LMFDB - Embedded newform 8034.2.a.ba.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-3.78531$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.78531 q^{5} +1.00000 q^{6} -3.09768 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.78531 q^{5} +1.00000 q^{6} -3.09768 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.78531 q^{10} -1.99141 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.09768 q^{14} -3.78531 q^{15} +1.00000 q^{16} -7.51222 q^{17} -1.00000 q^{18} +6.13877 q^{19} +3.78531 q^{20} +3.09768 q^{21} +1.99141 q^{22} +6.69447 q^{23} +1.00000 q^{24} +9.32855 q^{25} +1.00000 q^{26} -1.00000 q^{27} -3.09768 q^{28} +4.16226 q^{29} +3.78531 q^{30} +3.05022 q^{31} -1.00000 q^{32} +1.99141 q^{33} +7.51222 q^{34} -11.7257 q^{35} +1.00000 q^{36} -0.695449 q^{37} -6.13877 q^{38} +1.00000 q^{39} -3.78531 q^{40} +6.91346 q^{41} -3.09768 q^{42} +5.14209 q^{43} -1.99141 q^{44} +3.78531 q^{45} -6.69447 q^{46} -8.19852 q^{47} -1.00000 q^{48} +2.59560 q^{49} -9.32855 q^{50} +7.51222 q^{51} -1.00000 q^{52} -5.97715 q^{53} +1.00000 q^{54} -7.53812 q^{55} +3.09768 q^{56} -6.13877 q^{57} -4.16226 q^{58} +5.70653 q^{59} -3.78531 q^{60} -9.33645 q^{61} -3.05022 q^{62} -3.09768 q^{63} +1.00000 q^{64} -3.78531 q^{65} -1.99141 q^{66} +0.628166 q^{67} -7.51222 q^{68} -6.69447 q^{69} +11.7257 q^{70} -6.41206 q^{71} -1.00000 q^{72} -5.18377 q^{73} +0.695449 q^{74} -9.32855 q^{75} +6.13877 q^{76} +6.16876 q^{77} -1.00000 q^{78} -5.82259 q^{79} +3.78531 q^{80} +1.00000 q^{81} -6.91346 q^{82} +15.0761 q^{83} +3.09768 q^{84} -28.4361 q^{85} -5.14209 q^{86} -4.16226 q^{87} +1.99141 q^{88} -17.5821 q^{89} -3.78531 q^{90} +3.09768 q^{91} +6.69447 q^{92} -3.05022 q^{93} +8.19852 q^{94} +23.2371 q^{95} +1.00000 q^{96} +2.07965 q^{97} -2.59560 q^{98} -1.99141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - 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
$5$	3.78531	1.69284	0.846420	−	0.532515i	$-0.178753\pi$
$5$	3.78531	1.69284	0.846420	+	0.532515i	$0.178753\pi$
$6$	1.00000	0.408248
$7$	−3.09768	−1.17081	−0.585406	−	0.810740i	$-0.699065\pi$
$7$	−3.09768	−1.17081	−0.585406	+	0.810740i	$0.699065\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.78531	−1.19702
$11$	−1.99141	−0.600434	−0.300217	−	0.953871i	$-0.597059\pi$
$11$	−1.99141	−0.600434	−0.300217	+	0.953871i	$0.597059\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.09768	0.827889
$15$	−3.78531	−0.977362
$16$	1.00000	0.250000
$17$	−7.51222	−1.82198	−0.910991	−	0.412427i	$-0.864681\pi$
$17$	−7.51222	−1.82198	−0.910991	+	0.412427i	$0.864681\pi$
$18$	−1.00000	−0.235702
$19$	6.13877	1.40833	0.704165	−	0.710036i	$-0.251321\pi$
$19$	6.13877	1.40833	0.704165	+	0.710036i	$0.251321\pi$
$20$	3.78531	0.846420
$21$	3.09768	0.675969
$22$	1.99141	0.424571
$23$	6.69447	1.39589	0.697947	−	0.716149i	$-0.254097\pi$
$23$	6.69447	1.39589	0.697947	+	0.716149i	$0.254097\pi$
$24$	1.00000	0.204124
$25$	9.32855	1.86571
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−3.09768	−0.585406
$29$	4.16226	0.772913	0.386457	−	0.922308i	$-0.373699\pi$
$29$	4.16226	0.772913	0.386457	+	0.922308i	$0.373699\pi$
$30$	3.78531	0.691099
$31$	3.05022	0.547836	0.273918	−	0.961753i	$-0.411680\pi$
$31$	3.05022	0.547836	0.273918	+	0.961753i	$0.411680\pi$
$32$	−1.00000	−0.176777
$33$	1.99141	0.346661
$34$	7.51222	1.28834
$35$	−11.7257	−1.98200
$36$	1.00000	0.166667
$37$	−0.695449	−0.114331	−0.0571656	−	0.998365i	$-0.518206\pi$
$37$	−0.695449	−0.114331	−0.0571656	+	0.998365i	$0.518206\pi$
$38$	−6.13877	−0.995840
$39$	1.00000	0.160128
$40$	−3.78531	−0.598510
$41$	6.91346	1.07970	0.539850	−	0.841761i	$-0.318481\pi$
$41$	6.91346	1.07970	0.539850	+	0.841761i	$0.318481\pi$
$42$	−3.09768	−0.477982
$43$	5.14209	0.784162	0.392081	−	0.919931i	$-0.371755\pi$
$43$	5.14209	0.784162	0.392081	+	0.919931i	$0.371755\pi$
$44$	−1.99141	−0.300217
$45$	3.78531	0.564280
$46$	−6.69447	−0.987046
$47$	−8.19852	−1.19588	−0.597938	−	0.801542i	$-0.704013\pi$
$47$	−8.19852	−1.19588	−0.597938	+	0.801542i	$0.704013\pi$
$48$	−1.00000	−0.144338
$49$	2.59560	0.370800
$50$	−9.32855	−1.31926
$51$	7.51222	1.05192
$52$	−1.00000	−0.138675
$53$	−5.97715	−0.821025	−0.410512	−	0.911855i	$-0.634650\pi$
$53$	−5.97715	−0.821025	−0.410512	+	0.911855i	$0.634650\pi$
$54$	1.00000	0.136083
$55$	−7.53812	−1.01644
$56$	3.09768	0.413944
$57$	−6.13877	−0.813100
$58$	−4.16226	−0.546532
$59$	5.70653	0.742927	0.371463	−	0.928448i	$-0.378856\pi$
$59$	5.70653	0.742927	0.371463	+	0.928448i	$0.378856\pi$
$60$	−3.78531	−0.488681
$61$	−9.33645	−1.19541	−0.597705	−	0.801716i	$-0.703921\pi$
$61$	−9.33645	−1.19541	−0.597705	+	0.801716i	$0.703921\pi$
$62$	−3.05022	−0.387378
$63$	−3.09768	−0.390271
$64$	1.00000	0.125000
$65$	−3.78531	−0.469510
$66$	−1.99141	−0.245126
$67$	0.628166	0.0767427	0.0383713	−	0.999264i	$-0.487783\pi$
$67$	0.628166	0.0767427	0.0383713	+	0.999264i	$0.487783\pi$
$68$	−7.51222	−0.910991
$69$	−6.69447	−0.805920
$70$	11.7257	1.40148
$71$	−6.41206	−0.760972	−0.380486	−	0.924787i	$-0.624243\pi$
$71$	−6.41206	−0.760972	−0.380486	+	0.924787i	$0.624243\pi$
$72$	−1.00000	−0.117851
$73$	−5.18377	−0.606714	−0.303357	−	0.952877i	$-0.598108\pi$
$73$	−5.18377	−0.606714	−0.303357	+	0.952877i	$0.598108\pi$
$74$	0.695449	0.0808443
$75$	−9.32855	−1.07717
$76$	6.13877	0.704165
$77$	6.16876	0.702995
$78$	−1.00000	−0.113228
$79$	−5.82259	−0.655093	−0.327547	−	0.944835i	$-0.606222\pi$
$79$	−5.82259	−0.655093	−0.327547	+	0.944835i	$0.606222\pi$
