LMFDB - Embedded newform 4334.2.a.d.1.10

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} - 7 x^{16} - 7 x^{15} + 137 x^{14} - 98 x^{13} - 1048 x^{12} + 1313 x^{11} + 4085 x^{10} + \cdots - 400 $ x^17 - 7x^16 - 7x^15 + 137x^14 - 98x^13 - 1048x^12 + 1313x^11 + 4085x^10 - 6021x^9 - 8879x^8 + 13530x^7 + 11150x^6 - 15676x^5 - 8037x^4 + 8646x^3 + 3040x^2 - 1640x - 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.216237$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.216237 q^{3} +1.00000 q^{4} +0.737633 q^{5} +0.216237 q^{6} +0.342001 q^{7} +1.00000 q^{8} -2.95324 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.216237 q^{3} +1.00000 q^{4} +0.737633 q^{5} +0.216237 q^{6} +0.342001 q^{7} +1.00000 q^{8} -2.95324 q^{9} +0.737633 q^{10} -1.00000 q^{11} +0.216237 q^{12} -1.84461 q^{13} +0.342001 q^{14} +0.159503 q^{15} +1.00000 q^{16} -7.54522 q^{17} -2.95324 q^{18} +6.47208 q^{19} +0.737633 q^{20} +0.0739531 q^{21} -1.00000 q^{22} +0.711342 q^{23} +0.216237 q^{24} -4.45590 q^{25} -1.84461 q^{26} -1.28731 q^{27} +0.342001 q^{28} -3.71591 q^{29} +0.159503 q^{30} -3.28685 q^{31} +1.00000 q^{32} -0.216237 q^{33} -7.54522 q^{34} +0.252271 q^{35} -2.95324 q^{36} -10.4088 q^{37} +6.47208 q^{38} -0.398872 q^{39} +0.737633 q^{40} +7.49798 q^{41} +0.0739531 q^{42} +10.6585 q^{43} -1.00000 q^{44} -2.17841 q^{45} +0.711342 q^{46} -5.65113 q^{47} +0.216237 q^{48} -6.88304 q^{49} -4.45590 q^{50} -1.63156 q^{51} -1.84461 q^{52} -5.38294 q^{53} -1.28731 q^{54} -0.737633 q^{55} +0.342001 q^{56} +1.39950 q^{57} -3.71591 q^{58} +5.04425 q^{59} +0.159503 q^{60} -9.27249 q^{61} -3.28685 q^{62} -1.01001 q^{63} +1.00000 q^{64} -1.36064 q^{65} -0.216237 q^{66} +4.34994 q^{67} -7.54522 q^{68} +0.153818 q^{69} +0.252271 q^{70} -12.9494 q^{71} -2.95324 q^{72} -6.11038 q^{73} -10.4088 q^{74} -0.963529 q^{75} +6.47208 q^{76} -0.342001 q^{77} -0.398872 q^{78} -2.41874 q^{79} +0.737633 q^{80} +8.58136 q^{81} +7.49798 q^{82} +10.0640 q^{83} +0.0739531 q^{84} -5.56560 q^{85} +10.6585 q^{86} -0.803517 q^{87} -1.00000 q^{88} -8.31699 q^{89} -2.17841 q^{90} -0.630857 q^{91} +0.711342 q^{92} -0.710738 q^{93} -5.65113 q^{94} +4.77402 q^{95} +0.216237 q^{96} -13.3930 q^{97} -6.88304 q^{98} +2.95324 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19} - 4 q^{20} - 13 q^{21} - 17 q^{22} - 6 q^{23} - 7 q^{24} + 3 q^{25} - 18 q^{26} - 37 q^{27} - 5 q^{28} - 16 q^{29} - 16 q^{30} - 30 q^{31} + 17 q^{32} + 7 q^{33} - 10 q^{34} - 36 q^{35} + 12 q^{36} - 23 q^{37} - 31 q^{38} - 15 q^{39} - 4 q^{40} - 7 q^{41} - 13 q^{42} - 23 q^{43} - 17 q^{44} - 19 q^{45} - 6 q^{46} - 19 q^{47} - 7 q^{48} - 8 q^{49} + 3 q^{50} - 18 q^{51} - 18 q^{52} - 30 q^{53} - 37 q^{54} + 4 q^{55} - 5 q^{56} + 10 q^{57} - 16 q^{58} - 28 q^{59} - 16 q^{60} - 19 q^{61} - 30 q^{62} + 2 q^{63} + 17 q^{64} + 23 q^{65} + 7 q^{66} - 35 q^{67} - 10 q^{68} + q^{69} - 36 q^{70} + q^{71} + 12 q^{72} - 10 q^{73} - 23 q^{74} - 33 q^{75} - 31 q^{76} + 5 q^{77} - 15 q^{78} - 27 q^{79} - 4 q^{80} + 13 q^{81} - 7 q^{82} - 40 q^{83} - 13 q^{84} - 11 q^{85} - 23 q^{86} - 6 q^{87} - 17 q^{88} - 17 q^{89} - 19 q^{90} - 19 q^{91} - 6 q^{92} + 10 q^{93} - 19 q^{94} - 27 q^{95} - 7 q^{96} - 34 q^{97} - 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * 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
$3$	0.216237	0.124844	0.0624222	−	0.998050i	$-0.480117\pi$
$3$	0.216237	0.124844	0.0624222	+	0.998050i	$0.480117\pi$
$4$	1.00000	0.500000
$5$	0.737633	0.329879	0.164940	−	0.986304i	$-0.447257\pi$
$5$	0.737633	0.329879	0.164940	+	0.986304i	$0.447257\pi$
$6$	0.216237	0.0882783
$7$	0.342001	0.129264	0.0646320	−	0.997909i	$-0.479413\pi$
$7$	0.342001	0.129264	0.0646320	+	0.997909i	$0.479413\pi$
$8$	1.00000	0.353553
$9$	−2.95324	−0.984414
$10$	0.737633	0.233260
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.216237	0.0624222
$13$	−1.84461	−0.511602	−0.255801	−	0.966729i	$-0.582339\pi$
$13$	−1.84461	−0.511602	−0.255801	+	0.966729i	$0.582339\pi$
$14$	0.342001	0.0914035
$15$	0.159503	0.0411836
$16$	1.00000	0.250000
$17$	−7.54522	−1.82999	−0.914993	−	0.403470i	$-0.867804\pi$
$17$	−7.54522	−1.82999	−0.914993	+	0.403470i	$0.867804\pi$
$18$	−2.95324	−0.696086
$19$	6.47208	1.48480	0.742398	−	0.669959i	$-0.233688\pi$
$19$	6.47208	1.48480	0.742398	+	0.669959i	$0.233688\pi$
$20$	0.737633	0.164940
$21$	0.0739531	0.0161379
$22$	−1.00000	−0.213201
$23$	0.711342	0.148325	0.0741625	−	0.997246i	$-0.476372\pi$
$23$	0.711342	0.148325	0.0741625	+	0.997246i	$0.476372\pi$
$24$	0.216237	0.0441392
$25$	−4.45590	−0.891180
$26$	−1.84461	−0.361757
$27$	−1.28731	−0.247743
$28$	0.342001	0.0646320
$29$	−3.71591	−0.690028	−0.345014	−	0.938598i	$-0.612126\pi$
$29$	−3.71591	−0.690028	−0.345014	+	0.938598i	$0.612126\pi$
$30$	0.159503	0.0291212
$31$	−3.28685	−0.590336	−0.295168	−	0.955445i	$-0.595376\pi$
$31$	−3.28685	−0.590336	−0.295168	+	0.955445i	$0.595376\pi$
$32$	1.00000	0.176777
$33$	−0.216237	−0.0376420
$34$	−7.54522	−1.29400
$35$	0.252271	0.0426416
$36$	−2.95324	−0.492207
$37$	−10.4088	−1.71119	−0.855597	−	0.517642i	$-0.826810\pi$
$37$	−10.4088	−1.71119	−0.855597	+	0.517642i	$0.826810\pi$
$38$	6.47208	1.04991
$39$	−0.398872	−0.0638706
$40$	0.737633	0.116630
$41$	7.49798	1.17099	0.585494	−	0.810677i	$-0.300901\pi$
$41$	7.49798	1.17099	0.585494	+	0.810677i	$0.300901\pi$
$42$	0.0739531	0.0114112
$43$	10.6585	1.62541	0.812704	−	0.582677i	$-0.197995\pi$
$43$	10.6585	1.62541	0.812704	+	0.582677i	$0.197995\pi$
$44$	−1.00000	−0.150756
$45$	−2.17841	−0.324738
$46$	0.711342	0.104882
$47$	−5.65113	−0.824302	−0.412151	−	0.911116i	$-0.635222\pi$
$47$	−5.65113	−0.824302	−0.412151	+	0.911116i	$0.635222\pi$
$48$	0.216237	0.0312111
$49$	−6.88304	−0.983291
$50$	−4.45590	−0.630159
$51$	−1.63156	−0.228463
$52$	−1.84461	−0.255801
$53$	−5.38294	−0.739404	−0.369702	−	0.929150i	$-0.620540\pi$
