LMFDB - Embedded newform 403.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(1,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, 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("403.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 9x^{5} + 12x^{4} + 22x^{3} - 18x^{2} - 13x - 1 $ x^7 - 2x^6 - 9x^5 + 12x^4 + 22x^3 - 18x^2 - 13x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.51046$ of defining polynomial
Character	$\chi$	$=$	403.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09092 q^{2} -0.510463 q^{3} +2.37194 q^{4} +4.43975 q^{5} -1.06734 q^{6} -2.30124 q^{7} +0.777706 q^{8} -2.73943 q^{9} +O(q^{10})$	\(q+2.09092 q^{2} -0.510463 q^{3} +2.37194 q^{4} +4.43975 q^{5} -1.06734 q^{6} -2.30124 q^{7} +0.777706 q^{8} -2.73943 q^{9} +9.28317 q^{10} +5.75249 q^{11} -1.21079 q^{12} -1.00000 q^{13} -4.81170 q^{14} -2.26633 q^{15} -3.11777 q^{16} +0.581171 q^{17} -5.72792 q^{18} -3.67365 q^{19} +10.5308 q^{20} +1.17470 q^{21} +12.0280 q^{22} -7.44973 q^{23} -0.396990 q^{24} +14.7114 q^{25} -2.09092 q^{26} +2.92976 q^{27} -5.45840 q^{28} -1.17295 q^{29} -4.73871 q^{30} +1.00000 q^{31} -8.07441 q^{32} -2.93644 q^{33} +1.21518 q^{34} -10.2169 q^{35} -6.49777 q^{36} +6.63700 q^{37} -7.68131 q^{38} +0.510463 q^{39} +3.45282 q^{40} -6.46171 q^{41} +2.45619 q^{42} +0.352822 q^{43} +13.6446 q^{44} -12.1624 q^{45} -15.5768 q^{46} +0.562606 q^{47} +1.59151 q^{48} -1.70431 q^{49} +30.7604 q^{50} -0.296666 q^{51} -2.37194 q^{52} +7.57222 q^{53} +6.12590 q^{54} +25.5397 q^{55} -1.78968 q^{56} +1.87526 q^{57} -2.45255 q^{58} -10.3811 q^{59} -5.37561 q^{60} -1.24744 q^{61} +2.09092 q^{62} +6.30407 q^{63} -10.6474 q^{64} -4.43975 q^{65} -6.13985 q^{66} -9.53020 q^{67} +1.37851 q^{68} +3.80281 q^{69} -21.3628 q^{70} -4.04545 q^{71} -2.13047 q^{72} +3.12100 q^{73} +13.8774 q^{74} -7.50963 q^{75} -8.71370 q^{76} -13.2378 q^{77} +1.06734 q^{78} -7.08221 q^{79} -13.8421 q^{80} +6.72275 q^{81} -13.5109 q^{82} +2.29916 q^{83} +2.78631 q^{84} +2.58026 q^{85} +0.737723 q^{86} +0.598748 q^{87} +4.47375 q^{88} +0.601680 q^{89} -25.4306 q^{90} +2.30124 q^{91} -17.6703 q^{92} -0.510463 q^{93} +1.17636 q^{94} -16.3101 q^{95} +4.12169 q^{96} +12.4967 q^{97} -3.56358 q^{98} -15.7585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 5 q^{3} + 8 q^{4} + 11 q^{5} + 6 q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 + 5 * q^3 + 8 * q^4 + 11 * q^5 + 6 * q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9	\( 7 q + 2 q^{2} + 5 q^{3} + 8 q^{4} + 11 q^{5} + 6 q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} + 8 q^{11} - 3 q^{12} - 7 q^{13} - 5 q^{14} + 2 q^{16} + 7 q^{17} - 9 q^{18} + q^{19} - 2 q^{21} + 6 q^{22} + 6 q^{23} + 5 q^{24} + 10 q^{25} - 2 q^{26} + 11 q^{27} - 11 q^{28} - 2 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} + 6 q^{33} - 4 q^{34} - q^{35} - 20 q^{36} + 28 q^{37} - 8 q^{38} - 5 q^{39} - 5 q^{40} + 3 q^{41} + 13 q^{42} - q^{43} + 12 q^{44} + 9 q^{45} - 37 q^{46} - q^{47} + 11 q^{48} - 19 q^{49} + 21 q^{50} - 30 q^{51} - 8 q^{52} + 29 q^{53} + 2 q^{54} + 19 q^{55} - 20 q^{56} + 11 q^{57} + 3 q^{58} + 3 q^{59} - 43 q^{60} + 5 q^{61} + 2 q^{62} + q^{63} - 29 q^{64} - 11 q^{65} - 29 q^{66} - 32 q^{67} + 38 q^{68} + 17 q^{69} - 23 q^{70} + 5 q^{71} - 17 q^{72} + q^{73} - 4 q^{74} - 7 q^{75} - 12 q^{76} - 5 q^{77} - 6 q^{78} - 15 q^{79} - 11 q^{80} + 3 q^{81} - 36 q^{82} + 17 q^{83} + 2 q^{84} - q^{85} - 23 q^{86} - 42 q^{87} - 15 q^{88} + 26 q^{89} - 40 q^{90} - 4 q^{91} - 24 q^{92} + 5 q^{93} + 18 q^{94} - 21 q^{95} - 4 q^{96} + 11 q^{97} + 6 q^{98} - 28 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 5 * q^3 + 8 * q^4 + 11 * q^5 + 6 * q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9 + 8 * q^11 - 3 * q^12 - 7 * q^13 - 5 * q^14 + 2 * q^16 + 7 * q^17 - 9 * q^18 + q^19 - 2 * q^21 + 6 * q^22 + 6 * q^23 + 5 * q^24 + 10 * q^25 - 2 * q^26 + 11 * q^27 - 11 * q^28 - 2 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 + 6 * q^33 - 4 * q^34 - q^35 - 20 * q^36 + 28 * q^37 - 8 * q^38 - 5 * q^39 - 5 * q^40 + 3 * q^41 + 13 * q^42 - q^43 + 12 * q^44 + 9 * q^45 - 37 * q^46 - q^47 + 11 * q^48 - 19 * q^49 + 21 * q^50 - 30 * q^51 - 8 * q^52 + 29 * q^53 + 2 * q^54 + 19 * q^55 - 20 * q^56 + 11 * q^57 + 3 * q^58 + 3 * q^59 - 43 * q^60 + 5 * q^61 + 2 * q^62 + q^63 - 29 * q^64 - 11 * q^65 - 29 * q^66 - 32 * q^67 + 38 * q^68 + 17 * q^69 - 23 * q^70 + 5 * q^71 - 17 * q^72 + q^73 - 4 * q^74 - 7 * q^75 - 12 * q^76 - 5 * q^77 - 6 * q^78 - 15 * q^79 - 11 * q^80 + 3 * q^81 - 36 * q^82 + 17 * q^83 + 2 * q^84 - q^85 - 23 * q^86 - 42 * q^87 - 15 * q^88 + 26 * q^89 - 40 * q^90 - 4 * q^91 - 24 * q^92 + 5 * q^93 + 18 * q^94 - 21 * q^95 - 4 * q^96 + 11 * q^97 + 6 * q^98 - 28 * 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 $

$2$	2.09092	1.47850	0.739252	−	0.673429i	$-0.235179\pi$
$2$	2.09092	1.47850	0.739252	+	0.673429i	$0.235179\pi$
$3$	−0.510463	−0.294716	−0.147358	−	0.989083i	$-0.547077\pi$
$3$	−0.510463	−0.294716	−0.147358	+	0.989083i	$0.547077\pi$
$4$	2.37194	1.18597
$5$	4.43975	1.98552	0.992759	−	0.120121i	$-0.0383283\pi$
$5$	4.43975	1.98552	0.992759	+	0.120121i	$0.0383283\pi$
$6$	−1.06734	−0.435738
$7$	−2.30124	−0.869785	−0.434893	−	0.900482i	$-0.643214\pi$
$7$	−2.30124	−0.869785	−0.434893	+	0.900482i	$0.643214\pi$
$8$	0.777706	0.274960
$9$	−2.73943	−0.913143
$10$	9.28317	2.93560
$11$	5.75249	1.73444	0.867221	−	0.497923i	$-0.165904\pi$
$11$	5.75249	1.73444	0.867221	+	0.497923i	$0.165904\pi$
$12$	−1.21079	−0.349525
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.81170	−1.28598
$15$	−2.26633	−0.585164
$16$	−3.11777	−0.779442
$17$	0.581171	0.140955	0.0704774	−	0.997513i	$-0.477548\pi$
$17$	0.581171	0.140955	0.0704774	+	0.997513i	$0.477548\pi$
$18$	−5.72792	−1.35008
$19$	−3.67365	−0.842794	−0.421397	−	0.906876i	$-0.638460\pi$
$19$	−3.67365	−0.842794	−0.421397	+	0.906876i	$0.638460\pi$
$20$	10.5308	2.35477
$21$	1.17470	0.256340
$22$	12.0280	2.56438
$23$	−7.44973	−1.55338	−0.776688	−	0.629885i	$-0.783102\pi$
$23$	−7.44973	−1.55338	−0.776688	+	0.629885i	$0.783102\pi$
$24$	−0.396990	−0.0810352
$25$	14.7114	2.94228
$26$	−2.09092	−0.410063
$27$	2.92976	0.563833
$28$	−5.45840	−1.03154
