LMFDB - Embedded newform 1205.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57583 q^{2} +0.0567878 q^{3} +4.63488 q^{4} -1.00000 q^{5} -0.146276 q^{6} +2.85547 q^{7} -6.78699 q^{8} -2.99678 q^{9} +O(q^{10})$	\(q-2.57583 q^{2} +0.0567878 q^{3} +4.63488 q^{4} -1.00000 q^{5} -0.146276 q^{6} +2.85547 q^{7} -6.78699 q^{8} -2.99678 q^{9} +2.57583 q^{10} +6.31740 q^{11} +0.263205 q^{12} +5.29212 q^{13} -7.35520 q^{14} -0.0567878 q^{15} +8.21234 q^{16} -2.63097 q^{17} +7.71917 q^{18} +2.76600 q^{19} -4.63488 q^{20} +0.162156 q^{21} -16.2725 q^{22} -6.28590 q^{23} -0.385418 q^{24} +1.00000 q^{25} -13.6316 q^{26} -0.340544 q^{27} +13.2348 q^{28} +5.10150 q^{29} +0.146276 q^{30} +4.83893 q^{31} -7.57959 q^{32} +0.358751 q^{33} +6.77692 q^{34} -2.85547 q^{35} -13.8897 q^{36} +0.288024 q^{37} -7.12474 q^{38} +0.300528 q^{39} +6.78699 q^{40} +9.26642 q^{41} -0.417685 q^{42} -3.00110 q^{43} +29.2804 q^{44} +2.99678 q^{45} +16.1914 q^{46} +0.570278 q^{47} +0.466361 q^{48} +1.15371 q^{49} -2.57583 q^{50} -0.149407 q^{51} +24.5283 q^{52} -9.94711 q^{53} +0.877181 q^{54} -6.31740 q^{55} -19.3800 q^{56} +0.157075 q^{57} -13.1406 q^{58} -14.7070 q^{59} -0.263205 q^{60} -10.4353 q^{61} -12.4642 q^{62} -8.55720 q^{63} +3.09902 q^{64} -5.29212 q^{65} -0.924081 q^{66} -3.65107 q^{67} -12.1942 q^{68} -0.356962 q^{69} +7.35520 q^{70} +5.82789 q^{71} +20.3391 q^{72} +9.17223 q^{73} -0.741901 q^{74} +0.0567878 q^{75} +12.8201 q^{76} +18.0391 q^{77} -0.774107 q^{78} +7.79299 q^{79} -8.21234 q^{80} +8.97099 q^{81} -23.8687 q^{82} +2.57360 q^{83} +0.751573 q^{84} +2.63097 q^{85} +7.73032 q^{86} +0.289703 q^{87} -42.8761 q^{88} +15.4518 q^{89} -7.71917 q^{90} +15.1115 q^{91} -29.1344 q^{92} +0.274792 q^{93} -1.46894 q^{94} -2.76600 q^{95} -0.430428 q^{96} -4.84870 q^{97} -2.97176 q^{98} -18.9318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * 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 $

$2$	−2.57583	−1.82138	−0.910692	−	0.413086i	$-0.864451\pi$
$2$	−2.57583	−1.82138	−0.910692	+	0.413086i	$0.864451\pi$
$3$	0.0567878	0.0327865	0.0163932	−	0.999866i	$-0.494782\pi$
$3$	0.0567878	0.0327865	0.0163932	+	0.999866i	$0.494782\pi$
$4$	4.63488	2.31744
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.146276	−0.0597167
$7$	2.85547	1.07927	0.539633	−	0.841900i	$-0.318563\pi$
$7$	2.85547	1.07927	0.539633	+	0.841900i	$0.318563\pi$
$8$	−6.78699	−2.39956
$9$	−2.99678	−0.998925
$10$	2.57583	0.814548
$11$	6.31740	1.90477	0.952384	−	0.304902i	$-0.0986237\pi$
$11$	6.31740	1.90477	0.952384	+	0.304902i	$0.0986237\pi$
$12$	0.263205	0.0759806
$13$	5.29212	1.46777	0.733885	−	0.679274i	$-0.237705\pi$
$13$	5.29212	1.46777	0.733885	+	0.679274i	$0.237705\pi$
$14$	−7.35520	−1.96576
$15$	−0.0567878	−0.0146626
$16$	8.21234	2.05309
$17$	−2.63097	−0.638104	−0.319052	−	0.947737i	$-0.603364\pi$
$17$	−2.63097	−0.638104	−0.319052	+	0.947737i	$0.603364\pi$
$18$	7.71917	1.81943
$19$	2.76600	0.634565	0.317282	−	0.948331i	$-0.397230\pi$
$19$	2.76600	0.634565	0.317282	+	0.948331i	$0.397230\pi$
$20$	−4.63488	−1.03639
$21$	0.162156	0.0353853
$22$	−16.2725	−3.46931
$23$	−6.28590	−1.31070	−0.655350	−	0.755325i	$-0.727479\pi$
$23$	−6.28590	−1.31070	−0.655350	+	0.755325i	$0.727479\pi$
$24$	−0.385418	−0.0786732
$25$	1.00000	0.200000
$26$	−13.6316	−2.67337
$27$	−0.340544	−0.0655377
$28$	13.2348	2.50113
$29$	5.10150	0.947325	0.473663	−	0.880706i	$-0.342932\pi$
$29$	5.10150	0.947325	0.473663	+	0.880706i	$0.342932\pi$
$30$	0.146276	0.0267061
$31$	4.83893	0.869098	0.434549	−	0.900648i	$-0.356908\pi$
$31$	4.83893	0.869098	0.434549	+	0.900648i	$0.356908\pi$
$32$	−7.57959	−1.33989
$33$	0.358751	0.0624506
$34$	6.77692	1.16223
$35$	−2.85547	−0.482663
$36$	−13.8897	−2.31495
$37$	0.288024	0.0473509	0.0236755	−	0.999720i	$-0.492463\pi$
$37$	0.288024	0.0473509	0.0236755	+	0.999720i	$0.492463\pi$
$38$	−7.12474	−1.15579
$39$	0.300528	0.0481230
$40$	6.78699	1.07312
$41$	9.26642	1.44717	0.723586	−	0.690235i	$-0.242493\pi$
$41$	9.26642	1.44717	0.723586	+	0.690235i	$0.242493\pi$
$42$	−0.417685	−0.0644503
$43$	−3.00110	−0.457664	−0.228832	−	0.973466i	$-0.573491\pi$
$43$	−3.00110	−0.457664	−0.228832	+	0.973466i	$0.573491\pi$
$44$	29.2804	4.41418
$45$	2.99678	0.446733
$46$	16.1914	2.38729
$47$	0.570278	0.0831836	0.0415918	−	0.999135i	$-0.486757\pi$
$47$	0.570278	0.0831836	0.0415918	+	0.999135i	$0.486757\pi$
$48$	0.466361	0.0673134
$49$	1.15371	0.164816
$50$	−2.57583	−0.364277
$51$	−0.149407	−0.0209212
$52$	24.5283	3.40147
$53$	−9.94711	−1.36634	−0.683170	−	0.730259i	$-0.739399\pi$
$53$	−9.94711	−1.36634	−0.683170	+	0.730259i	$0.739399\pi$
$54$	0.877181	0.119369
$55$	−6.31740	−0.851838
$56$	−19.3800	−2.58977
$57$	0.157075	0.0208051
$58$	−13.1406	−1.72544
$59$	−14.7070	−1.91469	−0.957344	−	0.288950i	$-0.906694\pi$
$59$	−14.7070	−1.91469	−0.957344	+	0.288950i	$0.906694\pi$
$60$	−0.263205	−0.0339796
$61$	−10.4353	−1.33611	−0.668053	−	0.744114i	$-0.732872\pi$
$61$	−10.4353	−1.33611	−0.668053	+	0.744114i	$0.732872\pi$
$62$	−12.4642	−1.58296
$63$	−8.55720	−1.07811
$64$	3.09902	0.387377
$65$	−5.29212	−0.656407
$66$	−0.924081	−0.113746
$67$	−3.65107	−0.446050	−0.223025	−	0.974813i	$-0.571593\pi$
$67$	−3.65107	−0.446050	−0.223025	+	0.974813i	$0.571593\pi$
$68$	−12.1942	−1.47877
$69$	−0.356962	−0.0429732
$70$	7.35520	0.879114
$71$	5.82789	0.691643	0.345821	−	0.938300i	$-0.387600\pi$
$71$	5.82789	0.691643	0.345821	+	0.938300i	$0.387600\pi$
$72$	20.3391	2.39698
$73$	9.17223	1.07353	0.536764	−	0.843732i	$-0.319647\pi$
$73$	9.17223	1.07353	0.536764	+	0.843732i	$0.319647\pi$
