LMFDB - Embedded newform 403.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(1,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, 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("403.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.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:	$3.21797120146$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.5748973.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 4x - 1 $ x^6 - x^5 - 6x^4 + 4x^3 + 8x^2 - 4x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.32857$ of defining polynomial
Character	$\chi$	$=$	403.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45145 q^{2} -2.32857 q^{3} +4.00960 q^{4} -4.02200 q^{5} -5.70836 q^{6} -4.56194 q^{7} +4.92644 q^{8} +2.42222 q^{9} +O(q^{10})$	\(q+2.45145 q^{2} -2.32857 q^{3} +4.00960 q^{4} -4.02200 q^{5} -5.70836 q^{6} -4.56194 q^{7} +4.92644 q^{8} +2.42222 q^{9} -9.85973 q^{10} +2.49182 q^{11} -9.33663 q^{12} +1.00000 q^{13} -11.1834 q^{14} +9.36549 q^{15} +4.05771 q^{16} -6.88090 q^{17} +5.93795 q^{18} +1.91113 q^{19} -16.1266 q^{20} +10.6228 q^{21} +6.10858 q^{22} -4.25159 q^{23} -11.4715 q^{24} +11.1765 q^{25} +2.45145 q^{26} +1.34540 q^{27} -18.2916 q^{28} +0.363119 q^{29} +22.9590 q^{30} +1.00000 q^{31} +0.0943979 q^{32} -5.80238 q^{33} -16.8682 q^{34} +18.3481 q^{35} +9.71214 q^{36} -3.67601 q^{37} +4.68504 q^{38} -2.32857 q^{39} -19.8142 q^{40} +0.693941 q^{41} +26.0412 q^{42} -0.717340 q^{43} +9.99123 q^{44} -9.74217 q^{45} -10.4226 q^{46} +7.08350 q^{47} -9.44866 q^{48} +13.8113 q^{49} +27.3986 q^{50} +16.0226 q^{51} +4.00960 q^{52} -12.5951 q^{53} +3.29818 q^{54} -10.0221 q^{55} -22.4741 q^{56} -4.45020 q^{57} +0.890168 q^{58} -0.141609 q^{59} +37.5519 q^{60} -14.3222 q^{61} +2.45145 q^{62} -11.0500 q^{63} -7.88402 q^{64} -4.02200 q^{65} -14.2242 q^{66} -10.6671 q^{67} -27.5897 q^{68} +9.90011 q^{69} +44.9795 q^{70} +0.0239244 q^{71} +11.9329 q^{72} +0.444583 q^{73} -9.01156 q^{74} -26.0252 q^{75} +7.66288 q^{76} -11.3675 q^{77} -5.70836 q^{78} +6.70595 q^{79} -16.3201 q^{80} -10.3995 q^{81} +1.70116 q^{82} -6.57825 q^{83} +42.5931 q^{84} +27.6750 q^{85} -1.75852 q^{86} -0.845547 q^{87} +12.2758 q^{88} +0.210551 q^{89} -23.8824 q^{90} -4.56194 q^{91} -17.0472 q^{92} -2.32857 q^{93} +17.3648 q^{94} -7.68658 q^{95} -0.219812 q^{96} +10.1689 q^{97} +33.8576 q^{98} +6.03575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9} - 8 q^{10} - 5 q^{11} - 13 q^{12} + 6 q^{13} - 17 q^{14} + 4 q^{15} + 14 q^{16} - 23 q^{17} + 9 q^{18} + 7 q^{19} - 10 q^{20} + 2 q^{21} + 2 q^{22} - 18 q^{23} - 13 q^{24} + 11 q^{25} - 2 q^{26} - 5 q^{27} - 25 q^{28} - 18 q^{29} + 25 q^{30} + 6 q^{31} + 2 q^{32} - 2 q^{33} - 16 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 8 q^{38} - 5 q^{39} - 29 q^{40} - 5 q^{41} + 31 q^{42} - 7 q^{43} + 30 q^{44} - 5 q^{45} + 19 q^{46} - 9 q^{47} - 19 q^{48} + 16 q^{49} + 29 q^{50} + 26 q^{51} + 6 q^{52} - 31 q^{53} - 4 q^{54} + 7 q^{55} + 8 q^{56} - 5 q^{57} + 35 q^{58} - q^{59} + 33 q^{60} - 15 q^{61} - 2 q^{62} + 11 q^{63} - 5 q^{64} - 9 q^{65} - 29 q^{66} - 28 q^{67} - 12 q^{68} + 5 q^{69} + 73 q^{70} + q^{71} + 45 q^{72} - 20 q^{73} + 4 q^{74} + q^{75} + 38 q^{76} - 29 q^{77} - 15 q^{79} + 7 q^{80} + 2 q^{81} + 36 q^{82} + q^{83} + 68 q^{84} + 29 q^{85} + 3 q^{86} + 10 q^{87} + 9 q^{88} - q^{89} - 32 q^{90} - 60 q^{92} - 5 q^{93} + 54 q^{94} - 13 q^{95} + 36 q^{96} - 5 q^{97} + 20 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9 - 8 * q^10 - 5 * q^11 - 13 * q^12 + 6 * q^13 - 17 * q^14 + 4 * q^15 + 14 * q^16 - 23 * q^17 + 9 * q^18 + 7 * q^19 - 10 * q^20 + 2 * q^21 + 2 * q^22 - 18 * q^23 - 13 * q^24 + 11 * q^25 - 2 * q^26 - 5 * q^27 - 25 * q^28 - 18 * q^29 + 25 * q^30 + 6 * q^31 + 2 * q^32 - 2 * q^33 - 16 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 8 * q^38 - 5 * q^39 - 29 * q^40 - 5 * q^41 + 31 * q^42 - 7 * q^43 + 30 * q^44 - 5 * q^45 + 19 * q^46 - 9 * q^47 - 19 * q^48 + 16 * q^49 + 29 * q^50 + 26 * q^51 + 6 * q^52 - 31 * q^53 - 4 * q^54 + 7 * q^55 + 8 * q^56 - 5 * q^57 + 35 * q^58 - q^59 + 33 * q^60 - 15 * q^61 - 2 * q^62 + 11 * q^63 - 5 * q^64 - 9 * q^65 - 29 * q^66 - 28 * q^67 - 12 * q^68 + 5 * q^69 + 73 * q^70 + q^71 + 45 * q^72 - 20 * q^73 + 4 * q^74 + q^75 + 38 * q^76 - 29 * q^77 - 15 * q^79 + 7 * q^80 + 2 * q^81 + 36 * q^82 + q^83 + 68 * q^84 + 29 * q^85 + 3 * q^86 + 10 * q^87 + 9 * q^88 - q^89 - 32 * q^90 - 60 * q^92 - 5 * q^93 + 54 * q^94 - 13 * q^95 + 36 * q^96 - 5 * q^97 + 20 * q^98 - 15 * 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 $

$2$	2.45145	1.73344	0.866718	−	0.498798i	$-0.166225\pi$
$2$	2.45145	1.73344	0.866718	+	0.498798i	$0.166225\pi$
$3$	−2.32857	−1.34440	−0.672199	−	0.740370i	$-0.734650\pi$
$3$	−2.32857	−1.34440	−0.672199	+	0.740370i	$0.734650\pi$
$4$	4.00960	2.00480
$5$	−4.02200	−1.79869	−0.899347	−	0.437236i	$-0.855957\pi$
$5$	−4.02200	−1.79869	−0.899347	+	0.437236i	$0.855957\pi$
$6$	−5.70836	−2.33043
$7$	−4.56194	−1.72425	−0.862125	−	0.506696i	$-0.830867\pi$
$7$	−4.56194	−1.72425	−0.862125	+	0.506696i	$0.830867\pi$
$8$	4.92644	1.74176
$9$	2.42222	0.807407
$10$	−9.85973	−3.11792
$11$	2.49182	0.751313	0.375657	−	0.926759i	$-0.377417\pi$
$11$	2.49182	0.751313	0.375657	+	0.926759i	$0.377417\pi$
$12$	−9.33663	−2.69525
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−11.1834	−2.98888
$15$	9.36549	2.41816
$16$	4.05771	1.01443
$17$	−6.88090	−1.66886	−0.834431	−	0.551112i	$-0.814204\pi$
$17$	−6.88090	−1.66886	−0.834431	+	0.551112i	$0.814204\pi$
$18$	5.93795	1.39959
$19$	1.91113	0.438444	0.219222	−	0.975675i	$-0.429648\pi$
$19$	1.91113	0.438444	0.219222	+	0.975675i	$0.429648\pi$
$20$	−16.1266	−3.60602
$21$	10.6228	2.31808
$22$	6.10858	1.30235
$23$	−4.25159	−0.886518	−0.443259	−	0.896394i	$-0.646178\pi$
$23$	−4.25159	−0.886518	−0.443259	+	0.896394i	$0.646178\pi$
$24$	−11.4715	−2.34162
$25$	11.1765	2.23530
$26$	2.45145	0.480769
$27$	1.34540	0.258922
$28$	−18.2916	−3.45678
$29$	0.363119	0.0674295	0.0337148	−	0.999431i	$-0.489266\pi$
$29$	0.363119	0.0674295	0.0337148	+	0.999431i	$0.489266\pi$
$30$	22.9590	4.19173
