LMFDB - Embedded newform 966.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("966.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
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			1.1
Root			$3.37228$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.37228 q^{10} +4.00000 q^{11} -1.00000 q^{12} -4.37228 q^{13} -1.00000 q^{14} +4.37228 q^{15} +1.00000 q^{16} +6.74456 q^{17} +1.00000 q^{18} +4.00000 q^{19} -4.37228 q^{20} +1.00000 q^{21} +4.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +14.1168 q^{25} -4.37228 q^{26} -1.00000 q^{27} -1.00000 q^{28} +3.62772 q^{29} +4.37228 q^{30} -4.74456 q^{31} +1.00000 q^{32} -4.00000 q^{33} +6.74456 q^{34} +4.37228 q^{35} +1.00000 q^{36} +8.37228 q^{37} +4.00000 q^{38} +4.37228 q^{39} -4.37228 q^{40} +9.11684 q^{41} +1.00000 q^{42} -11.1168 q^{43} +4.00000 q^{44} -4.37228 q^{45} -1.00000 q^{46} +10.3723 q^{47} -1.00000 q^{48} +1.00000 q^{49} +14.1168 q^{50} -6.74456 q^{51} -4.37228 q^{52} -6.74456 q^{53} -1.00000 q^{54} -17.4891 q^{55} -1.00000 q^{56} -4.00000 q^{57} +3.62772 q^{58} +8.74456 q^{59} +4.37228 q^{60} -2.00000 q^{61} -4.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} +19.1168 q^{65} -4.00000 q^{66} -4.00000 q^{67} +6.74456 q^{68} +1.00000 q^{69} +4.37228 q^{70} +3.25544 q^{71} +1.00000 q^{72} -1.25544 q^{73} +8.37228 q^{74} -14.1168 q^{75} +4.00000 q^{76} -4.00000 q^{77} +4.37228 q^{78} +9.48913 q^{79} -4.37228 q^{80} +1.00000 q^{81} +9.11684 q^{82} +4.00000 q^{83} +1.00000 q^{84} -29.4891 q^{85} -11.1168 q^{86} -3.62772 q^{87} +4.00000 q^{88} -15.4891 q^{89} -4.37228 q^{90} +4.37228 q^{91} -1.00000 q^{92} +4.74456 q^{93} +10.3723 q^{94} -17.4891 q^{95} -1.00000 q^{96} -3.62772 q^{97} +1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + 8 q^{11} - 2 q^{12} - 3 q^{13} - 2 q^{14} + 3 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 8 q^{19} - 3 q^{20} + 2 q^{21} + 8 q^{22} - 2 q^{23} - 2 q^{24} + 11 q^{25} - 3 q^{26} - 2 q^{27} - 2 q^{28} + 13 q^{29} + 3 q^{30} + 2 q^{31} + 2 q^{32} - 8 q^{33} + 2 q^{34} + 3 q^{35} + 2 q^{36} + 11 q^{37} + 8 q^{38} + 3 q^{39} - 3 q^{40} + q^{41} + 2 q^{42} - 5 q^{43} + 8 q^{44} - 3 q^{45} - 2 q^{46} + 15 q^{47} - 2 q^{48} + 2 q^{49} + 11 q^{50} - 2 q^{51} - 3 q^{52} - 2 q^{53} - 2 q^{54} - 12 q^{55} - 2 q^{56} - 8 q^{57} + 13 q^{58} + 6 q^{59} + 3 q^{60} - 4 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 21 q^{65} - 8 q^{66} - 8 q^{67} + 2 q^{68} + 2 q^{69} + 3 q^{70} + 18 q^{71} + 2 q^{72} - 14 q^{73} + 11 q^{74} - 11 q^{75} + 8 q^{76} - 8 q^{77} + 3 q^{78} - 4 q^{79} - 3 q^{80} + 2 q^{81} + q^{82} + 8 q^{83} + 2 q^{84} - 36 q^{85} - 5 q^{86} - 13 q^{87} + 8 q^{88} - 8 q^{89} - 3 q^{90} + 3 q^{91} - 2 q^{92} - 2 q^{93} + 15 q^{94} - 12 q^{95} - 2 q^{96} - 13 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + 8 * q^11 - 2 * q^12 - 3 * q^13 - 2 * q^14 + 3 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 8 * q^19 - 3 * q^20 + 2 * q^21 + 8 * q^22 - 2 * q^23 - 2 * q^24 + 11 * q^25 - 3 * q^26 - 2 * q^27 - 2 * q^28 + 13 * q^29 + 3 * q^30 + 2 * q^31 + 2 * q^32 - 8 * q^33 + 2 * q^34 + 3 * q^35 + 2 * q^36 + 11 * q^37 + 8 * q^38 + 3 * q^39 - 3 * q^40 + q^41 + 2 * q^42 - 5 * q^43 + 8 * q^44 - 3 * q^45 - 2 * q^46 + 15 * q^47 - 2 * q^48 + 2 * q^49 + 11 * q^50 - 2 * q^51 - 3 * q^52 - 2 * q^53 - 2 * q^54 - 12 * q^55 - 2 * q^56 - 8 * q^57 + 13 * q^58 + 6 * q^59 + 3 * q^60 - 4 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 21 * q^65 - 8 * q^66 - 8 * q^67 + 2 * q^68 + 2 * q^69 + 3 * q^70 + 18 * q^71 + 2 * q^72 - 14 * q^73 + 11 * q^74 - 11 * q^75 + 8 * q^76 - 8 * q^77 + 3 * q^78 - 4 * q^79 - 3 * q^80 + 2 * q^81 + q^82 + 8 * q^83 + 2 * q^84 - 36 * q^85 - 5 * q^86 - 13 * q^87 + 8 * q^88 - 8 * q^89 - 3 * q^90 + 3 * q^91 - 2 * q^92 - 2 * q^93 + 15 * q^94 - 12 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 + 8 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−4.37228	−1.95534	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−4.37228	−1.95534	−0.977672	+	0.210138i	$0.932609\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.37228	−1.38264
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	−1.00000	−0.288675
$13$	−4.37228	−1.21265	−0.606326	−	0.795216i	$-0.707357\pi$
$13$	−4.37228	−1.21265	−0.606326	+	0.795216i	$0.707357\pi$
$14$	−1.00000	−0.267261
$15$	4.37228	1.12892
$16$	1.00000	0.250000
$17$	6.74456	1.63580	0.817898	−	0.575363i	$-0.195139\pi$
$17$	6.74456	1.63580	0.817898	+	0.575363i	$0.195139\pi$
$18$	1.00000	0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−4.37228	−0.977672
$21$	1.00000	0.218218
$22$	4.00000	0.852803
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	14.1168	2.82337
$26$	−4.37228	−0.857475
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	3.62772	0.673650	0.336825	−	0.941567i	$-0.390647\pi$
$29$	3.62772	0.673650	0.336825	+	0.941567i	$0.390647\pi$
$30$	4.37228	0.798266
$31$	−4.74456	−0.852149	−0.426074	−	0.904688i	$-0.640104\pi$
$31$	−4.74456	−0.852149	−0.426074	+	0.904688i	$0.640104\pi$
$32$	1.00000	0.176777
$33$	−4.00000	−0.696311
$34$	6.74456	1.15668
$35$	4.37228	0.739050
$36$	1.00000	0.166667
$37$	8.37228	1.37639	0.688197	−	0.725524i	$-0.258402\pi$
$37$	8.37228	1.37639	0.688197	+	0.725524i	$0.258402\pi$
$38$	4.00000	0.648886
$39$	4.37228	0.700125
$40$	−4.37228	−0.691318
$41$	9.11684	1.42381	0.711906	−	0.702275i	$-0.247832\pi$
$41$	9.11684	1.42381	0.711906	+	0.702275i	$0.247832\pi$
$42$	1.00000	0.154303
$43$	−11.1168	−1.69530	−0.847651	−	0.530554i	$-0.821984\pi$
$43$	−11.1168	−1.69530	−0.847651	+	0.530554i	$0.821984\pi$
$44$	4.00000	0.603023
$45$	−4.37228	−0.651781
$46$	−1.00000	−0.147442
$47$	10.3723	1.51295	0.756476	−	0.654021i	$-0.226919\pi$
$47$	10.3723	1.51295	0.756476	+	0.654021i	$0.226919\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	14.1168	1.99642
