LMFDB - Embedded newform 1502.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 $ x^11 - 4x^10 - 9x^9 + 58x^8 - 40x^7 - 146x^6 + 237x^5 - 47x^4 - 89x^3 + 39*x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.22814$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.24044 q^{3} +1.00000 q^{4} -4.22616 q^{5} +2.24044 q^{6} -3.19230 q^{7} -1.00000 q^{8} +2.01957 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.24044 q^{3} +1.00000 q^{4} -4.22616 q^{5} +2.24044 q^{6} -3.19230 q^{7} -1.00000 q^{8} +2.01957 q^{9} +4.22616 q^{10} +4.83468 q^{11} -2.24044 q^{12} +1.15811 q^{13} +3.19230 q^{14} +9.46846 q^{15} +1.00000 q^{16} -0.359718 q^{17} -2.01957 q^{18} -4.81240 q^{19} -4.22616 q^{20} +7.15216 q^{21} -4.83468 q^{22} +3.06784 q^{23} +2.24044 q^{24} +12.8604 q^{25} -1.15811 q^{26} +2.19659 q^{27} -3.19230 q^{28} +6.55078 q^{29} -9.46846 q^{30} +2.50947 q^{31} -1.00000 q^{32} -10.8318 q^{33} +0.359718 q^{34} +13.4912 q^{35} +2.01957 q^{36} +0.874448 q^{37} +4.81240 q^{38} -2.59467 q^{39} +4.22616 q^{40} -8.79337 q^{41} -7.15216 q^{42} -5.42719 q^{43} +4.83468 q^{44} -8.53504 q^{45} -3.06784 q^{46} +3.93189 q^{47} -2.24044 q^{48} +3.19079 q^{49} -12.8604 q^{50} +0.805926 q^{51} +1.15811 q^{52} -0.0537126 q^{53} -2.19659 q^{54} -20.4322 q^{55} +3.19230 q^{56} +10.7819 q^{57} -6.55078 q^{58} +7.13835 q^{59} +9.46846 q^{60} +4.08338 q^{61} -2.50947 q^{62} -6.44708 q^{63} +1.00000 q^{64} -4.89436 q^{65} +10.8318 q^{66} -4.48302 q^{67} -0.359718 q^{68} -6.87330 q^{69} -13.4912 q^{70} -7.13347 q^{71} -2.01957 q^{72} -16.4952 q^{73} -0.874448 q^{74} -28.8131 q^{75} -4.81240 q^{76} -15.4338 q^{77} +2.59467 q^{78} +9.83874 q^{79} -4.22616 q^{80} -10.9800 q^{81} +8.79337 q^{82} -1.75012 q^{83} +7.15216 q^{84} +1.52023 q^{85} +5.42719 q^{86} -14.6766 q^{87} -4.83468 q^{88} +15.5032 q^{89} +8.53504 q^{90} -3.69704 q^{91} +3.06784 q^{92} -5.62232 q^{93} -3.93189 q^{94} +20.3380 q^{95} +2.24044 q^{96} -11.5345 q^{97} -3.19079 q^{98} +9.76399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.24044	−1.29352	−0.646759	−	0.762694i	$-0.723876\pi$
$3$	−2.24044	−1.29352	−0.646759	+	0.762694i	$0.723876\pi$
$4$	1.00000	0.500000
$5$	−4.22616	−1.89000	−0.944999	−	0.327074i	$-0.893937\pi$
$5$	−4.22616	−1.89000	−0.944999	+	0.327074i	$0.893937\pi$
$6$	2.24044	0.914656
$7$	−3.19230	−1.20658	−0.603288	−	0.797523i	$-0.706143\pi$
$7$	−3.19230	−1.20658	−0.603288	+	0.797523i	$0.706143\pi$
$8$	−1.00000	−0.353553
$9$	2.01957	0.673190
$10$	4.22616	1.33643
$11$	4.83468	1.45771	0.728856	−	0.684667i	$-0.240052\pi$
$11$	4.83468	1.45771	0.728856	+	0.684667i	$0.240052\pi$
$12$	−2.24044	−0.646759
$13$	1.15811	0.321202	0.160601	−	0.987019i	$-0.448657\pi$
$13$	1.15811	0.321202	0.160601	+	0.987019i	$0.448657\pi$
$14$	3.19230	0.853179
$15$	9.46846	2.44475
$16$	1.00000	0.250000
$17$	−0.359718	−0.0872444	−0.0436222	−	0.999048i	$-0.513890\pi$
$17$	−0.359718	−0.0872444	−0.0436222	+	0.999048i	$0.513890\pi$
$18$	−2.01957	−0.476018
$19$	−4.81240	−1.10404	−0.552020	−	0.833831i	$-0.686143\pi$
$19$	−4.81240	−1.10404	−0.552020	+	0.833831i	$0.686143\pi$
$20$	−4.22616	−0.944999
$21$	7.15216	1.56073
$22$	−4.83468	−1.03076
$23$	3.06784	0.639688	0.319844	−	0.947470i	$-0.396370\pi$
$23$	3.06784	0.639688	0.319844	+	0.947470i	$0.396370\pi$
$24$	2.24044	0.457328
$25$	12.8604	2.57209
$26$	−1.15811	−0.227124
$27$	2.19659	0.422734
$28$	−3.19230	−0.603288
$29$	6.55078	1.21645	0.608225	−	0.793765i	$-0.291882\pi$
$29$	6.55078	1.21645	0.608225	+	0.793765i	$0.291882\pi$
$30$	−9.46846	−1.72870
$31$	2.50947	0.450714	0.225357	−	0.974276i	$-0.427645\pi$
$31$	2.50947	0.450714	0.225357	+	0.974276i	$0.427645\pi$
$32$	−1.00000	−0.176777
$33$	−10.8318	−1.88558
$34$	0.359718	0.0616911
$35$	13.4912	2.28043
$36$	2.01957	0.336595
$37$	0.874448	0.143758	0.0718792	−	0.997413i	$-0.477100\pi$
$37$	0.874448	0.143758	0.0718792	+	0.997413i	$0.477100\pi$
$38$	4.81240	0.780674
$39$	−2.59467	−0.415480
$40$	4.22616	0.668215
$41$	−8.79337	−1.37329	−0.686647	−	0.726991i	$-0.740918\pi$
$41$	−8.79337	−1.37329	−0.686647	+	0.726991i	$0.740918\pi$
$42$	−7.15216	−1.10360
$43$	−5.42719	−0.827639	−0.413819	−	0.910359i	$-0.635806\pi$
$43$	−5.42719	−0.827639	−0.413819	+	0.910359i	$0.635806\pi$
$44$	4.83468	0.728856
$45$	−8.53504	−1.27233
$46$	−3.06784	−0.452328
$47$	3.93189	0.573525	0.286762	−	0.958002i	$-0.407421\pi$
$47$	3.93189	0.573525	0.286762	+	0.958002i	$0.407421\pi$
$48$	−2.24044	−0.323380
$49$	3.19079	0.455828
$50$	−12.8604	−1.81874
$51$	0.805926	0.112852
$52$	1.15811	0.160601
$53$	−0.0537126	−0.00737799	−0.00368899	−	0.999993i	$-0.501174\pi$
$53$	−0.0537126	−0.00737799	−0.00368899	+	0.999993i	$0.501174\pi$
$54$	−2.19659	−0.298918
$55$	−20.4322	−2.75507
$56$	3.19230	0.426589
$57$	10.7819	1.42810
$58$	−6.55078	−0.860160
$59$	7.13835	0.929334	0.464667	−	0.885485i	$-0.346174\pi$
$59$	7.13835	0.929334	0.464667	+	0.885485i	$0.346174\pi$
$60$	9.46846	1.22237
$61$	4.08338	0.522823	0.261411	−	0.965227i	$-0.415812\pi$
$61$	4.08338	0.522823	0.261411	+	0.965227i	$0.415812\pi$
$62$	−2.50947	−0.318703
$63$	−6.44708	−0.812256
$64$	1.00000	0.125000
$65$	−4.89436	−0.607070
$66$	10.8318	1.33330
$67$	−4.48302	−0.547688	−0.273844	−	0.961774i	$-0.588295\pi$
$67$	−4.48302	−0.547688	−0.273844	+	0.961774i	$0.588295\pi$
$68$	−0.359718	−0.0436222
$69$	−6.87330	−0.827448
$70$	−13.4912	−1.61251
$71$	−7.13347	−0.846587	−0.423294	−	0.905992i	$-0.639126\pi$
$71$	−7.13347	−0.846587	−0.423294	+	0.905992i	$0.639126\pi$
$72$	−2.01957	−0.238009
$73$	−16.4952	−1.93062	−0.965311	−	0.261101i	$-0.915914\pi$
