LMFDB - Embedded newform 4334.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} + \cdots + 16 $ x^17 - 5x^16 - 19x^15 + 121x^14 + 112x^13 - 1172x^12 - 25x^11 + 5845x^10 - 2233x^9 - 16035x^8 + 9174x^7 + 23882x^6 - 15232x^5 - 17609x^4 + 10764x^3 + 4764x^2 - 2368x + 16
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			1.17
Root			$3.27281$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.27281 q^{3} +1.00000 q^{4} -0.718794 q^{5} -3.27281 q^{6} -3.71200 q^{7} -1.00000 q^{8} +7.71127 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.27281 q^{3} +1.00000 q^{4} -0.718794 q^{5} -3.27281 q^{6} -3.71200 q^{7} -1.00000 q^{8} +7.71127 q^{9} +0.718794 q^{10} -1.00000 q^{11} +3.27281 q^{12} -1.02767 q^{13} +3.71200 q^{14} -2.35248 q^{15} +1.00000 q^{16} -5.59499 q^{17} -7.71127 q^{18} -1.39286 q^{19} -0.718794 q^{20} -12.1487 q^{21} +1.00000 q^{22} +5.66611 q^{23} -3.27281 q^{24} -4.48333 q^{25} +1.02767 q^{26} +15.4191 q^{27} -3.71200 q^{28} +6.63878 q^{29} +2.35248 q^{30} -5.86146 q^{31} -1.00000 q^{32} -3.27281 q^{33} +5.59499 q^{34} +2.66816 q^{35} +7.71127 q^{36} +2.90613 q^{37} +1.39286 q^{38} -3.36335 q^{39} +0.718794 q^{40} -12.5051 q^{41} +12.1487 q^{42} +7.81271 q^{43} -1.00000 q^{44} -5.54282 q^{45} -5.66611 q^{46} -4.12250 q^{47} +3.27281 q^{48} +6.77894 q^{49} +4.48333 q^{50} -18.3113 q^{51} -1.02767 q^{52} -1.96763 q^{53} -15.4191 q^{54} +0.718794 q^{55} +3.71200 q^{56} -4.55856 q^{57} -6.63878 q^{58} -10.7645 q^{59} -2.35248 q^{60} -6.89262 q^{61} +5.86146 q^{62} -28.6242 q^{63} +1.00000 q^{64} +0.738680 q^{65} +3.27281 q^{66} +1.71202 q^{67} -5.59499 q^{68} +18.5441 q^{69} -2.66816 q^{70} -7.49643 q^{71} -7.71127 q^{72} -1.87944 q^{73} -2.90613 q^{74} -14.6731 q^{75} -1.39286 q^{76} +3.71200 q^{77} +3.36335 q^{78} -8.53461 q^{79} -0.718794 q^{80} +27.3299 q^{81} +12.5051 q^{82} -5.15930 q^{83} -12.1487 q^{84} +4.02165 q^{85} -7.81271 q^{86} +21.7275 q^{87} +1.00000 q^{88} -0.975999 q^{89} +5.54282 q^{90} +3.81469 q^{91} +5.66611 q^{92} -19.1834 q^{93} +4.12250 q^{94} +1.00118 q^{95} -3.27281 q^{96} -16.1433 q^{97} -6.77894 q^{98} -7.71127 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * 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
$3$	3.27281	1.88956	0.944778	−	0.327710i	$-0.106277\pi$
$3$	3.27281	1.88956	0.944778	+	0.327710i	$0.106277\pi$
$4$	1.00000	0.500000
$5$	−0.718794	−0.321455	−0.160727	−	0.986999i	$-0.551384\pi$
$5$	−0.718794	−0.321455	−0.160727	+	0.986999i	$0.551384\pi$
$6$	−3.27281	−1.33612
$7$	−3.71200	−1.40300	−0.701502	−	0.712668i	$-0.747487\pi$
$7$	−3.71200	−1.40300	−0.701502	+	0.712668i	$0.747487\pi$
$8$	−1.00000	−0.353553
$9$	7.71127	2.57042
$10$	0.718794	0.227303
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.27281	0.944778
$13$	−1.02767	−0.285023	−0.142512	−	0.989793i	$-0.545518\pi$
$13$	−1.02767	−0.285023	−0.142512	+	0.989793i	$0.545518\pi$
$14$	3.71200	0.992074
$15$	−2.35248	−0.607407
$16$	1.00000	0.250000
$17$	−5.59499	−1.35698	−0.678492	−	0.734608i	$-0.737366\pi$
$17$	−5.59499	−1.35698	−0.678492	+	0.734608i	$0.737366\pi$
$18$	−7.71127	−1.81756
$19$	−1.39286	−0.319543	−0.159772	−	0.987154i	$-0.551076\pi$
$19$	−1.39286	−0.319543	−0.159772	+	0.987154i	$0.551076\pi$
$20$	−0.718794	−0.160727
$21$	−12.1487	−2.65106
$22$	1.00000	0.213201
$23$	5.66611	1.18147	0.590733	−	0.806867i	$-0.298839\pi$
$23$	5.66611	1.18147	0.590733	+	0.806867i	$0.298839\pi$
$24$	−3.27281	−0.668059
$25$	−4.48333	−0.896667
$26$	1.02767	0.201542
$27$	15.4191	2.96740
$28$	−3.71200	−0.701502
$29$	6.63878	1.23279	0.616396	−	0.787437i	$-0.288592\pi$
$29$	6.63878	1.23279	0.616396	+	0.787437i	$0.288592\pi$
$30$	2.35248	0.429501
$31$	−5.86146	−1.05275	−0.526375	−	0.850253i	$-0.676449\pi$
$31$	−5.86146	−1.05275	−0.526375	+	0.850253i	$0.676449\pi$
$32$	−1.00000	−0.176777
$33$	−3.27281	−0.569723
$34$	5.59499	0.959533
$35$	2.66816	0.451002
$36$	7.71127	1.28521
$37$	2.90613	0.477765	0.238882	−	0.971049i	$-0.423219\pi$
$37$	2.90613	0.477765	0.238882	+	0.971049i	$0.423219\pi$
$38$	1.39286	0.225951
$39$	−3.36335	−0.538567
$40$	0.718794	0.113651
$41$	−12.5051	−1.95297	−0.976483	−	0.215595i	$-0.930831\pi$
$41$	−12.5051	−1.95297	−0.976483	+	0.215595i	$0.930831\pi$
$42$	12.1487	1.87458
$43$	7.81271	1.19143	0.595713	−	0.803197i	$-0.296869\pi$
$43$	7.81271	1.19143	0.595713	+	0.803197i	$0.296869\pi$
$44$	−1.00000	−0.150756
$45$	−5.54282	−0.826275
$46$	−5.66611	−0.835423
$47$	−4.12250	−0.601328	−0.300664	−	0.953730i	$-0.597208\pi$
$47$	−4.12250	−0.601328	−0.300664	+	0.953730i	$0.597208\pi$
$48$	3.27281	0.472389
$49$	6.77894	0.968420
$50$	4.48333	0.634039
$51$	−18.3113	−2.56410
$52$	−1.02767	−0.142512
$53$	−1.96763	−0.270275	−0.135137	−	0.990827i	$-0.543148\pi$
$53$	−1.96763	−0.270275	−0.135137	+	0.990827i	$0.543148\pi$
$54$	−15.4191	−2.09827
$55$	0.718794	0.0969222
$56$	3.71200	0.496037
$57$	−4.55856	−0.603795
$58$	−6.63878	−0.871715
$59$	−10.7645	−1.40142	−0.700711	−	0.713445i	$-0.747134\pi$
$59$	−10.7645	−1.40142	−0.700711	+	0.713445i	$0.747134\pi$
$60$	−2.35248	−0.303703
$61$	−6.89262	−0.882510	−0.441255	−	0.897382i	$-0.645467\pi$
$61$	−6.89262	−0.882510	−0.441255	+	0.897382i	$0.645467\pi$
$62$	5.86146	0.744406
$63$	−28.6242	−3.60631
$64$	1.00000	0.125000
$65$	0.738680	0.0916220
$66$	3.27281	0.402855
$67$	1.71202	0.209157	0.104578	−	0.994517i	$-0.466651\pi$
$67$	1.71202	0.209157	0.104578	+	0.994517i	$0.466651\pi$
$68$	−5.59499	−0.678492
$69$	18.5441	2.23245
$70$	−2.66816	−0.318907
$71$	−7.49643	−0.889662	−0.444831	−	0.895615i	$-0.646736\pi$