$51$	−6.74456	−0.944428
$52$	−4.37228	−0.606326
$53$	−6.74456	−0.926437	−0.463218	−	0.886244i	$-0.653305\pi$
$53$	−6.74456	−0.926437	−0.463218	+	0.886244i	$0.653305\pi$
$54$	−1.00000	−0.136083
$55$	−17.4891	−2.35823
$56$	−1.00000	−0.133631
$57$	−4.00000	−0.529813
$58$	3.62772	0.476343
$59$	8.74456	1.13845	0.569223	−	0.822183i	$-0.307244\pi$
$59$	8.74456	1.13845	0.569223	+	0.822183i	$0.307244\pi$
$60$	4.37228	0.564459
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−4.74456	−0.602560
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	19.1168	2.37115
$66$	−4.00000	−0.492366
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	6.74456	0.817898
$69$	1.00000	0.120386
$70$	4.37228	0.522588
$71$	3.25544	0.386349	0.193175	−	0.981164i	$-0.438122\pi$
$71$	3.25544	0.386349	0.193175	+	0.981164i	$0.438122\pi$
$72$	1.00000	0.117851
$73$	−1.25544	−0.146938	−0.0734689	−	0.997298i	$-0.523407\pi$
$73$	−1.25544	−0.146938	−0.0734689	+	0.997298i	$0.523407\pi$
$74$	8.37228	0.973258
$75$	−14.1168	−1.63007
$76$	4.00000	0.458831
$77$	−4.00000	−0.455842
$78$	4.37228	0.495063
$79$	9.48913	1.06761	0.533805	−	0.845608i	$-0.320762\pi$
$79$	9.48913	1.06761	0.533805	+	0.845608i	$0.320762\pi$
$80$	−4.37228	−0.488836
$81$	1.00000	0.111111
$82$	9.11684	1.00679
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	1.00000	0.109109
$85$	−29.4891	−3.19854
$86$	−11.1168	−1.19876
$87$	−3.62772	−0.388932
$88$	4.00000	0.426401
$89$	−15.4891	−1.64184	−0.820922	−	0.571040i	$-0.806540\pi$
$89$	−15.4891	−1.64184	−0.820922	+	0.571040i	$0.806540\pi$
$90$	−4.37228	−0.460879
$91$	4.37228	0.458340
$92$	−1.00000	−0.104257
$93$	4.74456	0.491988
$94$	10.3723	1.06982
$95$	−17.4891	−1.79435
$96$	−1.00000	−0.102062
$97$	−3.62772	−0.368339	−0.184170	−	0.982894i	$-0.558960\pi$
$97$	−3.62772	−0.368339	−0.184170	+	0.982894i	$0.558960\pi$
$98$	1.00000	0.101015
$99$	4.00000	0.402015
$100$	14.1168	1.41168
$101$	7.48913	0.745196	0.372598	−	0.927993i	$-0.378467\pi$
$101$	7.48913	0.745196	0.372598	+	0.927993i	$0.378467\pi$
$102$	−6.74456	−0.667811
$103$	7.11684	0.701243	0.350622	−	0.936517i	$-0.385970\pi$
$103$	7.11684	0.701243	0.350622	+	0.936517i	$0.385970\pi$
$104$	−4.37228	−0.428737
$105$	−4.37228	−0.426691
$106$	−6.74456	−0.655090
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−1.00000	−0.0962250
$109$	−9.11684	−0.873235	−0.436618	−	0.899647i	$-0.643824\pi$
$109$	−9.11684	−0.873235	−0.436618	+	0.899647i	$0.643824\pi$
$110$	−17.4891	−1.66752
$111$	−8.37228	−0.794662
$112$	−1.00000	−0.0944911
$113$	1.11684	0.105064	0.0525319	−	0.998619i	$-0.483271\pi$
$113$	1.11684	0.105064	0.0525319	+	0.998619i	$0.483271\pi$
$114$	−4.00000	−0.374634
$115$	4.37228	0.407717
$116$	3.62772	0.336825
$117$	−4.37228	−0.404218
$118$	8.74456	0.805002
$119$	−6.74456	−0.618273
$120$	4.37228	0.399133
$121$	5.00000	0.454545
$122$	−2.00000	−0.181071
$123$	−9.11684	−0.822038
$124$	−4.74456	−0.426074
$125$	−39.8614	−3.56531
$126$	−1.00000	−0.0890871
$127$	−5.62772	−0.499379	−0.249690	−	0.968326i	$-0.580329\pi$
$127$	−5.62772	−0.499379	−0.249690	+	0.968326i	$0.580329\pi$
$128$	1.00000	0.0883883
$129$	11.1168	0.978784
$130$	19.1168	1.67666
$131$	7.25544	0.633911	0.316955	−	0.948440i	$-0.397339\pi$
$131$	7.25544	0.633911	0.316955	+	0.948440i	$0.397339\pi$
$132$	−4.00000	−0.348155
$133$	−4.00000	−0.346844
$134$	−4.00000	−0.345547
$135$	4.37228	0.376306
$136$	6.74456	0.578341
$137$	9.11684	0.778905	0.389452	−	0.921047i	$-0.372664\pi$
$137$	9.11684	0.778905	0.389452	+	0.921047i	$0.372664\pi$
$138$	1.00000	0.0851257
$139$	14.3723	1.21904	0.609520	−	0.792770i	$-0.291362\pi$
$139$	14.3723	1.21904	0.609520	+	0.792770i	$0.291362\pi$
$140$	4.37228	0.369525
$141$	−10.3723	−0.873504
$142$	3.25544	0.273190
$143$	−17.4891	−1.46251
$144$	1.00000	0.0833333
$145$	−15.8614	−1.31722
$146$	−1.25544	−0.103901
$147$	−1.00000	−0.0824786
$148$	8.37228	0.688197
$149$	−16.2337	−1.32992	−0.664958	−	0.746881i	$-0.731550\pi$
$149$	−16.2337	−1.32992	−0.664958	+	0.746881i	$0.731550\pi$
$150$	−14.1168	−1.15264
$151$	2.37228	0.193054	0.0965268	−	0.995330i	$-0.469227\pi$
$151$	2.37228	0.193054	0.0965268	+	0.995330i	$0.469227\pi$
$152$	4.00000	0.324443
$153$	6.74456	0.545266
$154$	−4.00000	−0.322329
$155$	20.7446	1.66624
$156$	4.37228	0.350063
$157$	−22.7446	−1.81521	−0.907607	−	0.419821i	$-0.862093\pi$
$157$	−22.7446	−1.81521	−0.907607	+	0.419821i	$0.862093\pi$
$158$	9.48913	0.754914
$159$	6.74456	0.534879
$160$	−4.37228	−0.345659
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	9.11684	0.711906
$165$	17.4891	1.36153
$166$	4.00000	0.310460
$167$	17.4891	1.35335	0.676675	−	0.736282i	$-0.263420\pi$
$167$	17.4891	1.35335	0.676675	+	0.736282i	$0.263420\pi$
$168$	1.00000	0.0771517
$169$	6.11684	0.470526
$170$	−29.4891	−2.26171
$171$	4.00000	0.305888
$172$	−11.1168	−0.847651
$173$	15.4891	1.17762	0.588808	−	0.808273i	$-0.299597\pi$
$173$	15.4891	1.17762	0.588808	+	0.808273i	$0.299597\pi$
$174$	−3.62772	−0.275017
$175$	−14.1168	−1.06713
$176$	4.00000	0.301511
$177$	−8.74456	−0.657282
$178$	−15.4891	−1.16096
$179$	7.86141	0.587589	0.293795	−	0.955869i	$-0.405082\pi$
$179$	7.86141	0.587589	0.293795	+	0.955869i	$0.405082\pi$
$180$	−4.37228	−0.325891
$181$	24.9783	1.85662	0.928309	−	0.371809i	$-0.121262\pi$
$181$	24.9783	1.85662	0.928309	+	0.371809i	$0.121262\pi$
$182$	4.37228	0.324095
$183$	2.00000	0.147844
$184$	−1.00000	−0.0737210
$185$	−36.6060	−2.69132
$186$	4.74456	0.347888
$187$	26.9783	1.97285
$188$	10.3723	0.756476
$189$	1.00000	0.0727393
$190$	−17.4891	−1.26879
$191$	25.4891	1.84433	0.922164	−	0.386799i	$-0.126419\pi$
$191$	25.4891	1.84433	0.922164	+	0.386799i	$0.126419\pi$
$192$	−1.00000	−0.0721688
$193$	17.1168	1.23210	0.616049	−	0.787708i	$-0.288732\pi$
$193$	17.1168	1.23210	0.616049	+	0.787708i	$0.288732\pi$
$194$	−3.62772	−0.260455
$195$	−19.1168	−1.36899