$73$	−16.4952	−1.93062	−0.965311	+	0.261101i	$0.915914\pi$
$74$	−0.874448	−0.101653
$75$	−28.8131	−3.32705
$76$	−4.81240	−0.552020
$77$	−15.4338	−1.75884
$78$	2.59467	0.293789
$79$	9.83874	1.10694	0.553472	−	0.832868i	$-0.313302\pi$
$79$	9.83874	1.10694	0.553472	+	0.832868i	$0.313302\pi$
$80$	−4.22616	−0.472499
$81$	−10.9800	−1.22001
$82$	8.79337	0.971066
$83$	−1.75012	−0.192100	−0.0960501	−	0.995376i	$-0.530621\pi$
$83$	−1.75012	−0.192100	−0.0960501	+	0.995376i	$0.530621\pi$
$84$	7.15216	0.780365
$85$	1.52023	0.164892
$86$	5.42719	0.585229
$87$	−14.6766	−1.57350
$88$	−4.83468	−0.515379
$89$	15.5032	1.64334	0.821668	−	0.569967i	$-0.193044\pi$
$89$	15.5032	1.64334	0.821668	+	0.569967i	$0.193044\pi$
$90$	8.53504	0.899672
$91$	−3.69704	−0.387555
$92$	3.06784	0.319844
$93$	−5.62232	−0.583007
$94$	−3.93189	−0.405543
$95$	20.3380	2.08663
$96$	2.24044	0.228664
$97$	−11.5345	−1.17115	−0.585573	−	0.810620i	$-0.699131\pi$
$97$	−11.5345	−1.17115	−0.585573	+	0.810620i	$0.699131\pi$
$98$	−3.19079	−0.322319
$99$	9.76399	0.981317
$100$	12.8604	1.28604
$101$	5.93612	0.590666	0.295333	−	0.955394i	$-0.404569\pi$
$101$	5.93612	0.590666	0.295333	+	0.955394i	$0.404569\pi$
$102$	−0.805926	−0.0797986
$103$	12.1588	1.19805	0.599023	−	0.800732i	$-0.295556\pi$
$103$	12.1588	1.19805	0.599023	+	0.800732i	$0.295556\pi$
$104$	−1.15811	−0.113562
$105$	−30.2262	−2.94977
$106$	0.0537126	0.00521702
$107$	9.65014	0.932914	0.466457	−	0.884544i	$-0.345530\pi$
$107$	9.65014	0.932914	0.466457	+	0.884544i	$0.345530\pi$
$108$	2.19659	0.211367
$109$	1.66159	0.159151	0.0795757	−	0.996829i	$-0.474643\pi$
$109$	1.66159	0.159151	0.0795757	+	0.996829i	$0.474643\pi$
$110$	20.4322	1.94813
$111$	−1.95915	−0.185954
$112$	−3.19230	−0.301644
$113$	−3.07801	−0.289554	−0.144777	−	0.989464i	$-0.546247\pi$
$113$	−3.07801	−0.289554	−0.144777	+	0.989464i	$0.546247\pi$
$114$	−10.7819	−1.00982
$115$	−12.9652	−1.20901
$116$	6.55078	0.608225
$117$	2.33888	0.216230
$118$	−7.13835	−0.657138
$119$	1.14833	0.105267
$120$	−9.46846	−0.864348
$121$	12.3742	1.12492
$122$	−4.08338	−0.369692
$123$	19.7010	1.77638
$124$	2.50947	0.225357
$125$	−33.2195	−2.97124
$126$	6.44708	0.574352
$127$	−16.7539	−1.48667	−0.743333	−	0.668921i	$-0.766756\pi$
$127$	−16.7539	−1.48667	−0.743333	+	0.668921i	$0.766756\pi$
$128$	−1.00000	−0.0883883
$129$	12.1593	1.07057
$130$	4.89436	0.429264
$131$	−10.3796	−0.906867	−0.453433	−	0.891290i	$-0.649801\pi$
$131$	−10.3796	−0.906867	−0.453433	+	0.891290i	$0.649801\pi$
$132$	−10.8318	−0.942789
$133$	15.3626	1.33211
$134$	4.48302	0.387274
$135$	−9.28315	−0.798967
$136$	0.359718	0.0308455
$137$	7.02596	0.600268	0.300134	−	0.953897i	$-0.402969\pi$
$137$	7.02596	0.600268	0.300134	+	0.953897i	$0.402969\pi$
$138$	6.87330	0.585094
$139$	10.9322	0.927259	0.463630	−	0.886029i	$-0.346547\pi$
$139$	10.9322	0.927259	0.463630	+	0.886029i	$0.346547\pi$
$140$	13.4912	1.14021
$141$	−8.80916	−0.741865
$142$	7.13347	0.598628
$143$	5.59909	0.468219
$144$	2.01957	0.168298
$145$	−27.6847	−2.29909
$146$	16.4952	1.36516
$147$	−7.14878	−0.589622
$148$	0.874448	0.0718792
$149$	11.1132	0.910430	0.455215	−	0.890382i	$-0.349562\pi$
$149$	11.1132	0.910430	0.455215	+	0.890382i	$0.349562\pi$
$150$	28.8131	2.35258
$151$	−14.5029	−1.18023	−0.590114	−	0.807320i	$-0.700917\pi$
$151$	−14.5029	−1.18023	−0.590114	+	0.807320i	$0.700917\pi$
$152$	4.81240	0.390337
$153$	−0.726476	−0.0587321
$154$	15.4338	1.24369
$155$	−10.6054	−0.851848
$156$	−2.59467	−0.207740
$157$	−11.6657	−0.931026	−0.465513	−	0.885041i	$-0.654130\pi$
$157$	−11.6657	−0.931026	−0.465513	+	0.885041i	$0.654130\pi$
$158$	−9.83874	−0.782728
$159$	0.120340	0.00954356
$160$	4.22616	0.334107
$161$	−9.79346	−0.771833
$162$	10.9800	0.862674
$163$	−15.2790	−1.19675	−0.598373	−	0.801218i	$-0.704186\pi$
$163$	−15.2790	−1.19675	−0.598373	+	0.801218i	$0.704186\pi$
$164$	−8.79337	−0.686647
$165$	45.7770	3.56374
$166$	1.75012	0.135835
$167$	2.48824	0.192545	0.0962727	−	0.995355i	$-0.469308\pi$
$167$	2.48824	0.192545	0.0962727	+	0.995355i	$0.469308\pi$
$168$	−7.15216	−0.551801
$169$	−11.6588	−0.896829
$170$	−1.52023	−0.116596
$171$	−9.71898	−0.743229
$172$	−5.42719	−0.413819
$173$	−5.47415	−0.416192	−0.208096	−	0.978108i	$-0.566727\pi$
$173$	−5.47415	−0.416192	−0.208096	+	0.978108i	$0.566727\pi$
$174$	14.6766	1.11263
$175$	−41.0544	−3.10342
$176$	4.83468	0.364428
$177$	−15.9930	−1.20211
$178$	−15.5032	−1.16201
$179$	15.5084	1.15915	0.579577	−	0.814918i	$-0.303218\pi$
$179$	15.5084	1.15915	0.579577	+	0.814918i	$0.303218\pi$
$180$	−8.53504	−0.636164
$181$	−25.4860	−1.89436	−0.947180	−	0.320702i	$-0.896081\pi$
$181$	−25.4860	−1.89436	−0.947180	+	0.320702i	$0.896081\pi$
$182$	3.69704	0.274042
$183$	−9.14856	−0.676281
$184$	−3.06784	−0.226164
$185$	−3.69556	−0.271703
$186$	5.62232	0.412248
$187$	−1.73912	−0.127177
$188$	3.93189	0.286762
$189$	−7.01218	−0.510061
$190$	−20.3380	−1.47547
$191$	3.05773	0.221249	0.110625	−	0.993862i	$-0.464715\pi$
$191$	3.05773	0.221249	0.110625	+	0.993862i	$0.464715\pi$
$192$	−2.24044	−0.161690
$193$	20.0000	1.43963	0.719815	−	0.694166i	$-0.244227\pi$
$193$	20.0000	1.43963	0.719815	+	0.694166i	$0.244227\pi$
$194$	11.5345	0.828126
$195$	10.9655	0.785257
$196$	3.19079	0.227914
$197$	−22.9860	−1.63768	−0.818841	−	0.574020i	$-0.805383\pi$
$197$	−22.9860	−1.63768	−0.818841	+	0.574020i	$0.805383\pi$
$198$	−9.76399	−0.693896
$199$	10.8438	0.768696	0.384348	−	0.923188i	$-0.374426\pi$
$199$	10.8438	0.768696	0.384348	+	0.923188i	$0.374426\pi$
$200$	−12.8604	−0.909371
