LMFDB - Embedded newform 35.4.a.c.1.1

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			1.1
Root			$-3.62456$ 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)

$f(q)$	$=$	\(q-4.62456 q^{2} -8.38660 q^{3} +13.3866 q^{4} +5.00000 q^{5} +38.7844 q^{6} +7.00000 q^{7} -24.9107 q^{8} +43.3350 q^{9} -23.1228 q^{10} -30.1117 q^{11} -112.268 q^{12} +88.9295 q^{13} -32.3720 q^{14} -41.9330 q^{15} +8.10818 q^{16} -4.73699 q^{17} -200.405 q^{18} +124.818 q^{19} +66.9330 q^{20} -58.7062 q^{21} +139.253 q^{22} +20.2680 q^{23} +208.916 q^{24} +25.0000 q^{25} -411.260 q^{26} -136.995 q^{27} +93.7062 q^{28} +134.088 q^{29} +193.922 q^{30} -2.03767 q^{31} +161.788 q^{32} +252.534 q^{33} +21.9065 q^{34} +35.0000 q^{35} +580.108 q^{36} -141.137 q^{37} -577.228 q^{38} -745.816 q^{39} -124.553 q^{40} +95.2784 q^{41} +271.490 q^{42} -298.646 q^{43} -403.093 q^{44} +216.675 q^{45} -93.7305 q^{46} -129.054 q^{47} -68.0000 q^{48} +49.0000 q^{49} -115.614 q^{50} +39.7272 q^{51} +1190.46 q^{52} +388.429 q^{53} +633.542 q^{54} -150.558 q^{55} -174.375 q^{56} -1046.80 q^{57} -620.098 q^{58} +838.501 q^{59} -561.340 q^{60} +389.422 q^{61} +9.42333 q^{62} +303.345 q^{63} -813.067 q^{64} +444.647 q^{65} -1167.86 q^{66} +697.794 q^{67} -63.4122 q^{68} -169.979 q^{69} -161.860 q^{70} -523.450 q^{71} -1079.50 q^{72} +66.4684 q^{73} +652.699 q^{74} -209.665 q^{75} +1670.89 q^{76} -210.782 q^{77} +3449.07 q^{78} -526.982 q^{79} +40.5409 q^{80} -21.1236 q^{81} -440.621 q^{82} +70.0265 q^{83} -785.876 q^{84} -23.6850 q^{85} +1381.11 q^{86} -1124.54 q^{87} +750.101 q^{88} -9.27925 q^{89} -1002.03 q^{90} +622.506 q^{91} +271.319 q^{92} +17.0891 q^{93} +596.817 q^{94} +624.089 q^{95} -1356.85 q^{96} -4.19493 q^{97} -226.604 q^{98} -1304.89 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.62456	−1.63503	−0.817515	−	0.575907i	$-0.804649\pi$
$2$	−4.62456	−1.63503	−0.817515	+	0.575907i	$0.804649\pi$
$3$	−8.38660	−1.61400	−0.807001	−	0.590551i	$-0.798911\pi$
$3$	−8.38660	−1.61400	−0.807001	+	0.590551i	$0.798911\pi$
$4$	13.3866	1.67332
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	38.7844	2.63894
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−24.9107	−1.10091
$9$	43.3350	1.60500
$10$	−23.1228	−0.731208
$11$	−30.1117	−0.825364	−0.412682	−	0.910875i	$-0.635408\pi$
$11$	−30.1117	−0.825364	−0.412682	+	0.910875i	$0.635408\pi$
$12$	−112.268	−2.70075
$13$	88.9295	1.89728	0.948639	−	0.316362i	$-0.102461\pi$
$13$	88.9295	1.89728	0.948639	+	0.316362i	$0.102461\pi$
$14$	−32.3720	−0.617983
$15$	−41.9330	−0.721803
$16$	8.10818	0.126690
$17$	−4.73699	−0.0675817	−0.0337909	−	0.999429i	$-0.510758\pi$
$17$	−4.73699	−0.0675817	−0.0337909	+	0.999429i	$0.510758\pi$
$18$	−200.405	−2.62422
$19$	124.818	1.50711	0.753557	−	0.657382i	$-0.228336\pi$
$19$	124.818	1.50711	0.753557	+	0.657382i	$0.228336\pi$
$20$	66.9330	0.748333
$21$	−58.7062	−0.610035
$22$	139.253	1.34950
$23$	20.2680	0.183746	0.0918731	−	0.995771i	$-0.470715\pi$
$23$	20.2680	0.183746	0.0918731	+	0.995771i	$0.470715\pi$
$24$	208.916	1.77686
$25$	25.0000	0.200000
$26$	−411.260	−3.10211
$27$	−136.995	−0.976470
$28$	93.7062	0.632457
$29$	134.088	0.858603	0.429301	−	0.903161i	$-0.358760\pi$
$29$	134.088	0.858603	0.429301	+	0.903161i	$0.358760\pi$
$30$	193.922	1.18017
$31$	−2.03767	−0.0118057	−0.00590284	−	0.999983i	$-0.501879\pi$
$31$	−2.03767	−0.0118057	−0.00590284	+	0.999983i	$0.501879\pi$
$32$	161.788	0.893764
$33$	252.534	1.33214
$34$	21.9065	0.110498
$35$	35.0000	0.169031
$36$	580.108	2.68568
$37$	−141.137	−0.627104	−0.313552	−	0.949571i	$-0.601519\pi$
$37$	−141.137	−0.627104	−0.313552	+	0.949571i	$0.601519\pi$
$38$	−577.228	−2.46418
$39$	−745.816	−3.06221
$40$	−124.553	−0.492340
$41$	95.2784	0.362927	0.181463	−	0.983398i	$-0.441917\pi$
$41$	95.2784	0.362927	0.181463	+	0.983398i	$0.441917\pi$
$42$	271.490	0.997426
$43$	−298.646	−1.05914	−0.529571	−	0.848266i	$-0.677647\pi$
$43$	−298.646	−1.05914	−0.529571	+	0.848266i	$0.677647\pi$
$44$	−403.093	−1.38110
$45$	216.675	0.717778
$46$	−93.7305	−0.300431
$47$	−129.054	−0.400519	−0.200260	−	0.979743i	$-0.564179\pi$
$47$	−129.054	−0.400519	−0.200260	+	0.979743i	$0.564179\pi$
$48$	−68.0000	−0.204478
$49$	49.0000	0.142857
$50$	−115.614	−0.327006
$51$	39.7272	0.109077
$52$	1190.46	3.17476
$53$	388.429	1.00669	0.503347	−	0.864084i	$-0.332102\pi$
$53$	388.429	1.00669	0.503347	+	0.864084i	$0.332102\pi$
$54$	633.542	1.59656
$55$	−150.558	−0.369114
$56$	−174.375	−0.416103
$57$	−1046.80	−2.43248
$58$	−620.098	−1.40384
$59$	838.501	1.85023	0.925114	−	0.379688i	$-0.123969\pi$
$59$	838.501	1.85023	0.925114	+	0.379688i	$0.123969\pi$
$60$	−561.340	−1.20781
$61$	389.422	0.817384	0.408692	−	0.912672i	$-0.365985\pi$
$61$	389.422	0.817384	0.408692	+	0.912672i	$0.365985\pi$
$62$	9.42333	0.0193027
$63$	303.345	0.606633
$64$	−813.067	−1.58802
$65$	444.647	0.848488
$66$	−1167.86	−2.17809
$67$	697.794	1.27237	0.636187	−	0.771534i	$-0.280510\pi$
$67$	697.794	1.27237	0.636187	+	0.771534i	$0.280510\pi$
$68$	−63.4122	−0.113086
$69$	−169.979	−0.296567
$70$	−161.860	−0.276371
$71$	−523.450	−0.874959	−0.437479	−	0.899228i	$-0.644129\pi$
$71$	−523.450	−0.874959	−0.437479	+	0.899228i	$0.644129\pi$
$72$	−1079.50	−1.76695
$73$	66.4684	0.106569	0.0532845	−	0.998579i	$-0.483031\pi$
$73$	66.4684	0.106569	0.0532845	+	0.998579i	$0.483031\pi$
$74$	652.699	1.02533
$75$	−209.665	−0.322800
$76$	1670.89	2.52189
$77$	−210.782	−0.311958
$78$	3449.07	5.00680
$79$	−526.982	−0.750508	−0.375254	−	0.926922i	$-0.622444\pi$
$79$	−526.982	−0.750508	−0.375254	+	0.926922i	$0.622444\pi$
$80$	40.5409	0.0566576
$81$	−21.1236	−0.0289762
