LMFDB - Embedded newform 1859.4.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 59x^{7} - 12x^{6} + 1144x^{5} + 345x^{4} - 7888x^{3} - 2245x^{2} + 9710x - 2988 $ x^9 - 59x^7 - 12x^6 + 1144x^5 + 345x^4 - 7888x^3 - 2245x^2 + 9710*x - 2988
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-3.76323$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.76323 q^{2} -4.70664 q^{3} +6.16188 q^{4} -20.6048 q^{5} -17.7122 q^{6} +28.6315 q^{7} -6.91727 q^{8} -4.84752 q^{9} +O(q^{10})$	\(q+3.76323 q^{2} -4.70664 q^{3} +6.16188 q^{4} -20.6048 q^{5} -17.7122 q^{6} +28.6315 q^{7} -6.91727 q^{8} -4.84752 q^{9} -77.5406 q^{10} +11.0000 q^{11} -29.0018 q^{12} +107.747 q^{14} +96.9795 q^{15} -75.3263 q^{16} +50.0610 q^{17} -18.2423 q^{18} -5.38233 q^{19} -126.964 q^{20} -134.758 q^{21} +41.3955 q^{22} +183.575 q^{23} +32.5571 q^{24} +299.559 q^{25} +149.895 q^{27} +176.424 q^{28} -200.750 q^{29} +364.956 q^{30} +19.4064 q^{31} -228.132 q^{32} -51.7731 q^{33} +188.391 q^{34} -589.946 q^{35} -29.8698 q^{36} -258.301 q^{37} -20.2549 q^{38} +142.529 q^{40} -359.846 q^{41} -507.125 q^{42} +261.966 q^{43} +67.7807 q^{44} +99.8823 q^{45} +690.835 q^{46} +450.795 q^{47} +354.534 q^{48} +476.760 q^{49} +1127.31 q^{50} -235.619 q^{51} +725.364 q^{53} +564.088 q^{54} -226.653 q^{55} -198.051 q^{56} +25.3327 q^{57} -755.466 q^{58} -381.785 q^{59} +597.576 q^{60} +68.9130 q^{61} +73.0309 q^{62} -138.792 q^{63} -255.901 q^{64} -194.834 q^{66} -133.352 q^{67} +308.470 q^{68} -864.023 q^{69} -2220.10 q^{70} +142.258 q^{71} +33.5316 q^{72} -394.273 q^{73} -972.045 q^{74} -1409.92 q^{75} -33.1653 q^{76} +314.946 q^{77} -1151.89 q^{79} +1552.08 q^{80} -574.619 q^{81} -1354.18 q^{82} -519.150 q^{83} -830.363 q^{84} -1031.50 q^{85} +985.836 q^{86} +944.856 q^{87} -76.0899 q^{88} -248.303 q^{89} +375.880 q^{90} +1131.17 q^{92} -91.3392 q^{93} +1696.44 q^{94} +110.902 q^{95} +1073.73 q^{96} -848.603 q^{97} +1794.16 q^{98} -53.3227 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9}+O(q^{10}) $ 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9} - 22 q^{10} + 99 q^{11} + 181 q^{12} - 351 q^{15} + 130 q^{16} + 53 q^{17} - 33 q^{18} - 69 q^{19} - 282 q^{20} - 463 q^{21} + 216 q^{23} + 121 q^{24} + 617 q^{25} + 275 q^{27} - 279 q^{28} - 91 q^{29} + 29 q^{30} - 636 q^{31} - 663 q^{32} + 88 q^{33} - 423 q^{34} - 358 q^{35} - 252 q^{36} - 967 q^{37} - 101 q^{38} + 652 q^{40} + 226 q^{41} - 1186 q^{42} + 42 q^{43} + 506 q^{44} - 5 q^{45} + 1127 q^{46} + 269 q^{47} - 1820 q^{48} + 228 q^{49} + 1374 q^{50} - 589 q^{51} + 1227 q^{53} + 2438 q^{54} - 330 q^{55} - 659 q^{56} + 71 q^{57} - 471 q^{58} + 613 q^{59} + 859 q^{60} + 427 q^{61} - 1714 q^{62} - 305 q^{63} - 1194 q^{64} - 374 q^{66} + 271 q^{67} - 2835 q^{68} - 846 q^{69} + 102 q^{70} - 2279 q^{71} + 2400 q^{72} - 3602 q^{73} - 4955 q^{74} - 883 q^{75} - 1126 q^{76} - 275 q^{77} - 1182 q^{79} + 2360 q^{80} + 2697 q^{81} + 1007 q^{82} + 1877 q^{83} - 1618 q^{84} + 441 q^{85} - 830 q^{86} + 1942 q^{87} - 396 q^{88} - 1258 q^{89} - 5669 q^{90} + 1046 q^{92} - 1556 q^{93} + 1439 q^{94} + 2032 q^{95} + 3417 q^{96} - 4002 q^{97} + 1855 q^{98} + 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9 - 22 * q^10 + 99 * q^11 + 181 * q^12 - 351 * q^15 + 130 * q^16 + 53 * q^17 - 33 * q^18 - 69 * q^19 - 282 * q^20 - 463 * q^21 + 216 * q^23 + 121 * q^24 + 617 * q^25 + 275 * q^27 - 279 * q^28 - 91 * q^29 + 29 * q^30 - 636 * q^31 - 663 * q^32 + 88 * q^33 - 423 * q^34 - 358 * q^35 - 252 * q^36 - 967 * q^37 - 101 * q^38 + 652 * q^40 + 226 * q^41 - 1186 * q^42 + 42 * q^43 + 506 * q^44 - 5 * q^45 + 1127 * q^46 + 269 * q^47 - 1820 * q^48 + 228 * q^49 + 1374 * q^50 - 589 * q^51 + 1227 * q^53 + 2438 * q^54 - 330 * q^55 - 659 * q^56 + 71 * q^57 - 471 * q^58 + 613 * q^59 + 859 * q^60 + 427 * q^61 - 1714 * q^62 - 305 * q^63 - 1194 * q^64 - 374 * q^66 + 271 * q^67 - 2835 * q^68 - 846 * q^69 + 102 * q^70 - 2279 * q^71 + 2400 * q^72 - 3602 * q^73 - 4955 * q^74 - 883 * q^75 - 1126 * q^76 - 275 * q^77 - 1182 * q^79 + 2360 * q^80 + 2697 * q^81 + 1007 * q^82 + 1877 * q^83 - 1618 * q^84 + 441 * q^85 - 830 * q^86 + 1942 * q^87 - 396 * q^88 - 1258 * q^89 - 5669 * q^90 + 1046 * q^92 - 1556 * q^93 + 1439 * q^94 + 2032 * q^95 + 3417 * q^96 - 4002 * q^97 + 1855 * q^98 + 1001 * 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 $

$2$	3.76323	1.33050	0.665251	−	0.746620i	$-0.268325\pi$
$2$	3.76323	1.33050	0.665251	+	0.746620i	$0.268325\pi$
$3$	−4.70664	−0.905794	−0.452897	−	0.891563i	$-0.649609\pi$
$3$	−4.70664	−0.905794	−0.452897	+	0.891563i	$0.649609\pi$
$4$	6.16188	0.770235
$5$	−20.6048	−1.84295	−0.921476	−	0.388436i	$-0.873015\pi$
$5$	−20.6048	−1.84295	−0.921476	+	0.388436i	$0.873015\pi$
$6$	−17.7122	−1.20516
$7$	28.6315	1.54595	0.772977	−	0.634435i	$-0.218767\pi$
$7$	28.6315	1.54595	0.772977	+	0.634435i	$0.218767\pi$
$8$	−6.91727	−0.305703
$9$	−4.84752	−0.179538
$10$	−77.5406	−2.45205
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−29.0018	−0.697674
$13$	0	0
$13$	0	0
$14$	107.747	2.05689
$15$	96.9795	1.66933
$16$	−75.3263	−1.17697
$17$	50.0610	0.714210	0.357105	−	0.934064i	$-0.383764\pi$
$17$	50.0610	0.714210	0.357105	+	0.934064i	$0.383764\pi$
$18$	−18.2423	−0.238875
$19$	−5.38233	−0.0649891	−0.0324945	−	0.999472i	$-0.510345\pi$
$19$	−5.38233	−0.0649891	−0.0324945	+	0.999472i	$0.510345\pi$
$20$	−126.964	−1.41951
$21$	−134.758	−1.40031
$22$	41.3955	0.401161
$23$	183.575	1.66426	0.832132	−	0.554577i	$-0.187120\pi$
$23$	183.575	1.66426	0.832132	+	0.554577i	$0.187120\pi$
$24$	32.5571	0.276904
$25$	299.559	2.39647
$26$	0	0
$27$	149.895	1.06842
$28$	176.424	1.19075
$29$	−200.750	−1.28546	−0.642728	−	0.766094i	$-0.722198\pi$
$29$	−200.750	−1.28546	−0.642728	+	0.766094i	$0.722198\pi$
$30$	364.956	2.22105
$31$	19.4064	0.112435	0.0562177	−	0.998419i	$-0.482096\pi$
$31$	19.4064	0.112435	0.0562177	+	0.998419i	$0.482096\pi$
$32$	−228.132	−1.26026
$33$	−51.7731	−0.273107
$34$	188.391	0.950258
$35$	−589.946	−2.84912
