LMFDB - Embedded newform 946.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, 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("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 11x^{5} + 31x^{4} + 39x^{3} - 91x^{2} - 48x + 64 $ x^7 - 3x^6 - 11x^5 + 31x^4 + 39x^3 - 91x^2 - 48x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.23095$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.23095 q^{3} +1.00000 q^{4} +3.67721 q^{5} -1.23095 q^{6} -4.90006 q^{7} +1.00000 q^{8} -1.48475 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.23095 q^{3} +1.00000 q^{4} +3.67721 q^{5} -1.23095 q^{6} -4.90006 q^{7} +1.00000 q^{8} -1.48475 q^{9} +3.67721 q^{10} +1.00000 q^{11} -1.23095 q^{12} +5.58187 q^{13} -4.90006 q^{14} -4.52647 q^{15} +1.00000 q^{16} +2.65086 q^{17} -1.48475 q^{18} +2.61049 q^{19} +3.67721 q^{20} +6.03174 q^{21} +1.00000 q^{22} +8.29227 q^{23} -1.23095 q^{24} +8.52187 q^{25} +5.58187 q^{26} +5.52052 q^{27} -4.90006 q^{28} +3.76759 q^{29} -4.52647 q^{30} -2.62182 q^{31} +1.00000 q^{32} -1.23095 q^{33} +2.65086 q^{34} -18.0185 q^{35} -1.48475 q^{36} -4.98425 q^{37} +2.61049 q^{38} -6.87102 q^{39} +3.67721 q^{40} -4.31377 q^{41} +6.03174 q^{42} +1.00000 q^{43} +1.00000 q^{44} -5.45975 q^{45} +8.29227 q^{46} -12.4219 q^{47} -1.23095 q^{48} +17.0106 q^{49} +8.52187 q^{50} -3.26308 q^{51} +5.58187 q^{52} -3.39841 q^{53} +5.52052 q^{54} +3.67721 q^{55} -4.90006 q^{56} -3.21339 q^{57} +3.76759 q^{58} +4.30587 q^{59} -4.52647 q^{60} +4.48915 q^{61} -2.62182 q^{62} +7.27538 q^{63} +1.00000 q^{64} +20.5257 q^{65} -1.23095 q^{66} +0.438150 q^{67} +2.65086 q^{68} -10.2074 q^{69} -18.0185 q^{70} +11.2572 q^{71} -1.48475 q^{72} +1.10569 q^{73} -4.98425 q^{74} -10.4900 q^{75} +2.61049 q^{76} -4.90006 q^{77} -6.87102 q^{78} -0.722651 q^{79} +3.67721 q^{80} -2.34125 q^{81} -4.31377 q^{82} -14.5029 q^{83} +6.03174 q^{84} +9.74776 q^{85} +1.00000 q^{86} -4.63773 q^{87} +1.00000 q^{88} -11.4164 q^{89} -5.45975 q^{90} -27.3515 q^{91} +8.29227 q^{92} +3.22734 q^{93} -12.4219 q^{94} +9.59931 q^{95} -1.23095 q^{96} +10.4756 q^{97} +17.0106 q^{98} -1.48475 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9} + 8 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{15} + 7 q^{16} + 10 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} + 7 q^{22} - 4 q^{23} + 3 q^{24} + 11 q^{25} + 4 q^{26} + 15 q^{27} - 2 q^{28} + 5 q^{29} + 2 q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 10 q^{34} - 10 q^{35} + 10 q^{36} + 6 q^{37} - 2 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} + 7 q^{43} + 7 q^{44} - 2 q^{45} - 4 q^{46} - 6 q^{47} + 3 q^{48} + 31 q^{49} + 11 q^{50} - 14 q^{51} + 4 q^{52} + q^{53} + 15 q^{54} + 8 q^{55} - 2 q^{56} - 30 q^{57} + 5 q^{58} - 4 q^{59} + 2 q^{60} + 9 q^{61} - 2 q^{62} - 24 q^{63} + 7 q^{64} + 18 q^{65} + 3 q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 10 q^{70} + 10 q^{72} + 13 q^{73} + 6 q^{74} - 9 q^{75} - 2 q^{76} - 2 q^{77} - 8 q^{78} - 31 q^{79} + 8 q^{80} - 25 q^{81} + 4 q^{82} - 11 q^{83} - 24 q^{85} + 7 q^{86} - 13 q^{87} + 7 q^{88} + 10 q^{89} - 2 q^{90} - 12 q^{91} - 4 q^{92} + 12 q^{93} - 6 q^{94} - 18 q^{95} + 3 q^{96} + 23 q^{97} + 31 q^{98} + 10 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9 + 8 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^15 + 7 * q^16 + 10 * q^17 + 10 * q^18 - 2 * q^19 + 8 * q^20 + 7 * q^22 - 4 * q^23 + 3 * q^24 + 11 * q^25 + 4 * q^26 + 15 * q^27 - 2 * q^28 + 5 * q^29 + 2 * q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 10 * q^34 - 10 * q^35 + 10 * q^36 + 6 * q^37 - 2 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 + 7 * q^43 + 7 * q^44 - 2 * q^45 - 4 * q^46 - 6 * q^47 + 3 * q^48 + 31 * q^49 + 11 * q^50 - 14 * q^51 + 4 * q^52 + q^53 + 15 * q^54 + 8 * q^55 - 2 * q^56 - 30 * q^57 + 5 * q^58 - 4 * q^59 + 2 * q^60 + 9 * q^61 - 2 * q^62 - 24 * q^63 + 7 * q^64 + 18 * q^65 + 3 * q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 10 * q^70 + 10 * q^72 + 13 * q^73 + 6 * q^74 - 9 * q^75 - 2 * q^76 - 2 * q^77 - 8 * q^78 - 31 * q^79 + 8 * q^80 - 25 * q^81 + 4 * q^82 - 11 * q^83 - 24 * q^85 + 7 * q^86 - 13 * q^87 + 7 * q^88 + 10 * q^89 - 2 * q^90 - 12 * q^91 - 4 * q^92 + 12 * q^93 - 6 * q^94 - 18 * q^95 + 3 * q^96 + 23 * q^97 + 31 * q^98 + 10 * 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
$3$	−1.23095	−0.710691	−0.355346	−	0.934735i	$-0.615637\pi$
$3$	−1.23095	−0.710691	−0.355346	+	0.934735i	$0.615637\pi$
$4$	1.00000	0.500000
$5$	3.67721	1.64450	0.822249	−	0.569128i	$-0.192719\pi$
$5$	3.67721	1.64450	0.822249	+	0.569128i	$0.192719\pi$
$6$	−1.23095	−0.502535
$7$	−4.90006	−1.85205	−0.926024	−	0.377466i	$-0.876796\pi$
$7$	−4.90006	−1.85205	−0.926024	+	0.377466i	$0.876796\pi$
$8$	1.00000	0.353553
$9$	−1.48475	−0.494918
$10$	3.67721	1.16284
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.23095	−0.355346
$13$	5.58187	1.54813	0.774066	−	0.633105i	$-0.218220\pi$
$13$	5.58187	1.54813	0.774066	+	0.633105i	$0.218220\pi$
$14$	−4.90006	−1.30960
$15$	−4.52647	−1.16873
$16$	1.00000	0.250000
$17$	2.65086	0.642927	0.321464	−	0.946922i	$-0.395825\pi$
$17$	2.65086	0.642927	0.321464	+	0.946922i	$0.395825\pi$
$18$	−1.48475	−0.349960
$19$	2.61049	0.598887	0.299443	−	0.954114i	$-0.403199\pi$
$19$	2.61049	0.598887	0.299443	+	0.954114i	$0.403199\pi$
$20$	3.67721	0.822249
$21$	6.03174	1.31623
$22$	1.00000	0.213201
$23$	8.29227	1.72906	0.864529	−	0.502583i	$-0.167617\pi$
$23$	8.29227	1.72906	0.864529	+	0.502583i	$0.167617\pi$
$24$	−1.23095	−0.251267
$25$	8.52187	1.70437
$26$	5.58187	1.09469
$27$	5.52052	1.06243
$28$	−4.90006	−0.926024
$29$	3.76759	0.699624	0.349812	−	0.936820i	$-0.386245\pi$
$29$	3.76759	0.699624	0.349812	+	0.936820i	$0.386245\pi$
$30$	−4.52647	−0.826417
$31$	−2.62182	−0.470892	−0.235446	−	0.971887i	$-0.575655\pi$
$31$	−2.62182	−0.470892	−0.235446	+	0.971887i	$0.575655\pi$
$32$	1.00000	0.176777
$33$	−1.23095	−0.214281
$34$	2.65086	0.454618
$35$	−18.0185	−3.04569
$36$	−1.48475	−0.247459
$37$	−4.98425	−0.819405	−0.409703	−	0.912219i	$-0.634368\pi$
