LMFDB - Embedded newform 4030.2.a.r.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 8x^{7} + 39x^{6} + 13x^{5} - 106x^{4} + 9x^{3} + 74x^{2} - 3x - 7 $ x^9 - 4x^8 - 8x^7 + 39x^6 + 13x^5 - 106x^4 + 9x^3 + 74x^2 - 3x - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.27701$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.574493 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.574493 q^{6} +2.65097 q^{7} +1.00000 q^{8} -2.66996 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.574493 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.574493 q^{6} +2.65097 q^{7} +1.00000 q^{8} -2.66996 q^{9} +1.00000 q^{10} +5.46180 q^{11} +0.574493 q^{12} +1.00000 q^{13} +2.65097 q^{14} +0.574493 q^{15} +1.00000 q^{16} +6.09419 q^{17} -2.66996 q^{18} -2.11241 q^{19} +1.00000 q^{20} +1.52296 q^{21} +5.46180 q^{22} +1.90759 q^{23} +0.574493 q^{24} +1.00000 q^{25} +1.00000 q^{26} -3.25735 q^{27} +2.65097 q^{28} -1.58086 q^{29} +0.574493 q^{30} -1.00000 q^{31} +1.00000 q^{32} +3.13777 q^{33} +6.09419 q^{34} +2.65097 q^{35} -2.66996 q^{36} -1.86832 q^{37} -2.11241 q^{38} +0.574493 q^{39} +1.00000 q^{40} -2.18624 q^{41} +1.52296 q^{42} +3.93884 q^{43} +5.46180 q^{44} -2.66996 q^{45} +1.90759 q^{46} -9.99497 q^{47} +0.574493 q^{48} +0.0276456 q^{49} +1.00000 q^{50} +3.50107 q^{51} +1.00000 q^{52} -9.86129 q^{53} -3.25735 q^{54} +5.46180 q^{55} +2.65097 q^{56} -1.21356 q^{57} -1.58086 q^{58} -6.85309 q^{59} +0.574493 q^{60} +8.66537 q^{61} -1.00000 q^{62} -7.07798 q^{63} +1.00000 q^{64} +1.00000 q^{65} +3.13777 q^{66} -4.42904 q^{67} +6.09419 q^{68} +1.09590 q^{69} +2.65097 q^{70} +11.8069 q^{71} -2.66996 q^{72} -1.85312 q^{73} -1.86832 q^{74} +0.574493 q^{75} -2.11241 q^{76} +14.4791 q^{77} +0.574493 q^{78} +2.76301 q^{79} +1.00000 q^{80} +6.13855 q^{81} -2.18624 q^{82} +10.8906 q^{83} +1.52296 q^{84} +6.09419 q^{85} +3.93884 q^{86} -0.908195 q^{87} +5.46180 q^{88} -5.71941 q^{89} -2.66996 q^{90} +2.65097 q^{91} +1.90759 q^{92} -0.574493 q^{93} -9.99497 q^{94} -2.11241 q^{95} +0.574493 q^{96} -1.55602 q^{97} +0.0276456 q^{98} -14.5828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9} + 9 q^{10} + 10 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} + 14 q^{18} + 10 q^{19} + 9 q^{20} + 3 q^{21} + 10 q^{22} + 8 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 15 q^{27} + 9 q^{28} + 9 q^{29} + 3 q^{30} - 9 q^{31} + 9 q^{32} + 4 q^{33} + q^{34} + 9 q^{35} + 14 q^{36} - 3 q^{37} + 10 q^{38} + 3 q^{39} + 9 q^{40} + 3 q^{42} + 7 q^{43} + 10 q^{44} + 14 q^{45} + 8 q^{46} + 7 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} - 3 q^{51} + 9 q^{52} + 8 q^{53} + 15 q^{54} + 10 q^{55} + 9 q^{56} - 7 q^{57} + 9 q^{58} + 2 q^{59} + 3 q^{60} - 2 q^{61} - 9 q^{62} + 10 q^{63} + 9 q^{64} + 9 q^{65} + 4 q^{66} + 18 q^{67} + q^{68} - 16 q^{69} + 9 q^{70} + 14 q^{71} + 14 q^{72} + q^{73} - 3 q^{74} + 3 q^{75} + 10 q^{76} - 5 q^{77} + 3 q^{78} + 6 q^{79} + 9 q^{80} + q^{81} + 7 q^{83} + 3 q^{84} + q^{85} + 7 q^{86} + 11 q^{87} + 10 q^{88} - 19 q^{89} + 14 q^{90} + 9 q^{91} + 8 q^{92} - 3 q^{93} + 7 q^{94} + 10 q^{95} + 3 q^{96} - 6 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9 + 9 * q^10 + 10 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 + 3 * q^15 + 9 * q^16 + q^17 + 14 * q^18 + 10 * q^19 + 9 * q^20 + 3 * q^21 + 10 * q^22 + 8 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 15 * q^27 + 9 * q^28 + 9 * q^29 + 3 * q^30 - 9 * q^31 + 9 * q^32 + 4 * q^33 + q^34 + 9 * q^35 + 14 * q^36 - 3 * q^37 + 10 * q^38 + 3 * q^39 + 9 * q^40 + 3 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 + 8 * q^46 + 7 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 - 3 * q^51 + 9 * q^52 + 8 * q^53 + 15 * q^54 + 10 * q^55 + 9 * q^56 - 7 * q^57 + 9 * q^58 + 2 * q^59 + 3 * q^60 - 2 * q^61 - 9 * q^62 + 10 * q^63 + 9 * q^64 + 9 * q^65 + 4 * q^66 + 18 * q^67 + q^68 - 16 * q^69 + 9 * q^70 + 14 * q^71 + 14 * q^72 + q^73 - 3 * q^74 + 3 * q^75 + 10 * q^76 - 5 * q^77 + 3 * q^78 + 6 * q^79 + 9 * q^80 + q^81 + 7 * q^83 + 3 * q^84 + q^85 + 7 * q^86 + 11 * q^87 + 10 * q^88 - 19 * q^89 + 14 * q^90 + 9 * q^91 + 8 * q^92 - 3 * q^93 + 7 * q^94 + 10 * q^95 + 3 * q^96 - 6 * q^97 + 8 * q^98 - 5 * 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
$3$	0.574493	0.331684	0.165842	−	0.986152i	$-0.446966\pi$
$3$	0.574493	0.331684	0.165842	+	0.986152i	$0.446966\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.574493	0.234536
$7$	2.65097	1.00197	0.500986	−	0.865455i	$-0.332971\pi$
$7$	2.65097	1.00197	0.500986	+	0.865455i	$0.332971\pi$
$8$	1.00000	0.353553
$9$	−2.66996	−0.889986
$10$	1.00000	0.316228
$11$	5.46180	1.64680	0.823398	−	0.567465i	$-0.192076\pi$
$11$	5.46180	1.64680	0.823398	+	0.567465i	$0.192076\pi$
$12$	0.574493	0.165842
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.65097	0.708502
$15$	0.574493	0.148334
$16$	1.00000	0.250000
$17$	6.09419	1.47806	0.739030	−	0.673673i	$-0.235284\pi$
$17$	6.09419	1.47806	0.739030	+	0.673673i	$0.235284\pi$
$18$	−2.66996	−0.629315
$19$	−2.11241	−0.484619	−0.242310	−	0.970199i	$-0.577905\pi$
$19$	−2.11241	−0.484619	−0.242310	+	0.970199i	$0.577905\pi$
$20$	1.00000	0.223607
$21$	1.52296	0.332338
$22$	5.46180	1.16446
$23$	1.90759	0.397761	0.198880	−	0.980024i	$-0.436269\pi$
$23$	1.90759	0.397761	0.198880	+	0.980024i	$0.436269\pi$
$24$	0.574493	0.117268
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−3.25735	−0.626878
$28$	2.65097	0.500986
$29$	−1.58086	−0.293559	−0.146779	−	0.989169i	$-0.546891\pi$
$29$	−1.58086	−0.293559	−0.146779	+	0.989169i	$0.546891\pi$
$30$	0.574493	0.104888
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	3.13777	0.546215
$34$	6.09419	1.04515
$35$	2.65097	0.448096
$36$	−2.66996	−0.444993
$37$	−1.86832	−0.307150	−0.153575	−	0.988137i	$-0.549079\pi$
$37$	−1.86832	−0.307150	−0.153575	+	0.988137i	$0.549079\pi$
$38$	−2.11241	−0.342678
$39$	0.574493	0.0919926
$40$	1.00000	0.158114
$41$	−2.18624	−0.341433	−0.170716	−	0.985320i	$-0.554608\pi$
$41$	−2.18624	−0.341433	−0.170716	+	0.985320i	$0.554608\pi$
$42$	1.52296	0.234999
