LMFDB - Embedded newform 7935.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.3370660.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 9x^{3} - 2x^{2} + 16x + 6 $ x^5 - 9x^3 - 2x^2 + 16*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.388575$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.388575 q^{2} +1.00000 q^{3} -1.84901 q^{4} -1.00000 q^{5} +0.388575 q^{6} +2.84901 q^{7} -1.49563 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.388575 q^{2} +1.00000 q^{3} -1.84901 q^{4} -1.00000 q^{5} +0.388575 q^{6} +2.84901 q^{7} -1.49563 q^{8} +1.00000 q^{9} -0.388575 q^{10} -1.88420 q^{11} -1.84901 q^{12} -5.08166 q^{13} +1.10705 q^{14} -1.00000 q^{15} +3.11685 q^{16} +5.93067 q^{17} +0.388575 q^{18} -3.85881 q^{19} +1.84901 q^{20} +2.84901 q^{21} -0.732155 q^{22} -1.49563 q^{24} +1.00000 q^{25} -1.97461 q^{26} +1.00000 q^{27} -5.26785 q^{28} -0.964805 q^{29} -0.388575 q^{30} -4.84901 q^{31} +4.20239 q^{32} -1.88420 q^{33} +2.30451 q^{34} -2.84901 q^{35} -1.84901 q^{36} +7.03772 q^{37} -1.49944 q^{38} -5.08166 q^{39} +1.49563 q^{40} +5.93067 q^{41} +1.10705 q^{42} -7.19746 q^{43} +3.48391 q^{44} -1.00000 q^{45} +7.58222 q^{47} +3.11685 q^{48} +1.11685 q^{49} +0.388575 q^{50} +5.93067 q^{51} +9.39604 q^{52} +4.73321 q^{53} +0.388575 q^{54} +1.88420 q^{55} -4.26106 q^{56} -3.85881 q^{57} -0.374899 q^{58} +5.97567 q^{59} +1.84901 q^{60} +3.08166 q^{61} -1.88420 q^{62} +2.84901 q^{63} -4.60077 q^{64} +5.08166 q^{65} -0.732155 q^{66} +3.67115 q^{67} -10.9659 q^{68} -1.10705 q^{70} -14.6199 q^{71} -1.49563 q^{72} -6.63596 q^{73} +2.73468 q^{74} +1.00000 q^{75} +7.13498 q^{76} -5.36812 q^{77} -1.97461 q^{78} -15.9416 q^{79} -3.11685 q^{80} +1.00000 q^{81} +2.30451 q^{82} -11.5554 q^{83} -5.26785 q^{84} -5.93067 q^{85} -2.79675 q^{86} -0.964805 q^{87} +2.81807 q^{88} -15.8417 q^{89} -0.388575 q^{90} -14.4777 q^{91} -4.84901 q^{93} +2.94626 q^{94} +3.85881 q^{95} +4.20239 q^{96} -17.4410 q^{97} +0.433982 q^{98} -1.88420 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9	$ 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9} - 6 q^{11} + 8 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} + 10 q^{16} - 7 q^{17} + 4 q^{19} - 8 q^{20} - 3 q^{21} + 8 q^{22} - 6 q^{24} + 5 q^{25} + 10 q^{26} + 5 q^{27} - 38 q^{28} + 9 q^{29} - 7 q^{31} - 12 q^{32} - 6 q^{33} - 4 q^{34} + 3 q^{35} + 8 q^{36} - q^{37} - 26 q^{38} - 6 q^{39} + 6 q^{40} - 7 q^{41} + 6 q^{42} - 20 q^{43} - 18 q^{44} - 5 q^{45} + 10 q^{48} - 7 q^{51} - 22 q^{52} + 3 q^{53} + 6 q^{55} + 18 q^{56} + 4 q^{57} - 14 q^{58} + q^{59} - 8 q^{60} - 4 q^{61} - 6 q^{62} - 3 q^{63} + 18 q^{64} + 6 q^{65} + 8 q^{66} + 5 q^{67} - 32 q^{68} - 6 q^{70} + q^{71} - 6 q^{72} - 6 q^{73} - 48 q^{74} + 5 q^{75} + 6 q^{76} + 12 q^{77} + 10 q^{78} - 10 q^{80} + 5 q^{81} - 4 q^{82} - 41 q^{83} - 38 q^{84} + 7 q^{85} + 2 q^{86} + 9 q^{87} + 84 q^{88} - 18 q^{89} + 16 q^{91} - 7 q^{93} + 4 q^{94} - 4 q^{95} - 12 q^{96} - 26 q^{97} - 24 q^{98} - 6 q^{99}+O(q^{100}) $ 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9 - 6 * q^11 + 8 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 + 10 * q^16 - 7 * q^17 + 4 * q^19 - 8 * q^20 - 3 * q^21 + 8 * q^22 - 6 * q^24 + 5 * q^25 + 10 * q^26 + 5 * q^27 - 38 * q^28 + 9 * q^29 - 7 * q^31 - 12 * q^32 - 6 * q^33 - 4 * q^34 + 3 * q^35 + 8 * q^36 - q^37 - 26 * q^38 - 6 * q^39 + 6 * q^40 - 7 * q^41 + 6 * q^42 - 20 * q^43 - 18 * q^44 - 5 * q^45 + 10 * q^48 - 7 * q^51 - 22 * q^52 + 3 * q^53 + 6 * q^55 + 18 * q^56 + 4 * q^57 - 14 * q^58 + q^59 - 8 * q^60 - 4 * q^61 - 6 * q^62 - 3 * q^63 + 18 * q^64 + 6 * q^65 + 8 * q^66 + 5 * q^67 - 32 * q^68 - 6 * q^70 + q^71 - 6 * q^72 - 6 * q^73 - 48 * q^74 + 5 * q^75 + 6 * q^76 + 12 * q^77 + 10 * q^78 - 10 * q^80 + 5 * q^81 - 4 * q^82 - 41 * q^83 - 38 * q^84 + 7 * q^85 + 2 * q^86 + 9 * q^87 + 84 * q^88 - 18 * q^89 + 16 * q^91 - 7 * q^93 + 4 * q^94 - 4 * q^95 - 12 * q^96 - 26 * q^97 - 24 * q^98 - 6 * 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 $

$2$	0.388575	0.274764	0.137382	−	0.990518i	$-0.456131\pi$
$2$	0.388575	0.274764	0.137382	+	0.990518i	$0.456131\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.84901	−0.924505
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.388575	0.158635
$7$	2.84901	1.07682	0.538412	−	0.842682i	$-0.319024\pi$
$7$	2.84901	1.07682	0.538412	+	0.842682i	$0.319024\pi$
$8$	−1.49563	−0.528785
$9$	1.00000	0.333333
$10$	−0.388575	−0.122878
$11$	−1.88420	−0.568109	−0.284054	−	0.958808i	$-0.591680\pi$
$11$	−1.88420	−0.568109	−0.284054	+	0.958808i	$0.591680\pi$
$12$	−1.84901	−0.533763
$13$	−5.08166	−1.40940	−0.704699	−	0.709506i	$-0.748918\pi$
$13$	−5.08166	−1.40940	−0.704699	+	0.709506i	$0.748918\pi$
$14$	1.10705	0.295873
$15$	−1.00000	−0.258199
$16$	3.11685	0.779214
$17$	5.93067	1.43840	0.719199	−	0.694804i	$-0.244509\pi$
$17$	5.93067	1.43840	0.719199	+	0.694804i	$0.244509\pi$
$18$	0.388575	0.0915880
$19$	−3.85881	−0.885272	−0.442636	−	0.896701i	$-0.645957\pi$
$19$	−3.85881	−0.885272	−0.442636	+	0.896701i	$0.645957\pi$
$20$	1.84901	0.413451
$21$	2.84901	0.621705
$22$	−0.732155	−0.156096
$23$	0	0
$23$	0	0
$24$	−1.49563	−0.305294
$25$	1.00000	0.200000
$26$	−1.97461	−0.387252
$27$	1.00000	0.192450
$28$	−5.26785	−0.995529
$29$	−0.964805	−0.179160	−0.0895799	−	0.995980i	$-0.528552\pi$
$29$	−0.964805	−0.179160	−0.0895799	+	0.995980i	$0.528552\pi$
$30$	−0.388575	−0.0709438
$31$	−4.84901	−0.870908	−0.435454	−	0.900211i	$-0.643412\pi$
$31$	−4.84901	−0.870908	−0.435454	+	0.900211i	$0.643412\pi$
$32$	4.20239	0.742885
$33$	−1.88420	−0.327998
$34$	2.30451	0.395220
$35$	−2.84901	−0.481570
$36$	−1.84901	−0.308168
$37$	7.03772	1.15699	0.578497	−	0.815684i	$-0.303639\pi$
$37$	7.03772	1.15699	0.578497	+	0.815684i	$0.303639\pi$
$38$	−1.49944	−0.243241
$39$	−5.08166	−0.813717
$40$	1.49563	0.236480
$41$	5.93067	0.926215	0.463107	−	0.886302i	$-0.346734\pi$
$41$	5.93067	0.926215	0.463107	+	0.886302i	$0.346734\pi$
$42$	1.10705	0.170822
