	−0.259457
$96$	−760.627	−0.808658
$97$	128.506	0.134514	0.0672569	−	0.997736i	$-0.478575\pi$
$97$	128.506	0.134514	0.0672569	+	0.997736i	$0.478575\pi$
$98$	2925.19	3.01519
$99$	113.784	0.115512
$100$	193.252	0.193252
$101$	−584.973	−0.576307	−0.288153	−	0.957584i	$-0.593041\pi$
$101$	−584.973	−0.576307	−0.288153	+	0.957584i	$0.593041\pi$
$102$	−205.815	−0.199791
$103$	−1908.33	−1.82557	−0.912783	−	0.408446i	$-0.866071\pi$
$103$	−1908.33	−1.82557	−0.912783	+	0.408446i	$0.866071\pi$
$104$	55.9876	0.0527888
$105$	493.075	0.458278
$106$	1560.52	1.42992
$107$	646.934	0.584500	0.292250	−	0.956342i	$-0.405596\pi$
$107$	646.934	0.584500	0.292250	+	0.956342i	$0.405596\pi$
$108$	208.712	0.185957
$109$	−1065.19	−0.936028	−0.468014	−	0.883721i	$-0.655030\pi$
$109$	−1065.19	−0.936028	−0.468014	+	0.883721i	$0.655030\pi$
$110$	−250.710	−0.217312
$111$	−358.934	−0.306924
$112$	2172.37	1.83277
$113$	−1368.69	−1.13943	−0.569713	−	0.821844i	$-0.692946\pi$
$113$	−1368.69	−1.13943	−0.569713	+	0.821844i	$0.692946\pi$
$114$	571.699	0.469689
$115$	652.673	0.529236
$116$	−224.172	−0.179430
$117$	−470.681	−0.371919
$118$	2941.61	2.29489
$119$	568.606	0.438017
$120$	16.0583	0.0122159
$121$	−1171.16	−0.879913
$122$	3007.49	2.23184
$123$	−402.400	−0.294985
$124$	1519.84	1.10069
$125$	−125.000	−0.0894427
$126$	−1173.36	−0.829610
$127$	2118.32	1.48008	0.740040	−	0.672562i	$-0.234806\pi$
$127$	2118.32	1.48008	0.740040	+	0.672562i	$0.234806\pi$
$128$	136.953	0.0945704
$129$	−666.327	−0.454782
$130$	1037.10	0.699688
$131$	−2446.56	−1.63173	−0.815866	−	0.578241i	$-0.803740\pi$
$131$	−2446.56	−1.63173	−0.815866	+	0.578241i	$0.803740\pi$
$132$	293.185	0.193322
$133$	−1579.44	−1.02973
$134$	−296.302	−0.191019
$135$	−135.000	−0.0860663
$136$	18.5181	0.0116759
$137$	1586.44	0.989331	0.494665	−	0.869084i	$-0.335291\pi$
$137$	1586.44	0.989331	0.494665	+	0.869084i	$0.335291\pi$
$138$	−1553.15	−0.958063
$139$	1793.32	1.09430	0.547150	−	0.837034i	$-0.315713\pi$
$139$	1793.32	1.09430	0.547150	+	0.837034i	$0.315713\pi$
$140$	1270.50	0.766979
$141$	−1707.12	−1.01962
$142$	−469.280	−0.277332
$143$	−661.182	−0.386649
$144$	−594.779	−0.344201
$145$	145.000	0.0830455
$146$	−1976.71	−1.12050
$147$	2212.64	1.24146
$148$	−924.863	−0.513671
$149$	−2640.05	−1.45155	−0.725777	−	0.687930i	$-0.758520\pi$
$149$	−2640.05	−1.45155	−0.725777	+	0.687930i	$0.758520\pi$
$150$	297.459	0.161916
$151$	1132.79	0.610498	0.305249	−	0.952273i	$-0.401260\pi$
$151$	1132.79	0.610498	0.305249	+	0.952273i	$0.401260\pi$
$152$	−51.4385	−0.0274487
$153$	−155.680	−0.0822612
$154$	−1648.25	−0.862468
$155$	−983.072	−0.509434
$156$	−1212.80	−0.622447
$157$	912.652	0.463933	0.231967	−	0.972724i	$-0.425484\pi$
$157$	912.652	0.463933	0.231967	+	0.972724i	$0.425484\pi$
$158$	420.537	0.211748
$159$	1180.39	0.588750
$160$	1267.71	0.626384
$161$	4290.89	2.10043
$162$	321.255	0.155804
$163$	−2303.83	−1.10705	−0.553527	−	0.832831i	$-0.686718\pi$
$163$	−2303.83	−1.10705	−0.553527	+	0.832831i	$0.686718\pi$
$164$	−1036.86	−0.493690
$165$	−189.639	−0.0894751
$166$	168.564	0.0788138
$167$	381.558	0.176801	0.0884006	−	0.996085i	$-0.471824\pi$
$167$	381.558	0.176801	0.0884006	+	0.996085i	$0.471824\pi$
$168$	105.572	0.0484826
$169$	538.070	0.244911
$170$	343.025	0.154758
$171$	432.437	0.193388
$172$	−1716.92	−0.761128
$173$	−2697.02	−1.18526	−0.592631	−	0.805474i	$-0.701911\pi$
$173$	−2697.02	−1.18526	−0.592631	+	0.805474i	$0.701911\pi$
$174$	−345.052	−0.150335
$175$	−821.791	−0.354981
$176$	−835.506	−0.357833
$177$	2225.05	0.944888
$178$	−641.742	−0.270228
$179$	30.7370	0.0128346	0.00641729	−	0.999979i	$-0.497957\pi$
$179$	30.7370	0.0128346	0.00641729	+	0.999979i	$0.497957\pi$
$180$	−347.853	−0.144041
$181$	159.556	0.0655231	0.0327615	−	0.999463i	$-0.489570\pi$
$181$	159.556	0.0655231	0.0327615	+	0.999463i	$0.489570\pi$
$182$	6818.22	2.77692
$183$	2274.88	0.918931
$184$	139.744	0.0559895
$185$	598.224	0.237742
$186$	2339.39	0.922216
$187$	−218.689	−0.0855193
$188$	−4398.73	−1.70644
$189$	−887.535	−0.341580
$190$	−952.831	−0.363819
$191$	96.7632	0.0366573	0.0183286	−	0.999832i	$-0.494165\pi$
$191$	96.7632	0.0366573	0.0183286	+	0.999832i	$0.494165\pi$
$192$	−1430.66	−0.537755
$193$	1017.92	0.379646	0.189823	−	0.981818i	$-0.439209\pi$
$193$	1017.92	0.379646	0.189823	+	0.981818i	$0.439209\pi$
$194$	509.671	0.188620
$195$	784.468	0.288087
$196$	5701.29	2.07773
$197$	5012.65	1.81288	0.906438	−	0.422339i	$-0.138791\pi$
$197$	5012.65	1.81288	0.906438	+	0.422339i	$0.138791\pi$
$198$	451.279	0.161975
$199$	−4339.56	−1.54585	−0.772924	−	0.634499i	$-0.781206\pi$
$199$	−4339.56	−1.54585	−0.772924	+	0.634499i	$0.781206\pi$
$200$	−26.7638	−0.00946242
$201$	−224.125	−0.0786495
$202$	−2320.07	−0.808116
