LMFDB - Embedded newform 4334.2.a.h.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.09175 q^{3} +1.00000 q^{4} -0.380034 q^{5} +2.09175 q^{6} -1.49841 q^{7} -1.00000 q^{8} +1.37543 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.09175 q^{3} +1.00000 q^{4} -0.380034 q^{5} +2.09175 q^{6} -1.49841 q^{7} -1.00000 q^{8} +1.37543 q^{9} +0.380034 q^{10} +1.00000 q^{11} -2.09175 q^{12} +1.60830 q^{13} +1.49841 q^{14} +0.794938 q^{15} +1.00000 q^{16} +6.61065 q^{17} -1.37543 q^{18} -0.573057 q^{19} -0.380034 q^{20} +3.13431 q^{21} -1.00000 q^{22} -3.81272 q^{23} +2.09175 q^{24} -4.85557 q^{25} -1.60830 q^{26} +3.39819 q^{27} -1.49841 q^{28} +9.18345 q^{29} -0.794938 q^{30} -1.45824 q^{31} -1.00000 q^{32} -2.09175 q^{33} -6.61065 q^{34} +0.569448 q^{35} +1.37543 q^{36} +4.67286 q^{37} +0.573057 q^{38} -3.36416 q^{39} +0.380034 q^{40} +0.891793 q^{41} -3.13431 q^{42} -0.403055 q^{43} +1.00000 q^{44} -0.522712 q^{45} +3.81272 q^{46} -10.9075 q^{47} -2.09175 q^{48} -4.75476 q^{49} +4.85557 q^{50} -13.8278 q^{51} +1.60830 q^{52} -3.85363 q^{53} -3.39819 q^{54} -0.380034 q^{55} +1.49841 q^{56} +1.19869 q^{57} -9.18345 q^{58} -8.39980 q^{59} +0.794938 q^{60} +1.75728 q^{61} +1.45824 q^{62} -2.06097 q^{63} +1.00000 q^{64} -0.611207 q^{65} +2.09175 q^{66} -6.95751 q^{67} +6.61065 q^{68} +7.97527 q^{69} -0.569448 q^{70} +11.3788 q^{71} -1.37543 q^{72} +16.1455 q^{73} -4.67286 q^{74} +10.1567 q^{75} -0.573057 q^{76} -1.49841 q^{77} +3.36416 q^{78} -1.96995 q^{79} -0.380034 q^{80} -11.2345 q^{81} -0.891793 q^{82} -4.74281 q^{83} +3.13431 q^{84} -2.51227 q^{85} +0.403055 q^{86} -19.2095 q^{87} -1.00000 q^{88} +12.6759 q^{89} +0.522712 q^{90} -2.40989 q^{91} -3.81272 q^{92} +3.05028 q^{93} +10.9075 q^{94} +0.217781 q^{95} +2.09175 q^{96} -6.54696 q^{97} +4.75476 q^{98} +1.37543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.09175	−1.20767	−0.603837	−	0.797108i	$-0.706362\pi$
$3$	−2.09175	−1.20767	−0.603837	+	0.797108i	$0.706362\pi$
$4$	1.00000	0.500000
$5$	−0.380034	−0.169956	−0.0849782	−	0.996383i	$-0.527082\pi$
$5$	−0.380034	−0.169956	−0.0849782	+	0.996383i	$0.527082\pi$
$6$	2.09175	0.853955
$7$	−1.49841	−0.566347	−0.283174	−	0.959069i	$-0.591387\pi$
$7$	−1.49841	−0.566347	−0.283174	+	0.959069i	$0.591387\pi$
$8$	−1.00000	−0.353553
$9$	1.37543	0.458478
$10$	0.380034	0.120177
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.09175	−0.603837
$13$	1.60830	0.446061	0.223030	−	0.974811i	$-0.428405\pi$
$13$	1.60830	0.446061	0.223030	+	0.974811i	$0.428405\pi$
$14$	1.49841	0.400468
$15$	0.794938	0.205252
$16$	1.00000	0.250000
$17$	6.61065	1.60332	0.801659	−	0.597782i	$-0.203951\pi$
$17$	6.61065	1.60332	0.801659	+	0.597782i	$0.203951\pi$
$18$	−1.37543	−0.324193
$19$	−0.573057	−0.131468	−0.0657342	−	0.997837i	$-0.520939\pi$
$19$	−0.573057	−0.131468	−0.0657342	+	0.997837i	$0.520939\pi$
$20$	−0.380034	−0.0849782
$21$	3.13431	0.683963
$22$	−1.00000	−0.213201
$23$	−3.81272	−0.795007	−0.397504	−	0.917601i	$-0.630123\pi$
$23$	−3.81272	−0.795007	−0.397504	+	0.917601i	$0.630123\pi$
$24$	2.09175	0.426977
$25$	−4.85557	−0.971115
$26$	−1.60830	−0.315413
$27$	3.39819	0.653983
$28$	−1.49841	−0.283174
$29$	9.18345	1.70532	0.852662	−	0.522463i	$-0.174987\pi$
$29$	9.18345	1.70532	0.852662	+	0.522463i	$0.174987\pi$
$30$	−0.794938	−0.145135
$31$	−1.45824	−0.261908	−0.130954	−	0.991388i	$-0.541804\pi$
$31$	−1.45824	−0.261908	−0.130954	+	0.991388i	$0.541804\pi$
$32$	−1.00000	−0.176777
$33$	−2.09175	−0.364128
$34$	−6.61065	−1.13372
$35$	0.569448	0.0962543
$36$	1.37543	0.229239
$37$	4.67286	0.768213	0.384107	−	0.923289i	$-0.374509\pi$
$37$	4.67286	0.768213	0.384107	+	0.923289i	$0.374509\pi$
$38$	0.573057	0.0929622
$39$	−3.36416	−0.538696
$40$	0.380034	0.0600887
$41$	0.891793	0.139275	0.0696373	−	0.997572i	$-0.477816\pi$
$41$	0.891793	0.139275	0.0696373	+	0.997572i	$0.477816\pi$
$42$	−3.13431	−0.483635
$43$	−0.403055	−0.0614653	−0.0307326	−	0.999528i	$-0.509784\pi$
$43$	−0.403055	−0.0614653	−0.0307326	+	0.999528i	$0.509784\pi$
$44$	1.00000	0.150756
$45$	−0.522712	−0.0779212
$46$	3.81272	0.562155
$47$	−10.9075	−1.59102	−0.795511	−	0.605939i	$-0.792798\pi$
$47$	−10.9075	−1.59102	−0.795511	+	0.605939i	$0.792798\pi$
$48$	−2.09175	−0.301919
$49$	−4.75476	−0.679251
$50$	4.85557	0.686682
$51$	−13.8278	−1.93629
$52$	1.60830	0.223030
$53$	−3.85363	−0.529337	−0.264668	−	0.964339i	$-0.585263\pi$
$53$	−3.85363	−0.529337	−0.264668	+	0.964339i	$0.585263\pi$
$54$	−3.39819	−0.462436
$55$	−0.380034	−0.0512438
$56$	1.49841	0.200234
$57$	1.19869	0.158771
$58$	−9.18345	−1.20585
$59$	−8.39980	−1.09356	−0.546781	−	0.837276i	$-0.684147\pi$
$59$	−8.39980	−1.09356	−0.546781	+	0.837276i	$0.684147\pi$
$60$	0.794938	0.102626
$61$	1.75728	0.224997	0.112498	−	0.993652i	$-0.464115\pi$
$61$	1.75728	0.224997	0.112498	+	0.993652i	$0.464115\pi$
$62$	1.45824	0.185197
$63$	−2.06097	−0.259658
$64$	1.00000	0.125000
$65$	−0.611207	−0.0758109
$66$	2.09175	0.257477
$67$	−6.95751	−0.849995	−0.424997	−	0.905195i	$-0.639725\pi$
$67$	−6.95751	−0.849995	−0.424997	+	0.905195i	$0.639725\pi$
$68$	6.61065	0.801659
$69$	7.97527	0.960110
$70$	−0.569448	−0.0680621
$71$	11.3788	1.35041	0.675207	−	0.737628i	$-0.264054\pi$
$71$	11.3788	1.35041	0.675207	+	0.737628i	$0.264054\pi$
$72$	−1.37543	−0.162096
$73$	16.1455	1.88968	0.944841	−	0.327528i	$-0.106216\pi$
$73$	16.1455	1.88968	0.944841	+	0.327528i	$0.106216\pi$
$74$	−4.67286	−0.543209
$75$	10.1567	1.17279
$76$	−0.573057	−0.0657342
$77$	−1.49841	−0.170760
$78$	3.36416	0.380916
