LMFDB - Embedded newform 2015.4.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2015,4,Mod(1,2015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2015.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2015 = 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$118.888848662$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	2015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.829109 q^{2} -3.61767 q^{3} -7.31258 q^{4} -5.00000 q^{5} +2.99944 q^{6} -4.39822 q^{7} +12.6958 q^{8} -13.9125 q^{9} +O(q^{10})$	\(q-0.829109 q^{2} -3.61767 q^{3} -7.31258 q^{4} -5.00000 q^{5} +2.99944 q^{6} -4.39822 q^{7} +12.6958 q^{8} -13.9125 q^{9} +4.14555 q^{10} -4.67807 q^{11} +26.4545 q^{12} -13.0000 q^{13} +3.64661 q^{14} +18.0884 q^{15} +47.9744 q^{16} +24.5601 q^{17} +11.5350 q^{18} -157.447 q^{19} +36.5629 q^{20} +15.9113 q^{21} +3.87863 q^{22} +32.4425 q^{23} -45.9292 q^{24} +25.0000 q^{25} +10.7784 q^{26} +148.008 q^{27} +32.1623 q^{28} -153.795 q^{29} -14.9972 q^{30} +31.0000 q^{31} -141.342 q^{32} +16.9237 q^{33} -20.3630 q^{34} +21.9911 q^{35} +101.736 q^{36} -242.437 q^{37} +130.540 q^{38} +47.0297 q^{39} -63.4790 q^{40} +304.120 q^{41} -13.1922 q^{42} +350.846 q^{43} +34.2087 q^{44} +69.5623 q^{45} -26.8983 q^{46} +182.552 q^{47} -173.556 q^{48} -323.656 q^{49} -20.7277 q^{50} -88.8505 q^{51} +95.0635 q^{52} +265.910 q^{53} -122.715 q^{54} +23.3903 q^{55} -55.8389 q^{56} +569.590 q^{57} +127.513 q^{58} +159.751 q^{59} -132.272 q^{60} +732.433 q^{61} -25.7024 q^{62} +61.1901 q^{63} -266.607 q^{64} +65.0000 q^{65} -14.0316 q^{66} +114.275 q^{67} -179.598 q^{68} -117.366 q^{69} -18.2330 q^{70} -604.236 q^{71} -176.630 q^{72} +1158.49 q^{73} +201.007 q^{74} -90.4418 q^{75} +1151.34 q^{76} +20.5752 q^{77} -38.9928 q^{78} +521.596 q^{79} -239.872 q^{80} -159.807 q^{81} -252.149 q^{82} +709.181 q^{83} -116.353 q^{84} -122.801 q^{85} -290.889 q^{86} +556.380 q^{87} -59.3918 q^{88} -1209.88 q^{89} -57.6748 q^{90} +57.1769 q^{91} -237.238 q^{92} -112.148 q^{93} -151.355 q^{94} +787.233 q^{95} +511.330 q^{96} +231.784 q^{97} +268.346 q^{98} +65.0834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.829109	−0.293134	−0.146567	−	0.989201i	$-0.546822\pi$
$2$	−0.829109	−0.293134	−0.146567	+	0.989201i	$0.546822\pi$
$3$	−3.61767	−0.696221	−0.348110	−	0.937454i	$-0.613177\pi$
$3$	−3.61767	−0.696221	−0.348110	+	0.937454i	$0.613177\pi$
$4$	−7.31258	−0.914072
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	2.99944	0.204086
$7$	−4.39822	−0.237482	−0.118741	−	0.992925i	$-0.537886\pi$
$7$	−4.39822	−0.237482	−0.118741	+	0.992925i	$0.537886\pi$
$8$	12.6958	0.561080
$9$	−13.9125	−0.515276
$10$	4.14555	0.131094
$11$	−4.67807	−0.128226	−0.0641132	−	0.997943i	$-0.520422\pi$
$11$	−4.67807	−0.128226	−0.0641132	+	0.997943i	$0.520422\pi$
$12$	26.4545	0.636396
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	3.64661	0.0696140
$15$	18.0884	0.311359
$16$	47.9744	0.749600
$17$	24.5601	0.350395	0.175197	−	0.984533i	$-0.443944\pi$
$17$	24.5601	0.350395	0.175197	+	0.984533i	$0.443944\pi$
$18$	11.5350	0.151045
$19$	−157.447	−1.90109	−0.950545	−	0.310586i	$-0.899475\pi$
$19$	−157.447	−1.90109	−0.950545	+	0.310586i	$0.899475\pi$
$20$	36.5629	0.408786
$21$	15.9113	0.165340
$22$	3.87863	0.0375876
$23$	32.4425	0.294118	0.147059	−	0.989128i	$-0.453019\pi$
$23$	32.4425	0.294118	0.147059	+	0.989128i	$0.453019\pi$
$24$	−45.9292	−0.390636
$25$	25.0000	0.200000
$26$	10.7784	0.0813009
$27$	148.008	1.05497
$28$	32.1623	0.217075
$29$	−153.795	−0.984794	−0.492397	−	0.870371i	$-0.663879\pi$
$29$	−153.795	−0.984794	−0.492397	+	0.870371i	$0.663879\pi$
$30$	−14.9972	−0.0912702
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−141.342	−0.780814
$33$	16.9237	0.0892739
$34$	−20.3630	−0.102713
$35$	21.9911	0.106205
$36$	101.736	0.471000
$37$	−242.437	−1.07720	−0.538599	−	0.842562i	$-0.681046\pi$
$37$	−242.437	−1.07720	−0.538599	+	0.842562i	$0.681046\pi$
$38$	130.540	0.557275
$39$	47.0297	0.193097
$40$	−63.4790	−0.250923
$41$	304.120	1.15843	0.579214	−	0.815175i	$-0.303360\pi$
$41$	304.120	1.15843	0.579214	+	0.815175i	$0.303360\pi$
$42$	−13.1922	−0.0484668
$43$	350.846	1.24427	0.622133	−	0.782911i	$-0.286266\pi$
$43$	350.846	1.24427	0.622133	+	0.782911i	$0.286266\pi$
$44$	34.2087	0.117208
$45$	69.5623	0.230439
$46$	−26.8983	−0.0862162
$47$	182.552	0.566552	0.283276	−	0.959038i	$-0.408579\pi$
$47$	182.552	0.566552	0.283276	+	0.959038i	$0.408579\pi$
$48$	−173.556	−0.521887
$49$	−323.656	−0.943602
$50$	−20.7277	−0.0586269
$51$	−88.8505	−0.243952
$52$	95.0635	0.253518
$53$	265.910	0.689160	0.344580	−	0.938757i	$-0.388021\pi$
$53$	265.910	0.689160	0.344580	+	0.938757i	$0.388021\pi$
$54$	−122.715	−0.309247
$55$	23.3903	0.0573446
$56$	−55.8389	−0.133246
$57$	569.590	1.32358
$58$	127.513	0.288677
$59$	159.751	0.352506	0.176253	−	0.984345i	$-0.443602\pi$
$59$	159.751	0.352506	0.176253	+	0.984345i	$0.443602\pi$
$60$	−132.272	−0.284605
$61$	732.433	1.53735	0.768675	−	0.639639i	$-0.220916\pi$
$61$	732.433	1.53735	0.768675	+	0.639639i	$0.220916\pi$
$62$	−25.7024	−0.0526485
$63$	61.1901	0.122369
$64$	−266.607	−0.520717
$65$	65.0000	0.124035
$66$	−14.0316	−0.0261692
$67$	114.275	0.208372	0.104186	−	0.994558i	$-0.466776\pi$
$67$	114.275	0.208372	0.104186	+	0.994558i	$0.466776\pi$
$68$	−179.598	−0.320286
$69$	−117.366	−0.204771
$70$	−18.2330	−0.0311323
$71$	−604.236	−1.00999	−0.504997	−	0.863121i	$-0.668506\pi$
$71$	−604.236	−1.00999	−0.504997	+	0.863121i	$0.668506\pi$
$72$	−176.630	−0.289111
$73$	1158.49	1.85741	0.928703	−	0.370824i	$-0.120925\pi$