$29$	−1.17295	−0.217812	−0.108906	−	0.994052i	$-0.534735\pi$
$29$	−1.17295	−0.217812	−0.108906	+	0.994052i	$0.534735\pi$
$30$	−4.73871	−0.865167
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−8.07441	−1.42737
$33$	−2.93644	−0.511168
$34$	1.21518	0.208402
$35$	−10.2169	−1.72697
$36$	−6.49777	−1.08296
$37$	6.63700	1.09112	0.545558	−	0.838073i	$-0.316318\pi$
$37$	6.63700	1.09112	0.545558	+	0.838073i	$0.316318\pi$
$38$	−7.68131	−1.24607
$39$	0.510463	0.0817395
$40$	3.45282	0.545939
$41$	−6.46171	−1.00915	−0.504575	−	0.863368i	$-0.668351\pi$
$41$	−6.46171	−1.00915	−0.504575	+	0.863368i	$0.668351\pi$
$42$	2.45619	0.378999
$43$	0.352822	0.0538049	0.0269025	−	0.999638i	$-0.491436\pi$
$43$	0.352822	0.0538049	0.0269025	+	0.999638i	$0.491436\pi$
$44$	13.6446	2.05700
$45$	−12.1624	−1.81306
$46$	−15.5768	−2.29667
$47$	0.562606	0.0820645	0.0410322	−	0.999158i	$-0.486935\pi$
$47$	0.562606	0.0820645	0.0410322	+	0.999158i	$0.486935\pi$
$48$	1.59151	0.229714
$49$	−1.70431	−0.243473
$50$	30.7604	4.35018
$51$	−0.296666	−0.0415416
$52$	−2.37194	−0.328929
$53$	7.57222	1.04012	0.520062	−	0.854128i	$-0.325909\pi$
$53$	7.57222	1.04012	0.520062	+	0.854128i	$0.325909\pi$
$54$	6.12590	0.833630
$55$	25.5397	3.44377
$56$	−1.78968	−0.239157
$57$	1.87526	0.248385
$58$	−2.45255	−0.322035
$59$	−10.3811	−1.35151	−0.675754	−	0.737127i	$-0.736182\pi$
$59$	−10.3811	−1.35151	−0.675754	+	0.737127i	$0.736182\pi$
$60$	−5.37561	−0.693988
$61$	−1.24744	−0.159718	−0.0798591	−	0.996806i	$-0.525447\pi$
$61$	−1.24744	−0.159718	−0.0798591	+	0.996806i	$0.525447\pi$
$62$	2.09092	0.265547
$63$	6.30407	0.794238
$64$	−10.6474	−1.33093
$65$	−4.43975	−0.550684
$66$	−6.13985	−0.755763
$67$	−9.53020	−1.16430	−0.582150	−	0.813082i	$-0.697788\pi$
$67$	−9.53020	−1.16430	−0.582150	+	0.813082i	$0.697788\pi$
$68$	1.37851	0.167168
$69$	3.80281	0.457805
$70$	−21.3628	−2.55334
$71$	−4.04545	−0.480106	−0.240053	−	0.970760i	$-0.577165\pi$
$71$	−4.04545	−0.480106	−0.240053	+	0.970760i	$0.577165\pi$
$72$	−2.13047	−0.251078
$73$	3.12100	0.365285	0.182643	−	0.983179i	$-0.441535\pi$
$73$	3.12100	0.365285	0.182643	+	0.983179i	$0.441535\pi$
$74$	13.8774	1.61322
$75$	−7.50963	−0.867138
$76$	−8.71370	−0.999530
$77$	−13.2378	−1.50859
$78$	1.06734	0.120852
$79$	−7.08221	−0.796811	−0.398405	−	0.917209i	$-0.630436\pi$
$79$	−7.08221	−0.796811	−0.398405	+	0.917209i	$0.630436\pi$
$80$	−13.8421	−1.54760
$81$	6.72275	0.746972
$82$	−13.5109	−1.49203
$83$	2.29916	0.252365	0.126183	−	0.992007i	$-0.459727\pi$
$83$	2.29916	0.252365	0.126183	+	0.992007i	$0.459727\pi$
$84$	2.78631	0.304012
$85$	2.58026	0.279868
$86$	0.737723	0.0795508
$87$	0.598748	0.0641925
$88$	4.47375	0.476903
$89$	0.601680	0.0637779	0.0318890	−	0.999491i	$-0.489848\pi$
$89$	0.601680	0.0637779	0.0318890	+	0.999491i	$0.489848\pi$
$90$	−25.4306	−2.68062
$91$	2.30124	0.241235
$92$	−17.6703	−1.84226
$93$	−0.510463	−0.0529325
$94$	1.17636	0.121333
$95$	−16.3101	−1.67338
$96$	4.12169	0.420668
$97$	12.4967	1.26885	0.634423	−	0.772986i	$-0.281238\pi$
$97$	12.4967	1.26885	0.634423	+	0.772986i	$0.281238\pi$
$98$	−3.56358	−0.359976
$99$	−15.7585	−1.58379
$100$	34.8947	3.48947
$101$	6.04607	0.601607	0.300803	−	0.953686i	$-0.402745\pi$
$101$	6.04607	0.601607	0.300803	+	0.953686i	$0.402745\pi$
$102$	−0.620306	−0.0614194
$103$	13.6607	1.34603	0.673016	−	0.739628i	$-0.264998\pi$
$103$	13.6607	1.34603	0.673016	+	0.739628i	$0.264998\pi$
$104$	−0.777706	−0.0762603
$105$	5.21536	0.508967
$106$	15.8329	1.53783
$107$	−0.482553	−0.0466502	−0.0233251	−	0.999728i	$-0.507425\pi$
$107$	−0.482553	−0.0466502	−0.0233251	+	0.999728i	$0.507425\pi$
$108$	6.94924	0.668691
$109$	−11.4545	−1.09714	−0.548571	−	0.836104i	$-0.684828\pi$
$109$	−11.4545	−1.09714	−0.548571	+	0.836104i	$0.684828\pi$
$110$	53.4014	5.09162
$111$	−3.38794	−0.321569
$112$	7.17472	0.677947
$113$	−0.986560	−0.0928078	−0.0464039	−	0.998923i	$-0.514776\pi$
$113$	−0.986560	−0.0928078	−0.0464039	+	0.998923i	$0.514776\pi$
$114$	3.92103	0.367238
$115$	−33.0750	−3.08426
$116$	−2.78218	−0.258318
$117$	2.73943	0.253260
$118$	−21.7061	−1.99821
$119$	−1.33741	−0.122600
$120$	−1.76254	−0.160897
$121$	22.0912	2.00829
$122$	−2.60830	−0.236144
$123$	3.29846	0.297412
$124$	2.37194	0.213007
$125$	43.1163	3.85644
$126$	13.1813	1.17428
$127$	15.8978	1.41070	0.705350	−	0.708859i	$-0.250790\pi$
$127$	15.8978	1.41070	0.705350	+	0.708859i	$0.250790\pi$
$128$	−6.11405	−0.540411
$129$	−0.180103	−0.0158572
$130$	−9.28317	−0.814188
$131$	−17.0985	−1.49390	−0.746952	−	0.664878i	$-0.768484\pi$
$131$	−17.0985	−1.49390	−0.746952	+	0.664878i	$0.768484\pi$
$132$	−6.96506	−0.606231
$133$	8.45394	0.733050
$134$	−19.9269	−1.72142
$135$	13.0074	1.11950
$136$	0.451980	0.0387570
$137$	20.1010	1.71734	0.858671	−	0.512527i	$-0.171290\pi$
$137$	20.1010	1.71734	0.858671	+	0.512527i	$0.171290\pi$
$138$	7.95137	0.676866
$139$	13.9901	1.18662	0.593312	−	0.804972i	$-0.297820\pi$
$139$	13.9901	1.18662	0.593312	+	0.804972i	$0.297820\pi$
$140$	−24.2340	−2.04814
$141$	−0.287189	−0.0241857
$142$	−8.45870	−0.709839
$143$	−5.75249	−0.481048
$144$	8.54090	0.711742
$145$	−5.20762	−0.432469
$146$	6.52576	0.540075
$147$	0.869989	0.0717555
$148$	15.7426	1.29403
$149$	−4.68761	−0.384024	−0.192012	−	0.981393i	$-0.561501\pi$
$149$	−4.68761	−0.384024	−0.192012	+	0.981393i	$0.561501\pi$
$150$	−15.7020	−1.28207
$151$	−2.89606	−0.235678	−0.117839	−	0.993033i	$-0.537597\pi$
$151$	−2.89606	−0.235678	−0.117839	+	0.993033i	$0.537597\pi$
$152$	−2.85702	−0.231735
$153$	−1.59208	−0.128712
$154$	−27.6793	−2.23046
$155$	4.43975	0.356610
$156$	1.21079	0.0969407
$157$	5.12046	0.408657	0.204329	−	0.978902i	$-0.434499\pi$
$157$	5.12046	0.408657	0.204329	+	0.978902i	$0.434499\pi$
$158$	−14.8083	−1.17809
$159$	−3.86534	−0.306541
$160$	−35.8484	−2.83407
$161$	17.1436	1.35110
$162$	14.0567	1.10440
$163$	−7.47479	−0.585471	−0.292735	−	0.956193i	$-0.594566\pi$
$163$	−7.47479	−0.585471	−0.292735	+	0.956193i	$0.594566\pi$
$164$	−15.3268	−1.19682
$165$	−13.0370	−1.01493
$166$	4.80735	0.373123
$167$	14.9474	1.15666	0.578331	−	0.815802i	$-0.303704\pi$
$167$	14.9474	1.15666	0.578331	+	0.815802i	$0.303704\pi$
$168$	0.913567	0.0704832
$169$	1.00000	0.0769231
$170$	5.39511	0.413786
$171$	10.0637	0.769591
