LMFDB - Embedded newform 825.4.c.l.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.2230106176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 41x^{4} + 452x^{2} + 676 $ x^6 + 41x^4 + 452x^2 + 676
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.3
Root			$-1.32906i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.l.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32906i q^{2} +3.00000i q^{3} +2.57547 q^{4} +6.98719 q^{6} +22.4672i q^{7} -24.6309i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.32906i q^{2} +3.00000i q^{3} +2.57547 q^{4} +6.98719 q^{6} +22.4672i q^{7} -24.6309i q^{8} -9.00000 q^{9} +11.0000 q^{11} +7.72640i q^{12} +9.86030i q^{13} +52.3275 q^{14} -36.7633 q^{16} -128.137i q^{17} +20.9616i q^{18} -7.04001 q^{19} -67.4015 q^{21} -25.6197i q^{22} -0.654969i q^{23} +73.8928 q^{24} +22.9653 q^{26} -27.0000i q^{27} +57.8635i q^{28} +229.279 q^{29} +155.789 q^{31} -111.423i q^{32} +33.0000i q^{33} -298.438 q^{34} -23.1792 q^{36} -110.279i q^{37} +16.3966i q^{38} -29.5809 q^{39} +154.749 q^{41} +156.982i q^{42} +401.014i q^{43} +28.3301 q^{44} -1.52546 q^{46} -277.532i q^{47} -110.290i q^{48} -161.774 q^{49} +384.410 q^{51} +25.3949i q^{52} +651.566i q^{53} -62.8847 q^{54} +553.388 q^{56} -21.1200i q^{57} -534.005i q^{58} +423.869 q^{59} +681.851 q^{61} -362.842i q^{62} -202.205i q^{63} -553.618 q^{64} +76.8591 q^{66} +374.028i q^{67} -330.011i q^{68} +1.96491 q^{69} +96.6950 q^{71} +221.678i q^{72} +19.9460i q^{73} -256.848 q^{74} -18.1313 q^{76} +247.139i q^{77} +68.8958i q^{78} -24.4286 q^{79} +81.0000 q^{81} -360.419i q^{82} +1127.35i q^{83} -173.590 q^{84} +933.987 q^{86} +687.836i q^{87} -270.940i q^{88} +639.624 q^{89} -221.533 q^{91} -1.68685i q^{92} +467.366i q^{93} -646.389 q^{94} +334.270 q^{96} -730.865i q^{97} +376.783i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 44 q^{4} + 24 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 44 * q^4 + 24 * q^6 - 54 * q^9	$ 6 q - 44 q^{4} + 24 q^{6} - 54 q^{9} + 66 q^{11} + 112 q^{14} + 100 q^{16} - 292 q^{19} + 24 q^{21} - 288 q^{24} - 1016 q^{26} - 136 q^{29} - 136 q^{31} + 352 q^{34} + 396 q^{36} - 392 q^{41} - 484 q^{44} + 2320 q^{46} + 314 q^{49} + 1308 q^{51} - 216 q^{54} + 2736 q^{56} + 2088 q^{59} + 1284 q^{61} - 2332 q^{64} + 264 q^{66} - 1200 q^{69} - 1088 q^{71} - 3072 q^{74} + 3992 q^{76} + 3172 q^{79} + 486 q^{81} - 2040 q^{84} + 7136 q^{86} + 4244 q^{89} - 16 q^{91} + 4304 q^{94} + 4128 q^{96} - 594 q^{99}+O(q^{100}) $ 6 * q - 44 * q^4 + 24 * q^6 - 54 * q^9 + 66 * q^11 + 112 * q^14 + 100 * q^16 - 292 * q^19 + 24 * q^21 - 288 * q^24 - 1016 * q^26 - 136 * q^29 - 136 * q^31 + 352 * q^34 + 396 * q^36 - 392 * q^41 - 484 * q^44 + 2320 * q^46 + 314 * q^49 + 1308 * q^51 - 216 * q^54 + 2736 * q^56 + 2088 * q^59 + 1284 * q^61 - 2332 * q^64 + 264 * q^66 - 1200 * q^69 - 1088 * q^71 - 3072 * q^74 + 3992 * q^76 + 3172 * q^79 + 486 * q^81 - 2040 * q^84 + 7136 * q^86 + 4244 * q^89 - 16 * q^91 + 4304 * q^94 + 4128 * q^96 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	− 2.32906i	− 0.823448i	−0.911309	−	0.411724i	$-0.864927\pi$
$2$	− 2.32906i	− 0.823448i	0.911309	−	0.411724i	$-0.135073\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	2.57547	0.321933
$5$	0	0
$5$	0	0
$6$	6.98719	0.475418
$7$	22.4672i	1.21311i	0.795040	+	0.606557i	$0.207450\pi$
$7$	22.4672i	1.21311i	−0.795040	+	0.606557i	$0.792550\pi$
$8$	− 24.6309i	− 1.08854i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	7.72640i	0.185868i
$13$	9.86030i	0.210366i	0.994453	+	0.105183i	$0.0335428\pi$
$13$	9.86030i	0.210366i	−0.994453	+	0.105183i	$0.966457\pi$
$14$	52.3275	0.998936
$15$	0	0
$16$	−36.7633	−0.574426
$17$	− 128.137i	− 1.82810i	−0.405603	−	0.914049i	$-0.632938\pi$
$17$	− 128.137i	− 1.82810i	0.405603	−	0.914049i	$-0.367062\pi$
$18$	20.9616i	0.274483i
$19$	−7.04001	−0.0850047	−0.0425024	−	0.999096i	$-0.513533\pi$
$19$	−7.04001	−0.0850047	−0.0425024	+	0.999096i	$0.513533\pi$
$20$	0	0
$21$	−67.4015	−0.700392
$22$	− 25.6197i	− 0.248279i
$23$	− 0.654969i	− 0.00593785i	−0.999996	−	0.00296892i	$-0.999055\pi$
$23$	− 0.654969i	− 0.00593785i	0.999996	−	0.00296892i	$-0.000945039\pi$
$24$	73.8928	0.628471
$25$	0	0
$26$	22.9653	0.173225
$27$	− 27.0000i	− 0.192450i
$28$	57.8635i	0.390542i
$29$	229.279	1.46814	0.734069	−	0.679075i	$-0.237619\pi$
$29$	229.279	1.46814	0.734069	+	0.679075i	$0.237619\pi$
$30$	0	0
$31$	155.789	0.902596	0.451298	−	0.892373i	$-0.350961\pi$
$31$	155.789	0.902596	0.451298	+	0.892373i	$0.350961\pi$
$32$	− 111.423i	− 0.615534i
$33$	33.0000i	0.174078i
$34$	−298.438	−1.50534
$35$	0	0
$36$	−23.1792	−0.107311
$37$	− 110.279i	− 0.489995i	−0.969524	−	0.244998i	$-0.921213\pi$
$37$	− 110.279i	− 0.489995i	0.969524	−	0.244998i	$-0.0787872\pi$
$38$	16.3966i	0.0699970i
$39$	−29.5809	−0.121455
$40$	0	0
$41$	154.749	0.589456	0.294728	−	0.955581i	$-0.404771\pi$
$41$	154.749	0.589456	0.294728	+	0.955581i	$0.404771\pi$
$42$	156.982i	0.576736i
$43$	401.014i	1.42219i	0.703097	+	0.711094i	$0.251800\pi$
$43$	401.014i	1.42219i	−0.703097	+	0.711094i	$0.748200\pi$
$44$	28.3301	0.0970665
$45$	0	0
$46$	−1.52546	−0.00488951
$47$	− 277.532i	− 0.861323i	−0.902514	−	0.430661i	$-0.858280\pi$
$47$	− 277.532i	− 0.861323i	0.902514	−	0.430661i	$-0.141720\pi$
$48$	− 110.290i	− 0.331645i
$49$	−161.774	−0.471645
$50$	0	0
$51$	384.410	1.05545
$52$	25.3949i	0.0677237i
$53$	651.566i	1.68867i	0.535817	+	0.844334i	$0.320004\pi$
$53$	651.566i	1.68867i	−0.535817	+	0.844334i	$0.679996\pi$
$54$	−62.8847	−0.158473
$55$	0	0
$56$	553.388	1.32053
$57$	− 21.1200i	− 0.0490775i
$58$	− 534.005i	− 1.20894i
$59$	423.869	0.935307	0.467653	−	0.883912i	$-0.345100\pi$
