LMFDB - Embedded newform 8007.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49549 q^{2} -1.00000 q^{3} +4.22749 q^{4} +2.28895 q^{5} +2.49549 q^{6} -3.97589 q^{7} -5.55870 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49549 q^{2} -1.00000 q^{3} +4.22749 q^{4} +2.28895 q^{5} +2.49549 q^{6} -3.97589 q^{7} -5.55870 q^{8} +1.00000 q^{9} -5.71206 q^{10} -2.09788 q^{11} -4.22749 q^{12} +4.13048 q^{13} +9.92181 q^{14} -2.28895 q^{15} +5.41671 q^{16} -1.00000 q^{17} -2.49549 q^{18} +0.596243 q^{19} +9.67652 q^{20} +3.97589 q^{21} +5.23524 q^{22} -0.899600 q^{23} +5.55870 q^{24} +0.239296 q^{25} -10.3076 q^{26} -1.00000 q^{27} -16.8080 q^{28} -4.90674 q^{29} +5.71206 q^{30} +4.24984 q^{31} -2.39997 q^{32} +2.09788 q^{33} +2.49549 q^{34} -9.10062 q^{35} +4.22749 q^{36} +7.90469 q^{37} -1.48792 q^{38} -4.13048 q^{39} -12.7236 q^{40} +2.12540 q^{41} -9.92181 q^{42} -1.92823 q^{43} -8.86876 q^{44} +2.28895 q^{45} +2.24495 q^{46} +2.28987 q^{47} -5.41671 q^{48} +8.80771 q^{49} -0.597161 q^{50} +1.00000 q^{51} +17.4616 q^{52} +9.86265 q^{53} +2.49549 q^{54} -4.80194 q^{55} +22.1008 q^{56} -0.596243 q^{57} +12.2448 q^{58} +9.79550 q^{59} -9.67652 q^{60} -11.6143 q^{61} -10.6055 q^{62} -3.97589 q^{63} -4.84429 q^{64} +9.45447 q^{65} -5.23524 q^{66} -16.3430 q^{67} -4.22749 q^{68} +0.899600 q^{69} +22.7105 q^{70} -11.7706 q^{71} -5.55870 q^{72} -0.392144 q^{73} -19.7261 q^{74} -0.239296 q^{75} +2.52061 q^{76} +8.34093 q^{77} +10.3076 q^{78} +3.46759 q^{79} +12.3986 q^{80} +1.00000 q^{81} -5.30393 q^{82} +2.58974 q^{83} +16.8080 q^{84} -2.28895 q^{85} +4.81188 q^{86} +4.90674 q^{87} +11.6615 q^{88} -11.6634 q^{89} -5.71206 q^{90} -16.4223 q^{91} -3.80305 q^{92} -4.24984 q^{93} -5.71436 q^{94} +1.36477 q^{95} +2.39997 q^{96} +14.0736 q^{97} -21.9796 q^{98} -2.09788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * 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 $

$2$	−2.49549	−1.76458	−0.882291	−	0.470705i	$-0.844000\pi$
$2$	−2.49549	−1.76458	−0.882291	+	0.470705i	$0.844000\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.22749	2.11375
$5$	2.28895	1.02365	0.511825	−	0.859090i	$-0.328970\pi$
$5$	2.28895	1.02365	0.511825	+	0.859090i	$0.328970\pi$
$6$	2.49549	1.01878
$7$	−3.97589	−1.50275	−0.751373	−	0.659878i	$-0.770608\pi$
$7$	−3.97589	−1.50275	−0.751373	+	0.659878i	$0.770608\pi$
$8$	−5.55870	−1.96530
$9$	1.00000	0.333333
$10$	−5.71206	−1.80631
$11$	−2.09788	−0.632534	−0.316267	−	0.948670i	$-0.602430\pi$
$11$	−2.09788	−0.632534	−0.316267	+	0.948670i	$0.602430\pi$
$12$	−4.22749	−1.22037
$13$	4.13048	1.14559	0.572795	−	0.819699i	$-0.305859\pi$
$13$	4.13048	1.14559	0.572795	+	0.819699i	$0.305859\pi$
$14$	9.92181	2.65172
$15$	−2.28895	−0.591005
$16$	5.41671	1.35418
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.49549	−0.588194
$19$	0.596243	0.136788	0.0683938	−	0.997658i	$-0.478213\pi$
$19$	0.596243	0.136788	0.0683938	+	0.997658i	$0.478213\pi$
$20$	9.67652	2.16374
$21$	3.97589	0.867610
$22$	5.23524	1.11616
$23$	−0.899600	−0.187580	−0.0937898	−	0.995592i	$-0.529898\pi$
$23$	−0.899600	−0.187580	−0.0937898	+	0.995592i	$0.529898\pi$
$24$	5.55870	1.13466
$25$	0.239296	0.0478592
$26$	−10.3076	−2.02149
$27$	−1.00000	−0.192450
$28$	−16.8080	−3.17642
$29$	−4.90674	−0.911159	−0.455580	−	0.890195i	$-0.650568\pi$
$29$	−4.90674	−0.911159	−0.455580	+	0.890195i	$0.650568\pi$
$30$	5.71206	1.04288
$31$	4.24984	0.763295	0.381647	−	0.924308i	$-0.375357\pi$
$31$	4.24984	0.763295	0.381647	+	0.924308i	$0.375357\pi$
$32$	−2.39997	−0.424259
$33$	2.09788	0.365194
$34$	2.49549	0.427974
$35$	−9.10062	−1.53829
$36$	4.22749	0.704582
$37$	7.90469	1.29952	0.649761	−	0.760138i	$-0.274869\pi$
$37$	7.90469	1.29952	0.649761	+	0.760138i	$0.274869\pi$
$38$	−1.48792	−0.241373
$39$	−4.13048	−0.661406
$40$	−12.7236	−2.01177
$41$	2.12540	0.331932	0.165966	−	0.986131i	$-0.446926\pi$
$41$	2.12540	0.331932	0.165966	+	0.986131i	$0.446926\pi$
$42$	−9.92181	−1.53097
$43$	−1.92823	−0.294052	−0.147026	−	0.989133i	$-0.546970\pi$
$43$	−1.92823	−0.294052	−0.147026	+	0.989133i	$0.546970\pi$
$44$	−8.86876	−1.33702
$45$	2.28895	0.341217
$46$	2.24495	0.330999
$47$	2.28987	0.334012	0.167006	−	0.985956i	$-0.446590\pi$
$47$	2.28987	0.334012	0.167006	+	0.985956i	$0.446590\pi$
$48$	−5.41671	−0.781834
$49$	8.80771	1.25824
$50$	−0.597161	−0.0844514
$51$	1.00000	0.140028
$52$	17.4616	2.42149
$53$	9.86265	1.35474	0.677369	−	0.735643i	$-0.263120\pi$
$53$	9.86265	1.35474	0.677369	+	0.735643i	$0.263120\pi$
$54$	2.49549	0.339594
$55$	−4.80194	−0.647493
$56$	22.1008	2.95334
$57$	−0.596243	−0.0789743
$58$	12.2448	1.60781
$59$	9.79550	1.27527	0.637633	−	0.770340i	$-0.279914\pi$
$59$	9.79550	1.27527	0.637633	+	0.770340i	$0.279914\pi$
$60$	−9.67652	−1.24923
$61$	−11.6143	−1.48706	−0.743530	−	0.668702i	$-0.766850\pi$
$61$	−11.6143	−1.48706	−0.743530	+	0.668702i	$0.766850\pi$
$62$	−10.6055	−1.34690
$63$	−3.97589	−0.500915
$64$	−4.84429	−0.605537
$65$	9.45447	1.17268
$66$	−5.23524	−0.644414
$67$	−16.3430	−1.99661	−0.998305	−	0.0581999i	$-0.981464\pi$
$67$	−16.3430	−1.99661	−0.998305	+	0.0581999i	$0.981464\pi$
$68$	−4.22749	−0.512659
$69$	0.899600	0.108299
$70$	22.7105	2.71443
$71$	−11.7706	−1.39691	−0.698455	−	0.715654i	$-0.746129\pi$
$71$	−11.7706	−1.39691	−0.698455	+	0.715654i	$0.746129\pi$
$72$	−5.55870	−0.655098
$73$	−0.392144	−0.0458970	−0.0229485	−	0.999737i	$-0.507305\pi$
$73$	−0.392144	−0.0458970	−0.0229485	+	0.999737i	$0.507305\pi$
$74$	−19.7261	−2.29311
