LMFDB - Embedded newform 770.2.n.j.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, minimal)

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:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.1
Root			$-1.36475 - 0.991547i$ of defining polynomial
Character	$\chi$	$=$	770.631
Dual form			770.2.n.j.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.521287 + 1.60436i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.36475 + 0.991547i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.124831 + 0.0906951i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.521287 + 1.60436i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.36475 + 0.991547i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.124831 + 0.0906951i) q^{9} -1.00000 q^{10} +(-1.49776 + 2.95917i) q^{11} -1.68692 q^{12} +(-0.0344432 - 0.0250244i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-0.521287 - 1.60436i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.81887 - 2.77457i) q^{17} +(0.0476812 + 0.146748i) q^{18} +(-0.529469 + 1.62954i) q^{19} +(-0.809017 - 0.587785i) q^{20} -1.68692 q^{21} +(-2.95107 + 1.51366i) q^{22} -6.95966 q^{23} +(-1.36475 - 0.991547i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.0131561 - 0.0404904i) q^{26} +(-4.30482 + 3.12764i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-0.414939 - 1.27705i) q^{29} +(0.521287 - 1.60436i) q^{30} +(-4.86418 - 3.53403i) q^{31} -1.00000 q^{32} +(-3.96681 - 3.94552i) q^{33} +4.72038 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-0.0476812 + 0.146748i) q^{36} +(2.62188 + 8.06932i) q^{37} +(-1.38617 + 1.00711i) q^{38} +(0.0581029 - 0.0422142i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(1.20940 - 3.72216i) q^{41} +(-1.36475 - 0.991547i) q^{42} +6.42455 q^{43} +(-3.27718 - 0.510019i) q^{44} -0.154300 q^{45} +(-5.63049 - 4.09079i) q^{46} +(1.41879 - 4.36658i) q^{47} +(-0.521287 - 1.60436i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(2.46067 + 7.57317i) q^{51} +(0.0131561 - 0.0404904i) q^{52} +(11.4090 + 8.28916i) q^{53} -5.32105 q^{54} +(-0.527646 - 3.27438i) q^{55} -1.00000 q^{56} +(-2.33835 - 1.69891i) q^{57} +(0.414939 - 1.27705i) q^{58} +(-3.15745 - 9.71764i) q^{59} +(1.36475 - 0.991547i) q^{60} +(-11.2179 + 8.15030i) q^{61} +(-1.85795 - 5.71818i) q^{62} +(-0.0476812 + 0.146748i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.0425741 q^{65} +(-0.890097 - 5.52362i) q^{66} +6.39600 q^{67} +(3.81887 + 2.77457i) q^{68} +(3.62798 - 11.1658i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(-9.14519 + 6.64437i) q^{71} +(-0.124831 + 0.0906951i) q^{72} +(-0.614104 - 1.89002i) q^{73} +(-2.62188 + 8.06932i) q^{74} +(1.36475 + 0.991547i) q^{75} -1.71340 q^{76} +(-3.27718 - 0.510019i) q^{77} +0.0718191 q^{78} +(7.17650 + 5.21404i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-2.63075 - 8.09662i) q^{81} +(3.16626 - 2.30042i) q^{82} +(8.15543 - 5.92527i) q^{83} +(-0.521287 - 1.60436i) q^{84} +(-1.45868 + 4.48935i) q^{85} +(5.19757 + 3.77626i) q^{86} +2.26515 q^{87} +(-2.35151 - 2.33889i) q^{88} +2.93362 q^{89} +(-0.124831 - 0.0906951i) q^{90} +(0.0131561 - 0.0404904i) q^{91} +(-2.15065 - 6.61903i) q^{92} +(8.20548 - 5.96163i) q^{93} +(3.71443 - 2.69869i) q^{94} +(-0.529469 - 1.62954i) q^{95} +(0.521287 - 1.60436i) q^{96} +(14.1426 + 10.2752i) q^{97} -1.00000 q^{98} +(-0.455350 + 0.233558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 12 * q^10 - q^11 - 2 * q^12 + 2 * q^13 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 7 * q^17 + 9 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 7 * q^26 - 3 * q^27 - 3 * q^28 + 20 * q^29 - 3 * q^30 + 6 * q^31 - 12 * q^32 - 12 * q^33 + 18 * q^34 - 3 * q^35 - 9 * q^36 + 22 * q^37 - 6 * q^38 + 23 * q^39 + 3 * q^40 + 2 * q^41 + 2 * q^42 - 60 * q^43 - 11 * q^44 + 6 * q^45 + 2 * q^46 - 4 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 + 13 * q^51 + 7 * q^52 + 18 * q^53 + 8 * q^54 + 14 * q^55 - 12 * q^56 + 8 * q^57 - 20 * q^58 - 32 * q^59 - 2 * q^60 + 8 * q^61 + 14 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^65 - 8 * q^66 + 36 * q^67 + 7 * q^68 + 50 * q^69 + 3 * q^70 - 34 * q^71 - 6 * q^72 + 14 * q^73 - 22 * q^74 - 2 * q^75 - 24 * q^76 - 11 * q^77 - 38 * q^78 - 12 * q^79 - 3 * q^80 + 4 * q^81 - 2 * q^82 + 30 * q^83 + 3 * q^84 + 2 * q^85 - 28 * q^87 + q^88 - 36 * q^89 - 6 * q^90 + 7 * q^91 - 2 * q^92 + 12 * q^93 - 11 * q^94 + 6 * q^95 - 3 * q^96 + 39 * q^97 - 12 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.521287	+	1.60436i	−0.300965	+	0.926276i	0.680187	+	0.733039i	$0.261899\pi$
$3$	−0.521287	+	1.60436i	−0.300965	+	0.926276i	−0.981152	+	0.193237i	$0.938101\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$	−1.36475	+	0.991547i	−0.557156	+	0.404797i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.124831	+	0.0906951i	0.0416104	+	0.0302317i
$10$	−1.00000			−0.316228
$11$	−1.49776	+	2.95917i	−0.451592	+	0.892225i
$11$	−1.49776	+	2.95917i	−0.451592	+	0.892225i
$12$	−1.68692			−0.486972
$13$	−0.0344432	−	0.0250244i	−0.00955282	−	0.00694053i	0.582999	−	0.812473i	$-0.301879\pi$
$13$	−0.0344432	−	0.0250244i	−0.00955282	−	0.00694053i	−0.592551	+	0.805533i	$0.701879\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	−0.521287	−	1.60436i	−0.134596	−	0.414243i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.81887	−	2.77457i	0.926212	−	0.672932i	−0.0188508	−	0.999822i	$-0.506001\pi$
$17$	3.81887	−	2.77457i	0.926212	−	0.672932i	0.945062	+	0.326890i	$0.106001\pi$
$18$	0.0476812	+	0.146748i	0.0112386	+	0.0345888i
$19$	−0.529469	+	1.62954i	−0.121468	+	0.373841i	−0.993241	−	0.116069i	$-0.962971\pi$
$19$	−0.529469	+	1.62954i	−0.121468	+	0.373841i	0.871773	+	0.489911i	$0.162971\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	−1.68692			−0.368116
$22$	−2.95107	+	1.51366i	−0.629171	+	0.322714i
$23$	−6.95966			−1.45119			−0.725595	−	0.688122i	$-0.758435\pi$
$23$	−6.95966			−1.45119			−0.725595	+	0.688122i	$0.758435\pi$
$24$	−1.36475	−	0.991547i	−0.278578	−	0.202399i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.0131561	−	0.0404904i	−0.00258013	−	0.00794082i
$27$	−4.30482	+	3.12764i	−0.828463	+	0.601914i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	−0.414939	−	1.27705i	−0.0770523	−	0.237143i	0.905110	−	0.425177i	$-0.139788\pi$
$29$	−0.414939	−	1.27705i	−0.0770523	−	0.237143i	−0.982162	+	0.188035i	$0.939788\pi$
$30$	0.521287	−	1.60436i	0.0951736	−	0.292914i
$31$	−4.86418	−	3.53403i	−0.873632	−	0.634731i	0.0579271	−	0.998321i	$-0.481551\pi$
$31$	−4.86418	−	3.53403i	−0.873632	−	0.634731i	−0.931559	+	0.363590i	$0.881551\pi$
$32$	−1.00000			−0.176777
$33$	−3.96681	−	3.94552i	−0.690533	−	0.686827i
$34$	4.72038			0.809539
$35$	−0.809017	−	0.587785i	−0.136749	−	0.0993538i
$36$	−0.0476812	+	0.146748i	−0.00794687	+	0.0244580i
$37$	2.62188	+	8.06932i	0.431035	+	1.32659i	0.897096	+	0.441836i	$0.145673\pi$
$37$	2.62188	+	8.06932i	0.431035	+	1.32659i	−0.466061	+	0.884753i	$0.654327\pi$
$38$	−1.38617	+	1.00711i	−0.224866	+	0.163375i
$39$	0.0581029	−	0.0422142i	0.00930391	−	0.00675969i
$40$	−0.309017	−	0.951057i	−0.0488599	−	0.150375i
$41$	1.20940	−	3.72216i	0.188877	−	0.581304i	−0.811117	−	0.584885i	$-0.801140\pi$
$41$	1.20940	−	3.72216i	0.188877	−	0.581304i	0.999994	+	0.00358082i	$0.00113981\pi$
$42$	−1.36475	−	0.991547i	−0.210585	−	0.152999i
$43$	6.42455			0.979735			0.489867	−	0.871797i	$-0.337045\pi$
$43$	6.42455			0.979735			0.489867	+	0.871797i	$0.337045\pi$
$44$	−3.27718	−	0.510019i	−0.494053	−	0.0768883i
$45$	−0.154300			−0.0230016
$46$	−5.63049	−	4.09079i	−0.830170	−	0.603154i
$47$	1.41879	−	4.36658i	0.206951	−	0.636931i	−0.792676	−	0.609643i	$-0.791313\pi$
$47$	1.41879	−	4.36658i	0.206951	−	0.636931i	0.999628	−	0.0272881i	$-0.00868715\pi$
$48$	−0.521287	−	1.60436i	−0.0752413	−	0.231569i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$	2.46067	+	7.57317i	0.344563	+	1.06046i
$52$	0.0131561	−	0.0404904i	0.00182443	−	0.00561501i
$53$	11.4090	+	8.28916i	1.56715	+	1.13860i	0.929820	+	0.368015i	$0.119963\pi$
$53$	11.4090	+	8.28916i	1.56715	+	1.13860i	0.637333	+	0.770588i	$0.280037\pi$
$54$	−5.32105			−0.724104
$55$	−0.527646	−	3.27438i	−0.0711478	−	0.441518i
$56$	−1.00000			−0.133631
$57$	−2.33835	−	1.69891i	−0.309722	−	0.225027i
$58$	0.414939	−	1.27705i	0.0544842	−	0.167685i
$59$	−3.15745	−	9.71764i	−0.411065	−	1.26513i	−0.915723	−	0.401809i	$-0.868381\pi$
$59$	−3.15745	−	9.71764i	−0.411065	−	1.26513i	0.504658	−	0.863319i	$-0.331619\pi$
$60$	1.36475	−	0.991547i	0.176188	−	0.128008i
$61$	−11.2179	+	8.15030i	−1.43631	+	1.04354i	−0.447511	+	0.894278i	$0.647690\pi$
$61$	−11.2179	+	8.15030i	−1.43631	+	1.04354i	−0.988798	+	0.149261i	$0.952310\pi$
$62$	−1.85795	−	5.71818i	−0.235960	−	0.726210i
$63$	−0.0476812	+	0.146748i	−0.00600727	+	0.0184885i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.0425741			0.00528067
$66$	−0.890097	−	5.52362i	−0.109563	−	0.679911i
$67$	6.39600			0.781396			0.390698	−	0.920519i	$-0.372234\pi$
$67$	6.39600			0.781396			0.390698	+	0.920519i	$0.372234\pi$
$68$	3.81887	+	2.77457i	0.463106	+	0.336466i
