LMFDB - Embedded newform 35.4.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,4,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("35.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.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:	$2.06506685020$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.14360.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 17x - 14 $ x^3 - 17*x - 14
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			1.3
Root			$4.48565$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.48565 q^{2} +0.850238 q^{3} +4.14976 q^{4} +5.00000 q^{5} +2.96363 q^{6} +7.00000 q^{7} -13.4206 q^{8} -26.2771 q^{9} +17.4283 q^{10} -6.90764 q^{11} +3.52829 q^{12} -22.1364 q^{13} +24.3996 q^{14} +4.25119 q^{15} -79.9776 q^{16} +88.3030 q^{17} -91.5928 q^{18} +36.9560 q^{19} +20.7488 q^{20} +5.95167 q^{21} -24.0776 q^{22} -95.5283 q^{23} -11.4107 q^{24} +25.0000 q^{25} -77.1598 q^{26} -45.2982 q^{27} +29.0483 q^{28} +269.029 q^{29} +14.8182 q^{30} +197.114 q^{31} -171.409 q^{32} -5.87314 q^{33} +307.793 q^{34} +35.0000 q^{35} -109.044 q^{36} +2.14546 q^{37} +128.816 q^{38} -18.8212 q^{39} -67.1029 q^{40} +174.127 q^{41} +20.7454 q^{42} -17.0345 q^{43} -28.6650 q^{44} -131.385 q^{45} -332.978 q^{46} -528.029 q^{47} -68.0000 q^{48} +49.0000 q^{49} +87.1413 q^{50} +75.0786 q^{51} -91.8608 q^{52} -641.114 q^{53} -157.894 q^{54} -34.5382 q^{55} -93.9441 q^{56} +31.4214 q^{57} +937.742 q^{58} -642.975 q^{59} +17.6414 q^{60} +142.967 q^{61} +687.070 q^{62} -183.940 q^{63} +42.3480 q^{64} -110.682 q^{65} -20.4717 q^{66} +478.797 q^{67} +366.436 q^{68} -81.2218 q^{69} +121.998 q^{70} +105.550 q^{71} +352.654 q^{72} +986.512 q^{73} +7.47834 q^{74} +21.2560 q^{75} +153.358 q^{76} -48.3534 q^{77} -65.6042 q^{78} -1099.86 q^{79} -399.888 q^{80} +670.967 q^{81} +606.947 q^{82} -1236.62 q^{83} +24.6980 q^{84} +441.515 q^{85} -59.3763 q^{86} +228.739 q^{87} +92.7045 q^{88} -711.698 q^{89} -457.964 q^{90} -154.955 q^{91} -396.420 q^{92} +167.594 q^{93} -1840.52 q^{94} +184.780 q^{95} -145.739 q^{96} -636.553 q^{97} +170.797 q^{98} +181.513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} + 13 q^{4} + 15 q^{5} + 24 q^{6} + 21 q^{7} - 15 q^{8} + 81 q^{9} - 15 q^{10} - 74 q^{11} - 152 q^{12} + 44 q^{13} - 21 q^{14} + 10 q^{15} - 79 q^{16} - 52 q^{17} - 411 q^{18} + 168 q^{19}+ \cdots - 3488 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 2 * q^3 + 13 * q^4 + 15 * q^5 + 24 * q^6 + 21 * q^7 - 15 * q^8 + 81 * q^9 - 15 * q^10 - 74 * q^11 - 152 * q^12 + 44 * q^13 - 21 * q^14 + 10 * q^15 - 79 * q^16 - 52 * q^17 - 411 * q^18 + 168 * q^19 + 65 * q^20 + 14 * q^21 + 184 * q^22 - 124 * q^23 + 420 * q^24 + 75 * q^25 - 446 * q^26 + 170 * q^27 + 91 * q^28 + 332 * q^29 + 120 * q^30 + 320 * q^31 - 183 * q^32 - 106 * q^33 + 582 * q^34 + 105 * q^35 + 181 * q^36 - 54 * q^37 - 460 * q^38 - 982 * q^39 - 75 * q^40 + 362 * q^41 + 168 * q^42 - 16 * q^43 - 264 * q^44 + 405 * q^45 - 336 * q^46 - 730 * q^47 - 204 * q^48 + 147 * q^49 - 75 * q^50 - 1178 * q^51 + 1202 * q^52 + 110 * q^53 - 180 * q^54 - 370 * q^55 - 105 * q^56 - 956 * q^57 + 450 * q^58 - 180 * q^59 - 760 * q^60 + 1222 * q^61 + 464 * q^62 + 567 * q^63 - 391 * q^64 + 220 * q^65 - 532 * q^66 + 204 * q^67 + 918 * q^68 - 716 * q^69 - 105 * q^70 - 136 * q^71 + 765 * q^72 + 310 * q^73 + 502 * q^74 + 50 * q^75 + 1796 * q^76 - 518 * q^77 + 3788 * q^78 - 1034 * q^79 - 395 * q^80 + 2283 * q^81 - 6 * q^82 - 1660 * q^83 - 1064 * q^84 - 260 * q^85 + 764 * q^86 - 1574 * q^87 - 20 * q^88 + 242 * q^89 - 2055 * q^90 + 308 * q^91 + 96 * q^92 + 1376 * q^93 - 1108 * q^94 + 840 * q^95 - 3156 * q^96 + 100 * q^97 - 147 * q^98 - 3488 * 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 $

$2$	3.48565	1.23236	0.616182	−	0.787604i	$-0.288679\pi$
$2$	3.48565	1.23236	0.616182	+	0.787604i	$0.288679\pi$
$3$	0.850238	0.163628	0.0818142	−	0.996648i	$-0.473929\pi$
$3$	0.850238	0.163628	0.0818142	+	0.996648i	$0.473929\pi$
$4$	4.14976	0.518720
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	2.96363	0.201650
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−13.4206	−0.593112
$9$	−26.2771	−0.973226
$10$	17.4283	0.551130
$11$	−6.90764	−0.189339	−0.0946696	−	0.995509i	$-0.530179\pi$
$11$	−6.90764	−0.189339	−0.0946696	+	0.995509i	$0.530179\pi$
$12$	3.52829	0.0848774
$13$	−22.1364	−0.472272	−0.236136	−	0.971720i	$-0.575881\pi$
$13$	−22.1364	−0.472272	−0.236136	+	0.971720i	$0.575881\pi$
$14$	24.3996	0.465790
$15$	4.25119	0.0731769
$16$	−79.9776	−1.24965
$17$	88.3030	1.25980	0.629901	−	0.776676i	$-0.283096\pi$
$17$	88.3030	1.25980	0.629901	+	0.776676i	$0.283096\pi$
$18$	−91.5928	−1.19937
$19$	36.9560	0.446225	0.223113	−	0.974793i	$-0.428378\pi$
$19$	36.9560	0.446225	0.223113	+	0.974793i	$0.428378\pi$
$20$	20.7488	0.231979
$21$	5.95167	0.0618457
$22$	−24.0776	−0.233335
$23$	−95.5283	−0.866045	−0.433022	−	0.901383i	$-0.642553\pi$
$23$	−95.5283	−0.866045	−0.433022	+	0.901383i	$0.642553\pi$
$24$	−11.4107	−0.0970500
$25$	25.0000	0.200000
$26$	−77.1598	−0.582010
$27$	−45.2982	−0.322876
$28$	29.0483	0.196058
$29$	269.029	1.72267	0.861336	−	0.508035i	$-0.169628\pi$
$29$	269.029	1.72267	0.861336	+	0.508035i	$0.169628\pi$
$30$	14.8182	0.0901805
$31$	197.114	1.14202	0.571012	−	0.820942i	$-0.306551\pi$
$31$	197.114	1.14202	0.571012	+	0.820942i	$0.306551\pi$
$32$	−171.409	−0.946911
$33$	−5.87314	−0.0309813
$34$	307.793	1.55253
$35$	35.0000	0.169031
$36$	−109.044	−0.504832
$37$	2.14546	0.00953276	0.00476638	−	0.999989i	$-0.498483\pi$
$37$	2.14546	0.00953276	0.00476638	+	0.999989i	$0.498483\pi$
$38$	128.816	0.549912
$39$	−18.8212	−0.0772771
$40$	−67.1029	−0.265248
$41$	174.127	0.663271	0.331636	−	0.943408i	$-0.392400\pi$
$41$	174.127	0.663271	0.331636	+	0.943408i	$0.392400\pi$
$42$	20.7454	0.0762164
$43$	−17.0345	−0.0604125	−0.0302062	−	0.999544i	$-0.509616\pi$
$43$	−17.0345	−0.0604125	−0.0302062	+	0.999544i	$0.509616\pi$
$44$	−28.6650	−0.0982140
$45$	−131.385	−0.435240
$46$	−332.978	−1.06728
$47$	−528.029	−1.63874	−0.819371	−	0.573264i	$-0.805677\pi$
