LMFDB - Embedded newform 231.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,4,Mod(1,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("231.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.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:	$13.6294412113$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
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			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.561553 q^{2} -3.00000 q^{3} -7.68466 q^{4} +6.68466 q^{5} +1.68466 q^{6} +7.00000 q^{7} +8.80776 q^{8} +9.00000 q^{9} -3.75379 q^{10} -11.0000 q^{11} +23.0540 q^{12} +14.3002 q^{13} -3.93087 q^{14} -20.0540 q^{15} +56.5312 q^{16} -47.7538 q^{17} -5.05398 q^{18} +11.9157 q^{19} -51.3693 q^{20} -21.0000 q^{21} +6.17708 q^{22} -44.4924 q^{23} -26.4233 q^{24} -80.3153 q^{25} -8.03031 q^{26} -27.0000 q^{27} -53.7926 q^{28} -139.501 q^{29} +11.2614 q^{30} -208.600 q^{31} -102.207 q^{32} +33.0000 q^{33} +26.8163 q^{34} +46.7926 q^{35} -69.1619 q^{36} -253.086 q^{37} -6.69130 q^{38} -42.9006 q^{39} +58.8769 q^{40} -156.294 q^{41} +11.7926 q^{42} -263.386 q^{43} +84.5312 q^{44} +60.1619 q^{45} +24.9848 q^{46} +386.533 q^{47} -169.594 q^{48} +49.0000 q^{49} +45.1013 q^{50} +143.261 q^{51} -109.892 q^{52} -36.5701 q^{53} +15.1619 q^{54} -73.5312 q^{55} +61.6543 q^{56} -35.7471 q^{57} +78.3371 q^{58} -114.762 q^{59} +154.108 q^{60} -53.0758 q^{61} +117.140 q^{62} +63.0000 q^{63} -394.855 q^{64} +95.5919 q^{65} -18.5312 q^{66} +132.348 q^{67} +366.972 q^{68} +133.477 q^{69} -26.2765 q^{70} +583.447 q^{71} +79.2699 q^{72} -817.012 q^{73} +142.121 q^{74} +240.946 q^{75} -91.5682 q^{76} -77.0000 q^{77} +24.0909 q^{78} -369.633 q^{79} +377.892 q^{80} +81.0000 q^{81} +87.7671 q^{82} -69.1534 q^{83} +161.378 q^{84} -319.218 q^{85} +147.905 q^{86} +418.503 q^{87} -96.8854 q^{88} +467.295 q^{89} -33.7841 q^{90} +100.101 q^{91} +341.909 q^{92} +625.801 q^{93} -217.059 q^{94} +79.6525 q^{95} +306.622 q^{96} -1170.11 q^{97} -27.5161 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 6 q^{3} - 3 q^{4} + q^{5} - 9 q^{6} + 14 q^{7} - 3 q^{8} + 18 q^{9} - 24 q^{10} - 22 q^{11} + 9 q^{12} - 25 q^{13} + 21 q^{14} - 3 q^{15} - 23 q^{16} - 112 q^{17} + 27 q^{18} - 71 q^{19}+ \cdots - 198 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 + q^5 - 9 * q^6 + 14 * q^7 - 3 * q^8 + 18 * q^9 - 24 * q^10 - 22 * q^11 + 9 * q^12 - 25 * q^13 + 21 * q^14 - 3 * q^15 - 23 * q^16 - 112 * q^17 + 27 * q^18 - 71 * q^19 - 78 * q^20 - 42 * q^21 - 33 * q^22 - 56 * q^23 + 9 * q^24 - 173 * q^25 - 148 * q^26 - 54 * q^27 - 21 * q^28 - 11 * q^29 + 72 * q^30 - 310 * q^31 - 291 * q^32 + 66 * q^33 - 202 * q^34 + 7 * q^35 - 27 * q^36 - 65 * q^37 - 302 * q^38 + 75 * q^39 + 126 * q^40 + 42 * q^41 - 63 * q^42 - 32 * q^43 + 33 * q^44 + 9 * q^45 - 16 * q^46 + 101 * q^47 + 69 * q^48 + 98 * q^49 - 285 * q^50 + 336 * q^51 - 294 * q^52 + 166 * q^53 - 81 * q^54 - 11 * q^55 - 21 * q^56 + 213 * q^57 + 536 * q^58 - 11 * q^59 + 234 * q^60 - 436 * q^61 - 244 * q^62 + 126 * q^63 - 431 * q^64 + 319 * q^65 + 99 * q^66 - 127 * q^67 + 66 * q^68 + 168 * q^69 - 168 * q^70 + 936 * q^71 - 27 * q^72 - 327 * q^73 + 812 * q^74 + 519 * q^75 - 480 * q^76 - 154 * q^77 + 444 * q^78 - 228 * q^79 + 830 * q^80 + 162 * q^81 + 794 * q^82 - 262 * q^83 + 63 * q^84 + 46 * q^85 + 972 * q^86 + 33 * q^87 + 33 * q^88 + 44 * q^89 - 216 * q^90 - 175 * q^91 + 288 * q^92 + 930 * q^93 - 1234 * q^94 + 551 * q^95 + 873 * q^96 - 2266 * q^97 + 147 * q^98 - 198 * 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 $

$2$	−0.561553	−0.198539	−0.0992695	−	0.995061i	$-0.531651\pi$
$2$	−0.561553	−0.198539	−0.0992695	+	0.995061i	$0.531651\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.68466	−0.960582
$5$	6.68466	0.597894	0.298947	−	0.954270i	$-0.403365\pi$
$5$	6.68466	0.597894	0.298947	+	0.954270i	$0.403365\pi$
$6$	1.68466	0.114626
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.80776	0.389252
$9$	9.00000	0.333333
$10$	−3.75379	−0.118705
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	23.0540	0.554592
$13$	14.3002	0.305089	0.152545	−	0.988297i	$-0.451253\pi$
$13$	14.3002	0.305089	0.152545	+	0.988297i	$0.451253\pi$
$14$	−3.93087	−0.0750407
$15$	−20.0540	−0.345194
$16$	56.5312	0.883301
$17$	−47.7538	−0.681294	−0.340647	−	0.940191i	$-0.610646\pi$
$17$	−47.7538	−0.681294	−0.340647	+	0.940191i	$0.610646\pi$
$18$	−5.05398	−0.0661796
$19$	11.9157	0.143876	0.0719382	−	0.997409i	$-0.477082\pi$
$19$	11.9157	0.143876	0.0719382	+	0.997409i	$0.477082\pi$
$20$	−51.3693	−0.574326
$21$	−21.0000	−0.218218
$22$	6.17708	0.0598617
$23$	−44.4924	−0.403361	−0.201681	−	0.979451i	$-0.564640\pi$
$23$	−44.4924	−0.403361	−0.201681	+	0.979451i	$0.564640\pi$
$24$	−26.4233	−0.224735
$25$	−80.3153	−0.642523
$26$	−8.03031	−0.0605721
$27$	−27.0000	−0.192450
$28$	−53.7926	−0.363066
$29$	−139.501	−0.893265	−0.446632	−	0.894718i	$-0.647377\pi$
$29$	−139.501	−0.893265	−0.446632	+	0.894718i	$0.647377\pi$
$30$	11.2614	0.0685345
$31$	−208.600	−1.20857	−0.604286	−	0.796767i	$-0.706542\pi$
$31$	−208.600	−1.20857	−0.604286	+	0.796767i	$0.706542\pi$
$32$	−102.207	−0.564621
$33$	33.0000	0.174078
$34$	26.8163	0.135263
$35$	46.7926	0.225983
$36$	−69.1619	−0.320194
$37$	−253.086	−1.12452	−0.562258	−	0.826962i	$-0.690067\pi$
$37$	−253.086	−1.12452	−0.562258	+	0.826962i	$0.690067\pi$
$38$	−6.69130	−0.0285651
$39$	−42.9006	−0.176143
$40$	58.8769	0.232731
$41$	−156.294	−0.595340	−0.297670	−	0.954669i	$-0.596210\pi$
$41$	−156.294	−0.595340	−0.297670	+	0.954669i	$0.596210\pi$
$42$	11.7926	0.0433247
$43$	−263.386	−0.934094	−0.467047	−	0.884233i	$-0.654682\pi$
$43$	−263.386	−0.934094	−0.467047	+	0.884233i	$0.654682\pi$
$44$	84.5312	0.289626
$45$	60.1619	0.199298
$46$	24.9848	0.0800829
$47$	386.533	1.19961	0.599805	−	0.800146i	$-0.295245\pi$
$47$	386.533	1.19961	0.599805	+	0.800146i	$0.295245\pi$
$48$	−169.594	−0.509974
$49$	49.0000	0.142857
$50$	45.1013	0.127566
$51$	143.261	0.393345
