LMFDB - Embedded newform 8034.2.a.bb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 $ x^14 - 6x^13 - 29x^12 + 207x^11 + 269x^10 - 2601x^9 - 847x^8 + 14851x^7 + 678x^6 - 39390x^5 - 3280x^4 + 42456x^3 + 10816x^2 - 7296*x - 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.73527$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.73527 q^{5} -1.00000 q^{6} -3.07502 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.73527 q^{5} -1.00000 q^{6} -3.07502 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.73527 q^{10} -1.39192 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.07502 q^{14} -1.73527 q^{15} +1.00000 q^{16} -2.86227 q^{17} -1.00000 q^{18} +7.95620 q^{19} -1.73527 q^{20} -3.07502 q^{21} +1.39192 q^{22} +7.53997 q^{23} -1.00000 q^{24} -1.98884 q^{25} +1.00000 q^{26} +1.00000 q^{27} -3.07502 q^{28} +4.50668 q^{29} +1.73527 q^{30} -2.18944 q^{31} -1.00000 q^{32} -1.39192 q^{33} +2.86227 q^{34} +5.33598 q^{35} +1.00000 q^{36} -2.08178 q^{37} -7.95620 q^{38} -1.00000 q^{39} +1.73527 q^{40} -9.35900 q^{41} +3.07502 q^{42} +4.36597 q^{43} -1.39192 q^{44} -1.73527 q^{45} -7.53997 q^{46} -1.82148 q^{47} +1.00000 q^{48} +2.45574 q^{49} +1.98884 q^{50} -2.86227 q^{51} -1.00000 q^{52} +2.12579 q^{53} -1.00000 q^{54} +2.41535 q^{55} +3.07502 q^{56} +7.95620 q^{57} -4.50668 q^{58} -8.76579 q^{59} -1.73527 q^{60} -4.02706 q^{61} +2.18944 q^{62} -3.07502 q^{63} +1.00000 q^{64} +1.73527 q^{65} +1.39192 q^{66} +1.69460 q^{67} -2.86227 q^{68} +7.53997 q^{69} -5.33598 q^{70} +7.75467 q^{71} -1.00000 q^{72} +1.32518 q^{73} +2.08178 q^{74} -1.98884 q^{75} +7.95620 q^{76} +4.28017 q^{77} +1.00000 q^{78} +12.1297 q^{79} -1.73527 q^{80} +1.00000 q^{81} +9.35900 q^{82} -2.35921 q^{83} -3.07502 q^{84} +4.96681 q^{85} -4.36597 q^{86} +4.50668 q^{87} +1.39192 q^{88} +2.39147 q^{89} +1.73527 q^{90} +3.07502 q^{91} +7.53997 q^{92} -2.18944 q^{93} +1.82148 q^{94} -13.8061 q^{95} -1.00000 q^{96} +15.7125 q^{97} -2.45574 q^{98} -1.39192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * 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
$5$	−1.73527	−0.776036	−0.388018	−	0.921652i	$-0.626840\pi$
$5$	−1.73527	−0.776036	−0.388018	+	0.921652i	$0.626840\pi$
$6$	−1.00000	−0.408248
$7$	−3.07502	−1.16225	−0.581124	−	0.813815i	$-0.697387\pi$
$7$	−3.07502	−1.16225	−0.581124	+	0.813815i	$0.697387\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.73527	0.548740
$11$	−1.39192	−0.419678	−0.209839	−	0.977736i	$-0.567294\pi$
$11$	−1.39192	−0.419678	−0.209839	+	0.977736i	$0.567294\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.07502	0.821833
$15$	−1.73527	−0.448044
$16$	1.00000	0.250000
$17$	−2.86227	−0.694203	−0.347102	−	0.937828i	$-0.612834\pi$
$17$	−2.86227	−0.694203	−0.347102	+	0.937828i	$0.612834\pi$
$18$	−1.00000	−0.235702
$19$	7.95620	1.82528	0.912639	−	0.408767i	$-0.134041\pi$
$19$	7.95620	1.82528	0.912639	+	0.408767i	$0.134041\pi$
$20$	−1.73527	−0.388018
$21$	−3.07502	−0.671024
$22$	1.39192	0.296757
$23$	7.53997	1.57219	0.786097	−	0.618104i	$-0.212099\pi$
$23$	7.53997	1.57219	0.786097	+	0.618104i	$0.212099\pi$
$24$	−1.00000	−0.204124
$25$	−1.98884	−0.397769
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−3.07502	−0.581124
$29$	4.50668	0.836870	0.418435	−	0.908247i	$-0.362579\pi$
$29$	4.50668	0.836870	0.418435	+	0.908247i	$0.362579\pi$
$30$	1.73527	0.316815
$31$	−2.18944	−0.393236	−0.196618	−	0.980480i	$-0.562996\pi$
$31$	−2.18944	−0.393236	−0.196618	+	0.980480i	$0.562996\pi$
$32$	−1.00000	−0.176777
$33$	−1.39192	−0.242301
$34$	2.86227	0.490876
$35$	5.33598	0.901946
$36$	1.00000	0.166667
$37$	−2.08178	−0.342243	−0.171121	−	0.985250i	$-0.554739\pi$
$37$	−2.08178	−0.342243	−0.171121	+	0.985250i	$0.554739\pi$
$38$	−7.95620	−1.29067
$39$	−1.00000	−0.160128
$40$	1.73527	0.274370
$41$	−9.35900	−1.46163	−0.730815	−	0.682575i	$-0.760860\pi$
$41$	−9.35900	−1.46163	−0.730815	+	0.682575i	$0.760860\pi$
$42$	3.07502	0.474486
$43$	4.36597	0.665804	0.332902	−	0.942961i	$-0.391972\pi$
$43$	4.36597	0.665804	0.332902	+	0.942961i	$0.391972\pi$
$44$	−1.39192	−0.209839
$45$	−1.73527	−0.258679
$46$	−7.53997	−1.11171
$47$	−1.82148	−0.265690	−0.132845	−	0.991137i	$-0.542411\pi$
$47$	−1.82148	−0.265690	−0.132845	+	0.991137i	$0.542411\pi$
$48$	1.00000	0.144338
$49$	2.45574	0.350820
$50$	1.98884	0.281265
$51$	−2.86227	−0.400798
$52$	−1.00000	−0.138675
$53$	2.12579	0.292000	0.146000	−	0.989285i	$-0.453360\pi$
$53$	2.12579	0.292000	0.146000	+	0.989285i	$0.453360\pi$
$54$	−1.00000	−0.136083
$55$	2.41535	0.325685
$56$	3.07502	0.410917
$57$	7.95620	1.05382
$58$	−4.50668	−0.591756
$59$	−8.76579	−1.14121	−0.570604	−	0.821225i	$-0.693291\pi$
$59$	−8.76579	−1.14121	−0.570604	+	0.821225i	$0.693291\pi$
$60$	−1.73527	−0.224022
$61$	−4.02706	−0.515613	−0.257806	−	0.966197i	$-0.583000\pi$
$61$	−4.02706	−0.515613	−0.257806	+	0.966197i	$0.583000\pi$
$62$	2.18944	0.278060
$63$	−3.07502	−0.387416
$64$	1.00000	0.125000
$65$	1.73527	0.215234
$66$	1.39192	0.171333
$67$	1.69460	0.207029	0.103514	−	0.994628i	$-0.466991\pi$
$67$	1.69460	0.207029	0.103514	+	0.994628i	$0.466991\pi$
$68$	−2.86227	−0.347102
$69$	7.53997	0.907706
$70$	−5.33598	−0.637772
$71$	7.75467	0.920310	0.460155	−	0.887838i	$-0.347794\pi$
$71$	7.75467	0.920310	0.460155	+	0.887838i	$0.347794\pi$
$72$	−1.00000	−0.117851
$73$	1.32518	0.155100	0.0775500	−	0.996988i	$-0.475290\pi$
$73$	1.32518	0.155100	0.0775500	+	0.996988i	$0.475290\pi$
$74$	2.08178	0.242002
$75$	−1.98884	−0.229652
$76$	7.95620	0.912639
$77$	4.28017	0.487770
