LMFDB - Embedded newform 1859.4.a.o.1.8

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			1.8
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)

$f(q)$	$=$	$q-3.48032 q^{2} -2.00729 q^{3} +4.11265 q^{4} -5.42082 q^{5} +6.98601 q^{6} -27.8265 q^{7} +13.5292 q^{8} -22.9708 q^{9} +O(q^{10})$	\(q-3.48032 q^{2} -2.00729 q^{3} +4.11265 q^{4} -5.42082 q^{5} +6.98601 q^{6} -27.8265 q^{7} +13.5292 q^{8} -22.9708 q^{9} +18.8662 q^{10} -11.0000 q^{11} -8.25527 q^{12} +96.8452 q^{14} +10.8811 q^{15} -79.9873 q^{16} -53.2577 q^{17} +79.9458 q^{18} -1.47953 q^{19} -22.2939 q^{20} +55.8558 q^{21} +38.2836 q^{22} +30.0386 q^{23} -27.1571 q^{24} -95.6147 q^{25} +100.306 q^{27} -114.441 q^{28} -20.7365 q^{29} -37.8699 q^{30} +15.1132 q^{31} +170.148 q^{32} +22.0802 q^{33} +185.354 q^{34} +150.842 q^{35} -94.4708 q^{36} +316.249 q^{37} +5.14923 q^{38} -73.3396 q^{40} -13.2349 q^{41} -194.396 q^{42} -244.783 q^{43} -45.2391 q^{44} +124.520 q^{45} -104.544 q^{46} -140.160 q^{47} +160.558 q^{48} +431.315 q^{49} +332.770 q^{50} +106.904 q^{51} -137.662 q^{53} -349.096 q^{54} +59.6290 q^{55} -376.472 q^{56} +2.96984 q^{57} +72.1698 q^{58} +160.001 q^{59} +44.7503 q^{60} +243.281 q^{61} -52.5987 q^{62} +639.197 q^{63} +47.7296 q^{64} -76.8461 q^{66} +737.641 q^{67} -219.030 q^{68} -60.2962 q^{69} -524.980 q^{70} +331.001 q^{71} -310.778 q^{72} +557.931 q^{73} -1100.65 q^{74} +191.926 q^{75} -6.08477 q^{76} +306.092 q^{77} -95.3123 q^{79} +433.597 q^{80} +418.869 q^{81} +46.0616 q^{82} +86.4334 q^{83} +229.715 q^{84} +288.700 q^{85} +851.925 q^{86} +41.6242 q^{87} -148.822 q^{88} +43.6038 q^{89} -433.371 q^{90} +123.538 q^{92} -30.3365 q^{93} +487.801 q^{94} +8.02025 q^{95} -341.535 q^{96} -1822.96 q^{97} -1501.11 q^{98} +252.679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.48032	−1.23048	−0.615240	−	0.788340i	$-0.710941\pi$
$2$	−3.48032	−1.23048	−0.615240	+	0.788340i	$0.710941\pi$
$3$	−2.00729	−0.386303	−0.193151	−	0.981169i	$-0.561871\pi$
$3$	−2.00729	−0.386303	−0.193151	+	0.981169i	$0.561871\pi$
$4$	4.11265	0.514081
$5$	−5.42082	−0.484853	−0.242426	−	0.970170i	$-0.577943\pi$
$5$	−5.42082	−0.484853	−0.242426	+	0.970170i	$0.577943\pi$
$6$	6.98601	0.475338
$7$	−27.8265	−1.50249	−0.751245	−	0.660023i	$-0.770546\pi$
$7$	−27.8265	−1.50249	−0.751245	+	0.660023i	$0.770546\pi$
$8$	13.5292	0.597914
$9$	−22.9708	−0.850770
$10$	18.8662	0.596601
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−8.25527	−0.198591
$13$	0	0
$13$	0	0
$14$	96.8452	1.84878
$15$	10.8811	0.187300
$16$	−79.9873	−1.24980
$17$	−53.2577	−0.759817	−0.379909	−	0.925024i	$-0.624045\pi$
$17$	−53.2577	−0.759817	−0.379909	+	0.925024i	$0.624045\pi$
$18$	79.9458	1.04686
$19$	−1.47953	−0.0178646	−0.00893228	−	0.999960i	$-0.502843\pi$
$19$	−1.47953	−0.0178646	−0.00893228	+	0.999960i	$0.502843\pi$
$20$	−22.2939	−0.249253
$21$	55.8558	0.580416
$22$	38.2836	0.371004
$23$	30.0386	0.272325	0.136163	−	0.990686i	$-0.456523\pi$
$23$	30.0386	0.272325	0.136163	+	0.990686i	$0.456523\pi$
$24$	−27.1571	−0.230976
$25$	−95.6147	−0.764918
$26$	0	0
$27$	100.306	0.714958
$28$	−114.441	−0.772401
$29$	−20.7365	−0.132782	−0.0663909	−	0.997794i	$-0.521148\pi$
$29$	−20.7365	−0.132782	−0.0663909	+	0.997794i	$0.521148\pi$
$30$	−37.8699	−0.230469
$31$	15.1132	0.0875615	0.0437807	−	0.999041i	$-0.486060\pi$
$31$	15.1132	0.0875615	0.0437807	+	0.999041i	$0.486060\pi$
$32$	170.148	0.939942
$33$	22.0802	0.116475
$34$	185.354	0.934940
$35$	150.842	0.728486
$36$	−94.4708	−0.437365
$37$	316.249	1.40516	0.702581	−	0.711604i	$-0.252031\pi$
$37$	316.249	1.40516	0.702581	+	0.711604i	$0.252031\pi$
$38$	5.14923	0.0219820
$39$	0	0
$40$	−73.3396	−0.289900
$41$	−13.2349	−0.0504131	−0.0252065	−	0.999682i	$-0.508024\pi$
$41$	−13.2349	−0.0504131	−0.0252065	+	0.999682i	$0.508024\pi$
$42$	−194.396	−0.714190
$43$	−244.783	−0.868119	−0.434059	−	0.900884i	$-0.642919\pi$
$43$	−244.783	−0.868119	−0.434059	+	0.900884i	$0.642919\pi$
$44$	−45.2391	−0.155001
$45$	124.520	0.412498
$46$	−104.544	−0.335091
$47$	−140.160	−0.434987	−0.217494	−	0.976062i	$-0.569788\pi$
$47$	−140.160	−0.434987	−0.217494	+	0.976062i	$0.569788\pi$
$48$	160.558	0.482802
$49$	431.315	1.25748
$50$	332.770	0.941216
$51$	106.904	0.293519
$52$	0	0
$53$	−137.662	−0.356780	−0.178390	−	0.983960i	$-0.557089\pi$
$53$	−137.662	−0.356780	−0.178390	+	0.983960i	$0.557089\pi$
$54$	−349.096	−0.879741
$55$	59.6290	0.146189
$56$	−376.472	−0.898360
$57$	2.96984	0.00690113
$58$	72.1698	0.163385
$59$	160.001	0.353057	0.176528	−	0.984296i	$-0.443513\pi$
$59$	160.001	0.353057	0.176528	+	0.984296i	$0.443513\pi$
$60$	44.7503	0.0962873
$61$	243.281	0.510638	0.255319	−	0.966857i	$-0.417819\pi$
$61$	243.281	0.510638	0.255319	+	0.966857i	$0.417819\pi$
$62$	−52.5987	−0.107743
$63$	639.197	1.27827
$64$	47.7296	0.0932218
$65$	0	0
$66$	−76.8461	−0.143320
$67$	737.641	1.34503	0.672516	−	0.740082i	$-0.265213\pi$
$67$	737.641	1.34503	0.672516	+	0.740082i	$0.265213\pi$
$68$	−219.030	−0.390607
$69$	−60.2962	−0.105200
$70$	−524.980	−0.896388
$71$	331.001	0.553276	0.276638	−	0.960974i	$-0.410780\pi$
$71$	331.001	0.553276	0.276638	+	0.960974i	$0.410780\pi$
$72$	−310.778	−0.508687
$73$	557.931	0.894533	0.447266	−	0.894401i	$-0.352398\pi$
$73$	557.931	0.894533	0.447266	+	0.894401i	$0.352398\pi$
$74$	−1100.65	−1.72902
$75$	191.926	0.295490
$76$	−6.08477	−0.00918383
$77$	306.092	0.453018