$75$	−0.239296	−0.0276315
$76$	2.52061	0.289134
$77$	8.34093	0.950537
$78$	10.3076	1.16710
$79$	3.46759	0.390135	0.195067	−	0.980790i	$-0.437507\pi$
$79$	3.46759	0.390135	0.195067	+	0.980790i	$0.437507\pi$
$80$	12.3986	1.38620
$81$	1.00000	0.111111
$82$	−5.30393	−0.585721
$83$	2.58974	0.284261	0.142131	−	0.989848i	$-0.454605\pi$
$83$	2.58974	0.284261	0.142131	+	0.989848i	$0.454605\pi$
$84$	16.8080	1.83391
$85$	−2.28895	−0.248272
$86$	4.81188	0.518878
$87$	4.90674	0.526058
$88$	11.6615	1.24312
$89$	−11.6634	−1.23632	−0.618160	−	0.786052i	$-0.712122\pi$
$89$	−11.6634	−1.23632	−0.618160	+	0.786052i	$0.712122\pi$
$90$	−5.71206	−0.602104
$91$	−16.4223	−1.72153
$92$	−3.80305	−0.396496
$93$	−4.24984	−0.440688
$94$	−5.71436	−0.589392
$95$	1.36477	0.140023
$96$	2.39997	0.244946
$97$	14.0736	1.42896	0.714479	−	0.699657i	$-0.246664\pi$
$97$	14.0736	1.42896	0.714479	+	0.699657i	$0.246664\pi$
$98$	−21.9796	−2.22027
$99$	−2.09788	−0.210845
$100$	1.01162	0.101162
$101$	−13.9363	−1.38671	−0.693354	−	0.720597i	$-0.743868\pi$
$101$	−13.9363	−1.38671	−0.693354	+	0.720597i	$0.743868\pi$
$102$	−2.49549	−0.247091
$103$	9.21081	0.907568	0.453784	−	0.891112i	$-0.350074\pi$
$103$	9.21081	0.907568	0.453784	+	0.891112i	$0.350074\pi$
$104$	−22.9601	−2.25142
$105$	9.10062	0.888129
$106$	−24.6122	−2.39055
$107$	−8.16871	−0.789699	−0.394849	−	0.918746i	$-0.629203\pi$
$107$	−8.16871	−0.789699	−0.394849	+	0.918746i	$0.629203\pi$
$108$	−4.22749	−0.406791
$109$	15.5969	1.49391	0.746957	−	0.664873i	$-0.231514\pi$
$109$	15.5969	1.49391	0.746957	+	0.664873i	$0.231514\pi$
$110$	11.9832	1.14255
$111$	−7.90469	−0.750280
$112$	−21.5362	−2.03498
$113$	14.9837	1.40955	0.704773	−	0.709433i	$-0.251049\pi$
$113$	14.9837	1.40955	0.704773	+	0.709433i	$0.251049\pi$
$114$	1.48792	0.139357
$115$	−2.05914	−0.192016
$116$	−20.7432	−1.92596
$117$	4.13048	0.381863
$118$	−24.4446	−2.25031
$119$	3.97589	0.364469
$120$	12.7236	1.16150
$121$	−6.59891	−0.599901
$122$	28.9835	2.62404
$123$	−2.12540	−0.191641
$124$	17.9662	1.61341
$125$	−10.8970	−0.974659
$126$	9.92181	0.883905
$127$	−2.35845	−0.209278	−0.104639	−	0.994510i	$-0.533369\pi$
$127$	−2.35845	−0.209278	−0.104639	+	0.994510i	$0.533369\pi$
$128$	16.8889	1.49278
$129$	1.92823	0.169771
$130$	−23.5936	−2.06929
$131$	−22.1737	−1.93732	−0.968661	−	0.248388i	$-0.920099\pi$
$131$	−22.1737	−1.93732	−0.968661	+	0.248388i	$0.920099\pi$
$132$	8.86876	0.771926
$133$	−2.37060	−0.205557
$134$	40.7838	3.52318
$135$	−2.28895	−0.197002
$136$	5.55870	0.476654
$137$	0.226761	0.0193735	0.00968676	−	0.999953i	$-0.496917\pi$
$137$	0.226761	0.0193735	0.00968676	+	0.999953i	$0.496917\pi$
$138$	−2.24495	−0.191103
$139$	−8.38054	−0.710828	−0.355414	−	0.934709i	$-0.615660\pi$
$139$	−8.38054	−0.710828	−0.355414	+	0.934709i	$0.615660\pi$
$140$	−38.4728	−3.25154
$141$	−2.28987	−0.192842
$142$	29.3734	2.46496
$143$	−8.66524	−0.724624
$144$	5.41671	0.451392
$145$	−11.2313	−0.932708
$146$	0.978592	0.0809889
$147$	−8.80771	−0.726447
$148$	33.4170	2.74686
$149$	−3.47861	−0.284979	−0.142489	−	0.989796i	$-0.545511\pi$
$149$	−3.47861	−0.284979	−0.142489	+	0.989796i	$0.545511\pi$
$150$	0.597161	0.0487580
$151$	11.2622	0.916506	0.458253	−	0.888822i	$-0.348475\pi$
$151$	11.2622	0.916506	0.458253	+	0.888822i	$0.348475\pi$
$152$	−3.31433	−0.268828
$153$	−1.00000	−0.0808452
$154$	−20.8147	−1.67730
$155$	9.72768	0.781346
$156$	−17.4616	−1.39805
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−8.65336	−0.688424
$159$	−9.86265	−0.782159
$160$	−5.49342	−0.434293
$161$	3.57671	0.281884
$162$	−2.49549	−0.196065
$163$	19.3240	1.51358	0.756788	−	0.653661i	$-0.226768\pi$
$163$	19.3240	1.51358	0.756788	+	0.653661i	$0.226768\pi$
$164$	8.98512	0.701620
$165$	4.80194	0.373830
$166$	−6.46269	−0.501602
$167$	7.97629	0.617224	0.308612	−	0.951188i	$-0.400136\pi$
$167$	7.97629	0.617224	0.308612	+	0.951188i	$0.400136\pi$
$168$	−22.1008	−1.70511
$169$	4.06087	0.312375
$170$	5.71206	0.438095
$171$	0.596243	0.0455958
$172$	−8.15156	−0.621551
$173$	11.7731	0.895093	0.447547	−	0.894261i	$-0.352298\pi$
$173$	11.7731	0.895093	0.447547	+	0.894261i	$0.352298\pi$
$174$	−12.2448	−0.928272
$175$	−0.951414	−0.0719201
$176$	−11.3636	−0.856563
$177$	−9.79550	−0.736275
$178$	29.1060	2.18159
$179$	−13.9082	−1.03954	−0.519772	−	0.854305i	$-0.673983\pi$
$179$	−13.9082	−1.03954	−0.519772	+	0.854305i	$0.673983\pi$
$180$	9.67652	0.721245
$181$	15.1208	1.12392	0.561960	−	0.827164i	$-0.310047\pi$
$181$	15.1208	1.12392	0.561960	+	0.827164i	$0.310047\pi$
$182$	40.9819	3.03778
$183$	11.6143	0.858555
$184$	5.00060	0.368649
$185$	18.0934	1.33026
$186$	10.6055	0.777630
$187$	2.09788	0.153412
$188$	9.68042	0.706017
$189$	3.97589	0.289203
$190$	−3.40578	−0.247081
$191$	−8.25236	−0.597120	−0.298560	−	0.954391i	$-0.596506\pi$
$191$	−8.25236	−0.597120	−0.298560	+	0.954391i	$0.596506\pi$
$192$	4.84429	0.349607
$193$	2.14887	0.154679	0.0773395	−	0.997005i	$-0.475357\pi$
$193$	2.14887	0.154679	0.0773395	+	0.997005i	$0.475357\pi$
$194$	−35.1206	−2.52151
$195$	−9.45447	−0.677048
$196$	37.2345	2.65961
$197$	−1.78795	−0.127386	−0.0636932	−	0.997970i	$-0.520288\pi$
$197$	−1.78795	−0.127386	−0.0636932	+	0.997970i	$0.520288\pi$
$198$	5.23524	0.372052
$199$	13.7859	0.977253	0.488627	−	0.872493i	$-0.337498\pi$
$199$	13.7859	0.977253	0.488627	+	0.872493i	$0.337498\pi$
$200$	−1.33017	−0.0940574
$201$	16.3430	1.15274
$202$	34.7778	2.44696
$203$	19.5087	1.36924
$204$	4.22749	0.295984
$205$	4.86494	0.339782