$53$	−5.38294	−0.739404	−0.369702	+	0.929150i	$0.620540\pi$
$54$	−1.28731	−0.175181
$55$	−0.737633	−0.0994624
$56$	0.342001	0.0457018
$57$	1.39950	0.185369
$58$	−3.71591	−0.487923
$59$	5.04425	0.656705	0.328353	−	0.944555i	$-0.393507\pi$
$59$	5.04425	0.656705	0.328353	+	0.944555i	$0.393507\pi$
$60$	0.159503	0.0205918
$61$	−9.27249	−1.18722	−0.593611	−	0.804752i	$-0.702298\pi$
$61$	−9.27249	−1.18722	−0.593611	+	0.804752i	$0.702298\pi$
$62$	−3.28685	−0.417431
$63$	−1.01001	−0.127249
$64$	1.00000	0.125000
$65$	−1.36064	−0.168767
$66$	−0.216237	−0.0266169
$67$	4.34994	0.531430	0.265715	−	0.964052i	$-0.414392\pi$
$67$	4.34994	0.531430	0.265715	+	0.964052i	$0.414392\pi$
$68$	−7.54522	−0.914993
$69$	0.153818	0.0185175
$70$	0.252271	0.0301521
$71$	−12.9494	−1.53681	−0.768403	−	0.639966i	$-0.778948\pi$
$71$	−12.9494	−1.53681	−0.768403	+	0.639966i	$0.778948\pi$
$72$	−2.95324	−0.348043
$73$	−6.11038	−0.715165	−0.357583	−	0.933881i	$-0.616399\pi$
$73$	−6.11038	−0.715165	−0.357583	+	0.933881i	$0.616399\pi$
$74$	−10.4088	−1.21000
$75$	−0.963529	−0.111259
$76$	6.47208	0.742398
$77$	−0.342001	−0.0389746
$78$	−0.398872	−0.0451634
$79$	−2.41874	−0.272130	−0.136065	−	0.990700i	$-0.543446\pi$
$79$	−2.41874	−0.272130	−0.136065	+	0.990700i	$0.543446\pi$
$80$	0.737633	0.0824698
$81$	8.58136	0.953485
$82$	7.49798	0.828014
$83$	10.0640	1.10467	0.552334	−	0.833623i	$-0.313737\pi$
$83$	10.0640	1.10467	0.552334	+	0.833623i	$0.313737\pi$
$84$	0.0739531	0.00806895
$85$	−5.56560	−0.603674
$86$	10.6585	1.14934
$87$	−0.803517	−0.0861461
$88$	−1.00000	−0.106600
$89$	−8.31699	−0.881600	−0.440800	−	0.897605i	$-0.645305\pi$
$89$	−8.31699	−0.881600	−0.440800	+	0.897605i	$0.645305\pi$
$90$	−2.17841	−0.229624
$91$	−0.630857	−0.0661318
$92$	0.711342	0.0741625
$93$	−0.710738	−0.0737001
$94$	−5.65113	−0.582869
$95$	4.77402	0.489804
$96$	0.216237	0.0220696
$97$	−13.3930	−1.35985	−0.679924	−	0.733282i	$-0.737987\pi$
$97$	−13.3930	−1.35985	−0.679924	+	0.733282i	$0.737987\pi$
$98$	−6.88304	−0.695292
$99$	2.95324	0.296812
$100$	−4.45590	−0.445590
$101$	3.75853	0.373988	0.186994	−	0.982361i	$-0.440125\pi$
$101$	3.75853	0.373988	0.186994	+	0.982361i	$0.440125\pi$
$102$	−1.63156	−0.161548
$103$	4.05723	0.399771	0.199885	−	0.979819i	$-0.435943\pi$
$103$	4.05723	0.399771	0.199885	+	0.979819i	$0.435943\pi$
$104$	−1.84461	−0.180879
$105$	0.0545502	0.00532356
$106$	−5.38294	−0.522838
$107$	0.770693	0.0745057	0.0372528	−	0.999306i	$-0.488139\pi$
$107$	0.770693	0.0745057	0.0372528	+	0.999306i	$0.488139\pi$
$108$	−1.28731	−0.123871
$109$	12.1655	1.16524	0.582622	−	0.812743i	$-0.302027\pi$
$109$	12.1655	1.16524	0.582622	+	0.812743i	$0.302027\pi$
$110$	−0.737633	−0.0703305
$111$	−2.25076	−0.213633
$112$	0.342001	0.0323160
$113$	−1.34298	−0.126337	−0.0631684	−	0.998003i	$-0.520121\pi$
$113$	−1.34298	−0.126337	−0.0631684	+	0.998003i	$0.520121\pi$
$114$	1.39950	0.131075
$115$	0.524709	0.0489294
$116$	−3.71591	−0.345014
$117$	5.44757	0.503628
$118$	5.04425	0.464361
$119$	−2.58047	−0.236551
$120$	0.159503	0.0145606
$121$	1.00000	0.0909091
$122$	−9.27249	−0.839492
$123$	1.62134	0.146191
$124$	−3.28685	−0.295168
$125$	−6.97498	−0.623861
$126$	−1.01001	−0.0899789
$127$	−16.4826	−1.46260	−0.731299	−	0.682058i	$-0.761085\pi$
$127$	−16.4826	−1.46260	−0.731299	+	0.682058i	$0.761085\pi$
$128$	1.00000	0.0883883
$129$	2.30476	0.202923
$130$	−1.36064	−0.119336
$131$	15.0988	1.31919	0.659593	−	0.751623i	$-0.270729\pi$
$131$	15.0988	1.31919	0.659593	+	0.751623i	$0.270729\pi$
$132$	−0.216237	−0.0188210
$133$	2.21346	0.191931
$134$	4.34994	0.375778
$135$	−0.949562	−0.0817253
$136$	−7.54522	−0.646998
$137$	5.46081	0.466549	0.233274	−	0.972411i	$-0.425056\pi$
$137$	5.46081	0.466549	0.233274	+	0.972411i	$0.425056\pi$
$138$	0.153818	0.0130939
$139$	−14.3207	−1.21467	−0.607333	−	0.794448i	$-0.707761\pi$
$139$	−14.3207	−1.21467	−0.607333	+	0.794448i	$0.707761\pi$
$140$	0.252271	0.0213208
$141$	−1.22198	−0.102909
$142$	−12.9494	−1.08669
$143$	1.84461	0.154254
$144$	−2.95324	−0.246103
$145$	−2.74098	−0.227626
$146$	−6.11038	−0.505698
$147$	−1.48837	−0.122758
$148$	−10.4088	−0.855597
$149$	−19.7458	−1.61764	−0.808818	−	0.588058i	$-0.799893\pi$
$149$	−19.7458	−1.61764	−0.808818	+	0.588058i	$0.799893\pi$
$150$	−0.963529	−0.0786718
$151$	−11.0279	−0.897437	−0.448719	−	0.893673i	$-0.648119\pi$
$151$	−11.0279	−0.897437	−0.448719	+	0.893673i	$0.648119\pi$
$152$	6.47208	0.524955
$153$	22.2829	1.80146
$154$	−0.342001	−0.0275592
$155$	−2.42449	−0.194740
$156$	−0.398872	−0.0319353
$157$	12.0037	0.957998	0.478999	−	0.877815i	$-0.341000\pi$
$157$	12.0037	0.957998	0.478999	+	0.877815i	$0.341000\pi$
$158$	−2.41874	−0.192425
$159$	−1.16399	−0.0923105
$160$	0.737633	0.0583150
$161$	0.243279	0.0191731
$162$	8.58136	0.674215
$163$	−0.000924835 0	−7.24387e−5 0	−3.62193e−5	−	1.00000i	$-0.500012\pi$
$163$	−0.000924835 0	−7.24387e−5 0	−3.62193e−5		1.00000i	$0.500012\pi$
$164$	7.49798	0.585494
$165$	−0.159503	−0.0124173
$166$	10.0640	0.781118
$167$	7.00966	0.542424	0.271212	−	0.962520i	$-0.412576\pi$
$167$	7.00966	0.542424	0.271212	+	0.962520i	$0.412576\pi$
$168$	0.0739531	0.00570561
$169$	−9.59742	−0.738263
$170$	−5.56560	−0.426862
$171$	−19.1136	−1.46165
$172$	10.6585	0.812704
$173$	−6.85509	−0.521183	−0.260591	−	0.965449i	$-0.583918\pi$
$173$	−6.85509	−0.521183	−0.260591	+	0.965449i	$0.583918\pi$
$174$	−0.803517	−0.0609145
$175$	−1.52392	−0.115198
$176$	−1.00000	−0.0753778
$177$	1.09075	0.0819860
$178$	−8.31699	−0.623385
$179$	4.11888	0.307859	0.153930	−	0.988082i	$-0.450807\pi$
$179$	4.11888	0.307859	0.153930	+	0.988082i	$0.450807\pi$
$180$	−2.17841	−0.162369
$181$	9.83537	0.731057	0.365529	−	0.930800i	$-0.380888\pi$
$181$	9.83537	0.731057	0.365529	+	0.930800i	$0.380888\pi$
$182$	−0.630857	−0.0467622
$183$	−2.00505	−0.148218
$184$	0.711342	0.0524408
$185$	−7.67786	−0.564488
$186$	−0.710738	−0.0521139
$187$	7.54522	0.551761
