LMFDB - Embedded newform 7098.2.a.cn.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.13968.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 4 $ x^4 - 2x^3 - 7x^2 + 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.38651$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.78801 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.78801 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.78801 q^{10} +3.17452 q^{11} -1.00000 q^{12} +1.00000 q^{14} -1.78801 q^{15} +1.00000 q^{16} +5.56103 q^{17} -1.00000 q^{18} -6.18952 q^{19} +1.78801 q^{20} +1.00000 q^{21} -3.17452 q^{22} +6.13356 q^{23} +1.00000 q^{24} -1.80301 q^{25} -1.00000 q^{27} -1.00000 q^{28} +2.07759 q^{29} +1.78801 q^{30} +5.63862 q^{31} -1.00000 q^{32} -3.17452 q^{33} -5.56103 q^{34} -1.78801 q^{35} +1.00000 q^{36} -3.09693 q^{37} +6.18952 q^{38} -1.78801 q^{40} +1.49843 q^{41} -1.00000 q^{42} -9.63862 q^{43} +3.17452 q^{44} +1.78801 q^{45} -6.13356 q^{46} +10.5086 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.80301 q^{50} -5.56103 q^{51} +3.60200 q^{53} +1.00000 q^{54} +5.67609 q^{55} +1.00000 q^{56} +6.18952 q^{57} -2.07759 q^{58} +2.78138 q^{59} -1.78801 q^{60} +1.68879 q^{61} -5.63862 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.17452 q^{66} +11.5544 q^{67} +5.56103 q^{68} -6.13356 q^{69} +1.78801 q^{70} -0.598496 q^{71} -1.00000 q^{72} -0.423973 q^{73} +3.09693 q^{74} +1.80301 q^{75} -6.18952 q^{76} -3.17452 q^{77} +6.96254 q^{79} +1.78801 q^{80} +1.00000 q^{81} -1.49843 q^{82} -4.30228 q^{83} +1.00000 q^{84} +9.94320 q^{85} +9.63862 q^{86} -2.07759 q^{87} -3.17452 q^{88} -16.2931 q^{89} -1.78801 q^{90} +6.13356 q^{92} -5.63862 q^{93} -10.5086 q^{94} -11.0669 q^{95} +1.00000 q^{96} -17.4892 q^{97} -1.00000 q^{98} +3.17452 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{11} - 4 q^{12} + 4 q^{14} + 6 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} - 6 q^{20} + 4 q^{21} + 4 q^{22} + 8 q^{23} + 4 q^{24} + 12 q^{25} - 4 q^{27} - 4 q^{28} - 2 q^{29} - 6 q^{30} - 8 q^{31} - 4 q^{32} + 4 q^{33} - 2 q^{34} + 6 q^{35} + 4 q^{36} - 6 q^{37} + 2 q^{38} + 6 q^{40} - 10 q^{41} - 4 q^{42} - 8 q^{43} - 4 q^{44} - 6 q^{45} - 8 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} - 12 q^{50} - 2 q^{51} - 6 q^{53} + 4 q^{54} + 22 q^{55} + 4 q^{56} + 2 q^{57} + 2 q^{58} - 4 q^{59} + 6 q^{60} + 8 q^{61} + 8 q^{62} - 4 q^{63} + 4 q^{64} - 4 q^{66} + 24 q^{67} + 2 q^{68} - 8 q^{69} - 6 q^{70} - 12 q^{71} - 4 q^{72} - 28 q^{73} + 6 q^{74} - 12 q^{75} - 2 q^{76} + 4 q^{77} - 2 q^{79} - 6 q^{80} + 4 q^{81} + 10 q^{82} - 22 q^{83} + 4 q^{84} + 6 q^{85} + 8 q^{86} + 2 q^{87} + 4 q^{88} - 38 q^{89} + 6 q^{90} + 8 q^{92} + 8 q^{93} + 2 q^{94} - 50 q^{95} + 4 q^{96} - 22 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^11 - 4 * q^12 + 4 * q^14 + 6 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 - 6 * q^20 + 4 * q^21 + 4 * q^22 + 8 * q^23 + 4 * q^24 + 12 * q^25 - 4 * q^27 - 4 * q^28 - 2 * q^29 - 6 * q^30 - 8 * q^31 - 4 * q^32 + 4 * q^33 - 2 * q^34 + 6 * q^35 + 4 * q^36 - 6 * q^37 + 2 * q^38 + 6 * q^40 - 10 * q^41 - 4 * q^42 - 8 * q^43 - 4 * q^44 - 6 * q^45 - 8 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 - 12 * q^50 - 2 * q^51 - 6 * q^53 + 4 * q^54 + 22 * q^55 + 4 * q^56 + 2 * q^57 + 2 * q^58 - 4 * q^59 + 6 * q^60 + 8 * q^61 + 8 * q^62 - 4 * q^63 + 4 * q^64 - 4 * q^66 + 24 * q^67 + 2 * q^68 - 8 * q^69 - 6 * q^70 - 12 * q^71 - 4 * q^72 - 28 * q^73 + 6 * q^74 - 12 * q^75 - 2 * q^76 + 4 * q^77 - 2 * q^79 - 6 * q^80 + 4 * q^81 + 10 * q^82 - 22 * q^83 + 4 * q^84 + 6 * q^85 + 8 * q^86 + 2 * q^87 + 4 * q^88 - 38 * q^89 + 6 * q^90 + 8 * q^92 + 8 * q^93 + 2 * q^94 - 50 * q^95 + 4 * q^96 - 22 * q^97 - 4 * q^98 - 4 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.78801	0.799624	0.399812	−	0.916597i	$-0.369075\pi$
$5$	1.78801	0.799624	0.399812	+	0.916597i	$0.369075\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.78801	−0.565419
$11$	3.17452	0.957155	0.478577	−	0.878045i	$-0.341153\pi$
$11$	3.17452	0.957155	0.478577	+	0.878045i	$0.341153\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−1.78801	−0.461663
$16$	1.00000	0.250000
$17$	5.56103	1.34875	0.674374	−	0.738390i	$-0.264414\pi$
$17$	5.56103	1.34875	0.674374	+	0.738390i	$0.264414\pi$
$18$	−1.00000	−0.235702
$19$	−6.18952	−1.41997	−0.709986	−	0.704215i	$-0.751299\pi$
$19$	−6.18952	−1.41997	−0.709986	+	0.704215i	$0.751299\pi$
$20$	1.78801	0.399812
$21$	1.00000	0.218218
$22$	−3.17452	−0.676810
$23$	6.13356	1.27893	0.639467	−	0.768818i	$-0.279155\pi$
$23$	6.13356	1.27893	0.639467	+	0.768818i	$0.279155\pi$
$24$	1.00000	0.204124
$25$	−1.80301	−0.360602
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	2.07759	0.385799	0.192900	−	0.981218i	$-0.438211\pi$
$29$	2.07759	0.385799	0.192900	+	0.981218i	$0.438211\pi$
$30$	1.78801	0.326445
$31$	5.63862	1.01273	0.506363	−	0.862320i	$-0.330989\pi$
$31$	5.63862	1.01273	0.506363	+	0.862320i	$0.330989\pi$
$32$	−1.00000	−0.176777
$33$	−3.17452	−0.552613
$34$	−5.56103	−0.953709
$35$	−1.78801	−0.302229
$36$	1.00000	0.166667
$37$	−3.09693	−0.509132	−0.254566	−	0.967055i	$-0.581933\pi$
$37$	−3.09693	−0.509132	−0.254566	+	0.967055i	$0.581933\pi$
$38$	6.18952	1.00407
$39$	0	0
$40$	−1.78801	−0.282710
$41$	1.49843	0.234016	0.117008	−	0.993131i	$-0.462670\pi$
$41$	1.49843	0.234016	0.117008	+	0.993131i	$0.462670\pi$
$42$	−1.00000	−0.154303
$43$	−9.63862	−1.46988	−0.734938	−	0.678134i	$-0.762789\pi$
$43$	−9.63862	−1.46988	−0.734938	+	0.678134i	$0.762789\pi$
$44$	3.17452	0.478577
$45$	1.78801	0.266541
$46$	−6.13356	−0.904343
$47$	10.5086	1.53283	0.766416	−	0.642344i	$-0.222038\pi$
$47$	10.5086	1.53283	0.766416	+	0.642344i	$0.222038\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	1.80301	0.254984
$51$	−5.56103	−0.778700
$52$	0	0
$53$	3.60200	0.494773	0.247386	−	0.968917i	$-0.420428\pi$
