LMFDB - Embedded newform 1502.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.763932 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.763932 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.00000 q^{10} -6.23607 q^{11} -1.61803 q^{12} +3.47214 q^{13} -0.763932 q^{14} -1.61803 q^{15} +1.00000 q^{16} +3.38197 q^{17} -0.381966 q^{18} +2.38197 q^{19} +1.00000 q^{20} +1.23607 q^{21} -6.23607 q^{22} -7.23607 q^{23} -1.61803 q^{24} -4.00000 q^{25} +3.47214 q^{26} +5.47214 q^{27} -0.763932 q^{28} -10.2361 q^{29} -1.61803 q^{30} -8.70820 q^{31} +1.00000 q^{32} +10.0902 q^{33} +3.38197 q^{34} -0.763932 q^{35} -0.381966 q^{36} -2.14590 q^{37} +2.38197 q^{38} -5.61803 q^{39} +1.00000 q^{40} +10.7082 q^{41} +1.23607 q^{42} -3.76393 q^{43} -6.23607 q^{44} -0.381966 q^{45} -7.23607 q^{46} +1.85410 q^{47} -1.61803 q^{48} -6.41641 q^{49} -4.00000 q^{50} -5.47214 q^{51} +3.47214 q^{52} +8.56231 q^{53} +5.47214 q^{54} -6.23607 q^{55} -0.763932 q^{56} -3.85410 q^{57} -10.2361 q^{58} -3.23607 q^{59} -1.61803 q^{60} -15.0344 q^{61} -8.70820 q^{62} +0.291796 q^{63} +1.00000 q^{64} +3.47214 q^{65} +10.0902 q^{66} -7.00000 q^{67} +3.38197 q^{68} +11.7082 q^{69} -0.763932 q^{70} +1.76393 q^{71} -0.381966 q^{72} +6.38197 q^{73} -2.14590 q^{74} +6.47214 q^{75} +2.38197 q^{76} +4.76393 q^{77} -5.61803 q^{78} -9.61803 q^{79} +1.00000 q^{80} -7.70820 q^{81} +10.7082 q^{82} +7.47214 q^{83} +1.23607 q^{84} +3.38197 q^{85} -3.76393 q^{86} +16.5623 q^{87} -6.23607 q^{88} -3.94427 q^{89} -0.381966 q^{90} -2.65248 q^{91} -7.23607 q^{92} +14.0902 q^{93} +1.85410 q^{94} +2.38197 q^{95} -1.61803 q^{96} +1.29180 q^{97} -6.41641 q^{98} +2.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 6 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 6 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 6 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} - 8 q^{11} - q^{12} - 2 q^{13} - 6 q^{14} - q^{15} + 2 q^{16} + 9 q^{17} - 3 q^{18} + 7 q^{19} + 2 q^{20} - 2 q^{21} - 8 q^{22} - 10 q^{23} - q^{24} - 8 q^{25} - 2 q^{26} + 2 q^{27} - 6 q^{28} - 16 q^{29} - q^{30} - 4 q^{31} + 2 q^{32} + 9 q^{33} + 9 q^{34} - 6 q^{35} - 3 q^{36} - 11 q^{37} + 7 q^{38} - 9 q^{39} + 2 q^{40} + 8 q^{41} - 2 q^{42} - 12 q^{43} - 8 q^{44} - 3 q^{45} - 10 q^{46} - 3 q^{47} - q^{48} + 14 q^{49} - 8 q^{50} - 2 q^{51} - 2 q^{52} - 3 q^{53} + 2 q^{54} - 8 q^{55} - 6 q^{56} - q^{57} - 16 q^{58} - 2 q^{59} - q^{60} - q^{61} - 4 q^{62} + 14 q^{63} + 2 q^{64} - 2 q^{65} + 9 q^{66} - 14 q^{67} + 9 q^{68} + 10 q^{69} - 6 q^{70} + 8 q^{71} - 3 q^{72} + 15 q^{73} - 11 q^{74} + 4 q^{75} + 7 q^{76} + 14 q^{77} - 9 q^{78} - 17 q^{79} + 2 q^{80} - 2 q^{81} + 8 q^{82} + 6 q^{83} - 2 q^{84} + 9 q^{85} - 12 q^{86} + 13 q^{87} - 8 q^{88} + 10 q^{89} - 3 q^{90} + 26 q^{91} - 10 q^{92} + 17 q^{93} - 3 q^{94} + 7 q^{95} - q^{96} + 16 q^{97} + 14 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 6 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 - 8 * q^11 - q^12 - 2 * q^13 - 6 * q^14 - q^15 + 2 * q^16 + 9 * q^17 - 3 * q^18 + 7 * q^19 + 2 * q^20 - 2 * q^21 - 8 * q^22 - 10 * q^23 - q^24 - 8 * q^25 - 2 * q^26 + 2 * q^27 - 6 * q^28 - 16 * q^29 - q^30 - 4 * q^31 + 2 * q^32 + 9 * q^33 + 9 * q^34 - 6 * q^35 - 3 * q^36 - 11 * q^37 + 7 * q^38 - 9 * q^39 + 2 * q^40 + 8 * q^41 - 2 * q^42 - 12 * q^43 - 8 * q^44 - 3 * q^45 - 10 * q^46 - 3 * q^47 - q^48 + 14 * q^49 - 8 * q^50 - 2 * q^51 - 2 * q^52 - 3 * q^53 + 2 * q^54 - 8 * q^55 - 6 * q^56 - q^57 - 16 * q^58 - 2 * q^59 - q^60 - q^61 - 4 * q^62 + 14 * q^63 + 2 * q^64 - 2 * q^65 + 9 * q^66 - 14 * q^67 + 9 * q^68 + 10 * q^69 - 6 * q^70 + 8 * q^71 - 3 * q^72 + 15 * q^73 - 11 * q^74 + 4 * q^75 + 7 * q^76 + 14 * q^77 - 9 * q^78 - 17 * q^79 + 2 * q^80 - 2 * q^81 + 8 * q^82 + 6 * q^83 - 2 * q^84 + 9 * q^85 - 12 * q^86 + 13 * q^87 - 8 * q^88 + 10 * q^89 - 3 * q^90 + 26 * q^91 - 10 * q^92 + 17 * q^93 - 3 * q^94 + 7 * q^95 - q^96 + 16 * q^97 + 14 * 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
$3$	−1.61803	−0.934172	−0.467086	−	0.884212i	$-0.654696\pi$
$3$	−1.61803	−0.934172	−0.467086	+	0.884212i	$0.654696\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−1.61803	−0.660560
$7$	−0.763932	−0.288739	−0.144370	−	0.989524i	$-0.546115\pi$
$7$	−0.763932	−0.288739	−0.144370	+	0.989524i	$0.546115\pi$
$8$	1.00000	0.353553
$9$	−0.381966	−0.127322
$10$	1.00000	0.316228
$11$	−6.23607	−1.88025	−0.940123	−	0.340836i	$-0.889290\pi$
$11$	−6.23607	−1.88025	−0.940123	+	0.340836i	$0.889290\pi$
$12$	−1.61803	−0.467086
$13$	3.47214	0.962997	0.481499	−	0.876447i	$-0.340093\pi$
$13$	3.47214	0.962997	0.481499	+	0.876447i	$0.340093\pi$
$14$	−0.763932	−0.204169
$15$	−1.61803	−0.417775
$16$	1.00000	0.250000
$17$	3.38197	0.820247	0.410124	−	0.912030i	$-0.365486\pi$
$17$	3.38197	0.820247	0.410124	+	0.912030i	$0.365486\pi$
$18$	−0.381966	−0.0900303
$19$	2.38197	0.546460	0.273230	−	0.961949i	$-0.411908\pi$
$19$	2.38197	0.546460	0.273230	+	0.961949i	$0.411908\pi$
$20$	1.00000	0.223607
$21$	1.23607	0.269732
$22$	−6.23607	−1.32953
$23$	−7.23607	−1.50882	−0.754412	−	0.656401i	$-0.772078\pi$
$23$	−7.23607	−1.50882	−0.754412	+	0.656401i	$0.772078\pi$
$24$	−1.61803	−0.330280
$25$	−4.00000	−0.800000
$26$	3.47214	0.680942
$27$	5.47214	1.05311
$28$	−0.763932	−0.144370
$29$	−10.2361	−1.90079	−0.950395	−	0.311045i	$-0.899321\pi$
$29$	−10.2361	−1.90079	−0.950395	+	0.311045i	$0.899321\pi$
$30$	−1.61803	−0.295411
$31$	−8.70820	−1.56404	−0.782020	−	0.623254i	$-0.785810\pi$
$31$	−8.70820	−1.56404	−0.782020	+	0.623254i	$0.785810\pi$
$32$	1.00000	0.176777
$33$	10.0902	1.75647
$34$	3.38197	0.580002
$35$	−0.763932	−0.129128
$36$	−0.381966	−0.0636610
$37$	−2.14590	−0.352783	−0.176392	−	0.984320i	$-0.556443\pi$
$37$	−2.14590	−0.352783	−0.176392	+	0.984320i	$0.556443\pi$
$38$	2.38197	0.386406
$39$	−5.61803	−0.899605
$40$	1.00000	0.158114
$41$	10.7082	1.67234	0.836170	−	0.548470i	$-0.184790\pi$
$41$	10.7082	1.67234	0.836170	+	0.548470i	$0.184790\pi$
$42$	1.23607	0.190729
$43$	−3.76393	−0.573994	−0.286997	−	0.957931i	$-0.592657\pi$