$74$	−0.741901	−0.0862442
$75$	0.0567878	0.00655729
$76$	12.8201	1.47057
$77$	18.0391	2.05575
$78$	−0.774107	−0.0876504
$79$	7.79299	0.876780	0.438390	−	0.898785i	$-0.355549\pi$
$79$	7.79299	0.876780	0.438390	+	0.898785i	$0.355549\pi$
$80$	−8.21234	−0.918168
$81$	8.97099	0.996776
$82$	−23.8687	−2.63585
$83$	2.57360	0.282490	0.141245	−	0.989975i	$-0.454890\pi$
$83$	2.57360	0.282490	0.141245	+	0.989975i	$0.454890\pi$
$84$	0.751573	0.0820034
$85$	2.63097	0.285369
$86$	7.73032	0.833582
$87$	0.289703	0.0310595
$88$	−42.8761	−4.57061
$89$	15.4518	1.63789	0.818943	−	0.573874i	$-0.194560\pi$
$89$	15.4518	1.63789	0.818943	+	0.573874i	$0.194560\pi$
$90$	−7.71917	−0.813672
$91$	15.1115	1.58411
$92$	−29.1344	−3.03747
$93$	0.274792	0.0284946
$94$	−1.46894	−0.151509
$95$	−2.76600	−0.283786
$96$	−0.430428	−0.0439304
$97$	−4.84870	−0.492311	−0.246156	−	0.969230i	$-0.579167\pi$
$97$	−4.84870	−0.492311	−0.246156	+	0.969230i	$0.579167\pi$
$98$	−2.97176	−0.300193
$99$	−18.9318	−1.90272
$100$	4.63488	0.463488
$101$	13.2281	1.31625	0.658123	−	0.752910i	$-0.271351\pi$
$101$	13.2281	1.31625	0.658123	+	0.752910i	$0.271351\pi$
$102$	0.384846	0.0381055
$103$	−3.83008	−0.377389	−0.188694	−	0.982036i	$-0.560426\pi$
$103$	−3.83008	−0.377389	−0.188694	+	0.982036i	$0.560426\pi$
$104$	−35.9175	−3.52201
$105$	−0.162156	−0.0158248
$106$	25.6220	2.48863
$107$	14.9511	1.44538	0.722688	−	0.691175i	$-0.242906\pi$
$107$	14.9511	1.44538	0.722688	+	0.691175i	$0.242906\pi$
$108$	−1.57838	−0.151880
$109$	8.72545	0.835747	0.417873	−	0.908505i	$-0.362776\pi$
$109$	8.72545	0.835747	0.417873	+	0.908505i	$0.362776\pi$
$110$	16.2725	1.55152
$111$	0.0163563	0.00155247
$112$	23.4501	2.21583
$113$	−17.0295	−1.60200	−0.801001	−	0.598663i	$-0.795699\pi$
$113$	−17.0295	−1.60200	−0.801001	+	0.598663i	$0.795699\pi$
$114$	−0.404599	−0.0378941
$115$	6.28590	0.586163
$116$	23.6449	2.19537
$117$	−15.8593	−1.46619
$118$	37.8827	3.48738
$119$	−7.51265	−0.688684
$120$	0.385418	0.0351837
$121$	28.9095	2.62814
$122$	26.8796	2.43356
$123$	0.526220	0.0474476
$124$	22.4279	2.01408
$125$	−1.00000	−0.0894427
$126$	22.0419	1.96365
$127$	−5.90211	−0.523728	−0.261864	−	0.965105i	$-0.584337\pi$
$127$	−5.90211	−0.523728	−0.261864	+	0.965105i	$0.584337\pi$
$128$	7.17665	0.634333
$129$	−0.170426	−0.0150052
$130$	13.6316	1.19557
$131$	−9.65057	−0.843174	−0.421587	−	0.906788i	$-0.638527\pi$
$131$	−9.65057	−0.843174	−0.421587	+	0.906788i	$0.638527\pi$
$132$	1.66277	0.144725
$133$	7.89824	0.684864
$134$	9.40453	0.812427
$135$	0.340544	0.0293093
$136$	17.8564	1.53117
$137$	11.7258	1.00180	0.500901	−	0.865505i	$-0.333002\pi$
$137$	11.7258	1.00180	0.500901	+	0.865505i	$0.333002\pi$
$138$	0.919473	0.0782707
$139$	−12.6947	−1.07675	−0.538377	−	0.842704i	$-0.680962\pi$
$139$	−12.6947	−1.07675	−0.538377	+	0.842704i	$0.680962\pi$
$140$	−13.2348	−1.11854
$141$	0.0323848	0.00272730
$142$	−15.0116	−1.25975
$143$	33.4324	2.79576
$144$	−24.6105	−2.05088
$145$	−5.10150	−0.423657
$146$	−23.6261	−1.95531
$147$	0.0655168	0.00540374
$148$	1.33496	0.109733
$149$	−10.5196	−0.861800	−0.430900	−	0.902400i	$-0.641804\pi$
$149$	−10.5196	−0.861800	−0.430900	+	0.902400i	$0.641804\pi$
$150$	−0.146276	−0.0119433
$151$	22.7835	1.85410	0.927048	−	0.374942i	$-0.122337\pi$
$151$	22.7835	1.85410	0.927048	+	0.374942i	$0.122337\pi$
$152$	−18.7728	−1.52268
$153$	7.88442	0.637418
$154$	−46.4657	−3.74431
$155$	−4.83893	−0.388672
$156$	1.39291	0.111522
$157$	15.0725	1.20291	0.601456	−	0.798906i	$-0.294587\pi$
$157$	15.0725	1.20291	0.601456	+	0.798906i	$0.294587\pi$
$158$	−20.0734	−1.59695
$159$	−0.564875	−0.0447975
$160$	7.57959	0.599219
$161$	−17.9492	−1.41459
$162$	−23.1077	−1.81551
$163$	23.3387	1.82803	0.914014	−	0.405682i	$-0.132966\pi$
$163$	23.3387	1.82803	0.914014	+	0.405682i	$0.132966\pi$
$164$	42.9487	3.35373
$165$	−0.358751	−0.0279288
$166$	−6.62915	−0.514522
$167$	3.76500	0.291344	0.145672	−	0.989333i	$-0.453466\pi$
$167$	3.76500	0.291344	0.145672	+	0.989333i	$0.453466\pi$
$168$	−1.10055	−0.0849093
$169$	15.0065	1.15435
$170$	−6.77692	−0.519766
$171$	−8.28909	−0.633883
$172$	−13.9097	−1.06061
$173$	9.74258	0.740715	0.370358	−	0.928889i	$-0.379235\pi$
$173$	9.74258	0.740715	0.370358	+	0.928889i	$0.379235\pi$
$174$	−0.746225	−0.0565712
$175$	2.85547	0.215853
$176$	51.8807	3.91065
$177$	−0.835178	−0.0627758
$178$	−39.8011	−2.98322
$179$	2.35072	0.175701	0.0878506	−	0.996134i	$-0.472000\pi$
$179$	2.35072	0.175701	0.0878506	+	0.996134i	$0.472000\pi$
$180$	13.8897	1.03528
$181$	4.95437	0.368255	0.184128	−	0.982902i	$-0.441054\pi$
$181$	4.95437	0.368255	0.184128	+	0.982902i	$0.441054\pi$
$182$	−38.9246	−2.88528
$183$	−0.592599	−0.0438062
$184$	42.6623	3.14511
$185$	−0.288024	−0.0211760
$186$	−0.707817	−0.0518997
$187$	−16.6209	−1.21544
$188$	2.64317	0.192773
$189$	−0.972413	−0.0707326
$190$	7.12474	0.516883
$191$	0.808828	0.0585248	0.0292624	−	0.999572i	$-0.490684\pi$
$191$	0.808828	0.0585248	0.0292624	+	0.999572i	$0.490684\pi$
$192$	0.175986	0.0127007
$193$	10.6807	0.768814	0.384407	−	0.923164i	$-0.374406\pi$
$193$	10.6807	0.768814	0.384407	+	0.923164i	$0.374406\pi$
$194$	12.4894	0.896687
$195$	−0.300528	−0.0215212
$196$	5.34732	0.381951
$197$	9.00234	0.641390	0.320695	−	0.947182i	$-0.396083\pi$
$197$	9.00234	0.641390	0.320695	+	0.947182i	$0.396083\pi$
$198$	48.7651	3.46558
$199$	−24.4750	−1.73498	−0.867492	−	0.497451i	$-0.834269\pi$
$199$	−24.4750	−1.73498	−0.867492	+	0.497451i	$0.834269\pi$
$200$	−6.78699	−0.479913
$201$	−0.207336	−0.0146244
$202$	−34.0733	−2.39739
$203$	14.5672	1.02242