$196$	1.00000	0.0714286
$197$	−15.6277	−1.11343	−0.556714	−	0.830704i	$-0.687938\pi$
$197$	−15.6277	−1.11343	−0.556714	+	0.830704i	$0.687938\pi$
$198$	4.00000	0.284268
$199$	11.8614	0.840833	0.420416	−	0.907331i	$-0.361884\pi$
$199$	11.8614	0.840833	0.420416	+	0.907331i	$0.361884\pi$
$200$	14.1168	0.998212
$201$	4.00000	0.282138
$202$	7.48913	0.526933
$203$	−3.62772	−0.254616
$204$	−6.74456	−0.472214
$205$	−39.8614	−2.78404
$206$	7.11684	0.495854
$207$	−1.00000	−0.0695048
$208$	−4.37228	−0.303163
$209$	16.0000	1.10674
$210$	−4.37228	−0.301716
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−6.74456	−0.463218
$213$	−3.25544	−0.223059
$214$	4.00000	0.273434
$215$	48.6060	3.31490
$216$	−1.00000	−0.0680414
$217$	4.74456	0.322082
$218$	−9.11684	−0.617471
$219$	1.25544	0.0848346
$220$	−17.4891	−1.17912
$221$	−29.4891	−1.98365
$222$	−8.37228	−0.561911
$223$	−20.7446	−1.38916	−0.694579	−	0.719416i	$-0.744409\pi$
$223$	−20.7446	−1.38916	−0.694579	+	0.719416i	$0.744409\pi$
$224$	−1.00000	−0.0668153
$225$	14.1168	0.941123
$226$	1.11684	0.0742914
$227$	−11.1168	−0.737851	−0.368925	−	0.929459i	$-0.620274\pi$
$227$	−11.1168	−0.737851	−0.368925	+	0.929459i	$0.620274\pi$
$228$	−4.00000	−0.264906
$229$	10.7446	0.710021	0.355010	−	0.934862i	$-0.384477\pi$
$229$	10.7446	0.710021	0.355010	+	0.934862i	$0.384477\pi$
$230$	4.37228	0.288300
$231$	4.00000	0.263181
$232$	3.62772	0.238171
$233$	0.510875	0.0334685	0.0167343	−	0.999860i	$-0.494673\pi$
$233$	0.510875	0.0334685	0.0167343	+	0.999860i	$0.494673\pi$
$234$	−4.37228	−0.285825
$235$	−45.3505	−2.95834
$236$	8.74456	0.569223
$237$	−9.48913	−0.616385
$238$	−6.74456	−0.437185
$239$	−9.48913	−0.613800	−0.306900	−	0.951742i	$-0.599292\pi$
$239$	−9.48913	−0.613800	−0.306900	+	0.951742i	$0.599292\pi$
$240$	4.37228	0.282230
$241$	−8.37228	−0.539306	−0.269653	−	0.962958i	$-0.586909\pi$
$241$	−8.37228	−0.539306	−0.269653	+	0.962958i	$0.586909\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	−2.00000	−0.128037
$245$	−4.37228	−0.279335
$246$	−9.11684	−0.581269
$247$	−17.4891	−1.11281
$248$	−4.74456	−0.301280
$249$	−4.00000	−0.253490
$250$	−39.8614	−2.52106
$251$	−19.1168	−1.20664	−0.603322	−	0.797498i	$-0.706157\pi$
$251$	−19.1168	−1.20664	−0.603322	+	0.797498i	$0.706157\pi$
$252$	−1.00000	−0.0629941
$253$	−4.00000	−0.251478
$254$	−5.62772	−0.353114
$255$	29.4891	1.84668
$256$	1.00000	0.0625000
$257$	−16.9783	−1.05907	−0.529537	−	0.848287i	$-0.677634\pi$
$257$	−16.9783	−1.05907	−0.529537	+	0.848287i	$0.677634\pi$
$258$	11.1168	0.692104
$259$	−8.37228	−0.520228
$260$	19.1168	1.18558
$261$	3.62772	0.224550
$262$	7.25544	0.448242
$263$	−7.11684	−0.438843	−0.219422	−	0.975630i	$-0.570417\pi$
$263$	−7.11684	−0.438843	−0.219422	+	0.975630i	$0.570417\pi$
$264$	−4.00000	−0.246183
$265$	29.4891	1.81150
$266$	−4.00000	−0.245256
$267$	15.4891	0.947919
$268$	−4.00000	−0.244339
$269$	24.9783	1.52295	0.761475	−	0.648194i	$-0.224475\pi$
$269$	24.9783	1.52295	0.761475	+	0.648194i	$0.224475\pi$
$270$	4.37228	0.266089
$271$	18.9783	1.15285	0.576423	−	0.817151i	$-0.304448\pi$
$271$	18.9783	1.15285	0.576423	+	0.817151i	$0.304448\pi$
$272$	6.74456	0.408949
$273$	−4.37228	−0.264623
$274$	9.11684	0.550769
$275$	56.4674	3.40511
$276$	1.00000	0.0601929
$277$	17.2554	1.03678	0.518389	−	0.855145i	$-0.326532\pi$
$277$	17.2554	1.03678	0.518389	+	0.855145i	$0.326532\pi$
$278$	14.3723	0.861992
$279$	−4.74456	−0.284050
$280$	4.37228	0.261294
$281$	−11.6277	−0.693652	−0.346826	−	0.937930i	$-0.612740\pi$
$281$	−11.6277	−0.693652	−0.346826	+	0.937930i	$0.612740\pi$
$282$	−10.3723	−0.617660
$283$	−24.7446	−1.47091	−0.735456	−	0.677573i	$-0.763032\pi$
$283$	−24.7446	−1.47091	−0.735456	+	0.677573i	$0.763032\pi$
$284$	3.25544	0.193175
$285$	17.4891	1.03597
$286$	−17.4891	−1.03415
$287$	−9.11684	−0.538150
$288$	1.00000	0.0589256
$289$	28.4891	1.67583
$290$	−15.8614	−0.931414
$291$	3.62772	0.212661
$292$	−1.25544	−0.0734689
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	−1.00000	−0.0583212
$295$	−38.2337	−2.22605
$296$	8.37228	0.486629
$297$	−4.00000	−0.232104
$298$	−16.2337	−0.940392
$299$	4.37228	0.252856
$300$	−14.1168	−0.815036
$301$	11.1168	0.640764
$302$	2.37228	0.136509
$303$	−7.48913	−0.430239
$304$	4.00000	0.229416
$305$	8.74456	0.500712
$306$	6.74456	0.385561
$307$	1.62772	0.0928988	0.0464494	−	0.998921i	$-0.485209\pi$
$307$	1.62772	0.0928988	0.0464494	+	0.998921i	$0.485209\pi$
$308$	−4.00000	−0.227921
$309$	−7.11684	−0.404863
$310$	20.7446	1.17821
$311$	−17.4891	−0.991717	−0.495859	−	0.868403i	$-0.665147\pi$
$311$	−17.4891	−0.991717	−0.495859	+	0.868403i	$0.665147\pi$
$312$	4.37228	0.247532
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−22.7446	−1.28355
$315$	4.37228	0.246350
$316$	9.48913	0.533805
$317$	−1.11684	−0.0627282	−0.0313641	−	0.999508i	$-0.509985\pi$
$317$	−1.11684	−0.0627282	−0.0313641	+	0.999508i	$0.509985\pi$
$318$	6.74456	0.378216
$319$	14.5109	0.812453
$320$	−4.37228	−0.244418
$321$	−4.00000	−0.223258
$322$	1.00000	0.0557278
$323$	26.9783	1.50111
$324$	1.00000	0.0555556
$325$	−61.7228	−3.42377
$326$	4.00000	0.221540
$327$	9.11684	0.504163
$328$	9.11684	0.503393
$329$	−10.3723	−0.571842
$330$	17.4891	0.962745
$331$	−13.4891	−0.741429	−0.370715	−	0.928747i	$-0.620887\pi$
$331$	−13.4891	−0.741429	−0.370715	+	0.928747i	$0.620887\pi$
$332$	4.00000	0.219529
$333$	8.37228	0.458798
$334$	17.4891	0.956962
$335$	17.4891	0.955533
$336$	1.00000	0.0545545
$337$	−12.2337	−0.666411	−0.333206	−	0.942854i	$-0.608130\pi$
$337$	−12.2337	−0.666411	−0.333206	+	0.942854i	$0.608130\pi$
$338$	6.11684	0.332712
$339$	−1.11684	−0.0606586
$340$	−29.4891	−1.59927
$341$	−18.9783	−1.02773
$342$	4.00000	0.216295
$343$	−1.00000	−0.0539949
$344$	−11.1168	−0.599380
$345$	−4.37228	−0.235396
$346$	15.4891	0.832701
$347$	22.3723	1.20101	0.600503	−	0.799622i	$-0.294967\pi$
