LMFDB - Embedded newform 770.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(1,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("770.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	770.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.14637 q^{12} +4.68585 q^{13} -1.00000 q^{14} +1.14637 q^{15} +1.00000 q^{16} -0.292731 q^{17} -1.68585 q^{18} +6.51806 q^{19} +1.00000 q^{20} -1.14637 q^{21} +1.00000 q^{22} +2.85363 q^{23} +1.14637 q^{24} +1.00000 q^{25} +4.68585 q^{26} -5.37169 q^{27} -1.00000 q^{28} -1.43910 q^{29} +1.14637 q^{30} +0.978577 q^{31} +1.00000 q^{32} +1.14637 q^{33} -0.292731 q^{34} -1.00000 q^{35} -1.68585 q^{36} +0.853635 q^{37} +6.51806 q^{38} +5.37169 q^{39} +1.00000 q^{40} -6.22533 q^{41} -1.14637 q^{42} -10.3503 q^{43} +1.00000 q^{44} -1.68585 q^{45} +2.85363 q^{46} -9.95715 q^{47} +1.14637 q^{48} +1.00000 q^{49} +1.00000 q^{50} -0.335577 q^{51} +4.68585 q^{52} +5.43910 q^{53} -5.37169 q^{54} +1.00000 q^{55} -1.00000 q^{56} +7.47208 q^{57} -1.43910 q^{58} -9.37169 q^{59} +1.14637 q^{60} -11.9572 q^{61} +0.978577 q^{62} +1.68585 q^{63} +1.00000 q^{64} +4.68585 q^{65} +1.14637 q^{66} -0.585462 q^{67} -0.292731 q^{68} +3.27131 q^{69} -1.00000 q^{70} -0.335577 q^{71} -1.68585 q^{72} -3.70727 q^{73} +0.853635 q^{74} +1.14637 q^{75} +6.51806 q^{76} -1.00000 q^{77} +5.37169 q^{78} -2.51806 q^{79} +1.00000 q^{80} -1.10038 q^{81} -6.22533 q^{82} -1.70727 q^{83} -1.14637 q^{84} -0.292731 q^{85} -10.3503 q^{86} -1.64973 q^{87} +1.00000 q^{88} +13.0790 q^{89} -1.68585 q^{90} -4.68585 q^{91} +2.85363 q^{92} +1.12181 q^{93} -9.95715 q^{94} +6.51806 q^{95} +1.14637 q^{96} +9.10352 q^{97} +1.00000 q^{98} -1.68585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + 2 q^{17} + 7 q^{18} - 6 q^{19} + 3 q^{20} - 2 q^{21} + 3 q^{22} + 10 q^{23} + 2 q^{24} + 3 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} + 2 q^{30} - 12 q^{31} + 3 q^{32} + 2 q^{33} + 2 q^{34} - 3 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 8 q^{39} + 3 q^{40} + 4 q^{41} - 2 q^{42} + 8 q^{43} + 3 q^{44} + 7 q^{45} + 10 q^{46} + 2 q^{48} + 3 q^{49} + 3 q^{50} - 28 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{54} + 3 q^{55} - 3 q^{56} - 8 q^{57} - 4 q^{59} + 2 q^{60} - 6 q^{61} - 12 q^{62} - 7 q^{63} + 3 q^{64} + 2 q^{65} + 2 q^{66} + 4 q^{67} + 2 q^{68} - 8 q^{69} - 3 q^{70} - 28 q^{71} + 7 q^{72} - 14 q^{73} + 4 q^{74} + 2 q^{75} - 6 q^{76} - 3 q^{77} - 8 q^{78} + 18 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{82} - 8 q^{83} - 2 q^{84} + 2 q^{85} + 8 q^{86} - 44 q^{87} + 3 q^{88} + 18 q^{89} + 7 q^{90} - 2 q^{91} + 10 q^{92} + 12 q^{93} - 6 q^{95} + 2 q^{96} - 4 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + 2 * q^17 + 7 * q^18 - 6 * q^19 + 3 * q^20 - 2 * q^21 + 3 * q^22 + 10 * q^23 + 2 * q^24 + 3 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 + 2 * q^30 - 12 * q^31 + 3 * q^32 + 2 * q^33 + 2 * q^34 - 3 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 8 * q^39 + 3 * q^40 + 4 * q^41 - 2 * q^42 + 8 * q^43 + 3 * q^44 + 7 * q^45 + 10 * q^46 + 2 * q^48 + 3 * q^49 + 3 * q^50 - 28 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^54 + 3 * q^55 - 3 * q^56 - 8 * q^57 - 4 * q^59 + 2 * q^60 - 6 * q^61 - 12 * q^62 - 7 * q^63 + 3 * q^64 + 2 * q^65 + 2 * q^66 + 4 * q^67 + 2 * q^68 - 8 * q^69 - 3 * q^70 - 28 * q^71 + 7 * q^72 - 14 * q^73 + 4 * q^74 + 2 * q^75 - 6 * q^76 - 3 * q^77 - 8 * q^78 + 18 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^82 - 8 * q^83 - 2 * q^84 + 2 * q^85 + 8 * q^86 - 44 * q^87 + 3 * q^88 + 18 * q^89 + 7 * q^90 - 2 * q^91 + 10 * q^92 + 12 * q^93 - 6 * q^95 + 2 * q^96 - 4 * q^97 + 3 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.14637	0.661854	0.330927	−	0.943656i	$-0.392639\pi$
$3$	1.14637	0.661854	0.330927	+	0.943656i	$0.392639\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.14637	0.468002
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.68585	−0.561949
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.14637	0.330927
$13$	4.68585	1.29962	0.649810	−	0.760097i	$-0.274848\pi$
$13$	4.68585	1.29962	0.649810	+	0.760097i	$0.274848\pi$
$14$	−1.00000	−0.267261
$15$	1.14637	0.295990
$16$	1.00000	0.250000
$17$	−0.292731	−0.0709977	−0.0354988	−	0.999370i	$-0.511302\pi$
$17$	−0.292731	−0.0709977	−0.0354988	+	0.999370i	$0.511302\pi$
$18$	−1.68585	−0.397358
$19$	6.51806	1.49535	0.747673	−	0.664068i	$-0.231171\pi$
$19$	6.51806	1.49535	0.747673	+	0.664068i	$0.231171\pi$
$20$	1.00000	0.223607
$21$	−1.14637	−0.250157
$22$	1.00000	0.213201
$23$	2.85363	0.595024	0.297512	−	0.954718i	$-0.403843\pi$
$23$	2.85363	0.595024	0.297512	+	0.954718i	$0.403843\pi$
$24$	1.14637	0.234001
$25$	1.00000	0.200000
$26$	4.68585	0.918970
$27$	−5.37169	−1.03378
$28$	−1.00000	−0.188982
$29$	−1.43910	−0.267234	−0.133617	−	0.991033i	$-0.542659\pi$
$29$	−1.43910	−0.267234	−0.133617	+	0.991033i	$0.542659\pi$
$30$	1.14637	0.209297
$31$	0.978577	0.175758	0.0878788	−	0.996131i	$-0.471991\pi$
$31$	0.978577	0.175758	0.0878788	+	0.996131i	$0.471991\pi$
$32$	1.00000	0.176777
$33$	1.14637	0.199557
$34$	−0.292731	−0.0502029
$35$	−1.00000	−0.169031
$36$	−1.68585	−0.280974
$37$	0.853635	0.140337	0.0701683	−	0.997535i	$-0.477646\pi$
$37$	0.853635	0.140337	0.0701683	+	0.997535i	$0.477646\pi$
$38$	6.51806	1.05737
$39$	5.37169	0.860159
$40$	1.00000	0.158114
$41$	−6.22533	−0.972233	−0.486116	−	0.873894i	$-0.661587\pi$
$41$	−6.22533	−0.972233	−0.486116	+	0.873894i	$0.661587\pi$
$42$	−1.14637	−0.176888
$43$	−10.3503	−1.57840	−0.789201	−	0.614135i	$-0.789505\pi$
$43$	−10.3503	−1.57840	−0.789201	+	0.614135i	$0.789505\pi$
$44$	1.00000	0.150756
$45$	−1.68585	−0.251311
$46$	2.85363	0.420745
$47$	−9.95715	−1.45240	−0.726200	−	0.687483i	$-0.758715\pi$
$47$	−9.95715	−1.45240	−0.726200	+	0.687483i	$0.758715\pi$
$48$	1.14637	0.165464
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−0.335577	−0.0469901
$52$	4.68585	0.649810
$53$	5.43910	0.747117	0.373559	−	0.927607i	$-0.378137\pi$
