LMFDB - Embedded newform 231.4.a.f.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			$2.56155$ 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)

$f(q)$	$=$	\(q-3.56155 q^{2} +3.00000 q^{3} +4.68466 q^{4} -15.6847 q^{5} -10.6847 q^{6} +7.00000 q^{7} +11.8078 q^{8} +9.00000 q^{9} +55.8617 q^{10} +11.0000 q^{11} +14.0540 q^{12} +52.9157 q^{13} -24.9309 q^{14} -47.0540 q^{15} -79.5312 q^{16} -77.1231 q^{17} -32.0540 q^{18} +13.4081 q^{19} -73.4773 q^{20} +21.0000 q^{21} -39.1771 q^{22} -59.0152 q^{23} +35.4233 q^{24} +121.009 q^{25} -188.462 q^{26} +27.0000 q^{27} +32.7926 q^{28} -69.3305 q^{29} +167.585 q^{30} +75.9697 q^{31} +188.793 q^{32} +33.0000 q^{33} +274.678 q^{34} -109.793 q^{35} +42.1619 q^{36} -335.948 q^{37} -47.7538 q^{38} +158.747 q^{39} -185.201 q^{40} -318.617 q^{41} -74.7926 q^{42} -57.2614 q^{43} +51.5312 q^{44} -141.162 q^{45} +210.186 q^{46} -577.779 q^{47} -238.594 q^{48} +49.0000 q^{49} -430.978 q^{50} -231.369 q^{51} +247.892 q^{52} +315.555 q^{53} -96.1619 q^{54} -172.531 q^{55} +82.6543 q^{56} +40.2244 q^{57} +246.924 q^{58} -598.717 q^{59} -220.432 q^{60} -337.879 q^{61} -270.570 q^{62} +63.0000 q^{63} -36.1449 q^{64} -829.965 q^{65} -117.531 q^{66} -107.779 q^{67} -361.295 q^{68} -177.045 q^{69} +391.032 q^{70} +405.390 q^{71} +106.270 q^{72} -133.300 q^{73} +1196.50 q^{74} +363.026 q^{75} +62.8125 q^{76} +77.0000 q^{77} -565.386 q^{78} -922.038 q^{79} +1247.42 q^{80} +81.0000 q^{81} +1134.77 q^{82} -1221.17 q^{83} +98.3778 q^{84} +1209.65 q^{85} +203.939 q^{86} -207.991 q^{87} +129.885 q^{88} +1580.19 q^{89} +502.756 q^{90} +370.410 q^{91} -276.466 q^{92} +227.909 q^{93} +2057.79 q^{94} -210.302 q^{95} +566.378 q^{96} -287.097 q^{97} -174.516 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 6 q^{3} - 3 q^{4} - 19 q^{5} - 9 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 54 q^{10} + 22 q^{11} - 9 q^{12} + 11 q^{13} - 21 q^{14} - 57 q^{15} - 23 q^{16} - 146 q^{17} - 27 q^{18} - 101 q^{19}+ \cdots + 198 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 + 6 * q^3 - 3 * q^4 - 19 * q^5 - 9 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 54 * q^10 + 22 * q^11 - 9 * q^12 + 11 * q^13 - 21 * q^14 - 57 * q^15 - 23 * q^16 - 146 * q^17 - 27 * q^18 - 101 * q^19 - 48 * q^20 + 42 * q^21 - 33 * q^22 - 184 * q^23 + 9 * q^24 + 7 * q^25 - 212 * q^26 + 54 * q^27 - 21 * q^28 - 217 * q^29 + 162 * q^30 + 20 * q^31 + 291 * q^32 + 66 * q^33 + 236 * q^34 - 133 * q^35 - 27 * q^36 - 173 * q^37 - 112 * q^38 + 33 * q^39 - 156 * q^40 - 60 * q^41 - 63 * q^42 - 164 * q^43 - 33 * q^44 - 171 * q^45 + 140 * q^46 - 467 * q^47 - 69 * q^48 + 98 * q^49 - 495 * q^50 - 438 * q^51 + 570 * q^52 + 326 * q^53 - 81 * q^54 - 209 * q^55 + 21 * q^56 - 303 * q^57 + 164 * q^58 - 781 * q^59 - 144 * q^60 - 148 * q^61 - 302 * q^62 + 126 * q^63 - 431 * q^64 - 691 * q^65 - 99 * q^66 + 473 * q^67 + 168 * q^68 - 552 * q^69 + 378 * q^70 - 756 * q^71 + 27 * q^72 - 213 * q^73 + 1288 * q^74 + 21 * q^75 + 942 * q^76 + 154 * q^77 - 636 * q^78 + 168 * q^79 + 1060 * q^80 + 162 * q^81 + 1280 * q^82 - 2096 * q^83 - 63 * q^84 + 1438 * q^85 + 144 * q^86 - 651 * q^87 + 33 * q^88 + 736 * q^89 + 486 * q^90 + 77 * q^91 + 684 * q^92 + 60 * q^93 + 2120 * q^94 + 169 * q^95 + 873 * q^96 + 638 * 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 $

$2$	−3.56155	−1.25920	−0.629600	−	0.776920i	$-0.716781\pi$
$2$	−3.56155	−1.25920	−0.629600	+	0.776920i	$0.716781\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.68466	0.585582
$5$	−15.6847	−1.40288	−0.701439	−	0.712729i	$-0.747459\pi$
$5$	−15.6847	−1.40288	−0.701439	+	0.712729i	$0.747459\pi$
$6$	−10.6847	−0.726999
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	11.8078	0.521834
$9$	9.00000	0.333333
$10$	55.8617	1.76650
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	14.0540	0.338086
$13$	52.9157	1.12894	0.564468	−	0.825455i	$-0.309081\pi$
$13$	52.9157	1.12894	0.564468	+	0.825455i	$0.309081\pi$
$14$	−24.9309	−0.475933
$15$	−47.0540	−0.809952
$16$	−79.5312	−1.24268
$17$	−77.1231	−1.10030	−0.550150	−	0.835066i	$-0.685429\pi$
$17$	−77.1231	−1.10030	−0.550150	+	0.835066i	$0.685429\pi$
$18$	−32.0540	−0.419733
$19$	13.4081	0.161897	0.0809484	−	0.996718i	$-0.474205\pi$
$19$	13.4081	0.161897	0.0809484	+	0.996718i	$0.474205\pi$
$20$	−73.4773	−0.821501
$21$	21.0000	0.218218
$22$	−39.1771	−0.379663
$23$	−59.0152	−0.535022	−0.267511	−	0.963555i	$-0.586201\pi$
$23$	−59.0152	−0.535022	−0.267511	+	0.963555i	$0.586201\pi$
$24$	35.4233	0.301281
$25$	121.009	0.968068
$26$	−188.462	−1.42156
$27$	27.0000	0.192450
$28$	32.7926	0.221329
$29$	−69.3305	−0.443943	−0.221972	−	0.975053i	$-0.571249\pi$
$29$	−69.3305	−0.443943	−0.221972	+	0.975053i	$0.571249\pi$
$30$	167.585	1.01989
$31$	75.9697	0.440147	0.220074	−	0.975483i	$-0.429370\pi$
$31$	75.9697	0.440147	0.220074	+	0.975483i	$0.429370\pi$
$32$	188.793	1.04294
$33$	33.0000	0.174078
$34$	274.678	1.38550
$35$	−109.793	−0.530238
$36$	42.1619	0.195194
$37$	−335.948	−1.49269	−0.746344	−	0.665560i	$-0.768193\pi$
$37$	−335.948	−1.49269	−0.746344	+	0.665560i	$0.768193\pi$
$38$	−47.7538	−0.203860
$39$	158.747	0.651792
$40$	−185.201	−0.732070
$41$	−318.617	−1.21365	−0.606825	−	0.794835i	$-0.707557\pi$
$41$	−318.617	−1.21365	−0.606825	+	0.794835i	$0.707557\pi$
$42$	−74.7926	−0.274780
$43$	−57.2614	−0.203076	−0.101538	−	0.994832i	$-0.532376\pi$
$43$	−57.2614	−0.203076	−0.101538	+	0.994832i	$0.532376\pi$
$44$	51.5312	0.176560
$45$	−141.162	−0.467626
$46$	210.186	0.673699
$47$	−577.779	−1.79314	−0.896572	−	0.442898i	$-0.853950\pi$
$47$	−577.779	−1.79314	−0.896572	+	0.442898i	$0.853950\pi$
$48$	−238.594	−0.717459
$49$	49.0000	0.142857
$50$	−430.978	−1.21899
$51$	−231.369	−0.635259
$52$	247.892	0.661085
$53$	315.555	0.817826	0.408913	−	0.912573i	$-0.365908\pi$
$53$	315.555	0.817826	0.408913	+	0.912573i	$0.365908\pi$