$78$	1.00000	0.113228
$79$	12.1297	1.36470	0.682351	−	0.731025i	$-0.260958\pi$
$79$	12.1297	1.36470	0.682351	+	0.731025i	$0.260958\pi$
$80$	−1.73527	−0.194009
$81$	1.00000	0.111111
$82$	9.35900	1.03353
$83$	−2.35921	−0.258957	−0.129478	−	0.991582i	$-0.541330\pi$
$83$	−2.35921	−0.258957	−0.129478	+	0.991582i	$0.541330\pi$
$84$	−3.07502	−0.335512
$85$	4.96681	0.538726
$86$	−4.36597	−0.470795
$87$	4.50668	0.483167
$88$	1.39192	0.148379
$89$	2.39147	0.253495	0.126748	−	0.991935i	$-0.459546\pi$
$89$	2.39147	0.253495	0.126748	+	0.991935i	$0.459546\pi$
$90$	1.73527	0.182913
$91$	3.07502	0.322350
$92$	7.53997	0.786097
$93$	−2.18944	−0.227035
$94$	1.82148	0.187871
$95$	−13.8061	−1.41648
$96$	−1.00000	−0.102062
$97$	15.7125	1.59537	0.797683	−	0.603077i	$-0.206059\pi$
$97$	15.7125	1.59537	0.797683	+	0.603077i	$0.206059\pi$
$98$	−2.45574	−0.248067
$99$	−1.39192	−0.139893
$100$	−1.98884	−0.198884
$101$	0.387891	0.0385966	0.0192983	−	0.999814i	$-0.493857\pi$
$101$	0.387891	0.0385966	0.0192983	+	0.999814i	$0.493857\pi$
$102$	2.86227	0.283407
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	5.33598	0.520739
$106$	−2.12579	−0.206475
$107$	−1.94585	−0.188112	−0.0940562	−	0.995567i	$-0.529983\pi$
$107$	−1.94585	−0.188112	−0.0940562	+	0.995567i	$0.529983\pi$
$108$	1.00000	0.0962250
$109$	−8.84475	−0.847173	−0.423587	−	0.905856i	$-0.639229\pi$
$109$	−8.84475	−0.847173	−0.423587	+	0.905856i	$0.639229\pi$
$110$	−2.41535	−0.230294
$111$	−2.08178	−0.197594
$112$	−3.07502	−0.290562
$113$	−16.1754	−1.52165	−0.760825	−	0.648957i	$-0.775205\pi$
$113$	−16.1754	−1.52165	−0.760825	+	0.648957i	$0.775205\pi$
$114$	−7.95620	−0.745167
$115$	−13.0839	−1.22008
$116$	4.50668	0.418435
$117$	−1.00000	−0.0924500
$118$	8.76579	0.806956
$119$	8.80155	0.806836
$120$	1.73527	0.158408
$121$	−9.06257	−0.823870
$122$	4.02706	0.364593
$123$	−9.35900	−0.843873
$124$	−2.18944	−0.196618
$125$	12.1275	1.08472
$126$	3.07502	0.273944
$127$	21.3752	1.89674	0.948371	−	0.317165i	$-0.102731\pi$
$127$	21.3752	1.89674	0.948371	+	0.317165i	$0.102731\pi$
$128$	−1.00000	−0.0883883
$129$	4.36597	0.384402
$130$	−1.73527	−0.152193
$131$	14.8836	1.30039	0.650193	−	0.759769i	$-0.274688\pi$
$131$	14.8836	1.30039	0.650193	+	0.759769i	$0.274688\pi$
$132$	−1.39192	−0.121151
$133$	−24.4655	−2.12143
$134$	−1.69460	−0.146391
$135$	−1.73527	−0.149348
$136$	2.86227	0.245438
$137$	−6.09863	−0.521041	−0.260521	−	0.965468i	$-0.583894\pi$
$137$	−6.09863	−0.521041	−0.260521	+	0.965468i	$0.583894\pi$
$138$	−7.53997	−0.641845
$139$	17.4985	1.48421	0.742103	−	0.670286i	$-0.233829\pi$
$139$	17.4985	1.48421	0.742103	+	0.670286i	$0.233829\pi$
$140$	5.33598	0.450973
$141$	−1.82148	−0.153396
$142$	−7.75467	−0.650758
$143$	1.39192	0.116398
$144$	1.00000	0.0833333
$145$	−7.82030	−0.649441
$146$	−1.32518	−0.109672
$147$	2.45574	0.202546
$148$	−2.08178	−0.171121
$149$	−19.2645	−1.57821	−0.789106	−	0.614257i	$-0.789456\pi$
$149$	−19.2645	−1.57821	−0.789106	+	0.614257i	$0.789456\pi$
$150$	1.98884	0.162388
$151$	−17.8971	−1.45645	−0.728223	−	0.685340i	$-0.759654\pi$
$151$	−17.8971	−1.45645	−0.728223	+	0.685340i	$0.759654\pi$
$152$	−7.95620	−0.645333
$153$	−2.86227	−0.231401
$154$	−4.28017	−0.344906
$155$	3.79927	0.305165
$156$	−1.00000	−0.0800641
$157$	22.6039	1.80399	0.901995	−	0.431746i	$-0.142102\pi$
$157$	22.6039	1.80399	0.901995	+	0.431746i	$0.142102\pi$
$158$	−12.1297	−0.964990
$159$	2.12579	0.168586
$160$	1.73527	0.137185
$161$	−23.1856	−1.82728
$162$	−1.00000	−0.0785674
$163$	−0.465410	−0.0364537	−0.0182269	−	0.999834i	$-0.505802\pi$
$163$	−0.465410	−0.0364537	−0.0182269	+	0.999834i	$0.505802\pi$
$164$	−9.35900	−0.730815
$165$	2.41535	0.188035
$166$	2.35921	0.183110
$167$	4.36899	0.338082	0.169041	−	0.985609i	$-0.445933\pi$
$167$	4.36899	0.338082	0.169041	+	0.985609i	$0.445933\pi$
$168$	3.07502	0.237243
$169$	1.00000	0.0769231
$170$	−4.96681	−0.380937
$171$	7.95620	0.608426
$172$	4.36597	0.332902
$173$	−21.8891	−1.66419	−0.832097	−	0.554630i	$-0.812860\pi$
$173$	−21.8891	−1.66419	−0.832097	+	0.554630i	$0.812860\pi$
$174$	−4.50668	−0.341651
$175$	6.11573	0.462306
$176$	−1.39192	−0.104920
$177$	−8.76579	−0.658877
$178$	−2.39147	−0.179248
$179$	−5.18468	−0.387521	−0.193761	−	0.981049i	$-0.562069\pi$
$179$	−5.18468	−0.387521	−0.193761	+	0.981049i	$0.562069\pi$
$180$	−1.73527	−0.129339
$181$	−14.1375	−1.05083	−0.525417	−	0.850845i	$-0.676091\pi$
$181$	−14.1375	−1.05083	−0.525417	+	0.850845i	$0.676091\pi$
$182$	−3.07502	−0.227936
$183$	−4.02706	−0.297689
$184$	−7.53997	−0.555854
$185$	3.61245	0.265592
$186$	2.18944	0.160538
$187$	3.98404	0.291342
$188$	−1.82148	−0.132845
$189$	−3.07502	−0.223675
$190$	13.8061	1.00160
$191$	−15.0773	−1.09096	−0.545479	−	0.838124i	$-0.683652\pi$
$191$	−15.0773	−1.09096	−0.545479	+	0.838124i	$0.683652\pi$
$192$	1.00000	0.0721688
$193$	9.66116	0.695426	0.347713	−	0.937601i	$-0.386958\pi$
$193$	9.66116	0.695426	0.347713	+	0.937601i	$0.386958\pi$
$194$	−15.7125	−1.12809
$195$	1.73527	0.124265
$196$	2.45574	0.175410
$197$	−8.38028	−0.597070	−0.298535	−	0.954399i	$-0.596498\pi$
$197$	−8.38028	−0.597070	−0.298535	+	0.954399i	$0.596498\pi$
$198$	1.39192	0.0989191
$199$	−16.2017	−1.14851	−0.574255	−	0.818676i	$-0.694708\pi$
$199$	−16.2017	−1.14851	−0.574255	+	0.818676i	$0.694708\pi$
$200$	1.98884	0.140633
$201$	1.69460	0.119528
$202$	−0.387891	−0.0272919
$203$	−13.8581	−0.972650
$204$	−2.86227	−0.200399
$205$	16.2404	1.13428
$206$	−1.00000	−0.0696733
$207$	7.53997	0.524064
$208$	−1.00000	−0.0693375