$206$	−22.9855	−1.60148
$207$	−0.899600	−0.0625265
$208$	22.3736	1.55133
$209$	−1.25084	−0.0865227
$210$	−22.7105	−1.56718
$211$	7.90745	0.544371	0.272185	−	0.962245i	$-0.412254\pi$
$211$	7.90745	0.544371	0.272185	+	0.962245i	$0.412254\pi$
$212$	41.6943	2.86357
$213$	11.7706	0.806507
$214$	20.3850	1.39349
$215$	−4.41361	−0.301006
$216$	5.55870	0.378221
$217$	−16.8969	−1.14704
$218$	−38.9220	−2.63613
$219$	0.392144	0.0264986
$220$	−20.3002	−1.36864
$221$	−4.13048	−0.277846
$222$	19.7261	1.32393
$223$	9.37569	0.627843	0.313921	−	0.949449i	$-0.398357\pi$
$223$	9.37569	0.627843	0.313921	+	0.949449i	$0.398357\pi$
$224$	9.54203	0.637554
$225$	0.239296	0.0159531
$226$	−37.3917	−2.48726
$227$	−15.3381	−1.01803	−0.509013	−	0.860759i	$-0.669989\pi$
$227$	−15.3381	−1.01803	−0.509013	+	0.860759i	$0.669989\pi$
$228$	−2.52061	−0.166932
$229$	8.45160	0.558497	0.279249	−	0.960219i	$-0.409915\pi$
$229$	8.45160	0.558497	0.279249	+	0.960219i	$0.409915\pi$
$230$	5.13857	0.338827
$231$	−8.34093	−0.548793
$232$	27.2751	1.79070
$233$	20.5443	1.34590	0.672950	−	0.739688i	$-0.265027\pi$
$233$	20.5443	1.34590	0.672950	+	0.739688i	$0.265027\pi$
$234$	−10.3076	−0.673828
$235$	5.24140	0.341912
$236$	41.4104	2.69559
$237$	−3.46759	−0.225244
$238$	−9.92181	−0.643136
$239$	−5.66979	−0.366748	−0.183374	−	0.983043i	$-0.558702\pi$
$239$	−5.66979	−0.366748	−0.183374	+	0.983043i	$0.558702\pi$
$240$	−12.3986	−0.800325
$241$	26.3181	1.69530	0.847648	−	0.530559i	$-0.178018\pi$
$241$	26.3181	1.69530	0.847648	+	0.530559i	$0.178018\pi$
$242$	16.4675	1.05857
$243$	−1.00000	−0.0641500
$244$	−49.0994	−3.14327
$245$	20.1604	1.28800
$246$	5.30393	0.338166
$247$	2.46277	0.156702
$248$	−23.6236	−1.50010
$249$	−2.58974	−0.164118
$250$	27.1934	1.71986
$251$	−15.9749	−1.00833	−0.504163	−	0.863608i	$-0.668199\pi$
$251$	−15.9749	−1.00833	−0.504163	+	0.863608i	$0.668199\pi$
$252$	−16.8080	−1.05881
$253$	1.88725	0.118650
$254$	5.88549	0.369288
$255$	2.28895	0.143340
$256$	−32.4575	−2.02859
$257$	1.22344	0.0763158	0.0381579	−	0.999272i	$-0.487851\pi$
$257$	1.22344	0.0763158	0.0381579	+	0.999272i	$0.487851\pi$
$258$	−4.81188	−0.299574
$259$	−31.4282	−1.95285
$260$	39.9687	2.47875
$261$	−4.90674	−0.303720
$262$	55.3342	3.41856
$263$	1.42930	0.0881345	0.0440672	−	0.999029i	$-0.485968\pi$
$263$	1.42930	0.0881345	0.0440672	+	0.999029i	$0.485968\pi$
$264$	−11.6615	−0.717713
$265$	22.5751	1.38678
$266$	5.91581	0.362722
$267$	11.6634	0.713790
$268$	−69.0897	−4.22033
$269$	−1.18644	−0.0723386	−0.0361693	−	0.999346i	$-0.511516\pi$
$269$	−1.18644	−0.0723386	−0.0361693	+	0.999346i	$0.511516\pi$
$270$	5.71206	0.347625
$271$	9.17310	0.557226	0.278613	−	0.960403i	$-0.410125\pi$
$271$	9.17310	0.557226	0.278613	+	0.960403i	$0.410125\pi$
$272$	−5.41671	−0.328436
$273$	16.4223	0.993925
$274$	−0.565881	−0.0341861
$275$	−0.502013	−0.0302725
$276$	3.80305	0.228917
$277$	17.7208	1.06474	0.532371	−	0.846511i	$-0.321301\pi$
$277$	17.7208	1.06474	0.532371	+	0.846511i	$0.321301\pi$
$278$	20.9136	1.25431
$279$	4.24984	0.254432
$280$	50.5876	3.02319
$281$	−21.3320	−1.27256	−0.636281	−	0.771458i	$-0.719528\pi$
$281$	−21.3320	−1.27256	−0.636281	+	0.771458i	$0.719528\pi$
$282$	5.71436	0.340285
$283$	−9.29149	−0.552322	−0.276161	−	0.961111i	$-0.589062\pi$
$283$	−9.29149	−0.552322	−0.276161	+	0.961111i	$0.589062\pi$
$284$	−49.7600	−2.95271
$285$	−1.36477	−0.0808421
$286$	21.6241	1.27866
$287$	−8.45037	−0.498810
$288$	−2.39997	−0.141420
$289$	1.00000	0.0588235
$290$	28.0276	1.64584
$291$	−14.0736	−0.825009
$292$	−1.65778	−0.0970145
$293$	−10.1040	−0.590283	−0.295142	−	0.955454i	$-0.595367\pi$
$293$	−10.1040	−0.590283	−0.295142	+	0.955454i	$0.595367\pi$
$294$	21.9796	1.28188
$295$	22.4214	1.30543
$296$	−43.9398	−2.55395
$297$	2.09788	0.121731
$298$	8.68084	0.502868
$299$	−3.71578	−0.214889
$300$	−1.01162	−0.0584060
$301$	7.66642	0.441885
$302$	−28.1048	−1.61725
$303$	13.9363	0.800617
$304$	3.22967	0.185235
$305$	−26.5846	−1.52223
$306$	2.49549	0.142658
$307$	−21.0143	−1.19935	−0.599675	−	0.800244i	$-0.704703\pi$
$307$	−21.0143	−1.19935	−0.599675	+	0.800244i	$0.704703\pi$
$308$	35.2612	2.00919
$309$	−9.21081	−0.523984
$310$	−24.2754	−1.37875
$311$	8.34780	0.473360	0.236680	−	0.971588i	$-0.423941\pi$
$311$	8.34780	0.473360	0.236680	+	0.971588i	$0.423941\pi$
$312$	22.9601	1.29986
$313$	−10.6184	−0.600188	−0.300094	−	0.953910i	$-0.597018\pi$
$313$	−10.6184	−0.600188	−0.300094	+	0.953910i	$0.597018\pi$
$314$	−2.49549	−0.140829
$315$	−9.10062	−0.512762
$316$	14.6592	0.824646
$317$	3.76018	0.211193	0.105597	−	0.994409i	$-0.466325\pi$
$317$	3.76018	0.211193	0.105597	+	0.994409i	$0.466325\pi$
$318$	24.6122	1.38018
$319$	10.2937	0.576339
$320$	−11.0884	−0.619858
$321$	8.16871	0.455933
$322$	−8.92566	−0.497408
$323$	−0.596243	−0.0331758
$324$	4.22749	0.234861
$325$	0.988407	0.0548269
$326$	−48.2230	−2.67083
$327$	−15.5969	−0.862511
$328$	−11.8145	−0.652345
$329$	−9.10428	−0.501935
$330$	−11.9832	−0.659654
$331$	21.3573	1.17390	0.586950	−	0.809623i	$-0.300328\pi$
$331$	21.3573	1.17390	0.586950	+	0.809623i	$0.300328\pi$
$332$	10.9481	0.600856
$333$	7.90469	0.433174
$334$	−19.9048	−1.08914
$335$	−37.4082	−2.04383
$336$	21.5362	1.17490
$337$	0.693705	0.0377885	0.0188943	−	0.999821i	$-0.493985\pi$
$337$	0.693705	0.0377885	0.0188943	+	0.999821i	$0.493985\pi$
$338$	−10.1339	−0.551211
$339$	−14.9837	−0.813802
$340$	−9.67652	−0.524783
$341$	−8.91565	−0.482810
$342$	−1.48792	−0.0804576
$343$	−7.18725	−0.388075
$344$	10.7184	0.577899
