LMFDB - Embedded newform 4730.2.a.bc.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 24x^{9} - x^{8} + 200x^{7} + 14x^{6} - 653x^{5} - 26x^{4} + 620x^{3} - 177x^{2} - 90x + 32 $ x^11 - 24x^9 - x^8 + 200x^7 + 14x^6 - 653x^5 - 26x^4 + 620x^3 - 177x^2 - 90x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$3.01577$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.01577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.01577 q^{6} -4.16045 q^{7} -1.00000 q^{8} +6.09484 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.01577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.01577 q^{6} -4.16045 q^{7} -1.00000 q^{8} +6.09484 q^{9} +1.00000 q^{10} +1.00000 q^{11} +3.01577 q^{12} -0.969598 q^{13} +4.16045 q^{14} -3.01577 q^{15} +1.00000 q^{16} +1.39767 q^{17} -6.09484 q^{18} +4.13140 q^{19} -1.00000 q^{20} -12.5469 q^{21} -1.00000 q^{22} -3.83481 q^{23} -3.01577 q^{24} +1.00000 q^{25} +0.969598 q^{26} +9.33332 q^{27} -4.16045 q^{28} -3.54482 q^{29} +3.01577 q^{30} -0.299937 q^{31} -1.00000 q^{32} +3.01577 q^{33} -1.39767 q^{34} +4.16045 q^{35} +6.09484 q^{36} +3.35671 q^{37} -4.13140 q^{38} -2.92408 q^{39} +1.00000 q^{40} +0.0682677 q^{41} +12.5469 q^{42} -1.00000 q^{43} +1.00000 q^{44} -6.09484 q^{45} +3.83481 q^{46} +10.8022 q^{47} +3.01577 q^{48} +10.3093 q^{49} -1.00000 q^{50} +4.21504 q^{51} -0.969598 q^{52} +4.48604 q^{53} -9.33332 q^{54} -1.00000 q^{55} +4.16045 q^{56} +12.4593 q^{57} +3.54482 q^{58} +10.9299 q^{59} -3.01577 q^{60} +9.16751 q^{61} +0.299937 q^{62} -25.3573 q^{63} +1.00000 q^{64} +0.969598 q^{65} -3.01577 q^{66} +2.45837 q^{67} +1.39767 q^{68} -11.5649 q^{69} -4.16045 q^{70} +4.23234 q^{71} -6.09484 q^{72} +2.62611 q^{73} -3.35671 q^{74} +3.01577 q^{75} +4.13140 q^{76} -4.16045 q^{77} +2.92408 q^{78} +3.69703 q^{79} -1.00000 q^{80} +9.86258 q^{81} -0.0682677 q^{82} -2.57543 q^{83} -12.5469 q^{84} -1.39767 q^{85} +1.00000 q^{86} -10.6904 q^{87} -1.00000 q^{88} +9.56098 q^{89} +6.09484 q^{90} +4.03396 q^{91} -3.83481 q^{92} -0.904539 q^{93} -10.8022 q^{94} -4.13140 q^{95} -3.01577 q^{96} +13.9999 q^{97} -10.3093 q^{98} +6.09484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.01577	1.74115	0.870577	−	0.492033i	$-0.163746\pi$
$3$	3.01577	1.74115	0.870577	+	0.492033i	$0.163746\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.01577	−1.23118
$7$	−4.16045	−1.57250	−0.786251	−	0.617907i	$-0.787981\pi$
$7$	−4.16045	−1.57250	−0.786251	+	0.617907i	$0.787981\pi$
$8$	−1.00000	−0.353553
$9$	6.09484	2.03161
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.01577	0.870577
$13$	−0.969598	−0.268918	−0.134459	−	0.990919i	$-0.542930\pi$
$13$	−0.969598	−0.268918	−0.134459	+	0.990919i	$0.542930\pi$
$14$	4.16045	1.11193
$15$	−3.01577	−0.778667
$16$	1.00000	0.250000
$17$	1.39767	0.338984	0.169492	−	0.985532i	$-0.445787\pi$
$17$	1.39767	0.338984	0.169492	+	0.985532i	$0.445787\pi$
$18$	−6.09484	−1.43657
$19$	4.13140	0.947809	0.473904	−	0.880576i	$-0.342844\pi$
$19$	4.13140	0.947809	0.473904	+	0.880576i	$0.342844\pi$
$20$	−1.00000	−0.223607
$21$	−12.5469	−2.73797
$22$	−1.00000	−0.213201
$23$	−3.83481	−0.799613	−0.399806	−	0.916600i	$-0.630923\pi$
$23$	−3.83481	−0.799613	−0.399806	+	0.916600i	$0.630923\pi$
$24$	−3.01577	−0.615591
$25$	1.00000	0.200000
$26$	0.969598	0.190154
$27$	9.33332	1.79620
$28$	−4.16045	−0.786251
$29$	−3.54482	−0.658257	−0.329129	−	0.944285i	$-0.606755\pi$
$29$	−3.54482	−0.658257	−0.329129	+	0.944285i	$0.606755\pi$
$30$	3.01577	0.550601
$31$	−0.299937	−0.0538702	−0.0269351	−	0.999637i	$-0.508575\pi$
$31$	−0.299937	−0.0538702	−0.0269351	+	0.999637i	$0.508575\pi$
$32$	−1.00000	−0.176777
$33$	3.01577	0.524977
$34$	−1.39767	−0.239698
$35$	4.16045	0.703244
$36$	6.09484	1.01581
$37$	3.35671	0.551839	0.275920	−	0.961181i	$-0.411018\pi$
$37$	3.35671	0.551839	0.275920	+	0.961181i	$0.411018\pi$
$38$	−4.13140	−0.670202
$39$	−2.92408	−0.468228
$40$	1.00000	0.158114
$41$	0.0682677	0.0106616	0.00533081	−	0.999986i	$-0.498303\pi$
$41$	0.0682677	0.0106616	0.00533081	+	0.999986i	$0.498303\pi$
$42$	12.5469	1.93603
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−6.09484	−0.908566
$46$	3.83481	0.565412
$47$	10.8022	1.57566	0.787829	−	0.615894i	$-0.211205\pi$
$47$	10.8022	1.57566	0.787829	+	0.615894i	$0.211205\pi$
$48$	3.01577	0.435288
$49$	10.3093	1.47276
$50$	−1.00000	−0.141421
$51$	4.21504	0.590223
$52$	−0.969598	−0.134459
$53$	4.48604	0.616206	0.308103	−	0.951353i	$-0.400306\pi$
$53$	4.48604	0.616206	0.308103	+	0.951353i	$0.400306\pi$
$54$	−9.33332	−1.27010
$55$	−1.00000	−0.134840
$56$	4.16045	0.555963
$57$	12.4593	1.65028
$58$	3.54482	0.465458
$59$	10.9299	1.42295	0.711476	−	0.702710i	$-0.248027\pi$
$59$	10.9299	1.42295	0.711476	+	0.702710i	$0.248027\pi$
$60$	−3.01577	−0.389334
$61$	9.16751	1.17378	0.586889	−	0.809667i	$-0.300352\pi$
$61$	9.16751	1.17378	0.586889	+	0.809667i	$0.300352\pi$
$62$	0.299937	0.0380920
$63$	−25.3573	−3.19472
$64$	1.00000	0.125000
$65$	0.969598	0.120264
$66$	−3.01577	−0.371215
$67$	2.45837	0.300338	0.150169	−	0.988660i	$-0.452018\pi$
$67$	2.45837	0.300338	0.150169	+	0.988660i	$0.452018\pi$
$68$	1.39767	0.169492
$69$	−11.5649	−1.39225
$70$	−4.16045	−0.497269
$71$	4.23234	0.502286	0.251143	−	0.967950i	$-0.419194\pi$
$71$	4.23234	0.502286	0.251143	+	0.967950i	$0.419194\pi$
$72$	−6.09484	−0.718284
$73$	2.62611	0.307363	0.153681	−	0.988120i	$-0.450887\pi$
$73$	2.62611	0.307363	0.153681	+	0.988120i	$0.450887\pi$
$74$	−3.35671	−0.390209
$75$	3.01577	0.348231
$76$	4.13140	0.473904
$77$	−4.16045	−0.474127