$53$	3.60200	0.494773	0.247386	+	0.968917i	$0.420428\pi$
$54$	1.00000	0.136083
$55$	5.67609	0.765364
$56$	1.00000	0.133631
$57$	6.18952	0.819822
$58$	−2.07759	−0.272801
$59$	2.78138	0.362105	0.181052	−	0.983473i	$-0.442050\pi$
$59$	2.78138	0.362105	0.181052	+	0.983473i	$0.442050\pi$
$60$	−1.78801	−0.230832
$61$	1.68879	0.216228	0.108114	−	0.994139i	$-0.465519\pi$
$61$	1.68879	0.216228	0.108114	+	0.994139i	$0.465519\pi$
$62$	−5.63862	−0.716106
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	3.17452	0.390757
$67$	11.5544	1.41159	0.705797	−	0.708414i	$-0.250589\pi$
$67$	11.5544	1.41159	0.705797	+	0.708414i	$0.250589\pi$
$68$	5.56103	0.674374
$69$	−6.13356	−0.738393
$70$	1.78801	0.213708
$71$	−0.598496	−0.0710284	−0.0355142	−	0.999369i	$-0.511307\pi$
$71$	−0.598496	−0.0710284	−0.0355142	+	0.999369i	$0.511307\pi$
$72$	−1.00000	−0.117851
$73$	−0.423973	−0.0496223	−0.0248112	−	0.999692i	$-0.507898\pi$
$73$	−0.423973	−0.0496223	−0.0248112	+	0.999692i	$0.507898\pi$
$74$	3.09693	0.360011
$75$	1.80301	0.208193
$76$	−6.18952	−0.709986
$77$	−3.17452	−0.361770
$78$	0	0
$79$	6.96254	0.783346	0.391673	−	0.920104i	$-0.371896\pi$
$79$	6.96254	0.783346	0.391673	+	0.920104i	$0.371896\pi$
$80$	1.78801	0.199906
$81$	1.00000	0.111111
$82$	−1.49843	−0.165474
$83$	−4.30228	−0.472237	−0.236118	−	0.971724i	$-0.575875\pi$
$83$	−4.30228	−0.472237	−0.236118	+	0.971724i	$0.575875\pi$
$84$	1.00000	0.109109
$85$	9.94320	1.07849
$86$	9.63862	1.03936
$87$	−2.07759	−0.222741
$88$	−3.17452	−0.338405
$89$	−16.2931	−1.72706	−0.863532	−	0.504295i	$-0.831753\pi$
$89$	−16.2931	−1.72706	−0.863532	+	0.504295i	$0.831753\pi$
$90$	−1.78801	−0.188473
$91$	0	0
$92$	6.13356	0.639467
$93$	−5.63862	−0.584698
$94$	−10.5086	−1.08388
$95$	−11.0669	−1.13544
$96$	1.00000	0.102062
$97$	−17.4892	−1.77576	−0.887881	−	0.460072i	$-0.847823\pi$
$97$	−17.4892	−1.77576	−0.887881	+	0.460072i	$0.847823\pi$
$98$	−1.00000	−0.101015
$99$	3.17452	0.319052
$100$	−1.80301	−0.180301
$101$	−4.06866	−0.404847	−0.202424	−	0.979298i	$-0.564882\pi$
$101$	−4.06866	−0.404847	−0.202424	+	0.979298i	$0.564882\pi$
$102$	5.56103	0.550624
$103$	18.0768	1.78116	0.890578	−	0.454831i	$-0.150300\pi$
$103$	18.0768	1.78116	0.890578	+	0.454831i	$0.150300\pi$
$104$	0	0
$105$	1.78801	0.174492
$106$	−3.60200	−0.349857
$107$	−1.54169	−0.149041	−0.0745206	−	0.997219i	$-0.523743\pi$
$107$	−1.54169	−0.149041	−0.0745206	+	0.997219i	$0.523743\pi$
$108$	−1.00000	−0.0962250
$109$	7.37731	0.706618	0.353309	−	0.935507i	$-0.385056\pi$
$109$	7.37731	0.706618	0.353309	+	0.935507i	$0.385056\pi$
$110$	−5.67609	−0.541194
$111$	3.09693	0.293948
$112$	−1.00000	−0.0944911
$113$	−9.91321	−0.932556	−0.466278	−	0.884638i	$-0.654405\pi$
$113$	−9.91321	−0.932556	−0.466278	+	0.884638i	$0.654405\pi$
$114$	−6.18952	−0.579701
$115$	10.9669	1.02267
$116$	2.07759	0.192900
$117$	0	0
$118$	−2.78138	−0.256047
$119$	−5.56103	−0.509779
$120$	1.78801	0.163223
$121$	−0.922407	−0.0838552
$122$	−1.68879	−0.152896
$123$	−1.49843	−0.135109
$124$	5.63862	0.506363
$125$	−12.1639	−1.08797
$126$	1.00000	0.0890871
$127$	18.3490	1.62821	0.814107	−	0.580715i	$-0.197227\pi$
$127$	18.3490	1.62821	0.814107	+	0.580715i	$0.197227\pi$
$128$	−1.00000	−0.0883883
$129$	9.63862	0.848634
$130$	0	0
$131$	5.91928	0.517170	0.258585	−	0.965989i	$-0.416744\pi$
$131$	5.91928	0.517170	0.258585	+	0.965989i	$0.416744\pi$
$132$	−3.17452	−0.276307
$133$	6.18952	0.536699
$134$	−11.5544	−0.998148
$135$	−1.78801	−0.153888
$136$	−5.56103	−0.476855
$137$	−8.80301	−0.752092	−0.376046	−	0.926601i	$-0.622716\pi$
$137$	−8.80301	−0.752092	−0.376046	+	0.926601i	$0.622716\pi$
$138$	6.13356	0.522123
$139$	18.9744	1.60939	0.804694	−	0.593690i	$-0.202329\pi$
$139$	18.9744	1.60939	0.804694	+	0.593690i	$0.202329\pi$
$140$	−1.78801	−0.151115
$141$	−10.5086	−0.884981
$142$	0.598496	0.0502247
$143$	0	0
$144$	1.00000	0.0833333
$145$	3.71476	0.308494
$146$	0.423973	0.0350883
$147$	−1.00000	−0.0824786
$148$	−3.09693	−0.254566
$149$	13.9625	1.14386	0.571928	−	0.820304i	$-0.306196\pi$
$149$	13.9625	1.14386	0.571928	+	0.820304i	$0.306196\pi$
$150$	−1.80301	−0.147215
$151$	−17.8426	−1.45201	−0.726006	−	0.687688i	$-0.758626\pi$
$151$	−17.8426	−1.45201	−0.726006	+	0.687688i	$0.758626\pi$
$152$	6.18952	0.502036
$153$	5.56103	0.449583
$154$	3.17452	0.255810
$155$	10.0819	0.809800
$156$	0	0
$157$	4.57916	0.365457	0.182728	−	0.983163i	$-0.441507\pi$
$157$	4.57916	0.365457	0.182728	+	0.983163i	$0.441507\pi$
$158$	−6.96254	−0.553910
$159$	−3.60200	−0.285657
$160$	−1.78801	−0.141355
$161$	−6.13356	−0.483392
$162$	−1.00000	−0.0785674
$163$	−12.2706	−0.961109	−0.480554	−	0.876965i	$-0.659565\pi$
$163$	−12.2706	−0.961109	−0.480554	+	0.876965i	$0.659565\pi$
$164$	1.49843	0.117008
$165$	−5.67609	−0.441883
$166$	4.30228	0.333922
$167$	16.6981	1.29214	0.646068	−	0.763279i	$-0.276412\pi$
$167$	16.6981	1.29214	0.646068	+	0.763279i	$0.276412\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	−9.94320	−0.762609
$171$	−6.18952	−0.473324
$172$	−9.63862	−0.734938
$173$	7.37731	0.560886	0.280443	−	0.959871i	$-0.409519\pi$
$173$	7.37731	0.560886	0.280443	+	0.959871i	$0.409519\pi$
$174$	2.07759	0.157502
$175$	1.80301	0.136295
$176$	3.17452	0.239289
$177$	−2.78138	−0.209061
$178$	16.2931	1.22122
$179$	19.8202	1.48143	0.740714	−	0.671821i	$-0.234487\pi$
$179$	19.8202	1.48143	0.740714	+	0.671821i	$0.234487\pi$
$180$	1.78801	0.133271
$181$	18.3266	1.36220	0.681102	−	0.732189i	$-0.261501\pi$
$181$	18.3266	1.36220	0.681102	+	0.732189i	$0.261501\pi$
$182$	0	0
$183$	−1.68879	−0.124839
$184$	−6.13356	−0.452172
$185$	−5.53735	−0.407114
$186$	5.63862	0.413444
$187$	17.6536	1.29096
$188$	10.5086	0.766416
$189$	1.00000	0.0727393
$190$	11.0669	0.802880
$191$	−15.0304	−1.08756	−0.543779	−	0.839228i	$-0.683007\pi$
$191$	−15.0304	−1.08756	−0.543779	+	0.839228i	$0.683007\pi$