$52$	−109.892	−0.293063
$53$	−36.5701	−0.0947790	−0.0473895	−	0.998876i	$-0.515090\pi$
$53$	−36.5701	−0.0947790	−0.0473895	+	0.998876i	$0.515090\pi$
$54$	15.1619	0.0382088
$55$	−73.5312	−0.180272
$56$	61.6543	0.147123
$57$	−35.7471	−0.0830671
$58$	78.3371	0.177348
$59$	−114.762	−0.253234	−0.126617	−	0.991952i	$-0.540412\pi$
$59$	−114.762	−0.253234	−0.126617	+	0.991952i	$0.540412\pi$
$60$	154.108	0.331588
$61$	−53.0758	−0.111404	−0.0557021	−	0.998447i	$-0.517740\pi$
$61$	−53.0758	−0.111404	−0.0557021	+	0.998447i	$0.517740\pi$
$62$	117.140	0.239949
$63$	63.0000	0.125988
$64$	−394.855	−0.771201
$65$	95.5919	0.182411
$66$	−18.5312	−0.0345612
$67$	132.348	0.241326	0.120663	−	0.992694i	$-0.461498\pi$
$67$	132.348	0.241326	0.120663	+	0.992694i	$0.461498\pi$
$68$	366.972	0.654439
$69$	133.477	0.232881
$70$	−26.2765	−0.0448664
$71$	583.447	0.975245	0.487623	−	0.873055i	$-0.337864\pi$
$71$	583.447	0.975245	0.487623	+	0.873055i	$0.337864\pi$
$72$	79.2699	0.129751
$73$	−817.012	−1.30992	−0.654959	−	0.755664i	$-0.727314\pi$
$73$	−817.012	−1.30992	−0.654959	+	0.755664i	$0.727314\pi$
$74$	142.121	0.223260
$75$	240.946	0.370961
$76$	−91.5682	−0.138205
$77$	−77.0000	−0.113961
$78$	24.0909	0.0349713
$79$	−369.633	−0.526417	−0.263208	−	0.964739i	$-0.584781\pi$
$79$	−369.633	−0.526417	−0.263208	+	0.964739i	$0.584781\pi$
$80$	377.892	0.528120
$81$	81.0000	0.111111
$82$	87.7671	0.118198
$83$	−69.1534	−0.0914527	−0.0457263	−	0.998954i	$-0.514560\pi$
$83$	−69.1534	−0.0914527	−0.0457263	+	0.998954i	$0.514560\pi$
$84$	161.378	0.209616
$85$	−319.218	−0.407342
$86$	147.905	0.185454
$87$	418.503	0.515727
$88$	−96.8854	−0.117364
$89$	467.295	0.556553	0.278276	−	0.960501i	$-0.410237\pi$
$89$	467.295	0.556553	0.278276	+	0.960501i	$0.410237\pi$
$90$	−33.7841	−0.0395684
$91$	100.101	0.115313
$92$	341.909	0.387462
$93$	625.801	0.697769
$94$	−217.059	−0.238169
$95$	79.6525	0.0860229
$96$	306.622	0.325984
$97$	−1170.11	−1.22481	−0.612404	−	0.790545i	$-0.709798\pi$
$97$	−1170.11	−1.22481	−0.612404	+	0.790545i	$0.709798\pi$
$98$	−27.5161	−0.0283627
$99$	−99.0000	−0.100504
$100$	617.196	0.617196
$101$	181.299	0.178613	0.0893066	−	0.996004i	$-0.471535\pi$
$101$	181.299	0.178613	0.0893066	+	0.996004i	$0.471535\pi$
$102$	−80.4488	−0.0780943
$103$	−212.324	−0.203115	−0.101558	−	0.994830i	$-0.532383\pi$
$103$	−212.324	−0.203115	−0.101558	+	0.994830i	$0.532383\pi$
$104$	125.953	0.118756
$105$	−140.378	−0.130471
$106$	20.5360	0.0188173
$107$	220.111	0.198868	0.0994342	−	0.995044i	$-0.468297\pi$
$107$	220.111	0.198868	0.0994342	+	0.995044i	$0.468297\pi$
$108$	207.486	0.184864
$109$	−247.072	−0.217112	−0.108556	−	0.994090i	$-0.534623\pi$
$109$	−247.072	−0.217112	−0.108556	+	0.994090i	$0.534623\pi$
$110$	41.2917	0.0357910
$111$	759.258	0.649240
$112$	395.719	0.333856
$113$	−139.261	−0.115935	−0.0579673	−	0.998318i	$-0.518462\pi$
$113$	−139.261	−0.115935	−0.0579673	+	0.998318i	$0.518462\pi$
$114$	20.0739	0.0164921
$115$	−297.417	−0.241167
$116$	1072.02	0.858054
$117$	128.702	0.101696
$118$	64.4451	0.0502767
$119$	−334.277	−0.257505
$120$	−176.631	−0.134368
$121$	121.000	0.0909091
$122$	29.8049	0.0221181
$123$	468.881	0.343720
$124$	1603.02	1.16093
$125$	−1372.46	−0.982055
$126$	−35.3778	−0.0250136
$127$	676.918	0.472967	0.236483	−	0.971636i	$-0.424005\pi$
$127$	676.918	0.472967	0.236483	+	0.971636i	$0.424005\pi$
$128$	1039.39	0.717735
$129$	790.159	0.539299
$130$	−53.6799	−0.0362157
$131$	291.042	0.194110	0.0970551	−	0.995279i	$-0.469058\pi$
$131$	291.042	0.194110	0.0970551	+	0.995279i	$0.469058\pi$
$132$	−253.594	−0.167216
$133$	83.4100	0.0543802
$134$	−74.3201	−0.0479125
$135$	−180.486	−0.115065
$136$	−420.604	−0.265195
$137$	2322.41	1.44830	0.724148	−	0.689645i	$-0.242233\pi$
$137$	2322.41	1.44830	0.724148	+	0.689645i	$0.242233\pi$
$138$	−74.9545	−0.0462359
$139$	210.436	0.128409	0.0642047	−	0.997937i	$-0.479549\pi$
$139$	210.436	0.128409	0.0642047	+	0.997937i	$0.479549\pi$
$140$	−359.585	−0.217075
$141$	−1159.60	−0.692595
$142$	−327.636	−0.193624
$143$	−157.302	−0.0919878
$144$	508.781	0.294434
$145$	−932.516	−0.534078
$146$	458.796	0.260070
$147$	−147.000	−0.0824786
$148$	1944.88	1.08019
$149$	−929.815	−0.511231	−0.255616	−	0.966779i	$-0.582278\pi$
$149$	−929.815	−0.511231	−0.255616	+	0.966779i	$0.582278\pi$
$150$	−135.304	−0.0736501
$151$	2300.58	1.23986	0.619929	−	0.784658i	$-0.287161\pi$
$151$	2300.58	1.23986	0.619929	+	0.784658i	$0.287161\pi$
$152$	104.951	0.0560042
$153$	−429.784	−0.227098
$154$	43.2396	0.0226256
$155$	−1394.42	−0.722598
$156$	329.676	0.169200
$157$	−1947.83	−0.990150	−0.495075	−	0.868850i	$-0.664859\pi$
$157$	−1947.83	−0.990150	−0.495075	+	0.868850i	$0.664859\pi$
$158$	207.568	0.104514
$159$	109.710	0.0547207
$160$	−683.221	−0.337584
$161$	−311.447	−0.152456
$162$	−45.4858	−0.0220599
$163$	−2753.64	−1.32320	−0.661601	−	0.749856i	$-0.730123\pi$
$163$	−2753.64	−1.32320	−0.661601	+	0.749856i	$0.730123\pi$
$164$	1201.06	0.571873
$165$	220.594	0.104080
$166$	38.8333	0.0181569
$167$	−3883.50	−1.79948	−0.899742	−	0.436422i	$-0.856246\pi$
$167$	−3883.50	−1.79948	−0.899742	+	0.436422i	$0.856246\pi$
$168$	−184.963	−0.0849417
$169$	−1992.50	−0.906921
$170$	179.258	0.0808731
$171$	107.241	0.0479588
$172$	2024.03	0.897274
$173$	−3123.33	−1.37262	−0.686308	−	0.727311i	$-0.740770\pi$
$173$	−3123.33	−1.37262	−0.686308	+	0.727311i	$0.740770\pi$
$174$	−235.011	−0.102392
$175$	−562.207	−0.242851
$176$	−621.844	−0.266325
$177$	344.287	0.146204
$178$	−262.411	−0.110497
$179$	1631.29	0.681165	0.340582	−	0.940215i	$-0.389376\pi$
$179$	1631.29	0.681165	0.340582	+	0.940215i	$0.389376\pi$
$180$	−462.324	−0.191442
$181$	−853.165	−0.350360	−0.175180	−	0.984536i	$-0.556051\pi$
$181$	−853.165	−0.350360	−0.175180	+	0.984536i	$0.556051\pi$
$182$	−56.2122	−0.0228941
$183$	159.227	0.0643192
$184$	−391.879	−0.157009
$185$	−1691.79	−0.672342
$186$	−351.420	−0.138534
$187$	525.292	0.205418
$188$	−2970.37	−1.15232
