LMFDB - Embedded newform 8034.2.a.bd.1.12

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.32389$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32389 q^{5} +1.00000 q^{6} -0.374750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32389 q^{5} +1.00000 q^{6} -0.374750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.32389 q^{10} +5.67530 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.374750 q^{14} +2.32389 q^{15} +1.00000 q^{16} -6.54130 q^{17} +1.00000 q^{18} +5.75977 q^{19} +2.32389 q^{20} -0.374750 q^{21} +5.67530 q^{22} +4.54787 q^{23} +1.00000 q^{24} +0.400476 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.374750 q^{28} +5.38709 q^{29} +2.32389 q^{30} -7.19141 q^{31} +1.00000 q^{32} +5.67530 q^{33} -6.54130 q^{34} -0.870879 q^{35} +1.00000 q^{36} +1.20009 q^{37} +5.75977 q^{38} -1.00000 q^{39} +2.32389 q^{40} -3.11011 q^{41} -0.374750 q^{42} +12.1822 q^{43} +5.67530 q^{44} +2.32389 q^{45} +4.54787 q^{46} +1.27698 q^{47} +1.00000 q^{48} -6.85956 q^{49} +0.400476 q^{50} -6.54130 q^{51} -1.00000 q^{52} -11.2567 q^{53} +1.00000 q^{54} +13.1888 q^{55} -0.374750 q^{56} +5.75977 q^{57} +5.38709 q^{58} +13.7948 q^{59} +2.32389 q^{60} -5.86119 q^{61} -7.19141 q^{62} -0.374750 q^{63} +1.00000 q^{64} -2.32389 q^{65} +5.67530 q^{66} +11.4452 q^{67} -6.54130 q^{68} +4.54787 q^{69} -0.870879 q^{70} -3.03547 q^{71} +1.00000 q^{72} -5.01531 q^{73} +1.20009 q^{74} +0.400476 q^{75} +5.75977 q^{76} -2.12682 q^{77} -1.00000 q^{78} +3.90352 q^{79} +2.32389 q^{80} +1.00000 q^{81} -3.11011 q^{82} -2.10559 q^{83} -0.374750 q^{84} -15.2013 q^{85} +12.1822 q^{86} +5.38709 q^{87} +5.67530 q^{88} -3.18886 q^{89} +2.32389 q^{90} +0.374750 q^{91} +4.54787 q^{92} -7.19141 q^{93} +1.27698 q^{94} +13.3851 q^{95} +1.00000 q^{96} -4.91379 q^{97} -6.85956 q^{98} +5.67530 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * 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
$5$	2.32389	1.03928	0.519638	−	0.854386i	$-0.326067\pi$
$5$	2.32389	1.03928	0.519638	+	0.854386i	$0.326067\pi$
$6$	1.00000	0.408248
$7$	−0.374750	−0.141642	−0.0708212	−	0.997489i	$-0.522562\pi$
$7$	−0.374750	−0.141642	−0.0708212	+	0.997489i	$0.522562\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.32389	0.734879
$11$	5.67530	1.71117	0.855583	−	0.517665i	$-0.173199\pi$
$11$	5.67530	1.71117	0.855583	+	0.517665i	$0.173199\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.374750	−0.100156
$15$	2.32389	0.600026
$16$	1.00000	0.250000
$17$	−6.54130	−1.58650	−0.793250	−	0.608897i	$-0.791612\pi$
$17$	−6.54130	−1.58650	−0.793250	+	0.608897i	$0.791612\pi$
$18$	1.00000	0.235702
$19$	5.75977	1.32138	0.660691	−	0.750658i	$-0.270263\pi$
$19$	5.75977	1.32138	0.660691	+	0.750658i	$0.270263\pi$
$20$	2.32389	0.519638
$21$	−0.374750	−0.0817772
$22$	5.67530	1.20998
$23$	4.54787	0.948296	0.474148	−	0.880445i	$-0.342756\pi$
$23$	4.54787	0.948296	0.474148	+	0.880445i	$0.342756\pi$
$24$	1.00000	0.204124
$25$	0.400476	0.0800951
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−0.374750	−0.0708212
$29$	5.38709	1.00036	0.500179	−	0.865922i	$-0.333268\pi$
$29$	5.38709	1.00036	0.500179	+	0.865922i	$0.333268\pi$
$30$	2.32389	0.424283
$31$	−7.19141	−1.29162	−0.645808	−	0.763500i	$-0.723479\pi$
$31$	−7.19141	−1.29162	−0.645808	+	0.763500i	$0.723479\pi$
$32$	1.00000	0.176777
$33$	5.67530	0.987943
$34$	−6.54130	−1.12182
$35$	−0.870879	−0.147205
$36$	1.00000	0.166667
$37$	1.20009	0.197294	0.0986468	−	0.995123i	$-0.468549\pi$
$37$	1.20009	0.197294	0.0986468	+	0.995123i	$0.468549\pi$
$38$	5.75977	0.934359
$39$	−1.00000	−0.160128
$40$	2.32389	0.367440
$41$	−3.11011	−0.485718	−0.242859	−	0.970062i	$-0.578085\pi$
$41$	−3.11011	−0.485718	−0.242859	+	0.970062i	$0.578085\pi$
$42$	−0.374750	−0.0578252
$43$	12.1822	1.85777	0.928886	−	0.370366i	$-0.120768\pi$
$43$	12.1822	1.85777	0.928886	+	0.370366i	$0.120768\pi$
$44$	5.67530	0.855583
$45$	2.32389	0.346425
$46$	4.54787	0.670546
$47$	1.27698	0.186267	0.0931334	−	0.995654i	$-0.470312\pi$
$47$	1.27698	0.186267	0.0931334	+	0.995654i	$0.470312\pi$
$48$	1.00000	0.144338
$49$	−6.85956	−0.979937
$50$	0.400476	0.0566358
$51$	−6.54130	−0.915966
$52$	−1.00000	−0.138675
$53$	−11.2567	−1.54623	−0.773114	−	0.634267i	$-0.781302\pi$
$53$	−11.2567	−1.54623	−0.773114	+	0.634267i	$0.781302\pi$
$54$	1.00000	0.136083
$55$	13.1888	1.77837
$56$	−0.374750	−0.0500781
$57$	5.75977	0.762901
$58$	5.38709	0.707360
$59$	13.7948	1.79593	0.897966	−	0.440064i	$-0.145044\pi$
$59$	13.7948	1.79593	0.897966	+	0.440064i	$0.145044\pi$
$60$	2.32389	0.300013
$61$	−5.86119	−0.750448	−0.375224	−	0.926934i	$-0.622434\pi$
$61$	−5.86119	−0.750448	−0.375224	+	0.926934i	$0.622434\pi$
$62$	−7.19141	−0.913311
$63$	−0.374750	−0.0472141
$64$	1.00000	0.125000
$65$	−2.32389	−0.288243
$66$	5.67530	0.698581
$67$	11.4452	1.39826	0.699128	−	0.714996i	$-0.253572\pi$
$67$	11.4452	1.39826	0.699128	+	0.714996i	$0.253572\pi$
$68$	−6.54130	−0.793250
$69$	4.54787	0.547499
$70$	−0.870879	−0.104090
$71$	−3.03547	−0.360244	−0.180122	−	0.983644i	$-0.557649\pi$
$71$	−3.03547	−0.360244	−0.180122	+	0.983644i	$0.557649\pi$
$72$	1.00000	0.117851
$73$	−5.01531	−0.586998	−0.293499	−	0.955959i	$-0.594820\pi$
$73$	−5.01531	−0.586998	−0.293499	+	0.955959i	$0.594820\pi$
$74$	1.20009	0.139508
$75$	0.400476	0.0462429
$76$	5.75977	0.660691
$77$	−2.12682	−0.242374
$78$	−1.00000	−0.113228
$79$	3.90352	0.439180	0.219590	−	0.975592i	$-0.429528\pi$
$79$	3.90352	0.439180	0.219590	+	0.975592i	$0.429528\pi$
$80$	2.32389	0.259819
$81$	1.00000	0.111111
