LMFDB - Embedded newform 1859.4.a.n.1.2

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:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-5.01772 q^{2} +4.57830 q^{3} +17.1775 q^{4} +10.5311 q^{5} -22.9726 q^{6} +16.1445 q^{7} -46.0502 q^{8} -6.03920 q^{9} +O(q^{10})$	\(q-5.01772 q^{2} +4.57830 q^{3} +17.1775 q^{4} +10.5311 q^{5} -22.9726 q^{6} +16.1445 q^{7} -46.0502 q^{8} -6.03920 q^{9} -52.8420 q^{10} +11.0000 q^{11} +78.6438 q^{12} -81.0087 q^{14} +48.2144 q^{15} +93.6470 q^{16} +58.7153 q^{17} +30.3030 q^{18} -81.1068 q^{19} +180.898 q^{20} +73.9144 q^{21} -55.1949 q^{22} -150.138 q^{23} -210.832 q^{24} -14.0964 q^{25} -151.263 q^{27} +277.323 q^{28} -188.812 q^{29} -241.926 q^{30} +20.0127 q^{31} -101.493 q^{32} +50.3613 q^{33} -294.617 q^{34} +170.019 q^{35} -103.739 q^{36} +214.630 q^{37} +406.971 q^{38} -484.958 q^{40} +60.6943 q^{41} -370.882 q^{42} +11.1597 q^{43} +188.953 q^{44} -63.5993 q^{45} +753.351 q^{46} +158.284 q^{47} +428.744 q^{48} -82.3547 q^{49} +70.7320 q^{50} +268.816 q^{51} -326.954 q^{53} +758.997 q^{54} +115.842 q^{55} -743.458 q^{56} -371.331 q^{57} +947.406 q^{58} -489.035 q^{59} +828.204 q^{60} +94.4401 q^{61} -100.418 q^{62} -97.5000 q^{63} -239.914 q^{64} -252.699 q^{66} -604.408 q^{67} +1008.58 q^{68} -687.376 q^{69} -853.108 q^{70} +1103.36 q^{71} +278.107 q^{72} -1104.28 q^{73} -1076.95 q^{74} -64.5376 q^{75} -1393.21 q^{76} +177.590 q^{77} -904.398 q^{79} +986.204 q^{80} -529.470 q^{81} -304.547 q^{82} -545.710 q^{83} +1269.67 q^{84} +618.336 q^{85} -55.9962 q^{86} -864.437 q^{87} -506.552 q^{88} -1413.28 q^{89} +319.124 q^{90} -2579.00 q^{92} +91.6239 q^{93} -794.226 q^{94} -854.142 q^{95} -464.664 q^{96} +499.986 q^{97} +413.233 q^{98} -66.4312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * 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 $

$2$	−5.01772	−1.77403	−0.887016	−	0.461739i	$-0.847226\pi$
$2$	−5.01772	−1.77403	−0.887016	+	0.461739i	$0.847226\pi$
$3$	4.57830	0.881094	0.440547	−	0.897730i	$-0.354785\pi$
$3$	4.57830	0.881094	0.440547	+	0.897730i	$0.354785\pi$
$4$	17.1775	2.14719
$5$	10.5311	0.941928	0.470964	−	0.882152i	$-0.343906\pi$
$5$	10.5311	0.941928	0.470964	+	0.882152i	$0.343906\pi$
$6$	−22.9726	−1.56309
$7$	16.1445	0.871722	0.435861	−	0.900014i	$-0.356444\pi$
$7$	16.1445	0.871722	0.435861	+	0.900014i	$0.356444\pi$
$8$	−46.0502	−2.03515
$9$	−6.03920	−0.223674
$10$	−52.8420	−1.67101
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	78.6438	1.89188
$13$	0	0
$13$	0	0
$14$	−81.0087	−1.54646
$15$	48.2144	0.829927
$16$	93.6470	1.46323
$17$	58.7153	0.837680	0.418840	−	0.908060i	$-0.362437\pi$
$17$	58.7153	0.837680	0.418840	+	0.908060i	$0.362437\pi$
$18$	30.3030	0.396805
$19$	−81.1068	−0.979325	−0.489663	−	0.871912i	$-0.662880\pi$
$19$	−81.1068	−0.979325	−0.489663	+	0.871912i	$0.662880\pi$
$20$	180.898	2.02250
$21$	73.9144	0.768068
$22$	−55.1949	−0.534891
$23$	−150.138	−1.36113	−0.680564	−	0.732689i	$-0.738265\pi$
$23$	−150.138	−1.36113	−0.680564	+	0.732689i	$0.738265\pi$
$24$	−210.832	−1.79316
$25$	−14.0964	−0.112771
$26$	0	0
$27$	−151.263	−1.07817
$28$	277.323	1.87175
$29$	−188.812	−1.20902	−0.604509	−	0.796599i	$-0.706631\pi$
$29$	−188.812	−1.20902	−0.604509	+	0.796599i	$0.706631\pi$
$30$	−241.926	−1.47232
$31$	20.0127	0.115948	0.0579739	−	0.998318i	$-0.481536\pi$
$31$	20.0127	0.115948	0.0579739	+	0.998318i	$0.481536\pi$
$32$	−101.493	−0.560673
$33$	50.3613	0.265660
$34$	−294.617	−1.48607
$35$	170.019	0.821099
$36$	−103.739	−0.480271
$37$	214.630	0.953648	0.476824	−	0.878999i	$-0.341788\pi$
$37$	214.630	0.953648	0.476824	+	0.878999i	$0.341788\pi$
$38$	406.971	1.73735
$39$	0	0
$40$	−484.958	−1.91697
$41$	60.6943	0.231192	0.115596	−	0.993296i	$-0.463122\pi$
$41$	60.6943	0.231192	0.115596	+	0.993296i	$0.463122\pi$
$42$	−370.882	−1.36258
$43$	11.1597	0.0395776	0.0197888	−	0.999804i	$-0.493701\pi$
$43$	11.1597	0.0395776	0.0197888	+	0.999804i	$0.493701\pi$
$44$	188.953	0.647402
$45$	−63.5993	−0.210685
$46$	753.351	2.41468
$47$	158.284	0.491237	0.245618	−	0.969367i	$-0.421009\pi$
$47$	158.284	0.491237	0.245618	+	0.969367i	$0.421009\pi$
$48$	428.744	1.28925
$49$	−82.3547	−0.240101
$50$	70.7320	0.200060
$51$	268.816	0.738075
$52$	0	0
$53$	−326.954	−0.847370	−0.423685	−	0.905809i	$-0.639264\pi$
$53$	−326.954	−0.847370	−0.423685	+	0.905809i	$0.639264\pi$
$54$	758.997	1.91271
$55$	115.842	0.284002
$56$	−743.458	−1.77409
$57$	−371.331	−0.862877
$58$	947.406	2.14484
$59$	−489.035	−1.07910	−0.539550	−	0.841954i	$-0.681406\pi$
$59$	−489.035	−1.07910	−0.539550	+	0.841954i	$0.681406\pi$
$60$	828.204	1.78201
$61$	94.4401	0.198226	0.0991132	−	0.995076i	$-0.468399\pi$
$61$	94.4401	0.198226	0.0991132	+	0.995076i	$0.468399\pi$
$62$	−100.418	−0.205695
$63$	−97.5000	−0.194982
$64$	−239.914	−0.468582
$65$	0	0
$66$	−252.699	−0.471289
$67$	−604.408	−1.10209	−0.551047	−	0.834474i	$-0.685771\pi$
$67$	−604.408	−1.10209	−0.551047	+	0.834474i	$0.685771\pi$
$68$	1008.58	1.79866
$69$	−687.376	−1.19928
$70$	−853.108	−1.45666
$71$	1103.36	1.84429	0.922143	−	0.386850i	$-0.126437\pi$
$71$	1103.36	1.84429	0.922143	+	0.386850i	$0.126437\pi$
$72$	278.107	0.455211
$73$	−1104.28	−1.77050	−0.885250	−	0.465116i	$-0.846013\pi$
$73$	−1104.28	−1.77050	−0.885250	+	0.465116i	$0.846013\pi$
$74$	−1076.95	−1.69180
$75$	−64.5376	−0.0993622
$76$	−1393.21	−2.10280