$59$	423.869	0.935307	0.467653	+	0.883912i	$0.345100\pi$
$60$	0	0
$61$	681.851	1.43118	0.715590	−	0.698520i	$-0.246158\pi$
$61$	681.851	1.43118	0.715590	+	0.698520i	$0.246158\pi$
$62$	− 362.842i	− 0.743241i
$63$	− 202.205i	− 0.404371i
$64$	−553.618	−1.08129
$65$	0	0
$66$	76.8591	0.143344
$67$	374.028i	0.682012i	0.940061	+	0.341006i	$0.110768\pi$
$67$	374.028i	0.682012i	−0.940061	+	0.341006i	$0.889232\pi$
$68$	− 330.011i	− 0.588526i
$69$	1.96491	0.00342822
$70$	0	0
$71$	96.6950	0.161628	0.0808140	−	0.996729i	$-0.474248\pi$
$71$	96.6950	0.161628	0.0808140	+	0.996729i	$0.474248\pi$
$72$	221.678i	0.362848i
$73$	19.9460i	0.0319795i	0.999872	+	0.0159897i	$0.00508991\pi$
$73$	19.9460i	0.0319795i	−0.999872	+	0.0159897i	$0.994910\pi$
$74$	−256.848	−0.403486
$75$	0	0
$76$	−18.1313	−0.0273658
$77$	247.139i	0.365768i
$78$	68.8958i	0.100012i
$79$	−24.4286	−0.0347903	−0.0173951	−	0.999849i	$-0.505537\pi$
$79$	−24.4286	−0.0347903	−0.0173951	+	0.999849i	$0.505537\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 360.419i	− 0.485386i
$83$	1127.35i	1.49088i	0.666574	+	0.745439i	$0.267760\pi$
$83$	1127.35i	1.49088i	−0.666574	+	0.745439i	$0.732240\pi$
$84$	−173.590	−0.225479
$85$	0	0
$86$	933.987	1.17110
$87$	687.836i	0.847630i
$88$	− 270.940i	− 0.328208i
$89$	639.624	0.761798	0.380899	−	0.924617i	$-0.375615\pi$
$89$	639.624	0.761798	0.380899	+	0.924617i	$0.375615\pi$
$90$	0	0
$91$	−221.533	−0.255198
$92$	− 1.68685i	− 0.00191159i
$93$	467.366i	0.521114i
$94$	−646.389	−0.709255
$95$	0	0
$96$	334.270	0.355378
$97$	− 730.865i	− 0.765032i	−0.923949	−	0.382516i	$-0.875058\pi$
$97$	− 730.865i	− 0.765032i	0.923949	−	0.382516i	$-0.124942\pi$
$98$	376.783i	0.388375i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	−810.342	−0.798337	−0.399168	−	0.916878i	$-0.630701\pi$
$101$	−810.342	−0.798337	−0.399168	+	0.916878i	$0.630701\pi$
$102$	− 895.314i	− 0.869111i
$103$	1461.89i	1.39849i	0.714882	+	0.699245i	$0.246480\pi$
$103$	1461.89i	1.39849i	−0.714882	+	0.699245i	$0.753520\pi$
$104$	242.868	0.228992
$105$	0	0
$106$	1517.54	1.39053
$107$	1690.40i	1.52726i	0.645654	+	0.763630i	$0.276585\pi$
$107$	1690.40i	1.52726i	−0.645654	+	0.763630i	$0.723415\pi$
$108$	− 69.5376i	− 0.0619561i
$109$	1409.41	1.23851	0.619254	−	0.785190i	$-0.287435\pi$
$109$	1409.41	1.23851	0.619254	+	0.785190i	$0.287435\pi$
$110$	0	0
$111$	330.838	0.282899
$112$	− 825.967i	− 0.696844i
$113$	− 2185.67i	− 1.81956i	−0.415090	−	0.909780i	$-0.636250\pi$
$113$	− 2185.67i	− 1.81956i	0.415090	−	0.909780i	$-0.363750\pi$
$114$	−49.1899	−0.0404128
$115$	0	0
$116$	590.499	0.472642
$117$	− 88.7427i	− 0.0701219i
$118$	− 987.219i	− 0.770177i
$119$	2878.87	2.21769
$120$	0	0
$121$	121.000	0.0909091
$122$	− 1588.07i	− 1.17850i
$123$	464.246i	0.340322i
$124$	401.228	0.290576
$125$	0	0
$126$	−470.947	−0.332979
$127$	− 1918.85i	− 1.34071i	−0.742038	−	0.670357i	$-0.766141\pi$
$127$	− 1918.85i	− 1.34071i	0.742038	−	0.670357i	$-0.233859\pi$
$128$	398.024i	0.274849i
$129$	−1203.04	−0.821100
$130$	0	0
$131$	1339.41	0.893320	0.446660	−	0.894704i	$-0.352613\pi$
$131$	1339.41	0.893320	0.446660	+	0.894704i	$0.352613\pi$
$132$	84.9904i	0.0560414i
$133$	− 158.169i	− 0.103120i
$134$	871.135	0.561602
$135$	0	0
$136$	−3156.12	−1.98996
$137$	− 1100.56i	− 0.686330i	−0.939275	−	0.343165i	$-0.888501\pi$
$137$	− 1100.56i	− 0.686330i	0.939275	−	0.343165i	$-0.111499\pi$
$138$	− 4.57639i	− 0.00282296i
$139$	1284.51	0.783819	0.391910	−	0.920004i	$-0.371815\pi$
$139$	1284.51	0.783819	0.391910	+	0.920004i	$0.371815\pi$
$140$	0	0
$141$	832.595	0.497285
$142$	− 225.209i	− 0.133092i
$143$	108.463i	0.0634277i
$144$	330.869	0.191475
$145$	0	0
$146$	46.4554	0.0263334
$147$	− 485.323i	− 0.272305i
$148$	− 284.021i	− 0.157746i
$149$	−1277.21	−0.702236	−0.351118	−	0.936331i	$-0.614198\pi$
$149$	−1277.21	−0.702236	−0.351118	+	0.936331i	$0.614198\pi$
$150$	0	0
$151$	886.317	0.477665	0.238833	−	0.971061i	$-0.423235\pi$
$151$	886.317	0.477665	0.238833	+	0.971061i	$0.423235\pi$
$152$	173.402i	0.0925313i
$153$	1153.23i	0.609366i
$154$	575.602	0.301191
$155$	0	0
$156$	−76.1846	−0.0391003
$157$	− 1681.12i	− 0.854575i	−0.904116	−	0.427288i	$-0.859469\pi$
$157$	− 1681.12i	− 0.854575i	0.904116	−	0.427288i	$-0.140531\pi$
$158$	56.8958i	0.0286480i
$159$	−1954.70	−0.974953
$160$	0	0
$161$	14.7153	0.00720329
$162$	− 188.654i	− 0.0914942i
$163$	622.100i	0.298937i	0.988767	+	0.149468i	$0.0477562\pi$
$163$	622.100i	0.298937i	−0.988767	+	0.149468i	$0.952244\pi$
$164$	398.550	0.189765
$165$	0	0
$166$	2625.67	1.22766
$167$	− 2611.82i	− 1.21023i	−0.796138	−	0.605115i	$-0.793127\pi$
$167$	− 2611.82i	− 1.21023i	0.796138	−	0.605115i	$-0.206873\pi$
$168$	1660.16i	0.762407i
$169$	2099.77	0.955746
$170$	0	0
$171$	63.3601	0.0283349
$172$	1032.80i	0.457849i
$173$	− 2342.97i	− 1.02967i	−0.857290	−	0.514835i	$-0.827853\pi$
$173$	− 2342.97i	− 1.02967i	0.857290	−	0.514835i	$-0.172147\pi$
$174$	1602.01	0.697979
$175$	0	0
$176$	−404.396	−0.173196
$177$	1271.61i	0.540000i
$178$	− 1489.72i	− 0.627301i
$179$	−1314.75	−0.548991	−0.274495	−	0.961588i	$-0.588511\pi$
$179$	−1314.75	−0.548991	−0.274495	+	0.961588i	$0.588511\pi$
$180$	0	0
$181$	8.69006	0.00356866	0.00178433	−	0.999998i	$-0.499432\pi$
$181$	8.69006	0.00356866	0.00178433	+	0.999998i	$0.499432\pi$
$182$	515.965i	0.210142i
$183$	2045.55i	0.826292i
$184$	−16.1325	−0.00646361
$185$	0	0
$186$	1088.53	0.429110
$187$	− 1409.50i	− 0.551192i
$188$	− 714.774i	− 0.277288i
$189$	606.614	0.233464
$190$	0	0
$191$	644.102	0.244008	0.122004	−	0.992530i	$-0.461068\pi$
$191$	644.102	0.244008	0.122004	+	0.992530i	$0.461068\pi$
$192$	− 1660.85i	− 0.624281i
$193$	− 3970.76i	− 1.48094i	−0.672089	−	0.740470i	$-0.734603\pi$