$189$	−189.000	−0.0727393
$190$	−44.7291	−0.0170789
$191$	2826.32	1.07071	0.535354	−	0.844628i	$-0.320178\pi$
$191$	2826.32	1.07071	0.535354	+	0.844628i	$0.320178\pi$
$192$	1184.57	0.445253
$193$	2442.22	0.910856	0.455428	−	0.890273i	$-0.349486\pi$
$193$	2442.22	0.910856	0.455428	+	0.890273i	$0.349486\pi$
$194$	657.077	0.243172
$195$	−286.776	−0.105315
$196$	−376.548	−0.137226
$197$	2772.18	1.00259	0.501294	−	0.865277i	$-0.332858\pi$
$197$	2772.18	1.00259	0.501294	+	0.865277i	$0.332858\pi$
$198$	55.5937	0.0199539
$199$	−5579.98	−1.98771	−0.993855	−	0.110688i	$-0.964694\pi$
$199$	−5579.98	−1.98771	−0.993855	+	0.110688i	$0.964694\pi$
$200$	−707.399	−0.250103
$201$	−397.043	−0.139329
$202$	−101.809	−0.0354617
$203$	−976.507	−0.337622
$204$	−1100.91	−0.377840
$205$	−1044.77	−0.355950
$206$	119.231	0.0403263
$207$	−400.432	−0.134454
$208$	808.407	0.269485
$209$	−131.073	−0.0433804
$210$	78.8296	0.0259036
$211$	1573.05	0.513237	0.256619	−	0.966513i	$-0.417392\pi$
$211$	1573.05	0.513237	0.256619	+	0.966513i	$0.417392\pi$
$212$	281.028	0.0910430
$213$	−1750.34	−0.563058
$214$	−123.604	−0.0394831
$215$	−1760.65	−0.558489
$216$	−237.810	−0.0749116
$217$	−1460.20	−0.456797
$218$	138.744	0.0431052
$219$	2451.04	0.756282
$220$	565.062	0.173166
$221$	−682.888	−0.207855
$222$	−426.364	−0.128899
$223$	732.945	0.220097	0.110048	−	0.993926i	$-0.464899\pi$
$223$	732.945	0.220097	0.110048	+	0.993926i	$0.464899\pi$
$224$	−715.452	−0.213407
$225$	−722.838	−0.214174
$226$	78.2026	0.0230175
$227$	6548.97	1.91485	0.957423	−	0.288687i	$-0.0932188\pi$
$227$	6548.97	1.91485	0.957423	+	0.288687i	$0.0932188\pi$
$228$	274.705	0.0797928
$229$	−2326.27	−0.671285	−0.335643	−	0.941989i	$-0.608953\pi$
$229$	−2326.27	−0.671285	−0.335643	+	0.941989i	$0.608953\pi$
$230$	167.015	0.0478811
$231$	231.000	0.0657952
$232$	−1228.69	−0.347705
$233$	−3859.26	−1.08510	−0.542551	−	0.840023i	$-0.682541\pi$
$233$	−3859.26	−1.08510	−0.542551	+	0.840023i	$0.682541\pi$
$234$	−72.2728	−0.0201907
$235$	2583.84	0.717239
$236$	881.909	0.243252
$237$	1108.90	0.303927
$238$	187.714	0.0511247
$239$	−3688.00	−0.998147	−0.499074	−	0.866560i	$-0.666326\pi$
$239$	−3688.00	−0.998147	−0.499074	+	0.866560i	$0.666326\pi$
$240$	−1133.68	−0.304910
$241$	−1818.30	−0.486004	−0.243002	−	0.970026i	$-0.578132\pi$
$241$	−1818.30	−0.486004	−0.243002	+	0.970026i	$0.578132\pi$
$242$	−67.9479	−0.0180490
$243$	−243.000	−0.0641500
$244$	407.869	0.107013
$245$	327.548	0.0854134
$246$	−263.301	−0.0682418
$247$	170.397	0.0438951
$248$	−1837.30	−0.470439
$249$	207.460	0.0528002
$250$	770.710	0.194976
$251$	215.497	0.0541915	0.0270957	−	0.999633i	$-0.491374\pi$
$251$	215.497	0.0541915	0.0270957	+	0.999633i	$0.491374\pi$
$252$	−484.133	−0.121022
$253$	489.417	0.121618
$254$	−380.125	−0.0939023
$255$	957.653	0.235179
$256$	2575.17	0.628703
$257$	4699.31	1.14060	0.570301	−	0.821436i	$-0.306826\pi$
$257$	4699.31	1.14060	0.570301	+	0.821436i	$0.306826\pi$
$258$	−443.716	−0.107072
$259$	−1771.60	−0.425027
$260$	−734.591	−0.175221
$261$	−1255.51	−0.297755
$262$	−163.435	−0.0385384
$263$	7504.38	1.75947	0.879734	−	0.475466i	$-0.157721\pi$
$263$	7504.38	1.75947	0.879734	+	0.475466i	$0.157721\pi$
$264$	290.656	0.0677601
$265$	−244.458	−0.0566678
$266$	−46.8391	−0.0107966
$267$	−1401.89	−0.321326
$268$	−1017.05	−0.231813
$269$	−2513.64	−0.569736	−0.284868	−	0.958567i	$-0.591950\pi$
$269$	−2513.64	−0.569736	−0.284868	+	0.958567i	$0.591950\pi$
$270$	101.352	0.0228448
$271$	6385.39	1.43131	0.715654	−	0.698455i	$-0.246129\pi$
$271$	6385.39	1.43131	0.715654	+	0.698455i	$0.246129\pi$
$272$	−2699.58	−0.601787
$273$	−300.304	−0.0665759
$274$	−1304.15	−0.287543
$275$	883.469	0.193728
$276$	−1025.73	−0.223701
$277$	120.650	0.0261702	0.0130851	−	0.999914i	$-0.495835\pi$
$277$	120.650	0.0261702	0.0130851	+	0.999914i	$0.495835\pi$
$278$	−118.171	−0.0254943
$279$	−1877.40	−0.402857
$280$	412.138	0.0879642
$281$	−2387.75	−0.506908	−0.253454	−	0.967347i	$-0.581567\pi$
$281$	−2387.75	−0.506908	−0.253454	+	0.967347i	$0.581567\pi$
$282$	651.176	0.137507
$283$	781.711	0.164198	0.0820988	−	0.996624i	$-0.473838\pi$
$283$	781.711	0.164198	0.0820988	+	0.996624i	$0.473838\pi$
$284$	−4483.59	−0.936803
$285$	−238.957	−0.0496653
$286$	88.3334	0.0182632
$287$	−1094.05	−0.225017
$288$	−919.867	−0.188207
$289$	−2632.58	−0.535839
$290$	523.657	0.106035
$291$	3510.32	0.707144
$292$	6278.46	1.25828
$293$	2168.03	0.432278	0.216139	−	0.976363i	$-0.430653\pi$
$293$	2168.03	0.432278	0.216139	+	0.976363i	$0.430653\pi$
$294$	82.5483	0.0163752
$295$	−767.147	−0.151407
$296$	−2229.12	−0.437720
$297$	297.000	0.0580259
$298$	522.140	0.101499
$299$	−636.250	−0.123061
$300$	−1851.59	−0.356338
$301$	−1843.70	−0.353054
$302$	−1291.90	−0.246160
$303$	−543.897	−0.103122
$304$	673.610	0.127086
$305$	−354.793	−0.0666079
$306$	241.346	0.0450878
$307$	10309.9	1.91668	0.958338	−	0.285636i	$-0.0922047\pi$
$307$	10309.9	1.91668	0.958338	+	0.285636i	$0.0922047\pi$
$308$	591.719	0.109469
$309$	636.972	0.117269
$310$	783.042	0.143464
$311$	−6686.61	−1.21917	−0.609587	−	0.792719i	$-0.708665\pi$
$311$	−6686.61	−1.21917	−0.609587	+	0.792719i	$0.708665\pi$
$312$	−377.858	−0.0685641
$313$	6457.33	1.16610	0.583051	−	0.812436i	$-0.301859\pi$
$313$	6457.33	1.16610	0.583051	+	0.812436i	$0.301859\pi$
$314$	1093.81	0.196583
$315$	421.133	0.0753276
$316$	2840.50	0.505666
$317$	7170.30	1.27042	0.635212	−	0.772338i	$-0.280913\pi$
$317$	7170.30	1.27042	0.635212	+	0.772338i	$0.280913\pi$
$318$	−61.6081	−0.0108642
$319$	1534.51	0.269329
$320$	−2639.47	−0.461097
$321$	−660.333	−0.114817
$322$	174.894	0.0302685
$323$	−569.021	−0.0980221
$324$	−622.457	−0.106731
$325$	−1148.52	−0.196027
$326$	1546.32	0.262707
$327$	741.216	0.125350
$328$	−1376.60	−0.231737
$329$	2705.73	0.453410
$330$	−123.875	−0.0206639
$331$	5849.52	0.971355	0.485678	−	0.874138i	$-0.338573\pi$
$331$	5849.52	0.971355	0.485678	+	0.874138i	$0.338573\pi$
$332$	531.420	0.0878478