$37$	−4.98425	−0.819405	−0.409703	+	0.912219i	$0.634368\pi$
$38$	2.61049	0.423477
$39$	−6.87102	−1.10024
$40$	3.67721	0.581418
$41$	−4.31377	−0.673697	−0.336849	−	0.941559i	$-0.609361\pi$
$41$	−4.31377	−0.673697	−0.336849	+	0.941559i	$0.609361\pi$
$42$	6.03174	0.930718
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−5.45975	−0.813892
$46$	8.29227	1.22263
$47$	−12.4219	−1.81192	−0.905962	−	0.423358i	$-0.860851\pi$
$47$	−12.4219	−1.81192	−0.905962	+	0.423358i	$0.860851\pi$
$48$	−1.23095	−0.177673
$49$	17.0106	2.43008
$50$	8.52187	1.20518
$51$	−3.26308	−0.456923
$52$	5.58187	0.774066
$53$	−3.39841	−0.466807	−0.233404	−	0.972380i	$-0.574986\pi$
$53$	−3.39841	−0.466807	−0.233404	+	0.972380i	$0.574986\pi$
$54$	5.52052	0.751248
$55$	3.67721	0.495835
$56$	−4.90006	−0.654798
$57$	−3.21339	−0.425624
$58$	3.76759	0.494709
$59$	4.30587	0.560576	0.280288	−	0.959916i	$-0.409570\pi$
$59$	4.30587	0.560576	0.280288	+	0.959916i	$0.409570\pi$
$60$	−4.52647	−0.584365
$61$	4.48915	0.574777	0.287388	−	0.957814i	$-0.407213\pi$
$61$	4.48915	0.574777	0.287388	+	0.957814i	$0.407213\pi$
$62$	−2.62182	−0.332971
$63$	7.27538	0.916611
$64$	1.00000	0.125000
$65$	20.5257	2.54590
$66$	−1.23095	−0.151520
$67$	0.438150	0.0535285	0.0267642	−	0.999642i	$-0.491480\pi$
$67$	0.438150	0.0535285	0.0267642	+	0.999642i	$0.491480\pi$
$68$	2.65086	0.321464
$69$	−10.2074	−1.22883
$70$	−18.0185	−2.15363
$71$	11.2572	1.33598	0.667992	−	0.744168i	$-0.267154\pi$
$71$	11.2572	1.33598	0.667992	+	0.744168i	$0.267154\pi$
$72$	−1.48475	−0.174980
$73$	1.10569	0.129411	0.0647057	−	0.997904i	$-0.479389\pi$
$73$	1.10569	0.129411	0.0647057	+	0.997904i	$0.479389\pi$
$74$	−4.98425	−0.579407
$75$	−10.4900	−1.21128
$76$	2.61049	0.299443
$77$	−4.90006	−0.558413
$78$	−6.87102	−0.777990
$79$	−0.722651	−0.0813046	−0.0406523	−	0.999173i	$-0.512944\pi$
$79$	−0.722651	−0.0813046	−0.0406523	+	0.999173i	$0.512944\pi$
$80$	3.67721	0.411125
$81$	−2.34125	−0.260138
$82$	−4.31377	−0.476376
$83$	−14.5029	−1.59190	−0.795950	−	0.605362i	$-0.793028\pi$
$83$	−14.5029	−1.59190	−0.795950	+	0.605362i	$0.793028\pi$
$84$	6.03174	0.658117
$85$	9.74776	1.05729
$86$	1.00000	0.107833
$87$	−4.63773	−0.497217
$88$	1.00000	0.106600
$89$	−11.4164	−1.21013	−0.605066	−	0.796175i	$-0.706853\pi$
$89$	−11.4164	−1.21013	−0.605066	+	0.796175i	$0.706853\pi$
$90$	−5.45975	−0.575508
$91$	−27.3515	−2.86721
$92$	8.29227	0.864529
$93$	3.22734	0.334659
$94$	−12.4219	−1.28122
$95$	9.59931	0.984868
$96$	−1.23095	−0.125634
$97$	10.4756	1.06363	0.531816	−	0.846860i	$-0.321510\pi$
$97$	10.4756	1.06363	0.531816	+	0.846860i	$0.321510\pi$
$98$	17.0106	1.71833
$99$	−1.48475	−0.149223
$100$	8.52187	0.852187
$101$	−2.76409	−0.275037	−0.137518	−	0.990499i	$-0.543913\pi$
$101$	−2.76409	−0.275037	−0.137518	+	0.990499i	$0.543913\pi$
$102$	−3.26308	−0.323093
$103$	6.85795	0.675734	0.337867	−	0.941194i	$-0.390295\pi$
$103$	6.85795	0.675734	0.337867	+	0.941194i	$0.390295\pi$
$104$	5.58187	0.547347
$105$	22.1800	2.16454
$106$	−3.39841	−0.330083
$107$	−19.7588	−1.91016	−0.955079	−	0.296351i	$-0.904230\pi$
$107$	−19.7588	−1.91016	−0.955079	+	0.296351i	$0.904230\pi$
$108$	5.52052	0.531213
$109$	−11.8293	−1.13304	−0.566522	−	0.824047i	$-0.691711\pi$
$109$	−11.8293	−1.13304	−0.566522	+	0.824047i	$0.691711\pi$
$110$	3.67721	0.350608
$111$	6.13538	0.582344
$112$	−4.90006	−0.463012
$113$	10.3745	0.975947	0.487974	−	0.872858i	$-0.337736\pi$
$113$	10.3745	0.975947	0.487974	+	0.872858i	$0.337736\pi$
$114$	−3.21339	−0.300961
$115$	30.4924	2.84343
$116$	3.76759	0.349812
$117$	−8.28770	−0.766198
$118$	4.30587	0.396387
$119$	−12.9893	−1.19073
$120$	−4.52647	−0.413209
$121$	1.00000	0.0909091
$122$	4.48915	0.406429
$123$	5.31005	0.478791
$124$	−2.62182	−0.235446
$125$	12.9507	1.15834
$126$	7.27538	0.648142
$127$	−10.9297	−0.969858	−0.484929	−	0.874554i	$-0.661155\pi$
$127$	−10.9297	−0.969858	−0.484929	+	0.874554i	$0.661155\pi$
$128$	1.00000	0.0883883
$129$	−1.23095	−0.108379
$130$	20.5257	1.80022
$131$	−10.3916	−0.907922	−0.453961	−	0.891022i	$-0.649989\pi$
$131$	−10.3916	−0.907922	−0.453961	+	0.891022i	$0.649989\pi$
$132$	−1.23095	−0.107141
$133$	−12.7915	−1.10917
$134$	0.438150	0.0378504
$135$	20.3001	1.74716
$136$	2.65086	0.227309
$137$	−15.1656	−1.29568	−0.647841	−	0.761775i	$-0.724328\pi$
$137$	−15.1656	−1.29568	−0.647841	+	0.761775i	$0.724328\pi$
$138$	−10.2074	−0.868912
$139$	−10.8056	−0.916521	−0.458261	−	0.888818i	$-0.651527\pi$
$139$	−10.8056	−0.916521	−0.458261	+	0.888818i	$0.651527\pi$
$140$	−18.0185	−1.52284
$141$	15.2908	1.28772
$142$	11.2572	0.944684
$143$	5.58187	0.466779
$144$	−1.48475	−0.123729
$145$	13.8542	1.15053
$146$	1.10569	0.0915077
$147$	−20.9392	−1.72704
$148$	−4.98425	−0.409703
$149$	2.27519	0.186391	0.0931955	−	0.995648i	$-0.470292\pi$
$149$	2.27519	0.186391	0.0931955	+	0.995648i	$0.470292\pi$
$150$	−10.4900	−0.856507
$151$	7.24198	0.589344	0.294672	−	0.955598i	$-0.404790\pi$
$151$	7.24198	0.589344	0.294672	+	0.955598i	$0.404790\pi$
$152$	2.61049	0.211738
$153$	−3.93587	−0.318196
$154$	−4.90006	−0.394858
$155$	−9.64097	−0.774382
$156$	−6.87102	−0.550122
$157$	19.4435	1.55176	0.775881	−	0.630879i	$-0.217305\pi$
$157$	19.4435	1.55176	0.775881	+	0.630879i	$0.217305\pi$
$158$	−0.722651	−0.0574911
$159$	4.18328	0.331756
$160$	3.67721	0.290709
$161$	−40.6326	−3.20230
$162$	−2.34125	−0.183946
$163$	6.36605	0.498627	0.249314	−	0.968423i	$-0.419795\pi$
$163$	6.36605	0.498627	0.249314	+	0.968423i	$0.419795\pi$
$164$	−4.31377	−0.336849
$165$	−4.52647	−0.352386
$166$	−14.5029	−1.12564
$167$	1.58007	0.122270	0.0611348	−	0.998130i	$-0.480528\pi$
$167$	1.58007	0.122270	0.0611348	+	0.998130i	$0.480528\pi$
$168$	6.03174	0.465359
$169$	18.1572	1.39671
$170$	9.74776	0.747619
$171$	−3.87593	−0.296400
$172$	1.00000	0.0762493
$173$	−11.9285	−0.906910	−0.453455	−	0.891279i	$-0.649809\pi$
$173$	−11.9285	−0.906910	−0.453455	+	0.891279i	$0.649809\pi$
$174$	−4.63773	−0.351585
$175$	−41.7577	−3.15658
$176$	1.00000	0.0753778
$177$	−5.30032	−0.398397
$178$	−11.4164	−0.855693
$179$	25.3471	1.89453	0.947266	−	0.320449i	$-0.103834\pi$
