LMFDB - Embedded newform 8035.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54398 q^{2} +1.20144 q^{3} +4.47181 q^{4} -1.00000 q^{5} -3.05645 q^{6} -0.416723 q^{7} -6.28824 q^{8} -1.55653 q^{9} +O(q^{10})$	\(q-2.54398 q^{2} +1.20144 q^{3} +4.47181 q^{4} -1.00000 q^{5} -3.05645 q^{6} -0.416723 q^{7} -6.28824 q^{8} -1.55653 q^{9} +2.54398 q^{10} +2.46622 q^{11} +5.37264 q^{12} +1.05231 q^{13} +1.06013 q^{14} -1.20144 q^{15} +7.05349 q^{16} +1.69692 q^{17} +3.95978 q^{18} +0.454887 q^{19} -4.47181 q^{20} -0.500670 q^{21} -6.27400 q^{22} -0.913461 q^{23} -7.55497 q^{24} +1.00000 q^{25} -2.67705 q^{26} -5.47442 q^{27} -1.86351 q^{28} +1.20493 q^{29} +3.05645 q^{30} +1.18806 q^{31} -5.36745 q^{32} +2.96302 q^{33} -4.31692 q^{34} +0.416723 q^{35} -6.96052 q^{36} +1.75820 q^{37} -1.15722 q^{38} +1.26429 q^{39} +6.28824 q^{40} +8.34807 q^{41} +1.27369 q^{42} -8.17423 q^{43} +11.0285 q^{44} +1.55653 q^{45} +2.32382 q^{46} -8.08326 q^{47} +8.47438 q^{48} -6.82634 q^{49} -2.54398 q^{50} +2.03875 q^{51} +4.70573 q^{52} +2.10238 q^{53} +13.9268 q^{54} -2.46622 q^{55} +2.62046 q^{56} +0.546521 q^{57} -3.06532 q^{58} -2.24861 q^{59} -5.37264 q^{60} -4.50662 q^{61} -3.02239 q^{62} +0.648643 q^{63} -0.452328 q^{64} -1.05231 q^{65} -7.53786 q^{66} +1.24375 q^{67} +7.58830 q^{68} -1.09747 q^{69} -1.06013 q^{70} -14.3814 q^{71} +9.78784 q^{72} -4.00736 q^{73} -4.47281 q^{74} +1.20144 q^{75} +2.03417 q^{76} -1.02773 q^{77} -3.21633 q^{78} +15.7148 q^{79} -7.05349 q^{80} -1.90762 q^{81} -21.2373 q^{82} -6.82110 q^{83} -2.23890 q^{84} -1.69692 q^{85} +20.7950 q^{86} +1.44766 q^{87} -15.5082 q^{88} -4.04382 q^{89} -3.95978 q^{90} -0.438522 q^{91} -4.08483 q^{92} +1.42739 q^{93} +20.5636 q^{94} -0.454887 q^{95} -6.44869 q^{96} +7.72961 q^{97} +17.3660 q^{98} -3.83875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * 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 $

$2$	−2.54398	−1.79886	−0.899431	−	0.437062i	$-0.856019\pi$
$2$	−2.54398	−1.79886	−0.899431	+	0.437062i	$0.856019\pi$
$3$	1.20144	0.693654	0.346827	−	0.937929i	$-0.387259\pi$
$3$	1.20144	0.693654	0.346827	+	0.937929i	$0.387259\pi$
$4$	4.47181	2.23591
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.05645	−1.24779
$7$	−0.416723	−0.157507	−0.0787533	−	0.996894i	$-0.525094\pi$
$7$	−0.416723	−0.157507	−0.0787533	+	0.996894i	$0.525094\pi$
$8$	−6.28824	−2.22323
$9$	−1.55653	−0.518844
$10$	2.54398	0.804476
$11$	2.46622	0.743593	0.371796	−	0.928314i	$-0.378742\pi$
$11$	2.46622	0.743593	0.371796	+	0.928314i	$0.378742\pi$
$12$	5.37264	1.55095
$13$	1.05231	0.291858	0.145929	−	0.989295i	$-0.453383\pi$
$13$	1.05231	0.291858	0.145929	+	0.989295i	$0.453383\pi$
$14$	1.06013	0.283333
$15$	−1.20144	−0.310212
$16$	7.05349	1.76337
$17$	1.69692	0.411563	0.205782	−	0.978598i	$-0.434026\pi$
$17$	1.69692	0.411563	0.205782	+	0.978598i	$0.434026\pi$
$18$	3.95978	0.933329
$19$	0.454887	0.104358	0.0521791	−	0.998638i	$-0.483383\pi$
$19$	0.454887	0.104358	0.0521791	+	0.998638i	$0.483383\pi$
$20$	−4.47181	−0.999928
$21$	−0.500670	−0.109255
$22$	−6.27400	−1.33762
$23$	−0.913461	−0.190470	−0.0952349	−	0.995455i	$-0.530360\pi$
$23$	−0.913461	−0.190470	−0.0952349	+	0.995455i	$0.530360\pi$
$24$	−7.55497	−1.54215
$25$	1.00000	0.200000
$26$	−2.67705	−0.525013
$27$	−5.47442	−1.05355
$28$	−1.86351	−0.352170
$29$	1.20493	0.223750	0.111875	−	0.993722i	$-0.464314\pi$
$29$	1.20493	0.223750	0.111875	+	0.993722i	$0.464314\pi$
$30$	3.05645	0.558028
$31$	1.18806	0.213382	0.106691	−	0.994292i	$-0.465974\pi$
$31$	1.18806	0.213382	0.106691	+	0.994292i	$0.465974\pi$
$32$	−5.36745	−0.948840
$33$	2.96302	0.515796
$34$	−4.31692	−0.740346
$35$	0.416723	0.0704391
$36$	−6.96052	−1.16009
$37$	1.75820	0.289046	0.144523	−	0.989501i	$-0.453835\pi$
$37$	1.75820	0.289046	0.144523	+	0.989501i	$0.453835\pi$
$38$	−1.15722	−0.187726
$39$	1.26429	0.202449
$40$	6.28824	0.994257
$41$	8.34807	1.30375	0.651875	−	0.758327i	$-0.273983\pi$
$41$	8.34807	1.30375	0.651875	+	0.758327i	$0.273983\pi$
$42$	1.27369	0.196535
$43$	−8.17423	−1.24656	−0.623279	−	0.781999i	$-0.714200\pi$
$43$	−8.17423	−1.24656	−0.623279	+	0.781999i	$0.714200\pi$
$44$	11.0285	1.66260
$45$	1.55653	0.232034
$46$	2.32382	0.342629
$47$	−8.08326	−1.17907	−0.589533	−	0.807745i	$-0.700688\pi$
$47$	−8.08326	−1.17907	−0.589533	+	0.807745i	$0.700688\pi$
$48$	8.47438	1.22317
$49$	−6.82634	−0.975192
$50$	−2.54398	−0.359773
$51$	2.03875	0.285483
$52$	4.70573	0.652568
$53$	2.10238	0.288784	0.144392	−	0.989521i	$-0.453877\pi$
$53$	2.10238	0.288784	0.144392	+	0.989521i	$0.453877\pi$
$54$	13.9268	1.89520
$55$	−2.46622	−0.332545
$56$	2.62046	0.350173
$57$	0.546521	0.0723885
$58$	−3.06532	−0.402496
$59$	−2.24861	−0.292744	−0.146372	−	0.989230i	$-0.546760\pi$
$59$	−2.24861	−0.292744	−0.146372	+	0.989230i	$0.546760\pi$
$60$	−5.37264	−0.693604
$61$	−4.50662	−0.577013	−0.288507	−	0.957478i	$-0.593159\pi$
$61$	−4.50662	−0.577013	−0.288507	+	0.957478i	$0.593159\pi$
$62$	−3.02239	−0.383844
$63$	0.648643	0.0817213
$64$	−0.452328	−0.0565410
$65$	−1.05231	−0.130523
$66$	−7.53786	−0.927847
$67$	1.24375	0.151948	0.0759741	−	0.997110i	$-0.475793\pi$
$67$	1.24375	0.151948	0.0759741	+	0.997110i	$0.475793\pi$
$68$	7.58830	0.920217
$69$	−1.09747	−0.132120
$70$	−1.06013	−0.126710
$71$	−14.3814	−1.70675	−0.853377	−	0.521294i	$-0.825449\pi$
$71$	−14.3814	−1.70675	−0.853377	+	0.521294i	$0.825449\pi$
$72$	9.78784	1.15351
$73$	−4.00736	−0.469026	−0.234513	−	0.972113i	$-0.575350\pi$
$73$	−4.00736	−0.469026	−0.234513	+	0.972113i	$0.575350\pi$
$74$	−4.47281	−0.519953