$43$	−7.19746	−1.09760	−0.548801	−	0.835953i	$-0.684915\pi$
$43$	−7.19746	−1.09760	−0.548801	+	0.835953i	$0.684915\pi$
$44$	3.48391	0.525219
$45$	−1.00000	−0.149071
$46$	0	0
$47$	7.58222	1.10598	0.552990	−	0.833188i	$-0.313487\pi$
$47$	7.58222	1.10598	0.552990	+	0.833188i	$0.313487\pi$
$48$	3.11685	0.449879
$49$	1.11685	0.159551
$50$	0.388575	0.0549528
$51$	5.93067	0.830460
$52$	9.39604	1.30300
$53$	4.73321	0.650157	0.325078	−	0.945687i	$-0.394609\pi$
$53$	4.73321	0.650157	0.325078	+	0.945687i	$0.394609\pi$
$54$	0.388575	0.0528784
$55$	1.88420	0.254066
$56$	−4.26106	−0.569408
$57$	−3.85881	−0.511112
$58$	−0.374899	−0.0492267
$59$	5.97567	0.777965	0.388983	−	0.921245i	$-0.372827\pi$
$59$	5.97567	0.777965	0.388983	+	0.921245i	$0.372827\pi$
$60$	1.84901	0.238706
$61$	3.08166	0.394566	0.197283	−	0.980347i	$-0.436788\pi$
$61$	3.08166	0.394566	0.197283	+	0.980347i	$0.436788\pi$
$62$	−1.88420	−0.239294
$63$	2.84901	0.358941
$64$	−4.60077	−0.575096
$65$	5.08166	0.630302
$66$	−0.732155	−0.0901220
$67$	3.67115	0.448503	0.224251	−	0.974531i	$-0.428006\pi$
$67$	3.67115	0.448503	0.224251	+	0.974531i	$0.428006\pi$
$68$	−10.9659	−1.32981
$69$	0	0
$70$	−1.10705	−0.132318
$71$	−14.6199	−1.73507	−0.867534	−	0.497378i	$-0.834296\pi$
$71$	−14.6199	−1.73507	−0.867534	+	0.497378i	$0.834296\pi$
$72$	−1.49563	−0.176262
$73$	−6.63596	−0.776680	−0.388340	−	0.921516i	$-0.626951\pi$
$73$	−6.63596	−0.776680	−0.388340	+	0.921516i	$0.626951\pi$
$74$	2.73468	0.317901
$75$	1.00000	0.115470
$76$	7.13498	0.818438
$77$	−5.36812	−0.611753
$78$	−1.97461	−0.223580
$79$	−15.9416	−1.79357	−0.896785	−	0.442467i	$-0.854103\pi$
$79$	−15.9416	−1.79357	−0.896785	+	0.442467i	$0.854103\pi$
$80$	−3.11685	−0.348475
$81$	1.00000	0.111111
$82$	2.30451	0.254491
$83$	−11.5554	−1.26837	−0.634183	−	0.773183i	$-0.718663\pi$
$83$	−11.5554	−1.26837	−0.634183	+	0.773183i	$0.718663\pi$
$84$	−5.26785	−0.574769
$85$	−5.93067	−0.643271
$86$	−2.79675	−0.301582
$87$	−0.964805	−0.103438
$88$	2.81807	0.300407
$89$	−15.8417	−1.67922	−0.839610	−	0.543189i	$-0.817217\pi$
$89$	−15.8417	−1.67922	−0.839610	+	0.543189i	$0.817217\pi$
$90$	−0.388575	−0.0409594
$91$	−14.4777	−1.51768
$92$	0	0
$93$	−4.84901	−0.502819
$94$	2.94626	0.303884
$95$	3.85881	0.395906
$96$	4.20239	0.428905
$97$	−17.4410	−1.77087	−0.885434	−	0.464765i	$-0.846139\pi$
$97$	−17.4410	−1.77087	−0.885434	+	0.464765i	$0.846139\pi$
$98$	0.433982	0.0438388
$99$	−1.88420	−0.189370
$100$	−1.84901	−0.184901
$101$	−3.53576	−0.351821	−0.175910	−	0.984406i	$-0.556287\pi$
$101$	−3.53576	−0.351821	−0.175910	+	0.984406i	$0.556287\pi$
$102$	2.30451	0.228181
$103$	−2.58844	−0.255046	−0.127523	−	0.991836i	$-0.540703\pi$
$103$	−2.58844	−0.255046	−0.127523	+	0.991836i	$0.540703\pi$
$104$	7.60028	0.745269
$105$	−2.84901	−0.278035
$106$	1.83921	0.178640
$107$	8.66494	0.837672	0.418836	−	0.908062i	$-0.362438\pi$
$107$	8.66494	0.837672	0.418836	+	0.908062i	$0.362438\pi$
$108$	−1.84901	−0.177921
$109$	−1.52736	−0.146295	−0.0731473	−	0.997321i	$-0.523304\pi$
$109$	−1.52736	−0.146295	−0.0731473	+	0.997321i	$0.523304\pi$
$110$	0.732155	0.0698082
$111$	7.03772	0.667991
$112$	8.87995	0.839076
$113$	7.84181	0.737696	0.368848	−	0.929490i	$-0.379752\pi$
$113$	7.84181	0.737696	0.368848	+	0.929490i	$0.379752\pi$
$114$	−1.49944	−0.140435
$115$	0	0
$116$	1.78393	0.165634
$117$	−5.08166	−0.469800
$118$	2.32199	0.213757
$119$	16.8965	1.54890
$120$	1.49563	0.136532
$121$	−7.44978	−0.677252
$122$	1.19746	0.108413
$123$	5.93067	0.534750
$124$	8.96586	0.805158
$125$	−1.00000	−0.0894427
$126$	1.10705	0.0986242
$127$	18.1024	1.60633	0.803164	−	0.595759i	$-0.203148\pi$
$127$	18.1024	1.60633	0.803164	+	0.595759i	$0.203148\pi$
$128$	−10.1925	−0.900900
$129$	−7.19746	−0.633701
$130$	1.97461	0.173184
$131$	−0.475169	−0.0415157	−0.0207579	−	0.999785i	$-0.506608\pi$
$131$	−0.475169	−0.0415157	−0.0207579	+	0.999785i	$0.506608\pi$
$132$	3.48391	0.303236
$133$	−10.9938	−0.953282
$134$	1.42652	0.123232
$135$	−1.00000	−0.0860663
$136$	−8.87008	−0.760603
$137$	−16.1986	−1.38394	−0.691969	−	0.721927i	$-0.743257\pi$
$137$	−16.1986	−1.38394	−0.691969	+	0.721927i	$0.743257\pi$
$138$	0	0
$139$	7.79527	0.661186	0.330593	−	0.943773i	$-0.392751\pi$
$139$	7.79527	0.661186	0.330593	+	0.943773i	$0.392751\pi$
$140$	5.26785	0.445214
$141$	7.58222	0.638538
$142$	−5.68095	−0.476734
$143$	9.57488	0.800692
$144$	3.11685	0.259738
$145$	0.964805	0.0801227
$146$	−2.57857	−0.213404
$147$	1.11685	0.0921166
$148$	−13.0128	−1.06965
$149$	−7.88420	−0.645899	−0.322950	−	0.946416i	$-0.604674\pi$
$149$	−7.88420	−0.645899	−0.322950	+	0.946416i	$0.604674\pi$
$150$	0.388575	0.0317270
$151$	11.1271	0.905508	0.452754	−	0.891636i	$-0.350442\pi$
$151$	11.1271	0.905508	0.452754	+	0.891636i	$0.350442\pi$
$152$	5.77135	0.468118
$153$	5.93067	0.479466
$154$	−2.08592	−0.168088
$155$	4.84901	0.389482
$156$	9.39604	0.752285
$157$	16.4668	1.31419	0.657096	−	0.753807i	$-0.271785\pi$
$157$	16.4668	1.31419	0.657096	+	0.753807i	$0.271785\pi$
$158$	−6.19451	−0.492808
$159$	4.73321	0.375368
$160$	−4.20239	−0.332228
$161$	0	0
$162$	0.388575	0.0305293
$163$	18.0754	1.41578	0.707889	−	0.706324i	$-0.249648\pi$
$163$	18.0754	1.41578	0.707889	+	0.706324i	$0.249648\pi$
$164$	−10.9659	−0.856290
$165$	1.88420	0.146685
$166$	−4.49012	−0.348501
$167$	−11.6701	−0.903059	−0.451530	−	0.892256i	$-0.649121\pi$
$167$	−11.6701	−0.903059	−0.451530	+	0.892256i	$0.649121\pi$
$168$	−4.26106	−0.328748
$169$	12.8233	0.986405
$170$	−2.30451	−0.176748
$171$	−3.85881	−0.295091
$172$	13.3082	1.01474
$173$	−14.8526	−1.12922	−0.564611	−	0.825357i	$-0.690974\pi$
$173$	−14.8526	−1.12922	−0.564611	+	0.825357i	$0.690974\pi$
$174$	−0.374899	−0.0284210
$175$	2.84901	0.215365
$176$	−5.87279	−0.442678
$177$	5.97567	0.449158
$178$	−6.15570	−0.461390
$179$	0.722287	0.0539863	0.0269931	−	0.999636i	$-0.491407\pi$
$179$	0.722287	0.0539863	0.0269931	+	0.999636i	$0.491407\pi$
$180$	1.84901	0.137817