$79$	−1.96995	−0.221637	−0.110818	−	0.993841i	$-0.535347\pi$
$79$	−1.96995	−0.221637	−0.110818	+	0.993841i	$0.535347\pi$
$80$	−0.380034	−0.0424891
$81$	−11.2345	−1.24828
$82$	−0.891793	−0.0984820
$83$	−4.74281	−0.520591	−0.260295	−	0.965529i	$-0.583820\pi$
$83$	−4.74281	−0.520591	−0.260295	+	0.965529i	$0.583820\pi$
$84$	3.13431	0.341981
$85$	−2.51227	−0.272494
$86$	0.403055	0.0434625
$87$	−19.2095	−2.05948
$88$	−1.00000	−0.106600
$89$	12.6759	1.34364	0.671821	−	0.740713i	$-0.265512\pi$
$89$	12.6759	1.34364	0.671821	+	0.740713i	$0.265512\pi$
$90$	0.522712	0.0550986
$91$	−2.40989	−0.252625
$92$	−3.81272	−0.397504
$93$	3.05028	0.316299
$94$	10.9075	1.12502
$95$	0.217781	0.0223439
$96$	2.09175	0.213489
$97$	−6.54696	−0.664743	−0.332372	−	0.943149i	$-0.607849\pi$
$97$	−6.54696	−0.664743	−0.332372	+	0.943149i	$0.607849\pi$
$98$	4.75476	0.480303
$99$	1.37543	0.138236
$100$	−4.85557	−0.485557
$101$	−14.0190	−1.39494	−0.697469	−	0.716615i	$-0.745691\pi$
$101$	−14.0190	−1.39494	−0.697469	+	0.716615i	$0.745691\pi$
$102$	13.8278	1.36916
$103$	2.81132	0.277008	0.138504	−	0.990362i	$-0.455771\pi$
$103$	2.81132	0.277008	0.138504	+	0.990362i	$0.455771\pi$
$104$	−1.60830	−0.157706
$105$	−1.19115	−0.116244
$106$	3.85363	0.374298
$107$	11.4172	1.10374	0.551871	−	0.833930i	$-0.313914\pi$
$107$	11.4172	1.10374	0.551871	+	0.833930i	$0.313914\pi$
$108$	3.39819	0.326991
$109$	2.21551	0.212207	0.106104	−	0.994355i	$-0.466162\pi$
$109$	2.21551	0.212207	0.106104	+	0.994355i	$0.466162\pi$
$110$	0.380034	0.0362348
$111$	−9.77447	−0.927752
$112$	−1.49841	−0.141587
$113$	−17.7519	−1.66995	−0.834977	−	0.550284i	$-0.814519\pi$
$113$	−17.7519	−1.66995	−0.834977	+	0.550284i	$0.814519\pi$
$114$	−1.19869	−0.112268
$115$	1.44896	0.135117
$116$	9.18345	0.852662
$117$	2.21210	0.204509
$118$	8.39980	0.773265
$119$	−9.90548	−0.908034
$120$	−0.794938	−0.0725676
$121$	1.00000	0.0909091
$122$	−1.75728	−0.159097
$123$	−1.86541	−0.168198
$124$	−1.45824	−0.130954
$125$	3.74545	0.335004
$126$	2.06097	0.183606
$127$	7.93048	0.703717	0.351858	−	0.936053i	$-0.385550\pi$
$127$	7.93048	0.703717	0.351858	+	0.936053i	$0.385550\pi$
$128$	−1.00000	−0.0883883
$129$	0.843092	0.0742301
$130$	0.611207	0.0536064
$131$	10.3313	0.902649	0.451325	−	0.892360i	$-0.350952\pi$
$131$	10.3313	0.902649	0.451325	+	0.892360i	$0.350952\pi$
$132$	−2.09175	−0.182064
$133$	0.858677	0.0744567
$134$	6.95751	0.601037
$135$	−1.29143	−0.111149
$136$	−6.61065	−0.566858
$137$	−11.9671	−1.02242	−0.511210	−	0.859456i	$-0.670803\pi$
$137$	−11.9671	−1.02242	−0.511210	+	0.859456i	$0.670803\pi$
$138$	−7.97527	−0.678900
$139$	−17.9078	−1.51892	−0.759459	−	0.650555i	$-0.774536\pi$
$139$	−17.9078	−1.51892	−0.759459	+	0.650555i	$0.774536\pi$
$140$	0.569448	0.0481272
$141$	22.8158	1.92144
$142$	−11.3788	−0.954887
$143$	1.60830	0.134492
$144$	1.37543	0.114619
$145$	−3.49003	−0.289831
$146$	−16.1455	−1.33621
$147$	9.94578	0.820314
$148$	4.67286	0.384107
$149$	6.99173	0.572785	0.286392	−	0.958112i	$-0.407544\pi$
$149$	6.99173	0.572785	0.286392	+	0.958112i	$0.407544\pi$
$150$	−10.1567	−0.829288
$151$	−5.53111	−0.450115	−0.225057	−	0.974345i	$-0.572257\pi$
$151$	−5.53111	−0.450115	−0.225057	+	0.974345i	$0.572257\pi$
$152$	0.573057	0.0464811
$153$	9.09250	0.735085
$154$	1.49841	0.120746
$155$	0.554181	0.0445129
$156$	−3.36416	−0.269348
$157$	−19.0713	−1.52206	−0.761028	−	0.648719i	$-0.775305\pi$
$157$	−19.0713	−1.52206	−0.761028	+	0.648719i	$0.775305\pi$
$158$	1.96995	0.156721
$159$	8.06085	0.639267
$160$	0.380034	0.0300443
$161$	5.71303	0.450250
$162$	11.2345	0.882664
$163$	15.0209	1.17653	0.588266	−	0.808668i	$-0.299811\pi$
$163$	15.0209	1.17653	0.588266	+	0.808668i	$0.299811\pi$
$164$	0.891793	0.0696373
$165$	0.794938	0.0618858
$166$	4.74281	0.368113
$167$	0.992973	0.0768386	0.0384193	−	0.999262i	$-0.487768\pi$
$167$	0.992973	0.0768386	0.0384193	+	0.999262i	$0.487768\pi$
$168$	−3.13431	−0.241817
$169$	−10.4134	−0.801030
$170$	2.51227	0.192682
$171$	−0.788202	−0.0602753
$172$	−0.403055	−0.0307326
$173$	11.8301	0.899424	0.449712	−	0.893174i	$-0.351527\pi$
$173$	11.8301	0.899424	0.449712	+	0.893174i	$0.351527\pi$
$174$	19.2095	1.45627
$175$	7.27566	0.549988
$176$	1.00000	0.0753778
$177$	17.5703	1.32067
$178$	−12.6759	−0.950099
$179$	14.4489	1.07996	0.539981	−	0.841677i	$-0.318431\pi$
$179$	14.4489	1.07996	0.539981	+	0.841677i	$0.318431\pi$
$180$	−0.522712	−0.0389606
$181$	21.8327	1.62281	0.811406	−	0.584482i	$-0.198702\pi$
$181$	21.8327	1.62281	0.811406	+	0.584482i	$0.198702\pi$
$182$	2.40989	0.178633
$183$	−3.67580	−0.271723
$184$	3.81272	0.281078
$185$	−1.77585	−0.130563
$186$	−3.05028	−0.223657
$187$	6.61065	0.483418
$188$	−10.9075	−0.795511
$189$	−5.09190	−0.370381
$190$	−0.217781	−0.0157995
$191$	16.4174	1.18792	0.593960	−	0.804494i	$-0.297564\pi$
$191$	16.4174	1.18792	0.593960	+	0.804494i	$0.297564\pi$
$192$	−2.09175	−0.150959
$193$	8.62225	0.620643	0.310322	−	0.950632i	$-0.399563\pi$
$193$	8.62225	0.620643	0.310322	+	0.950632i	$0.399563\pi$
$194$	6.54696	0.470044
$195$	1.27849	0.0915549
$196$	−4.75476	−0.339626
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−1.37543	−0.0977478
$199$	11.1169	0.788053	0.394027	−	0.919099i	$-0.371082\pi$
$199$	11.1169	0.788053	0.394027	+	0.919099i	$0.371082\pi$
$200$	4.85557	0.343341
$201$	14.5534	1.02652
$202$	14.0190	0.986370
$203$	−13.7606	−0.965805
$204$	−13.8278	−0.968143
$205$	−0.338912	−0.0236706
$206$	−2.81132	−0.195874
$207$	−5.24414	−0.364493
$208$	1.60830	0.111515
$209$	−0.573057	−0.0396392
$210$	1.19115	0.0821968