$73$	1158.49	1.85741	0.928703	+	0.370824i	$0.120925\pi$
$74$	201.007	0.315764
$75$	−90.4418	−0.139244
$76$	1151.34	1.73773
$77$	20.5752	0.0304514
$78$	−38.9928	−0.0566034
$79$	521.596	0.742837	0.371419	−	0.928466i	$-0.378871\pi$
$79$	521.596	0.742837	0.371419	+	0.928466i	$0.378871\pi$
$80$	−239.872	−0.335231
$81$	−159.807	−0.219214
$82$	−252.149	−0.339575
$83$	709.181	0.937864	0.468932	−	0.883234i	$-0.344639\pi$
$83$	709.181	0.937864	0.468932	+	0.883234i	$0.344639\pi$
$84$	−116.353	−0.151132
$85$	−122.801	−0.156701
$86$	−290.889	−0.364737
$87$	556.380	0.685634
$88$	−59.3918	−0.0719453
$89$	−1209.88	−1.44098	−0.720488	−	0.693467i	$-0.756082\pi$
$89$	−1209.88	−1.44098	−0.720488	+	0.693467i	$0.756082\pi$
$90$	−57.6748	−0.0675495
$91$	57.1769	0.0658656
$92$	−237.238	−0.268845
$93$	−112.148	−0.125045
$94$	−151.355	−0.166076
$95$	787.233	0.850193
$96$	511.330	0.543619
$97$	231.784	0.242620	0.121310	−	0.992615i	$-0.461291\pi$
$97$	231.784	0.242620	0.121310	+	0.992615i	$0.461291\pi$
$98$	268.346	0.276602
$99$	65.0834	0.0660720
$100$	−182.814	−0.182814
$101$	479.764	0.472656	0.236328	−	0.971673i	$-0.424056\pi$
$101$	479.764	0.472656	0.236328	+	0.971673i	$0.424056\pi$
$102$	73.6668	0.0715107
$103$	798.894	0.764246	0.382123	−	0.924112i	$-0.375193\pi$
$103$	798.894	0.764246	0.382123	+	0.924112i	$0.375193\pi$
$104$	−165.045	−0.155616
$105$	−79.5566	−0.0739422
$106$	−220.468	−0.202017
$107$	−1903.60	−1.71988	−0.859942	−	0.510392i	$-0.829500\pi$
$107$	−1903.60	−1.71988	−0.859942	+	0.510392i	$0.829500\pi$
$108$	−1082.32	−0.964316
$109$	1440.01	1.26539	0.632697	−	0.774399i	$-0.281948\pi$
$109$	1440.01	1.26539	0.632697	+	0.774399i	$0.281948\pi$
$110$	−19.3931	−0.0168097
$111$	877.056	0.749969
$112$	−211.002	−0.178016
$113$	868.228	0.722797	0.361398	−	0.932412i	$-0.382299\pi$
$113$	868.228	0.722797	0.361398	+	0.932412i	$0.382299\pi$
$114$	−472.252	−0.387987
$115$	−162.212	−0.131534
$116$	1124.64	0.900173
$117$	180.862	0.142912
$118$	−132.451	−0.103331
$119$	−108.021	−0.0832123
$120$	229.646	0.174698
$121$	−1309.12	−0.983558
$122$	−607.267	−0.450650
$123$	−1100.21	−0.806522
$124$	−226.690	−0.164172
$125$	−125.000	−0.0894427
$126$	−50.7333	−0.0358705
$127$	1077.68	0.752984	0.376492	−	0.926420i	$-0.377130\pi$
$127$	1077.68	0.752984	0.376492	+	0.926420i	$0.377130\pi$
$128$	1351.79	0.933454
$129$	−1269.24	−0.866285
$130$	−53.8921	−0.0363588
$131$	−1532.85	−1.02233	−0.511165	−	0.859482i	$-0.670786\pi$
$131$	−1532.85	−1.02233	−0.511165	+	0.859482i	$0.670786\pi$
$132$	−123.756	−0.0816028
$133$	692.485	0.451474
$134$	−94.7464	−0.0610809
$135$	−740.039	−0.471796
$136$	311.811	0.196600
$137$	2638.90	1.64566	0.822832	−	0.568284i	$-0.192393\pi$
$137$	2638.90	1.64566	0.822832	+	0.568284i	$0.192393\pi$
$138$	97.3093	0.0600255
$139$	8.87287	0.00541429	0.00270715	−	0.999996i	$-0.499138\pi$
$139$	8.87287	0.00541429	0.00270715	+	0.999996i	$0.499138\pi$
$140$	−160.812	−0.0970791
$141$	−660.412	−0.394445
$142$	500.977	0.296064
$143$	60.8149	0.0355636
$144$	−667.442	−0.386251
$145$	768.975	0.440413
$146$	−960.513	−0.544470
$147$	1170.88	0.656956
$148$	1772.84	0.984638
$149$	1170.07	0.643325	0.321663	−	0.946854i	$-0.395758\pi$
$149$	1170.07	0.643325	0.321663	+	0.946854i	$0.395758\pi$
$150$	74.9861	0.0408173
$151$	−1429.96	−0.770655	−0.385327	−	0.922780i	$-0.625912\pi$
$151$	−1429.96	−0.770655	−0.385327	+	0.922780i	$0.625912\pi$
$152$	−1998.91	−1.06666
$153$	−341.692	−0.180550
$154$	−17.0591	−0.00892635
$155$	−155.000	−0.0803219
$156$	−343.908	−0.176505
$157$	−1463.28	−0.743840	−0.371920	−	0.928265i	$-0.621300\pi$
$157$	−1463.28	−0.743840	−0.371920	+	0.928265i	$0.621300\pi$
$158$	−432.460	−0.217751
$159$	−961.973	−0.479808
$160$	706.712	0.349191
$161$	−142.689	−0.0698477
$162$	132.497	0.0642591
$163$	1939.47	0.931969	0.465984	−	0.884793i	$-0.345700\pi$
$163$	1939.47	0.931969	0.465984	+	0.884793i	$0.345700\pi$
$164$	−2223.90	−1.05889
$165$	−84.6185	−0.0399245
$166$	−587.988	−0.274920
$167$	−2672.63	−1.23841	−0.619205	−	0.785230i	$-0.712545\pi$
$167$	−2672.63	−1.23841	−0.619205	+	0.785230i	$0.712545\pi$
$168$	202.007	0.0927689
$169$	169.000	0.0769231
$170$	101.815	0.0459345
$171$	2190.47	0.979587
$172$	−2565.59	−1.13735
$173$	−1746.27	−0.767438	−0.383719	−	0.923450i	$-0.625357\pi$
$173$	−1746.27	−0.767438	−0.383719	+	0.923450i	$0.625357\pi$
$174$	−461.300	−0.200983
$175$	−109.956	−0.0474963
$176$	−224.427	−0.0961185
$177$	−577.927	−0.245422
$178$	1003.12	0.422400
$179$	2457.31	1.02608	0.513040	−	0.858365i	$-0.328519\pi$
$179$	2457.31	1.02608	0.513040	+	0.858365i	$0.328519\pi$
$180$	−508.680	−0.210638
$181$	−1510.58	−0.620336	−0.310168	−	0.950682i	$-0.600385\pi$
$181$	−1510.58	−0.620336	−0.310168	+	0.950682i	$0.600385\pi$
$182$	−47.4059	−0.0193075
$183$	−2649.70	−1.07034
$184$	411.883	0.165024
$185$	1212.18	0.481738
$186$	92.9828	0.0366550
$187$	−114.894	−0.0449298
$188$	−1334.92	−0.517869
$189$	−650.971	−0.250535
$190$	−652.702	−0.249221
$191$	996.016	0.377325	0.188663	−	0.982042i	$-0.439585\pi$
$191$	996.016	0.377325	0.188663	+	0.982042i	$0.439585\pi$
$192$	964.496	0.362534
$193$	−3229.38	−1.20444	−0.602218	−	0.798332i	$-0.705716\pi$
$193$	−3229.38	−1.20444	−0.602218	+	0.798332i	$0.705716\pi$
$194$	−192.174	−0.0711201
$195$	−235.149	−0.0863556
$196$	2366.76	0.862521
$197$	1662.76	0.601353	0.300676	−	0.953726i	$-0.402788\pi$
$197$	1662.76	0.601353	0.300676	+	0.953726i	$0.402788\pi$
$198$	−53.9613	−0.0193680
$199$	−2033.52	−0.724384	−0.362192	−	0.932103i	$-0.617972\pi$
$199$	−2033.52	−0.724384	−0.362192	+	0.932103i	$0.617972\pi$