$193$	− 3970.76i	− 1.48094i	0.672089	−	0.740470i	$-0.265397\pi$
$194$	−1702.23	−0.629964
$195$	0	0
$196$	−416.644	−0.151838
$197$	3756.34i	1.35852i	0.733898	+	0.679260i	$0.237699\pi$
$197$	3756.34i	1.35852i	−0.733898	+	0.679260i	$0.762301\pi$
$198$	230.577i	0.0827596i
$199$	−4825.48	−1.71894	−0.859470	−	0.511186i	$-0.829206\pi$
$199$	−4825.48	−1.71894	−0.859470	+	0.511186i	$0.829206\pi$
$200$	0	0
$201$	−1122.08	−0.393760
$202$	1887.34i	0.657389i
$203$	5151.25i	1.78102i
$204$	990.034	0.339785
$205$	0	0
$206$	3404.84	1.15158
$207$	5.89472i	0.00197928i
$208$	− 362.497i	− 0.120840i
$209$	−77.4401	−0.0256299
$210$	0	0
$211$	−4394.02	−1.43363	−0.716817	−	0.697261i	$-0.754402\pi$
$211$	−4394.02	−1.43363	−0.716817	+	0.697261i	$0.754402\pi$
$212$	1678.08i	0.543638i
$213$	290.085i	0.0933160i
$214$	3937.04	1.25762
$215$	0	0
$216$	−665.035	−0.209490
$217$	3500.13i	1.09495i
$218$	− 3282.62i	− 1.01985i
$219$	−59.8379	−0.0184633
$220$	0	0
$221$	1263.46	0.384569
$222$	− 770.543i	− 0.232953i
$223$	− 2189.67i	− 0.657538i	−0.944410	−	0.328769i	$-0.893366\pi$
$223$	− 2189.67i	− 0.657538i	0.944410	−	0.328769i	$-0.106634\pi$
$224$	2503.37	0.746712
$225$	0	0
$226$	−5090.56	−1.49831
$227$	− 1139.27i	− 0.333110i	−0.986032	−	0.166555i	$-0.946736\pi$
$227$	− 1139.27i	− 0.333110i	0.986032	−	0.166555i	$-0.0532643\pi$
$228$	− 54.3939i	− 0.0157997i
$229$	−3416.10	−0.985773	−0.492886	−	0.870094i	$-0.664058\pi$
$229$	−3416.10	−0.985773	−0.492886	+	0.870094i	$0.664058\pi$
$230$	0	0
$231$	−741.417	−0.211176
$232$	− 5647.35i	− 1.59813i
$233$	− 6147.08i	− 1.72836i	−0.503181	−	0.864181i	$-0.667837\pi$
$233$	− 6147.08i	− 1.72836i	0.503181	−	0.864181i	$-0.332163\pi$
$234$	−206.687	−0.0577418
$235$	0	0
$236$	1091.66	0.301106
$237$	− 73.2858i	− 0.0200862i
$238$	− 6705.06i	− 1.82615i
$239$	2080.03	0.562954	0.281477	−	0.959568i	$-0.409176\pi$
$239$	2080.03	0.562954	0.281477	+	0.959568i	$0.409176\pi$
$240$	0	0
$241$	1846.28	0.493484	0.246742	−	0.969081i	$-0.420640\pi$
$241$	1846.28	0.493484	0.246742	+	0.969081i	$0.420640\pi$
$242$	− 281.817i	− 0.0748589i
$243$	243.000i	0.0641500i
$244$	1756.08	0.460745
$245$	0	0
$246$	1081.26	0.280238
$247$	− 69.4166i	− 0.0178821i
$248$	− 3837.22i	− 0.982515i
$249$	−3382.05	−0.860758
$250$	0	0
$251$	−2555.32	−0.642592	−0.321296	−	0.946979i	$-0.604118\pi$
$251$	−2555.32	−0.642592	−0.321296	+	0.946979i	$0.604118\pi$
$252$	− 520.771i	− 0.130181i
$253$	− 7.20466i	− 0.00179033i
$254$	−4469.13	−1.10401
$255$	0	0
$256$	−3501.92	−0.854962
$257$	− 1819.39i	− 0.441598i	−0.975319	−	0.220799i	$-0.929134\pi$
$257$	− 1819.39i	− 0.441598i	0.975319	−	0.220799i	$-0.0708664\pi$
$258$	2801.96i	0.676134i
$259$	2477.67	0.594420
$260$	0	0
$261$	−2063.51	−0.489379
$262$	− 3119.57i	− 0.735603i
$263$	6023.03i	1.41215i	0.708136	+	0.706076i	$0.249536\pi$
$263$	6023.03i	1.41215i	−0.708136	+	0.706076i	$0.750464\pi$
$264$	812.821	0.189491
$265$	0	0
$266$	−368.386	−0.0849143
$267$	1918.87i	0.439824i
$268$	963.297i	0.219562i
$269$	2978.38	0.675075	0.337537	−	0.941312i	$-0.390406\pi$
$269$	2978.38	0.675075	0.337537	+	0.941312i	$0.390406\pi$
$270$	0	0
$271$	−524.969	−0.117674	−0.0588369	−	0.998268i	$-0.518739\pi$
$271$	−524.969	−0.117674	−0.0588369	+	0.998268i	$0.518739\pi$
$272$	4710.72i	1.05011i
$273$	− 664.600i	− 0.147338i
$274$	−2563.28	−0.565157
$275$	0	0
$276$	5.06055	0.00110366
$277$	− 1693.07i	− 0.367245i	−0.982997	−	0.183623i	$-0.941218\pi$
$277$	− 1693.07i	− 0.367245i	0.982997	−	0.183623i	$-0.0587824\pi$
$278$	− 2991.71i	− 0.645435i
$279$	−1402.10	−0.300865
$280$	0	0
$281$	7346.60	1.55965	0.779824	−	0.625998i	$-0.215308\pi$
$281$	7346.60	1.55965	0.779824	+	0.625998i	$0.215308\pi$
$282$	− 1939.17i	− 0.409488i
$283$	1501.69i	0.315429i	0.987485	+	0.157714i	$0.0504125\pi$
$283$	1501.69i	0.315429i	−0.987485	+	0.157714i	$0.949587\pi$
$284$	249.035	0.0520334
$285$	0	0
$286$	252.618	0.0522294
$287$	3476.77i	0.715077i
$288$	1002.81i	0.205178i
$289$	−11506.0	−2.34194
$290$	0	0
$291$	2192.59	0.441691
$292$	51.3702i	0.0102952i
$293$	4481.03i	0.893462i	0.894668	+	0.446731i	$0.147412\pi$
$293$	4481.03i	0.893462i	−0.894668	+	0.446731i	$0.852588\pi$
$294$	−1130.35	−0.224229
$295$	0	0
$296$	−2716.28	−0.533381
$297$	− 297.000i	− 0.0580259i
$298$	2974.71i	0.578255i
$299$	6.45819	0.00124912
$300$	0	0
$301$	−9009.66	−1.72528
$302$	− 2064.29i	− 0.393333i
$303$	− 2431.02i	− 0.460920i
$304$	258.814	0.0488289
$305$	0	0
$306$	2685.94	0.501781
$307$	3052.17i	0.567416i	0.958911	+	0.283708i	$0.0915646\pi$
$307$	3052.17i	0.567416i	−0.958911	+	0.283708i	$0.908435\pi$
$308$	636.498i	0.117753i
$309$	−4385.67	−0.807418
$310$	0	0
$311$	10255.1	1.86983	0.934913	−	0.354878i	$-0.115477\pi$
$311$	10255.1	1.86983	0.934913	+	0.354878i	$0.115477\pi$
$312$	728.605i	0.132209i
$313$	6190.18i	1.11786i	0.829215	+	0.558929i	$0.188788\pi$
$313$	6190.18i	1.11786i	−0.829215	+	0.558929i	$0.811212\pi$
$314$	−3915.44	−0.703698
$315$	0	0
$316$	−62.9150	−0.0112001
$317$	− 6735.38i	− 1.19337i	−0.802477	−	0.596683i	$-0.796485\pi$
$317$	− 6735.38i	− 1.19337i	0.802477	−	0.596683i	$-0.203515\pi$
$318$	4552.61i	0.802823i
$319$	2522.07	0.442660
$320$	0	0
$321$	−5071.19	−0.881764
$322$	− 34.2729i	− 0.00593153i
$323$	902.083i	0.155397i
$324$	208.613	0.0357704
$325$	0	0
$326$	1448.91	0.246159
$327$	4228.24i	0.715053i
$328$	− 3811.60i	− 0.641648i
$329$	6235.36	1.04488
$330$	0	0
$331$	−4780.83	−0.793891	−0.396946	−	0.917842i	$-0.629930\pi$
$331$	−4780.83	−0.793891	−0.396946	+	0.917842i	$0.629930\pi$
$332$	2903.45i	0.479963i
$333$	992.515i	0.163332i
$334$	−6083.09	−0.996562
$335$	0	0
$336$	2477.90	0.402323
$337$	11890.3i	1.92197i	0.276604	+	0.960984i	$0.410791\pi$
