LMFDB - Embedded newform 830.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [830,2,Mod(1,830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(830, 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("830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 830 = 2 \cdot 5 \cdot 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	830.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:	$6.62758336777$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.887108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 13x^{2} + 6x - 9 $ x^5 - 2x^4 - 7x^3 + 13x^2 + 6x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.796077$ of defining polynomial
Character	$\chi$	$=$	830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.796077 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.796077 q^{6} +3.97241 q^{7} +1.00000 q^{8} -2.36626 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.796077 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.796077 q^{6} +3.97241 q^{7} +1.00000 q^{8} -2.36626 q^{9} +1.00000 q^{10} +0.897330 q^{11} +0.796077 q^{12} +2.67286 q^{13} +3.97241 q^{14} +0.796077 q^{15} +1.00000 q^{16} -2.78247 q^{17} -2.36626 q^{18} -2.66581 q^{19} +1.00000 q^{20} +3.16234 q^{21} +0.897330 q^{22} -7.39975 q^{23} +0.796077 q^{24} +1.00000 q^{25} +2.67286 q^{26} -4.27196 q^{27} +3.97241 q^{28} +1.16234 q^{29} +0.796077 q^{30} +6.14179 q^{31} +1.00000 q^{32} +0.714343 q^{33} -2.78247 q^{34} +3.97241 q^{35} -2.36626 q^{36} -2.22210 q^{37} -2.66581 q^{38} +2.12780 q^{39} +1.00000 q^{40} +8.31107 q^{41} +3.16234 q^{42} +2.94349 q^{43} +0.897330 q^{44} -2.36626 q^{45} -7.39975 q^{46} -9.86869 q^{47} +0.796077 q^{48} +8.78001 q^{49} +1.00000 q^{50} -2.21506 q^{51} +2.67286 q^{52} -0.539431 q^{53} -4.27196 q^{54} +0.897330 q^{55} +3.97241 q^{56} -2.12219 q^{57} +1.16234 q^{58} -6.69104 q^{59} +0.796077 q^{60} -7.96299 q^{61} +6.14179 q^{62} -9.39975 q^{63} +1.00000 q^{64} +2.67286 q^{65} +0.714343 q^{66} +9.87573 q^{67} -2.78247 q^{68} -5.89077 q^{69} +3.97241 q^{70} +3.52870 q^{71} -2.36626 q^{72} +0.0209368 q^{73} -2.22210 q^{74} +0.796077 q^{75} -2.66581 q^{76} +3.56456 q^{77} +2.12780 q^{78} -6.76050 q^{79} +1.00000 q^{80} +3.69798 q^{81} +8.31107 q^{82} +1.00000 q^{83} +3.16234 q^{84} -2.78247 q^{85} +2.94349 q^{86} +0.925311 q^{87} +0.897330 q^{88} -0.0551890 q^{89} -2.36626 q^{90} +10.6177 q^{91} -7.39975 q^{92} +4.88933 q^{93} -9.86869 q^{94} -2.66581 q^{95} +0.796077 q^{96} +5.01114 q^{97} +8.78001 q^{98} -2.12332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} + 2 q^{12} + 4 q^{13} + 5 q^{14} + 2 q^{15} + 5 q^{16} - q^{17} + 3 q^{18} + 7 q^{19} + 5 q^{20} - q^{21} + q^{22} + 8 q^{23} + 2 q^{24} + 5 q^{25} + 4 q^{26} - q^{27} + 5 q^{28} - 11 q^{29} + 2 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - q^{34} + 5 q^{35} + 3 q^{36} + 8 q^{37} + 7 q^{38} - 14 q^{39} + 5 q^{40} - 3 q^{41} - q^{42} - 2 q^{43} + q^{44} + 3 q^{45} + 8 q^{46} + 7 q^{47} + 2 q^{48} - 12 q^{49} + 5 q^{50} + 19 q^{51} + 4 q^{52} - 12 q^{53} - q^{54} + q^{55} + 5 q^{56} - 6 q^{57} - 11 q^{58} - 3 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 5 q^{64} + 4 q^{65} - 5 q^{66} + 4 q^{67} - q^{68} - 26 q^{69} + 5 q^{70} + 4 q^{71} + 3 q^{72} - 3 q^{73} + 8 q^{74} + 2 q^{75} + 7 q^{76} - q^{77} - 14 q^{78} - 12 q^{79} + 5 q^{80} - 19 q^{81} - 3 q^{82} + 5 q^{83} - q^{84} - q^{85} - 2 q^{86} + 9 q^{87} + q^{88} - 30 q^{89} + 3 q^{90} + 14 q^{91} + 8 q^{92} - 10 q^{93} + 7 q^{94} + 7 q^{95} + 2 q^{96} - 7 q^{97} - 12 q^{98} - 36 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 + 2 * q^12 + 4 * q^13 + 5 * q^14 + 2 * q^15 + 5 * q^16 - q^17 + 3 * q^18 + 7 * q^19 + 5 * q^20 - q^21 + q^22 + 8 * q^23 + 2 * q^24 + 5 * q^25 + 4 * q^26 - q^27 + 5 * q^28 - 11 * q^29 + 2 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - q^34 + 5 * q^35 + 3 * q^36 + 8 * q^37 + 7 * q^38 - 14 * q^39 + 5 * q^40 - 3 * q^41 - q^42 - 2 * q^43 + q^44 + 3 * q^45 + 8 * q^46 + 7 * q^47 + 2 * q^48 - 12 * q^49 + 5 * q^50 + 19 * q^51 + 4 * q^52 - 12 * q^53 - q^54 + q^55 + 5 * q^56 - 6 * q^57 - 11 * q^58 - 3 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 5 * q^64 + 4 * q^65 - 5 * q^66 + 4 * q^67 - q^68 - 26 * q^69 + 5 * q^70 + 4 * q^71 + 3 * q^72 - 3 * q^73 + 8 * q^74 + 2 * q^75 + 7 * q^76 - q^77 - 14 * q^78 - 12 * q^79 + 5 * q^80 - 19 * q^81 - 3 * q^82 + 5 * q^83 - q^84 - q^85 - 2 * q^86 + 9 * q^87 + q^88 - 30 * q^89 + 3 * q^90 + 14 * q^91 + 8 * q^92 - 10 * q^93 + 7 * q^94 + 7 * q^95 + 2 * q^96 - 7 * q^97 - 12 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.796077	0.459615	0.229807	−	0.973236i	$-0.426190\pi$
$3$	0.796077	0.459615	0.229807	+	0.973236i	$0.426190\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.796077	0.324997
$7$	3.97241	1.50143	0.750714	−	0.660627i	$-0.229710\pi$
$7$	3.97241	1.50143	0.750714	+	0.660627i	$0.229710\pi$
$8$	1.00000	0.353553
$9$	−2.36626	−0.788754
$10$	1.00000	0.316228
$11$	0.897330	0.270555	0.135278	−	0.990808i	$-0.456807\pi$
$11$	0.897330	0.270555	0.135278	+	0.990808i	$0.456807\pi$
$12$	0.796077	0.229807
$13$	2.67286	0.741317	0.370658	−	0.928769i	$-0.379132\pi$
$13$	2.67286	0.741317	0.370658	+	0.928769i	$0.379132\pi$
$14$	3.97241	1.06167
$15$	0.796077	0.205546
$16$	1.00000	0.250000
$17$	−2.78247	−0.674849	−0.337424	−	0.941353i	$-0.609556\pi$
$17$	−2.78247	−0.674849	−0.337424	+	0.941353i	$0.609556\pi$
$18$	−2.36626	−0.557733
$19$	−2.66581	−0.611579	−0.305790	−	0.952099i	$-0.598920\pi$
$19$	−2.66581	−0.611579	−0.305790	+	0.952099i	$0.598920\pi$
$20$	1.00000	0.223607
$21$	3.16234	0.690079
$22$	0.897330	0.191311
$23$	−7.39975	−1.54296	−0.771478	−	0.636257i	$-0.780482\pi$
$23$	−7.39975	−1.54296	−0.771478	+	0.636257i	$0.780482\pi$
$24$	0.796077	0.162498
$25$	1.00000	0.200000
$26$	2.67286	0.524190
$27$	−4.27196	−0.822138
$28$	3.97241	0.750714
$29$	1.16234	0.215841	0.107920	−	0.994160i	$-0.465581\pi$
$29$	1.16234	0.215841	0.107920	+	0.994160i	$0.465581\pi$
$30$	0.796077	0.145343
$31$	6.14179	1.10310	0.551549	−	0.834143i	$-0.314037\pi$
$31$	6.14179	1.10310	0.551549	+	0.834143i	$0.314037\pi$
$32$	1.00000	0.176777
$33$	0.714343	0.124351
$34$	−2.78247	−0.477190
$35$	3.97241	0.671459