$43$	−3.76393	−0.573994	−0.286997	+	0.957931i	$0.592657\pi$
$44$	−6.23607	−0.940123
$45$	−0.381966	−0.0569401
$46$	−7.23607	−1.06690
$47$	1.85410	0.270449	0.135224	−	0.990815i	$-0.456825\pi$
$47$	1.85410	0.270449	0.135224	+	0.990815i	$0.456825\pi$
$48$	−1.61803	−0.233543
$49$	−6.41641	−0.916630
$50$	−4.00000	−0.565685
$51$	−5.47214	−0.766252
$52$	3.47214	0.481499
$53$	8.56231	1.17612	0.588062	−	0.808816i	$-0.299891\pi$
$53$	8.56231	1.17612	0.588062	+	0.808816i	$0.299891\pi$
$54$	5.47214	0.744663
$55$	−6.23607	−0.840871
$56$	−0.763932	−0.102085
$57$	−3.85410	−0.510488
$58$	−10.2361	−1.34406
$59$	−3.23607	−0.421300	−0.210650	−	0.977562i	$-0.567558\pi$
$59$	−3.23607	−0.421300	−0.210650	+	0.977562i	$0.567558\pi$
$60$	−1.61803	−0.208887
$61$	−15.0344	−1.92496	−0.962482	−	0.271347i	$-0.912531\pi$
$61$	−15.0344	−1.92496	−0.962482	+	0.271347i	$0.912531\pi$
$62$	−8.70820	−1.10594
$63$	0.291796	0.0367628
$64$	1.00000	0.125000
$65$	3.47214	0.430665
$66$	10.0902	1.24201
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	3.38197	0.410124
$69$	11.7082	1.40950
$70$	−0.763932	−0.0913073
$71$	1.76393	0.209340	0.104670	−	0.994507i	$-0.466621\pi$
$71$	1.76393	0.209340	0.104670	+	0.994507i	$0.466621\pi$
$72$	−0.381966	−0.0450151
$73$	6.38197	0.746953	0.373476	−	0.927640i	$-0.378166\pi$
$73$	6.38197	0.746953	0.373476	+	0.927640i	$0.378166\pi$
$74$	−2.14590	−0.249456
$75$	6.47214	0.747338
$76$	2.38197	0.273230
$77$	4.76393	0.542900
$78$	−5.61803	−0.636117
$79$	−9.61803	−1.08211	−0.541057	−	0.840986i	$-0.681976\pi$
$79$	−9.61803	−1.08211	−0.541057	+	0.840986i	$0.681976\pi$
$80$	1.00000	0.111803
$81$	−7.70820	−0.856467
$82$	10.7082	1.18252
$83$	7.47214	0.820173	0.410087	−	0.912047i	$-0.365498\pi$
$83$	7.47214	0.820173	0.410087	+	0.912047i	$0.365498\pi$
$84$	1.23607	0.134866
$85$	3.38197	0.366826
$86$	−3.76393	−0.405875
$87$	16.5623	1.77567
$88$	−6.23607	−0.664767
$89$	−3.94427	−0.418092	−0.209046	−	0.977906i	$-0.567036\pi$
$89$	−3.94427	−0.418092	−0.209046	+	0.977906i	$0.567036\pi$
$90$	−0.381966	−0.0402628
$91$	−2.65248	−0.278055
$92$	−7.23607	−0.754412
$93$	14.0902	1.46108
$94$	1.85410	0.191236
$95$	2.38197	0.244385
$96$	−1.61803	−0.165140
$97$	1.29180	0.131162	0.0655810	−	0.997847i	$-0.479110\pi$
$97$	1.29180	0.131162	0.0655810	+	0.997847i	$0.479110\pi$
$98$	−6.41641	−0.648155
$99$	2.38197	0.239397
$100$	−4.00000	−0.400000
$101$	−5.61803	−0.559015	−0.279508	−	0.960143i	$-0.590171\pi$
$101$	−5.61803	−0.559015	−0.279508	+	0.960143i	$0.590171\pi$
$102$	−5.47214	−0.541822
$103$	−11.4721	−1.13038	−0.565192	−	0.824960i	$-0.691198\pi$
$103$	−11.4721	−1.13038	−0.565192	+	0.824960i	$0.691198\pi$
$104$	3.47214	0.340471
$105$	1.23607	0.120628
$106$	8.56231	0.831645
$107$	−3.29180	−0.318230	−0.159115	−	0.987260i	$-0.550864\pi$
$107$	−3.29180	−0.318230	−0.159115	+	0.987260i	$0.550864\pi$
$108$	5.47214	0.526557
$109$	−4.70820	−0.450964	−0.225482	−	0.974247i	$-0.572396\pi$
$109$	−4.70820	−0.450964	−0.225482	+	0.974247i	$0.572396\pi$
$110$	−6.23607	−0.594586
$111$	3.47214	0.329561
$112$	−0.763932	−0.0721848
$113$	7.09017	0.666987	0.333494	−	0.942752i	$-0.391772\pi$
$113$	7.09017	0.666987	0.333494	+	0.942752i	$0.391772\pi$
$114$	−3.85410	−0.360970
$115$	−7.23607	−0.674767
$116$	−10.2361	−0.950395
$117$	−1.32624	−0.122611
$118$	−3.23607	−0.297904
$119$	−2.58359	−0.236838
$120$	−1.61803	−0.147706
$121$	27.8885	2.53532
$122$	−15.0344	−1.36115
$123$	−17.3262	−1.56225
$124$	−8.70820	−0.782020
$125$	−9.00000	−0.804984
$126$	0.291796	0.0259953
$127$	−12.7082	−1.12767	−0.563835	−	0.825887i	$-0.690675\pi$
$127$	−12.7082	−1.12767	−0.563835	+	0.825887i	$0.690675\pi$
$128$	1.00000	0.0883883
$129$	6.09017	0.536210
$130$	3.47214	0.304526
$131$	7.09017	0.619471	0.309736	−	0.950823i	$-0.399759\pi$
$131$	7.09017	0.619471	0.309736	+	0.950823i	$0.399759\pi$
$132$	10.0902	0.878237
$133$	−1.81966	−0.157785
$134$	−7.00000	−0.604708
$135$	5.47214	0.470966
$136$	3.38197	0.290001
$137$	−8.41641	−0.719062	−0.359531	−	0.933133i	$-0.617063\pi$
$137$	−8.41641	−0.719062	−0.359531	+	0.933133i	$0.617063\pi$
$138$	11.7082	0.996669
$139$	6.00000	0.508913	0.254457	−	0.967084i	$-0.418103\pi$
$139$	6.00000	0.508913	0.254457	+	0.967084i	$0.418103\pi$
$140$	−0.763932	−0.0645640
$141$	−3.00000	−0.252646
$142$	1.76393	0.148026
$143$	−21.6525	−1.81067
$144$	−0.381966	−0.0318305
$145$	−10.2361	−0.850059
$146$	6.38197	0.528175
$147$	10.3820	0.856290
$148$	−2.14590	−0.176392
$149$	−6.56231	−0.537605	−0.268803	−	0.963195i	$-0.586628\pi$
$149$	−6.56231	−0.537605	−0.268803	+	0.963195i	$0.586628\pi$
$150$	6.47214	0.528448
$151$	−8.85410	−0.720537	−0.360268	−	0.932849i	$-0.617315\pi$
$151$	−8.85410	−0.720537	−0.360268	+	0.932849i	$0.617315\pi$
$152$	2.38197	0.193203
$153$	−1.29180	−0.104436
$154$	4.76393	0.383889
$155$	−8.70820	−0.699460
$156$	−5.61803	−0.449803
$157$	13.3820	1.06800	0.533999	−	0.845485i	$-0.320689\pi$
$157$	13.3820	1.06800	0.533999	+	0.845485i	$0.320689\pi$
$158$	−9.61803	−0.765170
$159$	−13.8541	−1.09870
$160$	1.00000	0.0790569
$161$	5.52786	0.435657
$162$	−7.70820	−0.605614
$163$	−3.14590	−0.246406	−0.123203	−	0.992382i	$-0.539317\pi$
$163$	−3.14590	−0.246406	−0.123203	+	0.992382i	$0.539317\pi$
$164$	10.7082	0.836170
$165$	10.0902	0.785519
$166$	7.47214	0.579950
$167$	14.4164	1.11558	0.557788	−	0.829984i	$-0.311650\pi$
$167$	14.4164	1.11558	0.557788	+	0.829984i	$0.311650\pi$
$168$	1.23607	0.0953647
$169$	−0.944272	−0.0726363
$170$	3.38197	0.259385
$171$	−0.909830	−0.0695764
$172$	−3.76393	−0.286997
$173$	15.5623	1.18318	0.591590	−	0.806239i	$-0.298500\pi$
$173$	15.5623	1.18318	0.591590	+	0.806239i	$0.298500\pi$
$174$	16.5623	1.25559
$175$	3.05573	0.230991
$176$	−6.23607	−0.470061
$177$	5.23607	0.393567
$178$	−3.94427	−0.295636
$179$	20.4721	1.53016	0.765080	−	0.643936i	$-0.222700\pi$
$179$	20.4721	1.53016	0.765080	+	0.643936i	$0.222700\pi$
$180$	−0.381966	−0.0284701
$181$	−1.29180	−0.0960184	−0.0480092	−	0.998847i	$-0.515288\pi$
$181$	−1.29180	−0.0960184	−0.0480092	+	0.998847i	$0.515288\pi$
$182$	−2.65248	−0.196615