$192$	−1.00000	−0.0721688
$193$	−5.45490	−0.392652	−0.196326	−	0.980539i	$-0.562901\pi$
$193$	−5.45490	−0.392652	−0.196326	+	0.980539i	$0.562901\pi$
$194$	17.4892	1.25565
$195$	0	0
$196$	1.00000	0.0714286
$197$	7.62970	0.543593	0.271797	−	0.962355i	$-0.412382\pi$
$197$	7.62970	0.543593	0.271797	+	0.962355i	$0.412382\pi$
$198$	−3.17452	−0.225603
$199$	5.99023	0.424636	0.212318	−	0.977201i	$-0.431899\pi$
$199$	5.99023	0.424636	0.212318	+	0.977201i	$0.431899\pi$
$200$	1.80301	0.127492
$201$	−11.5544	−0.814984
$202$	4.06866	0.286270
$203$	−2.07759	−0.145818
$204$	−5.56103	−0.389350
$205$	2.67922	0.187125
$206$	−18.0768	−1.25947
$207$	6.13356	0.426312
$208$	0	0
$209$	−19.6488	−1.35913
$210$	−1.78801	−0.123385
$211$	−2.77302	−0.190902	−0.0954512	−	0.995434i	$-0.530429\pi$
$211$	−2.77302	−0.190902	−0.0954512	+	0.995434i	$0.530429\pi$
$212$	3.60200	0.247386
$213$	0.598496	0.0410083
$214$	1.54169	0.105388
$215$	−17.2340	−1.17535
$216$	1.00000	0.0680414
$217$	−5.63862	−0.382775
$218$	−7.37731	−0.499654
$219$	0.423973	0.0286495
$220$	5.67609	0.382682
$221$	0	0
$222$	−3.09693	−0.207852
$223$	−22.5354	−1.50908	−0.754542	−	0.656252i	$-0.772141\pi$
$223$	−22.5354	−1.50908	−0.754542	+	0.656252i	$0.772141\pi$
$224$	1.00000	0.0668153
$225$	−1.80301	−0.120201
$226$	9.91321	0.659417
$227$	−1.83155	−0.121564	−0.0607820	−	0.998151i	$-0.519359\pi$
$227$	−1.83155	−0.121564	−0.0607820	+	0.998151i	$0.519359\pi$
$228$	6.18952	0.409911
$229$	−22.6060	−1.49385	−0.746924	−	0.664910i	$-0.768470\pi$
$229$	−22.6060	−1.49385	−0.746924	+	0.664910i	$0.768470\pi$
$230$	−10.9669	−0.723135
$231$	3.17452	0.208868
$232$	−2.07759	−0.136401
$233$	9.43897	0.618367	0.309184	−	0.951002i	$-0.399944\pi$
$233$	9.43897	0.618367	0.309184	+	0.951002i	$0.399944\pi$
$234$	0	0
$235$	18.7895	1.22569
$236$	2.78138	0.181052
$237$	−6.96254	−0.452265
$238$	5.56103	0.360468
$239$	15.8757	1.02692	0.513458	−	0.858115i	$-0.328364\pi$
$239$	15.8757	1.02692	0.513458	+	0.858115i	$0.328364\pi$
$240$	−1.78801	−0.115416
$241$	−23.9251	−1.54115	−0.770575	−	0.637350i	$-0.780031\pi$
$241$	−23.9251	−1.54115	−0.770575	+	0.637350i	$0.780031\pi$
$242$	0.922407	0.0592946
$243$	−1.00000	−0.0641500
$244$	1.68879	0.108114
$245$	1.78801	0.114232
$246$	1.49843	0.0955367
$247$	0	0
$248$	−5.63862	−0.358053
$249$	4.30228	0.272646
$250$	12.1639	0.769311
$251$	−20.5236	−1.29544	−0.647718	−	0.761880i	$-0.724277\pi$
$251$	−20.5236	−1.29544	−0.647718	+	0.761880i	$0.724277\pi$
$252$	−1.00000	−0.0629941
$253$	19.4711	1.22414
$254$	−18.3490	−1.15132
$255$	−9.94320	−0.622667
$256$	1.00000	0.0625000
$257$	−0.826688	−0.0515674	−0.0257837	−	0.999668i	$-0.508208\pi$
$257$	−0.826688	−0.0515674	−0.0257837	+	0.999668i	$0.508208\pi$
$258$	−9.63862	−0.600075
$259$	3.09693	0.192434
$260$	0	0
$261$	2.07759	0.128600
$262$	−5.91928	−0.365694
$263$	20.3609	1.25551	0.627754	−	0.778412i	$-0.283975\pi$
$263$	20.3609	1.25551	0.627754	+	0.778412i	$0.283975\pi$
$264$	3.17452	0.195378
$265$	6.44042	0.395632
$266$	−6.18952	−0.379504
$267$	16.2931	0.997120
$268$	11.5544	0.705797
$269$	−20.5175	−1.25097	−0.625487	−	0.780235i	$-0.715100\pi$
$269$	−20.5175	−1.25097	−0.625487	+	0.780235i	$0.715100\pi$
$270$	1.78801	0.108815
$271$	−12.1815	−0.739975	−0.369988	−	0.929037i	$-0.620638\pi$
$271$	−12.1815	−0.739975	−0.369988	+	0.929037i	$0.620638\pi$
$272$	5.56103	0.337187
$273$	0	0
$274$	8.80301	0.531809
$275$	−5.72369	−0.345152
$276$	−6.13356	−0.369197
$277$	8.62484	0.518216	0.259108	−	0.965848i	$-0.416571\pi$
$277$	8.62484	0.518216	0.259108	+	0.965848i	$0.416571\pi$
$278$	−18.9744	−1.13801
$279$	5.63862	0.337576
$280$	1.78801	0.106854
$281$	−24.2922	−1.44915	−0.724577	−	0.689194i	$-0.757965\pi$
$281$	−24.2922	−1.44915	−0.724577	+	0.689194i	$0.757965\pi$
$282$	10.5086	0.625776
$283$	10.7211	0.637302	0.318651	−	0.947872i	$-0.396770\pi$
$283$	10.7211	0.637302	0.318651	+	0.947872i	$0.396770\pi$
$284$	−0.598496	−0.0355142
$285$	11.0669	0.655549
$286$	0	0
$287$	−1.49843	−0.0884498
$288$	−1.00000	−0.0589256
$289$	13.9251	0.819122
$290$	−3.71476	−0.218138
$291$	17.4892	1.02524
$292$	−0.423973	−0.0248112
$293$	21.4278	1.25183	0.625914	−	0.779892i	$-0.284726\pi$
$293$	21.4278	1.25183	0.625914	+	0.779892i	$0.284726\pi$
$294$	1.00000	0.0583212
$295$	4.97314	0.289547
$296$	3.09693	0.180005
$297$	−3.17452	−0.184204
$298$	−13.9625	−0.808828
$299$	0	0
$300$	1.80301	0.104097
$301$	9.63862	0.555561
$302$	17.8426	1.02673
$303$	4.06866	0.233739
$304$	−6.18952	−0.354993
$305$	3.01958	0.172901
$306$	−5.56103	−0.317903
$307$	7.59364	0.433392	0.216696	−	0.976239i	$-0.430472\pi$
$307$	7.59364	0.433392	0.216696	+	0.976239i	$0.430472\pi$
$308$	−3.17452	−0.180885
$309$	−18.0768	−1.02835
$310$	−10.0819	−0.572615
$311$	−25.6355	−1.45366	−0.726828	−	0.686820i	$-0.759006\pi$
$311$	−25.6355	−1.45366	−0.726828	+	0.686820i	$0.759006\pi$
$312$	0	0
$313$	−1.71308	−0.0968293	−0.0484146	−	0.998827i	$-0.515417\pi$
$313$	−1.71308	−0.0968293	−0.0484146	+	0.998827i	$0.515417\pi$
$314$	−4.57916	−0.258417
$315$	−1.78801	−0.100743
$316$	6.96254	0.391673
$317$	33.2098	1.86525	0.932624	−	0.360850i	$-0.117513\pi$
$317$	33.2098	1.86525	0.932624	+	0.360850i	$0.117513\pi$
$318$	3.60200	0.201990
$319$	6.59536	0.369269
$320$	1.78801	0.0999530
$321$	1.54169	0.0860490
$322$	6.13356	0.341810
$323$	−34.4201	−1.91519
$324$	1.00000	0.0555556
$325$	0	0
$326$	12.2706	0.679606
$327$	−7.37731	−0.407966
$328$	−1.49843	−0.0827372
$329$	−10.5086	−0.579356
$330$	5.67609	0.312458
$331$	4.95987	0.272619	0.136310	−	0.990666i	$-0.456476\pi$
$331$	4.95987	0.272619	0.136310	+	0.990666i	$0.456476\pi$
$332$	−4.30228	−0.236118
$333$	−3.09693	−0.169711
$334$	−16.6981	−0.913679
$335$	20.6594	1.12874
$336$	1.00000	0.0545545
$337$	−23.6174	−1.28652	−0.643260	−	0.765648i	$-0.722419\pi$
$337$	−23.6174	−1.28652	−0.643260	+	0.765648i	$0.722419\pi$