$53$	5.43910	0.747117	0.373559	+	0.927607i	$0.378137\pi$
$54$	−5.37169	−0.730995
$55$	1.00000	0.134840
$56$	−1.00000	−0.133631
$57$	7.47208	0.989701
$58$	−1.43910	−0.188963
$59$	−9.37169	−1.22009	−0.610045	−	0.792367i	$-0.708849\pi$
$59$	−9.37169	−1.22009	−0.610045	+	0.792367i	$0.708849\pi$
$60$	1.14637	0.147995
$61$	−11.9572	−1.53096	−0.765478	−	0.643462i	$-0.777498\pi$
$61$	−11.9572	−1.53096	−0.765478	+	0.643462i	$0.777498\pi$
$62$	0.978577	0.124279
$63$	1.68585	0.212397
$64$	1.00000	0.125000
$65$	4.68585	0.581208
$66$	1.14637	0.141108
$67$	−0.585462	−0.0715256	−0.0357628	−	0.999360i	$-0.511386\pi$
$67$	−0.585462	−0.0715256	−0.0357628	+	0.999360i	$0.511386\pi$
$68$	−0.292731	−0.0354988
$69$	3.27131	0.393819
$70$	−1.00000	−0.119523
$71$	−0.335577	−0.0398256	−0.0199128	−	0.999802i	$-0.506339\pi$
$71$	−0.335577	−0.0398256	−0.0199128	+	0.999802i	$0.506339\pi$
$72$	−1.68585	−0.198679
$73$	−3.70727	−0.433903	−0.216952	−	0.976182i	$-0.569611\pi$
$73$	−3.70727	−0.433903	−0.216952	+	0.976182i	$0.569611\pi$
$74$	0.853635	0.0992330
$75$	1.14637	0.132371
$76$	6.51806	0.747673
$77$	−1.00000	−0.113961
$78$	5.37169	0.608224
$79$	−2.51806	−0.283304	−0.141652	−	0.989917i	$-0.545241\pi$
$79$	−2.51806	−0.283304	−0.141652	+	0.989917i	$0.545241\pi$
$80$	1.00000	0.111803
$81$	−1.10038	−0.122265
$82$	−6.22533	−0.687472
$83$	−1.70727	−0.187397	−0.0936986	−	0.995601i	$-0.529869\pi$
$83$	−1.70727	−0.187397	−0.0936986	+	0.995601i	$0.529869\pi$
$84$	−1.14637	−0.125079
$85$	−0.292731	−0.0317511
$86$	−10.3503	−1.11610
$87$	−1.64973	−0.176870
$88$	1.00000	0.106600
$89$	13.0790	1.38637	0.693184	−	0.720761i	$-0.256208\pi$
$89$	13.0790	1.38637	0.693184	+	0.720761i	$0.256208\pi$
$90$	−1.68585	−0.177704
$91$	−4.68585	−0.491210
$92$	2.85363	0.297512
$93$	1.12181	0.116326
$94$	−9.95715	−1.02700
$95$	6.51806	0.668739
$96$	1.14637	0.117000
$97$	9.10352	0.924322	0.462161	−	0.886796i	$-0.347074\pi$
$97$	9.10352	0.924322	0.462161	+	0.886796i	$0.347074\pi$
$98$	1.00000	0.101015
$99$	−1.68585	−0.169434
$100$	1.00000	0.100000
$101$	−10.7862	−1.07327	−0.536635	−	0.843814i	$-0.680305\pi$
$101$	−10.7862	−1.07327	−0.536635	+	0.843814i	$0.680305\pi$
$102$	−0.335577	−0.0332270
$103$	7.66442	0.755198	0.377599	−	0.925969i	$-0.376750\pi$
$103$	7.66442	0.755198	0.377599	+	0.925969i	$0.376750\pi$
$104$	4.68585	0.459485
$105$	−1.14637	−0.111874
$106$	5.43910	0.528292
$107$	9.56404	0.924591	0.462295	−	0.886726i	$-0.347026\pi$
$107$	9.56404	0.924591	0.462295	+	0.886726i	$0.347026\pi$
$108$	−5.37169	−0.516891
$109$	3.14637	0.301367	0.150684	−	0.988582i	$-0.451853\pi$
$109$	3.14637	0.301367	0.150684	+	0.988582i	$0.451853\pi$
$110$	1.00000	0.0953463
$111$	0.978577	0.0928824
$112$	−1.00000	−0.0944911
$113$	−2.58546	−0.243220	−0.121610	−	0.992578i	$-0.538806\pi$
$113$	−2.58546	−0.243220	−0.121610	+	0.992578i	$0.538806\pi$
$114$	7.47208	0.699824
$115$	2.85363	0.266103
$116$	−1.43910	−0.133617
$117$	−7.89962	−0.730320
$118$	−9.37169	−0.862734
$119$	0.292731	0.0268346
$120$	1.14637	0.104648
$121$	1.00000	0.0909091
$122$	−11.9572	−1.08255
$123$	−7.13650	−0.643477
$124$	0.978577	0.0878788
$125$	1.00000	0.0894427
$126$	1.68585	0.150187
$127$	−13.3717	−1.18655	−0.593273	−	0.805001i	$-0.702164\pi$
$127$	−13.3717	−1.18655	−0.593273	+	0.805001i	$0.702164\pi$
$128$	1.00000	0.0883883
$129$	−11.8652	−1.04467
$130$	4.68585	0.410976
$131$	−11.4391	−0.999438	−0.499719	−	0.866187i	$-0.666563\pi$
$131$	−11.4391	−0.999438	−0.499719	+	0.866187i	$0.666563\pi$
$132$	1.14637	0.0997783
$133$	−6.51806	−0.565187
$134$	−0.585462	−0.0505762
$135$	−5.37169	−0.462322
$136$	−0.292731	−0.0251015
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	3.27131	0.278472
$139$	−14.1825	−1.20294	−0.601471	−	0.798895i	$-0.705419\pi$
$139$	−14.1825	−1.20294	−0.601471	+	0.798895i	$0.705419\pi$
$140$	−1.00000	−0.0845154
$141$	−11.4145	−0.961278
$142$	−0.335577	−0.0281610
$143$	4.68585	0.391850
$144$	−1.68585	−0.140487
$145$	−1.43910	−0.119510
$146$	−3.70727	−0.306816
$147$	1.14637	0.0945506
$148$	0.853635	0.0701683
$149$	11.5970	0.950065	0.475032	−	0.879968i	$-0.342436\pi$
$149$	11.5970	0.950065	0.475032	+	0.879968i	$0.342436\pi$
$150$	1.14637	0.0936004
$151$	1.73183	0.140934	0.0704671	−	0.997514i	$-0.477551\pi$
$151$	1.73183	0.140934	0.0704671	+	0.997514i	$0.477551\pi$
$152$	6.51806	0.528684
$153$	0.493499	0.0398971
$154$	−1.00000	−0.0805823
$155$	0.978577	0.0786012
$156$	5.37169	0.430080
$157$	−12.2927	−0.981067	−0.490533	−	0.871422i	$-0.663198\pi$
$157$	−12.2927	−0.981067	−0.490533	+	0.871422i	$0.663198\pi$
$158$	−2.51806	−0.200326
$159$	6.23519	0.494483
$160$	1.00000	0.0790569
$161$	−2.85363	−0.224898
$162$	−1.10038	−0.0864543
$163$	23.9143	1.87311	0.936557	−	0.350516i	$-0.113994\pi$
$163$	23.9143	1.87311	0.936557	+	0.350516i	$0.113994\pi$
$164$	−6.22533	−0.486116
$165$	1.14637	0.0892444
$166$	−1.70727	−0.132510
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	−1.14637	−0.0884440
$169$	8.95715	0.689012
$170$	−0.292731	−0.0224514
$171$	−10.9884	−0.840307
$172$	−10.3503	−0.789201
$173$	−7.37169	−0.560459	−0.280230	−	0.959933i	$-0.590411\pi$
$173$	−7.37169	−0.560459	−0.280230	+	0.959933i	$0.590411\pi$
$174$	−1.64973	−0.125066
$175$	−1.00000	−0.0755929
$176$	1.00000	0.0753778
$177$	−10.7434	−0.807522
$178$	13.0790	0.980310
$179$	1.56404	0.116902	0.0584509	−	0.998290i	$-0.481384\pi$
$179$	1.56404	0.116902	0.0584509	+	0.998290i	$0.481384\pi$
$180$	−1.68585	−0.125656
$181$	14.7862	1.09905	0.549526	−	0.835477i	$-0.314808\pi$
$181$	14.7862	1.09905	0.549526	+	0.835477i	$0.314808\pi$
$182$	−4.68585	−0.347338
$183$	−13.7073	−1.01327
$184$	2.85363	0.210373
$185$	0.853635	0.0627605
$186$	1.12181	0.0822549
$187$	−0.292731	−0.0214066
$188$	−9.95715	−0.726200
$189$	5.37169	0.390733
$190$	6.51806	0.472870
$191$	−17.9572	−1.29933	−0.649667	−	0.760219i	$-0.725092\pi$
$191$	−17.9572	−1.29933	−0.649667	+	0.760219i	$0.725092\pi$
$192$	1.14637	0.0827318
$193$	18.6430	1.34195	0.670976	−	0.741479i	$-0.265875\pi$