$183$	24.3262	1.79825
$184$	−7.23607	−0.533450
$185$	−2.14590	−0.157770
$186$	14.0902	1.03314
$187$	−21.0902	−1.54227
$188$	1.85410	0.135224
$189$	−4.18034	−0.304075
$190$	2.38197	0.172806
$191$	9.88854	0.715510	0.357755	−	0.933816i	$-0.383542\pi$
$191$	9.88854	0.715510	0.357755	+	0.933816i	$0.383542\pi$
$192$	−1.61803	−0.116772
$193$	1.81966	0.130982	0.0654910	−	0.997853i	$-0.479139\pi$
$193$	1.81966	0.130982	0.0654910	+	0.997853i	$0.479139\pi$
$194$	1.29180	0.0927456
$195$	−5.61803	−0.402316
$196$	−6.41641	−0.458315
$197$	−9.94427	−0.708500	−0.354250	−	0.935151i	$-0.615264\pi$
$197$	−9.94427	−0.708500	−0.354250	+	0.935151i	$0.615264\pi$
$198$	2.38197	0.169279
$199$	23.1246	1.63926	0.819630	−	0.572893i	$-0.194179\pi$
$199$	23.1246	1.63926	0.819630	+	0.572893i	$0.194179\pi$
$200$	−4.00000	−0.282843
$201$	11.3262	0.798891
$202$	−5.61803	−0.395283
$203$	7.81966	0.548833
$204$	−5.47214	−0.383126
$205$	10.7082	0.747893
$206$	−11.4721	−0.799302
$207$	2.76393	0.192107
$208$	3.47214	0.240749
$209$	−14.8541	−1.02748
$210$	1.23607	0.0852968
$211$	16.1803	1.11390	0.556950	−	0.830546i	$-0.311971\pi$
$211$	16.1803	1.11390	0.556950	+	0.830546i	$0.311971\pi$
$212$	8.56231	0.588062
$213$	−2.85410	−0.195560
$214$	−3.29180	−0.225023
$215$	−3.76393	−0.256698
$216$	5.47214	0.372332
$217$	6.65248	0.451599
$218$	−4.70820	−0.318880
$219$	−10.3262	−0.697782
$220$	−6.23607	−0.420436
$221$	11.7426	0.789896
$222$	3.47214	0.233035
$223$	16.7984	1.12490	0.562451	−	0.826831i	$-0.309858\pi$
$223$	16.7984	1.12490	0.562451	+	0.826831i	$0.309858\pi$
$224$	−0.763932	−0.0510424
$225$	1.52786	0.101858
$226$	7.09017	0.471631
$227$	−2.00000	−0.132745	−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000	−0.132745	−0.0663723	+	0.997795i	$0.521143\pi$
$228$	−3.85410	−0.255244
$229$	1.00000	0.0660819	0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000	0.0660819	0.0330409	+	0.999454i	$0.489481\pi$
$230$	−7.23607	−0.477132
$231$	−7.70820	−0.507163
$232$	−10.2361	−0.672031
$233$	−25.9443	−1.69967	−0.849833	−	0.527052i	$-0.823297\pi$
$233$	−25.9443	−1.69967	−0.849833	+	0.527052i	$0.823297\pi$
$234$	−1.32624	−0.0866989
$235$	1.85410	0.120948
$236$	−3.23607	−0.210650
$237$	15.5623	1.01088
$238$	−2.58359	−0.167469
$239$	11.1803	0.723196	0.361598	−	0.932334i	$-0.382231\pi$
$239$	11.1803	0.723196	0.361598	+	0.932334i	$0.382231\pi$
$240$	−1.61803	−0.104444
$241$	21.2705	1.37015	0.685077	−	0.728471i	$-0.259769\pi$
$241$	21.2705	1.37015	0.685077	+	0.728471i	$0.259769\pi$
$242$	27.8885	1.79274
$243$	−3.94427	−0.253025
$244$	−15.0344	−0.962482
$245$	−6.41641	−0.409929
$246$	−17.3262	−1.10468
$247$	8.27051	0.526240
$248$	−8.70820	−0.552972
$249$	−12.0902	−0.766183
$250$	−9.00000	−0.569210
$251$	11.4721	0.724115	0.362057	−	0.932156i	$-0.382074\pi$
$251$	11.4721	0.724115	0.362057	+	0.932156i	$0.382074\pi$
$252$	0.291796	0.0183814
$253$	45.1246	2.83696
$254$	−12.7082	−0.797384
$255$	−5.47214	−0.342678
$256$	1.00000	0.0625000
$257$	11.3262	0.706511	0.353256	−	0.935527i	$-0.385075\pi$
$257$	11.3262	0.706511	0.353256	+	0.935527i	$0.385075\pi$
$258$	6.09017	0.379157
$259$	1.63932	0.101862
$260$	3.47214	0.215333
$261$	3.90983	0.242012
$262$	7.09017	0.438032
$263$	4.90983	0.302753	0.151377	−	0.988476i	$-0.451629\pi$
$263$	4.90983	0.302753	0.151377	+	0.988476i	$0.451629\pi$
$264$	10.0902	0.621007
$265$	8.56231	0.525978
$266$	−1.81966	−0.111571
$267$	6.38197	0.390570
$268$	−7.00000	−0.427593
$269$	−26.3262	−1.60514	−0.802570	−	0.596559i	$-0.796534\pi$
$269$	−26.3262	−1.60514	−0.802570	+	0.596559i	$0.796534\pi$
$270$	5.47214	0.333024
$271$	5.61803	0.341271	0.170636	−	0.985334i	$-0.445418\pi$
$271$	5.61803	0.341271	0.170636	+	0.985334i	$0.445418\pi$
$272$	3.38197	0.205062
$273$	4.29180	0.259751
$274$	−8.41641	−0.508454
$275$	24.9443	1.50420
$276$	11.7082	0.704751
$277$	−29.9787	−1.80125	−0.900623	−	0.434601i	$-0.856889\pi$
$277$	−29.9787	−1.80125	−0.900623	+	0.434601i	$0.856889\pi$
$278$	6.00000	0.359856
$279$	3.32624	0.199137
$280$	−0.763932	−0.0456537
$281$	28.8328	1.72002	0.860011	−	0.510276i	$-0.170457\pi$
$281$	28.8328	1.72002	0.860011	+	0.510276i	$0.170457\pi$
$282$	−3.00000	−0.178647
$283$	−24.5623	−1.46008	−0.730039	−	0.683406i	$-0.760498\pi$
$283$	−24.5623	−1.46008	−0.730039	+	0.683406i	$0.760498\pi$
$284$	1.76393	0.104670
$285$	−3.85410	−0.228297
$286$	−21.6525	−1.28034
$287$	−8.18034	−0.482870
$288$	−0.381966	−0.0225076
$289$	−5.56231	−0.327194
$290$	−10.2361	−0.601083
$291$	−2.09017	−0.122528
$292$	6.38197	0.373476
$293$	27.4721	1.60494	0.802470	−	0.596693i	$-0.203519\pi$
$293$	27.4721	1.60494	0.802470	+	0.596693i	$0.203519\pi$
$294$	10.3820	0.605489
$295$	−3.23607	−0.188411
$296$	−2.14590	−0.124728
$297$	−34.1246	−1.98011
$298$	−6.56231	−0.380144
$299$	−25.1246	−1.45299
$300$	6.47214	0.373669
$301$	2.87539	0.165735
$302$	−8.85410	−0.509496
$303$	9.09017	0.522217
$304$	2.38197	0.136615
$305$	−15.0344	−0.860870
$306$	−1.29180	−0.0738471
$307$	−4.67376	−0.266746	−0.133373	−	0.991066i	$-0.542581\pi$
$307$	−4.67376	−0.266746	−0.133373	+	0.991066i	$0.542581\pi$
$308$	4.76393	0.271450
$309$	18.5623	1.05597
$310$	−8.70820	−0.494593
$311$	−1.79837	−0.101976	−0.0509882	−	0.998699i	$-0.516237\pi$
$311$	−1.79837	−0.101976	−0.0509882	+	0.998699i	$0.516237\pi$
$312$	−5.61803	−0.318059
$313$	−3.67376	−0.207653	−0.103827	−	0.994595i	$-0.533109\pi$
$313$	−3.67376	−0.207653	−0.103827	+	0.994595i	$0.533109\pi$
$314$	13.3820	0.755188
$315$	0.291796	0.0164408
$316$	−9.61803	−0.541057
$317$	15.6525	0.879131	0.439565	−	0.898211i	$-0.355133\pi$
$317$	15.6525	0.879131	0.439565	+	0.898211i	$0.355133\pi$
$318$	−13.8541	−0.776899
$319$	63.8328	3.57395
$320$	1.00000	0.0559017
$321$	5.32624	0.297282
$322$	5.52786	0.308056
$323$	8.05573	0.448233
$324$	−7.70820	−0.428234
$325$	−13.8885	−0.770398
$326$	−3.14590	−0.174235
$327$	7.61803	0.421278
$328$	10.7082	0.591262
$329$	−1.41641	−0.0780891
$330$	10.0902	0.555446
$331$	−7.67376	−0.421788	−0.210894	−	0.977509i	$-0.567638\pi$
$331$	−7.67376	−0.421788	−0.210894	+	0.977509i	$0.567638\pi$