$338$	0	0
$339$	9.91321	0.538412
$340$	9.94320	0.539246
$341$	17.8999	0.969336
$342$	6.18952	0.334691
$343$	−1.00000	−0.0539949
$344$	9.63862	0.519680
$345$	−10.9669	−0.590437
$346$	−7.37731	−0.396607
$347$	−7.16967	−0.384888	−0.192444	−	0.981308i	$-0.561641\pi$
$347$	−7.16967	−0.384888	−0.192444	+	0.981308i	$0.561641\pi$
$348$	−2.07759	−0.111371
$349$	12.3732	0.662324	0.331162	−	0.943574i	$-0.392559\pi$
$349$	12.3732	0.662324	0.331162	+	0.943574i	$0.392559\pi$
$350$	−1.80301	−0.0963749
$351$	0	0
$352$	−3.17452	−0.169203
$353$	−26.2138	−1.39522	−0.697610	−	0.716477i	$-0.745753\pi$
$353$	−26.2138	−1.39522	−0.697610	+	0.716477i	$0.745753\pi$
$354$	2.78138	0.147829
$355$	−1.07012	−0.0567960
$356$	−16.2931	−0.863532
$357$	5.56103	0.294321
$358$	−19.8202	−1.04753
$359$	3.61956	0.191033	0.0955165	−	0.995428i	$-0.469550\pi$
$359$	3.61956	0.191033	0.0955165	+	0.995428i	$0.469550\pi$
$360$	−1.78801	−0.0942366
$361$	19.3101	1.01632
$362$	−18.3266	−0.963223
$363$	0.922407	0.0484138
$364$	0	0
$365$	−0.758070	−0.0396792
$366$	1.68879	0.0882745
$367$	−8.06489	−0.420984	−0.210492	−	0.977596i	$-0.567507\pi$
$367$	−8.06489	−0.420984	−0.210492	+	0.977596i	$0.567507\pi$
$368$	6.13356	0.319734
$369$	1.49843	0.0780054
$370$	5.53735	0.287873
$371$	−3.60200	−0.187006
$372$	−5.63862	−0.292349
$373$	29.1702	1.51037	0.755187	−	0.655509i	$-0.227546\pi$
$373$	29.1702	1.51037	0.755187	+	0.655509i	$0.227546\pi$
$374$	−17.6536	−0.912847
$375$	12.1639	0.628140
$376$	−10.5086	−0.541938
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	26.9966	1.38672	0.693361	−	0.720590i	$-0.256129\pi$
$379$	26.9966	1.38672	0.693361	+	0.720590i	$0.256129\pi$
$380$	−11.0669	−0.567722
$381$	−18.3490	−0.940050
$382$	15.0304	0.769020
$383$	26.1146	1.33439	0.667197	−	0.744882i	$-0.267494\pi$
$383$	26.1146	1.33439	0.667197	+	0.744882i	$0.267494\pi$
$384$	1.00000	0.0510310
$385$	−5.67609	−0.289280
$386$	5.45490	0.277647
$387$	−9.63862	−0.489959
$388$	−17.4892	−0.887881
$389$	32.7110	1.65852	0.829258	−	0.558866i	$-0.188764\pi$
$389$	32.7110	1.65852	0.829258	+	0.558866i	$0.188764\pi$
$390$	0	0
$391$	34.1089	1.72496
$392$	−1.00000	−0.0505076
$393$	−5.91928	−0.298588
$394$	−7.62970	−0.384379
$395$	12.4491	0.626383
$396$	3.17452	0.159526
$397$	0.606017	0.0304151	0.0152076	−	0.999884i	$-0.495159\pi$
$397$	0.606017	0.0304151	0.0152076	+	0.999884i	$0.495159\pi$
$398$	−5.99023	−0.300263
$399$	−6.18952	−0.309863
$400$	−1.80301	−0.0901504
$401$	10.2071	0.509720	0.254860	−	0.966978i	$-0.417971\pi$
$401$	10.2071	0.509720	0.254860	+	0.966978i	$0.417971\pi$
$402$	11.5544	0.576281
$403$	0	0
$404$	−4.06866	−0.202424
$405$	1.78801	0.0888471
$406$	2.07759	0.103109
$407$	−9.83127	−0.487318
$408$	5.56103	0.275312
$409$	9.25912	0.457834	0.228917	−	0.973446i	$-0.426482\pi$
$409$	9.25912	0.457834	0.228917	+	0.973446i	$0.426482\pi$
$410$	−2.67922	−0.132317
$411$	8.80301	0.434220
$412$	18.0768	0.890578
$413$	−2.78138	−0.136863
$414$	−6.13356	−0.301448
$415$	−7.69254	−0.377612
$416$	0	0
$417$	−18.9744	−0.929180
$418$	19.6488	0.961052
$419$	12.8489	0.627709	0.313855	−	0.949471i	$-0.398380\pi$
$419$	12.8489	0.627709	0.313855	+	0.949471i	$0.398380\pi$
$420$	1.78801	0.0872461
$421$	−7.21371	−0.351575	−0.175787	−	0.984428i	$-0.556247\pi$
$421$	−7.21371	−0.351575	−0.175787	+	0.984428i	$0.556247\pi$
$422$	2.77302	0.134988
$423$	10.5086	0.510944
$424$	−3.60200	−0.174929
$425$	−10.0266	−0.486361
$426$	−0.598496	−0.0289972
$427$	−1.68879	−0.0817263
$428$	−1.54169	−0.0745206
$429$	0	0
$430$	17.2340	0.831097
$431$	5.98066	0.288078	0.144039	−	0.989572i	$-0.453991\pi$
$431$	5.98066	0.288078	0.144039	+	0.989572i	$0.453991\pi$
$432$	−1.00000	−0.0481125
$433$	12.6029	0.605656	0.302828	−	0.953045i	$-0.402069\pi$
$433$	12.6029	0.605656	0.302828	+	0.953045i	$0.402069\pi$
$434$	5.63862	0.270663
$435$	−3.71476	−0.178109
$436$	7.37731	0.353309
$437$	−37.9637	−1.81605
$438$	−0.423973	−0.0202582
$439$	19.5593	0.933515	0.466757	−	0.884385i	$-0.345422\pi$
$439$	19.5593	0.933515	0.466757	+	0.884385i	$0.345422\pi$
$440$	−5.67609	−0.270597
$441$	1.00000	0.0476190
$442$	0	0
$443$	−40.2601	−1.91281	−0.956407	−	0.292038i	$-0.905666\pi$
$443$	−40.2601	−1.91281	−0.956407	+	0.292038i	$0.905666\pi$
$444$	3.09693	0.146974
$445$	−29.1322	−1.38100
$446$	22.5354	1.06708
$447$	−13.9625	−0.660405
$448$	−1.00000	−0.0472456
$449$	28.6159	1.35047	0.675234	−	0.737604i	$-0.264043\pi$
$449$	28.6159	1.35047	0.675234	+	0.737604i	$0.264043\pi$
$450$	1.80301	0.0849946
$451$	4.75681	0.223990
$452$	−9.91321	−0.466278
$453$	17.8426	0.838320
$454$	1.83155	0.0859587
$455$	0	0
$456$	−6.18952	−0.289851
$457$	−6.35040	−0.297059	−0.148530	−	0.988908i	$-0.547454\pi$
$457$	−6.35040	−0.297059	−0.148530	+	0.988908i	$0.547454\pi$
$458$	22.6060	1.05631
$459$	−5.56103	−0.259567
$460$	10.9669	0.511333
$461$	24.2238	1.12822	0.564109	−	0.825701i	$-0.309220\pi$
$461$	24.2238	1.12822	0.564109	+	0.825701i	$0.309220\pi$
$462$	−3.17452	−0.147692
$463$	17.3851	0.807954	0.403977	−	0.914769i	$-0.367628\pi$
$463$	17.3851	0.807954	0.403977	+	0.914769i	$0.367628\pi$
$464$	2.07759	0.0964498
$465$	−10.0819	−0.467539
$466$	−9.43897	−0.437252
$467$	14.8537	0.687349	0.343675	−	0.939089i	$-0.388328\pi$
$467$	14.8537	0.687349	0.343675	+	0.939089i	$0.388328\pi$
$468$	0	0
$469$	−11.5544	−0.533532
$470$	−18.7895	−0.866693
$471$	−4.57916	−0.210996
$472$	−2.78138	−0.128023
$473$	−30.5980	−1.40690
$474$	6.96254	0.319800
$475$	11.1598	0.512045
$476$	−5.56103	−0.254889
$477$	3.60200	0.164924
$478$	−15.8757	−0.726140
$479$	−38.6840	−1.76752	−0.883759	−	0.467942i	$-0.844996\pi$
$479$	−38.6840	−1.76752	−0.883759	+	0.467942i	$0.844996\pi$
$480$	1.78801	0.0816113
$481$	0	0
$482$	23.9251	1.08976
$483$	6.13356	0.279086
$484$	−0.922407	−0.0419276
$485$	−31.2710	−1.41994
$486$	1.00000	0.0453609
$487$	25.7244	1.16569	0.582843	−	0.812585i	$-0.301940\pi$