$75$	1.20144	0.138731
$76$	2.03417	0.233335
$77$	−1.02773	−0.117121
$78$	−3.21633	−0.364177
$79$	15.7148	1.76806	0.884028	−	0.467434i	$-0.154821\pi$
$79$	15.7148	1.76806	0.884028	+	0.467434i	$0.154821\pi$
$80$	−7.05349	−0.788605
$81$	−1.90762	−0.211957
$82$	−21.2373	−2.34527
$83$	−6.82110	−0.748712	−0.374356	−	0.927285i	$-0.622136\pi$
$83$	−6.82110	−0.748712	−0.374356	+	0.927285i	$0.622136\pi$
$84$	−2.23890	−0.244284
$85$	−1.69692	−0.184057
$86$	20.7950	2.24239
$87$	1.44766	0.155205
$88$	−15.5082	−1.65318
$89$	−4.04382	−0.428644	−0.214322	−	0.976763i	$-0.568754\pi$
$89$	−4.04382	−0.428644	−0.214322	+	0.976763i	$0.568754\pi$
$90$	−3.95978	−0.417397
$91$	−0.438522	−0.0459696
$92$	−4.08483	−0.425873
$93$	1.42739	0.148013
$94$	20.5636	2.12098
$95$	−0.454887	−0.0466704
$96$	−6.44869	−0.658167
$97$	7.72961	0.784823	0.392411	−	0.919790i	$-0.371641\pi$
$97$	7.72961	0.784823	0.392411	+	0.919790i	$0.371641\pi$
$98$	17.3660	1.75424
$99$	−3.83875	−0.385809
$100$	4.47181	0.447181
$101$	−0.710669	−0.0707143	−0.0353571	−	0.999375i	$-0.511257\pi$
$101$	−0.710669	−0.0707143	−0.0353571	+	0.999375i	$0.511257\pi$
$102$	−5.18654	−0.513544
$103$	15.3694	1.51439	0.757195	−	0.653189i	$-0.226569\pi$
$103$	15.3694	1.51439	0.757195	+	0.653189i	$0.226569\pi$
$104$	−6.61717	−0.648867
$105$	0.500670	0.0488604
$106$	−5.34840	−0.519482
$107$	−12.2372	−1.18301	−0.591505	−	0.806301i	$-0.701466\pi$
$107$	−12.2372	−1.18301	−0.591505	+	0.806301i	$0.701466\pi$
$108$	−24.4806	−2.35565
$109$	0.0112814	0.00108056	0.000540282	−	1.00000i	$-0.499828\pi$
$109$	0.0112814	0.00108056	0.000540282		1.00000i	$0.499828\pi$
$110$	6.27400	0.598203
$111$	2.11237	0.200498
$112$	−2.93936	−0.277743
$113$	−17.2288	−1.62075	−0.810375	−	0.585912i	$-0.800736\pi$
$113$	−17.2288	−1.62075	−0.810375	+	0.585912i	$0.800736\pi$
$114$	−1.39034	−0.130217
$115$	0.913461	0.0851807
$116$	5.38823	0.500285
$117$	−1.63795	−0.151429
$118$	5.72041	0.526606
$119$	−0.707146	−0.0648239
$120$	7.55497	0.689671
$121$	−4.91776	−0.447070
$122$	11.4647	1.03797
$123$	10.0297	0.904351
$124$	5.31278	0.477102
$125$	−1.00000	−0.0894427
$126$	−1.65013	−0.147005
$127$	21.7834	1.93296	0.966481	−	0.256738i	$-0.0826476\pi$
$127$	21.7834	1.93296	0.966481	+	0.256738i	$0.0826476\pi$
$128$	11.8856	1.05055
$129$	−9.82088	−0.864680
$130$	2.67705	0.234793
$131$	18.5830	1.62361	0.811803	−	0.583932i	$-0.198486\pi$
$131$	18.5830	1.62361	0.811803	+	0.583932i	$0.198486\pi$
$132$	13.2501	1.15327
$133$	−0.189562	−0.0164371
$134$	−3.16407	−0.273334
$135$	5.47442	0.471163
$136$	−10.6706	−0.914998
$137$	−11.1960	−0.956541	−0.478271	−	0.878213i	$-0.658736\pi$
$137$	−11.1960	−0.956541	−0.478271	+	0.878213i	$0.658736\pi$
$138$	2.79194	0.237666
$139$	6.56211	0.556591	0.278296	−	0.960495i	$-0.410230\pi$
$139$	6.56211	0.556591	0.278296	+	0.960495i	$0.410230\pi$
$140$	1.86351	0.157495
$141$	−9.71159	−0.817863
$142$	36.5858	3.07022
$143$	2.59522	0.217024
$144$	−10.9790	−0.914915
$145$	−1.20493	−0.100064
$146$	10.1946	0.843713
$147$	−8.20147	−0.676446
$148$	7.86233	0.646279
$149$	7.50371	0.614728	0.307364	−	0.951592i	$-0.400553\pi$
$149$	7.50371	0.614728	0.307364	+	0.951592i	$0.400553\pi$
$150$	−3.05645	−0.249558
$151$	16.3267	1.32865	0.664325	−	0.747444i	$-0.268719\pi$
$151$	16.3267	1.32865	0.664325	+	0.747444i	$0.268719\pi$
$152$	−2.86043	−0.232012
$153$	−2.64131	−0.213537
$154$	2.61452	0.210684
$155$	−1.18806	−0.0954272
$156$	5.65367	0.452656
$157$	6.08682	0.485781	0.242891	−	0.970054i	$-0.421904\pi$
$157$	6.08682	0.485781	0.242891	+	0.970054i	$0.421904\pi$
$158$	−39.9781	−3.18049
$159$	2.52589	0.200316
$160$	5.36745	0.424334
$161$	0.380661	0.0300003
$162$	4.85293	0.381282
$163$	−5.04923	−0.395486	−0.197743	−	0.980254i	$-0.563361\pi$
$163$	−5.04923	−0.395486	−0.197743	+	0.980254i	$0.563361\pi$
$164$	37.3310	2.91506
$165$	−2.96302	−0.230671
$166$	17.3527	1.34683
$167$	−13.4814	−1.04322	−0.521609	−	0.853185i	$-0.674668\pi$
$167$	−13.4814	−1.04322	−0.521609	+	0.853185i	$0.674668\pi$
$168$	3.14833	0.242899
$169$	−11.8926	−0.914819
$170$	4.31692	0.331093
$171$	−0.708045	−0.0541456
$172$	−36.5536	−2.78719
$173$	−6.61801	−0.503158	−0.251579	−	0.967837i	$-0.580950\pi$
$173$	−6.61801	−0.503158	−0.251579	+	0.967837i	$0.580950\pi$
$174$	−3.68281	−0.279193
$175$	−0.416723	−0.0315013
$176$	17.3955	1.31123
$177$	−2.70158	−0.203063
$178$	10.2874	0.771072
$179$	12.8842	0.963007	0.481503	−	0.876444i	$-0.340091\pi$
$179$	12.8842	0.963007	0.481503	+	0.876444i	$0.340091\pi$
$180$	6.96052	0.518806
$181$	18.0651	1.34277	0.671386	−	0.741108i	$-0.265699\pi$
$181$	18.0651	1.34277	0.671386	+	0.741108i	$0.265699\pi$
$182$	1.11559	0.0826930
$183$	−5.41445	−0.400248
$184$	5.74406	0.423458
$185$	−1.75820	−0.129265
$186$	−3.63124	−0.266255
$187$	4.18497	0.306035
$188$	−36.1468	−2.63628
$189$	2.28132	0.165942
$190$	1.15722	0.0839536
$191$	−13.2054	−0.955510	−0.477755	−	0.878493i	$-0.658549\pi$
$191$	−13.2054	−0.955510	−0.477755	+	0.878493i	$0.658549\pi$
$192$	−0.543447	−0.0392199
$193$	18.6160	1.34001	0.670004	−	0.742358i	$-0.266293\pi$
$193$	18.6160	1.34001	0.670004	+	0.742358i	$0.266293\pi$
$194$	−19.6639	−1.41179
$195$	−1.26429	−0.0905378
$196$	−30.5261	−2.18044
$197$	−4.91177	−0.349949	−0.174975	−	0.984573i	$-0.555984\pi$
$197$	−4.91177	−0.349949	−0.174975	+	0.984573i	$0.555984\pi$
$198$	9.76568	0.694017
$199$	−14.0483	−0.995859	−0.497930	−	0.867217i	$-0.665906\pi$
$199$	−14.0483	−0.995859	−0.497930	+	0.867217i	$0.665906\pi$
$200$	−6.28824	−0.444645
$201$	1.49430	0.105400
$202$	1.80793	0.127205
