LMFDB - Embedded newform 8027.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38066 q^{2} +0.526357 q^{3} +3.66755 q^{4} -2.52733 q^{5} -1.25308 q^{6} +3.59846 q^{7} -3.96986 q^{8} -2.72295 q^{9} +O(q^{10})$	\(q-2.38066 q^{2} +0.526357 q^{3} +3.66755 q^{4} -2.52733 q^{5} -1.25308 q^{6} +3.59846 q^{7} -3.96986 q^{8} -2.72295 q^{9} +6.01672 q^{10} +0.148692 q^{11} +1.93044 q^{12} -0.823438 q^{13} -8.56671 q^{14} -1.33028 q^{15} +2.11581 q^{16} -7.17794 q^{17} +6.48242 q^{18} -3.75432 q^{19} -9.26910 q^{20} +1.89408 q^{21} -0.353985 q^{22} +1.00000 q^{23} -2.08957 q^{24} +1.38740 q^{25} +1.96033 q^{26} -3.01232 q^{27} +13.1975 q^{28} -8.30713 q^{29} +3.16694 q^{30} -6.30144 q^{31} +2.90271 q^{32} +0.0782650 q^{33} +17.0882 q^{34} -9.09450 q^{35} -9.98654 q^{36} +7.50019 q^{37} +8.93776 q^{38} -0.433423 q^{39} +10.0332 q^{40} +2.30789 q^{41} -4.50915 q^{42} -7.76200 q^{43} +0.545334 q^{44} +6.88179 q^{45} -2.38066 q^{46} -12.7353 q^{47} +1.11367 q^{48} +5.94892 q^{49} -3.30292 q^{50} -3.77816 q^{51} -3.02000 q^{52} -6.43656 q^{53} +7.17130 q^{54} -0.375793 q^{55} -14.2854 q^{56} -1.97611 q^{57} +19.7765 q^{58} -5.91991 q^{59} -4.87886 q^{60} +11.6427 q^{61} +15.0016 q^{62} -9.79842 q^{63} -11.1420 q^{64} +2.08110 q^{65} -0.186322 q^{66} -8.93362 q^{67} -26.3254 q^{68} +0.526357 q^{69} +21.6509 q^{70} -11.5173 q^{71} +10.8097 q^{72} +2.53070 q^{73} -17.8554 q^{74} +0.730267 q^{75} -13.7691 q^{76} +0.535062 q^{77} +1.03183 q^{78} +8.17168 q^{79} -5.34734 q^{80} +6.58329 q^{81} -5.49431 q^{82} +0.954879 q^{83} +6.94661 q^{84} +18.1410 q^{85} +18.4787 q^{86} -4.37252 q^{87} -0.590286 q^{88} -4.90448 q^{89} -16.3832 q^{90} -2.96311 q^{91} +3.66755 q^{92} -3.31681 q^{93} +30.3184 q^{94} +9.48841 q^{95} +1.52786 q^{96} +15.3766 q^{97} -14.1624 q^{98} -0.404880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.38066	−1.68338	−0.841691	−	0.539960i	$-0.818439\pi$
$2$	−2.38066	−1.68338	−0.841691	+	0.539960i	$0.818439\pi$
$3$	0.526357	0.303893	0.151946	−	0.988389i	$-0.451446\pi$
$3$	0.526357	0.303893	0.151946	+	0.988389i	$0.451446\pi$
$4$	3.66755	1.83377
$5$	−2.52733	−1.13026	−0.565128	−	0.825003i	$-0.691173\pi$
$5$	−2.52733	−1.13026	−0.565128	+	0.825003i	$0.691173\pi$
$6$	−1.25308	−0.511567
$7$	3.59846	1.36009	0.680045	−	0.733170i	$-0.261960\pi$
$7$	3.59846	1.36009	0.680045	+	0.733170i	$0.261960\pi$
$8$	−3.96986	−1.40356
$9$	−2.72295	−0.907649
$10$	6.01672	1.90265
$11$	0.148692	0.0448323	0.0224161	−	0.999749i	$-0.492864\pi$
$11$	0.148692	0.0448323	0.0224161	+	0.999749i	$0.492864\pi$
$12$	1.93044	0.557270
$13$	−0.823438	−0.228381	−0.114190	−	0.993459i	$-0.536427\pi$
$13$	−0.823438	−0.228381	−0.114190	+	0.993459i	$0.536427\pi$
$14$	−8.56671	−2.28955
$15$	−1.33028	−0.343477
$16$	2.11581	0.528952
$17$	−7.17794	−1.74091	−0.870453	−	0.492252i	$-0.836174\pi$
$17$	−7.17794	−1.74091	−0.870453	+	0.492252i	$0.836174\pi$
$18$	6.48242	1.52792
$19$	−3.75432	−0.861300	−0.430650	−	0.902519i	$-0.641716\pi$
$19$	−3.75432	−0.861300	−0.430650	+	0.902519i	$0.641716\pi$
$20$	−9.26910	−2.07263
$21$	1.89408	0.413321
$22$	−0.353985	−0.0754698
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.08957	−0.426531
$25$	1.38740	0.277480
$26$	1.96033	0.384452
$27$	−3.01232	−0.579720
$28$	13.1975	2.49410
$29$	−8.30713	−1.54260	−0.771298	−	0.636474i	$-0.780392\pi$
$29$	−8.30713	−1.54260	−0.771298	+	0.636474i	$0.780392\pi$
$30$	3.16694	0.578202
$31$	−6.30144	−1.13177	−0.565886	−	0.824483i	$-0.691466\pi$
$31$	−6.30144	−1.13177	−0.565886	+	0.824483i	$0.691466\pi$
$32$	2.90271	0.513132
$33$	0.0782650	0.0136242
$34$	17.0882	2.93061
$35$	−9.09450	−1.53725
$36$	−9.98654	−1.66442
$37$	7.50019	1.23302	0.616512	−	0.787345i	$-0.288545\pi$
$37$	7.50019	1.23302	0.616512	+	0.787345i	$0.288545\pi$
$38$	8.93776	1.44990
$39$	−0.433423	−0.0694032
$40$	10.0332	1.58638
$41$	2.30789	0.360433	0.180216	−	0.983627i	$-0.442320\pi$
$41$	2.30789	0.360433	0.180216	+	0.983627i	$0.442320\pi$
$42$	−4.50915	−0.695777
$43$	−7.76200	−1.18369	−0.591847	−	0.806051i	$-0.701601\pi$
$43$	−7.76200	−1.18369	−0.591847	+	0.806051i	$0.701601\pi$
$44$	0.545334	0.0822122
$45$	6.88179	1.02588
$46$	−2.38066	−0.351009
$47$	−12.7353	−1.85763	−0.928817	−	0.370539i	$-0.879173\pi$
$47$	−12.7353	−1.85763	−0.928817	+	0.370539i	$0.879173\pi$
$48$	1.11367	0.160744
$49$	5.94892	0.849845
$50$	−3.30292	−0.467104
$51$	−3.77816	−0.529048
$52$	−3.02000	−0.418798
$53$	−6.43656	−0.884130	−0.442065	−	0.896983i	$-0.645754\pi$
$53$	−6.43656	−0.884130	−0.442065	+	0.896983i	$0.645754\pi$
$54$	7.17130	0.975891
$55$	−0.375793	−0.0506720
$56$	−14.2854	−1.90897
$57$	−1.97611	−0.261743
$58$	19.7765	2.59678
$59$	−5.91991	−0.770707	−0.385353	−	0.922769i	$-0.625920\pi$
$59$	−5.91991	−0.770707	−0.385353	+	0.922769i	$0.625920\pi$
$60$	−4.87886	−0.629858
$61$	11.6427	1.49070	0.745350	−	0.666673i	$-0.232282\pi$
$61$	11.6427	1.49070	0.745350	+	0.666673i	$0.232282\pi$
$62$	15.0016	1.90520
$63$	−9.79842	−1.23448
$64$	−11.1420	−1.39275
$65$	2.08110	0.258129
$66$	−0.186322	−0.0229347
$67$	−8.93362	−1.09142	−0.545708	−	0.837976i	$-0.683739\pi$
$67$	−8.93362	−1.09142	−0.545708	+	0.837976i	$0.683739\pi$
$68$	−26.3254	−3.19243
$69$	0.526357	0.0633660
$70$	21.6509	2.58778
$71$	−11.5173	−1.36685	−0.683427	−	0.730019i	$-0.739511\pi$
$71$	−11.5173	−1.36685	−0.683427	+	0.730019i	$0.739511\pi$
$72$	10.8097	1.27394
$73$	2.53070	0.296196	0.148098	−	0.988973i	$-0.452685\pi$
$73$	2.53070	0.296196	0.148098	+	0.988973i	$0.452685\pi$
$74$	−17.8554	−2.07565
