LMFDB - Embedded newform 946.2.a.g.1.4

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:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 1 $ x^4 - 5*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.456850$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.18890 q^{3} +1.00000 q^{4} -3.79129 q^{5} +1.18890 q^{6} -0.397613 q^{7} +1.00000 q^{8} -1.58651 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.18890 q^{3} +1.00000 q^{4} -3.79129 q^{5} +1.18890 q^{6} -0.397613 q^{7} +1.00000 q^{8} -1.58651 q^{9} -3.79129 q^{10} -1.00000 q^{11} +1.18890 q^{12} -5.64575 q^{13} -0.397613 q^{14} -4.50747 q^{15} +1.00000 q^{16} -5.00725 q^{17} -1.58651 q^{18} -2.37055 q^{19} -3.79129 q^{20} -0.472723 q^{21} -1.00000 q^{22} -2.14554 q^{23} +1.18890 q^{24} +9.37386 q^{25} -5.64575 q^{26} -5.45291 q^{27} -0.397613 q^{28} +9.88133 q^{29} -4.50747 q^{30} +5.01630 q^{31} +1.00000 q^{32} -1.18890 q^{33} -5.00725 q^{34} +1.50747 q^{35} -1.58651 q^{36} +9.71949 q^{37} -2.37055 q^{38} -6.71224 q^{39} -3.79129 q^{40} -4.47997 q^{41} -0.472723 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.01493 q^{45} -2.14554 q^{46} -4.77148 q^{47} +1.18890 q^{48} -6.84190 q^{49} +9.37386 q^{50} -5.95313 q^{51} -5.64575 q^{52} +0.138285 q^{53} -5.45291 q^{54} +3.79129 q^{55} -0.397613 q^{56} -2.81835 q^{57} +9.88133 q^{58} -8.19615 q^{59} -4.50747 q^{60} -3.44960 q^{61} +5.01630 q^{62} +0.630819 q^{63} +1.00000 q^{64} +21.4047 q^{65} -1.18890 q^{66} -1.05199 q^{67} -5.00725 q^{68} -2.55083 q^{69} +1.50747 q^{70} -2.88484 q^{71} -1.58651 q^{72} +0.937254 q^{73} +9.71949 q^{74} +11.1446 q^{75} -2.37055 q^{76} +0.397613 q^{77} -6.71224 q^{78} -12.2125 q^{79} -3.79129 q^{80} -1.72343 q^{81} -4.47997 q^{82} +5.28245 q^{83} -0.472723 q^{84} +18.9839 q^{85} +1.00000 q^{86} +11.7479 q^{87} -1.00000 q^{88} -4.31993 q^{89} +6.01493 q^{90} +2.24483 q^{91} -2.14554 q^{92} +5.96389 q^{93} -4.77148 q^{94} +8.98744 q^{95} +1.18890 q^{96} +10.6654 q^{97} -6.84190 q^{98} +1.58651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} - 2 q^{14} + 6 q^{15} + 4 q^{16} - 8 q^{17} + 2 q^{18} - 4 q^{19} - 6 q^{20} - 8 q^{21} - 4 q^{22} - 10 q^{23} - 4 q^{24} + 10 q^{25} - 12 q^{26} - 10 q^{27} - 2 q^{28} - 12 q^{29} + 6 q^{30} + 4 q^{31} + 4 q^{32} + 4 q^{33} - 8 q^{34} - 18 q^{35} + 2 q^{36} + 2 q^{37} - 4 q^{38} - 2 q^{39} - 6 q^{40} - 12 q^{41} - 8 q^{42} + 4 q^{43} - 4 q^{44} - 24 q^{45} - 10 q^{46} + 8 q^{47} - 4 q^{48} + 4 q^{49} + 10 q^{50} - 12 q^{52} + 14 q^{53} - 10 q^{54} + 6 q^{55} - 2 q^{56} - 8 q^{57} - 12 q^{58} - 12 q^{59} + 6 q^{60} - 24 q^{61} + 4 q^{62} + 40 q^{63} + 4 q^{64} + 18 q^{65} + 4 q^{66} - 14 q^{67} - 8 q^{68} + 24 q^{69} - 18 q^{70} + 6 q^{71} + 2 q^{72} - 28 q^{73} + 2 q^{74} - 10 q^{75} - 4 q^{76} + 2 q^{77} - 2 q^{78} - 12 q^{79} - 6 q^{80} + 20 q^{81} - 12 q^{82} + 4 q^{83} - 8 q^{84} + 12 q^{85} + 4 q^{86} + 48 q^{87} - 4 q^{88} - 34 q^{89} - 24 q^{90} + 20 q^{91} - 10 q^{92} + 22 q^{93} + 8 q^{94} + 6 q^{95} - 4 q^{96} - 6 q^{97} + 4 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 - 2 * q^14 + 6 * q^15 + 4 * q^16 - 8 * q^17 + 2 * q^18 - 4 * q^19 - 6 * q^20 - 8 * q^21 - 4 * q^22 - 10 * q^23 - 4 * q^24 + 10 * q^25 - 12 * q^26 - 10 * q^27 - 2 * q^28 - 12 * q^29 + 6 * q^30 + 4 * q^31 + 4 * q^32 + 4 * q^33 - 8 * q^34 - 18 * q^35 + 2 * q^36 + 2 * q^37 - 4 * q^38 - 2 * q^39 - 6 * q^40 - 12 * q^41 - 8 * q^42 + 4 * q^43 - 4 * q^44 - 24 * q^45 - 10 * q^46 + 8 * q^47 - 4 * q^48 + 4 * q^49 + 10 * q^50 - 12 * q^52 + 14 * q^53 - 10 * q^54 + 6 * q^55 - 2 * q^56 - 8 * q^57 - 12 * q^58 - 12 * q^59 + 6 * q^60 - 24 * q^61 + 4 * q^62 + 40 * q^63 + 4 * q^64 + 18 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 24 * q^69 - 18 * q^70 + 6 * q^71 + 2 * q^72 - 28 * q^73 + 2 * q^74 - 10 * q^75 - 4 * q^76 + 2 * q^77 - 2 * q^78 - 12 * q^79 - 6 * q^80 + 20 * q^81 - 12 * q^82 + 4 * q^83 - 8 * q^84 + 12 * q^85 + 4 * q^86 + 48 * q^87 - 4 * q^88 - 34 * q^89 - 24 * q^90 + 20 * q^91 - 10 * q^92 + 22 * q^93 + 8 * q^94 + 6 * q^95 - 4 * q^96 - 6 * q^97 + 4 * q^98 - 2 * 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
$3$	1.18890	0.686412	0.343206	−	0.939260i	$-0.388487\pi$
$3$	1.18890	0.686412	0.343206	+	0.939260i	$0.388487\pi$
$4$	1.00000	0.500000
$5$	−3.79129	−1.69552	−0.847758	−	0.530384i	$-0.822048\pi$
$5$	−3.79129	−1.69552	−0.847758	+	0.530384i	$0.822048\pi$
$6$	1.18890	0.485367
$7$	−0.397613	−0.150284	−0.0751418	−	0.997173i	$-0.523941\pi$
$7$	−0.397613	−0.150284	−0.0751418	+	0.997173i	$0.523941\pi$
$8$	1.00000	0.353553
$9$	−1.58651	−0.528838
$10$	−3.79129	−1.19891
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.18890	0.343206
$13$	−5.64575	−1.56585	−0.782925	−	0.622116i	$-0.786273\pi$
$13$	−5.64575	−1.56585	−0.782925	+	0.622116i	$0.786273\pi$
$14$	−0.397613	−0.106267
$15$	−4.50747	−1.16382
$16$	1.00000	0.250000
$17$	−5.00725	−1.21444	−0.607218	−	0.794535i	$-0.707715\pi$
$17$	−5.00725	−1.21444	−0.607218	+	0.794535i	$0.707715\pi$
$18$	−1.58651	−0.373945
$19$	−2.37055	−0.543842	−0.271921	−	0.962320i	$-0.587659\pi$
$19$	−2.37055	−0.543842	−0.271921	+	0.962320i	$0.587659\pi$
$20$	−3.79129	−0.847758
$21$	−0.472723	−0.103157
$22$	−1.00000	−0.213201
$23$	−2.14554	−0.447375	−0.223688	−	0.974661i	$-0.571810\pi$
$23$	−2.14554	−0.447375	−0.223688	+	0.974661i	$0.571810\pi$
$24$	1.18890	0.242683
$25$	9.37386	1.87477
$26$	−5.64575	−1.10722
$27$	−5.45291	−1.04941
$28$	−0.397613	−0.0751418
$29$	9.88133	1.83492	0.917458	−	0.397832i	$-0.130237\pi$
$29$	9.88133	1.83492	0.917458	+	0.397832i	$0.130237\pi$
$30$	−4.50747	−0.822947
$31$	5.01630	0.900954	0.450477	−	0.892788i	$-0.351254\pi$
$31$	5.01630	0.900954	0.450477	+	0.892788i	$0.351254\pi$
$32$	1.00000	0.176777
$33$	−1.18890	−0.206961
$34$	−5.00725	−0.858737
$35$	1.50747	0.254808
$36$	−1.58651	−0.264419
$37$	9.71949	1.59787	0.798937	−	0.601414i	$-0.205396\pi$
$37$	9.71949	1.59787	0.798937	+	0.601414i	$0.205396\pi$
$38$	−2.37055	−0.384554
$39$	−6.71224	−1.07482
$40$	−3.79129	−0.599455
$41$	−4.47997	−0.699654	−0.349827	−	0.936814i	$-0.613760\pi$