$333$	−2277.78	−0.374839
$334$	2180.79	0.357268
$335$	884.698	0.144287
$336$	−1187.16	−0.192752
$337$	9784.35	1.58157	0.790783	−	0.612097i	$-0.209674\pi$
$337$	9784.35	1.58157	0.790783	+	0.612097i	$0.209674\pi$
$338$	1118.90	0.180059
$339$	417.784	0.0669349
$340$	2453.08	0.391285
$341$	2294.60	0.364398
$342$	−60.2217	−0.00952169
$343$	343.000	0.0539949
$344$	−2319.84	−0.363598
$345$	892.250	0.139238
$346$	1753.92	0.272518
$347$	9431.05	1.45904	0.729518	−	0.683962i	$-0.239745\pi$
$347$	9431.05	1.45904	0.729518	+	0.683962i	$0.239745\pi$
$348$	−3216.05	−0.495398
$349$	3933.02	0.603238	0.301619	−	0.953429i	$-0.402473\pi$
$349$	3933.02	0.603238	0.301619	+	0.953429i	$0.402473\pi$
$350$	315.709	0.0482153
$351$	−386.105	−0.0587144
$352$	1124.28	0.170240
$353$	−6544.48	−0.986764	−0.493382	−	0.869813i	$-0.664240\pi$
$353$	−6544.48	−0.986764	−0.493382	+	0.869813i	$0.664240\pi$
$354$	−193.335	−0.0290273
$355$	3900.14	0.583093
$356$	−3591.01	−0.534615
$357$	1002.83	0.148671
$358$	−916.056	−0.135238
$359$	11013.2	1.61910	0.809548	−	0.587053i	$-0.199712\pi$
$359$	11013.2	1.61910	0.809548	+	0.587053i	$0.199712\pi$
$360$	529.892	0.0775771
$361$	−6717.02	−0.979300
$362$	479.097	0.0695602
$363$	−363.000	−0.0524864
$364$	−769.244	−0.110767
$365$	−5461.45	−0.783192
$366$	−89.4146	−0.0127699
$367$	−7733.24	−1.09992	−0.549962	−	0.835190i	$-0.685358\pi$
$367$	−7733.24	−1.09992	−0.549962	+	0.835190i	$0.685358\pi$
$368$	−2515.21	−0.356289
$369$	−1406.64	−0.198447
$370$	950.032	0.133486
$371$	−255.990	−0.0358231
$372$	−4809.07	−0.670265
$373$	2225.01	0.308865	0.154433	−	0.988003i	$-0.450645\pi$
$373$	2225.01	0.308865	0.154433	+	0.988003i	$0.450645\pi$
$374$	−294.979	−0.0407834
$375$	4117.39	0.566989
$376$	3404.49	0.466950
$377$	−1994.89	−0.272525
$378$	106.133	0.0144416
$379$	−1141.43	−0.154700	−0.0773500	−	0.997004i	$-0.524646\pi$
$379$	−1141.43	−0.154700	−0.0773500	+	0.997004i	$0.524646\pi$
$380$	−612.102	−0.0826320
$381$	−2030.76	−0.273068
$382$	−1587.13	−0.212577
$383$	−5445.56	−0.726515	−0.363257	−	0.931689i	$-0.618335\pi$
$383$	−5445.56	−0.726515	−0.363257	+	0.931689i	$0.618335\pi$
$384$	−3118.17	−0.414384
$385$	−514.719	−0.0681363
$386$	−1371.44	−0.180840
$387$	−2370.48	−0.311365
$388$	8991.88	1.17653
$389$	7194.64	0.937745	0.468872	−	0.883266i	$-0.344660\pi$
$389$	7194.64	0.937745	0.468872	+	0.883266i	$0.344660\pi$
$390$	161.040	0.0209091
$391$	2124.68	0.274808
$392$	431.580	0.0556074
$393$	−873.125	−0.112070
$394$	−1556.73	−0.199053
$395$	−2470.87	−0.314741
$396$	760.781	0.0965422
$397$	846.201	0.106976	0.0534882	−	0.998568i	$-0.482966\pi$
$397$	846.201	0.106976	0.0534882	+	0.998568i	$0.482966\pi$
$398$	3133.45	0.394638
$399$	−250.230	−0.0313964
$400$	−4540.33	−0.567541
$401$	4219.37	0.525450	0.262725	−	0.964871i	$-0.415379\pi$
$401$	4219.37	0.525450	0.262725	+	0.964871i	$0.415379\pi$
$402$	222.960	0.0276623
$403$	−2983.02	−0.368722
$404$	−1393.22	−0.171573
$405$	541.457	0.0664327
$406$	548.360	0.0670312
$407$	2783.95	0.339054
$408$	1261.81	0.153110
$409$	−8028.62	−0.970636	−0.485318	−	0.874338i	$-0.661296\pi$
$409$	−8028.62	−0.970636	−0.485318	+	0.874338i	$0.661296\pi$
$410$	586.693	0.0706700
$411$	−6967.22	−0.836174
$412$	1631.64	0.195109
$413$	−803.336	−0.0957133
$414$	224.864	0.0266943
$415$	−462.267	−0.0546790
$416$	−1461.58	−0.172260
$417$	−631.307	−0.0741372
$418$	73.6043	0.00861269
$419$	−11381.3	−1.32699	−0.663497	−	0.748179i	$-0.730929\pi$
$419$	−11381.3	−1.32699	−0.663497	+	0.748179i	$0.730929\pi$
$420$	1078.76	0.125328
$421$	−2476.59	−0.286702	−0.143351	−	0.989672i	$-0.545788\pi$
$421$	−2476.59	−0.286702	−0.143351	+	0.989672i	$0.545788\pi$
$422$	−883.349	−0.101898
$423$	3478.80	0.399870
$424$	−322.100	−0.0368929
$425$	3835.36	0.437747
$426$	982.909	0.111789
$427$	−371.530	−0.0421068
$428$	−1691.48	−0.191029
$429$	471.906	0.0531092
$430$	988.697	0.110882
$431$	−9698.52	−1.08390	−0.541951	−	0.840410i	$-0.682314\pi$
$431$	−9698.52	−1.08390	−0.541951	+	0.840410i	$0.682314\pi$
$432$	−1526.34	−0.169991
$433$	−14385.7	−1.59661	−0.798307	−	0.602251i	$-0.794271\pi$
$433$	−14385.7	−1.59661	−0.798307	+	0.602251i	$0.794271\pi$
$434$	819.981	0.0906920
$435$	2797.55	0.308350
$436$	1898.66	0.208554
$437$	−530.159	−0.0580342
$438$	−1376.39	−0.150151
$439$	−806.402	−0.0876708	−0.0438354	−	0.999039i	$-0.513958\pi$
$439$	−806.402	−0.0876708	−0.0438354	+	0.999039i	$0.513958\pi$
$440$	−647.646	−0.0701711
$441$	441.000	0.0476190
$442$	383.478	0.0412674
$443$	4748.19	0.509240	0.254620	−	0.967041i	$-0.418050\pi$
$443$	4748.19	0.509240	0.254620	+	0.967041i	$0.418050\pi$
$444$	−5834.64	−0.623648
$445$	3123.71	0.332760
$446$	−411.587	−0.0436978
$447$	2789.45	0.295159
$448$	−2763.99	−0.291487
$449$	−7104.43	−0.746724	−0.373362	−	0.927686i	$-0.621795\pi$
$449$	−7104.43	−0.746724	−0.373362	+	0.927686i	$0.621795\pi$
$450$	405.912	0.0425219
$451$	1719.23	0.179502
$452$	1070.18	0.111365
$453$	−6901.74	−0.715833
$454$	−3677.59	−0.380172
$455$	669.143	0.0689449
$456$	−314.852	−0.0323340
$457$	4600.05	0.470856	0.235428	−	0.971892i	$-0.424351\pi$
$457$	4600.05	0.470856	0.235428	+	0.971892i	$0.424351\pi$
$458$	1306.32	0.133276
$459$	1289.35	0.131115
$460$	2285.55	0.231661
$461$	7098.21	0.717130	0.358565	−	0.933505i	$-0.383266\pi$
$461$	7098.21	0.717130	0.358565	+	0.933505i	$0.383266\pi$
$462$	−129.719	−0.0130629
$463$	10036.0	1.00737	0.503684	−	0.863888i	$-0.331978\pi$
$463$	10036.0	1.00737	0.503684	+	0.863888i	$0.331978\pi$
$464$	−7886.16	−0.789021
$465$	4183.27	0.417192
$466$	2167.18	0.215435
$467$	255.074	0.0252750	0.0126375	−	0.999920i	$-0.495977\pi$
$467$	255.074	0.0252750	0.0126375	+	0.999920i	$0.495977\pi$
$468$	−989.028	−0.0976877
$469$	926.433	0.0912125
$470$	−1450.96	−0.142400
$471$	5843.48	0.571663
$472$	−1010.80	−0.0985716
$473$	2897.25	0.281640
$474$	−622.705	−0.0603413
$475$	−957.015	−0.0924439
$476$	2568.80	0.247355
$477$	−329.131	−0.0315930
$478$	2071.01	0.198171