$345$	2.05914	0.110860
$346$	−29.3797	−1.57946
$347$	4.23048	0.227104	0.113552	−	0.993532i	$-0.463777\pi$
$347$	4.23048	0.227104	0.113552	+	0.993532i	$0.463777\pi$
$348$	20.7432	1.11195
$349$	−11.3269	−0.606315	−0.303158	−	0.952940i	$-0.598041\pi$
$349$	−11.3269	−0.606315	−0.303158	+	0.952940i	$0.598041\pi$
$350$	2.37425	0.126909
$351$	−4.13048	−0.220469
$352$	5.03485	0.268358
$353$	10.6126	0.564854	0.282427	−	0.959289i	$-0.408860\pi$
$353$	10.6126	0.564854	0.282427	+	0.959289i	$0.408860\pi$
$354$	24.4446	1.29922
$355$	−26.9423	−1.42995
$356$	−49.3070	−2.61327
$357$	−3.97589	−0.210426
$358$	34.7077	1.83436
$359$	−32.7552	−1.72875	−0.864377	−	0.502844i	$-0.832287\pi$
$359$	−32.7552	−1.72875	−0.864377	+	0.502844i	$0.832287\pi$
$360$	−12.7236	−0.670592
$361$	−18.6445	−0.981289
$362$	−37.7339	−1.98325
$363$	6.59891	0.346353
$364$	−69.4253	−3.63888
$365$	−0.897598	−0.0469824
$366$	−28.9835	−1.51499
$367$	−16.5337	−0.863051	−0.431525	−	0.902101i	$-0.642024\pi$
$367$	−16.5337	−0.863051	−0.431525	+	0.902101i	$0.642024\pi$
$368$	−4.87287	−0.254016
$369$	2.12540	0.110644
$370$	−45.1521	−2.34735
$371$	−39.2128	−2.03583
$372$	−17.9662	−0.931503
$373$	13.7181	0.710298	0.355149	−	0.934810i	$-0.384430\pi$
$373$	13.7181	0.710298	0.355149	+	0.934810i	$0.384430\pi$
$374$	−5.23524	−0.270708
$375$	10.8970	0.562720
$376$	−12.7287	−0.656433
$377$	−20.2672	−1.04381
$378$	−9.92181	−0.510323
$379$	20.5527	1.05572	0.527862	−	0.849330i	$-0.322994\pi$
$379$	20.5527	1.05572	0.527862	+	0.849330i	$0.322994\pi$
$380$	5.76956	0.295972
$381$	2.35845	0.120827
$382$	20.5937	1.05367
$383$	10.2040	0.521401	0.260701	−	0.965420i	$-0.416046\pi$
$383$	10.2040	0.521401	0.260701	+	0.965420i	$0.416046\pi$
$384$	−16.8889	−0.861856
$385$	19.0920	0.973017
$386$	−5.36249	−0.272944
$387$	−1.92823	−0.0980172
$388$	59.4961	3.02045
$389$	−6.73322	−0.341388	−0.170694	−	0.985324i	$-0.554601\pi$
$389$	−6.73322	−0.341388	−0.170694	+	0.985324i	$0.554601\pi$
$390$	23.5936	1.19471
$391$	0.899600	0.0454947
$392$	−48.9594	−2.47282
$393$	22.1737	1.11851
$394$	4.46183	0.224784
$395$	7.93715	0.399361
$396$	−8.86876	−0.445672
$397$	−11.3217	−0.568221	−0.284111	−	0.958791i	$-0.591698\pi$
$397$	−11.3217	−0.568221	−0.284111	+	0.958791i	$0.591698\pi$
$398$	−34.4025	−1.72444
$399$	2.37060	0.118678
$400$	1.29620	0.0648098
$401$	−25.6960	−1.28320	−0.641599	−	0.767040i	$-0.721729\pi$
$401$	−25.6960	−1.28320	−0.641599	+	0.767040i	$0.721729\pi$
$402$	−40.7838	−2.03411
$403$	17.5539	0.874422
$404$	−58.9154	−2.93115
$405$	2.28895	0.113739
$406$	−48.6838	−2.41614
$407$	−16.5831	−0.821992
$408$	−5.55870	−0.275196
$409$	7.20371	0.356200	0.178100	−	0.984012i	$-0.443005\pi$
$409$	7.20371	0.356200	0.178100	+	0.984012i	$0.443005\pi$
$410$	−12.1404	−0.599573
$411$	−0.226761	−0.0111853
$412$	38.9386	1.91837
$413$	−38.9458	−1.91640
$414$	2.24495	0.110333
$415$	5.92780	0.290984
$416$	−9.91304	−0.486027
$417$	8.38054	0.410397
$418$	3.12148	0.152676
$419$	14.6594	0.716156	0.358078	−	0.933692i	$-0.383432\pi$
$419$	14.6594	0.716156	0.358078	+	0.933692i	$0.383432\pi$
$420$	38.4728	1.87728
$421$	28.3421	1.38131	0.690655	−	0.723185i	$-0.257322\pi$
$421$	28.3421	1.38131	0.690655	+	0.723185i	$0.257322\pi$
$422$	−19.7330	−0.960587
$423$	2.28987	0.111337
$424$	−54.8235	−2.66246
$425$	−0.239296	−0.0116076
$426$	−29.3734	−1.42315
$427$	46.1773	2.23467
$428$	−34.5332	−1.66922
$429$	8.66524	0.418362
$430$	11.0142	0.531150
$431$	17.6699	0.851131	0.425566	−	0.904928i	$-0.360075\pi$
$431$	17.6699	0.851131	0.425566	+	0.904928i	$0.360075\pi$
$432$	−5.41671	−0.260611
$433$	11.9186	0.572771	0.286385	−	0.958115i	$-0.407546\pi$
$433$	11.9186	0.572771	0.286385	+	0.958115i	$0.407546\pi$
$434$	42.1662	2.02404
$435$	11.2313	0.538499
$436$	65.9358	3.15775
$437$	−0.536380	−0.0256585
$438$	−0.978592	−0.0467590
$439$	39.7031	1.89492	0.947462	−	0.319869i	$-0.103639\pi$
$439$	39.7031	1.89492	0.947462	+	0.319869i	$0.103639\pi$
$440$	26.6925	1.27252
$441$	8.80771	0.419415
$442$	10.3076	0.490282
$443$	6.45246	0.306566	0.153283	−	0.988182i	$-0.451015\pi$
$443$	6.45246	0.306566	0.153283	+	0.988182i	$0.451015\pi$
$444$	−33.4170	−1.58590
$445$	−26.6970	−1.26556
$446$	−23.3970	−1.10788
$447$	3.47861	0.164532
$448$	19.2604	0.909968
$449$	24.8339	1.17199	0.585993	−	0.810316i	$-0.300705\pi$
$449$	24.8339	1.17199	0.585993	+	0.810316i	$0.300705\pi$
$450$	−0.597161	−0.0281505
$451$	−4.45883	−0.209958
$452$	63.3434	2.97942
$453$	−11.2622	−0.529145
$454$	38.2761	1.79639
$455$	−37.5899	−1.76224
$456$	3.31433	0.155208
$457$	−25.8728	−1.21028	−0.605139	−	0.796120i	$-0.706882\pi$
$457$	−25.8728	−1.21028	−0.605139	+	0.796120i	$0.706882\pi$
$458$	−21.0909	−0.985514
$459$	1.00000	0.0466760
$460$	−8.70500	−0.405873
$461$	6.11593	0.284847	0.142424	−	0.989806i	$-0.454510\pi$
$461$	6.11593	0.284847	0.142424	+	0.989806i	$0.454510\pi$
$462$	20.8147	0.968390
$463$	−31.2996	−1.45462	−0.727308	−	0.686312i	$-0.759229\pi$
$463$	−31.2996	−1.45462	−0.727308	+	0.686312i	$0.759229\pi$
$464$	−26.5784	−1.23387
$465$	−9.72768	−0.451111
$466$	−51.2681	−2.37495
$467$	−27.0814	−1.25318	−0.626588	−	0.779351i	$-0.715549\pi$
$467$	−27.0814	−1.25318	−0.626588	+	0.779351i	$0.715549\pi$
$468$	17.4616	0.807162
$469$	64.9778	3.00040
$470$	−13.0799	−0.603331
$471$	−1.00000	−0.0460776
$472$	−54.4502	−2.50627
$473$	4.04518	0.185998
$474$	8.65336	0.397462
$475$	0.142678	0.00654654
$476$	16.8080	0.770396
$477$	9.86265	0.451580
$478$	14.1489	0.647157