$181$	−6.67729	−0.496319	−0.248160	−	0.968719i	$-0.579826\pi$
$181$	−6.67729	−0.496319	−0.248160	+	0.968719i	$0.579826\pi$
$182$	−5.62567	−0.417003
$183$	3.08166	0.227803
$184$	0	0
$185$	−7.03772	−0.517424
$186$	−1.88420	−0.138157
$187$	−11.1746	−0.817167
$188$	−14.0196	−1.02248
$189$	2.84901	0.207235
$190$	1.49944	0.108781
$191$	−13.7455	−0.994593	−0.497296	−	0.867581i	$-0.665674\pi$
$191$	−13.7455	−0.994593	−0.497296	+	0.867581i	$0.665674\pi$
$192$	−4.60077	−0.332032
$193$	−0.0196017	−0.00141096	−0.000705482	−	1.00000i	$-0.500225\pi$
$193$	−0.0196017	−0.00141096	−0.000705482		1.00000i	$0.500225\pi$
$194$	−6.77715	−0.486571
$195$	5.08166	0.363905
$196$	−2.06508	−0.147505
$197$	−6.56516	−0.467748	−0.233874	−	0.972267i	$-0.575140\pi$
$197$	−6.56516	−0.467748	−0.233874	+	0.972267i	$0.575140\pi$
$198$	−0.732155	−0.0520320
$199$	−22.1049	−1.56698	−0.783488	−	0.621407i	$-0.786561\pi$
$199$	−22.1049	−1.56698	−0.783488	+	0.621407i	$0.786561\pi$
$200$	−1.49563	−0.105757
$201$	3.67115	0.258943
$202$	−1.37391	−0.0966678
$203$	−2.74874	−0.192924
$204$	−10.9659	−0.767764
$205$	−5.93067	−0.414216
$206$	−1.00580	−0.0700775
$207$	0	0
$208$	−15.8388	−1.09822
$209$	7.27079	0.502931
$210$	−1.10705	−0.0763940
$211$	15.6566	1.07785	0.538923	−	0.842355i	$-0.318831\pi$
$211$	15.6566	1.07785	0.538923	+	0.842355i	$0.318831\pi$
$212$	−8.75176	−0.601073
$213$	−14.6199	−1.00174
$214$	3.36698	0.230162
$215$	7.19746	0.490862
$216$	−1.49563	−0.101765
$217$	−13.8149	−0.937815
$218$	−0.593494	−0.0401965
$219$	−6.63596	−0.448417
$220$	−3.48391	−0.234885
$221$	−30.1376	−2.02728
$222$	2.73468	0.183540
$223$	12.1437	0.813204	0.406602	−	0.913605i	$-0.366714\pi$
$223$	12.1437	0.813204	0.406602	+	0.913605i	$0.366714\pi$
$224$	11.9726	0.799956
$225$	1.00000	0.0666667
$226$	3.04713	0.202692
$227$	−20.2874	−1.34652	−0.673262	−	0.739404i	$-0.735107\pi$
$227$	−20.2874	−1.34652	−0.673262	+	0.739404i	$0.735107\pi$
$228$	7.13498	0.472525
$229$	−3.76841	−0.249023	−0.124512	−	0.992218i	$-0.539736\pi$
$229$	−3.76841	−0.249023	−0.124512	+	0.992218i	$0.539736\pi$
$230$	0	0
$231$	−5.36812	−0.353196
$232$	1.44299	0.0947370
$233$	6.85048	0.448790	0.224395	−	0.974498i	$-0.427959\pi$
$233$	6.85048	0.448790	0.224395	+	0.974498i	$0.427959\pi$
$234$	−1.97461	−0.129084
$235$	−7.58222	−0.494610
$236$	−11.0491	−0.719233
$237$	−15.9416	−1.03552
$238$	6.56557	0.425583
$239$	−28.5496	−1.84672	−0.923359	−	0.383938i	$-0.874567\pi$
$239$	−28.5496	−1.84672	−0.923359	+	0.383938i	$0.874567\pi$
$240$	−3.11685	−0.201192
$241$	−22.7993	−1.46863	−0.734315	−	0.678808i	$-0.762497\pi$
$241$	−22.7993	−1.46863	−0.734315	+	0.678808i	$0.762497\pi$
$242$	−2.89480	−0.186085
$243$	1.00000	0.0641500
$244$	−5.69802	−0.364778
$245$	−1.11685	−0.0713532
$246$	2.30451	0.146930
$247$	19.6092	1.24770
$248$	7.25232	0.460523
$249$	−11.5554	−0.732291
$250$	−0.388575	−0.0245756
$251$	18.7383	1.18275	0.591377	−	0.806395i	$-0.298585\pi$
$251$	18.7383	1.18275	0.591377	+	0.806395i	$0.298585\pi$
$252$	−5.26785	−0.331843
$253$	0	0
$254$	7.03414	0.441361
$255$	−5.93067	−0.371393
$256$	5.24097	0.327561
$257$	−17.1121	−1.06742	−0.533712	−	0.845666i	$-0.679203\pi$
$257$	−17.1121	−1.06742	−0.533712	+	0.845666i	$0.679203\pi$
$258$	−2.79675	−0.174118
$259$	20.0505	1.24588
$260$	−9.39604	−0.582718
$261$	−0.964805	−0.0597200
$262$	−0.184639	−0.0114070
$263$	2.30712	0.142263	0.0711314	−	0.997467i	$-0.477339\pi$
$263$	2.30712	0.142263	0.0711314	+	0.997467i	$0.477339\pi$
$264$	2.81807	0.173440
$265$	−4.73321	−0.290759
$266$	−4.27191	−0.261928
$267$	−15.8417	−0.969499
$268$	−6.78800	−0.414643
$269$	22.3826	1.36469	0.682344	−	0.731031i	$-0.260960\pi$
$269$	22.3826	1.36469	0.682344	+	0.731031i	$0.260960\pi$
$270$	−0.388575	−0.0236479
$271$	3.28130	0.199325	0.0996624	−	0.995021i	$-0.468224\pi$
$271$	3.28130	0.199325	0.0996624	+	0.995021i	$0.468224\pi$
$272$	18.4850	1.12082
$273$	−14.4777	−0.876230
$274$	−6.29436	−0.380256
$275$	−1.88420	−0.113622
$276$	0	0
$277$	20.8821	1.25468	0.627341	−	0.778745i	$-0.284143\pi$
$277$	20.8821	1.25468	0.627341	+	0.778745i	$0.284143\pi$
$278$	3.02905	0.181670
$279$	−4.84901	−0.290303
$280$	4.26106	0.254647
$281$	−25.5336	−1.52320	−0.761602	−	0.648045i	$-0.775587\pi$
$281$	−25.5336	−1.52320	−0.761602	+	0.648045i	$0.775587\pi$
$282$	2.94626	0.175447
$283$	26.6204	1.58242	0.791208	−	0.611547i	$-0.209453\pi$
$283$	26.6204	1.58242	0.791208	+	0.611547i	$0.209453\pi$
$284$	27.0324	1.60408
$285$	3.85881	0.228576
$286$	3.72056	0.220001
$287$	16.8965	0.997371
$288$	4.20239	0.247628
$289$	18.1728	1.06899
$290$	0.374899	0.0220148
$291$	−17.4410	−1.02241
$292$	12.2700	0.718045
$293$	11.6287	0.679355	0.339678	−	0.940542i	$-0.389682\pi$
$293$	11.6287	0.679355	0.339678	+	0.940542i	$0.389682\pi$
$294$	0.433982	0.0253103
$295$	−5.97567	−0.347917
$296$	−10.5258	−0.611801
$297$	−1.88420	−0.109333
$298$	−3.06360	−0.177470
$299$	0	0
$300$	−1.84901	−0.106753
$301$	−20.5056	−1.18192
$302$	4.32370	0.248801
$303$	−3.53576	−0.203124
$304$	−12.0274	−0.689816
$305$	−3.08166	−0.176455
$306$	2.30451	0.131740
$307$	−2.00946	−0.114686	−0.0573429	−	0.998355i	$-0.518263\pi$
$307$	−2.00946	−0.114686	−0.0573429	+	0.998355i	$0.518263\pi$
$308$	9.92570	0.565569
$309$	−2.58844	−0.147251
$310$	1.88420	0.107016
$311$	−7.15246	−0.405579	−0.202789	−	0.979222i	$-0.565001\pi$
$311$	−7.15246	−0.405579	−0.202789	+	0.979222i	$0.565001\pi$
$312$	7.60028	0.430281
$313$	−3.08851	−0.174573	−0.0872865	−	0.996183i	$-0.527820\pi$
$313$	−3.08851	−0.174573	−0.0872865	+	0.996183i	$0.527820\pi$
$314$	6.39858	0.361093
$315$	−2.84901	−0.160523
$316$	29.4762	1.65816
$317$	−30.5278	−1.71461	−0.857305	−	0.514809i	$-0.827863\pi$
$317$	−30.5278	−1.71461	−0.857305	+	0.514809i	$0.827863\pi$
$318$	1.83921	0.103138
$319$	1.81789	0.101782
$320$	4.60077	0.257191
$321$	8.66494	0.483630
$322$	0	0
$323$	−22.8853	−1.27337
$324$	−1.84901	−0.102723
$325$	−5.08166	−0.281880
$326$	7.02367	0.389005
$327$	−1.52736	−0.0844632
$328$	−8.87008	−0.489768
$329$	21.6018	1.19095