$43$	3.93884	0.600667	0.300333	−	0.953834i	$-0.402902\pi$
$43$	3.93884	0.600667	0.300333	+	0.953834i	$0.402902\pi$
$44$	5.46180	0.823398
$45$	−2.66996	−0.398014
$46$	1.90759	0.281259
$47$	−9.99497	−1.45792	−0.728958	−	0.684558i	$-0.759995\pi$
$47$	−9.99497	−1.45792	−0.728958	+	0.684558i	$0.759995\pi$
$48$	0.574493	0.0829210
$49$	0.0276456	0.00394938
$50$	1.00000	0.141421
$51$	3.50107	0.490248
$52$	1.00000	0.138675
$53$	−9.86129	−1.35455	−0.677276	−	0.735729i	$-0.736840\pi$
$53$	−9.86129	−1.35455	−0.677276	+	0.735729i	$0.736840\pi$
$54$	−3.25735	−0.443270
$55$	5.46180	0.736469
$56$	2.65097	0.354251
$57$	−1.21356	−0.160740
$58$	−1.58086	−0.207578
$59$	−6.85309	−0.892196	−0.446098	−	0.894984i	$-0.647187\pi$
$59$	−6.85309	−0.892196	−0.446098	+	0.894984i	$0.647187\pi$
$60$	0.574493	0.0741668
$61$	8.66537	1.10949	0.554744	−	0.832021i	$-0.312816\pi$
$61$	8.66537	1.10949	0.554744	+	0.832021i	$0.312816\pi$
$62$	−1.00000	−0.127000
$63$	−7.07798	−0.891742
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	3.13777	0.386233
$67$	−4.42904	−0.541093	−0.270546	−	0.962707i	$-0.587204\pi$
$67$	−4.42904	−0.541093	−0.270546	+	0.962707i	$0.587204\pi$
$68$	6.09419	0.739030
$69$	1.09590	0.131931
$70$	2.65097	0.316852
$71$	11.8069	1.40122	0.700612	−	0.713543i	$-0.252911\pi$
$71$	11.8069	1.40122	0.700612	+	0.713543i	$0.252911\pi$
$72$	−2.66996	−0.314658
$73$	−1.85312	−0.216891	−0.108446	−	0.994102i	$-0.534587\pi$
$73$	−1.85312	−0.216891	−0.108446	+	0.994102i	$0.534587\pi$
$74$	−1.86832	−0.217188
$75$	0.574493	0.0663368
$76$	−2.11241	−0.242310
$77$	14.4791	1.65004
$78$	0.574493	0.0650486
$79$	2.76301	0.310863	0.155432	−	0.987847i	$-0.450323\pi$
$79$	2.76301	0.310863	0.155432	+	0.987847i	$0.450323\pi$
$80$	1.00000	0.111803
$81$	6.13855	0.682061
$82$	−2.18624	−0.241429
$83$	10.8906	1.19540	0.597699	−	0.801721i	$-0.296082\pi$
$83$	10.8906	1.19540	0.597699	+	0.801721i	$0.296082\pi$
$84$	1.52296	0.166169
$85$	6.09419	0.661008
$86$	3.93884	0.424736
$87$	−0.908195	−0.0973688
$88$	5.46180	0.582230
$89$	−5.71941	−0.606257	−0.303128	−	0.952950i	$-0.598031\pi$
$89$	−5.71941	−0.606257	−0.303128	+	0.952950i	$0.598031\pi$
$90$	−2.66996	−0.281438
$91$	2.65097	0.277897
$92$	1.90759	0.198880
$93$	−0.574493	−0.0595722
$94$	−9.99497	−1.03090
$95$	−2.11241	−0.216728
$96$	0.574493	0.0586340
$97$	−1.55602	−0.157990	−0.0789949	−	0.996875i	$-0.525171\pi$
$97$	−1.55602	−0.157990	−0.0789949	+	0.996875i	$0.525171\pi$
$98$	0.0276456	0.00279263
$99$	−14.5828	−1.46562
$100$	1.00000	0.100000
$101$	15.1649	1.50897	0.754483	−	0.656320i	$-0.227888\pi$
$101$	15.1649	1.50897	0.754483	+	0.656320i	$0.227888\pi$
$102$	3.50107	0.346658
$103$	−14.4472	−1.42353	−0.711764	−	0.702418i	$-0.752104\pi$
$103$	−14.4472	−1.42353	−0.711764	+	0.702418i	$0.752104\pi$
$104$	1.00000	0.0980581
$105$	1.52296	0.148626
$106$	−9.86129	−0.957813
$107$	−6.75721	−0.653244	−0.326622	−	0.945155i	$-0.605910\pi$
$107$	−6.75721	−0.653244	−0.326622	+	0.945155i	$0.605910\pi$
$108$	−3.25735	−0.313439
$109$	3.05614	0.292726	0.146363	−	0.989231i	$-0.453243\pi$
$109$	3.05614	0.292726	0.146363	+	0.989231i	$0.453243\pi$
$110$	5.46180	0.520762
$111$	−1.07334	−0.101877
$112$	2.65097	0.250493
$113$	−5.39957	−0.507949	−0.253974	−	0.967211i	$-0.581738\pi$
$113$	−5.39957	−0.507949	−0.253974	+	0.967211i	$0.581738\pi$
$114$	−1.21356	−0.113661
$115$	1.90759	0.177884
$116$	−1.58086	−0.146779
$117$	−2.66996	−0.246838
$118$	−6.85309	−0.630878
$119$	16.1555	1.48097
$120$	0.574493	0.0524438
$121$	18.8313	1.71193
$122$	8.66537	0.784526
$123$	−1.25598	−0.113248
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	−7.07798	−0.630556
$127$	9.99185	0.886634	0.443317	−	0.896365i	$-0.353802\pi$
$127$	9.99185	0.886634	0.443317	+	0.896365i	$0.353802\pi$
$128$	1.00000	0.0883883
$129$	2.26284	0.199232
$130$	1.00000	0.0877058
$131$	−15.5104	−1.35515	−0.677573	−	0.735455i	$-0.736968\pi$
$131$	−15.5104	−1.35515	−0.677573	+	0.735455i	$0.736968\pi$
$132$	3.13777	0.273108
$133$	−5.59993	−0.485576
$134$	−4.42904	−0.382610
$135$	−3.25735	−0.280348
$136$	6.09419	0.522573
$137$	9.64959	0.824421	0.412210	−	0.911089i	$-0.364757\pi$
$137$	9.64959	0.824421	0.412210	+	0.911089i	$0.364757\pi$
$138$	1.09590	0.0932892
$139$	−1.22773	−0.104134	−0.0520671	−	0.998644i	$-0.516581\pi$
$139$	−1.22773	−0.104134	−0.0520671	+	0.998644i	$0.516581\pi$
$140$	2.65097	0.224048
$141$	−5.74205	−0.483568
$142$	11.8069	0.990815
$143$	5.46180	0.456739
$144$	−2.66996	−0.222496
$145$	−1.58086	−0.131284
$146$	−1.85312	−0.153365
$147$	0.0158822	0.00130994
$148$	−1.86832	−0.153575
$149$	−12.1152	−0.992518	−0.496259	−	0.868174i	$-0.665293\pi$
$149$	−12.1152	−0.992518	−0.496259	+	0.868174i	$0.665293\pi$
$150$	0.574493	0.0469072
$151$	16.3675	1.33197	0.665986	−	0.745964i	$-0.268011\pi$
$151$	16.3675	1.33197	0.665986	+	0.745964i	$0.268011\pi$
$152$	−2.11241	−0.171339
$153$	−16.2712	−1.31545
$154$	14.4791	1.16676
$155$	−1.00000	−0.0803219
$156$	0.574493	0.0459963
$157$	3.69050	0.294534	0.147267	−	0.989097i	$-0.452952\pi$
$157$	3.69050	0.294534	0.147267	+	0.989097i	$0.452952\pi$
$158$	2.76301	0.219814
$159$	−5.66525	−0.449283
$160$	1.00000	0.0790569
$161$	5.05697	0.398545
$162$	6.13855	0.482290
$163$	23.7389	1.85938	0.929688	−	0.368348i	$-0.120077\pi$
$163$	23.7389	1.85938	0.929688	+	0.368348i	$0.120077\pi$
$164$	−2.18624	−0.170716
$165$	3.13777	0.244275
$166$	10.8906	0.845274
$167$	−14.5857	−1.12867	−0.564337	−	0.825545i	$-0.690868\pi$
$167$	−14.5857	−1.12867	−0.564337	+	0.825545i	$0.690868\pi$
$168$	1.52296	0.117499
$169$	1.00000	0.0769231
$170$	6.09419	0.467403
$171$	5.64004	0.431304
$172$	3.93884	0.300333
$173$	1.63786	0.124524	0.0622622	−	0.998060i	$-0.480169\pi$
$173$	1.63786	0.124524	0.0622622	+	0.998060i	$0.480169\pi$
$174$	−0.908195	−0.0688501
$175$	2.65097	0.200395
$176$	5.46180	0.411699
$177$	−3.93705	−0.295927
$178$	−5.71941	−0.428688
$179$	13.0508	0.975465	0.487733	−	0.872993i	$-0.337824\pi$
$179$	13.0508	0.975465	0.487733	+	0.872993i	$0.337824\pi$
$180$	−2.66996	−0.199007
$181$	6.55122	0.486948	0.243474	−	0.969907i	$-0.421713\pi$
