LMFDB - Embedded newform 151.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(1,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("151.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.713538$ of defining polynomial
Character	$\chi$	$=$	151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49086 q^{2} +2.00000 q^{3} +4.20440 q^{4} +3.77733 q^{5} -4.98173 q^{6} -2.00000 q^{7} -5.49086 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49086 q^{2} +2.00000 q^{3} +4.20440 q^{4} +3.77733 q^{5} -4.98173 q^{6} -2.00000 q^{7} -5.49086 q^{8} +1.00000 q^{9} -9.40880 q^{10} +2.91794 q^{11} +8.40880 q^{12} -6.40880 q^{13} +4.98173 q^{14} +7.55465 q^{15} +5.26819 q^{16} +5.49086 q^{17} -2.49086 q^{18} +2.14061 q^{19} +15.8814 q^{20} -4.00000 q^{21} -7.26819 q^{22} -4.98173 q^{23} -10.9817 q^{24} +9.26819 q^{25} +15.9635 q^{26} -4.00000 q^{27} -8.40880 q^{28} -2.84111 q^{29} -18.8176 q^{30} -3.20440 q^{31} -2.14061 q^{32} +5.83588 q^{33} -13.6770 q^{34} -7.55465 q^{35} +4.20440 q^{36} +8.47259 q^{37} -5.33198 q^{38} -12.8176 q^{39} -20.7408 q^{40} +9.96345 q^{42} -3.20440 q^{43} +12.2682 q^{44} +3.77733 q^{45} +12.4088 q^{46} -4.71354 q^{47} +10.5364 q^{48} -3.00000 q^{49} -23.0858 q^{50} +10.9817 q^{51} -26.9452 q^{52} -4.28123 q^{53} +9.96345 q^{54} +11.0220 q^{55} +10.9817 q^{56} +4.28123 q^{57} +7.07683 q^{58} +4.79560 q^{59} +31.7628 q^{60} +8.81761 q^{61} +7.98173 q^{62} -2.00000 q^{63} -5.20440 q^{64} -24.2081 q^{65} -14.5364 q^{66} -10.8176 q^{67} +23.0858 q^{68} -9.96345 q^{69} +18.8176 q^{70} +4.98173 q^{71} -5.49086 q^{72} -2.40880 q^{73} -21.1041 q^{74} +18.5364 q^{75} +9.00000 q^{76} -5.83588 q^{77} +31.9269 q^{78} -14.4088 q^{79} +19.8997 q^{80} -11.0000 q^{81} -1.39053 q^{83} -16.8176 q^{84} +20.7408 q^{85} +7.98173 q^{86} -5.68223 q^{87} -16.0220 q^{88} +7.01827 q^{89} -9.40880 q^{90} +12.8176 q^{91} -20.9452 q^{92} -6.40880 q^{93} +11.7408 q^{94} +8.08580 q^{95} -4.28123 q^{96} -3.98696 q^{97} +7.47259 q^{98} +2.91794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9	$ 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9} - 11 q^{10} - q^{11} + 8 q^{12} - 2 q^{13} + 10 q^{15} + 2 q^{16} + 9 q^{17} + 3 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{22} - 18 q^{24} + 14 q^{25} + 18 q^{26} - 12 q^{27} - 8 q^{28} + 3 q^{29} - 22 q^{30} - q^{31} - 3 q^{32} - 2 q^{33} - 10 q^{34} - 10 q^{35} + 4 q^{36} + 3 q^{37} + 3 q^{38} - 4 q^{39} - 26 q^{40} - q^{43} + 23 q^{44} + 5 q^{45} + 20 q^{46} - 13 q^{47} + 4 q^{48} - 9 q^{49} - 21 q^{50} + 18 q^{51} - 36 q^{52} - 6 q^{53} - 10 q^{55} + 18 q^{56} + 6 q^{57} + 23 q^{58} + 23 q^{59} + 16 q^{60} - 8 q^{61} + 9 q^{62} - 6 q^{63} - 7 q^{64} - 6 q^{65} - 16 q^{66} + 2 q^{67} + 21 q^{68} + 22 q^{70} - 9 q^{72} + 10 q^{73} - 30 q^{74} + 28 q^{75} + 27 q^{76} + 2 q^{77} + 36 q^{78} - 26 q^{79} + 35 q^{80} - 33 q^{81} + 28 q^{83} - 16 q^{84} + 26 q^{85} + 9 q^{86} + 6 q^{87} - 5 q^{88} + 36 q^{89} - 11 q^{90} + 4 q^{91} - 18 q^{92} - 2 q^{93} - q^{94} - 24 q^{95} - 6 q^{96} - 5 q^{97} - q^{99}+O(q^{100}) $ 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9 - 11 * q^10 - q^11 + 8 * q^12 - 2 * q^13 + 10 * q^15 + 2 * q^16 + 9 * q^17 + 3 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^22 - 18 * q^24 + 14 * q^25 + 18 * q^26 - 12 * q^27 - 8 * q^28 + 3 * q^29 - 22 * q^30 - q^31 - 3 * q^32 - 2 * q^33 - 10 * q^34 - 10 * q^35 + 4 * q^36 + 3 * q^37 + 3 * q^38 - 4 * q^39 - 26 * q^40 - q^43 + 23 * q^44 + 5 * q^45 + 20 * q^46 - 13 * q^47 + 4 * q^48 - 9 * q^49 - 21 * q^50 + 18 * q^51 - 36 * q^52 - 6 * q^53 - 10 * q^55 + 18 * q^56 + 6 * q^57 + 23 * q^58 + 23 * q^59 + 16 * q^60 - 8 * q^61 + 9 * q^62 - 6 * q^63 - 7 * q^64 - 6 * q^65 - 16 * q^66 + 2 * q^67 + 21 * q^68 + 22 * q^70 - 9 * q^72 + 10 * q^73 - 30 * q^74 + 28 * q^75 + 27 * q^76 + 2 * q^77 + 36 * q^78 - 26 * q^79 + 35 * q^80 - 33 * q^81 + 28 * q^83 - 16 * q^84 + 26 * q^85 + 9 * q^86 + 6 * q^87 - 5 * q^88 + 36 * q^89 - 11 * q^90 + 4 * q^91 - 18 * q^92 - 2 * q^93 - q^94 - 24 * q^95 - 6 * q^96 - 5 * q^97 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.49086	−1.76131	−0.880653	−	0.473761i	$-0.842896\pi$
$2$	−2.49086	−1.76131	−0.880653	+	0.473761i	$0.842896\pi$
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	4.20440	2.10220
$5$	3.77733	1.68927	0.844636	−	0.535342i	$-0.179817\pi$
$5$	3.77733	1.68927	0.844636	+	0.535342i	$0.179817\pi$
$6$	−4.98173	−2.03378
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−5.49086	−1.94131
$9$	1.00000	0.333333
$10$	−9.40880	−2.97532
$11$	2.91794	0.879792	0.439896	−	0.898049i	$-0.355015\pi$
$11$	2.91794	0.879792	0.439896	+	0.898049i	$0.355015\pi$
$12$	8.40880	2.42741
$13$	−6.40880	−1.77748	−0.888741	−	0.458410i	$-0.848419\pi$
$13$	−6.40880	−1.77748	−0.888741	+	0.458410i	$0.848419\pi$
$14$	4.98173	1.33142
$15$	7.55465	1.95060
$16$	5.26819	1.31705
$17$	5.49086	1.33173	0.665865	−	0.746072i	$-0.268063\pi$
$17$	5.49086	1.33173	0.665865	+	0.746072i	$0.268063\pi$
$18$	−2.49086	−0.587102
$19$	2.14061	0.491090	0.245545	−	0.969385i	$-0.421033\pi$
$19$	2.14061	0.491090	0.245545	+	0.969385i	$0.421033\pi$
$20$	15.8814	3.55119
$21$	−4.00000	−0.872872
$22$	−7.26819	−1.54958
$23$	−4.98173	−1.03876	−0.519381	−	0.854543i	$-0.673837\pi$
$23$	−4.98173	−1.03876	−0.519381	+	0.854543i	$0.673837\pi$
$24$	−10.9817	−2.24164
$25$	9.26819	1.85364
$26$	15.9635	3.13069
$27$	−4.00000	−0.769800
$28$	−8.40880	−1.58911
$29$	−2.84111	−0.527582	−0.263791	−	0.964580i	$-0.584973\pi$
$29$	−2.84111	−0.527582	−0.263791	+	0.964580i	$0.584973\pi$
$30$	−18.8176	−3.43561
$31$	−3.20440	−0.575528	−0.287764	−	0.957701i	$-0.592912\pi$
$31$	−3.20440	−0.575528	−0.287764	+	0.957701i	$0.592912\pi$
$32$	−2.14061	−0.378411
$33$	5.83588	1.01590
$34$	−13.6770	−2.34558
$35$	−7.55465	−1.27697
$36$	4.20440	0.700734
$37$	8.47259	1.39289	0.696443	−	0.717612i	$-0.254765\pi$
$37$	8.47259	1.39289	0.696443	+	0.717612i	$0.254765\pi$
$38$	−5.33198	−0.864961
$39$	−12.8176	−2.05246