$479$	−17.9859	−0.821798	−0.410899	−	0.911681i	$-0.634785\pi$
$479$	−17.9859	−0.821798	−0.410899	+	0.911681i	$0.634785\pi$
$480$	5.49342	0.250739
$481$	32.6502	1.48872
$482$	−65.6766	−2.99149
$483$	−3.57671	−0.162746
$484$	−27.8968	−1.26804
$485$	32.2138	1.46275
$486$	2.49549	0.113198
$487$	−18.4562	−0.836329	−0.418164	−	0.908371i	$-0.637326\pi$
$487$	−18.4562	−0.836329	−0.418164	+	0.908371i	$0.637326\pi$
$488$	64.5604	2.92251
$489$	−19.3240	−0.873863
$490$	−50.3102	−2.27278
$491$	22.9380	1.03518	0.517590	−	0.855629i	$-0.326829\pi$
$491$	22.9380	1.03518	0.517590	+	0.855629i	$0.326829\pi$
$492$	−8.98512	−0.405081
$493$	4.90674	0.220989
$494$	−6.14583	−0.276514
$495$	−4.80194	−0.215831
$496$	23.0202	1.03364
$497$	46.7985	2.09920
$498$	6.46269	0.289600
$499$	14.3853	0.643975	0.321988	−	0.946744i	$-0.395649\pi$
$499$	14.3853	0.643975	0.321988	+	0.946744i	$0.395649\pi$
$500$	−46.0671	−2.06018
$501$	−7.97629	−0.356354
$502$	39.8653	1.77927
$503$	24.4206	1.08886	0.544430	−	0.838806i	$-0.316746\pi$
$503$	24.4206	1.08886	0.544430	+	0.838806i	$0.316746\pi$
$504$	22.1008	0.984446
$505$	−31.8994	−1.41950
$506$	−4.70962	−0.209368
$507$	−4.06087	−0.180350
$508$	−9.97031	−0.442361
$509$	1.86289	0.0825710	0.0412855	−	0.999147i	$-0.486855\pi$
$509$	1.86289	0.0825710	0.0412855	+	0.999147i	$0.486855\pi$
$510$	−5.71206	−0.252934
$511$	1.55912	0.0689714
$512$	47.2197	2.08684
$513$	−0.596243	−0.0263248
$514$	−3.05308	−0.134665
$515$	21.0831	0.929032
$516$	8.15156	0.358853
$517$	−4.80387	−0.211274
$518$	78.4289	3.44597
$519$	−11.7731	−0.516782
$520$	−52.5545	−2.30467
$521$	−21.8144	−0.955708	−0.477854	−	0.878439i	$-0.658585\pi$
$521$	−21.8144	−0.955708	−0.477854	+	0.878439i	$0.658585\pi$
$522$	12.2448	0.535938
$523$	21.3018	0.931462	0.465731	−	0.884926i	$-0.345791\pi$
$523$	21.3018	0.931462	0.465731	+	0.884926i	$0.345791\pi$
$524$	−93.7390	−4.09501
$525$	0.951414	0.0415231
$526$	−3.56681	−0.155520
$527$	−4.24984	−0.185126
$528$	11.3636	0.494537
$529$	−22.1907	−0.964814
$530$	−56.3361	−2.44708
$531$	9.79550	0.425088
$532$	−10.0217	−0.434495
$533$	8.77894	0.380258
$534$	−29.1060	−1.25954
$535$	−18.6978	−0.808375
$536$	90.8455	3.92393
$537$	13.9082	0.600181
$538$	2.96076	0.127647
$539$	−18.4775	−0.795882
$540$	−9.67652	−0.416411
$541$	−22.0891	−0.949683	−0.474842	−	0.880071i	$-0.657495\pi$
$541$	−22.0891	−0.949683	−0.474842	+	0.880071i	$0.657495\pi$
$542$	−22.8914	−0.983271
$543$	−15.1208	−0.648896
$544$	2.39997	0.102898
$545$	35.7006	1.52924
$546$	−40.9819	−1.75386
$547$	22.4546	0.960090	0.480045	−	0.877244i	$-0.340620\pi$
$547$	22.4546	0.960090	0.480045	+	0.877244i	$0.340620\pi$
$548$	0.958631	0.0409507
$549$	−11.6143	−0.495687
$550$	1.25277	0.0534183
$551$	−2.92561	−0.124635
$552$	−5.00060	−0.212840
$553$	−13.7868	−0.586273
$554$	−44.2223	−1.87882
$555$	−18.0934	−0.768024
$556$	−35.4287	−1.50251
$557$	−27.8557	−1.18028	−0.590142	−	0.807300i	$-0.700928\pi$
$557$	−27.8557	−1.18028	−0.590142	+	0.807300i	$0.700928\pi$
$558$	−10.6055	−0.448965
$559$	−7.96450	−0.336863
$560$	−49.2954	−2.08311
$561$	−2.09788	−0.0885724
$562$	53.2339	2.24554
$563$	−40.7299	−1.71656	−0.858280	−	0.513182i	$-0.828466\pi$
$563$	−40.7299	−1.71656	−0.858280	+	0.513182i	$0.828466\pi$
$564$	−9.68042	−0.407619
$565$	34.2969	1.44288
$566$	23.1869	0.974616
$567$	−3.97589	−0.166972
$568$	65.4291	2.74534
$569$	39.2807	1.64673	0.823366	−	0.567510i	$-0.192093\pi$
$569$	39.2807	1.64673	0.823366	+	0.567510i	$0.192093\pi$
$570$	3.40578	0.142652
$571$	−22.7897	−0.953718	−0.476859	−	0.878980i	$-0.658225\pi$
$571$	−22.7897	−0.953718	−0.476859	+	0.878980i	$0.658225\pi$
$572$	−36.6322	−1.53167
$573$	8.25236	0.344747
$574$	21.0879	0.880190
$575$	−0.215270	−0.00897740
$576$	−4.84429	−0.201846
$577$	24.7742	1.03136	0.515682	−	0.856780i	$-0.327539\pi$
$577$	24.7742	1.03136	0.515682	+	0.856780i	$0.327539\pi$
$578$	−2.49549	−0.103799
$579$	−2.14887	−0.0893040
$580$	−47.4802	−1.97151
$581$	−10.2965	−0.427172
$582$	35.1206	1.45580
$583$	−20.6906	−0.856918
$584$	2.17981	0.0902011
$585$	9.45447	0.390894
$586$	25.2145	1.04160
$587$	23.8272	0.983454	0.491727	−	0.870749i	$-0.336366\pi$
$587$	23.8272	0.983454	0.491727	+	0.870749i	$0.336366\pi$
$588$	−37.2345	−1.53553
$589$	2.53394	0.104409
$590$	−55.9525	−2.30353
$591$	1.78795	0.0735465
$592$	42.8174	1.75978
$593$	31.1570	1.27947	0.639733	−	0.768598i	$-0.279045\pi$
$593$	31.1570	1.27947	0.639733	+	0.768598i	$0.279045\pi$
$594$	−5.23524	−0.214805
$595$	9.10062	0.373089
$596$	−14.7058	−0.602372
$597$	−13.7859	−0.564217
$598$	9.27271	0.379189
$599$	−8.58770	−0.350884	−0.175442	−	0.984490i	$-0.556135\pi$
$599$	−8.58770	−0.350884	−0.175442	+	0.984490i	$0.556135\pi$
$600$	1.33017	0.0543041
$601$	−35.0826	−1.43105	−0.715525	−	0.698587i	$-0.753813\pi$
$601$	−35.0826	−1.43105	−0.715525	+	0.698587i	$0.753813\pi$
$602$	−19.1315	−0.779742
$603$	−16.3430	−0.665537
$604$	47.6109	1.93726
$605$	−15.1046	−0.614089
$606$	−34.7778	−1.41275
$607$	27.1225	1.10087	0.550434	−	0.834879i	$-0.314462\pi$
$607$	27.1225	1.10087	0.550434	+	0.834879i	$0.314462\pi$
$608$	−1.43097	−0.0580334
$609$	−19.5087	−0.790532
$610$	66.3417	2.68610
$611$	9.45827	0.382641
$612$	−4.22749	−0.170886
$613$	−36.9362	−1.49184	−0.745919	−	0.666036i	$-0.767990\pi$
$613$	−36.9362	−1.49184	−0.745919	+	0.666036i	$0.767990\pi$
$614$	52.4411	2.11635
$615$	−4.86494	−0.196173
$616$	−46.3647	−1.86809
$617$	−18.9504	−0.762915	−0.381458	−	0.924386i	$-0.624578\pi$
$617$	−18.9504	−0.762915	−0.381458	+	0.924386i	$0.624578\pi$