$479$	−2390.02	−0.227981	−0.113991	−	0.993482i	$-0.536363\pi$
$479$	−2390.02	−0.227981	−0.113991	+	0.993482i	$0.536363\pi$
$480$	2049.66	0.194904
$481$	−3619.18	−0.343078
$482$	1021.07	0.0964907
$483$	934.341	0.0880207
$484$	−929.844	−0.0873257
$485$	−7821.77	−0.732306
$486$	136.457	0.0127363
$487$	−16853.6	−1.56819	−0.784095	−	0.620641i	$-0.786872\pi$
$487$	−16853.6	−1.56819	−0.784095	+	0.620641i	$0.786872\pi$
$488$	−467.479	−0.0433643
$489$	8260.93	0.763952
$490$	−183.936	−0.0169579
$491$	16965.7	1.55938	0.779688	−	0.626168i	$-0.215378\pi$
$491$	16965.7	1.55938	0.779688	+	0.626168i	$0.215378\pi$
$492$	−3603.19	−0.330171
$493$	6661.70	0.608576
$494$	−95.6869	−0.00871489
$495$	−661.781	−0.0600906
$496$	−11792.4	−1.06753
$497$	4084.13	0.368608
$498$	−116.500	−0.0104829
$499$	−18186.3	−1.63153	−0.815763	−	0.578386i	$-0.803683\pi$
$499$	−18186.3	−1.63153	−0.815763	+	0.578386i	$0.803683\pi$
$500$	10546.9	0.943344
$501$	11650.5	1.03893
$502$	−121.013	−0.0107591
$503$	−484.954	−0.0429881	−0.0214941	−	0.999769i	$-0.506842\pi$
$503$	−484.954	−0.0429881	−0.0214941	+	0.999769i	$0.506842\pi$
$504$	554.889	0.0490411
$505$	1211.92	0.106792
$506$	−274.833	−0.0241459
$507$	5977.51	0.523611
$508$	−5201.89	−0.454324
$509$	−7573.95	−0.659547	−0.329773	−	0.944060i	$-0.606972\pi$
$509$	−7573.95	−0.659547	−0.329773	+	0.944060i	$0.606972\pi$
$510$	−537.773	−0.0466921
$511$	−5719.09	−0.495103
$512$	−9761.22	−0.842557
$513$	−321.724	−0.0276890
$514$	−2638.91	−0.226454
$515$	−1419.31	−0.121442
$516$	−6072.10	−0.518041
$517$	−4251.86	−0.361696
$518$	994.849	0.0843844
$519$	9369.99	0.792480
$520$	841.951	0.0710038
$521$	−8619.11	−0.724779	−0.362390	−	0.932027i	$-0.618039\pi$
$521$	−8619.11	−0.724779	−0.362390	+	0.932027i	$0.618039\pi$
$522$	705.034	0.0591159
$523$	10682.2	0.893116	0.446558	−	0.894755i	$-0.352650\pi$
$523$	10682.2	0.893116	0.446558	+	0.894755i	$0.352650\pi$
$524$	−2236.56	−0.186459
$525$	1686.62	0.140210
$526$	−4214.11	−0.349323
$527$	9961.46	0.823393
$528$	1865.53	0.153763
$529$	−10187.4	−0.837300
$530$	137.276	0.0112508
$531$	−1032.86	−0.0844112
$532$	−640.977	−0.0522366
$533$	−2235.03	−0.181632
$534$	787.233	0.0637957
$535$	1471.37	0.118902
$536$	1165.69	0.0939365
$537$	−4893.88	−0.393271
$538$	1411.54	0.113115
$539$	−539.000	−0.0430730
$540$	1386.97	0.110529
$541$	−16632.0	−1.32175	−0.660873	−	0.750498i	$-0.729814\pi$
$541$	−16632.0	−1.32175	−0.660873	+	0.750498i	$0.729814\pi$
$542$	−3585.73	−0.284170
$543$	2559.49	0.202281
$544$	4880.79	0.384673
$545$	−1651.59	−0.129810
$546$	168.637	0.0132179
$547$	5814.76	0.454518	0.227259	−	0.973834i	$-0.427024\pi$
$547$	5814.76	0.454518	0.227259	+	0.973834i	$0.427024\pi$
$548$	−17846.9	−1.39121
$549$	−477.682	−0.0371347
$550$	−496.114	−0.0384625
$551$	−1662.25	−0.128520
$552$	1175.64	0.0906493
$553$	−2587.43	−0.198967
$554$	−67.7512	−0.00519580
$555$	5075.38	0.388177
$556$	−1617.13	−0.123348
$557$	−14323.2	−1.08958	−0.544788	−	0.838574i	$-0.683390\pi$
$557$	−14323.2	−1.08958	−0.544788	+	0.838574i	$0.683390\pi$
$558$	1054.26	0.0799829
$559$	−3766.47	−0.284982
$560$	2645.24	0.199611
$561$	−1575.88	−0.118598
$562$	1340.85	0.100641
$563$	12389.8	0.927476	0.463738	−	0.885972i	$-0.346508\pi$
$563$	12389.8	0.927476	0.463738	+	0.885972i	$0.346508\pi$
$564$	8911.12	0.665294
$565$	−930.915	−0.0693166
$566$	−438.972	−0.0325996
$567$	567.000	0.0419961
$568$	5138.86	0.379616
$569$	11823.1	0.871092	0.435546	−	0.900166i	$-0.356555\pi$
$569$	11823.1	0.871092	0.435546	+	0.900166i	$0.356555\pi$
$570$	134.187	0.00986050
$571$	−26117.3	−1.91414	−0.957069	−	0.289860i	$-0.906391\pi$
$571$	−26117.3	−1.91414	−0.957069	+	0.289860i	$0.906391\pi$
$572$	1208.81	0.0883619
$573$	−8478.95	−0.618173
$574$	614.370	0.0446747
$575$	3573.42	0.259169
$576$	−3553.70	−0.257067
$577$	11861.7	0.855821	0.427911	−	0.903821i	$-0.359250\pi$
$577$	11861.7	0.855821	0.427911	+	0.903821i	$0.359250\pi$
$578$	1478.33	0.106385
$579$	−7326.67	−0.525883
$580$	7166.07	0.513025
$581$	−484.074	−0.0345659
$582$	−1971.23	−0.140396
$583$	402.271	0.0285769
$584$	−7196.05	−0.509888
$585$	860.327	0.0608036
$586$	−1217.46	−0.0858241
$587$	365.737	0.0257165	0.0128582	−	0.999917i	$-0.495907\pi$
$587$	365.737	0.0257165	0.0128582	+	0.999917i	$0.495907\pi$
$588$	1129.64	0.0792275
$589$	−2485.62	−0.173885
$590$	430.793	0.0300601
$591$	−8316.54	−0.578844
$592$	−14307.3	−0.993286
$593$	−17264.3	−1.19554	−0.597772	−	0.801666i	$-0.703947\pi$
$593$	−17264.3	−1.19554	−0.597772	+	0.801666i	$0.703947\pi$
$594$	−166.781	−0.0115204
$595$	−2234.52	−0.153961
$596$	7145.31	0.491080
$597$	16739.9	1.14761
$598$	357.288	0.0244324
$599$	−53.8079	−0.00367033	−0.00183517	−	0.999998i	$-0.500584\pi$
$599$	−53.8079	−0.00367033	−0.00183517	+	0.999998i	$0.500584\pi$
$600$	2122.20	0.144397
$601$	3018.63	0.204879	0.102440	−	0.994739i	$-0.467335\pi$
$601$	3018.63	0.204879	0.102440	+	0.994739i	$0.467335\pi$
$602$	1035.34	0.0700950
$603$	1191.13	0.0804419
$604$	−17679.2	−1.19099
$605$	808.844	0.0543540
$606$	305.427	0.0204738
$607$	−8991.00	−0.601208	−0.300604	−	0.953749i	$-0.597188\pi$
$607$	−8991.00	−0.601208	−0.300604	+	0.953749i	$0.597188\pi$
$608$	−1217.87	−0.0812357
$609$	2929.52	0.194926
$610$	199.235	0.0132243
$611$	5527.50	0.365988
$612$	3302.74	0.218146
$613$	−16880.3	−1.11222	−0.556110	−	0.831109i	$-0.687707\pi$
$613$	−16880.3	−1.11222	−0.556110	+	0.831109i	$0.687707\pi$
$614$	−5789.58	−0.380535
$615$	3134.31	0.205508
$616$	−678.198	−0.0443594
$617$	23828.4	1.55477	0.777387	−	0.629022i	$-0.216545\pi$
$617$	23828.4	1.55477	0.777387	+	0.629022i	$0.216545\pi$
$618$	−357.693	−0.0232824
$619$	12588.4	0.817402	0.408701	−	0.912668i	$-0.365982\pi$
$619$	12588.4	0.817402	0.408701	+	0.912668i	$0.365982\pi$
$620$	10715.7	0.694115
$621$	1201.30	0.0776269
$622$	3754.89	0.242053
$623$	3271.07	0.210357
$624$	−2425.22	−0.155587
$625$	864.972	0.0553582
$626$	−3626.13	−0.231516
$627$	393.219	0.0250457
$628$	14968.4	0.951121
$629$	12085.8	0.766126
$630$	−236.489	−0.0149555
