LMFDB - Embedded newform 3610.2.a.bi.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.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:	$28.8259951297$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 $ x^9 - 24x^7 - 6x^6 + 183x^5 + 78x^4 - 455x^3 - 168x^2 + 228*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$3.42897$ of defining polynomial
Character	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.42897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42897 q^{6} +1.86700 q^{7} -1.00000 q^{8} +8.75785 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.42897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42897 q^{6} +1.86700 q^{7} -1.00000 q^{8} +8.75785 q^{9} -1.00000 q^{10} -3.60509 q^{11} +3.42897 q^{12} -2.83690 q^{13} -1.86700 q^{14} +3.42897 q^{15} +1.00000 q^{16} +5.98879 q^{17} -8.75785 q^{18} +1.00000 q^{20} +6.40189 q^{21} +3.60509 q^{22} +5.08775 q^{23} -3.42897 q^{24} +1.00000 q^{25} +2.83690 q^{26} +19.7435 q^{27} +1.86700 q^{28} +1.17848 q^{29} -3.42897 q^{30} -5.19863 q^{31} -1.00000 q^{32} -12.3617 q^{33} -5.98879 q^{34} +1.86700 q^{35} +8.75785 q^{36} +3.35231 q^{37} -9.72766 q^{39} -1.00000 q^{40} -3.72571 q^{41} -6.40189 q^{42} +0.671759 q^{43} -3.60509 q^{44} +8.75785 q^{45} -5.08775 q^{46} -6.32252 q^{47} +3.42897 q^{48} -3.51431 q^{49} -1.00000 q^{50} +20.5354 q^{51} -2.83690 q^{52} +2.56159 q^{53} -19.7435 q^{54} -3.60509 q^{55} -1.86700 q^{56} -1.17848 q^{58} -4.76825 q^{59} +3.42897 q^{60} +8.23638 q^{61} +5.19863 q^{62} +16.3509 q^{63} +1.00000 q^{64} -2.83690 q^{65} +12.3617 q^{66} +7.96385 q^{67} +5.98879 q^{68} +17.4458 q^{69} -1.86700 q^{70} -1.92698 q^{71} -8.75785 q^{72} -5.01201 q^{73} -3.35231 q^{74} +3.42897 q^{75} -6.73070 q^{77} +9.72766 q^{78} -0.601185 q^{79} +1.00000 q^{80} +41.4264 q^{81} +3.72571 q^{82} -1.90282 q^{83} +6.40189 q^{84} +5.98879 q^{85} -0.671759 q^{86} +4.04099 q^{87} +3.60509 q^{88} +0.985918 q^{89} -8.75785 q^{90} -5.29650 q^{91} +5.08775 q^{92} -17.8260 q^{93} +6.32252 q^{94} -3.42897 q^{96} -0.187561 q^{97} +3.51431 q^{98} -31.5728 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * 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
$3$	3.42897	1.97972	0.989859	−	0.142053i	$-0.0453703\pi$
$3$	3.42897	1.97972	0.989859	+	0.142053i	$0.0453703\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.42897	−1.39987
$7$	1.86700	0.705660	0.352830	−	0.935688i	$-0.385219\pi$
$7$	1.86700	0.705660	0.352830	+	0.935688i	$0.385219\pi$
$8$	−1.00000	−0.353553
$9$	8.75785	2.91928
$10$	−1.00000	−0.316228
$11$	−3.60509	−1.08698	−0.543488	−	0.839417i	$-0.682896\pi$
$11$	−3.60509	−1.08698	−0.543488	+	0.839417i	$0.682896\pi$
$12$	3.42897	0.989859
$13$	−2.83690	−0.786816	−0.393408	−	0.919364i	$-0.628704\pi$
$13$	−2.83690	−0.786816	−0.393408	+	0.919364i	$0.628704\pi$
$14$	−1.86700	−0.498977
$15$	3.42897	0.885357
$16$	1.00000	0.250000
$17$	5.98879	1.45249	0.726247	−	0.687433i	$-0.241263\pi$
$17$	5.98879	1.45249	0.726247	+	0.687433i	$0.241263\pi$
$18$	−8.75785	−2.06425
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	6.40189	1.39701
$22$	3.60509	0.768607
$23$	5.08775	1.06087	0.530435	−	0.847726i	$-0.322029\pi$
$23$	5.08775	1.06087	0.530435	+	0.847726i	$0.322029\pi$
$24$	−3.42897	−0.699936
$25$	1.00000	0.200000
$26$	2.83690	0.556363
$27$	19.7435	3.79964
$28$	1.86700	0.352830
$29$	1.17848	0.218839	0.109419	−	0.993996i	$-0.465101\pi$
$29$	1.17848	0.218839	0.109419	+	0.993996i	$0.465101\pi$
$30$	−3.42897	−0.626042
$31$	−5.19863	−0.933702	−0.466851	−	0.884336i	$-0.654612\pi$
$31$	−5.19863	−0.933702	−0.466851	+	0.884336i	$0.654612\pi$
$32$	−1.00000	−0.176777
$33$	−12.3617	−2.15190
$34$	−5.98879	−1.02707
$35$	1.86700	0.315581
$36$	8.75785	1.45964
$37$	3.35231	0.551116	0.275558	−	0.961285i	$-0.411137\pi$
$37$	3.35231	0.551116	0.275558	+	0.961285i	$0.411137\pi$
$38$	0	0
$39$	−9.72766	−1.55767
$40$	−1.00000	−0.158114
$41$	−3.72571	−0.581859	−0.290929	−	0.956745i	$-0.593964\pi$
$41$	−3.72571	−0.581859	−0.290929	+	0.956745i	$0.593964\pi$
$42$	−6.40189	−0.987833
$43$	0.671759	0.102442	0.0512211	−	0.998687i	$-0.483689\pi$
$43$	0.671759	0.102442	0.0512211	+	0.998687i	$0.483689\pi$
$44$	−3.60509	−0.543488
$45$	8.75785	1.30554
$46$	−5.08775	−0.750148
$47$	−6.32252	−0.922234	−0.461117	−	0.887339i	$-0.652551\pi$
$47$	−6.32252	−0.922234	−0.461117	+	0.887339i	$0.652551\pi$
$48$	3.42897	0.494930
$49$	−3.51431	−0.502045
$50$	−1.00000	−0.141421
$51$	20.5354	2.87553
$52$	−2.83690	−0.393408
$53$	2.56159	0.351862	0.175931	−	0.984403i	$-0.443706\pi$
$53$	2.56159	0.351862	0.175931	+	0.984403i	$0.443706\pi$
$54$	−19.7435	−2.68675
$55$	−3.60509	−0.486110
$56$	−1.86700	−0.249488
$57$	0	0
$58$	−1.17848	−0.154743
$59$	−4.76825	−0.620774	−0.310387	−	0.950610i	$-0.600459\pi$
$59$	−4.76825	−0.620774	−0.310387	+	0.950610i	$0.600459\pi$
$60$	3.42897	0.442678
$61$	8.23638	1.05456	0.527280	−	0.849692i	$-0.323212\pi$
$61$	8.23638	1.05456	0.527280	+	0.849692i	$0.323212\pi$
$62$	5.19863	0.660227
$63$	16.3509	2.06002
$64$	1.00000	0.125000
$65$	−2.83690	−0.351875
$66$	12.3617	1.52163
$67$	7.96385	0.972939	0.486470	−	0.873697i	$-0.338284\pi$
$67$	7.96385	0.972939	0.486470	+	0.873697i	$0.338284\pi$
$68$	5.98879	0.726247
$69$	17.4458	2.10022
$70$	−1.86700	−0.223149
$71$	−1.92698	−0.228690	−0.114345	−	0.993441i	$-0.536477\pi$
$71$	−1.92698	−0.228690	−0.114345	+	0.993441i	$0.536477\pi$
$72$	−8.75785	−1.03212
$73$	−5.01201	−0.586611	−0.293305	−	0.956019i	$-0.594755\pi$
$73$	−5.01201	−0.586611	−0.293305	+	0.956019i	$0.594755\pi$