$80$	3.78531	0.423210
$81$	1.00000	0.111111
$82$	−6.91346	−0.763463
$83$	15.0761	1.65482	0.827408	−	0.561601i	$-0.189814\pi$
$83$	15.0761	1.65482	0.827408	+	0.561601i	$0.189814\pi$
$84$	3.09768	0.337984
$85$	−28.4361	−3.08432
$86$	−5.14209	−0.554486
$87$	−4.16226	−0.446242
$88$	1.99141	0.212285
$89$	−17.5821	−1.86370	−0.931848	−	0.362848i	$-0.881805\pi$
$89$	−17.5821	−1.86370	−0.931848	+	0.362848i	$0.881805\pi$
$90$	−3.78531	−0.399006
$91$	3.09768	0.324725
$92$	6.69447	0.697947
$93$	−3.05022	−0.316293
$94$	8.19852	0.845612
$95$	23.2371	2.38408
$96$	1.00000	0.102062
$97$	2.07965	0.211157	0.105578	−	0.994411i	$-0.466331\pi$
$97$	2.07965	0.211157	0.105578	+	0.994411i	$0.466331\pi$
$98$	−2.59560	−0.262195
$99$	−1.99141	−0.200145
$100$	9.32855	0.932855
$101$	8.79029	0.874666	0.437333	−	0.899300i	$-0.355923\pi$
$101$	8.79029	0.874666	0.437333	+	0.899300i	$0.355923\pi$
$102$	−7.51222	−0.743821
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	11.7257	1.14431
$106$	5.97715	0.580552
$107$	9.62233	0.930226	0.465113	−	0.885251i	$-0.346014\pi$
$107$	9.62233	0.930226	0.465113	+	0.885251i	$0.346014\pi$
$108$	−1.00000	−0.0962250
$109$	−0.639705	−0.0612726	−0.0306363	−	0.999531i	$-0.509753\pi$
$109$	−0.639705	−0.0612726	−0.0306363	+	0.999531i	$0.509753\pi$
$110$	7.53812	0.718731
$111$	0.695449	0.0660091
$112$	−3.09768	−0.292703
$113$	−3.39898	−0.319750	−0.159875	−	0.987137i	$-0.551109\pi$
$113$	−3.39898	−0.319750	−0.159875	+	0.987137i	$0.551109\pi$
$114$	6.13877	0.574948
$115$	25.3406	2.36303
$116$	4.16226	0.386457
$117$	−1.00000	−0.0924500
$118$	−5.70653	−0.525328
$119$	23.2704	2.13320
$120$	3.78531	0.345550
$121$	−7.03427	−0.639479
$122$	9.33645	0.845282
$123$	−6.91346	−0.623365
$124$	3.05022	0.273918
$125$	16.3849	1.46551
$126$	3.09768	0.275963
$127$	−1.57275	−0.139559	−0.0697796	−	0.997562i	$-0.522230\pi$
$127$	−1.57275	−0.139559	−0.0697796	+	0.997562i	$0.522230\pi$
$128$	−1.00000	−0.0883883
$129$	−5.14209	−0.452736
$130$	3.78531	0.331993
$131$	9.95245	0.869549	0.434775	−	0.900539i	$-0.356828\pi$
$131$	9.95245	0.869549	0.434775	+	0.900539i	$0.356828\pi$
$132$	1.99141	0.173330
$133$	−19.0159	−1.64889
$134$	−0.628166	−0.0542653
$135$	−3.78531	−0.325787
$136$	7.51222	0.644168
$137$	−20.7496	−1.77275	−0.886377	−	0.462964i	$-0.846786\pi$
$137$	−20.7496	−1.77275	−0.886377	+	0.462964i	$0.846786\pi$
$138$	6.69447	0.569872
$139$	18.3189	1.55379	0.776894	−	0.629631i	$-0.216794\pi$
$139$	18.3189	1.55379	0.776894	+	0.629631i	$0.216794\pi$
$140$	−11.7257	−0.990999
$141$	8.19852	0.690440
$142$	6.41206	0.538088
$143$	1.99141	0.166530
$144$	1.00000	0.0833333
$145$	15.7554	1.30842
$146$	5.18377	0.429012
$147$	−2.59560	−0.214082
$148$	−0.695449	−0.0571656
$149$	−0.0161712	−0.00132479	−0.000662397	−	1.00000i	$-0.500211\pi$
$149$	−0.0161712	−0.00132479	−0.000662397		1.00000i	$0.500211\pi$
$150$	9.32855	0.761673
$151$	8.80074	0.716194	0.358097	−	0.933684i	$-0.383426\pi$
$151$	8.80074	0.716194	0.358097	+	0.933684i	$0.383426\pi$
$152$	−6.13877	−0.497920
$153$	−7.51222	−0.607327
$154$	−6.16876	−0.497093
$155$	11.5460	0.927399
$156$	1.00000	0.0800641
$157$	−8.35461	−0.666770	−0.333385	−	0.942791i	$-0.608191\pi$
$157$	−8.35461	−0.666770	−0.333385	+	0.942791i	$0.608191\pi$
$158$	5.82259	0.463221
$159$	5.97715	0.474019
$160$	−3.78531	−0.299255
$161$	−20.7373	−1.63433
$162$	−1.00000	−0.0785674
$163$	−22.9785	−1.79982	−0.899909	−	0.436078i	$-0.856367\pi$
$163$	−22.9785	−1.79982	−0.899909	+	0.436078i	$0.856367\pi$
$164$	6.91346	0.539850
$165$	7.53812	0.586842
$166$	−15.0761	−1.17013
$167$	22.5862	1.74778	0.873888	−	0.486127i	$-0.161591\pi$
$167$	22.5862	1.74778	0.873888	+	0.486127i	$0.161591\pi$
$168$	−3.09768	−0.238991
$169$	1.00000	0.0769231
$170$	28.4361	2.18095
$171$	6.13877	0.469443
$172$	5.14209	0.392081
$173$	16.2875	1.23832	0.619158	−	0.785267i	$-0.287474\pi$
$173$	16.2875	1.23832	0.619158	+	0.785267i	$0.287474\pi$
$174$	4.16226	0.315540
$175$	−28.8968	−2.18440
$176$	−1.99141	−0.150109
$177$	−5.70653	−0.428929
$178$	17.5821	1.31783
$179$	7.52632	0.562543	0.281272	−	0.959628i	$-0.409244\pi$
$179$	7.52632	0.562543	0.281272	+	0.959628i	$0.409244\pi$
$180$	3.78531	0.282140
$181$	−9.82936	−0.730610	−0.365305	−	0.930888i	$-0.619035\pi$
$181$	−9.82936	−0.730610	−0.365305	+	0.930888i	$0.619035\pi$
$182$	−3.09768	−0.229615
$183$	9.33645	0.690170
$184$	−6.69447	−0.493523
$185$	−2.63249	−0.193544
$186$	3.05022	0.223653
$187$	14.9599	1.09398
$188$	−8.19852	−0.597938
$189$	3.09768	0.225323
$190$	−23.2371	−1.68580
$191$	−0.940593	−0.0680589	−0.0340295	−	0.999421i	$-0.510834\pi$
$191$	−0.940593	−0.0680589	−0.0340295	+	0.999421i	$0.510834\pi$
$192$	−1.00000	−0.0721688
$193$	23.5134	1.69253	0.846267	−	0.532759i	$-0.178845\pi$
$193$	23.5134	1.69253	0.846267	+	0.532759i	$0.178845\pi$
$194$	−2.07965	−0.149310
$195$	3.78531	0.271071
$196$	2.59560	0.185400
$197$	24.1507	1.72066	0.860331	−	0.509735i	$-0.170257\pi$
$197$	24.1507	1.72066	0.860331	+	0.509735i	$0.170257\pi$
$198$	1.99141	0.141524
$199$	26.5695	1.88346	0.941732	−	0.336365i	$-0.109197\pi$
$199$	26.5695	1.88346	0.941732	+	0.336365i	$0.109197\pi$
$200$	−9.32855	−0.659628
$201$	−0.628166	−0.0443074
$202$	−8.79029	−0.618483
$203$	−12.8934	−0.904936
$204$	7.51222	0.525961
$205$	26.1696	1.82776
$206$	−1.00000	−0.0696733
$207$	6.69447	0.465298
$208$	−1.00000	−0.0693375
$209$	−12.2248	−0.845609
$210$	−11.7257	−0.809147
$211$	20.4472	1.40764	0.703821	−	0.710377i	$-0.251476\pi$
