LMFDB - Embedded newform 7381.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29392 q^{2} +2.84985 q^{3} -0.325780 q^{4} -3.15298 q^{5} -3.68746 q^{6} -5.03078 q^{7} +3.00937 q^{8} +5.12162 q^{9} +O(q^{10})$	\(q-1.29392 q^{2} +2.84985 q^{3} -0.325780 q^{4} -3.15298 q^{5} -3.68746 q^{6} -5.03078 q^{7} +3.00937 q^{8} +5.12162 q^{9} +4.07969 q^{10} -0.928422 q^{12} -5.37940 q^{13} +6.50941 q^{14} -8.98551 q^{15} -3.24231 q^{16} -3.74023 q^{17} -6.62696 q^{18} -4.04082 q^{19} +1.02718 q^{20} -14.3369 q^{21} -8.31179 q^{23} +8.57623 q^{24} +4.94128 q^{25} +6.96050 q^{26} +6.04630 q^{27} +1.63892 q^{28} +2.39261 q^{29} +11.6265 q^{30} -7.43729 q^{31} -1.82345 q^{32} +4.83955 q^{34} +15.8619 q^{35} -1.66852 q^{36} -1.77422 q^{37} +5.22848 q^{38} -15.3305 q^{39} -9.48847 q^{40} -0.711385 q^{41} +18.5508 q^{42} +5.80652 q^{43} -16.1484 q^{45} +10.7548 q^{46} -1.38780 q^{47} -9.24008 q^{48} +18.3087 q^{49} -6.39360 q^{50} -10.6591 q^{51} +1.75250 q^{52} -5.60689 q^{53} -7.82341 q^{54} -15.1394 q^{56} -11.5157 q^{57} -3.09583 q^{58} -7.84688 q^{59} +2.92729 q^{60} -1.00000 q^{61} +9.62324 q^{62} -25.7657 q^{63} +8.84401 q^{64} +16.9611 q^{65} -13.8486 q^{67} +1.21849 q^{68} -23.6873 q^{69} -20.5240 q^{70} -5.49805 q^{71} +15.4128 q^{72} -2.39993 q^{73} +2.29569 q^{74} +14.0819 q^{75} +1.31642 q^{76} +19.8364 q^{78} -0.369632 q^{79} +10.2229 q^{80} +1.86616 q^{81} +0.920473 q^{82} -9.97158 q^{83} +4.67068 q^{84} +11.7929 q^{85} -7.51316 q^{86} +6.81856 q^{87} +7.27038 q^{89} +20.8947 q^{90} +27.0626 q^{91} +2.70781 q^{92} -21.1951 q^{93} +1.79570 q^{94} +12.7406 q^{95} -5.19656 q^{96} -2.78798 q^{97} -23.6899 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9} - q^{10} + 6 q^{12} - 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} - q^{17} + 5 q^{18} - 15 q^{19} - 2 q^{20} - 16 q^{21} + 11 q^{23} + 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} + 16 q^{28} + 9 q^{29} - 16 q^{30} + 22 q^{31} - 3 q^{32} + 33 q^{34} + 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} + 28 q^{39} + 16 q^{40} - 7 q^{41} - 55 q^{42} - 16 q^{43} + 44 q^{45} + 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} + 33 q^{50} + 19 q^{51} - 60 q^{52} + 9 q^{53} - 13 q^{54} + 44 q^{56} - 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} - 21 q^{61} + 23 q^{62} - 24 q^{63} + 66 q^{64} - 25 q^{65} + 38 q^{67} + 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} + 75 q^{72} - 20 q^{73} + 12 q^{74} - 10 q^{75} - 59 q^{76} - 14 q^{78} - q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} + 19 q^{83} + 14 q^{84} - 38 q^{85} - 3 q^{86} - 4 q^{87} + 37 q^{89} + 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} + 64 q^{94} + 43 q^{95} + 38 q^{96} + 68 q^{97} + 2 q^{98}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9 - q^10 + 6 * q^12 - 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 - q^17 + 5 * q^18 - 15 * q^19 - 2 * q^20 - 16 * q^21 + 11 * q^23 + 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 + 16 * q^28 + 9 * q^29 - 16 * q^30 + 22 * q^31 - 3 * q^32 + 33 * q^34 + 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 + 28 * q^39 + 16 * q^40 - 7 * q^41 - 55 * q^42 - 16 * q^43 + 44 * q^45 + 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 + 33 * q^50 + 19 * q^51 - 60 * q^52 + 9 * q^53 - 13 * q^54 + 44 * q^56 - 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 - 21 * q^61 + 23 * q^62 - 24 * q^63 + 66 * q^64 - 25 * q^65 + 38 * q^67 + 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 + 75 * q^72 - 20 * q^73 + 12 * q^74 - 10 * q^75 - 59 * q^76 - 14 * q^78 - q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 + 19 * q^83 + 14 * q^84 - 38 * q^85 - 3 * q^86 - 4 * q^87 + 37 * q^89 + 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 + 64 * q^94 + 43 * q^95 + 38 * q^96 + 68 * q^97 + 2 * q^98

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 $

$2$	−1.29392	−0.914937	−0.457469	−	0.889226i	$-0.651244\pi$
$2$	−1.29392	−0.914937	−0.457469	+	0.889226i	$0.651244\pi$
$3$	2.84985	1.64536	0.822680	−	0.568505i	$-0.192478\pi$
$3$	2.84985	1.64536	0.822680	+	0.568505i	$0.192478\pi$
$4$	−0.325780	−0.162890
$5$	−3.15298	−1.41006	−0.705028	−	0.709180i	$-0.749065\pi$
$5$	−3.15298	−1.41006	−0.705028	+	0.709180i	$0.749065\pi$
$6$	−3.68746	−1.50540
$7$	−5.03078	−1.90145	−0.950727	−	0.310028i	$-0.899661\pi$
$7$	−5.03078	−1.90145	−0.950727	+	0.310028i	$0.899661\pi$
$8$	3.00937	1.06397
$9$	5.12162	1.70721
$10$	4.07969	1.29011
$11$	0	0
$11$	0	0
$12$	−0.928422	−0.268012
$13$	−5.37940	−1.49198	−0.745989	−	0.665958i	$-0.768023\pi$
$13$	−5.37940	−1.49198	−0.745989	+	0.665958i	$0.768023\pi$
$14$	6.50941	1.73971
$15$	−8.98551	−2.32005
$16$	−3.24231	−0.810577
$17$	−3.74023	−0.907139	−0.453570	−	0.891221i	$-0.649850\pi$
$17$	−3.74023	−0.907139	−0.453570	+	0.891221i	$0.649850\pi$
$18$	−6.62696	−1.56199
$19$	−4.04082	−0.927028	−0.463514	−	0.886090i	$-0.653412\pi$
$19$	−4.04082	−0.927028	−0.463514	+	0.886090i	$0.653412\pi$
$20$	1.02718	0.229684
$21$	−14.3369	−3.12858
$22$	0	0
$23$	−8.31179	−1.73313	−0.866564	−	0.499065i	$-0.833677\pi$
$23$	−8.31179	−1.73313	−0.866564	+	0.499065i	$0.833677\pi$
$24$	8.57623	1.75062
$25$	4.94128	0.988256
$26$	6.96050	1.36507
$27$	6.04630	1.16361
$28$	1.63892	0.309728
$29$	2.39261	0.444296	0.222148	−	0.975013i	$-0.428693\pi$
$29$	2.39261	0.444296	0.222148	+	0.975013i	$0.428693\pi$
$30$	11.6265	2.12270
$31$	−7.43729	−1.33578	−0.667889	−	0.744261i	$-0.732802\pi$
$31$	−7.43729	−1.33578	−0.667889	+	0.744261i	$0.732802\pi$
$32$	−1.82345	−0.322344
$33$	0	0
$34$	4.83955	0.829976
$35$	15.8619	2.68116
$36$	−1.66852	−0.278087
$37$	−1.77422	−0.291679	−0.145840	−	0.989308i	$-0.546588\pi$
$37$	−1.77422	−0.291679	−0.145840	+	0.989308i	$0.546588\pi$
$38$	5.22848	0.848172
$39$	−15.3305	−2.45484
$40$	−9.48847	−1.50026
$41$	−0.711385	−0.111100	−0.0555498	−	0.998456i	$-0.517691\pi$