$41$	−4.47997	−0.699654	−0.349827	+	0.936814i	$0.613760\pi$
$42$	−0.472723	−0.0729427
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	6.01493	0.896653
$46$	−2.14554	−0.316342
$47$	−4.77148	−0.695991	−0.347996	−	0.937496i	$-0.613138\pi$
$47$	−4.77148	−0.695991	−0.347996	+	0.937496i	$0.613138\pi$
$48$	1.18890	0.171603
$49$	−6.84190	−0.977415
$50$	9.37386	1.32566
$51$	−5.95313	−0.833604
$52$	−5.64575	−0.782925
$53$	0.138285	0.0189949	0.00949746	−	0.999955i	$-0.496977\pi$
$53$	0.138285	0.0189949	0.00949746	+	0.999955i	$0.496977\pi$
$54$	−5.45291	−0.742047
$55$	3.79129	0.511217
$56$	−0.397613	−0.0531333
$57$	−2.81835	−0.373300
$58$	9.88133	1.29748
$59$	−8.19615	−1.06705	−0.533524	−	0.845785i	$-0.679133\pi$
$59$	−8.19615	−1.06705	−0.533524	+	0.845785i	$0.679133\pi$
$60$	−4.50747	−0.581911
$61$	−3.44960	−0.441676	−0.220838	−	0.975311i	$-0.570879\pi$
$61$	−3.44960	−0.441676	−0.220838	+	0.975311i	$0.570879\pi$
$62$	5.01630	0.637071
$63$	0.630819	0.0794757
$64$	1.00000	0.125000
$65$	21.4047	2.65492
$66$	−1.18890	−0.146344
$67$	−1.05199	−0.128521	−0.0642603	−	0.997933i	$-0.520469\pi$
$67$	−1.05199	−0.128521	−0.0642603	+	0.997933i	$0.520469\pi$
$68$	−5.00725	−0.607218
$69$	−2.55083	−0.307084
$70$	1.50747	0.180177
$71$	−2.88484	−0.342367	−0.171184	−	0.985239i	$-0.554759\pi$
$71$	−2.88484	−0.342367	−0.171184	+	0.985239i	$0.554759\pi$
$72$	−1.58651	−0.186972
$73$	0.937254	0.109697	0.0548486	−	0.998495i	$-0.482532\pi$
$73$	0.937254	0.109697	0.0548486	+	0.998495i	$0.482532\pi$
$74$	9.71949	1.12987
$75$	11.1446	1.28687
$76$	−2.37055	−0.271921
$77$	0.397613	0.0453122
$78$	−6.71224	−0.760011
$79$	−12.2125	−1.37401	−0.687004	−	0.726653i	$-0.741075\pi$
$79$	−12.2125	−1.37401	−0.687004	+	0.726653i	$0.741075\pi$
$80$	−3.79129	−0.423879
$81$	−1.72343	−0.191492
$82$	−4.47997	−0.494730
$83$	5.28245	0.579824	0.289912	−	0.957053i	$-0.406374\pi$
$83$	5.28245	0.579824	0.289912	+	0.957053i	$0.406374\pi$
$84$	−0.472723	−0.0515783
$85$	18.9839	2.05910
$86$	1.00000	0.107833
$87$	11.7479	1.25951
$88$	−1.00000	−0.106600
$89$	−4.31993	−0.457912	−0.228956	−	0.973437i	$-0.573531\pi$
$89$	−4.31993	−0.457912	−0.228956	+	0.973437i	$0.573531\pi$
$90$	6.01493	0.634030
$91$	2.24483	0.235322
$92$	−2.14554	−0.223688
$93$	5.96389	0.618426
$94$	−4.77148	−0.492140
$95$	8.98744	0.922092
$96$	1.18890	0.121342
$97$	10.6654	1.08290	0.541452	−	0.840732i	$-0.317875\pi$
$97$	10.6654	1.08290	0.541452	+	0.840732i	$0.317875\pi$
$98$	−6.84190	−0.691137
$99$	1.58651	0.159451
$100$	9.37386	0.937386
$101$	−13.5826	−1.35152	−0.675758	−	0.737123i	$-0.736184\pi$
$101$	−13.5826	−1.35152	−0.675758	+	0.737123i	$0.736184\pi$
$102$	−5.95313	−0.589447
$103$	−2.05967	−0.202945	−0.101472	−	0.994838i	$-0.532355\pi$
$103$	−2.05967	−0.202945	−0.101472	+	0.994838i	$0.532355\pi$
$104$	−5.64575	−0.553611
$105$	1.79223	0.174904
$106$	0.138285	0.0134314
$107$	−11.2862	−1.09108	−0.545539	−	0.838086i	$-0.683675\pi$
$107$	−11.2862	−1.09108	−0.545539	+	0.838086i	$0.683675\pi$
$108$	−5.45291	−0.524707
$109$	−4.34894	−0.416553	−0.208276	−	0.978070i	$-0.566785\pi$
$109$	−4.34894	−0.416553	−0.208276	+	0.978070i	$0.566785\pi$
$110$	3.79129	0.361485
$111$	11.5555	1.09680
$112$	−0.397613	−0.0375709
$113$	12.7899	1.20317	0.601587	−	0.798807i	$-0.294535\pi$
$113$	12.7899	1.20317	0.601587	+	0.798807i	$0.294535\pi$
$114$	−2.81835	−0.263963
$115$	8.13435	0.758532
$116$	9.88133	0.917458
$117$	8.95707	0.828081
$118$	−8.19615	−0.754517
$119$	1.99095	0.182510
$120$	−4.50747	−0.411473
$121$	1.00000	0.0909091
$122$	−3.44960	−0.312312
$123$	−5.32625	−0.480251
$124$	5.01630	0.450477
$125$	−16.5826	−1.48319
$126$	0.630819	0.0561978
$127$	20.6567	1.83299	0.916495	−	0.400046i	$-0.131006\pi$
$127$	20.6567	1.83299	0.916495	+	0.400046i	$0.131006\pi$
$128$	1.00000	0.0883883
$129$	1.18890	0.104677
$130$	21.4047	1.87731
$131$	−4.86897	−0.425404	−0.212702	−	0.977117i	$-0.568226\pi$
$131$	−4.86897	−0.425404	−0.212702	+	0.977117i	$0.568226\pi$
$132$	−1.18890	−0.103481
$133$	0.942562	0.0817305
$134$	−1.05199	−0.0908777
$135$	20.6736	1.77930
$136$	−5.00725	−0.429368
$137$	−6.79640	−0.580656	−0.290328	−	0.956927i	$-0.593764\pi$
$137$	−6.79640	−0.580656	−0.290328	+	0.956927i	$0.593764\pi$
$138$	−2.55083	−0.217141
$139$	4.19615	0.355913	0.177957	−	0.984038i	$-0.443051\pi$
$139$	4.19615	0.355913	0.177957	+	0.984038i	$0.443051\pi$
$140$	1.50747	0.127404
$141$	−5.67281	−0.477737
$142$	−2.88484	−0.242090
$143$	5.64575	0.472121
$144$	−1.58651	−0.132210
$145$	−37.4630	−3.11113
$146$	0.937254	0.0775677
$147$	−8.13435	−0.670910
$148$	9.71949	0.798937
$149$	−4.83465	−0.396070	−0.198035	−	0.980195i	$-0.563456\pi$
$149$	−4.83465	−0.396070	−0.198035	+	0.980195i	$0.563456\pi$
$150$	11.1446	0.909952
$151$	18.4042	1.49772	0.748858	−	0.662731i	$-0.230603\pi$
$151$	18.4042	1.49772	0.748858	+	0.662731i	$0.230603\pi$
$152$	−2.37055	−0.192277
$153$	7.94408	0.642240
$154$	0.397613	0.0320406
$155$	−19.0182	−1.52758
$156$	−6.71224	−0.537409
$157$	11.5147	0.918975	0.459487	−	0.888184i	$-0.348033\pi$
$157$	11.5147	0.918975	0.459487	+	0.888184i	$0.348033\pi$
$158$	−12.2125	−0.971571
$159$	0.164407	0.0130384
$160$	−3.79129	−0.299728
$161$	0.853094	0.0672332
$162$	−1.72343	−0.135405
$163$	−19.3578	−1.51622	−0.758110	−	0.652127i	$-0.773877\pi$
$163$	−19.3578	−1.51622	−0.758110	+	0.652127i	$0.773877\pi$
$164$	−4.47997	−0.349827
$165$	4.50747	0.350906
$166$	5.28245	0.409998
$167$	17.4245	1.34835	0.674173	−	0.738573i	$-0.264500\pi$
$167$	17.4245	1.34835	0.674173	+	0.738573i	$0.264500\pi$
$168$	−0.472723	−0.0364714
$169$	18.8745	1.45189
$170$	18.9839	1.45600
$171$	3.76091	0.287604
$172$	1.00000	0.0762493
$173$	0.654372	0.0497510	0.0248755	−	0.999691i	$-0.492081\pi$
$173$	0.654372	0.0497510	0.0248755	+	0.999691i	$0.492081\pi$
$174$	11.7479	0.890608
$175$	−3.72717	−0.281748
$176$	−1.00000	−0.0753778
$177$	−9.74441	−0.732435
$178$	−4.31993	−0.323793
$179$	−21.1526	−1.58102	−0.790509	−	0.612450i	$-0.790184\pi$
$179$	−21.1526	−1.58102	−0.790509	+	0.612450i	$0.790184\pi$
$180$	6.01493	0.448327
$181$	−10.1540	−0.754738	−0.377369	−	0.926063i	$-0.623171\pi$