$200$	317.395	0.112216
$201$	−413.409	−0.145073
$202$	−397.777	−0.138552
$203$	676.425	0.233870
$204$	649.726	0.222990
$205$	−1520.60	−0.518065
$206$	−662.370	−0.224027
$207$	−451.354	−0.151552
$208$	−623.667	−0.207902
$209$	736.545	0.243770
$210$	65.9611	0.0216750
$211$	−858.774	−0.280192	−0.140096	−	0.990138i	$-0.544741\pi$
$211$	−858.774	−0.280192	−0.140096	+	0.990138i	$0.544741\pi$
$212$	−1944.48	−0.629942
$213$	2185.93	0.703179
$214$	1578.29	0.504157
$215$	−1754.23	−0.556453
$216$	1879.08	0.591921
$217$	−136.345	−0.0426530
$218$	−1193.93	−0.370931
$219$	−4191.03	−1.29317
$220$	−171.044	−0.0524171
$221$	−319.282	−0.0971820
$222$	−727.176	−0.219842
$223$	−3667.75	−1.10139	−0.550697	−	0.834705i	$-0.685638\pi$
$223$	−3667.75	−1.10139	−0.550697	+	0.834705i	$0.685638\pi$
$224$	621.655	0.185429
$225$	−347.812	−0.103055
$226$	−719.856	−0.211877
$227$	3682.62	1.07676	0.538380	−	0.842702i	$-0.319037\pi$
$227$	3682.62	1.07676	0.538380	+	0.842702i	$0.319037\pi$
$228$	−4165.17	−1.20985
$229$	815.744	0.235397	0.117698	−	0.993049i	$-0.462448\pi$
$229$	815.744	0.235397	0.117698	+	0.993049i	$0.462448\pi$
$230$	134.492	0.0385571
$231$	−74.4342	−0.0212009
$232$	−1952.55	−0.552548
$233$	1096.11	0.308191	0.154096	−	0.988056i	$-0.450754\pi$
$233$	1096.11	0.308191	0.154096	+	0.988056i	$0.450754\pi$
$234$	−149.954	−0.0418924
$235$	−912.759	−0.253370
$236$	−1168.19	−0.322216
$237$	−1886.96	−0.517179
$238$	89.5612	0.0243924
$239$	4203.42	1.13764	0.568822	−	0.822461i	$-0.307399\pi$
$239$	4203.42	1.13764	0.568822	+	0.822461i	$0.307399\pi$
$240$	867.778	0.233395
$241$	6374.03	1.70368	0.851841	−	0.523801i	$-0.175486\pi$
$241$	6374.03	1.70368	0.851841	+	0.523801i	$0.175486\pi$
$242$	1085.40	0.288315
$243$	−3418.08	−0.902346
$244$	−5355.97	−1.40525
$245$	1618.28	0.421992
$246$	912.191	0.236419
$247$	2046.81	0.527268
$248$	393.570	0.100773
$249$	−2565.58	−0.652960
$250$	103.639	0.0262187
$251$	506.100	0.127270	0.0636349	−	0.997973i	$-0.479731\pi$
$251$	506.100	0.127270	0.0636349	+	0.997973i	$0.479731\pi$
$252$	−447.457	−0.111854
$253$	−151.768	−0.0377137
$254$	−893.518	−0.220726
$255$	444.252	0.109099
$256$	1012.08	0.247089
$257$	−7790.45	−1.89087	−0.945437	−	0.325805i	$-0.894365\pi$
$257$	−7790.45	−1.89087	−0.945437	+	0.325805i	$0.894365\pi$
$258$	1052.34	0.253938
$259$	1066.29	0.255815
$260$	−475.318	−0.113377
$261$	2139.67	0.507441
$262$	1270.90	0.299680
$263$	−4534.10	−1.06306	−0.531529	−	0.847040i	$-0.678382\pi$
$263$	−4534.10	−1.06306	−0.531529	+	0.847040i	$0.678382\pi$
$264$	214.860	0.0500898
$265$	−1329.55	−0.308202
$266$	−574.146	−0.132343
$267$	4376.94	1.00324
$268$	−835.644	−0.190467
$269$	−4461.87	−1.01132	−0.505659	−	0.862733i	$-0.668751\pi$
$269$	−4461.87	−1.01132	−0.505659	+	0.862733i	$0.668751\pi$
$270$	613.573	0.138300
$271$	−3959.43	−0.887521	−0.443760	−	0.896145i	$-0.646356\pi$
$271$	−3959.43	−0.887521	−0.443760	+	0.896145i	$0.646356\pi$
$272$	1178.26	0.262656
$273$	−206.847	−0.0458570
$274$	−2187.93	−0.482401
$275$	−116.952	−0.0256453
$276$	858.249	0.187176
$277$	5406.56	1.17274	0.586370	−	0.810044i	$-0.300557\pi$
$277$	5406.56	1.17274	0.586370	+	0.810044i	$0.300557\pi$
$278$	−7.35658	−0.00158712
$279$	−431.286	−0.0925464
$280$	279.195	0.0595896
$281$	−8095.65	−1.71867	−0.859335	−	0.511413i	$-0.829122\pi$
$281$	−8095.65	−1.71867	−0.859335	+	0.511413i	$0.829122\pi$
$282$	547.554	0.115625
$283$	−3951.78	−0.830067	−0.415033	−	0.909806i	$-0.636230\pi$
$283$	−3951.78	−0.830067	−0.415033	+	0.909806i	$0.636230\pi$
$284$	4418.52	0.923208
$285$	−2847.95	−0.591923
$286$	−50.4222	−0.0104249
$287$	−1337.59	−0.275105
$288$	1966.42	0.402335
$289$	−4309.80	−0.877224
$290$	−637.564	−0.129100
$291$	−838.518	−0.168917
$292$	−8471.53	−1.69780
$293$	−4790.78	−0.955224	−0.477612	−	0.878571i	$-0.658498\pi$
$293$	−4790.78	−0.955224	−0.477612	+	0.878571i	$0.658498\pi$
$294$	−970.787	−0.192576
$295$	−798.756	−0.157645
$296$	−3077.93	−0.604395
$297$	−692.390	−0.135275
$298$	−970.112	−0.188581
$299$	−421.752	−0.0815737
$300$	661.362	0.127279
$301$	−1543.10	−0.295491
$302$	1185.60	0.225905
$303$	−1735.63	−0.329073
$304$	−7553.41	−1.42506
$305$	−3662.16	−0.687524
$306$	283.300	0.0529254
$307$	−3637.22	−0.676180	−0.338090	−	0.941114i	$-0.609781\pi$
$307$	−3637.22	−0.676180	−0.338090	+	0.941114i	$0.609781\pi$
$308$	−150.458	−0.0278348
$309$	−2890.13	−0.532084
$310$	128.512	0.0235451
$311$	−9600.60	−1.75048	−0.875241	−	0.483687i	$-0.839297\pi$
$311$	−9600.60	−1.75048	−0.875241	+	0.483687i	$0.839297\pi$
$312$	597.080	0.108343
$313$	6286.29	1.13521	0.567607	−	0.823300i	$-0.307869\pi$
$313$	6286.29	1.13521	0.567607	+	0.823300i	$0.307869\pi$
$314$	1213.22	0.218045
$315$	−305.950	−0.0547249
$316$	−3814.21	−0.679007
$317$	−2118.74	−0.375395	−0.187697	−	0.982227i	$-0.560102\pi$
$317$	−2118.74	−0.375395	−0.187697	+	0.982227i	$0.560102\pi$
$318$	797.581	0.140648
$319$	719.463	0.126276
$320$	1333.03	0.232872
$321$	6886.58	1.19742
$322$	118.305	0.0204748
$323$	−3866.91	−0.666132
$324$	1168.60	0.200377
$325$	−325.000	−0.0554700
$326$	−1608.03	−0.273192
$327$	−5209.48	−0.880994
$328$	3861.05	0.649971
$329$	−802.903	−0.134546
$330$	70.1580	0.0117032
$331$	8533.73	1.41709	0.708544	−	0.705667i	$-0.249352\pi$
$331$	8533.73	1.41709	0.708544	+	0.705667i	$0.249352\pi$
$332$	−5185.94	−0.857275
$333$	3372.89	0.555055
$334$	2215.90	0.363020
$335$	−571.375	−0.0931867
$336$	763.336	0.123939
$337$	−8515.27	−1.37643	−0.688214	−	0.725508i	$-0.741605\pi$
$337$	−8515.27	−1.37643	−0.688214	+	0.725508i	$0.741605\pi$
$338$	−140.119	−0.0225488