$41$	−0.711385	−0.111100	−0.0555498	+	0.998456i	$0.517691\pi$
$42$	18.5508	2.86245
$43$	5.80652	0.885486	0.442743	−	0.896648i	$-0.354005\pi$
$43$	5.80652	0.885486	0.442743	+	0.896648i	$0.354005\pi$
$44$	0	0
$45$	−16.1484	−2.40726
$46$	10.7548	1.58570
$47$	−1.38780	−0.202432	−0.101216	−	0.994864i	$-0.532273\pi$
$47$	−1.38780	−0.202432	−0.101216	+	0.994864i	$0.532273\pi$
$48$	−9.24008	−1.33369
$49$	18.3087	2.61553
$50$	−6.39360	−0.904192
$51$	−10.6591	−1.49257
$52$	1.75250	0.243028
$53$	−5.60689	−0.770166	−0.385083	−	0.922882i	$-0.625827\pi$
$53$	−5.60689	−0.770166	−0.385083	+	0.922882i	$0.625827\pi$
$54$	−7.82341	−1.06463
$55$	0	0
$56$	−15.1394	−2.02309
$57$	−11.5157	−1.52529
$58$	−3.09583	−0.406503
$59$	−7.84688	−1.02158	−0.510788	−	0.859707i	$-0.670646\pi$
$59$	−7.84688	−1.02158	−0.510788	+	0.859707i	$0.670646\pi$
$60$	2.92729	0.377912
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	9.62324	1.22215
$63$	−25.7657	−3.24618
$64$	8.84401	1.10550
$65$	16.9611	2.10377
$66$	0	0
$67$	−13.8486	−1.69188	−0.845940	−	0.533279i	$-0.820960\pi$
$67$	−13.8486	−1.69188	−0.845940	+	0.533279i	$0.820960\pi$
$68$	1.21849	0.147764
$69$	−23.6873	−2.85162
$70$	−20.5240	−2.45309
$71$	−5.49805	−0.652498	−0.326249	−	0.945284i	$-0.605785\pi$
$71$	−5.49805	−0.652498	−0.326249	+	0.945284i	$0.605785\pi$
$72$	15.4128	1.81642
$73$	−2.39993	−0.280891	−0.140446	−	0.990088i	$-0.544853\pi$
$73$	−2.39993	−0.280891	−0.140446	+	0.990088i	$0.544853\pi$
$74$	2.29569	0.266868
$75$	14.0819	1.62604
$76$	1.31642	0.151003
$77$	0	0
$78$	19.8364	2.24603
$79$	−0.369632	−0.0415869	−0.0207934	−	0.999784i	$-0.506619\pi$
$79$	−0.369632	−0.0415869	−0.0207934	+	0.999784i	$0.506619\pi$
$80$	10.2229	1.14296
$81$	1.86616	0.207352
$82$	0.920473	0.101649
$83$	−9.97158	−1.09452	−0.547261	−	0.836962i	$-0.684330\pi$
$83$	−9.97158	−1.09452	−0.547261	+	0.836962i	$0.684330\pi$
$84$	4.67068	0.509613
$85$	11.7929	1.27912
$86$	−7.51316	−0.810164
$87$	6.81856	0.731026
$88$	0	0
$89$	7.27038	0.770658	0.385329	−	0.922779i	$-0.374088\pi$
$89$	7.27038	0.770658	0.385329	+	0.922779i	$0.374088\pi$
$90$	20.8947	2.20249
$91$	27.0626	2.83693
$92$	2.70781	0.282309
$93$	−21.1951	−2.19783
$94$	1.79570	0.185212
$95$	12.7406	1.30716
$96$	−5.19656	−0.530372
$97$	−2.78798	−0.283076	−0.141538	−	0.989933i	$-0.545205\pi$
$97$	−2.78798	−0.283076	−0.141538	+	0.989933i	$0.545205\pi$
$98$	−23.6899	−2.39305
$99$	0	0
$100$	−1.60977	−0.160977
$101$	−7.38635	−0.734970	−0.367485	−	0.930030i	$-0.619781\pi$
$101$	−7.38635	−0.734970	−0.367485	+	0.930030i	$0.619781\pi$
$102$	13.7920	1.36561
$103$	13.7508	1.35491	0.677453	−	0.735566i	$-0.263084\pi$
$103$	13.7508	1.35491	0.677453	+	0.735566i	$0.263084\pi$
$104$	−16.1886	−1.58742
$105$	45.2041	4.41147
$106$	7.25485	0.704653
$107$	17.2838	1.67089	0.835443	−	0.549578i	$-0.185211\pi$
$107$	17.2838	1.67089	0.835443	+	0.549578i	$0.185211\pi$
$108$	−1.96976	−0.189540
$109$	6.93762	0.664503	0.332252	−	0.943191i	$-0.392192\pi$
$109$	6.93762	0.664503	0.332252	+	0.943191i	$0.392192\pi$
$110$	0	0
$111$	−5.05624	−0.479917
$112$	16.3113	1.54128
$113$	−7.67083	−0.721611	−0.360806	−	0.932641i	$-0.617498\pi$
$113$	−7.67083	−0.721611	−0.360806	+	0.932641i	$0.617498\pi$
$114$	14.9004	1.39555
$115$	26.2069	2.44381
$116$	−0.779462	−0.0723712
$117$	−27.5513	−2.54712
$118$	10.1532	0.934678
$119$	18.8163	1.72488
$120$	−27.0407	−2.46846
$121$	0	0
$122$	1.29392	0.117146
$123$	−2.02734	−0.182799
$124$	2.42292	0.217584
$125$	0.185143	0.0165597
$126$	33.3387	2.97005
$127$	−3.54653	−0.314704	−0.157352	−	0.987543i	$-0.550296\pi$
$127$	−3.54653	−0.314704	−0.157352	+	0.987543i	$0.550296\pi$
$128$	−7.79651	−0.689121
$129$	16.5477	1.45694
$130$	−21.9463	−1.92482
$131$	−14.8844	−1.30046	−0.650230	−	0.759738i	$-0.725327\pi$
$131$	−14.8844	−1.30046	−0.650230	+	0.759738i	$0.725327\pi$
$132$	0	0
$133$	20.3285	1.76270
$134$	17.9190	1.54796
$135$	−19.0639	−1.64076
$136$	−11.2557	−0.965170
$137$	6.65631	0.568687	0.284343	−	0.958722i	$-0.408224\pi$
$137$	6.65631	0.568687	0.284343	+	0.958722i	$0.408224\pi$
$138$	30.6494	2.60905
$139$	3.67190	0.311446	0.155723	−	0.987801i	$-0.450229\pi$
$139$	3.67190	0.311446	0.155723	+	0.987801i	$0.450229\pi$
$140$	−5.16749	−0.436733
$141$	−3.95502	−0.333073
$142$	7.11401	0.596995
$143$	0	0
$144$	−16.6059	−1.38382
$145$	−7.54384	−0.626482
$146$	3.10532	0.256998
$147$	52.1770	4.30349
$148$	0.578003	0.0475116
$149$	−18.1524	−1.48710	−0.743552	−	0.668678i	$-0.766861\pi$
$149$	−18.1524	−1.48710	−0.743552	+	0.668678i	$0.766861\pi$
$150$	−18.2208	−1.48772
$151$	1.81849	0.147987	0.0739934	−	0.997259i	$-0.476426\pi$
$151$	1.81849	0.147987	0.0739934	+	0.997259i	$0.476426\pi$
$152$	−12.1603	−0.986331
$153$	−19.1561	−1.54868
$154$	0	0
$155$	23.4496	1.88352
$156$	4.99436	0.399868
$157$	−5.49676	−0.438689	−0.219344	−	0.975647i	$-0.570392\pi$
$157$	−5.49676	−0.438689	−0.219344	+	0.975647i	$0.570392\pi$
$158$	0.478274	0.0380494
$159$	−15.9788	−1.26720
$160$	5.74931	0.454523
$161$	41.8148	3.29547
$162$	−2.41466	−0.189714
$163$	8.57144	0.671367	0.335683	−	0.941975i	$-0.391033\pi$
$163$	8.57144	0.671367	0.335683	+	0.941975i	$0.391033\pi$
$164$	0.231755	0.0180970
$165$	0	0
$166$	12.9024	1.00142
$167$	−15.2797	−1.18238	−0.591188	−	0.806534i	$-0.701341\pi$
$167$	−15.2797	−1.18238	−0.591188	+	0.806534i	$0.701341\pi$
$168$	−43.1451	−3.32872
$169$	15.9380	1.22600
$170$	−15.2590	−1.17031
$171$	−20.6956	−1.58263
$172$	−1.89165	−0.144237
$173$	−6.95831	−0.529031	−0.264515	−	0.964381i	$-0.585212\pi$
$173$	−6.95831	−0.529031	−0.264515	+	0.964381i	$0.585212\pi$
$174$	−8.82265	−0.668843
$175$	−24.8585	−1.87912
$176$	0	0
$177$	−22.3624	−1.68086
$178$	−9.40726	−0.705104
$179$	17.9416	1.34102	0.670509	−	0.741902i	$-0.266076\pi$
$179$	17.9416	1.34102	0.670509	+	0.741902i	$0.266076\pi$
$180$	5.26081	0.392118