$201$	10.0439	0.708445
$202$	−5.93612	−0.417664
$203$	−20.9121	−1.46774
$204$	0.805926	0.0564261
$205$	37.1622	2.59552
$206$	−12.1588	−0.847147
$207$	6.19571	0.430632
$208$	1.15811	0.0803004
$209$	−23.2664	−1.60937
$210$	30.2262	2.08581
$211$	13.6646	0.940712	0.470356	−	0.882477i	$-0.344126\pi$
$211$	13.6646	0.940712	0.470356	+	0.882477i	$0.344126\pi$
$212$	−0.0537126	−0.00368899
$213$	15.9821	1.09508
$214$	−9.65014	−0.659670
$215$	22.9362	1.56424
$216$	−2.19659	−0.149459
$217$	−8.01099	−0.543821
$218$	−1.66159	−0.112537
$219$	36.9566	2.49730
$220$	−20.4322	−1.37754
$221$	−0.416592	−0.0280230
$222$	1.95915	0.131489
$223$	−23.0463	−1.54329	−0.771646	−	0.636052i	$-0.780566\pi$
$223$	−23.0463	−1.54329	−0.771646	+	0.636052i	$0.780566\pi$
$224$	3.19230	0.213295
$225$	25.9726	1.73151
$226$	3.07801	0.204746
$227$	26.0769	1.73079	0.865394	−	0.501092i	$-0.167068\pi$
$227$	26.0769	1.73079	0.865394	+	0.501092i	$0.167068\pi$
$228$	10.7819	0.714048
$229$	3.16540	0.209175	0.104588	−	0.994516i	$-0.466648\pi$
$229$	3.16540	0.209175	0.104588	+	0.994516i	$0.466648\pi$
$230$	12.9652	0.854898
$231$	34.5784	2.27509
$232$	−6.55078	−0.430080
$233$	−8.48400	−0.555805	−0.277903	−	0.960609i	$-0.589639\pi$
$233$	−8.48400	−0.555805	−0.277903	+	0.960609i	$0.589639\pi$
$234$	−2.33888	−0.152898
$235$	−16.6168	−1.08396
$236$	7.13835	0.464667
$237$	−22.0431	−1.43185
$238$	−1.14833	−0.0744350
$239$	25.3573	1.64023	0.820113	−	0.572201i	$-0.193910\pi$
$239$	25.3573	1.64023	0.820113	+	0.572201i	$0.193910\pi$
$240$	9.46846	0.611187
$241$	−24.6895	−1.59039	−0.795195	−	0.606353i	$-0.792632\pi$
$241$	−24.6895	−1.59039	−0.795195	+	0.606353i	$0.792632\pi$
$242$	−12.3742	−0.795441
$243$	18.0104	1.15537
$244$	4.08338	0.261411
$245$	−13.4848	−0.861513
$246$	−19.7010	−1.25609
$247$	−5.57328	−0.354620
$248$	−2.50947	−0.159351
$249$	3.92103	0.248485
$250$	33.2195	2.10099
$251$	31.6355	1.99681	0.998407	−	0.0564170i	$-0.0179676\pi$
$251$	31.6355	1.99681	0.998407	+	0.0564170i	$0.0179676\pi$
$252$	−6.44708	−0.406128
$253$	14.8320	0.932480
$254$	16.7539	1.05123
$255$	−3.40597	−0.213290
$256$	1.00000	0.0625000
$257$	−27.1165	−1.69148	−0.845741	−	0.533594i	$-0.820841\pi$
$257$	−27.1165	−1.69148	−0.845741	+	0.533594i	$0.820841\pi$
$258$	−12.1593	−0.757005
$259$	−2.79150	−0.173456
$260$	−4.89436	−0.303535
$261$	13.2298	0.818902
$262$	10.3796	0.641252
$263$	−6.31552	−0.389432	−0.194716	−	0.980860i	$-0.562378\pi$
$263$	−6.31552	−0.389432	−0.194716	+	0.980860i	$0.562378\pi$
$264$	10.8318	0.666652
$265$	0.226998	0.0139444
$266$	−15.3626	−0.941943
$267$	−34.7340	−2.12568
$268$	−4.48302	−0.273844
$269$	6.47273	0.394649	0.197325	−	0.980338i	$-0.436775\pi$
$269$	6.47273	0.394649	0.197325	+	0.980338i	$0.436775\pi$
$270$	9.28315	0.564955
$271$	30.4808	1.85158	0.925789	−	0.378041i	$-0.123402\pi$
$271$	30.4808	1.85158	0.925789	+	0.378041i	$0.123402\pi$
$272$	−0.359718	−0.0218111
$273$	8.28299	0.501309
$274$	−7.02596	−0.424454
$275$	62.1762	3.74936
$276$	−6.87330	−0.413724
$277$	22.9398	1.37832	0.689161	−	0.724608i	$-0.257979\pi$
$277$	22.9398	1.37832	0.689161	+	0.724608i	$0.257979\pi$
$278$	−10.9322	−0.655671
$279$	5.06805	0.303416
$280$	−13.4912	−0.806253
$281$	−2.19073	−0.130688	−0.0653439	−	0.997863i	$-0.520814\pi$
$281$	−2.19073	−0.130688	−0.0653439	+	0.997863i	$0.520814\pi$
$282$	8.80916	0.524578
$283$	−9.33866	−0.555126	−0.277563	−	0.960707i	$-0.589527\pi$
$283$	−9.33866	−0.555126	−0.277563	+	0.960707i	$0.589527\pi$
$284$	−7.13347	−0.423294
$285$	−45.5660	−2.69910
$286$	−5.59909	−0.331081
$287$	28.0711	1.65698
$288$	−2.01957	−0.119004
$289$	−16.8706	−0.992388
$290$	27.6847	1.62570
$291$	25.8423	1.51490
$292$	−16.4952	−0.965311
$293$	10.8236	0.632319	0.316160	−	0.948706i	$-0.397606\pi$
$293$	10.8236	0.632319	0.316160	+	0.948706i	$0.397606\pi$
$294$	7.14878	0.416925
$295$	−30.1678	−1.75644
$296$	−0.874448	−0.0508263
$297$	10.6198	0.616225
$298$	−11.1132	−0.643771
$299$	3.55289	0.205469
$300$	−28.8131	−1.66352
$301$	17.3252	0.998610
$302$	14.5029	0.834547
$303$	−13.2995	−0.764037
$304$	−4.81240	−0.276010
$305$	−17.2570	−0.988134
$306$	0.726476	0.0415298
$307$	−1.28203	−0.0731691	−0.0365846	−	0.999331i	$-0.511648\pi$
$307$	−1.28203	−0.0731691	−0.0365846	+	0.999331i	$0.511648\pi$
$308$	−15.4338	−0.879420
$309$	−27.2412	−1.54970
$310$	10.6054	0.602348
$311$	−26.2231	−1.48697	−0.743487	−	0.668751i	$-0.766829\pi$
$311$	−26.2231	−1.48697	−0.743487	+	0.668751i	$0.766829\pi$
$312$	2.59467	0.146895
$313$	−21.7481	−1.22928	−0.614638	−	0.788810i	$-0.710698\pi$
$313$	−21.7481	−1.22928	−0.614638	+	0.788810i	$0.710698\pi$
$314$	11.6657	0.658335
$315$	27.2464	1.53516
$316$	9.83874	0.553472
$317$	14.6370	0.822098	0.411049	−	0.911613i	$-0.365163\pi$
$317$	14.6370	0.822098	0.411049	+	0.911613i	$0.365163\pi$
$318$	−0.120340	−0.00674832
$319$	31.6710	1.77323
$320$	−4.22616	−0.236250
$321$	−21.6206	−1.20674
$322$	9.79346	0.545768
$323$	1.73111	0.0963213
$324$	−10.9800	−0.610003
$325$	14.8938	0.826160
$326$	15.2790	0.846227
$327$	−3.72269	−0.205865
$328$	8.79337	0.485533
$329$	−12.5518	−0.692002
$330$	−45.7770	−2.51994
$331$	−13.7959	−0.758289	−0.379145	−	0.925337i	$-0.623782\pi$
$331$	−13.7959	−0.758289	−0.379145	+	0.925337i	$0.623782\pi$
$332$	−1.75012	−0.0960501
$333$	1.76601	0.0967768
$334$	−2.48824	−0.136150
$335$	18.9460	1.03513
$336$	7.15216	0.390182
$337$	−20.7483	−1.13023	−0.565117	−	0.825011i	$-0.691169\pi$
$337$	−20.7483	−1.13023	−0.565117	+	0.825011i	$0.691169\pi$
$338$	11.6588	0.634154
$339$	6.89609	0.374544