$40$	−20.7408	−3.27941
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	9.96345	1.53739
$43$	−3.20440	−0.488667	−0.244333	−	0.969691i	$-0.578569\pi$
$43$	−3.20440	−0.488667	−0.244333	+	0.969691i	$0.578569\pi$
$44$	12.2682	1.84950
$45$	3.77733	0.563090
$46$	12.4088	1.82958
$47$	−4.71354	−0.687540	−0.343770	−	0.939054i	$-0.611704\pi$
$47$	−4.71354	−0.687540	−0.343770	+	0.939054i	$0.611704\pi$
$48$	10.5364	1.52080
$49$	−3.00000	−0.428571
$50$	−23.0858	−3.26482
$51$	10.9817	1.53775
$52$	−26.9452	−3.73662
$53$	−4.28123	−0.588072	−0.294036	−	0.955794i	$-0.594999\pi$
$53$	−4.28123	−0.588072	−0.294036	+	0.955794i	$0.594999\pi$
$54$	9.96345	1.35585
$55$	11.0220	1.48621
$56$	10.9817	1.46750
$57$	4.28123	0.567062
$58$	7.07683	0.929233
$59$	4.79560	0.624334	0.312167	−	0.950027i	$-0.398945\pi$
$59$	4.79560	0.624334	0.312167	+	0.950027i	$0.398945\pi$
$60$	31.7628	4.10056
$61$	8.81761	1.12898	0.564489	−	0.825440i	$-0.309073\pi$
$61$	8.81761	1.12898	0.564489	+	0.825440i	$0.309073\pi$
$62$	7.98173	1.01368
$63$	−2.00000	−0.251976
$64$	−5.20440	−0.650550
$65$	−24.2081	−3.00265
$66$	−14.5364	−1.78930
$67$	−10.8176	−1.32158	−0.660790	−	0.750570i	$-0.729779\pi$
$67$	−10.8176	−1.32158	−0.660790	+	0.750570i	$0.729779\pi$
$68$	23.0858	2.79956
$69$	−9.96345	−1.19946
$70$	18.8176	2.24913
$71$	4.98173	0.591222	0.295611	−	0.955308i	$-0.404477\pi$
$71$	4.98173	0.591222	0.295611	+	0.955308i	$0.404477\pi$
$72$	−5.49086	−0.647104
$73$	−2.40880	−0.281929	−0.140965	−	0.990015i	$-0.545020\pi$
$73$	−2.40880	−0.281929	−0.140965	+	0.990015i	$0.545020\pi$
$74$	−21.1041	−2.45330
$75$	18.5364	2.14040
$76$	9.00000	1.03237
$77$	−5.83588	−0.665060
$78$	31.9269	3.61501
$79$	−14.4088	−1.62112	−0.810559	−	0.585658i	$-0.800836\pi$
$79$	−14.4088	−1.62112	−0.810559	+	0.585658i	$0.800836\pi$
$80$	19.8997	2.22485
$81$	−11.0000	−1.22222
$82$	0	0
$83$	−1.39053	−0.152631	−0.0763153	−	0.997084i	$-0.524316\pi$
$83$	−1.39053	−0.152631	−0.0763153	+	0.997084i	$0.524316\pi$
$84$	−16.8176	−1.83495
$85$	20.7408	2.24965
$86$	7.98173	0.860692
$87$	−5.68223	−0.609199
$88$	−16.0220	−1.70795
$89$	7.01827	0.743935	0.371968	−	0.928246i	$-0.378683\pi$
$89$	7.01827	0.743935	0.371968	+	0.928246i	$0.378683\pi$
$90$	−9.40880	−0.991775
$91$	12.8176	1.34365
$92$	−20.9452	−2.18369
$93$	−6.40880	−0.664562
$94$	11.7408	1.21097
$95$	8.08580	0.829585
$96$	−4.28123	−0.436951
$97$	−3.98696	−0.404815	−0.202407	−	0.979301i	$-0.564876\pi$
$97$	−3.98696	−0.404815	−0.202407	+	0.979301i	$0.564876\pi$
$98$	7.47259	0.754846
$99$	2.91794	0.293264
$100$	38.9672	3.89672
$101$	9.26295	0.921698	0.460849	−	0.887478i	$-0.347545\pi$
$101$	9.26295	0.921698	0.460849	+	0.887478i	$0.347545\pi$
$102$	−27.3540	−2.70845
$103$	−16.7538	−1.65080	−0.825401	−	0.564546i	$-0.809051\pi$
$103$	−16.7538	−1.65080	−0.825401	+	0.564546i	$0.809051\pi$
$104$	35.1899	3.45065
$105$	−15.1093	−1.47452
$106$	10.6640	1.03577
$107$	4.12758	0.399028	0.199514	−	0.979895i	$-0.436064\pi$
$107$	4.12758	0.399028	0.199514	+	0.979895i	$0.436064\pi$
$108$	−16.8176	−1.61827
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−27.4543	−2.61767
$111$	16.9452	1.60837
$112$	−10.5364	−0.995594
$113$	−5.68223	−0.534539	−0.267269	−	0.963622i	$-0.586121\pi$
$113$	−5.68223	−0.534539	−0.267269	+	0.963622i	$0.586121\pi$
$114$	−10.6640	−0.998771
$115$	−18.8176	−1.75475
$116$	−11.9452	−1.10908
$117$	−6.40880	−0.592494
$118$	−11.9452	−1.09964
$119$	−10.9817	−1.00669
$120$	−41.4816	−3.78673
$121$	−2.48563	−0.225966
$122$	−21.9635	−1.98848
$123$	0	0
$124$	−13.4726	−1.20987
$125$	16.1223	1.44203
$126$	4.98173	0.443808
$127$	5.61320	0.498091	0.249046	−	0.968492i	$-0.419883\pi$
$127$	5.61320	0.498091	0.249046	+	0.968492i	$0.419883\pi$
$128$	17.2447	1.52423
$129$	−6.40880	−0.564264
$130$	60.2992	5.28859
$131$	−7.87242	−0.687817	−0.343908	−	0.939003i	$-0.611751\pi$
$131$	−7.87242	−0.687817	−0.343908	+	0.939003i	$0.611751\pi$
$132$	24.5364	2.13562
$133$	−4.28123	−0.371230
$134$	26.9452	2.32771
$135$	−15.1093	−1.30040
$136$	−30.1496	−2.58531
$137$	18.1861	1.55375	0.776873	−	0.629657i	$-0.216805\pi$
$137$	18.1861	1.55375	0.776873	+	0.629657i	$0.216805\pi$
$138$	24.8176	2.11261
$139$	15.4946	1.31423	0.657117	−	0.753788i	$-0.271776\pi$
$139$	15.4946	1.31423	0.657117	+	0.753788i	$0.271776\pi$
$140$	−31.7628	−2.68445
$141$	−9.42708	−0.793903
$142$	−12.4088	−1.04132
$143$	−18.7005	−1.56381
$144$	5.26819	0.439016
$145$	−10.7318	−0.891228
$146$	6.00000	0.496564
$147$	−6.00000	−0.494872
$148$	35.6222	2.92812
$149$	13.5547	1.11044	0.555220	−	0.831703i	$-0.312634\pi$
$149$	13.5547	1.11044	0.555220	+	0.831703i	$0.312634\pi$
$150$	−46.1716	−3.76989
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−11.7538	−0.953361
$153$	5.49086	0.443910
$154$	14.5364	1.17137
$155$	−12.1041	−0.972222
$156$	−53.8904	−4.31468
$157$	16.5364	1.31975	0.659873	−	0.751377i	$-0.270610\pi$
$157$	16.5364	1.31975	0.659873	+	0.751377i	$0.270610\pi$
$158$	35.8904	2.85528
$159$	−8.56246	−0.679047
$160$	−8.08580	−0.639238
$161$	9.96345	0.785230
$162$	27.3995	2.15271
$163$	23.7628	1.86125	0.930623	−	0.365980i	$-0.119266\pi$
$163$	23.7628	1.86125	0.930623	+	0.365980i	$0.119266\pi$
$164$	0	0
$165$	22.0440	1.71612
$166$	3.46362	0.268829
$167$	3.10930	0.240605	0.120303	−	0.992737i	$-0.461614\pi$
$167$	3.10930	0.240605	0.120303	+	0.992737i	$0.461614\pi$
$168$	21.9635	1.69452
$169$	28.0728	2.15944
$170$	−51.6625	−3.96233
$171$	2.14061	0.163697
$172$	−13.4726	−1.02728
$173$	−17.9504	−1.36474	−0.682372	−	0.731005i	$-0.739052\pi$
$173$	−17.9504	−1.36474	−0.682372	+	0.731005i	$0.739052\pi$
$174$	14.1537	1.07299
$175$	−18.5364	−1.40122
$176$	15.3723	1.15873
$177$	9.59120	0.720919
$178$	−17.4816	−1.31030
$179$	1.87242	0.139952	0.0699758	−	0.997549i	$-0.477708\pi$
$179$	1.87242	0.139952	0.0699758	+	0.997549i	$0.477708\pi$
$180$	15.8814	1.18373
$181$	12.9452	0.962208	0.481104	−	0.876664i	$-0.340236\pi$
$181$	12.9452	0.962208	0.481104	+	0.876664i	$0.340236\pi$
$182$	−31.9269	−2.36658