$204$	−0.692483	−0.0484835
$205$	−9.26642	−0.647195
$206$	9.86561	0.687370
$207$	18.8374	1.30929
$208$	43.4607	3.01346
$209$	17.4739	1.20870
$210$	0.417685	0.0288230
$211$	−9.16836	−0.631176	−0.315588	−	0.948896i	$-0.602202\pi$
$211$	−9.16836	−0.631176	−0.315588	+	0.948896i	$0.602202\pi$
$212$	−46.1036	−3.16641
$213$	0.330953	0.0226765
$214$	−38.5114	−2.63258
$215$	3.00110	0.204674
$216$	2.31127	0.157262
$217$	13.8174	0.937988
$218$	−22.4752	−1.52222
$219$	0.520871	0.0351972
$220$	−29.2804	−1.97408
$221$	−13.9234	−0.936589
$222$	−0.0421309	−0.00282764
$223$	−16.0932	−1.07768	−0.538839	−	0.842409i	$-0.681137\pi$
$223$	−16.0932	−1.07768	−0.538839	+	0.842409i	$0.681137\pi$
$224$	−21.6433	−1.44610
$225$	−2.99678	−0.199785
$226$	43.8651	2.91786
$227$	2.05086	0.136121	0.0680603	−	0.997681i	$-0.478319\pi$
$227$	2.05086	0.136121	0.0680603	+	0.997681i	$0.478319\pi$
$228$	0.728025	0.0482146
$229$	17.5241	1.15803	0.579013	−	0.815318i	$-0.303438\pi$
$229$	17.5241	1.15803	0.579013	+	0.815318i	$0.303438\pi$
$230$	−16.1914	−1.06763
$231$	1.02440	0.0674008
$232$	−34.6238	−2.27317
$233$	8.81246	0.577324	0.288662	−	0.957431i	$-0.406790\pi$
$233$	8.81246	0.577324	0.288662	+	0.957431i	$0.406790\pi$
$234$	40.8508	2.67050
$235$	−0.570278	−0.0372008
$236$	−68.1652	−4.43717
$237$	0.442547	0.0287465
$238$	19.3513	1.25436
$239$	−0.0584768	−0.00378255	−0.00189128	−	0.999998i	$-0.500602\pi$
$239$	−0.0584768	−0.00378255	−0.00189128	+	0.999998i	$0.500602\pi$
$240$	−0.466361	−0.0301035
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−74.4659	−4.78685
$243$	1.53107	0.0982185
$244$	−48.3665	−3.09635
$245$	−1.15371	−0.0737080
$246$	−1.35545	−0.0864203
$247$	14.6380	0.931395
$248$	−32.8418	−2.08545
$249$	0.146149	0.00926184
$250$	2.57583	0.162910
$251$	−3.26034	−0.205791	−0.102895	−	0.994692i	$-0.532811\pi$
$251$	−3.26034	−0.205791	−0.102895	+	0.994692i	$0.532811\pi$
$252$	−39.6616	−2.49845
$253$	−39.7105	−2.49658
$254$	15.2028	0.953909
$255$	0.149407	0.00935623
$256$	−24.6838	−1.54274
$257$	−29.9266	−1.86677	−0.933384	−	0.358880i	$-0.883159\pi$
$257$	−29.9266	−1.86677	−0.933384	+	0.358880i	$0.883159\pi$
$258$	0.438988	0.0273302
$259$	0.822445	0.0511043
$260$	−24.5283	−1.52118
$261$	−15.2881	−0.946307
$262$	24.8582	1.53574
$263$	13.7319	0.846745	0.423372	−	0.905956i	$-0.360846\pi$
$263$	13.7319	0.846745	0.423372	+	0.905956i	$0.360846\pi$
$264$	−2.43484	−0.149854
$265$	9.94711	0.611046
$266$	−20.3445	−1.24740
$267$	0.877474	0.0537005
$268$	−16.9223	−1.03369
$269$	−18.2687	−1.11387	−0.556933	−	0.830558i	$-0.688022\pi$
$269$	−18.2687	−1.11387	−0.556933	+	0.830558i	$0.688022\pi$
$270$	−0.877181	−0.0533836
$271$	3.35235	0.203641	0.101820	−	0.994803i	$-0.467533\pi$
$271$	3.35235	0.203641	0.101820	+	0.994803i	$0.467533\pi$
$272$	−21.6064	−1.31008
$273$	0.858149	0.0519375
$274$	−30.2036	−1.82466
$275$	6.31740	0.380953
$276$	−1.65448	−0.0995878
$277$	11.8698	0.713185	0.356592	−	0.934260i	$-0.383939\pi$
$277$	11.8698	0.713185	0.356592	+	0.934260i	$0.383939\pi$
$278$	32.6994	1.96118
$279$	−14.5012	−0.868163
$280$	19.3800	1.15818
$281$	−21.1313	−1.26059	−0.630295	−	0.776356i	$-0.717066\pi$
$281$	−21.1313	−1.26059	−0.630295	+	0.776356i	$0.717066\pi$
$282$	−0.0834177	−0.00496745
$283$	21.6747	1.28843	0.644214	−	0.764845i	$-0.277185\pi$
$283$	21.6747	1.28843	0.644214	+	0.764845i	$0.277185\pi$
$284$	27.0115	1.60284
$285$	−0.157075	−0.00930434
$286$	−86.1161	−5.09215
$287$	26.4600	1.56188
$288$	22.7143	1.33845
$289$	−10.0780	−0.592824
$290$	13.1406	0.771642
$291$	−0.275347	−0.0161411
$292$	42.5122	2.48784
$293$	0.665779	0.0388952	0.0194476	−	0.999811i	$-0.493809\pi$
$293$	0.665779	0.0388952	0.0194476	+	0.999811i	$0.493809\pi$
$294$	−0.168760	−0.00984228
$295$	14.7070	0.856275
$296$	−1.95482	−0.113622
$297$	−2.15135	−0.124834
$298$	27.0967	1.56967
$299$	−33.2657	−1.92381
$300$	0.263205	0.0151961
$301$	−8.56956	−0.493941
$302$	−58.6864	−3.37702
$303$	0.751195	0.0431551
$304$	22.7154	1.30282
$305$	10.4353	0.597525
$306$	−20.3089	−1.16098
$307$	−16.9898	−0.969657	−0.484829	−	0.874609i	$-0.661118\pi$
$307$	−16.9898	−0.969657	−0.484829	+	0.874609i	$0.661118\pi$
$308$	83.6093	4.76408
$309$	−0.217502	−0.0123732
$310$	12.4642	0.707921
$311$	25.7836	1.46206	0.731028	−	0.682347i	$-0.239041\pi$
$311$	25.7836	1.46206	0.731028	+	0.682347i	$0.239041\pi$
$312$	−2.03968	−0.115474
$313$	−16.6484	−0.941021	−0.470511	−	0.882394i	$-0.655930\pi$
$313$	−16.6484	−0.941021	−0.470511	+	0.882394i	$0.655930\pi$
$314$	−38.8240	−2.19097
$315$	8.55720	0.482144
$316$	36.1196	2.03188
$317$	−4.86328	−0.273149	−0.136575	−	0.990630i	$-0.543609\pi$
$317$	−4.86328	−0.273149	−0.136575	+	0.990630i	$0.543609\pi$
$318$	1.45502	0.0815934
$319$	32.2282	1.80443
$320$	−3.09902	−0.173240
$321$	0.849039	0.0473888
$322$	46.2340	2.57652
$323$	−7.27727	−0.404918
$324$	41.5794	2.30997
$325$	5.29212	0.293554
$326$	−60.1164	−3.32954
$327$	0.495499	0.0274012
$328$	−62.8911	−3.47258
$329$	1.62841	0.0897773
$330$	0.924081	0.0508690
$331$	−8.57541	−0.471347	−0.235674	−	0.971832i	$-0.575730\pi$
$331$	−8.57541	−0.471347	−0.235674	+	0.971832i	$0.575730\pi$
$332$	11.9283	0.654653
$333$	−0.863144	−0.0473000
$334$	−9.69798	−0.530650
$335$	3.65107	0.199479
$336$	1.33168	0.0726491
$337$	−7.86001	−0.428162	−0.214081	−	0.976816i	$-0.568676\pi$
$337$	−7.86001	−0.428162	−0.214081	+	0.976816i	$0.568676\pi$
$338$	−38.6542	−2.10251
$339$	−0.967069	−0.0525240
$340$	12.1942	0.661324
$341$	30.5695	1.65543
$342$	21.3513	1.15454
$343$	−16.6939	−0.901386
$344$	20.3685	1.09819
$345$	0.356962	0.0192182