$181$	−10.1540	−0.754738	−0.377369	+	0.926063i	$0.623171\pi$
$182$	2.24483	0.166398
$183$	−4.10123	−0.303172
$184$	−2.14554	−0.158171
$185$	−36.8494	−2.70922
$186$	5.96389	0.437293
$187$	5.00725	0.366166
$188$	−4.77148	−0.347996
$189$	2.16815	0.157710
$190$	8.98744	0.652017
$191$	−9.02312	−0.652890	−0.326445	−	0.945216i	$-0.605851\pi$
$191$	−9.02312	−0.652890	−0.326445	+	0.945216i	$0.605851\pi$
$192$	1.18890	0.0858015
$193$	−15.0630	−1.08426	−0.542128	−	0.840296i	$-0.682381\pi$
$193$	−15.0630	−1.08426	−0.542128	+	0.840296i	$0.682381\pi$
$194$	10.6654	0.765729
$195$	25.4480	1.82237
$196$	−6.84190	−0.488707
$197$	−13.5231	−0.963484	−0.481742	−	0.876313i	$-0.659996\pi$
$197$	−13.5231	−0.963484	−0.481742	+	0.876313i	$0.659996\pi$
$198$	1.58651	0.112749
$199$	6.07597	0.430714	0.215357	−	0.976535i	$-0.430908\pi$
$199$	6.07597	0.430714	0.215357	+	0.976535i	$0.430908\pi$
$200$	9.37386	0.662832
$201$	−1.25071	−0.0882181
$202$	−13.5826	−0.955667
$203$	−3.92895	−0.275758
$204$	−5.95313	−0.416802
$205$	16.9849	1.18627
$206$	−2.05967	−0.143504
$207$	3.40392	0.236589
$208$	−5.64575	−0.391462
$209$	2.37055	0.163974
$210$	1.79223	0.123675
$211$	−0.335807	−0.0231179	−0.0115590	−	0.999933i	$-0.503679\pi$
$211$	−0.335807	−0.0231179	−0.0115590	+	0.999933i	$0.503679\pi$
$212$	0.138285	0.00949746
$213$	−3.42979	−0.235005
$214$	−11.2862	−0.771508
$215$	−3.79129	−0.258564
$216$	−5.45291	−0.371024
$217$	−1.99455	−0.135399
$218$	−4.34894	−0.294547
$219$	1.11430	0.0752976
$220$	3.79129	0.255609
$221$	28.2697	1.90163
$222$	11.5555	0.775555
$223$	4.35956	0.291938	0.145969	−	0.989289i	$-0.453370\pi$
$223$	4.35956	0.291938	0.145969	+	0.989289i	$0.453370\pi$
$224$	−0.397613	−0.0265667
$225$	−14.8718	−0.991451
$226$	12.7899	0.850773
$227$	−21.2670	−1.41154	−0.705770	−	0.708441i	$-0.749399\pi$
$227$	−21.2670	−1.41154	−0.705770	+	0.708441i	$0.749399\pi$
$228$	−2.81835	−0.186650
$229$	−9.37823	−0.619731	−0.309865	−	0.950780i	$-0.600284\pi$
$229$	−9.37823	−0.619731	−0.309865	+	0.950780i	$0.600284\pi$
$230$	8.13435	0.536363
$231$	0.472723	0.0311029
$232$	9.88133	0.648741
$233$	−21.1624	−1.38640	−0.693198	−	0.720747i	$-0.743799\pi$
$233$	−21.1624	−1.38640	−0.693198	+	0.720747i	$0.743799\pi$
$234$	8.95707	0.585542
$235$	18.0900	1.18006
$236$	−8.19615	−0.533524
$237$	−14.5194	−0.943136
$238$	1.99095	0.129054
$239$	−0.0468735	−0.00303200	−0.00151600	−	0.999999i	$-0.500483\pi$
$239$	−0.0468735	−0.00303200	−0.00151600	+	0.999999i	$0.500483\pi$
$240$	−4.50747	−0.290956
$241$	21.7932	1.40383	0.701913	−	0.712263i	$-0.252330\pi$
$241$	21.7932	1.40383	0.701913	+	0.712263i	$0.252330\pi$
$242$	1.00000	0.0642824
$243$	14.3097	0.917971
$244$	−3.44960	−0.220838
$245$	25.9396	1.65722
$246$	−5.32625	−0.339589
$247$	13.3835	0.851574
$248$	5.01630	0.318535
$249$	6.28031	0.397999
$250$	−16.5826	−1.04877
$251$	−15.9683	−1.00791	−0.503954	−	0.863731i	$-0.668122\pi$
$251$	−15.9683	−1.00791	−0.503954	+	0.863731i	$0.668122\pi$
$252$	0.630819	0.0397379
$253$	2.14554	0.134889
$254$	20.6567	1.29612
$255$	22.5700	1.41339
$256$	1.00000	0.0625000
$257$	−7.20477	−0.449421	−0.224711	−	0.974426i	$-0.572144\pi$
$257$	−7.20477	−0.449421	−0.224711	+	0.974426i	$0.572144\pi$
$258$	1.18890	0.0740177
$259$	−3.86460	−0.240134
$260$	21.4047	1.32746
$261$	−15.6769	−0.970374
$262$	−4.86897	−0.300806
$263$	3.21639	0.198331	0.0991656	−	0.995071i	$-0.468383\pi$
$263$	3.21639	0.198331	0.0991656	+	0.995071i	$0.468383\pi$
$264$	−1.18890	−0.0731718
$265$	−0.524279	−0.0322062
$266$	0.942562	0.0577922
$267$	−5.13598	−0.314317
$268$	−1.05199	−0.0642603
$269$	26.5302	1.61757	0.808787	−	0.588101i	$-0.200124\pi$
$269$	26.5302	1.61757	0.808787	+	0.588101i	$0.200124\pi$
$270$	20.6736	1.25815
$271$	10.4639	0.635637	0.317818	−	0.948152i	$-0.397050\pi$
$271$	10.4639	0.635637	0.317818	+	0.948152i	$0.397050\pi$
$272$	−5.00725	−0.303609
$273$	2.66888	0.161528
$274$	−6.79640	−0.410586
$275$	−9.37386	−0.565265
$276$	−2.55083	−0.153542
$277$	14.8182	0.890337	0.445168	−	0.895447i	$-0.353144\pi$
$277$	14.8182	0.890337	0.445168	+	0.895447i	$0.353144\pi$
$278$	4.19615	0.251668
$279$	−7.95843	−0.476459
$280$	1.50747	0.0900883
$281$	3.47092	0.207058	0.103529	−	0.994626i	$-0.466987\pi$
$281$	3.47092	0.207058	0.103529	+	0.994626i	$0.466987\pi$
$282$	−5.67281	−0.337811
$283$	−30.7197	−1.82610	−0.913049	−	0.407850i	$-0.866279\pi$
$283$	−30.7197	−1.82610	−0.913049	+	0.407850i	$0.866279\pi$
$284$	−2.88484	−0.171184
$285$	10.6852	0.632935
$286$	5.64575	0.333840
$287$	1.78130	0.105147
$288$	−1.58651	−0.0934862
$289$	8.07257	0.474857
$290$	−37.4630	−2.19990
$291$	12.6801	0.743319
$292$	0.937254	0.0548486
$293$	−24.5885	−1.43647	−0.718237	−	0.695799i	$-0.755050\pi$
$293$	−24.5885	−1.43647	−0.718237	+	0.695799i	$0.755050\pi$
$294$	−8.13435	−0.474405
$295$	31.0740	1.80920
$296$	9.71949	0.564934
$297$	5.45291	0.316410
$298$	−4.83465	−0.280064
$299$	12.1132	0.700522
$300$	11.1446	0.643434
$301$	−0.397613	−0.0229180
$302$	18.4042	1.05904
$303$	−16.1483	−0.927698
$304$	−2.37055	−0.135960
$305$	13.0784	0.748868
$306$	7.94408	0.454133
$307$	27.2160	1.55330	0.776650	−	0.629933i	$-0.216918\pi$
$307$	27.2160	1.55330	0.776650	+	0.629933i	$0.216918\pi$
$308$	0.397613	0.0226561
$309$	−2.44874	−0.139304
$310$	−19.0182	−1.08016
$311$	21.2338	1.20406	0.602029	−	0.798475i	$-0.294359\pi$
$311$	21.2338	1.20406	0.602029	+	0.798475i	$0.294359\pi$
$312$	−6.71224	−0.380006
$313$	20.0945	1.13581	0.567905	−	0.823094i	$-0.307754\pi$
$313$	20.0945	1.13581	0.567905	+	0.823094i	$0.307754\pi$
$314$	11.5147	0.649813
$315$	−2.39162	−0.134752
$316$	−12.2125	−0.687004
$317$	14.6936	0.825275	0.412637	−	0.910895i	$-0.364608\pi$
$317$	14.6936	0.825275	0.412637	+	0.910895i	$0.364608\pi$
$318$	0.164407	0.00921951
$319$	−9.88133	−0.553248
$320$	−3.79129	−0.211939
$321$	−13.4182	−0.748929
$322$	0.853094	0.0475411
$323$	11.8699	0.660461
$324$	−1.72343	−0.0957461
$325$	−52.9225	−2.93561
$326$	−19.3578	−1.07213
$327$	−5.17046	−0.285927
$328$	−4.47997	−0.247365
$329$	1.89720	0.104596
$330$	4.50747	0.248128
