LMFDB - Embedded newform 667.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 $ x^13 - 4x^12 - 11x^11 + 58x^10 + 24x^9 - 298x^8 + 97x^7 + 641x^6 - 402x^5 - 547x^4 + 352x^3 + 219x^2 - 88x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.397523$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.397523 q^{2} -0.0679369 q^{3} -1.84198 q^{4} -3.16986 q^{5} +0.0270065 q^{6} -1.67469 q^{7} +1.52727 q^{8} -2.99538 q^{9} +O(q^{10})$	\(q-0.397523 q^{2} -0.0679369 q^{3} -1.84198 q^{4} -3.16986 q^{5} +0.0270065 q^{6} -1.67469 q^{7} +1.52727 q^{8} -2.99538 q^{9} +1.26009 q^{10} +1.35258 q^{11} +0.125138 q^{12} -0.657616 q^{13} +0.665727 q^{14} +0.215350 q^{15} +3.07682 q^{16} +4.41950 q^{17} +1.19074 q^{18} -0.226826 q^{19} +5.83880 q^{20} +0.113773 q^{21} -0.537681 q^{22} -1.00000 q^{23} -0.103758 q^{24} +5.04800 q^{25} +0.261418 q^{26} +0.407308 q^{27} +3.08473 q^{28} +1.00000 q^{29} -0.0856067 q^{30} +9.64062 q^{31} -4.27766 q^{32} -0.0918898 q^{33} -1.75685 q^{34} +5.30852 q^{35} +5.51742 q^{36} +2.51972 q^{37} +0.0901685 q^{38} +0.0446764 q^{39} -4.84124 q^{40} -7.69417 q^{41} -0.0452274 q^{42} +1.41633 q^{43} -2.49141 q^{44} +9.49494 q^{45} +0.397523 q^{46} +1.67270 q^{47} -0.209030 q^{48} -4.19543 q^{49} -2.00670 q^{50} -0.300247 q^{51} +1.21131 q^{52} +7.39704 q^{53} -0.161914 q^{54} -4.28747 q^{55} -2.55771 q^{56} +0.0154098 q^{57} -0.397523 q^{58} +6.61560 q^{59} -0.396670 q^{60} +0.912075 q^{61} -3.83237 q^{62} +5.01633 q^{63} -4.45318 q^{64} +2.08455 q^{65} +0.0365283 q^{66} -3.75542 q^{67} -8.14060 q^{68} +0.0679369 q^{69} -2.11026 q^{70} +14.6425 q^{71} -4.57478 q^{72} -3.28531 q^{73} -1.00165 q^{74} -0.342945 q^{75} +0.417807 q^{76} -2.26514 q^{77} -0.0177599 q^{78} -14.7355 q^{79} -9.75309 q^{80} +8.95848 q^{81} +3.05861 q^{82} -10.3184 q^{83} -0.209567 q^{84} -14.0092 q^{85} -0.563026 q^{86} -0.0679369 q^{87} +2.06576 q^{88} +14.5878 q^{89} -3.77446 q^{90} +1.10130 q^{91} +1.84198 q^{92} -0.654954 q^{93} -0.664939 q^{94} +0.719005 q^{95} +0.290611 q^{96} -9.17309 q^{97} +1.66778 q^{98} -4.05149 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * 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 $

$2$	−0.397523	−0.281091	−0.140546	−	0.990074i	$-0.544886\pi$
$2$	−0.397523	−0.281091	−0.140546	+	0.990074i	$0.544886\pi$
$3$	−0.0679369	−0.0392234	−0.0196117	−	0.999808i	$-0.506243\pi$
$3$	−0.0679369	−0.0392234	−0.0196117	+	0.999808i	$0.506243\pi$
$4$	−1.84198	−0.920988
$5$	−3.16986	−1.41760	−0.708802	−	0.705408i	$-0.750764\pi$
$5$	−3.16986	−1.41760	−0.708802	+	0.705408i	$0.750764\pi$
$6$	0.0270065	0.0110254
$7$	−1.67469	−0.632972	−0.316486	−	0.948597i	$-0.602503\pi$
$7$	−1.67469	−0.632972	−0.316486	+	0.948597i	$0.602503\pi$
$8$	1.52727	0.539973
$9$	−2.99538	−0.998462
$10$	1.26009	0.398476
$11$	1.35258	0.407817	0.203909	−	0.978990i	$-0.434635\pi$
$11$	1.35258	0.407817	0.203909	+	0.978990i	$0.434635\pi$
$12$	0.125138	0.0361242
$13$	−0.657616	−0.182390	−0.0911949	−	0.995833i	$-0.529069\pi$
$13$	−0.657616	−0.182390	−0.0911949	+	0.995833i	$0.529069\pi$
$14$	0.665727	0.177923
$15$	0.215350	0.0556032
$16$	3.07682	0.769206
$17$	4.41950	1.07189	0.535943	−	0.844254i	$-0.319956\pi$
$17$	4.41950	1.07189	0.535943	+	0.844254i	$0.319956\pi$
$18$	1.19074	0.280659
$19$	−0.226826	−0.0520374	−0.0260187	−	0.999661i	$-0.508283\pi$
$19$	−0.226826	−0.0520374	−0.0260187	+	0.999661i	$0.508283\pi$
$20$	5.83880	1.30560
$21$	0.113773	0.0248273
$22$	−0.537681	−0.114634
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.103758	−0.0211796
$25$	5.04800	1.00960
$26$	0.261418	0.0512682
$27$	0.407308	0.0783864
$28$	3.08473	0.582959
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.0856067	−0.0156296
$31$	9.64062	1.73151	0.865754	−	0.500470i	$-0.166840\pi$
$31$	9.64062	1.73151	0.865754	+	0.500470i	$0.166840\pi$
$32$	−4.27766	−0.756190
$33$	−0.0918898	−0.0159960
$34$	−1.75685	−0.301298
$35$	5.30852	0.897303
$36$	5.51742	0.919571
$37$	2.51972	0.414240	0.207120	−	0.978316i	$-0.433591\pi$
$37$	2.51972	0.414240	0.207120	+	0.978316i	$0.433591\pi$
$38$	0.0901685	0.0146273
$39$	0.0446764	0.00715394
$40$	−4.84124	−0.765468
$41$	−7.69417	−1.20163	−0.600814	−	0.799389i	$-0.705157\pi$
$41$	−7.69417	−1.20163	−0.600814	+	0.799389i	$0.705157\pi$
$42$	−0.0452274	−0.00697874
$43$	1.41633	0.215989	0.107995	−	0.994151i	$-0.465557\pi$
$43$	1.41633	0.215989	0.107995	+	0.994151i	$0.465557\pi$
$44$	−2.49141	−0.375595
$45$	9.49494	1.41542
$46$	0.397523	0.0586116
$47$	1.67270	0.243989	0.121995	−	0.992531i	$-0.461071\pi$
$47$	1.67270	0.243989	0.121995	+	0.992531i	$0.461071\pi$
$48$	−0.209030	−0.0301708
$49$	−4.19543	−0.599347
$50$	−2.00670	−0.283790
$51$	−0.300247	−0.0420429
$52$	1.21131	0.167979
$53$	7.39704	1.01606	0.508031	−	0.861339i	$-0.330374\pi$
$53$	7.39704	1.01606	0.508031	+	0.861339i	$0.330374\pi$
$54$	−0.161914	−0.0220337
$55$	−4.28747	−0.578123
$56$	−2.55771	−0.341788
$57$	0.0154098	0.00204108
$58$	−0.397523	−0.0521974
$59$	6.61560	0.861278	0.430639	−	0.902524i	$-0.358288\pi$
$59$	6.61560	0.861278	0.430639	+	0.902524i	$0.358288\pi$
$60$	−0.396670	−0.0512098
$61$	0.912075	0.116779	0.0583896	−	0.998294i	$-0.481403\pi$
$61$	0.912075	0.116779	0.0583896	+	0.998294i	$0.481403\pi$
$62$	−3.83237	−0.486712
$63$	5.01633	0.631998
$64$	−4.45318	−0.556647
$65$	2.08455	0.258556
$66$	0.0365283	0.00449633
$67$	−3.75542	−0.458798	−0.229399	−	0.973332i	$-0.573676\pi$
$67$	−3.75542	−0.458798	−0.229399	+	0.973332i	$0.573676\pi$
$68$	−8.14060	−0.987193
$69$	0.0679369	0.00817864
$70$	−2.11026	−0.252224
$71$	14.6425	1.73774	0.868872	−	0.495036i	$-0.164845\pi$
$71$	14.6425	1.73774	0.868872	+	0.495036i	$0.164845\pi$
$72$	−4.57478	−0.539142