$75$	0.730267	0.0843240
$76$	−13.7691	−1.57943
$77$	0.535062	0.0609759
$78$	1.03183	0.116832
$79$	8.17168	0.919386	0.459693	−	0.888078i	$-0.347959\pi$
$79$	8.17168	0.919386	0.459693	+	0.888078i	$0.347959\pi$
$80$	−5.34734	−0.597851
$81$	6.58329	0.731477
$82$	−5.49431	−0.606745
$83$	0.954879	0.104812	0.0524058	−	0.998626i	$-0.483311\pi$
$83$	0.954879	0.104812	0.0524058	+	0.998626i	$0.483311\pi$
$84$	6.94661	0.757938
$85$	18.1410	1.96767
$86$	18.4787	1.99261
$87$	−4.37252	−0.468783
$88$	−0.590286	−0.0629247
$89$	−4.90448	−0.519873	−0.259937	−	0.965626i	$-0.583702\pi$
$89$	−4.90448	−0.519873	−0.259937	+	0.965626i	$0.583702\pi$
$90$	−16.3832	−1.72694
$91$	−2.96311	−0.310618
$92$	3.66755	0.382368
$93$	−3.31681	−0.343937
$94$	30.3184	3.12711
$95$	9.48841	0.973490
$96$	1.52786	0.155937
$97$	15.3766	1.56126	0.780630	−	0.624993i	$-0.214898\pi$
$97$	15.3766	1.56126	0.780630	+	0.624993i	$0.214898\pi$
$98$	−14.1624	−1.43061
$99$	−0.404880	−0.0406920
$100$	5.08835	0.508835
$101$	11.3044	1.12483	0.562416	−	0.826855i	$-0.309872\pi$
$101$	11.3044	1.12483	0.562416	+	0.826855i	$0.309872\pi$
$102$	8.99452	0.890590
$103$	−2.26848	−0.223520	−0.111760	−	0.993735i	$-0.535649\pi$
$103$	−2.26848	−0.223520	−0.111760	+	0.993735i	$0.535649\pi$
$104$	3.26894	0.320546
$105$	−4.78696	−0.467159
$106$	15.3233	1.48833
$107$	15.6792	1.51577	0.757883	−	0.652390i	$-0.226234\pi$
$107$	15.6792	1.51577	0.757883	+	0.652390i	$0.226234\pi$
$108$	−11.0478	−1.06308
$109$	11.5832	1.10947	0.554737	−	0.832026i	$-0.312819\pi$
$109$	11.5832	1.10947	0.554737	+	0.832026i	$0.312819\pi$
$110$	0.894636	0.0853002
$111$	3.94778	0.374707
$112$	7.61364	0.719422
$113$	1.53096	0.144021	0.0720105	−	0.997404i	$-0.477058\pi$
$113$	1.53096	0.144021	0.0720105	+	0.997404i	$0.477058\pi$
$114$	4.70446	0.440613
$115$	−2.52733	−0.235675
$116$	−30.4668	−2.82877
$117$	2.24218	0.207289
$118$	14.0933	1.29739
$119$	−25.8295	−2.36779
$120$	5.28103	0.482090
$121$	−10.9779	−0.997990
$122$	−27.7174	−2.50942
$123$	1.21478	0.109533
$124$	−23.1108	−2.07541
$125$	9.13024	0.816633
$126$	23.3267	2.07811
$127$	−13.2941	−1.17966	−0.589830	−	0.807527i	$-0.700805\pi$
$127$	−13.2941	−1.17966	−0.589830	+	0.807527i	$0.700805\pi$
$128$	20.7199	1.83139
$129$	−4.08558	−0.359716
$130$	−4.95439	−0.434529
$131$	−11.5503	−1.00916	−0.504578	−	0.863366i	$-0.668352\pi$
$131$	−11.5503	−1.00916	−0.504578	+	0.863366i	$0.668352\pi$
$132$	0.287041	0.0249837
$133$	−13.5098	−1.17145
$134$	21.2679	1.83727
$135$	7.61312	0.655233
$136$	28.4954	2.44346
$137$	10.2468	0.875441	0.437720	−	0.899111i	$-0.355786\pi$
$137$	10.2468	0.875441	0.437720	+	0.899111i	$0.355786\pi$
$138$	−1.25308	−0.106669
$139$	22.4477	1.90399	0.951996	−	0.306111i	$-0.0990278\pi$
$139$	22.4477	1.90399	0.951996	+	0.306111i	$0.0990278\pi$
$140$	−33.3545	−2.81897
$141$	−6.70332	−0.564521
$142$	27.4188	2.30094
$143$	−0.122438	−0.0102388
$144$	−5.76123	−0.480102
$145$	20.9949	1.74353
$146$	−6.02474	−0.498611
$147$	3.13126	0.258262
$148$	27.5073	2.26109
$149$	21.7101	1.77856	0.889278	−	0.457366i	$-0.151207\pi$
$149$	21.7101	1.77856	0.889278	+	0.457366i	$0.151207\pi$
$150$	−1.73852	−0.141949
$151$	−12.4342	−1.01188	−0.505942	−	0.862568i	$-0.668855\pi$
$151$	−12.4342	−1.01188	−0.505942	+	0.862568i	$0.668855\pi$
$152$	14.9041	1.20889
$153$	19.5452	1.58013
$154$	−1.27380	−0.102646
$155$	15.9258	1.27919
$156$	−1.58960	−0.127270
$157$	−8.42287	−0.672218	−0.336109	−	0.941823i	$-0.609111\pi$
$157$	−8.42287	−0.672218	−0.336109	+	0.941823i	$0.609111\pi$
$158$	−19.4540	−1.54768
$159$	−3.38793	−0.268680
$160$	−7.33611	−0.579970
$161$	3.59846	0.283598
$162$	−15.6726	−1.23135
$163$	−18.4711	−1.44677	−0.723384	−	0.690445i	$-0.757415\pi$
$163$	−18.4711	−1.44677	−0.723384	+	0.690445i	$0.757415\pi$
$164$	8.46431	0.660952
$165$	−0.197802	−0.0153988
$166$	−2.27324	−0.176438
$167$	6.02480	0.466213	0.233106	−	0.972451i	$-0.425111\pi$
$167$	6.02480	0.466213	0.233106	+	0.972451i	$0.425111\pi$
$168$	−7.51922	−0.580121
$169$	−12.3220	−0.947842
$170$	−43.1876	−3.31234
$171$	10.2228	0.781758
$172$	−28.4675	−2.17063
$173$	−5.61865	−0.427178	−0.213589	−	0.976924i	$-0.568515\pi$
$173$	−5.61865	−0.427178	−0.213589	+	0.976924i	$0.568515\pi$
$174$	10.4095	0.789141
$175$	4.99250	0.377397
$176$	0.314603	0.0237141
$177$	−3.11599	−0.234212
$178$	11.6759	0.875145
$179$	10.1063	0.755378	0.377689	−	0.925932i	$-0.376719\pi$
$179$	10.1063	0.755378	0.377689	+	0.925932i	$0.376719\pi$
$180$	25.2393	1.88123
$181$	22.3130	1.65851	0.829256	−	0.558869i	$-0.188765\pi$
$181$	22.3130	1.65851	0.829256	+	0.558869i	$0.188765\pi$
$182$	7.05416	0.522889
$183$	6.12824	0.453013
$184$	−3.96986	−0.292662
$185$	−18.9555	−1.39363
$186$	7.89620	0.578977
$187$	−1.06730	−0.0780487
$188$	−46.7073	−3.40648
$189$	−10.8397	−0.788472
$190$	−22.5887	−1.63876
$191$	21.4075	1.54899	0.774497	−	0.632578i	$-0.218003\pi$
$191$	21.4075	1.54899	0.774497	+	0.632578i	$0.218003\pi$
$192$	−5.86466	−0.423246
$193$	15.7581	1.13429	0.567146	−	0.823617i	$-0.308047\pi$
$193$	15.7581	1.13429	0.567146	+	0.823617i	$0.308047\pi$
$194$	−36.6065	−2.62820
$195$	1.09540	0.0784434
$196$	21.8179	1.55842
$197$	−7.96751	−0.567662	−0.283831	−	0.958874i	$-0.591605\pi$
$197$	−7.96751	−0.567662	−0.283831	+	0.958874i	$0.591605\pi$
$198$	0.963882	0.0685001
$199$	25.5094	1.80831	0.904157	−	0.427201i	$-0.140500\pi$
$199$	25.5094	1.80831	0.904157	+	0.427201i	$0.140500\pi$
$200$	−5.50778	−0.389459
$201$	−4.70228	−0.331673
$202$	−26.9120	−1.89352
$203$	−29.8929	−2.09807
$204$	−13.8566	−0.970155