$188$	−5.65113	−0.412151
$189$	−0.440261	−0.0320243
$190$	4.77402	0.346344
$191$	19.5130	1.41191	0.705956	−	0.708256i	$-0.250518\pi$
$191$	19.5130	1.41191	0.705956	+	0.708256i	$0.250518\pi$
$192$	0.216237	0.0156055
$193$	15.5318	1.11800	0.559001	−	0.829167i	$-0.311185\pi$
$193$	15.5318	1.11800	0.559001	+	0.829167i	$0.311185\pi$
$194$	−13.3930	−0.961558
$195$	−0.294221	−0.0210696
$196$	−6.88304	−0.491645
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.95324	0.209878
$199$	0.534442	0.0378856	0.0189428	−	0.999821i	$-0.493970\pi$
$199$	0.534442	0.0378856	0.0189428	+	0.999821i	$0.493970\pi$
$200$	−4.45590	−0.315080
$201$	0.940618	0.0663461
$202$	3.75853	0.264449
$203$	−1.27084	−0.0891958
$204$	−1.63156	−0.114232
$205$	5.53076	0.386285
$206$	4.05723	0.282681
$207$	−2.10076	−0.146013
$208$	−1.84461	−0.127901
$209$	−6.47208	−0.447683
$210$	0.0545502	0.00376432
$211$	6.86511	0.472614	0.236307	−	0.971679i	$-0.424063\pi$
$211$	6.86511	0.472614	0.236307	+	0.971679i	$0.424063\pi$
$212$	−5.38294	−0.369702
$213$	−2.80013	−0.191862
$214$	0.770693	0.0526835
$215$	7.86206	0.536188
$216$	−1.28731	−0.0875904
$217$	−1.12411	−0.0763093
$218$	12.1655	0.823952
$219$	−1.32129	−0.0892844
$220$	−0.737633	−0.0497312
$221$	13.9180	0.936224
$222$	−2.25076	−0.151061
$223$	6.50097	0.435337	0.217669	−	0.976023i	$-0.430155\pi$
$223$	6.50097	0.435337	0.217669	+	0.976023i	$0.430155\pi$
$224$	0.342001	0.0228509
$225$	13.1593	0.877290
$226$	−1.34298	−0.0893337
$227$	28.0331	1.86062	0.930311	−	0.366772i	$-0.119537\pi$
$227$	28.0331	1.86062	0.930311	+	0.366772i	$0.119537\pi$
$228$	1.39950	0.0926843
$229$	−6.80793	−0.449881	−0.224940	−	0.974373i	$-0.572219\pi$
$229$	−6.80793	−0.449881	−0.224940	+	0.974373i	$0.572219\pi$
$230$	0.524709	0.0345983
$231$	−0.0739531	−0.00486576
$232$	−3.71591	−0.243962
$233$	15.1939	0.995383	0.497691	−	0.867354i	$-0.334181\pi$
$233$	15.1939	0.995383	0.497691	+	0.867354i	$0.334181\pi$
$234$	5.44757	0.356119
$235$	−4.16846	−0.271920
$236$	5.04425	0.328353
$237$	−0.523021	−0.0339739
$238$	−2.58047	−0.167267
$239$	−1.97896	−0.128008	−0.0640041	−	0.997950i	$-0.520387\pi$
$239$	−1.97896	−0.128008	−0.0640041	+	0.997950i	$0.520387\pi$
$240$	0.159503	0.0102959
$241$	−22.7144	−1.46316	−0.731582	−	0.681754i	$-0.761217\pi$
$241$	−22.7144	−1.46316	−0.731582	+	0.681754i	$0.761217\pi$
$242$	1.00000	0.0642824
$243$	5.71754	0.366780
$244$	−9.27249	−0.593611
$245$	−5.07715	−0.324367
$246$	1.62134	0.103373
$247$	−11.9384	−0.759625
$248$	−3.28685	−0.208715
$249$	2.17621	0.137912
$250$	−6.97498	−0.441136
$251$	21.3152	1.34540	0.672702	−	0.739914i	$-0.265134\pi$
$251$	21.3152	1.34540	0.672702	+	0.739914i	$0.265134\pi$
$252$	−1.01001	−0.0636247
$253$	−0.711342	−0.0447217
$254$	−16.4826	−1.03421
$255$	−1.20349	−0.0753654
$256$	1.00000	0.0625000
$257$	−7.91019	−0.493424	−0.246712	−	0.969089i	$-0.579350\pi$
$257$	−7.91019	−0.493424	−0.246712	+	0.969089i	$0.579350\pi$
$258$	2.30476	0.143488
$259$	−3.55981	−0.221196
$260$	−1.36064	−0.0843835
$261$	10.9740	0.679273
$262$	15.0988	0.932805
$263$	−18.9873	−1.17081	−0.585403	−	0.810743i	$-0.699064\pi$
$263$	−18.9873	−1.17081	−0.585403	+	0.810743i	$0.699064\pi$
$264$	−0.216237	−0.0133085
$265$	−3.97063	−0.243914
$266$	2.21346	0.135716
$267$	−1.79844	−0.110063
$268$	4.34994	0.265715
$269$	7.80588	0.475933	0.237966	−	0.971273i	$-0.423519\pi$
$269$	7.80588	0.475933	0.237966	+	0.971273i	$0.423519\pi$
$270$	−0.949562	−0.0577885
$271$	−28.3426	−1.72169	−0.860845	−	0.508868i	$-0.830064\pi$
$271$	−28.3426	−1.72169	−0.860845	+	0.508868i	$0.830064\pi$
$272$	−7.54522	−0.457496
$273$	−0.136414	−0.00825618
$274$	5.46081	0.329900
$275$	4.45590	0.268701
$276$	0.153818	0.00925877
$277$	−29.6448	−1.78118	−0.890591	−	0.454804i	$-0.849709\pi$
$277$	−29.6448	−1.78118	−0.890591	+	0.454804i	$0.849709\pi$
$278$	−14.3207	−0.858898
$279$	9.70687	0.581135
$280$	0.252271	0.0150761
$281$	−23.3369	−1.39216	−0.696082	−	0.717962i	$-0.745075\pi$
$281$	−23.3369	−1.39216	−0.696082	+	0.717962i	$0.745075\pi$
$282$	−1.22198	−0.0727680
$283$	−3.65680	−0.217374	−0.108687	−	0.994076i	$-0.534665\pi$
$283$	−3.65680	−0.217374	−0.108687	+	0.994076i	$0.534665\pi$
$284$	−12.9494	−0.768403
$285$	1.03232	0.0611493
$286$	1.84461	0.109074
$287$	2.56432	0.151367
$288$	−2.95324	−0.174021
$289$	39.9304	2.34885
$290$	−2.74098	−0.160956
$291$	−2.89605	−0.169769
$292$	−6.11038	−0.357583
$293$	27.6266	1.61396	0.806982	−	0.590577i	$-0.201100\pi$
$293$	27.6266	1.61396	0.806982	+	0.590577i	$0.201100\pi$
$294$	−1.48837	−0.0868033
$295$	3.72080	0.216634
$296$	−10.4088	−0.604999
$297$	1.28731	0.0746973
$298$	−19.7458	−1.14384
$299$	−1.31215	−0.0758834
$300$	−0.963529	−0.0556294
$301$	3.64522	0.210107
$302$	−11.0279	−0.634584
$303$	0.812733	0.0466903
$304$	6.47208	0.371199
$305$	−6.83969	−0.391640
$306$	22.2829	1.27383
$307$	−30.5794	−1.74526	−0.872628	−	0.488385i	$-0.837586\pi$
$307$	−30.5794	−1.74526	−0.872628	+	0.488385i	$0.837586\pi$
$308$	−0.342001	−0.0194873
$309$	0.877322	0.0499091
$310$	−2.42449	−0.137702
$311$	10.7379	0.608893	0.304447	−	0.952529i	$-0.401528\pi$
$311$	10.7379	0.608893	0.304447	+	0.952529i	$0.401528\pi$
$312$	−0.398872	−0.0225817
$313$	−9.11280	−0.515086	−0.257543	−	0.966267i	$-0.582913\pi$
$313$	−9.11280	−0.515086	−0.257543	+	0.966267i	$0.582913\pi$
$314$	12.0037	0.677407
$315$	−0.745017	−0.0419769
$316$	−2.41874	−0.136065
$317$	29.6596	1.66585	0.832925	−	0.553386i	$-0.186665\pi$
$317$	29.6596	1.66585	0.832925	+	0.553386i	$0.186665\pi$
$318$	−1.16399	−0.0652733
$319$	3.71591	0.208051
$320$	0.737633	0.0412349
$321$	0.166652	0.00930161
$322$	0.243279	0.0135574
$323$	−48.8333	−2.71716
$324$	8.58136	0.476742
$325$	8.21938	0.455929
$326$	−0.000924835 0	−5.12219e−5 0
$327$	2.63063	0.145474
$328$	7.49798	0.414007
$329$	−1.93269	−0.106553
$330$	−0.159503	−0.00878037
$331$	−16.8523	−0.926284	−0.463142	−	0.886284i	$-0.653278\pi$
