LMFDB - Embedded newform 1911.4.a.bf.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,4,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, 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("1911.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1911.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:	$112.752650021$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.68266 q^{2} -3.00000 q^{3} +5.56198 q^{4} -10.3138 q^{5} -11.0480 q^{6} -8.97840 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.68266 q^{2} -3.00000 q^{3} +5.56198 q^{4} -10.3138 q^{5} -11.0480 q^{6} -8.97840 q^{8} +9.00000 q^{9} -37.9821 q^{10} -48.0250 q^{11} -16.6859 q^{12} -13.0000 q^{13} +30.9413 q^{15} -77.5602 q^{16} -22.5991 q^{17} +33.1439 q^{18} -148.338 q^{19} -57.3650 q^{20} -176.860 q^{22} +136.836 q^{23} +26.9352 q^{24} -18.6262 q^{25} -47.8746 q^{26} -27.0000 q^{27} +206.852 q^{29} +113.946 q^{30} +63.8589 q^{31} -213.801 q^{32} +144.075 q^{33} -83.2248 q^{34} +50.0578 q^{36} -183.495 q^{37} -546.280 q^{38} +39.0000 q^{39} +92.6012 q^{40} -308.829 q^{41} +312.359 q^{43} -267.114 q^{44} -92.8239 q^{45} +503.921 q^{46} -606.079 q^{47} +232.681 q^{48} -68.5939 q^{50} +67.7974 q^{51} -72.3057 q^{52} -175.835 q^{53} -99.4318 q^{54} +495.319 q^{55} +445.015 q^{57} +761.765 q^{58} +548.712 q^{59} +172.095 q^{60} -307.562 q^{61} +235.171 q^{62} -166.873 q^{64} +134.079 q^{65} +530.579 q^{66} +797.722 q^{67} -125.696 q^{68} -410.508 q^{69} +442.128 q^{71} -80.8056 q^{72} +612.791 q^{73} -675.751 q^{74} +55.8785 q^{75} -825.055 q^{76} +143.624 q^{78} +1054.69 q^{79} +799.938 q^{80} +81.0000 q^{81} -1137.31 q^{82} -892.242 q^{83} +233.082 q^{85} +1150.31 q^{86} -620.556 q^{87} +431.188 q^{88} +216.273 q^{89} -341.839 q^{90} +761.080 q^{92} -191.577 q^{93} -2231.98 q^{94} +1529.93 q^{95} +641.402 q^{96} -990.713 q^{97} -432.225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 66 q^{3} + 114 q^{4} - 36 q^{5} - 6 q^{6} + 66 q^{8} + 198 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 66 * q^3 + 114 * q^4 - 36 * q^5 - 6 * q^6 + 66 * q^8 + 198 * q^9	\( 22 q + 2 q^{2} - 66 q^{3} + 114 q^{4} - 36 q^{5} - 6 q^{6} + 66 q^{8} + 198 q^{9} - 48 q^{10} + 108 q^{11} - 342 q^{12} - 286 q^{13} + 108 q^{15} + 462 q^{16} + 18 q^{18} - 408 q^{19} - 416 q^{20} + 188 q^{22} + 304 q^{23} - 198 q^{24} + 882 q^{25} - 26 q^{26} - 594 q^{27} + 216 q^{29} + 144 q^{30} - 316 q^{31} + 770 q^{32} - 324 q^{33} - 776 q^{34} + 1026 q^{36} + 840 q^{37} + 436 q^{38} + 858 q^{39} - 40 q^{40} - 396 q^{41} + 768 q^{43} + 864 q^{44} - 324 q^{45} + 1380 q^{46} + 444 q^{47} - 1386 q^{48} + 70 q^{50} - 1482 q^{52} + 2612 q^{53} - 54 q^{54} - 1292 q^{55} + 1224 q^{57} + 1484 q^{58} - 1140 q^{59} + 1248 q^{60} + 392 q^{61} + 236 q^{62} + 2182 q^{64} + 468 q^{65} - 564 q^{66} + 2348 q^{67} + 3160 q^{68} - 912 q^{69} + 1624 q^{71} + 594 q^{72} - 1944 q^{73} + 3060 q^{74} - 2646 q^{75} - 2768 q^{76} + 78 q^{78} + 1904 q^{79} - 3820 q^{80} + 1782 q^{81} - 1360 q^{82} - 984 q^{83} + 1304 q^{85} + 2000 q^{86} - 648 q^{87} + 2164 q^{88} - 560 q^{89} - 432 q^{90} + 2608 q^{92} + 948 q^{93} - 1052 q^{94} + 2448 q^{95} - 2310 q^{96} - 2344 q^{97} + 972 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 66 * q^3 + 114 * q^4 - 36 * q^5 - 6 * q^6 + 66 * q^8 + 198 * q^9 - 48 * q^10 + 108 * q^11 - 342 * q^12 - 286 * q^13 + 108 * q^15 + 462 * q^16 + 18 * q^18 - 408 * q^19 - 416 * q^20 + 188 * q^22 + 304 * q^23 - 198 * q^24 + 882 * q^25 - 26 * q^26 - 594 * q^27 + 216 * q^29 + 144 * q^30 - 316 * q^31 + 770 * q^32 - 324 * q^33 - 776 * q^34 + 1026 * q^36 + 840 * q^37 + 436 * q^38 + 858 * q^39 - 40 * q^40 - 396 * q^41 + 768 * q^43 + 864 * q^44 - 324 * q^45 + 1380 * q^46 + 444 * q^47 - 1386 * q^48 + 70 * q^50 - 1482 * q^52 + 2612 * q^53 - 54 * q^54 - 1292 * q^55 + 1224 * q^57 + 1484 * q^58 - 1140 * q^59 + 1248 * q^60 + 392 * q^61 + 236 * q^62 + 2182 * q^64 + 468 * q^65 - 564 * q^66 + 2348 * q^67 + 3160 * q^68 - 912 * q^69 + 1624 * q^71 + 594 * q^72 - 1944 * q^73 + 3060 * q^74 - 2646 * q^75 - 2768 * q^76 + 78 * q^78 + 1904 * q^79 - 3820 * q^80 + 1782 * q^81 - 1360 * q^82 - 984 * q^83 + 1304 * q^85 + 2000 * q^86 - 648 * q^87 + 2164 * q^88 - 560 * q^89 - 432 * q^90 + 2608 * q^92 + 948 * q^93 - 1052 * q^94 + 2448 * q^95 - 2310 * q^96 - 2344 * q^97 + 972 * 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 $

$2$	3.68266	1.30202	0.651008	−	0.759071i	$-0.274346\pi$
$2$	3.68266	1.30202	0.651008	+	0.759071i	$0.274346\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	5.56198	0.695247
$5$	−10.3138	−0.922492	−0.461246	−	0.887272i	$-0.652597\pi$
$5$	−10.3138	−0.922492	−0.461246	+	0.887272i	$0.652597\pi$
$6$	−11.0480	−0.751720
$7$	0	0
$7$	0	0
$8$	−8.97840	−0.396793
$9$	9.00000	0.333333
$10$	−37.9821	−1.20110
$11$	−48.0250	−1.31637	−0.658186	−	0.752855i	$-0.728676\pi$
$11$	−48.0250	−1.31637	−0.658186	+	0.752855i	$0.728676\pi$
$12$	−16.6859	−0.401401
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	0	0
$15$	30.9413	0.532601
$16$	−77.5602	−1.21188
$17$	−22.5991	−0.322417	−0.161209	−	0.986920i	$-0.551539\pi$
$17$	−22.5991	−0.322417	−0.161209	+	0.986920i	$0.551539\pi$
$18$	33.1439	0.434006
$19$	−148.338	−1.79111	−0.895557	−	0.444946i	$-0.853223\pi$
$19$	−148.338	−1.79111	−0.895557	+	0.444946i	$0.853223\pi$
$20$	−57.3650	−0.641360
$21$	0	0
$22$	−176.860	−1.71394
$23$	136.836	1.24054	0.620268	−	0.784390i	$-0.287024\pi$
$23$	136.836	1.24054	0.620268	+	0.784390i	$0.287024\pi$
$24$	26.9352	0.229089
$25$	−18.6262	−0.149009
$26$	−47.8746	−0.361114
$27$	−27.0000	−0.192450
$28$	0	0
$29$	206.852	1.32453	0.662266	−	0.749269i	$-0.269595\pi$
$29$	206.852	1.32453	0.662266	+	0.749269i	$0.269595\pi$
$30$	113.946	0.693455
$31$	63.8589	0.369981	0.184990	−	0.982740i	$-0.440775\pi$
$31$	63.8589	0.369981	0.184990	+	0.982740i	$0.440775\pi$