$346$	−25.0952	−1.34913
$347$	12.4152	0.666485	0.333243	−	0.942841i	$-0.391857\pi$
$347$	12.4152	0.666485	0.333243	+	0.942841i	$0.391857\pi$
$348$	1.34274	0.0719784
$349$	−12.8552	−0.688123	−0.344061	−	0.938947i	$-0.611803\pi$
$349$	−12.8552	−0.688123	−0.344061	+	0.938947i	$0.611803\pi$
$350$	−7.35520	−0.393152
$351$	−1.80220	−0.0961942
$352$	−47.8833	−2.55219
$353$	24.3839	1.29782	0.648911	−	0.760864i	$-0.275225\pi$
$353$	24.3839	1.29782	0.648911	+	0.760864i	$0.275225\pi$
$354$	2.15127	0.114339
$355$	−5.82789	−0.309312
$356$	71.6172	3.79570
$357$	−0.426627	−0.0225795
$358$	−6.05505	−0.320019
$359$	−0.711017	−0.0375260	−0.0187630	−	0.999824i	$-0.505973\pi$
$359$	−0.711017	−0.0375260	−0.0187630	+	0.999824i	$0.505973\pi$
$360$	−20.3391	−1.07196
$361$	−11.3492	−0.597328
$362$	−12.7616	−0.670734
$363$	1.64171	0.0861674
$364$	70.0399	3.67109
$365$	−9.17223	−0.480096
$366$	1.52643	0.0797879
$367$	−24.5679	−1.28243	−0.641216	−	0.767361i	$-0.721570\pi$
$367$	−24.5679	−1.28243	−0.641216	+	0.767361i	$0.721570\pi$
$368$	−51.6219	−2.69098
$369$	−27.7694	−1.44562
$370$	0.741901	0.0385696
$371$	−28.4037	−1.47465
$372$	1.27363	0.0660346
$373$	−26.0063	−1.34655	−0.673277	−	0.739391i	$-0.735114\pi$
$373$	−26.0063	−1.34655	−0.673277	+	0.739391i	$0.735114\pi$
$374$	42.8125	2.21378
$375$	−0.0567878	−0.00293251
$376$	−3.87047	−0.199604
$377$	26.9978	1.39046
$378$	2.50477	0.128831
$379$	14.4859	0.744093	0.372046	−	0.928214i	$-0.378656\pi$
$379$	14.4859	0.744093	0.372046	+	0.928214i	$0.378656\pi$
$380$	−12.8201	−0.657657
$381$	−0.335168	−0.0171712
$382$	−2.08340	−0.106596
$383$	3.70509	0.189321	0.0946607	−	0.995510i	$-0.469823\pi$
$383$	3.70509	0.189321	0.0946607	+	0.995510i	$0.469823\pi$
$384$	0.407547	0.0207975
$385$	−18.0391	−0.919360
$386$	−27.5116	−1.40031
$387$	8.99363	0.457172
$388$	−22.4731	−1.14090
$389$	−14.8356	−0.752194	−0.376097	−	0.926580i	$-0.622734\pi$
$389$	−14.8356	−0.752194	−0.376097	+	0.926580i	$0.622734\pi$
$390$	0.774107	0.0391985
$391$	16.5380	0.836362
$392$	−7.83024	−0.395487
$393$	−0.548035	−0.0276447
$394$	−23.1885	−1.16822
$395$	−7.79299	−0.392108
$396$	−87.7467	−4.40944
$397$	15.8563	0.795804	0.397902	−	0.917428i	$-0.369738\pi$
$397$	15.8563	0.795804	0.397902	+	0.917428i	$0.369738\pi$
$398$	63.0432	3.16007
$399$	0.448524	0.0224543
$400$	8.21234	0.410617
$401$	11.1738	0.557991	0.278996	−	0.960292i	$-0.409999\pi$
$401$	11.1738	0.557991	0.278996	+	0.960292i	$0.409999\pi$
$402$	0.534063	0.0266366
$403$	25.6082	1.27563
$404$	61.3107	3.05032
$405$	−8.97099	−0.445772
$406$	−37.5226	−1.86221
$407$	1.81956	0.0901925
$408$	1.01402	0.0502016
$409$	−8.75983	−0.433146	−0.216573	−	0.976266i	$-0.569488\pi$
$409$	−8.75983	−0.433146	−0.216573	+	0.976266i	$0.569488\pi$
$410$	23.8687	1.17879
$411$	0.665882	0.0328455
$412$	−17.7519	−0.874575
$413$	−41.9954	−2.06646
$414$	−48.5219	−2.38472
$415$	−2.57360	−0.126333
$416$	−40.1121	−1.96666
$417$	−0.720906	−0.0353029
$418$	−45.0098	−2.20150
$419$	3.39398	0.165807	0.0829034	−	0.996558i	$-0.473581\pi$
$419$	3.39398	0.165807	0.0829034	+	0.996558i	$0.473581\pi$
$420$	−0.751573	−0.0366730
$421$	−26.1141	−1.27272	−0.636361	−	0.771392i	$-0.719561\pi$
$421$	−26.1141	−1.27272	−0.636361	+	0.771392i	$0.719561\pi$
$422$	23.6161	1.14961
$423$	−1.70899	−0.0830942
$424$	67.5109	3.27862
$425$	−2.63097	−0.127621
$426$	−0.852477	−0.0413027
$427$	−29.7978	−1.44201
$428$	69.2965	3.34957
$429$	1.89855	0.0916631
$430$	−7.73032	−0.372789
$431$	0.943969	0.0454694	0.0227347	−	0.999742i	$-0.492763\pi$
$431$	0.943969	0.0454694	0.0227347	+	0.999742i	$0.492763\pi$
$432$	−2.79666	−0.134554
$433$	−16.6745	−0.801323	−0.400661	−	0.916226i	$-0.631220\pi$
$433$	−16.6745	−0.801323	−0.400661	+	0.916226i	$0.631220\pi$
$434$	−35.5913	−1.70844
$435$	−0.289703	−0.0138902
$436$	40.4414	1.93679
$437$	−17.3868	−0.831724
$438$	−1.34167	−0.0641076
$439$	−11.3372	−0.541097	−0.270548	−	0.962706i	$-0.587205\pi$
$439$	−11.3372	−0.541097	−0.270548	+	0.962706i	$0.587205\pi$
$440$	42.8761	2.04404
$441$	−3.45742	−0.164639
$442$	35.8642	1.70589
$443$	9.57292	0.454823	0.227412	−	0.973799i	$-0.426974\pi$
$443$	9.57292	0.454823	0.227412	+	0.973799i	$0.426974\pi$
$444$	0.0758094	0.00359775
$445$	−15.4518	−0.732485
$446$	41.4532	1.96287
$447$	−0.597386	−0.0282554
$448$	8.84915	0.418083
$449$	20.1807	0.952386	0.476193	−	0.879341i	$-0.342016\pi$
$449$	20.1807	0.952386	0.476193	+	0.879341i	$0.342016\pi$
$450$	7.71917	0.363885
$451$	58.5397	2.75652
$452$	−78.9297	−3.71254
$453$	1.29383	0.0607893
$454$	−5.28266	−0.247928
$455$	−15.1115	−0.708438
$456$	−1.06607	−0.0499232
$457$	−25.7195	−1.20311	−0.601554	−	0.798832i	$-0.705451\pi$
$457$	−25.7195	−1.20311	−0.601554	+	0.798832i	$0.705451\pi$
$458$	−45.1391	−2.10921
$459$	0.895960	0.0418198
$460$	29.1344	1.35840
$461$	6.01569	0.280178	0.140089	−	0.990139i	$-0.455261\pi$
$461$	6.01569	0.280178	0.140089	+	0.990139i	$0.455261\pi$
$462$	−2.63869	−0.122763
$463$	27.1335	1.26100	0.630500	−	0.776189i	$-0.282850\pi$
$463$	27.1335	1.26100	0.630500	+	0.776189i	$0.282850\pi$
$464$	41.8953	1.94494
$465$	−0.274792	−0.0127432
$466$	−22.6994	−1.05153
$467$	−4.03434	−0.186687	−0.0933434	−	0.995634i	$-0.529755\pi$
$467$	−4.03434	−0.186687	−0.0933434	+	0.995634i	$0.529755\pi$
$468$	−73.5059	−3.39781
$469$	−10.4255	−0.481406
$470$	1.46894	0.0677570
$471$	0.855932	0.0394393
$472$	99.8162	4.59441
$473$	−18.9592	−0.871743
$474$	−1.13992	−0.0523584
$475$	2.76600	0.126913
$476$	−34.8202	−1.59598
$477$	29.8092	1.36487
$478$	0.150626	0.00688948
$479$	−5.89406	−0.269307	−0.134653	−	0.990893i	$-0.542992\pi$