$54$	−96.1619	−0.242333
$55$	−172.531	−0.422984
$56$	82.6543	0.197235
$57$	40.2244	0.0934711
$58$	246.924	0.559013
$59$	−598.717	−1.32112	−0.660562	−	0.750772i	$-0.729682\pi$
$59$	−598.717	−1.32112	−0.660562	+	0.750772i	$0.729682\pi$
$60$	−220.432	−0.474294
$61$	−337.879	−0.709196	−0.354598	−	0.935019i	$-0.615382\pi$
$61$	−337.879	−0.709196	−0.354598	+	0.935019i	$0.615382\pi$
$62$	−270.570	−0.554233
$63$	63.0000	0.125988
$64$	−36.1449	−0.0705955
$65$	−829.965	−1.58376
$66$	−117.531	−0.219198
$67$	−107.779	−0.196527	−0.0982637	−	0.995160i	$-0.531329\pi$
$67$	−107.779	−0.196527	−0.0982637	+	0.995160i	$0.531329\pi$
$68$	−361.295	−0.644316
$69$	−177.045	−0.308895
$70$	391.032	0.667675
$71$	405.390	0.677619	0.338810	−	0.940855i	$-0.389976\pi$
$71$	405.390	0.677619	0.338810	+	0.940855i	$0.389976\pi$
$72$	106.270	0.173945
$73$	−133.300	−0.213721	−0.106860	−	0.994274i	$-0.534080\pi$
$73$	−133.300	−0.213721	−0.106860	+	0.994274i	$0.534080\pi$
$74$	1196.50	1.87959
$75$	363.026	0.558914
$76$	62.8125	0.0948039
$77$	77.0000	0.113961
$78$	−565.386	−0.820736
$79$	−922.038	−1.31313	−0.656566	−	0.754269i	$-0.727991\pi$
$79$	−922.038	−1.31313	−0.656566	+	0.754269i	$0.727991\pi$
$80$	1247.42	1.74332
$81$	81.0000	0.111111
$82$	1134.77	1.52823
$83$	−1221.17	−1.61495	−0.807475	−	0.589902i	$-0.799167\pi$
$83$	−1221.17	−1.61495	−0.807475	+	0.589902i	$0.799167\pi$
$84$	98.3778	0.127785
$85$	1209.65	1.54359
$86$	203.939	0.255713
$87$	−207.991	−0.256311
$88$	129.885	0.157339
$89$	1580.19	1.88202	0.941012	−	0.338373i	$-0.109877\pi$
$89$	1580.19	1.88202	0.941012	+	0.338373i	$0.109877\pi$
$90$	502.756	0.588834
$91$	370.410	0.426698
$92$	−276.466	−0.313300
$93$	227.909	0.254119
$94$	2057.79	2.25793
$95$	−210.302	−0.227121
$96$	566.378	0.602143
$97$	−287.097	−0.300518	−0.150259	−	0.988647i	$-0.548011\pi$
$97$	−287.097	−0.300518	−0.150259	+	0.988647i	$0.548011\pi$
$98$	−174.516	−0.179886
$99$	99.0000	0.100504
$100$	566.884	0.566884
$101$	780.867	0.769299	0.384650	−	0.923063i	$-0.374322\pi$
$101$	780.867	0.769299	0.384650	+	0.923063i	$0.374322\pi$
$102$	824.034	0.799917
$103$	1218.22	1.16538	0.582691	−	0.812694i	$-0.302000\pi$
$103$	1218.22	1.16538	0.582691	+	0.812694i	$0.302000\pi$
$104$	624.816	0.589118
$105$	−329.378	−0.306133
$106$	−1123.87	−1.02981
$107$	−873.196	−0.788926	−0.394463	−	0.918912i	$-0.629069\pi$
$107$	−873.196	−0.788926	−0.394463	+	0.918912i	$0.629069\pi$
$108$	126.486	0.112695
$109$	126.424	0.111094	0.0555470	−	0.998456i	$-0.482310\pi$
$109$	126.424	0.111094	0.0555470	+	0.998456i	$0.482310\pi$
$110$	614.479	0.532621
$111$	−1007.84	−0.861804
$112$	−556.719	−0.469687
$113$	257.318	0.214217	0.107108	−	0.994247i	$-0.465841\pi$
$113$	257.318	0.214217	0.107108	+	0.994247i	$0.465841\pi$
$114$	−143.261	−0.117699
$115$	925.633	0.750571
$116$	−324.790	−0.259965
$117$	476.241	0.376312
$118$	2132.36	1.66356
$119$	−539.862	−0.415874
$120$	−555.602	−0.422661
$121$	121.000	0.0909091
$122$	1203.37	0.893019
$123$	−955.852	−0.700702
$124$	355.892	0.257742
$125$	62.6052	0.0447966
$126$	−224.378	−0.158644
$127$	74.9450	0.0523645	0.0261822	−	0.999657i	$-0.491665\pi$
$127$	74.9450	0.0523645	0.0261822	+	0.999657i	$0.491665\pi$
$128$	−1381.61	−0.954048
$129$	−171.784	−0.117246
$130$	2955.96	1.99427
$131$	−2636.30	−1.75828	−0.879141	−	0.476561i	$-0.841883\pi$
$131$	−2636.30	−1.75828	−0.879141	+	0.476561i	$0.841883\pi$
$132$	154.594	0.101937
$133$	93.8570	0.0611912
$134$	383.862	0.247467
$135$	−423.486	−0.269984
$136$	−910.651	−0.574174
$137$	1146.87	0.715210	0.357605	−	0.933873i	$-0.383593\pi$
$137$	1146.87	0.715210	0.357605	+	0.933873i	$0.383593\pi$
$138$	630.557	0.388961
$139$	−1013.00	−0.618139	−0.309070	−	0.951039i	$-0.600018\pi$
$139$	−1013.00	−0.618139	−0.309070	+	0.951039i	$0.600018\pi$
$140$	−514.341	−0.310498
$141$	−1733.34	−1.03527
$142$	−1443.82	−0.853257
$143$	582.073	0.340387
$144$	−715.781	−0.414225
$145$	1087.43	0.622798
$146$	474.756	0.269117
$147$	147.000	0.0824786
$148$	−1573.80	−0.874092
$149$	−2236.91	−1.22990	−0.614948	−	0.788568i	$-0.710823\pi$
$149$	−2236.91	−1.22990	−0.614948	+	0.788568i	$0.710823\pi$
$150$	−1292.93	−0.703784
$151$	636.657	0.343115	0.171558	−	0.985174i	$-0.445120\pi$
$151$	636.657	0.343115	0.171558	+	0.985174i	$0.445120\pi$
$152$	158.320	0.0844833
$153$	−694.108	−0.366767
$154$	−274.240	−0.143499
$155$	−1191.56	−0.617473
$156$	743.676	0.381678
$157$	−3561.59	−1.81048	−0.905241	−	0.424899i	$-0.860310\pi$
$157$	−3561.59	−1.81048	−0.905241	+	0.424899i	$0.860310\pi$
$158$	3283.89	1.65349
$159$	946.665	0.472172
$160$	−2961.15	−1.46312
$161$	−413.106	−0.202219
$162$	−288.486	−0.139911
$163$	2540.60	1.22083	0.610414	−	0.792082i	$-0.291003\pi$
$163$	2540.60	1.22083	0.610414	+	0.792082i	$0.291003\pi$
$164$	−1492.61	−0.710692
$165$	−517.594	−0.244210
$166$	4349.26	2.03354
$167$	1737.09	0.804913	0.402456	−	0.915439i	$-0.368157\pi$
$167$	1737.09	0.804913	0.402456	+	0.915439i	$0.368157\pi$
$168$	247.963	0.113874
$169$	603.073	0.274498
$170$	−4308.23	−1.94368
$171$	120.673	0.0539656
$172$	−268.250	−0.118918
$173$	4194.96	1.84357	0.921784	−	0.387704i	$-0.126732\pi$
$173$	4194.96	1.84357	0.921784	+	0.387704i	$0.126732\pi$
$174$	740.773	0.322746
$175$	847.060	0.365895
$176$	−874.844	−0.374681
$177$	−1796.15	−0.762751
$178$	−5627.94	−2.36984
$179$	1349.85	0.563645	0.281822	−	0.959467i	$-0.409061\pi$
$179$	1349.85	0.563645	0.281822	+	0.959467i	$0.409061\pi$
$180$	−661.295	−0.273834
$181$	−1198.06	−0.491994	−0.245997	−	0.969271i	$-0.579115\pi$
$181$	−1198.06	−0.491994	−0.245997	+	0.969271i	$0.579115\pi$
$182$	−1319.23	−0.537298
$183$	−1013.64	−0.409454
$184$	−696.837	−0.279193
$185$	5269.23	2.09406
$186$	−811.710	−0.319986
$187$	−848.354	−0.331753
$188$	−2706.70	−1.05003
$189$	189.000	0.0727393
$190$	749.002	0.285991
$191$	764.873	0.289761	0.144880	−	0.989449i	$-0.453720\pi$
$191$	764.873	0.289761	0.144880	+	0.989449i	$0.453720\pi$