$71$	−7.49643	−0.889662	−0.444831	+	0.895615i	$0.646736\pi$
$72$	−7.71127	−0.908782
$73$	−1.87944	−0.219971	−0.109986	−	0.993933i	$-0.535081\pi$
$73$	−1.87944	−0.219971	−0.109986	+	0.993933i	$0.535081\pi$
$74$	−2.90613	−0.337831
$75$	−14.6731	−1.69430
$76$	−1.39286	−0.159772
$77$	3.71200	0.423022
$78$	3.36335	0.380824
$79$	−8.53461	−0.960218	−0.480109	−	0.877209i	$-0.659403\pi$
$79$	−8.53461	−0.960218	−0.480109	+	0.877209i	$0.659403\pi$
$80$	−0.718794	−0.0803637
$81$	27.3299	3.03665
$82$	12.5051	1.38096
$83$	−5.15930	−0.566307	−0.283153	−	0.959075i	$-0.591381\pi$
$83$	−5.15930	−0.566307	−0.283153	+	0.959075i	$0.591381\pi$
$84$	−12.1487	−1.32553
$85$	4.02165	0.436209
$86$	−7.81271	−0.842466
$87$	21.7275	2.32943
$88$	1.00000	0.106600
$89$	−0.975999	−0.103456	−0.0517278	−	0.998661i	$-0.516473\pi$
$89$	−0.975999	−0.103456	−0.0517278	+	0.998661i	$0.516473\pi$
$90$	5.54282	0.584264
$91$	3.81469	0.399888
$92$	5.66611	0.590733
$93$	−19.1834	−1.98923
$94$	4.12250	0.425203
$95$	1.00118	0.102719
$96$	−3.27281	−0.334030
$97$	−16.1433	−1.63911	−0.819553	−	0.573003i	$-0.805778\pi$
$97$	−16.1433	−1.63911	−0.819553	+	0.573003i	$0.805778\pi$
$98$	−6.77894	−0.684776
$99$	−7.71127	−0.775012
$100$	−4.48333	−0.448333
$101$	11.4917	1.14347	0.571736	−	0.820438i	$-0.306270\pi$
$101$	11.4917	1.14347	0.571736	+	0.820438i	$0.306270\pi$
$102$	18.3113	1.81309
$103$	5.21145	0.513499	0.256750	−	0.966478i	$-0.417348\pi$
$103$	5.21145	0.513499	0.256750	+	0.966478i	$0.417348\pi$
$104$	1.02767	0.100771
$105$	8.73239	0.852194
$106$	1.96763	0.191113
$107$	−19.1794	−1.85414	−0.927071	−	0.374885i	$-0.877682\pi$
$107$	−19.1794	−1.85414	−0.927071	+	0.374885i	$0.877682\pi$
$108$	15.4191	1.48370
$109$	14.2650	1.36634	0.683170	−	0.730259i	$-0.260601\pi$
$109$	14.2650	1.36634	0.683170	+	0.730259i	$0.260601\pi$
$110$	−0.718794	−0.0685344
$111$	9.51120	0.902763
$112$	−3.71200	−0.350751
$113$	−1.88162	−0.177008	−0.0885038	−	0.996076i	$-0.528209\pi$
$113$	−1.88162	−0.177008	−0.0885038	+	0.996076i	$0.528209\pi$
$114$	4.55856	0.426948
$115$	−4.07277	−0.379788
$116$	6.63878	0.616396
$117$	−7.92460	−0.732630
$118$	10.7645	0.990956
$119$	20.7686	1.90385
$120$	2.35248	0.214751
$121$	1.00000	0.0909091
$122$	6.89262	0.624029
$123$	−40.9267	−3.69024
$124$	−5.86146	−0.526375
$125$	6.81657	0.609692
$126$	28.6242	2.55005
$127$	−7.01048	−0.622080	−0.311040	−	0.950397i	$-0.600677\pi$
$127$	−7.01048	−0.622080	−0.311040	+	0.950397i	$0.600677\pi$
$128$	−1.00000	−0.0883883
$129$	25.5695	2.25127
$130$	−0.738680	−0.0647865
$131$	3.17912	0.277761	0.138881	−	0.990309i	$-0.455650\pi$
$131$	3.17912	0.277761	0.138881	+	0.990309i	$0.455650\pi$
$132$	−3.27281	−0.284861
$133$	5.17029	0.448321
$134$	−1.71202	−0.147896
$135$	−11.0832	−0.953886
$136$	5.59499	0.479766
$137$	1.24022	0.105959	0.0529796	−	0.998596i	$-0.483128\pi$
$137$	1.24022	0.105959	0.0529796	+	0.998596i	$0.483128\pi$
$138$	−18.5441	−1.57858
$139$	−15.0489	−1.27643	−0.638217	−	0.769856i	$-0.720328\pi$
$139$	−15.0489	−1.27643	−0.638217	+	0.769856i	$0.720328\pi$
$140$	2.66816	0.225501
$141$	−13.4921	−1.13624
$142$	7.49643	0.629086
$143$	1.02767	0.0859377
$144$	7.71127	0.642606
$145$	−4.77192	−0.396287
$146$	1.87944	0.155543
$147$	22.1862	1.82988
$148$	2.90613	0.238882
$149$	−9.44795	−0.774006	−0.387003	−	0.922078i	$-0.626490\pi$
$149$	−9.44795	−0.774006	−0.387003	+	0.922078i	$0.626490\pi$
$150$	14.6731	1.19805
$151$	−9.98852	−0.812854	−0.406427	−	0.913683i	$-0.633225\pi$
$151$	−9.98852	−0.812854	−0.406427	+	0.913683i	$0.633225\pi$
$152$	1.39286	0.112976
$153$	−43.1445	−3.48802
$154$	−3.71200	−0.299121
$155$	4.21318	0.338411
$156$	−3.36335	−0.269284
$157$	3.14270	0.250815	0.125407	−	0.992105i	$-0.459976\pi$
$157$	3.14270	0.250815	0.125407	+	0.992105i	$0.459976\pi$
$158$	8.53461	0.678977
$159$	−6.43968	−0.510699
$160$	0.718794	0.0568257
$161$	−21.0326	−1.65760
$162$	−27.3299	−2.14724
$163$	−11.0035	−0.861863	−0.430931	−	0.902385i	$-0.641815\pi$
$163$	−11.0035	−0.861863	−0.430931	+	0.902385i	$0.641815\pi$
$164$	−12.5051	−0.976483
$165$	2.35248	0.183140
$166$	5.15930	0.400439
$167$	17.9456	1.38867	0.694336	−	0.719651i	$-0.255698\pi$
$167$	17.9456	1.38867	0.694336	+	0.719651i	$0.255698\pi$
$168$	12.1487	0.937289
$169$	−11.9439	−0.918762
$170$	−4.02165	−0.308446
$171$	−10.7407	−0.821362
$172$	7.81271	0.595713
$173$	−17.7078	−1.34630	−0.673149	−	0.739507i	$-0.735059\pi$
$173$	−17.7078	−1.34630	−0.673149	+	0.739507i	$0.735059\pi$
$174$	−21.7275	−1.64715
$175$	16.6421	1.25803
$176$	−1.00000	−0.0753778
$177$	−35.2302	−2.64807
$178$	0.975999	0.0731542
$179$	−2.64909	−0.198002	−0.0990010	−	0.995087i	$-0.531565\pi$
$179$	−2.64909	−0.198002	−0.0990010	+	0.995087i	$0.531565\pi$
$180$	−5.54282	−0.413137
$181$	7.49911	0.557405	0.278702	−	0.960378i	$-0.410096\pi$
$181$	7.49911	0.557405	0.278702	+	0.960378i	$0.410096\pi$
$182$	−3.81469	−0.282764
$183$	−22.5582	−1.66755
$184$	−5.66611	−0.417711
$185$	−2.08891	−0.153580
$186$	19.1834	1.40660
$187$	5.59499	0.409146
$188$	−4.12250	−0.300664
$189$	−57.2356	−4.16328
$190$	−1.00118	−0.0726331
$191$	18.3056	1.32455	0.662274	−	0.749262i	$-0.269592\pi$
$191$	18.3056	1.32455	0.662274	+	0.749262i	$0.269592\pi$
$192$	3.27281	0.236195
$193$	−11.1608	−0.803372	−0.401686	−	0.915778i	$-0.631576\pi$
$193$	−11.1608	−0.803372	−0.401686	+	0.915778i	$0.631576\pi$
$194$	16.1433	1.15902
$195$	2.41756	0.173125
$196$	6.77894	0.484210
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	7.71127	0.548016
$199$	23.3529	1.65544	0.827721	−	0.561140i	$-0.189637\pi$