$211$	24.3125	1.67374	0.836872	−	0.547398i	$-0.184382\pi$
$211$	24.3125	1.67374	0.836872	+	0.547398i	$0.184382\pi$
$212$	−3.85363	−0.264668
$213$	−23.8016	−1.63086
$214$	−11.4172	−0.780463
$215$	0.153175	0.0104464
$216$	−3.39819	−0.231218
$217$	2.18505	0.148331
$218$	−2.21551	−0.150053
$219$	−33.7723	−2.28212
$220$	−0.380034	−0.0256219
$221$	10.6319	0.715177
$222$	9.77447	0.656020
$223$	−15.5608	−1.04203	−0.521014	−	0.853548i	$-0.674446\pi$
$223$	−15.5608	−1.04203	−0.521014	+	0.853548i	$0.674446\pi$
$224$	1.49841	0.100117
$225$	−6.67852	−0.445235
$226$	17.7519	1.18084
$227$	−23.6135	−1.56728	−0.783641	−	0.621214i	$-0.786640\pi$
$227$	−23.6135	−1.56728	−0.783641	+	0.621214i	$0.786640\pi$
$228$	1.19869	0.0793855
$229$	23.3205	1.54107	0.770533	−	0.637401i	$-0.219990\pi$
$229$	23.3205	1.54107	0.770533	+	0.637401i	$0.219990\pi$
$230$	−1.44896	−0.0955419
$231$	3.13431	0.206223
$232$	−9.18345	−0.602923
$233$	−19.0879	−1.25049	−0.625244	−	0.780429i	$-0.715001\pi$
$233$	−19.0879	−1.25049	−0.625244	+	0.780429i	$0.715001\pi$
$234$	−2.21210	−0.144610
$235$	4.14522	0.270405
$236$	−8.39980	−0.546781
$237$	4.12065	0.267665
$238$	9.90548	0.642077
$239$	−30.6521	−1.98272	−0.991361	−	0.131161i	$-0.958130\pi$
$239$	−30.6521	−1.98272	−0.991361	+	0.131161i	$0.958130\pi$
$240$	0.794938	0.0513130
$241$	21.7962	1.40402	0.702009	−	0.712168i	$-0.252287\pi$
$241$	21.7962	1.40402	0.702009	+	0.712168i	$0.252287\pi$
$242$	−1.00000	−0.0642824
$243$	13.3052	0.853528
$244$	1.75728	0.112498
$245$	1.80697	0.115443
$246$	1.86541	0.118934
$247$	−0.921645	−0.0586429
$248$	1.45824	0.0925983
$249$	9.92078	0.628704
$250$	−3.74545	−0.236883
$251$	6.38407	0.402959	0.201480	−	0.979493i	$-0.435425\pi$
$251$	6.38407	0.402959	0.201480	+	0.979493i	$0.435425\pi$
$252$	−2.06097	−0.129829
$253$	−3.81272	−0.239704
$254$	−7.93048	−0.497603
$255$	5.25505	0.329084
$256$	1.00000	0.0625000
$257$	−4.02898	−0.251321	−0.125660	−	0.992073i	$-0.540105\pi$
$257$	−4.02898	−0.251321	−0.125660	+	0.992073i	$0.540105\pi$
$258$	−0.843092	−0.0524886
$259$	−7.00188	−0.435075
$260$	−0.611207	−0.0379055
$261$	12.6312	0.781853
$262$	−10.3313	−0.638269
$263$	−4.26970	−0.263281	−0.131641	−	0.991298i	$-0.542024\pi$
$263$	−4.26970	−0.263281	−0.131641	+	0.991298i	$0.542024\pi$
$264$	2.09175	0.128739
$265$	1.46451	0.0899642
$266$	−0.858677	−0.0526488
$267$	−26.5149	−1.62268
$268$	−6.95751	−0.424997
$269$	−24.5744	−1.49833	−0.749165	−	0.662383i	$-0.769545\pi$
$269$	−24.5744	−1.49833	−0.749165	+	0.662383i	$0.769545\pi$
$270$	1.29143	0.0785939
$271$	24.9683	1.51672	0.758360	−	0.651836i	$-0.226001\pi$
$271$	24.9683	1.51672	0.758360	+	0.651836i	$0.226001\pi$
$272$	6.61065	0.400829
$273$	5.04090	0.305089
$274$	11.9671	0.722961
$275$	−4.85557	−0.292802
$276$	7.97527	0.480055
$277$	8.68105	0.521594	0.260797	−	0.965394i	$-0.416015\pi$
$277$	8.68105	0.521594	0.260797	+	0.965394i	$0.416015\pi$
$278$	17.9078	1.07404
$279$	−2.00571	−0.120079
$280$	−0.569448	−0.0340310
$281$	10.3017	0.614547	0.307274	−	0.951621i	$-0.400583\pi$
$281$	10.3017	0.614547	0.307274	+	0.951621i	$0.400583\pi$
$282$	−22.8158	−1.35866
$283$	−27.4825	−1.63367	−0.816833	−	0.576874i	$-0.804272\pi$
$283$	−27.4825	−1.63367	−0.816833	+	0.576874i	$0.804272\pi$
$284$	11.3788	0.675207
$285$	−0.455545	−0.0269841
$286$	−1.60830	−0.0951005
$287$	−1.33627	−0.0788778
$288$	−1.37543	−0.0810482
$289$	26.7007	1.57063
$290$	3.49003	0.204941
$291$	13.6946	0.802793
$292$	16.1455	0.944841
$293$	−5.14872	−0.300792	−0.150396	−	0.988626i	$-0.548055\pi$
$293$	−5.14872	−0.300792	−0.150396	+	0.988626i	$0.548055\pi$
$294$	−9.94578	−0.580050
$295$	3.19221	0.185858
$296$	−4.67286	−0.271604
$297$	3.39819	0.197183
$298$	−6.99173	−0.405020
$299$	−6.13198	−0.354622
$300$	10.1567	0.586395
$301$	0.603943	0.0348107
$302$	5.53111	0.318279
$303$	29.3242	1.68463
$304$	−0.573057	−0.0328671
$305$	−0.667826	−0.0382396
$306$	−9.09250	−0.519784
$307$	4.72634	0.269746	0.134873	−	0.990863i	$-0.456937\pi$
$307$	4.72634	0.269746	0.134873	+	0.990863i	$0.456937\pi$
$308$	−1.49841	−0.0853800
$309$	−5.88060	−0.334536
$310$	−0.554181	−0.0314754
$311$	25.9021	1.46877	0.734386	−	0.678732i	$-0.237470\pi$
$311$	25.9021	1.46877	0.734386	+	0.678732i	$0.237470\pi$
$312$	3.36416	0.190458
$313$	20.0231	1.13177	0.565886	−	0.824484i	$-0.308534\pi$
$313$	20.0231	1.13177	0.565886	+	0.824484i	$0.308534\pi$
$314$	19.0713	1.07626
$315$	0.783238	0.0441305
$316$	−1.96995	−0.110818
$317$	14.8565	0.834422	0.417211	−	0.908810i	$-0.363008\pi$
$317$	14.8565	0.834422	0.417211	+	0.908810i	$0.363008\pi$
$318$	−8.06085	−0.452030
$319$	9.18345	0.514175
$320$	−0.380034	−0.0212446
$321$	−23.8819	−1.33296
$322$	−5.71303	−0.318375
$323$	−3.78828	−0.210785
$324$	−11.2345	−0.624138
$325$	−7.80920	−0.433176
$326$	−15.0209	−0.831933
$327$	−4.63430	−0.256278
$328$	−0.891793	−0.0492410
$329$	16.3439	0.901071
$330$	−0.794938	−0.0437599
$331$	28.9209	1.58964	0.794818	−	0.606847i	$-0.207566\pi$
$331$	28.9209	1.58964	0.794818	+	0.606847i	$0.207566\pi$
$332$	−4.74281	−0.260295
$333$	6.42721	0.352209
$334$	−0.992973	−0.0543331
$335$	2.64409	0.144462
$336$	3.13431	0.170991
$337$	32.0663	1.74676	0.873381	−	0.487038i	$-0.161923\pi$
$337$	32.0663	1.74676	0.873381	+	0.487038i	$0.161923\pi$
$338$	10.4134	0.566413
$339$	37.1325	2.01676
$340$	−2.51227	−0.136247
$341$	−1.45824	−0.0789681
$342$	0.788202	0.0426211
$343$	17.6135	0.951039
$344$	0.403055	0.0217313
$345$	−3.03088	−0.163177
$346$	−11.8301	−0.635989
$347$	0.297990	0.0159970	0.00799848	−	0.999968i	$-0.497454\pi$
$347$	0.297990	0.0159970	0.00799848	+	0.999968i	$0.497454\pi$
