LMFDB - Embedded newform 1003.2.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 $ x^18 - 5x^17 - 16x^16 + 112x^15 + 52x^14 - 984x^13 + 431x^12 + 4304x^11 - 3825x^10 - 9826x^9 + 11533x^8 + 11182x^7 - 15697x^6 - 5604x^5 + 9201x^4 + 1189x^3 - 1952x^2 - 100*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.101226$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.101226 q^{2} -0.700214 q^{3} -1.98975 q^{4} +0.497951 q^{5} -0.0708800 q^{6} -5.07659 q^{7} -0.403867 q^{8} -2.50970 q^{9} +O(q^{10})$	\(q+0.101226 q^{2} -0.700214 q^{3} -1.98975 q^{4} +0.497951 q^{5} -0.0708800 q^{6} -5.07659 q^{7} -0.403867 q^{8} -2.50970 q^{9} +0.0504057 q^{10} -0.805155 q^{11} +1.39325 q^{12} +1.59700 q^{13} -0.513883 q^{14} -0.348672 q^{15} +3.93862 q^{16} +1.00000 q^{17} -0.254047 q^{18} +3.21866 q^{19} -0.990800 q^{20} +3.55470 q^{21} -0.0815027 q^{22} +0.725538 q^{23} +0.282794 q^{24} -4.75204 q^{25} +0.161658 q^{26} +3.85797 q^{27} +10.1012 q^{28} +7.95964 q^{29} -0.0352948 q^{30} -3.36550 q^{31} +1.20643 q^{32} +0.563781 q^{33} +0.101226 q^{34} -2.52789 q^{35} +4.99368 q^{36} +9.30446 q^{37} +0.325812 q^{38} -1.11824 q^{39} -0.201106 q^{40} -3.11451 q^{41} +0.359828 q^{42} +0.820065 q^{43} +1.60206 q^{44} -1.24971 q^{45} +0.0734433 q^{46} +7.08506 q^{47} -2.75788 q^{48} +18.7718 q^{49} -0.481031 q^{50} -0.700214 q^{51} -3.17763 q^{52} -12.2987 q^{53} +0.390527 q^{54} -0.400928 q^{55} +2.05027 q^{56} -2.25375 q^{57} +0.805723 q^{58} -1.00000 q^{59} +0.693772 q^{60} -6.06900 q^{61} -0.340676 q^{62} +12.7407 q^{63} -7.75513 q^{64} +0.795228 q^{65} +0.0570693 q^{66} -4.30717 q^{67} -1.98975 q^{68} -0.508032 q^{69} -0.255889 q^{70} -4.14793 q^{71} +1.01359 q^{72} +11.5861 q^{73} +0.941854 q^{74} +3.32745 q^{75} -6.40434 q^{76} +4.08744 q^{77} -0.113195 q^{78} +1.85918 q^{79} +1.96124 q^{80} +4.82770 q^{81} -0.315270 q^{82} -17.3857 q^{83} -7.07297 q^{84} +0.497951 q^{85} +0.0830120 q^{86} -5.57345 q^{87} +0.325176 q^{88} +3.22980 q^{89} -0.126503 q^{90} -8.10731 q^{91} -1.44364 q^{92} +2.35657 q^{93} +0.717193 q^{94} +1.60273 q^{95} -0.844757 q^{96} +16.7437 q^{97} +1.90019 q^{98} +2.02070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * 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 $

$2$	0.101226	0.0715777	0.0357888	−	0.999359i	$-0.488606\pi$
$2$	0.101226	0.0715777	0.0357888	+	0.999359i	$0.488606\pi$
$3$	−0.700214	−0.404269	−0.202134	−	0.979358i	$-0.564788\pi$
$3$	−0.700214	−0.404269	−0.202134	+	0.979358i	$0.564788\pi$
$4$	−1.98975	−0.994877
$5$	0.497951	0.222691	0.111345	−	0.993782i	$-0.464484\pi$
$5$	0.497951	0.222691	0.111345	+	0.993782i	$0.464484\pi$
$6$	−0.0708800	−0.0289366
$7$	−5.07659	−1.91877	−0.959385	−	0.282100i	$-0.908969\pi$
$7$	−5.07659	−1.91877	−0.959385	+	0.282100i	$0.908969\pi$
$8$	−0.403867	−0.142789
$9$	−2.50970	−0.836567
$10$	0.0504057	0.0159397
$11$	−0.805155	−0.242763	−0.121382	−	0.992606i	$-0.538732\pi$
$11$	−0.805155	−0.242763	−0.121382	+	0.992606i	$0.538732\pi$
$12$	1.39325	0.402198
$13$	1.59700	0.442928	0.221464	−	0.975169i	$-0.428916\pi$
$13$	1.59700	0.442928	0.221464	+	0.975169i	$0.428916\pi$
$14$	−0.513883	−0.137341
$15$	−0.348672	−0.0900268
$16$	3.93862	0.984656
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.254047	−0.0598795
$19$	3.21866	0.738411	0.369205	−	0.929348i	$-0.379630\pi$
$19$	3.21866	0.738411	0.369205	+	0.929348i	$0.379630\pi$
$20$	−0.990800	−0.221550
$21$	3.55470	0.775699
$22$	−0.0815027	−0.0173764
$23$	0.725538	0.151285	0.0756425	−	0.997135i	$-0.475899\pi$
$23$	0.725538	0.151285	0.0756425	+	0.997135i	$0.475899\pi$
$24$	0.282794	0.0577250
$25$	−4.75204	−0.950409
$26$	0.161658	0.0317038
$27$	3.85797	0.742467
$28$	10.1012	1.90894
$29$	7.95964	1.47807	0.739034	−	0.673669i	$-0.235282\pi$
$29$	7.95964	1.47807	0.739034	+	0.673669i	$0.235282\pi$
$30$	−0.0352948	−0.00644391
$31$	−3.36550	−0.604462	−0.302231	−	0.953235i	$-0.597731\pi$
$31$	−3.36550	−0.604462	−0.302231	+	0.953235i	$0.597731\pi$
$32$	1.20643	0.213268
$33$	0.563781	0.0981416
$34$	0.101226	0.0173601
$35$	−2.52789	−0.427292
$36$	4.99368	0.832281
$37$	9.30446	1.52964	0.764822	−	0.644242i	$-0.222827\pi$
$37$	9.30446	1.52964	0.764822	+	0.644242i	$0.222827\pi$
$38$	0.325812	0.0528537
$39$	−1.11824	−0.179062
$40$	−0.201106	−0.0317977
$41$	−3.11451	−0.486405	−0.243202	−	0.969976i	$-0.578198\pi$
$41$	−3.11451	−0.486405	−0.243202	+	0.969976i	$0.578198\pi$
$42$	0.359828	0.0555227
$43$	0.820065	0.125059	0.0625293	−	0.998043i	$-0.480083\pi$
$43$	0.820065	0.125059	0.0625293	+	0.998043i	$0.480083\pi$
$44$	1.60206	0.241519
$45$	−1.24971	−0.186295
$46$	0.0734433	0.0108286
$47$	7.08506	1.03346	0.516731	−	0.856148i	$-0.327149\pi$
$47$	7.08506	1.03346	0.516731	+	0.856148i	$0.327149\pi$
$48$	−2.75788	−0.398066
$49$	18.7718	2.68168
$50$	−0.481031	−0.0680281
$51$	−0.700214	−0.0980496
$52$	−3.17763	−0.440659
$53$	−12.2987	−1.68935	−0.844675	−	0.535279i	$-0.820206\pi$
$53$	−12.2987	−1.68935	−0.844675	+	0.535279i	$0.820206\pi$
$54$	0.390527	0.0531440
$55$	−0.400928	−0.0540611
$56$	2.05027	0.273979
$57$	−2.25375	−0.298517
$58$	0.805723	0.105797
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0.693772	0.0895656
$61$	−6.06900	−0.777056	−0.388528	−	0.921437i	$-0.627016\pi$
$61$	−6.06900	−0.777056	−0.388528	+	0.921437i	$0.627016\pi$
$62$	−0.340676	−0.0432660
$63$	12.7407	1.60518
$64$	−7.75513	−0.969391
$65$	0.795228	0.0986359
$66$	0.0570693	0.00702475
$67$	−4.30717	−0.526204	−0.263102	−	0.964768i	$-0.584746\pi$
$67$	−4.30717	−0.526204	−0.263102	+	0.964768i	$0.584746\pi$
$68$	−1.98975	−0.241293
$69$	−0.508032	−0.0611598
$70$	−0.255889	−0.0305846
$71$	−4.14793	−0.492269	−0.246134	−	0.969236i	$-0.579160\pi$