$78$	0	0
$79$	−95.3123	−0.135740	−0.0678701	−	0.997694i	$-0.521620\pi$
$79$	−95.3123	−0.135740	−0.0678701	+	0.997694i	$0.521620\pi$
$80$	433.597	0.605970
$81$	418.869	0.574580
$82$	46.0616	0.0620323
$83$	86.4334	0.114305	0.0571524	−	0.998365i	$-0.481798\pi$
$83$	86.4334	0.114305	0.0571524	+	0.998365i	$0.481798\pi$
$84$	229.715	0.298381
$85$	288.700	0.368399
$86$	851.925	1.06820
$87$	41.6242	0.0512940
$88$	−148.822	−0.180278
$89$	43.6038	0.0519325	0.0259663	−	0.999663i	$-0.491734\pi$
$89$	43.6038	0.0519325	0.0259663	+	0.999663i	$0.491734\pi$
$90$	−433.371	−0.507571
$91$	0	0
$92$	123.538	0.139997
$93$	−30.3365	−0.0338252
$94$	487.801	0.535243
$95$	8.02025	0.00866168
$96$	−341.535	−0.363102
$97$	−1822.96	−1.90818	−0.954088	−	0.299526i	$-0.903172\pi$
$97$	−1822.96	−1.90818	−0.954088	+	0.299526i	$0.903172\pi$
$98$	−1501.11	−1.54730
$99$	252.679	0.256517
$100$	−393.230	−0.393230
$101$	1335.66	1.31587	0.657935	−	0.753075i	$-0.271430\pi$
$101$	1335.66	1.31587	0.657935	+	0.753075i	$0.271430\pi$
$102$	−372.059	−0.361170
$103$	−5.79633	−0.00554494	−0.00277247	−	0.999996i	$-0.500883\pi$
$103$	−5.79633	−0.00554494	−0.00277247	+	0.999996i	$0.500883\pi$
$104$	0	0
$105$	−302.784	−0.281416
$106$	479.108	0.439011
$107$	−893.665	−0.807419	−0.403710	−	0.914887i	$-0.632279\pi$
$107$	−893.665	−0.807419	−0.403710	+	0.914887i	$0.632279\pi$
$108$	412.522	0.367546
$109$	422.040	0.370863	0.185431	−	0.982657i	$-0.440632\pi$
$109$	422.040	0.370863	0.185431	+	0.982657i	$0.440632\pi$
$110$	−207.528	−0.179882
$111$	−634.802	−0.542818
$112$	2225.77	1.87782
$113$	−1495.26	−1.24480	−0.622398	−	0.782701i	$-0.713842\pi$
$113$	−1495.26	−1.24480	−0.622398	+	0.782701i	$0.713842\pi$
$114$	−10.3360	−0.00849170
$115$	−162.834	−0.132038
$116$	−85.2820	−0.0682606
$117$	0	0
$118$	−556.855	−0.434429
$119$	1481.98	1.14162
$120$	147.214	0.111989
$121$	121.000	0.0909091
$122$	−846.696	−0.628330
$123$	26.5662	0.0194747
$124$	62.1551	0.0450137
$125$	1195.91	0.855725
$126$	−2224.61	−1.57289
$127$	2783.50	1.94485	0.972424	−	0.233219i	$-0.0749258\pi$
$127$	2783.50	1.94485	0.972424	+	0.233219i	$0.0749258\pi$
$128$	−1527.30	−1.05465
$129$	491.351	0.335357
$130$	0	0
$131$	−1957.18	−1.30534	−0.652670	−	0.757642i	$-0.726351\pi$
$131$	−1957.18	−1.30534	−0.652670	+	0.757642i	$0.726351\pi$
$132$	90.8079	0.0598774
$133$	41.1701	0.0268413
$134$	−2567.23	−1.65504
$135$	−543.739	−0.346649
$136$	−720.537	−0.454305
$137$	2039.37	1.27179	0.635895	−	0.771776i	$-0.280631\pi$
$137$	2039.37	1.27179	0.635895	+	0.771776i	$0.280631\pi$
$138$	209.850	0.129447
$139$	−1736.20	−1.05944	−0.529721	−	0.848172i	$-0.677703\pi$
$139$	−1736.20	−1.05944	−0.529721	+	0.848172i	$0.677703\pi$
$140$	620.362	0.374501
$141$	281.341	0.168037
$142$	−1151.99	−0.680795
$143$	0	0
$144$	1837.37	1.06329
$145$	112.409	0.0643797
$146$	−1941.78	−1.10070
$147$	−865.773	−0.485767
$148$	1300.62	0.722367
$149$	3071.98	1.68903	0.844517	−	0.535529i	$-0.179888\pi$
$149$	3071.98	1.68903	0.844517	+	0.535529i	$0.179888\pi$
$150$	−667.966	−0.363594
$151$	3526.33	1.90045	0.950226	−	0.311560i	$-0.100851\pi$
$151$	3526.33	1.90045	0.950226	+	0.311560i	$0.100851\pi$
$152$	−20.0169	−0.0106815
$153$	1223.37	0.646430
$154$	−1065.30	−0.557429
$155$	−81.9257	−0.0424544
$156$	0	0
$157$	1317.87	0.669922	0.334961	−	0.942232i	$-0.391277\pi$
$157$	1317.87	0.669922	0.334961	+	0.942232i	$0.391277\pi$
$158$	331.718	0.167026
$159$	276.327	0.137825
$160$	−922.340	−0.455733
$161$	−835.870	−0.409166
$162$	−1457.80	−0.707009
$163$	2868.31	1.37830	0.689152	−	0.724617i	$-0.257983\pi$
$163$	2868.31	1.37830	0.689152	+	0.724617i	$0.257983\pi$
$164$	−54.4303	−0.0259164
$165$	−119.693	−0.0564730
$166$	−300.816	−0.140650
$167$	472.434	0.218911	0.109455	−	0.993992i	$-0.465089\pi$
$167$	472.434	0.218911	0.109455	+	0.993992i	$0.465089\pi$
$168$	755.687	0.347039
$169$	0	0
$170$	−1004.77	−0.453308
$171$	33.9859	0.0151986
$172$	−1006.71	−0.446283
$173$	1512.73	0.664800	0.332400	−	0.943138i	$-0.392142\pi$
$173$	1512.73	0.664800	0.332400	+	0.943138i	$0.392142\pi$
$174$	−144.866	−0.0631163
$175$	2660.62	1.14928
$176$	879.860	0.376829
$177$	−321.168	−0.136387
$178$	−151.755	−0.0639019
$179$	−632.898	−0.264274	−0.132137	−	0.991231i	$-0.542184\pi$
$179$	−632.898	−0.264274	−0.132137	+	0.991231i	$0.542184\pi$
$180$	512.109	0.212057
$181$	1207.72	0.495961	0.247980	−	0.968765i	$-0.420233\pi$
$181$	1207.72	0.495961	0.247980	+	0.968765i	$0.420233\pi$
$182$	0	0
$183$	−488.335	−0.197261
$184$	406.400	0.162827
$185$	−1714.33	−0.681296
$186$	105.581	0.0416213
$187$	585.835	0.229094
$188$	−576.428	−0.223619
$189$	−2791.16	−1.07422
$190$	−27.9130	−0.0106580
$191$	−1817.89	−0.688682	−0.344341	−	0.938845i	$-0.611898\pi$
$191$	−1817.89	−0.688682	−0.344341	+	0.938845i	$0.611898\pi$
$192$	−95.8070	−0.0360118
$193$	−1154.80	−0.430697	−0.215349	−	0.976537i	$-0.569089\pi$
$193$	−1154.80	−0.430697	−0.215349	+	0.976537i	$0.569089\pi$
$194$	6344.47	2.34797
$195$	0	0
$196$	1773.84	0.646445
$197$	−4111.89	−1.48711	−0.743554	−	0.668676i	$-0.766861\pi$
$197$	−4111.89	−1.48711	−0.743554	+	0.668676i	$0.766861\pi$
$198$	−879.404	−0.315639
$199$	−4290.78	−1.52847	−0.764234	−	0.644939i	$-0.776883\pi$
$199$	−4290.78	−1.52847	−0.764234	+	0.644939i	$0.776883\pi$
$200$	−1293.60	−0.457355
$201$	−1480.66	−0.519590
$202$	−4648.52	−1.61915
$203$	577.025	0.199504
$204$	439.657	0.150893
$205$	71.7437	0.0244429