$332$	7.47214	0.410087
$333$	0.819660	0.0449171
$334$	14.4164	0.788831
$335$	−7.00000	−0.382451
$336$	1.23607	0.0674330
$337$	19.7984	1.07849	0.539243	−	0.842150i	$-0.318710\pi$
$337$	19.7984	1.07849	0.539243	+	0.842150i	$0.318710\pi$
$338$	−0.944272	−0.0513616
$339$	−11.4721	−0.623081
$340$	3.38197	0.183413
$341$	54.3050	2.94078
$342$	−0.909830	−0.0491980
$343$	10.2492	0.553406
$344$	−3.76393	−0.202938
$345$	11.7082	0.630349
$346$	15.5623	0.836635
$347$	−9.67376	−0.519315	−0.259657	−	0.965701i	$-0.583610\pi$
$347$	−9.67376	−0.519315	−0.259657	+	0.965701i	$0.583610\pi$
$348$	16.5623	0.887833
$349$	9.65248	0.516685	0.258343	−	0.966053i	$-0.416824\pi$
$349$	9.65248	0.516685	0.258343	+	0.966053i	$0.416824\pi$
$350$	3.05573	0.163336
$351$	19.0000	1.01414
$352$	−6.23607	−0.332384
$353$	8.76393	0.466457	0.233229	−	0.972422i	$-0.425071\pi$
$353$	8.76393	0.466457	0.233229	+	0.972422i	$0.425071\pi$
$354$	5.23607	0.278294
$355$	1.76393	0.0936198
$356$	−3.94427	−0.209046
$357$	4.18034	0.221247
$358$	20.4721	1.08199
$359$	−15.7984	−0.833806	−0.416903	−	0.908951i	$-0.636885\pi$
$359$	−15.7984	−0.833806	−0.416903	+	0.908951i	$0.636885\pi$
$360$	−0.381966	−0.0201314
$361$	−13.3262	−0.701381
$362$	−1.29180	−0.0678953
$363$	−45.1246	−2.36843
$364$	−2.65248	−0.139028
$365$	6.38197	0.334047
$366$	24.3262	1.27155
$367$	−3.12461	−0.163103	−0.0815517	−	0.996669i	$-0.525988\pi$
$367$	−3.12461	−0.163103	−0.0815517	+	0.996669i	$0.525988\pi$
$368$	−7.23607	−0.377206
$369$	−4.09017	−0.212926
$370$	−2.14590	−0.111560
$371$	−6.54102	−0.339593
$372$	14.0902	0.730541
$373$	6.94427	0.359561	0.179780	−	0.983707i	$-0.442461\pi$
$373$	6.94427	0.359561	0.179780	+	0.983707i	$0.442461\pi$
$374$	−21.0902	−1.09055
$375$	14.5623	0.751994
$376$	1.85410	0.0956180
$377$	−35.5410	−1.83046
$378$	−4.18034	−0.215013
$379$	−14.6738	−0.753741	−0.376870	−	0.926266i	$-0.623000\pi$
$379$	−14.6738	−0.753741	−0.376870	+	0.926266i	$0.623000\pi$
$380$	2.38197	0.122192
$381$	20.5623	1.05344
$382$	9.88854	0.505942
$383$	3.27051	0.167115	0.0835576	−	0.996503i	$-0.473372\pi$
$383$	3.27051	0.167115	0.0835576	+	0.996503i	$0.473372\pi$
$384$	−1.61803	−0.0825700
$385$	4.76393	0.242792
$386$	1.81966	0.0926183
$387$	1.43769	0.0730821
$388$	1.29180	0.0655810
$389$	−8.29180	−0.420411	−0.210205	−	0.977657i	$-0.567413\pi$
$389$	−8.29180	−0.420411	−0.210205	+	0.977657i	$0.567413\pi$
$390$	−5.61803	−0.284480
$391$	−24.4721	−1.23761
$392$	−6.41641	−0.324078
$393$	−11.4721	−0.578693
$394$	−9.94427	−0.500985
$395$	−9.61803	−0.483936
$396$	2.38197	0.119698
$397$	−1.90983	−0.0958516	−0.0479258	−	0.998851i	$-0.515261\pi$
$397$	−1.90983	−0.0958516	−0.0479258	+	0.998851i	$0.515261\pi$
$398$	23.1246	1.15913
$399$	2.94427	0.147398
$400$	−4.00000	−0.200000
$401$	−18.4164	−0.919672	−0.459836	−	0.888004i	$-0.652092\pi$
$401$	−18.4164	−0.919672	−0.459836	+	0.888004i	$0.652092\pi$
$402$	11.3262	0.564901
$403$	−30.2361	−1.50617
$404$	−5.61803	−0.279508
$405$	−7.70820	−0.383024
$406$	7.81966	0.388083
$407$	13.3820	0.663319
$408$	−5.47214	−0.270911
$409$	2.70820	0.133912	0.0669560	−	0.997756i	$-0.478671\pi$
$409$	2.70820	0.133912	0.0669560	+	0.997756i	$0.478671\pi$
$410$	10.7082	0.528840
$411$	13.6180	0.671728
$412$	−11.4721	−0.565192
$413$	2.47214	0.121646
$414$	2.76393	0.135840
$415$	7.47214	0.366793
$416$	3.47214	0.170235
$417$	−9.70820	−0.475413
$418$	−14.8541	−0.726538
$419$	−21.9787	−1.07373	−0.536865	−	0.843668i	$-0.680392\pi$
$419$	−21.9787	−1.07373	−0.536865	+	0.843668i	$0.680392\pi$
$420$	1.23607	0.0603139
$421$	−1.05573	−0.0514530	−0.0257265	−	0.999669i	$-0.508190\pi$
$421$	−1.05573	−0.0514530	−0.0257265	+	0.999669i	$0.508190\pi$
$422$	16.1803	0.787647
$423$	−0.708204	−0.0344341
$424$	8.56231	0.415822
$425$	−13.5279	−0.656198
$426$	−2.85410	−0.138282
$427$	11.4853	0.555812
$428$	−3.29180	−0.159115
$429$	35.0344	1.69148
$430$	−3.76393	−0.181513
$431$	12.5967	0.606764	0.303382	−	0.952869i	$-0.401884\pi$
$431$	12.5967	0.606764	0.303382	+	0.952869i	$0.401884\pi$
$432$	5.47214	0.263278
$433$	−18.9443	−0.910404	−0.455202	−	0.890388i	$-0.650433\pi$
$433$	−18.9443	−0.910404	−0.455202	+	0.890388i	$0.650433\pi$
$434$	6.65248	0.319329
$435$	16.5623	0.794102
$436$	−4.70820	−0.225482
$437$	−17.2361	−0.824513
$438$	−10.3262	−0.493407
$439$	−21.0689	−1.00556	−0.502781	−	0.864414i	$-0.667690\pi$
$439$	−21.0689	−1.00556	−0.502781	+	0.864414i	$0.667690\pi$
$440$	−6.23607	−0.297293
$441$	2.45085	0.116707
$442$	11.7426	0.558541
$443$	−23.4164	−1.11255	−0.556274	−	0.830999i	$-0.687769\pi$
$443$	−23.4164	−1.11255	−0.556274	+	0.830999i	$0.687769\pi$
$444$	3.47214	0.164780
$445$	−3.94427	−0.186976
$446$	16.7984	0.795426
$447$	10.6180	0.502216
$448$	−0.763932	−0.0360924
$449$	36.8885	1.74088	0.870439	−	0.492276i	$-0.163835\pi$
$449$	36.8885	1.74088	0.870439	+	0.492276i	$0.163835\pi$
$450$	1.52786	0.0720242
$451$	−66.7771	−3.14441
$452$	7.09017	0.333494
$453$	14.3262	0.673105
$454$	−2.00000	−0.0938647
$455$	−2.65248	−0.124350
$456$	−3.85410	−0.180485
$457$	21.3262	0.997599	0.498800	−	0.866717i	$-0.333774\pi$
$457$	21.3262	0.997599	0.498800	+	0.866717i	$0.333774\pi$
$458$	1.00000	0.0467269
$459$	18.5066	0.863813
$460$	−7.23607	−0.337383
$461$	−21.6180	−1.00685	−0.503426	−	0.864038i	$-0.667927\pi$
$461$	−21.6180	−1.00685	−0.503426	+	0.864038i	$0.667927\pi$
$462$	−7.70820	−0.358618
$463$	−29.1803	−1.35613	−0.678063	−	0.735004i	$-0.737180\pi$
$463$	−29.1803	−1.35613	−0.678063	+	0.735004i	$0.737180\pi$
$464$	−10.2361	−0.475198
$465$	14.0902	0.653416
$466$	−25.9443	−1.20185
$467$	17.1246	0.792433	0.396216	−	0.918157i	$-0.370323\pi$
$467$	17.1246	0.792433	0.396216	+	0.918157i	$0.370323\pi$
$468$	−1.32624	−0.0613054
$469$	5.34752	0.246926
$470$	1.85410	0.0855233
$471$	−21.6525	−0.997693
$472$	−3.23607	−0.148952
$473$	23.4721	1.07925
$474$	15.5623	0.714800
$475$	−9.52786	−0.437168
$476$	−2.58359	−0.118419
$477$	−3.27051	−0.149746
$478$	11.1803	0.511377
$479$	−9.41641	−0.430247	−0.215123	−	0.976587i	$-0.569015\pi$
$479$	−9.41641	−0.430247	−0.215123	+	0.976587i	$0.569015\pi$