$183$	17.6352	1.30363
$184$	27.3540	2.01656
$185$	32.0037	2.35296
$186$	15.9635	1.17050
$187$	16.0220	1.17165
$188$	−19.8176	−1.44535
$189$	8.00000	0.581914
$190$	−20.1406	−1.46115
$191$	−5.24992	−0.379871	−0.189935	−	0.981797i	$-0.560828\pi$
$191$	−5.24992	−0.379871	−0.189935	+	0.981797i	$0.560828\pi$
$192$	−10.4088	−0.751191
$193$	5.74078	0.413230	0.206615	−	0.978422i	$-0.433755\pi$
$193$	5.74078	0.413230	0.206615	+	0.978422i	$0.433755\pi$
$194$	9.93098	0.713003
$195$	−48.4163	−3.46716
$196$	−12.6132	−0.900943
$197$	0.854152	0.0608558	0.0304279	−	0.999537i	$-0.490313\pi$
$197$	0.854152	0.0608558	0.0304279	+	0.999537i	$0.490313\pi$
$198$	−7.26819	−0.516528
$199$	−21.0728	−1.49381	−0.746904	−	0.664932i	$-0.768461\pi$
$199$	−21.0728	−1.49381	−0.746904	+	0.664932i	$0.768461\pi$
$200$	−50.8904	−3.59849
$201$	−21.6352	−1.52603
$202$	−23.0728	−1.62339
$203$	5.68223	0.398814
$204$	46.1716	3.23266
$205$	0	0
$206$	41.7315	2.90757
$207$	−4.98173	−0.346254
$208$	−33.7628	−2.34103
$209$	6.24618	0.432057
$210$	37.6352	2.59708
$211$	−10.2812	−0.707789	−0.353894	−	0.935285i	$-0.615143\pi$
$211$	−10.2812	−0.707789	−0.353894	+	0.935285i	$0.615143\pi$
$212$	−18.0000	−1.23625
$213$	9.96345	0.682685
$214$	−10.2812	−0.702810
$215$	−12.1041	−0.825491
$216$	21.9635	1.49442
$217$	6.40880	0.435058
$218$	−4.98173	−0.337405
$219$	−4.81761	−0.325544
$220$	46.3409	3.12431
$221$	−35.1899	−2.36713
$222$	−42.2081	−2.83282
$223$	15.9362	1.06717	0.533584	−	0.845747i	$-0.320845\pi$
$223$	15.9362	1.06717	0.533584	+	0.845747i	$0.320845\pi$
$224$	4.28123	0.286052
$225$	9.26819	0.617879
$226$	14.1537	0.941487
$227$	−2.91794	−0.193670	−0.0968352	−	0.995300i	$-0.530872\pi$
$227$	−2.91794	−0.193670	−0.0968352	+	0.995300i	$0.530872\pi$
$228$	18.0000	1.19208
$229$	−25.3409	−1.67458	−0.837288	−	0.546761i	$-0.815860\pi$
$229$	−25.3409	−1.67458	−0.837288	+	0.546761i	$0.815860\pi$
$230$	46.8721	3.09065
$231$	−11.6718	−0.767945
$232$	15.6002	1.02420
$233$	2.57292	0.168558	0.0842789	−	0.996442i	$-0.473141\pi$
$233$	2.57292	0.168558	0.0842789	+	0.996442i	$0.473141\pi$
$234$	15.9635	1.04356
$235$	−17.8046	−1.16144
$236$	20.1626	1.31247
$237$	−28.8176	−1.87190
$238$	27.3540	1.77310
$239$	7.73555	0.500371	0.250185	−	0.968198i	$-0.419508\pi$
$239$	7.73555	0.500371	0.250185	+	0.968198i	$0.419508\pi$
$240$	39.7993	2.56904
$241$	−17.4178	−1.12198	−0.560989	−	0.827823i	$-0.689579\pi$
$241$	−17.4178	−1.12198	−0.560989	+	0.827823i	$0.689579\pi$
$242$	6.19136	0.397996
$243$	−10.0000	−0.641500
$244$	37.0728	2.37334
$245$	−11.3320	−0.723973
$246$	0	0
$247$	−13.7188	−0.872905
$248$	17.5949	1.11728
$249$	−2.78106	−0.176243
$250$	−40.1586	−2.53985
$251$	5.14585	0.324803	0.162402	−	0.986725i	$-0.448076\pi$
$251$	5.14585	0.324803	0.162402	+	0.986725i	$0.448076\pi$
$252$	−8.40880	−0.529705
$253$	−14.5364	−0.913894
$254$	−13.9817	−0.877292
$255$	41.4816	2.59768
$256$	−32.5453	−2.03408
$257$	5.13538	0.320336	0.160168	−	0.987090i	$-0.448796\pi$
$257$	5.13538	0.320336	0.160168	+	0.987090i	$0.448796\pi$
$258$	15.9635	0.993841
$259$	−16.9452	−1.05292
$260$	−101.781	−6.31217
$261$	−2.84111	−0.175861
$262$	19.6091	1.21146
$263$	14.0910	0.868890	0.434445	−	0.900698i	$-0.356945\pi$
$263$	14.0910	0.868890	0.434445	+	0.900698i	$0.356945\pi$
$264$	−32.0440	−1.97217
$265$	−16.1716	−0.993413
$266$	10.6640	0.653849
$267$	14.0365	0.859023
$268$	−45.4816	−2.77823
$269$	21.6184	1.31810	0.659050	−	0.752099i	$-0.270959\pi$
$269$	21.6184	1.31810	0.659050	+	0.752099i	$0.270959\pi$
$270$	37.6352	2.29041
$271$	−3.30997	−0.201066	−0.100533	−	0.994934i	$-0.532055\pi$
$271$	−3.30997	−0.201066	−0.100533	+	0.994934i	$0.532055\pi$
$272$	28.9269	1.75395
$273$	25.6352	1.55151
$274$	−45.2992	−2.73662
$275$	27.0440	1.63082
$276$	−41.8904	−2.52150
$277$	12.9452	0.777801	0.388900	−	0.921280i	$-0.372855\pi$
$277$	12.9452	0.777801	0.388900	+	0.921280i	$0.372855\pi$
$278$	−38.5949	−2.31477
$279$	−3.20440	−0.191843
$280$	41.4816	2.47900
$281$	27.6457	1.64920	0.824602	−	0.565714i	$-0.191399\pi$
$281$	27.6457	1.64920	0.824602	+	0.565714i	$0.191399\pi$
$282$	23.4816	1.39831
$283$	−19.0728	−1.13376	−0.566879	−	0.823801i	$-0.691849\pi$
$283$	−19.0728	−1.13376	−0.566879	+	0.823801i	$0.691849\pi$
$284$	20.9452	1.24287
$285$	16.1716	0.957922
$286$	46.5804	2.75436
$287$	0	0
$288$	−2.14061	−0.126137
$289$	13.1496	0.773505
$290$	26.7315	1.56973
$291$	−7.97392	−0.467440
$292$	−10.1276	−0.592672
$293$	−7.87242	−0.459912	−0.229956	−	0.973201i	$-0.573858\pi$
$293$	−7.87242	−0.459912	−0.229956	+	0.973201i	$0.573858\pi$
$294$	14.9452	0.871621
$295$	18.1145	1.05467
$296$	−46.5218	−2.70403
$297$	−11.6718	−0.677264
$298$	−33.7628	−1.95583
$299$	31.9269	1.84638
$300$	77.9344	4.49954
$301$	6.40880	0.369397
$302$	−2.49086	−0.143333
$303$	18.5259	1.06429
$304$	11.2772	0.646789
$305$	33.3070	1.90715
$306$	−13.6770	−0.781862
$307$	8.88139	0.506888	0.253444	−	0.967350i	$-0.418437\pi$
$307$	8.88139	0.506888	0.253444	+	0.967350i	$0.418437\pi$
$308$	−24.5364	−1.39809
$309$	−33.5076	−1.90618
$310$	30.1496	1.71238
$311$	−14.4308	−0.818296	−0.409148	−	0.912468i	$-0.634174\pi$
$311$	−14.4308	−0.818296	−0.409148	+	0.912468i	$0.634174\pi$
$312$	70.3797	3.98447
$313$	14.3032	0.808467	0.404233	−	0.914656i	$-0.367538\pi$
$313$	14.3032	0.808467	0.404233	+	0.914656i	$0.367538\pi$
$314$	−41.1899	−2.32448
$315$	−7.55465	−0.425656
$316$	−60.5804	−3.40791
$317$	0.700500	0.0393440	0.0196720	−	0.999806i	$-0.493738\pi$
$317$	0.700500	0.0393440	0.0196720	+	0.999806i	$0.493738\pi$
$318$	21.3279	1.19601
$319$	−8.29020	−0.464162
$320$	−19.6587	−1.09896
$321$	8.25515	0.460758
$322$	−24.8176	−1.38303
$323$	11.7538	0.654000
$324$	−46.2484	−2.56936
$325$	−59.3980	−3.29481
$326$	−59.1899	−3.27822
$327$	4.00000	0.221201
$328$	0	0
$329$	9.42708	0.519732
$330$	−54.9086	−3.02262
$331$	24.1914	1.32968	0.664839	−	0.746987i	$-0.268500\pi$
$331$	24.1914	1.32968	0.664839	+	0.746987i	$0.268500\pi$
$332$	−5.84635	−0.320860