$179$	25.3471	1.89453	0.947266	+	0.320449i	$0.103834\pi$
$180$	−5.45975	−0.406946
$181$	−12.3135	−0.915252	−0.457626	−	0.889145i	$-0.651300\pi$
$181$	−12.3135	−0.915252	−0.457626	+	0.889145i	$0.651300\pi$
$182$	−27.3515	−2.02743
$183$	−5.52594	−0.408489
$184$	8.29227	0.611314
$185$	−18.3281	−1.34751
$186$	3.22734	0.236640
$187$	2.65086	0.193850
$188$	−12.4219	−0.905962
$189$	−27.0509	−1.96766
$190$	9.59931	0.696407
$191$	8.89008	0.643263	0.321632	−	0.946865i	$-0.395769\pi$
$191$	8.89008	0.643263	0.321632	+	0.946865i	$0.395769\pi$
$192$	−1.23095	−0.0888364
$193$	−13.2376	−0.952862	−0.476431	−	0.879212i	$-0.658070\pi$
$193$	−13.2376	−0.952862	−0.476431	+	0.879212i	$0.658070\pi$
$194$	10.4756	0.752101
$195$	−25.2662	−1.80935
$196$	17.0106	1.21504
$197$	−8.07873	−0.575586	−0.287793	−	0.957693i	$-0.592921\pi$
$197$	−8.07873	−0.575586	−0.287793	+	0.957693i	$0.592921\pi$
$198$	−1.48475	−0.105517
$199$	11.3471	0.804374	0.402187	−	0.915558i	$-0.368250\pi$
$199$	11.3471	0.804374	0.402187	+	0.915558i	$0.368250\pi$
$200$	8.52187	0.602588
$201$	−0.539342	−0.0380422
$202$	−2.76409	−0.194480
$203$	−18.4614	−1.29574
$204$	−3.26308	−0.228461
$205$	−15.8626	−1.10789
$206$	6.85795	0.477816
$207$	−12.3120	−0.855742
$208$	5.58187	0.387033
$209$	2.61049	0.180571
$210$	22.1800	1.53056
$211$	6.52220	0.449007	0.224503	−	0.974473i	$-0.427924\pi$
$211$	6.52220	0.449007	0.224503	+	0.974473i	$0.427924\pi$
$212$	−3.39841	−0.233404
$213$	−13.8571	−0.949472
$214$	−19.7588	−1.35069
$215$	3.67721	0.250784
$216$	5.52052	0.375624
$217$	12.8471	0.872115
$218$	−11.8293	−0.801183
$219$	−1.36106	−0.0919716
$220$	3.67721	0.247917
$221$	14.7967	0.995336
$222$	6.13538	0.411779
$223$	−16.0375	−1.07395	−0.536976	−	0.843597i	$-0.680434\pi$
$223$	−16.0375	−1.07395	−0.536976	+	0.843597i	$0.680434\pi$
$224$	−4.90006	−0.327399
$225$	−12.6529	−0.843526
$226$	10.3745	0.690099
$227$	1.36685	0.0907211	0.0453606	−	0.998971i	$-0.485556\pi$
$227$	1.36685	0.0907211	0.0453606	+	0.998971i	$0.485556\pi$
$228$	−3.21339	−0.212812
$229$	−13.8230	−0.913453	−0.456726	−	0.889607i	$-0.650978\pi$
$229$	−13.8230	−0.913453	−0.456726	+	0.889607i	$0.650978\pi$
$230$	30.4924	2.01061
$231$	6.03174	0.396859
$232$	3.76759	0.247355
$233$	−11.5284	−0.755252	−0.377626	−	0.925958i	$-0.623259\pi$
$233$	−11.5284	−0.755252	−0.377626	+	0.925958i	$0.623259\pi$
$234$	−8.28770	−0.541784
$235$	−45.6780	−2.97971
$236$	4.30587	0.280288
$237$	0.889550	0.0577825
$238$	−12.9893	−0.841974
$239$	−21.1701	−1.36938	−0.684688	−	0.728836i	$-0.740062\pi$
$239$	−21.1701	−1.36938	−0.684688	+	0.728836i	$0.740062\pi$
$240$	−4.52647	−0.292183
$241$	10.4452	0.672834	0.336417	−	0.941713i	$-0.390785\pi$
$241$	10.4452	0.672834	0.336417	+	0.941713i	$0.390785\pi$
$242$	1.00000	0.0642824
$243$	−13.6796	−0.877547
$244$	4.48915	0.287388
$245$	62.5514	3.99626
$246$	5.31005	0.338556
$247$	14.5714	0.927155
$248$	−2.62182	−0.166486
$249$	17.8524	1.13135
$250$	12.9507	0.819072
$251$	25.4394	1.60572	0.802861	−	0.596166i	$-0.203310\pi$
$251$	25.4394	1.60572	0.802861	+	0.596166i	$0.203310\pi$
$252$	7.27538	0.458306
$253$	8.29227	0.521331
$254$	−10.9297	−0.685793
$255$	−11.9990	−0.751409
$256$	1.00000	0.0625000
$257$	4.92848	0.307430	0.153715	−	0.988115i	$-0.450876\pi$
$257$	4.92848	0.307430	0.153715	+	0.988115i	$0.450876\pi$
$258$	−1.23095	−0.0766358
$259$	24.4231	1.51758
$260$	20.5257	1.27295
$261$	−5.59395	−0.346257
$262$	−10.3916	−0.641998
$263$	26.8654	1.65659	0.828294	−	0.560293i	$-0.189311\pi$
$263$	26.8654	1.65659	0.828294	+	0.560293i	$0.189311\pi$
$264$	−1.23095	−0.0757599
$265$	−12.4967	−0.767664
$266$	−12.7915	−0.784299
$267$	14.0530	0.860031
$268$	0.438150	0.0267642
$269$	30.0616	1.83289	0.916443	−	0.400166i	$-0.131048\pi$
$269$	30.0616	1.83289	0.916443	+	0.400166i	$0.131048\pi$
$270$	20.3001	1.23543
$271$	−20.6924	−1.25698	−0.628488	−	0.777819i	$-0.716326\pi$
$271$	−20.6924	−1.25698	−0.628488	+	0.777819i	$0.716326\pi$
$272$	2.65086	0.160732
$273$	33.6684	2.03770
$274$	−15.1656	−0.916186
$275$	8.52187	0.513888
$276$	−10.2074	−0.614413
$277$	−23.2518	−1.39706	−0.698532	−	0.715579i	$-0.746163\pi$
$277$	−23.2518	−1.39706	−0.698532	+	0.715579i	$0.746163\pi$
$278$	−10.8056	−0.648078
$279$	3.89275	0.233053
$280$	−18.0185	−1.07681
$281$	6.45528	0.385090	0.192545	−	0.981288i	$-0.438326\pi$
$281$	6.45528	0.385090	0.192545	+	0.981288i	$0.438326\pi$
$282$	15.2908	0.910555
$283$	−11.7944	−0.701102	−0.350551	−	0.936544i	$-0.614006\pi$
$283$	−11.7944	−0.701102	−0.350551	+	0.936544i	$0.614006\pi$
$284$	11.2572	0.667992
$285$	−11.8163	−0.699937
$286$	5.58187	0.330063
$287$	21.1377	1.24772
$288$	−1.48475	−0.0874899
$289$	−9.97296	−0.586645
$290$	13.8542	0.813548
$291$	−12.8949	−0.755913
$292$	1.10569	0.0647057
$293$	−8.02756	−0.468975	−0.234488	−	0.972119i	$-0.575341\pi$
$293$	−8.02756	−0.468975	−0.234488	+	0.972119i	$0.575341\pi$
$294$	−20.9392	−1.22120
$295$	15.8336	0.921867
$296$	−4.98425	−0.289703
$297$	5.52052	0.320333
$298$	2.27519	0.131798
$299$	46.2864	2.67681
$300$	−10.4900	−0.605642
$301$	−4.90006	−0.282435
$302$	7.24198	0.416729
$303$	3.40246	0.195466
$304$	2.61049	0.149722
$305$	16.5076	0.945220
$306$	−3.93587	−0.224999
$307$	−10.3199	−0.588988	−0.294494	−	0.955653i	$-0.595151\pi$
$307$	−10.3199	−0.588988	−0.294494	+	0.955653i	$0.595151\pi$
$308$	−4.90006	−0.279207
$309$	−8.44182	−0.480238
$310$	−9.64097	−0.547571
$311$	3.60431	0.204382	0.102191	−	0.994765i	$-0.467415\pi$
$311$	3.60431	0.204382	0.102191	+	0.994765i	$0.467415\pi$
$312$	−6.87102	−0.388995
$313$	12.2746	0.693800	0.346900	−	0.937902i	$-0.387234\pi$
$313$	12.2746	0.693800	0.346900	+	0.937902i	$0.387234\pi$
$314$	19.4435	1.09726
$315$	26.7531	1.50737
$316$	−0.722651	−0.0406523
$317$	−30.4516	−1.71033	−0.855167	−	0.518353i	$-0.826545\pi$
$317$	−30.4516	−1.71033	−0.855167	+	0.518353i	$0.826545\pi$
$318$	4.18328	0.234587
$319$	3.76759	0.210945
$320$	3.67721	0.205562
$321$	24.3222	1.35753
$322$	−40.6326	−2.26437
$323$	6.92003	0.385041
$324$	−2.34125	−0.130069
$325$	47.5680	2.63860
$326$	6.36605	0.352583
$327$	14.5614	0.805245
$328$	−4.31377	−0.238188
