LMFDB - Embedded newform 626.4.a.d.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [626,4,Mod(1,626)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("626.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(626, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 626 = 2 \cdot 313 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	626.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$36.9351956636$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	626.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -2.41450 q^{3} +4.00000 q^{4} +13.1695 q^{5} -4.82900 q^{6} +31.3107 q^{7} +8.00000 q^{8} -21.1702 q^{9} +26.3390 q^{10} +31.9442 q^{11} -9.65801 q^{12} +48.6300 q^{13} +62.6214 q^{14} -31.7977 q^{15} +16.0000 q^{16} -59.9639 q^{17} -42.3404 q^{18} +42.6947 q^{19} +52.6779 q^{20} -75.5997 q^{21} +63.8884 q^{22} +114.316 q^{23} -19.3160 q^{24} +48.4354 q^{25} +97.2601 q^{26} +116.307 q^{27} +125.243 q^{28} -100.304 q^{29} -63.5955 q^{30} -305.730 q^{31} +32.0000 q^{32} -77.1293 q^{33} -119.928 q^{34} +412.346 q^{35} -84.6807 q^{36} -217.137 q^{37} +85.3893 q^{38} -117.417 q^{39} +105.356 q^{40} -50.1667 q^{41} -151.199 q^{42} -43.0764 q^{43} +127.777 q^{44} -278.800 q^{45} +228.632 q^{46} +372.771 q^{47} -38.6320 q^{48} +637.359 q^{49} +96.8708 q^{50} +144.783 q^{51} +194.520 q^{52} -168.677 q^{53} +232.614 q^{54} +420.689 q^{55} +250.486 q^{56} -103.086 q^{57} -200.607 q^{58} -313.750 q^{59} -127.191 q^{60} +273.453 q^{61} -611.459 q^{62} -662.853 q^{63} +64.0000 q^{64} +640.433 q^{65} -154.259 q^{66} +361.493 q^{67} -239.856 q^{68} -276.016 q^{69} +824.691 q^{70} -449.493 q^{71} -169.361 q^{72} +549.733 q^{73} -434.275 q^{74} -116.947 q^{75} +170.779 q^{76} +1000.19 q^{77} -234.835 q^{78} +782.074 q^{79} +210.712 q^{80} +290.772 q^{81} -100.333 q^{82} -357.863 q^{83} -302.399 q^{84} -789.694 q^{85} -86.1528 q^{86} +242.183 q^{87} +255.554 q^{88} -975.788 q^{89} -557.601 q^{90} +1522.64 q^{91} +457.264 q^{92} +738.185 q^{93} +745.541 q^{94} +562.267 q^{95} -77.2640 q^{96} +1010.53 q^{97} +1274.72 q^{98} -676.264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 50 q^{2} + 16 q^{3} + 100 q^{4} + 40 q^{5} + 32 q^{6} + 51 q^{7} + 200 q^{8} + 351 q^{9} + 80 q^{10} + 178 q^{11} + 64 q^{12} + 142 q^{13} + 102 q^{14} + 151 q^{15} + 400 q^{16} + 339 q^{17} + 702 q^{18}+ \cdots + 2233 q^{99}+O(q^{100}) $ 25 * q + 50 * q^2 + 16 * q^3 + 100 * q^4 + 40 * q^5 + 32 * q^6 + 51 * q^7 + 200 * q^8 + 351 * q^9 + 80 * q^10 + 178 * q^11 + 64 * q^12 + 142 * q^13 + 102 * q^14 + 151 * q^15 + 400 * q^16 + 339 * q^17 + 702 * q^18 + 305 * q^19 + 160 * q^20 + 326 * q^21 + 356 * q^22 + 128 * q^23 + 128 * q^24 + 1181 * q^25 + 284 * q^26 + 505 * q^27 + 204 * q^28 + 700 * q^29 + 302 * q^30 + 944 * q^31 + 800 * q^32 + 526 * q^33 + 678 * q^34 + 529 * q^35 + 1404 * q^36 + 1165 * q^37 + 610 * q^38 + 872 * q^39 + 320 * q^40 + 970 * q^41 + 652 * q^42 + 855 * q^43 + 712 * q^44 + 1749 * q^45 + 256 * q^46 + 894 * q^47 + 256 * q^48 + 3132 * q^49 + 2362 * q^50 + 1939 * q^51 + 568 * q^52 + 1756 * q^53 + 1010 * q^54 + 1518 * q^55 + 408 * q^56 + 1813 * q^57 + 1400 * q^58 + 1364 * q^59 + 604 * q^60 + 1972 * q^61 + 1888 * q^62 + 2199 * q^63 + 1600 * q^64 + 3344 * q^65 + 1052 * q^66 + 2383 * q^67 + 1356 * q^68 + 2516 * q^69 + 1058 * q^70 + 1487 * q^71 + 2808 * q^72 + 2284 * q^73 + 2330 * q^74 + 3715 * q^75 + 1220 * q^76 + 3746 * q^77 + 1744 * q^78 + 373 * q^79 + 640 * q^80 + 4521 * q^81 + 1940 * q^82 + 1012 * q^83 + 1304 * q^84 - 364 * q^85 + 1710 * q^86 - 5697 * q^87 + 1424 * q^88 - 654 * q^89 + 3498 * q^90 - 835 * q^91 + 512 * q^92 - 480 * q^93 + 1788 * q^94 - 2436 * q^95 + 512 * q^96 - 609 * q^97 + 6264 * q^98 + 2233 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−2.41450	−0.464671	−0.232336	−	0.972636i	$-0.574637\pi$
$3$	−2.41450	−0.464671	−0.232336	+	0.972636i	$0.574637\pi$
$4$	4.00000	0.500000
$5$	13.1695	1.17791	0.588957	−	0.808164i	$-0.299539\pi$
$5$	13.1695	1.17791	0.588957	+	0.808164i	$0.299539\pi$
$6$	−4.82900	−0.328572
$7$	31.3107	1.69062	0.845309	−	0.534278i	$-0.179416\pi$
$7$	31.3107	1.69062	0.845309	+	0.534278i	$0.179416\pi$
$8$	8.00000	0.353553
$9$	−21.1702	−0.784081
$10$	26.3390	0.832911
$11$	31.9442	0.875594	0.437797	−	0.899074i	$-0.355759\pi$
$11$	31.9442	0.875594	0.437797	+	0.899074i	$0.355759\pi$
$12$	−9.65801	−0.232336
$13$	48.6300	1.03750	0.518752	−	0.854925i	$-0.326397\pi$
$13$	48.6300	1.03750	0.518752	+	0.854925i	$0.326397\pi$
$14$	62.6214	1.19545
$15$	−31.7977	−0.547343
$16$	16.0000	0.250000
$17$	−59.9639	−0.855493	−0.427747	−	0.903899i	$-0.640692\pi$
$17$	−59.9639	−0.855493	−0.427747	+	0.903899i	$0.640692\pi$
$18$	−42.3404	−0.554429
$19$	42.6947	0.515517	0.257759	−	0.966209i	$-0.417016\pi$
$19$	42.6947	0.515517	0.257759	+	0.966209i	$0.417016\pi$
$20$	52.6779	0.588957
$21$	−75.5997	−0.785581
$22$	63.8884	0.619139
$23$	114.316	1.03637	0.518185	−	0.855269i	$-0.326608\pi$
$23$	114.316	1.03637	0.518185	+	0.855269i	$0.326608\pi$
$24$	−19.3160	−0.164286
$25$	48.4354	0.387483
$26$	97.2601	0.733626
$27$	116.307	0.829011
$28$	125.243	0.845309
$29$	−100.304	−0.642273	−0.321136	−	0.947033i	$-0.604065\pi$
$29$	−100.304	−0.642273	−0.321136	+	0.947033i	$0.604065\pi$
$30$	−63.5955	−0.387030
$31$	−305.730	−1.77131	−0.885656	−	0.464342i	$-0.846291\pi$
$31$	−305.730	−1.77131	−0.885656	+	0.464342i	$0.846291\pi$
$32$	32.0000	0.176777
$33$	−77.1293	−0.406863
$34$	−119.928	−0.604925
$35$	412.346	1.99140
$36$	−84.6807	−0.392040
$37$	−217.137	−0.964788	−0.482394	−	0.875954i	$-0.660233\pi$
$37$	−217.137	−0.964788	−0.482394	+	0.875954i	$0.660233\pi$
$38$	85.3893	0.364526
$39$	−117.417	−0.482098
$40$	105.356	0.416456
$41$	−50.1667	−0.191091	−0.0955454	−	0.995425i	$-0.530460\pi$
$41$	−50.1667	−0.191091	−0.0955454	+	0.995425i	$0.530460\pi$
$42$	−151.199	−0.555490
$43$	−43.0764	−0.152770	−0.0763848	−	0.997078i	$-0.524338\pi$
$43$	−43.0764	−0.152770	−0.0763848	+	0.997078i	$0.524338\pi$