$192$	−108.435	−0.0407583
$193$	−2019.52	−0.753204	−0.376602	−	0.926375i	$-0.622907\pi$
$193$	−2019.52	−0.753204	−0.376602	+	0.926375i	$0.622907\pi$
$194$	1022.51	0.378412
$195$	−2489.89	−0.914385
$196$	229.548	0.0836546
$197$	1499.94	0.542470	0.271235	−	0.962513i	$-0.412568\pi$
$197$	1499.94	0.542470	0.271235	+	0.962513i	$0.412568\pi$
$198$	−352.594	−0.126554
$199$	−4574.41	−1.62950	−0.814752	−	0.579809i	$-0.803127\pi$
$199$	−4574.41	−1.62950	−0.814752	+	0.579809i	$0.803127\pi$
$200$	1428.84	0.505171
$201$	−323.338	−0.113465
$202$	−2781.10	−0.968701
$203$	−485.313	−0.167795
$204$	−1083.89	−0.371996
$205$	4997.40	1.70260
$206$	−4338.74	−1.46745
$207$	−531.136	−0.178341
$208$	−4208.45	−1.40290
$209$	147.490	0.0488137
$210$	1173.10	0.385483
$211$	−4456.96	−1.45417	−0.727084	−	0.686548i	$-0.759125\pi$
$211$	−4456.96	−1.45417	−0.727084	+	0.686548i	$0.759125\pi$
$212$	1478.27	0.478905
$213$	1216.17	0.391224
$214$	3109.93	0.993414
$215$	898.125	0.284891
$216$	318.810	0.100427
$217$	531.788	0.166360
$218$	−450.267	−0.139890
$219$	−399.901	−0.123392
$220$	−808.250	−0.247692
$221$	−4081.02	−1.24217
$222$	3589.49	1.08518
$223$	−3003.50	−0.901924	−0.450962	−	0.892543i	$-0.648919\pi$
$223$	−3003.50	−0.901924	−0.450962	+	0.892543i	$0.648919\pi$
$224$	1321.55	0.394195
$225$	1089.08	0.322689
$226$	−916.453	−0.269741
$227$	1252.20	0.366130	0.183065	−	0.983101i	$-0.441398\pi$
$227$	1252.20	0.366130	0.183065	+	0.983101i	$0.441398\pi$
$228$	188.438	0.0547350
$229$	2862.80	0.826110	0.413055	−	0.910706i	$-0.364462\pi$
$229$	2862.80	0.826110	0.413055	+	0.910706i	$0.364462\pi$
$230$	−3296.69	−0.945118
$231$	231.000	0.0657952
$232$	−818.638	−0.231665
$233$	4969.92	1.39738	0.698692	−	0.715423i	$-0.253766\pi$
$233$	4969.92	1.39738	0.698692	+	0.715423i	$0.253766\pi$
$234$	−1696.16	−0.473852
$235$	9062.27	2.51556
$236$	−2804.78	−0.773627
$237$	−2766.11	−0.758137
$238$	1922.75	0.523669
$239$	4602.18	1.24557	0.622783	−	0.782395i	$-0.286002\pi$
$239$	4602.18	1.24557	0.622783	+	0.782395i	$0.286002\pi$
$240$	3742.26	1.00651
$241$	−4147.29	−1.10851	−0.554254	−	0.832348i	$-0.686996\pi$
$241$	−4147.29	−1.10851	−0.554254	+	0.832348i	$0.686996\pi$
$242$	−430.948	−0.114473
$243$	243.000	0.0641500
$244$	−1582.85	−0.415292
$245$	−768.548	−0.200411
$246$	3404.32	0.882323
$247$	709.501	0.182771
$248$	897.032	0.229684
$249$	−3663.51	−0.932392
$250$	−222.972	−0.0564078
$251$	988.383	0.248551	0.124275	−	0.992248i	$-0.460339\pi$
$251$	988.383	0.248551	0.124275	+	0.992248i	$0.460339\pi$
$252$	295.133	0.0737764
$253$	−649.167	−0.161315
$254$	−266.920	−0.0659373
$255$	3628.95	0.891191
$256$	5209.83	1.27193
$257$	−2856.10	−0.693224	−0.346612	−	0.938009i	$-0.612668\pi$
$257$	−2856.10	−0.693224	−0.346612	+	0.938009i	$0.612668\pi$
$258$	611.818	0.147636
$259$	−2351.64	−0.564183
$260$	−3888.10	−0.927423
$261$	−623.974	−0.147981
$262$	9389.34	2.21403
$263$	5772.45	1.35340	0.676701	−	0.736258i	$-0.263409\pi$
$263$	5772.45	1.35340	0.676701	+	0.736258i	$0.263409\pi$
$264$	389.656	0.0908397
$265$	−4949.37	−1.14731
$266$	−334.277	−0.0770519
$267$	4740.58	1.08659
$268$	−504.909	−0.115083
$269$	−1626.04	−0.368555	−0.184278	−	0.982874i	$-0.558995\pi$
$269$	−1626.04	−0.368555	−0.184278	+	0.982874i	$0.558995\pi$
$270$	1508.27	0.339964
$271$	−1816.20	−0.407109	−0.203554	−	0.979064i	$-0.565249\pi$
$271$	−1816.20	−0.407109	−0.203554	+	0.979064i	$0.565249\pi$
$272$	6133.70	1.36732
$273$	1111.23	0.246354
$274$	−4084.64	−0.900592
$275$	1331.09	0.291884
$276$	−829.398	−0.180884
$277$	−8091.98	−1.75523	−0.877617	−	0.479362i	$-0.840868\pi$
$277$	−8091.98	−1.75523	−0.877617	+	0.479362i	$0.840868\pi$
$278$	3607.85	0.778361
$279$	683.727	0.146716
$280$	−1296.41	−0.276697
$281$	−8041.32	−1.70713	−0.853567	−	0.520982i	$-0.825566\pi$
$281$	−8041.32	−1.70713	−0.853567	+	0.520982i	$0.825566\pi$
$282$	6173.37	1.30361
$283$	644.465	0.135369	0.0676846	−	0.997707i	$-0.478439\pi$
$283$	644.465	0.135369	0.0676846	+	0.997707i	$0.478439\pi$
$284$	1899.11	0.396802
$285$	−630.906	−0.131129
$286$	−2073.08	−0.428615
$287$	−2230.32	−0.458717
$288$	1699.13	0.347647
$289$	1034.97	0.210660
$290$	−3872.92	−0.784227
$291$	−861.290	−0.173504
$292$	−624.466	−0.125151
$293$	−6451.96	−1.28644	−0.643221	−	0.765681i	$-0.722402\pi$
$293$	−6451.96	−1.28644	−0.643221	+	0.765681i	$0.722402\pi$
$294$	−523.548	−0.103857
$295$	9390.67	1.85338
$296$	−3966.79	−0.778936
$297$	297.000	0.0580259
$298$	7966.86	1.54868
$299$	−3122.83	−0.604006
$300$	1700.65	0.327290
$301$	−400.830	−0.0767556
$302$	−2267.49	−0.432051
$303$	2342.60	0.444155
$304$	−1066.37	−0.201185
$305$	5299.51	0.994916
$306$	2472.10	0.461832
$307$	4175.92	0.776327	0.388164	−	0.921590i	$-0.373110\pi$
$307$	4175.92	0.776327	0.388164	+	0.921590i	$0.373110\pi$
$308$	360.719	0.0667333
$309$	3654.65	0.672834
$310$	4243.80	0.777521
$311$	−8619.22	−1.57155	−0.785774	−	0.618514i	$-0.787735\pi$
$311$	−8619.22	−1.57155	−0.785774	+	0.618514i	$0.787735\pi$
$312$	1874.45	0.340127
$313$	−10300.8	−1.86019	−0.930093	−	0.367324i	$-0.880274\pi$
$313$	−10300.8	−1.86019	−0.930093	+	0.367324i	$0.880274\pi$
$314$	12684.8	2.27976
$315$	−988.133	−0.176746
$316$	−4319.43	−0.768946
$317$	7696.26	1.36361	0.681806	−	0.731533i	$-0.261195\pi$
$317$	7696.26	1.36361	0.681806	+	0.731533i	$0.261195\pi$
$318$	−3371.60	−0.594559
$319$	−762.635	−0.133854
$320$	566.920	0.0990369
$321$	−2619.59	−0.455486
$322$	1471.30	0.254634
$323$	−1034.08	−0.178135
$324$	379.457	0.0650647
$325$	6403.25	1.09289
$326$	−9048.48	−1.53727
$327$	379.273	0.0641402
$328$	−3762.16	−0.633325
$329$	−4044.46	−0.677745
$330$	1843.44	0.307509
$331$	6322.41	1.04988	0.524941	−	0.851138i	$-0.324087\pi$
$331$	6322.41	1.04988	0.524941	+	0.851138i	$0.324087\pi$
$332$	−5720.77	−0.945686
$333$	−3023.53	−0.497563
$334$	−6186.75	−1.01355
$335$	1690.48	0.275704
$336$	−1670.16	−0.271174
