LMFDB - Embedded newform 231.4.a.f.1.2

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			1.2
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)

$f(q)$	$=$	\(q+0.561553 q^{2} +3.00000 q^{3} -7.68466 q^{4} -3.31534 q^{5} +1.68466 q^{6} +7.00000 q^{7} -8.80776 q^{8} +9.00000 q^{9} -1.86174 q^{10} +11.0000 q^{11} -23.0540 q^{12} -41.9157 q^{13} +3.93087 q^{14} -9.94602 q^{15} +56.5312 q^{16} -68.8769 q^{17} +5.05398 q^{18} -114.408 q^{19} +25.4773 q^{20} +21.0000 q^{21} +6.17708 q^{22} -124.985 q^{23} -26.4233 q^{24} -114.009 q^{25} -23.5379 q^{26} +27.0000 q^{27} -53.7926 q^{28} -147.670 q^{29} -5.58522 q^{30} -55.9697 q^{31} +102.207 q^{32} +33.0000 q^{33} -38.6780 q^{34} -23.2074 q^{35} -69.1619 q^{36} +162.948 q^{37} -64.2462 q^{38} -125.747 q^{39} +29.2007 q^{40} +258.617 q^{41} +11.7926 q^{42} -106.739 q^{43} -84.5312 q^{44} -29.8381 q^{45} -70.1856 q^{46} +110.779 q^{47} +169.594 q^{48} +49.0000 q^{49} -64.0218 q^{50} -206.631 q^{51} +322.108 q^{52} +10.4451 q^{53} +15.1619 q^{54} -36.4688 q^{55} -61.6543 q^{56} -343.224 q^{57} -82.9242 q^{58} -182.283 q^{59} +76.4318 q^{60} +189.879 q^{61} -31.4299 q^{62} +63.0000 q^{63} -394.855 q^{64} +138.965 q^{65} +18.5312 q^{66} +580.779 q^{67} +529.295 q^{68} -374.955 q^{69} -13.0322 q^{70} -1161.39 q^{71} -79.2699 q^{72} -79.6998 q^{73} +91.5038 q^{74} -342.026 q^{75} +879.187 q^{76} +77.0000 q^{77} -70.6137 q^{78} +1090.04 q^{79} -187.420 q^{80} +81.0000 q^{81} +145.227 q^{82} -874.830 q^{83} -161.378 q^{84} +228.350 q^{85} -59.9394 q^{86} -443.009 q^{87} -96.8854 q^{88} -844.193 q^{89} -16.7557 q^{90} -293.410 q^{91} +960.466 q^{92} -167.909 q^{93} +62.2084 q^{94} +379.302 q^{95} +306.622 q^{96} +925.097 q^{97} +27.5161 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 6 q^{3} - 3 q^{4} - 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 $

$2$	0.561553	0.198539	0.0992695	−	0.995061i	$-0.468349\pi$
$2$	0.561553	0.198539	0.0992695	+	0.995061i	$0.468349\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.68466	−0.960582
$5$	−3.31534	−0.296533	−0.148267	−	0.988947i	$-0.547369\pi$
$5$	−3.31534	−0.296533	−0.148267	+	0.988947i	$0.547369\pi$
$6$	1.68466	0.114626
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.80776	−0.389252
$9$	9.00000	0.333333
$10$	−1.86174	−0.0588734
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−23.0540	−0.554592
$13$	−41.9157	−0.894256	−0.447128	−	0.894470i	$-0.647553\pi$
$13$	−41.9157	−0.894256	−0.447128	+	0.894470i	$0.647553\pi$
$14$	3.93087	0.0750407
$15$	−9.94602	−0.171204
$16$	56.5312	0.883301
$17$	−68.8769	−0.982653	−0.491326	−	0.870975i	$-0.663488\pi$
$17$	−68.8769	−0.982653	−0.491326	+	0.870975i	$0.663488\pi$
$18$	5.05398	0.0661796
$19$	−114.408	−1.38142	−0.690711	−	0.723131i	$-0.742702\pi$
$19$	−114.408	−1.38142	−0.690711	+	0.723131i	$0.742702\pi$
$20$	25.4773	0.284845
$21$	21.0000	0.218218
$22$	6.17708	0.0598617
$23$	−124.985	−1.13309	−0.566547	−	0.824030i	$-0.691721\pi$
$23$	−124.985	−1.13309	−0.566547	+	0.824030i	$0.691721\pi$
$24$	−26.4233	−0.224735
$25$	−114.009	−0.912068
$26$	−23.5379	−0.177545
$27$	27.0000	0.192450
$28$	−53.7926	−0.363066
$29$	−147.670	−0.945570	−0.472785	−	0.881178i	$-0.656751\pi$
$29$	−147.670	−0.945570	−0.472785	+	0.881178i	$0.656751\pi$
$30$	−5.58522	−0.0339906
$31$	−55.9697	−0.324273	−0.162136	−	0.986768i	$-0.551838\pi$
$31$	−55.9697	−0.324273	−0.162136	+	0.986768i	$0.551838\pi$
$32$	102.207	0.564621
$33$	33.0000	0.174078
$34$	−38.6780	−0.195095
$35$	−23.2074	−0.112079
$36$	−69.1619	−0.320194
$37$	162.948	0.724013	0.362006	−	0.932176i	$-0.382092\pi$
$37$	162.948	0.724013	0.362006	+	0.932176i	$0.382092\pi$
$38$	−64.2462	−0.274266
$39$	−125.747	−0.516299
$40$	29.2007	0.115426
$41$	258.617	0.985104	0.492552	−	0.870283i	$-0.336064\pi$
$41$	258.617	0.985104	0.492552	+	0.870283i	$0.336064\pi$
$42$	11.7926	0.0433247
$43$	−106.739	−0.378546	−0.189273	−	0.981924i	$-0.560613\pi$
$43$	−106.739	−0.378546	−0.189273	+	0.981924i	$0.560613\pi$
$44$	−84.5312	−0.289626
$45$	−29.8381	−0.0988444
$46$	−70.1856	−0.224963
$47$	110.779	0.343805	0.171902	−	0.985114i	$-0.445009\pi$
$47$	110.779	0.343805	0.171902	+	0.985114i	$0.445009\pi$
$48$	169.594	0.509974
$49$	49.0000	0.142857
$50$	−64.0218	−0.181081
$51$	−206.631	−0.567335
$52$	322.108	0.859006
$53$	10.4451	0.0270706	0.0135353	−	0.999908i	$-0.495691\pi$
$53$	10.4451	0.0270706	0.0135353	+	0.999908i	$0.495691\pi$
$54$	15.1619	0.0382088
$55$	−36.4688	−0.0894081
$56$	−61.6543	−0.147123
$57$	−343.224	−0.797565
$58$	−82.9242	−0.187732
$59$	−182.283	−0.402225	−0.201112	−	0.979568i	$-0.564456\pi$
$59$	−182.283	−0.402225	−0.201112	+	0.979568i	$0.564456\pi$
$60$	76.4318	0.164455
$61$	189.879	0.398549	0.199274	−	0.979944i	$-0.436141\pi$
$61$	189.879	0.398549	0.199274	+	0.979944i	$0.436141\pi$
$62$	−31.4299	−0.0643807
$63$	63.0000	0.125988
$64$	−394.855	−0.771201
$65$	138.965	0.265177
$66$	18.5312	0.0345612
$67$	580.779	1.05901	0.529504	−	0.848308i	$-0.322378\pi$
$67$	580.779	1.05901	0.529504	+	0.848308i	$0.322378\pi$
$68$	529.295	0.943919
$69$	−374.955	−0.654192
$70$	−13.0322	−0.0222520
$71$	−1161.39	−1.94129	−0.970645	−	0.240515i	$-0.922684\pi$
$71$	−1161.39	−1.94129	−0.970645	+	0.240515i	$0.922684\pi$
$72$	−79.2699	−0.129751
$73$	−79.6998	−0.127783	−0.0638915	−	0.997957i	$-0.520351\pi$
$73$	−79.6998	−0.127783	−0.0638915	+	0.997957i	$0.520351\pi$
$74$	91.5038	0.143745
$75$	−342.026	−0.526583
$76$	879.187	1.32697
$77$	77.0000	0.113961
$78$	−70.6137	−0.102505
$79$	1090.04	1.55239	0.776195	−	0.630493i	$-0.217147\pi$