$47$	−528.029	−1.63874	−0.819371	+	0.573264i	$0.805677\pi$
$48$	−68.0000	−0.204478
$49$	49.0000	0.142857
$50$	87.1413	0.246473
$51$	75.0786	0.206139
$52$	−91.8608	−0.244977
$53$	−641.114	−1.66158	−0.830790	−	0.556586i	$-0.812111\pi$
$53$	−641.114	−1.66158	−0.830790	+	0.556586i	$0.812111\pi$
$54$	−157.894	−0.397900
$55$	−34.5382	−0.0846750
$56$	−93.9441	−0.224175
$57$	31.4214	0.0730151
$58$	937.742	2.12296
$59$	−642.975	−1.41878	−0.709391	−	0.704815i	$-0.751030\pi$
$59$	−642.975	−1.41878	−0.709391	+	0.704815i	$0.751030\pi$
$60$	17.6414	0.0379583
$61$	142.967	0.300083	0.150042	−	0.988680i	$-0.452059\pi$
$61$	142.967	0.300083	0.150042	+	0.988680i	$0.452059\pi$
$62$	687.070	1.40739
$63$	−183.940	−0.367845
$64$	42.3480	0.0827109
$65$	−110.682	−0.211206
$66$	−20.4717	−0.0381802
$67$	478.797	0.873050	0.436525	−	0.899692i	$-0.356209\pi$
$67$	478.797	0.873050	0.436525	+	0.899692i	$0.356209\pi$
$68$	366.436	0.653484
$69$	−81.2218	−0.141710
$70$	121.998	0.208307
$71$	105.550	0.176430	0.0882150	−	0.996101i	$-0.471884\pi$
$71$	105.550	0.176430	0.0882150	+	0.996101i	$0.471884\pi$
$72$	352.654	0.577232
$73$	986.512	1.58168	0.790839	−	0.612024i	$-0.209644\pi$
$73$	986.512	1.58168	0.790839	+	0.612024i	$0.209644\pi$
$74$	7.47834	0.0117478
$75$	21.2560	0.0327257
$76$	153.358	0.231466
$77$	−48.3534	−0.0715635
$78$	−65.6042	−0.0952335
$79$	−1099.86	−1.56638	−0.783190	−	0.621783i	$-0.786409\pi$
$79$	−1099.86	−1.56638	−0.783190	+	0.621783i	$0.786409\pi$
$80$	−399.888	−0.558860
$81$	670.967	0.920394
$82$	606.947	0.817391
$83$	−1236.62	−1.63538	−0.817691	−	0.575657i	$-0.804746\pi$
$83$	−1236.62	−1.63538	−0.817691	+	0.575657i	$0.804746\pi$
$84$	24.6980	0.0320806
$85$	441.515	0.563400
$86$	−59.3763	−0.0744501
$87$	228.739	0.281878
$88$	92.7045	0.112299
$89$	−711.698	−0.847638	−0.423819	−	0.905747i	$-0.639311\pi$
$89$	−711.698	−0.847638	−0.423819	+	0.905747i	$0.639311\pi$
$90$	−457.964	−0.536374
$91$	−154.955	−0.178502
$92$	−396.420	−0.449235
$93$	167.594	0.186867
$94$	−1840.52	−2.01953
$95$	184.780	0.199558
$96$	−145.739	−0.154942
$97$	−636.553	−0.666311	−0.333156	−	0.942872i	$-0.608113\pi$
$97$	−636.553	−0.666311	−0.333156	+	0.942872i	$0.608113\pi$
$98$	170.797	0.176052
$99$	181.513	0.184270
$100$	103.744	0.103744
$101$	1742.05	1.71624	0.858121	−	0.513448i	$-0.171632\pi$
$101$	1742.05	1.71624	0.858121	+	0.513448i	$0.171632\pi$
$102$	261.698	0.254039
$103$	1454.62	1.39154	0.695769	−	0.718266i	$-0.255064\pi$
$103$	1454.62	1.39154	0.695769	+	0.718266i	$0.255064\pi$
$104$	297.083	0.280110
$105$	29.7583	0.0276583
$106$	−2234.70	−2.04767
$107$	−1181.67	−1.06763	−0.533813	−	0.845603i	$-0.679241\pi$
$107$	−1181.67	−1.06763	−0.533813	+	0.845603i	$0.679241\pi$
$108$	−187.977	−0.167482
$109$	2204.43	1.93712	0.968559	−	0.248784i	$-0.0800310\pi$
$109$	2204.43	1.93712	0.968559	+	0.248784i	$0.0800310\pi$
$110$	−120.388	−0.104350
$111$	1.82416	0.00155983
$112$	−559.843	−0.472323
$113$	236.886	0.197207	0.0986034	−	0.995127i	$-0.468562\pi$
$113$	236.886	0.197207	0.0986034	+	0.995127i	$0.468562\pi$
$114$	109.524	0.0899812
$115$	−477.641	−0.387307
$116$	1116.41	0.893585
$117$	581.680	0.459627
$118$	−2241.19	−1.74846
$119$	618.121	0.476160
$120$	−57.0535	−0.0434021
$121$	−1283.28	−0.964151
$122$	498.334	0.369811
$123$	148.050	0.108530
$124$	817.976	0.592390
$125$	125.000	0.0894427
$126$	−641.149	−0.453319
$127$	−1667.21	−1.16489	−0.582446	−	0.812869i	$-0.697904\pi$
$127$	−1667.21	−1.16489	−0.582446	+	0.812869i	$0.697904\pi$
$128$	1518.88	1.04884
$129$	−14.4834	−0.00988520
$130$	−385.799	−0.260283
$131$	891.722	0.594733	0.297367	−	0.954763i	$-0.403892\pi$
$131$	891.722	0.594733	0.297367	+	0.954763i	$0.403892\pi$
$132$	−24.3721	−0.0160706
$133$	258.692	0.168657
$134$	1668.92	1.07591
$135$	−226.491	−0.144394
$136$	−1185.08	−0.747203
$137$	−400.425	−0.249713	−0.124856	−	0.992175i	$-0.539847\pi$
$137$	−400.425	−0.249713	−0.124856	+	0.992175i	$0.539847\pi$
$138$	−283.111	−0.174638
$139$	515.050	0.314287	0.157144	−	0.987576i	$-0.449771\pi$
$139$	515.050	0.314287	0.157144	+	0.987576i	$0.449771\pi$
$140$	145.242	0.0876797
$141$	−448.950	−0.268145
$142$	367.912	0.217426
$143$	152.910	0.0894195
$144$	2101.58	1.21619
$145$	1345.15	0.770403
$146$	3438.64	1.94920
$147$	41.6617	0.0233755
$148$	8.90316	0.00494483
$149$	218.374	0.120066	0.0600332	−	0.998196i	$-0.480879\pi$
$149$	218.374	0.120066	0.0600332	+	0.998196i	$0.480879\pi$
$150$	74.0909	0.0403300
$151$	−175.011	−0.0943190	−0.0471595	−	0.998887i	$-0.515017\pi$
$151$	−175.011	−0.0943190	−0.0471595	+	0.998887i	$0.515017\pi$
$152$	−495.971	−0.264661
$153$	−2320.35	−1.22607
$154$	−168.543	−0.0881922
$155$	985.570	0.510728
$156$	−78.1036	−0.0400852
$157$	−919.642	−0.467487	−0.233743	−	0.972298i	$-0.575098\pi$
$157$	−919.642	−0.467487	−0.233743	+	0.972298i	$0.575098\pi$
$158$	−3833.73	−1.93035
$159$	−545.099	−0.271882
$160$	−857.046	−0.423471
$161$	−668.698	−0.327334
$162$	2338.76	1.13426
$163$	2368.51	1.13813	0.569067	−	0.822291i	$-0.307305\pi$
$163$	2368.51	1.13813	0.569067	+	0.822291i	$0.307305\pi$
$164$	722.587	0.344052
$165$	−29.3657	−0.0138552
$166$	−4310.43	−2.01539
$167$	1079.37	0.500144	0.250072	−	0.968227i	$-0.419546\pi$
$167$	1079.37	0.500144	0.250072	+	0.968227i	$0.419546\pi$
$168$	−79.8749	−0.0366814
$169$	−1706.98	−0.776959
$170$	1538.97	0.694314
$171$	−971.095	−0.434278
$172$	−70.6891	−0.0313372
$173$	−881.271	−0.387294	−0.193647	−	0.981071i	$-0.562032\pi$
$173$	−881.271	−0.387294	−0.193647	+	0.981071i	$0.562032\pi$
$174$	797.305	0.347376
$175$	175.000	0.0755929
$176$	552.456	0.236608
$177$	−546.682	−0.232153
$178$	−2480.73	−1.04460
$179$	−3377.72	−1.41041	−0.705203	−	0.709006i	$-0.749144\pi$
$179$	−3377.72	−1.41041	−0.705203	+	0.709006i	$0.749144\pi$
$180$	−545.218	−0.225768
$181$	1435.58	0.589533	0.294767	−	0.955569i	$-0.404758\pi$
$181$	1435.58	0.589533	0.294767	+	0.955569i	$0.404758\pi$
$182$	−540.118	−0.219979
$183$	121.556	0.0491021
$184$	1282.05	0.513661
$185$	10.7273	0.00426318
$186$	584.174	0.230289
$187$	−609.965	−0.238530
$188$	−2191.19	−0.850049
$189$	−317.088	−0.122036
$190$	644.078	0.245928