$203$	953.278	0.329591
$204$	−401.139	−0.137673
$205$	670.666	0.228494
$206$	−7568.65	−2.55987
$207$	−1174.81	−0.394469
$208$	3456.19	1.15213
$209$	607.460	0.201047
$210$	1955.59	0.642613
$211$	−2360.56	−0.770180	−0.385090	−	0.922879i	$-0.625830\pi$
$211$	−2360.56	−0.770180	−0.385090	+	0.922879i	$0.625830\pi$
$212$	3041.51	0.985338
$213$	−354.967	−0.114188
$214$	2565.82	0.819605
$215$	1110.55	0.352273
$216$	−28.9049	−0.00910522
$217$	−6463.04	−2.02184
$218$	−4224.68	−1.31253
$219$	−1495.20	−0.461352
$220$	−488.642	−0.149746
$221$	904.636	0.275350
$222$	−1423.58	−0.430379
$223$	−6063.08	−1.82069	−0.910345	−	0.413851i	$-0.864184\pi$
$223$	−6063.08	−1.82069	−0.910345	+	0.413851i	$0.864184\pi$
$224$	8334.36	2.48600
$225$	225.000	0.0666667
$226$	−5428.37	−1.59774
$227$	4428.61	1.29488	0.647438	−	0.762118i	$-0.275840\pi$
$227$	4428.61	1.29488	0.647438	+	0.762118i	$0.275840\pi$
$228$	1114.26	0.323656
$229$	−4517.28	−1.30354	−0.651768	−	0.758418i	$-0.725973\pi$
$229$	−4517.28	−1.30354	−0.651768	+	0.758418i	$0.725973\pi$
$230$	2588.58	0.742112
$231$	−1246.75	−0.355109
$232$	31.0460	0.00878564
$233$	4051.13	1.13905	0.569525	−	0.821974i	$-0.307127\pi$
$233$	4051.13	1.13905	0.569525	+	0.821974i	$0.307127\pi$
$234$	−1866.78	−0.521517
$235$	2845.21	0.789791
$236$	5733.28	1.58138
$237$	318.097	0.0871841
$238$	2255.16	0.614202
$239$	837.357	0.226628	0.113314	−	0.993559i	$-0.463853\pi$
$239$	837.357	0.226628	0.113314	+	0.993559i	$0.463853\pi$
$240$	991.298	0.266617
$241$	−2011.23	−0.537571	−0.268785	−	0.963200i	$-0.586622\pi$
$241$	−2011.23	−0.537571	−0.268785	+	0.963200i	$0.586622\pi$
$242$	−4644.97	−1.23384
$243$	243.000	0.0641500
$244$	5861.68	1.53793
$245$	−3687.73	−0.961634
$246$	−1595.96	−0.413638
$247$	−2512.84	−0.647321
$248$	−210.486	−0.0538946
$249$	127.503	0.0324505
$250$	−495.764	−0.125420
$251$	6458.29	1.62408	0.812039	−	0.583603i	$-0.198358\pi$
$251$	6458.29	1.62408	0.812039	+	0.583603i	$0.198358\pi$
$252$	−2286.90	−0.571672
$253$	−1650.30	−0.410093
$254$	8401.49	2.07542
$255$	259.466	0.0637193
$256$	4358.26	1.06403
$257$	1838.15	0.446150	0.223075	−	0.974801i	$-0.428390\pi$
$257$	1838.15	0.446150	0.223075	+	0.974801i	$0.428390\pi$
$258$	−2642.73	−0.637711
$259$	3932.92	0.943552
$260$	2021.33	0.482145
$261$	−261.000	−0.0618984
$262$	−9703.34	−2.28807
$263$	2263.00	0.530580	0.265290	−	0.964169i	$-0.414532\pi$
$263$	2263.00	0.530580	0.265290	+	0.964169i	$0.414532\pi$
$264$	−40.6037	−0.00946585
$265$	−1967.32	−0.456044
$266$	−6264.23	−1.44393
$267$	−485.419	−0.111263
$268$	−577.501	−0.131629
$269$	632.951	0.143464	0.0717318	−	0.997424i	$-0.477147\pi$
$269$	632.951	0.143464	0.0717318	+	0.997424i	$0.477147\pi$
$270$	−535.426	−0.120685
$271$	−987.158	−0.221275	−0.110638	−	0.993861i	$-0.535289\pi$
$271$	−987.158	−0.221275	−0.110638	+	0.993861i	$0.535289\pi$
$272$	1143.15	0.254829
$273$	5157.36	1.14336
$274$	6291.99	1.38727
$275$	316.065	0.0693071
$276$	−3027.13	−0.660187
$277$	8123.34	1.76204	0.881018	−	0.473083i	$-0.156859\pi$
$277$	8123.34	1.76204	0.881018	+	0.473083i	$0.156859\pi$
$278$	7112.53	1.53447
$279$	1769.53	0.379710
$280$	−175.954	−0.0375545
$281$	−5075.60	−1.07753	−0.538764	−	0.842457i	$-0.681108\pi$
$281$	−5075.60	−1.07753	−0.538764	+	0.842457i	$0.681108\pi$
$282$	−6770.65	−1.42974
$283$	−2077.30	−0.436335	−0.218168	−	0.975911i	$-0.570008\pi$
$283$	−2077.30	−0.436335	−0.218168	+	0.975911i	$0.570008\pi$
$284$	−914.641	−0.191105
$285$	−720.729	−0.149798
$286$	−2622.32	−0.542172
$287$	4409.18	0.906849
$288$	−2281.88	−0.466879
$289$	−4613.79	−0.939098
$290$	575.087	0.116449
$291$	385.519	0.0776615
$292$	−3852.66	−0.772123
$293$	−4097.60	−0.817011	−0.408505	−	0.912756i	$-0.633950\pi$
$293$	−4097.60	−0.817011	−0.408505	+	0.912756i	$0.633950\pi$
$294$	8775.58	1.74082
$295$	−3708.42	−0.731907
$296$	128.086	0.0251515
$297$	341.351	0.0666908
$298$	−10470.8	−2.03542
$299$	6826.69	1.32039
$300$	579.756	0.111574
$301$	7301.10	1.39810
$302$	4492.78	0.856061
$303$	−1754.92	−0.332731
$304$	−3175.36	−0.599078
$305$	−3791.47	−0.711801
$306$	−617.444	−0.115349
$307$	2800.27	0.520586	0.260293	−	0.965530i	$-0.416181\pi$
$307$	2800.27	0.520586	0.260293	+	0.965530i	$0.416181\pi$
$308$	−3212.49	−0.594314
$309$	−5724.99	−1.05399
$310$	−3898.98	−0.714345
$311$	−1007.23	−0.183649	−0.0918247	−	0.995775i	$-0.529270\pi$
$311$	−1007.23	−0.183649	−0.0918247	+	0.995775i	$0.529270\pi$
$312$	167.963	0.0304776
$313$	−8540.20	−1.54224	−0.771119	−	0.636691i	$-0.780303\pi$
$313$	−8540.20	−1.54224	−0.771119	+	0.636691i	$0.780303\pi$
$314$	3619.68	0.650543
$315$	1479.22	0.264587
$316$	819.639	0.145912
$317$	−6756.75	−1.19715	−0.598575	−	0.801067i	$-0.704266\pi$
$317$	−6756.75	−1.19715	−0.598575	+	0.801067i	$0.704266\pi$
$318$	4681.57	0.825565