$206$	20.1731	0.00682294
$207$	−690.011	−0.231686
$208$	0	0
$209$	16.2748	0.00538637
$210$	1053.79	0.346277
$211$	2323.37	0.758043	0.379022	−	0.925388i	$-0.376261\pi$
$211$	2323.37	0.758043	0.379022	+	0.925388i	$0.376261\pi$
$212$	−566.155	−0.183414
$213$	−664.414	−0.213732
$214$	3110.24	0.993513
$215$	1326.93	0.420910
$216$	1357.06	0.427483
$217$	−420.547	−0.131560
$218$	−1468.83	−0.456339
$219$	−1119.93	−0.345561
$220$	245.233	0.0751527
$221$	0	0
$222$	2209.32	0.667926
$223$	−2713.58	−0.814865	−0.407433	−	0.913235i	$-0.633576\pi$
$223$	−2713.58	−0.814865	−0.407433	+	0.913235i	$0.633576\pi$
$224$	−4734.62	−1.41225
$225$	2196.35	0.650769
$226$	5203.98	1.53170
$227$	4711.73	1.37766	0.688829	−	0.724924i	$-0.258125\pi$
$227$	4711.73	1.37766	0.688829	+	0.724924i	$0.258125\pi$
$228$	12.2139	0.00354774
$229$	6040.17	1.74299	0.871497	−	0.490401i	$-0.163150\pi$
$229$	6040.17	1.74299	0.871497	+	0.490401i	$0.163150\pi$
$230$	566.714	0.162470
$231$	−614.414	−0.175002
$232$	−280.549	−0.0793921
$233$	−2219.18	−0.623961	−0.311981	−	0.950088i	$-0.600992\pi$
$233$	−2219.18	−0.623961	−0.311981	+	0.950088i	$0.600992\pi$
$234$	0	0
$235$	759.781	0.210905
$236$	658.027	0.181500
$237$	191.319	0.0524368
$238$	−5157.76	−1.40474
$239$	3283.52	0.888673	0.444337	−	0.895860i	$-0.353439\pi$
$239$	3283.52	0.888673	0.444337	+	0.895860i	$0.353439\pi$
$240$	−870.353	−0.234088
$241$	−4833.24	−1.29185	−0.645925	−	0.763400i	$-0.723528\pi$
$241$	−4833.24	−1.29185	−0.645925	+	0.763400i	$0.723528\pi$
$242$	−421.119	−0.111862
$243$	−3549.05	−0.936919
$244$	1000.53	0.262509
$245$	−2338.08	−0.609691
$246$	−92.4588	−0.0239632
$247$	0	0
$248$	204.470	0.0523542
$249$	−173.497	−0.0441562
$250$	−4162.16	−1.05295
$251$	4625.78	1.16325	0.581627	−	0.813455i	$-0.302416\pi$
$251$	4625.78	1.16325	0.581627	+	0.813455i	$0.302416\pi$
$252$	2628.79	0.657136
$253$	−330.425	−0.0821092
$254$	−9687.48	−2.39310
$255$	−579.505	−0.142314
$256$	4933.65	1.20450
$257$	7568.81	1.83708	0.918539	−	0.395330i	$-0.129370\pi$
$257$	7568.81	1.83708	0.918539	+	0.395330i	$0.129370\pi$
$258$	−1710.06	−0.412650
$259$	−8800.10	−2.11124
$260$	0	0
$261$	476.334	0.112967
$262$	6811.61	1.60619
$263$	−2544.08	−0.596482	−0.298241	−	0.954491i	$-0.596400\pi$
$263$	−2544.08	−0.596482	−0.298241	+	0.954491i	$0.596400\pi$
$264$	298.728	0.0696418
$265$	746.241	0.172986
$266$	−143.285	−0.0330277
$267$	−87.5254	−0.0200617
$268$	3033.66	0.691455
$269$	−6373.49	−1.44460	−0.722302	−	0.691578i	$-0.756916\pi$
$269$	−6373.49	−1.44460	−0.722302	+	0.691578i	$0.756916\pi$
$270$	1892.39	0.426545
$271$	−5476.23	−1.22752	−0.613759	−	0.789493i	$-0.710343\pi$
$271$	−5476.23	−1.22752	−0.613759	+	0.789493i	$0.710343\pi$
$272$	4259.94	0.949621
$273$	0	0
$274$	−7097.67	−1.56491
$275$	1051.76	0.230631
$276$	−247.977	−0.0540813
$277$	1624.78	0.352431	0.176215	−	0.984352i	$-0.443614\pi$
$277$	1624.78	0.352431	0.176215	+	0.984352i	$0.443614\pi$
$278$	6042.53	1.30362
$279$	−347.161	−0.0744947
$280$	2040.78	0.435572
$281$	2244.79	0.476558	0.238279	−	0.971197i	$-0.423417\pi$
$281$	2244.79	0.476558	0.238279	+	0.971197i	$0.423417\pi$
$282$	−979.158	−0.206766
$283$	−2566.09	−0.539004	−0.269502	−	0.963000i	$-0.586859\pi$
$283$	−2566.09	−0.539004	−0.269502	+	0.963000i	$0.586859\pi$
$284$	1361.29	0.284428
$285$	−16.0989	−0.00334603
$286$	0	0
$287$	368.280	0.0757452
$288$	−3908.43	−0.799675
$289$	−2076.62	−0.422678
$290$	−391.219	−0.0792179
$291$	3659.20	0.737134
$292$	2294.57	0.459862
$293$	3504.91	0.698836	0.349418	−	0.936967i	$-0.386379\pi$
$293$	3504.91	0.698836	0.349418	+	0.936967i	$0.386379\pi$
$294$	3013.17	0.597726
$295$	−867.336	−0.171181
$296$	4278.61	0.840165
$297$	−1103.36	−0.215568
$298$	−10691.5	−2.07832
$299$	0	0
$300$	789.325	0.151906
$301$	6811.47	1.30434
$302$	−12272.8	−2.33847
$303$	−2681.05	−0.508324
$304$	118.343	0.0223272
$305$	−1318.78	−0.247584
$306$	−4257.73	−0.795419
$307$	−9606.11	−1.78583	−0.892915	−	0.450226i	$-0.851344\pi$
$307$	−9606.11	−1.78583	−0.892915	+	0.450226i	$0.851344\pi$
$308$	1258.85	0.232888
$309$	11.6349	0.00214203
$310$	285.128	0.0522393
$311$	−2296.74	−0.418766	−0.209383	−	0.977834i	$-0.567146\pi$
$311$	−2296.74	−0.418766	−0.209383	+	0.977834i	$0.567146\pi$
$312$	0	0
$313$	−6580.89	−1.18842	−0.594208	−	0.804312i	$-0.702534\pi$
$313$	−6580.89	−1.18842	−0.594208	+	0.804312i	$0.702534\pi$
$314$	−4586.62	−0.824325
$315$	−3464.97	−0.619774
$316$	−391.986	−0.0697814
$317$	379.186	0.0671837	0.0335918	−	0.999436i	$-0.489305\pi$
$317$	379.186	0.0671837	0.0335918	+	0.999436i	$0.489305\pi$
$318$	−961.709	−0.169591
$319$	228.102	0.0400352
$320$	−258.733	−0.0451988
$321$	1793.84	0.311908
$322$	2909.10	0.503471
$323$	78.7962	0.0135738
$324$	1722.66	0.295381
$325$	0	0
$326$	−9982.65	−1.69597
$327$	−847.155	−0.143265
$328$	−179.058	−0.0301427
$329$	3900.16	0.653564
$330$	416.569	0.0694889
$331$	−5639.23	−0.936435	−0.468218	−	0.883613i	$-0.655104\pi$
$331$	−5639.23	−0.936435	−0.468218	+	0.883613i	$0.655104\pi$
$332$	355.470	0.0587619
$333$	−7264.49	−1.19547
$334$	−1644.22	−0.269365
$335$	−3998.62	−0.652143
$336$	−4467.76	−0.725405
$337$	−6252.39	−1.01065	−0.505326	−	0.862929i	$-0.668628\pi$
$337$	−6252.39	−1.01065	−0.505326	+	0.862929i	$0.668628\pi$
$338$	0	0
$339$	3001.41	0.480868
$340$	1187.32	0.189387
$341$	−166.245	−0.0264008
$342$	−118.282	−0.0187016
$343$	−2457.49	−0.386857
$344$	−3311.73	−0.519060