$74$	−3.35231	−0.389698
$75$	3.42897	0.395944
$76$	0	0
$77$	−6.73070	−0.767034
$78$	9.72766	1.10144
$79$	−0.601185	−0.0676386	−0.0338193	−	0.999428i	$-0.510767\pi$
$79$	−0.601185	−0.0676386	−0.0338193	+	0.999428i	$0.510767\pi$
$80$	1.00000	0.111803
$81$	41.4264	4.60293
$82$	3.72571	0.411436
$83$	−1.90282	−0.208861	−0.104431	−	0.994532i	$-0.533302\pi$
$83$	−1.90282	−0.208861	−0.104431	+	0.994532i	$0.533302\pi$
$84$	6.40189	0.698503
$85$	5.98879	0.649575
$86$	−0.671759	−0.0724376
$87$	4.04099	0.433239
$88$	3.60509	0.384304
$89$	0.985918	0.104507	0.0522535	−	0.998634i	$-0.483360\pi$
$89$	0.985918	0.104507	0.0522535	+	0.998634i	$0.483360\pi$
$90$	−8.75785	−0.923159
$91$	−5.29650	−0.555224
$92$	5.08775	0.530435
$93$	−17.8260	−1.84847
$94$	6.32252	0.652118
$95$	0	0
$96$	−3.42897	−0.349968
$97$	−0.187561	−0.0190440	−0.00952199	−	0.999955i	$-0.503031\pi$
$97$	−0.187561	−0.0190440	−0.00952199	+	0.999955i	$0.503031\pi$
$98$	3.51431	0.354999
$99$	−31.5728	−3.17319
$100$	1.00000	0.100000
$101$	−1.96030	−0.195057	−0.0975287	−	0.995233i	$-0.531094\pi$
$101$	−1.96030	−0.195057	−0.0975287	+	0.995233i	$0.531094\pi$
$102$	−20.5354	−2.03331
$103$	17.5040	1.72472	0.862359	−	0.506297i	$-0.168986\pi$
$103$	17.5040	1.72472	0.862359	+	0.506297i	$0.168986\pi$
$104$	2.83690	0.278181
$105$	6.40189	0.624760
$106$	−2.56159	−0.248804
$107$	10.5897	1.02375	0.511873	−	0.859061i	$-0.328952\pi$
$107$	10.5897	1.02375	0.511873	+	0.859061i	$0.328952\pi$
$108$	19.7435	1.89982
$109$	−13.8754	−1.32902	−0.664509	−	0.747280i	$-0.731359\pi$
$109$	−13.8754	−1.32902	−0.664509	+	0.747280i	$0.731359\pi$
$110$	3.60509	0.343732
$111$	11.4950	1.09105
$112$	1.86700	0.176415
$113$	−15.9357	−1.49911	−0.749553	−	0.661944i	$-0.769732\pi$
$113$	−15.9357	−1.49911	−0.749553	+	0.661944i	$0.769732\pi$
$114$	0	0
$115$	5.08775	0.474435
$116$	1.17848	0.109419
$117$	−24.8452	−2.29694
$118$	4.76825	0.438953
$119$	11.1811	1.02497
$120$	−3.42897	−0.313021
$121$	1.99666	0.181515
$122$	−8.23638	−0.745686
$123$	−12.7754	−1.15192
$124$	−5.19863	−0.466851
$125$	1.00000	0.0894427
$126$	−16.3509	−1.45665
$127$	−16.8140	−1.49200	−0.746001	−	0.665944i	$-0.768029\pi$
$127$	−16.8140	−1.49200	−0.746001	+	0.665944i	$0.768029\pi$
$128$	−1.00000	−0.0883883
$129$	2.30344	0.202807
$130$	2.83690	0.248813
$131$	6.51376	0.569110	0.284555	−	0.958660i	$-0.408154\pi$
$131$	6.51376	0.569110	0.284555	+	0.958660i	$0.408154\pi$
$132$	−12.3617	−1.07595
$133$	0	0
$134$	−7.96385	−0.687972
$135$	19.7435	1.69925
$136$	−5.98879	−0.513534
$137$	20.2461	1.72975	0.864873	−	0.501991i	$-0.167399\pi$
$137$	20.2461	1.72975	0.864873	+	0.501991i	$0.167399\pi$
$138$	−17.4458	−1.48508
$139$	3.98847	0.338298	0.169149	−	0.985591i	$-0.445898\pi$
$139$	3.98847	0.338298	0.169149	+	0.985591i	$0.445898\pi$
$140$	1.86700	0.157790
$141$	−21.6797	−1.82576
$142$	1.92698	0.161708
$143$	10.2273	0.855249
$144$	8.75785	0.729821
$145$	1.17848	0.0978678
$146$	5.01201	0.414796
$147$	−12.0505	−0.993907
$148$	3.35231	0.275558
$149$	5.63256	0.461437	0.230719	−	0.973021i	$-0.425892\pi$
$149$	5.63256	0.461437	0.230719	+	0.973021i	$0.425892\pi$
$150$	−3.42897	−0.279974
$151$	−1.23848	−0.100786	−0.0503932	−	0.998729i	$-0.516047\pi$
$151$	−1.23848	−0.100786	−0.0503932	+	0.998729i	$0.516047\pi$
$152$	0	0
$153$	52.4489	4.24024
$154$	6.73070	0.542375
$155$	−5.19863	−0.417564
$156$	−9.72766	−0.778836
$157$	−21.5073	−1.71647	−0.858235	−	0.513256i	$-0.828439\pi$
$157$	−21.5073	−1.71647	−0.858235	+	0.513256i	$0.828439\pi$
$158$	0.601185	0.0478277
$159$	8.78363	0.696587
$160$	−1.00000	−0.0790569
$161$	9.49883	0.748613
$162$	−41.4264	−3.25477
$163$	18.0210	1.41151	0.705757	−	0.708454i	$-0.250607\pi$
$163$	18.0210	1.41151	0.705757	+	0.708454i	$0.250607\pi$
$164$	−3.72571	−0.290929
$165$	−12.3617	−0.962361
$166$	1.90282	0.147687
$167$	−10.9088	−0.844152	−0.422076	−	0.906560i	$-0.638698\pi$
$167$	−10.9088	−0.844152	−0.422076	+	0.906560i	$0.638698\pi$
$168$	−6.40189	−0.493917
$169$	−4.95198	−0.380921
$170$	−5.98879	−0.459319
$171$	0	0
$172$	0.671759	0.0512211
$173$	0.145902	0.0110927	0.00554637	−	0.999985i	$-0.498235\pi$
$173$	0.145902	0.0110927	0.00554637	+	0.999985i	$0.498235\pi$
$174$	−4.04099	−0.306347
$175$	1.86700	0.141132
$176$	−3.60509	−0.271744
$177$	−16.3502	−1.22896
$178$	−0.985918	−0.0738977
$179$	5.69949	0.426000	0.213000	−	0.977052i	$-0.431677\pi$
$179$	5.69949	0.426000	0.213000	+	0.977052i	$0.431677\pi$
$180$	8.75785	0.652772
$181$	−18.5013	−1.37519	−0.687594	−	0.726096i	$-0.741333\pi$
$181$	−18.5013	−1.37519	−0.687594	+	0.726096i	$0.741333\pi$
$182$	5.29650	0.392603
$183$	28.2423	2.08773
$184$	−5.08775	−0.375074
$185$	3.35231	0.246466
$186$	17.8260	1.30706
$187$	−21.5901	−1.57883
$188$	−6.32252	−0.461117
$189$	36.8611	2.68125
$190$	0	0
$191$	18.8820	1.36626	0.683128	−	0.730298i	$-0.260619\pi$
$191$	18.8820	1.36626	0.683128	+	0.730298i	$0.260619\pi$
$192$	3.42897	0.247465
$193$	4.88366	0.351533	0.175767	−	0.984432i	$-0.443760\pi$
$193$	4.88366	0.351533	0.175767	+	0.984432i	$0.443760\pi$
$194$	0.187561	0.0134661
$195$	−9.72766	−0.696613
$196$	−3.51431	−0.251022
$197$	−3.51747	−0.250609	−0.125305	−	0.992118i	$-0.539991\pi$
$197$	−3.51747	−0.250609	−0.125305	+	0.992118i	$0.539991\pi$
$198$	31.5728	2.24378
$199$	−0.840516	−0.0595826	−0.0297913	−	0.999556i	$-0.509484\pi$
$199$	−0.840516	−0.0595826	−0.0297913	+	0.999556i	$0.509484\pi$
$200$	−1.00000	−0.0707107
$201$	27.3078	1.92615
$202$	1.96030	0.137926
$203$	2.20023	0.154426
$204$	20.5354	1.43777
$205$	−3.72571	−0.260215