$82$	−440.621	−0.593396
$83$	70.0265	0.0926074	0.0463037	−	0.998927i	$-0.485256\pi$
$83$	70.0265	0.0926074	0.0463037	+	0.998927i	$0.485256\pi$
$84$	−785.876	−1.02079
$85$	−23.6850	−0.0302235
$86$	1381.11	1.73173
$87$	−1124.54	−1.38579
$88$	750.101	0.908649
$89$	−9.27925	−0.0110517	−0.00552584	−	0.999985i	$-0.501759\pi$
$89$	−9.27925	−0.0110517	−0.00552584	+	0.999985i	$0.501759\pi$
$90$	−1002.03	−1.17359
$91$	622.506	0.717103
$92$	271.319	0.307467
$93$	17.0891	0.0190544
$94$	596.817	0.654861
$95$	624.089	0.674002
$96$	−1356.85	−1.44254
$97$	−4.19493	−0.00439104	−0.00219552	−	0.999998i	$-0.500699\pi$
$97$	−4.19493	−0.00439104	−0.00219552	+	0.999998i	$0.500699\pi$
$98$	−226.604	−0.233576
$99$	−1304.89	−1.32471
$100$	334.665	0.334665
$101$	−865.844	−0.853016	−0.426508	−	0.904484i	$-0.640256\pi$
$101$	−865.844	−0.853016	−0.426508	+	0.904484i	$0.640256\pi$
$102$	−183.721	−0.178344
$103$	−1166.12	−1.11554	−0.557771	−	0.829995i	$-0.688343\pi$
$103$	−1166.12	−1.11554	−0.557771	+	0.829995i	$0.688343\pi$
$104$	−2215.29	−2.08872
$105$	−293.531	−0.272816
$106$	−1796.31	−1.64598
$107$	56.9652	0.0514676	0.0257338	−	0.999669i	$-0.491808\pi$
$107$	56.9652	0.0514676	0.0257338	+	0.999669i	$0.491808\pi$
$108$	−1833.90	−1.63395
$109$	−1358.89	−1.19411	−0.597055	−	0.802200i	$-0.703663\pi$
$109$	−1358.89	−1.19411	−0.597055	+	0.802200i	$0.703663\pi$
$110$	696.267	0.603513
$111$	1183.66	1.01215
$112$	56.7572	0.0478844
$113$	436.038	0.363000	0.181500	−	0.983391i	$-0.441905\pi$
$113$	436.038	0.363000	0.181500	+	0.983391i	$0.441905\pi$
$114$	4840.98	3.97719
$115$	101.340	0.0821738
$116$	1794.98	1.43672
$117$	3853.76	3.04513
$118$	−3877.70	−3.02518
$119$	−33.1590	−0.0255435
$120$	1044.58	0.794637
$121$	−424.288	−0.318774
$122$	−1800.91	−1.33645
$123$	−799.062	−0.585764
$124$	−27.2775	−0.0197547
$125$	125.000	0.0894427
$126$	−1402.84	−0.991863
$127$	1186.69	0.829144	0.414572	−	0.910017i	$-0.363931\pi$
$127$	1186.69	0.829144	0.414572	+	0.910017i	$0.363931\pi$
$128$	2465.77	1.70270
$129$	2504.62	1.70946
$130$	−2056.30	−1.38730
$131$	1034.56	0.689997	0.344999	−	0.938603i	$-0.387879\pi$
$131$	1034.56	0.689997	0.344999	+	0.938603i	$0.387879\pi$
$132$	3380.57	2.22910
$133$	873.725	0.569636
$134$	−3226.99	−2.08037
$135$	−684.975	−0.436691
$136$	118.002	0.0744011
$137$	646.219	0.402994	0.201497	−	0.979489i	$-0.435419\pi$
$137$	646.219	0.402994	0.201497	+	0.979489i	$0.435419\pi$
$138$	786.080	0.484895
$139$	506.484	0.309061	0.154530	−	0.987988i	$-0.450614\pi$
$139$	506.484	0.309061	0.154530	+	0.987988i	$0.450614\pi$
$140$	468.531	0.282843
$141$	1082.32	0.646439
$142$	2420.73	1.43058
$143$	−2677.81	−1.56594
$144$	351.368	0.203338
$145$	670.439	0.383979
$146$	−307.387	−0.174244
$147$	−410.943	−0.230572
$148$	−1889.35	−1.04935
$149$	−1828.12	−1.00513	−0.502567	−	0.864538i	$-0.667611\pi$
$149$	−1828.12	−1.00513	−0.502567	+	0.864538i	$0.667611\pi$
$150$	969.609	0.527788
$151$	2975.17	1.60342	0.801708	−	0.597716i	$-0.203925\pi$
$151$	2975.17	1.60342	0.801708	+	0.597716i	$0.203925\pi$
$152$	−3109.29	−1.65919
$153$	−205.278	−0.108469
$154$	974.773	0.510061
$155$	−10.1883	−0.00527966
$156$	−9983.93	−5.12407
$157$	−2131.74	−1.08364	−0.541820	−	0.840495i	$-0.682264\pi$
$157$	−2131.74	−1.08364	−0.541820	+	0.840495i	$0.682264\pi$
$158$	2437.06	1.22710
$159$	−3257.59	−1.62481
$160$	808.942	0.399703
$161$	141.876	0.0694495
$162$	97.6876	0.0473769
$163$	−593.939	−0.285404	−0.142702	−	0.989766i	$-0.545579\pi$
$163$	−593.939	−0.285404	−0.142702	+	0.989766i	$0.545579\pi$
$164$	1275.45	0.607294
$165$	1262.67	0.595751
$166$	−323.842	−0.151416
$167$	−2936.30	−1.36059	−0.680293	−	0.732941i	$-0.738147\pi$
$167$	−2936.30	−1.36059	−0.680293	+	0.732941i	$0.738147\pi$
$168$	1462.41	0.671591
$169$	5711.45	2.59966
$170$	109.533	0.0494163
$171$	5408.98	2.41892
$172$	−3997.85	−1.77229
$173$	2347.31	1.03158	0.515788	−	0.856716i	$-0.327499\pi$
$173$	2347.31	1.03158	0.515788	+	0.856716i	$0.327499\pi$
$174$	5200.51	2.26580
$175$	175.000	0.0755929
$176$	−244.151	−0.104566
$177$	−7032.17	−2.98627
$178$	42.9125	0.0180698
$179$	3036.56	1.26795	0.633975	−	0.773354i	$-0.281422\pi$
$179$	3036.56	1.26795	0.633975	+	0.773354i	$0.281422\pi$
$180$	2900.54	1.20107
$181$	−899.776	−0.369502	−0.184751	−	0.982785i	$-0.559148\pi$
$181$	−899.776	−0.369502	−0.184751	+	0.982785i	$0.559148\pi$
$182$	−2878.82	−1.17249
$183$	−3265.93	−1.31926
$184$	−504.888	−0.202287
$185$	−705.687	−0.280449
$186$	−79.0297	−0.0311545
$187$	142.639	0.0557796
$188$	−1727.59	−0.670199
$189$	−958.964	−0.369071
$190$	−2886.14	−1.10201
$191$	416.168	0.157659	0.0788294	−	0.996888i	$-0.474882\pi$
$191$	416.168	0.157659	0.0788294	+	0.996888i	$0.474882\pi$
$192$	6818.86	2.56307
$193$	−5181.05	−1.93233	−0.966166	−	0.257922i	$-0.916962\pi$
$193$	−5181.05	−1.93233	−0.966166	+	0.257922i	$0.916962\pi$
$194$	19.3997	0.00717948
$195$	−3729.08	−1.36946
$196$	655.943	0.239046
$197$	1452.34	0.525255	0.262627	−	0.964897i	$-0.415411\pi$
$197$	1452.34	0.525255	0.262627	+	0.964897i	$0.415411\pi$
$198$	6034.54	2.16594
$199$	−1277.23	−0.454978	−0.227489	−	0.973781i	$-0.573052\pi$
$199$	−1277.23	−0.454978	−0.227489	+	0.973781i	$0.573052\pi$
$200$	−622.766	−0.220181
$201$	−5852.12	−2.05361
$202$	4004.15	1.39471
$203$	938.615	0.324521
$204$	531.813	0.182521
$205$	476.392	0.162306
$206$	5392.78	1.82395
$207$	878.312	0.294913
$208$	721.056	0.240367
$209$	−3758.47	−1.24392
$210$	1357.45	0.446062
$211$	−3259.09	−1.06334	−0.531670	−	0.846951i	$-0.678436\pi$
$211$	−3259.09	−1.06334	−0.531670	+	0.846951i	$0.678436\pi$
$212$	5199.74	1.68453
$213$	4389.96	1.41218
$214$	−263.439	−0.0841511
$215$	−1493.23	−0.473663