$36$	−2.36626	−0.394377
$37$	−2.22210	−0.365312	−0.182656	−	0.983177i	$-0.558469\pi$
$37$	−2.22210	−0.365312	−0.182656	+	0.983177i	$0.558469\pi$
$38$	−2.66581	−0.432452
$39$	2.12780	0.340720
$40$	1.00000	0.158114
$41$	8.31107	1.29797	0.648986	−	0.760801i	$-0.275193\pi$
$41$	8.31107	1.29797	0.648986	+	0.760801i	$0.275193\pi$
$42$	3.16234	0.487959
$43$	2.94349	0.448878	0.224439	−	0.974488i	$-0.427945\pi$
$43$	2.94349	0.448878	0.224439	+	0.974488i	$0.427945\pi$
$44$	0.897330	0.135278
$45$	−2.36626	−0.352742
$46$	−7.39975	−1.09103
$47$	−9.86869	−1.43950	−0.719748	−	0.694236i	$-0.755743\pi$
$47$	−9.86869	−1.43950	−0.719748	+	0.694236i	$0.755743\pi$
$48$	0.796077	0.114904
$49$	8.78001	1.25429
$50$	1.00000	0.141421
$51$	−2.21506	−0.310171
$52$	2.67286	0.370658
$53$	−0.539431	−0.0740965	−0.0370483	−	0.999313i	$-0.511796\pi$
$53$	−0.539431	−0.0740965	−0.0370483	+	0.999313i	$0.511796\pi$
$54$	−4.27196	−0.581339
$55$	0.897330	0.120996
$56$	3.97241	0.530835
$57$	−2.12219	−0.281091
$58$	1.16234	0.152623
$59$	−6.69104	−0.871099	−0.435549	−	0.900165i	$-0.643446\pi$
$59$	−6.69104	−0.871099	−0.435549	+	0.900165i	$0.643446\pi$
$60$	0.796077	0.102773
$61$	−7.96299	−1.01956	−0.509778	−	0.860306i	$-0.670273\pi$
$61$	−7.96299	−1.01956	−0.509778	+	0.860306i	$0.670273\pi$
$62$	6.14179	0.780008
$63$	−9.39975	−1.18426
$64$	1.00000	0.125000
$65$	2.67286	0.331527
$66$	0.714343	0.0879296
$67$	9.87573	1.20651	0.603256	−	0.797547i	$-0.293870\pi$
$67$	9.87573	1.20651	0.603256	+	0.797547i	$0.293870\pi$
$68$	−2.78247	−0.337424
$69$	−5.89077	−0.709165
$70$	3.97241	0.474793
$71$	3.52870	0.418779	0.209390	−	0.977832i	$-0.432852\pi$
$71$	3.52870	0.418779	0.209390	+	0.977832i	$0.432852\pi$
$72$	−2.36626	−0.278867
$73$	0.0209368	0.00245047	0.00122524	−	0.999999i	$-0.499610\pi$
$73$	0.0209368	0.00245047	0.00122524	+	0.999999i	$0.499610\pi$
$74$	−2.22210	−0.258314
$75$	0.796077	0.0919230
$76$	−2.66581	−0.305790
$77$	3.56456	0.406219
$78$	2.12780	0.240926
$79$	−6.76050	−0.760616	−0.380308	−	0.924860i	$-0.624182\pi$
$79$	−6.76050	−0.760616	−0.380308	+	0.924860i	$0.624182\pi$
$80$	1.00000	0.111803
$81$	3.69798	0.410887
$82$	8.31107	0.917804
$83$	1.00000	0.109764
$83$	1.00000	0.109764
$84$	3.16234	0.345039
$85$	−2.78247	−0.301801
$86$	2.94349	0.317405
$87$	0.925311	0.0992037
$88$	0.897330	0.0956557
$89$	−0.0551890	−0.00585002	−0.00292501	−	0.999996i	$-0.500931\pi$
$89$	−0.0551890	−0.00585002	−0.00292501	+	0.999996i	$0.500931\pi$
$90$	−2.36626	−0.249426
$91$	10.6177	1.11303
$92$	−7.39975	−0.771478
$93$	4.88933	0.507000
$94$	−9.86869	−1.01788
$95$	−2.66581	−0.273507
$96$	0.796077	0.0812492
$97$	5.01114	0.508804	0.254402	−	0.967099i	$-0.418121\pi$
$97$	5.01114	0.508804	0.254402	+	0.967099i	$0.418121\pi$
$98$	8.78001	0.886914
$99$	−2.12332	−0.213401
$100$	1.00000	0.100000
$101$	−14.5014	−1.44294	−0.721471	−	0.692444i	$-0.756534\pi$
$101$	−14.5014	−1.44294	−0.721471	+	0.692444i	$0.756534\pi$
$102$	−2.21506	−0.219324
$103$	−1.86421	−0.183686	−0.0918428	−	0.995774i	$-0.529276\pi$
$103$	−1.86421	−0.183686	−0.0918428	+	0.995774i	$0.529276\pi$
$104$	2.67286	0.262095
$105$	3.16234	0.308613
$106$	−0.539431	−0.0523942
$107$	7.73384	0.747659	0.373829	−	0.927497i	$-0.378045\pi$
$107$	7.73384	0.747659	0.373829	+	0.927497i	$0.378045\pi$
$108$	−4.27196	−0.411069
$109$	−10.0321	−0.960898	−0.480449	−	0.877023i	$-0.659526\pi$
$109$	−10.0321	−0.960898	−0.480449	+	0.877023i	$0.659526\pi$
$110$	0.897330	0.0855571
$111$	−1.76897	−0.167903
$112$	3.97241	0.375357
$113$	−0.604341	−0.0568516	−0.0284258	−	0.999596i	$-0.509049\pi$
$113$	−0.604341	−0.0568516	−0.0284258	+	0.999596i	$0.509049\pi$
$114$	−2.12219	−0.198761
$115$	−7.39975	−0.690031
$116$	1.16234	0.107920
$117$	−6.32468	−0.584717
$118$	−6.69104	−0.615960
$119$	−11.0531	−1.01324
$120$	0.796077	0.0726715
$121$	−10.1948	−0.926800
$122$	−7.96299	−0.720935
$123$	6.61625	0.596567
$124$	6.14179	0.551549
$125$	1.00000	0.0894427
$126$	−9.39975	−0.837397
$127$	6.95137	0.616834	0.308417	−	0.951251i	$-0.400201\pi$
$127$	6.95137	0.616834	0.308417	+	0.951251i	$0.400201\pi$
$128$	1.00000	0.0883883
$129$	2.34324	0.206311
$130$	2.67286	0.234425
$131$	−12.1323	−1.06000	−0.530001	−	0.847997i	$-0.677808\pi$
$131$	−12.1323	−1.06000	−0.530001	+	0.847997i	$0.677808\pi$
$132$	0.714343	0.0621756
$133$	−10.5897	−0.918242
$134$	9.87573	0.853133
$135$	−4.27196	−0.367671
$136$	−2.78247	−0.238595
$137$	−6.24294	−0.533371	−0.266685	−	0.963784i	$-0.585928\pi$
$137$	−6.24294	−0.533371	−0.266685	+	0.963784i	$0.585928\pi$
$138$	−5.89077	−0.501456
$139$	−6.92989	−0.587785	−0.293893	−	0.955838i	$-0.594951\pi$
$139$	−6.92989	−0.587785	−0.293893	+	0.955838i	$0.594951\pi$
$140$	3.97241	0.335730
$141$	−7.85623	−0.661614
$142$	3.52870	0.296122
$143$	2.39843	0.200567
$144$	−2.36626	−0.197189
$145$	1.16234	0.0965270
$146$	0.0209368	0.00173274
$147$	6.98956	0.576489
$148$	−2.22210	−0.182656
$149$	−15.2499	−1.24932	−0.624660	−	0.780897i	$-0.714762\pi$
$149$	−15.2499	−1.24932	−0.624660	+	0.780897i	$0.714762\pi$
$150$	0.796077	0.0649994
$151$	15.4967	1.26110	0.630552	−	0.776147i	$-0.282829\pi$
$151$	15.4967	1.26110	0.630552	+	0.776147i	$0.282829\pi$
$152$	−2.66581	−0.216226
$153$	6.58406	0.532290
$154$	3.56456	0.287240
$155$	6.14179	0.493320
$156$	2.12780	0.170360
$157$	0.0719152	0.00573946	0.00286973	−	0.999996i	$-0.499087\pi$
$157$	0.0719152	0.00573946	0.00286973	+	0.999996i	$0.499087\pi$
$158$	−6.76050	−0.537837
$159$	−0.429428	−0.0340559
$160$	1.00000	0.0790569
$161$	−29.3948	−2.31664
$162$	3.69798	0.290541
$163$	−5.83091	−0.456712	−0.228356	−	0.973578i	$-0.573335\pi$
$163$	−5.83091	−0.456712	−0.228356	+	0.973578i	$0.573335\pi$
$164$	8.31107	0.648986
$165$	0.714343	0.0556116
$166$	1.00000	0.0776151
$167$	9.03075	0.698821	0.349410	−	0.936970i	$-0.386382\pi$
$167$	9.03075	0.698821	0.349410	+	0.936970i	$0.386382\pi$
$168$	3.16234	0.243980
$169$	−5.85584	−0.450449
$170$	−2.78247	−0.213406
$171$	6.30801	0.482386
$172$	2.94349	0.224439
$173$	3.98913	0.303288	0.151644	−	0.988435i	$-0.451543\pi$
$173$	3.98913	0.303288	0.151644	+	0.988435i	$0.451543\pi$
$174$	0.925311	0.0701476
$175$	3.97241	0.300286
$176$	0.897330	0.0676388
$177$	−5.32658	−0.400370