$172$	0.836875	0.0638111
$173$	24.7381	1.88081	0.940403	−	0.340063i	$-0.110448\pi$
$173$	24.7381	1.88081	0.940403	+	0.340063i	$0.110448\pi$
$174$	1.25193	0.0949089
$175$	−33.8544	−2.55916
$176$	−17.9349	−1.35190
$177$	5.29918	0.398311
$178$	1.25806	0.0942958
$179$	19.8633	1.48465	0.742325	−	0.670040i	$-0.233723\pi$
$179$	19.8633	1.48465	0.742325	+	0.670040i	$0.233723\pi$
$180$	−28.8485	−2.15024
$181$	2.12946	0.158281	0.0791406	−	0.996863i	$-0.474782\pi$
$181$	2.12946	0.158281	0.0791406	+	0.996863i	$0.474782\pi$
$182$	4.81170	0.356667
$183$	0.636772	0.0470715
$184$	−5.79370	−0.427117
$185$	29.4667	2.16643
$186$	−1.06734	−0.0782609
$187$	3.34319	0.244478
$188$	1.33447	0.0973262
$189$	−6.74208	−0.490414
$190$	−34.1031	−2.47410
$191$	2.42729	0.175633	0.0878164	−	0.996137i	$-0.472011\pi$
$191$	2.42729	0.175633	0.0878164	+	0.996137i	$0.472011\pi$
$192$	5.43511	0.392245
$193$	1.31201	0.0944406	0.0472203	−	0.998884i	$-0.484964\pi$
$193$	1.31201	0.0944406	0.0472203	+	0.998884i	$0.484964\pi$
$194$	26.1296	1.87599
$195$	2.26633	0.162295
$196$	−4.04254	−0.288753
$197$	−20.9215	−1.49060	−0.745299	−	0.666730i	$-0.767693\pi$
$197$	−20.9215	−1.49060	−0.745299	+	0.666730i	$0.767693\pi$
$198$	−32.9498	−2.34164
$199$	−0.576436	−0.0408625	−0.0204312	−	0.999791i	$-0.506504\pi$
$199$	−0.576436	−0.0408625	−0.0204312	+	0.999791i	$0.506504\pi$
$200$	11.4412	0.809012
$201$	4.86481	0.343137
$202$	12.6418	0.889477
$203$	2.69924	0.189449
$204$	−0.703676	−0.0492672
$205$	−28.6884	−2.00368
$206$	28.5635	1.99011
$207$	20.4080	1.41845
$208$	3.11777	0.216178
$209$	−21.1327	−1.46178
$210$	10.9049	0.752509
$211$	1.18942	0.0818832	0.0409416	−	0.999162i	$-0.486964\pi$
$211$	1.18942	0.0818832	0.0409416	+	0.999162i	$0.486964\pi$
$212$	17.9609	1.23356
$213$	2.06505	0.141495
$214$	−1.00898	−0.0689724
$215$	1.56644	0.106831
$216$	2.27849	0.155032
$217$	−2.30124	−0.156218
$218$	−23.9504	−1.62213
$219$	−1.59315	−0.107655
$220$	60.5787	4.08421
$221$	−0.581171	−0.0390938
$222$	−7.08392	−0.475441
$223$	10.9887	0.735860	0.367930	−	0.929853i	$-0.380067\pi$
$223$	10.9887	0.735860	0.367930	+	0.929853i	$0.380067\pi$
$224$	18.5811	1.24150
$225$	−40.3009	−2.68672
$226$	−2.06282	−0.137217
$227$	−3.87909	−0.257464	−0.128732	−	0.991679i	$-0.541091\pi$
$227$	−3.87909	−0.257464	−0.128732	+	0.991679i	$0.541091\pi$
$228$	4.44802	0.294577
$229$	−14.3665	−0.949365	−0.474682	−	0.880157i	$-0.657437\pi$
$229$	−14.3665	−0.949365	−0.474682	+	0.880157i	$0.657437\pi$
$230$	−69.1571	−4.56008
$231$	6.75743	0.444606
$232$	−0.912211	−0.0598896
$233$	−16.1138	−1.05565	−0.527826	−	0.849353i	$-0.676993\pi$
$233$	−16.1138	−1.05565	−0.527826	+	0.849353i	$0.676993\pi$
$234$	5.72792	0.374446
$235$	2.49783	0.162940
$236$	−24.6235	−1.60285
$237$	3.61520	0.234833
$238$	−2.79642	−0.181265
$239$	−12.3505	−0.798890	−0.399445	−	0.916757i	$-0.630797\pi$
$239$	−12.3505	−0.798890	−0.399445	+	0.916757i	$0.630797\pi$
$240$	7.06589	0.456101
$241$	14.9590	0.963596	0.481798	−	0.876282i	$-0.339984\pi$
$241$	14.9590	0.963596	0.481798	+	0.876282i	$0.339984\pi$
$242$	46.1909	2.96926
$243$	−12.2210	−0.783978
$244$	−2.95886	−0.189421
$245$	−7.56674	−0.483421
$246$	6.89682	0.439725
$247$	3.67365	0.233749
$248$	0.777706	0.0493844
$249$	−1.17363	−0.0743761
$250$	90.1527	5.70176
$251$	−17.9819	−1.13501	−0.567503	−	0.823371i	$-0.692090\pi$
$251$	−17.9819	−1.13501	−0.567503	+	0.823371i	$0.692090\pi$
$252$	14.9529	0.941944
$253$	−42.8545	−2.69424
$254$	33.2410	2.08573
$255$	−1.31713	−0.0824816
$256$	8.51083	0.531927
$257$	21.3724	1.33317	0.666586	−	0.745428i	$-0.267755\pi$
$257$	21.3724	1.33317	0.666586	+	0.745428i	$0.267755\pi$
$258$	−0.376580	−0.0234449
$259$	−15.2733	−0.949037
$260$	−10.5308	−0.653096
$261$	3.21322	0.198893
$262$	−35.7516	−2.20874
$263$	−27.3174	−1.68446	−0.842231	−	0.539117i	$-0.818758\pi$
$263$	−27.3174	−1.68446	−0.842231	+	0.539117i	$0.818758\pi$
$264$	−2.28368	−0.140551
$265$	33.6188	2.06519
$266$	17.6765	1.08382
$267$	−0.307135	−0.0187964
$268$	−22.6051	−1.38083
$269$	8.04213	0.490337	0.245169	−	0.969480i	$-0.421157\pi$
$269$	8.04213	0.490337	0.245169	+	0.969480i	$0.421157\pi$
$270$	27.1975	1.65519
$271$	9.35268	0.568135	0.284068	−	0.958804i	$-0.408316\pi$
$271$	9.35268	0.568135	0.284068	+	0.958804i	$0.408316\pi$
$272$	−1.81196	−0.109866
$273$	−1.17470	−0.0710958
$274$	42.0295	2.53910
$275$	84.6274	5.10322
$276$	9.02006	0.542944
$277$	−15.6248	−0.938805	−0.469402	−	0.882984i	$-0.655531\pi$
$277$	−15.6248	−0.938805	−0.469402	+	0.882984i	$0.655531\pi$
$278$	29.2522	1.75443
$279$	−2.73943	−0.164005
$280$	−7.94576	−0.474850
$281$	−0.501734	−0.0299310	−0.0149655	−	0.999888i	$-0.504764\pi$
$281$	−0.501734	−0.0299310	−0.0149655	+	0.999888i	$0.504764\pi$
$282$	−0.600490	−0.0357586
$283$	2.40276	0.142829	0.0714145	−	0.997447i	$-0.477249\pi$
$283$	2.40276	0.142829	0.0714145	+	0.997447i	$0.477249\pi$
$284$	−9.59558	−0.569393
$285$	8.32571	0.493172
$286$	−12.0280	−0.711231
$287$	14.8699	0.877743
$288$	22.1193	1.30339
$289$	−16.6622	−0.980132
$290$	−10.8887	−0.639407
$291$	−6.37910	−0.373949
$292$	7.40283	0.433218
$293$	−4.47081	−0.261187	−0.130594	−	0.991436i	$-0.541688\pi$
$293$	−4.47081	−0.261187	−0.130594	+	0.991436i	$0.541688\pi$
$294$	1.81908	0.106091
$295$	−46.0897	−2.68344
$296$	5.16163	0.300014
$297$	16.8535	0.977937
$298$	−9.80141	−0.567781
$299$	7.44973	0.430829
$300$	−17.8124	−1.02840
$301$	−0.811928	−0.0467987
$302$	−6.05542	−0.348451
$303$	−3.08629	−0.177303
$304$	11.4536	0.656909
$305$	−5.53832	−0.317124
$306$	−3.32891	−0.190301
$307$	19.9649	1.13945	0.569727	−	0.821834i	$-0.307049\pi$
$307$	19.9649	1.13945	0.569727	+	0.821834i	$0.307049\pi$
$308$	−31.3994	−1.78915
$309$	−6.97330	−0.396697
$310$	9.28317	0.527249
$311$	6.19191	0.351111	0.175555	−	0.984470i	$-0.443828\pi$
$311$	6.19191	0.351111	0.175555	+	0.984470i	$0.443828\pi$
$312$	0.396990	0.0224751
$313$	−19.8715	−1.12320	−0.561601	−	0.827408i	$-0.689814\pi$
$313$	−19.8715	−1.12320	−0.561601	+	0.827408i	$0.689814\pi$
$314$	10.7065	0.604201
$315$	27.9885	1.57697
$316$	−16.7986	−0.944995
$317$	−25.1763	−1.41404	−0.707021	−	0.707193i	$-0.749961\pi$
$317$	−25.1763	−1.41404	−0.707021	+	0.707193i	$0.749961\pi$
$318$	−8.08211	−0.453222
$319$	−6.74740	−0.377782