$77$	177.590	0.262834
$78$	0	0
$79$	−904.398	−1.28801	−0.644004	−	0.765022i	$-0.722728\pi$
$79$	−904.398	−1.28801	−0.644004	+	0.765022i	$0.722728\pi$
$80$	986.204	1.37826
$81$	−529.470	−0.726296
$82$	−304.547	−0.410141
$83$	−545.710	−0.721681	−0.360840	−	0.932628i	$-0.617510\pi$
$83$	−545.710	−0.721681	−0.360840	+	0.932628i	$0.617510\pi$
$84$	1269.67	1.64919
$85$	618.336	0.789034
$86$	−55.9962	−0.0702119
$87$	−864.437	−1.06526
$88$	−506.552	−0.613621
$89$	−1413.28	−1.68323	−0.841616	−	0.540077i	$-0.818395\pi$
$89$	−1413.28	−1.68323	−0.841616	+	0.540077i	$0.818395\pi$
$90$	319.124	0.373762
$91$	0	0
$92$	−2579.00	−2.92260
$93$	91.6239	0.102161
$94$	−794.226	−0.871470
$95$	−854.142	−0.922454
$96$	−464.664	−0.494006
$97$	499.986	0.523360	0.261680	−	0.965155i	$-0.415724\pi$
$97$	499.986	0.523360	0.261680	+	0.965155i	$0.415724\pi$
$98$	413.233	0.425947
$99$	−66.4312	−0.0674403
$100$	−242.142	−0.242142
$101$	1112.51	1.09603	0.548016	−	0.836468i	$-0.315383\pi$
$101$	1112.51	1.09603	0.548016	+	0.836468i	$0.315383\pi$
$102$	−1348.84	−1.30937
$103$	−1233.06	−1.17958	−0.589792	−	0.807555i	$-0.700790\pi$
$103$	−1233.06	−1.17958	−0.589792	+	0.807555i	$0.700790\pi$
$104$	0	0
$105$	778.398	0.723465
$106$	1640.57	1.50326
$107$	−774.437	−0.699697	−0.349849	−	0.936806i	$-0.613767\pi$
$107$	−774.437	−0.699697	−0.349849	+	0.936806i	$0.613767\pi$
$108$	−2598.33	−2.31504
$109$	1199.01	1.05361	0.526807	−	0.849985i	$-0.323389\pi$
$109$	1199.01	1.05361	0.526807	+	0.849985i	$0.323389\pi$
$110$	−581.262	−0.503829
$111$	982.640	0.840253
$112$	1511.89	1.27553
$113$	−1955.25	−1.62774	−0.813870	−	0.581047i	$-0.802643\pi$
$113$	−1955.25	−1.62774	−0.813870	+	0.581047i	$0.802643\pi$
$114$	1863.23	1.53077
$115$	−1581.12	−1.28208
$116$	−3243.32	−2.59599
$117$	0	0
$118$	2453.84	1.91436
$119$	947.931	0.730224
$120$	−2220.28	−1.68903
$121$	121.000	0.0909091
$122$	−473.874	−0.351660
$123$	277.876	0.203701
$124$	343.768	0.248962
$125$	−1464.84	−1.04815
$126$	489.228	0.345904
$127$	−375.753	−0.262541	−0.131271	−	0.991347i	$-0.541906\pi$
$127$	−375.753	−0.262541	−0.131271	+	0.991347i	$0.541906\pi$
$128$	2015.76	1.39195
$129$	51.0924	0.0348716
$130$	0	0
$131$	633.580	0.422566	0.211283	−	0.977425i	$-0.432236\pi$
$131$	633.580	0.422566	0.211283	+	0.977425i	$0.432236\pi$
$132$	865.082	0.570422
$133$	−1309.43	−0.853699
$134$	3032.75	1.95515
$135$	−1592.96	−1.01556
$136$	−2703.85	−1.70481
$137$	−1207.56	−0.753057	−0.376529	−	0.926405i	$-0.622882\pi$
$137$	−1207.56	−0.753057	−0.376529	+	0.926405i	$0.622882\pi$
$138$	3449.06	2.12756
$139$	1424.47	0.869224	0.434612	−	0.900618i	$-0.356886\pi$
$139$	1424.47	0.869224	0.434612	+	0.900618i	$0.356886\pi$
$140$	2920.51	1.76306
$141$	724.672	0.432825
$142$	−5536.33	−3.27182
$143$	0	0
$144$	−565.553	−0.327288
$145$	−1988.39	−1.13881
$146$	5540.98	3.14092
$147$	−377.044	−0.211552
$148$	3686.81	2.04766
$149$	2111.91	1.16117	0.580585	−	0.814200i	$-0.302824\pi$
$149$	2111.91	1.16117	0.580585	+	0.814200i	$0.302824\pi$
$150$	323.832	0.176272
$151$	−1500.77	−0.808813	−0.404406	−	0.914579i	$-0.632522\pi$
$151$	−1500.77	−0.808813	−0.404406	+	0.914579i	$0.632522\pi$
$152$	3734.99	1.99307
$153$	−354.594	−0.187367
$154$	−891.095	−0.466276
$155$	210.755	0.109214
$156$	0	0
$157$	−1009.26	−0.513045	−0.256523	−	0.966538i	$-0.582577\pi$
$157$	−1009.26	−0.513045	−0.256523	+	0.966538i	$0.582577\pi$
$158$	4538.01	2.28497
$159$	−1496.89	−0.746613
$160$	−1068.83	−0.528114
$161$	−2423.91	−1.18652
$162$	2656.73	1.28847
$163$	688.850	0.331012	0.165506	−	0.986209i	$-0.447074\pi$
$163$	688.850	0.331012	0.165506	+	0.986209i	$0.447074\pi$
$164$	1042.58	0.496412
$165$	530.358	0.250232
$166$	2738.22	1.28028
$167$	−489.476	−0.226807	−0.113404	−	0.993549i	$-0.536175\pi$
$167$	−489.476	−0.226807	−0.113404	+	0.993549i	$0.536175\pi$
$168$	−3403.77	−1.56314
$169$	0	0
$170$	−3102.64	−1.39977
$171$	489.820	0.219050
$172$	191.696	0.0849806
$173$	3800.04	1.67001	0.835004	−	0.550244i	$-0.185465\pi$
$173$	3800.04	1.67001	0.835004	+	0.550244i	$0.185465\pi$
$174$	4337.50	1.88980
$175$	−227.580	−0.0983053
$176$	1030.12	0.441182
$177$	−2238.95	−0.950788
$178$	7091.46	2.98611
$179$	3421.79	1.42881	0.714405	−	0.699733i	$-0.246698\pi$
$179$	3421.79	1.42881	0.714405	+	0.699733i	$0.246698\pi$
$180$	−1092.48	−0.452381
$181$	−2560.56	−1.05152	−0.525760	−	0.850633i	$-0.676219\pi$
$181$	−2560.56	−1.05152	−0.525760	+	0.850633i	$0.676219\pi$
$182$	0	0
$183$	432.375	0.174656
$184$	6913.89	2.77010
$185$	2260.29	0.898268
$186$	−459.743	−0.181237
$187$	645.869	0.252570
$188$	2718.93	1.05478
$189$	−2442.07	−0.939865
$190$	4285.85	1.63646
$191$	2671.38	1.01201	0.506006	−	0.862530i	$-0.331121\pi$
$191$	2671.38	1.01201	0.506006	+	0.862530i	$0.331121\pi$
$192$	−1098.40	−0.412865
$193$	−281.568	−0.105014	−0.0525069	−	0.998621i	$-0.516721\pi$
$193$	−281.568	−0.105014	−0.0525069	+	0.998621i	$0.516721\pi$
$194$	−2508.79	−0.928457
$195$	0	0
$196$	−1414.65	−0.515543
$197$	−2381.81	−0.861407	−0.430704	−	0.902493i	$-0.641735\pi$
$197$	−2381.81	−0.861407	−0.430704	+	0.902493i	$0.641735\pi$
$198$	333.333	0.119641
$199$	−5237.64	−1.86576	−0.932880	−	0.360188i	$-0.882713\pi$
$199$	−5237.64	−1.86576	−0.932880	+	0.360188i	$0.882713\pi$
$200$	649.144	0.229507
$201$	−2767.16	−0.971047
$202$	−5582.29	−1.94440
$203$	−3048.28	−1.05393
$204$	4617.60	1.58479
$205$	639.176	0.217766