$479$	−5.89406	−0.269307	−0.134653	+	0.990893i	$0.542992\pi$
$480$	0.430428	0.0196463
$481$	1.52426	0.0695002
$482$	−2.57583	−0.117326
$483$	−1.01930	−0.0463796
$484$	133.992	6.09055
$485$	4.84870	0.220168
$486$	−3.94378	−0.178894
$487$	33.3727	1.51226	0.756131	−	0.654420i	$-0.227087\pi$
$487$	33.3727	1.51226	0.756131	+	0.654420i	$0.227087\pi$
$488$	70.8244	3.20607
$489$	1.32535	0.0599346
$490$	2.97176	0.134251
$491$	−30.5655	−1.37940	−0.689700	−	0.724095i	$-0.742257\pi$
$491$	−30.5655	−1.37940	−0.689700	+	0.724095i	$0.742257\pi$
$492$	2.43896	0.109957
$493$	−13.4219	−0.604492
$494$	−37.7050	−1.69643
$495$	18.9318	0.850922
$496$	39.7390	1.78433
$497$	16.6414	0.746467
$498$	−0.376455	−0.0168694
$499$	−40.2138	−1.80022	−0.900109	−	0.435664i	$-0.856514\pi$
$499$	−40.2138	−1.80022	−0.900109	+	0.435664i	$0.856514\pi$
$500$	−4.63488	−0.207278
$501$	0.213806	0.00955215
$502$	8.39807	0.374824
$503$	−10.4628	−0.466513	−0.233256	−	0.972415i	$-0.574938\pi$
$503$	−10.4628	−0.466513	−0.233256	+	0.972415i	$0.574938\pi$
$504$	58.0776	2.58698
$505$	−13.2281	−0.588643
$506$	102.287	4.54723
$507$	0.852187	0.0378470
$508$	−27.3556	−1.21371
$509$	−30.3732	−1.34627	−0.673135	−	0.739520i	$-0.735053\pi$
$509$	−30.3732	−1.34627	−0.673135	+	0.739520i	$0.735053\pi$
$510$	−0.384846	−0.0170413
$511$	26.1910	1.15862
$512$	49.2280	2.17559
$513$	−0.941945	−0.0415879
$514$	77.0856	3.40010
$515$	3.83008	0.168773
$516$	−0.789904	−0.0347736
$517$	3.60267	0.158445
$518$	−2.11848	−0.0930805
$519$	0.553260	0.0242854
$520$	35.9175	1.57509
$521$	−11.1989	−0.490634	−0.245317	−	0.969443i	$-0.578892\pi$
$521$	−11.1989	−0.490634	−0.245317	+	0.969443i	$0.578892\pi$
$522$	39.3794	1.72359
$523$	29.9460	1.30945	0.654723	−	0.755869i	$-0.272785\pi$
$523$	29.9460	1.30945	0.654723	+	0.755869i	$0.272785\pi$
$524$	−44.7292	−1.95400
$525$	0.162156	0.00707707
$526$	−35.3710	−1.54225
$527$	−12.7311	−0.554574
$528$	2.94619	0.128216
$529$	16.5125	0.717934
$530$	−25.6220	−1.11295
$531$	44.0736	1.91263
$532$	36.6074	1.58713
$533$	49.0390	2.12411
$534$	−2.26022	−0.0978092
$535$	−14.9511	−0.646392
$536$	24.7798	1.07032
$537$	0.133492	0.00576062
$538$	47.0571	2.02878
$539$	7.28846	0.313936
$540$	1.57838	0.0679226
$541$	−41.1304	−1.76834	−0.884168	−	0.467170i	$-0.845274\pi$
$541$	−41.1304	−1.76834	−0.884168	+	0.467170i	$0.845274\pi$
$542$	−8.63507	−0.370908
$543$	0.281348	0.0120738
$544$	19.9417	0.854992
$545$	−8.72545	−0.373757
$546$	−2.21044	−0.0945981
$547$	−28.6702	−1.22585	−0.612925	−	0.790141i	$-0.710007\pi$
$547$	−28.6702	−1.22585	−0.612925	+	0.790141i	$0.710007\pi$
$548$	54.3476	2.32161
$549$	31.2723	1.33467
$550$	−16.2725	−0.693863
$551$	14.1108	0.601139
$552$	2.42270	0.103117
$553$	22.2527	0.946279
$554$	−30.5744	−1.29898
$555$	−0.0163563	−0.000694285 0
$556$	−58.8385	−2.49531
$557$	−35.4942	−1.50394	−0.751969	−	0.659198i	$-0.770896\pi$
$557$	−35.4942	−1.50394	−0.751969	+	0.659198i	$0.770896\pi$
$558$	37.3525	1.58126
$559$	−15.8822	−0.671745
$560$	−23.4501	−0.990948
$561$	−0.943863	−0.0398499
$562$	54.4306	2.29602
$563$	20.1987	0.851275	0.425638	−	0.904894i	$-0.360050\pi$
$563$	20.1987	0.851275	0.425638	+	0.904894i	$0.360050\pi$
$564$	0.150100	0.00632034
$565$	17.0295	0.716437
$566$	−55.8303	−2.34672
$567$	25.6164	1.07579
$568$	−39.5538	−1.65964
$569$	5.85009	0.245249	0.122624	−	0.992453i	$-0.460869\pi$
$569$	5.85009	0.245249	0.122624	+	0.992453i	$0.460869\pi$
$570$	0.404599	0.0169468
$571$	38.5546	1.61346	0.806729	−	0.590921i	$-0.201236\pi$
$571$	38.5546	1.61346	0.806729	+	0.590921i	$0.201236\pi$
$572$	154.955	6.47900
$573$	0.0459316	0.00191882
$574$	−68.1563	−2.84479
$575$	−6.28590	−0.262140
$576$	−9.28705	−0.386961
$577$	−38.9576	−1.62182	−0.810912	−	0.585168i	$-0.801029\pi$
$577$	−38.9576	−1.62182	−0.810912	+	0.585168i	$0.801029\pi$
$578$	25.9592	1.07976
$579$	0.606534	0.0252067
$580$	−23.6449	−0.981799
$581$	7.34885	0.304882
$582$	0.709246	0.0293992
$583$	−62.8398	−2.60256
$584$	−62.2518	−2.57600
$585$	15.8593	0.655701
$586$	−1.71493	−0.0708432
$587$	27.2679	1.12547	0.562733	−	0.826639i	$-0.309750\pi$
$587$	27.2679	1.12547	0.562733	+	0.826639i	$0.309750\pi$
$588$	0.303663	0.0125228
$589$	13.3845	0.551499
$590$	−37.8827	−1.55960
$591$	0.511223	0.0210289
$592$	2.36536	0.0972155
$593$	39.5572	1.62442	0.812210	−	0.583365i	$-0.198264\pi$
$593$	39.5572	1.62442	0.812210	+	0.583365i	$0.198264\pi$
$594$	5.54151	0.227371
$595$	7.51265	0.307989
$596$	−48.7571	−1.99717
$597$	−1.38988	−0.0568840
$598$	85.6867	3.50399
$599$	−6.27067	−0.256213	−0.128106	−	0.991760i	$-0.540890\pi$
$599$	−6.27067	−0.256213	−0.128106	+	0.991760i	$0.540890\pi$
$600$	−0.385418	−0.0157346
$601$	5.11174	0.208512	0.104256	−	0.994550i	$-0.466754\pi$
$601$	5.11174	0.208512	0.104256	+	0.994550i	$0.466754\pi$
$602$	22.0737	0.899657
$603$	10.9414	0.445570
$604$	105.599	4.29676
$605$	−28.9095	−1.17534
$606$	−1.93495	−0.0786019
$607$	−23.9456	−0.971922	−0.485961	−	0.873980i	$-0.661530\pi$
$607$	−23.9456	−0.971922	−0.485961	+	0.873980i	$0.661530\pi$
$608$	−20.9652	−0.850250
$609$	0.827239	0.0335214
$610$	−26.8796	−1.08832
$611$	3.01798	0.122094
$612$	36.5433	1.47718
$613$	−25.7417	−1.03970	−0.519849	−	0.854258i	$-0.674012\pi$
$613$	−25.7417	−1.03970	−0.519849	+	0.854258i	$0.674012\pi$
$614$	43.7627	1.76612
$615$	−0.526220	−0.0212192
$616$	−122.431	−4.93291
$617$	3.88797	0.156524	0.0782620	−	0.996933i	$-0.475063\pi$
$617$	3.88797	0.156524	0.0782620	+	0.996933i	$0.475063\pi$
$618$	0.560246	0.0225364
$619$	36.9583	1.48548	0.742740	−	0.669580i	$-0.233526\pi$