$319$	−366.636	−0.0643500
$320$	2384.43	0.416543
$321$	1940.80	0.337461
$322$	17018.2	2.94530
$323$	−831.133	−0.143175
$324$	626.136	0.107362
$325$	−1307.45	−0.223151
$326$	−9137.25	−1.55235
$327$	−3195.58	−0.540416
$328$	143.596	0.0241731
$329$	18705.3	3.13453
$330$	−752.131	−0.125465
$331$	−2186.58	−0.363097	−0.181548	−	0.983382i	$-0.558111\pi$
$331$	−2186.58	−0.363097	−0.181548	+	0.983382i	$0.558111\pi$
$332$	328.536	0.0543095
$333$	−1076.80	−0.177203
$334$	1513.30	0.247917
$335$	373.542	0.0609217
$336$	6517.12	1.05815
$337$	5592.65	0.904010	0.452005	−	0.892016i	$-0.350709\pi$
$337$	5592.65	0.904010	0.452005	+	0.892016i	$0.350709\pi$
$338$	2134.05	0.343423
$339$	−4106.06	−0.657848
$340$	668.565	0.106641
$341$	2485.72	0.394749
$342$	1715.10	0.271175
$343$	−12969.4	−2.04163
$344$	237.779	0.0372680
$345$	1958.02	0.305554
$346$	−10696.7	−1.66201
$347$	3744.53	0.579300	0.289650	−	0.957133i	$-0.406461\pi$
$347$	3744.53	0.579300	0.289650	+	0.957133i	$0.406461\pi$
$348$	−672.517	−0.103594
$349$	−11200.7	−1.71794	−0.858970	−	0.512025i	$-0.828895\pi$
$349$	−11200.7	−1.71794	−0.858970	+	0.512025i	$0.828895\pi$
$350$	−3259.32	−0.497766
$351$	−1412.04	−0.214727
$352$	−3205.44	−0.485371
$353$	1695.02	0.255572	0.127786	−	0.991802i	$-0.459213\pi$
$353$	1695.02	0.255572	0.127786	+	0.991802i	$0.459213\pi$
$354$	8824.82	1.32495
$355$	591.612	0.0884493
$356$	−1250.77	−0.186210
$357$	1705.82	0.252889
$358$	121.907	0.0179971
$359$	−331.341	−0.0487117	−0.0243559	−	0.999703i	$-0.507753\pi$
$359$	−331.341	−0.0487117	−0.0243559	+	0.999703i	$0.507753\pi$
$360$	48.1748	0.00705287
$361$	−4550.33	−0.663411
$362$	632.816	0.0918787
$363$	−3513.49	−0.508018
$364$	13288.9	1.91354
$365$	2491.99	0.357361
$366$	9022.46	1.28856
$367$	−11394.1	−1.62061	−0.810306	−	0.586006i	$-0.800699\pi$
$367$	−11394.1	−1.62061	−0.810306	+	0.586006i	$0.800699\pi$
$368$	8626.58	1.22199
$369$	−1207.20	−0.170310
$370$	2372.63	0.333370
$371$	−12933.8	−1.80995
$372$	4559.53	0.635486
$373$	6042.53	0.838794	0.419397	−	0.907803i	$-0.362241\pi$
$373$	6042.53	0.838794	0.419397	+	0.907803i	$0.362241\pi$
$374$	−867.345	−0.119918
$375$	−375.000	−0.0516398
$376$	609.188	0.0835544
$377$	1516.64	0.207191
$378$	−3520.07	−0.478975
$379$	3446.58	0.467121	0.233560	−	0.972342i	$-0.424962\pi$
$379$	3446.58	0.467121	0.233560	+	0.972342i	$0.424962\pi$
$380$	−1857.10	−0.250703
$381$	6354.95	0.854525
$382$	383.774	0.0514021
$383$	6068.80	0.809664	0.404832	−	0.914391i	$-0.367330\pi$
$383$	6068.80	0.809664	0.404832	+	0.914391i	$0.367330\pi$
$384$	410.858	0.0546002
$385$	2077.92	0.275066
$386$	4037.20	0.532352
$387$	−1998.98	−0.262568
$388$	993.363	0.129975
$389$	−4788.36	−0.624112	−0.312056	−	0.950064i	$-0.601018\pi$
$389$	−4788.36	−0.624112	−0.312056	+	0.950064i	$0.601018\pi$
$390$	3111.29	0.403965
$391$	2257.96	0.292046
$392$	−789.580	−0.101734
$393$	−7339.68	−0.942081
$394$	19880.8	2.54208
$395$	−530.162	−0.0675325
$396$	879.555	0.111614
$397$	206.388	0.0260914	0.0130457	−	0.999915i	$-0.495847\pi$
$397$	206.388	0.0260914	0.0130457	+	0.999915i	$0.495847\pi$
$398$	−17211.2	−2.16764
$399$	−4738.31	−0.594517
$400$	−1652.16	−0.206520
$401$	−10080.5	−1.25535	−0.627675	−	0.778475i	$-0.715993\pi$
$401$	−10080.5	−1.25535	−0.627675	+	0.778475i	$0.715993\pi$
$402$	−888.906	−0.110285
$403$	−10282.5	−1.27099
$404$	−4521.88	−0.556862
$405$	−405.000	−0.0496904
$406$	3780.81	0.462164
$407$	−1512.62	−0.184221
$408$	55.5544	0.00674106
$409$	15178.0	1.83497	0.917486	−	0.397769i	$-0.130215\pi$
$409$	15178.0	1.83497	0.917486	+	0.397769i	$0.130215\pi$
$410$	2659.94	0.320403
$411$	4759.31	0.571190
$412$	−14751.5	−1.76397
$413$	−24380.4	−2.90480
$414$	−4659.44	−0.553138
$415$	−212.505	−0.0251360
$416$	13259.7	1.56277
$417$	5379.97	0.631795
$418$	2409.26	0.281915
$419$	−6104.30	−0.711729	−0.355864	−	0.934538i	$-0.615814\pi$
$419$	−6104.30	−0.711729	−0.355864	+	0.934538i	$0.615814\pi$
$420$	3811.51	0.442815
$421$	8543.56	0.989045	0.494522	−	0.869165i	$-0.335343\pi$
$421$	8543.56	0.989045	0.494522	+	0.869165i	$0.335343\pi$
$422$	−9362.27	−1.07997
$423$	−5121.37	−0.588675
$424$	−421.223	−0.0482463
$425$	−432.444	−0.0493567
$426$	−1407.84	−0.160118
$427$	−24926.4	−2.82500
$428$	5000.85	0.564778
$429$	−1983.55	−0.223232
$430$	4404.55	0.493968
$431$	−7712.54	−0.861949	−0.430975	−	0.902364i	$-0.641830\pi$
$431$	−7712.54	−0.861949	−0.430975	+	0.902364i	$0.641830\pi$
$432$	−1784.34	−0.198724
$433$	−13294.5	−1.47551	−0.737753	−	0.675071i	$-0.764113\pi$
$433$	−13294.5	−1.47551	−0.737753	+	0.675071i	$0.764113\pi$
$434$	−25633.2	−2.83510
$435$	435.000	0.0479463
$436$	−8234.03	−0.904446
$437$	−6272.01	−0.686569
$438$	−5930.12	−0.646923
$439$	−18032.6	−1.96048	−0.980239	−	0.197816i	$-0.936615\pi$