$193$	18.6430	1.34195	0.670976	+	0.741479i	$0.265875\pi$
$194$	9.10352	0.653595
$195$	5.37169	0.384675
$196$	1.00000	0.0714286
$197$	−15.0361	−1.07128	−0.535639	−	0.844447i	$-0.679929\pi$
$197$	−15.0361	−1.07128	−0.535639	+	0.844447i	$0.679929\pi$
$198$	−1.68585	−0.119808
$199$	15.3288	1.08663	0.543317	−	0.839528i	$-0.317168\pi$
$199$	15.3288	1.08663	0.543317	+	0.839528i	$0.317168\pi$
$200$	1.00000	0.0707107
$201$	−0.671153	−0.0473395
$202$	−10.7862	−0.758917
$203$	1.43910	0.101005
$204$	−0.335577	−0.0234951
$205$	−6.22533	−0.434796
$206$	7.66442	0.534006
$207$	−4.81079	−0.334373
$208$	4.68585	0.324905
$209$	6.51806	0.450863
$210$	−1.14637	−0.0791067
$211$	2.04285	0.140635	0.0703176	−	0.997525i	$-0.477599\pi$
$211$	2.04285	0.140635	0.0703176	+	0.997525i	$0.477599\pi$
$212$	5.43910	0.373559
$213$	−0.384694	−0.0263588
$214$	9.56404	0.653784
$215$	−10.3503	−0.705883
$216$	−5.37169	−0.365497
$217$	−0.978577	−0.0664301
$218$	3.14637	0.213099
$219$	−4.24989	−0.287181
$220$	1.00000	0.0674200
$221$	−1.37169	−0.0922700
$222$	0.978577	0.0656778
$223$	11.0790	0.741902	0.370951	−	0.928652i	$-0.379032\pi$
$223$	11.0790	0.741902	0.370951	+	0.928652i	$0.379032\pi$
$224$	−1.00000	−0.0668153
$225$	−1.68585	−0.112390
$226$	−2.58546	−0.171982
$227$	−18.5426	−1.23072	−0.615358	−	0.788248i	$-0.710989\pi$
$227$	−18.5426	−1.23072	−0.615358	+	0.788248i	$0.710989\pi$
$228$	7.47208	0.494850
$229$	−8.01469	−0.529626	−0.264813	−	0.964300i	$-0.585310\pi$
$229$	−8.01469	−0.529626	−0.264813	+	0.964300i	$0.585310\pi$
$230$	2.85363	0.188163
$231$	−1.14637	−0.0754253
$232$	−1.43910	−0.0944813
$233$	27.9572	1.83153	0.915767	−	0.401710i	$-0.131584\pi$
$233$	27.9572	1.83153	0.915767	+	0.401710i	$0.131584\pi$
$234$	−7.89962	−0.516414
$235$	−9.95715	−0.649533
$236$	−9.37169	−0.610045
$237$	−2.88661	−0.187506
$238$	0.292731	0.0189749
$239$	−28.8108	−1.86362	−0.931808	−	0.362953i	$-0.881769\pi$
$239$	−28.8108	−1.86362	−0.931808	+	0.362953i	$0.881769\pi$
$240$	1.14637	0.0739976
$241$	−8.51806	−0.548696	−0.274348	−	0.961630i	$-0.588462\pi$
$241$	−8.51806	−0.548696	−0.274348	+	0.961630i	$0.588462\pi$
$242$	1.00000	0.0642824
$243$	14.8536	0.952861
$244$	−11.9572	−0.765478
$245$	1.00000	0.0638877
$246$	−7.13650	−0.455007
$247$	30.5426	1.94338
$248$	0.978577	0.0621397
$249$	−1.95715	−0.124030
$250$	1.00000	0.0632456
$251$	−23.1281	−1.45983	−0.729916	−	0.683537i	$-0.760441\pi$
$251$	−23.1281	−1.45983	−0.729916	+	0.683537i	$0.760441\pi$
$252$	1.68585	0.106198
$253$	2.85363	0.179406
$254$	−13.3717	−0.839015
$255$	−0.335577	−0.0210146
$256$	1.00000	0.0625000
$257$	14.8108	0.923872	0.461936	−	0.886913i	$-0.347155\pi$
$257$	14.8108	0.923872	0.461936	+	0.886913i	$0.347155\pi$
$258$	−11.8652	−0.738695
$259$	−0.853635	−0.0530423
$260$	4.68585	0.290604
$261$	2.42610	0.150172
$262$	−11.4391	−0.706710
$263$	18.7434	1.15577	0.577883	−	0.816119i	$-0.303879\pi$
$263$	18.7434	1.15577	0.577883	+	0.816119i	$0.303879\pi$
$264$	1.14637	0.0705539
$265$	5.43910	0.334121
$266$	−6.51806	−0.399648
$267$	14.9933	0.917573
$268$	−0.585462	−0.0357628
$269$	12.6858	0.773470	0.386735	−	0.922191i	$-0.373603\pi$
$269$	12.6858	0.773470	0.386735	+	0.922191i	$0.373603\pi$
$270$	−5.37169	−0.326911
$271$	1.12181	0.0681449	0.0340725	−	0.999419i	$-0.489152\pi$
$271$	1.12181	0.0681449	0.0340725	+	0.999419i	$0.489152\pi$
$272$	−0.292731	−0.0177494
$273$	−5.37169	−0.325110
$274$	10.0000	0.604122
$275$	1.00000	0.0603023
$276$	3.27131	0.196910
$277$	30.1151	1.80944	0.904720	−	0.426007i	$-0.140080\pi$
$277$	30.1151	1.80944	0.904720	+	0.426007i	$0.140080\pi$
$278$	−14.1825	−0.850609
$279$	−1.64973	−0.0987668
$280$	−1.00000	−0.0597614
$281$	−14.3356	−0.855189	−0.427594	−	0.903971i	$-0.640639\pi$
$281$	−14.3356	−0.855189	−0.427594	+	0.903971i	$0.640639\pi$
$282$	−11.4145	−0.679726
$283$	3.21377	0.191039	0.0955194	−	0.995428i	$-0.469549\pi$
$283$	3.21377	0.191039	0.0955194	+	0.995428i	$0.469549\pi$
$284$	−0.335577	−0.0199128
$285$	7.47208	0.442608
$286$	4.68585	0.277080
$287$	6.22533	0.367469
$288$	−1.68585	−0.0993394
$289$	−16.9143	−0.994959
$290$	−1.43910	−0.0845067
$291$	10.4360	0.611767
$292$	−3.70727	−0.216952
$293$	−16.6858	−0.974798	−0.487399	−	0.873179i	$-0.662054\pi$
$293$	−16.6858	−0.974798	−0.487399	+	0.873179i	$0.662054\pi$
$294$	1.14637	0.0668574
$295$	−9.37169	−0.545641
$296$	0.853635	0.0496165
$297$	−5.37169	−0.311697
$298$	11.5970	0.671797
$299$	13.3717	0.773305
$300$	1.14637	0.0661854
$301$	10.3503	0.596580
$302$	1.73183	0.0996555
$303$	−12.3650	−0.710349
$304$	6.51806	0.373836
$305$	−11.9572	−0.684665
$306$	0.493499	0.0282115
$307$	−6.29273	−0.359145	−0.179573	−	0.983745i	$-0.557471\pi$
$307$	−6.29273	−0.359145	−0.179573	+	0.983745i	$0.557471\pi$
$308$	−1.00000	−0.0569803
$309$	8.78623	0.499831
$310$	0.978577	0.0555794
$311$	−20.3931	−1.15639	−0.578194	−	0.815900i	$-0.696242\pi$
$311$	−20.3931	−1.15639	−0.578194	+	0.815900i	$0.696242\pi$
$312$	5.37169	0.304112
$313$	12.0674	0.682090	0.341045	−	0.940047i	$-0.389219\pi$
$313$	12.0674	0.682090	0.341045	+	0.940047i	$0.389219\pi$
$314$	−12.2927	−0.693719
$315$	1.68585	0.0949867
$316$	−2.51806	−0.141652
$317$	28.7679	1.61577	0.807884	−	0.589341i	$-0.200613\pi$
$317$	28.7679	1.61577	0.807884	+	0.589341i	$0.200613\pi$
$318$	6.23519	0.349652
$319$	−1.43910	−0.0805739
$320$	1.00000	0.0559017
$321$	10.9639	0.611944
$322$	−2.85363	−0.159027
$323$	−1.90804	−0.106166
$324$	−1.10038	−0.0611325
$325$	4.68585	0.259924
$326$	23.9143	1.32449
$327$	3.60688	0.199461
$328$	−6.22533	−0.343736
$329$	9.95715	0.548956
$330$	1.14637	0.0631053
$331$	−3.80765	−0.209288	−0.104644	−	0.994510i	$-0.533370\pi$
$331$	−3.80765	−0.209288	−0.104644	+	0.994510i	$0.533370\pi$
$332$	−1.70727	−0.0936986
$333$	−1.43910	−0.0788620
$334$	−8.00000	−0.437741
$335$	−0.585462	−0.0319872
$336$	−1.14637	−0.0625394
$337$	15.3717	0.837349	0.418675	−	0.908136i	$-0.362495\pi$
$337$	15.3717	0.837349	0.418675	+	0.908136i	$0.362495\pi$
$338$	8.95715	0.487205
$339$	−2.96388	−0.160976