$331$	−3.09418	−0.170071	−0.0850357	−	0.996378i	$-0.527100\pi$
$331$	−3.09418	−0.170071	−0.0850357	+	0.996378i	$0.527100\pi$
$332$	5.28245	0.289912
$333$	−15.4201	−0.845017
$334$	17.4245	0.953425
$335$	3.98838	0.217909
$336$	−0.472723	−0.0257891
$337$	−26.1552	−1.42476	−0.712381	−	0.701793i	$-0.752383\pi$
$337$	−26.1552	−1.42476	−0.712381	+	0.701793i	$0.752383\pi$
$338$	18.8745	1.02664
$339$	15.2059	0.825874
$340$	18.9839	1.02955
$341$	−5.01630	−0.271648
$342$	3.76091	0.203367
$343$	5.50372	0.297173
$344$	1.00000	0.0539164
$345$	9.67093	0.520666
$346$	0.654372	0.0351793
$347$	5.40273	0.290033	0.145017	−	0.989429i	$-0.453676\pi$
$347$	5.40273	0.290033	0.145017	+	0.989429i	$0.453676\pi$
$348$	11.7479	0.629755
$349$	−21.1799	−1.13373	−0.566866	−	0.823810i	$-0.691844\pi$
$349$	−21.1799	−1.13373	−0.566866	+	0.823810i	$0.691844\pi$
$350$	−3.72717	−0.199226
$351$	30.7858	1.64322
$352$	−1.00000	−0.0533002
$353$	25.4426	1.35417	0.677086	−	0.735904i	$-0.263243\pi$
$353$	25.4426	1.35417	0.677086	+	0.735904i	$0.263243\pi$
$354$	−9.74441	−0.517910
$355$	10.9373	0.580489
$356$	−4.31993	−0.228956
$357$	2.36704	0.125277
$358$	−21.1526	−1.11795
$359$	−35.4982	−1.87352	−0.936762	−	0.349967i	$-0.886193\pi$
$359$	−35.4982	−1.87352	−0.936762	+	0.349967i	$0.886193\pi$
$360$	6.01493	0.317015
$361$	−13.3805	−0.704236
$362$	−10.1540	−0.533680
$363$	1.18890	0.0624011
$364$	2.24483	0.117661
$365$	−3.55340	−0.185993
$366$	−4.10123	−0.214375
$367$	19.7248	1.02963	0.514813	−	0.857302i	$-0.327861\pi$
$367$	19.7248	1.02963	0.514813	+	0.857302i	$0.327861\pi$
$368$	−2.14554	−0.111844
$369$	7.10754	0.370004
$370$	−36.8494	−1.91571
$371$	−0.0549840	−0.00285463
$372$	5.96389	0.309213
$373$	−32.3611	−1.67559	−0.837797	−	0.545981i	$-0.816157\pi$
$373$	−32.3611	−1.67559	−0.837797	+	0.545981i	$0.816157\pi$
$374$	5.00725	0.258919
$375$	−19.7150	−1.01808
$376$	−4.77148	−0.246070
$377$	−55.7875	−2.87320
$378$	2.16815	0.111518
$379$	−22.6156	−1.16169	−0.580843	−	0.814016i	$-0.697277\pi$
$379$	−22.6156	−1.16169	−0.580843	+	0.814016i	$0.697277\pi$
$380$	8.98744	0.461046
$381$	24.5588	1.25819
$382$	−9.02312	−0.461663
$383$	10.7597	0.549793	0.274896	−	0.961474i	$-0.411356\pi$
$383$	10.7597	0.549793	0.274896	+	0.961474i	$0.411356\pi$
$384$	1.18890	0.0606709
$385$	−1.50747	−0.0768276
$386$	−15.0630	−0.766685
$387$	−1.58651	−0.0806471
$388$	10.6654	0.541452
$389$	3.29150	0.166886	0.0834429	−	0.996513i	$-0.473408\pi$
$389$	3.29150	0.166886	0.0834429	+	0.996513i	$0.473408\pi$
$390$	25.4480	1.28861
$391$	10.7432	0.543309
$392$	−6.84190	−0.345568
$393$	−5.78872	−0.292002
$394$	−13.5231	−0.681286
$395$	46.3009	2.32965
$396$	1.58651	0.0797253
$397$	−30.1574	−1.51356	−0.756778	−	0.653672i	$-0.773228\pi$
$397$	−30.1574	−1.51356	−0.756778	+	0.653672i	$0.773228\pi$
$398$	6.07597	0.304561
$399$	1.12061	0.0561008
$400$	9.37386	0.468693
$401$	11.1836	0.558482	0.279241	−	0.960221i	$-0.409917\pi$
$401$	11.1836	0.558482	0.279241	+	0.960221i	$0.409917\pi$
$402$	−1.25071	−0.0623796
$403$	−28.3208	−1.41076
$404$	−13.5826	−0.675758
$405$	6.53402	0.324678
$406$	−3.92895	−0.194990
$407$	−9.71949	−0.481777
$408$	−5.95313	−0.294724
$409$	−10.4084	−0.514661	−0.257330	−	0.966323i	$-0.582843\pi$
$409$	−10.4084	−0.514661	−0.257330	+	0.966323i	$0.582843\pi$
$410$	16.9849	0.838823
$411$	−8.08025	−0.398569
$412$	−2.05967	−0.101472
$413$	3.25890	0.160360
$414$	3.40392	0.167294
$415$	−20.0273	−0.983101
$416$	−5.64575	−0.276806
$417$	4.98881	0.244303
$418$	2.37055	0.115947
$419$	−32.3708	−1.58142	−0.790708	−	0.612193i	$-0.790287\pi$
$419$	−32.3708	−1.58142	−0.790708	+	0.612193i	$0.790287\pi$
$420$	1.79223	0.0874518
$421$	−2.82346	−0.137607	−0.0688036	−	0.997630i	$-0.521918\pi$
$421$	−2.82346	−0.137607	−0.0688036	+	0.997630i	$0.521918\pi$
$422$	−0.335807	−0.0163468
$423$	7.57002	0.368067
$424$	0.138285	0.00671572
$425$	−46.9373	−2.27679
$426$	−3.42979	−0.166174
$427$	1.37161	0.0663767
$428$	−11.2862	−0.545539
$429$	6.71224	0.324070
$430$	−3.79129	−0.182832
$431$	−32.0416	−1.54339	−0.771695	−	0.635993i	$-0.780591\pi$
$431$	−32.0416	−1.54339	−0.771695	+	0.635993i	$0.780591\pi$
$432$	−5.45291	−0.262353
$433$	−14.0998	−0.677595	−0.338797	−	0.940859i	$-0.610020\pi$
$433$	−14.0998	−0.677595	−0.338797	+	0.940859i	$0.610020\pi$
$434$	−1.99455	−0.0957414
$435$	−44.5398	−2.13552
$436$	−4.34894	−0.208276
$437$	5.08610	0.243301
$438$	1.11430	0.0532434
$439$	−0.563390	−0.0268892	−0.0134446	−	0.999910i	$-0.504280\pi$
$439$	−0.563390	−0.0268892	−0.0134446	+	0.999910i	$0.504280\pi$
$440$	3.79129	0.180743
$441$	10.8548	0.516894
$442$	28.2697	1.34465
$443$	34.7331	1.65022	0.825109	−	0.564974i	$-0.191114\pi$
$443$	34.7331	1.65022	0.825109	+	0.564974i	$0.191114\pi$
$444$	11.5555	0.548400
$445$	16.3781	0.776397
$446$	4.35956	0.206431
$447$	−5.74792	−0.271867
$448$	−0.397613	−0.0187855
$449$	−5.95375	−0.280975	−0.140487	−	0.990082i	$-0.544867\pi$
$449$	−5.95375	−0.280975	−0.140487	+	0.990082i	$0.544867\pi$
$450$	−14.8718	−0.701062
$451$	4.47997	0.210954
$452$	12.7899	0.601587
$453$	21.8808	1.02805
$454$	−21.2670	−0.998110
$455$	−8.51078	−0.398991
$456$	−2.81835	−0.131981
$457$	−22.5830	−1.05639	−0.528194	−	0.849124i	$-0.677131\pi$
$457$	−22.5830	−1.05639	−0.528194	+	0.849124i	$0.677131\pi$
$458$	−9.37823	−0.438216
$459$	27.3041	1.27445
$460$	8.13435	0.379266
$461$	−27.1057	−1.26244	−0.631220	−	0.775604i	$-0.717445\pi$
$461$	−27.1057	−1.26244	−0.631220	+	0.775604i	$0.717445\pi$
$462$	0.472723	0.0219931
$463$	40.9266	1.90202	0.951011	−	0.309157i	$-0.100047\pi$
$463$	40.9266	1.90202	0.951011	+	0.309157i	$0.100047\pi$
$464$	9.88133	0.458729
$465$	−22.6108	−1.04855
$466$	−21.1624	−0.980330
$467$	31.2686	1.44694	0.723469	−	0.690356i	$-0.242546\pi$
$467$	31.2686	1.44694	0.723469	+	0.690356i	$0.242546\pi$
$468$	8.95707	0.414040
$469$	0.418283	0.0193145
$470$	18.0900	0.834431
$471$	13.6899	0.630795
$472$	−8.19615	−0.377258
$473$	−1.00000	−0.0459800
$474$	−14.5194	−0.666898
$475$	−22.2212	−1.01958
$476$	1.99095	0.0912550
$477$	−0.219391	−0.0100452
$478$	−0.0468735	−0.00214395
$479$	17.9056	0.818129	0.409064	−	0.912505i	$-0.365855\pi$