$631$	−11576.5	−0.730354	−0.365177	−	0.930938i	$-0.618992\pi$
$631$	−11576.5	−0.730354	−0.365177	+	0.930938i	$0.618992\pi$
$632$	−3255.64	−0.204909
$633$	−4719.14	−0.296318
$634$	−4026.50	−0.252228
$635$	4524.97	0.282784
$636$	−843.085	−0.0525637
$637$	700.709	0.0435842
$638$	−861.709	−0.0534724
$639$	5251.02	0.325082
$640$	6947.97	0.429129
$641$	−9004.11	−0.554822	−0.277411	−	0.960751i	$-0.589476\pi$
$641$	−9004.11	−0.554822	−0.277411	+	0.960751i	$0.589476\pi$
$642$	370.812	0.0227956
$643$	19692.3	1.20776	0.603879	−	0.797076i	$-0.293621\pi$
$643$	19692.3	1.20776	0.603879	+	0.797076i	$0.293621\pi$
$644$	2393.36	0.146447
$645$	5281.94	0.322444
$646$	319.535	0.0194612
$647$	25548.5	1.55242	0.776208	−	0.630477i	$-0.217141\pi$
$647$	25548.5	1.55242	0.776208	+	0.630477i	$0.217141\pi$
$648$	713.429	0.0432502
$649$	1262.39	0.0763528
$650$	644.957	0.0389189
$651$	4380.61	0.263732
$652$	21160.8	1.27105
$653$	15206.7	0.911306	0.455653	−	0.890157i	$-0.349406\pi$
$653$	15206.7	0.911306	0.455653	+	0.890157i	$0.349406\pi$
$654$	−416.232	−0.0248868
$655$	1945.51	0.116057
$656$	−8835.47	−0.525864
$657$	−7353.11	−0.436639
$658$	−1519.41	−0.0900195
$659$	30126.4	1.78082	0.890408	−	0.455162i	$-0.150419\pi$
$659$	30126.4	1.78082	0.890408	+	0.455162i	$0.150419\pi$
$660$	−1695.19	−0.0999774
$661$	−5122.44	−0.301422	−0.150711	−	0.988578i	$-0.548156\pi$
$661$	−5122.44	−0.301422	−0.150711	+	0.988578i	$0.548156\pi$
$662$	−3284.81	−0.192852
$663$	2048.66	0.120005
$664$	−609.087	−0.0355981
$665$	557.567	0.0325136
$666$	1279.09	0.0744201
$667$	6206.73	0.360308
$668$	29843.3	1.72855
$669$	−2198.83	−0.127073
$670$	−496.805	−0.0286466
$671$	583.834	0.0335896
$672$	2146.36	0.123210
$673$	9238.65	0.529159	0.264579	−	0.964364i	$-0.414767\pi$
$673$	9238.65	0.529159	0.264579	+	0.964364i	$0.414767\pi$
$674$	−5494.43	−0.314002
$675$	2168.51	0.123654
$676$	15311.7	0.871172
$677$	−12245.5	−0.695171	−0.347586	−	0.937648i	$-0.612998\pi$
$677$	−12245.5	−0.695171	−0.347586	+	0.937648i	$0.612998\pi$
$678$	−234.608	−0.0132892
$679$	−8190.76	−0.462934
$680$	−2811.59	−0.158558
$681$	−19646.9	−1.10554
$682$	−1288.54	−0.0723472
$683$	−3210.33	−0.179853	−0.0899267	−	0.995948i	$-0.528663\pi$
$683$	−3210.33	−0.179853	−0.0899267	+	0.995948i	$0.528663\pi$
$684$	−824.114	−0.0460684
$685$	15524.5	0.865927
$686$	−192.613	−0.0107201
$687$	6978.81	0.387567
$688$	−14889.6	−0.825086
$689$	−522.959	−0.0289160
$690$	−501.045	−0.0276442
$691$	15819.4	0.870908	0.435454	−	0.900211i	$-0.356588\pi$
$691$	15819.4	0.870908	0.435454	+	0.900211i	$0.356588\pi$
$692$	24001.7	1.31851
$693$	−693.000	−0.0379869
$694$	−5296.03	−0.289675
$695$	1406.69	0.0767752
$696$	3686.07	0.200748
$697$	7463.61	0.405602
$698$	−2208.60	−0.119766
$699$	11577.8	0.626484
$700$	4320.37	0.233278
$701$	−13417.1	−0.722907	−0.361454	−	0.932390i	$-0.617719\pi$
$701$	−13417.1	−0.722907	−0.361454	+	0.932390i	$0.617719\pi$
$702$	216.818	0.0116571
$703$	−3015.70	−0.161791
$704$	4343.41	0.232526
$705$	−7751.53	−0.414098
$706$	3675.07	0.195911
$707$	1269.09	0.0675095
$708$	−2645.73	−0.140441
$709$	−25127.4	−1.33100	−0.665500	−	0.746398i	$-0.731782\pi$
$709$	−25127.4	−1.33100	−0.665500	+	0.746398i	$0.731782\pi$
$710$	−2190.14	−0.115767
$711$	−3326.69	−0.175472
$712$	4115.83	0.216639
$713$	9281.14	0.487491
$714$	−563.142	−0.0295169
$715$	−1051.51	−0.0549990
$716$	−12535.9	−0.654315
$717$	11064.0	0.576281
$718$	−6184.51	−0.321454
$719$	4894.82	0.253889	0.126944	−	0.991910i	$-0.459483\pi$
$719$	4894.82	0.253889	0.126944	+	0.991910i	$0.459483\pi$
$720$	3401.03	0.176040
$721$	−1486.27	−0.0767704
$722$	3771.96	0.194429
$723$	5454.90	0.280594
$724$	6556.28	0.336550
$725$	11204.1	0.573943
$726$	203.844	0.0104206
$727$	19968.3	1.01869	0.509343	−	0.860564i	$-0.329888\pi$
$727$	19968.3	1.01869	0.509343	+	0.860564i	$0.329888\pi$
$728$	881.669	0.0448857
$729$	729.000	0.0370370
$730$	3066.89	0.155494
$731$	12577.7	0.636392
$732$	−1223.61	−0.0617839
$733$	−3961.01	−0.199595	−0.0997975	−	0.995008i	$-0.531820\pi$
$733$	−3961.01	−0.199595	−0.0997975	+	0.995008i	$0.531820\pi$
$734$	4342.62	0.218378
$735$	−982.645	−0.0493135
$736$	4547.45	0.227746
$737$	−1455.82	−0.0727624
$738$	789.904	0.0393994
$739$	−30962.0	−1.54121	−0.770605	−	0.637313i	$-0.780046\pi$
$739$	−30962.0	−1.54121	−0.770605	+	0.637313i	$0.780046\pi$
$740$	13000.9	0.645839
$741$	−511.191	−0.0253429
$742$	143.752	0.00711227
$743$	−9800.99	−0.483935	−0.241967	−	0.970284i	$-0.577793\pi$
$743$	−9800.99	−0.483935	−0.241967	+	0.970284i	$0.577793\pi$
$744$	5511.91	0.271608
$745$	−6215.50	−0.305662
$746$	−1249.46	−0.0613217
$747$	−622.381	−0.0304842
$748$	−4036.69	−0.197321
$749$	1540.78	0.0751652
$750$	−2312.13	−0.112569
$751$	6366.71	0.309354	0.154677	−	0.987965i	$-0.450566\pi$
$751$	6366.71	0.309354	0.154677	+	0.987965i	$0.450566\pi$
$752$	21851.2	1.05962
$753$	−646.492	−0.0312875
$754$	1120.24	0.0541069
$755$	15378.6	0.741304
$756$	1452.40	0.0698721
$757$	18741.7	0.899838	0.449919	−	0.893069i	$-0.351453\pi$
$757$	18741.7	0.899838	0.449919	+	0.893069i	$0.351453\pi$
$758$	640.973	0.0307140
$759$	−1468.25	−0.0702162
$760$	701.560	0.0334846
$761$	−31269.0	−1.48949	−0.744745	−	0.667350i	$-0.767429\pi$
$761$	−31269.0	−1.48949	−0.744745	+	0.667350i	$0.767429\pi$
$762$	1140.38	0.0542145
$763$	−1729.50	−0.0820606
$764$	−21719.3	−1.02850
$765$	−2872.96	−0.135781
$766$	3057.97	0.144241
$767$	−1641.12	−0.0772588
$768$	−7725.50	−0.362982
$769$	6522.45	0.305859	0.152930	−	0.988237i	$-0.451129\pi$
$769$	6522.45	0.305859	0.152930	+	0.988237i	$0.451129\pi$
$770$	289.042	0.0135277
$771$	−14097.9	−0.658527
$772$	−18767.7	−0.874952
$773$	−27552.5	−1.28201	−0.641007	−	0.767535i	$-0.721483\pi$
$773$	−27552.5	−1.28201	−0.641007	+	0.767535i	$0.721483\pi$
$774$	1331.15	0.0618180
$775$	16753.8	0.776535
$776$	−10306.0	−0.476759
$777$	5314.81	0.245390
$778$	−4040.17	−0.186179
$779$	−1862.35	−0.0856554
$780$	2203.77	0.101164
$781$	−6417.92	−0.294048