$347$	22.3723	1.20101	0.600503	+	0.799622i	$0.294967\pi$
$348$	−3.62772	−0.194466
$349$	12.5109	0.669692	0.334846	−	0.942273i	$-0.391316\pi$
$349$	12.5109	0.669692	0.334846	+	0.942273i	$0.391316\pi$
$350$	−14.1168	−0.754577
$351$	4.37228	0.233375
$352$	4.00000	0.213201
$353$	18.8832	1.00505	0.502524	−	0.864563i	$-0.332405\pi$
$353$	18.8832	1.00505	0.502524	+	0.864563i	$0.332405\pi$
$354$	−8.74456	−0.464768
$355$	−14.2337	−0.755446
$356$	−15.4891	−0.820922
$357$	6.74456	0.356960
$358$	7.86141	0.415488
$359$	13.6277	0.719243	0.359622	−	0.933098i	$-0.382906\pi$
$359$	13.6277	0.719243	0.359622	+	0.933098i	$0.382906\pi$
$360$	−4.37228	−0.230439
$361$	−3.00000	−0.157895
$362$	24.9783	1.31283
$363$	−5.00000	−0.262432
$364$	4.37228	0.229170
$365$	5.48913	0.287314
$366$	2.00000	0.104542
$367$	−5.62772	−0.293765	−0.146882	−	0.989154i	$-0.546924\pi$
$367$	−5.62772	−0.293765	−0.146882	+	0.989154i	$0.546924\pi$
$368$	−1.00000	−0.0521286
$369$	9.11684	0.474604
$370$	−36.6060	−1.90305
$371$	6.74456	0.350160
$372$	4.74456	0.245994
$373$	−8.51087	−0.440676	−0.220338	−	0.975424i	$-0.570716\pi$
$373$	−8.51087	−0.440676	−0.220338	+	0.975424i	$0.570716\pi$
$374$	26.9783	1.39501
$375$	39.8614	2.05843
$376$	10.3723	0.534910
$377$	−15.8614	−0.816904
$378$	1.00000	0.0514344
$379$	9.62772	0.494543	0.247271	−	0.968946i	$-0.420466\pi$
$379$	9.62772	0.494543	0.247271	+	0.968946i	$0.420466\pi$
$380$	−17.4891	−0.897173
$381$	5.62772	0.288317
$382$	25.4891	1.30414
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	−1.00000	−0.0510310
$385$	17.4891	0.891328
$386$	17.1168	0.871224
$387$	−11.1168	−0.565101
$388$	−3.62772	−0.184170
$389$	−11.4891	−0.582522	−0.291261	−	0.956644i	$-0.594075\pi$
$389$	−11.4891	−0.582522	−0.291261	+	0.956644i	$0.594075\pi$
$390$	−19.1168	−0.968019
$391$	−6.74456	−0.341087
$392$	1.00000	0.0505076
$393$	−7.25544	−0.365988
$394$	−15.6277	−0.787313
$395$	−41.4891	−2.08754
$396$	4.00000	0.201008
$397$	−10.0000	−0.501886	−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000	−0.501886	−0.250943	+	0.968002i	$0.580741\pi$
$398$	11.8614	0.594559
$399$	4.00000	0.200250
$400$	14.1168	0.705842
$401$	20.9783	1.04760	0.523802	−	0.851840i	$-0.324513\pi$
$401$	20.9783	1.04760	0.523802	+	0.851840i	$0.324513\pi$
$402$	4.00000	0.199502
$403$	20.7446	1.03336
$404$	7.48913	0.372598
$405$	−4.37228	−0.217260
$406$	−3.62772	−0.180041
$407$	33.4891	1.65999
$408$	−6.74456	−0.333906
$409$	−10.7446	−0.531284	−0.265642	−	0.964072i	$-0.585584\pi$
$409$	−10.7446	−0.531284	−0.265642	+	0.964072i	$0.585584\pi$
$410$	−39.8614	−1.96861
$411$	−9.11684	−0.449701
$412$	7.11684	0.350622
$413$	−8.74456	−0.430292
$414$	−1.00000	−0.0491473
$415$	−17.4891	−0.858507
$416$	−4.37228	−0.214369
$417$	−14.3723	−0.703814
$418$	16.0000	0.782586
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	−4.37228	−0.213345
$421$	1.86141	0.0907194	0.0453597	−	0.998971i	$-0.485557\pi$
$421$	1.86141	0.0907194	0.0453597	+	0.998971i	$0.485557\pi$
$422$	−12.0000	−0.584151
$423$	10.3723	0.504318
$424$	−6.74456	−0.327545
$425$	95.2119	4.61846
$426$	−3.25544	−0.157726
$427$	2.00000	0.0967868
$428$	4.00000	0.193347
$429$	17.4891	0.844383
$430$	48.6060	2.34399
$431$	19.8614	0.956690	0.478345	−	0.878172i	$-0.341237\pi$
$431$	19.8614	0.956690	0.478345	+	0.878172i	$0.341237\pi$
$432$	−1.00000	−0.0481125
$433$	−17.8614	−0.858364	−0.429182	−	0.903218i	$-0.641198\pi$
$433$	−17.8614	−0.858364	−0.429182	+	0.903218i	$0.641198\pi$
$434$	4.74456	0.227746
$435$	15.8614	0.760496
$436$	−9.11684	−0.436618
$437$	−4.00000	−0.191346
$438$	1.25544	0.0599871
$439$	19.2554	0.919012	0.459506	−	0.888175i	$-0.348026\pi$
$439$	19.2554	0.919012	0.459506	+	0.888175i	$0.348026\pi$
$440$	−17.4891	−0.833761
$441$	1.00000	0.0476190
$442$	−29.4891	−1.40265
$443$	−14.3723	−0.682848	−0.341424	−	0.939909i	$-0.610909\pi$
$443$	−14.3723	−0.682848	−0.341424	+	0.939909i	$0.610909\pi$
$444$	−8.37228	−0.397331
$445$	67.7228	3.21037
$446$	−20.7446	−0.982284
$447$	16.2337	0.767827
$448$	−1.00000	−0.0472456
$449$	−16.9783	−0.801253	−0.400627	−	0.916241i	$-0.631208\pi$
$449$	−16.9783	−0.801253	−0.400627	+	0.916241i	$0.631208\pi$
$450$	14.1168	0.665474
$451$	36.4674	1.71718
$452$	1.11684	0.0525319
$453$	−2.37228	−0.111459
$454$	−11.1168	−0.521739
$455$	−19.1168	−0.896211
$456$	−4.00000	−0.187317
$457$	24.2337	1.13360	0.566802	−	0.823854i	$-0.308180\pi$
$457$	24.2337	1.13360	0.566802	+	0.823854i	$0.308180\pi$
$458$	10.7446	0.502060
$459$	−6.74456	−0.314809
$460$	4.37228	0.203859
$461$	−35.4891	−1.65289	−0.826447	−	0.563015i	$-0.809641\pi$
$461$	−35.4891	−1.65289	−0.826447	+	0.563015i	$0.809641\pi$
$462$	4.00000	0.186097
$463$	15.1168	0.702539	0.351270	−	0.936274i	$-0.385750\pi$
$463$	15.1168	0.702539	0.351270	+	0.936274i	$0.385750\pi$
$464$	3.62772	0.168413
$465$	−20.7446	−0.962006
$466$	0.510875	0.0236658
$467$	0.138593	0.00641334	0.00320667	−	0.999995i	$-0.498979\pi$
$467$	0.138593	0.00641334	0.00320667	+	0.999995i	$0.498979\pi$
$468$	−4.37228	−0.202109
$469$	4.00000	0.184703
$470$	−45.3505	−2.09186
$471$	22.7446	1.04801
$472$	8.74456	0.402501
$473$	−44.4674	−2.04461
$474$	−9.48913	−0.435850
$475$	56.4674	2.59090
$476$	−6.74456	−0.309137
$477$	−6.74456	−0.308812
$478$	−9.48913	−0.434022
$479$	4.74456	0.216785	0.108392	−	0.994108i	$-0.465430\pi$
$479$	4.74456	0.216785	0.108392	+	0.994108i	$0.465430\pi$
$480$	4.37228	0.199566
$481$	−36.6060	−1.66909
$482$	−8.37228	−0.381347
$483$	−1.00000	−0.0455016
$484$	5.00000	0.227273
$485$	15.8614	0.720229
$486$	−1.00000	−0.0453609
$487$	23.1168	1.04752	0.523762	−	0.851865i	$-0.324528\pi$
$487$	23.1168	1.04752	0.523762	+	0.851865i	$0.324528\pi$
$488$	−2.00000	−0.0905357
$489$	−4.00000	−0.180886
$490$	−4.37228	−0.197520
$491$	14.9783	0.675959	0.337979	−	0.941153i	$-0.390257\pi$
$491$	14.9783	0.675959	0.337979	+	0.941153i	$0.390257\pi$