$79$	1090.04	1.55239	0.776195	+	0.630493i	$0.217147\pi$
$80$	−187.420	−0.261928
$81$	81.0000	0.111111
$82$	145.227	0.195581
$83$	−874.830	−1.15693	−0.578464	−	0.815708i	$-0.696348\pi$
$83$	−874.830	−1.15693	−0.578464	+	0.815708i	$0.696348\pi$
$84$	−161.378	−0.209616
$85$	228.350	0.291389
$86$	−59.9394	−0.0751562
$87$	−443.009	−0.545925
$88$	−96.8854	−0.117364
$89$	−844.193	−1.00544	−0.502721	−	0.864449i	$-0.667668\pi$
$89$	−844.193	−1.00544	−0.502721	+	0.864449i	$0.667668\pi$
$90$	−16.7557	−0.0196245
$91$	−293.410	−0.337997
$92$	960.466	1.08843
$93$	−167.909	−0.187219
$94$	62.2084	0.0682586
$95$	379.302	0.409638
$96$	306.622	0.325984
$97$	925.097	0.968344	0.484172	−	0.874973i	$-0.339121\pi$
$97$	925.097	0.968344	0.484172	+	0.874973i	$0.339121\pi$
$98$	27.5161	0.0283627
$99$	99.0000	0.100504
$100$	876.116	0.876116
$101$	−884.867	−0.871758	−0.435879	−	0.900005i	$-0.643562\pi$
$101$	−884.867	−0.871758	−0.435879	+	0.900005i	$0.643562\pi$
$102$	−116.034	−0.112638
$103$	1069.78	1.02339	0.511694	−	0.859168i	$-0.329018\pi$
$103$	1069.78	1.02339	0.511694	+	0.859168i	$0.329018\pi$
$104$	369.184	0.348091
$105$	−69.6222	−0.0647088
$106$	5.86547	0.00537457
$107$	178.196	0.160999	0.0804993	−	0.996755i	$-0.474349\pi$
$107$	178.196	0.160999	0.0804993	+	0.996755i	$0.474349\pi$
$108$	−207.486	−0.184864
$109$	1973.58	1.73426	0.867130	−	0.498082i	$-0.165962\pi$
$109$	1973.58	1.73426	0.867130	+	0.498082i	$0.165962\pi$
$110$	−20.4791	−0.0177510
$111$	488.844	0.418009
$112$	395.719	0.333856
$113$	1642.68	1.36753	0.683763	−	0.729704i	$-0.260342\pi$
$113$	1642.68	1.36753	0.683763	+	0.729704i	$0.260342\pi$
$114$	−192.739	−0.158348
$115$	414.367	0.336000
$116$	1134.79	0.908298
$117$	−377.241	−0.298085
$118$	−102.362	−0.0798572
$119$	−482.138	−0.371408
$120$	87.6022	0.0666413
$121$	121.000	0.0909091
$122$	106.627	0.0791275
$123$	775.852	0.568750
$124$	430.108	0.311491
$125$	792.395	0.566992
$126$	35.3778	0.0250136
$127$	−1796.94	−1.25554	−0.627768	−	0.778400i	$-0.716031\pi$
$127$	−1796.94	−1.25554	−0.627768	+	0.778400i	$0.716031\pi$
$128$	−1039.39	−0.717735
$129$	−320.216	−0.218554
$130$	78.0361	0.0526479
$131$	934.305	0.623134	0.311567	−	0.950224i	$-0.399146\pi$
$131$	934.305	0.623134	0.311567	+	0.950224i	$0.399146\pi$
$132$	−253.594	−0.167216
$133$	−800.857	−0.522129
$134$	326.138	0.210254
$135$	−89.5142	−0.0570678
$136$	606.651	0.382499
$137$	−1590.87	−0.992097	−0.496048	−	0.868295i	$-0.665216\pi$
$137$	−1590.87	−0.992097	−0.496048	+	0.868295i	$0.665216\pi$
$138$	−210.557	−0.129882
$139$	−1549.00	−0.945213	−0.472607	−	0.881274i	$-0.656687\pi$
$139$	−1549.00	−0.945213	−0.472607	+	0.881274i	$0.656687\pi$
$140$	178.341	0.107661
$141$	332.338	0.198496
$142$	−652.182	−0.385422
$143$	−461.073	−0.269628
$144$	508.781	0.294434
$145$	489.575	0.280393
$146$	−44.7557	−0.0253699
$147$	147.000	0.0824786
$148$	−1252.20	−0.695474
$149$	−468.094	−0.257367	−0.128684	−	0.991686i	$-0.541075\pi$
$149$	−468.094	−0.257367	−0.128684	+	0.991686i	$0.541075\pi$
$150$	−192.065	−0.104547
$151$	1865.34	1.00529	0.502647	−	0.864492i	$-0.332360\pi$
$151$	1865.34	1.00529	0.502647	+	0.864492i	$0.332360\pi$
$152$	1007.68	0.537721
$153$	−619.892	−0.327551
$154$	43.2396	0.0226256
$155$	185.559	0.0961576
$156$	966.324	0.495948
$157$	1501.59	0.763310	0.381655	−	0.924305i	$-0.375354\pi$
$157$	1501.59	0.763310	0.381655	+	0.924305i	$0.375354\pi$
$158$	612.114	0.308210
$159$	31.3353	0.0156292
$160$	−338.852	−0.167429
$161$	−874.894	−0.428269
$162$	45.4858	0.0220599
$163$	524.401	0.251989	0.125995	−	0.992031i	$-0.459788\pi$
$163$	524.401	0.251989	0.125995	+	0.992031i	$0.459788\pi$
$164$	−1987.39	−0.946273
$165$	−109.406	−0.0516198
$166$	−491.263	−0.229695
$167$	−3293.09	−1.52591	−0.762956	−	0.646450i	$-0.776253\pi$
$167$	−3293.09	−1.52591	−0.762956	+	0.646450i	$0.776253\pi$
$168$	−184.963	−0.0849417
$169$	−440.073	−0.200306
$170$	128.231	0.0578521
$171$	−1029.67	−0.460474
$172$	820.250	0.363625
$173$	−3036.96	−1.33466	−0.667330	−	0.744762i	$-0.732563\pi$
$173$	−3036.96	−1.33466	−0.667330	+	0.744762i	$0.732563\pi$
$174$	−248.773	−0.108387
$175$	−798.060	−0.344729
$176$	621.844	0.266325
$177$	−546.849	−0.232224
$178$	−474.059	−0.199619
$179$	690.152	0.288181	0.144090	−	0.989565i	$-0.453974\pi$
$179$	690.152	0.288181	0.144090	+	0.989565i	$0.453974\pi$
$180$	229.295	0.0949482
$181$	−2533.94	−1.04059	−0.520294	−	0.853987i	$-0.674178\pi$
$181$	−2533.94	−1.04059	−0.520294	+	0.853987i	$0.674178\pi$
$182$	−164.765	−0.0671056
$183$	569.636	0.230102
$184$	1100.84	0.441059
$185$	−540.228	−0.214694
$186$	−94.2898	−0.0371702
$187$	−757.646	−0.296281
$188$	−851.301	−0.330253
$189$	189.000	0.0727393
$190$	212.998	0.0813290
$191$	1845.13	0.698998	0.349499	−	0.936937i	$-0.386352\pi$
$191$	1845.13	0.698998	0.349499	+	0.936937i	$0.386352\pi$
$192$	−1184.57	−0.445253
$193$	−2654.48	−0.990019	−0.495009	−	0.868888i	$-0.664835\pi$
$193$	−2654.48	−0.990019	−0.495009	+	0.868888i	$0.664835\pi$
$194$	519.491	0.192254
$195$	416.895	0.153100
$196$	−376.548	−0.137226
$197$	164.057	0.0593328	0.0296664	−	0.999560i	$-0.490555\pi$
$197$	164.057	0.0593328	0.0296664	+	0.999560i	$0.490555\pi$
$198$	55.5937	0.0199539
$199$	2888.41	1.02891	0.514457	−	0.857516i	$-0.327993\pi$
$199$	2888.41	1.02891	0.514457	+	0.857516i	$0.327993\pi$
$200$	1004.16	0.355024
$201$	1742.34	0.611418
$202$	−496.900	−0.173078
$203$	−1033.69	−0.357392
$204$	1587.89	0.544972
$205$	−857.405	−0.292116
$206$	600.740	0.203182
$207$	−1124.86	−0.377698
$208$	−2369.55	−0.789897
$209$	−1258.49	−0.416515
$210$	−39.0965	−0.0128472