$340$	1.52023	0.0824458
$341$	12.1325	0.657011
$342$	9.71898	0.525542
$343$	12.1601	0.656586
$344$	5.42719	0.292615
$345$	29.0477	1.56387
$346$	5.47415	0.294292
$347$	32.7747	1.75944	0.879718	−	0.475496i	$-0.157731\pi$
$347$	32.7747	1.75944	0.879718	+	0.475496i	$0.157731\pi$
$348$	−14.6766	−0.786750
$349$	−8.10451	−0.433824	−0.216912	−	0.976191i	$-0.569599\pi$
$349$	−8.10451	−0.433824	−0.216912	+	0.976191i	$0.569599\pi$
$350$	41.0544	2.19445
$351$	2.54389	0.135783
$352$	−4.83468	−0.257689
$353$	−30.7881	−1.63869	−0.819344	−	0.573303i	$-0.805662\pi$
$353$	−30.7881	−1.63869	−0.819344	+	0.573303i	$0.805662\pi$
$354$	15.9930	0.850021
$355$	30.1472	1.60005
$356$	15.5032	0.821668
$357$	−2.57276	−0.136165
$358$	−15.5084	−0.819645
$359$	−24.6486	−1.30090	−0.650452	−	0.759547i	$-0.725420\pi$
$359$	−24.6486	−1.30090	−0.650452	+	0.759547i	$0.725420\pi$
$360$	8.53504	0.449836
$361$	4.15918	0.218904
$362$	25.4860	1.33951
$363$	−27.7235	−1.45511
$364$	−3.69704	−0.193777
$365$	69.7116	3.64887
$366$	9.14856	0.478203
$367$	6.87619	0.358934	0.179467	−	0.983764i	$-0.442563\pi$
$367$	6.87619	0.358934	0.179467	+	0.983764i	$0.442563\pi$
$368$	3.06784	0.159922
$369$	−17.7588	−0.924488
$370$	3.69556	0.192123
$371$	0.171467	0.00890211
$372$	−5.62232	−0.291504
$373$	25.6932	1.33035	0.665173	−	0.746690i	$-0.268358\pi$
$373$	25.6932	1.33035	0.665173	+	0.746690i	$0.268358\pi$
$374$	1.73912	0.0899278
$375$	74.4263	3.84336
$376$	−3.93189	−0.202772
$377$	7.58652	0.390726
$378$	7.01218	0.360668
$379$	12.4152	0.637728	0.318864	−	0.947800i	$-0.396699\pi$
$379$	12.4152	0.637728	0.318864	+	0.947800i	$0.396699\pi$
$380$	20.3380	1.04332
$381$	37.5361	1.92303
$382$	−3.05773	−0.156447
$383$	−5.40838	−0.276355	−0.138178	−	0.990407i	$-0.544125\pi$
$383$	−5.40838	−0.276355	−0.138178	+	0.990407i	$0.544125\pi$
$384$	2.24044	0.114332
$385$	65.2256	3.32420
$386$	−20.0000	−1.01797
$387$	−10.9606	−0.557159
$388$	−11.5345	−0.585573
$389$	−0.438399	−0.0222277	−0.0111139	−	0.999938i	$-0.503538\pi$
$389$	−0.438399	−0.0222277	−0.0111139	+	0.999938i	$0.503538\pi$
$390$	−10.9655	−0.555260
$391$	−1.10355	−0.0558092
$392$	−3.19079	−0.161159
$393$	23.2548	1.17305
$394$	22.9860	1.15802
$395$	−41.5801	−2.09212
$396$	9.76399	0.490659
$397$	−21.1985	−1.06392	−0.531961	−	0.846769i	$-0.678545\pi$
$397$	−21.1985	−1.06392	−0.531961	+	0.846769i	$0.678545\pi$
$398$	−10.8438	−0.543550
$399$	−34.4191	−1.72311
$400$	12.8604	0.643022
$401$	−24.0656	−1.20178	−0.600889	−	0.799333i	$-0.705186\pi$
$401$	−24.0656	−1.20178	−0.600889	+	0.799333i	$0.705186\pi$
$402$	−10.0439	−0.500946
$403$	2.90624	0.144770
$404$	5.93612	0.295333
$405$	46.4035	2.30581
$406$	20.9121	1.03785
$407$	4.22768	0.209558
$408$	−0.805926	−0.0398993
$409$	−26.1273	−1.29191	−0.645957	−	0.763374i	$-0.723541\pi$
$409$	−26.1273	−1.29191	−0.645957	+	0.763374i	$0.723541\pi$
$410$	−37.1622	−1.83531
$411$	−15.7412	−0.776458
$412$	12.1588	0.599023
$413$	−22.7878	−1.12131
$414$	−6.19571	−0.304503
$415$	7.39628	0.363069
$416$	−1.15811	−0.0567810
$417$	−24.4930	−1.19943
$418$	23.2664	1.13800
$419$	−25.3572	−1.23878	−0.619390	−	0.785083i	$-0.712620\pi$
$419$	−25.3572	−1.23878	−0.619390	+	0.785083i	$0.712620\pi$
$420$	−30.2262	−1.47489
$421$	−2.10647	−0.102663	−0.0513316	−	0.998682i	$-0.516347\pi$
$421$	−2.10647	−0.102663	−0.0513316	+	0.998682i	$0.516347\pi$
$422$	−13.6646	−0.665184
$423$	7.94073	0.386091
$424$	0.0537126	0.00260851
$425$	−4.62613	−0.224400
$426$	−15.9821	−0.774336
$427$	−13.0354	−0.630826
$428$	9.65014	0.466457
$429$	−12.5444	−0.605651
$430$	−22.9362	−1.10608
$431$	−18.8166	−0.906364	−0.453182	−	0.891418i	$-0.649711\pi$
$431$	−18.8166	−0.906364	−0.453182	+	0.891418i	$0.649711\pi$
$432$	2.19659	0.105684
$433$	12.7156	0.611073	0.305536	−	0.952180i	$-0.401164\pi$
$433$	12.7156	0.611073	0.305536	+	0.952180i	$0.401164\pi$
$434$	8.01099	0.384540
$435$	62.0258	2.97391
$436$	1.66159	0.0795757
$437$	−14.7636	−0.706241
$438$	−36.9566	−1.76586
$439$	39.4225	1.88154	0.940768	−	0.339052i	$-0.110106\pi$
$439$	39.4225	1.88154	0.940768	+	0.339052i	$0.110106\pi$
$440$	20.4322	0.974065
$441$	6.44404	0.306859
$442$	0.416592	0.0198153
$443$	−3.05850	−0.145314	−0.0726568	−	0.997357i	$-0.523148\pi$
$443$	−3.05850	−0.145314	−0.0726568	+	0.997357i	$0.523148\pi$
$444$	−1.95915	−0.0929771
$445$	−65.5190	−3.10590
$446$	23.0463	1.09127
$447$	−24.8985	−1.17766
$448$	−3.19230	−0.150822
$449$	11.5376	0.544494	0.272247	−	0.962227i	$-0.412233\pi$
$449$	11.5376	0.544494	0.272247	+	0.962227i	$0.412233\pi$
$450$	−25.9726	−1.22436
$451$	−42.5132	−2.00187
$452$	−3.07801	−0.144777
$453$	32.4929	1.52665
$454$	−26.0769	−1.22385
$455$	15.6243	0.732477
$456$	−10.7819	−0.504908
$457$	7.66330	0.358474	0.179237	−	0.983806i	$-0.442637\pi$
$457$	7.66330	0.358474	0.179237	+	0.983806i	$0.442637\pi$
$458$	−3.16540	−0.147909
$459$	−0.790153	−0.0368812
$460$	−12.9652	−0.604504
$461$	−15.9765	−0.744101	−0.372051	−	0.928212i	$-0.621345\pi$
$461$	−15.9765	−0.744101	−0.372051	+	0.928212i	$0.621345\pi$
$462$	−34.5784	−1.60873
$463$	−13.8785	−0.644988	−0.322494	−	0.946572i	$-0.604521\pi$
$463$	−13.8785	−0.644988	−0.322494	+	0.946572i	$0.604521\pi$
$464$	6.55078	0.304112
$465$	23.7608	1.10188
$466$	8.48400	0.393014
$467$	2.96209	0.137069	0.0685345	−	0.997649i	$-0.478168\pi$
$467$	2.96209	0.137069	0.0685345	+	0.997649i	$0.478168\pi$
$468$	2.33888	0.108115
$469$	14.3112	0.660828
$470$	16.6168	0.766476
$471$	26.1363	1.20430
$472$	−7.13835	−0.328569
$473$	−26.2387	−1.20646
$474$	22.0431	1.01247
$475$	−61.8896	−2.83969
$476$	1.14833	0.0526335