$329$	60.8682	3.35577
$330$	−4.52647	−0.249174
$331$	−19.8001	−1.08831	−0.544155	−	0.838985i	$-0.683150\pi$
$331$	−19.8001	−1.08831	−0.544155	+	0.838985i	$0.683150\pi$
$332$	−14.5029	−0.795950
$333$	7.40038	0.405538
$334$	1.58007	0.0864577
$335$	1.61117	0.0880275
$336$	6.03174	0.329058
$337$	−13.2827	−0.723555	−0.361777	−	0.932264i	$-0.617830\pi$
$337$	−13.2827	−0.723555	−0.361777	+	0.932264i	$0.617830\pi$
$338$	18.1572	0.987623
$339$	−12.7705	−0.693597
$340$	9.74776	0.528646
$341$	−2.62182	−0.141979
$342$	−3.87593	−0.209586
$343$	−49.0523	−2.64857
$344$	1.00000	0.0539164
$345$	−37.5348	−2.02080
$346$	−11.9285	−0.641282
$347$	19.2213	1.03185	0.515926	−	0.856633i	$-0.327448\pi$
$347$	19.2213	1.03185	0.515926	+	0.856633i	$0.327448\pi$
$348$	−4.63773	−0.248608
$349$	−9.85669	−0.527617	−0.263808	−	0.964575i	$-0.584979\pi$
$349$	−9.85669	−0.527617	−0.263808	+	0.964575i	$0.584979\pi$
$350$	−41.7577	−2.23204
$351$	30.8148	1.64477
$352$	1.00000	0.0533002
$353$	−28.2926	−1.50586	−0.752932	−	0.658099i	$-0.771361\pi$
$353$	−28.2926	−1.50586	−0.752932	+	0.658099i	$0.771361\pi$
$354$	−5.30032	−0.281709
$355$	41.3951	2.19702
$356$	−11.4164	−0.605066
$357$	15.9893	0.846242
$358$	25.3471	1.33964
$359$	0.763328	0.0402869	0.0201435	−	0.999797i	$-0.493588\pi$
$359$	0.763328	0.0402869	0.0201435	+	0.999797i	$0.493588\pi$
$360$	−5.45975	−0.287754
$361$	−12.1854	−0.641335
$362$	−12.3135	−0.647181
$363$	−1.23095	−0.0646083
$364$	−27.3515	−1.43361
$365$	4.06586	0.212817
$366$	−5.52594	−0.288845
$367$	30.4433	1.58913	0.794563	−	0.607182i	$-0.207700\pi$
$367$	30.4433	1.58913	0.794563	+	0.607182i	$0.207700\pi$
$368$	8.29227	0.432265
$369$	6.40488	0.333425
$370$	−18.3281	−0.952834
$371$	16.6524	0.864549
$372$	3.22734	0.167330
$373$	−4.16889	−0.215857	−0.107928	−	0.994159i	$-0.534422\pi$
$373$	−4.16889	−0.215857	−0.107928	+	0.994159i	$0.534422\pi$
$374$	2.65086	0.137073
$375$	−15.9417	−0.823224
$376$	−12.4219	−0.640612
$377$	21.0302	1.08311
$378$	−27.0509	−1.39135
$379$	−11.1383	−0.572137	−0.286069	−	0.958209i	$-0.592348\pi$
$379$	−11.1383	−0.572137	−0.286069	+	0.958209i	$0.592348\pi$
$380$	9.59931	0.492434
$381$	13.4540	0.689270
$382$	8.89008	0.454856
$383$	−27.9543	−1.42840	−0.714200	−	0.699942i	$-0.753209\pi$
$383$	−27.9543	−1.42840	−0.714200	+	0.699942i	$0.753209\pi$
$384$	−1.23095	−0.0628168
$385$	−18.0185	−0.918310
$386$	−13.2376	−0.673775
$387$	−1.48475	−0.0754743
$388$	10.4756	0.531816
$389$	8.97453	0.455027	0.227513	−	0.973775i	$-0.426940\pi$
$389$	8.97453	0.455027	0.227513	+	0.973775i	$0.426940\pi$
$390$	−25.2662	−1.27940
$391$	21.9816	1.11166
$392$	17.0106	0.859163
$393$	12.7916	0.645252
$394$	−8.07873	−0.407001
$395$	−2.65734	−0.133705
$396$	−1.48475	−0.0746117
$397$	30.1593	1.51365	0.756826	−	0.653616i	$-0.226749\pi$
$397$	30.1593	1.51365	0.756826	+	0.653616i	$0.226749\pi$
$398$	11.3471	0.568778
$399$	15.7458	0.788275
$400$	8.52187	0.426094
$401$	−32.8112	−1.63851	−0.819255	−	0.573429i	$-0.805613\pi$
$401$	−32.8112	−1.63851	−0.819255	+	0.573429i	$0.805613\pi$
$402$	−0.539342	−0.0268999
$403$	−14.6346	−0.729003
$404$	−2.76409	−0.137518
$405$	−8.60925	−0.427797
$406$	−18.4614	−0.916225
$407$	−4.98425	−0.247060
$408$	−3.26308	−0.161547
$409$	13.4497	0.665047	0.332524	−	0.943095i	$-0.392100\pi$
$409$	13.4497	0.665047	0.332524	+	0.943095i	$0.392100\pi$
$410$	−15.8626	−0.783399
$411$	18.6681	0.920830
$412$	6.85795	0.337867
$413$	−21.0990	−1.03821
$414$	−12.3120	−0.605101
$415$	−53.3302	−2.61788
$416$	5.58187	0.273674
$417$	13.3012	0.651364
$418$	2.61049	0.127683
$419$	19.0618	0.931232	0.465616	−	0.884987i	$-0.345833\pi$
$419$	19.0618	0.931232	0.465616	+	0.884987i	$0.345833\pi$
$420$	22.1800	1.08227
$421$	7.14908	0.348425	0.174213	−	0.984708i	$-0.444262\pi$
$421$	7.14908	0.348425	0.174213	+	0.984708i	$0.444262\pi$
$422$	6.52220	0.317496
$423$	18.4435	0.896754
$424$	−3.39841	−0.165041
$425$	22.5903	1.09579
$426$	−13.8571	−0.671378
$427$	−21.9971	−1.06451
$428$	−19.7588	−0.955079
$429$	−6.87102	−0.331736
$430$	3.67721	0.177331
$431$	9.95384	0.479460	0.239730	−	0.970840i	$-0.422941\pi$
$431$	9.95384	0.479460	0.239730	+	0.970840i	$0.422941\pi$
$432$	5.52052	0.265606
$433$	−16.5172	−0.793765	−0.396883	−	0.917869i	$-0.629908\pi$
$433$	−16.5172	−0.793765	−0.396883	+	0.917869i	$0.629908\pi$
$434$	12.8471	0.616678
$435$	−17.0539	−0.817672
$436$	−11.8293	−0.566522
$437$	21.6469	1.03551
$438$	−1.36106	−0.0650337
$439$	34.7051	1.65638	0.828192	−	0.560445i	$-0.189370\pi$
$439$	34.7051	1.65638	0.828192	+	0.560445i	$0.189370\pi$
$440$	3.67721	0.175304
$441$	−25.2565	−1.20269
$442$	14.7967	0.703809
$443$	9.61478	0.456812	0.228406	−	0.973566i	$-0.426649\pi$
$443$	9.61478	0.456812	0.228406	+	0.973566i	$0.426649\pi$
$444$	6.13538	0.291172
$445$	−41.9804	−1.99006
$446$	−16.0375	−0.759399
$447$	−2.80066	−0.132467
$448$	−4.90006	−0.231506
$449$	13.3185	0.628539	0.314269	−	0.949334i	$-0.398241\pi$
$449$	13.3185	0.628539	0.314269	+	0.949334i	$0.398241\pi$
$450$	−12.6529	−0.596463
$451$	−4.31377	−0.203127
$452$	10.3745	0.487974
$453$	−8.91454	−0.418842
$454$	1.36685	0.0641495
$455$	−100.577	−4.71513
$456$	−3.21339	−0.150481
$457$	−23.6296	−1.10535	−0.552673	−	0.833398i	$-0.686392\pi$
$457$	−23.6296	−1.10535	−0.552673	+	0.833398i	$0.686392\pi$
$458$	−13.8230	−0.645908
$459$	14.6341	0.683062
$460$	30.4924	1.42172
$461$	−22.4828	−1.04713	−0.523565	−	0.851986i	$-0.675398\pi$
$461$	−22.4828	−1.04713	−0.523565	+	0.851986i	$0.675398\pi$
$462$	6.03174	0.280622
$463$	7.92592	0.368349	0.184174	−	0.982894i	$-0.441039\pi$
$463$	7.92592	0.368349	0.184174	+	0.982894i	$0.441039\pi$
$464$	3.76759	0.174906
$465$	11.8676	0.550346
$466$	−11.5284	−0.534044
$467$	−7.17044	−0.331809	−0.165904	−	0.986142i	$-0.553054\pi$
$467$	−7.17044	−0.331809	−0.165904	+	0.986142i	$0.553054\pi$
$468$	−8.28770	−0.383099
$469$	−2.14696	−0.0991373
$470$	−45.6780	−2.10697
$471$	−23.9341	−1.10282
$472$	4.30587	0.198194
$473$	1.00000	0.0459800
$474$	0.889550	0.0408584
$475$	22.2462	1.02073
$476$	−12.9893	−0.595366
$477$	5.04580	0.231031
$478$	−21.1701	−0.968296