$44$	127.777	0.437797
$45$	−278.800	−0.923580
$46$	228.632	0.732824
$47$	372.771	1.15690	0.578449	−	0.815719i	$-0.303658\pi$
$47$	372.771	1.15690	0.578449	+	0.815719i	$0.303658\pi$
$48$	−38.6320	−0.116168
$49$	637.359	1.85819
$50$	96.8708	0.273992
$51$	144.783	0.397523
$52$	194.520	0.518752
$53$	−168.677	−0.437161	−0.218581	−	0.975819i	$-0.570143\pi$
$53$	−168.677	−0.437161	−0.218581	+	0.975819i	$0.570143\pi$
$54$	232.614	0.586199
$55$	420.689	1.03138
$56$	250.486	0.597724
$57$	−103.086	−0.239546
$58$	−200.607	−0.454155
$59$	−313.750	−0.692319	−0.346159	−	0.938176i	$-0.612514\pi$
$59$	−313.750	−0.692319	−0.346159	+	0.938176i	$0.612514\pi$
$60$	−127.191	−0.273671
$61$	273.453	0.573967	0.286984	−	0.957935i	$-0.407347\pi$
$61$	273.453	0.573967	0.286984	+	0.957935i	$0.407347\pi$
$62$	−611.459	−1.25251
$63$	−662.853	−1.32558
$64$	64.0000	0.125000
$65$	640.433	1.22209
$66$	−154.259	−0.287696
$67$	361.493	0.659155	0.329578	−	0.944128i	$-0.393094\pi$
$67$	361.493	0.659155	0.329578	+	0.944128i	$0.393094\pi$
$68$	−239.856	−0.427747
$69$	−276.016	−0.481571
$70$	824.691	1.40814
$71$	−449.493	−0.751338	−0.375669	−	0.926754i	$-0.622587\pi$
$71$	−449.493	−0.751338	−0.375669	+	0.926754i	$0.622587\pi$
$72$	−169.361	−0.277214
$73$	549.733	0.881388	0.440694	−	0.897657i	$-0.354732\pi$
$73$	549.733	0.881388	0.440694	+	0.897657i	$0.354732\pi$
$74$	−434.275	−0.682208
$75$	−116.947	−0.180052
$76$	170.779	0.257759
$77$	1000.19	1.48030
$78$	−234.835	−0.340895
$79$	782.074	1.11380	0.556900	−	0.830580i	$-0.311991\pi$
$79$	782.074	1.11380	0.556900	+	0.830580i	$0.311991\pi$
$80$	210.712	0.294479
$81$	290.772	0.398864
$82$	−100.333	−0.135122
$83$	−357.863	−0.473260	−0.236630	−	0.971600i	$-0.576043\pi$
$83$	−357.863	−0.473260	−0.236630	+	0.971600i	$0.576043\pi$
$84$	−302.399	−0.392791
$85$	−789.694	−1.00770
$86$	−86.1528	−0.108024
$87$	242.183	0.298446
$88$	255.554	0.309569
$89$	−975.788	−1.16217	−0.581086	−	0.813842i	$-0.697372\pi$
$89$	−975.788	−1.16217	−0.581086	+	0.813842i	$0.697372\pi$
$90$	−557.601	−0.653070
$91$	1522.64	1.75402
$92$	457.264	0.518185
$93$	738.185	0.823077
$94$	745.541	0.818050
$95$	562.267	0.607235
$96$	−77.2640	−0.0821430
$97$	1010.53	1.05777	0.528887	−	0.848692i	$-0.322610\pi$
$97$	1010.53	1.05777	0.528887	+	0.848692i	$0.322610\pi$
$98$	1274.72	1.31394
$99$	−676.264	−0.686537
$100$	193.742	0.193742
$101$	878.455	0.865441	0.432720	−	0.901528i	$-0.357554\pi$
$101$	878.455	0.865441	0.432720	+	0.901528i	$0.357554\pi$
$102$	289.566	0.281091
$103$	604.590	0.578369	0.289184	−	0.957273i	$-0.406616\pi$
$103$	604.590	0.578369	0.289184	+	0.957273i	$0.406616\pi$
$104$	389.040	0.366813
$105$	−995.609	−0.925348
$106$	−337.354	−0.309120
$107$	1380.57	1.24733	0.623667	−	0.781690i	$-0.285642\pi$
$107$	1380.57	1.24733	0.623667	+	0.781690i	$0.285642\pi$
$108$	465.228	0.414505
$109$	−732.249	−0.643456	−0.321728	−	0.946832i	$-0.604264\pi$
$109$	−732.249	−0.643456	−0.321728	+	0.946832i	$0.604264\pi$
$110$	841.377	0.729293
$111$	524.278	0.448309
$112$	500.971	0.422655
$113$	1644.07	1.36868	0.684341	−	0.729162i	$-0.260090\pi$
$113$	1644.07	1.36868	0.684341	+	0.729162i	$0.260090\pi$
$114$	−206.173	−0.169385
$115$	1505.48	1.22076
$116$	−401.214	−0.321136
$117$	−1029.51	−0.813486
$118$	−627.500	−0.489543
$119$	−1877.51	−1.44631
$120$	−254.382	−0.193515
$121$	−310.568	−0.233335
$122$	546.905	0.405856
$123$	121.128	0.0887944
$124$	−1222.92	−0.885656
$125$	−1008.32	−0.721493
$126$	−1325.71	−0.937328
$127$	−2363.58	−1.65144	−0.825722	−	0.564077i	$-0.809232\pi$
$127$	−2363.58	−1.65144	−0.825722	+	0.564077i	$0.809232\pi$
$128$	128.000	0.0883883
$129$	104.008	0.0709876
$130$	1280.87	0.864148
$131$	−1243.40	−0.829285	−0.414643	−	0.909984i	$-0.636093\pi$
$131$	−1243.40	−0.829285	−0.414643	+	0.909984i	$0.636093\pi$
$132$	−308.517	−0.203432
$133$	1336.80	0.871543
$134$	722.986	0.466093
$135$	1531.70	0.976504
$136$	−479.711	−0.302463
$137$	311.125	0.194023	0.0970117	−	0.995283i	$-0.469072\pi$
$137$	311.125	0.194023	0.0970117	+	0.995283i	$0.469072\pi$
$138$	−552.032	−0.340522
$139$	−674.419	−0.411536	−0.205768	−	0.978601i	$-0.565969\pi$
$139$	−674.419	−0.411536	−0.205768	+	0.978601i	$0.565969\pi$
$140$	1649.38	0.995702
$141$	−900.055	−0.537577
$142$	−898.986	−0.531276
$143$	1553.45	0.908432
$144$	−338.723	−0.196020
$145$	−1320.95	−0.756542
$146$	1099.47	0.623236
$147$	−1538.90	−0.863447
$148$	−868.549	−0.482394
$149$	−777.281	−0.427365	−0.213682	−	0.976903i	$-0.568546\pi$
$149$	−777.281	−0.427365	−0.213682	+	0.976903i	$0.568546\pi$
$150$	−233.895	−0.127316
$151$	−899.823	−0.484944	−0.242472	−	0.970158i	$-0.577958\pi$
$151$	−899.823	−0.484944	−0.242472	+	0.970158i	$0.577958\pi$
$152$	341.557	0.182263
$153$	1269.45	0.670776
$154$	2000.39	1.04673
$155$	−4026.30	−2.08645
$156$	−469.669	−0.241049
$157$	1139.38	0.579187	0.289593	−	0.957150i	$-0.406480\pi$
$157$	1139.38	0.579187	0.289593	+	0.957150i	$0.406480\pi$
$158$	1564.15	0.787575
$159$	407.271	0.203136
$160$	421.424	0.208228
$161$	3579.31	1.75211
$162$	581.543	0.282039
$163$	−892.421	−0.428833	−0.214417	−	0.976742i	$-0.568785\pi$
$163$	−892.421	−0.428833	−0.214417	+	0.976742i	$0.568785\pi$
$164$	−200.667	−0.0955454
$165$	−1015.75	−0.479250
$166$	−715.726	−0.334645
$167$	1354.18	0.627484	0.313742	−	0.949508i	$-0.398417\pi$
$167$	1354.18	0.627484	0.313742	+	0.949508i	$0.398417\pi$
$168$	−604.798	−0.277745
$169$	167.880	0.0764131
$170$	−1579.39	−0.712550
$171$	−903.854	−0.404207
$172$	−172.306	−0.0763848
$173$	−3827.68	−1.68216	−0.841079	−	0.540913i	$-0.818079\pi$
$173$	−3827.68	−1.68216	−0.841079	+	0.540913i	$0.818079\pi$
$174$	484.366	0.211033
$175$	1516.55	0.655086
$176$	511.107	0.218899
$177$	757.550	0.321700
$178$	−1951.58	−0.821780
$179$	−3736.29	−1.56013	−0.780066	−	0.625697i	$-0.784815\pi$
$179$	−3736.29	−1.56013	−0.780066	+	0.625697i	$0.784815\pi$
$180$	−1115.20	−0.461790
$181$	−3855.37	−1.58325	−0.791623	−	0.611010i	$-0.790764\pi$