$206$	6187.16	2.09262
$207$	906.714	0.304449
$208$	0	0
$209$	−892.175	−0.295278
$210$	−3905.78	−1.28345
$211$	4028.30	1.31431	0.657155	−	0.753755i	$-0.271760\pi$
$211$	4028.30	1.31431	0.657155	+	0.753755i	$0.271760\pi$
$212$	−5616.26	−1.81947
$213$	5051.49	1.62499
$214$	3885.91	1.24129
$215$	117.524	0.0372792
$216$	6965.71	2.19424
$217$	323.095	0.101074
$218$	−6016.28	−1.86915
$219$	−5055.73	−1.55998
$220$	1989.88	0.609806
$221$	0	0
$222$	−4930.61	−1.49064
$223$	6565.25	1.97149	0.985743	−	0.168256i	$-0.0538134\pi$
$223$	6565.25	1.97149	0.985743	+	0.168256i	$0.0538134\pi$
$224$	−1638.55	−0.488751
$225$	85.1312	0.0252241
$226$	9810.91	2.88766
$227$	−1303.20	−0.381042	−0.190521	−	0.981683i	$-0.561018\pi$
$227$	−1303.20	−0.381042	−0.190521	+	0.981683i	$0.561018\pi$
$228$	−6378.54	−1.85276
$229$	−3386.32	−0.977181	−0.488591	−	0.872513i	$-0.662489\pi$
$229$	−3386.32	−0.977181	−0.488591	+	0.872513i	$0.662489\pi$
$230$	7933.59	2.27446
$231$	813.058	0.231581
$232$	8694.83	2.46053
$233$	2993.18	0.841587	0.420793	−	0.907156i	$-0.361752\pi$
$233$	2993.18	0.841587	0.420793	+	0.907156i	$0.361752\pi$
$234$	0	0
$235$	1666.90	0.462710
$236$	−8400.40	−2.31703
$237$	−4140.60	−1.13486
$238$	−4756.45	−1.29544
$239$	−682.724	−0.184777	−0.0923886	−	0.995723i	$-0.529450\pi$
$239$	−682.724	−0.184777	−0.0923886	+	0.995723i	$0.529450\pi$
$240$	4515.13	1.21438
$241$	−786.212	−0.210143	−0.105071	−	0.994465i	$-0.533507\pi$
$241$	−786.212	−0.210143	−0.105071	+	0.994465i	$0.533507\pi$
$242$	−607.144	−0.161276
$243$	1660.04	0.438237
$244$	1622.25	0.425630
$245$	−867.284	−0.226158
$246$	−1394.31	−0.361373
$247$	0	0
$248$	−921.588	−0.235971
$249$	−2498.42	−0.635868
$250$	7350.13	1.85945
$251$	−3350.73	−0.842616	−0.421308	−	0.906918i	$-0.638429\pi$
$251$	−3350.73	−0.842616	−0.421308	+	0.906918i	$0.638429\pi$
$252$	−1674.81	−0.418663
$253$	−1651.52	−0.410396
$254$	1885.43	0.465756
$255$	2830.92	0.695213
$256$	−8195.22	−2.00079
$257$	−2444.05	−0.593212	−0.296606	−	0.955000i	$-0.595855\pi$
$257$	−2444.05	−0.593212	−0.296606	+	0.955000i	$0.595855\pi$
$258$	−256.367	−0.0618633
$259$	3465.10	0.831316
$260$	0	0
$261$	1140.27	0.270426
$262$	−3179.13	−0.749646
$263$	7521.28	1.76343	0.881714	−	0.471783i	$-0.156390\pi$
$263$	7521.28	1.76343	0.881714	+	0.471783i	$0.156390\pi$
$264$	−2319.15	−0.540658
$265$	−3443.18	−0.798162
$266$	6570.35	1.51449
$267$	−6470.43	−1.48308
$268$	−10382.2	−2.36640
$269$	−4339.81	−0.983654	−0.491827	−	0.870693i	$-0.663671\pi$
$269$	−4339.81	−0.983654	−0.491827	+	0.870693i	$0.663671\pi$
$270$	7993.05	1.80164
$271$	3118.56	0.699037	0.349518	−	0.936929i	$-0.386345\pi$
$271$	3118.56	0.699037	0.349518	+	0.936929i	$0.386345\pi$
$272$	5498.52	1.22572
$273$	0	0
$274$	6059.20	1.33595
$275$	−155.061	−0.0340019
$276$	−11807.4	−2.57508
$277$	3585.62	0.777758	0.388879	−	0.921289i	$-0.372862\pi$
$277$	3585.62	0.777758	0.388879	+	0.921289i	$0.372862\pi$
$278$	−7147.60	−1.54203
$279$	−120.861	−0.0259345
$280$	−7829.42	−1.67106
$281$	8212.92	1.74356	0.871782	−	0.489894i	$-0.162964\pi$
$281$	8212.92	1.74356	0.871782	+	0.489894i	$0.162964\pi$
$282$	−3636.20	−0.767846
$283$	4593.59	0.964877	0.482439	−	0.875930i	$-0.339751\pi$
$283$	4593.59	0.964877	0.482439	+	0.875930i	$0.339751\pi$
$284$	18952.9	3.96003
$285$	−3910.51	−0.812768
$286$	0	0
$287$	979.880	0.201535
$288$	612.935	0.125408
$289$	−1465.51	−0.298292
$290$	9977.20	2.02028
$291$	2289.08	0.461129
$292$	−18968.8	−3.80160
$293$	7784.91	1.55222	0.776108	−	0.630600i	$-0.217191\pi$
$293$	7784.91	1.55222	0.776108	+	0.630600i	$0.217191\pi$
$294$	1891.90	0.375299
$295$	−5150.06	−1.01643
$296$	−9883.77	−1.94082
$297$	−1663.90	−0.325081
$298$	−10597.0	−2.05995
$299$	0	0
$300$	−1108.60	−0.213350
$301$	180.168	0.0345006
$302$	7530.43	1.43486
$303$	5093.42	0.965708
$304$	−7595.41	−1.43298
$305$	994.556	0.186715
$306$	1779.25	0.332396
$307$	−5467.23	−1.01639	−0.508195	−	0.861242i	$-0.669687\pi$
$307$	−5467.23	−1.01639	−0.508195	+	0.861242i	$0.669687\pi$
$308$	3050.55	0.564354
$309$	−5645.32	−1.03932
$310$	−1057.51	−0.193750
$311$	9293.28	1.69445	0.847224	−	0.531235i	$-0.178272\pi$
$311$	9293.28	1.69445	0.847224	+	0.531235i	$0.178272\pi$
$312$	0	0
$313$	−8254.57	−1.49066	−0.745329	−	0.666697i	$-0.767708\pi$
$313$	−8254.57	−1.49066	−0.745329	+	0.666697i	$0.767708\pi$
$314$	5064.21	0.910159
$315$	−1026.78	−0.183659
$316$	−15535.3	−2.76560
$317$	4440.99	0.786848	0.393424	−	0.919357i	$-0.371290\pi$
$317$	4440.99	0.786848	0.393424	+	0.919357i	$0.371290\pi$
$318$	7511.00	1.32451
$319$	−2076.93	−0.364532
$320$	−2526.55	−0.441371
$321$	−3545.60	−0.616499
$322$	12162.5	2.10493
$323$	−4762.21	−0.820361
$324$	−9094.97	−1.55949
$325$	0	0
$326$	−3456.46	−0.587225
$327$	5489.41	0.928333
$328$	−2794.99	−0.470510
$329$	2555.42	0.428222
$330$	−2661.19	−0.443920
$331$	1238.67	0.205691	0.102845	−	0.994697i	$-0.467205\pi$
$331$	1238.67	0.205691	0.102845	+	0.994697i	$0.467205\pi$
$332$	−9373.95	−1.54959
$333$	−1296.19	−0.213306
$334$	2456.06	0.402363
$335$	−6365.07	−1.03809
$336$	6921.86	1.12386
$337$	659.776	0.106648	0.0533239	−	0.998577i	$-0.483018\pi$
$337$	659.776	0.106648	0.0533239	+	0.998577i	$0.483018\pi$
$338$	0	0
$339$	−8951.72	−1.43419
$340$	10621.5	1.69421
$341$	220.139	0.0349596
$342$	−2457.78	−0.388601
$343$	−6867.14	−1.08102
$344$	−513.906	−0.0805464
$345$	−7238.81	−1.12964
