LMFDB - Embedded newform 605.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.46673$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52452 q^{2} -2.46673 q^{3} +4.37322 q^{4} +1.00000 q^{5} -6.22732 q^{6} +2.09351 q^{7} +5.99126 q^{8} +3.08477 q^{9} +O(q^{10})$	\(q+2.52452 q^{2} -2.46673 q^{3} +4.37322 q^{4} +1.00000 q^{5} -6.22732 q^{6} +2.09351 q^{7} +5.99126 q^{8} +3.08477 q^{9} +2.52452 q^{10} -10.7876 q^{12} +1.28846 q^{13} +5.28512 q^{14} -2.46673 q^{15} +6.37863 q^{16} -2.99126 q^{17} +7.78757 q^{18} +2.15130 q^{19} +4.37322 q^{20} -5.16413 q^{21} +8.77882 q^{23} -14.7788 q^{24} +1.00000 q^{25} +3.25274 q^{26} -0.209094 q^{27} +9.15538 q^{28} -0.612630 q^{29} -6.22732 q^{30} -3.64501 q^{31} +4.12048 q^{32} -7.55150 q^{34} +2.09351 q^{35} +13.4904 q^{36} -1.87077 q^{37} +5.43101 q^{38} -3.17828 q^{39} +5.99126 q^{40} -5.10684 q^{41} -13.0370 q^{42} +5.17287 q^{43} +3.08477 q^{45} +22.1623 q^{46} -7.30669 q^{47} -15.7344 q^{48} -2.61722 q^{49} +2.52452 q^{50} +7.37863 q^{51} +5.63470 q^{52} -2.94221 q^{53} -0.527864 q^{54} +12.5428 q^{56} -5.30669 q^{57} -1.54660 q^{58} -6.49421 q^{59} -10.7876 q^{60} -0.502449 q^{61} -9.20191 q^{62} +6.45799 q^{63} -2.35499 q^{64} +1.28846 q^{65} -7.80964 q^{67} -13.0814 q^{68} -21.6550 q^{69} +5.28512 q^{70} -11.3042 q^{71} +18.4816 q^{72} -11.1171 q^{73} -4.72281 q^{74} -2.46673 q^{75} +9.40812 q^{76} -8.02363 q^{78} +5.35907 q^{79} +6.37863 q^{80} -8.73852 q^{81} -12.8923 q^{82} +10.8454 q^{83} -22.5839 q^{84} -2.99126 q^{85} +13.0590 q^{86} +1.51119 q^{87} -4.32336 q^{89} +7.78757 q^{90} +2.69740 q^{91} +38.3917 q^{92} +8.99126 q^{93} -18.4459 q^{94} +2.15130 q^{95} -10.1641 q^{96} -0.351653 q^{97} -6.60723 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8	$ 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8} + 3 q^{10} - 14 q^{12} + 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 7 q^{20} - 6 q^{21} - 9 q^{23} - 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} + 7 q^{28} - 8 q^{29} - q^{30} + 3 q^{31} + 6 q^{32} - 10 q^{34} + 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} - 3 q^{39} + 9 q^{40} - 7 q^{41} + 2 q^{42} + 21 q^{43} + 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} + 3 q^{50} + 9 q^{51} + 27 q^{52} - 11 q^{53} - 20 q^{54} + 15 q^{56} + 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} + 4 q^{61} + 11 q^{62} + 3 q^{63} - 27 q^{64} + 7 q^{65} - q^{67} - 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} + 13 q^{72} - 9 q^{73} - 36 q^{74} - 2 q^{75} + 8 q^{76} + 6 q^{78} + 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} + 15 q^{83} - 47 q^{84} + 3 q^{85} - 3 q^{86} + 15 q^{87} + 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} - 11 q^{94} + 12 q^{95} - 26 q^{96} + 6 q^{97} - 42 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8 + 3 * q^10 - 14 * q^12 + 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 7 * q^20 - 6 * q^21 - 9 * q^23 - 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 + 7 * q^28 - 8 * q^29 - q^30 + 3 * q^31 + 6 * q^32 - 10 * q^34 + 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 - 3 * q^39 + 9 * q^40 - 7 * q^41 + 2 * q^42 + 21 * q^43 + 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 + 3 * q^50 + 9 * q^51 + 27 * q^52 - 11 * q^53 - 20 * q^54 + 15 * q^56 + 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 + 4 * q^61 + 11 * q^62 + 3 * q^63 - 27 * q^64 + 7 * q^65 - q^67 - 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 + 13 * q^72 - 9 * q^73 - 36 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^78 + 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 + 15 * q^83 - 47 * q^84 + 3 * q^85 - 3 * q^86 + 15 * q^87 + 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 - 11 * q^94 + 12 * q^95 - 26 * q^96 + 6 * q^97 - 42 * q^98

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 $

$2$	2.52452	1.78511	0.892554	−	0.450940i	$-0.148911\pi$
$2$	2.52452	1.78511	0.892554	+	0.450940i	$0.148911\pi$
$3$	−2.46673	−1.42417	−0.712084	−	0.702094i	$-0.752249\pi$
$3$	−2.46673	−1.42417	−0.712084	+	0.702094i	$0.752249\pi$
$4$	4.37322	2.18661
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.22732	−2.54229
$7$	2.09351	0.791272	0.395636	−	0.918407i	$-0.370524\pi$
$7$	2.09351	0.791272	0.395636	+	0.918407i	$0.370524\pi$
$8$	5.99126	2.11823
$9$	3.08477	1.02826
$10$	2.52452	0.798325
$11$	0	0
$11$	0	0
$12$	−10.7876	−3.11410
$13$	1.28846	0.357353	0.178677	−	0.983908i	$-0.442818\pi$
$13$	1.28846	0.357353	0.178677	+	0.983908i	$0.442818\pi$
$14$	5.28512	1.41251
$15$	−2.46673	−0.636907
$16$	6.37863	1.59466
$17$	−2.99126	−0.725486	−0.362743	−	0.931889i	$-0.618160\pi$
$17$	−2.99126	−0.725486	−0.362743	+	0.931889i	$0.618160\pi$
$18$	7.78757	1.83555
$19$	2.15130	0.493543	0.246771	−	0.969074i	$-0.420630\pi$
$19$	2.15130	0.493543	0.246771	+	0.969074i	$0.420630\pi$
$20$	4.37322	0.977882
$21$	−5.16413	−1.12690
$22$	0	0
$23$	8.77882	1.83051	0.915255	−	0.402874i	$-0.131989\pi$
$23$	8.77882	1.83051	0.915255	+	0.402874i	$0.131989\pi$
$24$	−14.7788	−3.01671
$25$	1.00000	0.200000
$26$	3.25274	0.637915
$27$	−0.209094	−0.0402403
$28$	9.15538	1.73020
$29$	−0.612630	−0.113763	−0.0568813	−	0.998381i	$-0.518116\pi$
$29$	−0.612630	−0.113763	−0.0568813	+	0.998381i	$0.518116\pi$
$30$	−6.22732	−1.13695
$31$	−3.64501	−0.654663	−0.327331	−	0.944910i	$-0.606149\pi$
$31$	−3.64501	−0.654663	−0.327331	+	0.944910i	$0.606149\pi$
$32$	4.12048	0.728405
$33$	0	0
$34$	−7.55150	−1.29507
$35$	2.09351	0.353868
$36$	13.4904	2.24839
$37$	−1.87077	−0.307553	−0.153777	−	0.988106i	$-0.549144\pi$
$37$	−1.87077	−0.307553	−0.153777	+	0.988106i	$0.549144\pi$
$38$	5.43101	0.881027
$39$	−3.17828	−0.508931
$40$	5.99126	0.947301
$41$	−5.10684	−0.797554	−0.398777	−	0.917048i	$-0.630565\pi$
$41$	−5.10684	−0.797554	−0.398777	+	0.917048i	$0.630565\pi$
$42$	−13.0370	−2.01165
$43$	5.17287	0.788856	0.394428	−	0.918927i	$-0.370943\pi$
$43$	5.17287	0.788856	0.394428	+	0.918927i	$0.370943\pi$
$44$	0	0
$45$	3.08477	0.459850
$46$	22.1623	3.26766