$619$	36.9583	1.48548	0.742740	+	0.669580i	$0.233526\pi$
$620$	−22.4279	−0.900724
$621$	2.14062	0.0859002
$622$	−66.4142	−2.66297
$623$	44.1221	1.76772
$624$	2.46804	0.0988006
$625$	1.00000	0.0400000
$626$	42.8833	1.71396
$627$	0.992307	0.0396289
$628$	69.8590	2.78768
$629$	−0.757783	−0.0302148
$630$	−22.0419	−0.878169
$631$	17.2992	0.688668	0.344334	−	0.938847i	$-0.388105\pi$
$631$	17.2992	0.688668	0.344334	+	0.938847i	$0.388105\pi$
$632$	−52.8909	−2.10389
$633$	−0.520651	−0.0206940
$634$	12.5270	0.497509
$635$	5.90211	0.234218
$636$	−2.61812	−0.103815
$637$	6.10559	0.241912
$638$	−83.0143	−3.28657
$639$	−17.4649	−0.690899
$640$	−7.17665	−0.283682
$641$	49.7420	1.96469	0.982346	−	0.187074i	$-0.0599004\pi$
$641$	49.7420	1.96469	0.982346	+	0.187074i	$0.0599004\pi$
$642$	−2.18698	−0.0863131
$643$	−7.31595	−0.288513	−0.144256	−	0.989540i	$-0.546079\pi$
$643$	−7.31595	−0.288513	−0.144256	+	0.989540i	$0.546079\pi$
$644$	−83.1923	−3.27824
$645$	0.170426	0.00671052
$646$	18.7450	0.737511
$647$	10.6013	0.416779	0.208389	−	0.978046i	$-0.433178\pi$
$647$	10.6013	0.416779	0.208389	+	0.978046i	$0.433178\pi$
$648$	−60.8860	−2.39183
$649$	−92.9100	−3.64704
$650$	−13.6316	−0.534674
$651$	0.784661	0.0307533
$652$	108.172	4.23634
$653$	40.6331	1.59010	0.795049	−	0.606546i	$-0.207445\pi$
$653$	40.6331	1.59010	0.795049	+	0.606546i	$0.207445\pi$
$654$	−1.27632	−0.0499081
$655$	9.65057	0.377079
$656$	76.0990	2.97117
$657$	−27.4871	−1.07237
$658$	−4.19451	−0.163519
$659$	3.15986	0.123091	0.0615454	−	0.998104i	$-0.480397\pi$
$659$	3.15986	0.123091	0.0615454	+	0.998104i	$0.480397\pi$
$660$	−1.66277	−0.0647232
$661$	−11.7495	−0.457004	−0.228502	−	0.973543i	$-0.573383\pi$
$661$	−11.7495	−0.457004	−0.228502	+	0.973543i	$0.573383\pi$
$662$	22.0888	0.858504
$663$	−0.790679	−0.0307074
$664$	−17.4670	−0.677852
$665$	−7.89824	−0.306281
$666$	2.22331	0.0861515
$667$	−32.0675	−1.24166
$668$	17.4503	0.675172
$669$	−0.913896	−0.0353333
$670$	−9.40453	−0.363329
$671$	−65.9241	−2.54497
$672$	−1.22908	−0.0474126
$673$	−21.9840	−0.847422	−0.423711	−	0.905797i	$-0.639273\pi$
$673$	−21.9840	−0.847422	−0.423711	+	0.905797i	$0.639273\pi$
$674$	20.2460	0.779847
$675$	−0.340544	−0.0131075
$676$	69.5534	2.67513
$677$	−1.54724	−0.0594654	−0.0297327	−	0.999558i	$-0.509466\pi$
$677$	−1.54724	−0.0594654	−0.0297327	+	0.999558i	$0.509466\pi$
$678$	2.49100	0.0956663
$679$	−13.8453	−0.531335
$680$	−17.8564	−0.684760
$681$	0.116464	0.00446291
$682$	−78.7416	−3.01517
$683$	−36.3614	−1.39133	−0.695666	−	0.718366i	$-0.744890\pi$
$683$	−36.3614	−1.39133	−0.695666	+	0.718366i	$0.744890\pi$
$684$	−38.4189	−1.46898
$685$	−11.7258	−0.448019
$686$	43.0006	1.64177
$687$	0.995156	0.0379676
$688$	−24.6461	−0.939623
$689$	−52.6413	−2.00547
$690$	−0.919473	−0.0350037
$691$	−3.07440	−0.116956	−0.0584778	−	0.998289i	$-0.518625\pi$
$691$	−3.07440	−0.116956	−0.0584778	+	0.998289i	$0.518625\pi$
$692$	45.1557	1.71656
$693$	−54.0593	−2.05354
$694$	−31.9795	−1.21393
$695$	12.6947	0.481539
$696$	−1.96621	−0.0745291
$697$	−24.3797	−0.923445
$698$	33.1127	1.25334
$699$	0.500440	0.0189284
$700$	13.2348	0.500227
$701$	−6.64963	−0.251153	−0.125577	−	0.992084i	$-0.540078\pi$
$701$	−6.64963	−0.251153	−0.125577	+	0.992084i	$0.540078\pi$
$702$	4.64215	0.175207
$703$	0.796676	0.0300472
$704$	19.5777	0.737863
$705$	−0.0323848	−0.00121968
$706$	−62.8086	−2.36383
$707$	37.7725	1.42058
$708$	−3.87095	−0.145479
$709$	38.3451	1.44008	0.720041	−	0.693932i	$-0.244123\pi$
$709$	38.3451	1.44008	0.720041	+	0.693932i	$0.244123\pi$
$710$	15.0116	0.563376
$711$	−23.3538	−0.875837
$712$	−104.871	−3.93021
$713$	−30.4170	−1.13913
$714$	1.09892	0.0411260
$715$	−33.4324	−1.25030
$716$	10.8953	0.407177
$717$	−0.00332077	−0.000124016 0
$718$	1.83146	0.0683493
$719$	1.60260	0.0597670	0.0298835	−	0.999553i	$-0.490486\pi$
$719$	1.60260	0.0597670	0.0298835	+	0.999553i	$0.490486\pi$
$720$	24.6105	0.917181
$721$	−10.9367	−0.407303
$722$	29.2336	1.08796
$723$	0.0567878	0.00211196
$724$	22.9629	0.853409
$725$	5.10150	0.189465
$726$	−4.22876	−0.156944
$727$	22.6800	0.841154	0.420577	−	0.907257i	$-0.361828\pi$
$727$	22.6800	0.841154	0.420577	+	0.907257i	$0.361828\pi$
$728$	−102.562	−3.80118
$729$	−26.8260	−0.993556
$730$	23.6261	0.874440
$731$	7.89581	0.292037
$732$	−2.74663	−0.101518
$733$	−17.7652	−0.656174	−0.328087	−	0.944647i	$-0.606404\pi$
$733$	−17.7652	−0.656174	−0.328087	+	0.944647i	$0.606404\pi$
$734$	63.2825	2.33580
$735$	−0.0655168	−0.00241663
$736$	47.6445	1.75620
$737$	−23.0653	−0.849621
$738$	71.5291	2.63302
$739$	−3.26920	−0.120259	−0.0601296	−	0.998191i	$-0.519151\pi$
$739$	−3.26920	−0.120259	−0.0601296	+	0.998191i	$0.519151\pi$
$740$	−1.33496	−0.0490740
$741$	0.831261	0.0305371
$742$	73.1629	2.68590
$743$	37.4880	1.37530	0.687650	−	0.726042i	$-0.258642\pi$
$743$	37.4880	1.37530	0.687650	+	0.726042i	$0.258642\pi$
$744$	−1.86501	−0.0683747
$745$	10.5196	0.385409
$746$	66.9876	2.45259
$747$	−7.71251	−0.282186
$748$	−77.0358	−2.81671
$749$	42.6924	1.55995
$750$	0.146276	0.00534123
$751$	38.8062	1.41606	0.708030	−	0.706182i	$-0.249584\pi$
$751$	38.8062	1.41606	0.708030	+	0.706182i	$0.249584\pi$
$752$	4.68332	0.170783
$753$	−0.185148	−0.00674715
$754$	−69.5415	−2.53255
$755$	−22.7835	−0.829177
$756$	−4.50702	−0.163919
$757$	0.0977984	0.00355454	0.00177727	−	0.999998i	$-0.499434\pi$
$757$	0.0977984	0.00355454	0.00177727	+	0.999998i	$0.499434\pi$
$758$	−37.3133	−1.35528
$759$	−2.25507	−0.0818540
$760$	18.7728	0.680962
$761$	−42.8817	−1.55446	−0.777230	−	0.629216i	$-0.783376\pi$