$203$	−0.502124	−0.0352422
$204$	9.11693	0.638312
$205$	−8.34807	−0.583054
$206$	−39.0993	−2.72418
$207$	1.42183	0.0988241
$208$	7.42246	0.514655
$209$	1.12185	0.0776000
$210$	−1.27369	−0.0878931
$211$	1.51560	0.104338	0.0521692	−	0.998638i	$-0.483386\pi$
$211$	1.51560	0.104338	0.0521692	+	0.998638i	$0.483386\pi$
$212$	9.40144	0.645694
$213$	−17.2784	−1.18390
$214$	31.1310	2.12807
$215$	8.17423	0.557478
$216$	34.4244	2.34229
$217$	−0.495092	−0.0336090
$218$	−0.0286997	−0.00194379
$219$	−4.81462	−0.325342
$220$	−11.0285	−0.743539
$221$	1.78568	0.120118
$222$	−5.37383	−0.360668
$223$	19.1985	1.28563	0.642814	−	0.766022i	$-0.277767\pi$
$223$	19.1985	1.28563	0.642814	+	0.766022i	$0.277767\pi$
$224$	2.23674	0.149449
$225$	−1.55653	−0.103769
$226$	43.8297	2.91551
$227$	−25.1061	−1.66635	−0.833175	−	0.553010i	$-0.813479\pi$
$227$	−25.1061	−1.66635	−0.833175	+	0.553010i	$0.813479\pi$
$228$	2.44394	0.161854
$229$	−1.31481	−0.0868854	−0.0434427	−	0.999056i	$-0.513833\pi$
$229$	−1.31481	−0.0868854	−0.0434427	+	0.999056i	$0.513833\pi$
$230$	−2.32382	−0.153228
$231$	−1.23476	−0.0812414
$232$	−7.57690	−0.497448
$233$	−23.7548	−1.55623	−0.778114	−	0.628123i	$-0.783823\pi$
$233$	−23.7548	−1.55623	−0.778114	+	0.628123i	$0.783823\pi$
$234$	4.16691	0.272399
$235$	8.08326	0.527294
$236$	−10.0554	−0.654549
$237$	18.8805	1.22642
$238$	1.79896	0.116609
$239$	−20.2054	−1.30698	−0.653491	−	0.756935i	$-0.726696\pi$
$239$	−20.2054	−1.30698	−0.653491	+	0.756935i	$0.726696\pi$
$240$	−8.47438	−0.547019
$241$	−25.5158	−1.64362	−0.821808	−	0.569764i	$-0.807034\pi$
$241$	−25.5158	−1.64362	−0.821808	+	0.569764i	$0.807034\pi$
$242$	12.5107	0.804217
$243$	14.1314	0.906527
$244$	−20.1528	−1.29015
$245$	6.82634	0.436119
$246$	−25.5154	−1.62680
$247$	0.478681	0.0304578
$248$	−7.47079	−0.474396
$249$	−8.19517	−0.519348
$250$	2.54398	0.160895
$251$	16.6332	1.04988	0.524940	−	0.851139i	$-0.324088\pi$
$251$	16.6332	1.04988	0.524940	+	0.851139i	$0.324088\pi$
$252$	2.90061	0.182721
$253$	−2.25280	−0.141632
$254$	−55.4164	−3.47713
$255$	−2.03875	−0.127672
$256$	−29.3320	−1.83325
$257$	−21.4257	−1.33650	−0.668251	−	0.743936i	$-0.732957\pi$
$257$	−21.4257	−1.33650	−0.668251	+	0.743936i	$0.732957\pi$
$258$	24.9841	1.55544
$259$	−0.732681	−0.0455266
$260$	−4.70573	−0.291837
$261$	−1.87551	−0.116091
$262$	−47.2747	−2.92064
$263$	−22.8517	−1.40910	−0.704548	−	0.709656i	$-0.748850\pi$
$263$	−22.8517	−1.40910	−0.704548	+	0.709656i	$0.748850\pi$
$264$	−18.6322	−1.14673
$265$	−2.10238	−0.129148
$266$	0.482241	0.0295681
$267$	−4.85842	−0.297331
$268$	5.56182	0.339742
$269$	−15.6217	−0.952469	−0.476235	−	0.879318i	$-0.657999\pi$
$269$	−15.6217	−0.952469	−0.476235	+	0.879318i	$0.657999\pi$
$270$	−13.9268	−0.847558
$271$	−0.429442	−0.0260868	−0.0130434	−	0.999915i	$-0.504152\pi$
$271$	−0.429442	−0.0260868	−0.0130434	+	0.999915i	$0.504152\pi$
$272$	11.9692	0.725740
$273$	−0.526860	−0.0318870
$274$	28.4824	1.72069
$275$	2.46622	0.148719
$276$	−4.90770	−0.295409
$277$	7.78685	0.467866	0.233933	−	0.972253i	$-0.424840\pi$
$277$	7.78685	0.467866	0.233933	+	0.972253i	$0.424840\pi$
$278$	−16.6939	−1.00123
$279$	−1.84925	−0.110712
$280$	−2.62046	−0.156602
$281$	11.3624	0.677821	0.338911	−	0.940819i	$-0.389942\pi$
$281$	11.3624	0.677821	0.338911	+	0.940819i	$0.389942\pi$
$282$	24.7061	1.47122
$283$	−10.3191	−0.613407	−0.306704	−	0.951805i	$-0.599226\pi$
$283$	−10.3191	−0.613407	−0.306704	+	0.951805i	$0.599226\pi$
$284$	−64.3108	−3.81614
$285$	−0.546521	−0.0323731
$286$	−6.60219	−0.390396
$287$	−3.47884	−0.205349
$288$	8.35460	0.492300
$289$	−14.1205	−0.830616
$290$	3.06532	0.180002
$291$	9.28669	0.544396
$292$	−17.9202	−1.04870
$293$	−17.4800	−1.02119	−0.510596	−	0.859821i	$-0.670575\pi$
$293$	−17.4800	−1.02119	−0.510596	+	0.859821i	$0.670575\pi$
$294$	20.8643	1.21683
$295$	2.24861	0.130919
$296$	−11.0560	−0.642614
$297$	−13.5011	−0.783414
$298$	−19.0893	−1.10581
$299$	−0.961244	−0.0555902
$300$	5.37264	0.310189
$301$	3.40639	0.196341
$302$	−41.5348	−2.39006
$303$	−0.853830	−0.0490512
$304$	3.20854	0.184022
$305$	4.50662	0.258048
$306$	6.71942	0.384124
$307$	−23.2495	−1.32692	−0.663461	−	0.748211i	$-0.730913\pi$
$307$	−23.2495	−1.32692	−0.663461	+	0.748211i	$0.730913\pi$
$308$	−4.59582	−0.261871
$309$	18.4654	1.05046
$310$	3.02239	0.171660
$311$	31.0576	1.76111	0.880556	−	0.473941i	$-0.157169\pi$
$311$	31.0576	1.76111	0.880556	+	0.473941i	$0.157169\pi$
$312$	−7.95016	−0.450089
$313$	24.9388	1.40962	0.704811	−	0.709395i	$-0.251032\pi$
$313$	24.9388	1.40962	0.704811	+	0.709395i	$0.251032\pi$
$314$	−15.4847	−0.873854
$315$	−0.648643	−0.0365469
$316$	70.2738	3.95321
$317$	−8.48769	−0.476716	−0.238358	−	0.971177i	$-0.576609\pi$
$317$	−8.48769	−0.476716	−0.238358	+	0.971177i	$0.576609\pi$
$318$	−6.42580	−0.360341
$319$	2.97163	0.166379
$320$	0.452328	0.0252859
$321$	−14.7023	−0.820601
$322$	−0.968392	−0.0539664
$323$	0.771905	0.0429500
$324$	−8.53051	−0.473917
$325$	1.05231	0.0583716
$326$	12.8451	0.711426
$327$	0.0135540	0.000749538 0
$328$	−52.4946	−2.89853
$329$	3.36848	0.185711
$330$	7.53786	0.414946
$331$	26.8073	1.47346	0.736730	−	0.676187i	$-0.236369\pi$
$331$	26.8073	1.47346	0.736730	+	0.676187i	$0.236369\pi$
$332$	−30.5027	−1.67405
$333$	−2.73669	−0.149970
$334$	34.2962	1.87661
$335$	−1.24375	−0.0679533
$336$	−3.53147	−0.192658
$337$	10.3116	0.561711	0.280855	−	0.959750i	$-0.409382\pi$
$337$	10.3116	0.561711	0.280855	+	0.959750i	$0.409382\pi$
$338$	30.2546	1.64563
$339$	−20.6994	−1.12424
$340$	−7.58830	−0.411534
$341$	2.93001	0.158669