$331$	−16.8523	−0.926284	−0.463142	+	0.886284i	$0.653278\pi$
$332$	10.0640	0.552334
$333$	30.7397	1.68452
$334$	7.00966	0.383551
$335$	3.20866	0.175308
$336$	0.0739531	0.00403447
$337$	−13.8605	−0.755027	−0.377514	−	0.926004i	$-0.623221\pi$
$337$	−13.8605	−0.755027	−0.377514	+	0.926004i	$0.623221\pi$
$338$	−9.59742	−0.522031
$339$	−0.290402	−0.0157725
$340$	−5.56560	−0.301837
$341$	3.28685	0.177993
$342$	−19.1136	−1.03355
$343$	−4.74801	−0.256368
$344$	10.6585	0.574668
$345$	0.113461	0.00610856
$346$	−6.85509	−0.368532
$347$	17.1461	0.920449	0.460225	−	0.887803i	$-0.347769\pi$
$347$	17.1461	0.920449	0.460225	+	0.887803i	$0.347769\pi$
$348$	−0.803517	−0.0430730
$349$	−23.8764	−1.27807	−0.639036	−	0.769177i	$-0.720666\pi$
$349$	−23.8764	−1.27807	−0.639036	+	0.769177i	$0.720666\pi$
$350$	−1.52392	−0.0814570
$351$	2.37458	0.126746
$352$	−1.00000	−0.0533002
$353$	9.15801	0.487432	0.243716	−	0.969847i	$-0.421634\pi$
$353$	9.15801	0.487432	0.243716	+	0.969847i	$0.421634\pi$
$354$	1.09075	0.0579729
$355$	−9.55187	−0.506961
$356$	−8.31699	−0.440800
$357$	−0.557993	−0.0295321
$358$	4.11888	0.217690
$359$	−11.1187	−0.586824	−0.293412	−	0.955986i	$-0.594791\pi$
$359$	−11.1187	−0.586824	−0.293412	+	0.955986i	$0.594791\pi$
$360$	−2.17841	−0.114812
$361$	22.8878	1.20462
$362$	9.83537	0.516935
$363$	0.216237	0.0113495
$364$	−0.630857	−0.0330659
$365$	−4.50721	−0.235918
$366$	−2.00505	−0.104806
$367$	−15.3813	−0.802900	−0.401450	−	0.915881i	$-0.631494\pi$
$367$	−15.3813	−0.802900	−0.401450	+	0.915881i	$0.631494\pi$
$368$	0.711342	0.0370813
$369$	−22.1434	−1.15274
$370$	−7.67786	−0.399153
$371$	−1.84097	−0.0955784
$372$	−0.710738	−0.0368501
$373$	26.3776	1.36578	0.682889	−	0.730522i	$-0.260723\pi$
$373$	26.3776	1.36578	0.682889	+	0.730522i	$0.260723\pi$
$374$	7.54522	0.390154
$375$	−1.50825	−0.0778856
$376$	−5.65113	−0.291435
$377$	6.85440	0.353020
$378$	−0.440261	−0.0226446
$379$	30.9513	1.58986	0.794930	−	0.606701i	$-0.207508\pi$
$379$	30.9513	1.58986	0.794930	+	0.606701i	$0.207508\pi$
$380$	4.77402	0.244902
$381$	−3.56415	−0.182597
$382$	19.5130	0.998373
$383$	−11.5329	−0.589302	−0.294651	−	0.955605i	$-0.595203\pi$
$383$	−11.5329	−0.589302	−0.294651	+	0.955605i	$0.595203\pi$
$384$	0.216237	0.0110348
$385$	−0.252271	−0.0128569
$386$	15.5318	0.790547
$387$	−31.4771	−1.60007
$388$	−13.3930	−0.679924
$389$	−36.3799	−1.84453	−0.922266	−	0.386556i	$-0.873665\pi$
$389$	−36.3799	−1.84453	−0.922266	+	0.386556i	$0.873665\pi$
$390$	−0.294221	−0.0148985
$391$	−5.36723	−0.271433
$392$	−6.88304	−0.347646
$393$	3.26491	0.164693
$394$	1.00000	0.0503793
$395$	−1.78414	−0.0897700
$396$	2.95324	0.148406
$397$	32.5974	1.63602	0.818009	−	0.575206i	$-0.195078\pi$
$397$	32.5974	1.63602	0.818009	+	0.575206i	$0.195078\pi$
$398$	0.534442	0.0267891
$399$	0.478631	0.0239615
$400$	−4.45590	−0.222795
$401$	−16.8072	−0.839314	−0.419657	−	0.907683i	$-0.637850\pi$
$401$	−16.8072	−0.839314	−0.419657	+	0.907683i	$0.637850\pi$
$402$	0.940618	0.0469137
$403$	6.06295	0.302017
$404$	3.75853	0.186994
$405$	6.32989	0.314535
$406$	−1.27084	−0.0630709
$407$	10.4088	0.515945
$408$	−1.63156	−0.0807740
$409$	37.1150	1.83522	0.917610	−	0.397483i	$-0.130116\pi$
$409$	37.1150	1.83522	0.917610	+	0.397483i	$0.130116\pi$
$410$	5.53076	0.273145
$411$	1.18083	0.0582460
$412$	4.05723	0.199885
$413$	1.72514	0.0848884
$414$	−2.10076	−0.103247
$415$	7.42354	0.364407
$416$	−1.84461	−0.0904393
$417$	−3.09666	−0.151644
$418$	−6.47208	−0.316560
$419$	−4.53436	−0.221518	−0.110759	−	0.993847i	$-0.535328\pi$
$419$	−4.53436	−0.221518	−0.110759	+	0.993847i	$0.535328\pi$
$420$	0.0545502	0.00266178
$421$	−12.4208	−0.605353	−0.302677	−	0.953093i	$-0.597880\pi$
$421$	−12.4208	−0.605353	−0.302677	+	0.953093i	$0.597880\pi$
$422$	6.86511	0.334188
$423$	16.6891	0.811454
$424$	−5.38294	−0.261419
$425$	33.6207	1.63085
$426$	−2.80013	−0.135667
$427$	−3.17120	−0.153465
$428$	0.770693	0.0372528
$429$	0.398872	0.0192577
$430$	7.86206	0.379142
$431$	0.860841	0.0414653	0.0207326	−	0.999785i	$-0.493400\pi$
$431$	0.860841	0.0414653	0.0207326	+	0.999785i	$0.493400\pi$
$432$	−1.28731	−0.0619357
$433$	5.63608	0.270853	0.135426	−	0.990787i	$-0.456760\pi$
$433$	5.63608	0.270853	0.135426	+	0.990787i	$0.456760\pi$
$434$	−1.12411	−0.0539588
$435$	−0.592700	−0.0284178
$436$	12.1655	0.582622
$437$	4.60386	0.220233
$438$	−1.32129	−0.0631336
$439$	−20.6190	−0.984091	−0.492045	−	0.870570i	$-0.663751\pi$
$439$	−20.6190	−0.984091	−0.492045	+	0.870570i	$0.663751\pi$
$440$	−0.737633	−0.0351653
$441$	20.3273	0.967965
$442$	13.9180	0.662011
$443$	25.0043	1.18799	0.593996	−	0.804468i	$-0.297549\pi$
$443$	25.0043	1.18799	0.593996	+	0.804468i	$0.297549\pi$
$444$	−2.25076	−0.106817
$445$	−6.13489	−0.290821
$446$	6.50097	0.307830
$447$	−4.26976	−0.201953
$448$	0.342001	0.0161580
$449$	−34.7163	−1.63836	−0.819181	−	0.573535i	$-0.805572\pi$
$449$	−34.7163	−1.63836	−0.819181	+	0.573535i	$0.805572\pi$
$450$	13.1593	0.620337
$451$	−7.49798	−0.353066
$452$	−1.34298	−0.0631684
$453$	−2.38464	−0.112040
$454$	28.0331	1.31566
$455$	−0.465341	−0.0218155
$456$	1.39950	0.0655377
$457$	6.97918	0.326472	0.163236	−	0.986587i	$-0.447807\pi$
$457$	6.97918	0.326472	0.163236	+	0.986587i	$0.447807\pi$
$458$	−6.80793	−0.318114
$459$	9.71304	0.453366
$460$	0.524709	0.0244647
$461$	−17.3901	−0.809939	−0.404970	−	0.914330i	$-0.632718\pi$
$461$	−17.3901	−0.809939	−0.404970	+	0.914330i	$0.632718\pi$
$462$	−0.0739531	−0.00344061
$463$	21.4363	0.996232	0.498116	−	0.867111i	$-0.334025\pi$
$463$	21.4363	0.996232	0.498116	+	0.867111i	$0.334025\pi$
$464$	−3.71591	−0.172507
$465$	−0.524264	−0.0243122
$466$	15.1939	0.703842
$467$	1.87676	0.0868460	0.0434230	−	0.999057i	$-0.486174\pi$
$467$	1.87676	0.0868460	0.0434230	+	0.999057i	$0.486174\pi$
$468$	5.44757	0.251814
$469$	1.48768	0.0686948
$470$	−4.16846	−0.192277
$471$	2.59564	0.119601