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	0.0943979	0.0166873
$33$	−5.80238	−1.01006
$34$	−16.8682	−2.89287
$35$	18.3481	3.10140
$36$	9.71214	1.61869
$37$	−3.67601	−0.604333	−0.302166	−	0.953255i	$-0.597710\pi$
$37$	−3.67601	−0.604333	−0.302166	+	0.953255i	$0.597710\pi$
$38$	4.68504	0.760015
$39$	−2.32857	−0.372869
$40$	−19.8142	−3.13289
$41$	0.693941	0.108375	0.0541877	−	0.998531i	$-0.482743\pi$
$41$	0.693941	0.108375	0.0541877	+	0.998531i	$0.482743\pi$
$42$	26.0412	4.01824
$43$	−0.717340	−0.109393	−0.0546966	−	0.998503i	$-0.517419\pi$
$43$	−0.717340	−0.109393	−0.0546966	+	0.998503i	$0.517419\pi$
$44$	9.99123	1.50623
$45$	−9.74217	−1.45228
$46$	−10.4226	−1.53672
$47$	7.08350	1.03323	0.516617	−	0.856217i	$-0.327191\pi$
$47$	7.08350	1.03323	0.516617	+	0.856217i	$0.327191\pi$
$48$	−9.44866	−1.36380
$49$	13.8113	1.97304
$50$	27.3986	3.87475
$51$	16.0226	2.24362
$52$	4.00960	0.556032
$53$	−12.5951	−1.73007	−0.865034	−	0.501714i	$-0.832703\pi$
$53$	−12.5951	−1.73007	−0.865034	+	0.501714i	$0.832703\pi$
$54$	3.29818	0.448825
$55$	−10.0221	−1.35138
$56$	−22.4741	−3.00323
$57$	−4.45020	−0.589443
$58$	0.890168	0.116885
$59$	−0.141609	−0.0184359	−0.00921797	−	0.999958i	$-0.502934\pi$
$59$	−0.141609	−0.0184359	−0.00921797	+	0.999958i	$0.502934\pi$
$60$	37.5519	4.84793
$61$	−14.3222	−1.83377	−0.916883	−	0.399156i	$-0.869303\pi$
$61$	−14.3222	−1.83377	−0.916883	+	0.399156i	$0.869303\pi$
$62$	2.45145	0.311334
$63$	−11.0500	−1.39217
$64$	−7.88402	−0.985502
$65$	−4.02200	−0.498868
$66$	−14.2242	−1.75088
$67$	−10.6671	−1.30320	−0.651598	−	0.758565i	$-0.725901\pi$
$67$	−10.6671	−1.30320	−0.651598	+	0.758565i	$0.725901\pi$
$68$	−27.5897	−3.34574
$69$	9.90011	1.19183
$70$	44.9795	5.37607
$71$	0.0239244	0.00283931	0.00141965	−	0.999999i	$-0.499548\pi$
$71$	0.0239244	0.00283931	0.00141965	+	0.999999i	$0.499548\pi$
$72$	11.9329	1.40631
$73$	0.444583	0.0520345	0.0260173	−	0.999661i	$-0.491718\pi$
$73$	0.444583	0.0520345	0.0260173	+	0.999661i	$0.491718\pi$
$74$	−9.01156	−1.04757
$75$	−26.0252	−3.00513
$76$	7.66288	0.878993
$77$	−11.3675	−1.29545
$78$	−5.70836	−0.646345
$79$	6.70595	0.754478	0.377239	−	0.926116i	$-0.376873\pi$
$79$	6.70595	0.754478	0.377239	+	0.926116i	$0.376873\pi$
$80$	−16.3201	−1.82465
$81$	−10.3995	−1.15550
$82$	1.70116	0.187862
$83$	−6.57825	−0.722057	−0.361028	−	0.932555i	$-0.617574\pi$
$83$	−6.57825	−0.722057	−0.361028	+	0.932555i	$0.617574\pi$
$84$	42.5931	4.64729
$85$	27.6750	3.00177
$86$	−1.75852	−0.189626
$87$	−0.845547	−0.0906521
$88$	12.2758	1.30861
$89$	0.210551	0.0223184	0.0111592	−	0.999938i	$-0.496448\pi$
$89$	0.210551	0.0223184	0.0111592	+	0.999938i	$0.496448\pi$
$90$	−23.8824	−2.51743
$91$	−4.56194	−0.478221
$92$	−17.0472	−1.77729
$93$	−2.32857	−0.241461
$94$	17.3648	1.79105
$95$	−7.68658	−0.788626
$96$	−0.219812	−0.0224344
$97$	10.1689	1.03250	0.516248	−	0.856439i	$-0.327328\pi$
$97$	10.1689	1.03250	0.516248	+	0.856439i	$0.327328\pi$
$98$	33.8576	3.42013
$99$	6.03575	0.606615
$100$	44.8133	4.48133
$101$	−6.16210	−0.613152	−0.306576	−	0.951846i	$-0.599183\pi$
$101$	−6.16210	−0.613152	−0.306576	+	0.951846i	$0.599183\pi$
$102$	39.2787	3.88917
$103$	12.8027	1.26149	0.630743	−	0.775992i	$-0.282750\pi$
$103$	12.8027	1.26149	0.630743	+	0.775992i	$0.282750\pi$
$104$	4.92644	0.483077
$105$	−42.7248	−4.16951
$106$	−30.8762	−2.99896
$107$	12.4349	1.20213	0.601066	−	0.799200i	$-0.294743\pi$
$107$	12.4349	1.20213	0.601066	+	0.799200i	$0.294743\pi$
$108$	5.39451	0.519087
$109$	−1.57882	−0.151223	−0.0756117	−	0.997137i	$-0.524091\pi$
$109$	−1.57882	−0.151223	−0.0756117	+	0.997137i	$0.524091\pi$
$110$	−24.5687	−2.34254
$111$	8.55984	0.812464
$112$	−18.5110	−1.74913
$113$	1.17964	0.110972	0.0554858	−	0.998459i	$-0.482329\pi$
$113$	1.17964	0.110972	0.0554858	+	0.998459i	$0.482329\pi$
$114$	−10.9094	−1.02176
$115$	17.0999	1.59457
$116$	1.45596	0.135183
$117$	2.42222	0.223934
$118$	−0.347148	−0.0319575
$119$	31.3902	2.87754
$120$	46.1386	4.21185
$121$	−4.79081	−0.435528
$122$	−35.1101	−3.17872
$123$	−1.61589	−0.145700
$124$	4.00960	0.360073
$125$	−24.8418	−2.22192
$126$	−27.0885	−2.41324
$127$	−6.78516	−0.602086	−0.301043	−	0.953611i	$-0.597335\pi$
$127$	−6.78516	−0.602086	−0.301043	+	0.953611i	$0.597335\pi$
$128$	−19.5161	−1.72499
$129$	1.67037	0.147068
$130$	−9.85973	−0.864756
$131$	−0.00665953	−0.000581846 0	−0.000290923	−	1.00000i	$-0.500093\pi$
$131$	−0.00665953	−0.000581846 0	−0.000290923		1.00000i	$0.500093\pi$
$132$	−23.2652	−2.02498
$133$	−8.71846	−0.755987
$134$	−26.1499	−2.25901
$135$	−5.41119	−0.465721
$136$	−33.8983	−2.90676
$137$	−11.2198	−0.958574	−0.479287	−	0.877658i	$-0.659105\pi$
$137$	−11.2198	−0.958574	−0.479287	+	0.877658i	$0.659105\pi$
$138$	24.2696	2.06597
$139$	−2.18133	−0.185018	−0.0925090	−	0.995712i	$-0.529489\pi$
$139$	−2.18133	−0.185018	−0.0925090	+	0.995712i	$0.529489\pi$
$140$	73.5686	6.21768
$141$	−16.4944	−1.38908
$142$	0.0586495	0.00492176
$143$	2.49182	0.208377
$144$	9.82868	0.819056
$145$	−1.46046	−0.121285
$146$	1.08987	0.0901985
$147$	−32.1604	−2.65255
$148$	−14.7394	−1.21157
$149$	4.20530	0.344512	0.172256	−	0.985052i	$-0.444894\pi$
$149$	4.20530	0.344512	0.172256	+	0.985052i	$0.444894\pi$
$150$	−63.7994	−5.20920
$151$	4.96105	0.403724	0.201862	−	0.979414i	$-0.435301\pi$
$151$	4.96105	0.403724	0.201862	+	0.979414i	$0.435301\pi$
$152$	9.41508	0.763664
$153$	−16.6671	−1.34745
$154$	−27.8670	−2.24558
$155$	−4.02200	−0.323055
$156$	−9.33663	−0.747528
$157$	−0.463395	−0.0369829	−0.0184915	−	0.999829i	$-0.505886\pi$
$157$	−0.463395	−0.0369829	−0.0184915	+	0.999829i	$0.505886\pi$
$158$	16.4393	1.30784
$159$	29.3285	2.32590
$160$	−0.379668	−0.0300154
$161$	19.3955	1.52858
$162$	−25.4939	−2.00299
$163$	20.2622	1.58706	0.793529	−	0.608532i	$-0.208241\pi$
$163$	20.2622	1.58706	0.793529	+	0.608532i	$0.208241\pi$
$164$	2.78243	0.217271
$165$	23.3372	1.81680
$166$	−16.1262	−1.25164
$167$	5.97803	0.462594	0.231297	−	0.972883i	$-0.425703\pi$
$167$	5.97803	0.462594	0.231297	+	0.972883i	$0.425703\pi$
$168$	52.3325	4.03754
$169$	1.00000	0.0769231
$170$	67.8438	5.20338
$171$	4.62918	0.354003
$172$	−2.87625	−0.219312