$82$	−3.11011	−0.343454
$83$	−2.10559	−0.231119	−0.115559	−	0.993301i	$-0.536866\pi$
$83$	−2.10559	−0.231119	−0.115559	+	0.993301i	$0.536866\pi$
$84$	−0.374750	−0.0408886
$85$	−15.2013	−1.64881
$86$	12.1822	1.31364
$87$	5.38709	0.577557
$88$	5.67530	0.604989
$89$	−3.18886	−0.338018	−0.169009	−	0.985614i	$-0.554057\pi$
$89$	−3.18886	−0.338018	−0.169009	+	0.985614i	$0.554057\pi$
$90$	2.32389	0.244960
$91$	0.374750	0.0392845
$92$	4.54787	0.474148
$93$	−7.19141	−0.745715
$94$	1.27698	0.131710
$95$	13.3851	1.37328
$96$	1.00000	0.102062
$97$	−4.91379	−0.498920	−0.249460	−	0.968385i	$-0.580253\pi$
$97$	−4.91379	−0.498920	−0.249460	+	0.968385i	$0.580253\pi$
$98$	−6.85956	−0.692920
$99$	5.67530	0.570389
$100$	0.400476	0.0400476
$101$	9.60630	0.955863	0.477931	−	0.878397i	$-0.341387\pi$
$101$	9.60630	0.955863	0.477931	+	0.878397i	$0.341387\pi$
$102$	−6.54130	−0.647686
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.870879	−0.0849891
$106$	−11.2567	−1.09335
$107$	−4.50856	−0.435859	−0.217930	−	0.975965i	$-0.569930\pi$
$107$	−4.50856	−0.435859	−0.217930	+	0.975965i	$0.569930\pi$
$108$	1.00000	0.0962250
$109$	5.01775	0.480613	0.240307	−	0.970697i	$-0.422752\pi$
$109$	5.01775	0.480613	0.240307	+	0.970697i	$0.422752\pi$
$110$	13.1888	1.25750
$111$	1.20009	0.113907
$112$	−0.374750	−0.0354106
$113$	−2.38912	−0.224750	−0.112375	−	0.993666i	$-0.535846\pi$
$113$	−2.38912	−0.224750	−0.112375	+	0.993666i	$0.535846\pi$
$114$	5.75977	0.539452
$115$	10.5688	0.985541
$116$	5.38709	0.500179
$117$	−1.00000	−0.0924500
$118$	13.7948	1.26992
$119$	2.45136	0.224715
$120$	2.32389	0.212141
$121$	21.2090	1.92809
$122$	−5.86119	−0.530647
$123$	−3.11011	−0.280429
$124$	−7.19141	−0.645808
$125$	−10.6888	−0.956035
$126$	−0.374750	−0.0333854
$127$	−4.32759	−0.384012	−0.192006	−	0.981394i	$-0.561499\pi$
$127$	−4.32759	−0.384012	−0.192006	+	0.981394i	$0.561499\pi$
$128$	1.00000	0.0883883
$129$	12.1822	1.07258
$130$	−2.32389	−0.203819
$131$	−6.45170	−0.563688	−0.281844	−	0.959460i	$-0.590946\pi$
$131$	−6.45170	−0.563688	−0.281844	+	0.959460i	$0.590946\pi$
$132$	5.67530	0.493971
$133$	−2.15848	−0.187164
$134$	11.4452	0.988717
$135$	2.32389	0.200009
$136$	−6.54130	−0.560912
$137$	−8.27244	−0.706762	−0.353381	−	0.935479i	$-0.614968\pi$
$137$	−8.27244	−0.706762	−0.353381	+	0.935479i	$0.614968\pi$
$138$	4.54787	0.387140
$139$	−0.432789	−0.0367087	−0.0183543	−	0.999832i	$-0.505843\pi$
$139$	−0.432789	−0.0367087	−0.0183543	+	0.999832i	$0.505843\pi$
$140$	−0.870879	−0.0736027
$141$	1.27698	0.107541
$142$	−3.03547	−0.254731
$143$	−5.67530	−0.474592
$144$	1.00000	0.0833333
$145$	12.5190	1.03965
$146$	−5.01531	−0.415070
$147$	−6.85956	−0.565767
$148$	1.20009	0.0986468
$149$	−8.83602	−0.723875	−0.361937	−	0.932202i	$-0.617885\pi$
$149$	−8.83602	−0.723875	−0.361937	+	0.932202i	$0.617885\pi$
$150$	0.400476	0.0326987
$151$	−15.4986	−1.26126	−0.630631	−	0.776083i	$-0.717204\pi$
$151$	−15.4986	−1.26126	−0.630631	+	0.776083i	$0.717204\pi$
$152$	5.75977	0.467179
$153$	−6.54130	−0.528833
$154$	−2.12682	−0.171384
$155$	−16.7121	−1.34235
$156$	−1.00000	−0.0800641
$157$	7.09884	0.566549	0.283275	−	0.959039i	$-0.408579\pi$
$157$	7.09884	0.566549	0.283275	+	0.959039i	$0.408579\pi$
$158$	3.90352	0.310547
$159$	−11.2567	−0.892715
$160$	2.32389	0.183720
$161$	−1.70431	−0.134319
$162$	1.00000	0.0785674
$163$	20.5467	1.60934	0.804669	−	0.593723i	$-0.202343\pi$
$163$	20.5467	1.60934	0.804669	+	0.593723i	$0.202343\pi$
$164$	−3.11011	−0.242859
$165$	13.1888	1.02675
$166$	−2.10559	−0.163425
$167$	5.35722	0.414554	0.207277	−	0.978282i	$-0.433540\pi$
$167$	5.35722	0.414554	0.207277	+	0.978282i	$0.433540\pi$
$168$	−0.374750	−0.0289126
$169$	1.00000	0.0769231
$170$	−15.2013	−1.16589
$171$	5.75977	0.440461
$172$	12.1822	0.928886
$173$	−1.65634	−0.125929	−0.0629645	−	0.998016i	$-0.520056\pi$
$173$	−1.65634	−0.125929	−0.0629645	+	0.998016i	$0.520056\pi$
$174$	5.38709	0.408394
$175$	−0.150078	−0.0113449
$176$	5.67530	0.427792
$177$	13.7948	1.03688
$178$	−3.18886	−0.239015
$179$	8.62400	0.644588	0.322294	−	0.946640i	$-0.395546\pi$
$179$	8.62400	0.644588	0.322294	+	0.946640i	$0.395546\pi$
$180$	2.32389	0.173213
$181$	−0.861819	−0.0640585	−0.0320293	−	0.999487i	$-0.510197\pi$
$181$	−0.861819	−0.0640585	−0.0320293	+	0.999487i	$0.510197\pi$
$182$	0.374750	0.0277783
$183$	−5.86119	−0.433272
$184$	4.54787	0.335273
$185$	2.78888	0.205043
$186$	−7.19141	−0.527300
$187$	−37.1238	−2.71476
$188$	1.27698	0.0931334
$189$	−0.374750	−0.0272591
$190$	13.3851	0.971057
$191$	−1.96669	−0.142305	−0.0711524	−	0.997465i	$-0.522668\pi$
$191$	−1.96669	−0.142305	−0.0711524	+	0.997465i	$0.522668\pi$
$192$	1.00000	0.0721688
$193$	10.7503	0.773821	0.386911	−	0.922117i	$-0.373542\pi$
$193$	10.7503	0.773821	0.386911	+	0.922117i	$0.373542\pi$
$194$	−4.91379	−0.352790
$195$	−2.32389	−0.166417
$196$	−6.85956	−0.489969
$197$	0.0128701	0.000916959 0	0.000458480	−	1.00000i	$-0.499854\pi$
$197$	0.0128701	0.000916959 0	0.000458480		1.00000i	$0.499854\pi$
$198$	5.67530	0.403326
$199$	12.0128	0.851562	0.425781	−	0.904826i	$-0.359999\pi$
$199$	12.0128	0.851562	0.425781	+	0.904826i	$0.359999\pi$
$200$	0.400476	0.0283179
$201$	11.4452	0.807284
$202$	9.60630	0.675897
$203$	−2.01881	−0.141693
$204$	−6.54130	−0.457983
$205$	−7.22756	−0.504795
$206$	1.00000	0.0696733
$207$	4.54787	0.316099
$208$	−1.00000	−0.0693375
$209$	32.6884	2.26111
$210$	−0.870879	−0.0600964
$211$	−2.95675	−0.203551	−0.101776	−	0.994807i	$-0.532452\pi$
$211$	−2.95675	−0.203551	−0.101776	+	0.994807i	$0.532452\pi$