$47$	−7.30669	−1.06579	−0.532895	−	0.846181i	$-0.678896\pi$
$47$	−7.30669	−1.06579	−0.532895	+	0.846181i	$0.678896\pi$
$48$	−15.7344	−2.27106
$49$	−2.61722	−0.373888
$50$	2.52452	0.357022
$51$	7.37863	1.03321
$52$	5.63470	0.781393
$53$	−2.94221	−0.404143	−0.202072	−	0.979371i	$-0.564767\pi$
$53$	−2.94221	−0.404143	−0.202072	+	0.979371i	$0.564767\pi$
$54$	−0.527864	−0.0718332
$55$	0	0
$56$	12.5428	1.67610
$57$	−5.30669	−0.702888
$58$	−1.54660	−0.203078
$59$	−6.49421	−0.845474	−0.422737	−	0.906252i	$-0.638931\pi$
$59$	−6.49421	−0.845474	−0.422737	+	0.906252i	$0.638931\pi$
$60$	−10.7876	−1.39267
$61$	−0.502449	−0.0643321	−0.0321660	−	0.999483i	$-0.510241\pi$
$61$	−0.502449	−0.0643321	−0.0321660	+	0.999483i	$0.510241\pi$
$62$	−9.20191	−1.16864
$63$	6.45799	0.813630
$64$	−2.35499	−0.294374
$65$	1.28846	0.159813
$66$	0	0
$67$	−7.80964	−0.954099	−0.477050	−	0.878876i	$-0.658294\pi$
$67$	−7.80964	−0.954099	−0.477050	+	0.878876i	$0.658294\pi$
$68$	−13.0814	−1.58636
$69$	−21.6550	−2.60696
$70$	5.28512	0.631692
$71$	−11.3042	−1.34156	−0.670779	−	0.741658i	$-0.734040\pi$
$71$	−11.3042	−1.34156	−0.670779	+	0.741658i	$0.734040\pi$
$72$	18.4816	2.17808
$73$	−11.1171	−1.30116	−0.650582	−	0.759436i	$-0.725475\pi$
$73$	−11.1171	−1.30116	−0.650582	+	0.759436i	$0.725475\pi$
$74$	−4.72281	−0.549016
$75$	−2.46673	−0.284834
$76$	9.40812	1.07919
$77$	0	0
$78$	−8.02363	−0.908498
$79$	5.35907	0.602943	0.301471	−	0.953475i	$-0.402522\pi$
$79$	5.35907	0.602943	0.301471	+	0.953475i	$0.402522\pi$
$80$	6.37863	0.713152
$81$	−8.73852	−0.970946
$82$	−12.8923	−1.42372
$83$	10.8454	1.19043	0.595216	−	0.803565i	$-0.297066\pi$
$83$	10.8454	1.19043	0.595216	+	0.803565i	$0.297066\pi$
$84$	−22.5839	−2.46410
$85$	−2.99126	−0.324447
$86$	13.0590	1.40819
$87$	1.51119	0.162017
$88$	0	0
$89$	−4.32336	−0.458275	−0.229137	−	0.973394i	$-0.573591\pi$
$89$	−4.32336	−0.458275	−0.229137	+	0.973394i	$0.573591\pi$
$90$	7.78757	0.820881
$91$	2.69740	0.282764
$92$	38.3917	4.00262
$93$	8.99126	0.932350
$94$	−18.4459	−1.90255
$95$	2.15130	0.220719
$96$	−10.1641	−1.03737
$97$	−0.351653	−0.0357049	−0.0178525	−	0.999841i	$-0.505683\pi$
$97$	−0.351653	−0.0357049	−0.0178525	+	0.999841i	$0.505683\pi$
$98$	−6.60723	−0.667431
$99$	0	0
$100$	4.37322	0.437322
$101$	−15.6995	−1.56215	−0.781077	−	0.624434i	$-0.785330\pi$
$101$	−15.6995	−1.56215	−0.781077	+	0.624434i	$0.785330\pi$
$102$	18.6275	1.84440
$103$	6.67991	0.658191	0.329095	−	0.944297i	$-0.393256\pi$
$103$	6.67991	0.658191	0.329095	+	0.944297i	$0.393256\pi$
$104$	7.71947	0.756956
$105$	−5.16413	−0.503967
$106$	−7.42767	−0.721439
$107$	15.6080	1.50888	0.754440	−	0.656370i	$-0.227909\pi$
$107$	15.6080	1.50888	0.754440	+	0.656370i	$0.227909\pi$
$108$	−0.914417	−0.0879898
$109$	11.5070	1.10217	0.551087	−	0.834448i	$-0.314213\pi$
$109$	11.5070	1.10217	0.551087	+	0.834448i	$0.314213\pi$
$110$	0	0
$111$	4.61469	0.438007
$112$	13.3537	1.26181
$113$	9.04823	0.851186	0.425593	−	0.904915i	$-0.360066\pi$
$113$	9.04823	0.851186	0.425593	+	0.904915i	$0.360066\pi$
$114$	−13.3969	−1.25473
$115$	8.77882	0.818629
$116$	−2.67917	−0.248754
$117$	3.97459	0.367451
$118$	−16.3948	−1.50926
$119$	−6.26222	−0.574057
$120$	−14.7788	−1.34912
$121$	0	0
$122$	−1.26845	−0.114840
$123$	12.5972	1.13585
$124$	−15.9404	−1.43149
$125$	1.00000	0.0894427
$126$	16.3033	1.45242
$127$	18.8341	1.67126	0.835628	−	0.549296i	$-0.185104\pi$
$127$	18.8341	1.67126	0.835628	+	0.549296i	$0.185104\pi$
$128$	−14.1862	−1.25389
$129$	−12.7601	−1.12346
$130$	3.25274	0.285284
$131$	−20.0997	−1.75612	−0.878058	−	0.478555i	$-0.841161\pi$
$131$	−20.0997	−1.75612	−0.878058	+	0.478555i	$0.841161\pi$
$132$	0	0
$133$	4.50377	0.390527
$134$	−19.7156	−1.70317
$135$	−0.209094	−0.0179960
$136$	−17.9214	−1.53675
$137$	−17.9712	−1.53539	−0.767694	−	0.640817i	$-0.778596\pi$
$137$	−17.9712	−1.53539	−0.767694	+	0.640817i	$0.778596\pi$
$138$	−54.6686	−4.65370
$139$	16.8631	1.43031	0.715154	−	0.698967i	$-0.246357\pi$
$139$	16.8631	1.43031	0.715154	+	0.698967i	$0.246357\pi$
$140$	9.15538	0.773771
$141$	18.0236	1.51786
$142$	−28.5376	−2.39482
$143$	0	0
$144$	19.6766	1.63971
$145$	−0.612630	−0.0508761
$146$	−28.0655	−2.32272
$147$	6.45597	0.532479
$148$	−8.18130	−0.672499
$149$	2.33366	0.191181	0.0955904	−	0.995421i	$-0.469526\pi$
$149$	2.33366	0.191181	0.0955904	+	0.995421i	$0.469526\pi$
$150$	−6.22732	−0.508459
$151$	−3.93887	−0.320541	−0.160270	−	0.987073i	$-0.551237\pi$
$151$	−3.93887	−0.320541	−0.160270	+	0.987073i	$0.551237\pi$
$152$	12.8890	1.04544
$153$	−9.22732	−0.745985
$154$	0	0
$155$	−3.64501	−0.292774
$156$	−13.8993	−1.11284
$157$	−4.88108	−0.389552	−0.194776	−	0.980848i	$-0.562398\pi$
$157$	−4.88108	−0.389552	−0.194776	+	0.980848i	$0.562398\pi$
$158$	13.5291	1.07632
$159$	7.25764	0.575568
$160$	4.12048	0.325753
$161$	18.3785	1.44843
$162$	−22.0606	−1.73324
$163$	−7.03572	−0.551080	−0.275540	−	0.961290i	$-0.588857\pi$
$163$	−7.03572	−0.551080	−0.275540	+	0.961290i	$0.588857\pi$
$164$	−22.3333	−1.74394
$165$	0	0
$166$	27.3794	2.12505
$167$	10.7195	0.829498	0.414749	−	0.909936i	$-0.363869\pi$
$167$	10.7195	0.829498	0.414749	+	0.909936i	$0.363869\pi$
$168$	−30.9396	−2.38704
$169$	−11.3399	−0.872299
$170$	−7.55150	−0.579173
$171$	6.63626	0.507488
$172$	22.6221	1.72492
$173$	8.41182	0.639539	0.319769	−	0.947495i	$-0.396395\pi$
$173$	8.41182	0.639539	0.319769	+	0.947495i	$0.396395\pi$
$174$	3.81504	0.289218
$175$	2.09351	0.158254
$176$	0	0
$177$	16.0195	1.20410
$178$	−10.9144	−0.818070
$179$	21.0365	1.57234	0.786169	−	0.618011i	$-0.212061\pi$
$179$	21.0365	1.57234	0.786169	+	0.618011i	$0.212061\pi$
$180$	13.4904	1.00551
$181$	−1.74310	−0.129564	−0.0647819	−	0.997899i	$-0.520635\pi$
$181$	−1.74310	−0.129564	−0.0647819	+	0.997899i	$0.520635\pi$
$182$	6.80964	0.504764
$183$	1.23941	0.0916197
$184$	52.5962	3.87744
$185$	−1.87077	−0.137542
$186$	22.6986	1.66435
$187$	0	0
$188$	−31.9538	−2.33047
$189$	−0.437741	−0.0318410
$190$	5.43101	0.394007
$191$	0.0249566	0.00180579	0.000902896	−	1.00000i	$-0.499713\pi$
$191$	0.0249566	0.00180579	0.000902896		1.00000i	$0.499713\pi$