$173$	−25.2223	−1.91762	−0.958809	−	0.284051i	$-0.908321\pi$
$173$	−25.2223	−1.91762	−0.958809	+	0.284051i	$0.908321\pi$
$174$	−2.07281	−0.157140
$175$	−50.9864	−3.85421
$176$	10.1111	0.762154
$177$	0.329746	0.0247852
$178$	0.516155	0.0386875
$179$	−13.7890	−1.03064	−0.515319	−	0.856998i	$-0.672327\pi$
$179$	−13.7890	−1.03064	−0.515319	+	0.856998i	$0.672327\pi$
$180$	−39.0622	−2.91153
$181$	−11.2073	−0.833029	−0.416515	−	0.909129i	$-0.636748\pi$
$181$	−11.2073	−0.833029	−0.416515	+	0.909129i	$0.636748\pi$
$182$	−11.1834	−0.828965
$183$	33.3501	2.46531
$184$	−20.9452	−1.54410
$185$	14.7849	1.08701
$186$	−5.70836	−0.418557
$187$	−17.1460	−1.25384
$188$	28.4020	2.07143
$189$	−6.13762	−0.446446
$190$	−18.8433	−1.36703
$191$	−18.9869	−1.37385	−0.686923	−	0.726730i	$-0.741039\pi$
$191$	−18.9869	−1.37385	−0.686923	+	0.726730i	$0.741039\pi$
$192$	18.3585	1.32491
$193$	13.1490	0.946487	0.473243	−	0.880932i	$-0.343083\pi$
$193$	13.1490	0.946487	0.473243	+	0.880932i	$0.343083\pi$
$194$	24.9286	1.78977
$195$	9.36549	0.670677
$196$	55.3777	3.95555
$197$	11.4860	0.818345	0.409173	−	0.912457i	$-0.365817\pi$
$197$	11.4860	0.818345	0.409173	+	0.912457i	$0.365817\pi$
$198$	14.7963	1.05153
$199$	6.97803	0.494660	0.247330	−	0.968931i	$-0.420447\pi$
$199$	6.97803	0.494660	0.247330	+	0.968931i	$0.420447\pi$
$200$	55.0603	3.89335
$201$	24.8391	1.75201
$202$	−15.1061	−1.06286
$203$	−1.65653	−0.116265
$204$	64.2444	4.49801
$205$	−2.79103	−0.194934
$206$	31.3851	2.18670
$207$	−10.2983	−0.715780
$208$	4.05771	0.281352
$209$	4.76221	0.329409
$210$	−104.738	−7.22758
$211$	4.05251	0.278986	0.139493	−	0.990223i	$-0.455453\pi$
$211$	4.05251	0.278986	0.139493	+	0.990223i	$0.455453\pi$
$212$	−50.5013	−3.46844
$213$	−0.0557096	−0.00381716
$214$	30.4836	2.08382
$215$	2.88514	0.196765
$216$	6.62803	0.450980
$217$	−4.56194	−0.309684
$218$	−3.87040	−0.262136
$219$	−1.03524	−0.0699551
$220$	−40.1847	−2.70925
$221$	−6.88090	−0.462859
$222$	20.9840	1.40836
$223$	18.3106	1.22617	0.613084	−	0.790017i	$-0.289929\pi$
$223$	18.3106	1.22617	0.613084	+	0.790017i	$0.289929\pi$
$224$	−0.430637	−0.0287732
$225$	27.0719	1.80479
$226$	2.89184	0.192362
$227$	−11.8667	−0.787619	−0.393810	−	0.919192i	$-0.628843\pi$
$227$	−11.8667	−0.787619	−0.393810	+	0.919192i	$0.628843\pi$
$228$	−17.8435	−1.18172
$229$	15.5344	1.02654	0.513271	−	0.858226i	$-0.328433\pi$
$229$	15.5344	1.02654	0.513271	+	0.858226i	$0.328433\pi$
$230$	41.9195	2.76409
$231$	26.4701	1.74160
$232$	1.78888	0.117446
$233$	−19.6069	−1.28449	−0.642246	−	0.766498i	$-0.721997\pi$
$233$	−19.6069	−1.28449	−0.642246	+	0.766498i	$0.721997\pi$
$234$	5.93795	0.388176
$235$	−28.4898	−1.85847
$236$	−0.567797	−0.0369604
$237$	−15.6152	−1.01432
$238$	76.9515	4.98803
$239$	2.82028	0.182429	0.0912145	−	0.995831i	$-0.470925\pi$
$239$	2.82028	0.182429	0.0912145	+	0.995831i	$0.470925\pi$
$240$	38.0025	2.45305
$241$	−8.17473	−0.526580	−0.263290	−	0.964717i	$-0.584808\pi$
$241$	−8.17473	−0.526580	−0.263290	+	0.964717i	$0.584808\pi$
$242$	−11.7444	−0.754960
$243$	20.1798	1.29453
$244$	−57.4262	−3.67634
$245$	−55.5489	−3.54889
$246$	−3.96127	−0.252561
$247$	1.91113	0.121602
$248$	4.92644	0.312829
$249$	15.3179	0.970732
$250$	−60.8985	−3.85156
$251$	−1.53099	−0.0966350	−0.0483175	−	0.998832i	$-0.515386\pi$
$251$	−1.53099	−0.0966350	−0.0483175	+	0.998832i	$0.515386\pi$
$252$	−44.3062	−2.79103
$253$	−10.5942	−0.666052
$254$	−16.6335	−1.04368
$255$	−64.4430	−4.03558
$256$	−32.0746	−2.00466
$257$	23.7519	1.48160	0.740802	−	0.671723i	$-0.234446\pi$
$257$	23.7519	1.48160	0.740802	+	0.671723i	$0.234446\pi$
$258$	4.09483	0.254933
$259$	16.7697	1.04202
$260$	−16.1266	−1.00013
$261$	0.879554	0.0544430
$262$	−0.0163255	−0.00100859
$263$	5.14286	0.317122	0.158561	−	0.987349i	$-0.449314\pi$
$263$	5.14286	0.317122	0.158561	+	0.987349i	$0.449314\pi$
$264$	−28.5851	−1.75929
$265$	50.6574	3.11186
$266$	−21.3729	−1.31045
$267$	−0.490282	−0.0300048
$268$	−42.7709	−2.61265
$269$	−3.70368	−0.225817	−0.112909	−	0.993605i	$-0.536017\pi$
$269$	−3.70368	−0.225817	−0.112909	+	0.993605i	$0.536017\pi$
$270$	−13.2653	−0.807298
$271$	−21.4881	−1.30531	−0.652656	−	0.757654i	$-0.726345\pi$
$271$	−21.4881	−1.30531	−0.652656	+	0.757654i	$0.726345\pi$
$272$	−27.9207	−1.69294
$273$	10.6228	0.642919
$274$	−27.5048	−1.66163
$275$	27.8498	1.67941
$276$	39.6955	2.38939
$277$	−6.10893	−0.367050	−0.183525	−	0.983015i	$-0.558751\pi$
$277$	−6.10893	−0.367050	−0.183525	+	0.983015i	$0.558751\pi$
$278$	−5.34742	−0.320717
$279$	2.42222	0.145015
$280$	90.3909	5.40189
$281$	26.0324	1.55296	0.776482	−	0.630139i	$-0.217002\pi$
$281$	26.0324	1.55296	0.776482	+	0.630139i	$0.217002\pi$
$282$	−40.4352	−2.40788
$283$	20.0160	1.18983	0.594914	−	0.803789i	$-0.297186\pi$
$283$	20.0160	1.18983	0.594914	+	0.803789i	$0.297186\pi$
$284$	0.0959274	0.00569225
$285$	17.8987	1.06023
$286$	6.10858	0.361208
$287$	−3.16571	−0.186866
$288$	0.228653	0.0134735
$289$	30.3468	1.78510
$290$	−3.58026	−0.210240
$291$	−23.6790	−1.38809
$292$	1.78260	0.104319
$293$	−17.8918	−1.04525	−0.522624	−	0.852563i	$-0.675047\pi$
$293$	−17.8918	−1.04525	−0.522624	+	0.852563i	$0.675047\pi$
$294$	−78.8397	−4.59802
$295$	0.569552	0.0331606
$296$	−18.1097	−1.05260
$297$	3.35250	0.194532
$298$	10.3091	0.597189
$299$	−4.25159	−0.245876
$300$	−104.351	−6.02469
$301$	3.27246	0.188621
$302$	12.1618	0.699831
$303$	14.3489	0.824320
$304$	7.75483	0.444770
$305$	57.6038	3.29838
$306$	−40.8584	−2.33572
$307$	22.2748	1.27129	0.635644	−	0.771982i	$-0.280735\pi$
$307$	22.2748	1.27129	0.635644	+	0.771982i	$0.280735\pi$
$308$	−45.5793	−2.59712
$309$	−29.8119	−1.69594
$310$	−9.85973	−0.559995
$311$	−21.0636	−1.19441	−0.597203	−	0.802090i	$-0.703721\pi$
$311$	−21.0636	−1.19441	−0.597203	+	0.802090i	$0.703721\pi$
$312$	−11.4715	−0.649448
$313$	−3.91675	−0.221388	−0.110694	−	0.993855i	$-0.535307\pi$
$313$	−3.91675	−0.221388	−0.110694	+	0.993855i	$0.535307\pi$
$314$	−1.13599	−0.0641076
$315$	44.4432	2.50409
$316$	26.8882	1.51258
$317$	−35.2233	−1.97834	−0.989170	−	0.146776i	$-0.953110\pi$
$317$	−35.2233	−1.97834	−0.989170	+	0.146776i	$0.953110\pi$
$318$	71.8973	4.03180