$337$	1576.06	0.254758	0.127379	−	0.991854i	$-0.459344\pi$
$337$	1576.06	0.254758	0.127379	+	0.991854i	$0.459344\pi$
$338$	−2147.88	−0.345648
$339$	771.955	0.123678
$340$	5666.80	0.903897
$341$	835.667	0.132709
$342$	−429.784	−0.0679534
$343$	343.000	0.0539949
$344$	−676.129	−0.105972
$345$	2776.90	0.433342
$346$	−14940.6	−2.32142
$347$	4989.29	0.771870	0.385935	−	0.922526i	$-0.373879\pi$
$347$	4989.29	0.771870	0.385935	+	0.922526i	$0.373879\pi$
$348$	−974.369	−0.150091
$349$	4348.98	0.667035	0.333518	−	0.942744i	$-0.391764\pi$
$349$	4348.98	0.667035	0.333518	+	0.942744i	$0.391764\pi$
$350$	−3016.85	−0.460735
$351$	1428.72	0.217264
$352$	2076.72	0.314459
$353$	−3724.71	−0.561604	−0.280802	−	0.959766i	$-0.590601\pi$
$353$	−3724.71	−0.561604	−0.280802	+	0.959766i	$0.590601\pi$
$354$	6397.08	0.960455
$355$	−6358.40	−0.950617
$356$	7402.66	1.10208
$357$	−1619.59	−0.240105
$358$	−4807.56	−0.709741
$359$	−5815.53	−0.854963	−0.427481	−	0.904024i	$-0.640599\pi$
$359$	−5815.53	−0.854963	−0.427481	+	0.904024i	$0.640599\pi$
$360$	−1666.81	−0.244023
$361$	−6679.22	−0.973789
$362$	4266.94	0.619518
$363$	363.000	0.0524864
$364$	1735.24	0.249867
$365$	2090.77	0.299824
$366$	3610.12	0.515585
$367$	9298.43	1.32255	0.661273	−	0.750146i	$-0.270017\pi$
$367$	9298.43	1.32255	0.661273	+	0.750146i	$0.270017\pi$
$368$	4693.55	0.664859
$369$	−2867.56	−0.404550
$370$	−18766.6	−2.63684
$371$	2208.88	0.309109
$372$	1067.68	0.148808
$373$	3697.85	0.513318	0.256659	−	0.966502i	$-0.417378\pi$
$373$	3697.85	0.513318	0.256659	+	0.966502i	$0.417378\pi$
$374$	3021.46	0.417743
$375$	187.815	0.0258633
$376$	−6822.28	−0.935724
$377$	−3668.67	−0.501184
$378$	−673.133	−0.0915933
$379$	2040.70	0.276580	0.138290	−	0.990392i	$-0.455839\pi$
$379$	2040.70	0.276580	0.138290	+	0.990392i	$0.455839\pi$
$380$	−985.193	−0.132998
$381$	224.835	0.0302327
$382$	−2724.14	−0.364866
$383$	−3311.92	−0.441857	−0.220928	−	0.975290i	$-0.570909\pi$
$383$	−3311.92	−0.441857	−0.220928	+	0.975290i	$0.570909\pi$
$384$	−4144.83	−0.550820
$385$	−1207.72	−0.159873
$386$	7192.63	0.948433
$387$	−515.352	−0.0676921
$388$	−1344.95	−0.175978
$389$	13095.1	1.70680	0.853401	−	0.521255i	$-0.174536\pi$
$389$	13095.1	1.70680	0.853401	+	0.521255i	$0.174536\pi$
$390$	8867.89	1.15139
$391$	4551.43	0.588685
$392$	578.580	0.0745478
$393$	−7908.91	−1.01514
$394$	−5342.13	−0.683077
$395$	14461.8	1.84216
$396$	463.781	0.0588532
$397$	15359.1	1.94169	0.970843	−	0.239716i	$-0.0770543\pi$
$397$	15359.1	1.94169	0.970843	+	0.239716i	$0.0770543\pi$
$398$	16292.0	2.05187
$399$	281.571	0.0353288
$400$	−9623.96	−1.20299
$401$	−11767.6	−1.46545	−0.732726	−	0.680524i	$-0.761752\pi$
$401$	−11767.6	−1.46545	−0.732726	+	0.680524i	$0.761752\pi$
$402$	1151.59	0.142875
$403$	4019.99	0.496898
$404$	3658.10	0.450488
$405$	−1270.46	−0.155875
$406$	1728.47	0.211287
$407$	−3695.43	−0.450063
$408$	−2731.95	−0.331500
$409$	5071.33	0.613108	0.306554	−	0.951853i	$-0.400824\pi$
$409$	5071.33	0.613108	0.306554	+	0.951853i	$0.400824\pi$
$410$	−17798.5	−2.14392
$411$	3440.61	0.412927
$412$	5706.93	0.682427
$413$	−4191.02	−0.499338
$414$	1891.67	0.224566
$415$	19153.6	2.26558
$416$	9990.10	1.17742
$417$	−3038.99	−0.356883
$418$	−525.292	−0.0614662
$419$	5085.27	0.592916	0.296458	−	0.955046i	$-0.404194\pi$
$419$	5085.27	0.592916	0.296458	+	0.955046i	$0.404194\pi$
$420$	−1543.02	−0.179266
$421$	15655.8	1.81239	0.906196	−	0.422859i	$-0.138973\pi$
$421$	15655.8	1.81239	0.906196	+	0.422859i	$0.138973\pi$
$422$	15873.7	1.83109
$423$	−5200.01	−0.597715
$424$	3726.00	0.426770
$425$	−9332.55	−1.06517
$426$	−4331.45	−0.492628
$427$	−2365.15	−0.268051
$428$	−4090.62	−0.461981
$429$	1746.22	0.196523
$430$	−3198.72	−0.358735
$431$	5775.20	0.645433	0.322717	−	0.946496i	$-0.395404\pi$
$431$	5775.20	0.645433	0.322717	+	0.946496i	$0.395404\pi$
$432$	−2147.34	−0.239153
$433$	−6756.97	−0.749929	−0.374964	−	0.927039i	$-0.622345\pi$
$433$	−6756.97	−0.749929	−0.374964	+	0.927039i	$0.622345\pi$
$434$	−1893.99	−0.209480
$435$	3262.28	0.359573
$436$	592.255	0.0650547
$437$	−791.283	−0.0866183
$438$	1424.27	0.155375
$439$	−9068.21	−0.985882	−0.492941	−	0.870063i	$-0.664078\pi$
$439$	−9068.21	−0.985882	−0.492941	+	0.870063i	$0.664078\pi$
$440$	−2037.21	−0.220727
$441$	441.000	0.0476190
$442$	14534.8	1.56414
$443$	−7095.86	−0.761026	−0.380513	−	0.924776i	$-0.624252\pi$
$443$	−7095.86	−0.761026	−0.380513	+	0.924776i	$0.624252\pi$
$444$	−4721.40	−0.504657
$445$	−24784.8	−2.64025
$446$	10697.1	1.13570
$447$	−6710.72	−0.710081
$448$	−253.014	−0.0266826
$449$	630.680	0.0662887	0.0331443	−	0.999451i	$-0.489448\pi$
$449$	630.680	0.0662887	0.0331443	+	0.999451i	$0.489448\pi$
$450$	−3878.80	−0.406330
$451$	−3504.79	−0.365929
$452$	1205.45	0.125441
$453$	1909.97	0.198098
$454$	−4459.78	−0.461030
$455$	−5809.75	−0.598605
$456$	474.960	0.0487764
$457$	12432.5	1.27258	0.636290	−	0.771450i	$-0.280468\pi$
$457$	12432.5	1.27258	0.636290	+	0.771450i	$0.280468\pi$
$458$	−10196.0	−1.04024
$459$	−2082.32	−0.211753
$460$	4336.27	0.439521
$461$	13057.3	1.31918	0.659588	−	0.751627i	$-0.270731\pi$
$461$	13057.3	1.31918	0.659588	+	0.751627i	$0.270731\pi$
$462$	−822.719	−0.0828492
$463$	8608.12	0.864046	0.432023	−	0.901863i	$-0.357800\pi$
$463$	8608.12	0.864046	0.432023	+	0.901863i	$0.357800\pi$
$464$	5513.94	0.551677
$465$	−3574.68	−0.356498
$466$	−17700.6	−1.75958
$467$	14997.6	1.48610	0.743049	−	0.669237i	$-0.233379\pi$
$467$	14997.6	1.48610	0.743049	+	0.669237i	$0.233379\pi$
$468$	2231.03	0.220362
$469$	−754.455	−0.0742804
$470$	−32275.8	−3.16760
$471$	−10684.8	−1.04528
$472$	−7069.51	−0.689408
$473$	−629.875	−0.0612298
$474$	9851.66	0.954645
$475$	1622.50	0.156727
$476$	−2529.07	−0.243529
$477$	2839.99	0.272609
$478$	−16390.9	−1.56841
$479$	−20698.8	−1.97443	−0.987216	−	0.159386i	$-0.949048\pi$
$479$	−20698.8	−1.97443	−0.987216	+	0.159386i	$0.949048\pi$