$36$	−29.8698	−0.138286
$37$	−258.301	−1.14769	−0.573843	−	0.818965i	$-0.694548\pi$
$37$	−258.301	−1.14769	−0.573843	+	0.818965i	$0.694548\pi$
$38$	−20.2549	−0.0864681
$39$	0	0
$40$	142.529	0.563396
$41$	−359.846	−1.37069	−0.685347	−	0.728217i	$-0.740349\pi$
$41$	−359.846	−1.37069	−0.685347	+	0.728217i	$0.740349\pi$
$42$	−507.125	−1.86312
$43$	261.966	0.929055	0.464528	−	0.885559i	$-0.346224\pi$
$43$	261.966	0.929055	0.464528	+	0.885559i	$0.346224\pi$
$44$	67.7807	0.232235
$45$	99.8823	0.330879
$46$	690.835	2.21431
$47$	450.795	1.39905	0.699524	−	0.714610i	$-0.253396\pi$
$47$	450.795	1.39905	0.699524	+	0.714610i	$0.253396\pi$
$48$	354.534	1.06609
$49$	476.760	1.38997
$50$	1127.31	3.18851
$51$	−235.619	−0.646927
$52$	0	0
$53$	725.364	1.87993	0.939966	−	0.341269i	$-0.110857\pi$
$53$	725.364	1.87993	0.939966	+	0.341269i	$0.110857\pi$
$54$	564.088	1.42153
$55$	−226.653	−0.555671
$56$	−198.051	−0.472602
$57$	25.3327	0.0588667
$58$	−755.466	−1.71030
$59$	−381.785	−0.842443	−0.421222	−	0.906958i	$-0.638399\pi$
$59$	−381.785	−0.842443	−0.421222	+	0.906958i	$0.638399\pi$
$60$	597.576	1.28578
$61$	68.9130	0.144646	0.0723229	−	0.997381i	$-0.476959\pi$
$61$	68.9130	0.144646	0.0723229	+	0.997381i	$0.476959\pi$
$62$	73.0309	0.149596
$63$	−138.792	−0.277557
$64$	−255.901	−0.499808
$65$	0	0
$66$	−194.834	−0.363369
$67$	−133.352	−0.243158	−0.121579	−	0.992582i	$-0.538796\pi$
$67$	−133.352	−0.243158	−0.121579	+	0.992582i	$0.538796\pi$
$68$	308.470	0.550109
$69$	−864.023	−1.50748
$70$	−2220.10	−3.79075
$71$	142.258	0.237788	0.118894	−	0.992907i	$-0.462065\pi$
$71$	142.258	0.237788	0.118894	+	0.992907i	$0.462065\pi$
$72$	33.5316	0.0548852
$73$	−394.273	−0.632139	−0.316070	−	0.948736i	$-0.602363\pi$
$73$	−394.273	−0.632139	−0.316070	+	0.948736i	$0.602363\pi$
$74$	−972.045	−1.52700
$75$	−1409.92	−2.17071
$76$	−33.1653	−0.0500568
$77$	314.946	0.466122
$78$	0	0
$79$	−1151.89	−1.64047	−0.820236	−	0.572025i	$-0.806158\pi$
$79$	−1151.89	−1.64047	−0.820236	+	0.572025i	$0.806158\pi$
$80$	1552.08	2.16910
$81$	−574.619	−0.788228
$82$	−1354.18	−1.82371
$83$	−519.150	−0.686556	−0.343278	−	0.939234i	$-0.611537\pi$
$83$	−519.150	−0.686556	−0.343278	+	0.939234i	$0.611537\pi$
$84$	−830.363	−1.07857
$85$	−1031.50	−1.31625
$86$	985.836	1.23611
$87$	944.856	1.16436
$88$	−76.0899	−0.0921729
$89$	−248.303	−0.295731	−0.147865	−	0.989008i	$-0.547240\pi$
$89$	−248.303	−0.295731	−0.147865	+	0.989008i	$0.547240\pi$
$90$	375.880	0.440235
$91$	0	0
$92$	1131.17	1.28187
$93$	−91.3392	−0.101843
$94$	1696.44	1.86143
$95$	110.902	0.119772
$96$	1073.73	1.14154
$97$	−848.603	−0.888274	−0.444137	−	0.895959i	$-0.646490\pi$
$97$	−848.603	−0.888274	−0.444137	+	0.895959i	$0.646490\pi$
$98$	1794.16	1.84936
$99$	−53.3227	−0.0541327
$100$	1845.85	1.84585
$101$	−158.629	−0.156279	−0.0781395	−	0.996942i	$-0.524898\pi$
$101$	−158.629	−0.156279	−0.0781395	+	0.996942i	$0.524898\pi$
$102$	−886.688	−0.860737
$103$	−439.878	−0.420801	−0.210400	−	0.977615i	$-0.567477\pi$
$103$	−439.878	−0.420801	−0.210400	+	0.977615i	$0.567477\pi$
$104$	0	0
$105$	2776.67	2.58071
$106$	2729.71	2.50125
$107$	−819.025	−0.739982	−0.369991	−	0.929035i	$-0.620639\pi$
$107$	−819.025	−0.739982	−0.369991	+	0.929035i	$0.620639\pi$
$108$	923.634	0.822933
$109$	−1753.26	−1.54066	−0.770329	−	0.637647i	$-0.779908\pi$
$109$	−1753.26	−1.54066	−0.770329	+	0.637647i	$0.779908\pi$
$110$	−852.947	−0.739321
$111$	1215.73	1.03957
$112$	−2156.70	−1.81955
$113$	−512.481	−0.426639	−0.213319	−	0.976983i	$-0.568427\pi$
$113$	−512.481	−0.426639	−0.213319	+	0.976983i	$0.568427\pi$
$114$	95.3328	0.0783222
$115$	−3782.54	−3.06716
$116$	−1236.99	−0.990104
$117$	0	0
$118$	−1436.74	−1.12087
$119$	1433.32	1.10414
$120$	−670.833	−0.510320
$121$	121.000	0.0909091
$122$	259.335	0.192452
$123$	1693.66	1.24157
$124$	119.580	0.0866017
$125$	−3596.75	−2.57363
$126$	−522.304	−0.369290
$127$	−1763.56	−1.23221	−0.616107	−	0.787663i	$-0.711291\pi$
$127$	−1763.56	−1.23221	−0.616107	+	0.787663i	$0.711291\pi$
$128$	862.039	0.595267
$129$	−1232.98	−0.841532
$130$	0	0
$131$	1291.41	0.861302	0.430651	−	0.902518i	$-0.358284\pi$
$131$	1291.41	0.861302	0.430651	+	0.902518i	$0.358284\pi$
$132$	−319.019	−0.210357
$133$	−154.104	−0.100470
$134$	−501.834	−0.323522
$135$	−3088.56	−1.96904
$136$	−346.285	−0.218336
$137$	682.436	0.425580	0.212790	−	0.977098i	$-0.431745\pi$
$137$	682.436	0.425580	0.212790	+	0.977098i	$0.431745\pi$
$138$	−3251.52	−2.00571
$139$	288.421	0.175997	0.0879983	−	0.996121i	$-0.471953\pi$
$139$	288.421	0.175997	0.0879983	+	0.996121i	$0.471953\pi$
$140$	−3635.18	−2.19449
$141$	−2121.73	−1.26725
$142$	535.349	0.316377
$143$	0	0
$144$	365.146	0.211311
$145$	4136.41	2.36903
$146$	−1483.74	−0.841063
$147$	−2243.94	−1.25903
$148$	−1591.62	−0.883988
$149$	224.765	0.123580	0.0617902	−	0.998089i	$-0.480319\pi$
$149$	224.765	0.123580	0.0617902	+	0.998089i	$0.480319\pi$
$150$	−5305.83	−2.88813
$151$	1527.86	0.823411	0.411706	−	0.911317i	$-0.364933\pi$
$151$	1527.86	0.823411	0.411706	+	0.911317i	$0.364933\pi$
$152$	37.2310	0.0198673
$153$	−242.671	−0.128228
$154$	1185.21	0.620177
$155$	−399.866	−0.207213
$156$	0	0
$157$	−1210.55	−0.615366	−0.307683	−	0.951489i	$-0.599554\pi$
$157$	−1210.55	−0.615366	−0.307683	+	0.951489i	$0.599554\pi$
$158$	−4334.81	−2.18265
$159$	−3414.03	−1.70283
$160$	4700.62	2.32260
$161$	5256.03	2.57288
$162$	−2162.42	−1.04874
$163$	−2302.18	−1.10626	−0.553132	−	0.833094i	$-0.686567\pi$
$163$	−2302.18	−1.10626	−0.553132	+	0.833094i	$0.686567\pi$
$164$	−2217.32	−1.05576
$165$	1066.77	0.503323
$166$	−1953.68	−0.913464
$167$	−1051.62	−0.487287	−0.243643	−	0.969865i	$-0.578343\pi$
$167$	−1051.62	−0.487287	−0.243643	+	0.969865i	$0.578343\pi$
$168$	932.157	0.428080
$169$	0	0
$170$	−3881.76	−1.75128
$171$	26.0910	0.0116680
$172$	1614.20	0.715591
$173$	−2545.99	−1.11889	−0.559445	−	0.828867i	$-0.688986\pi$
$173$	−2545.99	−1.11889	−0.559445	+	0.828867i	$0.688986\pi$
$174$	3555.71	1.54918
$175$	8576.80	3.70483
