LMFDB - Embedded newform 390.2.bd.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (of order $12$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$0.117630 - 0.893490i$ of defining polynomial
Character	$\chi$	$=$	390.37
Dual form			390.2.bd.b.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.13554 + 0.662933i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.648516 - 1.12326i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.13554 + 0.662933i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.648516 - 1.12326i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(1.51796 - 1.64189i) q^{10} +(2.28334 + 0.611818i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.97399 - 3.01718i) q^{13} +1.29703i q^{14} +(2.23435 - 0.0876265i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.79723 + 6.70736i) q^{17} -1.00000 q^{18} +(1.22132 + 4.55804i) q^{19} +(-0.493652 + 2.18090i) q^{20} +(-0.917141 + 0.917141i) q^{21} +(-2.28334 + 0.611818i) q^{22} +(-1.31661 + 4.91367i) q^{23} +(0.258819 - 0.965926i) q^{24} +(4.12104 - 2.83144i) q^{25} +(3.21811 + 1.62596i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.648516 - 1.12326i) q^{28} +(5.49047 - 3.16993i) q^{29} +(-1.89119 + 1.19306i) q^{30} +(6.24653 + 6.24653i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.04718 - 1.18194i) q^{33} +(-4.91013 - 4.91013i) q^{34} +(-0.640282 + 2.82869i) q^{35} +(0.866025 - 0.500000i) q^{36} +(1.61817 + 2.80275i) q^{37} +(-3.33672 - 3.33672i) q^{38} +(1.12582 + 3.42528i) q^{39} +(-0.662933 - 2.13554i) q^{40} +(-2.19059 + 8.17538i) q^{41} +(0.335697 - 1.25284i) q^{42} +(-0.778549 + 0.208612i) q^{43} +(1.67152 - 1.67152i) q^{44} +(-2.18090 - 0.493652i) q^{45} +(-1.31661 - 4.91367i) q^{46} -11.6095 q^{47} +(0.258819 + 0.965926i) q^{48} +(2.65885 + 4.60527i) q^{49} +(-2.15321 + 4.51262i) q^{50} -6.94397i q^{51} +(-3.59995 + 0.200935i) q^{52} +(8.79736 - 8.79736i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-5.28174 + 0.207139i) q^{55} +(1.12326 + 0.648516i) q^{56} -4.71883i q^{57} +(-3.16993 + 5.49047i) q^{58} +(5.81956 - 1.55935i) q^{59} +(1.04129 - 1.97882i) q^{60} +(2.10240 - 3.64147i) q^{61} +(-8.53291 - 2.28639i) q^{62} +(1.12326 - 0.648516i) q^{63} -1.00000 q^{64} +(6.21572 + 5.13467i) q^{65} +2.36388 q^{66} +(0.573907 - 0.331346i) q^{67} +(6.70736 + 1.79723i) q^{68} +(2.54350 - 4.40547i) q^{69} +(-0.859846 - 2.76986i) q^{70} +(-12.2489 + 3.28208i) q^{71} +(-0.500000 + 0.866025i) q^{72} +5.04229i q^{73} +(-2.80275 - 1.61817i) q^{74} +(-4.71345 + 1.66835i) q^{75} +(4.55804 + 1.22132i) q^{76} +(2.16801 - 2.16801i) q^{77} +(-2.68763 - 2.40346i) q^{78} -13.2885i q^{79} +(1.64189 + 1.51796i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.19059 - 8.17538i) q^{82} -2.04522 q^{83} +(0.335697 + 1.25284i) q^{84} +(-8.28459 - 13.1324i) q^{85} +(0.569937 - 0.569937i) q^{86} +(-6.12383 + 1.64087i) q^{87} +(-0.611818 + 2.28334i) q^{88} +(1.16115 - 4.33348i) q^{89} +(2.13554 - 0.662933i) q^{90} +(-4.66925 + 0.260620i) q^{91} +(3.59705 + 3.59705i) q^{92} +(-4.41696 - 7.65040i) q^{93} +(10.0541 - 5.80474i) q^{94} +(-5.62986 - 8.92421i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(5.19551 + 2.99963i) q^{97} +(-4.60527 - 2.65885i) q^{98} +(1.67152 + 1.67152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.13554	+	0.662933i	−0.955041	+	0.296473i
$5$	−2.13554	+	0.662933i	−0.955041	+	0.296473i
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	0.648516	−	1.12326i	0.245116	−	0.424554i	−0.717048	−	0.697024i	$-0.754507\pi$
$7$	0.648516	−	1.12326i	0.245116	−	0.424554i	0.962164	+	0.272470i	$0.0878406\pi$
$8$			1.00000i			0.353553i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	1.51796	−	1.64189i	0.480022	−	0.519210i
$11$	2.28334	+	0.611818i	0.688451	+	0.184470i	0.586052	−	0.810273i	$-0.300681\pi$
$11$	2.28334	+	0.611818i	0.688451	+	0.184470i	0.102399	+	0.994743i	$0.467348\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−1.97399	−	3.01718i	−0.547486	−	0.836815i
$13$	−1.97399	−	3.01718i	−0.547486	−	0.836815i
$14$			1.29703i			0.346647i
$15$	2.23435	−	0.0876265i	0.576907	−	0.0226251i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.79723	+	6.70736i	0.435893	+	1.62677i	0.738920	+	0.673793i	$0.235336\pi$
$17$	1.79723	+	6.70736i	0.435893	+	1.62677i	−0.303027	+	0.952982i	$0.597997\pi$
$18$	−1.00000			−0.235702
$19$	1.22132	+	4.55804i	0.280191	+	1.04569i	0.952282	+	0.305218i	$0.0987295\pi$
$19$	1.22132	+	4.55804i	0.280191	+	1.04569i	−0.672091	+	0.740468i	$0.734604\pi$
$20$	−0.493652	+	2.18090i	−0.110384	+	0.487663i
$21$	−0.917141	+	0.917141i	−0.200137	+	0.200137i
$22$	−2.28334	+	0.611818i	−0.486809	+	0.130440i