$205$	−5.83281	−0.407381
$206$	5.40048	0.376269
$207$	−2.72295	−0.189258
$208$	−1.74223	−0.120802
$209$	−0.558237	−0.0386140
$210$	11.3961	0.786407
$211$	−13.4498	−0.925924	−0.462962	−	0.886378i	$-0.653213\pi$
$211$	−13.4498	−0.925924	−0.462962	+	0.886378i	$0.653213\pi$
$212$	−23.6064	−1.62129
$213$	−6.06222	−0.415377
$214$	−37.3269	−2.55161
$215$	19.6171	1.33788
$216$	11.9585	0.813672
$217$	−22.6755	−1.53931
$218$	−27.5758	−1.86767
$219$	1.33205	0.0900118
$220$	−1.37824	−0.0929209
$221$	5.91059	0.397589
$222$	−9.39833	−0.630775
$223$	−11.4991	−0.770038	−0.385019	−	0.922909i	$-0.625805\pi$
$223$	−11.4991	−0.770038	−0.385019	+	0.922909i	$0.625805\pi$
$224$	10.4453	0.697905
$225$	−3.77781	−0.251854
$226$	−3.64471	−0.242442
$227$	−20.8312	−1.38261	−0.691307	−	0.722561i	$-0.742965\pi$
$227$	−20.8312	−1.38261	−0.691307	+	0.722561i	$0.742965\pi$
$228$	−7.24749	−0.479977
$229$	−16.8488	−1.11340	−0.556699	−	0.830714i	$-0.687932\pi$
$229$	−16.8488	−1.11340	−0.556699	+	0.830714i	$0.687932\pi$
$230$	6.01672	0.396731
$231$	0.281634	0.0185301
$232$	32.9782	2.16512
$233$	−1.92536	−0.126134	−0.0630671	−	0.998009i	$-0.520088\pi$
$233$	−1.92536	−0.126134	−0.0630671	+	0.998009i	$0.520088\pi$
$234$	−5.33787	−0.348947
$235$	32.1863	2.09960
$236$	−21.7115	−1.41330
$237$	4.30122	0.279395
$238$	61.4913	3.98589
$239$	14.1583	0.915826	0.457913	−	0.888997i	$-0.348597\pi$
$239$	14.1583	0.915826	0.457913	+	0.888997i	$0.348597\pi$
$240$	−2.81461	−0.181682
$241$	−6.43629	−0.414598	−0.207299	−	0.978278i	$-0.566467\pi$
$241$	−6.43629	−0.414598	−0.207299	+	0.978278i	$0.566467\pi$
$242$	26.1346	1.68000
$243$	12.5021	0.802011
$244$	42.7003	2.73361
$245$	−15.0349	−0.960543
$246$	−2.89197	−0.184385
$247$	3.09145	0.196704
$248$	25.0159	1.58851
$249$	0.502608	0.0318515
$250$	−21.7360	−1.37471
$251$	0.121232	0.00765208	0.00382604	−	0.999993i	$-0.498782\pi$
$251$	0.121232	0.00765208	0.00382604	+	0.999993i	$0.498782\pi$
$252$	−35.9362	−2.26377
$253$	0.148692	0.00934817
$254$	31.6487	1.98582
$255$	9.54866	0.597960
$256$	−27.0430	−1.69019
$257$	21.7696	1.35795	0.678976	−	0.734160i	$-0.262424\pi$
$257$	21.7696	1.35795	0.678976	+	0.734160i	$0.262424\pi$
$258$	9.72639	0.605539
$259$	26.9891	1.67702
$260$	7.63253	0.473349
$261$	22.6199	1.40014
$262$	27.4974	1.69879
$263$	−26.9245	−1.66024	−0.830118	−	0.557587i	$-0.811727\pi$
$263$	−26.9245	−1.66024	−0.830118	+	0.557587i	$0.811727\pi$
$264$	−0.310701	−0.0191224
$265$	16.2673	0.999293
$266$	32.1622	1.97199
$267$	−2.58151	−0.157986
$268$	−32.7645	−2.00141
$269$	−24.9459	−1.52098	−0.760489	−	0.649351i	$-0.775040\pi$
$269$	−24.9459	−1.52098	−0.760489	+	0.649351i	$0.775040\pi$
$270$	−18.1243	−1.10301
$271$	−4.79701	−0.291397	−0.145699	−	0.989329i	$-0.546543\pi$
$271$	−4.79701	−0.291397	−0.145699	+	0.989329i	$0.546543\pi$
$272$	−15.1871	−0.920855
$273$	−1.55965	−0.0943945
$274$	−24.3941	−1.47370
$275$	0.206295	0.0124400
$276$	1.93044	0.116199
$277$	8.37700	0.503325	0.251663	−	0.967815i	$-0.419023\pi$
$277$	8.37700	0.503325	0.251663	+	0.967815i	$0.419023\pi$
$278$	−53.4404	−3.20514
$279$	17.1585	1.02725
$280$	36.1039	2.15762
$281$	23.3875	1.39518	0.697591	−	0.716496i	$-0.254255\pi$
$281$	23.3875	1.39518	0.697591	+	0.716496i	$0.254255\pi$
$282$	15.9583	0.950305
$283$	−4.00799	−0.238250	−0.119125	−	0.992879i	$-0.538009\pi$
$283$	−4.00799	−0.238250	−0.119125	+	0.992879i	$0.538009\pi$
$284$	−42.2403	−2.50650
$285$	4.99429	0.295836
$286$	0.291484	0.0172358
$287$	8.30487	0.490221
$288$	−7.90393	−0.465743
$289$	34.5228	2.03075
$290$	−49.9817	−2.93502
$291$	8.09360	0.474455
$292$	9.28146	0.543156
$293$	−14.7643	−0.862539	−0.431269	−	0.902223i	$-0.641934\pi$
$293$	−14.7643	−0.862539	−0.431269	+	0.902223i	$0.641934\pi$
$294$	−7.45446	−0.434753
$295$	14.9616	0.871096
$296$	−29.7747	−1.73062
$297$	−0.447907	−0.0259902
$298$	−51.6843	−2.99399
$299$	−0.823438	−0.0476206
$300$	2.67829	0.154631
$301$	−27.9312	−1.60993
$302$	29.6017	1.70339
$303$	5.95016	0.341828
$304$	−7.94341	−0.455586
$305$	−29.4250	−1.68487
$306$	−46.5304	−2.65996
$307$	11.4218	0.651879	0.325939	−	0.945391i	$-0.394319\pi$
$307$	11.4218	0.651879	0.325939	+	0.945391i	$0.394319\pi$
$308$	1.96236	0.111816
$309$	−1.19403	−0.0679260
$310$	−37.9140	−2.15337
$311$	−25.4409	−1.44262	−0.721311	−	0.692612i	$-0.756460\pi$
$311$	−25.4409	−1.44262	−0.721311	+	0.692612i	$0.756460\pi$
$312$	1.72063	0.0974114
$313$	11.3398	0.640963	0.320481	−	0.947255i	$-0.396155\pi$
$313$	11.3398	0.640963	0.320481	+	0.947255i	$0.396155\pi$
$314$	20.0520	1.13160
$315$	24.7638	1.39528
$316$	29.9700	1.68595
$317$	−1.08207	−0.0607750	−0.0303875	−	0.999538i	$-0.509674\pi$
$317$	−1.08207	−0.0607750	−0.0303875	+	0.999538i	$0.509674\pi$
$318$	8.06552	0.452292
$319$	−1.23520	−0.0691581
$320$	28.1595	1.57416
$321$	8.25287	0.460630
$322$	−8.56671	−0.477404
$323$	26.9483	1.49944
$324$	24.1445	1.34136
$325$	−1.14244	−0.0633709
$326$	43.9735	2.43546
$327$	6.09693	0.337161
$328$	−9.16203	−0.505888
$329$	−45.8275	−2.52655
$330$	0.470898	0.0259221
$331$	−32.8450	−1.80533	−0.902663	−	0.430348i	$-0.858391\pi$
$331$	−32.8450	−1.80533	−0.902663	+	0.430348i	$0.858391\pi$
$332$	3.50207	0.192201
$333$	−20.4226	−1.11915
$334$	−14.3430	−0.784814
$335$	22.5782	1.23358
$336$	4.00750	0.218627
$337$	16.1015	0.877102	0.438551	−	0.898706i	$-0.355492\pi$
$337$	16.1015	0.877102	0.438551	+	0.898706i	$0.355492\pi$
$338$	29.3344	1.59558
$339$	0.805835	0.0437669
$340$	66.5330	3.60826
$341$	−0.936973	−0.0507399
$342$	−24.3371	−1.31600