$71$	−4.14793	−0.492269	−0.246134	+	0.969236i	$0.579160\pi$
$72$	1.01359	0.119452
$73$	11.5861	1.35605	0.678027	−	0.735037i	$-0.262835\pi$
$73$	11.5861	1.35605	0.678027	+	0.735037i	$0.262835\pi$
$74$	0.941854	0.109488
$75$	3.32745	0.384221
$76$	−6.40434	−0.734628
$77$	4.08744	0.465807
$78$	−0.113195	−0.0128168
$79$	1.85918	0.209174	0.104587	−	0.994516i	$-0.466648\pi$
$79$	1.85918	0.209174	0.104587	+	0.994516i	$0.466648\pi$
$80$	1.96124	0.219274
$81$	4.82770	0.536411
$82$	−0.315270	−0.0348157
$83$	−17.3857	−1.90833	−0.954164	−	0.299285i	$-0.903252\pi$
$83$	−17.3857	−1.90833	−0.954164	+	0.299285i	$0.903252\pi$
$84$	−7.07297	−0.771725
$85$	0.497951	0.0540104
$86$	0.0830120	0.00895141
$87$	−5.57345	−0.597536
$88$	0.325176	0.0346638
$89$	3.22980	0.342358	0.171179	−	0.985240i	$-0.445242\pi$
$89$	3.22980	0.342358	0.171179	+	0.985240i	$0.445242\pi$
$90$	−0.126503	−0.0133346
$91$	−8.10731	−0.849877
$92$	−1.44364	−0.150510
$93$	2.35657	0.244365
$94$	0.717193	0.0739728
$95$	1.60273	0.164437
$96$	−0.844757	−0.0862176
$97$	16.7437	1.70007	0.850035	−	0.526727i	$-0.176581\pi$
$97$	16.7437	1.70007	0.850035	+	0.526727i	$0.176581\pi$
$98$	1.90019	0.191948
$99$	2.02070	0.203088
$100$	9.45540	0.945540
$101$	5.87128	0.584215	0.292107	−	0.956386i	$-0.405644\pi$
$101$	5.87128	0.584215	0.292107	+	0.956386i	$0.405644\pi$
$102$	−0.0708800	−0.00701816
$103$	15.1836	1.49608	0.748041	−	0.663652i	$-0.230994\pi$
$103$	15.1836	1.49608	0.748041	+	0.663652i	$0.230994\pi$
$104$	−0.644976	−0.0632451
$105$	1.77007	0.172741
$106$	−1.24495	−0.120920
$107$	6.09609	0.589331	0.294666	−	0.955600i	$-0.404792\pi$
$107$	6.09609	0.589331	0.294666	+	0.955600i	$0.404792\pi$
$108$	−7.67641	−0.738663
$109$	10.6606	1.02110	0.510552	−	0.859847i	$-0.329441\pi$
$109$	10.6606	1.02110	0.510552	+	0.859847i	$0.329441\pi$
$110$	−0.0405843	−0.00386957
$111$	−6.51511	−0.618387
$112$	−19.9948	−1.88933
$113$	17.7341	1.66829	0.834143	−	0.551548i	$-0.185963\pi$
$113$	17.7341	1.66829	0.834143	+	0.551548i	$0.185963\pi$
$114$	−0.228138	−0.0213671
$115$	0.361282	0.0336897
$116$	−15.8377	−1.47049
$117$	−4.00799	−0.370539
$118$	−0.101226	−0.00931862
$119$	−5.07659	−0.465370
$120$	0.140817	0.0128548
$121$	−10.3517	−0.941066
$122$	−0.614342	−0.0556199
$123$	2.18082	0.196638
$124$	6.69651	0.601365
$125$	−4.85604	−0.434338
$126$	1.28969	0.114895
$127$	2.19329	0.194623	0.0973116	−	0.995254i	$-0.468976\pi$
$127$	2.19329	0.194623	0.0973116	+	0.995254i	$0.468976\pi$
$128$	−3.19787	−0.282655
$129$	−0.574221	−0.0505573
$130$	0.0804978	0.00706012
$131$	−9.23320	−0.806708	−0.403354	−	0.915044i	$-0.632156\pi$
$131$	−9.23320	−0.806708	−0.403354	+	0.915044i	$0.632156\pi$
$132$	−1.12178	−0.0976388
$133$	−16.3398	−1.41684
$134$	−0.435998	−0.0376645
$135$	1.92108	0.165340
$136$	−0.403867	−0.0346313
$137$	11.1687	0.954207	0.477104	−	0.878847i	$-0.341687\pi$
$137$	11.1687	0.954207	0.477104	+	0.878847i	$0.341687\pi$
$138$	−0.0514261	−0.00437768
$139$	19.3201	1.63871	0.819357	−	0.573284i	$-0.194331\pi$
$139$	19.3201	1.63871	0.819357	+	0.573284i	$0.194331\pi$
$140$	5.02988	0.425103
$141$	−4.96106	−0.417796
$142$	−0.419879	−0.0352354
$143$	−1.28583	−0.107527
$144$	−9.88477	−0.823731
$145$	3.96351	0.329152
$146$	1.17282	0.0970631
$147$	−13.1442	−1.08412
$148$	−18.5136	−1.52181
$149$	14.3390	1.17469	0.587347	−	0.809335i	$-0.300172\pi$
$149$	14.3390	1.17469	0.587347	+	0.809335i	$0.300172\pi$
$150$	0.336825	0.0275016
$151$	−8.00652	−0.651562	−0.325781	−	0.945445i	$-0.605627\pi$
$151$	−8.00652	−0.651562	−0.325781	+	0.945445i	$0.605627\pi$
$152$	−1.29991	−0.105437
$153$	−2.50970	−0.202897
$154$	0.413755	0.0333414
$155$	−1.67585	−0.134608
$156$	2.22502	0.178145
$157$	−14.1606	−1.13014	−0.565068	−	0.825044i	$-0.691150\pi$
$157$	−14.1606	−1.13014	−0.565068	+	0.825044i	$0.691150\pi$
$158$	0.188197	0.0149722
$159$	8.61169	0.682952
$160$	0.600741	0.0474928
$161$	−3.68326	−0.290281
$162$	0.488689	0.0383950
$163$	12.6580	0.991454	0.495727	−	0.868478i	$-0.334902\pi$
$163$	12.6580	0.991454	0.495727	+	0.868478i	$0.334902\pi$
$164$	6.19711	0.483913
$165$	0.280735	0.0218552
$166$	−1.75989	−0.136594
$167$	−22.4829	−1.73978	−0.869890	−	0.493246i	$-0.835810\pi$
$167$	−22.4829	−1.73978	−0.869890	+	0.493246i	$0.835810\pi$
$168$	−1.43563	−0.110761
$169$	−10.4496	−0.803815
$170$	0.0504057	0.00386594
$171$	−8.07787	−0.617730
$172$	−1.63173	−0.124418
$173$	−11.0765	−0.842129	−0.421065	−	0.907031i	$-0.638343\pi$
$173$	−11.0765	−0.842129	−0.421065	+	0.907031i	$0.638343\pi$
$174$	−0.564179	−0.0427703
$175$	24.1242	1.82362
$176$	−3.17120	−0.239038
$177$	0.700214	0.0526313
$178$	0.326940	0.0245052
$179$	0.510997	0.0381937	0.0190968	−	0.999818i	$-0.493921\pi$
$179$	0.510997	0.0381937	0.0190968	+	0.999818i	$0.493921\pi$
$180$	2.48661	0.185341
$181$	6.53304	0.485597	0.242799	−	0.970077i	$-0.421935\pi$
$181$	6.53304	0.485597	0.242799	+	0.970077i	$0.421935\pi$
$182$	−0.820671	−0.0608322
$183$	4.24960	0.314140
$184$	−0.293021	−0.0216018
$185$	4.63316	0.340637
$186$	0.238547	0.0174911
$187$	−0.805155	−0.0588787
$188$	−14.0975	−1.02817
$189$	−19.5853	−1.42462
$190$	0.162239	0.0117700
$191$	−9.03318	−0.653618	−0.326809	−	0.945090i	$-0.605973\pi$
$191$	−9.03318	−0.653618	−0.326809	+	0.945090i	$0.605973\pi$
$192$	5.43025	0.391895
$193$	−0.959811	−0.0690887	−0.0345443	−	0.999403i	$-0.510998\pi$
$193$	−0.959811	−0.0690887	−0.0345443	+	0.999403i	$0.510998\pi$
$194$	1.69490	0.121687
$195$	−0.556830	−0.0398754
$196$	−37.3512	−2.66794
$197$	12.9163	0.920245	0.460123	−	0.887855i	$-0.347805\pi$
$197$	12.9163	0.920245	0.460123	+	0.887855i	$0.347805\pi$
$198$	0.204547	0.0145365
$199$	−4.36269	−0.309263	−0.154632	−	0.987972i	$-0.549419\pi$