$73$	−3.28531	−0.384516	−0.192258	−	0.981344i	$-0.561581\pi$
$73$	−3.28531	−0.384516	−0.192258	+	0.981344i	$0.561581\pi$
$74$	−1.00165	−0.116439
$75$	−0.342945	−0.0395999
$76$	0.417807	0.0479258
$77$	−2.26514	−0.258137
$78$	−0.0177599	−0.00201091
$79$	−14.7355	−1.65788	−0.828939	−	0.559340i	$-0.811055\pi$
$79$	−14.7355	−1.65788	−0.828939	+	0.559340i	$0.811055\pi$
$80$	−9.75309	−1.09043
$81$	8.95848	0.995387
$82$	3.05861	0.337767
$83$	−10.3184	−1.13259	−0.566295	−	0.824203i	$-0.691624\pi$
$83$	−10.3184	−1.13259	−0.566295	+	0.824203i	$0.691624\pi$
$84$	−0.209567	−0.0228656
$85$	−14.0092	−1.51951
$86$	−0.563026	−0.0607127
$87$	−0.0679369	−0.00728360
$88$	2.06576	0.220210
$89$	14.5878	1.54630	0.773152	−	0.634221i	$-0.218679\pi$
$89$	14.5878	1.54630	0.773152	+	0.634221i	$0.218679\pi$
$90$	−3.77446	−0.397863
$91$	1.10130	0.115448
$92$	1.84198	0.192039
$93$	−0.654954	−0.0679155
$94$	−0.664939	−0.0685832
$95$	0.719005	0.0737683
$96$	0.290611	0.0296603
$97$	−9.17309	−0.931386	−0.465693	−	0.884946i	$-0.654195\pi$
$97$	−9.17309	−0.931386	−0.465693	+	0.884946i	$0.654195\pi$
$98$	1.66778	0.168471
$99$	−4.05149	−0.407190
$100$	−9.29829	−0.929829
$101$	0.636772	0.0633612	0.0316806	−	0.999498i	$-0.489914\pi$
$101$	0.636772	0.0633612	0.0316806	+	0.999498i	$0.489914\pi$
$102$	0.119355	0.0118179
$103$	12.3245	1.21437	0.607183	−	0.794562i	$-0.292299\pi$
$103$	12.3245	1.21437	0.607183	+	0.794562i	$0.292299\pi$
$104$	−1.00436	−0.0984856
$105$	−0.360644	−0.0351952
$106$	−2.94050	−0.285606
$107$	17.0007	1.64352	0.821760	−	0.569834i	$-0.192992\pi$
$107$	17.0007	1.64352	0.821760	+	0.569834i	$0.192992\pi$
$108$	−0.750250	−0.0721929
$109$	2.98969	0.286360	0.143180	−	0.989697i	$-0.454267\pi$
$109$	2.98969	0.286360	0.143180	+	0.989697i	$0.454267\pi$
$110$	1.70437	0.162505
$111$	−0.171182	−0.0162479
$112$	−5.15271	−0.486886
$113$	3.83318	0.360595	0.180298	−	0.983612i	$-0.442294\pi$
$113$	3.83318	0.360595	0.180298	+	0.983612i	$0.442294\pi$
$114$	−0.00612576	−0.000573730 0
$115$	3.16986	0.295591
$116$	−1.84198	−0.171023
$117$	1.96981	0.182109
$118$	−2.62986	−0.242098
$119$	−7.40127	−0.678473
$120$	0.328899	0.0300242
$121$	−9.17054	−0.833685
$122$	−0.362571	−0.0328257
$123$	0.522718	0.0471319
$124$	−17.7578	−1.59470
$125$	−0.152151	−0.0136088
$126$	−1.99411	−0.177649
$127$	9.31467	0.826543	0.413271	−	0.910608i	$-0.364386\pi$
$127$	9.31467	0.826543	0.413271	+	0.910608i	$0.364386\pi$
$128$	10.3256	0.912659
$129$	−0.0962213	−0.00847182
$130$	−0.828657	−0.0726780
$131$	4.17017	0.364349	0.182175	−	0.983266i	$-0.441686\pi$
$131$	4.17017	0.364349	0.182175	+	0.983266i	$0.441686\pi$
$132$	0.169259	0.0147321
$133$	0.379862	0.0329382
$134$	1.49287	0.128964
$135$	−1.29111	−0.111121
$136$	6.74979	0.578789
$137$	3.55809	0.303988	0.151994	−	0.988381i	$-0.451430\pi$
$137$	3.55809	0.303988	0.151994	+	0.988381i	$0.451430\pi$
$138$	−0.0270065	−0.00229894
$139$	0.173896	0.0147496	0.00737482	−	0.999973i	$-0.497652\pi$
$139$	0.173896	0.0147496	0.00737482	+	0.999973i	$0.497652\pi$
$140$	−9.77816	−0.826405
$141$	−0.113638	−0.00957007
$142$	−5.82073	−0.488465
$143$	−0.889476	−0.0743817
$144$	−9.21627	−0.768022
$145$	−3.16986	−0.263242
$146$	1.30599	0.108084
$147$	0.285024	0.0235084
$148$	−4.64126	−0.381510
$149$	3.06023	0.250704	0.125352	−	0.992112i	$-0.459994\pi$
$149$	3.06023	0.250704	0.125352	+	0.992112i	$0.459994\pi$
$150$	0.136329	0.0111312
$151$	11.2536	0.915808	0.457904	−	0.889002i	$-0.348600\pi$
$151$	11.2536	0.915808	0.457904	+	0.889002i	$0.348600\pi$
$152$	−0.346425	−0.0280988
$153$	−13.2381	−1.07024
$154$	0.900446	0.0725600
$155$	−30.5594	−2.45459
$156$	−0.0822927	−0.00658869
$157$	0.269281	0.0214909	0.0107455	−	0.999942i	$-0.496580\pi$
$157$	0.269281	0.0214909	0.0107455	+	0.999942i	$0.496580\pi$
$158$	5.85772	0.466015
$159$	−0.502532	−0.0398533
$160$	13.5596	1.07198
$161$	1.67469	0.131984
$162$	−3.56121	−0.279795
$163$	5.88692	0.461099	0.230550	−	0.973061i	$-0.425948\pi$
$163$	5.88692	0.461099	0.230550	+	0.973061i	$0.425948\pi$
$164$	14.1725	1.10668
$165$	0.291278	0.0226759
$166$	4.10180	0.318361
$167$	−10.6448	−0.823721	−0.411861	−	0.911247i	$-0.635121\pi$
$167$	−10.6448	−0.823721	−0.411861	+	0.911247i	$0.635121\pi$
$168$	0.173763	0.0134061
$169$	−12.5675	−0.966734
$170$	5.56897	0.427121
$171$	0.679430	0.0519573
$172$	−2.60885	−0.198923
$173$	−1.05240	−0.0800126	−0.0400063	−	0.999199i	$-0.512738\pi$
$173$	−1.05240	−0.0800126	−0.0400063	+	0.999199i	$0.512738\pi$
$174$	0.0270065	0.00204736
$175$	−8.45381	−0.639048
$176$	4.16164	0.313695
$177$	−0.449443	−0.0337822
$178$	−5.79899	−0.434653
$179$	−6.96566	−0.520638	−0.260319	−	0.965523i	$-0.583828\pi$
$179$	−6.96566	−0.520638	−0.260319	+	0.965523i	$0.583828\pi$
$180$	−17.4895	−1.30359
$181$	15.5790	1.15798	0.578989	−	0.815335i	$-0.303447\pi$
$181$	15.5790	1.15798	0.578989	+	0.815335i	$0.303447\pi$
$182$	−0.437793	−0.0324513
$183$	−0.0619635	−0.00458048
$184$	−1.52727	−0.112592
$185$	−7.98716	−0.587228
$186$	0.260359	0.0190905
$187$	5.97771	0.437133
$188$	−3.08108	−0.224711
$189$	−0.682112	−0.0496164
$190$	−0.285821	−0.0207356
$191$	5.98633	0.433156	0.216578	−	0.976265i	$-0.430511\pi$
$191$	5.98633	0.433156	0.216578	+	0.976265i	$0.430511\pi$
$192$	0.302535	0.0218336
$193$	−23.2496	−1.67354	−0.836770	−	0.547555i	$-0.815559\pi$
$193$	−23.2496	−1.67354	−0.836770	+	0.547555i	$0.815559\pi$
$194$	3.64652	0.261805
$195$	−0.141618	−0.0101415
$196$	7.72787	0.551991
$197$	24.4309	1.74063	0.870315	−	0.492495i	$-0.163915\pi$
$197$	24.4309	1.74063	0.870315	+	0.492495i	$0.163915\pi$
$198$	1.61056	0.114458
$199$	−4.61601	−0.327220	−0.163610	−	0.986525i	$-0.552314\pi$
$199$	−4.61601	−0.327220	−0.163610	+	0.986525i	$0.552314\pi$