$181$	−21.9095	−1.62852	−0.814259	−	0.580502i	$-0.802856\pi$
$181$	−21.9095	−1.62852	−0.814259	+	0.580502i	$0.802856\pi$
$182$	−35.0167	−2.59561
$183$	−2.84985	−0.210667
$184$	−25.0132	−1.84400
$185$	5.59407	0.411284
$186$	27.4248	2.01088
$187$	0	0
$188$	0.452118	0.0329741
$189$	−30.4176	−2.21255
$190$	−16.4853	−1.19597
$191$	4.31134	0.311958	0.155979	−	0.987760i	$-0.450147\pi$
$191$	4.31134	0.311958	0.155979	+	0.987760i	$0.450147\pi$
$192$	25.2041	1.81895
$193$	1.70398	0.122655	0.0613276	−	0.998118i	$-0.480467\pi$
$193$	1.70398	0.122655	0.0613276	+	0.998118i	$0.480467\pi$
$194$	3.60741	0.258997
$195$	48.3367	3.46146
$196$	−5.96460	−0.426043
$197$	16.9503	1.20766	0.603830	−	0.797113i	$-0.293641\pi$
$197$	16.9503	1.20766	0.603830	+	0.797113i	$0.293641\pi$
$198$	0	0
$199$	−19.5638	−1.38684	−0.693421	−	0.720533i	$-0.743897\pi$
$199$	−19.5638	−1.38684	−0.693421	+	0.720533i	$0.743897\pi$
$200$	14.8701	1.05148
$201$	−39.4665	−2.78375
$202$	9.55733	0.672451
$203$	−12.0367	−0.844808
$204$	3.47251	0.243124
$205$	2.24298	0.156657
$206$	−17.7924	−1.23965
$207$	−42.5699	−2.95881
$208$	17.4417	1.20936
$209$	0	0
$210$	−58.4903	−4.03621
$211$	18.5985	1.28037	0.640186	−	0.768220i	$-0.278857\pi$
$211$	18.5985	1.28037	0.640186	+	0.768220i	$0.278857\pi$
$212$	1.82661	0.125452
$213$	−15.6686	−1.07359
$214$	−22.3638	−1.52876
$215$	−18.3078	−1.24858
$216$	18.1955	1.23805
$217$	37.4154	2.53992
$218$	−8.97670	−0.607979
$219$	−6.83944	−0.462167
$220$	0	0
$221$	20.1202	1.35343
$222$	6.54236	0.439094
$223$	−11.6508	−0.780196	−0.390098	−	0.920773i	$-0.627559\pi$
$223$	−11.6508	−0.780196	−0.390098	+	0.920773i	$0.627559\pi$
$224$	9.17338	0.612922
$225$	25.3074	1.68716
$226$	9.92542	0.660229
$227$	−4.05285	−0.268997	−0.134499	−	0.990914i	$-0.542942\pi$
$227$	−4.05285	−0.268997	−0.134499	+	0.990914i	$0.542942\pi$
$228$	3.75158	0.248455
$229$	4.67351	0.308834	0.154417	−	0.988006i	$-0.450650\pi$
$229$	4.67351	0.308834	0.154417	+	0.988006i	$0.450650\pi$
$230$	−33.9096	−2.23593
$231$	0	0
$232$	7.20022	0.472718
$233$	−14.7430	−0.965847	−0.482923	−	0.875663i	$-0.660425\pi$
$233$	−14.7430	−0.965847	−0.482923	+	0.875663i	$0.660425\pi$
$234$	35.6491	2.33045
$235$	4.37571	0.285440
$236$	2.55635	0.166404
$237$	−1.05340	−0.0684254
$238$	−24.3467	−1.57816
$239$	−0.0283176	−0.00183171	−0.000915856	−	1.00000i	$-0.500292\pi$
$239$	−0.0283176	−0.00183171	−0.000915856		1.00000i	$0.500292\pi$
$240$	29.1338	1.88058
$241$	−13.0050	−0.837723	−0.418861	−	0.908050i	$-0.637571\pi$
$241$	−13.0050	−0.837723	−0.418861	+	0.908050i	$0.637571\pi$
$242$	0	0
$243$	−12.8206	−0.822444
$244$	0.325780	0.0208559
$245$	−57.7270	−3.68804
$246$	2.62321	0.167249
$247$	21.7372	1.38310
$248$	−22.3815	−1.42123
$249$	−28.4175	−1.80088
$250$	−0.239560	−0.0151511
$251$	9.82317	0.620033	0.310016	−	0.950731i	$-0.399665\pi$
$251$	9.82317	0.620033	0.310016	+	0.950731i	$0.399665\pi$
$252$	8.39395	0.528769
$253$	0	0
$254$	4.58892	0.287934
$255$	33.6079	2.10461
$256$	−7.59999	−0.474999
$257$	14.2555	0.889234	0.444617	−	0.895721i	$-0.353340\pi$
$257$	14.2555	0.889234	0.444617	+	0.895721i	$0.353340\pi$
$258$	−21.4113	−1.33301
$259$	8.92568	0.554615
$260$	−5.52560	−0.342683
$261$	12.2540	0.758505
$262$	19.2592	1.18984
$263$	15.4903	0.955176	0.477588	−	0.878584i	$-0.341511\pi$
$263$	15.4903	0.955176	0.477588	+	0.878584i	$0.341511\pi$
$264$	0	0
$265$	17.6784	1.08598
$266$	−26.3033	−1.61276
$267$	20.7195	1.26801
$268$	4.51160	0.275590
$269$	−13.4623	−0.820810	−0.410405	−	0.911903i	$-0.634613\pi$
$269$	−13.4623	−0.820810	−0.410405	+	0.911903i	$0.634613\pi$
$270$	24.6671	1.50119
$271$	24.3809	1.48103	0.740517	−	0.672037i	$-0.234581\pi$
$271$	24.3809	1.48103	0.740517	+	0.672037i	$0.234581\pi$
$272$	12.1270	0.735306
$273$	77.1242	4.66777
$274$	−8.61271	−0.520313
$275$	0	0
$276$	7.71685	0.464500
$277$	26.4547	1.58951	0.794756	−	0.606929i	$-0.207599\pi$
$277$	26.4547	1.58951	0.794756	+	0.606929i	$0.207599\pi$
$278$	−4.75113	−0.284954
$279$	−38.0910	−2.28045
$280$	47.7343	2.85267
$281$	−29.5269	−1.76143	−0.880714	−	0.473648i	$-0.842937\pi$
$281$	−29.5269	−1.76143	−0.880714	+	0.473648i	$0.842937\pi$
$282$	5.11747	0.304741
$283$	−14.6613	−0.871524	−0.435762	−	0.900062i	$-0.643521\pi$
$283$	−14.6613	−0.871524	−0.435762	+	0.900062i	$0.643521\pi$
$284$	1.79115	0.106285
$285$	36.3088	2.15075
$286$	0	0
$287$	3.57882	0.211251
$288$	−9.33904	−0.550308
$289$	−3.01067	−0.177098
$290$	9.76110	0.573191
$291$	−7.94531	−0.465762
$292$	0.781850	0.0457543
$293$	−16.1198	−0.941727	−0.470863	−	0.882206i	$-0.656058\pi$
$293$	−16.1198	−0.941727	−0.470863	+	0.882206i	$0.656058\pi$
$294$	−67.5127	−3.93742
$295$	24.7410	1.44048
$296$	−5.33926	−0.310338
$297$	0	0
$298$	23.4877	1.36061
$299$	44.7125	2.58579
$300$	−4.58759	−0.264865
$301$	−29.2113	−1.68371
$302$	−2.35298	−0.135399
$303$	−21.0500	−1.20929
$304$	13.1016	0.751427
$305$	3.15298	0.180539
$306$	24.7863	1.41694
$307$	−15.7370	−0.898160	−0.449080	−	0.893492i	$-0.648248\pi$
$307$	−15.7370	−0.898160	−0.449080	+	0.893492i	$0.648248\pi$
$308$	0	0
$309$	39.1876	2.22931
$310$	−30.3419	−1.72330
$311$	−3.98071	−0.225725	−0.112863	−	0.993611i	$-0.536002\pi$
$311$	−3.98071	−0.225725	−0.112863	+	0.993611i	$0.536002\pi$
$312$	−46.1350	−2.61188
$313$	28.0839	1.58740	0.793699	−	0.608311i	$-0.208153\pi$
$313$	28.0839	1.58740	0.793699	+	0.608311i	$0.208153\pi$
$314$	7.11234	0.401373
$315$	81.2389	4.57729
$316$	0.120419	0.00677408
$317$	−13.7782	−0.773858	−0.386929	−	0.922109i	$-0.626464\pi$
$317$	−13.7782	−0.773858	−0.386929	+	0.922109i	$0.626464\pi$
$318$	20.6752	1.15941
$319$	0	0
$320$	−27.8850	−1.55882
$321$	49.2561	2.74921
$322$	−54.1048	−3.01514
$323$	15.1136	0.840943
$324$	−0.607958	−0.0337754
$325$	−26.5811	−1.47446
$326$	−11.0907	−0.614258
$327$	19.7711	1.09335
$328$	−2.14082	−0.118207
$329$	6.98172	0.384915
$330$	0	0
$331$	2.44629	0.134460	0.0672301	−	0.997737i	$-0.478584\pi$