$477$	−0.108476	−0.00496679
$478$	−25.3573	−1.15982
$479$	−35.3712	−1.61615	−0.808075	−	0.589080i	$-0.799490\pi$
$479$	−35.3712	−1.61615	−0.808075	+	0.589080i	$0.799490\pi$
$480$	−9.46846	−0.432174
$481$	1.01271	0.0461754
$482$	24.6895	1.12458
$483$	21.9417	0.998380
$484$	12.3742	0.562461
$485$	48.7465	2.21346
$486$	−18.0104	−0.816966
$487$	−3.76095	−0.170425	−0.0852125	−	0.996363i	$-0.527157\pi$
$487$	−3.76095	−0.170425	−0.0852125	+	0.996363i	$0.527157\pi$
$488$	−4.08338	−0.184846
$489$	34.2318	1.54801
$490$	13.4848	0.609182
$491$	−28.2831	−1.27640	−0.638200	−	0.769871i	$-0.720321\pi$
$491$	−28.2831	−1.27640	−0.638200	+	0.769871i	$0.720321\pi$
$492$	19.7010	0.888191
$493$	−2.35643	−0.106128
$494$	5.57328	0.250754
$495$	−41.2642	−1.85469
$496$	2.50947	0.112679
$497$	22.7722	1.02147
$498$	−3.92103	−0.175706
$499$	−34.0033	−1.52220	−0.761098	−	0.648637i	$-0.775339\pi$
$499$	−34.0033	−1.52220	−0.761098	+	0.648637i	$0.775339\pi$
$500$	−33.2195	−1.48562
$501$	−5.57474	−0.249061
$502$	−31.6355	−1.41196
$503$	28.6910	1.27927	0.639633	−	0.768680i	$-0.279086\pi$
$503$	28.6910	1.27927	0.639633	+	0.768680i	$0.279086\pi$
$504$	6.44708	0.287176
$505$	−25.0870	−1.11636
$506$	−14.8320	−0.659363
$507$	26.1208	1.16007
$508$	−16.7539	−0.743333
$509$	21.3339	0.945609	0.472805	−	0.881167i	$-0.343242\pi$
$509$	21.3339	0.945609	0.472805	+	0.881167i	$0.343242\pi$
$510$	3.40597	0.150819
$511$	52.6578	2.32944
$512$	−1.00000	−0.0441942
$513$	−10.5709	−0.466716
$514$	27.1165	1.19606
$515$	−51.3853	−2.26430
$516$	12.1593	0.535283
$517$	19.0094	0.836034
$518$	2.79150	0.122652
$519$	12.2645	0.538352
$520$	4.89436	0.214632
$521$	−35.4810	−1.55445	−0.777226	−	0.629222i	$-0.783374\pi$
$521$	−35.4810	−1.55445	−0.777226	+	0.629222i	$0.783374\pi$
$522$	−13.2298	−0.579051
$523$	−16.2941	−0.712490	−0.356245	−	0.934393i	$-0.615943\pi$
$523$	−16.2941	−0.712490	−0.356245	+	0.934393i	$0.615943\pi$
$524$	−10.3796	−0.453433
$525$	91.9800	4.01434
$526$	6.31552	0.275370
$527$	−0.902701	−0.0393223
$528$	−10.8318	−0.471394
$529$	−13.5884	−0.590799
$530$	−0.226998	−0.00986016
$531$	14.4164	0.625619
$532$	15.3626	0.666055
$533$	−10.1837	−0.441104
$534$	34.7340	1.50309
$535$	−40.7830	−1.76320
$536$	4.48302	0.193637
$537$	−34.7457	−1.49939
$538$	−6.47273	−0.279059
$539$	15.4265	0.664465
$540$	−9.28315	−0.399483
$541$	16.8277	0.723481	0.361741	−	0.932279i	$-0.382183\pi$
$541$	16.8277	0.723481	0.361741	+	0.932279i	$0.382183\pi$
$542$	−30.4808	−1.30926
$543$	57.0999	2.45039
$544$	0.359718	0.0154228
$545$	−7.02215	−0.300796
$546$	−8.28299	−0.354479
$547$	15.1288	0.646859	0.323430	−	0.946252i	$-0.395164\pi$
$547$	15.1288	0.646859	0.323430	+	0.946252i	$0.395164\pi$
$548$	7.02596	0.300134
$549$	8.24667	0.351959
$550$	−62.1762	−2.65120
$551$	−31.5250	−1.34301
$552$	6.87330	0.292547
$553$	−31.4082	−1.33561
$554$	−22.9398	−0.974621
$555$	8.27968	0.351453
$556$	10.9322	0.463630
$557$	21.7052	0.919680	0.459840	−	0.888002i	$-0.347907\pi$
$557$	21.7052	0.919680	0.459840	+	0.888002i	$0.347907\pi$
$558$	−5.06805	−0.214548
$559$	−6.28528	−0.265839
$560$	13.4912	0.570107
$561$	3.89640	0.164506
$562$	2.19073	0.0924103
$563$	−4.24266	−0.178807	−0.0894033	−	0.995996i	$-0.528496\pi$
$563$	−4.24266	−0.178807	−0.0894033	+	0.995996i	$0.528496\pi$
$564$	−8.80916	−0.370933
$565$	13.0082	0.547257
$566$	9.33866	0.392533
$567$	35.0516	1.47203
$568$	7.13347	0.299314
$569$	−36.0825	−1.51266	−0.756330	−	0.654191i	$-0.773009\pi$
$569$	−36.0825	−1.51266	−0.756330	+	0.654191i	$0.773009\pi$
$570$	45.5660	1.90855
$571$	6.97143	0.291745	0.145873	−	0.989303i	$-0.453401\pi$
$571$	6.97143	0.291745	0.145873	+	0.989303i	$0.453401\pi$
$572$	5.59909	0.234110
$573$	−6.85066	−0.286190
$574$	−28.0711	−1.17167
$575$	39.4537	1.64533
$576$	2.01957	0.0841488
$577$	29.7346	1.23787	0.618933	−	0.785444i	$-0.287565\pi$
$577$	29.7346	1.23787	0.618933	+	0.785444i	$0.287565\pi$
$578$	16.8706	0.701725
$579$	−44.8088	−1.86219
$580$	−27.6847	−1.14954
$581$	5.58690	0.231784
$582$	−25.8423	−1.07120
$583$	−0.259683	−0.0107550
$584$	16.4952	0.682578
$585$	−9.88450	−0.408674
$586$	−10.8236	−0.447117
$587$	−29.4548	−1.21573	−0.607865	−	0.794041i	$-0.707974\pi$
$587$	−29.4548	−1.21573	−0.607865	+	0.794041i	$0.707974\pi$
$588$	−7.14878	−0.294811
$589$	−12.0766	−0.497606
$590$	30.1678	1.24199
$591$	51.4987	2.11837
$592$	0.874448	0.0359396
$593$	−15.5405	−0.638170	−0.319085	−	0.947726i	$-0.603376\pi$
$593$	−15.5405	−0.638170	−0.319085	+	0.947726i	$0.603376\pi$
$594$	−10.6198	−0.435737
$595$	−4.85302	−0.198954
$596$	11.1132	0.455215
$597$	−24.2949	−0.994323
$598$	−3.55289	−0.145288
$599$	−4.31322	−0.176233	−0.0881167	−	0.996110i	$-0.528085\pi$
$599$	−4.31322	−0.176233	−0.0881167	+	0.996110i	$0.528085\pi$
$600$	28.8131	1.17629
$601$	3.06059	0.124844	0.0624220	−	0.998050i	$-0.480118\pi$
$601$	3.06059	0.124844	0.0624220	+	0.998050i	$0.480118\pi$
$602$	−17.3252	−0.706124
$603$	−9.05378	−0.368699
$604$	−14.5029	−0.590114
$605$	−52.2952	−2.12610
$606$	13.2995	0.540256
$607$	0.0588208	0.00238746	0.00119373	−	0.999999i	$-0.499620\pi$
$607$	0.0588208	0.00238746	0.00119373	+	0.999999i	$0.499620\pi$
$608$	4.81240	0.195169
$609$	46.8523	1.89855
$610$	17.2570	0.698716
$611$	4.55356	0.184217
$612$	−0.726476	−0.0293660
$613$	31.3608	1.26665	0.633325	−	0.773886i	$-0.281690\pi$
$613$	31.3608	1.26665	0.633325	+	0.773886i	$0.281690\pi$
$614$	1.28203	0.0517384
$615$	−83.2597	−3.35736
$616$	15.4338	0.621844
$617$	−33.2320	−1.33787	−0.668935	−	0.743321i	$-0.733250\pi$