$32$	−213.801	−1.18109
$33$	144.075	0.760008
$34$	−83.2248	−0.419792
$35$	0	0
$36$	50.0578	0.231749
$37$	−183.495	−0.815309	−0.407655	−	0.913136i	$-0.633653\pi$
$37$	−183.495	−0.815309	−0.407655	+	0.913136i	$0.633653\pi$
$38$	−546.280	−2.33206
$39$	39.0000	0.160128
$40$	92.6012	0.366038
$41$	−308.829	−1.17637	−0.588183	−	0.808728i	$-0.700157\pi$
$41$	−308.829	−1.17637	−0.588183	+	0.808728i	$0.700157\pi$
$42$	0	0
$43$	312.359	1.10777	0.553887	−	0.832592i	$-0.313144\pi$
$43$	312.359	1.10777	0.553887	+	0.832592i	$0.313144\pi$
$44$	−267.114	−0.915204
$45$	−92.8239	−0.307497
$46$	503.921	1.61520
$47$	−606.079	−1.88097	−0.940487	−	0.339830i	$-0.889631\pi$
$47$	−606.079	−1.88097	−0.940487	+	0.339830i	$0.889631\pi$
$48$	232.681	0.699678
$49$	0	0
$50$	−68.5939	−0.194013
$51$	67.7974	0.186148
$52$	−72.3057	−0.192827
$53$	−175.835	−0.455714	−0.227857	−	0.973695i	$-0.573172\pi$
$53$	−175.835	−0.455714	−0.227857	+	0.973695i	$0.573172\pi$
$54$	−99.4318	−0.250573
$55$	495.319	1.21434
$56$	0	0
$57$	445.015	1.03410
$58$	761.765	1.72456
$59$	548.712	1.21078	0.605391	−	0.795928i	$-0.293017\pi$
$59$	548.712	1.21078	0.605391	+	0.795928i	$0.293017\pi$
$60$	172.095	0.370289
$61$	−307.562	−0.645562	−0.322781	−	0.946474i	$-0.604618\pi$
$61$	−307.562	−0.645562	−0.322781	+	0.946474i	$0.604618\pi$
$62$	235.171	0.481721
$63$	0	0
$64$	−166.873	−0.325924
$65$	134.079	0.255853
$66$	530.579	0.989543
$67$	797.722	1.45459	0.727293	−	0.686327i	$-0.240778\pi$
$67$	797.722	1.45459	0.727293	+	0.686327i	$0.240778\pi$
$68$	−125.696	−0.224160
$69$	−410.508	−0.716223
$70$	0	0
$71$	442.128	0.739028	0.369514	−	0.929225i	$-0.379524\pi$
$71$	442.128	0.739028	0.369514	+	0.929225i	$0.379524\pi$
$72$	−80.8056	−0.132264
$73$	612.791	0.982490	0.491245	−	0.871022i	$-0.336542\pi$
$73$	612.791	0.982490	0.491245	+	0.871022i	$0.336542\pi$
$74$	−675.751	−1.06155
$75$	55.8785	0.0860306
$76$	−825.055	−1.24527
$77$	0	0
$78$	143.624	0.208490
$79$	1054.69	1.50205	0.751024	−	0.660275i	$-0.229560\pi$
$79$	1054.69	1.50205	0.751024	+	0.660275i	$0.229560\pi$
$80$	799.938	1.11795
$81$	81.0000	0.111111
$82$	−1137.31	−1.53165
$83$	−892.242	−1.17996	−0.589978	−	0.807420i	$-0.700863\pi$
$83$	−892.242	−1.17996	−0.589978	+	0.807420i	$0.700863\pi$
$84$	0	0
$85$	233.082	0.297427
$86$	1150.31	1.44234
$87$	−620.556	−0.764719
$88$	431.188	0.522327
$89$	216.273	0.257583	0.128791	−	0.991672i	$-0.458890\pi$
$89$	216.273	0.257583	0.128791	+	0.991672i	$0.458890\pi$
$90$	−341.839	−0.400366
$91$	0	0
$92$	761.080	0.862479
$93$	−191.577	−0.213609
$94$	−2231.98	−2.44906
$95$	1529.93	1.65229
$96$	641.402	0.681904
$97$	−990.713	−1.03703	−0.518514	−	0.855069i	$-0.673515\pi$
$97$	−990.713	−1.03703	−0.518514	+	0.855069i	$0.673515\pi$
$98$	0	0
$99$	−432.225	−0.438791
$100$	−103.598	−0.103598
$101$	1288.89	1.26980	0.634899	−	0.772595i	$-0.281042\pi$
$101$	1288.89	1.26980	0.634899	+	0.772595i	$0.281042\pi$
$102$	249.675	0.242367
$103$	−331.294	−0.316925	−0.158463	−	0.987365i	$-0.550654\pi$
$103$	−331.294	−0.316925	−0.158463	+	0.987365i	$0.550654\pi$
$104$	116.719	0.110051
$105$	0	0
$106$	−647.542	−0.593348
$107$	−1986.52	−1.79481	−0.897405	−	0.441209i	$-0.854550\pi$
$107$	−1986.52	−1.79481	−0.897405	+	0.441209i	$0.854550\pi$
$108$	−150.173	−0.133800
$109$	−1742.58	−1.53127	−0.765637	−	0.643273i	$-0.777576\pi$
$109$	−1742.58	−1.53127	−0.765637	+	0.643273i	$0.777576\pi$
$110$	1824.09	1.58109
$111$	550.486	0.470719
$112$	0	0
$113$	1704.76	1.41920	0.709602	−	0.704603i	$-0.248875\pi$
$113$	1704.76	1.41920	0.709602	+	0.704603i	$0.248875\pi$
$114$	1638.84	1.34642
$115$	−1411.30	−1.14438
$116$	1150.51	0.920878
$117$	−117.000	−0.0924500
$118$	2020.72	1.57646
$119$	0	0
$120$	−277.804	−0.211332
$121$	975.403	0.732835
$122$	−1132.65	−0.840532
$123$	926.488	0.679176
$124$	355.182	0.257228
$125$	1481.33	1.05995
$126$	0	0
$127$	1326.73	0.926998	0.463499	−	0.886098i	$-0.346594\pi$
$127$	1326.73	0.926998	0.463499	+	0.886098i	$0.346594\pi$
$128$	1095.87	0.756734
$129$	−937.076	−0.639573
$130$	493.767	0.333125
$131$	485.923	0.324086	0.162043	−	0.986784i	$-0.448192\pi$
$131$	485.923	0.324086	0.162043	+	0.986784i	$0.448192\pi$
$132$	801.342	0.528393
$133$	0	0
$134$	2937.74	1.89389
$135$	278.472	0.177534
$136$	202.904	0.127933
$137$	−2752.81	−1.71670	−0.858351	−	0.513063i	$-0.828511\pi$
$137$	−2752.81	−1.71670	−0.858351	+	0.513063i	$0.828511\pi$
$138$	−1511.76	−0.932535
$139$	2805.05	1.71166	0.855831	−	0.517255i	$-0.173046\pi$
$139$	2805.05	1.71166	0.855831	+	0.517255i	$0.173046\pi$
$140$	0	0
$141$	1818.24	1.08598
$142$	1628.21	0.962227
$143$	624.325	0.365096
$144$	−698.042	−0.403960
$145$	−2133.42	−1.22187
$146$	2256.70	1.27922
$147$	0	0
$148$	−1020.60	−0.566842
$149$	1594.20	0.876525	0.438263	−	0.898847i	$-0.355594\pi$
$149$	1594.20	0.876525	0.438263	+	0.898847i	$0.355594\pi$
$150$	205.782	0.112013
$151$	−1409.62	−0.759693	−0.379846	−	0.925050i	$-0.624023\pi$
$151$	−1409.62	−0.759693	−0.379846	+	0.925050i	$0.624023\pi$
$152$	1331.84	0.710702
$153$	−203.392	−0.107472
$154$	0	0
$155$	−658.626	−0.341304
$156$	216.917	0.111329
$157$	863.985	0.439194	0.219597	−	0.975591i	$-0.429526\pi$
$157$	863.985	0.439194	0.219597	+	0.975591i	$0.429526\pi$
$158$	3884.06	1.95569
$159$	527.506	0.263107
$160$	2205.09	1.08955
$161$	0	0
$162$	298.295	0.144669
$163$	−1685.75	−0.810050	−0.405025	−	0.914306i	$-0.632737\pi$
$163$	−1685.75	−0.810050	−0.405025	+	0.914306i	$0.632737\pi$
$164$	−1717.70	−0.817866
$165$	−1485.96	−0.701101
$166$	−3285.82	−1.53632
$167$	653.800	0.302950	0.151475	−	0.988461i	$-0.451598\pi$
$167$	653.800	0.302950	0.151475	+	0.988461i	$0.451598\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	858.362	0.387255
$171$	−1335.05	−0.597038
$172$	1737.33	0.770177
$173$	−335.978	−0.147653	−0.0738265	−	0.997271i	$-0.523521\pi$
$173$	−335.978	−0.147653	−0.0738265	+	0.997271i	$0.523521\pi$