$320$	−47.2719	−2.64258
$321$	0.246325	0.0137485
$322$	35.8459	1.99761
$323$	−2.13502	−0.118796
$324$	15.9460	0.885888
$325$	−14.7114	−0.816043
$326$	−15.6292	−0.865621
$327$	5.84709	0.323345
$328$	−5.02531	−0.277476
$329$	−1.29469	−0.0713785
$330$	−27.2594	−1.50058
$331$	5.76319	0.316773	0.158387	−	0.987377i	$-0.449371\pi$
$331$	5.76319	0.316773	0.158387	+	0.987377i	$0.449371\pi$
$332$	5.45347	0.299298
$333$	−18.1816	−0.996345
$334$	31.2537	1.71013
$335$	−42.3117	−2.31174
$336$	−3.66243	−0.199802
$337$	−23.5689	−1.28388	−0.641940	−	0.766754i	$-0.721870\pi$
$337$	−23.5689	−1.28388	−0.641940	+	0.766754i	$0.721870\pi$
$338$	2.09092	0.113731
$339$	0.503602	0.0273519
$340$	6.12023	0.331916
$341$	5.75249	0.311515
$342$	21.0424	1.13784
$343$	20.0307	1.08155
$344$	0.274392	0.0147942
$345$	16.8835	0.908980
$346$	51.7254	2.78078
$347$	25.3637	1.36159	0.680797	−	0.732472i	$-0.261633\pi$
$347$	25.3637	1.36159	0.680797	+	0.732472i	$0.261633\pi$
$348$	1.42020	0.0761306
$349$	−27.6333	−1.47918	−0.739588	−	0.673060i	$-0.764979\pi$
$349$	−27.6333	−1.47918	−0.739588	+	0.673060i	$0.764979\pi$
$350$	−70.7869	−3.78372
$351$	−2.92976	−0.156379
$352$	−46.4480	−2.47569
$353$	3.86327	0.205621	0.102810	−	0.994701i	$-0.467216\pi$
$353$	3.86327	0.205621	0.102810	+	0.994701i	$0.467216\pi$
$354$	11.0802	0.588904
$355$	−17.9608	−0.953260
$356$	1.42715	0.0756388
$357$	0.682699	0.0361323
$358$	41.5325	2.19506
$359$	−21.7912	−1.15009	−0.575047	−	0.818120i	$-0.695016\pi$
$359$	−21.7912	−1.15009	−0.575047	+	0.818120i	$0.695016\pi$
$360$	−9.45875	−0.498520
$361$	−5.50427	−0.289699
$362$	4.45252	0.234019
$363$	−11.2767	−0.591875
$364$	5.45840	0.286098
$365$	13.8565	0.725281
$366$	1.33144	0.0695954
$367$	−20.9312	−1.09260	−0.546301	−	0.837589i	$-0.683965\pi$
$367$	−20.9312	−1.09260	−0.546301	+	0.837589i	$0.683965\pi$
$368$	23.2265	1.21077
$369$	17.7014	0.921497
$370$	61.6124	3.20308
$371$	−17.4255	−0.904685
$372$	−1.21079	−0.0627765
$373$	3.03023	0.156899	0.0784497	−	0.996918i	$-0.475003\pi$
$373$	3.03023	0.156899	0.0784497	+	0.996918i	$0.475003\pi$
$374$	6.99033	0.361461
$375$	−22.0093	−1.13655
$376$	0.437541	0.0225645
$377$	1.17295	0.0604101
$378$	−14.0971	−0.725079
$379$	−12.0359	−0.618243	−0.309121	−	0.951023i	$-0.600035\pi$
$379$	−12.0359	−0.618243	−0.309121	+	0.951023i	$0.600035\pi$
$380$	−38.6867	−1.98459
$381$	−8.11523	−0.415756
$382$	5.07527	0.259674
$383$	26.7161	1.36513	0.682565	−	0.730825i	$-0.260864\pi$
$383$	26.7161	1.36513	0.682565	+	0.730825i	$0.260864\pi$
$384$	3.12100	0.159268
$385$	−58.7728	−2.99534
$386$	2.74331	0.139631
$387$	−0.966532	−0.0491316
$388$	29.6415	1.50482
$389$	2.58533	0.131081	0.0655407	−	0.997850i	$-0.479123\pi$
$389$	2.58533	0.131081	0.0655407	+	0.997850i	$0.479123\pi$
$390$	4.73871	0.239954
$391$	−4.32957	−0.218956
$392$	−1.32545	−0.0669456
$393$	8.72816	0.440277
$394$	−43.7453	−2.20385
$395$	−31.4433	−1.58208
$396$	−37.3784	−1.87833
$397$	0.284430	0.0142751	0.00713756	−	0.999975i	$-0.497728\pi$
$397$	0.284430	0.0142751	0.00713756	+	0.999975i	$0.497728\pi$
$398$	−1.20528	−0.0604153
$399$	−4.31542	−0.216041
$400$	−45.8668	−2.29334
$401$	−36.3172	−1.81359	−0.906797	−	0.421567i	$-0.861480\pi$
$401$	−36.3172	−1.81359	−0.906797	+	0.421567i	$0.861480\pi$
$402$	10.1719	0.507330
$403$	−1.00000	−0.0498135
$404$	14.3409	0.713489
$405$	29.8473	1.48313
$406$	5.64389	0.280101
$407$	38.1793	1.89248
$408$	−0.230719	−0.0114223
$409$	22.6291	1.11894	0.559469	−	0.828851i	$-0.311005\pi$
$409$	22.6291	1.11894	0.559469	+	0.828851i	$0.311005\pi$
$410$	−59.9851	−2.96245
$411$	−10.2608	−0.506128
$412$	32.4025	1.59636
$413$	23.8894	1.17552
$414$	42.6715	2.09719
$415$	10.2077	0.501076
$416$	8.07441	0.395881
$417$	−7.14143	−0.349717
$418$	−44.1867	−2.16124
$419$	−3.38025	−0.165136	−0.0825680	−	0.996585i	$-0.526312\pi$
$419$	−3.38025	−0.165136	−0.0825680	+	0.996585i	$0.526312\pi$
$420$	12.3705	0.603621
$421$	23.6780	1.15399	0.576996	−	0.816747i	$-0.304225\pi$
$421$	23.6780	1.15399	0.576996	+	0.816747i	$0.304225\pi$
$422$	2.48699	0.121065
$423$	−1.54122	−0.0749365
$424$	5.88896	0.285993
$425$	8.54986	0.414729
$426$	4.31785	0.209201
$427$	2.87065	0.138921
$428$	−1.14459	−0.0553258
$429$	2.93644	0.141772
$430$	3.27531	0.157949
$431$	20.5219	0.988507	0.494253	−	0.869318i	$-0.335442\pi$
$431$	20.5219	0.988507	0.494253	+	0.869318i	$0.335442\pi$
$432$	−9.13433	−0.439476
$433$	−31.8415	−1.53020	−0.765102	−	0.643909i	$-0.777312\pi$
$433$	−31.8415	−1.53020	−0.765102	+	0.643909i	$0.777312\pi$
$434$	−4.81170	−0.230969
$435$	2.65829	0.127455
$436$	−27.1694	−1.30118
$437$	27.3677	1.30918
$438$	−3.33116	−0.159169
$439$	−5.95491	−0.284213	−0.142106	−	0.989851i	$-0.545387\pi$
$439$	−5.95491	−0.284213	−0.142106	+	0.989851i	$0.545387\pi$
$440$	19.8623	0.946900
$441$	4.66885	0.222326
$442$	−1.21518	−0.0578003
$443$	11.2815	0.535999	0.268000	−	0.963419i	$-0.413637\pi$
$443$	11.2815	0.535999	0.268000	+	0.963419i	$0.413637\pi$
$444$	−8.03601	−0.381372
$445$	2.67131	0.126632
$446$	22.9766	1.08797
$447$	2.39285	0.113178
$448$	24.5022	1.15762
$449$	19.8536	0.936951	0.468476	−	0.883476i	$-0.344803\pi$
$449$	19.8536	0.936951	0.468476	+	0.883476i	$0.344803\pi$
$450$	−84.2659	−3.97233
$451$	−37.1709	−1.75031
$452$	−2.34007	−0.110067
$453$	1.47833	0.0694580
$454$	−8.11086	−0.380661
$455$	10.2169	0.478977
$456$	1.45840	0.0682960
$457$	−28.4670	−1.33163	−0.665815	−	0.746117i	$-0.731916\pi$
$457$	−28.4670	−1.33163	−0.665815	+	0.746117i	$0.731916\pi$
$458$	−30.0392	−1.40364
$459$	1.70270	0.0794750
$460$	−78.4520	−3.65784
$461$	−28.9069	−1.34633	−0.673164	−	0.739493i	$-0.735065\pi$
$461$	−28.9069	−1.34633	−0.673164	+	0.739493i	$0.735065\pi$
$462$	14.1292	0.657352
$463$	−21.0250	−0.977113	−0.488557	−	0.872532i	$-0.662476\pi$
$463$	−21.0250	−0.977113	−0.488557	+	0.872532i	$0.662476\pi$
$464$	3.65699	0.169772
$465$	−2.26633	−0.105099
$466$	−33.6927	−1.56078
$467$	−20.0661	−0.928548	−0.464274	−	0.885692i	$-0.653685\pi$
$467$	−20.0661	−0.928548	−0.464274	+	0.885692i	$0.653685\pi$
$468$	6.49777	0.300360
$469$	21.9312	1.01269
$470$	5.22276	0.240908
$471$	−2.61380	−0.120438
$472$	−8.07346	−0.371611
$473$	2.02961	0.0933215
$474$	7.55910	0.347201
$475$	−54.0446	−2.47974