$330$	0.732155	0.0403038
$331$	−25.3362	−1.39260	−0.696301	−	0.717750i	$-0.745172\pi$
$331$	−25.3362	−1.39260	−0.696301	+	0.717750i	$0.745172\pi$
$332$	21.3660	1.17261
$333$	7.03772	0.385665
$334$	−4.53471	−0.248128
$335$	−3.67115	−0.200577
$336$	8.87995	0.484441
$337$	−20.0541	−1.09242	−0.546209	−	0.837649i	$-0.683930\pi$
$337$	−20.0541	−1.09242	−0.546209	+	0.837649i	$0.683930\pi$
$338$	4.98280	0.271029
$339$	7.84181	0.425909
$340$	10.9659	0.594707
$341$	9.13652	0.494770
$342$	−1.49944	−0.0810803
$343$	−16.7611	−0.905016
$344$	10.7647	0.580395
$345$	0	0
$346$	−5.77135	−0.310270
$347$	16.8087	0.902340	0.451170	−	0.892438i	$-0.351007\pi$
$347$	16.8087	0.902340	0.451170	+	0.892438i	$0.351007\pi$
$348$	1.78393	0.0956289
$349$	−13.5150	−0.723442	−0.361721	−	0.932286i	$-0.617811\pi$
$349$	−13.5150	−0.723442	−0.361721	+	0.932286i	$0.617811\pi$
$350$	1.10705	0.0591745
$351$	−5.08166	−0.271239
$352$	−7.91816	−0.422039
$353$	−32.0821	−1.70756	−0.853778	−	0.520638i	$-0.825694\pi$
$353$	−32.0821	−1.70756	−0.853778	+	0.520638i	$0.825694\pi$
$354$	2.32199	0.123413
$355$	14.6199	0.775946
$356$	29.2915	1.55245
$357$	16.8965	0.894259
$358$	0.280663	0.0148335
$359$	−24.6204	−1.29942	−0.649708	−	0.760184i	$-0.725109\pi$
$359$	−24.6204	−1.29942	−0.649708	+	0.760184i	$0.725109\pi$
$360$	1.49563	0.0788266
$361$	−4.10958	−0.216294
$362$	−2.59463	−0.136371
$363$	−7.44978	−0.391012
$364$	26.7694	1.40310
$365$	6.63596	0.347342
$366$	1.19746	0.0625920
$367$	−8.28018	−0.432222	−0.216111	−	0.976369i	$-0.569337\pi$
$367$	−8.28018	−0.432222	−0.216111	+	0.976369i	$0.569337\pi$
$368$	0	0
$369$	5.93067	0.308738
$370$	−2.73468	−0.142169
$371$	13.4850	0.700105
$372$	8.96586	0.464858
$373$	−27.1928	−1.40799	−0.703994	−	0.710206i	$-0.748602\pi$
$373$	−27.1928	−1.40799	−0.703994	+	0.710206i	$0.748602\pi$
$374$	−4.34217	−0.224528
$375$	−1.00000	−0.0516398
$376$	−11.3402	−0.584826
$377$	4.90281	0.252508
$378$	1.10705	0.0569407
$379$	−37.8733	−1.94542	−0.972711	−	0.232020i	$-0.925466\pi$
$379$	−37.8733	−1.94542	−0.972711	+	0.232020i	$0.925466\pi$
$380$	−7.13498	−0.366017
$381$	18.1024	0.927413
$382$	−5.34117	−0.273278
$383$	−21.1126	−1.07880	−0.539402	−	0.842049i	$-0.681350\pi$
$383$	−21.1126	−1.07880	−0.539402	+	0.842049i	$0.681350\pi$
$384$	−10.1925	−0.520135
$385$	5.36812	0.273584
$386$	−0.00761674	−0.000387682 0
$387$	−7.19746	−0.365867
$388$	32.2486	1.63718
$389$	−14.4682	−0.733569	−0.366784	−	0.930306i	$-0.619541\pi$
$389$	−14.4682	−0.733569	−0.366784	+	0.930306i	$0.619541\pi$
$390$	1.97461	0.0999881
$391$	0	0
$392$	−1.67040	−0.0843680
$393$	−0.475169	−0.0239691
$394$	−2.55106	−0.128520
$395$	15.9416	0.802109
$396$	3.48391	0.175073
$397$	1.39604	0.0700651	0.0350326	−	0.999386i	$-0.488847\pi$
$397$	1.39604	0.0700651	0.0350326	+	0.999386i	$0.488847\pi$
$398$	−8.58942	−0.430549
$399$	−10.9938	−0.550378
$400$	3.11685	0.155843
$401$	−34.3804	−1.71687	−0.858437	−	0.512919i	$-0.828564\pi$
$401$	−34.3804	−1.71687	−0.858437	+	0.512919i	$0.828564\pi$
$402$	1.42652	0.0711483
$403$	24.6410	1.22746
$404$	6.53765	0.325260
$405$	−1.00000	−0.0496904
$406$	−1.06809	−0.0530085
$407$	−13.2605	−0.657299
$408$	−8.87008	−0.439134
$409$	12.7063	0.628285	0.314142	−	0.949376i	$-0.398283\pi$
$409$	12.7063	0.628285	0.314142	+	0.949376i	$0.398283\pi$
$410$	−2.30451	−0.113812
$411$	−16.1986	−0.799017
$412$	4.78604	0.235791
$413$	17.0247	0.837732
$414$	0	0
$415$	11.5554	0.567230
$416$	−21.3551	−1.04702
$417$	7.79527	0.381736
$418$	2.82525	0.138187
$419$	−19.4436	−0.949880	−0.474940	−	0.880018i	$-0.657530\pi$
$419$	−19.4436	−0.949880	−0.474940	+	0.880018i	$0.657530\pi$
$420$	5.26785	0.257045
$421$	38.9430	1.89797	0.948983	−	0.315328i	$-0.102114\pi$
$421$	38.9430	1.89797	0.948983	+	0.315328i	$0.102114\pi$
$422$	6.08377	0.296153
$423$	7.58222	0.368660
$424$	−7.07913	−0.343793
$425$	5.93067	0.287680
$426$	−5.68095	−0.275243
$427$	8.77968	0.424878
$428$	−16.0216	−0.774431
$429$	9.57488	0.462280
$430$	2.79675	0.134871
$431$	−1.23483	−0.0594799	−0.0297400	−	0.999558i	$-0.509468\pi$
$431$	−1.23483	−0.0594799	−0.0297400	+	0.999558i	$0.509468\pi$
$432$	3.11685	0.149960
$433$	29.7016	1.42737	0.713684	−	0.700468i	$-0.247025\pi$
$433$	29.7016	1.42737	0.713684	+	0.700468i	$0.247025\pi$
$434$	−5.36812	−0.257678
$435$	0.964805	0.0462589
$436$	2.82410	0.135250
$437$	0	0
$438$	−2.57857	−0.123209
$439$	15.5553	0.742413	0.371207	−	0.928550i	$-0.378944\pi$
$439$	15.5553	0.742413	0.371207	+	0.928550i	$0.378944\pi$
$440$	−2.81807	−0.134346
$441$	1.11685	0.0531836
$442$	−11.7107	−0.557023
$443$	40.5768	1.92786	0.963932	−	0.266150i	$-0.0857518\pi$
$443$	40.5768	1.92786	0.963932	+	0.266150i	$0.0857518\pi$
$444$	−13.0128	−0.617561
$445$	15.8417	0.750970
$446$	4.71875	0.223439
$447$	−7.88420	−0.372910
$448$	−13.1076	−0.619277
$449$	−0.214184	−0.0101080	−0.00505398	−	0.999987i	$-0.501609\pi$
$449$	−0.214184	−0.0101080	−0.00505398	+	0.999987i	$0.501609\pi$
$450$	0.388575	0.0183176
$451$	−11.1746	−0.526191
$452$	−14.4996	−0.682003
$453$	11.1271	0.522795
$454$	−7.88319	−0.369977
$455$	14.4777	0.678725
$456$	5.77135	0.270268
$457$	21.1132	0.987632	0.493816	−	0.869566i	$-0.335602\pi$
$457$	21.1132	0.987632	0.493816	+	0.869566i	$0.335602\pi$
$458$	−1.46431	−0.0684227
$459$	5.93067	0.276820
$460$	0	0
$461$	−9.25444	−0.431022	−0.215511	−	0.976501i	$-0.569142\pi$
$461$	−9.25444	−0.431022	−0.215511	+	0.976501i	$0.569142\pi$
$462$	−2.08592	−0.0970456
$463$	−9.78080	−0.454553	−0.227276	−	0.973830i	$-0.572982\pi$
$463$	−9.78080	−0.454553	−0.227276	+	0.973830i	$0.572982\pi$
$464$	−3.00716	−0.139604
$465$	4.84901	0.224867
$466$	2.66193	0.123311
$467$	−11.3452	−0.524992	−0.262496	−	0.964933i	$-0.584546\pi$
$467$	−11.3452	−0.524992	−0.262496	+	0.964933i	$0.584546\pi$
$468$	9.39604	0.434332
$469$	10.4592	0.482959
$470$	−2.94626	−0.135901
$471$	16.4668	0.758749
$472$	−8.93738	−0.411376
$473$	13.5615	0.623557
$474$	−6.19451	−0.284523
$475$	−3.85881	−0.177054
$476$	−31.2419	−1.43197