$69$	3.62798	−	11.1658i	0.436758	−	1.34420i
$70$	−0.309017	−	0.951057i	−0.0369346	−	0.113673i
$71$	−9.14519	+	6.64437i	−1.08533	+	0.788542i	−0.978605	−	0.205746i	$-0.934038\pi$
$71$	−9.14519	+	6.64437i	−1.08533	+	0.788542i	−0.106729	+	0.994288i	$0.534038\pi$
$72$	−0.124831	+	0.0906951i	−0.0147115	+	0.0106885i
$73$	−0.614104	−	1.89002i	−0.0718754	−	0.221210i	0.908665	−	0.417525i	$-0.137102\pi$
$73$	−0.614104	−	1.89002i	−0.0718754	−	0.221210i	−0.980541	+	0.196315i	$0.937102\pi$
$74$	−2.62188	+	8.06932i	−0.304788	+	0.938040i
$75$	1.36475	+	0.991547i	0.157587	+	0.114494i
$76$	−1.71340			−0.196540
$77$	−3.27718	−	0.510019i	−0.373469	−	0.0581221i
$78$	0.0718191			0.00813192
$79$	7.17650	+	5.21404i	0.807420	+	0.586625i	0.913081	−	0.407777i	$-0.133696\pi$
$79$	7.17650	+	5.21404i	0.807420	+	0.586625i	−0.105662	+	0.994402i	$0.533696\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	−2.63075	−	8.09662i	−0.292306	−	0.899625i
$82$	3.16626	−	2.30042i	0.349655	−	0.254039i
$83$	8.15543	−	5.92527i	0.895175	−	0.650383i	−0.0420472	−	0.999116i	$-0.513388\pi$
$83$	8.15543	−	5.92527i	0.895175	−	0.650383i	0.937222	+	0.348733i	$0.113388\pi$
$84$	−0.521287	−	1.60436i	−0.0568771	−	0.175050i
$85$	−1.45868	+	4.48935i	−0.158216	+	0.486938i
$86$	5.19757	+	3.77626i	0.560469	+	0.407204i
$87$	2.26515			0.242849
$88$	−2.35151	−	2.33889i	−0.250672	−	0.249326i
$89$	2.93362			0.310963			0.155481	−	0.987839i	$-0.450307\pi$
$89$	2.93362			0.310963			0.155481	+	0.987839i	$0.450307\pi$
$90$	−0.124831	−	0.0906951i	−0.0131584	−	0.00956010i
$91$	0.0131561	−	0.0404904i	0.00137914	−	0.00424455i
$92$	−2.15065	−	6.61903i	−0.224221	−	0.690082i
$93$	8.20548	−	5.96163i	0.850868	−	0.618192i
$94$	3.71443	−	2.69869i	0.383115	−	0.278349i
$95$	−0.529469	−	1.62954i	−0.0543223	−	0.167187i
$96$	0.521287	−	1.60436i	0.0532036	−	0.163744i
$97$	14.1426	+	10.2752i	1.43596	+	1.04329i	0.988867	+	0.148803i	$0.0475422\pi$
$97$	14.1426	+	10.2752i	1.43596	+	1.04329i	0.447097	+	0.894485i	$0.352458\pi$
$98$	−1.00000			−0.101015
$99$	−0.455350	+	0.233558i	−0.0457644	+	0.0234734i
$100$	1.00000			0.100000
$101$	4.61879	+	3.35575i	0.459587	+	0.333909i	0.793369	−	0.608741i	$-0.208325\pi$
$101$	4.61879	+	3.35575i	0.459587	+	0.333909i	−0.333782	+	0.942650i	$0.608325\pi$
$102$	−2.46067	+	7.57317i	−0.243643	+	0.749856i
$103$	4.14242	+	12.7491i	0.408165	+	1.25620i	0.918223	+	0.396063i	$0.129624\pi$
$103$	4.14242	+	12.7491i	0.408165	+	1.25620i	−0.510058	+	0.860140i	$0.670376\pi$
$104$	0.0344432	−	0.0250244i	0.00337743	−	0.00245385i
$105$	1.36475	−	0.991547i	0.133186	−	0.0967651i
$106$	4.35787	+	13.4121i	0.423274	+	1.30270i
$107$	−4.93405	+	15.1854i	−0.476992	+	1.46803i	0.366259	+	0.930513i	$0.380638\pi$
$107$	−4.93405	+	15.1854i	−0.476992	+	1.46803i	−0.843252	+	0.537519i	$0.819362\pi$
$108$	−4.30482	−	3.12764i	−0.414232	−	0.300957i
$109$	15.9501			1.52774			0.763871	−	0.645369i	$-0.223297\pi$
$109$	15.9501			1.52774			0.763871	+	0.645369i	$0.223297\pi$
$110$	1.49776	−	2.95917i	0.142806	−	0.282146i
$111$	−14.3128			−1.35851
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	2.67326	−	8.22746i	0.251480	−	0.773975i	−0.743023	−	0.669266i	$-0.766609\pi$
$113$	2.67326	−	8.22746i	0.251480	−	0.773975i	0.994503	−	0.104709i	$-0.0333911\pi$
$114$	−0.893171	−	2.74890i	−0.0836532	−	0.257458i
$115$	5.63049	−	4.09079i	0.525046	−	0.381468i
$116$	1.08633	−	0.789261i	0.100863	−	0.0732811i
$117$	−0.00202999	−	0.00624766i	−0.000187672	−	0.000577596i
$118$	3.15745	−	9.71764i	0.290667	−	0.894581i
$119$	3.81887	+	2.77457i	0.350075	+	0.254344i
$120$	1.68692			0.153994
$121$	−6.51343	−	8.86427i	−0.592130	−	0.805842i
$122$	−13.8661			−1.25538
$123$	5.34123	+	3.88063i	0.481602	+	0.349904i
$124$	1.85795	−	5.71818i	0.166849	−	0.513508i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−0.124831	+	0.0906951i	−0.0111208	+	0.00807976i
$127$	1.47907	−	1.07461i	0.131247	−	0.0953563i	−0.520225	−	0.854029i	$-0.674152\pi$
$127$	1.47907	−	1.07461i	0.131247	−	0.0953563i	0.651472	+	0.758673i	$0.274152\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−3.34904	+	10.3073i	−0.294866	+	0.907505i
$130$	0.0344432	+	0.0250244i	0.00302087	+	0.00219479i
$131$	−1.61678			−0.141259			−0.0706294	−	0.997503i	$-0.522501\pi$
$131$	−1.61678			−0.141259			−0.0706294	+	0.997503i	$0.522501\pi$
$132$	2.52660	−	4.99189i	0.219912	−	0.434488i
$133$	−1.71340			−0.148570
$134$	5.17447	+	3.75947i	0.447006	+	0.324769i
$135$	1.64430	−	5.06062i	0.141518	−	0.435549i
$136$	1.45868	+	4.48935i	0.125081	+	0.384958i
$137$	−8.30594	+	6.03462i	−0.709624	+	0.515572i	−0.883053	−	0.469274i	$-0.844516\pi$
$137$	−8.30594	+	6.03462i	−0.709624	+	0.515572i	0.173428	+	0.984847i	$0.444516\pi$
$138$	9.49818	−	6.90083i	0.808539	−	0.587438i
$139$	−0.601835	−	1.85226i	−0.0510470	−	0.157106i	0.922283	−	0.386514i	$-0.126321\pi$
$139$	−0.601835	−	1.85226i	−0.0510470	−	0.157106i	−0.973330	+	0.229408i	$0.926321\pi$
$140$	0.309017	−	0.951057i	0.0261167	−	0.0803789i
$141$	6.26595	+	4.55248i	0.527689	+	0.383388i
$142$	−11.3041			−0.948617
$143$	0.125639	−	0.0644428i	0.0105065	−	0.00538898i
$144$	−0.154300			−0.0128583
$145$	1.08633	+	0.789261i	0.0902144	+	0.0655446i
$146$	0.614104	−	1.89002i	0.0508236	−	0.156419i
$147$	−0.521287	−	1.60436i	−0.0429950	−	0.132325i
$148$	−6.86418	+	4.98712i	−0.564232	+	0.409938i
$149$	5.23370	−	3.80250i	0.428761	−	0.311513i	−0.352392	−	0.935852i	$-0.614632\pi$
$149$	5.23370	−	3.80250i	0.428761	−	0.311513i	0.781153	+	0.624339i	$0.214632\pi$
$150$	0.521287	+	1.60436i	0.0425629	+	0.130995i
$151$	−7.29619	+	22.4554i	−0.593756	+	1.82739i	−0.0329305	+	0.999458i	$0.510484\pi$
$151$	−7.29619	+	22.4554i	−0.593756	+	1.82739i	−0.560825	+	0.827934i	$0.689516\pi$
$152$	−1.38617	−	1.00711i	−0.112433	−	0.0816873i
$153$	0.728353			0.0588839
$154$	−2.35151	−	2.33889i	−0.189490	−	0.188473i
$155$	6.01245			0.482932
$156$	0.0581029	+	0.0422142i	0.00465196	+	0.00337984i
$157$	3.55033	−	10.9268i	0.283347	−	0.872054i	−0.703542	−	0.710654i	$-0.748399\pi$
$157$	3.55033	−	10.9268i	0.283347	−	0.872054i	0.986889	−	0.161400i	$-0.0516009\pi$
$158$	2.74118	+	8.43649i	0.218077	+	0.671171i
$159$	−19.2462	+	13.9831i	−1.52632	+	1.10894i
$160$	0.809017	−	0.587785i	0.0639584	−	0.0464685i
$161$	−2.15065	−	6.61903i	−0.169495	−	0.521653i
$162$	2.63075	−	8.09662i	0.206691	−	0.636131i
$163$	11.4311	+	8.30519i	0.895354	+	0.650513i	0.937269	−	0.348608i	$-0.113346\pi$
$163$	11.4311	+	8.30519i	0.895354	+	0.650513i	−0.0419142	+	0.999121i	$0.513346\pi$
$164$	3.91371			0.305609
$165$	5.52833	+	0.860361i	0.430380	+	0.0669790i
$166$	10.0807			0.782412
$167$	12.6219	+	9.17034i	0.976711	+	0.709622i	0.956971	−	0.290183i	$-0.0937161\pi$
$167$	12.6219	+	9.17034i	0.976711	+	0.709622i	0.0197402	+	0.999805i	$0.493716\pi$
$168$	0.521287	−	1.60436i	0.0402182	−	0.123779i
$169$	−4.01666	−	12.3620i	−0.308974	−	0.950924i
$170$	−3.81887	+	2.77457i	−0.292894	+	0.212800i
$171$	−0.213885	+	0.155397i	−0.0163562	+	0.0118835i
$172$	1.98530	+	6.11011i	0.151377	+	0.465892i
$173$	1.91954	−	5.90774i	0.145940	−	0.449157i	−0.851191	−	0.524856i	$-0.824119\pi$
$173$	1.91954	−	5.90774i	0.145940	−	0.449157i	0.997131	+	0.0756996i	$0.0241190\pi$
$174$	1.83254	+	1.33142i	0.138925	+	0.100935i
$175$	1.00000			0.0755929
$176$	−0.527646	−	3.27438i	−0.0397728	−	0.246816i
$177$	17.2365			1.29557
$178$	2.37335	+	1.72434i	0.177890	+	0.129245i
$179$	4.91555	−	15.1285i	0.367406	−	1.13076i	−0.581055	−	0.813864i	$-0.697360\pi$
$179$	4.91555	−	15.1285i	0.367406	−	1.13076i	0.948461	−	0.316894i	$-0.102640\pi$
$180$	−0.0476812	−	0.146748i	−0.00355395	−	0.0109379i
$181$	5.33901	−	3.87902i	0.396845	−	0.288325i	−0.371409	−	0.928469i	$-0.621125\pi$
$181$	5.33901	−	3.87902i	0.396845	−	0.288325i	0.768255	+	0.640144i	$0.221125\pi$
$182$	0.0344432	−	0.0250244i	0.00255310	−	0.00185493i
$183$	−7.22823	−	22.2462i	−0.534326	−	1.64449i
$184$	2.15065	−	6.61903i	0.158548	−	0.487962i
$185$	−6.86418	−	4.98712i	−0.504664	−	0.366660i
$186$	10.1425			0.743686
$187$	2.49069	+	15.4563i	0.182137	+	1.13028i
$188$	4.59129			0.334854
$189$	−4.30482	−	3.12764i	−0.313130	−	0.227502i
$190$	0.529469	−	1.62954i	0.0384117	−	0.118219i
$191$	5.30552	+	16.3287i	0.383894	+	1.18150i	0.937280	+	0.348579i	$0.113336\pi$
$191$	5.30552	+	16.3287i	0.383894	+	1.18150i	−0.553386	+	0.832925i	$0.686664\pi$
$192$	1.36475	−	0.991547i	0.0984921	−	0.0715587i
$193$	8.26691	−	6.00626i	0.595065	−	0.432340i	−0.249059	−	0.968488i	$-0.580121\pi$
$193$	8.26691	−	6.00626i	0.595065	−	0.432340i	0.844124	+	0.536148i	$0.180121\pi$
$194$	5.40199	+	16.6256i	0.387841	+	1.19365i
$195$	−0.0221933	+	0.0683041i	−0.00158930	+	0.00489136i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−7.33268			−0.522432			−0.261216	−	0.965280i	$-0.584124\pi$
$197$	−7.33268			−0.522432			−0.261216	+	0.965280i	$0.584124\pi$
$198$	−0.505667	−	0.0786958i	−0.0359362	−	0.00559267i
$199$	−8.90352			−0.631154			−0.315577	−	0.948900i	$-0.602198\pi$
$199$	−8.90352			−0.631154			−0.315577	+	0.948900i	$0.602198\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$	−3.33415	+	10.2615i	−0.235173	+	0.723788i
$202$	1.76422	+	5.42972i	0.124130	+	0.382033i