$199$	−4.36269	−0.309263	−0.154632	+	0.987972i	$0.549419\pi$
$200$	1.91920	0.135708
$201$	3.01594	0.212728
$202$	0.594327	0.0418167
$203$	−40.4078	−2.83607
$204$	1.39325	0.0975472
$205$	−1.55087	−0.108318
$206$	1.53698	0.107086
$207$	−1.82088	−0.126560
$208$	6.28998	0.436132
$209$	−2.59152	−0.179259
$210$	0.179177	0.0123644
$211$	−23.4476	−1.61420	−0.807099	−	0.590416i	$-0.798964\pi$
$211$	−23.4476	−1.61420	−0.807099	+	0.590416i	$0.798964\pi$
$212$	24.4713	1.68070
$213$	2.90444	0.199009
$214$	0.617083	0.0421829
$215$	0.408352	0.0278494
$216$	−1.55811	−0.106016
$217$	17.0853	1.15982
$218$	1.07913	0.0730882
$219$	−8.11277	−0.548210
$220$	0.797747	0.0537841
$221$	1.59700	0.107426
$222$	−0.659500	−0.0442627
$223$	−6.23945	−0.417825	−0.208912	−	0.977934i	$-0.566992\pi$
$223$	−6.23945	−0.417825	−0.208912	+	0.977934i	$0.566992\pi$
$224$	−6.12453	−0.409212
$225$	11.9262	0.795080
$226$	1.79516	0.119412
$227$	−12.0308	−0.798515	−0.399257	−	0.916839i	$-0.630732\pi$
$227$	−12.0308	−0.798515	−0.399257	+	0.916839i	$0.630732\pi$
$228$	4.48441	0.296987
$229$	−25.2803	−1.67057	−0.835283	−	0.549820i	$-0.814696\pi$
$229$	−25.2803	−1.67057	−0.835283	+	0.549820i	$0.814696\pi$
$230$	0.0365712	0.00241143
$231$	−2.86208	−0.188311
$232$	−3.21464	−0.211051
$233$	20.9537	1.37272	0.686361	−	0.727261i	$-0.259207\pi$
$233$	20.9537	1.37272	0.686361	+	0.727261i	$0.259207\pi$
$234$	−0.405713	−0.0265223
$235$	3.52801	0.230142
$236$	1.98975	0.129522
$237$	−1.30182	−0.0845623
$238$	−0.513883	−0.0333101
$239$	14.7262	0.952558	0.476279	−	0.879294i	$-0.341985\pi$
$239$	14.7262	0.952558	0.476279	+	0.879294i	$0.341985\pi$
$240$	−1.37329	−0.0886455
$241$	−9.38876	−0.604783	−0.302392	−	0.953184i	$-0.597785\pi$
$241$	−9.38876	−0.604783	−0.302392	+	0.953184i	$0.597785\pi$
$242$	−1.04787	−0.0673593
$243$	−14.9543	−0.959321
$244$	12.0758	0.773075
$245$	9.34741	0.597184
$246$	0.220756	0.0140749
$247$	5.14020	0.327063
$248$	1.35922	0.0863102
$249$	12.1737	0.771477
$250$	−0.491558	−0.0310889
$251$	2.43125	0.153459	0.0767295	−	0.997052i	$-0.475552\pi$
$251$	2.43125	0.153459	0.0767295	+	0.997052i	$0.475552\pi$
$252$	−25.3509	−1.59696
$253$	−0.584170	−0.0367264
$254$	0.222018	0.0139307
$255$	−0.348672	−0.0218347
$256$	15.1865	0.949159
$257$	26.1123	1.62884	0.814419	−	0.580277i	$-0.197056\pi$
$257$	26.1123	1.62884	0.814419	+	0.580277i	$0.197056\pi$
$258$	−0.0581262	−0.00361878
$259$	−47.2349	−2.93503
$260$	−1.58231	−0.0981305
$261$	−19.9763	−1.23650
$262$	−0.934641	−0.0577423
$263$	18.5903	1.14633	0.573164	−	0.819441i	$-0.305716\pi$
$263$	18.5903	1.14633	0.573164	+	0.819441i	$0.305716\pi$
$264$	−0.227692	−0.0140135
$265$	−6.12413	−0.376202
$266$	−1.65402	−0.101414
$267$	−2.26155	−0.138405
$268$	8.57020	0.523508
$269$	22.9191	1.39741	0.698703	−	0.715412i	$-0.253761\pi$
$269$	22.9191	1.39741	0.698703	+	0.715412i	$0.253761\pi$
$270$	0.194464	0.0118347
$271$	12.0794	0.733770	0.366885	−	0.930266i	$-0.380424\pi$
$271$	12.0794	0.733770	0.366885	+	0.930266i	$0.380424\pi$
$272$	3.93862	0.238814
$273$	5.67685	0.343579
$274$	1.13057	0.0682999
$275$	3.82613	0.230724
$276$	1.01086	0.0608465
$277$	−1.35464	−0.0813924	−0.0406962	−	0.999172i	$-0.512958\pi$
$277$	−1.35464	−0.0813924	−0.0406962	+	0.999172i	$0.512958\pi$
$278$	1.95570	0.117295
$279$	8.44640	0.505673
$280$	1.02093	0.0610124
$281$	23.2819	1.38888	0.694441	−	0.719550i	$-0.255652\pi$
$281$	23.2819	1.38888	0.694441	+	0.719550i	$0.255652\pi$
$282$	−0.502188	−0.0299049
$283$	20.8855	1.24151	0.620756	−	0.784004i	$-0.286826\pi$
$283$	20.8855	1.24151	0.620756	+	0.784004i	$0.286826\pi$
$284$	8.25335	0.489746
$285$	−1.12226	−0.0664768
$286$	−0.130160	−0.00769651
$287$	15.8111	0.933299
$288$	−3.02777	−0.178413
$289$	1.00000	0.0588235
$290$	0.401211	0.0235599
$291$	−11.7242	−0.687285
$292$	−23.0535	−1.34911
$293$	32.0356	1.87154	0.935770	−	0.352611i	$-0.114706\pi$
$293$	32.0356	1.87154	0.935770	+	0.352611i	$0.114706\pi$
$294$	−1.33054	−0.0775987
$295$	−0.497951	−0.0289918
$296$	−3.75777	−0.218416
$297$	−3.10626	−0.180244
$298$	1.45148	0.0840818
$299$	1.15868	0.0670084
$300$	−6.62080	−0.382252
$301$	−4.16313	−0.239959
$302$	−0.810469	−0.0466373
$303$	−4.11116	−0.236180
$304$	12.6771	0.727081
$305$	−3.02207	−0.173043
$306$	−0.254047	−0.0145229
$307$	−20.3279	−1.16017	−0.580087	−	0.814554i	$-0.696982\pi$
$307$	−20.3279	−1.16017	−0.580087	+	0.814554i	$0.696982\pi$
$308$	−8.13299	−0.463420
$309$	−10.6318	−0.604820
$310$	−0.169640	−0.00963492
$311$	6.51834	0.369621	0.184811	−	0.982774i	$-0.440833\pi$
$311$	6.51834	0.369621	0.184811	+	0.982774i	$0.440833\pi$
$312$	0.451621	0.0255680
$313$	−16.4689	−0.930876	−0.465438	−	0.885081i	$-0.654103\pi$
$313$	−16.4689	−0.930876	−0.465438	+	0.885081i	$0.654103\pi$
$314$	−1.43342	−0.0808925
$315$	6.34425	0.357458
$316$	−3.69930	−0.208102
$317$	17.0313	0.956571	0.478286	−	0.878204i	$-0.341258\pi$
$317$	17.0313	0.956571	0.478286	+	0.878204i	$0.341258\pi$
$318$	0.871728	0.0488841
$319$	−6.40874	−0.358820
$320$	−3.86167	−0.215874
$321$	−4.26857	−0.238248
$322$	−0.372842	−0.0207777
$323$	3.21866	0.179091
$324$	−9.60592	−0.533662
$325$	−7.58901	−0.420963
$326$	1.28132	0.0709659
$327$	−7.46472	−0.412800
$328$	1.25785	0.0694531
$329$	−35.9679	−1.98298
$330$	0.0284177	0.00156434
$331$	−1.85906	−0.102183	−0.0510916	−	0.998694i	$-0.516270\pi$
$331$	−1.85906	−0.102183	−0.0510916	+	0.998694i	$0.516270\pi$
$332$	34.5932	1.89855
$333$	−23.3514	−1.27965
$334$	−2.27586	−0.124529
$335$	−2.14476	−0.117181
$336$	14.0006	0.763797
$337$	16.0242	0.872894	0.436447	−	0.899730i	$-0.356237\pi$
$337$	16.0242	0.872894	0.436447	+	0.899730i	$0.356237\pi$