$477$	4.73321	0.216719
$478$	−11.0936	−0.507412
$479$	5.13864	0.234790	0.117395	−	0.993085i	$-0.462546\pi$
$479$	5.13864	0.234790	0.117395	+	0.993085i	$0.462546\pi$
$480$	−4.20239	−0.191812
$481$	−35.7633	−1.63067
$482$	−8.85923	−0.403527
$483$	0	0
$484$	13.7747	0.626123
$485$	17.4410	0.791957
$486$	0.388575	0.0176261
$487$	9.06727	0.410877	0.205439	−	0.978670i	$-0.434138\pi$
$487$	9.06727	0.410877	0.205439	+	0.978670i	$0.434138\pi$
$488$	−4.60902	−0.208641
$489$	18.0754	0.817400
$490$	−0.433982	−0.0196053
$491$	0.0305279	0.00137771	0.000688853	−	1.00000i	$-0.499781\pi$
$491$	0.0305279	0.00137771	0.000688853		1.00000i	$0.499781\pi$
$492$	−10.9659	−0.494379
$493$	−5.72194	−0.257703
$494$	7.61963	0.342823
$495$	1.88420	0.0846887
$496$	−15.1137	−0.678623
$497$	−41.6524	−1.86836
$498$	−4.49012	−0.201207
$499$	−43.7848	−1.96008	−0.980039	−	0.198808i	$-0.936293\pi$
$499$	−43.7848	−1.96008	−0.980039	+	0.198808i	$0.936293\pi$
$500$	1.84901	0.0826902
$501$	−11.6701	−0.521381
$502$	7.28125	0.324978
$503$	−24.1115	−1.07508	−0.537539	−	0.843239i	$-0.680646\pi$
$503$	−24.1115	−1.07508	−0.537539	+	0.843239i	$0.680646\pi$
$504$	−4.26106	−0.189803
$505$	3.53576	0.157339
$506$	0	0
$507$	12.8233	0.569501
$508$	−33.4715	−1.48506
$509$	−23.8254	−1.05604	−0.528021	−	0.849231i	$-0.677066\pi$
$509$	−23.8254	−1.05604	−0.528021	+	0.849231i	$0.677066\pi$
$510$	−2.30451	−0.102045
$511$	−18.9059	−0.836348
$512$	22.4216	0.990902
$513$	−3.85881	−0.170371
$514$	−6.64934	−0.293290
$515$	2.58844	0.114060
$516$	13.3082	0.585859
$517$	−14.2865	−0.628318
$518$	7.79114	0.342323
$519$	−14.8526	−0.651957
$520$	−7.60028	−0.333294
$521$	12.9585	0.567723	0.283862	−	0.958865i	$-0.408384\pi$
$521$	12.9585	0.567723	0.283862	+	0.958865i	$0.408384\pi$
$522$	−0.374899	−0.0164089
$523$	12.4117	0.542726	0.271363	−	0.962477i	$-0.412526\pi$
$523$	12.4117	0.542726	0.271363	+	0.962477i	$0.412526\pi$
$524$	0.878592	0.0383815
$525$	2.84901	0.124341
$526$	0.896487	0.0390887
$527$	−28.7579	−1.25271
$528$	−5.87279	−0.255580
$529$	0	0
$530$	−1.83921	−0.0798901
$531$	5.97567	0.259322
$532$	20.3276	0.881314
$533$	−30.1376	−1.30541
$534$	−6.15570	−0.266383
$535$	−8.66494	−0.374618
$536$	−5.49069	−0.237162
$537$	0.722287	0.0311690
$538$	8.69731	0.374967
$539$	−2.10438	−0.0906422
$540$	1.84901	0.0795687
$541$	−34.6545	−1.48992	−0.744958	−	0.667112i	$-0.767530\pi$
$541$	−34.6545	−1.48992	−0.744958	+	0.667112i	$0.767530\pi$
$542$	1.27503	0.0547673
$543$	−6.67729	−0.286550
$544$	24.9230	1.06856
$545$	1.52736	0.0654249
$546$	−5.62567	−0.240757
$547$	−12.4704	−0.533194	−0.266597	−	0.963808i	$-0.585899\pi$
$547$	−12.4704	−0.533194	−0.266597	+	0.963808i	$0.585899\pi$
$548$	29.9513	1.27946
$549$	3.08166	0.131522
$550$	−0.732155	−0.0312192
$551$	3.72300	0.158605
$552$	0	0
$553$	−45.4178	−1.93136
$554$	8.11425	0.344741
$555$	−7.03772	−0.298735
$556$	−14.4135	−0.611270
$557$	45.7786	1.93970	0.969851	−	0.243700i	$-0.0783611\pi$
$557$	45.7786	1.93970	0.969851	+	0.243700i	$0.0783611\pi$
$558$	−1.88420	−0.0797647
$559$	36.5750	1.54696
$560$	−8.87995	−0.375246
$561$	−11.1746	−0.471792
$562$	−9.92170	−0.418522
$563$	−1.07228	−0.0451912	−0.0225956	−	0.999745i	$-0.507193\pi$
$563$	−1.07228	−0.0451912	−0.0225956	+	0.999745i	$0.507193\pi$
$564$	−14.0196	−0.590332
$565$	−7.84181	−0.329908
$566$	10.3440	0.434791
$567$	2.84901	0.119647
$568$	21.8660	0.917478
$569$	−21.7197	−0.910539	−0.455269	−	0.890354i	$-0.650457\pi$
$569$	−21.7197	−0.910539	−0.455269	+	0.890354i	$0.650457\pi$
$570$	1.49944	0.0628045
$571$	7.07193	0.295951	0.147975	−	0.988991i	$-0.452724\pi$
$571$	7.07193	0.295951	0.147975	+	0.988991i	$0.452724\pi$
$572$	−17.7041	−0.740244
$573$	−13.7455	−0.574228
$574$	6.56557	0.274042
$575$	0	0
$576$	−4.60077	−0.191699
$577$	11.9515	0.497546	0.248773	−	0.968562i	$-0.419973\pi$
$577$	11.9515	0.497546	0.248773	+	0.968562i	$0.419973\pi$
$578$	7.06151	0.293720
$579$	−0.0196017	−0.000814620 0
$580$	−1.78393	−0.0740738
$581$	−32.9213	−1.36581
$582$	−6.77715	−0.280922
$583$	−8.91834	−0.369360
$584$	9.92493	0.410697
$585$	5.08166	0.210101
$586$	4.51862	0.186662
$587$	16.2048	0.668843	0.334421	−	0.942424i	$-0.391459\pi$
$587$	16.2048	0.668843	0.334421	+	0.942424i	$0.391459\pi$
$588$	−2.06508	−0.0851623
$589$	18.7114	0.770990
$590$	−2.32199	−0.0955950
$591$	−6.56516	−0.270055
$592$	21.9356	0.901546
$593$	39.9942	1.64236	0.821182	−	0.570666i	$-0.193315\pi$
$593$	39.9942	1.64236	0.821182	+	0.570666i	$0.193315\pi$
$594$	−0.732155	−0.0300407
$595$	−16.8965	−0.692690
$596$	14.5780	0.597137
$597$	−22.1049	−0.904694
$598$	0	0
$599$	36.7118	1.50000	0.750002	−	0.661435i	$-0.230052\pi$
$599$	36.7118	1.50000	0.750002	+	0.661435i	$0.230052\pi$
$600$	−1.49563	−0.0610588
$601$	32.3576	1.31989	0.659947	−	0.751312i	$-0.270579\pi$
$601$	32.3576	1.31989	0.659947	+	0.751312i	$0.270579\pi$
$602$	−7.96797	−0.324750
$603$	3.67115	0.149501
$604$	−20.5741	−0.837146
$605$	7.44978	0.302876
$606$	−1.37391	−0.0558112
$607$	8.26277	0.335375	0.167688	−	0.985840i	$-0.446370\pi$
$607$	8.26277	0.335375	0.167688	+	0.985840i	$0.446370\pi$
$608$	−16.2162	−0.657655
$609$	−2.74874	−0.111385
$610$	−1.19746	−0.0484836
$611$	−38.5303	−1.55877
$612$	−10.9659	−0.443269
$613$	11.2962	0.456248	0.228124	−	0.973632i	$-0.426741\pi$
$613$	11.2962	0.456248	0.228124	+	0.973632i	$0.426741\pi$
$614$	−0.780824	−0.0315115
$615$	−5.93067	−0.239148
$616$	8.02871	0.323486
$617$	6.32489	0.254631	0.127315	−	0.991862i	$-0.459364\pi$
$617$	6.32489	0.254631	0.127315	+	0.991862i	$0.459364\pi$
$618$	−1.00580	−0.0404593
$619$	−27.7471	−1.11525	−0.557625	−	0.830093i	$-0.688287\pi$
$619$	−27.7471	−1.11525	−0.557625	+	0.830093i	$0.688287\pi$
$620$	−8.96586	−0.360078
$621$	0	0
$622$	−2.77927	−0.111438
$623$	−45.1333	−1.80823
$624$	−15.8388	−0.634059
$625$	1.00000	0.0400000
$626$	−1.20012	−0.0479664
$627$	7.27079	0.290367
$628$	−30.4472	−1.21498
$629$	41.7384	1.66422
$630$	−1.10705	−0.0441061
$631$	9.64682	0.384034	0.192017	−	0.981392i	$-0.438497\pi$