$343$	−3.78228	−0.204224
$344$	30.8141	1.66138
$345$	−1.33028	−0.0716198
$346$	13.3761	0.719104
$347$	27.1934	1.45982	0.729910	−	0.683543i	$-0.239562\pi$
$347$	27.1934	1.45982	0.729910	+	0.683543i	$0.239562\pi$
$348$	−16.0364	−0.859642
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−11.8854	−0.635304
$351$	2.48045	0.132397
$352$	0.431609	0.0230048
$353$	−5.23971	−0.278882	−0.139441	−	0.990230i	$-0.544530\pi$
$353$	−5.23971	−0.278882	−0.139441	+	0.990230i	$0.544530\pi$
$354$	7.41811	0.394268
$355$	29.1081	1.54490
$356$	−17.9874	−0.953330
$357$	−13.5956	−0.719553
$358$	−24.0596	−1.27159
$359$	−10.9081	−0.575707	−0.287854	−	0.957674i	$-0.592942\pi$
$359$	−10.9081	−0.575707	−0.287854	+	0.957674i	$0.592942\pi$
$360$	−27.3198	−1.43988
$361$	−4.90508	−0.258162
$362$	−53.1197	−2.79191
$363$	−5.77829	−0.303282
$364$	−10.8673	−0.569603
$365$	−6.39592	−0.334777
$366$	−14.5893	−0.762593
$367$	32.1036	1.67579	0.837896	−	0.545830i	$-0.183786\pi$
$367$	32.1036	1.67579	0.837896	+	0.545830i	$0.183786\pi$
$368$	2.11581	0.110294
$369$	−6.28428	−0.327146
$370$	45.1265	2.34602
$371$	−23.1617	−1.20250
$372$	−12.1646	−0.630703
$373$	−19.7458	−1.02240	−0.511199	−	0.859463i	$-0.670798\pi$
$373$	−19.7458	−1.02240	−0.511199	+	0.859463i	$0.670798\pi$
$374$	2.54088	0.131386
$375$	4.80577	0.248169
$376$	50.5574	2.60730
$377$	6.84041	0.352299
$378$	25.8056	1.32730
$379$	−26.2286	−1.34727	−0.673637	−	0.739063i	$-0.735269\pi$
$379$	−26.2286	−1.34727	−0.673637	+	0.739063i	$0.735269\pi$
$380$	34.7992	1.78516
$381$	−6.99745	−0.358490
$382$	−50.9640	−2.60755
$383$	22.6537	1.15755	0.578776	−	0.815487i	$-0.303531\pi$
$383$	22.6537	1.15755	0.578776	+	0.815487i	$0.303531\pi$
$384$	10.9061	0.556547
$385$	−1.35228	−0.0689184
$386$	−37.5147	−1.90945
$387$	21.1355	1.07438
$388$	56.3945	2.86300
$389$	−32.6874	−1.65732	−0.828660	−	0.559753i	$-0.810896\pi$
$389$	−32.6874	−1.65732	−0.828660	+	0.559753i	$0.810896\pi$
$390$	−2.60778	−0.132050
$391$	−7.17794	−0.363004
$392$	−23.6164	−1.19281
$393$	−6.07959	−0.306675
$394$	18.9679	0.955591
$395$	−20.6525	−1.03914
$396$	−1.48492	−0.0746199
$397$	−10.3538	−0.519642	−0.259821	−	0.965657i	$-0.583664\pi$
$397$	−10.3538	−0.519642	−0.259821	+	0.965657i	$0.583664\pi$
$398$	−60.7292	−3.04408
$399$	−7.11097	−0.355994
$400$	2.93547	0.146773
$401$	9.42277	0.470550	0.235275	−	0.971929i	$-0.424401\pi$
$401$	9.42277	0.470550	0.235275	+	0.971929i	$0.424401\pi$
$402$	11.1945	0.558332
$403$	5.18884	0.258475
$404$	41.4595	2.06269
$405$	−16.6381	−0.826756
$406$	71.1648	3.53185
$407$	1.11522	0.0552793
$408$	14.9988	0.742550
$409$	21.3950	1.05791	0.528957	−	0.848648i	$-0.322583\pi$
$409$	21.3950	1.05791	0.528957	+	0.848648i	$0.322583\pi$
$410$	13.8859	0.685778
$411$	5.39346	0.266040
$412$	−8.31975	−0.409885
$413$	−21.3026	−1.04823
$414$	6.48242	0.318593
$415$	−2.41330	−0.118464
$416$	−2.39020	−0.117189
$417$	11.8155	0.578609
$418$	1.32897	0.0650022
$419$	−13.6194	−0.665349	−0.332675	−	0.943042i	$-0.607951\pi$
$419$	−13.6194	−0.665349	−0.332675	+	0.943042i	$0.607951\pi$
$420$	−17.5564	−0.856664
$421$	39.3604	1.91831	0.959154	−	0.282884i	$-0.0912911\pi$
$421$	39.3604	1.91831	0.959154	+	0.282884i	$0.0912911\pi$
$422$	32.0195	1.55868
$423$	34.6776	1.68608
$424$	25.5523	1.24093
$425$	−9.95866	−0.483066
$426$	14.4321	0.699238
$427$	41.8959	2.02749
$428$	57.5042	2.77957
$429$	−0.0644464	−0.00311150
$430$	−46.7017	−2.25216
$431$	12.6374	0.608721	0.304360	−	0.952557i	$-0.401557\pi$
$431$	12.6374	0.608721	0.304360	+	0.952557i	$0.401557\pi$
$432$	−6.37348	−0.306644
$433$	13.5492	0.651133	0.325567	−	0.945519i	$-0.394445\pi$
$433$	13.5492	0.651133	0.325567	+	0.945519i	$0.394445\pi$
$434$	53.9826	2.59125
$435$	11.0508	0.529845
$436$	42.4821	2.03452
$437$	−3.75432	−0.179593
$438$	−3.17117	−0.151524
$439$	−29.5329	−1.40953	−0.704763	−	0.709442i	$-0.748947\pi$
$439$	−29.5329	−1.40953	−0.704763	+	0.709442i	$0.748947\pi$
$440$	1.49185	0.0711211
$441$	−16.1986	−0.771361
$442$	−14.0711	−0.669294
$443$	−18.0063	−0.855503	−0.427752	−	0.903896i	$-0.640694\pi$
$443$	−18.0063	−0.855503	−0.427752	+	0.903896i	$0.640694\pi$
$444$	14.4787	0.687127
$445$	12.3952	0.587590
$446$	27.3755	1.29627
$447$	11.4272	0.540490
$448$	−40.0940	−1.89426
$449$	1.37881	0.0650699	0.0325349	−	0.999471i	$-0.489642\pi$
$449$	1.37881	0.0650699	0.0325349	+	0.999471i	$0.489642\pi$
$450$	8.99369	0.423967
$451$	0.343165	0.0161590
$452$	5.61489	0.264102
$453$	−6.54485	−0.307504
$454$	49.5920	2.32747
$455$	7.48875	0.351078
$456$	7.84490	0.367371
$457$	−10.2483	−0.479396	−0.239698	−	0.970848i	$-0.577048\pi$
$457$	−10.2483	−0.479396	−0.239698	+	0.970848i	$0.577048\pi$
$458$	40.1112	1.87427
$459$	21.6222	1.00924
$460$	−9.26910	−0.432174
$461$	−15.5412	−0.723825	−0.361912	−	0.932212i	$-0.617876\pi$
$461$	−15.5412	−0.723825	−0.361912	+	0.932212i	$0.617876\pi$
$462$	−0.670474	−0.0311933
$463$	14.6072	0.678852	0.339426	−	0.940633i	$-0.389767\pi$
$463$	14.6072	0.678852	0.339426	+	0.940633i	$0.389767\pi$
$464$	−17.5763	−0.815958
$465$	8.38267	0.388737
$466$	4.58362	0.212332
$467$	−36.4257	−1.68558	−0.842789	−	0.538244i	$-0.819088\pi$
$467$	−36.4257	−1.68558	−0.842789	+	0.538244i	$0.819088\pi$
$468$	8.22329	0.380122
$469$	−32.1473	−1.48442
$470$	−76.6247	−3.53443
$471$	−4.43344	−0.204282
$472$	23.5012	1.08173
$473$	−1.15415	−0.0530677
$474$	−10.2398	−0.470328
$475$	−5.20874	−0.238993
$476$	−94.7310	−4.34199
$477$	17.5264	0.802480
$478$	−33.7062	−1.54168
$479$	0.704213	0.0321763	0.0160882	−	0.999871i	$-0.494879\pi$