$209$	−11.0744	−0.766030
$210$	−5.33598	−0.368218
$211$	3.60468	0.248156	0.124078	−	0.992272i	$-0.460403\pi$
$211$	3.60468	0.248156	0.124078	+	0.992272i	$0.460403\pi$
$212$	2.12579	0.146000
$213$	7.75467	0.531341
$214$	1.94585	0.133015
$215$	−7.57613	−0.516688
$216$	−1.00000	−0.0680414
$217$	6.73258	0.457037
$218$	8.84475	0.599042
$219$	1.32518	0.0895471
$220$	2.41535	0.162843
$221$	2.86227	0.192537
$222$	2.08178	0.139720
$223$	−0.759633	−0.0508688	−0.0254344	−	0.999676i	$-0.508097\pi$
$223$	−0.759633	−0.0508688	−0.0254344	+	0.999676i	$0.508097\pi$
$224$	3.07502	0.205458
$225$	−1.98884	−0.132590
$226$	16.1754	1.07597
$227$	−1.65329	−0.109733	−0.0548663	−	0.998494i	$-0.517473\pi$
$227$	−1.65329	−0.109733	−0.0548663	+	0.998494i	$0.517473\pi$
$228$	7.95620	0.526912
$229$	−15.3450	−1.01403	−0.507015	−	0.861937i	$-0.669251\pi$
$229$	−15.3450	−1.01403	−0.507015	+	0.861937i	$0.669251\pi$
$230$	13.0839	0.862725
$231$	4.28017	0.281614
$232$	−4.50668	−0.295878
$233$	18.9261	1.23989	0.619945	−	0.784645i	$-0.287155\pi$
$233$	18.9261	1.23989	0.619945	+	0.784645i	$0.287155\pi$
$234$	1.00000	0.0653720
$235$	3.16075	0.206185
$236$	−8.76579	−0.570604
$237$	12.1297	0.787911
$238$	−8.80155	−0.570519
$239$	−5.96484	−0.385833	−0.192917	−	0.981215i	$-0.561795\pi$
$239$	−5.96484	−0.385833	−0.192917	+	0.981215i	$0.561795\pi$
$240$	−1.73527	−0.112011
$241$	7.65509	0.493108	0.246554	−	0.969129i	$-0.420702\pi$
$241$	7.65509	0.493108	0.246554	+	0.969129i	$0.420702\pi$
$242$	9.06257	0.582564
$243$	1.00000	0.0641500
$244$	−4.02706	−0.257806
$245$	−4.26137	−0.272249
$246$	9.35900	0.596708
$247$	−7.95620	−0.506241
$248$	2.18944	0.139030
$249$	−2.35921	−0.149509
$250$	−12.1275	−0.767012
$251$	3.57823	0.225856	0.112928	−	0.993603i	$-0.463977\pi$
$251$	3.57823	0.225856	0.112928	+	0.993603i	$0.463977\pi$
$252$	−3.07502	−0.193708
$253$	−10.4950	−0.659815
$254$	−21.3752	−1.34120
$255$	4.96681	0.311034
$256$	1.00000	0.0625000
$257$	−28.6477	−1.78699	−0.893496	−	0.449070i	$-0.851755\pi$
$257$	−28.6477	−1.78699	−0.893496	+	0.449070i	$0.851755\pi$
$258$	−4.36597	−0.271813
$259$	6.40151	0.397771
$260$	1.73527	0.107617
$261$	4.50668	0.278957
$262$	−14.8836	−0.919512
$263$	−0.404957	−0.0249707	−0.0124854	−	0.999922i	$-0.503974\pi$
$263$	−0.404957	−0.0249707	−0.0124854	+	0.999922i	$0.503974\pi$
$264$	1.39192	0.0856665
$265$	−3.68882	−0.226602
$266$	24.4655	1.50007
$267$	2.39147	0.146356
$268$	1.69460	0.103514
$269$	−16.5365	−1.00825	−0.504124	−	0.863631i	$-0.668185\pi$
$269$	−16.5365	−1.00825	−0.504124	+	0.863631i	$0.668185\pi$
$270$	1.73527	0.105605
$271$	−29.3866	−1.78511	−0.892554	−	0.450941i	$-0.851088\pi$
$271$	−29.3866	−1.78511	−0.892554	+	0.450941i	$0.851088\pi$
$272$	−2.86227	−0.173551
$273$	3.07502	0.186109
$274$	6.09863	0.368432
$275$	2.76830	0.166935
$276$	7.53997	0.453853
$277$	−20.0366	−1.20388	−0.601941	−	0.798541i	$-0.705606\pi$
$277$	−20.0366	−1.20388	−0.601941	+	0.798541i	$0.705606\pi$
$278$	−17.4985	−1.04949
$279$	−2.18944	−0.131079
$280$	−5.33598	−0.318886
$281$	−19.4475	−1.16014	−0.580069	−	0.814567i	$-0.696974\pi$
$281$	−19.4475	−1.16014	−0.580069	+	0.814567i	$0.696974\pi$
$282$	1.82148	0.108467
$283$	−27.1883	−1.61618	−0.808090	−	0.589060i	$-0.799498\pi$
$283$	−27.1883	−1.61618	−0.808090	+	0.589060i	$0.799498\pi$
$284$	7.75467	0.460155
$285$	−13.8061	−0.817805
$286$	−1.39192	−0.0823057
$287$	28.7791	1.69878
$288$	−1.00000	−0.0589256
$289$	−8.80739	−0.518082
$290$	7.82030	0.459224
$291$	15.7125	0.921085
$292$	1.32518	0.0775500
$293$	−0.346988	−0.0202713	−0.0101356	−	0.999949i	$-0.503226\pi$
$293$	−0.346988	−0.0202713	−0.0101356	+	0.999949i	$0.503226\pi$
$294$	−2.45574	−0.143222
$295$	15.2110	0.885619
$296$	2.08178	0.121001
$297$	−1.39192	−0.0807671
$298$	19.2645	1.11596
$299$	−7.53997	−0.436048
$300$	−1.98884	−0.114826
$301$	−13.4254	−0.773830
$302$	17.8971	1.02986
$303$	0.387891	0.0222838
$304$	7.95620	0.456319
$305$	6.98803	0.400134
$306$	2.86227	0.163625
$307$	−20.0209	−1.14266	−0.571328	−	0.820722i	$-0.693571\pi$
$307$	−20.0209	−1.14266	−0.571328	+	0.820722i	$0.693571\pi$
$308$	4.28017	0.243885
$309$	1.00000	0.0568880
$310$	−3.79927	−0.215784
$311$	−7.63862	−0.433146	−0.216573	−	0.976266i	$-0.569488\pi$
$311$	−7.63862	−0.433146	−0.216573	+	0.976266i	$0.569488\pi$
$312$	1.00000	0.0566139
$313$	−13.9350	−0.787650	−0.393825	−	0.919185i	$-0.628848\pi$
$313$	−13.9350	−0.787650	−0.393825	+	0.919185i	$0.628848\pi$
$314$	−22.6039	−1.27561
$315$	5.33598	0.300649
$316$	12.1297	0.682351
$317$	−0.484365	−0.0272046	−0.0136023	−	0.999907i	$-0.504330\pi$
$317$	−0.484365	−0.0272046	−0.0136023	+	0.999907i	$0.504330\pi$
$318$	−2.12579	−0.119208
$319$	−6.27292	−0.351216
$320$	−1.73527	−0.0970044
$321$	−1.94585	−0.108607
$322$	23.1856	1.29208
$323$	−22.7728	−1.26711
$324$	1.00000	0.0555556
$325$	1.98884	0.110321
$326$	0.465410	0.0257767
$327$	−8.84475	−0.489116
$328$	9.35900	0.516764
$329$	5.60108	0.308797
$330$	−2.41535	−0.132960
$331$	−2.61559	−0.143766	−0.0718829	−	0.997413i	$-0.522901\pi$
$331$	−2.61559	−0.143766	−0.0718829	+	0.997413i	$0.522901\pi$
$332$	−2.35921	−0.129478
$333$	−2.08178	−0.114081
$334$	−4.36899	−0.239060
$335$	−2.94059	−0.160662
$336$	−3.07502	−0.167756
$337$	−11.5538	−0.629377	−0.314689	−	0.949195i	$-0.601900\pi$
$337$	−11.5538	−0.629377	−0.314689	+	0.949195i	$0.601900\pi$
$338$	−1.00000	−0.0543928
$339$	−16.1754	−0.878525
$340$	4.96681	0.269363
$341$	3.04752	0.165032
$342$	−7.95620	−0.430222
$343$	13.9737	0.754508
$344$	−4.36597	−0.235397
$345$	−13.0839	−0.704412