$199$	23.3529	1.65544	0.827721	+	0.561140i	$0.189637\pi$
$200$	4.48333	0.317020
$201$	5.60312	0.395214
$202$	−11.4917	−0.808556
$203$	−24.6432	−1.72961
$204$	−18.3113	−1.28205
$205$	8.98858	0.627790
$206$	−5.21145	−0.363099
$207$	43.6929	3.03687
$208$	−1.02767	−0.0712558
$209$	1.39286	0.0963460
$210$	−8.73239	−0.602592
$211$	−2.89161	−0.199067	−0.0995335	−	0.995034i	$-0.531735\pi$
$211$	−2.89161	−0.199067	−0.0995335	+	0.995034i	$0.531735\pi$
$212$	−1.96763	−0.135137
$213$	−24.5344	−1.68107
$214$	19.1794	1.31108
$215$	−5.61573	−0.382990
$216$	−15.4191	−1.04914
$217$	21.7577	1.47701
$218$	−14.2650	−0.966149
$219$	−6.15103	−0.415648
$220$	0.718794	0.0484611
$221$	5.74978	0.386772
$222$	−9.51120	−0.638350
$223$	−18.1897	−1.21807	−0.609035	−	0.793143i	$-0.708443\pi$
$223$	−18.1897	−1.21807	−0.609035	+	0.793143i	$0.708443\pi$
$224$	3.71200	0.248018
$225$	−34.5722	−2.30481
$226$	1.88162	0.125163
$227$	7.16501	0.475558	0.237779	−	0.971319i	$-0.423581\pi$
$227$	7.16501	0.475558	0.237779	+	0.971319i	$0.423581\pi$
$228$	−4.55856	−0.301898
$229$	−7.11306	−0.470044	−0.235022	−	0.971990i	$-0.575516\pi$
$229$	−7.11306	−0.470044	−0.235022	+	0.971990i	$0.575516\pi$
$230$	4.07277	0.268550
$231$	12.1487	0.799323
$232$	−6.63878	−0.435858
$233$	6.06437	0.397290	0.198645	−	0.980071i	$-0.436346\pi$
$233$	6.06437	0.397290	0.198645	+	0.980071i	$0.436346\pi$
$234$	7.92460	0.518048
$235$	2.96323	0.193300
$236$	−10.7645	−0.700711
$237$	−27.9321	−1.81439
$238$	−20.7686	−1.34623
$239$	24.6772	1.59624	0.798118	−	0.602501i	$-0.205829\pi$
$239$	24.6772	1.59624	0.798118	+	0.602501i	$0.205829\pi$
$240$	−2.35248	−0.151852
$241$	3.07444	0.198042	0.0990209	−	0.995085i	$-0.468429\pi$
$241$	3.07444	0.198042	0.0990209	+	0.995085i	$0.468429\pi$
$242$	−1.00000	−0.0642824
$243$	43.1882	2.77053
$244$	−6.89262	−0.441255
$245$	−4.87266	−0.311303
$246$	40.9267	2.60939
$247$	1.43139	0.0910772
$248$	5.86146	0.372203
$249$	−16.8854	−1.07007
$250$	−6.81657	−0.431118
$251$	−20.6094	−1.30086	−0.650428	−	0.759568i	$-0.725410\pi$
$251$	−20.6094	−1.30086	−0.650428	+	0.759568i	$0.725410\pi$
$252$	−28.6242	−1.80316
$253$	−5.66611	−0.356225
$254$	7.01048	0.439877
$255$	13.1621	0.824241
$256$	1.00000	0.0625000
$257$	9.58975	0.598192	0.299096	−	0.954223i	$-0.403315\pi$
$257$	9.58975	0.598192	0.299096	+	0.954223i	$0.403315\pi$
$258$	−25.5695	−1.59189
$259$	−10.7875	−0.670306
$260$	0.738680	0.0458110
$261$	51.1935	3.16880
$262$	−3.17912	−0.196407
$263$	6.98748	0.430867	0.215433	−	0.976519i	$-0.430884\pi$
$263$	6.98748	0.430867	0.215433	+	0.976519i	$0.430884\pi$
$264$	3.27281	0.201427
$265$	1.41432	0.0868811
$266$	−5.17029	−0.317011
$267$	−3.19426	−0.195485
$268$	1.71202	0.104578
$269$	−1.93784	−0.118152	−0.0590761	−	0.998253i	$-0.518815\pi$
$269$	−1.93784	−0.118152	−0.0590761	+	0.998253i	$0.518815\pi$
$270$	11.0832	0.674499
$271$	−3.24801	−0.197303	−0.0986513	−	0.995122i	$-0.531453\pi$
$271$	−3.24801	−0.197303	−0.0986513	+	0.995122i	$0.531453\pi$
$272$	−5.59499	−0.339246
$273$	12.4848	0.755612
$274$	−1.24022	−0.0749244
$275$	4.48333	0.270355
$276$	18.5441	1.11622
$277$	−31.4413	−1.88913	−0.944564	−	0.328328i	$-0.893515\pi$
$277$	−31.4413	−1.88913	−0.944564	+	0.328328i	$0.893515\pi$
$278$	15.0489	0.902576
$279$	−45.1993	−2.70601
$280$	−2.66816	−0.159453
$281$	28.5154	1.70109	0.850543	−	0.525905i	$-0.176273\pi$
$281$	28.5154	1.70109	0.850543	+	0.525905i	$0.176273\pi$
$282$	13.4921	0.803445
$283$	−10.1648	−0.604236	−0.302118	−	0.953271i	$-0.597694\pi$
$283$	−10.1648	−0.604236	−0.302118	+	0.953271i	$0.597694\pi$
$284$	−7.49643	−0.444831
$285$	3.27666	0.194093
$286$	−1.02767	−0.0607671
$287$	46.4189	2.74002
$288$	−7.71127	−0.454391
$289$	14.3039	0.841406
$290$	4.77192	0.280217
$291$	−52.8340	−3.09718
$292$	−1.87944	−0.109986
$293$	30.4672	1.77991	0.889957	−	0.456045i	$-0.150735\pi$
$293$	30.4672	1.77991	0.889957	+	0.456045i	$0.150735\pi$
$294$	−22.1862	−1.29392
$295$	7.73749	0.450494
$296$	−2.90613	−0.168915
$297$	−15.4191	−0.894706
$298$	9.44795	0.547305
$299$	−5.82287	−0.336745
$300$	−14.6731	−0.847151
$301$	−29.0008	−1.67158
$302$	9.98852	0.574775
$303$	37.6103	2.16065
$304$	−1.39286	−0.0798859
$305$	4.95438	0.283687
$306$	43.1445	2.46641
$307$	9.61702	0.548872	0.274436	−	0.961605i	$-0.411509\pi$
$307$	9.61702	0.548872	0.274436	+	0.961605i	$0.411509\pi$
$308$	3.71200	0.211511
$309$	17.0561	0.970286
$310$	−4.21318	−0.239293
$311$	25.1101	1.42386	0.711930	−	0.702250i	$-0.247821\pi$
$311$	25.1101	1.42386	0.711930	+	0.702250i	$0.247821\pi$
$312$	3.36335	0.190412
$313$	−9.09727	−0.514208	−0.257104	−	0.966384i	$-0.582768\pi$
$313$	−9.09727	−0.514208	−0.257104	+	0.966384i	$0.582768\pi$
$314$	−3.14270	−0.177353
$315$	20.5749	1.15927
$316$	−8.53461	−0.480109
$317$	1.09412	0.0614517	0.0307259	−	0.999528i	$-0.490218\pi$
$317$	1.09412	0.0614517	0.0307259	+	0.999528i	$0.490218\pi$
$318$	6.43968	0.361119
$319$	−6.63878	−0.371701
$320$	−0.718794	−0.0401818
$321$	−62.7705	−3.50351
$322$	21.0326	1.17210
$323$	7.79302	0.433615
$324$	27.3299	1.51833
$325$	4.60737	0.255571
$326$	11.0035	0.609429
$327$	46.6867	2.58178
$328$	12.5051	0.690478
$329$	15.3027	0.843666
$330$	−2.35248	−0.129500
$331$	5.49283	0.301913	0.150957	−	0.988540i	$-0.451765\pi$
$331$	5.49283	0.301913	0.150957	+	0.988540i	$0.451765\pi$
$332$	−5.15930	−0.283153
$333$	22.4099	1.22806
$334$	−17.9456	−0.981939
$335$	−1.23059	−0.0672345
$336$	−12.1487	−0.662764
$337$	15.2448	0.830438	0.415219	−	0.909722i	$-0.363705\pi$
$337$	15.2448	0.830438	0.415219	+	0.909722i	$0.363705\pi$
$338$	11.9439	0.649663