$203$	1.08633	−	0.789261i	0.0762451	−	0.0553953i
$204$	−6.44213	+	4.68048i	−0.451039	+	0.327699i
$205$	1.20940	+	3.72216i	0.0844684	+	0.259967i
$206$	−4.14242	+	12.7491i	−0.288616	+	0.888269i
$207$	−0.868782	−	0.631207i	−0.0603846	−	0.0438719i
$208$	0.0425741			0.00295198
$209$	−4.02907	−	4.00745i	−0.278696	−	0.277201i
$210$	1.68692			0.116409
$211$	−3.67914	−	2.67305i	−0.253283	−	0.184021i	0.453898	−	0.891054i	$-0.350033\pi$
$211$	−3.67914	−	2.67305i	−0.253283	−	0.184021i	−0.707180	+	0.707033i	$0.750033\pi$
$212$	−4.35787	+	13.4121i	−0.299300	+	0.921150i
$213$	−5.89267	−	18.1358i	−0.403759	−	1.24264i
$214$	−12.9175	+	9.38512i	−0.883022	+	0.641553i
$215$	−5.19757	+	3.77626i	−0.354471	+	0.257539i
$216$	−1.64430	−	5.06062i	−0.111880	−	0.344332i
$217$	1.85795	−	5.71818i	0.126126	−	0.388176i
$218$	12.9039	+	9.37523i	0.873962	+	0.634970i
$219$	3.35239			0.226533
$220$	2.95107	−	1.51366i	0.198961	−	0.102051i
$221$	−0.200966			−0.0135184
$222$	−11.5793	−	8.41287i	−0.777153	−	0.564635i
$223$	5.58399	−	17.1857i	0.373931	−	1.15084i	−0.570265	−	0.821461i	$-0.693160\pi$
$223$	5.58399	−	17.1857i	0.373931	−	1.15084i	0.944197	−	0.329382i	$-0.106840\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	0.124831	−	0.0906951i	0.00832207	−	0.00604634i
$226$	6.99870	−	5.08485i	0.465546	−	0.338239i
$227$	0.299901	+	0.923001i	0.0199052	+	0.0612618i	0.960516	−	0.278226i	$-0.0897464\pi$
$227$	0.299901	+	0.923001i	0.0199052	+	0.0612618i	−0.940611	+	0.339488i	$0.889746\pi$
$228$	0.893171	−	2.74890i	0.0591517	−	0.182050i
$229$	1.99255	+	1.44767i	0.131671	+	0.0956648i	0.651671	−	0.758501i	$-0.274068\pi$
$229$	1.99255	+	1.44767i	0.131671	+	0.0956648i	−0.520000	+	0.854166i	$0.674068\pi$
$230$	6.95966			0.458907
$231$	2.52660	−	4.99189i	0.166238	−	0.328442i
$232$	1.34277			0.0881573
$233$	5.38030	+	3.90901i	0.352475	+	0.256088i	0.749907	−	0.661544i	$-0.230098\pi$
$233$	5.38030	+	3.90901i	0.352475	+	0.256088i	−0.397432	+	0.917632i	$0.630098\pi$
$234$	0.00202999	−	0.00624766i	0.000132704	−	0.000408422i
$235$	1.41879	+	4.36658i	0.0925515	+	0.284844i
$236$	8.26632	−	6.00583i	0.538091	−	0.390946i
$237$	−12.1062	+	8.79566i	−0.786382	+	0.571340i
$238$	1.45868	+	4.48935i	0.0945520	+	0.291001i
$239$	6.50571	−	20.0225i	0.420819	−	1.29515i	−0.486122	−	0.873891i	$-0.661589\pi$
$239$	6.50571	−	20.0225i	0.420819	−	1.29515i	0.906941	−	0.421257i	$-0.138411\pi$
$240$	1.36475	+	0.991547i	0.0880941	+	0.0640041i
$241$	−7.93244			−0.510973			−0.255487	−	0.966813i	$-0.582236\pi$
$241$	−7.93244			−0.510973			−0.255487	+	0.966813i	$0.582236\pi$
$242$	−0.0591910	−	10.9998i	−0.00380494	−	0.707097i
$243$	−1.60191			−0.102763
$244$	−11.2179	−	8.15030i	−0.718154	−	0.521770i
$245$	0.309017	−	0.951057i	0.0197424	−	0.0607608i
$246$	2.04017	+	6.27899i	0.130076	+	0.400334i
$247$	0.0590148	−	0.0428768i	0.00375502	−	0.00272818i
$248$	4.86418	−	3.53403i	0.308876	−	0.224411i
$249$	5.25492	+	16.1730i	0.333017	+	1.02492i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−15.3253	−	11.1345i	−0.967323	−	0.702801i	−0.0124831	−	0.999922i	$-0.503974\pi$
$251$	−15.3253	−	11.1345i	−0.967323	−	0.702801i	−0.954840	+	0.297121i	$0.903974\pi$
$252$	−0.154300			−0.00971997
$253$	10.4239	−	20.5949i	0.655345	−	1.29479i
$254$	1.82824			0.114714
$255$	−6.44213	−	4.68048i	−0.403422	−	0.293103i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−8.30015	−	25.5452i	−0.517749	−	1.59347i	−0.778224	−	0.627987i	$-0.783879\pi$
$257$	−8.30015	−	25.5452i	−0.517749	−	1.59347i	0.260475	−	0.965481i	$-0.416121\pi$
$258$	−8.76789	+	6.37024i	−0.545865	+	0.396594i
$259$	−6.86418	+	4.98712i	−0.426519	+	0.309884i
$260$	0.0131561	+	0.0404904i	0.000815908	+	0.00251111i
$261$	0.0640250	−	0.197049i	0.00396305	−	0.0121970i
$262$	−1.30800	−	0.950320i	−0.0808087	−	0.0587109i
$263$	−13.3750			−0.824740			−0.412370	−	0.911017i	$-0.635299\pi$
$263$	−13.3750			−0.824740			−0.412370	+	0.911017i	$0.635299\pi$
$264$	4.97822	−	2.55343i	0.306389	−	0.157153i
$265$	−14.1024			−0.866301
$266$	−1.38617	−	1.00711i	−0.0849913	−	0.0617498i
$267$	−1.52926	+	4.70657i	−0.0935890	+	0.288037i
$268$	1.97647	+	6.08296i	0.120732	+	0.371576i
$269$	3.28444	−	2.38629i	0.200256	−	0.145494i	−0.483138	−	0.875544i	$-0.660503\pi$
$269$	3.28444	−	2.38629i	0.200256	−	0.145494i	0.683394	+	0.730050i	$0.260503\pi$
$270$	4.30482	−	3.12764i	0.261983	−	0.190342i
$271$	7.11437	+	21.8958i	0.432167	+	1.33007i	0.895962	+	0.444131i	$0.146488\pi$
$271$	7.11437	+	21.8958i	0.432167	+	1.33007i	−0.463794	+	0.885943i	$0.653512\pi$
$272$	−1.45868	+	4.48935i	−0.0884453	+	0.272207i
$273$	0.0581029	+	0.0422142i	0.00351655	+	0.00255492i
$274$	−10.2667			−0.620235
$275$	2.35151	+	2.33889i	0.141801	+	0.141040i
$276$	11.7404			0.706689
$277$	18.0299	+	13.0995i	1.08331	+	0.787073i	0.978258	−	0.207394i	$-0.0664981\pi$
$277$	18.0299	+	13.0995i	1.08331	+	0.787073i	0.105055	+	0.994466i	$0.466498\pi$
$278$	0.601835	−	1.85226i	0.0360956	−	0.111091i
$279$	−0.286681	−	0.882314i	−0.0171632	−	0.0528227i
$280$	0.809017	−	0.587785i	0.0483480	−	0.0351269i
$281$	1.81996	−	1.32228i	0.108569	−	0.0788803i	−0.532176	−	0.846634i	$-0.678625\pi$
$281$	1.81996	−	1.32228i	0.108569	−	0.0788803i	0.640745	+	0.767754i	$0.278625\pi$
$282$	2.39338	+	7.36607i	0.142524	+	0.438643i
$283$	−1.14656	+	3.52875i	−0.0681559	+	0.209762i	−0.979334	−	0.202251i	$-0.935174\pi$
$283$	−1.14656	+	3.52875i	−0.0681559	+	0.209762i	0.911178	+	0.412013i	$0.135174\pi$
$284$	−9.14519	−	6.64437i	−0.542667	−	0.394271i
$285$	2.89036			0.171210
$286$	0.139523	+	0.0217136i	0.00825016	+	0.00128395i
$287$	3.91371			0.231019
$288$	−0.124831	−	0.0906951i	−0.00735574	−	0.00534426i
$289$	1.63223	−	5.02347i	0.0960133	−	0.295498i
$290$	0.414939	+	1.27705i	0.0243661	+	0.0749911i
$291$	−23.8574	+	17.3334i	−1.39855	+	1.01610i
$292$	1.60774	−	1.16810i	0.0940862	−	0.0683576i
$293$	0.572205	+	1.76107i	0.0334286	+	0.102883i	0.966379	−	0.257123i	$-0.0827747\pi$
$293$	0.572205	+	1.76107i	0.0334286	+	0.102883i	−0.932950	+	0.360006i	$0.882775\pi$
$294$	0.521287	−	1.60436i	0.0304021	−	0.0935680i
$295$	8.26632	+	6.00583i	0.481284	+	0.349673i
$296$	−8.48459			−0.493157
$297$	−2.80763	−	17.4232i	−0.162915	−	1.01099i
$298$	6.46920			0.374751
$299$	0.239713	+	0.174162i	0.0138630	+	0.0100720i
$300$	−0.521287	+	1.60436i	−0.0300965	+	0.0926276i
$301$	1.98530	+	6.11011i	0.114431	+	0.352181i
$302$	−19.1017	+	13.8782i	−1.09918	+	0.798600i
$303$	−7.79153	+	5.66088i	−0.447612	+	0.325209i
$304$	−0.529469	−	1.62954i	−0.0303671	−	0.0934603i
$305$	4.28487	−	13.1875i	0.245351	−	0.755112i
$306$	0.589250	+	0.428115i	0.0336852	+	0.0244737i
$307$	−6.66980			−0.380666			−0.190333	−	0.981720i	$-0.560957\pi$
$307$	−6.66980			−0.380666			−0.190333	+	0.981720i	$0.560957\pi$
$308$	−0.527646	−	3.27438i	−0.0300654	−	0.186575i
$309$	−22.6134			−1.28643
$310$	4.86418	+	3.53403i	0.276267	+	0.200719i
$311$	4.66520	−	14.3580i	0.264539	−	0.814168i	−0.727260	−	0.686362i	$-0.759207\pi$
$311$	4.66520	−	14.3580i	0.264539	−	0.814168i	0.991799	−	0.127806i	$-0.0407935\pi$
$312$	0.0221933	+	0.0683041i	0.00125645	+	0.00386696i
$313$	−5.93611	+	4.31284i	−0.335529	+	0.243776i	−0.742773	−	0.669543i	$-0.766490\pi$
$313$	−5.93611	+	4.31284i	−0.335529	+	0.243776i	0.407244	+	0.913319i	$0.366490\pi$
$314$	9.29489	−	6.75314i	0.524541	−	0.381102i
$315$	−0.0476812	−	0.146748i	−0.00268653	−	0.00826830i
$316$	−2.74118	+	8.43649i	−0.154203	+	0.474589i
$317$	−18.1948	−	13.2193i	−1.02192	−	0.742468i	−0.0552441	−	0.998473i	$-0.517594\pi$
$317$	−18.1948	−	13.2193i	−1.02192	−	0.742468i	−0.966675	+	0.256005i	$0.917594\pi$
$318$	−23.7896			−1.33405
$319$	4.40050	+	0.684839i	0.246381	+	0.0383436i
$320$	1.00000			0.0559017
$321$	−21.7908	−	15.8319i	−1.21624	−	0.883653i
$322$	2.15065	−	6.61903i	0.119851	−	0.368864i
$323$	2.49929	+	7.69203i	0.139064	+	0.427996i
$324$	6.88740	−	5.00399i	0.382633	−	0.277999i
$325$	−0.0344432	+	0.0250244i	−0.00191056	+	0.00138811i
$326$	4.36630	+	13.4381i	0.241827	+	0.744267i
$327$	−8.31457	+	25.5896i	−0.459797	+	1.41511i
$328$	3.16626	+	2.30042i	0.174827	+	0.127020i
$329$	4.59129			0.253126
$330$	3.96681	+	3.94552i	0.218366	+	0.217194i
$331$	10.3154			0.566987			0.283494	−	0.958974i	$-0.408507\pi$
$331$	10.3154			0.566987			0.283494	+	0.958974i	$0.408507\pi$
$332$	8.15543	+	5.92527i	0.447587	+	0.325191i
$333$	−0.404556	+	1.24509i	−0.0221695	+	0.0682307i
$334$	4.82113	+	14.8379i	0.263801	+	0.811895i
$335$	−5.17447	+	3.75947i	−0.282712	+	0.205402i
$336$	1.36475	−	0.991547i	0.0744531	−	0.0540933i
$337$	−8.40752	−	25.8757i	−0.457987	−	1.40954i	−0.867593	−	0.497275i	$-0.834334\pi$
$337$	−8.40752	−	25.8757i	−0.457987	−	1.40954i	0.409606	−	0.912262i	$-0.365666\pi$
$338$	4.01666	−	12.3620i	0.218478	−	0.672405i
$339$	11.8062	+	8.57774i	0.641227	+	0.465879i
$340$	−4.72038			−0.255999
$341$	17.7432	−	9.10082i	0.960847	−	0.492837i
$342$	−0.264377			−0.0142958
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−1.98530	+	6.11011i	−0.107040	+	0.329435i
$345$	3.62798	+	11.1658i	0.195324	+	0.601146i
$346$	5.02542	−	3.65118i	0.270168	−	0.196289i
$347$	5.38238	−	3.91053i	0.288941	−	0.209928i	−0.433867	−	0.900977i	$-0.642851\pi$