$206$	−17.5040	−1.21956
$207$	44.5578	3.09698
$208$	−2.83690	−0.196704
$209$	0	0
$210$	−6.40189	−0.441772
$211$	−27.4095	−1.88695	−0.943474	−	0.331447i	$-0.892463\pi$
$211$	−27.4095	−1.88695	−0.943474	+	0.331447i	$0.892463\pi$
$212$	2.56159	0.175931
$213$	−6.60755	−0.452742
$214$	−10.5897	−0.723898
$215$	0.671759	0.0458136
$216$	−19.7435	−1.34338
$217$	−9.70585	−0.658876
$218$	13.8754	0.939757
$219$	−17.1860	−1.16132
$220$	−3.60509	−0.243055
$221$	−16.9896	−1.14285
$222$	−11.4950	−0.771491
$223$	−11.4351	−0.765754	−0.382877	−	0.923799i	$-0.625067\pi$
$223$	−11.4351	−0.765754	−0.382877	+	0.923799i	$0.625067\pi$
$224$	−1.86700	−0.124744
$225$	8.75785	0.583857
$226$	15.9357	1.06003
$227$	15.6154	1.03643	0.518214	−	0.855251i	$-0.326597\pi$
$227$	15.6154	1.03643	0.518214	+	0.855251i	$0.326597\pi$
$228$	0	0
$229$	5.50003	0.363452	0.181726	−	0.983349i	$-0.441832\pi$
$229$	5.50003	0.363452	0.181726	+	0.983349i	$0.441832\pi$
$230$	−5.08775	−0.335477
$231$	−23.0794	−1.51851
$232$	−1.17848	−0.0773713
$233$	−11.3286	−0.742162	−0.371081	−	0.928601i	$-0.621013\pi$
$233$	−11.3286	−0.742162	−0.371081	+	0.928601i	$0.621013\pi$
$234$	24.8452	1.62418
$235$	−6.32252	−0.412436
$236$	−4.76825	−0.310387
$237$	−2.06145	−0.133905
$238$	−11.1811	−0.724761
$239$	1.48334	0.0959493	0.0479747	−	0.998849i	$-0.484723\pi$
$239$	1.48334	0.0959493	0.0479747	+	0.998849i	$0.484723\pi$
$240$	3.42897	0.221339
$241$	−8.41913	−0.542324	−0.271162	−	0.962534i	$-0.587408\pi$
$241$	−8.41913	−0.542324	−0.271162	+	0.962534i	$0.587408\pi$
$242$	−1.99666	−0.128350
$243$	82.8195	5.31287
$244$	8.23638	0.527280
$245$	−3.51431	−0.224521
$246$	12.7754	0.814528
$247$	0	0
$248$	5.19863	0.330114
$249$	−6.52470	−0.413486
$250$	−1.00000	−0.0632456
$251$	11.0908	0.700044	0.350022	−	0.936741i	$-0.386174\pi$
$251$	11.0908	0.700044	0.350022	+	0.936741i	$0.386174\pi$
$252$	16.3509	1.03001
$253$	−18.3418	−1.15314
$254$	16.8140	1.05501
$255$	20.5354	1.28598
$256$	1.00000	0.0625000
$257$	11.4846	0.716390	0.358195	−	0.933647i	$-0.383392\pi$
$257$	11.4846	0.716390	0.358195	+	0.933647i	$0.383392\pi$
$258$	−2.30344	−0.143406
$259$	6.25875	0.388900
$260$	−2.83690	−0.175937
$261$	10.3210	0.638853
$262$	−6.51376	−0.402422
$263$	31.7383	1.95707	0.978533	−	0.206092i	$-0.0660746\pi$
$263$	31.7383	1.95707	0.978533	+	0.206092i	$0.0660746\pi$
$264$	12.3617	0.760813
$265$	2.56159	0.157357
$266$	0	0
$267$	3.38069	0.206895
$268$	7.96385	0.486470
$269$	−23.3579	−1.42416	−0.712079	−	0.702100i	$-0.752246\pi$
$269$	−23.3579	−1.42416	−0.712079	+	0.702100i	$0.752246\pi$
$270$	−19.7435	−1.20155
$271$	−22.0881	−1.34176	−0.670878	−	0.741567i	$-0.734083\pi$
$271$	−22.0881	−1.34176	−0.670878	+	0.741567i	$0.734083\pi$
$272$	5.98879	0.363124
$273$	−18.1615	−1.09919
$274$	−20.2461	−1.22311
$275$	−3.60509	−0.217395
$276$	17.4458	1.05011
$277$	−19.8124	−1.19041	−0.595207	−	0.803572i	$-0.702930\pi$
$277$	−19.8124	−1.19041	−0.595207	+	0.803572i	$0.702930\pi$
$278$	−3.98847	−0.239213
$279$	−45.5289	−2.72574
$280$	−1.86700	−0.111575
$281$	−21.1618	−1.26241	−0.631203	−	0.775617i	$-0.717439\pi$
$281$	−21.1618	−1.26241	−0.631203	+	0.775617i	$0.717439\pi$
$282$	21.6797	1.29101
$283$	−18.6499	−1.10862	−0.554310	−	0.832311i	$-0.687018\pi$
$283$	−18.6499	−1.10862	−0.554310	+	0.832311i	$0.687018\pi$
$284$	−1.92698	−0.114345
$285$	0	0
$286$	−10.2273	−0.604752
$287$	−6.95591	−0.410594
$288$	−8.75785	−0.516061
$289$	18.8656	1.10974
$290$	−1.17848	−0.0692030
$291$	−0.643143	−0.0377017
$292$	−5.01201	−0.293305
$293$	−29.7307	−1.73688	−0.868442	−	0.495791i	$-0.834878\pi$
$293$	−29.7307	−1.73688	−0.868442	+	0.495791i	$0.834878\pi$
$294$	12.0505	0.702798
$295$	−4.76825	−0.277619
$296$	−3.35231	−0.194849
$297$	−71.1771	−4.13011
$298$	−5.63256	−0.326285
$299$	−14.4335	−0.834709
$300$	3.42897	0.197972
$301$	1.25417	0.0722894
$302$	1.23848	0.0712668
$303$	−6.72182	−0.386159
$304$	0	0
$305$	8.23638	0.471614
$306$	−52.4489	−2.99831
$307$	−5.16143	−0.294578	−0.147289	−	0.989093i	$-0.547055\pi$
$307$	−5.16143	−0.294578	−0.147289	+	0.989093i	$0.547055\pi$
$308$	−6.73070	−0.383517
$309$	60.0207	3.41446
$310$	5.19863	0.295263
$311$	−26.0374	−1.47645	−0.738223	−	0.674557i	$-0.764335\pi$
$311$	−26.0374	−1.47645	−0.738223	+	0.674557i	$0.764335\pi$
$312$	9.72766	0.550721
$313$	−0.277126	−0.0156641	−0.00783204	−	0.999969i	$-0.502493\pi$
$313$	−0.277126	−0.0156641	−0.00783204	+	0.999969i	$0.502493\pi$
$314$	21.5073	1.21373
$315$	16.3509	0.921269
$316$	−0.601185	−0.0338193
$317$	24.9278	1.40009	0.700043	−	0.714101i	$-0.253164\pi$
$317$	24.9278	1.40009	0.700043	+	0.714101i	$0.253164\pi$
$318$	−8.78363	−0.492561
$319$	−4.24854	−0.237872
$320$	1.00000	0.0559017
$321$	36.3118	2.02673
$322$	−9.49883	−0.529349
$323$	0	0
$324$	41.4264	2.30147
$325$	−2.83690	−0.157363
$326$	−18.0210	−0.998091
$327$	−47.5782	−2.63108
$328$	3.72571	0.205718
$329$	−11.8041	−0.650783
$330$	12.3617	0.680492
$331$	−10.6969	−0.587956	−0.293978	−	0.955812i	$-0.594979\pi$
$331$	−10.6969	−0.587956	−0.293978	+	0.955812i	$0.594979\pi$
$332$	−1.90282	−0.104431
$333$	29.3590	1.60886
$334$	10.9088	0.596906
$335$	7.96385	0.435112
$336$	6.40189	0.349252
$337$	−4.55791	−0.248285	−0.124142	−	0.992264i	$-0.539618\pi$
$337$	−4.55791	−0.248285	−0.124142	+	0.992264i	$0.539618\pi$
$338$	4.95198	0.269352
$339$	−54.6431	−2.96781
$340$	5.98879	0.324788
$341$	18.7415	1.01491
$342$	0	0
$343$	−19.6302	−1.05993
$344$	−0.671759	−0.0362188
$345$	17.4458	0.939248
$346$	−0.145902	−0.00784376
$347$	20.8929	1.12159	0.560794	−	0.827956i	$-0.310496\pi$