$480$	−8883.44	−0.844733
$481$	−17776.9	−1.68515
$482$	14770.8	1.39583
$483$	−1239.32	−0.116751
$484$	566.844	0.0532348
$485$	4503.01	0.421590
$486$	−865.457	−0.0807777
$487$	15390.1	1.43202	0.716008	−	0.698092i	$-0.245968\pi$
$487$	15390.1	1.43202	0.716008	+	0.698092i	$0.245968\pi$
$488$	−3989.59	−0.370083
$489$	7621.80	0.704846
$490$	2737.23	0.252358
$491$	10771.4	0.990030	0.495015	−	0.868884i	$-0.335163\pi$
$491$	10771.4	0.990030	0.495015	+	0.868884i	$0.335163\pi$
$492$	−4477.84	−0.410318
$493$	5346.98	0.488471
$494$	−2526.93	−0.230145
$495$	−1552.78	−0.140995
$496$	−6041.96	−0.546960
$497$	2837.73	0.256116
$498$	13047.8	1.17407
$499$	−5999.79	−0.538251	−0.269126	−	0.963105i	$-0.586735\pi$
$499$	−5999.79	−0.538251	−0.269126	+	0.963105i	$0.586735\pi$
$500$	293.284	0.0262321
$501$	5211.28	0.464717
$502$	−3520.18	−0.312975
$503$	17610.5	1.56106	0.780528	−	0.625121i	$-0.214950\pi$
$503$	17610.5	1.56106	0.780528	+	0.625121i	$0.214950\pi$
$504$	743.889	0.0657450
$505$	−12247.6	−1.07923
$506$	2312.04	0.203128
$507$	1809.22	0.158482
$508$	351.092	0.0306637
$509$	−5920.42	−0.515556	−0.257778	−	0.966204i	$-0.582990\pi$
$509$	−5920.42	−0.515556	−0.257778	+	0.966204i	$0.582990\pi$
$510$	−12924.7	−1.12219
$511$	−933.101	−0.0807788
$512$	−7502.22	−0.647567
$513$	362.020	0.0311570
$514$	10172.1	0.872907
$515$	−19107.3	−1.63489
$516$	−804.750	−0.0686572
$517$	−6355.57	−0.540653
$518$	8375.47	0.710419
$519$	12584.9	1.06438
$520$	−9800.03	−0.826461
$521$	−15886.2	−1.33587	−0.667935	−	0.744220i	$-0.732821\pi$
$521$	−15886.2	−1.33587	−0.667935	+	0.744220i	$0.732821\pi$
$522$	2222.32	0.186338
$523$	1728.58	0.144523	0.0722613	−	0.997386i	$-0.476978\pi$
$523$	1728.58	0.144523	0.0722613	+	0.997386i	$0.476978\pi$
$524$	−12350.2	−1.02962
$525$	2541.18	0.211250
$526$	−20558.9	−1.70420
$527$	−5859.02	−0.484294
$528$	−2624.53	−0.216322
$529$	−8684.21	−0.713751
$530$	17627.4	1.44469
$531$	−5388.45	−0.440375
$532$	439.688	0.0358325
$533$	−16859.9	−1.37013
$534$	−16883.8	−1.36823
$535$	13695.8	1.10677
$536$	−1272.63	−0.102555
$537$	4049.55	0.325420
$538$	5791.23	0.464085
$539$	539.000	0.0430730
$540$	−1983.89	−0.158098
$541$	1941.99	0.154331	0.0771653	−	0.997018i	$-0.475413\pi$
$541$	1941.99	0.154331	0.0771653	+	0.997018i	$0.475413\pi$
$542$	6468.51	0.512631
$543$	−3594.17	−0.284053
$544$	−14560.3	−1.14755
$545$	−1982.92	−0.155852
$546$	−3957.70	−0.310209
$547$	−1450.56	−0.113384	−0.0566922	−	0.998392i	$-0.518055\pi$
$547$	−1450.56	−0.113384	−0.0566922	+	0.998392i	$0.518055\pi$
$548$	5372.70	0.418814
$549$	−3040.91	−0.236399
$550$	−4740.76	−0.367539
$551$	−929.593	−0.0718729
$552$	−2090.51	−0.161192
$553$	−6454.26	−0.496317
$554$	28820.0	2.21019
$555$	15807.7	1.20901
$556$	−4745.55	−0.361972
$557$	20821.8	1.58393	0.791965	−	0.610567i	$-0.209058\pi$
$557$	20821.8	1.58393	0.791965	+	0.610567i	$0.209058\pi$
$558$	−2435.13	−0.184744
$559$	−3030.03	−0.229260
$560$	8731.94	0.658914
$561$	−2545.06	−0.191538
$562$	28639.6	2.14962
$563$	−3694.11	−0.276533	−0.138267	−	0.990395i	$-0.544153\pi$
$563$	−3694.11	−0.276533	−0.138267	+	0.990395i	$0.544153\pi$
$564$	−8120.10	−0.606237
$565$	−4035.95	−0.300520
$566$	−2295.30	−0.170457
$567$	567.000	0.0419961
$568$	4786.75	0.353605
$569$	−16649.2	−1.22666	−0.613332	−	0.789825i	$-0.710171\pi$
$569$	−16649.2	−1.22666	−0.613332	+	0.789825i	$0.710171\pi$
$570$	2247.01	0.165117
$571$	546.005	0.0400168	0.0200084	−	0.999800i	$-0.493631\pi$
$571$	546.005	0.0400168	0.0200084	+	0.999800i	$0.493631\pi$
$572$	2726.81	0.199325
$573$	2294.62	0.167293
$574$	7943.41	0.577616
$575$	−7141.34	−0.517938
$576$	−325.304	−0.0235318
$577$	7910.36	0.570732	0.285366	−	0.958419i	$-0.407885\pi$
$577$	7910.36	0.570732	0.285366	+	0.958419i	$0.407885\pi$
$578$	−3686.11	−0.265263
$579$	−6058.56	−0.434862
$580$	5094.22	0.364700
$581$	−8548.19	−0.610394
$582$	3067.53	0.218476
$583$	3471.10	0.246584
$584$	−1573.98	−0.111527
$585$	−7469.68	−0.527920
$586$	22979.0	1.61989
$587$	−744.718	−0.0523642	−0.0261821	−	0.999657i	$-0.508335\pi$
$587$	−744.718	−0.0523642	−0.0261821	+	0.999657i	$0.508335\pi$
$588$	688.645	0.0482980
$589$	1018.61	0.0712584
$590$	−33445.4	−2.33377
$591$	4499.83	0.313195
$592$	26718.4	1.85493
$593$	−8167.66	−0.565608	−0.282804	−	0.959178i	$-0.591265\pi$
$593$	−8167.66	−0.565608	−0.282804	+	0.959178i	$0.591265\pi$
$594$	−1057.78	−0.0730661
$595$	8467.55	0.583421
$596$	−10479.1	−0.720205
$597$	−13723.2	−0.940795
$598$	11122.1	0.760564
$599$	12115.4	0.826413	0.413206	−	0.910637i	$-0.364409\pi$
$599$	12115.4	0.826413	0.413206	+	0.910637i	$0.364409\pi$
$600$	4286.52	0.291661
$601$	13606.0	0.923458	0.461729	−	0.887021i	$-0.347229\pi$
$601$	13606.0	0.923458	0.461729	+	0.887021i	$0.347229\pi$
$602$	1427.58	0.0966506
$603$	−970.014	−0.0655092
$604$	2982.52	0.200922
$605$	−1897.84	−0.127534
$606$	−8343.30	−0.559280
$607$	−11404.4	−0.762585	−0.381293	−	0.924454i	$-0.624521\pi$
$607$	−11404.4	−0.762585	−0.381293	+	0.924454i	$0.624521\pi$
$608$	2531.36	0.168849
$609$	−1455.94	−0.0968763
$610$	−18874.5	−1.25280
$611$	−30573.6	−2.02435
$612$	−3251.66	−0.214772
$613$	15266.2	1.00587	0.502934	−	0.864325i	$-0.332254\pi$
$613$	15266.2	1.00587	0.502934	+	0.864325i	$0.332254\pi$
$614$	−14872.8	−0.977550
$615$	14992.2	0.982999
$616$	909.198	0.0594685
$617$	23638.9	1.54241	0.771205	−	0.636586i	$-0.219654\pi$
$617$	23638.9	1.54241	0.771205	+	0.636586i	$0.219654\pi$
$618$	−13016.2	−0.847232
$619$	27681.1	1.79741	0.898706	−	0.438551i	$-0.144508\pi$
$619$	27681.1	1.79741	0.898706	+	0.438551i	$0.144508\pi$
$620$	−5582.05	−0.361581
$621$	−1593.41	−0.102965
$622$	30697.8	1.97889
$623$	11061.4	0.711338
$624$	−12625.4	−0.809966
$625$	−16108.0	−1.03091
$626$	36687.0	2.34235
$627$	442.469	0.0281826
$628$	−16684.8	−1.06019
$629$	25909.3	1.64241
$630$	3519.29	0.222558
$631$	18208.7	1.14877	0.574386	−	0.818585i	$-0.305241\pi$