$331$	2.44629	0.134460	0.0672301	+	0.997737i	$0.478584\pi$
$332$	3.24854	0.178287
$333$	−9.08687	−0.497957
$334$	19.7706	1.08180
$335$	43.6644	2.38564
$336$	46.4848	2.53595
$337$	−10.9925	−0.598798	−0.299399	−	0.954128i	$-0.596786\pi$
$337$	−10.9925	−0.598798	−0.299399	+	0.954128i	$0.596786\pi$
$338$	−20.6224	−1.12171
$339$	−21.8607	−1.18731
$340$	−3.84188	−0.208355
$341$	0	0
$342$	26.7783	1.44801
$343$	−56.8916	−3.07186
$344$	17.4739	0.942132
$345$	74.6857	4.02094
$346$	9.00348	0.484030
$347$	8.68794	0.466393	0.233196	−	0.972430i	$-0.425081\pi$
$347$	8.68794	0.466393	0.233196	+	0.972430i	$0.425081\pi$
$348$	−2.22135	−0.119077
$349$	7.57440	0.405448	0.202724	−	0.979236i	$-0.435021\pi$
$349$	7.57440	0.405448	0.202724	+	0.979236i	$0.435021\pi$
$350$	32.1648	1.71928
$351$	−32.5255	−1.73608
$352$	0	0
$353$	−0.0404881	−0.00215496	−0.00107748	−	0.999999i	$-0.500343\pi$
$353$	−0.0404881	−0.00215496	−0.00107748	+	0.999999i	$0.500343\pi$
$354$	28.9351	1.53788
$355$	17.3352	0.920058
$356$	−2.36854	−0.125532
$357$	53.6235	2.83805
$358$	−23.2149	−1.22695
$359$	25.6439	1.35343	0.676716	−	0.736244i	$-0.263402\pi$
$359$	25.6439	1.35343	0.676716	+	0.736244i	$0.263402\pi$
$360$	−48.5964	−2.56125
$361$	−2.67178	−0.140620
$362$	28.3490	1.48999
$363$	0	0
$364$	−8.81643	−0.462107
$365$	7.56694	0.396072
$366$	3.68746	0.192747
$367$	−16.9367	−0.884088	−0.442044	−	0.896993i	$-0.645747\pi$
$367$	−16.9367	−0.884088	−0.442044	+	0.896993i	$0.645747\pi$
$368$	26.9494	1.40483
$369$	−3.64345	−0.189670
$370$	−7.23826	−0.376299
$371$	28.2070	1.46444
$372$	6.90495	0.358005
$373$	−25.4130	−1.31583	−0.657917	−	0.753091i	$-0.728562\pi$
$373$	−25.4130	−1.31583	−0.657917	+	0.753091i	$0.728562\pi$
$374$	0	0
$375$	0.527629	0.0272466
$376$	−4.17640	−0.215382
$377$	−12.8708	−0.662880
$378$	39.3578	2.02435
$379$	−23.6354	−1.21407	−0.607035	−	0.794675i	$-0.707641\pi$
$379$	−23.6354	−1.21407	−0.607035	+	0.794675i	$0.707641\pi$
$380$	−4.15063	−0.212923
$381$	−10.1071	−0.517801
$382$	−5.57852	−0.285422
$383$	8.02500	0.410058	0.205029	−	0.978756i	$-0.434271\pi$
$383$	8.02500	0.410058	0.205029	+	0.978756i	$0.434271\pi$
$384$	−22.2189	−1.13385
$385$	0	0
$386$	−2.20481	−0.112222
$387$	29.7388	1.51171
$388$	0.908267	0.0461102
$389$	26.0896	1.32279	0.661397	−	0.750036i	$-0.269964\pi$
$389$	26.0896	1.32279	0.661397	+	0.750036i	$0.269964\pi$
$390$	−62.5436	−3.16702
$391$	31.0880	1.57219
$392$	55.0976	2.78285
$393$	−42.4184	−2.13972
$394$	−21.9323	−1.10493
$395$	1.16544	0.0586398
$396$	0	0
$397$	9.00408	0.451902	0.225951	−	0.974139i	$-0.427451\pi$
$397$	9.00408	0.451902	0.225951	+	0.974139i	$0.427451\pi$
$398$	25.3139	1.26887
$399$	57.9330	2.90028
$400$	−16.0212	−0.801058
$401$	28.5072	1.42358	0.711792	−	0.702391i	$-0.247884\pi$
$401$	28.5072	1.42358	0.711792	+	0.702391i	$0.247884\pi$
$402$	51.0663	2.54696
$403$	40.0082	1.99295
$404$	2.40632	0.119719
$405$	−5.88398	−0.292377
$406$	15.5744	0.772947
$407$	0	0
$408$	−32.0771	−1.58805
$409$	−22.9317	−1.13390	−0.566949	−	0.823753i	$-0.691876\pi$
$409$	−22.9317	−1.13390	−0.566949	+	0.823753i	$0.691876\pi$
$410$	−2.90223	−0.143331
$411$	18.9695	0.935695
$412$	−4.47973	−0.220700
$413$	39.4759	1.94248
$414$	55.0819	2.70713
$415$	31.4402	1.54334
$416$	9.80909	0.480930
$417$	10.4643	0.512441
$418$	0	0
$419$	−6.83008	−0.333671	−0.166836	−	0.985985i	$-0.553355\pi$
$419$	−6.83008	−0.333671	−0.166836	+	0.985985i	$0.553355\pi$
$420$	−14.7266	−0.718583
$421$	2.09584	0.102145	0.0510724	−	0.998695i	$-0.483736\pi$
$421$	2.09584	0.102145	0.0510724	+	0.998695i	$0.483736\pi$
$422$	−24.0649	−1.17146
$423$	−7.10780	−0.345593
$424$	−16.8732	−0.819434
$425$	−18.4815	−0.896486
$426$	20.2738	0.982271
$427$	5.03078	0.243456
$428$	−5.63070	−0.272170
$429$	0	0
$430$	23.6888	1.14238
$431$	19.5477	0.941580	0.470790	−	0.882245i	$-0.343969\pi$
$431$	19.5477	0.941580	0.470790	+	0.882245i	$0.343969\pi$
$432$	−19.6040	−0.943197
$433$	−22.9539	−1.10310	−0.551548	−	0.834143i	$-0.685963\pi$
$433$	−22.9539	−1.10310	−0.551548	+	0.834143i	$0.685963\pi$
$434$	−48.4124	−2.32387
$435$	−21.4988	−1.03079
$436$	−2.26013	−0.108241
$437$	33.5865	1.60666
$438$	8.84967	0.422854
$439$	−7.32646	−0.349673	−0.174836	−	0.984597i	$-0.555940\pi$
$439$	−7.32646	−0.349673	−0.174836	+	0.984597i	$0.555940\pi$
$440$	0	0
$441$	93.7703	4.46525
$442$	−26.0339	−1.23831
$443$	4.91021	0.233291	0.116645	−	0.993174i	$-0.462786\pi$
$443$	4.91021	0.233291	0.116645	+	0.993174i	$0.462786\pi$
$444$	1.64722	0.0781736
$445$	−22.9233	−1.08667
$446$	15.0752	0.713830
$447$	−51.7316	−2.44682
$448$	−44.4922	−2.10206
$449$	−4.43139	−0.209130	−0.104565	−	0.994518i	$-0.533345\pi$
$449$	−4.43139	−0.209130	−0.104565	+	0.994518i	$0.533345\pi$
$450$	−32.7456	−1.54364
$451$	0	0
$452$	2.49900	0.117543
$453$	5.18242	0.243492
$454$	5.24406	0.246116
$455$	−85.3277	−4.00023
$456$	−34.6550	−1.62287
$457$	−17.1757	−0.803445	−0.401722	−	0.915762i	$-0.631588\pi$
$457$	−17.1757	−0.803445	−0.401722	+	0.915762i	$0.631588\pi$
$458$	−6.04713	−0.282564
$459$	−22.6146	−1.05556
$460$	−8.53768	−0.398071
$461$	16.3294	0.760536	0.380268	−	0.924876i	$-0.375832\pi$
$461$	16.3294	0.760536	0.380268	+	0.924876i	$0.375832\pi$
$462$	0	0
$463$	34.7208	1.61361	0.806806	−	0.590816i	$-0.201194\pi$
$463$	34.7208	1.61361	0.806806	+	0.590816i	$0.201194\pi$
$464$	−7.75757	−0.360136
$465$	66.8279	3.09907
$466$	19.0762	0.883689
$467$	20.4386	0.945786	0.472893	−	0.881120i	$-0.343210\pi$
$467$	20.4386	0.945786	0.472893	+	0.881120i	$0.343210\pi$
$468$	8.97565	0.414899
$469$	69.6693	3.21703
$470$	−5.66181	−0.261160
$471$	−15.6649	−0.721801
$472$	−23.6141	−1.08693
$473$	0	0
$474$	1.36301	0.0626049
$475$	−19.9668	−0.916141
$476$	−6.12996	−0.280966
$477$	−28.7164	−1.31483
$478$	0.0366406	0.00167590
$479$	−12.8281	−0.586132	−0.293066	−	0.956092i	$-0.594676\pi$
$479$	−12.8281	−0.586132	−0.293066	+	0.956092i	$0.594676\pi$