$480$	−1.61803	−0.0738528
$481$	−7.45085	−0.339730
$482$	21.2705	0.968845
$483$	−8.94427	−0.406978
$484$	27.8885	1.26766
$485$	1.29180	0.0586574
$486$	−3.94427	−0.178916
$487$	25.0689	1.13598	0.567990	−	0.823036i	$-0.307721\pi$
$487$	25.0689	1.13598	0.567990	+	0.823036i	$0.307721\pi$
$488$	−15.0344	−0.680577
$489$	5.09017	0.230185
$490$	−6.41641	−0.289864
$491$	−32.7771	−1.47921	−0.739605	−	0.673042i	$-0.764987\pi$
$491$	−32.7771	−1.47921	−0.739605	+	0.673042i	$0.764987\pi$
$492$	−17.3262	−0.781127
$493$	−34.6180	−1.55912
$494$	8.27051	0.372108
$495$	2.38197	0.107061
$496$	−8.70820	−0.391010
$497$	−1.34752	−0.0604447
$498$	−12.0902	−0.541773
$499$	−19.1246	−0.856135	−0.428068	−	0.903747i	$-0.640805\pi$
$499$	−19.1246	−0.856135	−0.428068	+	0.903747i	$0.640805\pi$
$500$	−9.00000	−0.402492
$501$	−23.3262	−1.04214
$502$	11.4721	0.512026
$503$	−26.7984	−1.19488	−0.597440	−	0.801913i	$-0.703815\pi$
$503$	−26.7984	−1.19488	−0.597440	+	0.801913i	$0.703815\pi$
$504$	0.291796	0.0129976
$505$	−5.61803	−0.249999
$506$	45.1246	2.00603
$507$	1.52786	0.0678548
$508$	−12.7082	−0.563835
$509$	−16.2705	−0.721178	−0.360589	−	0.932725i	$-0.617424\pi$
$509$	−16.2705	−0.721178	−0.360589	+	0.932725i	$0.617424\pi$
$510$	−5.47214	−0.242310
$511$	−4.87539	−0.215674
$512$	1.00000	0.0441942
$513$	13.0344	0.575485
$514$	11.3262	0.499579
$515$	−11.4721	−0.505523
$516$	6.09017	0.268105
$517$	−11.5623	−0.508510
$518$	1.63932	0.0720276
$519$	−25.1803	−1.10529
$520$	3.47214	0.152263
$521$	40.3050	1.76579	0.882896	−	0.469569i	$-0.155591\pi$
$521$	40.3050	1.76579	0.882896	+	0.469569i	$0.155591\pi$
$522$	3.90983	0.171129
$523$	−41.8885	−1.83166	−0.915829	−	0.401568i	$-0.868465\pi$
$523$	−41.8885	−1.83166	−0.915829	+	0.401568i	$0.868465\pi$
$524$	7.09017	0.309736
$525$	−4.94427	−0.215786
$526$	4.90983	0.214079
$527$	−29.4508	−1.28290
$528$	10.0902	0.439118
$529$	29.3607	1.27655
$530$	8.56231	0.371923
$531$	1.23607	0.0536408
$532$	−1.81966	−0.0788923
$533$	37.1803	1.61046
$534$	6.38197	0.276175
$535$	−3.29180	−0.142317
$536$	−7.00000	−0.302354
$537$	−33.1246	−1.42943
$538$	−26.3262	−1.13500
$539$	40.0132	1.72349
$540$	5.47214	0.235483
$541$	−45.9787	−1.97678	−0.988390	−	0.151940i	$-0.951448\pi$
$541$	−45.9787	−1.97678	−0.988390	+	0.151940i	$0.951448\pi$
$542$	5.61803	0.241315
$543$	2.09017	0.0896978
$544$	3.38197	0.145001
$545$	−4.70820	−0.201677
$546$	4.29180	0.183672
$547$	−6.79837	−0.290677	−0.145339	−	0.989382i	$-0.546427\pi$
$547$	−6.79837	−0.290677	−0.145339	+	0.989382i	$0.546427\pi$
$548$	−8.41641	−0.359531
$549$	5.74265	0.245090
$550$	24.9443	1.06363
$551$	−24.3820	−1.03871
$552$	11.7082	0.498334
$553$	7.34752	0.312449
$554$	−29.9787	−1.27367
$555$	3.47214	0.147384
$556$	6.00000	0.254457
$557$	8.70820	0.368978	0.184489	−	0.982835i	$-0.440937\pi$
$557$	8.70820	0.368978	0.184489	+	0.982835i	$0.440937\pi$
$558$	3.32624	0.140811
$559$	−13.0689	−0.552755
$560$	−0.763932	−0.0322820
$561$	34.1246	1.44074
$562$	28.8328	1.21624
$563$	30.6180	1.29040	0.645198	−	0.764015i	$-0.276775\pi$
$563$	30.6180	1.29040	0.645198	+	0.764015i	$0.276775\pi$
$564$	−3.00000	−0.126323
$565$	7.09017	0.298286
$566$	−24.5623	−1.03243
$567$	5.88854	0.247296
$568$	1.76393	0.0740129
$569$	−10.9098	−0.457364	−0.228682	−	0.973501i	$-0.573442\pi$
$569$	−10.9098	−0.457364	−0.228682	+	0.973501i	$0.573442\pi$
$570$	−3.85410	−0.161431
$571$	0.673762	0.0281961	0.0140980	−	0.999901i	$-0.495512\pi$
$571$	0.673762	0.0281961	0.0140980	+	0.999901i	$0.495512\pi$
$572$	−21.6525	−0.905335
$573$	−16.0000	−0.668410
$574$	−8.18034	−0.341441
$575$	28.9443	1.20706
$576$	−0.381966	−0.0159153
$577$	−3.05573	−0.127212	−0.0636058	−	0.997975i	$-0.520260\pi$
$577$	−3.05573	−0.127212	−0.0636058	+	0.997975i	$0.520260\pi$
$578$	−5.56231	−0.231361
$579$	−2.94427	−0.122360
$580$	−10.2361	−0.425030
$581$	−5.70820	−0.236816
$582$	−2.09017	−0.0866403
$583$	−53.3951	−2.21140
$584$	6.38197	0.264088
$585$	−1.32624	−0.0548332
$586$	27.4721	1.13486
$587$	−46.0902	−1.90234	−0.951172	−	0.308660i	$-0.900119\pi$
$587$	−46.0902	−1.90234	−0.951172	+	0.308660i	$0.900119\pi$
$588$	10.3820	0.428145
$589$	−20.7426	−0.854686
$590$	−3.23607	−0.133227
$591$	16.0902	0.661861
$592$	−2.14590	−0.0881959
$593$	0.257354	0.0105683	0.00528414	−	0.999986i	$-0.498318\pi$
$593$	0.257354	0.0105683	0.00528414	+	0.999986i	$0.498318\pi$
$594$	−34.1246	−1.40015
$595$	−2.58359	−0.105917
$596$	−6.56231	−0.268803
$597$	−37.4164	−1.53135
$598$	−25.1246	−1.02742
$599$	−0.742646	−0.0303437	−0.0151718	−	0.999885i	$-0.504830\pi$
$599$	−0.742646	−0.0303437	−0.0151718	+	0.999885i	$0.504830\pi$
$600$	6.47214	0.264224
$601$	−26.0557	−1.06284	−0.531418	−	0.847110i	$-0.678341\pi$
$601$	−26.0557	−1.06284	−0.531418	+	0.847110i	$0.678341\pi$
$602$	2.87539	0.117192
$603$	2.67376	0.108884
$604$	−8.85410	−0.360268
$605$	27.8885	1.13383
$606$	9.09017	0.369263
$607$	5.20163	0.211127	0.105564	−	0.994413i	$-0.466335\pi$
$607$	5.20163	0.211127	0.105564	+	0.994413i	$0.466335\pi$
$608$	2.38197	0.0966015
$609$	−12.6525	−0.512704
$610$	−15.0344	−0.608727
$611$	6.43769	0.260441
$612$	−1.29180	−0.0522178
$613$	−22.9443	−0.926710	−0.463355	−	0.886173i	$-0.653355\pi$
$613$	−22.9443	−0.926710	−0.463355	+	0.886173i	$0.653355\pi$
$614$	−4.67376	−0.188618
$615$	−17.3262	−0.698661
$616$	4.76393	0.191944
$617$	39.8885	1.60585	0.802926	−	0.596079i	$-0.203275\pi$
$617$	39.8885	1.60585	0.802926	+	0.596079i	$0.203275\pi$
$618$	18.5623	0.746685
$619$	−12.8885	−0.518034	−0.259017	−	0.965873i	$-0.583399\pi$
$619$	−12.8885	−0.518034	−0.259017	+	0.965873i	$0.583399\pi$
$620$	−8.70820	−0.349730
$621$	−39.5967	−1.58896
$622$	−1.79837	−0.0721082
$623$	3.01316	0.120720
$624$	−5.61803	−0.224901
$625$	11.0000	0.440000
$626$	−3.67376	−0.146833
$627$	24.0344	0.959843
$628$	13.3820	0.533999
$629$	−7.25735	−0.289370
$630$	0.291796	0.0116254
$631$	40.9230	1.62912	0.814559	−	0.580080i	$-0.196979\pi$
$631$	40.9230	1.62912	0.814559	+	0.580080i	$0.196979\pi$
$632$	−9.61803	−0.382585
$633$	−26.1803	−1.04058
$634$	15.6525	0.621639