$174$	−2285.30	−0.995677
$175$	0	0
$176$	3724.83	1.59528
$177$	−1646.13	−0.699046
$178$	796.459	0.335377
$179$	−2945.59	−1.22997	−0.614983	−	0.788540i	$-0.710837\pi$
$179$	−2945.59	−1.22997	−0.614983	+	0.788540i	$0.710837\pi$
$180$	−516.285	−0.213787
$181$	1512.44	0.621099	0.310550	−	0.950557i	$-0.399487\pi$
$181$	1512.44	0.621099	0.310550	+	0.950557i	$0.399487\pi$
$182$	0	0
$183$	922.685	0.372715
$184$	−1228.57	−0.492236
$185$	1892.53	0.752116
$186$	−705.512	−0.278122
$187$	1085.32	0.424421
$188$	−3371.00	−1.30774
$189$	0	0
$190$	5634.21	2.15131
$191$	2365.40	0.896096	0.448048	−	0.894009i	$-0.352119\pi$
$191$	2365.40	0.896096	0.448048	+	0.894009i	$0.352119\pi$
$192$	500.619	0.188172
$193$	2991.45	1.11570	0.557848	−	0.829943i	$-0.311627\pi$
$193$	2991.45	1.11570	0.557848	+	0.829943i	$0.311627\pi$
$194$	−3648.46	−1.35023
$195$	−402.237	−0.147717
$196$	0	0
$197$	2015.28	0.728847	0.364424	−	0.931233i	$-0.381266\pi$
$197$	2015.28	0.728847	0.364424	+	0.931233i	$0.381266\pi$
$198$	−1591.74	−0.571313
$199$	−1373.61	−0.489308	−0.244654	−	0.969610i	$-0.578674\pi$
$199$	−1373.61	−0.489308	−0.244654	+	0.969610i	$0.578674\pi$
$200$	167.233	0.0591259
$201$	−2393.17	−0.839805
$202$	4746.55	1.65330
$203$	0	0
$204$	377.087	0.129419
$205$	3185.19	1.08519
$206$	−1220.04	−0.412642
$207$	1231.53	0.413512
$208$	1008.28	0.336115
$209$	7123.96	2.35777
$210$	0	0
$211$	−4275.28	−1.39489	−0.697447	−	0.716637i	$-0.745681\pi$
$211$	−4275.28	−1.39489	−0.697447	+	0.716637i	$0.745681\pi$
$212$	−977.993	−0.316834
$213$	−1326.39	−0.426678
$214$	−7315.69	−2.33687
$215$	−3221.60	−1.02191
$216$	242.417	0.0763629
$217$	0	0
$218$	−6417.32	−1.99374
$219$	−1838.37	−0.567241
$220$	2754.95	0.844268
$221$	293.789	0.0894224
$222$	2027.25	0.612884
$223$	3406.97	1.02308	0.511541	−	0.859259i	$-0.329075\pi$
$223$	3406.97	1.02308	0.511541	+	0.859259i	$0.329075\pi$
$224$	0	0
$225$	−167.636	−0.0496698
$226$	6278.04	1.84783
$227$	−3234.07	−0.945607	−0.472803	−	0.881168i	$-0.656758\pi$
$227$	−3234.07	−0.945607	−0.472803	+	0.881168i	$0.656758\pi$
$228$	2475.17	0.718956
$229$	5561.39	1.60483	0.802417	−	0.596764i	$-0.203547\pi$
$229$	5561.39	1.60483	0.802417	+	0.596764i	$0.203547\pi$
$230$	−5197.32	−1.49001
$231$	0	0
$232$	−1857.20	−0.525566
$233$	1431.89	0.402601	0.201300	−	0.979530i	$-0.435483\pi$
$233$	1431.89	0.402601	0.201300	+	0.979530i	$0.435483\pi$
$234$	−430.871	−0.120371
$235$	6250.96	1.73518
$236$	3051.92	0.841793
$237$	−3164.07	−0.867207
$238$	0	0
$239$	3789.69	1.02567	0.512834	−	0.858488i	$-0.328596\pi$
$239$	3789.69	1.02567	0.512834	+	0.858488i	$0.328596\pi$
$240$	−2399.81	−0.645447
$241$	−3058.77	−0.817563	−0.408782	−	0.912632i	$-0.634046\pi$
$241$	−3058.77	−0.817563	−0.408782	+	0.912632i	$0.634046\pi$
$242$	3592.08	0.954163
$243$	−243.000	−0.0641500
$244$	−1710.65	−0.448825
$245$	0	0
$246$	3411.94	0.884298
$247$	1928.40	0.496766
$248$	−573.351	−0.146806
$249$	2676.73	0.681248
$250$	5455.22	1.38007
$251$	4831.12	1.21489	0.607446	−	0.794361i	$-0.292194\pi$
$251$	4831.12	1.21489	0.607446	+	0.794361i	$0.292194\pi$
$252$	0	0
$253$	−6571.56	−1.63301
$254$	4885.91	1.20697
$255$	−699.246	−0.171720
$256$	5370.69	1.31120
$257$	2801.90	0.680069	0.340035	−	0.940413i	$-0.389561\pi$
$257$	2801.90	0.680069	0.340035	+	0.940413i	$0.389561\pi$
$258$	−3450.93	−0.832735
$259$	0	0
$260$	745.744	0.177881
$261$	1861.67	0.441511
$262$	1789.49	0.421966
$263$	455.758	0.106856	0.0534282	−	0.998572i	$-0.482985\pi$
$263$	455.758	0.106856	0.0534282	+	0.998572i	$0.482985\pi$
$264$	−1293.56	−0.301566
$265$	1813.53	0.420393
$266$	0	0
$267$	−648.818	−0.148715
$268$	4436.91	1.01130
$269$	−3481.93	−0.789207	−0.394604	−	0.918851i	$-0.629118\pi$
$269$	−3481.93	−0.789207	−0.394604	+	0.918851i	$0.629118\pi$
$270$	1025.52	0.231152
$271$	−3065.34	−0.687107	−0.343554	−	0.939133i	$-0.611631\pi$
$271$	−3065.34	−0.687107	−0.343554	+	0.939133i	$0.611631\pi$
$272$	1752.79	0.390730
$273$	0	0
$274$	−10137.6	−2.23517
$275$	894.523	0.196152
$276$	−2283.24	−0.497952
$277$	−1414.62	−0.306847	−0.153423	−	0.988161i	$-0.549030\pi$
$277$	−1414.62	−0.306847	−0.153423	+	0.988161i	$0.549030\pi$
$278$	10330.0	2.22861
$279$	574.730	0.123327
$280$	0	0
$281$	7215.15	1.53174	0.765872	−	0.642994i	$-0.222308\pi$
$281$	7215.15	1.53174	0.765872	+	0.642994i	$0.222308\pi$
$282$	6695.95	1.41396
$283$	−1536.25	−0.322688	−0.161344	−	0.986898i	$-0.551583\pi$
$283$	−1536.25	−0.322688	−0.161344	+	0.986898i	$0.551583\pi$
$284$	2459.11	0.513807
$285$	−4589.79	−0.953949
$286$	2299.18	0.475361
$287$	0	0
$288$	−1924.21	−0.393698
$289$	−4402.28	−0.896047
$290$	−7856.67	−1.59090
$291$	2972.14	0.598728
$292$	3408.33	0.683073
$293$	6200.32	1.23627	0.618134	−	0.786073i	$-0.287889\pi$
$293$	6200.32	1.23627	0.618134	+	0.786073i	$0.287889\pi$
$294$	0	0
$295$	−5659.28	−1.11694
$296$	1647.50	0.323509
$297$	1296.68	0.253336
$298$	5870.91	1.14125
$299$	−1778.87	−0.344063
$300$	310.795	0.0598126
$301$	0	0
$302$	−5191.17	−0.989133
$303$	−3866.68	−0.733118
$304$	11505.2	2.17061
$305$	3172.12	0.595525
$306$	−749.024	−0.139931
$307$	−8425.37	−1.56632	−0.783161	−	0.621818i	$-0.786394\pi$
$307$	−8425.37	−1.56632	−0.783161	+	0.621818i	$0.786394\pi$
$308$	0	0
$309$	993.881	0.182977
$310$	−2425.50	−0.444384
$311$	−9338.33	−1.70266	−0.851331	−	0.524629i	$-0.824204\pi$
$311$	−9338.33	−1.70266	−0.851331	+	0.524629i	$0.824204\pi$
$312$	−350.158	−0.0635378
$313$	−6117.60	−1.10475	−0.552376	−	0.833595i	$-0.686279\pi$
$313$	−6117.60	−1.10475	−0.552376	+	0.833595i	$0.686279\pi$
$314$	3181.76	0.571838
$315$	0	0
$316$	5866.15	1.04429
$317$	−5441.24	−0.964070	−0.482035	−	0.876152i	$-0.660102\pi$
$317$	−5441.24	−0.964070	−0.482035	+	0.876152i	$0.660102\pi$
$318$	1942.63	0.342569
$319$	−9934.07	−1.74358
$320$	1721.09	0.300662
$321$	5959.57	1.03623
$322$	0	0
$323$	3352.32	0.577486
$324$	450.520	0.0772497