$178$	−0.0551890	−0.00413659
$179$	14.5002	1.08380	0.541900	−	0.840443i	$-0.317705\pi$
$179$	14.5002	1.08380	0.541900	+	0.840443i	$0.317705\pi$
$180$	−2.36626	−0.176371
$181$	14.9978	1.11478	0.557390	−	0.830251i	$-0.311803\pi$
$181$	14.9978	1.11478	0.557390	+	0.830251i	$0.311803\pi$
$182$	10.6177	0.787034
$183$	−6.33915	−0.468604
$184$	−7.39975	−0.545517
$185$	−2.22210	−0.163372
$186$	4.88933	0.358503
$187$	−2.49680	−0.182584
$188$	−9.86869	−0.719748
$189$	−16.9699	−1.23438
$190$	−2.66581	−0.193398
$191$	14.3180	1.03601	0.518007	−	0.855376i	$-0.326674\pi$
$191$	14.3180	1.03601	0.518007	+	0.855376i	$0.326674\pi$
$192$	0.796077	0.0574519
$193$	−10.1222	−0.728610	−0.364305	−	0.931280i	$-0.618693\pi$
$193$	−10.1222	−0.728610	−0.364305	+	0.931280i	$0.618693\pi$
$194$	5.01114	0.359779
$195$	2.12780	0.152375
$196$	8.78001	0.627143
$197$	−5.77316	−0.411320	−0.205660	−	0.978623i	$-0.565934\pi$
$197$	−5.77316	−0.411320	−0.205660	+	0.978623i	$0.565934\pi$
$198$	−2.12332	−0.150898
$199$	8.64251	0.612651	0.306325	−	0.951927i	$-0.400900\pi$
$199$	8.64251	0.612651	0.306325	+	0.951927i	$0.400900\pi$
$200$	1.00000	0.0707107
$201$	7.86184	0.554531
$202$	−14.5014	−1.02031
$203$	4.61728	0.324070
$204$	−2.21506	−0.155085
$205$	8.31107	0.580471
$206$	−1.86421	−0.129885
$207$	17.5098	1.21701
$208$	2.67286	0.185329
$209$	−2.39211	−0.165466
$210$	3.16234	0.218222
$211$	−2.25092	−0.154960	−0.0774799	−	0.996994i	$-0.524687\pi$
$211$	−2.25092	−0.154960	−0.0774799	+	0.996994i	$0.524687\pi$
$212$	−0.539431	−0.0370483
$213$	2.80911	0.192477
$214$	7.73384	0.528675
$215$	2.94349	0.200744
$216$	−4.27196	−0.290670
$217$	24.3977	1.65622
$218$	−10.0321	−0.679458
$219$	0.0166673	0.00112627
$220$	0.897330	0.0604980
$221$	−7.43715	−0.500277
$222$	−1.76897	−0.118725
$223$	−8.20184	−0.549236	−0.274618	−	0.961553i	$-0.588551\pi$
$223$	−8.20184	−0.549236	−0.274618	+	0.961553i	$0.588551\pi$
$224$	3.97241	0.265418
$225$	−2.36626	−0.157751
$226$	−0.604341	−0.0402001
$227$	10.6705	0.708225	0.354113	−	0.935203i	$-0.384783\pi$
$227$	10.6705	0.708225	0.354113	+	0.935203i	$0.384783\pi$
$228$	−2.12219	−0.140545
$229$	−13.4856	−0.891151	−0.445575	−	0.895244i	$-0.647001\pi$
$229$	−13.4856	−0.891151	−0.445575	+	0.895244i	$0.647001\pi$
$230$	−7.39975	−0.487925
$231$	2.83766	0.186704
$232$	1.16234	0.0763113
$233$	−23.4533	−1.53647	−0.768237	−	0.640165i	$-0.778866\pi$
$233$	−23.4533	−1.53647	−0.768237	+	0.640165i	$0.778866\pi$
$234$	−6.32468	−0.413457
$235$	−9.86869	−0.643762
$236$	−6.69104	−0.435549
$237$	−5.38188	−0.349591
$238$	−11.0531	−0.716467
$239$	−26.5446	−1.71703	−0.858514	−	0.512790i	$-0.828612\pi$
$239$	−26.5446	−1.71703	−0.858514	+	0.512790i	$0.828612\pi$
$240$	0.796077	0.0513865
$241$	−24.6491	−1.58779	−0.793893	−	0.608057i	$-0.791949\pi$
$241$	−24.6491	−1.58779	−0.793893	+	0.608057i	$0.791949\pi$
$242$	−10.1948	−0.655346
$243$	15.7597	1.01099
$244$	−7.96299	−0.509778
$245$	8.78001	0.560934
$246$	6.61625	0.421837
$247$	−7.12533	−0.453374
$248$	6.14179	0.390004
$249$	0.796077	0.0504493
$250$	1.00000	0.0632456
$251$	7.11383	0.449021	0.224510	−	0.974472i	$-0.427922\pi$
$251$	7.11383	0.449021	0.224510	+	0.974472i	$0.427922\pi$
$252$	−9.39975	−0.592129
$253$	−6.64002	−0.417454
$254$	6.95137	0.436168
$255$	−2.21506	−0.138712
$256$	1.00000	0.0625000
$257$	2.65848	0.165831	0.0829157	−	0.996557i	$-0.473577\pi$
$257$	2.65848	0.165831	0.0829157	+	0.996557i	$0.473577\pi$
$258$	2.34324	0.145884
$259$	−8.82710	−0.548489
$260$	2.67286	0.165763
$261$	−2.75040	−0.170245
$262$	−12.1323	−0.749535
$263$	−25.7919	−1.59040	−0.795198	−	0.606350i	$-0.792633\pi$
$263$	−25.7919	−1.59040	−0.795198	+	0.606350i	$0.792633\pi$
$264$	0.714343	0.0439648
$265$	−0.539431	−0.0331370
$266$	−10.5897	−0.649295
$267$	−0.0439347	−0.00268876
$268$	9.87573	0.603256
$269$	7.93305	0.483686	0.241843	−	0.970315i	$-0.422248\pi$
$269$	7.93305	0.483686	0.241843	+	0.970315i	$0.422248\pi$
$270$	−4.27196	−0.259983
$271$	31.8540	1.93499	0.967495	−	0.252890i	$-0.0813812\pi$
$271$	31.8540	1.93499	0.967495	+	0.252890i	$0.0813812\pi$
$272$	−2.78247	−0.168712
$273$	8.45248	0.511567
$274$	−6.24294	−0.377150
$275$	0.897330	0.0541110
$276$	−5.89077	−0.354583
$277$	30.4696	1.83074	0.915371	−	0.402612i	$-0.131898\pi$
$277$	30.4696	1.83074	0.915371	+	0.402612i	$0.131898\pi$
$278$	−6.92989	−0.415627
$279$	−14.5331	−0.870073
$280$	3.97241	0.237397
$281$	26.5024	1.58100	0.790499	−	0.612463i	$-0.209821\pi$
$281$	26.5024	1.58100	0.790499	+	0.612463i	$0.209821\pi$
$282$	−7.85623	−0.467832
$283$	17.3016	1.02847	0.514237	−	0.857648i	$-0.328075\pi$
$283$	17.3016	1.02847	0.514237	+	0.857648i	$0.328075\pi$
$284$	3.52870	0.209390
$285$	−2.12219	−0.125708
$286$	2.39843	0.141822
$287$	33.0150	1.94881
$288$	−2.36626	−0.139433
$289$	−9.25785	−0.544579
$290$	1.16234	0.0682549
$291$	3.98925	0.233854
$292$	0.0209368	0.00122524
$293$	26.1467	1.52750	0.763752	−	0.645510i	$-0.223355\pi$
$293$	26.1467	1.52750	0.763752	+	0.645510i	$0.223355\pi$
$294$	6.98956	0.407639
$295$	−6.69104	−0.389567
$296$	−2.22210	−0.129157
$297$	−3.83335	−0.222434
$298$	−15.2499	−0.883402
$299$	−19.7785	−1.14382
$300$	0.796077	0.0459615
$301$	11.6927	0.673958
$302$	15.4967	0.891735
$303$	−11.5442	−0.663198
$304$	−2.66581	−0.152895
$305$	−7.96299	−0.455960
$306$	6.58406	0.376386
$307$	−21.2080	−1.21041	−0.605204	−	0.796071i	$-0.706908\pi$
$307$	−21.2080	−1.21041	−0.605204	+	0.796071i	$0.706908\pi$
$308$	3.56456	0.203110
$309$	−1.48405	−0.0844247
$310$	6.14179	0.348830
$311$	10.4805	0.594292	0.297146	−	0.954832i	$-0.403965\pi$
$311$	10.4805	0.594292	0.297146	+	0.954832i	$0.403965\pi$
$312$	2.12780	0.120463
$313$	−11.2611	−0.636514	−0.318257	−	0.948004i	$-0.603098\pi$
$313$	−11.2611	−0.636514	−0.318257	+	0.948004i	$0.603098\pi$
$314$	0.0719152	0.00405841
$315$	−9.39975	−0.529616
$316$	−6.76050	−0.380308
$317$	29.3462	1.64824	0.824122	−	0.566412i	$-0.191669\pi$
$317$	29.3462	1.64824	0.824122	+	0.566412i	$0.191669\pi$
$318$	−0.429428	−0.0240811
$319$	1.04300	0.0583969
$320$	1.00000	0.0559017
$321$	6.15673	0.343635
$322$	−29.3948	−1.63811
$323$	7.41755	0.412723
$324$	3.69798	0.205444
$325$	2.67286	0.148263
$326$	−5.83091	−0.322944
$327$	−7.98630	−0.441643