$631$	18208.7	1.14877	0.574386	+	0.818585i	$0.305241\pi$
$632$	−10887.2	−0.685237
$633$	−13370.9	−0.839564
$634$	−27410.6	−1.71706
$635$	−1175.49	−0.0734610
$636$	4434.80	0.276496
$637$	2592.87	0.161277
$638$	2716.17	0.168549
$639$	3648.51	0.225873
$640$	21670.1	1.33841
$641$	−23373.8	−1.44026	−0.720131	−	0.693838i	$-0.755918\pi$
$641$	−23373.8	−1.44026	−0.720131	+	0.693838i	$0.755918\pi$
$642$	9329.80	0.573548
$643$	6742.72	0.413541	0.206770	−	0.978389i	$-0.433705\pi$
$643$	6742.72	0.413541	0.206770	+	0.978389i	$0.433705\pi$
$644$	−1935.26	−0.118416
$645$	2694.37	0.164482
$646$	3682.92	0.224307
$647$	−17592.4	−1.06898	−0.534490	−	0.845175i	$-0.679496\pi$
$647$	−17592.4	−1.06898	−0.534490	+	0.845175i	$0.679496\pi$
$648$	956.429	0.0579816
$649$	−6585.89	−0.398334
$650$	−22805.5	−1.37616
$651$	1595.36	0.0960480
$652$	11901.8	0.714896
$653$	20074.0	1.20300	0.601498	−	0.798875i	$-0.294571\pi$
$653$	20074.0	1.20300	0.601498	+	0.798875i	$0.294571\pi$
$654$	−1350.80	−0.0807653
$655$	41349.5	2.46666
$656$	25340.0	1.50817
$657$	−1199.70	−0.0712402
$658$	14404.5	0.853416
$659$	−13778.4	−0.814460	−0.407230	−	0.913326i	$-0.633505\pi$
$659$	−13778.4	−0.814460	−0.407230	+	0.913326i	$0.633505\pi$
$660$	−2424.75	−0.143005
$661$	−7724.16	−0.454516	−0.227258	−	0.973835i	$-0.572976\pi$
$661$	−7724.16	−0.454516	−0.227258	+	0.973835i	$0.572976\pi$
$662$	−22517.6	−1.32201
$663$	−12243.1	−0.717167
$664$	−14419.3	−0.842737
$665$	−1472.11	−0.0858438
$666$	10768.5	0.626531
$667$	4091.55	0.237519
$668$	8137.69	0.471343
$669$	−9010.49	−0.520726
$670$	−6020.74	−0.347166
$671$	−3716.67	−0.213831
$672$	3964.64	0.227589
$673$	−18081.2	−1.03563	−0.517816	−	0.855492i	$-0.673255\pi$
$673$	−18081.2	−1.03563	−0.517816	+	0.855492i	$0.673255\pi$
$674$	−5613.21	−0.320791
$675$	3267.23	0.186305
$676$	2825.19	0.160741
$677$	−23199.8	−1.31705	−0.658523	−	0.752561i	$-0.728818\pi$
$677$	−23199.8	−1.31705	−0.658523	+	0.752561i	$0.728818\pi$
$678$	−2749.36	−0.155735
$679$	−2009.68	−0.113585
$680$	14283.3	0.805497
$681$	3756.60	0.211385
$682$	−2976.27	−0.167107
$683$	13339.6	0.747329	0.373665	−	0.927564i	$-0.378101\pi$
$683$	13339.6	0.747329	0.373665	+	0.927564i	$0.378101\pi$
$684$	565.313	0.0316013
$685$	−17988.3	−1.00335
$686$	−1221.61	−0.0679904
$687$	8588.40	0.476955
$688$	4554.07	0.252358
$689$	16697.8	0.923274
$690$	−9890.07	−0.545664
$691$	−17221.4	−0.948097	−0.474048	−	0.880499i	$-0.657208\pi$
$691$	−17221.4	−0.948097	−0.474048	+	0.880499i	$0.657208\pi$
$692$	19652.0	1.07956
$693$	693.000	0.0379869
$694$	−17769.6	−0.971938
$695$	15888.5	0.867175
$696$	−2455.91	−0.133752
$697$	24572.8	1.33538
$698$	−15489.1	−0.839930
$699$	14909.8	0.806780
$700$	3968.18	0.214262
$701$	−27196.5	−1.46533	−0.732665	−	0.680589i	$-0.761724\pi$
$701$	−27196.5	−1.46533	−0.732665	+	0.680589i	$0.761724\pi$
$702$	−5088.48	−0.273579
$703$	−4504.44	−0.241661
$704$	−397.594	−0.0212853
$705$	27186.8	1.45236
$706$	13265.8	0.707172
$707$	5466.07	0.290768
$708$	−8414.35	−0.446654
$709$	22682.8	1.20151	0.600755	−	0.799434i	$-0.294867\pi$
$709$	22682.8	1.20151	0.600755	+	0.799434i	$0.294867\pi$
$710$	22645.8	1.19702
$711$	−8298.34	−0.437710
$712$	18658.5	0.982105
$713$	−4483.36	−0.235488
$714$	5768.24	0.302340
$715$	−9129.61	−0.477522
$716$	6323.58	0.330060
$717$	13806.5	0.719127
$718$	20712.3	1.07657
$719$	10878.2	0.564241	0.282121	−	0.959379i	$-0.408962\pi$
$719$	10878.2	0.564241	0.282121	+	0.959379i	$0.408962\pi$
$720$	11226.8	0.581108
$721$	8527.51	0.440473
$722$	23788.4	1.22619
$723$	−12441.9	−0.639997
$724$	−5612.49	−0.288103
$725$	−8389.58	−0.429767
$726$	−1292.84	−0.0660908
$727$	−2793.35	−0.142503	−0.0712514	−	0.997458i	$-0.522699\pi$
$727$	−2793.35	−0.142503	−0.0712514	+	0.997458i	$0.522699\pi$
$728$	4373.71	0.222666
$729$	729.000	0.0370370
$730$	−7446.38	−0.377538
$731$	4416.17	0.223445
$732$	−4748.54	−0.239769
$733$	−7597.31	−0.382828	−0.191414	−	0.981509i	$-0.561307\pi$
$733$	−7597.31	−0.382828	−0.191414	+	0.981509i	$0.561307\pi$
$734$	−33116.9	−1.66535
$735$	−2305.64	−0.115707
$736$	−11141.6	−0.557997
$737$	−1185.57	−0.0592553
$738$	10213.0	0.509409
$739$	−14304.7	−0.712052	−0.356026	−	0.934476i	$-0.615868\pi$
$739$	−14304.7	−0.712052	−0.356026	+	0.934476i	$0.615868\pi$
$740$	24684.5	1.22625
$741$	2128.50	0.105523
$742$	−7867.06	−0.389230
$743$	31212.2	1.54114	0.770569	−	0.637357i	$-0.219972\pi$
$743$	31212.2	1.54114	0.770569	+	0.637357i	$0.219972\pi$
$744$	2691.10	0.132608
$745$	35085.1	1.72539
$746$	−13170.1	−0.646369
$747$	−10990.5	−0.538317
$748$	−3974.25	−0.194269
$749$	−6112.37	−0.298186
$750$	−668.915	−0.0325671
$751$	30743.1	1.49378	0.746891	−	0.664946i	$-0.231546\pi$
$751$	30743.1	1.49378	0.746891	+	0.664946i	$0.231546\pi$
$752$	45951.5	2.22830
$753$	2965.15	0.143501
$754$	13066.2	0.631090
$755$	−9985.75	−0.481349
$756$	885.400	0.0425948
$757$	13176.9	0.632657	0.316328	−	0.948650i	$-0.397550\pi$
$757$	13176.9	0.632657	0.316328	+	0.948650i	$0.397550\pi$
$758$	−7268.07	−0.348270
$759$	−1947.50	−0.0931354
$760$	−2483.20	−0.118520
$761$	−10696.4	−0.509520	−0.254760	−	0.967004i	$-0.581996\pi$
$761$	−10696.4	−0.509520	−0.254760	+	0.967004i	$0.581996\pi$
$762$	−800.761	−0.0380689
$763$	884.970	0.0419896
$764$	3583.17	0.169679
$765$	10886.8	0.514529
$766$	11795.6	0.556385
$767$	−31681.5	−1.49147
$768$	15629.5	0.734350
$769$	−7724.46	−0.362225	−0.181113	−	0.983462i	$-0.557970\pi$
$769$	−7724.46	−0.362225	−0.181113	+	0.983462i	$0.557970\pi$
$770$	4301.35	0.201312
$771$	−8568.30	−0.400233
$772$	−9460.77	−0.441063
$773$	28801.0	1.34010	0.670051	−	0.742315i	$-0.266272\pi$
$773$	28801.0	1.34010	0.670051	+	0.742315i	$0.266272\pi$
$774$	1835.45	0.0852378
$775$	9192.98	0.426092
$776$	−3389.97	−0.156821
$777$	−7054.91	−0.325731
$778$	−46638.7	−2.14920
$779$	−4272.07	−0.196486
$780$	−11664.3	−0.535448
$781$	4459.29	0.204310
$782$	−16210.2	−0.741272