$325$	242.140	0.0413278
$326$	−6208.04	−1.05470
$327$	5227.74	0.884081
$328$	2772.80	0.466774
$329$	0	0
$330$	−5472.27	−0.912845
$331$	4218.96	0.700588	0.350294	−	0.936640i	$-0.386082\pi$
$331$	4218.96	0.700588	0.350294	+	0.936640i	$0.386082\pi$
$332$	−4962.63	−0.820361
$333$	−1651.46	−0.271770
$334$	2407.72	0.394446
$335$	−8227.52	−1.34184
$336$	0	0
$337$	88.2347	0.0142625	0.00713123	−	0.999975i	$-0.497730\pi$
$337$	88.2347	0.0142625	0.00713123	+	0.999975i	$0.497730\pi$
$338$	622.369	0.100155
$339$	−5114.27	−0.819377
$340$	1296.40	0.206785
$341$	−3066.83	−0.487032
$342$	−4916.52	−0.777354
$343$	0	0
$344$	−2804.48	−0.439557
$345$	4233.89	0.660710
$346$	−1237.29	−0.192247
$347$	3952.59	0.611488	0.305744	−	0.952114i	$-0.401095\pi$
$347$	3952.59	0.611488	0.305744	+	0.952114i	$0.401095\pi$
$348$	−3451.52	−0.531669
$349$	−4617.67	−0.708247	−0.354123	−	0.935199i	$-0.615221\pi$
$349$	−4617.67	−0.708247	−0.354123	+	0.935199i	$0.615221\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	10267.8	1.55476
$353$	3856.84	0.581526	0.290763	−	0.956795i	$-0.406091\pi$
$353$	3856.84	0.581526	0.290763	+	0.956795i	$0.406091\pi$
$354$	−6062.15	−0.910169
$355$	−4560.01	−0.681747
$356$	1202.90	0.179084
$357$	0	0
$358$	−10847.6	−1.60144
$359$	−7517.35	−1.10515	−0.552577	−	0.833462i	$-0.686356\pi$
$359$	−7517.35	−1.10515	−0.552577	+	0.833462i	$0.686356\pi$
$360$	833.411	0.122013
$361$	15145.3	2.20809
$362$	5569.81	0.808682
$363$	−2926.21	−0.423102
$364$	0	0
$365$	−6320.18	−0.906338
$366$	3397.94	0.485281
$367$	3637.09	0.517315	0.258657	−	0.965969i	$-0.416720\pi$
$367$	3637.09	0.517315	0.258657	+	0.965969i	$0.416720\pi$
$368$	−10613.0	−1.50338
$369$	−2779.46	−0.392122
$370$	6969.54	0.979267
$371$	0	0
$372$	−1065.55	−0.148511
$373$	1143.36	0.158716	0.0793580	−	0.996846i	$-0.474713\pi$
$373$	1143.36	0.158716	0.0793580	+	0.996846i	$0.474713\pi$
$374$	3996.88	0.552603
$375$	−4443.98	−0.611963
$376$	5441.63	0.746358
$377$	−2689.08	−0.367359
$378$	0	0
$379$	−11263.4	−1.52655	−0.763273	−	0.646076i	$-0.776409\pi$
$379$	−11263.4	−1.52655	−0.763273	+	0.646076i	$0.776409\pi$
$380$	8509.43	1.14875
$381$	−3980.20	−0.535202
$382$	8710.96	1.16673
$383$	6243.86	0.833019	0.416510	−	0.909131i	$-0.363253\pi$
$383$	6243.86	0.833019	0.416510	+	0.909131i	$0.363253\pi$
$384$	−3287.61	−0.436901
$385$	0	0
$386$	11016.5	1.45265
$387$	2811.23	0.369258
$388$	−5510.33	−0.720991
$389$	245.619	0.0320138	0.0160069	−	0.999872i	$-0.494905\pi$
$389$	245.619	0.0320138	0.0160069	+	0.999872i	$0.494905\pi$
$390$	−1481.30	−0.192330
$391$	−3092.38	−0.399970
$392$	0	0
$393$	−1457.77	−0.187111
$394$	7421.60	0.948971
$395$	−10877.8	−1.38563
$396$	−2404.03	−0.305068
$397$	−9759.82	−1.23383	−0.616916	−	0.787029i	$-0.711618\pi$
$397$	−9759.82	−1.23383	−0.616916	+	0.787029i	$0.711618\pi$
$398$	−5058.52	−0.637087
$399$	0	0
$400$	1444.65	0.180581
$401$	856.787	0.106698	0.0533490	−	0.998576i	$-0.483010\pi$
$401$	856.787	0.106698	0.0533490	+	0.998576i	$0.483010\pi$
$402$	−8813.21	−1.09344
$403$	−830.166	−0.102614
$404$	7168.79	0.882823
$405$	−835.415	−0.102499
$406$	0	0
$407$	8812.37	1.07325
$408$	−608.712	−0.0738621
$409$	−13492.8	−1.63124	−0.815621	−	0.578587i	$-0.803604\pi$
$409$	−13492.8	−1.63124	−0.815621	+	0.578587i	$0.803604\pi$
$410$	11730.0	1.41293
$411$	8258.42	0.991138
$412$	−1842.65	−0.220342
$413$	0	0
$414$	4535.29	0.538399
$415$	9202.38	1.08850
$416$	2779.41	0.327576
$417$	−8415.15	−0.988229
$418$	26235.1	3.06986
$419$	7560.21	0.881481	0.440740	−	0.897635i	$-0.354716\pi$
$419$	7560.21	0.881481	0.440740	+	0.897635i	$0.354716\pi$
$420$	0	0
$421$	6060.81	0.701629	0.350814	−	0.936445i	$-0.385905\pi$
$421$	6060.81	0.701629	0.350814	+	0.936445i	$0.385905\pi$
$422$	−15744.4	−1.81617
$423$	−5454.71	−0.626991
$424$	1578.72	0.180824
$425$	420.935	0.0480432
$426$	−4884.62	−0.555542
$427$	0	0
$428$	−11049.0	−1.24784
$429$	−1872.98	−0.210788
$430$	−11864.0	−1.33055
$431$	−7309.40	−0.816895	−0.408447	−	0.912782i	$-0.633930\pi$
$431$	−7309.40	−0.816895	−0.408447	+	0.912782i	$0.633930\pi$
$432$	2094.13	0.233226
$433$	3111.16	0.345295	0.172648	−	0.984984i	$-0.444768\pi$
$433$	3111.16	0.345295	0.172648	+	0.984984i	$0.444768\pi$
$434$	0	0
$435$	6400.27	0.705447
$436$	−9692.19	−1.06461
$437$	−20298.1	−2.22194
$438$	−6770.10	−0.738557
$439$	7332.12	0.797136	0.398568	−	0.917139i	$-0.369507\pi$
$439$	7332.12	0.797136	0.398568	+	0.917139i	$0.369507\pi$
$440$	−4447.17	−0.481843
$441$	0	0
$442$	1081.92	0.116429
$443$	−1046.60	−0.112247	−0.0561235	−	0.998424i	$-0.517874\pi$
$443$	−1046.60	−0.112247	−0.0561235	+	0.998424i	$0.517874\pi$
$444$	3061.79	0.327266
$445$	−2230.59	−0.237618
$446$	12546.7	1.33207
$447$	−4782.61	−0.506062
$448$	0	0
$449$	1057.03	0.111101	0.0555504	−	0.998456i	$-0.482309\pi$
$449$	1057.03	0.111101	0.0555504	+	0.998456i	$0.482309\pi$
$450$	−617.345	−0.0646709
$451$	14831.5	1.54854
$452$	9481.82	0.986697
$453$	4228.87	0.438609
$454$	−11910.0	−1.23120
$455$	0	0
$456$	−3995.53	−0.410324
$457$	−2640.07	−0.270235	−0.135118	−	0.990830i	$-0.543141\pi$
$457$	−2640.07	−0.270235	−0.135118	+	0.990830i	$0.543141\pi$
$458$	20480.7	2.08952
$459$	610.176	0.0620492
$460$	−7849.60	−0.795629
$461$	−14396.0	−1.45442	−0.727209	−	0.686416i	$-0.759183\pi$
$461$	−14396.0	−1.45442	−0.727209	+	0.686416i	$0.759183\pi$
$462$	0	0
$463$	−10031.3	−1.00690	−0.503450	−	0.864025i	$-0.667936\pi$
$463$	−10031.3	−1.00690	−0.503450	+	0.864025i	$0.667936\pi$
$464$	−16043.5	−1.60517
$465$	1975.88	0.197052
$466$	5273.15	0.524193
$467$	16478.8	1.63287	0.816434	−	0.577439i	$-0.195948\pi$
$467$	16478.8	1.63287	0.816434	+	0.577439i	$0.195948\pi$
$468$	−650.751	−0.0642756
$469$	0	0
$470$	23020.2	2.25924
$471$	−2591.95	−0.253569
$472$	−4926.55	−0.480430
$473$	−15001.0	−1.45824
$474$	−11652.2	−1.12912
$475$	2762.98	0.266893
$476$	0	0
$477$	−1582.52	−0.151905