$337$	11890.3i	1.92197i	−0.276604	+	0.960984i	$0.589209\pi$
$338$	− 4890.51i	− 0.787007i
$339$	6557.00	1.05052
$340$	0	0
$341$	1713.68	0.272143
$342$	− 147.570i	− 0.0233323i
$343$	4071.63i	0.640954i
$344$	9877.35	1.54811
$345$	0	0
$346$	−5456.93	−0.847879
$347$	8462.47i	1.30919i	0.755979	+	0.654595i	$0.227161\pi$
$347$	8462.47i	1.30919i	−0.755979	+	0.654595i	$0.772839\pi$
$348$	1771.50i	0.272880i
$349$	3291.90	0.504903	0.252452	−	0.967610i	$-0.418763\pi$
$349$	3291.90	0.504903	0.252452	+	0.967610i	$0.418763\pi$
$350$	0	0
$351$	266.228	0.0404849
$352$	− 1225.66i	− 0.185590i
$353$	8193.52i	1.23540i	0.786413	+	0.617701i	$0.211936\pi$
$353$	8193.52i	1.23540i	−0.786413	+	0.617701i	$0.788064\pi$
$354$	2961.66	0.444662
$355$	0	0
$356$	1647.33	0.245248
$357$	8636.60i	1.28038i
$358$	3062.15i	0.452066i
$359$	−12817.6	−1.88437	−0.942185	−	0.335093i	$-0.891232\pi$
$359$	−12817.6	−1.88437	−0.942185	+	0.335093i	$0.891232\pi$
$360$	0	0
$361$	−6809.44	−0.992774
$362$	− 20.2397i	− 0.00293861i
$363$	363.000i	0.0524864i
$364$	−570.551	−0.0821566
$365$	0	0
$366$	4764.22	0.680409
$367$	− 2801.22i	− 0.398427i	−0.979956	−	0.199213i	$-0.936161\pi$
$367$	− 2801.22i	− 0.398427i	0.979956	−	0.199213i	$-0.0638387\pi$
$368$	24.0788i	0.00341085i
$369$	−1392.74	−0.196485
$370$	0	0
$371$	−14638.8	−2.04855
$372$	1203.69i	0.167764i
$373$	− 6838.03i	− 0.949222i	−0.880196	−	0.474611i	$-0.842589\pi$
$373$	− 6838.03i	− 0.949222i	0.880196	−	0.474611i	$-0.157411\pi$
$374$	−3282.82	−0.453878
$375$	0	0
$376$	−6835.86	−0.937587
$377$	2260.76i	0.308846i
$378$	− 1412.84i	− 0.192245i
$379$	7465.79	1.01185	0.505926	−	0.862577i	$-0.331151\pi$
$379$	7465.79	1.01185	0.505926	+	0.862577i	$0.331151\pi$
$380$	0	0
$381$	5756.56	0.774062
$382$	− 1500.16i	− 0.200928i
$383$	8646.55i	1.15357i	0.816895	+	0.576786i	$0.195693\pi$
$383$	8646.55i	1.15357i	−0.816895	+	0.576786i	$0.804307\pi$
$384$	−1194.07	−0.158684
$385$	0	0
$386$	−9248.15	−1.21948
$387$	− 3609.13i	− 0.474063i
$388$	− 1882.32i	− 0.246289i
$389$	−4382.78	−0.571248	−0.285624	−	0.958342i	$-0.592201\pi$
$389$	−4382.78	−0.571248	−0.285624	+	0.958342i	$0.592201\pi$
$390$	0	0
$391$	−83.9255	−0.0108550
$392$	3984.65i	0.513406i
$393$	4018.24i	0.515759i
$394$	8748.76	1.11867
$395$	0	0
$396$	−254.971	−0.0323555
$397$	− 4432.58i	− 0.560365i	−0.959947	−	0.280182i	$-0.909605\pi$
$397$	− 4432.58i	− 0.560365i	0.959947	−	0.280182i	$-0.0903950\pi$
$398$	11238.8i	1.41546i
$399$	474.508	0.0595366
$400$	0	0
$401$	−5034.93	−0.627013	−0.313507	−	0.949586i	$-0.601504\pi$
$401$	−5034.93	−0.627013	−0.313507	+	0.949586i	$0.601504\pi$
$402$	2613.41i	0.324241i
$403$	1536.12i	0.189875i
$404$	−2087.01	−0.257011
$405$	0	0
$406$	11997.6	1.46658
$407$	− 1213.07i	− 0.147739i
$408$	− 9468.36i	− 1.14891i
$409$	−6474.64	−0.782764	−0.391382	−	0.920228i	$-0.628003\pi$
$409$	−6474.64	−0.782764	−0.391382	+	0.920228i	$0.628003\pi$
$410$	0	0
$411$	3301.68	0.396253
$412$	3765.05i	0.450220i
$413$	9523.15i	1.13463i
$414$	13.7292	0.00162984
$415$	0	0
$416$	1098.67	0.129487
$417$	3853.54i	0.452538i
$418$	180.363i	0.0211049i
$419$	8257.80	0.962816	0.481408	−	0.876497i	$-0.340126\pi$
$419$	8257.80	0.962816	0.481408	+	0.876497i	$0.340126\pi$
$420$	0	0
$421$	−3429.36	−0.397000	−0.198500	−	0.980101i	$-0.563607\pi$
$421$	−3429.36	−0.397000	−0.198500	+	0.980101i	$0.563607\pi$
$422$	10233.9i	1.18052i
$423$	2497.79i	0.287108i
$424$	16048.7	1.83819
$425$	0	0
$426$	675.626	0.0768408
$427$	15319.3i	1.73618i
$428$	4353.56i	0.491676i
$429$	−325.390	−0.0366200
$430$	0	0
$431$	−11260.4	−1.25846	−0.629230	−	0.777219i	$-0.716630\pi$
$431$	−11260.4	−1.25846	−0.629230	+	0.777219i	$0.716630\pi$
$432$	992.608i	0.110548i
$433$	− 12598.5i	− 1.39826i	−0.714996	−	0.699128i	$-0.753572\pi$
$433$	− 12598.5i	− 1.39826i	0.714996	−	0.699128i	$-0.246428\pi$
$434$	8152.03	0.901636
$435$	0	0
$436$	3629.90	0.398717
$437$	4.61099i	0 0.000504745i
$438$	139.366i	0.0152036i
$439$	−4176.90	−0.454106	−0.227053	−	0.973882i	$-0.572909\pi$
$439$	−4176.90	−0.454106	−0.227053	+	0.973882i	$0.572909\pi$
$440$	0	0
$441$	1455.97	0.157215
$442$	− 2942.69i	− 0.316673i
$443$	− 2354.16i	− 0.252482i	−0.992000	−	0.126241i	$-0.959709\pi$
$443$	− 2354.16i	− 0.252482i	0.992000	−	0.126241i	$-0.0402913\pi$
$444$	852.062	0.0910745
$445$	0	0
$446$	−5099.88	−0.541449
$447$	− 3831.63i	− 0.405436i
$448$	− 12438.2i	− 1.31172i
$449$	−9286.18	−0.976040	−0.488020	−	0.872832i	$-0.662281\pi$
$449$	−9286.18	−0.976040	−0.488020	+	0.872832i	$0.662281\pi$
$450$	0	0
$451$	1702.24	0.177728
$452$	− 5629.11i	− 0.585777i
$453$	2658.95i	0.275780i
$454$	−2653.43	−0.274299
$455$	0	0
$456$	−520.206	−0.0534230
$457$	14378.4i	1.47176i	0.677115	+	0.735878i	$0.263230\pi$
$457$	14378.4i	1.47176i	−0.677115	+	0.735878i	$0.736770\pi$
$458$	7956.30i	0.811733i
$459$	−3459.69	−0.351818
$460$	0	0
$461$	−5383.19	−0.543861	−0.271931	−	0.962317i	$-0.587662\pi$
$461$	−5383.19	−0.543861	−0.271931	+	0.962317i	$0.587662\pi$
$462$	1726.81i	0.173892i
$463$	− 18360.5i	− 1.84294i	−0.388446	−	0.921471i	$-0.626988\pi$
$463$	− 18360.5i	− 1.84294i	0.388446	−	0.921471i	$-0.373012\pi$
$464$	−8429.03	−0.843336
$465$	0	0
$466$	−14316.9	−1.42322
$467$	9063.65i	0.898106i	0.893505	+	0.449053i	$0.148239\pi$
$467$	9063.65i	0.898106i	−0.893505	+	0.449053i	$0.851761\pi$
$468$	− 228.554i	− 0.0225746i
$469$	−8403.36	−0.827358
$470$	0	0
$471$	5043.37	0.493389
$472$	− 10440.3i	− 1.01812i
$473$	4411.15i	0.428806i
$474$	−170.687	−0.0165399
$475$	0	0
$476$	7414.42	0.713949
$477$	− 5864.09i	− 0.562889i
$478$	− 4844.53i	− 0.463564i
$479$	−12608.2	−1.20268	−0.601341	−	0.798992i	$-0.705367\pi$
$479$	−12608.2	−1.20268	−0.601341	+	0.798992i	$0.705367\pi$