$347$	5.38238	−	3.91053i	0.288941	−	0.209928i	0.722808	+	0.691049i	$0.242851\pi$
$348$	0.699970	+	2.15428i	0.0375223	+	0.115482i
$349$	−7.86699	+	24.2121i	−0.421110	+	1.29604i	0.485560	+	0.874204i	$0.338616\pi$
$349$	−7.86699	+	24.2121i	−0.421110	+	1.29604i	−0.906670	+	0.421841i	$0.861384\pi$
$350$	0.809017	+	0.587785i	0.0432438	+	0.0314184i
$351$	0.226539			0.0120918
$352$	1.49776	−	2.95917i	0.0798309	−	0.157725i
$353$	−29.0584			−1.54662			−0.773311	−	0.634026i	$-0.781401\pi$
$353$	−29.0584			−1.54662			−0.773311	+	0.634026i	$0.781401\pi$
$354$	13.9446	+	10.1314i	0.741148	+	0.538476i
$355$	3.49315	−	10.7508i	0.185397	−	0.570594i
$356$	0.906538	+	2.79004i	0.0480464	+	0.147872i
$357$	−6.44213	+	4.68048i	−0.340953	+	0.247717i
$358$	12.8691	−	9.34994i	0.680152	−	0.494160i
$359$	−8.75211	−	26.9362i	−0.461918	−	1.42164i	−0.862817	−	0.505516i	$-0.831302\pi$
$359$	−8.75211	−	26.9362i	−0.461918	−	1.42164i	0.400898	−	0.916122i	$-0.368698\pi$
$360$	0.0476812	−	0.146748i	0.00251302	−	0.00773428i
$361$	12.9963	+	9.44234i	0.684014	+	0.496965i
$362$	6.59938			0.346856
$363$	17.6168	−	5.82904i	0.924643	−	0.305945i
$364$	0.0425741			0.00223149
$365$	1.60774	+	1.16810i	0.0841532	+	0.0611409i
$366$	7.22823	−	22.2462i	0.377826	−	1.16283i
$367$	−8.50364	−	26.1715i	−0.443887	−	1.36614i	−0.883700	−	0.468053i	$-0.844956\pi$
$367$	−8.50364	−	26.1715i	−0.443887	−	1.36614i	0.439814	−	0.898089i	$-0.355044\pi$
$368$	5.63049	−	4.09079i	0.293509	−	0.213247i
$369$	0.488553	−	0.354954i	0.0254330	−	0.0184782i
$370$	−2.62188	−	8.06932i	−0.136305	−	0.419504i
$371$	−4.35787	+	13.4121i	−0.226249	+	0.696324i
$372$	8.20548	+	5.96163i	0.425434	+	0.309096i
$373$	−22.9306			−1.18730			−0.593650	−	0.804724i	$-0.702313\pi$
$373$	−22.9306			−1.18730			−0.593650	+	0.804724i	$0.702313\pi$
$374$	−7.07000	+	13.9684i	−0.365581	+	0.722290i
$375$	−1.68692			−0.0871122
$376$	3.71443	+	2.69869i	0.191557	+	0.139175i
$377$	−0.0176657	+	0.0543694i	−0.000909829	+	0.00280016i
$378$	−1.64430	−	5.06062i	−0.0845734	−	0.260290i
$379$	−12.4702	+	9.06012i	−0.640550	+	0.465387i	−0.860039	−	0.510228i	$-0.829561\pi$
$379$	−12.4702	+	9.06012i	−0.640550	+	0.465387i	0.219489	+	0.975615i	$0.429561\pi$
$380$	1.38617	−	1.00711i	0.0711089	−	0.0516636i
$381$	0.953036	+	2.93314i	0.0488255	+	0.150270i
$382$	−5.30552	+	16.3287i	−0.271454	+	0.835449i
$383$	24.9927	+	18.1582i	1.27707	+	0.927843i	0.999460	−	0.0328519i	$-0.0104590\pi$
$383$	24.9927	+	18.1582i	1.27707	+	0.927843i	0.277606	+	0.960695i	$0.410459\pi$
$384$	1.68692			0.0860853
$385$	2.95107	−	1.51366i	0.150401	−	0.0771433i
$386$	10.2185			0.520106
$387$	0.801984	+	0.582675i	0.0407671	+	0.0296190i
$388$	−5.40199	+	16.6256i	−0.274245	+	0.844038i
$389$	0.139877	+	0.430497i	0.00709204	+	0.0218270i	0.954540	−	0.298083i	$-0.0963473\pi$
$389$	0.139877	+	0.430497i	0.00709204	+	0.0218270i	−0.947448	+	0.319910i	$0.896347\pi$
$390$	−0.0581029	+	0.0422142i	−0.00294216	+	0.00213760i
$391$	−26.5780	+	19.3101i	−1.34411	+	0.976553i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	0.842807	−	2.59389i	0.0425140	−	0.130845i
$394$	−5.93227	−	4.31004i	−0.298863	−	0.217137i
$395$	−8.87065			−0.446331
$396$	−0.362837	−	0.360890i	−0.0182333	−	0.0181354i
$397$	24.1263			1.21086			0.605431	−	0.795897i	$-0.293001\pi$
$397$	24.1263			1.21086			0.605431	+	0.795897i	$0.293001\pi$
$398$	−7.20310	−	5.23336i	−0.361059	−	0.262325i
$399$	0.893171	−	2.74890i	0.0447145	−	0.137617i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	9.08207	−	6.59851i	0.453537	−	0.329514i	−0.337454	−	0.941342i	$-0.609566\pi$
$401$	9.08207	−	6.59851i	0.453537	−	0.329514i	0.790991	+	0.611828i	$0.209566\pi$
$402$	−8.72892	+	6.34193i	−0.435359	+	0.316307i
$403$	0.0791006	+	0.243447i	0.00394028	+	0.0121269i
$404$	−1.76422	+	5.42972i	−0.0877733	+	0.270138i
$405$	6.88740	+	5.00399i	0.342238	+	0.248650i
$406$	1.34277			0.0666406
$407$	−27.8055	−	4.32730i	−1.37827	−	0.214496i
$408$	−7.96291			−0.394223
$409$	24.6566	+	17.9140i	1.21919	+	0.885792i	0.996032	−	0.0889907i	$-0.0283641\pi$
$409$	24.6566	+	17.9140i	1.21919	+	0.885792i	0.223156	+	0.974783i	$0.428364\pi$
$410$	−1.20940	+	3.72216i	−0.0597282	+	0.183824i
$411$	−5.35190	−	16.4715i	−0.263990	−	0.812477i
$412$	−10.8450	+	7.87936i	−0.534295	+	0.388188i
$413$	8.26632	−	6.00583i	0.406759	−	0.295528i
$414$	−0.331845	−	1.02132i	−0.0163093	−	0.0501949i
$415$	−3.11510	+	9.58728i	−0.152914	+	0.470621i
$416$	0.0344432	+	0.0250244i	0.00168872	+	0.00122692i
$417$	3.28541			0.160887
$418$	−0.904067	−	5.61032i	−0.0442194	−	0.274410i
$419$	11.8710			0.579937			0.289968	−	0.957036i	$-0.406355\pi$
$419$	11.8710			0.579937			0.289968	+	0.957036i	$0.406355\pi$
$420$	1.36475	+	0.991547i	0.0665928	+	0.0483825i
$421$	7.34459	−	22.6043i	0.357953	−	1.10167i	−0.596324	−	0.802744i	$-0.703373\pi$
$421$	7.34459	−	22.6043i	0.357953	−	1.10167i	0.954277	−	0.298923i	$-0.0966274\pi$
$422$	−1.40531	−	4.32509i	−0.0684093	−	0.210542i
$423$	0.573136	−	0.416408i	0.0278668	−	0.0202464i
$424$	−11.4090	+	8.28916i	−0.554072	+	0.402557i
$425$	−1.45868	−	4.48935i	−0.0707563	−	0.217765i
$426$	5.89267	−	18.1358i	0.285501	−	0.878681i
$427$	−11.2179	−	8.15030i	−0.542874	−	0.394421i
$428$	−15.9669			−0.771790
$429$	0.0378951	+	0.235163i	0.00182959	+	0.0113538i
$430$	−6.42455			−0.309819
$431$	−22.0004	−	15.9842i	−1.05972	−	0.769932i	−0.0856833	−	0.996322i	$-0.527307\pi$
$431$	−22.0004	−	15.9842i	−1.05972	−	0.769932i	−0.974037	+	0.226391i	$0.927307\pi$
$432$	1.64430	−	5.06062i	0.0791112	−	0.243479i
$433$	−0.683128	−	2.10245i	−0.0328290	−	0.101037i	0.933299	−	0.359099i	$-0.116916\pi$
$433$	−0.683128	−	2.10245i	−0.0328290	−	0.101037i	−0.966128	+	0.258062i	$0.916916\pi$
$434$	4.86418	−	3.53403i	0.233488	−	0.169639i
$435$	−1.83254	+	1.33142i	−0.0878638	+	0.0638368i
$436$	4.92885	+	15.1694i	0.236049	+	0.726484i
$437$	3.68492	−	11.3410i	0.176274	−	0.542515i
$438$	2.71214	+	1.97048i	0.129591	+	0.0941533i
$439$	−6.47985			−0.309267			−0.154633	−	0.987972i	$-0.549420\pi$
$439$	−6.47985			−0.309267			−0.154633	+	0.987972i	$0.549420\pi$
$440$	3.27718	+	0.510019i	0.156233	+	0.0243142i
$441$	−0.154300			−0.00734760
$442$	−0.162585	−	0.118125i	−0.00773338	−	0.00561863i
$443$	5.27776	−	16.2433i	0.250754	−	0.771741i	−0.743883	−	0.668310i	$-0.767018\pi$
$443$	5.27776	−	16.2433i	0.250754	−	0.771741i	0.994637	−	0.103431i	$-0.0329820\pi$
$444$	−4.42291	−	13.6123i	−0.209902	−	0.646011i
$445$	−2.37335	+	1.72434i	−0.112507	+	0.0817414i
$446$	14.6191	−	10.6214i	0.692233	−	0.502937i
$447$	3.37231	+	10.3789i	0.159505	+	0.490906i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	−10.6246	−	7.71925i	−0.501408	−	0.364294i	0.308147	−	0.951339i	$-0.400291\pi$
$449$	−10.6246	−	7.71925i	−0.501408	−	0.364294i	−0.809554	+	0.587045i	$0.800291\pi$
$450$	0.154300			0.00727376
$451$	9.20313	+	9.15374i	0.433358	+	0.431033i
$452$	8.65087			0.406903
$453$	−32.2230	−	23.4114i	−1.51397	−	1.09996i
$454$	−0.299901	+	0.923001i	−0.0140751	+	0.0433186i
$455$	0.0131561	+	0.0404904i	0.000616769	+	0.00189822i
$456$	2.33835	−	1.69891i	0.109503	−	0.0795589i
$457$	−12.5000	+	9.08176i	−0.584724	+	0.424827i	−0.840424	−	0.541929i	$-0.817694\pi$
$457$	−12.5000	+	9.08176i	−0.584724	+	0.424827i	0.255700	+	0.966756i	$0.417694\pi$
$458$	0.761085	+	2.34238i	0.0355632	+	0.109452i
$459$	−7.76170	+	23.8881i	−0.362285	+	1.11500i
$460$	5.63049	+	4.09079i	0.262523	+	0.190734i
$461$	−33.8352			−1.57586			−0.787932	−	0.615763i	$-0.788848\pi$
$461$	−33.8352			−1.57586			−0.787932	+	0.615763i	$0.788848\pi$
$462$	4.97822	−	2.55343i	0.231608	−	0.118796i
$463$	31.7915			1.47748			0.738738	−	0.673993i	$-0.235422\pi$
$463$	31.7915			1.47748			0.738738	+	0.673993i	$0.235422\pi$
$464$	1.08633	+	0.789261i	0.0504314	+	0.0366405i
$465$	−3.13421	+	9.64612i	−0.145346	+	0.447328i
$466$	2.05509	+	6.32492i	0.0952002	+	0.292996i
$467$	13.7772	−	10.0097i	0.637531	−	0.463194i	−0.221470	−	0.975167i	$-0.571085\pi$
$467$	13.7772	−	10.0097i	0.637531	−	0.463194i	0.859001	+	0.511974i	$0.171085\pi$
$468$	0.00531457	−	0.00386126i	0.000245666	−	0.000178487i
$469$	1.97647	+	6.08296i	0.0912650	+	0.280885i
$470$	−1.41879	+	4.36658i	−0.0654438	+	0.201415i
$471$	15.6797	+	11.3920i	0.722485	+	0.524916i
$472$	10.2177			0.470309
$473$	−9.62244	+	19.0114i	−0.442440	+	0.874144i
$474$	−14.9641			−0.687323
$475$	1.38617	+	1.00711i	0.0636017	+	0.0462093i
$476$	−1.45868	+	4.48935i	−0.0668584	+	0.205769i
$477$	0.672418	+	2.06949i	0.0307879	+	0.0947554i
$478$	17.0322	−	12.3746i	0.779033	−	0.566001i
$479$	−24.2477	+	17.6170i	−1.10791	+	0.804942i	−0.982333	−	0.187143i	$-0.940077\pi$
$479$	−24.2477	+	17.6170i	−1.10791	+	0.804942i	−0.125574	+	0.992084i	$0.540077\pi$
$480$	0.521287	+	1.60436i	0.0237934	+	0.0732285i
$481$	0.111624	−	0.343544i	0.00508963	−	0.0156643i
$482$	−6.41748	−	4.66257i	−0.292308	−	0.212374i
$483$	11.7404			0.534207
$484$	6.41766	−	8.93385i	0.291712	−	0.406084i
$485$	−17.4812			−0.793781
$486$	−1.29597	−	0.941579i	−0.0587865	−	0.0427109i
$487$	0.226524	−	0.697170i	0.0102648	−	0.0315918i	−0.945793	−	0.324770i	$-0.894713\pi$