$783$	−1871.92	−0.0854369
$784$	−3897.03	−0.177525
$785$	55862.3	2.53989
$786$	28168.0	1.27827
$787$	−11812.0	−0.535007	−0.267504	−	0.963557i	$-0.586199\pi$
$787$	−11812.0	−0.535007	−0.267504	+	0.963557i	$0.586199\pi$
$788$	7026.72	0.317661
$789$	17317.4	0.781387
$790$	−51506.6	−2.31965
$791$	1801.23	0.0809662
$792$	1168.97	0.0524463
$793$	−17879.1	−0.800637
$794$	−54702.1	−2.44497
$795$	−14848.1	−0.662400
$796$	−21429.6	−0.954209
$797$	−26884.2	−1.19484	−0.597420	−	0.801928i	$-0.703808\pi$
$797$	−26884.2	−1.19484	−0.597420	+	0.801928i	$0.703808\pi$
$798$	−1002.83	−0.0444859
$799$	44560.1	1.97300
$800$	22845.5	1.00964
$801$	14221.7	0.627341
$802$	41910.9	1.84530
$803$	−1466.30	−0.0644392
$804$	−1514.73	−0.0664432
$805$	6479.43	0.283689
$806$	−14317.4	−0.625694
$807$	−4878.12	−0.212786
$808$	9220.30	0.401447
$809$	−18360.8	−0.797936	−0.398968	−	0.916965i	$-0.630632\pi$
$809$	−18360.8	−0.797936	−0.398968	+	0.916965i	$0.630632\pi$
$810$	4524.80	0.196278
$811$	17033.7	0.737528	0.368764	−	0.929523i	$-0.379781\pi$
$811$	17033.7	0.737528	0.368764	+	0.929523i	$0.379781\pi$
$812$	−2273.53	−0.0982576
$813$	−5448.61	−0.235044
$814$	13161.5	0.566718
$815$	−39848.4	−1.71267
$816$	18401.1	0.789420
$817$	−767.768	−0.0328774
$818$	−18061.8	−0.772026
$819$	3333.69	0.142233
$820$	23411.1	0.997015
$821$	−29675.1	−1.26147	−0.630735	−	0.775998i	$-0.717246\pi$
$821$	−29675.1	−1.26147	−0.630735	+	0.775998i	$0.717246\pi$
$822$	−12253.9	−0.519957
$823$	−24677.2	−1.04519	−0.522596	−	0.852581i	$-0.675036\pi$
$823$	−24677.2	−1.04519	−0.522596	+	0.852581i	$0.675036\pi$
$824$	14384.4	0.608137
$825$	3993.28	0.168519
$826$	14926.5	0.628766
$827$	−9168.43	−0.385511	−0.192755	−	0.981247i	$-0.561742\pi$
$827$	−9168.43	−0.385511	−0.192755	+	0.981247i	$0.561742\pi$
$828$	−2488.19	−0.104433
$829$	8065.03	0.337889	0.168945	−	0.985626i	$-0.445964\pi$
$829$	8065.03	0.337889	0.168945	+	0.985626i	$0.445964\pi$
$830$	−68216.7	−2.85281
$831$	−24275.9	−1.01338
$832$	−1912.63	−0.0796979
$833$	−3779.03	−0.157186
$834$	10823.5	0.449387
$835$	−27245.7	−1.12919
$836$	690.938	0.0285844
$837$	2051.18	0.0847063
$838$	−18111.5	−0.746599
$839$	−29665.7	−1.22071	−0.610354	−	0.792129i	$-0.708973\pi$
$839$	−29665.7	−1.22071	−0.610354	+	0.792129i	$0.708973\pi$
$840$	−3889.22	−0.159751
$841$	−19582.3	−0.802915
$842$	−55758.9	−2.28216
$843$	−24124.0	−0.985615
$844$	−20879.3	−0.851535
$845$	−9458.99	−0.385088
$846$	18520.1	0.752642
$847$	847.000	0.0343604
$848$	−25096.5	−1.01629
$849$	1933.39	0.0781554
$850$	33238.4	1.34126
$851$	19826.0	0.798622
$852$	5697.34	0.229094
$853$	−33087.0	−1.32811	−0.664056	−	0.747683i	$-0.731166\pi$
$853$	−33087.0	−1.32811	−0.664056	+	0.747683i	$0.731166\pi$
$854$	8423.61	0.337529
$855$	−1892.72	−0.0757071
$856$	−10310.5	−0.411689
$857$	−8204.78	−0.327036	−0.163518	−	0.986540i	$-0.552284\pi$
$857$	−8204.78	−0.327036	−0.163518	+	0.986540i	$0.552284\pi$
$858$	−6219.25	−0.247461
$859$	19406.0	0.770808	0.385404	−	0.922748i	$-0.374062\pi$
$859$	19406.0	0.770808	0.385404	+	0.922748i	$0.374062\pi$
$860$	4207.41	0.166827
$861$	−6690.97	−0.264840
$862$	−20568.7	−0.812729
$863$	−3352.45	−0.132235	−0.0661174	−	0.997812i	$-0.521061\pi$
$863$	−3352.45	−0.132235	−0.0661174	+	0.997812i	$0.521061\pi$
$864$	5097.40	0.200714
$865$	−65796.6	−2.58630
$866$	24065.3	0.944310
$867$	3104.92	0.121625
$868$	2491.24	0.0974174
$869$	−10142.4	−0.395924
$870$	−11618.8	−0.452774
$871$	−5703.22	−0.221867
$872$	1492.79	0.0579727
$873$	−2583.87	−0.100173
$874$	2818.20	0.109070
$875$	438.236	0.0169315
$876$	−1873.40	−0.0722560
$877$	−20076.9	−0.773033	−0.386516	−	0.922283i	$-0.626322\pi$
$877$	−20076.9	−0.773033	−0.386516	+	0.922283i	$0.626322\pi$
$878$	32296.9	1.24142
$879$	−19355.9	−0.742728
$880$	13721.6	0.525632
$881$	−14800.2	−0.565982	−0.282991	−	0.959123i	$-0.591327\pi$
$881$	−14800.2	−0.565982	−0.282991	+	0.959123i	$0.591327\pi$
$882$	−1570.64	−0.0599619
$883$	−19955.4	−0.760534	−0.380267	−	0.924877i	$-0.624168\pi$
$883$	−19955.4	−0.760534	−0.380267	+	0.924877i	$0.624168\pi$
$884$	−19118.2	−0.727392
$885$	28172.0	1.07005
$886$	25272.3	0.958283
$887$	−9205.47	−0.348466	−0.174233	−	0.984704i	$-0.555745\pi$
$887$	−9205.47	−0.348466	−0.174233	+	0.984704i	$0.555745\pi$
$888$	−11900.4	−0.449719
$889$	524.615	0.0197919
$890$	88272.3	3.32460
$891$	891.000	0.0335013
$892$	−14070.4	−0.528151
$893$	−7746.94	−0.290304
$894$	23900.6	0.894133
$895$	−21171.9	−0.790725
$896$	−9671.26	−0.360596
$897$	−9368.49	−0.348723
$898$	−2246.20	−0.0834706
$899$	−5267.02	−0.195400
$900$	5101.95	0.188961
$901$	−24336.6	−0.899854
$902$	12482.5	0.460778
$903$	−1202.49	−0.0443149
$904$	3038.35	0.111786
$905$	18791.1	0.690207
$906$	−6802.47	−0.249445
$907$	6722.78	0.246115	0.123057	−	0.992400i	$-0.460730\pi$
$907$	6722.78	0.246115	0.123057	+	0.992400i	$0.460730\pi$
$908$	5866.13	0.214399
$909$	7027.81	0.256433
$910$	20691.7	0.753763
$911$	51855.3	1.88589	0.942944	−	0.332952i	$-0.108045\pi$
$911$	51855.3	1.88589	0.942944	+	0.332952i	$0.108045\pi$
$912$	−3199.10	−0.116154
$913$	−13432.9	−0.486926
$914$	−44279.1	−1.60243
$915$	15898.5	0.574415
$916$	13411.2	0.483755
$917$	−18454.1	−0.664568
$918$	7416.31	0.266639
$919$	−55119.5	−1.97848	−0.989240	−	0.146302i	$-0.953263\pi$
$919$	−55119.5	−1.97848	−0.989240	+	0.146302i	$0.953263\pi$
$920$	10929.7	0.391674
$921$	12527.8	0.448213
$922$	−46504.4	−1.66111
$923$	21451.5	0.764989
$924$	1082.16	0.0385285
$925$	−40652.6	−1.44502
$926$	−30658.3	−1.08801
$927$	10963.9	0.388461
$928$	−13089.1	−0.463007
$929$	31459.7	1.11104	0.555522	−	0.831502i	$-0.312518\pi$
$929$	31459.7	1.11104	0.555522	+	0.831502i	$0.312518\pi$
$930$	12731.4	0.448902
$931$	656.999	0.0231281
$932$	23282.4	0.818283
$933$	−25857.7	−0.907333
$934$	−53414.9	−1.87129
$935$	13306.1	0.465409
$936$	5623.35	0.196373
$937$	−13745.6	−0.479242	−0.239621	−	0.970867i	$-0.577023\pi$