$631$	9.64682	0.384034	0.192017	+	0.981392i	$0.438497\pi$
$632$	23.8427	0.948412
$633$	15.6566	0.622294
$634$	−11.8623	−0.471113
$635$	−18.1024	−0.718371
$636$	−8.75176	−0.347030
$637$	−5.67548	−0.224871
$638$	0.706387	0.0279661
$639$	−14.6199	−0.578356
$640$	10.1925	0.402895
$641$	25.9089	1.02334	0.511669	−	0.859182i	$-0.329027\pi$
$641$	25.9089	1.02334	0.511669	+	0.859182i	$0.329027\pi$
$642$	3.36698	0.132884
$643$	25.3321	0.999000	0.499500	−	0.866314i	$-0.333517\pi$
$643$	25.3321	0.999000	0.499500	+	0.866314i	$0.333517\pi$
$644$	0	0
$645$	7.19746	0.283400
$646$	−8.89267	−0.349877
$647$	−25.1416	−0.988418	−0.494209	−	0.869343i	$-0.664542\pi$
$647$	−25.1416	−0.988418	−0.494209	+	0.869343i	$0.664542\pi$
$648$	−1.49563	−0.0587539
$649$	−11.2594	−0.441969
$650$	−1.97461	−0.0774504
$651$	−13.8149	−0.541448
$652$	−33.4217	−1.30889
$653$	38.5648	1.50916	0.754579	−	0.656209i	$-0.227841\pi$
$653$	38.5648	1.50916	0.754579	+	0.656209i	$0.227841\pi$
$654$	−0.593494	−0.0232075
$655$	0.475169	0.0185664
$656$	18.4850	0.721719
$657$	−6.63596	−0.258893
$658$	8.39393	0.327229
$659$	−28.2304	−1.09970	−0.549851	−	0.835263i	$-0.685316\pi$
$659$	−28.2304	−1.09970	−0.549851	+	0.835263i	$0.685316\pi$
$660$	−3.48391	−0.135611
$661$	−15.0547	−0.585561	−0.292780	−	0.956180i	$-0.594580\pi$
$661$	−15.0547	−0.585561	−0.292780	+	0.956180i	$0.594580\pi$
$662$	−9.84500	−0.382637
$663$	−30.1376	−1.17045
$664$	17.2825	0.670692
$665$	10.9938	0.426321
$666$	2.73468	0.105967
$667$	0	0
$668$	21.5781	0.834882
$669$	12.1437	0.469503
$670$	−1.42652	−0.0551112
$671$	−5.80648	−0.224157
$672$	11.9726	0.461855
$673$	−7.38658	−0.284732	−0.142366	−	0.989814i	$-0.545471\pi$
$673$	−7.38658	−0.284732	−0.142366	+	0.989814i	$0.545471\pi$
$674$	−7.79253	−0.300157
$675$	1.00000	0.0384900
$676$	−23.7103	−0.911936
$677$	7.64731	0.293910	0.146955	−	0.989143i	$-0.453053\pi$
$677$	7.64731	0.293910	0.146955	+	0.989143i	$0.453053\pi$
$678$	3.04713	0.117024
$679$	−49.6897	−1.90691
$680$	8.87008	0.340152
$681$	−20.2874	−0.777416
$682$	3.55022	0.135945
$683$	43.2149	1.65357	0.826786	−	0.562516i	$-0.190167\pi$
$683$	43.2149	1.65357	0.826786	+	0.562516i	$0.190167\pi$
$684$	7.13498	0.272813
$685$	16.1986	0.618916
$686$	−6.51296	−0.248666
$687$	−3.76841	−0.143774
$688$	−22.4334	−0.855266
$689$	−24.0526	−0.916330
$690$	0	0
$691$	−14.9513	−0.568775	−0.284388	−	0.958709i	$-0.591790\pi$
$691$	−14.9513	−0.568775	−0.284388	+	0.958709i	$0.591790\pi$
$692$	27.4626	1.04397
$693$	−5.36812	−0.203918
$694$	6.53146	0.247931
$695$	−7.79527	−0.295692
$696$	1.44299	0.0546964
$697$	35.1728	1.33227
$698$	−5.25160	−0.198776
$699$	6.85048	0.259109
$700$	−5.26785	−0.199106
$701$	−33.4806	−1.26455	−0.632273	−	0.774745i	$-0.717878\pi$
$701$	−33.4806	−1.26455	−0.632273	+	0.774745i	$0.717878\pi$
$702$	−1.97461	−0.0745267
$703$	−27.1572	−1.02425
$704$	8.66878	0.326717
$705$	−7.58222	−0.285563
$706$	−12.4663	−0.469175
$707$	−10.0734	−0.378849
$708$	−11.0491	−0.415249
$709$	34.2440	1.28606	0.643030	−	0.765841i	$-0.277677\pi$
$709$	34.2440	1.28606	0.643030	+	0.765841i	$0.277677\pi$
$710$	5.68095	0.213202
$711$	−15.9416	−0.597857
$712$	23.6934	0.887946
$713$	0	0
$714$	6.56557	0.245710
$715$	−9.57488	−0.358080
$716$	−1.33552	−0.0499106
$717$	−28.5496	−1.06620
$718$	−9.56689	−0.357033
$719$	32.8693	1.22582	0.612909	−	0.790153i	$-0.289999\pi$
$719$	32.8693	1.22582	0.612909	+	0.790153i	$0.289999\pi$
$720$	−3.11685	−0.116158
$721$	−7.37448	−0.274640
$722$	−1.59688	−0.0594298
$723$	−22.7993	−0.847914
$724$	12.3464	0.458849
$725$	−0.964805	−0.0358320
$726$	−2.89480	−0.107436
$727$	22.1913	0.823030	0.411515	−	0.911403i	$-0.365000\pi$
$727$	22.1913	0.823030	0.411515	+	0.911403i	$0.365000\pi$
$728$	21.6533	0.802523
$729$	1.00000	0.0370370
$730$	2.57857	0.0954371
$731$	−42.6857	−1.57879
$732$	−5.69802	−0.210605
$733$	−27.8094	−1.02716	−0.513581	−	0.858041i	$-0.671682\pi$
$733$	−27.8094	−1.02716	−0.513581	+	0.858041i	$0.671682\pi$
$734$	−3.21747	−0.118759
$735$	−1.11685	−0.0411958
$736$	0	0
$737$	−6.91720	−0.254799
$738$	2.30451	0.0848302
$739$	−53.1446	−1.95496	−0.977478	−	0.211038i	$-0.932316\pi$
$739$	−53.1446	−1.95496	−0.977478	+	0.211038i	$0.932316\pi$
$740$	13.0128	0.478361
$741$	19.6092	0.720361
$742$	5.23992	0.192364
$743$	36.4364	1.33672	0.668360	−	0.743838i	$-0.266996\pi$
$743$	36.4364	1.33672	0.668360	+	0.743838i	$0.266996\pi$
$744$	7.25232	0.265883
$745$	7.88420	0.288855
$746$	−10.5664	−0.386865
$747$	−11.5554	−0.422788
$748$	20.6619	0.755475
$749$	24.6865	0.902025
$750$	−0.388575	−0.0141888
$751$	8.28785	0.302428	0.151214	−	0.988501i	$-0.451682\pi$
$751$	8.28785	0.302428	0.151214	+	0.988501i	$0.451682\pi$
$752$	23.6327	0.861795
$753$	18.7383	0.682863
$754$	1.90511	0.0693800
$755$	−11.1271	−0.404955
$756$	−5.26785	−0.191590
$757$	7.72121	0.280632	0.140316	−	0.990107i	$-0.455188\pi$
$757$	7.72121	0.280632	0.140316	+	0.990107i	$0.455188\pi$
$758$	−14.7166	−0.534532
$759$	0	0
$760$	−5.77135	−0.209349
$761$	−18.7187	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$761$	−18.7187	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$762$	7.03414	0.254820
$763$	−4.35146	−0.157534
$764$	25.4156	0.919506
$765$	−5.93067	−0.214424
$766$	−8.20383	−0.296416
$767$	−30.3663	−1.09646
$768$	5.24097	0.189117
$769$	−17.8519	−0.643755	−0.321878	−	0.946781i	$-0.604314\pi$
$769$	−17.8519	−0.643755	−0.321878	+	0.946781i	$0.604314\pi$
$770$	2.08592	0.0751712
$771$	−17.1121	−0.616278
$772$	0.0362438	0.00130444
$773$	7.93679	0.285466	0.142733	−	0.989761i	$-0.454411\pi$
$773$	7.93679	0.285466	0.142733	+	0.989761i	$0.454411\pi$
$774$	−2.79675	−0.100527
$775$	−4.84901	−0.174182
$776$	26.0853	0.936408
$777$	20.0505	0.719309
$778$	−5.62200	−0.201558
$779$	−22.8853	−0.819952
$780$	−9.39604	−0.336432
$781$	27.5470	0.985708
$782$	0	0
$783$	−0.964805	−0.0344793
$784$	3.48107	0.124324
$785$	−16.4668	−0.587724
$786$	−0.184639	−0.00658585
$787$	−9.35026	−0.333301	−0.166650	−	0.986016i	$-0.553295\pi$