$476$	−3.17227	−0.145401
$477$	−20.7435	−0.949782
$478$	−25.8240	−1.18116
$479$	38.5191	1.75998	0.879992	−	0.474989i	$-0.157548\pi$
$479$	38.5191	1.75998	0.879992	+	0.474989i	$0.157548\pi$
$480$	18.2993	0.835244
$481$	−6.63700	−0.302621
$482$	31.2781	1.42468
$483$	−8.75116	−0.398192
$484$	52.3991	2.38178
$485$	55.4822	2.51932
$486$	−25.5531	−1.15911
$487$	−20.1387	−0.912570	−0.456285	−	0.889834i	$-0.650820\pi$
$487$	−20.1387	−0.912570	−0.456285	+	0.889834i	$0.650820\pi$
$488$	−0.970141	−0.0439162
$489$	3.81560	0.172548
$490$	−15.8214	−0.714740
$491$	−29.5191	−1.33218	−0.666088	−	0.745873i	$-0.732033\pi$
$491$	−29.5191	−1.33218	−0.666088	+	0.745873i	$0.732033\pi$
$492$	7.82377	0.352723
$493$	−0.681686	−0.0307016
$494$	7.68131	0.345599
$495$	−69.9641	−3.14465
$496$	−3.11777	−0.139992
$497$	9.30953	0.417589
$498$	−2.45397	−0.109965
$499$	4.62447	0.207020	0.103510	−	0.994628i	$-0.466993\pi$
$499$	4.62447	0.207020	0.103510	+	0.994628i	$0.466993\pi$
$500$	102.269	4.57363
$501$	−7.63008	−0.340887
$502$	−37.5987	−1.67811
$503$	14.0185	0.625056	0.312528	−	0.949909i	$-0.398824\pi$
$503$	14.0185	0.625056	0.312528	+	0.949909i	$0.398824\pi$
$504$	4.90271	0.218384
$505$	26.8431	1.19450
$506$	−89.6054	−3.98345
$507$	−0.510463	−0.0226705
$508$	37.7087	1.67305
$509$	38.4131	1.70263	0.851316	−	0.524653i	$-0.175805\pi$
$509$	38.4131	1.70263	0.851316	+	0.524653i	$0.175805\pi$
$510$	−2.75400	−0.121949
$511$	−7.18215	−0.317720
$512$	30.0236	1.32687
$513$	−10.7629	−0.475195
$514$	44.6879	1.97110
$515$	60.6503	2.67257
$516$	−0.427194	−0.0188062
$517$	3.23639	0.142336
$518$	−31.9353	−1.40315
$519$	−12.6279	−0.554303
$520$	−3.45282	−0.151416
$521$	−0.824701	−0.0361308	−0.0180654	−	0.999837i	$-0.505751\pi$
$521$	−0.824701	−0.0361308	−0.0180654	+	0.999837i	$0.505751\pi$
$522$	6.71857	0.294064
$523$	−14.2490	−0.623066	−0.311533	−	0.950235i	$-0.600842\pi$
$523$	−14.2490	−0.623066	−0.311533	+	0.950235i	$0.600842\pi$
$524$	−40.5567	−1.77173
$525$	17.2814	0.754224
$526$	−57.1184	−2.49048
$527$	0.581171	0.0253162
$528$	9.15513	0.398426
$529$	32.4985	1.41298
$530$	70.2942	3.05338
$531$	28.4384	1.23412
$532$	20.0523	0.869377
$533$	6.46171	0.279888
$534$	−0.642195	−0.0277905
$535$	−2.14242	−0.0926247
$536$	−7.41169	−0.320136
$537$	−10.1395	−0.437550
$538$	16.8155	0.724966
$539$	−9.80406	−0.422291
$540$	30.8529	1.32770
$541$	39.6237	1.70356	0.851778	−	0.523902i	$-0.175524\pi$
$541$	39.6237	1.70356	0.851778	+	0.523902i	$0.175524\pi$
$542$	19.5557	0.839990
$543$	−1.08701	−0.0466480
$544$	−4.69262	−0.201194
$545$	−50.8551	−2.17839
$546$	−2.45619	−0.105115
$547$	15.8308	0.676875	0.338437	−	0.940989i	$-0.390102\pi$
$547$	15.8308	0.676875	0.338437	+	0.940989i	$0.390102\pi$
$548$	47.6784	2.03672
$549$	3.41727	0.145846
$550$	176.949	7.54513
$551$	4.30902	0.183570
$552$	2.95747	0.125878
$553$	16.2978	0.693054
$554$	−32.6703	−1.38803
$555$	−15.0416	−0.638482
$556$	33.1837	1.40730
$557$	20.0498	0.849537	0.424769	−	0.905302i	$-0.360355\pi$
$557$	20.0498	0.849537	0.424769	+	0.905302i	$0.360355\pi$
$558$	−5.72792	−0.242482
$559$	−0.352822	−0.0149228
$560$	31.8540	1.34608
$561$	−1.70657	−0.0720515
$562$	−1.04909	−0.0442530
$563$	−0.996796	−0.0420099	−0.0210050	−	0.999779i	$-0.506687\pi$
$563$	−0.996796	−0.0420099	−0.0210050	+	0.999779i	$0.506687\pi$
$564$	−0.681197	−0.0286836
$565$	−4.38009	−0.184272
$566$	5.02397	0.211173
$567$	−15.4706	−0.649705
$568$	−3.14617	−0.132010
$569$	−14.7566	−0.618627	−0.309313	−	0.950960i	$-0.600099\pi$
$569$	−14.7566	−0.618627	−0.309313	+	0.950960i	$0.600099\pi$
$570$	17.4084	0.729157
$571$	−4.38828	−0.183644	−0.0918220	−	0.995775i	$-0.529269\pi$
$571$	−4.38828	−0.183644	−0.0918220	+	0.995775i	$0.529269\pi$
$572$	−13.6446	−0.570509
$573$	−1.23904	−0.0517618
$574$	31.0918	1.29775
$575$	−109.596	−4.57047
$576$	29.1678	1.21533
$577$	18.2000	0.757677	0.378839	−	0.925463i	$-0.376324\pi$
$577$	18.2000	0.757677	0.378839	+	0.925463i	$0.376324\pi$
$578$	−34.8394	−1.44913
$579$	−0.669733	−0.0278331
$580$	−12.3522	−0.512896
$581$	−5.29090	−0.219504
$582$	−13.3382	−0.552885
$583$	43.5591	1.80404
$584$	2.42722	0.100439
$585$	12.1624	0.502853
$586$	−9.34810	−0.386166
$587$	31.7805	1.31172	0.655861	−	0.754882i	$-0.272306\pi$
$587$	31.7805	1.31172	0.655861	+	0.754882i	$0.272306\pi$
$588$	2.06357	0.0851000
$589$	−3.67365	−0.151370
$590$	−96.3698	−3.96748
$591$	10.6797	0.439303
$592$	−20.6926	−0.850462
$593$	−33.9347	−1.39353	−0.696765	−	0.717300i	$-0.745378\pi$
$593$	−33.9347	−1.39353	−0.696765	+	0.717300i	$0.745378\pi$
$594$	35.2392	1.44588
$595$	−5.93778	−0.243425
$596$	−11.1187	−0.455442
$597$	0.294249	0.0120428
$598$	15.5768	0.636982
$599$	−21.0150	−0.858649	−0.429325	−	0.903150i	$-0.641248\pi$
$599$	−21.0150	−0.858649	−0.429325	+	0.903150i	$0.641248\pi$
$600$	−5.84028	−0.238429
$601$	−0.0972081	−0.00396520	−0.00198260	−	0.999998i	$-0.500631\pi$
$601$	−0.0972081	−0.00396520	−0.00198260	+	0.999998i	$0.500631\pi$
$602$	−1.69768	−0.0691921
$603$	26.1073	1.06317
$604$	−6.86929	−0.279507
$605$	98.0795	3.98750
$606$	−6.45319	−0.262143
$607$	−16.8042	−0.682061	−0.341031	−	0.940052i	$-0.610776\pi$
$607$	−16.8042	−0.682061	−0.341031	+	0.940052i	$0.610776\pi$
$608$	29.6626	1.20298
$609$	−1.37786	−0.0558337
$610$	−11.5802	−0.468868
$611$	−0.562606	−0.0227606
$612$	−3.77632	−0.152649
$613$	−38.6389	−1.56061	−0.780306	−	0.625398i	$-0.784937\pi$
$613$	−38.6389	−1.56061	−0.780306	+	0.625398i	$0.784937\pi$
$614$	41.7449	1.68469
$615$	14.6444	0.590518
$616$	−10.2951	−0.414803
$617$	−40.6277	−1.63561	−0.817804	−	0.575496i	$-0.804809\pi$
$617$	−40.6277	−1.63561	−0.817804	+	0.575496i	$0.804809\pi$
$618$	−14.5806	−0.586518
$619$	20.8650	0.838635	0.419317	−	0.907840i	$-0.362269\pi$
$619$	20.8650	0.838635	0.419317	+	0.907840i	$0.362269\pi$
$620$	10.5308	0.422929
$621$	−21.8260	−0.875846
$622$	12.9468	0.519119
$623$	−1.38461	−0.0554731
$624$	−1.59151	−0.0637112
$625$	117.869	4.71475
$626$	−41.5496	−1.66066
$627$	10.7874	0.430809
$628$	12.1454	0.484656
$629$	3.85724	0.153798
$630$	58.5217	2.33156
$631$	39.1620	1.55901	0.779507	−	0.626393i	$-0.215469\pi$
$631$	39.1620	1.55901	0.779507	+	0.626393i	$0.215469\pi$
$632$	−5.50787	−0.219091
$633$	−0.607156	−0.0241323
$634$	−52.6416	−2.09067