$472$	5.04425	0.232180
$473$	−10.6585	−0.490079
$474$	−0.523021	−0.0240232
$475$	−28.8389	−1.32322
$476$	−2.58047	−0.118276
$477$	15.8971	0.727880
$478$	−1.97896	−0.0905155
$479$	20.6866	0.945196	0.472598	−	0.881278i	$-0.343316\pi$
$479$	20.6866	0.945196	0.472598	+	0.881278i	$0.343316\pi$
$480$	0.159503	0.00728030
$481$	19.2001	0.875451
$482$	−22.7144	−1.03461
$483$	0.0526060	0.00239365
$484$	1.00000	0.0454545
$485$	−9.87908	−0.448586
$486$	5.71754	0.259353
$487$	16.2294	0.735425	0.367713	−	0.929939i	$-0.380141\pi$
$487$	16.2294	0.735425	0.367713	+	0.929939i	$0.380141\pi$
$488$	−9.27249	−0.419746
$489$	−0.000199983 0	−9.04356e−6 0
$490$	−5.07715	−0.229362
$491$	−31.3158	−1.41326	−0.706631	−	0.707582i	$-0.749786\pi$
$491$	−31.3158	−1.41326	−0.706631	+	0.707582i	$0.749786\pi$
$492$	1.62134	0.0730957
$493$	28.0374	1.26274
$494$	−11.9384	−0.537136
$495$	2.17841	0.0979121
$496$	−3.28685	−0.147584
$497$	−4.42869	−0.198654
$498$	2.17621	0.0975182
$499$	−10.4370	−0.467226	−0.233613	−	0.972330i	$-0.575055\pi$
$499$	−10.4370	−0.467226	−0.233613	+	0.972330i	$0.575055\pi$
$500$	−6.97498	−0.311931
$501$	1.51575	0.0677185
$502$	21.3152	0.951344
$503$	−35.4622	−1.58118	−0.790591	−	0.612345i	$-0.790226\pi$
$503$	−35.4622	−1.58118	−0.790591	+	0.612345i	$0.790226\pi$
$504$	−1.01001	−0.0449894
$505$	2.77242	0.123371
$506$	−0.711342	−0.0316230
$507$	−2.07532	−0.0921680
$508$	−16.4826	−0.731299
$509$	7.43800	0.329683	0.164842	−	0.986320i	$-0.447289\pi$
$509$	7.43800	0.329683	0.164842	+	0.986320i	$0.447289\pi$
$510$	−1.20349	−0.0532914
$511$	−2.08975	−0.0924452
$512$	1.00000	0.0441942
$513$	−8.33157	−0.367848
$514$	−7.91019	−0.348904
$515$	2.99274	0.131876
$516$	2.30476	0.101461
$517$	5.65113	0.248536
$518$	−3.55981	−0.156409
$519$	−1.48232	−0.0650667
$520$	−1.36064	−0.0596681
$521$	−28.9393	−1.26785	−0.633927	−	0.773393i	$-0.718558\pi$
$521$	−28.9393	−1.26785	−0.633927	+	0.773393i	$0.718558\pi$
$522$	10.9740	0.480318
$523$	−36.8434	−1.61105	−0.805526	−	0.592561i	$-0.798117\pi$
$523$	−36.8434	−1.61105	−0.805526	+	0.592561i	$0.798117\pi$
$524$	15.0988	0.659593
$525$	−0.329528	−0.0143818
$526$	−18.9873	−0.827885
$527$	24.8000	1.08031
$528$	−0.216237	−0.00941050
$529$	−22.4940	−0.978000
$530$	−3.97063	−0.172473
$531$	−14.8969	−0.646470
$532$	2.21346	0.0959655
$533$	−13.8308	−0.599080
$534$	−1.79844	−0.0778261
$535$	0.568488	0.0245779
$536$	4.34994	0.187889
$537$	0.890653	0.0384345
$538$	7.80588	0.336535
$539$	6.88304	0.296473
$540$	−0.949562	−0.0408626
$541$	34.1023	1.46617	0.733085	−	0.680137i	$-0.238080\pi$
$541$	34.1023	1.46617	0.733085	+	0.680137i	$0.238080\pi$
$542$	−28.3426	−1.21742
$543$	2.12677	0.0912684
$544$	−7.54522	−0.323499
$545$	8.97368	0.384390
$546$	−0.136414	−0.00583800
$547$	6.90042	0.295041	0.147520	−	0.989059i	$-0.452871\pi$
$547$	6.90042	0.295041	0.147520	+	0.989059i	$0.452871\pi$
$548$	5.46081	0.233274
$549$	27.3839	1.16872
$550$	4.45590	0.190000
$551$	−24.0497	−1.02455
$552$	0.153818	0.00654694
$553$	−0.827211	−0.0351766
$554$	−29.6448	−1.25949
$555$	−1.66024	−0.0704731
$556$	−14.3207	−0.607333
$557$	−14.2874	−0.605378	−0.302689	−	0.953089i	$-0.597884\pi$
$557$	−14.2874	−0.605378	−0.302689	+	0.953089i	$0.597884\pi$
$558$	9.70687	0.410924
$559$	−19.6608	−0.831562
$560$	0.252271	0.0106604
$561$	1.63156	0.0688843
$562$	−23.3369	−0.984409
$563$	−9.61469	−0.405211	−0.202605	−	0.979260i	$-0.564941\pi$
$563$	−9.61469	−0.405211	−0.202605	+	0.979260i	$0.564941\pi$
$564$	−1.22198	−0.0514547
$565$	−0.990625	−0.0416759
$566$	−3.65680	−0.153707
$567$	2.93483	0.123251
$568$	−12.9494	−0.543343
$569$	−17.7332	−0.743412	−0.371706	−	0.928350i	$-0.621227\pi$
$569$	−17.7332	−0.743412	−0.371706	+	0.928350i	$0.621227\pi$
$570$	1.03232	0.0432391
$571$	28.9140	1.21001	0.605006	−	0.796221i	$-0.293171\pi$
$571$	28.9140	1.21001	0.605006	+	0.796221i	$0.293171\pi$
$572$	1.84461	0.0771269
$573$	4.21943	0.176269
$574$	2.56432	0.107032
$575$	−3.16967	−0.132184
$576$	−2.95324	−0.123052
$577$	39.5918	1.64823	0.824113	−	0.566425i	$-0.191674\pi$
$577$	39.5918	1.64823	0.824113	+	0.566425i	$0.191674\pi$
$578$	39.9304	1.66089
$579$	3.35854	0.139576
$580$	−2.74098	−0.113813
$581$	3.44190	0.142794
$582$	−2.89605	−0.120045
$583$	5.38294	0.222939
$584$	−6.11038	−0.252849
$585$	4.01831	0.166137
$586$	27.6266	1.14124
$587$	16.6125	0.685672	0.342836	−	0.939395i	$-0.388612\pi$
$587$	16.6125	0.685672	0.342836	+	0.939395i	$0.388612\pi$
$588$	−1.48837	−0.0613792
$589$	−21.2728	−0.876529
$590$	3.72080	0.153183
$591$	0.216237	0.00889479
$592$	−10.4088	−0.427799
$593$	19.5658	0.803473	0.401737	−	0.915755i	$-0.368407\pi$
$593$	19.5658	0.803473	0.401737	+	0.915755i	$0.368407\pi$
$594$	1.28731	0.0528190
$595$	−1.90344	−0.0780334
$596$	−19.7458	−0.808818
$597$	0.115566	0.00472980
$598$	−1.31215	−0.0536577
$599$	27.8626	1.13844	0.569218	−	0.822186i	$-0.307246\pi$
$599$	27.8626	1.13844	0.569218	+	0.822186i	$0.307246\pi$
$600$	−0.963529	−0.0393359
$601$	5.31733	0.216899	0.108449	−	0.994102i	$-0.465411\pi$
$601$	5.31733	0.216899	0.108449	+	0.994102i	$0.465411\pi$
$602$	3.64522	0.148568
$603$	−12.8464	−0.523147
$604$	−11.0279	−0.448719
$605$	0.737633	0.0299890
$606$	0.812733	0.0330150
$607$	32.1644	1.30551	0.652757	−	0.757567i	$-0.273612\pi$
$607$	32.1644	1.30551	0.652757	+	0.757567i	$0.273612\pi$
$608$	6.47208	0.262477
$609$	−0.274803	−0.0111356
$610$	−6.83969	−0.276931
$611$	10.4241	0.421715
$612$	22.2829	0.900732
$613$	37.0445	1.49621	0.748106	−	0.663579i	$-0.230963\pi$
$613$	37.0445	1.49621	0.748106	+	0.663579i	$0.230963\pi$
$614$	−30.5794	−1.23408
$615$	1.19595	0.0482255
$616$	−0.342001	−0.0137796
$617$	−34.7215	−1.39784	−0.698918	−	0.715202i	$-0.746335\pi$
$617$	−34.7215	−1.39784	−0.698918	+	0.715202i	$0.746335\pi$
$618$	0.877322	0.0352911
$619$	−42.0573	−1.69043	−0.845213	−	0.534429i	$-0.820527\pi$
$619$	−42.0573	−1.69043	−0.845213	+	0.534429i	$0.820527\pi$