$191$	−1588.14	−0.601642	−0.300821	−	0.953681i	$-0.597261\pi$
$191$	−1588.14	−0.601642	−0.300821	+	0.953681i	$0.597261\pi$
$192$	36.0059	0.0135339
$193$	−977.704	−0.364646	−0.182323	−	0.983239i	$-0.558362\pi$
$193$	−977.704	−0.364646	−0.182323	+	0.983239i	$0.558362\pi$
$194$	−2218.80	−0.821138
$195$	−94.1061	−0.0345594
$196$	203.338	0.0741029
$197$	359.682	0.130083	0.0650413	−	0.997883i	$-0.479282\pi$
$197$	359.682	0.130083	0.0650413	+	0.997883i	$0.479282\pi$
$198$	632.689	0.227087
$199$	2818.38	1.00397	0.501983	−	0.864877i	$-0.332604\pi$
$199$	2818.38	1.00397	0.501983	+	0.864877i	$0.332604\pi$
$200$	−335.515	−0.118622
$201$	407.091	0.142856
$202$	6072.18	2.11503
$203$	1883.21	0.651109
$204$	311.558	0.106929
$205$	870.637	0.296624
$206$	5070.31	1.71488
$207$	2510.21	0.842857
$208$	1770.42	0.590174
$209$	−255.278	−0.0844879
$210$	103.727	0.0340850
$211$	−1009.64	−0.329415	−0.164708	−	0.986342i	$-0.552668\pi$
$211$	−1009.64	−0.329415	−0.164708	+	0.986342i	$0.552668\pi$
$212$	−2660.47	−0.861895
$213$	89.7430	0.0288690
$214$	−4118.88	−1.31570
$215$	−85.1725	−0.0270173
$216$	607.929	0.191501
$217$	1379.80	0.431644
$218$	7683.86	2.38723
$219$	838.770	0.258808
$220$	−143.325	−0.0439226
$221$	−1954.71	−0.594969
$222$	6.35837	0.00192228
$223$	1277.28	0.383555	0.191778	−	0.981438i	$-0.438575\pi$
$223$	1277.28	0.383555	0.191778	+	0.981438i	$0.438575\pi$
$224$	−1199.86	−0.357899
$225$	−656.927	−0.194645
$226$	825.702	0.243030
$227$	1399.87	0.409307	0.204654	−	0.978834i	$-0.434393\pi$
$227$	1399.87	0.409307	0.204654	+	0.978834i	$0.434393\pi$
$228$	130.391	0.0378744
$229$	3182.00	0.918222	0.459111	−	0.888379i	$-0.348168\pi$
$229$	3182.00	0.918222	0.459111	+	0.888379i	$0.348168\pi$
$230$	−1664.89	−0.477303
$231$	−41.1120	−0.0117098
$232$	−3610.53	−1.02174
$233$	−3027.84	−0.851332	−0.425666	−	0.904880i	$-0.639960\pi$
$233$	−3027.84	−0.851332	−0.425666	+	0.904880i	$0.639960\pi$
$234$	2027.53	0.566428
$235$	−2640.14	−0.732868
$236$	−2668.19	−0.735951
$237$	−935.144	−0.256304
$238$	2154.55	0.586802
$239$	−4995.69	−1.35207	−0.676034	−	0.736870i	$-0.736303\pi$
$239$	−4995.69	−1.35207	−0.676034	+	0.736870i	$0.736303\pi$
$240$	−340.000	−0.0914454
$241$	−3756.52	−1.00406	−0.502030	−	0.864850i	$-0.667413\pi$
$241$	−3756.52	−1.00406	−0.502030	+	0.864850i	$0.667413\pi$
$242$	−4473.08	−1.18818
$243$	1793.53	0.473479
$244$	593.280	0.155659
$245$	245.000	0.0638877
$246$	516.050	0.133748
$247$	−818.072	−0.210740
$248$	−2645.39	−0.677347
$249$	−1051.42	−0.267595
$250$	435.706	0.110226
$251$	6565.46	1.65103	0.825514	−	0.564381i	$-0.190885\pi$
$251$	6565.46	1.65103	0.825514	+	0.564381i	$0.190885\pi$
$252$	−763.306	−0.190809
$253$	659.875	0.163976
$254$	−5811.33	−1.43557
$255$	375.393	0.0921883
$256$	4955.51	1.20984
$257$	−6879.44	−1.66976	−0.834879	−	0.550433i	$-0.814463\pi$
$257$	−6879.44	−1.66976	−0.834879	+	0.550433i	$0.814463\pi$
$258$	−50.4840	−0.0121822
$259$	15.0182	0.00360304
$260$	−459.304	−0.109557
$261$	−7069.31	−1.67655
$262$	3108.23	0.732928
$263$	3080.15	0.722169	0.361084	−	0.932533i	$-0.382407\pi$
$263$	3080.15	0.722169	0.361084	+	0.932533i	$0.382407\pi$
$264$	78.8209	0.0183754
$265$	−3205.57	−0.743081
$266$	901.709	0.207847
$267$	−605.113	−0.138698
$268$	1986.89	0.452869
$269$	6710.33	1.52095	0.760476	−	0.649366i	$-0.224966\pi$
$269$	6710.33	1.52095	0.760476	+	0.649366i	$0.224966\pi$
$270$	−789.469	−0.177947
$271$	7842.95	1.75803	0.879014	−	0.476796i	$-0.158202\pi$
$271$	7842.95	1.75803	0.879014	+	0.476796i	$0.158202\pi$
$272$	−7062.26	−1.57431
$273$	−131.749	−0.0292080
$274$	−1395.74	−0.307737
$275$	−172.691	−0.0378678
$276$	−337.051	−0.0735076
$277$	5446.87	1.18148	0.590742	−	0.806861i	$-0.298835\pi$
$277$	5446.87	1.18148	0.590742	+	0.806861i	$0.298835\pi$
$278$	1795.28	0.387316
$279$	−5179.58	−1.11145
$280$	−469.721	−0.100254
$281$	2126.76	0.451501	0.225751	−	0.974185i	$-0.427517\pi$
$281$	2126.76	0.451501	0.225751	+	0.974185i	$0.427517\pi$
$282$	−1564.88	−0.330452
$283$	−3426.38	−0.719707	−0.359853	−	0.933009i	$-0.617173\pi$
$283$	−3426.38	−0.719707	−0.359853	+	0.933009i	$0.617173\pi$
$284$	438.009	0.0915178
$285$	157.107	0.0326534
$286$	532.991	0.110197
$287$	1218.89	0.250693
$288$	4504.14	0.921558
$289$	2884.42	0.587099
$290$	4688.71	0.949416
$291$	−541.222	−0.109028
$292$	4093.79	0.820448
$293$	−1749.82	−0.348894	−0.174447	−	0.984667i	$-0.555814\pi$
$293$	−1749.82	−0.348894	−0.174447	+	0.984667i	$0.555814\pi$
$294$	145.218	0.0288071
$295$	−3214.87	−0.634499
$296$	−28.7934	−0.00565399
$297$	312.904	0.0611330
$298$	761.176	0.147966
$299$	2114.65	0.409008
$300$	88.2072	0.0169755
$301$	−119.241	−0.0228338
$302$	−610.026	−0.116235
$303$	1481.16	0.280826
$304$	−2955.65	−0.557625
$305$	714.836	0.134201
$306$	−8087.92	−1.51097
$307$	7970.33	1.48173	0.740864	−	0.671655i	$-0.234416\pi$
$307$	7970.33	1.48173	0.740864	+	0.671655i	$0.234416\pi$
$308$	−200.655	−0.0371214
$309$	1236.78	0.227695
$310$	3435.35	0.629403
$311$	−2560.72	−0.466898	−0.233449	−	0.972369i	$-0.575001\pi$
$311$	−2560.72	−0.466898	−0.233449	+	0.972369i	$0.575001\pi$
$312$	252.592	0.0458339
$313$	−4861.11	−0.877848	−0.438924	−	0.898524i	$-0.644640\pi$
$313$	−4861.11	−0.877848	−0.438924	+	0.898524i	$0.644640\pi$
$314$	−3205.55	−0.576114
$315$	−919.698	−0.164505
$316$	−4564.16	−0.812513
$317$	8166.16	1.44687	0.723434	−	0.690394i	$-0.242563\pi$
$317$	8166.16	1.44687	0.723434	+	0.690394i	$0.242563\pi$
$318$	−1900.03	−0.335057
$319$	−1858.36	−0.326169
$320$	211.740	0.0369894
$321$	−1004.70	−0.174694
$322$	−2330.85	−0.403395
$323$	3263.32	0.562155
$324$	2784.35	0.477427
$325$	−553.410	−0.0944543
$326$	8255.79	1.40259
$327$	1874.29	0.316968
$328$	−2336.89	−0.393394
$329$	−3696.20	−0.619386
$330$	−102.359	−0.0170747
$331$	2974.89	0.494002	0.247001	−	0.969015i	$-0.420555\pi$
$331$	2974.89	0.494002	0.247001	+	0.969015i	$0.420555\pi$
$332$	−5131.68	−0.848306
$333$	−56.3766	−0.00927753
$334$	3762.30	0.616359
$335$	2393.98	0.390440
$336$	−476.000	−0.0772855
$337$	3496.34	0.565157	0.282578	−	0.959244i	$-0.408810\pi$
$337$	3496.34	0.565157	0.282578	+	0.959244i	$0.408810\pi$