$787$	−9.35026	−0.333301	−0.166650	+	0.986016i	$0.553295\pi$
$788$	12.1390	0.432435
$789$	2.30712	0.0821355
$790$	6.19451	0.220391
$791$	22.3414	0.794369
$792$	2.81807	0.100136
$793$	−15.6600	−0.556101
$794$	0.542465	0.0192514
$795$	−4.73321	−0.167870
$796$	40.8722	1.44868
$797$	−29.0796	−1.03005	−0.515026	−	0.857175i	$-0.672218\pi$
$797$	−29.0796	−1.03005	−0.515026	+	0.857175i	$0.672218\pi$
$798$	−4.27191	−0.151224
$799$	44.9677	1.59084
$800$	4.20239	0.148577
$801$	−15.8417	−0.559740
$802$	−13.3594	−0.471735
$803$	12.5035	0.441239
$804$	−6.78800	−0.239394
$805$	0	0
$806$	9.57488	0.337261
$807$	22.3826	0.787904
$808$	5.28818	0.186038
$809$	28.7517	1.01086	0.505428	−	0.862869i	$-0.331335\pi$
$809$	28.7517	1.01086	0.505428	+	0.862869i	$0.331335\pi$
$810$	−0.388575	−0.0136531
$811$	−30.5307	−1.07208	−0.536039	−	0.844193i	$-0.680080\pi$
$811$	−30.5307	−1.07208	−0.536039	+	0.844193i	$0.680080\pi$
$812$	5.08245	0.178359
$813$	3.28130	0.115080
$814$	−5.15270	−0.180602
$815$	−18.0754	−0.633155
$816$	18.4850	0.647106
$817$	27.7736	0.971676
$818$	4.93734	0.172630
$819$	−14.4777	−0.505892
$820$	10.9659	0.382945
$821$	−18.0795	−0.630980	−0.315490	−	0.948929i	$-0.602169\pi$
$821$	−18.0795	−0.630980	−0.315490	+	0.948929i	$0.602169\pi$
$822$	−6.29436	−0.219541
$823$	16.1321	0.562331	0.281165	−	0.959659i	$-0.409279\pi$
$823$	16.1321	0.562331	0.281165	+	0.959659i	$0.409279\pi$
$824$	3.87134	0.134865
$825$	−1.88420	−0.0655996
$826$	6.61538	0.230179
$827$	36.3297	1.26331	0.631653	−	0.775251i	$-0.282377\pi$
$827$	36.3297	1.26331	0.631653	+	0.775251i	$0.282377\pi$
$828$	0	0
$829$	21.2469	0.737934	0.368967	−	0.929442i	$-0.379712\pi$
$829$	21.2469	0.737934	0.368967	+	0.929442i	$0.379712\pi$
$830$	4.49012	0.155854
$831$	20.8821	0.724391
$832$	23.3795	0.810539
$833$	6.62370	0.229497
$834$	3.02905	0.104887
$835$	11.6701	0.403860
$836$	−13.4438	−0.464962
$837$	−4.84901	−0.167606
$838$	−7.55528	−0.260993
$839$	54.9400	1.89674	0.948370	−	0.317165i	$-0.102731\pi$
$839$	54.9400	1.89674	0.948370	+	0.317165i	$0.102731\pi$
$840$	4.26106	0.147021
$841$	−28.0692	−0.967902
$842$	15.1323	0.521493
$843$	−25.5336	−0.879422
$844$	−28.9492	−0.996473
$845$	−12.8233	−0.441134
$846$	2.94626	0.101295
$847$	−21.2245	−0.729282
$848$	14.7527	0.506611
$849$	26.6204	0.913608
$850$	2.30451	0.0790440
$851$	0	0
$852$	27.0324	0.926115
$853$	−29.5079	−1.01033	−0.505165	−	0.863023i	$-0.668568\pi$
$853$	−29.5079	−1.01033	−0.505165	+	0.863023i	$0.668568\pi$
$854$	3.41156	0.116741
$855$	3.85881	0.131969
$856$	−12.9595	−0.442948
$857$	−56.6117	−1.93382	−0.966909	−	0.255122i	$-0.917884\pi$
$857$	−56.6117	−1.93382	−0.966909	+	0.255122i	$0.917884\pi$
$858$	3.72056	0.127018
$859$	25.6930	0.876634	0.438317	−	0.898820i	$-0.355575\pi$
$859$	25.6930	0.876634	0.438317	+	0.898820i	$0.355575\pi$
$860$	−13.3082	−0.453805
$861$	16.8965	0.575832
$862$	−0.479826	−0.0163429
$863$	17.3175	0.589494	0.294747	−	0.955575i	$-0.404765\pi$
$863$	17.3175	0.589494	0.294747	+	0.955575i	$0.404765\pi$
$864$	4.20239	0.142968
$865$	14.8526	0.505003
$866$	11.5413	0.392189
$867$	18.1728	0.617182
$868$	25.5438	0.867014
$869$	30.0372	1.01894
$870$	0.374899	0.0127103
$871$	−18.6556	−0.632120
$872$	2.28436	0.0773583
$873$	−17.4410	−0.590290
$874$	0	0
$875$	−2.84901	−0.0963141
$876$	12.2700	0.414563
$877$	57.4992	1.94161	0.970806	−	0.239867i	$-0.0771040\pi$
$877$	57.4992	1.94161	0.970806	+	0.239867i	$0.0771040\pi$
$878$	6.04439	0.203988
$879$	11.6287	0.392226
$880$	5.87279	0.197972
$881$	−26.0134	−0.876413	−0.438207	−	0.898874i	$-0.644386\pi$
$881$	−26.0134	−0.876413	−0.438207	+	0.898874i	$0.644386\pi$
$882$	0.433982	0.0146129
$883$	−3.41989	−0.115088	−0.0575441	−	0.998343i	$-0.518327\pi$
$883$	−3.41989	−0.115088	−0.0575441	+	0.998343i	$0.518327\pi$
$884$	55.7248	1.87423
$885$	−5.97567	−0.200870
$886$	15.7671	0.529707
$887$	−0.109726	−0.00368422	−0.00184211	−	0.999998i	$-0.500586\pi$
$887$	−0.109726	−0.00368422	−0.00184211	+	0.999998i	$0.500586\pi$
$888$	−10.5258	−0.353224
$889$	51.5739	1.72973
$890$	6.15570	0.206340
$891$	−1.88420	−0.0631232
$892$	−22.4539	−0.751811
$893$	−29.2584	−0.979094
$894$	−3.06360	−0.102462
$895$	−0.722287	−0.0241434
$896$	−29.0386	−0.970111
$897$	0	0
$898$	−0.0832265	−0.00277731
$899$	4.67835	0.156032
$900$	−1.84901	−0.0616336
$901$	28.0711	0.935185
$902$	−4.34217	−0.144578
$903$	−20.5056	−0.682384
$904$	−11.7284	−0.390082
$905$	6.67729	0.221961
$906$	4.32370	0.143645
$907$	−12.4436	−0.413184	−0.206592	−	0.978427i	$-0.566237\pi$
$907$	−12.4436	−0.413184	−0.206592	+	0.978427i	$0.566237\pi$
$908$	37.5117	1.24487
$909$	−3.53576	−0.117274
$910$	5.62567	0.186489
$911$	−22.9721	−0.761098	−0.380549	−	0.924761i	$-0.624265\pi$
$911$	−22.9721	−0.761098	−0.380549	+	0.924761i	$0.624265\pi$
$912$	−12.0274	−0.398265
$913$	21.7727	0.720570
$914$	8.20405	0.271366
$915$	−3.08166	−0.101877
$916$	6.96782	0.230223
$917$	−1.35376	−0.0447051
$918$	2.30451	0.0760602
$919$	19.1699	0.632358	0.316179	−	0.948700i	$-0.397600\pi$
$919$	19.1699	0.632358	0.316179	+	0.948700i	$0.397600\pi$
$920$	0	0
$921$	−2.00946	−0.0662138
$922$	−3.59604	−0.118429
$923$	74.2936	2.44540
$924$	9.92570	0.326531
$925$	7.03772	0.231399
$926$	−3.80058	−0.124895
$927$	−2.58844	−0.0850154
$928$	−4.05449	−0.133095
$929$	−45.5420	−1.49418	−0.747091	−	0.664721i	$-0.768550\pi$
$929$	−45.5420	−1.49418	−0.747091	+	0.664721i	$0.768550\pi$
$930$	1.88420	0.0617855
$931$	−4.30973	−0.141246
$932$	−12.6666	−0.414908
$933$	−7.15246	−0.234161
$934$	−4.40845	−0.144249
$935$	11.1746	0.365448
$936$	7.60028	0.248423
$937$	−26.8464	−0.877034	−0.438517	−	0.898723i	$-0.644496\pi$
$937$	−26.8464	−0.877034	−0.438517	+	0.898723i	$0.644496\pi$
$938$	4.06417	0.132700
$939$	−3.08851	−0.100790
$940$	14.0196	0.457269
$941$	8.30818	0.270839	0.135420	−	0.990788i	$-0.456762\pi$
$941$	8.30818	0.270839	0.135420	+	0.990788i	$0.456762\pi$
$942$	6.39858	0.208477
$943$	0	0
$944$	18.6253	0.606201
$945$	−2.84901	−0.0926783