$216$	3412.63	1.07500
$217$	−14.2637	−0.00446213
$218$	6284.27	1.95241
$219$	−557.444	−0.172002
$220$	−2015.46	−0.617648
$221$	−421.258	−0.128221
$222$	−5473.92	−1.65489
$223$	4373.35	1.31328	0.656639	−	0.754205i	$-0.271977\pi$
$223$	4373.35	1.31328	0.656639	+	0.754205i	$0.271977\pi$
$224$	1132.52	0.337811
$225$	1083.37	0.321000
$226$	−2016.48	−0.593516
$227$	−61.1145	−0.0178692	−0.00893461	−	0.999960i	$-0.502844\pi$
$227$	−61.1145	−0.0178692	−0.00893461	+	0.999960i	$0.502844\pi$
$228$	−14013.0	−4.07034
$229$	3019.41	0.871302	0.435651	−	0.900116i	$-0.356518\pi$
$229$	3019.41	0.871302	0.435651	+	0.900116i	$0.356518\pi$
$230$	−468.653	−0.134357
$231$	1767.74	0.503501
$232$	−3340.22	−0.945241
$233$	−3531.17	−0.992851	−0.496426	−	0.868079i	$-0.665354\pi$
$233$	−3531.17	−0.992851	−0.496426	+	0.868079i	$0.665354\pi$
$234$	−17822.0	−4.97888
$235$	−645.268	−0.179118
$236$	11224.7	3.09603
$237$	4419.58	1.21132
$238$	153.346	0.0417644
$239$	2282.62	0.617785	0.308893	−	0.951097i	$-0.400042\pi$
$239$	2282.62	0.617785	0.308893	+	0.951097i	$0.400042\pi$
$240$	−340.000	−0.0914454
$241$	−2215.68	−0.592217	−0.296109	−	0.955154i	$-0.595689\pi$
$241$	−2215.68	−0.592217	−0.296109	+	0.955154i	$0.595689\pi$
$242$	1962.15	0.521205
$243$	3876.02	1.02324
$244$	5213.04	1.36775
$245$	245.000	0.0638877
$246$	3695.31	0.957742
$247$	11100.0	2.85941
$248$	50.7597	0.0129970
$249$	−587.284	−0.149468
$250$	−578.071	−0.146242
$251$	−3082.55	−0.775174	−0.387587	−	0.921833i	$-0.626691\pi$
$251$	−3082.55	−0.775174	−0.387587	+	0.921833i	$0.626691\pi$
$252$	4060.76	1.01509
$253$	−610.302	−0.151658
$254$	−5487.90	−1.35568
$255$	198.636	0.0487807
$256$	−4898.58	−1.19594
$257$	−6032.40	−1.46417	−0.732083	−	0.681215i	$-0.761452\pi$
$257$	−6032.40	−1.46417	−0.732083	+	0.681215i	$0.761452\pi$
$258$	−11582.8	−2.79501
$259$	−987.962	−0.237023
$260$	5952.32	1.41980
$261$	5810.69	1.37806
$262$	−4784.37	−1.12817
$263$	5923.81	1.38889	0.694445	−	0.719546i	$-0.255650\pi$
$263$	5923.81	1.38889	0.694445	+	0.719546i	$0.255650\pi$
$264$	−6290.80	−1.46656
$265$	1942.14	0.450207
$266$	−4040.60	−0.931372
$267$	77.8213	0.0178374
$268$	9341.09	2.12910
$269$	3252.80	0.737273	0.368637	−	0.929574i	$-0.379825\pi$
$269$	3252.80	0.737273	0.368637	+	0.929574i	$0.379825\pi$
$270$	3167.71	0.714002
$271$	−6246.26	−1.40012	−0.700061	−	0.714083i	$-0.746844\pi$
$271$	−6246.26	−1.40012	−0.700061	+	0.714083i	$0.746844\pi$
$272$	−38.4084	−0.00856195
$273$	−5220.71	−1.15741
$274$	−2988.48	−0.658907
$275$	−752.792	−0.165073
$276$	−2275.44	−0.496252
$277$	−1572.17	−0.341020	−0.170510	−	0.985356i	$-0.554541\pi$
$277$	−1572.17	−0.341020	−0.170510	+	0.985356i	$0.554541\pi$
$278$	−2342.27	−0.505324
$279$	−88.3024	−0.0189481
$280$	−871.873	−0.186087
$281$	−7846.03	−1.66567	−0.832837	−	0.553518i	$-0.813285\pi$
$281$	−7846.03	−1.66567	−0.832837	+	0.553518i	$0.813285\pi$
$282$	−5005.26	−1.05695
$283$	6265.58	1.31608	0.658039	−	0.752984i	$-0.271386\pi$
$283$	6265.58	1.31608	0.658039	+	0.752984i	$0.271386\pi$
$284$	−7007.21	−1.46409
$285$	−5233.98	−1.08784
$286$	12383.7	2.56037
$287$	666.949	0.137173
$288$	7011.10	1.43449
$289$	−4890.56	−0.995433
$290$	−3100.49	−0.627817
$291$	35.1812	0.00708714
$292$	889.785	0.178325
$293$	−7264.99	−1.44855	−0.724276	−	0.689511i	$-0.757826\pi$
$293$	−7264.99	−1.44855	−0.724276	+	0.689511i	$0.757826\pi$
$294$	1900.43	0.376992
$295$	4192.50	0.827448
$296$	3515.83	0.690382
$297$	4125.14	0.805943
$298$	8454.24	1.64343
$299$	1802.42	0.348617
$300$	−2806.70	−0.540149
$301$	−2090.52	−0.400318
$302$	−13758.9	−2.62163
$303$	7261.48	1.37677
$304$	1012.05	0.190937
$305$	1947.11	0.365545
$306$	949.319	0.177350
$307$	1328.32	0.246943	0.123471	−	0.992348i	$-0.460597\pi$
$307$	1328.32	0.246943	0.123471	+	0.992348i	$0.460597\pi$
$308$	−2821.65	−0.522008
$309$	9779.75	1.80049
$310$	47.1167	0.00863241
$311$	4868.68	0.887709	0.443855	−	0.896099i	$-0.353611\pi$
$311$	4868.68	0.887709	0.443855	+	0.896099i	$0.353611\pi$
$312$	18578.8	3.37120
$313$	7733.39	1.39654	0.698270	−	0.715835i	$-0.253954\pi$
$313$	7733.39	1.39654	0.698270	+	0.715835i	$0.253954\pi$
$314$	9858.37	1.77178
$315$	1516.72	0.271294
$316$	−7054.49	−1.25584
$317$	−8175.03	−1.44844	−0.724220	−	0.689569i	$-0.757800\pi$
$317$	−8175.03	−1.44844	−0.724220	+	0.689569i	$0.757800\pi$
$318$	15065.0	2.65661
$319$	−4037.61	−0.708660
$320$	−4065.33	−0.710184
$321$	−477.744	−0.0830688
$322$	−656.114	−0.113552
$323$	−591.261	−0.101853
$324$	−282.774	−0.0484865
$325$	2223.24	0.379455
$326$	2746.71	0.466644
$327$	11396.5	1.92729
$328$	−2373.45	−0.399548
$329$	−903.375	−0.151382
$330$	−5839.31	−0.974070
$331$	−2040.76	−0.338884	−0.169442	−	0.985540i	$-0.554197\pi$
$331$	−2040.76	−0.338884	−0.169442	+	0.985540i	$0.554197\pi$
$332$	937.417	0.154962
$333$	−6116.19	−1.00650
$334$	13579.1	2.22460
$335$	3488.97	0.569023
$336$	−476.000	−0.0772855
$337$	7349.73	1.18803	0.594013	−	0.804455i	$-0.297543\pi$
$337$	7349.73	1.18803	0.594013	+	0.804455i	$0.297543\pi$
$338$	−26413.0	−4.25052
$339$	−3656.87	−0.585882
$340$	−317.061	−0.0505737
$341$	61.3576	0.00974399
$342$	−25014.2	−3.95500
$343$	343.000	0.0539949
$344$	7439.47	1.16602
$345$	−849.896	−0.132629
$346$	−10855.3	−1.68666
$347$	−12069.9	−1.86728	−0.933642	−	0.358207i	$-0.883388\pi$
$347$	−12069.9	−1.86728	−0.933642	+	0.358207i	$0.883388\pi$
$348$	−15053.8	−2.31887
$349$	−4484.96	−0.687892	−0.343946	−	0.938989i	$-0.611764\pi$
$349$	−4484.96	−0.687892	−0.343946	+	0.938989i	$0.611764\pi$
$350$	−809.299	−0.123597
$351$	−12182.9	−1.85263
$352$	−4871.72	−0.737681
$353$	−12762.5	−1.92430	−0.962151	−	0.272517i	$-0.912144\pi$