$338$	−5949.94	−0.957497
$339$	201.410	0.0322686
$340$	1832.18	0.292247
$341$	−1361.59	−0.216230
$342$	−3384.90	−0.535188
$343$	343.000	0.0539949
$344$	228.613	0.0358314
$345$	−406.109	−0.0633744
$346$	−3071.80	−0.477287
$347$	3959.08	0.612491	0.306246	−	0.951953i	$-0.400927\pi$
$347$	3959.08	0.612491	0.306246	+	0.951953i	$0.400927\pi$
$348$	949.213	0.146216
$349$	5581.65	0.856099	0.428050	−	0.903755i	$-0.359201\pi$
$349$	5581.65	0.856099	0.428050	+	0.903755i	$0.359201\pi$
$350$	609.989	0.0931579
$351$	1002.74	0.152485
$352$	1184.03	0.179287
$353$	−9896.43	−1.49216	−0.746082	−	0.665854i	$-0.768067\pi$
$353$	−9896.43	−1.49216	−0.746082	+	0.665854i	$0.768067\pi$
$354$	−1905.54	−0.286097
$355$	527.752	0.0789019
$356$	−2953.38	−0.439687
$357$	525.550	0.0779133
$358$	−11773.5	−1.73813
$359$	11917.6	1.75205	0.876025	−	0.482265i	$-0.160186\pi$
$359$	11917.6	1.75205	0.876025	+	0.482265i	$0.160186\pi$
$360$	1763.27	0.258146
$361$	−5493.26	−0.800883
$362$	5003.92	0.726519
$363$	−1091.10	−0.157762
$364$	−643.025	−0.0925926
$365$	4932.56	0.707348
$366$	423.702	0.0605117
$367$	−7101.58	−1.01008	−0.505040	−	0.863096i	$-0.668522\pi$
$367$	−7101.58	−1.01008	−0.505040	+	0.863096i	$0.668522\pi$
$368$	7640.12	1.08225
$369$	−4575.56	−0.645513
$370$	37.3917	0.00525379
$371$	−4487.80	−0.628018
$372$	695.475	0.0969319
$373$	294.316	0.0408555	0.0204277	−	0.999791i	$-0.493497\pi$
$373$	294.316	0.0408555	0.0204277	+	0.999791i	$0.493497\pi$
$374$	−2126.12	−0.293955
$375$	106.280	0.0146354
$376$	7086.45	0.971957
$377$	−5955.34	−0.813569
$378$	−1105.26	−0.150392
$379$	−9436.57	−1.27896	−0.639478	−	0.768810i	$-0.720849\pi$
$379$	−9436.57	−1.27896	−0.639478	+	0.768810i	$0.720849\pi$
$380$	766.792	0.103515
$381$	−1417.53	−0.190610
$382$	−5535.70	−0.741442
$383$	−3160.82	−0.421699	−0.210849	−	0.977519i	$-0.567623\pi$
$383$	−3160.82	−0.421699	−0.210849	+	0.977519i	$0.567623\pi$
$384$	1291.41	0.171620
$385$	−241.767	−0.0320042
$386$	−3407.93	−0.449376
$387$	447.617	0.0587950
$388$	−2641.55	−0.345629
$389$	7822.76	1.01961	0.509807	−	0.860289i	$-0.329717\pi$
$389$	7822.76	1.01961	0.509807	+	0.860289i	$0.329717\pi$
$390$	−328.021	−0.0425897
$391$	−8435.43	−1.09104
$392$	−657.609	−0.0847302
$393$	758.176	0.0973153
$394$	1253.73	0.160309
$395$	−5499.30	−0.700506
$396$	753.234	0.0955844
$397$	−7935.18	−1.00316	−0.501581	−	0.865111i	$-0.667248\pi$
$397$	−7935.18	−1.00316	−0.501581	+	0.865111i	$0.667248\pi$
$398$	9823.87	1.23725
$399$	219.950	0.0275971
$400$	−1999.44	−0.249930
$401$	−488.380	−0.0608193	−0.0304097	−	0.999538i	$-0.509681\pi$
$401$	−488.380	−0.0608193	−0.0304097	+	0.999538i	$0.509681\pi$
$402$	1418.98	0.176050
$403$	−4363.39	−0.539345
$404$	7229.09	0.890249
$405$	3354.84	0.411613
$406$	6564.20	0.802403
$407$	−14.8201	−0.00180492
$408$	−1007.60	−0.122264
$409$	11230.6	1.35775	0.678874	−	0.734254i	$-0.262468\pi$
$409$	11230.6	1.35775	0.678874	+	0.734254i	$0.262468\pi$
$410$	3034.74	0.365549
$411$	−340.457	−0.0408601
$412$	6036.34	0.721818
$413$	−4500.82	−0.536249
$414$	8749.70	1.03871
$415$	−6183.10	−0.731365
$416$	3794.38	0.447199
$417$	437.915	0.0514263
$418$	−889.811	−0.104120
$419$	−7369.62	−0.859259	−0.429629	−	0.903005i	$-0.641356\pi$
$419$	−7369.62	−0.859259	−0.429629	+	0.903005i	$0.641356\pi$
$420$	123.490	0.0143469
$421$	11972.5	1.38599	0.692997	−	0.720941i	$-0.256290\pi$
$421$	11972.5	1.38599	0.692997	+	0.720941i	$0.256290\pi$
$422$	−3519.26	−0.405959
$423$	13875.1	1.59487
$424$	8604.12	0.985503
$425$	2207.57	0.251960
$426$	312.813	0.0355770
$427$	1000.77	0.113421
$428$	−4903.63	−0.553799
$429$	130.010	0.0146316
$430$	−296.882	−0.0332951
$431$	−3568.60	−0.398825	−0.199412	−	0.979916i	$-0.563903\pi$
$431$	−3568.60	−0.398825	−0.199412	+	0.979916i	$0.563903\pi$
$432$	3622.84	0.403482
$433$	2291.60	0.254335	0.127168	−	0.991881i	$-0.459411\pi$
$433$	2291.60	0.254335	0.127168	+	0.991881i	$0.459411\pi$
$434$	4809.49	0.531943
$435$	1143.70	0.126060
$436$	9147.85	1.00482
$437$	−3530.34	−0.386451
$438$	2923.66	0.318945
$439$	−7329.66	−0.796870	−0.398435	−	0.917197i	$-0.630446\pi$
$439$	−7329.66	−0.796870	−0.398435	+	0.917197i	$0.630446\pi$
$440$	463.523	0.0502218
$441$	−1287.58	−0.139032
$442$	−6813.44	−0.733218
$443$	8297.38	0.889889	0.444944	−	0.895558i	$-0.353223\pi$
$443$	8297.38	0.889889	0.444944	+	0.895558i	$0.353223\pi$
$444$	7.56981	0.000809116 0
$445$	−3558.49	−0.379075
$446$	4452.14	0.472679
$447$	185.670	0.0196463
$448$	296.436	0.0312618
$449$	9758.62	1.02570	0.512848	−	0.858479i	$-0.328590\pi$
$449$	9758.62	1.02570	0.512848	+	0.858479i	$0.328590\pi$
$450$	−2289.82	−0.239874
$451$	−1202.81	−0.125583
$452$	983.021	0.102295
$453$	−148.801	−0.0154333
$454$	4879.47	0.504416
$455$	−774.774	−0.0798285
$456$	−421.693	−0.0433061
$457$	−11745.0	−1.20220	−0.601102	−	0.799172i	$-0.705272\pi$
$457$	−11745.0	−1.20220	−0.601102	+	0.799172i	$0.705272\pi$
$458$	11091.4	1.13158
$459$	−3999.97	−0.406759
$460$	−1982.10	−0.200904
$461$	−10748.6	−1.08593	−0.542963	−	0.839756i	$-0.682698\pi$
$461$	−10748.6	−1.08593	−0.542963	+	0.839756i	$0.682698\pi$
$462$	−143.302	−0.0144308
$463$	−9862.51	−0.989957	−0.494978	−	0.868905i	$-0.664824\pi$
$463$	−9862.51	−0.989957	−0.494978	+	0.868905i	$0.664824\pi$
$464$	−21516.3	−2.15274
$465$	837.969	0.0835697
$466$	−10554.0	−1.04915
$467$	−4660.78	−0.461831	−0.230916	−	0.972974i	$-0.574172\pi$
$467$	−4660.78	−0.461831	−0.230916	+	0.972974i	$0.574172\pi$
$468$	2413.83	0.238418
$469$	3351.58	0.329982
$470$	−9202.62	−0.903160
$471$	−781.915	−0.0764941
$472$	8629.10	0.841497
$473$	117.668	0.0114384
$474$	−3259.58	−0.315860
$475$	923.899	0.0892451
$476$	2565.05	0.246994
$477$	16846.6	1.61709
$478$	−17413.2	−1.66624
$479$	−16293.2	−1.55419	−0.777094	−	0.629385i	$-0.783307\pi$
$479$	−16293.2	−1.55419	−0.777094	+	0.629385i	$0.783307\pi$
$480$	−728.693	−0.0692920
$481$	−47.4928	−0.00450205
$482$	−13093.9	−1.23737
$483$	−568.553	−0.0535612
$484$	−5325.33	−0.500124
$485$	−3182.77	−0.297984
$486$	6251.63	0.583498
$487$	−3515.00	−0.327063	−0.163531	−	0.986538i	$-0.552289\pi$