$347$	20.8929	1.12159	0.560794	+	0.827956i	$0.310496\pi$
$348$	4.04099	0.216620
$349$	−11.2844	−0.604038	−0.302019	−	0.953302i	$-0.597661\pi$
$349$	−11.2844	−0.604038	−0.302019	+	0.953302i	$0.597661\pi$
$350$	−1.86700	−0.0997953
$351$	−56.0104	−2.98962
$352$	3.60509	0.192152
$353$	−8.21584	−0.437285	−0.218642	−	0.975805i	$-0.570163\pi$
$353$	−8.21584	−0.437285	−0.218642	+	0.975805i	$0.570163\pi$
$354$	16.3502	0.869004
$355$	−1.92698	−0.102273
$356$	0.985918	0.0522535
$357$	38.3396	2.02915
$358$	−5.69949	−0.301227
$359$	−10.7491	−0.567314	−0.283657	−	0.958926i	$-0.591548\pi$
$359$	−10.7491	−0.567314	−0.283657	+	0.958926i	$0.591548\pi$
$360$	−8.75785	−0.461579
$361$	0	0
$362$	18.5013	0.972405
$363$	6.84650	0.359348
$364$	−5.29650	−0.277612
$365$	−5.01201	−0.262340
$366$	−28.2423	−1.47625
$367$	−14.9478	−0.780268	−0.390134	−	0.920758i	$-0.627571\pi$
$367$	−14.9478	−0.780268	−0.390134	+	0.920758i	$0.627571\pi$
$368$	5.08775	0.265217
$369$	−32.6293	−1.69861
$370$	−3.35231	−0.174278
$371$	4.78249	0.248295
$372$	−17.8260	−0.924234
$373$	8.72226	0.451622	0.225811	−	0.974171i	$-0.427497\pi$
$373$	8.72226	0.451622	0.225811	+	0.974171i	$0.427497\pi$
$374$	21.5901	1.11640
$375$	3.42897	0.177071
$376$	6.32252	0.326059
$377$	−3.34325	−0.172186
$378$	−36.8611	−1.89593
$379$	15.9169	0.817597	0.408799	−	0.912625i	$-0.365948\pi$
$379$	15.9169	0.817597	0.408799	+	0.912625i	$0.365948\pi$
$380$	0	0
$381$	−57.6548	−2.95375
$382$	−18.8820	−0.966090
$383$	−1.74388	−0.0891081	−0.0445540	−	0.999007i	$-0.514187\pi$
$383$	−1.74388	−0.0891081	−0.0445540	+	0.999007i	$0.514187\pi$
$384$	−3.42897	−0.174984
$385$	−6.73070	−0.343028
$386$	−4.88366	−0.248572
$387$	5.88316	0.299058
$388$	−0.187561	−0.00952199
$389$	32.4754	1.64657	0.823284	−	0.567630i	$-0.192139\pi$
$389$	32.4754	1.64657	0.823284	+	0.567630i	$0.192139\pi$
$390$	9.72766	0.492579
$391$	30.4695	1.54091
$392$	3.51431	0.177500
$393$	22.3355	1.12668
$394$	3.51747	0.177208
$395$	−0.601185	−0.0302489
$396$	−31.5728	−1.58659
$397$	−4.10529	−0.206039	−0.103019	−	0.994679i	$-0.532850\pi$
$397$	−4.10529	−0.206039	−0.103019	+	0.994679i	$0.532850\pi$
$398$	0.840516	0.0421313
$399$	0	0
$400$	1.00000	0.0500000
$401$	31.1991	1.55801	0.779003	−	0.627020i	$-0.215725\pi$
$401$	31.1991	1.55801	0.779003	+	0.627020i	$0.215725\pi$
$402$	−27.3078	−1.36199
$403$	14.7480	0.734652
$404$	−1.96030	−0.0975287
$405$	41.4264	2.05849
$406$	−2.20023	−0.109196
$407$	−12.0854	−0.599049
$408$	−20.5354	−1.01665
$409$	8.77338	0.433816	0.216908	−	0.976192i	$-0.430403\pi$
$409$	8.77338	0.433816	0.216908	+	0.976192i	$0.430403\pi$
$410$	3.72571	0.184000
$411$	69.4235	3.42441
$412$	17.5040	0.862359
$413$	−8.90233	−0.438055
$414$	−44.5578	−2.18990
$415$	−1.90282	−0.0934055
$416$	2.83690	0.139091
$417$	13.6764	0.669734
$418$	0	0
$419$	−6.13252	−0.299593	−0.149797	−	0.988717i	$-0.547862\pi$
$419$	−6.13252	−0.299593	−0.149797	+	0.988717i	$0.547862\pi$
$420$	6.40189	0.312380
$421$	−3.83612	−0.186961	−0.0934805	−	0.995621i	$-0.529799\pi$
$421$	−3.83612	−0.186961	−0.0934805	+	0.995621i	$0.529799\pi$
$422$	27.4095	1.33427
$423$	−55.3717	−2.69226
$424$	−2.56159	−0.124402
$425$	5.98879	0.290499
$426$	6.60755	0.320137
$427$	15.3773	0.744160
$428$	10.5897	0.511873
$429$	35.0691	1.69315
$430$	−0.671759	−0.0323951
$431$	−25.5855	−1.23241	−0.616205	−	0.787586i	$-0.711331\pi$
$431$	−25.5855	−1.23241	−0.616205	+	0.787586i	$0.711331\pi$
$432$	19.7435	0.949910
$433$	28.4636	1.36787	0.683937	−	0.729541i	$-0.260266\pi$
$433$	28.4636	1.36787	0.683937	+	0.729541i	$0.260266\pi$
$434$	9.70585	0.465896
$435$	4.04099	0.193751
$436$	−13.8754	−0.664509
$437$	0	0
$438$	17.1860	0.821180
$439$	38.1049	1.81865	0.909324	−	0.416090i	$-0.136600\pi$
$439$	38.1049	1.81865	0.909324	+	0.416090i	$0.136600\pi$
$440$	3.60509	0.171866
$441$	−30.7778	−1.46561
$442$	16.9896	0.808114
$443$	22.7785	1.08224	0.541119	−	0.840946i	$-0.318001\pi$
$443$	22.7785	1.08224	0.541119	+	0.840946i	$0.318001\pi$
$444$	11.4950	0.545527
$445$	0.985918	0.0467370
$446$	11.4351	0.541470
$447$	19.3139	0.913516
$448$	1.86700	0.0882074
$449$	−31.1821	−1.47157	−0.735787	−	0.677213i	$-0.763188\pi$
$449$	−31.1821	−1.47157	−0.735787	+	0.677213i	$0.763188\pi$
$450$	−8.75785	−0.412849
$451$	13.4315	0.632466
$452$	−15.9357	−0.749553
$453$	−4.24673	−0.199529
$454$	−15.6154	−0.732865
$455$	−5.29650	−0.248304
$456$	0	0
$457$	−13.0810	−0.611902	−0.305951	−	0.952047i	$-0.598974\pi$
$457$	−13.0810	−0.611902	−0.305951	+	0.952047i	$0.598974\pi$
$458$	−5.50003	−0.257000
$459$	118.240	5.51896
$460$	5.08775	0.237218
$461$	18.2208	0.848626	0.424313	−	0.905516i	$-0.360516\pi$
$461$	18.2208	0.848626	0.424313	+	0.905516i	$0.360516\pi$
$462$	23.0794	1.07375
$463$	−23.0080	−1.06927	−0.534636	−	0.845083i	$-0.679551\pi$
$463$	−23.0080	−1.06927	−0.534636	+	0.845083i	$0.679551\pi$
$464$	1.17848	0.0547097
$465$	−17.8260	−0.826660
$466$	11.3286	0.524788
$467$	−25.0530	−1.15932	−0.579658	−	0.814860i	$-0.696814\pi$
$467$	−25.0530	−1.15932	−0.579658	+	0.814860i	$0.696814\pi$
$468$	−24.8452	−1.14847
$469$	14.8685	0.686564
$470$	6.32252	0.291636
$471$	−73.7480	−3.39813
$472$	4.76825	0.219477
$473$	−2.42175	−0.111352
$474$	2.06145	0.0946854
$475$	0	0
$476$	11.1811	0.512483
$477$	22.4340	1.02718
$478$	−1.48334	−0.0678464
$479$	21.6632	0.989815	0.494907	−	0.868946i	$-0.335202\pi$
$479$	21.6632	0.989815	0.494907	+	0.868946i	$0.335202\pi$
$480$	−3.42897	−0.156510
$481$	−9.51017	−0.433626
$482$	8.41913	0.383481
$483$	32.5712	1.48204
$484$	1.99666	0.0907574