$176$	−828.589	−0.354871
$177$	1796.92	0.763080
$178$	−934.419	−0.393470
$179$	−1107.54	−0.462464	−0.231232	−	0.972899i	$-0.574276\pi$
$179$	−1107.54	−0.462464	−0.231232	+	0.972899i	$0.574276\pi$
$180$	615.462	0.254855
$181$	−3398.72	−1.39572	−0.697860	−	0.716235i	$-0.745864\pi$
$181$	−3398.72	−1.39572	−0.697860	+	0.716235i	$0.745864\pi$
$182$	0	0
$183$	−324.349	−0.131019
$184$	−1269.84	−0.508770
$185$	5322.24	2.11513
$186$	−343.730	−0.135503
$187$	550.671	0.215342
$188$	2777.74	1.07759
$189$	4291.71	1.65172
$190$	417.350	0.159356
$191$	4137.36	1.56738	0.783688	−	0.621154i	$-0.213336\pi$
$191$	4137.36	1.56738	0.783688	+	0.621154i	$0.213336\pi$
$192$	1204.44	0.452723
$193$	1041.79	0.388549	0.194274	−	0.980947i	$-0.437765\pi$
$193$	1041.79	0.388549	0.194274	+	0.980947i	$0.437765\pi$
$194$	−3193.49	−1.18185
$195$	0	0
$196$	2937.74	1.07060
$197$	456.359	0.165047	0.0825234	−	0.996589i	$-0.473702\pi$
$197$	456.359	0.165047	0.0825234	+	0.996589i	$0.473702\pi$
$198$	−200.665	−0.0720236
$199$	3146.51	1.12086	0.560428	−	0.828203i	$-0.310637\pi$
$199$	3146.51	1.12086	0.560428	+	0.828203i	$0.310637\pi$
$200$	−2072.13	−0.732608
$201$	627.641	0.220251
$202$	−596.957	−0.207929
$203$	−5747.75	−1.98726
$204$	−1451.86	−0.498286
$205$	7414.55	2.52612
$206$	−1655.36	−0.559876
$207$	−889.884	−0.298798
$208$	0	0
$209$	−59.2057	−0.0195949
$210$	10449.2	3.43364
$211$	559.375	0.182507	0.0912535	−	0.995828i	$-0.470913\pi$
$211$	559.375	0.182507	0.0912535	+	0.995828i	$0.470913\pi$
$212$	4469.60	1.44799
$213$	−669.558	−0.215387
$214$	−3082.18	−0.984548
$215$	−5397.75	−1.71220
$216$	−1036.86	−0.326618
$217$	555.635	0.173820
$218$	−6597.91	−2.04985
$219$	1855.70	0.572588
$220$	−1396.61	−0.427997
$221$	0	0
$222$	4575.07	1.38315
$223$	−4530.55	−1.36048	−0.680242	−	0.732987i	$-0.738125\pi$
$223$	−4530.55	−1.36048	−0.680242	+	0.732987i	$0.738125\pi$
$224$	−6531.74	−1.94831
$225$	−1452.12	−0.430257
$226$	−1928.58	−0.567643
$227$	−2872.86	−0.839994	−0.419997	−	0.907526i	$-0.637969\pi$
$227$	−2872.86	−0.839994	−0.419997	+	0.907526i	$0.637969\pi$
$228$	156.097	0.0453412
$229$	2252.72	0.650061	0.325030	−	0.945704i	$-0.394625\pi$
$229$	2252.72	0.650061	0.325030	+	0.945704i	$0.394625\pi$
$230$	−14234.5	−4.08086
$231$	−1482.34	−0.422211
$232$	1388.64	0.392968
$233$	−3277.35	−0.921486	−0.460743	−	0.887534i	$-0.652417\pi$
$233$	−3277.35	−0.921486	−0.460743	+	0.887534i	$0.652417\pi$
$234$	0	0
$235$	−9288.55	−2.57838
$236$	−2352.51	−0.648879
$237$	5421.51	1.48593
$238$	5393.90	1.46905
$239$	−2721.58	−0.736588	−0.368294	−	0.929709i	$-0.620058\pi$
$239$	−2721.58	−0.736588	−0.368294	+	0.929709i	$0.620058\pi$
$240$	−7305.11	−1.96476
$241$	2829.78	0.756357	0.378179	−	0.925733i	$-0.376550\pi$
$241$	2829.78	0.756357	0.378179	+	0.925733i	$0.376550\pi$
$242$	455.350	0.120955
$243$	−1342.64	−0.354445
$244$	424.633	0.111411
$245$	−9823.56	−2.56165
$246$	6373.64	1.65190
$247$	0	0
$248$	−134.240	−0.0343718
$249$	2443.45	0.621878
$250$	−13535.4	−3.42422
$251$	−1657.88	−0.416910	−0.208455	−	0.978032i	$-0.566844\pi$
$251$	−1657.88	−0.416910	−0.208455	+	0.978032i	$0.566844\pi$
$252$	−855.216	−0.213784
$253$	2019.33	0.501795
$254$	−6636.69	−1.63946
$255$	4854.89	1.19225
$256$	5291.26	1.29181
$257$	4195.11	1.01822	0.509112	−	0.860700i	$-0.329974\pi$
$257$	4195.11	1.01822	0.509112	+	0.860700i	$0.329974\pi$
$258$	−4639.98	−1.11966
$259$	−7395.53	−1.77427
$260$	0	0
$261$	973.137	0.230788
$262$	4859.85	1.14596
$263$	2463.36	0.577557	0.288779	−	0.957396i	$-0.406751\pi$
$263$	2463.36	0.577557	0.288779	+	0.957396i	$0.406751\pi$
$264$	358.128	0.0834896
$265$	−14946.0	−3.46462
$266$	−579.929	−0.133676
$267$	1168.67	0.267871
$268$	−821.700	−0.187288
$269$	1449.56	0.328555	0.164277	−	0.986414i	$-0.447471\pi$
$269$	1449.56	0.328555	0.164277	+	0.986414i	$0.447471\pi$
$270$	−11622.9	−2.61981
$271$	−2428.13	−0.544275	−0.272137	−	0.962258i	$-0.587731\pi$
$271$	−2428.13	−0.544275	−0.272137	+	0.962258i	$0.587731\pi$
$272$	−3770.91	−0.840606
$273$	0	0
$274$	2568.16	0.566235
$275$	3295.15	0.722563
$276$	−5324.01	−1.16111
$277$	3081.58	0.668426	0.334213	−	0.942497i	$-0.391529\pi$
$277$	3081.58	0.668426	0.334213	+	0.942497i	$0.391529\pi$
$278$	1085.39	0.234164
$279$	−94.0731	−0.0201864
$280$	4080.81	0.870983
$281$	7005.97	1.48733	0.743667	−	0.668550i	$-0.233085\pi$
$281$	7005.97	1.48733	0.743667	+	0.668550i	$0.233085\pi$
$282$	−7984.56	−1.68608
$283$	2397.37	0.503564	0.251782	−	0.967784i	$-0.418983\pi$
$283$	2397.37	0.503564	0.251782	+	0.967784i	$0.418983\pi$
$284$	876.577	0.183152
$285$	−521.976	−0.108488
$286$	0	0
$287$	−10302.9	−2.11903
$288$	1105.87	0.226265
$289$	−2406.90	−0.489904
$290$	15566.2	3.15201
$291$	3994.07	0.804593
$292$	−2429.46	−0.486896
$293$	−5825.38	−1.16151	−0.580755	−	0.814078i	$-0.697243\pi$
$293$	−5825.38	−1.16151	−0.580755	+	0.814078i	$0.697243\pi$
$294$	−8444.46	−1.67514
$295$	7866.61	1.55258
$296$	1786.74	0.350851
$297$	1648.84	0.322140
$298$	845.842	0.164424
$299$	0	0
$300$	−8687.73	−1.67195
$301$	7500.46	1.43628
$302$	5749.67	1.09555
$303$	746.610	0.141556
$304$	405.431	0.0764904
$305$	−1419.94	−0.266575
$306$	−913.228	−0.170607
$307$	−9578.26	−1.78065	−0.890326	−	0.455323i	$-0.849524\pi$
$307$	−9578.26	−1.78065	−0.890326	+	0.455323i	$0.849524\pi$
$308$	1940.66	0.359024
$309$	2070.35	0.381158
$310$	−1504.79	−0.275697
$311$	−918.897	−0.167543	−0.0837715	−	0.996485i	$-0.526697\pi$
$311$	−918.897	−0.167543	−0.0837715	+	0.996485i	$0.526697\pi$
$312$	0	0
$313$	−4384.64	−0.791803	−0.395902	−	0.918293i	$-0.629568\pi$
$313$	−4384.64	−0.791803	−0.395902	+	0.918293i	$0.629568\pi$
$314$	−4555.58	−0.818746
$315$	2859.77	0.511524
$316$	−7097.78	−1.26355
$317$	9818.48	1.73962	0.869812	−	0.493384i	$-0.164240\pi$
$317$	9818.48	1.73962	0.869812	+	0.493384i	$0.164240\pi$
$318$	−12847.8	−2.26562
$319$	−2208.24	−0.387580
$320$	5272.80	0.921121
$321$	3854.86	0.670271
$322$	19779.6	3.42322
$323$	−269.445	−0.0464158
$324$	−3540.73	−0.607121
$325$	0	0
$326$	−8663.64	−1.47189