$339$	−3140.96	−0.503226
$340$	897.990	0.143236
$341$	−145.020	−0.0230301
$342$	−1816.14	−0.287151
$343$	2932.10	0.461570
$344$	4454.27	0.698134
$345$	586.831	0.0915765
$346$	1447.85	0.224962
$347$	1319.11	0.204073	0.102036	−	0.994781i	$-0.467464\pi$
$347$	1319.11	0.204073	0.102036	+	0.994781i	$0.467464\pi$
$348$	−4068.57	−0.626719
$349$	613.469	0.0940925	0.0470462	−	0.998893i	$-0.485019\pi$
$349$	613.469	0.0940925	0.0470462	+	0.998893i	$0.485019\pi$
$350$	91.1652	0.0139228
$351$	−1924.10	−0.292595
$352$	661.209	0.100121
$353$	−9024.09	−1.36063	−0.680317	−	0.732918i	$-0.738158\pi$
$353$	−9024.09	−1.36063	−0.680317	+	0.732918i	$0.738158\pi$
$354$	479.165	0.0719416
$355$	3021.18	0.451683
$356$	8847.33	1.31716
$357$	390.784	0.0579341
$358$	−2037.38	−0.300779
$359$	−2481.59	−0.364828	−0.182414	−	0.983222i	$-0.558391\pi$
$359$	−2481.59	−0.364828	−0.182414	+	0.983222i	$0.558391\pi$
$360$	883.149	0.129295
$361$	17930.4	2.61414
$362$	1252.44	0.181842
$363$	4735.95	0.684774
$364$	−418.110	−0.0602059
$365$	−5792.44	−0.830658
$366$	2196.89	0.313752
$367$	10449.8	1.48631	0.743156	−	0.669118i	$-0.233328\pi$
$367$	10449.8	1.48631	0.743156	+	0.669118i	$0.233328\pi$
$368$	1556.41	0.220471
$369$	−4231.06	−0.596911
$370$	−1005.03	−0.141214
$371$	−1169.53	−0.163663
$372$	820.089	0.114300
$373$	4246.16	0.589431	0.294715	−	0.955585i	$-0.404775\pi$
$373$	4246.16	0.589431	0.294715	+	0.955585i	$0.404775\pi$
$374$	95.2596	0.0131705
$375$	452.209	0.0622719
$376$	2317.64	0.317881
$377$	1999.34	0.273133
$378$	539.726	0.0734405
$379$	8049.06	1.09090	0.545452	−	0.838142i	$-0.316358\pi$
$379$	8049.06	1.09090	0.545452	+	0.838142i	$0.316358\pi$
$380$	−5756.70	−0.777138
$381$	−3898.71	−0.524243
$382$	−825.806	−0.110607
$383$	13379.6	1.78503	0.892515	−	0.451018i	$-0.148939\pi$
$383$	13379.6	1.78503	0.892515	+	0.451018i	$0.148939\pi$
$384$	−4890.32	−0.649890
$385$	−102.876	−0.0136183
$386$	2677.51	0.353062
$387$	−4881.13	−0.641141
$388$	−1694.94	−0.221772
$389$	5745.69	0.748890	0.374445	−	0.927249i	$-0.377833\pi$
$389$	5745.69	0.748890	0.374445	+	0.927249i	$0.377833\pi$
$390$	194.964	0.0253138
$391$	796.791	0.103057
$392$	−4109.07	−0.529437
$393$	5545.33	0.711768
$394$	−1378.61	−0.176277
$395$	−2607.98	−0.332207
$396$	−475.927	−0.0603946
$397$	2736.58	0.345957	0.172979	−	0.984926i	$-0.444661\pi$
$397$	2736.58	0.345957	0.172979	+	0.984926i	$0.444661\pi$
$398$	1686.01	0.212342
$399$	−2505.18	−0.314326
$400$	1199.36	0.149920
$401$	−7457.92	−0.928755	−0.464377	−	0.885637i	$-0.653722\pi$
$401$	−7457.92	−0.928755	−0.464377	+	0.885637i	$0.653722\pi$
$402$	342.761	0.0425258
$403$	−403.000	−0.0498135
$404$	−3508.31	−0.432042
$405$	799.035	0.0980354
$406$	−560.830	−0.0685555
$407$	1134.14	0.138125
$408$	−1128.03	−0.136877
$409$	−11075.4	−1.33898	−0.669489	−	0.742822i	$-0.733487\pi$
$409$	−11075.4	−1.33898	−0.669489	+	0.742822i	$0.733487\pi$
$410$	1260.74	0.151863
$411$	−9546.65	−1.14575
$412$	−5841.97	−0.698576
$413$	−702.621	−0.0837136
$414$	374.222	0.0444252
$415$	−3545.90	−0.419425
$416$	1837.45	0.216559
$417$	−32.0991	−0.00376954
$418$	−610.677	−0.0714573
$419$	−4510.68	−0.525922	−0.262961	−	0.964806i	$-0.584699\pi$
$419$	−4510.68	−0.525922	−0.262961	+	0.964806i	$0.584699\pi$
$420$	581.764	0.0675885
$421$	−12853.7	−1.48801	−0.744003	−	0.668176i	$-0.767075\pi$
$421$	−12853.7	−1.48801	−0.744003	+	0.668176i	$0.767075\pi$
$422$	712.017	0.0821338
$423$	−2539.75	−0.291931
$424$	3375.94	0.386674
$425$	614.003	0.0700789
$426$	−1812.37	−0.206126
$427$	−3221.40	−0.365093
$428$	13920.2	1.57210
$429$	−220.008	−0.0247601
$430$	1454.45	0.163116
$431$	2314.25	0.258640	0.129320	−	0.991603i	$-0.458721\pi$
$431$	2314.25	0.258640	0.129320	+	0.991603i	$0.458721\pi$
$432$	7100.59	0.790804
$433$	−2714.03	−0.301219	−0.150610	−	0.988593i	$-0.548124\pi$
$433$	−2714.03	−0.301219	−0.150610	+	0.988593i	$0.548124\pi$
$434$	113.045	0.0125031
$435$	−2781.90	−0.306625
$436$	−10530.2	−1.15666
$437$	−5107.95	−0.559145
$438$	3474.82	0.379071
$439$	−651.515	−0.0708317	−0.0354158	−	0.999373i	$-0.511276\pi$
$439$	−651.515	−0.0708317	−0.0354158	+	0.999373i	$0.511276\pi$
$440$	296.959	0.0321749
$441$	4502.85	0.486216
$442$	264.720	0.0284874
$443$	13586.6	1.45716	0.728578	−	0.684963i	$-0.240182\pi$
$443$	13586.6	1.45716	0.728578	+	0.684963i	$0.240182\pi$
$444$	−6413.54	−0.685525
$445$	6049.39	0.644424
$446$	3040.97	0.322856
$447$	−4232.91	−0.447897
$448$	1172.60	0.123661
$449$	−5301.75	−0.557250	−0.278625	−	0.960400i	$-0.589879\pi$
$449$	−5301.75	−0.557250	−0.278625	+	0.960400i	$0.589879\pi$
$450$	288.374	0.0302090
$451$	−1422.69	−0.148541
$452$	−6348.98	−0.660688
$453$	5173.14	0.536546
$454$	−3053.30	−0.315635
$455$	−285.884	−0.0294560
$456$	7231.40	0.742634
$457$	−17051.5	−1.74537	−0.872685	−	0.488284i	$-0.837623\pi$
$457$	−17051.5	−1.74537	−0.872685	+	0.488284i	$0.837623\pi$
$458$	−676.341	−0.0690029
$459$	3635.09	0.369655
$460$	1186.19	0.120231
$461$	16398.3	1.65671	0.828356	−	0.560202i	$-0.189276\pi$
$461$	16398.3	1.65671	0.828356	+	0.560202i	$0.189276\pi$
$462$	61.7141	0.00621472
$463$	7124.72	0.715149	0.357574	−	0.933885i	$-0.383604\pi$
$463$	7124.72	0.715149	0.357574	+	0.933885i	$0.383604\pi$
$464$	−7378.23	−0.738202
$465$	560.739	0.0559218
$466$	−908.794	−0.0903414
$467$	12999.4	1.28810	0.644048	−	0.764985i	$-0.277254\pi$
$467$	12999.4	1.28810	0.644048	+	0.764985i	$0.277254\pi$
$468$	−1322.57	−0.130632
$469$	−502.607	−0.0494845
$470$	756.777	0.0742713
$471$	5293.68	0.517877
$472$	2028.17	0.197784
$473$	−1641.28	−0.159548
$474$	1564.50	0.151603
$475$	−3936.16	−0.380218