$333$	8.47259	0.464295
$334$	−7.74485	−0.423779
$335$	−40.8616	−2.23251
$336$	−21.0728	−1.14961
$337$	4.94518	0.269381	0.134691	−	0.990888i	$-0.456996\pi$
$337$	4.94518	0.269381	0.134691	+	0.990888i	$0.456996\pi$
$338$	−69.9254	−3.80344
$339$	−11.3645	−0.617232
$340$	87.2026	4.72922
$341$	−9.35025	−0.506344
$342$	−5.33198	−0.288320
$343$	20.0000	1.07990
$344$	17.5949	0.948655
$345$	−37.6352	−2.02621
$346$	44.7120	2.40373
$347$	3.10930	0.166916	0.0834581	−	0.996511i	$-0.473404\pi$
$347$	3.10930	0.166916	0.0834581	+	0.996511i	$0.473404\pi$
$348$	−23.8904	−1.28066
$349$	3.52741	0.188818	0.0944089	−	0.995534i	$-0.469904\pi$
$349$	3.52741	0.188818	0.0944089	+	0.995534i	$0.469904\pi$
$350$	46.1716	2.46798
$351$	25.6352	1.36831
$352$	−6.24618	−0.332923
$353$	−11.6718	−0.621225	−0.310612	−	0.950537i	$-0.600534\pi$
$353$	−11.6718	−0.621225	−0.310612	+	0.950537i	$0.600534\pi$
$354$	−23.8904	−1.26976
$355$	18.8176	0.998735
$356$	29.5076	1.56390
$357$	−21.9635	−1.16243
$358$	−4.66395	−0.246498
$359$	−14.2552	−0.752358	−0.376179	−	0.926547i	$-0.622762\pi$
$359$	−14.2552	−0.752358	−0.376179	+	0.926547i	$0.622762\pi$
$360$	−20.7408	−1.09314
$361$	−14.4178	−0.758830
$362$	−32.2447	−1.69474
$363$	−4.97126	−0.260923
$364$	53.8904	2.82462
$365$	−9.09883	−0.476255
$366$	−43.9269	−2.29610
$367$	28.2812	1.47627	0.738134	−	0.674654i	$-0.235707\pi$
$367$	28.2812	1.47627	0.738134	+	0.674654i	$0.235707\pi$
$368$	−26.2447	−1.36810
$369$	0	0
$370$	−79.7169	−4.14429
$371$	8.56246	0.444541
$372$	−26.9452	−1.39704
$373$	15.2264	0.788394	0.394197	−	0.919026i	$-0.371023\pi$
$373$	15.2264	0.788394	0.394197	+	0.919026i	$0.371023\pi$
$374$	−39.9086	−2.06363
$375$	32.2447	1.66511
$376$	25.8814	1.33473
$377$	18.2081	0.937767
$378$	−19.9269	−1.02493
$379$	−5.87242	−0.301646	−0.150823	−	0.988561i	$-0.548192\pi$
$379$	−5.87242	−0.301646	−0.150823	+	0.988561i	$0.548192\pi$
$380$	33.9959	1.74395
$381$	11.2264	0.575146
$382$	13.0768	0.669069
$383$	32.9777	1.68508	0.842540	−	0.538634i	$-0.181059\pi$
$383$	32.9777	1.68508	0.842540	+	0.538634i	$0.181059\pi$
$384$	34.4894	1.76003
$385$	−22.0440	−1.12347
$386$	−14.2995	−0.727825
$387$	−3.20440	−0.162889
$388$	−16.7628	−0.851002
$389$	−10.6640	−0.540684	−0.270342	−	0.962764i	$-0.587137\pi$
$389$	−10.6640	−0.540684	−0.270342	+	0.962764i	$0.587137\pi$
$390$	120.598	6.10673
$391$	−27.3540	−1.38335
$392$	16.4726	0.831991
$393$	−15.7448	−0.794223
$394$	−2.12758	−0.107186
$395$	−54.4267	−2.73851
$396$	12.2682	0.616500
$397$	13.6222	0.683677	0.341839	−	0.939759i	$-0.388950\pi$
$397$	13.6222	0.683677	0.341839	+	0.939759i	$0.388950\pi$
$398$	52.4894	2.63105
$399$	−8.56246	−0.428659
$400$	48.8266	2.44133
$401$	38.5129	1.92324	0.961621	−	0.274383i	$-0.0884736\pi$
$401$	38.5129	1.92324	0.961621	+	0.274383i	$0.0884736\pi$
$402$	53.8904	2.68781
$403$	20.5364	1.02299
$404$	38.9452	1.93760
$405$	−41.5506	−2.06467
$406$	−14.1537	−0.702434
$407$	24.7225	1.22545
$408$	−60.2992	−2.98525
$409$	2.56246	0.126705	0.0633526	−	0.997991i	$-0.479821\pi$
$409$	2.56246	0.126705	0.0633526	+	0.997991i	$0.479821\pi$
$410$	0	0
$411$	36.3723	1.79411
$412$	−70.4398	−3.47032
$413$	−9.59120	−0.471952
$414$	12.4088	0.609859
$415$	−5.25249	−0.257834
$416$	13.7188	0.672618
$417$	30.9892	1.51755
$418$	−15.5584	−0.760986
$419$	−7.01827	−0.342865	−0.171433	−	0.985196i	$-0.554840\pi$
$419$	−7.01827	−0.342865	−0.171433	+	0.985196i	$0.554840\pi$
$420$	−63.5256	−3.09973
$421$	−29.4816	−1.43684	−0.718422	−	0.695608i	$-0.755135\pi$
$421$	−29.4816	−1.43684	−0.718422	+	0.695608i	$0.755135\pi$
$422$	25.6091	1.24663
$423$	−4.71354	−0.229180
$424$	23.5076	1.14163
$425$	50.8904	2.46855
$426$	−24.8176	−1.20242
$427$	−17.6352	−0.853428
$428$	17.3540	0.838837
$429$	−37.4010	−1.80574
$430$	30.1496	1.45394
$431$	−14.2447	−0.686142	−0.343071	−	0.939309i	$-0.611467\pi$
$431$	−14.2447	−0.686142	−0.343071	+	0.939309i	$0.611467\pi$
$432$	−21.0728	−1.01386
$433$	−31.2264	−1.50065	−0.750323	−	0.661072i	$-0.770102\pi$
$433$	−31.2264	−1.50065	−0.750323	+	0.661072i	$0.770102\pi$
$434$	−15.9635	−0.766270
$435$	−21.4636	−1.02910
$436$	8.40880	0.402709
$437$	−10.6640	−0.510126
$438$	12.0000	0.573382
$439$	25.0090	1.19361	0.596806	−	0.802385i	$-0.296436\pi$
$439$	25.0090	1.19361	0.596806	+	0.802385i	$0.296436\pi$
$440$	−60.5203	−2.88519
$441$	−3.00000	−0.142857
$442$	87.6532	4.16924
$443$	9.26295	0.440096	0.220048	−	0.975489i	$-0.429379\pi$
$443$	9.26295	0.440096	0.220048	+	0.975489i	$0.429379\pi$
$444$	71.2443	3.38111
$445$	26.5103	1.25671
$446$	−39.6949	−1.87961
$447$	27.1093	1.28223
$448$	10.4088	0.491770
$449$	−4.98173	−0.235102	−0.117551	−	0.993067i	$-0.537504\pi$
$449$	−4.98173	−0.235102	−0.117551	+	0.993067i	$0.537504\pi$
$450$	−23.0858	−1.08827
$451$	0	0
$452$	−23.8904	−1.12371
$453$	2.00000	0.0939682
$454$	7.26819	0.341113
$455$	48.4163	2.26979
$456$	−23.5076	−1.10085
$457$	3.85042	0.180115	0.0900574	−	0.995937i	$-0.471295\pi$
$457$	3.85042	0.180115	0.0900574	+	0.995937i	$0.471295\pi$
$458$	63.1208	2.94944
$459$	−21.9635	−1.02517
$460$	−79.1168	−3.68884
$461$	−3.78256	−0.176171	−0.0880857	−	0.996113i	$-0.528075\pi$
$461$	−3.78256	−0.176171	−0.0880857	+	0.996113i	$0.528075\pi$
$462$	29.0728	1.35259
$463$	−9.00897	−0.418682	−0.209341	−	0.977843i	$-0.567132\pi$
$463$	−9.00897	−0.418682	−0.209341	+	0.977843i	$0.567132\pi$
$464$	−14.9675	−0.694850
$465$	−24.2081	−1.12263
$466$	−6.40880	−0.296882
$467$	1.39053	0.0643461	0.0321730	−	0.999482i	$-0.489757\pi$
$467$	1.39053	0.0643461	0.0321730	+	0.999482i	$0.489757\pi$
$468$	−26.9452	−1.24554
$469$	21.6352	0.999021
$470$	44.3488	2.04566
$471$	33.0728	1.52391
$472$	−26.3320	−1.21203
$473$	−9.35025	−0.429925
$474$	71.7807	3.29700
$475$	19.8396	0.910304
$476$	−46.1716	−2.11627
$477$	−4.28123	−0.196024
$478$	−19.2682	−0.881306
$479$	−26.9452	−1.23116	−0.615578	−	0.788076i	$-0.711078\pi$
$479$	−26.9452	−1.23116	−0.615578	+	0.788076i	$0.711078\pi$
$480$	−16.1716	−0.738129
$481$	−54.2992	−2.47583