$348$	−19.2095	−1.02974
$349$	18.2340	0.976043	0.488022	−	0.872832i	$-0.337719\pi$
$349$	18.2340	0.976043	0.488022	+	0.872832i	$0.337719\pi$
$350$	−7.27566	−0.388900
$351$	5.46530	0.291716
$352$	−1.00000	−0.0533002
$353$	16.1112	0.857514	0.428757	−	0.903420i	$-0.358952\pi$
$353$	16.1112	0.857514	0.428757	+	0.903420i	$0.358952\pi$
$354$	−17.5703	−0.933852
$355$	−4.32433	−0.229512
$356$	12.6759	0.671821
$357$	20.7198	1.09661
$358$	−14.4489	−0.763648
$359$	−5.19060	−0.273949	−0.136975	−	0.990575i	$-0.543738\pi$
$359$	−5.19060	−0.273949	−0.136975	+	0.990575i	$0.543738\pi$
$360$	0.522712	0.0275493
$361$	−18.6716	−0.982716
$362$	−21.8327	−1.14750
$363$	−2.09175	−0.109789
$364$	−2.40989	−0.126313
$365$	−6.13582	−0.321164
$366$	3.67580	0.192137
$367$	−12.8577	−0.671165	−0.335582	−	0.942011i	$-0.608933\pi$
$367$	−12.8577	−0.671165	−0.335582	+	0.942011i	$0.608933\pi$
$368$	−3.81272	−0.198752
$369$	1.22660	0.0638543
$370$	1.77585	0.0923218
$371$	5.77433	0.299788
$372$	3.05028	0.158150
$373$	27.9807	1.44879	0.724393	−	0.689388i	$-0.242120\pi$
$373$	27.9807	1.44879	0.724393	+	0.689388i	$0.242120\pi$
$374$	−6.61065	−0.341828
$375$	−7.83457	−0.404575
$376$	10.9075	0.562511
$377$	14.7697	0.760679
$378$	5.09190	0.261899
$379$	11.8170	0.606998	0.303499	−	0.952832i	$-0.401845\pi$
$379$	11.8170	0.606998	0.303499	+	0.952832i	$0.401845\pi$
$380$	0.217781	0.0111719
$381$	−16.5886	−0.849861
$382$	−16.4174	−0.839986
$383$	0.798495	0.0408012	0.0204006	−	0.999792i	$-0.493506\pi$
$383$	0.798495	0.0408012	0.0204006	+	0.999792i	$0.493506\pi$
$384$	2.09175	0.106744
$385$	0.569448	0.0290218
$386$	−8.62225	−0.438861
$387$	−0.554375	−0.0281805
$388$	−6.54696	−0.332372
$389$	25.2877	1.28214	0.641068	−	0.767484i	$-0.278491\pi$
$389$	25.2877	1.28214	0.641068	+	0.767484i	$0.278491\pi$
$390$	−1.27849	−0.0647391
$391$	−25.2046	−1.27465
$392$	4.75476	0.240152
$393$	−21.6105	−1.09011
$394$	1.00000	0.0503793
$395$	0.748648	0.0376686
$396$	1.37543	0.0691181
$397$	1.61247	0.0809273	0.0404637	−	0.999181i	$-0.487116\pi$
$397$	1.61247	0.0809273	0.0404637	+	0.999181i	$0.487116\pi$
$398$	−11.1169	−0.557238
$399$	−1.79614	−0.0899195
$400$	−4.85557	−0.242779
$401$	31.3434	1.56522	0.782608	−	0.622515i	$-0.213889\pi$
$401$	31.3434	1.56522	0.782608	+	0.622515i	$0.213889\pi$
$402$	−14.5534	−0.725857
$403$	−2.34528	−0.116827
$404$	−14.0190	−0.697469
$405$	4.26949	0.212153
$406$	13.7606	0.682928
$407$	4.67286	0.231625
$408$	13.8278	0.684580
$409$	−0.918545	−0.0454191	−0.0227096	−	0.999742i	$-0.507229\pi$
$409$	−0.918545	−0.0454191	−0.0227096	+	0.999742i	$0.507229\pi$
$410$	0.338912	0.0167377
$411$	25.0323	1.23475
$412$	2.81132	0.138504
$413$	12.5864	0.619335
$414$	5.24414	0.257736
$415$	1.80243	0.0884777
$416$	−1.60830	−0.0788532
$417$	37.4587	1.83436
$418$	0.573057	0.0280291
$419$	4.23530	0.206908	0.103454	−	0.994634i	$-0.467011\pi$
$419$	4.23530	0.206908	0.103454	+	0.994634i	$0.467011\pi$
$420$	−1.19115	−0.0581219
$421$	35.4799	1.72919	0.864593	−	0.502473i	$-0.167576\pi$
$421$	35.4799	1.72919	0.864593	+	0.502473i	$0.167576\pi$
$422$	−24.3125	−1.18352
$423$	−15.0025	−0.729448
$424$	3.85363	0.187149
$425$	−32.0985	−1.55701
$426$	23.8016	1.15319
$427$	−2.63313	−0.127426
$428$	11.4172	0.551871
$429$	−3.36416	−0.162423
$430$	−0.153175	−0.00738674
$431$	−20.0951	−0.967948	−0.483974	−	0.875083i	$-0.660807\pi$
$431$	−20.0951	−0.967948	−0.483974	+	0.875083i	$0.660807\pi$
$432$	3.39819	0.163496
$433$	12.8202	0.616098	0.308049	−	0.951371i	$-0.400324\pi$
$433$	12.8202	0.616098	0.308049	+	0.951371i	$0.400324\pi$
$434$	−2.18505	−0.104886
$435$	7.30027	0.350021
$436$	2.21551	0.106104
$437$	2.18491	0.104518
$438$	33.7723	1.61370
$439$	−0.840206	−0.0401008	−0.0200504	−	0.999799i	$-0.506383\pi$
$439$	−0.840206	−0.0401008	−0.0200504	+	0.999799i	$0.506383\pi$
$440$	0.380034	0.0181174
$441$	−6.53985	−0.311421
$442$	−10.6319	−0.505707
$443$	−34.1949	−1.62465	−0.812323	−	0.583207i	$-0.801798\pi$
$443$	−34.1949	−1.62465	−0.812323	+	0.583207i	$0.801798\pi$
$444$	−9.77447	−0.463876
$445$	−4.81727	−0.228361
$446$	15.5608	0.736826
$447$	−14.6250	−0.691738
$448$	−1.49841	−0.0707934
$449$	1.61098	0.0760269	0.0380134	−	0.999277i	$-0.487897\pi$
$449$	1.61098	0.0760269	0.0380134	+	0.999277i	$0.487897\pi$
$450$	6.67852	0.314828
$451$	0.891793	0.0419929
$452$	−17.7519	−0.834977
$453$	11.5697	0.543592
$454$	23.6135	1.10824
$455$	0.915841	0.0429353
$456$	−1.19869	−0.0561340
$457$	20.5285	0.960283	0.480142	−	0.877191i	$-0.340585\pi$
$457$	20.5285	0.960283	0.480142	+	0.877191i	$0.340585\pi$
$458$	−23.3205	−1.08970
$459$	22.4643	1.04854
$460$	1.44896	0.0675583
$461$	−3.59147	−0.167271	−0.0836357	−	0.996496i	$-0.526653\pi$
$461$	−3.59147	−0.167271	−0.0836357	+	0.996496i	$0.526653\pi$
$462$	−3.13431	−0.145821
$463$	12.5127	0.581515	0.290757	−	0.956797i	$-0.406093\pi$
$463$	12.5127	0.581515	0.290757	+	0.956797i	$0.406093\pi$
$464$	9.18345	0.426331
$465$	−1.15921	−0.0537571
$466$	19.0879	0.884229
$467$	38.7635	1.79376	0.896880	−	0.442274i	$-0.145828\pi$
$467$	38.7635	1.79376	0.896880	+	0.442274i	$0.145828\pi$
$468$	2.21210	0.102255
$469$	10.4252	0.481392
$470$	−4.14522	−0.191205
$471$	39.8925	1.83815
$472$	8.39980	0.386632
$473$	−0.403055	−0.0185325
$474$	−4.12065	−0.189268
$475$	2.78252	0.127671
$476$	−9.90548	−0.454017
$477$	−5.30041	−0.242689
$478$	30.6521	1.40200
$479$	43.2609	1.97664	0.988320	−	0.152392i	$-0.0486976\pi$
$479$	43.2609	1.97664	0.988320	+	0.152392i	$0.0486976\pi$
$480$	−0.794938	−0.0362838
$481$	7.51534	0.342670