$212$	−11.2567	−0.773114
$213$	−3.03547	−0.207987
$214$	−4.50856	−0.308199
$215$	28.3102	1.93074
$216$	1.00000	0.0680414
$217$	2.69499	0.182948
$218$	5.01775	0.339845
$219$	−5.01531	−0.338903
$220$	13.1888	0.889187
$221$	6.54130	0.440016
$222$	1.20009	0.0805448
$223$	−11.4459	−0.766471	−0.383236	−	0.923651i	$-0.625190\pi$
$223$	−11.4459	−0.766471	−0.383236	+	0.923651i	$0.625190\pi$
$224$	−0.374750	−0.0250391
$225$	0.400476	0.0266984
$226$	−2.38912	−0.158922
$227$	−1.02550	−0.0680646	−0.0340323	−	0.999421i	$-0.510835\pi$
$227$	−1.02550	−0.0680646	−0.0340323	+	0.999421i	$0.510835\pi$
$228$	5.75977	0.381450
$229$	−27.0378	−1.78671	−0.893355	−	0.449352i	$-0.851655\pi$
$229$	−27.0378	−1.78671	−0.893355	+	0.449352i	$0.851655\pi$
$230$	10.5688	0.696883
$231$	−2.12682	−0.139934
$232$	5.38709	0.353680
$233$	1.16247	0.0761557	0.0380779	−	0.999275i	$-0.487877\pi$
$233$	1.16247	0.0761557	0.0380779	+	0.999275i	$0.487877\pi$
$234$	−1.00000	−0.0653720
$235$	2.96756	0.193583
$236$	13.7948	0.897966
$237$	3.90352	0.253561
$238$	2.45136	0.158898
$239$	−1.38196	−0.0893915	−0.0446958	−	0.999001i	$-0.514232\pi$
$239$	−1.38196	−0.0893915	−0.0446958	+	0.999001i	$0.514232\pi$
$240$	2.32389	0.150007
$241$	−27.7699	−1.78882	−0.894408	−	0.447253i	$-0.852402\pi$
$241$	−27.7699	−1.78882	−0.894408	+	0.447253i	$0.852402\pi$
$242$	21.2090	1.36337
$243$	1.00000	0.0641500
$244$	−5.86119	−0.375224
$245$	−15.9409	−1.01843
$246$	−3.11011	−0.198293
$247$	−5.75977	−0.366486
$248$	−7.19141	−0.456655
$249$	−2.10559	−0.133436
$250$	−10.6888	−0.676019
$251$	24.5538	1.54982	0.774910	−	0.632072i	$-0.217795\pi$
$251$	24.5538	1.54982	0.774910	+	0.632072i	$0.217795\pi$
$252$	−0.374750	−0.0236071
$253$	25.8105	1.62269
$254$	−4.32759	−0.271537
$255$	−15.2013	−0.951941
$256$	1.00000	0.0625000
$257$	−5.29370	−0.330212	−0.165106	−	0.986276i	$-0.552797\pi$
$257$	−5.29370	−0.330212	−0.165106	+	0.986276i	$0.552797\pi$
$258$	12.1822	0.758432
$259$	−0.449734	−0.0279451
$260$	−2.32389	−0.144122
$261$	5.38709	0.333453
$262$	−6.45170	−0.398588
$263$	−27.4819	−1.69461	−0.847305	−	0.531107i	$-0.821776\pi$
$263$	−27.4819	−1.69461	−0.847305	+	0.531107i	$0.821776\pi$
$264$	5.67530	0.349290
$265$	−26.1594	−1.60696
$266$	−2.15848	−0.132345
$267$	−3.18886	−0.195155
$268$	11.4452	0.699128
$269$	−9.96162	−0.607371	−0.303685	−	0.952772i	$-0.598217\pi$
$269$	−9.96162	−0.607371	−0.303685	+	0.952772i	$0.598217\pi$
$270$	2.32389	0.141428
$271$	15.0010	0.911243	0.455622	−	0.890174i	$-0.349417\pi$
$271$	15.0010	0.911243	0.455622	+	0.890174i	$0.349417\pi$
$272$	−6.54130	−0.396625
$273$	0.374750	0.0226809
$274$	−8.27244	−0.499756
$275$	2.27282	0.137056
$276$	4.54787	0.273749
$277$	8.27269	0.497058	0.248529	−	0.968624i	$-0.420053\pi$
$277$	8.27269	0.497058	0.248529	+	0.968624i	$0.420053\pi$
$278$	−0.432789	−0.0259569
$279$	−7.19141	−0.430539
$280$	−0.870879	−0.0520450
$281$	−0.956702	−0.0570721	−0.0285360	−	0.999593i	$-0.509085\pi$
$281$	−0.956702	−0.0570721	−0.0285360	+	0.999593i	$0.509085\pi$
$282$	1.27698	0.0760431
$283$	−12.3188	−0.732275	−0.366138	−	0.930561i	$-0.619320\pi$
$283$	−12.3188	−0.732275	−0.366138	+	0.930561i	$0.619320\pi$
$284$	−3.03547	−0.180122
$285$	13.3851	0.792865
$286$	−5.67530	−0.335587
$287$	1.16551	0.0687982
$288$	1.00000	0.0589256
$289$	25.7886	1.51698
$290$	12.5190	0.735142
$291$	−4.91379	−0.288052
$292$	−5.01531	−0.293499
$293$	16.1483	0.943396	0.471698	−	0.881760i	$-0.343641\pi$
$293$	16.1483	0.943396	0.471698	+	0.881760i	$0.343641\pi$
$294$	−6.85956	−0.400058
$295$	32.0577	1.86647
$296$	1.20009	0.0697538
$297$	5.67530	0.329314
$298$	−8.83602	−0.511857
$299$	−4.54787	−0.263010
$300$	0.400476	0.0231215
$301$	−4.56529	−0.263139
$302$	−15.4986	−0.891847
$303$	9.60630	0.551868
$304$	5.75977	0.330346
$305$	−13.6208	−0.779923
$306$	−6.54130	−0.373941
$307$	17.3930	0.992673	0.496336	−	0.868130i	$-0.334678\pi$
$307$	17.3930	0.992673	0.496336	+	0.868130i	$0.334678\pi$
$308$	−2.12682	−0.121187
$309$	1.00000	0.0568880
$310$	−16.7121	−0.949182
$311$	−26.2190	−1.48674	−0.743372	−	0.668878i	$-0.766775\pi$
$311$	−26.2190	−1.48674	−0.743372	+	0.668878i	$0.766775\pi$
$312$	−1.00000	−0.0566139
$313$	23.4796	1.32714	0.663572	−	0.748113i	$-0.269040\pi$
$313$	23.4796	1.32714	0.663572	+	0.748113i	$0.269040\pi$
$314$	7.09884	0.400611
$315$	−0.870879	−0.0490685
$316$	3.90352	0.219590
$317$	−25.8367	−1.45113	−0.725566	−	0.688152i	$-0.758422\pi$
$317$	−25.8367	−1.45113	−0.725566	+	0.688152i	$0.758422\pi$
$318$	−11.2567	−0.631245
$319$	30.5734	1.71178
$320$	2.32389	0.129910
$321$	−4.50856	−0.251643
$322$	−1.70431	−0.0949777
$323$	−37.6764	−2.09637
$324$	1.00000	0.0555556
$325$	−0.400476	−0.0222144
$326$	20.5467	1.13797
$327$	5.01775	0.277482
$328$	−3.11011	−0.171727
$329$	−0.478549	−0.0263832
$330$	13.1888	0.726019
$331$	−21.8397	−1.20042	−0.600209	−	0.799843i	$-0.704916\pi$
$331$	−21.8397	−1.20042	−0.600209	+	0.799843i	$0.704916\pi$
$332$	−2.10559	−0.115559
$333$	1.20009	0.0657645
$334$	5.35722	0.293134
$335$	26.5975	1.45317
$336$	−0.374750	−0.0204443
$337$	28.2816	1.54060	0.770298	−	0.637685i	$-0.220108\pi$
$337$	28.2816	1.54060	0.770298	+	0.637685i	$0.220108\pi$
$338$	1.00000	0.0543928
$339$	−2.38912	−0.129759
$340$	−15.2013	−0.824405
$341$	−40.8134	−2.21017
$342$	5.75977	0.311453
$343$	5.19388	0.280443
$344$	12.1822	0.656821
$345$	10.5688	0.569002
$346$	−1.65634	−0.0890453
$347$	−21.5079	−1.15460	−0.577302	−	0.816531i	$-0.695894\pi$
$347$	−21.5079	−1.15460	−0.577302	+	0.816531i	$0.695894\pi$