$487$	0.226524	−	0.697170i	0.0102648	−	0.0315918i	0.956058	+	0.293178i	$0.0947130\pi$
$488$	−4.28487	−	13.1875i	−0.193967	−	0.596969i
$489$	−19.2834	+	14.0102i	−0.872025	+	0.633563i
$490$	0.809017	−	0.587785i	0.0365477	−	0.0265534i
$491$	3.13633	+	9.65263i	0.141541	+	0.435617i	0.996550	−	0.0829954i	$-0.0264487\pi$
$491$	3.13633	+	9.65263i	0.141541	+	0.435617i	−0.855009	+	0.518613i	$0.826449\pi$
$492$	−2.04017	+	6.27899i	−0.0919778	+	0.283079i
$493$	−5.12787	−	3.72561i	−0.230948	−	0.167793i
$494$	0.0729463			0.00328201
$495$	0.231104	−	0.456600i	0.0103873	−	0.0205226i
$496$	6.01245			0.269967
$497$	−9.14519	−	6.64437i	−0.410218	−	0.298041i
$498$	−5.25492	+	16.1730i	−0.235479	+	0.724729i
$499$	−3.45090	−	10.6208i	−0.154483	−	0.475451i	0.843625	−	0.536933i	$-0.180417\pi$
$499$	−3.45090	−	10.6208i	−0.154483	−	0.475451i	−0.998108	+	0.0614823i	$0.980417\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	−21.2921	+	15.4696i	−0.951262	+	0.691132i
$502$	−5.85374	−	18.0159i	−0.261265	−	0.804091i
$503$	−2.30604	+	7.09725i	−0.102821	+	0.316451i	−0.989213	−	0.146485i	$-0.953204\pi$
$503$	−2.30604	+	7.09725i	−0.102821	+	0.316451i	0.886392	+	0.462936i	$0.153204\pi$
$504$	−0.124831	−	0.0906951i	−0.00556042	−	0.00403988i
$505$	−5.70914			−0.254053
$506$	20.5385	−	10.5346i	0.913047	−	0.468319i
$507$	21.9269			0.973808
$508$	1.47907	+	1.07461i	0.0656233	+	0.0476781i
$509$	−9.52514	+	29.3154i	−0.422194	+	1.29938i	0.483461	+	0.875366i	$0.339380\pi$
$509$	−9.52514	+	29.3154i	−0.422194	+	1.29938i	−0.905655	+	0.424015i	$0.860620\pi$
$510$	−2.46067	−	7.57317i	−0.108960	−	0.335346i
$511$	1.60774	−	1.16810i	0.0711224	−	0.0516735i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.81733	−	8.67085i	−0.124388	−	0.382827i
$514$	8.30015	−	25.5452i	0.366104	−	1.12675i
$515$	−10.8450	−	7.87936i	−0.477888	−	0.347206i
$516$	−10.8377			−0.477103
$517$	10.7965	+	10.7385i	0.474828	+	0.472280i
$518$	−8.48459			−0.372791
$519$	8.47748	+	6.15925i	0.372120	+	0.270361i
$520$	−0.0131561	+	0.0404904i	−0.000576934	+	0.00177562i
$521$	−4.50694	−	13.8709i	−0.197453	−	0.607697i	−0.999939	−	0.0110266i	$-0.996490\pi$
$521$	−4.50694	−	13.8709i	−0.197453	−	0.607697i	0.802487	−	0.596670i	$-0.203510\pi$
$522$	0.167620	−	0.121783i	0.00733651	−	0.00533029i
$523$	7.75498	−	5.63432i	0.339102	−	0.246372i	−0.405181	−	0.914236i	$-0.632792\pi$
$523$	7.75498	−	5.63432i	0.339102	−	0.246372i	0.744283	+	0.667865i	$0.232792\pi$
$524$	−0.499613	−	1.53765i	−0.0218257	−	0.0671725i
$525$	−0.521287	+	1.60436i	−0.0227508	+	0.0700199i
$526$	−10.8206	−	7.86164i	−0.471802	−	0.342784i
$527$	−28.3811			−1.23630
$528$	5.52833	+	0.860361i	0.240590	+	0.0374424i
$529$	25.4369			1.10595
$530$	−11.4090	−	8.28916i	−0.495577	−	0.360058i
$531$	0.487194	−	1.49943i	0.0211424	−	0.0650697i
$532$	−0.529469	−	1.62954i	−0.0229554	−	0.0706494i
$533$	−0.134801	+	0.0979384i	−0.00583886	+	0.00424218i
$534$	−4.00365	+	2.90882i	−0.173255	+	0.125877i
$535$	−4.93405	−	15.1854i	−0.213317	−	0.656524i
$536$	−1.97647	+	6.08296i	−0.0853706	+	0.262744i
$537$	21.7091	+	15.7726i	0.936818	+	0.680638i
$538$	4.05979			0.175030
$539$	−0.527646	−	3.27438i	−0.0227273	−	0.141038i
$540$	5.32105			0.228982
$541$	−1.38485	−	1.00615i	−0.0595394	−	0.0432579i	0.557617	−	0.830098i	$-0.311716\pi$
$541$	−1.38485	−	1.00615i	−0.0595394	−	0.0432579i	−0.617157	+	0.786840i	$0.711716\pi$
$542$	−7.11437	+	21.8958i	−0.305588	+	0.940505i
$543$	3.44017	+	10.5878i	0.147632	+	0.454364i
$544$	−3.81887	+	2.77457i	−0.163733	+	0.118959i
$545$	−12.9039	+	9.37523i	−0.552742	+	0.401591i
$546$	0.0221933	+	0.0683041i	0.000949787	+	0.00292314i
$547$	5.40069	−	16.6216i	0.230917	−	0.710688i	−0.766720	−	0.641981i	$-0.778113\pi$
$547$	5.40069	−	16.6216i	0.230917	−	0.710688i	0.997637	−	0.0687070i	$-0.0218873\pi$
$548$	−8.30594	−	6.03462i	−0.354812	−	0.257786i
$549$	−2.13954			−0.0913133
$550$	0.527646	+	3.27438i	0.0224989	+	0.139620i
$551$	2.30070			0.0980131
$552$	9.49818	+	6.90083i	0.404270	+	0.293719i
$553$	−2.74118	+	8.43649i	−0.116567	+	0.358756i
$554$	6.88682	+	21.1954i	0.292593	+	0.900508i
$555$	11.5793	−	8.41287i	0.491515	−	0.357106i
$556$	1.57562	−	1.14476i	0.0668213	−	0.0485485i
$557$	−7.93849	−	24.4322i	−0.336365	−	1.03522i	−0.966046	−	0.258371i	$-0.916814\pi$
$557$	−7.93849	−	24.4322i	−0.336365	−	1.03522i	0.629681	−	0.776854i	$-0.283186\pi$
$558$	0.286681	−	0.882314i	0.0121362	−	0.0373513i
$559$	−0.221282	−	0.160771i	−0.00935923	−	0.00679988i
$560$	1.00000			0.0422577
$561$	−26.0958	−	4.06123i	−1.10177	−	0.171465i
$562$	2.24959			0.0948932
$563$	15.6491	+	11.3697i	0.659531	+	0.479177i	0.866505	−	0.499169i	$-0.166361\pi$
$563$	15.6491	+	11.3697i	0.659531	+	0.479177i	−0.206973	+	0.978347i	$0.566361\pi$
$564$	−2.39338	+	7.36607i	−0.100780	+	0.310168i
$565$	2.67326	+	8.22746i	0.112465	+	0.346132i
$566$	−3.00173	+	2.18089i	−0.126172	+	0.0916695i
$567$	6.88740	−	5.00399i	0.289244	−	0.210148i
$568$	−3.49315	−	10.7508i	−0.146569	−	0.451094i
$569$	0.469462	−	1.44485i	0.0196809	−	0.0605714i	−0.940734	−	0.339146i	$-0.889862\pi$
$569$	0.469462	−	1.44485i	0.0196809	−	0.0605714i	0.960415	+	0.278575i	$0.0898619\pi$
$570$	2.33835	+	1.69891i	0.0979428	+	0.0711596i
$571$	4.97687			0.208276			0.104138	−	0.994563i	$-0.466792\pi$
$571$	4.97687			0.208276			0.104138	+	0.994563i	$0.466792\pi$
$572$	0.100113	+	0.0995762i	0.00418595	+	0.00416349i
$573$	−28.9628			−1.20994
$574$	3.16626	+	2.30042i	0.132157	+	0.0960177i
$575$	−2.15065	+	6.61903i	−0.0896885	+	0.276033i
$576$	−0.0476812	−	0.146748i	−0.00198672	−	0.00611449i
$577$	25.5732	−	18.5800i	1.06463	−	0.773497i	0.0896883	−	0.995970i	$-0.471413\pi$
$577$	25.5732	−	18.5800i	1.06463	−	0.773497i	0.974939	+	0.222473i	$0.0714129\pi$
$578$	4.27322	−	3.10468i	0.177743	−	0.129138i
$579$	5.32675	+	16.3941i	0.221372	+	0.681314i
$580$	−0.414939	+	1.27705i	−0.0172294	+	0.0530267i
$581$	8.15543	+	5.92527i	0.338344	+	0.245822i
$582$	−29.4894			−1.22238
$583$	−41.6171	+	21.3462i	−1.72360	+	0.884069i
$584$	1.98728			0.0822343
$585$	0.00531457	+	0.00386126i	0.000219731	+	0.000159644i
$586$	−0.572205	+	1.76107i	−0.0236376	+	0.0727490i
$587$	2.19984	+	6.77043i	0.0907973	+	0.279445i	0.986136	−	0.165941i	$-0.0530662\pi$
$587$	2.19984	+	6.77043i	0.0907973	+	0.279445i	−0.895338	+	0.445387i	$0.853066\pi$
$588$	1.36475	−	0.991547i	0.0562812	−	0.0408907i
$589$	8.33426	−	6.05520i	0.343407	−	0.249500i
$590$	3.15745	+	9.71764i	0.129990	+	0.400069i
$591$	3.82243	−	11.7642i	0.157234	−	0.483916i
$592$	−6.86418	−	4.98712i	−0.282116	−	0.204969i
$593$	−18.4209			−0.756456			−0.378228	−	0.925713i	$-0.623466\pi$
$593$	−18.4209			−0.756456			−0.378228	+	0.925713i	$0.623466\pi$
$594$	7.96966	−	15.7459i	0.326999	−	0.646063i
$595$	−4.72038			−0.193517
$596$	5.23370	+	3.80250i	0.214381	+	0.155757i
$597$	4.64129	−	14.2844i	0.189955	−	0.584623i
$598$	0.0915622	+	0.281800i	0.00374426	+	0.0115236i
$599$	0.989585	−	0.718975i	0.0404333	−	0.0293765i	−0.567385	−	0.823453i	$-0.692045\pi$
$599$	0.989585	−	0.718975i	0.0404333	−	0.0293765i	0.607818	+	0.794076i	$0.292045\pi$
$600$	−1.36475	+	0.991547i	−0.0557156	+	0.0404797i
$601$	−6.39321	−	19.6763i	−0.260784	−	0.802612i	−0.992635	−	0.121146i	$-0.961343\pi$
$601$	−6.39321	−	19.6763i	−0.260784	−	0.802612i	0.731850	−	0.681465i	$-0.238657\pi$
$602$	−1.98530	+	6.11011i	−0.0809146	+	0.249030i
$603$	0.798420	+	0.580086i	0.0325142	+	0.0236229i
$604$	−23.6110			−0.960717
$605$	10.4798	+	3.34284i	0.426063	+	0.135906i
$606$	−9.63087			−0.391227
$607$	8.33557	+	6.05615i	0.338330	+	0.245811i	0.743957	−	0.668227i	$-0.232947\pi$
$607$	8.33557	+	6.05615i	0.338330	+	0.245811i	−0.405627	+	0.914039i	$0.632947\pi$
$608$	0.529469	−	1.62954i	0.0214728	−	0.0660864i
$609$	0.699970	+	2.15428i	0.0283642	+	0.0872960i
$610$	11.2179	−	8.15030i	0.454201	−	0.329996i
$611$	−0.158139	+	0.114895i	−0.00639761	+	0.00464814i
$612$	0.225074	+	0.692705i	0.00909806	+	0.0280009i
$613$	−13.2106	+	40.6579i	−0.533569	+	1.64216i	0.213151	+	0.977019i	$0.431627\pi$
$613$	−13.2106	+	40.6579i	−0.533569	+	1.64216i	−0.746720	+	0.665138i	$0.768373\pi$
$614$	−5.39598	−	3.92041i	−0.217764	−	0.158215i
$615$	−6.60212			−0.266223
$616$	1.49776	−	2.95917i	0.0603465	−	0.119229i
$617$	10.3582			0.417004			0.208502	−	0.978022i	$-0.433141\pi$
$617$	10.3582			0.417004			0.208502	+	0.978022i	$0.433141\pi$
$618$	−18.2947	−	13.2918i	−0.735919	−	0.534676i
$619$	4.41589	−	13.5907i	0.177490	−	0.546257i	−0.822249	−	0.569128i	$-0.807281\pi$
$619$	4.41589	−	13.5907i	0.177490	−	0.546257i	0.999738	+	0.0228714i	$0.00728084\pi$
$620$	1.85795	+	5.71818i	0.0746171	+	0.229648i
$621$	29.9601	−	21.7673i	1.20226	−	0.873492i
$622$	12.2137	−	8.87374i	0.489723	−	0.355805i
$623$	0.906538	+	2.79004i	0.0363197	+	0.111780i
$624$	−0.0221933	+	0.0683041i	−0.000888445	+	0.00273435i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−7.33744			−0.293263
$627$	8.52967	−	4.37503i	0.340642	−	0.174722i
$628$	11.4891			0.458466
$629$	32.4015	+	23.5411i	1.29193	+	0.938645i
$630$	0.0476812	−	0.146748i	0.00189967	−	0.00584657i
$631$	−3.59946	−	11.0780i	−0.143292	−	0.441008i	0.853495	−	0.521100i	$-0.174478\pi$