$346$	−19067.5	−2.96265
$347$	−2440.68	−0.377587	−0.188793	−	0.982017i	$-0.560458\pi$
$347$	−2440.68	−0.377587	−0.188793	+	0.982017i	$0.560458\pi$
$348$	−14848.9	−2.28731
$349$	−5077.10	−0.778714	−0.389357	−	0.921087i	$-0.627303\pi$
$349$	−5077.10	−0.778714	−0.389357	+	0.921087i	$0.627303\pi$
$350$	1141.93	0.174397
$351$	0	0
$352$	−1116.42	−0.169049
$353$	−2109.09	−0.318004	−0.159002	−	0.987278i	$-0.550828\pi$
$353$	−2109.09	−0.318004	−0.159002	+	0.987278i	$0.550828\pi$
$354$	11234.4	1.68673
$355$	11619.5	1.73718
$356$	−24276.7	−3.61422
$357$	4339.91	0.643396
$358$	−17169.6	−2.53475
$359$	−2098.69	−0.308537	−0.154268	−	0.988029i	$-0.549302\pi$
$359$	−2098.69	−0.308537	−0.154268	+	0.988029i	$0.549302\pi$
$360$	2928.76	0.428776
$361$	−280.687	−0.0409225
$362$	12848.2	1.86543
$363$	553.974	0.0800994
$364$	0	0
$365$	−11629.3	−1.66768
$366$	−2169.54	−0.309845
$367$	−6448.35	−0.917169	−0.458584	−	0.888651i	$-0.651643\pi$
$367$	−6448.35	−0.917169	−0.458584	+	0.888651i	$0.651643\pi$
$368$	−14060.0	−1.99165
$369$	−366.545	−0.0517116
$370$	−11341.5	−1.59356
$371$	−5278.52	−0.738671
$372$	1573.87	0.219359
$373$	5889.56	0.817560	0.408780	−	0.912633i	$-0.365954\pi$
$373$	5889.56	0.817560	0.408780	+	0.912633i	$0.365954\pi$
$374$	−3240.79	−0.448067
$375$	−6706.45	−0.923519
$376$	−7289.02	−0.999741
$377$	0	0
$378$	12253.6	1.66735
$379$	−8175.67	−1.10806	−0.554032	−	0.832496i	$-0.686911\pi$
$379$	−8175.67	−1.10806	−0.554032	+	0.832496i	$0.686911\pi$
$380$	−14672.0	−1.98068
$381$	−1720.31	−0.231323
$382$	−13404.2	−1.79534
$383$	6497.48	0.866856	0.433428	−	0.901188i	$-0.357304\pi$
$383$	6497.48	0.866856	0.433428	+	0.901188i	$0.357304\pi$
$384$	9228.76	1.22644
$385$	1870.21	0.247571
$386$	1412.83	0.186298
$387$	−67.3956	−0.00885248
$388$	8588.52	1.12375
$389$	13761.1	1.79361	0.896806	−	0.442425i	$-0.145882\pi$
$389$	13761.1	1.79361	0.896806	+	0.442425i	$0.145882\pi$
$390$	0	0
$391$	−8815.41	−1.14019
$392$	3792.45	0.488642
$393$	2900.72	0.372320
$394$	11951.3	1.52816
$395$	−9524.28	−1.21321
$396$	−1141.12	−0.144807
$397$	−9008.92	−1.13890	−0.569452	−	0.822025i	$-0.692844\pi$
$397$	−9008.92	−1.13890	−0.569452	+	0.822025i	$0.692844\pi$
$398$	26281.0	3.30992
$399$	−5994.96	−0.752189
$400$	−1320.09	−0.165011
$401$	−3103.71	−0.386513	−0.193256	−	0.981148i	$-0.561905\pi$
$401$	−3103.71	−0.386513	−0.193256	+	0.981148i	$0.561905\pi$
$402$	13884.8	1.72267
$403$	0	0
$404$	19110.2	2.35339
$405$	−5575.88	−0.684118
$406$	15295.4	1.86970
$407$	2360.93	0.287536
$408$	−12379.0	−1.50209
$409$	−10219.8	−1.23554	−0.617771	−	0.786358i	$-0.711964\pi$
$409$	−10219.8	−1.23554	−0.617771	+	0.786358i	$0.711964\pi$
$410$	−3207.21	−0.386324
$411$	−5528.57	−0.663514
$412$	−21180.9	−2.53279
$413$	−7895.22	−0.940675
$414$	−4549.64	−0.540103
$415$	−5746.92	−0.679771
$416$	0	0
$417$	6521.65	0.765867
$418$	4476.68	0.523832
$419$	−13946.4	−1.62608	−0.813039	−	0.582210i	$-0.802188\pi$
$419$	−13946.4	−1.62608	−0.813039	+	0.582210i	$0.802188\pi$
$420$	13370.9	1.55342
$421$	−3823.17	−0.442588	−0.221294	−	0.975207i	$-0.571028\pi$
$421$	−3823.17	−0.442588	−0.221294	+	0.975207i	$0.571028\pi$
$422$	−20212.9	−2.33163
$423$	−955.910	−0.109877
$424$	15056.3	1.72453
$425$	−827.677	−0.0944664
$426$	−25347.0	−2.88278
$427$	1524.69	0.172798
$428$	−13302.9	−1.50238
$429$	0	0
$430$	−589.700	−0.0661346
$431$	−12544.0	−1.40191	−0.700955	−	0.713206i	$-0.747243\pi$
$431$	−12544.0	−1.40191	−0.700955	+	0.713206i	$0.747243\pi$
$432$	−14165.4	−1.57762
$433$	1742.05	0.193343	0.0966715	−	0.995316i	$-0.469180\pi$
$433$	1742.05	0.193343	0.0966715	+	0.995316i	$0.469180\pi$
$434$	−1621.20	−0.179309
$435$	−9103.45	−1.00340
$436$	20596.0	2.26231
$437$	12177.2	1.33299
$438$	25368.3	2.76745
$439$	−9084.98	−0.987704	−0.493852	−	0.869546i	$-0.664412\pi$
$439$	−9084.98	−0.987704	−0.493852	+	0.869546i	$0.664412\pi$
$440$	−5334.54	−0.577987
$441$	497.357	0.0537044
$442$	0	0
$443$	−9652.36	−1.03521	−0.517604	−	0.855620i	$-0.673176\pi$
$443$	−9652.36	−1.03521	−0.517604	+	0.855620i	$0.673176\pi$
$444$	16879.3	1.80418
$445$	−14883.4	−1.58548
$446$	−32942.6	−3.49748
$447$	9668.94	1.02310
$448$	−3873.30	−0.408473
$449$	18542.0	1.94889	0.974445	−	0.224627i	$-0.0721162\pi$
$449$	18542.0	1.94889	0.974445	+	0.224627i	$0.0721162\pi$
$450$	−427.165	−0.0447483
$451$	667.637	0.0697069
$452$	−33586.4	−3.49507
$453$	−6870.96	−0.712640
$454$	6539.10	0.675981
$455$	0	0
$456$	17099.9	1.75609
$457$	−6314.10	−0.646304	−0.323152	−	0.946347i	$-0.604743\pi$
$457$	−6314.10	−0.646304	−0.323152	+	0.946347i	$0.604743\pi$
$458$	16991.6	1.73355
$459$	−8881.47	−0.903163
$460$	−27159.6	−2.75288
$461$	15672.4	1.58338	0.791689	−	0.610924i	$-0.209202\pi$
$461$	15672.4	1.58338	0.791689	+	0.610924i	$0.209202\pi$
$462$	−4079.70	−0.410833
$463$	11690.9	1.17348	0.586740	−	0.809775i	$-0.300411\pi$
$463$	11690.9	1.17348	0.586740	+	0.809775i	$0.300411\pi$
$464$	−17681.7	−1.76908
$465$	964.898	0.0962281
$466$	−15018.9	−1.49300
$467$	2492.83	0.247012	0.123506	−	0.992344i	$-0.460586\pi$
$467$	2492.83	0.247012	0.123506	+	0.992344i	$0.460586\pi$
$468$	0	0
$469$	−9757.88	−0.960719
$470$	−8364.05	−0.820862
$471$	−4620.71	−0.452041
$472$	22520.2	2.19613
$473$	122.757	0.0119331
$474$	20776.4	2.01327
$475$	1143.32	0.110440
$476$	16283.1	1.56793
$477$	1974.54	0.189535
$478$	3425.72	0.327801
$479$	1055.81	0.100712	0.0503562	−	0.998731i	$-0.483964\pi$