$327$	8251.96	1.39552
$328$	2489.15	0.419025
$329$	12906.9	2.16286
$330$	4014.52	0.669672
$331$	670.303	0.111309	0.0556544	−	0.998450i	$-0.482275\pi$
$331$	670.303	0.111309	0.0556544	+	0.998450i	$0.482275\pi$
$332$	−3198.94	−0.528809
$333$	1252.12	0.206053
$334$	−3957.49	−0.648336
$335$	2747.70	0.448128
$336$	10150.8	1.64813
$337$	8392.85	1.35664	0.678320	−	0.734767i	$-0.262708\pi$
$337$	8392.85	1.35664	0.678320	+	0.734767i	$0.262708\pi$
$338$	0	0
$339$	2412.07	0.386447
$340$	−6355.96	−1.01383
$341$	213.471	0.0339006
$342$	98.1862	0.0155243
$343$	3829.75	0.602878
$344$	−1812.09	−0.284015
$345$	17803.0	2.77821
$346$	−9581.14	−1.48869
$347$	−8123.92	−1.25682	−0.628408	−	0.777884i	$-0.716293\pi$
$347$	−8123.92	−1.25682	−0.628408	+	0.777884i	$0.716293\pi$
$348$	5822.09	0.896830
$349$	−6458.56	−0.990598	−0.495299	−	0.868723i	$-0.664941\pi$
$349$	−6458.56	−0.990598	−0.495299	+	0.868723i	$0.664941\pi$
$350$	32276.5	4.92928
$351$	0	0
$352$	−2509.45	−0.379983
$353$	−9218.68	−1.38997	−0.694987	−	0.719022i	$-0.744590\pi$
$353$	−9218.68	−1.38997	−0.694987	+	0.719022i	$0.744590\pi$
$354$	6762.24	1.01528
$355$	−2931.20	−0.438231
$356$	−1530.01	−0.227782
$357$	−6746.12	−1.00012
$358$	−4167.91	−0.615309
$359$	−4605.15	−0.677022	−0.338511	−	0.940962i	$-0.609923\pi$
$359$	−4605.15	−0.677022	−0.338511	+	0.940962i	$0.609923\pi$
$360$	−690.912	−0.101151
$361$	−6830.03	−0.995776
$362$	−12790.2	−1.85701
$363$	−569.504	−0.0823449
$364$	0	0
$365$	8123.93	1.16500
$366$	−1220.60	−0.174321
$367$	−5253.39	−0.747206	−0.373603	−	0.927589i	$-0.621878\pi$
$367$	−5253.39	−0.747206	−0.373603	+	0.927589i	$0.621878\pi$
$368$	−13828.0	−1.95879
$369$	1744.36	0.246091
$370$	20028.8	2.81419
$371$	20768.2	2.90629
$372$	−562.821	−0.0784433
$373$	5930.74	0.823277	0.411638	−	0.911347i	$-0.364957\pi$
$373$	5930.74	0.823277	0.411638	+	0.911347i	$0.364957\pi$
$374$	2072.30	0.286513
$375$	16928.6	2.33118
$376$	−3118.27	−0.427693
$377$	0	0
$378$	16150.7	2.19762
$379$	−9107.92	−1.23441	−0.617207	−	0.786801i	$-0.711736\pi$
$379$	−9107.92	−1.23441	−0.617207	+	0.786801i	$0.711736\pi$
$380$	683.365	0.0922523
$381$	8300.47	1.11613
$382$	15569.8	2.08540
$383$	258.180	0.0344448	0.0172224	−	0.999852i	$-0.494518\pi$
$383$	258.180	0.0344448	0.0172224	+	0.999852i	$0.494518\pi$
$384$	−4057.31	−0.539189
$385$	−6489.41	−0.859041
$386$	3920.50	0.516965
$387$	−1269.88	−0.166800
$388$	−5228.99	−0.684180
$389$	9198.82	1.19897	0.599484	−	0.800387i	$-0.295372\pi$
$389$	9198.82	1.19897	0.599484	+	0.800387i	$0.295372\pi$
$390$	0	0
$391$	9189.96	1.18863
$392$	−3297.88	−0.424918
$393$	−6078.18	−0.780162
$394$	1717.38	0.219595
$395$	23734.4	3.02331
$396$	−328.568	−0.0416949
$397$	2022.92	0.255737	0.127869	−	0.991791i	$-0.459186\pi$
$397$	2022.92	0.255737	0.127869	+	0.991791i	$0.459186\pi$
$398$	11841.0	1.49130
$399$	725.313	0.0910052
$400$	−22564.6	−2.82058
$401$	10837.6	1.34964	0.674819	−	0.737984i	$-0.264222\pi$
$401$	10837.6	1.34964	0.674819	+	0.737984i	$0.264222\pi$
$402$	2361.95	0.293044
$403$	0	0
$404$	−977.452	−0.120371
$405$	11839.9	1.45267
$406$	−21630.1	−2.64405
$407$	−2841.31	−0.346041
$408$	1629.84	0.197767
$409$	2783.88	0.336562	0.168281	−	0.985739i	$-0.446178\pi$
$409$	2783.88	0.336562	0.168281	+	0.985739i	$0.446178\pi$
$410$	27902.6	3.36101
$411$	−3211.98	−0.385488
$412$	−2710.47	−0.324115
$413$	−10931.1	−1.30238
$414$	−3348.84	−0.397552
$415$	10697.0	1.26529
$416$	0	0
$417$	−1357.49	−0.159417
$418$	−222.804	−0.0260711
$419$	2581.90	0.301035	0.150518	−	0.988607i	$-0.451906\pi$
$419$	2581.90	0.301035	0.150518	+	0.988607i	$0.451906\pi$
$420$	17109.5	1.98775
$421$	−269.615	−0.0312119	−0.0156060	−	0.999878i	$-0.504968\pi$
$421$	−269.615	−0.0312119	−0.0156060	+	0.999878i	$0.504968\pi$
$422$	2105.06	0.242826
$423$	−2185.24	−0.251182
$424$	−5017.53	−0.574700
$425$	14996.2	1.71158
$426$	−2519.70	−0.286572
$427$	1973.08	0.223616
$428$	−5046.73	−0.569960
$429$	0	0
$430$	−20313.0	−2.27809
$431$	3746.07	0.418659	0.209329	−	0.977845i	$-0.432872\pi$
$431$	3746.07	0.418659	0.209329	+	0.977845i	$0.432872\pi$
$432$	−11291.0	−1.25750
$433$	−10180.4	−1.12988	−0.564940	−	0.825132i	$-0.691101\pi$
$433$	−10180.4	−1.12988	−0.564940	+	0.825132i	$0.691101\pi$
$434$	2090.98	0.231268
$435$	−19468.6	−2.14586
$436$	−10803.4	−1.18667
$437$	−988.064	−0.108159
$438$	6983.43	0.761829
$439$	−5215.63	−0.567035	−0.283517	−	0.958967i	$-0.591501\pi$
$439$	−5215.63	−0.567035	−0.283517	+	0.958967i	$0.591501\pi$
$440$	1567.82	0.169870
$441$	−2311.10	−0.249552
$442$	0	0
$443$	−13641.5	−1.46304	−0.731521	−	0.681819i	$-0.761189\pi$
$443$	−13641.5	−1.46304	−0.731521	+	0.681819i	$0.761189\pi$
$444$	7491.18	0.800711
$445$	5116.23	0.545017
$446$	−17049.5	−1.81013
$447$	−1057.89	−0.111938
$448$	−7326.83	−0.772679
$449$	−5396.27	−0.567184	−0.283592	−	0.958945i	$-0.591526\pi$
$449$	−5396.27	−0.567184	−0.283592	+	0.958945i	$0.591526\pi$
$450$	−5464.64	−0.572457
$451$	−3958.30	−0.413280
$452$	−3157.85	−0.328612
$453$	−7191.07	−0.745841
$454$	−10811.2	−1.11761
$455$	0	0
$456$	−175.233	−0.0179957
$457$	−6361.44	−0.651150	−0.325575	−	0.945516i	$-0.605558\pi$
$457$	−6361.44	−0.651150	−0.325575	+	0.945516i	$0.605558\pi$
$458$	8477.50	0.864907
$459$	7503.88	0.763075
$460$	−23307.5	−2.36243
$461$	10064.2	1.01678	0.508392	−	0.861126i	$-0.330240\pi$
$461$	10064.2	1.01678	0.508392	+	0.861126i	$0.330240\pi$
$462$	−5578.38	−0.561752
$463$	11767.5	1.18117	0.590584	−	0.806976i	$-0.298897\pi$
$463$	11767.5	1.18117	0.590584	+	0.806976i	$0.298897\pi$
$464$	15121.7	1.51295
$465$	1882.03	0.187692
$466$	−12333.4	−1.22604
$467$	−1410.44	−0.139759	−0.0698794	−	0.997555i	$-0.522261\pi$
$467$	−1410.44	−0.139759	−0.0698794	+	0.997555i	$0.522261\pi$
$468$	0	0
$469$	−3818.07	−0.375910
$470$	−34954.9	−3.43053
$471$	5697.63	0.557395
$472$	2640.91	0.257537
$473$	2881.62	0.280121
$474$	20402.4	1.97703
$475$	−1612.33	−0.155744
$476$	8831.94	0.850444
$477$	−3516.21	−0.337519
$478$	−10241.9	−0.980031