$635$	70.5823	2.80097
$636$	−9.16836	−0.363549
$637$	1.70431	0.0675274
$638$	−14.1083	−0.558551
$639$	11.0822	0.438405
$640$	−27.1449	−1.07300
$641$	−18.8415	−0.744196	−0.372098	−	0.928193i	$-0.621362\pi$
$641$	−18.8415	−0.744196	−0.372098	+	0.928193i	$0.621362\pi$
$642$	0.515046	0.0203273
$643$	3.89976	0.153792	0.0768958	−	0.997039i	$-0.475499\pi$
$643$	3.89976	0.153792	0.0768958	+	0.997039i	$0.475499\pi$
$644$	40.6636	1.60237
$645$	−0.799612	−0.0314847
$646$	−4.46416	−0.175640
$647$	10.6716	0.419543	0.209771	−	0.977750i	$-0.432728\pi$
$647$	10.6716	0.419543	0.209771	+	0.977750i	$0.432728\pi$
$648$	5.22832	0.205388
$649$	−59.7174	−2.34411
$650$	−30.7604	−1.20652
$651$	1.17470	0.0460399
$652$	−17.7298	−0.694352
$653$	−13.2372	−0.518011	−0.259005	−	0.965876i	$-0.583395\pi$
$653$	−13.2372	−0.518011	−0.259005	+	0.965876i	$0.583395\pi$
$654$	12.2258	0.478067
$655$	−75.9132	−2.96617
$656$	20.1461	0.786574
$657$	−8.54975	−0.333558
$658$	−2.70709	−0.105533
$659$	−32.1036	−1.25058	−0.625289	−	0.780394i	$-0.715019\pi$
$659$	−32.1036	−1.25058	−0.625289	+	0.780394i	$0.715019\pi$
$660$	−30.9232	−1.20368
$661$	−2.49712	−0.0971268	−0.0485634	−	0.998820i	$-0.515464\pi$
$661$	−2.49712	−0.0971268	−0.0485634	+	0.998820i	$0.515464\pi$
$662$	12.0504	0.468351
$663$	0.296666	0.0115216
$664$	1.78807	0.0693905
$665$	37.5334	1.45548
$666$	−38.0162	−1.47310
$667$	8.73817	0.338343
$668$	35.4543	1.37177
$669$	−5.60934	−0.216870
$670$	−88.4705	−3.41791
$671$	−7.17589	−0.277022
$672$	−9.48498	−0.365891
$673$	11.1156	0.428476	0.214238	−	0.976782i	$-0.431273\pi$
$673$	11.1156	0.428476	0.214238	+	0.976782i	$0.431273\pi$
$674$	−49.2807	−1.89822
$675$	43.1010	1.65896
$676$	2.37194	0.0912286
$677$	1.90992	0.0734040	0.0367020	−	0.999326i	$-0.488315\pi$
$677$	1.90992	0.0734040	0.0367020	+	0.999326i	$0.488315\pi$
$678$	1.05299	0.0404399
$679$	−28.7578	−1.10362
$680$	2.00668	0.0769527
$681$	1.98013	0.0758787
$682$	12.0280	0.460576
$683$	−15.5813	−0.596202	−0.298101	−	0.954534i	$-0.596353\pi$
$683$	−15.5813	−0.596202	−0.298101	+	0.954534i	$0.596353\pi$
$684$	23.8706	0.912713
$685$	89.2434	3.40982
$686$	41.8825	1.59908
$687$	7.33356	0.279793
$688$	−1.10002	−0.0419378
$689$	−7.57222	−0.288479
$690$	35.3021	1.34393
$691$	−7.69570	−0.292758	−0.146379	−	0.989229i	$-0.546762\pi$
$691$	−7.69570	−0.292758	−0.146379	+	0.989229i	$0.546762\pi$
$692$	58.6775	2.23058
$693$	36.2641	1.37756
$694$	53.0335	2.01312
$695$	62.1126	2.35607
$696$	0.465650	0.0176504
$697$	−3.75536	−0.142244
$698$	−57.7790	−2.18697
$699$	8.22550	0.311117
$700$	−80.3008	−3.03509
$701$	7.83452	0.295906	0.147953	−	0.988994i	$-0.452732\pi$
$701$	7.83452	0.295906	0.147953	+	0.988994i	$0.452732\pi$
$702$	−6.12590	−0.231207
$703$	−24.3820	−0.919586
$704$	−61.2492	−2.30842
$705$	−1.27505	−0.0480211
$706$	8.07778	0.304011
$707$	−13.9134	−0.523269
$708$	12.5694	0.472386
$709$	49.7188	1.86723	0.933615	−	0.358277i	$-0.116636\pi$
$709$	49.7188	1.86723	0.933615	+	0.358277i	$0.116636\pi$
$710$	−37.5546	−1.40940
$711$	19.4012	0.727602
$712$	0.467930	0.0175364
$713$	−7.44973	−0.278995
$714$	1.42747	0.0534217
$715$	−25.5397	−0.955129
$716$	47.1146	1.76075
$717$	6.30450	0.235446
$718$	−45.5636	−1.70042
$719$	−12.2555	−0.457051	−0.228526	−	0.973538i	$-0.573390\pi$
$719$	−12.2555	−0.457051	−0.228526	+	0.973538i	$0.573390\pi$
$720$	37.9195	1.41318
$721$	−31.4366	−1.17076
$722$	−11.5090	−0.428320
$723$	−7.63603	−0.283987
$724$	5.05095	0.187717
$725$	−17.2558	−0.640863
$726$	−23.5787	−0.875089
$727$	−32.4770	−1.20451	−0.602253	−	0.798306i	$-0.705730\pi$
$727$	−32.4770	−1.20451	−0.602253	+	0.798306i	$0.705730\pi$
$728$	1.78968	0.0663301
$729$	−13.9299	−0.515921
$730$	28.9728	1.07233
$731$	0.205050	0.00758406
$732$	1.51039	0.0558255
$733$	11.9205	0.440295	0.220147	−	0.975467i	$-0.429346\pi$
$733$	11.9205	0.440295	0.220147	+	0.975467i	$0.429346\pi$
$734$	−43.7656	−1.61542
$735$	3.86254	0.142472
$736$	60.1522	2.21724
$737$	−54.8224	−2.01941
$738$	37.0122	1.36244
$739$	5.01188	0.184365	0.0921824	−	0.995742i	$-0.470616\pi$
$739$	5.01188	0.184365	0.0921824	+	0.995742i	$0.470616\pi$
$740$	69.8933	2.56933
$741$	−1.87526	−0.0688895
$742$	−36.4352	−1.33758
$743$	−3.46845	−0.127245	−0.0636225	−	0.997974i	$-0.520265\pi$
$743$	−3.46845	−0.127245	−0.0636225	+	0.997974i	$0.520265\pi$
$744$	−0.396990	−0.0145544
$745$	−20.8118	−0.762487
$746$	6.33597	0.231976
$747$	−6.29837	−0.230445
$748$	7.92985	0.289944
$749$	1.11047	0.0405756
$750$	−46.0196	−1.68040
$751$	−19.7013	−0.718910	−0.359455	−	0.933162i	$-0.617037\pi$
$751$	−19.7013	−0.718910	−0.359455	+	0.933162i	$0.617037\pi$
$752$	−1.75407	−0.0639645
$753$	9.17908	0.334504
$754$	2.45255	0.0893165
$755$	−12.8578	−0.467943
$756$	−15.9918	−0.581617
$757$	17.4380	0.633795	0.316898	−	0.948460i	$-0.397359\pi$
$757$	17.4380	0.633795	0.316898	+	0.948460i	$0.397359\pi$
$758$	−25.1661	−0.914074
$759$	21.8757	0.794036
$760$	−12.6845	−0.460114
$761$	−16.1771	−0.586421	−0.293210	−	0.956048i	$-0.594724\pi$
$761$	−16.1771	−0.586421	−0.293210	+	0.956048i	$0.594724\pi$
$762$	−16.9683	−0.614696
$763$	26.3595	0.954277
$764$	5.75740	0.208296
$765$	−7.06843	−0.255560
$766$	55.8613	2.01835
$767$	10.3811	0.374841
$768$	−4.34446	−0.156767
$769$	−26.8584	−0.968540	−0.484270	−	0.874919i	$-0.660915\pi$
$769$	−26.8584	−0.968540	−0.484270	+	0.874919i	$0.660915\pi$
$770$	−122.889	−4.42862
$771$	−10.9098	−0.392907
$772$	3.11202	0.112004
$773$	−15.3913	−0.553586	−0.276793	−	0.960930i	$-0.589272\pi$
$773$	−15.3913	−0.553586	−0.276793	+	0.960930i	$0.589272\pi$
$774$	−2.02094	−0.0726412
$775$	14.7114	0.528450
$776$	9.71875	0.348883
$777$	7.79646	0.279696
$778$	5.40572	0.193804
$779$	23.7381	0.850505
$780$	5.37561	0.192478
$781$	−23.2714	−0.832717
$782$	−9.05278	−0.323727
$783$	−3.43647	−0.122809
$784$	5.31366	0.189773
$785$	22.7336	0.811396
$786$	18.2499	0.650951
$787$	−3.13429	−0.111725	−0.0558626	−	0.998438i	$-0.517791\pi$
$787$	−3.13429	−0.111725	−0.0558626	+	0.998438i	$0.517791\pi$
$788$	−49.6247	−1.76781
$789$	13.9445	0.496437
$790$	−65.7453	−2.33911
$791$	2.27031	0.0807228
$792$	−12.2555	−0.435480
$793$	1.24744	0.0442979
$794$	0.594720	0.0211058
$795$	−17.1611	−0.608643
$796$	−1.36727	−0.0484617