$478$	13956.1	1.33544
$479$	17446.0	1.66415	0.832076	−	0.554661i	$-0.187152\pi$
$479$	17446.0	1.66415	0.832076	+	0.554661i	$0.187152\pi$
$480$	−6615.27	−0.629051
$481$	2385.44	0.226126
$482$	−11264.4	−1.06448
$483$	0	0
$484$	5425.17	0.509501
$485$	10218.0	0.956649
$486$	−894.886	−0.0835244
$487$	5994.27	0.557754	0.278877	−	0.960327i	$-0.410038\pi$
$487$	5994.27	0.557754	0.278877	+	0.960327i	$0.410038\pi$
$488$	2761.41	0.256154
$489$	5057.25	0.467683
$490$	0	0
$491$	−15253.9	−1.40203	−0.701015	−	0.713146i	$-0.747270\pi$
$491$	−15253.9	−1.40203	−0.701015	+	0.713146i	$0.747270\pi$
$492$	5153.11	0.472195
$493$	−4674.67	−0.427052
$494$	7101.64	0.646797
$495$	4457.87	0.404781
$496$	−4952.91	−0.448372
$497$	0	0
$498$	9857.47	0.886996
$499$	−19162.7	−1.71912	−0.859560	−	0.511034i	$-0.829263\pi$
$499$	−19162.7	−1.71912	−0.859560	+	0.511034i	$0.829263\pi$
$500$	8239.11	0.736928
$501$	−1961.40	−0.174908
$502$	17791.4	1.58181
$503$	16615.8	1.47288	0.736442	−	0.676501i	$-0.236504\pi$
$503$	16615.8	1.47288	0.736442	+	0.676501i	$0.236504\pi$
$504$	0	0
$505$	−13293.3	−1.17138
$506$	−24200.8	−2.12620
$507$	−507.000	−0.0444116
$508$	7379.27	0.644492
$509$	5184.56	0.451477	0.225738	−	0.974188i	$-0.427521\pi$
$509$	5184.56	0.451477	0.225738	+	0.974188i	$0.427521\pi$
$510$	−2575.09	−0.223582
$511$	0	0
$512$	11011.5	0.950476
$513$	4005.14	0.344700
$514$	10318.4	0.885461
$515$	3416.88	0.292361
$516$	−5212.00	−0.444662
$517$	29107.0	2.47606
$518$	0	0
$519$	1007.93	0.0852474
$520$	−1203.82	−0.101521
$521$	−4827.57	−0.405949	−0.202975	−	0.979184i	$-0.565061\pi$
$521$	−4827.57	−0.405949	−0.202975	+	0.979184i	$0.565061\pi$
$522$	6855.89	0.574854
$523$	−6467.28	−0.540716	−0.270358	−	0.962760i	$-0.587142\pi$
$523$	−6467.28	−0.540716	−0.270358	+	0.962760i	$0.587142\pi$
$524$	2702.69	0.225320
$525$	0	0
$526$	1678.40	0.139129
$527$	−1443.16	−0.119288
$528$	−11174.5	−0.921037
$529$	6557.13	0.538927
$530$	6678.60	0.547358
$531$	4938.40	0.403594
$532$	0	0
$533$	4014.78	0.326265
$534$	−2389.38	−0.193630
$535$	20488.6	1.65570
$536$	−7162.27	−0.577170
$537$	8836.78	0.710121
$538$	−12822.7	−1.02756
$539$	0	0
$540$	1548.85	0.123430
$541$	1842.65	0.146436	0.0732180	−	0.997316i	$-0.476673\pi$
$541$	1842.65	0.146436	0.0732180	+	0.997316i	$0.476673\pi$
$542$	−11288.6	−0.894625
$543$	−4537.33	−0.358592
$544$	4831.71	0.380805
$545$	17972.6	1.41259
$546$	0	0
$547$	−15851.6	−1.23906	−0.619528	−	0.784974i	$-0.712676\pi$
$547$	−15851.6	−1.23906	−0.619528	+	0.784974i	$0.712676\pi$
$548$	−15311.1	−1.19353
$549$	−2768.06	−0.215187
$550$	3294.22	0.255393
$551$	−30684.1	−2.37239
$552$	3685.71	0.284193
$553$	0	0
$554$	−5209.58	−0.399520
$555$	−5677.58	−0.434234
$556$	15601.6	1.19003
$557$	18003.8	1.36956	0.684779	−	0.728751i	$-0.259899\pi$
$557$	18003.8	1.36956	0.684779	+	0.728751i	$0.259899\pi$
$558$	2116.54	0.160574
$559$	−4060.66	−0.307241
$560$	0	0
$561$	−3255.97	−0.245039
$562$	26570.9	1.99435
$563$	9437.81	0.706494	0.353247	−	0.935530i	$-0.385078\pi$
$563$	9437.81	0.706494	0.353247	+	0.935530i	$0.385078\pi$
$564$	10113.0	0.755025
$565$	−17582.5	−1.30920
$566$	−5657.50	−0.420146
$567$	0	0
$568$	−3969.61	−0.293241
$569$	−9442.99	−0.695731	−0.347865	−	0.937544i	$-0.613093\pi$
$569$	−9442.99	−0.695731	−0.347865	+	0.937544i	$0.613093\pi$
$570$	−16902.6	−1.24206
$571$	−25254.2	−1.85089	−0.925443	−	0.378886i	$-0.876307\pi$
$571$	−25254.2	−1.85089	−0.925443	+	0.378886i	$0.876307\pi$
$572$	3472.48	0.253832
$573$	−7096.20	−0.517361
$574$	0	0
$575$	−2548.73	−0.184851
$576$	−1501.86	−0.108641
$577$	14635.5	1.05595	0.527977	−	0.849259i	$-0.322951\pi$
$577$	14635.5	1.05595	0.527977	+	0.849259i	$0.322951\pi$
$578$	−16212.1	−1.16667
$579$	−8974.35	−0.644147
$580$	−11866.1	−0.849502
$581$	0	0
$582$	10945.4	0.779554
$583$	8444.50	0.599890
$584$	−5501.89	−0.389845
$585$	1206.71	0.0852844
$586$	22833.7	1.60964
$587$	−2615.89	−0.183934	−0.0919670	−	0.995762i	$-0.529315\pi$
$587$	−2615.89	−0.183934	−0.0919670	+	0.995762i	$0.529315\pi$
$588$	0	0
$589$	−9472.74	−0.662678
$590$	−20841.2	−1.45427
$591$	−6045.85	−0.420800
$592$	14231.9	0.988056
$593$	−21508.3	−1.48944	−0.744721	−	0.667376i	$-0.767417\pi$
$593$	−21508.3	−1.48944	−0.744721	+	0.667376i	$0.767417\pi$
$594$	4775.21	0.329848
$595$	0	0
$596$	8866.92	0.609402
$597$	4120.82	0.282502
$598$	−6550.97	−0.447975
$599$	8571.23	0.584659	0.292330	−	0.956318i	$-0.405570\pi$
$599$	8571.23	0.584659	0.292330	+	0.956318i	$0.405570\pi$
$600$	−501.700	−0.0341364
$601$	−17054.9	−1.15754	−0.578772	−	0.815489i	$-0.696468\pi$
$601$	−17054.9	−1.15754	−0.578772	+	0.815489i	$0.696468\pi$
$602$	0	0
$603$	7179.50	0.484862
$604$	−7840.30	−0.528174
$605$	−10060.1	−0.676034
$606$	−14239.7	−0.954532
$607$	14278.8	0.954794	0.477397	−	0.878688i	$-0.341580\pi$
$607$	14278.8	0.954794	0.477397	+	0.878688i	$0.341580\pi$
$608$	31714.9	2.11547
$609$	0	0
$610$	11681.8	0.775384
$611$	7879.03	0.521688
$612$	−1131.26	−0.0747199
$613$	17041.4	1.12283	0.561417	−	0.827533i	$-0.310257\pi$
$613$	17041.4	1.12283	0.561417	+	0.827533i	$0.310257\pi$
$614$	−31027.8	−2.03938
$615$	−9555.58	−0.626534
$616$	0	0
$617$	2925.16	0.190863	0.0954315	−	0.995436i	$-0.469577\pi$
$617$	2925.16	0.190863	0.0954315	+	0.995436i	$0.469577\pi$
$618$	3660.12	0.238239
$619$	−5877.15	−0.381620	−0.190810	−	0.981627i	$-0.561111\pi$
$619$	−5877.15	−0.381620	−0.190810	+	0.981627i	$0.561111\pi$
$620$	−3663.27	−0.237291
$621$	−3694.58	−0.238741
$622$	−34389.9	−2.21689
$623$	0	0
$624$	−3024.85	−0.194056
$625$	−12949.8	−0.828787
$626$	−22529.0	−1.43841
$627$	−21371.9	−1.36126
$628$	4805.47	0.305349
$629$	4146.83	0.262870
$630$	0	0
$631$	−12967.1	−0.818083	−0.409041	−	0.912516i	$-0.634137\pi$
$631$	−12967.1	−0.818083	−0.409041	+	0.912516i	$0.634137\pi$
$632$	−9469.42	−0.596002
$633$	12825.8	0.805342
$634$	−20038.2	−1.25524
$635$	−13683.6	−0.855147