$353$	−12762.5	−1.92430	−0.962151	+	0.272517i	$0.912144\pi$
$354$	32520.7	4.88264
$355$	−2617.25	−0.391293
$356$	−124.218	−0.0184930
$357$	278.091	0.0412272
$358$	−14042.8	−2.07314
$359$	−2419.42	−0.355689	−0.177844	−	0.984059i	$-0.556912\pi$
$359$	−2419.42	−0.355689	−0.177844	+	0.984059i	$0.556912\pi$
$360$	−5397.52	−0.790206
$361$	8720.49	1.27139
$362$	4161.07	0.604147
$363$	3558.33	0.514501
$364$	8333.24	1.19995
$365$	332.342	0.0476591
$366$	15103.5	2.15703
$367$	−7129.74	−1.01409	−0.507043	−	0.861921i	$-0.669261\pi$
$367$	−7129.74	−1.01409	−0.507043	+	0.861921i	$0.669261\pi$
$368$	164.336	0.0232789
$369$	4128.89	0.582497
$370$	3263.50	0.458543
$371$	2719.00	0.380495
$372$	228.765	0.0318842
$373$	11596.9	1.60983	0.804914	−	0.593391i	$-0.202211\pi$
$373$	11596.9	1.60983	0.804914	+	0.593391i	$0.202211\pi$
$374$	−659.642	−0.0912013
$375$	−1048.32	−0.144361
$376$	3214.81	0.440934
$377$	11924.4	1.62901
$378$	4434.79	0.603442
$379$	−12770.8	−1.73085	−0.865424	−	0.501040i	$-0.832951\pi$
$379$	−12770.8	−1.73085	−0.865424	+	0.501040i	$0.832951\pi$
$380$	8354.43	1.12782
$381$	−9952.25	−1.33824
$382$	−1924.59	−0.257777
$383$	7470.10	0.996617	0.498308	−	0.867000i	$-0.333955\pi$
$383$	7470.10	0.996617	0.498308	+	0.867000i	$0.333955\pi$
$384$	−20679.4	−2.74816
$385$	−1053.91	−0.139512
$386$	23960.1	3.15942
$387$	−12941.8	−1.69992
$388$	−56.1558	−0.00734763
$389$	8749.77	1.14044	0.570220	−	0.821492i	$-0.306858\pi$
$389$	8749.77	1.14044	0.570220	+	0.821492i	$0.306858\pi$
$390$	17245.4	2.23911
$391$	−96.0092	−0.0124179
$392$	−1220.62	−0.157272
$393$	−8676.41	−1.11366
$394$	−6716.46	−0.858808
$395$	−2634.91	−0.335637
$396$	−17468.0	−2.21667
$397$	5375.25	0.679537	0.339769	−	0.940509i	$-0.389651\pi$
$397$	5375.25	0.679537	0.339769	+	0.940509i	$0.389651\pi$
$398$	5906.65	0.743903
$399$	−7327.58	−0.919393
$400$	202.704	0.0253381
$401$	7361.33	0.916727	0.458363	−	0.888765i	$-0.348436\pi$
$401$	7361.33	0.916727	0.458363	+	0.888765i	$0.348436\pi$
$402$	27063.5	3.35772
$403$	−181.209	−0.0223987
$404$	−11590.7	−1.42737
$405$	−105.618	−0.0129585
$406$	−4340.68	−0.530602
$407$	4249.88	0.517589
$408$	−989.632	−0.120084
$409$	−2612.45	−0.315837	−0.157919	−	0.987452i	$-0.550478\pi$
$409$	−2612.45	−0.315837	−0.157919	+	0.987452i	$0.550478\pi$
$410$	−2203.11	−0.265375
$411$	−5419.57	−0.650433
$412$	−15610.3	−1.86667
$413$	5869.51	0.699321
$414$	−4061.81	−0.482191
$415$	350.133	0.0414153
$416$	14387.8	1.69572
$417$	−4247.68	−0.498824
$418$	17381.3	2.03384
$419$	4398.21	0.512808	0.256404	−	0.966570i	$-0.417462\pi$
$419$	4398.21	0.512808	0.256404	+	0.966570i	$0.417462\pi$
$420$	−3929.38	−0.456510
$421$	9723.32	1.12562	0.562810	−	0.826587i	$-0.309720\pi$
$421$	9723.32	1.12562	0.562810	+	0.826587i	$0.309720\pi$
$422$	15071.9	1.73859
$423$	−5592.54	−0.642833
$424$	−9676.01	−1.10828
$425$	−118.425	−0.0135163
$426$	−20301.7	−2.30896
$427$	2725.96	0.308942
$428$	762.570	0.0861220
$429$	22457.7	2.52744
$430$	6905.54	0.774453
$431$	−14314.5	−1.59978	−0.799892	−	0.600144i	$-0.795110\pi$
$431$	−14314.5	−1.59978	−0.799892	+	0.600144i	$0.795110\pi$
$432$	−1110.78	−0.123709
$433$	−2373.62	−0.263438	−0.131719	−	0.991287i	$-0.542050\pi$
$433$	−2373.62	−0.263438	−0.131719	+	0.991287i	$0.542050\pi$
$434$	65.9633	0.00729572
$435$	−5622.70	−0.619742
$436$	−18190.9	−1.99813
$437$	2529.80	0.276927
$438$	2577.93	0.281229
$439$	−9533.46	−1.03646	−0.518231	−	0.855240i	$-0.673409\pi$
$439$	−9533.46	−1.03646	−0.518231	+	0.855240i	$0.673409\pi$
$440$	3750.51	0.406360
$441$	2123.41	0.229286
$442$	1948.14	0.209646
$443$	6647.94	0.712987	0.356493	−	0.934298i	$-0.383972\pi$
$443$	6647.94	0.712987	0.356493	+	0.934298i	$0.383972\pi$
$444$	15845.2	1.69365
$445$	−46.3963	−0.00494246
$446$	−20224.8	−2.14725
$447$	15331.7	1.62229
$448$	−5691.47	−0.600215
$449$	−768.256	−0.0807489	−0.0403744	−	0.999185i	$-0.512855\pi$
$449$	−768.256	−0.0807489	−0.0403744	+	0.999185i	$0.512855\pi$
$450$	−5010.14	−0.524845
$451$	−2868.99	−0.299547
$452$	5837.06	0.607416
$453$	−24951.5	−2.58791
$454$	282.628	0.0292167
$455$	3112.53	0.320698
$456$	26076.4	2.67794
$457$	−3323.50	−0.340190	−0.170095	−	0.985428i	$-0.554407\pi$
$457$	−3323.50	−0.340190	−0.170095	+	0.985428i	$0.554407\pi$
$458$	−13963.5	−1.42461
$459$	648.944	0.0659915
$460$	1356.60	0.137503
$461$	−18840.7	−1.90347	−0.951733	−	0.306926i	$-0.900700\pi$
$461$	−18840.7	−1.90347	−0.951733	+	0.306926i	$0.900700\pi$
$462$	−8175.03	−0.823240
$463$	−10759.1	−1.07995	−0.539977	−	0.841679i	$-0.681567\pi$
$463$	−10759.1	−1.07995	−0.539977	+	0.841679i	$0.681567\pi$
$464$	1087.21	0.108777
$465$	85.4456	0.00852138
$466$	16330.1	1.62334
$467$	7441.70	0.737390	0.368695	−	0.929550i	$-0.379805\pi$
$467$	7441.70	0.737390	0.368695	+	0.929550i	$0.379805\pi$
$468$	51588.7	5.09549
$469$	4884.56	0.480913
$470$	2984.08	0.292863
$471$	17878.0	1.74899
$472$	−20887.6	−2.03693
$473$	8992.73	0.874178
$474$	−20438.7	−1.98055
$475$	3120.45	0.301423
$476$	−443.885	−0.0427426
$477$	16832.6	1.61574
$478$	−10556.1	−1.01010
$479$	5691.97	0.542949	0.271475	−	0.962446i	$-0.412489\pi$
$479$	5691.97	0.542949	0.271475	+	0.962446i	$0.412489\pi$
$480$	−6784.27	−0.645121
$481$	−12551.3	−1.18979
$482$	10246.5	0.968293
$483$	−1189.85	−0.112092
$484$	−5679.77	−0.533412
$485$	−20.9746	−0.00196373
$486$	−17924.9	−1.67302
$487$	−2020.25	−0.187980	−0.0939899	−	0.995573i	$-0.529962\pi$
$487$	−2020.25	−0.187980	−0.0939899	+	0.995573i	$0.529962\pi$
$488$	−9700.77	−0.899863
$489$	4981.12	0.460642
$490$	−1133.02	−0.104458
$491$	7636.02	0.701851	0.350925	−	0.936403i	$-0.385867\pi$
$491$	7636.02	0.701851	0.350925	+	0.936403i	$0.385867\pi$