$23$	−1.31661	+	4.91367i	−0.274533	+	1.02457i	0.681621	+	0.731705i	$0.261275\pi$
$23$	−1.31661	+	4.91367i	−0.274533	+	1.02457i	−0.956154	+	0.292865i	$0.905391\pi$
$24$	0.258819	−	0.965926i	0.0528312	−	0.197169i
$25$	4.12104	−	2.83144i	0.824208	−	0.566287i
$26$	3.21811	+	1.62596i	0.631124	+	0.318877i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−0.648516	−	1.12326i	−0.122558	−	0.212277i
$29$	5.49047	−	3.16993i	1.01956	−	0.588640i	0.105580	−	0.994411i	$-0.466330\pi$
$29$	5.49047	−	3.16993i	1.01956	−	0.588640i	0.913975	+	0.405770i	$0.132997\pi$
$30$	−1.89119	+	1.19306i	−0.345283	+	0.217822i
$31$	6.24653	+	6.24653i	1.12191	+	1.12191i	0.991454	+	0.130455i	$0.0416439\pi$
$31$	6.24653	+	6.24653i	1.12191	+	1.12191i	0.130455	+	0.991454i	$0.458356\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.04718	−	1.18194i	−0.356369	−	0.205750i
$34$	−4.91013	−	4.91013i	−0.842081	−	0.842081i
$35$	−0.640282	+	2.82869i	−0.108227	+	0.478137i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	1.61817	+	2.80275i	0.266025	+	0.460769i	0.967832	−	0.251599i	$-0.0809563\pi$
$37$	1.61817	+	2.80275i	0.266025	+	0.460769i	−0.701807	+	0.712367i	$0.747623\pi$
$38$	−3.33672	−	3.33672i	−0.541287	−	0.541287i
$39$	1.12582	+	3.42528i	0.180276	+	0.548483i
$40$	−0.662933	−	2.13554i	−0.104819	−	0.337658i
$41$	−2.19059	+	8.17538i	−0.342112	+	1.27678i	0.553838	+	0.832625i	$0.313163\pi$
$41$	−2.19059	+	8.17538i	−0.342112	+	1.27678i	−0.895950	+	0.444155i	$0.853504\pi$
$42$	0.335697	−	1.25284i	0.0517991	−	0.193317i
$43$	−0.778549	+	0.208612i	−0.118728	+	0.0318130i	−0.317694	−	0.948193i	$-0.602908\pi$
$43$	−0.778549	+	0.208612i	−0.118728	+	0.0318130i	0.198966	+	0.980006i	$0.436242\pi$
$44$	1.67152	−	1.67152i	0.251991	−	0.251991i
$45$	−2.18090	−	0.493652i	−0.325109	−	0.0735892i
$46$	−1.31661	−	4.91367i	−0.194124	−	0.724480i
$47$	−11.6095			−1.69342			−0.846709	−	0.532056i	$-0.821419\pi$
$47$	−11.6095			−1.69342			−0.846709	+	0.532056i	$0.821419\pi$
$48$	0.258819	+	0.965926i	0.0373573	+	0.139419i
$49$	2.65885	+	4.60527i	0.379836	+	0.657895i
$50$	−2.15321	+	4.51262i	−0.304509	+	0.638180i
$51$		−	6.94397i		−	0.972351i
$52$	−3.59995	+	0.200935i	−0.499223	+	0.0278647i
$53$	8.79736	−	8.79736i	1.20841	−	1.20841i	0.236869	−	0.971542i	$-0.423879\pi$
$53$	8.79736	−	8.79736i	1.20841	−	1.20841i	0.971542	−	0.236869i	$-0.0761211\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	−5.28174	+	0.207139i	−0.712190	+	0.0279306i
$56$	1.12326	+	0.648516i	0.150102	+	0.0866617i
$57$		−	4.71883i		−	0.625025i
$58$	−3.16993	+	5.49047i	−0.416232	+	0.720934i
$59$	5.81956	−	1.55935i	0.757642	−	0.203010i	0.140737	−	0.990047i	$-0.455053\pi$
$59$	5.81956	−	1.55935i	0.757642	−	0.203010i	0.616905	+	0.787038i	$0.288386\pi$
$60$	1.04129	−	1.97882i	0.134430	−	0.255464i
$61$	2.10240	−	3.64147i	0.269185	−	0.466243i	−0.699466	−	0.714665i	$-0.746579\pi$
$61$	2.10240	−	3.64147i	0.269185	−	0.466243i	0.968652	+	0.248423i	$0.0799123\pi$
$62$	−8.53291	−	2.28639i	−1.08368	−	0.290372i
$63$	1.12326	−	0.648516i	0.141518	−	0.0817054i
$64$	−1.00000			−0.125000
$65$	6.21572	+	5.13467i	0.770965	+	0.636878i
$66$	2.36388			0.290974
$67$	0.573907	−	0.331346i	0.0701140	−	0.0404803i	−0.464533	−	0.885556i	$-0.653778\pi$
$67$	0.573907	−	0.331346i	0.0701140	−	0.0404803i	0.534647	+	0.845075i	$0.320445\pi$
$68$	6.70736	+	1.79723i	0.813387	+	0.217946i
$69$	2.54350	−	4.40547i	0.306201	−	0.530357i
$70$	−0.859846	−	2.76986i	−0.102771	−	0.331062i
$71$	−12.2489	+	3.28208i	−1.45367	+	0.389511i	−0.897300	−	0.441421i	$-0.854475\pi$
$71$	−12.2489	+	3.28208i	−1.45367	+	0.389511i	−0.556374	+	0.830932i	$0.687808\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$			5.04229i			0.590155i	0.955473	+	0.295077i	$0.0953454\pi$
$73$			5.04229i			0.590155i	−0.955473	+	0.295077i	$0.904655\pi$
$74$	−2.80275	−	1.61817i	−0.325813	−	0.188108i
$75$	−4.71345	+	1.66835i	−0.544262	+	0.192645i
$76$	4.55804	+	1.22132i	0.522843	+	0.140095i
$77$	2.16801	−	2.16801i	0.247068	−	0.247068i
$78$	−2.68763	−	2.40346i	−0.304314	−	0.272139i
$79$		−	13.2885i		−	1.49507i	−0.664222	−	0.747536i	$-0.731237\pi$
$79$		−	13.2885i		−	1.49507i	0.664222	−	0.747536i	$-0.268763\pi$
$80$	1.64189	+	1.51796i	0.183568	+	0.169713i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−2.19059	−	8.17538i	−0.241910	−	0.902820i
$83$	−2.04522			−0.224492			−0.112246	−	0.993680i	$-0.535804\pi$
$83$	−2.04522			−0.224492			−0.112246	+	0.993680i	$0.535804\pi$
$84$	0.335697	+	1.25284i	0.0366275	+	0.136696i
$85$	−8.28459	−	13.1324i	−0.898590	−	1.42441i
$86$	0.569937	−	0.569937i	0.0614579	−	0.0614579i
$87$	−6.12383	+	1.64087i	−0.656543	+	0.175920i
$88$	−0.611818	+	2.28334i	−0.0652200	+	0.243404i