$439$	−18032.6	−1.96048	−0.980239	+	0.197816i	$0.936615\pi$
$440$	67.6728	0.00733221
$441$	6637.91	0.716760
$442$	3587.89	0.386106
$443$	16475.7	1.76700	0.883502	−	0.468427i	$-0.155179\pi$
$443$	16475.7	1.76700	0.883502	+	0.468427i	$0.155179\pi$
$444$	−2774.59	−0.296568
$445$	809.031	0.0861837
$446$	−24046.9	−2.55303
$447$	−7920.16	−0.838055
$448$	15676.1	1.65318
$449$	−2651.74	−0.278716	−0.139358	−	0.990242i	$-0.544504\pi$
$449$	−2651.74	−0.278716	−0.139358	+	0.990242i	$0.544504\pi$
$450$	892.376	0.0934822
$451$	−1695.79	−0.177055
$452$	−10580.0	−1.10098
$453$	3398.37	0.352471
$454$	17564.4	1.81572
$455$	−8595.59	−0.885643
$456$	−154.315	−0.0158475
$457$	−582.597	−0.0596340	−0.0298170	−	0.999555i	$-0.509492\pi$
$457$	−582.597	−0.0596340	−0.0298170	+	0.999555i	$0.509492\pi$
$458$	−17916.0	−1.82786
$459$	−467.040	−0.0474935
$460$	5045.21	0.511379
$461$	−6537.72	−0.660504	−0.330252	−	0.943893i	$-0.607134\pi$
$461$	−6537.72	−0.660504	−0.330252	+	0.943893i	$0.607134\pi$
$462$	−4944.76	−0.497946
$463$	−11895.3	−1.19400	−0.596998	−	0.802243i	$-0.703640\pi$
$463$	−11895.3	−1.19400	−0.596998	+	0.802243i	$0.703640\pi$
$464$	1916.51	0.191749
$465$	−2949.22	−0.294122
$466$	16067.3	1.59721
$467$	−14742.5	−1.46081	−0.730406	−	0.683013i	$-0.760669\pi$
$467$	−14742.5	−1.46081	−0.730406	+	0.683013i	$0.760669\pi$
$468$	−3638.40	−0.359370
$469$	2455.79	0.241786
$470$	11284.4	1.10747
$471$	2737.96	0.267852
$472$	−794.011	−0.0774307
$473$	−2808.04	−0.272968
$474$	1261.61	0.122253
$475$	1201.21	0.116033
$476$	4395.37	0.423238
$477$	3541.18	0.339915
$478$	3321.06	0.317786
$479$	5864.41	0.559398	0.279699	−	0.960088i	$-0.409765\pi$
$479$	5864.41	0.559398	0.279699	+	0.960088i	$0.409765\pi$
$480$	3803.14	0.361643
$481$	6257.17	0.593144
$482$	−7976.76	−0.753800
$483$	12872.7	1.21269
$484$	−9053.19	−0.850224
$485$	−642.531	−0.0601564
$486$	963.766	0.0899533
$487$	−15495.7	−1.44184	−0.720920	−	0.693018i	$-0.756281\pi$
$487$	−15495.7	−1.44184	−0.720920	+	0.693018i	$0.756281\pi$
$488$	−811.793	−0.0753036
$489$	−6911.49	−0.639158
$490$	−14626.0	−1.34844
$491$	951.715	0.0874751	0.0437376	−	0.999043i	$-0.486073\pi$
$491$	951.715	0.0874751	0.0437376	+	0.999043i	$0.486073\pi$
$492$	−3110.58	−0.285032
$493$	501.635	0.0458266
$494$	−9966.22	−0.907695
$495$	−568.918	−0.0516585
$496$	−12993.6	−1.17627
$497$	3889.45	0.351038
$498$	505.692	0.0455032
$499$	12667.6	1.13643	0.568216	−	0.822880i	$-0.307634\pi$
$499$	12667.6	1.13643	0.568216	+	0.822880i	$0.307634\pi$
$500$	−966.259	−0.0864249
$501$	1144.67	0.102076
$502$	25614.3	2.27734
$503$	17478.7	1.54938	0.774690	−	0.632341i	$-0.217906\pi$
$503$	17478.7	1.54938	0.774690	+	0.632341i	$0.217906\pi$
$504$	316.717	0.0279915
$505$	2924.86	0.257732
$506$	−6545.28	−0.575046
$507$	1614.21	0.141399
$508$	16374.8	1.43014
$509$	11463.1	0.998219	0.499110	−	0.866539i	$-0.333661\pi$
$509$	11463.1	0.998219	0.499110	+	0.866539i	$0.333661\pi$
$510$	1029.07	0.0893493
$511$	16383.2	1.41830
$512$	16189.8	1.39745
$513$	1297.31	0.111652
$514$	7290.32	0.625607
$515$	9541.64	0.816418
$516$	−5150.76	−0.439437
$517$	−7194.17	−0.611991
$518$	15598.4	1.32308
$519$	−8091.05	−0.684312
$520$	−279.938	−0.0236079
$521$	13465.1	1.13228	0.566141	−	0.824309i	$-0.308436\pi$
$521$	13465.1	1.13228	0.566141	+	0.824309i	$0.308436\pi$
$522$	−1035.16	−0.0867961
$523$	19829.8	1.65793	0.828963	−	0.559303i	$-0.188931\pi$
$523$	19829.8	1.65793	0.828963	+	0.559303i	$0.188931\pi$
$524$	−18912.1	−1.57668
$525$	−2465.37	−0.204948
$526$	8975.32	0.743997
$527$	−3400.99	−0.281118
$528$	−2506.52	−0.206595
$529$	4872.30	0.400452
$530$	−7802.62	−0.639480
$531$	6675.16	0.545532
$532$	−12209.2	−0.994990
$533$	7014.89	0.570072
$534$	−1925.23	−0.156016
$535$	−3234.67	−0.261396
$536$	79.9790	0.00644509
$537$	92.2110	0.00741005
$538$	2510.36	0.201170
$539$	9324.51	0.745148
$540$	−1043.56	−0.0831624
$541$	−8464.80	−0.672699	−0.336349	−	0.941737i	$-0.609192\pi$
$541$	−8464.80	−0.672699	−0.336349	+	0.941737i	$0.609192\pi$
$542$	−3915.18	−0.310280
$543$	478.667	0.0378298
$544$	4385.72	0.345654
$545$	5325.97	0.418605
$546$	20454.7	1.60326
$547$	7649.90	0.597964	0.298982	−	0.954259i	$-0.403353\pi$
$547$	7649.90	0.597964	0.298982	+	0.954259i	$0.403353\pi$
$548$	12263.3	0.955950
$549$	6824.65	0.530545
$550$	1253.55	0.0971848
$551$	−1393.41	−0.107734
$552$	419.232	0.0323255
$553$	−3485.46	−0.268023
$554$	32218.1	2.47079
$555$	1794.67	0.137261
$556$	13862.5	1.05738
$557$	6293.95	0.478785	0.239393	−	0.970923i	$-0.423052\pi$
$557$	6293.95	0.478785	0.239393	+	0.970923i	$0.423052\pi$
$558$	7018.16	0.532442
$559$	11615.8	0.878887
$560$	−10861.9	−0.819639
$561$	−656.067	−0.0493746
$562$	−20130.4	−1.51095
$563$	−4688.80	−0.350993	−0.175497	−	0.984480i	$-0.556153\pi$