$342$	1.80125	0.0974004
$343$	5.76176	0.311106
$344$	51.4015	2.77138
$345$	1.09747	0.0590860
$346$	16.8360	0.905112
$347$	−10.5604	−0.566911	−0.283455	−	0.958985i	$-0.591481\pi$
$347$	−10.5604	−0.566911	−0.283455	+	0.958985i	$0.591481\pi$
$348$	6.47366	0.347025
$349$	−24.6482	−1.31939	−0.659694	−	0.751534i	$-0.729314\pi$
$349$	−24.6482	−1.31939	−0.659694	+	0.751534i	$0.729314\pi$
$350$	1.06013	0.0566666
$351$	−5.76078	−0.307488
$352$	−13.2373	−0.705551
$353$	−11.9899	−0.638157	−0.319078	−	0.947728i	$-0.603373\pi$
$353$	−11.9899	−0.638157	−0.319078	+	0.947728i	$0.603373\pi$
$354$	6.87276	0.365283
$355$	14.3814	0.763284
$356$	−18.0832	−0.958408
$357$	−0.849596	−0.0449654
$358$	−32.7770	−1.73232
$359$	25.8987	1.36688	0.683440	−	0.730006i	$-0.260483\pi$
$359$	25.8987	1.36688	0.683440	+	0.730006i	$0.260483\pi$
$360$	−9.78784	−0.515864
$361$	−18.7931	−0.989109
$362$	−45.9573	−2.41546
$363$	−5.90842	−0.310112
$364$	−1.96099	−0.102784
$365$	4.00736	0.209755
$366$	13.7742	0.719991
$367$	−34.8021	−1.81665	−0.908326	−	0.418262i	$-0.862639\pi$
$367$	−34.8021	−1.81665	−0.908326	+	0.418262i	$0.862639\pi$
$368$	−6.44309	−0.335869
$369$	−12.9940	−0.676442
$370$	4.47281	0.232530
$371$	−0.876110	−0.0454854
$372$	6.38301	0.330944
$373$	−14.1151	−0.730851	−0.365426	−	0.930841i	$-0.619077\pi$
$373$	−14.1151	−0.730851	−0.365426	+	0.930841i	$0.619077\pi$
$374$	−10.6465	−0.550516
$375$	−1.20144	−0.0620423
$376$	50.8295	2.62133
$377$	1.26796	0.0653033
$378$	−5.80362	−0.298506
$379$	−5.73253	−0.294460	−0.147230	−	0.989102i	$-0.547036\pi$
$379$	−5.73253	−0.294460	−0.147230	+	0.989102i	$0.547036\pi$
$380$	−2.03417	−0.104351
$381$	26.1715	1.34081
$382$	33.5943	1.71883
$383$	−3.72949	−0.190568	−0.0952841	−	0.995450i	$-0.530376\pi$
$383$	−3.72949	−0.190568	−0.0952841	+	0.995450i	$0.530376\pi$
$384$	14.2799	0.728718
$385$	1.02773	0.0523780
$386$	−47.3586	−2.41049
$387$	12.7234	0.646769
$388$	34.5654	1.75479
$389$	−12.5855	−0.638110	−0.319055	−	0.947736i	$-0.603365\pi$
$389$	−12.5855	−0.638110	−0.319055	+	0.947736i	$0.603365\pi$
$390$	3.21633	0.162865
$391$	−1.55007	−0.0783904
$392$	42.9257	2.16807
$393$	22.3265	1.12622
$394$	12.4954	0.629511
$395$	−15.7148	−0.790699
$396$	−17.1662	−0.862632
$397$	−26.9353	−1.35184	−0.675922	−	0.736973i	$-0.736254\pi$
$397$	−26.9353	−1.35184	−0.675922	+	0.736973i	$0.736254\pi$
$398$	35.7386	1.79141
$399$	−0.227748	−0.0114017
$400$	7.05349	0.352675
$401$	37.1468	1.85502	0.927512	−	0.373794i	$-0.121943\pi$
$401$	37.1468	1.85502	0.927512	+	0.373794i	$0.121943\pi$
$402$	−3.80145	−0.189599
$403$	1.25021	0.0622772
$404$	−3.17798	−0.158111
$405$	1.90762	0.0947902
$406$	1.27739	0.0633958
$407$	4.33610	0.214932
$408$	−12.8202	−0.634693
$409$	15.5231	0.767568	0.383784	−	0.923423i	$-0.374621\pi$
$409$	15.5231	0.767568	0.383784	+	0.923423i	$0.374621\pi$
$410$	21.2373	1.04883
$411$	−13.4514	−0.663509
$412$	68.7290	3.38603
$413$	0.937048	0.0461091
$414$	−3.61710	−0.177771
$415$	6.82110	0.334834
$416$	−5.64822	−0.276927
$417$	7.88402	0.386082
$418$	−2.85396	−0.139592
$419$	−32.8545	−1.60505	−0.802523	−	0.596621i	$-0.796510\pi$
$419$	−32.8545	−1.60505	−0.802523	+	0.596621i	$0.796510\pi$
$420$	2.23890	0.109247
$421$	5.21821	0.254320	0.127160	−	0.991882i	$-0.459414\pi$
$421$	5.21821	0.254320	0.127160	+	0.991882i	$0.459414\pi$
$422$	−3.85566	−0.187691
$423$	12.5819	0.611750
$424$	−13.2203	−0.642032
$425$	1.69692	0.0823126
$426$	43.9559	2.12967
$427$	1.87801	0.0908834
$428$	−54.7223	−2.64510
$429$	3.11802	0.150539
$430$	−20.7950	−1.00283
$431$	−9.70882	−0.467657	−0.233829	−	0.972278i	$-0.575125\pi$
$431$	−9.70882	−0.467657	−0.233829	+	0.972278i	$0.575125\pi$
$432$	−38.6138	−1.85781
$433$	27.8262	1.33724	0.668620	−	0.743604i	$-0.266885\pi$
$433$	27.8262	1.33724	0.668620	+	0.743604i	$0.266885\pi$
$434$	1.25950	0.0604580
$435$	−1.44766	−0.0694100
$436$	0.0504484	0.00241604
$437$	−0.415521	−0.0198771
$438$	12.2483	0.585245
$439$	5.38210	0.256873	0.128437	−	0.991718i	$-0.459004\pi$
$439$	5.38210	0.256873	0.128437	+	0.991718i	$0.459004\pi$
$440$	15.5082	0.739323
$441$	10.6254	0.505972
$442$	−4.54273	−0.216076
$443$	15.0943	0.717154	0.358577	−	0.933500i	$-0.383262\pi$
$443$	15.0943	0.717154	0.358577	+	0.933500i	$0.383262\pi$
$444$	9.44615	0.448294
$445$	4.04382	0.191695
$446$	−48.8406	−2.31267
$447$	9.01529	0.426408
$448$	0.188496	0.00890559
$449$	11.7372	0.553915	0.276957	−	0.960882i	$-0.410674\pi$
$449$	11.7372	0.553915	0.276957	+	0.960882i	$0.410674\pi$
$450$	3.95978	0.186666
$451$	20.5882	0.969459
$452$	−77.0440	−3.62385
$453$	19.6156	0.921623
$454$	63.8693	2.99753
$455$	0.438522	0.0205582
$456$	−3.43665	−0.160936
$457$	17.9753	0.840851	0.420425	−	0.907327i	$-0.361881\pi$
$457$	17.9753	0.840851	0.420425	+	0.907327i	$0.361881\pi$
$458$	3.34486	0.156295
$459$	−9.28964	−0.433603
$460$	4.08483	0.190456
$461$	13.0810	0.609241	0.304621	−	0.952474i	$-0.401470\pi$
$461$	13.0810	0.609241	0.304621	+	0.952474i	$0.401470\pi$
$462$	3.14120	0.146142
$463$	−26.9804	−1.25388	−0.626942	−	0.779066i	$-0.715694\pi$
$463$	−26.9804	−1.25388	−0.626942	+	0.779066i	$0.715694\pi$
$464$	8.49898	0.394555
$465$	−1.42739	−0.0661935
$466$	60.4316	2.79944
$467$	4.19220	0.193992	0.0969960	−	0.995285i	$-0.469077\pi$
$467$	4.19220	0.193992	0.0969960	+	0.995285i	$0.469077\pi$
$468$	−7.32462	−0.338581
$469$	−0.518300	−0.0239329
$470$	−20.5636	−0.948529
$471$	7.31298	0.336964
$472$	14.1398	0.650837
$473$	−20.1594	−0.926932
$474$	−48.0315	−2.20616
$475$	0.454887	0.0208716
$476$	−3.16222	−0.144940
$477$	−3.27242	−0.149834
$478$	51.4022	2.35108