$89$	1.16115	−	4.33348i	0.123082	−	0.459348i	−0.876682	−	0.481070i	$-0.840248\pi$
$89$	1.16115	−	4.33348i	0.123082	−	0.459348i	0.999764	+	0.0217223i	$0.00691497\pi$
$90$	2.13554	−	0.662933i	0.225105	−	0.0698793i
$91$	−4.66925	+	0.260620i	−0.489470	+	0.0273204i
$92$	3.59705	+	3.59705i	0.375019	+	0.375019i
$93$	−4.41696	−	7.65040i	−0.458018	−	0.793310i
$94$	10.0541	−	5.80474i	1.03700	−	0.598714i
$95$	−5.62986	−	8.92421i	−0.577611	−	0.915605i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	5.19551	+	2.99963i	0.527524	+	0.304566i	0.740007	−	0.672599i	$-0.234822\pi$
$97$	5.19551	+	2.99963i	0.527524	+	0.304566i	−0.212484	+	0.977165i	$0.568155\pi$
$98$	−4.60527	−	2.65885i	−0.465202	−	0.268585i
$99$	1.67152	+	1.67152i	0.167994	+	0.167994i
$100$	−0.391577	−	4.98464i	−0.0391577	−	0.498464i
$101$	12.2279	−	7.05976i	1.21672	−	0.702473i	0.252504	−	0.967596i	$-0.418746\pi$
$101$	12.2279	−	7.05976i	1.21672	−	0.702473i	0.964215	+	0.265123i	$0.0854126\pi$
$102$	3.47199	+	6.01366i	0.343778	+	0.595441i
$103$	−0.223293	−	0.223293i	−0.0220017	−	0.0220017i	0.696020	−	0.718022i	$-0.254952\pi$
$103$	−0.223293	−	0.223293i	−0.0220017	−	0.0220017i	−0.718022	+	0.696020i	$0.754952\pi$
$104$	3.01718	−	1.97399i	0.295859	−	0.193566i
$105$	1.35059	−	2.56659i	0.131804	−	0.250474i
$106$	−3.22006	+	12.0174i	−0.312760	+	1.16723i
$107$	−3.47715	+	12.9769i	−0.336149	+	1.25453i	0.566469	+	0.824083i	$0.308309\pi$
$107$	−3.47715	+	12.9769i	−0.336149	+	1.25453i	−0.902618	+	0.430442i	$0.858358\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	−2.20681	+	2.20681i	−0.211374	+	0.211374i	−0.804851	−	0.593477i	$-0.797755\pi$
$109$	−2.20681	+	2.20681i	−0.211374	+	0.211374i	0.593477	+	0.804851i	$0.297755\pi$
$110$	4.47055	−	2.82026i	0.426251	−	0.268901i
$111$	−0.837624	−	3.12606i	−0.0795038	−	0.296712i
$112$	−1.29703			−0.122558
$113$	−2.62886	−	9.81102i	−0.247302	−	0.922943i	−0.972212	−	0.234100i	$-0.924786\pi$
$113$	−2.62886	−	9.81102i	−0.247302	−	0.922943i	0.724911	−	0.688843i	$-0.241881\pi$
$114$	2.35942	+	4.08663i	0.220980	+	0.382748i
$115$	−0.445756	−	11.3661i	−0.0415670	−	1.05990i
$116$		−	6.33985i		−	0.588640i
$117$	−0.200935	−	3.59995i	−0.0185765	−	0.332815i
$118$	−4.26021	+	4.26021i	−0.392184	+	0.392184i
$119$	8.69967	+	2.33107i	0.797498	+	0.213689i
$120$	0.0876265	+	2.23435i	0.00799917	+	0.203967i
$121$	−4.68698	−	2.70603i	−0.426089	−	0.246003i
$122$			4.20481i			0.380685i
$123$	4.23189	−	7.32985i	0.381577	−	0.660910i
$124$	8.53291	−	2.28639i	0.766278	−	0.205324i
$125$	−6.92358	+	8.77861i	−0.619264	+	0.785183i
$126$	−0.648516	+	1.12326i	−0.0577744	+	0.100068i
$127$	12.9430	+	3.46805i	1.14850	+	0.307740i	0.782364	−	0.622821i	$-0.214013\pi$
$127$	12.9430	+	3.46805i	1.14850	+	0.307740i	0.366137	+	0.930561i	$0.380680\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	0.806013			0.0709655
$130$	−7.95030	−	1.33890i	−0.697288	−	0.117429i
$131$	−13.0083			−1.13654			−0.568272	−	0.822841i	$-0.692388\pi$
$131$	−13.0083			−1.13654			−0.568272	+	0.822841i	$0.692388\pi$
$132$	−2.04718	+	1.18194i	−0.178184	+	0.102875i
$133$	5.91193	+	1.58410i	0.512629	+	0.137359i
$134$	−0.331346	+	0.573907i	−0.0286239	+	0.0495781i
$135$	1.97882	+	1.04129i	0.170309	+	0.0896198i
$136$	−6.70736	+	1.79723i	−0.575152	+	0.154111i
$137$	1.36061	−	2.35665i	0.116245	−	0.201342i	−0.802032	−	0.597282i	$-0.796248\pi$
$137$	1.36061	−	2.35665i	0.116245	−	0.201342i	0.918277	+	0.395939i	$0.129581\pi$
$138$			5.08700i			0.433034i
$139$	1.84444	+	1.06489i	0.156443	+	0.0903225i	0.576178	−	0.817324i	$-0.304544\pi$
$139$	1.84444	+	1.06489i	0.156443	+	0.0903225i	−0.419735	+	0.907647i	$0.637877\pi$
$140$	2.12958	+	1.96885i	0.179982	+	0.166398i
$141$	11.2139	+	3.00476i	0.944381	+	0.253046i
$142$	8.96680	−	8.96680i	0.752477	−	0.752477i
$143$	−2.66132	−	8.09695i	−0.222550	−	0.677101i
$144$		−	1.00000i		−	0.0833333i
$145$	−9.62366	+	10.4093i	−0.799201	+	0.864446i
$146$	−2.52114	−	4.36675i	−0.208651	−	0.361395i
$147$	−1.37632	−	5.13651i	−0.113517	−	0.423652i
$148$	3.23633			0.266025
$149$	−1.18180	−	4.41052i	−0.0968164	−	0.361324i	0.900472	−	0.434914i	$-0.143221\pi$
$149$	−1.18180	−	4.41052i	−0.0968164	−	0.361324i	−0.997289	+	0.0735898i	$0.976554\pi$
$150$	3.24779	−	3.80156i	0.265181	−	0.310396i
$151$	−13.3144	+	13.3144i	−1.08351	+	1.08351i	−0.0873303	+	0.996179i	$0.527834\pi$
$151$	−13.3144	+	13.3144i	−1.08351	+	1.08351i	−0.996179	+	0.0873303i	$0.972166\pi$
$152$	−4.55804	+	1.22132i	−0.369706	+	0.0990624i
$153$	−1.79723	+	6.70736i	−0.145298	+	0.542258i
$154$	−0.793548	+	2.96156i	−0.0639459	+	0.238649i
$155$	−17.4807	−	9.19866i	−1.40409	−	0.738854i
$156$	3.52929	+	0.737646i	0.282569	+	0.0590590i