$480$	16.3846	0.747854
$481$	9.54423	0.435179
$482$	16.8273	0.766464
$483$	119.166	5.42223
$484$	0	0
$485$	8.79044	0.399153
$486$	16.5888	0.752485
$487$	16.3096	0.739058	0.369529	−	0.929219i	$-0.379519\pi$
$487$	16.3096	0.739058	0.369529	+	0.929219i	$0.379519\pi$
$488$	−3.00937	−0.136228
$489$	24.4273	1.10464
$490$	74.6939	3.37433
$491$	24.6215	1.11115	0.555576	−	0.831466i	$-0.312498\pi$
$491$	24.6215	1.11115	0.555576	+	0.831466i	$0.312498\pi$
$492$	0.660465	0.0297761
$493$	−8.94890	−0.403038
$494$	−28.1261	−1.26545
$495$	0	0
$496$	24.1140	1.08275
$497$	27.6594	1.24070
$498$	36.7698	1.64770
$499$	27.1576	1.21574	0.607871	−	0.794036i	$-0.292024\pi$
$499$	27.1576	1.21574	0.607871	+	0.794036i	$0.292024\pi$
$500$	−0.0603158	−0.00269740
$501$	−43.5447	−1.94543
$502$	−12.7104	−0.567291
$503$	−14.1547	−0.631125	−0.315563	−	0.948905i	$-0.602193\pi$
$503$	−14.1547	−0.631125	−0.315563	+	0.948905i	$0.602193\pi$
$504$	−77.5385	−3.45384
$505$	23.2890	1.03635
$506$	0	0
$507$	45.4208	2.01721
$508$	1.15539	0.0512621
$509$	−8.64166	−0.383035	−0.191517	−	0.981489i	$-0.561341\pi$
$509$	−8.64166	−0.383035	−0.191517	+	0.981489i	$0.561341\pi$
$510$	−43.4858	−1.92558
$511$	12.0735	0.534102
$512$	25.4268	1.12372
$513$	−24.4320	−1.07870
$514$	−18.4454	−0.813593
$515$	−43.3560	−1.91049
$516$	−5.39090	−0.237321
$517$	0	0
$518$	−11.5491	−0.507438
$519$	−19.8301	−0.870446
$520$	51.0423	2.23835
$521$	−28.1013	−1.23114	−0.615571	−	0.788082i	$-0.711075\pi$
$521$	−28.1013	−1.23114	−0.615571	+	0.788082i	$0.711075\pi$
$522$	−15.8557	−0.693985
$523$	−25.0944	−1.09730	−0.548651	−	0.836051i	$-0.684859\pi$
$523$	−25.0944	−1.09730	−0.548651	+	0.836051i	$0.684859\pi$
$524$	4.84905	0.211832
$525$	−70.8428	−3.09183
$526$	−20.0432	−0.873926
$527$	27.8172	1.21174
$528$	0	0
$529$	46.0859	2.00374
$530$	−22.8744	−0.993600
$531$	−40.1888	−1.74404
$532$	−6.62260	−0.287126
$533$	3.82683	0.165758
$534$	−26.8092	−1.16015
$535$	−54.4954	−2.35604
$536$	−41.6756	−1.80011
$537$	51.1308	2.20646
$538$	17.4191	0.750990
$539$	0	0
$540$	6.21062	0.267263
$541$	21.2427	0.913294	0.456647	−	0.889648i	$-0.349050\pi$
$541$	21.2427	0.913294	0.456647	+	0.889648i	$0.349050\pi$
$542$	−31.5469	−1.35505
$543$	−62.4386	−2.67950
$544$	6.82014	0.292411
$545$	−21.8742	−0.936986
$546$	−99.7923	−4.27071
$547$	−20.8371	−0.890929	−0.445464	−	0.895300i	$-0.646961\pi$
$547$	−20.8371	−0.890929	−0.445464	+	0.895300i	$0.646961\pi$
$548$	−2.16849	−0.0926333
$549$	−5.12162	−0.218586
$550$	0	0
$551$	−9.66809	−0.411874
$552$	−71.2838	−3.03404
$553$	1.85954	0.0790756
$554$	−34.2302	−1.45430
$555$	15.9422	0.676710
$556$	−1.19623	−0.0507314
$557$	−17.8131	−0.754766	−0.377383	−	0.926057i	$-0.623176\pi$
$557$	−17.8131	−0.754766	−0.377383	+	0.926057i	$0.623176\pi$
$558$	49.2866	2.08647
$559$	−31.2356	−1.32113
$560$	−51.4293	−2.17328
$561$	0	0
$562$	38.2054	1.61160
$563$	−26.1629	−1.10263	−0.551317	−	0.834296i	$-0.685874\pi$
$563$	−26.1629	−1.10263	−0.551317	+	0.834296i	$0.685874\pi$
$564$	1.28847	0.0542542
$565$	24.1860	1.01751
$566$	18.9705	0.797389
$567$	−9.38825	−0.394270
$568$	−16.5456	−0.694239
$569$	−37.5330	−1.57347	−0.786733	−	0.617293i	$-0.788229\pi$
$569$	−37.5330	−1.57347	−0.786733	+	0.617293i	$0.788229\pi$
$570$	−46.9806	−1.96780
$571$	16.3419	0.683887	0.341944	−	0.939720i	$-0.388915\pi$
$571$	16.3419	0.683887	0.341944	+	0.939720i	$0.388915\pi$
$572$	0	0
$573$	12.2867	0.513283
$574$	−4.63069	−0.193281
$575$	−41.0709	−1.71278
$576$	45.2957	1.88732
$577$	−39.5536	−1.64664	−0.823320	−	0.567578i	$-0.807881\pi$
$577$	−39.5536	−1.64664	−0.823320	+	0.567578i	$0.807881\pi$
$578$	3.89556	0.162034
$579$	4.85608	0.201812
$580$	2.45763	0.102047
$581$	50.1648	2.08119
$582$	10.2806	0.426143
$583$	0	0
$584$	−7.22228	−0.298860
$585$	86.8686	3.59158
$586$	20.8576	0.861621
$587$	−11.4662	−0.473263	−0.236631	−	0.971600i	$-0.576043\pi$
$587$	−11.4662	−0.473263	−0.236631	+	0.971600i	$0.576043\pi$
$588$	−16.9982	−0.700994
$589$	30.0528	1.23830
$590$	−32.0129	−1.31795
$591$	48.3058	1.98703
$592$	5.75256	0.236429
$593$	−32.0395	−1.31571	−0.657853	−	0.753147i	$-0.728535\pi$
$593$	−32.0395	−1.31571	−0.657853	+	0.753147i	$0.728535\pi$
$594$	0	0
$595$	−59.3273	−2.43218
$596$	5.91369	0.242234
$597$	−55.7538	−2.28185
$598$	−57.8542	−2.36584
$599$	2.76637	0.113031	0.0565153	−	0.998402i	$-0.482001\pi$
$599$	2.76637	0.113031	0.0565153	+	0.998402i	$0.482001\pi$
$600$	42.3775	1.73006
$601$	−12.5085	−0.510230	−0.255115	−	0.966911i	$-0.582113\pi$
$601$	−12.5085	−0.510230	−0.255115	+	0.966911i	$0.582113\pi$
$602$	37.7970	1.54049
$603$	−70.9275	−2.88839
$604$	−0.592428	−0.0241055
$605$	0	0
$606$	27.2369	1.10642
$607$	−37.2492	−1.51190	−0.755950	−	0.654630i	$-0.772824\pi$
$607$	−37.2492	−1.51190	−0.755950	+	0.654630i	$0.772824\pi$
$608$	7.36824	0.298822
$609$	−34.3026	−1.39001
$610$	−4.07969	−0.165182
$611$	7.46555	0.302024
$612$	6.24065	0.252263
$613$	−31.6955	−1.28017	−0.640084	−	0.768305i	$-0.721100\pi$
$613$	−31.6955	−1.28017	−0.640084	+	0.768305i	$0.721100\pi$
$614$	20.3624	0.821760
$615$	6.39215	0.257756
$616$	0	0
$617$	−9.04103	−0.363978	−0.181989	−	0.983301i	$-0.558254\pi$
$617$	−9.04103	−0.363978	−0.181989	+	0.983301i	$0.558254\pi$
$618$	−50.7055	−2.03968
$619$	−11.5307	−0.463459	−0.231730	−	0.972780i	$-0.574438\pi$
$619$	−11.5307	−0.463459	−0.231730	+	0.972780i	$0.574438\pi$
$620$	−7.63941	−0.306806
$621$	−50.2556	−2.01669
$622$	5.15071	0.206525
$623$	−36.5756	−1.46537
$624$	49.7061	1.98984
$625$	−25.2902	−1.01161
$626$	−36.3383	−1.45237
$627$	0	0
$628$	1.79073	0.0714579
$629$	6.63598	0.264594
$630$	−105.116	−4.18793
$631$	−19.6315	−0.781519	−0.390760	−	0.920493i	$-0.627788\pi$
$631$	−19.6315	−0.781519	−0.390760	+	0.920493i	$0.627788\pi$
$632$	−1.11236	−0.0442473
$633$	53.0028	2.10667
$634$	17.8278	0.708032
$635$	11.1821	0.443750
$636$	5.20556	0.206414