$479$	18.4220	0.841724	0.420862	−	0.907125i	$-0.361728\pi$
$479$	18.4220	0.841724	0.420862	+	0.907125i	$0.361728\pi$
$480$	6.44869	0.294341
$481$	1.85017	0.0843603
$482$	64.9115	2.95664
$483$	0.457343	0.0208098
$484$	−21.9913	−0.999606
$485$	−7.72961	−0.350983
$486$	−35.9498	−1.63072
$487$	−30.5393	−1.38387	−0.691934	−	0.721961i	$-0.743241\pi$
$487$	−30.5393	−1.38387	−0.691934	+	0.721961i	$0.743241\pi$
$488$	28.3387	1.28283
$489$	−6.06637	−0.274331
$490$	−17.3660	−0.784518
$491$	−5.75816	−0.259862	−0.129931	−	0.991523i	$-0.541476\pi$
$491$	−5.75816	−0.259862	−0.129931	+	0.991523i	$0.541476\pi$
$492$	44.8511	2.02205
$493$	2.04467	0.0920874
$494$	−1.21775	−0.0547893
$495$	3.83875	0.172539
$496$	8.37997	0.376272
$497$	5.99305	0.268825
$498$	20.8483	0.934235
$499$	−4.44118	−0.198815	−0.0994073	−	0.995047i	$-0.531695\pi$
$499$	−4.44118	−0.198815	−0.0994073	+	0.995047i	$0.531695\pi$
$500$	−4.47181	−0.199986
$501$	−16.1971	−0.723633
$502$	−42.3145	−1.88859
$503$	−37.6891	−1.68047	−0.840237	−	0.542219i	$-0.817584\pi$
$503$	−37.6891	−1.68047	−0.840237	+	0.542219i	$0.817584\pi$
$504$	−4.07882	−0.181685
$505$	0.710669	0.0316244
$506$	5.73106	0.254777
$507$	−14.2884	−0.634568
$508$	97.4112	4.32192
$509$	3.13553	0.138980	0.0694901	−	0.997583i	$-0.477863\pi$
$509$	3.13553	0.138980	0.0694901	+	0.997583i	$0.477863\pi$
$510$	5.18654	0.229664
$511$	1.66996	0.0738747
$512$	50.8488	2.24722
$513$	−2.49024	−0.109947
$514$	54.5066	2.40418
$515$	−15.3694	−0.677255
$516$	−43.9172	−1.93335
$517$	−19.9351	−0.876744
$518$	1.86392	0.0818961
$519$	−7.95117	−0.349017
$520$	6.61717	0.290182
$521$	7.51615	0.329289	0.164644	−	0.986353i	$-0.447352\pi$
$521$	7.51615	0.329289	0.164644	+	0.986353i	$0.447352\pi$
$522$	4.77126	0.208833
$523$	−30.7982	−1.34671	−0.673355	−	0.739319i	$-0.735148\pi$
$523$	−30.7982	−1.34671	−0.673355	+	0.739319i	$0.735148\pi$
$524$	83.0998	3.63023
$525$	−0.500670	−0.0218510
$526$	58.1342	2.53477
$527$	2.01604	0.0878200
$528$	20.8997	0.909542
$529$	−22.1656	−0.963721
$530$	5.34840	0.232320
$531$	3.50003	0.151888
$532$	−0.847686	−0.0367518
$533$	8.78475	0.380510
$534$	12.3597	0.534857
$535$	12.2372	0.529059
$536$	−7.82099	−0.337815
$537$	15.4796	0.667994
$538$	39.7411	1.71336
$539$	−16.8353	−0.725146
$540$	24.4806	1.05348
$541$	−25.0316	−1.07619	−0.538096	−	0.842884i	$-0.680856\pi$
$541$	−25.0316	−1.07619	−0.538096	+	0.842884i	$0.680856\pi$
$542$	1.09249	0.0469265
$543$	21.7043	0.931419
$544$	−9.10812	−0.390508
$545$	−0.0112814	−0.000483243 0
$546$	1.34032	0.0573603
$547$	−22.7675	−0.973469	−0.486734	−	0.873550i	$-0.661812\pi$
$547$	−22.7675	−0.973469	−0.486734	+	0.873550i	$0.661812\pi$
$548$	−50.0666	−2.13874
$549$	7.01469	0.299380
$550$	−6.27400	−0.267524
$551$	0.548108	0.0233502
$552$	6.90117	0.293733
$553$	−6.54874	−0.278481
$554$	−19.8095	−0.841627
$555$	−2.11237	−0.0896653
$556$	29.3446	1.24449
$557$	−19.3338	−0.819198	−0.409599	−	0.912266i	$-0.634331\pi$
$557$	−19.3338	−0.819198	−0.409599	+	0.912266i	$0.634331\pi$
$558$	4.70445	0.199155
$559$	−8.60182	−0.363818
$560$	2.93936	0.124210
$561$	5.02801	0.212283
$562$	−28.9056	−1.21931
$563$	6.81133	0.287063	0.143532	−	0.989646i	$-0.454154\pi$
$563$	6.81133	0.287063	0.143532	+	0.989646i	$0.454154\pi$
$564$	−43.4284	−1.82867
$565$	17.2288	0.724821
$566$	26.2516	1.10344
$567$	0.794949	0.0333847
$568$	90.4334	3.79450
$569$	11.8086	0.495041	0.247520	−	0.968883i	$-0.420384\pi$
$569$	11.8086	0.495041	0.247520	+	0.968883i	$0.420384\pi$
$570$	1.39034	0.0582348
$571$	30.0155	1.25611	0.628056	−	0.778169i	$-0.283851\pi$
$571$	30.0155	1.25611	0.628056	+	0.778169i	$0.283851\pi$
$572$	11.6054	0.485245
$573$	−15.8656	−0.662794
$574$	8.85007	0.369395
$575$	−0.913461	−0.0380940
$576$	0.704063	0.0293360
$577$	6.84797	0.285085	0.142542	−	0.989789i	$-0.454472\pi$
$577$	6.84797	0.285085	0.142542	+	0.989789i	$0.454472\pi$
$578$	35.9221	1.49416
$579$	22.3661	0.929502
$580$	−5.38823	−0.223734
$581$	2.84251	0.117927
$582$	−23.6251	−0.979293
$583$	5.18492	0.214738
$584$	25.1992	1.04275
$585$	1.63795	0.0677210
$586$	44.4687	1.83698
$587$	−30.0913	−1.24200	−0.621001	−	0.783810i	$-0.713274\pi$
$587$	−30.0913	−1.24200	−0.621001	+	0.783810i	$0.713274\pi$
$588$	−36.6755	−1.51247
$589$	0.540432	0.0222681
$590$	−5.72041	−0.235506
$591$	−5.90122	−0.242744
$592$	12.4014	0.509695
$593$	32.2248	1.32331	0.661657	−	0.749807i	$-0.269853\pi$
$593$	32.2248	1.32331	0.661657	+	0.749807i	$0.269853\pi$
$594$	34.3465	1.40925
$595$	0.707146	0.0289901
$596$	33.5552	1.37447
$597$	−16.8783	−0.690782
$598$	2.44538	0.0999991
$599$	−32.3590	−1.32215	−0.661076	−	0.750319i	$-0.729900\pi$
$599$	−32.3590	−1.32215	−0.661076	+	0.750319i	$0.729900\pi$
$600$	−7.55497	−0.308430
$601$	34.2478	1.39700	0.698498	−	0.715612i	$-0.253852\pi$
$601$	34.2478	1.39700	0.698498	+	0.715612i	$0.253852\pi$
$602$	−8.66578	−0.353191
$603$	−1.93594	−0.0788374
$604$	73.0100	2.97074
$605$	4.91776	0.199936
$606$	2.17212	0.0882365
$607$	−23.5949	−0.957688	−0.478844	−	0.877900i	$-0.658944\pi$
$607$	−23.5949	−0.957688	−0.478844	+	0.877900i	$0.658944\pi$
$608$	−2.44158	−0.0990192
$609$	−0.603274	−0.0244459
$610$	−11.4647	−0.464193
$611$	−8.50609	−0.344120
$612$	−11.8114	−0.477449
$613$	−36.6192	−1.47903	−0.739517	−	0.673138i	$-0.764946\pi$
$613$	−36.6192	−1.47903	−0.739517	+	0.673138i	$0.764946\pi$
$614$	59.1463	2.38695
$615$	−10.0297	−0.404438
$616$	6.46262	0.260386
$617$	10.4014	0.418746	0.209373	−	0.977836i	$-0.432858\pi$
$617$	10.4014	0.418746	0.209373	+	0.977836i	$0.432858\pi$
$618$	−46.9757	−1.88964