$78$	2.92408	0.331087
$79$	3.69703	0.415948	0.207974	−	0.978134i	$-0.433313\pi$
$79$	3.69703	0.415948	0.207974	+	0.978134i	$0.433313\pi$
$80$	−1.00000	−0.111803
$81$	9.86258	1.09584
$82$	−0.0682677	−0.00753890
$83$	−2.57543	−0.282690	−0.141345	−	0.989960i	$-0.545143\pi$
$83$	−2.57543	−0.282690	−0.141345	+	0.989960i	$0.545143\pi$
$84$	−12.5469	−1.36898
$85$	−1.39767	−0.151598
$86$	1.00000	0.107833
$87$	−10.6904	−1.14613
$88$	−1.00000	−0.106600
$89$	9.56098	1.01346	0.506731	−	0.862104i	$-0.330854\pi$
$89$	9.56098	1.01346	0.506731	+	0.862104i	$0.330854\pi$
$90$	6.09484	0.642453
$91$	4.03396	0.422874
$92$	−3.83481	−0.399806
$93$	−0.904539	−0.0937963
$94$	−10.8022	−1.11416
$95$	−4.13140	−0.423873
$96$	−3.01577	−0.307795
$97$	13.9999	1.42147	0.710737	−	0.703458i	$-0.248361\pi$
$97$	13.9999	1.42147	0.710737	+	0.703458i	$0.248361\pi$
$98$	−10.3093	−1.04140
$99$	6.09484	0.612555
$100$	1.00000	0.100000
$101$	5.40782	0.538098	0.269049	−	0.963126i	$-0.413291\pi$
$101$	5.40782	0.538098	0.269049	+	0.963126i	$0.413291\pi$
$102$	−4.21504	−0.417351
$103$	−5.70244	−0.561878	−0.280939	−	0.959726i	$-0.590646\pi$
$103$	−5.70244	−0.561878	−0.280939	+	0.959726i	$0.590646\pi$
$104$	0.969598	0.0950769
$105$	12.5469	1.22446
$106$	−4.48604	−0.435723
$107$	−5.59518	−0.540907	−0.270453	−	0.962733i	$-0.587174\pi$
$107$	−5.59518	−0.540907	−0.270453	+	0.962733i	$0.587174\pi$
$108$	9.33332	0.898099
$109$	−6.40781	−0.613757	−0.306878	−	0.951749i	$-0.599284\pi$
$109$	−6.40781	−0.613757	−0.306878	+	0.951749i	$0.599284\pi$
$110$	1.00000	0.0953463
$111$	10.1230	0.960837
$112$	−4.16045	−0.393125
$113$	−16.0752	−1.51223	−0.756116	−	0.654438i	$-0.772905\pi$
$113$	−16.0752	−1.51223	−0.756116	+	0.654438i	$0.772905\pi$
$114$	−12.4593	−1.16692
$115$	3.83481	0.357598
$116$	−3.54482	−0.329129
$117$	−5.90955	−0.546338
$118$	−10.9299	−1.00618
$119$	−5.81492	−0.533053
$120$	3.01577	0.275300
$121$	1.00000	0.0909091
$122$	−9.16751	−0.829987
$123$	0.205879	0.0185635
$124$	−0.299937	−0.0269351
$125$	−1.00000	−0.0894427
$126$	25.3573	2.25901
$127$	−10.3994	−0.922797	−0.461399	−	0.887193i	$-0.652652\pi$
$127$	−10.3994	−0.922797	−0.461399	+	0.887193i	$0.652652\pi$
$128$	−1.00000	−0.0883883
$129$	−3.01577	−0.265523
$130$	−0.969598	−0.0850394
$131$	13.0346	1.13884	0.569420	−	0.822047i	$-0.307168\pi$
$131$	13.0346	1.13884	0.569420	+	0.822047i	$0.307168\pi$
$132$	3.01577	0.262489
$133$	−17.1885	−1.49043
$134$	−2.45837	−0.212371
$135$	−9.33332	−0.803284
$136$	−1.39767	−0.119849
$137$	10.3677	0.885775	0.442888	−	0.896577i	$-0.353954\pi$
$137$	10.3677	0.885775	0.442888	+	0.896577i	$0.353954\pi$
$138$	11.5649	0.984468
$139$	−2.91272	−0.247054	−0.123527	−	0.992341i	$-0.539420\pi$
$139$	−2.91272	−0.247054	−0.123527	+	0.992341i	$0.539420\pi$
$140$	4.16045	0.351622
$141$	32.5768	2.74346
$142$	−4.23234	−0.355170
$143$	−0.969598	−0.0810819
$144$	6.09484	0.507904
$145$	3.54482	0.294382
$146$	−2.62611	−0.217338
$147$	31.0905	2.56430
$148$	3.35671	0.275920
$149$	12.2913	1.00694	0.503469	−	0.864013i	$-0.332057\pi$
$149$	12.2913	1.00694	0.503469	+	0.864013i	$0.332057\pi$
$150$	−3.01577	−0.246236
$151$	8.74373	0.711555	0.355777	−	0.934571i	$-0.384216\pi$
$151$	8.74373	0.711555	0.355777	+	0.934571i	$0.384216\pi$
$152$	−4.13140	−0.335101
$153$	8.51856	0.688685
$154$	4.16045	0.335258
$155$	0.299937	0.0240915
$156$	−2.92408	−0.234114
$157$	−4.50911	−0.359866	−0.179933	−	0.983679i	$-0.557588\pi$
$157$	−4.50911	−0.359866	−0.179933	+	0.983679i	$0.557588\pi$
$158$	−3.69703	−0.294120
$159$	13.5289	1.07291
$160$	1.00000	0.0790569
$161$	15.9545	1.25739
$162$	−9.86258	−0.774877
$163$	19.5471	1.53104	0.765522	−	0.643409i	$-0.222481\pi$
$163$	19.5471	1.53104	0.765522	+	0.643409i	$0.222481\pi$
$164$	0.0682677	0.00533081
$165$	−3.01577	−0.234777
$166$	2.57543	0.199892
$167$	−6.43628	−0.498054	−0.249027	−	0.968497i	$-0.580111\pi$
$167$	−6.43628	−0.498054	−0.249027	+	0.968497i	$0.580111\pi$
$168$	12.5469	0.968017
$169$	−12.0599	−0.927683
$170$	1.39767	0.107196
$171$	25.1803	1.92558
$172$	−1.00000	−0.0762493
$173$	−9.94712	−0.756266	−0.378133	−	0.925751i	$-0.623434\pi$
$173$	−9.94712	−0.756266	−0.378133	+	0.925751i	$0.623434\pi$
$174$	10.6904	0.810434
$175$	−4.16045	−0.314500
$176$	1.00000	0.0753778
$177$	32.9620	2.47758
$178$	−9.56098	−0.716626
$179$	−21.6591	−1.61888	−0.809438	−	0.587206i	$-0.800228\pi$
$179$	−21.6591	−1.61888	−0.809438	+	0.587206i	$0.800228\pi$
$180$	−6.09484	−0.454283
$181$	3.73078	0.277307	0.138653	−	0.990341i	$-0.455723\pi$
$181$	3.73078	0.277307	0.138653	+	0.990341i	$0.455723\pi$
$182$	−4.03396	−0.299017
$183$	27.6471	2.04373
$184$	3.83481	0.282706
$185$	−3.35671	−0.246790
$186$	0.904539	0.0663240
$187$	1.39767	0.102208
$188$	10.8022	0.787829
$189$	−38.8308	−2.82452
$190$	4.13140	0.299723
$191$	1.11021	0.0803323	0.0401662	−	0.999193i	$-0.487211\pi$
$191$	1.11021	0.0803323	0.0401662	+	0.999193i	$0.487211\pi$
$192$	3.01577	0.217644
$193$	−0.308152	−0.0221813	−0.0110906	−	0.999938i	$-0.503530\pi$
$193$	−0.308152	−0.0221813	−0.0110906	+	0.999938i	$0.503530\pi$
$194$	−13.9999	−1.00513
$195$	2.92408	0.209398
$196$	10.3093	0.736381
$197$	−10.7639	−0.766897	−0.383449	−	0.923562i	$-0.625264\pi$
$197$	−10.7639	−0.766897	−0.383449	+	0.923562i	$0.625264\pi$
$198$	−6.09484	−0.433142
$199$	9.58888	0.679737	0.339869	−	0.940473i	$-0.389617\pi$
$199$	9.58888	0.679737	0.339869	+	0.940473i	$0.389617\pi$
$200$	−1.00000	−0.0707107
$201$	7.41387	0.522934
$202$	−5.40782	−0.380493
$203$	14.7481	1.03511
$204$	4.21504	0.295112
$205$	−0.0682677	−0.00476802
$206$	5.70244	0.397308