$157$	10.5530	+	10.5530i	0.842224	+	0.842224i	0.989148	−	0.146924i	$-0.0469372\pi$
$157$	10.5530	+	10.5530i	0.842224	+	0.842224i	−0.146924	+	0.989148i	$0.546937\pi$
$158$	6.64424	+	11.5082i	0.528587	+	0.915540i
$159$	−10.7745	+	6.22067i	−0.854475	+	0.493331i
$160$	−2.18090	−	0.493652i	−0.172415	−	0.0390266i
$161$	4.66550	+	4.66550i	0.367693	+	0.367693i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−1.52221	−	0.878849i	−0.119229	−	0.0688368i	0.439200	−	0.898390i	$-0.355262\pi$
$163$	−1.52221	−	0.878849i	−0.119229	−	0.0688368i	−0.558428	+	0.829553i	$0.688595\pi$
$164$	5.98479	+	5.98479i	0.467334	+	0.467334i
$165$	5.15538	+	1.16693i	0.401346	+	0.0908457i
$166$	1.77121	−	1.02261i	0.137473	−	0.0793699i
$167$	6.87400	+	11.9061i	0.531926	+	0.921324i	0.999305	+	0.0372665i	$0.0118650\pi$
$167$	6.87400	+	11.9061i	0.531926	+	0.921324i	−0.467379	+	0.884057i	$0.654802\pi$
$168$	−0.917141	−	0.917141i	−0.0707589	−	0.0707589i
$169$	−5.20673	+	11.9118i	−0.400518	+	0.916289i
$170$	13.7409	+	7.23068i	1.05388	+	0.554568i
$171$	−1.22132	+	4.55804i	−0.0933970	+	0.348562i
$172$	−0.208612	+	0.778549i	−0.0159065	+	0.0593638i
$173$	8.58782	−	2.30110i	0.652920	−	0.174949i	0.0828711	−	0.996560i	$-0.473591\pi$
$173$	8.58782	−	2.30110i	0.652920	−	0.174949i	0.570049	+	0.821611i	$0.306924\pi$
$174$	4.48295	−	4.48295i	0.339852	−	0.339852i
$175$	−0.507888	−	6.46525i	−0.0383927	−	0.488727i
$176$	−0.611818	−	2.28334i	−0.0461175	−	0.172113i
$177$	−6.02485			−0.452855
$178$	1.16115	+	4.33348i	0.0870320	+	0.324808i
$179$	−1.43583	−	2.48692i	−0.107319	−	0.185881i	0.807364	−	0.590053i	$-0.200893\pi$
$179$	−1.43583	−	2.48692i	−0.107319	−	0.185881i	−0.914683	+	0.404172i	$0.867560\pi$
$180$	−1.51796	+	1.64189i	−0.113142	+	0.122379i
$181$			15.2820i			1.13590i	0.823062	+	0.567952i	$0.192264\pi$
$181$			15.2820i			1.13590i	−0.823062	+	0.567952i	$0.807736\pi$
$182$	3.91338	−	2.56033i	0.290079	−	0.189784i
$183$	−2.97325	+	2.97325i	−0.219789	+	0.219789i
$184$	−4.91367	−	1.31661i	−0.362240	−	0.0970620i
$185$	−5.31369	−	4.91263i	−0.390670	−	0.361184i
$186$	7.65040	+	4.41696i	0.560955	+	0.323867i
$187$			16.4147i			1.20036i
$188$	−5.80474	+	10.0541i	−0.423354	+	0.733271i
$189$	−1.25284	+	0.335697i	−0.0911305	+	0.0244184i
$190$	9.33771	+	4.91367i	0.677429	+	0.356475i
$191$	−2.84601	+	4.92943i	−0.205930	+	0.356681i	−0.950429	−	0.310943i	$-0.899355\pi$
$191$	−2.84601	+	4.92943i	−0.205930	+	0.356681i	0.744499	+	0.667624i	$0.232689\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	3.75328	−	2.16696i	0.270167	−	0.155981i	−0.358797	−	0.933416i	$-0.616813\pi$
$193$	3.75328	−	2.16696i	0.270167	−	0.155981i	0.628963	+	0.777435i	$0.283479\pi$
$194$	−5.99925			−0.430721
$195$	−4.67497	−	6.56846i	−0.334781	−	0.470377i
$196$	5.31771			0.379836
$197$	0.358186	−	0.206799i	0.0255197	−	0.0147338i	−0.487186	−	0.873298i	$-0.661977\pi$
$197$	0.358186	−	0.206799i	0.0255197	−	0.0147338i	0.512706	+	0.858564i	$0.328643\pi$
$198$	−2.28334	−	0.611818i	−0.162270	−	0.0434800i
$199$	−8.50824	+	14.7367i	−0.603133	+	1.04466i	0.389210	+	0.921149i	$0.372748\pi$
$199$	−8.50824	+	14.7367i	−0.603133	+	1.04466i	−0.992343	+	0.123509i	$0.960585\pi$
$200$	2.83144	+	4.12104i	0.200213	+	0.291401i
$201$	−0.640111	+	0.171517i	−0.0451499	+	0.0120979i
$202$	−7.05976	+	12.2279i	−0.496723	+	0.860350i
$203$		−	8.22300i		−	0.577141i
$204$	−6.01366	−	3.47199i	−0.421040	−	0.243088i
$205$	−0.741652	−	18.9110i	−0.0517992	−	1.32080i
$206$	0.305024	+	0.0817310i	0.0212520	+	0.00569447i
$207$	−3.59705	+	3.59705i	−0.250012	+	0.250012i
$208$	−1.62596	+	3.21811i	−0.112740	+	0.223136i
$209$			11.1548i			0.771591i
$210$	0.113655	+	2.89803i	0.00784291	+	0.199983i
$211$	5.51865	+	9.55858i	0.379919	+	0.658040i	0.991050	−	0.133490i	$-0.0426184\pi$
$211$	5.51865	+	9.55858i	0.379919	+	0.658040i	−0.611131	+	0.791530i	$0.709285\pi$
$212$	−3.22006	−	12.0174i	−0.221154	−	0.825360i
$213$	12.6810			0.868886
$214$	−3.47715	−	12.9769i	−0.237693	−	0.887083i
$215$	1.52432	−	0.961624i	0.103958	−	0.0655822i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	11.0675	−	2.96552i	0.751309	−	0.201313i
$218$	0.807747	−	3.01455i	0.0547076	−	0.204171i
$219$	1.30504	−	4.87047i	0.0881864	−	0.329116i
$220$	−2.46148	+	4.67769i	−0.165953	+	0.315370i
$221$	16.6896	−	18.6628i	1.12266	−	1.25540i
$222$	2.28843	+	2.28843i	0.153590	+	0.153590i
$223$	5.99361	+	10.3812i	0.401362	+	0.695179i	0.993891	−	0.110370i	$-0.0352037\pi$
$223$	5.99361	+	10.3812i	0.401362	+	0.695179i	−0.592529	+	0.805549i	$0.701870\pi$
$224$	1.12326	−	0.648516i	0.0750512	−	0.0433308i
$225$	4.98464	−	0.391577i	0.332310	−	0.0261051i
$226$	7.18217	+	7.18217i	0.477751	+	0.477751i
