LMFDB - Embedded newform 946.2.a.k.1.7

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			1.7
Root			$3.07023$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.07023 q^{3} +1.00000 q^{4} +2.26020 q^{5} +3.07023 q^{6} -4.26455 q^{7} +1.00000 q^{8} +6.42629 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.07023 q^{3} +1.00000 q^{4} +2.26020 q^{5} +3.07023 q^{6} -4.26455 q^{7} +1.00000 q^{8} +6.42629 q^{9} +2.26020 q^{10} +1.00000 q^{11} +3.07023 q^{12} +0.476943 q^{13} -4.26455 q^{14} +6.93932 q^{15} +1.00000 q^{16} +2.57281 q^{17} +6.42629 q^{18} -7.32518 q^{19} +2.26020 q^{20} -13.0931 q^{21} +1.00000 q^{22} -9.23230 q^{23} +3.07023 q^{24} +0.108489 q^{25} +0.476943 q^{26} +10.5195 q^{27} -4.26455 q^{28} -0.0534837 q^{29} +6.93932 q^{30} +5.15606 q^{31} +1.00000 q^{32} +3.07023 q^{33} +2.57281 q^{34} -9.63873 q^{35} +6.42629 q^{36} +5.06385 q^{37} -7.32518 q^{38} +1.46432 q^{39} +2.26020 q^{40} -0.892876 q^{41} -13.0931 q^{42} +1.00000 q^{43} +1.00000 q^{44} +14.5247 q^{45} -9.23230 q^{46} -3.37304 q^{47} +3.07023 q^{48} +11.1864 q^{49} +0.108489 q^{50} +7.89912 q^{51} +0.476943 q^{52} +6.48213 q^{53} +10.5195 q^{54} +2.26020 q^{55} -4.26455 q^{56} -22.4900 q^{57} -0.0534837 q^{58} -14.5527 q^{59} +6.93932 q^{60} +1.34893 q^{61} +5.15606 q^{62} -27.4053 q^{63} +1.00000 q^{64} +1.07799 q^{65} +3.07023 q^{66} +8.40501 q^{67} +2.57281 q^{68} -28.3452 q^{69} -9.63873 q^{70} -15.9176 q^{71} +6.42629 q^{72} -6.90034 q^{73} +5.06385 q^{74} +0.333087 q^{75} -7.32518 q^{76} -4.26455 q^{77} +1.46432 q^{78} -0.381383 q^{79} +2.26020 q^{80} +13.0184 q^{81} -0.892876 q^{82} +11.1991 q^{83} -13.0931 q^{84} +5.81507 q^{85} +1.00000 q^{86} -0.164207 q^{87} +1.00000 q^{88} +12.6308 q^{89} +14.5247 q^{90} -2.03395 q^{91} -9.23230 q^{92} +15.8303 q^{93} -3.37304 q^{94} -16.5563 q^{95} +3.07023 q^{96} +8.66932 q^{97} +11.1864 q^{98} +6.42629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.07023	1.77260	0.886298	−	0.463115i	$-0.153268\pi$
$3$	3.07023	1.77260	0.886298	+	0.463115i	$0.153268\pi$
$4$	1.00000	0.500000
$5$	2.26020	1.01079	0.505395	−	0.862888i	$-0.331347\pi$
$5$	2.26020	1.01079	0.505395	+	0.862888i	$0.331347\pi$
$6$	3.07023	1.25341
$7$	−4.26455	−1.61185	−0.805925	−	0.592018i	$-0.798331\pi$
$7$	−4.26455	−1.61185	−0.805925	+	0.592018i	$0.798331\pi$
$8$	1.00000	0.353553
$9$	6.42629	2.14210
$10$	2.26020	0.714737
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.07023	0.886298
$13$	0.476943	0.132280	0.0661402	−	0.997810i	$-0.478932\pi$
$13$	0.476943	0.132280	0.0661402	+	0.997810i	$0.478932\pi$
$14$	−4.26455	−1.13975
$15$	6.93932	1.79172
$16$	1.00000	0.250000
$17$	2.57281	0.623999	0.312000	−	0.950082i	$-0.399001\pi$
$17$	2.57281	0.623999	0.312000	+	0.950082i	$0.399001\pi$
$18$	6.42629	1.51469
$19$	−7.32518	−1.68051	−0.840255	−	0.542191i	$-0.817595\pi$
$19$	−7.32518	−1.68051	−0.840255	+	0.542191i	$0.817595\pi$
$20$	2.26020	0.505395
$21$	−13.0931	−2.85716
$22$	1.00000	0.213201
$23$	−9.23230	−1.92507	−0.962533	−	0.271163i	$-0.912592\pi$
$23$	−9.23230	−1.92507	−0.962533	+	0.271163i	$0.912592\pi$
$24$	3.07023	0.626707
$25$	0.108489	0.0216979
$26$	0.476943	0.0935363
$27$	10.5195	2.02448
$28$	−4.26455	−0.805925
$29$	−0.0534837	−0.00993168	−0.00496584	−	0.999988i	$-0.501581\pi$
$29$	−0.0534837	−0.00993168	−0.00496584	+	0.999988i	$0.501581\pi$
$30$	6.93932	1.26694
$31$	5.15606	0.926056	0.463028	−	0.886344i	$-0.346763\pi$
$31$	5.15606	0.926056	0.463028	+	0.886344i	$0.346763\pi$
$32$	1.00000	0.176777
$33$	3.07023	0.534458
$34$	2.57281	0.441234
$35$	−9.63873	−1.62924
$36$	6.42629	1.07105
$37$	5.06385	0.832491	0.416246	−	0.909252i	$-0.363346\pi$
$37$	5.06385	0.832491	0.416246	+	0.909252i	$0.363346\pi$
$38$	−7.32518	−1.18830
$39$	1.46432	0.234480
$40$	2.26020	0.357368
$41$	−0.892876	−0.139444	−0.0697219	−	0.997566i	$-0.522211\pi$
$41$	−0.892876	−0.139444	−0.0697219	+	0.997566i	$0.522211\pi$
$42$	−13.0931	−2.02032
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	14.5247	2.16521
$46$	−9.23230	−1.36123
$47$	−3.37304	−0.492009	−0.246004	−	0.969269i	$-0.579118\pi$
$47$	−3.37304	−0.492009	−0.246004	+	0.969269i	$0.579118\pi$
$48$	3.07023	0.443149
$49$	11.1864	1.59806
$50$	0.108489	0.0153427
$51$	7.89912	1.10610
$52$	0.476943	0.0661402
$53$	6.48213	0.890389	0.445195	−	0.895434i	$-0.353134\pi$
$53$	6.48213	0.890389	0.445195	+	0.895434i	$0.353134\pi$
$54$	10.5195	1.43152
$55$	2.26020	0.304765
$56$	−4.26455	−0.569875
$57$	−22.4900	−2.97887
$58$	−0.0534837	−0.00702276
$59$	−14.5527	−1.89460	−0.947299	−	0.320350i	$-0.896199\pi$
$59$	−14.5527	−1.89460	−0.947299	+	0.320350i	$0.896199\pi$
$60$	6.93932	0.895862
$61$	1.34893	0.172713	0.0863563	−	0.996264i	$-0.472478\pi$
$61$	1.34893	0.172713	0.0863563	+	0.996264i	$0.472478\pi$
$62$	5.15606	0.654821
$63$	−27.4053	−3.45274
$64$	1.00000	0.125000
$65$	1.07799	0.133708
$66$	3.07023	0.377919
$67$	8.40501	1.02684	0.513418	−	0.858139i	$-0.328379\pi$
$67$	8.40501	1.02684	0.513418	+	0.858139i	$0.328379\pi$
$68$	2.57281	0.312000
$69$	−28.3452	−3.41237
$70$	−9.63873	−1.15205
$71$	−15.9176	−1.88907	−0.944534	−	0.328414i	$-0.893486\pi$
$71$	−15.9176	−1.88907	−0.944534	+	0.328414i	$0.893486\pi$
$72$	6.42629	0.757346
$73$	−6.90034	−0.807624	−0.403812	−	0.914842i	$-0.632315\pi$
$73$	−6.90034	−0.807624	−0.403812	+	0.914842i	$0.632315\pi$
$74$	5.06385	0.588660
$75$	0.333087	0.0384616
$76$	−7.32518	−0.840255
$77$	−4.26455	−0.485991
$78$	1.46432	0.165802
$79$	−0.381383	−0.0429089	−0.0214545	−	0.999770i	$-0.506830\pi$
$79$	−0.381383	−0.0429089	−0.0214545	+	0.999770i	$0.506830\pi$