$211$	630.956	0.205862	0.102931	−	0.994689i	$-0.467178\pi$
$211$	630.956	0.205862	0.102931	+	0.994689i	$0.467178\pi$
$212$	−80.2670	−0.0260036
$213$	−3484.17	−1.12080
$214$	100.066	0.0319645
$215$	353.875	0.112252
$216$	−237.810	−0.0749116
$217$	−391.788	−0.122564
$218$	1108.27	0.344318
$219$	−239.099	−0.0737755
$220$	280.250	0.0858839
$221$	2887.02	0.878743
$222$	274.512	0.0829910
$223$	−6252.50	−1.87757	−0.938786	−	0.344501i	$-0.888048\pi$
$223$	−6252.50	−1.87757	−0.938786	+	0.344501i	$0.888048\pi$
$224$	715.452	0.213407
$225$	−1026.08	−0.304023
$226$	922.453	0.271507
$227$	−3316.20	−0.969621	−0.484810	−	0.874619i	$-0.661111\pi$
$227$	−3316.20	−0.969621	−0.484810	+	0.874619i	$0.661111\pi$
$228$	2637.56	0.766126
$229$	3077.20	0.887979	0.443989	−	0.896032i	$-0.353563\pi$
$229$	3077.20	0.887979	0.443989	+	0.896032i	$0.353563\pi$
$230$	232.689	0.0667090
$231$	231.000	0.0657952
$232$	1300.64	0.368065
$233$	1358.08	0.381849	0.190924	−	0.981605i	$-0.438851\pi$
$233$	1358.08	0.381849	0.190924	+	0.981605i	$0.438851\pi$
$234$	−211.841	−0.0591815
$235$	−367.271	−0.101950
$236$	1400.78	0.386370
$237$	3270.11	0.896273
$238$	−270.746	−0.0737389
$239$	−4151.18	−1.12350	−0.561752	−	0.827306i	$-0.689872\pi$
$239$	−4151.18	−1.12350	−0.561752	+	0.827306i	$0.689872\pi$
$240$	−562.261	−0.151224
$241$	−3491.71	−0.933282	−0.466641	−	0.884447i	$-0.654536\pi$
$241$	−3491.71	−0.933282	−0.466641	+	0.884447i	$0.654536\pi$
$242$	67.9479	0.0180490
$243$	243.000	0.0641500
$244$	−1459.15	−0.382839
$245$	−162.452	−0.0423619
$246$	435.682	0.112919
$247$	4795.50	1.23535
$248$	492.968	0.126224
$249$	−2624.49	−0.667953
$250$	444.972	0.112570
$251$	−879.383	−0.221140	−0.110570	−	0.993868i	$-0.535268\pi$
$251$	−879.383	−0.221140	−0.110570	+	0.993868i	$0.535268\pi$
$252$	−484.133	−0.121022
$253$	−1374.83	−0.341640
$254$	−1009.08	−0.249273
$255$	685.051	0.168234
$256$	2575.17	0.628703
$257$	5691.10	1.38133	0.690663	−	0.723176i	$-0.257319\pi$
$257$	5691.10	1.38133	0.690663	+	0.723176i	$0.257319\pi$
$258$	−179.818	−0.0433914
$259$	1140.64	0.273651
$260$	−1067.90	−0.254724
$261$	−1329.03	−0.315190
$262$	524.661	0.123716
$263$	2024.55	0.474673	0.237337	−	0.971427i	$-0.423726\pi$
$263$	2024.55	0.474673	0.237337	+	0.971427i	$0.423726\pi$
$264$	−290.656	−0.0677601
$265$	−34.6290	−0.00802734
$266$	−449.723	−0.103663
$267$	−2532.58	−0.580492
$268$	−4463.09	−1.01726
$269$	−3431.96	−0.777882	−0.388941	−	0.921263i	$-0.627159\pi$
$269$	−3431.96	−0.777882	−0.388941	+	0.921263i	$0.627159\pi$
$270$	−50.2670	−0.0113302
$271$	−2974.80	−0.666812	−0.333406	−	0.942783i	$-0.608198\pi$
$271$	−2974.80	−0.666812	−0.333406	+	0.942783i	$0.608198\pi$
$272$	−3893.70	−0.867978
$273$	−880.230	−0.195143
$274$	−893.358	−0.196970
$275$	−1254.09	−0.274999
$276$	2881.40	0.628405
$277$	7781.98	1.68799	0.843996	−	0.536350i	$-0.180197\pi$
$277$	7781.98	1.68799	0.843996	+	0.536350i	$0.180197\pi$
$278$	−869.846	−0.187662
$279$	−503.727	−0.108091
$280$	204.405	0.0436270
$281$	−2627.68	−0.557845	−0.278922	−	0.960314i	$-0.589977\pi$
$281$	−2627.68	−0.557845	−0.278922	+	0.960314i	$0.589977\pi$
$282$	186.625	0.0394091
$283$	−2501.46	−0.525430	−0.262715	−	0.964873i	$-0.584618\pi$
$283$	−2501.46	−0.525430	−0.262715	+	0.964873i	$0.584618\pi$
$284$	8924.89	1.86477
$285$	1137.91	0.236504
$286$	−258.917	−0.0535317
$287$	1810.32	0.372334
$288$	919.867	0.188207
$289$	−168.973	−0.0343931
$290$	274.922	0.0556689
$291$	2775.29	0.559073
$292$	612.466	0.122746
$293$	−4646.04	−0.926364	−0.463182	−	0.886263i	$-0.653292\pi$
$293$	−4646.04	−0.926364	−0.463182	+	0.886263i	$0.653292\pi$
$294$	82.5483	0.0163752
$295$	604.331	0.119273
$296$	−1435.21	−0.281823
$297$	297.000	0.0580259
$298$	−262.859	−0.0510974
$299$	5238.83	1.01328
$300$	2628.35	0.505826
$301$	−747.170	−0.143077
$302$	1047.49	0.199590
$303$	−2654.60	−0.503310
$304$	−6467.63	−1.22021
$305$	−629.513	−0.118183
$306$	−348.102	−0.0650316
$307$	−4325.92	−0.804213	−0.402107	−	0.915593i	$-0.631722\pi$
$307$	−4325.92	−0.804213	−0.402107	+	0.915593i	$0.631722\pi$
$308$	−591.719	−0.109469
$309$	3209.35	0.590853
$310$	104.201	0.0190910
$311$	1845.22	0.336440	0.168220	−	0.985749i	$-0.446198\pi$
$311$	1845.22	0.336440	0.168220	+	0.985749i	$0.446198\pi$
$312$	1107.55	0.200970
$313$	−5287.15	−0.954784	−0.477392	−	0.878690i	$-0.658418\pi$
$313$	−5287.15	−0.954784	−0.477392	+	0.878690i	$0.658418\pi$
$314$	843.220	0.151547
$315$	−208.867	−0.0373597
$316$	−8376.57	−1.49120
$317$	9353.74	1.65728	0.828641	−	0.559780i	$-0.189114\pi$
$317$	9353.74	1.65728	0.828641	+	0.559780i	$0.189114\pi$
$318$	17.5964	0.00310301
$319$	−1624.36	−0.285100
$320$	1309.08	0.228687
$321$	534.588	0.0929526
$322$	−491.299	−0.0850280
$323$	7880.08	1.35746
$324$	−622.457	−0.106731
$325$	4778.75	0.815622
$326$	294.479	0.0500296
$327$	5920.73	1.00128
$328$	−2277.84	−0.383453
$329$	775.455	0.129946
$330$	−61.4374	−0.0102485
$331$	11385.6	1.89066	0.945330	−	0.326115i	$-0.105740\pi$
$331$	11385.6	1.89066	0.945330	+	0.326115i	$0.105740\pi$
$332$	6722.77	1.11132
$333$	1466.53	0.241338
$334$	−1849.25	−0.302953
$335$	−1925.48	−0.314031
$336$	1187.16	0.192752
$337$	−10686.1	−1.72732	−0.863660	−	0.504075i	$-0.831833\pi$
$337$	−10686.1	−1.72732	−0.863660	+	0.504075i	$0.831833\pi$
$338$	−247.124	−0.0397686
$339$	4928.05	0.789542
$340$	−1754.80	−0.279903
$341$	−615.667	−0.0977719
$342$	−578.216	−0.0914220
$343$	343.000	0.0539949
$344$	940.129	0.147350
$345$	1243.10	0.193990
$346$	−1705.42	−0.264982
$347$	6242.71	0.965782	0.482891	−	0.875680i	$-0.339587\pi$