$480$	0	0
$481$	1087.39	0.103078
$482$	− 4300.11i	− 0.406358i
$483$	44.1459i	0.00415882i
$484$	311.631	0.0292667
$485$	0	0
$486$	565.962	0.0528242
$487$	− 13214.2i	− 1.22955i	−0.788703	−	0.614775i	$-0.789247\pi$
$487$	− 13214.2i	− 1.22955i	0.788703	−	0.614775i	$-0.210753\pi$
$488$	− 16794.6i	− 1.55790i
$489$	−1866.30	−0.172591
$490$	0	0
$491$	6553.27	0.602332	0.301166	−	0.953572i	$-0.402624\pi$
$491$	6553.27	0.602332	0.301166	+	0.953572i	$0.402624\pi$
$492$	1195.65i	0.109561i
$493$	− 29379.0i	− 2.68390i
$494$	−161.676	−0.0147250
$495$	0	0
$496$	−5727.30	−0.518474
$497$	2172.46i	0.196073i
$498$	7877.01i	0.708790i
$499$	2596.63	0.232948	0.116474	−	0.993194i	$-0.462841\pi$
$499$	2596.63	0.232948	0.116474	+	0.993194i	$0.462841\pi$
$500$	0	0
$501$	7835.45	0.698727
$502$	5951.51i	0.529141i
$503$	659.714i	0.0584795i	0.999572	+	0.0292398i	$0.00930863\pi$
$503$	659.714i	0.0584795i	−0.999572	+	0.0292398i	$0.990691\pi$
$504$	−4980.49	−0.440176
$505$	0	0
$506$	−16.7801	−0.00147424
$507$	6299.32i	0.551800i
$508$	− 4941.94i	− 0.431621i
$509$	−4825.41	−0.420201	−0.210101	−	0.977680i	$-0.567379\pi$
$509$	−4825.41	−0.420201	−0.210101	+	0.977680i	$0.567379\pi$
$510$	0	0
$511$	−448.130	−0.0387947
$512$	11340.4i	0.978866i
$513$	190.080i	0.0163592i
$514$	−4237.48	−0.363633
$515$	0	0
$516$	−3098.39	−0.264339
$517$	− 3052.85i	− 0.259699i
$518$	− 5770.64i	− 0.489474i
$519$	7028.91	0.594480
$520$	0	0
$521$	−2329.24	−0.195866	−0.0979328	−	0.995193i	$-0.531223\pi$
$521$	−2329.24	−0.195866	−0.0979328	+	0.995193i	$0.531223\pi$
$522$	4806.04i	0.402978i
$523$	15104.6i	1.26287i	0.775429	+	0.631434i	$0.217533\pi$
$523$	15104.6i	1.26287i	−0.775429	+	0.631434i	$0.782467\pi$
$524$	3449.61	0.287589
$525$	0	0
$526$	14028.0	1.16283
$527$	− 19962.2i	− 1.65003i
$528$	− 1213.19i	− 0.0999947i
$529$	12166.6	0.999965
$530$	0	0
$531$	−3814.82	−0.311769
$532$	− 407.359i	− 0.0331979i
$533$	1525.87i	0.124001i
$534$	4469.17	0.362172
$535$	0	0
$536$	9212.66	0.742400
$537$	− 3944.26i	− 0.316960i
$538$	− 6936.84i	− 0.555889i
$539$	−1779.52	−0.142206
$540$	0	0
$541$	10712.1	0.851293	0.425647	−	0.904889i	$-0.360047\pi$
$541$	10712.1	0.851293	0.425647	+	0.904889i	$0.360047\pi$
$542$	1222.69i	0.0968983i
$543$	26.0702i	0.00206037i
$544$	−14277.4	−1.12526
$545$	0	0
$546$	−1547.89	−0.121326
$547$	− 17251.6i	− 1.34849i	−0.738508	−	0.674245i	$-0.764469\pi$
$547$	− 17251.6i	− 1.34849i	0.738508	−	0.674245i	$-0.235531\pi$
$548$	− 2834.46i	− 0.220953i
$549$	−6136.65	−0.477060
$550$	0	0
$551$	−1614.12	−0.124799
$552$	− 48.3975i	− 0.00373177i
$553$	− 548.842i	− 0.0422046i
$554$	−3943.27	−0.302407
$555$	0	0
$556$	3308.22	0.252337
$557$	− 8179.34i	− 0.622208i	−0.950376	−	0.311104i	$-0.899301\pi$
$557$	− 8179.34i	− 0.622208i	0.950376	−	0.311104i	$-0.100699\pi$
$558$	3265.58i	0.247747i
$559$	−3954.12	−0.299180
$560$	0	0
$561$	4228.51	0.318231
$562$	− 17110.7i	− 1.28429i
$563$	− 4939.38i	− 0.369752i	−0.982762	−	0.184876i	$-0.940812\pi$
$563$	− 4939.38i	− 0.369752i	0.982762	−	0.184876i	$-0.0591883\pi$
$564$	2144.32	0.160093
$565$	0	0
$566$	3497.54	0.259739
$567$	1819.84i	0.134790i
$568$	− 2381.69i	− 0.175939i
$569$	7658.76	0.564274	0.282137	−	0.959374i	$-0.408957\pi$
$569$	7658.76	0.564274	0.282137	+	0.959374i	$0.408957\pi$
$570$	0	0
$571$	−1744.16	−0.127830	−0.0639149	−	0.997955i	$-0.520359\pi$
$571$	−1744.16	−0.127830	−0.0639149	+	0.997955i	$0.520359\pi$
$572$	279.344i	0.0204195i
$573$	1932.31i	0.140878i
$574$	8097.61	0.588829
$575$	0	0
$576$	4982.56	0.360429
$577$	1264.61i	0.0912414i	0.998959	+	0.0456207i	$0.0145266\pi$
$577$	1264.61i	0.0912414i	−0.998959	+	0.0456207i	$0.985473\pi$
$578$	26798.1i	1.92847i
$579$	11912.3	0.855022
$580$	0	0
$581$	−25328.4	−1.80860
$582$	− 5106.69i	− 0.363710i
$583$	7167.22i	0.509153i
$584$	491.288	0.0348110
$585$	0	0
$586$	10436.6	0.735720
$587$	− 17167.4i	− 1.20711i	−0.797320	−	0.603557i	$-0.793750\pi$
$587$	− 17167.4i	− 1.20711i	0.797320	−	0.603557i	$-0.206250\pi$
$588$	− 1249.93i	− 0.0876639i
$589$	−1096.75	−0.0767249
$590$	0	0
$591$	−11269.0	−0.784342
$592$	4054.23i	0.281466i
$593$	21429.5i	1.48399i	0.670406	+	0.741995i	$0.266120\pi$
$593$	21429.5i	1.48399i	−0.670406	+	0.741995i	$0.733880\pi$
$594$	−691.732	−0.0477813
$595$	0	0
$596$	−3289.41	−0.226073
$597$	− 14476.4i	− 0.992431i
$598$	− 15.0415i	− 0.00102859i
$599$	7994.61	0.545327	0.272664	−	0.962109i	$-0.412095\pi$
$599$	7994.61	0.545327	0.272664	+	0.962109i	$0.412095\pi$
$600$	0	0
$601$	−24313.4	−1.65019	−0.825094	−	0.564996i	$-0.808878\pi$
$601$	−24313.4	−1.65019	−0.825094	+	0.564996i	$0.808878\pi$
$602$	20984.1i	1.42067i
$603$	− 3366.25i	− 0.227337i
$604$	2282.68	0.153776
$605$	0	0
$606$	−5662.01	−0.379544
$607$	24569.7i	1.64292i	0.570266	+	0.821460i	$0.306840\pi$
$607$	24569.7i	1.64292i	−0.570266	+	0.821460i	$0.693160\pi$
$608$	784.423i	0.0523232i
$609$	−15453.7	−1.02827
$610$	0	0
$611$	2736.55	0.181193
$612$	2970.10i	0.196175i
$613$	12746.7i	0.839859i	0.907557	+	0.419929i	$0.137945\pi$
$613$	12746.7i	0.839859i	−0.907557	+	0.419929i	$0.862055\pi$
$614$	7108.70	0.467237
$615$	0	0
$616$	6087.26	0.398154
$617$	− 15607.4i	− 1.01837i	−0.860658	−	0.509183i	$-0.829948\pi$
$617$	− 15607.4i	− 1.01837i	0.860658	−	0.509183i	$-0.170052\pi$
$618$	10214.5i	0.664867i
$619$	11909.7	0.773329	0.386665	−	0.922220i	$-0.373627\pi$
$619$	11909.7	0.773329	0.386665	+	0.922220i	$0.373627\pi$
$620$	0	0
$621$	−17.6842	−0.00114274
$622$	− 23884.9i	− 1.53970i
$623$	14370.5i	0.924147i
$624$	1087.49	0.0697667
$625$	0	0
$626$	14417.3	0.920499
$627$	− 232.320i	− 0.0147974i
$628$	− 4329.68i	− 0.275116i
$629$	−14130.8	−0.895759
$630$	0	0
$631$	−19304.2	−1.21789	−0.608946	−	0.793212i	$-0.708407\pi$