$328$	8.31107	0.458902
$329$	−39.2024	−2.16130
$330$	0.714343	0.0393233
$331$	23.2125	1.27587	0.637937	−	0.770088i	$-0.279788\pi$
$331$	23.2125	1.27587	0.637937	+	0.770088i	$0.279788\pi$
$332$	1.00000	0.0548821
$333$	5.25808	0.288141
$334$	9.03075	0.494141
$335$	9.87573	0.539569
$336$	3.16234	0.172520
$337$	13.6467	0.743382	0.371691	−	0.928357i	$-0.378778\pi$
$337$	13.6467	0.743382	0.371691	+	0.928357i	$0.378778\pi$
$338$	−5.85584	−0.318516
$339$	−0.481101	−0.0261298
$340$	−2.78247	−0.150901
$341$	5.51121	0.298449
$342$	6.30801	0.341098
$343$	7.07090	0.381793
$344$	2.94349	0.158702
$345$	−5.89077	−0.317148
$346$	3.98913	0.214457
$347$	−1.17945	−0.0633162	−0.0316581	−	0.999499i	$-0.510079\pi$
$347$	−1.17945	−0.0633162	−0.0316581	+	0.999499i	$0.510079\pi$
$348$	0.925311	0.0496019
$349$	16.2886	0.871910	0.435955	−	0.899968i	$-0.356411\pi$
$349$	16.2886	0.871910	0.435955	+	0.899968i	$0.356411\pi$
$350$	3.97241	0.212334
$351$	−11.4183	−0.609465
$352$	0.897330	0.0478278
$353$	6.66964	0.354989	0.177494	−	0.984122i	$-0.443201\pi$
$353$	6.66964	0.354989	0.177494	+	0.984122i	$0.443201\pi$
$354$	−5.32658	−0.283104
$355$	3.52870	0.187284
$356$	−0.0551890	−0.00292501
$357$	−8.79912	−0.465699
$358$	14.5002	0.766362
$359$	14.1881	0.748820	0.374410	−	0.927263i	$-0.377845\pi$
$359$	14.1881	0.748820	0.374410	+	0.927263i	$0.377845\pi$
$360$	−2.36626	−0.124713
$361$	−11.8934	−0.625971
$362$	14.9978	0.788268
$363$	−8.11584	−0.425971
$364$	10.6177	0.556517
$365$	0.0209368	0.00109588
$366$	−6.33915	−0.331353
$367$	11.2212	0.585742	0.292871	−	0.956152i	$-0.405389\pi$
$367$	11.2212	0.585742	0.292871	+	0.956152i	$0.405389\pi$
$368$	−7.39975	−0.385739
$369$	−19.6662	−1.02378
$370$	−2.22210	−0.115522
$371$	−2.14284	−0.111251
$372$	4.88933	0.253500
$373$	4.50309	0.233161	0.116581	−	0.993181i	$-0.462807\pi$
$373$	4.50309	0.233161	0.116581	+	0.993181i	$0.462807\pi$
$374$	−2.49680	−0.129106
$375$	0.796077	0.0411092
$376$	−9.86869	−0.508939
$377$	3.10676	0.160006
$378$	−16.9699	−0.872839
$379$	33.5547	1.72359	0.861794	−	0.507259i	$-0.169341\pi$
$379$	33.5547	1.72359	0.861794	+	0.507259i	$0.169341\pi$
$380$	−2.66581	−0.136753
$381$	5.53382	0.283506
$382$	14.3180	0.732573
$383$	6.65012	0.339805	0.169903	−	0.985461i	$-0.445655\pi$
$383$	6.65012	0.339805	0.169903	+	0.985461i	$0.445655\pi$
$384$	0.796077	0.0406246
$385$	3.56456	0.181667
$386$	−10.1222	−0.515205
$387$	−6.96507	−0.354055
$388$	5.01114	0.254402
$389$	−5.94359	−0.301352	−0.150676	−	0.988583i	$-0.548145\pi$
$389$	−5.94359	−0.301352	−0.150676	+	0.988583i	$0.548145\pi$
$390$	2.12780	0.107745
$391$	20.5896	1.04126
$392$	8.78001	0.443457
$393$	−9.65822	−0.487193
$394$	−5.77316	−0.290847
$395$	−6.76050	−0.340158
$396$	−2.12332	−0.106701
$397$	4.44866	0.223272	0.111636	−	0.993749i	$-0.464391\pi$
$397$	4.44866	0.223272	0.111636	+	0.993749i	$0.464391\pi$
$398$	8.64251	0.433210
$399$	−8.43020	−0.422038
$400$	1.00000	0.0500000
$401$	−28.8690	−1.44165	−0.720825	−	0.693117i	$-0.756237\pi$
$401$	−28.8690	−1.44165	−0.720825	+	0.693117i	$0.756237\pi$
$402$	7.86184	0.392113
$403$	16.4161	0.817745
$404$	−14.5014	−0.721471
$405$	3.69798	0.183754
$406$	4.61728	0.229152
$407$	−1.99396	−0.0988370
$408$	−2.21506	−0.109662
$409$	0.880179	0.0435221	0.0217610	−	0.999763i	$-0.493073\pi$
$409$	0.880179	0.0435221	0.0217610	+	0.999763i	$0.493073\pi$
$410$	8.31107	0.410455
$411$	−4.96986	−0.245145
$412$	−1.86421	−0.0918428
$413$	−26.5795	−1.30789
$414$	17.5098	0.860558
$415$	1.00000	0.0490881
$416$	2.67286	0.131048
$417$	−5.51672	−0.270155
$418$	−2.39211	−0.117002
$419$	30.9874	1.51383	0.756916	−	0.653512i	$-0.226705\pi$
$419$	30.9874	1.51383	0.756916	+	0.653512i	$0.226705\pi$
$420$	3.16234	0.154306
$421$	−18.4984	−0.901557	−0.450779	−	0.892636i	$-0.648854\pi$
$421$	−18.4984	−0.901557	−0.450779	+	0.892636i	$0.648854\pi$
$422$	−2.25092	−0.109573
$423$	23.3519	1.13541
$424$	−0.539431	−0.0261971
$425$	−2.78247	−0.134970
$426$	2.80911	0.136102
$427$	−31.6322	−1.53079
$428$	7.73384	0.373829
$429$	1.90934	0.0921836
$430$	2.94349	0.141948
$431$	−32.0779	−1.54514	−0.772569	−	0.634931i	$-0.781028\pi$
$431$	−32.0779	−1.54514	−0.772569	+	0.634931i	$0.781028\pi$
$432$	−4.27196	−0.205535
$433$	37.2469	1.78997	0.894987	−	0.446093i	$-0.147185\pi$
$433$	37.2469	1.78997	0.894987	+	0.446093i	$0.147185\pi$
$434$	24.3977	1.17113
$435$	0.925311	0.0443652
$436$	−10.0321	−0.480449
$437$	19.7263	0.943639
$438$	0.0166673	0.000796395 0
$439$	17.3568	0.828395	0.414198	−	0.910187i	$-0.364062\pi$
$439$	17.3568	0.828395	0.414198	+	0.910187i	$0.364062\pi$
$440$	0.897330	0.0427785
$441$	−20.7758	−0.989324
$442$	−7.43715	−0.353749
$443$	28.4154	1.35005	0.675027	−	0.737793i	$-0.264132\pi$
$443$	28.4154	1.35005	0.675027	+	0.737793i	$0.264132\pi$
$444$	−1.76897	−0.0839514
$445$	−0.0551890	−0.00261621
$446$	−8.20184	−0.388369
$447$	−12.1401	−0.574206
$448$	3.97241	0.187679
$449$	−14.8296	−0.699851	−0.349926	−	0.936777i	$-0.613793\pi$
$449$	−14.8296	−0.699851	−0.349926	+	0.936777i	$0.613793\pi$
$450$	−2.36626	−0.111547
$451$	7.45778	0.351173
$452$	−0.604341	−0.0284258
$453$	12.3366	0.579622
$454$	10.6705	0.500791
$455$	10.6177	0.497764
$456$	−2.12219	−0.0993807
$457$	28.5209	1.33415	0.667075	−	0.744990i	$-0.267546\pi$
$457$	28.5209	1.33415	0.667075	+	0.744990i	$0.267546\pi$
$458$	−13.4856	−0.630139
$459$	11.8866	0.554819
$460$	−7.39975	−0.345015
$461$	−25.0697	−1.16761	−0.583805	−	0.811894i	$-0.698437\pi$
$461$	−25.0697	−1.16761	−0.583805	+	0.811894i	$0.698437\pi$
$462$	2.83766	0.132020
$463$	26.8147	1.24618	0.623092	−	0.782148i	$-0.285876\pi$
$463$	26.8147	1.24618	0.623092	+	0.782148i	$0.285876\pi$
$464$	1.16234	0.0539602
$465$	4.88933	0.226737
$466$	−23.4533	−1.08645
$467$	−5.24038	−0.242496	−0.121248	−	0.992622i	$-0.538690\pi$
$467$	−5.24038	−0.242496	−0.121248	+	0.992622i	$0.538690\pi$
$468$	−6.32468	−0.292358
$469$	39.2304	1.81149
$470$	−9.86869	−0.455209
$471$	0.0572500	0.00263794
$472$	−6.69104	−0.307980
$473$	2.64128	0.121446
$474$	−5.38188	−0.247198
$475$	−2.66581	−0.122316
$476$	−11.0531	−0.506618
$477$	1.27643	0.0584439
$478$	−26.5446	−1.21412
$479$	−30.5482	−1.39579	−0.697893	−	0.716203i	$-0.745879\pi$