$487$	25.7244	1.16569	0.582843	+	0.812585i	$0.301940\pi$
$488$	−1.68879	−0.0764480
$489$	12.2706	0.554896
$490$	−1.78801	−0.0807742
$491$	−18.3490	−0.828081	−0.414040	−	0.910259i	$-0.635883\pi$
$491$	−18.3490	−0.828081	−0.414040	+	0.910259i	$0.635883\pi$
$492$	−1.49843	−0.0675546
$493$	11.5536	0.520346
$494$	0	0
$495$	5.67609	0.255121
$496$	5.63862	0.253182
$497$	0.598496	0.0268462
$498$	−4.30228	−0.192790
$499$	17.8096	0.797269	0.398635	−	0.917110i	$-0.369484\pi$
$499$	17.8096	0.797269	0.398635	+	0.917110i	$0.369484\pi$
$500$	−12.1639	−0.543985
$501$	−16.6981	−0.746016
$502$	20.5236	0.916012
$503$	30.9422	1.37965	0.689823	−	0.723978i	$-0.257689\pi$
$503$	30.9422	1.37965	0.689823	+	0.723978i	$0.257689\pi$
$504$	1.00000	0.0445435
$505$	−7.27483	−0.323726
$506$	−19.4711	−0.865596
$507$	0	0
$508$	18.3490	0.814107
$509$	−13.8083	−0.612042	−0.306021	−	0.952025i	$-0.598998\pi$
$509$	−13.8083	−0.612042	−0.306021	+	0.952025i	$0.598998\pi$
$510$	9.94320	0.440292
$511$	0.423973	0.0187555
$512$	−1.00000	−0.0441942
$513$	6.18952	0.273274
$514$	0.826688	0.0364636
$515$	32.3215	1.42425
$516$	9.63862	0.424317
$517$	33.3597	1.46716
$518$	−3.09693	−0.136071
$519$	−7.37731	−0.323828
$520$	0	0
$521$	−11.4549	−0.501848	−0.250924	−	0.968007i	$-0.580734\pi$
$521$	−11.4549	−0.501848	−0.250924	+	0.968007i	$0.580734\pi$
$522$	−2.07759	−0.0909338
$523$	0.930396	0.0406834	0.0203417	−	0.999793i	$-0.493525\pi$
$523$	0.930396	0.0406834	0.0203417	+	0.999793i	$0.493525\pi$
$524$	5.91928	0.258585
$525$	−1.80301	−0.0786897
$526$	−20.3609	−0.887778
$527$	31.3566	1.36591
$528$	−3.17452	−0.138153
$529$	14.6205	0.635674
$530$	−6.44042	−0.279754
$531$	2.78138	0.120702
$532$	6.18952	0.268350
$533$	0	0
$534$	−16.2931	−0.705071
$535$	−2.75657	−0.119177
$536$	−11.5544	−0.499074
$537$	−19.8202	−0.855303
$538$	20.5175	0.884572
$539$	3.17452	0.136736
$540$	−1.78801	−0.0769438
$541$	−22.7965	−0.980097	−0.490048	−	0.871695i	$-0.663021\pi$
$541$	−22.7965	−0.980097	−0.490048	+	0.871695i	$0.663021\pi$
$542$	12.1815	0.523241
$543$	−18.3266	−0.786469
$544$	−5.56103	−0.238427
$545$	13.1907	0.565029
$546$	0	0
$547$	31.6698	1.35410	0.677052	−	0.735935i	$-0.263257\pi$
$547$	31.6698	1.35410	0.677052	+	0.735935i	$0.263257\pi$
$548$	−8.80301	−0.376046
$549$	1.68879	0.0720758
$550$	5.72369	0.244059
$551$	−12.8593	−0.547824
$552$	6.13356	0.261061
$553$	−6.96254	−0.296077
$554$	−8.62484	−0.366434
$555$	5.53735	0.235047
$556$	18.9744	0.804694
$557$	−10.8383	−0.459233	−0.229616	−	0.973281i	$-0.573747\pi$
$557$	−10.8383	−0.459233	−0.229616	+	0.973281i	$0.573747\pi$
$558$	−5.63862	−0.238702
$559$	0	0
$560$	−1.78801	−0.0755574
$561$	−17.6536	−0.745336
$562$	24.2922	1.02471
$563$	15.4725	0.652089	0.326044	−	0.945354i	$-0.394284\pi$
$563$	15.4725	0.652089	0.326044	+	0.945354i	$0.394284\pi$
$564$	−10.5086	−0.442491
$565$	−17.7249	−0.745694
$566$	−10.7211	−0.450640
$567$	−1.00000	−0.0419961
$568$	0.598496	0.0251123
$569$	33.7334	1.41418	0.707088	−	0.707126i	$-0.250008\pi$
$569$	33.7334	1.41418	0.707088	+	0.707126i	$0.250008\pi$
$570$	−11.0669	−0.463543
$571$	43.6140	1.82519	0.912594	−	0.408868i	$-0.134076\pi$
$571$	43.6140	1.82519	0.912594	+	0.408868i	$0.134076\pi$
$572$	0	0
$573$	15.0304	0.627902
$574$	1.49843	0.0625434
$575$	−11.0589	−0.461186
$576$	1.00000	0.0416667
$577$	−10.8368	−0.451143	−0.225571	−	0.974227i	$-0.572425\pi$
$577$	−10.8368	−0.451143	−0.225571	+	0.974227i	$0.572425\pi$
$578$	−13.9251	−0.579207
$579$	5.45490	0.226698
$580$	3.71476	0.154247
$581$	4.30228	0.178489
$582$	−17.4892	−0.724952
$583$	11.4346	0.473574
$584$	0.423973	0.0175441
$585$	0	0
$586$	−21.4278	−0.885176
$587$	−26.0538	−1.07535	−0.537677	−	0.843151i	$-0.680698\pi$
$587$	−26.0538	−1.07535	−0.537677	+	0.843151i	$0.680698\pi$
$588$	−1.00000	−0.0412393
$589$	−34.9004	−1.43804
$590$	−4.97314	−0.204741
$591$	−7.62970	−0.313844
$592$	−3.09693	−0.127283
$593$	−1.68393	−0.0691509	−0.0345754	−	0.999402i	$-0.511008\pi$
$593$	−1.68393	−0.0691509	−0.0345754	+	0.999402i	$0.511008\pi$
$594$	3.17452	0.130252
$595$	−9.94320	−0.407631
$596$	13.9625	0.571928
$597$	−5.99023	−0.245164
$598$	0	0
$599$	−6.54081	−0.267250	−0.133625	−	0.991032i	$-0.542662\pi$
$599$	−6.54081	−0.267250	−0.133625	+	0.991032i	$0.542662\pi$
$600$	−1.80301	−0.0736075
$601$	38.4774	1.56953	0.784763	−	0.619796i	$-0.212784\pi$
$601$	38.4774	1.56953	0.784763	+	0.619796i	$0.212784\pi$
$602$	−9.63862	−0.392841
$603$	11.5544	0.470531
$604$	−17.8426	−0.726006
$605$	−1.64928	−0.0670526
$606$	−4.06866	−0.165278
$607$	−9.43594	−0.382993	−0.191496	−	0.981493i	$-0.561334\pi$
$607$	−9.43594	−0.382993	−0.191496	+	0.981493i	$0.561334\pi$
$608$	6.18952	0.251018
$609$	2.07759	0.0841883
$610$	−3.01958	−0.122259
$611$	0	0
$612$	5.56103	0.224791
$613$	25.4254	1.02692	0.513462	−	0.858113i	$-0.328363\pi$
$613$	25.4254	1.02692	0.513462	+	0.858113i	$0.328363\pi$
$614$	−7.59364	−0.306454
$615$	−2.67922	−0.108037
$616$	3.17452	0.127905
$617$	28.6995	1.15540	0.577699	−	0.816250i	$-0.303951\pi$
$617$	28.6995	1.15540	0.577699	+	0.816250i	$0.303951\pi$
$618$	18.0768	0.727154
$619$	−9.61494	−0.386457	−0.193229	−	0.981154i	$-0.561896\pi$
$619$	−9.61494	−0.386457	−0.193229	+	0.981154i	$0.561896\pi$
$620$	10.0819	0.404900
$621$	−6.13356	−0.246131
$622$	25.6355	1.02789
$623$	16.2931	0.652769
$624$	0	0
$625$	−12.7341	−0.509365
$626$	1.71308	0.0684686
$627$	19.6488	0.784696
$628$	4.57916	0.182728
$629$	−17.2221	−0.686691
$630$	1.78801	0.0712362
$631$	−34.5770	−1.37649	−0.688244	−	0.725480i	$-0.741618\pi$
$631$	−34.5770	−1.37649	−0.688244	+	0.725480i	$0.741618\pi$
$632$	−6.96254	−0.276955
$633$	2.77302	0.110218
$634$	−33.2098	−1.31893
$635$	32.8083	1.30196
$636$	−3.60200	−0.142829
$637$	0	0
$638$	−6.59536	−0.261113
$639$	−0.598496	−0.0236761
$640$	−1.78801	−0.0706774
$641$	6.51291	0.257245	0.128622	−	0.991694i	$-0.458945\pi$