$80$	2.26020	0.252698
$81$	13.0184	1.44649
$82$	−0.892876	−0.0986017
$83$	11.1991	1.22926	0.614628	−	0.788817i	$-0.289306\pi$
$83$	11.1991	1.22926	0.614628	+	0.788817i	$0.289306\pi$
$84$	−13.0931	−1.42858
$85$	5.81507	0.630732
$86$	1.00000	0.107833
$87$	−0.164207	−0.0176049
$88$	1.00000	0.106600
$89$	12.6308	1.33886	0.669432	−	0.742873i	$-0.266537\pi$
$89$	12.6308	1.33886	0.669432	+	0.742873i	$0.266537\pi$
$90$	14.5247	1.53104
$91$	−2.03395	−0.213216
$92$	−9.23230	−0.962533
$93$	15.8303	1.64152
$94$	−3.37304	−0.347903
$95$	−16.5563	−1.69864
$96$	3.07023	0.313354
$97$	8.66932	0.880236	0.440118	−	0.897940i	$-0.354937\pi$
$97$	8.66932	0.880236	0.440118	+	0.897940i	$0.354937\pi$
$98$	11.1864	1.13000
$99$	6.42629	0.645867
$100$	0.108489	0.0108489
$101$	−0.973293	−0.0968463	−0.0484232	−	0.998827i	$-0.515420\pi$
$101$	−0.973293	−0.0968463	−0.0484232	+	0.998827i	$0.515420\pi$
$102$	7.89912	0.782130
$103$	−2.48667	−0.245019	−0.122510	−	0.992467i	$-0.539094\pi$
$103$	−2.48667	−0.245019	−0.122510	+	0.992467i	$0.539094\pi$
$104$	0.476943	0.0467682
$105$	−29.5931	−2.88799
$106$	6.48213	0.629600
$107$	1.29039	0.124747	0.0623735	−	0.998053i	$-0.480133\pi$
$107$	1.29039	0.124747	0.0623735	+	0.998053i	$0.480133\pi$
$108$	10.5195	1.01224
$109$	−7.31544	−0.700692	−0.350346	−	0.936620i	$-0.613936\pi$
$109$	−7.31544	−0.700692	−0.350346	+	0.936620i	$0.613936\pi$
$110$	2.26020	0.215501
$111$	15.5472	1.47567
$112$	−4.26455	−0.402962
$113$	13.5219	1.27203	0.636015	−	0.771677i	$-0.280582\pi$
$113$	13.5219	1.27203	0.636015	+	0.771677i	$0.280582\pi$
$114$	−22.4900	−2.10638
$115$	−20.8668	−1.94584
$116$	−0.0534837	−0.00496584
$117$	3.06498	0.283357
$118$	−14.5527	−1.33968
$119$	−10.9719	−1.00579
$120$	6.93932	0.633470
$121$	1.00000	0.0909091
$122$	1.34893	0.122126
$123$	−2.74133	−0.247178
$124$	5.15606	0.463028
$125$	−11.0558	−0.988859
$126$	−27.4053	−2.44146
$127$	−1.32189	−0.117299	−0.0586496	−	0.998279i	$-0.518679\pi$
$127$	−1.32189	−0.117299	−0.0586496	+	0.998279i	$0.518679\pi$
$128$	1.00000	0.0883883
$129$	3.07023	0.270318
$130$	1.07799	0.0945456
$131$	22.3026	1.94859	0.974293	−	0.225287i	$-0.0723318\pi$
$131$	22.3026	1.94859	0.974293	+	0.225287i	$0.0723318\pi$
$132$	3.07023	0.267229
$133$	31.2386	2.70873
$134$	8.40501	0.726082
$135$	23.7761	2.04632
$136$	2.57281	0.220617
$137$	−15.3235	−1.30918	−0.654589	−	0.755985i	$-0.727158\pi$
$137$	−15.3235	−1.30918	−0.654589	+	0.755985i	$0.727158\pi$
$138$	−28.3452	−2.41291
$139$	10.7783	0.914205	0.457103	−	0.889414i	$-0.348887\pi$
$139$	10.7783	0.914205	0.457103	+	0.889414i	$0.348887\pi$
$140$	−9.63873	−0.814621
$141$	−10.3560	−0.872133
$142$	−15.9176	−1.33577
$143$	0.476943	0.0398840
$144$	6.42629	0.535525
$145$	−0.120884	−0.0100389
$146$	−6.90034	−0.571076
$147$	34.3448	2.83271
$148$	5.06385	0.416246
$149$	−8.76562	−0.718107	−0.359054	−	0.933317i	$-0.616901\pi$
$149$	−8.76562	−0.718107	−0.359054	+	0.933317i	$0.616901\pi$
$150$	0.333087	0.0271964
$151$	−8.61281	−0.700900	−0.350450	−	0.936581i	$-0.613971\pi$
$151$	−8.61281	−0.700900	−0.350450	+	0.936581i	$0.613971\pi$
$152$	−7.32518	−0.594150
$153$	16.5337	1.33667
$154$	−4.26455	−0.343647
$155$	11.6537	0.936049
$156$	1.46432	0.117240
$157$	−17.5567	−1.40117	−0.700587	−	0.713567i	$-0.747078\pi$
$157$	−17.5567	−1.40117	−0.700587	+	0.713567i	$0.747078\pi$
$158$	−0.381383	−0.0303412
$159$	19.9016	1.57830
$160$	2.26020	0.178684
$161$	39.3716	3.10292
$162$	13.0184	1.02282
$163$	20.7474	1.62506	0.812531	−	0.582918i	$-0.198089\pi$
$163$	20.7474	1.62506	0.812531	+	0.582918i	$0.198089\pi$
$164$	−0.892876	−0.0697219
$165$	6.93932	0.540225
$166$	11.1991	0.869215
$167$	−5.76255	−0.445920	−0.222960	−	0.974828i	$-0.571572\pi$
$167$	−5.76255	−0.445920	−0.222960	+	0.974828i	$0.571572\pi$
$168$	−13.0931	−1.01016
$169$	−12.7725	−0.982502
$170$	5.81507	0.445995
$171$	−47.0737	−3.59982
$172$	1.00000	0.0762493
$173$	−18.2167	−1.38499	−0.692494	−	0.721424i	$-0.743488\pi$
$173$	−18.2167	−1.38499	−0.692494	+	0.721424i	$0.743488\pi$
$174$	−0.164207	−0.0124485
$175$	−0.462659	−0.0349737
$176$	1.00000	0.0753778
$177$	−44.6801	−3.35836
$178$	12.6308	0.946720
$179$	12.8623	0.961370	0.480685	−	0.876893i	$-0.340388\pi$
$179$	12.8623	0.961370	0.480685	+	0.876893i	$0.340388\pi$
$180$	14.5247	1.08261
$181$	4.81882	0.358180	0.179090	−	0.983833i	$-0.442685\pi$
$181$	4.81882	0.358180	0.179090	+	0.983833i	$0.442685\pi$
$182$	−2.03395	−0.150766
$183$	4.14152	0.306150
$184$	−9.23230	−0.680614
$185$	11.4453	0.841474
$186$	15.8303	1.16073
$187$	2.57281	0.188143
$188$	−3.37304	−0.246004
$189$	−44.8610	−3.26316
$190$	−16.5563	−1.20112
$191$	26.2401	1.89867	0.949334	−	0.314268i	$-0.101759\pi$
$191$	26.2401	1.89867	0.949334	+	0.314268i	$0.101759\pi$
$192$	3.07023	0.221575
$193$	7.38803	0.531802	0.265901	−	0.964000i	$-0.414331\pi$
$193$	7.38803	0.531802	0.265901	+	0.964000i	$0.414331\pi$
$194$	8.66932	0.622421
$195$	3.30966	0.237010
$196$	11.1864	0.799030
$197$	−18.8955	−1.34625	−0.673124	−	0.739529i	$-0.735048\pi$
$197$	−18.8955	−1.34625	−0.673124	+	0.739529i	$0.735048\pi$
$198$	6.42629	0.456697
$199$	−8.45622	−0.599446	−0.299723	−	0.954026i	$-0.596894\pi$
$199$	−8.45622	−0.599446	−0.299723	+	0.954026i	$0.596894\pi$
$200$	0.108489	0.00767135
$201$	25.8053	1.82016
$202$	−0.973293	−0.0684807
$203$	0.228084	0.0160084
$204$	7.89912	0.553049
$205$	−2.01808	−0.140949
$206$	−2.48667	−0.173255
$207$	−59.3295	−4.12368
$208$	0.476943	0.0330701
$209$	−7.32518	−0.506693
$210$	−29.5931	−2.04212
$211$	3.58878	0.247062	0.123531	−	0.992341i	$-0.460578\pi$