$479$	1055.81	0.100712	0.0503562	+	0.998731i	$0.483964\pi$
$480$	−4893.41	−0.465318
$481$	0	0
$482$	3944.99	0.372800
$483$	−11097.4	−1.04544
$484$	2078.48	0.195199
$485$	5265.39	0.492967
$486$	−8329.61	−0.777446
$487$	3975.06	0.369871	0.184936	−	0.982751i	$-0.440792\pi$
$487$	3975.06	0.369871	0.184936	+	0.982751i	$0.440792\pi$
$488$	−4348.99	−0.403421
$489$	3153.76	0.291652
$490$	4351.79	0.401212
$491$	−18002.0	−1.65462	−0.827312	−	0.561742i	$-0.810131\pi$
$491$	−18002.0	−1.65462	−0.827312	+	0.561742i	$0.810131\pi$
$492$	4773.23	0.437386
$493$	−11086.2	−1.01277
$494$	0	0
$495$	−699.592	−0.0635239
$496$	1874.13	0.169659
$497$	17813.1	1.60770
$498$	12536.4	1.12805
$499$	18012.1	1.61589	0.807947	−	0.589255i	$-0.200579\pi$
$499$	18012.1	1.61589	0.807947	+	0.589255i	$0.200579\pi$
$500$	−25162.2	−2.25058
$501$	−2240.97	−0.199838
$502$	16813.1	1.49483
$503$	10434.5	0.924956	0.462478	−	0.886631i	$-0.346960\pi$
$503$	10434.5	0.924956	0.462478	+	0.886631i	$0.346960\pi$
$504$	4489.90	0.396817
$505$	11716.0	1.03238
$506$	8286.86	0.728055
$507$	0	0
$508$	−6454.51	−0.563726
$509$	−16933.4	−1.47458	−0.737291	−	0.675576i	$-0.763895\pi$
$509$	−16933.4	−1.47458	−0.737291	+	0.675576i	$0.763895\pi$
$510$	−14204.8	−1.23333
$511$	−17828.1	−1.54338
$512$	24995.2	2.15751
$513$	12268.5	1.05588
$514$	12263.5	1.05238
$515$	−12985.5	−1.11108
$516$	877.640	0.0748759
$517$	1741.13	0.148113
$518$	−17386.9	−1.47478
$519$	17397.7	1.47143
$520$	0	0
$521$	−11370.2	−0.956120	−0.478060	−	0.878327i	$-0.658660\pi$
$521$	−11370.2	−0.956120	−0.478060	+	0.878327i	$0.658660\pi$
$522$	−5721.57	−0.479744
$523$	−1214.79	−0.101566	−0.0507829	−	0.998710i	$-0.516172\pi$
$523$	−1214.79	−0.101566	−0.0507829	+	0.998710i	$0.516172\pi$
$524$	10883.3	0.907330
$525$	−1041.93	−0.0866162
$526$	−37739.7	−3.12838
$527$	1175.05	0.0971271
$528$	4716.18	0.388722
$529$	10374.4	0.852669
$530$	17276.9	1.41597
$531$	2953.38	0.241367
$532$	−22492.8	−1.83305
$533$	0	0
$534$	32466.8	2.63104
$535$	−8155.65	−0.659065
$536$	27833.1	2.24293
$537$	15666.0	1.25891
$538$	21776.0	1.74503
$539$	−905.902	−0.0723932
$540$	−27363.2	−2.18060
$541$	20242.5	1.60867	0.804336	−	0.594174i	$-0.202521\pi$
$541$	20242.5	1.60867	0.804336	+	0.594174i	$0.202521\pi$
$542$	−15648.1	−1.24011
$543$	−11723.0	−0.926488
$544$	−5959.18	−0.469665
$545$	12626.8	0.992429
$546$	0	0
$547$	−19235.3	−1.50355	−0.751775	−	0.659420i	$-0.770802\pi$
$547$	−19235.3	−1.50355	−0.751775	+	0.659420i	$0.770802\pi$
$548$	−20742.9	−1.61696
$549$	−570.343	−0.0443381
$550$	778.052	0.0603204
$551$	15313.9	1.18402
$552$	31653.8	2.44072
$553$	−14601.1	−1.12278
$554$	−17991.6	−1.37977
$555$	10348.3	0.791458
$556$	24468.9	1.86639
$557$	44.6665	0.00339781	0.00169891	−	0.999999i	$-0.499459\pi$
$557$	44.6665	0.00339781	0.00169891	+	0.999999i	$0.499459\pi$
$558$	606.444	0.0460087
$559$	0	0
$560$	15921.8	1.20146
$561$	2956.98	0.222538
$562$	−41210.1	−3.09314
$563$	4421.01	0.330947	0.165473	−	0.986214i	$-0.447085\pi$
$563$	4421.01	0.330947	0.165473	+	0.986214i	$0.447085\pi$
$564$	12448.1	0.929358
$565$	−20590.9	−1.53321
$566$	−23049.3	−1.71172
$567$	−8548.03	−0.633128
$568$	−50809.8	−3.75340
$569$	162.232	0.0119528	0.00597638	−	0.999982i	$-0.498098\pi$
$569$	162.232	0.0119528	0.00597638	+	0.999982i	$0.498098\pi$
$570$	19621.9	1.44188
$571$	−1604.25	−0.117576	−0.0587879	−	0.998270i	$-0.518724\pi$
$571$	−1604.25	−0.117576	−0.0587879	+	0.998270i	$0.518724\pi$
$572$	0	0
$573$	12230.4	0.891677
$574$	−4916.76	−0.357529
$575$	2116.41	0.153496
$576$	1448.89	0.104810
$577$	7558.95	0.545378	0.272689	−	0.962102i	$-0.412087\pi$
$577$	7558.95	0.545378	0.272689	+	0.962102i	$0.412087\pi$
$578$	7353.51	0.529179
$579$	−1289.10	−0.0925270
$580$	−34155.7	−2.44524
$581$	−8810.23	−0.629105
$582$	−11486.0	−0.818057
$583$	−3596.50	−0.255492
$584$	50852.5	3.60324
$585$	0	0
$586$	−39062.5	−2.75368
$587$	24469.0	1.72052	0.860260	−	0.509856i	$-0.170301\pi$
$587$	24469.0	1.72052	0.860260	+	0.509856i	$0.170301\pi$
$588$	−6476.69	−0.454242
$589$	−1623.16	−0.113551
$590$	25841.6	1.80319
$591$	−10904.6	−0.758980
$592$	20099.5	1.39541
$593$	−24894.9	−1.72397	−0.861983	−	0.506937i	$-0.830778\pi$
$593$	−24894.9	−1.72397	−0.861983	+	0.506937i	$0.830778\pi$
$594$	8348.96	0.576704
$595$	9982.73	0.687818
$596$	36277.3	2.49325
$597$	−23979.5	−1.64391
$598$	0	0
$599$	15767.4	1.07552	0.537762	−	0.843097i	$-0.319270\pi$
$599$	15767.4	1.07552	0.537762	+	0.843097i	$0.319270\pi$
$600$	2971.97	0.202217
$601$	5376.20	0.364892	0.182446	−	0.983216i	$-0.441599\pi$
$601$	5376.20	0.364892	0.182446	+	0.983216i	$0.441599\pi$
$602$	−904.031	−0.0612052
$603$	3650.15	0.246510
$604$	−25779.5	−1.73668
$605$	1274.26	0.0856298
$606$	−25557.4	−1.71320
$607$	−25422.2	−1.69992	−0.849962	−	0.526844i	$-0.823375\pi$
$607$	−25422.2	−1.69992	−0.849962	+	0.526844i	$0.823375\pi$
$608$	8231.75	0.549081
$609$	−13955.9	−0.928608
$610$	−4990.40	−0.331239
$611$	0	0
$612$	−6091.04	−0.402313
$613$	−20749.1	−1.36713	−0.683563	−	0.729891i	$-0.739571\pi$
$613$	−20749.1	−1.36713	−0.683563	+	0.729891i	$0.739571\pi$
$614$	27433.0	1.80311
$615$	2926.34	0.191872
$616$	−8178.04	−0.534907
$617$	24983.9	1.63017	0.815085	−	0.579342i	$-0.196690\pi$
$617$	24983.9	1.63017	0.815085	+	0.579342i	$0.196690\pi$
$618$	28326.7	1.84379
$619$	−10478.6	−0.680404	−0.340202	−	0.940352i	$-0.610495\pi$