$563$	−4688.80	−0.350993	−0.175497	+	0.984480i	$0.556153\pi$
$564$	−13196.2	−0.985213
$565$	6843.43	0.509567
$566$	−8238.83	−0.611844
$567$	−2662.60	−0.197211
$568$	126.670	0.00935732
$569$	−20371.9	−1.50094	−0.750470	−	0.660904i	$-0.770173\pi$
$569$	−20371.9	−1.50094	−0.750470	+	0.660904i	$0.770173\pi$
$570$	−2858.49	−0.210051
$571$	−5658.25	−0.414694	−0.207347	−	0.978267i	$-0.566483\pi$
$571$	−5658.25	−0.414694	−0.207347	+	0.978267i	$0.566483\pi$
$572$	−5110.99	−0.373603
$573$	290.290	0.0211641
$574$	17487.3	1.27161
$575$	−3263.37	−0.236681
$576$	−4291.98	−0.310473
$577$	809.648	0.0584161	0.0292081	−	0.999573i	$-0.490701\pi$
$577$	809.648	0.0584161	0.0292081	+	0.999573i	$0.490701\pi$
$578$	−18298.8	−1.31683
$579$	3053.77	0.219189
$580$	1120.86	0.0802435
$581$	−1397.08	−0.0997600
$582$	1529.01	0.108900
$583$	4974.42	0.353378
$584$	533.561	0.0378064
$585$	2353.41	0.166327
$586$	−16251.5	−1.14564
$587$	9794.78	0.688712	0.344356	−	0.938839i	$-0.388097\pi$
$587$	9794.78	0.688712	0.344356	+	0.938839i	$0.388097\pi$
$588$	17103.9	1.19958
$589$	9447.05	0.660881
$590$	−14708.0	−1.02631
$591$	15038.0	1.04666
$592$	7906.91	0.548939
$593$	−19668.3	−1.36202	−0.681011	−	0.732273i	$-0.738459\pi$
$593$	−19668.3	−1.36202	−0.681011	+	0.732273i	$0.738459\pi$
$594$	1353.84	0.0935161
$595$	−2843.03	−0.195887
$596$	−20407.8	−1.40258
$597$	−13018.7	−0.892495
$598$	27075.4	1.85150
$599$	3461.98	0.236148	0.118074	−	0.993005i	$-0.462328\pi$
$599$	3461.98	0.236148	0.118074	+	0.993005i	$0.462328\pi$
$600$	−80.2913	−0.00546313
$601$	1598.93	0.108522	0.0542611	−	0.998527i	$-0.482720\pi$
$601$	1598.93	0.108522	0.0542611	+	0.998527i	$0.482720\pi$
$602$	28957.0	1.96046
$603$	−672.375	−0.0454083
$604$	8756.56	0.589900
$605$	5855.82	0.393509
$606$	−6960.21	−0.466566
$607$	−9756.63	−0.652405	−0.326202	−	0.945300i	$-0.605769\pi$
$607$	−9756.63	−0.652405	−0.326202	+	0.945300i	$0.605769\pi$
$608$	−12182.4	−0.812598
$609$	2859.83	0.190290
$610$	−15037.4	−0.998111
$611$	29759.7	1.97045
$612$	−1203.42	−0.0794857
$613$	−1209.23	−0.0796744	−0.0398372	−	0.999206i	$-0.512684\pi$
$613$	−1209.23	−0.0796744	−0.0398372	+	0.999206i	$0.512684\pi$
$614$	11106.2	0.729984
$615$	2012.00	0.131921
$616$	444.903	0.0291001
$617$	12543.6	0.818456	0.409228	−	0.912432i	$-0.365798\pi$
$617$	12543.6	0.818456	0.409228	+	0.912432i	$0.365798\pi$
$618$	−22706.0	−1.47794
$619$	11124.6	0.722353	0.361176	−	0.932498i	$-0.382375\pi$
$619$	11124.6	0.722353	0.361176	+	0.932498i	$0.382375\pi$
$620$	−7599.22	−0.492245
$621$	−3524.44	−0.227747
$622$	−3994.80	−0.257519
$623$	5318.84	0.342046
$624$	10368.6	0.665184
$625$	625.000	0.0400000
$626$	−33871.4	−2.16258
$627$	1822.38	0.116075
$628$	7054.87	0.448280
$629$	2069.59	0.131192
$630$	5866.78	0.371013
$631$	5229.61	0.329932	0.164966	−	0.986299i	$-0.447249\pi$
$631$	5229.61	0.329932	0.164966	+	0.986299i	$0.447249\pi$
$632$	−113.513	−0.00714447
$633$	−7081.69	−0.444663
$634$	−26798.0	−1.67868
$635$	−10591.6	−0.661912
$636$	9124.53	0.568885
$637$	−38572.1	−2.39919
$638$	−1454.12	−0.0902338
$639$	−1064.90	−0.0659262
$640$	−684.763	−0.0422931
$641$	8390.44	0.517008	0.258504	−	0.966010i	$-0.416770\pi$
$641$	8390.44	0.517008	0.258504	+	0.966010i	$0.416770\pi$
$642$	7697.45	0.473199
$643$	25647.2	1.57298	0.786490	−	0.617602i	$-0.211896\pi$
$643$	25647.2	1.57298	0.786490	+	0.617602i	$0.211896\pi$
$644$	33168.9	2.02956
$645$	3331.64	0.203385
$646$	−3296.37	−0.200765
$647$	24363.6	1.48042	0.740210	−	0.672376i	$-0.234726\pi$
$647$	24363.6	1.48042	0.740210	+	0.672376i	$0.234726\pi$
$648$	−86.7146	−0.00525690
$649$	9376.83	0.567138
$650$	−5185.49	−0.312910
$651$	−19389.1	−1.16731
$652$	−17808.8	−1.06970
$653$	−20699.7	−1.24049	−0.620246	−	0.784407i	$-0.712967\pi$
$653$	−20699.7	−1.24049	−0.620246	+	0.784407i	$0.712967\pi$
$654$	−12674.1	−0.757790
$655$	12232.8	0.729733
$656$	8864.40	0.527586
$657$	−4485.59	−0.266361
$658$	74187.5	4.39534
$659$	18977.9	1.12181	0.560905	−	0.827880i	$-0.310453\pi$
$659$	18977.9	1.12181	0.560905	+	0.827880i	$0.310453\pi$
$660$	−1465.93	−0.0864562
$661$	19769.9	1.16333	0.581665	−	0.813428i	$-0.302401\pi$
$661$	19769.9	1.16333	0.581665	+	0.813428i	$0.302401\pi$
$662$	−8672.21	−0.509147
$663$	2713.91	0.158974
$664$	−45.4995	−0.00265922
$665$	7897.18	0.460511
$666$	−4270.73	−0.248479
$667$	3785.51	0.219753
$668$	2949.47	0.170836
$669$	−18189.2	−1.05118
$670$	1481.51	0.0854264
$671$	9586.83	0.551558
$672$	25003.1	1.43529
$673$	5776.20	0.330841	0.165420	−	0.986223i	$-0.447102\pi$
$673$	5776.20	0.330841	0.165420	+	0.986223i	$0.447102\pi$
$674$	22181.1	1.26763
$675$	675.000	0.0384900
$676$	4159.32	0.236648
$677$	20304.8	1.15270	0.576349	−	0.817203i	$-0.304477\pi$
$677$	20304.8	1.15270	0.576349	+	0.817203i	$0.304477\pi$