$319$	0.904829	0.0506607
$320$	31.7095	1.77262
$321$	−28.9556	−1.61614
$322$	47.5470	2.64969
$323$	−13.1503	−0.731703
$324$	−41.6979	−2.31655
$325$	11.1765	0.619960
$326$	49.6718	2.75107
$327$	3.67638	0.203305
$328$	3.41866	0.188764
$329$	−32.3145	−1.78155
$330$	57.2099	3.14930
$331$	−18.0487	−0.992044	−0.496022	−	0.868310i	$-0.665207\pi$
$331$	−18.0487	−0.992044	−0.496022	+	0.868310i	$0.665207\pi$
$332$	−26.3762	−1.44758
$333$	−8.90412	−0.487942
$334$	14.6548	0.801877
$335$	42.9032	2.34405
$336$	43.1042	2.35152
$337$	−0.916184	−0.0499077	−0.0249539	−	0.999689i	$-0.507944\pi$
$337$	−0.916184	−0.0499077	−0.0249539	+	0.999689i	$0.507944\pi$
$338$	2.45145	0.133341
$339$	−2.74688	−0.149190
$340$	110.966	6.01796
$341$	2.49182	0.134940
$342$	11.3482	0.613641
$343$	−31.0725	−1.67776
$344$	−3.53393	−0.190537
$345$	−39.8182	−2.14374
$346$	−61.8313	−3.32407
$347$	4.30335	0.231016	0.115508	−	0.993307i	$-0.463150\pi$
$347$	4.30335	0.231016	0.115508	+	0.993307i	$0.463150\pi$
$348$	−3.39031	−0.181740
$349$	25.4507	1.36234	0.681172	−	0.732123i	$-0.261470\pi$
$349$	25.4507	1.36234	0.681172	+	0.732123i	$0.261470\pi$
$350$	−124.991	−6.68103
$351$	1.34540	0.0718121
$352$	0.235223	0.0125374
$353$	−1.93469	−0.102973	−0.0514867	−	0.998674i	$-0.516396\pi$
$353$	−1.93469	−0.102973	−0.0514867	+	0.998674i	$0.516396\pi$
$354$	0.808356	0.0429636
$355$	−0.0962240	−0.00510704
$356$	0.844226	0.0447439
$357$	−73.0942	−3.86855
$358$	−33.8030	−1.78655
$359$	4.34024	0.229069	0.114534	−	0.993419i	$-0.463462\pi$
$359$	4.34024	0.229069	0.114534	+	0.993419i	$0.463462\pi$
$360$	−47.9942	−2.52952
$361$	−15.3476	−0.807767
$362$	−27.4740	−1.44400
$363$	11.1557	0.585523
$364$	−18.2916	−0.958738
$365$	−1.78811	−0.0935941
$366$	81.7561	4.27346
$367$	26.7938	1.39862	0.699312	−	0.714817i	$-0.253490\pi$
$367$	26.7938	1.39862	0.699312	+	0.714817i	$0.253490\pi$
$368$	−17.2517	−0.899309
$369$	1.68088	0.0875030
$370$	36.2445	1.88426
$371$	57.4580	2.98307
$372$	−9.33663	−0.484082
$373$	9.96333	0.515882	0.257941	−	0.966161i	$-0.416956\pi$
$373$	9.96333	0.515882	0.257941	+	0.966161i	$0.416956\pi$
$374$	−42.0325	−2.17345
$375$	57.8459	2.98715
$376$	34.8964	1.79965
$377$	0.363119	0.0187016
$378$	−15.0461	−0.773886
$379$	21.7156	1.11546	0.557728	−	0.830024i	$-0.311673\pi$
$379$	21.7156	1.11546	0.557728	+	0.830024i	$0.311673\pi$
$380$	−30.8201	−1.58104
$381$	15.7997	0.809443
$382$	−46.5455	−2.38147
$383$	−31.8495	−1.62743	−0.813717	−	0.581261i	$-0.802559\pi$
$383$	−31.8495	−1.62743	−0.813717	+	0.581261i	$0.802559\pi$
$384$	45.4444	2.31908
$385$	45.7203	2.33012
$386$	32.2341	1.64067
$387$	−1.73755	−0.0883249
$388$	40.7733	2.06995
$389$	−19.7995	−1.00387	−0.501937	−	0.864904i	$-0.667379\pi$
$389$	−19.7995	−1.00387	−0.501937	+	0.864904i	$0.667379\pi$
$390$	22.9590	1.16258
$391$	29.2547	1.47948
$392$	68.0404	3.43656
$393$	0.0155071	0.000782232 0
$394$	28.1574	1.41855
$395$	−26.9713	−1.35708
$396$	24.2010	1.21614
$397$	−26.6765	−1.33886	−0.669428	−	0.742877i	$-0.733461\pi$
$397$	−26.6765	−1.33886	−0.669428	+	0.742877i	$0.733461\pi$
$398$	17.1063	0.857461
$399$	20.3015	1.01635
$400$	45.3510	2.26755
$401$	3.95638	0.197572	0.0987861	−	0.995109i	$-0.468504\pi$
$401$	3.95638	0.197572	0.0987861	+	0.995109i	$0.468504\pi$
$402$	60.8918	3.03701
$403$	1.00000	0.0498135
$404$	−24.7076	−1.22925
$405$	41.8268	2.07839
$406$	−4.06089	−0.201539
$407$	−9.15998	−0.454043
$408$	78.9345	3.90784
$409$	−8.11338	−0.401181	−0.200590	−	0.979675i	$-0.564286\pi$
$409$	−8.11338	−0.401181	−0.200590	+	0.979675i	$0.564286\pi$
$410$	−6.84207	−0.337906
$411$	26.1261	1.28871
$412$	51.3337	2.52903
$413$	0.646012	0.0317882
$414$	−25.2457	−1.24076
$415$	26.4577	1.29876
$416$	0.0943979	0.00462824
$417$	5.07937	0.248738
$418$	11.6743	0.571009
$419$	8.77985	0.428924	0.214462	−	0.976732i	$-0.431200\pi$
$419$	8.77985	0.428924	0.214462	+	0.976732i	$0.431200\pi$
$420$	−171.309	−8.35904
$421$	14.1314	0.688723	0.344362	−	0.938837i	$-0.388095\pi$
$421$	14.1314	0.688723	0.344362	+	0.938837i	$0.388095\pi$
$422$	9.93452	0.483605
$423$	17.1578	0.834240
$424$	−62.0489	−3.01336
$425$	−76.9043	−3.73041
$426$	−0.136569	−0.00661680
$427$	65.3368	3.16187
$428$	49.8592	2.41004
$429$	−5.80238	−0.280141
$430$	7.07278	0.341080
$431$	16.2326	0.781895	0.390947	−	0.920413i	$-0.372147\pi$
$431$	16.2326	0.781895	0.390947	+	0.920413i	$0.372147\pi$
$432$	5.45924	0.262658
$433$	3.10283	0.149112	0.0745562	−	0.997217i	$-0.476246\pi$
$433$	3.10283	0.149112	0.0745562	+	0.997217i	$0.476246\pi$
$434$	−11.1834	−0.536818
$435$	3.40079	0.163055
$436$	−6.33044	−0.303173
$437$	−8.12535	−0.388688
$438$	−2.53784	−0.121263
$439$	−37.0769	−1.76958	−0.884792	−	0.465986i	$-0.845700\pi$
$439$	−37.0769	−1.76958	−0.884792	+	0.465986i	$0.845700\pi$
$440$	−49.3734	−2.35378
$441$	33.4539	1.59304
$442$	−16.8682	−0.802337
$443$	10.7662	0.511517	0.255759	−	0.966741i	$-0.417675\pi$
$443$	10.7662	0.511517	0.255759	+	0.966741i	$0.417675\pi$
$444$	34.3216	1.62883
$445$	−0.846836	−0.0401439
$446$	44.8875	2.12549
$447$	−9.79232	−0.463161
$448$	35.9664	1.69925
$449$	16.2319	0.766029	0.383014	−	0.923742i	$-0.374886\pi$
$449$	16.2319	0.766029	0.383014	+	0.923742i	$0.374886\pi$
$450$	66.3654	3.12850
$451$	1.72918	0.0814239
$452$	4.72990	0.222476
$453$	−11.5521	−0.542766
$454$	−29.0906	−1.36529
$455$	18.3481	0.860173
$456$	−21.9236	−1.02667
$457$	−22.8952	−1.07099	−0.535495	−	0.844538i	$-0.679875\pi$
$457$	−22.8952	−1.07099	−0.535495	+	0.844538i	$0.679875\pi$
$458$	38.0818	1.77945
$459$	−9.25755	−0.432105
$460$	68.5638	3.19680
$461$	−5.72159	−0.266481	−0.133240	−	0.991084i	$-0.542538\pi$
$461$	−5.72159	−0.266481	−0.133240	+	0.991084i	$0.542538\pi$
$462$	64.8901	3.01896
$463$	−2.23325	−0.103788	−0.0518940	−	0.998653i	$-0.516526\pi$
$463$	−2.23325	−0.103788	−0.0518940	+	0.998653i	$0.516526\pi$
$464$	1.47343	0.0684024
$465$	9.36549	0.434314
$466$	−48.0654	−2.22659
$467$	−28.2147	−1.30562	−0.652810	−	0.757521i	$-0.726410\pi$
$467$	−28.2147	−1.30562	−0.652810	+	0.757521i	$0.726410\pi$
$468$	9.71214	0.448944
$469$	48.6627	2.24703
$470$	−69.8414	−3.22154
$471$	1.07905	0.0497198
$472$	−0.697629	−0.0321110