$338$	−1.05777	−0.0575352
$339$	−12.4177	−0.674436
$340$	−0.990800	−0.0537337
$341$	2.70975	0.146741
$342$	−0.817691	−0.0442157
$343$	−59.7603	−3.22675
$344$	−0.331197	−0.0178570
$345$	−0.252975	−0.0136197
$346$	−1.12123	−0.0602777
$347$	22.9413	1.23155	0.615777	−	0.787920i	$-0.288842\pi$
$347$	22.9413	1.23155	0.615777	+	0.787920i	$0.288842\pi$
$348$	11.0898	0.594475
$349$	24.0851	1.28925	0.644623	−	0.764500i	$-0.277014\pi$
$349$	24.0851	1.28925	0.644623	+	0.764500i	$0.277014\pi$
$350$	2.44200	0.130530
$351$	6.16118	0.328859
$352$	−0.971359	−0.0517736
$353$	−16.6436	−0.885851	−0.442925	−	0.896558i	$-0.646059\pi$
$353$	−16.6436	−0.885851	−0.442925	+	0.896558i	$0.646059\pi$
$354$	0.0708800	0.00376723
$355$	−2.06547	−0.109624
$356$	−6.42651	−0.340604
$357$	3.55470	0.188135
$358$	0.0517262	0.00273381
$359$	16.0835	0.848853	0.424426	−	0.905463i	$-0.360476\pi$
$359$	16.0835	0.848853	0.424426	+	0.905463i	$0.360476\pi$
$360$	0.504716	0.0266009
$361$	−8.64024	−0.454749
$362$	0.661315	0.0347579
$363$	7.24843	0.380444
$364$	16.1315	0.845523
$365$	5.76932	0.301980
$366$	0.430171	0.0224854
$367$	−9.89890	−0.516718	−0.258359	−	0.966049i	$-0.583182\pi$
$367$	−9.89890	−0.516718	−0.258359	+	0.966049i	$0.583182\pi$
$368$	2.85762	0.148964
$369$	7.81649	0.406910
$370$	0.468997	0.0243820
$371$	62.4352	3.24148
$372$	−4.68899	−0.243113
$373$	11.7588	0.608850	0.304425	−	0.952536i	$-0.401536\pi$
$373$	11.7588	0.608850	0.304425	+	0.952536i	$0.401536\pi$
$374$	−0.0815027	−0.00421440
$375$	3.40027	0.175589
$376$	−2.86142	−0.147567
$377$	12.7115	0.654677
$378$	−1.98255	−0.101971
$379$	27.2318	1.39880	0.699402	−	0.714728i	$-0.253450\pi$
$379$	27.2318	1.39880	0.699402	+	0.714728i	$0.253450\pi$
$380$	−3.18905	−0.163595
$381$	−1.53577	−0.0786801
$382$	−0.914394	−0.0467845
$383$	0.739956	0.0378100	0.0189050	−	0.999821i	$-0.493982\pi$
$383$	0.739956	0.0378100	0.0189050	+	0.999821i	$0.493982\pi$
$384$	2.23920	0.114269
$385$	2.03534	0.103731
$386$	−0.0971579	−0.00494521
$387$	−2.05812	−0.104620
$388$	−33.3159	−1.69136
$389$	−12.0859	−0.612778	−0.306389	−	0.951906i	$-0.599121\pi$
$389$	−12.0859	−0.612778	−0.306389	+	0.951906i	$0.599121\pi$
$390$	−0.0563657	−0.00285419
$391$	0.725538	0.0366920
$392$	−7.58130	−0.382913
$393$	6.46522	0.326127
$394$	1.30746	0.0658690
$395$	0.925778	0.0465810
$396$	−4.02069	−0.202047
$397$	−1.37747	−0.0691331	−0.0345666	−	0.999402i	$-0.511005\pi$
$397$	−1.37747	−0.0691331	−0.0345666	+	0.999402i	$0.511005\pi$
$398$	−0.441618	−0.0221363
$399$	11.4414	0.572785
$400$	−18.7165	−0.935826
$401$	−25.0578	−1.25133	−0.625663	−	0.780093i	$-0.715171\pi$
$401$	−25.0578	−1.25133	−0.625663	+	0.780093i	$0.715171\pi$
$402$	0.305292	0.0152266
$403$	−5.37470	−0.267733
$404$	−11.6824	−0.581221
$405$	2.40396	0.119454
$406$	−4.09032	−0.202999
$407$	−7.49153	−0.371341
$408$	0.282794	0.0140004
$409$	−8.17728	−0.404340	−0.202170	−	0.979350i	$-0.564799\pi$
$409$	−8.17728	−0.404340	−0.202170	+	0.979350i	$0.564799\pi$
$410$	−0.156989	−0.00775313
$411$	−7.82049	−0.385756
$412$	−30.2116	−1.48842
$413$	5.07659	0.249803
$414$	−0.184321	−0.00905887
$415$	−8.65722	−0.424966
$416$	1.92666	0.0944624
$417$	−13.5282	−0.662481
$418$	−0.262329	−0.0128309
$419$	−16.2665	−0.794672	−0.397336	−	0.917673i	$-0.630065\pi$
$419$	−16.2665	−0.794672	−0.397336	+	0.917673i	$0.630065\pi$
$420$	−3.52200	−0.171856
$421$	8.94341	0.435875	0.217938	−	0.975963i	$-0.430067\pi$
$421$	8.94341	0.435875	0.217938	+	0.975963i	$0.430067\pi$
$422$	−2.37351	−0.115541
$423$	−17.7814	−0.864560
$424$	4.96702	0.241220
$425$	−4.75204	−0.230508
$426$	0.294005	0.0142446
$427$	30.8098	1.49099
$428$	−12.1297	−0.586312
$429$	0.900357	0.0434697
$430$	0.0413359	0.00199339
$431$	19.6717	0.947554	0.473777	−	0.880645i	$-0.342890\pi$
$431$	19.6717	0.947554	0.473777	+	0.880645i	$0.342890\pi$
$432$	15.1951	0.731074
$433$	1.12453	0.0540413	0.0270207	−	0.999635i	$-0.491398\pi$
$433$	1.12453	0.0540413	0.0270207	+	0.999635i	$0.491398\pi$
$434$	1.72947	0.0830174
$435$	−2.77531	−0.133066
$436$	−21.2120	−1.01587
$437$	2.33526	0.111711
$438$	−0.821224	−0.0392396
$439$	−6.32287	−0.301774	−0.150887	−	0.988551i	$-0.548213\pi$
$439$	−6.32287	−0.301774	−0.150887	+	0.988551i	$0.548213\pi$
$440$	0.161922	0.00771931
$441$	−47.1115	−2.24340
$442$	0.161658	0.00768929
$443$	22.2094	1.05520	0.527601	−	0.849492i	$-0.323092\pi$
$443$	22.2094	1.05520	0.527601	+	0.849492i	$0.323092\pi$
$444$	12.9635	0.615219
$445$	1.60828	0.0762399
$446$	−0.631596	−0.0299069
$447$	−10.0403	−0.474892
$448$	39.3696	1.86004
$449$	−11.9126	−0.562189	−0.281095	−	0.959680i	$-0.590697\pi$
$449$	−11.9126	−0.562189	−0.281095	+	0.959680i	$0.590697\pi$
$450$	1.20724	0.0569100
$451$	2.50766	0.118081
$452$	−35.2865	−1.65974
$453$	5.60628	0.263406
$454$	−1.21783	−0.0571558
$455$	−4.03704	−0.189260
$456$	0.910216	0.0426248
$457$	−15.1135	−0.706980	−0.353490	−	0.935438i	$-0.615005\pi$
$457$	−15.1135	−0.706980	−0.353490	+	0.935438i	$0.615005\pi$
$458$	−2.55902	−0.119575
$459$	3.85797	0.180075
$460$	−0.718862	−0.0335171
$461$	−11.6613	−0.543120	−0.271560	−	0.962421i	$-0.587540\pi$
$461$	−11.6613	−0.543120	−0.271560	+	0.962421i	$0.587540\pi$
$462$	−0.289717	−0.0134789
$463$	13.3254	0.619283	0.309642	−	0.950853i	$-0.399791\pi$
$463$	13.3254	0.619283	0.309642	+	0.950853i	$0.399791\pi$
$464$	31.3500	1.45539
$465$	1.17346	0.0544178
$466$	2.12106	0.0982562
$467$	24.9828	1.15607	0.578033	−	0.816013i	$-0.303820\pi$
$467$	24.9828	1.15607	0.578033	+	0.816013i	$0.303820\pi$
$468$	7.97491	0.368640
$469$	21.8657	1.00967
$470$	0.357127	0.0164730
$471$	9.91543	0.456879
$472$	0.403867	0.0185895
$473$	−0.660279	−0.0303597
$474$	−0.131778	−0.00605278