$479$	−8503.84	−0.811170	−0.405585	−	0.914057i	$-0.632932\pi$
$479$	−8503.84	−0.811170	−0.405585	+	0.914057i	$0.632932\pi$
$480$	−22124.1	−2.10380
$481$	0	0
$482$	10649.1	1.00633
$483$	−24738.2	−2.33049
$484$	745.587	0.0700214
$485$	17485.3	1.63705
$486$	−5052.65	−0.471590
$487$	−7097.68	−0.660424	−0.330212	−	0.943907i	$-0.607120\pi$
$487$	−7097.68	−0.660424	−0.330212	+	0.943907i	$0.607120\pi$
$488$	−476.689	−0.0442187
$489$	10835.6	1.00205
$490$	−36968.3	−3.40828
$491$	−7371.16	−0.677507	−0.338753	−	0.940875i	$-0.610005\pi$
$491$	−7371.16	−0.677507	−0.338753	+	0.940875i	$0.610005\pi$
$492$	10436.2	0.956297
$493$	−10049.7	−0.918086
$494$	0	0
$495$	1098.70	0.0997639
$496$	−1461.82	−0.132334
$497$	4073.06	0.367609
$498$	9195.27	0.827410
$499$	5810.17	0.521240	0.260620	−	0.965441i	$-0.416073\pi$
$499$	5810.17	0.521240	0.260620	+	0.965441i	$0.416073\pi$
$500$	−22162.8	−1.98230
$501$	4949.61	0.441381
$502$	−6238.98	−0.554700
$503$	17754.7	1.57384	0.786921	−	0.617054i	$-0.211674\pi$
$503$	17754.7	1.57384	0.786921	+	0.617054i	$0.211674\pi$
$504$	960.058	0.0848499
$505$	3268.52	0.288014
$506$	7599.19	0.667639
$507$	0	0
$508$	−10866.9	−0.949094
$509$	18959.9	1.65105	0.825523	−	0.564368i	$-0.190880\pi$
$509$	18959.9	1.65105	0.825523	+	0.564368i	$0.190880\pi$
$510$	18270.1	1.58630
$511$	−11288.6	−0.977258
$512$	13015.9	1.12349
$513$	−806.784	−0.0694355
$514$	15787.1	1.35475
$515$	9063.61	0.775515
$516$	−7597.46	−0.648178
$517$	4958.75	0.421829
$518$	−27831.1	−2.36067
$519$	11983.1	1.01348
$520$	0	0
$521$	−9488.06	−0.797849	−0.398925	−	0.916984i	$-0.630617\pi$
$521$	−9488.06	−0.797849	−0.398925	+	0.916984i	$0.630617\pi$
$522$	3662.14	0.307064
$523$	11375.1	0.951050	0.475525	−	0.879702i	$-0.342258\pi$
$523$	11375.1	0.951050	0.475525	+	0.879702i	$0.342258\pi$
$524$	7957.48	0.663405
$525$	−40367.9	−3.35581
$526$	9270.20	0.768441
$527$	971.505	0.0803025
$528$	3899.87	0.321440
$529$	21532.9	1.76978
$530$	−56245.2	−4.60969
$531$	1850.71	0.151250
$532$	−949.571	−0.0773855
$533$	0	0
$534$	4397.98	0.356403
$535$	16875.9	1.36375
$536$	922.432	0.0743340
$537$	5212.77	0.418897
$538$	5455.02	0.437142
$539$	5244.36	0.419092
$540$	−19031.3	−1.51663
$541$	−3435.71	−0.273036	−0.136518	−	0.990638i	$-0.543591\pi$
$541$	−3435.71	−0.273036	−0.136518	+	0.990638i	$0.543591\pi$
$542$	−9137.61	−0.724159
$543$	15996.6	1.26423
$544$	−11420.5	−0.900092
$545$	36125.6	2.83936
$546$	0	0
$547$	3002.79	0.234717	0.117358	−	0.993090i	$-0.462557\pi$
$547$	3002.79	0.234717	0.117358	+	0.993090i	$0.462557\pi$
$548$	4205.09	0.327796
$549$	−334.057	−0.0259694
$550$	12400.4	0.961371
$551$	1080.50	0.0835407
$552$	5976.68	0.460841
$553$	−32980.2	−2.53609
$554$	11596.7	0.889343
$555$	−25049.9	−1.91587
$556$	1777.21	0.135559
$557$	−18394.6	−1.39929	−0.699643	−	0.714493i	$-0.746658\pi$
$557$	−18394.6	−1.39929	−0.699643	+	0.714493i	$0.746658\pi$
$558$	−354.018	−0.0268581
$559$	0	0
$560$	44438.4	3.35333
$561$	−2591.81	−0.195056
$562$	26365.0	1.97890
$563$	−17413.3	−1.30353	−0.651763	−	0.758423i	$-0.725970\pi$
$563$	−17413.3	−1.30353	−0.651763	+	0.758423i	$0.725970\pi$
$564$	−13073.8	−0.976079
$565$	10559.6	0.786274
$566$	9021.84	0.669993
$567$	−16452.2	−1.21856
$568$	−984.037	−0.0726924
$569$	10346.9	0.762329	0.381164	−	0.924507i	$-0.375523\pi$
$569$	10346.9	0.762329	0.381164	+	0.924507i	$0.375523\pi$
$570$	−1964.32	−0.144344
$571$	−4005.00	−0.293527	−0.146764	−	0.989172i	$-0.546886\pi$
$571$	−4005.00	−0.293527	−0.146764	+	0.989172i	$0.546886\pi$
$572$	0	0
$573$	−19473.1	−1.41972
$574$	−38772.2	−2.81937
$575$	54991.6	3.98836
$576$	1240.49	0.0897343
$577$	−6772.05	−0.488603	−0.244302	−	0.969699i	$-0.578559\pi$
$577$	−6772.05	−0.488603	−0.244302	+	0.969699i	$0.578559\pi$
$578$	−9057.71	−0.651818
$579$	−4903.35	−0.351945
$580$	25488.1	1.82471
$581$	−14864.0	−1.06138
$582$	15030.6	1.07051
$583$	7979.00	0.566821
$584$	2727.29	0.193247
$585$	0	0
$586$	−21922.2	−1.54539
$587$	2148.77	0.151089	0.0755445	−	0.997142i	$-0.475930\pi$
$587$	2148.77	0.151089	0.0755445	+	0.997142i	$0.475930\pi$
$588$	−13826.9	−0.969747
$589$	−104.452	−0.00730708
$590$	29603.8	2.06571
$591$	−2147.92	−0.149498
$592$	19456.8	1.35080
$593$	1188.43	0.0822985	0.0411493	−	0.999153i	$-0.486898\pi$
$593$	1188.43	0.0822985	0.0411493	+	0.999153i	$0.486898\pi$
$594$	6204.97	0.428608
$595$	−29533.3	−2.03487
$596$	1384.98	0.0951859
$597$	−14809.5	−1.01526
$598$	0	0
$599$	−23587.7	−1.60896	−0.804479	−	0.593981i	$-0.797555\pi$
$599$	−23587.7	−1.60896	−0.804479	+	0.593981i	$0.797555\pi$
$600$	9752.76	0.663592
$601$	−19790.4	−1.34321	−0.671604	−	0.740911i	$-0.734394\pi$
$601$	−19790.4	−1.34321	−0.671604	+	0.740911i	$0.734394\pi$
$602$	28225.9	1.91097
$603$	646.427	0.0436559
$604$	9414.46	0.634220
$605$	−2493.18	−0.167541
$606$	2809.66	0.188341
$607$	4775.53	0.319329	0.159665	−	0.987171i	$-0.448959\pi$
$607$	4775.53	0.319329	0.159665	+	0.987171i	$0.448959\pi$
$608$	1227.88	0.0819032
$609$	27052.6	1.80004
$610$	−5343.55	−0.354679
$611$	0	0
$612$	−1495.31	−0.0987654
$613$	1778.03	0.117152	0.0585758	−	0.998283i	$-0.481344\pi$
$613$	1778.03	0.117152	0.0585758	+	0.998283i	$0.481344\pi$
$614$	−36045.2	−2.36916
$615$	−34897.6	−2.28814
$616$	−2178.57	−0.142495
$617$	26795.0	1.74834	0.874170	−	0.485621i	$-0.161406\pi$
$617$	26795.0	1.74834	0.874170	+	0.485621i	$0.161406\pi$
$618$	7791.19	0.507132
$619$	−24263.3	−1.57548	−0.787742	−	0.616005i	$-0.788750\pi$
$619$	−24263.3	−1.57548	−0.787742	+	0.616005i	$0.788750\pi$
$620$	−2463.93	−0.159603
$621$	27517.0	1.77813
$622$	−3458.02	−0.222916
$623$	−7109.26	−0.457186
$624$	0	0
$625$	36665.6	2.34660
$626$	−16500.4	−1.05350
$627$	278.660	0.0177490
$628$	−7459.27	−0.473977
$629$	−12930.8	−0.819689
$630$	10762.0	0.680583
$631$	−12952.8	−0.817181	−0.408591	−	0.912718i	$-0.633980\pi$
$631$	−12952.8	−0.817181	−0.408591	+	0.912718i	$0.633980\pi$
$632$	7967.90	0.501497
$633$	−2632.78	−0.165314
$634$	36949.2	2.31457
$635$	36337.9	2.27091
$636$	−21036.8	−1.31158
$637$	0	0
$638$	−8310.13	−0.515676