$207$	−23.3726	−1.62450
$208$	−0.969598	−0.0672295
$209$	4.13140	0.285775
$210$	−12.5469	−0.865821
$211$	20.1978	1.39047	0.695236	−	0.718781i	$-0.255300\pi$
$211$	20.1978	1.39047	0.695236	+	0.718781i	$0.255300\pi$
$212$	4.48604	0.308103
$213$	12.7637	0.874556
$214$	5.59518	0.382479
$215$	1.00000	0.0681994
$216$	−9.33332	−0.635052
$217$	1.24787	0.0847110
$218$	6.40781	0.433992
$219$	7.91973	0.535166
$220$	−1.00000	−0.0674200
$221$	−1.35518	−0.0911590
$222$	−10.1230	−0.679414
$223$	7.03064	0.470806	0.235403	−	0.971898i	$-0.424359\pi$
$223$	7.03064	0.470806	0.235403	+	0.971898i	$0.424359\pi$
$224$	4.16045	0.277982
$225$	6.09484	0.406323
$226$	16.0752	1.06931
$227$	13.2412	0.878851	0.439426	−	0.898279i	$-0.355182\pi$
$227$	13.2412	0.878851	0.439426	+	0.898279i	$0.355182\pi$
$228$	12.4593	0.825140
$229$	18.6685	1.23365	0.616825	−	0.787100i	$-0.288419\pi$
$229$	18.6685	1.23365	0.616825	+	0.787100i	$0.288419\pi$
$230$	−3.83481	−0.252860
$231$	−12.5469	−0.825528
$232$	3.54482	0.232729
$233$	1.47505	0.0966338	0.0483169	−	0.998832i	$-0.484614\pi$
$233$	1.47505	0.0966338	0.0483169	+	0.998832i	$0.484614\pi$
$234$	5.90955	0.386319
$235$	−10.8022	−0.704656
$236$	10.9299	0.711476
$237$	11.1494	0.724229
$238$	5.81492	0.376925
$239$	9.27014	0.599636	0.299818	−	0.953996i	$-0.403074\pi$
$239$	9.27014	0.599636	0.299818	+	0.953996i	$0.403074\pi$
$240$	−3.01577	−0.194667
$241$	−5.50283	−0.354469	−0.177234	−	0.984169i	$-0.556715\pi$
$241$	−5.50283	−0.354469	−0.177234	+	0.984169i	$0.556715\pi$
$242$	−1.00000	−0.0642824
$243$	1.74327	0.111831
$244$	9.16751	0.586889
$245$	−10.3093	−0.658639
$246$	−0.205879	−0.0131264
$247$	−4.00580	−0.254883
$248$	0.299937	0.0190460
$249$	−7.76689	−0.492207
$250$	1.00000	0.0632456
$251$	10.3039	0.650374	0.325187	−	0.945650i	$-0.394573\pi$
$251$	10.3039	0.650374	0.325187	+	0.945650i	$0.394573\pi$
$252$	−25.3573	−1.59736
$253$	−3.83481	−0.241092
$254$	10.3994	0.652516
$255$	−4.21504	−0.263956
$256$	1.00000	0.0625000
$257$	17.6110	1.09854	0.549272	−	0.835644i	$-0.314905\pi$
$257$	17.6110	1.09854	0.549272	+	0.835644i	$0.314905\pi$
$258$	3.01577	0.187753
$259$	−13.9654	−0.867768
$260$	0.969598	0.0601319
$261$	−21.6051	−1.33733
$262$	−13.0346	−0.805281
$263$	9.94643	0.613323	0.306662	−	0.951819i	$-0.400788\pi$
$263$	9.94643	0.613323	0.306662	+	0.951819i	$0.400788\pi$
$264$	−3.01577	−0.185608
$265$	−4.48604	−0.275575
$266$	17.1885	1.05389
$267$	28.8337	1.76459
$268$	2.45837	0.150169
$269$	13.5269	0.824750	0.412375	−	0.911014i	$-0.364699\pi$
$269$	13.5269	0.824750	0.412375	+	0.911014i	$0.364699\pi$
$270$	9.33332	0.568008
$271$	11.7607	0.714409	0.357204	−	0.934026i	$-0.383730\pi$
$271$	11.7607	0.714409	0.357204	+	0.934026i	$0.383730\pi$
$272$	1.39767	0.0847460
$273$	12.1655	0.736289
$274$	−10.3677	−0.626338
$275$	1.00000	0.0603023
$276$	−11.5649	−0.696124
$277$	1.61331	0.0969341	0.0484671	−	0.998825i	$-0.484566\pi$
$277$	1.61331	0.0969341	0.0484671	+	0.998825i	$0.484566\pi$
$278$	2.91272	0.174693
$279$	−1.82807	−0.109443
$280$	−4.16045	−0.248634
$281$	−25.6898	−1.53253	−0.766263	−	0.642527i	$-0.777886\pi$
$281$	−25.6898	−1.53253	−0.766263	+	0.642527i	$0.777886\pi$
$282$	−32.5768	−1.93992
$283$	3.17076	0.188482	0.0942411	−	0.995549i	$-0.469958\pi$
$283$	3.17076	0.188482	0.0942411	+	0.995549i	$0.469958\pi$
$284$	4.23234	0.251143
$285$	−12.4593	−0.738028
$286$	0.969598	0.0573335
$287$	−0.284024	−0.0167654
$288$	−6.09484	−0.359142
$289$	−15.0465	−0.885090
$290$	−3.54482	−0.208159
$291$	42.2204	2.47500
$292$	2.62611	0.153681
$293$	−27.9345	−1.63195	−0.815976	−	0.578085i	$-0.803800\pi$
$293$	−27.9345	−1.63195	−0.815976	+	0.578085i	$0.803800\pi$
$294$	−31.0905	−1.81324
$295$	−10.9299	−0.636364
$296$	−3.35671	−0.195105
$297$	9.33332	0.541574
$298$	−12.2913	−0.712013
$299$	3.71822	0.215030
$300$	3.01577	0.174115
$301$	4.16045	0.239804
$302$	−8.74373	−0.503145
$303$	16.3087	0.936911
$304$	4.13140	0.236952
$305$	−9.16751	−0.524930
$306$	−8.51856	−0.486974
$307$	−1.86969	−0.106709	−0.0533544	−	0.998576i	$-0.516991\pi$
$307$	−1.86969	−0.106709	−0.0533544	+	0.998576i	$0.516991\pi$
$308$	−4.16045	−0.237064
$309$	−17.1972	−0.978316
$310$	−0.299937	−0.0170353
$311$	−5.04072	−0.285833	−0.142916	−	0.989735i	$-0.545648\pi$
$311$	−5.04072	−0.285833	−0.142916	+	0.989735i	$0.545648\pi$
$312$	2.92408	0.165544
$313$	24.5485	1.38756	0.693781	−	0.720186i	$-0.255944\pi$
$313$	24.5485	1.38756	0.693781	+	0.720186i	$0.255944\pi$
$314$	4.50911	0.254464
$315$	25.3573	1.42872
$316$	3.69703	0.207974
$317$	−28.1083	−1.57872	−0.789360	−	0.613931i	$-0.789587\pi$
$317$	−28.1083	−1.57872	−0.789360	+	0.613931i	$0.789587\pi$
$318$	−13.5289	−0.758661
$319$	−3.54482	−0.198472
$320$	−1.00000	−0.0559017
$321$	−16.8738	−0.941801
$322$	−15.9545	−0.889111
$323$	5.77433	0.321292
$324$	9.86258	0.547921
$325$	−0.969598	−0.0537836
$326$	−19.5471	−1.08261
$327$	−19.3244	−1.06864
$328$	−0.0682677	−0.00376945
$329$	−44.9419	−2.47773
$330$	3.01577	0.166012
$331$	13.9751	0.768142	0.384071	−	0.923304i	$-0.374522\pi$
$331$	13.9751	0.768142	0.384071	+	0.923304i	$0.374522\pi$
$332$	−2.57543	−0.141345
$333$	20.4586	1.12112
$334$	6.43628	0.352177
$335$	−2.45837	−0.134315
$336$	−12.5469	−0.684492
$337$	20.6043	1.12239	0.561195	−	0.827684i	$-0.310342\pi$
$337$	20.6043	1.12239	0.561195	+	0.827684i	$0.310342\pi$
$338$	12.0599	0.655971
$339$	−48.4792	−2.63303
$340$	−1.39767	−0.0757992
$341$	−0.299937	−0.0162425
$342$	−25.1803	−1.36159
$343$	−13.7683	−0.743418
$344$	1.00000	0.0539164
$345$	11.5649	0.622632
$346$	9.94712	0.534761