$181$	−3855.37	−1.58325	−0.791623	+	0.611010i	$0.790764\pi$
$182$	3045.28	1.24028
$183$	−660.252	−0.266706
$184$	914.527	0.366412
$185$	−2859.59	−1.13644
$186$	1476.37	0.582003
$187$	−1915.50	−0.749065
$188$	1491.08	0.578449
$189$	3641.65	1.40154
$190$	1124.53	0.429380
$191$	−358.483	−0.135806	−0.0679029	−	0.997692i	$-0.521631\pi$
$191$	−358.483	−0.135806	−0.0679029	+	0.997692i	$0.521631\pi$
$192$	−154.528	−0.0580839
$193$	485.330	0.181010	0.0905048	−	0.995896i	$-0.471152\pi$
$193$	485.330	0.181010	0.0905048	+	0.995896i	$0.471152\pi$
$194$	2021.06	0.747959
$195$	−1546.33	−0.567870
$196$	2549.44	0.929095
$197$	1630.34	0.589628	0.294814	−	0.955555i	$-0.404742\pi$
$197$	1630.34	0.589628	0.294814	+	0.955555i	$0.404742\pi$
$198$	−1352.53	−0.485455
$199$	3915.98	1.39496	0.697479	−	0.716605i	$-0.254305\pi$
$199$	3915.98	1.39496	0.697479	+	0.716605i	$0.254305\pi$
$200$	387.483	0.136996
$201$	−872.825	−0.306290
$202$	1756.91	0.611959
$203$	−3140.57	−1.08584
$204$	579.132	0.198761
$205$	−660.670	−0.225089
$206$	1209.18	0.408968
$207$	−2420.09	−0.812598
$208$	778.080	0.259376
$209$	1363.85	0.451384
$210$	−1991.22	−0.654320
$211$	−2837.92	−0.925927	−0.462963	−	0.886377i	$-0.653214\pi$
$211$	−2837.92	−0.925927	−0.462963	+	0.886377i	$0.653214\pi$
$212$	−674.707	−0.218581
$213$	1085.30	0.349125
$214$	2761.14	0.881998
$215$	−567.294	−0.179950
$216$	930.456	0.293100
$217$	−9572.60	−2.99461
$218$	−1464.50	−0.454992
$219$	−1327.33	−0.409556
$220$	1682.75	0.515688
$221$	−2916.05	−0.887577
$222$	1048.56	0.317002
$223$	1470.72	0.441645	0.220822	−	0.975314i	$-0.429126\pi$
$223$	1470.72	0.441645	0.220822	+	0.975314i	$0.429126\pi$
$224$	1001.94	0.298862
$225$	−1025.39	−0.303818
$226$	3288.14	0.967805
$227$	−1176.66	−0.344043	−0.172021	−	0.985093i	$-0.555030\pi$
$227$	−1176.66	−0.344043	−0.172021	+	0.985093i	$0.555030\pi$
$228$	−412.345	−0.119773
$229$	1563.34	0.451129	0.225565	−	0.974228i	$-0.427577\pi$
$229$	1563.34	0.451129	0.225565	+	0.974228i	$0.427577\pi$
$230$	3010.96	0.863205
$231$	−2414.97	−0.687851
$232$	−802.429	−0.227078
$233$	1205.41	0.338924	0.169462	−	0.985537i	$-0.445797\pi$
$233$	1205.41	0.338924	0.169462	+	0.985537i	$0.445797\pi$
$234$	−2059.01	−0.575222
$235$	4909.20	1.36273
$236$	−1255.00	−0.346159
$237$	−1888.32	−0.517550
$238$	−3755.02	−1.02270
$239$	−6209.66	−1.68062	−0.840312	−	0.542102i	$-0.817628\pi$
$239$	−6209.66	−1.68062	−0.840312	+	0.542102i	$0.817628\pi$
$240$	−508.764	−0.136836
$241$	−3873.34	−1.03529	−0.517643	−	0.855597i	$-0.673190\pi$
$241$	−3873.34	−1.03529	−0.517643	+	0.855597i	$0.673190\pi$
$242$	−621.137	−0.164993
$243$	−3842.36	−1.01435
$244$	1093.81	0.286984
$245$	8393.69	2.18879
$246$	242.255	0.0627871
$247$	2076.24	0.534851
$248$	−2445.84	−0.626253
$249$	864.060	0.219910
$250$	−2016.63	−0.510172
$251$	−4704.21	−1.18298	−0.591489	−	0.806313i	$-0.701460\pi$
$251$	−4704.21	−1.18298	−0.591489	+	0.806313i	$0.701460\pi$
$252$	−2651.41	−0.662791
$253$	3651.73	0.907440
$254$	−4727.15	−1.16775
$255$	1906.72	0.468248
$256$	256.000	0.0625000
$257$	649.133	0.157556	0.0787779	−	0.996892i	$-0.474898\pi$
$257$	649.133	0.157556	0.0787779	+	0.996892i	$0.474898\pi$
$258$	208.016	0.0501958
$259$	−6798.72	−1.63109
$260$	2561.73	0.611045
$261$	2123.45	0.503594
$262$	−2486.80	−0.586393
$263$	−5152.41	−1.20803	−0.604014	−	0.796974i	$-0.706433\pi$
$263$	−5152.41	−1.20803	−0.604014	+	0.796974i	$0.706433\pi$
$264$	−617.034	−0.143848
$265$	−2221.39	−0.514939
$266$	2673.60	0.616274
$267$	2356.04	0.540028
$268$	1445.97	0.329578
$269$	6092.70	1.38096	0.690480	−	0.723351i	$-0.257399\pi$
$269$	6092.70	1.38096	0.690480	+	0.723351i	$0.257399\pi$
$270$	3063.41	0.690493
$271$	6681.27	1.49763	0.748816	−	0.662778i	$-0.230623\pi$
$271$	6681.27	1.49763	0.748816	+	0.662778i	$0.230623\pi$
$272$	−959.423	−0.213873
$273$	−3676.42	−0.815043
$274$	622.250	0.137195
$275$	1547.23	0.339278
$276$	−1104.06	−0.240786
$277$	5127.44	1.11219	0.556097	−	0.831117i	$-0.312298\pi$
$277$	5127.44	1.11219	0.556097	+	0.831117i	$0.312298\pi$
$278$	−1348.84	−0.291000
$279$	6472.35	1.38885
$280$	3298.77	0.704068
$281$	6161.22	1.30800	0.653999	−	0.756495i	$-0.273090\pi$
$281$	6161.22	1.30800	0.653999	+	0.756495i	$0.273090\pi$
$282$	−1800.11	−0.380124
$283$	−669.144	−0.140553	−0.0702764	−	0.997528i	$-0.522388\pi$
$283$	−669.144	−0.140553	−0.0702764	+	0.997528i	$0.522388\pi$
$284$	−1797.97	−0.375669
$285$	−1357.59	−0.282165
$286$	3106.89	0.642358
$287$	−1570.75	−0.323062
$288$	−677.446	−0.138607
$289$	−1317.33	−0.268131
$290$	−2641.89	−0.534956
$291$	−2439.93	−0.491517
$292$	2198.93	0.440694
$293$	6111.15	1.21849	0.609244	−	0.792982i	$-0.291473\pi$
$293$	6111.15	1.21849	0.609244	+	0.792982i	$0.291473\pi$
$294$	−3077.81	−0.610549
$295$	−4131.93	−0.815492
$296$	−1737.10	−0.341104
$297$	3715.33	0.725877
$298$	−1554.56	−0.302192
$299$	5559.18	1.07524
$300$	−467.789	−0.0900261
$301$	−1348.75	−0.258275
$302$	−1799.65	−0.342907
$303$	−2121.03	−0.402145
$304$	683.115	0.128879
$305$	3601.23	0.676085
$306$	2538.89	0.474310
$307$	−5430.67	−1.00959	−0.504796	−	0.863238i	$-0.668432\pi$
$307$	−5430.67	−1.00959	−0.504796	+	0.863238i	$0.668432\pi$
$308$	4000.78	0.740148
$309$	−1459.78	−0.268751
$310$	−8052.60	−1.47535
$311$	−9228.67	−1.68267	−0.841335	−	0.540515i	$-0.818230\pi$
$311$	−9228.67	−1.68267	−0.841335	+	0.540515i	$0.818230\pi$
$312$	−939.338	−0.170447
$313$	313.000	0.0565233
$313$	313.000	0.0565233
$314$	2278.76	0.409547
$315$	−8729.43	−1.56142
$316$	3128.29	0.556900
$317$	5573.47	0.987499	0.493749	−	0.869604i	$-0.335626\pi$
$317$	5573.47	0.987499	0.493749	+	0.869604i	$0.335626\pi$
$318$	814.541	0.143639
$319$	−3204.12	−0.562370
$320$	842.847	0.147239
$321$	−3333.39	−0.579600
$322$	7158.62	1.23893
$323$	−2560.14	−0.441022
$324$	1163.09	0.199432
$325$	2355.41	0.402015
$326$	−1784.84	−0.303231
$327$	1768.02	0.298995
$328$	−401.334	−0.0675608
$329$	11671.7	1.95587
$330$	−2031.51	−0.338881