$339$	−6.15817	−0.334466
$340$	4.02165	0.218104
$341$	5.86146	0.317416
$342$	10.7407	0.580791
$343$	0.820579	0.0443071
$344$	−7.81271	−0.421233
$345$	−13.3294	−0.717630
$346$	17.7078	0.951976
$347$	32.3057	1.73426	0.867130	−	0.498081i	$-0.165962\pi$
$347$	32.3057	1.73426	0.867130	+	0.498081i	$0.165962\pi$
$348$	21.7275	1.16471
$349$	27.2244	1.45729	0.728644	−	0.684892i	$-0.240151\pi$
$349$	27.2244	1.45729	0.728644	+	0.684892i	$0.240151\pi$
$350$	−16.6421	−0.889560
$351$	−15.8457	−0.845779
$352$	1.00000	0.0533002
$353$	4.79750	0.255345	0.127673	−	0.991816i	$-0.459249\pi$
$353$	4.79750	0.255345	0.127673	+	0.991816i	$0.459249\pi$
$354$	35.2302	1.87247
$355$	5.38839	0.285986
$356$	−0.975999	−0.0517278
$357$	67.9716	3.59744
$358$	2.64909	0.140009
$359$	25.6919	1.35597	0.677984	−	0.735076i	$-0.262854\pi$
$359$	25.6919	1.35597	0.677984	+	0.735076i	$0.262854\pi$
$360$	5.54282	0.292132
$361$	−17.0599	−0.897892
$362$	−7.49911	−0.394145
$363$	3.27281	0.171778
$364$	3.81469	0.199944
$365$	1.35093	0.0707108
$366$	22.5582	1.17914
$367$	26.8474	1.40142	0.700712	−	0.713445i	$-0.252866\pi$
$367$	26.8474	1.40142	0.700712	+	0.713445i	$0.252866\pi$
$368$	5.66611	0.295366
$369$	−96.4301	−5.01995
$370$	2.08891	0.108597
$371$	7.30384	0.379197
$372$	−19.1834	−0.994614
$373$	−24.7254	−1.28023	−0.640117	−	0.768277i	$-0.721114\pi$
$373$	−24.7254	−1.28023	−0.640117	+	0.768277i	$0.721114\pi$
$374$	−5.59499	−0.289310
$375$	22.3093	1.15205
$376$	4.12250	0.212602
$377$	−6.82245	−0.351374
$378$	57.2356	2.94388
$379$	0.232164	0.0119254	0.00596272	−	0.999982i	$-0.498102\pi$
$379$	0.232164	0.0119254	0.00596272	+	0.999982i	$0.498102\pi$
$380$	1.00118	0.0513594
$381$	−22.9440	−1.17545
$382$	−18.3056	−0.936597
$383$	−22.0370	−1.12604	−0.563020	−	0.826443i	$-0.690361\pi$
$383$	−22.0370	−1.12604	−0.563020	+	0.826443i	$0.690361\pi$
$384$	−3.27281	−0.167015
$385$	−2.66816	−0.135982
$386$	11.1608	0.568069
$387$	60.2459	3.06247
$388$	−16.1433	−0.819553
$389$	2.36319	0.119819	0.0599093	−	0.998204i	$-0.480919\pi$
$389$	2.36319	0.119819	0.0599093	+	0.998204i	$0.480919\pi$
$390$	−2.41756	−0.122418
$391$	−31.7018	−1.60323
$392$	−6.77894	−0.342388
$393$	10.4047	0.524845
$394$	1.00000	0.0503793
$395$	6.13463	0.308667
$396$	−7.71127	−0.387506
$397$	22.6563	1.13709	0.568544	−	0.822653i	$-0.307507\pi$
$397$	22.6563	1.13709	0.568544	+	0.822653i	$0.307507\pi$
$398$	−23.3529	−1.17057
$399$	16.9214	0.847127
$400$	−4.48333	−0.224167
$401$	6.10327	0.304783	0.152392	−	0.988320i	$-0.451303\pi$
$401$	6.10327	0.304783	0.152392	+	0.988320i	$0.451303\pi$
$402$	−5.60312	−0.279458
$403$	6.02362	0.300058
$404$	11.4917	0.571736
$405$	−19.6446	−0.976147
$406$	24.6432	1.22302
$407$	−2.90613	−0.144051
$408$	18.3113	0.906546
$409$	20.5396	1.01562	0.507809	−	0.861470i	$-0.330455\pi$
$409$	20.5396	1.01562	0.507809	+	0.861470i	$0.330455\pi$
$410$	−8.98858	−0.443915
$411$	4.05900	0.200216
$412$	5.21145	0.256750
$413$	39.9579	1.96620
$414$	−43.6929	−2.14739
$415$	3.70847	0.182042
$416$	1.02767	0.0503854
$417$	−49.2523	−2.41190
$418$	−1.39286	−0.0681269
$419$	−21.0039	−1.02611	−0.513053	−	0.858357i	$-0.671486\pi$
$419$	−21.0039	−1.02611	−0.513053	+	0.858357i	$0.671486\pi$
$420$	8.73239	0.426097
$421$	−7.56037	−0.368470	−0.184235	−	0.982882i	$-0.558981\pi$
$421$	−7.56037	−0.368470	−0.184235	+	0.982882i	$0.558981\pi$
$422$	2.89161	0.140762
$423$	−31.7897	−1.54567
$424$	1.96763	0.0955566
$425$	25.0842	1.21676
$426$	24.5344	1.18869
$427$	25.5854	1.23817
$428$	−19.1794	−0.927071
$429$	3.36335	0.162384
$430$	5.61573	0.270815
$431$	4.55686	0.219496	0.109748	−	0.993959i	$-0.464996\pi$
$431$	4.55686	0.219496	0.109748	+	0.993959i	$0.464996\pi$
$432$	15.4191	0.741851
$433$	−27.9350	−1.34247	−0.671235	−	0.741244i	$-0.734236\pi$
$433$	−27.9350	−1.34247	−0.671235	+	0.741244i	$0.734236\pi$
$434$	−21.7577	−1.04440
$435$	−15.6176	−0.748806
$436$	14.2650	0.683170
$437$	−7.89209	−0.377530
$438$	6.15103	0.293908
$439$	−20.1194	−0.960245	−0.480123	−	0.877201i	$-0.659408\pi$
$439$	−20.1194	−0.960245	−0.480123	+	0.877201i	$0.659408\pi$
$440$	−0.718794	−0.0342672
$441$	52.2742	2.48925
$442$	−5.74978	−0.273489
$443$	3.76389	0.178828	0.0894140	−	0.995995i	$-0.471501\pi$
$443$	3.76389	0.178828	0.0894140	+	0.995995i	$0.471501\pi$
$444$	9.51120	0.451382
$445$	0.701543	0.0332563
$446$	18.1897	0.861305
$447$	−30.9213	−1.46253
$448$	−3.71200	−0.175375
$449$	31.9611	1.50834	0.754169	−	0.656681i	$-0.228040\pi$
$449$	31.9611	1.50834	0.754169	+	0.656681i	$0.228040\pi$
$450$	34.5722	1.62975
$451$	12.5051	0.588841
$452$	−1.88162	−0.0885038
$453$	−32.6905	−1.53593
$454$	−7.16501	−0.336271
$455$	−2.74198	−0.128546
$456$	4.55856	0.213474
$457$	35.2334	1.64815	0.824075	−	0.566481i	$-0.191696\pi$
$457$	35.2334	1.64815	0.824075	+	0.566481i	$0.191696\pi$
$458$	7.11306	0.332371
$459$	−86.2696	−4.02672
$460$	−4.07277	−0.189894
$461$	−33.4828	−1.55945	−0.779724	−	0.626123i	$-0.784641\pi$
$461$	−33.4828	−1.55945	−0.779724	+	0.626123i	$0.784641\pi$
$462$	−12.1487	−0.565207
$463$	−2.21488	−0.102934	−0.0514671	−	0.998675i	$-0.516390\pi$
$463$	−2.21488	−0.102934	−0.0514671	+	0.998675i	$0.516390\pi$
$464$	6.63878	0.308198
$465$	13.7889	0.639447
$466$	−6.06437	−0.280927
$467$	11.3173	0.523702	0.261851	−	0.965108i	$-0.415667\pi$
$467$	11.3173	0.523702	0.261851	+	0.965108i	$0.415667\pi$
$468$	−7.92460	−0.366315
$469$	−6.35503	−0.293448
$470$	−2.96323	−0.136684
$471$	10.2854	0.473928
$472$	10.7645	0.495478
$473$	−7.81271	−0.359229
$474$	27.9321	1.28297
$475$	6.24465	0.286524
$476$	20.7686	0.951927