$618$	22.9855	0.924613
$619$	32.7318	1.31560	0.657802	−	0.753191i	$-0.271486\pi$
$619$	32.7318	1.31560	0.657802	+	0.753191i	$0.271486\pi$
$620$	41.1237	1.65157
$621$	0.899600	0.0360997
$622$	−20.8319	−0.835283
$623$	46.3725	1.85788
$624$	−22.3736	−0.895661
$625$	−26.1392	−1.04557
$626$	26.4982	1.05908
$627$	1.25084	0.0499539
$628$	4.22749	0.168695
$629$	−7.90469	−0.315181
$630$	22.7105	0.904810
$631$	8.05952	0.320844	0.160422	−	0.987048i	$-0.448714\pi$
$631$	8.05952	0.320844	0.160422	+	0.987048i	$0.448714\pi$
$632$	−19.2753	−0.766730
$633$	−7.90745	−0.314293
$634$	−9.38352	−0.372667
$635$	−5.39837	−0.214228
$636$	−41.6943	−1.65329
$637$	36.3801	1.44143
$638$	−25.6880	−1.01700
$639$	−11.7706	−0.465637
$640$	38.6578	1.52808
$641$	26.0860	1.03034	0.515168	−	0.857089i	$-0.327729\pi$
$641$	26.0860	1.03034	0.515168	+	0.857089i	$0.327729\pi$
$642$	−20.3850	−0.804531
$643$	−8.46999	−0.334024	−0.167012	−	0.985955i	$-0.553412\pi$
$643$	−8.46999	−0.334024	−0.167012	+	0.985955i	$0.553412\pi$
$644$	15.1205	0.595832
$645$	4.41361	0.173786
$646$	1.48792	0.0585415
$647$	9.54660	0.375315	0.187658	−	0.982234i	$-0.439910\pi$
$647$	9.54660	0.375315	0.187658	+	0.982234i	$0.439910\pi$
$648$	−5.55870	−0.218366
$649$	−20.5498	−0.806649
$650$	−2.46656	−0.0967466
$651$	16.8969	0.662242
$652$	81.6922	3.19931
$653$	39.4107	1.54226	0.771130	−	0.636678i	$-0.219692\pi$
$653$	39.4107	1.54226	0.771130	+	0.636678i	$0.219692\pi$
$654$	38.9220	1.52197
$655$	−50.7544	−1.98314
$656$	11.5127	0.449495
$657$	−0.392144	−0.0152990
$658$	22.7197	0.885705
$659$	35.9160	1.39909	0.699544	−	0.714589i	$-0.253386\pi$
$659$	35.9160	1.39909	0.699544	+	0.714589i	$0.253386\pi$
$660$	20.3002	0.790182
$661$	0.756861	0.0294385	0.0147192	−	0.999892i	$-0.495315\pi$
$661$	0.756861	0.0294385	0.0147192	+	0.999892i	$0.495315\pi$
$662$	−53.2969	−2.07144
$663$	4.13048	0.160415
$664$	−14.3956	−0.558657
$665$	−5.42618	−0.210418
$666$	−19.7261	−0.764371
$667$	4.41411	0.170915
$668$	33.7197	1.30465
$669$	−9.37569	−0.362485
$670$	93.3520	3.60650
$671$	24.3654	0.940616
$672$	−9.54203	−0.368092
$673$	46.9803	1.81096	0.905478	−	0.424393i	$-0.139513\pi$
$673$	46.9803	1.81096	0.905478	+	0.424393i	$0.139513\pi$
$674$	−1.73114	−0.0666809
$675$	−0.239296	−0.00921050
$676$	17.1673	0.660281
$677$	29.7466	1.14325	0.571627	−	0.820514i	$-0.306313\pi$
$677$	29.7466	1.14325	0.571627	+	0.820514i	$0.306313\pi$
$678$	37.3917	1.43602
$679$	−55.9551	−2.14736
$680$	12.7236	0.487927
$681$	15.3381	0.587757
$682$	22.2490	0.851957
$683$	−28.5625	−1.09291	−0.546457	−	0.837487i	$-0.684024\pi$
$683$	−28.5625	−1.09291	−0.546457	+	0.837487i	$0.684024\pi$
$684$	2.52061	0.0963780
$685$	0.519045	0.0198317
$686$	17.9357	0.684790
$687$	−8.45160	−0.322449
$688$	−10.4446	−0.398198
$689$	40.7375	1.55197
$690$	−5.13857	−0.195622
$691$	40.0576	1.52386	0.761931	−	0.647658i	$-0.224252\pi$
$691$	40.0576	1.52386	0.761931	+	0.647658i	$0.224252\pi$
$692$	49.7707	1.89200
$693$	8.34093	0.316846
$694$	−10.5571	−0.400744
$695$	−19.1826	−0.727639
$696$	−27.2751	−1.03386
$697$	−2.12540	−0.0805054
$698$	28.2662	1.06989
$699$	−20.5443	−0.777055
$700$	−4.02210	−0.152021
$701$	37.2628	1.40740	0.703699	−	0.710498i	$-0.251530\pi$
$701$	37.2628	1.40740	0.703699	+	0.710498i	$0.251530\pi$
$702$	10.3076	0.389035
$703$	4.71312	0.177759
$704$	10.1627	0.383023
$705$	−5.24140	−0.197403
$706$	−26.4838	−0.996731
$707$	55.4090	2.08387
$708$	−41.4104	−1.55630
$709$	29.5209	1.10868	0.554340	−	0.832290i	$-0.312971\pi$
$709$	29.5209	1.10868	0.554340	+	0.832290i	$0.312971\pi$
$710$	67.2343	2.52326
$711$	3.46759	0.130045
$712$	64.8334	2.42974
$713$	−3.82316	−0.143178
$714$	9.92181	0.371315
$715$	−19.8343	−0.741761
$716$	−58.7966	−2.19733
$717$	5.66979	0.211742
$718$	81.7405	3.05053
$719$	1.07639	0.0401426	0.0200713	−	0.999799i	$-0.493611\pi$
$719$	1.07639	0.0401426	0.0200713	+	0.999799i	$0.493611\pi$
$720$	12.3986	0.462068
$721$	−36.6212	−1.36384
$722$	46.5272	1.73156
$723$	−26.3181	−0.978780
$724$	63.9231	2.37568
$725$	−1.17416	−0.0436073
$726$	−16.4675	−0.611168
$727$	21.7500	0.806665	0.403332	−	0.915054i	$-0.367852\pi$
$727$	21.7500	0.806665	0.403332	+	0.915054i	$0.367852\pi$
$728$	91.2868	3.38331
$729$	1.00000	0.0370370
$730$	2.23995	0.0829043
$731$	1.92823	0.0713180
$732$	49.0994	1.81477
$733$	10.9645	0.404983	0.202492	−	0.979284i	$-0.435096\pi$
$733$	10.9645	0.404983	0.202492	+	0.979284i	$0.435096\pi$
$734$	41.2597	1.52292
$735$	−20.1604	−0.743628
$736$	2.15902	0.0795824
$737$	34.2855	1.26292
$738$	−5.30393	−0.195240
$739$	−27.9372	−1.02769	−0.513844	−	0.857884i	$-0.671779\pi$
$739$	−27.9372	−1.02769	−0.513844	+	0.857884i	$0.671779\pi$
$740$	76.4899	2.81182
$741$	−2.46277	−0.0904721
$742$	97.8554	3.59238
$743$	−17.1717	−0.629969	−0.314984	−	0.949097i	$-0.601999\pi$
$743$	−17.1717	−0.629969	−0.314984	+	0.949097i	$0.601999\pi$
$744$	23.6236	0.866083
$745$	−7.96236	−0.291718
$746$	−34.2335	−1.25338
$747$	2.58974	0.0947538
$748$	8.86876	0.324274
$749$	32.4779	1.18672
$750$	−27.1934	−0.992964
$751$	34.5845	1.26201	0.631003	−	0.775781i	$-0.282644\pi$
$751$	34.5845	1.26201	0.631003	+	0.775781i	$0.282644\pi$
$752$	12.4036	0.452312
$753$	15.9749	0.582158
$754$	50.5767	1.84190
$755$	25.7787	0.938182
$756$	16.8080	0.611303
$757$	−37.7428	−1.37178	−0.685892	−	0.727703i	$-0.740588\pi$
$757$	−37.7428	−1.37178	−0.685892	+	0.727703i	$0.740588\pi$
$758$	−51.2893	−1.86291
$759$	−1.88725	−0.0685028
$760$	−7.58635	−0.275186