$479$	−30.5482	−1.39579	−0.697893	+	0.716203i	$0.745879\pi$
$480$	0.796077	0.0363358
$481$	−5.93936	−0.270812
$482$	−24.6491	−1.12273
$483$	−23.4005	−1.06476
$484$	−10.1948	−0.463400
$485$	5.01114	0.227544
$486$	15.7597	0.714876
$487$	27.2045	1.23275	0.616377	−	0.787451i	$-0.288600\pi$
$487$	27.2045	1.23275	0.616377	+	0.787451i	$0.288600\pi$
$488$	−7.96299	−0.360468
$489$	−4.64185	−0.209912
$490$	8.78001	0.396640
$491$	−9.85466	−0.444734	−0.222367	−	0.974963i	$-0.571378\pi$
$491$	−9.85466	−0.444734	−0.222367	+	0.974963i	$0.571378\pi$
$492$	6.61625	0.298284
$493$	−3.23418	−0.145660
$494$	−7.12533	−0.320584
$495$	−2.12332	−0.0954360
$496$	6.14179	0.275774
$497$	14.0174	0.628767
$498$	0.796077	0.0356730
$499$	−23.3802	−1.04664	−0.523320	−	0.852136i	$-0.675307\pi$
$499$	−23.3802	−1.04664	−0.523320	+	0.852136i	$0.675307\pi$
$500$	1.00000	0.0447214
$501$	7.18917	0.321189
$502$	7.11383	0.317506
$503$	18.7826	0.837473	0.418737	−	0.908108i	$-0.362473\pi$
$503$	18.7826	0.837473	0.418737	+	0.908108i	$0.362473\pi$
$504$	−9.39975	−0.418698
$505$	−14.5014	−0.645303
$506$	−6.64002	−0.295185
$507$	−4.66170	−0.207033
$508$	6.95137	0.308417
$509$	−18.1849	−0.806030	−0.403015	−	0.915193i	$-0.632038\pi$
$509$	−18.1849	−0.806030	−0.403015	+	0.915193i	$0.632038\pi$
$510$	−2.21506	−0.0980845
$511$	0.0831696	0.00367921
$512$	1.00000	0.0441942
$513$	11.3882	0.502803
$514$	2.65848	0.117260
$515$	−1.86421	−0.0821467
$516$	2.34324	0.103156
$517$	−8.85547	−0.389463
$518$	−8.82710	−0.387841
$519$	3.17565	0.139396
$520$	2.67286	0.117212
$521$	−3.93911	−0.172576	−0.0862878	−	0.996270i	$-0.527500\pi$
$521$	−3.93911	−0.172576	−0.0862878	+	0.996270i	$0.527500\pi$
$522$	−2.75040	−0.120382
$523$	23.8084	1.04107	0.520535	−	0.853840i	$-0.325732\pi$
$523$	23.8084	1.04107	0.520535	+	0.853840i	$0.325732\pi$
$524$	−12.1323	−0.530001
$525$	3.16234	0.138016
$526$	−25.7919	−1.12458
$527$	−17.0894	−0.744424
$528$	0.714343	0.0310878
$529$	31.7563	1.38071
$530$	−0.539431	−0.0234314
$531$	15.8327	0.687083
$532$	−10.5897	−0.459121
$533$	22.2143	0.962208
$534$	−0.0439347	−0.00190124
$535$	7.73384	0.334363
$536$	9.87573	0.426567
$537$	11.5433	0.498130
$538$	7.93305	0.342018
$539$	7.87856	0.339354
$540$	−4.27196	−0.183836
$541$	36.8602	1.58474	0.792372	−	0.610038i	$-0.208846\pi$
$541$	36.8602	1.58474	0.792372	+	0.610038i	$0.208846\pi$
$542$	31.8540	1.36824
$543$	11.9394	0.512369
$544$	−2.78247	−0.119298
$545$	−10.0321	−0.429727
$546$	8.45248	0.361733
$547$	−24.4346	−1.04475	−0.522373	−	0.852717i	$-0.674953\pi$
$547$	−24.4346	−1.04475	−0.522373	+	0.852717i	$0.674953\pi$
$548$	−6.24294	−0.266685
$549$	18.8425	0.804179
$550$	0.897330	0.0382623
$551$	−3.09858	−0.132004
$552$	−5.89077	−0.250728
$553$	−26.8555	−1.14201
$554$	30.4696	1.29453
$555$	−1.76897	−0.0750884
$556$	−6.92989	−0.293893
$557$	−1.78369	−0.0755776	−0.0377888	−	0.999286i	$-0.512031\pi$
$557$	−1.78369	−0.0755776	−0.0377888	+	0.999286i	$0.512031\pi$
$558$	−14.5331	−0.615234
$559$	7.86753	0.332761
$560$	3.97241	0.167865
$561$	−1.98764	−0.0839182
$562$	26.5024	1.11793
$563$	42.8152	1.80445	0.902223	−	0.431270i	$-0.141934\pi$
$563$	42.8152	1.80445	0.902223	+	0.431270i	$0.141934\pi$
$564$	−7.85623	−0.330807
$565$	−0.604341	−0.0254248
$566$	17.3016	0.727241
$567$	14.6899	0.616917
$568$	3.52870	0.148061
$569$	33.8845	1.42051	0.710256	−	0.703944i	$-0.248579\pi$
$569$	33.8845	1.42051	0.710256	+	0.703944i	$0.248579\pi$
$570$	−2.12219	−0.0888888
$571$	−2.99853	−0.125484	−0.0627422	−	0.998030i	$-0.519985\pi$
$571$	−2.99853	−0.125484	−0.0627422	+	0.998030i	$0.519985\pi$
$572$	2.39843	0.100284
$573$	11.3982	0.476168
$574$	33.0150	1.37802
$575$	−7.39975	−0.308591
$576$	−2.36626	−0.0985943
$577$	−20.7612	−0.864302	−0.432151	−	0.901801i	$-0.642245\pi$
$577$	−20.7612	−0.864302	−0.432151	+	0.901801i	$0.642245\pi$
$578$	−9.25785	−0.385076
$579$	−8.05802	−0.334880
$580$	1.16234	0.0482635
$581$	3.97241	0.164803
$582$	3.98925	0.165360
$583$	−0.484048	−0.0200472
$584$	0.0209368	0.000866372 0
$585$	−6.32468	−0.261493
$586$	26.1467	1.08011
$587$	−15.3343	−0.632913	−0.316456	−	0.948607i	$-0.602493\pi$
$587$	−15.3343	−0.632913	−0.316456	+	0.948607i	$0.602493\pi$
$588$	6.98956	0.288244
$589$	−16.3729	−0.674632
$590$	−6.69104	−0.275466
$591$	−4.59587	−0.189049
$592$	−2.22210	−0.0913279
$593$	38.2011	1.56873	0.784366	−	0.620299i	$-0.212989\pi$
$593$	38.2011	1.56873	0.784366	+	0.620299i	$0.212989\pi$
$594$	−3.83335	−0.157284
$595$	−11.0531	−0.453133
$596$	−15.2499	−0.624660
$597$	6.88010	0.281584
$598$	−19.7785	−0.808802
$599$	−21.6235	−0.883511	−0.441755	−	0.897136i	$-0.645644\pi$
$599$	−21.6235	−0.883511	−0.441755	+	0.897136i	$0.645644\pi$
$600$	0.796077	0.0324997
$601$	−2.77830	−0.113329	−0.0566646	−	0.998393i	$-0.518047\pi$
$601$	−2.77830	−0.113329	−0.0566646	+	0.998393i	$0.518047\pi$
$602$	11.6927	0.476561
$603$	−23.3686	−0.951641
$604$	15.4967	0.630552
$605$	−10.1948	−0.414478
$606$	−11.5442	−0.468952
$607$	29.5039	1.19753	0.598763	−	0.800927i	$-0.295659\pi$
$607$	29.5039	1.19753	0.598763	+	0.800927i	$0.295659\pi$
$608$	−2.66581	−0.108113
$609$	3.67571	0.148947
$610$	−7.96299	−0.322412
$611$	−26.3776	−1.06712
$612$	6.58406	0.266145
$613$	−22.3506	−0.902731	−0.451365	−	0.892339i	$-0.649063\pi$
$613$	−22.3506	−0.902731	−0.451365	+	0.892339i	$0.649063\pi$
$614$	−21.2080	−0.855887
$615$	6.61625	0.266793
$616$	3.56456	0.143620
$617$	−28.7449	−1.15722	−0.578612	−	0.815603i	$-0.696406\pi$
$617$	−28.7449	−1.15722	−0.578612	+	0.815603i	$0.696406\pi$
$618$	−1.48405	−0.0596973
$619$	38.8823	1.56281	0.781406	−	0.624023i	$-0.214503\pi$
$619$	38.8823	1.56281	0.781406	+	0.624023i	$0.214503\pi$
$620$	6.14179	0.246660
$621$	31.6114	1.26852
$622$	10.4805	0.420228
$623$	−0.219233	−0.00878339
$624$	2.12780	0.0851801
$625$	1.00000	0.0400000
$626$	−11.2611	−0.450084
$627$	−1.90430	−0.0760506
$628$	0.0719152	0.00286973
$629$	6.18294	0.246530
$630$	−9.39975	−0.374495
$631$	8.92474	0.355288	0.177644	−	0.984095i	$-0.443152\pi$
$631$	8.92474	0.355288	0.177644	+	0.984095i	$0.443152\pi$
$632$	−6.76050	−0.268918
$633$	−1.79191	−0.0712219
$634$	29.3462	1.16548
$635$	6.95137	0.275857
$636$	−0.429428	−0.0170279
$637$	23.4677	0.929824
$638$	1.04300	0.0412928