$473$	−1.78748	−0.0821886
$474$	−38.2800	−1.75826
$475$	21.3598	0.980053
$476$	125.862	5.76889
$477$	−30.5081	−1.39687
$478$	6.91378	0.316229
$479$	27.4383	1.25369	0.626844	−	0.779145i	$-0.284346\pi$
$479$	27.4383	1.25369	0.626844	+	0.779145i	$0.284346\pi$
$480$	0.884083	0.0403527
$481$	−3.67601	−0.167612
$482$	−20.0399	−0.912794
$483$	−45.1636	−2.05502
$484$	−19.2093	−0.873148
$485$	−40.8994	−1.85714
$486$	49.4696	2.24399
$487$	13.9188	0.630722	0.315361	−	0.948972i	$-0.397874\pi$
$487$	13.9188	0.630722	0.315361	+	0.948972i	$0.397874\pi$
$488$	−70.5573	−3.19398
$489$	−47.1819	−2.13364
$490$	−136.175	−6.15177
$491$	−41.9079	−1.89128	−0.945640	−	0.325217i	$-0.894563\pi$
$491$	−41.9079	−1.89128	−0.945640	+	0.325217i	$0.894563\pi$
$492$	−6.47907	−0.292099
$493$	−2.49858	−0.112531
$494$	4.68504	0.210790
$495$	−24.2758	−1.09112
$496$	4.05771	0.182197
$497$	−0.109142	−0.00489567
$498$	37.5510	1.68270
$499$	−9.87793	−0.442197	−0.221099	−	0.975251i	$-0.570964\pi$
$499$	−9.87793	−0.442197	−0.221099	+	0.975251i	$0.570964\pi$
$500$	−99.6059	−4.45451
$501$	−13.9202	−0.621911
$502$	−3.75313	−0.167511
$503$	−4.32370	−0.192784	−0.0963922	−	0.995343i	$-0.530730\pi$
$503$	−4.32370	−0.192784	−0.0963922	+	0.995343i	$0.530730\pi$
$504$	−54.4372	−2.42483
$505$	24.7840	1.10287
$506$	−25.9712	−1.15456
$507$	−2.32857	−0.103415
$508$	−27.2058	−1.20706
$509$	−32.6873	−1.44884	−0.724419	−	0.689360i	$-0.757892\pi$
$509$	−32.6873	−1.44884	−0.724419	+	0.689360i	$0.757892\pi$
$510$	−157.979	−6.99542
$511$	−2.02816	−0.0897205
$512$	−39.5971	−1.74996
$513$	2.57123	0.113523
$514$	58.2266	2.56827
$515$	−51.4924	−2.26903
$516$	6.69753	0.294842
$517$	17.6508	0.776283
$518$	41.1102	1.80628
$519$	58.7319	2.57804
$520$	−19.8142	−0.868908
$521$	−41.6245	−1.82360	−0.911802	−	0.410629i	$-0.865309\pi$
$521$	−41.6245	−1.82360	−0.911802	+	0.410629i	$0.865309\pi$
$522$	2.15618	0.0943735
$523$	−31.1438	−1.36182	−0.680912	−	0.732365i	$-0.738417\pi$
$523$	−31.1438	−1.36182	−0.680912	+	0.732365i	$0.738417\pi$
$524$	−0.0267021	−0.00116648
$525$	118.725	5.18159
$526$	12.6075	0.549711
$527$	−6.88090	−0.299737
$528$	−23.5444	−1.02464
$529$	−4.92399	−0.214087
$530$	124.184	5.39421
$531$	−0.343009	−0.0148853
$532$	−34.9576	−1.51560
$533$	0.693941	0.0300579
$534$	−1.20190	−0.0520114
$535$	−50.0133	−2.16227
$536$	−52.5509	−2.26985
$537$	32.1086	1.38559
$538$	−9.07939	−0.391440
$539$	34.4152	1.48237
$540$	−21.6967	−0.933679
$541$	−13.5731	−0.583553	−0.291777	−	0.956487i	$-0.594246\pi$
$541$	−13.5731	−0.583553	−0.291777	+	0.956487i	$0.594246\pi$
$542$	−52.6771	−2.26268
$543$	26.0968	1.11992
$544$	−0.649542	−0.0278489
$545$	6.35001	0.272005
$546$	26.0412	1.11446
$547$	1.91030	0.0816786	0.0408393	−	0.999166i	$-0.486997\pi$
$547$	1.91030	0.0816786	0.0408393	+	0.999166i	$0.486997\pi$
$548$	−44.9870	−1.92175
$549$	−34.6915	−1.48060
$550$	68.2725	2.91115
$551$	0.693969	0.0295641
$552$	48.7723	2.07589
$553$	−30.5921	−1.30091
$554$	−14.9757	−0.636258
$555$	−34.4277	−1.46137
$556$	−8.74627	−0.370924
$557$	44.6368	1.89132	0.945660	−	0.325157i	$-0.105417\pi$
$557$	44.6368	1.89132	0.945660	+	0.325157i	$0.105417\pi$
$558$	5.93795	0.251373
$559$	−0.717340	−0.0303402
$560$	74.4514	3.14614
$561$	39.9256	1.68566
$562$	63.8172	2.69197
$563$	24.1490	1.01776	0.508879	−	0.860838i	$-0.330060\pi$
$563$	24.1490	1.01776	0.508879	+	0.860838i	$0.330060\pi$
$564$	−66.1360	−2.78483
$565$	−4.74453	−0.199604
$566$	49.0682	2.06249
$567$	47.4419	1.99237
$568$	0.117862	0.00494539
$569$	45.4418	1.90502	0.952509	−	0.304509i	$-0.0984925\pi$
$569$	45.4418	1.90502	0.952509	+	0.304509i	$0.0984925\pi$
$570$	43.8778	1.83784
$571$	−36.7469	−1.53781	−0.768905	−	0.639363i	$-0.779198\pi$
$571$	−36.7469	−1.53781	−0.768905	+	0.639363i	$0.779198\pi$
$572$	9.99123	0.417754
$573$	44.2123	1.84700
$574$	−7.76059	−0.323921
$575$	−47.5178	−1.98163
$576$	−19.0968	−0.795701
$577$	−7.10064	−0.295604	−0.147802	−	0.989017i	$-0.547220\pi$
$577$	−7.10064	−0.295604	−0.147802	+	0.989017i	$0.547220\pi$
$578$	74.3935	3.09436
$579$	−30.6184	−1.27246
$580$	−5.85588	−0.243152
$581$	30.0096	1.24501
$582$	−58.0478	−2.40616
$583$	−31.3847	−1.29982
$584$	2.19021	0.0906316
$585$	−9.74217	−0.402789
$586$	−43.8607	−1.81187
$587$	−33.3544	−1.37668	−0.688342	−	0.725387i	$-0.741661\pi$
$587$	−33.3544	−1.37668	−0.688342	+	0.725387i	$0.741661\pi$
$588$	−128.951	−5.31783
$589$	1.91113	0.0787468
$590$	1.39623	0.0574818
$591$	−26.7460	−1.10018
$592$	−14.9162	−0.613053
$593$	13.0650	0.536515	0.268257	−	0.963347i	$-0.413552\pi$
$593$	13.0650	0.536515	0.268257	+	0.963347i	$0.413552\pi$
$594$	8.21848	0.337208
$595$	−126.251	−5.17581
$596$	16.8616	0.690678
$597$	−16.2488	−0.665020
$598$	−10.4226	−0.426210
$599$	31.7429	1.29698	0.648490	−	0.761223i	$-0.275401\pi$
$599$	31.7429	1.29698	0.648490	+	0.761223i	$0.275401\pi$
$600$	−128.212	−5.23422
$601$	−0.188711	−0.00769767	−0.00384884	−	0.999993i	$-0.501225\pi$
$601$	−0.188711	−0.00769767	−0.00384884	+	0.999993i	$0.501225\pi$
$602$	8.02226	0.326963
$603$	−25.8381	−1.05221
$604$	19.8918	0.809388
$605$	19.2686	0.783382
$606$	35.1755	1.42891
$607$	12.7465	0.517363	0.258681	−	0.965963i	$-0.416712\pi$
$607$	12.7465	0.517363	0.258681	+	0.965963i	$0.416712\pi$
$608$	0.180407	0.00731647
$609$	3.85733	0.156307
$610$	141.213	5.71754
$611$	7.08350	0.286568
$612$	−66.8283	−2.70137
$613$	28.7496	1.16119	0.580593	−	0.814194i	$-0.302821\pi$
$613$	28.7496	1.16119	0.580593	+	0.814194i	$0.302821\pi$
$614$	54.6055	2.20370
$615$	6.49910	0.262069
$616$	−56.0015	−2.25637
$617$	30.7822	1.23925	0.619623	−	0.784899i	$-0.287285\pi$
$617$	30.7822	1.23925	0.619623	+	0.784899i	$0.287285\pi$
$618$	−73.0823	−2.93980
$619$	−7.96174	−0.320009	−0.160005	−	0.987116i	$-0.551151\pi$
$619$	−7.96174	−0.320009	−0.160005	+	0.987116i	$0.551151\pi$
$620$	−16.1266	−0.647661
$621$	−5.72008	−0.229539
$622$	−51.6363	−2.07043
$623$	−0.960520	−0.0384824
$624$	−9.44866	−0.378249
$625$	44.0314	1.76126
$626$	−9.60171	−0.383762
$627$	−11.0891	−0.442857
$628$	−1.85803	−0.0741435
$629$	25.2943	1.00855
$630$	108.950	4.34068
$631$	−18.6796	−0.743621	−0.371811	−	0.928309i	$-0.621263\pi$