$619$	−23.2271	−0.933577	−0.466788	−	0.884369i	$-0.654589\pi$
$619$	−23.2271	−0.933577	−0.466788	+	0.884369i	$0.654589\pi$
$620$	−5.31278	−0.213366
$621$	5.00067	0.200670
$622$	−79.0097	−3.16800
$623$	1.68515	0.0675143
$624$	8.91767	0.356993
$625$	1.00000	0.0400000
$626$	−63.4436	−2.53572
$627$	1.34784	0.0538276
$628$	27.2191	1.08616
$629$	2.98352	0.118961
$630$	1.65013	0.0657428
$631$	9.97069	0.396927	0.198463	−	0.980108i	$-0.436405\pi$
$631$	9.97069	0.396927	0.198463	+	0.980108i	$0.436405\pi$
$632$	−98.8185	−3.93079
$633$	1.82091	0.0723748
$634$	21.5925	0.857547
$635$	−21.7834	−0.864447
$636$	11.2953	0.447888
$637$	−7.18342	−0.284618
$638$	−7.55975	−0.299293
$639$	22.3850	0.885539
$640$	−11.8856	−0.469820
$641$	32.1537	1.26999	0.634997	−	0.772515i	$-0.281001\pi$
$641$	32.1537	1.26999	0.634997	+	0.772515i	$0.281001\pi$
$642$	37.4022	1.47615
$643$	−39.6478	−1.56356	−0.781778	−	0.623557i	$-0.785687\pi$
$643$	−39.6478	−1.56356	−0.781778	+	0.623557i	$0.785687\pi$
$644$	1.70224	0.0670778
$645$	9.82088	0.386697
$646$	−1.96371	−0.0772611
$647$	−19.1244	−0.751857	−0.375928	−	0.926649i	$-0.622676\pi$
$647$	−19.1244	−0.751857	−0.375928	+	0.926649i	$0.622676\pi$
$648$	11.9955	0.471230
$649$	−5.54556	−0.217682
$650$	−2.67705	−0.105003
$651$	−0.594825	−0.0233130
$652$	−22.5792	−0.884271
$653$	33.4141	1.30759	0.653797	−	0.756670i	$-0.273175\pi$
$653$	33.4141	1.30759	0.653797	+	0.756670i	$0.273175\pi$
$654$	−0.0344810	−0.00134832
$655$	−18.5830	−0.726098
$656$	58.8831	2.29900
$657$	6.23758	0.243351
$658$	−8.56934	−0.334068
$659$	−35.1477	−1.36916	−0.684579	−	0.728938i	$-0.740014\pi$
$659$	−35.1477	−1.36916	−0.684579	+	0.728938i	$0.740014\pi$
$660$	−13.2501	−0.515759
$661$	−36.0135	−1.40076	−0.700382	−	0.713768i	$-0.746987\pi$
$661$	−36.0135	−1.40076	−0.700382	+	0.713768i	$0.746987\pi$
$662$	−68.1970	−2.65055
$663$	2.14540	0.0833204
$664$	42.8927	1.66456
$665$	0.189562	0.00735089
$666$	6.96207	0.269775
$667$	−1.10066	−0.0426177
$668$	−60.2861	−2.33254
$669$	23.0660	0.891782
$670$	3.16407	0.122239
$671$	−11.1143	−0.429063
$672$	2.68732	0.103666
$673$	2.69201	0.103770	0.0518848	−	0.998653i	$-0.483477\pi$
$673$	2.69201	0.103770	0.0518848	+	0.998653i	$0.483477\pi$
$674$	−26.2326	−1.01044
$675$	−5.47442	−0.210710
$676$	−53.1817	−2.04545
$677$	−12.2223	−0.469742	−0.234871	−	0.972027i	$-0.575467\pi$
$677$	−12.2223	−0.469742	−0.234871	+	0.972027i	$0.575467\pi$
$678$	52.6589	2.02235
$679$	−3.22111	−0.123615
$680$	10.6706	0.409200
$681$	−30.1636	−1.15587
$682$	−7.45388	−0.285424
$683$	43.5969	1.66819	0.834095	−	0.551621i	$-0.185990\pi$
$683$	43.5969	1.66819	0.834095	+	0.551621i	$0.185990\pi$
$684$	−3.16625	−0.121064
$685$	11.1960	0.427778
$686$	−14.6578	−0.559637
$687$	−1.57968	−0.0602684
$688$	−57.6569	−2.19815
$689$	2.21235	0.0842839
$690$	−2.79194	−0.106288
$691$	45.6023	1.73479	0.867396	−	0.497618i	$-0.165792\pi$
$691$	45.6023	1.73479	0.867396	+	0.497618i	$0.165792\pi$
$692$	−29.5945	−1.12501
$693$	1.59970	0.0607674
$694$	26.8653	1.01979
$695$	−6.56211	−0.248915
$696$	−9.10322	−0.345057
$697$	14.1660	0.536575
$698$	62.7045	2.37340
$699$	−28.5401	−1.07948
$700$	−1.86351	−0.0704340
$701$	−10.9518	−0.413643	−0.206822	−	0.978379i	$-0.566312\pi$
$701$	−10.9518	−0.413643	−0.206822	+	0.978379i	$0.566312\pi$
$702$	14.6553	0.553128
$703$	0.799780	0.0301643
$704$	−1.11554	−0.0420435
$705$	9.71159	0.365760
$706$	30.5020	1.14796
$707$	0.296153	0.0111380
$708$	−12.0810	−0.454030
$709$	21.1173	0.793079	0.396539	−	0.918018i	$-0.370211\pi$
$709$	21.1173	0.793079	0.396539	+	0.918018i	$0.370211\pi$
$710$	−36.5858	−1.37304
$711$	−24.4606	−0.917345
$712$	25.4285	0.952973
$713$	−1.08525	−0.0406428
$714$	2.16135	0.0808866
$715$	−2.59522	−0.0970559
$716$	57.6155	2.15319
$717$	−24.2757	−0.906593
$718$	−65.8856	−2.45883
$719$	−25.0359	−0.933683	−0.466842	−	0.884341i	$-0.654608\pi$
$719$	−25.0359	−0.933683	−0.466842	+	0.884341i	$0.654608\pi$
$720$	10.9790	0.409163
$721$	−6.40478	−0.238526
$722$	47.8091	1.77927
$723$	−30.6558	−1.14010
$724$	80.7840	3.00231
$725$	1.20493	0.0447501
$726$	15.0309	0.557848
$727$	−38.6905	−1.43495	−0.717475	−	0.696584i	$-0.754702\pi$
$727$	−38.6905	−1.43495	−0.717475	+	0.696584i	$0.754702\pi$
$728$	2.75753	0.102201
$729$	22.7009	0.840774
$730$	−10.1946	−0.377320
$731$	−13.8710	−0.513037
$732$	−24.2124	−0.894917
$733$	23.5226	0.868829	0.434414	−	0.900713i	$-0.356955\pi$
$733$	23.5226	0.868829	0.434414	+	0.900713i	$0.356955\pi$
$734$	88.5356	3.26791
$735$	8.20147	0.302516
$736$	4.90296	0.180725
$737$	3.06736	0.112988
$738$	33.0565	1.21683
$739$	34.3127	1.26221	0.631107	−	0.775696i	$-0.282601\pi$
$739$	34.3127	1.26221	0.631107	+	0.775696i	$0.282601\pi$
$740$	−7.86233	−0.289025
$741$	0.575109	0.0211272
$742$	2.22880	0.0818219
$743$	4.08680	0.149930	0.0749651	−	0.997186i	$-0.476115\pi$
$743$	4.08680	0.149930	0.0749651	+	0.997186i	$0.476115\pi$
$744$	−8.97575	−0.329067
$745$	−7.50371	−0.274915
$746$	35.9084	1.31470
$747$	10.6172	0.388465
$748$	18.7144	0.684267
$749$	5.09951	0.186332
$750$	3.05645	0.111606
$751$	−38.1437	−1.39188	−0.695942	−	0.718098i	$-0.745013\pi$
$751$	−38.1437	−1.39188	−0.695942	+	0.718098i	$0.745013\pi$
$752$	−57.0152	−2.07913
$753$	19.9839	0.728254
$754$	−3.22566	−0.117472
$755$	−16.3267	−0.594190
$756$	10.2016	0.371030
$757$	35.4737	1.28931	0.644657	−	0.764472i	$-0.277000\pi$
$757$	35.4737	1.28931	0.644657	+	0.764472i	$0.277000\pi$
$758$	14.5834	0.529694
$759$	−2.70661	−0.0982437
$760$	2.86043	0.103759
$761$	−19.2267	−0.696969	−0.348484	−	0.937315i	$-0.613304\pi$