$348$	5.38709	0.288778
$349$	−29.5596	−1.58229	−0.791144	−	0.611630i	$-0.790514\pi$
$349$	−29.5596	−1.58229	−0.791144	+	0.611630i	$0.790514\pi$
$350$	−0.150078	−0.00802203
$351$	−1.00000	−0.0533761
$352$	5.67530	0.302494
$353$	−0.961649	−0.0511834	−0.0255917	−	0.999672i	$-0.508147\pi$
$353$	−0.961649	−0.0511834	−0.0255917	+	0.999672i	$0.508147\pi$
$354$	13.7948	0.733186
$355$	−7.05410	−0.374393
$356$	−3.18886	−0.169009
$357$	2.45136	0.129739
$358$	8.62400	0.455793
$359$	16.7319	0.883077	0.441539	−	0.897242i	$-0.354433\pi$
$359$	16.7319	0.883077	0.441539	+	0.897242i	$0.354433\pi$
$360$	2.32389	0.122480
$361$	14.1750	0.746053
$362$	−0.861819	−0.0452962
$363$	21.2090	1.11318
$364$	0.374750	0.0196423
$365$	−11.6550	−0.610053
$366$	−5.86119	−0.306369
$367$	28.5471	1.49015	0.745073	−	0.666982i	$-0.232414\pi$
$367$	28.5471	1.49015	0.745073	+	0.666982i	$0.232414\pi$
$368$	4.54787	0.237074
$369$	−3.11011	−0.161906
$370$	2.78888	0.144987
$371$	4.21846	0.219011
$372$	−7.19141	−0.372857
$373$	−2.39693	−0.124109	−0.0620543	−	0.998073i	$-0.519765\pi$
$373$	−2.39693	−0.124109	−0.0620543	+	0.998073i	$0.519765\pi$
$374$	−37.1238	−1.91963
$375$	−10.6888	−0.551967
$376$	1.27698	0.0658552
$377$	−5.38709	−0.277449
$378$	−0.374750	−0.0192751
$379$	31.9484	1.64108	0.820539	−	0.571591i	$-0.193674\pi$
$379$	31.9484	1.64108	0.820539	+	0.571591i	$0.193674\pi$
$380$	13.3851	0.686641
$381$	−4.32759	−0.221709
$382$	−1.96669	−0.100625
$383$	15.8580	0.810304	0.405152	−	0.914249i	$-0.367219\pi$
$383$	15.8580	0.810304	0.405152	+	0.914249i	$0.367219\pi$
$384$	1.00000	0.0510310
$385$	−4.94250	−0.251893
$386$	10.7503	0.547174
$387$	12.1822	0.619257
$388$	−4.91379	−0.249460
$389$	11.7709	0.596808	0.298404	−	0.954440i	$-0.403546\pi$
$389$	11.7709	0.596808	0.298404	+	0.954440i	$0.403546\pi$
$390$	−2.32389	−0.117675
$391$	−29.7490	−1.50447
$392$	−6.85956	−0.346460
$393$	−6.45170	−0.325445
$394$	0.0128701	0.000648388 0
$395$	9.07136	0.456430
$396$	5.67530	0.285194
$397$	−20.8461	−1.04623	−0.523117	−	0.852261i	$-0.675231\pi$
$397$	−20.8461	−1.04623	−0.523117	+	0.852261i	$0.675231\pi$
$398$	12.0128	0.602145
$399$	−2.15848	−0.108059
$400$	0.400476	0.0200238
$401$	−32.6364	−1.62978	−0.814891	−	0.579614i	$-0.803203\pi$
$401$	−32.6364	−1.62978	−0.814891	+	0.579614i	$0.803203\pi$
$402$	11.4452	0.570836
$403$	7.19141	0.358230
$404$	9.60630	0.477931
$405$	2.32389	0.115475
$406$	−2.01881	−0.100192
$407$	6.81087	0.337602
$408$	−6.54130	−0.323843
$409$	−15.6682	−0.774743	−0.387371	−	0.921924i	$-0.626617\pi$
$409$	−15.6682	−0.774743	−0.387371	+	0.921924i	$0.626617\pi$
$410$	−7.22756	−0.356944
$411$	−8.27244	−0.408049
$412$	1.00000	0.0492665
$413$	−5.16961	−0.254380
$414$	4.54787	0.223515
$415$	−4.89316	−0.240196
$416$	−1.00000	−0.0490290
$417$	−0.432789	−0.0211938
$418$	32.6884	1.59884
$419$	−31.8520	−1.55607	−0.778037	−	0.628219i	$-0.783784\pi$
$419$	−31.8520	−1.55607	−0.778037	+	0.628219i	$0.783784\pi$
$420$	−0.870879	−0.0424946
$421$	9.44236	0.460193	0.230096	−	0.973168i	$-0.426096\pi$
$421$	9.44236	0.460193	0.230096	+	0.973168i	$0.426096\pi$
$422$	−2.95675	−0.143932
$423$	1.27698	0.0620889
$424$	−11.2567	−0.546674
$425$	−2.61963	−0.127071
$426$	−3.03547	−0.147069
$427$	2.19648	0.106295
$428$	−4.50856	−0.217930
$429$	−5.67530	−0.274006
$430$	28.3102	1.36524
$431$	−11.5799	−0.557782	−0.278891	−	0.960323i	$-0.589967\pi$
$431$	−11.5799	−0.557782	−0.278891	+	0.960323i	$0.589967\pi$
$432$	1.00000	0.0481125
$433$	−30.6151	−1.47127	−0.735635	−	0.677379i	$-0.763116\pi$
$433$	−30.6151	−1.47127	−0.735635	+	0.677379i	$0.763116\pi$
$434$	2.69499	0.129363
$435$	12.5190	0.600241
$436$	5.01775	0.240307
$437$	26.1947	1.25306
$438$	−5.01531	−0.239641
$439$	6.12116	0.292147	0.146074	−	0.989274i	$-0.453336\pi$
$439$	6.12116	0.292147	0.146074	+	0.989274i	$0.453336\pi$
$440$	13.1888	0.628751
$441$	−6.85956	−0.326646
$442$	6.54130	0.311138
$443$	−15.3458	−0.729100	−0.364550	−	0.931184i	$-0.618777\pi$
$443$	−15.3458	−0.729100	−0.364550	+	0.931184i	$0.618777\pi$
$444$	1.20009	0.0569537
$445$	−7.41056	−0.351294
$446$	−11.4459	−0.541977
$447$	−8.83602	−0.417929
$448$	−0.374750	−0.0177053
$449$	10.8492	0.512004	0.256002	−	0.966676i	$-0.417595\pi$
$449$	10.8492	0.512004	0.256002	+	0.966676i	$0.417595\pi$
$450$	0.400476	0.0188786
$451$	−17.6508	−0.831144
$452$	−2.38912	−0.112375
$453$	−15.4986	−0.728190
$454$	−1.02550	−0.0481289
$455$	0.870879	0.0408275
$456$	5.75977	0.269726
$457$	−3.60474	−0.168623	−0.0843113	−	0.996439i	$-0.526869\pi$
$457$	−3.60474	−0.168623	−0.0843113	+	0.996439i	$0.526869\pi$
$458$	−27.0378	−1.26339
$459$	−6.54130	−0.305322
$460$	10.5688	0.492771
$461$	29.5826	1.37780	0.688900	−	0.724857i	$-0.258094\pi$
$461$	29.5826	1.37780	0.688900	+	0.724857i	$0.258094\pi$
$462$	−2.12682	−0.0989486
$463$	2.58748	0.120251	0.0601253	−	0.998191i	$-0.480850\pi$
$463$	2.58748	0.120251	0.0601253	+	0.998191i	$0.480850\pi$
$464$	5.38709	0.250089
$465$	−16.7121	−0.775004
$466$	1.16247	0.0538502
$467$	25.9862	1.20250	0.601249	−	0.799061i	$-0.294670\pi$
$467$	25.9862	1.20250	0.601249	+	0.799061i	$0.294670\pi$
$468$	−1.00000	−0.0462250
$469$	−4.28910	−0.198052
$470$	2.96756	0.136884
$471$	7.09884	0.327097
$472$	13.7948	0.634958
$473$	69.1377	3.17896
$474$	3.90352	0.179295
$475$	2.30665	0.105836
$476$	2.45136	0.112358
$477$	−11.2567	−0.515409
$478$	−1.38196	−0.0632094
$479$	−15.4621	−0.706482	−0.353241	−	0.935532i	$-0.614920\pi$
$479$	−15.4621	−0.706482	−0.353241	+	0.935532i	$0.614920\pi$
$480$	2.32389	0.106071
$481$	−1.20009	−0.0547194