$345$	326.854	0.0510065
$346$	−5264.77	−0.818023
$347$	−6457.42	−0.998998	−0.499499	−	0.866314i	$-0.666483\pi$
$347$	−6457.42	−0.998998	−0.499499	+	0.866314i	$0.666483\pi$
$348$	171.185	0.0263693
$349$	−603.157	−0.0925108	−0.0462554	−	0.998930i	$-0.514729\pi$
$349$	−603.157	−0.0925108	−0.0462554	+	0.998930i	$0.514729\pi$
$350$	−9259.83	−1.41417
$351$	0	0
$352$	−1871.62	−0.283403
$353$	−1605.35	−0.242051	−0.121026	−	0.992649i	$-0.538618\pi$
$353$	−1605.35	−0.242051	−0.121026	+	0.992649i	$0.538618\pi$
$354$	1117.77	0.167821
$355$	−1794.30	−0.268257
$356$	179.327	0.0266975
$357$	−2974.75	−0.441010
$358$	2202.69	0.325184
$359$	−4486.16	−0.659527	−0.329764	−	0.944064i	$-0.606969\pi$
$359$	−4486.16	−0.659527	−0.329764	+	0.944064i	$0.606969\pi$
$360$	1684.67	0.246638
$361$	−6856.81	−0.999681
$362$	−4203.24	−0.610270
$363$	−242.882	−0.0351184
$364$	0	0
$365$	−3024.44	−0.433717
$366$	1699.56	0.242726
$367$	6358.06	0.904327	0.452163	−	0.891935i	$-0.350652\pi$
$367$	6358.06	0.904327	0.452163	+	0.891935i	$0.350652\pi$
$368$	−2402.71	−0.340353
$369$	304.015	0.0428899
$370$	5966.41	0.838321
$371$	3830.66	0.536059
$372$	−124.763	−0.0173889
$373$	1540.77	0.213882	0.106941	−	0.994265i	$-0.465894\pi$
$373$	1540.77	0.213882	0.106941	+	0.994265i	$0.465894\pi$
$374$	−2038.89	−0.281895
$375$	−2400.54	−0.330569
$376$	−1896.26	−0.260085
$377$	0	0
$378$	9714.14	1.32180
$379$	−5144.42	−0.697232	−0.348616	−	0.937266i	$-0.613348\pi$
$379$	−5144.42	−0.697232	−0.348616	+	0.937266i	$0.613348\pi$
$380$	32.9844	0.00445281
$381$	−5587.29	−0.751300
$382$	6326.86	0.847409
$383$	−8782.20	−1.17167	−0.585835	−	0.810431i	$-0.699233\pi$
$383$	−8782.20	−1.17167	−0.585835	+	0.810431i	$0.699233\pi$
$384$	3065.72	0.407414
$385$	−1659.27	−0.219647
$386$	4019.09	0.529965
$387$	5622.87	0.738570
$388$	−7497.17	−0.980957
$389$	1409.63	0.183730	0.0918651	−	0.995771i	$-0.470717\pi$
$389$	1409.63	0.183730	0.0918651	+	0.995771i	$0.470717\pi$
$390$	0	0
$391$	−1599.79	−0.206918
$392$	5835.36	0.751863
$393$	3928.62	0.504256
$394$	14310.7	1.82986
$395$	516.671	0.0658140
$396$	1039.18	0.131870
$397$	6558.73	0.829152	0.414576	−	0.910015i	$-0.363930\pi$
$397$	6558.73	0.829152	0.414576	+	0.910015i	$0.363930\pi$
$398$	14933.3	1.88075
$399$	−82.6402	−0.0103689
$400$	7647.97	0.955996
$401$	−5288.58	−0.658602	−0.329301	−	0.944225i	$-0.606813\pi$
$401$	−5288.58	−0.658602	−0.329301	+	0.944225i	$0.606813\pi$
$402$	5153.17	0.639345
$403$	0	0
$404$	5493.09	0.676463
$405$	−2270.61	−0.278587
$406$	−2008.23	−0.245485
$407$	−3478.74	−0.423672
$408$	1446.32	0.175499
$409$	−11942.0	−1.44375	−0.721875	−	0.692024i	$-0.756719\pi$
$409$	−11942.0	−1.44375	−0.721875	+	0.692024i	$0.756719\pi$
$410$	−249.691	−0.0300765
$411$	−4093.61	−0.491296
$412$	−23.8382	−0.00285055
$413$	−4452.27	−0.530464
$414$	2401.46	0.285085
$415$	−468.539	−0.0554209
$416$	0	0
$417$	3485.05	0.409265
$418$	−56.6416	−0.00662782
$419$	8106.64	0.945191	0.472596	−	0.881279i	$-0.343317\pi$
$419$	8106.64	0.945191	0.472596	+	0.881279i	$0.343317\pi$
$420$	−1245.24	−0.144671
$421$	−6222.05	−0.720294	−0.360147	−	0.932895i	$-0.617274\pi$
$421$	−6222.05	−0.720294	−0.360147	+	0.932895i	$0.617274\pi$
$422$	−8086.06	−0.932757
$423$	3219.58	0.370074
$424$	−1862.46	−0.213324
$425$	5092.22	0.581198
$426$	2312.38	0.262993
$427$	−6769.66	−0.767229
$428$	−3675.33	−0.415079
$429$	0	0
$430$	−4618.13	−0.517921
$431$	−3488.05	−0.389823	−0.194911	−	0.980821i	$-0.562442\pi$
$431$	−3488.05	−0.389823	−0.194911	+	0.980821i	$0.562442\pi$
$432$	−8023.19	−0.893555
$433$	7957.11	0.883127	0.441564	−	0.897230i	$-0.354424\pi$
$433$	7957.11	0.883127	0.441564	+	0.897230i	$0.354424\pi$
$434$	1463.64	0.161882
$435$	−225.637	−0.0248700
$436$	1735.70	0.190654
$437$	−44.4429	−0.00486498
$438$	3897.71	0.425205
$439$	−5979.94	−0.650130	−0.325065	−	0.945692i	$-0.605386\pi$
$439$	−5979.94	−0.650130	−0.325065	+	0.945692i	$0.605386\pi$
$440$	806.735	0.0874082
$441$	−9907.64	−1.06982
$442$	0	0
$443$	14283.8	1.53192	0.765961	−	0.642887i	$-0.222263\pi$
$443$	14283.8	1.53192	0.765961	+	0.642887i	$0.222263\pi$
$444$	−2610.72	−0.279052
$445$	−236.368	−0.0251796
$446$	9444.14	1.00268
$447$	−6166.34	−0.652479
$448$	−1328.15	−0.140065
$449$	−16894.9	−1.77577	−0.887885	−	0.460066i	$-0.847826\pi$
$449$	−16894.9	−1.77577	−0.887885	+	0.460066i	$0.847826\pi$
$450$	−7644.00	−0.800759
$451$	145.583	0.0152001
$452$	−6149.47	−0.639926
$453$	−7078.35	−0.734150
$454$	−16398.3	−1.69518
$455$	0	0
$456$	40.1797	0.00412628
$457$	8790.53	0.899789	0.449894	−	0.893082i	$-0.351462\pi$
$457$	8790.53	0.899789	0.449894	+	0.893082i	$0.351462\pi$
$458$	−21021.7	−2.14472
$459$	−5342.06	−0.543237
$460$	−669.678	−0.0678780
$461$	−14509.0	−1.46583	−0.732917	−	0.680318i	$-0.761842\pi$
$461$	−14509.0	−1.46583	−0.732917	+	0.680318i	$0.761842\pi$
$462$	2138.36	0.215337
$463$	4998.67	0.501745	0.250872	−	0.968020i	$-0.419283\pi$
$463$	4998.67	0.501745	0.250872	+	0.968020i	$0.419283\pi$
$464$	1658.66	0.165951
$465$	164.449	0.0164003
$466$	7723.45	0.767772
$467$	2191.36	0.217140	0.108570	−	0.994089i	$-0.465373\pi$
$467$	2191.36	0.217140	0.108570	+	0.994089i	$0.465373\pi$
$468$	0	0
$469$	−20526.0	−2.02090
$470$	−2644.28	−0.259514
$471$	−2645.35	−0.258793
$472$	2164.69	0.211098
$473$	2692.62	0.261748
$474$	−665.853	−0.0645224
$475$	141.465	0.0136649
$476$	6094.85	0.586884
$477$	3162.21	0.303538