$492$	−9.11684	−0.411019
$493$	24.4674	1.10196
$494$	−17.4891	−0.786873
$495$	−17.4891	−0.786078
$496$	−4.74456	−0.213037
$497$	−3.25544	−0.146026
$498$	−4.00000	−0.179244
$499$	−35.7228	−1.59917	−0.799586	−	0.600551i	$-0.794948\pi$
$499$	−35.7228	−1.59917	−0.799586	+	0.600551i	$0.794948\pi$
$500$	−39.8614	−1.78266
$501$	−17.4891	−0.781356
$502$	−19.1168	−0.853227
$503$	−12.7446	−0.568252	−0.284126	−	0.958787i	$-0.591703\pi$
$503$	−12.7446	−0.568252	−0.284126	+	0.958787i	$0.591703\pi$
$504$	−1.00000	−0.0445435
$505$	−32.7446	−1.45711
$506$	−4.00000	−0.177822
$507$	−6.11684	−0.271659
$508$	−5.62772	−0.249690
$509$	−8.23369	−0.364952	−0.182476	−	0.983210i	$-0.558411\pi$
$509$	−8.23369	−0.364952	−0.182476	+	0.983210i	$0.558411\pi$
$510$	29.4891	1.30580
$511$	1.25544	0.0555373
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	−16.9783	−0.748879
$515$	−31.1168	−1.37117
$516$	11.1168	0.489392
$517$	41.4891	1.82469
$518$	−8.37228	−0.367857
$519$	−15.4891	−0.679897
$520$	19.1168	0.838329
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	3.62772	0.158781
$523$	−5.76631	−0.252143	−0.126072	−	0.992021i	$-0.540237\pi$
$523$	−5.76631	−0.252143	−0.126072	+	0.992021i	$0.540237\pi$
$524$	7.25544	0.316955
$525$	14.1168	0.616110
$526$	−7.11684	−0.310309
$527$	−32.0000	−1.39394
$528$	−4.00000	−0.174078
$529$	1.00000	0.0434783
$530$	29.4891	1.28093
$531$	8.74456	0.379482
$532$	−4.00000	−0.173422
$533$	−39.8614	−1.72659
$534$	15.4891	0.670280
$535$	−17.4891	−0.756121
$536$	−4.00000	−0.172774
$537$	−7.86141	−0.339245
$538$	24.9783	1.07689
$539$	4.00000	0.172292
$540$	4.37228	0.188153
$541$	−16.2337	−0.697941	−0.348970	−	0.937134i	$-0.613469\pi$
$541$	−16.2337	−0.697941	−0.348970	+	0.937134i	$0.613469\pi$
$542$	18.9783	0.815186
$543$	−24.9783	−1.07192
$544$	6.74456	0.289171
$545$	39.8614	1.70748
$546$	−4.37228	−0.187116
$547$	−32.7446	−1.40006	−0.700028	−	0.714115i	$-0.746829\pi$
$547$	−32.7446	−1.40006	−0.700028	+	0.714115i	$0.746829\pi$
$548$	9.11684	0.389452
$549$	−2.00000	−0.0853579
$550$	56.4674	2.40778
$551$	14.5109	0.618184
$552$	1.00000	0.0425628
$553$	−9.48913	−0.403519
$554$	17.2554	0.733113
$555$	36.6060	1.55384
$556$	14.3723	0.609520
$557$	20.2337	0.857329	0.428664	−	0.903464i	$-0.358984\pi$
$557$	20.2337	0.857329	0.428664	+	0.903464i	$0.358984\pi$
$558$	−4.74456	−0.200853
$559$	48.6060	2.05581
$560$	4.37228	0.184763
$561$	−26.9783	−1.13902
$562$	−11.6277	−0.490486
$563$	30.3723	1.28004	0.640020	−	0.768359i	$-0.278926\pi$
$563$	30.3723	1.28004	0.640020	+	0.768359i	$0.278926\pi$
$564$	−10.3723	−0.436752
$565$	−4.88316	−0.205436
$566$	−24.7446	−1.04009
$567$	−1.00000	−0.0419961
$568$	3.25544	0.136595
$569$	−37.1168	−1.55602	−0.778010	−	0.628252i	$-0.783770\pi$
$569$	−37.1168	−1.55602	−0.778010	+	0.628252i	$0.783770\pi$
$570$	17.4891	0.732539
$571$	22.9783	0.961610	0.480805	−	0.876828i	$-0.340345\pi$
$571$	22.9783	0.961610	0.480805	+	0.876828i	$0.340345\pi$
$572$	−17.4891	−0.731257
$573$	−25.4891	−1.06482
$574$	−9.11684	−0.380530
$575$	−14.1168	−0.588713
$576$	1.00000	0.0416667
$577$	−26.4674	−1.10185	−0.550926	−	0.834554i	$-0.685725\pi$
$577$	−26.4674	−1.10185	−0.550926	+	0.834554i	$0.685725\pi$
$578$	28.4891	1.18499
$579$	−17.1168	−0.711352
$580$	−15.8614	−0.658609
$581$	−4.00000	−0.165948
$582$	3.62772	0.150374
$583$	−26.9783	−1.11732
$584$	−1.25544	−0.0519504
$585$	19.1168	0.790384
$586$	−10.0000	−0.413096
$587$	29.4891	1.21715	0.608573	−	0.793498i	$-0.291742\pi$
$587$	29.4891	1.21715	0.608573	+	0.793498i	$0.291742\pi$
$588$	−1.00000	−0.0412393
$589$	−18.9783	−0.781985
$590$	−38.2337	−1.57406
$591$	15.6277	0.642838
$592$	8.37228	0.344099
$593$	−8.37228	−0.343808	−0.171904	−	0.985114i	$-0.554992\pi$
$593$	−8.37228	−0.343808	−0.171904	+	0.985114i	$0.554992\pi$
$594$	−4.00000	−0.164122
$595$	29.4891	1.20894
$596$	−16.2337	−0.664958
$597$	−11.8614	−0.485455
$598$	4.37228	0.178796
$599$	20.4674	0.836274	0.418137	−	0.908384i	$-0.362683\pi$
$599$	20.4674	0.836274	0.418137	+	0.908384i	$0.362683\pi$
$600$	−14.1168	−0.576318
$601$	−4.23369	−0.172696	−0.0863479	−	0.996265i	$-0.527520\pi$
$601$	−4.23369	−0.172696	−0.0863479	+	0.996265i	$0.527520\pi$
$602$	11.1168	0.453089
$603$	−4.00000	−0.162893
$604$	2.37228	0.0965268
$605$	−21.8614	−0.888793
$606$	−7.48913	−0.304225
$607$	11.2554	0.456844	0.228422	−	0.973562i	$-0.426643\pi$
$607$	11.2554	0.456844	0.228422	+	0.973562i	$0.426643\pi$
$608$	4.00000	0.162221
$609$	3.62772	0.147003
$610$	8.74456	0.354057
$611$	−45.3505	−1.83469
$612$	6.74456	0.272633
$613$	45.1168	1.82225	0.911126	−	0.412128i	$-0.135214\pi$
$613$	45.1168	1.82225	0.911126	+	0.412128i	$0.135214\pi$
$614$	1.62772	0.0656894
$615$	39.8614	1.60737
$616$	−4.00000	−0.161165
$617$	−12.5109	−0.503669	−0.251834	−	0.967770i	$-0.581034\pi$
$617$	−12.5109	−0.503669	−0.251834	+	0.967770i	$0.581034\pi$
$618$	−7.11684	−0.286281
$619$	23.2554	0.934715	0.467357	−	0.884068i	$-0.345206\pi$
$619$	23.2554	0.934715	0.467357	+	0.884068i	$0.345206\pi$
$620$	20.7446	0.833122
$621$	1.00000	0.0401286
$622$	−17.4891	−0.701250
$623$	15.4891	0.620559
$624$	4.37228	0.175031
$625$	103.701	4.14804
$626$	−6.00000	−0.239808
$627$	−16.0000	−0.638978
$628$	−22.7446	−0.907607
$629$	56.4674	2.25150
$630$	4.37228	0.174196
$631$	10.9783	0.437037	0.218519	−	0.975833i	$-0.429878\pi$
$631$	10.9783	0.437037	0.218519	+	0.975833i	$0.429878\pi$
$632$	9.48913	0.377457
$633$	12.0000	0.476957
$634$	−1.11684	−0.0443555
$635$	24.6060	0.976458
$636$	6.74456	0.267439
$637$	−4.37228	−0.173236
$638$	14.5109	0.574491
$639$	3.25544	0.128783
$640$	−4.37228	−0.172830
$641$	31.3505	1.23827	0.619136	−	0.785284i	$-0.287483\pi$
$641$	31.3505	1.23827	0.619136	+	0.785284i	$0.287483\pi$
$642$	−4.00000	−0.157867
$643$	−42.2337	−1.66553	−0.832767	−	0.553624i	$-0.813245\pi$
$643$	−42.2337	−1.66553	−0.832767	+	0.553624i	$0.813245\pi$