$211$	3.58878	0.247062	0.123531	+	0.992341i	$0.460578\pi$
$212$	6.48213	0.445195
$213$	−48.8705	−3.34855
$214$	1.29039	0.0882095
$215$	2.26020	0.154144
$216$	10.5195	0.715761
$217$	−21.9883	−1.49266
$218$	−7.31544	−0.495464
$219$	−21.1856	−1.43159
$220$	2.26020	0.152382
$221$	1.22709	0.0825428
$222$	15.5472	1.04346
$223$	−0.884649	−0.0592405	−0.0296202	−	0.999561i	$-0.509430\pi$
$223$	−0.884649	−0.0592405	−0.0296202	+	0.999561i	$0.509430\pi$
$224$	−4.26455	−0.284937
$225$	0.697184	0.0464790
$226$	13.5219	0.899460
$227$	6.98695	0.463740	0.231870	−	0.972747i	$-0.425516\pi$
$227$	6.98695	0.463740	0.231870	+	0.972747i	$0.425516\pi$
$228$	−22.4900	−1.48943
$229$	4.74998	0.313888	0.156944	−	0.987608i	$-0.449836\pi$
$229$	4.74998	0.313888	0.156944	+	0.987608i	$0.449836\pi$
$230$	−20.8668	−1.37592
$231$	−13.0931	−0.861466
$232$	−0.0534837	−0.00351138
$233$	−4.78393	−0.313406	−0.156703	−	0.987646i	$-0.550087\pi$
$233$	−4.78393	−0.313406	−0.156703	+	0.987646i	$0.550087\pi$
$234$	3.06498	0.200364
$235$	−7.62374	−0.497318
$236$	−14.5527	−0.947299
$237$	−1.17093	−0.0760602
$238$	−10.9719	−0.711203
$239$	−0.787044	−0.0509096	−0.0254548	−	0.999676i	$-0.508103\pi$
$239$	−0.787044	−0.0509096	−0.0254548	+	0.999676i	$0.508103\pi$
$240$	6.93932	0.447931
$241$	27.3153	1.75953	0.879767	−	0.475405i	$-0.157698\pi$
$241$	27.3153	1.75953	0.879767	+	0.475405i	$0.157698\pi$
$242$	1.00000	0.0642824
$243$	8.41087	0.539557
$244$	1.34893	0.0863563
$245$	25.2835	1.61530
$246$	−2.74133	−0.174781
$247$	−3.49369	−0.222298
$248$	5.15606	0.327410
$249$	34.3836	2.17897
$250$	−11.0558	−0.699229
$251$	−13.9711	−0.881848	−0.440924	−	0.897544i	$-0.645349\pi$
$251$	−13.9711	−0.881848	−0.440924	+	0.897544i	$0.645349\pi$
$252$	−27.4053	−1.72637
$253$	−9.23230	−0.580429
$254$	−1.32189	−0.0829430
$255$	17.8536	1.11803
$256$	1.00000	0.0625000
$257$	−11.3975	−0.710958	−0.355479	−	0.934684i	$-0.615682\pi$
$257$	−11.3975	−0.710958	−0.355479	+	0.934684i	$0.615682\pi$
$258$	3.07023	0.191144
$259$	−21.5950	−1.34185
$260$	1.07799	0.0668539
$261$	−0.343702	−0.0212746
$262$	22.3026	1.37786
$263$	22.8713	1.41030	0.705151	−	0.709057i	$-0.250879\pi$
$263$	22.8713	1.41030	0.705151	+	0.709057i	$0.250879\pi$
$264$	3.07023	0.188959
$265$	14.6509	0.899997
$266$	31.2386	1.91536
$267$	38.7795	2.37327
$268$	8.40501	0.513418
$269$	13.1303	0.800571	0.400285	−	0.916391i	$-0.368911\pi$
$269$	13.1303	0.800571	0.400285	+	0.916391i	$0.368911\pi$
$270$	23.7761	1.44697
$271$	7.59444	0.461330	0.230665	−	0.973033i	$-0.425910\pi$
$271$	7.59444	0.461330	0.230665	+	0.973033i	$0.425910\pi$
$272$	2.57281	0.156000
$273$	−6.24469	−0.377946
$274$	−15.3235	−0.925729
$275$	0.108489	0.00654215
$276$	−28.3452	−1.70618
$277$	16.0874	0.966598	0.483299	−	0.875455i	$-0.339438\pi$
$277$	16.0874	0.966598	0.483299	+	0.875455i	$0.339438\pi$
$278$	10.7783	0.646441
$279$	33.1344	1.98370
$280$	−9.63873	−0.576024
$281$	27.8704	1.66261	0.831304	−	0.555818i	$-0.187595\pi$
$281$	27.8704	1.66261	0.831304	+	0.555818i	$0.187595\pi$
$282$	−10.3560	−0.616691
$283$	−19.1649	−1.13923	−0.569617	−	0.821910i	$-0.692909\pi$
$283$	−19.1649	−1.13923	−0.569617	+	0.821910i	$0.692909\pi$
$284$	−15.9176	−0.944534
$285$	−50.8317	−3.01101
$286$	0.476943	0.0282023
$287$	3.80772	0.224763
$288$	6.42629	0.378673
$289$	−10.3806	−0.610625
$290$	−0.120884	−0.00709854
$291$	26.6168	1.56030
$292$	−6.90034	−0.403812
$293$	−4.48566	−0.262055	−0.131027	−	0.991379i	$-0.541828\pi$
$293$	−4.48566	−0.262055	−0.131027	+	0.991379i	$0.541828\pi$
$294$	34.3448	2.00303
$295$	−32.8919	−1.91504
$296$	5.06385	0.294330
$297$	10.5195	0.610403
$298$	−8.76562	−0.507779
$299$	−4.40328	−0.254648
$300$	0.333087	0.0192308
$301$	−4.26455	−0.245805
$302$	−8.61281	−0.495611
$303$	−2.98823	−0.171669
$304$	−7.32518	−0.420128
$305$	3.04884	0.174576
$306$	16.5337	0.945166
$307$	−7.66857	−0.437669	−0.218834	−	0.975762i	$-0.570225\pi$
$307$	−7.66857	−0.437669	−0.218834	+	0.975762i	$0.570225\pi$
$308$	−4.26455	−0.242995
$309$	−7.63466	−0.434320
$310$	11.6537	0.661887
$311$	26.1881	1.48499	0.742495	−	0.669852i	$-0.233642\pi$
$311$	26.1881	1.48499	0.742495	+	0.669852i	$0.233642\pi$
$312$	1.46432	0.0829011
$313$	16.3891	0.926365	0.463182	−	0.886263i	$-0.346707\pi$
$313$	16.3891	0.926365	0.463182	+	0.886263i	$0.346707\pi$
$314$	−17.5567	−0.990779
$315$	−61.9413	−3.49000
$316$	−0.381383	−0.0214545
$317$	−18.8049	−1.05619	−0.528096	−	0.849185i	$-0.677094\pi$
$317$	−18.8049	−1.05619	−0.528096	+	0.849185i	$0.677094\pi$
$318$	19.9016	1.11603
$319$	−0.0534837	−0.00299451
$320$	2.26020	0.126349
$321$	3.96180	0.221126
$322$	39.3716	2.19409
$323$	−18.8463	−1.04864
$324$	13.0184	0.723243
$325$	0.0517433	0.00287020
$326$	20.7474	1.14909
$327$	−22.4601	−1.24205
$328$	−0.892876	−0.0493008
$329$	14.3845	0.793044
$330$	6.93932	0.381997
$331$	−12.2901	−0.675524	−0.337762	−	0.941232i	$-0.609670\pi$
$331$	−12.2901	−0.675524	−0.337762	+	0.941232i	$0.609670\pi$
$332$	11.1991	0.614628
$333$	32.5418	1.78328
$334$	−5.76255	−0.315313
$335$	18.9970	1.03792
$336$	−13.0931	−0.714290
$337$	−29.1270	−1.58665	−0.793325	−	0.608798i	$-0.791652\pi$
$337$	−29.1270	−1.58665	−0.793325	+	0.608798i	$0.791652\pi$
$338$	−12.7725	−0.694734
$339$	41.5152	2.25479
$340$	5.81507	0.315366
$341$	5.15606	0.279217
$342$	−47.0737	−2.54546
$343$	−17.8532	−0.963982
$344$	1.00000	0.0539164
$345$	−64.0658	−3.44919
$346$	−18.2167	−0.979334
$347$	−16.9726	−0.911134	−0.455567	−	0.890201i	$-0.650564\pi$
$347$	−16.9726	−0.911134	−0.455567	+	0.890201i	$0.650564\pi$