$678$	−16285.1	−0.922456
$679$	−4224.21	−0.238749
$680$	−92.5907	−0.00522160
$681$	13285.8	0.747598
$682$	9858.65	0.553530
$683$	2014.43	0.112855	0.0564276	−	0.998407i	$-0.482029\pi$
$683$	2014.43	0.112855	0.0564276	+	0.998407i	$0.482029\pi$
$684$	3342.77	0.186863
$685$	−7932.18	−0.442442
$686$	−51438.1	−2.86285
$687$	−13551.8	−0.752597
$688$	14678.4	0.813386
$689$	−20577.4	−1.13779
$690$	7765.73	0.428459
$691$	−25073.6	−1.38038	−0.690190	−	0.723628i	$-0.742473\pi$
$691$	−25073.6	−1.38038	−0.690190	+	0.723628i	$0.742473\pi$
$692$	−20848.1	−1.14527
$693$	−3740.25	−0.205022
$694$	14851.2	0.812314
$695$	−8966.62	−0.489386
$696$	93.1379	0.00507239
$697$	2320.20	0.126089
$698$	−44423.4	−2.40895
$699$	12153.4	0.657631
$700$	−6352.51	−0.343003
$701$	−507.308	−0.0273335	−0.0136667	−	0.999907i	$-0.504350\pi$
$701$	−507.308	−0.0273335	−0.0136667	+	0.999907i	$0.504350\pi$
$702$	−5600.33	−0.301098
$703$	−5748.76	−0.308419
$704$	−6029.09	−0.322770
$705$	8535.62	0.455986
$706$	6722.65	0.358372
$707$	19229.0	1.02289
$708$	17199.8	0.913007
$709$	−24972.7	−1.32280	−0.661402	−	0.750032i	$-0.730038\pi$
$709$	−24972.7	−1.32280	−0.661402	+	0.750032i	$0.730038\pi$
$710$	2346.40	0.124027
$711$	954.292	0.0503358
$712$	173.222	0.00911764
$713$	−25665.0	−1.34805
$714$	6765.47	0.354610
$715$	3305.91	0.172915
$716$	237.599	0.0124015
$717$	2512.07	0.130844
$718$	−1314.14	−0.0683052
$719$	13494.0	0.699917	0.349958	−	0.936765i	$-0.386196\pi$
$719$	13494.0	0.699917	0.349958	+	0.936765i	$0.386196\pi$
$720$	2973.89	0.153931
$721$	62729.9	3.24020
$722$	−18047.1	−0.930257
$723$	−6033.68	−0.310367
$724$	1233.38	0.0633123
$725$	−725.000	−0.0371391
$726$	−13934.9	−0.712360
$727$	5717.08	0.291657	0.145829	−	0.989310i	$-0.453415\pi$
$727$	5717.08	0.291657	0.145829	+	0.989310i	$0.453415\pi$
$728$	−1840.40	−0.0936949
$729$	729.000	0.0370370
$730$	9883.53	0.501104
$731$	3841.99	0.194393
$732$	17585.0	0.887925
$733$	10147.2	0.511318	0.255659	−	0.966767i	$-0.417708\pi$
$733$	10147.2	0.511318	0.255659	+	0.966767i	$0.417708\pi$
$734$	−45190.1	−2.27248
$735$	−11063.2	−0.555200
$736$	33096.1	1.65752
$737$	−944.508	−0.0472068
$738$	−4787.89	−0.238814
$739$	39280.9	1.95531	0.977654	−	0.210222i	$-0.0674187\pi$
$739$	39280.9	1.95531	0.977654	+	0.210222i	$0.0674187\pi$
$740$	4624.32	0.229721
$741$	−7538.52	−0.373731
$742$	−51297.0	−2.53797
$743$	27166.1	1.34136	0.670679	−	0.741748i	$-0.266003\pi$
$743$	27166.1	1.34136	0.670679	+	0.741748i	$0.266003\pi$
$744$	−631.457	−0.0311161
$745$	13200.3	0.649155
$746$	23965.4	1.17619
$747$	382.509	0.0187353
$748$	−1690.48	−0.0826339
$749$	−21265.8	−1.03743
$750$	−1487.29	−0.0724110
$751$	−2310.40	−0.112261	−0.0561303	−	0.998423i	$-0.517876\pi$
$751$	−2310.40	−0.112261	−0.0561303	+	0.998423i	$0.517876\pi$
$752$	37606.0	1.82360
$753$	19374.9	0.937662
$754$	6015.17	0.290530
$755$	−5663.95	−0.273023
$756$	−6860.71	−0.330055
$757$	28647.5	1.37545	0.687723	−	0.725973i	$-0.258610\pi$
$757$	28647.5	1.37545	0.687723	+	0.725973i	$0.258610\pi$
$758$	13669.5	0.655012
$759$	−4950.90	−0.236767
$760$	257.192	0.0122755
$761$	−28161.6	−1.34147	−0.670733	−	0.741699i	$-0.734020\pi$
$761$	−28161.6	−1.34147	−0.670733	+	0.741699i	$0.734020\pi$
$762$	25204.5	1.19824
$763$	35014.7	1.66136
$764$	747.987	0.0354205
$765$	778.399	0.0367883
$766$	24069.6	1.13534
$767$	−38788.5	−1.82604
$768$	13074.8	0.614317
$769$	−12197.5	−0.571981	−0.285990	−	0.958233i	$-0.592323\pi$
$769$	−12197.5	−0.571981	−0.285990	+	0.958233i	$0.592323\pi$
$770$	8241.26	0.385707
$771$	5514.45	0.257585
$772$	7868.62	0.366837
$773$	21367.3	0.994216	0.497108	−	0.867689i	$-0.334395\pi$
$773$	21367.3	0.994216	0.497108	+	0.867689i	$0.334395\pi$
$774$	−7928.20	−0.368182
$775$	4915.36	0.227826
$776$	−137.572	−0.00636413
$777$	11798.8	0.544760
$778$	−18991.2	−0.875151
$779$	−6444.91	−0.296422
$780$	6064.00	0.278367
$781$	−1495.90	−0.0685373
$782$	8955.32	0.409516
$783$	−783.000	−0.0357371
$784$	−48741.9	−2.22038
$785$	−4563.26	−0.207477
$786$	−29110.0	−1.32102
$787$	−20891.1	−0.946236	−0.473118	−	0.880999i	$-0.656872\pi$
$787$	−20891.1	−0.946236	−0.473118	+	0.880999i	$0.656872\pi$
$788$	38748.2	1.75171
$789$	6789.00	0.306331
$790$	−2102.68	−0.0946964
$791$	44991.0	2.02237
$792$	−121.811	−0.00546511
$793$	−39657.2	−1.77588
$794$	818.557	0.0365863
$795$	−5901.96	−0.263297
$796$	−33545.2	−1.49369
$797$	−12968.8	−0.576386	−0.288193	−	0.957572i	$-0.593054\pi$
$797$	−12968.8	−0.576386	−0.288193	+	0.957572i	$0.593054\pi$
$798$	−18792.7	−0.833652
$799$	9843.14	0.435827
$800$	−6338.56	−0.280127
$801$	−1456.26	−0.0642376
$802$	−39980.4	−1.76029
$803$	−6301.06	−0.276911
$804$	−1732.50	−0.0759959
$805$	−21454.5	−0.939342
$806$	−40781.7	−1.78222
$807$	1898.85	0.0828288
$808$	626.243	0.0272663