$637$	−98.4899	−3.90231
$638$	0	0
$639$	−28.1589	−1.11395
$640$	24.5822	0.971698
$641$	3.04359	0.120215	0.0601073	−	0.998192i	$-0.480856\pi$
$641$	3.04359	0.120215	0.0601073	+	0.998192i	$0.480856\pi$
$642$	−63.7333	−2.51535
$643$	−13.3214	−0.525345	−0.262672	−	0.964885i	$-0.584604\pi$
$643$	−13.3214	−0.525345	−0.262672	+	0.964885i	$0.584604\pi$
$644$	−13.6224	−0.536798
$645$	−52.1746	−2.05437
$646$	−19.5557	−0.769410
$647$	49.2657	1.93683	0.968417	−	0.249335i	$-0.0802120\pi$
$647$	49.2657	1.93683	0.968417	+	0.249335i	$0.0802120\pi$
$648$	5.61597	0.220616
$649$	0	0
$650$	34.3938	1.34904
$651$	106.628	4.17908
$652$	−2.79240	−0.109359
$653$	−31.5895	−1.23619	−0.618096	−	0.786103i	$-0.712096\pi$
$653$	−31.5895	−1.23619	−0.618096	+	0.786103i	$0.712096\pi$
$654$	−25.5822	−1.00034
$655$	46.9303	1.83372
$656$	2.30653	0.0900548
$657$	−12.2916	−0.479540
$658$	−9.03377	−0.352173
$659$	4.83782	0.188455	0.0942274	−	0.995551i	$-0.469962\pi$
$659$	4.83782	0.188455	0.0942274	+	0.995551i	$0.469962\pi$
$660$	0	0
$661$	8.00928	0.311525	0.155762	−	0.987795i	$-0.450217\pi$
$661$	8.00928	0.311525	0.155762	+	0.987795i	$0.450217\pi$
$662$	−3.16530	−0.123023
$663$	57.3395	2.22688
$664$	−30.0081	−1.16454
$665$	−64.0952	−2.48551
$666$	11.7577	0.455600
$667$	−19.8868	−0.770022
$668$	4.97781	0.192597
$669$	−33.2030	−1.28370
$670$	−56.4981	−2.18271
$671$	0	0
$672$	26.1427	1.00848
$673$	−7.62088	−0.293763	−0.146882	−	0.989154i	$-0.546924\pi$
$673$	−7.62088	−0.293763	−0.146882	+	0.989154i	$0.546924\pi$
$674$	14.2233	0.547862
$675$	29.8765	1.14995
$676$	−5.19227	−0.199703
$677$	29.8047	1.14549	0.572745	−	0.819734i	$-0.305879\pi$
$677$	29.8047	1.14549	0.572745	+	0.819734i	$0.305879\pi$
$678$	28.2859	1.08631
$679$	14.0257	0.538257
$680$	35.4891	1.36094
$681$	−11.5500	−0.442597
$682$	0	0
$683$	−28.0157	−1.07199	−0.535995	−	0.844221i	$-0.680063\pi$
$683$	−28.0157	−1.07199	−0.535995	+	0.844221i	$0.680063\pi$
$684$	6.74219	0.257794
$685$	−20.9872	−0.801880
$686$	73.6130	2.81056
$687$	13.3188	0.508143
$688$	−18.8265	−0.717755
$689$	30.1617	1.14907
$690$	−96.6371	−3.67891
$691$	27.5320	1.04737	0.523684	−	0.851913i	$-0.324557\pi$
$691$	27.5320	1.04737	0.523684	+	0.851913i	$0.324557\pi$
$692$	2.26688	0.0861737
$693$	0	0
$694$	−11.2415	−0.426720
$695$	−11.5774	−0.439157
$696$	20.5195	0.777791
$697$	2.66074	0.100783
$698$	−9.80065	−0.370960
$699$	−42.0153	−1.58917
$700$	8.09838	0.306090
$701$	23.7575	0.897307	0.448654	−	0.893706i	$-0.351904\pi$
$701$	23.7575	0.897307	0.448654	+	0.893706i	$0.351904\pi$
$702$	42.0853	1.58841
$703$	7.16929	0.270395
$704$	0	0
$705$	12.4701	0.469651
$706$	0.0523882	0.00197165
$707$	37.1591	1.39751
$708$	7.28521	0.273795
$709$	17.2900	0.649340	0.324670	−	0.945827i	$-0.394747\pi$
$709$	17.2900	0.649340	0.324670	+	0.945827i	$0.394747\pi$
$710$	−22.4303	−0.841796
$711$	−1.89312	−0.0709975
$712$	21.8792	0.819958
$713$	61.8173	2.31507
$714$	−69.3843	−2.59664
$715$	0	0
$716$	−5.84501	−0.218438
$717$	−0.0807007	−0.00301382
$718$	−33.1811	−1.23831
$719$	21.2476	0.792400	0.396200	−	0.918164i	$-0.370329\pi$
$719$	21.2476	0.792400	0.396200	+	0.918164i	$0.370329\pi$
$720$	52.3580	1.95127
$721$	−69.1772	−2.57629
$722$	3.45706	0.128658
$723$	−37.0621	−1.37836
$724$	7.13765	0.265269
$725$	11.8225	0.439078
$726$	0	0
$727$	−32.5988	−1.20902	−0.604510	−	0.796597i	$-0.706631\pi$
$727$	−32.5988	−1.20902	−0.604510	+	0.796597i	$0.706631\pi$
$728$	81.4412	3.01841
$729$	−42.1353	−1.56057
$730$	−9.79100	−0.362381
$731$	−21.7177	−0.803260
$732$	0.928422	0.0343155
$733$	25.1980	0.930709	0.465355	−	0.885124i	$-0.345927\pi$
$733$	25.1980	0.930709	0.465355	+	0.885124i	$0.345927\pi$
$734$	21.9147	0.808885
$735$	−164.513	−6.06815
$736$	15.1562	0.558664
$737$	0	0
$738$	4.71431	0.173536
$739$	43.7239	1.60841	0.804204	−	0.594353i	$-0.202592\pi$
$739$	43.7239	1.60841	0.804204	+	0.594353i	$0.202592\pi$
$740$	−1.82243	−0.0669940
$741$	61.9477	2.27570
$742$	−36.4975	−1.33987
$743$	6.25851	0.229603	0.114801	−	0.993388i	$-0.463377\pi$
$743$	6.25851	0.229603	0.114801	+	0.993388i	$0.463377\pi$
$744$	−63.7839	−2.33843
$745$	57.2342	2.09690
$746$	32.8823	1.20391
$747$	−51.0707	−1.86858
$748$	0	0
$749$	−86.9508	−3.17711
$750$	−0.682708	−0.0249290
$751$	−7.65511	−0.279339	−0.139670	−	0.990198i	$-0.544604\pi$
$751$	−7.65511	−0.279339	−0.139670	+	0.990198i	$0.544604\pi$
$752$	4.49968	0.164087
$753$	27.9945	1.02018
$754$	16.6537	0.606493
$755$	−5.73367	−0.208670
$756$	9.90943	0.360403
$757$	33.6873	1.22439	0.612193	−	0.790708i	$-0.290288\pi$
$757$	33.6873	1.22439	0.612193	+	0.790708i	$0.290288\pi$
$758$	30.5823	1.11080
$759$	0	0
$760$	38.3412	1.39078
$761$	−28.3400	−1.02733	−0.513663	−	0.857992i	$-0.671712\pi$
$761$	−28.3400	−1.02733	−0.513663	+	0.857992i	$0.671712\pi$
$762$	13.0777	0.473756
$763$	−34.9016	−1.26352
$764$	−1.40455	−0.0508148
$765$	60.3987	2.18372
$766$	−10.3837	−0.375178
$767$	42.2115	1.52417
$768$	−21.6588	−0.781545
$769$	−2.44448	−0.0881501	−0.0440751	−	0.999028i	$-0.514034\pi$
$769$	−2.44448	−0.0881501	−0.0440751	+	0.999028i	$0.514034\pi$
$770$	0	0
$771$	40.6260	1.46311
$772$	−0.555122	−0.0199793
$773$	−30.7973	−1.10770	−0.553851	−	0.832616i	$-0.686842\pi$
$773$	−30.7973	−1.10770	−0.553851	+	0.832616i	$0.686842\pi$
$774$	−38.4796	−1.38312
$775$	−36.7498	−1.32009
$776$	−8.39005	−0.301185
$777$	25.4368	0.912541
$778$	−33.7577	−1.21027
$779$	2.87458	0.102992
$780$	−15.7471	−0.563837
$781$	0	0
$782$	−40.2253	−1.43845
$783$	14.4664	0.516988
$784$	−59.3625	−2.12009
$785$	17.3312	0.618576
$786$	54.8858	1.95771
$787$	−24.7391	−0.881853	−0.440926	−	0.897543i	$-0.645350\pi$
$787$	−24.7391	−0.881853	−0.440926	+	0.897543i	$0.645350\pi$
$788$	−5.52206	−0.196715
$789$	44.1451	1.57161
$790$	−1.50799	−0.0536518
$791$	38.5902	1.37211
$792$	0	0
$793$	5.37940	0.191028
$794$	−11.6505	−0.413462
$795$	50.3808	1.78682