$631$	−3.59946	−	11.0780i	−0.143292	−	0.441008i	−0.996787	+	0.0800929i	$0.974478\pi$
$632$	−7.17650	+	5.21404i	−0.285466	+	0.207403i
$633$	6.20642	−	4.50923i	0.246683	−	0.179226i
$634$	−6.94978	−	21.3892i	−0.276011	−	0.849475i
$635$	−0.564956	+	1.73876i	−0.0224196	+	0.0690005i
$636$	−19.2462	−	13.9831i	−0.763160	−	0.554468i
$637$	0.0425741			0.00168685
$638$	3.15754	+	3.14060i	0.125008	+	0.124337i
$639$	−1.74422			−0.0690001
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	5.56992	−	17.1425i	0.219999	−	0.677087i	−0.778762	−	0.627319i	$-0.784152\pi$
$641$	5.56992	−	17.1425i	0.219999	−	0.677087i	0.998761	−	0.0497672i	$-0.0158479\pi$
$642$	−8.32335	−	25.6166i	−0.328496	−	1.01101i
$643$	8.62576	−	6.26698i	0.340167	−	0.247146i	−0.404565	−	0.914509i	$-0.632577\pi$
$643$	8.62576	−	6.26698i	0.340167	−	0.247146i	0.744732	+	0.667363i	$0.232577\pi$
$644$	5.63049	−	4.09079i	0.221872	−	0.161200i
$645$	−3.34904	−	10.3073i	−0.131868	−	0.405848i
$646$	−2.49929	+	7.69203i	−0.0983334	+	0.302639i
$647$	17.5810	+	12.7734i	0.691182	+	0.502173i	0.877048	−	0.480402i	$-0.159509\pi$
$647$	17.5810	+	12.7734i	0.691182	+	0.502173i	−0.185867	+	0.982575i	$0.559509\pi$
$648$	8.51329			0.334434
$649$	33.4853	+	5.21124i	1.31441	+	0.204559i
$650$	−0.0425741			−0.00166989
$651$	8.20548	+	5.96163i	0.321598	+	0.233655i
$652$	−4.36630	+	13.4381i	−0.170997	+	0.526276i
$653$	0.328175	+	1.01002i	0.0128425	+	0.0395251i	0.957272	−	0.289188i	$-0.0933852\pi$
$653$	0.328175	+	1.01002i	0.0128425	+	0.0395251i	−0.944430	+	0.328713i	$0.893385\pi$
$654$	−21.7678	+	15.8153i	−0.851190	+	0.618426i
$655$	1.30800	−	0.950320i	0.0511079	−	0.0371321i
$656$	1.20940	+	3.72216i	0.0472193	+	0.145326i
$657$	0.0947560	−	0.291629i	0.00369679	−	0.0113775i
$658$	3.71443	+	2.69869i	0.144804	+	0.105206i
$659$	33.2641			1.29578			0.647892	−	0.761732i	$-0.275651\pi$
$659$	33.2641			1.29578			0.647892	+	0.761732i	$0.275651\pi$
$660$	0.890097	+	5.52362i	0.0346470	+	0.215007i
$661$	−8.99126			−0.349719			−0.174860	−	0.984593i	$-0.555947\pi$
$661$	−8.99126			−0.349719			−0.174860	+	0.984593i	$0.555947\pi$
$662$	8.34536	+	6.06326i	0.324351	+	0.235655i
$663$	0.104761	−	0.322421i	0.00406858	−	0.0125218i
$664$	3.11510	+	9.58728i	0.120889	+	0.372059i
$665$	1.38617	−	1.00711i	0.0537532	−	0.0390540i
$666$	−1.05914	+	0.769511i	−0.0410409	+	0.0298179i
$667$	2.88784	+	8.88785i	0.111818	+	0.344139i
$668$	−4.82113	+	14.8379i	−0.186535	+	0.574097i
$669$	24.6612	+	17.9174i	0.953457	+	0.692727i
$670$	−6.39600			−0.247099
$671$	−7.31641	−	45.4030i	−0.282447	−	1.75276i
$672$	1.68692			0.0650744
$673$	7.59648	+	5.51916i	0.292823	+	0.212748i	0.724491	−	0.689284i	$-0.242075\pi$
$673$	7.59648	+	5.51916i	0.292823	+	0.212748i	−0.431668	+	0.902032i	$0.642075\pi$
$674$	8.40752	−	25.8757i	0.323845	−	0.996694i
$675$	1.64430	+	5.06062i	0.0632890	+	0.194783i
$676$	10.5158	−	7.64014i	0.404452	−	0.293852i
$677$	−30.5048	+	22.1630i	−1.17239	+	0.851794i	−0.991294	−	0.131670i	$-0.957966\pi$
$677$	−30.5048	+	22.1630i	−1.17239	+	0.851794i	−0.181101	+	0.983465i	$0.557966\pi$
$678$	4.50958	+	13.8791i	0.173190	+	0.533023i
$679$	−5.40199	+	16.6256i	−0.207310	+	0.638033i
$680$	−3.81887	−	2.77457i	−0.146447	−	0.106400i
$681$	−1.63716			−0.0627360
$682$	19.7039	+	3.06647i	0.754500	+	0.117421i
$683$	11.5317			0.441248			0.220624	−	0.975359i	$-0.429191\pi$
$683$	11.5317			0.441248			0.220624	+	0.975359i	$0.429191\pi$
$684$	−0.213885	−	0.155397i	−0.00817810	−	0.00594174i
$685$	3.17259	−	9.76422i	0.121218	−	0.373072i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−3.36127	+	2.44211i	−0.128240	+	0.0931721i
$688$	−5.19757	+	3.77626i	−0.198156	+	0.143968i
$689$	−0.185532	−	0.571010i	−0.00706822	−	0.0217537i
$690$	−3.62798	+	11.1658i	−0.138115	+	0.425074i
$691$	10.2972	+	7.48133i	0.391722	+	0.284603i	0.766161	−	0.642649i	$-0.222165\pi$
$691$	10.2972	+	7.48133i	0.391722	+	0.284603i	−0.374439	+	0.927252i	$0.622165\pi$
$692$	6.21176			0.236136
$693$	−0.362837	−	0.360890i	−0.0137830	−	0.0137091i
$694$	6.65299			0.252544
$695$	1.57562	+	1.14476i	0.0597668	+	0.0434231i
$696$	−0.699970	+	2.15428i	−0.0265323	+	0.0816580i
$697$	−5.70884	−	17.5700i	−0.216238	−	0.665512i
$698$	−20.5960	+	14.9639i	−0.779572	+	0.566392i
$699$	−9.07613	+	6.59420i	−0.343291	+	0.249415i
$700$	0.309017	+	0.951057i	0.0116797	+	0.0359466i
$701$	3.46061	−	10.6507i	0.130705	−	0.402270i	−0.864192	−	0.503162i	$-0.832170\pi$
$701$	3.46061	−	10.6507i	0.130705	−	0.402270i	0.994897	+	0.100892i	$0.0321697\pi$
$702$	0.183274	+	0.133156i	0.00691723	+	0.00502566i
$703$	−14.5375			−0.548291
$704$	2.95107	−	1.51366i	0.111223	−	0.0570483i
$705$	−7.74515			−0.291699
$706$	−23.5087	−	17.0801i	−0.884763	−	0.642818i
$707$	−1.76422	+	5.42972i	−0.0663504	+	0.204205i
$708$	5.32637	+	16.3929i	0.200177	+	0.616082i
$709$	23.0362	−	16.7368i	0.865144	−	0.628564i	−0.0641354	−	0.997941i	$-0.520429\pi$
$709$	23.0362	−	16.7368i	0.865144	−	0.628564i	0.929280	+	0.369377i	$0.120429\pi$
$710$	9.14519	−	6.64437i	0.343213	−	0.249359i
$711$	0.422963	+	1.30175i	0.0158624	+	0.0488193i
$712$	−0.906538	+	2.79004i	−0.0339739	+	0.104561i
$713$	33.8530	+	24.5957i	1.26781	+	0.921115i
$714$	−7.96291			−0.298004
$715$	−0.0637658	+	0.125984i	−0.00238471	+	0.00471154i
$716$	15.9071			0.594475
$717$	28.7319	+	20.8749i	1.07301	+	0.779589i
$718$	8.75211	−	26.9362i	0.326626	−	1.00525i
$719$	−13.7812	−	42.4140i	−0.513951	−	1.58178i	−0.785183	−	0.619263i	$-0.787431\pi$
$719$	−13.7812	−	42.4140i	−0.513951	−	1.58178i	0.271233	−	0.962514i	$-0.412569\pi$
$720$	0.124831	−	0.0906951i	0.00465218	−	0.00338001i
$721$	−10.8450	+	7.87936i	−0.403889	+	0.293443i
$722$	4.96413	+	15.2780i	0.184746	+	0.568589i
$723$	4.13508	−	12.7265i	0.153785	−	0.473302i
$724$	5.33901	+	3.87902i	0.198423	+	0.144163i
$725$	−1.34277			−0.0498693
$726$	17.6785	+	5.63911i	0.656112	+	0.209287i
$727$	50.4565			1.87133			0.935664	−	0.352892i	$-0.114802\pi$
$727$	50.4565			1.87133			0.935664	+	0.352892i	$0.114802\pi$
$728$	0.0344432	+	0.0250244i	0.00127655	+	0.000927467i
$729$	8.72731	−	26.8599i	0.323234	−	0.994811i
$730$	0.614104	+	1.89002i	0.0227290	+	0.0699527i
$731$	24.5345	−	17.8254i	0.907442	−	0.659295i
$732$	18.9238	−	13.7489i	0.699442	−	0.508174i
$733$	11.7734	+	36.2348i	0.434860	+	1.33836i	0.893230	+	0.449600i	$0.148434\pi$
$733$	11.7734	+	36.2348i	0.434860	+	1.33836i	−0.458370	+	0.888762i	$0.651566\pi$
$734$	8.50364	−	26.1715i	0.313875	−	0.966008i
$735$	1.36475	+	0.991547i	0.0503395	+	0.0365738i
$736$	6.95966			0.256537
$737$	−9.57967	+	18.9269i	−0.352872	+	0.697181i
$738$	0.603884			0.0222293
$739$	−0.613466	−	0.445709i	−0.0225667	−	0.0163957i	0.576445	−	0.817136i	$-0.304440\pi$
$739$	−0.613466	−	0.445709i	−0.0225667	−	0.0163957i	−0.599011	+	0.800740i	$0.704440\pi$
$740$	2.62188	−	8.06932i	0.0963823	−	0.296634i
$741$	0.0380260	+	0.117032i	0.00139692	+	0.00429928i
$742$	−11.4090	+	8.28916i	−0.418839	+	0.304305i
$743$	28.0830	−	20.4035i	1.03027	−	0.748532i	0.0619040	−	0.998082i	$-0.480283\pi$
$743$	28.0830	−	20.4035i	1.03027	−	0.748532i	0.968362	+	0.249550i	$0.0802827\pi$
$744$	3.13421	+	9.64612i	0.114906	+	0.353644i
$745$	−1.99909	+	6.15258i	−0.0732411	+	0.225413i
$746$	−18.5512	−	13.4782i	−0.679208	−	0.493473i
$747$	1.55544			0.0569107
$748$	−13.9302	+	7.14506i	−0.509338	+	0.261249i
$749$	−15.9669			−0.583418
$750$	−1.36475	−	0.991547i	−0.0498335	−	0.0362062i
$751$	−14.2175	+	43.7570i	−0.518804	+	1.59672i	0.257447	+	0.966292i	$0.417119\pi$
$751$	−14.2175	+	43.7570i	−0.518804	+	1.59672i	−0.776252	+	0.630423i	$0.782881\pi$
$752$	1.41879	+	4.36658i	0.0517379	+	0.159233i
$753$	25.8525	−	18.7830i	0.942118	−	0.684489i
$754$	−0.0462493	+	0.0336021i	−0.00168430	+	0.00122372i
$755$	−7.29619	−	22.4554i	−0.265536	−	0.817235i
$756$	1.64430	−	5.06062i	0.0598025	−	0.184053i
$757$	18.7292	+	13.6075i	0.680723	+	0.494574i	0.873597	−	0.486649i	$-0.161781\pi$
$757$	18.7292	+	13.6075i	0.680723	+	0.494574i	−0.192874	+	0.981223i	$0.561781\pi$
$758$	−15.4140			−0.559862
$759$	27.6077	+	27.4595i	1.00209	+	0.996717i
$760$	1.71340			0.0621514
$761$	−5.82188	−	4.22984i	−0.211043	−	0.153332i	0.477242	−	0.878772i	$-0.341636\pi$
$761$	−5.82188	−	4.22984i	−0.211043	−	0.153332i	−0.688285	+	0.725440i	$0.741636\pi$
$762$	−0.953036	+	2.93314i	−0.0345249	+	0.106257i
$763$	4.92885	+	15.1694i	0.178436	+	0.549170i
$764$	−13.8900	+	10.0917i	−0.502524	+	0.365105i
$765$	−0.589250	+	0.428115i	−0.0213044	+	0.0154785i
$766$	9.54636	+	29.3807i	0.344924	+	1.06157i
$767$	−0.134426	+	0.413720i	−0.00485383	+	0.0149386i
$768$	1.36475	+	0.991547i	0.0492461	+	0.0357794i
$769$	8.64296			0.311673			0.155837	−	0.987783i	$-0.450193\pi$
$769$	8.64296			0.311673			0.155837	+	0.987783i	$0.450193\pi$
$770$	3.27718	+	0.510019i	0.118101	+	0.0183798i
$771$	45.3104			1.63181
$772$	8.26691	+	6.00626i	0.297533	+	0.216170i
$773$	−12.1811	+	37.4897i	−0.438125	+	1.34841i	0.451725	+	0.892157i	$0.350809\pi$
$773$	−12.1811	+	37.4897i	−0.438125	+	1.34841i	−0.889850	+	0.456253i	$0.849191\pi$
$774$	0.306331	+	0.942788i	0.0110108	+	0.0338878i
$775$	−4.86418	+	3.53403i	−0.174726	+	0.126946i
$776$	−14.1426	+	10.2752i	−0.507690	+	0.368858i