$487$	−3515.00	−0.327063	−0.163531	+	0.986538i	$0.552289\pi$
$488$	−1918.70	−0.177983
$489$	2013.80	0.186231
$490$	853.984	0.0787328
$491$	−2516.79	−0.231326	−0.115663	−	0.993288i	$-0.536899\pi$
$491$	−2516.79	−0.231326	−0.115663	+	0.993288i	$0.536899\pi$
$492$	614.371	0.0562967
$493$	23756.1	2.17023
$494$	−2851.51	−0.259708
$495$	907.563	0.0824079
$496$	−15764.7	−1.42713
$497$	738.853	0.0666842
$498$	−3664.89	−0.329775
$499$	−8747.48	−0.784751	−0.392376	−	0.919805i	$-0.628347\pi$
$499$	−8747.48	−0.784751	−0.392376	+	0.919805i	$0.628347\pi$
$500$	518.720	0.0463957
$501$	917.720	0.0818377
$502$	22884.9	2.03467
$503$	11426.1	1.01285	0.506426	−	0.862284i	$-0.330966\pi$
$503$	11426.1	1.01285	0.506426	+	0.862284i	$0.330966\pi$
$504$	2468.58	0.218173
$505$	8710.25	0.767526
$506$	2300.09	0.202078
$507$	−1451.34	−0.127133
$508$	−6918.54	−0.604254
$509$	−8078.44	−0.703478	−0.351739	−	0.936098i	$-0.614410\pi$
$509$	−8078.44	−0.703478	−0.351739	+	0.936098i	$0.614410\pi$
$510$	1308.49	0.113610
$511$	6905.58	0.597818
$512$	5122.12	0.442125
$513$	−1674.04	−0.144075
$514$	−23979.3	−2.05775
$515$	7273.12	0.622314
$516$	−60.1026	−0.00512765
$517$	3647.43	0.310278
$518$	52.3484	0.00444026
$519$	−749.290	−0.0633723
$520$	1485.42	0.125269
$521$	7226.14	0.607645	0.303822	−	0.952729i	$-0.401737\pi$
$521$	7226.14	0.607645	0.303822	+	0.952729i	$0.401737\pi$
$522$	−24641.1	−2.06612
$523$	9333.06	0.780318	0.390159	−	0.920748i	$-0.372420\pi$
$523$	9333.06	0.780318	0.390159	+	0.920748i	$0.372420\pi$
$524$	3700.43	0.308500
$525$	148.792	0.0123691
$526$	10736.3	0.889974
$527$	17405.8	1.43872
$528$	469.719	0.0387157
$529$	−3041.35	−0.249967
$530$	−11173.5	−0.915746
$531$	16895.5	1.38080
$532$	1073.51	0.0874859
$533$	−3854.55	−0.313244
$534$	−2109.21	−0.170926
$535$	−5908.33	−0.477457
$536$	−6425.73	−0.517816
$537$	−2871.87	−0.230782
$538$	23389.9	1.87437
$539$	−338.474	−0.0270484
$540$	−939.884	−0.0749003
$541$	15263.1	1.21296	0.606482	−	0.795097i	$-0.292580\pi$
$541$	15263.1	1.21296	0.606482	+	0.795097i	$0.292580\pi$
$542$	27337.8	2.16653
$543$	1220.58	0.0964644
$544$	−15135.9	−1.19292
$545$	11022.1	0.866305
$546$	−459.229	−0.0359949
$547$	−13226.0	−1.03382	−0.516912	−	0.856039i	$-0.672918\pi$
$547$	−13226.0	−1.03382	−0.516912	+	0.856039i	$0.672918\pi$
$548$	−1661.67	−0.129531
$549$	−3756.76	−0.292049
$550$	−601.940	−0.0466669
$551$	9942.24	0.768700
$552$	1090.04	0.0840496
$553$	−7699.03	−0.592036
$554$	18985.9	1.45602
$555$	9.12078	0.000697577 0
$556$	2137.33	0.163027
$557$	6993.63	0.532010	0.266005	−	0.963972i	$-0.414296\pi$
$557$	6993.63	0.532010	0.266005	+	0.963972i	$0.414296\pi$
$558$	−18054.2	−1.36971
$559$	377.082	0.0285311
$560$	−2799.22	−0.211229
$561$	−518.616	−0.0390302
$562$	7413.14	0.556413
$563$	392.197	0.0293590	0.0146795	−	0.999892i	$-0.495327\pi$
$563$	392.197	0.0293590	0.0146795	+	0.999892i	$0.495327\pi$
$564$	−1863.04	−0.139092
$565$	1184.43	0.0881935
$566$	−11943.2	−0.886940
$567$	4696.77	0.347876
$568$	−1416.55	−0.104643
$569$	8811.72	0.649221	0.324610	−	0.945848i	$-0.394767\pi$
$569$	8811.72	0.649221	0.324610	+	0.945848i	$0.394767\pi$
$570$	547.620	0.0402408
$571$	−24775.6	−1.81581	−0.907905	−	0.419175i	$-0.862319\pi$
$571$	−24775.6	−1.81581	−0.907905	+	0.419175i	$0.862319\pi$
$572$	634.541	0.0463837
$573$	−1350.30	−0.0984458
$574$	4248.63	0.308945
$575$	−2388.21	−0.173209
$576$	−1112.78	−0.0804964
$577$	−8850.62	−0.638572	−0.319286	−	0.947658i	$-0.603443\pi$
$577$	−8850.62	−0.638572	−0.319286	+	0.947658i	$0.603443\pi$
$578$	10054.1	0.723520
$579$	−831.281	−0.0596664
$580$	5582.04	0.399623
$581$	−8656.35	−0.618117
$582$	−1886.51	−0.134362
$583$	4428.58	0.314602
$584$	−13239.6	−0.938112
$585$	2908.40	0.205551
$586$	−6099.28	−0.429964
$587$	−46.0232	−0.00323608	−0.00161804	−	0.999999i	$-0.500515\pi$
$587$	−46.0232	−0.00323608	−0.00161804	+	0.999999i	$0.500515\pi$
$588$	172.886	0.0121253
$589$	7284.54	0.509600
$590$	−11205.9	−0.781933
$591$	305.815	0.0212852
$592$	−171.589	−0.0119126
$593$	−2729.93	−0.189047	−0.0945235	−	0.995523i	$-0.530133\pi$
$593$	−2729.93	−0.189047	−0.0945235	+	0.995523i	$0.530133\pi$
$594$	1090.67	0.0753381
$595$	3090.60	0.212945
$596$	906.200	0.0622809
$597$	2396.29	0.164277
$598$	7370.94	0.504047
$599$	−5505.07	−0.375511	−0.187756	−	0.982216i	$-0.560121\pi$
$599$	−5505.07	−0.375511	−0.187756	+	0.982216i	$0.560121\pi$
$600$	−285.267	−0.0194100
$601$	−7446.97	−0.505438	−0.252719	−	0.967540i	$-0.581325\pi$
$601$	−7446.97	−0.505438	−0.252719	+	0.967540i	$0.581325\pi$
$602$	−415.634	−0.0281395
$603$	−12581.4	−0.849674
$604$	−726.253	−0.0489252
$605$	−6416.42	−0.431181
$606$	5162.80	0.346080
$607$	−24071.4	−1.60960	−0.804799	−	0.593547i	$-0.797727\pi$
$607$	−24071.4	−1.60960	−0.804799	+	0.593547i	$0.797727\pi$
$608$	−6334.59	−0.422536
$609$	1601.17	0.106540
$610$	2491.67	0.165385
$611$	11688.7	0.773932
$612$	−9628.88	−0.635988
$613$	−4108.61	−0.270710	−0.135355	−	0.990797i	$-0.543218\pi$
$613$	−4108.61	−0.270710	−0.135355	+	0.990797i	$0.543218\pi$
$614$	27781.8	1.82603
$615$	740.249	0.0485361
$616$	648.932	0.0424451
$617$	3542.46	0.231141	0.115571	−	0.993299i	$-0.463130\pi$
$617$	3542.46	0.231141	0.115571	+	0.993299i	$0.463130\pi$
$618$	4310.97	0.280603
$619$	6484.81	0.421077	0.210538	−	0.977586i	$-0.432478\pi$
$619$	6484.81	0.421077	0.210538	+	0.977586i	$0.432478\pi$
$620$	4089.88	0.264925
$621$	4327.26	0.279625
$622$	−8925.79	−0.575388
$623$	−4981.88	−0.320377
$624$	1505.28	0.0965693
$625$	625.000	0.0400000
$626$	−16944.1	−1.08183
$627$	−217.047	−0.0138246
$628$	−3816.29	−0.242495
$629$	189.451	0.0120094
$630$	−3205.75	−0.202730
$631$	3250.84	0.205094	0.102547	−	0.994728i	$-0.467301\pi$
$631$	3250.84	0.205094	0.102547	+	0.994728i	$0.467301\pi$
$632$	14760.8	0.929038
$633$	−858.436	−0.0539017
$634$	28464.4	1.78307
$635$	−8336.07	−0.520956
$636$	−2262.03	−0.141031
$637$	−1084.68	−0.0674674
$638$	−6477.58	−0.401959
$639$	−2773.56	−0.171706
$640$	7594.42	0.469056
$641$	2800.61	0.172570	0.0862852	−	0.996270i	$-0.472500\pi$
$641$	2800.61	0.172570	0.0862852	+	0.996270i	$0.472500\pi$
$642$	−3502.03	−0.215287