$347$	6242.71	0.965782	0.482891	+	0.875680i	$0.339587\pi$
$348$	3404.37	0.524406
$349$	4518.02	0.692964	0.346482	−	0.938057i	$-0.387376\pi$
$349$	4518.02	0.692964	0.346482	+	0.938057i	$0.387376\pi$
$350$	−448.153	−0.0684422
$351$	−1131.72	−0.172100
$352$	1124.28	0.170240
$353$	−9270.29	−1.39776	−0.698878	−	0.715241i	$-0.746317\pi$
$353$	−9270.29	−1.39776	−0.698878	+	0.715241i	$0.746317\pi$
$354$	−307.085	−0.0461056
$355$	3850.40	0.575657
$356$	6487.34	0.965809
$357$	−1446.41	−0.214432
$358$	387.557	0.0572151
$359$	8219.53	1.20838	0.604192	−	0.796839i	$-0.293496\pi$
$359$	8219.53	1.20838	0.604192	+	0.796839i	$0.293496\pi$
$360$	262.807	0.0384754
$361$	6230.22	0.908328
$362$	−1422.94	−0.206597
$363$	363.000	0.0524864
$364$	2254.76	0.324674
$365$	264.232	0.0378919
$366$	319.881	0.0456843
$367$	9001.57	1.28032	0.640161	−	0.768241i	$-0.278868\pi$
$367$	9001.57	1.28032	0.640161	+	0.768241i	$0.278868\pi$
$368$	−7065.55	−1.00086
$369$	2327.56	0.328368
$370$	−303.367	−0.0426251
$371$	73.1156	0.0102317
$372$	1290.32	0.179839
$373$	1966.15	0.272931	0.136466	−	0.990645i	$-0.456426\pi$
$373$	1966.15	0.272931	0.136466	+	0.990645i	$0.456426\pi$
$374$	−425.458	−0.0588233
$375$	2377.18	0.327353
$376$	−975.718	−0.133827
$377$	6189.67	0.845582
$378$	106.133	0.0144416
$379$	1022.30	0.138554	0.0692768	−	0.997597i	$-0.477931\pi$
$379$	1022.30	0.138554	0.0692768	+	0.997597i	$0.477931\pi$
$380$	−2914.81	−0.393491
$381$	−5390.83	−0.724884
$382$	1036.14	0.138778
$383$	12825.9	1.71116	0.855579	−	0.517672i	$-0.173201\pi$
$383$	12825.9	1.71116	0.855579	+	0.517672i	$0.173201\pi$
$384$	−3118.17	−0.414384
$385$	−255.281	−0.0337931
$386$	−1490.63	−0.196557
$387$	−960.648	−0.126182
$388$	−7109.05	−0.930174
$389$	−12229.1	−1.59393	−0.796964	−	0.604027i	$-0.793562\pi$
$389$	−12229.1	−1.59393	−0.796964	+	0.604027i	$0.793562\pi$
$390$	234.108	0.0303963
$391$	8608.57	1.11344
$392$	−431.580	−0.0556074
$393$	2802.91	0.359767
$394$	92.1266	0.0117799
$395$	−3613.85	−0.460335
$396$	−760.781	−0.0965422
$397$	−3401.07	−0.429961	−0.214981	−	0.976618i	$-0.568969\pi$
$397$	−3401.07	−0.429961	−0.214981	+	0.976618i	$0.568969\pi$
$398$	1622.00	0.204280
$399$	−2402.57	−0.301451
$400$	−6445.04	−0.805630
$401$	−6234.40	−0.776386	−0.388193	−	0.921578i	$-0.626901\pi$
$401$	−6234.40	−0.776386	−0.388193	+	0.921578i	$0.626901\pi$
$402$	978.415	0.121390
$403$	2346.01	0.289983
$404$	6799.90	0.837396
$405$	−268.543	−0.0329481
$406$	−580.470	−0.0709562
$407$	1792.43	0.218298
$408$	1819.95	0.220836
$409$	−11429.3	−1.38177	−0.690885	−	0.722964i	$-0.742779\pi$
$409$	−11429.3	−1.38177	−0.690885	+	0.722964i	$0.742779\pi$
$410$	−481.478	−0.0579964
$411$	−4772.61	−0.572787
$412$	−8220.93	−0.983048
$413$	−1275.98	−0.152027
$414$	−631.670	−0.0749877
$415$	2900.36	0.343068
$416$	−4284.10	−0.504916
$417$	−4647.01	−0.545719
$418$	−706.708	−0.0826943
$419$	3827.73	0.446293	0.223146	−	0.974785i	$-0.428367\pi$
$419$	3827.73	0.446293	0.223146	+	0.974785i	$0.428367\pi$
$420$	535.023	0.0621582
$421$	−11626.8	−1.34597	−0.672987	−	0.739654i	$-0.734989\pi$
$421$	−11626.8	−1.34597	−0.672987	+	0.739654i	$0.734989\pi$
$422$	354.315	0.0408716
$423$	997.014	0.114602
$424$	−91.9979	−0.0105373
$425$	7852.55	0.896246
$426$	−1956.55	−0.222523
$427$	1329.15	0.150637
$428$	−1369.38	−0.154652
$429$	−1383.22	−0.155670
$430$	198.720	0.0222863
$431$	7469.80	0.834820	0.417410	−	0.908718i	$-0.362938\pi$
$431$	7469.80	0.834820	0.417410	+	0.908718i	$0.362938\pi$
$432$	1526.34	0.169991
$433$	1546.97	0.171692	0.0858459	−	0.996308i	$-0.472641\pi$
$433$	1546.97	0.171692	0.0858459	+	0.996308i	$0.472641\pi$
$434$	−220.010	−0.0243336
$435$	1468.72	0.161885
$436$	−15166.3	−1.66590
$437$	14299.3	1.56528
$438$	−134.267	−0.0146473
$439$	−8082.79	−0.878748	−0.439374	−	0.898304i	$-0.644800\pi$
$439$	−8082.79	−0.878748	−0.439374	+	0.898304i	$0.644800\pi$
$440$	321.208	0.0348023
$441$	441.000	0.0476190
$442$	1621.22	0.174465
$443$	−13000.1	−1.39426	−0.697128	−	0.716947i	$-0.745539\pi$
$443$	−13000.1	−1.39426	−0.697128	+	0.716947i	$0.745539\pi$
$444$	−3756.60	−0.401532
$445$	2798.79	0.298147
$446$	−3511.11	−0.372771
$447$	−1404.28	−0.148591
$448$	−2763.99	−0.291487
$449$	−4572.68	−0.480619	−0.240310	−	0.970696i	$-0.577249\pi$
$449$	−4572.68	−0.480619	−0.240310	+	0.970696i	$0.577249\pi$
$450$	−576.196	−0.0603603
$451$	2844.79	0.297020
$452$	−12623.4	−1.31362
$453$	5596.03	0.580407
$454$	−1862.22	−0.192507
$455$	972.754	0.100227
$456$	3023.04	0.310454
$457$	−10846.5	−1.11024	−0.555119	−	0.831771i	$-0.687327\pi$
$457$	−10846.5	−1.11024	−0.555119	+	0.831771i	$0.687327\pi$
$458$	1728.01	0.176298
$459$	−1859.68	−0.189112
$460$	−3184.27	−0.322755
$461$	−1299.33	−0.131270	−0.0656352	−	0.997844i	$-0.520907\pi$
$461$	−1299.33	−0.131270	−0.0656352	+	0.997844i	$0.520907\pi$
$462$	129.719	0.0130629
$463$	12116.9	1.21624	0.608120	−	0.793845i	$-0.291924\pi$
$463$	12116.9	1.21624	0.608120	+	0.793845i	$0.291924\pi$
$464$	−8347.94	−0.835223
$465$	556.676	0.0555166
$466$	762.633	0.0758118
$467$	−13546.6	−1.34232	−0.671160	−	0.741313i	$-0.734204\pi$
$467$	−13546.6	−1.34232	−0.671160	+	0.741313i	$0.734204\pi$
$468$	2898.97	0.286335
$469$	4065.46	0.400267
$470$	−206.242	−0.0202409
$471$	4504.76	0.440697
$472$	1605.51	0.156567
$473$	−1174.12	−0.114136
$474$	1836.34	0.177945
$475$	13043.5	1.25995
$476$	3705.07	0.356768
$477$	94.0058	0.00902355
$478$	−2331.10	−0.223059
$479$	−10663.2	−1.01715	−0.508573	−	0.861019i	$-0.669827\pi$
$479$	−10663.2	−1.01715	−0.508573	+	0.861019i	$0.669827\pi$
$480$	−1016.56	−0.0966652
$481$	−6830.08	−0.647453