$641$	6.51291	0.257245	0.128622	+	0.991694i	$0.458945\pi$
$642$	−1.54169	−0.0608458
$643$	−25.2869	−0.997219	−0.498609	−	0.866827i	$-0.666156\pi$
$643$	−25.2869	−0.997219	−0.498609	+	0.866827i	$0.666156\pi$
$644$	−6.13356	−0.241696
$645$	17.2340	0.678588
$646$	34.4201	1.35424
$647$	11.9159	0.468461	0.234231	−	0.972181i	$-0.424743\pi$
$647$	11.9159	0.468461	0.234231	+	0.972181i	$0.424743\pi$
$648$	−1.00000	−0.0392837
$649$	8.82955	0.346590
$650$	0	0
$651$	5.63862	0.220995
$652$	−12.2706	−0.480554
$653$	41.5017	1.62409	0.812043	−	0.583598i	$-0.198356\pi$
$653$	41.5017	1.62409	0.812043	+	0.583598i	$0.198356\pi$
$654$	7.37731	0.288476
$655$	10.5837	0.413541
$656$	1.49843	0.0585040
$657$	−0.423973	−0.0165408
$658$	10.5086	0.409667
$659$	15.7356	0.612970	0.306485	−	0.951875i	$-0.400847\pi$
$659$	15.7356	0.612970	0.306485	+	0.951875i	$0.400847\pi$
$660$	−5.67609	−0.220941
$661$	−26.1045	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$661$	−26.1045	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$662$	−4.95987	−0.192771
$663$	0	0
$664$	4.30228	0.166961
$665$	11.0669	0.429158
$666$	3.09693	0.120004
$667$	12.7430	0.493412
$668$	16.6981	0.646068
$669$	22.5354	0.871270
$670$	−20.6594	−0.798143
$671$	5.36110	0.206963
$672$	−1.00000	−0.0385758
$673$	1.24171	0.0478642	0.0239321	−	0.999714i	$-0.492381\pi$
$673$	1.24171	0.0478642	0.0239321	+	0.999714i	$0.492381\pi$
$674$	23.6174	0.909707
$675$	1.80301	0.0693978
$676$	0	0
$677$	29.2845	1.12550	0.562748	−	0.826629i	$-0.309744\pi$
$677$	29.2845	1.12550	0.562748	+	0.826629i	$0.309744\pi$
$678$	−9.91321	−0.380714
$679$	17.4892	0.671175
$680$	−9.94320	−0.381304
$681$	1.83155	0.0701850
$682$	−17.8999	−0.685424
$683$	42.7800	1.63693	0.818466	−	0.574555i	$-0.194825\pi$
$683$	42.7800	1.63693	0.818466	+	0.574555i	$0.194825\pi$
$684$	−6.18952	−0.236662
$685$	−15.7399	−0.601391
$686$	1.00000	0.0381802
$687$	22.6060	0.862473
$688$	−9.63862	−0.367469
$689$	0	0
$690$	10.9669	0.417502
$691$	18.8965	0.718858	0.359429	−	0.933172i	$-0.382971\pi$
$691$	18.8965	0.718858	0.359429	+	0.933172i	$0.382971\pi$
$692$	7.37731	0.280443
$693$	−3.17452	−0.120590
$694$	7.16967	0.272157
$695$	33.9265	1.28690
$696$	2.07759	0.0787509
$697$	8.33284	0.315629
$698$	−12.3732	−0.468334
$699$	−9.43897	−0.357015
$700$	1.80301	0.0681473
$701$	3.35161	0.126589	0.0632943	−	0.997995i	$-0.479839\pi$
$701$	3.35161	0.126589	0.0632943	+	0.997995i	$0.479839\pi$
$702$	0	0
$703$	19.1685	0.722954
$704$	3.17452	0.119644
$705$	−18.7895	−0.707652
$706$	26.2138	0.986570
$707$	4.06866	0.153018
$708$	−2.78138	−0.104531
$709$	−36.7735	−1.38106	−0.690529	−	0.723305i	$-0.742622\pi$
$709$	−36.7735	−1.38106	−0.690529	+	0.723305i	$0.742622\pi$
$710$	1.07012	0.0401608
$711$	6.96254	0.261115
$712$	16.2931	0.610609
$713$	34.5848	1.29521
$714$	−5.56103	−0.208116
$715$	0	0
$716$	19.8202	0.740714
$717$	−15.8757	−0.592891
$718$	−3.61956	−0.135081
$719$	16.1697	0.603029	0.301514	−	0.953462i	$-0.402508\pi$
$719$	16.1697	0.603029	0.301514	+	0.953462i	$0.402508\pi$
$720$	1.78801	0.0666353
$721$	−18.0768	−0.673213
$722$	−19.3101	−0.718649
$723$	23.9251	0.889783
$724$	18.3266	0.681102
$725$	−3.74592	−0.139120
$726$	−0.922407	−0.0342338
$727$	−27.2522	−1.01073	−0.505363	−	0.862907i	$-0.668642\pi$
$727$	−27.2522	−1.01073	−0.505363	+	0.862907i	$0.668642\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.758070	0.0280574
$731$	−53.6007	−1.98249
$732$	−1.68879	−0.0624195
$733$	39.6734	1.46537	0.732686	−	0.680567i	$-0.238267\pi$
$733$	39.6734	1.46537	0.732686	+	0.680567i	$0.238267\pi$
$734$	8.06489	0.297681
$735$	−1.78801	−0.0659519
$736$	−6.13356	−0.226086
$737$	36.6797	1.35111
$738$	−1.49843	−0.0551581
$739$	−25.4178	−0.935009	−0.467505	−	0.883991i	$-0.654847\pi$
$739$	−25.4178	−0.935009	−0.467505	+	0.883991i	$0.654847\pi$
$740$	−5.53735	−0.203557
$741$	0	0
$742$	3.60200	0.132234
$743$	24.8426	0.911387	0.455694	−	0.890137i	$-0.349391\pi$
$743$	24.8426	0.911387	0.455694	+	0.890137i	$0.349391\pi$
$744$	5.63862	0.206722
$745$	24.9652	0.914654
$746$	−29.1702	−1.06800
$747$	−4.30228	−0.157412
$748$	17.6536	0.645480
$749$	1.54169	0.0563323
$750$	−12.1639	−0.444162
$751$	−45.4421	−1.65821	−0.829103	−	0.559096i	$-0.811148\pi$
$751$	−45.4421	−1.65821	−0.829103	+	0.559096i	$0.811148\pi$
$752$	10.5086	0.383208
$753$	20.5236	0.747920
$754$	0	0
$755$	−31.9028	−1.16106
$756$	1.00000	0.0363696
$757$	6.41285	0.233079	0.116540	−	0.993186i	$-0.462820\pi$
$757$	6.41285	0.233079	0.116540	+	0.993186i	$0.462820\pi$
$758$	−26.9966	−0.980561
$759$	−19.4711	−0.706756
$760$	11.0669	0.401440
$761$	−32.1368	−1.16496	−0.582479	−	0.812846i	$-0.697917\pi$
$761$	−32.1368	−1.16496	−0.582479	+	0.812846i	$0.697917\pi$
$762$	18.3490	0.664716
$763$	−7.37731	−0.267077
$764$	−15.0304	−0.543779
$765$	9.94320	0.359497
$766$	−26.1146	−0.943558
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	38.9771	1.40555	0.702774	−	0.711413i	$-0.251944\pi$
$769$	38.9771	1.40555	0.702774	+	0.711413i	$0.251944\pi$
$770$	5.67609	0.204552
$771$	0.826688	0.0297724
$772$	−5.45490	−0.196326
$773$	2.42397	0.0871843	0.0435921	−	0.999049i	$-0.486120\pi$
$773$	2.42397	0.0871843	0.0435921	+	0.999049i	$0.486120\pi$
$774$	9.63862	0.346453
$775$	−10.1665	−0.365191
$776$	17.4892	0.627827
$777$	−3.09693	−0.111102
$778$	−32.7110	−1.17275
$779$	−9.27458	−0.332296
$780$	0	0
$781$	−1.89994	−0.0679851
$782$	−34.1089	−1.21973
$783$	−2.07759	−0.0742471
$784$	1.00000	0.0357143
$785$	8.18760	0.292228
$786$	5.91928	0.211134
$787$	50.7677	1.80967	0.904837	−	0.425758i	$-0.139992\pi$
$787$	50.7677	1.80967	0.904837	+	0.425758i	$0.139992\pi$
$788$	7.62970	0.271797
$789$	−20.3609	−0.724868
$790$	−12.4491	−0.442919
$791$	9.91321	0.352473
$792$	−3.17452	−0.112802
$793$	0	0
$794$	−0.606017	−0.0215067
$795$	−6.44042	−0.228418
$796$	5.99023	0.212318