$635$	−12.7082	−0.504310
$636$	−13.8541	−0.549351
$637$	−22.2786	−0.882712
$638$	63.8328	2.52717
$639$	−0.673762	−0.0266536
$640$	1.00000	0.0395285
$641$	−36.3607	−1.43616	−0.718080	−	0.695960i	$-0.754979\pi$
$641$	−36.3607	−1.43616	−0.718080	+	0.695960i	$0.754979\pi$
$642$	5.32624	0.210210
$643$	−34.7984	−1.37231	−0.686157	−	0.727454i	$-0.740704\pi$
$643$	−34.7984	−1.37231	−0.686157	+	0.727454i	$0.740704\pi$
$644$	5.52786	0.217828
$645$	6.09017	0.239800
$646$	8.05573	0.316948
$647$	22.9098	0.900678	0.450339	−	0.892858i	$-0.351303\pi$
$647$	22.9098	0.900678	0.450339	+	0.892858i	$0.351303\pi$
$648$	−7.70820	−0.302807
$649$	20.1803	0.792148
$650$	−13.8885	−0.544754
$651$	−10.7639	−0.421872
$652$	−3.14590	−0.123203
$653$	15.8197	0.619071	0.309536	−	0.950888i	$-0.399826\pi$
$653$	15.8197	0.619071	0.309536	+	0.950888i	$0.399826\pi$
$654$	7.61803	0.297889
$655$	7.09017	0.277036
$656$	10.7082	0.418085
$657$	−2.43769	−0.0951035
$658$	−1.41641	−0.0552173
$659$	32.3607	1.26059	0.630297	−	0.776354i	$-0.282933\pi$
$659$	32.3607	1.26059	0.630297	+	0.776354i	$0.282933\pi$
$660$	10.0902	0.392759
$661$	8.79837	0.342217	0.171109	−	0.985252i	$-0.445265\pi$
$661$	8.79837	0.342217	0.171109	+	0.985252i	$0.445265\pi$
$662$	−7.67376	−0.298249
$663$	−19.0000	−0.737899
$664$	7.47214	0.289975
$665$	−1.81966	−0.0705634
$666$	0.819660	0.0317612
$667$	74.0689	2.86796
$668$	14.4164	0.557788
$669$	−27.1803	−1.05085
$670$	−7.00000	−0.270434
$671$	93.7558	3.61940
$672$	1.23607	0.0476824
$673$	−14.4377	−0.556532	−0.278266	−	0.960504i	$-0.589760\pi$
$673$	−14.4377	−0.556532	−0.278266	+	0.960504i	$0.589760\pi$
$674$	19.7984	0.762605
$675$	−21.8885	−0.842490
$676$	−0.944272	−0.0363182
$677$	0.111456	0.00428361	0.00214180	−	0.999998i	$-0.499318\pi$
$677$	0.111456	0.00428361	0.00214180	+	0.999998i	$0.499318\pi$
$678$	−11.4721	−0.440585
$679$	−0.986844	−0.0378716
$680$	3.38197	0.129692
$681$	3.23607	0.124006
$682$	54.3050	2.07944
$683$	9.74265	0.372792	0.186396	−	0.982475i	$-0.440319\pi$
$683$	9.74265	0.372792	0.186396	+	0.982475i	$0.440319\pi$
$684$	−0.909830	−0.0347882
$685$	−8.41641	−0.321574
$686$	10.2492	0.391317
$687$	−1.61803	−0.0617318
$688$	−3.76393	−0.143499
$689$	29.7295	1.13260
$690$	11.7082	0.445724
$691$	29.2705	1.11350	0.556751	−	0.830679i	$-0.312048\pi$
$691$	29.2705	1.11350	0.556751	+	0.830679i	$0.312048\pi$
$692$	15.5623	0.591590
$693$	−1.81966	−0.0691232
$694$	−9.67376	−0.367211
$695$	6.00000	0.227593
$696$	16.5623	0.627793
$697$	36.2148	1.37173
$698$	9.65248	0.365352
$699$	41.9787	1.58778
$700$	3.05573	0.115496
$701$	−46.2492	−1.74681	−0.873405	−	0.486995i	$-0.838093\pi$
$701$	−46.2492	−1.74681	−0.873405	+	0.486995i	$0.838093\pi$
$702$	19.0000	0.717109
$703$	−5.11146	−0.192782
$704$	−6.23607	−0.235031
$705$	−3.00000	−0.112987
$706$	8.76393	0.329835
$707$	4.29180	0.161410
$708$	5.23607	0.196783
$709$	20.4721	0.768847	0.384424	−	0.923157i	$-0.374400\pi$
$709$	20.4721	0.768847	0.384424	+	0.923157i	$0.374400\pi$
$710$	1.76393	0.0661992
$711$	3.67376	0.137777
$712$	−3.94427	−0.147818
$713$	63.0132	2.35986
$714$	4.18034	0.156445
$715$	−21.6525	−0.809757
$716$	20.4721	0.765080
$717$	−18.0902	−0.675590
$718$	−15.7984	−0.589590
$719$	7.59675	0.283311	0.141655	−	0.989916i	$-0.454757\pi$
$719$	7.59675	0.283311	0.141655	+	0.989916i	$0.454757\pi$
$720$	−0.381966	−0.0142350
$721$	8.76393	0.326386
$722$	−13.3262	−0.495951
$723$	−34.4164	−1.27996
$724$	−1.29180	−0.0480092
$725$	40.9443	1.52063
$726$	−45.1246	−1.67473
$727$	37.4721	1.38976	0.694882	−	0.719123i	$-0.255456\pi$
$727$	37.4721	1.38976	0.694882	+	0.719123i	$0.255456\pi$
$728$	−2.65248	−0.0983073
$729$	29.5066	1.09284
$730$	6.38197	0.236207
$731$	−12.7295	−0.470817
$732$	24.3262	0.899124
$733$	3.97871	0.146957	0.0734786	−	0.997297i	$-0.476590\pi$
$733$	3.97871	0.146957	0.0734786	+	0.997297i	$0.476590\pi$
$734$	−3.12461	−0.115332
$735$	10.3820	0.382945
$736$	−7.23607	−0.266725
$737$	43.6525	1.60796
$738$	−4.09017	−0.150561
$739$	37.7082	1.38712	0.693559	−	0.720399i	$-0.256042\pi$
$739$	37.7082	1.38712	0.693559	+	0.720399i	$0.256042\pi$
$740$	−2.14590	−0.0788848
$741$	−13.3820	−0.491599
$742$	−6.54102	−0.240128
$743$	−23.1803	−0.850404	−0.425202	−	0.905098i	$-0.639797\pi$
$743$	−23.1803	−0.850404	−0.425202	+	0.905098i	$0.639797\pi$
$744$	14.0902	0.516571
$745$	−6.56231	−0.240424
$746$	6.94427	0.254248
$747$	−2.85410	−0.104426
$748$	−21.0902	−0.771133
$749$	2.51471	0.0918854
$750$	14.5623	0.531740
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	1.85410	0.0676121
$753$	−18.5623	−0.676448
$754$	−35.5410	−1.29433
$755$	−8.85410	−0.322234
$756$	−4.18034	−0.152037
$757$	−22.9230	−0.833150	−0.416575	−	0.909101i	$-0.636770\pi$
$757$	−22.9230	−0.833150	−0.416575	+	0.909101i	$0.636770\pi$
$758$	−14.6738	−0.532975
$759$	−73.0132	−2.65021
$760$	2.38197	0.0864030
$761$	−11.1246	−0.403267	−0.201633	−	0.979461i	$-0.564625\pi$
$761$	−11.1246	−0.403267	−0.201633	+	0.979461i	$0.564625\pi$
$762$	20.5623	0.744894
$763$	3.59675	0.130211
$764$	9.88854	0.357755
$765$	−1.29180	−0.0467050
$766$	3.27051	0.118168
$767$	−11.2361	−0.405711
$768$	−1.61803	−0.0583858
$769$	−4.21478	−0.151989	−0.0759945	−	0.997108i	$-0.524213\pi$
$769$	−4.21478	−0.151989	−0.0759945	+	0.997108i	$0.524213\pi$
$770$	4.76393	0.171680
$771$	−18.3262	−0.660003
$772$	1.81966	0.0654910
$773$	−25.3607	−0.912160	−0.456080	−	0.889939i	$-0.650747\pi$
$773$	−25.3607	−0.912160	−0.456080	+	0.889939i	$0.650747\pi$
$774$	1.43769	0.0516768
$775$	34.8328	1.25123
$776$	1.29180	0.0463728
$777$	−2.65248	−0.0951570
$778$	−8.29180	−0.297275
$779$	25.5066	0.913868
$780$	−5.61803	−0.201158
$781$	−11.0000	−0.393611
$782$	−24.4721	−0.875122
$783$	−56.0132	−2.00175
$784$	−6.41641	−0.229157
$785$	13.3820	0.477623
$786$	−11.4721	−0.409198
$787$	−50.0902	−1.78552	−0.892761	−	0.450531i	$-0.851235\pi$
$787$	−50.0902	−1.78552	−0.892761	+	0.450531i	$0.851235\pi$
$788$	−9.94427	−0.354250
$789$	−7.94427	−0.282824
$790$	−9.61803	−0.342194
$791$	−5.41641	−0.192585
$792$	2.38197	0.0846395
$793$	−52.2016	−1.85373