$478$	−11427.7	−1.09349
$479$	−8735.00	−0.833220	−0.416610	−	0.909085i	$-0.636782\pi$
$479$	−8735.00	−0.833220	−0.416610	+	0.909085i	$0.636782\pi$
$480$	1851.40	0.176051
$481$	0	0
$482$	16821.2	1.58960
$483$	1677.83	0.158062
$484$	497.630	0.0467346
$485$	9881.91	0.925184
$486$	12351.8	1.15286
$487$	−4040.90	−0.375997	−0.187998	−	0.982169i	$-0.560200\pi$
$487$	−4040.90	−0.375997	−0.187998	+	0.982169i	$0.560200\pi$
$488$	3291.41	0.305318
$489$	−5757.53	−0.532442
$490$	8137.27	0.750213
$491$	9650.24	0.886984	0.443492	−	0.896278i	$-0.353739\pi$
$491$	9650.24	0.886984	0.443492	+	0.896278i	$0.353739\pi$
$492$	109.257	0.0100116
$493$	1104.38	0.100890
$494$	0	0
$495$	−1369.73	−0.124373
$496$	−1208.86	−0.109434
$497$	−9210.60	−0.831292
$498$	603.824	0.0543334
$499$	17654.8	1.58384	0.791921	−	0.610624i	$-0.209081\pi$
$499$	17654.8	1.58384	0.791921	+	0.610624i	$0.209081\pi$
$500$	4918.36	0.439912
$501$	−948.312	−0.0845658
$502$	−16099.2	−1.43136
$503$	−9760.07	−0.865169	−0.432584	−	0.901593i	$-0.642398\pi$
$503$	−9760.07	−0.865169	−0.432584	+	0.901593i	$0.642398\pi$
$504$	8647.85	0.764298
$505$	−7240.35	−0.638003
$506$	1149.98	0.101034
$507$	0	0
$508$	11447.6	0.999809
$509$	−14116.3	−1.22926	−0.614629	−	0.788816i	$-0.710694\pi$
$509$	−14116.3	−1.22926	−0.614629	+	0.788816i	$0.710694\pi$
$510$	2016.86	0.175114
$511$	−15525.3	−1.34403
$512$	−4952.31	−0.427468
$513$	−148.405	−0.0127724
$514$	−26341.9	−2.26049
$515$	31.4208	0.00268848
$516$	2020.75	0.172400
$517$	1541.76	0.131154
$518$	30627.2	2.59784
$519$	−3036.48	−0.256814
$520$	0	0
$521$	16598.4	1.39576	0.697879	−	0.716216i	$-0.254127\pi$
$521$	16598.4	1.39576	0.697879	+	0.716216i	$0.254127\pi$
$522$	−1657.80	−0.139003
$523$	1224.52	0.102379	0.0511896	−	0.998689i	$-0.483699\pi$
$523$	1224.52	0.102379	0.0511896	+	0.998689i	$0.483699\pi$
$524$	−8049.18	−0.671050
$525$	−5340.64	−0.443971
$526$	8854.23	0.733960
$527$	−804.893	−0.0665307
$528$	−1766.13	−0.145570
$529$	−11264.7	−0.925839
$530$	−2597.16	−0.212855
$531$	−3675.35	−0.300370
$532$	169.318	0.0137986
$533$	0	0
$534$	304.617	0.0246855
$535$	4844.39	0.391479
$536$	9979.72	0.804214
$537$	1270.41	0.102090
$538$	22181.8	1.77756
$539$	−4744.46	−0.379144
$540$	−2236.21	−0.178206
$541$	15359.5	1.22062	0.610310	−	0.792163i	$-0.291045\pi$
$541$	15359.5	1.22062	0.610310	+	0.792163i	$0.291045\pi$
$542$	19059.1	1.51044
$543$	−2424.24	−0.191591
$544$	−9061.68	−0.714184
$545$	−2287.80	−0.179814
$546$	0	0
$547$	−8098.22	−0.633007	−0.316504	−	0.948591i	$-0.602509\pi$
$547$	−8098.22	−0.633007	−0.316504	+	0.948591i	$0.602509\pi$
$548$	8387.21	0.653803
$549$	−5588.36	−0.434436
$550$	−3660.47	−0.283787
$551$	30.6802	0.00237209
$552$	−815.761	−0.0629006
$553$	2652.21	0.203948
$554$	−5654.74	−0.433659
$555$	3441.15	0.263187
$556$	−7140.37	−0.544638
$557$	2897.41	0.220408	0.110204	−	0.993909i	$-0.464850\pi$
$557$	2897.41	0.220408	0.110204	+	0.993909i	$0.464850\pi$
$558$	1208.23	0.0916642
$559$	0	0
$560$	−12065.5	−0.910464
$561$	−1175.94	−0.0884995
$562$	−7812.58	−0.586395
$563$	24360.8	1.82360	0.911800	−	0.410634i	$-0.134692\pi$
$563$	24360.8	1.82360	0.911800	+	0.410634i	$0.134692\pi$
$564$	1157.06	0.0863845
$565$	8105.52	0.603543
$566$	8930.81	0.663233
$567$	−11655.7	−0.863301
$568$	4478.19	0.330811
$569$	−17100.7	−1.25993	−0.629963	−	0.776625i	$-0.716930\pi$
$569$	−17100.7	−1.25993	−0.629963	+	0.776625i	$0.716930\pi$
$570$	56.0295	0.00411723
$571$	17051.6	1.24972	0.624858	−	0.780738i	$-0.285157\pi$
$571$	17051.6	1.24972	0.624858	+	0.780738i	$0.285157\pi$
$572$	0	0
$573$	3649.04	0.266040
$574$	−1281.73	−0.0932029
$575$	−2872.13	−0.208307
$576$	−1096.39	−0.0793103
$577$	−21905.8	−1.58051	−0.790253	−	0.612780i	$-0.790051\pi$
$577$	−21905.8	−1.58051	−0.790253	+	0.612780i	$0.790051\pi$
$578$	7227.29	0.520096
$579$	2318.02	0.166380
$580$	462.298	0.0330963
$581$	−2405.14	−0.171742
$582$	−12735.2	−0.907028
$583$	1514.28	0.107573
$584$	7548.39	0.534854
$585$	0	0
$586$	−12198.2	−0.859904
$587$	16756.5	1.17822	0.589109	−	0.808054i	$-0.299479\pi$
$587$	16756.5	1.17822	0.589109	+	0.808054i	$0.299479\pi$
$588$	−3560.62	−0.249723
$589$	−22.3603	−0.00156425
$590$	3018.61	0.210634
$591$	8253.76	0.574474
$592$	−25295.9	−1.75617
$593$	19120.8	1.32411	0.662054	−	0.749456i	$-0.269685\pi$
$593$	19120.8	1.32411	0.662054	+	0.749456i	$0.269685\pi$
$594$	3840.06	0.265252
$595$	−8033.52	−0.553517
$596$	12634.0	0.868300
$597$	8612.83	0.590452
$598$	0	0
$599$	5951.96	0.405994	0.202997	−	0.979179i	$-0.434932\pi$
$599$	5951.96	0.405994	0.202997	+	0.979179i	$0.434932\pi$
$600$	2596.62	0.176677
$601$	−3344.37	−0.226988	−0.113494	−	0.993539i	$-0.536204\pi$
$601$	−3344.37	−0.226988	−0.113494	+	0.993539i	$0.536204\pi$
$602$	−23706.1	−1.60496
$603$	−16944.2	−1.14431
$604$	14502.5	0.976986
$605$	−655.919	−0.0440775
$606$	9330.91	0.625483
$607$	6128.63	0.409808	0.204904	−	0.978782i	$-0.434312\pi$
$607$	6128.63	0.409808	0.204904	+	0.978782i	$0.434312\pi$
$608$	−251.738	−0.0167917
$609$	−1158.26	−0.0770688
$610$	4589.78	0.304647
$611$	0	0
$612$	5031.30	0.332317
$613$	−22818.4	−1.50347	−0.751735	−	0.659466i	$-0.770783\pi$
$613$	−22818.4	−1.50347	−0.751735	+	0.659466i	$0.770783\pi$
$614$	33432.4	2.19743
$615$	−144.010	−0.00944237
$616$	4141.19	0.270866
$617$	−16451.2	−1.07342	−0.536709	−	0.843768i	$-0.680333\pi$
$617$	−16451.2	−1.07342	−0.536709	+	0.843768i	$0.680333\pi$
$618$	−40.4932	−0.00263572