$761$	1.57113	0.0569535	0.0284767	−	0.999594i	$-0.490934\pi$
$761$	1.57113	0.0569535	0.0284767	+	0.999594i	$0.490934\pi$
$762$	−5.88549	−0.213209
$763$	−62.0116	−2.24497
$764$	−34.8868	−1.26216
$765$	−2.28895	−0.0827572
$766$	−25.4641	−0.920054
$767$	40.4601	1.46093
$768$	32.4575	1.17121
$769$	47.0999	1.69847	0.849233	−	0.528019i	$-0.177065\pi$
$769$	47.0999	1.69847	0.849233	+	0.528019i	$0.177065\pi$
$770$	−47.6439	−1.71697
$771$	−1.22344	−0.0440609
$772$	9.08433	0.326952
$773$	44.3393	1.59477	0.797387	−	0.603468i	$-0.206215\pi$
$773$	44.3393	1.59477	0.797387	+	0.603468i	$0.206215\pi$
$774$	4.81188	0.172959
$775$	1.01697	0.0365306
$776$	−78.2309	−2.80832
$777$	31.4282	1.12748
$778$	16.8027	0.602406
$779$	1.26726	0.0454042
$780$	−39.9687	−1.43111
$781$	24.6932	0.883593
$782$	−2.24495	−0.0802791
$783$	4.90674	0.175353
$784$	47.7088	1.70388
$785$	2.28895	0.0816962
$786$	−55.3342	−1.97371
$787$	−4.97973	−0.177508	−0.0887540	−	0.996054i	$-0.528289\pi$
$787$	−4.97973	−0.177508	−0.0887540	+	0.996054i	$0.528289\pi$
$788$	−7.55856	−0.269262
$789$	−1.42930	−0.0508845
$790$	−19.8071	−0.704706
$791$	−59.5735	−2.11819
$792$	11.6615	0.414372
$793$	−47.9727	−1.70356
$794$	28.2533	1.00267
$795$	−22.5751	−0.800657
$796$	58.2796	2.06566
$797$	33.6541	1.19209	0.596045	−	0.802951i	$-0.296738\pi$
$797$	33.6541	1.19209	0.596045	+	0.802951i	$0.296738\pi$
$798$	−5.91581	−0.209417
$799$	−2.28987	−0.0810098
$800$	−0.574304	−0.0203047
$801$	−11.6634	−0.412107
$802$	64.1242	2.26431
$803$	0.822669	0.0290314
$804$	69.0897	2.43661
$805$	8.18691	0.288551
$806$	−43.8057	−1.54299
$807$	1.18644	0.0417647
$808$	77.4674	2.72529
$809$	−10.9571	−0.385231	−0.192615	−	0.981274i	$-0.561697\pi$
$809$	−10.9571	−0.385231	−0.192615	+	0.981274i	$0.561697\pi$
$810$	−5.71206	−0.200701
$811$	−20.2163	−0.709890	−0.354945	−	0.934887i	$-0.615500\pi$
$811$	−20.2163	−0.709890	−0.354945	+	0.934887i	$0.615500\pi$
$812$	82.4728	2.89423
$813$	−9.17310	−0.321715
$814$	41.3830	1.45047
$815$	44.2318	1.54937
$816$	5.41671	0.189623
$817$	−1.14969	−0.0402226
$818$	−17.9768	−0.628545
$819$	−16.4223	−0.573843
$820$	20.5665	0.718214
$821$	21.2270	0.740827	0.370413	−	0.928867i	$-0.379216\pi$
$821$	21.2270	0.740827	0.370413	+	0.928867i	$0.379216\pi$
$822$	0.565881	0.0197374
$823$	24.1802	0.842869	0.421435	−	0.906859i	$-0.361527\pi$
$823$	24.1802	0.842869	0.421435	+	0.906859i	$0.361527\pi$
$824$	−51.2001	−1.78364
$825$	0.502013	0.0174779
$826$	97.1891	3.38164
$827$	−10.0475	−0.349386	−0.174693	−	0.984623i	$-0.555893\pi$
$827$	−10.0475	−0.349386	−0.174693	+	0.984623i	$0.555893\pi$
$828$	−3.80305	−0.132165
$829$	27.2764	0.947348	0.473674	−	0.880700i	$-0.342927\pi$
$829$	27.2764	0.947348	0.473674	+	0.880700i	$0.342927\pi$
$830$	−14.7928	−0.513465
$831$	−17.7208	−0.614729
$832$	−20.0093	−0.693696
$833$	−8.80771	−0.305169
$834$	−20.9136	−0.724178
$835$	18.2573	0.631821
$836$	−5.28794	−0.182887
$837$	−4.24984	−0.146896
$838$	−36.5823	−1.26372
$839$	48.9554	1.69013	0.845065	−	0.534664i	$-0.179562\pi$
$839$	48.9554	1.69013	0.845065	+	0.534664i	$0.179562\pi$
$840$	−50.5876	−1.74544
$841$	−4.92386	−0.169788
$842$	−70.7276	−2.43743
$843$	21.3320	0.734714
$844$	33.4287	1.15066
$845$	9.29514	0.319762
$846$	−5.71436	−0.196464
$847$	26.2365	0.901499
$848$	53.4231	1.83456
$849$	9.29149	0.318883
$850$	0.597161	0.0204825
$851$	−7.11106	−0.243764
$852$	49.7600	1.70475
$853$	10.0226	0.343168	0.171584	−	0.985170i	$-0.445112\pi$
$853$	10.0226	0.343168	0.171584	+	0.985170i	$0.445112\pi$
$854$	−115.235	−3.94326
$855$	1.36477	0.0466742
$856$	45.4074	1.55199
$857$	−22.9102	−0.782597	−0.391299	−	0.920264i	$-0.627974\pi$
$857$	−22.9102	−0.782597	−0.391299	+	0.920264i	$0.627974\pi$
$858$	−21.6241	−0.738233
$859$	2.94992	0.100650	0.0503250	−	0.998733i	$-0.483974\pi$
$859$	2.94992	0.100650	0.0503250	+	0.998733i	$0.483974\pi$
$860$	−18.6585	−0.636250
$861$	8.45037	0.287988
$862$	−44.0952	−1.50189
$863$	11.2571	0.383198	0.191599	−	0.981473i	$-0.438633\pi$
$863$	11.2571	0.383198	0.191599	+	0.981473i	$0.438633\pi$
$864$	2.39997	0.0816488
$865$	26.9481	0.916262
$866$	−29.7428	−1.01070
$867$	−1.00000	−0.0339618
$868$	−71.4316	−2.42455
$869$	−7.27459	−0.246773
$870$	−28.0276	−0.950226
$871$	−67.5043	−2.28729
$872$	−86.6985	−2.93598
$873$	14.0736	0.476319
$874$	1.33853	0.0452766
$875$	43.3254	1.46466
$876$	1.65778	0.0560114
$877$	−22.0202	−0.743570	−0.371785	−	0.928319i	$-0.621254\pi$
$877$	−22.0202	−0.743570	−0.371785	+	0.928319i	$0.621254\pi$
$878$	−99.0788	−3.34375
$879$	10.1040	0.340800
$880$	−26.0107	−0.876820
$881$	18.7679	0.632306	0.316153	−	0.948708i	$-0.397609\pi$
$881$	18.7679	0.632306	0.316153	+	0.948708i	$0.397609\pi$
$882$	−21.9796	−0.740091
$883$	−48.5145	−1.63264	−0.816321	−	0.577598i	$-0.803990\pi$
$883$	−48.5145	−1.63264	−0.816321	+	0.577598i	$0.803990\pi$
$884$	−17.4616	−0.587296
$885$	−22.4214	−0.753688
$886$	−16.1021	−0.540960
$887$	38.9880	1.30909	0.654544	−	0.756024i	$-0.272860\pi$
$887$	38.9880	1.30909	0.654544	+	0.756024i	$0.272860\pi$
$888$	43.9398	1.47452
$889$	9.37692	0.314492
$890$	66.6222	2.23318
$891$	−2.09788	−0.0702815
$892$	39.6357	1.32710
$893$	1.36532	0.0456887
$894$	−8.68084	−0.290331
$895$	−31.8351	−1.06413
$896$	−67.1483	−2.24327
$897$	3.71578	0.124066
$898$	−61.9729	−2.06806
$899$	−20.8529	−0.695483
$900$	1.01162	0.0337207
$901$	−9.86265	−0.328572
$902$	11.1270	0.370488
$903$	−7.66642	−0.255122
$904$	−83.2897	−2.77018
$905$	34.6108	1.15050
$906$	28.1048	0.933720
$907$	12.4223	0.412475	0.206238	−	0.978502i	$-0.433878\pi$