$200$	7.70968	0.545157
$201$	0.255132	0.0179956
$202$	−0.253132	−0.0178103
$203$	−1.67469	−0.117540
$204$	0.553047	0.0387210
$205$	24.3894	1.70343
$206$	−4.89926	−0.341348
$207$	2.99538	0.208194
$208$	−2.02337	−0.140295
$209$	−0.306799	−0.0212217
$210$	0.143364	0.00989308
$211$	−28.4009	−1.95520	−0.977599	−	0.210477i	$-0.932498\pi$
$211$	−28.4009	−1.95520	−0.977599	+	0.210477i	$0.932498\pi$
$212$	−13.6252	−0.935780
$213$	−0.994765	−0.0681602
$214$	−6.75818	−0.461979
$215$	−4.48958	−0.306187
$216$	0.622071	0.0423265
$217$	−16.1450	−1.09600
$218$	−1.18847	−0.0804934
$219$	0.223193	0.0150820
$220$	7.89742	0.532444
$221$	−2.90633	−0.195501
$222$	0.0680488	0.00456714
$223$	−15.4282	−1.03315	−0.516573	−	0.856243i	$-0.672793\pi$
$223$	−15.4282	−1.03315	−0.516573	+	0.856243i	$0.672793\pi$
$224$	7.16374	0.478647
$225$	−15.1207	−1.00805
$226$	−1.52378	−0.101360
$227$	−14.9603	−0.992950	−0.496475	−	0.868051i	$-0.665373\pi$
$227$	−14.9603	−0.992950	−0.496475	+	0.868051i	$0.665373\pi$
$228$	−0.0283845	−0.00187981
$229$	9.10667	0.601786	0.300893	−	0.953658i	$-0.402715\pi$
$229$	9.10667	0.601786	0.300893	+	0.953658i	$0.402715\pi$
$230$	−1.26009	−0.0830880
$231$	0.153887	0.0101250
$232$	1.52727	0.100271
$233$	−8.00051	−0.524131	−0.262065	−	0.965050i	$-0.584404\pi$
$233$	−8.00051	−0.524131	−0.262065	+	0.965050i	$0.584404\pi$
$234$	−0.783046	−0.0511893
$235$	−5.30224	−0.345880
$236$	−12.1858	−0.793226
$237$	1.00109	0.0650275
$238$	2.94218	0.190713
$239$	−4.11046	−0.265884	−0.132942	−	0.991124i	$-0.542442\pi$
$239$	−4.11046	−0.265884	−0.132942	+	0.991124i	$0.542442\pi$
$240$	0.662594	0.0427703
$241$	26.8825	1.73165	0.865827	−	0.500343i	$-0.166793\pi$
$241$	26.8825	1.73165	0.865827	+	0.500343i	$0.166793\pi$
$242$	3.64550	0.234342
$243$	−1.83053	−0.117429
$244$	−1.68002	−0.107552
$245$	13.2989	0.849636
$246$	−0.207792	−0.0132484
$247$	0.149164	0.00949108
$248$	14.7239	0.934968
$249$	0.700999	0.0444240
$250$	0.0604835	0.00382531
$251$	2.97370	0.187698	0.0938492	−	0.995586i	$-0.470083\pi$
$251$	2.97370	0.187698	0.0938492	+	0.995586i	$0.470083\pi$
$252$	−9.23995	−0.582062
$253$	−1.35258	−0.0850357
$254$	−3.70280	−0.232334
$255$	0.951739	0.0596002
$256$	4.80170	0.300106
$257$	22.6761	1.41450	0.707248	−	0.706965i	$-0.249936\pi$
$257$	22.6761	1.41450	0.707248	+	0.706965i	$0.249936\pi$
$258$	0.0382502	0.00238136
$259$	−4.21974	−0.262202
$260$	−3.83969	−0.238127
$261$	−2.99538	−0.185410
$262$	−1.65774	−0.102415
$263$	25.7248	1.58626	0.793130	−	0.609053i	$-0.208450\pi$
$263$	25.7248	1.58626	0.793130	+	0.609053i	$0.208450\pi$
$264$	−0.140341	−0.00863739
$265$	−23.4476	−1.44037
$266$	−0.151004	−0.00925864
$267$	−0.991049	−0.0606512
$268$	6.91740	0.422547
$269$	20.1571	1.22900	0.614500	−	0.788917i	$-0.289358\pi$
$269$	20.1571	1.22900	0.614500	+	0.788917i	$0.289358\pi$
$270$	0.513245	0.0312351
$271$	−2.32005	−0.140933	−0.0704664	−	0.997514i	$-0.522449\pi$
$271$	−2.32005	−0.140933	−0.0704664	+	0.997514i	$0.522449\pi$
$272$	13.5980	0.824500
$273$	−0.0748189	−0.00452824
$274$	−1.41443	−0.0854485
$275$	6.82780	0.411732
$276$	−0.125138	−0.00753242
$277$	8.38015	0.503514	0.251757	−	0.967790i	$-0.418992\pi$
$277$	8.38015	0.503514	0.251757	+	0.967790i	$0.418992\pi$
$278$	−0.0691276	−0.00414600
$279$	−28.8774	−1.72884
$280$	8.10756	0.484520
$281$	13.7243	0.818724	0.409362	−	0.912372i	$-0.365751\pi$
$281$	13.7243	0.818724	0.409362	+	0.912372i	$0.365751\pi$
$282$	0.0451739	0.00269007
$283$	17.4806	1.03912	0.519558	−	0.854435i	$-0.326097\pi$
$283$	17.4806	1.03912	0.519558	+	0.854435i	$0.326097\pi$
$284$	−26.9711	−1.60044
$285$	−0.0488469	−0.00289344
$286$	0.353587	0.0209081
$287$	12.8853	0.760596
$288$	12.8132	0.755027
$289$	2.53195	0.148938
$290$	1.26009	0.0739952
$291$	0.623191	0.0365321
$292$	6.05145	0.354135
$293$	25.2785	1.47679	0.738393	−	0.674370i	$-0.235585\pi$
$293$	25.2785	1.47679	0.738393	+	0.674370i	$0.235585\pi$
$294$	−0.113304	−0.00660801
$295$	−20.9705	−1.22095
$296$	3.84831	0.223678
$297$	0.550915	0.0319673
$298$	−1.21651	−0.0704707
$299$	0.657616	0.0380309
$300$	0.631697	0.0364710
$301$	−2.37192	−0.136715
$302$	−4.47358	−0.257426
$303$	−0.0432603	−0.00248524
$304$	−0.697902	−0.0400274
$305$	−2.89115	−0.165547
$306$	5.26245	0.300834
$307$	0.488401	0.0278745	0.0139373	−	0.999903i	$-0.495563\pi$
$307$	0.488401	0.0278745	0.0139373	+	0.999903i	$0.495563\pi$
$308$	4.17233	0.237741
$309$	−0.837286	−0.0476315
$310$	12.1481	0.689965
$311$	5.22317	0.296179	0.148089	−	0.988974i	$-0.452688\pi$
$311$	5.22317	0.296179	0.148089	+	0.988974i	$0.452688\pi$
$312$	0.0682331	0.00386294
$313$	31.4710	1.77885	0.889424	−	0.457083i	$-0.151106\pi$
$313$	31.4710	1.77885	0.889424	+	0.457083i	$0.151106\pi$
$314$	−0.107045	−0.00604092
$315$	−15.9011	−0.895923
$316$	27.1425	1.52688
$317$	23.1945	1.30273	0.651366	−	0.758764i	$-0.274196\pi$
$317$	23.1945	1.30273	0.651366	+	0.758764i	$0.274196\pi$
$318$	0.199768	0.0112024
$319$	1.35258	0.0757297
$320$	14.1159	0.789105
$321$	−1.15497	−0.0644644
$322$	−0.665727	−0.0370995
$323$	−1.00245	−0.0557781
$324$	−16.5013	−0.916739
$325$	−3.31964	−0.184141
$326$	−2.34019	−0.129611
$327$	−0.203110	−0.0112320
$328$	−11.7511	−0.648847
$329$	−2.80126	−0.154438
$330$	−0.115790	−0.00637401
$331$	−8.40340	−0.461893	−0.230946	−	0.972966i	$-0.574182\pi$
$331$	−8.40340	−0.461893	−0.230946	+	0.972966i	$0.574182\pi$
$332$	19.0062	1.04310
$333$	−7.54753	−0.413602
$334$	4.23157	0.231541
$335$	11.9042	0.650394
$336$	0.350059	0.0190973
$337$	9.69433	0.528084	0.264042	−	0.964511i	$-0.414944\pi$
$337$	9.69433	0.528084	0.264042	+	0.964511i	$0.414944\pi$
$338$	4.99589	0.271741
$339$	−0.260414	−0.0141438
$340$	25.8046	1.39945