$347$	−20.9511	−1.12471	−0.562356	−	0.826895i	$-0.690105\pi$
$347$	−20.9511	−1.12471	−0.562356	+	0.826895i	$0.690105\pi$
$348$	−10.6904	−0.573063
$349$	1.46715	0.0785347	0.0392674	−	0.999229i	$-0.487498\pi$
$349$	1.46715	0.0785347	0.0392674	+	0.999229i	$0.487498\pi$
$350$	4.16045	0.222385
$351$	−9.04957	−0.483030
$352$	−1.00000	−0.0533002
$353$	−11.4508	−0.609463	−0.304731	−	0.952438i	$-0.598567\pi$
$353$	−11.4508	−0.609463	−0.304731	+	0.952438i	$0.598567\pi$
$354$	−32.9620	−1.75191
$355$	−4.23234	−0.224629
$356$	9.56098	0.506731
$357$	−17.5364	−0.928127
$358$	21.6591	1.14472
$359$	16.7416	0.883587	0.441794	−	0.897117i	$-0.354342\pi$
$359$	16.7416	0.883587	0.441794	+	0.897117i	$0.354342\pi$
$360$	6.09484	0.321226
$361$	−1.93151	−0.101658
$362$	−3.73078	−0.196085
$363$	3.01577	0.158287
$364$	4.03396	0.211437
$365$	−2.62611	−0.137457
$366$	−27.6471	−1.44513
$367$	−13.8394	−0.722410	−0.361205	−	0.932486i	$-0.617635\pi$
$367$	−13.8394	−0.722410	−0.361205	+	0.932486i	$0.617635\pi$
$368$	−3.83481	−0.199903
$369$	0.416081	0.0216603
$370$	3.35671	0.174507
$371$	−18.6640	−0.968984
$372$	−0.904539	−0.0468981
$373$	−2.22418	−0.115163	−0.0575817	−	0.998341i	$-0.518339\pi$
$373$	−2.22418	−0.115163	−0.0575817	+	0.998341i	$0.518339\pi$
$374$	−1.39767	−0.0722717
$375$	−3.01577	−0.155733
$376$	−10.8022	−0.557079
$377$	3.43706	0.177017
$378$	38.8308	1.99724
$379$	−32.5986	−1.67448	−0.837239	−	0.546837i	$-0.815832\pi$
$379$	−32.5986	−1.67448	−0.837239	+	0.546837i	$0.815832\pi$
$380$	−4.13140	−0.211936
$381$	−31.3621	−1.60673
$382$	−1.11021	−0.0568035
$383$	−14.4827	−0.740032	−0.370016	−	0.929025i	$-0.620648\pi$
$383$	−14.4827	−0.740032	−0.370016	+	0.929025i	$0.620648\pi$
$384$	−3.01577	−0.153898
$385$	4.16045	0.212036
$386$	0.308152	0.0156845
$387$	−6.09484	−0.309818
$388$	13.9999	0.710737
$389$	2.74052	0.138950	0.0694750	−	0.997584i	$-0.477868\pi$
$389$	2.74052	0.138950	0.0694750	+	0.997584i	$0.477868\pi$
$390$	−2.92408	−0.148067
$391$	−5.35979	−0.271056
$392$	−10.3093	−0.520700
$393$	39.3093	1.98289
$394$	10.7639	0.542278
$395$	−3.69703	−0.186018
$396$	6.09484	0.306277
$397$	13.6671	0.685931	0.342966	−	0.939348i	$-0.388569\pi$
$397$	13.6671	0.685931	0.342966	+	0.939348i	$0.388569\pi$
$398$	−9.58888	−0.480647
$399$	−51.8365	−2.59507
$400$	1.00000	0.0500000
$401$	2.25366	0.112543	0.0562713	−	0.998416i	$-0.482079\pi$
$401$	2.25366	0.112543	0.0562713	+	0.998416i	$0.482079\pi$
$402$	−7.41387	−0.369770
$403$	0.290818	0.0144867
$404$	5.40782	0.269049
$405$	−9.86258	−0.490076
$406$	−14.7481	−0.731934
$407$	3.35671	0.166386
$408$	−4.21504	−0.208675
$409$	−24.2131	−1.19726	−0.598630	−	0.801025i	$-0.704288\pi$
$409$	−24.2131	−1.19726	−0.598630	+	0.801025i	$0.704288\pi$
$410$	0.0682677	0.00337150
$411$	31.2666	1.54227
$412$	−5.70244	−0.280939
$413$	−45.4733	−2.23760
$414$	23.3726	1.14870
$415$	2.57543	0.126423
$416$	0.969598	0.0475385
$417$	−8.78408	−0.430158
$418$	−4.13140	−0.202074
$419$	9.83853	0.480644	0.240322	−	0.970693i	$-0.422747\pi$
$419$	9.83853	0.480644	0.240322	+	0.970693i	$0.422747\pi$
$420$	12.5469	0.612228
$421$	−32.9433	−1.60556	−0.802780	−	0.596275i	$-0.796647\pi$
$421$	−32.9433	−1.60556	−0.802780	+	0.596275i	$0.796647\pi$
$422$	−20.1978	−0.983212
$423$	65.8375	3.20113
$424$	−4.48604	−0.217862
$425$	1.39767	0.0677968
$426$	−12.7637	−0.618405
$427$	−38.1409	−1.84577
$428$	−5.59518	−0.270453
$429$	−2.92408	−0.141176
$430$	−1.00000	−0.0482243
$431$	4.95464	0.238657	0.119328	−	0.992855i	$-0.461926\pi$
$431$	4.95464	0.238657	0.119328	+	0.992855i	$0.461926\pi$
$432$	9.33332	0.449050
$433$	25.1634	1.20928	0.604638	−	0.796500i	$-0.293318\pi$
$433$	25.1634	1.20928	0.604638	+	0.796500i	$0.293318\pi$
$434$	−1.24787	−0.0598997
$435$	10.6904	0.512564
$436$	−6.40781	−0.306878
$437$	−15.8431	−0.757880
$438$	−7.91973	−0.378419
$439$	−24.6473	−1.17635	−0.588177	−	0.808732i	$-0.700154\pi$
$439$	−24.6473	−1.17635	−0.588177	+	0.808732i	$0.700154\pi$
$440$	1.00000	0.0476731
$441$	62.8337	2.99208
$442$	1.35518	0.0644592
$443$	−4.36972	−0.207612	−0.103806	−	0.994598i	$-0.533102\pi$
$443$	−4.36972	−0.207612	−0.103806	+	0.994598i	$0.533102\pi$
$444$	10.1230	0.480418
$445$	−9.56098	−0.453234
$446$	−7.03064	−0.332910
$447$	37.0675	1.75323
$448$	−4.16045	−0.196563
$449$	13.3900	0.631913	0.315956	−	0.948774i	$-0.397675\pi$
$449$	13.3900	0.631913	0.315956	+	0.948774i	$0.397675\pi$
$450$	−6.09484	−0.287314
$451$	0.0682677	0.00321460
$452$	−16.0752	−0.756116
$453$	26.3690	1.23893
$454$	−13.2412	−0.621442
$455$	−4.03396	−0.189115
$456$	−12.4593	−0.583462
$457$	−19.2007	−0.898169	−0.449084	−	0.893489i	$-0.648250\pi$
$457$	−19.2007	−0.898169	−0.449084	+	0.893489i	$0.648250\pi$
$458$	−18.6685	−0.872323
$459$	13.0449	0.608883
$460$	3.83481	0.178799
$461$	37.3739	1.74068	0.870339	−	0.492453i	$-0.163900\pi$
$461$	37.3739	1.74068	0.870339	+	0.492453i	$0.163900\pi$
$462$	12.5469	0.583736
$463$	−2.53427	−0.117778	−0.0588888	−	0.998265i	$-0.518756\pi$
$463$	−2.53427	−0.117778	−0.0588888	+	0.998265i	$0.518756\pi$
$464$	−3.54482	−0.164564
$465$	0.904539	0.0419470
$466$	−1.47505	−0.0683304
$467$	35.0679	1.62275	0.811374	−	0.584528i	$-0.198720\pi$
$467$	35.0679	1.62275	0.811374	+	0.584528i	$0.198720\pi$
$468$	−5.90955	−0.273169
$469$	−10.2279	−0.472282
$470$	10.8022	0.498267
$471$	−13.5984	−0.626582
$472$	−10.9299	−0.503090
$473$	−1.00000	−0.0459800
$474$	−11.1494	−0.512107
$475$	4.13140	0.189562
$476$	−5.81492	−0.266527
$477$	27.3417	1.25189
$478$	−9.27014	−0.424006
$479$	−21.2750	−0.972077	−0.486039	−	0.873937i	$-0.661559\pi$