$482$	−21.7962	−0.992791
$483$	−11.9503	−0.543755
$484$	1.00000	0.0454545
$485$	2.48807	0.112977
$486$	−13.3052	−0.603536
$487$	−25.6206	−1.16098	−0.580489	−	0.814268i	$-0.697139\pi$
$487$	−25.6206	−1.16098	−0.580489	+	0.814268i	$0.697139\pi$
$488$	−1.75728	−0.0795483
$489$	−31.4201	−1.42087
$490$	−1.80697	−0.0816306
$491$	−21.6586	−0.977440	−0.488720	−	0.872441i	$-0.662536\pi$
$491$	−21.6586	−0.977440	−0.488720	+	0.872441i	$0.662536\pi$
$492$	−1.86541	−0.0840992
$493$	60.7086	2.73418
$494$	0.921645	0.0414668
$495$	−0.522712	−0.0234941
$496$	−1.45824	−0.0654769
$497$	−17.0501	−0.764803
$498$	−9.92078	−0.444561
$499$	6.72973	0.301264	0.150632	−	0.988590i	$-0.451869\pi$
$499$	6.72973	0.301264	0.150632	+	0.988590i	$0.451869\pi$
$500$	3.74545	0.167502
$501$	−2.07706	−0.0927960
$502$	−6.38407	−0.284935
$503$	12.5712	0.560520	0.280260	−	0.959924i	$-0.409579\pi$
$503$	12.5712	0.560520	0.280260	+	0.959924i	$0.409579\pi$
$504$	2.06097	0.0918028
$505$	5.32768	0.237079
$506$	3.81272	0.169496
$507$	21.7822	0.967383
$508$	7.93048	0.351858
$509$	−22.0507	−0.977378	−0.488689	−	0.872458i	$-0.662525\pi$
$509$	−22.0507	−0.977378	−0.488689	+	0.872458i	$0.662525\pi$
$510$	−5.25505	−0.232698
$511$	−24.1926	−1.07022
$512$	−1.00000	−0.0441942
$513$	−1.94736	−0.0859780
$514$	4.02898	0.177711
$515$	−1.06840	−0.0470793
$516$	0.843092	0.0371150
$517$	−10.9075	−0.479711
$518$	7.00188	0.307645
$519$	−24.7456	−1.08621
$520$	0.611207	0.0268032
$521$	−21.1089	−0.924798	−0.462399	−	0.886672i	$-0.653011\pi$
$521$	−21.1089	−0.924798	−0.462399	+	0.886672i	$0.653011\pi$
$522$	−12.6312	−0.552854
$523$	−1.14752	−0.0501777	−0.0250889	−	0.999685i	$-0.507987\pi$
$523$	−1.14752	−0.0501777	−0.0250889	+	0.999685i	$0.507987\pi$
$524$	10.3313	0.451325
$525$	−15.2189	−0.664206
$526$	4.26970	0.186168
$527$	−9.63991	−0.419921
$528$	−2.09175	−0.0910319
$529$	−8.46316	−0.367963
$530$	−1.46451	−0.0636143
$531$	−11.5534	−0.501373
$532$	0.858677	0.0372284
$533$	1.43427	0.0621250
$534$	26.5149	1.14741
$535$	−4.33892	−0.187588
$536$	6.95751	0.300519
$537$	−30.2235	−1.30424
$538$	24.5744	1.05948
$539$	−4.75476	−0.204802
$540$	−1.29143	−0.0555743
$541$	−45.9963	−1.97753	−0.988767	−	0.149467i	$-0.952244\pi$
$541$	−45.9963	−1.97753	−0.988767	+	0.149467i	$0.952244\pi$
$542$	−24.9683	−1.07248
$543$	−45.6687	−1.95983
$544$	−6.61065	−0.283429
$545$	−0.841970	−0.0360660
$546$	−5.04090	−0.215731
$547$	33.0958	1.41507	0.707537	−	0.706676i	$-0.249806\pi$
$547$	33.0958	1.41507	0.707537	+	0.706676i	$0.249806\pi$
$548$	−11.9671	−0.511210
$549$	2.41702	0.103156
$550$	4.85557	0.207042
$551$	−5.26264	−0.224196
$552$	−7.97527	−0.339450
$553$	2.95180	0.125523
$554$	−8.68105	−0.368822
$555$	3.71463	0.157677
$556$	−17.9078	−0.759459
$557$	−3.92662	−0.166376	−0.0831881	−	0.996534i	$-0.526510\pi$
$557$	−3.92662	−0.166376	−0.0831881	+	0.996534i	$0.526510\pi$
$558$	2.00571	0.0849085
$559$	−0.648231	−0.0274173
$560$	0.569448	0.0240636
$561$	−13.8278	−0.583812
$562$	−10.3017	−0.434550
$563$	−10.0467	−0.423418	−0.211709	−	0.977333i	$-0.567903\pi$
$563$	−10.0467	−0.423418	−0.211709	+	0.977333i	$0.567903\pi$
$564$	22.8158	0.960719
$565$	6.74631	0.283820
$566$	27.4825	1.15518
$567$	16.8339	0.706957
$568$	−11.3788	−0.477444
$569$	37.6849	1.57983	0.789917	−	0.613214i	$-0.210124\pi$
$569$	37.6849	1.57983	0.789917	+	0.613214i	$0.210124\pi$
$570$	0.455545	0.0190807
$571$	22.0205	0.921527	0.460764	−	0.887523i	$-0.347576\pi$
$571$	22.0205	0.921527	0.460764	+	0.887523i	$0.347576\pi$
$572$	1.60830	0.0672462
$573$	−34.3411	−1.43462
$574$	1.33627	0.0557750
$575$	18.5129	0.772043
$576$	1.37543	0.0573097
$577$	8.92536	0.371568	0.185784	−	0.982591i	$-0.440518\pi$
$577$	8.92536	0.371568	0.185784	+	0.982591i	$0.440518\pi$
$578$	−26.7007	−1.11060
$579$	−18.0356	−0.749535
$580$	−3.49003	−0.144915
$581$	7.10669	0.294835
$582$	−13.6946	−0.567661
$583$	−3.85363	−0.159601
$584$	−16.1455	−0.668104
$585$	−0.840675	−0.0347576
$586$	5.14872	0.212692
$587$	−20.5394	−0.847753	−0.423877	−	0.905720i	$-0.639331\pi$
$587$	−20.5394	−0.847753	−0.423877	+	0.905720i	$0.639331\pi$
$588$	9.94578	0.410157
$589$	0.835655	0.0344326
$590$	−3.19221	−0.131421
$591$	2.09175	0.0860432
$592$	4.67286	0.192053
$593$	16.1011	0.661194	0.330597	−	0.943772i	$-0.392750\pi$
$593$	16.1011	0.661194	0.330597	+	0.943772i	$0.392750\pi$
$594$	−3.39819	−0.139430
$595$	3.76442	0.154326
$596$	6.99173	0.286392
$597$	−23.2537	−0.951712
$598$	6.13198	0.250755
$599$	−15.5620	−0.635847	−0.317923	−	0.948116i	$-0.602985\pi$
$599$	−15.5620	−0.635847	−0.317923	+	0.948116i	$0.602985\pi$
$600$	−10.1567	−0.414644
$601$	30.4861	1.24356	0.621778	−	0.783194i	$-0.286411\pi$
$601$	30.4861	1.24356	0.621778	+	0.783194i	$0.286411\pi$
$602$	−0.603943	−0.0246149
$603$	−9.56959	−0.389704
$604$	−5.53111	−0.225057
$605$	−0.380034	−0.0154506
$606$	−29.3242	−1.19121
$607$	22.8879	0.928990	0.464495	−	0.885576i	$-0.346236\pi$
$607$	22.8879	0.928990	0.464495	+	0.885576i	$0.346236\pi$
$608$	0.573057	0.0232405
$609$	28.7838	1.16638
$610$	0.667826	0.0270395
$611$	−17.5425	−0.709693
$612$	9.09250	0.367543
$613$	20.8190	0.840872	0.420436	−	0.907322i	$-0.361877\pi$
$613$	20.8190	0.840872	0.420436	+	0.907322i	$0.361877\pi$
$614$	−4.72634	−0.190740
$615$	0.708920	0.0285864
$616$	1.49841	0.0603728
$617$	−10.7404	−0.432392	−0.216196	−	0.976350i	$-0.569365\pi$
$617$	−10.7404	−0.432392	−0.216196	+	0.976350i	$0.569365\pi$
$618$	5.88060	0.236552
$619$	34.9649	1.40536	0.702678	−	0.711508i	$-0.251987\pi$
$619$	34.9649	1.40536	0.702678	+	0.711508i	$0.251987\pi$