$797$	27.2089	0.963787	0.481894	−	0.876230i	$-0.339949\pi$
$797$	27.2089	0.963787	0.481894	+	0.876230i	$0.339949\pi$
$798$	6.18952	0.219107
$799$	58.4385	2.06741
$800$	1.80301	0.0637460
$801$	−16.2931	−0.575688
$802$	−10.2071	−0.360426
$803$	−1.34591	−0.0474962
$804$	−11.5544	−0.407492
$805$	−10.9669	−0.386532
$806$	0	0
$807$	20.5175	0.722250
$808$	4.06866	0.143135
$809$	−43.4097	−1.52620	−0.763102	−	0.646278i	$-0.776325\pi$
$809$	−43.4097	−1.52620	−0.763102	+	0.646278i	$0.776325\pi$
$810$	−1.78801	−0.0628244
$811$	38.1252	1.33876	0.669378	−	0.742922i	$-0.266561\pi$
$811$	38.1252	1.33876	0.669378	+	0.742922i	$0.266561\pi$
$812$	−2.07759	−0.0729092
$813$	12.1815	0.427225
$814$	9.83127	0.344586
$815$	−21.9400	−0.768525
$816$	−5.56103	−0.194675
$817$	59.6584	2.08718
$818$	−9.25912	−0.323738
$819$	0	0
$820$	2.67922	0.0935624
$821$	−24.5879	−0.858123	−0.429062	−	0.903275i	$-0.641156\pi$
$821$	−24.5879	−0.858123	−0.429062	+	0.903275i	$0.641156\pi$
$822$	−8.80301	−0.307040
$823$	−31.2929	−1.09080	−0.545402	−	0.838175i	$-0.683623\pi$
$823$	−31.2929	−1.09080	−0.545402	+	0.838175i	$0.683623\pi$
$824$	−18.0768	−0.629734
$825$	5.72369	0.199273
$826$	2.78138	0.0967765
$827$	10.9236	0.379851	0.189926	−	0.981798i	$-0.439175\pi$
$827$	10.9236	0.379851	0.189926	+	0.981798i	$0.439175\pi$
$828$	6.13356	0.213156
$829$	43.7677	1.52011	0.760057	−	0.649856i	$-0.225171\pi$
$829$	43.7677	1.52011	0.760057	+	0.649856i	$0.225171\pi$
$830$	7.69254	0.267012
$831$	−8.62484	−0.299192
$832$	0	0
$833$	5.56103	0.192678
$834$	18.9744	0.657030
$835$	29.8564	1.03322
$836$	−19.6488	−0.679567
$837$	−5.63862	−0.194899
$838$	−12.8489	−0.443857
$839$	19.3002	0.666318	0.333159	−	0.942871i	$-0.391885\pi$
$839$	19.3002	0.666318	0.333159	+	0.942871i	$0.391885\pi$
$840$	−1.78801	−0.0616923
$841$	−24.6836	−0.851159
$842$	7.21371	0.248601
$843$	24.2922	0.836669
$844$	−2.77302	−0.0954512
$845$	0	0
$846$	−10.5086	−0.361292
$847$	0.922407	0.0316943
$848$	3.60200	0.123693
$849$	−10.7211	−0.367946
$850$	10.0266	0.343909
$851$	−18.9952	−0.651147
$852$	0.598496	0.0205041
$853$	28.9164	0.990078	0.495039	−	0.868871i	$-0.335154\pi$
$853$	28.9164	0.990078	0.495039	+	0.868871i	$0.335154\pi$
$854$	1.68879	0.0577892
$855$	−11.0669	−0.378481
$856$	1.54169	0.0526940
$857$	16.6946	0.570278	0.285139	−	0.958486i	$-0.407960\pi$
$857$	16.6946	0.570278	0.285139	+	0.958486i	$0.407960\pi$
$858$	0	0
$859$	27.5825	0.941103	0.470552	−	0.882372i	$-0.344055\pi$
$859$	27.5825	0.941103	0.470552	+	0.882372i	$0.344055\pi$
$860$	−17.2340	−0.587674
$861$	1.49843	0.0510665
$862$	−5.98066	−0.203702
$863$	31.9313	1.08696	0.543478	−	0.839424i	$-0.317107\pi$
$863$	31.9313	1.08696	0.543478	+	0.839424i	$0.317107\pi$
$864$	1.00000	0.0340207
$865$	13.1907	0.448498
$866$	−12.6029	−0.428263
$867$	−13.9251	−0.472920
$868$	−5.63862	−0.191387
$869$	22.1027	0.749784
$870$	3.71476	0.125942
$871$	0	0
$872$	−7.37731	−0.249827
$873$	−17.4892	−0.591921
$874$	37.9637	1.28414
$875$	12.1639	0.411214
$876$	0.423973	0.0143247
$877$	29.6196	1.00018	0.500091	−	0.865973i	$-0.333300\pi$
$877$	29.6196	1.00018	0.500091	+	0.865973i	$0.333300\pi$
$878$	−19.5593	−0.660095
$879$	−21.4278	−0.722743
$880$	5.67609	0.191341
$881$	−10.0974	−0.340192	−0.170096	−	0.985428i	$-0.554408\pi$
$881$	−10.0974	−0.340192	−0.170096	+	0.985428i	$0.554408\pi$
$882$	−1.00000	−0.0336718
$883$	−46.5103	−1.56520	−0.782598	−	0.622527i	$-0.786106\pi$
$883$	−46.5103	−1.56520	−0.782598	+	0.622527i	$0.786106\pi$
$884$	0	0
$885$	−4.97314	−0.167170
$886$	40.2601	1.35256
$887$	−26.5383	−0.891069	−0.445534	−	0.895265i	$-0.646986\pi$
$887$	−26.5383	−0.891069	−0.445534	+	0.895265i	$0.646986\pi$
$888$	−3.09693	−0.103926
$889$	−18.3490	−0.615407
$890$	29.1322	0.976515
$891$	3.17452	0.106351
$892$	−22.5354	−0.754542
$893$	−65.0430	−2.17658
$894$	13.9625	0.466977
$895$	35.4387	1.18458
$896$	1.00000	0.0334077
$897$	0	0
$898$	−28.6159	−0.954924
$899$	11.7148	0.390709
$900$	−1.80301	−0.0601003
$901$	20.0308	0.667324
$902$	−4.75681	−0.158385
$903$	−9.63862	−0.320753
$904$	9.91321	0.329708
$905$	32.7682	1.08925
$906$	−17.8426	−0.592781
$907$	−23.6391	−0.784923	−0.392462	−	0.919768i	$-0.628376\pi$
$907$	−23.6391	−0.784923	−0.392462	+	0.919768i	$0.628376\pi$
$908$	−1.83155	−0.0607820
$909$	−4.06866	−0.134949
$910$	0	0
$911$	−1.46896	−0.0486688	−0.0243344	−	0.999704i	$-0.507747\pi$
$911$	−1.46896	−0.0486688	−0.0243344	+	0.999704i	$0.507747\pi$
$912$	6.18952	0.204955
$913$	−13.6577	−0.452004
$914$	6.35040	0.210053
$915$	−3.01958	−0.0998242
$916$	−22.6060	−0.746924
$917$	−5.91928	−0.195472
$918$	5.56103	0.183541
$919$	43.0377	1.41968	0.709841	−	0.704362i	$-0.248767\pi$
$919$	43.0377	1.41968	0.709841	+	0.704362i	$0.248767\pi$
$920$	−10.9669	−0.361567
$921$	−7.59364	−0.250219
$922$	−24.2238	−0.797770
$923$	0	0
$924$	3.17452	0.104434
$925$	5.58379	0.183594
$926$	−17.3851	−0.571310
$927$	18.0768	0.593718
$928$	−2.07759	−0.0682003
$929$	−1.71851	−0.0563825	−0.0281912	−	0.999603i	$-0.508975\pi$
$929$	−1.71851	−0.0563825	−0.0281912	+	0.999603i	$0.508975\pi$
$930$	10.0819	0.330600
$931$	−6.18952	−0.202853
$932$	9.43897	0.309184
$933$	25.6355	0.839268
$934$	−14.8537	−0.486029
$935$	31.5649	1.03228
$936$	0	0
$937$	−20.0024	−0.653451	−0.326725	−	0.945119i	$-0.605945\pi$
$937$	−20.0024	−0.653451	−0.326725	+	0.945119i	$0.605945\pi$
$938$	11.5544	0.377264
$939$	1.71308	0.0559044
$940$	18.7895	0.612845
$941$	−11.8846	−0.387428	−0.193714	−	0.981058i	$-0.562053\pi$
$941$	−11.8846	−0.387428	−0.193714	+	0.981058i	$0.562053\pi$
$942$	4.57916	0.149197
$943$	9.19073	0.299291
$944$	2.78138	0.0905262
$945$	1.78801	0.0581641
$946$	30.5980	0.994828
$947$	6.17065	0.200519	0.100260	−	0.994961i	$-0.468033\pi$
$947$	6.17065	0.200519	0.100260	+	0.994961i	$0.468033\pi$
$948$	−6.96254	−0.226133
$949$	0	0
$950$	−11.1598	−0.362070
$951$	−33.2098	−1.07690