$331$	−2722.75	−0.452132	−0.226066	−	0.974112i	$-0.572587\pi$
$331$	−2722.75	−0.452132	−0.226066	+	0.974112i	$0.572587\pi$
$332$	−1431.45	−0.236630
$333$	4596.84	0.756472
$334$	2708.36	0.443698
$335$	4760.68	0.776429
$336$	−1209.60	−0.196395
$337$	−4755.70	−0.768722	−0.384361	−	0.923183i	$-0.625578\pi$
$337$	−4755.70	−0.768722	−0.384361	+	0.923183i	$0.625578\pi$
$338$	335.759	0.0540322
$339$	−3969.61	−0.635987
$340$	−3158.78	−0.503849
$341$	−9766.29	−1.55095
$342$	−1807.71	−0.285818
$343$	9216.59	1.45087
$344$	−344.611	−0.0540122
$345$	−3634.99	−0.567250
$346$	−7655.36	−1.18946
$347$	9543.31	1.47640	0.738201	−	0.674581i	$-0.235676\pi$
$347$	9543.31	1.47640	0.738201	+	0.674581i	$0.235676\pi$
$348$	968.733	0.149223
$349$	1659.02	0.254456	0.127228	−	0.991873i	$-0.459392\pi$
$349$	1659.02	0.254456	0.127228	+	0.991873i	$0.459392\pi$
$350$	3033.09	0.463216
$351$	5656.01	0.860101
$352$	1022.21	0.154785
$353$	3483.10	0.525174	0.262587	−	0.964908i	$-0.415424\pi$
$353$	3483.10	0.525174	0.262587	+	0.964908i	$0.415424\pi$
$354$	1515.10	0.227477
$355$	−5919.59	−0.885012
$356$	−3903.15	−0.581086
$357$	4533.25	0.672060
$358$	−7472.59	−1.10318
$359$	6864.34	1.00915	0.504577	−	0.863367i	$-0.331649\pi$
$359$	6864.34	1.00915	0.504577	+	0.863367i	$0.331649\pi$
$360$	−2230.40	−0.326535
$361$	−5036.17	−0.734242
$362$	−7710.74	−1.11952
$363$	749.868	0.108424
$364$	6090.56	0.877011
$365$	7239.70	1.03820
$366$	−1320.50	−0.188590
$367$	−1332.52	−0.189528	−0.0947641	−	0.995500i	$-0.530210\pi$
$367$	−1332.52	−0.189528	−0.0947641	+	0.995500i	$0.530210\pi$
$368$	1829.05	0.259093
$369$	1062.04	0.149831
$370$	−5719.18	−0.803583
$371$	−5281.39	−0.739073
$372$	2952.74	0.411539
$373$	3635.23	0.504625	0.252313	−	0.967646i	$-0.418809\pi$
$373$	3635.23	0.504625	0.252313	+	0.967646i	$0.418809\pi$
$374$	−3831.00	−0.529669
$375$	2434.58	0.335257
$376$	2982.16	0.409025
$377$	−4877.77	−0.666360
$378$	7283.30	0.991039
$379$	−6746.47	−0.914361	−0.457181	−	0.889374i	$-0.651141\pi$
$379$	−6746.47	−0.914361	−0.457181	+	0.889374i	$0.651141\pi$
$380$	2249.07	0.303618
$381$	5706.86	0.767378
$382$	−716.966	−0.0960292
$383$	−14523.4	−1.93763	−0.968816	−	0.247780i	$-0.920299\pi$
$383$	−14523.4	−1.93763	−0.968816	+	0.247780i	$0.920299\pi$
$384$	−309.056	−0.0410715
$385$	13172.1	1.74366
$386$	970.660	0.127993
$387$	911.936	0.119784
$388$	4042.13	0.528887
$389$	−9524.62	−1.24143	−0.620717	−	0.784035i	$-0.713158\pi$
$389$	−9524.62	−1.24143	−0.620717	+	0.784035i	$0.713158\pi$
$390$	−3092.65	−0.401545
$391$	−6854.83	−0.886608
$392$	5098.87	0.656969
$393$	3002.19	0.385345
$394$	3260.67	0.416930
$395$	10299.5	1.31196
$396$	−2705.06	−0.343268
$397$	1990.99	0.251699	0.125850	−	0.992049i	$-0.459834\pi$
$397$	1990.99	0.251699	0.125850	+	0.992049i	$0.459834\pi$
$398$	7831.97	0.986384
$399$	−3227.70	−0.404981
$400$	774.966	0.0968708
$401$	−14394.5	−1.79259	−0.896296	−	0.443456i	$-0.853752\pi$
$401$	−14394.5	−1.79259	−0.896296	+	0.443456i	$0.853752\pi$
$402$	−1745.65	−0.216580
$403$	−14867.6	−1.83774
$404$	3513.82	0.432720
$405$	3829.31	0.469827
$406$	−6281.15	−0.767803
$407$	−6936.28	−0.844763
$408$	1158.26	0.140546
$409$	−9881.22	−1.19461	−0.597305	−	0.802015i	$-0.703762\pi$
$409$	−9881.22	−1.19461	−0.597305	+	0.802015i	$0.703762\pi$
$410$	−1321.34	−0.159162
$411$	−751.212	−0.0901570
$412$	2418.36	0.289184
$413$	−9823.74	−1.17045
$414$	−4840.18	−0.574593
$415$	−4712.87	−0.557459
$416$	1556.16	0.183406
$417$	1628.39	0.191229
$418$	2727.69	0.319177
$419$	−8409.17	−0.980465	−0.490232	−	0.871592i	$-0.663088\pi$
$419$	−8409.17	−0.980465	−0.490232	+	0.871592i	$0.663088\pi$
$420$	−3982.44	−0.462674
$421$	−2527.03	−0.292541	−0.146271	−	0.989245i	$-0.546727\pi$
$421$	−2527.03	−0.292541	−0.146271	+	0.989245i	$0.546727\pi$
$422$	−5675.84	−0.654729
$423$	−7891.62	−0.907101
$424$	−1349.41	−0.154560
$425$	−2904.38	−0.331489
$426$	2170.60	0.246869
$427$	8561.99	0.970360
$428$	5522.28	0.623667
$429$	−3750.80	−0.422122
$430$	−1134.59	−0.127244
$431$	−612.663	−0.0684709	−0.0342355	−	0.999414i	$-0.510900\pi$
$431$	−612.663	−0.0684709	−0.0342355	+	0.999414i	$0.510900\pi$
$432$	1860.91	0.207253
$433$	6878.34	0.763399	0.381700	−	0.924286i	$-0.375339\pi$
$433$	6878.34	0.763399	0.381700	+	0.924286i	$0.375339\pi$
$434$	−19145.2	−2.11751
$435$	3189.43	0.351543
$436$	−2929.00	−0.321728
$437$	4880.68	0.534267
$438$	−2654.66	−0.289600
$439$	10905.3	1.18561	0.592804	−	0.805347i	$-0.298021\pi$
$439$	10905.3	1.18561	0.592804	+	0.805347i	$0.298021\pi$
$440$	3365.51	0.364646
$441$	−13493.0	−1.45697
$442$	−5832.09	−0.627612
$443$	4473.36	0.479765	0.239882	−	0.970802i	$-0.422891\pi$
$443$	4473.36	0.479765	0.239882	+	0.970802i	$0.422891\pi$
$444$	2097.11	0.224155
$445$	−12850.6	−1.36894
$446$	2941.44	0.312290
$447$	1876.75	0.198584
$448$	2003.88	0.211327
$449$	−13836.8	−1.45434	−0.727171	−	0.686456i	$-0.759165\pi$
$449$	−13836.8	−1.45434	−0.727171	+	0.686456i	$0.759165\pi$
$450$	−2050.77	−0.214832
$451$	−1602.54	−0.167318
$452$	6576.28	0.684341
$453$	2172.62	0.225340
$454$	−2353.32	−0.243275
$455$	20052.4	2.06609
$456$	−824.691	−0.0846923
$457$	10802.0	1.10568	0.552842	−	0.833286i	$-0.313543\pi$
$457$	10802.0	1.10568	0.552842	+	0.833286i	$0.313543\pi$
$458$	3126.69	0.318997
$459$	−6974.22	−0.709213
$460$	6021.93	0.610378
$461$	−1528.99	−0.154473	−0.0772366	−	0.997013i	$-0.524610\pi$
$461$	−1528.99	−0.154473	−0.0772366	+	0.997013i	$0.524610\pi$
$462$	−4829.94	−0.486384
$463$	2301.24	0.230989	0.115494	−	0.993308i	$-0.463155\pi$
$463$	2301.24	0.230989	0.115494	+	0.993308i	$0.463155\pi$
$464$	−1604.86	−0.160568
$465$	9721.51	0.969515
$466$	2410.83	0.239655
$467$	−3794.11	−0.375954	−0.187977	−	0.982173i	$-0.560193\pi$
$467$	−3794.11	−0.375954	−0.187977	+	0.982173i	$0.560193\pi$
$468$	−4118.03	−0.406743
$469$	11318.6	1.11438
$470$	9818.40	0.963593
$471$	−2751.03	−0.269131
$472$	−2510.00	−0.244772
$473$	−1376.04	−0.133764
$474$	−3776.64	−0.365963
$475$	2067.93	0.199754