$485$	−0.187561	−0.00851672
$486$	−82.8195	−3.75677
$487$	−3.32533	−0.150685	−0.0753425	−	0.997158i	$-0.524005\pi$
$487$	−3.32533	−0.150685	−0.0753425	+	0.997158i	$0.524005\pi$
$488$	−8.23638	−0.372843
$489$	61.7935	2.79440
$490$	3.51431	0.158760
$491$	−5.03905	−0.227409	−0.113705	−	0.993515i	$-0.536272\pi$
$491$	−5.03905	−0.227409	−0.113705	+	0.993515i	$0.536272\pi$
$492$	−12.7754	−0.575958
$493$	7.05769	0.317862
$494$	0	0
$495$	−31.5728	−1.41909
$496$	−5.19863	−0.233426
$497$	−3.59766	−0.161377
$498$	6.52470	0.292379
$499$	−10.2386	−0.458343	−0.229171	−	0.973386i	$-0.573602\pi$
$499$	−10.2386	−0.458343	−0.229171	+	0.973386i	$0.573602\pi$
$500$	1.00000	0.0447214
$501$	−37.4061	−1.67118
$502$	−11.0908	−0.495006
$503$	6.70316	0.298879	0.149439	−	0.988771i	$-0.452253\pi$
$503$	6.70316	0.298879	0.149439	+	0.988771i	$0.452253\pi$
$504$	−16.3509	−0.728327
$505$	−1.96030	−0.0872323
$506$	18.3418	0.815392
$507$	−16.9802	−0.754117
$508$	−16.8140	−0.746001
$509$	24.0556	1.06625	0.533124	−	0.846037i	$-0.321018\pi$
$509$	24.0556	1.06625	0.533124	+	0.846037i	$0.321018\pi$
$510$	−20.5354	−0.909322
$511$	−9.35741	−0.413948
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−11.4846	−0.506564
$515$	17.5040	0.771317
$516$	2.30344	0.101403
$517$	22.7932	1.00245
$518$	−6.25875	−0.274994
$519$	0.500295	0.0219605
$520$	2.83690	0.124406
$521$	26.4750	1.15989	0.579945	−	0.814656i	$-0.303074\pi$
$521$	26.4750	1.15989	0.579945	+	0.814656i	$0.303074\pi$
$522$	−10.3210	−0.451737
$523$	−15.6235	−0.683166	−0.341583	−	0.939852i	$-0.610963\pi$
$523$	−15.6235	−0.683166	−0.341583	+	0.939852i	$0.610963\pi$
$524$	6.51376	0.284555
$525$	6.40189	0.279401
$526$	−31.7383	−1.38385
$527$	−31.1335	−1.35620
$528$	−12.3617	−0.537976
$529$	2.88523	0.125445
$530$	−2.56159	−0.111268
$531$	−41.7597	−1.81222
$532$	0	0
$533$	10.5695	0.457816
$534$	−3.38069	−0.146297
$535$	10.5897	0.457833
$536$	−7.96385	−0.343986
$537$	19.5434	0.843359
$538$	23.3579	1.00703
$539$	12.6694	0.545710
$540$	19.7435	0.849626
$541$	−14.8243	−0.637347	−0.318673	−	0.947865i	$-0.603237\pi$
$541$	−14.8243	−0.637347	−0.318673	+	0.947865i	$0.603237\pi$
$542$	22.0881	0.948765
$543$	−63.4403	−2.72248
$544$	−5.98879	−0.256767
$545$	−13.8754	−0.594355
$546$	18.1615	0.777242
$547$	−19.3818	−0.828707	−0.414353	−	0.910116i	$-0.635992\pi$
$547$	−19.3818	−0.828707	−0.414353	+	0.910116i	$0.635992\pi$
$548$	20.2461	0.864873
$549$	72.1330	3.07856
$550$	3.60509	0.153721
$551$	0	0
$552$	−17.4458	−0.742541
$553$	−1.12241	−0.0477298
$554$	19.8124	0.841750
$555$	11.4950	0.487934
$556$	3.98847	0.169149
$557$	−38.1240	−1.61536	−0.807682	−	0.589618i	$-0.799278\pi$
$557$	−38.1240	−1.61536	−0.807682	+	0.589618i	$0.799278\pi$
$558$	45.5289	1.92739
$559$	−1.90572	−0.0806032
$560$	1.86700	0.0788951
$561$	−74.0319	−3.12563
$562$	21.1618	0.892656
$563$	12.3292	0.519613	0.259806	−	0.965661i	$-0.416341\pi$
$563$	12.3292	0.519613	0.259806	+	0.965661i	$0.416341\pi$
$564$	−21.6797	−0.912882
$565$	−15.9357	−0.670421
$566$	18.6499	0.783912
$567$	77.3431	3.24810
$568$	1.92698	0.0808541
$569$	−3.18778	−0.133639	−0.0668194	−	0.997765i	$-0.521285\pi$
$569$	−3.18778	−0.133639	−0.0668194	+	0.997765i	$0.521285\pi$
$570$	0	0
$571$	3.67370	0.153740	0.0768698	−	0.997041i	$-0.475507\pi$
$571$	3.67370	0.153740	0.0768698	+	0.997041i	$0.475507\pi$
$572$	10.2273	0.427624
$573$	64.7460	2.70480
$574$	6.95591	0.290334
$575$	5.08775	0.212174
$576$	8.75785	0.364910
$577$	−2.15105	−0.0895492	−0.0447746	−	0.998997i	$-0.514257\pi$
$577$	−2.15105	−0.0895492	−0.0447746	+	0.998997i	$0.514257\pi$
$578$	−18.8656	−0.784705
$579$	16.7459	0.695937
$580$	1.17848	0.0489339
$581$	−3.55256	−0.147385
$582$	0.643143	0.0266591
$583$	−9.23477	−0.382465
$584$	5.01201	0.207398
$585$	−24.8452	−1.02722
$586$	29.7307	1.22816
$587$	−28.5242	−1.17732	−0.588659	−	0.808381i	$-0.700344\pi$
$587$	−28.5242	−1.17732	−0.588659	+	0.808381i	$0.700344\pi$
$588$	−12.0505	−0.496953
$589$	0	0
$590$	4.76825	0.196306
$591$	−12.0613	−0.496136
$592$	3.35231	0.137779
$593$	10.0915	0.414410	0.207205	−	0.978298i	$-0.433563\pi$
$593$	10.0915	0.414410	0.207205	+	0.978298i	$0.433563\pi$
$594$	71.1771	2.92043
$595$	11.1811	0.458379
$596$	5.63256	0.230719
$597$	−2.88211	−0.117957
$598$	14.4335	0.590228
$599$	2.76324	0.112903	0.0564514	−	0.998405i	$-0.482021\pi$
$599$	2.76324	0.112903	0.0564514	+	0.998405i	$0.482021\pi$
$600$	−3.42897	−0.139987
$601$	17.0215	0.694321	0.347160	−	0.937806i	$-0.387146\pi$
$601$	17.0215	0.694321	0.347160	+	0.937806i	$0.387146\pi$
$602$	−1.25417	−0.0511163
$603$	69.7462	2.84029
$604$	−1.23848	−0.0503932
$605$	1.99666	0.0811758
$606$	6.72182	0.273055
$607$	−45.0807	−1.82977	−0.914884	−	0.403717i	$-0.867718\pi$
$607$	−45.0807	−1.82977	−0.914884	+	0.403717i	$0.867718\pi$
$608$	0	0
$609$	7.54452	0.305720
$610$	−8.23638	−0.333481
$611$	17.9364	0.725628
$612$	52.4489	2.12012
$613$	−1.22843	−0.0496158	−0.0248079	−	0.999692i	$-0.507897\pi$
$613$	−1.22843	−0.0496158	−0.0248079	+	0.999692i	$0.507897\pi$
$614$	5.16143	0.208298
$615$	−12.7754	−0.515153
$616$	6.73070	0.271188
$617$	23.7192	0.954899	0.477449	−	0.878659i	$-0.341561\pi$
$617$	23.7192	0.954899	0.477449	+	0.878659i	$0.341561\pi$
$618$	−60.0207	−2.41439
$619$	12.6509	0.508482	0.254241	−	0.967141i	$-0.418174\pi$
$619$	12.6509	0.508482	0.254241	+	0.967141i	$0.418174\pi$
$620$	−5.19863	−0.208782
$621$	100.450	4.03092
$622$	26.0374	1.04400
$623$	1.84071	0.0737464
$624$	−9.72766	−0.389418
$625$	1.00000	0.0400000
$626$	0.277126	0.0110762
$627$	0	0
$628$	−21.5073	−0.858235