$181$	6.55122	0.486948	0.243474	+	0.969907i	$0.421713\pi$
$182$	2.65097	0.196503
$183$	4.97820	0.367999
$184$	1.90759	0.140630
$185$	−1.86832	−0.137362
$186$	−0.574493	−0.0421239
$187$	33.2853	2.43406
$188$	−9.99497	−0.728958
$189$	−8.63515	−0.628114
$190$	−2.11241	−0.153250
$191$	−25.1493	−1.81974	−0.909870	−	0.414894i	$-0.863819\pi$
$191$	−25.1493	−1.81974	−0.909870	+	0.414894i	$0.863819\pi$
$192$	0.574493	0.0414605
$193$	−0.569528	−0.0409955	−0.0204978	−	0.999790i	$-0.506525\pi$
$193$	−0.569528	−0.0409955	−0.0204978	+	0.999790i	$0.506525\pi$
$194$	−1.55602	−0.111716
$195$	0.574493	0.0411403
$196$	0.0276456	0.00197469
$197$	−16.6544	−1.18658	−0.593289	−	0.804990i	$-0.702171\pi$
$197$	−16.6544	−1.18658	−0.593289	+	0.804990i	$0.702171\pi$
$198$	−14.5828	−1.03635
$199$	−17.6114	−1.24844	−0.624219	−	0.781249i	$-0.714583\pi$
$199$	−17.6114	−1.24844	−0.624219	+	0.781249i	$0.714583\pi$
$200$	1.00000	0.0707107
$201$	−2.54445	−0.179472
$202$	15.1649	1.06700
$203$	−4.19082	−0.294138
$204$	3.50107	0.245124
$205$	−2.18624	−0.152693
$206$	−14.4472	−1.00659
$207$	−5.09319	−0.354001
$208$	1.00000	0.0693375
$209$	−11.5375	−0.798069
$210$	1.52296	0.105095
$211$	−20.3142	−1.39849	−0.699243	−	0.714884i	$-0.746480\pi$
$211$	−20.3142	−1.39849	−0.699243	+	0.714884i	$0.746480\pi$
$212$	−9.86129	−0.677276
$213$	6.78300	0.464763
$214$	−6.75721	−0.461913
$215$	3.93884	0.268626
$216$	−3.25735	−0.221635
$217$	−2.65097	−0.179960
$218$	3.05614	0.206988
$219$	−1.06461	−0.0719394
$220$	5.46180	0.368235
$221$	6.09419	0.409940
$222$	−1.07334	−0.0720377
$223$	18.0022	1.20552	0.602759	−	0.797923i	$-0.294068\pi$
$223$	18.0022	1.20552	0.602759	+	0.797923i	$0.294068\pi$
$224$	2.65097	0.177125
$225$	−2.66996	−0.177997
$226$	−5.39957	−0.359174
$227$	−4.23392	−0.281015	−0.140508	−	0.990080i	$-0.544873\pi$
$227$	−4.23392	−0.281015	−0.140508	+	0.990080i	$0.544873\pi$
$228$	−1.21356	−0.0803702
$229$	11.2182	0.741318	0.370659	−	0.928769i	$-0.379132\pi$
$229$	11.2182	0.741318	0.370659	+	0.928769i	$0.379132\pi$
$230$	1.90759	0.125783
$231$	8.31813	0.547293
$232$	−1.58086	−0.103789
$233$	19.0696	1.24929	0.624646	−	0.780908i	$-0.285243\pi$
$233$	19.0696	1.24929	0.624646	+	0.780908i	$0.285243\pi$
$234$	−2.66996	−0.174541
$235$	−9.99497	−0.652000
$236$	−6.85309	−0.446098
$237$	1.58733	0.103108
$238$	16.1555	1.04721
$239$	−4.55128	−0.294398	−0.147199	−	0.989107i	$-0.547026\pi$
$239$	−4.55128	−0.294398	−0.147199	+	0.989107i	$0.547026\pi$
$240$	0.574493	0.0370834
$241$	15.8198	1.01904	0.509522	−	0.860458i	$-0.329822\pi$
$241$	15.8198	1.01904	0.509522	+	0.860458i	$0.329822\pi$
$242$	18.8313	1.21052
$243$	13.2986	0.853106
$244$	8.66537	0.554744
$245$	0.0276456	0.00176621
$246$	−1.25598	−0.0800782
$247$	−2.11241	−0.134409
$248$	−1.00000	−0.0635001
$249$	6.25657	0.396494
$250$	1.00000	0.0632456
$251$	−16.7453	−1.05695	−0.528477	−	0.848948i	$-0.677237\pi$
$251$	−16.7453	−1.05695	−0.528477	+	0.848948i	$0.677237\pi$
$252$	−7.07798	−0.445871
$253$	10.4189	0.655030
$254$	9.99185	0.626945
$255$	3.50107	0.219246
$256$	1.00000	0.0625000
$257$	2.59139	0.161646	0.0808231	−	0.996728i	$-0.474245\pi$
$257$	2.59139	0.161646	0.0808231	+	0.996728i	$0.474245\pi$
$258$	2.26284	0.140878
$259$	−4.95287	−0.307756
$260$	1.00000	0.0620174
$261$	4.22084	0.261263
$262$	−15.5104	−0.958233
$263$	−13.3832	−0.825246	−0.412623	−	0.910902i	$-0.635387\pi$
$263$	−13.3832	−0.825246	−0.412623	+	0.910902i	$0.635387\pi$
$264$	3.13777	0.193116
$265$	−9.86129	−0.605774
$266$	−5.59993	−0.343354
$267$	−3.28577	−0.201086
$268$	−4.42904	−0.270546
$269$	11.4529	0.698297	0.349149	−	0.937067i	$-0.386471\pi$
$269$	11.4529	0.698297	0.349149	+	0.937067i	$0.386471\pi$
$270$	−3.25735	−0.198236
$271$	−5.81599	−0.353296	−0.176648	−	0.984274i	$-0.556525\pi$
$271$	−5.81599	−0.353296	−0.176648	+	0.984274i	$0.556525\pi$
$272$	6.09419	0.369515
$273$	1.52296	0.0921740
$274$	9.64959	0.582953
$275$	5.46180	0.329359
$276$	1.09590	0.0659654
$277$	−28.3232	−1.70177	−0.850887	−	0.525349i	$-0.823935\pi$
$277$	−28.3232	−1.70177	−0.850887	+	0.525349i	$0.823935\pi$
$278$	−1.22773	−0.0736341
$279$	2.66996	0.159846
$280$	2.65097	0.158426
$281$	−13.6691	−0.815429	−0.407715	−	0.913109i	$-0.633674\pi$
$281$	−13.6691	−0.815429	−0.407715	+	0.913109i	$0.633674\pi$
$282$	−5.74205	−0.341934
$283$	−31.5935	−1.87804	−0.939018	−	0.343868i	$-0.888263\pi$
$283$	−31.5935	−1.87804	−0.939018	+	0.343868i	$0.888263\pi$
$284$	11.8069	0.700612
$285$	−1.21356	−0.0718853
$286$	5.46180	0.322963
$287$	−5.79565	−0.342106
$288$	−2.66996	−0.157329
$289$	20.1392	1.18466
$290$	−1.58086	−0.0928315
$291$	−0.893922	−0.0524027
$292$	−1.85312	−0.108446
$293$	9.09822	0.531524	0.265762	−	0.964039i	$-0.414376\pi$
$293$	9.09822	0.531524	0.265762	+	0.964039i	$0.414376\pi$
$294$	0.0158822	0.000926270 0
$295$	−6.85309	−0.399002
$296$	−1.86832	−0.108594
$297$	−17.7910	−1.03234
$298$	−12.1152	−0.701816
$299$	1.90759	0.110319
$300$	0.574493	0.0331684
$301$	10.4417	0.601852
$302$	16.3675	0.941846
$303$	8.71214	0.500499
$304$	−2.11241	−0.121155
$305$	8.66537	0.496178
$306$	−16.2712	−0.930165
$307$	−18.9973	−1.08423	−0.542116	−	0.840304i	$-0.682376\pi$
$307$	−18.9973	−1.08423	−0.542116	+	0.840304i	$0.682376\pi$
$308$	14.4791	0.825022
$309$	−8.29984	−0.472161
$310$	−1.00000	−0.0567962
$311$	27.7546	1.57382	0.786909	−	0.617068i	$-0.211680\pi$
$311$	27.7546	1.57382	0.786909	+	0.617068i	$0.211680\pi$
$312$	0.574493	0.0325243
$313$	2.64737	0.149638	0.0748192	−	0.997197i	$-0.476162\pi$
$313$	2.64737	0.149638	0.0748192	+	0.997197i	$0.476162\pi$
$314$	3.69050	0.208267
$315$	−7.07798	−0.398799
$316$	2.76301	0.155432
$317$	21.8541	1.22745	0.613724	−	0.789521i	$-0.289671\pi$
$317$	21.8541	1.22745	0.613724	+	0.789521i	$0.289671\pi$
$318$	−5.66525	−0.317691
$319$	−8.63436	−0.483431
$320$	1.00000	0.0559017
$321$	−3.88197	−0.216671
$322$	5.05697	0.281814
$323$	−12.8734	−0.716296
$324$	6.13855	0.341030
$325$	1.00000	0.0554700
$326$	23.7389	1.31478
$327$	1.75573	0.0970923
$328$	−2.18624	−0.120715
$329$	−26.4964	−1.46079
$330$	3.13777	0.172728
$331$	−20.5451	−1.12926	−0.564631	−	0.825343i	$-0.690982\pi$