$192$	5.80913	0.419238
$193$	1.45725	0.104895	0.0524474	−	0.998624i	$-0.483298\pi$
$193$	1.45725	0.104895	0.0524474	+	0.998624i	$0.483298\pi$
$194$	−0.887755	−0.0637371
$195$	−3.17828	−0.227601
$196$	−11.4457	−0.817548
$197$	22.7027	1.61750	0.808751	−	0.588151i	$-0.200144\pi$
$197$	22.7027	1.61750	0.808751	+	0.588151i	$0.200144\pi$
$198$	0	0
$199$	−6.62834	−0.469870	−0.234935	−	0.972011i	$-0.575488\pi$
$199$	−6.62834	−0.469870	−0.234935	+	0.972011i	$0.575488\pi$
$200$	5.99126	0.423646
$201$	19.2643	1.35880
$202$	−39.6337	−2.78861
$203$	−1.28255	−0.0900171
$204$	32.2684	2.25924
$205$	−5.10684	−0.356677
$206$	16.8636	1.17494
$207$	27.0806	1.88223
$208$	8.21858	0.569856
$209$	0	0
$210$	−13.0370	−0.899636
$211$	5.65760	0.389485	0.194743	−	0.980854i	$-0.437613\pi$
$211$	5.65760	0.389485	0.194743	+	0.980854i	$0.437613\pi$
$212$	−12.8669	−0.883704
$213$	27.8843	1.91060
$214$	39.4027	2.69351
$215$	5.17287	0.352787
$216$	−1.25274	−0.0852381
$217$	−7.63086	−0.518016
$218$	29.0498	1.96750
$219$	27.4230	1.85308
$220$	0	0
$221$	−3.85410	−0.259255
$222$	11.6499	0.781891
$223$	7.88442	0.527980	0.263990	−	0.964525i	$-0.414961\pi$
$223$	7.88442	0.527980	0.263990	+	0.964525i	$0.414961\pi$
$224$	8.62627	0.576367
$225$	3.08477	0.205651
$226$	22.8425	1.51946
$227$	−11.2114	−0.744126	−0.372063	−	0.928207i	$-0.621350\pi$
$227$	−11.2114	−0.744126	−0.372063	+	0.928207i	$0.621350\pi$
$228$	−23.2073	−1.53694
$229$	26.9907	1.78360	0.891799	−	0.452433i	$-0.149444\pi$
$229$	26.9907	1.78360	0.891799	+	0.452433i	$0.149444\pi$
$230$	22.1623	1.46134
$231$	0	0
$232$	−3.67042	−0.240975
$233$	−10.8508	−0.710857	−0.355429	−	0.934703i	$-0.615665\pi$
$233$	−10.8508	−0.710857	−0.355429	+	0.934703i	$0.615665\pi$
$234$	10.0339	0.655939
$235$	−7.30669	−0.476636
$236$	−28.4006	−1.84872
$237$	−13.2194	−0.858692
$238$	−15.8091	−1.02475
$239$	−11.4663	−0.741692	−0.370846	−	0.928694i	$-0.620932\pi$
$239$	−11.4663	−0.741692	−0.370846	+	0.928694i	$0.620932\pi$
$240$	−15.7344	−1.01565
$241$	12.7542	0.821572	0.410786	−	0.911732i	$-0.365254\pi$
$241$	12.7542	0.821572	0.410786	+	0.911732i	$0.365254\pi$
$242$	0	0
$243$	22.1829	1.42303
$244$	−2.19732	−0.140669
$245$	−2.61722	−0.167208
$246$	31.8019	2.02762
$247$	2.77186	0.176369
$248$	−21.8382	−1.38673
$249$	−26.7526	−1.69538
$250$	2.52452	0.159665
$251$	−12.2016	−0.770158	−0.385079	−	0.922884i	$-0.625826\pi$
$251$	−12.2016	−0.770158	−0.385079	+	0.922884i	$0.625826\pi$
$252$	28.2422	1.77909
$253$	0	0
$254$	47.5471	2.98337
$255$	7.37863	0.462067
$256$	−31.1034	−1.94396
$257$	−5.89604	−0.367785	−0.183892	−	0.982946i	$-0.558870\pi$
$257$	−5.89604	−0.367785	−0.183892	+	0.982946i	$0.558870\pi$
$258$	−32.2131	−2.00550
$259$	−3.91648	−0.243358
$260$	5.63470	0.349450
$261$	−1.88982	−0.116977
$262$	−50.7421	−3.13486
$263$	−21.7305	−1.33996	−0.669980	−	0.742379i	$-0.733698\pi$
$263$	−21.7305	−1.33996	−0.669980	+	0.742379i	$0.733698\pi$
$264$	0	0
$265$	−2.94221	−0.180738
$266$	11.3699	0.697132
$267$	10.6646	0.652660
$268$	−34.1533	−2.08624
$269$	−4.52452	−0.275865	−0.137933	−	0.990442i	$-0.544046\pi$
$269$	−4.52452	−0.275865	−0.137933	+	0.990442i	$0.544046\pi$
$270$	−0.527864	−0.0321248
$271$	−21.7608	−1.32188	−0.660938	−	0.750440i	$-0.729841\pi$
$271$	−21.7608	−1.32188	−0.660938	+	0.750440i	$0.729841\pi$
$272$	−19.0801	−1.15690
$273$	−6.65375	−0.402703
$274$	−45.3688	−2.74083
$275$	0	0
$276$	−94.7021	−5.70040
$277$	−13.0346	−0.783172	−0.391586	−	0.920141i	$-0.628074\pi$
$277$	−13.0346	−0.783172	−0.391586	+	0.920141i	$0.628074\pi$
$278$	42.5713	2.55325
$279$	−11.2440	−0.673160
$280$	12.5428	0.749573
$281$	9.38559	0.559897	0.279949	−	0.960015i	$-0.409683\pi$
$281$	9.38559	0.559897	0.279949	+	0.960015i	$0.409683\pi$
$282$	45.5011	2.70955
$283$	13.9397	0.828628	0.414314	−	0.910134i	$-0.364021\pi$
$283$	13.9397	0.828628	0.414314	+	0.910134i	$0.364021\pi$
$284$	−49.4356	−2.93346
$285$	−5.30669	−0.314341
$286$	0	0
$287$	−10.6912	−0.631083
$288$	12.7107	0.748987
$289$	−8.05239	−0.473670
$290$	−1.54660	−0.0908194
$291$	0.867433	0.0508498
$292$	−48.6177	−2.84514
$293$	30.4700	1.78008	0.890039	−	0.455884i	$-0.150677\pi$
$293$	30.4700	1.78008	0.890039	+	0.455884i	$0.150677\pi$
$294$	16.2983	0.950533
$295$	−6.49421	−0.378108
$296$	−11.2083	−0.651468
$297$	0	0
$298$	5.89138	0.341278
$299$	11.3111	0.654139
$300$	−10.7876	−0.622820
$301$	10.8295	0.624200
$302$	−9.94377	−0.572199
$303$	38.7264	2.22477
$304$	13.7224	0.787031
$305$	−0.502449	−0.0287702
$306$	−23.2946	−1.33166
$307$	5.08609	0.290278	0.145139	−	0.989411i	$-0.453637\pi$
$307$	5.08609	0.290278	0.145139	+	0.989411i	$0.453637\pi$
$308$	0	0
$309$	−16.4775	−0.937375
$310$	−9.20191	−0.522633
$311$	13.7613	0.780334	0.390167	−	0.920744i	$-0.372417\pi$
$311$	13.7613	0.780334	0.390167	+	0.920744i	$0.372417\pi$
$312$	−19.0419	−1.07803
$313$	15.9527	0.901700	0.450850	−	0.892600i	$-0.351121\pi$
$313$	15.9527	0.901700	0.450850	+	0.892600i	$0.351121\pi$
$314$	−12.3224	−0.695393
$315$	6.45799	0.363866
$316$	23.4364	1.31840
$317$	10.7074	0.601387	0.300693	−	0.953721i	$-0.402782\pi$
$317$	10.7074	0.601387	0.300693	+	0.953721i	$0.402782\pi$
$318$	18.3221	1.02745
$319$	0	0
$320$	−2.35499	−0.131648
$321$	−38.5007	−2.14890
$322$	46.3971	2.58561
$323$	−6.43510	−0.358058
$324$	−38.2155	−2.12308
$325$	1.28846	0.0714707
$326$	−17.7618	−0.983737
$327$	−28.3848	−1.56968
$328$	−30.5964	−1.68940
$329$	−15.2966	−0.843330
$330$	0	0
$331$	−8.84618	−0.486230	−0.243115	−	0.969997i	$-0.578169\pi$
$331$	−8.84618	−0.486230	−0.243115	+	0.969997i	$0.578169\pi$
$332$	47.4292	2.60301
$333$	−5.77090	−0.316243
$334$	27.0616	1.48074
$335$	−7.80964	−0.426686
$336$	−32.9400	−1.79703
$337$	−11.5897	−0.631333	−0.315667	−	0.948870i	$-0.602228\pi$
$337$	−11.5897	−0.631333	−0.315667	+	0.948870i	$0.602228\pi$
$338$	−28.6278	−1.55715
$339$	−22.3196	−1.21223
$340$	−13.0814	−0.709440
$341$	0	0
$342$	16.7534	0.905920
$343$	−20.1337	−1.08712
$344$	30.9920	1.67098
$345$	−21.6550	−1.16587
$346$	21.2358	1.14165