$227$	−9.07894	−	5.24173i	−0.602591	−	0.347906i	0.167469	−	0.985877i	$-0.446440\pi$
$227$	−9.07894	−	5.24173i	−0.602591	−	0.347906i	−0.770060	+	0.637971i	$0.779774\pi$
$228$	−4.08663	−	2.35942i	−0.270644	−	0.156256i
$229$	−8.70469	−	8.70469i	−0.575222	−	0.575222i	0.358361	−	0.933583i	$-0.383336\pi$
$229$	−8.70469	−	8.70469i	−0.575222	−	0.575222i	−0.933583	+	0.358361i	$0.883336\pi$
$230$	6.06911	+	9.62049i	0.400185	+	0.634356i
$231$	−2.65526	+	1.53302i	−0.174703	+	0.100865i
$232$	3.16993	+	5.49047i	0.208116	+	0.360467i
$233$	−18.0690	−	18.0690i	−1.18374	−	1.18374i	−0.978768	−	0.204973i	$-0.934289\pi$
$233$	−18.0690	−	18.0690i	−1.18374	−	1.18374i	−0.204973	−	0.978768i	$-0.565711\pi$
$234$	1.97399	+	3.01718i	0.129044	+	0.197239i
$235$	24.7925	−	7.69631i	1.61728	−	0.502052i
$236$	1.55935	−	5.81956i	0.101505	−	0.378821i
$237$	−3.43931	+	12.8357i	−0.223407	+	0.833768i
$238$	−8.69967	+	2.33107i	−0.563916	+	0.151101i
$239$	9.68691	−	9.68691i	0.626594	−	0.626594i	−0.320615	−	0.947209i	$-0.603890\pi$
$239$	9.68691	−	9.68691i	0.626594	−	0.626594i	0.947209	+	0.320615i	$0.103890\pi$
$240$	−1.19306	−	1.89119i	−0.0770118	−	0.122076i
$241$	−3.00649	−	11.2204i	−0.193665	−	0.722769i	−0.992608	−	0.121362i	$-0.961274\pi$
$241$	−3.00649	−	11.2204i	−0.193665	−	0.722769i	0.798943	−	0.601407i	$-0.205393\pi$
$242$	5.41206			0.347900
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	−2.10240	−	3.64147i	−0.134593	−	0.233121i
$245$	−8.73106	−	8.07208i	−0.557807	−	0.515706i
$246$			8.46378i			0.539631i
$247$	11.3415	−	12.6825i	0.721645	−	0.806967i
$248$	−6.24653	+	6.24653i	−0.396655	+	0.396655i
$249$	1.97553	+	0.529342i	0.125194	+	0.0335457i
$250$	1.60669	−	11.0643i	0.101616	−	0.699767i
$251$	−14.5774	−	8.41627i	−0.920118	−	0.531230i	−0.0364452	−	0.999336i	$-0.511603\pi$
$251$	−14.5774	−	8.41627i	−0.920118	−	0.531230i	−0.883673	+	0.468105i	$0.844937\pi$
$252$		−	1.29703i		−	0.0817054i
$253$	−6.01254	+	10.4140i	−0.378005	+	0.654724i
$254$	−12.9430	+	3.46805i	−0.812113	+	0.217605i
$255$	4.60339	+	14.8291i	0.288275	+	0.928635i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00363	+	1.60867i	0.374496	+	0.100346i	0.441158	−	0.897430i	$-0.354568\pi$
$257$	6.00363	+	1.60867i	0.374496	+	0.100346i	−0.0666611	+	0.997776i	$0.521235\pi$
$258$	−0.698028	+	0.403007i	−0.0434573	+	0.0250901i
$259$	4.19763			0.260828
$260$	7.55462	−	2.81563i	0.468517	−	0.174618i
$261$	6.33985			0.392427
$262$	11.2655	−	6.50417i	0.695988	−	0.401829i
$263$	12.4555	+	3.33744i	0.768038	+	0.205795i	0.621505	−	0.783410i	$-0.286522\pi$
$263$	12.4555	+	3.33744i	0.768038	+	0.205795i	0.146534	+	0.989206i	$0.453188\pi$
$264$	1.18194	−	2.04718i	0.0727435	−	0.125995i
$265$	−12.9550	+	24.6192i	−0.795821	+	1.51234i
$266$	−5.91193	+	1.58410i	−0.362484	+	0.0971272i
$267$	−2.24317	+	3.88529i	−0.137280	+	0.237776i
$268$		−	0.662691i		−	0.0404803i
$269$	0.184766	+	0.106675i	0.0112654	+	0.00650406i	0.505622	−	0.862755i	$-0.331263\pi$
$269$	0.184766	+	0.106675i	0.0112654	+	0.00650406i	−0.494357	+	0.869259i	$0.664596\pi$
$270$	−2.23435	+	0.0876265i	−0.135978	+	0.00533278i
$271$	1.83744	+	0.492340i	0.111616	+	0.0299075i	0.314195	−	0.949358i	$-0.398265\pi$
$271$	1.83744	+	0.492340i	0.111616	+	0.0299075i	−0.202578	+	0.979266i	$0.564932\pi$
$272$	4.91013	−	4.91013i	0.297720	−	0.297720i
$273$	4.57760	+	0.956752i	0.277049	+	0.0579052i
$274$			2.72123i			0.164395i
$275$	11.1420	−	3.94379i	0.671890	−	0.237820i
$276$	−2.54350	−	4.40547i	−0.153101	−	0.265178i
$277$	−6.22473	−	23.2310i	−0.374008	−	1.39582i	−0.854789	−	0.518976i	$-0.826314\pi$
$277$	−6.22473	−	23.2310i	−0.374008	−	1.39582i	0.480781	−	0.876841i	$-0.340353\pi$
$278$	−2.12977			−0.127735
$279$	2.28639	+	8.53291i	0.136882	+	0.510852i
$280$	−2.82869	−	0.640282i	−0.169047	−	0.0382642i
$281$	−6.72882	+	6.72882i	−0.401408	+	0.401408i	−0.878729	−	0.477321i	$-0.841608\pi$
$281$	−6.72882	+	6.72882i	−0.401408	+	0.401408i	0.477321	+	0.878729i	$0.341608\pi$
$282$	−11.2139	+	3.00476i	−0.667778	+	0.178931i
$283$	−3.36636	+	12.5634i	−0.200109	+	0.746818i	0.790775	+	0.612106i	$0.209678\pi$
$283$	−3.36636	+	12.5634i	−0.200109	+	0.746818i	−0.990885	+	0.134712i	$0.956989\pi$
$284$	−3.28208	+	12.2489i	−0.194755	+	0.726837i
$285$	3.12827	+	10.0772i	0.185303	+	0.596924i
$286$	6.35324	+	5.68151i	0.375675	+	0.335955i
$287$	7.76247	+	7.76247i	0.458204	+	0.458204i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−27.0362	+	15.6094i	−1.59037	+	0.918199i
$290$	3.12968	−	13.8266i	0.183781	−	0.811923i
$291$	−4.24211	−	4.24211i	−0.248677	−	0.248677i
$292$	4.36675	+	2.52114i	0.255545	+	0.147539i
$293$	6.08742	+	3.51457i	0.355631	+	0.205324i	0.667162	−	0.744912i	$-0.267509\pi$