$619$	−10478.6	−0.680404	−0.340202	+	0.940352i	$0.610495\pi$
$620$	3620.25	0.234504
$621$	22710.4	1.46753
$622$	−46631.1	−3.00601
$623$	−22816.8	−1.46731
$624$	0	0
$625$	−13664.2	−0.874511
$626$	41419.1	2.64448
$627$	−4084.64	−0.260167
$628$	−17336.7	−1.10161
$629$	12602.1	0.798852
$630$	5152.09	0.325816
$631$	−13113.1	−0.827296	−0.413648	−	0.910437i	$-0.635746\pi$
$631$	−13113.1	−0.827296	−0.413648	+	0.910437i	$0.635746\pi$
$632$	41647.7	2.62129
$633$	18442.7	1.15803
$634$	−22283.6	−1.39589
$635$	−3957.09	−0.247295
$636$	−25712.9	−1.60312
$637$	0	0
$638$	10421.5	0.646692
$639$	−6663.39	−0.412519
$640$	21228.2	1.31112
$641$	−15840.3	−0.976057	−0.488029	−	0.872828i	$-0.662284\pi$
$641$	−15840.3	−0.976057	−0.488029	+	0.872828i	$0.662284\pi$
$642$	17790.8	1.09369
$643$	4678.62	0.286947	0.143473	−	0.989654i	$-0.454173\pi$
$643$	4678.62	0.286947	0.143473	+	0.989654i	$0.454173\pi$
$644$	−41636.7	−2.54769
$645$	538.057	0.0328465
$646$	23895.5	1.45535
$647$	1441.09	0.0875658	0.0437829	−	0.999041i	$-0.486059\pi$
$647$	1441.09	0.0875658	0.0437829	+	0.999041i	$0.486059\pi$
$648$	24382.2	1.47812
$649$	−5379.38	−0.325361
$650$	0	0
$651$	1479.22	0.0890558
$652$	11832.7	0.710745
$653$	−7753.38	−0.464645	−0.232323	−	0.972639i	$-0.574632\pi$
$653$	−7753.38	−0.464645	−0.232323	+	0.972639i	$0.574632\pi$
$654$	−27544.3	−1.64689
$655$	6672.28	0.398027
$656$	5683.84	0.338288
$657$	6668.99	0.396015
$658$	−12822.4	−0.759679
$659$	−8218.44	−0.485804	−0.242902	−	0.970051i	$-0.578099\pi$
$659$	−8218.44	−0.485804	−0.242902	+	0.970051i	$0.578099\pi$
$660$	9110.24	0.537296
$661$	8047.49	0.473542	0.236771	−	0.971566i	$-0.423911\pi$
$661$	8047.49	0.473542	0.236771	+	0.971566i	$0.423911\pi$
$662$	−6215.32	−0.364902
$663$	0	0
$664$	25130.1	1.46873
$665$	−13789.7	−0.804123
$666$	6503.94	0.378412
$667$	28347.9	1.64563
$668$	−8407.99	−0.486998
$669$	30057.7	1.73706
$670$	31938.2	1.84161
$671$	1038.84	0.0597675
$672$	−7501.77	−0.430635
$673$	−20927.6	−1.19866	−0.599331	−	0.800501i	$-0.704567\pi$
$673$	−20927.6	−1.19866	−0.599331	+	0.800501i	$0.704567\pi$
$674$	−3310.57	−0.189197
$675$	2132.27	0.121587
$676$	0	0
$677$	−8251.48	−0.468435	−0.234217	−	0.972184i	$-0.575253\pi$
$677$	−8251.48	−0.468435	−0.234217	+	0.972184i	$0.575253\pi$
$678$	44917.3	2.54430
$679$	8072.03	0.456224
$680$	−28474.5	−1.60580
$681$	−5966.44	−0.335734
$682$	−1104.60	−0.0620194
$683$	−2823.57	−0.158186	−0.0790928	−	0.996867i	$-0.525202\pi$
$683$	−2823.57	−0.158186	−0.0790928	+	0.996867i	$0.525202\pi$
$684$	8413.90	0.470341
$685$	−12716.9	−0.709326
$686$	34457.4	1.91777
$687$	−15503.6	−0.860988
$688$	1045.07	0.0579113
$689$	0	0
$690$	36322.3	2.00401
$691$	5631.68	0.310042	0.155021	−	0.987911i	$-0.450455\pi$
$691$	5631.68	0.310042	0.155021	+	0.987911i	$0.450455\pi$
$692$	65275.2	3.58582
$693$	−1072.50	−0.0587892
$694$	12246.6	0.669851
$695$	15001.2	0.818746
$696$	39807.5	2.16796
$697$	3563.69	0.193665
$698$	25475.5	1.38146
$699$	13703.7	0.741517
$700$	−3909.26	−0.211080
$701$	30182.9	1.62624	0.813119	−	0.582098i	$-0.197768\pi$
$701$	30182.9	1.62624	0.813119	+	0.582098i	$0.197768\pi$
$702$	0	0
$703$	−17408.0	−0.933931
$704$	−2639.05	−0.141283
$705$	7631.58	0.407690
$706$	10582.8	0.564150
$707$	17961.0	0.955436
$708$	−38459.5	−2.04152
$709$	26706.4	1.41464	0.707320	−	0.706894i	$-0.249904\pi$
$709$	26706.4	1.41464	0.707320	+	0.706894i	$0.249904\pi$
$710$	−58303.5	−3.08182
$711$	5461.84	0.288094
$712$	65082.0	3.42563
$713$	−3004.66	−0.157820
$714$	−21776.4	−1.14140
$715$	0	0
$716$	58777.9	3.06792
$717$	−3125.71	−0.162806
$718$	10530.7	0.547354
$719$	−23268.3	−1.20690	−0.603451	−	0.797400i	$-0.706208\pi$
$719$	−23268.3	−1.20690	−0.603451	+	0.797400i	$0.706208\pi$
$720$	−5955.88	−0.308282
$721$	−19907.2	−1.02827
$722$	1408.41	0.0725978
$723$	−3599.51	−0.185155
$724$	−43984.2	−2.25782
$725$	2661.58	0.136343
$726$	−2779.69	−0.142099
$727$	25642.2	1.30814	0.654068	−	0.756435i	$-0.273061\pi$
$727$	25642.2	1.30814	0.654068	+	0.756435i	$0.273061\pi$
$728$	0	0
$729$	21895.8	1.11242
$730$	58352.5	2.95852
$731$	655.245	0.0331534
$732$	7427.13	0.375020
$733$	2894.18	0.145838	0.0729188	−	0.997338i	$-0.476769\pi$
$733$	2894.18	0.145838	0.0729188	+	0.997338i	$0.476769\pi$
$734$	32356.0	1.62709
$735$	−3970.68	−0.199266
$736$	15237.9	0.763148
$737$	−6648.49	−0.332294
$738$	1839.22	0.0917380
$739$	37471.8	1.86525	0.932626	−	0.360845i	$-0.117512\pi$
$739$	37471.8	1.86525	0.932626	+	0.360845i	$0.117512\pi$
$740$	38826.1	1.92875
$741$	0	0
$742$	26486.1	1.31043
$743$	−9000.92	−0.444430	−0.222215	−	0.974998i	$-0.571329\pi$
$743$	−9000.92	−0.444430	−0.222215	+	0.974998i	$0.571329\pi$
$744$	−4219.30	−0.207913
$745$	22240.7	1.09374
$746$	−29552.2	−1.45038
$747$	3295.66	0.161421
$748$	11094.4	0.542316
$749$	−12502.9	−0.609941
$750$	33651.1	1.63835
$751$	−8837.83	−0.429424	−0.214712	−	0.976677i	$-0.568881\pi$
$751$	−8837.83	−0.429424	−0.214712	+	0.976677i	$0.568881\pi$
$752$	14822.8	0.718794
$753$	−15340.7	−0.742423
$754$	0	0
$755$	−15804.7	−0.761844
$756$	−41948.7	−2.01807
$757$	17122.5	0.822096	0.411048	−	0.911614i	$-0.365163\pi$
$757$	17122.5	0.822096	0.411048	+	0.911614i	$0.365163\pi$
$758$	41023.2	1.96574
$759$	−7561.14	−0.361597
$760$	39333.4	1.87733
$761$	26203.3	1.24819	0.624093	−	0.781350i	$-0.285469\pi$
$761$	26203.3	1.24819	0.624093	+	0.781350i	$0.285469\pi$