$946$	5.26965	0.171331
$947$	22.3260	0.725496	0.362748	−	0.931887i	$-0.381839\pi$
$947$	22.3260	0.725496	0.362748	+	0.931887i	$0.381839\pi$
$948$	29.4762	0.957341
$949$	33.7217	1.09465
$950$	−1.49944	−0.0486482
$951$	−30.5278	−0.989930
$952$	−25.2709	−0.819036
$953$	33.6008	1.08844	0.544219	−	0.838943i	$-0.316826\pi$
$953$	33.6008	1.08844	0.544219	+	0.838943i	$0.316826\pi$
$954$	1.83921	0.0595466
$955$	13.7455	0.444795
$956$	52.7884	1.70730
$957$	1.81789	0.0587640
$958$	1.99675	0.0645120
$959$	−46.1499	−1.49026
$960$	4.60077	0.148489
$961$	−7.48711	−0.241520
$962$	−13.8967	−0.448049
$963$	8.66494	0.279224
$964$	42.1561	1.35776
$965$	0.0196017	0.000631002 0
$966$	0	0
$967$	−2.71141	−0.0871930	−0.0435965	−	0.999049i	$-0.513882\pi$
$967$	−2.71141	−0.0871930	−0.0435965	+	0.999049i	$0.513882\pi$
$968$	11.1421	0.358121
$969$	−22.8853	−0.735183
$970$	6.77715	0.217601
$971$	51.3235	1.64705	0.823525	−	0.567281i	$-0.192004\pi$
$971$	51.3235	1.64705	0.823525	+	0.567281i	$0.192004\pi$
$972$	−1.84901	−0.0593070
$973$	22.2088	0.711982
$974$	3.52331	0.112894
$975$	−5.08166	−0.162743
$976$	9.60509	0.307451
$977$	−20.9295	−0.669595	−0.334798	−	0.942290i	$-0.608668\pi$
$977$	−20.9295	−0.669595	−0.334798	+	0.942290i	$0.608668\pi$
$978$	7.02367	0.224592
$979$	29.8491	0.953980
$980$	2.06508	0.0659664
$981$	−1.52736	−0.0487649
$982$	0.0118624	0.000378544 0
$983$	11.2367	0.358396	0.179198	−	0.983813i	$-0.442650\pi$
$983$	11.2367	0.358396	0.179198	+	0.983813i	$0.442650\pi$
$984$	−8.87008	−0.282768
$985$	6.56516	0.209183
$986$	−2.22340	−0.0708076
$987$	21.6018	0.687594
$988$	−36.2575	−1.15351
$989$	0	0
$990$	0.732155	0.0232694
$991$	15.7663	0.500834	0.250417	−	0.968138i	$-0.419432\pi$
$991$	15.7663	0.500834	0.250417	+	0.968138i	$0.419432\pi$
$992$	−20.3774	−0.646984
$993$	−25.3362	−0.804019
$994$	−16.1851	−0.513359
$995$	22.1049	0.700773
$996$	21.3660	0.677007
$997$	29.4011	0.931142	0.465571	−	0.885011i	$-0.345849\pi$
$997$	29.4011	0.931142	0.465571	+	0.885011i	$0.345849\pi$
$998$	−17.0137	−0.538559
$999$	7.03772	0.222664

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bb.1.3	✓	5
23.22	odd	2		7935.2.a.bc.1.3	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bb.1.3	✓	5	1.1	even	1	trivial
7935.2.a.bc.1.3	yes	5	23.22	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.388575 q^{2} +1.00000 q^{3} -1.84901 q^{4} -1.00000 q^{5} +0.388575 q^{6} +2.84901 q^{7} -1.49563 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.388575 q^{2} +1.00000 q^{3} -1.84901 q^{4} -1.00000 q^{5} +0.388575 q^{6} +2.84901 q^{7} -1.49563 q^{8} +1.00000 q^{9} -0.388575 q^{10} -1.88420 q^{11} -1.84901 q^{12} -5.08166 q^{13} +1.10705 q^{14} -1.00000 q^{15} +3.11685 q^{16} +5.93067 q^{17} +0.388575 q^{18} -3.85881 q^{19} +1.84901 q^{20} +2.84901 q^{21} -0.732155 q^{22} -1.49563 q^{24} +1.00000 q^{25} -1.97461 q^{26} +1.00000 q^{27} -5.26785 q^{28} -0.964805 q^{29} -0.388575 q^{30} -4.84901 q^{31} +4.20239 q^{32} -1.88420 q^{33} +2.30451 q^{34} -2.84901 q^{35} -1.84901 q^{36} +7.03772 q^{37} -1.49944 q^{38} -5.08166 q^{39} +1.49563 q^{40} +5.93067 q^{41} +1.10705 q^{42} -7.19746 q^{43} +3.48391 q^{44} -1.00000 q^{45} +7.58222 q^{47} +3.11685 q^{48} +1.11685 q^{49} +0.388575 q^{50} +5.93067 q^{51} +9.39604 q^{52} +4.73321 q^{53} +0.388575 q^{54} +1.88420 q^{55} -4.26106 q^{56} -3.85881 q^{57} -0.374899 q^{58} +5.97567 q^{59} +1.84901 q^{60} +3.08166 q^{61} -1.88420 q^{62} +2.84901 q^{63} -4.60077 q^{64} +5.08166 q^{65} -0.732155 q^{66} +3.67115 q^{67} -10.9659 q^{68} -1.10705 q^{70} -14.6199 q^{71} -1.49563 q^{72} -6.63596 q^{73} +2.73468 q^{74} +1.00000 q^{75} +7.13498 q^{76} -5.36812 q^{77} -1.97461 q^{78} -15.9416 q^{79} -3.11685 q^{80} +1.00000 q^{81} +2.30451 q^{82} -11.5554 q^{83} -5.26785 q^{84} -5.93067 q^{85} -2.79675 q^{86} -0.964805 q^{87} +2.81807 q^{88} -15.8417 q^{89} -0.388575 q^{90} -14.4777 q^{91} -4.84901 q^{93} +2.94626 q^{94} +3.85881 q^{95} +4.20239 q^{96} -17.4410 q^{97} +0.433982 q^{98} -1.88420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9} - 6 q^{11} + 8 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} + 10 q^{16} - 7 q^{17} + 4 q^{19} - 8 q^{20} - 3 q^{21} + 8 q^{22} - 6 q^{24} + 5 q^{25} + 10 q^{26} + 5 q^{27} - 38 q^{28} + 9 q^{29} - 7 q^{31} - 12 q^{32} - 6 q^{33} - 4 q^{34} + 3 q^{35} + 8 q^{36} - q^{37} - 26 q^{38} - 6 q^{39} + 6 q^{40} - 7 q^{41} + 6 q^{42} - 20 q^{43} - 18 q^{44} - 5 q^{45} + 10 q^{48} - 7 q^{51} - 22 q^{52} + 3 q^{53} + 6 q^{55} + 18 q^{56} + 4 q^{57} - 14 q^{58} + q^{59} - 8 q^{60} - 4 q^{61} - 6 q^{62} - 3 q^{63} + 18 q^{64} + 6 q^{65} + 8 q^{66} + 5 q^{67} - 32 q^{68} - 6 q^{70} + q^{71} - 6 q^{72} - 6 q^{73} - 48 q^{74} + 5 q^{75} + 6 q^{76} + 12 q^{77} + 10 q^{78} - 10 q^{80} + 5 q^{81} - 4 q^{82} - 41 q^{83} - 38 q^{84} + 7 q^{85} + 2 q^{86} + 9 q^{87} + 84 q^{88} - 18 q^{89} + 16 q^{91} - 7 q^{93} + 4 q^{94} - 4 q^{95} - 12 q^{96} - 26 q^{97} - 24 q^{98} - 6 q^{99}+O(q^{100}) \) 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9 - 6 * q^11 + 8 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 + 10 * q^16 - 7 * q^17 + 4 * q^19 - 8 * q^20 - 3 * q^21 + 8 * q^22 - 6 * q^24 + 5 * q^25 + 10 * q^26 + 5 * q^27 - 38 * q^28 + 9 * q^29 - 7 * q^31 - 12 * q^32 - 6 * q^33 - 4 * q^34 + 3 * q^35 + 8 * q^36 - q^37 - 26 * q^38 - 6 * q^39 + 6 * q^40 - 7 * q^41 + 6 * q^42 - 20 * q^43 - 18 * q^44 - 5 * q^45 + 10 * q^48 - 7 * q^51 - 22 * q^52 + 3 * q^53 + 6 * q^55 + 18 * q^56 + 4 * q^57 - 14 * q^58 + q^59 - 8 * q^60 - 4 * q^61 - 6 * q^62 - 3 * q^63 + 18 * q^64 + 6 * q^65 + 8 * q^66 + 5 * q^67 - 32 * q^68 - 6 * q^70 + q^71 - 6 * q^72 - 6 * q^73 - 48 * q^74 + 5 * q^75 + 6 * q^76 + 12 * q^77 + 10 * q^78 - 10 * q^80 + 5 * q^81 - 4 * q^82 - 41 * q^83 - 38 * q^84 + 7 * q^85 + 2 * q^86 + 9 * q^87 + 84 * q^88 - 18 * q^89 + 16 * q^91 - 7 * q^93 + 4 * q^94 - 4 * q^95 - 12 * q^96 - 26 * q^97 - 24 * q^98 - 6 * q^99

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