$639$	−689.599	−0.0426919
$640$	−17762.2	−1.09705
$641$	6799.14	0.418955	0.209477	−	0.977813i	$-0.432824\pi$
$641$	6799.14	0.418955	0.209477	+	0.977813i	$0.432824\pi$
$642$	14506.7	0.891797
$643$	−25190.6	−1.54498	−0.772490	−	0.635027i	$-0.780989\pi$
$643$	−25190.6	−1.54498	−0.772490	+	0.635027i	$0.780989\pi$
$644$	32387.0	1.98172
$645$	25405.3	1.55090
$646$	−1013.98	−0.0617564
$647$	1749.28	0.106293	0.0531464	−	0.998587i	$-0.483075\pi$
$647$	1749.28	0.106293	0.0531464	+	0.998587i	$0.483075\pi$
$648$	3974.79	0.240964
$649$	−4199.63	−0.254006
$650$	0	0
$651$	−2615.17	−0.157445
$652$	−14185.8	−0.852083
$653$	−2872.69	−0.172154	−0.0860772	−	0.996288i	$-0.527433\pi$
$653$	−2872.69	−0.172154	−0.0860772	+	0.996288i	$0.527433\pi$
$654$	31054.0	1.85674
$655$	−26609.2	−1.58734
$656$	27105.8	1.61327
$657$	1911.25	0.113493
$658$	48571.7	2.87769
$659$	27313.4	1.61453	0.807267	−	0.590187i	$-0.200946\pi$
$659$	27313.4	1.61453	0.807267	+	0.590187i	$0.200946\pi$
$660$	6573.34	0.387677
$661$	−6827.99	−0.401782	−0.200891	−	0.979614i	$-0.564384\pi$
$661$	−6827.99	−0.401782	−0.200891	+	0.979614i	$0.564384\pi$
$662$	2522.50	0.148097
$663$	0	0
$664$	3591.10	0.209882
$665$	3175.29	0.185161
$666$	4712.01	0.274154
$667$	−36852.6	−2.13934
$668$	−6479.96	−0.375325
$669$	21323.7	1.23232
$670$	10340.2	0.596234
$671$	758.043	0.0436124
$672$	30742.6	1.76476
$673$	20894.3	1.19676	0.598379	−	0.801213i	$-0.295812\pi$
$673$	20894.3	1.19676	0.598379	+	0.801213i	$0.295812\pi$
$674$	31584.2	1.80501
$675$	44902.3	2.56043
$676$	0	0
$677$	−23016.4	−1.30664	−0.653318	−	0.757084i	$-0.726624\pi$
$677$	−23016.4	−1.30664	−0.653318	+	0.757084i	$0.726624\pi$
$678$	9077.15	0.514168
$679$	−24296.7	−1.37323
$680$	7135.14	0.402383
$681$	13521.5	0.760861
$682$	803.339	0.0451048
$683$	−19368.6	−1.08509	−0.542546	−	0.840026i	$-0.682540\pi$
$683$	−19368.6	−1.08509	−0.542546	+	0.840026i	$0.682540\pi$
$684$	160.769	0.00898709
$685$	−14061.5	−0.784323
$686$	14412.2	0.802130
$687$	−10602.7	−0.588821
$688$	−19732.9	−1.09347
$689$	0	0
$690$	66996.9	3.69642
$691$	6141.58	0.338114	0.169057	−	0.985606i	$-0.445928\pi$
$691$	6141.58	0.338114	0.169057	+	0.985606i	$0.445928\pi$
$692$	−15688.1	−0.861808
$693$	−1526.71	−0.0836866
$694$	−30572.2	−1.67219
$695$	−5942.86	−0.324353
$696$	−6535.82	−0.355948
$697$	−18014.2	−0.978963
$698$	−24305.0	−1.31799
$699$	15425.3	0.834676
$700$	52849.2	2.85359
$701$	8753.79	0.471649	0.235825	−	0.971796i	$-0.424221\pi$
$701$	8753.79	0.471649	0.235825	+	0.971796i	$0.424221\pi$
$702$	0	0
$703$	1390.26	0.0745871
$704$	−2814.92	−0.150698
$705$	43717.9	2.33548
$706$	−34692.0	−1.84936
$707$	−4541.78	−0.241600
$708$	11072.4	0.587751
$709$	−11557.2	−0.612188	−0.306094	−	0.952001i	$-0.599022\pi$
$709$	−11557.2	−0.612188	−0.306094	+	0.952001i	$0.599022\pi$
$710$	−11030.8	−0.583067
$711$	5583.79	0.294527
$712$	1717.57	0.0904057
$713$	3562.54	0.187122
$714$	−25387.2	−1.33066
$715$	0	0
$716$	−6824.50	−0.356206
$717$	12809.5	0.667197
$718$	−17330.2	−0.900779
$719$	−5045.15	−0.261686	−0.130843	−	0.991403i	$-0.541768\pi$
$719$	−5045.15	−0.261686	−0.130843	+	0.991403i	$0.541768\pi$
$720$	−7523.76	−0.389436
$721$	−12594.3	−0.650538
$722$	−25703.0	−1.32488
$723$	−13318.8	−0.685104
$724$	−20942.5	−1.07503
$725$	−60136.3	−3.08056
$726$	−2143.17	−0.109560
$727$	25829.3	1.31768	0.658841	−	0.752282i	$-0.271047\pi$
$727$	25829.3	1.31768	0.658841	+	0.752282i	$0.271047\pi$
$728$	0	0
$729$	21834.0	1.10928
$730$	30572.2	1.55004
$731$	13114.3	0.663541
$732$	−1998.60	−0.100916
$733$	−9573.49	−0.482408	−0.241204	−	0.970474i	$-0.577542\pi$
$733$	−9573.49	−0.482408	−0.241204	+	0.970474i	$0.577542\pi$
$734$	−19769.7	−0.994159
$735$	46236.0	2.32033
$736$	−41879.3	−2.09741
$737$	−1466.87	−0.0733148
$738$	6564.41	0.327425
$739$	5965.38	0.296942	0.148471	−	0.988917i	$-0.452565\pi$
$739$	5965.38	0.296942	0.148471	+	0.988917i	$0.452565\pi$
$740$	32795.0	1.62915
$741$	0	0
$742$	78155.5	3.86682
$743$	−9637.00	−0.475838	−0.237919	−	0.971285i	$-0.576465\pi$
$743$	−9637.00	−0.475838	−0.237919	+	0.971285i	$0.576465\pi$
$744$	631.817	0.0311338
$745$	−4631.25	−0.227753
$746$	22318.7	1.09537
$747$	2516.59	0.123263
$748$	3393.17	0.165864
$749$	−23449.9	−1.14398
$750$	63706.3	3.10163
$751$	−11586.3	−0.562968	−0.281484	−	0.959566i	$-0.590827\pi$
$751$	−11586.3	−0.562968	−0.281484	+	0.959566i	$0.590827\pi$
$752$	−33956.7	−1.64664
$753$	7803.05	0.377635
$754$	0	0
$755$	−31481.2	−1.51751
$756$	26445.0	1.27222
$757$	−14966.5	−0.718584	−0.359292	−	0.933225i	$-0.616982\pi$
$757$	−14966.5	−0.718584	−0.359292	+	0.933225i	$0.616982\pi$
$758$	−34275.2	−1.64239
$759$	−9504.25	−0.454522
$760$	−767.139	−0.0366146
$761$	−29341.7	−1.39768	−0.698841	−	0.715277i	$-0.746300\pi$
$761$	−29341.7	−1.39768	−0.698841	+	0.715277i	$0.746300\pi$
$762$	31236.5	1.48501
$763$	−50198.3	−2.38179
$764$	25493.9	1.20725
$765$	5000.20	0.236317
$766$	971.588	0.0458289
$767$	0	0
$768$	−24904.1	−1.17011
$769$	7314.13	0.342983	0.171492	−	0.985186i	$-0.445141\pi$
$769$	7314.13	0.342983	0.171492	+	0.985186i	$0.445141\pi$
$770$	−24421.1	−1.14296
$771$	−19744.9	−0.922301
$772$	6419.40	0.299274
$773$	33505.7	1.55901	0.779505	−	0.626395i	$-0.215470\pi$
$773$	33505.7	1.55901	0.779505	+	0.626395i	$0.215470\pi$
$774$	−4778.86	−0.221928
$775$	5813.37	0.269448
$776$	5870.01	0.271548
$777$	34808.1	1.60712
$778$	34617.2	1.59523
$779$	1936.81	0.0890801
$780$	0	0
$781$	1564.84	0.0716957
$782$	34583.9	1.58148
$783$	−30091.3	−1.37341
$784$	−35912.6	−1.63596
$785$	24943.2	1.13409
$786$	−22873.6	−1.03801
$787$	37790.7	1.71168	0.855840	−	0.517240i	$-0.173041\pi$
$787$	37790.7	1.71168	0.855840	+	0.517240i	$0.173041\pi$
$788$	2812.03	0.127125
$789$	−11594.2	−0.523148
$790$	89318.0	4.02252
$791$	−14673.1	−0.659563
$792$	368.847	0.0165485
$793$	0	0
$794$	7612.72	0.340259
$795$	70345.4	3.13823
$796$	19388.4	0.863322
$797$	−37688.3	−1.67502	−0.837508	−	0.546425i	$-0.815988\pi$
$797$	−37688.3	−1.67502	−0.837508	+	0.546425i	$0.815988\pi$
$798$	2729.52	0.121083