$639$	−8.34982	−0.330314
$640$	1.00000	0.0395285
$641$	−25.6678	−1.01382	−0.506908	−	0.862000i	$-0.669212\pi$
$641$	−25.6678	−1.01382	−0.506908	+	0.862000i	$0.669212\pi$
$642$	6.15673	0.242987
$643$	−39.8015	−1.56962	−0.784809	−	0.619737i	$-0.787239\pi$
$643$	−39.8015	−1.56962	−0.784809	+	0.619737i	$0.787239\pi$
$644$	−29.3948	−1.15832
$645$	2.34324	0.0922652
$646$	7.41755	0.291840
$647$	−31.9330	−1.25542	−0.627708	−	0.778449i	$-0.716007\pi$
$647$	−31.9330	−1.25542	−0.627708	+	0.778449i	$0.716007\pi$
$648$	3.69798	0.145271
$649$	−6.00407	−0.235680
$650$	2.67286	0.104838
$651$	19.4224	0.761224
$652$	−5.83091	−0.228356
$653$	36.9926	1.44763	0.723816	−	0.689993i	$-0.242386\pi$
$653$	36.9926	1.44763	0.723816	+	0.689993i	$0.242386\pi$
$654$	−7.98630	−0.312289
$655$	−12.1323	−0.474047
$656$	8.31107	0.324493
$657$	−0.0495420	−0.00193282
$658$	−39.2024	−1.52827
$659$	31.1573	1.21372	0.606859	−	0.794810i	$-0.292429\pi$
$659$	31.1573	1.21372	0.606859	+	0.794810i	$0.292429\pi$
$660$	0.714343	0.0278058
$661$	−30.8435	−1.19967	−0.599837	−	0.800122i	$-0.704768\pi$
$661$	−30.8435	−1.19967	−0.599837	+	0.800122i	$0.704768\pi$
$662$	23.2125	0.902179
$663$	−5.92054	−0.229935
$664$	1.00000	0.0388075
$665$	−10.5897	−0.410650
$666$	5.25808	0.203747
$667$	−8.60102	−0.333033
$668$	9.03075	0.349410
$669$	−6.52929	−0.252437
$670$	9.87573	0.381533
$671$	−7.14543	−0.275846
$672$	3.16234	0.121990
$673$	−37.9720	−1.46371	−0.731856	−	0.681460i	$-0.761345\pi$
$673$	−37.9720	−1.46371	−0.731856	+	0.681460i	$0.761345\pi$
$674$	13.6467	0.525650
$675$	−4.27196	−0.164428
$676$	−5.85584	−0.225225
$677$	−47.5253	−1.82654	−0.913272	−	0.407350i	$-0.866453\pi$
$677$	−47.5253	−1.82654	−0.913272	+	0.407350i	$0.866453\pi$
$678$	−0.481101	−0.0184766
$679$	19.9063	0.763933
$680$	−2.78247	−0.106703
$681$	8.49452	0.325511
$682$	5.51121	0.211035
$683$	33.2602	1.27267	0.636334	−	0.771414i	$-0.280450\pi$
$683$	33.2602	1.27267	0.636334	+	0.771414i	$0.280450\pi$
$684$	6.30801	0.241193
$685$	−6.24294	−0.238531
$686$	7.07090	0.269968
$687$	−10.7355	−0.409586
$688$	2.94349	0.112220
$689$	−1.44182	−0.0549290
$690$	−5.89077	−0.224258
$691$	−32.8288	−1.24887	−0.624433	−	0.781078i	$-0.714670\pi$
$691$	−32.8288	−1.24887	−0.624433	+	0.781078i	$0.714670\pi$
$692$	3.98913	0.151644
$693$	−8.43468	−0.320407
$694$	−1.17945	−0.0447713
$695$	−6.92989	−0.262866
$696$	0.925311	0.0350738
$697$	−23.1253	−0.875934
$698$	16.2886	0.616533
$699$	−18.6706	−0.706187
$700$	3.97241	0.150143
$701$	−6.50130	−0.245551	−0.122775	−	0.992434i	$-0.539179\pi$
$701$	−6.50130	−0.245551	−0.122775	+	0.992434i	$0.539179\pi$
$702$	−11.4183	−0.430957
$703$	5.92371	0.223417
$704$	0.897330	0.0338194
$705$	−7.85623	−0.295883
$706$	6.66964	0.251015
$707$	−57.6054	−2.16647
$708$	−5.32658	−0.200185
$709$	−28.1457	−1.05703	−0.528517	−	0.848923i	$-0.677252\pi$
$709$	−28.1457	−1.05703	−0.528517	+	0.848923i	$0.677252\pi$
$710$	3.52870	0.132430
$711$	15.9971	0.599939
$712$	−0.0551890	−0.00206830
$713$	−45.4477	−1.70203
$714$	−8.79912	−0.329299
$715$	2.39843	0.0896963
$716$	14.5002	0.541900
$717$	−21.1315	−0.789172
$718$	14.1881	0.529496
$719$	−4.40711	−0.164358	−0.0821788	−	0.996618i	$-0.526188\pi$
$719$	−4.40711	−0.164358	−0.0821788	+	0.996618i	$0.526188\pi$
$720$	−2.36626	−0.0881854
$721$	−7.40538	−0.275791
$722$	−11.8934	−0.442628
$723$	−19.6226	−0.729771
$724$	14.9978	0.557390
$725$	1.16234	0.0431682
$726$	−8.11584	−0.301207
$727$	42.4008	1.57256	0.786280	−	0.617871i	$-0.212004\pi$
$727$	42.4008	1.57256	0.786280	+	0.617871i	$0.212004\pi$
$728$	10.6177	0.393517
$729$	1.45201	0.0537782
$730$	0.0209368	0.000774907 0
$731$	−8.19018	−0.302925
$732$	−6.33915	−0.234302
$733$	21.0830	0.778718	0.389359	−	0.921086i	$-0.372697\pi$
$733$	21.0830	0.778718	0.389359	+	0.921086i	$0.372697\pi$
$734$	11.2212	0.414182
$735$	6.98956	0.257814
$736$	−7.39975	−0.272759
$737$	8.86179	0.326428
$738$	−19.6662	−0.723922
$739$	41.8417	1.53917	0.769585	−	0.638544i	$-0.220463\pi$
$739$	41.8417	1.53917	0.769585	+	0.638544i	$0.220463\pi$
$740$	−2.22210	−0.0816862
$741$	−5.67231	−0.208377
$742$	−2.14284	−0.0786661
$743$	−34.7828	−1.27606	−0.638029	−	0.770012i	$-0.720250\pi$
$743$	−34.7828	−1.27606	−0.638029	+	0.770012i	$0.720250\pi$
$744$	4.88933	0.179252
$745$	−15.2499	−0.558713
$746$	4.50309	0.164870
$747$	−2.36626	−0.0865770
$748$	−2.49680	−0.0912919
$749$	30.7220	1.12256
$750$	0.796077	0.0290686
$751$	32.6859	1.19272	0.596362	−	0.802715i	$-0.296612\pi$
$751$	32.6859	1.19272	0.596362	+	0.802715i	$0.296612\pi$
$752$	−9.86869	−0.359874
$753$	5.66315	0.206377
$754$	3.10676	0.113142
$755$	15.4967	0.563983
$756$	−16.9699	−0.617191
$757$	8.34006	0.303125	0.151562	−	0.988448i	$-0.451570\pi$
$757$	8.34006	0.303125	0.151562	+	0.988448i	$0.451570\pi$
$758$	33.5547	1.21876
$759$	−5.28596	−0.191868
$760$	−2.66581	−0.0966992
$761$	−21.3544	−0.774095	−0.387047	−	0.922060i	$-0.626505\pi$
$761$	−21.3544	−0.774095	−0.387047	+	0.922060i	$0.626505\pi$
$762$	5.53382	0.200469
$763$	−39.8515	−1.44272
$764$	14.3180	0.518007
$765$	6.58406	0.238047
$766$	6.65012	0.240278
$767$	−17.8842	−0.645760
$768$	0.796077	0.0287259
$769$	29.4548	1.06217	0.531083	−	0.847320i	$-0.321785\pi$
$769$	29.4548	1.06217	0.531083	+	0.847320i	$0.321785\pi$
$770$	3.56456	0.128458
$771$	2.11635	0.0762186
$772$	−10.1222	−0.364305
$773$	−41.7187	−1.50052	−0.750259	−	0.661144i	$-0.770071\pi$
$773$	−41.7187	−1.50052	−0.750259	+	0.661144i	$0.770071\pi$
$774$	−6.96507	−0.250354
$775$	6.14179	0.220620
$776$	5.01114	0.179889
$777$	−7.02705	−0.252094
$778$	−5.94359	−0.213088
$779$	−22.1558	−0.793812
$780$	2.12780	0.0761874
$781$	3.16641	0.113303
$782$	20.5896	0.736283
$783$	−4.96546	−0.177451
$784$	8.78001	0.313572
$785$	0.0719152	0.00256677
$786$	−9.65822	−0.344497
$787$	−19.5296	−0.696154	−0.348077	−	0.937466i	$-0.613165\pi$
$787$	−19.5296	−0.696154	−0.348077	+	0.937466i	$0.613165\pi$
$788$	−5.77316	−0.205660
$789$	−20.5323	−0.730970
$790$	−6.76050	−0.240528
$791$	−2.40069	−0.0853586
$792$	−2.12332	−0.0754488
$793$	−21.2839	−0.755814
$794$	4.44866	0.157877
$795$	−0.429428	−0.0152303
$796$	8.64251	0.306325
$797$	27.6606	0.979788	0.489894	−	0.871782i	$-0.337035\pi$