$644$	1.00000	0.0394055
$645$	−48.6060	−1.91386
$646$	26.9783	1.06145
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	1.00000	0.0392837
$649$	34.9783	1.37302
$650$	−61.7228	−2.42097
$651$	−4.74456	−0.185954
$652$	4.00000	0.156652
$653$	32.0951	1.25598	0.627989	−	0.778222i	$-0.283878\pi$
$653$	32.0951	1.25598	0.627989	+	0.778222i	$0.283878\pi$
$654$	9.11684	0.356497
$655$	−31.7228	−1.23951
$656$	9.11684	0.355953
$657$	−1.25544	−0.0489793
$658$	−10.3723	−0.404354
$659$	−22.9783	−0.895106	−0.447553	−	0.894258i	$-0.647704\pi$
$659$	−22.9783	−0.895106	−0.447553	+	0.894258i	$0.647704\pi$
$660$	17.4891	0.680763
$661$	−19.4891	−0.758039	−0.379020	−	0.925389i	$-0.623739\pi$
$661$	−19.4891	−0.758039	−0.379020	+	0.925389i	$0.623739\pi$
$662$	−13.4891	−0.524270
$663$	29.4891	1.14526
$664$	4.00000	0.155230
$665$	17.4891	0.678199
$666$	8.37228	0.324419
$667$	−3.62772	−0.140466
$668$	17.4891	0.676675
$669$	20.7446	0.802031
$670$	17.4891	0.675664
$671$	−8.00000	−0.308837
$672$	1.00000	0.0385758
$673$	26.6060	1.02558	0.512792	−	0.858513i	$-0.328611\pi$
$673$	26.6060	1.02558	0.512792	+	0.858513i	$0.328611\pi$
$674$	−12.2337	−0.471224
$675$	−14.1168	−0.543358
$676$	6.11684	0.235263
$677$	−12.9783	−0.498795	−0.249397	−	0.968401i	$-0.580233\pi$
$677$	−12.9783	−0.498795	−0.249397	+	0.968401i	$0.580233\pi$
$678$	−1.11684	−0.0428921
$679$	3.62772	0.139219
$680$	−29.4891	−1.13086
$681$	11.1168	0.425998
$682$	−18.9783	−0.726715
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	4.00000	0.152944
$685$	−39.8614	−1.52303
$686$	−1.00000	−0.0381802
$687$	−10.7446	−0.409931
$688$	−11.1168	−0.423826
$689$	29.4891	1.12345
$690$	−4.37228	−0.166450
$691$	−42.8397	−1.62970	−0.814849	−	0.579674i	$-0.803180\pi$
$691$	−42.8397	−1.62970	−0.814849	+	0.579674i	$0.803180\pi$
$692$	15.4891	0.588808
$693$	−4.00000	−0.151947
$694$	22.3723	0.849240
$695$	−62.8397	−2.38364
$696$	−3.62772	−0.137508
$697$	61.4891	2.32907
$698$	12.5109	0.473544
$699$	−0.510875	−0.0193231
$700$	−14.1168	−0.533567
$701$	−40.2337	−1.51961	−0.759803	−	0.650154i	$-0.774704\pi$
$701$	−40.2337	−1.51961	−0.759803	+	0.650154i	$0.774704\pi$
$702$	4.37228	0.165021
$703$	33.4891	1.26307
$704$	4.00000	0.150756
$705$	45.3505	1.70800
$706$	18.8832	0.710677
$707$	−7.48913	−0.281658
$708$	−8.74456	−0.328641
$709$	−27.4891	−1.03238	−0.516188	−	0.856475i	$-0.672649\pi$
$709$	−27.4891	−1.03238	−0.516188	+	0.856475i	$0.672649\pi$
$710$	−14.2337	−0.534181
$711$	9.48913	0.355870
$712$	−15.4891	−0.580480
$713$	4.74456	0.177685
$714$	6.74456	0.252409
$715$	76.4674	2.85972
$716$	7.86141	0.293795
$717$	9.48913	0.354378
$718$	13.6277	0.508582
$719$	−5.62772	−0.209878	−0.104939	−	0.994479i	$-0.533465\pi$
$719$	−5.62772	−0.209878	−0.104939	+	0.994479i	$0.533465\pi$
$720$	−4.37228	−0.162945
$721$	−7.11684	−0.265045
$722$	−3.00000	−0.111648
$723$	8.37228	0.311368
$724$	24.9783	0.928309
$725$	51.2119	1.90196
$726$	−5.00000	−0.185567
$727$	33.4891	1.24204	0.621021	−	0.783794i	$-0.286718\pi$
$727$	33.4891	1.24204	0.621021	+	0.783794i	$0.286718\pi$
$728$	4.37228	0.162048
$729$	1.00000	0.0370370
$730$	5.48913	0.203162
$731$	−74.9783	−2.77317
$732$	2.00000	0.0739221
$733$	−16.2337	−0.599605	−0.299802	−	0.954001i	$-0.596921\pi$
$733$	−16.2337	−0.599605	−0.299802	+	0.954001i	$0.596921\pi$
$734$	−5.62772	−0.207723
$735$	4.37228	0.161274
$736$	−1.00000	−0.0368605
$737$	−16.0000	−0.589368
$738$	9.11684	0.335596
$739$	−16.7446	−0.615959	−0.307979	−	0.951393i	$-0.599653\pi$
$739$	−16.7446	−0.615959	−0.307979	+	0.951393i	$0.599653\pi$
$740$	−36.6060	−1.34566
$741$	17.4891	0.642479
$742$	6.74456	0.247601
$743$	−45.9565	−1.68598	−0.842990	−	0.537929i	$-0.819207\pi$
$743$	−45.9565	−1.68598	−0.842990	+	0.537929i	$0.819207\pi$
$744$	4.74456	0.173944
$745$	70.9783	2.60044
$746$	−8.51087	−0.311605
$747$	4.00000	0.146352
$748$	26.9783	0.986423
$749$	−4.00000	−0.146157
$750$	39.8614	1.45553
$751$	−9.48913	−0.346263	−0.173132	−	0.984899i	$-0.555389\pi$
$751$	−9.48913	−0.346263	−0.173132	+	0.984899i	$0.555389\pi$
$752$	10.3723	0.378238
$753$	19.1168	0.696657
$754$	−15.8614	−0.577638
$755$	−10.3723	−0.377486
$756$	1.00000	0.0363696
$757$	−50.0000	−1.81728	−0.908640	−	0.417579i	$-0.862879\pi$
$757$	−50.0000	−1.81728	−0.908640	+	0.417579i	$0.862879\pi$
$758$	9.62772	0.349694
$759$	4.00000	0.145191
$760$	−17.4891	−0.634397
$761$	−40.9783	−1.48546	−0.742730	−	0.669591i	$-0.766469\pi$
$761$	−40.9783	−1.48546	−0.742730	+	0.669591i	$0.766469\pi$
$762$	5.62772	0.203871
$763$	9.11684	0.330052
$764$	25.4891	0.922164
$765$	−29.4891	−1.06618
$766$	16.0000	0.578103
$767$	−38.2337	−1.38054
$768$	−1.00000	−0.0360844
$769$	−45.1168	−1.62696	−0.813478	−	0.581596i	$-0.802428\pi$
$769$	−45.1168	−1.62696	−0.813478	+	0.581596i	$0.802428\pi$
$770$	17.4891	0.630264
$771$	16.9783	0.611457
$772$	17.1168	0.616049
$773$	−1.39403	−0.0501398	−0.0250699	−	0.999686i	$-0.507981\pi$
$773$	−1.39403	−0.0501398	−0.0250699	+	0.999686i	$0.507981\pi$
$774$	−11.1168	−0.399587
$775$	−66.9783	−2.40593
$776$	−3.62772	−0.130228
$777$	8.37228	0.300354
$778$	−11.4891	−0.411905
$779$	36.4674	1.30658
$780$	−19.1168	−0.684493
$781$	13.0217	0.465955
$782$	−6.74456	−0.241185
$783$	−3.62772	−0.129644
$784$	1.00000	0.0357143
$785$	99.4456	3.54937
$786$	−7.25544	−0.258793
$787$	29.4891	1.05117	0.525587	−	0.850740i	$-0.323846\pi$
$787$	29.4891	1.05117	0.525587	+	0.850740i	$0.323846\pi$
$788$	−15.6277	−0.556714
$789$	7.11684	0.253366
$790$	−41.4891	−1.47612
$791$	−1.11684	−0.0397104
$792$	4.00000	0.142134
$793$	8.74456	0.310529
$794$	−10.0000	−0.354887
$795$	−29.4891	−1.04587
$796$	11.8614	0.420416
$797$	−21.8614	−0.774371	−0.387185	−	0.922002i	$-0.626553\pi$
$797$	−21.8614	−0.774371	−0.387185	+	0.922002i	$0.626553\pi$
$798$	4.00000	0.141598
$799$	69.9565	2.47488
$800$	14.1168	0.499106