$479$	42.0090	1.91944	0.959719	−	0.280961i	$-0.0906530\pi$
$479$	42.0090	1.91944	0.959719	+	0.280961i	$0.0906530\pi$
$480$	−4.52647	−0.206604
$481$	−27.8214	−1.26855
$482$	10.4452	0.475765
$483$	50.0168	2.27585
$484$	1.00000	0.0454545
$485$	38.5208	1.74914
$486$	−13.6796	−0.620519
$487$	−23.3107	−1.05631	−0.528153	−	0.849149i	$-0.677115\pi$
$487$	−23.3107	−1.05631	−0.528153	+	0.849149i	$0.677115\pi$
$488$	4.48915	0.203214
$489$	−7.83631	−0.354370
$490$	62.5514	2.82578
$491$	11.2005	0.505470	0.252735	−	0.967536i	$-0.418670\pi$
$491$	11.2005	0.505470	0.252735	+	0.967536i	$0.418670\pi$
$492$	5.31005	0.239395
$493$	9.98735	0.449807
$494$	14.5714	0.655598
$495$	−5.45975	−0.245398
$496$	−2.62182	−0.117723
$497$	−55.1609	−2.47431
$498$	17.8524	0.799985
$499$	−5.02700	−0.225039	−0.112520	−	0.993649i	$-0.535892\pi$
$499$	−5.02700	−0.225039	−0.112520	+	0.993649i	$0.535892\pi$
$500$	12.9507	0.579172
$501$	−1.94500	−0.0868960
$502$	25.4394	1.13542
$503$	39.8436	1.77654	0.888270	−	0.459322i	$-0.151908\pi$
$503$	39.8436	1.77654	0.888270	+	0.459322i	$0.151908\pi$
$504$	7.27538	0.324071
$505$	−10.1641	−0.452298
$506$	8.29227	0.368636
$507$	−22.3507	−0.992630
$508$	−10.9297	−0.484929
$509$	44.0609	1.95296	0.976482	−	0.215598i	$-0.0691702\pi$
$509$	44.0609	1.95296	0.976482	+	0.215598i	$0.0691702\pi$
$510$	−11.9990	−0.531326
$511$	−5.41795	−0.239676
$512$	1.00000	0.0441942
$513$	14.4113	0.636272
$514$	4.92848	0.217386
$515$	25.2181	1.11124
$516$	−1.23095	−0.0541897
$517$	−12.4219	−0.546316
$518$	24.4231	1.07309
$519$	14.6835	0.644533
$520$	20.5257	0.900111
$521$	−9.29601	−0.407266	−0.203633	−	0.979047i	$-0.565275\pi$
$521$	−9.29601	−0.407266	−0.203633	+	0.979047i	$0.565275\pi$
$522$	−5.59395	−0.244840
$523$	−35.3725	−1.54673	−0.773367	−	0.633959i	$-0.781429\pi$
$523$	−35.3725	−1.54673	−0.773367	+	0.633959i	$0.781429\pi$
$524$	−10.3916	−0.453961
$525$	51.4017	2.24336
$526$	26.8654	1.17139
$527$	−6.95006	−0.302749
$528$	−1.23095	−0.0535704
$529$	45.7618	1.98964
$530$	−12.4967	−0.542820
$531$	−6.39316	−0.277439
$532$	−12.7915	−0.554583
$533$	−24.0789	−1.04297
$534$	14.0530	0.608133
$535$	−72.6574	−3.14125
$536$	0.438150	0.0189252
$537$	−31.2011	−1.34643
$538$	30.0616	1.29605
$539$	17.0106	0.732696
$540$	20.3001	0.873578
$541$	22.9104	0.984995	0.492498	−	0.870314i	$-0.336084\pi$
$541$	22.9104	0.984995	0.492498	+	0.870314i	$0.336084\pi$
$542$	−20.6924	−0.888817
$543$	15.1573	0.650462
$544$	2.65086	0.113655
$545$	−43.4989	−1.86329
$546$	33.6684	1.44087
$547$	24.7808	1.05955	0.529774	−	0.848139i	$-0.322277\pi$
$547$	24.7808	1.05955	0.529774	+	0.848139i	$0.322277\pi$
$548$	−15.1656	−0.647841
$549$	−6.66528	−0.284467
$550$	8.52187	0.363374
$551$	9.83525	0.418996
$552$	−10.2074	−0.434456
$553$	3.54103	0.150580
$554$	−23.2518	−0.987873
$555$	22.5611	0.957664
$556$	−10.8056	−0.458261
$557$	4.67034	0.197889	0.0989443	−	0.995093i	$-0.468453\pi$
$557$	4.67034	0.197889	0.0989443	+	0.995093i	$0.468453\pi$
$558$	3.89275	0.164793
$559$	5.58187	0.236088
$560$	−18.0185	−0.761422
$561$	−3.26308	−0.137767
$562$	6.45528	0.272300
$563$	5.51651	0.232493	0.116247	−	0.993220i	$-0.462914\pi$
$563$	5.51651	0.232493	0.116247	+	0.993220i	$0.462914\pi$
$564$	15.2908	0.643860
$565$	38.1491	1.60494
$566$	−11.7944	−0.495754
$567$	11.4722	0.481789
$568$	11.2572	0.472342
$569$	35.4930	1.48795	0.743973	−	0.668210i	$-0.232939\pi$
$569$	35.4930	1.48795	0.743973	+	0.668210i	$0.232939\pi$
$570$	−11.8163	−0.494930
$571$	−27.0554	−1.13223	−0.566117	−	0.824325i	$-0.691555\pi$
$571$	−27.0554	−1.13223	−0.566117	+	0.824325i	$0.691555\pi$
$572$	5.58187	0.233390
$573$	−10.9433	−0.457162
$574$	21.1377	0.882271
$575$	70.6657	2.94696
$576$	−1.48475	−0.0618647
$577$	−7.09929	−0.295547	−0.147774	−	0.989021i	$-0.547211\pi$
$577$	−7.09929	−0.295547	−0.147774	+	0.989021i	$0.547211\pi$
$578$	−9.97296	−0.414820
$579$	16.2948	0.677191
$580$	13.8542	0.575266
$581$	71.0650	2.94827
$582$	−12.8949	−0.534512
$583$	−3.39841	−0.140748
$584$	1.10569	0.0457539
$585$	−30.4756	−1.26001
$586$	−8.02756	−0.331615
$587$	−29.5750	−1.22069	−0.610346	−	0.792135i	$-0.708969\pi$
$587$	−29.5750	−1.22069	−0.610346	+	0.792135i	$0.708969\pi$
$588$	−20.9392	−0.863518
$589$	−6.84422	−0.282011
$590$	15.8336	0.651858
$591$	9.94454	0.409064
$592$	−4.98425	−0.204851
$593$	−33.5870	−1.37925	−0.689626	−	0.724166i	$-0.742225\pi$
$593$	−33.5870	−1.37925	−0.689626	+	0.724166i	$0.742225\pi$
$594$	5.52052	0.226510
$595$	−47.7646	−1.95816
$596$	2.27519	0.0931955
$597$	−13.9677	−0.571662
$598$	46.2864	1.89279
$599$	3.92728	0.160464	0.0802321	−	0.996776i	$-0.474434\pi$
$599$	3.92728	0.160464	0.0802321	+	0.996776i	$0.474434\pi$
$600$	−10.4900	−0.428254
$601$	22.1126	0.901992	0.450996	−	0.892526i	$-0.351069\pi$
$601$	22.1126	0.901992	0.450996	+	0.892526i	$0.351069\pi$
$602$	−4.90006	−0.199711
$603$	−0.650544	−0.0264922
$604$	7.24198	0.294672
$605$	3.67721	0.149500
$606$	3.40246	0.138216
$607$	−0.613336	−0.0248945	−0.0124473	−	0.999923i	$-0.503962\pi$
$607$	−0.613336	−0.0248945	−0.0124473	+	0.999923i	$0.503962\pi$
$608$	2.61049	0.105869
$609$	22.7251	0.920869
$610$	16.5076	0.668371
$611$	−69.3376	−2.80510
$612$	−3.93587	−0.159098
$613$	−34.7685	−1.40429	−0.702143	−	0.712036i	$-0.747773\pi$
$613$	−34.7685	−1.40429	−0.702143	+	0.712036i	$0.747773\pi$
$614$	−10.3199	−0.416478
$615$	19.5262	0.787371
$616$	−4.90006	−0.197429
$617$	6.34277	0.255350	0.127675	−	0.991816i	$-0.459249\pi$
$617$	6.34277	0.255350	0.127675	+	0.991816i	$0.459249\pi$
$618$	−8.44182	−0.339580
$619$	33.3537	1.34060	0.670299	−	0.742091i	$-0.266166\pi$
$619$	33.3537	1.34060	0.670299	+	0.742091i	$0.266166\pi$
$620$	−9.64097	−0.387191
$621$	45.7777	1.83699
$622$	3.60431	0.144520
$623$	55.9408	2.24122
$624$	−6.87102	−0.275061
$625$	5.01297	0.200519
$626$	12.2746	0.490590
$627$	−3.21339	−0.128330
$628$	19.4435	0.775881
$629$	−13.2125	−0.526818
$630$	26.7531	1.06587
$631$	−22.9465	−0.913484	−0.456742	−	0.889599i	$-0.650984\pi$
$631$	−22.9465	−0.913484	−0.456742	+	0.889599i	$0.650984\pi$
$632$	−0.722651	−0.0287455
$633$	−8.02852	−0.319105
$634$	−30.4516	−1.20939