$643$	18910.6	1.15982	0.579908	−	0.814682i	$-0.303089\pi$
$643$	18910.6	1.15982	0.579908	+	0.814682i	$0.303089\pi$
$644$	−2774.94	−0.169795
$645$	−72.4169	−0.00442080
$646$	11374.8	0.692780
$647$	−24522.7	−1.49009	−0.745043	−	0.667016i	$-0.767571\pi$
$647$	−24522.7	−1.49009	−0.745043	+	0.667016i	$0.767571\pi$
$648$	−9004.77	−0.545897
$649$	4441.43	0.268631
$650$	−1928.99	−0.116402
$651$	1173.16	0.0706293
$652$	9828.74	0.590373
$653$	−15299.6	−0.916875	−0.458438	−	0.888727i	$-0.651591\pi$
$653$	−15299.6	−0.916875	−0.458438	+	0.888727i	$0.651591\pi$
$654$	6533.12	0.390619
$655$	4458.61	0.265973
$656$	−13926.3	−0.828857
$657$	−25922.7	−1.53933
$658$	−12883.7	−0.763309
$659$	−2203.13	−0.130230	−0.0651151	−	0.997878i	$-0.520741\pi$
$659$	−2203.13	−0.130230	−0.0651151	+	0.997878i	$0.520741\pi$
$660$	−121.861	−0.00718699
$661$	−3162.36	−0.186084	−0.0930421	−	0.995662i	$-0.529659\pi$
$661$	−3162.36	−0.186084	−0.0930421	+	0.995662i	$0.529659\pi$
$662$	10369.4	0.608790
$663$	−1661.97	−0.0973538
$664$	16596.2	0.969965
$665$	1293.46	0.0754258
$666$	−196.509	−0.0114333
$667$	−25699.9	−1.49191
$668$	4479.12	0.259435
$669$	1085.99	0.0627605
$670$	8344.59	0.481164
$671$	−987.565	−0.0568175
$672$	−1020.17	−0.0585624
$673$	−4443.07	−0.254484	−0.127242	−	0.991872i	$-0.540613\pi$
$673$	−4443.07	−0.254484	−0.127242	+	0.991872i	$0.540613\pi$
$674$	12187.0	0.696479
$675$	−1132.46	−0.0645752
$676$	−7083.56	−0.403025
$677$	4456.32	0.252984	0.126492	−	0.991968i	$-0.459628\pi$
$677$	4456.32	0.252984	0.126492	+	0.991968i	$0.459628\pi$
$678$	702.044	0.0397667
$679$	−4455.87	−0.251842
$680$	−5925.39	−0.334159
$681$	1190.23	0.0669743
$682$	−4746.03	−0.266474
$683$	−10046.8	−0.562858	−0.281429	−	0.959582i	$-0.590808\pi$
$683$	−10046.8	−0.562858	−0.281429	+	0.959582i	$0.590808\pi$
$684$	−4029.81	−0.225269
$685$	−2002.13	−0.111675
$686$	1195.58	0.0665414
$687$	2705.46	0.150247
$688$	1362.38	0.0754944
$689$	14191.9	0.784717
$690$	−1415.55	−0.0781003
$691$	31811.2	1.75131	0.875655	−	0.482938i	$-0.160430\pi$
$691$	31811.2	1.75131	0.875655	+	0.482938i	$0.160430\pi$
$692$	−3657.06	−0.200897
$693$	1270.59	0.0696474
$694$	13800.0	0.754812
$695$	2575.25	0.140554
$696$	−3069.81	−0.167185
$697$	15376.0	0.835590
$698$	19455.7	1.05503
$699$	−2574.39	−0.139302
$700$	726.208	0.0392116
$701$	−13907.2	−0.749312	−0.374656	−	0.927164i	$-0.622239\pi$
$701$	−13907.2	−0.749312	−0.374656	+	0.927164i	$0.622239\pi$
$702$	3495.20	0.187917
$703$	79.2877	0.00425376
$704$	−292.524	−0.0156604
$705$	−2244.75	−0.119918
$706$	−34495.5	−1.83889
$707$	12194.3	0.648678
$708$	−2268.60	−0.120423
$709$	−228.952	−0.0121276	−0.00606381	−	0.999982i	$-0.501930\pi$
$709$	−228.952	−0.0121276	−0.00606381	+	0.999982i	$0.501930\pi$
$710$	1839.56	0.0972358
$711$	28901.1	1.52444
$712$	9551.40	0.502744
$713$	−18830.0	−0.989043
$714$	1831.88	0.0960176
$715$	764.551	0.0399896
$716$	−14016.7	−0.731606
$717$	−4247.53	−0.221237
$718$	41540.5	2.15916
$719$	36162.2	1.87569	0.937846	−	0.347052i	$-0.112817\pi$
$719$	36162.2	1.87569	0.937846	+	0.347052i	$0.112817\pi$
$720$	10507.9	0.543897
$721$	10182.4	0.525952
$722$	−19147.6	−0.986979
$723$	−3193.93	−0.164293
$724$	5957.30	0.305803
$725$	6725.73	0.344534
$726$	−3803.19	−0.194421
$727$	22268.3	1.13602	0.568010	−	0.823021i	$-0.307713\pi$
$727$	22268.3	1.13602	0.568010	+	0.823021i	$0.307713\pi$
$728$	2079.58	0.105872
$729$	−16591.2	−0.842919
$730$	17193.2	0.871710
$731$	−1504.20	−0.0761077
$732$	504.429	0.0254703
$733$	−2333.20	−0.117570	−0.0587848	−	0.998271i	$-0.518723\pi$
$733$	−2333.20	−0.117570	−0.0587848	+	0.998271i	$0.518723\pi$
$734$	−24753.6	−1.24479
$735$	208.308	0.0104538
$736$	16374.4	0.820067
$737$	−3307.35	−0.165302
$738$	−15948.8	−0.795506
$739$	−4829.15	−0.240383	−0.120192	−	0.992751i	$-0.538351\pi$
$739$	−4829.15	−0.240383	−0.120192	+	0.992751i	$0.538351\pi$
$740$	44.5158	0.00221140
$741$	−695.556	−0.0344830
$742$	−15642.9	−0.773947
$743$	−25459.0	−1.25707	−0.628533	−	0.777783i	$-0.716344\pi$
$743$	−25459.0	−1.25707	−0.628533	+	0.777783i	$0.716344\pi$
$744$	−2249.21	−0.110833
$745$	1091.87	0.0536953
$746$	1025.88	0.0503488
$747$	32494.8	1.59160
$748$	−2531.21	−0.123730
$749$	−8271.66	−0.403525
$750$	370.454	0.0180361
$751$	−5707.08	−0.277303	−0.138651	−	0.990341i	$-0.544277\pi$
$751$	−5707.08	−0.277303	−0.138651	+	0.990341i	$0.544277\pi$
$752$	42230.4	2.04785
$753$	5582.21	0.270155
$754$	−20758.2	−1.00261
$755$	−875.054	−0.0421808
$756$	−1315.84	−0.0633023
$757$	−1900.91	−0.0912677	−0.0456339	−	0.998958i	$-0.514531\pi$
$757$	−1900.91	−0.0912677	−0.0456339	+	0.998958i	$0.514531\pi$
$758$	−32892.6	−1.57614
$759$	561.051	0.0268312
$760$	−2479.85	−0.118360
$761$	−11583.8	−0.551791	−0.275896	−	0.961188i	$-0.588974\pi$
$761$	−11583.8	−0.551791	−0.275896	+	0.961188i	$0.588974\pi$
$762$	−4941.01	−0.234900
$763$	15431.0	0.732162
$764$	−6590.40	−0.312084
$765$	−11601.7	−0.548316
$766$	−11017.5	−0.519686
$767$	14233.1	0.670051
$768$	4213.37	0.197965
$769$	−26059.7	−1.22202	−0.611012	−	0.791622i	$-0.709237\pi$
$769$	−26059.7	−1.22202	−0.611012	+	0.791622i	$0.709237\pi$
$770$	−842.716	−0.0394408
$771$	−5849.17	−0.273220
$772$	−4057.24	−0.189149
$773$	−16213.6	−0.754413	−0.377206	−	0.926129i	$-0.623115\pi$
$773$	−16213.6	−0.754413	−0.377206	+	0.926129i	$0.623115\pi$
$774$	1560.24	0.0724568
$775$	4927.85	0.228405
$776$	8542.92	0.395197
$777$	12.7691	0.000589561 0
$778$	27267.4	1.25653
$779$	6435.04	0.295968
$780$	−390.518	−0.0179266
$781$	−729.103	−0.0334051
$782$	−29403.0	−1.34456
$783$	−12186.6	−0.556209
$784$	−3918.90	−0.178521
$785$	−4598.21	−0.209066
$786$	2642.74	0.119928
$787$	−1371.34	−0.0621131	−0.0310565	−	0.999518i	$-0.509887\pi$
$787$	−1371.34	−0.0621131	−0.0310565	+	0.999518i	$0.509887\pi$
$788$	1492.59	0.0674765
$789$	2618.86	0.118167
$790$	−19168.7	−0.863279
$791$	1658.20	0.0745371
$792$	−2436.01	−0.109293
$793$	−3164.78	−0.141721
$794$	−27659.3	−1.23626
$795$	−2725.50	−0.121589
$796$	11695.6	0.520778
$797$	7991.49	0.355173	0.177587	−	0.984105i	$-0.443171\pi$
$797$	7991.49	0.355173	0.177587	+	0.984105i	$0.443171\pi$