$482$	−1960.78	−0.185293
$483$	−2624.68	−0.247261
$484$	−929.844	−0.0873257
$485$	−3067.01	−0.287146
$486$	136.457	0.0127363
$487$	8149.91	0.758332	0.379166	−	0.925329i	$-0.376211\pi$
$487$	8149.91	0.758332	0.379166	+	0.925329i	$0.376211\pi$
$488$	−1672.41	−0.155136
$489$	1573.20	0.145486
$490$	−91.2252	−0.00841048
$491$	−15142.4	−1.39178	−0.695891	−	0.718147i	$-0.744990\pi$
$491$	−15142.4	−1.39178	−0.695891	+	0.718147i	$0.744990\pi$
$492$	−5962.16	−0.546331
$493$	10171.0	0.929167
$494$	2692.93	0.245264
$495$	−328.219	−0.0298027
$496$	−3164.04	−0.286430
$497$	−8129.73	−0.733739
$498$	−1473.79	−0.132615
$499$	10430.8	0.935764	0.467882	−	0.883791i	$-0.345017\pi$
$499$	10430.8	0.935764	0.467882	+	0.883791i	$0.345017\pi$
$500$	−6089.28	−0.544642
$501$	−9879.28	−0.880986
$502$	−493.820	−0.0439049
$503$	2173.55	0.192671	0.0963356	−	0.995349i	$-0.469288\pi$
$503$	2173.55	0.192671	0.0963356	+	0.995349i	$0.469288\pi$
$504$	−554.889	−0.0490411
$505$	2933.64	0.258505
$506$	−772.042	−0.0678289
$507$	−1320.22	−0.115647
$508$	13808.9	1.20605
$509$	−13729.6	−1.19559	−0.597793	−	0.801651i	$-0.703955\pi$
$509$	−13729.6	−1.19559	−0.597793	+	0.801651i	$0.703955\pi$
$510$	384.692	0.0334009
$511$	−557.899	−0.0482974
$512$	9761.22	0.842557
$513$	−3089.02	−0.265855
$514$	3195.85	0.274247
$515$	−3546.70	−0.303468
$516$	2460.75	0.209939
$517$	1218.57	0.103661
$518$	640.527	0.0543304
$519$	−9110.89	−0.770566
$520$	−1223.97	−0.103220
$521$	18257.2	1.53525	0.767623	−	0.640902i	$-0.221439\pi$
$521$	18257.2	1.53525	0.767623	+	0.640902i	$0.221439\pi$
$522$	−746.318	−0.0625775
$523$	−19979.6	−1.67045	−0.835225	−	0.549908i	$-0.814663\pi$
$523$	−19979.6	−1.67045	−0.835225	+	0.549908i	$0.814663\pi$
$524$	−7179.81	−0.598572
$525$	−2394.18	−0.199030
$526$	1136.89	0.0942411
$527$	3855.02	0.318648
$528$	1865.53	0.153763
$529$	3454.21	0.283900
$530$	−19.4460	−0.00159374
$531$	−1640.55	−0.134075
$532$	6154.31	0.501548
$533$	−10840.1	−0.880935
$534$	−1422.18	−0.115250
$535$	−590.780	−0.0477414
$536$	−5115.37	−0.412221
$537$	2070.45	0.166381
$538$	−1927.23	−0.154440
$539$	539.000	0.0430730
$540$	687.886	0.0548184
$541$	7904.01	0.628133	0.314066	−	0.949401i	$-0.398309\pi$
$541$	7904.01	0.628133	0.314066	+	0.949401i	$0.398309\pi$
$542$	−1670.51	−0.132388
$543$	−7601.83	−0.600784
$544$	−7039.73	−0.554827
$545$	−6543.08	−0.514265
$546$	−494.296	−0.0387434
$547$	16806.6	1.31370	0.656852	−	0.754019i	$-0.271887\pi$
$547$	16806.6	1.31370	0.656852	+	0.754019i	$0.271887\pi$
$548$	12225.3	0.952991
$549$	1708.91	0.132850
$550$	−704.240	−0.0545980
$551$	16894.6	1.30623
$552$	3302.51	0.254645
$553$	7630.26	0.586748
$554$	4369.99	0.335132
$555$	−1620.68	−0.123954
$556$	11903.6	0.907955
$557$	−8002.82	−0.608780	−0.304390	−	0.952548i	$-0.598453\pi$
$557$	−8002.82	−0.608780	−0.304390	+	0.952548i	$0.598453\pi$
$558$	−282.869	−0.0214602
$559$	4474.03	0.338517
$560$	−1311.94	−0.0989995
$561$	−2272.94	−0.171058
$562$	−1475.58	−0.110754
$563$	−12327.9	−0.922840	−0.461420	−	0.887182i	$-0.652660\pi$
$563$	−12327.9	−0.922840	−0.461420	+	0.887182i	$0.652660\pi$
$564$	−2553.90	−0.190672
$565$	−5446.05	−0.405517
$566$	−1404.70	−0.104318
$567$	567.000	0.0419961
$568$	10229.2	0.755651
$569$	−6786.77	−0.500028	−0.250014	−	0.968242i	$-0.580435\pi$
$569$	−6786.77	−0.500028	−0.250014	+	0.968242i	$0.580435\pi$
$570$	638.994	0.0469553
$571$	16890.0	1.23787	0.618935	−	0.785442i	$-0.287564\pi$
$571$	16890.0	1.23787	0.618935	+	0.785442i	$0.287564\pi$
$572$	3543.19	0.259000
$573$	5535.38	0.403567
$574$	1016.59	0.0739228
$575$	14249.3	1.03346
$576$	−3553.70	−0.257067
$577$	1857.64	0.134029	0.0670144	−	0.997752i	$-0.478653\pi$
$577$	1857.64	0.134029	0.0670144	+	0.997752i	$0.478653\pi$
$578$	−94.8875	−0.00682837
$579$	−7963.44	−0.571588
$580$	−3762.22	−0.269341
$581$	−6123.81	−0.437278
$582$	1558.47	0.110998
$583$	114.896	0.00816210
$584$	701.977	0.0497398
$585$	1250.68	0.0883922
$586$	−2609.00	−0.183919
$587$	21977.7	1.54534	0.772672	−	0.634805i	$-0.218920\pi$
$587$	21977.7	1.54534	0.772672	+	0.634805i	$0.218920\pi$
$588$	−1129.64	−0.0792275
$589$	6403.39	0.447958
$590$	339.364	0.0236803
$591$	492.171	0.0342558
$592$	9211.65	0.639521
$593$	17263.7	1.19550	0.597752	−	0.801681i	$-0.296061\pi$
$593$	17263.7	1.19550	0.597752	+	0.801681i	$0.296061\pi$
$594$	166.781	0.0115204
$595$	1598.45	0.110135
$596$	3597.14	0.247223
$597$	8665.23	0.594044
$598$	2941.88	0.201175
$599$	−23211.4	−1.58329	−0.791646	−	0.610981i	$-0.790775\pi$
$599$	−23211.4	−1.58329	−0.791646	+	0.610981i	$0.790775\pi$
$600$	3012.48	0.204973
$601$	−20051.0	−1.36089	−0.680446	−	0.732799i	$-0.738214\pi$
$601$	−20051.0	−1.36089	−0.680446	+	0.732799i	$0.738214\pi$
$602$	−419.576	−0.0284064
$603$	5227.01	0.353002
$604$	−14334.5	−0.965668
$605$	−401.156	−0.0269576
$606$	−1490.70	−0.0999266
$607$	−7862.63	−0.525756	−0.262878	−	0.964829i	$-0.584672\pi$
$607$	−7862.63	−0.525756	−0.262878	+	0.964829i	$0.584672\pi$
$608$	−11693.4	−0.779981
$609$	−3101.06	−0.206340
$610$	−353.505	−0.0234639
$611$	−4643.39	−0.307449
$612$	4763.66	0.314640
$613$	−16366.2	−1.07835	−0.539173	−	0.842195i	$-0.681263\pi$
$613$	−16366.2	−1.07835	−0.539173	+	0.842195i	$0.681263\pi$
$614$	−2429.23	−0.159668
$615$	−2572.21	−0.168653
$616$	−678.198	−0.0443594
$617$	3749.07	0.244622	0.122311	−	0.992492i	$-0.460969\pi$
$617$	3749.07	0.244622	0.122311	+	0.992492i	$0.460969\pi$
$618$	1802.22	0.117307
$619$	20036.9	1.30105	0.650525	−	0.759485i	$-0.274549\pi$
$619$	20036.9	1.30105	0.650525	+	0.759485i	$0.274549\pi$
$620$	−1425.95	−0.0923673