$340$	−0.292731	−0.0158756
$341$	0.978577	0.0529929
$342$	−10.9884	−0.594187
$343$	−1.00000	−0.0539949
$344$	−10.3503	−0.558049
$345$	3.27131	0.176121
$346$	−7.37169	−0.396305
$347$	3.02142	0.162198	0.0810992	−	0.996706i	$-0.474157\pi$
$347$	3.02142	0.162198	0.0810992	+	0.996706i	$0.474157\pi$
$348$	−1.64973	−0.0884348
$349$	11.0361	0.590750	0.295375	−	0.955381i	$-0.404555\pi$
$349$	11.0361	0.590750	0.295375	+	0.955381i	$0.404555\pi$
$350$	−1.00000	−0.0534522
$351$	−25.1709	−1.34352
$352$	1.00000	0.0533002
$353$	23.9817	1.27642	0.638209	−	0.769863i	$-0.279676\pi$
$353$	23.9817	1.27642	0.638209	+	0.769863i	$0.279676\pi$
$354$	−10.7434	−0.571004
$355$	−0.335577	−0.0178106
$356$	13.0790	0.693184
$357$	0.335577	0.0177606
$358$	1.56404	0.0826620
$359$	−10.5181	−0.555122	−0.277561	−	0.960708i	$-0.589526\pi$
$359$	−10.5181	−0.555122	−0.277561	+	0.960708i	$0.589526\pi$
$360$	−1.68585	−0.0888519
$361$	23.4851	1.23606
$362$	14.7862	0.777147
$363$	1.14637	0.0601686
$364$	−4.68585	−0.245605
$365$	−3.70727	−0.194047
$366$	−13.7073	−0.716490
$367$	−35.5787	−1.85719	−0.928597	−	0.371089i	$-0.878985\pi$
$367$	−35.5787	−1.85719	−0.928597	+	0.371089i	$0.878985\pi$
$368$	2.85363	0.148756
$369$	10.4949	0.546345
$370$	0.853635	0.0443783
$371$	−5.43910	−0.282384
$372$	1.12181	0.0581630
$373$	7.50650	0.388672	0.194336	−	0.980935i	$-0.437745\pi$
$373$	7.50650	0.388672	0.194336	+	0.980935i	$0.437745\pi$
$374$	−0.292731	−0.0151368
$375$	1.14637	0.0591981
$376$	−9.95715	−0.513501
$377$	−6.74338	−0.347302
$378$	5.37169	0.276290
$379$	33.4868	1.72010	0.860050	−	0.510210i	$-0.170432\pi$
$379$	33.4868	1.72010	0.860050	+	0.510210i	$0.170432\pi$
$380$	6.51806	0.334369
$381$	−15.3288	−0.785321
$382$	−17.9572	−0.918768
$383$	15.6644	0.800415	0.400207	−	0.916425i	$-0.368938\pi$
$383$	15.6644	0.800415	0.400207	+	0.916425i	$0.368938\pi$
$384$	1.14637	0.0585002
$385$	−1.00000	−0.0509647
$386$	18.6430	0.948904
$387$	17.4490	0.886981
$388$	9.10352	0.462161
$389$	−19.6216	−0.994853	−0.497427	−	0.867506i	$-0.665722\pi$
$389$	−19.6216	−0.994853	−0.497427	+	0.867506i	$0.665722\pi$
$390$	5.37169	0.272006
$391$	−0.835347	−0.0422453
$392$	1.00000	0.0505076
$393$	−13.1134	−0.661483
$394$	−15.0361	−0.757509
$395$	−2.51806	−0.126697
$396$	−1.68585	−0.0847170
$397$	10.2499	0.514427	0.257213	−	0.966355i	$-0.417196\pi$
$397$	10.2499	0.514427	0.257213	+	0.966355i	$0.417196\pi$
$398$	15.3288	0.768366
$399$	−7.47208	−0.374072
$400$	1.00000	0.0500000
$401$	−16.8866	−0.843277	−0.421639	−	0.906764i	$-0.638545\pi$
$401$	−16.8866	−0.843277	−0.421639	+	0.906764i	$0.638545\pi$
$402$	−0.671153	−0.0334741
$403$	4.58546	0.228418
$404$	−10.7862	−0.536635
$405$	−1.10038	−0.0546785
$406$	1.43910	0.0714212
$407$	0.853635	0.0423131
$408$	−0.335577	−0.0166135
$409$	18.2744	0.903613	0.451807	−	0.892116i	$-0.350780\pi$
$409$	18.2744	0.903613	0.451807	+	0.892116i	$0.350780\pi$
$410$	−6.22533	−0.307447
$411$	11.4637	0.565460
$412$	7.66442	0.377599
$413$	9.37169	0.461151
$414$	−4.81079	−0.236437
$415$	−1.70727	−0.0838065
$416$	4.68585	0.229743
$417$	−16.2583	−0.796173
$418$	6.51806	0.318809
$419$	−37.2860	−1.82154	−0.910770	−	0.412914i	$-0.864511\pi$
$419$	−37.2860	−1.82154	−0.910770	+	0.412914i	$0.864511\pi$
$420$	−1.14637	−0.0559369
$421$	−2.78623	−0.135793	−0.0678963	−	0.997692i	$-0.521629\pi$
$421$	−2.78623	−0.135793	−0.0678963	+	0.997692i	$0.521629\pi$
$422$	2.04285	0.0994442
$423$	16.7862	0.816174
$424$	5.43910	0.264146
$425$	−0.292731	−0.0141995
$426$	−0.384694	−0.0186385
$427$	11.9572	0.578647
$428$	9.56404	0.462295
$429$	5.37169	0.259348
$430$	−10.3503	−0.499134
$431$	38.0477	1.83269	0.916346	−	0.400387i	$-0.131124\pi$
$431$	38.0477	1.83269	0.916346	+	0.400387i	$0.131124\pi$
$432$	−5.37169	−0.258446
$433$	−10.8108	−0.519533	−0.259767	−	0.965671i	$-0.583646\pi$
$433$	−10.8108	−0.519533	−0.259767	+	0.965671i	$0.583646\pi$
$434$	−0.978577	−0.0469732
$435$	−1.64973	−0.0790985
$436$	3.14637	0.150684
$437$	18.6002	0.889766
$438$	−4.24989	−0.203067
$439$	30.9933	1.47923	0.739614	−	0.673031i	$-0.235008\pi$
$439$	30.9933	1.47923	0.739614	+	0.673031i	$0.235008\pi$
$440$	1.00000	0.0476731
$441$	−1.68585	−0.0802784
$442$	−1.37169	−0.0652448
$443$	25.3717	1.20545	0.602723	−	0.797951i	$-0.294083\pi$
$443$	25.3717	1.20545	0.602723	+	0.797951i	$0.294083\pi$
$444$	0.978577	0.0464412
$445$	13.0790	0.620002
$446$	11.0790	0.524604
$447$	13.2944	0.628805
$448$	−1.00000	−0.0472456
$449$	−0.886615	−0.0418419	−0.0209210	−	0.999781i	$-0.506660\pi$
$449$	−0.886615	−0.0418419	−0.0209210	+	0.999781i	$0.506660\pi$
$450$	−1.68585	−0.0794716
$451$	−6.22533	−0.293139
$452$	−2.58546	−0.121610
$453$	1.98531	0.0932779
$454$	−18.5426	−0.870248
$455$	−4.68585	−0.219676
$456$	7.47208	0.349912
$457$	29.9143	1.39933	0.699666	−	0.714470i	$-0.253332\pi$
$457$	29.9143	1.39933	0.699666	+	0.714470i	$0.253332\pi$
$458$	−8.01469	−0.374502
$459$	1.57246	0.0733962
$460$	2.85363	0.133051
$461$	−2.33558	−0.108779	−0.0543893	−	0.998520i	$-0.517321\pi$
$461$	−2.33558	−0.108779	−0.0543893	+	0.998520i	$0.517321\pi$
$462$	−1.14637	−0.0533337
$463$	0.110250	0.00512374	0.00256187	−	0.999997i	$-0.499185\pi$
$463$	0.110250	0.00512374	0.00256187	+	0.999997i	$0.499185\pi$
$464$	−1.43910	−0.0668084
$465$	1.12181	0.0520226
$466$	27.9572	1.29509
$467$	36.6760	1.69716	0.848581	−	0.529066i	$-0.177457\pi$
$467$	36.6760	1.69716	0.848581	+	0.529066i	$0.177457\pi$
$468$	−7.89962	−0.365160
$469$	0.585462	0.0270341
$470$	−9.95715	−0.459289
$471$	−14.0920	−0.649323
$472$	−9.37169	−0.431367
$473$	−10.3503	−0.475906
$474$	−2.88661	−0.132587
$475$	6.51806	0.299069
$476$	0.292731	0.0134173
$477$	−9.16948	−0.419842
$478$	−28.8108	−1.31777
$479$	−42.7434	−1.95300	−0.976498	−	0.215529i	$-0.930853\pi$
$479$	−42.7434	−1.95300	−0.976498	+	0.215529i	$0.930853\pi$
$480$	1.14637	0.0523242
$481$	4.00000	0.182384
$482$	−8.51806	−0.387987
$483$	−3.27131	−0.148850
$484$	1.00000	0.0454545
$485$	9.10352	0.413370
$486$	14.8536	0.673775