$782$	−1193.12	−0.0545600
$783$	3766.53	0.171909
$784$	2770.03	0.126186
$785$	−13020.6	−0.592005
$786$	490.306	0.0222502
$787$	−31775.6	−1.43923	−0.719616	−	0.694372i	$-0.755682\pi$
$787$	−31775.6	−1.43923	−0.719616	+	0.694372i	$0.755682\pi$
$788$	−21303.3	−0.963068
$789$	−22513.1	−1.01583
$790$	1387.52	0.0624884
$791$	−974.830	−0.0438192
$792$	−871.969	−0.0391213
$793$	−758.993	−0.0339882
$794$	−475.187	−0.0212390
$795$	733.375	0.0327172
$796$	42880.2	1.90936
$797$	−26583.5	−1.18147	−0.590737	−	0.806864i	$-0.701163\pi$
$797$	−26583.5	−1.18147	−0.590737	+	0.806864i	$0.701163\pi$
$798$	140.517	0.00623341
$799$	−18458.4	−0.817287
$800$	8208.82	0.362782
$801$	4205.66	0.185518
$802$	−2369.40	−0.104322
$803$	8987.13	0.394955
$804$	3051.14	0.133837
$805$	−2081.92	−0.0911527
$806$	1675.13	0.0732057
$807$	7540.91	0.328938
$808$	1596.84	0.0695255
$809$	−4580.99	−0.199084	−0.0995421	−	0.995033i	$-0.531738\pi$
$809$	−4580.99	−0.199084	−0.0995421	+	0.995033i	$0.531738\pi$
$810$	−304.057	−0.0131895
$811$	−11867.9	−0.513855	−0.256928	−	0.966431i	$-0.582710\pi$
$811$	−11867.9	−0.513855	−0.256928	+	0.966431i	$0.582710\pi$
$812$	7504.12	0.324314
$813$	−19156.2	−0.826366
$814$	−1563.33	−0.0673155
$815$	−18407.2	−0.791135
$816$	8098.74	0.347442
$817$	−3138.44	−0.134394
$818$	4508.50	0.192709
$819$	900.912	0.0384376
$820$	8028.69	0.341920
$821$	6389.94	0.271633	0.135816	−	0.990734i	$-0.456634\pi$
$821$	6389.94	0.271633	0.135816	+	0.990734i	$0.456634\pi$
$822$	3912.46	0.166013
$823$	−35488.9	−1.50312	−0.751558	−	0.659667i	$-0.770697\pi$
$823$	−35488.9	−1.50312	−0.751558	+	0.659667i	$0.770697\pi$
$824$	−1870.10	−0.0790631
$825$	−2650.41	−0.111849
$826$	451.116	0.0190028
$827$	−506.928	−0.0213151	−0.0106576	−	0.999943i	$-0.503392\pi$
$827$	−506.928	−0.0213151	−0.0106576	+	0.999943i	$0.503392\pi$
$828$	3077.18	0.129154
$829$	−18129.2	−0.759535	−0.379768	−	0.925082i	$-0.623996\pi$
$829$	−18129.2	−0.759535	−0.379768	+	0.925082i	$0.623996\pi$
$830$	259.587	0.0108559
$831$	−361.949	−0.0151094
$832$	−5646.50	−0.235285
$833$	−2339.94	−0.0973277
$834$	354.512	0.0147191
$835$	−25959.8	−1.07590
$836$	1007.25	0.0416704
$837$	5632.21	0.232590
$838$	6391.18	0.263460
$839$	−4031.98	−0.165911	−0.0829556	−	0.996553i	$-0.526436\pi$
$839$	−4031.98	−0.165911	−0.0829556	+	0.996553i	$0.526436\pi$
$840$	−1236.41	−0.0507861
$841$	−4928.49	−0.202078
$842$	1390.74	0.0569216
$843$	7163.25	0.292664
$844$	−12088.3	−0.493006
$845$	−13319.2	−0.542242
$846$	−1953.53	−0.0793897
$847$	847.000	0.0343604
$848$	−2067.35	−0.0837183
$849$	−2345.13	−0.0947995
$850$	−2153.76	−0.0869098
$851$	11260.4	0.453586
$852$	13450.8	0.540864
$853$	20432.0	0.820140	0.410070	−	0.912054i	$-0.365504\pi$
$853$	20432.0	0.820140	0.410070	+	0.912054i	$0.365504\pi$
$854$	208.634	0.00835984
$855$	716.872	0.0286743
$856$	1938.68	0.0774099
$857$	27874.2	1.11105	0.555523	−	0.831501i	$-0.312518\pi$
$857$	27874.2	1.11105	0.555523	+	0.831501i	$0.312518\pi$
$858$	−265.000	−0.0105442
$859$	−7972.63	−0.316674	−0.158337	−	0.987385i	$-0.550613\pi$
$859$	−7972.63	−0.316674	−0.158337	+	0.987385i	$0.550613\pi$
$860$	13530.0	0.536475
$861$	3282.16	0.129914
$862$	5446.23	0.215197
$863$	−45524.5	−1.79568	−0.897840	−	0.440322i	$-0.854864\pi$
$863$	−45524.5	−1.79568	−0.897840	+	0.440322i	$0.854864\pi$
$864$	2759.60	0.108661
$865$	−20878.4	−0.820679
$866$	8078.34	0.316990
$867$	7897.73	0.309367
$868$	11221.2	0.438791
$869$	4065.96	0.158721
$870$	−1570.97	−0.0612194
$871$	1892.59	0.0736258
$872$	−2176.15	−0.0845113
$873$	−10531.0	−0.408270
$874$	297.712	0.0115220
$875$	−9607.24	−0.371182
$876$	−18835.4	−0.726471
$877$	24262.3	0.934186	0.467093	−	0.884208i	$-0.345301\pi$
$877$	24262.3	0.934186	0.467093	+	0.884208i	$0.345301\pi$
$878$	452.837	0.0174061
$879$	−6504.09	−0.249576
$880$	−4156.81	−0.159234
$881$	−6944.67	−0.265575	−0.132788	−	0.991145i	$-0.542393\pi$
$881$	−6944.67	−0.265575	−0.132788	+	0.991145i	$0.542393\pi$
$882$	−247.645	−0.00945423
$883$	−11539.6	−0.439794	−0.219897	−	0.975523i	$-0.570572\pi$
$883$	−11539.6	−0.439794	−0.219897	+	0.975523i	$0.570572\pi$
$884$	5247.76	0.199662
$885$	2301.44	0.0874148
$886$	−2666.36	−0.101104
$887$	−259.602	−0.00982702	−0.00491351	−	0.999988i	$-0.501564\pi$
$887$	−259.602	−0.00982702	−0.00491351	+	0.999988i	$0.501564\pi$
$888$	6687.37	0.252718
$889$	4738.43	0.178765
$890$	−1754.13	−0.0660657
$891$	−891.000	−0.0335013
$892$	−5632.43	−0.211421
$893$	4605.82	0.172596
$894$	−1566.42	−0.0586006
$895$	10904.6	0.407264
$896$	7275.74	0.271278
$897$	1908.75	0.0710494
$898$	3989.51	0.148254
$899$	29099.9	1.07957
$900$	5554.76	0.205732
$901$	1746.36	0.0645723
$902$	−965.438	−0.0356381
$903$	5531.11	0.203836
$904$	−1226.58	−0.0451277
$905$	−5703.11	−0.209478
$906$	3875.69	0.142121
$907$	−20655.5	−0.756179	−0.378089	−	0.925769i	$-0.623419\pi$
$907$	−20655.5	−0.756179	−0.378089	+	0.925769i	$0.623419\pi$
$908$	−50326.6	−1.83937
$909$	1631.69	0.0595378
$910$	−375.759	−0.0136882
$911$	−14371.0	−0.522648	−0.261324	−	0.965251i	$-0.584159\pi$
$911$	−14371.0	−0.522648	−0.261324	+	0.965251i	$0.584159\pi$
$912$	−2020.83	−0.0733732
$913$	760.688	0.0275740
$914$	−2583.17	−0.0934833
$915$	1064.38	0.0384561
$916$	17876.6	0.644825
$917$	2037.29	0.0733668
$918$	−724.039	−0.0260314
$919$	12066.1	0.433107	0.216553	−	0.976271i	$-0.430518\pi$
$919$	12066.1	0.433107	0.216553	+	0.976271i	$0.430518\pi$
$920$	−2619.58	−0.0938748
$921$	−30929.8	−1.10659
$922$	−3986.02	−0.142378
$923$	8343.40	0.297537
$924$	−1775.16	−0.0632017
$925$	20326.7	0.722527
$926$	−5635.73	−0.200002
$927$	−1910.91	−0.0677051
$928$	14258.0	0.504356
$929$	−53667.0	−1.89532	−0.947662	−	0.319275i	$-0.896561\pi$
$929$	−53667.0	−1.89532	−0.947662	+	0.319275i	$0.896561\pi$
$930$	−2349.13	−0.0828289
$931$	583.870	0.0205538
$932$	29657.1	1.04233
$933$	20059.8	0.703890
$934$	−143.238	−0.00501808
$935$	3511.40	0.122818
$936$	1133.57	0.0395855
$937$	26617.1	0.928007	0.464004	−	0.885833i	$-0.346412\pi$