$621$	−3374.59	−0.218064
$622$	1036.19	0.0667965
$623$	−5909.35	−0.380021
$624$	−7108.64	−0.456047
$625$	11624.0	0.743936
$626$	−2969.01	−0.189562
$627$	−3775.47	−0.240475
$628$	−11539.2	−0.733222
$629$	−11223.3	−0.711453
$630$	−117.290	−0.00741735
$631$	5839.34	0.368400	0.184200	−	0.982889i	$-0.441031\pi$
$631$	5839.34	0.368400	0.184200	+	0.982889i	$0.441031\pi$
$632$	−9600.80	−0.604271
$633$	1892.87	0.118854
$634$	5252.62	0.329035
$635$	5957.49	0.372308
$636$	−240.801	−0.0150132
$637$	−2053.87	−0.127751
$638$	−912.166	−0.0566035
$639$	−10452.5	−0.647097
$640$	3445.94	0.212832
$641$	−14682.2	−0.904702	−0.452351	−	0.891840i	$-0.649415\pi$
$641$	−14682.2	−0.904702	−0.452351	+	0.891840i	$0.649415\pi$
$642$	300.199	0.0184547
$643$	30541.3	1.87314	0.936571	−	0.350477i	$-0.113981\pi$
$643$	30541.3	1.87314	0.936571	+	0.350477i	$0.113981\pi$
$644$	6723.26	0.411388
$645$	1061.63	0.0648084
$646$	4425.08	0.269508
$647$	7991.44	0.485588	0.242794	−	0.970078i	$-0.421936\pi$
$647$	7991.44	0.485588	0.242794	+	0.970078i	$0.421936\pi$
$648$	−713.429	−0.0432502
$649$	−2005.11	−0.121275
$650$	2683.52	0.161933
$651$	−1175.36	−0.0707621
$652$	−4029.84	−0.242056
$653$	18400.0	1.10268	0.551338	−	0.834282i	$-0.314117\pi$
$653$	18400.0	1.10268	0.551338	+	0.834282i	$0.314117\pi$
$654$	3324.80	0.198792
$655$	−3097.54	−0.184780
$656$	14620.0	0.870143
$657$	−717.298	−0.0425943
$658$	435.459	0.0257993
$659$	15887.4	0.939126	0.469563	−	0.882899i	$-0.344411\pi$
$659$	15887.4	0.939126	0.469563	+	0.882899i	$0.344411\pi$
$660$	840.750	0.0495851
$661$	−14947.8	−0.879582	−0.439791	−	0.898100i	$-0.644947\pi$
$661$	−14947.8	−0.879582	−0.439791	+	0.898100i	$0.644947\pi$
$662$	6393.61	0.375370
$663$	8661.07	0.507343
$664$	7705.29	0.450336
$665$	2655.11	0.154828
$666$	823.535	0.0479149
$667$	18456.4	1.07142
$668$	25306.3	1.46576
$669$	−18757.5	−1.08402
$670$	−1081.26	−0.0623473
$671$	2088.67	0.120167
$672$	2146.36	0.123210
$673$	1091.22	0.0625014	0.0312507	−	0.999512i	$-0.490051\pi$
$673$	1091.22	0.0625014	0.0312507	+	0.999512i	$0.490051\pi$
$674$	−6000.79	−0.342940
$675$	−3078.23	−0.175528
$676$	3381.81	0.192411
$677$	−26564.2	−1.50804	−0.754022	−	0.656849i	$-0.771889\pi$
$677$	−26564.2	−1.50804	−0.754022	+	0.656849i	$0.771889\pi$
$678$	2767.36	0.156755
$679$	6475.68	0.365999
$680$	−2011.26	−0.113424
$681$	−9948.60	−0.559811
$682$	−345.729	−0.0194115
$683$	−20461.6	−1.14633	−0.573164	−	0.819441i	$-0.694284\pi$
$683$	−20461.6	−1.14633	−0.573164	+	0.819441i	$0.694284\pi$
$684$	7912.69	0.442323
$685$	5274.28	0.294190
$686$	192.613	0.0107201
$687$	9231.60	0.512675
$688$	−6034.07	−0.334370
$689$	−437.813	−0.0242081
$690$	698.068	0.0385145
$691$	−12100.6	−0.666175	−0.333087	−	0.942896i	$-0.608090\pi$
$691$	−12100.6	−0.666175	−0.333087	+	0.942896i	$0.608090\pi$
$692$	23338.0	1.28205
$693$	693.000	0.0379869
$694$	3505.61	0.191745
$695$	5135.47	0.280287
$696$	3901.91	0.212502
$697$	−17812.8	−0.968015
$698$	2537.11	0.137580
$699$	4074.24	0.220460
$700$	6132.82	0.331141
$701$	27360.5	1.47417	0.737083	−	0.675802i	$-0.236203\pi$
$701$	27360.5	1.47417	0.737083	+	0.675802i	$0.236203\pi$
$702$	−635.523	−0.0341685
$703$	−18642.6	−1.00017
$704$	−4343.41	−0.232526
$705$	−1101.81	−0.0588606
$706$	−5205.76	−0.277509
$707$	−6194.07	−0.329494
$708$	4202.35	0.223071
$709$	19314.2	1.02308	0.511538	−	0.859261i	$-0.329076\pi$
$709$	19314.2	1.02308	0.511538	+	0.859261i	$0.329076\pi$
$710$	2162.21	0.114290
$711$	9810.34	0.517463
$712$	7435.45	0.391370
$713$	6995.36	0.367431
$714$	−812.238	−0.0425732
$715$	1528.61	0.0799537
$716$	−5303.58	−0.276821
$717$	−12453.5	−0.648655
$718$	4615.70	0.239911
$719$	−11811.2	−0.612635	−0.306317	−	0.951929i	$-0.599097\pi$
$719$	−11811.2	−0.612635	−0.306317	+	0.951929i	$0.599097\pi$
$720$	−1686.78	−0.0873093
$721$	7488.49	0.386804
$722$	3498.60	0.180338
$723$	−10475.1	−0.538831
$724$	19472.5	0.999571
$725$	16835.6	0.862424
$726$	203.844	0.0104206
$727$	17995.3	0.918034	0.459017	−	0.888428i	$-0.348202\pi$
$727$	17995.3	0.918034	0.459017	+	0.888428i	$0.348202\pi$
$728$	2584.29	0.131566
$729$	729.000	0.0370370
$730$	148.380	0.00752301
$731$	7351.83	0.371980
$732$	−4377.46	−0.221032
$733$	−28542.7	−1.43827	−0.719133	−	0.694873i	$-0.755461\pi$
$733$	−28542.7	−1.43827	−0.719133	+	0.694873i	$0.755461\pi$
$734$	5054.86	0.254194
$735$	−487.355	−0.0244576
$736$	−12774.4	−0.639769
$737$	6388.57	0.319303
$738$	1307.05	0.0651938
$739$	−5283.32	−0.262991	−0.131495	−	0.991317i	$-0.541978\pi$
$739$	−5283.32	−0.262991	−0.131495	+	0.991317i	$0.541978\pi$
$740$	4151.47	0.206231
$741$	14386.5	0.713227
$742$	41.0583	0.00203140
$743$	−8423.21	−0.415905	−0.207953	−	0.978139i	$-0.566680\pi$
$743$	−8423.21	−0.415905	−0.207953	+	0.978139i	$0.566680\pi$
$744$	1478.90	0.0728753
$745$	1551.89	0.0763180
$746$	1104.10	0.0541874
$747$	−7873.47	−0.385643
$748$	5822.25	0.284602
$749$	1247.37	0.0608518
$750$	1334.91	0.0649923
$751$	26417.9	1.28363	0.641814	−	0.766861i	$-0.278182\pi$
$751$	26417.9	1.28363	0.641814	+	0.766861i	$0.278182\pi$
$752$	6262.49	0.303683
$753$	−2638.15	−0.127675
$754$	3475.83	0.167881
$755$	−6184.25	−0.298103
$756$	−1452.40	−0.0698721
$757$	−24157.9	−1.15988	−0.579942	−	0.814658i	$-0.696925\pi$
$757$	−24157.9	−1.15988	−0.579942	+	0.814658i	$0.696925\pi$
$758$	574.073	0.0275083
$759$	−4124.50	−0.197246
$760$	−3340.80	−0.159452
$761$	−9195.59	−0.438029	−0.219014	−	0.975722i	$-0.570284\pi$
$761$	−9195.59	−0.438029	−0.219014	+	0.975722i	$0.570284\pi$
$762$	−3027.24	−0.143918
$763$	13815.0	0.655488
$764$	−14179.2	−0.671445