$348$	−0.164207	−0.00880243
$349$	3.52397	0.188634	0.0943169	−	0.995542i	$-0.469933\pi$
$349$	3.52397	0.188634	0.0943169	+	0.995542i	$0.469933\pi$
$350$	−0.462659	−0.0247301
$351$	5.01721	0.267799
$352$	1.00000	0.0533002
$353$	20.9514	1.11513	0.557566	−	0.830132i	$-0.311735\pi$
$353$	20.9514	1.11513	0.557566	+	0.830132i	$0.311735\pi$
$354$	−44.6801	−2.37472
$355$	−35.9768	−1.90945
$356$	12.6308	0.669432
$357$	−33.6862	−1.78286
$358$	12.8623	0.679791
$359$	37.6841	1.98889	0.994446	−	0.105252i	$-0.0335650\pi$
$359$	37.6841	1.98889	0.994446	+	0.105252i	$0.0335650\pi$
$360$	14.5247	0.765518
$361$	34.6582	1.82412
$362$	4.81882	0.253271
$363$	3.07023	0.161145
$364$	−2.03395	−0.106608
$365$	−15.5961	−0.816339
$366$	4.14152	0.216481
$367$	−20.0016	−1.04408	−0.522038	−	0.852922i	$-0.674828\pi$
$367$	−20.0016	−1.04408	−0.522038	+	0.852922i	$0.674828\pi$
$368$	−9.23230	−0.481267
$369$	−5.73789	−0.298702
$370$	11.4453	0.595012
$371$	−27.6434	−1.43517
$372$	15.8303	0.820762
$373$	16.2704	0.842447	0.421224	−	0.906957i	$-0.361601\pi$
$373$	16.2704	0.842447	0.421224	+	0.906957i	$0.361601\pi$
$374$	2.57281	0.133037
$375$	−33.9437	−1.75285
$376$	−3.37304	−0.173951
$377$	−0.0255087	−0.00131377
$378$	−44.8610	−2.30740
$379$	−17.1987	−0.883436	−0.441718	−	0.897154i	$-0.645631\pi$
$379$	−17.1987	−0.883436	−0.441718	+	0.897154i	$0.645631\pi$
$380$	−16.5563	−0.849322
$381$	−4.05851	−0.207924
$382$	26.2401	1.34256
$383$	19.3101	0.986702	0.493351	−	0.869830i	$-0.335772\pi$
$383$	19.3101	0.986702	0.493351	+	0.869830i	$0.335772\pi$
$384$	3.07023	0.156677
$385$	−9.63873	−0.491235
$386$	7.38803	0.376041
$387$	6.42629	0.326667
$388$	8.66932	0.440118
$389$	2.63060	0.133377	0.0666884	−	0.997774i	$-0.478757\pi$
$389$	2.63060	0.133377	0.0666884	+	0.997774i	$0.478757\pi$
$390$	3.30966	0.167591
$391$	−23.7530	−1.20124
$392$	11.1864	0.564999
$393$	68.4740	3.45406
$394$	−18.8955	−0.951941
$395$	−0.862000	−0.0433719
$396$	6.42629	0.322933
$397$	−36.1512	−1.81438	−0.907189	−	0.420724i	$-0.861776\pi$
$397$	−36.1512	−1.81438	−0.907189	+	0.420724i	$0.861776\pi$
$398$	−8.45622	−0.423872
$399$	95.9096	4.80149
$400$	0.108489	0.00542447
$401$	−29.4806	−1.47219	−0.736095	−	0.676878i	$-0.763333\pi$
$401$	−29.4806	−1.47219	−0.736095	+	0.676878i	$0.763333\pi$
$402$	25.8053	1.28705
$403$	2.45915	0.122499
$404$	−0.973293	−0.0484232
$405$	29.4241	1.46209
$406$	0.228084	0.0113196
$407$	5.06385	0.251005
$408$	7.89912	0.391065
$409$	−32.3899	−1.60158	−0.800788	−	0.598948i	$-0.795586\pi$
$409$	−32.3899	−1.60158	−0.800788	+	0.598948i	$0.795586\pi$
$410$	−2.01808	−0.0996657
$411$	−47.0468	−2.32065
$412$	−2.48667	−0.122510
$413$	62.0607	3.05381
$414$	−59.3295	−2.91588
$415$	25.3121	1.24252
$416$	0.476943	0.0233841
$417$	33.0919	1.62052
$418$	−7.32518	−0.358286
$419$	20.0410	0.979067	0.489533	−	0.871985i	$-0.337167\pi$
$419$	20.0410	0.979067	0.489533	+	0.871985i	$0.337167\pi$
$420$	−29.5931	−1.44399
$421$	0.353028	0.0172055	0.00860276	−	0.999963i	$-0.497262\pi$
$421$	0.353028	0.0172055	0.00860276	+	0.999963i	$0.497262\pi$
$422$	3.58878	0.174699
$423$	−21.6762	−1.05393
$424$	6.48213	0.314800
$425$	0.279123	0.0135394
$426$	−48.8705	−2.36779
$427$	−5.75258	−0.278387
$428$	1.29039	0.0623735
$429$	1.46432	0.0706983
$430$	2.26020	0.108996
$431$	9.81726	0.472881	0.236440	−	0.971646i	$-0.424019\pi$
$431$	9.81726	0.472881	0.236440	+	0.971646i	$0.424019\pi$
$432$	10.5195	0.506120
$433$	−1.96841	−0.0945958	−0.0472979	−	0.998881i	$-0.515061\pi$
$433$	−1.96841	−0.0945958	−0.0472979	+	0.998881i	$0.515061\pi$
$434$	−21.9883	−1.05547
$435$	−0.371141	−0.0177948
$436$	−7.31544	−0.350346
$437$	67.6282	3.23510
$438$	−21.1856	−1.01229
$439$	21.2871	1.01598	0.507988	−	0.861364i	$-0.330389\pi$
$439$	21.2871	1.01598	0.507988	+	0.861364i	$0.330389\pi$
$440$	2.26020	0.107751
$441$	71.8872	3.42320
$442$	1.22709	0.0583666
$443$	−30.7777	−1.46229	−0.731147	−	0.682220i	$-0.761015\pi$
$443$	−30.7777	−1.46229	−0.731147	+	0.682220i	$0.761015\pi$
$444$	15.5472	0.737835
$445$	28.5481	1.35331
$446$	−0.884649	−0.0418893
$447$	−26.9124	−1.27291
$448$	−4.26455	−0.201481
$449$	−15.5445	−0.733590	−0.366795	−	0.930302i	$-0.619545\pi$
$449$	−15.5445	−0.733590	−0.366795	+	0.930302i	$0.619545\pi$
$450$	0.697184	0.0328656
$451$	−0.892876	−0.0420439
$452$	13.5219	0.636015
$453$	−26.4433	−1.24241
$454$	6.98695	0.327914
$455$	−4.59713	−0.215517
$456$	−22.4900	−1.05319
$457$	37.9869	1.77695	0.888476	−	0.458923i	$-0.151765\pi$
$457$	37.9869	1.77695	0.888476	+	0.458923i	$0.151765\pi$
$458$	4.74998	0.221952
$459$	27.0647	1.26327
$460$	−20.8668	−0.972920
$461$	−13.1749	−0.613617	−0.306809	−	0.951771i	$-0.599261\pi$
$461$	−13.1749	−0.613617	−0.306809	+	0.951771i	$0.599261\pi$
$462$	−13.0931	−0.609148
$463$	−20.6815	−0.961151	−0.480575	−	0.876953i	$-0.659572\pi$
$463$	−20.6815	−0.961151	−0.480575	+	0.876953i	$0.659572\pi$
$464$	−0.0534837	−0.00248292
$465$	35.7796	1.65924
$466$	−4.78393	−0.221611
$467$	7.32327	0.338880	0.169440	−	0.985540i	$-0.445804\pi$
$467$	7.32327	0.338880	0.169440	+	0.985540i	$0.445804\pi$
$468$	3.06498	0.141679
$469$	−35.8436	−1.65510
$470$	−7.62374	−0.351657
$471$	−53.9029	−2.48372
$472$	−14.5527	−0.669842
$473$	1.00000	0.0459800
$474$	−1.17093	−0.0537827
$475$	−0.794703	−0.0364635
$476$	−10.9719	−0.502896
$477$	41.6561	1.90730
$478$	−0.787044	−0.0359985
$479$	−15.5590	−0.710907	−0.355454	−	0.934694i	$-0.615674\pi$
$479$	−15.5590	−0.710907	−0.355454	+	0.934694i	$0.615674\pi$
$480$	6.93932	0.316735
$481$	2.41517	0.110122
$482$	27.3153	1.24418
$483$	120.880	5.50022