$620$	0.554181	0.0222564
$621$	−12.9564	−0.519921
$622$	−25.9021	−1.03858
$623$	−18.9937	−0.760968
$624$	−3.36416	−0.134674
$625$	22.8545	0.914179
$626$	−20.0231	−0.800283
$627$	1.19869	0.0478712
$628$	−19.0713	−0.761028
$629$	30.8906	1.23169
$630$	−0.783238	−0.0312049
$631$	−26.2104	−1.04342	−0.521710	−	0.853123i	$-0.674706\pi$
$631$	−26.2104	−1.04342	−0.521710	+	0.853123i	$0.674706\pi$
$632$	1.96995	0.0783604
$633$	−50.8559	−2.02134
$634$	−14.8565	−0.590026
$635$	−3.01385	−0.119601
$636$	8.06085	0.319633
$637$	−7.64705	−0.302987
$638$	−9.18345	−0.363576
$639$	15.6508	0.619135
$640$	0.380034	0.0150222
$641$	37.2047	1.46950	0.734749	−	0.678339i	$-0.237300\pi$
$641$	37.2047	1.46950	0.734749	+	0.678339i	$0.237300\pi$
$642$	23.8819	0.942545
$643$	−8.81707	−0.347711	−0.173856	−	0.984771i	$-0.555623\pi$
$643$	−8.81707	−0.347711	−0.173856	+	0.984771i	$0.555623\pi$
$644$	5.71303	0.225125
$645$	−0.320404	−0.0126159
$646$	3.78828	0.149048
$647$	37.3374	1.46788	0.733942	−	0.679212i	$-0.237678\pi$
$647$	37.3374	1.46788	0.733942	+	0.679212i	$0.237678\pi$
$648$	11.2345	0.441332
$649$	−8.39980	−0.329721
$650$	7.80920	0.306302
$651$	−4.57058	−0.179135
$652$	15.0209	0.588266
$653$	−46.0838	−1.80340	−0.901700	−	0.432363i	$-0.857680\pi$
$653$	−46.0838	−1.80340	−0.901700	+	0.432363i	$0.857680\pi$
$654$	4.63430	0.181216
$655$	−3.92624	−0.153411
$656$	0.891793	0.0348187
$657$	22.2070	0.866378
$658$	−16.3439	−0.637153
$659$	−2.71355	−0.105705	−0.0528525	−	0.998602i	$-0.516831\pi$
$659$	−2.71355	−0.105705	−0.0528525	+	0.998602i	$0.516831\pi$
$660$	0.794938	0.0309429
$661$	−21.8131	−0.848433	−0.424216	−	0.905561i	$-0.639450\pi$
$661$	−21.8131	−0.848433	−0.424216	+	0.905561i	$0.639450\pi$
$662$	−28.9209	−1.12404
$663$	−22.2393	−0.863701
$664$	4.74281	0.184057
$665$	−0.326326	−0.0126544
$666$	−6.42721	−0.249049
$667$	−35.0139	−1.35575
$668$	0.992973	0.0384193
$669$	32.5494	1.25843
$670$	−2.64409	−0.102150
$671$	1.75728	0.0678390
$672$	−3.13431	−0.120909
$673$	−12.3371	−0.475562	−0.237781	−	0.971319i	$-0.576420\pi$
$673$	−12.3371	−0.475562	−0.237781	+	0.971319i	$0.576420\pi$
$674$	−32.0663	−1.23515
$675$	−16.5002	−0.635092
$676$	−10.4134	−0.400515
$677$	33.5748	1.29039	0.645193	−	0.764020i	$-0.276777\pi$
$677$	33.5748	1.29039	0.645193	+	0.764020i	$0.276777\pi$
$678$	−37.1325	−1.42607
$679$	9.81005	0.376475
$680$	2.51227	0.0963412
$681$	49.3936	1.89277
$682$	1.45824	0.0558389
$683$	−23.5535	−0.901250	−0.450625	−	0.892713i	$-0.648799\pi$
$683$	−23.5535	−0.901250	−0.450625	+	0.892713i	$0.648799\pi$
$684$	−0.788202	−0.0301377
$685$	4.54792	0.173767
$686$	−17.6135	−0.672486
$687$	−48.7808	−1.86111
$688$	−0.403055	−0.0153663
$689$	−6.19778	−0.236116
$690$	3.03088	0.115383
$691$	−4.09107	−0.155632	−0.0778158	−	0.996968i	$-0.524795\pi$
$691$	−4.09107	−0.155632	−0.0778158	+	0.996968i	$0.524795\pi$
$692$	11.8301	0.449712
$693$	−2.06097	−0.0782897
$694$	−0.297990	−0.0113116
$695$	6.80557	0.258150
$696$	19.2095	0.728135
$697$	5.89533	0.223301
$698$	−18.2340	−0.690167
$699$	39.9272	1.51018
$700$	7.27566	0.274994
$701$	−21.3404	−0.806015	−0.403007	−	0.915197i	$-0.632035\pi$
$701$	−21.3404	−0.806015	−0.403007	+	0.915197i	$0.632035\pi$
$702$	−5.46530	−0.206274
$703$	−2.67782	−0.100996
$704$	1.00000	0.0376889
$705$	−8.67078	−0.326561
$706$	−16.1112	−0.606354
$707$	21.0062	0.790019
$708$	17.5703	0.660333
$709$	−32.4020	−1.21688	−0.608441	−	0.793599i	$-0.708205\pi$
$709$	−32.4020	−1.21688	−0.608441	+	0.793599i	$0.708205\pi$
$710$	4.32433	0.162289
$711$	−2.70953	−0.101615
$712$	−12.6759	−0.475049
$713$	5.55986	0.208218
$714$	−20.7198	−0.775420
$715$	−0.611207	−0.0228579
$716$	14.4489	0.539981
$717$	64.1167	2.39448
$718$	5.19060	0.193711
$719$	31.6933	1.18196	0.590980	−	0.806686i	$-0.298741\pi$
$719$	31.6933	1.18196	0.590980	+	0.806686i	$0.298741\pi$
$720$	−0.522712	−0.0194803
$721$	−4.21253	−0.156883
$722$	18.6716	0.694885
$723$	−45.5923	−1.69560
$724$	21.8327	0.811406
$725$	−44.5909	−1.65607
$726$	2.09175	0.0776323
$727$	−46.1809	−1.71276	−0.856378	−	0.516349i	$-0.827291\pi$
$727$	−46.1809	−1.71276	−0.856378	+	0.516349i	$0.827291\pi$
$728$	2.40989	0.0893165
$729$	5.87227	0.217491
$730$	6.13582	0.227097
$731$	−2.66445	−0.0985484
$732$	−3.67580	−0.135861
$733$	−20.4942	−0.756969	−0.378485	−	0.925608i	$-0.623555\pi$
$733$	−20.4942	−0.756969	−0.378485	+	0.925608i	$0.623555\pi$
$734$	12.8577	0.474585
$735$	−3.77974	−0.139418
$736$	3.81272	0.140539
$737$	−6.95751	−0.256283
$738$	−1.22660	−0.0451518
$739$	−49.1990	−1.80981	−0.904906	−	0.425610i	$-0.860059\pi$
$739$	−49.1990	−1.80981	−0.904906	+	0.425610i	$0.860059\pi$
$740$	−1.77585	−0.0652814
$741$	1.92786	0.0708215
$742$	−5.77433	−0.211982
$743$	−19.3068	−0.708296	−0.354148	−	0.935189i	$-0.615229\pi$
$743$	−19.3068	−0.708296	−0.354148	+	0.935189i	$0.615229\pi$
$744$	−3.05028	−0.111829
$745$	−2.65710	−0.0973485
$746$	−27.9807	−1.02445
$747$	−6.52341	−0.238679
$748$	6.61065	0.241709
$749$	−17.1077	−0.625101
$750$	7.83457	0.286078
$751$	11.2797	0.411601	0.205800	−	0.978594i	$-0.434020\pi$
$751$	11.2797	0.411601	0.205800	+	0.978594i	$0.434020\pi$
$752$	−10.9075	−0.397756
$753$	−13.3539	−0.486643
$754$	−14.7697	−0.537881
$755$	2.10201	0.0764999
$756$	−5.09190	−0.185191
$757$	12.2202	0.444152	0.222076	−	0.975029i	$-0.428717\pi$
$757$	12.2202	0.444152	0.222076	+	0.975029i	$0.428717\pi$
$758$	−11.8170	−0.429212
$759$	7.97527	0.289484
$760$	−0.217781	−0.00789976
$761$	14.2073	0.515014	0.257507	−	0.966276i	$-0.417099\pi$
$761$	14.2073	0.515014	0.257507	+	0.966276i	$0.417099\pi$