$636$	2933.98	0.182924
$637$	0	0
$638$	−36583.8	−2.27017
$639$	3979.16	0.246343
$640$	−11302.5	−0.698081
$641$	−15817.3	−0.974642	−0.487321	−	0.873223i	$-0.662026\pi$
$641$	−15817.3	−0.974642	−0.487321	+	0.873223i	$0.662026\pi$
$642$	21947.1	1.34919
$643$	−12171.1	−0.746472	−0.373236	−	0.927736i	$-0.621752\pi$
$643$	−12171.1	−0.746472	−0.373236	+	0.927736i	$0.621752\pi$
$644$	0	0
$645$	9664.79	0.590001
$646$	12345.4	0.751897
$647$	−12381.8	−0.752366	−0.376183	−	0.926545i	$-0.622764\pi$
$647$	−12381.8	−0.752366	−0.376183	+	0.926545i	$0.622764\pi$
$648$	−727.251	−0.0440881
$649$	−26351.9	−1.59384
$650$	891.720	0.0538094
$651$	0	0
$652$	−9376.10	−0.563185
$653$	5485.28	0.328722	0.164361	−	0.986400i	$-0.447444\pi$
$653$	5485.28	0.328722	0.164361	+	0.986400i	$0.447444\pi$
$654$	19252.0	1.15109
$655$	−5011.70	−0.298967
$656$	23952.9	1.42561
$657$	5515.12	0.327497
$658$	0	0
$659$	10091.3	0.596512	0.298256	−	0.954486i	$-0.403595\pi$
$659$	10091.3	0.596512	0.298256	+	0.954486i	$0.403595\pi$
$660$	−8264.86	−0.487438
$661$	9985.62	0.587588	0.293794	−	0.955869i	$-0.405082\pi$
$661$	9985.62	0.587588	0.293794	+	0.955869i	$0.405082\pi$
$662$	15537.0	0.912178
$663$	−881.366	−0.0516281
$664$	8010.91	0.468198
$665$	0	0
$666$	−6081.76	−0.353849
$667$	28304.8	1.64313
$668$	3636.42	0.210625
$669$	−10220.9	−0.590677
$670$	−30299.1	−1.74710
$671$	14770.7	0.849799
$672$	0	0
$673$	18123.1	1.03803	0.519014	−	0.854766i	$-0.326299\pi$
$673$	18123.1	1.03803	0.519014	+	0.854766i	$0.326299\pi$
$674$	324.938	0.0185700
$675$	502.907	0.0286769
$676$	939.974	0.0534806
$677$	20845.7	1.18340	0.591702	−	0.806156i	$-0.298456\pi$
$677$	20845.7	1.18340	0.591702	+	0.806156i	$0.298456\pi$
$678$	−18834.1	−1.06684
$679$	0	0
$680$	−2092.71	−0.118017
$681$	9702.21	0.545946
$682$	−11294.1	−0.634124
$683$	−13824.3	−0.774484	−0.387242	−	0.921978i	$-0.626572\pi$
$683$	−13824.3	−0.774484	−0.387242	+	0.921978i	$0.626572\pi$
$684$	−7425.50	−0.415089
$685$	28391.8	1.58364
$686$	0	0
$687$	−16684.2	−0.926551
$688$	−24226.6	−1.34249
$689$	2285.86	0.126392
$690$	15592.0	0.860255
$691$	−406.726	−0.0223916	−0.0111958	−	0.999937i	$-0.503564\pi$
$691$	−406.726	−0.0223916	−0.0111958	+	0.999937i	$0.503564\pi$
$692$	−1868.70	−0.102655
$693$	0	0
$694$	14556.1	0.796168
$695$	−28930.6	−1.57899
$696$	5571.60	0.303435
$697$	6979.27	0.379281
$698$	−17005.3	−0.922149
$699$	−4295.66	−0.232442
$700$	0	0
$701$	−4016.68	−0.216416	−0.108208	−	0.994128i	$-0.534511\pi$
$701$	−4016.68	−0.216416	−0.108208	+	0.994128i	$0.534511\pi$
$702$	1292.61	0.0694965
$703$	27219.4	1.46031
$704$	8014.08	0.429037
$705$	−18752.9	−1.00181
$706$	14203.4	0.757157
$707$	0	0
$708$	−9155.76	−0.486009
$709$	8436.79	0.446898	0.223449	−	0.974716i	$-0.428268\pi$
$709$	8436.79	0.446898	0.223449	+	0.974716i	$0.428268\pi$
$710$	−16793.0	−0.887646
$711$	9492.20	0.500682
$712$	−1941.78	−0.102207
$713$	8738.21	0.458974
$714$	0	0
$715$	−6439.15	−0.336798
$716$	−16383.3	−0.855130
$717$	−11369.1	−0.592169
$718$	−27683.8	−1.43893
$719$	−4237.71	−0.219805	−0.109903	−	0.993942i	$-0.535054\pi$
$719$	−4237.71	−0.219805	−0.109903	+	0.993942i	$0.535054\pi$
$720$	7199.44	0.372649
$721$	0	0
$722$	55775.0	2.87497
$723$	9176.31	0.472020
$724$	8412.17	0.431818
$725$	−3852.86	−0.197368
$726$	−10776.2	−0.550886
$727$	15531.4	0.792333	0.396167	−	0.918179i	$-0.370340\pi$
$727$	15531.4	0.792333	0.396167	+	0.918179i	$0.370340\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−23275.1	−1.18007
$731$	−7059.03	−0.357165
$732$	5131.96	0.259129
$733$	−21470.1	−1.08188	−0.540939	−	0.841062i	$-0.681931\pi$
$733$	−21470.1	−1.08188	−0.540939	+	0.841062i	$0.681931\pi$
$734$	13394.2	0.673553
$735$	0	0
$736$	−29255.7	−1.46519
$737$	−38310.6	−1.91478
$738$	−10235.8	−0.510550
$739$	−34124.2	−1.69862	−0.849310	−	0.527895i	$-0.822982\pi$
$739$	−34124.2	−1.69862	−0.849310	+	0.527895i	$0.822982\pi$
$740$	10526.2	0.522907
$741$	−5785.20	−0.286808
$742$	0	0
$743$	27631.3	1.36433	0.682163	−	0.731200i	$-0.261039\pi$
$743$	27631.3	1.36433	0.682163	+	0.731200i	$0.261039\pi$
$744$	1720.05	0.0847584
$745$	−16442.2	−0.808587
$746$	4210.61	0.206651
$747$	−8030.18	−0.393318
$748$	6036.54	0.295077
$749$	0	0
$750$	−16365.7	−0.796786
$751$	4970.53	0.241514	0.120757	−	0.992682i	$-0.461468\pi$
$751$	4970.53	0.241514	0.120757	+	0.992682i	$0.461468\pi$
$752$	47007.7	2.27951
$753$	−14493.4	−0.701418
$754$	−9902.95	−0.478308
$755$	14538.5	0.700810
$756$	0	0
$757$	23086.2	1.10843	0.554215	−	0.832374i	$-0.313019\pi$
$757$	23086.2	1.10843	0.554215	+	0.832374i	$0.313019\pi$
$758$	−41479.2	−1.98759
$759$	19714.7	0.942816
$760$	−13736.3	−0.655617
$761$	1829.68	0.0871562	0.0435781	−	0.999050i	$-0.486124\pi$
$761$	1829.68	0.0871562	0.0435781	+	0.999050i	$0.486124\pi$
$762$	−14657.7	−0.696842
$763$	0	0
$764$	13156.3	0.623008
$765$	2097.74	0.0991424
$766$	22994.0	1.08460
$767$	−7133.25	−0.335811
$768$	−16112.1	−0.757024
$769$	12626.0	0.592073	0.296037	−	0.955177i	$-0.404335\pi$
$769$	12626.0	0.592073	0.296037	+	0.955177i	$0.404335\pi$
$770$	0	0
$771$	−8405.70	−0.392638
$772$	16638.4	0.775685
$773$	17918.6	0.833747	0.416873	−	0.908965i	$-0.363126\pi$
$773$	17918.6	0.833747	0.416873	+	0.908965i	$0.363126\pi$
$774$	10352.8	0.480780
$775$	−1189.45	−0.0551306
$776$	8895.03	0.411486
$777$	0	0
$778$	904.530	0.0416825
$779$	45811.3	2.10701
$780$	−2237.23	−0.102700
$781$	−21233.2	−0.972836
$782$	−11388.2	−0.520767
$783$	−5585.00	−0.254906
$784$	0	0
$785$	−8910.94	−0.405153
$786$	−5368.47	−0.243622
$787$	11338.7	0.513570	0.256785	−	0.966468i	$-0.417337\pi$
$787$	11338.7	0.513570	0.256785	+	0.966468i	$0.417337\pi$
$788$	11209.0	0.506729
$789$	−1367.27	−0.0616935
$790$	−40059.3	−1.80411
$791$	0	0
$792$	3880.69	0.174109
$793$	3998.30	0.179047
$794$	−35942.1	−1.60647
$795$	−5440.58	−0.242714
$796$	−7639.96	−0.340190
$797$	7046.33	0.313167	0.156583	−	0.987665i	$-0.449952\pi$