$797$	26.3760	0.934286	0.467143	−	0.884182i	$-0.345283\pi$
$797$	26.3760	0.934286	0.467143	+	0.884182i	$0.345283\pi$
$798$	−9.02320	−0.319418
$799$	0.326970	0.0115674
$800$	−118.786	−4.19972
$801$	−1.64826	−0.0582383
$802$	−75.9364	−2.68141
$803$	17.9535	0.633566
$804$	11.5391	0.406951
$805$	76.1133	2.68264
$806$	−2.09092	−0.0736495
$807$	−4.10521	−0.144510
$808$	4.70206	0.165418
$809$	−28.5048	−1.00217	−0.501087	−	0.865397i	$-0.667066\pi$
$809$	−28.5048	−1.00217	−0.501087	+	0.865397i	$0.667066\pi$
$810$	62.4084	2.19281
$811$	−22.2678	−0.781929	−0.390964	−	0.920406i	$-0.627858\pi$
$811$	−22.2678	−0.781929	−0.390964	+	0.920406i	$0.627858\pi$
$812$	6.40244	0.224682
$813$	−4.77420	−0.167438
$814$	79.8299	2.79804
$815$	−33.1862	−1.16246
$816$	0.924937	0.0323793
$817$	−1.29615	−0.0453465
$818$	47.3157	1.65435
$819$	−6.30407	−0.220282
$820$	−68.0473	−2.37631
$821$	−12.4105	−0.433130	−0.216565	−	0.976268i	$-0.569485\pi$
$821$	−12.4105	−0.433130	−0.216565	+	0.976268i	$0.569485\pi$
$822$	−21.4545	−0.748312
$823$	8.72428	0.304109	0.152055	−	0.988372i	$-0.451411\pi$
$823$	8.72428	0.304109	0.152055	+	0.988372i	$0.451411\pi$
$824$	10.6240	0.370106
$825$	−43.1991	−1.50400
$826$	49.9509	1.73801
$827$	1.00784	0.0350461	0.0175231	−	0.999846i	$-0.494422\pi$
$827$	1.00784	0.0350461	0.0175231	+	0.999846i	$0.494422\pi$
$828$	48.4066	1.68225
$829$	−51.1646	−1.77702	−0.888510	−	0.458857i	$-0.848259\pi$
$829$	−51.1646	−1.77702	−0.888510	+	0.458857i	$0.848259\pi$
$830$	21.3435	0.740842
$831$	7.97589	0.276681
$832$	10.6474	0.369133
$833$	−0.990499	−0.0343187
$834$	−14.9321	−0.517058
$835$	66.3626	2.29657
$836$	−50.1255	−1.73363
$837$	2.92976	0.101267
$838$	−7.06783	−0.244154
$839$	−2.77793	−0.0959046	−0.0479523	−	0.998850i	$-0.515270\pi$
$839$	−2.77793	−0.0959046	−0.0479523	+	0.998850i	$0.515270\pi$
$840$	4.05601	0.139946
$841$	−27.6242	−0.952558
$842$	49.5087	1.70618
$843$	0.256117	0.00882113
$844$	2.82124	0.0971112
$845$	4.43975	0.152732
$846$	−3.22256	−0.110794
$847$	−50.8371	−1.74678
$848$	−23.6084	−0.810717
$849$	−1.22652	−0.0420940
$850$	17.8771	0.613178
$851$	−49.4439	−1.69491
$852$	4.89818	0.167809
$853$	−36.0880	−1.23563	−0.617815	−	0.786323i	$-0.711982\pi$
$853$	−36.0880	−1.23563	−0.617815	+	0.786323i	$0.711982\pi$
$854$	6.00230	0.205395
$855$	44.6804	1.52804
$856$	−0.375284	−0.0128269
$857$	35.5618	1.21477	0.607384	−	0.794408i	$-0.292219\pi$
$857$	35.5618	1.21477	0.607384	+	0.794408i	$0.292219\pi$
$858$	6.13985	0.209611
$859$	4.37889	0.149406	0.0747028	−	0.997206i	$-0.476199\pi$
$859$	4.37889	0.149406	0.0747028	+	0.997206i	$0.476199\pi$
$860$	3.71552	0.126698
$861$	−7.59054	−0.258685
$862$	42.9097	1.46151
$863$	24.1676	0.822674	0.411337	−	0.911483i	$-0.365062\pi$
$863$	24.1676	0.822674	0.411337	+	0.911483i	$0.365062\pi$
$864$	−23.6561	−0.804798
$865$	109.831	3.73437
$866$	−66.5780	−2.26241
$867$	8.50545	0.288860
$868$	−5.45840	−0.185270
$869$	−40.7404	−1.38202
$870$	5.55828	0.188443
$871$	9.53020	0.322919
$872$	−8.90822	−0.301670
$873$	−34.2338	−1.15864
$874$	57.2237	1.93562
$875$	−99.2208	−3.35427
$876$	−3.77887	−0.127676
$877$	6.43577	0.217321	0.108660	−	0.994079i	$-0.465344\pi$
$877$	6.43577	0.217321	0.108660	+	0.994079i	$0.465344\pi$
$878$	−12.4512	−0.420209
$879$	2.28218	0.0769761
$880$	−79.6268	−2.68422
$881$	−5.38389	−0.181388	−0.0906939	−	0.995879i	$-0.528908\pi$
$881$	−5.38389	−0.181388	−0.0906939	+	0.995879i	$0.528908\pi$
$882$	9.76218	0.328710
$883$	21.0551	0.708560	0.354280	−	0.935139i	$-0.384726\pi$
$883$	21.0551	0.708560	0.354280	+	0.935139i	$0.384726\pi$
$884$	−1.37851	−0.0463642
$885$	23.5271	0.790854
$886$	23.5887	0.792476
$887$	45.0494	1.51261	0.756306	−	0.654218i	$-0.227002\pi$
$887$	45.0494	1.51261	0.756306	+	0.654218i	$0.227002\pi$
$888$	−2.63482	−0.0884189
$889$	−36.5846	−1.22701
$890$	5.58549	0.187226
$891$	38.6726	1.29558
$892$	26.0647	0.872710
$893$	−2.06682	−0.0691634
$894$	5.00326	0.167334
$895$	88.1880	2.94780
$896$	14.0699	0.470042
$897$	−3.80281	−0.126972
$898$	41.5124	1.38529
$899$	−1.17295	−0.0391201
$900$	−95.5914	−3.18638
$901$	4.40076	0.146610
$902$	−77.7215	−2.58784
$903$	0.414459	0.0137923
$904$	−0.767253	−0.0255185
$905$	9.45426	0.314270
$906$	3.09107	0.102694
$907$	5.77631	0.191799	0.0958996	−	0.995391i	$-0.469427\pi$
$907$	5.77631	0.191799	0.0958996	+	0.995391i	$0.469427\pi$
$908$	−9.20098	−0.305345
$909$	−16.5628	−0.549353
$910$	21.3628	0.708169
$911$	−39.8214	−1.31934	−0.659671	−	0.751555i	$-0.729304\pi$
$911$	−39.8214	−1.31934	−0.659671	+	0.751555i	$0.729304\pi$
$912$	−5.84664	−0.193602
$913$	13.2259	0.437713
$914$	−59.5222	−1.96882
$915$	2.82711	0.0934613
$916$	−34.0765	−1.12592
$917$	39.3477	1.29938
$918$	3.56020	0.117504
$919$	37.9635	1.25230	0.626150	−	0.779703i	$-0.284630\pi$
$919$	37.9635	1.25230	0.626150	+	0.779703i	$0.284630\pi$
$920$	−25.7226	−0.848049
$921$	−10.1913	−0.335815
$922$	−60.4420	−1.99055
$923$	4.04545	0.133158
$924$	16.0282	0.527291
$925$	97.6397	3.21037
$926$	−43.9615	−1.44467
$927$	−37.4226	−1.22912
$928$	9.47090	0.310897
$929$	54.2112	1.77861	0.889305	−	0.457314i	$-0.151188\pi$
$929$	54.2112	1.77861	0.889305	+	0.457314i	$0.151188\pi$
$930$	−4.73871	−0.155389
$931$	6.26106	0.205198
$932$	−38.2211	−1.25197
$933$	−3.16074	−0.103478
$934$	−41.9566	−1.37286
$935$	14.8429	0.485416
$936$	2.13047	0.0696365
$937$	5.71619	0.186740	0.0933699	−	0.995631i	$-0.470236\pi$
$937$	5.71619	0.186740	0.0933699	+	0.995631i	$0.470236\pi$
$938$	45.8565	1.49727
$939$	10.1436	0.331025
$940$	5.92471	0.193243
$941$	−7.24462	−0.236168	−0.118084	−	0.993004i	$-0.537675\pi$
$941$	−7.24462	−0.236168	−0.118084	+	0.993004i	$0.537675\pi$
$942$	−5.46525	−0.178068
$943$	48.1380	1.56759
$944$	32.3660	1.05342
$945$	−29.9332	−0.973726
$946$	4.24375	0.137976
$947$	40.2621	1.30834	0.654171	−	0.756346i	$-0.273018\pi$
$947$	40.2621	1.30834	0.654171	+	0.756346i	$0.273018\pi$
$948$	8.57506	0.278505
$949$	−3.12100	−0.101312
$950$	−113.003	−3.66630
$951$	12.8516	0.416741
$952$	−1.04011	−0.0337103
$953$	8.44348	0.273511	0.136756	−	0.990605i	$-0.456332\pi$
$953$	8.44348	0.273511	0.136756	+	0.990605i	$0.456332\pi$
$954$	−43.3731	−1.40426
$955$	10.7766	0.348722
$956$	−29.2948	−0.947462
$957$	3.44430	0.111338
$958$	80.5404	2.60214