$762$	16.5886	0.600942
$763$	−3.31975	−0.120183
$764$	16.4174	0.593960
$765$	−3.45546	−0.124932
$766$	−0.798495	−0.0288508
$767$	−13.5094	−0.487795
$768$	−2.09175	−0.0754797
$769$	34.6902	1.25096	0.625481	−	0.780240i	$-0.284903\pi$
$769$	34.6902	1.25096	0.625481	+	0.780240i	$0.284903\pi$
$770$	−0.569448	−0.0205215
$771$	8.42763	0.303514
$772$	8.62225	0.310322
$773$	12.5791	0.452438	0.226219	−	0.974076i	$-0.427363\pi$
$773$	12.5791	0.452438	0.226219	+	0.974076i	$0.427363\pi$
$774$	0.554375	0.0199266
$775$	7.08059	0.254342
$776$	6.54696	0.235022
$777$	14.6462	0.525429
$778$	−25.2877	−0.906608
$779$	−0.511048	−0.0183102
$780$	1.27849	0.0457775
$781$	11.3788	0.407165
$782$	25.2046	0.901313
$783$	31.2071	1.11525
$784$	−4.75476	−0.169813
$785$	7.24775	0.258683
$786$	21.6105	0.770822
$787$	−45.7590	−1.63113	−0.815565	−	0.578665i	$-0.803574\pi$
$787$	−45.7590	−1.63113	−0.815565	+	0.578665i	$0.803574\pi$
$788$	−1.00000	−0.0356235
$789$	8.93117	0.317958
$790$	−0.748648	−0.0266357
$791$	26.5996	0.945774
$792$	−1.37543	−0.0488739
$793$	2.82623	0.100362
$794$	−1.61247	−0.0572243
$795$	−3.06340	−0.108647
$796$	11.1169	0.394027
$797$	−37.6553	−1.33382	−0.666909	−	0.745139i	$-0.732383\pi$
$797$	−37.6553	−1.33382	−0.666909	+	0.745139i	$0.732383\pi$
$798$	1.79614	0.0635827
$799$	−72.1056	−2.55091
$800$	4.85557	0.171670
$801$	17.4348	0.616030
$802$	−31.3434	−1.10678
$803$	16.1455	0.569761
$804$	14.5534	0.513259
$805$	−2.17115	−0.0765229
$806$	2.34528	0.0826090
$807$	51.4037	1.80950
$808$	14.0190	0.493185
$809$	−0.136521	−0.00479981	−0.00239990	−	0.999997i	$-0.500764\pi$
$809$	−0.136521	−0.00479981	−0.00239990	+	0.999997i	$0.500764\pi$
$810$	−4.26949	−0.150014
$811$	26.3172	0.924122	0.462061	−	0.886848i	$-0.347110\pi$
$811$	26.3172	0.924122	0.462061	+	0.886848i	$0.347110\pi$
$812$	−13.7606	−0.482903
$813$	−52.2276	−1.83170
$814$	−4.67286	−0.163784
$815$	−5.70847	−0.199959
$816$	−13.8278	−0.484071
$817$	0.230974	0.00808074
$818$	0.918545	0.0321162
$819$	−3.31465	−0.115823
$820$	−0.338912	−0.0118353
$821$	−25.6423	−0.894921	−0.447461	−	0.894304i	$-0.647672\pi$
$821$	−25.6423	−0.894921	−0.447461	+	0.894304i	$0.647672\pi$
$822$	−25.0323	−0.873101
$823$	54.4151	1.89679	0.948395	−	0.317091i	$-0.102706\pi$
$823$	54.4151	1.89679	0.948395	+	0.317091i	$0.102706\pi$
$824$	−2.81132	−0.0979371
$825$	10.1567	0.353610
$826$	−12.5864	−0.437936
$827$	23.7993	0.827581	0.413791	−	0.910372i	$-0.364205\pi$
$827$	23.7993	0.827581	0.413791	+	0.910372i	$0.364205\pi$
$828$	−5.24414	−0.182247
$829$	−21.5230	−0.747524	−0.373762	−	0.927525i	$-0.621932\pi$
$829$	−21.5230	−0.747524	−0.373762	+	0.927525i	$0.621932\pi$
$830$	−1.80243	−0.0625632
$831$	−18.1586	−0.629915
$832$	1.60830	0.0557576
$833$	−31.4320	−1.08906
$834$	−37.4587	−1.29709
$835$	−0.377364	−0.0130592
$836$	−0.573057	−0.0198196
$837$	−4.95538	−0.171283
$838$	−4.23530	−0.146306
$839$	24.6353	0.850507	0.425253	−	0.905074i	$-0.360185\pi$
$839$	24.6353	0.850507	0.425253	+	0.905074i	$0.360185\pi$
$840$	1.19115	0.0410984
$841$	55.3358	1.90813
$842$	−35.4799	−1.22272
$843$	−21.5486	−0.742173
$844$	24.3125	0.836872
$845$	3.95744	0.136140
$846$	15.0025	0.515798
$847$	−1.49841	−0.0514861
$848$	−3.85363	−0.132334
$849$	57.4867	1.97294
$850$	32.0985	1.10097
$851$	−17.8163	−0.610735
$852$	−23.8016	−0.815430
$853$	22.7597	0.779276	0.389638	−	0.920968i	$-0.372600\pi$
$853$	22.7597	0.779276	0.389638	+	0.920968i	$0.372600\pi$
$854$	2.63313	0.0901039
$855$	0.299544	0.0102442
$856$	−11.4172	−0.390232
$857$	−47.6672	−1.62828	−0.814140	−	0.580669i	$-0.802791\pi$
$857$	−47.6672	−1.62828	−0.814140	+	0.580669i	$0.802791\pi$
$858$	3.36416	0.114850
$859$	−40.3161	−1.37557	−0.687784	−	0.725915i	$-0.741416\pi$
$859$	−40.3161	−1.37557	−0.687784	+	0.725915i	$0.741416\pi$
$860$	0.153175	0.00522321
$861$	2.79516	0.0952587
$862$	20.0951	0.684442
$863$	−19.8744	−0.676534	−0.338267	−	0.941050i	$-0.609841\pi$
$863$	−19.8744	−0.676534	−0.338267	+	0.941050i	$0.609841\pi$
$864$	−3.39819	−0.115609
$865$	−4.49583	−0.152863
$866$	−12.8202	−0.435647
$867$	−55.8512	−1.89681
$868$	2.18505	0.0741653
$869$	−1.96995	−0.0668259
$870$	−7.30027	−0.247502
$871$	−11.1897	−0.379150
$872$	−2.21551	−0.0750267
$873$	−9.00491	−0.304770
$874$	−2.18491	−0.0739056
$875$	−5.61224	−0.189728
$876$	−33.7723	−1.14106
$877$	11.8240	0.399268	0.199634	−	0.979870i	$-0.436025\pi$
$877$	11.8240	0.399268	0.199634	+	0.979870i	$0.436025\pi$
$878$	0.840206	0.0283556
$879$	10.7699	0.363258
$880$	−0.380034	−0.0128109
$881$	39.7213	1.33824	0.669122	−	0.743152i	$-0.266670\pi$
$881$	39.7213	1.33824	0.669122	+	0.743152i	$0.266670\pi$
$882$	6.53985	0.220208
$883$	−18.1263	−0.609997	−0.304999	−	0.952353i	$-0.598656\pi$
$883$	−18.1263	−0.609997	−0.304999	+	0.952353i	$0.598656\pi$
$884$	10.6319	0.357589
$885$	−6.67732	−0.224456
$886$	34.1949	1.14880
$887$	−53.1326	−1.78402	−0.892010	−	0.452016i	$-0.850705\pi$
$887$	−53.1326	−1.78402	−0.892010	+	0.452016i	$0.850705\pi$
$888$	9.77447	0.328010
$889$	−11.8831	−0.398548
$890$	4.81727	0.161475
$891$	−11.2345	−0.376369
$892$	−15.5608	−0.521014
$893$	6.25062	0.209169
$894$	14.6250	0.489132
$895$	−5.49108	−0.183546
$896$	1.49841	0.0500585
$897$	12.8266	0.428268
$898$	−1.61098	−0.0537591
$899$	−13.3917	−0.446637
$900$	−6.67852	−0.222617
$901$	−25.4750	−0.848695
$902$	−0.891793	−0.0296934
$903$	−1.26330	−0.0420400
$904$	17.7519	0.590418
$905$	−8.29718	−0.275807
$906$	−11.5697	−0.384378
$907$	25.0428	0.831532	0.415766	−	0.909472i	$-0.363513\pi$
$907$	25.0428	0.831532	0.415766	+	0.909472i	$0.363513\pi$