$487$	−36.1396	−1.63764	−0.818822	−	0.574048i	$-0.805372\pi$
$487$	−36.1396	−1.63764	−0.818822	+	0.574048i	$0.805372\pi$
$488$	−11.9572	−0.541275
$489$	27.4145	1.23973
$490$	1.00000	0.0451754
$491$	2.54262	0.114747	0.0573733	−	0.998353i	$-0.481727\pi$
$491$	2.54262	0.114747	0.0573733	+	0.998353i	$0.481727\pi$
$492$	−7.13650	−0.321738
$493$	0.421268	0.0189730
$494$	30.5426	1.37418
$495$	−1.68585	−0.0757732
$496$	0.978577	0.0439394
$497$	0.335577	0.0150527
$498$	−1.95715	−0.0877022
$499$	3.13650	0.140409	0.0702045	−	0.997533i	$-0.477635\pi$
$499$	3.13650	0.140409	0.0702045	+	0.997533i	$0.477635\pi$
$500$	1.00000	0.0447214
$501$	−9.17092	−0.409727
$502$	−23.1281	−1.03226
$503$	−28.5855	−1.27456	−0.637281	−	0.770631i	$-0.719941\pi$
$503$	−28.5855	−1.27456	−0.637281	+	0.770631i	$0.719941\pi$
$504$	1.68585	0.0750936
$505$	−10.7862	−0.479981
$506$	2.85363	0.126860
$507$	10.2682	0.456026
$508$	−13.3717	−0.593273
$509$	2.20077	0.0975473	0.0487737	−	0.998810i	$-0.484469\pi$
$509$	2.20077	0.0975473	0.0487737	+	0.998810i	$0.484469\pi$
$510$	−0.335577	−0.0148596
$511$	3.70727	0.164000
$512$	1.00000	0.0441942
$513$	−35.0130	−1.54586
$514$	14.8108	0.653276
$515$	7.66442	0.337735
$516$	−11.8652	−0.522336
$517$	−9.95715	−0.437915
$518$	−0.853635	−0.0375065
$519$	−8.45065	−0.370943
$520$	4.68585	0.205488
$521$	37.1940	1.62950	0.814750	−	0.579812i	$-0.196874\pi$
$521$	37.1940	1.62950	0.814750	+	0.579812i	$0.196874\pi$
$522$	2.42610	0.106187
$523$	30.4078	1.32964	0.664820	−	0.747003i	$-0.268508\pi$
$523$	30.4078	1.32964	0.664820	+	0.747003i	$0.268508\pi$
$524$	−11.4391	−0.499719
$525$	−1.14637	−0.0500315
$526$	18.7434	0.817250
$527$	−0.286460	−0.0124784
$528$	1.14637	0.0498892
$529$	−14.8568	−0.645947
$530$	5.43910	0.236259
$531$	15.7992	0.685628
$532$	−6.51806	−0.282594
$533$	−29.1709	−1.26353
$534$	14.9933	0.648822
$535$	9.56404	0.413489
$536$	−0.585462	−0.0252881
$537$	1.79296	0.0773720
$538$	12.6858	0.546926
$539$	1.00000	0.0430730
$540$	−5.37169	−0.231161
$541$	39.0607	1.67935	0.839675	−	0.543090i	$-0.182746\pi$
$541$	39.0607	1.67935	0.839675	+	0.543090i	$0.182746\pi$
$542$	1.12181	0.0481857
$543$	16.9504	0.727412
$544$	−0.292731	−0.0125507
$545$	3.14637	0.134775
$546$	−5.37169	−0.229887
$547$	−0.585462	−0.0250325	−0.0125163	−	0.999922i	$-0.503984\pi$
$547$	−0.585462	−0.0250325	−0.0125163	+	0.999922i	$0.503984\pi$
$548$	10.0000	0.427179
$549$	20.1579	0.860319
$550$	1.00000	0.0426401
$551$	−9.38011	−0.399606
$552$	3.27131	0.139236
$553$	2.51806	0.107079
$554$	30.1151	1.27947
$555$	0.978577	0.0415383
$556$	−14.1825	−0.601471
$557$	17.4637	0.739959	0.369979	−	0.929040i	$-0.379365\pi$
$557$	17.4637	0.739959	0.369979	+	0.929040i	$0.379365\pi$
$558$	−1.64973	−0.0698387
$559$	−48.4998	−2.05132
$560$	−1.00000	−0.0422577
$561$	−0.335577	−0.0141681
$562$	−14.3356	−0.604710
$563$	−18.1579	−0.765265	−0.382633	−	0.923901i	$-0.624982\pi$
$563$	−18.1579	−0.765265	−0.382633	+	0.923901i	$0.624982\pi$
$564$	−11.4145	−0.480639
$565$	−2.58546	−0.108771
$566$	3.21377	0.135085
$567$	1.10038	0.0462118
$568$	−0.335577	−0.0140805
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	7.47208	0.312971
$571$	−9.03612	−0.378150	−0.189075	−	0.981963i	$-0.560549\pi$
$571$	−9.03612	−0.378150	−0.189075	+	0.981963i	$0.560549\pi$
$572$	4.68585	0.195925
$573$	−20.5855	−0.859970
$574$	6.22533	0.259840
$575$	2.85363	0.119005
$576$	−1.68585	−0.0702436
$577$	19.3963	0.807476	0.403738	−	0.914875i	$-0.367711\pi$
$577$	19.3963	0.807476	0.403738	+	0.914875i	$0.367711\pi$
$578$	−16.9143	−0.703542
$579$	21.3717	0.888177
$580$	−1.43910	−0.0597552
$581$	1.70727	0.0708295
$582$	10.4360	0.432584
$583$	5.43910	0.225264
$584$	−3.70727	−0.153408
$585$	−7.89962	−0.326609
$586$	−16.6858	−0.689286
$587$	17.2614	0.712456	0.356228	−	0.934399i	$-0.384063\pi$
$587$	17.2614	0.712456	0.356228	+	0.934399i	$0.384063\pi$
$588$	1.14637	0.0472753
$589$	6.37842	0.262818
$590$	−9.37169	−0.385826
$591$	−17.2369	−0.709031
$592$	0.853635	0.0350842
$593$	−11.0361	−0.453199	−0.226599	−	0.973988i	$-0.572761\pi$
$593$	−11.0361	−0.453199	−0.226599	+	0.973988i	$0.572761\pi$
$594$	−5.37169	−0.220403
$595$	0.292731	0.0120008
$596$	11.5970	0.475032
$597$	17.5725	0.719193
$598$	13.3717	0.546809
$599$	−41.7367	−1.70531	−0.852657	−	0.522472i	$-0.825010\pi$
$599$	−41.7367	−1.70531	−0.852657	+	0.522472i	$0.825010\pi$
$600$	1.14637	0.0468002
$601$	39.3106	1.60351	0.801756	−	0.597652i	$-0.203900\pi$
$601$	39.3106	1.60351	0.801756	+	0.597652i	$0.203900\pi$
$602$	10.3503	0.421845
$603$	0.986999	0.0401937
$604$	1.73183	0.0704671
$605$	1.00000	0.0406558
$606$	−12.3650	−0.502292
$607$	−6.35027	−0.257749	−0.128875	−	0.991661i	$-0.541137\pi$
$607$	−6.35027	−0.257749	−0.128875	+	0.991661i	$0.541137\pi$
$608$	6.51806	0.264342
$609$	1.64973	0.0668505
$610$	−11.9572	−0.484131
$611$	−46.6577	−1.88757
$612$	0.493499	0.0199485
$613$	−42.4507	−1.71457	−0.857283	−	0.514846i	$-0.827849\pi$
$613$	−42.4507	−1.71457	−0.857283	+	0.514846i	$0.827849\pi$
$614$	−6.29273	−0.253954
$615$	−7.13650	−0.287771
$616$	−1.00000	−0.0402911
$617$	−0.677425	−0.0272721	−0.0136360	−	0.999907i	$-0.504341\pi$
$617$	−0.677425	−0.0272721	−0.0136360	+	0.999907i	$0.504341\pi$
$618$	8.78623	0.353434
$619$	−18.5426	−0.745291	−0.372645	−	0.927974i	$-0.621549\pi$
$619$	−18.5426	−0.745291	−0.372645	+	0.927974i	$0.621549\pi$
$620$	0.978577	0.0393006
$621$	−15.3288	−0.615125
$622$	−20.3931	−0.817689
$623$	−13.0790	−0.523998
$624$	5.37169	0.215040
$625$	1.00000	0.0400000
$626$	12.0674	0.482310
$627$	7.47208	0.298406
$628$	−12.2927	−0.490533
$629$	−0.249885	−0.00996358
$630$	1.68585	0.0671657
$631$	21.3717	0.850794	0.425397	−	0.905007i	$-0.360135\pi$
$631$	21.3717	0.850794	0.425397	+	0.905007i	$0.360135\pi$
$632$	−2.51806	−0.100163
$633$	2.34185	0.0930801
$634$	28.7679	1.14252
$635$	−13.3717	−0.530639
$636$	6.23519	0.247241
$637$	4.68585	0.185660
$638$	−1.43910	−0.0569744
$639$	0.565731	0.0223800
$640$	1.00000	0.0395285
$641$	23.8715	0.942866	0.471433	−	0.881902i	$-0.343737\pi$