$346$	21.8891	1.17676
$347$	−19.4830	−1.04590	−0.522950	−	0.852363i	$-0.675169\pi$
$347$	−19.4830	−1.04590	−0.522950	+	0.852363i	$0.675169\pi$
$348$	4.50668	0.241584
$349$	17.3821	0.930444	0.465222	−	0.885194i	$-0.345974\pi$
$349$	17.3821	0.930444	0.465222	+	0.885194i	$0.345974\pi$
$350$	−6.11573	−0.326900
$351$	−1.00000	−0.0533761
$352$	1.39192	0.0741894
$353$	6.06344	0.322724	0.161362	−	0.986895i	$-0.448411\pi$
$353$	6.06344	0.322724	0.161362	+	0.986895i	$0.448411\pi$
$354$	8.76579	0.465897
$355$	−13.4564	−0.714194
$356$	2.39147	0.126748
$357$	8.80155	0.465827
$358$	5.18468	0.274019
$359$	−31.4171	−1.65813	−0.829067	−	0.559149i	$-0.811128\pi$
$359$	−31.4171	−1.65813	−0.829067	+	0.559149i	$0.811128\pi$
$360$	1.73527	0.0914567
$361$	44.3011	2.33164
$362$	14.1375	0.743052
$363$	−9.06257	−0.475662
$364$	3.07502	0.161175
$365$	−2.29953	−0.120363
$366$	4.02706	0.210498
$367$	11.4259	0.596428	0.298214	−	0.954499i	$-0.403609\pi$
$367$	11.4259	0.596428	0.298214	+	0.954499i	$0.403609\pi$
$368$	7.53997	0.393048
$369$	−9.35900	−0.487210
$370$	−3.61245	−0.187802
$371$	−6.53685	−0.339376
$372$	−2.18944	−0.113517
$373$	−19.7682	−1.02356	−0.511778	−	0.859117i	$-0.671013\pi$
$373$	−19.7682	−1.02356	−0.511778	+	0.859117i	$0.671013\pi$
$374$	−3.98404	−0.206010
$375$	12.1275	0.626262
$376$	1.82148	0.0939355
$377$	−4.50668	−0.232106
$378$	3.07502	0.158162
$379$	14.0604	0.722234	0.361117	−	0.932520i	$-0.382395\pi$
$379$	14.0604	0.722234	0.361117	+	0.932520i	$0.382395\pi$
$380$	−13.8061	−0.708240
$381$	21.3752	1.09508
$382$	15.0773	0.771424
$383$	−3.11366	−0.159101	−0.0795503	−	0.996831i	$-0.525348\pi$
$383$	−3.11366	−0.159101	−0.0795503	+	0.996831i	$0.525348\pi$
$384$	−1.00000	−0.0510310
$385$	−7.42724	−0.378527
$386$	−9.66116	−0.491740
$387$	4.36597	0.221935
$388$	15.7125	0.797683
$389$	−28.1927	−1.42943	−0.714713	−	0.699418i	$-0.753443\pi$
$389$	−28.1927	−1.42943	−0.714713	+	0.699418i	$0.753443\pi$
$390$	−1.73527	−0.0878687
$391$	−21.5815	−1.09142
$392$	−2.45574	−0.124034
$393$	14.8836	0.750778
$394$	8.38028	0.422193
$395$	−21.0483	−1.05906
$396$	−1.39192	−0.0699464
$397$	−22.4025	−1.12435	−0.562174	−	0.827019i	$-0.690035\pi$
$397$	−22.4025	−1.12435	−0.562174	+	0.827019i	$0.690035\pi$
$398$	16.2017	0.812120
$399$	−24.4655	−1.22481
$400$	−1.98884	−0.0994422
$401$	14.9573	0.746934	0.373467	−	0.927644i	$-0.378169\pi$
$401$	14.9573	0.746934	0.373467	+	0.927644i	$0.378169\pi$
$402$	−1.69460	−0.0845192
$403$	2.18944	0.109064
$404$	0.387891	0.0192983
$405$	−1.73527	−0.0862262
$406$	13.8581	0.687768
$407$	2.89766	0.143632
$408$	2.86227	0.141704
$409$	−33.0154	−1.63251	−0.816254	−	0.577693i	$-0.803953\pi$
$409$	−33.0154	−1.63251	−0.816254	+	0.577693i	$0.803953\pi$
$410$	−16.2404	−0.802055
$411$	−6.09863	−0.300823
$412$	1.00000	0.0492665
$413$	26.9550	1.32637
$414$	−7.53997	−0.370569
$415$	4.09386	0.200960
$416$	1.00000	0.0490290
$417$	17.4985	0.856907
$418$	11.0744	0.541665
$419$	−9.83287	−0.480367	−0.240184	−	0.970727i	$-0.577208\pi$
$419$	−9.83287	−0.480367	−0.240184	+	0.970727i	$0.577208\pi$
$420$	5.33598	0.260369
$421$	12.5841	0.613311	0.306656	−	0.951821i	$-0.400790\pi$
$421$	12.5841	0.613311	0.306656	+	0.951821i	$0.400790\pi$
$422$	−3.60468	−0.175473
$423$	−1.82148	−0.0885633
$424$	−2.12579	−0.103237
$425$	5.69262	0.276132
$426$	−7.75467	−0.375715
$427$	12.3833	0.599270
$428$	−1.94585	−0.0940562
$429$	1.39192	0.0672023
$430$	7.57613	0.365353
$431$	−28.4668	−1.37120	−0.685598	−	0.727981i	$-0.740459\pi$
$431$	−28.4668	−1.37120	−0.685598	+	0.727981i	$0.740459\pi$
$432$	1.00000	0.0481125
$433$	30.6051	1.47079	0.735393	−	0.677641i	$-0.236997\pi$
$433$	30.6051	1.47079	0.735393	+	0.677641i	$0.236997\pi$
$434$	−6.73258	−0.323174
$435$	−7.82030	−0.374955
$436$	−8.84475	−0.423587
$437$	59.9895	2.86969
$438$	−1.32518	−0.0633193
$439$	−4.75581	−0.226982	−0.113491	−	0.993539i	$-0.536203\pi$
$439$	−4.75581	−0.226982	−0.113491	+	0.993539i	$0.536203\pi$
$440$	−2.41535	−0.115147
$441$	2.45574	0.116940
$442$	−2.86227	−0.136144
$443$	−27.1927	−1.29196	−0.645981	−	0.763353i	$-0.723552\pi$
$443$	−27.1927	−1.29196	−0.645981	+	0.763353i	$0.723552\pi$
$444$	−2.08178	−0.0987969
$445$	−4.14984	−0.196721
$446$	0.759633	0.0359697
$447$	−19.2645	−0.911181
$448$	−3.07502	−0.145281
$449$	22.7037	1.07146	0.535728	−	0.844391i	$-0.320037\pi$
$449$	22.7037	1.07146	0.535728	+	0.844391i	$0.320037\pi$
$450$	1.98884	0.0937550
$451$	13.0269	0.613415
$452$	−16.1754	−0.760825
$453$	−17.8971	−0.840880
$454$	1.65329	0.0775927
$455$	−5.33598	−0.250155
$456$	−7.95620	−0.372583
$457$	12.8305	0.600188	0.300094	−	0.953910i	$-0.402982\pi$
$457$	12.8305	0.600188	0.300094	+	0.953910i	$0.402982\pi$
$458$	15.3450	0.717027
$459$	−2.86227	−0.133599
$460$	−13.0839	−0.610039
$461$	16.5024	0.768594	0.384297	−	0.923210i	$-0.374444\pi$
$461$	16.5024	0.768594	0.384297	+	0.923210i	$0.374444\pi$
$462$	−4.28017	−0.199131
$463$	−24.0249	−1.11653	−0.558266	−	0.829662i	$-0.688533\pi$
$463$	−24.0249	−1.11653	−0.558266	+	0.829662i	$0.688533\pi$
$464$	4.50668	0.209217
$465$	3.79927	0.176187
$466$	−18.9261	−0.876735
$467$	−2.17328	−0.100567	−0.0502836	−	0.998735i	$-0.516013\pi$
$467$	−2.17328	−0.100567	−0.0502836	+	0.998735i	$0.516013\pi$
$468$	−1.00000	−0.0462250
$469$	−5.21094	−0.240619
$470$	−3.16075	−0.145795
$471$	22.6039	1.04153
$472$	8.76579	0.403478
$473$	−6.07706	−0.279424
$474$	−12.1297	−0.557137
$475$	−15.8236	−0.726039
$476$	8.80155	0.403418
$477$	2.12579	0.0973332
$478$	5.96484	0.272825