$347$	−4.88900	−0.262455	−0.131228	−	0.991352i	$-0.541892\pi$
$347$	−4.88900	−0.262455	−0.131228	+	0.991352i	$0.541892\pi$
$348$	6.60878	0.354268
$349$	0.953521	0.0510408	0.0255204	−	0.999674i	$-0.491876\pi$
$349$	0.953521	0.0510408	0.0255204	+	0.999674i	$0.491876\pi$
$350$	5.28512	0.282501
$351$	−0.269409	−0.0143800
$352$	0	0
$353$	−15.5166	−0.825865	−0.412933	−	0.910762i	$-0.635495\pi$
$353$	−15.5166	−0.825865	−0.412933	+	0.910762i	$0.635495\pi$
$354$	40.4416	2.14944
$355$	−11.3042	−0.599963
$356$	−18.9070	−1.00207
$357$	15.4472	0.817554
$358$	53.1070	2.80679
$359$	20.2550	1.06902	0.534510	−	0.845162i	$-0.320496\pi$
$359$	20.2550	1.06902	0.534510	+	0.845162i	$0.320496\pi$
$360$	18.4816	0.974067
$361$	−14.3719	−0.756416
$362$	−4.40051	−0.231286
$363$	0	0
$364$	11.7963	0.618295
$365$	−11.1171	−0.581898
$366$	3.12892	0.163551
$367$	35.6550	1.86118	0.930588	−	0.366069i	$-0.119296\pi$
$367$	35.6550	1.86118	0.930588	+	0.366069i	$0.119296\pi$
$368$	55.9968	2.91904
$369$	−15.7534	−0.820090
$370$	−4.72281	−0.245527
$371$	−6.15954	−0.319787
$372$	39.3208	2.03869
$373$	12.1358	0.628370	0.314185	−	0.949362i	$-0.398269\pi$
$373$	12.1358	0.628370	0.314185	+	0.949362i	$0.398269\pi$
$374$	0	0
$375$	−2.46673	−0.127381
$376$	−43.7762	−2.25759
$377$	−0.789347	−0.0406534
$378$	−1.10509	−0.0568396
$379$	7.14412	0.366969	0.183484	−	0.983023i	$-0.441262\pi$
$379$	7.14412	0.366969	0.183484	+	0.983023i	$0.441262\pi$
$380$	9.40812	0.482626
$381$	−46.4587	−2.38015
$382$	0.0630034	0.00322354
$383$	15.9630	0.815669	0.407835	−	0.913056i	$-0.366284\pi$
$383$	15.9630	0.815669	0.407835	+	0.913056i	$0.366284\pi$
$384$	34.9936	1.78576
$385$	0	0
$386$	3.67885	0.187249
$387$	15.9571	0.811145
$388$	−1.53785	−0.0780727
$389$	−25.0904	−1.27213	−0.636067	−	0.771634i	$-0.719440\pi$
$389$	−25.0904	−1.27213	−0.636067	+	0.771634i	$0.719440\pi$
$390$	−8.02363	−0.406292
$391$	−26.2597	−1.32801
$392$	−15.6804	−0.791980
$393$	49.5805	2.50100
$394$	57.3136	2.88742
$395$	5.35907	0.269644
$396$	0	0
$397$	3.57490	0.179419	0.0897094	−	0.995968i	$-0.471406\pi$
$397$	3.57490	0.179419	0.0897094	+	0.995968i	$0.471406\pi$
$398$	−16.7334	−0.838769
$399$	−11.1096	−0.556176
$400$	6.37863	0.318931
$401$	28.8838	1.44239	0.721195	−	0.692732i	$-0.243593\pi$
$401$	28.8838	1.44239	0.721195	+	0.692732i	$0.243593\pi$
$402$	48.6332	2.42560
$403$	−4.69643	−0.233946
$404$	−68.6572	−3.41582
$405$	−8.73852	−0.434220
$406$	−3.23782	−0.160690
$407$	0	0
$408$	44.2072	2.18858
$409$	9.61904	0.475631	0.237816	−	0.971310i	$-0.423569\pi$
$409$	9.61904	0.475631	0.237816	+	0.971310i	$0.423569\pi$
$410$	−12.8923	−0.636707
$411$	44.3302	2.18665
$412$	29.2127	1.43921
$413$	−13.5957	−0.669000
$414$	68.3656	3.35999
$415$	10.8454	0.532378
$416$	5.30906	0.260298
$417$	−41.5967	−2.03700
$418$	0	0
$419$	−30.6537	−1.49753	−0.748765	−	0.662836i	$-0.769353\pi$
$419$	−30.6537	−1.49753	−0.748765	+	0.662836i	$0.769353\pi$
$420$	−22.5839	−1.10198
$421$	−6.94963	−0.338704	−0.169352	−	0.985556i	$-0.554168\pi$
$421$	−6.94963	−0.338704	−0.169352	+	0.985556i	$0.554168\pi$
$422$	14.2827	0.695273
$423$	−22.5394	−1.09590
$424$	−17.6275	−0.856068
$425$	−2.99126	−0.145097
$426$	70.3947	3.41063
$427$	−1.05188	−0.0509042
$428$	68.2571	3.29933
$429$	0	0
$430$	13.0590	0.629763
$431$	−3.23400	−0.155776	−0.0778882	−	0.996962i	$-0.524818\pi$
$431$	−3.23400	−0.155776	−0.0778882	+	0.996962i	$0.524818\pi$
$432$	−1.33374	−0.0641694
$433$	−30.3919	−1.46054	−0.730270	−	0.683158i	$-0.760606\pi$
$433$	−30.3919	−1.46054	−0.730270	+	0.683158i	$0.760606\pi$
$434$	−19.2643	−0.924715
$435$	1.51119	0.0724562
$436$	50.3228	2.41003
$437$	18.8859	0.903435
$438$	69.2301	3.30794
$439$	36.5311	1.74353	0.871767	−	0.489921i	$-0.162974\pi$
$439$	36.5311	1.74353	0.871767	+	0.489921i	$0.162974\pi$
$440$	0	0
$441$	−8.07350	−0.384452
$442$	−9.72977	−0.462798
$443$	−2.16153	−0.102697	−0.0513487	−	0.998681i	$-0.516352\pi$
$443$	−2.16153	−0.102697	−0.0513487	+	0.998681i	$0.516352\pi$
$444$	20.1811	0.957752
$445$	−4.32336	−0.204947
$446$	19.9044	0.942501
$447$	−5.75651	−0.272274
$448$	−4.93020	−0.232930
$449$	−11.5217	−0.543742	−0.271871	−	0.962334i	$-0.587642\pi$
$449$	−11.5217	−0.543742	−0.271871	+	0.962334i	$0.587642\pi$
$450$	7.78757	0.367109
$451$	0	0
$452$	39.5699	1.86121
$453$	9.71613	0.456504
$454$	−28.3034	−1.32835
$455$	2.69740	0.126456
$456$	−31.7937	−1.48888
$457$	−15.9314	−0.745242	−0.372621	−	0.927984i	$-0.621541\pi$
$457$	−15.9314	−0.745242	−0.372621	+	0.927984i	$0.621541\pi$
$458$	68.1387	3.18391
$459$	0.625455	0.0291937
$460$	38.3917	1.79002
$461$	1.52527	0.0710387	0.0355193	−	0.999369i	$-0.488691\pi$
$461$	1.52527	0.0710387	0.0355193	+	0.999369i	$0.488691\pi$
$462$	0	0
$463$	14.2073	0.660268	0.330134	−	0.943934i	$-0.392906\pi$
$463$	14.2073	0.660268	0.330134	+	0.943934i	$0.392906\pi$
$464$	−3.90774	−0.181412
$465$	8.99126	0.416960
$466$	−27.3930	−1.26896
$467$	−6.05697	−0.280283	−0.140142	−	0.990131i	$-0.544756\pi$
$467$	−6.05697	−0.280283	−0.140142	+	0.990131i	$0.544756\pi$
$468$	17.3817	0.803471
$469$	−16.3496	−0.754952
$470$	−18.4459	−0.850846
$471$	12.0403	0.554788
$472$	−38.9085	−1.79091
$473$	0	0
$474$	−33.3727	−1.53286
$475$	2.15130	0.0987085
$476$	−27.3861	−1.25524
$477$	−9.07602	−0.415562
$478$	−28.9469	−1.32400
$479$	−17.6084	−0.804549	−0.402275	−	0.915519i	$-0.631780\pi$
$479$	−17.6084	−0.804549	−0.402275	+	0.915519i	$0.631780\pi$
$480$	−10.1641	−0.463927
$481$	−2.41041	−0.109905
$482$	32.1983	1.46659
$483$	−45.3350	−2.06281
$484$	0	0
$485$	−0.351653	−0.0159677
$486$	56.0012	2.54026
$487$	6.78341	0.307386	0.153693	−	0.988119i	$-0.450883\pi$
$487$	6.78341	0.307386	0.153693	+	0.988119i	$0.450883\pi$
$488$	−3.01030	−0.136270
$489$	17.3552	0.784831
$490$	−6.60723	−0.298484
$491$	0.518615	0.0234047	0.0117024	−	0.999932i	$-0.496275\pi$
$491$	0.518615	0.0234047	0.0117024	+	0.999932i	$0.496275\pi$
$492$	55.0904	2.48367
$493$	1.83253	0.0825331
$494$	6.99762	0.314838
$495$	0	0
$496$	−23.2501	−1.04396
$497$	−23.6654	−1.06154
$498$	−67.5376	−3.02643
$499$	21.8608	0.978622	0.489311	−	0.872109i	$-0.337248\pi$