$641$	23.8715	0.942866	0.471433	+	0.881902i	$0.343737\pi$
$642$	10.9639	0.432710
$643$	0.311018	0.0122654	0.00613268	−	0.999981i	$-0.498048\pi$
$643$	0.311018	0.0122654	0.00613268	+	0.999981i	$0.498048\pi$
$644$	−2.85363	−0.112449
$645$	−11.8652	−0.467191
$646$	−1.90804	−0.0750707
$647$	−9.62158	−0.378263	−0.189132	−	0.981952i	$-0.560567\pi$
$647$	−9.62158	−0.378263	−0.189132	+	0.981952i	$0.560567\pi$
$648$	−1.10038	−0.0432272
$649$	−9.37169	−0.367871
$650$	4.68585	0.183794
$651$	−1.12181	−0.0439671
$652$	23.9143	0.936557
$653$	−27.0607	−1.05897	−0.529483	−	0.848321i	$-0.677614\pi$
$653$	−27.0607	−1.05897	−0.529483	+	0.848321i	$0.677614\pi$
$654$	3.60688	0.141040
$655$	−11.4391	−0.446962
$656$	−6.22533	−0.243058
$657$	6.24989	0.243831
$658$	9.95715	0.388170
$659$	−26.4935	−1.03204	−0.516020	−	0.856576i	$-0.672587\pi$
$659$	−26.4935	−1.03204	−0.516020	+	0.856576i	$0.672587\pi$
$660$	1.14637	0.0446222
$661$	35.0852	1.36466	0.682329	−	0.731046i	$-0.260967\pi$
$661$	35.0852	1.36466	0.682329	+	0.731046i	$0.260967\pi$
$662$	−3.80765	−0.147989
$663$	−1.57246	−0.0610693
$664$	−1.70727	−0.0662549
$665$	−6.51806	−0.252759
$666$	−1.43910	−0.0557639
$667$	−4.10666	−0.159010
$668$	−8.00000	−0.309529
$669$	12.7005	0.491031
$670$	−0.585462	−0.0226184
$671$	−11.9572	−0.461601
$672$	−1.14637	−0.0442220
$673$	32.6577	1.25886	0.629431	−	0.777057i	$-0.283288\pi$
$673$	32.6577	1.25886	0.629431	+	0.777057i	$0.283288\pi$
$674$	15.3717	0.592095
$675$	−5.37169	−0.206757
$676$	8.95715	0.344506
$677$	9.12808	0.350821	0.175410	−	0.984495i	$-0.443875\pi$
$677$	9.12808	0.350821	0.175410	+	0.984495i	$0.443875\pi$
$678$	−2.96388	−0.113827
$679$	−9.10352	−0.349361
$680$	−0.292731	−0.0112257
$681$	−21.2566	−0.814555
$682$	0.978577	0.0374717
$683$	10.4935	0.401523	0.200761	−	0.979640i	$-0.435658\pi$
$683$	10.4935	0.401523	0.200761	+	0.979640i	$0.435658\pi$
$684$	−10.9884	−0.420154
$685$	10.0000	0.382080
$686$	−1.00000	−0.0381802
$687$	−9.18777	−0.350535
$688$	−10.3503	−0.394600
$689$	25.4868	0.970969
$690$	3.27131	0.124537
$691$	1.70727	0.0649476	0.0324738	−	0.999473i	$-0.489661\pi$
$691$	1.70727	0.0649476	0.0324738	+	0.999473i	$0.489661\pi$
$692$	−7.37169	−0.280230
$693$	1.68585	0.0640400
$694$	3.02142	0.114692
$695$	−14.1825	−0.537972
$696$	−1.64973	−0.0625329
$697$	1.82235	0.0690263
$698$	11.0361	0.417723
$699$	32.0491	1.21221
$700$	−1.00000	−0.0377964
$701$	−37.3534	−1.41082	−0.705409	−	0.708800i	$-0.749237\pi$
$701$	−37.3534	−1.41082	−0.705409	+	0.708800i	$0.749237\pi$
$702$	−25.1709	−0.950015
$703$	5.56404	0.209852
$704$	1.00000	0.0376889
$705$	−11.4145	−0.429896
$706$	23.9817	0.902564
$707$	10.7862	0.405658
$708$	−10.7434	−0.403761
$709$	−8.20704	−0.308222	−0.154111	−	0.988054i	$-0.549251\pi$
$709$	−8.20704	−0.308222	−0.154111	+	0.988054i	$0.549251\pi$
$710$	−0.335577	−0.0125940
$711$	4.24506	0.159202
$712$	13.0790	0.490155
$713$	2.79250	0.104580
$714$	0.335577	0.0125586
$715$	4.68585	0.175241
$716$	1.56404	0.0584509
$717$	−33.0277	−1.23344
$718$	−10.5181	−0.392530
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	−1.68585	−0.0628278
$721$	−7.66442	−0.285438
$722$	23.4851	0.874024
$723$	−9.76481	−0.363157
$724$	14.7862	0.549526
$725$	−1.43910	−0.0534467
$726$	1.14637	0.0425456
$727$	−46.9442	−1.74106	−0.870531	−	0.492113i	$-0.836225\pi$
$727$	−46.9442	−1.74106	−0.870531	+	0.492113i	$0.836225\pi$
$728$	−4.68585	−0.173669
$729$	20.3288	0.752920
$730$	−3.70727	−0.137212
$731$	3.02984	0.112063
$732$	−13.7073	−0.506635
$733$	−42.0000	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$734$	−35.5787	−1.31323
$735$	1.14637	0.0422843
$736$	2.85363	0.105186
$737$	−0.585462	−0.0215658
$738$	10.4949	0.386324
$739$	−0.871922	−0.0320742	−0.0160371	−	0.999871i	$-0.505105\pi$
$739$	−0.871922	−0.0320742	−0.0160371	+	0.999871i	$0.505105\pi$
$740$	0.853635	0.0313802
$741$	35.0130	1.28623
$742$	−5.43910	−0.199676
$743$	−24.6712	−0.905097	−0.452548	−	0.891740i	$-0.649485\pi$
$743$	−24.6712	−0.905097	−0.452548	+	0.891740i	$0.649485\pi$
$744$	1.12181	0.0411274
$745$	11.5970	0.424882
$746$	7.50650	0.274833
$747$	2.87819	0.105308
$748$	−0.292731	−0.0107033
$749$	−9.56404	−0.349462
$750$	1.14637	0.0418593
$751$	−3.75011	−0.136844	−0.0684218	−	0.997656i	$-0.521796\pi$
$751$	−3.75011	−0.136844	−0.0684218	+	0.997656i	$0.521796\pi$
$752$	−9.95715	−0.363100
$753$	−26.5132	−0.966196
$754$	−6.74338	−0.245580
$755$	1.73183	0.0630277
$756$	5.37169	0.195367
$757$	15.7318	0.571783	0.285891	−	0.958262i	$-0.407710\pi$
$757$	15.7318	0.571783	0.285891	+	0.958262i	$0.407710\pi$
$758$	33.4868	1.21629
$759$	3.27131	0.118741
$760$	6.51806	0.236435
$761$	15.2614	0.553227	0.276613	−	0.960981i	$-0.410788\pi$
$761$	15.2614	0.553227	0.276613	+	0.960981i	$0.410788\pi$
$762$	−15.3288	−0.555306
$763$	−3.14637	−0.113906
$764$	−17.9572	−0.649667
$765$	0.493499	0.0178425
$766$	15.6644	0.565979
$767$	−43.9143	−1.58565
$768$	1.14637	0.0413659
$769$	−9.63986	−0.347622	−0.173811	−	0.984779i	$-0.555608\pi$
$769$	−9.63986	−0.347622	−0.173811	+	0.984779i	$0.555608\pi$
$770$	−1.00000	−0.0360375
$771$	16.9786	0.611469
$772$	18.6430	0.670976
$773$	12.8291	0.461430	0.230715	−	0.973021i	$-0.425894\pi$
$773$	12.8291	0.461430	0.230715	+	0.973021i	$0.425894\pi$
$774$	17.4490	0.627190
$775$	0.978577	0.0351515
$776$	9.10352	0.326797
$777$	−0.978577	−0.0351063
$778$	−19.6216	−0.703468
$779$	−40.5770	−1.45382
$780$	5.37169	0.192337
$781$	−0.335577	−0.0120079
$782$	−0.835347	−0.0298720
$783$	7.73038	0.276261
$784$	1.00000	0.0357143
$785$	−12.2927	−0.438746
$786$	−13.1134	−0.467739
$787$	10.8291	0.386015	0.193007	−	0.981197i	$-0.438176\pi$
$787$	10.8291	0.386015	0.193007	+	0.981197i	$0.438176\pi$
$788$	−15.0361	−0.535639
$789$	21.4868	0.764949
$790$	−2.51806	−0.0895885
$791$	2.58546	0.0919284
$792$	−1.68585	−0.0599039
$793$	−56.0294	−1.98966
$794$	10.2499	0.363755
$795$	6.23519	0.221139
$796$	15.3288	0.543317
$797$	−21.0790	−0.746655	−0.373328	−	0.927700i	$-0.621783\pi$