$475$	−15.2952	−0.701792
$476$	10.1012	0.462986
$477$	30.8659	1.41325
$478$	1.49068	0.0681819
$479$	18.8978	0.863460	0.431730	−	0.902003i	$-0.357903\pi$
$479$	18.8978	0.863460	0.431730	+	0.902003i	$0.357903\pi$
$480$	−0.420648	−0.0191998
$481$	14.8592	0.677522
$482$	−0.950388	−0.0432890
$483$	2.57907	0.117352
$484$	20.5974	0.936245
$485$	8.33757	0.378589
$486$	−1.51377	−0.0686659
$487$	33.3508	1.51127	0.755634	−	0.654994i	$-0.227329\pi$
$487$	33.3508	1.51127	0.755634	+	0.654994i	$0.227329\pi$
$488$	2.45107	0.110955
$489$	−8.86333	−0.400814
$490$	0.946202	0.0427451
$491$	−29.5338	−1.33284	−0.666420	−	0.745577i	$-0.732174\pi$
$491$	−29.5338	−1.33284	−0.666420	+	0.745577i	$0.732174\pi$
$492$	−4.33930	−0.195631
$493$	7.95964	0.358484
$494$	0.520322	0.0234104
$495$	1.00621	0.0452257
$496$	−13.2554	−0.595187
$497$	21.0573	0.944550
$498$	1.23230	0.0552206
$499$	7.93841	0.355372	0.177686	−	0.984087i	$-0.443139\pi$
$499$	7.93841	0.355372	0.177686	+	0.984087i	$0.443139\pi$
$500$	9.66232	0.432112
$501$	15.7428	0.703339
$502$	0.246106	0.0109842
$503$	19.5270	0.870665	0.435333	−	0.900270i	$-0.356631\pi$
$503$	19.5270	0.870665	0.435333	+	0.900270i	$0.356631\pi$
$504$	−5.14556	−0.229201
$505$	2.92361	0.130099
$506$	−0.0591332	−0.00262879
$507$	7.31695	0.324957
$508$	−4.36411	−0.193626
$509$	−19.4324	−0.861326	−0.430663	−	0.902513i	$-0.641720\pi$
$509$	−19.4324	−0.861326	−0.430663	+	0.902513i	$0.641720\pi$
$510$	−0.0352948	−0.00156288
$511$	−58.8180	−2.60195
$512$	7.93302	0.350593
$513$	12.4175	0.548246
$514$	2.64324	0.116588
$515$	7.56068	0.333163
$516$	1.14256	0.0502983
$517$	−5.70456	−0.250886
$518$	−4.78141	−0.210083
$519$	7.75591	0.340447
$520$	−0.321166	−0.0140841
$521$	36.4551	1.59713	0.798563	−	0.601911i	$-0.205594\pi$
$521$	36.4551	1.59713	0.798563	+	0.601911i	$0.205594\pi$
$522$	−2.02212	−0.0885059
$523$	−9.76614	−0.427044	−0.213522	−	0.976938i	$-0.568493\pi$
$523$	−9.76614	−0.427044	−0.213522	+	0.976938i	$0.568493\pi$
$524$	18.3718	0.802575
$525$	−16.8921	−0.737231
$526$	1.88182	0.0820514
$527$	−3.36550	−0.146603
$528$	2.22052	0.0966357
$529$	−22.4736	−0.977113
$530$	−0.619922	−0.0269277
$531$	2.50970	0.108912
$532$	32.5122	1.40958
$533$	−4.97387	−0.215442
$534$	−0.228928	−0.00990669
$535$	3.03555	0.131238
$536$	1.73952	0.0751360
$537$	−0.357807	−0.0154405
$538$	2.32002	0.100023
$539$	−15.1142	−0.651013
$540$	−3.82248	−0.164493
$541$	39.9207	1.71632	0.858162	−	0.513380i	$-0.171607\pi$
$541$	39.9207	1.71632	0.858162	+	0.513380i	$0.171607\pi$
$542$	1.22275	0.0525215
$543$	−4.57453	−0.196312
$544$	1.20643	0.0517251
$545$	5.30847	0.227390
$546$	0.574646	0.0245926
$547$	7.63482	0.326441	0.163221	−	0.986590i	$-0.447812\pi$
$547$	7.63482	0.326441	0.163221	+	0.986590i	$0.447812\pi$
$548$	−22.2230	−0.949318
$549$	15.2314	0.650059
$550$	0.387304	0.0165147
$551$	25.6193	1.09142
$552$	0.205177	0.00873293
$553$	−9.43827	−0.401356
$554$	−0.137125	−0.00582588
$555$	−3.24421	−0.137709
$556$	−38.4423	−1.63032
$557$	8.96407	0.379820	0.189910	−	0.981802i	$-0.439180\pi$
$557$	8.96407	0.379820	0.189910	+	0.981802i	$0.439180\pi$
$558$	0.854996	0.0361949
$559$	1.30964	0.0553920
$560$	−9.95642	−0.420736
$561$	0.563781	0.0238028
$562$	2.35674	0.0994129
$563$	−23.0293	−0.970569	−0.485285	−	0.874356i	$-0.661284\pi$
$563$	−23.0293	−0.970569	−0.485285	+	0.874356i	$0.661284\pi$
$564$	9.87128	0.415656
$565$	8.83073	0.371512
$566$	2.11415	0.0888645
$567$	−24.5082	−1.02925
$568$	1.67521	0.0702904
$569$	−5.64870	−0.236806	−0.118403	−	0.992966i	$-0.537777\pi$
$569$	−5.64870	−0.236806	−0.118403	+	0.992966i	$0.537777\pi$
$570$	−0.113602	−0.00475825
$571$	−20.2640	−0.848020	−0.424010	−	0.905658i	$-0.639378\pi$
$571$	−20.2640	−0.848020	−0.424010	+	0.905658i	$0.639378\pi$
$572$	2.55849	0.106976
$573$	6.32516	0.264237
$574$	1.60049	0.0668034
$575$	−3.44779	−0.143783
$576$	19.4630	0.810960
$577$	−4.29295	−0.178718	−0.0893589	−	0.995999i	$-0.528482\pi$
$577$	−4.29295	−0.178718	−0.0893589	+	0.995999i	$0.528482\pi$
$578$	0.101226	0.00421045
$579$	0.672073	0.0279304
$580$	−7.88641	−0.327465
$581$	88.2600	3.66164
$582$	−1.18680	−0.0491943
$583$	9.90232	0.410112
$584$	−4.67926	−0.193629
$585$	−1.99578	−0.0825155
$586$	3.24284	0.133960
$587$	−16.9877	−0.701159	−0.350580	−	0.936533i	$-0.614015\pi$
$587$	−16.9877	−0.701159	−0.350580	+	0.936533i	$0.614015\pi$
$588$	26.1538	1.07856
$589$	−10.8324	−0.446341
$590$	−0.0504057	−0.00207517
$591$	−9.04415	−0.372026
$592$	36.6468	1.50617
$593$	14.1992	0.583092	0.291546	−	0.956557i	$-0.405830\pi$
$593$	14.1992	0.583092	0.291546	+	0.956557i	$0.405830\pi$
$594$	−0.314435	−0.0129014
$595$	−2.52789	−0.103634
$596$	−28.5310	−1.16868
$597$	3.05482	0.125025
$598$	0.117289	0.00479630
$599$	2.26885	0.0927028	0.0463514	−	0.998925i	$-0.485241\pi$
$599$	2.26885	0.0927028	0.0463514	+	0.998925i	$0.485241\pi$
$600$	−1.34385	−0.0548623
$601$	19.6459	0.801374	0.400687	−	0.916215i	$-0.368771\pi$
$601$	19.6459	0.801374	0.400687	+	0.916215i	$0.368771\pi$
$602$	−0.421418	−0.0171757
$603$	10.8097	0.440205
$604$	15.9310	0.648224
$605$	−5.15465	−0.209566
$606$	−0.416156	−0.0169052
$607$	39.8668	1.61814	0.809071	−	0.587710i	$-0.199970\pi$
$607$	39.8668	1.61814	0.809071	+	0.587710i	$0.199970\pi$
$608$	3.88307	0.157479
$609$	28.2941	1.14654
$610$	−0.305912	−0.0123860
$611$	11.3148	0.457749
$612$	4.99368	0.201858
$613$	−38.4279	−1.55209	−0.776045	−	0.630678i	$-0.782777\pi$
$613$	−38.4279	−1.55209	−0.776045	+	0.630678i	$0.782777\pi$
$614$	−2.05771	−0.0830426
$615$	1.08594	0.0437895
$616$	−1.65078	−0.0665119
$617$	−36.2362	−1.45882	−0.729408	−	0.684079i	$-0.760204\pi$
$617$	−36.2362	−1.45882	−0.729408	+	0.684079i	$0.760204\pi$