$629$	20.0763	0.800493
$630$	−16.3509	−0.651436
$631$	38.2412	1.52236	0.761179	−	0.648542i	$-0.224621\pi$
$631$	38.2412	1.52236	0.761179	+	0.648542i	$0.224621\pi$
$632$	0.601185	0.0239139
$633$	−93.9864	−3.73562
$634$	−24.9278	−0.990010
$635$	−16.8140	−0.667244
$636$	8.78363	0.348294
$637$	9.96977	0.395017
$638$	4.24854	0.168201
$639$	−16.8762	−0.667611
$640$	−1.00000	−0.0395285
$641$	10.2621	0.405327	0.202663	−	0.979248i	$-0.435040\pi$
$641$	10.2621	0.405327	0.202663	+	0.979248i	$0.435040\pi$
$642$	−36.3118	−1.43311
$643$	−14.5679	−0.574502	−0.287251	−	0.957855i	$-0.592741\pi$
$643$	−14.5679	−0.574502	−0.287251	+	0.957855i	$0.592741\pi$
$644$	9.49883	0.374306
$645$	2.30344	0.0906980
$646$	0	0
$647$	4.44223	0.174642	0.0873211	−	0.996180i	$-0.472169\pi$
$647$	4.44223	0.174642	0.0873211	+	0.996180i	$0.472169\pi$
$648$	−41.4264	−1.62738
$649$	17.1900	0.674766
$650$	2.83690	0.111273
$651$	−33.2811	−1.30439
$652$	18.0210	0.705757
$653$	19.4483	0.761072	0.380536	−	0.924766i	$-0.375740\pi$
$653$	19.4483	0.761072	0.380536	+	0.924766i	$0.375740\pi$
$654$	47.5782	1.86045
$655$	6.51376	0.254514
$656$	−3.72571	−0.145465
$657$	−43.8944	−1.71248
$658$	11.8041	0.460173
$659$	12.4606	0.485395	0.242698	−	0.970102i	$-0.421968\pi$
$659$	12.4606	0.485395	0.242698	+	0.970102i	$0.421968\pi$
$660$	−12.3617	−0.481180
$661$	8.25110	0.320931	0.160465	−	0.987041i	$-0.448701\pi$
$661$	8.25110	0.320931	0.160465	+	0.987041i	$0.448701\pi$
$662$	10.6969	0.415748
$663$	−58.2569	−2.26251
$664$	1.90282	0.0738436
$665$	0	0
$666$	−29.3590	−1.13764
$667$	5.99584	0.232160
$668$	−10.9088	−0.422076
$669$	−39.2108	−1.51598
$670$	−7.96385	−0.307670
$671$	−29.6929	−1.14628
$672$	−6.40189	−0.246958
$673$	−1.23314	−0.0475341	−0.0237671	−	0.999718i	$-0.507566\pi$
$673$	−1.23314	−0.0475341	−0.0237671	+	0.999718i	$0.507566\pi$
$674$	4.55791	0.175564
$675$	19.7435	0.759928
$676$	−4.95198	−0.190461
$677$	−17.8526	−0.686131	−0.343065	−	0.939312i	$-0.611465\pi$
$677$	−17.8526	−0.686131	−0.343065	+	0.939312i	$0.611465\pi$
$678$	54.6431	2.09856
$679$	−0.350177	−0.0134386
$680$	−5.98879	−0.229660
$681$	53.5446	2.05184
$682$	−18.7415	−0.717651
$683$	27.7712	1.06264	0.531318	−	0.847173i	$-0.321697\pi$
$683$	27.7712	1.06264	0.531318	+	0.847173i	$0.321697\pi$
$684$	0	0
$685$	20.2461	0.773566
$686$	19.6302	0.749485
$687$	18.8595	0.719533
$688$	0.671759	0.0256106
$689$	−7.26699	−0.276850
$690$	−17.4458	−0.664149
$691$	42.6796	1.62361	0.811805	−	0.583929i	$-0.198485\pi$
$691$	42.6796	1.62361	0.811805	+	0.583929i	$0.198485\pi$
$692$	0.145902	0.00554637
$693$	−58.9465	−2.23919
$694$	−20.8929	−0.793082
$695$	3.98847	0.151291
$696$	−4.04099	−0.153173
$697$	−22.3125	−0.845147
$698$	11.2844	0.427120
$699$	−38.8455	−1.46927
$700$	1.86700	0.0705660
$701$	−39.8475	−1.50502	−0.752509	−	0.658582i	$-0.771157\pi$
$701$	−39.8475	−1.50502	−0.752509	+	0.658582i	$0.771157\pi$
$702$	56.0104	2.11398
$703$	0	0
$704$	−3.60509	−0.135872
$705$	−21.6797	−0.816506
$706$	8.21584	0.309207
$707$	−3.65988	−0.137644
$708$	−16.3502	−0.614479
$709$	48.0511	1.80460	0.902298	−	0.431113i	$-0.141879\pi$
$709$	48.0511	1.80460	0.902298	+	0.431113i	$0.141879\pi$
$710$	1.92698	0.0723181
$711$	−5.26509	−0.197456
$712$	−0.985918	−0.0369488
$713$	−26.4494	−0.990537
$714$	−38.3396	−1.43482
$715$	10.2273	0.382479
$716$	5.69949	0.213000
$717$	5.08633	0.189953
$718$	10.7491	0.401152
$719$	−30.3742	−1.13277	−0.566383	−	0.824142i	$-0.691658\pi$
$719$	−30.3742	−1.13277	−0.566383	+	0.824142i	$0.691658\pi$
$720$	8.75785	0.326386
$721$	32.6799	1.21706
$722$	0	0
$723$	−28.8690	−1.07365
$724$	−18.5013	−0.687594
$725$	1.17848	0.0437678
$726$	−6.84650	−0.254097
$727$	−30.5670	−1.13367	−0.566834	−	0.823832i	$-0.691832\pi$
$727$	−30.5670	−1.13367	−0.566834	+	0.823832i	$0.691832\pi$
$728$	5.29650	0.196301
$729$	159.706	5.91505
$730$	5.01201	0.185503
$731$	4.02302	0.148797
$732$	28.2423	1.04387
$733$	−43.9998	−1.62517	−0.812586	−	0.582842i	$-0.801941\pi$
$733$	−43.9998	−1.62517	−0.812586	+	0.582842i	$0.801941\pi$
$734$	14.9478	0.551733
$735$	−12.0505	−0.444489
$736$	−5.08775	−0.187537
$737$	−28.7104	−1.05756
$738$	32.6293	1.20110
$739$	29.3015	1.07787	0.538936	−	0.842347i	$-0.318826\pi$
$739$	29.3015	1.07787	0.538936	+	0.842347i	$0.318826\pi$
$740$	3.35231	0.123233
$741$	0	0
$742$	−4.78249	−0.175571
$743$	13.1228	0.481430	0.240715	−	0.970596i	$-0.422618\pi$
$743$	13.1228	0.481430	0.240715	+	0.970596i	$0.422618\pi$
$744$	17.8260	0.653532
$745$	5.63256	0.206361
$746$	−8.72226	−0.319345
$747$	−16.6646	−0.609725
$748$	−21.5901	−0.789413
$749$	19.7710	0.722416
$750$	−3.42897	−0.125208
$751$	20.0098	0.730167	0.365084	−	0.930975i	$-0.381040\pi$
$751$	20.0098	0.730167	0.365084	+	0.930975i	$0.381040\pi$
$752$	−6.32252	−0.230559
$753$	38.0300	1.38589
$754$	3.34325	0.121754
$755$	−1.23848	−0.0450731
$756$	36.8611	1.34063
$757$	−36.4883	−1.32619	−0.663095	−	0.748536i	$-0.730757\pi$
$757$	−36.4883	−1.32619	−0.663095	+	0.748536i	$0.730757\pi$
$758$	−15.9169	−0.578128
$759$	−62.8935	−2.28289
$760$	0	0
$761$	3.91470	0.141908	0.0709540	−	0.997480i	$-0.477396\pi$
$761$	3.91470	0.141908	0.0709540	+	0.997480i	$0.477396\pi$
$762$	57.6548	2.08861
$763$	−25.9053	−0.937834
$764$	18.8820	0.683128
$765$	52.4489	1.89629
$766$	1.74388	0.0630089
$767$	13.5271	0.488435
$768$	3.42897	0.123732
$769$	−22.7389	−0.819987	−0.409993	−	0.912088i	$-0.634469\pi$
$769$	−22.7389	−0.819987	−0.409993	+	0.912088i	$0.634469\pi$
$770$	6.73070	0.242558
$771$	39.3804	1.41825
$772$	4.88366	0.175767