$482$	43.3853	1.97615
$483$	19.9269	0.906706
$484$	−10.4506	−0.475027
$485$	−15.0601	−0.683842
$486$	24.9086	1.12988
$487$	−24.0310	−1.08895	−0.544474	−	0.838778i	$-0.683271\pi$
$487$	−24.0310	−1.08895	−0.544474	+	0.838778i	$0.683271\pi$
$488$	−48.4163	−2.19170
$489$	47.5256	2.14918
$490$	28.2264	1.27514
$491$	24.3502	1.09891	0.549456	−	0.835523i	$-0.314835\pi$
$491$	24.3502	1.09891	0.549456	+	0.835523i	$0.314835\pi$
$492$	0	0
$493$	−15.6002	−0.702596
$494$	34.1716	1.53745
$495$	11.0220	0.495402
$496$	−16.8814	−0.757997
$497$	−9.96345	−0.446922
$498$	6.92724	0.310417
$499$	−41.7889	−1.87073	−0.935363	−	0.353689i	$-0.884927\pi$
$499$	−41.7889	−1.87073	−0.935363	+	0.353689i	$0.884927\pi$
$500$	67.7848	3.03143
$501$	6.21861	0.277827
$502$	−12.8176	−0.572078
$503$	9.61320	0.428632	0.214316	−	0.976764i	$-0.431248\pi$
$503$	9.61320	0.428632	0.214316	+	0.976764i	$0.431248\pi$
$504$	10.9817	0.489165
$505$	34.9892	1.55700
$506$	36.2081	1.60965
$507$	56.1455	2.49351
$508$	23.6002	1.04709
$509$	−27.4711	−1.21763	−0.608817	−	0.793310i	$-0.708356\pi$
$509$	−27.4711	−1.21763	−0.608817	+	0.793310i	$0.708356\pi$
$510$	−103.325	−4.57530
$511$	4.81761	0.213118
$512$	46.5767	2.05842
$513$	−8.56246	−0.378042
$514$	−12.7915	−0.564210
$515$	−63.2846	−2.78865
$516$	−26.9452	−1.18620
$517$	−13.7538	−0.604892
$518$	42.2081	1.85452
$519$	−35.9008	−1.57587
$520$	132.924	5.82908
$521$	19.9870	0.875645	0.437822	−	0.899062i	$-0.355750\pi$
$521$	19.9870	0.875645	0.437822	+	0.899062i	$0.355750\pi$
$522$	7.07683	0.309744
$523$	11.8463	0.518005	0.259002	−	0.965877i	$-0.416606\pi$
$523$	11.8463	0.518005	0.259002	+	0.965877i	$0.416606\pi$
$524$	−33.0988	−1.44593
$525$	−37.0728	−1.61799
$526$	−35.0988	−1.53038
$527$	−17.5949	−0.766447
$528$	30.7445	1.33798
$529$	1.81761	0.0790264
$530$	40.2812	1.74970
$531$	4.79560	0.208111
$532$	−18.0000	−0.780399
$533$	0	0
$534$	−34.9631	−1.51300
$535$	15.5912	0.674066
$536$	59.3980	2.56560
$537$	3.74485	0.161602
$538$	−53.8486	−2.32158
$539$	−8.75382	−0.377054
$540$	−63.5256	−2.73371
$541$	−2.51437	−0.108101	−0.0540506	−	0.998538i	$-0.517213\pi$
$541$	−2.51437	−0.108101	−0.0540506	+	0.998538i	$0.517213\pi$
$542$	8.24468	0.354139
$543$	25.8904	1.11106
$544$	−11.7538	−0.503941
$545$	7.55465	0.323606
$546$	−63.8538	−2.73269
$547$	34.6770	1.48268	0.741341	−	0.671129i	$-0.234190\pi$
$547$	34.6770	1.48268	0.741341	+	0.671129i	$0.234190\pi$
$548$	76.4618	3.26629
$549$	8.81761	0.376326
$550$	−67.3630	−2.87237
$551$	−6.08173	−0.259090
$552$	54.7080	2.32853
$553$	28.8176	1.22545
$554$	−32.2447	−1.36995
$555$	64.0075	2.71697
$556$	65.1455	2.76279
$557$	−36.7445	−1.55692	−0.778458	−	0.627697i	$-0.783998\pi$
$557$	−36.7445	−1.55692	−0.778458	+	0.627697i	$0.783998\pi$
$558$	7.98173	0.337893
$559$	20.5364	0.868596
$560$	−39.7993	−1.68183
$561$	32.0440	1.35290
$562$	−68.8616	−2.90475
$563$	15.2134	0.641167	0.320584	−	0.947220i	$-0.396121\pi$
$563$	15.2134	0.641167	0.320584	+	0.947220i	$0.396121\pi$
$564$	−39.6352	−1.66894
$565$	−21.4636	−0.902981
$566$	47.5076	1.99689
$567$	22.0000	0.923913
$568$	−27.3540	−1.14775
$569$	−39.5088	−1.65630	−0.828148	−	0.560510i	$-0.810605\pi$
$569$	−39.5088	−1.65630	−0.828148	+	0.560510i	$0.810605\pi$
$570$	−40.2812	−1.68719
$571$	−11.4596	−0.479567	−0.239784	−	0.970826i	$-0.577077\pi$
$571$	−11.4596	−0.479567	−0.239784	+	0.970826i	$0.577077\pi$
$572$	−78.6244	−3.28745
$573$	−10.4998	−0.438637
$574$	0	0
$575$	−46.1716	−1.92549
$576$	−5.20440	−0.216850
$577$	−0.549417	−0.0228725	−0.0114363	−	0.999935i	$-0.503640\pi$
$577$	−0.549417	−0.0228725	−0.0114363	+	0.999935i	$0.503640\pi$
$578$	−32.7538	−1.36238
$579$	11.4816	0.477157
$580$	−45.1208	−1.87354
$581$	2.78106	0.115378
$582$	19.8620	0.823305
$583$	−12.4924	−0.517381
$584$	13.2264	0.547313
$585$	−24.2081	−1.00088
$586$	19.6091	0.810046
$587$	−8.03655	−0.331704	−0.165852	−	0.986151i	$-0.553037\pi$
$587$	−8.03655	−0.331704	−0.165852	+	0.986151i	$0.553037\pi$
$588$	−25.2264	−1.04032
$589$	−6.85939	−0.282636
$590$	−45.1208	−1.85760
$591$	1.70830	0.0702702
$592$	44.6352	1.83450
$593$	−7.86196	−0.322852	−0.161426	−	0.986885i	$-0.551609\pi$
$593$	−7.86196	−0.322852	−0.161426	+	0.986885i	$0.551609\pi$
$594$	29.0728	1.19287
$595$	−41.4816	−1.70058
$596$	56.9892	2.33437
$597$	−42.1455	−1.72490
$598$	−79.5256	−3.25204
$599$	4.11711	0.168220	0.0841102	−	0.996456i	$-0.473195\pi$
$599$	4.11711	0.168220	0.0841102	+	0.996456i	$0.473195\pi$
$600$	−101.781	−4.15518
$601$	−43.6311	−1.77975	−0.889876	−	0.456203i	$-0.849209\pi$
$601$	−43.6311	−1.77975	−0.889876	+	0.456203i	$0.849209\pi$
$602$	−15.9635	−0.650622
$603$	−10.8176	−0.440527
$604$	4.20440	0.171075
$605$	−9.38903	−0.381718
$606$	−46.1455	−1.87453
$607$	10.6640	0.432837	0.216418	−	0.976301i	$-0.430563\pi$
$607$	10.6640	0.432837	0.216418	+	0.976301i	$0.430563\pi$
$608$	−4.58223	−0.185834
$609$	11.3645	0.460511
$610$	−82.9631	−3.35908
$611$	30.2081	1.22209
$612$	23.0858	0.933188
$613$	−43.0728	−1.73969	−0.869846	−	0.493323i	$-0.835782\pi$
$613$	−43.0728	−1.73969	−0.869846	+	0.493323i	$0.835782\pi$
$614$	−22.1223	−0.892785
$615$	0	0
$616$	32.0440	1.29109
$617$	27.6457	1.11297	0.556487	−	0.830857i	$-0.312149\pi$
$617$	27.6457	1.11297	0.556487	+	0.830857i	$0.312149\pi$
$618$	83.4630	3.35737
$619$	7.35398	0.295582	0.147791	−	0.989019i	$-0.452784\pi$
$619$	7.35398	0.295582	0.147791	+	0.989019i	$0.452784\pi$
$620$	−50.8904	−2.04381
$621$	19.9269	0.799639
$622$	35.9452	1.44127
$623$	−14.0365	−0.562362
$624$	−67.5256	−2.70319
$625$	14.5584	0.582335
$626$	−35.6274	−1.42396
$627$	12.4924	0.498897
$628$	69.5256	2.77437
$629$	46.5218	1.85495
$630$	18.8176	0.749711
$631$	−0.536379	−0.0213529	−0.0106764	−	0.999943i	$-0.503398\pi$
$631$	−0.536379	−0.0213529	−0.0106764	+	0.999943i	$0.503398\pi$
$632$	79.1168	3.14710
$633$	−20.5625	−0.817284
$634$	−1.74485	−0.0692968
$635$	21.2029	0.841412
$636$	−36.0000	−1.42749
$637$	19.2264	0.761778
$638$	20.6498	0.817531
$639$	4.98173	0.197074
$640$	65.1388	2.57484