$798$	766.668	0.0340097
$799$	−46626.5	−2.06449
$800$	−4285.23	−0.189382
$801$	18701.3	0.824943
$802$	−1702.32	−0.0749515
$803$	−6814.47	−0.299474
$804$	1689.33	0.0741022
$805$	−3343.49	−0.146388
$806$	−15209.3	−0.664669
$807$	5705.38	0.248871
$808$	−23379.3	−1.01792
$809$	−17661.4	−0.767542	−0.383771	−	0.923428i	$-0.625375\pi$
$809$	−17661.4	−0.767542	−0.383771	+	0.923428i	$0.625375\pi$
$810$	11693.8	0.507257
$811$	−24180.6	−1.04697	−0.523486	−	0.852034i	$-0.675369\pi$
$811$	−24180.6	−1.04697	−0.523486	+	0.852034i	$0.675369\pi$
$812$	7814.85	0.337743
$813$	6668.38	0.287663
$814$	−51.6576	−0.00222432
$815$	11842.5	0.508989
$816$	−6004.60	−0.257602
$817$	−629.526	−0.0269576
$818$	39146.1	1.67324
$819$	4071.76	0.173723
$820$	3612.93	0.153865
$821$	−23340.9	−0.992208	−0.496104	−	0.868263i	$-0.665237\pi$
$821$	−23340.9	−0.992208	−0.496104	+	0.868263i	$0.665237\pi$
$822$	−1186.71	−0.0503545
$823$	20630.4	0.873792	0.436896	−	0.899512i	$-0.356078\pi$
$823$	20630.4	0.873792	0.436896	+	0.899512i	$0.356078\pi$
$824$	−19521.9	−0.825337
$825$	−146.828	−0.00619625
$826$	−15688.3	−0.660854
$827$	24113.7	1.01393	0.506963	−	0.861968i	$-0.330768\pi$
$827$	24113.7	1.01393	0.506963	+	0.861968i	$0.330768\pi$
$828$	10416.8	0.437207
$829$	41738.9	1.74868	0.874338	−	0.485317i	$-0.161296\pi$
$829$	41738.9	1.74868	0.874338	+	0.485317i	$0.161296\pi$
$830$	−21552.1	−0.901308
$831$	4631.14	0.193324
$832$	−937.432	−0.0390620
$833$	4326.85	0.179972
$834$	1526.42	0.0633760
$835$	5396.84	0.223671
$836$	−1059.34	−0.0438256
$837$	−8928.91	−0.368732
$838$	−25687.9	−1.05892
$839$	30403.0	1.25105	0.625523	−	0.780205i	$-0.284886\pi$
$839$	30403.0	1.25105	0.625523	+	0.780205i	$0.284886\pi$
$840$	−399.374	−0.0164044
$841$	47987.8	1.96760
$842$	41731.9	1.70805
$843$	1808.25	0.0738784
$844$	−4189.77	−0.170874
$845$	−8534.90	−0.347467
$846$	48363.6	1.96545
$847$	−8982.99	−0.364415
$848$	51274.7	2.07639
$849$	−2913.24	−0.117764
$850$	7694.84	0.310507
$851$	−204.952	−0.00825579
$852$	372.412	0.0149749
$853$	5900.43	0.236843	0.118421	−	0.992963i	$-0.462217\pi$
$853$	5900.43	0.236843	0.118421	+	0.992963i	$0.462217\pi$
$854$	3488.33	0.139776
$855$	−4855.48	−0.194215
$856$	15858.7	0.633221
$857$	−18226.2	−0.726480	−0.363240	−	0.931696i	$-0.618330\pi$
$857$	−18226.2	−0.726480	−0.363240	+	0.931696i	$0.618330\pi$
$858$	453.170	0.0180314
$859$	−19944.2	−0.792186	−0.396093	−	0.918210i	$-0.629634\pi$
$859$	−19944.2	−0.792186	−0.396093	+	0.918210i	$0.629634\pi$
$860$	−353.446	−0.0140144
$861$	1036.35	0.0410205
$862$	−12438.9	−0.491497
$863$	30830.3	1.21608	0.608038	−	0.793908i	$-0.291957\pi$
$863$	30830.3	1.21608	0.608038	+	0.793908i	$0.291957\pi$
$864$	7764.53	0.305735
$865$	−4406.36	−0.173203
$866$	7987.70	0.313433
$867$	2452.44	0.0960662
$868$	5725.83	0.223903
$869$	7597.44	0.296577
$870$	3986.52	0.155351
$871$	−10598.8	−0.412317
$872$	−29584.7	−1.14893
$873$	16726.8	0.648471
$874$	−12305.5	−0.476248
$875$	875.000	0.0338062
$876$	3480.70	0.134249
$877$	−45885.6	−1.76676	−0.883379	−	0.468659i	$-0.844737\pi$
$877$	−45885.6	−1.76676	−0.883379	+	0.468659i	$0.844737\pi$
$878$	−25548.6	−0.982033
$879$	−1487.77	−0.0570889
$880$	2762.28	0.105814
$881$	41132.6	1.57298	0.786489	−	0.617605i	$-0.211897\pi$
$881$	41132.6	1.57298	0.786489	+	0.617605i	$0.211897\pi$
$882$	−4488.05	−0.171338
$883$	19850.0	0.756520	0.378260	−	0.925699i	$-0.376523\pi$
$883$	19850.0	0.756520	0.378260	+	0.925699i	$0.376523\pi$
$884$	−8111.58	−0.308622
$885$	−2733.41	−0.103822
$886$	28921.8	1.09667
$887$	29029.3	1.09888	0.549441	−	0.835532i	$-0.314841\pi$
$887$	29029.3	1.09888	0.549441	+	0.835532i	$0.314841\pi$
$888$	−24.4812	−0.000925154 0
$889$	−11670.5	−0.440288
$890$	−12403.6	−0.467159
$891$	−4634.80	−0.174267
$892$	5300.40	0.198958
$893$	−19513.8	−0.731248
$894$	647.181	0.0242114
$895$	−16888.6	−0.630752
$896$	10632.2	0.396425
$897$	1797.96	0.0669254
$898$	34015.2	1.26403
$899$	53029.4	1.96733
$900$	−2726.09	−0.100966
$901$	−56612.3	−2.09326
$902$	−4192.57	−0.154764
$903$	−101.384	−0.00373625
$904$	−3179.15	−0.116966
$905$	7177.88	0.263647
$906$	−518.668	−0.0190194
$907$	−21029.1	−0.769856	−0.384928	−	0.922947i	$-0.625774\pi$
$907$	−21029.1	−0.769856	−0.384928	+	0.922947i	$0.625774\pi$
$908$	5809.14	0.212316
$909$	−45776.0	−1.67029
$910$	−2700.59	−0.0983777
$911$	−19225.5	−0.699198	−0.349599	−	0.936899i	$-0.613682\pi$
$911$	−19225.5	−0.699198	−0.349599	+	0.936899i	$0.613682\pi$
$912$	−2513.01	−0.0912433
$913$	8542.13	0.309642
$914$	−40938.9	−1.48155
$915$	607.781	0.0219591
$916$	13204.6	0.476300
$917$	6242.05	0.224788
$918$	−13942.5	−0.501276
$919$	21316.8	0.765154	0.382577	−	0.923924i	$-0.375037\pi$
$919$	21316.8	0.765154	0.382577	+	0.923924i	$0.375037\pi$
$920$	6410.23	0.229716
$921$	6776.68	0.242453
$922$	−37465.9	−1.33826
$923$	−2336.50	−0.0833229
$924$	−170.605	−0.00607412
$925$	53.6366	0.00190655
$926$	−34377.3	−1.21999
$927$	−38223.3	−1.35428
$928$	−46114.1	−1.63122
$929$	19989.6	0.705959	0.352979	−	0.935631i	$-0.385169\pi$
$929$	19989.6	0.705959	0.352979	+	0.935631i	$0.385169\pi$
$930$	2920.87	0.102988
$931$	1810.84	0.0637465
$932$	−12564.8	−0.441603
$933$	−2177.23	−0.0763978
$934$	−16245.9	−0.569144
$935$	−3049.82	−0.106674
$936$	−7806.49	−0.272610
$937$	55676.4	1.94116	0.970580	−	0.240779i	$-0.0774027\pi$
$937$	55676.4	1.94116	0.970580	+	0.240779i	$0.0774027\pi$
$938$	11682.4	0.406658
$939$	−4133.10	−0.143641
$940$	−10956.0	−0.380153
$941$	−108.842	−0.00377062	−0.00188531	−	0.999998i	$-0.500600\pi$
$941$	−108.842	−0.00377062	−0.00188531	+	0.999998i	$0.500600\pi$
$942$	−2725.48	−0.0942686
$943$	−16634.1	−0.574422
$944$	51423.6	1.77298
$945$	−1585.44	−0.0545760
$946$	410.150	0.0140963
$947$	−7785.95	−0.267169	−0.133585	−	0.991037i	$-0.542649\pi$
$947$	−7785.95	−0.267169	−0.133585	+	0.991037i	$0.542649\pi$
$948$	−3880.62	−0.132950
$949$	−21837.8	−0.746982
$950$	3220.39	0.109982
$951$	6943.18	0.236749
$952$	−8295.55	−0.282416
$953$	41445.5	1.40876	0.704381	−	0.709822i	$-0.251224\pi$
$953$	41445.5	1.40876	0.704381	+	0.709822i	$0.251224\pi$
$954$	58721.4	1.99285