$617$	−33.2320	−1.33787	−0.668935	+	0.743321i	$0.733250\pi$
$618$	27.2412	1.09580
$619$	0.931679	0.0374473	0.0187237	−	0.999825i	$-0.494040\pi$
$619$	0.931679	0.0374473	0.0187237	+	0.999825i	$0.494040\pi$
$620$	−10.6054	−0.425924
$621$	6.73878	0.270418
$622$	26.2231	1.05145
$623$	−49.4909	−1.98281
$624$	−2.59467	−0.103870
$625$	76.0888	3.04355
$626$	21.7481	0.869229
$627$	52.1270	2.08175
$628$	−11.6657	−0.465513
$629$	−0.314554	−0.0125421
$630$	−27.2464	−1.08552
$631$	24.2532	0.965503	0.482752	−	0.875757i	$-0.339637\pi$
$631$	24.2532	0.965503	0.482752	+	0.875757i	$0.339637\pi$
$632$	−9.83874	−0.391364
$633$	−30.6148	−1.21683
$634$	−14.6370	−0.581311
$635$	70.8046	2.80980
$636$	0.120340	0.00477178
$637$	3.69529	0.146413
$638$	−31.6710	−1.25387
$639$	−14.4066	−0.569915
$640$	4.22616	0.167054
$641$	−7.67092	−0.302983	−0.151492	−	0.988459i	$-0.548408\pi$
$641$	−7.67092	−0.302983	−0.151492	+	0.988459i	$0.548408\pi$
$642$	21.6206	0.853295
$643$	−6.05339	−0.238722	−0.119361	−	0.992851i	$-0.538085\pi$
$643$	−6.05339	−0.238722	−0.119361	+	0.992851i	$0.538085\pi$
$644$	−9.79346	−0.385916
$645$	−51.3872	−2.02337
$646$	−1.73111	−0.0681094
$647$	32.9776	1.29648	0.648241	−	0.761435i	$-0.275505\pi$
$647$	32.9776	1.29648	0.648241	+	0.761435i	$0.275505\pi$
$648$	10.9800	0.431337
$649$	34.5117	1.35470
$650$	−14.8938	−0.584183
$651$	17.9481	0.703443
$652$	−15.2790	−0.598373
$653$	−24.3109	−0.951360	−0.475680	−	0.879618i	$-0.657798\pi$
$653$	−24.3109	−0.951360	−0.475680	+	0.879618i	$0.657798\pi$
$654$	3.72269	0.145569
$655$	43.8657	1.71398
$656$	−8.79337	−0.343324
$657$	−33.3133	−1.29968
$658$	12.5518	0.489319
$659$	−8.51171	−0.331569	−0.165785	−	0.986162i	$-0.553016\pi$
$659$	−8.51171	−0.331569	−0.165785	+	0.986162i	$0.553016\pi$
$660$	45.7770	1.78187
$661$	−23.5848	−0.917342	−0.458671	−	0.888606i	$-0.651674\pi$
$661$	−23.5848	−0.917342	−0.458671	+	0.888606i	$0.651674\pi$
$662$	13.7959	0.536192
$663$	0.933350	0.0362483
$664$	1.75012	0.0679177
$665$	−64.9250	−2.51768
$666$	−1.76601	−0.0684315
$667$	20.0967	0.778148
$668$	2.48824	0.0962727
$669$	51.6338	1.99628
$670$	−18.9460	−0.731947
$671$	19.7418	0.762125
$672$	−7.15216	−0.275901
$673$	−5.75333	−0.221774	−0.110887	−	0.993833i	$-0.535369\pi$
$673$	−5.75333	−0.221774	−0.110887	+	0.993833i	$0.535369\pi$
$674$	20.7483	0.799196
$675$	28.2491	1.08731
$676$	−11.6588	−0.448415
$677$	−28.0521	−1.07813	−0.539064	−	0.842265i	$-0.681222\pi$
$677$	−28.0521	−1.07813	−0.539064	+	0.842265i	$0.681222\pi$
$678$	−6.89609	−0.264843
$679$	36.8215	1.41308
$680$	−1.52023	−0.0582980
$681$	−58.4238	−2.23881
$682$	−12.1325	−0.464577
$683$	−9.31798	−0.356542	−0.178271	−	0.983981i	$-0.557050\pi$
$683$	−9.31798	−0.356542	−0.178271	+	0.983981i	$0.557050\pi$
$684$	−9.71898	−0.371615
$685$	−29.6928	−1.13450
$686$	−12.1601	−0.464276
$687$	−7.09188	−0.270572
$688$	−5.42719	−0.206910
$689$	−0.0622050	−0.00236982
$690$	−29.0477	−1.10583
$691$	−50.5423	−1.92272	−0.961361	−	0.275292i	$-0.911225\pi$
$691$	−50.5423	−1.92272	−0.961361	+	0.275292i	$0.911225\pi$
$692$	−5.47415	−0.208096
$693$	−31.1696	−1.18403
$694$	−32.7747	−1.24411
$695$	−46.2014	−1.75252
$696$	14.6766	0.556316
$697$	3.16313	0.119812
$698$	8.10451	0.306760
$699$	19.0079	0.718945
$700$	−41.0544	−1.55171
$701$	−31.3214	−1.18299	−0.591496	−	0.806308i	$-0.701462\pi$
$701$	−31.3214	−1.18299	−0.591496	+	0.806308i	$0.701462\pi$
$702$	−2.54389	−0.0960131
$703$	−4.20819	−0.158715
$704$	4.83468	0.182214
$705$	37.2289	1.40212
$706$	30.7881	1.15873
$707$	−18.9499	−0.712684
$708$	−15.9930	−0.601055
$709$	−44.8013	−1.68255	−0.841275	−	0.540608i	$-0.818194\pi$
$709$	−44.8013	−1.68255	−0.841275	+	0.540608i	$0.818194\pi$
$710$	−30.1472	−1.13140
$711$	19.8700	0.745185
$712$	−15.5032	−0.581007
$713$	7.69864	0.288316
$714$	2.57276	0.0962831
$715$	−23.6627	−0.884933
$716$	15.5084	0.579577
$717$	−56.8115	−2.12166
$718$	24.6486	0.919878
$719$	−1.16417	−0.0434163	−0.0217082	−	0.999764i	$-0.506910\pi$
$719$	−1.16417	−0.0434163	−0.0217082	+	0.999764i	$0.506910\pi$
$720$	−8.53504	−0.318082
$721$	−38.8147	−1.44554
$722$	−4.15918	−0.154789
$723$	55.3153	2.05720
$724$	−25.4860	−0.947180
$725$	84.2460	3.12882
$726$	27.7235	1.02892
$727$	19.7708	0.733260	0.366630	−	0.930367i	$-0.380511\pi$
$727$	19.7708	0.733260	0.366630	+	0.930367i	$0.380511\pi$
$728$	3.69704	0.137021
$729$	−7.41099	−0.274481
$730$	−69.7116	−2.58014
$731$	1.95226	0.0722068
$732$	−9.14856	−0.338141
$733$	15.4406	0.570310	0.285155	−	0.958481i	$-0.407955\pi$
$733$	15.4406	0.570310	0.285155	+	0.958481i	$0.407955\pi$
$734$	−6.87619	−0.253805
$735$	30.2119	1.11438
$736$	−3.06784	−0.113082
$737$	−21.6740	−0.798372
$738$	17.7588	0.653712
$739$	−38.5797	−1.41918	−0.709589	−	0.704616i	$-0.751119\pi$
$739$	−38.5797	−1.41918	−0.709589	+	0.704616i	$0.751119\pi$
$740$	−3.69556	−0.135851
$741$	12.4866	0.458707
$742$	−0.171467	−0.00629474
$743$	−47.6628	−1.74858	−0.874289	−	0.485405i	$-0.838672\pi$
$743$	−47.6628	−1.74858	−0.874289	+	0.485405i	$0.838672\pi$
$744$	5.62232	0.206124
$745$	−46.9662	−1.72071
$746$	−25.6932	−0.940696
$747$	−3.53449	−0.129320
$748$	−1.73912	−0.0635886
$749$	−30.8062	−1.12563
$750$	−74.4263	−2.71767
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	3.93189	0.143381
$753$	−70.8774	−2.58292
$754$	−7.58652	−0.276285
$755$	61.2916	2.23063
$756$	−7.01218	−0.255031
$757$	−19.6029	−0.712481	−0.356240	−	0.934394i	$-0.615942\pi$
$757$	−19.6029	−0.712481	−0.356240	+	0.934394i	$0.615942\pi$
$758$	−12.4152	−0.450942
$759$	−33.2302	−1.20618
$760$	−20.3380	−0.737736