$635$	−40.1910	−1.59493
$636$	4.18328	0.165878
$637$	94.9506	3.76208
$638$	3.76759	0.149160
$639$	−16.7142	−0.661203
$640$	3.67721	0.145354
$641$	−18.1033	−0.715037	−0.357519	−	0.933906i	$-0.616377\pi$
$641$	−18.1033	−0.715037	−0.357519	+	0.933906i	$0.616377\pi$
$642$	24.3222	0.959921
$643$	21.6470	0.853673	0.426837	−	0.904329i	$-0.359628\pi$
$643$	21.6470	0.853673	0.426837	+	0.904329i	$0.359628\pi$
$644$	−40.6326	−1.60115
$645$	−4.52647	−0.178230
$646$	6.92003	0.272265
$647$	−31.3397	−1.23209	−0.616046	−	0.787710i	$-0.711266\pi$
$647$	−31.3397	−1.23209	−0.616046	+	0.787710i	$0.711266\pi$
$648$	−2.34125	−0.0919728
$649$	4.30587	0.169020
$650$	47.5680	1.86577
$651$	−15.8141	−0.619804
$652$	6.36605	0.249314
$653$	−8.34527	−0.326576	−0.163288	−	0.986578i	$-0.552210\pi$
$653$	−8.34527	−0.326576	−0.163288	+	0.986578i	$0.552210\pi$
$654$	14.5614	0.569394
$655$	−38.2122	−1.49308
$656$	−4.31377	−0.168424
$657$	−1.64168	−0.0640480
$658$	60.8682	2.37289
$659$	−18.2964	−0.712725	−0.356362	−	0.934348i	$-0.615983\pi$
$659$	−18.2964	−0.712725	−0.356362	+	0.934348i	$0.615983\pi$
$660$	−4.52647	−0.176193
$661$	19.5809	0.761610	0.380805	−	0.924655i	$-0.375647\pi$
$661$	19.5809	0.761610	0.380805	+	0.924655i	$0.375647\pi$
$662$	−19.8001	−0.769551
$663$	−18.2141	−0.707376
$664$	−14.5029	−0.562822
$665$	−47.0372	−1.82402
$666$	7.40038	0.286759
$667$	31.2419	1.20969
$668$	1.58007	0.0611348
$669$	19.7415	0.763249
$670$	1.61117	0.0622449
$671$	4.48915	0.173302
$672$	6.03174	0.232679
$673$	43.8224	1.68923	0.844616	−	0.535373i	$-0.179829\pi$
$673$	43.8224	1.68923	0.844616	+	0.535373i	$0.179829\pi$
$674$	−13.2827	−0.511631
$675$	47.0452	1.81077
$676$	18.1572	0.698355
$677$	17.0421	0.654980	0.327490	−	0.944855i	$-0.393797\pi$
$677$	17.0421	0.654980	0.327490	+	0.944855i	$0.393797\pi$
$678$	−12.7705	−0.490447
$679$	−51.3308	−1.96990
$680$	9.74776	0.373809
$681$	−1.68253	−0.0644747
$682$	−2.62182	−0.100395
$683$	−35.5104	−1.35877	−0.679383	−	0.733784i	$-0.737753\pi$
$683$	−35.5104	−1.35877	−0.679383	+	0.733784i	$0.737753\pi$
$684$	−3.87593	−0.148200
$685$	−55.7670	−2.13075
$686$	−49.0523	−1.87282
$687$	17.0155	0.649183
$688$	1.00000	0.0381246
$689$	−18.9695	−0.722679
$690$	−37.5348	−1.42892
$691$	21.3308	0.811462	0.405731	−	0.913992i	$-0.367017\pi$
$691$	21.3308	0.811462	0.405731	+	0.913992i	$0.367017\pi$
$692$	−11.9285	−0.453455
$693$	7.27538	0.276369
$694$	19.2213	0.729630
$695$	−39.7345	−1.50722
$696$	−4.63773	−0.175793
$697$	−11.4352	−0.433138
$698$	−9.85669	−0.373081
$699$	14.1909	0.536751
$700$	−41.7577	−1.57829
$701$	−4.84417	−0.182962	−0.0914810	−	0.995807i	$-0.529160\pi$
$701$	−4.84417	−0.182962	−0.0914810	+	0.995807i	$0.529160\pi$
$702$	30.8148	1.16303
$703$	−13.0113	−0.490731
$704$	1.00000	0.0376889
$705$	56.2276	2.11765
$706$	−28.2926	−1.06481
$707$	13.5442	0.509381
$708$	−5.30032	−0.199198
$709$	−33.3072	−1.25088	−0.625438	−	0.780274i	$-0.715080\pi$
$709$	−33.3072	−1.25088	−0.625438	+	0.780274i	$0.715080\pi$
$710$	41.3951	1.55353
$711$	1.07296	0.0402391
$712$	−11.4164	−0.427846
$713$	−21.7408	−0.814200
$714$	15.9893	0.598384
$715$	20.5257	0.767618
$716$	25.3471	0.947266
$717$	26.0593	0.973204
$718$	0.763328	0.0284872
$719$	−42.4213	−1.58205	−0.791024	−	0.611785i	$-0.790452\pi$
$719$	−42.4213	−1.58205	−0.791024	+	0.611785i	$0.790452\pi$
$720$	−5.45975	−0.203473
$721$	−33.6043	−1.25149
$722$	−12.1854	−0.453492
$723$	−12.8575	−0.478177
$724$	−12.3135	−0.457626
$725$	32.1069	1.19242
$726$	−1.23095	−0.0456850
$727$	−14.0586	−0.521406	−0.260703	−	0.965419i	$-0.583954\pi$
$727$	−14.0586	−0.521406	−0.260703	+	0.965419i	$0.583954\pi$
$728$	−27.3515	−1.01371
$729$	23.8627	0.883803
$730$	4.06586	0.150484
$731$	2.65086	0.0980455
$732$	−5.52594	−0.204244
$733$	−29.1876	−1.07807	−0.539034	−	0.842284i	$-0.681210\pi$
$733$	−29.1876	−1.07807	−0.539034	+	0.842284i	$0.681210\pi$
$734$	30.4433	1.12368
$735$	−76.9978	−2.84011
$736$	8.29227	0.305657
$737$	0.438150	0.0161394
$738$	6.40488	0.235767
$739$	−6.64186	−0.244325	−0.122162	−	0.992510i	$-0.538983\pi$
$739$	−6.64186	−0.244325	−0.122162	+	0.992510i	$0.538983\pi$
$740$	−18.3281	−0.673755
$741$	−17.9367	−0.658921
$742$	16.6524	0.611328
$743$	−18.8868	−0.692890	−0.346445	−	0.938070i	$-0.612611\pi$
$743$	−18.8868	−0.692890	−0.346445	+	0.938070i	$0.612611\pi$
$744$	3.22734	0.118320
$745$	8.36636	0.306520
$746$	−4.16889	−0.152634
$747$	21.5332	0.787860
$748$	2.65086	0.0969249
$749$	96.8194	3.53770
$750$	−15.9417	−0.582108
$751$	−36.3383	−1.32600	−0.663001	−	0.748618i	$-0.730718\pi$
$751$	−36.3383	−1.32600	−0.663001	+	0.748618i	$0.730718\pi$
$752$	−12.4219	−0.452981
$753$	−31.3148	−1.14117
$754$	21.0302	0.765875
$755$	26.6303	0.969175
$756$	−27.0509	−0.983831
$757$	12.5056	0.454522	0.227261	−	0.973834i	$-0.427023\pi$
$757$	12.5056	0.454522	0.227261	+	0.973834i	$0.427023\pi$
$758$	−11.1383	−0.404562
$759$	−10.2074	−0.370505
$760$	9.59931	0.348204
$761$	50.9872	1.84828	0.924142	−	0.382050i	$-0.124782\pi$
$761$	50.9872	1.84828	0.924142	+	0.382050i	$0.124782\pi$
$762$	13.4540	0.487387
$763$	57.9644	2.09845
$764$	8.89008	0.321632
$765$	−14.4730	−0.523273
$766$	−27.9543	−1.01003
$767$	24.0348	0.867846
$768$	−1.23095	−0.0444182
$769$	17.7403	0.639732	0.319866	−	0.947463i	$-0.396362\pi$
$769$	17.7403	0.639732	0.319866	+	0.947463i	$0.396362\pi$
$770$	−18.0185	−0.649343
$771$	−6.06673	−0.218488
$772$	−13.2376	−0.476431
$773$	46.7620	1.68191	0.840956	−	0.541103i	$-0.181993\pi$
$773$	46.7620	1.68191	0.840956	+	0.541103i	$0.181993\pi$
$774$	−1.48475	−0.0533684
$775$	−22.3428	−0.802577
$776$	10.4756	0.376050
$777$	−30.0637	−1.07853
$778$	8.97453	0.321752
$779$	−11.2610	−0.403468
$780$	−25.2662	−0.904674
$781$	11.2572	0.402814
$782$	21.9816	0.786061
$783$	20.7991	0.743298
$784$	17.0106	0.607520
$785$	71.4980	2.55187
$786$	12.7916	0.456262
$787$	−5.49607	−0.195914	−0.0979569	−	0.995191i	$-0.531231\pi$
$787$	−5.49607	−0.195914	−0.0979569	+	0.995191i	$0.531231\pi$
$788$	−8.07873	−0.287793
$789$	−33.0700	−1.17732
$790$	−2.65734	−0.0945440
$791$	−50.8354	−1.80750
$792$	−1.48475	−0.0527584