$499$	21.8608	0.978622	0.489311	+	0.872109i	$0.337248\pi$
$500$	4.37322	0.195576
$501$	−26.4421	−1.18134
$502$	−30.8032	−1.37482
$503$	3.01667	0.134507	0.0672533	−	0.997736i	$-0.478576\pi$
$503$	3.01667	0.134507	0.0672533	+	0.997736i	$0.478576\pi$
$504$	38.6915	1.72345
$505$	−15.6995	−0.698617
$506$	0	0
$507$	27.9724	1.24230
$508$	82.3657	3.65439
$509$	−25.7079	−1.13948	−0.569741	−	0.821824i	$-0.692957\pi$
$509$	−25.7079	−1.13948	−0.569741	+	0.821824i	$0.692957\pi$
$510$	18.6275	0.824840
$511$	−23.2738	−1.02957
$512$	−50.1489	−2.21629
$513$	−0.449825	−0.0198603
$514$	−14.8847	−0.656536
$515$	6.67991	0.294352
$516$	−55.8027	−2.45658
$517$	0	0
$518$	−9.88725	−0.434421
$519$	−20.7497	−0.910811
$520$	7.71947	0.338521
$521$	11.1326	0.487729	0.243864	−	0.969809i	$-0.421585\pi$
$521$	11.1326	0.487729	0.243864	+	0.969809i	$0.421585\pi$
$522$	−4.77090	−0.208816
$523$	−6.53840	−0.285904	−0.142952	−	0.989730i	$-0.545660\pi$
$523$	−6.53840	−0.285904	−0.142952	+	0.989730i	$0.545660\pi$
$524$	−87.9003	−3.83994
$525$	−5.16413	−0.225381
$526$	−54.8592	−2.39198
$527$	10.9032	0.474949
$528$	0	0
$529$	54.0677	2.35077
$530$	−7.42767	−0.322638
$531$	−20.0331	−0.869363
$532$	19.6960	0.853930
$533$	−6.57994	−0.285009
$534$	26.9229	1.16507
$535$	15.6080	0.674791
$536$	−46.7896	−2.02100
$537$	−51.8913	−2.23927
$538$	−11.4223	−0.492449
$539$	0	0
$540$	−0.914417	−0.0393502
$541$	41.7400	1.79454	0.897271	−	0.441479i	$-0.145546\pi$
$541$	41.7400	1.79454	0.897271	+	0.441479i	$0.145546\pi$
$542$	−54.9357	−2.35969
$543$	4.29977	0.184521
$544$	−12.3254	−0.528448
$545$	11.5070	0.492907
$546$	−16.7976	−0.718869
$547$	−4.45616	−0.190532	−0.0952658	−	0.995452i	$-0.530370\pi$
$547$	−4.45616	−0.190532	−0.0952658	+	0.995452i	$0.530370\pi$
$548$	−78.5922	−3.35729
$549$	−1.54994	−0.0661498
$550$	0	0
$551$	−1.31795	−0.0561466
$552$	−129.741	−5.52213
$553$	11.2193	0.477092
$554$	−32.9061	−1.39805
$555$	4.61469	0.195883
$556$	73.7460	3.12753
$557$	19.3714	0.820791	0.410396	−	0.911908i	$-0.365391\pi$
$557$	19.3714	0.820791	0.410396	+	0.911908i	$0.365391\pi$
$558$	−28.3857	−1.20166
$559$	6.66502	0.281900
$560$	13.3537	0.564298
$561$	0	0
$562$	23.6941	0.999477
$563$	20.7432	0.874220	0.437110	−	0.899408i	$-0.356002\pi$
$563$	20.7432	0.874220	0.437110	+	0.899408i	$0.356002\pi$
$564$	78.8213	3.31898
$565$	9.04823	0.380662
$566$	35.1911	1.47919
$567$	−18.2942	−0.768283
$568$	−67.7261	−2.84173
$569$	−42.3747	−1.77644	−0.888220	−	0.459418i	$-0.848058\pi$
$569$	−42.3747	−1.77644	−0.888220	+	0.459418i	$0.848058\pi$
$570$	−13.3969	−0.561133
$571$	−5.03980	−0.210909	−0.105455	−	0.994424i	$-0.533630\pi$
$571$	−5.03980	−0.210909	−0.105455	+	0.994424i	$0.533630\pi$
$572$	0	0
$573$	−0.0615611	−0.00257175
$574$	−26.9902	−1.12655
$575$	8.77882	0.366102
$576$	−7.26460	−0.302692
$577$	34.8419	1.45049	0.725245	−	0.688491i	$-0.241727\pi$
$577$	34.8419	1.45049	0.725245	+	0.688491i	$0.241727\pi$
$578$	−20.3284	−0.845552
$579$	−3.59464	−0.149388
$580$	−2.67917	−0.111246
$581$	22.7049	0.941956
$582$	2.18985	0.0907724
$583$	0	0
$584$	−66.6057	−2.75616
$585$	3.97459	0.164329
$586$	76.9224	3.17763
$587$	−13.7783	−0.568690	−0.284345	−	0.958722i	$-0.591776\pi$
$587$	−13.7783	−0.568690	−0.284345	+	0.958722i	$0.591776\pi$
$588$	28.2334	1.16433
$589$	−7.84151	−0.323104
$590$	−16.3948	−0.674963
$591$	−56.0015	−2.30360
$592$	−11.9330	−0.490442
$593$	−25.1595	−1.03318	−0.516588	−	0.856234i	$-0.672798\pi$
$593$	−25.1595	−1.03318	−0.516588	+	0.856234i	$0.672798\pi$
$594$	0	0
$595$	−6.26222	−0.256726
$596$	10.2056	0.418038
$597$	16.3503	0.669174
$598$	28.5552	1.16771
$599$	−16.5063	−0.674429	−0.337214	−	0.941428i	$-0.609485\pi$
$599$	−16.5063	−0.674429	−0.337214	+	0.941428i	$0.609485\pi$
$600$	−14.7788	−0.603343
$601$	39.6449	1.61715	0.808574	−	0.588395i	$-0.200240\pi$
$601$	39.6449	1.61715	0.808574	+	0.588395i	$0.200240\pi$
$602$	27.3392	1.11426
$603$	−24.0909	−0.981058
$604$	−17.2255	−0.700897
$605$	0	0
$606$	97.7656	3.97146
$607$	14.1895	0.575933	0.287966	−	0.957641i	$-0.407021\pi$
$607$	14.1895	0.575933	0.287966	+	0.957641i	$0.407021\pi$
$608$	8.86440	0.359499
$609$	3.16370	0.128200
$610$	−1.26845	−0.0513579
$611$	−9.41434	−0.380864
$612$	−40.3531	−1.63118
$613$	30.1543	1.21792	0.608961	−	0.793200i	$-0.291586\pi$
$613$	30.1543	1.21792	0.608961	+	0.793200i	$0.291586\pi$
$614$	12.8400	0.518178
$615$	12.5972	0.507968
$616$	0	0
$617$	−31.3844	−1.26349	−0.631744	−	0.775177i	$-0.717661\pi$
$617$	−31.3844	−1.26349	−0.631744	+	0.775177i	$0.717661\pi$
$618$	−41.5979	−1.67331
$619$	35.2332	1.41614	0.708070	−	0.706142i	$-0.249566\pi$
$619$	35.2332	1.41614	0.708070	+	0.706142i	$0.249566\pi$
$620$	−15.9404	−0.640183
$621$	−1.83560	−0.0736602
$622$	34.7408	1.39298
$623$	−9.05099	−0.362620
$624$	−20.2730	−0.811571
$625$	1.00000	0.0400000
$626$	40.2730	1.60963
$627$	0	0
$628$	−21.3460	−0.851799
$629$	5.59596	0.223126
$630$	16.3033	0.649541
$631$	5.73472	0.228296	0.114148	−	0.993464i	$-0.463586\pi$
$631$	5.73472	0.228296	0.114148	+	0.993464i	$0.463586\pi$
$632$	32.1076	1.27717
$633$	−13.9558	−0.554692
$634$	27.0311	1.07354
$635$	18.8341	0.747408
$636$	31.7393	1.25854
$637$	−3.37217	−0.133610
$638$	0	0
$639$	−34.8707	−1.37946
$640$	−14.1862	−0.560759
$641$	−7.12476	−0.281411	−0.140706	−	0.990051i	$-0.544937\pi$
$641$	−7.12476	−0.281411	−0.140706	+	0.990051i	$0.544937\pi$
$642$	−97.1959	−3.83601
$643$	−21.1895	−0.835634	−0.417817	−	0.908531i	$-0.637205\pi$
$643$	−21.1895	−0.835634	−0.417817	+	0.908531i	$0.637205\pi$
$644$	80.3735	3.16716
$645$	−12.7601	−0.502428
$646$	−16.2456	−0.639173
$647$	−5.64974	−0.222114	−0.111057	−	0.993814i	$-0.535424\pi$
$647$	−5.64974	−0.222114	−0.111057	+	0.993814i	$0.535424\pi$
$648$	−52.3547	−2.05669
$649$	0	0
$650$	3.25274	0.127583
$651$	18.8233	0.737743
$652$	−30.7688	−1.20500
$653$	−15.7131	−0.614903	−0.307452	−	0.951564i	$-0.599476\pi$
$653$	−15.7131	−0.614903	−0.307452	+	0.951564i	$0.599476\pi$
$654$	−71.6580	−2.80205
$655$	−20.0997	−0.785359
$656$	−32.5746	−1.27183
$657$	−34.2938	−1.33793