$479$	−26.2126	−1.19769	−0.598843	−	0.800867i	$-0.704373\pi$
$479$	−26.2126	−1.19769	−0.598843	+	0.800867i	$0.704373\pi$
$480$	1.73527	0.0792038
$481$	2.08178	0.0949210
$482$	−7.65509	−0.348680
$483$	−23.1856	−1.05498
$484$	−9.06257	−0.411935
$485$	−27.2655	−1.23806
$486$	−1.00000	−0.0453609
$487$	−6.06624	−0.274887	−0.137444	−	0.990510i	$-0.543889\pi$
$487$	−6.06624	−0.274887	−0.137444	+	0.990510i	$0.543889\pi$
$488$	4.02706	0.182297
$489$	−0.465410	−0.0210466
$490$	4.26137	0.192509
$491$	−26.8159	−1.21019	−0.605093	−	0.796155i	$-0.706864\pi$
$491$	−26.8159	−1.21019	−0.605093	+	0.796155i	$0.706864\pi$
$492$	−9.35900	−0.421936
$493$	−12.8994	−0.580958
$494$	7.95620	0.357966
$495$	2.41535	0.108562
$496$	−2.18944	−0.0983089
$497$	−23.8458	−1.06963
$498$	2.35921	0.105719
$499$	−3.58161	−0.160335	−0.0801675	−	0.996781i	$-0.525546\pi$
$499$	−3.58161	−0.160335	−0.0801675	+	0.996781i	$0.525546\pi$
$500$	12.1275	0.542359
$501$	4.36899	0.195192
$502$	−3.57823	−0.159704
$503$	−8.19566	−0.365426	−0.182713	−	0.983166i	$-0.558488\pi$
$503$	−8.19566	−0.365426	−0.182713	+	0.983166i	$0.558488\pi$
$504$	3.07502	0.136972
$505$	−0.673095	−0.0299523
$506$	10.4950	0.466560
$507$	1.00000	0.0444116
$508$	21.3752	0.948371
$509$	−23.6251	−1.04716	−0.523582	−	0.851975i	$-0.675405\pi$
$509$	−23.6251	−1.04716	−0.523582	+	0.851975i	$0.675405\pi$
$510$	−4.96681	−0.219934
$511$	−4.07494	−0.180265
$512$	−1.00000	−0.0441942
$513$	7.95620	0.351275
$514$	28.6477	1.26359
$515$	−1.73527	−0.0764651
$516$	4.36597	0.192201
$517$	2.53534	0.111504
$518$	−6.40151	−0.281266
$519$	−21.8891	−0.960823
$520$	−1.73527	−0.0760965
$521$	24.3813	1.06817	0.534083	−	0.845432i	$-0.320657\pi$
$521$	24.3813	1.06817	0.534083	+	0.845432i	$0.320657\pi$
$522$	−4.50668	−0.197252
$523$	38.3222	1.67571	0.837856	−	0.545892i	$-0.183809\pi$
$523$	38.3222	1.67571	0.837856	+	0.545892i	$0.183809\pi$
$524$	14.8836	0.650193
$525$	6.11573	0.266913
$526$	0.404957	0.0176570
$527$	6.26679	0.272985
$528$	−1.39192	−0.0605754
$529$	33.8512	1.47179
$530$	3.68882	0.160232
$531$	−8.76579	−0.380403
$532$	−24.4655	−1.06071
$533$	9.35900	0.405383
$534$	−2.39147	−0.103489
$535$	3.37657	0.145982
$536$	−1.69460	−0.0731957
$537$	−5.18468	−0.223736
$538$	16.5365	0.712939
$539$	−3.41819	−0.147232
$540$	−1.73527	−0.0746741
$541$	−9.56555	−0.411255	−0.205627	−	0.978630i	$-0.565924\pi$
$541$	−9.56555	−0.411255	−0.205627	+	0.978630i	$0.565924\pi$
$542$	29.3866	1.26226
$543$	−14.1375	−0.606700
$544$	2.86227	0.122719
$545$	15.3480	0.657437
$546$	−3.07502	−0.131599
$547$	11.1149	0.475241	0.237620	−	0.971358i	$-0.423633\pi$
$547$	11.1149	0.475241	0.237620	+	0.971358i	$0.423633\pi$
$548$	−6.09863	−0.260521
$549$	−4.02706	−0.171871
$550$	−2.76830	−0.118041
$551$	35.8561	1.52752
$552$	−7.53997	−0.320923
$553$	−37.2992	−1.58612
$554$	20.0366	0.851273
$555$	3.61245	0.153340
$556$	17.4985	0.742103
$557$	22.6461	0.959547	0.479774	−	0.877392i	$-0.340719\pi$
$557$	22.6461	0.959547	0.479774	+	0.877392i	$0.340719\pi$
$558$	2.18944	0.0926865
$559$	−4.36597	−0.184661
$560$	5.33598	0.225486
$561$	3.98404	0.168206
$562$	19.4475	0.820341
$563$	31.8934	1.34415	0.672074	−	0.740484i	$-0.265404\pi$
$563$	31.8934	1.34415	0.672074	+	0.740484i	$0.265404\pi$
$564$	−1.82148	−0.0766980
$565$	28.0686	1.18085
$566$	27.1883	1.14281
$567$	−3.07502	−0.129139
$568$	−7.75467	−0.325379
$569$	21.6956	0.909526	0.454763	−	0.890612i	$-0.349724\pi$
$569$	21.6956	0.909526	0.454763	+	0.890612i	$0.349724\pi$
$570$	13.8061	0.578276
$571$	−25.0997	−1.05039	−0.525195	−	0.850982i	$-0.676008\pi$
$571$	−25.0997	−1.05039	−0.525195	+	0.850982i	$0.676008\pi$
$572$	1.39192	0.0581989
$573$	−15.0773	−0.629865
$574$	−28.7791	−1.20122
$575$	−14.9958	−0.625369
$576$	1.00000	0.0416667
$577$	43.5561	1.81327	0.906633	−	0.421921i	$-0.138644\pi$
$577$	43.5561	1.81327	0.906633	+	0.421921i	$0.138644\pi$
$578$	8.80739	0.366339
$579$	9.66116	0.401504
$580$	−7.82030	−0.324720
$581$	7.25462	0.300972
$582$	−15.7125	−0.651306
$583$	−2.95892	−0.122546
$584$	−1.32518	−0.0548361
$585$	1.73527	0.0717445
$586$	0.346988	0.0143340
$587$	18.1913	0.750836	0.375418	−	0.926856i	$-0.377499\pi$
$587$	18.1913	0.750836	0.375418	+	0.926856i	$0.377499\pi$
$588$	2.45574	0.101273
$589$	−17.4197	−0.717764
$590$	−15.2110	−0.626227
$591$	−8.38028	−0.344719
$592$	−2.08178	−0.0855606
$593$	−1.33417	−0.0547876	−0.0273938	−	0.999625i	$-0.508721\pi$
$593$	−1.33417	−0.0547876	−0.0273938	+	0.999625i	$0.508721\pi$
$594$	1.39192	0.0571110
$595$	−15.2730	−0.626134
$596$	−19.2645	−0.789106
$597$	−16.2017	−0.663093
$598$	7.53997	0.308332
$599$	−32.9561	−1.34655	−0.673274	−	0.739393i	$-0.735113\pi$
$599$	−32.9561	−1.34655	−0.673274	+	0.739393i	$0.735113\pi$
$600$	1.98884	0.0811942
$601$	17.7894	0.725647	0.362823	−	0.931858i	$-0.381813\pi$
$601$	17.7894	0.725647	0.362823	+	0.931858i	$0.381813\pi$
$602$	13.4254	0.547180
$603$	1.69460	0.0690096
$604$	−17.8971	−0.728223
$605$	15.7260	0.639352
$606$	−0.387891	−0.0157570
$607$	46.3524	1.88138	0.940692	−	0.339261i	$-0.110177\pi$
$607$	46.3524	1.88138	0.940692	+	0.339261i	$0.110177\pi$
$608$	−7.95620	−0.322667
$609$	−13.8581	−0.561560
$610$	−6.98803	−0.282937
$611$	1.82148	0.0736891
$612$	−2.86227	−0.115701
$613$	−42.6244	−1.72158	−0.860791	−	0.508958i	$-0.830031\pi$
$613$	−42.6244	−1.72158	−0.860791	+	0.508958i	$0.830031\pi$
$614$	20.0209	0.807979
$615$	16.2404	0.654875
$616$	−4.28017	−0.172453
$617$	−2.70299	−0.108818	−0.0544092	−	0.998519i	$-0.517328\pi$
$617$	−2.70299	−0.108818	−0.0544092	+	0.998519i	$0.517328\pi$