$293$	6.08742	+	3.51457i	0.355631	+	0.205324i	−0.311532	+	0.950236i	$0.600842\pi$
$294$	3.76019	+	3.76019i	0.219298	+	0.219298i
$295$	−11.3941	+	7.18802i	−0.663392	+	0.418503i
$296$	−2.80275	+	1.61817i	−0.162906	+	0.0940540i
$297$	−1.18194	−	2.04718i	−0.0685832	−	0.118790i
$298$	3.22872	+	3.22872i	0.187035	+	0.187035i
$299$	17.4244	−	5.72707i	1.00768	−	0.331205i
$300$	−0.911886	+	4.91614i	−0.0526478	+	0.283834i
$301$	−0.270576	+	1.00980i	−0.0155957	+	0.0582041i
$302$	4.87341	−	18.1878i	0.280433	−	1.04659i
$303$	−13.6384	+	3.65440i	−0.783507	+	0.209940i
$304$	3.33672	−	3.33672i	0.191374	−	0.191374i
$305$	−2.07571	+	9.17025i	−0.118855	+	0.525087i
$306$	−1.79723	−	6.70736i	−0.102741	−	0.383434i
$307$	−13.5523			−0.773472			−0.386736	−	0.922190i	$-0.626398\pi$
$307$	−13.5523			−0.773472			−0.386736	+	0.922190i	$0.626398\pi$
$308$	−0.793548	−	2.96156i	−0.0452166	−	0.168751i
$309$	0.157892	+	0.273477i	0.00898217	+	0.0155576i
$310$	19.7381	−	0.774086i	1.12105	−	0.0439651i
$311$		−	30.2666i		−	1.71626i	−0.513433	−	0.858129i	$-0.671627\pi$
$311$		−	30.2666i		−	1.71626i	0.513433	−	0.858129i	$-0.328373\pi$
$312$	−3.42528	+	1.12582i	−0.193918	+	0.0637372i
$313$	16.4458	−	16.4458i	0.929571	−	0.929571i	−0.0681069	−	0.997678i	$-0.521696\pi$
$313$	16.4458	−	16.4458i	0.929571	−	0.929571i	0.997678	+	0.0681069i	$0.0216959\pi$
$314$	−14.4157	−	3.86268i	−0.813526	−	0.217984i
$315$	−1.96885	+	2.12958i	−0.110932	+	0.119988i
$316$	−11.5082	−	6.64424i	−0.647385	−	0.373768i
$317$		−	14.9396i		−	0.839094i	−0.907734	−	0.419547i	$-0.862189\pi$
$317$		−	14.9396i		−	0.839094i	0.907734	−	0.419547i	$-0.137811\pi$
$318$	6.22067	−	10.7745i	0.348838	−	0.604205i
$319$	14.4760	−	3.87883i	0.810501	−	0.217173i
$320$	2.13554	−	0.662933i	0.119380	−	0.0370591i
$321$	6.71734	−	11.6348i	0.374926	−	0.649390i
$322$	−6.37319	−	1.70769i	−0.355164	−	0.0951658i
$323$	−28.3774	+	16.3837i	−1.57896	+	0.911615i
$324$	1.00000			0.0555556
$325$	−16.6778	−	6.84469i	−0.925120	−	0.379675i
$326$	1.75770			0.0973499
$327$	2.70278	−	1.56045i	0.149464	−	0.0862930i
$328$	−8.17538	−	2.19059i	−0.451410	−	0.120955i
$329$	−7.52894	+	13.0405i	−0.415084	+	0.718947i
$330$	−5.04816	+	1.56710i	−0.277892	+	0.0862658i
$331$	11.0457	−	2.95968i	0.607125	−	0.162679i	0.0578568	−	0.998325i	$-0.481573\pi$
$331$	11.0457	−	2.95968i	0.607125	−	0.162679i	0.549268	+	0.835646i	$0.314907\pi$
$332$	−1.02261	+	1.77121i	−0.0561230	+	0.0972079i
$333$			3.23633i			0.177350i
$334$	−11.9061	−	6.87400i	−0.651474	−	0.376129i
$335$	−1.00594	+	1.08806i	−0.0549604	+	0.0594472i
$336$	1.25284	+	0.335697i	0.0683479	+	0.0183138i
$337$	20.3283	−	20.3283i	1.10735	−	1.10735i	0.113854	−	0.993497i	$-0.463680\pi$
$337$	20.3283	−	20.3283i	1.10735	−	1.10735i	0.993497	−	0.113854i	$-0.0363196\pi$
$338$	−1.44671	−	12.9192i	−0.0786909	−	0.702715i
$339$			10.1571i			0.551659i
$340$	−15.5153	+	0.608476i	−0.841434	+	0.0329993i
$341$	10.4412	+	18.0847i	0.565422	+	0.979339i
$342$	−1.22132	−	4.55804i	−0.0660416	−	0.246471i
$343$	15.9765			0.862648
$344$	−0.208612	−	0.778549i	−0.0112476	−	0.0419765i
$345$	−2.51121	+	11.0942i	−0.135199	+	0.597293i
$346$	−6.28672	+	6.28672i	−0.337976	+	0.337976i
$347$	13.4434	−	3.60214i	0.721677	−	0.193373i	0.120757	−	0.992682i	$-0.461468\pi$
$347$	13.4434	−	3.60214i	0.721677	−	0.193373i	0.600920	+	0.799309i	$0.294801\pi$
$348$	−1.64087	+	6.12383i	−0.0879601	+	0.328272i
$349$	7.74172	−	28.8925i	0.414405	−	1.54658i	−0.371620	−	0.928385i	$-0.621198\pi$
$349$	7.74172	−	28.8925i	0.414405	−	1.54658i	0.786025	−	0.618195i	$-0.212136\pi$
$350$	3.67247	+	5.34512i	0.196302	+	0.285709i
$351$	−0.737646	+	3.52929i	−0.0393727	+	0.188379i
$352$	1.67152	+	1.67152i	0.0890922	+	0.0890922i
$353$	13.4248	+	23.2525i	0.714532	+	1.23760i	0.963140	+	0.269001i	$0.0866934\pi$
$353$	13.4248	+	23.2525i	0.714532	+	1.23760i	−0.248608	+	0.968604i	$0.579973\pi$
$354$	5.21767	−	3.01242i	0.277316	−	0.160109i
$355$	23.9821	−	15.1292i	1.27284	−	0.802974i
$356$	−3.17233	−	3.17233i	−0.168133	−	0.168133i
$357$	−7.79991	−	4.50328i	−0.412815	−	0.238339i
$358$	2.48692	+	1.43583i	0.131438	+	0.0758858i
$359$	−5.81339	−	5.81339i	−0.306819	−	0.306819i	0.536855	−	0.843674i	$-0.319612\pi$
$359$	−5.81339	−	5.81339i	−0.306819	−	0.306819i	−0.843674	+	0.536855i	$0.819612\pi$
$360$	0.493652	−	2.18090i	0.0260177	−	0.114943i
$361$	−2.82964	+	1.63369i	−0.148928	+	0.0859837i
$362$	−7.64101	−	13.2346i	−0.401602	−	0.695596i
$363$	3.82690	+	3.82690i	0.200860	+	0.200860i
$364$	−2.10892	+	4.17400i	−0.110538	+	0.218777i
$365$	−3.34270	−	10.7680i	−0.174965	−	0.563622i
$366$	1.08828	−	4.06153i	0.0568855	−	0.212300i
$367$	7.61596	−	28.4231i	0.397550	−	1.48368i	−0.419844	−	0.907596i	$-0.637915\pi$