$482$	−27.7699	−1.26488
$483$	−1.70431	−0.0775490
$484$	21.2090	0.964046
$485$	−11.4191	−0.518516
$486$	1.00000	0.0453609
$487$	20.0582	0.908925	0.454462	−	0.890766i	$-0.349831\pi$
$487$	20.0582	0.908925	0.454462	+	0.890766i	$0.349831\pi$
$488$	−5.86119	−0.265324
$489$	20.5467	0.929152
$490$	−15.9409	−0.720136
$491$	20.6114	0.930181	0.465091	−	0.885263i	$-0.346022\pi$
$491$	20.6114	0.930181	0.465091	+	0.885263i	$0.346022\pi$
$492$	−3.11011	−0.140215
$493$	−35.2386	−1.58707
$494$	−5.75977	−0.259145
$495$	13.1888	0.592792
$496$	−7.19141	−0.322904
$497$	1.13754	0.0510257
$498$	−2.10559	−0.0943537
$499$	28.0107	1.25393	0.626966	−	0.779047i	$-0.284297\pi$
$499$	28.0107	1.25393	0.626966	+	0.779047i	$0.284297\pi$
$500$	−10.6888	−0.478018
$501$	5.35722	0.239343
$502$	24.5538	1.09589
$503$	1.16792	0.0520748	0.0260374	−	0.999661i	$-0.491711\pi$
$503$	1.16792	0.0520748	0.0260374	+	0.999661i	$0.491711\pi$
$504$	−0.374750	−0.0166927
$505$	22.3240	0.993405
$506$	25.8105	1.14742
$507$	1.00000	0.0444116
$508$	−4.32759	−0.192006
$509$	42.0500	1.86383	0.931916	−	0.362674i	$-0.118136\pi$
$509$	42.0500	1.86383	0.931916	+	0.362674i	$0.118136\pi$
$510$	−15.2013	−0.673124
$511$	1.87949	0.0831437
$512$	1.00000	0.0441942
$513$	5.75977	0.254300
$514$	−5.29370	−0.233495
$515$	2.32389	0.102403
$516$	12.1822	0.536292
$517$	7.24724	0.318733
$518$	−0.449734	−0.0197602
$519$	−1.65634	−0.0727052
$520$	−2.32389	−0.101909
$521$	−10.8207	−0.474062	−0.237031	−	0.971502i	$-0.576174\pi$
$521$	−10.8207	−0.474062	−0.237031	+	0.971502i	$0.576174\pi$
$522$	5.38709	0.235787
$523$	−4.44549	−0.194388	−0.0971939	−	0.995265i	$-0.530987\pi$
$523$	−4.44549	−0.194388	−0.0971939	+	0.995265i	$0.530987\pi$
$524$	−6.45170	−0.281844
$525$	−0.150078	−0.00654996
$526$	−27.4819	−1.19827
$527$	47.0412	2.04915
$528$	5.67530	0.246986
$529$	−2.31691	−0.100735
$530$	−26.1594	−1.13629
$531$	13.7948	0.598644
$532$	−2.15848	−0.0935819
$533$	3.11011	0.134714
$534$	−3.18886	−0.137995
$535$	−10.4774	−0.452978
$536$	11.4452	0.494358
$537$	8.62400	0.372153
$538$	−9.96162	−0.429476
$539$	−38.9301	−1.67684
$540$	2.32389	0.100004
$541$	5.56717	0.239351	0.119676	−	0.992813i	$-0.461815\pi$
$541$	5.56717	0.239351	0.119676	+	0.992813i	$0.461815\pi$
$542$	15.0010	0.644346
$543$	−0.861819	−0.0369842
$544$	−6.54130	−0.280456
$545$	11.6607	0.499490
$546$	0.374750	0.0160378
$547$	−21.7508	−0.929997	−0.464998	−	0.885311i	$-0.653945\pi$
$547$	−21.7508	−0.929997	−0.464998	+	0.885311i	$0.653945\pi$
$548$	−8.27244	−0.353381
$549$	−5.86119	−0.250149
$550$	2.27282	0.0969133
$551$	31.0284	1.32186
$552$	4.54787	0.193570
$553$	−1.46285	−0.0622065
$554$	8.27269	0.351473
$555$	2.78888	0.118381
$556$	−0.432789	−0.0183543
$557$	−11.1788	−0.473660	−0.236830	−	0.971551i	$-0.576108\pi$
$557$	−11.1788	−0.473660	−0.236830	+	0.971551i	$0.576108\pi$
$558$	−7.19141	−0.304437
$559$	−12.1822	−0.515253
$560$	−0.870879	−0.0368014
$561$	−37.1238	−1.56737
$562$	−0.956702	−0.0403560
$563$	−9.18804	−0.387230	−0.193615	−	0.981078i	$-0.562021\pi$
$563$	−9.18804	−0.387230	−0.193615	+	0.981078i	$0.562021\pi$
$564$	1.27698	0.0537706
$565$	−5.55207	−0.233577
$566$	−12.3188	−0.517797
$567$	−0.374750	−0.0157380
$568$	−3.03547	−0.127365
$569$	11.4550	0.480220	0.240110	−	0.970746i	$-0.422816\pi$
$569$	11.4550	0.480220	0.240110	+	0.970746i	$0.422816\pi$
$570$	13.3851	0.560640
$571$	38.9224	1.62885	0.814427	−	0.580266i	$-0.197051\pi$
$571$	38.9224	1.62885	0.814427	+	0.580266i	$0.197051\pi$
$572$	−5.67530	−0.237296
$573$	−1.96669	−0.0821597
$574$	1.16551	0.0486476
$575$	1.82131	0.0759539
$576$	1.00000	0.0416667
$577$	−25.7209	−1.07078	−0.535388	−	0.844606i	$-0.679834\pi$
$577$	−25.7209	−1.07078	−0.535388	+	0.844606i	$0.679834\pi$
$578$	25.7886	1.07267
$579$	10.7503	0.446766
$580$	12.5190	0.519824
$581$	0.789071	0.0327362
$582$	−4.91379	−0.203683
$583$	−63.8852	−2.64585
$584$	−5.01531	−0.207535
$585$	−2.32389	−0.0960811
$586$	16.1483	0.667082
$587$	−24.3013	−1.00302	−0.501512	−	0.865151i	$-0.667223\pi$
$587$	−24.3013	−1.00302	−0.501512	+	0.865151i	$0.667223\pi$
$588$	−6.85956	−0.282884
$589$	−41.4209	−1.70672
$590$	32.0577	1.31979
$591$	0.0128701	0.000529407 0
$592$	1.20009	0.0493234
$593$	−7.03102	−0.288729	−0.144365	−	0.989525i	$-0.546114\pi$
$593$	−7.03102	−0.288729	−0.144365	+	0.989525i	$0.546114\pi$
$594$	5.67530	0.232860
$595$	5.69669	0.233541
$596$	−8.83602	−0.361937
$597$	12.0128	0.491649
$598$	−4.54787	−0.185976
$599$	16.3812	0.669316	0.334658	−	0.942340i	$-0.391379\pi$
$599$	16.3812	0.669316	0.334658	+	0.942340i	$0.391379\pi$
$600$	0.400476	0.0163494
$601$	22.5219	0.918688	0.459344	−	0.888259i	$-0.348085\pi$
$601$	22.5219	0.918688	0.459344	+	0.888259i	$0.348085\pi$
$602$	−4.56529	−0.186067
$603$	11.4452	0.466086
$604$	−15.4986	−0.630631
$605$	49.2875	2.00382
$606$	9.60630	0.390229
$607$	5.93990	0.241093	0.120547	−	0.992708i	$-0.461535\pi$
$607$	5.93990	0.241093	0.120547	+	0.992708i	$0.461535\pi$
$608$	5.75977	0.233590
$609$	−2.01881	−0.0818065
$610$	−13.6208	−0.551489
$611$	−1.27698	−0.0516611
$612$	−6.54130	−0.264417
$613$	15.9520	0.644295	0.322148	−	0.946689i	$-0.395595\pi$
$613$	15.9520	0.644295	0.322148	+	0.946689i	$0.395595\pi$
$614$	17.3930	0.701926
$615$	−7.22756	−0.291443
$616$	−2.12682	−0.0856920
$617$	20.1056	0.809422	0.404711	−	0.914445i	$-0.367372\pi$
$617$	20.1056	0.809422	0.404711	+	0.914445i	$0.367372\pi$
$618$	1.00000	0.0402259
$619$	−30.6448	−1.23172	−0.615859	−	0.787857i	$-0.711191\pi$
$619$	−30.6448	−1.23172	−0.615859	+	0.787857i	$0.711191\pi$