$619$	−23920.5	−1.55323	−0.776614	−	0.629977i	$-0.783064\pi$
$619$	−23920.5	−1.55323	−0.776614	+	0.629977i	$0.783064\pi$
$620$	−336.932	−0.0218250
$621$	3013.05	0.194701
$622$	7993.40	0.515283
$623$	−1213.34	−0.0780281
$624$	0	0
$625$	5469.02	0.350017
$626$	22903.6	1.46232
$627$	−32.6682	−0.00208077
$628$	5419.95	0.344394
$629$	−16842.7	−1.06767
$630$	12059.2	0.762620
$631$	15690.3	0.989889	0.494944	−	0.868925i	$-0.335188\pi$
$631$	15690.3	0.989889	0.494944	+	0.868925i	$0.335188\pi$
$632$	−1289.50	−0.0811609
$633$	−4663.66	−0.292834
$634$	−1319.69	−0.0826682
$635$	−15088.8	−0.942965
$636$	1136.44	0.0708532
$637$	0	0
$638$	−793.868	−0.0492626
$639$	−7603.35	−0.470711
$640$	8279.19	0.511350
$641$	24238.4	1.49354	0.746770	−	0.665083i	$-0.231604\pi$
$641$	24238.4	1.49354	0.746770	+	0.665083i	$0.231604\pi$
$642$	−6243.15	−0.383797
$643$	23979.6	1.47071	0.735353	−	0.677684i	$-0.237016\pi$
$643$	23979.6	1.47071	0.735353	+	0.677684i	$0.237016\pi$
$644$	−3437.64	−0.210345
$645$	−2663.52	−0.162599
$646$	−274.236	−0.0167023
$647$	25068.5	1.52325	0.761626	−	0.648016i	$-0.224401\pi$
$647$	25068.5	1.52325	0.761626	+	0.648016i	$0.224401\pi$
$648$	5666.98	0.343549
$649$	−1760.01	−0.106451
$650$	0	0
$651$	844.158	0.0508221
$652$	11796.3	0.708559
$653$	9787.92	0.586571	0.293286	−	0.956025i	$-0.405251\pi$
$653$	9787.92	0.586571	0.293286	+	0.956025i	$0.405251\pi$
$654$	2948.37	0.176285
$655$	10609.5	0.632897
$656$	1058.62	0.0630064
$657$	−12816.1	−0.761042
$658$	−13573.8	−0.804198
$659$	−14504.0	−0.857354	−0.428677	−	0.903458i	$-0.641020\pi$
$659$	−14504.0	−0.857354	−0.428677	+	0.903458i	$0.641020\pi$
$660$	−492.253	−0.0290317
$661$	16299.0	0.959091	0.479545	−	0.877517i	$-0.340802\pi$
$661$	16299.0	0.959091	0.479545	+	0.877517i	$0.340802\pi$
$662$	19626.3	1.15226
$663$	0	0
$664$	1169.38	0.0683444
$665$	−223.175	−0.0130141
$666$	25282.8	1.47100
$667$	−622.896	−0.0361599
$668$	1942.96	0.112538
$669$	5446.94	0.314785
$670$	13916.5	0.802448
$671$	−2676.09	−0.153963
$672$	9503.74	0.545558
$673$	−21674.3	−1.24143	−0.620716	−	0.784036i	$-0.713158\pi$
$673$	−21674.3	−1.24143	−0.620716	+	0.784036i	$0.713158\pi$
$674$	21760.3	1.24359
$675$	−9590.71	−0.546884
$676$	0	0
$677$	22774.7	1.29291	0.646457	−	0.762950i	$-0.276250\pi$
$677$	22774.7	1.29291	0.646457	+	0.762950i	$0.276250\pi$
$678$	−10445.9	−0.591699
$679$	50726.5	2.86702
$680$	3905.90	0.220271
$681$	−9457.80	−0.532193
$682$	578.586	0.0324856
$683$	22355.7	1.25244	0.626219	−	0.779647i	$-0.284601\pi$
$683$	22355.7	1.25244	0.626219	+	0.779647i	$0.284601\pi$
$684$	139.772	0.00781333
$685$	−11055.1	−0.616631
$686$	8552.86	0.476020
$687$	−12124.4	−0.673323
$688$	19579.6	1.08498
$689$	0	0
$690$	−1137.56	−0.0627625
$691$	−15408.4	−0.848283	−0.424141	−	0.905596i	$-0.639424\pi$
$691$	−15408.4	−0.848283	−0.424141	+	0.905596i	$0.639424\pi$
$692$	6221.31	0.341761
$693$	−7031.17	−0.385414
$694$	22473.9	1.22925
$695$	9411.61	0.513673
$696$	563.144	0.0306694
$697$	704.858	0.0383047
$698$	2099.18	0.113833
$699$	4454.52	0.241038
$700$	10942.2	0.590824
$701$	−9607.49	−0.517646	−0.258823	−	0.965925i	$-0.583335\pi$
$701$	−9607.49	−0.517646	−0.258823	+	0.965925i	$0.583335\pi$
$702$	0	0
$703$	−467.899	−0.0251026
$704$	−525.025	−0.0281074
$705$	−1525.10	−0.0814731
$706$	5587.13	0.297839
$707$	−37166.7	−1.97708
$708$	−1320.85	−0.0701139
$709$	−4914.88	−0.260342	−0.130171	−	0.991492i	$-0.541553\pi$
$709$	−4914.88	−0.260342	−0.130171	+	0.991492i	$0.541553\pi$
$710$	6244.73	0.330085
$711$	2189.40	0.115484
$712$	589.927	0.0310512
$713$	453.979	0.0238452
$714$	10353.1	0.542654
$715$	0	0
$716$	−2602.89	−0.135858
$717$	−6590.96	−0.343297
$718$	15613.3	0.811535
$719$	8126.92	0.421534	0.210767	−	0.977536i	$-0.432404\pi$
$719$	8126.92	0.421534	0.210767	+	0.977536i	$0.432404\pi$
$720$	−9960.06	−0.515541
$721$	161.292	0.00833122
$722$	23863.9	1.23009
$723$	9701.70	0.499046
$724$	4966.91	0.254964
$725$	1982.72	0.101567
$726$	845.307	0.0432125
$727$	−18767.2	−0.957412	−0.478706	−	0.877975i	$-0.658894\pi$
$727$	−18767.2	−0.957412	−0.478706	+	0.877975i	$0.658894\pi$
$728$	0	0
$729$	−4185.50	−0.212645
$730$	10526.0	0.533680
$731$	13036.6	0.659612
$732$	−2008.35	−0.101408
$733$	−29741.1	−1.49865	−0.749325	−	0.662202i	$-0.769622\pi$
$733$	−29741.1	−1.49865	−0.749325	+	0.662202i	$0.769622\pi$
$734$	−22128.1	−1.11276
$735$	4693.20	0.235525
$736$	5111.00	0.255970
$737$	−8114.05	−0.405543
$738$	−1058.07	−0.0527752
$739$	8644.26	0.430290	0.215145	−	0.976582i	$-0.430978\pi$
$739$	8644.26	0.430290	0.215145	+	0.976582i	$0.430978\pi$
$740$	−7050.42	−0.350241
$741$	0	0
$742$	−13331.9	−0.659609
$743$	−2817.71	−0.139128	−0.0695638	−	0.997578i	$-0.522161\pi$
$743$	−2817.71	−0.139128	−0.0695638	+	0.997578i	$0.522161\pi$
$744$	−410.430	−0.0202246
$745$	−16652.6	−0.818933
$746$	−5362.37	−0.263178
$747$	−1985.44	−0.0972471
$748$	2409.33	0.117773
$749$	24867.6	1.21314
$750$	8354.65	0.406758
$751$	30956.7	1.50416	0.752081	−	0.659070i	$-0.229050\pi$
$751$	30956.7	1.50416	0.752081	+	0.659070i	$0.229050\pi$
$752$	11211.0	0.543648
$753$	−9285.28	−0.449369
$754$	0	0
$755$	−19115.6	−0.921440
$756$	−11479.1	−0.552234
$757$	−3739.15	−0.179527	−0.0897635	−	0.995963i	$-0.528611\pi$
$757$	−3739.15	−0.179527	−0.0897635	+	0.995963i	$0.528611\pi$
$758$	17904.2	0.857930
$759$	663.258	0.0317190
$760$	108.508	0.00517894
$761$	35580.7	1.69487	0.847437	−	0.530896i	$-0.178145\pi$