$658$	−38.6167	−1.50543
$659$	−41.7884	−1.62784	−0.813922	−	0.580975i	$-0.802671\pi$
$659$	−41.7884	−1.62784	−0.813922	+	0.580975i	$0.802671\pi$
$660$	0	0
$661$	15.8742	0.617435	0.308717	−	0.951154i	$-0.400100\pi$
$661$	15.8742	0.617435	0.308717	+	0.951154i	$0.400100\pi$
$662$	−22.3324	−0.867973
$663$	9.50704	0.369223
$664$	64.9773	2.52161
$665$	4.50377	0.174649
$666$	−14.5688	−0.564528
$667$	−5.37817	−0.208243
$668$	46.8786	1.81379
$669$	−19.4487	−0.751932
$670$	−19.7156	−0.761681
$671$	0	0
$672$	−21.2787	−0.820844
$673$	32.2446	1.24294	0.621469	−	0.783439i	$-0.286536\pi$
$673$	32.2446	1.24294	0.621469	+	0.783439i	$0.286536\pi$
$674$	−29.2586	−1.12700
$675$	−0.209094	−0.00804805
$676$	−49.5918	−1.90738
$677$	17.5625	0.674983	0.337492	−	0.941329i	$-0.390422\pi$
$677$	17.5625	0.674983	0.337492	+	0.941329i	$0.390422\pi$
$678$	−56.3463	−2.16397
$679$	−0.736188	−0.0282523
$680$	−17.9214	−0.687254
$681$	27.6555	1.05976
$682$	0	0
$683$	−5.93856	−0.227233	−0.113616	−	0.993525i	$-0.536243\pi$
$683$	−5.93856	−0.227233	−0.113616	+	0.993525i	$0.536243\pi$
$684$	29.0219	1.10968
$685$	−17.9712	−0.686646
$686$	−50.8281	−1.94063
$687$	−66.5789	−2.54014
$688$	32.9958	1.25795
$689$	−3.79091	−0.144422
$690$	−54.6686	−2.08120
$691$	21.9356	0.834469	0.417235	−	0.908799i	$-0.362999\pi$
$691$	21.9356	0.834469	0.417235	+	0.908799i	$0.362999\pi$
$692$	36.7868	1.39842
$693$	0	0
$694$	−12.3424	−0.468511
$695$	16.8631	0.639653
$696$	9.05395	0.343189
$697$	15.2759	0.578615
$698$	2.40719	0.0911134
$699$	26.7659	1.01238
$700$	9.15538	0.346041
$701$	32.4209	1.22452	0.612260	−	0.790657i	$-0.290261\pi$
$701$	32.4209	1.22452	0.612260	+	0.790657i	$0.290261\pi$
$702$	−0.680130	−0.0256698
$703$	−4.02460	−0.151791
$704$	0	0
$705$	18.0236	0.678809
$706$	−39.1720	−1.47426
$707$	−32.8670	−1.23609
$708$	70.0567	2.63289
$709$	−16.1005	−0.604666	−0.302333	−	0.953202i	$-0.597765\pi$
$709$	−16.1005	−0.604666	−0.302333	+	0.953202i	$0.597765\pi$
$710$	−28.5376	−1.07100
$711$	16.5315	0.619979
$712$	−25.9023	−0.970731
$713$	−31.9989	−1.19837
$714$	38.9969	1.45942
$715$	0	0
$716$	91.9971	3.43809
$717$	28.2842	1.05629
$718$	51.1343	1.90832
$719$	−7.81216	−0.291345	−0.145672	−	0.989333i	$-0.546534\pi$
$719$	−7.81216	−0.291345	−0.145672	+	0.989333i	$0.546534\pi$
$720$	19.6766	0.733302
$721$	13.9845	0.520808
$722$	−36.2822	−1.35028
$723$	−31.4613	−1.17006
$724$	−7.62298	−0.283306
$725$	−0.612630	−0.0227525
$726$	0	0
$727$	−49.1218	−1.82183	−0.910914	−	0.412597i	$-0.864622\pi$
$727$	−49.1218	−1.82183	−0.910914	+	0.412597i	$0.864622\pi$
$728$	16.1608	0.598959
$729$	−28.5036	−1.05569
$730$	−28.0655	−1.03875
$731$	−15.4734	−0.572304
$732$	5.42021	0.200337
$733$	−0.667947	−0.0246712	−0.0123356	−	0.999924i	$-0.503927\pi$
$733$	−0.667947	−0.0246712	−0.0123356	+	0.999924i	$0.503927\pi$
$734$	90.0119	3.32240
$735$	6.45597	0.238132
$736$	36.1730	1.33335
$737$	0	0
$738$	−39.7699	−1.46395
$739$	38.0939	1.40131	0.700654	−	0.713501i	$-0.252892\pi$
$739$	38.0939	1.40131	0.700654	+	0.713501i	$0.252892\pi$
$740$	−8.18130	−0.300751
$741$	−6.83743	−0.251179
$742$	−15.5499	−0.570855
$743$	−31.3356	−1.14959	−0.574797	−	0.818296i	$-0.694919\pi$
$743$	−31.3356	−1.14959	−0.574797	+	0.818296i	$0.694919\pi$
$744$	53.8689	1.97493
$745$	2.33366	0.0854987
$746$	30.6372	1.12171
$747$	33.4554	1.22407
$748$	0	0
$749$	32.6754	1.19393
$750$	−6.22732	−0.227390
$751$	−37.1874	−1.35699	−0.678494	−	0.734606i	$-0.737367\pi$
$751$	−37.1874	−1.35699	−0.678494	+	0.734606i	$0.737367\pi$
$752$	−46.6066	−1.69957
$753$	30.0981	1.09683
$754$	−1.99272	−0.0725708
$755$	−3.93887	−0.143350
$756$	−1.91434	−0.0696239
$757$	6.68068	0.242813	0.121407	−	0.992603i	$-0.461259\pi$
$757$	6.68068	0.242813	0.121407	+	0.992603i	$0.461259\pi$
$758$	18.0355	0.655079
$759$	0	0
$760$	12.8890	0.467533
$761$	−22.8936	−0.829894	−0.414947	−	0.909846i	$-0.636200\pi$
$761$	−22.8936	−0.829894	−0.414947	+	0.909846i	$0.636200\pi$
$762$	−117.286	−4.24882
$763$	24.0901	0.872120
$764$	0.109141	0.00394857
$765$	−9.22732	−0.333615
$766$	40.2989	1.45606
$767$	−8.36751	−0.302133
$768$	76.7238	2.76853
$769$	−13.1946	−0.475808	−0.237904	−	0.971289i	$-0.576460\pi$
$769$	−13.1946	−0.475808	−0.237904	+	0.971289i	$0.576460\pi$
$770$	0	0
$771$	14.5440	0.523788
$772$	6.37286	0.229364
$773$	−12.4209	−0.446749	−0.223374	−	0.974733i	$-0.571707\pi$
$773$	−12.4209	−0.446749	−0.223374	+	0.974733i	$0.571707\pi$
$774$	40.2841	1.44798
$775$	−3.64501	−0.130933
$776$	−2.10684	−0.0756312
$777$	9.66091	0.346583
$778$	−63.3413	−2.27090
$779$	−10.9864	−0.393627
$780$	−13.8993	−0.497675
$781$	0	0
$782$	−66.2932	−2.37064
$783$	0.128098	0.00457783
$784$	−16.6942	−0.596223
$785$	−4.88108	−0.174213
$786$	125.167	4.46456
$787$	21.4851	0.765861	0.382931	−	0.923777i	$-0.374915\pi$
$787$	21.4851	0.765861	0.382931	+	0.923777i	$0.374915\pi$
$788$	99.2840	3.53685
$789$	53.6034	1.90833
$790$	13.5291	0.481344
$791$	18.9426	0.673520
$792$	0	0
$793$	−0.647384	−0.0229893
$794$	9.02491	0.320282
$795$	7.25764	0.257402
$796$	−28.9872	−1.02742
$797$	2.12930	0.0754238	0.0377119	−	0.999289i	$-0.487993\pi$
$797$	2.12930	0.0754238	0.0377119	+	0.999289i	$0.487993\pi$
$798$	−28.0464	−0.992834
$799$	21.8562	0.773216
$800$	4.12048	0.145681
$801$	−13.3365	−0.471224
$802$	72.9179	2.57482
$803$	0	0
$804$	84.2470	2.97116
$805$	18.3785	0.647759
$806$	−11.8563	−0.417619
$807$	11.1608	0.392878
$808$	−94.0595	−3.30900
$809$	−5.36232	−0.188529	−0.0942645	−	0.995547i	$-0.530050\pi$
$809$	−5.36232	−0.188529	−0.0942645	+	0.995547i	$0.530050\pi$
$810$	−22.0606	−0.775130
$811$	19.5797	0.687538	0.343769	−	0.939054i	$-0.388296\pi$
$811$	19.5797	0.687538	0.343769	+	0.939054i	$0.388296\pi$
$812$	−5.60886	−0.196832
$813$	53.6781	1.88257
$814$	0	0
$815$	−7.03572	−0.246450
$816$	47.0655	1.64762
$817$	11.1284	0.389334
$818$	24.2835	0.849053
$819$	8.32083	0.290753
$820$	−22.3333	−0.779914
$821$	−16.6365	−0.580616	−0.290308	−	0.956933i	$-0.593758\pi$
$821$	−16.6365	−0.580616	−0.290308	+	0.956933i	$0.593758\pi$
$822$	111.913	3.90341