$631$	−19304.2	−1.21789	−0.608946	+	0.793212i	$0.708407\pi$
$632$	601.699i	0.0378707i
$633$	− 13182.1i	− 0.827709i
$634$	−15687.1	−0.982674
$635$	0	0
$636$	−5034.25	−0.313870
$637$	− 1595.14i	− 0.0992180i
$638$	− 5874.05i	− 0.364508i
$639$	−870.255	−0.0538760
$640$	0	0
$641$	26678.6	1.64390	0.821950	−	0.569560i	$-0.192886\pi$
$641$	26678.6	1.64390	0.821950	+	0.569560i	$0.192886\pi$
$642$	11811.1i	0.726087i
$643$	26456.2i	1.62260i	0.584631	+	0.811299i	$0.301239\pi$
$643$	26456.2i	1.62260i	−0.584631	+	0.811299i	$0.698761\pi$
$644$	37.8988	0.00231898
$645$	0	0
$646$	2101.01	0.127961
$647$	− 23523.7i	− 1.42939i	−0.699438	−	0.714694i	$-0.746566\pi$
$647$	− 23523.7i	− 1.42939i	0.699438	−	0.714694i	$-0.253434\pi$
$648$	− 1995.10i	− 0.120949i
$649$	4662.56	0.282006
$650$	0	0
$651$	−10500.4	−0.632171
$652$	1602.20i	0.0962376i
$653$	− 18071.1i	− 1.08296i	−0.840712	−	0.541482i	$-0.817863\pi$
$653$	− 18071.1i	− 1.08296i	0.840712	−	0.541482i	$-0.182137\pi$
$654$	9847.85	0.588809
$655$	0	0
$656$	−5689.07	−0.338599
$657$	− 179.514i	− 0.0106598i
$658$	− 14522.5i	− 0.860407i
$659$	−17023.1	−1.00626	−0.503130	−	0.864210i	$-0.667818\pi$
$659$	−17023.1	−1.00626	−0.503130	+	0.864210i	$0.667818\pi$
$660$	0	0
$661$	2137.74	0.125792	0.0628959	−	0.998020i	$-0.479966\pi$
$661$	2137.74	0.125792	0.0628959	+	0.998020i	$0.479966\pi$
$662$	11134.8i	0.653728i
$663$	3790.39i	0.222031i
$664$	27767.7	1.62288
$665$	0	0
$666$	2311.63	0.134495
$667$	− 150.171i	− 0.00871758i
$668$	− 6726.65i	− 0.389614i
$669$	6569.01	0.379630
$670$	0	0
$671$	7500.36	0.431517
$672$	7510.11i	0.431115i
$673$	− 31790.1i	− 1.82083i	−0.413698	−	0.910414i	$-0.635763\pi$
$673$	− 31790.1i	− 1.82083i	0.413698	−	0.910414i	$-0.364237\pi$
$674$	27693.1	1.58264
$675$	0	0
$676$	5407.90	0.307686
$677$	− 10225.1i	− 0.580476i	−0.956955	−	0.290238i	$-0.906266\pi$
$677$	− 10225.1i	− 0.580476i	0.956955	−	0.290238i	$-0.0937344\pi$
$678$	− 15271.7i	− 0.865052i
$679$	16420.5	0.928071
$680$	0	0
$681$	3417.81	0.192321
$682$	− 3991.26i	− 0.224096i
$683$	− 21274.0i	− 1.19184i	−0.803044	−	0.595919i	$-0.796788\pi$
$683$	− 21274.0i	− 1.19184i	0.803044	−	0.595919i	$-0.203212\pi$
$684$	163.182	0.00912195
$685$	0	0
$686$	9483.08	0.527793
$687$	− 10248.3i	− 0.569136i
$688$	− 14742.6i	− 0.816941i
$689$	−6424.63	−0.355238
$690$	0	0
$691$	−22568.1	−1.24245	−0.621224	−	0.783633i	$-0.713364\pi$
$691$	−22568.1	−1.24245	−0.621224	+	0.783633i	$0.713364\pi$
$692$	− 6034.24i	− 0.331485i
$693$	− 2224.25i	− 0.121923i
$694$	19709.6	1.07805
$695$	0	0
$696$	16942.0	0.922682
$697$	− 19829.0i	− 1.07758i
$698$	− 7667.03i	− 0.415761i
$699$	18441.2	0.997870
$700$	0	0
$701$	−7735.03	−0.416759	−0.208380	−	0.978048i	$-0.566819\pi$
$701$	−7735.03	−0.416759	−0.208380	+	0.978048i	$0.566819\pi$
$702$	− 620.062i	− 0.0333372i
$703$	776.368i	0.0416519i
$704$	−6089.80	−0.326020
$705$	0	0
$706$	19083.2	1.01729
$707$	− 18206.1i	− 0.968473i
$708$	3274.98i	0.173844i
$709$	−35115.1	−1.86005	−0.930025	−	0.367497i	$-0.880215\pi$
$709$	−35115.1	−1.86005	−0.930025	+	0.367497i	$0.880215\pi$
$710$	0	0
$711$	219.857	0.0115968
$712$	− 15754.5i	− 0.829250i
$713$	− 102.037i	− 0.00535948i
$714$	20115.2	1.05433
$715$	0	0
$716$	−3386.11	−0.176738
$717$	6240.10i	0.325022i
$718$	29853.1i	1.55168i
$719$	−15334.3	−0.795370	−0.397685	−	0.917522i	$-0.630186\pi$
$719$	−15334.3	−0.795370	−0.397685	+	0.917522i	$0.630186\pi$
$720$	0	0
$721$	−32844.6	−1.69653
$722$	15859.6i	0.817498i
$723$	5538.85i	0.284913i
$724$	22.3810	0.00114887
$725$	0	0
$726$	845.450	0.0432198
$727$	− 12360.4i	− 0.630567i	−0.948997	−	0.315284i	$-0.897900\pi$
$727$	− 12360.4i	− 0.630567i	0.948997	−	0.315284i	$-0.102100\pi$
$728$	5456.57i	0.277794i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	51384.6	2.59990
$732$	5268.25i	0.266011i
$733$	15097.6i	0.760769i	0.924828	+	0.380384i	$0.124208\pi$
$733$	15097.6i	0.760769i	−0.924828	+	0.380384i	$0.875792\pi$
$734$	−6524.23	−0.328084
$735$	0	0
$736$	−72.9790	−0.00365495
$737$	4114.31i	0.205634i
$738$	3243.78i	0.161795i
$739$	3667.49	0.182559	0.0912793	−	0.995825i	$-0.470904\pi$
$739$	3667.49	0.182559	0.0912793	+	0.995825i	$0.470904\pi$
$740$	0	0
$741$	208.250	0.0103242
$742$	34094.8i	1.68687i
$743$	− 10172.1i	− 0.502257i	−0.967954	−	0.251128i	$-0.919198\pi$
$743$	− 10172.1i	− 0.502257i	0.967954	−	0.251128i	$-0.0808016\pi$
$744$	11511.7	0.567255
$745$	0	0
$746$	−15926.2	−0.781635
$747$	− 10146.2i	− 0.496959i
$748$	− 3630.12i	− 0.177447i
$749$	−37978.5	−1.85274
$750$	0	0
$751$	31430.3	1.52718	0.763588	−	0.645704i	$-0.223436\pi$
$751$	31430.3	1.52718	0.763588	+	0.645704i	$0.223436\pi$
$752$	10203.0i	0.494766i
$753$	− 7665.97i	− 0.371000i
$754$	5265.45	0.254319
$755$	0	0
$756$	1562.31	0.0751598
$757$	− 28362.0i	− 1.36174i	−0.732406	−	0.680868i	$-0.761603\pi$
$757$	− 28362.0i	− 1.36174i	0.732406	−	0.680868i	$-0.238397\pi$
$758$	− 17388.3i	− 0.833207i
$759$	21.6140	0.00103365
$760$	0	0
$761$	30722.6	1.46346	0.731731	−	0.681594i	$-0.238713\pi$
$761$	30722.6	1.46346	0.731731	+	0.681594i	$0.238713\pi$
$762$	− 13407.4i	− 0.637400i
$763$	31665.6i	1.50245i
$764$	1658.86	0.0785544
$765$	0	0
$766$	20138.4	0.949906
$767$	4179.48i	0.196757i
$768$	− 10505.8i	− 0.493612i
$769$	18443.1	0.864855	0.432427	−	0.901669i	$-0.357657\pi$
$769$	18443.1	0.864855	0.432427	+	0.901669i	$0.357657\pi$
$770$	0	0
$771$	5458.18	0.254956
$772$	− 10226.6i	− 0.476764i
$773$	545.742i	0.0253932i	0.999919	+	0.0126966i	$0.00404156\pi$
$773$	545.742i	0.0253932i	−0.999919	+	0.0126966i	$0.995958\pi$
$774$	−8405.88	−0.390366
$775$	0	0
$776$	−18001.9	−0.832770
$777$	7433.00i	0.343189i
$778$	10207.8i	0.470393i
$779$	−1089.43	−0.0501065
$780$	0	0