$331$	−20.5451	−1.12926	−0.564631	+	0.825343i	$0.690982\pi$
$332$	10.8906	0.597699
$333$	4.98834	0.273359
$334$	−14.5857	−0.798093
$335$	−4.42904	−0.241984
$336$	1.52296	0.0830845
$337$	−12.6765	−0.690530	−0.345265	−	0.938505i	$-0.612211\pi$
$337$	−12.6765	−0.690530	−0.345265	+	0.938505i	$0.612211\pi$
$338$	1.00000	0.0543928
$339$	−3.10202	−0.168478
$340$	6.09419	0.330504
$341$	−5.46180	−0.295773
$342$	5.64004	0.304978
$343$	−18.4835	−0.998016
$344$	3.93884	0.212368
$345$	1.09590	0.0590012
$346$	1.63786	0.0880520
$347$	−1.24387	−0.0667747	−0.0333873	−	0.999442i	$-0.510629\pi$
$347$	−1.24387	−0.0667747	−0.0333873	+	0.999442i	$0.510629\pi$
$348$	−0.908195	−0.0486844
$349$	11.1025	0.594305	0.297153	−	0.954830i	$-0.403963\pi$
$349$	11.1025	0.594305	0.297153	+	0.954830i	$0.403963\pi$
$350$	2.65097	0.141700
$351$	−3.25735	−0.173865
$352$	5.46180	0.291115
$353$	5.79077	0.308212	0.154106	−	0.988054i	$-0.450750\pi$
$353$	5.79077	0.308212	0.154106	+	0.988054i	$0.450750\pi$
$354$	−3.93705	−0.209252
$355$	11.8069	0.626646
$356$	−5.71941	−0.303128
$357$	9.28124	0.491215
$358$	13.0508	0.689758
$359$	−2.07598	−0.109566	−0.0547829	−	0.998498i	$-0.517447\pi$
$359$	−2.07598	−0.109566	−0.0547829	+	0.998498i	$0.517447\pi$
$360$	−2.66996	−0.140719
$361$	−14.5377	−0.765144
$362$	6.55122	0.344324
$363$	10.8184	0.567821
$364$	2.65097	0.138949
$365$	−1.85312	−0.0969968
$366$	4.97820	0.260215
$367$	17.6437	0.920994	0.460497	−	0.887661i	$-0.347671\pi$
$367$	17.6437	0.920994	0.460497	+	0.887661i	$0.347671\pi$
$368$	1.90759	0.0994402
$369$	5.83716	0.303870
$370$	−1.86832	−0.0971294
$371$	−26.1420	−1.35722
$372$	−0.574493	−0.0297861
$373$	−7.66397	−0.396825	−0.198413	−	0.980119i	$-0.563579\pi$
$373$	−7.66397	−0.396825	−0.198413	+	0.980119i	$0.563579\pi$
$374$	33.2853	1.72114
$375$	0.574493	0.0296667
$376$	−9.99497	−0.515451
$377$	−1.58086	−0.0814186
$378$	−8.63515	−0.444144
$379$	3.68946	0.189515	0.0947574	−	0.995500i	$-0.469792\pi$
$379$	3.68946	0.189515	0.0947574	+	0.995500i	$0.469792\pi$
$380$	−2.11241	−0.108364
$381$	5.74025	0.294082
$382$	−25.1493	−1.28675
$383$	7.99773	0.408665	0.204332	−	0.978902i	$-0.434498\pi$
$383$	7.99773	0.408665	0.204332	+	0.978902i	$0.434498\pi$
$384$	0.574493	0.0293170
$385$	14.4791	0.737922
$386$	−0.569528	−0.0289882
$387$	−10.5165	−0.534585
$388$	−1.55602	−0.0789949
$389$	20.7990	1.05455	0.527277	−	0.849694i	$-0.323213\pi$
$389$	20.7990	1.05455	0.527277	+	0.849694i	$0.323213\pi$
$390$	0.574493	0.0290906
$391$	11.6252	0.587914
$392$	0.0276456	0.00139632
$393$	−8.91060	−0.449480
$394$	−16.6544	−0.839037
$395$	2.76301	0.139022
$396$	−14.5828	−0.732812
$397$	4.85991	0.243912	0.121956	−	0.992536i	$-0.461083\pi$
$397$	4.85991	0.243912	0.121956	+	0.992536i	$0.461083\pi$
$398$	−17.6114	−0.882779
$399$	−3.21712	−0.161058
$400$	1.00000	0.0500000
$401$	−1.50310	−0.0750612	−0.0375306	−	0.999295i	$-0.511949\pi$
$401$	−1.50310	−0.0750612	−0.0375306	+	0.999295i	$0.511949\pi$
$402$	−2.54445	−0.126906
$403$	−1.00000	−0.0498135
$404$	15.1649	0.754483
$405$	6.13855	0.305027
$406$	−4.19082	−0.207987
$407$	−10.2044	−0.505813
$408$	3.50107	0.173329
$409$	−30.8261	−1.52425	−0.762125	−	0.647430i	$-0.775844\pi$
$409$	−30.8261	−1.52425	−0.762125	+	0.647430i	$0.775844\pi$
$410$	−2.18624	−0.107970
$411$	5.54363	0.273447
$412$	−14.4472	−0.711764
$413$	−18.1673	−0.893956
$414$	−5.09319	−0.250317
$415$	10.8906	0.534598
$416$	1.00000	0.0490290
$417$	−0.705320	−0.0345397
$418$	−11.5375	−0.564320
$419$	21.3064	1.04088	0.520442	−	0.853897i	$-0.325767\pi$
$419$	21.3064	1.04088	0.520442	+	0.853897i	$0.325767\pi$
$420$	1.52296	0.0743131
$421$	11.1970	0.545708	0.272854	−	0.962055i	$-0.412032\pi$
$421$	11.1970	0.545708	0.272854	+	0.962055i	$0.412032\pi$
$422$	−20.3142	−0.988879
$423$	26.6862	1.29753
$424$	−9.86129	−0.478907
$425$	6.09419	0.295612
$426$	6.78300	0.328637
$427$	22.9717	1.11168
$428$	−6.75721	−0.326622
$429$	3.13777	0.151493
$430$	3.93884	0.189948
$431$	36.1462	1.74110	0.870549	−	0.492081i	$-0.163764\pi$
$431$	36.1462	1.74110	0.870549	+	0.492081i	$0.163764\pi$
$432$	−3.25735	−0.156719
$433$	−25.2596	−1.21390	−0.606949	−	0.794740i	$-0.707607\pi$
$433$	−25.2596	−1.21390	−0.606949	+	0.794740i	$0.707607\pi$
$434$	−2.65097	−0.127251
$435$	−0.908195	−0.0435446
$436$	3.05614	0.146363
$437$	−4.02961	−0.192763
$438$	−1.06461	−0.0508688
$439$	−4.22167	−0.201489	−0.100745	−	0.994912i	$-0.532122\pi$
$439$	−4.22167	−0.201489	−0.100745	+	0.994912i	$0.532122\pi$
$440$	5.46180	0.260381
$441$	−0.0738126	−0.00351489
$442$	6.09419	0.289871
$443$	7.90570	0.375611	0.187806	−	0.982206i	$-0.439862\pi$
$443$	7.90570	0.375611	0.187806	+	0.982206i	$0.439862\pi$
$444$	−1.07334	−0.0509384
$445$	−5.71941	−0.271126
$446$	18.0022	0.852430
$447$	−6.96012	−0.329202
$448$	2.65097	0.125247
$449$	−5.10945	−0.241130	−0.120565	−	0.992705i	$-0.538471\pi$
$449$	−5.10945	−0.241130	−0.120565	+	0.992705i	$0.538471\pi$
$450$	−2.66996	−0.125863
$451$	−11.9408	−0.562270
$452$	−5.39957	−0.253974
$453$	9.40304	0.441794
$454$	−4.23392	−0.198708
$455$	2.65097	0.124279
$456$	−1.21356	−0.0568303
$457$	−25.9473	−1.21376	−0.606881	−	0.794793i	$-0.707580\pi$
$457$	−25.9473	−1.21376	−0.606881	+	0.794793i	$0.707580\pi$
$458$	11.2182	0.524191
$459$	−19.8509	−0.926562
$460$	1.90759	0.0889420
$461$	−16.4812	−0.767605	−0.383803	−	0.923415i	$-0.625386\pi$
$461$	−16.4812	−0.767605	−0.383803	+	0.923415i	$0.625386\pi$
$462$	8.31813	0.386995
$463$	−36.8600	−1.71303	−0.856515	−	0.516122i	$-0.827375\pi$
$463$	−36.8600	−1.71303	−0.856515	+	0.516122i	$0.827375\pi$
$464$	−1.58086	−0.0733897
$465$	−0.574493	−0.0266415
$466$	19.0696	0.883383
$467$	−0.401555	−0.0185818	−0.00929088	−	0.999957i	$-0.502957\pi$
$467$	−0.401555	−0.0185818	−0.00929088	+	0.999957i	$0.502957\pi$
$468$	−2.66996	−0.123419
$469$	−11.7412	−0.542160
$470$	−9.99497	−0.461034
$471$	2.12017	0.0976921
$472$	−6.85309	−0.315439
$473$	21.5131	0.989175
$474$	1.58733	0.0729086
$475$	−2.11241	−0.0969239
$476$	16.1555	0.740487
$477$	26.3292	1.20553
$478$	−4.55128	−0.208171
$479$	−35.6527	−1.62901	−0.814507	−	0.580154i	$-0.802992\pi$