$479$	−21.2750	−0.972077	−0.486039	+	0.873937i	$0.661559\pi$
$480$	3.01577	0.137650
$481$	−3.25466	−0.148400
$482$	5.50283	0.250647
$483$	48.1151	2.18931
$484$	1.00000	0.0454545
$485$	−13.9999	−0.635703
$486$	−1.74327	−0.0790762
$487$	41.0650	1.86083	0.930417	−	0.366504i	$-0.119445\pi$
$487$	41.0650	1.86083	0.930417	+	0.366504i	$0.119445\pi$
$488$	−9.16751	−0.414994
$489$	58.9494	2.66578
$490$	10.3093	0.465728
$491$	29.3669	1.32531	0.662655	−	0.748925i	$-0.269429\pi$
$491$	29.3669	1.32531	0.662655	+	0.748925i	$0.269429\pi$
$492$	0.205879	0.00928176
$493$	−4.95449	−0.223139
$494$	4.00580	0.180230
$495$	−6.09484	−0.273943
$496$	−0.299937	−0.0134676
$497$	−17.6084	−0.789845
$498$	7.76689	0.348043
$499$	16.8729	0.755335	0.377668	−	0.925941i	$-0.376726\pi$
$499$	16.8729	0.755335	0.377668	+	0.925941i	$0.376726\pi$
$500$	−1.00000	−0.0447214
$501$	−19.4103	−0.867189
$502$	−10.3039	−0.459884
$503$	−14.9126	−0.664919	−0.332459	−	0.943118i	$-0.607878\pi$
$503$	−14.9126	−0.664919	−0.332459	+	0.943118i	$0.607878\pi$
$504$	25.3573	1.12950
$505$	−5.40782	−0.240645
$506$	3.83481	0.170478
$507$	−36.3698	−1.61524
$508$	−10.3994	−0.461399
$509$	−15.5860	−0.690836	−0.345418	−	0.938449i	$-0.612263\pi$
$509$	−15.5860	−0.690836	−0.345418	+	0.938449i	$0.612263\pi$
$510$	4.21504	0.186645
$511$	−10.9258	−0.483329
$512$	−1.00000	−0.0441942
$513$	38.5597	1.70245
$514$	−17.6110	−0.776788
$515$	5.70244	0.251280
$516$	−3.01577	−0.132762
$517$	10.8022	0.475079
$518$	13.9654	0.613605
$519$	−29.9982	−1.31677
$520$	−0.969598	−0.0425197
$521$	−31.3165	−1.37200	−0.686000	−	0.727601i	$-0.740635\pi$
$521$	−31.3165	−1.37200	−0.686000	+	0.727601i	$0.740635\pi$
$522$	21.6051	0.945632
$523$	−33.8977	−1.48224	−0.741121	−	0.671372i	$-0.765705\pi$
$523$	−33.8977	−1.48224	−0.741121	+	0.671372i	$0.765705\pi$
$524$	13.0346	0.569420
$525$	−12.5469	−0.547593
$526$	−9.94643	−0.433685
$527$	−0.419212	−0.0182611
$528$	3.01577	0.131244
$529$	−8.29425	−0.360620
$530$	4.48604	0.194861
$531$	66.6161	2.89089
$532$	−17.1885	−0.745215
$533$	−0.0661922	−0.00286710
$534$	−28.8337	−1.24776
$535$	5.59518	0.241901
$536$	−2.45837	−0.106186
$537$	−65.3187	−2.81871
$538$	−13.5269	−0.583186
$539$	10.3093	0.444054
$540$	−9.33332	−0.401642
$541$	25.6722	1.10374	0.551868	−	0.833932i	$-0.313915\pi$
$541$	25.6722	1.10374	0.551868	+	0.833932i	$0.313915\pi$
$542$	−11.7607	−0.505163
$543$	11.2512	0.482833
$544$	−1.39767	−0.0599245
$545$	6.40781	0.274480
$546$	−12.1655	−0.520635
$547$	19.5926	0.837720	0.418860	−	0.908051i	$-0.362430\pi$
$547$	19.5926	0.837720	0.418860	+	0.908051i	$0.362430\pi$
$548$	10.3677	0.442888
$549$	55.8745	2.38467
$550$	−1.00000	−0.0426401
$551$	−14.6451	−0.623902
$552$	11.5649	0.492234
$553$	−15.3813	−0.654079
$554$	−1.61331	−0.0685428
$555$	−10.1230	−0.429699
$556$	−2.91272	−0.123527
$557$	−25.9476	−1.09943	−0.549717	−	0.835351i	$-0.685264\pi$
$557$	−25.9476	−1.09943	−0.549717	+	0.835351i	$0.685264\pi$
$558$	1.82807	0.0773882
$559$	0.969598	0.0410096
$560$	4.16045	0.175811
$561$	4.21504	0.177959
$562$	25.6898	1.08366
$563$	−5.35203	−0.225561	−0.112781	−	0.993620i	$-0.535976\pi$
$563$	−5.35203	−0.225561	−0.112781	+	0.993620i	$0.535976\pi$
$564$	32.5768	1.37173
$565$	16.0752	0.676290
$566$	−3.17076	−0.133277
$567$	−41.0328	−1.72321
$568$	−4.23234	−0.177585
$569$	14.6247	0.613100	0.306550	−	0.951854i	$-0.400825\pi$
$569$	14.6247	0.613100	0.306550	+	0.951854i	$0.400825\pi$
$570$	12.4593	0.521864
$571$	−11.5957	−0.485265	−0.242633	−	0.970118i	$-0.578011\pi$
$571$	−11.5957	−0.485265	−0.242633	+	0.970118i	$0.578011\pi$
$572$	−0.969598	−0.0405409
$573$	3.34815	0.139871
$574$	0.284024	0.0118549
$575$	−3.83481	−0.159923
$576$	6.09484	0.253952
$577$	41.0762	1.71002	0.855012	−	0.518608i	$-0.173549\pi$
$577$	41.0762	1.71002	0.855012	+	0.518608i	$0.173549\pi$
$578$	15.0465	0.625853
$579$	−0.929315	−0.0386210
$580$	3.54482	0.147191
$581$	10.7149	0.444531
$582$	−42.2204	−1.75009
$583$	4.48604	0.185793
$584$	−2.62611	−0.108669
$585$	5.90955	0.244330
$586$	27.9345	1.15396
$587$	2.38218	0.0983230	0.0491615	−	0.998791i	$-0.484345\pi$
$587$	2.38218	0.0983230	0.0491615	+	0.998791i	$0.484345\pi$
$588$	31.0905	1.28215
$589$	−1.23916	−0.0510587
$590$	10.9299	0.449977
$591$	−32.4615	−1.33529
$592$	3.35671	0.137960
$593$	15.2599	0.626649	0.313324	−	0.949646i	$-0.398557\pi$
$593$	15.2599	0.626649	0.313324	+	0.949646i	$0.398557\pi$
$594$	−9.33332	−0.382951
$595$	5.81492	0.238389
$596$	12.2913	0.503469
$597$	28.9178	1.18353
$598$	−3.71822	−0.152049
$599$	−24.4664	−0.999668	−0.499834	−	0.866121i	$-0.666606\pi$
$599$	−24.4664	−0.999668	−0.499834	+	0.866121i	$0.666606\pi$
$600$	−3.01577	−0.123118
$601$	44.8737	1.83044	0.915218	−	0.402960i	$-0.132019\pi$
$601$	44.8737	1.83044	0.915218	+	0.402960i	$0.132019\pi$
$602$	−4.16045	−0.169567
$603$	14.9834	0.610171
$604$	8.74373	0.355777
$605$	−1.00000	−0.0406558
$606$	−16.3087	−0.662496
$607$	22.2795	0.904299	0.452149	−	0.891942i	$-0.350657\pi$
$607$	22.2795	0.904299	0.452149	+	0.891942i	$0.350657\pi$
$608$	−4.13140	−0.167551
$609$	44.4767	1.80229
$610$	9.16751	0.371181
$611$	−10.4738	−0.423723
$612$	8.51856	0.344343
$613$	29.0772	1.17442	0.587209	−	0.809435i	$-0.300227\pi$
$613$	29.0772	1.17442	0.587209	+	0.809435i	$0.300227\pi$
$614$	1.86969	0.0754545
$615$	−0.205879	−0.00830186
$616$	4.16045	0.167629
$617$	−46.0738	−1.85486	−0.927431	−	0.373994i	$-0.877988\pi$
$617$	−46.0738	−1.85486	−0.927431	+	0.373994i	$0.877988\pi$
$618$	17.1972	0.691774
$619$	−5.06413	−0.203544	−0.101772	−	0.994808i	$-0.532451\pi$