$952$	5.56103	0.180234
$953$	41.0723	1.33046	0.665231	−	0.746638i	$-0.268333\pi$
$953$	41.0723	1.33046	0.665231	+	0.746638i	$0.268333\pi$
$954$	−3.60200	−0.116619
$955$	−26.8745	−0.869638
$956$	15.8757	0.513458
$957$	−6.59536	−0.213198
$958$	38.6840	1.24982
$959$	8.80301	0.284264
$960$	−1.78801	−0.0577079
$961$	0.794081	0.0256155
$962$	0	0
$963$	−1.54169	−0.0496804
$964$	−23.9251	−0.770575
$965$	−9.75344	−0.313974
$966$	−6.13356	−0.197344
$967$	34.4847	1.10895	0.554477	−	0.832199i	$-0.312919\pi$
$967$	34.4847	1.10895	0.554477	+	0.832199i	$0.312919\pi$
$968$	0.922407	0.0296473
$969$	34.4201	1.10573
$970$	31.2710	1.00405
$971$	3.89555	0.125014	0.0625071	−	0.998045i	$-0.480090\pi$
$971$	3.89555	0.125014	0.0625071	+	0.998045i	$0.480090\pi$
$972$	−1.00000	−0.0320750
$973$	−18.9744	−0.608291
$974$	−25.7244	−0.824264
$975$	0	0
$976$	1.68879	0.0540569
$977$	−52.8223	−1.68994	−0.844968	−	0.534816i	$-0.820381\pi$
$977$	−52.8223	−1.68994	−0.844968	+	0.534816i	$0.820381\pi$
$978$	−12.2706	−0.392371
$979$	−51.7228	−1.65307
$980$	1.78801	0.0571160
$981$	7.37731	0.235539
$982$	18.3490	0.585542
$983$	−40.2176	−1.28274	−0.641371	−	0.767231i	$-0.721634\pi$
$983$	−40.2176	−1.28274	−0.641371	+	0.767231i	$0.721634\pi$
$984$	1.49843	0.0477683
$985$	13.6420	0.434670
$986$	−11.5536	−0.367940
$987$	10.5086	0.334492
$988$	0	0
$989$	−59.1190	−1.87988
$990$	−5.67609	−0.180398
$991$	37.1818	1.18112	0.590559	−	0.806994i	$-0.298907\pi$
$991$	37.1818	1.18112	0.590559	+	0.806994i	$0.298907\pi$
$992$	−5.63862	−0.179026
$993$	−4.95987	−0.157397
$994$	−0.598496	−0.0189831
$995$	10.7106	0.339549
$996$	4.30228	0.136323
$997$	−0.0740894	−0.00234644	−0.00117322	−	0.999999i	$-0.500373\pi$
$997$	−0.0740894	−0.00234644	−0.00117322	+	0.999999i	$0.500373\pi$
$998$	−17.8096	−0.563754
$999$	3.09693	0.0979825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cn.1.4		4
13.6	odd	12		546.2.s.e.127.3	yes	8
13.11	odd	12		546.2.s.e.43.4	✓	8
13.12	even	2		7098.2.a.co.1.1		4
39.11	even	12		1638.2.bj.f.1135.1		8
39.32	even	12		1638.2.bj.f.127.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.e.43.4	✓	8	13.11	odd	12
546.2.s.e.127.3	yes	8	13.6	odd	12
1638.2.bj.f.127.2		8	39.32	even	12
1638.2.bj.f.1135.1		8	39.11	even	12
7098.2.a.cn.1.4		4	1.1	even	1	trivial
7098.2.a.co.1.1		4	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.78801 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.78801 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.78801 q^{10} +3.17452 q^{11} -1.00000 q^{12} +1.00000 q^{14} -1.78801 q^{15} +1.00000 q^{16} +5.56103 q^{17} -1.00000 q^{18} -6.18952 q^{19} +1.78801 q^{20} +1.00000 q^{21} -3.17452 q^{22} +6.13356 q^{23} +1.00000 q^{24} -1.80301 q^{25} -1.00000 q^{27} -1.00000 q^{28} +2.07759 q^{29} +1.78801 q^{30} +5.63862 q^{31} -1.00000 q^{32} -3.17452 q^{33} -5.56103 q^{34} -1.78801 q^{35} +1.00000 q^{36} -3.09693 q^{37} +6.18952 q^{38} -1.78801 q^{40} +1.49843 q^{41} -1.00000 q^{42} -9.63862 q^{43} +3.17452 q^{44} +1.78801 q^{45} -6.13356 q^{46} +10.5086 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.80301 q^{50} -5.56103 q^{51} +3.60200 q^{53} +1.00000 q^{54} +5.67609 q^{55} +1.00000 q^{56} +6.18952 q^{57} -2.07759 q^{58} +2.78138 q^{59} -1.78801 q^{60} +1.68879 q^{61} -5.63862 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.17452 q^{66} +11.5544 q^{67} +5.56103 q^{68} -6.13356 q^{69} +1.78801 q^{70} -0.598496 q^{71} -1.00000 q^{72} -0.423973 q^{73} +3.09693 q^{74} +1.80301 q^{75} -6.18952 q^{76} -3.17452 q^{77} +6.96254 q^{79} +1.78801 q^{80} +1.00000 q^{81} -1.49843 q^{82} -4.30228 q^{83} +1.00000 q^{84} +9.94320 q^{85} +9.63862 q^{86} -2.07759 q^{87} -3.17452 q^{88} -16.2931 q^{89} -1.78801 q^{90} +6.13356 q^{92} -5.63862 q^{93} -10.5086 q^{94} -11.0669 q^{95} +1.00000 q^{96} -17.4892 q^{97} -1.00000 q^{98} +3.17452 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{11} - 4 q^{12} + 4 q^{14} + 6 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} - 6 q^{20} + 4 q^{21} + 4 q^{22} + 8 q^{23} + 4 q^{24} + 12 q^{25} - 4 q^{27} - 4 q^{28} - 2 q^{29} - 6 q^{30} - 8 q^{31} - 4 q^{32} + 4 q^{33} - 2 q^{34} + 6 q^{35} + 4 q^{36} - 6 q^{37} + 2 q^{38} + 6 q^{40} - 10 q^{41} - 4 q^{42} - 8 q^{43} - 4 q^{44} - 6 q^{45} - 8 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} - 12 q^{50} - 2 q^{51} - 6 q^{53} + 4 q^{54} + 22 q^{55} + 4 q^{56} + 2 q^{57} + 2 q^{58} - 4 q^{59} + 6 q^{60} + 8 q^{61} + 8 q^{62} - 4 q^{63} + 4 q^{64} - 4 q^{66} + 24 q^{67} + 2 q^{68} - 8 q^{69} - 6 q^{70} - 12 q^{71} - 4 q^{72} - 28 q^{73} + 6 q^{74} - 12 q^{75} - 2 q^{76} + 4 q^{77} - 2 q^{79} - 6 q^{80} + 4 q^{81} + 10 q^{82} - 22 q^{83} + 4 q^{84} + 6 q^{85} + 8 q^{86} + 2 q^{87} + 4 q^{88} - 38 q^{89} + 6 q^{90} + 8 q^{92} + 8 q^{93} + 2 q^{94} - 50 q^{95} + 4 q^{96} - 22 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^11 - 4 * q^12 + 4 * q^14 + 6 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 - 6 * q^20 + 4 * q^21 + 4 * q^22 + 8 * q^23 + 4 * q^24 + 12 * q^25 - 4 * q^27 - 4 * q^28 - 2 * q^29 - 6 * q^30 - 8 * q^31 - 4 * q^32 + 4 * q^33 - 2 * q^34 + 6 * q^35 + 4 * q^36 - 6 * q^37 + 2 * q^38 + 6 * q^40 - 10 * q^41 - 4 * q^42 - 8 * q^43 - 4 * q^44 - 6 * q^45 - 8 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 - 12 * q^50 - 2 * q^51 - 6 * q^53 + 4 * q^54 + 22 * q^55 + 4 * q^56 + 2 * q^57 + 2 * q^58 - 4 * q^59 + 6 * q^60 + 8 * q^61 + 8 * q^62 - 4 * q^63 + 4 * q^64 - 4 * q^66 + 24 * q^67 + 2 * q^68 - 8 * q^69 - 6 * q^70 - 12 * q^71 - 4 * q^72 - 28 * q^73 + 6 * q^74 - 12 * q^75 - 2 * q^76 + 4 * q^77 - 2 * q^79 - 6 * q^80 + 4 * q^81 + 10 * q^82 - 22 * q^83 + 4 * q^84 + 6 * q^85 + 8 * q^86 + 2 * q^87 + 4 * q^88 - 38 * q^89 + 6 * q^90 + 8 * q^92 + 8 * q^93 + 2 * q^94 - 50 * q^95 + 4 * q^96 - 22 * q^97 - 4 * q^98 - 4 * q^99

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