$618$	−1.00000	−0.0402259
$619$	−16.8035	−0.675390	−0.337695	−	0.941256i	$-0.609647\pi$
$619$	−16.8035	−0.675390	−0.337695	+	0.941256i	$0.609647\pi$
$620$	3.79927	0.152582
$621$	7.53997	0.302569
$622$	7.63862	0.306281
$623$	−7.35382	−0.294624
$624$	−1.00000	−0.0400320
$625$	−11.1003	−0.444011
$626$	13.9350	0.556953
$627$	−11.0744	−0.442267
$628$	22.6039	0.901995
$629$	5.95862	0.237586
$630$	−5.33598	−0.212591
$631$	32.9522	1.31181	0.655904	−	0.754844i	$-0.272288\pi$
$631$	32.9522	1.31181	0.655904	+	0.754844i	$0.272288\pi$
$632$	−12.1297	−0.482495
$633$	3.60468	0.143273
$634$	0.484365	0.0192366
$635$	−37.0917	−1.47194
$636$	2.12579	0.0842931
$637$	−2.45574	−0.0973001
$638$	6.27292	0.248347
$639$	7.75467	0.306770
$640$	1.73527	0.0685925
$641$	−40.0729	−1.58279	−0.791393	−	0.611308i	$-0.790644\pi$
$641$	−40.0729	−1.58279	−0.791393	+	0.611308i	$0.790644\pi$
$642$	1.94585	0.0767965
$643$	22.1042	0.871706	0.435853	−	0.900018i	$-0.356447\pi$
$643$	22.1042	0.871706	0.435853	+	0.900018i	$0.356447\pi$
$644$	−23.1856	−0.913639
$645$	−7.57613	−0.298310
$646$	22.7728	0.895985
$647$	32.3252	1.27083	0.635417	−	0.772169i	$-0.280828\pi$
$647$	32.3252	1.27083	0.635417	+	0.772169i	$0.280828\pi$
$648$	−1.00000	−0.0392837
$649$	12.2012	0.478941
$650$	−1.98884	−0.0780089
$651$	6.73258	0.263871
$652$	−0.465410	−0.0182269
$653$	−29.7996	−1.16615	−0.583074	−	0.812419i	$-0.698150\pi$
$653$	−29.7996	−1.16615	−0.583074	+	0.812419i	$0.698150\pi$
$654$	8.84475	0.345857
$655$	−25.8270	−1.00915
$656$	−9.35900	−0.365408
$657$	1.32518	0.0517000
$658$	−5.60108	−0.218353
$659$	−9.02261	−0.351471	−0.175735	−	0.984437i	$-0.556230\pi$
$659$	−9.02261	−0.351471	−0.175735	+	0.984437i	$0.556230\pi$
$660$	2.41535	0.0940173
$661$	−28.4282	−1.10573	−0.552864	−	0.833272i	$-0.686465\pi$
$661$	−28.4282	−1.10573	−0.552864	+	0.833272i	$0.686465\pi$
$662$	2.61559	0.101658
$663$	2.86227	0.111161
$664$	2.35921	0.0915551
$665$	42.4542	1.64630
$666$	2.08178	0.0806674
$667$	33.9803	1.31572
$668$	4.36899	0.169041
$669$	−0.759633	−0.0293691
$670$	2.94059	0.113605
$671$	5.60533	0.216391
$672$	3.07502	0.118621
$673$	31.2855	1.20597	0.602984	−	0.797753i	$-0.293978\pi$
$673$	31.2855	1.20597	0.602984	+	0.797753i	$0.293978\pi$
$674$	11.5538	0.445037
$675$	−1.98884	−0.0765507
$676$	1.00000	0.0384615
$677$	−20.5785	−0.790898	−0.395449	−	0.918488i	$-0.629411\pi$
$677$	−20.5785	−0.790898	−0.395449	+	0.918488i	$0.629411\pi$
$678$	16.1754	0.621211
$679$	−48.3164	−1.85421
$680$	−4.96681	−0.190469
$681$	−1.65329	−0.0633542
$682$	−3.04752	−0.116696
$683$	31.4617	1.20385	0.601923	−	0.798554i	$-0.294401\pi$
$683$	31.4617	1.20385	0.601923	+	0.798554i	$0.294401\pi$
$684$	7.95620	0.304213
$685$	10.5828	0.404347
$686$	−13.9737	−0.533517
$687$	−15.3450	−0.585450
$688$	4.36597	0.166451
$689$	−2.12579	−0.0809862
$690$	13.0839	0.498095
$691$	38.2907	1.45665	0.728323	−	0.685234i	$-0.240300\pi$
$691$	38.2907	1.45665	0.728323	+	0.685234i	$0.240300\pi$
$692$	−21.8891	−0.832097
$693$	4.28017	0.162590
$694$	19.4830	0.739564
$695$	−30.3646	−1.15180
$696$	−4.50668	−0.170825
$697$	26.7880	1.01467
$698$	−17.3821	−0.657923
$699$	18.9261	0.715851
$700$	6.11573	0.231153
$701$	−29.3169	−1.10729	−0.553643	−	0.832754i	$-0.686763\pi$
$701$	−29.3169	−1.10729	−0.553643	+	0.832754i	$0.686763\pi$
$702$	1.00000	0.0377426
$703$	−16.5631	−0.624688
$704$	−1.39192	−0.0524598
$705$	3.16075	0.119041
$706$	−6.06344	−0.228200
$707$	−1.19277	−0.0448588
$708$	−8.76579	−0.329439
$709$	5.97285	0.224315	0.112158	−	0.993690i	$-0.464224\pi$
$709$	5.97285	0.224315	0.112158	+	0.993690i	$0.464224\pi$
$710$	13.4564	0.505011
$711$	12.1297	0.454901
$712$	−2.39147	−0.0896241
$713$	−16.5083	−0.618242
$714$	−8.80155	−0.329390
$715$	−2.41535	−0.0903289
$716$	−5.18468	−0.193761
$717$	−5.96484	−0.222761
$718$	31.4171	1.17248
$719$	35.6420	1.32922	0.664612	−	0.747189i	$-0.268597\pi$
$719$	35.6420	1.32922	0.664612	+	0.747189i	$0.268597\pi$
$720$	−1.73527	−0.0646696
$721$	−3.07502	−0.114520
$722$	−44.3011	−1.64872
$723$	7.65509	0.284696
$724$	−14.1375	−0.525417
$725$	−8.96309	−0.332881
$726$	9.06257	0.336344
$727$	41.5022	1.53923	0.769615	−	0.638508i	$-0.220448\pi$
$727$	41.5022	1.53923	0.769615	+	0.638508i	$0.220448\pi$
$728$	−3.07502	−0.113968
$729$	1.00000	0.0370370
$730$	2.29953	0.0851096
$731$	−12.4966	−0.462204
$732$	−4.02706	−0.148845
$733$	−38.7797	−1.43236	−0.716180	−	0.697916i	$-0.754111\pi$
$733$	−38.7797	−1.43236	−0.716180	+	0.697916i	$0.754111\pi$
$734$	−11.4259	−0.421738
$735$	−4.26137	−0.157183
$736$	−7.53997	−0.277927
$737$	−2.35875	−0.0868855
$738$	9.35900	0.344510
$739$	27.9553	1.02835	0.514175	−	0.857685i	$-0.328098\pi$
$739$	27.9553	1.02835	0.514175	+	0.857685i	$0.328098\pi$
$740$	3.61245	0.132796
$741$	−7.95620	−0.292278
$742$	6.53685	0.239975
$743$	−41.6662	−1.52858	−0.764291	−	0.644871i	$-0.776911\pi$
$743$	−41.6662	−1.52858	−0.764291	+	0.644871i	$0.776911\pi$
$744$	2.18944	0.0802689
$745$	33.4291	1.22475
$746$	19.7682	0.723764
$747$	−2.35921	−0.0863190
$748$	3.98404	0.145671
$749$	5.98352	0.218633
$750$	−12.1275	−0.442834
$751$	30.4446	1.11094	0.555470	−	0.831536i	$-0.312538\pi$
$751$	30.4446	1.11094	0.555470	+	0.831536i	$0.312538\pi$
$752$	−1.82148	−0.0664225
$753$	3.57823	0.130398
$754$	4.50668	0.164124
$755$	31.0563	1.13025
$756$	−3.07502	−0.111837
$757$	−32.6952	−1.18833	−0.594164	−	0.804344i	$-0.702517\pi$
$757$	−32.6952	−1.18833	−0.594164	+	0.804344i	$0.702517\pi$
$758$	−14.0604	−0.510697
$759$	−10.4950	−0.380945
$760$	13.8061	0.500801