$341$	13.0397	0.706138
$342$	−0.270089	−0.0146048
$343$	18.7488	1.01234
$344$	2.16313	0.116628
$345$	−0.215350	−0.0115941
$346$	0.418354	0.0224908
$347$	14.0015	0.751642	0.375821	−	0.926692i	$-0.377361\pi$
$347$	14.0015	0.751642	0.375821	+	0.926692i	$0.377361\pi$
$348$	0.125138	0.00670810
$349$	−0.389464	−0.0208475	−0.0104238	−	0.999946i	$-0.503318\pi$
$349$	−0.389464	−0.0208475	−0.0104238	+	0.999946i	$0.503318\pi$
$350$	3.36059	0.179631
$351$	−0.267852	−0.0142969
$352$	−5.78586	−0.308387
$353$	17.2560	0.918446	0.459223	−	0.888321i	$-0.348128\pi$
$353$	17.2560	0.918446	0.459223	+	0.888321i	$0.348128\pi$
$354$	0.178664	0.00949589
$355$	−46.4146	−2.46343
$356$	−26.8704	−1.42413
$357$	0.502819	0.0266120
$358$	2.76901	0.146347
$359$	−30.6718	−1.61879	−0.809397	−	0.587262i	$-0.800206\pi$
$359$	−30.6718	−1.61879	−0.809397	+	0.587262i	$0.800206\pi$
$360$	14.5014	0.764290
$361$	−18.9486	−0.997292
$362$	−6.19301	−0.325498
$363$	0.623017	0.0326999
$364$	−2.02857	−0.106326
$365$	10.4140	0.545091
$366$	0.0246319	0.00128753
$367$	−9.11035	−0.475557	−0.237778	−	0.971319i	$-0.576419\pi$
$367$	−9.11035	−0.475557	−0.237778	+	0.971319i	$0.576419\pi$
$368$	−3.07682	−0.160390
$369$	23.0470	1.19978
$370$	3.17508	0.165065
$371$	−12.3877	−0.643138
$372$	1.20641	0.0625494
$373$	5.35362	0.277200	0.138600	−	0.990348i	$-0.455740\pi$
$373$	5.35362	0.277200	0.138600	+	0.990348i	$0.455740\pi$
$374$	−2.37628	−0.122874
$375$	0.0103367	0.000533782 0
$376$	2.55468	0.131748
$377$	−0.657616	−0.0338689
$378$	0.271156	0.0139467
$379$	−11.6032	−0.596016	−0.298008	−	0.954563i	$-0.596322\pi$
$379$	−11.6032	−0.596016	−0.298008	+	0.954563i	$0.596322\pi$
$380$	−1.32439	−0.0679397
$381$	−0.632809	−0.0324198
$382$	−2.37971	−0.121756
$383$	−8.31496	−0.424874	−0.212437	−	0.977175i	$-0.568140\pi$
$383$	−8.31496	−0.424874	−0.212437	+	0.977175i	$0.568140\pi$
$384$	−0.701486	−0.0357976
$385$	7.18017	0.365936
$386$	9.24224	0.470418
$387$	−4.24247	−0.215657
$388$	16.8966	0.857795
$389$	−2.26821	−0.115003	−0.0575014	−	0.998345i	$-0.518313\pi$
$389$	−2.26821	−0.115003	−0.0575014	+	0.998345i	$0.518313\pi$
$390$	0.0562963	0.00285068
$391$	−4.41950	−0.223504
$392$	−6.40757	−0.323631
$393$	−0.283308	−0.0142910
$394$	−9.71186	−0.489276
$395$	46.7096	2.35021
$396$	7.46274	0.375017
$397$	−12.9717	−0.651032	−0.325516	−	0.945537i	$-0.605538\pi$
$397$	−12.9717	−0.651032	−0.325516	+	0.945537i	$0.605538\pi$
$398$	1.83497	0.0919788
$399$	−0.0258066	−0.00129195
$400$	15.5318	0.776590
$401$	−0.997267	−0.0498011	−0.0249006	−	0.999690i	$-0.507927\pi$
$401$	−0.997267	−0.0498011	−0.0249006	+	0.999690i	$0.507927\pi$
$402$	−0.101421	−0.00505841
$403$	−6.33983	−0.315809
$404$	−1.17292	−0.0583548
$405$	−28.3971	−1.41106
$406$	0.665727	0.0330395
$407$	3.40812	0.168934
$408$	−0.458559	−0.0227021
$409$	15.6229	0.772502	0.386251	−	0.922394i	$-0.373770\pi$
$409$	15.6229	0.772502	0.386251	+	0.922394i	$0.373770\pi$
$410$	−9.69536	−0.478820
$411$	−0.241726	−0.0119234
$412$	−22.7014	−1.11842
$413$	−11.0791	−0.545165
$414$	−1.19074	−0.0585214
$415$	32.7078	1.60556
$416$	2.81306	0.137921
$417$	−0.0118139	−0.000578531 0
$418$	0.121960	0.00596524
$419$	14.2200	0.694693	0.347347	−	0.937737i	$-0.387083\pi$
$419$	14.2200	0.694693	0.347347	+	0.937737i	$0.387083\pi$
$420$	0.664297	0.0324144
$421$	32.2664	1.57257	0.786284	−	0.617866i	$-0.212002\pi$
$421$	32.2664	1.57257	0.786284	+	0.617866i	$0.212002\pi$
$422$	11.2900	0.549589
$423$	−5.01039	−0.243614
$424$	11.2973	0.548646
$425$	22.3096	1.08218
$426$	0.395442	0.0191592
$427$	−1.52744	−0.0739180
$428$	−31.3149	−1.51366
$429$	0.0604282	0.00291750
$430$	1.78471	0.0860665
$431$	−35.5584	−1.71279	−0.856393	−	0.516325i	$-0.827300\pi$
$431$	−35.5584	−1.71279	−0.856393	+	0.516325i	$0.827300\pi$
$432$	1.25321	0.0602953
$433$	4.61554	0.221809	0.110904	−	0.993831i	$-0.464625\pi$
$433$	4.61554	0.221809	0.110904	+	0.993831i	$0.464625\pi$
$434$	6.41802	0.308075
$435$	0.215350	0.0103253
$436$	−5.50693	−0.263734
$437$	0.226826	0.0108505
$438$	−0.0887246	−0.00423943
$439$	−2.30348	−0.109939	−0.0549695	−	0.998488i	$-0.517506\pi$
$439$	−2.30348	−0.109939	−0.0549695	+	0.998488i	$0.517506\pi$
$440$	−6.54815	−0.312171
$441$	12.5669	0.598425
$442$	1.15533	0.0549537
$443$	8.59573	0.408395	0.204198	−	0.978930i	$-0.434541\pi$
$443$	8.59573	0.408395	0.204198	+	0.978930i	$0.434541\pi$
$444$	0.315313	0.0149641
$445$	−46.2413	−2.19205
$446$	6.13306	0.290409
$447$	−0.207903	−0.00983345
$448$	7.45767	0.352342
$449$	−16.1317	−0.761303	−0.380651	−	0.924719i	$-0.624300\pi$
$449$	−16.1317	−0.761303	−0.380651	+	0.924719i	$0.624300\pi$
$450$	6.01083	0.283353
$451$	−10.4070	−0.490044
$452$	−7.06062	−0.332104
$453$	−0.764536	−0.0359210
$454$	5.94707	0.279110
$455$	−3.49097	−0.163659
$456$	0.0235350	0.00110213
$457$	−27.4394	−1.28356	−0.641780	−	0.766889i	$-0.721804\pi$
$457$	−27.4394	−1.28356	−0.641780	+	0.766889i	$0.721804\pi$
$458$	−3.62011	−0.169157
$459$	1.80009	0.0840212
$460$	−5.83880	−0.272235
$461$	−17.7923	−0.828669	−0.414334	−	0.910125i	$-0.635986\pi$
$461$	−17.7923	−0.828669	−0.414334	+	0.910125i	$0.635986\pi$
$462$	−0.0611735	−0.00284605
$463$	−3.23767	−0.150467	−0.0752336	−	0.997166i	$-0.523970\pi$
$463$	−3.23767	−0.150467	−0.0752336	+	0.997166i	$0.523970\pi$
$464$	3.07682	0.142838
$465$	2.07611	0.0962773
$466$	3.18039	0.147329
$467$	16.3389	0.756075	0.378038	−	0.925790i	$-0.376599\pi$
$467$	16.3389	0.756075	0.378038	+	0.925790i	$0.376599\pi$
$468$	−3.62835	−0.167720
$469$	6.28916	0.290406
$470$	2.10776	0.0972238
$471$	−0.0182941	−0.000842947 0
$472$	10.1038	0.465067
$473$	1.91570	0.0880840
$474$	−0.397955	−0.0182787
$475$	−1.14502	−0.0525369
$476$	13.6330	0.624865