$801$	−15.4891	−0.547281
$802$	20.9783	0.740768
$803$	−5.02175	−0.177214
$804$	4.00000	0.141069
$805$	−4.37228	−0.154103
$806$	20.7446	0.730696
$807$	−24.9783	−0.879276
$808$	7.48913	0.263467
$809$	−1.25544	−0.0441388	−0.0220694	−	0.999756i	$-0.507025\pi$
$809$	−1.25544	−0.0441388	−0.0220694	+	0.999756i	$0.507025\pi$
$810$	−4.37228	−0.153626
$811$	−20.6060	−0.723573	−0.361787	−	0.932261i	$-0.617833\pi$
$811$	−20.6060	−0.723573	−0.361787	+	0.932261i	$0.617833\pi$
$812$	−3.62772	−0.127308
$813$	−18.9783	−0.665596
$814$	33.4891	1.17379
$815$	−17.4891	−0.612617
$816$	−6.74456	−0.236107
$817$	−44.4674	−1.55572
$818$	−10.7446	−0.375675
$819$	4.37228	0.152780
$820$	−39.8614	−1.39202
$821$	−0.510875	−0.0178297	−0.00891483	−	0.999960i	$-0.502838\pi$
$821$	−0.510875	−0.0178297	−0.00891483	+	0.999960i	$0.502838\pi$
$822$	−9.11684	−0.317986
$823$	5.35053	0.186508	0.0932539	−	0.995642i	$-0.470273\pi$
$823$	5.35053	0.186508	0.0932539	+	0.995642i	$0.470273\pi$
$824$	7.11684	0.247927
$825$	−56.4674	−1.96594
$826$	−8.74456	−0.304262
$827$	18.2337	0.634047	0.317024	−	0.948418i	$-0.397317\pi$
$827$	18.2337	0.634047	0.317024	+	0.948418i	$0.397317\pi$
$828$	−1.00000	−0.0347524
$829$	47.4891	1.64937	0.824683	−	0.565596i	$-0.191354\pi$
$829$	47.4891	1.64937	0.824683	+	0.565596i	$0.191354\pi$
$830$	−17.4891	−0.607056
$831$	−17.2554	−0.598584
$832$	−4.37228	−0.151582
$833$	6.74456	0.233685
$834$	−14.3723	−0.497671
$835$	−76.4674	−2.64626
$836$	16.0000	0.553372
$837$	4.74456	0.163996
$838$	4.00000	0.138178
$839$	44.7446	1.54475	0.772377	−	0.635164i	$-0.219068\pi$
$839$	44.7446	1.54475	0.772377	+	0.635164i	$0.219068\pi$
$840$	−4.37228	−0.150858
$841$	−15.8397	−0.546195
$842$	1.86141	0.0641483
$843$	11.6277	0.400480
$844$	−12.0000	−0.413057
$845$	−26.7446	−0.920041
$846$	10.3723	0.356606
$847$	−5.00000	−0.171802
$848$	−6.74456	−0.231609
$849$	24.7446	0.849231
$850$	95.2119	3.26574
$851$	−8.37228	−0.286998
$852$	−3.25544	−0.111529
$853$	−45.5842	−1.56077	−0.780387	−	0.625297i	$-0.784978\pi$
$853$	−45.5842	−1.56077	−0.780387	+	0.625297i	$0.784978\pi$
$854$	2.00000	0.0684386
$855$	−17.4891	−0.598115
$856$	4.00000	0.136717
$857$	−6.88316	−0.235124	−0.117562	−	0.993066i	$-0.537508\pi$
$857$	−6.88316	−0.235124	−0.117562	+	0.993066i	$0.537508\pi$
$858$	17.4891	0.597069
$859$	4.88316	0.166611	0.0833056	−	0.996524i	$-0.473452\pi$
$859$	4.88316	0.166611	0.0833056	+	0.996524i	$0.473452\pi$
$860$	48.6060	1.65745
$861$	9.11684	0.310701
$862$	19.8614	0.676482
$863$	−9.48913	−0.323014	−0.161507	−	0.986872i	$-0.551635\pi$
$863$	−9.48913	−0.323014	−0.161507	+	0.986872i	$0.551635\pi$
$864$	−1.00000	−0.0340207
$865$	−67.7228	−2.30264
$866$	−17.8614	−0.606955
$867$	−28.4891	−0.967541
$868$	4.74456	0.161041
$869$	37.9565	1.28759
$870$	15.8614	0.537752
$871$	17.4891	0.592596
$872$	−9.11684	−0.308735
$873$	−3.62772	−0.122780
$874$	−4.00000	−0.135302
$875$	39.8614	1.34756
$876$	1.25544	0.0424173
$877$	12.2337	0.413102	0.206551	−	0.978436i	$-0.433776\pi$
$877$	12.2337	0.413102	0.206551	+	0.978436i	$0.433776\pi$
$878$	19.2554	0.649840
$879$	10.0000	0.337292
$880$	−17.4891	−0.589558
$881$	4.97825	0.167722	0.0838608	−	0.996477i	$-0.473275\pi$
$881$	4.97825	0.167722	0.0838608	+	0.996477i	$0.473275\pi$
$882$	1.00000	0.0336718
$883$	−32.7446	−1.10194	−0.550971	−	0.834524i	$-0.685743\pi$
$883$	−32.7446	−1.10194	−0.550971	+	0.834524i	$0.685743\pi$
$884$	−29.4891	−0.991827
$885$	38.2337	1.28521
$886$	−14.3723	−0.482846
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	−8.37228	−0.280955
$889$	5.62772	0.188748
$890$	67.7228	2.27007
$891$	4.00000	0.134005
$892$	−20.7446	−0.694579
$893$	41.4891	1.38838
$894$	16.2337	0.542936
$895$	−34.3723	−1.14894
$896$	−1.00000	−0.0334077
$897$	−4.37228	−0.145986
$898$	−16.9783	−0.566572
$899$	−17.2119	−0.574050
$900$	14.1168	0.470561
$901$	−45.4891	−1.51546
$902$	36.4674	1.21423
$903$	−11.1168	−0.369945
$904$	1.11684	0.0371457
$905$	−109.212	−3.63033
$906$	−2.37228	−0.0788138
$907$	22.0951	0.733656	0.366828	−	0.930289i	$-0.380444\pi$
$907$	22.0951	0.733656	0.366828	+	0.930289i	$0.380444\pi$
$908$	−11.1168	−0.368925
$909$	7.48913	0.248399
$910$	−19.1168	−0.633717
$911$	−48.3288	−1.60120	−0.800602	−	0.599196i	$-0.795487\pi$
$911$	−48.3288	−1.60120	−0.800602	+	0.599196i	$0.795487\pi$
$912$	−4.00000	−0.132453
$913$	16.0000	0.529523
$914$	24.2337	0.801579
$915$	−8.74456	−0.289086
$916$	10.7446	0.355010
$917$	−7.25544	−0.239596
$918$	−6.74456	−0.222604
$919$	45.9565	1.51597	0.757983	−	0.652275i	$-0.226185\pi$
$919$	45.9565	1.51597	0.757983	+	0.652275i	$0.226185\pi$
$920$	4.37228	0.144150
$921$	−1.62772	−0.0536352
$922$	−35.4891	−1.16877
$923$	−14.2337	−0.468508
$924$	4.00000	0.131590
$925$	118.190	3.88607
$926$	15.1168	0.496770
$927$	7.11684	0.233748
$928$	3.62772	0.119086
$929$	33.1168	1.08653	0.543264	−	0.839562i	$-0.317188\pi$
$929$	33.1168	1.08653	0.543264	+	0.839562i	$0.317188\pi$
$930$	−20.7446	−0.680241
$931$	4.00000	0.131095
$932$	0.510875	0.0167343
$933$	17.4891	0.572568
$934$	0.138593	0.00453491
$935$	−117.957	−3.85759
$936$	−4.37228	−0.142912
$937$	−27.6277	−0.902558	−0.451279	−	0.892383i	$-0.649032\pi$
$937$	−27.6277	−0.902558	−0.451279	+	0.892383i	$0.649032\pi$
$938$	4.00000	0.130605
$939$	6.00000	0.195803
$940$	−45.3505	−1.47917
$941$	−60.3723	−1.96808	−0.984040	−	0.177947i	$-0.943054\pi$
$941$	−60.3723	−1.96808	−0.984040	+	0.177947i	$0.943054\pi$
$942$	22.7446	0.741058
$943$	−9.11684	−0.296885
$944$	8.74456	0.284611
$945$	−4.37228	−0.142230
$946$	−44.4674	−1.44576
$947$	−57.3505	−1.86364	−0.931821	−	0.362918i	$-0.881780\pi$
$947$	−57.3505	−1.86364	−0.931821	+	0.362918i	$0.881780\pi$
$948$	−9.48913	−0.308192
$949$	5.48913	0.178185
$950$	56.4674	1.83204
$951$	1.11684	0.0362161
$952$	−6.74456	−0.218593
$953$	0.510875	0.0165489	0.00827443	−	0.999966i	$-0.497366\pi$