$823$	−18.2929	−0.637650	−0.318825	−	0.947814i	$-0.603288\pi$
$823$	−18.2929	−0.637650	−0.318825	+	0.947814i	$0.603288\pi$
$824$	40.0210	1.39420
$825$	0	0
$826$	−34.3227	−1.19424
$827$	−38.0184	−1.32203	−0.661014	−	0.750373i	$-0.729874\pi$
$827$	−38.0184	−1.32203	−0.661014	+	0.750373i	$0.729874\pi$
$828$	118.430	4.11571
$829$	51.7002	1.79562	0.897811	−	0.440382i	$-0.145157\pi$
$829$	51.7002	1.79562	0.897811	+	0.440382i	$0.145157\pi$
$830$	27.3794	0.950352
$831$	32.1528	1.11537
$832$	−3.03430	−0.105196
$833$	7.82876	0.271251
$834$	−105.012	−3.63626
$835$	10.7195	0.370963
$836$	0	0
$837$	0.762151	0.0263438
$838$	−77.3859	−2.67325
$839$	38.6025	1.33271	0.666354	−	0.745636i	$-0.267854\pi$
$839$	38.6025	1.33271	0.666354	+	0.745636i	$0.267854\pi$
$840$	−30.9396	−1.06752
$841$	−28.6247	−0.987058
$842$	−17.5445	−0.604624
$843$	−23.1517	−0.797388
$844$	24.7419	0.851652
$845$	−11.3399	−0.390104
$846$	−56.9013	−1.95631
$847$	0	0
$848$	−18.7672	−0.644470
$849$	−34.3855	−1.18011
$850$	−7.55150	−0.259014
$851$	−16.4232	−0.562979
$852$	121.944	4.17775
$853$	33.9058	1.16091	0.580456	−	0.814292i	$-0.302874\pi$
$853$	33.9058	1.16091	0.580456	+	0.814292i	$0.302874\pi$
$854$	−2.65550	−0.0908695
$855$	6.63626	0.226955
$856$	93.5113	3.19615
$857$	−56.7117	−1.93723	−0.968617	−	0.248558i	$-0.920043\pi$
$857$	−56.7117	−1.93723	−0.968617	+	0.248558i	$0.920043\pi$
$858$	0	0
$859$	−25.7505	−0.878597	−0.439298	−	0.898341i	$-0.644773\pi$
$859$	−25.7505	−0.878597	−0.439298	+	0.898341i	$0.644773\pi$
$860$	22.6221	0.771408
$861$	26.3724	0.898768
$862$	−8.16432	−0.278078
$863$	35.7650	1.21746	0.608728	−	0.793379i	$-0.291680\pi$
$863$	35.7650	1.21746	0.608728	+	0.793379i	$0.291680\pi$
$864$	−0.861570	−0.0293112
$865$	8.41182	0.286011
$866$	−76.7250	−2.60722
$867$	19.8631	0.674586
$868$	−33.3714	−1.13270
$869$	0	0
$870$	3.81504	0.129342
$871$	−10.0624	−0.340951
$872$	68.9416	2.33466
$873$	−1.08477	−0.0367138
$874$	47.6779	1.61273
$875$	2.09351	0.0707736
$876$	119.927	4.05195
$877$	17.3101	0.584522	0.292261	−	0.956339i	$-0.405592\pi$
$877$	17.3101	0.584522	0.292261	+	0.956339i	$0.405592\pi$
$878$	92.2236	3.11240
$879$	−75.1614	−2.53513
$880$	0	0
$881$	−4.15822	−0.140094	−0.0700470	−	0.997544i	$-0.522315\pi$
$881$	−4.15822	−0.140094	−0.0700470	+	0.997544i	$0.522315\pi$
$882$	−20.3817	−0.686289
$883$	−41.2704	−1.38886	−0.694430	−	0.719560i	$-0.744344\pi$
$883$	−41.2704	−1.38886	−0.694430	+	0.719560i	$0.744344\pi$
$884$	−16.8548	−0.566890
$885$	16.0195	0.538489
$886$	−5.45683	−0.183326
$887$	30.4790	1.02339	0.511693	−	0.859169i	$-0.329019\pi$
$887$	30.4790	1.02339	0.511693	+	0.859169i	$0.329019\pi$
$888$	27.6478	0.927800
$889$	39.4294	1.32242
$890$	−10.9144	−0.365852
$891$	0	0
$892$	34.4803	1.15449
$893$	−15.7189	−0.526013
$894$	−14.5325	−0.486038
$895$	21.0365	0.703171
$896$	−29.6990	−0.992172
$897$	−27.9015	−0.931604
$898$	−29.0868	−0.970639
$899$	2.23304	0.0744761
$900$	13.4904	0.449679
$901$	8.80090	0.293200
$902$	0	0
$903$	−26.7134	−0.888965
$904$	54.2103	1.80301
$905$	−1.74310	−0.0579427
$906$	24.5286	0.814908
$907$	11.2895	0.374861	0.187430	−	0.982278i	$-0.439984\pi$
$907$	11.2895	0.374861	0.187430	+	0.982278i	$0.439984\pi$
$908$	−49.0299	−1.62711
$909$	−48.4292	−1.60629
$910$	6.80964	0.225737
$911$	50.6067	1.67667	0.838337	−	0.545152i	$-0.183528\pi$
$911$	50.6067	1.67667	0.838337	+	0.545152i	$0.183528\pi$
$912$	−33.8494	−1.12086
$913$	0	0
$914$	−40.2193	−1.33034
$915$	1.23941	0.0409736
$916$	118.036	3.90003
$917$	−42.0788	−1.38957
$918$	1.57898	0.0521140
$919$	−27.2180	−0.897837	−0.448919	−	0.893573i	$-0.648191\pi$
$919$	−27.2180	−0.897837	−0.448919	+	0.893573i	$0.648191\pi$
$920$	52.5962	1.73404
$921$	−12.5460	−0.413405
$922$	3.85057	0.126812
$923$	−14.5649	−0.479410
$924$	0	0
$925$	−1.87077	−0.0615106
$926$	35.8666	1.17865
$927$	20.6059	0.676788
$928$	−2.52433	−0.0828652
$929$	−23.2104	−0.761508	−0.380754	−	0.924676i	$-0.624336\pi$
$929$	−23.2104	−0.761508	−0.380754	+	0.924676i	$0.624336\pi$
$930$	22.6986	0.744318
$931$	−5.63042	−0.184530
$932$	−47.4528	−1.55437
$933$	−33.9455	−1.11133
$934$	−15.2910	−0.500336
$935$	0	0
$936$	23.8128	0.778344
$937$	−42.2117	−1.37900	−0.689498	−	0.724287i	$-0.742169\pi$
$937$	−42.2117	−1.37900	−0.689498	+	0.724287i	$0.742169\pi$
$938$	−41.2749	−1.34767
$939$	−39.3510	−1.28417
$940$	−31.9538	−1.04222
$941$	−29.2128	−0.952310	−0.476155	−	0.879361i	$-0.657970\pi$
$941$	−29.2128	−0.952310	−0.476155	+	0.879361i	$0.657970\pi$
$942$	30.3960	0.990356
$943$	−44.8320	−1.45993
$944$	−41.4241	−1.34824
$945$	−0.437741	−0.0142397
$946$	0	0
$947$	9.63809	0.313196	0.156598	−	0.987662i	$-0.449947\pi$
$947$	9.63809	0.313196	0.156598	+	0.987662i	$0.449947\pi$
$948$	−57.8114	−1.87763
$949$	−14.3240	−0.464975
$950$	5.43101	0.176205
$951$	−26.4123	−0.856476
$952$	−37.5186	−1.21598
$953$	5.22149	0.169141	0.0845703	−	0.996418i	$-0.473048\pi$
$953$	5.22149	0.169141	0.0845703	+	0.996418i	$0.473048\pi$
$954$	−22.9126	−0.741824
$955$	0.0249566	0.000807575 0
$956$	−50.1446	−1.62179
$957$	0	0
$958$	−44.4529	−1.43621
$959$	−37.6230	−1.21491
$960$	5.80913	0.187489
$961$	−17.7139	−0.571417
$962$	−6.08513	−0.196193
$963$	48.1469	1.55151
$964$	55.7771	1.79646
$965$	1.45725	0.0469104
$966$	−114.449	−3.68234
$967$	38.4583	1.23674	0.618368	−	0.785889i	$-0.287794\pi$
$967$	38.4583	1.23674	0.618368	+	0.785889i	$0.287794\pi$
$968$	0	0
$969$	15.8737	0.509935
$970$	−0.887755	−0.0285041
$971$	43.6637	1.40124	0.700618	−	0.713536i	$-0.252908\pi$
$971$	43.6637	1.40124	0.700618	+	0.713536i	$0.252908\pi$
$972$	97.0106	3.11162
$973$	35.3030	1.13176
$974$	17.1249	0.548716
$975$	−3.17828	−0.101786
$976$	−3.20494	−0.102588
$977$	−11.7467	−0.375811	−0.187906	−	0.982187i	$-0.560170\pi$
$977$	−11.7467	−0.375811	−0.187906	+	0.982187i	$0.560170\pi$
$978$	43.8137	1.40101
$979$	0	0
$980$	−11.4457	−0.365618
$981$	35.4965	1.13332
$982$	1.30926	0.0417800
$983$	9.35189	0.298279	0.149139	−	0.988816i	$-0.452350\pi$
$983$	9.35189	0.298279	0.149139	+	0.988816i	$0.452350\pi$
$984$	75.4731	2.40599
$985$	22.7027	0.723369