$761$	−19.2267	−0.696969	−0.348484	+	0.937315i	$0.613304\pi$
$762$	−66.5797	−2.41193
$763$	−0.00470123	−0.000170196 0
$764$	−59.0522	−2.13643
$765$	2.64131	0.0954966
$766$	9.48774	0.342806
$767$	−2.36623	−0.0854397
$768$	−35.2408	−1.27164
$769$	−44.9686	−1.62161	−0.810805	−	0.585316i	$-0.800971\pi$
$769$	−44.9686	−1.62161	−0.810805	+	0.585316i	$0.800971\pi$
$770$	−2.61452	−0.0942209
$771$	−25.7418	−0.927070
$772$	83.2472	2.99613
$773$	38.8613	1.39774	0.698872	−	0.715247i	$-0.253686\pi$
$773$	38.8613	1.39774	0.698872	+	0.715247i	$0.253686\pi$
$774$	−32.3681	−1.16345
$775$	1.18806	0.0426763
$776$	−48.6056	−1.74484
$777$	−0.880276	−0.0315797
$778$	32.0172	1.14787
$779$	3.79742	0.136057
$780$	−5.65367	−0.202434
$781$	−35.4676	−1.26913
$782$	3.94334	0.141014
$783$	−6.59630	−0.235733
$784$	−48.1496	−1.71963
$785$	−6.08682	−0.217248
$786$	−56.7980	−2.02592
$787$	16.1443	0.575482	0.287741	−	0.957708i	$-0.407096\pi$
$787$	16.1443	0.575482	0.287741	+	0.957708i	$0.407096\pi$
$788$	−21.9645	−0.782454
$789$	−27.4551	−0.977426
$790$	39.9781	1.42236
$791$	7.17965	0.255279
$792$	24.1389	0.857740
$793$	−4.74236	−0.168406
$794$	68.5227	2.43178
$795$	−2.52589	−0.0895841
$796$	−62.8215	−2.22665
$797$	−50.6496	−1.79410	−0.897051	−	0.441927i	$-0.854295\pi$
$797$	−50.6496	−1.79410	−0.897051	+	0.441927i	$0.854295\pi$
$798$	0.579386	0.0205100
$799$	−13.7166	−0.485260
$800$	−5.36745	−0.189768
$801$	6.29433	0.222399
$802$	−94.5006	−3.33693
$803$	−9.88302	−0.348764
$804$	6.68222	0.235664
$805$	−0.380661	−0.0134165
$806$	−3.18049	−0.112028
$807$	−18.7686	−0.660684
$808$	4.46886	0.157214
$809$	−10.4031	−0.365755	−0.182877	−	0.983136i	$-0.558541\pi$
$809$	−10.4031	−0.365755	−0.182877	+	0.983136i	$0.558541\pi$
$810$	−4.85293	−0.170515
$811$	20.8231	0.731200	0.365600	−	0.930772i	$-0.380864\pi$
$811$	20.8231	0.731200	0.365600	+	0.930772i	$0.380864\pi$
$812$	−2.24540	−0.0787982
$813$	−0.515951	−0.0180952
$814$	−11.0309	−0.386634
$815$	5.04923	0.176867
$816$	14.3803	0.503412
$817$	−3.71835	−0.130088
$818$	−39.4904	−1.38075
$819$	0.682573	0.0238510
$820$	−37.3310	−1.30366
$821$	−23.8105	−0.830992	−0.415496	−	0.909595i	$-0.636392\pi$
$821$	−23.8105	−0.830992	−0.415496	+	0.909595i	$0.636392\pi$
$822$	34.2201	1.19356
$823$	−33.5611	−1.16987	−0.584934	−	0.811081i	$-0.698879\pi$
$823$	−33.5611	−1.16987	−0.584934	+	0.811081i	$0.698879\pi$
$824$	−96.6462	−3.36683
$825$	2.96302	0.103159
$826$	−2.38383	−0.0829440
$827$	−52.5984	−1.82903	−0.914513	−	0.404557i	$-0.867426\pi$
$827$	−52.5984	−1.82903	−0.914513	+	0.404557i	$0.867426\pi$
$828$	6.35816	0.220961
$829$	−41.0159	−1.42454	−0.712270	−	0.701906i	$-0.752333\pi$
$829$	−41.0159	−1.42454	−0.712270	+	0.701906i	$0.752333\pi$
$830$	−17.3527	−0.602321
$831$	9.35546	0.324537
$832$	−0.475989	−0.0165020
$833$	−11.5837	−0.401353
$834$	−20.0567	−0.694508
$835$	13.4814	0.466541
$836$	5.01670	0.173506
$837$	−6.50393	−0.224809
$838$	83.5810	2.88726
$839$	−10.9419	−0.377758	−0.188879	−	0.982000i	$-0.560485\pi$
$839$	−10.9419	−0.377758	−0.188879	+	0.982000i	$0.560485\pi$
$840$	−3.14833	−0.108628
$841$	−27.5481	−0.949936
$842$	−13.2750	−0.457487
$843$	13.6512	0.470174
$844$	6.77750	0.233291
$845$	11.8926	0.409119
$846$	−32.0079	−1.10046
$847$	2.04935	0.0704164
$848$	14.8291	0.509234
$849$	−12.3978	−0.425493
$850$	−4.31692	−0.148069
$851$	−1.60604	−0.0550545
$852$	−77.2658	−2.64708
$853$	−33.6662	−1.15271	−0.576354	−	0.817200i	$-0.695525\pi$
$853$	−33.6662	−1.15271	−0.576354	+	0.817200i	$0.695525\pi$
$854$	−4.77762	−0.163487
$855$	0.708045	0.0242146
$856$	76.9502	2.63010
$857$	−3.66150	−0.125074	−0.0625372	−	0.998043i	$-0.519919\pi$
$857$	−3.66150	−0.125074	−0.0625372	+	0.998043i	$0.519919\pi$
$858$	−7.93216	−0.270800
$859$	39.1044	1.33422	0.667112	−	0.744957i	$-0.267530\pi$
$859$	39.1044	1.33422	0.667112	+	0.744957i	$0.267530\pi$
$860$	36.5536	1.24647
$861$	−4.17963	−0.142441
$862$	24.6990	0.841251
$863$	28.2093	0.960254	0.480127	−	0.877199i	$-0.340591\pi$
$863$	28.2093	0.960254	0.480127	+	0.877199i	$0.340591\pi$
$864$	29.3837	0.999653
$865$	6.61801	0.225019
$866$	−70.7891	−2.40551
$867$	−16.9650	−0.576160
$868$	−2.21396	−0.0751467
$869$	38.7562	1.31471
$870$	3.68281	0.124859
$871$	1.30881	0.0443473
$872$	−0.0709402	−0.00240234
$873$	−12.0314	−0.407200
$874$	1.05708	0.0357561
$875$	0.416723	0.0140878
$876$	−21.5301	−0.727434
$877$	33.6606	1.13664	0.568318	−	0.822809i	$-0.307594\pi$
$877$	33.6606	1.13664	0.568318	+	0.822809i	$0.307594\pi$
$878$	−13.6919	−0.462080
$879$	−21.0012	−0.708354
$880$	−17.3955	−0.586401
$881$	−6.20498	−0.209051	−0.104525	−	0.994522i	$-0.533332\pi$
$881$	−6.20498	−0.209051	−0.104525	+	0.994522i	$0.533332\pi$
$882$	−27.0308	−0.910174
$883$	30.8376	1.03777	0.518884	−	0.854845i	$-0.326348\pi$
$883$	30.8376	1.03777	0.518884	+	0.854845i	$0.326348\pi$
$884$	7.98524	0.268573
$885$	2.70158	0.0908126
$886$	−38.3996	−1.29006
$887$	43.6515	1.46567	0.732837	−	0.680404i	$-0.238196\pi$
$887$	43.6515	1.46567	0.732837	+	0.680404i	$0.238196\pi$
$888$	−13.2831	−0.445752
$889$	−9.07764	−0.304454
$890$	−10.2874	−0.344834
$891$	−4.70460	−0.157610
$892$	85.8522	2.87455
$893$	−3.67697	−0.123045
$894$	−22.9347	−0.767050
$895$	−12.8842	−0.430670
$896$	−4.95301	−0.165469
$897$	−1.15488	−0.0385604
$898$	−29.8593	−0.996416
$899$	1.43153	0.0477442
$900$	−6.96052	−0.232017
$901$	3.56756	0.118853
$902$	−52.3758	−1.74392
$903$	4.09259	0.136193
$904$	108.339	3.60329
$905$	−18.0651	−0.600506
$906$	−49.9017	−1.65787
$907$	−43.1030	−1.43121	−0.715606	−	0.698504i	$-0.753849\pi$