$620$	−16.7121	−0.671173
$621$	4.54787	0.182500
$622$	−26.2190	−1.05129
$623$	1.19503	0.0478777
$624$	−1.00000	−0.0400320
$625$	−26.8420	−1.07368
$626$	23.4796	0.938432
$627$	32.6884	1.30545
$628$	7.09884	0.283275
$629$	−7.85015	−0.313006
$630$	−0.870879	−0.0346967
$631$	−37.1034	−1.47706	−0.738531	−	0.674220i	$-0.764480\pi$
$631$	−37.1034	−1.47706	−0.738531	+	0.674220i	$0.764480\pi$
$632$	3.90352	0.155274
$633$	−2.95675	−0.117520
$634$	−25.8367	−1.02611
$635$	−10.0569	−0.399094
$636$	−11.2567	−0.446357
$637$	6.85956	0.271786
$638$	30.5734	1.21041
$639$	−3.03547	−0.120081
$640$	2.32389	0.0918599
$641$	22.2057	0.877072	0.438536	−	0.898714i	$-0.355497\pi$
$641$	22.2057	0.877072	0.438536	+	0.898714i	$0.355497\pi$
$642$	−4.50856	−0.177939
$643$	−50.0517	−1.97385	−0.986924	−	0.161187i	$-0.948468\pi$
$643$	−50.0517	−1.97385	−0.986924	+	0.161187i	$0.948468\pi$
$644$	−1.70431	−0.0671594
$645$	28.3102	1.11471
$646$	−37.6764	−1.48236
$647$	−0.749594	−0.0294696	−0.0147348	−	0.999891i	$-0.504690\pi$
$647$	−0.749594	−0.0294696	−0.0147348	+	0.999891i	$0.504690\pi$
$648$	1.00000	0.0392837
$649$	78.2897	3.07314
$650$	−0.400476	−0.0157079
$651$	2.69499	0.105625
$652$	20.5467	0.804669
$653$	42.8450	1.67665	0.838327	−	0.545167i	$-0.183534\pi$
$653$	42.8450	1.67665	0.838327	+	0.545167i	$0.183534\pi$
$654$	5.01775	0.196210
$655$	−14.9931	−0.585828
$656$	−3.11011	−0.121429
$657$	−5.01531	−0.195666
$658$	−0.478549	−0.0186558
$659$	10.4012	0.405174	0.202587	−	0.979264i	$-0.435065\pi$
$659$	10.4012	0.405174	0.202587	+	0.979264i	$0.435065\pi$
$660$	13.1888	0.513373
$661$	−33.3836	−1.29847	−0.649235	−	0.760588i	$-0.724911\pi$
$661$	−33.3836	−1.29847	−0.649235	+	0.760588i	$0.724911\pi$
$662$	−21.8397	−0.848824
$663$	6.54130	0.254043
$664$	−2.10559	−0.0817127
$665$	−5.01607	−0.194515
$666$	1.20009	0.0465025
$667$	24.4998	0.948635
$668$	5.35722	0.207277
$669$	−11.4459	−0.442522
$670$	26.5975	1.02755
$671$	−33.2640	−1.28414
$672$	−0.374750	−0.0144563
$673$	10.4191	0.401628	0.200814	−	0.979629i	$-0.435641\pi$
$673$	10.4191	0.401628	0.200814	+	0.979629i	$0.435641\pi$
$674$	28.2816	1.08937
$675$	0.400476	0.0154143
$676$	1.00000	0.0384615
$677$	−19.2232	−0.738809	−0.369405	−	0.929269i	$-0.620438\pi$
$677$	−19.2232	−0.738809	−0.369405	+	0.929269i	$0.620438\pi$
$678$	−2.38912	−0.0917537
$679$	1.84145	0.0706682
$680$	−15.2013	−0.582943
$681$	−1.02550	−0.0392971
$682$	−40.8134	−1.56283
$683$	−43.3442	−1.65852	−0.829259	−	0.558864i	$-0.811237\pi$
$683$	−43.3442	−1.65852	−0.829259	+	0.558864i	$0.811237\pi$
$684$	5.75977	0.220230
$685$	−19.2243	−0.734521
$686$	5.19388	0.198303
$687$	−27.0378	−1.03156
$688$	12.1822	0.464443
$689$	11.2567	0.428846
$690$	10.5688	0.402346
$691$	−11.8457	−0.450633	−0.225317	−	0.974286i	$-0.572342\pi$
$691$	−11.8457	−0.450633	−0.225317	+	0.974286i	$0.572342\pi$
$692$	−1.65634	−0.0629645
$693$	−2.12682	−0.0807912
$694$	−21.5079	−0.816428
$695$	−1.00575	−0.0381504
$696$	5.38709	0.204197
$697$	20.3442	0.770590
$698$	−29.5596	−1.11885
$699$	1.16247	0.0439685
$700$	−0.150078	−0.00567243
$701$	25.9293	0.979336	0.489668	−	0.871909i	$-0.337118\pi$
$701$	25.9293	0.979336	0.489668	+	0.871909i	$0.337118\pi$
$702$	−1.00000	−0.0377426
$703$	6.91225	0.260700
$704$	5.67530	0.213896
$705$	2.96756	0.111765
$706$	−0.961649	−0.0361922
$707$	−3.59996	−0.135391
$708$	13.7948	0.518441
$709$	−33.7776	−1.26854	−0.634271	−	0.773110i	$-0.718700\pi$
$709$	−33.7776	−1.26854	−0.634271	+	0.773110i	$0.718700\pi$
$710$	−7.05410	−0.264736
$711$	3.90352	0.146393
$712$	−3.18886	−0.119508
$713$	−32.7056	−1.22483
$714$	2.45136	0.0917397
$715$	−13.1888	−0.493232
$716$	8.62400	0.322294
$717$	−1.38196	−0.0516102
$718$	16.7319	0.624430
$719$	47.0520	1.75474	0.877372	−	0.479810i	$-0.159294\pi$
$719$	47.0520	1.75474	0.877372	+	0.479810i	$0.159294\pi$
$720$	2.32389	0.0866064
$721$	−0.374750	−0.0139564
$722$	14.1750	0.527539
$723$	−27.7699	−1.03277
$724$	−0.861819	−0.0320293
$725$	2.15740	0.0801238
$726$	21.2090	0.787140
$727$	1.37503	0.0509972	0.0254986	−	0.999675i	$-0.491883\pi$
$727$	1.37503	0.0509972	0.0254986	+	0.999675i	$0.491883\pi$
$728$	0.374750	0.0138892
$729$	1.00000	0.0370370
$730$	−11.6550	−0.431373
$731$	−79.6876	−2.94735
$732$	−5.86119	−0.216636
$733$	−37.2913	−1.37739	−0.688693	−	0.725053i	$-0.741815\pi$
$733$	−37.2913	−1.37739	−0.688693	+	0.725053i	$0.741815\pi$
$734$	28.5471	1.05369
$735$	−15.9409	−0.587988
$736$	4.54787	0.167637
$737$	64.9551	2.39265
$738$	−3.11011	−0.114485
$739$	−11.6566	−0.428795	−0.214397	−	0.976747i	$-0.568779\pi$
$739$	−11.6566	−0.428795	−0.214397	+	0.976747i	$0.568779\pi$
$740$	2.78888	0.102521
$741$	−5.75977	−0.211591
$742$	4.21846	0.154864
$743$	−49.4737	−1.81502	−0.907508	−	0.420035i	$-0.862018\pi$
$743$	−49.4737	−1.81502	−0.907508	+	0.420035i	$0.862018\pi$
$744$	−7.19141	−0.263650
$745$	−20.5340	−0.752306
$746$	−2.39693	−0.0877580
$747$	−2.10559	−0.0770395
$748$	−37.1238	−1.35738
$749$	1.68958	0.0617361
$750$	−10.6888	−0.390300
$751$	−22.6637	−0.827010	−0.413505	−	0.910502i	$-0.635696\pi$
$751$	−22.6637	−0.827010	−0.413505	+	0.910502i	$0.635696\pi$
$752$	1.27698	0.0465667
$753$	24.5538	0.894789
$754$	−5.38709	−0.196186
$755$	−36.0172	−1.31080
$756$	−0.374750	−0.0136295
$757$	−34.8399	−1.26628	−0.633139	−	0.774038i	$-0.718234\pi$
$757$	−34.8399	−1.26628	−0.633139	+	0.774038i	$0.718234\pi$
$758$	31.9484	1.16042
$759$	25.8105	0.936862
$760$	13.3851	0.485528
$761$	−9.35927	−0.339273	−0.169637	−	0.985507i	$-0.554259\pi$
$761$	−9.35927	−0.339273	−0.169637	+	0.985507i	$0.554259\pi$