$761$	−42.8817	−1.55446	−0.777230	+	0.629216i	$0.783376\pi$
$762$	0.863334	0.0312753
$763$	24.9153	0.901994
$764$	3.74882	0.135628
$765$	−7.88442	−0.285062
$766$	−9.54368	−0.344827
$767$	−77.8312	−2.81032
$768$	−1.40174	−0.0505810
$769$	16.1034	0.580703	0.290351	−	0.956920i	$-0.406228\pi$
$769$	16.1034	0.580703	0.290351	+	0.956920i	$0.406228\pi$
$770$	46.4657	1.67451
$771$	−1.69946	−0.0612047
$772$	49.5038	1.78168
$773$	−15.4797	−0.556766	−0.278383	−	0.960470i	$-0.589798\pi$
$773$	−15.4797	−0.556766	−0.278383	+	0.960470i	$0.589798\pi$
$774$	−23.1660	−0.832686
$775$	4.83893	0.173820
$776$	32.9081	1.18133
$777$	0.0467049	0.00167553
$778$	38.2139	1.37003
$779$	25.6309	0.918324
$780$	−1.39291	−0.0498742
$781$	36.8171	1.31742
$782$	−42.5990	−1.52334
$783$	−1.73729	−0.0620855
$784$	9.47469	0.338382
$785$	−15.0725	−0.537959
$786$	1.41164	0.0503516
$787$	17.0488	0.607724	0.303862	−	0.952716i	$-0.401724\pi$
$787$	17.0488	0.607724	0.303862	+	0.952716i	$0.401724\pi$
$788$	41.7248	1.48638
$789$	0.779804	0.0277618
$790$	20.0734	0.714179
$791$	−48.6273	−1.72899
$792$	128.490	4.56570
$793$	−55.2250	−1.96110
$794$	−40.8430	−1.44946
$795$	0.564875	0.0200340
$796$	−113.438	−4.02072
$797$	−9.43249	−0.334116	−0.167058	−	0.985947i	$-0.553427\pi$
$797$	−9.43249	−0.334116	−0.167058	+	0.985947i	$0.553427\pi$
$798$	−1.15532	−0.0408979
$799$	−1.50038	−0.0530798
$800$	−7.57959	−0.267979
$801$	−46.3055	−1.63613
$802$	−28.7817	−1.01632
$803$	57.9446	2.04482
$804$	−0.960979	−0.0338911
$805$	17.9492	0.632626
$806$	−65.9622	−2.32342
$807$	−1.03744	−0.0365197
$808$	−89.7790	−3.15842
$809$	−44.6400	−1.56946	−0.784729	−	0.619839i	$-0.787198\pi$
$809$	−44.6400	−1.56946	−0.784729	+	0.619839i	$0.787198\pi$
$810$	23.1077	0.811922
$811$	−28.5796	−1.00357	−0.501783	−	0.864994i	$-0.667322\pi$
$811$	−28.5796	−1.00357	−0.501783	+	0.864994i	$0.667322\pi$
$812$	67.5172	2.36939
$813$	0.190373	0.00667666
$814$	−4.68688	−0.164275
$815$	−23.3387	−0.817519
$816$	−1.22698	−0.0429529
$817$	−8.30106	−0.290417
$818$	22.5638	0.788924
$819$	−45.2857	−1.58241
$820$	−42.9487	−1.49983
$821$	25.2876	0.882543	0.441272	−	0.897374i	$-0.354528\pi$
$821$	25.2876	0.882543	0.441272	+	0.897374i	$0.354528\pi$
$822$	−1.71520	−0.0598243
$823$	−40.0376	−1.39562	−0.697811	−	0.716282i	$-0.745843\pi$
$823$	−40.0376	−1.39562	−0.697811	+	0.716282i	$0.745843\pi$
$824$	25.9947	0.905568
$825$	0.358751	0.0124901
$826$	108.173	3.76381
$827$	−2.89165	−0.100552	−0.0502762	−	0.998735i	$-0.516010\pi$
$827$	−2.89165	−0.100552	−0.0502762	+	0.998735i	$0.516010\pi$
$828$	87.3091	3.03420
$829$	−10.1793	−0.353540	−0.176770	−	0.984252i	$-0.556565\pi$
$829$	−10.1793	−0.353540	−0.176770	+	0.984252i	$0.556565\pi$
$830$	6.62915	0.230101
$831$	0.674058	0.0233828
$832$	16.4004	0.568580
$833$	−3.03538	−0.105170
$834$	1.85693	0.0643002
$835$	−3.76500	−0.130293
$836$	80.9896	2.80108
$837$	−1.64787	−0.0569586
$838$	−8.74230	−0.301998
$839$	−44.4615	−1.53498	−0.767491	−	0.641060i	$-0.778495\pi$
$839$	−44.4615	−1.53498	−0.767491	+	0.641060i	$0.778495\pi$
$840$	1.10055	0.0379726
$841$	−2.97466	−0.102575
$842$	67.2653	2.31811
$843$	−1.20000	−0.0413303
$844$	−42.4943	−1.46271
$845$	−15.0065	−0.516240
$846$	4.40207	0.151346
$847$	82.5503	2.83646
$848$	−81.6891	−2.80521
$849$	1.23086	0.0422430
$850$	6.77692	0.232446
$851$	−1.81049	−0.0620628
$852$	1.53393	0.0525515
$853$	22.1019	0.756756	0.378378	−	0.925651i	$-0.376482\pi$
$853$	22.1019	0.756756	0.378378	+	0.925651i	$0.376482\pi$
$854$	76.7538	2.62646
$855$	8.28909	0.283481
$856$	−101.473	−3.46827
$857$	43.4931	1.48570	0.742848	−	0.669460i	$-0.233475\pi$
$857$	43.4931	1.48570	0.742848	+	0.669460i	$0.233475\pi$
$858$	−4.89035	−0.166954
$859$	45.5992	1.55583	0.777913	−	0.628372i	$-0.216279\pi$
$859$	45.5992	1.55583	0.777913	+	0.628372i	$0.216279\pi$
$860$	13.9097	0.474318
$861$	1.50260	0.0512086
$862$	−2.43150	−0.0828172
$863$	−47.2295	−1.60771	−0.803855	−	0.594825i	$-0.797221\pi$
$863$	−47.2295	−1.60771	−0.803855	+	0.594825i	$0.797221\pi$
$864$	2.58118	0.0878136
$865$	−9.74258	−0.331258
$866$	42.9505	1.45952
$867$	−0.572308	−0.0194366
$868$	64.0421	2.17373
$869$	49.2314	1.67006
$870$	0.746225	0.0252994
$871$	−19.3219	−0.654698
$872$	−59.2196	−2.00543
$873$	14.5305	0.491782
$874$	44.7854	1.51489
$875$	−2.85547	−0.0965325
$876$	2.41417	0.0815673
$877$	−7.31219	−0.246915	−0.123458	−	0.992350i	$-0.539398\pi$
$877$	−7.31219	−0.246915	−0.123458	+	0.992350i	$0.539398\pi$
$878$	29.2027	0.985545
$879$	0.0378082	0.00127524
$880$	−51.8807	−1.74890
$881$	21.1239	0.711684	0.355842	−	0.934546i	$-0.384194\pi$
$881$	21.1239	0.711684	0.355842	+	0.934546i	$0.384194\pi$
$882$	8.90571	0.299871
$883$	−12.1100	−0.407533	−0.203767	−	0.979020i	$-0.565318\pi$
$883$	−12.1100	−0.407533	−0.203767	+	0.979020i	$0.565318\pi$
$884$	−64.5333	−2.17049
$885$	0.835178	0.0280742
$886$	−24.6582	−0.828408
$887$	13.9372	0.467965	0.233983	−	0.972241i	$-0.424824\pi$
$887$	13.9372	0.467965	0.233983	+	0.972241i	$0.424824\pi$
$888$	−0.111010	−0.00372525
$889$	−16.8533	−0.565242
$890$	39.8011	1.33414
$891$	56.6733	1.89863
$892$	−74.5899	−2.49745
$893$	1.57739	0.0527854
$894$	1.53876	0.0514639
$895$	−2.35072	−0.0785760
$896$	20.4927	0.684614
$897$	−1.88909	−0.0630748
$898$	−51.9820	−1.73466
$899$	24.6858	0.823318
$900$	−13.8897	−0.462990
$901$	26.1705	0.871867
$902$	−150.788	−5.02069
$903$	−0.486647	−0.0161946
$904$	115.579	3.84411
$905$	−4.95437	−0.164689
$906$	−3.33267	−0.110721
$907$	−0.670578	−0.0222662	−0.0111331	−	0.999938i	$-0.503544\pi$
$907$	−0.670578	−0.0222662	−0.0111331	+	0.999938i	$0.503544\pi$