$477$	−15.1729	−0.694721
$478$	−24.6772	−1.12871
$479$	15.0116	0.685899	0.342949	−	0.939354i	$-0.388574\pi$
$479$	15.0116	0.685899	0.342949	+	0.939354i	$0.388574\pi$
$480$	2.35248	0.107375
$481$	−2.98653	−0.136174
$482$	−3.07444	−0.140037
$483$	−68.8357	−3.13213
$484$	1.00000	0.0454545
$485$	11.6037	0.526898
$486$	−43.1882	−1.95906
$487$	1.76000	0.0797531	0.0398765	−	0.999205i	$-0.487304\pi$
$487$	1.76000	0.0797531	0.0398765	+	0.999205i	$0.487304\pi$
$488$	6.89262	0.312014
$489$	−36.0124	−1.62854
$490$	4.87266	0.220125
$491$	−39.6118	−1.78765	−0.893827	−	0.448411i	$-0.851990\pi$
$491$	−39.6118	−1.78765	−0.893827	+	0.448411i	$0.851990\pi$
$492$	−40.9267	−1.84512
$493$	−37.1439	−1.67288
$494$	−1.43139	−0.0644013
$495$	5.54282	0.249131
$496$	−5.86146	−0.263187
$497$	27.8267	1.24820
$498$	16.8854	0.756652
$499$	−13.8249	−0.618889	−0.309444	−	0.950918i	$-0.600143\pi$
$499$	−13.8249	−0.618889	−0.309444	+	0.950918i	$0.600143\pi$
$500$	6.81657	0.304846
$501$	58.7325	2.62397
$502$	20.6094	0.919844
$503$	−4.63612	−0.206714	−0.103357	−	0.994644i	$-0.532958\pi$
$503$	−4.63612	−0.206714	−0.103357	+	0.994644i	$0.532958\pi$
$504$	28.6242	1.27502
$505$	−8.26020	−0.367574
$506$	5.66611	0.251889
$507$	−39.0901	−1.73605
$508$	−7.01048	−0.311040
$509$	−15.2055	−0.673971	−0.336986	−	0.941510i	$-0.609407\pi$
$509$	−15.2055	−0.673971	−0.336986	+	0.941510i	$0.609407\pi$
$510$	−13.1621	−0.582827
$511$	6.97647	0.308621
$512$	−1.00000	−0.0441942
$513$	−21.4766	−0.948215
$514$	−9.58975	−0.422986
$515$	−3.74596	−0.165067
$516$	25.5695	1.12563
$517$	4.12250	0.181307
$518$	10.7875	0.473978
$519$	−57.9542	−2.54391
$520$	−0.738680	−0.0323933
$521$	−21.1634	−0.927184	−0.463592	−	0.886049i	$-0.653440\pi$
$521$	−21.1634	−0.927184	−0.463592	+	0.886049i	$0.653440\pi$
$522$	−51.1935	−2.24068
$523$	10.1485	0.443762	0.221881	−	0.975074i	$-0.428780\pi$
$523$	10.1485	0.443762	0.221881	+	0.975074i	$0.428780\pi$
$524$	3.17912	0.138881
$525$	54.4665	2.37711
$526$	−6.98748	−0.304669
$527$	32.7948	1.42856
$528$	−3.27281	−0.142431
$529$	9.10482	0.395862
$530$	−1.41432	−0.0614342
$531$	−83.0082	−3.60225
$532$	5.17029	0.224160
$533$	12.8510	0.556640
$534$	3.19426	0.138229
$535$	13.7860	0.596023
$536$	−1.71202	−0.0739481
$537$	−8.66995	−0.374136
$538$	1.93784	0.0835462
$539$	−6.77894	−0.291990
$540$	−11.0832	−0.476943
$541$	7.79842	0.335280	0.167640	−	0.985848i	$-0.446385\pi$
$541$	7.79842	0.335280	0.167640	+	0.985848i	$0.446385\pi$
$542$	3.24801	0.139514
$543$	24.5431	1.05325
$544$	5.59499	0.239883
$545$	−10.2536	−0.439217
$546$	−12.4848	−0.534298
$547$	−29.3207	−1.25366	−0.626832	−	0.779154i	$-0.715649\pi$
$547$	−29.3207	−1.25366	−0.626832	+	0.779154i	$0.715649\pi$
$548$	1.24022	0.0529796
$549$	−53.1509	−2.26842
$550$	−4.48333	−0.191170
$551$	−9.24688	−0.393930
$552$	−18.5441	−0.789289
$553$	31.6805	1.34719
$554$	31.4413	1.33581
$555$	−6.83660	−0.290197
$556$	−15.0489	−0.638217
$557$	−27.3511	−1.15890	−0.579451	−	0.815007i	$-0.696733\pi$
$557$	−27.3511	−1.15890	−0.579451	+	0.815007i	$0.696733\pi$
$558$	45.1993	1.91344
$559$	−8.02885	−0.339584
$560$	2.66816	0.112751
$561$	18.3113	0.773105
$562$	−28.5154	−1.20285
$563$	30.5399	1.28710	0.643552	−	0.765403i	$-0.277460\pi$
$563$	30.5399	1.28710	0.643552	+	0.765403i	$0.277460\pi$
$564$	−13.4921	−0.568122
$565$	1.35249	0.0568999
$566$	10.1648	0.427259
$567$	−101.449	−4.26044
$568$	7.49643	0.314543
$569$	−8.80295	−0.369039	−0.184520	−	0.982829i	$-0.559073\pi$
$569$	−8.80295	−0.369039	−0.184520	+	0.982829i	$0.559073\pi$
$570$	−3.27666	−0.137244
$571$	−13.1289	−0.549428	−0.274714	−	0.961526i	$-0.588583\pi$
$571$	−13.1289	−0.549428	−0.274714	+	0.961526i	$0.588583\pi$
$572$	1.02767	0.0429688
$573$	59.9108	2.50281
$574$	−46.4189	−1.93749
$575$	−25.4031	−1.05938
$576$	7.71127	0.321303
$577$	−46.6812	−1.94336	−0.971682	−	0.236294i	$-0.924067\pi$
$577$	−46.6812	−1.94336	−0.971682	+	0.236294i	$0.924067\pi$
$578$	−14.3039	−0.594964
$579$	−36.5271	−1.51802
$580$	−4.77192	−0.198143
$581$	19.1513	0.794530
$582$	52.8340	2.19004
$583$	1.96763	0.0814909
$584$	1.87944	0.0777716
$585$	5.69616	0.235507
$586$	−30.4672	−1.25859
$587$	39.8092	1.64310	0.821552	−	0.570134i	$-0.193109\pi$
$587$	39.8092	1.64310	0.821552	+	0.570134i	$0.193109\pi$
$588$	22.1862	0.914942
$589$	8.16418	0.336399
$590$	−7.73749	−0.318547
$591$	−3.27281	−0.134625
$592$	2.90613	0.119441
$593$	−13.0302	−0.535087	−0.267543	−	0.963546i	$-0.586212\pi$
$593$	−13.0302	−0.535087	−0.267543	+	0.963546i	$0.586212\pi$
$594$	15.4191	0.632653
$595$	−14.9284	−0.612003
$596$	−9.44795	−0.387003
$597$	76.4295	3.12805
$598$	5.82287	0.238115
$599$	−25.1393	−1.02716	−0.513582	−	0.858040i	$-0.671682\pi$
$599$	−25.1393	−1.02716	−0.513582	+	0.858040i	$0.671682\pi$
$600$	14.6731	0.599026
$601$	32.9381	1.34357	0.671786	−	0.740745i	$-0.265527\pi$
$601$	32.9381	1.34357	0.671786	+	0.740745i	$0.265527\pi$
$602$	29.0008	1.18198
$603$	13.2019	0.537622
$604$	−9.98852	−0.406427
$605$	−0.718794	−0.0292232
$606$	−37.6103	−1.52781
$607$	−39.0993	−1.58699	−0.793496	−	0.608575i	$-0.791741\pi$
$607$	−39.0993	−1.58699	−0.793496	+	0.608575i	$0.791741\pi$
$608$	1.39286	0.0564878
$609$	−80.6523	−3.26820
$610$	−4.95438	−0.200597
$611$	4.23655	0.171392
$612$	−43.1445	−1.74401
$613$	23.8347	0.962673	0.481337	−	0.876536i	$-0.340151\pi$
$613$	23.8347	0.962673	0.481337	+	0.876536i	$0.340151\pi$
$614$	−9.61702	−0.388111
$615$	29.4179	1.18624
$616$	−3.71200	−0.149561
$617$	41.9728	1.68976	0.844880	−	0.534955i	$-0.179671\pi$
$617$	41.9728	1.68976	0.844880	+	0.534955i	$0.179671\pi$