$484$	1.00000	0.0454545
$485$	19.5944	0.889734
$486$	8.41087	0.381525
$487$	−11.4685	−0.519687	−0.259843	−	0.965651i	$-0.583671\pi$
$487$	−11.4685	−0.519687	−0.259843	+	0.965651i	$0.583671\pi$
$488$	1.34893	0.0610631
$489$	63.6992	2.88058
$490$	25.2835	1.14219
$491$	−8.37788	−0.378088	−0.189044	−	0.981969i	$-0.560539\pi$
$491$	−8.37788	−0.378088	−0.189044	+	0.981969i	$0.560539\pi$
$492$	−2.74133	−0.123589
$493$	−0.137604	−0.00619736
$494$	−3.49369	−0.157189
$495$	14.5247	0.652836
$496$	5.15606	0.231514
$497$	67.8813	3.04489
$498$	34.3836	1.54077
$499$	28.3634	1.26972	0.634860	−	0.772627i	$-0.281058\pi$
$499$	28.3634	1.26972	0.634860	+	0.772627i	$0.281058\pi$
$500$	−11.0558	−0.494429
$501$	−17.6923	−0.790436
$502$	−13.9711	−0.623561
$503$	10.0744	0.449197	0.224599	−	0.974451i	$-0.427893\pi$
$503$	10.0744	0.449197	0.224599	+	0.974451i	$0.427893\pi$
$504$	−27.4053	−1.22073
$505$	−2.19983	−0.0978913
$506$	−9.23230	−0.410426
$507$	−39.2146	−1.74158
$508$	−1.32189	−0.0586496
$509$	16.9710	0.752227	0.376114	−	0.926574i	$-0.377260\pi$
$509$	16.9710	0.752227	0.376114	+	0.926574i	$0.377260\pi$
$510$	17.8536	0.790569
$511$	29.4269	1.30177
$512$	1.00000	0.0441942
$513$	−77.0572	−3.40216
$514$	−11.3975	−0.502723
$515$	−5.62037	−0.247663
$516$	3.07023	0.135159
$517$	−3.37304	−0.148346
$518$	−21.5950	−0.948832
$519$	−55.9293	−2.45502
$520$	1.07799	0.0472728
$521$	−25.9116	−1.13521	−0.567603	−	0.823302i	$-0.692129\pi$
$521$	−25.9116	−1.13521	−0.567603	+	0.823302i	$0.692129\pi$
$522$	−0.343702	−0.0150434
$523$	19.3010	0.843973	0.421987	−	0.906602i	$-0.361333\pi$
$523$	19.3010	0.843973	0.421987	+	0.906602i	$0.361333\pi$
$524$	22.3026	0.974293
$525$	−1.42047	−0.0619943
$526$	22.8713	0.997234
$527$	13.2656	0.577858
$528$	3.07023	0.133614
$529$	62.2353	2.70588
$530$	14.6509	0.636394
$531$	−93.5198	−4.05842
$532$	31.2386	1.35437
$533$	−0.425851	−0.0184457
$534$	38.7795	1.67815
$535$	2.91654	0.126093
$536$	8.40501	0.363041
$537$	39.4900	1.70412
$538$	13.1303	0.566089
$539$	11.1864	0.481833
$540$	23.7761	1.02316
$541$	34.1183	1.46686	0.733431	−	0.679764i	$-0.237918\pi$
$541$	34.1183	1.46686	0.733431	+	0.679764i	$0.237918\pi$
$542$	7.59444	0.326209
$543$	14.7949	0.634908
$544$	2.57281	0.110308
$545$	−16.5343	−0.708253
$546$	−6.24469	−0.267248
$547$	7.65036	0.327106	0.163553	−	0.986535i	$-0.447705\pi$
$547$	7.65036	0.327106	0.163553	+	0.986535i	$0.447705\pi$
$548$	−15.3235	−0.654589
$549$	8.66861	0.369967
$550$	0.108489	0.00462600
$551$	0.391778	0.0166903
$552$	−28.3452	−1.20645
$553$	1.62643	0.0691627
$554$	16.0874	0.683488
$555$	35.1396	1.49159
$556$	10.7783	0.457103
$557$	−17.3836	−0.736568	−0.368284	−	0.929713i	$-0.620055\pi$
$557$	−17.3836	−0.736568	−0.368284	+	0.929713i	$0.620055\pi$
$558$	33.1344	1.40269
$559$	0.476943	0.0201726
$560$	−9.63873	−0.407311
$561$	7.89912	0.333501
$562$	27.8704	1.17564
$563$	−25.7184	−1.08390	−0.541951	−	0.840410i	$-0.682314\pi$
$563$	−25.7184	−1.08390	−0.541951	+	0.840410i	$0.682314\pi$
$564$	−10.3560	−0.436067
$565$	30.5621	1.28576
$566$	−19.1649	−0.805561
$567$	−55.5176	−2.33152
$568$	−15.9176	−0.667886
$569$	1.10088	0.0461515	0.0230757	−	0.999734i	$-0.492654\pi$
$569$	1.10088	0.0461515	0.0230757	+	0.999734i	$0.492654\pi$
$570$	−50.8317	−2.12911
$571$	1.72953	0.0723786	0.0361893	−	0.999345i	$-0.488478\pi$
$571$	1.72953	0.0723786	0.0361893	+	0.999345i	$0.488478\pi$
$572$	0.476943	0.0199420
$573$	80.5631	3.36557
$574$	3.80772	0.158931
$575$	−1.00161	−0.0417698
$576$	6.42629	0.267762
$577$	7.25757	0.302137	0.151068	−	0.988523i	$-0.451729\pi$
$577$	7.25757	0.302137	0.151068	+	0.988523i	$0.451729\pi$
$578$	−10.3806	−0.431777
$579$	22.6829	0.942671
$580$	−0.120884	−0.00501943
$581$	−47.7590	−1.98138
$582$	26.6168	1.10330
$583$	6.48213	0.268462
$584$	−6.90034	−0.285538
$585$	6.92746	0.286415
$586$	−4.48566	−0.185301
$587$	15.4125	0.636142	0.318071	−	0.948067i	$-0.396965\pi$
$587$	15.4125	0.636142	0.318071	+	0.948067i	$0.396965\pi$
$588$	34.3448	1.41636
$589$	−37.7691	−1.55625
$590$	−32.8919	−1.35414
$591$	−58.0135	−2.38636
$592$	5.06385	0.208123
$593$	20.7023	0.850143	0.425072	−	0.905160i	$-0.360249\pi$
$593$	20.7023	0.850143	0.425072	+	0.905160i	$0.360249\pi$
$594$	10.5195	0.431620
$595$	−24.7987	−1.01665
$596$	−8.76562	−0.359054
$597$	−25.9625	−1.06258
$598$	−4.40328	−0.180064
$599$	37.2990	1.52399	0.761997	−	0.647580i	$-0.224219\pi$
$599$	37.2990	1.52399	0.761997	+	0.647580i	$0.224219\pi$
$600$	0.333087	0.0135982
$601$	26.5328	1.08230	0.541148	−	0.840928i	$-0.317990\pi$
$601$	26.5328	1.08230	0.541148	+	0.840928i	$0.317990\pi$
$602$	−4.26455	−0.173810
$603$	54.0131	2.19958
$604$	−8.61281	−0.350450
$605$	2.26020	0.0918901
$606$	−2.98823	−0.121389
$607$	−37.8794	−1.53748	−0.768738	−	0.639564i	$-0.779115\pi$
$607$	−37.8794	−1.53748	−0.768738	+	0.639564i	$0.779115\pi$
$608$	−7.32518	−0.297075
$609$	0.700270	0.0283764
$610$	3.04884	0.123444
$611$	−1.60875	−0.0650831
$612$	16.5337	0.668334
$613$	40.8460	1.64976	0.824878	−	0.565311i	$-0.191244\pi$
$613$	40.8460	1.64976	0.824878	+	0.565311i	$0.191244\pi$
$614$	−7.66857	−0.309478
$615$	−6.19595	−0.249845
$616$	−4.26455	−0.171824
$617$	23.0521	0.928044	0.464022	−	0.885824i	$-0.346406\pi$
$617$	23.0521	0.928044	0.464022	+	0.885824i	$0.346406\pi$
$618$	−7.63466	−0.307111
$619$	−42.1314	−1.69340	−0.846701	−	0.532069i	$-0.821415\pi$
$619$	−42.1314	−1.69340	−0.846701	+	0.532069i	$0.821415\pi$
$620$	11.6537	0.468025
$621$	−97.1192	−3.89726
$622$	26.1881	1.05005
$623$	−53.8648	−2.15805
$624$	1.46432	0.0586199