$479$	0.704213	0.0321763	0.0160882	+	0.999871i	$0.494879\pi$
$480$	−3.86141	−0.176249
$481$	−6.17594	−0.281599
$482$	15.3226	0.697926
$483$	1.89408	0.0861834
$484$	−40.2619	−1.83009
$485$	−38.8618	−1.76462
$486$	−29.7633	−1.35009
$487$	13.0887	0.593104	0.296552	−	0.955017i	$-0.404163\pi$
$487$	13.0887	0.593104	0.296552	+	0.955017i	$0.404163\pi$
$488$	−46.2201	−2.09228
$489$	−9.72240	−0.439662
$490$	35.7929	1.61696
$491$	21.3450	0.963286	0.481643	−	0.876367i	$-0.340040\pi$
$491$	21.3450	0.963286	0.481643	+	0.876367i	$0.340040\pi$
$492$	4.45525	0.200858
$493$	59.6281	2.68551
$494$	−7.35969	−0.331128
$495$	1.02327	0.0459924
$496$	−13.3326	−0.598653
$497$	−41.4446	−1.85904
$498$	−1.19654	−0.0536182
$499$	−3.09987	−0.138769	−0.0693846	−	0.997590i	$-0.522104\pi$
$499$	−3.09987	−0.138769	−0.0693846	+	0.997590i	$0.522104\pi$
$500$	33.4856	1.49752
$501$	3.17120	0.141679
$502$	−0.288612	−0.0128814
$503$	7.56887	0.337479	0.168740	−	0.985661i	$-0.446030\pi$
$503$	7.56887	0.337479	0.168740	+	0.985661i	$0.446030\pi$
$504$	38.8984	1.73267
$505$	−28.5700	−1.27135
$506$	−0.353985	−0.0157365
$507$	−6.48575	−0.288042
$508$	−48.7567	−2.16323
$509$	1.98557	0.0880086	0.0440043	−	0.999031i	$-0.485988\pi$
$509$	1.98557	0.0880086	0.0440043	+	0.999031i	$0.485988\pi$
$510$	−22.7321	−1.00660
$511$	9.10662	0.402853
$512$	22.9405	1.01384
$513$	11.3092	0.499313
$514$	−51.8261	−2.28595
$515$	5.73319	0.252635
$516$	−14.9841	−0.659637
$517$	−1.89363	−0.0832819
$518$	−64.2520	−2.82307
$519$	−2.95742	−0.129816
$520$	−8.26168	−0.362299
$521$	35.4309	1.55226	0.776129	−	0.630574i	$-0.217181\pi$
$521$	35.4309	1.55226	0.776129	+	0.630574i	$0.217181\pi$
$522$	−53.8503	−2.35696
$523$	6.60112	0.288647	0.144323	−	0.989531i	$-0.453899\pi$
$523$	6.60112	0.288647	0.144323	+	0.989531i	$0.453899\pi$
$524$	−42.3613	−1.85056
$525$	2.62784	0.114688
$526$	64.0981	2.79481
$527$	45.2313	1.97031
$528$	0.165594	0.00720654
$529$	1.00000	0.0434783
$530$	−38.7270	−1.68219
$531$	16.1196	0.699531
$532$	−49.5477	−2.14817
$533$	−1.90041	−0.0823158
$534$	6.14569	0.265950
$535$	−39.6265	−1.71320
$536$	35.4652	1.53187
$537$	5.31951	0.229554
$538$	59.3877	2.56038
$539$	0.884555	0.0381005
$540$	27.9215	1.20155
$541$	−13.2356	−0.569044	−0.284522	−	0.958670i	$-0.591835\pi$
$541$	−13.2356	−0.569044	−0.284522	+	0.958670i	$0.591835\pi$
$542$	11.4200	0.490533
$543$	11.7446	0.504009
$544$	−20.8355	−0.893314
$545$	−29.2747	−1.25399
$546$	3.71301	0.158902
$547$	24.9942	1.06867	0.534337	−	0.845272i	$-0.320561\pi$
$547$	24.9942	1.06867	0.534337	+	0.845272i	$0.320561\pi$
$548$	37.5805	1.60536
$549$	−31.7026	−1.35303
$550$	−0.491118	−0.0209413
$551$	31.1876	1.32864
$552$	−2.08957	−0.0889379
$553$	29.4055	1.25045
$554$	−19.9428	−0.847289
$555$	−9.97735	−0.423515
$556$	82.3281	3.49149
$557$	17.1028	0.724667	0.362333	−	0.932049i	$-0.381980\pi$
$557$	17.1028	0.724667	0.362333	+	0.932049i	$0.381980\pi$
$558$	−40.8486	−1.72926
$559$	6.39152	0.270333
$560$	−19.2422	−0.813131
$561$	−0.561781	−0.0237184
$562$	−55.6777	−2.34862
$563$	−22.3885	−0.943561	−0.471780	−	0.881716i	$-0.656388\pi$
$563$	−22.3885	−0.943561	−0.471780	+	0.881716i	$0.656388\pi$
$564$	−24.5847	−1.03520
$565$	−3.86925	−0.162781
$566$	9.54167	0.401066
$567$	23.6897	0.994874
$568$	45.7222	1.91846
$569$	−26.7090	−1.11970	−0.559850	−	0.828594i	$-0.689141\pi$
$569$	−26.7090	−1.11970	−0.559850	+	0.828594i	$0.689141\pi$
$570$	−11.8897	−0.498006
$571$	−6.80257	−0.284679	−0.142339	−	0.989818i	$-0.545462\pi$
$571$	−6.80257	−0.284679	−0.142339	+	0.989818i	$0.545462\pi$
$572$	−0.449049	−0.0187757
$573$	11.2680	0.470728
$574$	−19.7711	−0.825229
$575$	1.38740	0.0578585
$576$	30.3390	1.26413
$577$	−9.16556	−0.381567	−0.190784	−	0.981632i	$-0.561103\pi$
$577$	−9.16556	−0.381567	−0.190784	+	0.981632i	$0.561103\pi$
$578$	−82.1871	−3.41853
$579$	8.29439	0.344703
$580$	76.9997	3.19724
$581$	3.43610	0.142553
$582$	−19.2681	−0.798689
$583$	−0.957064	−0.0396375
$584$	−10.0465	−0.415729
$585$	−5.66672	−0.234290
$586$	35.1488	1.45198
$587$	27.6788	1.14243	0.571214	−	0.820801i	$-0.306473\pi$
$587$	27.6788	1.14243	0.571214	+	0.820801i	$0.306473\pi$
$588$	11.4840	0.473593
$589$	23.6576	0.974795
$590$	−35.6184	−1.46639
$591$	−4.19376	−0.172508
$592$	15.8690	0.652210
$593$	−5.17627	−0.212564	−0.106282	−	0.994336i	$-0.533895\pi$
$593$	−5.17627	−0.212564	−0.106282	+	0.994336i	$0.533895\pi$
$594$	1.06631	0.0437514
$595$	65.2797	2.67621
$596$	79.6226	3.26147
$597$	13.4271	0.549533
$598$	1.96033	0.0801637
$599$	−32.4991	−1.32788	−0.663940	−	0.747786i	$-0.731117\pi$
$599$	−32.4991	−1.32788	−0.663940	+	0.747786i	$0.731117\pi$
$600$	−2.89906	−0.118354
$601$	36.6637	1.49554	0.747772	−	0.663955i	$-0.231123\pi$
$601$	36.6637	1.49554	0.747772	+	0.663955i	$0.231123\pi$
$602$	66.4948	2.71013
$603$	24.3258	0.990622
$604$	−45.6031	−1.85556
$605$	27.7448	1.12798
$606$	−14.1653	−0.575427
$607$	9.26373	0.376003	0.188002	−	0.982169i	$-0.439799\pi$
$607$	9.26373	0.376003	0.188002	+	0.982169i	$0.439799\pi$
$608$	−10.8977	−0.441960
$609$	−15.7343	−0.637588
$610$	70.0511	2.83628
$611$	10.4867	0.424247
$612$	71.6828	2.89760
$613$	−17.8512	−0.721003	−0.360501	−	0.932759i	$-0.617394\pi$
$613$	−17.8512	−0.721003	−0.360501	+	0.932759i	$0.617394\pi$
$614$	−27.1915	−1.09736
$615$	−3.07014	−0.123800
$616$	−2.12412	−0.0855833
$617$	22.3190	0.898528	0.449264	−	0.893399i	$-0.351686\pi$
$617$	22.3190	0.898528	0.449264	+	0.893399i	$0.351686\pi$
$618$	2.84258	0.114345
$619$	2.02348	0.0813306	0.0406653	−	0.999173i	$-0.487052\pi$