$937$	−13745.6	−0.479242	−0.239621	+	0.970867i	$0.577023\pi$
$938$	2687.03	0.0935338
$939$	−30902.5	−1.07398
$940$	42453.6	1.47307
$941$	−29814.2	−1.03285	−0.516427	−	0.856331i	$-0.672738\pi$
$941$	−29814.2	−1.03285	−0.516427	+	0.856331i	$0.672738\pi$
$942$	38054.3	1.31622
$943$	18803.3	0.649330
$944$	47616.7	1.64173
$945$	−2964.40	−0.102044
$946$	2243.33	0.0771005
$947$	32410.4	1.11214	0.556070	−	0.831135i	$-0.312309\pi$
$947$	32410.4	1.11214	0.556070	+	0.831135i	$0.312309\pi$
$948$	−12958.3	−0.443951
$949$	−7053.67	−0.241277
$950$	−5778.61	−0.197351
$951$	23088.8	0.787281
$952$	−6374.56	−0.217018
$953$	8931.28	0.303581	0.151790	−	0.988413i	$-0.451496\pi$
$953$	8931.28	0.303581	0.151790	+	0.988413i	$0.451496\pi$
$954$	−10114.8	−0.343269
$955$	−11996.8	−0.406499
$956$	21559.6	0.729381
$957$	−2287.91	−0.0772806
$958$	73719.9	2.48620
$959$	8028.10	0.270324
$960$	1700.76	0.0571790
$961$	−24019.6	−0.806271
$962$	63313.4	2.12194
$963$	−7858.76	−0.262975
$964$	−19428.6	−0.649122
$965$	31675.5	1.05665
$966$	4413.90	0.147013
$967$	28665.0	0.953262	0.476631	−	0.879104i	$-0.341858\pi$
$967$	28665.0	0.953262	0.476631	+	0.879104i	$0.341858\pi$
$968$	1428.74	0.0474395
$969$	−3102.23	−0.102846
$970$	−16037.7	−0.530866
$971$	−40925.2	−1.35258	−0.676288	−	0.736637i	$-0.736413\pi$
$971$	−40925.2	−1.35258	−0.676288	+	0.736637i	$0.736413\pi$
$972$	1138.37	0.0375651
$973$	−7090.99	−0.233635
$974$	−54812.6	−1.80319
$975$	19209.8	0.630979
$976$	26871.9	0.881300
$977$	−21288.8	−0.697124	−0.348562	−	0.937286i	$-0.613330\pi$
$977$	−21288.8	−0.697124	−0.348562	+	0.937286i	$0.613330\pi$
$978$	−27145.4	−0.887541
$979$	17382.1	0.567452
$980$	−3600.39	−0.117357
$981$	1137.82	0.0370314
$982$	−38362.8	−1.24664
$983$	−53128.8	−1.72385	−0.861925	−	0.507035i	$-0.830741\pi$
$983$	−53128.8	−1.72385	−0.861925	+	0.507035i	$0.830741\pi$
$984$	−11286.5	−0.365650
$985$	−23526.1	−0.761019
$986$	−19043.6	−0.615082
$987$	−12133.4	−0.391296
$988$	3323.77	0.107028
$989$	3379.29	0.108650
$990$	5530.31	0.177540
$991$	−17978.4	−0.576290	−0.288145	−	0.957587i	$-0.593039\pi$
$991$	−17978.4	−0.576290	−0.288145	+	0.957587i	$0.593039\pi$
$992$	14342.5	0.459048
$993$	18967.2	0.606150
$994$	−10106.7	−0.322501
$995$	71748.1	2.28600
$996$	−17162.3	−0.545992
$997$	10063.9	0.319687	0.159844	−	0.987142i	$-0.448901\pi$
$997$	10063.9	0.319687	0.159844	+	0.987142i	$0.448901\pi$
$998$	21368.6	0.677766
$999$	−9070.59	−0.287268

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.f.1.1	✓	2	1.1	even	1	trivial
693.4.a.k.1.2		2	3.2	odd	2
1617.4.a.i.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)

\(f(q)\)	\(=\)	\(q-3.56155 q^{2} +3.00000 q^{3} +4.68466 q^{4} -15.6847 q^{5} -10.6847 q^{6} +7.00000 q^{7} +11.8078 q^{8} +9.00000 q^{9} +55.8617 q^{10} +11.0000 q^{11} +14.0540 q^{12} +52.9157 q^{13} -24.9309 q^{14} -47.0540 q^{15} -79.5312 q^{16} -77.1231 q^{17} -32.0540 q^{18} +13.4081 q^{19} -73.4773 q^{20} +21.0000 q^{21} -39.1771 q^{22} -59.0152 q^{23} +35.4233 q^{24} +121.009 q^{25} -188.462 q^{26} +27.0000 q^{27} +32.7926 q^{28} -69.3305 q^{29} +167.585 q^{30} +75.9697 q^{31} +188.793 q^{32} +33.0000 q^{33} +274.678 q^{34} -109.793 q^{35} +42.1619 q^{36} -335.948 q^{37} -47.7538 q^{38} +158.747 q^{39} -185.201 q^{40} -318.617 q^{41} -74.7926 q^{42} -57.2614 q^{43} +51.5312 q^{44} -141.162 q^{45} +210.186 q^{46} -577.779 q^{47} -238.594 q^{48} +49.0000 q^{49} -430.978 q^{50} -231.369 q^{51} +247.892 q^{52} +315.555 q^{53} -96.1619 q^{54} -172.531 q^{55} +82.6543 q^{56} +40.2244 q^{57} +246.924 q^{58} -598.717 q^{59} -220.432 q^{60} -337.879 q^{61} -270.570 q^{62} +63.0000 q^{63} -36.1449 q^{64} -829.965 q^{65} -117.531 q^{66} -107.779 q^{67} -361.295 q^{68} -177.045 q^{69} +391.032 q^{70} +405.390 q^{71} +106.270 q^{72} -133.300 q^{73} +1196.50 q^{74} +363.026 q^{75} +62.8125 q^{76} +77.0000 q^{77} -565.386 q^{78} -922.038 q^{79} +1247.42 q^{80} +81.0000 q^{81} +1134.77 q^{82} -1221.17 q^{83} +98.3778 q^{84} +1209.65 q^{85} +203.939 q^{86} -207.991 q^{87} +129.885 q^{88} +1580.19 q^{89} +502.756 q^{90} +370.410 q^{91} -276.466 q^{92} +227.909 q^{93} +2057.79 q^{94} -210.302 q^{95} +566.378 q^{96} -287.097 q^{97} -174.516 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 6 q^{3} - 3 q^{4} - 19 q^{5} - 9 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 54 q^{10} + 22 q^{11} - 9 q^{12} + 11 q^{13} - 21 q^{14} - 57 q^{15} - 23 q^{16} - 146 q^{17} - 27 q^{18} - 101 q^{19}+ \cdots + 198 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 6 * q^3 - 3 * q^4 - 19 * q^5 - 9 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 54 * q^10 + 22 * q^11 - 9 * q^12 + 11 * q^13 - 21 * q^14 - 57 * q^15 - 23 * q^16 - 146 * q^17 - 27 * q^18 - 101 * q^19 - 48 * q^20 + 42 * q^21 - 33 * q^22 - 184 * q^23 + 9 * q^24 + 7 * q^25 - 212 * q^26 + 54 * q^27 - 21 * q^28 - 217 * q^29 + 162 * q^30 + 20 * q^31 + 291 * q^32 + 66 * q^33 + 236 * q^34 - 133 * q^35 - 27 * q^36 - 173 * q^37 - 112 * q^38 + 33 * q^39 - 156 * q^40 - 60 * q^41 - 63 * q^42 - 164 * q^43 - 33 * q^44 - 171 * q^45 + 140 * q^46 - 467 * q^47 - 69 * q^48 + 98 * q^49 - 495 * q^50 - 438 * q^51 + 570 * q^52 + 326 * q^53 - 81 * q^54 - 209 * q^55 + 21 * q^56 - 303 * q^57 + 164 * q^58 - 781 * q^59 - 144 * q^60 - 148 * q^61 - 302 * q^62 + 126 * q^63 - 431 * q^64 - 691 * q^65 - 99 * q^66 + 473 * q^67 + 168 * q^68 - 552 * q^69 + 378 * q^70 - 756 * q^71 + 27 * q^72 - 213 * q^73 + 1288 * q^74 + 21 * q^75 + 942 * q^76 + 154 * q^77 - 636 * q^78 + 168 * q^79 + 1060 * q^80 + 162 * q^81 + 1280 * q^82 - 2096 * q^83 - 63 * q^84 + 1438 * q^85 + 144 * q^86 - 651 * q^87 + 33 * q^88 + 736 * q^89 + 486 * q^90 + 77 * q^91 + 684 * q^92 + 60 * q^93 + 2120 * q^94 + 169 * q^95 + 873 * q^96 + 638 * q^97 - 147 * q^98 + 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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