$619$	−5.06413	−0.203544	−0.101772	+	0.994808i	$0.532451\pi$
$620$	0.299937	0.0120457
$621$	−35.7915	−1.43626
$622$	5.04072	0.202114
$623$	−39.7780	−1.59367
$624$	−2.92408	−0.117057
$625$	1.00000	0.0400000
$626$	−24.5485	−0.981155
$627$	12.4593	0.497578
$628$	−4.50911	−0.179933
$629$	4.69156	0.187065
$630$	−25.3573	−1.01026
$631$	−18.0847	−0.719940	−0.359970	−	0.932964i	$-0.617213\pi$
$631$	−18.0847	−0.719940	−0.359970	+	0.932964i	$0.617213\pi$
$632$	−3.69703	−0.147060
$633$	60.9118	2.42103
$634$	28.1083	1.11632
$635$	10.3994	0.412687
$636$	13.5289	0.536454
$637$	−9.99591	−0.396052
$638$	3.54482	0.140341
$639$	25.7954	1.02045
$640$	1.00000	0.0395285
$641$	−24.7457	−0.977398	−0.488699	−	0.872452i	$-0.662528\pi$
$641$	−24.7457	−0.977398	−0.488699	+	0.872452i	$0.662528\pi$
$642$	16.8738	0.665954
$643$	−18.7532	−0.739554	−0.369777	−	0.929120i	$-0.620566\pi$
$643$	−18.7532	−0.739554	−0.369777	+	0.929120i	$0.620566\pi$
$644$	15.9545	0.628696
$645$	3.01577	0.118746
$646$	−5.77433	−0.227188
$647$	24.6252	0.968118	0.484059	−	0.875035i	$-0.339162\pi$
$647$	24.6252	0.968118	0.484059	+	0.875035i	$0.339162\pi$
$648$	−9.86258	−0.387439
$649$	10.9299	0.429036
$650$	0.969598	0.0380308
$651$	3.76329	0.147495
$652$	19.5471	0.765522
$653$	−38.1476	−1.49283	−0.746415	−	0.665481i	$-0.768227\pi$
$653$	−38.1476	−1.49283	−0.746415	+	0.665481i	$0.768227\pi$
$654$	19.3244	0.755646
$655$	−13.0346	−0.509304
$656$	0.0682677	0.00266541
$657$	16.0057	0.624443
$658$	44.9419	1.75202
$659$	−42.8639	−1.66974	−0.834870	−	0.550448i	$-0.814457\pi$
$659$	−42.8639	−1.66974	−0.834870	+	0.550448i	$0.814457\pi$
$660$	−3.01577	−0.117389
$661$	48.9659	1.90455	0.952276	−	0.305239i	$-0.0987365\pi$
$661$	48.9659	1.90455	0.952276	+	0.305239i	$0.0987365\pi$
$662$	−13.9751	−0.543158
$663$	−4.08689	−0.158722
$664$	2.57543	0.0999461
$665$	17.1885	0.666541
$666$	−20.4586	−0.792755
$667$	13.5937	0.526351
$668$	−6.43628	−0.249027
$669$	21.2028	0.819746
$670$	2.45837	0.0949752
$671$	9.16751	0.353908
$672$	12.5469	0.484009
$673$	−16.0005	−0.616772	−0.308386	−	0.951261i	$-0.599789\pi$
$673$	−16.0005	−0.616772	−0.308386	+	0.951261i	$0.599789\pi$
$674$	−20.6043	−0.793649
$675$	9.33332	0.359240
$676$	−12.0599	−0.463842
$677$	8.66280	0.332939	0.166469	−	0.986047i	$-0.446763\pi$
$677$	8.66280	0.332939	0.166469	+	0.986047i	$0.446763\pi$
$678$	48.4792	1.86183
$679$	−58.2459	−2.23527
$680$	1.39767	0.0535981
$681$	39.9324	1.53021
$682$	0.299937	0.0114852
$683$	−25.5350	−0.977071	−0.488536	−	0.872544i	$-0.662469\pi$
$683$	−25.5350	−0.977071	−0.488536	+	0.872544i	$0.662469\pi$
$684$	25.1803	0.962791
$685$	−10.3677	−0.396131
$686$	13.7683	0.525676
$687$	56.2999	2.14797
$688$	−1.00000	−0.0381246
$689$	−4.34966	−0.165709
$690$	−11.5649	−0.440268
$691$	−27.0110	−1.02755	−0.513774	−	0.857925i	$-0.671753\pi$
$691$	−27.0110	−1.02755	−0.513774	+	0.857925i	$0.671753\pi$
$692$	−9.94712	−0.378133
$693$	−25.3573	−0.963243
$694$	20.9511	0.795292
$695$	2.91272	0.110486
$696$	10.6904	0.405217
$697$	0.0954155	0.00361412
$698$	−1.46715	−0.0555324
$699$	4.44841	0.168254
$700$	−4.16045	−0.157250
$701$	−30.5838	−1.15513	−0.577567	−	0.816343i	$-0.695998\pi$
$701$	−30.5838	−1.15513	−0.577567	+	0.816343i	$0.695998\pi$
$702$	9.04957	0.341554
$703$	13.8679	0.523038
$704$	1.00000	0.0376889
$705$	−32.5768	−1.22691
$706$	11.4508	0.430955
$707$	−22.4989	−0.846160
$708$	32.9620	1.23879
$709$	31.5218	1.18382	0.591912	−	0.806003i	$-0.298373\pi$
$709$	31.5218	1.18382	0.591912	+	0.806003i	$0.298373\pi$
$710$	4.23234	0.158837
$711$	22.5328	0.845046
$712$	−9.56098	−0.358313
$713$	1.15020	0.0430753
$714$	17.5364	0.656285
$715$	0.969598	0.0362609
$716$	−21.6591	−0.809438
$717$	27.9566	1.04406
$718$	−16.7416	−0.624791
$719$	−2.92660	−0.109144	−0.0545718	−	0.998510i	$-0.517379\pi$
$719$	−2.92660	−0.109144	−0.0545718	+	0.998510i	$0.517379\pi$
$720$	−6.09484	−0.227141
$721$	23.7247	0.883554
$722$	1.93151	0.0718833
$723$	−16.5953	−0.617184
$724$	3.73078	0.138653
$725$	−3.54482	−0.131651
$726$	−3.01577	−0.111926
$727$	−11.8575	−0.439771	−0.219885	−	0.975526i	$-0.570568\pi$
$727$	−11.8575	−0.439771	−0.219885	+	0.975526i	$0.570568\pi$
$728$	−4.03396	−0.149509
$729$	−24.3305	−0.901128
$730$	2.62611	0.0971967
$731$	−1.39767	−0.0516946
$732$	27.6471	1.02186
$733$	12.4075	0.458282	0.229141	−	0.973393i	$-0.426408\pi$
$733$	12.4075	0.458282	0.229141	+	0.973393i	$0.426408\pi$
$734$	13.8394	0.510821
$735$	−31.0905	−1.14679
$736$	3.83481	0.141353
$737$	2.45837	0.0905553
$738$	−0.416081	−0.0153161
$739$	−6.47141	−0.238055	−0.119027	−	0.992891i	$-0.537978\pi$
$739$	−6.47141	−0.238055	−0.119027	+	0.992891i	$0.537978\pi$
$740$	−3.35671	−0.123395
$741$	−12.0806	−0.443790
$742$	18.6640	0.685175
$743$	−39.0560	−1.43283	−0.716413	−	0.697676i	$-0.754217\pi$
$743$	−39.0560	−1.43283	−0.716413	+	0.697676i	$0.754217\pi$
$744$	0.904539	0.0331620
$745$	−12.2913	−0.450317
$746$	2.22418	0.0814329
$747$	−15.6968	−0.574317
$748$	1.39767	0.0511038
$749$	23.2785	0.850577
$750$	3.01577	0.110120
$751$	15.9117	0.580626	0.290313	−	0.956932i	$-0.406241\pi$
$751$	15.9117	0.580626	0.290313	+	0.956932i	$0.406241\pi$
$752$	10.8022	0.393915
$753$	31.0740	1.13240
$754$	−3.43706	−0.125170
$755$	−8.74373	−0.318217
$756$	−38.8308	−1.41226
$757$	−23.2497	−0.845025	−0.422513	−	0.906357i	$-0.638852\pi$
$757$	−23.2497	−0.845025	−0.422513	+	0.906357i	$0.638852\pi$
$758$	32.5986	1.18404
$759$	−11.5649	−0.419779
$760$	4.13140	0.149862
$761$	20.2067	0.732494	0.366247	−	0.930518i	$-0.380643\pi$