$796$	6.37349	0.225902
$797$	−31.1840	−1.10459	−0.552296	−	0.833648i	$-0.686248\pi$
$797$	−31.1840	−1.10459	−0.552296	+	0.833648i	$0.686248\pi$
$798$	−74.9605	−2.65357
$799$	5.19070	0.183634
$800$	−9.01019	−0.318558
$801$	37.2361	1.31567
$802$	−36.8860	−1.30249
$803$	0	0
$804$	12.8574	0.453444
$805$	−131.841	−4.64679
$806$	−51.7673	−1.82342
$807$	−38.3655	−1.35053
$808$	−22.2282	−0.781986
$809$	22.6010	0.794610	0.397305	−	0.917687i	$-0.369946\pi$
$809$	22.6010	0.794610	0.397305	+	0.917687i	$0.369946\pi$
$810$	7.61338	0.267507
$811$	31.9391	1.12153	0.560767	−	0.827974i	$-0.310506\pi$
$811$	31.9391	1.12153	0.560767	+	0.827974i	$0.310506\pi$
$812$	3.92130	0.137611
$813$	69.4818	2.43683
$814$	0	0
$815$	−27.0256	−0.946664
$816$	34.5600	1.20984
$817$	−23.4631	−0.820870
$818$	29.6717	1.03745
$819$	138.604	4.84323
$820$	−0.730718	−0.0255178
$821$	32.6809	1.14057	0.570285	−	0.821447i	$-0.306833\pi$
$821$	32.6809	1.14057	0.570285	+	0.821447i	$0.306833\pi$
$822$	−24.5449	−0.856102
$823$	21.3237	0.743297	0.371649	−	0.928373i	$-0.378793\pi$
$823$	21.3237	0.743297	0.371649	+	0.928373i	$0.378793\pi$
$824$	41.3812	1.44158
$825$	0	0
$826$	−51.0785	−1.77725
$827$	−20.8252	−0.724163	−0.362081	−	0.932146i	$-0.617934\pi$
$827$	−20.8252	−0.724163	−0.362081	+	0.932146i	$0.617934\pi$
$828$	13.8684	0.481960
$829$	−21.2732	−0.738849	−0.369424	−	0.929261i	$-0.620445\pi$
$829$	−21.2732	−0.738849	−0.369424	+	0.929261i	$0.620445\pi$
$830$	−40.6810	−1.41206
$831$	75.3920	2.61532
$832$	−47.5755	−1.64938
$833$	−68.4788	−2.37265
$834$	−13.5400	−0.468852
$835$	48.1765	1.66722
$836$	0	0
$837$	−44.9681	−1.55433
$838$	8.83756	0.305288
$839$	57.8074	1.99573	0.997866	−	0.0652934i	$-0.0207983\pi$
$839$	57.8074	1.99573	0.997866	+	0.0652934i	$0.0207983\pi$
$840$	136.036	4.69367
$841$	−23.2754	−0.802601
$842$	−2.71184	−0.0934561
$843$	−84.1472	−2.89818
$844$	−6.05901	−0.208560
$845$	−50.2521	−1.72873
$846$	9.19690	0.316196
$847$	0	0
$848$	18.1793	0.624279
$849$	−41.7824	−1.43397
$850$	23.9136	0.820228
$851$	14.7469	0.505518
$852$	5.10451	0.174878
$853$	−5.94693	−0.203619	−0.101809	−	0.994804i	$-0.532463\pi$
$853$	−5.94693	−0.203619	−0.101809	+	0.994804i	$0.532463\pi$
$854$	−6.50941	−0.222747
$855$	65.2527	2.23159
$856$	52.0132	1.77777
$857$	55.1181	1.88280	0.941400	−	0.337293i	$-0.109511\pi$
$857$	55.1181	1.88280	0.941400	+	0.337293i	$0.109511\pi$
$858$	0	0
$859$	3.34358	0.114082	0.0570408	−	0.998372i	$-0.481833\pi$
$859$	3.34358	0.114082	0.0570408	+	0.998372i	$0.481833\pi$
$860$	5.96432	0.203382
$861$	10.1991	0.347584
$862$	−25.2931	−0.861487
$863$	18.3209	0.623651	0.311825	−	0.950139i	$-0.399060\pi$
$863$	18.3209	0.623651	0.311825	+	0.950139i	$0.399060\pi$
$864$	−11.0252	−0.375083
$865$	21.9394	0.745963
$866$	29.7005	1.00926
$867$	−8.57995	−0.291390
$868$	−12.1892	−0.413727
$869$	0	0
$870$	27.8176	0.943106
$871$	74.4974	2.52425
$872$	20.8778	0.707012
$873$	−14.2790	−0.483270
$874$	−43.4581	−1.46999
$875$	−0.931413	−0.0314875
$876$	2.22815	0.0752823
$877$	−11.0283	−0.372401	−0.186200	−	0.982512i	$-0.559617\pi$
$877$	−11.0283	−0.372401	−0.186200	+	0.982512i	$0.559617\pi$
$878$	9.47983	0.319929
$879$	−45.9389	−1.54948
$880$	0	0
$881$	−42.1619	−1.42047	−0.710235	−	0.703964i	$-0.751411\pi$
$881$	−42.1619	−1.42047	−0.710235	+	0.703964i	$0.751411\pi$
$882$	−121.331	−4.08543
$883$	−50.5867	−1.70238	−0.851189	−	0.524859i	$-0.824118\pi$
$883$	−50.5867	−1.70238	−0.851189	+	0.524859i	$0.824118\pi$
$884$	−6.55475	−0.220460
$885$	70.5082	2.37011
$886$	−6.35340	−0.213447
$887$	20.5497	0.689993	0.344996	−	0.938604i	$-0.387880\pi$
$887$	20.5497	0.689993	0.344996	+	0.938604i	$0.387880\pi$
$888$	−15.2161	−0.510618
$889$	17.8418	0.598395
$890$	29.6609	0.994236
$891$	0	0
$892$	3.79559	0.127086
$893$	5.60786	0.187660
$894$	66.9364	2.23869
$895$	−56.5695	−1.89091
$896$	39.2225	1.31033
$897$	127.424	4.25455
$898$	5.73385	0.191341
$899$	−17.7945	−0.593480
$900$	−8.24463	−0.274821
$901$	20.9711	0.698648
$902$	0	0
$903$	−83.2478	−2.77031
$904$	−23.0843	−0.767773
$905$	69.0801	2.29630
$906$	−6.70562	−0.222779
$907$	8.06583	0.267821	0.133911	−	0.990993i	$-0.457246\pi$
$907$	8.06583	0.267821	0.133911	+	0.990993i	$0.457246\pi$
$908$	1.32034	0.0438169
$909$	−37.8301	−1.25475
$910$	110.407	3.65996
$911$	24.4560	0.810264	0.405132	−	0.914258i	$-0.367226\pi$
$911$	24.4560	0.810264	0.405132	+	0.914258i	$0.367226\pi$
$912$	37.3375	1.23637
$913$	0	0
$914$	22.2239	0.735102
$915$	8.98551	0.297052
$916$	−1.52253	−0.0503060
$917$	74.8803	2.47276
$918$	29.2614	0.965769
$919$	−6.99410	−0.230714	−0.115357	−	0.993324i	$-0.536801\pi$
$919$	−6.99410	−0.230714	−0.115357	+	0.993324i	$0.536801\pi$
$920$	78.8662	2.60014
$921$	−44.8481	−1.47780
$922$	−21.1289	−0.695842
$923$	29.5762	0.973513
$924$	0	0
$925$	−8.76690	−0.288254
$926$	−44.9258	−1.47635
$927$	70.4264	2.31311
$928$	−4.36280	−0.143216
$929$	41.4648	1.36042	0.680209	−	0.733019i	$-0.261889\pi$
$929$	41.4648	1.36042	0.680209	+	0.733019i	$0.261889\pi$
$930$	−86.4697	−2.83545
$931$	−73.9822	−2.42467
$932$	4.80297	0.157327
$933$	−11.3444	−0.371399
$934$	−26.4458	−0.865334
$935$	0	0
$936$	−82.9119	−2.71006
$937$	42.3323	1.38293	0.691467	−	0.722408i	$-0.256965\pi$
$937$	42.3323	1.38293	0.691467	+	0.722408i	$0.256965\pi$
$938$	−90.1463	−2.94338
$939$	80.0349	2.61184
$940$	−1.42552	−0.0464953
$941$	−11.6346	−0.379278	−0.189639	−	0.981854i	$-0.560732\pi$
$941$	−11.6346	−0.379278	−0.189639	+	0.981854i	$0.560732\pi$
$942$	20.2691	0.660403
$943$	5.91288	0.192550
$944$	25.4420	0.828067
$945$	95.9061	3.11982
$946$	0	0
$947$	−29.1141	−0.946081	−0.473040	−	0.881041i	$-0.656844\pi$
$947$	−29.1141	−0.946081	−0.473040	+	0.881041i	$0.656844\pi$
$948$	0.343175	0.0111458
$949$	12.9102	0.419083
$950$	25.8354	0.838211
$951$	−39.2656	−1.27328
$952$	56.6250	1.83523
$953$	−5.14787	−0.166756	−0.0833779	−	0.996518i	$-0.526571\pi$