$797$	7046.33	0.313167	0.156583	+	0.987665i	$0.449952\pi$
$798$	0	0
$799$	13696.9	0.606458
$800$	3982.29	0.175994
$801$	1946.45	0.0858609
$802$	3155.26	0.138923
$803$	−29429.3	−1.29332
$804$	−13310.7	−0.583872
$805$	0	0
$806$	−3057.22	−0.133605
$807$	10445.8	0.455649
$808$	−11572.2	−0.503847
$809$	36139.4	1.57057	0.785287	−	0.619133i	$-0.212516\pi$
$809$	36139.4	1.57057	0.785287	+	0.619133i	$0.212516\pi$
$810$	−3076.55	−0.133455
$811$	−5634.30	−0.243954	−0.121977	−	0.992533i	$-0.538923\pi$
$811$	−5634.30	−0.243954	−0.121977	+	0.992533i	$0.538923\pi$
$812$	0	0
$813$	9196.01	0.396701
$814$	32452.9	1.39739
$815$	17386.4	0.747264
$816$	−5258.38	−0.225588
$817$	−46334.8	−1.98415
$818$	−49689.5	−2.12390
$819$	0	0
$820$	17716.0	0.754474
$821$	−4.23158	−0.000179882 0	−8.99411e−5	−	1.00000i	$-0.500029\pi$
$821$	−4.23158	−0.000179882 0	−8.99411e−5		1.00000i	$0.500029\pi$
$822$	30412.9	1.29048
$823$	19329.2	0.818678	0.409339	−	0.912382i	$-0.365759\pi$
$823$	19329.2	0.818678	0.409339	+	0.912382i	$0.365759\pi$
$824$	2974.49	0.125754
$825$	−2683.57	−0.113248
$826$	0	0
$827$	35545.8	1.49462	0.747308	−	0.664478i	$-0.231346\pi$
$827$	35545.8	1.49462	0.747308	+	0.664478i	$0.231346\pi$
$828$	6849.72	0.287493
$829$	34394.2	1.44097	0.720483	−	0.693472i	$-0.243920\pi$
$829$	34394.2	1.44097	0.720483	+	0.693472i	$0.243920\pi$
$830$	33889.2	1.41724
$831$	4243.87	0.177158
$832$	2169.35	0.0903950
$833$	0	0
$834$	−30990.1	−1.28669
$835$	−6743.15	−0.279469
$836$	39623.3	1.63924
$837$	−1724.19	−0.0712028
$838$	27841.7	1.14770
$839$	23926.2	0.984532	0.492266	−	0.870445i	$-0.336169\pi$
$839$	23926.2	0.984532	0.492266	+	0.870445i	$0.336169\pi$
$840$	0	0
$841$	18398.7	0.754387
$842$	22319.9	0.913532
$843$	−21645.5	−0.884352
$844$	−23779.0	−0.969796
$845$	−1743.03	−0.0709609
$846$	−20087.9	−0.816353
$847$	0	0
$848$	13637.8	0.552270
$849$	4608.76	0.186304
$850$	1550.16	0.0625530
$851$	−25108.8	−1.01142
$852$	−7377.33	−0.296647
$853$	−8933.95	−0.358608	−0.179304	−	0.983794i	$-0.557385\pi$
$853$	−8933.95	−0.358608	−0.179304	+	0.983794i	$0.557385\pi$
$854$	0	0
$855$	13769.4	0.550763
$856$	17835.8	0.712168
$857$	−2121.36	−0.0845559	−0.0422779	−	0.999106i	$-0.513462\pi$
$857$	−2121.36	−0.0845559	−0.0422779	+	0.999106i	$0.513462\pi$
$858$	−6897.53	−0.274450
$859$	32265.5	1.28159	0.640795	−	0.767712i	$-0.278605\pi$
$859$	32265.5	1.28159	0.640795	+	0.767712i	$0.278605\pi$
$860$	−17918.4	−0.710481
$861$	0	0
$862$	−26918.0	−1.06361
$863$	−3734.46	−0.147303	−0.0736515	−	0.997284i	$-0.523465\pi$
$863$	−3734.46	−0.147303	−0.0736515	+	0.997284i	$0.523465\pi$
$864$	5772.62	0.227301
$865$	3465.20	0.136209
$866$	11457.3	0.449580
$867$	13206.8	0.517333
$868$	0	0
$869$	−50651.5	−1.97725
$870$	23570.0	0.918504
$871$	−10370.4	−0.403429
$872$	15645.6	0.607599
$873$	−8916.42	−0.345676
$874$	−74750.9	−2.89300
$875$	0	0
$876$	−10225.0	−0.394373
$877$	−15276.6	−0.588205	−0.294102	−	0.955774i	$-0.595021\pi$
$877$	−15276.6	−0.588205	−0.294102	+	0.955774i	$0.595021\pi$
$878$	27001.7	1.03788
$879$	−18601.0	−0.713760
$880$	−38417.1	−1.47163
$881$	8565.86	0.327572	0.163786	−	0.986496i	$-0.447629\pi$
$881$	8565.86	0.327572	0.163786	+	0.986496i	$0.447629\pi$
$882$	0	0
$883$	−12700.6	−0.484043	−0.242022	−	0.970271i	$-0.577811\pi$
$883$	−12700.6	−0.484043	−0.242022	+	0.970271i	$0.577811\pi$
$884$	1634.05	0.0621707
$885$	16977.9	0.644864
$886$	−3854.27	−0.146148
$887$	3443.30	0.130344	0.0651719	−	0.997874i	$-0.479240\pi$
$887$	3443.30	0.130344	0.0651719	+	0.997874i	$0.479240\pi$
$888$	−4942.49	−0.186778
$889$	0	0
$890$	−8214.49	−0.309382
$891$	−3890.03	−0.146264
$892$	18949.5	0.711296
$893$	89904.9	3.36904
$894$	−17612.7	−0.658901
$895$	30380.2	1.13463
$896$	0	0
$897$	5336.61	0.198645
$898$	3892.67	0.144655
$899$	13209.3	0.490052
$900$	−932.385	−0.0345328
$901$	3973.73	0.146930
$902$	54619.5	2.01622
$903$	0	0
$904$	−15306.0	−0.563130
$905$	−15599.0	−0.572959
$906$	15573.5	0.571076
$907$	−43547.3	−1.59423	−0.797114	−	0.603829i	$-0.793641\pi$
$907$	−43547.3	−1.59423	−0.797114	+	0.603829i	$0.793641\pi$
$908$	−17987.8	−0.657431
$909$	11600.0	0.423266
$910$	0	0
$911$	14305.7	0.520274	0.260137	−	0.965572i	$-0.416232\pi$
$911$	14305.7	0.520274	0.260137	+	0.965572i	$0.416232\pi$
$912$	−34515.5	−1.25320
$913$	42850.0	1.55326
$914$	−9722.49	−0.351851
$915$	−9516.36	−0.343827
$916$	30932.3	1.11576
$917$	0	0
$918$	2247.07	0.0807891
$919$	27012.6	0.969601	0.484800	−	0.874625i	$-0.338892\pi$
$919$	27012.6	0.969601	0.484800	+	0.874625i	$0.338892\pi$
$920$	12671.2	0.454083
$921$	25276.1	0.904317
$922$	−53015.4	−1.89368
$923$	−5747.67	−0.204969
$924$	0	0
$925$	3417.82	0.121489
$926$	−36941.9	−1.31100
$927$	−2981.64	−0.105642
$928$	−44225.1	−1.56440
$929$	11299.7	0.399065	0.199532	−	0.979891i	$-0.436058\pi$
$929$	11299.7	0.399065	0.199532	+	0.979891i	$0.436058\pi$
$930$	7276.49	0.256565
$931$	0	0
$932$	7964.12	0.279907
$933$	28015.0	0.983033
$934$	60685.9	2.12602
$935$	−11193.8	−0.391525
$936$	1050.47	0.0366835
$937$	−2250.61	−0.0784677	−0.0392338	−	0.999230i	$-0.512492\pi$
$937$	−2250.61	−0.0784677	−0.0392338	+	0.999230i	$0.512492\pi$
$938$	0	0
$939$	18352.8	0.637829
$940$	34767.7	1.20638
$941$	16286.6	0.564218	0.282109	−	0.959382i	$-0.408966\pi$
$941$	16286.6	0.564218	0.282109	+	0.959382i	$0.408966\pi$
$942$	−9545.29	−0.330151
$943$	−42259.0	−1.45932
$944$	−42558.2	−1.46732
$945$	0	0
$946$	−55243.7	−1.89866
$947$	35115.1	1.20495	0.602475	−	0.798138i	$-0.294181\pi$
$947$	35115.1	1.20495	0.602475	+	0.798138i	$0.294181\pi$
$948$	−17598.5	−0.602924
$949$	−7966.28	−0.272494
$950$	10175.1	0.347499
$951$	16323.7	0.556606
$952$	0	0
$953$	−3720.61	−0.126466	−0.0632331	−	0.997999i	$-0.520141\pi$
$953$	−3720.61	−0.126466	−0.0632331	+	0.997999i	$0.520141\pi$
$954$	−5827.88	−0.197783
$955$	−24396.2	−0.826641
$956$	21078.2	0.713093