$797$	27.6606	0.979788	0.489894	+	0.871782i	$0.337035\pi$
$798$	−8.43020	−0.298426
$799$	27.4593	0.971442
$800$	1.00000	0.0353553
$801$	0.130592	0.00461423
$802$	−28.8690	−1.01940
$803$	0.0187872	0.000662987 0
$804$	7.86184	0.277266
$805$	−29.3948	−1.03603
$806$	16.4161	0.578233
$807$	6.31531	0.222310
$808$	−14.5014	−0.510157
$809$	−47.9163	−1.68465	−0.842324	−	0.538972i	$-0.818813\pi$
$809$	−47.9163	−1.68465	−0.842324	+	0.538972i	$0.818813\pi$
$810$	3.69798	0.129934
$811$	2.63719	0.0926042	0.0463021	−	0.998927i	$-0.485256\pi$
$811$	2.63719	0.0926042	0.0463021	+	0.998927i	$0.485256\pi$
$812$	4.61728	0.162035
$813$	25.3582	0.889350
$814$	−1.99396	−0.0698883
$815$	−5.83091	−0.204248
$816$	−2.21506	−0.0775426
$817$	−7.84680	−0.274525
$818$	0.880179	0.0307748
$819$	−25.1242	−0.877910
$820$	8.31107	0.290235
$821$	−43.5903	−1.52131	−0.760656	−	0.649156i	$-0.775122\pi$
$821$	−43.5903	−1.52131	−0.760656	+	0.649156i	$0.775122\pi$
$822$	−4.96986	−0.173344
$823$	27.7470	0.967199	0.483599	−	0.875290i	$-0.339329\pi$
$823$	27.7470	0.967199	0.483599	+	0.875290i	$0.339329\pi$
$824$	−1.86421	−0.0649427
$825$	0.714343	0.0248702
$826$	−26.5795	−0.924819
$827$	−28.3909	−0.987249	−0.493625	−	0.869675i	$-0.664328\pi$
$827$	−28.3909	−0.987249	−0.493625	+	0.869675i	$0.664328\pi$
$828$	17.5098	0.608506
$829$	−14.7073	−0.510806	−0.255403	−	0.966835i	$-0.582208\pi$
$829$	−14.7073	−0.510806	−0.255403	+	0.966835i	$0.582208\pi$
$830$	1.00000	0.0347105
$831$	24.2561	0.841436
$832$	2.67286	0.0926646
$833$	−24.4301	−0.846454
$834$	−5.51672	−0.191028
$835$	9.03075	0.312522
$836$	−2.39211	−0.0827330
$837$	−26.2374	−0.906899
$838$	30.9874	1.07044
$839$	−5.74755	−0.198427	−0.0992136	−	0.995066i	$-0.531633\pi$
$839$	−5.74755	−0.198427	−0.0992136	+	0.995066i	$0.531633\pi$
$840$	3.16234	0.109111
$841$	−27.6490	−0.953413
$842$	−18.4984	−0.637497
$843$	21.0979	0.726650
$844$	−2.25092	−0.0774799
$845$	−5.85584	−0.201447
$846$	23.3519	0.802855
$847$	−40.4979	−1.39152
$848$	−0.539431	−0.0185241
$849$	13.7734	0.472702
$850$	−2.78247	−0.0954380
$851$	16.4430	0.563660
$852$	2.80911	0.0962386
$853$	46.3269	1.58620	0.793102	−	0.609089i	$-0.208465\pi$
$853$	46.3269	1.58620	0.793102	+	0.609089i	$0.208465\pi$
$854$	−31.6322	−1.08243
$855$	6.30801	0.215729
$856$	7.73384	0.264337
$857$	−4.89188	−0.167104	−0.0835518	−	0.996503i	$-0.526626\pi$
$857$	−4.89188	−0.167104	−0.0835518	+	0.996503i	$0.526626\pi$
$858$	1.90934	0.0651837
$859$	23.2881	0.794579	0.397289	−	0.917693i	$-0.369951\pi$
$859$	23.2881	0.794579	0.397289	+	0.917693i	$0.369951\pi$
$860$	2.94349	0.100372
$861$	26.2824	0.895703
$862$	−32.0779	−1.09258
$863$	35.1988	1.19818	0.599091	−	0.800681i	$-0.295529\pi$
$863$	35.1988	1.19818	0.599091	+	0.800681i	$0.295529\pi$
$864$	−4.27196	−0.145335
$865$	3.98913	0.135635
$866$	37.2469	1.26570
$867$	−7.36996	−0.250297
$868$	24.3977	0.828111
$869$	−6.06640	−0.205789
$870$	0.925311	0.0313710
$871$	26.3964	0.894408
$872$	−10.0321	−0.339729
$873$	−11.8577	−0.401321
$874$	19.7263	0.667254
$875$	3.97241	0.134292
$876$	0.0166673	0.000563137 0
$877$	1.29140	0.0436074	0.0218037	−	0.999762i	$-0.493059\pi$
$877$	1.29140	0.0436074	0.0218037	+	0.999762i	$0.493059\pi$
$878$	17.3568	0.585764
$879$	20.8147	0.702064
$880$	0.897330	0.0302490
$881$	−5.29516	−0.178399	−0.0891993	−	0.996014i	$-0.528431\pi$
$881$	−5.29516	−0.178399	−0.0891993	+	0.996014i	$0.528431\pi$
$882$	−20.7758	−0.699557
$883$	−40.8853	−1.37590	−0.687950	−	0.725759i	$-0.741489\pi$
$883$	−40.8853	−1.37590	−0.687950	+	0.725759i	$0.741489\pi$
$884$	−7.43715	−0.250138
$885$	−5.32658	−0.179051
$886$	28.4154	0.954632
$887$	−2.74708	−0.0922380	−0.0461190	−	0.998936i	$-0.514685\pi$
$887$	−2.74708	−0.0922380	−0.0461190	+	0.998936i	$0.514685\pi$
$888$	−1.76897	−0.0593626
$889$	27.6137	0.926133
$890$	−0.0551890	−0.00184994
$891$	3.31831	0.111168
$892$	−8.20184	−0.274618
$893$	26.3081	0.880366
$894$	−12.1401	−0.406025
$895$	14.5002	0.484690
$896$	3.97241	0.132709
$897$	−15.7452	−0.525716
$898$	−14.8296	−0.494870
$899$	7.13884	0.238094
$900$	−2.36626	−0.0788754
$901$	1.50095	0.0500039
$902$	7.45778	0.248317
$903$	9.30832	0.309761
$904$	−0.604341	−0.0201001
$905$	14.9978	0.498544
$906$	12.3366	0.409855
$907$	−23.6901	−0.786617	−0.393308	−	0.919407i	$-0.628670\pi$
$907$	−23.6901	−0.786617	−0.393308	+	0.919407i	$0.628670\pi$
$908$	10.6705	0.354113
$909$	34.3141	1.13813
$910$	10.6177	0.351972
$911$	−30.3560	−1.00574	−0.502869	−	0.864363i	$-0.667722\pi$
$911$	−30.3560	−1.00574	−0.502869	+	0.864363i	$0.667722\pi$
$912$	−2.12219	−0.0702727
$913$	0.897330	0.0296973
$914$	28.5209	0.943387
$915$	−6.33915	−0.209566
$916$	−13.4856	−0.445575
$917$	−48.1943	−1.59152
$918$	11.8866	0.392316
$919$	−33.0969	−1.09177	−0.545884	−	0.837861i	$-0.683806\pi$
$919$	−33.0969	−1.09177	−0.545884	+	0.837861i	$0.683806\pi$
$920$	−7.39975	−0.243963
$921$	−16.8832	−0.556321
$922$	−25.0697	−0.825625
$923$	9.43170	0.310448
$924$	2.83766	0.0933522
$925$	−2.22210	−0.0730623
$926$	26.8147	0.881186
$927$	4.41120	0.144883
$928$	1.16234	0.0381556
$929$	−6.70752	−0.220067	−0.110033	−	0.993928i	$-0.535096\pi$
$929$	−6.70752	−0.220067	−0.110033	+	0.993928i	$0.535096\pi$
$930$	4.88933	0.160328
$931$	−23.4058	−0.767096
$932$	−23.4533	−0.768237
$933$	8.34324	0.273146
$934$	−5.24038	−0.171471
$935$	−2.49680	−0.0816540
$936$	−6.32468	−0.206729
$937$	−5.98074	−0.195382	−0.0976912	−	0.995217i	$-0.531146\pi$
$937$	−5.98074	−0.195382	−0.0976912	+	0.995217i	$0.531146\pi$
$938$	39.2304	1.28092
$939$	−8.96469	−0.292551
$940$	−9.86869	−0.321881
$941$	52.9964	1.72763	0.863816	−	0.503808i	$-0.168068\pi$
$941$	52.9964	1.72763	0.863816	+	0.503808i	$0.168068\pi$
$942$	0.0572500	0.00186531
$943$	−61.4999	−2.00271
$944$	−6.69104	−0.217775
$945$	−16.9699	−0.552032
$946$	2.64128	0.0858755
$947$	2.49788	0.0811700	0.0405850	−	0.999176i	$-0.487078\pi$
$947$	2.49788	0.0811700	0.0405850	+	0.999176i	$0.487078\pi$
$948$	−5.38188	−0.174795
$949$	0.0559611	0.00181658
$950$	−2.66581	−0.0864904
$951$	23.3618	0.757558
$952$	−11.0531	−0.358233
$953$	−24.3678	−0.789350	−0.394675	−	0.918821i	$-0.629143\pi$
$953$	−24.3678	−0.789350	−0.394675	+	0.918821i	$0.629143\pi$
$954$	1.27643	0.0413261
$955$	14.3180	0.463320