$477$	−22.1570	−1.01450
$478$	1.63401	0.0747377
$479$	7.83185	0.357846	0.178923	−	0.983863i	$-0.442739\pi$
$479$	7.83185	0.357846	0.178923	+	0.983863i	$0.442739\pi$
$480$	−0.921195	−0.0420466
$481$	−1.65701	−0.0755531
$482$	−10.6864	−0.486753
$483$	−0.113773	−0.00517685
$484$	16.8919	0.767814
$485$	29.0774	1.32034
$486$	0.727680	0.0330082
$487$	38.3921	1.73971	0.869856	−	0.493305i	$-0.164211\pi$
$487$	38.3921	1.73971	0.869856	+	0.493305i	$0.164211\pi$
$488$	1.39299	0.0630577
$489$	−0.399939	−0.0180859
$490$	−5.28663	−0.238825
$491$	−32.4833	−1.46595	−0.732975	−	0.680256i	$-0.761869\pi$
$491$	−32.4833	−1.46595	−0.732975	+	0.680256i	$0.761869\pi$
$492$	−0.962833	−0.0434079
$493$	4.41950	0.199044
$494$	−0.0592962	−0.00266786
$495$	12.8426	0.577234
$496$	29.6625	1.33189
$497$	−24.5216	−1.09994
$498$	−0.278663	−0.0124872
$499$	−8.26214	−0.369864	−0.184932	−	0.982751i	$-0.559207\pi$
$499$	−8.26214	−0.369864	−0.184932	+	0.982751i	$0.559207\pi$
$500$	0.280258	0.0125335
$501$	0.723176	0.0323091
$502$	−1.18212	−0.0527604
$503$	0.275633	0.0122899	0.00614493	−	0.999981i	$-0.498044\pi$
$503$	0.275633	0.0122899	0.00614493	+	0.999981i	$0.498044\pi$
$504$	7.66131	0.341262
$505$	−2.01848	−0.0898210
$506$	0.537681	0.0239028
$507$	0.853799	0.0379186
$508$	−17.1574	−0.761236
$509$	2.03889	0.0903720	0.0451860	−	0.998979i	$-0.485612\pi$
$509$	2.03889	0.0903720	0.0451860	+	0.998979i	$0.485612\pi$
$510$	−0.378339	−0.0167531
$511$	5.50186	0.243388
$512$	−22.5599	−0.997016
$513$	−0.0923878	−0.00407902
$514$	−9.01428	−0.397603
$515$	−39.0668	−1.72149
$516$	0.177237	0.00780244
$517$	2.26246	0.0995029
$518$	1.67745	0.0737027
$519$	0.0714968	0.00313836
$520$	3.18368	0.139614
$521$	−36.2346	−1.58747	−0.793734	−	0.608265i	$-0.791866\pi$
$521$	−36.2346	−1.58747	−0.793734	+	0.608265i	$0.791866\pi$
$522$	1.19074	0.0521171
$523$	−23.2807	−1.01800	−0.508998	−	0.860768i	$-0.669984\pi$
$523$	−23.2807	−1.01800	−0.508998	+	0.860768i	$0.669984\pi$
$524$	−7.68134	−0.335561
$525$	0.574326	0.0250656
$526$	−10.2262	−0.445884
$527$	42.6067	1.85598
$528$	−0.282729	−0.0123042
$529$	1.00000	0.0434783
$530$	9.32095	0.404876
$531$	−19.8163	−0.859953
$532$	−0.699696	−0.0303357
$533$	5.05981	0.219165
$534$	0.393965	0.0170485
$535$	−53.8898	−2.32986
$536$	−5.73557	−0.247739
$537$	0.473225	0.0204212
$538$	−8.01291	−0.345461
$539$	−5.67463	−0.244424
$540$	2.37819	0.102341
$541$	−26.0846	−1.12146	−0.560732	−	0.827997i	$-0.689480\pi$
$541$	−26.0846	−1.12146	−0.560732	+	0.827997i	$0.689480\pi$
$542$	0.922272	0.0396150
$543$	−1.05839	−0.0454198
$544$	−18.9051	−0.810549
$545$	−9.47689	−0.405945
$546$	0.0297422	0.00127285
$547$	10.3897	0.444230	0.222115	−	0.975020i	$-0.428704\pi$
$547$	10.3897	0.444230	0.222115	+	0.975020i	$0.428704\pi$
$548$	−6.55392	−0.279970
$549$	−2.73202	−0.116600
$550$	−2.71421	−0.115734
$551$	−0.226826	−0.00966309
$552$	0.103758	0.00441624
$553$	24.6774	1.04939
$554$	−3.33130	−0.141534
$555$	0.542622	0.0230330
$556$	−0.320312	−0.0135842
$557$	−7.93520	−0.336225	−0.168113	−	0.985768i	$-0.553767\pi$
$557$	−7.93520	−0.336225	−0.168113	+	0.985768i	$0.553767\pi$
$558$	11.4794	0.485963
$559$	−0.931404	−0.0393942
$560$	16.3334	0.690211
$561$	−0.406107	−0.0171458
$562$	−5.45574	−0.230136
$563$	30.9842	1.30583	0.652915	−	0.757431i	$-0.273546\pi$
$563$	30.9842	1.30583	0.652915	+	0.757431i	$0.273546\pi$
$564$	0.209319	0.00881392
$565$	−12.1506	−0.511181
$566$	−6.94896	−0.292087
$567$	−15.0026	−0.630052
$568$	22.3631	0.938336
$569$	36.3560	1.52412	0.762061	−	0.647505i	$-0.224187\pi$
$569$	36.3560	1.52412	0.762061	+	0.647505i	$0.224187\pi$
$570$	0.0194178	0.000813322 0
$571$	2.76541	0.115729	0.0578644	−	0.998324i	$-0.481571\pi$
$571$	2.76541	0.115729	0.0578644	+	0.998324i	$0.481571\pi$
$572$	1.63839	0.0685046
$573$	−0.406692	−0.0169898
$574$	−5.12221	−0.213797
$575$	−5.04800	−0.210516
$576$	13.3390	0.555791
$577$	−17.1204	−0.712730	−0.356365	−	0.934347i	$-0.615984\pi$
$577$	−17.1204	−0.712730	−0.356365	+	0.934347i	$0.615984\pi$
$578$	−1.00651	−0.0418652
$579$	1.57950	0.0656419
$580$	5.83880	0.242443
$581$	17.2801	0.716898
$582$	−0.247733	−0.0102689
$583$	10.0051	0.414367
$584$	−5.01757	−0.207628
$585$	−6.24403	−0.258159
$586$	−10.0488	−0.415112
$587$	−28.2800	−1.16724	−0.583621	−	0.812026i	$-0.698365\pi$
$587$	−28.2800	−1.16724	−0.583621	+	0.812026i	$0.698365\pi$
$588$	−0.525007	−0.0216509
$589$	−2.18674	−0.0901031
$590$	8.33627	0.343199
$591$	−1.65976	−0.0682734
$592$	7.75274	0.318635
$593$	36.0830	1.48175	0.740876	−	0.671642i	$-0.234411\pi$
$593$	36.0830	1.48175	0.740876	+	0.671642i	$0.234411\pi$
$594$	−0.219001	−0.00898574
$595$	23.4610	0.961806
$596$	−5.63687	−0.230895
$597$	0.313597	0.0128347
$598$	−0.261418	−0.0106902
$599$	−42.6659	−1.74328	−0.871641	−	0.490145i	$-0.836944\pi$
$599$	−42.6659	−1.74328	−0.871641	+	0.490145i	$0.836944\pi$
$600$	−0.523772	−0.0213829
$601$	11.0225	0.449615	0.224808	−	0.974403i	$-0.427825\pi$
$601$	11.0225	0.449615	0.224808	+	0.974403i	$0.427825\pi$
$602$	0.942892	0.0384294
$603$	11.2489	0.458092
$604$	−20.7289	−0.843447
$605$	29.0693	1.18184
$606$	0.0171970	0.000698579 0
$607$	1.73655	0.0704844	0.0352422	−	0.999379i	$-0.488780\pi$
$607$	1.73655	0.0704844	0.0352422	+	0.999379i	$0.488780\pi$
$608$	0.970282	0.0393501
$609$	0.113773	0.00461031
$610$	1.14930	0.0465338
$611$	−1.10000	−0.0445011
$612$	24.3842	0.985674
$613$	−35.0712	−1.41651	−0.708257	−	0.705955i	$-0.750518\pi$
$613$	−35.0712	−1.41651	−0.708257	+	0.705955i	$0.750518\pi$
$614$	−0.194151	−0.00783529
$615$	−1.65694	−0.0668143
$616$	−3.45949	−0.139387
$617$	−32.4852	−1.30780	−0.653902	−	0.756580i	$-0.726869\pi$
$617$	−32.4852	−1.30780	−0.653902	+	0.756580i	$0.726869\pi$