$492$	−10696.7	−0.980173
$493$	−635.173	−0.0580259
$494$	−51332.6	−4.67523
$495$	−6524.44	−0.592428
$496$	−16.5218	−0.00149567
$497$	−3664.15	−0.330703
$498$	2715.93	0.244385
$499$	6284.56	0.563799	0.281900	−	0.959444i	$-0.409036\pi$
$499$	6284.56	0.563799	0.281900	+	0.959444i	$0.409036\pi$
$500$	1673.32	0.149667
$501$	24625.6	2.19599
$502$	14255.4	1.26743
$503$	11310.9	1.00264	0.501319	−	0.865262i	$-0.332848\pi$
$503$	11310.9	1.00264	0.501319	+	0.865262i	$0.332848\pi$
$504$	−7556.52	−0.667846
$505$	−4329.22	−0.381481
$506$	2822.38	0.247965
$507$	−47899.7	−4.19586
$508$	15885.7	1.38743
$509$	10712.7	0.932876	0.466438	−	0.884554i	$-0.345537\pi$
$509$	10712.7	0.932876	0.466438	+	0.884554i	$0.345537\pi$
$510$	−918.606	−0.0797580
$511$	465.279	0.0402793
$512$	2927.65	0.252705
$513$	−17099.4	−1.47165
$514$	27897.2	2.39396
$515$	−5830.58	−0.498886
$516$	33528.4	2.86047
$517$	3886.02	0.330574
$518$	4568.89	0.387540
$519$	−19685.9	−1.66496
$520$	−11076.5	−0.934106
$521$	17721.9	1.49023	0.745116	−	0.666935i	$-0.232394\pi$
$521$	17721.9	1.49023	0.745116	+	0.666935i	$0.232394\pi$
$522$	−26871.9	−2.25317
$523$	237.193	0.0198312	0.00991562	−	0.999951i	$-0.496844\pi$
$523$	237.193	0.0198312	0.00991562	+	0.999951i	$0.496844\pi$
$524$	13849.2	1.15459
$525$	−1467.65	−0.122007
$526$	−27395.0	−2.27088
$527$	9.65243	0.000797849 0
$528$	2047.59	0.168769
$529$	−11756.2	−0.966237
$530$	−8981.57	−0.736103
$531$	36336.4	2.96962
$532$	11696.2	0.953185
$533$	8473.06	0.688572
$534$	−359.890	−0.0291647
$535$	284.826	0.0230170
$536$	−17382.5	−1.40077
$537$	−25466.4	−2.04647
$538$	−15042.8	−1.20546
$539$	−1475.47	−0.117909
$540$	−9169.48	−0.730725
$541$	−5352.94	−0.425399	−0.212699	−	0.977118i	$-0.568226\pi$
$541$	−5352.94	−0.425399	−0.212699	+	0.977118i	$0.568226\pi$
$542$	28886.2	2.28924
$543$	7546.06	0.596376
$544$	−766.391	−0.0604021
$545$	−6794.45	−0.534022
$546$	24143.5	1.89239
$547$	−192.162	−0.0150206	−0.00751030	−	0.999972i	$-0.502391\pi$
$547$	−192.162	−0.0150206	−0.00751030	+	0.999972i	$0.502391\pi$
$548$	8650.67	0.674340
$549$	16875.6	1.31190
$550$	3481.33	0.269899
$551$	16736.5	1.29401
$552$	4234.29	0.326492
$553$	−3688.87	−0.283665
$554$	7270.60	0.557578
$555$	5918.31	0.452646
$556$	6780.10	0.517159
$557$	−4850.62	−0.368990	−0.184495	−	0.982833i	$-0.559065\pi$
$557$	−4850.62	−0.368990	−0.184495	+	0.982833i	$0.559065\pi$
$558$	408.360	0.0309808
$559$	−26558.4	−2.00949
$560$	283.786	0.0214146
$561$	−1196.25	−0.0900283
$562$	36284.4	2.72343
$563$	9699.11	0.726055	0.363027	−	0.931778i	$-0.381743\pi$
$563$	9699.11	0.726055	0.363027	+	0.931778i	$0.381743\pi$
$564$	14488.6	1.08170
$565$	2180.19	0.162338
$566$	−28975.6	−2.15183
$567$	−147.865	−0.0109520
$568$	13039.5	0.963247
$569$	3109.53	0.229100	0.114550	−	0.993417i	$-0.463457\pi$
$569$	3109.53	0.229100	0.114550	+	0.993417i	$0.463457\pi$
$570$	24204.9	1.77865
$571$	−14476.2	−1.06097	−0.530483	−	0.847695i	$-0.677990\pi$
$571$	−14476.2	−1.06097	−0.530483	+	0.847695i	$0.677990\pi$
$572$	−35846.8	−2.62033
$573$	−3490.23	−0.254461
$574$	−3084.35	−0.224283
$575$	506.699	0.0367492
$576$	−35234.2	−2.54877
$577$	−2208.23	−0.159323	−0.0796617	−	0.996822i	$-0.525384\pi$
$577$	−2208.23	−0.159323	−0.0796617	+	0.996822i	$0.525384\pi$
$578$	22616.7	1.62756
$579$	43451.4	3.11879
$580$	8974.90	0.642521
$581$	490.186	0.0350023
$582$	−162.698	−0.0115877
$583$	−11696.2	−0.830889
$584$	−1655.77	−0.117322
$585$	19268.8	1.36182
$586$	33597.4	2.36843
$587$	−23988.7	−1.68675	−0.843374	−	0.537327i	$-0.819434\pi$
$587$	−23988.7	−1.68675	−0.843374	+	0.537327i	$0.819434\pi$
$588$	−5501.13	−0.385821
$589$	−254.338	−0.0177925
$590$	−19388.5	−1.35290
$591$	−12180.2	−0.847762
$592$	−1144.37	−0.0794480
$593$	−15869.4	−1.09895	−0.549474	−	0.835511i	$-0.685172\pi$
$593$	−15869.4	−1.09895	−0.549474	+	0.835511i	$0.685172\pi$
$594$	−19077.0	−1.31774
$595$	−165.795	−0.0114234
$596$	−24472.2	−1.68192
$597$	10711.6	0.734335
$598$	−8335.41	−0.570000
$599$	−15236.6	−1.03932	−0.519660	−	0.854373i	$-0.673941\pi$
$599$	−15236.6	−1.03932	−0.519660	+	0.854373i	$0.673941\pi$
$600$	5222.89	0.355373
$601$	12258.8	0.832026	0.416013	−	0.909359i	$-0.363427\pi$
$601$	12258.8	0.832026	0.416013	+	0.909359i	$0.363427\pi$
$602$	9667.75	0.654532
$603$	30238.9	2.04216
$604$	39827.4	2.68303
$605$	−2121.44	−0.142560
$606$	−33581.2	−2.25106
$607$	23487.2	1.57054	0.785269	−	0.619155i	$-0.212525\pi$
$607$	23487.2	1.57054	0.785269	+	0.619155i	$0.212525\pi$
$608$	20194.1	1.34700
$609$	−7871.78	−0.523778
$610$	−9004.54	−0.597678
$611$	−11476.7	−0.759896
$612$	−2747.97	−0.181503
$613$	−22305.3	−1.46966	−0.734830	−	0.678251i	$-0.762738\pi$
$613$	−22305.3	−1.46966	−0.734830	+	0.678251i	$0.762738\pi$
$614$	−6142.92	−0.403759
$615$	−3995.31	−0.261962
$616$	5250.71	0.343437
$617$	3285.91	0.214402	0.107201	−	0.994237i	$-0.465811\pi$
$617$	3285.91	0.214402	0.107201	+	0.994237i	$0.465811\pi$
$618$	−45227.1	−2.94385
$619$	−11613.1	−0.754069	−0.377035	−	0.926199i	$-0.623056\pi$
$619$	−11613.1	−0.754069	−0.377035	+	0.926199i	$0.623056\pi$
$620$	−136.387	−0.00883459
$621$	−2776.61	−0.179423
$622$	−22515.5	−1.45143
$623$	−64.9548	−0.00417714
$624$	−6047.21	−0.387952
$625$	625.000	0.0400000
$626$	−35763.5	−2.28338
$627$	31520.8	2.00769
$628$	−28536.7	−1.81328
$629$	668.567	0.0423808
$630$	−7014.19	−0.443575
$631$	6890.91	0.434743	0.217372	−	0.976089i	$-0.430252\pi$
$631$	6890.91	0.434743	0.217372	+	0.976089i	$0.430252\pi$
$632$	13127.5	0.826238
$633$	27332.7	1.71623
$634$	37805.9	2.36824
$635$	5933.43	0.370804
$636$	−43608.1	−2.71883
$637$	4357.55	0.271040
$638$	18672.2	1.15868
$639$	−22683.7	−1.40431