$620$	−2.42449	−0.0973698
$621$	−0.915718	−0.0367465
$622$	10.7379	0.430553
$623$	−2.84442	−0.113959
$624$	−0.398872	−0.0159677
$625$	17.1345	0.685381
$626$	−9.11280	−0.364221
$627$	−1.39950	−0.0558907
$628$	12.0037	0.478999
$629$	78.5366	3.13146
$630$	−0.745017	−0.0296822
$631$	−21.1799	−0.843160	−0.421580	−	0.906791i	$-0.638524\pi$
$631$	−21.1799	−0.843160	−0.421580	+	0.906791i	$0.638524\pi$
$632$	−2.41874	−0.0962124
$633$	1.48449	0.0590031
$634$	29.6596	1.17793
$635$	−12.1581	−0.482481
$636$	−1.16399	−0.0461552
$637$	12.6965	0.503054
$638$	3.71591	0.147114
$639$	38.2426	1.51285
$640$	0.737633	0.0291575
$641$	−25.2941	−0.999057	−0.499529	−	0.866297i	$-0.666493\pi$
$641$	−25.2941	−0.999057	−0.499529	+	0.866297i	$0.666493\pi$
$642$	0.166652	0.00657723
$643$	33.6443	1.32680	0.663401	−	0.748264i	$-0.269112\pi$
$643$	33.6443	1.32680	0.663401	+	0.748264i	$0.269112\pi$
$644$	0.243279	0.00958655
$645$	1.70007	0.0669401
$646$	−48.8333	−1.92132
$647$	19.1871	0.754324	0.377162	−	0.926147i	$-0.376900\pi$
$647$	19.1871	0.754324	0.377162	+	0.926147i	$0.376900\pi$
$648$	8.58136	0.337108
$649$	−5.04425	−0.198004
$650$	8.21938	0.322391
$651$	−0.243073	−0.00952678
$652$	−0.000924835 0	−3.62193e−5 0
$653$	30.7339	1.20271	0.601356	−	0.798981i	$-0.294627\pi$
$653$	30.7339	1.20271	0.601356	+	0.798981i	$0.294627\pi$
$654$	2.63063	0.102866
$655$	11.1373	0.435172
$656$	7.49798	0.292747
$657$	18.0454	0.704019
$658$	−1.93269	−0.0753441
$659$	49.8101	1.94033	0.970163	−	0.242455i	$-0.0779525\pi$
$659$	49.8101	1.94033	0.970163	+	0.242455i	$0.0779525\pi$
$660$	−0.159503	−0.00620866
$661$	−15.9255	−0.619429	−0.309715	−	0.950830i	$-0.600234\pi$
$661$	−15.9255	−0.619429	−0.309715	+	0.950830i	$0.600234\pi$
$662$	−16.8523	−0.654982
$663$	3.00958	0.116882
$664$	10.0640	0.390559
$665$	1.63272	0.0633140
$666$	30.7397	1.19114
$667$	−2.64328	−0.102348
$668$	7.00966	0.271212
$669$	1.40575	0.0543494
$670$	3.20866	0.123961
$671$	9.27249	0.357961
$672$	0.0739531	0.00285280
$673$	11.5379	0.444753	0.222376	−	0.974961i	$-0.428619\pi$
$673$	11.5379	0.444753	0.222376	+	0.974961i	$0.428619\pi$
$674$	−13.8605	−0.533885
$675$	5.73612	0.220783
$676$	−9.59742	−0.369132
$677$	45.6120	1.75301	0.876506	−	0.481390i	$-0.159868\pi$
$677$	45.6120	1.75301	0.876506	+	0.481390i	$0.159868\pi$
$678$	−0.290402	−0.0111528
$679$	−4.58040	−0.175780
$680$	−5.56560	−0.213431
$681$	6.06179	0.232288
$682$	3.28685	0.125860
$683$	−0.398554	−0.0152503	−0.00762513	−	0.999971i	$-0.502427\pi$
$683$	−0.398554	−0.0152503	−0.00762513	+	0.999971i	$0.502427\pi$
$684$	−19.1136	−0.730827
$685$	4.02807	0.153905
$686$	−4.74801	−0.181280
$687$	−1.47213	−0.0561651
$688$	10.6585	0.406352
$689$	9.92942	0.378281
$690$	0.113461	0.00431940
$691$	4.60493	0.175180	0.0875899	−	0.996157i	$-0.472084\pi$
$691$	4.60493	0.175180	0.0875899	+	0.996157i	$0.472084\pi$
$692$	−6.85509	−0.260591
$693$	1.01001	0.0383671
$694$	17.1461	0.650856
$695$	−10.5634	−0.400693
$696$	−0.803517	−0.0304572
$697$	−56.5740	−2.14289
$698$	−23.8764	−0.903733
$699$	3.28547	0.124268
$700$	−1.52392	−0.0575988
$701$	−7.42517	−0.280445	−0.140222	−	0.990120i	$-0.544782\pi$
$701$	−7.42517	−0.280445	−0.140222	+	0.990120i	$0.544782\pi$
$702$	2.37458	0.0896228
$703$	−67.3665	−2.54078
$704$	−1.00000	−0.0376889
$705$	−0.901374	−0.0339477
$706$	9.15801	0.344666
$707$	1.28542	0.0483432
$708$	1.09075	0.0409930
$709$	50.0863	1.88103	0.940516	−	0.339749i	$-0.110342\pi$
$709$	50.0863	1.88103	0.940516	+	0.339749i	$0.110342\pi$
$710$	−9.55187	−0.358475
$711$	7.14313	0.267888
$712$	−8.31699	−0.311693
$713$	−2.33808	−0.0875616
$714$	−0.557993	−0.0208824
$715$	1.36064	0.0508851
$716$	4.11888	0.153930
$717$	−0.427924	−0.0159811
$718$	−11.1187	−0.414947
$719$	12.8032	0.477480	0.238740	−	0.971084i	$-0.423266\pi$
$719$	12.8032	0.477480	0.238740	+	0.971084i	$0.423266\pi$
$720$	−2.17841	−0.0811844
$721$	1.38758	0.0516760
$722$	22.8878	0.851796
$723$	−4.91169	−0.182668
$724$	9.83537	0.365529
$725$	16.5577	0.614939
$726$	0.216237	0.00802530
$727$	−14.1133	−0.523433	−0.261716	−	0.965145i	$-0.584289\pi$
$727$	−14.1133	−0.523433	−0.261716	+	0.965145i	$0.584289\pi$
$728$	−0.630857	−0.0233811
$729$	−24.5077	−0.907694
$730$	−4.50721	−0.166819
$731$	−80.4208	−2.97447
$732$	−2.00505	−0.0741090
$733$	8.52819	0.314996	0.157498	−	0.987519i	$-0.449657\pi$
$733$	8.52819	0.314996	0.157498	+	0.987519i	$0.449657\pi$
$734$	−15.3813	−0.567736
$735$	−1.09787	−0.0404954
$736$	0.711342	0.0262204
$737$	−4.34994	−0.160232
$738$	−22.1434	−0.815108
$739$	16.7194	0.615032	0.307516	−	0.951543i	$-0.400502\pi$
$739$	16.7194	0.615032	0.307516	+	0.951543i	$0.400502\pi$
$740$	−7.67786	−0.282244
$741$	−2.58153	−0.0948349
$742$	−1.84097	−0.0675841
$743$	−27.0060	−0.990753	−0.495376	−	0.868678i	$-0.664970\pi$
$743$	−27.0060	−0.990753	−0.495376	+	0.868678i	$0.664970\pi$
$744$	−0.710738	−0.0260569
$745$	−14.5651	−0.533625
$746$	26.3776	0.965751
$747$	−29.7214	−1.08745
$748$	7.54522	0.275881
$749$	0.263577	0.00963091
$750$	−1.50825	−0.0550734
$751$	12.8416	0.468595	0.234297	−	0.972165i	$-0.424721\pi$
$751$	12.8416	0.468595	0.234297	+	0.972165i	$0.424721\pi$
$752$	−5.65113	−0.206075
$753$	4.60913	0.167966
$754$	6.85440	0.249622
$755$	−8.13453	−0.296046
$756$	−0.440261	−0.0160121
$757$	−25.1195	−0.912983	−0.456492	−	0.889728i	$-0.650894\pi$
$757$	−25.1195	−0.912983	−0.456492	+	0.889728i	$0.650894\pi$
$758$	30.9513	1.12420
$759$	−0.153818	−0.00558325
$760$	4.77402	0.173172
$761$	−37.1927	−1.34823	−0.674117	−	0.738625i	$-0.735475\pi$
$761$	−37.1927	−1.34823	−0.674117	+	0.738625i	$0.735475\pi$
$762$	−3.56415	−0.129116
$763$	4.16061	0.150624
$764$	19.5130	0.705956
$765$	16.4366	0.594265
$766$	−11.5329	−0.416699
$767$	−9.30466	−0.335972
$768$	0.216237	0.00780277
$769$	−31.3251	−1.12961	−0.564807	−	0.825223i	$-0.691049\pi$
$769$	−31.3251	−1.12961	−0.564807	+	0.825223i	$0.691049\pi$