$618$	0.332841	0.0133888
$619$	31.7143	1.27470	0.637352	−	0.770573i	$-0.280030\pi$
$619$	31.7143	1.27470	0.637352	+	0.770573i	$0.280030\pi$
$620$	56.2897	2.26065
$621$	−0.407308	−0.0163447
$622$	−2.07633	−0.0832534
$623$	−24.4300	−0.978767
$624$	0.137461	0.00550285
$625$	−24.7577	−0.990308
$626$	−12.5105	−0.500019
$627$	0.0208430	0.000832387 0
$628$	−0.496008	−0.0197929
$629$	11.1359	0.444017
$630$	6.32104	0.251836
$631$	1.92400	0.0765931	0.0382965	−	0.999266i	$-0.487807\pi$
$631$	1.92400	0.0765931	0.0382965	+	0.999266i	$0.487807\pi$
$632$	−22.5052	−0.895209
$633$	1.92947	0.0766894
$634$	−9.22034	−0.366187
$635$	−29.5262	−1.17171
$636$	0.925651	0.0367044
$637$	2.75898	0.109315
$638$	−0.537681	−0.0212870
$639$	−43.8599	−1.73507
$640$	−32.7306	−1.29379
$641$	41.4326	1.63649	0.818245	−	0.574869i	$-0.194947\pi$
$641$	41.4326	1.63649	0.818245	+	0.574869i	$0.194947\pi$
$642$	0.459129	0.0181204
$643$	−13.2866	−0.523972	−0.261986	−	0.965072i	$-0.584377\pi$
$643$	−13.2866	−0.523972	−0.261986	+	0.965072i	$0.584377\pi$
$644$	−3.08473	−0.121555
$645$	0.305008	0.0120097
$646$	0.398499	0.0156787
$647$	−33.4357	−1.31449	−0.657246	−	0.753676i	$-0.728279\pi$
$647$	−33.4357	−1.31449	−0.657246	+	0.753676i	$0.728279\pi$
$648$	13.6821	0.537482
$649$	8.94810	0.351244
$650$	1.31964	0.0517604
$651$	1.09684	0.0429886
$652$	−10.8436	−0.424667
$653$	40.6149	1.58938	0.794692	−	0.607013i	$-0.207632\pi$
$653$	40.6149	1.58938	0.794692	+	0.607013i	$0.207632\pi$
$654$	0.0807410	0.00315722
$655$	−13.2188	−0.516502
$656$	−23.6736	−0.924299
$657$	9.84076	0.383925
$658$	1.11356	0.0434113
$659$	−37.2253	−1.45009	−0.725045	−	0.688701i	$-0.758181\pi$
$659$	−37.2253	−1.45009	−0.725045	+	0.688701i	$0.758181\pi$
$660$	−0.536526	−0.0208842
$661$	14.0154	0.545137	0.272569	−	0.962136i	$-0.412127\pi$
$661$	14.0154	0.545137	0.272569	+	0.962136i	$0.412127\pi$
$662$	3.34055	0.129834
$663$	0.197447	0.00766821
$664$	−15.7590	−0.611568
$665$	−1.20411	−0.0466933
$666$	3.00032	0.116260
$667$	−1.00000	−0.0387202
$668$	19.6075	0.758637
$669$	1.04814	0.0405235
$670$	−4.73218	−0.182820
$671$	1.23365	0.0476246
$672$	−0.486682	−0.0187742
$673$	−3.86624	−0.149033	−0.0745164	−	0.997220i	$-0.523741\pi$
$673$	−3.86624	−0.149033	−0.0745164	+	0.997220i	$0.523741\pi$
$674$	−3.85372	−0.148440
$675$	2.05609	0.0791389
$676$	23.1491	0.890350
$677$	4.47723	0.172074	0.0860369	−	0.996292i	$-0.472580\pi$
$677$	4.47723	0.172074	0.0860369	+	0.996292i	$0.472580\pi$
$678$	0.103521	0.00397569
$679$	15.3620	0.589541
$680$	−21.3959	−0.820494
$681$	1.01636	0.0389468
$682$	−5.18358	−0.198489
$683$	26.2668	1.00507	0.502536	−	0.864556i	$-0.332401\pi$
$683$	26.2668	1.00507	0.502536	+	0.864556i	$0.332401\pi$
$684$	−1.25149	−0.0478520
$685$	−11.2787	−0.430935
$686$	−7.45310	−0.284561
$687$	−0.618679	−0.0236041
$688$	4.35781	0.166140
$689$	−4.86441	−0.185319
$690$	0.0856067	0.00325899
$691$	−50.2708	−1.91239	−0.956196	−	0.292727i	$-0.905437\pi$
$691$	−50.2708	−1.91239	−0.956196	+	0.292727i	$0.905437\pi$
$692$	1.93850	0.0736906
$693$	6.78497	0.257740
$694$	−5.56594	−0.211280
$695$	−0.551225	−0.0209092
$696$	−0.103758	−0.00393295
$697$	−34.0044	−1.28801
$698$	0.154821	0.00586006
$699$	0.543529	0.0205582
$700$	15.5717	0.588556
$701$	−1.25281	−0.0473180	−0.0236590	−	0.999720i	$-0.507532\pi$
$701$	−1.25281	−0.0473180	−0.0236590	+	0.999720i	$0.507532\pi$
$702$	0.106477	0.00401873
$703$	−0.571537	−0.0215559
$704$	−6.02326	−0.227010
$705$	0.360217	0.0135666
$706$	−6.85967	−0.258167
$707$	−1.06639	−0.0401058
$708$	0.827863	0.0311130
$709$	−10.1837	−0.382457	−0.191228	−	0.981546i	$-0.561247\pi$
$709$	−10.1837	−0.382457	−0.191228	+	0.981546i	$0.561247\pi$
$710$	18.4509	0.692450
$711$	44.1386	1.65533
$712$	22.2796	0.834963
$713$	−9.64062	−0.361044
$714$	−0.199882	−0.00748041
$715$	2.81951	0.105444
$716$	12.8306	0.479501
$717$	0.279252	0.0104289
$718$	12.1927	0.455029
$719$	−1.72692	−0.0644032	−0.0322016	−	0.999481i	$-0.510252\pi$
$719$	−1.72692	−0.0644032	−0.0322016	+	0.999481i	$0.510252\pi$
$720$	29.2143	1.08875
$721$	−20.6396	−0.768660
$722$	7.53249	0.280330
$723$	−1.82631	−0.0679213
$724$	−28.6961	−1.06648
$725$	5.04800	0.187478
$726$	−0.247664	−0.00919167
$727$	−4.32804	−0.160518	−0.0802592	−	0.996774i	$-0.525575\pi$
$727$	−4.32804	−0.160518	−0.0802592	+	0.996774i	$0.525575\pi$
$728$	1.68199	0.0623386
$729$	−26.7511	−0.990781
$730$	−4.13979	−0.153221
$731$	6.25949	0.231516
$732$	0.114135	0.00421856
$733$	44.0511	1.62707	0.813533	−	0.581519i	$-0.197541\pi$
$733$	44.0511	1.62707	0.813533	+	0.581519i	$0.197541\pi$
$734$	3.62158	0.133675
$735$	−0.903486	−0.0333256
$736$	4.27766	0.157677
$737$	−5.07950	−0.187106
$738$	−9.16172	−0.337248
$739$	−36.1834	−1.33103	−0.665514	−	0.746385i	$-0.731788\pi$
$739$	−36.1834	−1.33103	−0.665514	+	0.746385i	$0.731788\pi$
$740$	14.7121	0.540829
$741$	−0.0101337	−0.000372272 0
$742$	4.92441	0.180781
$743$	−14.8073	−0.543227	−0.271614	−	0.962406i	$-0.587557\pi$
$743$	−14.8073	−0.543227	−0.271614	+	0.962406i	$0.587557\pi$
$744$	−1.00029	−0.0366726
$745$	−9.70050	−0.355399
$746$	−2.12819	−0.0779185
$747$	30.9075	1.13085
$748$	−11.0108	−0.402594
$749$	−28.4708	−1.04030
$750$	−0.00410906	−0.000150042 0
$751$	−30.7780	−1.12311	−0.561553	−	0.827441i	$-0.689796\pi$
$751$	−30.7780	−1.12311	−0.561553	+	0.827441i	$0.689796\pi$
$752$	5.14662	0.187678
$753$	−0.202024	−0.00736216
$754$	0.261418	0.00952027
$755$	−35.6724	−1.29825
$756$	1.25643	0.0456961
$757$	15.6080	0.567281	0.283640	−	0.958931i	$-0.408458\pi$
$757$	15.6080	0.567281	0.283640	+	0.958931i	$0.408458\pi$
$758$	4.61254	0.167535
$759$	0.0918898	0.00333539
$760$	1.09812	0.0398329
$761$	−21.6974	−0.786529	−0.393264	−	0.919425i	$-0.628654\pi$