$640$	12328.9	0.761470
$641$	18769.3	1.15654	0.578269	−	0.815846i	$-0.303728\pi$
$641$	18769.3	1.15654	0.578269	+	0.815846i	$0.303728\pi$
$642$	2209.36	0.135820
$643$	−3142.30	−0.192722	−0.0963609	−	0.995346i	$-0.530720\pi$
$643$	−3142.30	−0.192722	−0.0963609	+	0.995346i	$0.530720\pi$
$644$	1899.23	0.116212
$645$	12523.1	0.764492
$646$	2734.33	0.166533
$647$	19038.1	1.15683	0.578413	−	0.815744i	$-0.303672\pi$
$647$	19038.1	1.15683	0.578413	+	0.815744i	$0.303672\pi$
$648$	526.204	0.0319000
$649$	−25248.7	−1.52711
$650$	−10281.5	−0.620421
$651$	119.624	0.00720188
$652$	−7950.82	−0.477574
$653$	−20538.6	−1.23084	−0.615420	−	0.788199i	$-0.711014\pi$
$653$	−20538.6	−1.23084	−0.615420	+	0.788199i	$0.711014\pi$
$654$	−52703.6	−3.15119
$655$	5172.78	0.308576
$656$	772.534	0.0459793
$657$	2880.41	0.171043
$658$	4177.72	0.247514
$659$	−937.046	−0.0553902	−0.0276951	−	0.999616i	$-0.508817\pi$
$659$	−937.046	−0.0553902	−0.0276951	+	0.999616i	$0.508817\pi$
$660$	16902.9	0.996884
$661$	21116.5	1.24257	0.621283	−	0.783586i	$-0.286612\pi$
$661$	21116.5	1.24257	0.621283	+	0.783586i	$0.286612\pi$
$662$	9437.65	0.554085
$663$	3532.92	0.206949
$664$	−1744.41	−0.101952
$665$	4368.62	0.254749
$666$	28284.7	1.64566
$667$	2717.69	0.157765
$668$	−39307.1	−2.27670
$669$	−36677.5	−2.11963
$670$	−16135.0	−0.930371
$671$	−11726.2	−0.674640
$672$	−9497.98	−0.545227
$673$	13825.9	0.791903	0.395952	−	0.918271i	$-0.370415\pi$
$673$	13825.9	0.791903	0.395952	+	0.918271i	$0.370415\pi$
$674$	−33989.3	−1.94246
$675$	−3424.87	−0.195294
$676$	76456.9	4.35008
$677$	−16928.4	−0.961021	−0.480510	−	0.876989i	$-0.659549\pi$
$677$	−16928.4	−0.961021	−0.480510	+	0.876989i	$0.659549\pi$
$678$	16911.4	0.957935
$679$	−29.3645	−0.00165966
$680$	590.008	0.0332732
$681$	512.543	0.0288409
$682$	−283.752	−0.0159317
$683$	−13817.3	−0.774091	−0.387045	−	0.922061i	$-0.626504\pi$
$683$	−13817.3	−0.774091	−0.387045	+	0.922061i	$0.626504\pi$
$684$	72407.8	4.04763
$685$	3231.09	0.180224
$686$	−1586.23	−0.0882833
$687$	−25322.6	−1.40628
$688$	−2421.47	−0.134183
$689$	34542.8	1.90998
$690$	3930.40	0.216852
$691$	−23671.6	−1.30320	−0.651600	−	0.758563i	$-0.725902\pi$
$691$	−23671.6	−1.30320	−0.651600	+	0.758563i	$0.725902\pi$
$692$	31422.5	1.72616
$693$	−9134.22	−0.500693
$694$	55818.2	3.05307
$695$	2532.42	0.138216
$696$	28013.0	1.52562
$697$	−451.333	−0.0245272
$698$	20741.0	1.12472
$699$	29614.5	1.60246
$700$	2342.65	0.126491
$701$	−17009.7	−0.916472	−0.458236	−	0.888831i	$-0.651519\pi$
$701$	−17009.7	−0.916472	−0.458236	+	0.888831i	$0.651519\pi$
$702$	56340.6	3.02911
$703$	−17616.5	−0.945117
$704$	24482.8	1.31070
$705$	5411.60	0.289096
$706$	59020.9	3.14629
$707$	−6060.91	−0.322410
$708$	−94136.8	−4.99700
$709$	22038.9	1.16740	0.583701	−	0.811969i	$-0.301604\pi$
$709$	22038.9	1.16740	0.583701	+	0.811969i	$0.301604\pi$
$710$	12103.6	0.639777
$711$	−22836.8	−1.20456
$712$	231.152	0.0121669
$713$	−41.2994	−0.00216925
$714$	−1286.05	−0.0674078
$715$	−13389.1	−0.700312
$716$	40649.2	2.12169
$717$	−19143.4	−0.997106
$718$	11188.8	0.581562
$719$	7287.44	0.377991	0.188996	−	0.981978i	$-0.439477\pi$
$719$	7287.44	0.377991	0.188996	+	0.981978i	$0.439477\pi$
$720$	1756.84	0.0909354
$721$	−8162.82	−0.421636
$722$	−40328.5	−2.07877
$723$	18582.0	0.955839
$724$	−12044.9	−0.618297
$725$	3352.20	0.171721
$726$	−16455.7	−0.841225
$727$	−29676.7	−1.51396	−0.756980	−	0.653438i	$-0.773326\pi$
$727$	−29676.7	−1.51396	−0.756980	+	0.653438i	$0.773326\pi$
$728$	−15507.0	−0.789463
$729$	−31936.3	−1.62253
$730$	−1536.94	−0.0779241
$731$	1414.68	0.0715786
$732$	−43719.7	−2.20755
$733$	23111.8	1.16460	0.582300	−	0.812974i	$-0.302153\pi$
$733$	23111.8	1.16460	0.582300	+	0.812974i	$0.302153\pi$
$734$	32971.9	1.65806
$735$	−2054.72	−0.103115
$736$	3279.12	0.164226
$737$	−21011.7	−1.05017
$738$	−19094.3	−0.952400
$739$	−31171.4	−1.55164	−0.775818	−	0.630957i	$-0.782662\pi$
$739$	−31171.4	−1.55164	−0.775818	+	0.630957i	$0.782662\pi$
$740$	−9446.75	−0.469283
$741$	−93091.1	−4.61510
$742$	−12574.2	−0.622120
$743$	−31324.4	−1.54668	−0.773338	−	0.633993i	$-0.781415\pi$
$743$	−31324.4	−1.54668	−0.773338	+	0.633993i	$0.781415\pi$
$744$	−425.701	−0.0209771
$745$	−9140.58	−0.449510
$746$	−53630.7	−2.63212
$747$	3034.60	0.148635
$748$	1909.45	0.0933373
$749$	398.756	0.0194529
$750$	4848.04	0.236034
$751$	4032.20	0.195922	0.0979608	−	0.995190i	$-0.468768\pi$
$751$	4032.20	0.195922	0.0979608	+	0.995190i	$0.468768\pi$
$752$	−1046.39	−0.0507419
$753$	25852.1	1.25113
$754$	−55145.0	−2.66348
$755$	14875.8	0.717069
$756$	−12837.3	−0.617575
$757$	34263.7	1.64509	0.822546	−	0.568699i	$-0.192553\pi$
$757$	34263.7	1.64509	0.822546	+	0.568699i	$0.192553\pi$
$758$	59059.3	2.82999
$759$	5118.36	0.244775
$760$	−15546.5	−0.742013
$761$	7265.88	0.346108	0.173054	−	0.984912i	$-0.444637\pi$
$761$	7265.88	0.346108	0.173054	+	0.984912i	$0.444637\pi$
$762$	46024.8	2.18806
$763$	−9512.22	−0.451331
$764$	5571.07	0.263814
$765$	−1026.39	−0.0485087
$766$	−34546.0	−1.62950
$767$	74567.5	3.51040
$768$	41082.4	1.93025
$769$	38116.2	1.78739	0.893695	−	0.448674i	$-0.148104\pi$
$769$	38116.2	1.78739	0.893695	+	0.448674i	$0.148104\pi$
$770$	4873.87	0.228106
$771$	50591.3	2.36317
$772$	−69356.6	−3.23342
$773$	16158.2	0.751838	0.375919	−	0.926652i	$-0.377327\pi$
$773$	16158.2	0.751838	0.375919	+	0.926652i	$0.377327\pi$
$774$	59850.3	2.77942
$775$	−50.9417	−0.00236114
$776$	104.498	0.00483412
$777$	8285.64	0.382555
$778$	−40463.9	−1.86465
$779$	11892.4	0.546972
$780$	−49919.7	−2.29155
$781$	15761.9	0.722160
$782$	444.001	0.0203036
$783$	−18369.3	−0.838400
$784$	397.301	0.0180986
$785$	−10658.7	−0.484618