$631$	−18.6796	−0.743621	−0.371811	+	0.928309i	$0.621263\pi$
$632$	33.0365	1.31412
$633$	−9.43654	−0.375069
$634$	−86.3482	−3.42933
$635$	27.2899	1.08297
$636$	117.596	4.66297
$637$	13.8113	0.547222
$638$	2.21814	0.0878171
$639$	0.0579502	0.00229248
$640$	78.4936	3.10273
$641$	−35.8629	−1.41650	−0.708250	−	0.705962i	$-0.750515\pi$
$641$	−35.8629	−1.41650	−0.708250	+	0.705962i	$0.750515\pi$
$642$	−70.9832	−2.80148
$643$	5.28078	0.208254	0.104127	−	0.994564i	$-0.466795\pi$
$643$	5.28078	0.208254	0.104127	+	0.994564i	$0.466795\pi$
$644$	77.7682	3.06450
$645$	−6.71824	−0.264530
$646$	−32.2373	−1.26836
$647$	−26.4640	−1.04041	−0.520204	−	0.854042i	$-0.674144\pi$
$647$	−26.4640	−1.04041	−0.520204	+	0.854042i	$0.674144\pi$
$648$	−51.2326	−2.01261
$649$	−0.352865	−0.0138512
$650$	27.3986	1.07466
$651$	10.6228	0.416339
$652$	81.2434	3.18174
$653$	−20.4933	−0.801966	−0.400983	−	0.916085i	$-0.631331\pi$
$653$	−20.4933	−0.801966	−0.400983	+	0.916085i	$0.631331\pi$
$654$	9.01247	0.352415
$655$	0.0267846	0.00104656
$656$	2.81581	0.109939
$657$	1.07688	0.0420130
$658$	−79.2172	−3.08821
$659$	15.3329	0.597285	0.298643	−	0.954365i	$-0.403466\pi$
$659$	15.3329	0.597285	0.298643	+	0.954365i	$0.403466\pi$
$660$	93.5728	3.64232
$661$	8.06223	0.313584	0.156792	−	0.987632i	$-0.449885\pi$
$661$	8.06223	0.313584	0.156792	+	0.987632i	$0.449885\pi$
$662$	−44.2454	−1.71965
$663$	16.0226	0.622267
$664$	−32.4074	−1.25765
$665$	35.0657	1.35979
$666$	−21.8280	−0.845817
$667$	−1.54383	−0.0597774
$668$	23.9695	0.927410
$669$	−42.6375	−1.64846
$670$	105.175	4.06326
$671$	−35.6883	−1.37773
$672$	1.00277	0.0386826
$673$	38.9747	1.50237	0.751183	−	0.660094i	$-0.229484\pi$
$673$	38.9747	1.50237	0.751183	+	0.660094i	$0.229484\pi$
$674$	−2.24598	−0.0865118
$675$	15.0368	0.578768
$676$	4.00960	0.154216
$677$	24.7184	0.950005	0.475002	−	0.879984i	$-0.342447\pi$
$677$	24.7184	0.950005	0.475002	+	0.879984i	$0.342447\pi$
$678$	−6.73383	−0.258611
$679$	−46.3899	−1.78028
$680$	136.339	5.22837
$681$	27.6324	1.05887
$682$	6.10858	0.233910
$683$	7.61868	0.291521	0.145760	−	0.989320i	$-0.453437\pi$
$683$	7.61868	0.291521	0.145760	+	0.989320i	$0.453437\pi$
$684$	18.5612	0.709705
$685$	45.1261	1.72418
$686$	−76.1727	−2.90829
$687$	−36.1729	−1.38008
$688$	−2.91076	−0.110972
$689$	−12.5951	−0.479834
$690$	−97.6124	−3.71604
$691$	−28.4083	−1.08070	−0.540351	−	0.841440i	$-0.681708\pi$
$691$	−28.4083	−1.08070	−0.540351	+	0.841440i	$0.681708\pi$
$692$	−101.132	−3.84444
$693$	−27.5347	−1.04596
$694$	10.5494	0.400451
$695$	8.77331	0.332791
$696$	−4.16554	−0.157894
$697$	−4.77494	−0.180864
$698$	62.3911	2.36154
$699$	45.6560	1.72687
$700$	−204.435	−7.72693
$701$	−28.7226	−1.08484	−0.542419	−	0.840108i	$-0.682491\pi$
$701$	−28.7226	−1.08484	−0.542419	+	0.840108i	$0.682491\pi$
$702$	3.29818	0.124482
$703$	−7.02535	−0.264966
$704$	−19.6456	−0.740421
$705$	66.3404	2.49853
$706$	−4.74281	−0.178498
$707$	28.1111	1.05723
$708$	1.32215	0.0496895
$709$	−28.7853	−1.08105	−0.540527	−	0.841327i	$-0.681775\pi$
$709$	−28.7853	−1.08105	−0.540527	+	0.841327i	$0.681775\pi$
$710$	−0.235888	−0.00885273
$711$	16.2433	0.609171
$712$	1.03727	0.0388732
$713$	−4.25159	−0.159223
$714$	−179.187	−6.70589
$715$	−10.0221	−0.374806
$716$	−55.2884	−2.06622
$717$	−6.56721	−0.245257
$718$	10.6399	0.397076
$719$	5.89125	0.219706	0.109853	−	0.993948i	$-0.464962\pi$
$719$	5.89125	0.219706	0.109853	+	0.993948i	$0.464962\pi$
$720$	−39.5309	−1.47323
$721$	−58.4050	−2.17512
$722$	−37.6238	−1.40021
$723$	19.0354	0.707934
$724$	−44.9367	−1.67006
$725$	4.05840	0.150725
$726$	27.3477	1.01497
$727$	−25.5686	−0.948288	−0.474144	−	0.880447i	$-0.657242\pi$
$727$	−25.5686	−0.948288	−0.474144	+	0.880447i	$0.657242\pi$
$728$	−22.4741	−0.832946
$729$	−15.7914	−0.584865
$730$	−4.38347	−0.162239
$731$	4.93594	0.182562
$732$	133.721	4.94246
$733$	2.54782	0.0941058	0.0470529	−	0.998892i	$-0.485017\pi$
$733$	2.54782	0.0941058	0.0470529	+	0.998892i	$0.485017\pi$
$734$	65.6836	2.42442
$735$	129.349	4.77112
$736$	−0.401341	−0.0147936
$737$	−26.5806	−0.979108
$738$	4.12059	0.151681
$739$	−11.8751	−0.436834	−0.218417	−	0.975856i	$-0.570089\pi$
$739$	−11.8751	−0.436834	−0.218417	+	0.975856i	$0.570089\pi$
$740$	59.2817	2.17924
$741$	−4.45020	−0.163482
$742$	140.855	5.17096
$743$	−53.6861	−1.96955	−0.984775	−	0.173832i	$-0.944385\pi$
$743$	−53.6861	−1.96955	−0.984775	+	0.173832i	$0.944385\pi$
$744$	−11.4715	−0.420567
$745$	−16.9137	−0.619671
$746$	24.4246	0.894248
$747$	−15.9340	−0.582993
$748$	−68.7486	−2.51370
$749$	−56.7274	−2.07277
$750$	141.806	5.17803
$751$	43.9362	1.60326	0.801628	−	0.597823i	$-0.203967\pi$
$751$	43.9362	1.60326	0.801628	+	0.597823i	$0.203967\pi$
$752$	28.7428	1.04814
$753$	3.56500	0.129916
$754$	0.890168	0.0324180
$755$	−19.9533	−0.726176
$756$	−24.6094	−0.895036
$757$	40.6872	1.47880	0.739401	−	0.673265i	$-0.235109\pi$
$757$	40.6872	1.47880	0.739401	+	0.673265i	$0.235109\pi$
$758$	53.2347	1.93357
$759$	24.6693	0.895440
$760$	−37.8675	−1.37360
$761$	3.89805	0.141304	0.0706520	−	0.997501i	$-0.477492\pi$
$761$	3.89805	0.141304	0.0706520	+	0.997501i	$0.477492\pi$
$762$	38.7322	1.40312
$763$	7.20247	0.260747
$764$	−76.1301	−2.75429
$765$	67.0349	2.42365
$766$	−78.0774	−2.82105
$767$	−0.141609	−0.00511321
$768$	74.6878	2.69507
$769$	8.16608	0.294476	0.147238	−	0.989101i	$-0.452962\pi$
$769$	8.16608	0.294476	0.147238	+	0.989101i	$0.452962\pi$
$770$	112.081	4.03912
$771$	−55.3079	−1.99187
$772$	52.7223	1.89752
$773$	−31.4283	−1.13040	−0.565198	−	0.824955i	$-0.691200\pi$
$773$	−31.4283	−1.13040	−0.565198	+	0.824955i	$0.691200\pi$
$774$	−4.25953	−0.153106
$775$	11.1765	0.401471
$776$	50.0965	1.79836
$777$	−39.0494	−1.40089
$778$	−48.5374	−1.74015
$779$	1.32621	0.0475165
$780$	37.5519	1.34457
$781$	0.0596155	0.00213321
$782$	71.7165	2.56458
$783$	0.488540	0.0174590
$784$	56.0421	2.00150
$785$	1.86377	0.0665210
$786$	0.0380150	0.00135595
$787$	42.6592	1.52064	0.760318	−	0.649551i	$-0.225043\pi$
$787$	42.6592	1.52064	0.760318	+	0.649551i	$0.225043\pi$
$788$	46.0544	1.64062
$789$	−11.9755	−0.426339
$790$	−66.1189	−2.35240