$211$	20.4472	1.40764	0.703821	+	0.710377i	$0.251476\pi$
$212$	−5.97715	−0.410512
$213$	6.41206	0.439347
$214$	−9.62233	−0.657769
$215$	19.4644	1.32746
$216$	1.00000	0.0680414
$217$	−9.44860	−0.641413
$218$	0.639705	0.0433263
$219$	5.18377	0.350287
$220$	−7.53812	−0.508220
$221$	7.51222	0.505327
$222$	−0.695449	−0.0466755
$223$	19.4070	1.29959	0.649793	−	0.760111i	$-0.274855\pi$
$223$	19.4070	1.29959	0.649793	+	0.760111i	$0.274855\pi$
$224$	3.09768	0.206972
$225$	9.32855	0.621903
$226$	3.39898	0.226097
$227$	−15.5048	−1.02909	−0.514544	−	0.857464i	$-0.672039\pi$
$227$	−15.5048	−1.02909	−0.514544	+	0.857464i	$0.672039\pi$
$228$	−6.13877	−0.406550
$229$	23.4503	1.54964	0.774818	−	0.632184i	$-0.217841\pi$
$229$	23.4503	1.54964	0.774818	+	0.632184i	$0.217841\pi$
$230$	−25.3406	−1.67091
$231$	−6.16876	−0.405875
$232$	−4.16226	−0.273266
$233$	−1.15040	−0.0753649	−0.0376825	−	0.999290i	$-0.511998\pi$
$233$	−1.15040	−0.0753649	−0.0376825	+	0.999290i	$0.511998\pi$
$234$	1.00000	0.0653720
$235$	−31.0339	−2.02443
$236$	5.70653	0.371463
$237$	5.82259	0.378218
$238$	−23.2704	−1.50840
$239$	22.2279	1.43780	0.718901	−	0.695112i	$-0.244645\pi$
$239$	22.2279	1.43780	0.718901	+	0.695112i	$0.244645\pi$
$240$	−3.78531	−0.244341
$241$	−0.626194	−0.0403367	−0.0201684	−	0.999797i	$-0.506420\pi$
$241$	−0.626194	−0.0403367	−0.0201684	+	0.999797i	$0.506420\pi$
$242$	7.03427	0.452180
$243$	−1.00000	−0.0641500
$244$	−9.33645	−0.597705
$245$	9.82515	0.627706
$246$	6.91346	0.440786
$247$	−6.13877	−0.390601
$248$	−3.05022	−0.193689
$249$	−15.0761	−0.955409
$250$	−16.3849	−1.03627
$251$	−10.8422	−0.684355	−0.342178	−	0.939635i	$-0.611164\pi$
$251$	−10.8422	−0.684355	−0.342178	+	0.939635i	$0.611164\pi$
$252$	−3.09768	−0.195135
$253$	−13.3315	−0.838143
$254$	1.57275	0.0986833
$255$	28.4361	1.78074
$256$	1.00000	0.0625000
$257$	−27.6196	−1.72286	−0.861432	−	0.507874i	$-0.830432\pi$
$257$	−27.6196	−1.72286	−0.861432	+	0.507874i	$0.830432\pi$
$258$	5.14209	0.320133
$259$	2.15428	0.133860
$260$	−3.78531	−0.234755
$261$	4.16226	0.257638
$262$	−9.95245	−0.614864
$263$	−15.2570	−0.940786	−0.470393	−	0.882457i	$-0.655888\pi$
$263$	−15.2570	−0.940786	−0.470393	+	0.882457i	$0.655888\pi$
$264$	−1.99141	−0.122563
$265$	−22.6254	−1.38986
$266$	19.0159	1.16594
$267$	17.5821	1.07601
$268$	0.628166	0.0383713
$269$	−1.32901	−0.0810311	−0.0405155	−	0.999179i	$-0.512900\pi$
$269$	−1.32901	−0.0810311	−0.0405155	+	0.999179i	$0.512900\pi$
$270$	3.78531	0.230366
$271$	−23.7281	−1.44138	−0.720688	−	0.693259i	$-0.756174\pi$
$271$	−23.7281	−1.44138	−0.720688	+	0.693259i	$0.756174\pi$
$272$	−7.51222	−0.455495
$273$	−3.09768	−0.187480
$274$	20.7496	1.25353
$275$	−18.5770	−1.12024
$276$	−6.69447	−0.402960
$277$	20.9041	1.25600	0.628002	−	0.778212i	$-0.283873\pi$
$277$	20.9041	1.25600	0.628002	+	0.778212i	$0.283873\pi$
$278$	−18.3189	−1.09869
$279$	3.05022	0.182612
$280$	11.7257	0.700742
$281$	−7.33988	−0.437861	−0.218930	−	0.975740i	$-0.570257\pi$
$281$	−7.33988	−0.437861	−0.218930	+	0.975740i	$0.570257\pi$
$282$	−8.19852	−0.488215
$283$	−1.97292	−0.117278	−0.0586389	−	0.998279i	$-0.518676\pi$
$283$	−1.97292	−0.117278	−0.0586389	+	0.998279i	$0.518676\pi$
$284$	−6.41206	−0.380486
$285$	−23.2371	−1.37645
$286$	−1.99141	−0.117755
$287$	−21.4157	−1.26413
$288$	−1.00000	−0.0589256
$289$	39.4335	2.31962
$290$	−15.7554	−0.925192
$291$	−2.07965	−0.121911
$292$	−5.18377	−0.303357
$293$	9.65800	0.564226	0.282113	−	0.959381i	$-0.408965\pi$
$293$	9.65800	0.564226	0.282113	+	0.959381i	$0.408965\pi$
$294$	2.59560	0.151379
$295$	21.6010	1.25766
$296$	0.695449	0.0404222
$297$	1.99141	0.115554
$298$	0.0161712	0.000936771 0
$299$	−6.69447	−0.387151
$300$	−9.32855	−0.538584
$301$	−15.9285	−0.918106
$302$	−8.80074	−0.506426
$303$	−8.79029	−0.504989
$304$	6.13877	0.352083
$305$	−35.3413	−2.02364
$306$	7.51222	0.429445
$307$	−14.6185	−0.834324	−0.417162	−	0.908832i	$-0.636975\pi$
$307$	−14.6185	−0.834324	−0.417162	+	0.908832i	$0.636975\pi$
$308$	6.16876	0.351498
$309$	−1.00000	−0.0568880
$310$	−11.5460	−0.655770
$311$	18.8745	1.07027	0.535136	−	0.844766i	$-0.320260\pi$
$311$	18.8745	1.07027	0.535136	+	0.844766i	$0.320260\pi$
$312$	−1.00000	−0.0566139
$313$	22.3554	1.26360	0.631801	−	0.775130i	$-0.282316\pi$
$313$	22.3554	1.26360	0.631801	+	0.775130i	$0.282316\pi$
$314$	8.35461	0.471478
$315$	−11.7257	−0.660666
$316$	−5.82259	−0.327547
$317$	−18.8230	−1.05720	−0.528602	−	0.848870i	$-0.677284\pi$
$317$	−18.8230	−1.05720	−0.528602	+	0.848870i	$0.677284\pi$
$318$	−5.97715	−0.335182
$319$	−8.28879	−0.464083
$320$	3.78531	0.211605
$321$	−9.62233	−0.537066
$322$	20.7373	1.15565
$323$	−46.1158	−2.56595
$324$	1.00000	0.0555556
$325$	−9.32855	−0.517455
$326$	22.9785	1.27266
$327$	0.639705	0.0353758
$328$	−6.91346	−0.381732
$329$	25.3964	1.40015
$330$	−7.53812	−0.414960
$331$	30.7156	1.68828	0.844141	−	0.536121i	$-0.180111\pi$
$331$	30.7156	1.68828	0.844141	+	0.536121i	$0.180111\pi$
$332$	15.0761	0.827408
$333$	−0.695449	−0.0381104
$334$	−22.5862	−1.23586
$335$	2.37780	0.129913
$336$	3.09768	0.168992
$337$	−26.9596	−1.46858	−0.734290	−	0.678836i	$-0.762485\pi$
$337$	−26.9596	−1.46858	−0.734290	+	0.678836i	$0.762485\pi$
$338$	−1.00000	−0.0543928
$339$	3.39898	0.184607
$340$	−28.4361	−1.54216
$341$	−6.07425	−0.328939
$342$	−6.13877	−0.331947
$343$	13.6434	0.736674
$344$	−5.14209	−0.277243
$345$	−25.3406	−1.36429
$346$	−16.2875	−0.875621
$347$	−33.3690	−1.79134	−0.895670	−	0.444720i	$-0.853303\pi$