$786$	40124.6	1.82086
$787$	5092.49	0.230658	0.115329	−	0.993327i	$-0.463208\pi$
$787$	5092.49	0.230658	0.115329	+	0.993327i	$0.463208\pi$
$788$	19441.9	0.878922
$789$	−49680.6	−2.24167
$790$	12185.3	0.548777
$791$	3052.26	0.137201
$792$	32505.6	1.45838
$793$	34631.1	1.55080
$794$	−24858.2	−1.11106
$795$	−16288.0	−0.726635
$796$	−17097.8	−0.761326
$797$	−34666.2	−1.54070	−0.770350	−	0.637621i	$-0.779919\pi$
$797$	−34666.2	−1.54070	−0.770350	+	0.637621i	$0.779919\pi$
$798$	33886.9	1.50323
$799$	611.326	0.0270678
$800$	4044.71	0.178753
$801$	−402.116	−0.0177379
$802$	−34043.0	−1.49888
$803$	−2001.47	−0.0879582
$804$	−78339.9	−3.43636
$805$	709.379	0.0310588
$806$	838.012	0.0366225
$807$	−27279.9	−1.18996
$808$	21568.7	0.939091
$809$	15126.2	0.657365	0.328683	−	0.944440i	$-0.393395\pi$
$809$	15126.2	0.657365	0.328683	+	0.944440i	$0.393395\pi$
$810$	488.438	0.0211876
$811$	29416.5	1.27368	0.636840	−	0.770996i	$-0.280241\pi$
$811$	29416.5	1.27368	0.636840	+	0.770996i	$0.280241\pi$
$812$	12564.9	0.543030
$813$	52384.9	2.25980
$814$	−19653.9	−0.846274
$815$	−2969.69	−0.127637
$816$	322.116	0.0138190
$817$	−37276.3	−1.59625
$818$	12081.5	0.516404
$819$	26976.3	1.15095
$820$	6377.27	0.271590
$821$	−15334.4	−0.651856	−0.325928	−	0.945395i	$-0.605677\pi$
$821$	−15334.4	−0.651856	−0.325928	+	0.945395i	$0.605677\pi$
$822$	25063.2	1.06348
$823$	−11003.7	−0.466056	−0.233028	−	0.972470i	$-0.574863\pi$
$823$	−11003.7	−0.466056	−0.233028	+	0.972470i	$0.574863\pi$
$824$	29048.7	1.22811
$825$	6313.36	0.266428
$826$	−27143.9	−1.14341
$827$	−3261.59	−0.137142	−0.0685711	−	0.997646i	$-0.521844\pi$
$827$	−3261.59	−0.137142	−0.0685711	+	0.997646i	$0.521844\pi$
$828$	11757.6	0.493484
$829$	5163.30	0.216319	0.108160	−	0.994134i	$-0.465504\pi$
$829$	5163.30	0.216319	0.108160	+	0.994134i	$0.465504\pi$
$830$	−1619.21	−0.0677152
$831$	13185.1	0.550406
$832$	−72305.6	−3.01292
$833$	−232.113	−0.00965453
$834$	19643.7	0.815593
$835$	−14681.5	−0.608472
$836$	−50313.1	−2.08148
$837$	279.150	0.0115279
$838$	−20339.8	−0.838457
$839$	−5641.70	−0.232149	−0.116075	−	0.993241i	$-0.537031\pi$
$839$	−5641.70	−0.232149	−0.116075	+	0.993241i	$0.537031\pi$
$840$	7312.05	0.300345
$841$	−6409.46	−0.262801
$842$	−44966.1	−1.84042
$843$	65801.4	2.68840
$844$	−43628.1	−1.77931
$845$	28557.3	1.16260
$846$	25863.0	1.05105
$847$	−2970.01	−0.120485
$848$	3149.45	0.127538
$849$	−52546.8	−2.12415
$850$	547.663	0.0220996
$851$	−2860.57	−0.115228
$852$	58766.7	2.36304
$853$	−7799.52	−0.313072	−0.156536	−	0.987672i	$-0.550033\pi$
$853$	−7799.52	−0.313072	−0.156536	+	0.987672i	$0.550033\pi$
$854$	−12606.4	−0.505130
$855$	27044.9	1.08177
$856$	−1419.04	−0.0566610
$857$	−21540.0	−0.858568	−0.429284	−	0.903170i	$-0.641234\pi$
$857$	−21540.0	−0.858568	−0.429284	+	0.903170i	$0.641234\pi$
$858$	−103857.	−4.13244
$859$	4447.97	0.176674	0.0883370	−	0.996091i	$-0.471845\pi$
$859$	4447.97	0.176674	0.0883370	+	0.996091i	$0.471845\pi$
$860$	−19989.3	−0.792591
$861$	−5593.43	−0.221398
$862$	66198.5	2.61569
$863$	−9425.21	−0.371770	−0.185885	−	0.982571i	$-0.559515\pi$
$863$	−9425.21	−0.371770	−0.185885	+	0.982571i	$0.559515\pi$
$864$	−22164.2	−0.872733
$865$	11736.5	0.461335
$866$	10977.0	0.430730
$867$	41015.2	1.60663
$868$	−190.942	−0.00746659
$869$	15868.3	0.619442
$870$	26002.5	1.01330
$871$	62054.5	2.41405
$872$	33850.8	1.31460
$873$	−181.787	−0.00704761
$874$	−11699.2	−0.452783
$875$	875.000	0.0338062
$876$	−7462.27	−0.287816
$877$	22346.1	0.860403	0.430201	−	0.902733i	$-0.358443\pi$
$877$	22346.1	0.860403	0.430201	+	0.902733i	$0.358443\pi$
$878$	44088.1	1.69465
$879$	60928.6	2.33796
$880$	−1220.75	−0.0467632
$881$	12074.9	0.461762	0.230881	−	0.972982i	$-0.425839\pi$
$881$	12074.9	0.461762	0.230881	+	0.972982i	$0.425839\pi$
$882$	−9819.87	−0.374889
$883$	−30499.6	−1.16239	−0.581196	−	0.813764i	$-0.697415\pi$
$883$	−30499.6	−1.16239	−0.581196	+	0.813764i	$0.697415\pi$
$884$	−5639.22	−0.214556
$885$	−35160.8	−1.33550
$886$	−30743.8	−1.16576
$887$	23344.2	0.883675	0.441838	−	0.897095i	$-0.354327\pi$
$887$	23344.2	0.883675	0.441838	+	0.897095i	$0.354327\pi$
$888$	−29485.8	−1.11428
$889$	8306.80	0.313387
$890$	214.562	0.00808107
$891$	636.068	0.0239159
$892$	58544.3	2.19754
$893$	−16108.2	−0.603628
$894$	−70902.3	−2.65249
$895$	15182.8	0.567044
$896$	17260.4	0.643560
$897$	−15116.2	−0.562669
$898$	3552.85	0.132027
$899$	−273.227	−0.0101364
$900$	14502.7	0.537137
$901$	−1839.98	−0.0680341
$902$	13267.8	0.489768
$903$	17532.4	0.646113
$904$	−10862.0	−0.399629
$905$	−4498.88	−0.165246
$906$	115390.	4.23132
$907$	−15092.5	−0.552523	−0.276262	−	0.961082i	$-0.589096\pi$
$907$	−15092.5	−0.552523	−0.276262	+	0.961082i	$0.589096\pi$
$908$	−818.115	−0.0299010
$909$	−37521.3	−1.36909
$910$	−14394.1	−0.524352
$911$	−15207.8	−0.553081	−0.276541	−	0.961002i	$-0.589188\pi$
$911$	−15207.8	−0.553081	−0.276541	+	0.961002i	$0.589188\pi$
$912$	−8487.61	−0.308172
$913$	−2108.62	−0.0764348
$914$	15369.7	0.556221
$915$	−16329.6	−0.589990
$916$	40419.6	1.45797
$917$	7241.90	0.260794
$918$	−3001.08	−0.107898
$919$	24818.1	0.890831	0.445415	−	0.895324i	$-0.353056\pi$
$919$	24818.1	0.890831	0.445415	+	0.895324i	$0.353056\pi$
$920$	−2524.44	−0.0904656
$921$	−11140.1	−0.398566
$922$	87130.0	3.11223
$923$	−46550.1	−1.66004
$924$	23664.0	0.842521
$925$	−3528.44	−0.125421
$926$	49756.3	1.76576
$927$	−50533.7	−1.79045
$928$	21693.9	0.767388
$929$	39906.4	1.40935	0.704675	−	0.709530i	$-0.251093\pi$
$929$	39906.4	1.40935	0.704675	+	0.709530i	$0.251093\pi$
$930$	−395.148	−0.0139327
$931$	6116.07	0.215302
$932$	−47270.3	−1.66136
$933$	−40831.7	−1.43276