$791$	−5.38146	−0.191343
$792$	29.7348	1.05658
$793$	−14.3222	−0.508595
$794$	−65.3962	−2.32082
$795$	−117.959	−4.18358
$796$	27.9791	0.991695
$797$	−9.95392	−0.352586	−0.176293	−	0.984338i	$-0.556411\pi$
$797$	−9.95392	−0.352586	−0.176293	+	0.984338i	$0.556411\pi$
$798$	49.7681	1.76177
$799$	−48.7408	−1.72433
$800$	1.05504	0.0373012
$801$	0.510001	0.0180200
$802$	9.69887	0.342479
$803$	1.10782	0.0390942
$804$	99.5949	3.51244
$805$	−78.0086	−2.74944
$806$	2.45145	0.0863486
$807$	8.62427	0.303589
$808$	−30.3572	−1.06796
$809$	−39.4734	−1.38781	−0.693906	−	0.720066i	$-0.744112\pi$
$809$	−39.4734	−1.38781	−0.693906	+	0.720066i	$0.744112\pi$
$810$	102.536	3.60276
$811$	−1.43206	−0.0502864	−0.0251432	−	0.999684i	$-0.508004\pi$
$811$	−1.43206	−0.0502864	−0.0251432	+	0.999684i	$0.508004\pi$
$812$	−6.64201	−0.233089
$813$	50.0366	1.75486
$814$	−22.4552	−0.787055
$815$	−81.4946	−2.85463
$816$	65.0152	2.27599
$817$	−1.37093	−0.0479628
$818$	−19.8895	−0.695421
$819$	−11.0500	−0.386119
$820$	−11.1909	−0.390804
$821$	7.10826	0.248080	0.124040	−	0.992277i	$-0.460415\pi$
$821$	7.10826	0.248080	0.124040	+	0.992277i	$0.460415\pi$
$822$	64.0468	2.23389
$823$	1.20406	0.0419707	0.0209854	−	0.999780i	$-0.493320\pi$
$823$	1.20406	0.0419707	0.0209854	+	0.999780i	$0.493320\pi$
$824$	63.0716	2.19720
$825$	−64.8502	−2.25779
$826$	1.58367	0.0551028
$827$	−5.58627	−0.194254	−0.0971269	−	0.995272i	$-0.530965\pi$
$827$	−5.58627	−0.194254	−0.0971269	+	0.995272i	$0.530965\pi$
$828$	−41.2920	−1.43500
$829$	−13.0402	−0.452904	−0.226452	−	0.974022i	$-0.572713\pi$
$829$	−13.0402	−0.452904	−0.226452	+	0.974022i	$0.572713\pi$
$830$	64.8598	2.25132
$831$	14.2251	0.493462
$832$	−7.88402	−0.273329
$833$	−95.0339	−3.29273
$834$	12.4518	0.431171
$835$	−24.0437	−0.832065
$836$	19.0946	0.660399
$837$	1.34540	0.0465038
$838$	21.5234	0.743512
$839$	−7.48966	−0.258572	−0.129286	−	0.991607i	$-0.541268\pi$
$839$	−7.48966	−0.258572	−0.129286	+	0.991607i	$0.541268\pi$
$840$	−210.481	−7.26229
$841$	−28.8681	−0.995453
$842$	34.6424	1.19386
$843$	−60.6182	−2.08780
$844$	16.2490	0.559312
$845$	−4.02200	−0.138361
$846$	42.0614	1.44610
$847$	21.8554	0.750959
$848$	−51.1072	−1.75503
$849$	−46.6086	−1.59960
$850$	−188.527	−6.46642
$851$	15.6289	0.535752
$852$	−0.223373	−0.00765265
$853$	−42.9816	−1.47166	−0.735832	−	0.677164i	$-0.763209\pi$
$853$	−42.9816	−1.47166	−0.735832	+	0.677164i	$0.763209\pi$
$854$	160.170	5.48090
$855$	−18.6186	−0.636742
$856$	61.2600	2.09382
$857$	−6.45241	−0.220410	−0.110205	−	0.993909i	$-0.535151\pi$
$857$	−6.45241	−0.220410	−0.110205	+	0.993909i	$0.535151\pi$
$858$	−14.2242	−0.485607
$859$	24.1300	0.823306	0.411653	−	0.911341i	$-0.364952\pi$
$859$	24.1300	0.823306	0.411653	+	0.911341i	$0.364952\pi$
$860$	11.5683	0.394475
$861$	7.37158	0.251223
$862$	39.7933	1.35536
$863$	−13.2286	−0.450307	−0.225153	−	0.974323i	$-0.572288\pi$
$863$	−13.2286	−0.450307	−0.225153	+	0.974323i	$0.572288\pi$
$864$	0.127003	0.00432072
$865$	101.444	3.44921
$866$	7.60643	0.258477
$867$	−70.6644	−2.39989
$868$	−18.2916	−0.620856
$869$	16.7101	0.566850
$870$	8.33686	0.282646
$871$	−10.6671	−0.361441
$872$	−7.77796	−0.263395
$873$	24.6313	0.833644
$874$	−19.9189	−0.673766
$875$	113.327	3.83115
$876$	−4.15091	−0.140246
$877$	32.1933	1.08709	0.543546	−	0.839380i	$-0.317082\pi$
$877$	32.1933	1.08709	0.543546	+	0.839380i	$0.317082\pi$
$878$	−90.8922	−3.06746
$879$	41.6621	1.40523
$880$	−40.6669	−1.37088
$881$	−12.9016	−0.434665	−0.217333	−	0.976098i	$-0.569736\pi$
$881$	−12.9016	−0.434665	−0.217333	+	0.976098i	$0.569736\pi$
$882$	82.0106	2.76144
$883$	−43.9455	−1.47888	−0.739441	−	0.673221i	$-0.764910\pi$
$883$	−43.9455	−1.47888	−0.739441	+	0.673221i	$0.764910\pi$
$884$	−27.5897	−0.927941
$885$	−1.32624	−0.0445811
$886$	26.3928	0.886683
$887$	19.5931	0.657873	0.328936	−	0.944352i	$-0.393310\pi$
$887$	19.5931	0.657873	0.328936	+	0.944352i	$0.393310\pi$
$888$	42.1696	1.41512
$889$	30.9535	1.03815
$890$	−2.07598	−0.0695869
$891$	−25.9138	−0.868143
$892$	73.4183	2.45823
$893$	13.5375	0.453015
$894$	−24.0054	−0.802860
$895$	55.4593	1.85380
$896$	89.0310	2.97432
$897$	9.90011	0.330555
$898$	39.7916	1.32786
$899$	0.363119	0.0121107
$900$	108.548	3.61825
$901$	86.6655	2.88725
$902$	4.23900	0.141143
$903$	−7.62013	−0.253582
$904$	5.81144	0.193286
$905$	45.0756	1.49836
$906$	−28.3195	−0.940851
$907$	−20.0083	−0.664363	−0.332182	−	0.943215i	$-0.607785\pi$
$907$	−20.0083	−0.664363	−0.332182	+	0.943215i	$0.607785\pi$
$908$	−47.5807	−1.57902
$909$	−14.9260	−0.495063
$910$	44.9795	1.49105
$911$	−16.3269	−0.540934	−0.270467	−	0.962729i	$-0.587178\pi$
$911$	−16.3269	−0.540934	−0.270467	+	0.962729i	$0.587178\pi$
$912$	−18.0576	−0.597948
$913$	−16.3918	−0.542491
$914$	−56.1263	−1.85649
$915$	−134.134	−4.43434
$916$	62.2868	2.05801
$917$	0.0303803	0.00100325
$918$	−22.6944	−0.749027
$919$	42.7719	1.41092	0.705458	−	0.708752i	$-0.250741\pi$
$919$	42.7719	1.41092	0.705458	+	0.708752i	$0.250741\pi$
$920$	84.2416	2.77736
$921$	−51.8683	−1.70912
$922$	−14.0262	−0.461928
$923$	0.0239244	0.000787482 0
$924$	106.135	3.49157
$925$	−41.0849	−1.35086
$926$	−5.47470	−0.179910
$927$	31.0109	1.01853
$928$	0.0342777	0.00112522
$929$	11.0876	0.363774	0.181887	−	0.983319i	$-0.441780\pi$
$929$	11.0876	0.363774	0.181887	+	0.983319i	$0.441780\pi$
$930$	22.9590	0.752856
$931$	26.3951	0.865066
$932$	−78.6160	−2.57515
$933$	49.0479	1.60576
$934$	−69.1669	−2.26321
$935$	68.9612	2.25527
$936$	11.9329	0.390040
$937$	−13.5085	−0.441304	−0.220652	−	0.975353i	$-0.570818\pi$
$937$	−13.5085	−0.441304	−0.220652	+	0.975353i	$0.570818\pi$
$938$	119.294	3.89509
$939$	9.12041	0.297633
$940$	−114.233	−3.72587
$941$	19.8761	0.647941	0.323971	−	0.946067i	$-0.394982\pi$
$941$	19.8761	0.647941	0.323971	+	0.946067i	$0.394982\pi$
$942$	2.64523	0.0861861
$943$	−2.95035	−0.0960767
$944$	−0.574609	−0.0187019
$945$	24.6855	0.803020
$946$	−4.38193	−0.142469
$947$	−50.9037	−1.65415	−0.827074	−	0.562093i	$-0.809996\pi$
$947$	−50.9037	−1.65415	−0.827074	+	0.562093i	$0.809996\pi$
$948$	−62.6110	−2.03351
$949$	0.444583	0.0144318
$950$	52.3623	1.69886
$951$	82.0199	2.65968