$761$	35580.7	1.69487	0.847437	+	0.530896i	$0.178145\pi$
$762$	19445.6	0.924460
$763$	−11743.9	−0.557218
$764$	−7476.36	−0.354038
$765$	−6631.68	−0.313423
$766$	30564.9	1.44172
$767$	0	0
$768$	−9903.25	−0.465303
$769$	−38845.9	−1.82161	−0.910805	−	0.412838i	$-0.864538\pi$
$769$	−38845.9	−1.82161	−0.910805	+	0.412838i	$0.864538\pi$
$770$	5774.78	0.270271
$771$	−15192.8	−0.709668
$772$	−4749.30	−0.221413
$773$	21646.1	1.00719	0.503594	−	0.863941i	$-0.332011\pi$
$773$	21646.1	1.00719	0.503594	+	0.863941i	$0.332011\pi$
$774$	−19569.4	−0.908795
$775$	−1445.04	−0.0669773
$776$	−24663.2	−1.14092
$777$	17664.3	0.815578
$778$	−4905.97	−0.226076
$779$	19.5813	0.000900608 0
$780$	0	0
$781$	−3641.01	−0.166819
$782$	5567.78	0.254608
$783$	−2079.99	−0.0949334
$784$	−34499.7	−1.57160
$785$	−7143.95	−0.324813
$786$	−13672.9	−0.620477
$787$	29081.0	1.31719	0.658593	−	0.752500i	$-0.271152\pi$
$787$	29081.0	1.31719	0.658593	+	0.752500i	$0.271152\pi$
$788$	−16910.8	−0.764494
$789$	5106.71	0.230423
$790$	−1798.18	−0.0809828
$791$	41607.8	1.87030
$792$	3418.55	0.153375
$793$	0	0
$794$	−22826.5	−1.02025
$795$	−1497.92	−0.0668249
$796$	−17646.5	−0.785756
$797$	24462.7	1.08722	0.543609	−	0.839339i	$-0.317058\pi$
$797$	24462.7	1.08722	0.543609	+	0.839339i	$0.317058\pi$
$798$	287.615	0.0127587
$799$	7464.59	0.330511
$800$	−16268.6	−0.718979
$801$	−1001.61	−0.0441827
$802$	18406.0	0.810396
$803$	−6137.24	−0.269712
$804$	−6089.42	−0.267111
$805$	4531.10	0.198385
$806$	0	0
$807$	12793.4	0.558054
$808$	18070.4	0.786777
$809$	−33136.4	−1.44006	−0.720032	−	0.693941i	$-0.755873\pi$
$809$	−33136.4	−1.44006	−0.720032	+	0.693941i	$0.755873\pi$
$810$	7902.46	0.342795
$811$	10499.7	0.454616	0.227308	−	0.973823i	$-0.427008\pi$
$811$	10499.7	0.454616	0.227308	+	0.973823i	$0.427008\pi$
$812$	2373.10	0.102561
$813$	10992.4	0.474194
$814$	12107.1	0.521320
$815$	−15548.6	−0.668274
$816$	−8550.93	−0.366841
$817$	362.164	0.0155086
$818$	41562.0	1.77650
$819$	0	0
$820$	295.056	0.0125656
$821$	16718.4	0.710690	0.355345	−	0.934735i	$-0.384363\pi$
$821$	16718.4	0.710690	0.355345	+	0.934735i	$0.384363\pi$
$822$	14247.1	0.604530
$823$	−38160.0	−1.61625	−0.808126	−	0.589009i	$-0.799518\pi$
$823$	−38160.0	−1.61625	−0.808126	+	0.589009i	$0.799518\pi$
$824$	−78.4199	−0.00331540
$825$	−2111.19	−0.0890936
$826$	15495.3	0.652726
$827$	26314.4	1.10646	0.553229	−	0.833029i	$-0.313395\pi$
$827$	26314.4	1.10646	0.553229	+	0.833029i	$0.313395\pi$
$828$	−2837.77	−0.119105
$829$	34630.3	1.45086	0.725428	−	0.688298i	$-0.241642\pi$
$829$	34630.3	1.45086	0.725428	+	0.688298i	$0.241642\pi$
$830$	1630.67	0.0681944
$831$	−3261.39	−0.136145
$832$	0	0
$833$	−22970.8	−0.955453
$834$	−12129.1	−0.503592
$835$	−2560.98	−0.106139
$836$	66.9325	0.00276903
$837$	1515.94	0.0626027
$838$	−28213.7	−1.16304
$839$	16788.4	0.690824	0.345412	−	0.938451i	$-0.387739\pi$
$839$	16788.4	0.690824	0.345412	+	0.938451i	$0.387739\pi$
$840$	−4096.44	−0.168263
$841$	−23959.0	−0.982369
$842$	21654.7	0.886308
$843$	−4505.93	−0.184096
$844$	9555.18	0.389695
$845$	0	0
$846$	−11205.2	−0.455369
$847$	−3367.01	−0.136590
$848$	11011.2	0.445904
$849$	5150.88	0.208219
$850$	−17722.6	−0.715152
$851$	9499.67	0.382661
$852$	−2732.50	−0.109876
$853$	−5728.65	−0.229947	−0.114974	−	0.993369i	$-0.536678\pi$
$853$	−5728.65	−0.229947	−0.114974	+	0.993369i	$0.536678\pi$
$854$	23560.6	0.944060
$855$	−184.231	−0.00736910
$856$	−12090.6	−0.482767
$857$	26476.1	1.05532	0.527658	−	0.849457i	$-0.323070\pi$
$857$	26476.1	1.05532	0.527658	+	0.849457i	$0.323070\pi$
$858$	0	0
$859$	−26503.6	−1.05273	−0.526363	−	0.850260i	$-0.676445\pi$
$859$	−26503.6	−1.05273	−0.526363	+	0.850260i	$0.676445\pi$
$860$	5457.18	0.216382
$861$	−739.243	−0.0292606
$862$	12139.5	0.479669
$863$	23480.4	0.926165	0.463083	−	0.886315i	$-0.346743\pi$
$863$	23480.4	0.926165	0.463083	+	0.886315i	$0.346743\pi$
$864$	17066.8	0.672019
$865$	−8200.21	−0.322330
$866$	−27693.3	−1.08667
$867$	4168.37	0.163282
$868$	−1729.56	−0.0676326
$869$	1048.44	0.0409272
$870$	785.290	0.0306021
$871$	0	0
$872$	5709.88	0.221744
$873$	41874.7	1.62342
$874$	154.676	0.00598626
$875$	−33278.1	−1.28572
$876$	−4605.87	−0.177646
$877$	3989.11	0.153595	0.0767973	−	0.997047i	$-0.475531\pi$
$877$	3989.11	0.153595	0.0767973	+	0.997047i	$0.475531\pi$
$878$	20812.1	0.799972
$879$	−7035.36	−0.269962
$880$	−4769.56	−0.182707
$881$	−32116.4	−1.22818	−0.614092	−	0.789235i	$-0.710478\pi$
$881$	−32116.4	−1.22818	−0.614092	+	0.789235i	$0.710478\pi$
$882$	34481.8	1.31640
$883$	31229.1	1.19019	0.595097	−	0.803654i	$-0.297114\pi$
$883$	31229.1	1.19019	0.595097	+	0.803654i	$0.297114\pi$
$884$	0	0
$885$	1740.99	0.0661275
$886$	−49712.1	−1.88500
$887$	22513.6	0.852234	0.426117	−	0.904668i	$-0.359881\pi$
$887$	22513.6	0.852234	0.426117	+	0.904668i	$0.359881\pi$
$888$	−8588.40	−0.324558
$889$	−77455.1	−2.92212
$890$	822.638	0.0309830
$891$	−4607.56	−0.173242
$892$	−11160.0	−0.418907
$893$	207.370	0.00777086
$894$	21460.9	0.802862
$895$	3430.82	0.128134
$896$	42499.3	1.58460
$897$	0	0
$898$	58799.8	2.18505
$899$	−313.395	−0.0116266
$900$	9032.80	0.334548
$901$	7331.57	0.271088
$902$	−506.677	−0.0187034
$903$	−13672.6	−0.503870
$904$	−20229.7	−0.744281
$905$	−6546.81	−0.240468
$906$	24635.0	0.903357
$907$	−28677.5	−1.04986	−0.524929	−	0.851146i	$-0.675908\pi$
$907$	−28677.5	−1.04986	−0.524929	+	0.851146i	$0.675908\pi$