$934$	−34414.6	−1.20565
$935$	713.194	0.0249454
$936$	−95999.7	−3.35240
$937$	16923.0	0.590020	0.295010	−	0.955494i	$-0.404677\pi$
$937$	16923.0	0.590020	0.295010	+	0.955494i	$0.404677\pi$
$938$	−22589.0	−0.786307
$939$	−64856.8	−2.25402
$940$	−8637.94	−0.299722
$941$	−53014.1	−1.83657	−0.918285	−	0.395921i	$-0.870426\pi$
$941$	−53014.1	−1.83657	−0.918285	+	0.395921i	$0.870426\pi$
$942$	−82678.1	−2.85966
$943$	1931.10	0.0666864
$944$	6798.71	0.234406
$945$	−4794.82	−0.165054
$946$	−41587.4	−1.42931
$947$	−25798.9	−0.885271	−0.442636	−	0.896702i	$-0.645957\pi$
$947$	−25798.9	−0.885271	−0.442636	+	0.896702i	$0.645957\pi$
$948$	59163.2	2.02693
$949$	5911.00	0.202191
$950$	−14430.7	−0.492836
$951$	68560.6	2.33778
$952$	826.011	0.0281210
$953$	−17942.7	−0.609885	−0.304943	−	0.952371i	$-0.598637\pi$
$953$	−17942.7	−0.609885	−0.304943	+	0.952371i	$0.598637\pi$
$954$	−77843.2	−2.64179
$955$	2080.84	0.0705072
$956$	30556.6	1.03375
$957$	33861.8	1.14378
$958$	−26322.9	−0.887739
$959$	4523.53	0.152317
$960$	34094.3	1.14624
$961$	−29786.8	−0.999861
$962$	58044.2	1.94534
$963$	2468.59	0.0826055
$964$	−29660.4	−0.990971
$965$	−25905.2	−0.864165
$966$	5502.56	0.183273
$967$	19668.3	0.654073	0.327036	−	0.945012i	$-0.393950\pi$
$967$	19668.3	0.654073	0.327036	+	0.945012i	$0.393950\pi$
$968$	10569.3	0.350940
$969$	4958.67	0.164392
$970$	96.9986	0.00321076
$971$	6332.97	0.209304	0.104652	−	0.994509i	$-0.466627\pi$
$971$	6332.97	0.209304	0.104652	+	0.994509i	$0.466627\pi$
$972$	51886.7	1.71221
$973$	3545.39	0.116814
$974$	9342.76	0.307353
$975$	−18645.4	−0.612441
$976$	3157.51	0.103555
$977$	−11334.1	−0.371145	−0.185573	−	0.982631i	$-0.559414\pi$
$977$	−11334.1	−0.371145	−0.185573	+	0.982631i	$0.559414\pi$
$978$	−23035.5	−0.753164
$979$	279.414	0.00912166
$980$	3279.72	0.106905
$981$	−58887.4	−1.91655
$982$	−35313.3	−1.14755
$983$	−37654.3	−1.22175	−0.610877	−	0.791725i	$-0.709183\pi$
$983$	−37654.3	−1.22175	−0.610877	+	0.791725i	$0.709183\pi$
$984$	19905.1	0.644871
$985$	7261.72	0.234901
$986$	2937.40	0.0948741
$987$	7576.24	0.244331
$988$	148591.	4.78473
$989$	−6052.95	−0.194613
$990$	30172.7	0.968638
$991$	−53441.5	−1.71304	−0.856522	−	0.516111i	$-0.827379\pi$
$991$	−53441.5	−1.71304	−0.856522	+	0.516111i	$0.827379\pi$
$992$	−329.671	−0.0105515
$993$	17115.1	0.546959
$994$	16945.1	0.540710
$995$	−6386.16	−0.203472
$996$	−7861.74	−0.250109
$997$	37919.3	1.20453	0.602266	−	0.798296i	$-0.294265\pi$
$997$	37919.3	1.20453	0.602266	+	0.798296i	$0.294265\pi$
$998$	−29063.4	−0.921829
$999$	19335.1	0.612348

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.a.c.1.1	✓	3
3.2	odd	2		315.4.a.p.1.3		3
4.3	odd	2		560.4.a.u.1.3		3
5.2	odd	4		175.4.b.e.99.1		6
5.3	odd	4		175.4.b.e.99.6		6
5.4	even	2		175.4.a.f.1.3		3
7.2	even	3		245.4.e.m.116.3		6
7.3	odd	6		245.4.e.n.226.3		6
7.4	even	3		245.4.e.m.226.3		6
7.5	odd	6		245.4.e.n.116.3		6
7.6	odd	2		245.4.a.l.1.1		3
8.3	odd	2		2240.4.a.bv.1.1		3
8.5	even	2		2240.4.a.bt.1.3		3
15.14	odd	2		1575.4.a.ba.1.1		3
21.20	even	2		2205.4.a.bm.1.3		3
35.34	odd	2		1225.4.a.y.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.1	✓	3	1.1	even	1	trivial
175.4.a.f.1.3		3	5.4	even	2
175.4.b.e.99.1		6	5.2	odd	4
175.4.b.e.99.6		6	5.3	odd	4
245.4.a.l.1.1		3	7.6	odd	2
245.4.e.m.116.3		6	7.2	even	3
245.4.e.m.226.3		6	7.4	even	3
245.4.e.n.116.3		6	7.5	odd	6
245.4.e.n.226.3		6	7.3	odd	6
315.4.a.p.1.3		3	3.2	odd	2
560.4.a.u.1.3		3	4.3	odd	2
1225.4.a.y.1.3		3	35.34	odd	2
1575.4.a.ba.1.1		3	15.14	odd	2
2205.4.a.bm.1.3		3	21.20	even	2
2240.4.a.bt.1.3		3	8.5	even	2
2240.4.a.bv.1.1		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)

\(f(q)\)	\(=\)	\(q-4.62456 q^{2} -8.38660 q^{3} +13.3866 q^{4} +5.00000 q^{5} +38.7844 q^{6} +7.00000 q^{7} -24.9107 q^{8} +43.3350 q^{9} -23.1228 q^{10} -30.1117 q^{11} -112.268 q^{12} +88.9295 q^{13} -32.3720 q^{14} -41.9330 q^{15} +8.10818 q^{16} -4.73699 q^{17} -200.405 q^{18} +124.818 q^{19} +66.9330 q^{20} -58.7062 q^{21} +139.253 q^{22} +20.2680 q^{23} +208.916 q^{24} +25.0000 q^{25} -411.260 q^{26} -136.995 q^{27} +93.7062 q^{28} +134.088 q^{29} +193.922 q^{30} -2.03767 q^{31} +161.788 q^{32} +252.534 q^{33} +21.9065 q^{34} +35.0000 q^{35} +580.108 q^{36} -141.137 q^{37} -577.228 q^{38} -745.816 q^{39} -124.553 q^{40} +95.2784 q^{41} +271.490 q^{42} -298.646 q^{43} -403.093 q^{44} +216.675 q^{45} -93.7305 q^{46} -129.054 q^{47} -68.0000 q^{48} +49.0000 q^{49} -115.614 q^{50} +39.7272 q^{51} +1190.46 q^{52} +388.429 q^{53} +633.542 q^{54} -150.558 q^{55} -174.375 q^{56} -1046.80 q^{57} -620.098 q^{58} +838.501 q^{59} -561.340 q^{60} +389.422 q^{61} +9.42333 q^{62} +303.345 q^{63} -813.067 q^{64} +444.647 q^{65} -1167.86 q^{66} +697.794 q^{67} -63.4122 q^{68} -169.979 q^{69} -161.860 q^{70} -523.450 q^{71} -1079.50 q^{72} +66.4684 q^{73} +652.699 q^{74} -209.665 q^{75} +1670.89 q^{76} -210.782 q^{77} +3449.07 q^{78} -526.982 q^{79} +40.5409 q^{80} -21.1236 q^{81} -440.621 q^{82} +70.0265 q^{83} -785.876 q^{84} -23.6850 q^{85} +1381.11 q^{86} -1124.54 q^{87} +750.101 q^{88} -9.27925 q^{89} -1002.03 q^{90} +622.506 q^{91} +271.319 q^{92} +17.0891 q^{93} +596.817 q^{94} +624.089 q^{95} -1356.85 q^{96} -4.19493 q^{97} -226.604 q^{98} -1304.89 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 13 q^{4} + 15 q^{5} + 24 q^{6} + 21 q^{7} - 15 q^{8} + 81 q^{9} - 15 q^{10} - 74 q^{11} - 152 q^{12} + 44 q^{13} - 21 q^{14} + 10 q^{15} - 79 q^{16} - 52 q^{17} - 411 q^{18} + 168 q^{19}+ \cdots - 3488 q^{99}+O(q^{100}) \) 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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