$762$	8632.04	0.410375
$763$	19357.4	0.918459
$764$	45887.7	2.17298
$765$	−3734.25	−0.176487
$766$	−32602.5	−1.53783
$767$	0	0
$768$	−37520.2	−1.76288
$769$	−7503.24	−0.351851	−0.175926	−	0.984403i	$-0.556292\pi$
$769$	−7503.24	−0.351851	−0.175926	+	0.984403i	$0.556292\pi$
$770$	−9384.19	−0.439198
$771$	−11189.6	−0.522675
$772$	−4836.63	−0.225485
$773$	−9523.35	−0.443119	−0.221560	−	0.975147i	$-0.571115\pi$
$773$	−9523.35	−0.443119	−0.221560	+	0.975147i	$0.571115\pi$
$774$	338.172	0.0157046
$775$	−282.107	−0.0130756
$776$	−23024.5	−1.06512
$777$	15864.2	0.732467
$778$	−69049.3	−3.18192
$779$	−4922.72	−0.226412
$780$	0	0
$781$	12136.9	0.556073
$782$	44233.2	2.02273
$783$	28560.3	1.30353
$784$	−7712.27	−0.351324
$785$	−10628.6	−0.483252
$786$	−14555.0	−0.660508
$787$	−39644.6	−1.79565	−0.897827	−	0.440349i	$-0.854855\pi$
$787$	−39644.6	−1.79565	−0.897827	+	0.440349i	$0.854855\pi$
$788$	−40913.6	−1.84960
$789$	34434.6	1.55375
$790$	47790.2	2.15228
$791$	−31566.6	−1.41894
$792$	3059.17	0.137251
$793$	0	0
$794$	45204.2	2.02045
$795$	−15763.9	−0.703255
$796$	−89969.6	−4.00614
$797$	−6627.44	−0.294550	−0.147275	−	0.989096i	$-0.547050\pi$
$797$	−6627.44	−0.294550	−0.147275	+	0.989096i	$0.547050\pi$
$798$	30081.0	1.33441
$799$	9293.71	0.411499
$800$	1430.69	0.0632279
$801$	8535.10	0.376495
$802$	15573.5	0.685686
$803$	−12147.1	−0.533826
$804$	−47533.0	−2.08502
$805$	−25526.3	−1.11762
$806$	0	0
$807$	−19868.9	−0.866692
$808$	−51231.5	−2.23059
$809$	−32676.9	−1.42010	−0.710048	−	0.704153i	$-0.751327\pi$
$809$	−32676.9	−1.42010	−0.710048	+	0.704153i	$0.751327\pi$
$810$	27978.2	1.21365
$811$	16267.1	0.704335	0.352168	−	0.935937i	$-0.385445\pi$
$811$	16267.1	0.704335	0.352168	+	0.935937i	$0.385445\pi$
$812$	−52361.8	−2.26298
$813$	14277.7	0.615917
$814$	−11846.5	−0.510098
$815$	7254.33	0.311789
$816$	25173.8	1.07998
$817$	−905.126	−0.0387593
$818$	51280.1	2.19189
$819$	0	0
$820$	10979.5	0.467585
$821$	−33261.1	−1.41391	−0.706955	−	0.707259i	$-0.749932\pi$
$821$	−33261.1	−1.41391	−0.706955	+	0.707259i	$0.749932\pi$
$822$	27740.8	1.17710
$823$	−21702.7	−0.919210	−0.459605	−	0.888123i	$-0.652009\pi$
$823$	−21702.7	−0.919210	−0.459605	+	0.888123i	$0.652009\pi$
$824$	56782.8	2.40063
$825$	−709.914	−0.0299588
$826$	39616.0	1.66879
$827$	25955.0	1.09135	0.545674	−	0.837998i	$-0.316274\pi$
$827$	25955.0	1.09135	0.545674	+	0.837998i	$0.316274\pi$
$828$	15575.1	0.653710
$829$	−15680.5	−0.656944	−0.328472	−	0.944514i	$-0.606534\pi$
$829$	−15680.5	−0.656944	−0.328472	+	0.944514i	$0.606534\pi$
$830$	28836.4	1.20594
$831$	16416.0	0.685277
$832$	0	0
$833$	−4835.49	−0.201128
$834$	−32723.8	−1.35867
$835$	−5154.71	−0.213636
$836$	−15325.3	−0.634017
$837$	−3027.18	−0.125012
$838$	69979.2	2.88471
$839$	−20911.7	−0.860491	−0.430245	−	0.902712i	$-0.641573\pi$
$839$	−20911.7	−0.860491	−0.430245	+	0.902712i	$0.641573\pi$
$840$	−35845.4	−1.47236
$841$	11261.0	0.461723
$842$	19183.6	0.785166
$843$	37601.2	1.53624
$844$	69196.2	2.82207
$845$	0	0
$846$	4796.49	0.194925
$847$	1953.49	0.0792474
$848$	−30618.3	−1.23990
$849$	21030.8	0.850147
$850$	4153.05	0.167586
$851$	−32224.1	−1.29804
$852$	86772.1	3.48916
$853$	−29411.4	−1.18057	−0.590285	−	0.807195i	$-0.700985\pi$
$853$	−29411.4	−1.18057	−0.590285	+	0.807195i	$0.700985\pi$
$854$	−7650.46	−0.306550
$855$	5158.34	0.206329
$856$	35663.0	1.42399
$857$	−7780.31	−0.310117	−0.155059	−	0.987905i	$-0.549557\pi$
$857$	−7780.31	−0.310117	−0.155059	+	0.987905i	$0.549557\pi$
$858$	0	0
$859$	−34947.2	−1.38811	−0.694053	−	0.719924i	$-0.744177\pi$
$859$	−34947.2	−1.38811	−0.694053	+	0.719924i	$0.744177\pi$
$860$	2018.76	0.0800456
$861$	4486.18	0.177571
$862$	62942.3	2.48703
$863$	9197.61	0.362793	0.181397	−	0.983410i	$-0.441938\pi$
$863$	9197.61	0.362793	0.181397	+	0.983410i	$0.441938\pi$
$864$	15352.1	0.604502
$865$	40018.5	1.57303
$866$	−8741.11	−0.342997
$867$	−6709.53	−0.262823
$868$	5549.97	0.217025
$869$	−9948.37	−0.388349
$870$	45678.6	1.78006
$871$	0	0
$872$	−55214.5	−2.14427
$873$	−3019.52	−0.117062
$874$	−61101.9	−2.36476
$875$	−23649.0	−0.913696
$876$	−86844.9	−3.34956
$877$	26770.8	1.03077	0.515386	−	0.856958i	$-0.327649\pi$
$877$	26770.8	1.03077	0.515386	+	0.856958i	$0.327649\pi$
$878$	45585.9	1.75222
$879$	35641.6	1.36765
$880$	10848.2	0.415562
$881$	46566.0	1.78076	0.890379	−	0.455219i	$-0.150439\pi$
$881$	46566.0	1.78076	0.890379	+	0.455219i	$0.150439\pi$
$882$	−2495.60	−0.0952734
$883$	−12910.2	−0.492031	−0.246016	−	0.969266i	$-0.579121\pi$
$883$	−12910.2	−0.492031	−0.246016	+	0.969266i	$0.579121\pi$
$884$	0	0
$885$	−23578.5	−0.895574
$886$	48432.8	1.83649
$887$	−16756.5	−0.634303	−0.317152	−	0.948375i	$-0.602726\pi$
$887$	−16756.5	−0.634303	−0.317152	+	0.948375i	$0.602726\pi$
$888$	−45250.8	−1.71004
$889$	−6066.36	−0.228863
$890$	74680.7	2.81270
$891$	−5824.17	−0.218986
$892$	112775.	4.23316
$893$	−12837.9	−0.481080
$894$	−48516.0	−1.81501
$895$	36035.2	1.34584
$896$	32543.5	1.21340
$897$	0	0
$898$	−93038.6	−3.45739
$899$	−3778.63	−0.140183
$900$	1462.34	0.0541608
$901$	−19197.2	−0.709825
$902$	−3350.02	−0.123662
$903$	824.861	0.0303983
$904$	90039.8	3.31270
$905$	−26965.5	−0.990457
$906$	34476.6	1.26425
$907$	−5659.77	−0.207199	−0.103600	−	0.994619i	$-0.533036\pi$
$907$	−5659.77	−0.207199	−0.103600	+	0.994619i	$0.533036\pi$
$908$	−22385.8	−0.818169
$909$	−6718.70	−0.245154