$799$	22567.2	0.999213
$800$	−68338.9	−3.02018
$801$	1203.65	0.0530948
$802$	40784.4	1.79569
$803$	−4337.00	−0.190597
$804$	3867.45	0.169645
$805$	−108300.	−4.74168
$806$	0	0
$807$	−6822.56	−0.297603
$808$	1097.28	0.0477749
$809$	21146.6	0.919006	0.459503	−	0.888176i	$-0.348028\pi$
$809$	21146.6	0.919006	0.459503	+	0.888176i	$0.348028\pi$
$810$	44556.3	1.93278
$811$	−21621.2	−0.936157	−0.468078	−	0.883687i	$-0.655054\pi$
$811$	−21621.2	−0.936157	−0.468078	+	0.883687i	$0.655054\pi$
$812$	−35416.9	−1.53065
$813$	11428.3	0.493001
$814$	−10692.5	−0.460408
$815$	47436.1	2.03879
$816$	17748.3	0.761416
$817$	−1409.99	−0.0603784
$818$	10476.4	0.447796
$819$	0	0
$820$	45687.6	1.94571
$821$	12075.3	0.513314	0.256657	−	0.966503i	$-0.417379\pi$
$821$	12075.3	0.513314	0.256657	+	0.966503i	$0.417379\pi$
$822$	−12087.4	−0.512892
$823$	24199.0	1.02494	0.512469	−	0.858706i	$-0.328731\pi$
$823$	24199.0	1.02494	0.512469	+	0.858706i	$0.328731\pi$
$824$	3042.75	0.128640
$825$	−15509.1	−0.654493
$826$	−41136.1	−1.73282
$827$	−9099.35	−0.382606	−0.191303	−	0.981531i	$-0.561271\pi$
$827$	−9099.35	−0.382606	−0.191303	+	0.981531i	$0.561271\pi$
$828$	−5483.36	−0.230145
$829$	−35389.6	−1.48267	−0.741334	−	0.671137i	$-0.765806\pi$
$829$	−35389.6	−1.48267	−0.741334	+	0.671137i	$0.765806\pi$
$830$	40255.2	1.68347
$831$	−14503.9	−0.605457
$832$	0	0
$833$	23867.1	0.992732
$834$	−5108.55	−0.212104
$835$	21668.5	0.898046
$836$	−364.818	−0.0150927
$837$	2908.93	0.120128
$838$	9716.26	0.400528
$839$	−19700.0	−0.810632	−0.405316	−	0.914177i	$-0.632838\pi$
$839$	−19700.0	−0.810632	−0.405316	+	0.914177i	$0.632838\pi$
$840$	−19206.9	−0.788931
$841$	15911.4	0.652400
$842$	−1014.62	−0.0415275
$843$	−32974.6	−1.34722
$844$	3446.80	0.140573
$845$	0	0
$846$	−8223.54	−0.334198
$847$	3464.41	0.140541
$848$	−54638.9	−2.21263
$849$	−11283.5	−0.456125
$850$	56434.1	2.27726
$851$	−47417.7	−1.91005
$852$	−4125.73	−0.165898
$853$	−33819.4	−1.35751	−0.678753	−	0.734367i	$-0.737479\pi$
$853$	−33819.4	−1.35751	−0.678753	+	0.734367i	$0.737479\pi$
$854$	7425.14	0.297521
$855$	−537.600	−0.0215035
$856$	5665.41	0.226215
$857$	−5431.01	−0.216476	−0.108238	−	0.994125i	$-0.534521\pi$
$857$	−5431.01	−0.216476	−0.108238	+	0.994125i	$0.534521\pi$
$858$	0	0
$859$	−22206.7	−0.882054	−0.441027	−	0.897494i	$-0.645386\pi$
$859$	−22206.7	−0.882054	−0.441027	+	0.897494i	$0.645386\pi$
$860$	−33260.3	−1.31880
$861$	48492.1	1.91940
$862$	14097.3	0.557026
$863$	−359.080	−0.0141636	−0.00708182	−	0.999975i	$-0.502254\pi$
$863$	−359.080	−0.0141636	−0.00708182	+	0.999975i	$0.502254\pi$
$864$	−34195.8	−1.34649
$865$	52459.7	2.06206
$866$	−38311.1	−1.50331
$867$	11328.4	0.443752
$868$	3423.75	0.133882
$869$	−12670.7	−0.494621
$870$	−73264.8	−2.85507
$871$	0	0
$872$	12127.8	0.470984
$873$	4113.62	0.159479
$874$	−3718.31	−0.143906
$875$	−102980.	−3.97871
$876$	11434.6	0.441027
$877$	6543.64	0.251953	0.125977	−	0.992033i	$-0.459794\pi$
$877$	6543.64	0.251953	0.125977	+	0.992033i	$0.459794\pi$
$878$	−19627.6	−0.754441
$879$	27418.0	1.05209
$880$	17072.9	0.654010
$881$	43684.7	1.67057	0.835287	−	0.549815i	$-0.185302\pi$
$881$	43684.7	1.67057	0.835287	+	0.549815i	$0.185302\pi$
$882$	−8697.21	−0.332030
$883$	41992.6	1.60041	0.800206	−	0.599726i	$-0.204724\pi$
$883$	41992.6	1.60041	0.800206	+	0.599726i	$0.204724\pi$
$884$	0	0
$885$	−37025.3	−1.40632
$886$	−51336.1	−1.94658
$887$	39052.7	1.47831	0.739156	−	0.673534i	$-0.235225\pi$
$887$	39052.7	1.47831	0.739156	+	0.673534i	$0.235225\pi$
$888$	−8409.53	−0.317799
$889$	−50493.4	−1.90494
$890$	19253.5	0.725146
$891$	−6320.80	−0.237660
$892$	−27916.7	−1.04789
$893$	−2426.33	−0.0909228
$894$	−3981.08	−0.148934
$895$	22820.6	0.852299
$896$	24681.4	0.920255
$897$	0	0
$898$	−20307.4	−0.754640
$899$	−3895.83	−0.144531
$900$	−8947.77	−0.331399
$901$	36312.4	1.34267
$902$	−14896.0	−0.549869
$903$	−35302.0	−1.30097
$904$	3544.97	0.130425
$905$	70030.1	2.57224
$906$	−27061.6	−0.992343
$907$	−14371.6	−0.526132	−0.263066	−	0.964778i	$-0.584734\pi$
$907$	−14371.6	−0.526132	−0.263066	+	0.964778i	$0.584734\pi$
$908$	−17702.2	−0.646993
$909$	768.957	0.0280580
$910$	0	0
$911$	−23703.3	−0.862046	−0.431023	−	0.902341i	$-0.641847\pi$
$911$	−23703.3	−0.862046	−0.431023	+	0.902341i	$0.641847\pi$
$912$	−1908.22	−0.0692845
$913$	−5710.65	−0.207004
$914$	−23939.5	−0.866356
$915$	6683.15	0.241462
$916$	13881.0	0.500700
$917$	36974.8	1.33153
$918$	28238.8	1.01527
$919$	−38644.0	−1.38710	−0.693551	−	0.720407i	$-0.743955\pi$
$919$	−38644.0	−1.38710	−0.693551	+	0.720407i	$0.743955\pi$
$920$	26164.8	0.937639
$921$	45081.5	1.61290
$922$	37873.9	1.35283
$923$	0	0
$924$	−9133.99	−0.325201
$925$	−77376.3	−2.75040
$926$	44283.7	1.57155
$927$	2132.32	0.0755496
$928$	45797.3	1.62001
$929$	−436.870	−0.0154287	−0.00771434	−	0.999970i	$-0.502456\pi$
$929$	−436.870	−0.0154287	−0.00771434	+	0.999970i	$0.502456\pi$
$930$	7082.50	0.249725
$931$	−2566.08	−0.0903329
$932$	−20194.6	−0.709760
$933$	4324.92	0.151759
$934$	−5307.81	−0.185949
$935$	−11346.5	−0.396866
$936$	0	0
$937$	8675.83	0.302484	0.151242	−	0.988497i	$-0.451673\pi$
$937$	8675.83	0.302484	0.151242	+	0.988497i	$0.451673\pi$
$938$	−14368.2	−0.500149
$939$	20636.9	0.717210
$940$	−57234.9	−1.98596
$941$	−43446.9	−1.50513	−0.752566	−	0.658517i	$-0.771184\pi$
$941$	−43446.9	−1.50513	−0.752566	+	0.658517i	$0.771184\pi$
$942$	21441.5	0.741615
$943$	−66058.7	−2.28120
$944$	28758.4	0.991533
$945$	−88429.9	−3.04405
$946$	10844.2	0.372701
$947$	55657.1	1.90983	0.954917	−	0.296872i	$-0.0959435\pi$
$947$	55657.1	1.90983	0.954917	+	0.296872i	$0.0959435\pi$
$948$	33406.7	1.14451
$949$	0	0
$950$	−6067.55	−0.207218
$951$	−46212.1	−1.57574
$952$	−9914.65	−0.337537
$953$	−14337.4	−0.487338	−0.243669	−	0.969858i	$-0.578351\pi$
$953$	−14337.4	−0.487338	−0.243669	+	0.969858i	$0.578351\pi$
$954$	−13232.3	−0.449069
$955$	−85249.6	−2.88860
$956$	−16770.1	−0.567346
$957$	10393.4	0.351067
$958$	−32001.9	−1.07926
$959$	19539.1	0.657926