$797$	−21.0790	−0.746655	−0.373328	+	0.927700i	$0.621783\pi$
$798$	−7.47208	−0.264509
$799$	2.91477	0.103117
$800$	1.00000	0.0353553
$801$	−22.0491	−0.779067
$802$	−16.8866	−0.596287
$803$	−3.70727	−0.130827
$804$	−0.671153	−0.0236698
$805$	−2.85363	−0.100577
$806$	4.58546	0.161516
$807$	14.5426	0.511924
$808$	−10.7862	−0.379458
$809$	3.62158	0.127328	0.0636639	−	0.997971i	$-0.479721\pi$
$809$	3.62158	0.127328	0.0636639	+	0.997971i	$0.479721\pi$
$810$	−1.10038	−0.0386636
$811$	34.7188	1.21914	0.609571	−	0.792731i	$-0.291342\pi$
$811$	34.7188	1.21914	0.609571	+	0.792731i	$0.291342\pi$
$812$	1.43910	0.0505024
$813$	1.28600	0.0451020
$814$	0.853635	0.0299199
$815$	23.9143	0.837682
$816$	−0.335577	−0.0117475
$817$	−67.4637	−2.36025
$818$	18.2744	0.638951
$819$	7.89962	0.276035
$820$	−6.22533	−0.217398
$821$	−37.7549	−1.31766	−0.658828	−	0.752293i	$-0.728948\pi$
$821$	−37.7549	−1.31766	−0.658828	+	0.752293i	$0.728948\pi$
$822$	11.4637	0.399841
$823$	11.1892	0.390031	0.195016	−	0.980800i	$-0.437524\pi$
$823$	11.1892	0.390031	0.195016	+	0.980800i	$0.437524\pi$
$824$	7.66442	0.267003
$825$	1.14637	0.0399113
$826$	9.37169	0.326083
$827$	−7.91431	−0.275207	−0.137604	−	0.990487i	$-0.543940\pi$
$827$	−7.91431	−0.275207	−0.137604	+	0.990487i	$0.543940\pi$
$828$	−4.81079	−0.167186
$829$	−44.7152	−1.55302	−0.776512	−	0.630102i	$-0.783013\pi$
$829$	−44.7152	−1.55302	−0.776512	+	0.630102i	$0.783013\pi$
$830$	−1.70727	−0.0592602
$831$	34.5229	1.19759
$832$	4.68585	0.162452
$833$	−0.292731	−0.0101425
$834$	−16.2583	−0.562979
$835$	−8.00000	−0.276851
$836$	6.51806	0.225432
$837$	−5.25662	−0.181695
$838$	−37.2860	−1.28802
$839$	21.6791	0.748446	0.374223	−	0.927339i	$-0.377909\pi$
$839$	21.6791	0.748446	0.374223	+	0.927339i	$0.377909\pi$
$840$	−1.14637	−0.0395534
$841$	−26.9290	−0.928586
$842$	−2.78623	−0.0960198
$843$	−16.4338	−0.566010
$844$	2.04285	0.0703176
$845$	8.95715	0.308135
$846$	16.7862	0.577122
$847$	−1.00000	−0.0343604
$848$	5.43910	0.186779
$849$	3.68415	0.126440
$850$	−0.292731	−0.0100406
$851$	2.43596	0.0835037
$852$	−0.384694	−0.0131794
$853$	9.41454	0.322348	0.161174	−	0.986926i	$-0.448472\pi$
$853$	9.41454	0.322348	0.161174	+	0.986926i	$0.448472\pi$
$854$	11.9572	0.409165
$855$	−10.9884	−0.375797
$856$	9.56404	0.326892
$857$	−25.8652	−0.883538	−0.441769	−	0.897129i	$-0.645649\pi$
$857$	−25.8652	−0.883538	−0.441769	+	0.897129i	$0.645649\pi$
$858$	5.37169	0.183387
$859$	−29.2860	−0.999225	−0.499613	−	0.866249i	$-0.666524\pi$
$859$	−29.2860	−0.999225	−0.499613	+	0.866249i	$0.666524\pi$
$860$	−10.3503	−0.352941
$861$	7.13650	0.243211
$862$	38.0477	1.29591
$863$	−20.3110	−0.691395	−0.345698	−	0.938346i	$-0.612358\pi$
$863$	−20.3110	−0.691395	−0.345698	+	0.938346i	$0.612358\pi$
$864$	−5.37169	−0.182749
$865$	−7.37169	−0.250645
$866$	−10.8108	−0.367366
$867$	−19.3900	−0.658518
$868$	−0.978577	−0.0332151
$869$	−2.51806	−0.0854193
$870$	−1.64973	−0.0559311
$871$	−2.74338	−0.0929560
$872$	3.14637	0.106549
$873$	−15.3471	−0.519422
$874$	18.6002	0.629160
$875$	−1.00000	−0.0338062
$876$	−4.24989	−0.143590
$877$	−38.3650	−1.29549	−0.647746	−	0.761856i	$-0.724288\pi$
$877$	−38.3650	−1.29549	−0.647746	+	0.761856i	$0.724288\pi$
$878$	30.9933	1.04597
$879$	−19.1281	−0.645174
$880$	1.00000	0.0337100
$881$	40.5426	1.36592	0.682958	−	0.730458i	$-0.260693\pi$
$881$	40.5426	1.36592	0.682958	+	0.730458i	$0.260693\pi$
$882$	−1.68585	−0.0567654
$883$	28.0491	0.943928	0.471964	−	0.881618i	$-0.343545\pi$
$883$	28.0491	0.943928	0.471964	+	0.881618i	$0.343545\pi$
$884$	−1.37169	−0.0461350
$885$	−10.7434	−0.361135
$886$	25.3717	0.852379
$887$	−6.65769	−0.223543	−0.111772	−	0.993734i	$-0.535653\pi$
$887$	−6.65769	−0.223543	−0.111772	+	0.993734i	$0.535653\pi$
$888$	0.978577	0.0328389
$889$	13.3717	0.448472
$890$	13.0790	0.438408
$891$	−1.10038	−0.0368643
$892$	11.0790	0.370951
$893$	−64.9013	−2.17184
$894$	13.2944	0.444632
$895$	1.56404	0.0522801
$896$	−1.00000	−0.0334077
$897$	15.3288	0.511815
$898$	−0.886615	−0.0295867
$899$	−1.40827	−0.0469683
$900$	−1.68585	−0.0561949
$901$	−1.59219	−0.0530436
$902$	−6.22533	−0.207281
$903$	11.8652	0.394849
$904$	−2.58546	−0.0859912
$905$	14.7862	0.491511
$906$	1.98531	0.0659574
$907$	39.5787	1.31419	0.657095	−	0.753808i	$-0.271785\pi$
$907$	39.5787	1.31419	0.657095	+	0.753808i	$0.271785\pi$
$908$	−18.5426	−0.615358
$909$	18.1839	0.603123
$910$	−4.68585	−0.155334
$911$	−24.3356	−0.806274	−0.403137	−	0.915140i	$-0.632080\pi$
$911$	−24.3356	−0.806274	−0.403137	+	0.915140i	$0.632080\pi$
$912$	7.47208	0.247425
$913$	−1.70727	−0.0565024
$914$	29.9143	0.989477
$915$	−13.7073	−0.453148
$916$	−8.01469	−0.264813
$917$	11.4391	0.377752
$918$	1.57246	0.0518989
$919$	50.6331	1.67023	0.835117	−	0.550073i	$-0.185400\pi$
$919$	50.6331	1.67023	0.835117	+	0.550073i	$0.185400\pi$
$920$	2.85363	0.0940815
$921$	−7.21377	−0.237702
$922$	−2.33558	−0.0769181
$923$	−1.57246	−0.0517582
$924$	−1.14637	−0.0377127
$925$	0.853635	0.0280673
$926$	0.110250	0.00362303
$927$	−12.9210	−0.424383
$928$	−1.43910	−0.0472407
$929$	47.1512	1.54698	0.773490	−	0.633808i	$-0.218509\pi$
$929$	47.1512	1.54698	0.773490	+	0.633808i	$0.218509\pi$
$930$	1.12181	0.0367855
$931$	6.51806	0.213621
$932$	27.9572	0.915767
$933$	−23.3780	−0.765360
$934$	36.6760	1.20007
$935$	−0.292731	−0.00957333
$936$	−7.89962	−0.258207
$937$	−42.0294	−1.37304	−0.686520	−	0.727111i	$-0.740863\pi$
$937$	−42.0294	−1.37304	−0.686520	+	0.727111i	$0.740863\pi$
$938$	0.585462	0.0191160
$939$	13.8337	0.451444
$940$	−9.95715	−0.324767
$941$	−36.7434	−1.19780	−0.598900	−	0.800824i	$-0.704395\pi$
$941$	−36.7434	−1.19780	−0.598900	+	0.800824i	$0.704395\pi$
$942$	−14.0920	−0.459141
$943$	−17.7648	−0.578502
$944$	−9.37169	−0.305023
$945$	5.37169	0.174741
$946$	−10.3503	−0.336516
$947$	18.8782	0.613459	0.306729	−	0.951797i	$-0.400765\pi$
$947$	18.8782	0.613459	0.306729	+	0.951797i	$0.400765\pi$
$948$	−2.88661	−0.0937529
$949$	−17.3717	−0.563909
$950$	6.51806	0.211474