$956$	−26.5446	−0.858514
$957$	0.830309	0.0268401
$958$	−30.5482	−0.986969
$959$	−24.7995	−0.800818
$960$	0.796077	0.0256933
$961$	6.72156	0.216824
$962$	−5.93936	−0.191493
$963$	−18.3003	−0.589719
$964$	−24.6491	−0.793893
$965$	−10.1222	−0.325844
$966$	−23.4005	−0.752900
$967$	−19.8923	−0.639694	−0.319847	−	0.947469i	$-0.603632\pi$
$967$	−19.8923	−0.639694	−0.319847	+	0.947469i	$0.603632\pi$
$968$	−10.1948	−0.327673
$969$	5.90494	0.189694
$970$	5.01114	0.160898
$971$	49.1410	1.57701	0.788504	−	0.615029i	$-0.210856\pi$
$971$	49.1410	1.57701	0.788504	+	0.615029i	$0.210856\pi$
$972$	15.7597	0.505494
$973$	−27.5283	−0.882518
$974$	27.2045	0.871689
$975$	2.12780	0.0681441
$976$	−7.96299	−0.254889
$977$	−22.1627	−0.709046	−0.354523	−	0.935047i	$-0.615357\pi$
$977$	−22.1627	−0.709046	−0.354523	+	0.935047i	$0.615357\pi$
$978$	−4.64185	−0.148430
$979$	−0.0495228	−0.00158275
$980$	8.78001	0.280467
$981$	23.7385	0.757913
$982$	−9.85466	−0.314475
$983$	−8.25200	−0.263198	−0.131599	−	0.991303i	$-0.542011\pi$
$983$	−8.25200	−0.263198	−0.131599	+	0.991303i	$0.542011\pi$
$984$	6.61625	0.210918
$985$	−5.77316	−0.183948
$986$	−3.23418	−0.102997
$987$	−31.2081	−0.993366
$988$	−7.12533	−0.226687
$989$	−21.7811	−0.692599
$990$	−2.12332	−0.0674835
$991$	−58.8743	−1.87020	−0.935102	−	0.354380i	$-0.884692\pi$
$991$	−58.8743	−1.87020	−0.935102	+	0.354380i	$0.884692\pi$
$992$	6.14179	0.195002
$993$	18.4789	0.586411
$994$	14.0174	0.444606
$995$	8.64251	0.273986
$996$	0.796077	0.0252246
$997$	33.6482	1.06565	0.532825	−	0.846226i	$-0.321131\pi$
$997$	33.6482	1.06565	0.532825	+	0.846226i	$0.321131\pi$
$998$	−23.3802	−0.740086
$999$	9.49273	0.300337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	830.2.a.k.1.3	✓	5
3.2	odd	2		7470.2.a.bv.1.5		5
4.3	odd	2		6640.2.a.z.1.3		5
5.4	even	2		4150.2.a.bd.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
830.2.a.k.1.3	✓	5	1.1	even	1	trivial
4150.2.a.bd.1.3		5	5.4	even	2
6640.2.a.z.1.3		5	4.3	odd	2
7470.2.a.bv.1.5		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 830 = 2 \cdot 5 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	830.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.796077 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.796077 q^{6} +3.97241 q^{7} +1.00000 q^{8} -2.36626 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.796077 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.796077 q^{6} +3.97241 q^{7} +1.00000 q^{8} -2.36626 q^{9} +1.00000 q^{10} +0.897330 q^{11} +0.796077 q^{12} +2.67286 q^{13} +3.97241 q^{14} +0.796077 q^{15} +1.00000 q^{16} -2.78247 q^{17} -2.36626 q^{18} -2.66581 q^{19} +1.00000 q^{20} +3.16234 q^{21} +0.897330 q^{22} -7.39975 q^{23} +0.796077 q^{24} +1.00000 q^{25} +2.67286 q^{26} -4.27196 q^{27} +3.97241 q^{28} +1.16234 q^{29} +0.796077 q^{30} +6.14179 q^{31} +1.00000 q^{32} +0.714343 q^{33} -2.78247 q^{34} +3.97241 q^{35} -2.36626 q^{36} -2.22210 q^{37} -2.66581 q^{38} +2.12780 q^{39} +1.00000 q^{40} +8.31107 q^{41} +3.16234 q^{42} +2.94349 q^{43} +0.897330 q^{44} -2.36626 q^{45} -7.39975 q^{46} -9.86869 q^{47} +0.796077 q^{48} +8.78001 q^{49} +1.00000 q^{50} -2.21506 q^{51} +2.67286 q^{52} -0.539431 q^{53} -4.27196 q^{54} +0.897330 q^{55} +3.97241 q^{56} -2.12219 q^{57} +1.16234 q^{58} -6.69104 q^{59} +0.796077 q^{60} -7.96299 q^{61} +6.14179 q^{62} -9.39975 q^{63} +1.00000 q^{64} +2.67286 q^{65} +0.714343 q^{66} +9.87573 q^{67} -2.78247 q^{68} -5.89077 q^{69} +3.97241 q^{70} +3.52870 q^{71} -2.36626 q^{72} +0.0209368 q^{73} -2.22210 q^{74} +0.796077 q^{75} -2.66581 q^{76} +3.56456 q^{77} +2.12780 q^{78} -6.76050 q^{79} +1.00000 q^{80} +3.69798 q^{81} +8.31107 q^{82} +1.00000 q^{83} +3.16234 q^{84} -2.78247 q^{85} +2.94349 q^{86} +0.925311 q^{87} +0.897330 q^{88} -0.0551890 q^{89} -2.36626 q^{90} +10.6177 q^{91} -7.39975 q^{92} +4.88933 q^{93} -9.86869 q^{94} -2.66581 q^{95} +0.796077 q^{96} +5.01114 q^{97} +8.78001 q^{98} -2.12332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} + 5 q^{5} + 2 q^{6} + 5 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} + 2 q^{12} + 4 q^{13} + 5 q^{14} + 2 q^{15} + 5 q^{16} - q^{17} + 3 q^{18} + 7 q^{19} + 5 q^{20} - q^{21} + q^{22} + 8 q^{23} + 2 q^{24} + 5 q^{25} + 4 q^{26} - q^{27} + 5 q^{28} - 11 q^{29} + 2 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - q^{34} + 5 q^{35} + 3 q^{36} + 8 q^{37} + 7 q^{38} - 14 q^{39} + 5 q^{40} - 3 q^{41} - q^{42} - 2 q^{43} + q^{44} + 3 q^{45} + 8 q^{46} + 7 q^{47} + 2 q^{48} - 12 q^{49} + 5 q^{50} + 19 q^{51} + 4 q^{52} - 12 q^{53} - q^{54} + q^{55} + 5 q^{56} - 6 q^{57} - 11 q^{58} - 3 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 5 q^{64} + 4 q^{65} - 5 q^{66} + 4 q^{67} - q^{68} - 26 q^{69} + 5 q^{70} + 4 q^{71} + 3 q^{72} - 3 q^{73} + 8 q^{74} + 2 q^{75} + 7 q^{76} - q^{77} - 14 q^{78} - 12 q^{79} + 5 q^{80} - 19 q^{81} - 3 q^{82} + 5 q^{83} - q^{84} - q^{85} - 2 q^{86} + 9 q^{87} + q^{88} - 30 q^{89} + 3 q^{90} + 14 q^{91} + 8 q^{92} - 10 q^{93} + 7 q^{94} + 7 q^{95} + 2 q^{96} - 7 q^{97} - 12 q^{98} - 36 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 + 5 * q^5 + 2 * q^6 + 5 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 + 2 * q^12 + 4 * q^13 + 5 * q^14 + 2 * q^15 + 5 * q^16 - q^17 + 3 * q^18 + 7 * q^19 + 5 * q^20 - q^21 + q^22 + 8 * q^23 + 2 * q^24 + 5 * q^25 + 4 * q^26 - q^27 + 5 * q^28 - 11 * q^29 + 2 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - q^34 + 5 * q^35 + 3 * q^36 + 8 * q^37 + 7 * q^38 - 14 * q^39 + 5 * q^40 - 3 * q^41 - q^42 - 2 * q^43 + q^44 + 3 * q^45 + 8 * q^46 + 7 * q^47 + 2 * q^48 - 12 * q^49 + 5 * q^50 + 19 * q^51 + 4 * q^52 - 12 * q^53 - q^54 + q^55 + 5 * q^56 - 6 * q^57 - 11 * q^58 - 3 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 5 * q^64 + 4 * q^65 - 5 * q^66 + 4 * q^67 - q^68 - 26 * q^69 + 5 * q^70 + 4 * q^71 + 3 * q^72 - 3 * q^73 + 8 * q^74 + 2 * q^75 + 7 * q^76 - q^77 - 14 * q^78 - 12 * q^79 + 5 * q^80 - 19 * q^81 - 3 * q^82 + 5 * q^83 - q^84 - q^85 - 2 * q^86 + 9 * q^87 + q^88 - 30 * q^89 + 3 * q^90 + 14 * q^91 + 8 * q^92 - 10 * q^93 + 7 * q^94 + 7 * q^95 + 2 * q^96 - 7 * q^97 - 12 * q^98 - 36 * q^99

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