$794$	−1.90983	−0.0677773
$795$	−13.8541	−0.491354
$796$	23.1246	0.819630
$797$	50.9787	1.80576	0.902879	−	0.429894i	$-0.141449\pi$
$797$	50.9787	1.80576	0.902879	+	0.429894i	$0.141449\pi$
$798$	2.94427	0.104226
$799$	6.27051	0.221835
$800$	−4.00000	−0.141421
$801$	1.50658	0.0532323
$802$	−18.4164	−0.650306
$803$	−39.7984	−1.40445
$804$	11.3262	0.399446
$805$	5.52786	0.194832
$806$	−30.2361	−1.06502
$807$	42.5967	1.49948
$808$	−5.61803	−0.197642
$809$	−43.0689	−1.51422	−0.757111	−	0.653287i	$-0.773390\pi$
$809$	−43.0689	−1.51422	−0.757111	+	0.653287i	$0.773390\pi$
$810$	−7.70820	−0.270839
$811$	26.2705	0.922482	0.461241	−	0.887275i	$-0.347404\pi$
$811$	26.2705	0.922482	0.461241	+	0.887275i	$0.347404\pi$
$812$	7.81966	0.274416
$813$	−9.09017	−0.318806
$814$	13.3820	0.469038
$815$	−3.14590	−0.110196
$816$	−5.47214	−0.191563
$817$	−8.96556	−0.313665
$818$	2.70820	0.0946901
$819$	1.01316	0.0354025
$820$	10.7082	0.373947
$821$	−24.2918	−0.847790	−0.423895	−	0.905711i	$-0.639337\pi$
$821$	−24.2918	−0.847790	−0.423895	+	0.905711i	$0.639337\pi$
$822$	13.6180	0.474983
$823$	−33.1459	−1.15539	−0.577697	−	0.816252i	$-0.696048\pi$
$823$	−33.1459	−1.15539	−0.577697	+	0.816252i	$0.696048\pi$
$824$	−11.4721	−0.399651
$825$	−40.3607	−1.40518
$826$	2.47214	0.0860166
$827$	8.88854	0.309085	0.154542	−	0.987986i	$-0.450610\pi$
$827$	8.88854	0.309085	0.154542	+	0.987986i	$0.450610\pi$
$828$	2.76393	0.0960533
$829$	−6.05573	−0.210324	−0.105162	−	0.994455i	$-0.533536\pi$
$829$	−6.05573	−0.210324	−0.105162	+	0.994455i	$0.533536\pi$
$830$	7.47214	0.259362
$831$	48.5066	1.68267
$832$	3.47214	0.120375
$833$	−21.7001	−0.751863
$834$	−9.70820	−0.336168
$835$	14.4164	0.498900
$836$	−14.8541	−0.513740
$837$	−47.6525	−1.64711
$838$	−21.9787	−0.759242
$839$	−22.9098	−0.790935	−0.395468	−	0.918480i	$-0.629417\pi$
$839$	−22.9098	−0.790935	−0.395468	+	0.918480i	$0.629417\pi$
$840$	1.23607	0.0426484
$841$	75.7771	2.61300
$842$	−1.05573	−0.0363828
$843$	−46.6525	−1.60680
$844$	16.1803	0.556950
$845$	−0.944272	−0.0324839
$846$	−0.708204	−0.0243486
$847$	−21.3050	−0.732047
$848$	8.56231	0.294031
$849$	39.7426	1.36396
$850$	−13.5279	−0.464002
$851$	15.5279	0.532288
$852$	−2.85410	−0.0977799
$853$	−33.3951	−1.14343	−0.571714	−	0.820453i	$-0.693721\pi$
$853$	−33.3951	−1.14343	−0.571714	+	0.820453i	$0.693721\pi$
$854$	11.4853	0.393019
$855$	−0.909830	−0.0311155
$856$	−3.29180	−0.112511
$857$	−44.2148	−1.51035	−0.755174	−	0.655524i	$-0.772448\pi$
$857$	−44.2148	−1.51035	−0.755174	+	0.655524i	$0.772448\pi$
$858$	35.0344	1.19606
$859$	−9.21478	−0.314404	−0.157202	−	0.987566i	$-0.550247\pi$
$859$	−9.21478	−0.314404	−0.157202	+	0.987566i	$0.550247\pi$
$860$	−3.76393	−0.128349
$861$	13.2361	0.451084
$862$	12.5967	0.429047
$863$	−23.6180	−0.803967	−0.401984	−	0.915647i	$-0.631679\pi$
$863$	−23.6180	−0.803967	−0.401984	+	0.915647i	$0.631679\pi$
$864$	5.47214	0.186166
$865$	15.5623	0.529134
$866$	−18.9443	−0.643753
$867$	9.00000	0.305656
$868$	6.65248	0.225800
$869$	59.9787	2.03464
$870$	16.5623	0.561515
$871$	−24.3050	−0.823542
$872$	−4.70820	−0.159440
$873$	−0.493422	−0.0166998
$874$	−17.2361	−0.583019
$875$	6.87539	0.232431
$876$	−10.3262	−0.348891
$877$	−37.3951	−1.26274	−0.631372	−	0.775480i	$-0.717508\pi$
$877$	−37.3951	−1.26274	−0.631372	+	0.775480i	$0.717508\pi$
$878$	−21.0689	−0.711040
$879$	−44.4508	−1.49929
$880$	−6.23607	−0.210218
$881$	−0.381966	−0.0128688	−0.00643438	−	0.999979i	$-0.502048\pi$
$881$	−0.381966	−0.0128688	−0.00643438	+	0.999979i	$0.502048\pi$
$882$	2.45085	0.0825244
$883$	34.7771	1.17034	0.585171	−	0.810910i	$-0.301027\pi$
$883$	34.7771	1.17034	0.585171	+	0.810910i	$0.301027\pi$
$884$	11.7426	0.394948
$885$	5.23607	0.176008
$886$	−23.4164	−0.786690
$887$	11.9443	0.401049	0.200525	−	0.979689i	$-0.435735\pi$
$887$	11.9443	0.401049	0.200525	+	0.979689i	$0.435735\pi$
$888$	3.47214	0.116517
$889$	9.70820	0.325603
$890$	−3.94427	−0.132212
$891$	48.0689	1.61037
$892$	16.7984	0.562451
$893$	4.41641	0.147789
$894$	10.6180	0.355120
$895$	20.4721	0.684308
$896$	−0.763932	−0.0255212
$897$	40.6525	1.35735
$898$	36.8885	1.23099
$899$	89.1378	2.97291
$900$	1.52786	0.0509288
$901$	28.9574	0.964712
$902$	−66.7771	−2.22343
$903$	−4.65248	−0.154825
$904$	7.09017	0.235816
$905$	−1.29180	−0.0429408
$906$	14.3262	0.475957
$907$	−7.00000	−0.232431	−0.116216	−	0.993224i	$-0.537076\pi$
$907$	−7.00000	−0.232431	−0.116216	+	0.993224i	$0.537076\pi$
$908$	−2.00000	−0.0663723
$909$	2.14590	0.0711749
$910$	−2.65248	−0.0879287
$911$	−12.6738	−0.419900	−0.209950	−	0.977712i	$-0.567330\pi$
$911$	−12.6738	−0.419900	−0.209950	+	0.977712i	$0.567330\pi$
$912$	−3.85410	−0.127622
$913$	−46.5967	−1.54213
$914$	21.3262	0.705409
$915$	24.3262	0.804201
$916$	1.00000	0.0330409
$917$	−5.41641	−0.178866
$918$	18.5066	0.610808
$919$	−41.7214	−1.37626	−0.688130	−	0.725587i	$-0.741568\pi$
$919$	−41.7214	−1.37626	−0.688130	+	0.725587i	$0.741568\pi$
$920$	−7.23607	−0.238566
$921$	7.56231	0.249186
$922$	−21.6180	−0.711952
$923$	6.12461	0.201594
$924$	−7.70820	−0.253581
$925$	8.58359	0.282227
$926$	−29.1803	−0.958925
$927$	4.38197	0.143923
$928$	−10.2361	−0.336015
$929$	5.65248	0.185452	0.0927259	−	0.995692i	$-0.470442\pi$
$929$	5.65248	0.185452	0.0927259	+	0.995692i	$0.470442\pi$
$930$	14.0902	0.462035
$931$	−15.2837	−0.500902
$932$	−25.9443	−0.849833
$933$	2.90983	0.0952636
$934$	17.1246	0.560334
$935$	−21.0902	−0.689722
$936$	−1.32624	−0.0433494
$937$	−22.3050	−0.728671	−0.364336	−	0.931268i	$-0.618704\pi$
$937$	−22.3050	−0.728671	−0.364336	+	0.931268i	$0.618704\pi$
$938$	5.34752	0.174603
$939$	5.94427	0.193984
$940$	1.85410	0.0604741
$941$	11.1246	0.362652	0.181326	−	0.983423i	$-0.441961\pi$
$941$	11.1246	0.362652	0.181326	+	0.983423i	$0.441961\pi$
$942$	−21.6525	−0.705476
$943$	−77.4853	−2.52327
$944$	−3.23607	−0.105325
$945$	−4.18034	−0.135986
$946$	23.4721	0.763145
$947$	5.70820	0.185492	0.0927459	−	0.995690i	$-0.470436\pi$
$947$	5.70820	0.185492	0.0927459	+	0.995690i	$0.470436\pi$
$948$	15.5623	0.505440
$949$	22.1591	0.719313