$761$	20.2067	0.732494	0.366247	+	0.930518i	$0.380643\pi$
$762$	31.3621	1.13613
$763$	26.6594	0.965134
$764$	1.11021	0.0401662
$765$	−8.51856	−0.307989
$766$	14.4827	0.523282
$767$	−10.5976	−0.382658
$768$	3.01577	0.108822
$769$	27.6357	0.996568	0.498284	−	0.867014i	$-0.333964\pi$
$769$	27.6357	0.996568	0.498284	+	0.867014i	$0.333964\pi$
$770$	−4.16045	−0.149932
$771$	53.1106	1.91273
$772$	−0.308152	−0.0110906
$773$	−50.2984	−1.80911	−0.904554	−	0.426359i	$-0.859796\pi$
$773$	−50.2984	−1.80911	−0.904554	+	0.426359i	$0.859796\pi$
$774$	6.09484	0.219075
$775$	−0.299937	−0.0107740
$776$	−13.9999	−0.502567
$777$	−42.1164	−1.51092
$778$	−2.74052	−0.0982526
$779$	0.282041	0.0101052
$780$	2.92408	0.104699
$781$	4.23234	0.151445
$782$	5.35979	0.191666
$783$	−33.0850	−1.18236
$784$	10.3093	0.368190
$785$	4.50911	0.160937
$786$	−39.3093	−1.40212
$787$	−19.6774	−0.701424	−0.350712	−	0.936483i	$-0.614060\pi$
$787$	−19.6774	−0.701424	−0.350712	+	0.936483i	$0.614060\pi$
$788$	−10.7639	−0.383449
$789$	29.9961	1.06789
$790$	3.69703	0.131534
$791$	66.8802	2.37799
$792$	−6.09484	−0.216571
$793$	−8.88880	−0.315650
$794$	−13.6671	−0.485027
$795$	−13.5289	−0.479819
$796$	9.58888	0.339869
$797$	−27.9230	−0.989082	−0.494541	−	0.869154i	$-0.664664\pi$
$797$	−27.9230	−0.989082	−0.494541	+	0.869154i	$0.664664\pi$
$798$	51.8365	1.83499
$799$	15.0978	0.534123
$800$	−1.00000	−0.0353553
$801$	58.2727	2.05896
$802$	−2.25366	−0.0795796
$803$	2.62611	0.0926734
$804$	7.41387	0.261467
$805$	−15.9545	−0.562323
$806$	−0.290818	−0.0102436
$807$	40.7940	1.43602
$808$	−5.40782	−0.190246
$809$	13.5120	0.475056	0.237528	−	0.971381i	$-0.423663\pi$
$809$	13.5120	0.475056	0.237528	+	0.971381i	$0.423663\pi$
$810$	9.86258	0.346536
$811$	28.2676	0.992609	0.496304	−	0.868149i	$-0.334690\pi$
$811$	28.2676	0.992609	0.496304	+	0.868149i	$0.334690\pi$
$812$	14.7481	0.517555
$813$	35.4674	1.24389
$814$	−3.35671	−0.117653
$815$	−19.5471	−0.684704
$816$	4.21504	0.147556
$817$	−4.13140	−0.144539
$818$	24.2131	0.846591
$819$	24.5864	0.859117
$820$	−0.0682677	−0.00238401
$821$	−45.6690	−1.59386	−0.796929	−	0.604073i	$-0.793544\pi$
$821$	−45.6690	−1.59386	−0.796929	+	0.604073i	$0.793544\pi$
$822$	−31.2666	−1.09055
$823$	18.6474	0.650006	0.325003	−	0.945713i	$-0.394635\pi$
$823$	18.6474	0.650006	0.325003	+	0.945713i	$0.394635\pi$
$824$	5.70244	0.198654
$825$	3.01577	0.104995
$826$	45.4733	1.58222
$827$	40.5365	1.40959	0.704796	−	0.709410i	$-0.251038\pi$
$827$	40.5365	1.40959	0.704796	+	0.709410i	$0.251038\pi$
$828$	−23.3726	−0.812252
$829$	−5.38633	−0.187075	−0.0935375	−	0.995616i	$-0.529817\pi$
$829$	−5.38633	−0.187075	−0.0935375	+	0.995616i	$0.529817\pi$
$830$	−2.57543	−0.0893945
$831$	4.86535	0.168777
$832$	−0.969598	−0.0336148
$833$	14.4090	0.499243
$834$	8.78408	0.304168
$835$	6.43628	0.222737
$836$	4.13140	0.142888
$837$	−2.79940	−0.0967616
$838$	−9.83853	−0.339866
$839$	21.1022	0.728528	0.364264	−	0.931296i	$-0.381321\pi$
$839$	21.1022	0.728528	0.364264	+	0.931296i	$0.381321\pi$
$840$	−12.5469	−0.432910
$841$	−16.4342	−0.566697
$842$	32.9433	1.13530
$843$	−77.4744	−2.66836
$844$	20.1978	0.695236
$845$	12.0599	0.414872
$846$	−65.8375	−2.26354
$847$	−4.16045	−0.142955
$848$	4.48604	0.154051
$849$	9.56228	0.328177
$850$	−1.39767	−0.0479396
$851$	−12.8723	−0.441258
$852$	12.7637	0.437278
$853$	−9.12391	−0.312397	−0.156198	−	0.987726i	$-0.549924\pi$
$853$	−9.12391	−0.312397	−0.156198	+	0.987726i	$0.549924\pi$
$854$	38.1409	1.30516
$855$	−25.1803	−0.861146
$856$	5.59518	0.191239
$857$	−3.07577	−0.105066	−0.0525331	−	0.998619i	$-0.516730\pi$
$857$	−3.07577	−0.105066	−0.0525331	+	0.998619i	$0.516730\pi$
$858$	2.92408	0.0998265
$859$	−9.41907	−0.321374	−0.160687	−	0.987005i	$-0.551371\pi$
$859$	−9.41907	−0.321374	−0.160687	+	0.987005i	$0.551371\pi$
$860$	1.00000	0.0340997
$861$	−0.856550	−0.0291912
$862$	−4.95464	−0.168756
$863$	22.6984	0.772663	0.386331	−	0.922360i	$-0.373742\pi$
$863$	22.6984	0.772663	0.386331	+	0.922360i	$0.373742\pi$
$864$	−9.33332	−0.317526
$865$	9.94712	0.338212
$866$	−25.1634	−0.855088
$867$	−45.3768	−1.54108
$868$	1.24787	0.0423555
$869$	3.69703	0.125413
$870$	−10.6904	−0.362437
$871$	−2.38363	−0.0807663
$872$	6.40781	0.216996
$873$	85.3272	2.88789
$874$	15.8431	0.535902
$875$	4.16045	0.140649
$876$	7.91973	0.267583
$877$	−11.8510	−0.400181	−0.200090	−	0.979777i	$-0.564124\pi$
$877$	−11.8510	−0.400181	−0.200090	+	0.979777i	$0.564124\pi$
$878$	24.6473	0.831808
$879$	−84.2440	−2.84148
$880$	−1.00000	−0.0337100
$881$	36.1088	1.21654	0.608269	−	0.793731i	$-0.291864\pi$
$881$	36.1088	1.21654	0.608269	+	0.793731i	$0.291864\pi$
$882$	−62.8337	−2.11572
$883$	20.7678	0.698892	0.349446	−	0.936956i	$-0.386370\pi$
$883$	20.7678	0.698892	0.349446	+	0.936956i	$0.386370\pi$
$884$	−1.35518	−0.0455795
$885$	−32.9620	−1.10801
$886$	4.36972	0.146804
$887$	−28.4854	−0.956445	−0.478223	−	0.878239i	$-0.658719\pi$
$887$	−28.4854	−0.956445	−0.478223	+	0.878239i	$0.658719\pi$
$888$	−10.1230	−0.339707
$889$	43.2661	1.45110
$890$	9.56098	0.320485
$891$	9.86258	0.330409
$892$	7.03064	0.235403
$893$	44.6281	1.49342
$894$	−37.0675	−1.23972
$895$	21.6591	0.723983
$896$	4.16045	0.138991
$897$	11.2133	0.374401
$898$	−13.3900	−0.446830
$899$	1.06322	0.0354605
$900$	6.09484	0.203161
$901$	6.27000	0.208884
$902$	−0.0682677	−0.00227307
$903$	12.5469	0.417536
$904$	16.0752	0.534654
$905$	−3.73078	−0.124015
$906$	−26.3690	−0.876053
$907$	36.6002	1.21529	0.607645	−	0.794209i	$-0.292114\pi$
$907$	36.6002	1.21529	0.607645	+	0.794209i	$0.292114\pi$
$908$	13.2412	0.439426