$955$	−7940.69	−0.269063
$956$	−20730.9	−0.701345
$957$	−1580.05	−0.0533706
$958$	−56792.5	−1.91532
$959$	−2802.98	−0.0943825
$960$	180.029	0.00605252
$961$	9062.92	0.304217
$962$	−165.543	−0.00554817
$963$	31050.8	1.03904
$964$	−15588.7	−0.520826
$965$	−4888.52	−0.163075
$966$	−1981.78	−0.0660068
$967$	39155.0	1.30211	0.651055	−	0.759030i	$-0.274327\pi$
$967$	39155.0	1.30211	0.651055	+	0.759030i	$0.274327\pi$
$968$	17222.4	0.571849
$969$	2774.60	0.0919846
$970$	−11094.0	−0.367224
$971$	−43440.8	−1.43572	−0.717859	−	0.696189i	$-0.754878\pi$
$971$	−43440.8	−1.43572	−0.717859	+	0.696189i	$0.754878\pi$
$972$	7442.74	0.245603
$973$	3605.35	0.118789
$974$	−12252.0	−0.403061
$975$	−470.530	−0.0154554
$976$	−11434.2	−0.374999
$977$	11297.8	0.369957	0.184978	−	0.982743i	$-0.440778\pi$
$977$	11297.8	0.369957	0.184978	+	0.982743i	$0.440778\pi$
$978$	7019.39	0.229504
$979$	4916.15	0.160491
$980$	1016.69	0.0331398
$981$	−57925.9	−1.88525
$982$	−8772.66	−0.285078
$983$	10865.9	0.352563	0.176282	−	0.984340i	$-0.443593\pi$
$983$	10865.9	0.352563	0.176282	+	0.984340i	$0.443593\pi$
$984$	−1986.91	−0.0643704
$985$	1798.41	0.0581747
$986$	82805.5	2.67451
$987$	−3142.65	−0.101349
$988$	−3394.80	−0.109315
$989$	1627.28	0.0523199
$990$	3163.45	0.101557
$991$	13884.1	0.445048	0.222524	−	0.974927i	$-0.428570\pi$
$991$	13884.1	0.445048	0.222524	+	0.974927i	$0.428570\pi$
$992$	−33787.1	−1.08139
$993$	2529.36	0.0808328
$994$	2575.38	0.0821792
$995$	14091.9	0.448987
$996$	−4363.15	−0.138807
$997$	31665.7	1.00588	0.502940	−	0.864321i	$-0.332252\pi$
$997$	31665.7	1.00588	0.502940	+	0.864321i	$0.332252\pi$
$998$	−30490.7	−0.967099
$999$	−97.1857	−0.00307790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.a.c.1.3	✓	3
3.2	odd	2		315.4.a.p.1.1		3
4.3	odd	2		560.4.a.u.1.2		3
5.2	odd	4		175.4.b.e.99.5		6
5.3	odd	4		175.4.b.e.99.2		6
5.4	even	2		175.4.a.f.1.1		3
7.2	even	3		245.4.e.m.116.1		6
7.3	odd	6		245.4.e.n.226.1		6
7.4	even	3		245.4.e.m.226.1		6
7.5	odd	6		245.4.e.n.116.1		6
7.6	odd	2		245.4.a.l.1.3		3
8.3	odd	2		2240.4.a.bv.1.2		3
8.5	even	2		2240.4.a.bt.1.2		3
15.14	odd	2		1575.4.a.ba.1.3		3
21.20	even	2		2205.4.a.bm.1.1		3
35.34	odd	2		1225.4.a.y.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.3	✓	3	1.1	even	1	trivial
175.4.a.f.1.1		3	5.4	even	2
175.4.b.e.99.2		6	5.3	odd	4
175.4.b.e.99.5		6	5.2	odd	4
245.4.a.l.1.3		3	7.6	odd	2
245.4.e.m.116.1		6	7.2	even	3
245.4.e.m.226.1		6	7.4	even	3
245.4.e.n.116.1		6	7.5	odd	6
245.4.e.n.226.1		6	7.3	odd	6
315.4.a.p.1.1		3	3.2	odd	2
560.4.a.u.1.2		3	4.3	odd	2
1225.4.a.y.1.1		3	35.34	odd	2
1575.4.a.ba.1.3		3	15.14	odd	2
2205.4.a.bm.1.1		3	21.20	even	2
2240.4.a.bt.1.2		3	8.5	even	2
2240.4.a.bv.1.2		3	8.3	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q+3.48565 q^{2} +0.850238 q^{3} +4.14976 q^{4} +5.00000 q^{5} +2.96363 q^{6} +7.00000 q^{7} -13.4206 q^{8} -26.2771 q^{9} +17.4283 q^{10} -6.90764 q^{11} +3.52829 q^{12} -22.1364 q^{13} +24.3996 q^{14} +4.25119 q^{15} -79.9776 q^{16} +88.3030 q^{17} -91.5928 q^{18} +36.9560 q^{19} +20.7488 q^{20} +5.95167 q^{21} -24.0776 q^{22} -95.5283 q^{23} -11.4107 q^{24} +25.0000 q^{25} -77.1598 q^{26} -45.2982 q^{27} +29.0483 q^{28} +269.029 q^{29} +14.8182 q^{30} +197.114 q^{31} -171.409 q^{32} -5.87314 q^{33} +307.793 q^{34} +35.0000 q^{35} -109.044 q^{36} +2.14546 q^{37} +128.816 q^{38} -18.8212 q^{39} -67.1029 q^{40} +174.127 q^{41} +20.7454 q^{42} -17.0345 q^{43} -28.6650 q^{44} -131.385 q^{45} -332.978 q^{46} -528.029 q^{47} -68.0000 q^{48} +49.0000 q^{49} +87.1413 q^{50} +75.0786 q^{51} -91.8608 q^{52} -641.114 q^{53} -157.894 q^{54} -34.5382 q^{55} -93.9441 q^{56} +31.4214 q^{57} +937.742 q^{58} -642.975 q^{59} +17.6414 q^{60} +142.967 q^{61} +687.070 q^{62} -183.940 q^{63} +42.3480 q^{64} -110.682 q^{65} -20.4717 q^{66} +478.797 q^{67} +366.436 q^{68} -81.2218 q^{69} +121.998 q^{70} +105.550 q^{71} +352.654 q^{72} +986.512 q^{73} +7.47834 q^{74} +21.2560 q^{75} +153.358 q^{76} -48.3534 q^{77} -65.6042 q^{78} -1099.86 q^{79} -399.888 q^{80} +670.967 q^{81} +606.947 q^{82} -1236.62 q^{83} +24.6980 q^{84} +441.515 q^{85} -59.3763 q^{86} +228.739 q^{87} +92.7045 q^{88} -711.698 q^{89} -457.964 q^{90} -154.955 q^{91} -396.420 q^{92} +167.594 q^{93} -1840.52 q^{94} +184.780 q^{95} -145.739 q^{96} -636.553 q^{97} +170.797 q^{98} +181.513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 13 q^{4} + 15 q^{5} + 24 q^{6} + 21 q^{7} - 15 q^{8} + 81 q^{9} - 15 q^{10} - 74 q^{11} - 152 q^{12} + 44 q^{13} - 21 q^{14} + 10 q^{15} - 79 q^{16} - 52 q^{17} - 411 q^{18} + 168 q^{19}+ \cdots - 3488 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 13 * q^4 + 15 * q^5 + 24 * q^6 + 21 * q^7 - 15 * q^8 + 81 * q^9 - 15 * q^10 - 74 * q^11 - 152 * q^12 + 44 * q^13 - 21 * q^14 + 10 * q^15 - 79 * q^16 - 52 * q^17 - 411 * q^18 + 168 * q^19 + 65 * q^20 + 14 * q^21 + 184 * q^22 - 124 * q^23 + 420 * q^24 + 75 * q^25 - 446 * q^26 + 170 * q^27 + 91 * q^28 + 332 * q^29 + 120 * q^30 + 320 * q^31 - 183 * q^32 - 106 * q^33 + 582 * q^34 + 105 * q^35 + 181 * q^36 - 54 * q^37 - 460 * q^38 - 982 * q^39 - 75 * q^40 + 362 * q^41 + 168 * q^42 - 16 * q^43 - 264 * q^44 + 405 * q^45 - 336 * q^46 - 730 * q^47 - 204 * q^48 + 147 * q^49 - 75 * q^50 - 1178 * q^51 + 1202 * q^52 + 110 * q^53 - 180 * q^54 - 370 * q^55 - 105 * q^56 - 956 * q^57 + 450 * q^58 - 180 * q^59 - 760 * q^60 + 1222 * q^61 + 464 * q^62 + 567 * q^63 - 391 * q^64 + 220 * q^65 - 532 * q^66 + 204 * q^67 + 918 * q^68 - 716 * q^69 - 105 * q^70 - 136 * q^71 + 765 * q^72 + 310 * q^73 + 502 * q^74 + 50 * q^75 + 1796 * q^76 - 518 * q^77 + 3788 * q^78 - 1034 * q^79 - 395 * q^80 + 2283 * q^81 - 6 * q^82 - 1660 * q^83 - 1064 * q^84 - 260 * q^85 + 764 * q^86 - 1574 * q^87 - 20 * q^88 + 242 * q^89 - 2055 * q^90 + 308 * q^91 + 96 * q^92 + 1376 * q^93 - 1108 * q^94 + 840 * q^95 - 3156 * q^96 + 100 * q^97 - 147 * q^98 - 3488 * q^99

Introduction

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Varieties

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Database

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