$960$	−24817.2	−0.834346
$961$	−29414.4	−0.987358
$962$	0	0
$963$	3970.24	0.132855
$964$	17436.8	0.582573
$965$	−21466.0	−0.716076
$966$	−93095.6	−3.10073
$967$	7336.97	0.243993	0.121996	−	0.992531i	$-0.461070\pi$
$967$	7336.97	0.243993	0.121996	+	0.992531i	$0.461070\pi$
$968$	−836.989	−0.0277912
$969$	1268.18	0.0420432
$970$	65801.2	2.17809
$971$	37800.0	1.24929	0.624644	−	0.780909i	$-0.285244\pi$
$971$	37800.0	1.24929	0.624644	+	0.780909i	$0.285244\pi$
$972$	−8273.17	−0.273006
$973$	8257.90	0.272082
$974$	−26710.2	−0.878696
$975$	0	0
$976$	−5190.96	−0.170244
$977$	−24842.4	−0.813490	−0.406745	−	0.913542i	$-0.633336\pi$
$977$	−24842.4	−0.813490	−0.406745	+	0.913542i	$0.633336\pi$
$978$	40776.7	1.33322
$979$	−2731.33	−0.0891661
$980$	−60531.6	−1.97307
$981$	8498.95	0.276606
$982$	−27739.4	−0.901424
$983$	31895.5	1.03490	0.517452	−	0.855712i	$-0.326881\pi$
$983$	31895.5	1.03490	0.517452	+	0.855712i	$0.326881\pi$
$984$	−11715.5	−0.379550
$985$	−9403.19	−0.304173
$986$	−37819.4	−1.22152
$987$	−60748.2	−1.95911
$988$	0	0
$989$	48090.4	1.54619
$990$	4134.68	0.132736
$991$	−7205.49	−0.230969	−0.115484	−	0.993309i	$-0.536842\pi$
$991$	−7205.49	−0.230969	−0.115484	+	0.993309i	$0.536842\pi$
$992$	−4427.23	−0.141698
$993$	−3154.88	−0.100823
$994$	15327.8	0.489104
$995$	−64833.3	−2.06568
$996$	15056.3	0.478992
$997$	−32447.4	−1.03071	−0.515355	−	0.856977i	$-0.672340\pi$
$997$	−32447.4	−1.03071	−0.515355	+	0.856977i	$0.672340\pi$
$998$	21865.0	0.693511
$999$	−38718.0	−1.22621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.d.1.7		9
13.12	even	2		143.4.a.c.1.3	✓	9
39.38	odd	2		1287.4.a.k.1.7		9
52.51	odd	2		2288.4.a.r.1.8		9
143.142	odd	2		1573.4.a.e.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.3	✓	9	13.12	even	2
1287.4.a.k.1.7		9	39.38	odd	2
1573.4.a.e.1.7		9	143.142	odd	2
1859.4.a.d.1.7		9	1.1	even	1	trivial
2288.4.a.r.1.8		9	52.51	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+3.76323 q^{2} -4.70664 q^{3} +6.16188 q^{4} -20.6048 q^{5} -17.7122 q^{6} +28.6315 q^{7} -6.91727 q^{8} -4.84752 q^{9} +O(q^{10})\)	\(q+3.76323 q^{2} -4.70664 q^{3} +6.16188 q^{4} -20.6048 q^{5} -17.7122 q^{6} +28.6315 q^{7} -6.91727 q^{8} -4.84752 q^{9} -77.5406 q^{10} +11.0000 q^{11} -29.0018 q^{12} +107.747 q^{14} +96.9795 q^{15} -75.3263 q^{16} +50.0610 q^{17} -18.2423 q^{18} -5.38233 q^{19} -126.964 q^{20} -134.758 q^{21} +41.3955 q^{22} +183.575 q^{23} +32.5571 q^{24} +299.559 q^{25} +149.895 q^{27} +176.424 q^{28} -200.750 q^{29} +364.956 q^{30} +19.4064 q^{31} -228.132 q^{32} -51.7731 q^{33} +188.391 q^{34} -589.946 q^{35} -29.8698 q^{36} -258.301 q^{37} -20.2549 q^{38} +142.529 q^{40} -359.846 q^{41} -507.125 q^{42} +261.966 q^{43} +67.7807 q^{44} +99.8823 q^{45} +690.835 q^{46} +450.795 q^{47} +354.534 q^{48} +476.760 q^{49} +1127.31 q^{50} -235.619 q^{51} +725.364 q^{53} +564.088 q^{54} -226.653 q^{55} -198.051 q^{56} +25.3327 q^{57} -755.466 q^{58} -381.785 q^{59} +597.576 q^{60} +68.9130 q^{61} +73.0309 q^{62} -138.792 q^{63} -255.901 q^{64} -194.834 q^{66} -133.352 q^{67} +308.470 q^{68} -864.023 q^{69} -2220.10 q^{70} +142.258 q^{71} +33.5316 q^{72} -394.273 q^{73} -972.045 q^{74} -1409.92 q^{75} -33.1653 q^{76} +314.946 q^{77} -1151.89 q^{79} +1552.08 q^{80} -574.619 q^{81} -1354.18 q^{82} -519.150 q^{83} -830.363 q^{84} -1031.50 q^{85} +985.836 q^{86} +944.856 q^{87} -76.0899 q^{88} -248.303 q^{89} +375.880 q^{90} +1131.17 q^{92} -91.3392 q^{93} +1696.44 q^{94} +110.902 q^{95} +1073.73 q^{96} -848.603 q^{97} +1794.16 q^{98} -53.3227 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9}+O(q^{10}) \) 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9} - 22 q^{10} + 99 q^{11} + 181 q^{12} - 351 q^{15} + 130 q^{16} + 53 q^{17} - 33 q^{18} - 69 q^{19} - 282 q^{20} - 463 q^{21} + 216 q^{23} + 121 q^{24} + 617 q^{25} + 275 q^{27} - 279 q^{28} - 91 q^{29} + 29 q^{30} - 636 q^{31} - 663 q^{32} + 88 q^{33} - 423 q^{34} - 358 q^{35} - 252 q^{36} - 967 q^{37} - 101 q^{38} + 652 q^{40} + 226 q^{41} - 1186 q^{42} + 42 q^{43} + 506 q^{44} - 5 q^{45} + 1127 q^{46} + 269 q^{47} - 1820 q^{48} + 228 q^{49} + 1374 q^{50} - 589 q^{51} + 1227 q^{53} + 2438 q^{54} - 330 q^{55} - 659 q^{56} + 71 q^{57} - 471 q^{58} + 613 q^{59} + 859 q^{60} + 427 q^{61} - 1714 q^{62} - 305 q^{63} - 1194 q^{64} - 374 q^{66} + 271 q^{67} - 2835 q^{68} - 846 q^{69} + 102 q^{70} - 2279 q^{71} + 2400 q^{72} - 3602 q^{73} - 4955 q^{74} - 883 q^{75} - 1126 q^{76} - 275 q^{77} - 1182 q^{79} + 2360 q^{80} + 2697 q^{81} + 1007 q^{82} + 1877 q^{83} - 1618 q^{84} + 441 q^{85} - 830 q^{86} + 1942 q^{87} - 396 q^{88} - 1258 q^{89} - 5669 q^{90} + 1046 q^{92} - 1556 q^{93} + 1439 q^{94} + 2032 q^{95} + 3417 q^{96} - 4002 q^{97} + 1855 q^{98} + 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9 - 22 * q^10 + 99 * q^11 + 181 * q^12 - 351 * q^15 + 130 * q^16 + 53 * q^17 - 33 * q^18 - 69 * q^19 - 282 * q^20 - 463 * q^21 + 216 * q^23 + 121 * q^24 + 617 * q^25 + 275 * q^27 - 279 * q^28 - 91 * q^29 + 29 * q^30 - 636 * q^31 - 663 * q^32 + 88 * q^33 - 423 * q^34 - 358 * q^35 - 252 * q^36 - 967 * q^37 - 101 * q^38 + 652 * q^40 + 226 * q^41 - 1186 * q^42 + 42 * q^43 + 506 * q^44 - 5 * q^45 + 1127 * q^46 + 269 * q^47 - 1820 * q^48 + 228 * q^49 + 1374 * q^50 - 589 * q^51 + 1227 * q^53 + 2438 * q^54 - 330 * q^55 - 659 * q^56 + 71 * q^57 - 471 * q^58 + 613 * q^59 + 859 * q^60 + 427 * q^61 - 1714 * q^62 - 305 * q^63 - 1194 * q^64 - 374 * q^66 + 271 * q^67 - 2835 * q^68 - 846 * q^69 + 102 * q^70 - 2279 * q^71 + 2400 * q^72 - 3602 * q^73 - 4955 * q^74 - 883 * q^75 - 1126 * q^76 - 275 * q^77 - 1182 * q^79 + 2360 * q^80 + 2697 * q^81 + 1007 * q^82 + 1877 * q^83 - 1618 * q^84 + 441 * q^85 - 830 * q^86 + 1942 * q^87 - 396 * q^88 - 1258 * q^89 - 5669 * q^90 + 1046 * q^92 - 1556 * q^93 + 1439 * q^94 + 2032 * q^95 + 3417 * q^96 - 4002 * q^97 + 1855 * q^98 + 1001 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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