$619$	2.02348	0.0813306	0.0406653	+	0.999173i	$0.487052\pi$
$620$	58.4087	2.34575
$621$	−3.01232	−0.120880
$622$	60.5662	2.42848
$623$	−17.6486	−0.707075
$624$	−0.917038	−0.0367109
$625$	−30.0121	−1.20048
$626$	−26.9962	−1.07898
$627$	−0.293832	−0.0117345
$628$	−30.8913	−1.23270
$629$	−53.8359	−2.14658
$630$	−58.9543	−2.34880
$631$	−15.9928	−0.636661	−0.318331	−	0.947980i	$-0.603122\pi$
$631$	−15.9928	−0.636661	−0.318331	+	0.947980i	$0.603122\pi$
$632$	−32.4405	−1.29041
$633$	−7.07941	−0.281381
$634$	2.57604	0.102308
$635$	33.5986	1.33332
$636$	−12.4254	−0.492699
$637$	−4.89856	−0.194088
$638$	2.94060	0.116419
$639$	31.3611	1.24062
$640$	−52.3659	−2.06995
$641$	−44.3589	−1.75207	−0.876036	−	0.482245i	$-0.839822\pi$
$641$	−44.3589	−1.75207	−0.876036	+	0.482245i	$0.839822\pi$
$642$	−19.6473	−0.775416
$643$	−1.39985	−0.0552048	−0.0276024	−	0.999619i	$-0.508787\pi$
$643$	−1.39985	−0.0552048	−0.0276024	+	0.999619i	$0.508787\pi$
$644$	13.1975	0.520055
$645$	10.3256	0.406571
$646$	−64.1547	−2.52413
$647$	−49.3759	−1.94117	−0.970584	−	0.240762i	$-0.922603\pi$
$647$	−49.3759	−1.94117	−0.970584	+	0.240762i	$0.922603\pi$
$648$	−26.1348	−1.02667
$649$	−0.880242	−0.0345525
$650$	2.71975	0.106677
$651$	−11.9354	−0.467786
$652$	−67.7437	−2.65305
$653$	−1.24204	−0.0486047	−0.0243023	−	0.999705i	$-0.507736\pi$
$653$	−1.24204	−0.0486047	−0.0243023	+	0.999705i	$0.507736\pi$
$654$	−14.5147	−0.567570
$655$	29.1914	1.14060
$656$	4.88306	0.190651
$657$	−6.89096	−0.268842
$658$	109.100	4.25315
$659$	21.7765	0.848291	0.424145	−	0.905594i	$-0.360575\pi$
$659$	21.7765	0.848291	0.424145	+	0.905594i	$0.360575\pi$
$660$	−0.725447	−0.0282380
$661$	−16.6446	−0.647398	−0.323699	−	0.946160i	$-0.604927\pi$
$661$	−16.6446	−0.647398	−0.323699	+	0.946160i	$0.604927\pi$
$662$	78.1929	3.03905
$663$	3.11108	0.120824
$664$	−3.79074	−0.147109
$665$	34.1437	1.32403
$666$	48.6194	1.88396
$667$	−8.30713	−0.321653
$668$	22.0962	0.854929
$669$	−6.05265	−0.234009
$670$	−53.7510	−2.07658
$671$	1.73118	0.0668315
$672$	5.49795	0.212088
$673$	21.3316	0.822272	0.411136	−	0.911574i	$-0.365132\pi$
$673$	21.3316	0.822272	0.411136	+	0.911574i	$0.365132\pi$
$674$	−38.3321	−1.47650
$675$	−4.17928	−0.160861
$676$	−45.1913	−1.73813
$677$	4.54169	0.174551	0.0872757	−	0.996184i	$-0.472184\pi$
$677$	4.54169	0.174551	0.0872757	+	0.996184i	$0.472184\pi$
$678$	−1.91842	−0.0736764
$679$	55.3322	2.12345
$680$	−72.0174	−2.76174
$681$	−10.9646	−0.420166
$682$	2.23061	0.0854146
$683$	−24.3951	−0.933451	−0.466725	−	0.884402i	$-0.654566\pi$
$683$	−24.3951	−0.933451	−0.466725	+	0.884402i	$0.654566\pi$
$684$	37.4927	1.43357
$685$	−25.8970	−0.989473
$686$	9.00433	0.343787
$687$	−8.86847	−0.338353
$688$	−16.4229	−0.626116
$689$	5.30011	0.201918
$690$	3.16694	0.120563
$691$	−18.5155	−0.704362	−0.352181	−	0.935932i	$-0.614560\pi$
$691$	−18.5155	−0.704362	−0.352181	+	0.935932i	$0.614560\pi$
$692$	−20.6067	−0.783348
$693$	−1.45694	−0.0553448
$694$	−64.7383	−2.45743
$695$	−56.7328	−2.15200
$696$	17.3583	0.657965
$697$	−16.5659	−0.627479
$698$	2.38066	0.0901093
$699$	−1.01343	−0.0383313
$700$	18.3102	0.692061
$701$	3.90953	0.147661	0.0738304	−	0.997271i	$-0.476478\pi$
$701$	3.90953	0.147661	0.0738304	+	0.997271i	$0.476478\pi$
$702$	−5.90512	−0.222874
$703$	−28.1581	−1.06200
$704$	−1.65672	−0.0624400
$705$	16.9415	0.638054
$706$	12.4740	0.469464
$707$	40.6785	1.52987
$708$	−11.4280	−0.429492
$709$	31.3969	1.17913	0.589567	−	0.807719i	$-0.299298\pi$
$709$	31.3969	1.17913	0.589567	+	0.807719i	$0.299298\pi$
$710$	−69.2964	−2.60065
$711$	−22.2511	−0.834480
$712$	19.4701	0.729673
$713$	−6.30144	−0.235991
$714$	32.3664	1.21128
$715$	0.309442	0.0115725
$716$	37.0652	1.38519
$717$	7.45234	0.278313
$718$	25.9685	0.969135
$719$	−8.42710	−0.314278	−0.157139	−	0.987576i	$-0.550227\pi$
$719$	−8.42710	−0.314278	−0.157139	+	0.987576i	$0.550227\pi$
$720$	14.5605	0.542639
$721$	−8.16303	−0.304007
$722$	11.6773	0.434585
$723$	−3.38779	−0.125993
$724$	81.8339	3.04133
$725$	−11.5253	−0.428039
$726$	13.7562	0.510539
$727$	−19.4107	−0.719903	−0.359951	−	0.932971i	$-0.617207\pi$
$727$	−19.4107	−0.719903	−0.359951	+	0.932971i	$0.617207\pi$
$728$	11.7631	0.435971
$729$	−13.1693	−0.487751
$730$	15.2265	0.563558
$731$	55.7151	2.06070
$732$	22.4756	0.830723
$733$	−11.2020	−0.413754	−0.206877	−	0.978367i	$-0.566330\pi$
$733$	−11.2020	−0.413754	−0.206877	+	0.978367i	$0.566330\pi$
$734$	−76.4277	−2.82100
$735$	−7.91372	−0.291902
$736$	2.90271	0.106995
$737$	−1.32836	−0.0489306
$738$	14.9607	0.550712
$739$	24.5501	0.903092	0.451546	−	0.892248i	$-0.350873\pi$
$739$	24.5501	0.903092	0.451546	+	0.892248i	$0.350873\pi$
$740$	−69.5200	−2.55561
$741$	1.62721	0.0597769
$742$	55.1402	2.02426
$743$	−45.7963	−1.68010	−0.840051	−	0.542507i	$-0.817475\pi$
$743$	−45.7963	−1.68010	−0.840051	+	0.542507i	$0.817475\pi$
$744$	13.1673	0.482736
$745$	−54.8685	−2.01023
$746$	47.0080	1.72108
$747$	−2.60009	−0.0951322
$748$	−3.91437	−0.143124
$749$	56.4210	2.06158
$750$	−11.4409	−0.417763
$751$	−22.4773	−0.820209	−0.410104	−	0.912039i	$-0.634508\pi$
$751$	−22.4773	−0.820209	−0.410104	+	0.912039i	$0.634508\pi$
$752$	−26.9454	−0.982598
$753$	0.0638112	0.00232541
$754$	−16.2847	−0.593053
$755$	31.4254	1.14369
$756$	−39.7551	−1.44588
$757$	−12.6804	−0.460875	−0.230438	−	0.973087i	$-0.574016\pi$
$757$	−12.6804	−0.460875	−0.230438	+	0.973087i	$0.574016\pi$
$758$	62.4414	2.26797
$759$	0.0782650	0.00284084
$760$	−37.6677	−1.36635
$761$	−12.7970	−0.463891	−0.231946	−	0.972729i	$-0.574509\pi$