$618$	−1.07621	−0.0432916
$619$	42.1966	1.69603	0.848013	−	0.529975i	$-0.177799\pi$
$619$	42.1966	1.69603	0.848013	+	0.529975i	$0.177799\pi$
$620$	3.33454	0.133918
$621$	2.79910	0.112324
$622$	0.659827	0.0264566
$623$	−16.3964	−0.656907
$624$	−4.40433	−0.176314
$625$	21.3422	0.853686
$626$	−1.66708	−0.0666299
$627$	1.81462	0.0724688
$628$	28.1760	1.12435
$629$	9.30446	0.370993
$630$	0.642204	0.0255860
$631$	−42.8558	−1.70606	−0.853032	−	0.521858i	$-0.825239\pi$
$631$	−42.8558	−1.70606	−0.853032	+	0.521858i	$0.825239\pi$
$632$	−0.750860	−0.0298676
$633$	16.4183	0.652570
$634$	1.72401	0.0684691
$635$	1.09215	0.0433407
$636$	−17.1351	−0.679453
$637$	29.9785	1.18779
$638$	−0.648731	−0.0256835
$639$	10.4101	0.411815
$640$	−1.59238	−0.0629445
$641$	−21.5584	−0.851504	−0.425752	−	0.904840i	$-0.639990\pi$
$641$	−21.5584	−0.851504	−0.425752	+	0.904840i	$0.639990\pi$
$642$	−0.432090	−0.0170532
$643$	9.50640	0.374896	0.187448	−	0.982275i	$-0.439978\pi$
$643$	9.50640	0.374896	0.187448	+	0.982275i	$0.439978\pi$
$644$	7.32877	0.288794
$645$	−0.285934	−0.0112586
$646$	0.325812	0.0128189
$647$	35.4153	1.39232	0.696159	−	0.717887i	$-0.254891\pi$
$647$	35.4153	1.39232	0.696159	+	0.717887i	$0.254891\pi$
$648$	−1.94975	−0.0765933
$649$	0.805155	0.0316051
$650$	−0.768206	−0.0301315
$651$	−11.9633	−0.468880
$652$	−25.1864	−0.986374
$653$	16.3986	0.641728	0.320864	−	0.947125i	$-0.396027\pi$
$653$	16.3986	0.641728	0.320864	+	0.947125i	$0.396027\pi$
$654$	−0.755625	−0.0295473
$655$	−4.59768	−0.179646
$656$	−12.2669	−0.478941
$657$	−29.0777	−1.13443
$658$	−3.64089	−0.141937
$659$	−11.0176	−0.429183	−0.214592	−	0.976704i	$-0.568842\pi$
$659$	−11.0176	−0.429183	−0.214592	+	0.976704i	$0.568842\pi$
$660$	−0.558594	−0.0217432
$661$	18.0053	0.700325	0.350162	−	0.936689i	$-0.386126\pi$
$661$	18.0053	0.700325	0.350162	+	0.936689i	$0.386126\pi$
$662$	−0.188185	−0.00731403
$663$	−1.11824	−0.0434289
$664$	7.02151	0.272487
$665$	−8.13642	−0.315517
$666$	−2.36377	−0.0915943
$667$	5.77501	0.223609
$668$	44.7354	1.73087
$669$	4.36895	0.168914
$670$	−0.217106	−0.00838752
$671$	4.88649	0.188641
$672$	4.28848	0.165432
$673$	−21.4929	−0.828492	−0.414246	−	0.910165i	$-0.635955\pi$
$673$	−21.4929	−0.828492	−0.414246	+	0.910165i	$0.635955\pi$
$674$	1.62207	0.0624797
$675$	−18.3332	−0.705647
$676$	20.7921	0.799697
$677$	5.51201	0.211844	0.105922	−	0.994374i	$-0.466221\pi$
$677$	5.51201	0.211844	0.105922	+	0.994374i	$0.466221\pi$
$678$	−1.25699	−0.0482746
$679$	−85.0011	−3.26204
$680$	−0.201106	−0.00771207
$681$	8.42416	0.322815
$682$	0.274297	0.0105034
$683$	−48.9045	−1.87128	−0.935639	−	0.352959i	$-0.885175\pi$
$683$	−48.9045	−1.87128	−0.935639	+	0.352959i	$0.885175\pi$
$684$	16.0730	0.614565
$685$	5.56147	0.212493
$686$	−6.04931	−0.230964
$687$	17.7016	0.675358
$688$	3.22993	0.123140
$689$	−19.6410	−0.748261
$690$	−0.0256077	−0.000974867 0
$691$	45.9266	1.74713	0.873566	−	0.486706i	$-0.161802\pi$
$691$	45.9266	1.74713	0.873566	+	0.486706i	$0.161802\pi$
$692$	22.0395	0.837815
$693$	−10.2582	−0.389678
$694$	2.32226	0.0881518
$695$	9.62049	0.364926
$696$	2.25093	0.0853214
$697$	−3.11451	−0.117970
$698$	2.43804	0.0922813
$699$	−14.6721	−0.554948
$700$	−48.0012	−1.81427
$701$	−42.3853	−1.60087	−0.800435	−	0.599420i	$-0.795398\pi$
$701$	−42.3853	−1.60087	−0.800435	+	0.599420i	$0.795398\pi$
$702$	0.623672	0.0235390
$703$	29.9479	1.12951
$704$	6.24408	0.235332
$705$	−2.47036	−0.0930393
$706$	−1.68477	−0.0634071
$707$	−29.8061	−1.12097
$708$	−1.39325	−0.0523617
$709$	14.1197	0.530277	0.265139	−	0.964210i	$-0.414582\pi$
$709$	14.1197	0.530277	0.265139	+	0.964210i	$0.414582\pi$
$710$	−0.209079	−0.00784660
$711$	−4.66597	−0.174988
$712$	−1.30441	−0.0488848
$713$	−2.44180	−0.0914460
$714$	0.359828	0.0134662
$715$	−0.640281	−0.0239452
$716$	−1.01676	−0.0379980
$717$	−10.3115	−0.385090
$718$	1.62807	0.0607589
$719$	−26.5400	−0.989775	−0.494887	−	0.868957i	$-0.664791\pi$
$719$	−26.5400	−0.989775	−0.494887	+	0.868957i	$0.664791\pi$
$720$	−4.92213	−0.183437
$721$	−77.0808	−2.87064
$722$	−0.874618	−0.0325499
$723$	6.57414	0.244495
$724$	−12.9991	−0.483109
$725$	−37.8245	−1.40477
$726$	0.733730	0.0272313
$727$	−46.1904	−1.71311	−0.856553	−	0.516060i	$-0.827398\pi$
$727$	−46.1904	−1.71311	−0.856553	+	0.516060i	$0.827398\pi$
$728$	3.27428	0.121353
$729$	−4.01185	−0.148587
$730$	0.584006	0.0216150
$731$	0.820065	0.0303312
$732$	−8.45566	−0.312530
$733$	−16.8969	−0.624100	−0.312050	−	0.950066i	$-0.601016\pi$
$733$	−16.8969	−0.624100	−0.312050	+	0.950066i	$0.601016\pi$
$734$	−1.00203	−0.0369855
$735$	−6.54519	−0.241423
$736$	0.875307	0.0322643
$737$	3.46794	0.127743
$738$	0.791232	0.0291257
$739$	−27.5013	−1.01165	−0.505825	−	0.862636i	$-0.668812\pi$
$739$	−27.5013	−1.01165	−0.505825	+	0.862636i	$0.668812\pi$
$740$	−9.21885	−0.338892
$741$	−3.59924	−0.132221
$742$	6.32008	0.232017
$743$	21.6789	0.795321	0.397661	−	0.917533i	$-0.369822\pi$
$743$	21.6789	0.795321	0.397661	+	0.917533i	$0.369822\pi$
$744$	−0.951742	−0.0348925
$745$	7.14010	0.261593
$746$	1.19030	0.0435800
$747$	43.6329	1.59644
$748$	1.60206	0.0585771
$749$	−30.9473	−1.13079
$750$	0.344196	0.0125683
$751$	−38.0047	−1.38681	−0.693405	−	0.720548i	$-0.743890\pi$
$751$	−38.0047	−1.38681	−0.693405	+	0.720548i	$0.743890\pi$
$752$	27.9054	1.01760
$753$	−1.70239	−0.0620387
$754$	1.28674	0.0468603
$755$	−3.98686	−0.145097
$756$	38.9700	1.41732
$757$	33.2694	1.20920	0.604599	−	0.796530i	$-0.293333\pi$
$757$	33.2694	1.20920	0.604599	+	0.796530i	$0.293333\pi$
$758$	2.75657	0.100123
$759$	0.409044	0.0148474
$760$	−0.647292	−0.0234797
$761$	2.89533	0.104956	0.0524779	−	0.998622i	$-0.483288\pi$