$479$	−35.6527	−1.62901	−0.814507	+	0.580154i	$0.802992\pi$
$480$	0.574493	0.0262219
$481$	−1.86832	−0.0851881
$482$	15.8198	0.720573
$483$	2.90520	0.132191
$484$	18.8313	0.855967
$485$	−1.55602	−0.0706552
$486$	13.2986	0.603237
$487$	32.5500	1.47498	0.737490	−	0.675358i	$-0.236011\pi$
$487$	32.5500	1.47498	0.737490	+	0.675358i	$0.236011\pi$
$488$	8.66537	0.392263
$489$	13.6378	0.616725
$490$	0.0276456	0.00124890
$491$	21.6706	0.977979	0.488990	−	0.872290i	$-0.337366\pi$
$491$	21.6706	0.977979	0.488990	+	0.872290i	$0.337366\pi$
$492$	−1.25598	−0.0566238
$493$	−9.63409	−0.433897
$494$	−2.11241	−0.0950417
$495$	−14.5828	−0.655447
$496$	−1.00000	−0.0449013
$497$	31.2998	1.40399
$498$	6.25657	0.280364
$499$	−7.01650	−0.314102	−0.157051	−	0.987591i	$-0.550199\pi$
$499$	−7.01650	−0.314102	−0.157051	+	0.987591i	$0.550199\pi$
$500$	1.00000	0.0447214
$501$	−8.37937	−0.374363
$502$	−16.7453	−0.747379
$503$	10.1133	0.450931	0.225466	−	0.974251i	$-0.427610\pi$
$503$	10.1133	0.450931	0.225466	+	0.974251i	$0.427610\pi$
$504$	−7.07798	−0.315278
$505$	15.1649	0.674830
$506$	10.4189	0.463176
$507$	0.574493	0.0255141
$508$	9.99185	0.443317
$509$	−28.0381	−1.24277	−0.621383	−	0.783507i	$-0.713429\pi$
$509$	−28.0381	−1.24277	−0.621383	+	0.783507i	$0.713429\pi$
$510$	3.50107	0.155030
$511$	−4.91257	−0.217319
$512$	1.00000	0.0441942
$513$	6.88086	0.303797
$514$	2.59139	0.114301
$515$	−14.4472	−0.636621
$516$	2.26284	0.0996158
$517$	−54.5906	−2.40089
$518$	−4.95287	−0.217616
$519$	0.940941	0.0413027
$520$	1.00000	0.0438529
$521$	−14.6391	−0.641352	−0.320676	−	0.947189i	$-0.603910\pi$
$521$	−14.6391	−0.641352	−0.320676	+	0.947189i	$0.603910\pi$
$522$	4.22084	0.184741
$523$	41.5429	1.81654	0.908271	−	0.418381i	$-0.137402\pi$
$523$	41.5429	1.81654	0.908271	+	0.418381i	$0.137402\pi$
$524$	−15.5104	−0.677573
$525$	1.52296	0.0664676
$526$	−13.3832	−0.583537
$527$	−6.09419	−0.265467
$528$	3.13777	0.136554
$529$	−19.3611	−0.841786
$530$	−9.86129	−0.428347
$531$	18.2975	0.794042
$532$	−5.59993	−0.242788
$533$	−2.18624	−0.0946964
$534$	−3.28577	−0.142189
$535$	−6.75721	−0.292140
$536$	−4.42904	−0.191305
$537$	7.49762	0.323546
$538$	11.4529	0.493771
$539$	0.150995	0.00650381
$540$	−3.25735	−0.140174
$541$	−21.8516	−0.939475	−0.469738	−	0.882806i	$-0.655651\pi$
$541$	−21.8516	−0.939475	−0.469738	+	0.882806i	$0.655651\pi$
$542$	−5.81599	−0.249818
$543$	3.76363	0.161513
$544$	6.09419	0.261286
$545$	3.05614	0.130911
$546$	1.52296	0.0651769
$547$	19.7480	0.844365	0.422182	−	0.906511i	$-0.361264\pi$
$547$	19.7480	0.844365	0.422182	+	0.906511i	$0.361264\pi$
$548$	9.64959	0.412210
$549$	−23.1362	−0.987428
$550$	5.46180	0.232892
$551$	3.33943	0.142264
$552$	1.09590	0.0466446
$553$	7.32467	0.311477
$554$	−28.3232	−1.20334
$555$	−1.07334	−0.0455607
$556$	−1.22773	−0.0520671
$557$	21.6809	0.918647	0.459324	−	0.888269i	$-0.348092\pi$
$557$	21.6809	0.918647	0.459324	+	0.888269i	$0.348092\pi$
$558$	2.66996	0.113028
$559$	3.93884	0.166595
$560$	2.65097	0.112024
$561$	19.1222	0.807339
$562$	−13.6691	−0.576596
$563$	−1.00319	−0.0422794	−0.0211397	−	0.999777i	$-0.506729\pi$
$563$	−1.00319	−0.0422794	−0.0211397	+	0.999777i	$0.506729\pi$
$564$	−5.74205	−0.241784
$565$	−5.39957	−0.227162
$566$	−31.5935	−1.32797
$567$	16.2731	0.683406
$568$	11.8069	0.495407
$569$	−13.4489	−0.563807	−0.281903	−	0.959443i	$-0.590966\pi$
$569$	−13.4489	−0.563807	−0.281903	+	0.959443i	$0.590966\pi$
$570$	−1.21356	−0.0508306
$571$	−0.213456	−0.00893286	−0.00446643	−	0.999990i	$-0.501422\pi$
$571$	−0.213456	−0.00893286	−0.00446643	+	0.999990i	$0.501422\pi$
$572$	5.46180	0.228369
$573$	−14.4481	−0.603578
$574$	−5.79565	−0.241906
$575$	1.90759	0.0795521
$576$	−2.66996	−0.111248
$577$	23.8040	0.990972	0.495486	−	0.868616i	$-0.334990\pi$
$577$	23.8040	0.990972	0.495486	+	0.868616i	$0.334990\pi$
$578$	20.1392	0.837680
$579$	−0.327190	−0.0135975
$580$	−1.58086	−0.0656418
$581$	28.8706	1.19776
$582$	−0.893922	−0.0370543
$583$	−53.8604	−2.23067
$584$	−1.85312	−0.0766827
$585$	−2.66996	−0.110389
$586$	9.09822	0.375844
$587$	3.46568	0.143044	0.0715220	−	0.997439i	$-0.477214\pi$
$587$	3.46568	0.143044	0.0715220	+	0.997439i	$0.477214\pi$
$588$	0.0158822	0.000654972 0
$589$	2.11241	0.0870402
$590$	−6.85309	−0.282137
$591$	−9.56785	−0.393569
$592$	−1.86832	−0.0767875
$593$	−16.3183	−0.670113	−0.335056	−	0.942198i	$-0.608755\pi$
$593$	−16.3183	−0.670113	−0.335056	+	0.942198i	$0.608755\pi$
$594$	−17.7910	−0.729974
$595$	16.1555	0.662312
$596$	−12.1152	−0.496259
$597$	−10.1176	−0.414087
$598$	1.90759	0.0780073
$599$	−12.9927	−0.530865	−0.265433	−	0.964129i	$-0.585515\pi$
$599$	−12.9927	−0.530865	−0.265433	+	0.964129i	$0.585515\pi$
$600$	0.574493	0.0234536
$601$	−31.0785	−1.26772	−0.633859	−	0.773449i	$-0.718530\pi$
$601$	−31.0785	−1.26772	−0.633859	+	0.773449i	$0.718530\pi$
$602$	10.4417	0.425574
$603$	11.8253	0.481565
$604$	16.3675	0.665986
$605$	18.8313	0.765600
$606$	8.71214	0.353907
$607$	−13.6270	−0.553101	−0.276551	−	0.960999i	$-0.589191\pi$
$607$	−13.6270	−0.553101	−0.276551	+	0.960999i	$0.589191\pi$
$608$	−2.11241	−0.0856694
$609$	−2.40760	−0.0975609
$610$	8.66537	0.350851
$611$	−9.99497	−0.404353
$612$	−16.2712	−0.657726
$613$	−12.0228	−0.485597	−0.242798	−	0.970077i	$-0.578065\pi$
$613$	−12.0228	−0.485597	−0.242798	+	0.970077i	$0.578065\pi$
$614$	−18.9973	−0.766667
$615$	−1.25598	−0.0506459
$616$	14.4791	0.583379
$617$	9.88752	0.398057	0.199028	−	0.979994i	$-0.436221\pi$
$617$	9.88752	0.398057	0.199028	+	0.979994i	$0.436221\pi$
$618$	−8.29984	−0.333869
$619$	23.9439	0.962385	0.481192	−	0.876615i	$-0.340204\pi$
$619$	23.9439	0.962385	0.481192	+	0.876615i	$0.340204\pi$
$620$	−1.00000	−0.0401610
$621$	−6.21370	−0.249347
$622$	27.7546	1.11286
$623$	−15.1620	−0.607453
$624$	0.574493	0.0229981
$625$	1.00000	0.0400000
$626$	2.64737	0.105810
$627$	−6.62825	−0.264707
$628$	3.69050	0.147267
$629$	−11.3859	−0.453986
$630$	−7.07798	−0.281993
$631$	32.4434	1.29155	0.645776	−	0.763527i	$-0.276534\pi$
$631$	32.4434	1.29155	0.645776	+	0.763527i	$0.276534\pi$
$632$	2.76301	0.109907