$908$	−23.6135	−0.783641
$909$	−19.2821	−0.639548
$910$	−0.915841	−0.0303598
$911$	−29.0017	−0.960868	−0.480434	−	0.877031i	$-0.659521\pi$
$911$	−29.0017	−0.960868	−0.480434	+	0.877031i	$0.659521\pi$
$912$	1.19869	0.0396927
$913$	−4.74281	−0.156964
$914$	−20.5285	−0.679023
$915$	1.39693	0.0461810
$916$	23.3205	0.770533
$917$	−15.4805	−0.511213
$918$	−22.4643	−0.741431
$919$	−23.6550	−0.780305	−0.390153	−	0.920750i	$-0.627578\pi$
$919$	−23.6550	−0.780305	−0.390153	+	0.920750i	$0.627578\pi$
$920$	−1.44896	−0.0477709
$921$	−9.88634	−0.325766
$922$	3.59147	0.118279
$923$	18.3005	0.602367
$924$	3.13431	0.103111
$925$	−22.6894	−0.746023
$926$	−12.5127	−0.411193
$927$	3.86679	0.127002
$928$	−9.18345	−0.301462
$929$	17.6477	0.579003	0.289502	−	0.957178i	$-0.406510\pi$
$929$	17.6477	0.579003	0.289502	+	0.957178i	$0.406510\pi$
$930$	1.15921	0.0380120
$931$	2.72475	0.0893000
$932$	−19.0879	−0.625244
$933$	−54.1807	−1.77380
$934$	−38.7635	−1.26838
$935$	−2.51227	−0.0821601
$936$	−2.21210	−0.0723049
$937$	−13.0004	−0.424703	−0.212352	−	0.977193i	$-0.568112\pi$
$937$	−13.0004	−0.424703	−0.212352	+	0.977193i	$0.568112\pi$
$938$	−10.4252	−0.340396
$939$	−41.8834	−1.36681
$940$	4.14522	0.135202
$941$	36.1676	1.17903	0.589514	−	0.807758i	$-0.299319\pi$
$941$	36.1676	1.17903	0.589514	+	0.807758i	$0.299319\pi$
$942$	−39.8925	−1.29977
$943$	−3.40016	−0.110724
$944$	−8.39980	−0.273390
$945$	1.93510	0.0629487
$946$	0.403055	0.0131044
$947$	19.0330	0.618490	0.309245	−	0.950982i	$-0.399924\pi$
$947$	19.0330	0.618490	0.309245	+	0.950982i	$0.399924\pi$
$948$	4.12065	0.133832
$949$	25.9667	0.842914
$950$	−2.78252	−0.0902769
$951$	−31.0761	−1.00771
$952$	9.90548	0.321039
$953$	−51.2242	−1.65931	−0.829657	−	0.558274i	$-0.811464\pi$
$953$	−51.2242	−1.65931	−0.829657	+	0.558274i	$0.811464\pi$
$954$	5.30041	0.171607
$955$	−6.23917	−0.201895
$956$	−30.6521	−0.991361
$957$	−19.2095	−0.620956
$958$	−43.2609	−1.39770
$959$	17.9317	0.579045
$960$	0.794938	0.0256565
$961$	−28.8735	−0.931404
$962$	−7.51534	−0.242304
$963$	15.7036	0.506041
$964$	21.7962	0.702009
$965$	−3.27675	−0.105482
$966$	11.9503	0.384493
$967$	47.3768	1.52353	0.761767	−	0.647851i	$-0.224332\pi$
$967$	47.3768	1.52353	0.761767	+	0.647851i	$0.224332\pi$
$968$	−1.00000	−0.0321412
$969$	7.92415	0.254560
$970$	−2.48807	−0.0798871
$971$	21.3070	0.683775	0.341888	−	0.939741i	$-0.388934\pi$
$971$	21.3070	0.683775	0.341888	+	0.939741i	$0.388934\pi$
$972$	13.3052	0.426764
$973$	26.8333	0.860235
$974$	25.6206	0.820936
$975$	16.3349	0.523136
$976$	1.75728	0.0562492
$977$	39.1335	1.25199	0.625996	−	0.779826i	$-0.284693\pi$
$977$	39.1335	1.25199	0.625996	+	0.779826i	$0.284693\pi$
$978$	31.4201	1.00470
$979$	12.6759	0.405123
$980$	1.80697	0.0577215
$981$	3.04729	0.0972924
$982$	21.6586	0.691154
$983$	7.79606	0.248656	0.124328	−	0.992241i	$-0.460323\pi$
$983$	7.79606	0.248656	0.124328	+	0.992241i	$0.460323\pi$
$984$	1.86541	0.0594671
$985$	0.380034	0.0121089
$986$	−60.7086	−1.93335
$987$	−34.1875	−1.08820
$988$	−0.921645	−0.0293214
$989$	1.53674	0.0488654
$990$	0.522712	0.0166129
$991$	−53.5270	−1.70034	−0.850171	−	0.526507i	$-0.823501\pi$
$991$	−53.5270	−1.70034	−0.850171	+	0.526507i	$0.823501\pi$
$992$	1.45824	0.0462992
$993$	−60.4954	−1.91976
$994$	17.0501	0.540797
$995$	−4.22479	−0.133935
$996$	9.92078	0.314352
$997$	−4.12771	−0.130726	−0.0653629	−	0.997862i	$-0.520820\pi$
$997$	−4.12771	−0.130726	−0.0653629	+	0.997862i	$0.520820\pi$
$998$	−6.72973	−0.213026
$999$	15.8793	0.502398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.h.1.7	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.h.1.7	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.09175 q^{3} +1.00000 q^{4} -0.380034 q^{5} +2.09175 q^{6} -1.49841 q^{7} -1.00000 q^{8} +1.37543 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.09175 q^{3} +1.00000 q^{4} -0.380034 q^{5} +2.09175 q^{6} -1.49841 q^{7} -1.00000 q^{8} +1.37543 q^{9} +0.380034 q^{10} +1.00000 q^{11} -2.09175 q^{12} +1.60830 q^{13} +1.49841 q^{14} +0.794938 q^{15} +1.00000 q^{16} +6.61065 q^{17} -1.37543 q^{18} -0.573057 q^{19} -0.380034 q^{20} +3.13431 q^{21} -1.00000 q^{22} -3.81272 q^{23} +2.09175 q^{24} -4.85557 q^{25} -1.60830 q^{26} +3.39819 q^{27} -1.49841 q^{28} +9.18345 q^{29} -0.794938 q^{30} -1.45824 q^{31} -1.00000 q^{32} -2.09175 q^{33} -6.61065 q^{34} +0.569448 q^{35} +1.37543 q^{36} +4.67286 q^{37} +0.573057 q^{38} -3.36416 q^{39} +0.380034 q^{40} +0.891793 q^{41} -3.13431 q^{42} -0.403055 q^{43} +1.00000 q^{44} -0.522712 q^{45} +3.81272 q^{46} -10.9075 q^{47} -2.09175 q^{48} -4.75476 q^{49} +4.85557 q^{50} -13.8278 q^{51} +1.60830 q^{52} -3.85363 q^{53} -3.39819 q^{54} -0.380034 q^{55} +1.49841 q^{56} +1.19869 q^{57} -9.18345 q^{58} -8.39980 q^{59} +0.794938 q^{60} +1.75728 q^{61} +1.45824 q^{62} -2.06097 q^{63} +1.00000 q^{64} -0.611207 q^{65} +2.09175 q^{66} -6.95751 q^{67} +6.61065 q^{68} +7.97527 q^{69} -0.569448 q^{70} +11.3788 q^{71} -1.37543 q^{72} +16.1455 q^{73} -4.67286 q^{74} +10.1567 q^{75} -0.573057 q^{76} -1.49841 q^{77} +3.36416 q^{78} -1.96995 q^{79} -0.380034 q^{80} -11.2345 q^{81} -0.891793 q^{82} -4.74281 q^{83} +3.13431 q^{84} -2.51227 q^{85} +0.403055 q^{86} -19.2095 q^{87} -1.00000 q^{88} +12.6759 q^{89} +0.522712 q^{90} -2.40989 q^{91} -3.81272 q^{92} +3.05028 q^{93} +10.9075 q^{94} +0.217781 q^{95} +2.09175 q^{96} -6.54696 q^{97} +4.75476 q^{98} +1.37543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

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