$761$	2.89533	0.104956	0.0524779	+	0.998622i	$0.483288\pi$
$762$	−0.155460	−0.00563174
$763$	−54.1196	−1.95926
$764$	17.9738	0.650270
$765$	−1.24971	−0.0451833
$766$	0.0749029	0.00270635
$767$	−1.59700	−0.0576643
$768$	−10.6338	−0.383715
$769$	−24.4024	−0.879973	−0.439986	−	0.898004i	$-0.645017\pi$
$769$	−24.4024	−0.879973	−0.439986	+	0.898004i	$0.645017\pi$
$770$	0.206030	0.00742481
$771$	−18.2842	−0.658488
$772$	1.90979	0.0687347
$773$	22.1151	0.795425	0.397712	−	0.917510i	$-0.369804\pi$
$773$	22.1151	0.795425	0.397712	+	0.917510i	$0.369804\pi$
$774$	−0.208335	−0.00748845
$775$	15.9930	0.574486
$776$	−6.76225	−0.242751
$777$	33.0745	1.18654
$778$	−1.22341	−0.0438612
$779$	−10.0245	−0.359167
$780$	1.10795	0.0396711
$781$	3.33972	0.119505
$782$	0.0734433	0.00262633
$783$	30.7080	1.09742
$784$	73.9349	2.64053
$785$	−7.05127	−0.251671
$786$	0.654449	0.0233434
$787$	11.7135	0.417542	0.208771	−	0.977965i	$-0.433054\pi$
$787$	11.7135	0.417542	0.208771	+	0.977965i	$0.433054\pi$
$788$	−25.7002	−0.915531
$789$	−13.0172	−0.463424
$790$	0.0937129	0.00333416
$791$	−90.0289	−3.20106
$792$	−0.816093	−0.0289986
$793$	−9.69220	−0.344180
$794$	−0.139436	−0.00494839
$795$	4.28820	0.152087
$796$	8.68068	0.307679
$797$	41.6557	1.47552	0.737761	−	0.675062i	$-0.235883\pi$
$797$	41.6557	1.47552	0.737761	+	0.675062i	$0.235883\pi$
$798$	1.15816	0.0409986
$799$	7.08506	0.250651
$800$	−5.73299	−0.202692
$801$	−8.10583	−0.286405
$802$	−2.53650	−0.0895670
$803$	−9.32862	−0.329200
$804$	−6.00098	−0.211638
$805$	−1.83408	−0.0646429
$806$	−0.544060	−0.0191637
$807$	−16.0483	−0.564927
$808$	−2.37122	−0.0834192
$809$	−52.4682	−1.84468	−0.922342	−	0.386373i	$-0.873728\pi$
$809$	−52.4682	−1.84468	−0.922342	+	0.386373i	$0.873728\pi$
$810$	0.243343	0.00855021
$811$	16.5697	0.581841	0.290920	−	0.956747i	$-0.406038\pi$
$811$	16.5697	0.581841	0.290920	+	0.956747i	$0.406038\pi$
$812$	80.4015	2.82154
$813$	−8.45815	−0.296640
$814$	−0.758338	−0.0265797
$815$	6.30308	0.220787
$816$	−2.75788	−0.0965451
$817$	2.63951	0.0923447
$818$	−0.827754	−0.0289417
$819$	20.3469	0.710979
$820$	3.08586	0.107763
$821$	20.0888	0.701105	0.350552	−	0.936543i	$-0.385994\pi$
$821$	20.0888	0.701105	0.350552	+	0.936543i	$0.385994\pi$
$822$	−0.791638	−0.0276115
$823$	−4.94027	−0.172207	−0.0861036	−	0.996286i	$-0.527442\pi$
$823$	−4.94027	−0.172207	−0.0861036	+	0.996286i	$0.527442\pi$
$824$	−6.13215	−0.213624
$825$	−2.67911	−0.0932747
$826$	0.513883	0.0178803
$827$	2.60361	0.0905363	0.0452681	−	0.998975i	$-0.485586\pi$
$827$	2.60361	0.0905363	0.0452681	+	0.998975i	$0.485586\pi$
$828$	3.62311	0.125912
$829$	3.54325	0.123062	0.0615311	−	0.998105i	$-0.480402\pi$
$829$	3.54325	0.123062	0.0615311	+	0.998105i	$0.480402\pi$
$830$	−0.876337	−0.0304181
$831$	0.948538	0.0329044
$832$	−12.3849	−0.429370
$833$	18.7718	0.650403
$834$	−1.36941	−0.0474188
$835$	−11.1954	−0.387432
$836$	5.15648	0.178341
$837$	−12.9840	−0.448793
$838$	−1.64660	−0.0568807
$839$	−23.1773	−0.800169	−0.400085	−	0.916478i	$-0.631019\pi$
$839$	−23.1773	−0.800169	−0.400085	+	0.916478i	$0.631019\pi$
$840$	−0.714872	−0.0246654
$841$	34.3558	1.18468
$842$	0.905307	0.0311989
$843$	−16.3023	−0.561482
$844$	46.6549	1.60593
$845$	−5.20339	−0.179002
$846$	−1.79994	−0.0618832
$847$	52.5515	1.80569
$848$	−48.4398	−1.66343
$849$	−14.6243	−0.501904
$850$	−0.481031	−0.0164992
$851$	6.75073	0.231412
$852$	−5.77912	−0.197989
$853$	−9.20536	−0.315186	−0.157593	−	0.987504i	$-0.550373\pi$
$853$	−9.20536	−0.315186	−0.157593	+	0.987504i	$0.550373\pi$
$854$	3.11876	0.106722
$855$	−4.02238	−0.137563
$856$	−2.46201	−0.0841498
$857$	23.0042	0.785809	0.392904	−	0.919579i	$-0.371470\pi$
$857$	23.0042	0.785809	0.392904	+	0.919579i	$0.371470\pi$
$858$	0.0911397	0.00311146
$859$	−48.5022	−1.65487	−0.827437	−	0.561558i	$-0.810202\pi$
$859$	−48.5022	−1.65487	−0.827437	+	0.561558i	$0.810202\pi$
$860$	−0.812520	−0.0277067
$861$	−11.0711	−0.377304
$862$	1.99129	0.0678237
$863$	8.00245	0.272407	0.136203	−	0.990681i	$-0.456510\pi$
$863$	8.00245	0.272407	0.136203	+	0.990681i	$0.456510\pi$
$864$	4.65436	0.158344
$865$	−5.51555	−0.187534
$866$	0.113832	0.00386815
$867$	−0.700214	−0.0237805
$868$	−33.9955	−1.15388
$869$	−1.49692	−0.0507796
$870$	−0.280933	−0.00952453
$871$	−6.87855	−0.233071
$872$	−4.30548	−0.145802
$873$	−42.0218	−1.42222
$874$	0.236389	0.00799598
$875$	24.6521	0.833394
$876$	16.1424	0.545401
$877$	8.33408	0.281422	0.140711	−	0.990051i	$-0.455061\pi$
$877$	8.33408	0.281422	0.140711	+	0.990051i	$0.455061\pi$
$878$	−0.640040	−0.0216003
$879$	−22.4318	−0.756605
$880$	−1.57910	−0.0532316
$881$	−41.7581	−1.40686	−0.703432	−	0.710762i	$-0.748350\pi$
$881$	−41.7581	−1.40686	−0.703432	+	0.710762i	$0.748350\pi$
$882$	−4.76891	−0.160578
$883$	−25.6248	−0.862343	−0.431172	−	0.902270i	$-0.641900\pi$
$883$	−25.6248	−0.862343	−0.431172	+	0.902270i	$0.641900\pi$
$884$	−3.17763	−0.106875
$885$	0.348672	0.0117205
$886$	2.24817	0.0755289
$887$	46.6816	1.56741	0.783707	−	0.621131i	$-0.213326\pi$
$887$	46.6816	1.56741	0.783707	+	0.621131i	$0.213326\pi$
$888$	2.63124	0.0882986
$889$	−11.1344	−0.373437
$890$	0.162800	0.00545707
$891$	−3.88704	−0.130221
$892$	12.4150	0.415684
$893$	22.8044	0.763119
$894$	−1.01635	−0.0339917
$895$	0.254451	0.00850537
$896$	16.2343	0.542350
$897$	−0.811326	−0.0270894
$898$	−1.20586	−0.0402402
$899$	−26.7882	−0.893435
$900$	−23.7302	−0.791007
$901$	−12.2987	−0.409728
$902$	0.253841	0.00845198
$903$	2.91508	0.0970079
$904$	−7.16223	−0.238212
$905$	3.25314	0.108138
$906$	0.567502	0.0188540
$907$	−30.8735	−1.02514	−0.512569	−	0.858646i	$-0.671306\pi$
$907$	−30.8735	−1.02514	−0.512569	+	0.858646i	$0.671306\pi$