$809$	−13867.9	−0.602683	−0.301342	−	0.953516i	$-0.597434\pi$
$809$	−13867.9	−0.602683	−0.301342	+	0.953516i	$0.597434\pi$
$810$	−1606.28	−0.0696776
$811$	−32657.3	−1.41400	−0.707000	−	0.707213i	$-0.749952\pi$
$811$	−32657.3	−1.41400	−0.707000	+	0.707213i	$0.749952\pi$
$812$	7368.91	0.318471
$813$	−2961.47	−0.127753
$814$	−5999.24	−0.258321
$815$	11519.1	0.495090
$816$	3429.45	0.147126
$817$	−10672.0	−0.456998
$818$	60197.7	2.57306
$819$	15472.1	0.660119
$820$	5184.30	0.220785
$821$	13615.5	0.578788	0.289394	−	0.957210i	$-0.406546\pi$
$821$	13615.5	0.578788	0.289394	+	0.957210i	$0.406546\pi$
$822$	18876.0	0.800942
$823$	−13661.8	−0.578640	−0.289320	−	0.957232i	$-0.593429\pi$
$823$	−13661.8	−0.578640	−0.289320	+	0.957232i	$0.593429\pi$
$824$	2042.96	0.0863713
$825$	948.196	0.0400145
$826$	−96695.5	−4.07320
$827$	31693.6	1.33264	0.666320	−	0.745666i	$-0.267869\pi$
$827$	31693.6	1.33264	0.666320	+	0.745666i	$0.267869\pi$
$828$	−9081.39	−0.381159
$829$	−18908.6	−0.792185	−0.396093	−	0.918211i	$-0.629634\pi$
$829$	−18908.6	−0.792185	−0.396093	+	0.918211i	$0.629634\pi$
$830$	−842.819	−0.0352466
$831$	24370.0	1.01731
$832$	24940.2	1.03924
$833$	−12757.9	−0.530654
$834$	21337.6	0.885924
$835$	−1907.79	−0.0790679
$836$	4695.71	0.194264
$837$	5308.59	0.219225
$838$	−24210.3	−0.998010
$839$	29382.9	1.20907	0.604534	−	0.796579i	$-0.293359\pi$
$839$	29382.9	1.20907	0.604534	+	0.796579i	$0.293359\pi$
$840$	−527.862	−0.0216821
$841$	841.000	0.0344828
$842$	33884.8	1.38687
$843$	−15226.8	−0.622111
$844$	−18247.3	−0.744193
$845$	−2690.35	−0.109528
$846$	−20312.0	−0.825461
$847$	38498.1	1.56176
$848$	−26002.7	−1.05299
$849$	−6231.91	−0.251918
$850$	−1715.12	−0.0692097
$851$	15617.8	0.629108
$852$	−2743.92	−0.110335
$853$	421.011	0.0168994	0.00844968	−	0.999964i	$-0.497310\pi$
$853$	421.011	0.0168994	0.00844968	+	0.999964i	$0.497310\pi$
$854$	−98861.0	−3.96131
$855$	−2162.19	−0.0864856
$856$	−692.576	−0.0276539
$857$	−41115.0	−1.63881	−0.819405	−	0.573215i	$-0.805696\pi$
$857$	−41115.0	−1.63881	−0.819405	+	0.573215i	$0.805696\pi$
$858$	−7866.97	−0.313023
$859$	−578.823	−0.0229909	−0.0114954	−	0.999934i	$-0.503659\pi$
$859$	−578.823	−0.0229909	−0.0114954	+	0.999934i	$0.503659\pi$
$860$	8584.60	0.340387
$861$	13227.5	0.523570
$862$	−30588.8	−1.20865
$863$	−30773.6	−1.21384	−0.606921	−	0.794762i	$-0.707596\pi$
$863$	−30773.6	−1.21384	−0.606921	+	0.794762i	$0.707596\pi$
$864$	−6845.65	−0.269553
$865$	13485.1	0.530065
$866$	−52727.6	−2.06900
$867$	−13841.4	−0.542188
$868$	−49959.8	−1.95362
$869$	1340.53	0.0523294
$870$	1725.26	0.0672320
$871$	3907.09	0.151994
$872$	1140.34	0.0442855
$873$	1156.56	0.0448379
$874$	−24875.5	−0.962731
$875$	4108.96	0.158752
$876$	−11558.0	−0.445785
$877$	−21118.7	−0.813146	−0.406573	−	0.913618i	$-0.633276\pi$
$877$	−21118.7	−0.813146	−0.406573	+	0.913618i	$0.633276\pi$
$878$	−71519.5	−2.74905
$879$	−12292.8	−0.471701
$880$	4177.53	0.160028
$881$	−42520.5	−1.62605	−0.813026	−	0.582228i	$-0.802181\pi$
$881$	−42520.5	−1.62605	−0.813026	+	0.582228i	$0.802181\pi$
$882$	26326.7	1.00506
$883$	25473.5	0.970840	0.485420	−	0.874281i	$-0.338667\pi$
$883$	25473.5	0.970840	0.485420	+	0.874281i	$0.338667\pi$
$884$	6992.91	0.266060
$885$	−11125.3	−0.422567
$886$	65344.5	2.47775
$887$	36451.4	1.37984	0.689920	−	0.723885i	$-0.257646\pi$
$887$	36451.4	1.37984	0.689920	+	0.723885i	$0.257646\pi$
$888$	384.258	0.0145212
$889$	−69632.6	−2.62700
$890$	3208.71	0.120850
$891$	1024.05	0.0385039
$892$	−46868.1	−1.75926
$893$	−27341.6	−1.02458
$894$	−31412.3	−1.17515
$895$	−153.685	−0.00573980
$896$	−4501.86	−0.167853
$897$	20480.1	0.762329
$898$	−10517.1	−0.390825
$899$	−5701.82	−0.211531
$900$	1739.27	0.0644173
$901$	−6806.05	−0.251656
$902$	−6725.72	−0.248273
$903$	21903.3	0.807194
$904$	1465.25	0.0539086
$905$	−797.778	−0.0293028
$906$	13478.3	0.494247
$907$	36563.0	1.33854	0.669270	−	0.743020i	$-0.266607\pi$
$907$	36563.0	1.33854	0.669270	+	0.743020i	$0.266607\pi$
$908$	34233.5	1.25119
$909$	−5264.75	−0.192102
$910$	−34091.1	−1.24188
$911$	25321.6	0.920902	0.460451	−	0.887685i	$-0.347688\pi$
$911$	25321.6	0.920902	0.460451	+	0.887685i	$0.347688\pi$
$912$	−9526.09	−0.345878
$913$	537.324	0.0194773
$914$	−2310.65	−0.0836208
$915$	−11374.4	−0.410958
$916$	−34918.9	−1.25955
$917$	80422.5	2.89617
$918$	−1852.33	−0.0665971
$919$	16527.1	0.593230	0.296615	−	0.954997i	$-0.404142\pi$
$919$	16527.1	0.593230	0.296615	+	0.954997i	$0.404142\pi$
$920$	−698.720	−0.0250393
$921$	8400.82	0.300561
$922$	−25929.4	−0.926181
$923$	6188.01	0.220673
$924$	−9637.48	−0.343127
$925$	−2991.12	−0.106322
$926$	−47178.0	−1.67426
$927$	−17175.0	−0.608522
$928$	7352.73	0.260092
$929$	−32080.4	−1.13297	−0.566483	−	0.824073i	$-0.691696\pi$