$762$	−4.32759	−0.156772
$763$	−1.88040	−0.0680752
$764$	−1.96669	−0.0711524
$765$	−15.2013	−0.549604
$766$	15.8580	0.572972
$767$	−13.7948	−0.498102
$768$	1.00000	0.0360844
$769$	−26.1241	−0.942058	−0.471029	−	0.882118i	$-0.656117\pi$
$769$	−26.1241	−0.942058	−0.471029	+	0.882118i	$0.656117\pi$
$770$	−4.94250	−0.178115
$771$	−5.29370	−0.190648
$772$	10.7503	0.386911
$773$	14.9171	0.536529	0.268265	−	0.963345i	$-0.413550\pi$
$773$	14.9171	0.536529	0.268265	+	0.963345i	$0.413550\pi$
$774$	12.1822	0.437881
$775$	−2.87999	−0.103452
$776$	−4.91379	−0.176395
$777$	−0.449734	−0.0161341
$778$	11.7709	0.422007
$779$	−17.9135	−0.641819
$780$	−2.32389	−0.0832087
$781$	−17.2272	−0.616437
$782$	−29.7490	−1.06382
$783$	5.38709	0.192519
$784$	−6.85956	−0.244984
$785$	16.4969	0.588801
$786$	−6.45170	−0.230125
$787$	−35.1774	−1.25394	−0.626970	−	0.779043i	$-0.715705\pi$
$787$	−35.1774	−1.25394	−0.626970	+	0.779043i	$0.715705\pi$
$788$	0.0128701	0.000458480 0
$789$	−27.4819	−0.978383
$790$	9.07136	0.322745
$791$	0.895325	0.0318341
$792$	5.67530	0.201663
$793$	5.86119	0.208137
$794$	−20.8461	−0.739800
$795$	−26.1594	−0.927777
$796$	12.0128	0.425781
$797$	−29.8581	−1.05763	−0.528814	−	0.848738i	$-0.677363\pi$
$797$	−29.8581	−1.05763	−0.528814	+	0.848738i	$0.677363\pi$
$798$	−2.15848	−0.0764093
$799$	−8.35311	−0.295512
$800$	0.400476	0.0141590
$801$	−3.18886	−0.112673
$802$	−32.6364	−1.15243
$803$	−28.4634	−1.00445
$804$	11.4452	0.403642
$805$	−3.96064	−0.139594
$806$	7.19141	0.253307
$807$	−9.96162	−0.350666
$808$	9.60630	0.337948
$809$	−38.8585	−1.36619	−0.683095	−	0.730329i	$-0.739367\pi$
$809$	−38.8585	−1.36619	−0.683095	+	0.730329i	$0.739367\pi$
$810$	2.32389	0.0816533
$811$	20.8496	0.732128	0.366064	−	0.930590i	$-0.380705\pi$
$811$	20.8496	0.732128	0.366064	+	0.930590i	$0.380705\pi$
$812$	−2.01881	−0.0708465
$813$	15.0010	0.526106
$814$	6.81087	0.238721
$815$	47.7482	1.67255
$816$	−6.54130	−0.228991
$817$	70.1669	2.45483
$818$	−15.6682	−0.547826
$819$	0.374750	0.0130948
$820$	−7.22756	−0.252397
$821$	−31.1460	−1.08700	−0.543501	−	0.839409i	$-0.682901\pi$
$821$	−31.1460	−1.08700	−0.543501	+	0.839409i	$0.682901\pi$
$822$	−8.27244	−0.288535
$823$	−42.5703	−1.48391	−0.741953	−	0.670452i	$-0.766100\pi$
$823$	−42.5703	−1.48391	−0.741953	+	0.670452i	$0.766100\pi$
$824$	1.00000	0.0348367
$825$	2.27282	0.0791294
$826$	−5.16961	−0.179874
$827$	8.42762	0.293057	0.146528	−	0.989206i	$-0.453190\pi$
$827$	8.42762	0.293057	0.146528	+	0.989206i	$0.453190\pi$
$828$	4.54787	0.158049
$829$	−0.772210	−0.0268199	−0.0134100	−	0.999910i	$-0.504269\pi$
$829$	−0.772210	−0.0268199	−0.0134100	+	0.999910i	$0.504269\pi$
$830$	−4.89316	−0.169844
$831$	8.27269	0.286977
$832$	−1.00000	−0.0346688
$833$	44.8705	1.55467
$834$	−0.432789	−0.0149863
$835$	12.4496	0.430836
$836$	32.6884	1.13055
$837$	−7.19141	−0.248572
$838$	−31.8520	−1.10031
$839$	13.2590	0.457753	0.228877	−	0.973455i	$-0.426495\pi$
$839$	13.2590	0.457753	0.228877	+	0.973455i	$0.426495\pi$
$840$	−0.870879	−0.0300482
$841$	0.0207663	0.000716078 0
$842$	9.44236	0.325405
$843$	−0.956702	−0.0329506
$844$	−2.95675	−0.101776
$845$	2.32389	0.0799443
$846$	1.27698	0.0439035
$847$	−7.94808	−0.273099
$848$	−11.2567	−0.386557
$849$	−12.3188	−0.422779
$850$	−2.61963	−0.0898527
$851$	5.45785	0.187093
$852$	−3.03547	−0.103993
$853$	−14.9163	−0.510726	−0.255363	−	0.966845i	$-0.582195\pi$
$853$	−14.9163	−0.510726	−0.255363	+	0.966845i	$0.582195\pi$
$854$	2.19648	0.0751621
$855$	13.3851	0.457761
$856$	−4.50856	−0.154099
$857$	−39.5285	−1.35027	−0.675135	−	0.737694i	$-0.735915\pi$
$857$	−39.5285	−1.35027	−0.675135	+	0.737694i	$0.735915\pi$
$858$	−5.67530	−0.193751
$859$	−12.8137	−0.437196	−0.218598	−	0.975815i	$-0.570148\pi$
$859$	−12.8137	−0.437196	−0.218598	+	0.975815i	$0.570148\pi$
$860$	28.3102	0.965369
$861$	1.16551	0.0397206
$862$	−11.5799	−0.394412
$863$	6.71961	0.228738	0.114369	−	0.993438i	$-0.463515\pi$
$863$	6.71961	0.228738	0.114369	+	0.993438i	$0.463515\pi$
$864$	1.00000	0.0340207
$865$	−3.84915	−0.130875
$866$	−30.6151	−1.04034
$867$	25.7886	0.875828
$868$	2.69499	0.0914738
$869$	22.1536	0.751511
$870$	12.5190	0.424435
$871$	−11.4452	−0.387807
$872$	5.01775	0.169922
$873$	−4.91379	−0.166307
$874$	26.1947	0.886048
$875$	4.00563	0.135415
$876$	−5.01531	−0.169452
$877$	−19.2487	−0.649983	−0.324991	−	0.945717i	$-0.605361\pi$
$877$	−19.2487	−0.649983	−0.324991	+	0.945717i	$0.605361\pi$
$878$	6.12116	0.206579
$879$	16.1483	0.544670
$880$	13.1888	0.444594
$881$	39.4480	1.32904	0.664518	−	0.747272i	$-0.268637\pi$
$881$	39.4480	1.32904	0.664518	+	0.747272i	$0.268637\pi$
$882$	−6.85956	−0.230973
$883$	−2.05725	−0.0692319	−0.0346159	−	0.999401i	$-0.511021\pi$
$883$	−2.05725	−0.0692319	−0.0346159	+	0.999401i	$0.511021\pi$
$884$	6.54130	0.220008
$885$	32.0577	1.07761
$886$	−15.3458	−0.515552
$887$	−42.5977	−1.43029	−0.715146	−	0.698975i	$-0.753640\pi$
$887$	−42.5977	−1.43029	−0.715146	+	0.698975i	$0.753640\pi$
$888$	1.20009	0.0402724
$889$	1.62177	0.0543923
$890$	−7.41056	−0.248403
$891$	5.67530	0.190130
$892$	−11.4459	−0.383236
$893$	7.35512	0.246130
$894$	−8.83602	−0.295521
$895$	20.0413	0.669905
$896$	−0.374750	−0.0125195
$897$	−4.54787	−0.151849
$898$	10.8492	0.362042
$899$	−38.7408	−1.29208
$900$	0.400476	0.0133492
$901$	73.6335	2.45309
$902$	−17.6508	−0.587707
$903$	−4.56529	−0.151923
$904$	−2.38912	−0.0794611
$905$	−2.00278	−0.0665745
$906$	−15.4986	−0.514908
$907$	40.7959	1.35461	0.677303	−	0.735704i	$-0.263149\pi$