$761$	24.1851	0.876710	0.438355	−	0.898802i	$-0.355561\pi$
$761$	24.1851	0.876710	0.438355	+	0.898802i	$0.355561\pi$
$762$	−37.5361	−1.35979
$763$	−5.30430	−0.192028
$764$	3.05773	0.110625
$765$	3.07020	0.111003
$766$	5.40838	0.195413
$767$	8.26699	0.298504
$768$	−2.24044	−0.0808449
$769$	33.3831	1.20383	0.601913	−	0.798562i	$-0.294405\pi$
$769$	33.3831	1.20383	0.601913	+	0.798562i	$0.294405\pi$
$770$	−65.2256	−2.35057
$771$	60.7529	2.18796
$772$	20.0000	0.719815
$773$	23.0422	0.828771	0.414385	−	0.910101i	$-0.363997\pi$
$773$	23.0422	0.828771	0.414385	+	0.910101i	$0.363997\pi$
$774$	10.9606	0.393971
$775$	32.2729	1.15928
$776$	11.5345	0.414063
$777$	6.25419	0.224368
$778$	0.438399	0.0157174
$779$	42.3172	1.51617
$780$	10.9655	0.392628
$781$	−34.4881	−1.23408
$782$	1.10355	0.0394630
$783$	14.3894	0.514235
$784$	3.19079	0.113957
$785$	49.3012	1.75964
$786$	−23.2548	−0.829471
$787$	20.2871	0.723156	0.361578	−	0.932342i	$-0.382238\pi$
$787$	20.2871	0.723156	0.361578	+	0.932342i	$0.382238\pi$
$788$	−22.9860	−0.818841
$789$	14.1495	0.503737
$790$	41.5801	1.47935
$791$	9.82593	0.349370
$792$	−9.76399	−0.346948
$793$	4.72900	0.167932
$794$	21.1985	0.752306
$795$	−0.508575	−0.0180373
$796$	10.8438	0.384348
$797$	−19.1610	−0.678716	−0.339358	−	0.940657i	$-0.610210\pi$
$797$	−19.1610	−0.678716	−0.339358	+	0.940657i	$0.610210\pi$
$798$	34.4191	1.21842
$799$	−1.41437	−0.0500368
$800$	−12.8604	−0.454685
$801$	31.3098	1.10628
$802$	24.0656	0.849785
$803$	−79.7493	−2.81429
$804$	10.0439	0.354223
$805$	41.3887	1.45876
$806$	−2.90624	−0.102368
$807$	−14.5018	−0.510486
$808$	−5.93612	−0.208832
$809$	−9.17677	−0.322638	−0.161319	−	0.986902i	$-0.551575\pi$
$809$	−9.17677	−0.322638	−0.161319	+	0.986902i	$0.551575\pi$
$810$	−46.4035	−1.63045
$811$	6.94595	0.243905	0.121953	−	0.992536i	$-0.461084\pi$
$811$	6.94595	0.243905	0.121953	+	0.992536i	$0.461084\pi$
$812$	−20.9121	−0.733870
$813$	−68.2904	−2.39505
$814$	−4.22768	−0.148180
$815$	64.5717	2.26185
$816$	0.805926	0.0282131
$817$	26.1178	0.913746
$818$	26.1273	0.913520
$819$	−7.46643	−0.260898
$820$	37.1622	1.29776
$821$	22.7039	0.792371	0.396186	−	0.918170i	$-0.370334\pi$
$821$	22.7039	0.792371	0.396186	+	0.918170i	$0.370334\pi$
$822$	15.7412	0.549039
$823$	−29.5839	−1.03123	−0.515615	−	0.856820i	$-0.672437\pi$
$823$	−29.5839	−1.03123	−0.515615	+	0.856820i	$0.672437\pi$
$824$	−12.1588	−0.423573
$825$	−139.302	−4.84987
$826$	22.7878	0.792888
$827$	0.460859	0.0160256	0.00801281	−	0.999968i	$-0.497449\pi$
$827$	0.460859	0.0160256	0.00801281	+	0.999968i	$0.497449\pi$
$828$	6.19571	0.215316
$829$	−15.9600	−0.554313	−0.277156	−	0.960825i	$-0.589392\pi$
$829$	−15.9600	−0.554313	−0.277156	+	0.960825i	$0.589392\pi$
$830$	−7.39628	−0.256729
$831$	−51.3954	−1.78289
$832$	1.15811	0.0401502
$833$	−1.14779	−0.0397684
$834$	24.4930	0.848123
$835$	−10.5157	−0.363910
$836$	−23.2664	−0.804686
$837$	5.51228	0.190532
$838$	25.3572	0.875950
$839$	−26.6817	−0.921153	−0.460577	−	0.887620i	$-0.652357\pi$
$839$	−26.6817	−0.921153	−0.460577	+	0.887620i	$0.652357\pi$
$840$	30.2262	1.04290
$841$	13.9128	0.479750
$842$	2.10647	0.0725939
$843$	4.90819	0.169047
$844$	13.6646	0.470356
$845$	49.2719	1.69501
$846$	−7.94073	−0.273008
$847$	−39.5020	−1.35731
$848$	−0.0537126	−0.00184450
$849$	20.9227	0.718066
$850$	4.62613	0.158675
$851$	2.68266	0.0919605
$852$	15.9821	0.547538
$853$	42.6969	1.46191	0.730956	−	0.682424i	$-0.239074\pi$
$853$	42.6969	1.46191	0.730956	+	0.682424i	$0.239074\pi$
$854$	13.0354	0.446061
$855$	41.0740	1.40470
$856$	−9.65014	−0.329835
$857$	23.5777	0.805399	0.402699	−	0.915332i	$-0.368072\pi$
$857$	23.5777	0.805399	0.402699	+	0.915332i	$0.368072\pi$
$858$	12.5444	0.428260
$859$	−19.3780	−0.661169	−0.330585	−	0.943776i	$-0.607246\pi$
$859$	−19.3780	−0.661169	−0.330585	+	0.943776i	$0.607246\pi$
$860$	22.9362	0.782118
$861$	−62.8916	−2.14334
$862$	18.8166	0.640896
$863$	23.0764	0.785529	0.392765	−	0.919639i	$-0.371519\pi$
$863$	23.0764	0.785529	0.392765	+	0.919639i	$0.371519\pi$
$864$	−2.19659	−0.0747296
$865$	23.1346	0.786602
$866$	−12.7156	−0.432094
$867$	37.7976	1.28367
$868$	−8.01099	−0.271911
$869$	47.5672	1.61361
$870$	−62.0258	−2.10287
$871$	−5.19183	−0.175918
$872$	−1.66159	−0.0562685
$873$	−23.2947	−0.788405
$874$	14.7636	0.499388
$875$	106.047	3.58503
$876$	36.9566	1.24865
$877$	−26.8866	−0.907897	−0.453948	−	0.891028i	$-0.649985\pi$
$877$	−26.8866	−0.907897	−0.453948	+	0.891028i	$0.649985\pi$
$878$	−39.4225	−1.33045
$879$	−24.2495	−0.817917
$880$	−20.4322	−0.688768
$881$	−56.3640	−1.89895	−0.949476	−	0.313839i	$-0.898385\pi$
$881$	−56.3640	−1.89895	−0.949476	+	0.313839i	$0.898385\pi$
$882$	−6.44404	−0.216982
$883$	39.4854	1.32879	0.664394	−	0.747382i	$-0.268690\pi$
$883$	39.4854	1.32879	0.664394	+	0.747382i	$0.268690\pi$
$884$	−0.416592	−0.0140115
$885$	67.5892	2.27199
$886$	3.05850	0.102752
$887$	21.3940	0.718340	0.359170	−	0.933272i	$-0.383060\pi$
$887$	21.3940	0.718340	0.359170	+	0.933272i	$0.383060\pi$
$888$	1.95915	0.0657447
$889$	53.4835	1.79378
$890$	65.5190	2.19620
$891$	−53.0850	−1.77842
$892$	−23.0463	−0.771646
$893$	−18.9218	−0.633194
$894$	24.8985	0.832730
$895$	−65.5411	−2.19080
$896$	3.19230	0.106647
$897$	−7.96003	−0.265778
$898$	−11.5376	−0.385015
$899$	16.4390	0.548271
$900$	25.9726	0.865753
$901$	0.0193214	0.000643688 0
$902$	42.5132	1.41553
$903$	−38.8162	−1.29172
$904$	3.07801	0.102373
$905$	107.708	3.58034
$906$	−32.4929	−1.07950
$907$	−29.7332	−0.987275	−0.493637	−	0.869668i	$-0.664333\pi$
$907$	−29.7332	−0.987275	−0.493637	+	0.869668i	$0.664333\pi$