$793$	25.0578	0.889830
$794$	30.1593	1.07031
$795$	15.3828	0.545572
$796$	11.3471	0.402187
$797$	−31.4103	−1.11261	−0.556305	−	0.830979i	$-0.687781\pi$
$797$	−31.4103	−1.11261	−0.556305	+	0.830979i	$0.687781\pi$
$798$	15.7458	0.557395
$799$	−32.9288	−1.16494
$800$	8.52187	0.301294
$801$	16.9505	0.598916
$802$	−32.8112	−1.15860
$803$	1.10569	0.0390190
$804$	−0.539342	−0.0190211
$805$	−149.415	−5.26617
$806$	−14.6346	−0.515483
$807$	−37.0044	−1.30262
$808$	−2.76409	−0.0972402
$809$	−12.3400	−0.433850	−0.216925	−	0.976188i	$-0.569603\pi$
$809$	−12.3400	−0.433850	−0.216925	+	0.976188i	$0.569603\pi$
$810$	−8.60925	−0.302498
$811$	32.1130	1.12764	0.563819	−	0.825898i	$-0.309331\pi$
$811$	32.1130	1.12764	0.563819	+	0.825898i	$0.309331\pi$
$812$	−18.4614	−0.647869
$813$	25.4714	0.893322
$814$	−4.98425	−0.174698
$815$	23.4093	0.819992
$816$	−3.26308	−0.114231
$817$	2.61049	0.0913294
$818$	13.4497	0.470259
$819$	40.6102	1.41903
$820$	−15.8626	−0.553947
$821$	−37.9639	−1.32495	−0.662475	−	0.749084i	$-0.730494\pi$
$821$	−37.9639	−1.32495	−0.662475	+	0.749084i	$0.730494\pi$
$822$	18.6681	0.651125
$823$	23.1160	0.805774	0.402887	−	0.915250i	$-0.368007\pi$
$823$	23.1160	0.805774	0.402887	+	0.915250i	$0.368007\pi$
$824$	6.85795	0.238908
$825$	−10.4900	−0.365216
$826$	−21.0990	−0.734128
$827$	24.5982	0.855364	0.427682	−	0.903929i	$-0.359330\pi$
$827$	24.5982	0.855364	0.427682	+	0.903929i	$0.359330\pi$
$828$	−12.3120	−0.427871
$829$	24.1221	0.837795	0.418897	−	0.908034i	$-0.362417\pi$
$829$	24.1221	0.837795	0.418897	+	0.908034i	$0.362417\pi$
$830$	−53.3302	−1.85112
$831$	28.6218	0.992881
$832$	5.58187	0.193516
$833$	45.0925	1.56236
$834$	13.3012	0.460584
$835$	5.81026	0.201072
$836$	2.61049	0.0902856
$837$	−14.4738	−0.500288
$838$	19.0618	0.658480
$839$	−14.4289	−0.498142	−0.249071	−	0.968485i	$-0.580125\pi$
$839$	−14.4289	−0.498142	−0.249071	+	0.968485i	$0.580125\pi$
$840$	22.1800	0.765282
$841$	−14.8052	−0.510526
$842$	7.14908	0.246374
$843$	−7.94615	−0.273680
$844$	6.52220	0.224503
$845$	66.7680	2.29689
$846$	18.4435	0.634101
$847$	−4.90006	−0.168368
$848$	−3.39841	−0.116702
$849$	14.5183	0.498267
$850$	22.5903	0.774840
$851$	−41.3307	−1.41680
$852$	−13.8571	−0.474736
$853$	−14.4791	−0.495755	−0.247877	−	0.968791i	$-0.579733\pi$
$853$	−14.4791	−0.495755	−0.247877	+	0.968791i	$0.579733\pi$
$854$	−21.9971	−0.752725
$855$	−14.2526	−0.487429
$856$	−19.7588	−0.675343
$857$	30.3071	1.03527	0.517636	−	0.855601i	$-0.326812\pi$
$857$	30.3071	1.03527	0.517636	+	0.855601i	$0.326812\pi$
$858$	−6.87102	−0.234573
$859$	−3.52173	−0.120160	−0.0600799	−	0.998194i	$-0.519136\pi$
$859$	−3.52173	−0.120160	−0.0600799	+	0.998194i	$0.519136\pi$
$860$	3.67721	0.125392
$861$	−26.0195	−0.886743
$862$	9.95384	0.339029
$863$	−57.7466	−1.96572	−0.982858	−	0.184365i	$-0.940977\pi$
$863$	−57.7466	−1.96572	−0.982858	+	0.184365i	$0.940977\pi$
$864$	5.52052	0.187812
$865$	−43.8638	−1.49141
$866$	−16.5172	−0.561277
$867$	12.2763	0.416923
$868$	12.8471	0.436057
$869$	−0.722651	−0.0245143
$870$	−17.0539	−0.578182
$871$	2.44569	0.0828691
$872$	−11.8293	−0.400592
$873$	−15.5536	−0.526410
$874$	21.6469	0.732216
$875$	−63.4590	−2.14531
$876$	−1.36106	−0.0459858
$877$	15.1694	0.512234	0.256117	−	0.966646i	$-0.417557\pi$
$877$	15.1694	0.512234	0.256117	+	0.966646i	$0.417557\pi$
$878$	34.7051	1.17124
$879$	9.88155	0.333296
$880$	3.67721	0.123959
$881$	11.5773	0.390049	0.195024	−	0.980798i	$-0.437521\pi$
$881$	11.5773	0.390049	0.195024	+	0.980798i	$0.437521\pi$
$882$	−25.2565	−0.850430
$883$	−14.3177	−0.481831	−0.240915	−	0.970546i	$-0.577448\pi$
$883$	−14.3177	−0.481831	−0.240915	+	0.970546i	$0.577448\pi$
$884$	14.7967	0.497668
$885$	−19.4904	−0.655163
$886$	9.61478	0.323015
$887$	−19.5712	−0.657135	−0.328568	−	0.944480i	$-0.606566\pi$
$887$	−19.5712	−0.657135	−0.328568	+	0.944480i	$0.606566\pi$
$888$	6.13538	0.205890
$889$	53.5564	1.79622
$890$	−41.9804	−1.40719
$891$	−2.34125	−0.0784347
$892$	−16.0375	−0.536976
$893$	−32.4273	−1.08514
$894$	−2.80066	−0.0936680
$895$	93.2066	3.11555
$896$	−4.90006	−0.163699
$897$	−56.9764	−1.90238
$898$	13.3185	0.444444
$899$	−9.87794	−0.329448
$900$	−12.6529	−0.421763
$901$	−9.00869	−0.300123
$902$	−4.31377	−0.143633
$903$	6.03174	0.200724
$904$	10.3745	0.345049
$905$	−45.2792	−1.50513
$906$	−8.91454	−0.296166
$907$	−17.0067	−0.564698	−0.282349	−	0.959312i	$-0.591114\pi$
$907$	−17.0067	−0.564698	−0.282349	+	0.959312i	$0.591114\pi$
$908$	1.36685	0.0453606
$909$	4.10399	0.136121
$910$	−100.577	−3.33410
$911$	−36.2711	−1.20172	−0.600858	−	0.799356i	$-0.705174\pi$
$911$	−36.2711	−1.20172	−0.600858	+	0.799356i	$0.705174\pi$
$912$	−3.21339	−0.106406
$913$	−14.5029	−0.479976
$914$	−23.6296	−0.781598
$915$	−20.3200	−0.671759
$916$	−13.8230	−0.456726
$917$	50.9196	1.68151
$918$	14.6341	0.482998
$919$	−27.5029	−0.907237	−0.453618	−	0.891196i	$-0.649867\pi$
$919$	−27.5029	−0.907237	−0.453618	+	0.891196i	$0.649867\pi$
$920$	30.4924	1.00531
$921$	12.7033	0.418589
$922$	−22.4828	−0.740433
$923$	62.8362	2.06828
$924$	6.03174	0.198430
$925$	−42.4751	−1.39657
$926$	7.92592	0.260462
$927$	−10.1824	−0.334433
$928$	3.76759	0.123677
$929$	14.0810	0.461982	0.230991	−	0.972956i	$-0.425803\pi$
$929$	14.0810	0.461982	0.230991	+	0.972956i	$0.425803\pi$
$930$	11.8676	0.389154
$931$	44.4058	1.45534
$932$	−11.5284	−0.377626
$933$	−4.43674	−0.145252
$934$	−7.17044	−0.234624
$935$	9.74776	0.318786
$936$	−8.28770	−0.270892
$937$	24.7779	0.809457	0.404729	−	0.914437i	$-0.367366\pi$
$937$	24.7779	0.809457	0.404729	+	0.914437i	$0.367366\pi$
$938$	−2.14696	−0.0701007
$939$	−15.1094	−0.493077
$940$	−45.6780	−1.48985
$941$	−14.8423	−0.483846	−0.241923	−	0.970295i	$-0.577778\pi$
$941$	−14.8423	−0.483846	−0.241923	+	0.970295i	$0.577778\pi$
$942$	−23.9341	−0.779815
$943$	−35.7709	−1.16486
$944$	4.30587	0.140144
$945$	−99.4717	−3.23582
$946$	1.00000	0.0325128
$947$	1.43561	0.0466512	0.0233256	−	0.999728i	$-0.492575\pi$
$947$	1.43561	0.0466512	0.0233256	+	0.999728i	$0.492575\pi$
$948$	0.889550	0.0288912
$949$	6.17182	0.200346
$950$	22.2462	0.721763