$641$	−13.4125	−0.529763	−0.264882	−	0.964281i	$-0.585333\pi$
$641$	−13.4125	−0.529763	−0.264882	+	0.964281i	$0.585333\pi$
$642$	−20.5625	−0.811535
$643$	−22.3697	−0.882174	−0.441087	−	0.897464i	$-0.645407\pi$
$643$	−22.3697	−0.882174	−0.441087	+	0.897464i	$0.645407\pi$
$644$	41.8904	1.65071
$645$	−24.2081	−0.953194
$646$	−29.2772	−1.15189
$647$	−31.4282	−1.23557	−0.617786	−	0.786346i	$-0.711970\pi$
$647$	−31.4282	−1.23557	−0.617786	+	0.786346i	$0.711970\pi$
$648$	60.3995	2.37272
$649$	13.9933	0.549284
$650$	147.952	5.80317
$651$	12.8176	0.502362
$652$	99.9083	3.91271
$653$	21.8538	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$653$	21.8538	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$654$	−9.96345	−0.389602
$655$	−29.7367	−1.16191
$656$	0	0
$657$	−2.40880	−0.0939764
$658$	−23.4816	−0.915407
$659$	−28.4674	−1.10893	−0.554465	−	0.832207i	$-0.687077\pi$
$659$	−28.4674	−1.10893	−0.554465	+	0.832207i	$0.687077\pi$
$660$	92.6819	3.60764
$661$	33.4816	1.30228	0.651141	−	0.758957i	$-0.274291\pi$
$661$	33.4816	1.30228	0.651141	+	0.758957i	$0.274291\pi$
$662$	−60.2574	−2.34197
$663$	−70.3797	−2.73332
$664$	7.63521	0.296304
$665$	−16.1716	−0.627107
$666$	−21.1041	−0.817766
$667$	14.1537	0.548032
$668$	13.0728	0.505800
$669$	31.8724	1.23226
$670$	101.781	3.93213
$671$	25.7292	0.993266
$672$	8.56246	0.330304
$673$	−13.9802	−0.538898	−0.269449	−	0.963015i	$-0.586842\pi$
$673$	−13.9802	−0.538898	−0.269449	+	0.963015i	$0.586842\pi$
$674$	−12.3178	−0.474463
$675$	−37.0728	−1.42693
$676$	118.029	4.53958
$677$	−17.1354	−0.658566	−0.329283	−	0.944231i	$-0.606807\pi$
$677$	−17.1354	−0.658566	−0.329283	+	0.944231i	$0.606807\pi$
$678$	28.3073	1.08714
$679$	7.97392	0.306011
$680$	−113.885	−4.36728
$681$	−5.83588	−0.223631
$682$	23.2902	0.891828
$683$	16.6640	0.637628	0.318814	−	0.947817i	$-0.396715\pi$
$683$	16.6640	0.637628	0.318814	+	0.947817i	$0.396715\pi$
$684$	9.00000	0.344124
$685$	68.6949	2.62470
$686$	−49.8173	−1.90203
$687$	−50.6819	−1.93363
$688$	−16.8814	−0.643597
$689$	27.4375	1.04529
$690$	93.7442	3.56878
$691$	−14.9713	−0.569534	−0.284767	−	0.958597i	$-0.591916\pi$
$691$	−14.9713	−0.569534	−0.284767	+	0.958597i	$0.591916\pi$
$692$	−75.4708	−2.86897
$693$	−5.83588	−0.221687
$694$	−7.74485	−0.293990
$695$	58.5281	2.22010
$696$	31.2003	1.18265
$697$	0	0
$698$	−8.78630	−0.332566
$699$	5.14585	0.194634
$700$	−77.9344	−2.94564
$701$	0.295765	0.0111709	0.00558545	−	0.999984i	$-0.498222\pi$
$701$	0.295765	0.0111709	0.00558545	+	0.999984i	$0.498222\pi$
$702$	−63.8538	−2.41001
$703$	18.1365	0.684033
$704$	−15.1861	−0.572349
$705$	−35.6091	−1.34112
$706$	29.0728	1.09417
$707$	−18.5259	−0.696739
$708$	40.3252	1.51552
$709$	3.91014	0.146848	0.0734241	−	0.997301i	$-0.476607\pi$
$709$	3.91014	0.146848	0.0734241	+	0.997301i	$0.476607\pi$
$710$	−46.8721	−1.75908
$711$	−14.4088	−0.540372
$712$	−38.5364	−1.44421
$713$	15.9635	0.597836
$714$	54.7080	2.04739
$715$	−70.6379	−2.64171
$716$	7.87242	0.294206
$717$	15.4711	0.577778
$718$	35.5076	1.32513
$719$	22.3357	0.832982	0.416491	−	0.909140i	$-0.363260\pi$
$719$	22.3357	0.832982	0.416491	+	0.909140i	$0.363260\pi$
$720$	19.8997	0.741617
$721$	33.5076	1.24789
$722$	35.9127	1.33653
$723$	−34.8355	−1.29555
$724$	54.4267	2.02275
$725$	−26.3320	−0.977945
$726$	12.3827	0.459566
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	−70.3797	−2.60845
$729$	13.0000	0.481481
$730$	22.6640	0.838831
$731$	−17.5949	−0.650772
$732$	74.1455	2.74050
$733$	46.5804	1.72049	0.860243	−	0.509884i	$-0.170312\pi$
$733$	46.5804	1.72049	0.860243	+	0.509884i	$0.170312\pi$
$734$	−70.4447	−2.60016
$735$	−22.6640	−0.835973
$736$	10.6640	0.393079
$737$	−31.5651	−1.16272
$738$	0	0
$739$	18.0179	0.662801	0.331400	−	0.943490i	$-0.392479\pi$
$739$	18.0179	0.662801	0.331400	+	0.943490i	$0.392479\pi$
$740$	134.557	4.94640
$741$	−27.4375	−1.00794
$742$	−21.3279	−0.782972
$743$	−31.7900	−1.16626	−0.583132	−	0.812378i	$-0.698173\pi$
$743$	−31.7900	−1.16626	−0.583132	+	0.812378i	$0.698173\pi$
$744$	35.1899	1.29012
$745$	51.2003	1.87584
$746$	−37.9269	−1.38860
$747$	−1.39053	−0.0508768
$748$	67.3630	2.46303
$749$	−8.25515	−0.301637
$750$	−80.3171	−2.93277
$751$	7.84635	0.286317	0.143159	−	0.989700i	$-0.454274\pi$
$751$	7.84635	0.286317	0.143159	+	0.989700i	$0.454274\pi$
$752$	−24.8318	−0.905523
$753$	10.2917	0.375050
$754$	−45.3540	−1.65169
$755$	3.77733	0.137471
$756$	33.6352	1.22330
$757$	−15.6393	−0.568419	−0.284210	−	0.958762i	$-0.591731\pi$
$757$	−15.6393	−0.568419	−0.284210	+	0.958762i	$0.591731\pi$
$758$	14.6274	0.531291
$759$	−29.0728	−1.05527
$760$	−44.3980	−1.61048
$761$	14.7370	0.534217	0.267109	−	0.963666i	$-0.413932\pi$
$761$	14.7370	0.534217	0.267109	+	0.963666i	$0.413932\pi$
$762$	−27.9635	−1.01301
$763$	−4.00000	−0.144810
$764$	−22.0728	−0.798564
$765$	20.7408	0.749884
$766$	−82.1428	−2.96794
$767$	−30.7340	−1.10974
$768$	−65.0907	−2.34876
$769$	−30.1716	−1.08802	−0.544008	−	0.839080i	$-0.683094\pi$
$769$	−30.1716	−1.08802	−0.544008	+	0.839080i	$0.683094\pi$
$770$	54.9086	1.97877
$771$	10.2708	0.369892
$772$	24.1365	0.868693
$773$	36.5259	1.31375	0.656873	−	0.754001i	$-0.271879\pi$
$773$	36.5259	1.31375	0.656873	+	0.754001i	$0.271879\pi$
$774$	7.98173	0.286897
$775$	−29.6990	−1.06682
$776$	21.8919	0.785872
$777$	−33.8904	−1.21581
$778$	26.5625	0.952310
$779$	0	0
$780$	−203.561	−7.28867
$781$	14.5364	0.520153
$782$	68.1350	2.43650
$783$	11.3645	0.406132
$784$	−15.8046	−0.564449
$785$	62.4633	2.22941
$786$	39.2183	1.39887
$787$	46.0817	1.64264	0.821318	−	0.570471i	$-0.193239\pi$
$787$	46.0817	1.64264	0.821318	+	0.570471i	$0.193239\pi$
$788$	3.59120	0.127931
$789$	28.1821	1.00331
$790$	135.570	4.82335
$791$	11.3645	0.404073
$792$	−16.0220	−0.569317
$793$	−56.5103	−2.00674
$794$	−33.9310	−1.20417
$795$	−32.3432	−1.14709
$796$	−88.5983	−3.14028
$797$	−51.5856	−1.82726	−0.913628	−	0.406550i	$-0.866732\pi$
$797$	−51.5856	−1.82726	−0.913628	+	0.406550i	$0.866732\pi$