$476$	−7510.05	−0.723156
$477$	3570.92	0.342770
$478$	−12419.3	−1.18838
$479$	5385.96	0.513760	0.256880	−	0.966443i	$-0.417305\pi$
$479$	5385.96	0.513760	0.256880	+	0.966443i	$0.417305\pi$
$480$	−1017.53	−0.0967575
$481$	−10559.4	−1.00097
$482$	−7746.68	−0.732058
$483$	−8642.25	−0.814153
$484$	−1242.27	−0.116667
$485$	13308.2	1.24597
$486$	−7684.71	−0.717254
$487$	13683.2	1.27319	0.636595	−	0.771199i	$-0.280342\pi$
$487$	13683.2	1.27319	0.636595	+	0.771199i	$0.280342\pi$
$488$	2187.62	0.202928
$489$	2154.75	0.199266
$490$	16787.4	1.54771
$491$	6428.10	0.590827	0.295413	−	0.955370i	$-0.404543\pi$
$491$	6428.10	0.590827	0.295413	+	0.955370i	$0.404543\pi$
$492$	484.510	0.0443972
$493$	6014.60	0.549460
$494$	4152.49	0.378197
$495$	−8906.06	−0.808682
$496$	−4891.67	−0.442828
$497$	−14073.9	−1.27023
$498$	1728.12	0.155500
$499$	12256.6	1.09956	0.549782	−	0.835308i	$-0.314711\pi$
$499$	12256.6	1.09956	0.549782	+	0.835308i	$0.314711\pi$
$500$	−4033.27	−0.360746
$501$	−3269.67	−0.291573
$502$	−9408.43	−0.836491
$503$	−2499.20	−0.221539	−0.110769	−	0.993846i	$-0.535331\pi$
$503$	−2499.20	−0.221539	−0.110769	+	0.993846i	$0.535331\pi$
$504$	−5302.82	−0.468664
$505$	11568.8	1.01942
$506$	7303.46	0.641657
$507$	−405.345	−0.0355069
$508$	−9454.30	−0.825722
$509$	17573.2	1.53029	0.765146	−	0.643857i	$-0.222667\pi$
$509$	17573.2	1.53029	0.765146	+	0.643857i	$0.222667\pi$
$510$	3813.43	0.331101
$511$	17212.5	1.49009
$512$	512.000	0.0441942
$513$	4965.69	0.427369
$514$	1298.27	0.111409
$515$	7962.13	0.681269
$516$	416.032	0.0354938
$517$	11907.9	1.01297
$518$	−13597.4	−1.15335
$519$	9241.94	0.781650
$520$	5123.46	0.432074
$521$	−12697.2	−1.06770	−0.533851	−	0.845578i	$-0.679256\pi$
$521$	−12697.2	−1.06770	−0.533851	+	0.845578i	$0.679256\pi$
$522$	4246.89	0.356095
$523$	11541.7	0.964978	0.482489	−	0.875902i	$-0.339733\pi$
$523$	11541.7	0.964978	0.482489	+	0.875902i	$0.339733\pi$
$524$	−4973.60	−0.414643
$525$	−3661.70	−0.304399
$526$	−10304.8	−0.854205
$527$	18332.7	1.51535
$528$	−1234.07	−0.101716
$529$	901.123	0.0740628
$530$	−4442.78	−0.364117
$531$	6642.15	0.542834
$532$	5347.20	0.435771
$533$	−2439.61	−0.198257
$534$	4712.08	0.381857
$535$	18181.4	1.46925
$536$	2891.94	0.233047
$537$	9021.29	0.724948
$538$	12185.4	0.976486
$539$	20359.9	1.62702
$540$	6126.81	0.488252
$541$	−18020.6	−1.43210	−0.716051	−	0.698048i	$-0.754052\pi$
$541$	−18020.6	−1.43210	−0.716051	+	0.698048i	$0.754052\pi$
$542$	13362.5	1.05899
$543$	9308.80	0.735689
$544$	−1918.85	−0.151231
$545$	−9643.34	−0.757936
$546$	−7352.83	−0.576323
$547$	17542.8	1.37126	0.685629	−	0.727951i	$-0.259527\pi$
$547$	17542.8	1.37126	0.685629	+	0.727951i	$0.259527\pi$
$548$	1244.50	0.0970117
$549$	−5789.04	−0.450037
$550$	3094.46	0.239906
$551$	−4282.43	−0.331103
$552$	−2208.13	−0.170261
$553$	24487.3	1.88301
$554$	10254.9	0.786441
$555$	6904.48	0.528070
$556$	−2697.68	−0.205768
$557$	−12860.7	−0.978321	−0.489160	−	0.872194i	$-0.662697\pi$
$557$	−12860.7	−0.978321	−0.489160	+	0.872194i	$0.662697\pi$
$558$	12944.7	0.982066
$559$	−2094.81	−0.158499
$560$	6597.53	0.497851
$561$	4624.98	0.348069
$562$	12322.4	0.924894
$563$	7577.64	0.567246	0.283623	−	0.958936i	$-0.408464\pi$
$563$	7577.64	0.567246	0.283623	+	0.958936i	$0.408464\pi$
$564$	−3600.22	−0.268788
$565$	21651.6	1.61219
$566$	−1338.29	−0.0993859
$567$	9104.26	0.674326
$568$	−3595.94	−0.265638
$569$	2939.67	0.216586	0.108293	−	0.994119i	$-0.465462\pi$
$569$	2939.67	0.216586	0.108293	+	0.994119i	$0.465462\pi$
$570$	−2715.19	−0.199521
$571$	−24699.3	−1.81022	−0.905108	−	0.425181i	$-0.860210\pi$
$571$	−24699.3	−1.81022	−0.905108	+	0.425181i	$0.860210\pi$
$572$	6213.79	0.454216
$573$	865.558	0.0631050
$574$	−3141.51	−0.228439
$575$	5536.93	0.401576
$576$	−1354.89	−0.0980101
$577$	2379.15	0.171656	0.0858279	−	0.996310i	$-0.472646\pi$
$577$	2379.15	0.171656	0.0858279	+	0.996310i	$0.472646\pi$
$578$	−2634.66	−0.189597
$579$	−1171.83	−0.0841099
$580$	−5283.79	−0.378271
$581$	−11204.9	−0.800101
$582$	−4879.86	−0.347555
$583$	−5388.25	−0.382776
$584$	4397.86	0.311618
$585$	−13558.1	−0.958218
$586$	12222.3	0.861602
$587$	−1807.02	−0.127059	−0.0635295	−	0.997980i	$-0.520236\pi$
$587$	−1807.02	−0.127059	−0.0635295	+	0.997980i	$0.520236\pi$
$588$	−6155.62	−0.431724
$589$	−13053.0	−0.913142
$590$	−8263.86	−0.576640
$591$	−3936.45	−0.273983
$592$	−3474.20	−0.241197
$593$	−12579.2	−0.871104	−0.435552	−	0.900164i	$-0.643447\pi$
$593$	−12579.2	−0.871104	−0.435552	+	0.900164i	$0.643447\pi$
$594$	7430.67	0.513273
$595$	−24725.9	−1.70363
$596$	−3109.12	−0.213682
$597$	−9455.15	−0.648197
$598$	11118.4	0.760308
$599$	12501.1	0.852723	0.426361	−	0.904553i	$-0.359795\pi$
$599$	12501.1	0.852723	0.426361	+	0.904553i	$0.359795\pi$
$600$	−935.578	−0.0636581
$601$	19561.0	1.32764	0.663818	−	0.747894i	$-0.268935\pi$
$601$	19561.0	1.32764	0.663818	+	0.747894i	$0.268935\pi$
$602$	−2697.50	−0.182628
$603$	−7652.87	−0.516831
$604$	−3599.29	−0.242472
$605$	−4090.03	−0.274848
$606$	−4242.06	−0.284360
$607$	−26049.7	−1.74188	−0.870942	−	0.491386i	$-0.836490\pi$
$607$	−26049.7	−1.74188	−0.870942	+	0.491386i	$0.836490\pi$
$608$	1366.23	0.0911314
$609$	7582.92	0.504557
$610$	7202.46	0.478064
$611$	18127.8	1.20028
$612$	5077.79	0.335388
$613$	−10439.2	−0.687823	−0.343911	−	0.939002i	$-0.611752\pi$
$613$	−10439.2	−0.687823	−0.343911	+	0.939002i	$0.611752\pi$
$614$	−10861.3	−0.713890
$615$	1595.19	0.104592
$616$	8001.56	0.523364
$617$	24810.8	1.61887	0.809437	−	0.587207i	$-0.199772\pi$
$617$	24810.8	1.61887	0.809437	+	0.587207i	$0.199772\pi$
$618$	−2919.56	−0.190036
$619$	27224.0	1.76773	0.883864	−	0.467744i	$-0.154933\pi$
$619$	27224.0	1.76773	0.883864	+	0.467744i	$0.154933\pi$
$620$	−16105.2	−1.04323
$621$	13295.7	0.859162
$622$	−18457.3	−1.18983
$623$	−30552.6	−1.96479
$624$	−1878.68	−0.120524
$625$	−19333.4	−1.23734
$626$	626.000	0.0399680
$627$	−3293.01	−0.209745
$628$	4557.52	0.289593
$629$	13020.4	0.825370