$908$	23.9384	0.794424
$909$	−14.7352	−0.488735
$910$	−0.408654	−0.0135468
$911$	23.9816	0.794547	0.397273	−	0.917700i	$-0.369956\pi$
$911$	23.9816	0.794547	0.397273	+	0.917700i	$0.369956\pi$
$912$	−8.87668	−0.293936
$913$	13.9982	0.463272
$914$	−1.52988	−0.0506039
$915$	2.11609	0.0699559
$916$	50.3015	1.66201
$917$	46.8732	1.54789
$918$	0.390527	0.0128893
$919$	25.8937	0.854156	0.427078	−	0.904215i	$-0.359543\pi$
$919$	25.8937	0.854156	0.427078	+	0.904215i	$0.359543\pi$
$920$	−0.145910	−0.00481051
$921$	14.2339	0.469022
$922$	−1.18043	−0.0388753
$923$	−6.62424	−0.218040
$924$	5.69484	0.187346
$925$	−44.2152	−1.45379
$926$	1.34888	0.0443268
$927$	−38.1062	−1.25157
$928$	9.60271	0.315224
$929$	29.5688	0.970120	0.485060	−	0.874481i	$-0.338798\pi$
$929$	29.5688	0.970120	0.485060	+	0.874481i	$0.338798\pi$
$930$	0.118784	0.00389510
$931$	60.4199	1.98018
$932$	−41.6927	−1.36569
$933$	−4.56424	−0.149426
$934$	2.52891	0.0827486
$935$	−0.400928	−0.0131117
$936$	1.61870	0.0529087
$937$	26.3471	0.860723	0.430361	−	0.902657i	$-0.358386\pi$
$937$	26.3471	0.860723	0.430361	+	0.902657i	$0.358386\pi$
$938$	2.21338	0.0722695
$939$	11.5317	0.376324
$940$	−7.01987	−0.228963
$941$	3.49565	0.113955	0.0569774	−	0.998375i	$-0.481854\pi$
$941$	3.49565	0.113955	0.0569774	+	0.998375i	$0.481854\pi$
$942$	1.00370	0.0327023
$943$	−2.25969	−0.0735858
$944$	−3.93862	−0.128191
$945$	−9.75253	−0.317250
$946$	−0.0668375	−0.00217307
$947$	27.6564	0.898711	0.449356	−	0.893353i	$-0.351654\pi$
$947$	27.6564	0.898711	0.449356	+	0.893353i	$0.351654\pi$
$948$	2.59030	0.0841291
$949$	18.5030	0.600634
$950$	−1.54827	−0.0502327
$951$	−11.9255	−0.386712
$952$	2.05027	0.0664496
$953$	−24.4122	−0.790790	−0.395395	−	0.918511i	$-0.629392\pi$
$953$	−24.4122	−0.790790	−0.395395	+	0.918511i	$0.629392\pi$
$954$	3.12444	0.101157
$955$	−4.49808	−0.145555
$956$	−29.3015	−0.947678
$957$	4.48749	0.145060
$958$	1.91295	0.0618045
$959$	−56.6989	−1.83090
$960$	2.70400	0.0872712
$961$	−19.6734	−0.634626
$962$	1.50414	0.0484954
$963$	−15.2994	−0.493015
$964$	18.6813	0.601685
$965$	−0.477939	−0.0153854
$966$	0.261069	0.00839976
$967$	3.23378	0.103991	0.0519957	−	0.998647i	$-0.483442\pi$
$967$	3.23378	0.103991	0.0519957	+	0.998647i	$0.483442\pi$
$968$	4.18072	0.134374
$969$	−2.25375	−0.0724009
$970$	0.843979	0.0270985
$971$	27.6928	0.888706	0.444353	−	0.895852i	$-0.353434\pi$
$971$	27.6928	0.888706	0.444353	+	0.895852i	$0.353434\pi$
$972$	29.7554	0.954406
$973$	−98.0804	−3.14431
$974$	3.37597	0.108173
$975$	5.31393	0.170182
$976$	−23.9035	−0.765133
$977$	33.6511	1.07659	0.538297	−	0.842756i	$-0.319068\pi$
$977$	33.6511	1.07659	0.538297	+	0.842756i	$0.319068\pi$
$978$	−0.897201	−0.0286893
$979$	−2.60049	−0.0831120
$980$	−18.5990	−0.594125
$981$	−26.7550	−0.854221
$982$	−2.98959	−0.0954016
$983$	40.3545	1.28711	0.643555	−	0.765400i	$-0.277459\pi$
$983$	40.3545	1.28711	0.643555	+	0.765400i	$0.277459\pi$
$984$	−0.880763	−0.0280777
$985$	6.43167	0.204930
$986$	0.805723	0.0256594
$987$	25.1852	0.801655
$988$	−10.2277	−0.325387
$989$	0.594988	0.0189195
$990$	0.101855	0.00323715
$991$	−1.94847	−0.0618951	−0.0309476	−	0.999521i	$-0.509852\pi$
$991$	−1.94847	−0.0618951	−0.0309476	+	0.999521i	$0.509852\pi$
$992$	−4.06023	−0.128912
$993$	1.30174	0.0413095
$994$	2.13155	0.0676087
$995$	−2.17241	−0.0688699
$996$	−24.2227	−0.767525
$997$	−26.4315	−0.837093	−0.418546	−	0.908195i	$-0.637460\pi$
$997$	−26.4315	−0.837093	−0.418546	+	0.908195i	$0.637460\pi$
$998$	0.803574	0.0254367
$999$	35.8963	1.13571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.9	✓	18
3.2	odd	2		9027.2.a.q.1.10		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.9	✓	18	1.1	even	1	trivial
9027.2.a.q.1.10		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+0.101226 q^{2} -0.700214 q^{3} -1.98975 q^{4} +0.497951 q^{5} -0.0708800 q^{6} -5.07659 q^{7} -0.403867 q^{8} -2.50970 q^{9} +O(q^{10})\)	\(q+0.101226 q^{2} -0.700214 q^{3} -1.98975 q^{4} +0.497951 q^{5} -0.0708800 q^{6} -5.07659 q^{7} -0.403867 q^{8} -2.50970 q^{9} +0.0504057 q^{10} -0.805155 q^{11} +1.39325 q^{12} +1.59700 q^{13} -0.513883 q^{14} -0.348672 q^{15} +3.93862 q^{16} +1.00000 q^{17} -0.254047 q^{18} +3.21866 q^{19} -0.990800 q^{20} +3.55470 q^{21} -0.0815027 q^{22} +0.725538 q^{23} +0.282794 q^{24} -4.75204 q^{25} +0.161658 q^{26} +3.85797 q^{27} +10.1012 q^{28} +7.95964 q^{29} -0.0352948 q^{30} -3.36550 q^{31} +1.20643 q^{32} +0.563781 q^{33} +0.101226 q^{34} -2.52789 q^{35} +4.99368 q^{36} +9.30446 q^{37} +0.325812 q^{38} -1.11824 q^{39} -0.201106 q^{40} -3.11451 q^{41} +0.359828 q^{42} +0.820065 q^{43} +1.60206 q^{44} -1.24971 q^{45} +0.0734433 q^{46} +7.08506 q^{47} -2.75788 q^{48} +18.7718 q^{49} -0.481031 q^{50} -0.700214 q^{51} -3.17763 q^{52} -12.2987 q^{53} +0.390527 q^{54} -0.400928 q^{55} +2.05027 q^{56} -2.25375 q^{57} +0.805723 q^{58} -1.00000 q^{59} +0.693772 q^{60} -6.06900 q^{61} -0.340676 q^{62} +12.7407 q^{63} -7.75513 q^{64} +0.795228 q^{65} +0.0570693 q^{66} -4.30717 q^{67} -1.98975 q^{68} -0.508032 q^{69} -0.255889 q^{70} -4.14793 q^{71} +1.01359 q^{72} +11.5861 q^{73} +0.941854 q^{74} +3.32745 q^{75} -6.40434 q^{76} +4.08744 q^{77} -0.113195 q^{78} +1.85918 q^{79} +1.96124 q^{80} +4.82770 q^{81} -0.315270 q^{82} -17.3857 q^{83} -7.07297 q^{84} +0.497951 q^{85} +0.0830120 q^{86} -5.57345 q^{87} +0.325176 q^{88} +3.22980 q^{89} -0.126503 q^{90} -8.10731 q^{91} -1.44364 q^{92} +2.35657 q^{93} +0.717193 q^{94} +1.60273 q^{95} -0.844757 q^{96} +16.7437 q^{97} +1.90019 q^{98} +2.02070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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