$770$	−0.252271	−0.00909121
$771$	−1.71047	−0.0616012
$772$	15.5318	0.559001
$773$	−14.0670	−0.505957	−0.252978	−	0.967472i	$-0.581410\pi$
$773$	−14.0670	−0.505957	−0.252978	+	0.967472i	$0.581410\pi$
$774$	−31.4771	−1.13142
$775$	14.6459	0.526095
$776$	−13.3930	−0.480779
$777$	−0.769763	−0.0276151
$778$	−36.3799	−1.30428
$779$	48.5275	1.73868
$780$	−0.294221	−0.0105348
$781$	12.9494	0.463365
$782$	−5.36723	−0.191932
$783$	4.78353	0.170949
$784$	−6.88304	−0.245823
$785$	8.85431	0.316024
$786$	3.26491	0.116455
$787$	45.4187	1.61900	0.809500	−	0.587119i	$-0.199738\pi$
$787$	45.4187	1.61900	0.809500	+	0.587119i	$0.199738\pi$
$788$	1.00000	0.0356235
$789$	−4.10575	−0.146169
$790$	−1.78414	−0.0634770
$791$	−0.459300	−0.0163308
$792$	2.95324	0.104939
$793$	17.1041	0.607385
$794$	32.5974	1.15684
$795$	−0.858597	−0.0304513
$796$	0.534442	0.0189428
$797$	22.0450	0.780873	0.390437	−	0.920630i	$-0.372324\pi$
$797$	22.0450	0.780873	0.390437	+	0.920630i	$0.372324\pi$
$798$	0.478631	0.0169433
$799$	42.6390	1.50846
$800$	−4.45590	−0.157540
$801$	24.5621	0.867859
$802$	−16.8072	−0.593485
$803$	6.11038	0.215630
$804$	0.940618	0.0331730
$805$	0.179451	0.00632481
$806$	6.06295	0.213558
$807$	1.68792	0.0594175
$808$	3.75853	0.132225
$809$	1.29571	0.0455548	0.0227774	−	0.999741i	$-0.492749\pi$
$809$	1.29571	0.0455548	0.0227774	+	0.999741i	$0.492749\pi$
$810$	6.32989	0.222410
$811$	16.2203	0.569571	0.284786	−	0.958591i	$-0.408078\pi$
$811$	16.2203	0.569571	0.284786	+	0.958591i	$0.408078\pi$
$812$	−1.27084	−0.0445979
$813$	−6.12871	−0.214943
$814$	10.4088	0.364828
$815$	−0.000682189 0	−2.38960e−5 0
$816$	−1.63156	−0.0571159
$817$	68.9827	2.41340
$818$	37.1150	1.29770
$819$	1.86307	0.0651010
$820$	5.53076	0.193142
$821$	47.9692	1.67414	0.837069	−	0.547098i	$-0.184267\pi$
$821$	47.9692	1.67414	0.837069	+	0.547098i	$0.184267\pi$
$822$	1.18083	0.0411861
$823$	3.07292	0.107115	0.0535576	−	0.998565i	$-0.482944\pi$
$823$	3.07292	0.107115	0.0535576	+	0.998565i	$0.482944\pi$
$824$	4.05723	0.141340
$825$	0.963529	0.0335458
$826$	1.72514	0.0600252
$827$	−47.7460	−1.66029	−0.830146	−	0.557547i	$-0.811743\pi$
$827$	−47.7460	−1.66029	−0.830146	+	0.557547i	$0.811743\pi$
$828$	−2.10076	−0.0730066
$829$	−17.4398	−0.605709	−0.302855	−	0.953037i	$-0.597940\pi$
$829$	−17.4398	−0.605709	−0.302855	+	0.953037i	$0.597940\pi$
$830$	7.42354	0.257675
$831$	−6.41030	−0.222371
$832$	−1.84461	−0.0639503
$833$	51.9340	1.79941
$834$	−3.09666	−0.107229
$835$	5.17055	0.178934
$836$	−6.47208	−0.223842
$837$	4.23120	0.146252
$838$	−4.53436	−0.156637
$839$	39.5208	1.36441	0.682204	−	0.731162i	$-0.261022\pi$
$839$	39.5208	1.36441	0.682204	+	0.731162i	$0.261022\pi$
$840$	0.0545502	0.00188216
$841$	−15.1920	−0.523862
$842$	−12.4208	−0.428049
$843$	−5.04630	−0.173804
$844$	6.86511	0.236307
$845$	−7.07937	−0.243538
$846$	16.6891	0.573785
$847$	0.342001	0.0117513
$848$	−5.38294	−0.184851
$849$	−0.790735	−0.0271380
$850$	33.6207	1.15318
$851$	−7.40421	−0.253813
$852$	−2.80013	−0.0959308
$853$	−7.88396	−0.269942	−0.134971	−	0.990850i	$-0.543094\pi$
$853$	−7.88396	−0.269942	−0.134971	+	0.990850i	$0.543094\pi$
$854$	−3.17120	−0.108516
$855$	−14.0988	−0.482170
$856$	0.770693	0.0263417
$857$	2.99137	0.102183	0.0510917	−	0.998694i	$-0.483730\pi$
$857$	2.99137	0.102183	0.0510917	+	0.998694i	$0.483730\pi$
$858$	0.398872	0.0136173
$859$	30.0731	1.02608	0.513040	−	0.858365i	$-0.328519\pi$
$859$	30.0731	1.02608	0.513040	+	0.858365i	$0.328519\pi$
$860$	7.86206	0.268094
$861$	0.554499	0.0188973
$862$	0.860841	0.0293204
$863$	−3.87408	−0.131875	−0.0659376	−	0.997824i	$-0.521004\pi$
$863$	−3.87408	−0.131875	−0.0659376	+	0.997824i	$0.521004\pi$
$864$	−1.28731	−0.0437952
$865$	−5.05654	−0.171927
$866$	5.63608	0.191522
$867$	8.63442	0.293240
$868$	−1.12411	−0.0381546
$869$	2.41874	0.0820502
$870$	−0.592700	−0.0200944
$871$	−8.02393	−0.271881
$872$	12.1655	0.411976
$873$	39.5526	1.33865
$874$	4.60386	0.155728
$875$	−2.38545	−0.0806428
$876$	−1.32129	−0.0446422
$877$	−56.5889	−1.91087	−0.955436	−	0.295199i	$-0.904614\pi$
$877$	−56.5889	−1.91087	−0.955436	+	0.295199i	$0.904614\pi$
$878$	−20.6190	−0.695857
$879$	5.97389	0.201494
$880$	−0.737633	−0.0248656
$881$	−37.3960	−1.25990	−0.629951	−	0.776635i	$-0.716925\pi$
$881$	−37.3960	−1.25990	−0.629951	+	0.776635i	$0.716925\pi$
$882$	20.3273	0.684455
$883$	−53.7470	−1.80873	−0.904365	−	0.426761i	$-0.859655\pi$
$883$	−53.7470	−1.80873	−0.904365	+	0.426761i	$0.859655\pi$
$884$	13.9180	0.468112
$885$	0.804575	0.0270455
$886$	25.0043	0.840038
$887$	−46.0107	−1.54489	−0.772444	−	0.635083i	$-0.780966\pi$
$887$	−46.0107	−1.54489	−0.772444	+	0.635083i	$0.780966\pi$
$888$	−2.25076	−0.0755307
$889$	−5.63707	−0.189061
$890$	−6.13489	−0.205642
$891$	−8.58136	−0.287486
$892$	6.50097	0.217669
$893$	−36.5746	−1.22392
$894$	−4.26976	−0.142802
$895$	3.03822	0.101556
$896$	0.342001	0.0114254
$897$	−0.283734	−0.00947362
$898$	−34.7163	−1.15850
$899$	12.2137	0.407348
$900$	13.1593	0.438645
$901$	40.6155	1.35310
$902$	−7.49798	−0.249656
$903$	0.788230	0.0262307
$904$	−1.34298	−0.0446668
$905$	7.25489	0.241161
$906$	−2.38464	−0.0792242
$907$	41.4232	1.37543	0.687717	−	0.725979i	$-0.258613\pi$
$907$	41.4232	1.37543	0.687717	+	0.725979i	$0.258613\pi$
$908$	28.0331	0.930311
$909$	−11.0999	−0.368159
$910$	−0.465341	−0.0154259
$911$	−26.2781	−0.870633	−0.435317	−	0.900277i	$-0.643364\pi$
$911$	−26.2781	−0.870633	−0.435317	+	0.900277i	$0.643364\pi$
$912$	1.39950	0.0463421
$913$	−10.0640	−0.333070
$914$	6.97918	0.230851
$915$	−1.47899	−0.0488940
$916$	−6.80793	−0.224940
$917$	5.16379	0.170523
$918$	9.71304	0.320578
$919$	14.6871	0.484484	0.242242	−	0.970216i	$-0.422117\pi$
$919$	14.6871	0.484484	0.242242	+	0.970216i	$0.422117\pi$
$920$	0.524709	0.0172991
$921$	−6.61238	−0.217885
$922$	−17.3901	−0.572714
$923$	23.8865	0.786233
$924$	−0.0739531	−0.00243288