$798$	21.3279	0.755000
$799$	−25.8814	−0.915618
$800$	−19.8396	−0.701436
$801$	7.01827	0.247978
$802$	−95.9303	−3.38742
$803$	−7.02874	−0.248039
$804$	−90.9631	−3.20802
$805$	37.6352	1.32647
$806$	−51.1533	−1.80180
$807$	43.2369	1.52201
$808$	−50.8616	−1.78931
$809$	−27.3174	−0.960430	−0.480215	−	0.877151i	$-0.659441\pi$
$809$	−27.3174	−0.960430	−0.480215	+	0.877151i	$0.659441\pi$
$810$	103.497	3.63651
$811$	−49.4816	−1.73753	−0.868766	−	0.495222i	$-0.835087\pi$
$811$	−49.4816	−1.73753	−0.868766	+	0.495222i	$0.835087\pi$
$812$	23.8904	0.838387
$813$	−6.61994	−0.232171
$814$	−61.5804	−2.15839
$815$	89.7598	3.14415
$816$	57.8538	2.02529
$817$	−6.85939	−0.239980
$818$	−6.38273	−0.223167
$819$	12.8176	0.447883
$820$	0	0
$821$	2.62741	0.0916972	0.0458486	−	0.998948i	$-0.485401\pi$
$821$	2.62741	0.0916972	0.0458486	+	0.998948i	$0.485401\pi$
$822$	−90.5983	−3.15998
$823$	30.1145	1.04973	0.524863	−	0.851186i	$-0.324116\pi$
$823$	30.1145	1.04973	0.524863	+	0.851186i	$0.324116\pi$
$824$	91.9929	3.20473
$825$	54.0880	1.88310
$826$	23.8904	0.831252
$827$	−13.3801	−0.465270	−0.232635	−	0.972564i	$-0.574735\pi$
$827$	−13.3801	−0.465270	−0.232635	+	0.972564i	$0.574735\pi$
$828$	−20.9452	−0.727895
$829$	−41.2704	−1.43338	−0.716691	−	0.697391i	$-0.754344\pi$
$829$	−41.2704	−1.43338	−0.716691	+	0.697391i	$0.754344\pi$
$830$	13.0832	0.454125
$831$	25.8904	0.898127
$832$	33.3540	1.15634
$833$	−16.4726	−0.570741
$834$	−77.1899	−2.67287
$835$	11.7448	0.406447
$836$	26.2615	0.908271
$837$	12.8176	0.443041
$838$	17.4816	0.603890
$839$	23.7758	0.820833	0.410416	−	0.911898i	$-0.365383\pi$
$839$	23.7758	0.820833	0.410416	+	0.911898i	$0.365383\pi$
$840$	82.9631	2.86250
$841$	−20.9281	−0.721658
$842$	73.4345	2.53072
$843$	55.2914	1.90434
$844$	−43.2264	−1.48791
$845$	106.040	3.64789
$846$	11.7408	0.403656
$847$	4.97126	0.170814
$848$	−22.5543	−0.774518
$849$	−38.1455	−1.30915
$850$	−126.761	−4.34786
$851$	−42.2081	−1.44688
$852$	41.8904	1.43514
$853$	−14.8135	−0.507206	−0.253603	−	0.967308i	$-0.581616\pi$
$853$	−14.8135	−0.507206	−0.253603	+	0.967308i	$0.581616\pi$
$854$	43.9269	1.50315
$855$	8.08580	0.276528
$856$	−22.6640	−0.774638
$857$	−42.5259	−1.45266	−0.726329	−	0.687348i	$-0.758775\pi$
$857$	−42.5259	−1.45266	−0.726329	+	0.687348i	$0.758775\pi$
$858$	93.1608	3.18046
$859$	5.87242	0.200365	0.100182	−	0.994969i	$-0.468057\pi$
$859$	5.87242	0.200365	0.100182	+	0.994969i	$0.468057\pi$
$860$	−50.8904	−1.73535
$861$	0	0
$862$	35.4816	1.20851
$863$	0.635546	0.0216342	0.0108171	−	0.999941i	$-0.496557\pi$
$863$	0.635546	0.0216342	0.0108171	+	0.999941i	$0.496557\pi$
$864$	8.56246	0.291301
$865$	−67.8046	−2.30542
$866$	77.7807	2.64310
$867$	26.2992	0.893167
$868$	26.9452	0.914579
$869$	−42.0440	−1.42625
$870$	53.4630	1.81256
$871$	69.3279	2.34909
$872$	−10.9817	−0.371888
$873$	−3.98696	−0.134938
$874$	26.5625	0.898488
$875$	−32.2447	−1.09007
$876$	−20.2552	−0.684358
$877$	−8.97126	−0.302938	−0.151469	−	0.988462i	$-0.548400\pi$
$877$	−8.97126	−0.302938	−0.151469	+	0.988462i	$0.548400\pi$
$878$	−62.2939	−2.10232
$879$	−15.7448	−0.531061
$880$	58.0660	1.95741
$881$	48.2626	1.62601	0.813005	−	0.582257i	$-0.197830\pi$
$881$	48.2626	1.62601	0.813005	+	0.582257i	$0.197830\pi$
$882$	7.47259	0.251615
$883$	16.4465	0.553469	0.276735	−	0.960946i	$-0.410748\pi$
$883$	16.4465	0.553469	0.276735	+	0.960946i	$0.410748\pi$
$884$	−147.952	−4.97617
$885$	36.2291	1.21783
$886$	−23.0728	−0.775144
$887$	26.9452	0.904731	0.452365	−	0.891833i	$-0.350580\pi$
$887$	26.9452	0.904731	0.452365	+	0.891833i	$0.350580\pi$
$888$	−93.0437	−3.12234
$889$	−11.2264	−0.376522
$890$	−66.0335	−2.21345
$891$	−32.0973	−1.07530
$892$	67.0022	2.24340
$893$	−10.0899	−0.337644
$894$	−67.5256	−2.25839
$895$	7.07276	0.236416
$896$	−34.4894	−1.15221
$897$	63.8538	2.13202
$898$	12.4088	0.414087
$899$	9.10407	0.303638
$900$	38.9672	1.29891
$901$	−23.5076	−0.783153
$902$	0	0
$903$	12.8176	0.426543
$904$	31.2003	1.03771
$905$	48.8982	1.62543
$906$	−4.98173	−0.165507
$907$	−33.1037	−1.09919	−0.549596	−	0.835431i	$-0.685218\pi$
$907$	−33.1037	−1.09919	−0.549596	+	0.835431i	$0.685218\pi$
$908$	−12.2682	−0.407134
$909$	9.26295	0.307233
$910$	−120.598	−3.99780
$911$	−52.9217	−1.75337	−0.876687	−	0.481062i	$-0.840251\pi$
$911$	−52.9217	−1.75337	−0.876687	+	0.481062i	$0.840251\pi$
$912$	22.5543	0.746848
$913$	−4.05748	−0.134283
$914$	−9.59086	−0.317238
$915$	66.6139	2.20219
$916$	−106.544	−3.52030
$917$	15.7448	0.519941
$918$	54.7080	1.80563
$919$	21.7628	0.717888	0.358944	−	0.933359i	$-0.383137\pi$
$919$	21.7628	0.717888	0.358944	+	0.933359i	$0.383137\pi$
$920$	103.325	3.40652
$921$	17.7628	0.585304
$922$	9.42184	0.310292
$923$	−31.9269	−1.05089
$924$	−49.0728	−1.61438
$925$	78.5256	2.58191
$926$	22.4401	0.737428
$927$	−16.7538	−0.550268
$928$	6.08173	0.199642
$929$	37.5987	1.23357	0.616786	−	0.787131i	$-0.288434\pi$
$929$	37.5987	1.23357	0.616786	+	0.787131i	$0.288434\pi$
$930$	60.2992	1.97729
$931$	−6.42184	−0.210467
$932$	10.8176	0.354342
$933$	−28.8616	−0.944887
$934$	−3.46362	−0.113333
$935$	60.5203	1.97923
$936$	35.1899	1.15022
$937$	7.42451	0.242548	0.121274	−	0.992619i	$-0.461302\pi$
$937$	7.42451	0.242548	0.121274	+	0.992619i	$0.461302\pi$
$938$	−53.8904	−1.75958
$939$	28.6065	0.933537
$940$	−74.8576	−2.44158
$941$	13.9269	0.454004	0.227002	−	0.973894i	$-0.427108\pi$
$941$	13.9269	0.454004	0.227002	+	0.973894i	$0.427108\pi$
$942$	−82.3797	−2.68408
$943$	0	0
$944$	25.2641	0.822277
$945$	30.2186	0.983011
$946$	23.2902	0.757230
$947$	−8.79153	−0.285686	−0.142843	−	0.989745i	$-0.545624\pi$
$947$	−8.79153	−0.285686	−0.142843	+	0.989745i	$0.545624\pi$
$948$	−121.161	−3.93512
$949$	15.4375	0.501124
$950$	−49.4178	−1.60332
$951$	1.40100	0.0454305
$952$	60.2992	1.95431
$953$	−13.4401	−0.435368	−0.217684	−	0.976019i	$-0.569850\pi$
$953$	−13.4401	−0.435368	−0.217684	+	0.976019i	$0.569850\pi$
$954$	10.6640	0.345258
$955$	−19.8306	−0.641705