$761$	−12.7970	−0.463891	−0.231946	+	0.972729i	$0.574509\pi$
$762$	16.6586	0.603476
$763$	41.6818	1.50898
$764$	78.5131	2.84050
$765$	−49.3971	−1.78595
$766$	−53.9309	−1.94860
$767$	4.87468	0.176014
$768$	−14.2343	−0.513635
$769$	−31.1800	−1.12438	−0.562190	−	0.827008i	$-0.690041\pi$
$769$	−31.1800	−1.12438	−0.562190	+	0.827008i	$0.690041\pi$
$770$	3.21931	0.116016
$771$	11.4586	0.412672
$772$	57.7935	2.08003
$773$	42.0824	1.51360	0.756799	−	0.653647i	$-0.226762\pi$
$773$	42.0824	1.51360	0.756799	+	0.653647i	$0.226762\pi$
$774$	−50.3165	−1.80859
$775$	−8.74261	−0.314044
$776$	−61.0431	−2.19132
$777$	14.2059	0.509635
$778$	77.8177	2.78990
$779$	−8.66457	−0.310441
$780$	4.01744	0.143847
$781$	−1.71253	−0.0612792
$782$	17.0882	0.611074
$783$	25.0237	0.894274
$784$	12.5868	0.449527
$785$	21.2874	0.759779
$786$	14.4734	0.516251
$787$	−49.7131	−1.77208	−0.886040	−	0.463609i	$-0.846554\pi$
$787$	−49.7131	−1.77208	−0.886040	+	0.463609i	$0.846554\pi$
$788$	−29.2212	−1.04096
$789$	−14.1719	−0.504534
$790$	49.1667	1.74927
$791$	5.50912	0.195882
$792$	1.60732	0.0571136
$793$	−9.58707	−0.340447
$794$	24.6489	0.874756
$795$	8.56242	0.303678
$796$	93.5569	3.31604
$797$	7.09248	0.251228	0.125614	−	0.992079i	$-0.459910\pi$
$797$	7.09248	0.251228	0.125614	+	0.992079i	$0.459910\pi$
$798$	16.9288	0.599273
$799$	91.4132	3.23397
$800$	4.02721	0.142384
$801$	13.3546	0.471863
$802$	−22.4324	−0.792116
$803$	0.376294	0.0132791
$804$	−17.2458	−0.608213
$805$	−9.09450	−0.320539
$806$	−12.3529	−0.435112
$807$	−13.1304	−0.462214
$808$	−44.8770	−1.57877
$809$	16.4853	0.579593	0.289796	−	0.957088i	$-0.406412\pi$
$809$	16.4853	0.579593	0.289796	+	0.957088i	$0.406412\pi$
$810$	39.6098	1.39175
$811$	15.5992	0.547761	0.273881	−	0.961764i	$-0.411693\pi$
$811$	15.5992	0.547761	0.273881	+	0.961764i	$0.411693\pi$
$812$	−109.634	−3.84738
$813$	−2.52494	−0.0885535
$814$	−2.65495	−0.0930561
$815$	46.6826	1.63522
$816$	−7.99385	−0.279841
$817$	29.1410	1.01952
$818$	−50.9342	−1.78087
$819$	8.06839	0.281932
$820$	−21.3921	−0.747045
$821$	−17.8246	−0.622084	−0.311042	−	0.950396i	$-0.600678\pi$
$821$	−17.8246	−0.622084	−0.311042	+	0.950396i	$0.600678\pi$
$822$	−12.8400	−0.447847
$823$	−8.12631	−0.283265	−0.141633	−	0.989919i	$-0.545235\pi$
$823$	−8.12631	−0.283265	−0.141633	+	0.989919i	$0.545235\pi$
$824$	9.00555	0.313723
$825$	0.108585	0.00378044
$826$	50.7142	1.76457
$827$	48.0760	1.67177	0.835883	−	0.548907i	$-0.184956\pi$
$827$	48.0760	1.67177	0.835883	+	0.548907i	$0.184956\pi$
$828$	−9.98654	−0.347056
$829$	27.6879	0.961640	0.480820	−	0.876819i	$-0.340339\pi$
$829$	27.6879	0.961640	0.480820	+	0.876819i	$0.340339\pi$
$830$	5.74524	0.199420
$831$	4.40930	0.152957
$832$	9.17473	0.318076
$833$	−42.7010	−1.47950
$834$	−28.1288	−0.974020
$835$	−15.2267	−0.526940
$836$	−2.04736	−0.0708094
$837$	18.9819	0.656111
$838$	32.4231	1.12004
$839$	−38.4127	−1.32615	−0.663077	−	0.748552i	$-0.730750\pi$
$839$	−38.4127	−1.32615	−0.663077	+	0.748552i	$0.730750\pi$
$840$	19.0036	0.655685
$841$	40.0084	1.37960
$842$	−93.7038	−3.22924
$843$	12.3102	0.423985
$844$	−49.3278	−1.69793
$845$	31.1416	1.07130
$846$	−82.5555	−2.83832
$847$	−39.5035	−1.35736
$848$	−13.6185	−0.467662
$849$	−2.10964	−0.0724025
$850$	23.7082	0.813184
$851$	7.50019	0.257103
$852$	−22.2335	−0.761707
$853$	9.77625	0.334732	0.167366	−	0.985895i	$-0.446474\pi$
$853$	9.77625	0.334732	0.167366	+	0.985895i	$0.446474\pi$
$854$	−99.7400	−3.41303
$855$	−25.8364	−0.883588
$856$	−62.2443	−2.12747
$857$	−10.5722	−0.361138	−0.180569	−	0.983562i	$-0.557794\pi$
$857$	−10.5722	−0.361138	−0.180569	+	0.983562i	$0.557794\pi$
$858$	0.153425	0.00523784
$859$	39.7160	1.35509	0.677546	−	0.735480i	$-0.263043\pi$
$859$	39.7160	1.35509	0.677546	+	0.735480i	$0.263043\pi$
$860$	71.9467	2.45336
$861$	4.37133	0.148974
$862$	−30.0853	−1.02471
$863$	25.6876	0.874415	0.437208	−	0.899361i	$-0.355967\pi$
$863$	25.6876	0.874415	0.437208	+	0.899361i	$0.355967\pi$
$864$	−8.74388	−0.297473
$865$	14.2002	0.482821
$866$	−32.2561	−1.09611
$867$	18.1713	0.617131
$868$	−83.1634	−2.82275
$869$	1.21506	0.0412182
$870$	−26.3082	−0.891932
$871$	7.35628	0.249258
$872$	−45.9839	−1.55721
$873$	−41.8698	−1.41708
$874$	8.93776	0.302324
$875$	32.8548	1.11069
$876$	4.88537	0.165061
$877$	12.9469	0.437185	0.218592	−	0.975816i	$-0.429853\pi$
$877$	12.9469	0.437185	0.218592	+	0.975816i	$0.429853\pi$
$878$	70.3077	2.37277
$879$	−7.77129	−0.262119
$880$	−0.795106	−0.0268030
$881$	48.4011	1.63068	0.815338	−	0.578986i	$-0.196551\pi$
$881$	48.4011	1.63068	0.815338	+	0.578986i	$0.196551\pi$
$882$	38.5634	1.29850
$883$	7.84105	0.263873	0.131936	−	0.991258i	$-0.457881\pi$
$883$	7.84105	0.263873	0.131936	+	0.991258i	$0.457881\pi$
$884$	21.6773	0.729088
$885$	7.87513	0.264720
$886$	42.8668	1.44014
$887$	45.4165	1.52494	0.762468	−	0.647026i	$-0.223987\pi$
$887$	45.4165	1.52494	0.762468	+	0.647026i	$0.223987\pi$
$888$	−15.6722	−0.525923
$889$	−47.8383	−1.60444
$890$	−29.5088	−0.989138
$891$	0.978881	0.0327938
$892$	−42.1736	−1.41208
$893$	47.8124	1.59998
$894$	−27.2044	−0.909851
$895$	−25.5419	−0.853771
$896$	74.5596	2.49086
$897$	−0.433423	−0.0144716
$898$	−3.28247	−0.109537
$899$	52.3469	1.74587
$900$	−13.8553	−0.461844
$901$	46.2012	1.53919
$902$	−0.816959	−0.0272018
$903$	−14.7018	−0.489246
$904$	−6.07772	−0.202142
$905$	−56.3923	−1.87454
$906$	15.5811	0.517646
$907$	17.5644	0.583217	0.291609	−	0.956538i	$-0.405809\pi$
$907$	17.5644	0.583217	0.291609	+	0.956538i	$0.405809\pi$