$761$	−21.6974	−0.786529	−0.393264	+	0.919425i	$0.628654\pi$
$762$	0.251556	0.00911293
$763$	−5.00679	−0.181258
$764$	−11.0267	−0.398931
$765$	41.9629	1.51717
$766$	3.30539	0.119429
$767$	−4.35052	−0.157088
$768$	−0.326213	−0.0117712
$769$	−41.3361	−1.49062	−0.745309	−	0.666720i	$-0.767698\pi$
$769$	−41.3361	−1.49062	−0.745309	+	0.666720i	$0.767698\pi$
$770$	−2.85429	−0.102861
$771$	−1.54054	−0.0554813
$772$	42.8251	1.54131
$773$	9.27907	0.333745	0.166873	−	0.985978i	$-0.446633\pi$
$773$	9.27907	0.333745	0.166873	+	0.985978i	$0.446633\pi$
$774$	1.68648	0.0606193
$775$	48.6659	1.74813
$776$	−14.0098	−0.502924
$777$	0.286676	0.0102844
$778$	0.901666	0.0323263
$779$	1.74523	0.0625295
$780$	0.260856	0.00934015
$781$	19.8051	0.708682
$782$	1.75685	0.0628249
$783$	0.407308	0.0145560
$784$	−12.9086	−0.461021
$785$	−0.853582	−0.0304656
$786$	0.112621	0.00401708
$787$	33.1118	1.18031	0.590153	−	0.807291i	$-0.299067\pi$
$787$	33.1118	1.18031	0.590153	+	0.807291i	$0.299067\pi$
$788$	−45.0011	−1.60310
$789$	−1.74766	−0.0622184
$790$	−18.5681	−0.660625
$791$	−6.41937	−0.228247
$792$	−6.18773	−0.219872
$793$	−0.599795	−0.0212993
$794$	5.15656	0.182999
$795$	1.59295	0.0564962
$796$	8.50257	0.301366
$797$	21.4212	0.758779	0.379390	−	0.925237i	$-0.376134\pi$
$797$	21.4212	0.758779	0.379390	+	0.925237i	$0.376134\pi$
$798$	0.0102587	0.000363155 0
$799$	7.39251	0.261528
$800$	−21.5936	−0.763450
$801$	−43.6961	−1.54392
$802$	0.396437	0.0139987
$803$	−4.44363	−0.156812
$804$	−0.469946	−0.0165737
$805$	−5.30852	−0.187101
$806$	2.52023	0.0887713
$807$	−1.36941	−0.0482055
$808$	0.972525	0.0342133
$809$	−22.5673	−0.793423	−0.396712	−	0.917943i	$-0.629849\pi$
$809$	−22.5673	−0.793423	−0.396712	+	0.917943i	$0.629849\pi$
$810$	11.2885	0.396638
$811$	24.3804	0.856112	0.428056	−	0.903752i	$-0.359199\pi$
$811$	24.3804	0.856112	0.428056	+	0.903752i	$0.359199\pi$
$812$	3.08473	0.108253
$813$	0.157617	0.00552786
$814$	−1.35481	−0.0474859
$815$	−18.6607	−0.653656
$816$	−0.923806	−0.0323397
$817$	−0.321261	−0.0112395
$818$	−6.21047	−0.217144
$819$	−3.29882	−0.115270
$820$	−44.9247	−1.56884
$821$	36.5337	1.27504	0.637518	−	0.770436i	$-0.279961\pi$
$821$	36.5337	1.27504	0.637518	+	0.770436i	$0.279961\pi$
$822$	0.0960916	0.00335158
$823$	−40.5937	−1.41501	−0.707503	−	0.706710i	$-0.750178\pi$
$823$	−40.5937	−1.41501	−0.707503	+	0.706710i	$0.750178\pi$
$824$	18.8229	0.655725
$825$	−0.463860	−0.0161495
$826$	4.40418	0.153241
$827$	29.0707	1.01089	0.505444	−	0.862860i	$-0.331329\pi$
$827$	29.0707	1.01089	0.505444	+	0.862860i	$0.331329\pi$
$828$	−5.51742	−0.191744
$829$	35.3536	1.22788	0.613940	−	0.789352i	$-0.289584\pi$
$829$	35.3536	1.22788	0.613940	+	0.789352i	$0.289584\pi$
$830$	−13.0021	−0.451310
$831$	−0.569321	−0.0197495
$832$	2.92848	0.101527
$833$	−18.5417	−0.642431
$834$	0.00469631	0.000162620 0
$835$	33.7426	1.16771
$836$	0.565116	0.0195449
$837$	3.92670	0.135727
$838$	−5.65279	−0.195272
$839$	−11.1677	−0.385553	−0.192776	−	0.981243i	$-0.561749\pi$
$839$	−11.1677	−0.385553	−0.192776	+	0.981243i	$0.561749\pi$
$840$	−0.550802	−0.0190045
$841$	1.00000	0.0344828
$842$	−12.8266	−0.442035
$843$	−0.932387	−0.0321131
$844$	52.3137	1.80071
$845$	39.8373	1.37045
$846$	1.99175	0.0684777
$847$	15.3578	0.527699
$848$	22.7594	0.781560
$849$	−1.18758	−0.0407576
$850$	−8.86859	−0.304190
$851$	−2.51972	−0.0863749
$852$	1.83233	0.0627747
$853$	36.4163	1.24687	0.623436	−	0.781875i	$-0.285736\pi$
$853$	36.4163	1.24687	0.623436	+	0.781875i	$0.285736\pi$
$854$	0.607193	0.0207777
$855$	−2.15370	−0.0736548
$856$	25.9647	0.887457
$857$	17.1591	0.586144	0.293072	−	0.956090i	$-0.405322\pi$
$857$	17.1591	0.586144	0.293072	+	0.956090i	$0.405322\pi$
$858$	−0.0240216	−0.000820084 0
$859$	35.2599	1.20305	0.601525	−	0.798854i	$-0.294560\pi$
$859$	35.2599	1.20305	0.601525	+	0.798854i	$0.294560\pi$
$860$	8.26970	0.281994
$861$	−0.875388	−0.0298331
$862$	14.1353	0.481449
$863$	4.02541	0.137027	0.0685133	−	0.997650i	$-0.478174\pi$
$863$	4.02541	0.137027	0.0685133	+	0.997650i	$0.478174\pi$
$864$	−1.74232	−0.0592750
$865$	3.33596	0.113426
$866$	−1.83479	−0.0623485
$867$	−0.172013	−0.00584186
$868$	29.7387	1.00940
$869$	−19.9309	−0.676111
$870$	−0.0856067	−0.00290234
$871$	2.46963	0.0836801
$872$	4.56607	0.154627
$873$	27.4769	0.929953
$874$	−0.0901685	−0.00304999
$875$	0.254805	0.00861398
$876$	−0.411117	−0.0138903
$877$	−35.1631	−1.18737	−0.593687	−	0.804696i	$-0.702328\pi$
$877$	−35.1631	−1.18737	−0.593687	+	0.804696i	$0.702328\pi$
$878$	0.915686	0.0309029
$879$	−1.71734	−0.0579245
$880$	−13.1918	−0.444696
$881$	−11.8258	−0.398422	−0.199211	−	0.979957i	$-0.563838\pi$
$881$	−11.8258	−0.398422	−0.199211	+	0.979957i	$0.563838\pi$
$882$	−4.99564	−0.168212
$883$	27.9925	0.942023	0.471012	−	0.882127i	$-0.343889\pi$
$883$	27.9925	0.942023	0.471012	+	0.882127i	$0.343889\pi$
$884$	5.35339	0.180054
$885$	1.42467	0.0478898
$886$	−3.41700	−0.114796
$887$	−22.6326	−0.759927	−0.379963	−	0.925001i	$-0.624063\pi$
$887$	−22.6326	−0.759927	−0.379963	+	0.925001i	$0.624063\pi$
$888$	−0.261442	−0.00877341
$889$	−15.5991	−0.523178
$890$	18.3820	0.616165
$891$	12.1170	0.405936
$892$	28.4183	0.951515
$893$	−0.379412	−0.0126965
$894$	0.0826461	0.00276410
$895$	22.0801	0.738058
$896$	−17.2921	−0.577688
$897$	−0.0446764	−0.00149170
$898$	6.41273	0.213996
$899$	9.64062	0.321533
$900$	27.8520	0.928398
$901$	32.6912	1.08910
$902$	4.13701	0.137747
$903$	0.161141	0.00536242
$904$	5.85432	0.194712
$905$	−49.3832	−1.64155
$906$	0.303921	0.0100971
$907$	51.0746	1.69590	0.847952	−	0.530073i	$-0.177836\pi$
$907$	51.0746	1.69590	0.847952	+	0.530073i	$0.177836\pi$
$908$	27.5565	0.914495