$907$	12.4223	0.412475	0.206238	+	0.978502i	$0.433878\pi$
$908$	−64.8417	−2.15185
$909$	−13.9363	−0.462236
$910$	93.8055	3.10962
$911$	−2.11142	−0.0699543	−0.0349772	−	0.999388i	$-0.511136\pi$
$911$	−2.11142	−0.0699543	−0.0349772	+	0.999388i	$0.511136\pi$
$912$	−3.22967	−0.106945
$913$	−5.43296	−0.179805
$914$	64.5654	2.13563
$915$	26.5846	0.878860
$916$	35.7291	1.18052
$917$	88.1600	2.91130
$918$	−2.49549	−0.0823636
$919$	28.8910	0.953026	0.476513	−	0.879167i	$-0.341901\pi$
$919$	28.8910	0.953026	0.476513	+	0.879167i	$0.341901\pi$
$920$	11.4461	0.377368
$921$	21.0143	0.692445
$922$	−15.2623	−0.502636
$923$	−48.6181	−1.60029
$924$	−35.2612	−1.16001
$925$	1.89156	0.0621941
$926$	78.1080	2.56679
$927$	9.21081	0.302523
$928$	11.7761	0.386568
$929$	−16.2154	−0.532011	−0.266005	−	0.963972i	$-0.585704\pi$
$929$	−16.2154	−0.532011	−0.266005	+	0.963972i	$0.585704\pi$
$930$	24.2754	0.796021
$931$	5.25153	0.172112
$932$	86.8507	2.84489
$933$	−8.34780	−0.273295
$934$	67.5814	2.21133
$935$	4.80194	0.157040
$936$	−22.9601	−0.750474
$937$	38.5316	1.25877	0.629386	−	0.777093i	$-0.283306\pi$
$937$	38.5316	1.25877	0.629386	+	0.777093i	$0.283306\pi$
$938$	−162.152	−5.29444
$939$	10.6184	0.346519
$940$	22.1580	0.722714
$941$	25.3666	0.826929	0.413464	−	0.910520i	$-0.364319\pi$
$941$	25.3666	0.826929	0.413464	+	0.910520i	$0.364319\pi$
$942$	2.49549	0.0813076
$943$	−1.91201	−0.0622637
$944$	53.0594	1.72694
$945$	9.10062	0.296043
$946$	−10.0947	−0.328208
$947$	50.3579	1.63641	0.818205	−	0.574926i	$-0.194969\pi$
$947$	50.3579	1.63641	0.818205	+	0.574926i	$0.194969\pi$
$948$	−14.6592	−0.476110
$949$	−1.61974	−0.0525791
$950$	−0.356053	−0.0115519
$951$	−3.76018	−0.121932
$952$	−22.1008	−0.716290
$953$	−43.9038	−1.42218	−0.711092	−	0.703099i	$-0.751799\pi$
$953$	−43.9038	−1.42218	−0.711092	+	0.703099i	$0.751799\pi$
$954$	−24.6122	−0.796849
$955$	−18.8893	−0.611242
$956$	−23.9690	−0.775213
$957$	−10.2937	−0.332750
$958$	44.8838	1.45013
$959$	−0.901578	−0.0291135
$960$	11.0884	0.357875
$961$	−12.9388	−0.417381
$962$	−81.4783	−2.62697
$963$	−8.16871	−0.263233
$964$	111.259	3.58343
$965$	4.91866	0.158337
$966$	8.92566	0.287178
$967$	26.2750	0.844948	0.422474	−	0.906375i	$-0.361162\pi$
$967$	26.2750	0.844948	0.422474	+	0.906375i	$0.361162\pi$
$968$	36.6813	1.17898
$969$	0.596243	0.0191541
$970$	−80.3893	−2.58115
$971$	8.52272	0.273507	0.136754	−	0.990605i	$-0.456333\pi$
$971$	8.52272	0.273507	0.136754	+	0.990605i	$0.456333\pi$
$972$	−4.22749	−0.135597
$973$	33.3201	1.06819
$974$	46.0573	1.47577
$975$	−0.988407	−0.0316543
$976$	−62.9114	−2.01374
$977$	−33.9487	−1.08611	−0.543057	−	0.839696i	$-0.682733\pi$
$977$	−33.9487	−1.08611	−0.543057	+	0.839696i	$0.682733\pi$
$978$	48.2230	1.54200
$979$	24.4684	0.782015
$980$	85.2280	2.72251
$981$	15.5969	0.497971
$982$	−57.2418	−1.82666
$983$	−0.748729	−0.0238807	−0.0119404	−	0.999929i	$-0.503801\pi$
$983$	−0.748729	−0.0238807	−0.0119404	+	0.999929i	$0.503801\pi$
$984$	11.8145	0.376631
$985$	−4.09254	−0.130399
$986$	−12.2448	−0.389952
$987$	9.10428	0.289792
$988$	10.4113	0.331229
$989$	1.73463	0.0551581
$990$	11.9832	0.380851
$991$	−28.3216	−0.899665	−0.449832	−	0.893113i	$-0.648516\pi$
$991$	−28.3216	−0.899665	−0.449832	+	0.893113i	$0.648516\pi$
$992$	−10.1995	−0.323835
$993$	−21.3573	−0.677752
$994$	−116.785	−3.70421
$995$	31.5551	1.00036
$996$	−10.9481	−0.346905
$997$	−4.47201	−0.141630	−0.0708149	−	0.997489i	$-0.522560\pi$
$997$	−4.47201	−0.141630	−0.0708149	+	0.997489i	$0.522560\pi$
$998$	−35.8985	−1.13635
$999$	−7.90469	−0.250093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.5	✓	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49549 q^{2} -1.00000 q^{3} +4.22749 q^{4} +2.28895 q^{5} +2.49549 q^{6} -3.97589 q^{7} -5.55870 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49549 q^{2} -1.00000 q^{3} +4.22749 q^{4} +2.28895 q^{5} +2.49549 q^{6} -3.97589 q^{7} -5.55870 q^{8} +1.00000 q^{9} -5.71206 q^{10} -2.09788 q^{11} -4.22749 q^{12} +4.13048 q^{13} +9.92181 q^{14} -2.28895 q^{15} +5.41671 q^{16} -1.00000 q^{17} -2.49549 q^{18} +0.596243 q^{19} +9.67652 q^{20} +3.97589 q^{21} +5.23524 q^{22} -0.899600 q^{23} +5.55870 q^{24} +0.239296 q^{25} -10.3076 q^{26} -1.00000 q^{27} -16.8080 q^{28} -4.90674 q^{29} +5.71206 q^{30} +4.24984 q^{31} -2.39997 q^{32} +2.09788 q^{33} +2.49549 q^{34} -9.10062 q^{35} +4.22749 q^{36} +7.90469 q^{37} -1.48792 q^{38} -4.13048 q^{39} -12.7236 q^{40} +2.12540 q^{41} -9.92181 q^{42} -1.92823 q^{43} -8.86876 q^{44} +2.28895 q^{45} +2.24495 q^{46} +2.28987 q^{47} -5.41671 q^{48} +8.80771 q^{49} -0.597161 q^{50} +1.00000 q^{51} +17.4616 q^{52} +9.86265 q^{53} +2.49549 q^{54} -4.80194 q^{55} +22.1008 q^{56} -0.596243 q^{57} +12.2448 q^{58} +9.79550 q^{59} -9.67652 q^{60} -11.6143 q^{61} -10.6055 q^{62} -3.97589 q^{63} -4.84429 q^{64} +9.45447 q^{65} -5.23524 q^{66} -16.3430 q^{67} -4.22749 q^{68} +0.899600 q^{69} +22.7105 q^{70} -11.7706 q^{71} -5.55870 q^{72} -0.392144 q^{73} -19.7261 q^{74} -0.239296 q^{75} +2.52061 q^{76} +8.34093 q^{77} +10.3076 q^{78} +3.46759 q^{79} +12.3986 q^{80} +1.00000 q^{81} -5.30393 q^{82} +2.58974 q^{83} +16.8080 q^{84} -2.28895 q^{85} +4.81188 q^{86} +4.90674 q^{87} +11.6615 q^{88} -11.6634 q^{89} -5.71206 q^{90} -16.4223 q^{91} -3.80305 q^{92} -4.24984 q^{93} -5.71436 q^{94} +1.36477 q^{95} +2.39997 q^{96} +14.0736 q^{97} -21.9796 q^{98} -2.09788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more