$907$	40.7959	1.35461	0.677303	+	0.735704i	$0.263149\pi$
$908$	−1.02550	−0.0340323
$909$	9.60630	0.318621
$910$	0.870879	0.0288694
$911$	46.5465	1.54216	0.771078	−	0.636741i	$-0.219718\pi$
$911$	46.5465	1.54216	0.771078	+	0.636741i	$0.219718\pi$
$912$	5.75977	0.190725
$913$	−11.9499	−0.395482
$914$	−3.60474	−0.119234
$915$	−13.6208	−0.450289
$916$	−27.0378	−0.893355
$917$	2.41778	0.0798421
$918$	−6.54130	−0.215895
$919$	20.4477	0.674509	0.337254	−	0.941414i	$-0.390502\pi$
$919$	20.4477	0.674509	0.337254	+	0.941414i	$0.390502\pi$
$920$	10.5688	0.348441
$921$	17.3930	0.573120
$922$	29.5826	0.974251
$923$	3.03547	0.0999136
$924$	−2.12682	−0.0699672
$925$	0.480607	0.0158023
$926$	2.58748	0.0850300
$927$	1.00000	0.0328443
$928$	5.38709	0.176840
$929$	58.1442	1.90765	0.953824	−	0.300366i	$-0.0971088\pi$
$929$	58.1442	1.90765	0.953824	+	0.300366i	$0.0971088\pi$
$930$	−16.7121	−0.548010
$931$	−39.5095	−1.29487
$932$	1.16247	0.0380779
$933$	−26.2190	−0.858372
$934$	25.9862	0.850295
$935$	−86.2718	−2.82139
$936$	−1.00000	−0.0326860
$937$	−19.0655	−0.622843	−0.311421	−	0.950272i	$-0.600805\pi$
$937$	−19.0655	−0.622843	−0.311421	+	0.950272i	$0.600805\pi$
$938$	−4.28910	−0.140044
$939$	23.4796	0.766227
$940$	2.96756	0.0967913
$941$	15.6561	0.510374	0.255187	−	0.966892i	$-0.417863\pi$
$941$	15.6561	0.510374	0.255187	+	0.966892i	$0.417863\pi$
$942$	7.09884	0.231293
$943$	−14.1444	−0.460604
$944$	13.7948	0.448983
$945$	−0.870879	−0.0283297
$946$	69.1377	2.24786
$947$	12.2700	0.398721	0.199360	−	0.979926i	$-0.436114\pi$
$947$	12.2700	0.398721	0.199360	+	0.979926i	$0.436114\pi$
$948$	3.90352	0.126780
$949$	5.01531	0.162804
$950$	2.30665	0.0748376
$951$	−25.8367	−0.837812
$952$	2.45136	0.0794489
$953$	26.1182	0.846051	0.423025	−	0.906118i	$-0.360968\pi$
$953$	26.1182	0.846051	0.423025	+	0.906118i	$0.360968\pi$
$954$	−11.2567	−0.364449
$955$	−4.57038	−0.147894
$956$	−1.38196	−0.0446958
$957$	30.5734	0.988296
$958$	−15.4621	−0.499558
$959$	3.10010	0.100107
$960$	2.32389	0.0750033
$961$	20.7164	0.668272
$962$	−1.20009	−0.0386925
$963$	−4.50856	−0.145286
$964$	−27.7699	−0.894408
$965$	24.9825	0.804214
$966$	−1.70431	−0.0548354
$967$	17.1598	0.551823	0.275911	−	0.961183i	$-0.411020\pi$
$967$	17.1598	0.551823	0.275911	+	0.961183i	$0.411020\pi$
$968$	21.2090	0.681683
$969$	−37.6764	−1.21034
$970$	−11.4191	−0.366646
$971$	32.2017	1.03340	0.516700	−	0.856166i	$-0.327160\pi$
$971$	32.2017	1.03340	0.516700	+	0.856166i	$0.327160\pi$
$972$	1.00000	0.0320750
$973$	0.162188	0.00519950
$974$	20.0582	0.642707
$975$	−0.400476	−0.0128255
$976$	−5.86119	−0.187612
$977$	15.9225	0.509406	0.254703	−	0.967019i	$-0.418022\pi$
$977$	15.9225	0.509406	0.254703	+	0.967019i	$0.418022\pi$
$978$	20.5467	0.657010
$979$	−18.0977	−0.578406
$980$	−15.9409	−0.509213
$981$	5.01775	0.160204
$982$	20.6114	0.657738
$983$	−30.3765	−0.968860	−0.484430	−	0.874830i	$-0.660973\pi$
$983$	−30.3765	−0.968860	−0.484430	+	0.874830i	$0.660973\pi$
$984$	−3.11011	−0.0991467
$985$	0.0299088	0.000952974 0
$986$	−35.2386	−1.12223
$987$	−0.478549	−0.0152324
$988$	−5.75977	−0.183243
$989$	55.4031	1.76172
$990$	13.1888	0.419167
$991$	6.27611	0.199367	0.0996836	−	0.995019i	$-0.468217\pi$
$991$	6.27611	0.199367	0.0996836	+	0.995019i	$0.468217\pi$
$992$	−7.19141	−0.228328
$993$	−21.8397	−0.693062
$994$	1.13754	0.0360806
$995$	27.9164	0.885008
$996$	−2.10559	−0.0667182
$997$	−29.0509	−0.920052	−0.460026	−	0.887905i	$-0.652160\pi$
$997$	−29.0509	−0.920052	−0.460026	+	0.887905i	$0.652160\pi$
$998$	28.0107	0.886663
$999$	1.20009	0.0379692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.12	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.12	✓	16	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32389 q^{5} +1.00000 q^{6} -0.374750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32389 q^{5} +1.00000 q^{6} -0.374750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.32389 q^{10} +5.67530 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.374750 q^{14} +2.32389 q^{15} +1.00000 q^{16} -6.54130 q^{17} +1.00000 q^{18} +5.75977 q^{19} +2.32389 q^{20} -0.374750 q^{21} +5.67530 q^{22} +4.54787 q^{23} +1.00000 q^{24} +0.400476 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.374750 q^{28} +5.38709 q^{29} +2.32389 q^{30} -7.19141 q^{31} +1.00000 q^{32} +5.67530 q^{33} -6.54130 q^{34} -0.870879 q^{35} +1.00000 q^{36} +1.20009 q^{37} +5.75977 q^{38} -1.00000 q^{39} +2.32389 q^{40} -3.11011 q^{41} -0.374750 q^{42} +12.1822 q^{43} +5.67530 q^{44} +2.32389 q^{45} +4.54787 q^{46} +1.27698 q^{47} +1.00000 q^{48} -6.85956 q^{49} +0.400476 q^{50} -6.54130 q^{51} -1.00000 q^{52} -11.2567 q^{53} +1.00000 q^{54} +13.1888 q^{55} -0.374750 q^{56} +5.75977 q^{57} +5.38709 q^{58} +13.7948 q^{59} +2.32389 q^{60} -5.86119 q^{61} -7.19141 q^{62} -0.374750 q^{63} +1.00000 q^{64} -2.32389 q^{65} +5.67530 q^{66} +11.4452 q^{67} -6.54130 q^{68} +4.54787 q^{69} -0.870879 q^{70} -3.03547 q^{71} +1.00000 q^{72} -5.01531 q^{73} +1.20009 q^{74} +0.400476 q^{75} +5.75977 q^{76} -2.12682 q^{77} -1.00000 q^{78} +3.90352 q^{79} +2.32389 q^{80} +1.00000 q^{81} -3.11011 q^{82} -2.10559 q^{83} -0.374750 q^{84} -15.2013 q^{85} +12.1822 q^{86} +5.38709 q^{87} +5.67530 q^{88} -3.18886 q^{89} +2.32389 q^{90} +0.374750 q^{91} +4.54787 q^{92} -7.19141 q^{93} +1.27698 q^{94} +13.3851 q^{95} +1.00000 q^{96} -4.91379 q^{97} -6.85956 q^{98} +5.67530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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