$951$	32.9786	1.06940
$952$	0.292731	0.00948747
$953$	−43.2285	−1.40031	−0.700154	−	0.713992i	$-0.746885\pi$
$953$	−43.2285	−1.40031	−0.700154	+	0.713992i	$0.746885\pi$
$954$	−9.16948	−0.296873
$955$	−17.9572	−0.581080
$956$	−28.8108	−0.931808
$957$	−1.64973	−0.0533282
$958$	−42.7434	−1.38098
$959$	−10.0000	−0.322917
$960$	1.14637	0.0369988
$961$	−30.0424	−0.969109
$962$	4.00000	0.128965
$963$	−16.1235	−0.519572
$964$	−8.51806	−0.274348
$965$	18.6430	0.600139
$966$	−3.27131	−0.105253
$967$	48.7299	1.56705	0.783524	−	0.621361i	$-0.213420\pi$
$967$	48.7299	1.56705	0.783524	+	0.621361i	$0.213420\pi$
$968$	1.00000	0.0321412
$969$	−2.18731	−0.0702665
$970$	9.10352	0.292296
$971$	−25.9865	−0.833948	−0.416974	−	0.908918i	$-0.636909\pi$
$971$	−25.9865	−0.833948	−0.416974	+	0.908918i	$0.636909\pi$
$972$	14.8536	0.476431
$973$	14.1825	0.454669
$974$	−36.1396	−1.15799
$975$	5.37169	0.172032
$976$	−11.9572	−0.382739
$977$	2.67115	0.0854578	0.0427289	−	0.999087i	$-0.486395\pi$
$977$	2.67115	0.0854578	0.0427289	+	0.999087i	$0.486395\pi$
$978$	27.4145	0.876620
$979$	13.0790	0.418005
$980$	1.00000	0.0319438
$981$	−5.30429	−0.169353
$982$	2.54262	0.0811381
$983$	−8.33558	−0.265864	−0.132932	−	0.991125i	$-0.542439\pi$
$983$	−8.33558	−0.265864	−0.132932	+	0.991125i	$0.542439\pi$
$984$	−7.13650	−0.227503
$985$	−15.0361	−0.479090
$986$	0.421268	0.0134159
$987$	11.4145	0.363329
$988$	30.5426	0.971690
$989$	−29.5359	−0.939187
$990$	−1.68585	−0.0535797
$991$	46.2730	1.46991	0.734955	−	0.678116i	$-0.237203\pi$
$991$	46.2730	1.46991	0.734955	+	0.678116i	$0.237203\pi$
$992$	0.978577	0.0310699
$993$	−4.36496	−0.138518
$994$	0.335577	0.0106438
$995$	15.3288	0.485957
$996$	−1.95715	−0.0620148
$997$	35.8715	1.13606	0.568030	−	0.823008i	$-0.307706\pi$
$997$	35.8715	1.13606	0.568030	+	0.823008i	$0.307706\pi$
$998$	3.13650	0.0992842
$999$	−4.58546	−0.145078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.a.m.1.2	✓	3
3.2	odd	2		6930.2.a.ce.1.3		3
4.3	odd	2		6160.2.a.bf.1.2		3
5.2	odd	4		3850.2.c.ba.1849.5		6
5.3	odd	4		3850.2.c.ba.1849.2		6
5.4	even	2		3850.2.a.bt.1.2		3
7.6	odd	2		5390.2.a.ca.1.2		3
11.10	odd	2		8470.2.a.ci.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.m.1.2	✓	3	1.1	even	1	trivial
3850.2.a.bt.1.2		3	5.4	even	2
3850.2.c.ba.1849.2		6	5.3	odd	4
3850.2.c.ba.1849.5		6	5.2	odd	4
5390.2.a.ca.1.2		3	7.6	odd	2
6160.2.a.bf.1.2		3	4.3	odd	2
6930.2.a.ce.1.3		3	3.2	odd	2
8470.2.a.ci.1.2		3	11.10	odd	2

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.14637 q^{12} +4.68585 q^{13} -1.00000 q^{14} +1.14637 q^{15} +1.00000 q^{16} -0.292731 q^{17} -1.68585 q^{18} +6.51806 q^{19} +1.00000 q^{20} -1.14637 q^{21} +1.00000 q^{22} +2.85363 q^{23} +1.14637 q^{24} +1.00000 q^{25} +4.68585 q^{26} -5.37169 q^{27} -1.00000 q^{28} -1.43910 q^{29} +1.14637 q^{30} +0.978577 q^{31} +1.00000 q^{32} +1.14637 q^{33} -0.292731 q^{34} -1.00000 q^{35} -1.68585 q^{36} +0.853635 q^{37} +6.51806 q^{38} +5.37169 q^{39} +1.00000 q^{40} -6.22533 q^{41} -1.14637 q^{42} -10.3503 q^{43} +1.00000 q^{44} -1.68585 q^{45} +2.85363 q^{46} -9.95715 q^{47} +1.14637 q^{48} +1.00000 q^{49} +1.00000 q^{50} -0.335577 q^{51} +4.68585 q^{52} +5.43910 q^{53} -5.37169 q^{54} +1.00000 q^{55} -1.00000 q^{56} +7.47208 q^{57} -1.43910 q^{58} -9.37169 q^{59} +1.14637 q^{60} -11.9572 q^{61} +0.978577 q^{62} +1.68585 q^{63} +1.00000 q^{64} +4.68585 q^{65} +1.14637 q^{66} -0.585462 q^{67} -0.292731 q^{68} +3.27131 q^{69} -1.00000 q^{70} -0.335577 q^{71} -1.68585 q^{72} -3.70727 q^{73} +0.853635 q^{74} +1.14637 q^{75} +6.51806 q^{76} -1.00000 q^{77} +5.37169 q^{78} -2.51806 q^{79} +1.00000 q^{80} -1.10038 q^{81} -6.22533 q^{82} -1.70727 q^{83} -1.14637 q^{84} -0.292731 q^{85} -10.3503 q^{86} -1.64973 q^{87} +1.00000 q^{88} +13.0790 q^{89} -1.68585 q^{90} -4.68585 q^{91} +2.85363 q^{92} +1.12181 q^{93} -9.95715 q^{94} +6.51806 q^{95} +1.14637 q^{96} +9.10352 q^{97} +1.00000 q^{98} -1.68585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + 2 q^{17} + 7 q^{18} - 6 q^{19} + 3 q^{20} - 2 q^{21} + 3 q^{22} + 10 q^{23} + 2 q^{24} + 3 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} + 2 q^{30} - 12 q^{31} + 3 q^{32} + 2 q^{33} + 2 q^{34} - 3 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 8 q^{39} + 3 q^{40} + 4 q^{41} - 2 q^{42} + 8 q^{43} + 3 q^{44} + 7 q^{45} + 10 q^{46} + 2 q^{48} + 3 q^{49} + 3 q^{50} - 28 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{54} + 3 q^{55} - 3 q^{56} - 8 q^{57} - 4 q^{59} + 2 q^{60} - 6 q^{61} - 12 q^{62} - 7 q^{63} + 3 q^{64} + 2 q^{65} + 2 q^{66} + 4 q^{67} + 2 q^{68} - 8 q^{69} - 3 q^{70} - 28 q^{71} + 7 q^{72} - 14 q^{73} + 4 q^{74} + 2 q^{75} - 6 q^{76} - 3 q^{77} - 8 q^{78} + 18 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{82} - 8 q^{83} - 2 q^{84} + 2 q^{85} + 8 q^{86} - 44 q^{87} + 3 q^{88} + 18 q^{89} + 7 q^{90} - 2 q^{91} + 10 q^{92} + 12 q^{93} - 6 q^{95} + 2 q^{96} - 4 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + 2 * q^17 + 7 * q^18 - 6 * q^19 + 3 * q^20 - 2 * q^21 + 3 * q^22 + 10 * q^23 + 2 * q^24 + 3 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 + 2 * q^30 - 12 * q^31 + 3 * q^32 + 2 * q^33 + 2 * q^34 - 3 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 8 * q^39 + 3 * q^40 + 4 * q^41 - 2 * q^42 + 8 * q^43 + 3 * q^44 + 7 * q^45 + 10 * q^46 + 2 * q^48 + 3 * q^49 + 3 * q^50 - 28 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^54 + 3 * q^55 - 3 * q^56 - 8 * q^57 - 4 * q^59 + 2 * q^60 - 6 * q^61 - 12 * q^62 - 7 * q^63 + 3 * q^64 + 2 * q^65 + 2 * q^66 + 4 * q^67 + 2 * q^68 - 8 * q^69 - 3 * q^70 - 28 * q^71 + 7 * q^72 - 14 * q^73 + 4 * q^74 + 2 * q^75 - 6 * q^76 - 3 * q^77 - 8 * q^78 + 18 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^82 - 8 * q^83 - 2 * q^84 + 2 * q^85 + 8 * q^86 - 44 * q^87 + 3 * q^88 + 18 * q^89 + 7 * q^90 - 2 * q^91 + 10 * q^92 + 12 * q^93 - 6 * q^95 + 2 * q^96 - 4 * q^97 + 3 * q^98 + 7 * q^99

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