$347$	−33.3690	−1.79134	−0.895670	+	0.444720i	$0.853303\pi$
$348$	−4.16226	−0.223121
$349$	16.5858	0.887817	0.443909	−	0.896072i	$-0.353591\pi$
$349$	16.5858	0.887817	0.443909	+	0.896072i	$0.353591\pi$
$350$	28.8968	1.54460
$351$	1.00000	0.0533761
$352$	1.99141	0.106143
$353$	16.7491	0.891465	0.445733	−	0.895166i	$-0.352943\pi$
$353$	16.7491	0.891465	0.445733	+	0.895166i	$0.352943\pi$
$354$	5.70653	0.303299
$355$	−24.2716	−1.28820
$356$	−17.5821	−0.931848
$357$	−23.2704	−1.23160
$358$	−7.52632	−0.397778
$359$	25.7189	1.35739	0.678697	−	0.734419i	$-0.262545\pi$
$359$	25.7189	1.35739	0.678697	+	0.734419i	$0.262545\pi$
$360$	−3.78531	−0.199503
$361$	18.6845	0.983394
$362$	9.82936	0.516619
$363$	7.03427	0.369203
$364$	3.09768	0.162362
$365$	−19.6222	−1.02707
$366$	−9.33645	−0.488024
$367$	14.3211	0.747557	0.373779	−	0.927518i	$-0.378062\pi$
$367$	14.3211	0.747557	0.373779	+	0.927518i	$0.378062\pi$
$368$	6.69447	0.348974
$369$	6.91346	0.359900
$370$	2.63249	0.136857
$371$	18.5153	0.961266
$372$	−3.05022	−0.158147
$373$	24.5108	1.26912	0.634561	−	0.772872i	$-0.281181\pi$
$373$	24.5108	1.26912	0.634561	+	0.772872i	$0.281181\pi$
$374$	−14.9599	−0.773560
$375$	−16.3849	−0.846113
$376$	8.19852	0.422806
$377$	−4.16226	−0.214368
$378$	−3.09768	−0.159327
$379$	7.15639	0.367599	0.183800	−	0.982964i	$-0.441160\pi$
$379$	7.15639	0.367599	0.183800	+	0.982964i	$0.441160\pi$
$380$	23.2371	1.19204
$381$	1.57275	0.0805746
$382$	0.940593	0.0481249
$383$	−0.745504	−0.0380935	−0.0190467	−	0.999819i	$-0.506063\pi$
$383$	−0.745504	−0.0380935	−0.0190467	+	0.999819i	$0.506063\pi$
$384$	1.00000	0.0510310
$385$	23.3506	1.19006
$386$	−23.5134	−1.19680
$387$	5.14209	0.261387
$388$	2.07965	0.105578
$389$	19.9258	1.01028	0.505140	−	0.863038i	$-0.331441\pi$
$389$	19.9258	1.01028	0.505140	+	0.863038i	$0.331441\pi$
$390$	−3.78531	−0.191676
$391$	−50.2904	−2.54329
$392$	−2.59560	−0.131098
$393$	−9.95245	−0.502034
$394$	−24.1507	−1.21669
$395$	−22.0403	−1.10897
$396$	−1.99141	−0.100072
$397$	6.58175	0.330329	0.165164	−	0.986266i	$-0.447185\pi$
$397$	6.58175	0.330329	0.165164	+	0.986266i	$0.447185\pi$
$398$	−26.5695	−1.33181
$399$	19.0159	0.951987
$400$	9.32855	0.466428
$401$	25.0372	1.25030	0.625149	−	0.780506i	$-0.285038\pi$
$401$	25.0372	1.25030	0.625149	+	0.780506i	$0.285038\pi$
$402$	0.628166	0.0313301
$403$	−3.05022	−0.151942
$404$	8.79029	0.437333
$405$	3.78531	0.188093
$406$	12.8934	0.639886
$407$	1.38493	0.0686483
$408$	−7.51222	−0.371910
$409$	18.2340	0.901614	0.450807	−	0.892622i	$-0.351136\pi$
$409$	18.2340	0.901614	0.450807	+	0.892622i	$0.351136\pi$
$410$	−26.1696	−1.29242
$411$	20.7496	1.02350
$412$	1.00000	0.0492665
$413$	−17.6770	−0.869827
$414$	−6.69447	−0.329015
$415$	57.0677	2.80134
$416$	1.00000	0.0490290
$417$	−18.3189	−0.897080
$418$	12.2248	0.597936
$419$	31.4533	1.53659	0.768297	−	0.640094i	$-0.221105\pi$
$419$	31.4533	1.53659	0.768297	+	0.640094i	$0.221105\pi$
$420$	11.7257	0.572154
$421$	−17.7470	−0.864933	−0.432467	−	0.901650i	$-0.642357\pi$
$421$	−17.7470	−0.864933	−0.432467	+	0.901650i	$0.642357\pi$
$422$	−20.4472	−0.995354
$423$	−8.19852	−0.398625
$424$	5.97715	0.290276
$425$	−70.0782	−3.39929
$426$	−6.41206	−0.310665
$427$	28.9213	1.39960
$428$	9.62233	0.465113
$429$	−1.99141	−0.0961464
$430$	−19.4644	−0.938657
$431$	−17.6107	−0.848279	−0.424140	−	0.905597i	$-0.639423\pi$
$431$	−17.6107	−0.848279	−0.424140	+	0.905597i	$0.639423\pi$
$432$	−1.00000	−0.0481125
$433$	21.0987	1.01394	0.506970	−	0.861964i	$-0.330766\pi$
$433$	21.0987	1.01394	0.506970	+	0.861964i	$0.330766\pi$
$434$	9.44860	0.453547
$435$	−15.7554	−0.755416
$436$	−0.639705	−0.0306363
$437$	41.0958	1.96588
$438$	−5.18377	−0.247690
$439$	3.92954	0.187547	0.0937734	−	0.995594i	$-0.470107\pi$
$439$	3.92954	0.187547	0.0937734	+	0.995594i	$0.470107\pi$
$440$	7.53812	0.359366
$441$	2.59560	0.123600
$442$	−7.51222	−0.357320
$443$	24.9289	1.18441	0.592205	−	0.805788i	$-0.298258\pi$
$443$	24.9289	1.18441	0.592205	+	0.805788i	$0.298258\pi$
$444$	0.695449	0.0330046
$445$	−66.5536	−3.15494
$446$	−19.4070	−0.918946
$447$	0.0161712	0.000764870 0
$448$	−3.09768	−0.146351
$449$	15.4427	0.728784	0.364392	−	0.931246i	$-0.381277\pi$
$449$	15.4427	0.728784	0.364392	+	0.931246i	$0.381277\pi$
$450$	−9.32855	−0.439752
$451$	−13.7676	−0.648289
$452$	−3.39898	−0.159875
$453$	−8.80074	−0.413495
$454$	15.5048	0.727675
$455$	11.7257	0.549707
$456$	6.13877	0.287474
$457$	21.6250	1.01158	0.505788	−	0.862658i	$-0.331202\pi$
$457$	21.6250	1.01158	0.505788	+	0.862658i	$0.331202\pi$
$458$	−23.4503	−1.09576
$459$	7.51222	0.350640
$460$	25.3406	1.18151
$461$	−22.2887	−1.03809	−0.519043	−	0.854748i	$-0.673712\pi$
$461$	−22.2887	−1.03809	−0.519043	+	0.854748i	$0.673712\pi$
$462$	6.16876	0.286997
$463$	10.6074	0.492969	0.246485	−	0.969147i	$-0.420725\pi$
$463$	10.6074	0.492969	0.246485	+	0.969147i	$0.420725\pi$
$464$	4.16226	0.193228
$465$	−11.5460	−0.535434
$466$	1.15040	0.0532911
$467$	−1.80493	−0.0835224	−0.0417612	−	0.999128i	$-0.513297\pi$
$467$	−1.80493	−0.0835224	−0.0417612	+	0.999128i	$0.513297\pi$
$468$	−1.00000	−0.0462250
$469$	−1.94586	−0.0898512
$470$	31.0339	1.43149
$471$	8.35461	0.384960
$472$	−5.70653	−0.262664
$473$	−10.2400	−0.470837
$474$	−5.82259	−0.267441
$475$	57.2658	2.62754
$476$	23.2704	1.06660
$477$	−5.97715	−0.273675
$478$	−22.2279	−1.01668
$479$	−37.0283	−1.69187	−0.845934	−	0.533288i	$-0.820956\pi$
$479$	−37.0283	−1.69187	−0.845934	+	0.533288i	$0.820956\pi$
$480$	3.78531	0.172775