$953$	−5.14787	−0.166756	−0.0833779	+	0.996518i	$0.526571\pi$
$954$	37.1566	1.20299
$955$	−13.5936	−0.439878
$956$	0.00922528	0.000298367 0
$957$	0	0
$958$	16.5985	0.536274
$959$	−33.4864	−1.08133
$960$	−79.4679	−2.56482
$961$	24.3133	0.784301
$962$	−12.3494	−0.398162
$963$	88.5210	2.85255
$964$	4.23675	0.136456
$965$	−5.37261	−0.172951
$966$	−154.190	−4.96100
$967$	−25.7412	−0.827783	−0.413891	−	0.910326i	$-0.635831\pi$
$967$	−25.7412	−0.827783	−0.413891	+	0.910326i	$0.635831\pi$
$968$	0	0
$969$	43.0714	1.38365
$970$	−11.3741	−0.365200
$971$	11.3852	0.365369	0.182685	−	0.983172i	$-0.441521\pi$
$971$	11.3852	0.365369	0.182685	+	0.983172i	$0.441521\pi$
$972$	4.17670	0.133968
$973$	−18.4725	−0.592201
$974$	−21.1032	−0.676191
$975$	−75.7522	−2.42601
$976$	3.24231	0.103784
$977$	−32.2201	−1.03081	−0.515407	−	0.856946i	$-0.672359\pi$
$977$	−32.2201	−1.03081	−0.515407	+	0.856946i	$0.672359\pi$
$978$	−31.6069	−1.01068
$979$	0	0
$980$	18.8063	0.600744
$981$	35.5319	1.13445
$982$	−31.8581	−1.01663
$983$	−27.9462	−0.891344	−0.445672	−	0.895196i	$-0.647035\pi$
$983$	−27.9462	−0.891344	−0.445672	+	0.895196i	$0.647035\pi$
$984$	−6.10100	−0.194493
$985$	−53.4440	−1.70287
$986$	11.5791	0.368755
$987$	19.8968	0.633323
$988$	−7.08154	−0.225294
$989$	−48.2626	−1.53466
$990$	0	0
$991$	35.9854	1.14311	0.571556	−	0.820563i	$-0.306340\pi$
$991$	35.9854	1.14311	0.571556	+	0.820563i	$0.306340\pi$
$992$	13.5616	0.430580
$993$	6.97155	0.221235
$994$	−35.7890	−1.13516
$995$	61.6843	1.95552
$996$	9.25783	0.293346
$997$	1.62823	0.0515667	0.0257834	−	0.999668i	$-0.491792\pi$
$997$	1.62823	0.0515667	0.0257834	+	0.999668i	$0.491792\pi$
$998$	−35.1397	−1.11233
$999$	−10.7275	−0.339402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.j.1.7		21
11.10	odd	2		671.2.a.d.1.15	✓	21
33.32	even	2		6039.2.a.l.1.7		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.15	✓	21	11.10	odd	2
6039.2.a.l.1.7		21	33.32	even	2
7381.2.a.j.1.7		21	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.29392 q^{2} +2.84985 q^{3} -0.325780 q^{4} -3.15298 q^{5} -3.68746 q^{6} -5.03078 q^{7} +3.00937 q^{8} +5.12162 q^{9} +O(q^{10})\)	\(q-1.29392 q^{2} +2.84985 q^{3} -0.325780 q^{4} -3.15298 q^{5} -3.68746 q^{6} -5.03078 q^{7} +3.00937 q^{8} +5.12162 q^{9} +4.07969 q^{10} -0.928422 q^{12} -5.37940 q^{13} +6.50941 q^{14} -8.98551 q^{15} -3.24231 q^{16} -3.74023 q^{17} -6.62696 q^{18} -4.04082 q^{19} +1.02718 q^{20} -14.3369 q^{21} -8.31179 q^{23} +8.57623 q^{24} +4.94128 q^{25} +6.96050 q^{26} +6.04630 q^{27} +1.63892 q^{28} +2.39261 q^{29} +11.6265 q^{30} -7.43729 q^{31} -1.82345 q^{32} +4.83955 q^{34} +15.8619 q^{35} -1.66852 q^{36} -1.77422 q^{37} +5.22848 q^{38} -15.3305 q^{39} -9.48847 q^{40} -0.711385 q^{41} +18.5508 q^{42} +5.80652 q^{43} -16.1484 q^{45} +10.7548 q^{46} -1.38780 q^{47} -9.24008 q^{48} +18.3087 q^{49} -6.39360 q^{50} -10.6591 q^{51} +1.75250 q^{52} -5.60689 q^{53} -7.82341 q^{54} -15.1394 q^{56} -11.5157 q^{57} -3.09583 q^{58} -7.84688 q^{59} +2.92729 q^{60} -1.00000 q^{61} +9.62324 q^{62} -25.7657 q^{63} +8.84401 q^{64} +16.9611 q^{65} -13.8486 q^{67} +1.21849 q^{68} -23.6873 q^{69} -20.5240 q^{70} -5.49805 q^{71} +15.4128 q^{72} -2.39993 q^{73} +2.29569 q^{74} +14.0819 q^{75} +1.31642 q^{76} +19.8364 q^{78} -0.369632 q^{79} +10.2229 q^{80} +1.86616 q^{81} +0.920473 q^{82} -9.97158 q^{83} +4.67068 q^{84} +11.7929 q^{85} -7.51316 q^{86} +6.81856 q^{87} +7.27038 q^{89} +20.8947 q^{90} +27.0626 q^{91} +2.70781 q^{92} -21.1951 q^{93} +1.79570 q^{94} +12.7406 q^{95} -5.19656 q^{96} -2.78798 q^{97} -23.6899 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9} - q^{10} + 6 q^{12} - 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} - q^{17} + 5 q^{18} - 15 q^{19} - 2 q^{20} - 16 q^{21} + 11 q^{23} + 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} + 16 q^{28} + 9 q^{29} - 16 q^{30} + 22 q^{31} - 3 q^{32} + 33 q^{34} + 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} + 28 q^{39} + 16 q^{40} - 7 q^{41} - 55 q^{42} - 16 q^{43} + 44 q^{45} + 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} + 33 q^{50} + 19 q^{51} - 60 q^{52} + 9 q^{53} - 13 q^{54} + 44 q^{56} - 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} - 21 q^{61} + 23 q^{62} - 24 q^{63} + 66 q^{64} - 25 q^{65} + 38 q^{67} + 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} + 75 q^{72} - 20 q^{73} + 12 q^{74} - 10 q^{75} - 59 q^{76} - 14 q^{78} - q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} + 19 q^{83} + 14 q^{84} - 38 q^{85} - 3 q^{86} - 4 q^{87} + 37 q^{89} + 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} + 64 q^{94} + 43 q^{95} + 38 q^{96} + 68 q^{97} + 2 q^{98}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9 - q^10 + 6 * q^12 - 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 - q^17 + 5 * q^18 - 15 * q^19 - 2 * q^20 - 16 * q^21 + 11 * q^23 + 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 + 16 * q^28 + 9 * q^29 - 16 * q^30 + 22 * q^31 - 3 * q^32 + 33 * q^34 + 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 + 28 * q^39 + 16 * q^40 - 7 * q^41 - 55 * q^42 - 16 * q^43 + 44 * q^45 + 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 + 33 * q^50 + 19 * q^51 - 60 * q^52 + 9 * q^53 - 13 * q^54 + 44 * q^56 - 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 - 21 * q^61 + 23 * q^62 - 24 * q^63 + 66 * q^64 - 25 * q^65 + 38 * q^67 + 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 + 75 * q^72 - 20 * q^73 + 12 * q^74 - 10 * q^75 - 59 * q^76 - 14 * q^78 - q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 + 19 * q^83 + 14 * q^84 - 38 * q^85 - 3 * q^86 - 4 * q^87 + 37 * q^89 + 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 + 64 * q^94 + 43 * q^95 + 38 * q^96 + 68 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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