$907$	−43.1030	−1.43121	−0.715606	+	0.698504i	$0.753849\pi$
$908$	−112.270	−3.72580
$909$	1.10618	0.0366896
$910$	−1.11559	−0.0369814
$911$	9.31967	0.308775	0.154387	−	0.988010i	$-0.450660\pi$
$911$	9.31967	0.308775	0.154387	+	0.988010i	$0.450660\pi$
$912$	3.85488	0.127648
$913$	−16.8223	−0.556737
$914$	−45.7288	−1.51257
$915$	5.41445	0.178996
$916$	−5.87961	−0.194268
$917$	−7.74398	−0.255729
$918$	23.6326	0.779993
$919$	−42.2892	−1.39499	−0.697496	−	0.716589i	$-0.745703\pi$
$919$	−42.2892	−1.39499	−0.697496	+	0.716589i	$0.745703\pi$
$920$	−5.74406	−0.189376
$921$	−27.9330	−0.920425
$922$	−33.2777	−1.09594
$923$	−15.1336	−0.498130
$924$	−5.52163	−0.181648
$925$	1.75820	0.0578091
$926$	68.6374	2.25557
$927$	−23.9229	−0.785731
$928$	−6.46741	−0.212303
$929$	52.9540	1.73736	0.868682	−	0.495371i	$-0.164968\pi$
$929$	52.9540	1.73736	0.868682	+	0.495371i	$0.164968\pi$
$930$	3.63124	0.119073
$931$	−3.10521	−0.101769
$932$	−106.227	−3.47958
$933$	37.3139	1.22160
$934$	−10.6649	−0.348965
$935$	−4.18497	−0.136863
$936$	10.2998	0.336660
$937$	−53.4939	−1.74757	−0.873785	−	0.486312i	$-0.838342\pi$
$937$	−53.4939	−1.74757	−0.873785	+	0.486312i	$0.838342\pi$
$938$	1.31854	0.0430519
$939$	29.9625	0.977791
$940$	36.1468	1.17898
$941$	−29.5386	−0.962930	−0.481465	−	0.876465i	$-0.659895\pi$
$941$	−29.5386	−0.962930	−0.481465	+	0.876465i	$0.659895\pi$
$942$	−18.6040	−0.606152
$943$	−7.62564	−0.248325
$944$	−15.8606	−0.516217
$945$	−2.28132	−0.0742113
$946$	51.2851	1.66742
$947$	−22.5541	−0.732910	−0.366455	−	0.930436i	$-0.619429\pi$
$947$	−22.5541	−0.732910	−0.366455	+	0.930436i	$0.619429\pi$
$948$	84.4301	2.74216
$949$	−4.21698	−0.136889
$950$	−1.15722	−0.0375452
$951$	−10.1975	−0.330676
$952$	4.44670	0.144118
$953$	46.1370	1.49452	0.747262	−	0.664530i	$-0.231368\pi$
$953$	46.1370	1.49452	0.747262	+	0.664530i	$0.231368\pi$
$954$	8.32495	0.269530
$955$	13.2054	0.427317
$956$	−90.3550	−2.92229
$957$	3.57024	0.115410
$958$	−46.8652	−1.51415
$959$	4.66565	0.150662
$960$	0.543447	0.0175397
$961$	−29.5885	−0.954468
$962$	−4.70678	−0.151753
$963$	19.0475	0.613798
$964$	−114.102	−3.67497
$965$	−18.6160	−0.599270
$966$	−1.16347	−0.0374340
$967$	15.8404	0.509392	0.254696	−	0.967021i	$-0.418025\pi$
$967$	15.8404	0.509392	0.254696	+	0.967021i	$0.418025\pi$
$968$	30.9241	0.993937
$969$	0.927401	0.0297924
$970$	19.6639	0.631371
$971$	−20.9119	−0.671094	−0.335547	−	0.942024i	$-0.608921\pi$
$971$	−20.9119	−0.671094	−0.335547	+	0.942024i	$0.608921\pi$
$972$	63.1928	2.02691
$973$	−2.73459	−0.0876668
$974$	77.6913	2.48939
$975$	1.26429	0.0404897
$976$	−31.7874	−1.01749
$977$	−36.7965	−1.17722	−0.588612	−	0.808416i	$-0.700325\pi$
$977$	−36.7965	−1.17722	−0.588612	+	0.808416i	$0.700325\pi$
$978$	15.4327	0.493484
$979$	−9.97294	−0.318737
$980$	30.5261	0.975122
$981$	−0.0175599	−0.000560644 0
$982$	14.6486	0.467456
$983$	44.8540	1.43062	0.715310	−	0.698808i	$-0.246286\pi$
$983$	44.8540	1.43062	0.715310	+	0.698808i	$0.246286\pi$
$984$	−63.0694	−2.01058
$985$	4.91177	0.156502
$986$	−5.20160	−0.165653
$987$	4.04705	0.128819
$988$	2.14057	0.0681007
$989$	7.46684	0.237432
$990$	−9.76568	−0.310374
$991$	−16.7936	−0.533467	−0.266733	−	0.963770i	$-0.585944\pi$
$991$	−16.7936	−0.533467	−0.266733	+	0.963770i	$0.585944\pi$
$992$	−6.37684	−0.202465
$993$	32.2074	1.02207
$994$	−15.2462	−0.483579
$995$	14.0483	0.445362
$996$	−36.6473	−1.16121
$997$	−30.7182	−0.972855	−0.486427	−	0.873721i	$-0.661700\pi$
$997$	−30.7182	−0.972855	−0.486427	+	0.873721i	$0.661700\pi$
$998$	11.2983	0.357640
$999$	−9.62510	−0.304525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.12	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.12	✓	140	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54398 q^{2} +1.20144 q^{3} +4.47181 q^{4} -1.00000 q^{5} -3.05645 q^{6} -0.416723 q^{7} -6.28824 q^{8} -1.55653 q^{9} +O(q^{10})\)	\(q-2.54398 q^{2} +1.20144 q^{3} +4.47181 q^{4} -1.00000 q^{5} -3.05645 q^{6} -0.416723 q^{7} -6.28824 q^{8} -1.55653 q^{9} +2.54398 q^{10} +2.46622 q^{11} +5.37264 q^{12} +1.05231 q^{13} +1.06013 q^{14} -1.20144 q^{15} +7.05349 q^{16} +1.69692 q^{17} +3.95978 q^{18} +0.454887 q^{19} -4.47181 q^{20} -0.500670 q^{21} -6.27400 q^{22} -0.913461 q^{23} -7.55497 q^{24} +1.00000 q^{25} -2.67705 q^{26} -5.47442 q^{27} -1.86351 q^{28} +1.20493 q^{29} +3.05645 q^{30} +1.18806 q^{31} -5.36745 q^{32} +2.96302 q^{33} -4.31692 q^{34} +0.416723 q^{35} -6.96052 q^{36} +1.75820 q^{37} -1.15722 q^{38} +1.26429 q^{39} +6.28824 q^{40} +8.34807 q^{41} +1.27369 q^{42} -8.17423 q^{43} +11.0285 q^{44} +1.55653 q^{45} +2.32382 q^{46} -8.08326 q^{47} +8.47438 q^{48} -6.82634 q^{49} -2.54398 q^{50} +2.03875 q^{51} +4.70573 q^{52} +2.10238 q^{53} +13.9268 q^{54} -2.46622 q^{55} +2.62046 q^{56} +0.546521 q^{57} -3.06532 q^{58} -2.24861 q^{59} -5.37264 q^{60} -4.50662 q^{61} -3.02239 q^{62} +0.648643 q^{63} -0.452328 q^{64} -1.05231 q^{65} -7.53786 q^{66} +1.24375 q^{67} +7.58830 q^{68} -1.09747 q^{69} -1.06013 q^{70} -14.3814 q^{71} +9.78784 q^{72} -4.00736 q^{73} -4.47281 q^{74} +1.20144 q^{75} +2.03417 q^{76} -1.02773 q^{77} -3.21633 q^{78} +15.7148 q^{79} -7.05349 q^{80} -1.90762 q^{81} -21.2373 q^{82} -6.82110 q^{83} -2.23890 q^{84} -1.69692 q^{85} +20.7950 q^{86} +1.44766 q^{87} -15.5082 q^{88} -4.04382 q^{89} -3.95978 q^{90} -0.438522 q^{91} -4.08483 q^{92} +1.42739 q^{93} +20.5636 q^{94} -0.454887 q^{95} -6.44869 q^{96} +7.72961 q^{97} +17.3660 q^{98} -3.83875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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