$481$	0.695449	0.0317097
$482$	0.626194	0.0285224
$483$	20.7373	0.943581
$484$	−7.03427	−0.319739
$485$	7.87212	0.357455
$486$	1.00000	0.0453609
$487$	−29.9059	−1.35516	−0.677582	−	0.735447i	$-0.736972\pi$
$487$	−29.9059	−1.35516	−0.677582	+	0.735447i	$0.736972\pi$
$488$	9.33645	0.422641
$489$	22.9785	1.03913
$490$	−9.82515	−0.443855
$491$	13.9979	0.631715	0.315857	−	0.948807i	$-0.397708\pi$
$491$	13.9979	0.631715	0.315857	+	0.948807i	$0.397708\pi$
$492$	−6.91346	−0.311683
$493$	−31.2679	−1.40823
$494$	6.13877	0.276196
$495$	−7.53812	−0.338813
$496$	3.05022	0.136959
$497$	19.8625	0.890955
$498$	15.0761	0.675576
$499$	−1.26434	−0.0565998	−0.0282999	−	0.999599i	$-0.509009\pi$
$499$	−1.26434	−0.0565998	−0.0282999	+	0.999599i	$0.509009\pi$
$500$	16.3849	0.732755
$501$	−22.5862	−1.00908
$502$	10.8422	0.483912
$503$	−31.4677	−1.40307	−0.701537	−	0.712633i	$-0.747502\pi$
$503$	−31.4677	−1.40307	−0.701537	+	0.712633i	$0.747502\pi$
$504$	3.09768	0.137981
$505$	33.2739	1.48067
$506$	13.3315	0.592656
$507$	−1.00000	−0.0444116
$508$	−1.57275	−0.0697796
$509$	22.3915	0.992484	0.496242	−	0.868184i	$-0.334713\pi$
$509$	22.3915	0.992484	0.496242	+	0.868184i	$0.334713\pi$
$510$	−28.4361	−1.25917
$511$	16.0576	0.710348
$512$	−1.00000	−0.0441942
$513$	−6.13877	−0.271033
$514$	27.6196	1.21825
$515$	3.78531	0.166801
$516$	−5.14209	−0.226368
$517$	16.3266	0.718045
$518$	−2.15428	−0.0946535
$519$	−16.2875	−0.714942
$520$	3.78531	0.165997
$521$	8.92353	0.390947	0.195474	−	0.980709i	$-0.437376\pi$
$521$	8.92353	0.390947	0.195474	+	0.980709i	$0.437376\pi$
$522$	−4.16226	−0.182177
$523$	20.5910	0.900381	0.450191	−	0.892933i	$-0.351356\pi$
$523$	20.5910	0.900381	0.450191	+	0.892933i	$0.351356\pi$
$524$	9.95245	0.434775
$525$	28.8968	1.26116
$526$	15.2570	0.665236
$527$	−22.9139	−0.998147
$528$	1.99141	0.0866652
$529$	21.8160	0.948521
$530$	22.6254	0.982783
$531$	5.70653	0.247642
$532$	−19.0159	−0.824445
$533$	−6.91346	−0.299455
$534$	−17.5821	−0.760851
$535$	36.4235	1.57472
$536$	−0.628166	−0.0271326
$537$	−7.52632	−0.324784
$538$	1.32901	0.0572976
$539$	−5.16892	−0.222641
$540$	−3.78531	−0.162894
$541$	−13.3913	−0.575737	−0.287869	−	0.957670i	$-0.592947\pi$
$541$	−13.3913	−0.575737	−0.287869	+	0.957670i	$0.592947\pi$
$542$	23.7281	1.01921
$543$	9.82936	0.421818
$544$	7.51222	0.322084
$545$	−2.42148	−0.103725
$546$	3.09768	0.132568
$547$	4.44388	0.190007	0.0950033	−	0.995477i	$-0.469714\pi$
$547$	4.44388	0.190007	0.0950033	+	0.995477i	$0.469714\pi$
$548$	−20.7496	−0.886377
$549$	−9.33645	−0.398470
$550$	18.5770	0.792127
$551$	25.5512	1.08852
$552$	6.69447	0.284936
$553$	18.0365	0.766991
$554$	−20.9041	−0.888129
$555$	2.63249	0.111743
$556$	18.3189	0.776894
$557$	−22.9310	−0.971618	−0.485809	−	0.874065i	$-0.661475\pi$
$557$	−22.9310	−0.971618	−0.485809	+	0.874065i	$0.661475\pi$
$558$	−3.05022	−0.129126
$559$	−5.14209	−0.217487
$560$	−11.7257	−0.495500
$561$	−14.9599	−0.631609
$562$	7.33988	0.309614
$563$	19.5396	0.823496	0.411748	−	0.911298i	$-0.364918\pi$
$563$	19.5396	0.823496	0.411748	+	0.911298i	$0.364918\pi$
$564$	8.19852	0.345220
$565$	−12.8662	−0.541285
$566$	1.97292	0.0829279
$567$	−3.09768	−0.130090
$568$	6.41206	0.269044
$569$	21.4904	0.900925	0.450462	−	0.892795i	$-0.351259\pi$
$569$	21.4904	0.900925	0.450462	+	0.892795i	$0.351259\pi$
$570$	23.2371	0.973296
$571$	36.5476	1.52947	0.764735	−	0.644345i	$-0.222870\pi$
$571$	36.5476	1.52947	0.764735	+	0.644345i	$0.222870\pi$
$572$	1.99141	0.0832652
$573$	0.940593	0.0392938
$574$	21.4157	0.893872
$575$	62.4498	2.60433
$576$	1.00000	0.0416667
$577$	19.8309	0.825573	0.412787	−	0.910828i	$-0.364556\pi$
$577$	19.8309	0.825573	0.412787	+	0.910828i	$0.364556\pi$
$578$	−39.4335	−1.64022
$579$	−23.5134	−0.977185
$580$	15.7554	0.654209
$581$	−46.7009	−1.93748
$582$	2.07965	0.0862044
$583$	11.9030	0.492971
$584$	5.18377	0.214506
$585$	−3.78531	−0.156503
$586$	−9.65800	−0.398968
$587$	7.15353	0.295258	0.147629	−	0.989043i	$-0.452836\pi$
$587$	7.15353	0.295258	0.147629	+	0.989043i	$0.452836\pi$
$588$	−2.59560	−0.107041
$589$	18.7246	0.771534
$590$	−21.6010	−0.889298
$591$	−24.1507	−0.993425
$592$	−0.695449	−0.0285828
$593$	−17.2185	−0.707078	−0.353539	−	0.935420i	$-0.615022\pi$
$593$	−17.2185	−0.707078	−0.353539	+	0.935420i	$0.615022\pi$
$594$	−1.99141	−0.0817087
$595$	88.0858	3.61116
$596$	−0.0161712	−0.000662397 0
$597$	−26.5695	−1.08742
$598$	6.69447	0.273757
$599$	−38.9159	−1.59006	−0.795030	−	0.606570i	$-0.792545\pi$
$599$	−38.9159	−1.59006	−0.795030	+	0.606570i	$0.792545\pi$
$600$	9.32855	0.380837
$601$	−39.4760	−1.61026	−0.805129	−	0.593100i	$-0.797904\pi$
$601$	−39.4760	−1.61026	−0.805129	+	0.593100i	$0.797904\pi$
$602$	15.9285	0.649199
$603$	0.628166	0.0255809
$604$	8.80074	0.358097
$605$	−26.6269	−1.08254
$606$	8.79029	0.357081
$607$	−21.5363	−0.874129	−0.437065	−	0.899430i	$-0.643982\pi$
$607$	−21.5363	−0.874129	−0.437065	+	0.899430i	$0.643982\pi$
$608$	−6.13877	−0.248960
$609$	12.8934	0.522465
$610$	35.3413	1.43093
$611$	8.19852	0.331676
$612$	−7.51222	−0.303664
$613$	39.3064	1.58757	0.793786	−	0.608197i	$-0.208107\pi$
$613$	39.3064	1.58757	0.793786	+	0.608197i	$0.208107\pi$
$614$	14.6185	0.589956
$615$	−26.1696	−1.05526
$616$	−6.16876	−0.248546
$617$	−23.0807	−0.929192	−0.464596	−	0.885523i	$-0.653800\pi$
$617$	−23.0807	−0.929192	−0.464596	+	0.885523i	$0.653800\pi$
$618$	1.00000	0.0402259
$619$	11.6374	0.467748	0.233874	−	0.972267i	$-0.424860\pi$