$630$	−17458.9	−1.10409
$631$	−20277.6	−1.27930	−0.639650	−	0.768667i	$-0.720921\pi$
$631$	−20277.6	−1.27930	−0.639650	+	0.768667i	$0.720921\pi$
$632$	6256.59	0.393788
$633$	6852.16	0.430251
$634$	11146.9	0.698267
$635$	−31127.1	−1.94526
$636$	1629.08	0.101568
$637$	30994.8	1.92788
$638$	−6408.23	−0.397656
$639$	9515.85	0.589110
$640$	1685.69	0.104114
$641$	8812.26	0.543001	0.271500	−	0.962438i	$-0.412480\pi$
$641$	8812.26	0.543001	0.271500	+	0.962438i	$0.412480\pi$
$642$	−6666.78	−0.409839
$643$	−22072.2	−1.35372	−0.676861	−	0.736111i	$-0.736660\pi$
$643$	−22072.2	−1.35372	−0.676861	+	0.736111i	$0.736660\pi$
$644$	14317.2	0.876053
$645$	1369.73	0.0836173
$646$	−5120.28	−0.311849
$647$	8614.02	0.523419	0.261710	−	0.965147i	$-0.415714\pi$
$647$	8614.02	0.523419	0.261710	+	0.965147i	$0.415714\pi$
$648$	2326.17	0.141020
$649$	−10022.5	−0.606190
$650$	4710.83	0.284268
$651$	23113.1	1.39151
$652$	−3569.69	−0.214417
$653$	−9785.80	−0.586444	−0.293222	−	0.956044i	$-0.594728\pi$
$653$	−9785.80	−0.586444	−0.293222	+	0.956044i	$0.594728\pi$
$654$	3536.03	0.211422
$655$	−16374.9	−0.976827
$656$	−802.667	−0.0477727
$657$	−11637.9	−0.691080
$658$	23343.4	1.38301
$659$	−5647.85	−0.333853	−0.166926	−	0.985969i	$-0.553384\pi$
$659$	−5647.85	−0.333853	−0.166926	+	0.985969i	$0.553384\pi$
$660$	−4063.01	−0.239625
$661$	3365.97	0.198065	0.0990325	−	0.995084i	$-0.468425\pi$
$661$	3365.97	0.198065	0.0990325	+	0.995084i	$0.468425\pi$
$662$	−5445.49	−0.319706
$663$	7040.80	0.412431
$664$	−2862.90	−0.167323
$665$	17605.0	1.02660
$666$	9193.68	0.534906
$667$	−11466.3	−0.665632
$668$	5416.73	0.313742
$669$	−3551.06	−0.205219
$670$	9521.36	0.549018
$671$	8735.22	0.502563
$672$	−2419.19	−0.138872
$673$	10650.6	0.610030	0.305015	−	0.952348i	$-0.401339\pi$
$673$	10650.6	0.610030	0.305015	+	0.952348i	$0.401339\pi$
$674$	−9511.40	−0.543569
$675$	5633.37	0.321228
$676$	671.518	0.0382065
$677$	12454.3	0.707028	0.353514	−	0.935429i	$-0.384987\pi$
$677$	12454.3	0.707028	0.353514	+	0.935429i	$0.384987\pi$
$678$	−7939.22	−0.449711
$679$	31640.5	1.78829
$680$	−6317.55	−0.356275
$681$	2841.05	0.159867
$682$	−19532.6	−1.09669
$683$	−24732.9	−1.38562	−0.692810	−	0.721120i	$-0.743628\pi$
$683$	−24732.9	−1.38562	−0.692810	+	0.721120i	$0.743628\pi$
$684$	−3615.42	−0.202104
$685$	4097.36	0.228543
$686$	18433.2	1.02592
$687$	−3774.69	−0.209627
$688$	−689.223	−0.0381924
$689$	−8202.76	−0.453556
$690$	−7269.98	−0.401106
$691$	23654.6	1.30226	0.651130	−	0.758966i	$-0.274295\pi$
$691$	23654.6	1.30226	0.651130	+	0.758966i	$0.274295\pi$
$692$	−15310.7	−0.841079
$693$	−21174.3	−1.16067
$694$	19086.6	1.04397
$695$	−8881.76	−0.484754
$696$	1937.47	0.105516
$697$	3008.19	0.163477
$698$	3318.04	0.179928
$699$	−2910.47	−0.157488
$700$	6066.18	0.327543
$701$	9197.68	0.495566	0.247783	−	0.968816i	$-0.420298\pi$
$701$	9197.68	0.495566	0.247783	+	0.968816i	$0.420298\pi$
$702$	11312.0	0.608183
$703$	−9270.61	−0.497365
$704$	2044.43	0.109449
$705$	−11853.3	−0.633220
$706$	6966.19	0.371354
$707$	27505.0	1.46313
$708$	3030.20	0.160850
$709$	33840.9	1.79255	0.896277	−	0.443496i	$-0.146262\pi$
$709$	33840.9	1.79255	0.896277	+	0.443496i	$0.146262\pi$
$710$	−11839.2	−0.625798
$711$	−16556.6	−0.873309
$712$	−7806.30	−0.410890
$713$	−34949.8	−1.83573
$714$	9066.51	0.475218
$715$	20458.1	1.07006
$716$	−14945.2	−0.780066
$717$	14993.2	0.780938
$718$	13728.7	0.713579
$719$	−32933.1	−1.70820	−0.854102	−	0.520105i	$-0.825893\pi$
$719$	−32933.1	−1.70820	−0.854102	+	0.520105i	$0.825893\pi$
$720$	−4460.81	−0.230895
$721$	18930.1	0.977801
$722$	−10072.3	−0.519187
$723$	9352.19	0.481067
$724$	−15421.5	−0.791623
$725$	−4858.24	−0.248870
$726$	1499.74	0.0766672
$727$	34287.8	1.74919	0.874596	−	0.484852i	$-0.161126\pi$
$727$	34287.8	1.74919	0.874596	+	0.484852i	$0.161126\pi$
$728$	12181.1	0.620140
$729$	1426.54	0.0724759
$730$	14479.4	0.734119
$731$	2583.03	0.130693
$732$	−2641.01	−0.133353
$733$	21750.3	1.09600	0.547998	−	0.836480i	$-0.315390\pi$
$733$	21750.3	1.09600	0.547998	+	0.836480i	$0.315390\pi$
$734$	−2665.03	−0.134017
$735$	−20266.6	−1.01707
$736$	3658.11	0.183206
$737$	11547.6	0.577153
$738$	2124.08	0.105946
$739$	15996.8	0.796280	0.398140	−	0.917325i	$-0.369656\pi$
$739$	15996.8	0.796280	0.398140	+	0.917325i	$0.369656\pi$
$740$	−11438.4	−0.568219
$741$	−5013.09	−0.248530
$742$	−10562.8	−0.522603
$743$	−24335.4	−1.20159	−0.600793	−	0.799405i	$-0.705148\pi$
$743$	−24335.4	−1.20159	−0.600793	+	0.799405i	$0.705148\pi$
$744$	5905.48	0.291002
$745$	−10236.4	−0.503399
$746$	7270.47	0.356824
$747$	7576.02	0.371074
$748$	−7662.00	−0.374533
$749$	43226.6	2.10877
$750$	4869.16	0.237062
$751$	−7852.93	−0.381568	−0.190784	−	0.981632i	$-0.561103\pi$
$751$	−7852.93	−0.381568	−0.190784	+	0.981632i	$0.561103\pi$
$752$	5964.33	0.289224
$753$	11358.3	0.549695
$754$	−9755.53	−0.471188
$755$	−11850.2	−0.571223
$756$	14566.6	0.700770
$757$	28080.7	1.34823	0.674116	−	0.738625i	$-0.264525\pi$
$757$	28080.7	1.34823	0.674116	+	0.738625i	$0.264525\pi$
$758$	−13492.9	−0.646551
$759$	−8817.11	−0.421661
$760$	4498.13	0.214690
$761$	−36954.5	−1.76032	−0.880158	−	0.474681i	$-0.842563\pi$
$761$	−36954.5	−1.76032	−0.880158	+	0.474681i	$0.842563\pi$
$762$	11413.7	0.542618
$763$	−22927.2	−1.08784
$764$	−1433.93	−0.0679029
$765$	16718.0	0.790117
$766$	−29046.9	−1.37011
$767$	−15257.7	−0.718283
$768$	−618.112	−0.0290419
$769$	23536.0	1.10368	0.551841	−	0.833950i	$-0.313926\pi$
$769$	23536.0	1.10368	0.551841	+	0.833950i	$0.313926\pi$
$770$	26344.1	1.23296
$771$	−1567.33	−0.0732116
$772$	1941.32	0.0905048
$773$	−33874.0	−1.57615	−0.788074	−	0.615580i	$-0.788922\pi$
$773$	−33874.0	−1.57615	−0.788074	+	0.615580i	$0.788922\pi$
$774$	1823.87	0.0846999
$775$	−14808.1	−0.686353
$776$	8084.26	0.373979
$777$	16415.5	0.757920
$778$	−19049.2	−0.877826
$779$	−2141.85	−0.0985106
$780$	−6185.30	−0.283935
$781$	−14358.7	−0.657867
$782$	−13709.7	−0.626926
$783$	−11666.0	−0.532451