$909$	32.9598	1.09321
$910$	4.03396	0.133725
$911$	−58.8380	−1.94939	−0.974694	−	0.223542i	$-0.928238\pi$
$911$	−58.8380	−1.94939	−0.974694	+	0.223542i	$0.928238\pi$
$912$	12.4593	0.412570
$913$	−2.57543	−0.0852343
$914$	19.2007	0.635101
$915$	−27.6471	−0.913983
$916$	18.6685	0.616825
$917$	−54.2298	−1.79083
$918$	−13.0449	−0.430545
$919$	41.3354	1.36353	0.681765	−	0.731572i	$-0.261213\pi$
$919$	41.3354	1.36353	0.681765	+	0.731572i	$0.261213\pi$
$920$	−3.83481	−0.126430
$921$	−5.63854	−0.185796
$922$	−37.3739	−1.23085
$923$	−4.10366	−0.135074
$924$	−12.5469	−0.412764
$925$	3.35671	0.110368
$926$	2.53427	0.0832813
$927$	−34.7555	−1.14152
$928$	3.54482	0.116365
$929$	27.2519	0.894105	0.447052	−	0.894508i	$-0.352474\pi$
$929$	27.2519	0.894105	0.447052	+	0.894508i	$0.352474\pi$
$930$	−0.904539	−0.0296610
$931$	42.5920	1.39590
$932$	1.47505	0.0483169
$933$	−15.2016	−0.497679
$934$	−35.0679	−1.14746
$935$	−1.39767	−0.0457086
$936$	5.90955	0.193160
$937$	−42.3768	−1.38439	−0.692195	−	0.721710i	$-0.743356\pi$
$937$	−42.3768	−1.38439	−0.692195	+	0.721710i	$0.743356\pi$
$938$	10.2279	0.333954
$939$	74.0325	2.41596
$940$	−10.8022	−0.352328
$941$	−10.0898	−0.328918	−0.164459	−	0.986384i	$-0.552588\pi$
$941$	−10.0898	−0.328918	−0.164459	+	0.986384i	$0.552588\pi$
$942$	13.5984	0.443060
$943$	−0.261793	−0.00852517
$944$	10.9299	0.355738
$945$	38.8308	1.26317
$946$	1.00000	0.0325128
$947$	−41.4088	−1.34561	−0.672803	−	0.739821i	$-0.734910\pi$
$947$	−41.4088	−1.34561	−0.672803	+	0.739821i	$0.734910\pi$
$948$	11.1494	0.362115
$949$	−2.54627	−0.0826555
$950$	−4.13140	−0.134040
$951$	−84.7681	−2.74879
$952$	5.81492	0.188463
$953$	−21.5864	−0.699252	−0.349626	−	0.936889i	$-0.613691\pi$
$953$	−21.5864	−0.699252	−0.349626	+	0.936889i	$0.613691\pi$
$954$	−27.3417	−0.885221
$955$	−1.11021	−0.0359257
$956$	9.27014	0.299818
$957$	−10.6904	−0.345570
$958$	21.2750	0.687363
$959$	−43.1344	−1.39288
$960$	−3.01577	−0.0973334
$961$	−30.9100	−0.997098
$962$	3.25466	0.104934
$963$	−34.1018	−1.09891
$964$	−5.50283	−0.177234
$965$	0.308152	0.00991977
$966$	−48.1151	−1.54808
$967$	−31.4721	−1.01208	−0.506038	−	0.862511i	$-0.668890\pi$
$967$	−31.4721	−1.01208	−0.506038	+	0.862511i	$0.668890\pi$
$968$	−1.00000	−0.0321412
$969$	17.4140	0.559419
$970$	13.9999	0.449510
$971$	−20.2979	−0.651392	−0.325696	−	0.945475i	$-0.605599\pi$
$971$	−20.2979	−0.651392	−0.325696	+	0.945475i	$0.605599\pi$
$972$	1.74327	0.0559153
$973$	12.1182	0.388492
$974$	−41.0650	−1.31581
$975$	−2.92408	−0.0936455
$976$	9.16751	0.293445
$977$	−37.5288	−1.20065	−0.600327	−	0.799755i	$-0.704963\pi$
$977$	−37.5288	−1.20065	−0.600327	+	0.799755i	$0.704963\pi$
$978$	−58.9494	−1.88499
$979$	9.56098	0.305570
$980$	−10.3093	−0.329319
$981$	−39.0546	−1.24692
$982$	−29.3669	−0.937136
$983$	−17.2700	−0.550827	−0.275413	−	0.961326i	$-0.588815\pi$
$983$	−17.2700	−0.550827	−0.275413	+	0.961326i	$0.588815\pi$
$984$	−0.205879	−0.00656319
$985$	10.7639	0.342967
$986$	4.95449	0.157783
$987$	−135.534	−4.31410
$988$	−4.00580	−0.127442
$989$	3.83481	0.121940
$990$	6.09484	0.193707
$991$	−3.92900	−0.124809	−0.0624044	−	0.998051i	$-0.519877\pi$
$991$	−3.92900	−0.124809	−0.0624044	+	0.998051i	$0.519877\pi$
$992$	0.299937	0.00952300
$993$	42.1457	1.33745
$994$	17.6084	0.558505
$995$	−9.58888	−0.303988
$996$	−7.76689	−0.246103
$997$	16.5238	0.523314	0.261657	−	0.965161i	$-0.415731\pi$
$997$	16.5238	0.523314	0.261657	+	0.965161i	$0.415731\pi$
$998$	−16.8729	−0.534103
$999$	31.3292	0.991213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bc.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bc.1.11	✓	11	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.01577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.01577 q^{6} -4.16045 q^{7} -1.00000 q^{8} +6.09484 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.01577 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.01577 q^{6} -4.16045 q^{7} -1.00000 q^{8} +6.09484 q^{9} +1.00000 q^{10} +1.00000 q^{11} +3.01577 q^{12} -0.969598 q^{13} +4.16045 q^{14} -3.01577 q^{15} +1.00000 q^{16} +1.39767 q^{17} -6.09484 q^{18} +4.13140 q^{19} -1.00000 q^{20} -12.5469 q^{21} -1.00000 q^{22} -3.83481 q^{23} -3.01577 q^{24} +1.00000 q^{25} +0.969598 q^{26} +9.33332 q^{27} -4.16045 q^{28} -3.54482 q^{29} +3.01577 q^{30} -0.299937 q^{31} -1.00000 q^{32} +3.01577 q^{33} -1.39767 q^{34} +4.16045 q^{35} +6.09484 q^{36} +3.35671 q^{37} -4.13140 q^{38} -2.92408 q^{39} +1.00000 q^{40} +0.0682677 q^{41} +12.5469 q^{42} -1.00000 q^{43} +1.00000 q^{44} -6.09484 q^{45} +3.83481 q^{46} +10.8022 q^{47} +3.01577 q^{48} +10.3093 q^{49} -1.00000 q^{50} +4.21504 q^{51} -0.969598 q^{52} +4.48604 q^{53} -9.33332 q^{54} -1.00000 q^{55} +4.16045 q^{56} +12.4593 q^{57} +3.54482 q^{58} +10.9299 q^{59} -3.01577 q^{60} +9.16751 q^{61} +0.299937 q^{62} -25.3573 q^{63} +1.00000 q^{64} +0.969598 q^{65} -3.01577 q^{66} +2.45837 q^{67} +1.39767 q^{68} -11.5649 q^{69} -4.16045 q^{70} +4.23234 q^{71} -6.09484 q^{72} +2.62611 q^{73} -3.35671 q^{74} +3.01577 q^{75} +4.13140 q^{76} -4.16045 q^{77} +2.92408 q^{78} +3.69703 q^{79} -1.00000 q^{80} +9.86258 q^{81} -0.0682677 q^{82} -2.57543 q^{83} -12.5469 q^{84} -1.39767 q^{85} +1.00000 q^{86} -10.6904 q^{87} -1.00000 q^{88} +9.56098 q^{89} +6.09484 q^{90} +4.03396 q^{91} -3.83481 q^{92} -0.904539 q^{93} -10.8022 q^{94} -4.13140 q^{95} -3.01577 q^{96} +13.9999 q^{97} -10.3093 q^{98} +6.09484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * q^99

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