$619$	11.6374	0.467748	0.233874	+	0.972267i	$0.424860\pi$
$620$	11.5460	0.463700
$621$	−6.69447	−0.268640
$622$	−18.8745	−0.756797
$623$	54.4636	2.18204
$624$	1.00000	0.0400320
$625$	15.3791	0.615165
$626$	−22.3554	−0.893502
$627$	12.2248	0.488213
$628$	−8.35461	−0.333385
$629$	5.22437	0.208309
$630$	11.7257	0.467161
$631$	13.7616	0.547841	0.273920	−	0.961752i	$-0.411680\pi$
$631$	13.7616	0.547841	0.273920	+	0.961752i	$0.411680\pi$
$632$	5.82259	0.231610
$633$	−20.4472	−0.812703
$634$	18.8230	0.747556
$635$	−5.95335	−0.236252
$636$	5.97715	0.237009
$637$	−2.59560	−0.102842
$638$	8.28879	0.328156
$639$	−6.41206	−0.253657
$640$	−3.78531	−0.149627
$641$	−10.5027	−0.414833	−0.207417	−	0.978253i	$-0.566506\pi$
$641$	−10.5027	−0.414833	−0.207417	+	0.978253i	$0.566506\pi$
$642$	9.62233	0.379763
$643$	−36.6778	−1.44643	−0.723216	−	0.690622i	$-0.757337\pi$
$643$	−36.6778	−1.44643	−0.723216	+	0.690622i	$0.757337\pi$
$644$	−20.7373	−0.817165
$645$	−19.4644	−0.766410
$646$	46.1158	1.81440
$647$	−31.8916	−1.25379	−0.626895	−	0.779104i	$-0.715674\pi$
$647$	−31.8916	−1.25379	−0.626895	+	0.779104i	$0.715674\pi$
$648$	−1.00000	−0.0392837
$649$	−11.3641	−0.446078
$650$	9.32855	0.365896
$651$	9.44860	0.370320
$652$	−22.9785	−0.899909
$653$	21.2444	0.831359	0.415680	−	0.909511i	$-0.363544\pi$
$653$	21.2444	0.831359	0.415680	+	0.909511i	$0.363544\pi$
$654$	−0.639705	−0.0250144
$655$	37.6731	1.47201
$656$	6.91346	0.269925
$657$	−5.18377	−0.202238
$658$	−25.3964	−0.990053
$659$	−32.4731	−1.26497	−0.632486	−	0.774572i	$-0.717965\pi$
$659$	−32.4731	−1.26497	−0.632486	+	0.774572i	$0.717965\pi$
$660$	7.53812	0.293421
$661$	7.26850	0.282712	0.141356	−	0.989959i	$-0.454854\pi$
$661$	7.26850	0.282712	0.141356	+	0.989959i	$0.454854\pi$
$662$	−30.7156	−1.19380
$663$	−7.51222	−0.291751
$664$	−15.0761	−0.585066
$665$	−71.9811	−2.79131
$666$	0.695449	0.0269481
$667$	27.8642	1.07891
$668$	22.5862	0.873888
$669$	−19.4070	−0.750317
$670$	−2.37780	−0.0918625
$671$	18.5927	0.717765
$672$	−3.09768	−0.119495
$673$	−8.81926	−0.339957	−0.169979	−	0.985448i	$-0.554370\pi$
$673$	−8.81926	−0.339957	−0.169979	+	0.985448i	$0.554370\pi$
$674$	26.9596	1.03844
$675$	−9.32855	−0.359056
$676$	1.00000	0.0384615
$677$	23.8125	0.915187	0.457594	−	0.889161i	$-0.348711\pi$
$677$	23.8125	0.915187	0.457594	+	0.889161i	$0.348711\pi$
$678$	−3.39898	−0.130537
$679$	−6.44209	−0.247225
$680$	28.4361	1.09047
$681$	15.5048	0.594144
$682$	6.07425	0.232595
$683$	22.4760	0.860020	0.430010	−	0.902824i	$-0.358510\pi$
$683$	22.4760	0.860020	0.430010	+	0.902824i	$0.358510\pi$
$684$	6.13877	0.234722
$685$	−78.5435	−3.00099
$686$	−13.6434	−0.520907
$687$	−23.4503	−0.894683
$688$	5.14209	0.196040
$689$	5.97715	0.227711
$690$	25.3406	0.964702
$691$	29.1132	1.10752	0.553759	−	0.832677i	$-0.313193\pi$
$691$	29.1132	1.10752	0.553759	+	0.832677i	$0.313193\pi$
$692$	16.2875	0.619158
$693$	6.16876	0.234332
$694$	33.3690	1.26667
$695$	69.3426	2.63032
$696$	4.16226	0.157770
$697$	−51.9354	−1.96719
$698$	−16.5858	−0.627782
$699$	1.15040	0.0435120
$700$	−28.8968	−1.09220
$701$	16.7388	0.632217	0.316109	−	0.948723i	$-0.397624\pi$
$701$	16.7388	0.632217	0.316109	+	0.948723i	$0.397624\pi$
$702$	−1.00000	−0.0377426
$703$	−4.26920	−0.161016
$704$	−1.99141	−0.0750543
$705$	31.0339	1.16880
$706$	−16.7491	−0.630361
$707$	−27.2295	−1.02407
$708$	−5.70653	−0.214464
$709$	25.3836	0.953303	0.476651	−	0.879092i	$-0.341850\pi$
$709$	25.3836	0.953303	0.476651	+	0.879092i	$0.341850\pi$
$710$	24.2716	0.910898
$711$	−5.82259	−0.218364
$712$	17.5821	0.658916
$713$	20.4196	0.764721
$714$	23.2704	0.870874
$715$	7.53812	0.281910
$716$	7.52632	0.281272
$717$	−22.2279	−0.830116
$718$	−25.7189	−0.959822
$719$	−32.2426	−1.20245	−0.601224	−	0.799081i	$-0.705320\pi$
$719$	−32.2426	−1.20245	−0.601224	+	0.799081i	$0.705320\pi$
$720$	3.78531	0.141070
$721$	−3.09768	−0.115364
$722$	−18.6845	−0.695364
$723$	0.626194	0.0232884
$724$	−9.82936	−0.365305
$725$	38.8279	1.44203
$726$	−7.03427	−0.261066
$727$	−38.8037	−1.43915	−0.719576	−	0.694414i	$-0.755664\pi$
$727$	−38.8037	−1.43915	−0.719576	+	0.694414i	$0.755664\pi$
$728$	−3.09768	−0.114808
$729$	1.00000	0.0370370
$730$	19.6222	0.726249
$731$	−38.6285	−1.42873
$732$	9.33645	0.345085
$733$	33.8085	1.24874	0.624372	−	0.781127i	$-0.285355\pi$
$733$	33.8085	1.24874	0.624372	+	0.781127i	$0.285355\pi$
$734$	−14.3211	−0.528603
$735$	−9.82515	−0.362406
$736$	−6.69447	−0.246762
$737$	−1.25094	−0.0460789
$738$	−6.91346	−0.254488
$739$	12.3286	0.453515	0.226758	−	0.973951i	$-0.427187\pi$
$739$	12.3286	0.453515	0.226758	+	0.973951i	$0.427187\pi$
$740$	−2.63249	−0.0967722
$741$	6.13877	0.225513
$742$	−18.5153	−0.679717
$743$	5.10838	0.187408	0.0937042	−	0.995600i	$-0.470129\pi$
$743$	5.10838	0.187408	0.0937042	+	0.995600i	$0.470129\pi$
$744$	3.05022	0.111827
$745$	−0.0612128	−0.00224267
$746$	−24.5108	−0.897405
$747$	15.0761	0.551606
$748$	14.9599	0.546990
$749$	−29.8069	−1.08912
$750$	16.3849	0.598292
$751$	−35.7973	−1.30626	−0.653132	−	0.757244i	$-0.726545\pi$
$751$	−35.7973	−1.30626	−0.653132	+	0.757244i	$0.726545\pi$
$752$	−8.19852	−0.298969
$753$	10.8422	0.395113
$754$	4.16226	0.151581
$755$	33.3135	1.21240
$756$	3.09768	0.112661
$757$	46.0475	1.67363	0.836813	−	0.547488i	$-0.184416\pi$
$757$	46.0475	1.67363	0.836813	+	0.547488i	$0.184416\pi$
$758$	−7.15639	−0.259932
$759$	13.3315	0.483902
$760$	−23.2371	−0.842899
$761$	30.1154	1.09168	0.545841	−	0.837889i	$-0.316210\pi$
$761$	30.1154	1.09168	0.545841	+	0.837889i	$0.316210\pi$