$908$	9.50550	0.315451
$909$	−39.6417	−1.31483
$910$	38.9246	1.29034
$911$	−24.8335	−0.822772	−0.411386	−	0.911461i	$-0.634955\pi$
$911$	−24.8335	−0.822772	−0.411386	+	0.911461i	$0.634955\pi$
$912$	1.28996	0.0427147
$913$	16.2585	0.538077
$914$	66.2489	2.19132
$915$	0.592599	0.0195907
$916$	81.2221	2.68365
$917$	−27.5569	−0.910009
$918$	−2.30784	−0.0761700
$919$	−6.86443	−0.226437	−0.113218	−	0.993570i	$-0.536116\pi$
$919$	−6.86443	−0.226437	−0.113218	+	0.993570i	$0.536116\pi$
$920$	−42.6623	−1.40653
$921$	−0.964812	−0.0317916
$922$	−15.4954	−0.510312
$923$	30.8419	1.01517
$924$	4.74799	0.156197
$925$	0.288024	0.00947018
$926$	−69.8912	−2.29677
$927$	11.4779	0.376983
$928$	−38.6673	−1.26932
$929$	38.1633	1.25210	0.626048	−	0.779784i	$-0.284671\pi$
$929$	38.1633	1.25210	0.626048	+	0.779784i	$0.284671\pi$
$930$	0.707817	0.0232102
$931$	3.19117	0.104587
$932$	40.8447	1.33791
$933$	1.46420	0.0479356
$934$	10.3917	0.340028
$935$	16.6209	0.543561
$936$	107.637	3.51822
$937$	47.0735	1.53782	0.768912	−	0.639355i	$-0.220798\pi$
$937$	47.0735	1.53782	0.768912	+	0.639355i	$0.220798\pi$
$938$	26.8544	0.876826
$939$	−0.945424	−0.0308528
$940$	−2.64317	−0.0862107
$941$	35.5232	1.15802	0.579012	−	0.815319i	$-0.303439\pi$
$941$	35.5232	1.15802	0.579012	+	0.815319i	$0.303439\pi$
$942$	−2.20473	−0.0718340
$943$	−58.2477	−1.89681
$944$	−120.779	−3.93102
$945$	0.972413	0.0316326
$946$	48.8355	1.58778
$947$	15.6140	0.507388	0.253694	−	0.967285i	$-0.418354\pi$
$947$	15.6140	0.507388	0.253694	+	0.967285i	$0.418354\pi$
$948$	2.05115	0.0666183
$949$	48.5405	1.57569
$950$	−7.12474	−0.231157
$951$	−0.276175	−0.00895559
$952$	50.9883	1.65254
$953$	−1.63849	−0.0530758	−0.0265379	−	0.999648i	$-0.508448\pi$
$953$	−1.63849	−0.0530758	−0.0265379	+	0.999648i	$0.508448\pi$
$954$	−76.7834	−2.48595
$955$	−0.808828	−0.0261731
$956$	−0.271033	−0.00876583
$957$	1.83017	0.0591610
$958$	15.1821	0.490511
$959$	33.4826	1.08121
$960$	−0.175986	−0.00567994
$961$	−7.58475	−0.244669
$962$	−3.92623	−0.126587
$963$	−44.8050	−1.44382
$964$	4.63488	0.149279
$965$	−10.6807	−0.343824
$966$	2.62553	0.0844750
$967$	−57.4835	−1.84855	−0.924273	−	0.381733i	$-0.875327\pi$
$967$	−57.4835	−1.84855	−0.924273	+	0.381733i	$0.875327\pi$
$968$	−196.209	−6.30639
$969$	−0.413260	−0.0132758
$970$	−12.4894	−0.401011
$971$	−13.2419	−0.424952	−0.212476	−	0.977166i	$-0.568153\pi$
$971$	−13.2419	−0.424952	−0.212476	+	0.977166i	$0.568153\pi$
$972$	7.09634	0.227615
$973$	−36.2494	−1.16210
$974$	−85.9624	−2.75441
$975$	0.300528	0.00962459
$976$	−85.6985	−2.74314
$977$	−40.2047	−1.28626	−0.643132	−	0.765756i	$-0.722365\pi$
$977$	−40.2047	−1.28626	−0.643132	+	0.765756i	$0.722365\pi$
$978$	−3.41388	−0.109164
$979$	97.6151	3.11979
$980$	−5.34732	−0.170814
$981$	−26.1482	−0.834848
$982$	78.7313	2.51242
$983$	−47.6778	−1.52068	−0.760342	−	0.649523i	$-0.774969\pi$
$983$	−47.6778	−1.52068	−0.760342	+	0.649523i	$0.774969\pi$
$984$	−3.57145	−0.113854
$985$	−9.00234	−0.286838
$986$	34.5725	1.10101
$987$	0.0924740	0.00294348
$988$	67.8454	2.15845
$989$	18.8646	0.599860
$990$	−48.7651	−1.54986
$991$	−6.74810	−0.214360	−0.107180	−	0.994240i	$-0.534182\pi$
$991$	−6.74810	−0.214360	−0.107180	+	0.994240i	$0.534182\pi$
$992$	−36.6771	−1.16450
$993$	−0.486979	−0.0154538
$994$	−42.8652	−1.35960
$995$	24.4750	0.775908
$996$	0.677384	0.0214637
$997$	6.93342	0.219584	0.109792	−	0.993955i	$-0.464982\pi$
$997$	6.93342	0.219584	0.109792	+	0.993955i	$0.464982\pi$
$998$	103.584	3.27889
$999$	−0.0980849	−0.00310327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.3	✓	25
5.4	even	2		6025.2.a.k.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.3	✓	25	1.1	even	1	trivial
6025.2.a.k.1.23		25	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57583 q^{2} +0.0567878 q^{3} +4.63488 q^{4} -1.00000 q^{5} -0.146276 q^{6} +2.85547 q^{7} -6.78699 q^{8} -2.99678 q^{9} +O(q^{10})\)	\(q-2.57583 q^{2} +0.0567878 q^{3} +4.63488 q^{4} -1.00000 q^{5} -0.146276 q^{6} +2.85547 q^{7} -6.78699 q^{8} -2.99678 q^{9} +2.57583 q^{10} +6.31740 q^{11} +0.263205 q^{12} +5.29212 q^{13} -7.35520 q^{14} -0.0567878 q^{15} +8.21234 q^{16} -2.63097 q^{17} +7.71917 q^{18} +2.76600 q^{19} -4.63488 q^{20} +0.162156 q^{21} -16.2725 q^{22} -6.28590 q^{23} -0.385418 q^{24} +1.00000 q^{25} -13.6316 q^{26} -0.340544 q^{27} +13.2348 q^{28} +5.10150 q^{29} +0.146276 q^{30} +4.83893 q^{31} -7.57959 q^{32} +0.358751 q^{33} +6.77692 q^{34} -2.85547 q^{35} -13.8897 q^{36} +0.288024 q^{37} -7.12474 q^{38} +0.300528 q^{39} +6.78699 q^{40} +9.26642 q^{41} -0.417685 q^{42} -3.00110 q^{43} +29.2804 q^{44} +2.99678 q^{45} +16.1914 q^{46} +0.570278 q^{47} +0.466361 q^{48} +1.15371 q^{49} -2.57583 q^{50} -0.149407 q^{51} +24.5283 q^{52} -9.94711 q^{53} +0.877181 q^{54} -6.31740 q^{55} -19.3800 q^{56} +0.157075 q^{57} -13.1406 q^{58} -14.7070 q^{59} -0.263205 q^{60} -10.4353 q^{61} -12.4642 q^{62} -8.55720 q^{63} +3.09902 q^{64} -5.29212 q^{65} -0.924081 q^{66} -3.65107 q^{67} -12.1942 q^{68} -0.356962 q^{69} +7.35520 q^{70} +5.82789 q^{71} +20.3391 q^{72} +9.17223 q^{73} -0.741901 q^{74} +0.0567878 q^{75} +12.8201 q^{76} +18.0391 q^{77} -0.774107 q^{78} +7.79299 q^{79} -8.21234 q^{80} +8.97099 q^{81} -23.8687 q^{82} +2.57360 q^{83} +0.751573 q^{84} +2.63097 q^{85} +7.73032 q^{86} +0.289703 q^{87} -42.8761 q^{88} +15.4518 q^{89} -7.71917 q^{90} +15.1115 q^{91} -29.1344 q^{92} +0.274792 q^{93} -1.46894 q^{94} -2.76600 q^{95} -0.430428 q^{96} -4.84870 q^{97} -2.97176 q^{98} -18.9318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more