$937$	26617.1	0.928007	0.464004	+	0.885833i	$0.346412\pi$
$938$	−520.241	−0.0181092
$939$	−19372.0	−0.673249
$940$	−19855.9	−0.688967
$941$	−39750.7	−1.37709	−0.688543	−	0.725196i	$-0.741749\pi$
$941$	−39750.7	−1.37709	−0.688543	+	0.725196i	$0.741749\pi$
$942$	−3281.42	−0.113497
$943$	6953.88	0.240137
$944$	−6487.66	−0.223681
$945$	−1263.40	−0.0434904
$946$	−1626.96	−0.0559165
$947$	18606.6	0.638471	0.319235	−	0.947675i	$-0.396574\pi$
$947$	18606.6	0.638471	0.319235	+	0.947675i	$0.396574\pi$
$948$	−8521.50	−0.291947
$949$	−11683.4	−0.399642
$950$	537.414	0.0183537
$951$	−21510.9	−0.733479
$952$	−2944.23	−0.100234
$953$	−46514.2	−1.58105	−0.790526	−	0.612428i	$-0.790193\pi$
$953$	−46514.2	−1.58105	−0.790526	+	0.612428i	$0.790193\pi$
$954$	184.824	0.00627244
$955$	18893.0	0.640169
$956$	28341.1	0.958803
$957$	−4603.53	−0.155497
$958$	1342.12	0.0452631
$959$	16256.8	0.547404
$960$	7918.41	0.266214
$961$	13723.1	0.460646
$962$	2032.36	0.0681143
$963$	1981.00	0.0662895
$964$	13973.0	0.466847
$965$	16325.4	0.544595
$966$	−524.682	−0.0174755
$967$	34299.6	1.14064	0.570321	−	0.821422i	$-0.306819\pi$
$967$	34299.6	1.14064	0.570321	+	0.821422i	$0.306819\pi$
$968$	1065.74	0.0353865
$969$	1707.06	0.0565931
$970$	4392.34	0.145391
$971$	−27751.4	−0.917182	−0.458591	−	0.888648i	$-0.651646\pi$
$971$	−27751.4	−0.917182	−0.458591	+	0.888648i	$0.651646\pi$
$972$	1867.37	0.0616214
$973$	1473.05	0.0485342
$974$	9464.17	0.311347
$975$	3445.57	0.113176
$976$	−3000.44	−0.0984034
$977$	−4009.25	−0.131287	−0.0656434	−	0.997843i	$-0.520910\pi$
$977$	−4009.25	−0.131287	−0.0656434	+	0.997843i	$0.520910\pi$
$978$	−4638.95	−0.151674
$979$	−5140.25	−0.167807
$980$	−2517.10	−0.0820466
$981$	−2223.65	−0.0723707
$982$	−9527.16	−0.309597
$983$	9792.68	0.317739	0.158870	−	0.987300i	$-0.449215\pi$
$983$	9792.68	0.317739	0.158870	+	0.987300i	$0.449215\pi$
$984$	4129.79	0.133794
$985$	18531.1	0.599441
$986$	−3740.90	−0.120826
$987$	−8117.20	−0.261776
$988$	−1309.44	−0.0421649
$989$	11718.7	0.376777
$990$	371.625	0.0119303
$991$	51763.7	1.65926	0.829631	−	0.558312i	$-0.188551\pi$
$991$	51763.7	1.65926	0.829631	+	0.558312i	$0.188551\pi$
$992$	21320.5	0.682386
$993$	−17548.6	−0.560812
$994$	−2293.45	−0.0731830
$995$	−37300.3	−1.18844
$996$	−1594.26	−0.0507190
$997$	−17369.9	−0.551767	−0.275884	−	0.961191i	$-0.588970\pi$
$997$	−17369.9	−0.551767	−0.275884	+	0.961191i	$0.588970\pi$
$998$	10212.6	0.323921
$999$	6833.33	0.216413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.a.h.1.1	✓	2
3.2	odd	2		693.4.a.g.1.2		2
7.6	odd	2		1617.4.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.h.1.1	✓	2	1.1	even	1	trivial
693.4.a.g.1.2		2	3.2	odd	2
1617.4.a.m.1.1		2	7.6	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.a (trivial)

\(f(q)\)	\(=\)	\(q-0.561553 q^{2} -3.00000 q^{3} -7.68466 q^{4} +6.68466 q^{5} +1.68466 q^{6} +7.00000 q^{7} +8.80776 q^{8} +9.00000 q^{9} -3.75379 q^{10} -11.0000 q^{11} +23.0540 q^{12} +14.3002 q^{13} -3.93087 q^{14} -20.0540 q^{15} +56.5312 q^{16} -47.7538 q^{17} -5.05398 q^{18} +11.9157 q^{19} -51.3693 q^{20} -21.0000 q^{21} +6.17708 q^{22} -44.4924 q^{23} -26.4233 q^{24} -80.3153 q^{25} -8.03031 q^{26} -27.0000 q^{27} -53.7926 q^{28} -139.501 q^{29} +11.2614 q^{30} -208.600 q^{31} -102.207 q^{32} +33.0000 q^{33} +26.8163 q^{34} +46.7926 q^{35} -69.1619 q^{36} -253.086 q^{37} -6.69130 q^{38} -42.9006 q^{39} +58.8769 q^{40} -156.294 q^{41} +11.7926 q^{42} -263.386 q^{43} +84.5312 q^{44} +60.1619 q^{45} +24.9848 q^{46} +386.533 q^{47} -169.594 q^{48} +49.0000 q^{49} +45.1013 q^{50} +143.261 q^{51} -109.892 q^{52} -36.5701 q^{53} +15.1619 q^{54} -73.5312 q^{55} +61.6543 q^{56} -35.7471 q^{57} +78.3371 q^{58} -114.762 q^{59} +154.108 q^{60} -53.0758 q^{61} +117.140 q^{62} +63.0000 q^{63} -394.855 q^{64} +95.5919 q^{65} -18.5312 q^{66} +132.348 q^{67} +366.972 q^{68} +133.477 q^{69} -26.2765 q^{70} +583.447 q^{71} +79.2699 q^{72} -817.012 q^{73} +142.121 q^{74} +240.946 q^{75} -91.5682 q^{76} -77.0000 q^{77} +24.0909 q^{78} -369.633 q^{79} +377.892 q^{80} +81.0000 q^{81} +87.7671 q^{82} -69.1534 q^{83} +161.378 q^{84} -319.218 q^{85} +147.905 q^{86} +418.503 q^{87} -96.8854 q^{88} +467.295 q^{89} -33.7841 q^{90} +100.101 q^{91} +341.909 q^{92} +625.801 q^{93} -217.059 q^{94} +79.6525 q^{95} +306.622 q^{96} -1170.11 q^{97} -27.5161 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 6 q^{3} - 3 q^{4} + q^{5} - 9 q^{6} + 14 q^{7} - 3 q^{8} + 18 q^{9} - 24 q^{10} - 22 q^{11} + 9 q^{12} - 25 q^{13} + 21 q^{14} - 3 q^{15} - 23 q^{16} - 112 q^{17} + 27 q^{18} - 71 q^{19}+ \cdots - 198 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 + q^5 - 9 * q^6 + 14 * q^7 - 3 * q^8 + 18 * q^9 - 24 * q^10 - 22 * q^11 + 9 * q^12 - 25 * q^13 + 21 * q^14 - 3 * q^15 - 23 * q^16 - 112 * q^17 + 27 * q^18 - 71 * q^19 - 78 * q^20 - 42 * q^21 - 33 * q^22 - 56 * q^23 + 9 * q^24 - 173 * q^25 - 148 * q^26 - 54 * q^27 - 21 * q^28 - 11 * q^29 + 72 * q^30 - 310 * q^31 - 291 * q^32 + 66 * q^33 - 202 * q^34 + 7 * q^35 - 27 * q^36 - 65 * q^37 - 302 * q^38 + 75 * q^39 + 126 * q^40 + 42 * q^41 - 63 * q^42 - 32 * q^43 + 33 * q^44 + 9 * q^45 - 16 * q^46 + 101 * q^47 + 69 * q^48 + 98 * q^49 - 285 * q^50 + 336 * q^51 - 294 * q^52 + 166 * q^53 - 81 * q^54 - 11 * q^55 - 21 * q^56 + 213 * q^57 + 536 * q^58 - 11 * q^59 + 234 * q^60 - 436 * q^61 - 244 * q^62 + 126 * q^63 - 431 * q^64 + 319 * q^65 + 99 * q^66 - 127 * q^67 + 66 * q^68 + 168 * q^69 - 168 * q^70 + 936 * q^71 - 27 * q^72 - 327 * q^73 + 812 * q^74 + 519 * q^75 - 480 * q^76 - 154 * q^77 + 444 * q^78 - 228 * q^79 + 830 * q^80 + 162 * q^81 + 794 * q^82 - 262 * q^83 + 63 * q^84 + 46 * q^85 + 972 * q^86 + 33 * q^87 + 33 * q^88 + 44 * q^89 - 216 * q^90 - 175 * q^91 + 288 * q^92 + 930 * q^93 - 1234 * q^94 + 551 * q^95 + 873 * q^96 - 2266 * q^97 + 147 * q^98 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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