$957$	29802.2	1.00665
$958$	64247.8	2.16675
$959$	0	0
$960$	−5163.27	−0.173587
$961$	−25713.0	−0.863114
$962$	8784.76	0.294420
$963$	−17878.7	−0.598270
$964$	−17012.8	−0.568408
$965$	−30853.1	−1.02922
$966$	0	0
$967$	38092.5	1.26678	0.633388	−	0.773834i	$-0.281664\pi$
$967$	38092.5	1.26678	0.633388	+	0.773834i	$0.281664\pi$
$968$	−8757.56	−0.290784
$969$	−10057.0	−0.333412
$970$	37629.4	1.24557
$971$	−7141.09	−0.236013	−0.118006	−	0.993013i	$-0.537650\pi$
$971$	−7141.09	−0.236013	−0.118006	+	0.993013i	$0.537650\pi$
$972$	−1351.56	−0.0446001
$973$	0	0
$974$	22074.9	0.726205
$975$	−726.421	−0.0238606
$976$	23854.6	0.782342
$977$	10836.9	0.354866	0.177433	−	0.984133i	$-0.443221\pi$
$977$	10836.9	0.354866	0.177433	+	0.984133i	$0.443221\pi$
$978$	18624.1	0.608930
$979$	−10386.5	−0.339075
$980$	0	0
$981$	−15683.2	−0.510424
$982$	−56174.8	−1.82547
$983$	58367.5	1.89383	0.946915	−	0.321485i	$-0.104182\pi$
$983$	58367.5	1.89383	0.946915	+	0.321485i	$0.104182\pi$
$984$	−8318.39	−0.269492
$985$	−20785.2	−0.672356
$986$	−17215.2	−0.556029
$987$	0	0
$988$	10725.7	0.345375
$989$	42742.0	1.37423
$990$	16416.8	0.527031
$991$	41999.4	1.34627	0.673135	−	0.739519i	$-0.264947\pi$
$991$	41999.4	1.34627	0.673135	+	0.739519i	$0.264947\pi$
$992$	−13653.1	−0.436982
$993$	−12656.9	−0.404485
$994$	0	0
$995$	14167.1	0.451383
$996$	14887.9	0.473635
$997$	−14469.4	−0.459631	−0.229815	−	0.973234i	$-0.573812\pi$
$997$	−14469.4	−0.459631	−0.229815	+	0.973234i	$0.573812\pi$
$998$	−70569.8	−2.23832
$999$	4954.37	0.156906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.4.a.bf.1.18	✓	22
7.6	odd	2		1911.4.a.bg.1.18	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.4.a.bf.1.18	✓	22	1.1	even	1	trivial
1911.4.a.bg.1.18	yes	22	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q+3.68266 q^{2} -3.00000 q^{3} +5.56198 q^{4} -10.3138 q^{5} -11.0480 q^{6} -8.97840 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.68266 q^{2} -3.00000 q^{3} +5.56198 q^{4} -10.3138 q^{5} -11.0480 q^{6} -8.97840 q^{8} +9.00000 q^{9} -37.9821 q^{10} -48.0250 q^{11} -16.6859 q^{12} -13.0000 q^{13} +30.9413 q^{15} -77.5602 q^{16} -22.5991 q^{17} +33.1439 q^{18} -148.338 q^{19} -57.3650 q^{20} -176.860 q^{22} +136.836 q^{23} +26.9352 q^{24} -18.6262 q^{25} -47.8746 q^{26} -27.0000 q^{27} +206.852 q^{29} +113.946 q^{30} +63.8589 q^{31} -213.801 q^{32} +144.075 q^{33} -83.2248 q^{34} +50.0578 q^{36} -183.495 q^{37} -546.280 q^{38} +39.0000 q^{39} +92.6012 q^{40} -308.829 q^{41} +312.359 q^{43} -267.114 q^{44} -92.8239 q^{45} +503.921 q^{46} -606.079 q^{47} +232.681 q^{48} -68.5939 q^{50} +67.7974 q^{51} -72.3057 q^{52} -175.835 q^{53} -99.4318 q^{54} +495.319 q^{55} +445.015 q^{57} +761.765 q^{58} +548.712 q^{59} +172.095 q^{60} -307.562 q^{61} +235.171 q^{62} -166.873 q^{64} +134.079 q^{65} +530.579 q^{66} +797.722 q^{67} -125.696 q^{68} -410.508 q^{69} +442.128 q^{71} -80.8056 q^{72} +612.791 q^{73} -675.751 q^{74} +55.8785 q^{75} -825.055 q^{76} +143.624 q^{78} +1054.69 q^{79} +799.938 q^{80} +81.0000 q^{81} -1137.31 q^{82} -892.242 q^{83} +233.082 q^{85} +1150.31 q^{86} -620.556 q^{87} +431.188 q^{88} +216.273 q^{89} -341.839 q^{90} +761.080 q^{92} -191.577 q^{93} -2231.98 q^{94} +1529.93 q^{95} +641.402 q^{96} -990.713 q^{97} -432.225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 66 q^{3} + 114 q^{4} - 36 q^{5} - 6 q^{6} + 66 q^{8} + 198 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 66 * q^3 + 114 * q^4 - 36 * q^5 - 6 * q^6 + 66 * q^8 + 198 * q^9	\( 22 q + 2 q^{2} - 66 q^{3} + 114 q^{4} - 36 q^{5} - 6 q^{6} + 66 q^{8} + 198 q^{9} - 48 q^{10} + 108 q^{11} - 342 q^{12} - 286 q^{13} + 108 q^{15} + 462 q^{16} + 18 q^{18} - 408 q^{19} - 416 q^{20} + 188 q^{22} + 304 q^{23} - 198 q^{24} + 882 q^{25} - 26 q^{26} - 594 q^{27} + 216 q^{29} + 144 q^{30} - 316 q^{31} + 770 q^{32} - 324 q^{33} - 776 q^{34} + 1026 q^{36} + 840 q^{37} + 436 q^{38} + 858 q^{39} - 40 q^{40} - 396 q^{41} + 768 q^{43} + 864 q^{44} - 324 q^{45} + 1380 q^{46} + 444 q^{47} - 1386 q^{48} + 70 q^{50} - 1482 q^{52} + 2612 q^{53} - 54 q^{54} - 1292 q^{55} + 1224 q^{57} + 1484 q^{58} - 1140 q^{59} + 1248 q^{60} + 392 q^{61} + 236 q^{62} + 2182 q^{64} + 468 q^{65} - 564 q^{66} + 2348 q^{67} + 3160 q^{68} - 912 q^{69} + 1624 q^{71} + 594 q^{72} - 1944 q^{73} + 3060 q^{74} - 2646 q^{75} - 2768 q^{76} + 78 q^{78} + 1904 q^{79} - 3820 q^{80} + 1782 q^{81} - 1360 q^{82} - 984 q^{83} + 1304 q^{85} + 2000 q^{86} - 648 q^{87} + 2164 q^{88} - 560 q^{89} - 432 q^{90} + 2608 q^{92} + 948 q^{93} - 1052 q^{94} + 2448 q^{95} - 2310 q^{96} - 2344 q^{97} + 972 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 66 * q^3 + 114 * q^4 - 36 * q^5 - 6 * q^6 + 66 * q^8 + 198 * q^9 - 48 * q^10 + 108 * q^11 - 342 * q^12 - 286 * q^13 + 108 * q^15 + 462 * q^16 + 18 * q^18 - 408 * q^19 - 416 * q^20 + 188 * q^22 + 304 * q^23 - 198 * q^24 + 882 * q^25 - 26 * q^26 - 594 * q^27 + 216 * q^29 + 144 * q^30 - 316 * q^31 + 770 * q^32 - 324 * q^33 - 776 * q^34 + 1026 * q^36 + 840 * q^37 + 436 * q^38 + 858 * q^39 - 40 * q^40 - 396 * q^41 + 768 * q^43 + 864 * q^44 - 324 * q^45 + 1380 * q^46 + 444 * q^47 - 1386 * q^48 + 70 * q^50 - 1482 * q^52 + 2612 * q^53 - 54 * q^54 - 1292 * q^55 + 1224 * q^57 + 1484 * q^58 - 1140 * q^59 + 1248 * q^60 + 392 * q^61 + 236 * q^62 + 2182 * q^64 + 468 * q^65 - 564 * q^66 + 2348 * q^67 + 3160 * q^68 - 912 * q^69 + 1624 * q^71 + 594 * q^72 - 1944 * q^73 + 3060 * q^74 - 2646 * q^75 - 2768 * q^76 + 78 * q^78 + 1904 * q^79 - 3820 * q^80 + 1782 * q^81 - 1360 * q^82 - 984 * q^83 + 1304 * q^85 + 2000 * q^86 - 648 * q^87 + 2164 * q^88 - 560 * q^89 - 432 * q^90 + 2608 * q^92 + 948 * q^93 - 1052 * q^94 + 2448 * q^95 - 2310 * q^96 - 2344 * q^97 + 972 * q^99

Introduction

L-functions

Modular forms

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