$950$	−9.52786	−0.309125
$951$	−25.3262	−0.821260
$952$	−2.58359	−0.0837347
$953$	−29.4721	−0.954696	−0.477348	−	0.878714i	$-0.658402\pi$
$953$	−29.4721	−0.954696	−0.477348	+	0.878714i	$0.658402\pi$
$954$	−3.27051	−0.105887
$955$	9.88854	0.319986
$956$	11.1803	0.361598
$957$	−103.284	−3.33869
$958$	−9.41641	−0.304230
$959$	6.42956	0.207621
$960$	−1.61803	−0.0522218
$961$	44.8328	1.44622
$962$	−7.45085	−0.240225
$963$	1.25735	0.0405177
$964$	21.2705	0.685077
$965$	1.81966	0.0585769
$966$	−8.94427	−0.287777
$967$	3.20163	0.102957	0.0514787	−	0.998674i	$-0.483607\pi$
$967$	3.20163	0.102957	0.0514787	+	0.998674i	$0.483607\pi$
$968$	27.8885	0.896372
$969$	−13.0344	−0.418727
$970$	1.29180	0.0414771
$971$	34.4721	1.10626	0.553132	−	0.833094i	$-0.313433\pi$
$971$	34.4721	1.10626	0.553132	+	0.833094i	$0.313433\pi$
$972$	−3.94427	−0.126513
$973$	−4.58359	−0.146943
$974$	25.0689	0.803259
$975$	22.4721	0.719684
$976$	−15.0344	−0.481241
$977$	−31.9787	−1.02309	−0.511545	−	0.859257i	$-0.670927\pi$
$977$	−31.9787	−1.02309	−0.511545	+	0.859257i	$0.670927\pi$
$978$	5.09017	0.162766
$979$	24.5967	0.786115
$980$	−6.41641	−0.204965
$981$	1.79837	0.0574177
$982$	−32.7771	−1.04596
$983$	−20.5279	−0.654737	−0.327369	−	0.944897i	$-0.606162\pi$
$983$	−20.5279	−0.654737	−0.327369	+	0.944897i	$0.606162\pi$
$984$	−17.3262	−0.552340
$985$	−9.94427	−0.316851
$986$	−34.6180	−1.10246
$987$	2.29180	0.0729487
$988$	8.27051	0.263120
$989$	27.2361	0.866057
$990$	2.38197	0.0757038
$991$	5.03444	0.159924	0.0799622	−	0.996798i	$-0.474520\pi$
$991$	5.03444	0.159924	0.0799622	+	0.996798i	$0.474520\pi$
$992$	−8.70820	−0.276486
$993$	12.4164	0.394023
$994$	−1.34752	−0.0427409
$995$	23.1246	0.733099
$996$	−12.0902	−0.383092
$997$	53.6312	1.69852	0.849258	−	0.527977i	$-0.177049\pi$
$997$	53.6312	1.69852	0.849258	+	0.527977i	$0.177049\pi$
$998$	−19.1246	−0.605379
$999$	−11.7426	−0.371521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.d.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.d.1.1	✓	2	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.763932 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.61803 q^{6} -0.763932 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.00000 q^{10} -6.23607 q^{11} -1.61803 q^{12} +3.47214 q^{13} -0.763932 q^{14} -1.61803 q^{15} +1.00000 q^{16} +3.38197 q^{17} -0.381966 q^{18} +2.38197 q^{19} +1.00000 q^{20} +1.23607 q^{21} -6.23607 q^{22} -7.23607 q^{23} -1.61803 q^{24} -4.00000 q^{25} +3.47214 q^{26} +5.47214 q^{27} -0.763932 q^{28} -10.2361 q^{29} -1.61803 q^{30} -8.70820 q^{31} +1.00000 q^{32} +10.0902 q^{33} +3.38197 q^{34} -0.763932 q^{35} -0.381966 q^{36} -2.14590 q^{37} +2.38197 q^{38} -5.61803 q^{39} +1.00000 q^{40} +10.7082 q^{41} +1.23607 q^{42} -3.76393 q^{43} -6.23607 q^{44} -0.381966 q^{45} -7.23607 q^{46} +1.85410 q^{47} -1.61803 q^{48} -6.41641 q^{49} -4.00000 q^{50} -5.47214 q^{51} +3.47214 q^{52} +8.56231 q^{53} +5.47214 q^{54} -6.23607 q^{55} -0.763932 q^{56} -3.85410 q^{57} -10.2361 q^{58} -3.23607 q^{59} -1.61803 q^{60} -15.0344 q^{61} -8.70820 q^{62} +0.291796 q^{63} +1.00000 q^{64} +3.47214 q^{65} +10.0902 q^{66} -7.00000 q^{67} +3.38197 q^{68} +11.7082 q^{69} -0.763932 q^{70} +1.76393 q^{71} -0.381966 q^{72} +6.38197 q^{73} -2.14590 q^{74} +6.47214 q^{75} +2.38197 q^{76} +4.76393 q^{77} -5.61803 q^{78} -9.61803 q^{79} +1.00000 q^{80} -7.70820 q^{81} +10.7082 q^{82} +7.47214 q^{83} +1.23607 q^{84} +3.38197 q^{85} -3.76393 q^{86} +16.5623 q^{87} -6.23607 q^{88} -3.94427 q^{89} -0.381966 q^{90} -2.65248 q^{91} -7.23607 q^{92} +14.0902 q^{93} +1.85410 q^{94} +2.38197 q^{95} -1.61803 q^{96} +1.29180 q^{97} -6.41641 q^{98} +2.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 6 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 6 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} - q^{6} - 6 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} - 8 q^{11} - q^{12} - 2 q^{13} - 6 q^{14} - q^{15} + 2 q^{16} + 9 q^{17} - 3 q^{18} + 7 q^{19} + 2 q^{20} - 2 q^{21} - 8 q^{22} - 10 q^{23} - q^{24} - 8 q^{25} - 2 q^{26} + 2 q^{27} - 6 q^{28} - 16 q^{29} - q^{30} - 4 q^{31} + 2 q^{32} + 9 q^{33} + 9 q^{34} - 6 q^{35} - 3 q^{36} - 11 q^{37} + 7 q^{38} - 9 q^{39} + 2 q^{40} + 8 q^{41} - 2 q^{42} - 12 q^{43} - 8 q^{44} - 3 q^{45} - 10 q^{46} - 3 q^{47} - q^{48} + 14 q^{49} - 8 q^{50} - 2 q^{51} - 2 q^{52} - 3 q^{53} + 2 q^{54} - 8 q^{55} - 6 q^{56} - q^{57} - 16 q^{58} - 2 q^{59} - q^{60} - q^{61} - 4 q^{62} + 14 q^{63} + 2 q^{64} - 2 q^{65} + 9 q^{66} - 14 q^{67} + 9 q^{68} + 10 q^{69} - 6 q^{70} + 8 q^{71} - 3 q^{72} + 15 q^{73} - 11 q^{74} + 4 q^{75} + 7 q^{76} + 14 q^{77} - 9 q^{78} - 17 q^{79} + 2 q^{80} - 2 q^{81} + 8 q^{82} + 6 q^{83} - 2 q^{84} + 9 q^{85} - 12 q^{86} + 13 q^{87} - 8 q^{88} + 10 q^{89} - 3 q^{90} + 26 q^{91} - 10 q^{92} + 17 q^{93} - 3 q^{94} + 7 q^{95} - q^{96} + 16 q^{97} + 14 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 - q^6 - 6 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 - 8 * q^11 - q^12 - 2 * q^13 - 6 * q^14 - q^15 + 2 * q^16 + 9 * q^17 - 3 * q^18 + 7 * q^19 + 2 * q^20 - 2 * q^21 - 8 * q^22 - 10 * q^23 - q^24 - 8 * q^25 - 2 * q^26 + 2 * q^27 - 6 * q^28 - 16 * q^29 - q^30 - 4 * q^31 + 2 * q^32 + 9 * q^33 + 9 * q^34 - 6 * q^35 - 3 * q^36 - 11 * q^37 + 7 * q^38 - 9 * q^39 + 2 * q^40 + 8 * q^41 - 2 * q^42 - 12 * q^43 - 8 * q^44 - 3 * q^45 - 10 * q^46 - 3 * q^47 - q^48 + 14 * q^49 - 8 * q^50 - 2 * q^51 - 2 * q^52 - 3 * q^53 + 2 * q^54 - 8 * q^55 - 6 * q^56 - q^57 - 16 * q^58 - 2 * q^59 - q^60 - q^61 - 4 * q^62 + 14 * q^63 + 2 * q^64 - 2 * q^65 + 9 * q^66 - 14 * q^67 + 9 * q^68 + 10 * q^69 - 6 * q^70 + 8 * q^71 - 3 * q^72 + 15 * q^73 - 11 * q^74 + 4 * q^75 + 7 * q^76 + 14 * q^77 - 9 * q^78 - 17 * q^79 + 2 * q^80 - 2 * q^81 + 8 * q^82 + 6 * q^83 - 2 * q^84 + 9 * q^85 - 12 * q^86 + 13 * q^87 - 8 * q^88 + 10 * q^89 - 3 * q^90 + 26 * q^91 - 10 * q^92 + 17 * q^93 - 3 * q^94 + 7 * q^95 - q^96 + 16 * q^97 + 14 * q^98 + 7 * q^99

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