$781$	1063.65	0.0487327
$782$	195.468i	0.00893851i
$783$	− 6190.53i	− 0.282543i
$784$	5947.35	0.270925
$785$	0	0
$786$	9358.72	0.424701
$787$	17365.2i	0.786536i	0.919424	+	0.393268i	$0.128655\pi$
$787$	17365.2i	0.786536i	−0.919424	+	0.393268i	$0.871345\pi$
$788$	9674.33i	0.437352i
$789$	−18069.1	−0.815306
$790$	0	0
$791$	49105.8	2.20733
$792$	2438.46i	0.109403i
$793$	6723.25i	0.301071i
$794$	−10323.8	−0.461431
$795$	0	0
$796$	−12427.9	−0.553384
$797$	7055.12i	0.313557i	0.987634	+	0.156779i	$0.0501109\pi$
$797$	7055.12i	0.313557i	−0.987634	+	0.156779i	$0.949889\pi$
$798$	− 1105.16i	− 0.0490253i
$799$	−35562.0	−1.57458
$800$	0	0
$801$	−5756.61	−0.253933
$802$	11726.7i	0.516313i
$803$	219.406i	0.00964217i
$804$	−2889.89	−0.126764
$805$	0	0
$806$	3577.73	0.156353
$807$	8935.14i	0.389755i
$808$	19959.5i	0.869024i
$809$	6937.17	0.301481	0.150740	−	0.988573i	$-0.451834\pi$
$809$	6937.17	0.301481	0.150740	+	0.988573i	$0.451834\pi$
$810$	0	0
$811$	5610.44	0.242921	0.121461	−	0.992596i	$-0.461242\pi$
$811$	5610.44	0.242921	0.121461	+	0.992596i	$0.461242\pi$
$812$	13266.9i	0.573369i
$813$	− 1574.91i	− 0.0679390i
$814$	−2825.32	−0.121655
$815$	0	0
$816$	−14132.1	−0.606280
$817$	− 2823.14i	− 0.120893i
$818$	15079.8i	0.644565i
$819$	1993.80	0.0850659
$820$	0	0
$821$	−17001.8	−0.722735	−0.361368	−	0.932423i	$-0.617690\pi$
$821$	−17001.8	−0.722735	−0.361368	+	0.932423i	$0.617690\pi$
$822$	− 7689.83i	− 0.326294i
$823$	− 14567.3i	− 0.616991i	−0.951226	−	0.308496i	$-0.900175\pi$
$823$	− 14567.3i	− 0.616991i	0.951226	−	0.308496i	$-0.0998255\pi$
$824$	36007.7	1.52232
$825$	0	0
$826$	22180.0	0.934312
$827$	− 7345.87i	− 0.308877i	−0.988002	−	0.154438i	$-0.950643\pi$
$827$	− 7345.87i	− 0.308877i	0.988002	−	0.154438i	$-0.0493568\pi$
$828$	15.1817i	0 0.000637197i
$829$	13903.2	0.582482	0.291241	−	0.956650i	$-0.405932\pi$
$829$	13903.2	0.582482	0.291241	+	0.956650i	$0.405932\pi$
$830$	0	0
$831$	5079.22	0.212029
$832$	− 5458.84i	− 0.227466i
$833$	20729.2i	0.862214i
$834$	8975.13	0.372642
$835$	0	0
$836$	−199.444	−0.00825111
$837$	− 4206.30i	− 0.173705i
$838$	− 19232.9i	− 0.792829i
$839$	25111.9	1.03332	0.516662	−	0.856190i	$-0.327175\pi$
$839$	25111.9	1.03332	0.516662	+	0.856190i	$0.327175\pi$
$840$	0	0
$841$	28179.7	1.15543
$842$	7987.20i	0.326909i
$843$	22039.8i	0.900464i
$844$	−11316.6	−0.461534
$845$	0	0
$846$	5817.50	0.236418
$847$	2718.53i	0.110283i
$848$	− 23953.7i	− 0.970014i
$849$	−4505.08	−0.182113
$850$	0	0
$851$	−72.2296	−0.00290952
$852$	747.104i	0.0300415i
$853$	27545.3i	1.10567i	0.833292	+	0.552833i	$0.186453\pi$
$853$	27545.3i	1.10567i	−0.833292	+	0.552833i	$0.813547\pi$
$854$	35679.5	1.42966
$855$	0	0
$856$	41636.1	1.66249
$857$	1808.04i	0.0720669i	0.999351	+	0.0360334i	$0.0114723\pi$
$857$	1808.04i	0.0720669i	−0.999351	+	0.0360334i	$0.988528\pi$
$858$	757.854i	0.0301547i
$859$	−32160.8	−1.27743	−0.638716	−	0.769443i	$-0.720534\pi$
$859$	−32160.8	−1.27743	−0.638716	+	0.769443i	$0.720534\pi$
$860$	0	0
$861$	−10430.3	−0.412850
$862$	26226.3i	1.03628i
$863$	− 33734.8i	− 1.33064i	−0.746557	−	0.665321i	$-0.768294\pi$
$863$	− 33734.8i	− 1.33064i	0.746557	−	0.665321i	$-0.231706\pi$
$864$	−3008.43	−0.118459
$865$	0	0
$866$	−29342.7	−1.15139
$867$	− 34517.9i	− 1.35212i
$868$	9014.47i	0.352501i
$869$	−268.715	−0.0104897
$870$	0	0
$871$	−3688.03	−0.143472
$872$	− 34715.2i	− 1.34817i
$873$	6577.78i	0.255011i
$874$	10.7393	0.000415631 0
$875$	0	0
$876$	−154.111	−0.00594397
$877$	46573.5i	1.79325i	0.442795	+	0.896623i	$0.353987\pi$
$877$	46573.5i	1.79325i	−0.442795	+	0.896623i	$0.646013\pi$
$878$	9728.26i	0.373933i
$879$	−13443.1	−0.515841
$880$	0	0
$881$	−9949.72	−0.380493	−0.190247	−	0.981736i	$-0.560929\pi$
$881$	−9949.72	−0.380493	−0.190247	+	0.981736i	$0.560929\pi$
$882$	− 3391.04i	− 0.129458i
$883$	49269.1i	1.87773i	0.344282	+	0.938866i	$0.388122\pi$
$883$	49269.1i	1.87773i	−0.344282	+	0.938866i	$0.611878\pi$
$884$	3254.01	0.123806
$885$	0	0
$886$	−5483.00	−0.207906
$887$	27347.5i	1.03522i	0.855617	+	0.517609i	$0.173178\pi$
$887$	27347.5i	1.03522i	−0.855617	+	0.517609i	$0.826822\pi$
$888$	− 8148.85i	− 0.307948i
$889$	43111.2	1.62644
$890$	0	0
$891$	891.000	0.0335013
$892$	− 5639.42i	− 0.211683i
$893$	1953.83i	0.0732165i
$894$	−8924.12	−0.333856
$895$	0	0
$896$	−8942.48	−0.333423
$897$	19.3746i	0 0.000721180i
$898$	21628.1i	0.803718i
$899$	35719.0	1.32514
$900$	0	0
$901$	83489.4	3.08705
$902$	− 3964.61i	− 0.146349i
$903$	− 27029.0i	− 0.996088i
$904$	−53835.0	−1.98067
$905$	0	0
$906$	6192.86	0.227091
$907$	− 25516.6i	− 0.934141i	−0.884220	−	0.467071i	$-0.845309\pi$
$907$	− 25516.6i	− 0.934141i	0.884220	−	0.467071i	$-0.154691\pi$
$908$	− 2934.15i	− 0.107239i
$909$	7293.07	0.266112
$910$	0	0
$911$	22379.0	0.813885	0.406942	−	0.913454i	$-0.366595\pi$
$911$	22379.0	0.813885	0.406942	+	0.913454i	$0.366595\pi$
$912$	776.441i	0.0281914i
$913$	12400.9i	0.449516i
$914$	33488.1	1.21191
$915$	0	0
$916$	−8798.04	−0.317353
$917$	30092.8i	1.08370i
$918$	8057.83i	0.289704i
$919$	6244.97	0.224159	0.112080	−	0.993699i	$-0.464249\pi$
$919$	6244.97	0.224159	0.112080	+	0.993699i	$0.464249\pi$
$920$	0	0
$921$	−9156.52	−0.327598
$922$	12537.8i	0.447841i
$923$	953.442i	0.0340010i
$924$	−1909.49	−0.0679846
$925$	0	0
$926$	−42762.6	−1.51757
$927$	− 13157.0i	− 0.466163i
$928$	− 25547.0i	− 0.903688i
$929$	−16122.2	−0.569378	−0.284689	−	0.958620i	$-0.591890\pi$
$929$	−16122.2	−0.569378	−0.284689	+	0.958620i	$0.591890\pi$
$930$	0	0
$931$	1138.89	0.0400921
$932$	− 15831.6i	− 0.556417i
$933$	30765.4i	1.07954i
$934$	21109.8	0.739544
$935$	0	0
$936$	−2185.82	−0.0763308
$937$	56379.6i	1.96568i	0.184466	+	0.982839i	$0.440945\pi$