$910$	0	0
$911$	−5396.54	−0.196263	−0.0981314	−	0.995173i	$-0.531287\pi$
$911$	−5396.54	−0.196263	−0.0981314	+	0.995173i	$0.531287\pi$
$912$	−34774.0	−1.26259
$913$	−6002.82	−0.217595
$914$	31682.4	1.14656
$915$	4553.37	0.164513
$916$	−58168.6	−2.09819
$917$	10228.8	0.368360
$918$	44564.8	1.60224
$919$	−34927.5	−1.25370	−0.626851	−	0.779139i	$-0.715656\pi$
$919$	−34927.5	−1.25370	−0.626851	+	0.779139i	$0.715656\pi$
$920$	72810.7	2.60924
$921$	−25030.6	−0.895534
$922$	−78639.9	−2.80897
$923$	0	0
$924$	13966.3	0.497249
$925$	−3025.52	−0.107544
$926$	−58661.6	−2.08179
$927$	7446.71	0.263843
$928$	19163.0	0.677864
$929$	−9208.41	−0.325208	−0.162604	−	0.986691i	$-0.551989\pi$
$929$	−9208.41	−0.325208	−0.162604	+	0.986691i	$0.551989\pi$
$930$	−4841.59	−0.170712
$931$	6679.53	0.235137
$932$	51415.4	1.80705
$933$	42547.4	1.49297
$934$	−12508.3	−0.438207
$935$	6801.69	0.237903
$936$	0	0
$937$	4060.11	0.141556	0.0707780	−	0.997492i	$-0.477452\pi$
$937$	4060.11	0.141556	0.0707780	+	0.997492i	$0.477452\pi$
$938$	48962.3	1.70435
$939$	−37791.9	−1.31341
$940$	28633.3	0.993525
$941$	1212.63	0.0420090	0.0210045	−	0.999779i	$-0.493314\pi$
$941$	1212.63	0.0420090	0.0210045	+	0.999779i	$0.493314\pi$
$942$	23185.4	0.801935
$943$	−9112.52	−0.314681
$944$	−45796.6	−1.57898
$945$	−25717.6	−0.885286
$946$	−615.958	−0.0211697
$947$	−44452.1	−1.52534	−0.762671	−	0.646787i	$-0.776112\pi$
$947$	−44452.1	−1.52534	−0.762671	+	0.646787i	$0.776112\pi$
$948$	−71125.2	−2.43675
$949$	0	0
$950$	−5736.84	−0.195924
$951$	20332.2	0.693287
$952$	−43652.4	−1.48612
$953$	−5101.64	−0.173408	−0.0867042	−	0.996234i	$-0.527634\pi$
$953$	−5101.64	−0.173408	−0.0867042	+	0.996234i	$0.527634\pi$
$954$	−9907.71	−0.336241
$955$	28132.5	0.953242
$956$	−11727.5	−0.396752
$957$	−9508.81	−0.321187
$958$	−5297.76	−0.178667
$959$	−19495.5	−0.656456
$960$	−11567.3	−0.388889
$961$	−29390.5	−0.986556
$962$	0	0
$963$	4676.98	0.156504
$964$	−13505.2	−0.451216
$965$	−2965.21	−0.0989155
$966$	55683.4	1.85464
$967$	6445.09	0.214333	0.107167	−	0.994241i	$-0.465822\pi$
$967$	6445.09	0.214333	0.107167	+	0.994241i	$0.465822\pi$
$968$	−5572.08	−0.185014
$969$	−21802.8	−0.722815
$970$	−26420.3	−0.874540
$971$	−8687.53	−0.287123	−0.143561	−	0.989641i	$-0.545855\pi$
$971$	−8687.53	−0.287123	−0.143561	+	0.989641i	$0.545855\pi$
$972$	28515.4	0.940978
$973$	22997.4	0.757721
$974$	−19945.7	−0.656163
$975$	0	0
$976$	8844.03	0.290052
$977$	27024.8	0.884955	0.442477	−	0.896780i	$-0.354100\pi$
$977$	27024.8	0.884955	0.442477	+	0.896780i	$0.354100\pi$
$978$	−15824.7	−0.517400
$979$	−15546.1	−0.507513
$980$	−14897.8	−0.485604
$981$	−7241.04	−0.235666
$982$	90329.2	2.93536
$983$	7460.18	0.242058	0.121029	−	0.992649i	$-0.461381\pi$
$983$	7460.18	0.242058	0.121029	+	0.992649i	$0.461381\pi$
$984$	−12796.3	−0.414563
$985$	−25083.1	−0.811384
$986$	55627.3	1.79669
$987$	11699.5	0.377303
$988$	0	0
$989$	−1675.49	−0.0538702
$990$	3510.36	0.112693
$991$	53498.6	1.71487	0.857437	−	0.514589i	$-0.172055\pi$
$991$	53498.6	1.71487	0.857437	+	0.514589i	$0.172055\pi$
$992$	−2031.14	−0.0650088
$993$	5671.01	0.181233
$994$	−89381.4	−2.85212
$995$	−55157.9	−1.75741
$996$	−42916.7	−1.36533
$997$	−10736.6	−0.341055	−0.170527	−	0.985353i	$-0.554547\pi$
$997$	−10736.6	−0.341055	−0.170527	+	0.985353i	$0.554547\pi$
$998$	−90379.6	−2.86665
$999$	−32465.7	−1.02820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.n.1.2	✓	39
13.12	even	2		1859.4.a.o.1.38	yes	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.2	✓	39	1.1	even	1	trivial
1859.4.a.o.1.38	yes	39	13.12	even	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)

\(f(q)\)	\(=\)	\(q-5.01772 q^{2} +4.57830 q^{3} +17.1775 q^{4} +10.5311 q^{5} -22.9726 q^{6} +16.1445 q^{7} -46.0502 q^{8} -6.03920 q^{9} +O(q^{10})\)	\(q-5.01772 q^{2} +4.57830 q^{3} +17.1775 q^{4} +10.5311 q^{5} -22.9726 q^{6} +16.1445 q^{7} -46.0502 q^{8} -6.03920 q^{9} -52.8420 q^{10} +11.0000 q^{11} +78.6438 q^{12} -81.0087 q^{14} +48.2144 q^{15} +93.6470 q^{16} +58.7153 q^{17} +30.3030 q^{18} -81.1068 q^{19} +180.898 q^{20} +73.9144 q^{21} -55.1949 q^{22} -150.138 q^{23} -210.832 q^{24} -14.0964 q^{25} -151.263 q^{27} +277.323 q^{28} -188.812 q^{29} -241.926 q^{30} +20.0127 q^{31} -101.493 q^{32} +50.3613 q^{33} -294.617 q^{34} +170.019 q^{35} -103.739 q^{36} +214.630 q^{37} +406.971 q^{38} -484.958 q^{40} +60.6943 q^{41} -370.882 q^{42} +11.1597 q^{43} +188.953 q^{44} -63.5993 q^{45} +753.351 q^{46} +158.284 q^{47} +428.744 q^{48} -82.3547 q^{49} +70.7320 q^{50} +268.816 q^{51} -326.954 q^{53} +758.997 q^{54} +115.842 q^{55} -743.458 q^{56} -371.331 q^{57} +947.406 q^{58} -489.035 q^{59} +828.204 q^{60} +94.4401 q^{61} -100.418 q^{62} -97.5000 q^{63} -239.914 q^{64} -252.699 q^{66} -604.408 q^{67} +1008.58 q^{68} -687.376 q^{69} -853.108 q^{70} +1103.36 q^{71} +278.107 q^{72} -1104.28 q^{73} -1076.95 q^{74} -64.5376 q^{75} -1393.21 q^{76} +177.590 q^{77} -904.398 q^{79} +986.204 q^{80} -529.470 q^{81} -304.547 q^{82} -545.710 q^{83} +1269.67 q^{84} +618.336 q^{85} -55.9962 q^{86} -864.437 q^{87} -506.552 q^{88} -1413.28 q^{89} +319.124 q^{90} -2579.00 q^{92} +91.6239 q^{93} -794.226 q^{94} -854.142 q^{95} -464.664 q^{96} +499.986 q^{97} +413.233 q^{98} -66.4312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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