$986$	4.62627	0.147331
$987$	37.7327	1.20104
$988$	12.1220	0.385651
$989$	45.4117	1.44401
$990$	0	0
$991$	−32.3450	−1.02747	−0.513737	−	0.857948i	$-0.671739\pi$
$991$	−32.3450	−1.02747	−0.513737	+	0.857948i	$0.671739\pi$
$992$	−15.0192	−0.476860
$993$	21.8211	0.692473
$994$	−59.7438	−1.89496
$995$	−6.62834	−0.210132
$996$	−116.995	−3.70713
$997$	−29.1174	−0.922157	−0.461078	−	0.887359i	$-0.652537\pi$
$997$	−29.1174	−0.922157	−0.461078	+	0.887359i	$0.652537\pi$
$998$	55.1880	1.74695
$999$	0.391168	0.0123760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.l.1.4		4
3.2	odd	2		5445.2.a.bg.1.1		4
4.3	odd	2		9680.2.a.cs.1.4		4
5.4	even	2		3025.2.a.v.1.1		4
11.2	odd	10		605.2.g.n.81.2		8
11.3	even	5		605.2.g.j.251.2		8
11.4	even	5		605.2.g.j.511.2		8
11.5	even	5		55.2.g.a.36.1	yes	8
11.6	odd	10		605.2.g.n.366.2		8
11.7	odd	10		605.2.g.g.511.1		8
11.8	odd	10		605.2.g.g.251.1		8
11.9	even	5		55.2.g.a.26.1	✓	8
11.10	odd	2		605.2.a.i.1.1		4
33.5	odd	10		495.2.n.f.91.2		8
33.20	odd	10		495.2.n.f.136.2		8
33.32	even	2		5445.2.a.bu.1.4		4
44.27	odd	10		880.2.bo.e.641.2		8
44.31	odd	10		880.2.bo.e.81.2		8
44.43	even	2		9680.2.a.cv.1.4		4
55.9	even	10		275.2.h.b.26.2		8
55.27	odd	20		275.2.z.b.124.1		16
55.38	odd	20		275.2.z.b.124.4		16
55.42	odd	20		275.2.z.b.224.4		16
55.49	even	10		275.2.h.b.201.2		8
55.53	odd	20		275.2.z.b.224.1		16
55.54	odd	2		3025.2.a.be.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	11.9	even	5
55.2.g.a.36.1	yes	8	11.5	even	5
275.2.h.b.26.2		8	55.9	even	10
275.2.h.b.201.2		8	55.49	even	10
275.2.z.b.124.1		16	55.27	odd	20
275.2.z.b.124.4		16	55.38	odd	20
275.2.z.b.224.1		16	55.53	odd	20
275.2.z.b.224.4		16	55.42	odd	20
495.2.n.f.91.2		8	33.5	odd	10
495.2.n.f.136.2		8	33.20	odd	10
605.2.a.i.1.1		4	11.10	odd	2
605.2.a.l.1.4		4	1.1	even	1	trivial
605.2.g.g.251.1		8	11.8	odd	10
605.2.g.g.511.1		8	11.7	odd	10
605.2.g.j.251.2		8	11.3	even	5
605.2.g.j.511.2		8	11.4	even	5
605.2.g.n.81.2		8	11.2	odd	10
605.2.g.n.366.2		8	11.6	odd	10
880.2.bo.e.81.2		8	44.31	odd	10
880.2.bo.e.641.2		8	44.27	odd	10
3025.2.a.v.1.1		4	5.4	even	2
3025.2.a.be.1.4		4	55.54	odd	2
5445.2.a.bg.1.1		4	3.2	odd	2
5445.2.a.bu.1.4		4	33.32	even	2
9680.2.a.cs.1.4		4	4.3	odd	2
9680.2.a.cv.1.4		4	44.43	even	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+2.52452 q^{2} -2.46673 q^{3} +4.37322 q^{4} +1.00000 q^{5} -6.22732 q^{6} +2.09351 q^{7} +5.99126 q^{8} +3.08477 q^{9} +O(q^{10})\)	\(q+2.52452 q^{2} -2.46673 q^{3} +4.37322 q^{4} +1.00000 q^{5} -6.22732 q^{6} +2.09351 q^{7} +5.99126 q^{8} +3.08477 q^{9} +2.52452 q^{10} -10.7876 q^{12} +1.28846 q^{13} +5.28512 q^{14} -2.46673 q^{15} +6.37863 q^{16} -2.99126 q^{17} +7.78757 q^{18} +2.15130 q^{19} +4.37322 q^{20} -5.16413 q^{21} +8.77882 q^{23} -14.7788 q^{24} +1.00000 q^{25} +3.25274 q^{26} -0.209094 q^{27} +9.15538 q^{28} -0.612630 q^{29} -6.22732 q^{30} -3.64501 q^{31} +4.12048 q^{32} -7.55150 q^{34} +2.09351 q^{35} +13.4904 q^{36} -1.87077 q^{37} +5.43101 q^{38} -3.17828 q^{39} +5.99126 q^{40} -5.10684 q^{41} -13.0370 q^{42} +5.17287 q^{43} +3.08477 q^{45} +22.1623 q^{46} -7.30669 q^{47} -15.7344 q^{48} -2.61722 q^{49} +2.52452 q^{50} +7.37863 q^{51} +5.63470 q^{52} -2.94221 q^{53} -0.527864 q^{54} +12.5428 q^{56} -5.30669 q^{57} -1.54660 q^{58} -6.49421 q^{59} -10.7876 q^{60} -0.502449 q^{61} -9.20191 q^{62} +6.45799 q^{63} -2.35499 q^{64} +1.28846 q^{65} -7.80964 q^{67} -13.0814 q^{68} -21.6550 q^{69} +5.28512 q^{70} -11.3042 q^{71} +18.4816 q^{72} -11.1171 q^{73} -4.72281 q^{74} -2.46673 q^{75} +9.40812 q^{76} -8.02363 q^{78} +5.35907 q^{79} +6.37863 q^{80} -8.73852 q^{81} -12.8923 q^{82} +10.8454 q^{83} -22.5839 q^{84} -2.99126 q^{85} +13.0590 q^{86} +1.51119 q^{87} -4.32336 q^{89} +7.78757 q^{90} +2.69740 q^{91} +38.3917 q^{92} +8.99126 q^{93} -18.4459 q^{94} +2.15130 q^{95} -10.1641 q^{96} -0.351653 q^{97} -6.60723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8	\( 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8} + 3 q^{10} - 14 q^{12} + 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 7 q^{20} - 6 q^{21} - 9 q^{23} - 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} + 7 q^{28} - 8 q^{29} - q^{30} + 3 q^{31} + 6 q^{32} - 10 q^{34} + 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} - 3 q^{39} + 9 q^{40} - 7 q^{41} + 2 q^{42} + 21 q^{43} + 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} + 3 q^{50} + 9 q^{51} + 27 q^{52} - 11 q^{53} - 20 q^{54} + 15 q^{56} + 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} + 4 q^{61} + 11 q^{62} + 3 q^{63} - 27 q^{64} + 7 q^{65} - q^{67} - 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} + 13 q^{72} - 9 q^{73} - 36 q^{74} - 2 q^{75} + 8 q^{76} + 6 q^{78} + 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} + 15 q^{83} - 47 q^{84} + 3 q^{85} - 3 q^{86} + 15 q^{87} + 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} - 11 q^{94} + 12 q^{95} - 26 q^{96} + 6 q^{97} - 42 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8 + 3 * q^10 - 14 * q^12 + 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 7 * q^20 - 6 * q^21 - 9 * q^23 - 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 + 7 * q^28 - 8 * q^29 - q^30 + 3 * q^31 + 6 * q^32 - 10 * q^34 + 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 - 3 * q^39 + 9 * q^40 - 7 * q^41 + 2 * q^42 + 21 * q^43 + 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 + 3 * q^50 + 9 * q^51 + 27 * q^52 - 11 * q^53 - 20 * q^54 + 15 * q^56 + 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 + 4 * q^61 + 11 * q^62 + 3 * q^63 - 27 * q^64 + 7 * q^65 - q^67 - 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 + 13 * q^72 - 9 * q^73 - 36 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^78 + 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 + 15 * q^83 - 47 * q^84 + 3 * q^85 - 3 * q^86 + 15 * q^87 + 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 - 11 * q^94 + 12 * q^95 - 26 * q^96 + 6 * q^97 - 42 * q^98

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