$367$	7.61596	−	28.4231i	0.397550	−	1.48368i	0.817393	−	0.576080i	$-0.195418\pi$
$368$	4.91367	−	1.31661i	0.256143	−	0.0686332i
$369$	−5.98479	+	5.98479i	−0.311556	+	0.311556i
$370$	7.05810	+	1.59762i	0.366933	+	0.0830564i
$371$	−4.17652	−	15.5870i	−0.216834	−	0.809236i
$372$	−8.83392			−0.458018
$373$	2.73310	+	10.2001i	0.141515	+	0.528140i	0.999886	+	0.0151105i	$0.00481002\pi$
$373$	2.73310	+	10.2001i	0.141515	+	0.528140i	−0.858371	+	0.513029i	$0.828523\pi$
$374$	−8.20737	−	14.2156i	−0.424393	−	0.735070i
$375$	8.95974	−	6.68753i	0.462679	−	0.345343i
$376$		−	11.6095i		−	0.598714i
$377$	−20.4024	−	10.3083i	−1.05078	−	0.530906i
$378$	0.917141	−	0.917141i	0.0471726	−	0.0471726i
$379$	−6.58577	−	1.76465i	−0.338288	−	0.0906440i	0.0856759	−	0.996323i	$-0.472695\pi$
$379$	−6.58577	−	1.76465i	−0.338288	−	0.0906440i	−0.423964	+	0.905679i	$0.639362\pi$
$380$	−10.5435	+	0.413495i	−0.540871	+	0.0212118i
$381$	−11.6043	−	6.69977i	−0.594508	−	0.343239i
$382$		−	5.69202i		−	0.291229i
$383$	9.91784	−	17.1782i	0.506778	−	0.877765i	−0.493191	−	0.869921i	$-0.664170\pi$
$383$	9.91784	−	17.1782i	0.506778	−	0.877765i	0.999969	−	0.00784427i	$-0.00249694\pi$
$384$	−0.965926	+	0.258819i	−0.0492922	+	0.0132078i
$385$	−3.19262	+	6.06712i	−0.162711	+	0.309209i
$386$	−2.16696	+	3.75328i	−0.110295	+	0.191037i
$387$	−0.778549	−	0.208612i	−0.0395759	−	0.0106043i
$388$	5.19551	−	2.99963i	0.263762	−	0.152283i
$389$	−26.5912			−1.34823			−0.674113	−	0.738628i	$-0.735474\pi$
$389$	−26.5912			−1.34823			−0.674113	+	0.738628i	$0.735474\pi$
$390$	7.33287	+	3.35097i	0.371314	+	0.169683i
$391$	−35.3240			−1.78641
$392$	−4.60527	+	2.65885i	−0.232601	+	0.134292i
$393$	12.5651	+	3.36680i	0.633825	+	0.169833i
$394$	−0.206799	+	0.358186i	−0.0104184	+	0.0180451i
$395$	8.80938	+	28.3781i	0.443248	+	1.42785i
$396$	2.28334	−	0.611818i	0.114742	−	0.0307450i
$397$	−4.98507	+	8.63440i	−0.250194	+	0.433348i	−0.963579	−	0.267424i	$-0.913828\pi$
$397$	−4.98507	+	8.63440i	−0.250194	+	0.433348i	0.713385	+	0.700772i	$0.247161\pi$
$398$		−	17.0165i		−	0.852959i
$399$	−5.30049	−	3.06024i	−0.265357	−	0.153204i
$400$	−4.51262	−	2.15321i	−0.225631	−	0.107660i
$401$	17.9265	+	4.80339i	0.895206	+	0.239870i	0.676956	−	0.736023i	$-0.263299\pi$
$401$	17.9265	+	4.80339i	0.895206	+	0.239870i	0.218250	+	0.975893i	$0.429965\pi$
$402$	0.468594	−	0.468594i	0.0233713	−	0.0233713i
$403$	6.51631	−	31.1775i	0.324601	−	1.55306i
$404$		−	14.1195i		−	0.702473i
$405$	−1.64189	−	1.51796i	−0.0815860	−	0.0754282i
$406$	4.11150	+	7.12132i	0.204050	+	0.353425i
$407$	1.98005	+	7.38963i	0.0981472	+	0.366290i
$408$	6.94397			0.343778
$409$	2.53797	+	9.47184i	0.125495	+	0.468352i	0.999857	−	0.0169217i	$-0.00538659\pi$
$409$	2.53797	+	9.47184i	0.125495	+	0.468352i	−0.874362	+	0.485274i	$0.838720\pi$
$410$	10.0978	+	16.0066i	0.498695	+	0.790510i
$411$	−1.92420	+	1.92420i	−0.0949137	+	0.0949137i
$412$	−0.305024	+	0.0817310i	−0.0150275	+	0.00402659i
$413$	2.02252	−	7.54816i	0.0995218	−	0.371421i
$414$	1.31661	−	4.91367i	0.0647080	−	0.241493i
$415$	4.36764	−	1.35584i	0.214399	−	0.0665558i
$416$	−0.200935	−	3.59995i	−0.00985167	−	0.176502i
$417$	−1.50598	−	1.50598i	−0.0737480	−	0.0737480i
$418$	−5.57738	−	9.66031i	−0.272799	−	0.472501i
$419$	−5.99767	+	3.46276i	−0.293005	+	0.169167i	−0.639296	−	0.768960i	$-0.720774\pi$
$419$	−5.99767	+	3.46276i	−0.293005	+	0.169167i	0.346291	+	0.938127i	$0.387441\pi$
$420$	−1.54744	−	2.45294i	−0.0755074	−	0.119691i
$421$	−19.5137	−	19.5137i	−0.951041	−	0.951041i	0.0478153	−	0.998856i	$-0.484774\pi$
$421$	−19.5137	−	19.5137i	−0.951041	−	0.951041i	−0.998856	+	0.0478153i	$0.984774\pi$
$422$	−9.55858	−	5.51865i	−0.465304	−	0.268644i
$423$	−10.0541	−	5.80474i	−0.488848	−	0.282236i
$424$	8.79736	+	8.79736i	0.427238	+	0.427238i
$425$	26.3979	+	22.5526i	1.28049	+	1.09396i
$426$	−10.9820	+	6.34049i	−0.532082	+	0.307198i
$427$	−2.72689	−	4.72311i	−0.131963	−	0.228567i
$428$	9.49976	+	9.49976i	0.459188	+	0.459188i
$429$	0.474988	+	8.50985i	0.0229326	+	0.410860i
$430$	−0.839292	+	1.59495i	−0.0404743	+	0.0769155i
$431$	0.563587	−	2.10333i	0.0271470	−	0.101314i	−0.951023	−	0.309120i	$-0.899966\pi$
$431$	0.563587	−	2.10333i	0.0271470	−	0.101314i	0.978170	+	0.207806i	$0.0666322\pi$
$432$	−0.258819	+	0.965926i	−0.0124524	+	0.0464731i
$433$	−34.9027	+	9.35214i	−1.67731	+	0.449435i	−0.967068	−	0.254518i	$-0.918083\pi$
$433$	−34.9027	+	9.35214i	−1.67731	+	0.449435i	−0.710246	+	0.703953i	$0.751417\pi$
$434$	−8.10195	+	8.10195i	−0.388906	+	0.388906i
$435$	11.9899	−	7.56384i	0.574870	−	0.362658i
$436$	0.807747	+	3.01455i	0.0386841	+	0.144371i
$437$	−24.0047			−1.14830