$633$	−11.6704	−0.463855
$634$	21.8541	0.867937
$635$	9.99185	0.396515
$636$	−5.66525	−0.224642
$637$	0.0276456	0.00109536
$638$	−8.63436	−0.341838
$639$	−31.5240	−1.24707
$640$	1.00000	0.0395285
$641$	11.7690	0.464846	0.232423	−	0.972615i	$-0.425335\pi$
$641$	11.7690	0.464846	0.232423	+	0.972615i	$0.425335\pi$
$642$	−3.88197	−0.153209
$643$	−25.5912	−1.00922	−0.504608	−	0.863348i	$-0.668363\pi$
$643$	−25.5912	−1.00922	−0.504608	+	0.863348i	$0.668363\pi$
$644$	5.05697	0.199273
$645$	2.26284	0.0890991
$646$	−12.8734	−0.506498
$647$	10.3291	0.406079	0.203040	−	0.979171i	$-0.434918\pi$
$647$	10.3291	0.406079	0.203040	+	0.979171i	$0.434918\pi$
$648$	6.13855	0.241145
$649$	−37.4302	−1.46926
$650$	1.00000	0.0392232
$651$	−1.52296	−0.0596897
$652$	23.7389	0.929688
$653$	−35.6050	−1.39333	−0.696665	−	0.717396i	$-0.745334\pi$
$653$	−35.6050	−1.39333	−0.696665	+	0.717396i	$0.745334\pi$
$654$	1.75573	0.0686547
$655$	−15.5104	−0.606040
$656$	−2.18624	−0.0853581
$657$	4.94776	0.193030
$658$	−26.4964	−1.03294
$659$	5.17288	0.201507	0.100753	−	0.994911i	$-0.467875\pi$
$659$	5.17288	0.201507	0.100753	+	0.994911i	$0.467875\pi$
$660$	3.13777	0.122137
$661$	−29.0936	−1.13161	−0.565804	−	0.824540i	$-0.691434\pi$
$661$	−29.0936	−1.13161	−0.565804	+	0.824540i	$0.691434\pi$
$662$	−20.5451	−0.798509
$663$	3.50107	0.135970
$664$	10.8906	0.422637
$665$	−5.59993	−0.217156
$666$	4.98834	0.193294
$667$	−3.01564	−0.116766
$668$	−14.5857	−0.564337
$669$	10.3422	0.399851
$670$	−4.42904	−0.171109
$671$	47.3286	1.82710
$672$	1.52296	0.0587496
$673$	2.96957	0.114468	0.0572342	−	0.998361i	$-0.481772\pi$
$673$	2.96957	0.114468	0.0572342	+	0.998361i	$0.481772\pi$
$674$	−12.6765	−0.488279
$675$	−3.25735	−0.125376
$676$	1.00000	0.0384615
$677$	−5.40749	−0.207827	−0.103913	−	0.994586i	$-0.533136\pi$
$677$	−5.40749	−0.207827	−0.103913	+	0.994586i	$0.533136\pi$
$678$	−3.10202	−0.119132
$679$	−4.12496	−0.158301
$680$	6.09419	0.233702
$681$	−2.43236	−0.0932083
$682$	−5.46180	−0.209143
$683$	19.5993	0.749946	0.374973	−	0.927036i	$-0.377652\pi$
$683$	19.5993	0.749946	0.374973	+	0.927036i	$0.377652\pi$
$684$	5.64004	0.215652
$685$	9.64959	0.368692
$686$	−18.4835	−0.705704
$687$	6.44476	0.245883
$688$	3.93884	0.150167
$689$	−9.86129	−0.375685
$690$	1.09590	0.0417202
$691$	−35.2005	−1.33909	−0.669545	−	0.742771i	$-0.733511\pi$
$691$	−35.2005	−1.33909	−0.669545	+	0.742771i	$0.733511\pi$
$692$	1.63786	0.0622622
$693$	−38.6585	−1.46852
$694$	−1.24387	−0.0472168
$695$	−1.22773	−0.0465703
$696$	−0.908195	−0.0344251
$697$	−13.3233	−0.504658
$698$	11.1025	0.420237
$699$	10.9554	0.414370
$700$	2.65097	0.100197
$701$	−33.0743	−1.24920	−0.624599	−	0.780946i	$-0.714737\pi$
$701$	−33.0743	−1.24920	−0.624599	+	0.780946i	$0.714737\pi$
$702$	−3.25735	−0.122941
$703$	3.94666	0.148851
$704$	5.46180	0.205849
$705$	−5.74205	−0.216258
$706$	5.79077	0.217938
$707$	40.2017	1.51194
$708$	−3.93705	−0.147964
$709$	−5.67506	−0.213132	−0.106566	−	0.994306i	$-0.533985\pi$
$709$	−5.67506	−0.213132	−0.106566	+	0.994306i	$0.533985\pi$
$710$	11.8069	0.443106
$711$	−7.37713	−0.276664
$712$	−5.71941	−0.214344
$713$	−1.90759	−0.0714399
$714$	9.28124	0.347342
$715$	5.46180	0.204260
$716$	13.0508	0.487733
$717$	−2.61468	−0.0976470
$718$	−2.07598	−0.0774748
$719$	−28.6757	−1.06942	−0.534712	−	0.845034i	$-0.679580\pi$
$719$	−28.6757	−1.06942	−0.534712	+	0.845034i	$0.679580\pi$
$720$	−2.66996	−0.0995034
$721$	−38.2992	−1.42634
$722$	−14.5377	−0.541038
$723$	9.08838	0.338000
$724$	6.55122	0.243474
$725$	−1.58086	−0.0587118
$726$	10.8184	0.401510
$727$	−6.09449	−0.226032	−0.113016	−	0.993593i	$-0.536051\pi$
$727$	−6.09449	−0.226032	−0.113016	+	0.993593i	$0.536051\pi$
$728$	2.65097	0.0982515
$729$	−10.7757	−0.399099
$730$	−1.85312	−0.0685871
$731$	24.0040	0.887821
$732$	4.97820	0.184000
$733$	−26.7358	−0.987509	−0.493754	−	0.869601i	$-0.664376\pi$
$733$	−26.7358	−0.987509	−0.493754	+	0.869601i	$0.664376\pi$
$734$	17.6437	0.651241
$735$	0.0158822	0.000585825 0
$736$	1.90759	0.0703148
$737$	−24.1905	−0.891069
$738$	5.83716	0.214869
$739$	3.79203	0.139492	0.0697460	−	0.997565i	$-0.477781\pi$
$739$	3.79203	0.139492	0.0697460	+	0.997565i	$0.477781\pi$
$740$	−1.86832	−0.0686809
$741$	−1.21356	−0.0445814
$742$	−26.1420	−0.959703
$743$	31.2853	1.14775	0.573873	−	0.818944i	$-0.305440\pi$
$743$	31.2853	1.14775	0.573873	+	0.818944i	$0.305440\pi$
$744$	−0.574493	−0.0210619
$745$	−12.1152	−0.443868
$746$	−7.66397	−0.280598
$747$	−29.0774	−1.06389
$748$	33.2853	1.21703
$749$	−17.9132	−0.654533
$750$	0.574493	0.0209775
$751$	−7.11777	−0.259731	−0.129866	−	0.991532i	$-0.541455\pi$
$751$	−7.11777	−0.259731	−0.129866	+	0.991532i	$0.541455\pi$
$752$	−9.99497	−0.364479
$753$	−9.62006	−0.350574
$754$	−1.58086	−0.0575717
$755$	16.3675	0.595676
$756$	−8.63515	−0.314057
$757$	−30.0722	−1.09299	−0.546496	−	0.837462i	$-0.684039\pi$
$757$	−30.0722	−1.09299	−0.546496	+	0.837462i	$0.684039\pi$
$758$	3.68946	0.134007
$759$	5.98559	0.217263
$760$	−2.11241	−0.0766251
$761$	−32.1167	−1.16423	−0.582114	−	0.813107i	$-0.697774\pi$
$761$	−32.1167	−1.16423	−0.582114	+	0.813107i	$0.697774\pi$
$762$	5.74025	0.207947
$763$	8.10175	0.293303
$764$	−25.1493	−0.909870
$765$	−16.2712	−0.588288
$766$	7.99773	0.288970
$767$	−6.85309	−0.247451
$768$	0.574493	0.0207302
$769$	35.4075	1.27683	0.638414	−	0.769693i	$-0.279591\pi$
$769$	35.4075	1.27683	0.638414	+	0.769693i	$0.279591\pi$
$770$	14.4791	0.521790
$771$	1.48873	0.0536154
$772$	−0.569528	−0.0204978
$773$	16.6930	0.600407	0.300204	−	0.953875i	$-0.402945\pi$
$773$	16.6930	0.600407	0.300204	+	0.953875i	$0.402945\pi$
$774$	−10.5165	−0.378009
$775$	−1.00000	−0.0359211
$776$	−1.55602	−0.0558578
$777$	−2.84539	−0.102078
$778$	20.7990	0.745682
$779$	4.61822	0.165465
$780$	0.574493	0.0205702
$781$	64.4871	2.30753
$782$	11.6252	0.415718
$783$	5.14943	0.184026
$784$	0.0276456	0.000987344 0
$785$	3.69050	0.131720
$786$	−8.91060	−0.317831
$787$	14.7485	0.525729	0.262864	−	0.964833i	$-0.415333\pi$
$787$	14.7485	0.525729	0.262864	+	0.964833i	$0.415333\pi$
$788$	−16.6544	−0.593289