$925$	46.3805	1.52498
$926$	21.4363	0.704442
$927$	−11.9820	−0.393540
$928$	−3.71591	−0.121981
$929$	33.9514	1.11391	0.556954	−	0.830543i	$-0.311970\pi$
$929$	33.9514	1.11391	0.556954	+	0.830543i	$0.311970\pi$
$930$	−0.524264	−0.0171913
$931$	−44.5476	−1.45999
$932$	15.1939	0.497691
$933$	2.32194	0.0760169
$934$	1.87676	0.0614094
$935$	5.56560	0.182015
$936$	5.44757	0.178059
$937$	−58.8888	−1.92381	−0.961907	−	0.273378i	$-0.911859\pi$
$937$	−58.8888	−1.92381	−0.961907	+	0.273378i	$0.911859\pi$
$938$	1.48768	0.0485746
$939$	−1.97052	−0.0643056
$940$	−4.16846	−0.135960
$941$	17.6254	0.574572	0.287286	−	0.957845i	$-0.407247\pi$
$941$	17.6254	0.574572	0.287286	+	0.957845i	$0.407247\pi$
$942$	2.59564	0.0845705
$943$	5.33363	0.173687
$944$	5.04425	0.164176
$945$	−0.324751	−0.0105641
$946$	−10.6585	−0.346538
$947$	43.7343	1.42117	0.710587	−	0.703610i	$-0.248430\pi$
$947$	43.7343	1.42117	0.710587	+	0.703610i	$0.248430\pi$
$948$	−0.523021	−0.0169869
$949$	11.2712	0.365880
$950$	−28.8389	−0.935658
$951$	6.41350	0.207972
$952$	−2.58047	−0.0836336
$953$	21.3901	0.692894	0.346447	−	0.938069i	$-0.387388\pi$
$953$	21.3901	0.692894	0.346447	+	0.938069i	$0.387388\pi$
$954$	15.8971	0.514689
$955$	14.3934	0.465761
$956$	−1.97896	−0.0640041
$957$	0.803517	0.0259740
$958$	20.6866	0.668355
$959$	1.86760	0.0603080
$960$	0.159503	0.00514795
$961$	−20.1966	−0.651503
$962$	19.2001	0.619037
$963$	−2.27604	−0.0733444
$964$	−22.7144	−0.731582
$965$	11.4567	0.368806
$966$	0.0526060	0.00169257
$967$	13.9287	0.447917	0.223959	−	0.974599i	$-0.428102\pi$
$967$	13.9287	0.447917	0.223959	+	0.974599i	$0.428102\pi$
$968$	1.00000	0.0321412
$969$	−10.5596	−0.339222
$970$	−9.87908	−0.317198
$971$	39.3135	1.26163	0.630815	−	0.775933i	$-0.282721\pi$
$971$	39.3135	1.26163	0.630815	+	0.775933i	$0.282721\pi$
$972$	5.71754	0.183390
$973$	−4.89769	−0.157013
$974$	16.2294	0.520024
$975$	1.77733	0.0569202
$976$	−9.27249	−0.296805
$977$	9.73215	0.311359	0.155680	−	0.987808i	$-0.450243\pi$
$977$	9.73215	0.311359	0.155680	+	0.987808i	$0.450243\pi$
$978$	−0.000199983 0	−6.39477e−6 0
$979$	8.31699	0.265812
$980$	−5.07715	−0.162184
$981$	−35.9277	−1.14708
$982$	−31.3158	−0.999328
$983$	−1.30517	−0.0416284	−0.0208142	−	0.999783i	$-0.506626\pi$
$983$	−1.30517	−0.0416284	−0.0208142	+	0.999783i	$0.506626\pi$
$984$	1.62134	0.0516864
$985$	0.737633	0.0235029
$986$	28.0374	0.892892
$987$	−0.417919	−0.0133025
$988$	−11.9384	−0.379813
$989$	7.58184	0.241089
$990$	2.17841	0.0692343
$991$	13.1695	0.418342	0.209171	−	0.977879i	$-0.432923\pi$
$991$	13.1695	0.418342	0.209171	+	0.977879i	$0.432923\pi$
$992$	−3.28685	−0.104358
$993$	−3.64408	−0.115641
$994$	−4.42869	−0.140469
$995$	0.394222	0.0124977
$996$	2.17621	0.0689558
$997$	−58.7003	−1.85906	−0.929529	−	0.368748i	$-0.879786\pi$
$997$	−58.7003	−1.85906	−0.929529	+	0.368748i	$0.879786\pi$
$998$	−10.4370	−0.330379
$999$	13.3993	0.423936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.d.1.10	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.216237 q^{3} +1.00000 q^{4} +0.737633 q^{5} +0.216237 q^{6} +0.342001 q^{7} +1.00000 q^{8} -2.95324 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.216237 q^{3} +1.00000 q^{4} +0.737633 q^{5} +0.216237 q^{6} +0.342001 q^{7} +1.00000 q^{8} -2.95324 q^{9} +0.737633 q^{10} -1.00000 q^{11} +0.216237 q^{12} -1.84461 q^{13} +0.342001 q^{14} +0.159503 q^{15} +1.00000 q^{16} -7.54522 q^{17} -2.95324 q^{18} +6.47208 q^{19} +0.737633 q^{20} +0.0739531 q^{21} -1.00000 q^{22} +0.711342 q^{23} +0.216237 q^{24} -4.45590 q^{25} -1.84461 q^{26} -1.28731 q^{27} +0.342001 q^{28} -3.71591 q^{29} +0.159503 q^{30} -3.28685 q^{31} +1.00000 q^{32} -0.216237 q^{33} -7.54522 q^{34} +0.252271 q^{35} -2.95324 q^{36} -10.4088 q^{37} +6.47208 q^{38} -0.398872 q^{39} +0.737633 q^{40} +7.49798 q^{41} +0.0739531 q^{42} +10.6585 q^{43} -1.00000 q^{44} -2.17841 q^{45} +0.711342 q^{46} -5.65113 q^{47} +0.216237 q^{48} -6.88304 q^{49} -4.45590 q^{50} -1.63156 q^{51} -1.84461 q^{52} -5.38294 q^{53} -1.28731 q^{54} -0.737633 q^{55} +0.342001 q^{56} +1.39950 q^{57} -3.71591 q^{58} +5.04425 q^{59} +0.159503 q^{60} -9.27249 q^{61} -3.28685 q^{62} -1.01001 q^{63} +1.00000 q^{64} -1.36064 q^{65} -0.216237 q^{66} +4.34994 q^{67} -7.54522 q^{68} +0.153818 q^{69} +0.252271 q^{70} -12.9494 q^{71} -2.95324 q^{72} -6.11038 q^{73} -10.4088 q^{74} -0.963529 q^{75} +6.47208 q^{76} -0.342001 q^{77} -0.398872 q^{78} -2.41874 q^{79} +0.737633 q^{80} +8.58136 q^{81} +7.49798 q^{82} +10.0640 q^{83} +0.0739531 q^{84} -5.56560 q^{85} +10.6585 q^{86} -0.803517 q^{87} -1.00000 q^{88} -8.31699 q^{89} -2.17841 q^{90} -0.630857 q^{91} +0.711342 q^{92} -0.710738 q^{93} -5.65113 q^{94} +4.77402 q^{95} +0.216237 q^{96} -13.3930 q^{97} -6.88304 q^{98} +2.95324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19} - 4 q^{20} - 13 q^{21} - 17 q^{22} - 6 q^{23} - 7 q^{24} + 3 q^{25} - 18 q^{26} - 37 q^{27} - 5 q^{28} - 16 q^{29} - 16 q^{30} - 30 q^{31} + 17 q^{32} + 7 q^{33} - 10 q^{34} - 36 q^{35} + 12 q^{36} - 23 q^{37} - 31 q^{38} - 15 q^{39} - 4 q^{40} - 7 q^{41} - 13 q^{42} - 23 q^{43} - 17 q^{44} - 19 q^{45} - 6 q^{46} - 19 q^{47} - 7 q^{48} - 8 q^{49} + 3 q^{50} - 18 q^{51} - 18 q^{52} - 30 q^{53} - 37 q^{54} + 4 q^{55} - 5 q^{56} + 10 q^{57} - 16 q^{58} - 28 q^{59} - 16 q^{60} - 19 q^{61} - 30 q^{62} + 2 q^{63} + 17 q^{64} + 23 q^{65} + 7 q^{66} - 35 q^{67} - 10 q^{68} + q^{69} - 36 q^{70} + q^{71} + 12 q^{72} - 10 q^{73} - 23 q^{74} - 33 q^{75} - 31 q^{76} + 5 q^{77} - 15 q^{78} - 27 q^{79} - 4 q^{80} + 13 q^{81} - 7 q^{82} - 40 q^{83} - 13 q^{84} - 11 q^{85} - 23 q^{86} - 6 q^{87} - 17 q^{88} - 17 q^{89} - 19 q^{90} - 19 q^{91} - 6 q^{92} + 10 q^{93} - 19 q^{94} - 27 q^{95} - 7 q^{96} - 34 q^{97} - 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

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