$929$	−32080.4	−1.13297	−0.566483	+	0.824073i	$0.691696\pi$
$930$	−11696.9	−0.412428
$931$	35438.0	1.24751
$932$	31315.6	1.10062
$933$	−3021.70	−0.106030
$934$	−58470.3	−2.04840
$935$	1093.44	0.0382454
$936$	503.888	0.0175963
$937$	31282.2	1.09066	0.545328	−	0.838223i	$-0.316405\pi$
$937$	31282.2	1.09066	0.545328	+	0.838223i	$0.316405\pi$
$938$	9739.93	0.339041
$939$	−25620.6	−0.890411
$940$	21993.7	0.763143
$941$	23786.8	0.824047	0.412024	−	0.911173i	$-0.364822\pi$
$941$	23786.8	0.824047	0.412024	+	0.911173i	$0.364822\pi$
$942$	10859.0	0.375591
$943$	17509.0	0.604637
$944$	−49015.4	−1.68995
$945$	4437.67	0.152759
$946$	−11137.0	−0.382765
$947$	38442.2	1.31912	0.659558	−	0.751654i	$-0.270744\pi$
$947$	38442.2	1.31912	0.659558	+	0.751654i	$0.270744\pi$
$948$	2458.92	0.0842425
$949$	26065.2	0.891583
$950$	4764.16	0.162705
$951$	−20270.2	−0.691175
$952$	−608.722	−0.0207235
$953$	41175.0	1.39957	0.699784	−	0.714355i	$-0.253280\pi$
$953$	41175.0	1.39957	0.699784	+	0.714355i	$0.253280\pi$
$954$	14044.7	0.476640
$955$	−483.816	−0.0163936
$956$	6472.84	0.218982
$957$	−1099.91	−0.0371525
$958$	23258.9	0.784407
$959$	−52148.8	−1.75597
$960$	7153.30	0.240491
$961$	8866.24	0.297615
$962$	24816.7	0.831727
$963$	5822.41	0.194833
$964$	−15546.9	−0.519433
$965$	−5089.61	−0.169783
$966$	51054.5	1.70047
$967$	20553.4	0.683508	0.341754	−	0.939790i	$-0.388979\pi$
$967$	20553.4	0.683508	0.341754	+	0.939790i	$0.388979\pi$
$968$	1253.79	0.0416305
$969$	−2493.40	−0.0826620
$970$	−2548.35	−0.0843533
$971$	7678.14	0.253762	0.126881	−	0.991918i	$-0.459503\pi$
$971$	7678.14	0.253762	0.126881	+	0.991918i	$0.459503\pi$
$972$	1878.41	0.0619856
$973$	−58949.5	−1.94228
$974$	−61457.7	−2.02180
$975$	−3922.34	−0.128836
$976$	−50113.1	−1.64353
$977$	46149.6	1.51121	0.755607	−	0.655025i	$-0.227342\pi$
$977$	46149.6	1.51121	0.755607	+	0.655025i	$0.227342\pi$
$978$	−27411.8	−0.896249
$979$	−2045.65	−0.0667818
$980$	−28506.4	−0.929188
$981$	−9586.75	−0.312009
$982$	3774.61	0.122661
$983$	−17189.7	−0.557747	−0.278874	−	0.960328i	$-0.589961\pi$
$983$	−17189.7	−0.557747	−0.278874	+	0.960328i	$0.589961\pi$
$984$	430.789	0.0139564
$985$	−25063.3	−0.810743
$986$	1989.54	0.0642596
$987$	56116.0	1.80972
$988$	−19424.4	−0.625480
$989$	28992.9	0.932176
$990$	−2256.39	−0.0724372
$991$	−14818.9	−0.475012	−0.237506	−	0.971386i	$-0.576330\pi$
$991$	−14818.9	−0.475012	−0.237506	+	0.971386i	$0.576330\pi$
$992$	−49850.1	−1.59551
$993$	−6559.73	−0.209634
$994$	15426.0	0.492237
$995$	21697.8	0.691324
$996$	985.608	0.0313556
$997$	−60460.3	−1.92056	−0.960280	−	0.279038i	$-0.909984\pi$
$997$	−60460.3	−1.92056	−0.960280	+	0.279038i	$0.909984\pi$
$998$	50241.2	1.59354
$999$	−3230.41	−0.102308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.j.1.7	✓	7
3.2	odd	2		1305.4.a.m.1.1		7
5.4	even	2		2175.4.a.m.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.j.1.7	✓	7	1.1	even	1	trivial
1305.4.a.m.1.1		7	3.2	odd	2
2175.4.a.m.1.1		7	5.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q+3.96612 q^{2} +3.00000 q^{3} +7.73008 q^{4} -5.00000 q^{5} +11.8983 q^{6} -32.8717 q^{7} -1.07055 q^{8} +9.00000 q^{9} -19.8306 q^{10} +12.6426 q^{11} +23.1902 q^{12} -52.2979 q^{13} -130.373 q^{14} -15.0000 q^{15} -66.0865 q^{16} -17.2978 q^{17} +35.6950 q^{18} +48.0486 q^{19} -38.6504 q^{20} -98.6150 q^{21} +50.1421 q^{22} -130.535 q^{23} -3.21165 q^{24} +25.0000 q^{25} -207.420 q^{26} +27.0000 q^{27} -254.100 q^{28} -29.0000 q^{29} -59.4917 q^{30} +196.614 q^{31} -253.542 q^{32} +37.9278 q^{33} -68.6049 q^{34} +164.358 q^{35} +69.5707 q^{36} -119.645 q^{37} +190.566 q^{38} -156.894 q^{39} +5.35275 q^{40} -134.133 q^{41} -391.118 q^{42} -222.109 q^{43} +97.7283 q^{44} -45.0000 q^{45} -517.716 q^{46} -569.042 q^{47} -198.260 q^{48} +737.546 q^{49} +99.1529 q^{50} -51.8933 q^{51} -404.267 q^{52} +393.464 q^{53} +107.085 q^{54} -63.2131 q^{55} +35.1908 q^{56} +144.146 q^{57} -115.017 q^{58} +741.684 q^{59} -115.951 q^{60} +758.295 q^{61} +779.796 q^{62} -295.845 q^{63} -476.886 q^{64} +261.489 q^{65} +150.426 q^{66} -74.7083 q^{67} -133.713 q^{68} -391.604 q^{69} +651.864 q^{70} -118.322 q^{71} -9.63496 q^{72} -498.399 q^{73} -474.525 q^{74} +75.0000 q^{75} +371.419 q^{76} -415.584 q^{77} -622.259 q^{78} +106.032 q^{79} +330.433 q^{80} +81.0000 q^{81} -531.988 q^{82} +42.5010 q^{83} -762.301 q^{84} +86.4888 q^{85} -880.911 q^{86} -87.0000 q^{87} -13.5346 q^{88} -161.806 q^{89} -178.475 q^{90} +1719.12 q^{91} -1009.04 q^{92} +589.843 q^{93} -2256.88 q^{94} -240.243 q^{95} -760.627 q^{96} +128.506 q^{97} +2925.19 q^{98} +113.784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) \) 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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