$773$	21.8627	0.786347	0.393174	−	0.919464i	$-0.371377\pi$
$773$	21.8627	0.786347	0.393174	+	0.919464i	$0.371377\pi$
$774$	−5.88316	−0.211466
$775$	−5.19863	−0.186740
$776$	0.187561	0.00673306
$777$	21.4611	0.769912
$778$	−32.4754	−1.16430
$779$	0	0
$780$	−9.72766	−0.348306
$781$	6.94692	0.248580
$782$	−30.4695	−1.08959
$783$	23.2674	0.831510
$784$	−3.51431	−0.125511
$785$	−21.5073	−0.767629
$786$	−22.3355	−0.796681
$787$	−30.1350	−1.07420	−0.537098	−	0.843520i	$-0.680480\pi$
$787$	−30.1350	−1.07420	−0.537098	+	0.843520i	$0.680480\pi$
$788$	−3.51747	−0.125305
$789$	108.830	3.87444
$790$	0.601185	0.0213892
$791$	−29.7520	−1.05786
$792$	31.5728	1.12189
$793$	−23.3658	−0.829744
$794$	4.10529	0.145691
$795$	8.78363	0.311523
$796$	−0.840516	−0.0297913
$797$	−19.4641	−0.689456	−0.344728	−	0.938703i	$-0.612029\pi$
$797$	−19.4641	−0.689456	−0.344728	+	0.938703i	$0.612029\pi$
$798$	0	0
$799$	−37.8642	−1.33954
$800$	−1.00000	−0.0353553
$801$	8.63452	0.305086
$802$	−31.1991	−1.10168
$803$	18.0687	0.637631
$804$	27.3078	0.963073
$805$	9.49883	0.334790
$806$	−14.7480	−0.519477
$807$	−80.0937	−2.81943
$808$	1.96030	0.0689632
$809$	−40.3232	−1.41769	−0.708844	−	0.705365i	$-0.750783\pi$
$809$	−40.3232	−1.41769	−0.708844	+	0.705365i	$0.750783\pi$
$810$	−41.4264	−1.45558
$811$	−19.2857	−0.677212	−0.338606	−	0.940928i	$-0.609955\pi$
$811$	−19.2857	−0.677212	−0.338606	+	0.940928i	$0.609955\pi$
$812$	2.20023	0.0772129
$813$	−75.7395	−2.65630
$814$	12.0854	0.423592
$815$	18.0210	0.631248
$816$	20.5354	0.718883
$817$	0	0
$818$	−8.77338	−0.306754
$819$	−46.3859	−1.62086
$820$	−3.72571	−0.130108
$821$	41.9192	1.46299	0.731495	−	0.681847i	$-0.238823\pi$
$821$	41.9192	1.46299	0.731495	+	0.681847i	$0.238823\pi$
$822$	−69.4235	−2.42142
$823$	23.9246	0.833960	0.416980	−	0.908916i	$-0.363088\pi$
$823$	23.9246	0.833960	0.416980	+	0.908916i	$0.363088\pi$
$824$	−17.5040	−0.609780
$825$	−12.3617	−0.430381
$826$	8.90233	0.309752
$827$	24.6024	0.855508	0.427754	−	0.903895i	$-0.359305\pi$
$827$	24.6024	0.855508	0.427754	+	0.903895i	$0.359305\pi$
$828$	44.5578	1.54849
$829$	−35.1963	−1.22242	−0.611209	−	0.791469i	$-0.709317\pi$
$829$	−35.1963	−1.22242	−0.611209	+	0.791469i	$0.709317\pi$
$830$	1.90282	0.0660477
$831$	−67.9363	−2.35669
$832$	−2.83690	−0.0983519
$833$	−21.0465	−0.729217
$834$	−13.6764	−0.473573
$835$	−10.9088	−0.377516
$836$	0	0
$837$	−102.639	−3.54773
$838$	6.13252	0.211844
$839$	−23.8974	−0.825030	−0.412515	−	0.910951i	$-0.635350\pi$
$839$	−23.8974	−0.825030	−0.412515	+	0.910951i	$0.635350\pi$
$840$	−6.40189	−0.220886
$841$	−27.6112	−0.952110
$842$	3.83612	0.132201
$843$	−72.5632	−2.49921
$844$	−27.4095	−0.943474
$845$	−4.95198	−0.170353
$846$	55.3717	1.90372
$847$	3.72777	0.128088
$848$	2.56159	0.0879654
$849$	−63.9499	−2.19475
$850$	−5.98879	−0.205414
$851$	17.0557	0.584662
$852$	−6.60755	−0.226371
$853$	26.1190	0.894297	0.447148	−	0.894460i	$-0.352440\pi$
$853$	26.1190	0.894297	0.447148	+	0.894460i	$0.352440\pi$
$854$	−15.3773	−0.526201
$855$	0	0
$856$	−10.5897	−0.361949
$857$	−49.1708	−1.67964	−0.839821	−	0.542863i	$-0.817340\pi$
$857$	−49.1708	−1.67964	−0.839821	+	0.542863i	$0.817340\pi$
$858$	−35.0691	−1.19724
$859$	−14.5141	−0.495213	−0.247607	−	0.968861i	$-0.579644\pi$
$859$	−14.5141	−0.495213	−0.247607	+	0.968861i	$0.579644\pi$
$860$	0.671759	0.0229068
$861$	−23.8516	−0.812861
$862$	25.5855	0.871445
$863$	−10.9036	−0.371161	−0.185581	−	0.982629i	$-0.559417\pi$
$863$	−10.9036	−0.371161	−0.185581	+	0.982629i	$0.559417\pi$
$864$	−19.7435	−0.671688
$865$	0.145902	0.00496083
$866$	−28.4636	−0.967233
$867$	64.6896	2.19697
$868$	−9.70585	−0.329438
$869$	2.16733	0.0735215
$870$	−4.04099	−0.137002
$871$	−22.5927	−0.765524
$872$	13.8754	0.469879
$873$	−1.64263	−0.0555948
$874$	0	0
$875$	1.86700	0.0631161
$876$	−17.1860	−0.580662
$877$	11.2484	0.379831	0.189915	−	0.981800i	$-0.439179\pi$
$877$	11.2484	0.379831	0.189915	+	0.981800i	$0.439179\pi$
$878$	−38.1049	−1.28598
$879$	−101.946	−3.43854
$880$	−3.60509	−0.121528
$881$	−9.81993	−0.330842	−0.165421	−	0.986223i	$-0.552898\pi$
$881$	−9.81993	−0.330842	−0.165421	+	0.986223i	$0.552898\pi$
$882$	30.7778	1.03634
$883$	30.4524	1.02481	0.512403	−	0.858745i	$-0.328755\pi$
$883$	30.4524	1.02481	0.512403	+	0.858745i	$0.328755\pi$
$884$	−16.9896	−0.571423
$885$	−16.3502	−0.549606
$886$	−22.7785	−0.765258
$887$	12.3099	0.413327	0.206663	−	0.978412i	$-0.433740\pi$
$887$	12.3099	0.413327	0.206663	+	0.978412i	$0.433740\pi$
$888$	−11.4950	−0.385746
$889$	−31.3918	−1.05285
$890$	−0.985918	−0.0330480
$891$	−149.346	−5.00327
$892$	−11.4351	−0.382877
$893$	0	0
$894$	−19.3139	−0.645953
$895$	5.69949	0.190513
$896$	−1.86700	−0.0623721
$897$	−49.4920	−1.65249
$898$	31.1821	1.04056
$899$	−6.12651	−0.204330
$900$	8.75785	0.291928
$901$	15.3408	0.511077
$902$	−13.4315	−0.447221
$903$	4.30053	0.143113
$904$	15.9357	0.530014
$905$	−18.5013	−0.615003
$906$	4.24673	0.141088
$907$	−40.8180	−1.35534	−0.677670	−	0.735366i	$-0.737010\pi$
$907$	−40.8180	−1.35534	−0.677670	+	0.735366i	$0.737010\pi$
$908$	15.6154	0.518214
$909$	−17.1680	−0.569428
$910$	5.29650	0.175577
$911$	1.58058	0.0523671	0.0261836	−	0.999657i	$-0.491665\pi$
$911$	1.58058	0.0523671	0.0261836	+	0.999657i	$0.491665\pi$
$912$	0	0
$913$	6.85982	0.227027
$914$	13.0810	0.432680
$915$	28.2423	0.933662
$916$	5.50003	0.181726
$917$	12.1612	0.401598
$918$	−118.240	−3.90249
$919$	−47.7782	−1.57606	−0.788029	−	0.615638i	$-0.788899\pi$
$919$	−47.7782	−1.57606	−0.788029	+	0.615638i	$0.788899\pi$
$920$	−5.08775	−0.167738