$625$	−25.5307	−1.02123
$626$	16.3891	0.655039
$627$	−22.4900	−0.898162
$628$	−17.5567	−0.700587
$629$	13.0283	0.519474
$630$	−61.9413	−2.46780
$631$	−12.2987	−0.489605	−0.244802	−	0.969573i	$-0.578723\pi$
$631$	−12.2987	−0.489605	−0.244802	+	0.969573i	$0.578723\pi$
$632$	−0.381383	−0.0151706
$633$	11.0184	0.437941
$634$	−18.8049	−0.746840
$635$	−2.98774	−0.118565
$636$	19.9016	0.789150
$637$	5.33529	0.211392
$638$	−0.0534837	−0.00211744
$639$	−102.291	−4.04657
$640$	2.26020	0.0893421
$641$	48.0185	1.89662	0.948308	−	0.317352i	$-0.102794\pi$
$641$	48.0185	1.89662	0.948308	+	0.317352i	$0.102794\pi$
$642$	3.96180	0.156360
$643$	−27.9980	−1.10413	−0.552066	−	0.833800i	$-0.686160\pi$
$643$	−27.9980	−1.10413	−0.552066	+	0.833800i	$0.686160\pi$
$644$	39.3716	1.55146
$645$	6.93932	0.273235
$646$	−18.8463	−0.741498
$647$	−39.3736	−1.54793	−0.773967	−	0.633226i	$-0.781730\pi$
$647$	−39.3736	−1.54793	−0.773967	+	0.633226i	$0.781730\pi$
$648$	13.0184	0.511410
$649$	−14.5527	−0.571243
$650$	0.0517433	0.00202954
$651$	−67.5091	−2.64589
$652$	20.7474	0.812531
$653$	0.0233887	0.000915269 0	0.000457635	−	1.00000i	$-0.499854\pi$
$653$	0.0233887	0.000915269 0	0.000457635		1.00000i	$0.499854\pi$
$654$	−22.4601	−0.878258
$655$	50.4082	1.96961
$656$	−0.892876	−0.0348610
$657$	−44.3436	−1.73001
$658$	14.3845	0.560767
$659$	26.5015	1.03235	0.516175	−	0.856483i	$-0.327355\pi$
$659$	26.5015	1.03235	0.516175	+	0.856483i	$0.327355\pi$
$660$	6.93932	0.270113
$661$	−3.94272	−0.153354	−0.0766770	−	0.997056i	$-0.524431\pi$
$661$	−3.94272	−0.153354	−0.0766770	+	0.997056i	$0.524431\pi$
$662$	−12.2901	−0.477668
$663$	3.76743	0.146315
$664$	11.1991	0.434607
$665$	70.6054	2.73796
$666$	32.5418	1.26097
$667$	0.493778	0.0191191
$668$	−5.76255	−0.222960
$669$	−2.71607	−0.105009
$670$	18.9970	0.733917
$671$	1.34893	0.0520748
$672$	−13.0931	−0.505079
$673$	51.6824	1.99221	0.996105	−	0.0881795i	$-0.0281049\pi$
$673$	51.6824	1.99221	0.996105	+	0.0881795i	$0.0281049\pi$
$674$	−29.1270	−1.12193
$675$	1.14125	0.0439269
$676$	−12.7725	−0.491251
$677$	−7.05190	−0.271027	−0.135513	−	0.990776i	$-0.543268\pi$
$677$	−7.05190	−0.271027	−0.135513	+	0.990776i	$0.543268\pi$
$678$	41.5152	1.59438
$679$	−36.9708	−1.41881
$680$	5.81507	0.222998
$681$	21.4515	0.822024
$682$	5.15606	0.197436
$683$	1.47046	0.0562654	0.0281327	−	0.999604i	$-0.491044\pi$
$683$	1.47046	0.0562654	0.0281327	+	0.999604i	$0.491044\pi$
$684$	−47.0737	−1.79991
$685$	−34.6342	−1.32331
$686$	−17.8532	−0.681638
$687$	14.5835	0.556396
$688$	1.00000	0.0381246
$689$	3.09161	0.117781
$690$	−64.0658	−2.43894
$691$	27.5313	1.04734	0.523670	−	0.851921i	$-0.324562\pi$
$691$	27.5313	1.04734	0.523670	+	0.851921i	$0.324562\pi$
$692$	−18.2167	−0.692494
$693$	−27.4053	−1.04104
$694$	−16.9726	−0.644269
$695$	24.3611	0.924070
$696$	−0.164207	−0.00622426
$697$	−2.29720	−0.0870128
$698$	3.52397	0.133384
$699$	−14.6878	−0.555542
$700$	−0.462659	−0.0174869
$701$	−7.77626	−0.293705	−0.146853	−	0.989158i	$-0.546914\pi$
$701$	−7.77626	−0.293705	−0.146853	+	0.989158i	$0.546914\pi$
$702$	5.01721	0.189362
$703$	−37.0936	−1.39901
$704$	1.00000	0.0376889
$705$	−23.4066	−0.881544
$706$	20.9514	0.788518
$707$	4.15066	0.156102
$708$	−44.6801	−1.67918
$709$	−24.4912	−0.919786	−0.459893	−	0.887974i	$-0.652112\pi$
$709$	−24.4912	−0.919786	−0.459893	+	0.887974i	$0.652112\pi$
$710$	−35.9768	−1.35019
$711$	−2.45088	−0.0919151
$712$	12.6308	0.473360
$713$	−47.6023	−1.78272
$714$	−33.6862	−1.26068
$715$	1.07799	0.0403144
$716$	12.8623	0.480685
$717$	−2.41640	−0.0902422
$718$	37.6841	1.40636
$719$	23.0184	0.858441	0.429220	−	0.903200i	$-0.358788\pi$
$719$	23.0184	0.858441	0.429220	+	0.903200i	$0.358788\pi$
$720$	14.5247	0.541303
$721$	10.6046	0.394934
$722$	34.6582	1.28984
$723$	83.8642	3.11894
$724$	4.81882	0.179090
$725$	−0.00580242	−0.000215496 0
$726$	3.07023	0.113947
$727$	8.20356	0.304253	0.152127	−	0.988361i	$-0.451388\pi$
$727$	8.20356	0.304253	0.152127	+	0.988361i	$0.451388\pi$
$728$	−2.03395	−0.0753832
$729$	−13.2319	−0.490069
$730$	−15.5961	−0.577239
$731$	2.57281	0.0951590
$732$	4.14152	0.153075
$733$	−28.2464	−1.04330	−0.521652	−	0.853159i	$-0.674684\pi$
$733$	−28.2464	−1.04330	−0.521652	+	0.853159i	$0.674684\pi$
$734$	−20.0016	−0.738273
$735$	77.6261	2.86328
$736$	−9.23230	−0.340307
$737$	8.40501	0.309602
$738$	−5.73789	−0.211214
$739$	−23.8128	−0.875969	−0.437985	−	0.898982i	$-0.644308\pi$
$739$	−23.8128	−0.875969	−0.437985	+	0.898982i	$0.644308\pi$
$740$	11.4453	0.420737
$741$	−10.7264	−0.394045
$742$	−27.6434	−1.01482
$743$	12.9355	0.474556	0.237278	−	0.971442i	$-0.423745\pi$
$743$	12.9355	0.474556	0.237278	+	0.971442i	$0.423745\pi$
$744$	15.8303	0.580366
$745$	−19.8120	−0.725856
$746$	16.2704	0.595700
$747$	71.9684	2.63319
$748$	2.57281	0.0940714
$749$	−5.50295	−0.201074
$750$	−33.9437	−1.23945
$751$	40.3349	1.47184	0.735921	−	0.677067i	$-0.236749\pi$
$751$	40.3349	1.47184	0.735921	+	0.677067i	$0.236749\pi$
$752$	−3.37304	−0.123002
$753$	−42.8944	−1.56316
$754$	−0.0255087	−0.000928973 0
$755$	−19.4666	−0.708464
$756$	−44.8610	−1.63158
$757$	−14.5955	−0.530484	−0.265242	−	0.964182i	$-0.585452\pi$
$757$	−14.5955	−0.530484	−0.265242	+	0.964182i	$0.585452\pi$
$758$	−17.1987	−0.624684
$759$	−28.3452	−1.02887
$760$	−16.5563	−0.600562
$761$	−47.8044	−1.73291	−0.866454	−	0.499256i	$-0.833607\pi$
$761$	−47.8044	−1.73291	−0.866454	+	0.499256i	$0.833607\pi$
$762$	−4.05851	−0.147024
$763$	31.1971	1.12941
$764$	26.2401	0.949334
$765$	37.3693	1.35109
$766$	19.3101	0.697704
$767$	−6.94081	−0.250618