$761$	24.8127	0.899460	0.449730	−	0.893165i	$-0.351520\pi$
$761$	24.8127	0.899460	0.449730	+	0.893165i	$0.351520\pi$
$762$	−21.3752	−0.774341
$763$	27.1978	0.984626
$764$	−15.0773	−0.545479
$765$	4.96681	0.179575
$766$	3.11366	0.112501
$767$	8.76579	0.316514
$768$	1.00000	0.0360844
$769$	29.8213	1.07538	0.537691	−	0.843142i	$-0.319297\pi$
$769$	29.8213	1.07538	0.537691	+	0.843142i	$0.319297\pi$
$770$	7.42724	0.267659
$771$	−28.6477	−1.03172
$772$	9.66116	0.347713
$773$	−21.1377	−0.760270	−0.380135	−	0.924931i	$-0.624123\pi$
$773$	−21.1377	−0.760270	−0.380135	+	0.924931i	$0.624123\pi$
$774$	−4.36597	−0.156932
$775$	4.35446	0.156417
$776$	−15.7125	−0.564047
$777$	6.40151	0.229653
$778$	28.1927	1.01076
$779$	−74.4621	−2.66788
$780$	1.73527	0.0621326
$781$	−10.7939	−0.386234
$782$	21.5815	0.771752
$783$	4.50668	0.161056
$784$	2.45574	0.0877051
$785$	−39.2239	−1.39996
$786$	−14.8836	−0.530880
$787$	−11.5624	−0.412155	−0.206077	−	0.978536i	$-0.566070\pi$
$787$	−11.5624	−0.412155	−0.206077	+	0.978536i	$0.566070\pi$
$788$	−8.38028	−0.298535
$789$	−0.404957	−0.0144169
$790$	21.0483	0.748866
$791$	49.7395	1.76853
$792$	1.39192	0.0494596
$793$	4.02706	0.143005
$794$	22.4025	0.795035
$795$	−3.68882	−0.130829
$796$	−16.2017	−0.574255
$797$	5.88631	0.208504	0.104252	−	0.994551i	$-0.466755\pi$
$797$	5.88631	0.208504	0.104252	+	0.994551i	$0.466755\pi$
$798$	24.4655	0.866068
$799$	5.21357	0.184443
$800$	1.98884	0.0703163
$801$	2.39147	0.0844985
$802$	−14.9573	−0.528162
$803$	−1.84453	−0.0650921
$804$	1.69460	0.0597641
$805$	40.2332	1.41803
$806$	−2.18944	−0.0771199
$807$	−16.5365	−0.582112
$808$	−0.387891	−0.0136460
$809$	10.4046	0.365807	0.182904	−	0.983131i	$-0.441450\pi$
$809$	10.4046	0.365807	0.182904	+	0.983131i	$0.441450\pi$
$810$	1.73527	0.0609711
$811$	−32.8319	−1.15288	−0.576442	−	0.817138i	$-0.695559\pi$
$811$	−32.8319	−1.15288	−0.576442	+	0.817138i	$0.695559\pi$
$812$	−13.8581	−0.486325
$813$	−29.3866	−1.03063
$814$	−2.89766	−0.101563
$815$	0.807612	0.0282894
$816$	−2.86227	−0.100200
$817$	34.7365	1.21528
$818$	33.0154	1.15436
$819$	3.07502	0.107450
$820$	16.2404	0.567139
$821$	14.5787	0.508800	0.254400	−	0.967099i	$-0.418122\pi$
$821$	14.5787	0.508800	0.254400	+	0.967099i	$0.418122\pi$
$822$	6.09863	0.212714
$823$	−25.8828	−0.902216	−0.451108	−	0.892469i	$-0.648971\pi$
$823$	−25.8828	−0.902216	−0.451108	+	0.892469i	$0.648971\pi$
$824$	−1.00000	−0.0348367
$825$	2.76830	0.0963800
$826$	−26.9550	−0.937884
$827$	−11.7465	−0.408467	−0.204233	−	0.978922i	$-0.565470\pi$
$827$	−11.7465	−0.408467	−0.204233	+	0.978922i	$0.565470\pi$
$828$	7.53997	0.262032
$829$	8.62805	0.299665	0.149832	−	0.988711i	$-0.452127\pi$
$829$	8.62805	0.299665	0.149832	+	0.988711i	$0.452127\pi$
$830$	−4.09386	−0.142100
$831$	−20.0366	−0.695062
$832$	−1.00000	−0.0346688
$833$	−7.02901	−0.243541
$834$	−17.4985	−0.605924
$835$	−7.58136	−0.262364
$836$	−11.0744	−0.383015
$837$	−2.18944	−0.0756782
$838$	9.83287	0.339671
$839$	−38.9905	−1.34610	−0.673050	−	0.739597i	$-0.735016\pi$
$839$	−38.9905	−1.34610	−0.673050	+	0.739597i	$0.735016\pi$
$840$	−5.33598	−0.184109
$841$	−8.68981	−0.299649
$842$	−12.5841	−0.433676
$843$	−19.4475	−0.669806
$844$	3.60468	0.124078
$845$	−1.73527	−0.0596950
$846$	1.82148	0.0626237
$847$	27.8676	0.957541
$848$	2.12579	0.0729999
$849$	−27.1883	−0.933101
$850$	−5.69262	−0.195255
$851$	−15.6966	−0.538071
$852$	7.75467	0.265671
$853$	49.1807	1.68392	0.841958	−	0.539543i	$-0.181403\pi$
$853$	49.1807	1.68392	0.841958	+	0.539543i	$0.181403\pi$
$854$	−12.3833	−0.423748
$855$	−13.8061	−0.472160
$856$	1.94585	0.0665077
$857$	15.6294	0.533891	0.266946	−	0.963712i	$-0.413986\pi$
$857$	15.6294	0.533891	0.266946	+	0.963712i	$0.413986\pi$
$858$	−1.39192	−0.0475192
$859$	−31.8384	−1.08631	−0.543156	−	0.839632i	$-0.682771\pi$
$859$	−31.8384	−1.08631	−0.543156	+	0.839632i	$0.682771\pi$
$860$	−7.57613	−0.258344
$861$	28.7791	0.980790
$862$	28.4668	0.969581
$863$	−7.02071	−0.238988	−0.119494	−	0.992835i	$-0.538127\pi$
$863$	−7.02071	−0.238988	−0.119494	+	0.992835i	$0.538127\pi$
$864$	−1.00000	−0.0340207
$865$	37.9834	1.29147
$866$	−30.6051	−1.04000
$867$	−8.80739	−0.299115
$868$	6.73258	0.228519
$869$	−16.8836	−0.572736
$870$	7.82030	0.265133
$871$	−1.69460	−0.0574195
$872$	8.84475	0.299521
$873$	15.7125	0.531789
$874$	−59.9895	−2.02918
$875$	−37.2924	−1.26071
$876$	1.32518	0.0447735
$877$	−18.4449	−0.622840	−0.311420	−	0.950272i	$-0.600805\pi$
$877$	−18.4449	−0.622840	−0.311420	+	0.950272i	$0.600805\pi$
$878$	4.75581	0.160501
$879$	−0.346988	−0.0117036
$880$	2.41535	0.0814213
$881$	−31.8807	−1.07409	−0.537045	−	0.843554i	$-0.680459\pi$
$881$	−31.8807	−1.07409	−0.537045	+	0.843554i	$0.680459\pi$
$882$	−2.45574	−0.0826892
$883$	52.2620	1.75876	0.879378	−	0.476124i	$-0.157959\pi$
$883$	52.2620	1.75876	0.879378	+	0.476124i	$0.157959\pi$
$884$	2.86227	0.0962687
$885$	15.2110	0.511312
$886$	27.1927	0.913555
$887$	15.9162	0.534414	0.267207	−	0.963639i	$-0.413899\pi$
$887$	15.9162	0.534414	0.267207	+	0.963639i	$0.413899\pi$
$888$	2.08178	0.0698600
$889$	−65.7291	−2.20448
$890$	4.14984	0.139103
$891$	−1.39192	−0.0466309
$892$	−0.759633	−0.0254344
$893$	−14.4920	−0.484958
$894$	19.2645	0.644302
$895$	8.99681	0.300730
$896$	3.07502	0.102729
$897$	−7.53997	−0.251752
$898$	−22.7037	−0.757634
$899$	−9.86713	−0.329087
$900$	−1.98884	−0.0662948
$901$	−6.08459	−0.202707
$902$	−13.0269	−0.433750
$903$	−13.4254	−0.446771
$904$	16.1754	0.537985
$905$	24.5324	0.815485
$906$	17.8971	0.594592