$959$	−46.2571	−1.49372
$960$	24.1305	0.778810
$961$	1.00000	0.0322581
$962$	−13.8774	−0.447427
$963$	1.32192	0.0425982
$964$	35.4820	1.14280
$965$	5.82501	0.187514
$966$	−18.2980	−0.588728
$967$	−39.3088	−1.26409	−0.632043	−	0.774933i	$-0.717784\pi$
$967$	−39.3088	−1.26409	−0.632043	+	0.774933i	$0.717784\pi$
$968$	17.1804	0.552200
$969$	1.08985	0.0350110
$970$	116.009	3.72482
$971$	−25.1181	−0.806078	−0.403039	−	0.915183i	$-0.632046\pi$
$971$	−25.1181	−0.806078	−0.403039	+	0.915183i	$0.632046\pi$
$972$	−28.9875	−0.929776
$973$	−32.1945	−1.03211
$974$	−42.1083	−1.34924
$975$	7.50963	0.240501
$976$	3.88923	0.124491
$977$	7.43073	0.237730	0.118865	−	0.992910i	$-0.462074\pi$
$977$	7.43073	0.237730	0.118865	+	0.992910i	$0.462074\pi$
$978$	7.97812	0.255112
$979$	3.46116	0.110619
$980$	−17.9479	−0.573324
$981$	31.3788	1.00185
$982$	−61.7220	−1.96963
$983$	29.0005	0.924972	0.462486	−	0.886627i	$-0.346958\pi$
$983$	29.0005	0.924972	0.462486	+	0.886627i	$0.346958\pi$
$984$	2.56523	0.0817766
$985$	−92.8865	−2.95961
$986$	−1.42535	−0.0453924
$987$	0.660890	0.0210364
$988$	8.71370	0.277220
$989$	−2.62843	−0.0835793
$990$	−146.289	−4.64938
$991$	42.8637	1.36161	0.680806	−	0.732464i	$-0.261630\pi$
$991$	42.8637	1.36161	0.680806	+	0.732464i	$0.261630\pi$
$992$	−8.07441	−0.256363
$993$	−2.94189	−0.0933582
$994$	19.4655	0.617407
$995$	−2.55923	−0.0811332
$996$	−2.78380	−0.0882079
$997$	−35.7909	−1.13351	−0.566755	−	0.823887i	$-0.691801\pi$
$997$	−35.7909	−1.13351	−0.566755	+	0.823887i	$0.691801\pi$
$998$	9.66939	0.306079
$999$	19.4449	0.615208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.c.1.6	✓	7
3.2	odd	2		3627.2.a.n.1.2		7
4.3	odd	2		6448.2.a.ba.1.5		7
13.12	even	2		5239.2.a.h.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.c.1.6	✓	7	1.1	even	1	trivial
3627.2.a.n.1.2		7	3.2	odd	2
5239.2.a.h.1.2		7	13.12	even	2
6448.2.a.ba.1.5		7	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09092 q^{2} -0.510463 q^{3} +2.37194 q^{4} +4.43975 q^{5} -1.06734 q^{6} -2.30124 q^{7} +0.777706 q^{8} -2.73943 q^{9} +O(q^{10})\)	\(q+2.09092 q^{2} -0.510463 q^{3} +2.37194 q^{4} +4.43975 q^{5} -1.06734 q^{6} -2.30124 q^{7} +0.777706 q^{8} -2.73943 q^{9} +9.28317 q^{10} +5.75249 q^{11} -1.21079 q^{12} -1.00000 q^{13} -4.81170 q^{14} -2.26633 q^{15} -3.11777 q^{16} +0.581171 q^{17} -5.72792 q^{18} -3.67365 q^{19} +10.5308 q^{20} +1.17470 q^{21} +12.0280 q^{22} -7.44973 q^{23} -0.396990 q^{24} +14.7114 q^{25} -2.09092 q^{26} +2.92976 q^{27} -5.45840 q^{28} -1.17295 q^{29} -4.73871 q^{30} +1.00000 q^{31} -8.07441 q^{32} -2.93644 q^{33} +1.21518 q^{34} -10.2169 q^{35} -6.49777 q^{36} +6.63700 q^{37} -7.68131 q^{38} +0.510463 q^{39} +3.45282 q^{40} -6.46171 q^{41} +2.45619 q^{42} +0.352822 q^{43} +13.6446 q^{44} -12.1624 q^{45} -15.5768 q^{46} +0.562606 q^{47} +1.59151 q^{48} -1.70431 q^{49} +30.7604 q^{50} -0.296666 q^{51} -2.37194 q^{52} +7.57222 q^{53} +6.12590 q^{54} +25.5397 q^{55} -1.78968 q^{56} +1.87526 q^{57} -2.45255 q^{58} -10.3811 q^{59} -5.37561 q^{60} -1.24744 q^{61} +2.09092 q^{62} +6.30407 q^{63} -10.6474 q^{64} -4.43975 q^{65} -6.13985 q^{66} -9.53020 q^{67} +1.37851 q^{68} +3.80281 q^{69} -21.3628 q^{70} -4.04545 q^{71} -2.13047 q^{72} +3.12100 q^{73} +13.8774 q^{74} -7.50963 q^{75} -8.71370 q^{76} -13.2378 q^{77} +1.06734 q^{78} -7.08221 q^{79} -13.8421 q^{80} +6.72275 q^{81} -13.5109 q^{82} +2.29916 q^{83} +2.78631 q^{84} +2.58026 q^{85} +0.737723 q^{86} +0.598748 q^{87} +4.47375 q^{88} +0.601680 q^{89} -25.4306 q^{90} +2.30124 q^{91} -17.6703 q^{92} -0.510463 q^{93} +1.17636 q^{94} -16.3101 q^{95} +4.12169 q^{96} +12.4967 q^{97} -3.56358 q^{98} -15.7585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 5 q^{3} + 8 q^{4} + 11 q^{5} + 6 q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 + 5 * q^3 + 8 * q^4 + 11 * q^5 + 6 * q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9	\( 7 q + 2 q^{2} + 5 q^{3} + 8 q^{4} + 11 q^{5} + 6 q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} + 8 q^{11} - 3 q^{12} - 7 q^{13} - 5 q^{14} + 2 q^{16} + 7 q^{17} - 9 q^{18} + q^{19} - 2 q^{21} + 6 q^{22} + 6 q^{23} + 5 q^{24} + 10 q^{25} - 2 q^{26} + 11 q^{27} - 11 q^{28} - 2 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} + 6 q^{33} - 4 q^{34} - q^{35} - 20 q^{36} + 28 q^{37} - 8 q^{38} - 5 q^{39} - 5 q^{40} + 3 q^{41} + 13 q^{42} - q^{43} + 12 q^{44} + 9 q^{45} - 37 q^{46} - q^{47} + 11 q^{48} - 19 q^{49} + 21 q^{50} - 30 q^{51} - 8 q^{52} + 29 q^{53} + 2 q^{54} + 19 q^{55} - 20 q^{56} + 11 q^{57} + 3 q^{58} + 3 q^{59} - 43 q^{60} + 5 q^{61} + 2 q^{62} + q^{63} - 29 q^{64} - 11 q^{65} - 29 q^{66} - 32 q^{67} + 38 q^{68} + 17 q^{69} - 23 q^{70} + 5 q^{71} - 17 q^{72} + q^{73} - 4 q^{74} - 7 q^{75} - 12 q^{76} - 5 q^{77} - 6 q^{78} - 15 q^{79} - 11 q^{80} + 3 q^{81} - 36 q^{82} + 17 q^{83} + 2 q^{84} - q^{85} - 23 q^{86} - 42 q^{87} - 15 q^{88} + 26 q^{89} - 40 q^{90} - 4 q^{91} - 24 q^{92} + 5 q^{93} + 18 q^{94} - 21 q^{95} - 4 q^{96} + 11 q^{97} + 6 q^{98} - 28 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 5 * q^3 + 8 * q^4 + 11 * q^5 + 6 * q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9 + 8 * q^11 - 3 * q^12 - 7 * q^13 - 5 * q^14 + 2 * q^16 + 7 * q^17 - 9 * q^18 + q^19 - 2 * q^21 + 6 * q^22 + 6 * q^23 + 5 * q^24 + 10 * q^25 - 2 * q^26 + 11 * q^27 - 11 * q^28 - 2 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 + 6 * q^33 - 4 * q^34 - q^35 - 20 * q^36 + 28 * q^37 - 8 * q^38 - 5 * q^39 - 5 * q^40 + 3 * q^41 + 13 * q^42 - q^43 + 12 * q^44 + 9 * q^45 - 37 * q^46 - q^47 + 11 * q^48 - 19 * q^49 + 21 * q^50 - 30 * q^51 - 8 * q^52 + 29 * q^53 + 2 * q^54 + 19 * q^55 - 20 * q^56 + 11 * q^57 + 3 * q^58 + 3 * q^59 - 43 * q^60 + 5 * q^61 + 2 * q^62 + q^63 - 29 * q^64 - 11 * q^65 - 29 * q^66 - 32 * q^67 + 38 * q^68 + 17 * q^69 - 23 * q^70 + 5 * q^71 - 17 * q^72 + q^73 - 4 * q^74 - 7 * q^75 - 12 * q^76 - 5 * q^77 - 6 * q^78 - 15 * q^79 - 11 * q^80 + 3 * q^81 - 36 * q^82 + 17 * q^83 + 2 * q^84 - q^85 - 23 * q^86 - 42 * q^87 - 15 * q^88 + 26 * q^89 - 40 * q^90 - 4 * q^91 - 24 * q^92 + 5 * q^93 + 18 * q^94 - 21 * q^95 - 4 * q^96 + 11 * q^97 + 6 * q^98 - 28 * q^99

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