$479$	17.9056	0.818129	0.409064	+	0.912505i	$0.365855\pi$
$480$	−4.50747	−0.205737
$481$	−54.8738	−2.50203
$482$	21.7932	0.992654
$483$	1.01424	0.0461497
$484$	1.00000	0.0454545
$485$	−40.4355	−1.83608
$486$	14.3097	0.649103
$487$	36.3437	1.64689	0.823446	−	0.567395i	$-0.192049\pi$
$487$	36.3437	1.64689	0.823446	+	0.567395i	$0.192049\pi$
$488$	−3.44960	−0.156156
$489$	−23.0145	−1.04075
$490$	25.9396	1.17183
$491$	−22.4494	−1.01313	−0.506564	−	0.862203i	$-0.669084\pi$
$491$	−22.4494	−1.01313	−0.506564	+	0.862203i	$0.669084\pi$
$492$	−5.32625	−0.240126
$493$	−49.4783	−2.22839
$494$	13.3835	0.602154
$495$	−6.01493	−0.270351
$496$	5.01630	0.225239
$497$	1.14705	0.0514522
$498$	6.28031	0.281428
$499$	32.8908	1.47239	0.736197	−	0.676767i	$-0.236619\pi$
$499$	32.8908	1.47239	0.736197	+	0.676767i	$0.236619\pi$
$500$	−16.5826	−0.741595
$501$	20.7160	0.925522
$502$	−15.9683	−0.712698
$503$	−23.1136	−1.03058	−0.515292	−	0.857015i	$-0.672317\pi$
$503$	−23.1136	−1.03058	−0.515292	+	0.857015i	$0.672317\pi$
$504$	0.630819	0.0280989
$505$	51.4955	2.29152
$506$	2.14554	0.0953807
$507$	22.4399	0.996592
$508$	20.6567	0.916495
$509$	15.3612	0.680871	0.340436	−	0.940268i	$-0.389425\pi$
$509$	15.3612	0.680871	0.340436	+	0.940268i	$0.389425\pi$
$510$	22.5700	0.999417
$511$	−0.372665	−0.0164857
$512$	1.00000	0.0441942
$513$	12.9264	0.570715
$514$	−7.20477	−0.317789
$515$	7.80879	0.344096
$516$	1.18890	0.0523385
$517$	4.77148	0.209849
$518$	−3.86460	−0.169801
$519$	0.777984	0.0341497
$520$	21.4047	0.938657
$521$	10.8527	0.475465	0.237733	−	0.971331i	$-0.423596\pi$
$521$	10.8527	0.475465	0.237733	+	0.971331i	$0.423596\pi$
$522$	−15.6769	−0.686158
$523$	−27.4520	−1.20039	−0.600195	−	0.799853i	$-0.704911\pi$
$523$	−27.4520	−1.20039	−0.600195	+	0.799853i	$0.704911\pi$
$524$	−4.86897	−0.212702
$525$	−4.43124	−0.193395
$526$	3.21639	0.140241
$527$	−25.1179	−1.09415
$528$	−1.18890	−0.0517403
$529$	−18.3967	−0.799855
$530$	−0.524279	−0.0227732
$531$	13.0033	0.564296
$532$	0.942562	0.0408653
$533$	25.2928	1.09555
$534$	−5.13598	−0.222255
$535$	42.7892	1.84994
$536$	−1.05199	−0.0454389
$537$	−25.1483	−1.08523
$538$	26.5302	1.14380
$539$	6.84190	0.294702
$540$	20.6736	0.889648
$541$	27.4497	1.18016	0.590078	−	0.807346i	$-0.299097\pi$
$541$	27.4497	1.18016	0.590078	+	0.807346i	$0.299097\pi$
$542$	10.4639	0.449463
$543$	−12.0721	−0.518061
$544$	−5.00725	−0.214684
$545$	16.4881	0.706272
$546$	2.66888	0.114217
$547$	−8.70319	−0.372121	−0.186061	−	0.982538i	$-0.559572\pi$
$547$	−8.70319	−0.372121	−0.186061	+	0.982538i	$0.559572\pi$
$548$	−6.79640	−0.290328
$549$	5.47284	0.233575
$550$	−9.37386	−0.399703
$551$	−23.4242	−0.997904
$552$	−2.55083	−0.108571
$553$	4.85583	0.206491
$554$	14.8182	0.629563
$555$	−43.8103	−1.85964
$556$	4.19615	0.177957
$557$	−25.4769	−1.07949	−0.539745	−	0.841828i	$-0.681479\pi$
$557$	−25.4769	−1.07949	−0.539745	+	0.841828i	$0.681479\pi$
$558$	−7.95843	−0.336907
$559$	−5.64575	−0.238790
$560$	1.50747	0.0637021
$561$	5.95313	0.251341
$562$	3.47092	0.146412
$563$	22.7032	0.956825	0.478413	−	0.878135i	$-0.341212\pi$
$563$	22.7032	0.956825	0.478413	+	0.878135i	$0.341212\pi$
$564$	−5.67281	−0.238869
$565$	−48.4903	−2.04000
$566$	−30.7197	−1.29125
$567$	0.685258	0.0287781
$568$	−2.88484	−0.121045
$569$	−1.20203	−0.0503919	−0.0251959	−	0.999683i	$-0.508021\pi$
$569$	−1.20203	−0.0503919	−0.0251959	+	0.999683i	$0.508021\pi$
$570$	10.6852	0.447553
$571$	−43.9007	−1.83719	−0.918595	−	0.395201i	$-0.870675\pi$
$571$	−43.9007	−1.83719	−0.918595	+	0.395201i	$0.870675\pi$
$572$	5.64575	0.236061
$573$	−10.7276	−0.448152
$574$	1.78130	0.0743499
$575$	−20.1120	−0.838727
$576$	−1.58651	−0.0661048
$577$	4.00117	0.166571	0.0832855	−	0.996526i	$-0.473459\pi$
$577$	4.00117	0.166571	0.0832855	+	0.996526i	$0.473459\pi$
$578$	8.07257	0.335774
$579$	−17.9084	−0.744247
$580$	−37.4630	−1.55556
$581$	−2.10037	−0.0871381
$582$	12.6801	0.525606
$583$	−0.138285	−0.00572719
$584$	0.937254	0.0387838
$585$	−33.9588	−1.40402
$586$	−24.5885	−1.01574
$587$	30.6367	1.26451	0.632257	−	0.774759i	$-0.282129\pi$
$587$	30.6367	1.26451	0.632257	+	0.774759i	$0.282129\pi$
$588$	−8.13435	−0.335455
$589$	−11.8914	−0.489977
$590$	31.0740	1.27930
$591$	−16.0777	−0.661347
$592$	9.71949	0.399469
$593$	−13.1677	−0.540733	−0.270367	−	0.962757i	$-0.587145\pi$
$593$	−13.1677	−0.540733	−0.270367	+	0.962757i	$0.587145\pi$
$594$	5.45291	0.223736
$595$	−7.54826	−0.309449
$596$	−4.83465	−0.198035
$597$	7.22373	0.295647
$598$	12.1132	0.495344
$599$	−15.9908	−0.653364	−0.326682	−	0.945134i	$-0.605931\pi$
$599$	−15.9908	−0.653364	−0.326682	+	0.945134i	$0.605931\pi$
$600$	11.1446	0.454976
$601$	38.4435	1.56814	0.784071	−	0.620671i	$-0.213140\pi$
$601$	38.4435	1.56814	0.784071	+	0.620671i	$0.213140\pi$
$602$	−0.397613	−0.0162055
$603$	1.66899	0.0679665
$604$	18.4042	0.748858
$605$	−3.79129	−0.154138
$606$	−16.1483	−0.655981
$607$	12.7952	0.519342	0.259671	−	0.965697i	$-0.416386\pi$
$607$	12.7952	0.519342	0.259671	+	0.965697i	$0.416386\pi$
$608$	−2.37055	−0.0961385
$609$	−4.67113	−0.189284
$610$	13.0784	0.529530
$611$	26.9386	1.08982
$612$	7.94408	0.321120
$613$	24.8238	1.00263	0.501313	−	0.865266i	$-0.332851\pi$
$613$	24.8238	1.00263	0.501313	+	0.865266i	$0.332851\pi$
$614$	27.2160	1.09835
$615$	20.1933	0.814274
$616$	0.397613	0.0160203
$617$	40.4979	1.63038	0.815192	−	0.579191i	$-0.196631\pi$
$617$	40.4979	1.63038	0.815192	+	0.579191i	$0.196631\pi$
$618$	−2.44874	−0.0985028
$619$	8.21885	0.330343	0.165172	−	0.986265i	$-0.447182\pi$
$619$	8.21885	0.330343	0.165172	+	0.986265i	$0.447182\pi$
$620$	−19.0182	−0.763791
$621$	11.6994	0.469482
$622$	21.2338	0.851397
$623$	1.71766	0.0688167
$624$	−6.71224	−0.268705
$625$	16.0000	0.640000
$626$	20.0945	0.803139
$627$	2.81835	0.112554
$628$	11.5147	0.459487
$629$	−48.6679	−1.94052
$630$	−2.39162	−0.0952843
$631$	25.9406	1.03268	0.516339	−	0.856384i	$-0.327295\pi$
$631$	25.9406	1.03268	0.516339	+	0.856384i	$0.327295\pi$
$632$	−12.2125	−0.485785
$633$	−0.399242	−0.0158684
$634$	14.6936	0.583557