$777$	−4.42291	−	13.6123i	−0.158671	−	0.488339i
$778$	−0.139877	+	0.430497i	−0.00501483	+	0.0154341i
$779$	5.42506	+	3.94153i	0.194373	+	0.141220i
$780$	−0.0718191			−0.00257154
$781$	−5.96455	−	37.0139i	−0.213428	−	1.32446i
$782$	−32.8523			−1.17479
$783$	5.78039	+	4.19970i	0.206574	+	0.150085i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	3.55033	+	10.9268i	0.126717	+	0.389994i
$786$	2.20650	−	1.60311i	0.0787031	−	0.0571812i
$787$	35.8244	−	26.0279i	1.27700	−	0.927796i	0.277543	−	0.960713i	$-0.410480\pi$
$787$	35.8244	−	26.0279i	1.27700	−	0.927796i	0.999458	+	0.0329175i	$0.0104798\pi$
$788$	−2.26592	−	6.97380i	−0.0807202	−	0.248431i
$789$	6.97223	−	21.4583i	0.248218	−	0.763936i
$790$	−7.17650	−	5.21404i	−0.255329	−	0.185507i
$791$	8.65087			0.307589
$792$	−0.0814156	−	0.505236i	−0.00289298	−	0.0179528i
$793$	0.590338			0.0209635
$794$	19.5186	+	14.1811i	0.692688	+	0.503267i
$795$	7.35138	−	22.6252i	0.260726	−	0.802434i
$796$	−2.75134	−	8.46775i	−0.0975186	−	0.300132i
$797$	16.9716	−	12.3306i	0.601165	−	0.436772i	−0.245127	−	0.969491i	$-0.578830\pi$
$797$	16.9716	−	12.3306i	0.601165	−	0.436772i	0.846292	+	0.532719i	$0.178830\pi$
$798$	2.33835	−	1.69891i	0.0827768	−	0.0601409i
$799$	−6.69722	−	20.6119i	−0.236931	−	0.729197i
$800$	−0.309017	+	0.951057i	−0.0109254	+	0.0336249i
$801$	0.366207	+	0.266065i	0.0129393	+	0.00940093i
$802$	11.2261			0.396406
$803$	6.51267	+	1.01355i	0.229827	+	0.0357675i
$804$	−10.7895			−0.380518
$805$	5.63049	+	4.09079i	0.198449	+	0.144181i
$806$	−0.0791006	+	0.243447i	−0.00278620	+	0.00857504i
$807$	2.11632	+	6.51335i	0.0744979	+	0.229281i
$808$	−4.61879	+	3.35575i	−0.162489	+	0.118055i
$809$	19.6326	−	14.2639i	0.690245	−	0.501492i	−0.186496	−	0.982456i	$-0.559713\pi$
$809$	19.6326	−	14.2639i	0.690245	−	0.501492i	0.876741	+	0.480963i	$0.159713\pi$
$810$	2.63075	+	8.09662i	0.0924352	+	0.284486i
$811$	−11.4434	+	35.2190i	−0.401830	+	1.23671i	0.521682	+	0.853140i	$0.325305\pi$
$811$	−11.4434	+	35.2190i	−0.401830	+	1.23671i	−0.923513	+	0.383567i	$0.874695\pi$
$812$	1.08633	+	0.789261i	0.0381225	+	0.0276976i
$813$	−38.8373			−1.36208
$814$	−19.9516	−	19.8445i	−0.699303	−	0.695550i
$815$	−14.1296			−0.494940
$816$	−6.44213	−	4.68048i	−0.225520	−	0.163850i
$817$	−3.40160	+	10.4690i	−0.119007	+	0.366265i
$818$	9.41797	+	28.9855i	0.329291	+	1.01345i
$819$	0.00531457	−	0.00386126i	0.000185706	−	0.000134923i
$820$	−3.16626	+	2.30042i	−0.110571	+	0.0803342i
$821$	6.80912	+	20.9563i	0.237640	+	0.731380i	0.996760	+	0.0804300i	$0.0256293\pi$
$821$	6.80912	+	20.9563i	0.237640	+	0.731380i	−0.759120	+	0.650950i	$0.774371\pi$
$822$	5.35190	−	16.4715i	0.186669	−	0.574508i
$823$	−20.7880	−	15.1034i	−0.724624	−	0.526470i	0.163234	−	0.986587i	$-0.447807\pi$
$823$	−20.7880	−	15.1034i	−0.724624	−	0.526470i	−0.887858	+	0.460117i	$0.847807\pi$
$824$	−13.4052			−0.466991
$825$	−4.97822	+	2.55343i	−0.173320	+	0.0888989i
$826$	10.2177			0.355520
$827$	13.6641	+	9.92753i	0.475146	+	0.345214i	0.799444	−	0.600741i	$-0.205128\pi$
$827$	13.6641	+	9.92753i	0.475146	+	0.345214i	−0.324297	+	0.945955i	$0.605128\pi$
$828$	0.331845	−	1.02132i	0.0115324	−	0.0354932i
$829$	−6.32362	−	19.4621i	−0.219628	−	0.675947i	−0.998793	−	0.0491267i	$-0.984356\pi$
$829$	−6.32362	−	19.4621i	−0.219628	−	0.675947i	0.779164	−	0.626820i	$-0.215644\pi$
$830$	−8.15543	+	5.92527i	−0.283079	+	0.205669i
$831$	−30.4150	+	22.0978i	−1.05509	+	0.766565i
$832$	0.0131561	+	0.0404904i	0.000456107	+	0.00140375i
$833$	−1.45868	+	4.48935i	−0.0505402	+	0.155547i
$834$	2.65795	+	1.93111i	0.0920373	+	0.0668690i
$835$	−15.6015			−0.539913
$836$	2.56626	−	5.07024i	0.0887558	−	0.175358i
$837$	31.9926			1.10583
$838$	9.60385	+	6.97761i	0.331759	+	0.241037i
$839$	10.5187	−	32.3733i	0.363147	−	1.11765i	−0.587987	−	0.808870i	$-0.700079\pi$
$839$	10.5187	−	32.3733i	0.363147	−	1.11765i	0.951134	−	0.308780i	$-0.0999207\pi$
$840$	0.521287	+	1.60436i	0.0179861	+	0.0553556i
$841$	22.0028	−	15.9860i	0.758717	−	0.551240i
$842$	19.2284	−	13.9702i	0.662654	−	0.481446i
$843$	1.17268	+	3.60914i	0.0403893	+	0.124305i
$844$	1.40531	−	4.32509i	0.0483727	−	0.148876i
$845$	10.5158	+	7.64014i	0.361753	+	0.262829i
$846$	0.708435			0.0243565
$847$	6.41766	−	8.93385i	0.220513	−	0.306971i
$848$	−14.1024			−0.484277
$849$	−5.06368	−	3.67898i	−0.173785	−	0.126262i
$850$	1.45868	−	4.48935i	0.0500322	−	0.153983i
$851$	−18.2474	−	56.1598i	−0.625514	−	1.92513i
$852$	15.4272	−	11.2085i	0.528527	−	0.383998i
$853$	16.7298	−	12.1549i	0.572816	−	0.416175i	−0.263311	−	0.964711i	$-0.584814\pi$
$853$	16.7298	−	12.1549i	0.572816	−	0.416175i	0.836127	+	0.548536i	$0.184814\pi$
$854$	−4.28487	−	13.1875i	−0.146625	−	0.451266i
$855$	0.0816968	−	0.251437i	0.00279397	−	0.00859897i
$856$	−12.9175	−	9.38512i	−0.441511	−	0.320777i
$857$	−44.5639			−1.52227			−0.761136	−	0.648592i	$-0.775358\pi$
$857$	−44.5639			−1.52227			−0.761136	+	0.648592i	$0.775358\pi$
$858$	−0.107568	+	0.212525i	−0.00367231	+	0.00725550i
$859$	0.992443			0.0338617			0.0169309	−	0.999857i	$-0.494610\pi$
$859$	0.992443			0.0338617			0.0169309	+	0.999857i	$0.494610\pi$
$860$	−5.19757	−	3.77626i	−0.177236	−	0.128769i
$861$	−2.04017	+	6.27899i	−0.0695287	+	0.213987i
$862$	−8.40339	−	25.8630i	−0.286221	−	0.880896i
$863$	−27.5193	+	19.9939i	−0.936767	+	0.680601i	−0.947640	−	0.319340i	$-0.896539\pi$
$863$	−27.5193	+	19.9939i	−0.936767	+	0.680601i	0.0108730	+	0.999941i	$0.496539\pi$
$864$	4.30482	−	3.12764i	0.146453	−	0.106404i
$865$	1.91954	+	5.90774i	0.0652663	+	0.200869i
$866$	0.683128	−	2.10245i	0.0232136	−	0.0714442i
$867$	7.20858	+	5.23734i	0.244816	+	0.177870i
$868$	6.01245			0.204076
$869$	−26.1779	+	13.4272i	−0.888025	+	0.455485i
$870$	−2.26515			−0.0767957
$871$	−0.220299	−	0.160056i	−0.00746453	−	0.00542330i
$872$	−4.92885	+	15.1694i	−0.166912	+	0.513702i
$873$	0.833526	+	2.56533i	0.0282106	+	0.0868232i
$874$	9.64726	−	7.00914i	0.326323	−	0.237088i
$875$	−0.809017	+	0.587785i	−0.0273498	+	0.0198708i
$876$	1.03594	+	3.18831i	0.0350013	+	0.107723i
$877$	11.6614	−	35.8900i	0.393777	−	1.21192i	−0.536133	−	0.844133i	$-0.680116\pi$
$877$	11.6614	−	35.8900i	0.393777	−	1.21192i	0.929910	−	0.367787i	$-0.119884\pi$
$878$	−5.24231	−	3.80876i	−0.176919	−	0.128540i
$879$	−3.12366			−0.105359
$880$	2.35151	+	2.33889i	0.0792694	+	0.0788440i
$881$	12.1850			0.410522			0.205261	−	0.978707i	$-0.434196\pi$
$881$	12.1850			0.410522			0.205261	+	0.978707i	$0.434196\pi$
$882$	−0.124831	−	0.0906951i	−0.00420328	−	0.00305386i
$883$	−7.41317	+	22.8154i	−0.249473	+	0.767799i	0.745396	+	0.666622i	$0.232261\pi$
$883$	−7.41317	+	22.8154i	−0.249473	+	0.767799i	−0.994869	+	0.101176i	$0.967739\pi$
$884$	−0.0621019	−	0.191130i	−0.00208871	−	0.00642840i
$885$	−13.9446	+	10.1314i	−0.468743	+	0.340562i
$886$	13.8173	−	10.0389i	0.464203	−	0.337263i
$887$	−13.2650	−	40.8256i	−0.445396	−	1.37079i	−0.882049	−	0.471158i	$-0.843836\pi$
$887$	−13.2650	−	40.8256i	−0.445396	−	1.37079i	0.436653	−	0.899630i	$-0.356164\pi$
$888$	4.42291	−	13.6123i	0.148423	−	0.456799i
$889$	1.47907	+	1.07461i	0.0496066	+	0.0360413i
$890$	−2.93362			−0.0983351
$891$	27.8996	+	4.34194i	0.934670	+	0.145460i
$892$	18.0702			0.605034
$893$	6.36430	+	4.62393i	0.212973	+	0.154734i
$894$	−3.37231	+	10.3789i	−0.112787	+	0.347123i
$895$	4.91555	+	15.1285i	0.164309	+	0.505691i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−0.404377	+	0.293797i	−0.0135017	+	0.00980959i
$898$	−4.05825	−	12.4900i	−0.135426	−	0.416797i
$899$	−2.49480	+	7.67821i	−0.0832063	+	0.256083i
$900$	0.124831	+	0.0906951i	0.00416104	+	0.00302317i
$901$	66.5685			2.21772
$902$	2.06505	+	12.8150i	0.0687588	+	0.426693i
$903$	−10.8377			−0.360656
$904$	6.99870	+	5.08485i	0.232773	+	0.169120i
$905$	−2.03932	+	6.27638i	−0.0677893	+	0.208634i
$906$	−12.3081	−	37.8804i	−0.408909	−	1.25849i
$907$	−14.4630	+	10.5080i	−0.480238	+	0.348913i	−0.801418	−	0.598105i	$-0.795921\pi$
$907$	−14.4630	+	10.5080i	−0.480238	+	0.348913i	0.321180	+	0.947018i	$0.395921\pi$
$908$	−0.785152	+	0.570446i	−0.0260562	+	0.0189309i
$909$	0.272219	+	0.837803i	0.00902893	+	0.0277882i
$910$	−0.0131561	+	0.0404904i	−0.000436121	+	0.00134224i
$911$	21.7267	+	15.7854i	0.719838	+	0.522993i	0.886333	−	0.463049i	$-0.153245\pi$
$911$	21.7267	+	15.7854i	0.719838	+	0.522993i	−0.166494	+	0.986042i	$0.553245\pi$
$912$	2.89036			0.0957095
$913$	5.31903	+	33.0080i	0.176034	+	1.09240i
$914$	−15.4508			−0.511067
$915$	18.9238	+	13.7489i	0.625600	+	0.454525i
$916$	−0.761085	+	2.34238i	−0.0251470	+	0.0773944i
$917$	−0.499613	−	1.53765i	−0.0164987	−	0.0507777i
$918$	−20.3204	+	14.7636i	−0.670673	+	0.487272i
$919$	−13.1724	+	9.57027i	−0.434516	+	0.315694i	−0.783452	−	0.621452i	$-0.786543\pi$
$919$	−13.1724	+	9.57027i	−0.434516	+	0.315694i	0.348936	+	0.937146i	$0.386543\pi$
$920$	2.15065	+	6.61903i	0.0709050	+	0.218223i
$921$	3.47688	−	10.7007i	0.114567	−	0.352602i
$922$	−27.3733	−	19.8878i	−0.901491	−	0.654971i
$923$	0.481261			0.0158409
$924$	5.52833	+	0.860361i	0.181869	+	0.0283038i
$925$	8.48459			0.278972
$926$	25.7198	+	18.6866i	0.845207	+	0.614078i
$927$	−0.639175	+	1.96718i	−0.0209932	+	0.0646106i