$956$	32.5233	1.05188
$957$	−16.5804	−0.535968
$958$	67.1168	2.16844
$959$	−36.3723	−1.17452
$960$	−39.3174	−1.26896
$961$	−20.7318	−0.668768
$962$	135.252	4.36069
$963$	4.12758	0.133009
$964$	−73.2313	−2.35862
$965$	21.6848	0.698058
$966$	−49.6352	−1.59699
$967$	30.9713	0.995969	0.497984	−	0.867186i	$-0.334074\pi$
$967$	30.9713	0.995969	0.497984	+	0.867186i	$0.334074\pi$
$968$	13.6483	0.438671
$969$	23.5076	0.755174
$970$	37.5125	1.20445
$971$	−34.6430	−1.11175	−0.555874	−	0.831267i	$-0.687616\pi$
$971$	−34.6430	−1.11175	−0.555874	+	0.831267i	$0.687616\pi$
$972$	−42.0440	−1.34856
$973$	−30.9892	−0.993468
$974$	59.8579	1.91797
$975$	−118.796	−3.80452
$976$	46.4528	1.48692
$977$	−45.7002	−1.46208	−0.731039	−	0.682336i	$-0.760964\pi$
$977$	−45.7002	−1.46208	−0.731039	+	0.682336i	$0.760964\pi$
$978$	−118.380	−3.78537
$979$	20.4789	0.654508
$980$	−47.6442	−1.52194
$981$	2.00000	0.0638551
$982$	−60.6532	−1.93552
$983$	54.4163	1.73561	0.867805	−	0.496905i	$-0.165530\pi$
$983$	54.4163	1.73561	0.867805	+	0.496905i	$0.165530\pi$
$984$	0	0
$985$	3.22641	0.102802
$986$	38.8579	1.23749
$987$	18.8542	0.600134
$988$	−57.6792	−1.83502
$989$	15.9635	0.507608
$990$	−27.4543	−0.872556
$991$	60.3383	1.91671	0.958354	−	0.285582i	$-0.0921868\pi$
$991$	60.3383	1.91671	0.958354	+	0.285582i	$0.0921868\pi$
$992$	6.85939	0.217786
$993$	48.3827	1.53538
$994$	24.8176	0.787167
$995$	−79.5987	−2.52345
$996$	−11.6927	−0.370497
$997$	−50.1078	−1.58693	−0.793465	−	0.608616i	$-0.791725\pi$
$997$	−50.1078	−1.58693	−0.793465	+	0.608616i	$0.791725\pi$
$998$	104.090	3.29492
$999$	−33.8904	−1.07224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.a.b.1.1	✓	3
3.2	odd	2		1359.2.a.e.1.3		3
4.3	odd	2		2416.2.a.f.1.3		3
5.4	even	2		3775.2.a.j.1.3		3
7.6	odd	2		7399.2.a.c.1.1		3
8.3	odd	2		9664.2.a.v.1.1		3
8.5	even	2		9664.2.a.m.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.a.b.1.1	✓	3	1.1	even	1	trivial
1359.2.a.e.1.3		3	3.2	odd	2
2416.2.a.f.1.3		3	4.3	odd	2
3775.2.a.j.1.3		3	5.4	even	2
7399.2.a.c.1.1		3	7.6	odd	2
9664.2.a.m.1.1		3	8.5	even	2
9664.2.a.v.1.1		3	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49086 q^{2} +2.00000 q^{3} +4.20440 q^{4} +3.77733 q^{5} -4.98173 q^{6} -2.00000 q^{7} -5.49086 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49086 q^{2} +2.00000 q^{3} +4.20440 q^{4} +3.77733 q^{5} -4.98173 q^{6} -2.00000 q^{7} -5.49086 q^{8} +1.00000 q^{9} -9.40880 q^{10} +2.91794 q^{11} +8.40880 q^{12} -6.40880 q^{13} +4.98173 q^{14} +7.55465 q^{15} +5.26819 q^{16} +5.49086 q^{17} -2.49086 q^{18} +2.14061 q^{19} +15.8814 q^{20} -4.00000 q^{21} -7.26819 q^{22} -4.98173 q^{23} -10.9817 q^{24} +9.26819 q^{25} +15.9635 q^{26} -4.00000 q^{27} -8.40880 q^{28} -2.84111 q^{29} -18.8176 q^{30} -3.20440 q^{31} -2.14061 q^{32} +5.83588 q^{33} -13.6770 q^{34} -7.55465 q^{35} +4.20440 q^{36} +8.47259 q^{37} -5.33198 q^{38} -12.8176 q^{39} -20.7408 q^{40} +9.96345 q^{42} -3.20440 q^{43} +12.2682 q^{44} +3.77733 q^{45} +12.4088 q^{46} -4.71354 q^{47} +10.5364 q^{48} -3.00000 q^{49} -23.0858 q^{50} +10.9817 q^{51} -26.9452 q^{52} -4.28123 q^{53} +9.96345 q^{54} +11.0220 q^{55} +10.9817 q^{56} +4.28123 q^{57} +7.07683 q^{58} +4.79560 q^{59} +31.7628 q^{60} +8.81761 q^{61} +7.98173 q^{62} -2.00000 q^{63} -5.20440 q^{64} -24.2081 q^{65} -14.5364 q^{66} -10.8176 q^{67} +23.0858 q^{68} -9.96345 q^{69} +18.8176 q^{70} +4.98173 q^{71} -5.49086 q^{72} -2.40880 q^{73} -21.1041 q^{74} +18.5364 q^{75} +9.00000 q^{76} -5.83588 q^{77} +31.9269 q^{78} -14.4088 q^{79} +19.8997 q^{80} -11.0000 q^{81} -1.39053 q^{83} -16.8176 q^{84} +20.7408 q^{85} +7.98173 q^{86} -5.68223 q^{87} -16.0220 q^{88} +7.01827 q^{89} -9.40880 q^{90} +12.8176 q^{91} -20.9452 q^{92} -6.40880 q^{93} +11.7408 q^{94} +8.08580 q^{95} -4.28123 q^{96} -3.98696 q^{97} +7.47259 q^{98} +2.91794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9	\( 3 q + 6 q^{3} + 4 q^{4} + 5 q^{5} - 6 q^{7} - 9 q^{8} + 3 q^{9} - 11 q^{10} - q^{11} + 8 q^{12} - 2 q^{13} + 10 q^{15} + 2 q^{16} + 9 q^{17} + 3 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{22} - 18 q^{24} + 14 q^{25} + 18 q^{26} - 12 q^{27} - 8 q^{28} + 3 q^{29} - 22 q^{30} - q^{31} - 3 q^{32} - 2 q^{33} - 10 q^{34} - 10 q^{35} + 4 q^{36} + 3 q^{37} + 3 q^{38} - 4 q^{39} - 26 q^{40} - q^{43} + 23 q^{44} + 5 q^{45} + 20 q^{46} - 13 q^{47} + 4 q^{48} - 9 q^{49} - 21 q^{50} + 18 q^{51} - 36 q^{52} - 6 q^{53} - 10 q^{55} + 18 q^{56} + 6 q^{57} + 23 q^{58} + 23 q^{59} + 16 q^{60} - 8 q^{61} + 9 q^{62} - 6 q^{63} - 7 q^{64} - 6 q^{65} - 16 q^{66} + 2 q^{67} + 21 q^{68} + 22 q^{70} - 9 q^{72} + 10 q^{73} - 30 q^{74} + 28 q^{75} + 27 q^{76} + 2 q^{77} + 36 q^{78} - 26 q^{79} + 35 q^{80} - 33 q^{81} + 28 q^{83} - 16 q^{84} + 26 q^{85} + 9 q^{86} + 6 q^{87} - 5 q^{88} + 36 q^{89} - 11 q^{90} + 4 q^{91} - 18 q^{92} - 2 q^{93} - q^{94} - 24 q^{95} - 6 q^{96} - 5 q^{97} - q^{99}+O(q^{100}) \) 3 * q + 6 * q^3 + 4 * q^4 + 5 * q^5 - 6 * q^7 - 9 * q^8 + 3 * q^9 - 11 * q^10 - q^11 + 8 * q^12 - 2 * q^13 + 10 * q^15 + 2 * q^16 + 9 * q^17 + 3 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^22 - 18 * q^24 + 14 * q^25 + 18 * q^26 - 12 * q^27 - 8 * q^28 + 3 * q^29 - 22 * q^30 - q^31 - 3 * q^32 - 2 * q^33 - 10 * q^34 - 10 * q^35 + 4 * q^36 + 3 * q^37 + 3 * q^38 - 4 * q^39 - 26 * q^40 - q^43 + 23 * q^44 + 5 * q^45 + 20 * q^46 - 13 * q^47 + 4 * q^48 - 9 * q^49 - 21 * q^50 + 18 * q^51 - 36 * q^52 - 6 * q^53 - 10 * q^55 + 18 * q^56 + 6 * q^57 + 23 * q^58 + 23 * q^59 + 16 * q^60 - 8 * q^61 + 9 * q^62 - 6 * q^63 - 7 * q^64 - 6 * q^65 - 16 * q^66 + 2 * q^67 + 21 * q^68 + 22 * q^70 - 9 * q^72 + 10 * q^73 - 30 * q^74 + 28 * q^75 + 27 * q^76 + 2 * q^77 + 36 * q^78 - 26 * q^79 + 35 * q^80 - 33 * q^81 + 28 * q^83 - 16 * q^84 + 26 * q^85 + 9 * q^86 + 6 * q^87 - 5 * q^88 + 36 * q^89 - 11 * q^90 + 4 * q^91 - 18 * q^92 - 2 * q^93 - q^94 - 24 * q^95 - 6 * q^96 - 5 * q^97 - q^99

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