$765$	2055.15	0.0971297
$766$	7202.43	0.339732
$767$	7640.53	0.359692
$768$	7725.50	0.362982
$769$	−15430.5	−0.723589	−0.361794	−	0.932258i	$-0.617836\pi$
$769$	−15430.5	−0.723589	−0.361794	+	0.932258i	$0.617836\pi$
$770$	−143.354	−0.00670924
$771$	17073.3	0.797509
$772$	20398.8	0.950994
$773$	−14100.0	−0.656068	−0.328034	−	0.944666i	$-0.606386\pi$
$773$	−14100.0	−0.656068	−0.328034	+	0.944666i	$0.606386\pi$
$774$	−539.454	−0.0250521
$775$	6381.02	0.295759
$776$	−8148.03	−0.376930
$777$	3421.91	0.157993
$778$	−6867.26	−0.316457
$779$	−29587.9	−1.36084
$780$	−3203.69	−0.147065
$781$	−12775.3	−0.585321
$782$	4834.17	0.221061
$783$	−3987.08	−0.181975
$784$	2770.03	0.126186
$785$	−4978.27	−0.226347
$786$	1573.98	0.0714277
$787$	4428.96	0.200604	0.100302	−	0.994957i	$-0.468019\pi$
$787$	4428.96	0.200604	0.100302	+	0.994957i	$0.468019\pi$
$788$	−1260.72	−0.0569941
$789$	6073.65	0.274053
$790$	−2029.37	−0.0913944
$791$	11498.8	0.516876
$792$	−871.969	−0.0391213
$793$	−7958.90	−0.356405
$794$	−1909.88	−0.0853640
$795$	−103.887	−0.00463459
$796$	−22196.4	−0.988357
$797$	32311.2	1.43604	0.718019	−	0.696024i	$-0.245049\pi$
$797$	32311.2	1.43604	0.718019	+	0.696024i	$0.245049\pi$
$798$	−1349.17	−0.0598498
$799$	−7630.14	−0.337841
$800$	−11652.5	−0.514973
$801$	−7597.74	−0.335147
$802$	−3500.94	−0.154143
$803$	−876.698	−0.0385280
$804$	−13389.3	−0.587317
$805$	2900.57	0.126996
$806$	1317.41	0.0575729
$807$	−10295.9	−0.449110
$808$	7793.70	0.339334
$809$	−45404.2	−1.97321	−0.986605	−	0.163125i	$-0.947843\pi$
$809$	−45404.2	−1.97321	−0.986605	+	0.163125i	$0.947843\pi$
$810$	−150.801	−0.00654149
$811$	−36636.7	−1.58630	−0.793150	−	0.609026i	$-0.791560\pi$
$811$	−36636.7	−1.58630	−0.793150	+	0.609026i	$0.791560\pi$
$812$	7943.53	0.343304
$813$	−8924.39	−0.384984
$814$	1006.54	0.0433407
$815$	−1738.57	−0.0747231
$816$	−11681.1	−0.501127
$817$	12211.8	0.522932
$818$	−6418.17	−0.274335
$819$	−2640.69	−0.112666
$820$	6588.86	0.280601
$821$	−14967.9	−0.636279	−0.318139	−	0.948044i	$-0.603058\pi$
$821$	−14967.9	−0.636279	−0.318139	+	0.948044i	$0.603058\pi$
$822$	−2680.07	−0.113721
$823$	−8353.81	−0.353822	−0.176911	−	0.984227i	$-0.556610\pi$
$823$	−8353.81	−0.353822	−0.176911	+	0.984227i	$0.556610\pi$
$824$	−9422.41	−0.398356
$825$	−3762.28	−0.158771
$826$	−716.531	−0.0301832
$827$	26797.4	1.12677	0.563384	−	0.826195i	$-0.309499\pi$
$827$	26797.4	1.12677	0.563384	+	0.826195i	$0.309499\pi$
$828$	8644.19	0.362810
$829$	−14645.0	−0.613562	−0.306781	−	0.951780i	$-0.599252\pi$
$829$	−14645.0	−0.613562	−0.306781	+	0.951780i	$0.599252\pi$
$830$	1628.70	0.0681122
$831$	23345.9	0.974563
$832$	16550.6	0.689651
$833$	−3374.97	−0.140379
$834$	−2609.54	−0.108346
$835$	10917.7	0.452484
$836$	9671.06	0.400097
$837$	−1511.18	−0.0624063
$838$	2149.47	0.0886065
$839$	−10093.3	−0.415327	−0.207664	−	0.978200i	$-0.566586\pi$
$839$	−10093.3	−0.415327	−0.207664	+	0.978200i	$0.566586\pi$
$840$	613.216	0.0251880
$841$	−2582.72	−0.105897
$842$	−6529.06	−0.267228
$843$	−7883.04	−0.322072
$844$	−4848.68	−0.197747
$845$	1458.99	0.0593975
$846$	559.876	0.0227529
$847$	847.000	0.0343604
$848$	590.474	0.0239115
$849$	−7504.39	−0.303357
$850$	4409.62	0.177940
$851$	−20366.0	−0.820374
$852$	26774.7	1.07663
$853$	28743.0	1.15374	0.576872	−	0.816835i	$-0.304273\pi$
$853$	28743.0	1.15374	0.576872	+	0.816835i	$0.304273\pi$
$854$	746.389	0.0299074
$855$	3413.72	0.136546
$856$	−1569.51	−0.0626690
$857$	−19741.2	−0.786870	−0.393435	−	0.919352i	$-0.628713\pi$
$857$	−19741.2	−0.786870	−0.393435	+	0.919352i	$0.628713\pi$
$858$	−776.750	−0.0309065
$859$	−41550.0	−1.65037	−0.825185	−	0.564863i	$-0.808929\pi$
$859$	−41550.0	−1.65037	−0.825185	+	0.564863i	$0.808929\pi$
$860$	−2719.41	−0.107827
$861$	5430.97	0.214967
$862$	4194.69	0.165744
$863$	45844.4	1.80830	0.904150	−	0.427215i	$-0.140505\pi$
$863$	45844.4	1.80830	0.904150	+	0.427215i	$0.140505\pi$
$864$	2759.60	0.108661
$865$	10068.6	0.395771
$866$	868.704	0.0340875
$867$	−506.920	−0.0198569
$868$	3010.76	0.117732
$869$	11990.4	0.468063
$870$	824.766	0.0321405
$871$	−24343.8	−0.947024
$872$	−17382.8	−0.675064
$873$	8325.87	0.322781
$874$	8029.80	0.310769
$875$	5546.76	0.214303
$876$	1837.40	0.0708675
$877$	2558.92	0.0985277	0.0492638	−	0.998786i	$-0.484312\pi$
$877$	2558.92	0.0985277	0.0492638	+	0.998786i	$0.484312\pi$
$878$	−4538.91	−0.174466
$879$	−13938.1	−0.534836
$880$	−2061.62	−0.0789742
$881$	1119.16	0.0427983	0.0213992	−	0.999771i	$-0.493188\pi$
$881$	1119.16	0.0427983	0.0213992	+	0.999771i	$0.493188\pi$
$882$	247.645	0.00945423
$883$	−1677.64	−0.0639377	−0.0319688	−	0.999489i	$-0.510178\pi$
$883$	−1677.64	−0.0639377	−0.0319688	+	0.999489i	$0.510178\pi$
$884$	−22185.8	−0.844105
$885$	1812.99	0.0688622
$886$	−7300.27	−0.276814
$887$	12127.5	0.459076	0.229538	−	0.973300i	$-0.426278\pi$
$887$	12127.5	0.459076	0.229538	+	0.973300i	$0.426278\pi$
$888$	−4305.62	−0.162711
$889$	−12578.6	−0.474548
$890$	1571.67	0.0591937
$891$	891.000	0.0335013
$892$	48048.4	1.80356
$893$	−12674.1	−0.474940
$894$	−788.578	−0.0295011
$895$	−2288.09	−0.0854551
$896$	−7275.74	−0.271278
$897$	15716.5	0.585015
$898$	−2567.80	−0.0954216
$899$	8265.02	0.306623
$900$	7885.05	0.292039
$901$	−719.425	−0.0266010
$902$	1597.50	0.0589700
$903$	−2241.51	−0.0826056
$904$	−14468.4	−0.532312
$905$	8400.89	0.308569
$906$	3142.47	0.115233
$907$	−13826.8	−0.506186	−0.253093	−	0.967442i	$-0.581448\pi$
$907$	−13826.8	−0.506186	−0.253093	+	0.967442i	$0.581448\pi$
$908$	25483.9	0.931401
$909$	−7963.81	−0.290586
$910$	546.253	0.0198990