$768$	3.07023	0.110787
$769$	2.21811	0.0799872	0.0399936	−	0.999200i	$-0.487266\pi$
$769$	2.21811	0.0799872	0.0399936	+	0.999200i	$0.487266\pi$
$770$	−9.63873	−0.347356
$771$	−34.9930	−1.26024
$772$	7.38803	0.265901
$773$	−22.3913	−0.805359	−0.402679	−	0.915341i	$-0.631921\pi$
$773$	−22.3913	−0.805359	−0.402679	+	0.915341i	$0.631921\pi$
$774$	6.42629	0.230988
$775$	0.559378	0.0200935
$776$	8.66932	0.311210
$777$	−66.3017	−2.37856
$778$	2.63060	0.0943116
$779$	6.54048	0.234337
$780$	3.30966	0.118505
$781$	−15.9176	−0.569575
$782$	−23.7530	−0.849405
$783$	−0.562622	−0.0201065
$784$	11.1864	0.399515
$785$	−39.6815	−1.41629
$786$	68.4740	2.44239
$787$	12.6040	0.449285	0.224642	−	0.974441i	$-0.427879\pi$
$787$	12.6040	0.449285	0.224642	+	0.974441i	$0.427879\pi$
$788$	−18.8955	−0.673124
$789$	70.2200	2.49990
$790$	−0.862000	−0.0306686
$791$	−57.6647	−2.05032
$792$	6.42629	0.228348
$793$	0.643363	0.0228465
$794$	−36.1512	−1.28296
$795$	44.9816	1.59533
$796$	−8.45622	−0.299723
$797$	29.0033	1.02735	0.513675	−	0.857985i	$-0.328284\pi$
$797$	29.0033	1.02735	0.513675	+	0.857985i	$0.328284\pi$
$798$	95.9096	3.39516
$799$	−8.67821	−0.307013
$800$	0.108489	0.00383568
$801$	81.1694	2.86798
$802$	−29.4806	−1.04100
$803$	−6.90034	−0.243508
$804$	25.8053	0.910082
$805$	88.9876	3.13640
$806$	2.45915	0.0866199
$807$	40.3131	1.41909
$808$	−0.973293	−0.0342403
$809$	−28.0169	−0.985021	−0.492510	−	0.870307i	$-0.663921\pi$
$809$	−28.0169	−0.985021	−0.492510	+	0.870307i	$0.663921\pi$
$810$	29.4241	1.03386
$811$	4.01238	0.140894	0.0704469	−	0.997516i	$-0.477557\pi$
$811$	4.01238	0.140894	0.0704469	+	0.997516i	$0.477557\pi$
$812$	0.228084	0.00800419
$813$	23.3167	0.817751
$814$	5.06385	0.177488
$815$	46.8932	1.64260
$816$	7.89912	0.276525
$817$	−7.32518	−0.256275
$818$	−32.3899	−1.13249
$819$	−13.0708	−0.456730
$820$	−2.01808	−0.0704743
$821$	19.6873	0.687092	0.343546	−	0.939136i	$-0.388372\pi$
$821$	19.6873	0.687092	0.343546	+	0.939136i	$0.388372\pi$
$822$	−47.0468	−1.64094
$823$	−22.4189	−0.781473	−0.390736	−	0.920503i	$-0.627780\pi$
$823$	−22.4189	−0.781473	−0.390736	+	0.920503i	$0.627780\pi$
$824$	−2.48667	−0.0866274
$825$	0.333087	0.0115966
$826$	62.0607	2.15937
$827$	21.1109	0.734099	0.367050	−	0.930201i	$-0.380368\pi$
$827$	21.1109	0.734099	0.367050	+	0.930201i	$0.380368\pi$
$828$	−59.3295	−2.06184
$829$	−3.20846	−0.111434	−0.0557171	−	0.998447i	$-0.517745\pi$
$829$	−3.20846	−0.111434	−0.0557171	+	0.998447i	$0.517745\pi$
$830$	25.3121	0.878594
$831$	49.3920	1.71339
$832$	0.476943	0.0165350
$833$	28.7806	0.997187
$834$	33.0919	1.14588
$835$	−13.0245	−0.450731
$836$	−7.32518	−0.253346
$837$	54.2392	1.87478
$838$	20.0410	0.692305
$839$	22.5448	0.778333	0.389166	−	0.921167i	$-0.372763\pi$
$839$	22.5448	0.778333	0.389166	+	0.921167i	$0.372763\pi$
$840$	−29.5931	−1.02106
$841$	−28.9971	−0.999901
$842$	0.353028	0.0121661
$843$	85.5684	2.94713
$844$	3.58878	0.123531
$845$	−28.8684	−0.993104
$846$	−21.6762	−0.745242
$847$	−4.26455	−0.146532
$848$	6.48213	0.222597
$849$	−58.8406	−2.01940
$850$	0.279123	0.00957384
$851$	−46.7509	−1.60260
$852$	−48.8705	−1.67428
$853$	−18.2278	−0.624107	−0.312053	−	0.950065i	$-0.601017\pi$
$853$	−18.2278	−0.624107	−0.312053	+	0.950065i	$0.601017\pi$
$854$	−5.75258	−0.196849
$855$	−106.396	−3.63866
$856$	1.29039	0.0441047
$857$	36.4474	1.24502	0.622510	−	0.782612i	$-0.286113\pi$
$857$	36.4474	1.24502	0.622510	+	0.782612i	$0.286113\pi$
$858$	1.46432	0.0499912
$859$	−43.5172	−1.48479	−0.742394	−	0.669963i	$-0.766310\pi$
$859$	−43.5172	−1.48479	−0.742394	+	0.669963i	$0.766310\pi$
$860$	2.26020	0.0770721
$861$	11.6906	0.398413
$862$	9.81726	0.334377
$863$	3.89806	0.132692	0.0663458	−	0.997797i	$-0.478866\pi$
$863$	3.89806	0.132692	0.0663458	+	0.997797i	$0.478866\pi$
$864$	10.5195	0.357881
$865$	−41.1732	−1.39993
$866$	−1.96841	−0.0668894
$867$	−31.8709	−1.08239
$868$	−21.9883	−0.746332
$869$	−0.381383	−0.0129375
$870$	−0.371141	−0.0125828
$871$	4.00871	0.135830
$872$	−7.31544	−0.247732
$873$	55.7116	1.88555
$874$	67.6282	2.28756
$875$	47.1479	1.59389
$876$	−21.1856	−0.715796
$877$	2.96043	0.0999666	0.0499833	−	0.998750i	$-0.484083\pi$
$877$	2.96043	0.0999666	0.0499833	+	0.998750i	$0.484083\pi$
$878$	21.2871	0.718404
$879$	−13.7720	−0.464518
$880$	2.26020	0.0761912
$881$	−28.2299	−0.951090	−0.475545	−	0.879691i	$-0.657749\pi$
$881$	−28.2299	−0.951090	−0.475545	+	0.879691i	$0.657749\pi$
$882$	71.8872	2.42057
$883$	−56.7084	−1.90839	−0.954195	−	0.299186i	$-0.903285\pi$
$883$	−56.7084	−1.90839	−0.954195	+	0.299186i	$0.903285\pi$
$884$	1.22709	0.0412714
$885$	−100.986	−3.39460
$886$	−30.7777	−1.03400
$887$	51.0572	1.71433	0.857167	−	0.515039i	$-0.172223\pi$
$887$	51.0572	1.71433	0.857167	+	0.515039i	$0.172223\pi$
$888$	15.5472	0.521728
$889$	5.63729	0.189069
$890$	28.5481	0.956936
$891$	13.0184	0.436132
$892$	−0.884649	−0.0296202
$893$	24.7081	0.826826
$894$	−26.9124	−0.900087
$895$	29.0712	0.971744
$896$	−4.26455	−0.142469
$897$	−13.5191	−0.451389
$898$	−15.5445	−0.518726
$899$	−0.275766	−0.00919730
$900$	0.697184	0.0232395
$901$	16.6773	0.555602
$902$	−0.892876	−0.0297295
$903$	−13.0931	−0.435713
$904$	13.5219	0.449730
$905$	10.8915	0.362045
$906$	−26.4433	−0.878519
$907$	−11.2340	−0.373019	−0.186509	−	0.982453i	$-0.559717\pi$
$907$	−11.2340	−0.373019	−0.186509	+	0.982453i	$0.559717\pi$
$908$	6.98695	0.231870
$909$	−6.25467	−0.207454
$910$	−4.59713	−0.152393
$911$	9.92407	0.328799	0.164400	−	0.986394i	$-0.447431\pi$
$911$	9.92407	0.328799	0.164400	+	0.986394i	$0.447431\pi$