$476$	789.911	0.0760620
$477$	−3699.46	−0.355108
$478$	−3485.10	−0.333483
$479$	14241.7	1.35849	0.679247	−	0.733909i	$-0.262306\pi$
$479$	14241.7	1.35849	0.679247	+	0.733909i	$0.262306\pi$
$480$	−2556.65	−0.243114
$481$	3151.68	0.298761
$482$	−5284.77	−0.499408
$483$	516.202	0.0486294
$484$	9573.01	0.899043
$485$	−1158.92	−0.108503
$486$	2833.96	0.264509
$487$	4599.14	0.427940	0.213970	−	0.976840i	$-0.431360\pi$
$487$	4599.14	0.427940	0.213970	+	0.976840i	$0.431360\pi$
$488$	9298.82	0.862577
$489$	−7016.36	−0.648856
$490$	−1341.73	−0.123700
$491$	−10963.5	−1.00769	−0.503845	−	0.863794i	$-0.668082\pi$
$491$	−10963.5	−1.00769	−0.503845	+	0.863794i	$0.668082\pi$
$492$	8045.34	0.737219
$493$	−3777.23	−0.345066
$494$	−1697.03	−0.154560
$495$	−325.417	−0.0295483
$496$	1487.21	0.134632
$497$	2657.56	0.239855
$498$	2127.15	0.191405
$499$	4256.18	0.381829	0.190915	−	0.981607i	$-0.438855\pi$
$499$	4256.18	0.381829	0.190915	+	0.981607i	$0.438855\pi$
$500$	914.072	0.0817571
$501$	9668.70	0.862206
$502$	−419.612	−0.0373072
$503$	−11144.6	−0.987902	−0.493951	−	0.869490i	$-0.664448\pi$
$503$	−11144.6	−0.987902	−0.493951	+	0.869490i	$0.664448\pi$
$504$	776.857	0.0686587
$505$	−2398.82	−0.211378
$506$	125.832	0.0110552
$507$	−611.386	−0.0535555
$508$	−7880.65	−0.688282
$509$	−15308.8	−1.33311	−0.666553	−	0.745457i	$-0.732231\pi$
$509$	−15308.8	−1.33311	−0.666553	+	0.745457i	$0.732231\pi$
$510$	−368.334	−0.0319806
$511$	−5095.28	−0.441100
$512$	−11653.4	−1.00588
$513$	−23303.3	−2.00559
$514$	6459.13	0.554280
$515$	−3994.47	−0.341781
$516$	9281.45	0.791847
$517$	−853.989	−0.0726468
$518$	−884.072	−0.0749882
$519$	6317.44	0.534306
$520$	825.227	0.0695935
$521$	4098.97	0.344682	0.172341	−	0.985037i	$-0.444867\pi$
$521$	4098.97	0.344682	0.172341	+	0.985037i	$0.444867\pi$
$522$	−1774.02	−0.148748
$523$	−12750.2	−1.06602	−0.533010	−	0.846109i	$-0.678939\pi$
$523$	−12750.2	−1.06602	−0.533010	+	0.846109i	$0.678939\pi$
$524$	11209.1	0.934484
$525$	397.783	0.0330679
$526$	3759.26	0.311619
$527$	761.364	0.0629327
$528$	811.905	0.0669197
$529$	−11114.5	−0.913494
$530$	1102.34	0.0903446
$531$	−2222.53	−0.181638
$532$	−5063.85	−0.412680
$533$	−3953.56	−0.321290
$534$	−3628.96	−0.294084
$535$	9517.98	0.769155
$536$	1450.81	0.116913
$537$	−8889.75	−0.714378
$538$	3699.37	0.296452
$539$	1514.08	0.120995
$540$	5411.59	0.431255
$541$	11373.6	0.903859	0.451930	−	0.892054i	$-0.350736\pi$
$541$	11373.6	0.903859	0.451930	+	0.892054i	$0.350736\pi$
$542$	3282.80	0.260163
$543$	5464.80	0.431891
$544$	−3471.39	−0.273593
$545$	−7200.05	−0.565901
$546$	171.499	0.0134423
$547$	−15286.5	−1.19489	−0.597444	−	0.801911i	$-0.703817\pi$
$547$	−15286.5	−1.19489	−0.597444	+	0.801911i	$0.703817\pi$
$548$	−19297.1	−1.50426
$549$	−10189.9	−0.792160
$550$	96.9657	0.00751751
$551$	24214.5	1.87218
$552$	−1490.06	−0.114893
$553$	−2294.09	−0.176410
$554$	−4482.63	−0.343770
$555$	−4385.28	−0.335396
$556$	−64.8835	−0.00494905
$557$	−3011.08	−0.229055	−0.114527	−	0.993420i	$-0.536535\pi$
$557$	−3011.08	−0.229055	−0.114527	+	0.993420i	$0.536535\pi$
$558$	357.584	0.0271285
$559$	−4560.99	−0.345098
$560$	1055.01	0.0796113
$561$	415.648	0.0312811
$562$	6712.18	0.503801
$563$	6951.83	0.520399	0.260199	−	0.965555i	$-0.416212\pi$
$563$	6951.83	0.520399	0.260199	+	0.965555i	$0.416212\pi$
$564$	4829.32	0.360551
$565$	−4341.14	−0.323244
$566$	3276.46	0.243321
$567$	702.866	0.0520593
$568$	−7671.26	−0.566688
$569$	26435.8	1.94771	0.973853	−	0.227178i	$-0.0729498\pi$
$569$	26435.8	1.94771	0.973853	+	0.227178i	$0.0729498\pi$
$570$	2361.26	0.173513
$571$	13494.5	0.989012	0.494506	−	0.869174i	$-0.335349\pi$
$571$	13494.5	0.989012	0.494506	+	0.869174i	$0.335349\pi$
$572$	−444.713	−0.0325077
$573$	−3603.26	−0.262702
$574$	1109.01	0.0806429
$575$	811.062	0.0588237
$576$	3709.16	0.268313
$577$	4806.55	0.346792	0.173396	−	0.984852i	$-0.444526\pi$
$577$	4806.55	0.346792	0.173396	+	0.984852i	$0.444526\pi$
$578$	3573.30	0.257144
$579$	11682.8	0.838553
$580$	−5623.19	−0.402569
$581$	−3119.13	−0.222725
$582$	695.223	0.0495153
$583$	−1243.94	−0.0883685
$584$	14707.9	1.04215
$585$	−904.310	−0.0639122
$586$	3972.08	0.280009
$587$	8615.01	0.605757	0.302878	−	0.953029i	$-0.402052\pi$
$587$	8615.01	0.605757	0.302878	+	0.953029i	$0.402052\pi$
$588$	−8562.15	−0.600505
$589$	−4880.84	−0.341446
$590$	662.256	0.0462113
$591$	−6015.31	−0.418675
$592$	−11630.8	−0.807469
$593$	−4521.13	−0.313087	−0.156544	−	0.987671i	$-0.550035\pi$
$593$	−4521.13	−0.313087	−0.156544	+	0.987671i	$0.550035\pi$
$594$	574.067	0.0396536
$595$	540.105	0.0372137
$596$	−8556.19	−0.588046
$597$	7356.61	0.504331
$598$	349.679	0.0239121
$599$	−5998.85	−0.409192	−0.204596	−	0.978846i	$-0.565588\pi$
$599$	−5998.85	−0.409192	−0.204596	+	0.978846i	$0.565588\pi$
$600$	−1148.23	−0.0781272
$601$	18477.2	1.25408	0.627038	−	0.778989i	$-0.284267\pi$
$601$	18477.2	1.25408	0.627038	+	0.778989i	$0.284267\pi$
$602$	1279.40	0.0866185
$603$	−1589.85	−0.107369
$604$	10456.7	0.704434
$605$	6545.58	0.439861
$606$	1439.02	0.0964627
$607$	−23253.3	−1.55490	−0.777449	−	0.628946i	$-0.783487\pi$
$607$	−23253.3	−1.55490	−0.777449	+	0.628946i	$0.783487\pi$
$608$	22253.9	1.48440
$609$	−2447.08	−0.162825
$610$	3036.33	0.201537
$611$	−2373.17	−0.157133
$612$	2498.65	0.165036
$613$	−7939.97	−0.523152	−0.261576	−	0.965183i	$-0.584242\pi$
$613$	−7939.97	−0.523152	−0.261576	+	0.965183i	$0.584242\pi$
$614$	3015.65	0.198211
$615$	5501.03	0.360688
$616$	261.218	0.0170857
$617$	−17726.1	−1.15660	−0.578302	−	0.815823i	$-0.696284\pi$