$909$	−1.90738	−0.0632637
$910$	1.38774	0.0460031
$911$	−36.9765	−1.22509	−0.612543	−	0.790437i	$-0.709853\pi$
$911$	−36.9765	−1.22509	−0.612543	+	0.790437i	$0.709853\pi$
$912$	0.0474133	0.00157001
$913$	−13.9564	−0.461890
$914$	10.9078	0.360798
$915$	0.196416	0.00649330
$916$	−16.7743	−0.554237
$917$	−6.98372	−0.230623
$918$	−0.715580	−0.0236176
$919$	−31.0396	−1.02390	−0.511951	−	0.859014i	$-0.671077\pi$
$919$	−31.0396	−1.02390	−0.511951	+	0.859014i	$0.671077\pi$
$920$	4.84124	0.159611
$921$	−0.0331804	−0.00109333
$922$	7.07284	0.232932
$923$	−9.62914	−0.316947
$924$	−0.283455	−0.00932499
$925$	12.7196	0.418216
$926$	1.28705	0.0422950
$927$	−36.9165	−1.21250
$928$	−4.27766	−0.140421
$929$	−52.2135	−1.71307	−0.856535	−	0.516090i	$-0.827387\pi$
$929$	−52.2135	−1.71307	−0.856535	+	0.516090i	$0.827387\pi$
$930$	−0.825302	−0.0270627
$931$	0.951630	0.0311884
$932$	14.7367	0.482718
$933$	−0.354846	−0.0116171
$934$	−6.49510	−0.212526
$935$	−18.9485	−0.619682
$936$	3.00844	0.0983341
$937$	12.6887	0.414520	0.207260	−	0.978286i	$-0.433545\pi$
$937$	12.6887	0.414520	0.207260	+	0.978286i	$0.433545\pi$
$938$	−2.50009	−0.0816307
$939$	−2.13804	−0.0697724
$940$	9.76659	0.318551
$941$	41.5030	1.35296	0.676479	−	0.736462i	$-0.263505\pi$
$941$	41.5030	1.35296	0.676479	+	0.736462i	$0.263505\pi$
$942$	0.00727233	0.000236945 0
$943$	7.69417	0.250557
$944$	20.3550	0.662500
$945$	2.16220	0.0703363
$946$	−0.761536	−0.0247597
$947$	−40.5269	−1.31695	−0.658474	−	0.752604i	$-0.728798\pi$
$947$	−40.5269	−1.31695	−0.658474	+	0.752604i	$0.728798\pi$
$948$	−1.84398	−0.0598895
$949$	2.16047	0.0701318
$950$	0.455170	0.0147677
$951$	−1.57576	−0.0510975
$952$	−11.3038	−0.366357
$953$	24.8116	0.803728	0.401864	−	0.915699i	$-0.368363\pi$
$953$	24.8116	0.803728	0.401864	+	0.915699i	$0.368363\pi$
$954$	8.80791	0.285167
$955$	−18.9758	−0.614043
$956$	7.57137	0.244876
$957$	−0.0918898	−0.00297037
$958$	−3.11334	−0.100588
$959$	−5.95869	−0.192416
$960$	−0.958992	−0.0309513
$961$	61.9416	1.99812
$962$	0.658700	0.0212373
$963$	−50.9236	−1.64099
$964$	−49.5169	−1.59483
$965$	73.6978	2.37242
$966$	0.0452274	0.00145517
$967$	40.2551	1.29452	0.647259	−	0.762270i	$-0.275915\pi$
$967$	40.2551	1.29452	0.647259	+	0.762270i	$0.275915\pi$
$968$	−14.0059	−0.450168
$969$	0.0681036	0.00218780
$970$	−11.5589	−0.371135
$971$	−28.3848	−0.910910	−0.455455	−	0.890259i	$-0.650523\pi$
$971$	−28.3848	−0.910910	−0.455455	+	0.890259i	$0.650523\pi$
$972$	3.37180	0.108150
$973$	−0.291221	−0.00933611
$974$	−15.2618	−0.489018
$975$	0.225526	0.00722262
$976$	2.80629	0.0898273
$977$	49.2960	1.57712	0.788560	−	0.614958i	$-0.210827\pi$
$977$	49.2960	1.57712	0.788560	+	0.614958i	$0.210827\pi$
$978$	0.158985	0.00508378
$979$	19.7311	0.630609
$980$	−24.4963	−0.782504
$981$	−8.95526	−0.285920
$982$	12.9129	0.412066
$983$	−6.95652	−0.221878	−0.110939	−	0.993827i	$-0.535386\pi$
$983$	−6.95652	−0.221878	−0.110939	+	0.993827i	$0.535386\pi$
$984$	0.798333	0.0254499
$985$	−77.4425	−2.46752
$986$	−1.75685	−0.0559496
$987$	0.190308	0.00605759
$988$	−0.274757	−0.00874117
$989$	−1.41633	−0.0450368
$990$	−5.10525	−0.162255
$991$	−18.9477	−0.601894	−0.300947	−	0.953641i	$-0.597303\pi$
$991$	−18.9477	−0.601894	−0.300947	+	0.953641i	$0.597303\pi$
$992$	−41.2393	−1.30935
$993$	0.570901	0.0181170
$994$	9.74790	0.309185
$995$	14.6321	0.463868
$996$	−1.29122	−0.0409139
$997$	−27.6170	−0.874640	−0.437320	−	0.899306i	$-0.644072\pi$
$997$	−27.6170	−0.874640	−0.437320	+	0.899306i	$0.644072\pi$
$998$	3.28439	0.103966
$999$	1.02630	0.0324707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.6	✓	13
3.2	odd	2		6003.2.a.o.1.8		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.6	✓	13	1.1	even	1	trivial
6003.2.a.o.1.8		13	3.2	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.397523 q^{2} -0.0679369 q^{3} -1.84198 q^{4} -3.16986 q^{5} +0.0270065 q^{6} -1.67469 q^{7} +1.52727 q^{8} -2.99538 q^{9} +O(q^{10})\)	\(q-0.397523 q^{2} -0.0679369 q^{3} -1.84198 q^{4} -3.16986 q^{5} +0.0270065 q^{6} -1.67469 q^{7} +1.52727 q^{8} -2.99538 q^{9} +1.26009 q^{10} +1.35258 q^{11} +0.125138 q^{12} -0.657616 q^{13} +0.665727 q^{14} +0.215350 q^{15} +3.07682 q^{16} +4.41950 q^{17} +1.19074 q^{18} -0.226826 q^{19} +5.83880 q^{20} +0.113773 q^{21} -0.537681 q^{22} -1.00000 q^{23} -0.103758 q^{24} +5.04800 q^{25} +0.261418 q^{26} +0.407308 q^{27} +3.08473 q^{28} +1.00000 q^{29} -0.0856067 q^{30} +9.64062 q^{31} -4.27766 q^{32} -0.0918898 q^{33} -1.75685 q^{34} +5.30852 q^{35} +5.51742 q^{36} +2.51972 q^{37} +0.0901685 q^{38} +0.0446764 q^{39} -4.84124 q^{40} -7.69417 q^{41} -0.0452274 q^{42} +1.41633 q^{43} -2.49141 q^{44} +9.49494 q^{45} +0.397523 q^{46} +1.67270 q^{47} -0.209030 q^{48} -4.19543 q^{49} -2.00670 q^{50} -0.300247 q^{51} +1.21131 q^{52} +7.39704 q^{53} -0.161914 q^{54} -4.28747 q^{55} -2.55771 q^{56} +0.0154098 q^{57} -0.397523 q^{58} +6.61560 q^{59} -0.396670 q^{60} +0.912075 q^{61} -3.83237 q^{62} +5.01633 q^{63} -4.45318 q^{64} +2.08455 q^{65} +0.0365283 q^{66} -3.75542 q^{67} -8.14060 q^{68} +0.0679369 q^{69} -2.11026 q^{70} +14.6425 q^{71} -4.57478 q^{72} -3.28531 q^{73} -1.00165 q^{74} -0.342945 q^{75} +0.417807 q^{76} -2.26514 q^{77} -0.0177599 q^{78} -14.7355 q^{79} -9.75309 q^{80} +8.95848 q^{81} +3.05861 q^{82} -10.3184 q^{83} -0.209567 q^{84} -14.0092 q^{85} -0.563026 q^{86} -0.0679369 q^{87} +2.06576 q^{88} +14.5878 q^{89} -3.77446 q^{90} +1.10130 q^{91} +1.84198 q^{92} -0.654954 q^{93} -0.664939 q^{94} +0.719005 q^{95} +0.290611 q^{96} -9.17309 q^{97} +1.66778 q^{98} -4.05149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

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