$912$	−22.4900	−0.744717
$913$	11.1991	0.370635
$914$	37.9869	1.25649
$915$	9.36064	0.309453
$916$	4.74998	0.156944
$917$	−95.1105	−3.14083
$918$	27.0647	0.893269
$919$	−39.9930	−1.31925	−0.659624	−	0.751596i	$-0.729284\pi$
$919$	−39.9930	−1.31925	−0.659624	+	0.751596i	$0.729284\pi$
$920$	−20.8668	−0.687958
$921$	−23.5443	−0.775810
$922$	−13.1749	−0.433893
$923$	−7.59178	−0.249886
$924$	−13.0931	−0.430733
$925$	0.549373	0.0180633
$926$	−20.6815	−0.679636
$927$	−15.9801	−0.524855
$928$	−0.0534837	−0.00175569
$929$	−5.42486	−0.177984	−0.0889919	−	0.996032i	$-0.528365\pi$
$929$	−5.42486	−0.177984	−0.0889919	+	0.996032i	$0.528365\pi$
$930$	35.7796	1.17326
$931$	−81.9425	−2.68556
$932$	−4.78393	−0.156703
$933$	80.4033	2.63229
$934$	7.32327	0.239625
$935$	5.81507	0.190173
$936$	3.06498	0.100182
$937$	−31.1254	−1.01682	−0.508412	−	0.861114i	$-0.669767\pi$
$937$	−31.1254	−1.01682	−0.508412	+	0.861114i	$0.669767\pi$
$938$	−35.8436	−1.17034
$939$	50.3182	1.64207
$940$	−7.62374	−0.248659
$941$	−7.40660	−0.241448	−0.120724	−	0.992686i	$-0.538522\pi$
$941$	−7.40660	−0.241448	−0.120724	+	0.992686i	$0.538522\pi$
$942$	−53.9029	−1.75625
$943$	8.24330	0.268439
$944$	−14.5527	−0.473650
$945$	−101.395	−3.29837
$946$	1.00000	0.0325128
$947$	−35.1543	−1.14236	−0.571180	−	0.820825i	$-0.693514\pi$
$947$	−35.1543	−1.14236	−0.571180	+	0.820825i	$0.693514\pi$
$948$	−1.17093	−0.0380301
$949$	−3.29107	−0.106833
$950$	−0.794703	−0.0257836
$951$	−57.7355	−1.87220
$952$	−10.9719	−0.355601
$953$	−52.5715	−1.70296	−0.851480	−	0.524388i	$-0.824294\pi$
$953$	−52.5715	−1.70296	−0.851480	+	0.524388i	$0.824294\pi$
$954$	41.6561	1.34867
$955$	59.3078	1.91916
$956$	−0.787044	−0.0254548
$957$	−0.164207	−0.00530807
$958$	−15.5590	−0.502687
$959$	65.3481	2.11020
$960$	6.93932	0.223966
$961$	−4.41500	−0.142419
$962$	2.41517	0.0778681
$963$	8.29245	0.267220
$964$	27.3153	0.879767
$965$	16.6984	0.537541
$966$	120.880	3.88924
$967$	13.4310	0.431912	0.215956	−	0.976403i	$-0.430713\pi$
$967$	13.4310	0.431912	0.215956	+	0.976403i	$0.430713\pi$
$968$	1.00000	0.0321412
$969$	−57.8625	−1.85881
$970$	19.5944	0.629137
$971$	12.1328	0.389360	0.194680	−	0.980867i	$-0.437633\pi$
$971$	12.1328	0.389360	0.194680	+	0.980867i	$0.437633\pi$
$972$	8.41087	0.269779
$973$	−45.9647	−1.47356
$974$	−11.4685	−0.367474
$975$	0.158864	0.00508771
$976$	1.34893	0.0431782
$977$	−18.3514	−0.587112	−0.293556	−	0.955942i	$-0.594839\pi$
$977$	−18.3514	−0.587112	−0.293556	+	0.955942i	$0.594839\pi$
$978$	63.6992	2.03688
$979$	12.6308	0.403683
$980$	25.2835	0.807652
$981$	−47.0112	−1.50095
$982$	−8.37788	−0.267349
$983$	−26.9397	−0.859244	−0.429622	−	0.903009i	$-0.641353\pi$
$983$	−26.9397	−0.859244	−0.429622	+	0.903009i	$0.641353\pi$
$984$	−2.74133	−0.0873905
$985$	−42.7075	−1.36078
$986$	−0.137604	−0.00438219
$987$	44.1637	1.40575
$988$	−3.49369	−0.111149
$989$	−9.23230	−0.293570
$990$	14.5247	0.461625
$991$	−28.0949	−0.892465	−0.446233	−	0.894917i	$-0.647235\pi$
$991$	−28.0949	−0.892465	−0.446233	+	0.894917i	$0.647235\pi$
$992$	5.15606	0.163705
$993$	−37.7334	−1.19743
$994$	67.8813	2.15306
$995$	−19.1127	−0.605914
$996$	34.3836	1.08949
$997$	−20.9738	−0.664246	−0.332123	−	0.943236i	$-0.607765\pi$
$997$	−20.9738	−0.664246	−0.332123	+	0.943236i	$0.607765\pi$
$998$	28.3634	0.897827
$999$	53.2691	1.68536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.k.1.7	✓	7
3.2	odd	2		8514.2.a.bl.1.4		7
4.3	odd	2		7568.2.a.bg.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.k.1.7	✓	7	1.1	even	1	trivial
7568.2.a.bg.1.1		7	4.3	odd	2
8514.2.a.bl.1.4		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.07023 q^{3} +1.00000 q^{4} +2.26020 q^{5} +3.07023 q^{6} -4.26455 q^{7} +1.00000 q^{8} +6.42629 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.07023 q^{3} +1.00000 q^{4} +2.26020 q^{5} +3.07023 q^{6} -4.26455 q^{7} +1.00000 q^{8} +6.42629 q^{9} +2.26020 q^{10} +1.00000 q^{11} +3.07023 q^{12} +0.476943 q^{13} -4.26455 q^{14} +6.93932 q^{15} +1.00000 q^{16} +2.57281 q^{17} +6.42629 q^{18} -7.32518 q^{19} +2.26020 q^{20} -13.0931 q^{21} +1.00000 q^{22} -9.23230 q^{23} +3.07023 q^{24} +0.108489 q^{25} +0.476943 q^{26} +10.5195 q^{27} -4.26455 q^{28} -0.0534837 q^{29} +6.93932 q^{30} +5.15606 q^{31} +1.00000 q^{32} +3.07023 q^{33} +2.57281 q^{34} -9.63873 q^{35} +6.42629 q^{36} +5.06385 q^{37} -7.32518 q^{38} +1.46432 q^{39} +2.26020 q^{40} -0.892876 q^{41} -13.0931 q^{42} +1.00000 q^{43} +1.00000 q^{44} +14.5247 q^{45} -9.23230 q^{46} -3.37304 q^{47} +3.07023 q^{48} +11.1864 q^{49} +0.108489 q^{50} +7.89912 q^{51} +0.476943 q^{52} +6.48213 q^{53} +10.5195 q^{54} +2.26020 q^{55} -4.26455 q^{56} -22.4900 q^{57} -0.0534837 q^{58} -14.5527 q^{59} +6.93932 q^{60} +1.34893 q^{61} +5.15606 q^{62} -27.4053 q^{63} +1.00000 q^{64} +1.07799 q^{65} +3.07023 q^{66} +8.40501 q^{67} +2.57281 q^{68} -28.3452 q^{69} -9.63873 q^{70} -15.9176 q^{71} +6.42629 q^{72} -6.90034 q^{73} +5.06385 q^{74} +0.333087 q^{75} -7.32518 q^{76} -4.26455 q^{77} +1.46432 q^{78} -0.381383 q^{79} +2.26020 q^{80} +13.0184 q^{81} -0.892876 q^{82} +11.1991 q^{83} -13.0931 q^{84} +5.81507 q^{85} +1.00000 q^{86} -0.164207 q^{87} +1.00000 q^{88} +12.6308 q^{89} +14.5247 q^{90} -2.03395 q^{91} -9.23230 q^{92} +15.8303 q^{93} -3.37304 q^{94} -16.5563 q^{95} +3.07023 q^{96} +8.66932 q^{97} +11.1864 q^{98} +6.42629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9}+O(q^{10}) \) 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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