$789$	−7.68858	−0.273721
$790$	2.76301	0.0983036
$791$	−14.3141	−0.508951
$792$	−14.5828	−0.518176
$793$	8.66537	0.307716
$794$	4.85991	0.172472
$795$	−5.66525	−0.200926
$796$	−17.6114	−0.624219
$797$	−44.4794	−1.57554	−0.787771	−	0.615969i	$-0.788765\pi$
$797$	−44.4794	−1.57554	−0.787771	+	0.615969i	$0.788765\pi$
$798$	−3.21712	−0.113885
$799$	−60.9113	−2.15489
$800$	1.00000	0.0353553
$801$	15.2706	0.539560
$802$	−1.50310	−0.0530763
$803$	−10.1214	−0.357176
$804$	−2.54445	−0.0897359
$805$	5.05697	0.178235
$806$	−1.00000	−0.0352235
$807$	6.57963	0.231614
$808$	15.1649	0.533500
$809$	21.8448	0.768023	0.384012	−	0.923328i	$-0.374542\pi$
$809$	21.8448	0.768023	0.384012	+	0.923328i	$0.374542\pi$
$810$	6.13855	0.215686
$811$	−6.53612	−0.229514	−0.114757	−	0.993394i	$-0.536609\pi$
$811$	−6.53612	−0.229514	−0.114757	+	0.993394i	$0.536609\pi$
$812$	−4.19082	−0.147069
$813$	−3.34125	−0.117183
$814$	−10.2044	−0.357664
$815$	23.7389	0.831538
$816$	3.50107	0.122562
$817$	−8.32043	−0.291095
$818$	−30.8261	−1.07781
$819$	−7.07798	−0.247325
$820$	−2.18624	−0.0763466
$821$	12.1753	0.424920	0.212460	−	0.977170i	$-0.431853\pi$
$821$	12.1753	0.424920	0.212460	+	0.977170i	$0.431853\pi$
$822$	5.54363	0.193356
$823$	30.0875	1.04878	0.524392	−	0.851477i	$-0.324293\pi$
$823$	30.0875	1.04878	0.524392	+	0.851477i	$0.324293\pi$
$824$	−14.4472	−0.503293
$825$	3.13777	0.109243
$826$	−18.1673	−0.632122
$827$	20.2642	0.704655	0.352328	−	0.935877i	$-0.385390\pi$
$827$	20.2642	0.704655	0.352328	+	0.935877i	$0.385390\pi$
$828$	−5.09319	−0.177001
$829$	−26.0892	−0.906116	−0.453058	−	0.891481i	$-0.649667\pi$
$829$	−26.0892	−0.906116	−0.453058	+	0.891481i	$0.649667\pi$
$830$	10.8906	0.378018
$831$	−16.2715	−0.564451
$832$	1.00000	0.0346688
$833$	0.168478	0.00583741
$834$	−0.705320	−0.0244232
$835$	−14.5857	−0.504758
$836$	−11.5375	−0.399035
$837$	3.25735	0.112591
$838$	21.3064	0.736016
$839$	51.7662	1.78717	0.893583	−	0.448897i	$-0.148183\pi$
$839$	51.7662	1.78717	0.893583	+	0.448897i	$0.148183\pi$
$840$	1.52296	0.0525473
$841$	−26.5009	−0.913823
$842$	11.1970	0.385874
$843$	−7.85280	−0.270465
$844$	−20.3142	−0.699243
$845$	1.00000	0.0344010
$846$	26.6862	0.917489
$847$	49.9212	1.71531
$848$	−9.86129	−0.338638
$849$	−18.1502	−0.622914
$850$	6.09419	0.209029
$851$	−3.56400	−0.122172
$852$	6.78300	0.232382
$853$	−41.7393	−1.42913	−0.714564	−	0.699570i	$-0.753375\pi$
$853$	−41.7393	−1.42913	−0.714564	+	0.699570i	$0.753375\pi$
$854$	22.9717	0.786074
$855$	5.64004	0.192885
$856$	−6.75721	−0.230957
$857$	5.96129	0.203634	0.101817	−	0.994803i	$-0.467534\pi$
$857$	5.96129	0.203634	0.101817	+	0.994803i	$0.467534\pi$
$858$	3.13777	0.107122
$859$	13.6214	0.464756	0.232378	−	0.972626i	$-0.425349\pi$
$859$	13.6214	0.464756	0.232378	+	0.972626i	$0.425349\pi$
$860$	3.93884	0.134313
$861$	−3.32956	−0.113471
$862$	36.1462	1.23114
$863$	−10.0963	−0.343683	−0.171842	−	0.985125i	$-0.554972\pi$
$863$	−10.0963	−0.343683	−0.171842	+	0.985125i	$0.554972\pi$
$864$	−3.25735	−0.110817
$865$	1.63786	0.0556890
$866$	−25.2596	−0.858356
$867$	11.5698	0.392932
$868$	−2.65097	−0.0899798
$869$	15.0910	0.511928
$870$	−0.908195	−0.0307907
$871$	−4.42904	−0.150072
$872$	3.05614	0.103494
$873$	4.15450	0.140609
$874$	−4.02961	−0.136304
$875$	2.65097	0.0896192
$876$	−1.06461	−0.0359697
$877$	30.3366	1.02439	0.512197	−	0.858868i	$-0.328832\pi$
$877$	30.3366	1.02439	0.512197	+	0.858868i	$0.328832\pi$
$878$	−4.22167	−0.142474
$879$	5.22687	0.176298
$880$	5.46180	0.184117
$881$	11.2613	0.379402	0.189701	−	0.981842i	$-0.439248\pi$
$881$	11.2613	0.379402	0.189701	+	0.981842i	$0.439248\pi$
$882$	−0.0738126	−0.00248540
$883$	−36.0314	−1.21255	−0.606277	−	0.795253i	$-0.707338\pi$
$883$	−36.0314	−1.21255	−0.606277	+	0.795253i	$0.707338\pi$
$884$	6.09419	0.204970
$885$	−3.93705	−0.132343
$886$	7.90570	0.265597
$887$	32.8651	1.10350	0.551751	−	0.834009i	$-0.313960\pi$
$887$	32.8651	1.10350	0.551751	+	0.834009i	$0.313960\pi$
$888$	−1.07334	−0.0360189
$889$	26.4881	0.888383
$890$	−5.71941	−0.191715
$891$	33.5275	1.12321
$892$	18.0022	0.602759
$893$	21.1135	0.706535
$894$	−6.96012	−0.232781
$895$	13.0508	0.436241
$896$	2.65097	0.0885627
$897$	1.09590	0.0365910
$898$	−5.10945	−0.170505
$899$	1.58086	0.0527247
$900$	−2.66996	−0.0889986
$901$	−60.0966	−2.00211
$902$	−11.9408	−0.397585
$903$	5.99871	0.199625
$904$	−5.39957	−0.179587
$905$	6.55122	0.217770
$906$	9.40304	0.312395
$907$	34.3636	1.14103	0.570513	−	0.821289i	$-0.306744\pi$
$907$	34.3636	1.14103	0.570513	+	0.821289i	$0.306744\pi$
$908$	−4.23392	−0.140508
$909$	−40.4897	−1.34296
$910$	2.65097	0.0878788
$911$	13.0274	0.431618	0.215809	−	0.976436i	$-0.430761\pi$
$911$	13.0274	0.431618	0.215809	+	0.976436i	$0.430761\pi$
$912$	−1.21356	−0.0401851
$913$	59.4822	1.96857
$914$	−25.9473	−0.858259
$915$	4.97820	0.164574
$916$	11.2182	0.370659
$917$	−41.1175	−1.35782
$918$	−19.8509	−0.655179
$919$	−39.8232	−1.31365	−0.656823	−	0.754045i	$-0.728100\pi$
$919$	−39.8232	−1.31365	−0.656823	+	0.754045i	$0.728100\pi$
$920$	1.90759	0.0628915
$921$	−10.9138	−0.359622
$922$	−16.4812	−0.542779
$923$	11.8069	0.388629
$924$	8.31813	0.273646
$925$	−1.86832	−0.0614300
$926$	−36.8600	−1.21130
$927$	38.5735	1.26692
$928$	−1.58086	−0.0518944
$929$	−13.8021	−0.452833	−0.226416	−	0.974031i	$-0.572701\pi$
$929$	−13.8021	−0.452833	−0.226416	+	0.974031i	$0.572701\pi$
$930$	−0.574493	−0.0188384
$931$	−0.0583988	−0.00191394
$932$	19.0696	0.624646
$933$	15.9448	0.522010
$934$	−0.401555	−0.0131393
$935$	33.2853	1.08854
$936$	−2.66996	−0.0872703
$937$	50.0929	1.63646	0.818232	−	0.574888i	$-0.194954\pi$
$937$	50.0929	1.63646	0.818232	+	0.574888i	$0.194954\pi$
$938$	−11.7412	−0.383365
$939$	1.52090	0.0496327
$940$	−9.99497	−0.326000
$941$	−41.0898	−1.33949	−0.669745	−	0.742591i	$-0.733597\pi$
$941$	−41.0898	−1.33949	−0.669745	+	0.742591i	$0.733597\pi$
$942$	2.12017	0.0690788
$943$	−4.17045	−0.135808
$944$	−6.85309	−0.223049
$945$	−8.63515	−0.280901
$946$	21.5131	0.699453
$947$	11.2480	0.365510	0.182755	−	0.983158i	$-0.441498\pi$
$947$	11.2480	0.365510	0.182755	+	0.983158i	$0.441498\pi$