$952$	154.642	5.01198
$953$	33.6205	1.08908	0.544538	−	0.838736i	$-0.316705\pi$
$953$	33.6205	1.08908	0.544538	+	0.838736i	$0.316705\pi$
$954$	−74.7890	−2.42138
$955$	76.3654	2.47113
$956$	11.3082	0.365734
$957$	−2.10695	−0.0681081
$958$	67.2636	2.17319
$959$	51.1841	1.65282
$960$	−73.8377	−2.38310
$961$	1.00000	0.0322581
$962$	−9.01156	−0.290544
$963$	30.1202	0.970609
$964$	−32.7774	−1.05569
$965$	−52.8853	−1.70244
$966$	−110.716	−3.56224
$967$	9.55882	0.307391	0.153695	−	0.988118i	$-0.450883\pi$
$967$	9.55882	0.307391	0.153695	+	0.988118i	$0.450883\pi$
$968$	−23.6016	−0.758586
$969$	30.6214	0.983700
$970$	−100.263	−3.21924
$971$	43.2506	1.38798	0.693989	−	0.719986i	$-0.255852\pi$
$971$	43.2506	1.38798	0.693989	+	0.719986i	$0.255852\pi$
$972$	80.9128	2.59528
$973$	9.95109	0.319017
$974$	34.1213	1.09332
$975$	−26.0252	−0.833473
$976$	−58.1153	−1.86022
$977$	19.1455	0.612517	0.306259	−	0.951948i	$-0.400923\pi$
$977$	19.1455	0.612517	0.306259	+	0.951948i	$0.400923\pi$
$978$	−115.664	−3.69853
$979$	0.524656	0.0167681
$980$	−222.729	−7.11482
$981$	−3.82425	−0.122099
$982$	−102.735	−3.27841
$983$	29.2196	0.931961	0.465981	−	0.884795i	$-0.345702\pi$
$983$	29.2196	0.931961	0.465981	+	0.884795i	$0.345702\pi$
$984$	−7.96058	−0.253774
$985$	−46.1968	−1.47195
$986$	−6.12515	−0.195065
$987$	75.2463	2.39512
$988$	7.66288	0.243789
$989$	3.04983	0.0969791
$990$	−59.5108	−1.89138
$991$	−18.2190	−0.578745	−0.289373	−	0.957217i	$-0.593447\pi$
$991$	−18.2190	−0.578745	−0.289373	+	0.957217i	$0.593447\pi$
$992$	0.0943979	0.00299714
$993$	42.0275	1.33370
$994$	−0.267555	−0.00848634
$995$	−28.0657	−0.889741
$996$	61.4187	1.94613
$997$	−28.4108	−0.899780	−0.449890	−	0.893084i	$-0.648537\pi$
$997$	−28.4108	−0.899780	−0.449890	+	0.893084i	$0.648537\pi$
$998$	−24.2153	−0.766521
$999$	−4.94570	−0.156475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.b.1.6	✓	6
3.2	odd	2		3627.2.a.m.1.1		6
4.3	odd	2		6448.2.a.y.1.5		6
13.12	even	2		5239.2.a.g.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.b.1.6	✓	6	1.1	even	1	trivial
3627.2.a.m.1.1		6	3.2	odd	2
5239.2.a.g.1.1		6	13.12	even	2
6448.2.a.y.1.5		6	4.3	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45145 q^{2} -2.32857 q^{3} +4.00960 q^{4} -4.02200 q^{5} -5.70836 q^{6} -4.56194 q^{7} +4.92644 q^{8} +2.42222 q^{9} +O(q^{10})\)	\(q+2.45145 q^{2} -2.32857 q^{3} +4.00960 q^{4} -4.02200 q^{5} -5.70836 q^{6} -4.56194 q^{7} +4.92644 q^{8} +2.42222 q^{9} -9.85973 q^{10} +2.49182 q^{11} -9.33663 q^{12} +1.00000 q^{13} -11.1834 q^{14} +9.36549 q^{15} +4.05771 q^{16} -6.88090 q^{17} +5.93795 q^{18} +1.91113 q^{19} -16.1266 q^{20} +10.6228 q^{21} +6.10858 q^{22} -4.25159 q^{23} -11.4715 q^{24} +11.1765 q^{25} +2.45145 q^{26} +1.34540 q^{27} -18.2916 q^{28} +0.363119 q^{29} +22.9590 q^{30} +1.00000 q^{31} +0.0943979 q^{32} -5.80238 q^{33} -16.8682 q^{34} +18.3481 q^{35} +9.71214 q^{36} -3.67601 q^{37} +4.68504 q^{38} -2.32857 q^{39} -19.8142 q^{40} +0.693941 q^{41} +26.0412 q^{42} -0.717340 q^{43} +9.99123 q^{44} -9.74217 q^{45} -10.4226 q^{46} +7.08350 q^{47} -9.44866 q^{48} +13.8113 q^{49} +27.3986 q^{50} +16.0226 q^{51} +4.00960 q^{52} -12.5951 q^{53} +3.29818 q^{54} -10.0221 q^{55} -22.4741 q^{56} -4.45020 q^{57} +0.890168 q^{58} -0.141609 q^{59} +37.5519 q^{60} -14.3222 q^{61} +2.45145 q^{62} -11.0500 q^{63} -7.88402 q^{64} -4.02200 q^{65} -14.2242 q^{66} -10.6671 q^{67} -27.5897 q^{68} +9.90011 q^{69} +44.9795 q^{70} +0.0239244 q^{71} +11.9329 q^{72} +0.444583 q^{73} -9.01156 q^{74} -26.0252 q^{75} +7.66288 q^{76} -11.3675 q^{77} -5.70836 q^{78} +6.70595 q^{79} -16.3201 q^{80} -10.3995 q^{81} +1.70116 q^{82} -6.57825 q^{83} +42.5931 q^{84} +27.6750 q^{85} -1.75852 q^{86} -0.845547 q^{87} +12.2758 q^{88} +0.210551 q^{89} -23.8824 q^{90} -4.56194 q^{91} -17.0472 q^{92} -2.32857 q^{93} +17.3648 q^{94} -7.68658 q^{95} -0.219812 q^{96} +10.1689 q^{97} +33.8576 q^{98} +6.03575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9} - 8 q^{10} - 5 q^{11} - 13 q^{12} + 6 q^{13} - 17 q^{14} + 4 q^{15} + 14 q^{16} - 23 q^{17} + 9 q^{18} + 7 q^{19} - 10 q^{20} + 2 q^{21} + 2 q^{22} - 18 q^{23} - 13 q^{24} + 11 q^{25} - 2 q^{26} - 5 q^{27} - 25 q^{28} - 18 q^{29} + 25 q^{30} + 6 q^{31} + 2 q^{32} - 2 q^{33} - 16 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 8 q^{38} - 5 q^{39} - 29 q^{40} - 5 q^{41} + 31 q^{42} - 7 q^{43} + 30 q^{44} - 5 q^{45} + 19 q^{46} - 9 q^{47} - 19 q^{48} + 16 q^{49} + 29 q^{50} + 26 q^{51} + 6 q^{52} - 31 q^{53} - 4 q^{54} + 7 q^{55} + 8 q^{56} - 5 q^{57} + 35 q^{58} - q^{59} + 33 q^{60} - 15 q^{61} - 2 q^{62} + 11 q^{63} - 5 q^{64} - 9 q^{65} - 29 q^{66} - 28 q^{67} - 12 q^{68} + 5 q^{69} + 73 q^{70} + q^{71} + 45 q^{72} - 20 q^{73} + 4 q^{74} + q^{75} + 38 q^{76} - 29 q^{77} - 15 q^{79} + 7 q^{80} + 2 q^{81} + 36 q^{82} + q^{83} + 68 q^{84} + 29 q^{85} + 3 q^{86} + 10 q^{87} + 9 q^{88} - q^{89} - 32 q^{90} - 60 q^{92} - 5 q^{93} + 54 q^{94} - 13 q^{95} + 36 q^{96} - 5 q^{97} + 20 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9 - 8 * q^10 - 5 * q^11 - 13 * q^12 + 6 * q^13 - 17 * q^14 + 4 * q^15 + 14 * q^16 - 23 * q^17 + 9 * q^18 + 7 * q^19 - 10 * q^20 + 2 * q^21 + 2 * q^22 - 18 * q^23 - 13 * q^24 + 11 * q^25 - 2 * q^26 - 5 * q^27 - 25 * q^28 - 18 * q^29 + 25 * q^30 + 6 * q^31 + 2 * q^32 - 2 * q^33 - 16 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 8 * q^38 - 5 * q^39 - 29 * q^40 - 5 * q^41 + 31 * q^42 - 7 * q^43 + 30 * q^44 - 5 * q^45 + 19 * q^46 - 9 * q^47 - 19 * q^48 + 16 * q^49 + 29 * q^50 + 26 * q^51 + 6 * q^52 - 31 * q^53 - 4 * q^54 + 7 * q^55 + 8 * q^56 - 5 * q^57 + 35 * q^58 - q^59 + 33 * q^60 - 15 * q^61 - 2 * q^62 + 11 * q^63 - 5 * q^64 - 9 * q^65 - 29 * q^66 - 28 * q^67 - 12 * q^68 + 5 * q^69 + 73 * q^70 + q^71 + 45 * q^72 - 20 * q^73 + 4 * q^74 + q^75 + 38 * q^76 - 29 * q^77 - 15 * q^79 + 7 * q^80 + 2 * q^81 + 36 * q^82 + q^83 + 68 * q^84 + 29 * q^85 + 3 * q^86 + 10 * q^87 + 9 * q^88 - q^89 - 32 * q^90 - 60 * q^92 - 5 * q^93 + 54 * q^94 - 13 * q^95 + 36 * q^96 - 5 * q^97 + 20 * q^98 - 15 * q^99

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