$907$	55.4817	1.84224	0.921120	−	0.389279i	$-0.127276\pi$
$907$	55.4817	1.84224	0.921120	+	0.389279i	$0.127276\pi$
$908$	−1.65329	−0.0548663
$909$	0.387891	0.0128655
$910$	5.33598	0.176886
$911$	6.17396	0.204552	0.102276	−	0.994756i	$-0.467387\pi$
$911$	6.17396	0.204552	0.102276	+	0.994756i	$0.467387\pi$
$912$	7.95620	0.263456
$913$	3.28382	0.108679
$914$	−12.8305	−0.424397
$915$	6.98803	0.231017
$916$	−15.3450	−0.507015
$917$	−45.7673	−1.51137
$918$	2.86227	0.0944691
$919$	5.11440	0.168708	0.0843542	−	0.996436i	$-0.473117\pi$
$919$	5.11440	0.168708	0.0843542	+	0.996436i	$0.473117\pi$
$920$	13.0839	0.431363
$921$	−20.0209	−0.659712
$922$	−16.5024	−0.543478
$923$	−7.75467	−0.255248
$924$	4.28017	0.140807
$925$	4.14034	0.136133
$926$	24.0249	0.789508
$927$	1.00000	0.0328443
$928$	−4.50668	−0.147939
$929$	43.7867	1.43660	0.718298	−	0.695736i	$-0.244922\pi$
$929$	43.7867	1.43660	0.718298	+	0.695736i	$0.244922\pi$
$930$	−3.79927	−0.124583
$931$	19.5384	0.640345
$932$	18.9261	0.619945
$933$	−7.63862	−0.250077
$934$	2.17328	0.0711117
$935$	−6.91338	−0.226092
$936$	1.00000	0.0326860
$937$	35.3010	1.15323	0.576616	−	0.817015i	$-0.304373\pi$
$937$	35.3010	1.15323	0.576616	+	0.817015i	$0.304373\pi$
$938$	5.21094	0.170143
$939$	−13.9350	−0.454750
$940$	3.16075	0.103092
$941$	27.4067	0.893432	0.446716	−	0.894676i	$-0.352594\pi$
$941$	27.4067	0.893432	0.446716	+	0.894676i	$0.352594\pi$
$942$	−22.6039	−0.736476
$943$	−70.5666	−2.29797
$944$	−8.76579	−0.285302
$945$	5.33598	0.173580
$946$	6.07706	0.197582
$947$	−15.4629	−0.502478	−0.251239	−	0.967925i	$-0.580838\pi$
$947$	−15.4629	−0.502478	−0.251239	+	0.967925i	$0.580838\pi$
$948$	12.1297	0.393955
$949$	−1.32518	−0.0430170
$950$	15.8236	0.513387
$951$	−0.484365	−0.0157066
$952$	−8.80155	−0.285260
$953$	20.7975	0.673697	0.336848	−	0.941559i	$-0.390639\pi$
$953$	20.7975	0.673697	0.336848	+	0.941559i	$0.390639\pi$
$954$	−2.12579	−0.0688250
$955$	26.1632	0.846622
$956$	−5.96484	−0.192917
$957$	−6.27292	−0.202775
$958$	26.2126	0.846891
$959$	18.7534	0.605579
$960$	−1.73527	−0.0560055
$961$	−26.2063	−0.845366
$962$	−2.08178	−0.0671193
$963$	−1.94585	−0.0627041
$964$	7.65509	0.246554
$965$	−16.7647	−0.539675
$966$	23.1856	0.745983
$967$	5.25688	0.169050	0.0845249	−	0.996421i	$-0.473063\pi$
$967$	5.25688	0.169050	0.0845249	+	0.996421i	$0.473063\pi$
$968$	9.06257	0.291282
$969$	−22.7728	−0.731568
$970$	27.2655	0.875441
$971$	21.7767	0.698849	0.349425	−	0.936965i	$-0.386377\pi$
$971$	21.7767	0.698849	0.349425	+	0.936965i	$0.386377\pi$
$972$	1.00000	0.0320750
$973$	−53.8083	−1.72502
$974$	6.06624	0.194375
$975$	1.98884	0.0636940
$976$	−4.02706	−0.128903
$977$	23.6820	0.757654	0.378827	−	0.925468i	$-0.376328\pi$
$977$	23.6820	0.757654	0.378827	+	0.925468i	$0.376328\pi$
$978$	0.465410	0.0148822
$979$	−3.32872	−0.106387
$980$	−4.26137	−0.136125
$981$	−8.84475	−0.282391
$982$	26.8159	0.855731
$983$	−52.7443	−1.68228	−0.841142	−	0.540815i	$-0.818116\pi$
$983$	−52.7443	−1.68228	−0.841142	+	0.540815i	$0.818116\pi$
$984$	9.35900	0.298354
$985$	14.5420	0.463348
$986$	12.8994	0.410799
$987$	5.60108	0.178284
$988$	−7.95620	−0.253120
$989$	32.9193	1.04677
$990$	−2.41535	−0.0767648
$991$	−53.9155	−1.71268	−0.856341	−	0.516411i	$-0.827268\pi$
$991$	−53.9155	−1.71268	−0.856341	+	0.516411i	$0.827268\pi$
$992$	2.18944	0.0695149
$993$	−2.61559	−0.0830032
$994$	23.8458	0.756342
$995$	28.1144	0.891285
$996$	−2.35921	−0.0747544
$997$	25.1433	0.796297	0.398149	−	0.917321i	$-0.369653\pi$
$997$	25.1433	0.796297	0.398149	+	0.917321i	$0.369653\pi$
$998$	3.58161	0.113374
$999$	−2.08178	−0.0658646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bb.1.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bb.1.6	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.73527 q^{5} -1.00000 q^{6} -3.07502 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.73527 q^{5} -1.00000 q^{6} -3.07502 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.73527 q^{10} -1.39192 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.07502 q^{14} -1.73527 q^{15} +1.00000 q^{16} -2.86227 q^{17} -1.00000 q^{18} +7.95620 q^{19} -1.73527 q^{20} -3.07502 q^{21} +1.39192 q^{22} +7.53997 q^{23} -1.00000 q^{24} -1.98884 q^{25} +1.00000 q^{26} +1.00000 q^{27} -3.07502 q^{28} +4.50668 q^{29} +1.73527 q^{30} -2.18944 q^{31} -1.00000 q^{32} -1.39192 q^{33} +2.86227 q^{34} +5.33598 q^{35} +1.00000 q^{36} -2.08178 q^{37} -7.95620 q^{38} -1.00000 q^{39} +1.73527 q^{40} -9.35900 q^{41} +3.07502 q^{42} +4.36597 q^{43} -1.39192 q^{44} -1.73527 q^{45} -7.53997 q^{46} -1.82148 q^{47} +1.00000 q^{48} +2.45574 q^{49} +1.98884 q^{50} -2.86227 q^{51} -1.00000 q^{52} +2.12579 q^{53} -1.00000 q^{54} +2.41535 q^{55} +3.07502 q^{56} +7.95620 q^{57} -4.50668 q^{58} -8.76579 q^{59} -1.73527 q^{60} -4.02706 q^{61} +2.18944 q^{62} -3.07502 q^{63} +1.00000 q^{64} +1.73527 q^{65} +1.39192 q^{66} +1.69460 q^{67} -2.86227 q^{68} +7.53997 q^{69} -5.33598 q^{70} +7.75467 q^{71} -1.00000 q^{72} +1.32518 q^{73} +2.08178 q^{74} -1.98884 q^{75} +7.95620 q^{76} +4.28017 q^{77} +1.00000 q^{78} +12.1297 q^{79} -1.73527 q^{80} +1.00000 q^{81} +9.35900 q^{82} -2.35921 q^{83} -3.07502 q^{84} +4.96681 q^{85} -4.36597 q^{86} +4.50668 q^{87} +1.39192 q^{88} +2.39147 q^{89} +1.73527 q^{90} +3.07502 q^{91} +7.53997 q^{92} -2.18944 q^{93} +1.82148 q^{94} -13.8061 q^{95} -1.00000 q^{96} +15.7125 q^{97} -2.45574 q^{98} -1.39192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

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