$951$	37.4845	1.21552
$952$	−12.9893	−0.420987
$953$	24.0381	0.778672	0.389336	−	0.921096i	$-0.372705\pi$
$953$	24.0381	0.778672	0.389336	+	0.921096i	$0.372705\pi$
$954$	5.04580	0.163364
$955$	32.6907	1.05785
$956$	−21.1701	−0.684688
$957$	−4.63773	−0.149917
$958$	42.0090	1.35725
$959$	74.3122	2.39967
$960$	−4.52647	−0.146091
$961$	−24.1261	−0.778260
$962$	−27.8214	−0.896998
$963$	29.3370	0.945371
$964$	10.4452	0.336417
$965$	−48.6774	−1.56698
$966$	50.0168	1.60927
$967$	53.8556	1.73188	0.865939	−	0.500149i	$-0.166721\pi$
$967$	53.8556	1.73188	0.865939	+	0.500149i	$0.166721\pi$
$968$	1.00000	0.0321412
$969$	−8.51823	−0.273645
$970$	38.5208	1.23683
$971$	−8.81600	−0.282919	−0.141460	−	0.989944i	$-0.545180\pi$
$971$	−8.81600	−0.282919	−0.141460	+	0.989944i	$0.545180\pi$
$972$	−13.6796	−0.438774
$973$	52.9482	1.69744
$974$	−23.3107	−0.746922
$975$	−58.5540	−1.87523
$976$	4.48915	0.143694
$977$	13.2456	0.423765	0.211882	−	0.977295i	$-0.432041\pi$
$977$	13.2456	0.423765	0.211882	+	0.977295i	$0.432041\pi$
$978$	−7.83631	−0.250577
$979$	−11.4164	−0.364869
$980$	62.5514	1.99813
$981$	17.5636	0.560764
$982$	11.2005	0.357421
$983$	22.2168	0.708606	0.354303	−	0.935131i	$-0.384718\pi$
$983$	22.2168	0.708606	0.354303	+	0.935131i	$0.384718\pi$
$984$	5.31005	0.169278
$985$	−29.7072	−0.946550
$986$	9.98735	0.318062
$987$	−74.9259	−2.38492
$988$	14.5714	0.463578
$989$	8.29227	0.263679
$990$	−5.45975	−0.173522
$991$	36.4701	1.15851	0.579256	−	0.815146i	$-0.303343\pi$
$991$	36.4701	1.15851	0.579256	+	0.815146i	$0.303343\pi$
$992$	−2.62182	−0.0832428
$993$	24.3730	0.773452
$994$	−55.1609	−1.74960
$995$	41.7256	1.32279
$996$	17.8524	0.565675
$997$	−16.1413	−0.511199	−0.255600	−	0.966783i	$-0.582273\pi$
$997$	−16.1413	−0.511199	−0.255600	+	0.966783i	$0.582273\pi$
$998$	−5.02700	−0.159127
$999$	−27.5157	−0.870557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.k.1.3	✓	7
3.2	odd	2		8514.2.a.bl.1.1		7
4.3	odd	2		7568.2.a.bg.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.k.1.3	✓	7	1.1	even	1	trivial
7568.2.a.bg.1.5		7	4.3	odd	2
8514.2.a.bl.1.1		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.23095 q^{3} +1.00000 q^{4} +3.67721 q^{5} -1.23095 q^{6} -4.90006 q^{7} +1.00000 q^{8} -1.48475 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.23095 q^{3} +1.00000 q^{4} +3.67721 q^{5} -1.23095 q^{6} -4.90006 q^{7} +1.00000 q^{8} -1.48475 q^{9} +3.67721 q^{10} +1.00000 q^{11} -1.23095 q^{12} +5.58187 q^{13} -4.90006 q^{14} -4.52647 q^{15} +1.00000 q^{16} +2.65086 q^{17} -1.48475 q^{18} +2.61049 q^{19} +3.67721 q^{20} +6.03174 q^{21} +1.00000 q^{22} +8.29227 q^{23} -1.23095 q^{24} +8.52187 q^{25} +5.58187 q^{26} +5.52052 q^{27} -4.90006 q^{28} +3.76759 q^{29} -4.52647 q^{30} -2.62182 q^{31} +1.00000 q^{32} -1.23095 q^{33} +2.65086 q^{34} -18.0185 q^{35} -1.48475 q^{36} -4.98425 q^{37} +2.61049 q^{38} -6.87102 q^{39} +3.67721 q^{40} -4.31377 q^{41} +6.03174 q^{42} +1.00000 q^{43} +1.00000 q^{44} -5.45975 q^{45} +8.29227 q^{46} -12.4219 q^{47} -1.23095 q^{48} +17.0106 q^{49} +8.52187 q^{50} -3.26308 q^{51} +5.58187 q^{52} -3.39841 q^{53} +5.52052 q^{54} +3.67721 q^{55} -4.90006 q^{56} -3.21339 q^{57} +3.76759 q^{58} +4.30587 q^{59} -4.52647 q^{60} +4.48915 q^{61} -2.62182 q^{62} +7.27538 q^{63} +1.00000 q^{64} +20.5257 q^{65} -1.23095 q^{66} +0.438150 q^{67} +2.65086 q^{68} -10.2074 q^{69} -18.0185 q^{70} +11.2572 q^{71} -1.48475 q^{72} +1.10569 q^{73} -4.98425 q^{74} -10.4900 q^{75} +2.61049 q^{76} -4.90006 q^{77} -6.87102 q^{78} -0.722651 q^{79} +3.67721 q^{80} -2.34125 q^{81} -4.31377 q^{82} -14.5029 q^{83} +6.03174 q^{84} +9.74776 q^{85} +1.00000 q^{86} -4.63773 q^{87} +1.00000 q^{88} -11.4164 q^{89} -5.45975 q^{90} -27.3515 q^{91} +8.29227 q^{92} +3.22734 q^{93} -12.4219 q^{94} +9.59931 q^{95} -1.23095 q^{96} +10.4756 q^{97} +17.0106 q^{98} -1.48475 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9} + 8 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{15} + 7 q^{16} + 10 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} + 7 q^{22} - 4 q^{23} + 3 q^{24} + 11 q^{25} + 4 q^{26} + 15 q^{27} - 2 q^{28} + 5 q^{29} + 2 q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 10 q^{34} - 10 q^{35} + 10 q^{36} + 6 q^{37} - 2 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} + 7 q^{43} + 7 q^{44} - 2 q^{45} - 4 q^{46} - 6 q^{47} + 3 q^{48} + 31 q^{49} + 11 q^{50} - 14 q^{51} + 4 q^{52} + q^{53} + 15 q^{54} + 8 q^{55} - 2 q^{56} - 30 q^{57} + 5 q^{58} - 4 q^{59} + 2 q^{60} + 9 q^{61} - 2 q^{62} - 24 q^{63} + 7 q^{64} + 18 q^{65} + 3 q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 10 q^{70} + 10 q^{72} + 13 q^{73} + 6 q^{74} - 9 q^{75} - 2 q^{76} - 2 q^{77} - 8 q^{78} - 31 q^{79} + 8 q^{80} - 25 q^{81} + 4 q^{82} - 11 q^{83} - 24 q^{85} + 7 q^{86} - 13 q^{87} + 7 q^{88} + 10 q^{89} - 2 q^{90} - 12 q^{91} - 4 q^{92} + 12 q^{93} - 6 q^{94} - 18 q^{95} + 3 q^{96} + 23 q^{97} + 31 q^{98} + 10 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9 + 8 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^15 + 7 * q^16 + 10 * q^17 + 10 * q^18 - 2 * q^19 + 8 * q^20 + 7 * q^22 - 4 * q^23 + 3 * q^24 + 11 * q^25 + 4 * q^26 + 15 * q^27 - 2 * q^28 + 5 * q^29 + 2 * q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 10 * q^34 - 10 * q^35 + 10 * q^36 + 6 * q^37 - 2 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 + 7 * q^43 + 7 * q^44 - 2 * q^45 - 4 * q^46 - 6 * q^47 + 3 * q^48 + 31 * q^49 + 11 * q^50 - 14 * q^51 + 4 * q^52 + q^53 + 15 * q^54 + 8 * q^55 - 2 * q^56 - 30 * q^57 + 5 * q^58 - 4 * q^59 + 2 * q^60 + 9 * q^61 - 2 * q^62 - 24 * q^63 + 7 * q^64 + 18 * q^65 + 3 * q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 10 * q^70 + 10 * q^72 + 13 * q^73 + 6 * q^74 - 9 * q^75 - 2 * q^76 - 2 * q^77 - 8 * q^78 - 31 * q^79 + 8 * q^80 - 25 * q^81 + 4 * q^82 - 11 * q^83 - 24 * q^85 + 7 * q^86 - 13 * q^87 + 7 * q^88 + 10 * q^89 - 2 * q^90 - 12 * q^91 - 4 * q^92 + 12 * q^93 - 6 * q^94 - 18 * q^95 + 3 * q^96 + 23 * q^97 + 31 * q^98 + 10 * q^99

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