$618$	−17.0561	−0.686096
$619$	−12.1306	−0.487568	−0.243784	−	0.969829i	$-0.578389\pi$
$619$	−12.1306	−0.487568	−0.243784	+	0.969829i	$0.578389\pi$
$620$	4.21318	0.169206
$621$	87.3663	3.50589
$622$	−25.1101	−1.00682
$623$	3.62291	0.145149
$624$	−3.36335	−0.134642
$625$	17.5170	0.700678
$626$	9.09727	0.363600
$627$	4.55856	0.182051
$628$	3.14270	0.125407
$629$	−16.2598	−0.648319
$630$	−20.5749	−0.819725
$631$	−11.8126	−0.470251	−0.235126	−	0.971965i	$-0.575550\pi$
$631$	−11.8126	−0.470251	−0.235126	+	0.971965i	$0.575550\pi$
$632$	8.53461	0.339488
$633$	−9.46370	−0.376148
$634$	−1.09412	−0.0434529
$635$	5.03910	0.199970
$636$	−6.43968	−0.255350
$637$	−6.96648	−0.276022
$638$	6.63878	0.262832
$639$	−57.8070	−2.28681
$640$	0.718794	0.0284128
$641$	9.27251	0.366242	0.183121	−	0.983090i	$-0.441380\pi$
$641$	9.27251	0.366242	0.183121	+	0.983090i	$0.441380\pi$
$642$	62.7705	2.47735
$643$	17.2497	0.680263	0.340131	−	0.940378i	$-0.389528\pi$
$643$	17.2497	0.680263	0.340131	+	0.940378i	$0.389528\pi$
$644$	−21.0326	−0.828801
$645$	−18.3792	−0.723681
$646$	−7.79302	−0.306612
$647$	37.6956	1.48197	0.740983	−	0.671524i	$-0.234360\pi$
$647$	37.6956	1.48197	0.740983	+	0.671524i	$0.234360\pi$
$648$	−27.3299	−1.07362
$649$	10.7645	0.422545
$650$	−4.60737	−0.180716
$651$	71.2089	2.79090
$652$	−11.0035	−0.430931
$653$	−20.3881	−0.797849	−0.398924	−	0.916984i	$-0.630616\pi$
$653$	−20.3881	−0.797849	−0.398924	+	0.916984i	$0.630616\pi$
$654$	−46.6867	−1.82559
$655$	−2.28514	−0.0892876
$656$	−12.5051	−0.488241
$657$	−14.4928	−0.565420
$658$	−15.3027	−0.596562
$659$	33.6419	1.31050	0.655251	−	0.755412i	$-0.272563\pi$
$659$	33.6419	1.31050	0.655251	+	0.755412i	$0.272563\pi$
$660$	2.35248	0.0915700
$661$	−31.4834	−1.22456	−0.612282	−	0.790640i	$-0.709748\pi$
$661$	−31.4834	−1.22456	−0.612282	+	0.790640i	$0.709748\pi$
$662$	−5.49283	−0.213485
$663$	18.8179	0.730827
$664$	5.15930	0.200220
$665$	−3.71637	−0.144115
$666$	−22.4099	−0.868368
$667$	37.6161	1.45650
$668$	17.9456	0.694336
$669$	−59.5313	−2.30161
$670$	1.23059	0.0475419
$671$	6.89262	0.266087
$672$	12.1487	0.468645
$673$	40.3883	1.55685	0.778427	−	0.627735i	$-0.216018\pi$
$673$	40.3883	1.55685	0.778427	+	0.627735i	$0.216018\pi$
$674$	−15.2448	−0.587208
$675$	−69.1289	−2.66077
$676$	−11.9439	−0.459381
$677$	−12.4640	−0.479029	−0.239514	−	0.970893i	$-0.576988\pi$
$677$	−12.4640	−0.479029	−0.239514	+	0.970893i	$0.576988\pi$
$678$	6.15817	0.236503
$679$	59.9240	2.29967
$680$	−4.02165	−0.154223
$681$	23.4497	0.898595
$682$	−5.86146	−0.224447
$683$	−6.91333	−0.264531	−0.132266	−	0.991214i	$-0.542225\pi$
$683$	−6.91333	−0.264531	−0.132266	+	0.991214i	$0.542225\pi$
$684$	−10.7407	−0.410681
$685$	−0.891463	−0.0340611
$686$	−0.820579	−0.0313298
$687$	−23.2797	−0.888175
$688$	7.81271	0.297857
$689$	2.02207	0.0770345
$690$	13.3294	0.507441
$691$	−13.2740	−0.504966	−0.252483	−	0.967601i	$-0.581247\pi$
$691$	−13.2740	−0.504966	−0.252483	+	0.967601i	$0.581247\pi$
$692$	−17.7078	−0.673149
$693$	28.6242	1.08734
$694$	−32.3057	−1.22631
$695$	10.8171	0.410316
$696$	−21.7275	−0.823577
$697$	69.9658	2.65014
$698$	−27.2244	−1.03046
$699$	19.8475	0.750703
$700$	16.6421	0.629014
$701$	−41.9900	−1.58594	−0.792970	−	0.609261i	$-0.791466\pi$
$701$	−41.9900	−1.58594	−0.792970	+	0.609261i	$0.791466\pi$
$702$	15.8457	0.598056
$703$	−4.04782	−0.152667
$704$	−1.00000	−0.0376889
$705$	9.69808	0.365251
$706$	−4.79750	−0.180556
$707$	−42.6574	−1.60430
$708$	−35.2302	−1.32403
$709$	8.79873	0.330443	0.165222	−	0.986256i	$-0.447166\pi$
$709$	8.79873	0.330443	0.165222	+	0.986256i	$0.447166\pi$
$710$	−5.38839	−0.202223
$711$	−65.8127	−2.46817
$712$	0.975999	0.0365771
$713$	−33.2117	−1.24379
$714$	−67.9716	−2.54377
$715$	−0.738680	−0.0276251
$716$	−2.64909	−0.0990010
$717$	80.7638	3.01618
$718$	−25.6919	−0.958814
$719$	1.24025	0.0462537	0.0231268	−	0.999733i	$-0.492638\pi$
$719$	1.24025	0.0462537	0.0231268	+	0.999733i	$0.492638\pi$
$720$	−5.54282	−0.206569
$721$	−19.3449	−0.720442
$722$	17.0599	0.634906
$723$	10.0620	0.374211
$724$	7.49911	0.278702
$725$	−29.7639	−1.10540
$726$	−3.27281	−0.121465
$727$	−46.6120	−1.72874	−0.864371	−	0.502854i	$-0.832283\pi$
$727$	−46.6120	−1.72874	−0.864371	+	0.502854i	$0.832283\pi$
$728$	−3.81469	−0.141382
$729$	59.3571	2.19841
$730$	−1.35093	−0.0500001
$731$	−43.7120	−1.61675
$732$	−22.5582	−0.833776
$733$	12.9922	0.479877	0.239938	−	0.970788i	$-0.422873\pi$
$733$	12.9922	0.479877	0.239938	+	0.970788i	$0.422873\pi$
$734$	−26.8474	−0.990956
$735$	−15.9473	−0.588225
$736$	−5.66611	−0.208856
$737$	−1.71202	−0.0630632
$738$	96.4301	3.54964
$739$	23.9574	0.881286	0.440643	−	0.897682i	$-0.354750\pi$
$739$	23.9574	0.881286	0.440643	+	0.897682i	$0.354750\pi$
$740$	−2.08891	−0.0767898
$741$	4.68467	0.172096
$742$	−7.30384	−0.268132
$743$	34.9884	1.28360	0.641800	−	0.766872i	$-0.278188\pi$
$743$	34.9884	1.28360	0.641800	+	0.766872i	$0.278188\pi$
$744$	19.1834	0.703299
$745$	6.79113	0.248808
$746$	24.7254	0.905263
$747$	−39.7847	−1.45565
$748$	5.59499	0.204573
$749$	71.1939	2.60137
$750$	−22.3093	−0.814621
$751$	−48.5792	−1.77268	−0.886340	−	0.463034i	$-0.846761\pi$
$751$	−48.5792	−1.77268	−0.886340	+	0.463034i	$0.846761\pi$
$752$	−4.12250	−0.150332
$753$	−67.4507	−2.45804
$754$	6.82245	0.248459
$755$	7.17969	0.261296
$756$	−57.2356	−2.08164
$757$	10.6166	0.385868	0.192934	−	0.981212i	$-0.438200\pi$
$757$	10.6166	0.385868	0.192934	+	0.981212i	$0.438200\pi$
$758$	−0.232164	−0.00843256
$759$	−18.5441	−0.673108
$760$	−1.00118	−0.0363166