$937$	56379.6i	1.96568i	−0.184466	+	0.982839i	$0.559055\pi$
$938$	19572.0i	0.681287i
$939$	−18570.5	−0.645396
$940$	0	0
$941$	25527.0	0.884332	0.442166	−	0.896933i	$-0.354210\pi$
$941$	25527.0	0.884332	0.442166	+	0.896933i	$0.354210\pi$
$942$	− 11746.3i	− 0.406280i
$943$	− 101.356i	− 0.00350010i
$944$	−15582.8	−0.537264
$945$	0	0
$946$	10273.9	0.353099
$947$	46411.3i	1.59257i	0.604921	+	0.796285i	$0.293205\pi$
$947$	46411.3i	1.59257i	−0.604921	+	0.796285i	$0.706795\pi$
$948$	− 188.745i	− 0.00646641i
$949$	−196.673	−0.00672738
$950$	0	0
$951$	20206.1	0.688990
$952$	− 70909.2i	− 2.41405i
$953$	21266.1i	0.722850i	0.932401	+	0.361425i	$0.117710\pi$
$953$	21266.1i	0.722850i	−0.932401	+	0.361425i	$0.882290\pi$
$954$	−13657.8	−0.463510
$955$	0	0
$956$	5357.05	0.181234
$957$	7566.20i	0.255570i
$958$	29365.4i	0.990347i
$959$	24726.5	0.832597
$960$	0	0
$961$	−5520.88	−0.185320
$962$	− 2532.60i	− 0.0848796i
$963$	− 15213.6i	− 0.509087i
$964$	4755.04	0.158869
$965$	0	0
$966$	102.819	0.00342457
$967$	20035.9i	0.666300i	0.942874	+	0.333150i	$0.108112\pi$
$967$	20035.9i	0.666300i	−0.942874	+	0.333150i	$0.891888\pi$
$968$	− 2980.34i	− 0.0989585i
$969$	−2706.25	−0.0897185
$970$	0	0
$971$	21354.1	0.705751	0.352876	−	0.935670i	$-0.385204\pi$
$971$	21354.1	0.705751	0.352876	+	0.935670i	$0.385204\pi$
$972$	625.838i	0.0206520i
$973$	28859.4i	0.950862i
$974$	−30776.6	−1.01247
$975$	0	0
$976$	−25067.0	−0.822107
$977$	− 34057.7i	− 1.11525i	−0.830092	−	0.557626i	$-0.811712\pi$
$977$	− 34057.7i	− 1.11525i	0.830092	−	0.557626i	$-0.188288\pi$
$978$	4346.73i	0.142120i
$979$	7035.86	0.229691
$980$	0	0
$981$	−12684.7	−0.412836
$982$	− 15263.0i	− 0.495989i
$983$	− 31846.5i	− 1.03331i	−0.856193	−	0.516657i	$-0.827176\pi$
$983$	− 31846.5i	− 1.03331i	0.856193	−	0.516657i	$-0.172824\pi$
$984$	11434.8	0.370456
$985$	0	0
$986$	−68425.5	−2.21005
$987$	18706.1i	0.603263i
$988$	− 178.780i	− 0.00575684i
$989$	262.652	0.00844474
$990$	0	0
$991$	−20462.5	−0.655915	−0.327957	−	0.944693i	$-0.606360\pi$
$991$	−20462.5	−0.655915	−0.327957	+	0.944693i	$0.606360\pi$
$992$	− 17358.5i	− 0.555578i
$993$	− 14342.5i	− 0.458353i
$994$	5059.81	0.161456
$995$	0	0
$996$	−8710.36	−0.277107
$997$	35227.4i	1.11902i	0.828824	+	0.559510i	$0.189011\pi$
$997$	35227.4i	1.11902i	−0.828824	+	0.559510i	$0.810989\pi$
$998$	− 6047.71i	− 0.191820i
$999$	−2977.54	−0.0942996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.l.199.3		6
5.2	odd	4		825.4.a.s.1.2		3
5.3	odd	4		165.4.a.d.1.2	✓	3
5.4	even	2	inner	825.4.c.l.199.4		6
15.2	even	4		2475.4.a.s.1.2		3
15.8	even	4		495.4.a.l.1.2		3
55.43	even	4		1815.4.a.s.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.d.1.2	✓	3	5.3	odd	4
495.4.a.l.1.2		3	15.8	even	4
825.4.a.s.1.2		3	5.2	odd	4
825.4.c.l.199.3		6	1.1	even	1	trivial
825.4.c.l.199.4		6	5.4	even	2	inner
1815.4.a.s.1.2		3	55.43	even	4
2475.4.a.s.1.2		3	15.2	even	4

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.32906i q^{2} +3.00000i q^{3} +2.57547 q^{4} +6.98719 q^{6} +22.4672i q^{7} -24.6309i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.32906i q^{2} +3.00000i q^{3} +2.57547 q^{4} +6.98719 q^{6} +22.4672i q^{7} -24.6309i q^{8} -9.00000 q^{9} +11.0000 q^{11} +7.72640i q^{12} +9.86030i q^{13} +52.3275 q^{14} -36.7633 q^{16} -128.137i q^{17} +20.9616i q^{18} -7.04001 q^{19} -67.4015 q^{21} -25.6197i q^{22} -0.654969i q^{23} +73.8928 q^{24} +22.9653 q^{26} -27.0000i q^{27} +57.8635i q^{28} +229.279 q^{29} +155.789 q^{31} -111.423i q^{32} +33.0000i q^{33} -298.438 q^{34} -23.1792 q^{36} -110.279i q^{37} +16.3966i q^{38} -29.5809 q^{39} +154.749 q^{41} +156.982i q^{42} +401.014i q^{43} +28.3301 q^{44} -1.52546 q^{46} -277.532i q^{47} -110.290i q^{48} -161.774 q^{49} +384.410 q^{51} +25.3949i q^{52} +651.566i q^{53} -62.8847 q^{54} +553.388 q^{56} -21.1200i q^{57} -534.005i q^{58} +423.869 q^{59} +681.851 q^{61} -362.842i q^{62} -202.205i q^{63} -553.618 q^{64} +76.8591 q^{66} +374.028i q^{67} -330.011i q^{68} +1.96491 q^{69} +96.6950 q^{71} +221.678i q^{72} +19.9460i q^{73} -256.848 q^{74} -18.1313 q^{76} +247.139i q^{77} +68.8958i q^{78} -24.4286 q^{79} +81.0000 q^{81} -360.419i q^{82} +1127.35i q^{83} -173.590 q^{84} +933.987 q^{86} +687.836i q^{87} -270.940i q^{88} +639.624 q^{89} -221.533 q^{91} -1.68685i q^{92} +467.366i q^{93} -646.389 q^{94} +334.270 q^{96} -730.865i q^{97} +376.783i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 44 q^{4} + 24 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 44 * q^4 + 24 * q^6 - 54 * q^9	\( 6 q - 44 q^{4} + 24 q^{6} - 54 q^{9} + 66 q^{11} + 112 q^{14} + 100 q^{16} - 292 q^{19} + 24 q^{21} - 288 q^{24} - 1016 q^{26} - 136 q^{29} - 136 q^{31} + 352 q^{34} + 396 q^{36} - 392 q^{41} - 484 q^{44} + 2320 q^{46} + 314 q^{49} + 1308 q^{51} - 216 q^{54} + 2736 q^{56} + 2088 q^{59} + 1284 q^{61} - 2332 q^{64} + 264 q^{66} - 1200 q^{69} - 1088 q^{71} - 3072 q^{74} + 3992 q^{76} + 3172 q^{79} + 486 q^{81} - 2040 q^{84} + 7136 q^{86} + 4244 q^{89} - 16 q^{91} + 4304 q^{94} + 4128 q^{96} - 594 q^{99}+O(q^{100}) \) 6 * q - 44 * q^4 + 24 * q^6 - 54 * q^9 + 66 * q^11 + 112 * q^14 + 100 * q^16 - 292 * q^19 + 24 * q^21 - 288 * q^24 - 1016 * q^26 - 136 * q^29 - 136 * q^31 + 352 * q^34 + 396 * q^36 - 392 * q^41 - 484 * q^44 + 2320 * q^46 + 314 * q^49 + 1308 * q^51 - 216 * q^54 + 2736 * q^56 + 2088 * q^59 + 1284 * q^61 - 2332 * q^64 + 264 * q^66 - 1200 * q^69 - 1088 * q^71 - 3072 * q^74 + 3992 * q^76 + 3172 * q^79 + 486 * q^81 - 2040 * q^84 + 7136 * q^86 + 4244 * q^89 - 16 * q^91 + 4304 * q^94 + 4128 * q^96 - 594 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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