$948$	1.58733	0.0515542
$949$	−1.85312	−0.0601549
$950$	−2.11241	−0.0685355
$951$	12.5550	0.407125
$952$	16.1555	0.523604
$953$	−22.2592	−0.721045	−0.360522	−	0.932751i	$-0.617402\pi$
$953$	−22.2592	−0.721045	−0.360522	+	0.932751i	$0.617402\pi$
$954$	26.3292	0.852440
$955$	−25.1493	−0.813812
$956$	−4.55128	−0.147199
$957$	−4.96038	−0.160346
$958$	−35.6527	−1.15189
$959$	25.5808	0.826047
$960$	0.574493	0.0185417
$961$	1.00000	0.0322581
$962$	−1.86832	−0.0602371
$963$	18.0415	0.581378
$964$	15.8198	0.509522
$965$	−0.569528	−0.0183337
$966$	2.90520	0.0934732
$967$	34.3610	1.10498	0.552488	−	0.833521i	$-0.313679\pi$
$967$	34.3610	1.10498	0.552488	+	0.833521i	$0.313679\pi$
$968$	18.8313	0.605260
$969$	−7.39569	−0.237584
$970$	−1.55602	−0.0499607
$971$	15.1132	0.485005	0.242503	−	0.970151i	$-0.422032\pi$
$971$	15.1132	0.485005	0.242503	+	0.970151i	$0.422032\pi$
$972$	13.2986	0.426553
$973$	−3.25466	−0.104340
$974$	32.5500	1.04297
$975$	0.574493	0.0183985
$976$	8.66537	0.277372
$977$	−16.6835	−0.533751	−0.266876	−	0.963731i	$-0.585991\pi$
$977$	−16.6835	−0.533751	−0.266876	+	0.963731i	$0.585991\pi$
$978$	13.6378	0.436090
$979$	−31.2383	−0.998381
$980$	0.0276456	0.000883107 0
$981$	−8.15978	−0.260522
$982$	21.6706	0.691536
$983$	−22.4386	−0.715681	−0.357841	−	0.933783i	$-0.616487\pi$
$983$	−22.4386	−0.715681	−0.357841	+	0.933783i	$0.616487\pi$
$984$	−1.25598	−0.0400391
$985$	−16.6544	−0.530654
$986$	−9.63409	−0.306812
$987$	−15.2220	−0.484521
$988$	−2.11241	−0.0672046
$989$	7.51370	0.238922
$990$	−14.5828	−0.463471
$991$	23.2263	0.737807	0.368903	−	0.929468i	$-0.379733\pi$
$991$	23.2263	0.737807	0.368903	+	0.929468i	$0.379733\pi$
$992$	−1.00000	−0.0317500
$993$	−11.8030	−0.374558
$994$	31.2998	0.992769
$995$	−17.6114	−0.558318
$996$	6.25657	0.198247
$997$	−6.59004	−0.208709	−0.104354	−	0.994540i	$-0.533278\pi$
$997$	−6.59004	−0.208709	−0.104354	+	0.994540i	$0.533278\pi$
$998$	−7.01650	−0.222103
$999$	6.08578	0.192546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.r.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.r.1.5	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.574493 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.574493 q^{6} +2.65097 q^{7} +1.00000 q^{8} -2.66996 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.574493 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.574493 q^{6} +2.65097 q^{7} +1.00000 q^{8} -2.66996 q^{9} +1.00000 q^{10} +5.46180 q^{11} +0.574493 q^{12} +1.00000 q^{13} +2.65097 q^{14} +0.574493 q^{15} +1.00000 q^{16} +6.09419 q^{17} -2.66996 q^{18} -2.11241 q^{19} +1.00000 q^{20} +1.52296 q^{21} +5.46180 q^{22} +1.90759 q^{23} +0.574493 q^{24} +1.00000 q^{25} +1.00000 q^{26} -3.25735 q^{27} +2.65097 q^{28} -1.58086 q^{29} +0.574493 q^{30} -1.00000 q^{31} +1.00000 q^{32} +3.13777 q^{33} +6.09419 q^{34} +2.65097 q^{35} -2.66996 q^{36} -1.86832 q^{37} -2.11241 q^{38} +0.574493 q^{39} +1.00000 q^{40} -2.18624 q^{41} +1.52296 q^{42} +3.93884 q^{43} +5.46180 q^{44} -2.66996 q^{45} +1.90759 q^{46} -9.99497 q^{47} +0.574493 q^{48} +0.0276456 q^{49} +1.00000 q^{50} +3.50107 q^{51} +1.00000 q^{52} -9.86129 q^{53} -3.25735 q^{54} +5.46180 q^{55} +2.65097 q^{56} -1.21356 q^{57} -1.58086 q^{58} -6.85309 q^{59} +0.574493 q^{60} +8.66537 q^{61} -1.00000 q^{62} -7.07798 q^{63} +1.00000 q^{64} +1.00000 q^{65} +3.13777 q^{66} -4.42904 q^{67} +6.09419 q^{68} +1.09590 q^{69} +2.65097 q^{70} +11.8069 q^{71} -2.66996 q^{72} -1.85312 q^{73} -1.86832 q^{74} +0.574493 q^{75} -2.11241 q^{76} +14.4791 q^{77} +0.574493 q^{78} +2.76301 q^{79} +1.00000 q^{80} +6.13855 q^{81} -2.18624 q^{82} +10.8906 q^{83} +1.52296 q^{84} +6.09419 q^{85} +3.93884 q^{86} -0.908195 q^{87} +5.46180 q^{88} -5.71941 q^{89} -2.66996 q^{90} +2.65097 q^{91} +1.90759 q^{92} -0.574493 q^{93} -9.99497 q^{94} -2.11241 q^{95} +0.574493 q^{96} -1.55602 q^{97} +0.0276456 q^{98} -14.5828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9} + 9 q^{10} + 10 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} + 14 q^{18} + 10 q^{19} + 9 q^{20} + 3 q^{21} + 10 q^{22} + 8 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 15 q^{27} + 9 q^{28} + 9 q^{29} + 3 q^{30} - 9 q^{31} + 9 q^{32} + 4 q^{33} + q^{34} + 9 q^{35} + 14 q^{36} - 3 q^{37} + 10 q^{38} + 3 q^{39} + 9 q^{40} + 3 q^{42} + 7 q^{43} + 10 q^{44} + 14 q^{45} + 8 q^{46} + 7 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} - 3 q^{51} + 9 q^{52} + 8 q^{53} + 15 q^{54} + 10 q^{55} + 9 q^{56} - 7 q^{57} + 9 q^{58} + 2 q^{59} + 3 q^{60} - 2 q^{61} - 9 q^{62} + 10 q^{63} + 9 q^{64} + 9 q^{65} + 4 q^{66} + 18 q^{67} + q^{68} - 16 q^{69} + 9 q^{70} + 14 q^{71} + 14 q^{72} + q^{73} - 3 q^{74} + 3 q^{75} + 10 q^{76} - 5 q^{77} + 3 q^{78} + 6 q^{79} + 9 q^{80} + q^{81} + 7 q^{83} + 3 q^{84} + q^{85} + 7 q^{86} + 11 q^{87} + 10 q^{88} - 19 q^{89} + 14 q^{90} + 9 q^{91} + 8 q^{92} - 3 q^{93} + 7 q^{94} + 10 q^{95} + 3 q^{96} - 6 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9 + 9 * q^10 + 10 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 + 3 * q^15 + 9 * q^16 + q^17 + 14 * q^18 + 10 * q^19 + 9 * q^20 + 3 * q^21 + 10 * q^22 + 8 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 15 * q^27 + 9 * q^28 + 9 * q^29 + 3 * q^30 - 9 * q^31 + 9 * q^32 + 4 * q^33 + q^34 + 9 * q^35 + 14 * q^36 - 3 * q^37 + 10 * q^38 + 3 * q^39 + 9 * q^40 + 3 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 + 8 * q^46 + 7 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 - 3 * q^51 + 9 * q^52 + 8 * q^53 + 15 * q^54 + 10 * q^55 + 9 * q^56 - 7 * q^57 + 9 * q^58 + 2 * q^59 + 3 * q^60 - 2 * q^61 - 9 * q^62 + 10 * q^63 + 9 * q^64 + 9 * q^65 + 4 * q^66 + 18 * q^67 + q^68 - 16 * q^69 + 9 * q^70 + 14 * q^71 + 14 * q^72 + q^73 - 3 * q^74 + 3 * q^75 + 10 * q^76 - 5 * q^77 + 3 * q^78 + 6 * q^79 + 9 * q^80 + q^81 + 7 * q^83 + 3 * q^84 + q^85 + 7 * q^86 + 11 * q^87 + 10 * q^88 - 19 * q^89 + 14 * q^90 + 9 * q^91 + 8 * q^92 - 3 * q^93 + 7 * q^94 + 10 * q^95 + 3 * q^96 - 6 * q^97 + 8 * q^98 - 5 * q^99

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