$635$	−78.3157	−3.10786
$636$	0.164407	0.00651918
$637$	38.6277	1.53048
$638$	−9.88133	−0.391206
$639$	4.57684	0.181057
$640$	−3.79129	−0.149864
$641$	−25.7219	−1.01595	−0.507976	−	0.861371i	$-0.669606\pi$
$641$	−25.7219	−1.01595	−0.507976	+	0.861371i	$0.669606\pi$
$642$	−13.4182	−0.529573
$643$	9.67836	0.381677	0.190839	−	0.981621i	$-0.438879\pi$
$643$	9.67836	0.381677	0.190839	+	0.981621i	$0.438879\pi$
$644$	0.853094	0.0336166
$645$	−4.50747	−0.177481
$646$	11.8699	0.467017
$647$	22.1759	0.871827	0.435913	−	0.899989i	$-0.356425\pi$
$647$	22.1759	0.871827	0.435913	+	0.899989i	$0.356425\pi$
$648$	−1.72343	−0.0677027
$649$	8.19615	0.321727
$650$	−52.9225	−2.07579
$651$	−2.37132	−0.0929394
$652$	−19.3578	−0.758110
$653$	−42.1370	−1.64895	−0.824473	−	0.565901i	$-0.808528\pi$
$653$	−42.1370	−1.64895	−0.824473	+	0.565901i	$0.808528\pi$
$654$	−5.17046	−0.202181
$655$	18.4597	0.721278
$656$	−4.47997	−0.174914
$657$	−1.48697	−0.0580121
$658$	1.89720	0.0739606
$659$	−1.01376	−0.0394904	−0.0197452	−	0.999805i	$-0.506286\pi$
$659$	−1.01376	−0.0394904	−0.0197452	+	0.999805i	$0.506286\pi$
$660$	4.50747	0.175453
$661$	8.19498	0.318748	0.159374	−	0.987218i	$-0.449052\pi$
$661$	8.19498	0.318748	0.159374	+	0.987218i	$0.449052\pi$
$662$	−3.09418	−0.120259
$663$	33.6099	1.30530
$664$	5.28245	0.204999
$665$	−3.57352	−0.138575
$666$	−15.4201	−0.597517
$667$	−21.2008	−0.820896
$668$	17.4245	0.674173
$669$	5.18308	0.200390
$670$	3.98838	0.154085
$671$	3.44960	0.133170
$672$	−0.472723	−0.0182357
$673$	−16.8113	−0.648028	−0.324014	−	0.946052i	$-0.605032\pi$
$673$	−16.8113	−0.648028	−0.324014	+	0.946052i	$0.605032\pi$
$674$	−26.1552	−1.00746
$675$	−51.1148	−1.96741
$676$	18.8745	0.725943
$677$	−7.16460	−0.275358	−0.137679	−	0.990477i	$-0.543964\pi$
$677$	−7.16460	−0.275358	−0.137679	+	0.990477i	$0.543964\pi$
$678$	15.2059	0.583981
$679$	−4.24069	−0.162743
$680$	18.9839	0.728001
$681$	−25.2844	−0.968899
$682$	−5.01630	−0.192084
$683$	−15.5141	−0.593630	−0.296815	−	0.954935i	$-0.595925\pi$
$683$	−15.5141	−0.593630	−0.296815	+	0.954935i	$0.595925\pi$
$684$	3.76091	0.143802
$685$	25.7671	0.984511
$686$	5.50372	0.210133
$687$	−11.1498	−0.425391
$688$	1.00000	0.0381246
$689$	−0.780724	−0.0297432
$690$	9.67093	0.368166
$691$	−16.4315	−0.625085	−0.312543	−	0.949904i	$-0.601181\pi$
$691$	−16.4315	−0.625085	−0.312543	+	0.949904i	$0.601181\pi$
$692$	0.654372	0.0248755
$693$	−0.630819	−0.0239628
$694$	5.40273	0.205085
$695$	−15.9088	−0.603456
$696$	11.7479	0.445304
$697$	22.4324	0.849686
$698$	−21.1799	−0.801669
$699$	−25.1600	−0.951639
$700$	−3.72717	−0.140874
$701$	−30.8633	−1.16569	−0.582846	−	0.812583i	$-0.698061\pi$
$701$	−30.8633	−1.16569	−0.582846	+	0.812583i	$0.698061\pi$
$702$	30.7858	1.16193
$703$	−23.0405	−0.868991
$704$	−1.00000	−0.0376889
$705$	21.5073	0.810011
$706$	25.4426	0.957544
$707$	5.40061	0.203111
$708$	−9.74441	−0.366218
$709$	34.0059	1.27712	0.638560	−	0.769572i	$-0.279531\pi$
$709$	34.0059	1.27712	0.638560	+	0.769572i	$0.279531\pi$
$710$	10.9373	0.410468
$711$	19.3752	0.726628
$712$	−4.31993	−0.161896
$713$	−10.7627	−0.403065
$714$	2.36704	0.0885843
$715$	−21.4047	−0.800489
$716$	−21.1526	−0.790509
$717$	−0.0557280	−0.00208120
$718$	−35.4982	−1.32478
$719$	−12.6883	−0.473195	−0.236598	−	0.971608i	$-0.576032\pi$
$719$	−12.6883	−0.473195	−0.236598	+	0.971608i	$0.576032\pi$
$720$	6.01493	0.224163
$721$	0.818951	0.0304993
$722$	−13.3805	−0.497970
$723$	25.9100	0.963603
$724$	−10.1540	−0.377369
$725$	92.6262	3.44005
$726$	1.18890	0.0441243
$727$	−51.1024	−1.89528	−0.947642	−	0.319334i	$-0.896541\pi$
$727$	−51.1024	−1.89528	−0.947642	+	0.319334i	$0.896541\pi$
$728$	2.24483	0.0831988
$729$	22.1832	0.821599
$730$	−3.55340	−0.131517
$731$	−5.00725	−0.185200
$732$	−4.10123	−0.151586
$733$	−29.2191	−1.07923	−0.539616	−	0.841911i	$-0.681430\pi$
$733$	−29.2191	−1.07923	−0.539616	+	0.841911i	$0.681430\pi$
$734$	19.7248	0.728056
$735$	30.8396	1.13754
$736$	−2.14554	−0.0790855
$737$	1.05199	0.0387504
$738$	7.10754	0.261632
$739$	28.1931	1.03710	0.518549	−	0.855048i	$-0.326472\pi$
$739$	28.1931	1.03710	0.518549	+	0.855048i	$0.326472\pi$
$740$	−36.8494	−1.35461
$741$	15.9117	0.584531
$742$	−0.0549840	−0.00201853
$743$	2.28694	0.0838996	0.0419498	−	0.999120i	$-0.486643\pi$
$743$	2.28694	0.0838996	0.0419498	+	0.999120i	$0.486643\pi$
$744$	5.96389	0.218647
$745$	18.3296	0.671543
$746$	−32.3611	−1.18482
$747$	−8.38069	−0.306633
$748$	5.00725	0.183083
$749$	4.48754	0.163971
$750$	−19.7150	−0.719892
$751$	44.1152	1.60979	0.804893	−	0.593420i	$-0.202223\pi$
$751$	44.1152	1.60979	0.804893	+	0.593420i	$0.202223\pi$
$752$	−4.77148	−0.173998
$753$	−18.9847	−0.691840
$754$	−55.7875	−2.03166
$755$	−69.7758	−2.53940
$756$	2.16815	0.0788548
$757$	−5.77596	−0.209931	−0.104965	−	0.994476i	$-0.533473\pi$
$757$	−5.77596	−0.209931	−0.104965	+	0.994476i	$0.533473\pi$
$758$	−22.6156	−0.821436
$759$	2.55083	0.0925893
$760$	8.98744	0.326009
$761$	44.2879	1.60544	0.802718	−	0.596358i	$-0.203386\pi$
$761$	44.2879	1.60544	0.802718	+	0.596358i	$0.203386\pi$
$762$	24.5588	0.889672
$763$	1.72920	0.0626011
$764$	−9.02312	−0.326445
$765$	−30.1183	−1.08893
$766$	10.7597	0.388762
$767$	46.2734	1.67084
$768$	1.18890	0.0429008
$769$	8.74005	0.315174	0.157587	−	0.987505i	$-0.449629\pi$
$769$	8.74005	0.315174	0.157587	+	0.987505i	$0.449629\pi$
$770$	−1.50747	−0.0543253
$771$	−8.56576	−0.308488
$772$	−15.0630	−0.542128
$773$	30.6187	1.10128	0.550639	−	0.834744i	$-0.314384\pi$
$773$	30.6187	1.10128	0.550639	+	0.834744i	$0.314384\pi$
$774$	−1.58651	−0.0570261
$775$	47.0221	1.68908
$776$	10.6654	0.382864
$777$	−4.59462	−0.164831
$778$	3.29150	0.118006
$779$	10.6200	0.380501
$780$	25.4480	0.911186
$781$	2.88484	0.103228
$782$	10.7432	0.384178
$783$	−53.8820	−1.92559
$784$	−6.84190	−0.244354
$785$	−43.6556	−1.55814
$786$	−5.78872	−0.206477
$787$	−11.8201	−0.421340	−0.210670	−	0.977557i	$-0.567564\pi$
$787$	−11.8201	−0.421340	−0.210670	+	0.977557i	$0.567564\pi$
$788$	−13.5231	−0.481742
$789$	3.82397	0.136137
$790$	46.3009	1.64731
$791$	−5.08544	−0.180817