$762$	−1.57275	−0.0569748
$763$	1.98160	0.0717387
$764$	−0.940593	−0.0340295
$765$	−28.4361	−1.02811
$766$	0.745504	0.0269361
$767$	−5.70653	−0.206051
$768$	−1.00000	−0.0360844
$769$	−3.24995	−0.117196	−0.0585981	−	0.998282i	$-0.518663\pi$
$769$	−3.24995	−0.117196	−0.0585981	+	0.998282i	$0.518663\pi$
$770$	−23.3506	−0.841499
$771$	27.6196	0.994695
$772$	23.5134	0.846267
$773$	−19.3295	−0.695233	−0.347617	−	0.937637i	$-0.613009\pi$
$773$	−19.3295	−0.695233	−0.347617	+	0.937637i	$0.613009\pi$
$774$	−5.14209	−0.184829
$775$	28.4541	1.02210
$776$	−2.07965	−0.0746552
$777$	−2.15428	−0.0772842
$778$	−19.9258	−0.714375
$779$	42.4401	1.52057
$780$	3.78531	0.135536
$781$	12.7691	0.456913
$782$	50.2904	1.79838
$783$	−4.16226	−0.148747
$784$	2.59560	0.0927001
$785$	−31.6248	−1.12874
$786$	9.95245	0.354992
$787$	−6.83414	−0.243611	−0.121805	−	0.992554i	$-0.538868\pi$
$787$	−6.83414	−0.243611	−0.121805	+	0.992554i	$0.538868\pi$
$788$	24.1507	0.860331
$789$	15.2570	0.543163
$790$	22.0403	0.784159
$791$	10.5290	0.374367
$792$	1.99141	0.0707618
$793$	9.33645	0.331547
$794$	−6.58175	−0.233578
$795$	22.6254	0.802439
$796$	26.5695	0.941732
$797$	37.5899	1.33150	0.665752	−	0.746173i	$-0.268111\pi$
$797$	37.5899	1.33150	0.665752	+	0.746173i	$0.268111\pi$
$798$	−19.0159	−0.673156
$799$	61.5891	2.17886
$800$	−9.32855	−0.329814
$801$	−17.5821	−0.621232
$802$	−25.0372	−0.884094
$803$	10.3230	0.364292
$804$	−0.628166	−0.0221537
$805$	−78.4971	−2.76666
$806$	3.05022	0.107439
$807$	1.32901	0.0467833
$808$	−8.79029	−0.309241
$809$	10.1718	0.357620	0.178810	−	0.983884i	$-0.442775\pi$
$809$	10.1718	0.357620	0.178810	+	0.983884i	$0.442775\pi$
$810$	−3.78531	−0.133002
$811$	30.6570	1.07651	0.538257	−	0.842781i	$-0.319083\pi$
$811$	30.6570	1.07651	0.538257	+	0.842781i	$0.319083\pi$
$812$	−12.8934	−0.452468
$813$	23.7281	0.832179
$814$	−1.38493	−0.0485417
$815$	−86.9808	−3.04680
$816$	7.51222	0.262980
$817$	31.5661	1.10436
$818$	−18.2340	−0.637537
$819$	3.09768	0.108242
$820$	26.1696	0.913880
$821$	−48.2456	−1.68378	−0.841892	−	0.539646i	$-0.818558\pi$
$821$	−48.2456	−1.68378	−0.841892	+	0.539646i	$0.818558\pi$
$822$	−20.7496	−0.723724
$823$	46.0802	1.60626	0.803128	−	0.595807i	$-0.203168\pi$
$823$	46.0802	1.60626	0.803128	+	0.595807i	$0.203168\pi$
$824$	−1.00000	−0.0348367
$825$	18.5770	0.646769
$826$	17.6770	0.615061
$827$	27.8281	0.967679	0.483840	−	0.875157i	$-0.339242\pi$
$827$	27.8281	0.967679	0.483840	+	0.875157i	$0.339242\pi$
$828$	6.69447	0.232649
$829$	−10.5642	−0.366912	−0.183456	−	0.983028i	$-0.558728\pi$
$829$	−10.5642	−0.366912	−0.183456	+	0.983028i	$0.558728\pi$
$830$	−57.0677	−1.98085
$831$	−20.9041	−0.725154
$832$	−1.00000	−0.0346688
$833$	−19.4987	−0.675591
$834$	18.3189	0.634331
$835$	85.4959	2.95871
$836$	−12.2248	−0.422805
$837$	−3.05022	−0.105431
$838$	−31.4533	−1.08654
$839$	−40.4266	−1.39568	−0.697841	−	0.716253i	$-0.745856\pi$
$839$	−40.4266	−1.39568	−0.697841	+	0.716253i	$0.745856\pi$
$840$	−11.7257	−0.404574
$841$	−11.6756	−0.402605
$842$	17.7470	0.611600
$843$	7.33988	0.252799
$844$	20.4472	0.703821
$845$	3.78531	0.130219
$846$	8.19852	0.281871
$847$	21.7899	0.748710
$848$	−5.97715	−0.205256
$849$	1.97292	0.0677104
$850$	70.0782	2.40366
$851$	−4.65567	−0.159594
$852$	6.41206	0.219674
$853$	−8.79975	−0.301298	−0.150649	−	0.988587i	$-0.548136\pi$
$853$	−8.79975	−0.301298	−0.150649	+	0.988587i	$0.548136\pi$
$854$	−28.9213	−0.989667
$855$	23.2371	0.794693
$856$	−9.62233	−0.328884
$857$	−11.7712	−0.402096	−0.201048	−	0.979581i	$-0.564435\pi$
$857$	−11.7712	−0.402096	−0.201048	+	0.979581i	$0.564435\pi$
$858$	1.99141	0.0679858
$859$	47.8822	1.63372	0.816859	−	0.576837i	$-0.195713\pi$
$859$	47.8822	1.63372	0.816859	+	0.576837i	$0.195713\pi$
$860$	19.4644	0.663731
$861$	21.4157	0.729843
$862$	17.6107	0.599824
$863$	43.5993	1.48414	0.742069	−	0.670324i	$-0.233845\pi$
$863$	43.5993	1.48414	0.742069	+	0.670324i	$0.233845\pi$
$864$	1.00000	0.0340207
$865$	61.6532	2.09627
$866$	−21.0987	−0.716963
$867$	−39.4335	−1.33923
$868$	−9.44860	−0.320706
$869$	11.5952	0.393340
$870$	15.7554	0.534160
$871$	−0.628166	−0.0212846
$872$	0.639705	0.0216631
$873$	2.07965	0.0703856
$874$	−41.0958	−1.39009
$875$	−50.7551	−1.71584
$876$	5.18377	0.175143
$877$	37.1295	1.25377	0.626886	−	0.779111i	$-0.284329\pi$
$877$	37.1295	1.25377	0.626886	+	0.779111i	$0.284329\pi$
$878$	−3.92954	−0.132616
$879$	−9.65800	−0.325756
$880$	−7.53812	−0.254110
$881$	−9.10636	−0.306801	−0.153400	−	0.988164i	$-0.549022\pi$
$881$	−9.10636	−0.306801	−0.153400	+	0.988164i	$0.549022\pi$
$882$	−2.59560	−0.0873985
$883$	4.05430	0.136438	0.0682190	−	0.997670i	$-0.478268\pi$
$883$	4.05430	0.136438	0.0682190	+	0.997670i	$0.478268\pi$
$884$	7.51222	0.252663
$885$	−21.6010	−0.726108
$886$	−24.9289	−0.837504
$887$	−2.52846	−0.0848974	−0.0424487	−	0.999099i	$-0.513516\pi$
$887$	−2.52846	−0.0848974	−0.0424487	+	0.999099i	$0.513516\pi$
$888$	−0.695449	−0.0233377
$889$	4.87188	0.163398
$890$	66.5536	2.23088
$891$	−1.99141	−0.0667149
$892$	19.4070	0.649793
$893$	−50.3288	−1.68419
$894$	−0.0161712	−0.000540845 0
$895$	28.4894	0.952296
$896$	3.09768	0.103486
$897$	6.69447	0.223522
$898$	−15.4427	−0.515328
$899$	12.6958	0.423430
$900$	9.32855	0.310952
$901$	44.9017	1.49589
$902$	13.7676	0.458409
$903$	15.9285	0.530069
$904$	3.39898	0.113049
$905$	−37.2071	−1.23681
$906$	8.80074	0.292385
$907$	−33.9238	−1.12642	−0.563210	−	0.826314i	$-0.690434\pi$