$761$	14.7744	0.535571	0.267785	−	0.963479i	$-0.413708\pi$
$761$	14.7744	0.535571	0.267785	+	0.963479i	$0.413708\pi$
$762$	22.9440	0.831172
$763$	−52.9517	−1.91698
$764$	18.3056	0.662274
$765$	31.0120	1.12124
$766$	22.0370	0.796230
$767$	11.0623	0.399438
$768$	3.27281	0.118097
$769$	−30.2319	−1.09019	−0.545095	−	0.838374i	$-0.683507\pi$
$769$	−30.2319	−1.09019	−0.545095	+	0.838374i	$0.683507\pi$
$770$	2.66816	0.0961540
$771$	31.3854	1.13032
$772$	−11.1608	−0.401686
$773$	42.6276	1.53321	0.766605	−	0.642119i	$-0.221945\pi$
$773$	42.6276	1.53321	0.766605	+	0.642119i	$0.221945\pi$
$774$	−60.2459	−2.16549
$775$	26.2789	0.943965
$776$	16.1433	0.579511
$777$	−35.3056	−1.26658
$778$	−2.36319	−0.0847246
$779$	17.4178	0.624057
$780$	2.41756	0.0865625
$781$	7.49643	0.268243
$782$	31.7018	1.13366
$783$	102.364	3.65819
$784$	6.77894	0.242105
$785$	−2.25895	−0.0806255
$786$	−10.4047	−0.371122
$787$	34.7737	1.23955	0.619775	−	0.784780i	$-0.287224\pi$
$787$	34.7737	1.23955	0.619775	+	0.784780i	$0.287224\pi$
$788$	−1.00000	−0.0356235
$789$	22.8687	0.814147
$790$	−6.13463	−0.218260
$791$	6.98456	0.248342
$792$	7.71127	0.274008
$793$	7.08331	0.251536
$794$	−22.6563	−0.804043
$795$	4.62880	0.164167
$796$	23.3529	0.827721
$797$	−8.59610	−0.304490	−0.152245	−	0.988343i	$-0.548650\pi$
$797$	−8.59610	−0.304490	−0.152245	+	0.988343i	$0.548650\pi$
$798$	−16.9214	−0.599009
$799$	23.0653	0.815993
$800$	4.48333	0.158510
$801$	−7.52619	−0.265925
$802$	−6.10327	−0.215514
$803$	1.87944	0.0663239
$804$	5.60312	0.197607
$805$	15.1181	0.532844
$806$	−6.02362	−0.212173
$807$	−6.34217	−0.223255
$808$	−11.4917	−0.404278
$809$	−43.5846	−1.53235	−0.766176	−	0.642631i	$-0.777843\pi$
$809$	−43.5846	−1.53235	−0.766176	+	0.642631i	$0.777843\pi$
$810$	19.6446	0.690240
$811$	−24.0149	−0.843277	−0.421638	−	0.906764i	$-0.638545\pi$
$811$	−24.0149	−0.843277	−0.421638	+	0.906764i	$0.638545\pi$
$812$	−24.6432	−0.864805
$813$	−10.6301	−0.372814
$814$	2.90613	0.101860
$815$	7.90928	0.277050
$816$	−18.3113	−0.641025
$817$	−10.8820	−0.380713
$818$	−20.5396	−0.718151
$819$	29.4161	1.02788
$820$	8.98858	0.313895
$821$	−14.2392	−0.496952	−0.248476	−	0.968638i	$-0.579930\pi$
$821$	−14.2392	−0.496952	−0.248476	+	0.968638i	$0.579930\pi$
$822$	−4.05900	−0.141574
$823$	−16.5979	−0.578566	−0.289283	−	0.957244i	$-0.593417\pi$
$823$	−16.5979	−0.578566	−0.289283	+	0.957244i	$0.593417\pi$
$824$	−5.21145	−0.181549
$825$	14.6731	0.510851
$826$	−39.9579	−1.39031
$827$	47.3659	1.64707	0.823537	−	0.567263i	$-0.191998\pi$
$827$	47.3659	1.64707	0.823537	+	0.567263i	$0.191998\pi$
$828$	43.6929	1.51843
$829$	−17.0269	−0.591370	−0.295685	−	0.955286i	$-0.595548\pi$
$829$	−17.0269	−0.591370	−0.295685	+	0.955286i	$0.595548\pi$
$830$	−3.70847	−0.128723
$831$	−102.901	−3.56961
$832$	−1.02767	−0.0356279
$833$	−37.9281	−1.31413
$834$	49.2523	1.70547
$835$	−12.8992	−0.446395
$836$	1.39286	0.0481730
$837$	−90.3783	−3.12393
$838$	21.0039	0.725567
$839$	12.4509	0.429854	0.214927	−	0.976630i	$-0.431049\pi$
$839$	12.4509	0.429854	0.214927	+	0.976630i	$0.431049\pi$
$840$	−8.73239	−0.301296
$841$	15.0735	0.519774
$842$	7.56037	0.260547
$843$	93.3254	3.21430
$844$	−2.89161	−0.0995335
$845$	8.58521	0.295340
$846$	31.7897	1.09295
$847$	−3.71200	−0.127546
$848$	−1.96763	−0.0675687
$849$	−33.2675	−1.14174
$850$	−25.0842	−0.860381
$851$	16.4665	0.564463
$852$	−24.5344	−0.840533
$853$	−8.29840	−0.284132	−0.142066	−	0.989857i	$-0.545374\pi$
$853$	−8.29840	−0.284132	−0.142066	+	0.989857i	$0.545374\pi$
$854$	−25.5854	−0.875515
$855$	7.72036	0.264031
$856$	19.1794	0.655539
$857$	−43.5023	−1.48601	−0.743005	−	0.669286i	$-0.766600\pi$
$857$	−43.5023	−1.48601	−0.743005	+	0.669286i	$0.766600\pi$
$858$	−3.36335	−0.114823
$859$	9.74960	0.332652	0.166326	−	0.986071i	$-0.446810\pi$
$859$	9.74960	0.332652	0.166326	+	0.986071i	$0.446810\pi$
$860$	−5.61573	−0.191495
$861$	151.920	5.17742
$862$	−4.55686	−0.155207
$863$	−41.0375	−1.39693	−0.698467	−	0.715642i	$-0.746134\pi$
$863$	−41.0375	−1.39693	−0.698467	+	0.715642i	$0.746134\pi$
$864$	−15.4191	−0.524568
$865$	12.7283	0.432774
$866$	27.9350	0.949270
$867$	46.8139	1.58988
$868$	21.7577	0.738505
$869$	8.53461	0.289517
$870$	15.6176	0.529486
$871$	−1.75939	−0.0596145
$872$	−14.2650	−0.483074
$873$	−124.486	−4.21320
$874$	7.89209	0.266954
$875$	−25.3031	−0.855401
$876$	−6.15103	−0.207824
$877$	25.6087	0.864744	0.432372	−	0.901695i	$-0.357677\pi$
$877$	25.6087	0.864744	0.432372	+	0.901695i	$0.357677\pi$
$878$	20.1194	0.678996
$879$	99.7133	3.36325
$880$	0.718794	0.0242306
$881$	−23.5484	−0.793365	−0.396683	−	0.917956i	$-0.629839\pi$
$881$	−23.5484	−0.793365	−0.396683	+	0.917956i	$0.629839\pi$
$882$	−52.2742	−1.76017
$883$	14.3716	0.483642	0.241821	−	0.970321i	$-0.422255\pi$
$883$	14.3716	0.483642	0.241821	+	0.970321i	$0.422255\pi$
$884$	5.74978	0.193386
$885$	25.3233	0.851234
$886$	−3.76389	−0.126451
$887$	21.9663	0.737555	0.368778	−	0.929518i	$-0.379776\pi$
$887$	21.9663	0.737555	0.368778	+	0.929518i	$0.379776\pi$
$888$	−9.51120	−0.319175
$889$	26.0229	0.872780
$890$	−0.701543	−0.0235158
$891$	−27.3299	−0.915586
$892$	−18.1897	−0.609035
$893$	5.74205	0.192150
$894$	30.9213	1.03416
$895$	1.90415	0.0636487
$896$	3.71200	0.124009
$897$	−19.0571	−0.636299
$898$	−31.9611	−1.06656
$899$	−38.9130	−1.29782
$900$	−34.5722	−1.15241
$901$	11.0089	0.366759
$902$	−12.5051	−0.416374
$903$	−94.9139	−3.15854
$904$	1.88162	0.0625816
$905$	−5.39032	−0.179180
$906$	32.6905	1.08607
$907$	8.99847	0.298789	0.149395	−	0.988778i	$-0.452268\pi$