$617$	−17726.1	−1.15660	−0.578302	+	0.815823i	$0.696284\pi$
$618$	2396.24	0.155972
$619$	−4850.20	−0.314937	−0.157469	−	0.987524i	$-0.550333\pi$
$619$	−4850.20	−0.314937	−0.157469	+	0.987524i	$0.550333\pi$
$620$	1133.45	0.0734200
$621$	4801.74	0.310285
$622$	7959.95	0.513127
$623$	5321.31	0.342205
$624$	2256.22	0.144746
$625$	625.000	0.0400000
$626$	−5212.02	−0.332770
$627$	−2664.58	−0.169718
$628$	10700.4	0.679923
$629$	−5954.28	−0.377445
$630$	253.666	0.0160418
$631$	−16791.4	−1.05936	−0.529679	−	0.848198i	$-0.677688\pi$
$631$	−16791.4	−1.05936	−0.529679	+	0.848198i	$0.677688\pi$
$632$	6622.08	0.416791
$633$	3106.76	0.195075
$634$	1756.66	0.110041
$635$	−5388.42	−0.336745
$636$	7034.50	0.438579
$637$	4207.52	0.261708
$638$	−596.514	−0.0370160
$639$	8406.41	0.520426
$640$	−6758.93	−0.417453
$641$	127.000	0.00782559	0.00391280	−	0.999992i	$-0.498755\pi$
$641$	127.000	0.00782559	0.00391280	+	0.999992i	$0.498755\pi$
$642$	−5709.73	−0.351005
$643$	4634.43	0.284237	0.142118	−	0.989850i	$-0.454609\pi$
$643$	4634.43	0.284237	0.142118	+	0.989850i	$0.454609\pi$
$644$	1043.43	0.0638458
$645$	6346.22	0.387414
$646$	3206.09	0.195266
$647$	−3377.62	−0.205236	−0.102618	−	0.994721i	$-0.532722\pi$
$647$	−3377.62	−0.205236	−0.102618	+	0.994721i	$0.532722\pi$
$648$	−2028.88	−0.122997
$649$	−747.326	−0.0452005
$650$	269.461	0.0162602
$651$	493.251	0.0296959
$652$	−14182.5	−0.851887
$653$	11418.3	0.684275	0.342137	−	0.939650i	$-0.388849\pi$
$653$	11418.3	0.684275	0.342137	+	0.939650i	$0.388849\pi$
$654$	4319.23	0.258250
$655$	7664.23	0.457200
$656$	14590.0	0.868358
$657$	−16117.4	−0.957078
$658$	665.695	0.0394399
$659$	−14154.6	−0.836701	−0.418350	−	0.908286i	$-0.637392\pi$
$659$	−14154.6	−0.836701	−0.418350	+	0.908286i	$0.637392\pi$
$660$	618.779	0.0364939
$661$	18610.1	1.09508	0.547541	−	0.836779i	$-0.315564\pi$
$661$	18610.1	1.09508	0.547541	+	0.836779i	$0.315564\pi$
$662$	−7075.39	−0.415397
$663$	1155.06	0.0676601
$664$	9003.62	0.526217
$665$	−3462.42	−0.201905
$666$	−2796.50	−0.162706
$667$	−4989.49	−0.289646
$668$	19543.8	1.13200
$669$	13268.7	0.766814
$670$	473.732	0.0273162
$671$	−3426.37	−0.197129
$672$	−2248.94	−0.129100
$673$	−3514.53	−0.201300	−0.100650	−	0.994922i	$-0.532092\pi$
$673$	−3514.53	−0.201300	−0.100650	+	0.994922i	$0.532092\pi$
$674$	7060.09	0.403478
$675$	3700.19	0.210993
$676$	−1235.83	−0.0703132
$677$	10276.5	0.583393	0.291696	−	0.956511i	$-0.405780\pi$
$677$	10276.5	0.583393	0.291696	+	0.956511i	$0.405780\pi$
$678$	2604.20	0.147513
$679$	−1019.44	−0.0576177
$680$	−1559.05	−0.0879220
$681$	−13322.5	−0.749662
$682$	120.237	0.00675092
$683$	−21705.7	−1.21602	−0.608012	−	0.793928i	$-0.708033\pi$
$683$	−21705.7	−1.21602	−0.608012	+	0.793928i	$0.708033\pi$
$684$	−16018.0	−0.895413
$685$	−13194.5	−0.735964
$686$	−2431.03	−0.135302
$687$	−2951.09	−0.163888
$688$	16831.6	0.932703
$689$	−3456.82	−0.191139
$690$	−486.547	−0.0268442
$691$	−26107.4	−1.43730	−0.718650	−	0.695372i	$-0.755240\pi$
$691$	−26107.4	−1.43730	−0.718650	+	0.695372i	$0.755240\pi$
$692$	12769.8	0.701494
$693$	−286.251	−0.0156909
$694$	−1093.68	−0.0598208
$695$	−44.3643	−0.00242135
$696$	7063.68	0.384696
$697$	7469.23	0.405907
$698$	−508.633	−0.0275817
$699$	−3965.36	−0.214569
$700$	804.058	0.0434151
$701$	13453.6	0.724871	0.362435	−	0.932009i	$-0.381945\pi$
$701$	13453.6	0.724871	0.362435	+	0.932009i	$0.381945\pi$
$702$	1595.29	0.0857697
$703$	38170.8	2.04785
$704$	1247.20	0.0667696
$705$	3302.06	0.176401
$706$	7481.96	0.398849
$707$	−2110.11	−0.112247
$708$	4226.14	0.224333
$709$	30761.6	1.62945	0.814723	−	0.579850i	$-0.196889\pi$
$709$	30761.6	1.62945	0.814723	+	0.579850i	$0.196889\pi$
$710$	−2504.89	−0.132404
$711$	−7256.68	−0.382766
$712$	−15360.4	−0.808504
$713$	1005.72	0.0528252
$714$	−324.003	−0.0169825
$715$	−304.074	−0.0159045
$716$	−17969.3	−0.937910
$717$	−15206.6	−0.792052
$718$	2057.51	0.106944
$719$	−1831.38	−0.0949918	−0.0474959	−	0.998871i	$-0.515124\pi$
$719$	−1831.38	−0.0949918	−0.0474959	+	0.998871i	$0.515124\pi$
$720$	3337.21	0.172737
$721$	−3513.71	−0.181494
$722$	−14866.3	−0.766296
$723$	−23059.1	−1.18614
$724$	11046.3	0.567032
$725$	−3844.88	−0.196959
$726$	−3926.62	−0.200731
$727$	−34711.6	−1.77081	−0.885407	−	0.464816i	$-0.846120\pi$
$727$	−34711.6	−1.77081	−0.885407	+	0.464816i	$0.846120\pi$
$728$	725.906	0.0369559
$729$	16680.3	0.847446
$730$	4802.56	0.243494
$731$	8616.82	0.435984
$732$	19376.1	0.978364
$733$	21978.6	1.10750	0.553751	−	0.832682i	$-0.313196\pi$
$733$	21978.6	1.10750	0.553751	+	0.832682i	$0.313196\pi$
$734$	−8664.05	−0.435689
$735$	−5854.40	−0.293800
$736$	−4585.50	−0.229652
$737$	−534.586	−0.0267187
$738$	3508.01	0.174975
$739$	−7578.84	−0.377256	−0.188628	−	0.982049i	$-0.560404\pi$
$739$	−7578.84	−0.377256	−0.188628	+	0.982049i	$0.560404\pi$
$740$	−8864.19	−0.440343
$741$	−7404.67	−0.367095
$742$	969.668	0.0479752
$743$	−20844.3	−1.02921	−0.514605	−	0.857427i	$-0.672062\pi$
$743$	−20844.3	−1.02921	−0.514605	+	0.857427i	$0.672062\pi$
$744$	−1423.81	−0.0701603
$745$	−5850.33	−0.287704
$746$	−3520.53	−0.172782
$747$	−9866.45	−0.483259
$748$	840.171	0.0410691
$749$	8372.44	0.408441
$750$	−374.931	−0.0182540
$751$	−35197.2	−1.71020	−0.855102	−	0.518460i	$-0.826506\pi$
$751$	−35197.2	−1.71020	−0.855102	+	0.518460i	$0.826506\pi$
$752$	8757.82	0.424687
$753$	−1830.90	−0.0886079
$754$	−1657.67	−0.0800646
$755$	7149.82	0.344647
$756$	4760.28	0.229007
$757$	25022.2	1.20138	0.600691	−	0.799482i	$-0.294892\pi$
$757$	25022.2	1.20138	0.600691	+	0.799482i	$0.294892\pi$
$758$	−6673.55	−0.319781