$784$	10197.7	0.464548
$785$	15005.0	0.682233
$786$	6004.38	0.272480
$787$	−37968.0	−1.71971	−0.859857	−	0.510536i	$-0.829447\pi$
$787$	−37968.0	−1.71971	−0.859857	+	0.510536i	$0.829447\pi$
$788$	6521.34	0.294814
$789$	12440.5	0.561336
$790$	20599.0	0.927696
$791$	51477.0	2.31392
$792$	−5410.12	−0.242727
$793$	13298.0	0.595493
$794$	3981.97	0.177978
$795$	5363.54	0.239277
$796$	15663.9	0.697479
$797$	5028.90	0.223504	0.111752	−	0.993736i	$-0.464354\pi$
$797$	5028.90	0.223504	0.111752	+	0.993736i	$0.464354\pi$
$798$	−6455.41	−0.286365
$799$	−22352.8	−0.989718
$800$	1549.93	0.0684980
$801$	20657.6	0.911237
$802$	−28789.1	−1.26755
$803$	17560.8	0.771739
$804$	−3491.30	−0.153145
$805$	47137.7	2.06383
$806$	−29735.3	−1.29948
$807$	−14710.8	−0.641692
$808$	7027.64	0.305980
$809$	−31912.2	−1.38686	−0.693432	−	0.720522i	$-0.743902\pi$
$809$	−31912.2	−1.38686	−0.693432	+	0.720522i	$0.743902\pi$
$810$	7658.62	0.332218
$811$	−13259.7	−0.574121	−0.287061	−	0.957912i	$-0.592678\pi$
$811$	−13259.7	−0.574121	−0.287061	+	0.957912i	$0.592678\pi$
$812$	−12562.3	−0.542919
$813$	−16131.9	−0.695906
$814$	−13872.6	−0.597338
$815$	−11752.7	−0.505129
$816$	2316.53	0.0993807
$817$	−1839.13	−0.0787554
$818$	−19762.4	−0.844716
$819$	−32234.6	−1.37530
$820$	−2642.68	−0.112544
$821$	33014.7	1.40344	0.701718	−	0.712455i	$-0.252417\pi$
$821$	33014.7	1.40344	0.701718	+	0.712455i	$0.252417\pi$
$822$	−1502.42	−0.0637506
$823$	42448.5	1.79789	0.898943	−	0.438065i	$-0.144336\pi$
$823$	42448.5	1.79789	0.898943	+	0.438065i	$0.144336\pi$
$824$	4836.72	0.204484
$825$	−3735.79	−0.157653
$826$	−19647.5	−0.827631
$827$	5124.77	0.215485	0.107742	−	0.994179i	$-0.465638\pi$
$827$	5124.77	0.215485	0.107742	+	0.994179i	$0.465638\pi$
$828$	−9680.35	−0.406299
$829$	−11237.9	−0.470817	−0.235409	−	0.971896i	$-0.575643\pi$
$829$	−11237.9	−0.470817	−0.235409	+	0.971896i	$0.575643\pi$
$830$	−9425.74	−0.394183
$831$	−12380.2	−0.516805
$832$	3112.32	0.129688
$833$	−38218.6	−1.58967
$834$	3256.77	0.135219
$835$	17833.9	0.739122
$836$	5455.39	0.225692
$837$	−35558.5	−1.46844
$838$	−16818.3	−0.693293
$839$	−12030.2	−0.495030	−0.247515	−	0.968884i	$-0.579614\pi$
$839$	−12030.2	−0.495030	−0.247515	+	0.968884i	$0.579614\pi$
$840$	−7964.87	−0.327160
$841$	−14328.2	−0.587486
$842$	−5054.06	−0.206858
$843$	−14876.3	−0.607789
$844$	−11351.7	−0.462963
$845$	2210.89	0.0900081
$846$	−15783.2	−0.641417
$847$	−9724.11	−0.394480
$848$	−2698.83	−0.109290
$849$	1615.65	0.0653108
$850$	−5808.75	−0.234398
$851$	−24822.3	−0.999878
$852$	4341.21	0.174563
$853$	39445.0	1.58332	0.791659	−	0.610963i	$-0.209217\pi$
$853$	39445.0	1.58332	0.791659	+	0.610963i	$0.209217\pi$
$854$	17124.0	0.686148
$855$	−11903.3	−0.476122
$856$	11044.6	0.440999
$857$	−4905.92	−0.195546	−0.0977732	−	0.995209i	$-0.531172\pi$
$857$	−4905.92	−0.195546	−0.0977732	+	0.995209i	$0.531172\pi$
$858$	−7501.60	−0.298485
$859$	−3407.05	−0.135328	−0.0676642	−	0.997708i	$-0.521555\pi$
$859$	−3407.05	−0.135328	−0.0676642	+	0.997708i	$0.521555\pi$
$860$	−2269.18	−0.0899748
$861$	3792.59	0.150117
$862$	−1225.33	−0.0484162
$863$	7821.25	0.308503	0.154252	−	0.988032i	$-0.450703\pi$
$863$	7821.25	0.308503	0.154252	+	0.988032i	$0.450703\pi$
$864$	3721.82	0.146550
$865$	−50408.6	−1.98144
$866$	13756.7	0.539805
$867$	3180.69	0.124593
$868$	−38290.4	−1.49731
$869$	24982.7	0.975236
$870$	6378.86	0.248579
$871$	17579.4	0.683876
$872$	−5857.99	−0.227496
$873$	−21393.2	−0.829380
$874$	9761.36	0.377784
$875$	−31571.1	−1.21977
$876$	−5309.32	−0.204778
$877$	21958.9	0.845494	0.422747	−	0.906248i	$-0.361066\pi$
$877$	21958.9	0.845494	0.422747	+	0.906248i	$0.361066\pi$
$878$	21810.6	0.838351
$879$	−14755.4	−0.566196
$880$	6731.02	0.257844
$881$	−28068.9	−1.07340	−0.536700	−	0.843773i	$-0.680329\pi$
$881$	−28068.9	−1.07340	−0.536700	+	0.843773i	$0.680329\pi$
$882$	−26986.0	−1.03023
$883$	−32976.9	−1.25681	−0.628405	−	0.777887i	$-0.716292\pi$
$883$	−32976.9	−1.25681	−0.628405	+	0.777887i	$0.716292\pi$
$884$	−11664.2	−0.443789
$885$	9976.55	0.378936
$886$	8946.72	0.339245
$887$	−24303.8	−0.920002	−0.460001	−	0.887918i	$-0.652151\pi$
$887$	−24303.8	−0.920002	−0.460001	+	0.887918i	$0.652151\pi$
$888$	4194.23	0.158501
$889$	−74005.2	−2.79196
$890$	−25701.3	−0.967987
$891$	9288.46	0.349243
$892$	5882.88	0.220822
$893$	15915.3	0.596401
$894$	3753.49	0.140420
$895$	−49205.1	−1.83770
$896$	4007.77	0.149431
$897$	−13422.7	−0.499632
$898$	−27673.6	−1.02838
$899$	30665.8	1.13767
$900$	−4101.54	−0.151909
$901$	10114.5	0.373989
$902$	−3205.07	−0.118312
$903$	3256.56	0.120013
$904$	13152.6	0.483902
$905$	−50773.3	−1.86493
$906$	4345.25	0.159339
$907$	18529.5	0.678347	0.339173	−	0.940724i	$-0.389853\pi$
$907$	18529.5	0.678347	0.339173	+	0.940724i	$0.389853\pi$
$908$	−4706.64	−0.172021
$909$	−18597.0	−0.678575
$910$	40104.8	1.46095
$911$	23987.1	0.872367	0.436184	−	0.899858i	$-0.356330\pi$
$911$	23987.1	0.872367	0.436184	+	0.899858i	$0.356330\pi$
$912$	−1649.38	−0.0598865
$913$	−11431.6	−0.414383
$914$	21604.0	0.781836
$915$	−8695.18	−0.314157
$916$	6253.37	0.225565
$917$	−38931.7	−1.40201
$918$	−13948.4	−0.501489
$919$	−11836.0	−0.424847	−0.212424	−	0.977178i	$-0.568136\pi$
$919$	−11836.0	−0.424847	−0.212424	+	0.977178i	$0.568136\pi$
$920$	12043.9	0.431602
$921$	13112.4	0.469128
$922$	−3057.98	−0.109229
$923$	−21858.9	−0.779516
$924$	−9659.89	−0.343925
$925$	−10517.1	−0.373839
$926$	4602.48	0.163334
$927$	−12799.3	−0.453488
$928$	−3209.71	−0.113539
$929$	32429.5	1.14529	0.572647	−	0.819802i	$-0.305917\pi$
$929$	32429.5	1.14529	0.572647	+	0.819802i	$0.305917\pi$
$930$	19443.0	0.685550
$931$	27211.8	0.957929
$932$	4821.65	0.169462
$933$	22282.6	0.781888
$934$	−7588.22	−0.265839
$935$	−25226.1	−0.882335
$936$	−8236.05	−0.287611
$937$	−42685.6	−1.48824	−0.744118	−	0.668048i	$-0.767130\pi$
$937$	−42685.6	−1.48824	−0.744118	+	0.668048i	$0.767130\pi$
$938$	22637.2	0.787986
$939$	−755.739	−0.0262648