$911$	−41945.3	−1.52548	−0.762739	−	0.646706i	$-0.776146\pi$
$911$	−41945.3	−1.52548	−0.762739	+	0.646706i	$0.776146\pi$
$912$	−19402.9	−0.704489
$913$	−9623.13	−0.348827
$914$	−6090.90	−0.220426
$915$	−1888.54	−0.0682330
$916$	−23647.2	−0.852977
$917$	6540.13	0.235523
$918$	−1044.31	−0.0375460
$919$	−8132.54	−0.291913	−0.145956	−	0.989291i	$-0.546626\pi$
$919$	−8132.54	−0.291913	−0.145956	+	0.989291i	$0.546626\pi$
$920$	−3649.65	−0.130789
$921$	−12977.8	−0.464313
$922$	−729.641	−0.0260623
$923$	48680.5	1.73601
$924$	−1775.16	−0.0632017
$925$	−18577.4	−0.660349
$926$	6804.27	0.241471
$927$	9628.06	0.341129
$928$	−15092.9	−0.533889
$929$	−48334.7	−1.70701	−0.853504	−	0.521086i	$-0.825527\pi$
$929$	−48334.7	−1.70701	−0.853504	+	0.521086i	$0.825527\pi$
$930$	312.603	0.0110222
$931$	−5606.00	−0.197346
$932$	−10436.4	−0.366797
$933$	5535.66	0.194244
$934$	−7607.15	−0.266503
$935$	2511.85	0.0878571
$936$	3322.65	0.116030
$937$	−6068.39	−0.211575	−0.105787	−	0.994389i	$-0.533736\pi$
$937$	−6068.39	−0.211575	−0.105787	+	0.994389i	$0.533736\pi$
$938$	2282.97	0.0794686
$939$	−15861.5	−0.551245
$940$	2822.35	0.0979309
$941$	15416.2	0.534065	0.267032	−	0.963688i	$-0.413957\pi$
$941$	15416.2	0.534065	0.267032	+	0.963688i	$0.413957\pi$
$942$	2529.66	0.0874955
$943$	−32323.3	−1.11621
$944$	−10304.7	−0.355285
$945$	−626.600	−0.0215696
$946$	−659.333	−0.0226604
$947$	−45788.4	−1.57120	−0.785598	−	0.618737i	$-0.787645\pi$
$947$	−45788.4	−1.57120	−0.785598	+	0.618737i	$0.787645\pi$
$948$	−25129.7	−0.860944
$949$	3340.67	0.114271
$950$	7324.61	0.250149
$951$	28061.2	0.956833
$952$	4246.56	0.144571
$953$	36543.7	1.24215	0.621074	−	0.783752i	$-0.286697\pi$
$953$	36543.7	1.24215	0.621074	+	0.783752i	$0.286697\pi$
$954$	52.7892	0.00179152
$955$	−6117.23	−0.207276
$956$	31900.4	1.07922
$957$	−4873.09	−0.164603
$958$	−5987.94	−0.201943
$959$	−11136.1	−0.374977
$960$	3927.24	0.132032
$961$	−26658.4	−0.894847
$962$	−3835.45	−0.128545
$963$	1603.76	0.0536662
$964$	26832.6	0.896494
$965$	8800.50	0.293573
$966$	−1473.90	−0.0490910
$967$	3077.00	0.102327	0.0511633	−	0.998690i	$-0.483707\pi$
$967$	3077.00	0.102327	0.0511633	+	0.998690i	$0.483707\pi$
$968$	−1065.74	−0.0353865
$969$	23640.2	0.783729
$970$	−1722.29	−0.0570096
$971$	41714.2	1.37865	0.689327	−	0.724451i	$-0.257906\pi$
$971$	41714.2	1.37865	0.689327	+	0.724451i	$0.257906\pi$
$972$	−1867.37	−0.0616214
$973$	−10843.0	−0.357257
$974$	4576.61	0.150558
$975$	14336.2	0.470900
$976$	10734.1	0.352039
$977$	−22237.2	−0.728178	−0.364089	−	0.931364i	$-0.618620\pi$
$977$	−22237.2	−0.728178	−0.364089	+	0.931364i	$0.618620\pi$
$978$	883.436	0.0288846
$979$	−9286.12	−0.303152
$980$	1248.39	0.0406921
$981$	17762.2	0.578086
$982$	−8503.23	−0.276323
$983$	−26617.2	−0.863639	−0.431820	−	0.901960i	$-0.642128\pi$
$983$	−26617.2	−0.863639	−0.431820	+	0.901960i	$0.642128\pi$
$984$	−6833.52	−0.221387
$985$	−543.905	−0.0175942
$986$	5711.56	0.184476
$987$	2326.37	0.0750244
$988$	−36851.8	−1.18665
$989$	13340.7	0.428928
$990$	−184.312	−0.00591700
$991$	28839.4	0.924435	0.462217	−	0.886767i	$-0.347054\pi$
$991$	28839.4	0.924435	0.462217	+	0.886767i	$0.347054\pi$
$992$	−5720.52	−0.183091
$993$	34156.8	1.09157
$994$	−4565.27	−0.145676
$995$	−9576.07	−0.305107
$996$	20168.3	0.641624
$997$	35924.1	1.14115	0.570575	−	0.821246i	$-0.306720\pi$
$997$	35924.1	1.14115	0.570575	+	0.821246i	$0.306720\pi$
$998$	5857.44	0.185786
$999$	4399.59	0.139336

Twists

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

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

\(f(q)\)	\(=\)	\(q+0.561553 q^{2} +3.00000 q^{3} -7.68466 q^{4} -3.31534 q^{5} +1.68466 q^{6} +7.00000 q^{7} -8.80776 q^{8} +9.00000 q^{9} -1.86174 q^{10} +11.0000 q^{11} -23.0540 q^{12} -41.9157 q^{13} +3.93087 q^{14} -9.94602 q^{15} +56.5312 q^{16} -68.8769 q^{17} +5.05398 q^{18} -114.408 q^{19} +25.4773 q^{20} +21.0000 q^{21} +6.17708 q^{22} -124.985 q^{23} -26.4233 q^{24} -114.009 q^{25} -23.5379 q^{26} +27.0000 q^{27} -53.7926 q^{28} -147.670 q^{29} -5.58522 q^{30} -55.9697 q^{31} +102.207 q^{32} +33.0000 q^{33} -38.6780 q^{34} -23.2074 q^{35} -69.1619 q^{36} +162.948 q^{37} -64.2462 q^{38} -125.747 q^{39} +29.2007 q^{40} +258.617 q^{41} +11.7926 q^{42} -106.739 q^{43} -84.5312 q^{44} -29.8381 q^{45} -70.1856 q^{46} +110.779 q^{47} +169.594 q^{48} +49.0000 q^{49} -64.0218 q^{50} -206.631 q^{51} +322.108 q^{52} +10.4451 q^{53} +15.1619 q^{54} -36.4688 q^{55} -61.6543 q^{56} -343.224 q^{57} -82.9242 q^{58} -182.283 q^{59} +76.4318 q^{60} +189.879 q^{61} -31.4299 q^{62} +63.0000 q^{63} -394.855 q^{64} +138.965 q^{65} +18.5312 q^{66} +580.779 q^{67} +529.295 q^{68} -374.955 q^{69} -13.0322 q^{70} -1161.39 q^{71} -79.2699 q^{72} -79.6998 q^{73} +91.5038 q^{74} -342.026 q^{75} +879.187 q^{76} +77.0000 q^{77} -70.6137 q^{78} +1090.04 q^{79} -187.420 q^{80} +81.0000 q^{81} +145.227 q^{82} -874.830 q^{83} -161.378 q^{84} +228.350 q^{85} -59.9394 q^{86} -443.009 q^{87} -96.8854 q^{88} -844.193 q^{89} -16.7557 q^{90} -293.410 q^{91} +960.466 q^{92} -167.909 q^{93} +62.2084 q^{94} +379.302 q^{95} +306.622 q^{96} +925.097 q^{97} +27.5161 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 6 q^{3} - 3 q^{4} - 19 q^{5} - 9 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 54 q^{10} + 22 q^{11} - 9 q^{12} + 11 q^{13} - 21 q^{14} - 57 q^{15} - 23 q^{16} - 146 q^{17} - 27 q^{18} - 101 q^{19}+ \cdots + 198 q^{99}+O(q^{100}) \) 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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