$759$	549.046	0.0262571
$760$	9994.55	0.477027
$761$	30424.1	1.44924	0.724620	−	0.689149i	$-0.242015\pi$
$761$	30424.1	1.44924	0.724620	+	0.689149i	$0.242015\pi$
$762$	3232.45	0.153674
$763$	−6333.48	−0.300508
$764$	−7283.44	−0.344903
$765$	1708.46	0.0807444
$766$	−11093.2	−0.523254
$767$	−2076.76	−0.0977674
$768$	−3661.36	−0.172029
$769$	18815.0	0.882299	0.441150	−	0.897434i	$-0.354571\pi$
$769$	18815.0	0.882299	0.441150	+	0.897434i	$0.354571\pi$
$770$	85.2953	0.00399199
$771$	28183.3	1.31647
$772$	23615.1	1.10094
$773$	5627.41	0.261842	0.130921	−	0.991393i	$-0.458207\pi$
$773$	5627.41	0.261842	0.130921	+	0.991393i	$0.458207\pi$
$774$	4046.99	0.187941
$775$	775.000	0.0359211
$776$	2942.68	0.136129
$777$	−3857.49	−0.178104
$778$	−4763.81	−0.219525
$779$	−47882.6	−2.20228
$780$	1719.54	0.0789352
$781$	2826.65	0.129508
$782$	−660.627	−0.0302097
$783$	−22762.9	−1.03892
$784$	−15527.2	−0.707325
$785$	7316.42	0.332655
$786$	−4597.68	−0.208644
$787$	17404.6	0.788320	0.394160	−	0.919042i	$-0.371036\pi$
$787$	17404.6	0.788320	0.394160	+	0.919042i	$0.371036\pi$
$788$	−12159.0	−0.549680
$789$	16402.9	0.740124
$790$	2162.30	0.0973813
$791$	−3818.66	−0.171651
$792$	826.286	0.0370717
$793$	−9521.62	−0.426384
$794$	−2268.92	−0.101412
$795$	4809.87	0.214577
$796$	14870.3	0.662139
$797$	12954.0	0.575726	0.287863	−	0.957672i	$-0.407055\pi$
$797$	12954.0	0.575726	0.287863	+	0.957672i	$0.407055\pi$
$798$	2077.07	0.0921397
$799$	4483.50	0.198517
$800$	−3533.56	−0.156163
$801$	16832.4	0.742501
$802$	6183.43	0.272250
$803$	−5419.48	−0.238168
$804$	3023.09	0.132607
$805$	713.446	0.0312368
$806$	334.131	0.0146021
$807$	16141.6	0.704101
$808$	6090.98	0.265198
$809$	26955.7	1.17146	0.585731	−	0.810506i	$-0.300808\pi$
$809$	26955.7	1.17146	0.585731	+	0.810506i	$0.300808\pi$
$810$	−662.487	−0.0287376
$811$	16880.5	0.730891	0.365446	−	0.930833i	$-0.380917\pi$
$811$	16880.5	0.730891	0.365446	+	0.930833i	$0.380917\pi$
$812$	−4946.41	−0.213774
$813$	14323.9	0.617911
$814$	−940.322	−0.0404893
$815$	−9697.34	−0.416789
$816$	−4262.55	−0.182867
$817$	−55239.5	−2.36546
$818$	9182.69	0.392500
$819$	−795.471	−0.0339390
$820$	11119.5	0.473549
$821$	−11818.5	−0.502396	−0.251198	−	0.967936i	$-0.580824\pi$
$821$	−11818.5	−0.502396	−0.251198	+	0.967936i	$0.580824\pi$
$822$	7915.22	0.335858
$823$	37013.0	1.56767	0.783834	−	0.620970i	$-0.213261\pi$
$823$	37013.0	1.56767	0.783834	+	0.620970i	$0.213261\pi$
$824$	10142.6	0.428803
$825$	423.092	0.0178548
$826$	582.550	0.0245393
$827$	−26600.7	−1.11850	−0.559248	−	0.829000i	$-0.688910\pi$
$827$	−26600.7	−1.11850	−0.559248	+	0.829000i	$0.688910\pi$
$828$	3300.56	0.138530
$829$	7368.71	0.308716	0.154358	−	0.988015i	$-0.450669\pi$
$829$	7368.71	0.308716	0.154358	+	0.988015i	$0.450669\pi$
$830$	2939.94	0.122948
$831$	−19559.2	−0.816485
$832$	3465.89	0.144421
$833$	−7949.03	−0.330633
$834$	26.6137	0.00110498
$835$	13363.2	0.553833
$836$	−5386.04	−0.222823
$837$	4588.24	0.189478
$838$	3739.85	0.154166
$839$	18785.5	0.773001	0.386500	−	0.922289i	$-0.373684\pi$
$839$	18785.5	0.773001	0.386500	+	0.922289i	$0.373684\pi$
$840$	−1010.03	−0.0414875
$841$	−736.097	−0.0301815
$842$	10657.1	0.436186
$843$	29287.4	1.19657
$844$	6279.85	0.256115
$845$	−845.000	−0.0344010
$846$	2105.73	0.0855749
$847$	5757.78	0.233577
$848$	12756.9	0.516595
$849$	14296.2	0.577910
$850$	−509.076	−0.0205425
$851$	−7865.25	−0.316824
$852$	−15984.7	−0.642756
$853$	−21616.7	−0.867694	−0.433847	−	0.900987i	$-0.642844\pi$
$853$	−21616.7	−0.867694	−0.433847	+	0.900987i	$0.642844\pi$
$854$	2670.89	0.107021
$855$	−10952.3	−0.438085
$856$	−24167.7	−0.964993
$857$	−37498.2	−1.49465	−0.747324	−	0.664459i	$-0.768662\pi$
$857$	−37498.2	−1.49465	−0.747324	+	0.664459i	$0.768662\pi$
$858$	182.411	0.00725804
$859$	25811.5	1.02523	0.512617	−	0.858617i	$-0.328676\pi$
$859$	25811.5	1.02523	0.512617	+	0.858617i	$0.328676\pi$
$860$	12827.9	0.508638
$861$	4838.95	0.191534
$862$	−1918.77	−0.0758162
$863$	−42222.9	−1.66545	−0.832725	−	0.553687i	$-0.813220\pi$
$863$	−42222.9	−1.66545	−0.832725	+	0.553687i	$0.813220\pi$
$864$	−20919.8	−0.823733
$865$	8731.37	0.343209
$866$	2250.23	0.0882977
$867$	15591.4	0.610741
$868$	997.033	0.0389879
$869$	−2440.06	−0.0952513
$870$	2306.50	0.0898823
$871$	−1485.57	−0.0577919
$872$	18282.1	0.709988
$873$	−3224.69	−0.125016
$874$	4235.05	0.163905
$875$	549.778	0.0212410
$876$	30647.2	1.18205
$877$	9510.80	0.366199	0.183100	−	0.983094i	$-0.441387\pi$
$877$	9510.80	0.366199	0.183100	+	0.983094i	$0.441387\pi$
$878$	540.177	0.0207632
$879$	17331.5	0.665047
$880$	1122.14	0.0429855
$881$	8538.76	0.326536	0.163268	−	0.986582i	$-0.447796\pi$
$881$	8538.76	0.326536	0.163268	+	0.986582i	$0.447796\pi$
$882$	−3733.35	−0.142527
$883$	26078.6	0.993900	0.496950	−	0.867779i	$-0.334453\pi$
$883$	26078.6	0.993900	0.496950	+	0.867779i	$0.334453\pi$
$884$	2334.77	0.0888313
$885$	2889.63	0.109756
$886$	−11264.8	−0.427142
$887$	22046.4	0.834548	0.417274	−	0.908781i	$-0.362985\pi$
$887$	22046.4	0.834548	0.417274	+	0.908781i	$0.362985\pi$
$888$	11134.9	0.420793
$889$	−4739.89	−0.178820
$890$	−5015.61	−0.188903
$891$	747.587	0.0281090
$892$	26820.7	1.00675
$893$	−28742.2	−1.07707
$894$	3509.54	0.131294
$895$	−12286.6	−0.458877
$896$	−5945.45	−0.221678
$897$	1525.76	0.0567933
$898$	4395.73	0.163349
$899$	−4767.65	−0.176874
$900$	2543.40	0.0942000
$901$	6530.78	0.241478
$902$	1179.57	0.0435425
$903$	5582.42	0.205727
$904$	11022.8	0.405547
$905$	7552.92	0.277423
$906$	−4289.10	−0.157280
$907$	−32186.2	−1.17831	−0.589154	−	0.808021i	$-0.700539\pi$