$907$	−33.9238	−1.12642	−0.563210	+	0.826314i	$0.690434\pi$
$908$	−15.5048	−0.514544
$909$	8.79029	0.291555
$910$	−11.7257	−0.388702
$911$	11.7450	0.389129	0.194565	−	0.980890i	$-0.437671\pi$
$911$	11.7450	0.389129	0.194565	+	0.980890i	$0.437671\pi$
$912$	−6.13877	−0.203275
$913$	−30.0228	−0.993608
$914$	−21.6250	−0.715293
$915$	35.3413	1.16835
$916$	23.4503	0.774818
$917$	−30.8295	−1.01808
$918$	−7.51222	−0.247940
$919$	20.3117	0.670022	0.335011	−	0.942214i	$-0.391260\pi$
$919$	20.3117	0.670022	0.335011	+	0.942214i	$0.391260\pi$
$920$	−25.3406	−0.835456
$921$	14.6185	0.481697
$922$	22.2887	0.734038
$923$	6.41206	0.211056
$924$	−6.16876	−0.202937
$925$	−6.48753	−0.213309
$926$	−10.6074	−0.348582
$927$	1.00000	0.0328443
$928$	−4.16226	−0.136633
$929$	−36.1337	−1.18551	−0.592755	−	0.805383i	$-0.701960\pi$
$929$	−36.1337	−1.18551	−0.592755	+	0.805383i	$0.701960\pi$
$930$	11.5460	0.378609
$931$	15.9338	0.522209
$932$	−1.15040	−0.0376825
$933$	−18.8745	−0.617922
$934$	1.80493	0.0590592
$935$	56.6280	1.85193
$936$	1.00000	0.0326860
$937$	−53.8613	−1.75957	−0.879785	−	0.475371i	$-0.842314\pi$
$937$	−53.8613	−1.75957	−0.879785	+	0.475371i	$0.842314\pi$
$938$	1.94586	0.0635344
$939$	−22.3554	−0.729541
$940$	−31.0339	−1.01221
$941$	−28.1101	−0.916365	−0.458182	−	0.888858i	$-0.651499\pi$
$941$	−28.1101	−0.916365	−0.458182	+	0.888858i	$0.651499\pi$
$942$	−8.35461	−0.272208
$943$	46.2820	1.50715
$944$	5.70653	0.185732
$945$	11.7257	0.381436
$946$	10.2400	0.332932
$947$	−18.4966	−0.601058	−0.300529	−	0.953773i	$-0.597163\pi$
$947$	−18.4966	−0.601058	−0.300529	+	0.953773i	$0.597163\pi$
$948$	5.82259	0.189109
$949$	5.18377	0.168272
$950$	−57.2658	−1.85795
$951$	18.8230	0.610377
$952$	−23.2704	−0.754199
$953$	−51.4008	−1.66504	−0.832518	−	0.553998i	$-0.813102\pi$
$953$	−51.4008	−1.66504	−0.832518	+	0.553998i	$0.813102\pi$
$954$	5.97715	0.193517
$955$	−3.56043	−0.115213
$956$	22.2279	0.718901
$957$	8.28879	0.267939
$958$	37.0283	1.19633
$959$	64.2754	2.07556
$960$	−3.78531	−0.122170
$961$	−21.6962	−0.699876
$962$	−0.695449	−0.0224222
$963$	9.62233	0.310075
$964$	−0.626194	−0.0201684
$965$	89.0056	2.86519
$966$	−20.7373	−0.667212
$967$	31.7026	1.01949	0.509744	−	0.860326i	$-0.329740\pi$
$967$	31.7026	1.01949	0.509744	+	0.860326i	$0.329740\pi$
$968$	7.03427	0.226090
$969$	46.1158	1.48145
$970$	−7.87212	−0.252759
$971$	4.46345	0.143239	0.0716195	−	0.997432i	$-0.477183\pi$
$971$	4.46345	0.143239	0.0716195	+	0.997432i	$0.477183\pi$
$972$	−1.00000	−0.0320750
$973$	−56.7460	−1.81919
$974$	29.9059	0.958246
$975$	9.32855	0.298753
$976$	−9.33645	−0.298852
$977$	8.96137	0.286700	0.143350	−	0.989672i	$-0.454213\pi$
$977$	8.96137	0.286700	0.143350	+	0.989672i	$0.454213\pi$
$978$	−22.9785	−0.734772
$979$	35.0132	1.11903
$980$	9.82515	0.313853
$981$	−0.639705	−0.0204242
$982$	−13.9979	−0.446690
$983$	−27.9612	−0.891823	−0.445912	−	0.895077i	$-0.647120\pi$
$983$	−27.9612	−0.891823	−0.445912	+	0.895077i	$0.647120\pi$
$984$	6.91346	0.220393
$985$	91.4177	2.91281
$986$	31.2679	0.995771
$987$	−25.3964	−0.808375
$988$	−6.13877	−0.195300
$989$	34.4236	1.09461
$990$	7.53812	0.239577
$991$	−3.92413	−0.124654	−0.0623271	−	0.998056i	$-0.519852\pi$
$991$	−3.92413	−0.124654	−0.0623271	+	0.998056i	$0.519852\pi$
$992$	−3.05022	−0.0968446
$993$	−30.7156	−0.974730
$994$	−19.8625	−0.630000
$995$	100.574	3.18840
$996$	−15.0761	−0.477704
$997$	21.5902	0.683768	0.341884	−	0.939742i	$-0.388935\pi$
$997$	21.5902	0.683768	0.341884	+	0.939742i	$0.388935\pi$
$998$	1.26434	0.0400221
$999$	0.695449	0.0220030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.14	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.14	✓	14	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.78531 q^{5} +1.00000 q^{6} -3.09768 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.78531 q^{5} +1.00000 q^{6} -3.09768 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.78531 q^{10} -1.99141 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.09768 q^{14} -3.78531 q^{15} +1.00000 q^{16} -7.51222 q^{17} -1.00000 q^{18} +6.13877 q^{19} +3.78531 q^{20} +3.09768 q^{21} +1.99141 q^{22} +6.69447 q^{23} +1.00000 q^{24} +9.32855 q^{25} +1.00000 q^{26} -1.00000 q^{27} -3.09768 q^{28} +4.16226 q^{29} +3.78531 q^{30} +3.05022 q^{31} -1.00000 q^{32} +1.99141 q^{33} +7.51222 q^{34} -11.7257 q^{35} +1.00000 q^{36} -0.695449 q^{37} -6.13877 q^{38} +1.00000 q^{39} -3.78531 q^{40} +6.91346 q^{41} -3.09768 q^{42} +5.14209 q^{43} -1.99141 q^{44} +3.78531 q^{45} -6.69447 q^{46} -8.19852 q^{47} -1.00000 q^{48} +2.59560 q^{49} -9.32855 q^{50} +7.51222 q^{51} -1.00000 q^{52} -5.97715 q^{53} +1.00000 q^{54} -7.53812 q^{55} +3.09768 q^{56} -6.13877 q^{57} -4.16226 q^{58} +5.70653 q^{59} -3.78531 q^{60} -9.33645 q^{61} -3.05022 q^{62} -3.09768 q^{63} +1.00000 q^{64} -3.78531 q^{65} -1.99141 q^{66} +0.628166 q^{67} -7.51222 q^{68} -6.69447 q^{69} +11.7257 q^{70} -6.41206 q^{71} -1.00000 q^{72} -5.18377 q^{73} +0.695449 q^{74} -9.32855 q^{75} +6.13877 q^{76} +6.16876 q^{77} -1.00000 q^{78} -5.82259 q^{79} +3.78531 q^{80} +1.00000 q^{81} -6.91346 q^{82} +15.0761 q^{83} +3.09768 q^{84} -28.4361 q^{85} -5.14209 q^{86} -4.16226 q^{87} +1.99141 q^{88} -17.5821 q^{89} -3.78531 q^{90} +3.09768 q^{91} +6.69447 q^{92} -3.05022 q^{93} +8.19852 q^{94} +23.2371 q^{95} +1.00000 q^{96} +2.07965 q^{97} -2.59560 q^{98} -1.99141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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