$792$	1.58651	0.0563743
$793$	19.4756	0.691598
$794$	−30.1574	−1.07025
$795$	−0.623316	−0.0221067
$796$	6.07597	0.215357
$797$	50.5710	1.79132	0.895658	−	0.444743i	$-0.146705\pi$
$797$	50.5710	1.79132	0.895658	+	0.444743i	$0.146705\pi$
$798$	1.12061	0.0396693
$799$	23.8920	0.845238
$800$	9.37386	0.331416
$801$	6.85364	0.242161
$802$	11.1836	0.394906
$803$	−0.937254	−0.0330750
$804$	−1.25071	−0.0441090
$805$	−3.23432	−0.113995
$806$	−28.3208	−0.997557
$807$	31.5418	1.11032
$808$	−13.5826	−0.477833
$809$	−7.19047	−0.252803	−0.126402	−	0.991979i	$-0.540343\pi$
$809$	−7.19047	−0.252803	−0.126402	+	0.991979i	$0.540343\pi$
$810$	6.53402	0.229582
$811$	42.1477	1.48001	0.740003	−	0.672603i	$-0.234824\pi$
$811$	42.1477	1.48001	0.740003	+	0.672603i	$0.234824\pi$
$812$	−3.92895	−0.137879
$813$	12.4405	0.436309
$814$	−9.71949	−0.340668
$815$	73.3910	2.57077
$816$	−5.95313	−0.208401
$817$	−2.37055	−0.0829351
$818$	−10.4084	−0.363920
$819$	−3.56145	−0.124447
$820$	16.9849	0.593137
$821$	−3.96326	−0.138319	−0.0691594	−	0.997606i	$-0.522032\pi$
$821$	−3.96326	−0.138319	−0.0691594	+	0.997606i	$0.522032\pi$
$822$	−8.08025	−0.281831
$823$	−5.67290	−0.197745	−0.0988725	−	0.995100i	$-0.531524\pi$
$823$	−5.67290	−0.197745	−0.0988725	+	0.995100i	$0.531524\pi$
$824$	−2.05967	−0.0717519
$825$	−11.1446	−0.388005
$826$	3.25890	0.113392
$827$	38.0942	1.32467	0.662333	−	0.749210i	$-0.269567\pi$
$827$	38.0942	1.32467	0.662333	+	0.749210i	$0.269567\pi$
$828$	3.40392	0.118295
$829$	−53.5531	−1.85998	−0.929988	−	0.367589i	$-0.880183\pi$
$829$	−53.5531	−1.85998	−0.929988	+	0.367589i	$0.880183\pi$
$830$	−20.0273	−0.695158
$831$	17.6173	0.611138
$832$	−5.64575	−0.195731
$833$	34.2591	1.18701
$834$	4.98881	0.172748
$835$	−66.0612	−2.28614
$836$	2.37055	0.0819872
$837$	−27.3535	−0.945474
$838$	−32.3708	−1.11823
$839$	−51.8325	−1.78946	−0.894728	−	0.446612i	$-0.852630\pi$
$839$	−51.8325	−1.78946	−0.894728	+	0.446612i	$0.852630\pi$
$840$	1.79223	0.0618377
$841$	68.6407	2.36692
$842$	−2.82346	−0.0973029
$843$	4.12658	0.142127
$844$	−0.335807	−0.0115590
$845$	−71.5587	−2.46169
$846$	7.57002	0.260263
$847$	−0.397613	−0.0136622
$848$	0.138285	0.00474873
$849$	−36.5227	−1.25346
$850$	−46.9373	−1.60994
$851$	−20.8535	−0.714850
$852$	−3.42979	−0.117503
$853$	9.32942	0.319433	0.159717	−	0.987163i	$-0.448942\pi$
$853$	9.32942	0.319433	0.159717	+	0.987163i	$0.448942\pi$
$854$	1.37161	0.0469354
$855$	−14.2587	−0.487637
$856$	−11.2862	−0.385754
$857$	39.6856	1.35563	0.677817	−	0.735230i	$-0.262926\pi$
$857$	39.6856	1.35563	0.677817	+	0.735230i	$0.262926\pi$
$858$	6.71224	0.229152
$859$	−33.7761	−1.15242	−0.576212	−	0.817300i	$-0.695470\pi$
$859$	−33.7761	−1.15242	−0.576212	+	0.817300i	$0.695470\pi$
$860$	−3.79129	−0.129282
$861$	2.11779	0.0721739
$862$	−32.0416	−1.09134
$863$	−13.0719	−0.444974	−0.222487	−	0.974936i	$-0.571417\pi$
$863$	−13.0719	−0.444974	−0.222487	+	0.974936i	$0.571417\pi$
$864$	−5.45291	−0.185512
$865$	−2.48091	−0.0843536
$866$	−14.0998	−0.479132
$867$	9.59748	0.325948
$868$	−1.99455	−0.0676994
$869$	12.2125	0.414279
$870$	−44.5398	−1.51004
$871$	5.93925	0.201244
$872$	−4.34894	−0.147274
$873$	−16.9208	−0.572681
$874$	5.08610	0.172040
$875$	6.59345	0.222899
$876$	1.11430	0.0376488
$877$	−19.5419	−0.659884	−0.329942	−	0.944001i	$-0.607029\pi$
$877$	−19.5419	−0.659884	−0.329942	+	0.944001i	$0.607029\pi$
$878$	−0.563390	−0.0190135
$879$	−29.2332	−0.986013
$880$	3.79129	0.127804
$881$	−15.9102	−0.536028	−0.268014	−	0.963415i	$-0.586367\pi$
$881$	−15.9102	−0.536028	−0.268014	+	0.963415i	$0.586367\pi$
$882$	10.8548	0.365499
$883$	56.3156	1.89517	0.947586	−	0.319501i	$-0.103515\pi$
$883$	56.3156	1.89517	0.947586	+	0.319501i	$0.103515\pi$
$884$	28.2697	0.950813
$885$	36.9439	1.24185
$886$	34.7331	1.16688
$887$	−0.196009	−0.00658133	−0.00329067	−	0.999995i	$-0.501047\pi$
$887$	−0.196009	−0.00658133	−0.00329067	+	0.999995i	$0.501047\pi$
$888$	11.5555	0.387778
$889$	−8.21339	−0.275468
$890$	16.3781	0.548996
$891$	1.72343	0.0577371
$892$	4.35956	0.145969
$893$	11.3110	0.378509
$894$	−5.74792	−0.192239
$895$	80.1956	2.68064
$896$	−0.397613	−0.0132833
$897$	14.4014	0.480847
$898$	−5.95375	−0.198679
$899$	49.5677	1.65318
$900$	−14.8718	−0.495726
$901$	−0.692429	−0.0230681
$902$	4.47997	0.149167
$903$	−0.472723	−0.0157312
$904$	12.7899	0.425386
$905$	38.4966	1.27967
$906$	21.8808	0.726942
$907$	−35.7450	−1.18689	−0.593447	−	0.804873i	$-0.702233\pi$
$907$	−35.7450	−1.18689	−0.593447	+	0.804873i	$0.702233\pi$
$908$	−21.2670	−0.705770
$909$	21.5490	0.714734
$910$	−8.51078	−0.282130
$911$	30.8106	1.02080	0.510400	−	0.859937i	$-0.329497\pi$
$911$	30.8106	1.02080	0.510400	+	0.859937i	$0.329497\pi$
$912$	−2.81835	−0.0933249
$913$	−5.28245	−0.174824
$914$	−22.5830	−0.746979
$915$	15.5490	0.514032
$916$	−9.37823	−0.309865
$917$	1.93597	0.0639312
$918$	27.3041	0.901170
$919$	28.7673	0.948947	0.474474	−	0.880270i	$-0.342638\pi$
$919$	28.7673	0.948947	0.474474	+	0.880270i	$0.342638\pi$
$920$	8.13435	0.268181
$921$	32.3571	1.06620
$922$	−27.1057	−0.892679
$923$	16.2871	0.536096
$924$	0.472723	0.0155514
$925$	91.1092	2.99565
$926$	40.9266	1.34493
$927$	3.26769	0.107325
$928$	9.88133	0.324371
$929$	−49.8333	−1.63498	−0.817489	−	0.575944i	$-0.804635\pi$
$929$	−49.8333	−1.63498	−0.817489	+	0.575944i	$0.804635\pi$
$930$	−22.6108	−0.741438
$931$	16.2191	0.531559
$932$	−21.1624	−0.693198
$933$	25.2449	0.826480
$934$	31.2686	1.02314
$935$	−18.9839	−0.620841
$936$	8.95707	0.292771
$937$	40.7911	1.33259	0.666293	−	0.745690i	$-0.267880\pi$
$937$	40.7911	1.33259	0.666293	+	0.745690i	$0.267880\pi$
$938$	0.418283	0.0136574
$939$	23.8904	0.779634
$940$	18.0900	0.590032
$941$	−2.45750	−0.0801124	−0.0400562	−	0.999197i	$-0.512754\pi$
$941$	−2.45750	−0.0801124	−0.0400562	+	0.999197i	$0.512754\pi$
$942$	13.6899	0.446040
$943$	9.61195	0.313008
$944$	−8.19615	−0.266762
$945$	−8.22008	−0.267399
$946$	−1.00000	−0.0325128
$947$	−1.65769	−0.0538675	−0.0269338	−	0.999637i	$-0.508574\pi$
$947$	−1.65769	−0.0538675	−0.0269338	+	0.999637i	$0.508574\pi$