$907$	−32186.2	−1.17831	−0.589154	+	0.808021i	$0.700539\pi$
$908$	−26929.5	−0.984236
$909$	−6674.69	−0.243549
$910$	237.029	0.00863456
$911$	42633.5	1.55051	0.775254	−	0.631650i	$-0.217622\pi$
$911$	42633.5	1.55051	0.775254	+	0.631650i	$0.217622\pi$
$912$	27325.7	0.992155
$913$	−3317.59	−0.120259
$914$	14137.5	0.511628
$915$	13248.5	0.478669
$916$	−5965.19	−0.215170
$917$	6741.79	0.242785
$918$	−3013.89	−0.108359
$919$	−47349.7	−1.69959	−0.849794	−	0.527115i	$-0.823274\pi$
$919$	−47349.7	−1.69959	−0.849794	+	0.527115i	$0.823274\pi$
$920$	−2059.42	−0.0738010
$921$	13158.3	0.470770
$922$	−13596.0	−0.485639
$923$	7855.06	0.280122
$924$	544.306	0.0193792
$925$	−6060.92	−0.215440
$926$	−5907.17	−0.209635
$927$	−11114.6	−0.393798
$928$	21737.8	0.768941
$929$	29973.3	1.05855	0.529275	−	0.848450i	$-0.322464\pi$
$929$	29973.3	1.05855	0.529275	+	0.848450i	$0.322464\pi$
$930$	−464.914	−0.0163926
$931$	50958.5	1.79387
$932$	−8015.38	−0.281709
$933$	34731.8	1.21872
$934$	−10777.9	−0.377585
$935$	574.470	0.0200932
$936$	2296.19	0.0801851
$937$	13665.0	0.476431	0.238215	−	0.971212i	$-0.423438\pi$
$937$	13665.0	0.476431	0.238215	+	0.971212i	$0.423438\pi$
$938$	416.716	0.0145056
$939$	−22741.7	−0.790360
$940$	6674.62	0.231598
$941$	−4410.25	−0.152784	−0.0763922	−	0.997078i	$-0.524340\pi$
$941$	−4410.25	−0.152784	−0.0763922	+	0.997078i	$0.524340\pi$
$942$	−4389.04	−0.151808
$943$	9866.40	0.340715
$944$	7663.97	0.264238
$945$	3254.86	0.112043
$946$	1360.80	0.0467689
$947$	40956.9	1.40541	0.702703	−	0.711483i	$-0.251976\pi$
$947$	40956.9	1.40541	0.702703	+	0.711483i	$0.251976\pi$
$948$	13798.6	0.472739
$949$	−15060.3	−0.515152
$950$	3263.51	0.111455
$951$	7664.89	0.261358
$952$	−1371.41	−0.0466888
$953$	−36439.3	−1.23860	−0.619299	−	0.785155i	$-0.712583\pi$
$953$	−36439.3	−1.23860	−0.619299	+	0.785155i	$0.712583\pi$
$954$	3067.25	0.104094
$955$	−4980.08	−0.168745
$956$	−30737.9	−1.03989
$957$	−2602.78	−0.0879163
$958$	−11807.9	−0.398222
$959$	−11606.4	−0.390815
$960$	−4822.48	−0.162130
$961$	961.000	0.0322581
$962$	−2613.09	−0.0875772
$963$	26483.7	0.886216
$964$	−46610.6	−1.55729
$965$	16146.9	0.538640
$966$	−427.988	−0.0142550
$967$	15322.5	0.509555	0.254778	−	0.967000i	$-0.417998\pi$
$967$	15322.5	0.509555	0.254778	+	0.967000i	$0.417998\pi$
$968$	−16620.3	−0.551855
$969$	13989.2	0.463775
$970$	960.871	0.0318059
$971$	10846.6	0.358481	0.179241	−	0.983805i	$-0.442636\pi$
$971$	10846.6	0.358481	0.179241	+	0.983805i	$0.442636\pi$
$972$	24995.0	0.824809
$973$	−39.0248	−0.00128580
$974$	−3813.19	−0.125444
$975$	1175.74	0.0386194
$976$	35138.0	1.15240
$977$	9506.09	0.311286	0.155643	−	0.987813i	$-0.450255\pi$
$977$	9506.09	0.311286	0.155643	+	0.987813i	$0.450255\pi$
$978$	5817.33	0.190202
$979$	5659.89	0.184771
$980$	−11833.8	−0.385731
$981$	−20034.1	−0.652028
$982$	9089.94	0.295389
$983$	−32674.4	−1.06017	−0.530087	−	0.847943i	$-0.677841\pi$
$983$	−32674.4	−1.06017	−0.530087	+	0.847943i	$0.677841\pi$
$984$	−13968.0	−0.452524
$985$	−8313.79	−0.268933
$986$	3131.73	0.101151
$987$	2904.64	0.0936735
$988$	−14967.4	−0.481961
$989$	11382.3	0.365962
$990$	269.806	0.00866162
$991$	52279.3	1.67579	0.837894	−	0.545833i	$-0.183787\pi$
$991$	52279.3	1.67579	0.837894	+	0.545833i	$0.183787\pi$
$992$	−4381.62	−0.140238
$993$	−30872.2	−0.986606
$994$	−2203.41	−0.0703098
$995$	10167.6	0.323954
$996$	18761.0	0.596853
$997$	−14367.4	−0.456391	−0.228195	−	0.973615i	$-0.573283\pi$
$997$	−14367.4	−0.456391	−0.228195	+	0.973615i	$0.573283\pi$
$998$	−3528.84	−0.111927
$999$	−35882.5	−1.13641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.18	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.18	✓	40	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2015 = 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.829109 q^{2} -3.61767 q^{3} -7.31258 q^{4} -5.00000 q^{5} +2.99944 q^{6} -4.39822 q^{7} +12.6958 q^{8} -13.9125 q^{9} +O(q^{10})\)	\(q-0.829109 q^{2} -3.61767 q^{3} -7.31258 q^{4} -5.00000 q^{5} +2.99944 q^{6} -4.39822 q^{7} +12.6958 q^{8} -13.9125 q^{9} +4.14555 q^{10} -4.67807 q^{11} +26.4545 q^{12} -13.0000 q^{13} +3.64661 q^{14} +18.0884 q^{15} +47.9744 q^{16} +24.5601 q^{17} +11.5350 q^{18} -157.447 q^{19} +36.5629 q^{20} +15.9113 q^{21} +3.87863 q^{22} +32.4425 q^{23} -45.9292 q^{24} +25.0000 q^{25} +10.7784 q^{26} +148.008 q^{27} +32.1623 q^{28} -153.795 q^{29} -14.9972 q^{30} +31.0000 q^{31} -141.342 q^{32} +16.9237 q^{33} -20.3630 q^{34} +21.9911 q^{35} +101.736 q^{36} -242.437 q^{37} +130.540 q^{38} +47.0297 q^{39} -63.4790 q^{40} +304.120 q^{41} -13.1922 q^{42} +350.846 q^{43} +34.2087 q^{44} +69.5623 q^{45} -26.8983 q^{46} +182.552 q^{47} -173.556 q^{48} -323.656 q^{49} -20.7277 q^{50} -88.8505 q^{51} +95.0635 q^{52} +265.910 q^{53} -122.715 q^{54} +23.3903 q^{55} -55.8389 q^{56} +569.590 q^{57} +127.513 q^{58} +159.751 q^{59} -132.272 q^{60} +732.433 q^{61} -25.7024 q^{62} +61.1901 q^{63} -266.607 q^{64} +65.0000 q^{65} -14.0316 q^{66} +114.275 q^{67} -179.598 q^{68} -117.366 q^{69} -18.2330 q^{70} -604.236 q^{71} -176.630 q^{72} +1158.49 q^{73} +201.007 q^{74} -90.4418 q^{75} +1151.34 q^{76} +20.5752 q^{77} -38.9928 q^{78} +521.596 q^{79} -239.872 q^{80} -159.807 q^{81} -252.149 q^{82} +709.181 q^{83} -116.353 q^{84} -122.801 q^{85} -290.889 q^{86} +556.380 q^{87} -59.3918 q^{88} -1209.88 q^{89} -57.6748 q^{90} +57.1769 q^{91} -237.238 q^{92} -112.148 q^{93} -151.355 q^{94} +787.233 q^{95} +511.330 q^{96} +231.784 q^{97} +268.346 q^{98} +65.0834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more