$940$	19636.8	0.681363
$941$	4872.38	0.168794	0.0843970	−	0.996432i	$-0.473104\pi$
$941$	4872.38	0.168794	0.0843970	+	0.996432i	$0.473104\pi$
$942$	−5502.06	−0.190305
$943$	−5734.85	−0.198041
$944$	−5020.00	−0.173080
$945$	47958.7	1.65090
$946$	−2752.08	−0.0945855
$947$	−49189.9	−1.68792	−0.843959	−	0.536408i	$-0.819781\pi$
$947$	−49189.9	−1.68792	−0.843959	+	0.536408i	$0.819781\pi$
$948$	−7553.27	−0.258775
$949$	26733.5	0.914443
$950$	4135.87	0.141248
$951$	−13457.1	−0.458862
$952$	−15020.1	−0.511349
$953$	27492.4	0.934486	0.467243	−	0.884129i	$-0.345247\pi$
$953$	27492.4	0.934486	0.467243	+	0.884129i	$0.345247\pi$
$954$	7141.84	0.242375
$955$	−4721.04	−0.159968
$956$	−24838.6	−0.840312
$957$	7736.35	0.261317
$958$	10771.9	0.363283
$959$	9741.54	0.328019
$960$	−2035.06	−0.0684179
$961$	63679.6	2.13754
$962$	−21118.8	−0.707793
$963$	−29226.9	−0.978011
$964$	−15493.4	−0.517643
$965$	6391.55	0.213214
$966$	−17284.5	−0.575693
$967$	33211.6	1.10446	0.552230	−	0.833692i	$-0.313777\pi$
$967$	33211.6	1.10446	0.552230	+	0.833692i	$0.313777\pi$
$968$	−2484.55	−0.0824963
$969$	6181.46	0.204930
$970$	26616.4	0.881032
$971$	−25814.8	−0.853180	−0.426590	−	0.904445i	$-0.640285\pi$
$971$	−25814.8	−0.853180	−0.426590	+	0.904445i	$0.640285\pi$
$972$	−15369.4	−0.507176
$973$	−21116.5	−0.695750
$974$	27366.3	0.900281
$975$	−5687.15	−0.186805
$976$	4375.24	0.143492
$977$	29129.0	0.953858	0.476929	−	0.878942i	$-0.341750\pi$
$977$	29129.0	0.953858	0.476929	+	0.878942i	$0.341750\pi$
$978$	4309.51	0.140903
$979$	−31170.8	−1.01759
$980$	33574.8	1.09439
$981$	15501.8	0.504522
$982$	12856.2	0.417778
$983$	−30415.4	−0.986876	−0.493438	−	0.869781i	$-0.664260\pi$
$983$	−30415.4	−0.986876	−0.493438	+	0.869781i	$0.664260\pi$
$984$	969.021	0.0313936
$985$	21470.7	0.694531
$986$	12029.2	0.388527
$987$	−28181.3	−0.908837
$988$	8304.97	0.267425
$989$	−4924.32	−0.158326
$990$	−17812.1	−0.571824
$991$	−28364.3	−0.909206	−0.454603	−	0.890694i	$-0.650219\pi$
$991$	−28364.3	−0.909206	−0.454603	+	0.890694i	$0.650219\pi$
$992$	−9783.35	−0.313127
$993$	6574.08	0.210093
$994$	−28147.9	−0.898185
$995$	51571.5	1.64314
$996$	3456.24	0.109955
$997$	34690.3	1.10196	0.550979	−	0.834519i	$-0.314255\pi$
$997$	34690.3	1.10196	0.550979	+	0.834519i	$0.314255\pi$
$998$	24513.3	0.777509
$999$	−25254.6	−0.799820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	626.4.a.d.1.11	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
626.4.a.d.1.11	✓	25	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 626 = 2 \cdot 313 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	626.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -2.41450 q^{3} +4.00000 q^{4} +13.1695 q^{5} -4.82900 q^{6} +31.3107 q^{7} +8.00000 q^{8} -21.1702 q^{9} +26.3390 q^{10} +31.9442 q^{11} -9.65801 q^{12} +48.6300 q^{13} +62.6214 q^{14} -31.7977 q^{15} +16.0000 q^{16} -59.9639 q^{17} -42.3404 q^{18} +42.6947 q^{19} +52.6779 q^{20} -75.5997 q^{21} +63.8884 q^{22} +114.316 q^{23} -19.3160 q^{24} +48.4354 q^{25} +97.2601 q^{26} +116.307 q^{27} +125.243 q^{28} -100.304 q^{29} -63.5955 q^{30} -305.730 q^{31} +32.0000 q^{32} -77.1293 q^{33} -119.928 q^{34} +412.346 q^{35} -84.6807 q^{36} -217.137 q^{37} +85.3893 q^{38} -117.417 q^{39} +105.356 q^{40} -50.1667 q^{41} -151.199 q^{42} -43.0764 q^{43} +127.777 q^{44} -278.800 q^{45} +228.632 q^{46} +372.771 q^{47} -38.6320 q^{48} +637.359 q^{49} +96.8708 q^{50} +144.783 q^{51} +194.520 q^{52} -168.677 q^{53} +232.614 q^{54} +420.689 q^{55} +250.486 q^{56} -103.086 q^{57} -200.607 q^{58} -313.750 q^{59} -127.191 q^{60} +273.453 q^{61} -611.459 q^{62} -662.853 q^{63} +64.0000 q^{64} +640.433 q^{65} -154.259 q^{66} +361.493 q^{67} -239.856 q^{68} -276.016 q^{69} +824.691 q^{70} -449.493 q^{71} -169.361 q^{72} +549.733 q^{73} -434.275 q^{74} -116.947 q^{75} +170.779 q^{76} +1000.19 q^{77} -234.835 q^{78} +782.074 q^{79} +210.712 q^{80} +290.772 q^{81} -100.333 q^{82} -357.863 q^{83} -302.399 q^{84} -789.694 q^{85} -86.1528 q^{86} +242.183 q^{87} +255.554 q^{88} -975.788 q^{89} -557.601 q^{90} +1522.64 q^{91} +457.264 q^{92} +738.185 q^{93} +745.541 q^{94} +562.267 q^{95} -77.2640 q^{96} +1010.53 q^{97} +1274.72 q^{98} -676.264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 50 q^{2} + 16 q^{3} + 100 q^{4} + 40 q^{5} + 32 q^{6} + 51 q^{7} + 200 q^{8} + 351 q^{9} + 80 q^{10} + 178 q^{11} + 64 q^{12} + 142 q^{13} + 102 q^{14} + 151 q^{15} + 400 q^{16} + 339 q^{17} + 702 q^{18}+ \cdots + 2233 q^{99}+O(q^{100}) \) 25 * q + 50 * q^2 + 16 * q^3 + 100 * q^4 + 40 * q^5 + 32 * q^6 + 51 * q^7 + 200 * q^8 + 351 * q^9 + 80 * q^10 + 178 * q^11 + 64 * q^12 + 142 * q^13 + 102 * q^14 + 151 * q^15 + 400 * q^16 + 339 * q^17 + 702 * q^18 + 305 * q^19 + 160 * q^20 + 326 * q^21 + 356 * q^22 + 128 * q^23 + 128 * q^24 + 1181 * q^25 + 284 * q^26 + 505 * q^27 + 204 * q^28 + 700 * q^29 + 302 * q^30 + 944 * q^31 + 800 * q^32 + 526 * q^33 + 678 * q^34 + 529 * q^35 + 1404 * q^36 + 1165 * q^37 + 610 * q^38 + 872 * q^39 + 320 * q^40 + 970 * q^41 + 652 * q^42 + 855 * q^43 + 712 * q^44 + 1749 * q^45 + 256 * q^46 + 894 * q^47 + 256 * q^48 + 3132 * q^49 + 2362 * q^50 + 1939 * q^51 + 568 * q^52 + 1756 * q^53 + 1010 * q^54 + 1518 * q^55 + 408 * q^56 + 1813 * q^57 + 1400 * q^58 + 1364 * q^59 + 604 * q^60 + 1972 * q^61 + 1888 * q^62 + 2199 * q^63 + 1600 * q^64 + 3344 * q^65 + 1052 * q^66 + 2383 * q^67 + 1356 * q^68 + 2516 * q^69 + 1058 * q^70 + 1487 * q^71 + 2808 * q^72 + 2284 * q^73 + 2330 * q^74 + 3715 * q^75 + 1220 * q^76 + 3746 * q^77 + 1744 * q^78 + 373 * q^79 + 640 * q^80 + 4521 * q^81 + 1940 * q^82 + 1012 * q^83 + 1304 * q^84 - 364 * q^85 + 1710 * q^86 - 5697 * q^87 + 1424 * q^88 - 654 * q^89 + 3498 * q^90 - 835 * q^91 + 512 * q^92 - 480 * q^93 + 1788 * q^94 - 2436 * q^95 + 512 * q^96 - 609 * q^97 + 6264 * q^98 + 2233 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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