$908$	−76.3993	−2.53540
$909$	−30.7813	−1.02095
$910$	−17.8282	−0.590998
$911$	1.79720	0.0595440	0.0297720	−	0.999557i	$-0.490522\pi$
$911$	1.79720	0.0595440	0.0297720	+	0.999557i	$0.490522\pi$
$912$	−4.18107	−0.138449
$913$	0.141983	0.00469894
$914$	24.3978	0.807006
$915$	−15.4881	−0.512020
$916$	−61.7936	−2.04172
$917$	−41.5633	−1.37254
$918$	−51.4752	−1.69893
$919$	32.3367	1.06669	0.533344	−	0.845898i	$-0.320935\pi$
$919$	32.3367	1.06669	0.533344	+	0.845898i	$0.320935\pi$
$920$	10.0332	0.330783
$921$	6.01197	0.198101
$922$	36.9983	1.21847
$923$	9.48379	0.312163
$924$	1.03290	0.0339801
$925$	10.4058	0.342139
$926$	−34.7747	−1.14277
$927$	6.17695	0.202878
$928$	−24.1132	−0.791555
$929$	10.4570	0.343081	0.171541	−	0.985177i	$-0.445125\pi$
$929$	10.4570	0.343081	0.171541	+	0.985177i	$0.445125\pi$
$930$	−19.9563	−0.654393
$931$	−22.3341	−0.731972
$932$	−7.06133	−0.231302
$933$	−13.3910	−0.438402
$934$	86.7172	2.83747
$935$	2.69742	0.0882151
$936$	−8.90114	−0.290943
$937$	38.6340	1.26212	0.631058	−	0.775735i	$-0.282621\pi$
$937$	38.6340	1.26212	0.631058	+	0.775735i	$0.282621\pi$
$938$	76.5317	2.49885
$939$	5.96878	0.194784
$940$	118.045	3.85020
$941$	−1.49539	−0.0487484	−0.0243742	−	0.999703i	$-0.507759\pi$
$941$	−1.49539	−0.0487484	−0.0243742	+	0.999703i	$0.507759\pi$
$942$	10.5545	0.343885
$943$	2.30789	0.0751554
$944$	−12.5254	−0.407666
$945$	27.3955	0.891176
$946$	2.74763	0.0893331
$947$	14.4837	0.470659	0.235329	−	0.971916i	$-0.424383\pi$
$947$	14.4837	0.470659	0.235329	+	0.971916i	$0.424383\pi$
$948$	15.7749	0.512346
$949$	−2.08387	−0.0676454
$950$	12.4002	0.402317
$951$	−0.569555	−0.0184691
$952$	102.540	3.32333
$953$	46.5250	1.50709	0.753546	−	0.657395i	$-0.228342\pi$
$953$	46.5250	1.50709	0.753546	+	0.657395i	$0.228342\pi$
$954$	−41.7245	−1.35088
$955$	−54.1039	−1.75076
$956$	51.9263	1.67942
$957$	−0.650158	−0.0210166
$958$	−1.67649	−0.0541650
$959$	36.8726	1.19068
$960$	14.8219	0.478376
$961$	8.70815	0.280908
$962$	14.7028	0.474038
$963$	−42.6937	−1.37578
$964$	−23.6054	−0.760278
$965$	−39.8259	−1.28204
$966$	−4.50915	−0.145080
$967$	41.1326	1.32273	0.661367	−	0.750062i	$-0.269977\pi$
$967$	41.1326	1.32273	0.661367	+	0.750062i	$0.269977\pi$
$968$	43.5807	1.40074
$969$	14.1844	0.455669
$970$	92.5168	2.97054
$971$	−1.39650	−0.0448158	−0.0224079	−	0.999749i	$-0.507133\pi$
$971$	−1.39650	−0.0448158	−0.0224079	+	0.999749i	$0.507133\pi$
$972$	45.8521	1.47071
$973$	80.7773	2.58960
$974$	−31.1597	−0.998421
$975$	−0.601330	−0.0192580
$976$	24.6338	0.788508
$977$	−16.7603	−0.536211	−0.268105	−	0.963390i	$-0.586398\pi$
$977$	−16.7603	−0.536211	−0.268105	+	0.963390i	$0.586398\pi$
$978$	23.1457	0.740119
$979$	−0.729255	−0.0233071
$980$	−55.1411	−1.76142
$981$	−31.5406	−1.00701
$982$	−50.8152	−1.62158
$983$	46.8166	1.49322	0.746609	−	0.665263i	$-0.231680\pi$
$983$	46.8166	1.49322	0.746609	+	0.665263i	$0.231680\pi$
$984$	−4.82250	−0.153736
$985$	20.1365	0.641603
$986$	−141.954	−4.52074
$987$	−24.1216	−0.767800
$988$	11.3380	0.360711
$989$	−7.76200	−0.246817
$990$	−2.43605	−0.0774227
$991$	−15.0694	−0.478694	−0.239347	−	0.970934i	$-0.576933\pi$
$991$	−15.0694	−0.478694	−0.239347	+	0.970934i	$0.576933\pi$
$992$	−18.2913	−0.580748
$993$	−17.2882	−0.548625
$994$	98.6656	3.12948
$995$	−64.4707	−2.04386
$996$	1.84334	0.0584084
$997$	30.8870	0.978202	0.489101	−	0.872227i	$-0.337325\pi$
$997$	30.8870	0.978202	0.489101	+	0.872227i	$0.337325\pi$
$998$	7.37974	0.233602
$999$	−22.5929	−0.714809

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.17	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.17	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38066 q^{2} +0.526357 q^{3} +3.66755 q^{4} -2.52733 q^{5} -1.25308 q^{6} +3.59846 q^{7} -3.96986 q^{8} -2.72295 q^{9} +O(q^{10})\)	\(q-2.38066 q^{2} +0.526357 q^{3} +3.66755 q^{4} -2.52733 q^{5} -1.25308 q^{6} +3.59846 q^{7} -3.96986 q^{8} -2.72295 q^{9} +6.01672 q^{10} +0.148692 q^{11} +1.93044 q^{12} -0.823438 q^{13} -8.56671 q^{14} -1.33028 q^{15} +2.11581 q^{16} -7.17794 q^{17} +6.48242 q^{18} -3.75432 q^{19} -9.26910 q^{20} +1.89408 q^{21} -0.353985 q^{22} +1.00000 q^{23} -2.08957 q^{24} +1.38740 q^{25} +1.96033 q^{26} -3.01232 q^{27} +13.1975 q^{28} -8.30713 q^{29} +3.16694 q^{30} -6.30144 q^{31} +2.90271 q^{32} +0.0782650 q^{33} +17.0882 q^{34} -9.09450 q^{35} -9.98654 q^{36} +7.50019 q^{37} +8.93776 q^{38} -0.433423 q^{39} +10.0332 q^{40} +2.30789 q^{41} -4.50915 q^{42} -7.76200 q^{43} +0.545334 q^{44} +6.88179 q^{45} -2.38066 q^{46} -12.7353 q^{47} +1.11367 q^{48} +5.94892 q^{49} -3.30292 q^{50} -3.77816 q^{51} -3.02000 q^{52} -6.43656 q^{53} +7.17130 q^{54} -0.375793 q^{55} -14.2854 q^{56} -1.97611 q^{57} +19.7765 q^{58} -5.91991 q^{59} -4.87886 q^{60} +11.6427 q^{61} +15.0016 q^{62} -9.79842 q^{63} -11.1420 q^{64} +2.08110 q^{65} -0.186322 q^{66} -8.93362 q^{67} -26.3254 q^{68} +0.526357 q^{69} +21.6509 q^{70} -11.5173 q^{71} +10.8097 q^{72} +2.53070 q^{73} -17.8554 q^{74} +0.730267 q^{75} -13.7691 q^{76} +0.535062 q^{77} +1.03183 q^{78} +8.17168 q^{79} -5.34734 q^{80} +6.58329 q^{81} -5.49431 q^{82} +0.954879 q^{83} +6.94661 q^{84} +18.1410 q^{85} +18.4787 q^{86} -4.37252 q^{87} -0.590286 q^{88} -4.90448 q^{89} -16.3832 q^{90} -2.96311 q^{91} +3.66755 q^{92} -3.31681 q^{93} +30.3184 q^{94} +9.48841 q^{95} +1.52786 q^{96} +15.3766 q^{97} -14.1624 q^{98} -0.404880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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