$908$	19377.7	0.708228
$909$	−30681.1	−1.11950
$910$	0	0
$911$	17188.5	0.625116	0.312558	−	0.949899i	$-0.398814\pi$
$911$	17188.5	0.625116	0.312558	+	0.949899i	$0.398814\pi$
$912$	−237.549	−0.00862505
$913$	−950.767	−0.0344642
$914$	−30593.9	−1.10717
$915$	2647.17	0.0956425
$916$	24841.1	0.896040
$917$	54461.5	1.96126
$918$	18592.1	0.668442
$919$	−7814.39	−0.280493	−0.140246	−	0.990117i	$-0.544789\pi$
$919$	−7814.39	−0.280493	−0.140246	+	0.990117i	$0.544789\pi$
$920$	−2203.02	−0.0789472
$921$	19282.2	0.689871
$922$	50495.9	1.80368
$923$	0	0
$924$	−2526.87	−0.0899652
$925$	−30238.0	−1.07483
$926$	−17397.0	−0.617387
$927$	133.146	0.00471747
$928$	−3528.27	−0.124807
$929$	19972.3	0.705351	0.352676	−	0.935746i	$-0.385272\pi$
$929$	19972.3	0.705351	0.352676	+	0.935746i	$0.385272\pi$
$930$	−572.334	−0.0201802
$931$	−638.142	−0.0224643
$932$	−9126.68	−0.320767
$933$	4610.22	0.161770
$934$	−7626.65	−0.267186
$935$	−3175.70	−0.111077
$936$	0	0
$937$	−27263.5	−0.950543	−0.475272	−	0.879839i	$-0.657650\pi$
$937$	−27263.5	−0.950543	−0.475272	+	0.879839i	$0.657650\pi$
$938$	71437.0	2.48667
$939$	13209.7	0.459088
$940$	3124.71	0.108422
$941$	10468.4	0.362657	0.181329	−	0.983423i	$-0.441960\pi$
$941$	10468.4	0.362657	0.181329	+	0.983423i	$0.441960\pi$
$942$	9206.67	0.318439
$943$	−397.557	−0.0137288
$944$	−12798.0	−0.441251
$945$	15130.4	0.520837
$946$	−9371.18	−0.322075
$947$	10093.9	0.346365	0.173183	−	0.984890i	$-0.444595\pi$
$947$	10093.9	0.346365	0.173183	+	0.984890i	$0.444595\pi$
$948$	786.828	0.0269567
$949$	0	0
$950$	−492.343	−0.0168144
$951$	−761.136	−0.0259532
$952$	20050.0	0.682589
$953$	32203.5	1.09462	0.547311	−	0.836930i	$-0.315652\pi$
$953$	32203.5	1.09462	0.547311	+	0.836930i	$0.315652\pi$
$954$	−11005.5	−0.373497
$955$	9854.47	0.333909
$956$	13503.9	0.456850
$957$	−457.866	−0.0154657
$958$	30400.6	1.02526
$959$	−56748.6	−1.91085
$960$	519.352	0.0174604
$961$	−29562.6	−0.992333
$962$	0	0
$963$	20528.2	0.686928
$964$	−19877.4	−0.664116
$965$	6259.98	0.208825
$966$	−5839.40	−0.194492
$967$	−28002.5	−0.931231	−0.465615	−	0.884987i	$-0.654167\pi$
$967$	−28002.5	−0.931231	−0.465615	+	0.884987i	$0.654167\pi$
$968$	1637.04	0.0543558
$969$	−158.167	−0.00524360
$970$	−34392.2	−1.13842
$971$	−2548.89	−0.0842409	−0.0421205	−	0.999113i	$-0.513411\pi$
$971$	−2548.89	−0.0842409	−0.0421205	+	0.999113i	$0.513411\pi$
$972$	−14596.0	−0.481652
$973$	48312.3	1.59180
$974$	14063.6	0.462657
$975$	0	0
$976$	−19459.4	−0.638197
$977$	37461.7	1.22672	0.613361	−	0.789803i	$-0.289817\pi$
$977$	37461.7	1.22672	0.613361	+	0.789803i	$0.289817\pi$
$978$	20038.0	0.655160
$979$	−479.642	−0.0156582
$980$	−9615.69	−0.313431
$981$	−9694.58	−0.315519
$982$	−33585.9	−1.09142
$983$	−38714.0	−1.25614	−0.628069	−	0.778157i	$-0.716155\pi$
$983$	−38714.0	−1.25614	−0.628069	+	0.778157i	$0.716155\pi$
$984$	359.420	0.0116442
$985$	22289.8	0.721028
$986$	−3843.60	−0.124143
$987$	−7828.74	−0.252474
$988$	0	0
$989$	−7352.95	−0.236411
$990$	4767.09	0.153038
$991$	28354.5	0.908890	0.454445	−	0.890775i	$-0.349838\pi$
$991$	28354.5	0.908890	0.454445	+	0.890775i	$0.349838\pi$
$992$	2571.47	0.0823027
$993$	11319.6	0.361747
$994$	32055.9	1.02289
$995$	23259.5	0.741082
$996$	−713.530	−0.0226999
$997$	14978.3	0.475796	0.237898	−	0.971290i	$-0.423542\pi$
$997$	14978.3	0.475796	0.237898	+	0.971290i	$0.423542\pi$
$998$	−61444.4	−1.94889
$999$	31721.6	1.00463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.8	yes	39
13.12	even	2		1859.4.a.n.1.32	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.32	✓	39	13.12	even	2
1859.4.a.o.1.8	yes	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-3.48032 q^{2} -2.00729 q^{3} +4.11265 q^{4} -5.42082 q^{5} +6.98601 q^{6} -27.8265 q^{7} +13.5292 q^{8} -22.9708 q^{9} +O(q^{10})\)	\(q-3.48032 q^{2} -2.00729 q^{3} +4.11265 q^{4} -5.42082 q^{5} +6.98601 q^{6} -27.8265 q^{7} +13.5292 q^{8} -22.9708 q^{9} +18.8662 q^{10} -11.0000 q^{11} -8.25527 q^{12} +96.8452 q^{14} +10.8811 q^{15} -79.9873 q^{16} -53.2577 q^{17} +79.9458 q^{18} -1.47953 q^{19} -22.2939 q^{20} +55.8558 q^{21} +38.2836 q^{22} +30.0386 q^{23} -27.1571 q^{24} -95.6147 q^{25} +100.306 q^{27} -114.441 q^{28} -20.7365 q^{29} -37.8699 q^{30} +15.1132 q^{31} +170.148 q^{32} +22.0802 q^{33} +185.354 q^{34} +150.842 q^{35} -94.4708 q^{36} +316.249 q^{37} +5.14923 q^{38} -73.3396 q^{40} -13.2349 q^{41} -194.396 q^{42} -244.783 q^{43} -45.2391 q^{44} +124.520 q^{45} -104.544 q^{46} -140.160 q^{47} +160.558 q^{48} +431.315 q^{49} +332.770 q^{50} +106.904 q^{51} -137.662 q^{53} -349.096 q^{54} +59.6290 q^{55} -376.472 q^{56} +2.96984 q^{57} +72.1698 q^{58} +160.001 q^{59} +44.7503 q^{60} +243.281 q^{61} -52.5987 q^{62} +639.197 q^{63} +47.7296 q^{64} -76.8461 q^{66} +737.641 q^{67} -219.030 q^{68} -60.2962 q^{69} -524.980 q^{70} +331.001 q^{71} -310.778 q^{72} +557.931 q^{73} -1100.65 q^{74} +191.926 q^{75} -6.08477 q^{76} +306.092 q^{77} -95.3123 q^{79} +433.597 q^{80} +418.869 q^{81} +46.0616 q^{82} +86.4334 q^{83} +229.715 q^{84} +288.700 q^{85} +851.925 q^{86} +41.6242 q^{87} -148.822 q^{88} +43.6038 q^{89} -433.371 q^{90} +123.538 q^{92} -30.3365 q^{93} +487.801 q^{94} +8.02025 q^{95} -341.535 q^{96} -1822.96 q^{97} -1501.11 q^{98} +252.679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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