$928$	0.414939	+	1.27705i	0.0136211	+	0.0419213i
$929$	29.6732	−	21.5588i	0.973545	−	0.707322i	0.0172881	−	0.999851i	$-0.494497\pi$
$929$	29.6732	−	21.5588i	0.973545	−	0.707322i	0.956257	+	0.292529i	$0.0944968\pi$
$930$	−8.20548	+	5.96163i	−0.269068	+	0.195490i
$931$	−0.529469	−	1.62954i	−0.0173526	−	0.0534059i
$932$	−2.05509	+	6.32492i	−0.0673167	+	0.207180i
$933$	20.6035	+	14.9693i	0.674527	+	0.490073i
$934$	17.0295			0.557223
$935$	−11.1000	−	11.0404i	−0.363009	−	0.361061i
$936$	0.00656917			0.000214720
$937$	23.5394	+	17.1024i	0.769000	+	0.558711i	0.901657	−	0.432451i	$-0.142351\pi$
$937$	23.5394	+	17.1024i	0.769000	+	0.558711i	−0.132658	+	0.991162i	$0.542351\pi$
$938$	−1.97647	+	6.08296i	−0.0645341	+	0.198616i
$939$	−3.82491	−	11.7719i	−0.124821	−	0.384160i
$940$	−3.71443	+	2.69869i	−0.121151	+	0.0880217i
$941$	4.55576	−	3.30996i	0.148514	−	0.107901i	−0.511047	−	0.859553i	$-0.670742\pi$
$941$	4.55576	−	3.30996i	0.148514	−	0.107901i	0.659561	+	0.751651i	$0.270742\pi$
$942$	5.98913	+	18.4326i	0.195136	+	0.600568i
$943$	−8.41704	+	25.9050i	−0.274097	+	0.843582i
$944$	8.26632	+	6.00583i	0.269046	+	0.195473i
$945$	5.32105			0.173094
$946$	−18.9593	+	9.72460i	−0.616421	+	0.316174i
$947$	−25.4396			−0.826677			−0.413338	−	0.910577i	$-0.635637\pi$
$947$	−25.4396			−0.826677			−0.413338	+	0.910577i	$0.635637\pi$
$948$	−12.1062	−	8.79566i	−0.393191	−	0.285670i
$949$	−0.0261449	+	0.0804658i	−0.000848700	+	0.00261203i
$950$	0.529469	+	1.62954i	0.0171782	+	0.0528692i
$951$	30.6931	−	22.2999i	0.995292	−	0.723122i
$952$	−3.81887	+	2.77457i	−0.123770	+	0.0899243i
$953$	−11.3365	−	34.8902i	−0.367226	−	1.13021i	−0.948575	−	0.316551i	$-0.897475\pi$
$953$	−11.3365	−	34.8902i	−0.367226	−	1.13021i	0.581349	−	0.813654i	$-0.302525\pi$
$954$	−0.672418	+	2.06949i	−0.0217703	+	0.0670022i
$955$	−13.8900	−	10.0917i	−0.449471	−	0.326560i
$956$	21.0529			0.680900
$957$	−3.39265	+	6.70297i	−0.109669	+	0.216676i
$958$	−29.9718			−0.968346
$959$	−8.30594	−	6.03462i	−0.268213	−	0.194868i
$960$	−0.521287	+	1.60436i	−0.0168245	+	0.0517804i
$961$	1.59131	+	4.89755i	0.0513326	+	0.157986i
$962$	0.292236	−	0.212322i	0.00942208	−	0.00684554i
$963$	−1.99317	+	1.44812i	−0.0642289	+	0.0466650i
$964$	−2.45126	−	7.54420i	−0.0789497	−	0.242982i
$965$	−3.15768	+	9.71834i	−0.101649	+	0.312844i
$966$	9.49818	+	6.90083i	0.305599	+	0.222031i
$967$	23.5537			0.757438			0.378719	−	0.925512i	$-0.376365\pi$
$967$	23.5537			0.757438			0.378719	+	0.925512i	$0.376365\pi$
$968$	10.4432	−	3.45543i	0.335656	−	0.111062i
$969$	−13.6436			−0.438296
$970$	−14.1426	−	10.2752i	−0.454092	−	0.329917i
$971$	2.45974	−	7.57030i	0.0789368	−	0.242943i	−0.903799	−	0.427957i	$-0.859233\pi$
$971$	2.45974	−	7.57030i	0.0789368	−	0.242943i	0.982736	+	0.185015i	$0.0592333\pi$
$972$	−0.495018	−	1.52351i	−0.0158777	−	0.0488665i
$973$	1.57562	−	1.14476i	0.0505122	−	0.0366992i
$974$	0.593048	−	0.430874i	0.0190025	−	0.0138061i
$975$	−0.0221933	−	0.0683041i	−0.000710756	−	0.00218748i
$976$	4.28487	−	13.1875i	0.137155	−	0.422121i
$977$	−13.5939	−	9.87652i	−0.434906	−	0.315978i	0.348701	−	0.937234i	$-0.386623\pi$
$977$	−13.5939	−	9.87652i	−0.434906	−	0.315978i	−0.783608	+	0.621256i	$0.786623\pi$
$978$	−23.8356			−0.762178
$979$	−4.39385	+	8.68109i	−0.140428	+	0.277449i
$980$	1.00000			0.0319438
$981$	1.99107	+	1.44659i	0.0635699	+	0.0461862i
$982$	−3.13633	+	9.65263i	−0.100084	+	0.308028i
$983$	−2.05189	−	6.31507i	−0.0654452	−	0.201420i	0.912987	−	0.407989i	$-0.133770\pi$
$983$	−2.05189	−	6.31507i	−0.0654452	−	0.201420i	−0.978432	+	0.206570i	$0.933770\pi$
$984$	−5.34123	+	3.88063i	−0.170272	+	0.123710i
$985$	5.93227	−	4.31004i	0.189018	−	0.137329i
$986$	−1.95867	−	6.02817i	−0.0623768	−	0.191976i
$987$	−2.39338	+	7.36607i	−0.0761822	+	0.234465i
$988$	0.0590148	+	0.0428768i	0.00187751	+	0.00136409i
$989$	−44.7127			−1.42178
$990$	0.455350	−	0.233558i	0.0144720	−	0.00742295i
$991$	−49.2695			−1.56510			−0.782548	−	0.622590i	$-0.786080\pi$
$991$	−49.2695			−1.56510			−0.782548	+	0.622590i	$0.786080\pi$
$992$	4.86418	+	3.53403i	0.154438	+	0.112206i
$993$	−5.37730	+	16.5496i	−0.170643	+	0.525186i
$994$	−3.49315	−	10.7508i	−0.110796	−	0.340995i
$995$	7.20310	−	5.23336i	0.228354	−	0.165909i
$996$	−13.7576	+	9.99546i	−0.435925	+	0.316718i
$997$	10.0592	+	30.9591i	0.318578	+	0.980483i	0.974256	+	0.225443i	$0.0723829\pi$
$997$	10.0592	+	30.9591i	0.318578	+	0.980483i	−0.655678	+	0.755041i	$0.727617\pi$
$998$	3.45090	−	10.6208i	0.109236	−	0.336194i
$999$	−36.5246	−	26.5367i	−1.15559	−	0.839584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.j.631.1	yes	12
11.3	even	5	inner	770.2.n.j.421.1	✓	12
11.5	even	5		8470.2.a.cw.1.2		6
11.6	odd	10		8470.2.a.dc.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.j.421.1	✓	12	11.3	even	5	inner
770.2.n.j.631.1	yes	12	1.1	even	1	trivial
8470.2.a.cw.1.2		6	11.5	even	5
8470.2.a.dc.1.2		6	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.521287 + 1.60436i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.36475 + 0.991547i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.124831 + 0.0906951i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.521287 + 1.60436i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.36475 + 0.991547i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.124831 + 0.0906951i) q^{9} -1.00000 q^{10} +(-1.49776 + 2.95917i) q^{11} -1.68692 q^{12} +(-0.0344432 - 0.0250244i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-0.521287 - 1.60436i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.81887 - 2.77457i) q^{17} +(0.0476812 + 0.146748i) q^{18} +(-0.529469 + 1.62954i) q^{19} +(-0.809017 - 0.587785i) q^{20} -1.68692 q^{21} +(-2.95107 + 1.51366i) q^{22} -6.95966 q^{23} +(-1.36475 - 0.991547i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.0131561 - 0.0404904i) q^{26} +(-4.30482 + 3.12764i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-0.414939 - 1.27705i) q^{29} +(0.521287 - 1.60436i) q^{30} +(-4.86418 - 3.53403i) q^{31} -1.00000 q^{32} +(-3.96681 - 3.94552i) q^{33} +4.72038 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-0.0476812 + 0.146748i) q^{36} +(2.62188 + 8.06932i) q^{37} +(-1.38617 + 1.00711i) q^{38} +(0.0581029 - 0.0422142i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(1.20940 - 3.72216i) q^{41} +(-1.36475 - 0.991547i) q^{42} +6.42455 q^{43} +(-3.27718 - 0.510019i) q^{44} -0.154300 q^{45} +(-5.63049 - 4.09079i) q^{46} +(1.41879 - 4.36658i) q^{47} +(-0.521287 - 1.60436i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(2.46067 + 7.57317i) q^{51} +(0.0131561 - 0.0404904i) q^{52} +(11.4090 + 8.28916i) q^{53} -5.32105 q^{54} +(-0.527646 - 3.27438i) q^{55} -1.00000 q^{56} +(-2.33835 - 1.69891i) q^{57} +(0.414939 - 1.27705i) q^{58} +(-3.15745 - 9.71764i) q^{59} +(1.36475 - 0.991547i) q^{60} +(-11.2179 + 8.15030i) q^{61} +(-1.85795 - 5.71818i) q^{62} +(-0.0476812 + 0.146748i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.0425741 q^{65} +(-0.890097 - 5.52362i) q^{66} +6.39600 q^{67} +(3.81887 + 2.77457i) q^{68} +(3.62798 - 11.1658i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(-9.14519 + 6.64437i) q^{71} +(-0.124831 + 0.0906951i) q^{72} +(-0.614104 - 1.89002i) q^{73} +(-2.62188 + 8.06932i) q^{74} +(1.36475 + 0.991547i) q^{75} -1.71340 q^{76} +(-3.27718 - 0.510019i) q^{77} +0.0718191 q^{78} +(7.17650 + 5.21404i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-2.63075 - 8.09662i) q^{81} +(3.16626 - 2.30042i) q^{82} +(8.15543 - 5.92527i) q^{83} +(-0.521287 - 1.60436i) q^{84} +(-1.45868 + 4.48935i) q^{85} +(5.19757 + 3.77626i) q^{86} +2.26515 q^{87} +(-2.35151 - 2.33889i) q^{88} +2.93362 q^{89} +(-0.124831 - 0.0906951i) q^{90} +(0.0131561 - 0.0404904i) q^{91} +(-2.15065 - 6.61903i) q^{92} +(8.20548 - 5.96163i) q^{93} +(3.71443 - 2.69869i) q^{94} +(-0.529469 - 1.62954i) q^{95} +(0.521287 - 1.60436i) q^{96} +(14.1426 + 10.2752i) q^{97} -1.00000 q^{98} +(-0.455350 + 0.233558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 12 * q^10 - q^11 - 2 * q^12 + 2 * q^13 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 7 * q^17 + 9 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 7 * q^26 - 3 * q^27 - 3 * q^28 + 20 * q^29 - 3 * q^30 + 6 * q^31 - 12 * q^32 - 12 * q^33 + 18 * q^34 - 3 * q^35 - 9 * q^36 + 22 * q^37 - 6 * q^38 + 23 * q^39 + 3 * q^40 + 2 * q^41 + 2 * q^42 - 60 * q^43 - 11 * q^44 + 6 * q^45 + 2 * q^46 - 4 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 + 13 * q^51 + 7 * q^52 + 18 * q^53 + 8 * q^54 + 14 * q^55 - 12 * q^56 + 8 * q^57 - 20 * q^58 - 32 * q^59 - 2 * q^60 + 8 * q^61 + 14 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^65 - 8 * q^66 + 36 * q^67 + 7 * q^68 + 50 * q^69 + 3 * q^70 - 34 * q^71 - 6 * q^72 + 14 * q^73 - 22 * q^74 - 2 * q^75 - 24 * q^76 - 11 * q^77 - 38 * q^78 - 12 * q^79 - 3 * q^80 + 4 * q^81 - 2 * q^82 + 30 * q^83 + 3 * q^84 + 2 * q^85 - 28 * q^87 + q^88 - 36 * q^89 - 6 * q^90 + 7 * q^91 - 2 * q^92 + 12 * q^93 - 11 * q^94 + 6 * q^95 - 3 * q^96 + 39 * q^97 - 12 * q^98 - 15 * q^99

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