$953$	0.510875	0.0165489	0.00827443	+	0.999966i	$0.497366\pi$
$954$	−6.74456	−0.218363
$955$	−111.446	−3.60630
$956$	−9.48913	−0.306900
$957$	−14.5109	−0.469070
$958$	4.74456	0.153290
$959$	−9.11684	−0.294398
$960$	4.37228	0.141115
$961$	−8.48913	−0.273843
$962$	−36.6060	−1.18022
$963$	4.00000	0.128898
$964$	−8.37228	−0.269653
$965$	−74.8397	−2.40917
$966$	−1.00000	−0.0321745
$967$	−30.5109	−0.981164	−0.490582	−	0.871395i	$-0.663216\pi$
$967$	−30.5109	−0.981164	−0.490582	+	0.871395i	$0.663216\pi$
$968$	5.00000	0.160706
$969$	−26.9783	−0.866666
$970$	15.8614	0.509279
$971$	40.4674	1.29866	0.649330	−	0.760507i	$-0.275049\pi$
$971$	40.4674	1.29866	0.649330	+	0.760507i	$0.275049\pi$
$972$	−1.00000	−0.0320750
$973$	−14.3723	−0.460754
$974$	23.1168	0.740711
$975$	61.7228	1.97671
$976$	−2.00000	−0.0640184
$977$	−43.3505	−1.38691	−0.693453	−	0.720502i	$-0.743912\pi$
$977$	−43.3505	−1.38691	−0.693453	+	0.720502i	$0.743912\pi$
$978$	−4.00000	−0.127906
$979$	−61.9565	−1.98014
$980$	−4.37228	−0.139667
$981$	−9.11684	−0.291078
$982$	14.9783	0.477975
$983$	−38.2337	−1.21947	−0.609733	−	0.792607i	$-0.708723\pi$
$983$	−38.2337	−1.21947	−0.609733	+	0.792607i	$0.708723\pi$
$984$	−9.11684	−0.290634
$985$	68.3288	2.17714
$986$	24.4674	0.779200
$987$	10.3723	0.330153
$988$	−17.4891	−0.556403
$989$	11.1168	0.353495
$990$	−17.4891	−0.555841
$991$	9.48913	0.301432	0.150716	−	0.988577i	$-0.451842\pi$
$991$	9.48913	0.301432	0.150716	+	0.988577i	$0.451842\pi$
$992$	−4.74456	−0.150640
$993$	13.4891	0.428064
$994$	−3.25544	−0.103256
$995$	−51.8614	−1.64412
$996$	−4.00000	−0.126745
$997$	−50.0000	−1.58352	−0.791758	−	0.610835i	$-0.790834\pi$
$997$	−50.0000	−1.58352	−0.791758	+	0.610835i	$0.790834\pi$
$998$	−35.7228	−1.13079
$999$	−8.37228	−0.264887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.a.o.1.1	✓	2
3.2	odd	2		2898.2.a.x.1.2		2
4.3	odd	2		7728.2.a.bh.1.1		2
7.6	odd	2		6762.2.a.cd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.o.1.1	✓	2	1.1	even	1	trivial
2898.2.a.x.1.2		2	3.2	odd	2
6762.2.a.cd.1.2		2	7.6	odd	2
7728.2.a.bh.1.1		2	4.3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37228 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.37228 q^{10} +4.00000 q^{11} -1.00000 q^{12} -4.37228 q^{13} -1.00000 q^{14} +4.37228 q^{15} +1.00000 q^{16} +6.74456 q^{17} +1.00000 q^{18} +4.00000 q^{19} -4.37228 q^{20} +1.00000 q^{21} +4.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +14.1168 q^{25} -4.37228 q^{26} -1.00000 q^{27} -1.00000 q^{28} +3.62772 q^{29} +4.37228 q^{30} -4.74456 q^{31} +1.00000 q^{32} -4.00000 q^{33} +6.74456 q^{34} +4.37228 q^{35} +1.00000 q^{36} +8.37228 q^{37} +4.00000 q^{38} +4.37228 q^{39} -4.37228 q^{40} +9.11684 q^{41} +1.00000 q^{42} -11.1168 q^{43} +4.00000 q^{44} -4.37228 q^{45} -1.00000 q^{46} +10.3723 q^{47} -1.00000 q^{48} +1.00000 q^{49} +14.1168 q^{50} -6.74456 q^{51} -4.37228 q^{52} -6.74456 q^{53} -1.00000 q^{54} -17.4891 q^{55} -1.00000 q^{56} -4.00000 q^{57} +3.62772 q^{58} +8.74456 q^{59} +4.37228 q^{60} -2.00000 q^{61} -4.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} +19.1168 q^{65} -4.00000 q^{66} -4.00000 q^{67} +6.74456 q^{68} +1.00000 q^{69} +4.37228 q^{70} +3.25544 q^{71} +1.00000 q^{72} -1.25544 q^{73} +8.37228 q^{74} -14.1168 q^{75} +4.00000 q^{76} -4.00000 q^{77} +4.37228 q^{78} +9.48913 q^{79} -4.37228 q^{80} +1.00000 q^{81} +9.11684 q^{82} +4.00000 q^{83} +1.00000 q^{84} -29.4891 q^{85} -11.1168 q^{86} -3.62772 q^{87} +4.00000 q^{88} -15.4891 q^{89} -4.37228 q^{90} +4.37228 q^{91} -1.00000 q^{92} +4.74456 q^{93} +10.3723 q^{94} -17.4891 q^{95} -1.00000 q^{96} -3.62772 q^{97} +1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + 8 q^{11} - 2 q^{12} - 3 q^{13} - 2 q^{14} + 3 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 8 q^{19} - 3 q^{20} + 2 q^{21} + 8 q^{22} - 2 q^{23} - 2 q^{24} + 11 q^{25} - 3 q^{26} - 2 q^{27} - 2 q^{28} + 13 q^{29} + 3 q^{30} + 2 q^{31} + 2 q^{32} - 8 q^{33} + 2 q^{34} + 3 q^{35} + 2 q^{36} + 11 q^{37} + 8 q^{38} + 3 q^{39} - 3 q^{40} + q^{41} + 2 q^{42} - 5 q^{43} + 8 q^{44} - 3 q^{45} - 2 q^{46} + 15 q^{47} - 2 q^{48} + 2 q^{49} + 11 q^{50} - 2 q^{51} - 3 q^{52} - 2 q^{53} - 2 q^{54} - 12 q^{55} - 2 q^{56} - 8 q^{57} + 13 q^{58} + 6 q^{59} + 3 q^{60} - 4 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 21 q^{65} - 8 q^{66} - 8 q^{67} + 2 q^{68} + 2 q^{69} + 3 q^{70} + 18 q^{71} + 2 q^{72} - 14 q^{73} + 11 q^{74} - 11 q^{75} + 8 q^{76} - 8 q^{77} + 3 q^{78} - 4 q^{79} - 3 q^{80} + 2 q^{81} + q^{82} + 8 q^{83} + 2 q^{84} - 36 q^{85} - 5 q^{86} - 13 q^{87} + 8 q^{88} - 8 q^{89} - 3 q^{90} + 3 q^{91} - 2 q^{92} - 2 q^{93} + 15 q^{94} - 12 q^{95} - 2 q^{96} - 13 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + 8 * q^11 - 2 * q^12 - 3 * q^13 - 2 * q^14 + 3 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 8 * q^19 - 3 * q^20 + 2 * q^21 + 8 * q^22 - 2 * q^23 - 2 * q^24 + 11 * q^25 - 3 * q^26 - 2 * q^27 - 2 * q^28 + 13 * q^29 + 3 * q^30 + 2 * q^31 + 2 * q^32 - 8 * q^33 + 2 * q^34 + 3 * q^35 + 2 * q^36 + 11 * q^37 + 8 * q^38 + 3 * q^39 - 3 * q^40 + q^41 + 2 * q^42 - 5 * q^43 + 8 * q^44 - 3 * q^45 - 2 * q^46 + 15 * q^47 - 2 * q^48 + 2 * q^49 + 11 * q^50 - 2 * q^51 - 3 * q^52 - 2 * q^53 - 2 * q^54 - 12 * q^55 - 2 * q^56 - 8 * q^57 + 13 * q^58 + 6 * q^59 + 3 * q^60 - 4 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 21 * q^65 - 8 * q^66 - 8 * q^67 + 2 * q^68 + 2 * q^69 + 3 * q^70 + 18 * q^71 + 2 * q^72 - 14 * q^73 + 11 * q^74 - 11 * q^75 + 8 * q^76 - 8 * q^77 + 3 * q^78 - 4 * q^79 - 3 * q^80 + 2 * q^81 + q^82 + 8 * q^83 + 2 * q^84 - 36 * q^85 - 5 * q^86 - 13 * q^87 + 8 * q^88 - 8 * q^89 - 3 * q^90 + 3 * q^91 - 2 * q^92 - 2 * q^93 + 15 * q^94 - 12 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 + 8 * q^99

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