$908$	26.0769	0.865394
$909$	11.9884	0.397631
$910$	−15.6243	−0.517939
$911$	−45.7264	−1.51498	−0.757491	−	0.652845i	$-0.773575\pi$
$911$	−45.7264	−1.51498	−0.757491	+	0.652845i	$0.773575\pi$
$912$	10.7819	0.357024
$913$	−8.46126	−0.280027
$914$	−7.66330	−0.253480
$915$	38.6633	1.27817
$916$	3.16540	0.104588
$917$	33.1347	1.09420
$918$	0.790153	0.0260789
$919$	−0.980241	−0.0323352	−0.0161676	−	0.999869i	$-0.505147\pi$
$919$	−0.980241	−0.0323352	−0.0161676	+	0.999869i	$0.505147\pi$
$920$	12.9652	0.427449
$921$	2.87230	0.0946456
$922$	15.9765	0.526159
$923$	−8.26134	−0.271925
$924$	34.5784	1.13755
$925$	11.2458	0.369759
$926$	13.8785	0.456075
$927$	24.5557	0.806514
$928$	−6.55078	−0.215040
$929$	−21.0568	−0.690853	−0.345426	−	0.938446i	$-0.612266\pi$
$929$	−21.0568	−0.690853	−0.345426	+	0.938446i	$0.612266\pi$
$930$	−23.7608	−0.779148
$931$	−15.3554	−0.503252
$932$	−8.48400	−0.277903
$933$	58.7512	1.92343
$934$	−2.96209	−0.0969225
$935$	7.34981	0.240364
$936$	−2.33888	−0.0764488
$937$	29.4872	0.963304	0.481652	−	0.876363i	$-0.340037\pi$
$937$	29.4872	0.963304	0.481652	+	0.876363i	$0.340037\pi$
$938$	−14.3112	−0.467276
$939$	48.7253	1.59009
$940$	−16.6168	−0.541980
$941$	−10.5526	−0.344003	−0.172002	−	0.985097i	$-0.555023\pi$
$941$	−10.5526	−0.344003	−0.172002	+	0.985097i	$0.555023\pi$
$942$	−26.1363	−0.851568
$943$	−26.9766	−0.878480
$944$	7.13835	0.232334
$945$	29.6346	0.964015
$946$	26.2387	0.853095
$947$	16.6377	0.540652	0.270326	−	0.962769i	$-0.412868\pi$
$947$	16.6377	0.540652	0.270326	+	0.962769i	$0.412868\pi$
$948$	−22.0431	−0.715927
$949$	−19.1033	−0.620119
$950$	61.8896	2.00796
$951$	−32.7934	−1.06340
$952$	−1.14833	−0.0372175
$953$	14.6516	0.474611	0.237306	−	0.971435i	$-0.423736\pi$
$953$	14.6516	0.474611	0.237306	+	0.971435i	$0.423736\pi$
$954$	0.108476	0.00351205
$955$	−12.9225	−0.418161
$956$	25.3573	0.820113
$957$	−70.9569	−2.29371
$958$	35.3712	1.14279
$959$	−22.4290	−0.724270
$960$	9.46846	0.305593
$961$	−24.7026	−0.796857
$962$	−1.01271	−0.0326510
$963$	19.4891	0.628029
$964$	−24.6895	−0.795195
$965$	−84.5232	−2.72090
$966$	−21.9417	−0.705961
$967$	−22.9480	−0.737958	−0.368979	−	0.929438i	$-0.620293\pi$
$967$	−22.9480	−0.737958	−0.368979	+	0.929438i	$0.620293\pi$
$968$	−12.3742	−0.397720
$969$	−3.87844	−0.124593
$970$	−48.7465	−1.56516
$971$	−25.2525	−0.810390	−0.405195	−	0.914230i	$-0.632796\pi$
$971$	−25.2525	−0.810390	−0.405195	+	0.914230i	$0.632796\pi$
$972$	18.0104	0.577683
$973$	−34.8990	−1.11881
$974$	3.76095	0.120509
$975$	−33.3687	−1.06865
$976$	4.08338	0.130706
$977$	58.3709	1.86745	0.933725	−	0.357990i	$-0.116538\pi$
$977$	58.3709	1.86745	0.933725	+	0.357990i	$0.116538\pi$
$978$	−34.2318	−1.09461
$979$	74.9530	2.39551
$980$	−13.4848	−0.430757
$981$	3.35570	0.107139
$982$	28.2831	0.902551
$983$	45.3644	1.44690	0.723450	−	0.690377i	$-0.242555\pi$
$983$	45.3644	1.44690	0.723450	+	0.690377i	$0.242555\pi$
$984$	−19.7010	−0.628046
$985$	97.1425	3.09522
$986$	2.35643	0.0750441
$987$	28.1215	0.895117
$988$	−5.57328	−0.177310
$989$	−16.6497	−0.529431
$990$	41.2642	1.31146
$991$	0.287519	0.00913336	0.00456668	−	0.999990i	$-0.498546\pi$
$991$	0.287519	0.00913336	0.00456668	+	0.999990i	$0.498546\pi$
$992$	−2.50947	−0.0796757
$993$	30.9088	0.980861
$994$	−22.7722	−0.722290
$995$	−45.8276	−1.45283
$996$	3.92103	0.124243
$997$	0.993867	0.0314761	0.0157380	−	0.999876i	$-0.494990\pi$
$997$	0.993867	0.0314761	0.0157380	+	0.999876i	$0.494990\pi$
$998$	34.0033	1.07636
$999$	1.92081	0.0607716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.e.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.e.1.3	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.24044 q^{3} +1.00000 q^{4} -4.22616 q^{5} +2.24044 q^{6} -3.19230 q^{7} -1.00000 q^{8} +2.01957 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.24044 q^{3} +1.00000 q^{4} -4.22616 q^{5} +2.24044 q^{6} -3.19230 q^{7} -1.00000 q^{8} +2.01957 q^{9} +4.22616 q^{10} +4.83468 q^{11} -2.24044 q^{12} +1.15811 q^{13} +3.19230 q^{14} +9.46846 q^{15} +1.00000 q^{16} -0.359718 q^{17} -2.01957 q^{18} -4.81240 q^{19} -4.22616 q^{20} +7.15216 q^{21} -4.83468 q^{22} +3.06784 q^{23} +2.24044 q^{24} +12.8604 q^{25} -1.15811 q^{26} +2.19659 q^{27} -3.19230 q^{28} +6.55078 q^{29} -9.46846 q^{30} +2.50947 q^{31} -1.00000 q^{32} -10.8318 q^{33} +0.359718 q^{34} +13.4912 q^{35} +2.01957 q^{36} +0.874448 q^{37} +4.81240 q^{38} -2.59467 q^{39} +4.22616 q^{40} -8.79337 q^{41} -7.15216 q^{42} -5.42719 q^{43} +4.83468 q^{44} -8.53504 q^{45} -3.06784 q^{46} +3.93189 q^{47} -2.24044 q^{48} +3.19079 q^{49} -12.8604 q^{50} +0.805926 q^{51} +1.15811 q^{52} -0.0537126 q^{53} -2.19659 q^{54} -20.4322 q^{55} +3.19230 q^{56} +10.7819 q^{57} -6.55078 q^{58} +7.13835 q^{59} +9.46846 q^{60} +4.08338 q^{61} -2.50947 q^{62} -6.44708 q^{63} +1.00000 q^{64} -4.89436 q^{65} +10.8318 q^{66} -4.48302 q^{67} -0.359718 q^{68} -6.87330 q^{69} -13.4912 q^{70} -7.13347 q^{71} -2.01957 q^{72} -16.4952 q^{73} -0.874448 q^{74} -28.8131 q^{75} -4.81240 q^{76} -15.4338 q^{77} +2.59467 q^{78} +9.83874 q^{79} -4.22616 q^{80} -10.9800 q^{81} +8.79337 q^{82} -1.75012 q^{83} +7.15216 q^{84} +1.52023 q^{85} +5.42719 q^{86} -14.6766 q^{87} -4.83468 q^{88} +15.5032 q^{89} +8.53504 q^{90} -3.69704 q^{91} +3.06784 q^{92} -5.62232 q^{93} -3.93189 q^{94} +20.3380 q^{95} +2.24044 q^{96} -11.5345 q^{97} -3.19079 q^{98} +9.76399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

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