$907$	8.99847	0.298789	0.149395	+	0.988778i	$0.452268\pi$
$908$	7.16501	0.237779
$909$	88.6160	2.93921
$910$	2.74198	0.0908957
$911$	1.84920	0.0612669	0.0306334	−	0.999531i	$-0.490248\pi$
$911$	1.84920	0.0612669	0.0306334	+	0.999531i	$0.490248\pi$
$912$	−4.55856	−0.150949
$913$	5.15930	0.170748
$914$	−35.2334	−1.16542
$915$	16.2147	0.536043
$916$	−7.11306	−0.235022
$917$	−11.8009	−0.389700
$918$	86.2696	2.84732
$919$	−56.1065	−1.85078	−0.925391	−	0.379015i	$-0.876263\pi$
$919$	−56.1065	−1.85078	−0.925391	+	0.379015i	$0.876263\pi$
$920$	4.07277	0.134275
$921$	31.4746	1.03712
$922$	33.4828	1.10270
$923$	7.70382	0.253574
$924$	12.1487	0.399662
$925$	−13.0291	−0.428396
$926$	2.21488	0.0727855
$927$	40.1869	1.31991
$928$	−6.63878	−0.217929
$929$	−43.2914	−1.42034	−0.710172	−	0.704028i	$-0.751383\pi$
$929$	−43.2914	−1.42034	−0.710172	+	0.704028i	$0.751383\pi$
$930$	−13.7889	−0.452157
$931$	−9.44210	−0.309452
$932$	6.06437	0.198645
$933$	82.1804	2.69047
$934$	−11.3173	−0.370313
$935$	−4.02165	−0.131522
$936$	7.92460	0.259024
$937$	12.4483	0.406669	0.203334	−	0.979109i	$-0.434822\pi$
$937$	12.4483	0.406669	0.203334	+	0.979109i	$0.434822\pi$
$938$	6.35503	0.207499
$939$	−29.7736	−0.971626
$940$	2.96323	0.0966499
$941$	−14.6574	−0.477819	−0.238910	−	0.971042i	$-0.576790\pi$
$941$	−14.6574	−0.477819	−0.238910	+	0.971042i	$0.576790\pi$
$942$	−10.2854	−0.335118
$943$	−70.8552	−2.30736
$944$	−10.7645	−0.350356
$945$	41.1407	1.33831
$946$	7.81271	0.254013
$947$	−47.3307	−1.53804	−0.769020	−	0.639224i	$-0.779255\pi$
$947$	−47.3307	−1.53804	−0.769020	+	0.639224i	$0.779255\pi$
$948$	−27.9321	−0.907193
$949$	1.93143	0.0626969
$950$	−6.24465	−0.202603
$951$	3.58083	0.116116
$952$	−20.7686	−0.673114
$953$	24.3246	0.787950	0.393975	−	0.919121i	$-0.371100\pi$
$953$	24.3246	0.787950	0.393975	+	0.919121i	$0.371100\pi$
$954$	15.1729	0.491242
$955$	−13.1580	−0.425782
$956$	24.6772	0.798118
$957$	−21.7275	−0.702349
$958$	−15.0116	−0.485004
$959$	−4.60369	−0.148661
$960$	−2.35248	−0.0759258
$961$	3.35670	0.108281
$962$	2.98653	0.0962895
$963$	−147.898	−4.76593
$964$	3.07444	0.0990209
$965$	8.02232	0.258248
$966$	68.8357	2.21475
$967$	−24.4182	−0.785236	−0.392618	−	0.919702i	$-0.628431\pi$
$967$	−24.4182	−0.785236	−0.392618	+	0.919702i	$0.628431\pi$
$968$	−1.00000	−0.0321412
$969$	25.5051	0.819341
$970$	−11.6037	−0.372573
$971$	50.0338	1.60566	0.802830	−	0.596208i	$-0.203327\pi$
$971$	50.0338	1.60566	0.802830	+	0.596208i	$0.203327\pi$
$972$	43.1882	1.38526
$973$	55.8617	1.79084
$974$	−1.76000	−0.0563939
$975$	15.0790	0.482915
$976$	−6.89262	−0.220628
$977$	13.2516	0.423956	0.211978	−	0.977274i	$-0.432009\pi$
$977$	13.2516	0.423956	0.211978	+	0.977274i	$0.432009\pi$
$978$	36.0124	1.15155
$979$	0.975999	0.0311931
$980$	−4.87266	−0.155652
$981$	110.001	3.51207
$982$	39.6118	1.26406
$983$	48.1751	1.53655	0.768273	−	0.640122i	$-0.221116\pi$
$983$	48.1751	1.53655	0.768273	+	0.640122i	$0.221116\pi$
$984$	40.9267	1.30470
$985$	0.718794	0.0229027
$986$	37.1439	1.18290
$987$	50.0828	1.59415
$988$	1.43139	0.0455386
$989$	44.2677	1.40763
$990$	−5.54282	−0.176162
$991$	45.1543	1.43437	0.717186	−	0.696881i	$-0.245430\pi$
$991$	45.1543	1.43437	0.717186	+	0.696881i	$0.245430\pi$
$992$	5.86146	0.186101
$993$	17.9770	0.570482
$994$	−27.8267	−0.882610
$995$	−16.7859	−0.532149
$996$	−16.8854	−0.535034
$997$	−9.94080	−0.314828	−0.157414	−	0.987533i	$-0.550316\pi$
$997$	−9.94080	−0.314828	−0.157414	+	0.987533i	$0.550316\pi$
$998$	13.8249	0.437620
$999$	44.8098	1.41772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.17	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.17	✓	17	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.27281 q^{3} +1.00000 q^{4} -0.718794 q^{5} -3.27281 q^{6} -3.71200 q^{7} -1.00000 q^{8} +7.71127 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.27281 q^{3} +1.00000 q^{4} -0.718794 q^{5} -3.27281 q^{6} -3.71200 q^{7} -1.00000 q^{8} +7.71127 q^{9} +0.718794 q^{10} -1.00000 q^{11} +3.27281 q^{12} -1.02767 q^{13} +3.71200 q^{14} -2.35248 q^{15} +1.00000 q^{16} -5.59499 q^{17} -7.71127 q^{18} -1.39286 q^{19} -0.718794 q^{20} -12.1487 q^{21} +1.00000 q^{22} +5.66611 q^{23} -3.27281 q^{24} -4.48333 q^{25} +1.02767 q^{26} +15.4191 q^{27} -3.71200 q^{28} +6.63878 q^{29} +2.35248 q^{30} -5.86146 q^{31} -1.00000 q^{32} -3.27281 q^{33} +5.59499 q^{34} +2.66816 q^{35} +7.71127 q^{36} +2.90613 q^{37} +1.39286 q^{38} -3.36335 q^{39} +0.718794 q^{40} -12.5051 q^{41} +12.1487 q^{42} +7.81271 q^{43} -1.00000 q^{44} -5.54282 q^{45} -5.66611 q^{46} -4.12250 q^{47} +3.27281 q^{48} +6.77894 q^{49} +4.48333 q^{50} -18.3113 q^{51} -1.02767 q^{52} -1.96763 q^{53} -15.4191 q^{54} +0.718794 q^{55} +3.71200 q^{56} -4.55856 q^{57} -6.63878 q^{58} -10.7645 q^{59} -2.35248 q^{60} -6.89262 q^{61} +5.86146 q^{62} -28.6242 q^{63} +1.00000 q^{64} +0.738680 q^{65} +3.27281 q^{66} +1.71202 q^{67} -5.59499 q^{68} +18.5441 q^{69} -2.66816 q^{70} -7.49643 q^{71} -7.71127 q^{72} -1.87944 q^{73} -2.90613 q^{74} -14.6731 q^{75} -1.39286 q^{76} +3.71200 q^{77} +3.36335 q^{78} -8.53461 q^{79} -0.718794 q^{80} +27.3299 q^{81} +12.5051 q^{82} -5.15930 q^{83} -12.1487 q^{84} +4.02165 q^{85} -7.81271 q^{86} +21.7275 q^{87} +1.00000 q^{88} -0.975999 q^{89} +5.54282 q^{90} +3.81469 q^{91} +5.66611 q^{92} -19.1834 q^{93} +4.12250 q^{94} +1.00118 q^{95} -3.27281 q^{96} -16.1433 q^{97} -6.77894 q^{98} -7.71127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

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