$948$	−14.5194	−0.471568
$949$	−5.29150	−0.171769
$950$	−22.2212	−0.720952
$951$	17.4692	0.566479
$952$	1.99095	0.0645270
$953$	22.5500	0.730466	0.365233	−	0.930916i	$-0.380989\pi$
$953$	22.5500	0.730466	0.365233	+	0.930916i	$0.380989\pi$
$954$	−0.219391	−0.00710306
$955$	34.2093	1.10699
$956$	−0.0468735	−0.00151600
$957$	−11.7479	−0.379756
$958$	17.9056	0.578505
$959$	2.70234	0.0872631
$960$	−4.50747	−0.145478
$961$	−5.83671	−0.188281
$962$	−54.8738	−1.76920
$963$	17.9057	0.577003
$964$	21.7932	0.701913
$965$	57.1081	1.83837
$966$	1.01424	0.0326328
$967$	38.9363	1.25211	0.626054	−	0.779780i	$-0.284669\pi$
$967$	38.9363	1.25211	0.626054	+	0.779780i	$0.284669\pi$
$968$	1.00000	0.0321412
$969$	14.1122	0.453349
$970$	−40.4355	−1.29830
$971$	32.4275	1.04065	0.520324	−	0.853969i	$-0.325811\pi$
$971$	32.4275	1.04065	0.520324	+	0.853969i	$0.325811\pi$
$972$	14.3097	0.458985
$973$	−1.66845	−0.0534879
$974$	36.3437	1.16453
$975$	−62.9196	−2.01504
$976$	−3.44960	−0.110419
$977$	34.1514	1.09260	0.546300	−	0.837589i	$-0.316036\pi$
$977$	34.1514	1.09260	0.546300	+	0.837589i	$0.316036\pi$
$978$	−23.0145	−0.735923
$979$	4.31993	0.138066
$980$	25.9396	0.828611
$981$	6.89966	0.220289
$982$	−22.4494	−0.716389
$983$	−36.4614	−1.16294	−0.581469	−	0.813569i	$-0.697522\pi$
$983$	−36.4614	−1.16294	−0.581469	+	0.813569i	$0.697522\pi$
$984$	−5.32625	−0.169795
$985$	51.2701	1.63360
$986$	−49.4783	−1.57571
$987$	2.25559	0.0717961
$988$	13.3835	0.425787
$989$	−2.14554	−0.0682241
$990$	−6.01493	−0.191167
$991$	20.1562	0.640283	0.320142	−	0.947370i	$-0.396269\pi$
$991$	20.1562	0.640283	0.320142	+	0.947370i	$0.396269\pi$
$992$	5.01630	0.159268
$993$	−3.67867	−0.116739
$994$	1.14705	0.0363822
$995$	−23.0357	−0.730282
$996$	6.28031	0.198999
$997$	8.40849	0.266300	0.133150	−	0.991096i	$-0.457491\pi$
$997$	8.40849	0.266300	0.133150	+	0.991096i	$0.457491\pi$
$998$	32.8908	1.04114
$999$	−52.9995	−1.67683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.g.1.4	✓	4
3.2	odd	2		8514.2.a.bd.1.3		4
4.3	odd	2		7568.2.a.z.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.g.1.4	✓	4	1.1	even	1	trivial
7568.2.a.z.1.1		4	4.3	odd	2
8514.2.a.bd.1.3		4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.18890 q^{3} +1.00000 q^{4} -3.79129 q^{5} +1.18890 q^{6} -0.397613 q^{7} +1.00000 q^{8} -1.58651 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.18890 q^{3} +1.00000 q^{4} -3.79129 q^{5} +1.18890 q^{6} -0.397613 q^{7} +1.00000 q^{8} -1.58651 q^{9} -3.79129 q^{10} -1.00000 q^{11} +1.18890 q^{12} -5.64575 q^{13} -0.397613 q^{14} -4.50747 q^{15} +1.00000 q^{16} -5.00725 q^{17} -1.58651 q^{18} -2.37055 q^{19} -3.79129 q^{20} -0.472723 q^{21} -1.00000 q^{22} -2.14554 q^{23} +1.18890 q^{24} +9.37386 q^{25} -5.64575 q^{26} -5.45291 q^{27} -0.397613 q^{28} +9.88133 q^{29} -4.50747 q^{30} +5.01630 q^{31} +1.00000 q^{32} -1.18890 q^{33} -5.00725 q^{34} +1.50747 q^{35} -1.58651 q^{36} +9.71949 q^{37} -2.37055 q^{38} -6.71224 q^{39} -3.79129 q^{40} -4.47997 q^{41} -0.472723 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.01493 q^{45} -2.14554 q^{46} -4.77148 q^{47} +1.18890 q^{48} -6.84190 q^{49} +9.37386 q^{50} -5.95313 q^{51} -5.64575 q^{52} +0.138285 q^{53} -5.45291 q^{54} +3.79129 q^{55} -0.397613 q^{56} -2.81835 q^{57} +9.88133 q^{58} -8.19615 q^{59} -4.50747 q^{60} -3.44960 q^{61} +5.01630 q^{62} +0.630819 q^{63} +1.00000 q^{64} +21.4047 q^{65} -1.18890 q^{66} -1.05199 q^{67} -5.00725 q^{68} -2.55083 q^{69} +1.50747 q^{70} -2.88484 q^{71} -1.58651 q^{72} +0.937254 q^{73} +9.71949 q^{74} +11.1446 q^{75} -2.37055 q^{76} +0.397613 q^{77} -6.71224 q^{78} -12.2125 q^{79} -3.79129 q^{80} -1.72343 q^{81} -4.47997 q^{82} +5.28245 q^{83} -0.472723 q^{84} +18.9839 q^{85} +1.00000 q^{86} +11.7479 q^{87} -1.00000 q^{88} -4.31993 q^{89} +6.01493 q^{90} +2.24483 q^{91} -2.14554 q^{92} +5.96389 q^{93} -4.77148 q^{94} +8.98744 q^{95} +1.18890 q^{96} +10.6654 q^{97} -6.84190 q^{98} +1.58651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} - 2 q^{14} + 6 q^{15} + 4 q^{16} - 8 q^{17} + 2 q^{18} - 4 q^{19} - 6 q^{20} - 8 q^{21} - 4 q^{22} - 10 q^{23} - 4 q^{24} + 10 q^{25} - 12 q^{26} - 10 q^{27} - 2 q^{28} - 12 q^{29} + 6 q^{30} + 4 q^{31} + 4 q^{32} + 4 q^{33} - 8 q^{34} - 18 q^{35} + 2 q^{36} + 2 q^{37} - 4 q^{38} - 2 q^{39} - 6 q^{40} - 12 q^{41} - 8 q^{42} + 4 q^{43} - 4 q^{44} - 24 q^{45} - 10 q^{46} + 8 q^{47} - 4 q^{48} + 4 q^{49} + 10 q^{50} - 12 q^{52} + 14 q^{53} - 10 q^{54} + 6 q^{55} - 2 q^{56} - 8 q^{57} - 12 q^{58} - 12 q^{59} + 6 q^{60} - 24 q^{61} + 4 q^{62} + 40 q^{63} + 4 q^{64} + 18 q^{65} + 4 q^{66} - 14 q^{67} - 8 q^{68} + 24 q^{69} - 18 q^{70} + 6 q^{71} + 2 q^{72} - 28 q^{73} + 2 q^{74} - 10 q^{75} - 4 q^{76} + 2 q^{77} - 2 q^{78} - 12 q^{79} - 6 q^{80} + 20 q^{81} - 12 q^{82} + 4 q^{83} - 8 q^{84} + 12 q^{85} + 4 q^{86} + 48 q^{87} - 4 q^{88} - 34 q^{89} - 24 q^{90} + 20 q^{91} - 10 q^{92} + 22 q^{93} + 8 q^{94} + 6 q^{95} - 4 q^{96} - 6 q^{97} + 4 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 - 2 * q^14 + 6 * q^15 + 4 * q^16 - 8 * q^17 + 2 * q^18 - 4 * q^19 - 6 * q^20 - 8 * q^21 - 4 * q^22 - 10 * q^23 - 4 * q^24 + 10 * q^25 - 12 * q^26 - 10 * q^27 - 2 * q^28 - 12 * q^29 + 6 * q^30 + 4 * q^31 + 4 * q^32 + 4 * q^33 - 8 * q^34 - 18 * q^35 + 2 * q^36 + 2 * q^37 - 4 * q^38 - 2 * q^39 - 6 * q^40 - 12 * q^41 - 8 * q^42 + 4 * q^43 - 4 * q^44 - 24 * q^45 - 10 * q^46 + 8 * q^47 - 4 * q^48 + 4 * q^49 + 10 * q^50 - 12 * q^52 + 14 * q^53 - 10 * q^54 + 6 * q^55 - 2 * q^56 - 8 * q^57 - 12 * q^58 - 12 * q^59 + 6 * q^60 - 24 * q^61 + 4 * q^62 + 40 * q^63 + 4 * q^64 + 18 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 24 * q^69 - 18 * q^70 + 6 * q^71 + 2 * q^72 - 28 * q^73 + 2 * q^74 - 10 * q^75 - 4 * q^76 + 2 * q^77 - 2 * q^78 - 12 * q^79 - 6 * q^80 + 20 * q^81 - 12 * q^82 + 4 * q^83 - 8 * q^84 + 12 * q^85 + 4 * q^86 + 48 * q^87 - 4 * q^88 - 34 * q^89 - 24 * q^90 + 20 * q^91 - 10 * q^92 + 22 * q^93 + 8 * q^94 + 6 * q^95 - 4 * q^96 - 6 * q^97 + 4 * q^98 - 2 * q^99

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