$921$	−17.6984	−0.583182
$922$	−18.2208	−0.600069
$923$	5.46665	0.179937
$924$	−23.0794	−0.759256
$925$	3.35231	0.110223
$926$	23.0080	0.756089
$927$	153.297	5.03494
$928$	−1.17848	−0.0386856
$929$	−47.9567	−1.57341	−0.786705	−	0.617330i	$-0.788214\pi$
$929$	−47.9567	−1.57341	−0.786705	+	0.617330i	$0.788214\pi$
$930$	17.8260	0.584537
$931$	0	0
$932$	−11.3286	−0.371081
$933$	−89.2815	−2.92295
$934$	25.0530	0.819761
$935$	−21.5901	−0.706072
$936$	24.8452	0.812090
$937$	38.0767	1.24391	0.621955	−	0.783053i	$-0.286339\pi$
$937$	38.0767	1.24391	0.621955	+	0.783053i	$0.286339\pi$
$938$	−14.8685	−0.485474
$939$	−0.950257	−0.0310105
$940$	−6.32252	−0.206218
$941$	−39.2730	−1.28026	−0.640132	−	0.768265i	$-0.721120\pi$
$941$	−39.2730	−1.28026	−0.640132	+	0.768265i	$0.721120\pi$
$942$	73.7480	2.40284
$943$	−18.9555	−0.617276
$944$	−4.76825	−0.155193
$945$	36.8611	1.19909
$946$	2.42175	0.0787379
$947$	−7.16095	−0.232700	−0.116350	−	0.993208i	$-0.537119\pi$
$947$	−7.16095	−0.232700	−0.116350	+	0.993208i	$0.537119\pi$
$948$	−2.06145	−0.0669527
$949$	14.2186	0.461555
$950$	0	0
$951$	85.4768	2.77178
$952$	−11.1811	−0.362380
$953$	−33.2331	−1.07653	−0.538263	−	0.842777i	$-0.680919\pi$
$953$	−33.2331	−1.07653	−0.538263	+	0.842777i	$0.680919\pi$
$954$	−22.4340	−0.726329
$955$	18.8820	0.611009
$956$	1.48334	0.0479747
$957$	−14.5681	−0.470920
$958$	−21.6632	−0.699905
$959$	37.7996	1.22061
$960$	3.42897	0.110670
$961$	−3.97420	−0.128200
$962$	9.51017	0.306620
$963$	92.7431	2.98860
$964$	−8.41913	−0.271162
$965$	4.88366	0.157211
$966$	−32.5712	−1.04796
$967$	−25.2252	−0.811188	−0.405594	−	0.914053i	$-0.632935\pi$
$967$	−25.2252	−0.811188	−0.405594	+	0.914053i	$0.632935\pi$
$968$	−1.99666	−0.0641751
$969$	0	0
$970$	0.187561	0.00602223
$971$	43.7283	1.40331	0.701654	−	0.712518i	$-0.252445\pi$
$971$	43.7283	1.40331	0.701654	+	0.712518i	$0.252445\pi$
$972$	82.8195	2.65644
$973$	7.44647	0.238723
$974$	3.32533	0.106550
$975$	−9.72766	−0.311535
$976$	8.23638	0.263640
$977$	−0.00478368	−0.000153043 0	−7.65217e−5	−	1.00000i	$-0.500024\pi$
$977$	−0.00478368	−0.000153043 0	−7.65217e−5		1.00000i	$0.500024\pi$
$978$	−61.7935	−1.97594
$979$	−3.55432	−0.113597
$980$	−3.51431	−0.112261
$981$	−121.518	−3.87978
$982$	5.03905	0.160803
$983$	36.9839	1.17960	0.589801	−	0.807548i	$-0.299206\pi$
$983$	36.9839	1.17960	0.589801	+	0.807548i	$0.299206\pi$
$984$	12.7754	0.407264
$985$	−3.51747	−0.112076
$986$	−7.05769	−0.224763
$987$	−40.4761	−1.28837
$988$	0	0
$989$	3.41774	0.108678
$990$	31.5728	1.00345
$991$	−5.84928	−0.185809	−0.0929043	−	0.995675i	$-0.529615\pi$
$991$	−5.84928	−0.185809	−0.0929043	+	0.995675i	$0.529615\pi$
$992$	5.19863	0.165057
$993$	−36.6795	−1.16399
$994$	3.59766	0.114111
$995$	−0.840516	−0.0266462
$996$	−6.52470	−0.206743
$997$	−57.9390	−1.83495	−0.917473	−	0.397798i	$-0.869775\pi$
$997$	−57.9390	−1.83495	−0.917473	+	0.397798i	$0.869775\pi$
$998$	10.2386	0.324097
$999$	66.1863	2.09404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.bi.1.9		9
19.6	even	9		190.2.k.d.131.3	✓	18
19.16	even	9		190.2.k.d.161.3	yes	18
19.18	odd	2		3610.2.a.bj.1.1		9
95.44	even	18		950.2.l.i.701.1		18
95.54	even	18		950.2.l.i.351.1		18
95.63	odd	36		950.2.u.g.549.4		36
95.73	odd	36		950.2.u.g.199.3		36
95.82	odd	36		950.2.u.g.549.3		36
95.92	odd	36		950.2.u.g.199.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.3	✓	18	19.6	even	9
190.2.k.d.161.3	yes	18	19.16	even	9
950.2.l.i.351.1		18	95.54	even	18
950.2.l.i.701.1		18	95.44	even	18
950.2.u.g.199.3		36	95.73	odd	36
950.2.u.g.199.4		36	95.92	odd	36
950.2.u.g.549.3		36	95.82	odd	36
950.2.u.g.549.4		36	95.63	odd	36
3610.2.a.bi.1.9		9	1.1	even	1	trivial
3610.2.a.bj.1.1		9	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.42897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42897 q^{6} +1.86700 q^{7} -1.00000 q^{8} +8.75785 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.42897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42897 q^{6} +1.86700 q^{7} -1.00000 q^{8} +8.75785 q^{9} -1.00000 q^{10} -3.60509 q^{11} +3.42897 q^{12} -2.83690 q^{13} -1.86700 q^{14} +3.42897 q^{15} +1.00000 q^{16} +5.98879 q^{17} -8.75785 q^{18} +1.00000 q^{20} +6.40189 q^{21} +3.60509 q^{22} +5.08775 q^{23} -3.42897 q^{24} +1.00000 q^{25} +2.83690 q^{26} +19.7435 q^{27} +1.86700 q^{28} +1.17848 q^{29} -3.42897 q^{30} -5.19863 q^{31} -1.00000 q^{32} -12.3617 q^{33} -5.98879 q^{34} +1.86700 q^{35} +8.75785 q^{36} +3.35231 q^{37} -9.72766 q^{39} -1.00000 q^{40} -3.72571 q^{41} -6.40189 q^{42} +0.671759 q^{43} -3.60509 q^{44} +8.75785 q^{45} -5.08775 q^{46} -6.32252 q^{47} +3.42897 q^{48} -3.51431 q^{49} -1.00000 q^{50} +20.5354 q^{51} -2.83690 q^{52} +2.56159 q^{53} -19.7435 q^{54} -3.60509 q^{55} -1.86700 q^{56} -1.17848 q^{58} -4.76825 q^{59} +3.42897 q^{60} +8.23638 q^{61} +5.19863 q^{62} +16.3509 q^{63} +1.00000 q^{64} -2.83690 q^{65} +12.3617 q^{66} +7.96385 q^{67} +5.98879 q^{68} +17.4458 q^{69} -1.86700 q^{70} -1.92698 q^{71} -8.75785 q^{72} -5.01201 q^{73} -3.35231 q^{74} +3.42897 q^{75} -6.73070 q^{77} +9.72766 q^{78} -0.601185 q^{79} +1.00000 q^{80} +41.4264 q^{81} +3.72571 q^{82} -1.90282 q^{83} +6.40189 q^{84} +5.98879 q^{85} -0.671759 q^{86} +4.04099 q^{87} +3.60509 q^{88} +0.985918 q^{89} -8.75785 q^{90} -5.29650 q^{91} +5.08775 q^{92} -17.8260 q^{93} +6.32252 q^{94} -3.42897 q^{96} -0.187561 q^{97} +3.51431 q^{98} -31.5728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

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