$438$	1.30504	+	4.87047i	0.0623572	+	0.232720i
$439$	−8.21571	−	14.2300i	−0.392114	−	0.679162i	0.600614	−	0.799539i	$-0.294923\pi$
$439$	−8.21571	−	14.2300i	−0.392114	−	0.679162i	−0.992728	+	0.120377i	$0.961590\pi$
$440$	−0.207139	−	5.28174i	−0.00987496	−	0.251797i
$441$			5.31771i			0.253224i
$442$	−5.12220	+	24.5073i	−0.243638	+	1.16569i
$443$	−27.3942	+	27.3942i	−1.30154	+	1.30154i	−0.374187	+	0.927353i	$0.622078\pi$
$443$	−27.3942	+	27.3942i	−1.30154	+	1.30154i	−0.927353	+	0.374187i	$0.877922\pi$
$444$	−3.12606	−	0.837624i	−0.148356	−	0.0397519i
$445$	0.393123	+	10.0241i	0.0186358	+	0.475186i
$446$	−10.3812	−	5.99361i	−0.491566	−	0.283806i
$447$			4.56611i			0.215969i
$448$	−0.648516	+	1.12326i	−0.0306395	+	0.0530692i
$449$	39.0040	−	10.4511i	1.84071	−	0.493218i	0.841800	−	0.539790i	$-0.181496\pi$
$449$	39.0040	−	10.4511i	1.84071	−	0.493218i	0.998915	+	0.0465717i	$0.0148296\pi$
$450$	−4.12104	+	2.83144i	−0.194268	+	0.133475i
$451$	−10.0037	+	17.3269i	−0.471055	+	0.815892i
$452$	−9.81102	−	2.62886i	−0.461472	−	0.123651i
$453$	16.3067	−	9.41470i	0.766157	−	0.442341i
$454$	10.4835			0.492013
$455$	9.79859	−	3.65196i	0.459365	−	0.171207i
$456$	4.71883			0.220980
$457$	6.12025	−	3.53353i	0.286293	−	0.165291i	−0.349976	−	0.936759i	$-0.613810\pi$
$457$	6.12025	−	3.53353i	0.286293	−	0.165291i	0.636269	+	0.771467i	$0.280477\pi$
$458$	11.8908	+	3.18614i	0.555622	+	0.148878i
$459$	3.47199	−	6.01366i	0.162058	−	0.280694i
$460$	−10.0662	−	5.29703i	−0.469341	−	0.246976i
$461$	−15.1853	+	4.06888i	−0.707249	+	0.189507i	−0.594475	−	0.804114i	$-0.702640\pi$
$461$	−15.1853	+	4.06888i	−0.707249	+	0.189507i	−0.112774	+	0.993621i	$0.535974\pi$
$462$	1.53302	−	2.65526i	0.0713224	−	0.123534i
$463$			13.2887i			0.617577i	0.951131	+	0.308788i	$0.0999235\pi$
$463$			13.2887i			0.617577i	−0.951131	+	0.308788i	$0.900077\pi$
$464$	−5.49047	−	3.16993i	−0.254889	−	0.147160i
$465$	14.5043	+	13.4096i	0.672620	+	0.621854i
$466$	24.6827	+	6.61372i	1.14341	+	0.306375i
$467$	11.5225	−	11.5225i	0.533200	−	0.533200i	−0.388324	−	0.921523i	$-0.626946\pi$
$467$	11.5225	−	11.5225i	0.533200	−	0.533200i	0.921523	+	0.388324i	$0.126946\pi$
$468$	−3.21811	−	1.62596i	−0.148757	−	0.0751600i
$469$		−	0.859532i		−	0.0396895i
$470$	−17.6228	+	19.0615i	−0.812878	+	0.879239i
$471$	−7.46212	−	12.9248i	−0.343837	−	0.595542i
$472$	1.55935	+	5.81956i	0.0717747	+	0.267867i
$473$	−1.90532			−0.0876067
$474$	−3.43931	−	12.8357i	−0.157973	−	0.589563i
$475$	17.9389	+	15.3258i	0.823095	+	0.703195i
$476$	6.36860	−	6.36860i	0.291904	−	0.291904i
$477$	12.0174	−	3.22006i	0.550240	−	0.147436i
$478$	−3.54566	+	13.2326i	−0.162175	+	0.605244i
$479$	−8.77511	+	32.7492i	−0.400945	+	1.49635i	0.410468	+	0.911875i	$0.365365\pi$
$479$	−8.77511	+	32.7492i	−0.400945	+	1.49635i	−0.811413	+	0.584473i	$0.801301\pi$
$480$	1.97882	+	1.04129i	0.0903202	+	0.0475281i
$481$	5.26214	−	10.4149i	0.239933	−	0.474878i
$482$	8.21390	+	8.21390i	0.374133	+	0.374133i
$483$	−3.29900	−	5.71404i	−0.150110	−	0.259998i
$484$	−4.68698	+	2.70603i	−0.213045	+	0.123001i
$485$	−13.0837	−	2.96154i	−0.594102	−	0.134477i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	34.0102	+	19.6358i	1.54115	+	0.889783i	0.998767	+	0.0496516i	$0.0158111\pi$
$487$	34.0102	+	19.6358i	1.54115	+	0.889783i	0.542383	+	0.840131i	$0.317522\pi$
$488$	3.64147	+	2.10240i	0.164842	+	0.0951714i
$489$	1.24288	+	1.24288i	0.0562050	+	0.0562050i
$490$	11.5974	+	2.62509i	0.523915	+	0.118590i
$491$	34.8781	−	20.1369i	1.57403	−	0.908765i	0.578359	−	0.815782i	$-0.303693\pi$
$491$	34.8781	−	20.1369i	1.57403	−	0.908765i	0.995668	−	0.0929826i	$-0.0296401\pi$
$492$	−4.23189	−	7.32985i	−0.190788	−	0.330455i
$493$	31.1295	+	31.1295i	1.40200	+	1.40200i
$494$	−3.48083	+	16.6541i	−0.156610	+	0.749304i
$495$	−4.67769	−	2.46148i	−0.210247	−	0.110635i
$496$	2.28639	−	8.53291i	0.102662	−	0.383139i
$497$	−4.25696	+	15.8872i	−0.190951	+	0.712638i
$498$	−1.97553	+	0.529342i	−0.0885257	+	0.0237204i
$499$	−14.8255	+	14.8255i	−0.663679	+	0.663679i	−0.956245	−	0.292566i	$-0.905491\pi$
$499$	−14.8255	+	14.8255i	−0.663679	+	0.663679i	0.292566	+	0.956245i	$0.405491\pi$
$500$	4.14071	+	10.3853i	0.185178	+	0.464445i
$501$	−3.55825	−	13.2796i	−0.158971	−	0.593287i
$502$	16.8325			0.751273
$503$	2.29209	+	8.55419i	0.102199	+	0.381412i	0.998012	−	0.0630184i	$-0.0200727\pi$
$503$	2.29209	+	8.55419i	0.102199	+	0.381412i	−0.895813	+	0.444431i	$0.853406\pi$
$504$	0.648516	+	1.12326i	0.0288872	+	0.0500341i
$505$	−21.4329	+	23.1826i	−0.953752	+	1.03161i
$506$		−	12.0251i		−	0.534580i
$507$	8.11231	−	10.1583i	0.360280	−	0.451145i
$508$	9.47490	−	9.47490i	0.420381	−	0.420381i
$509$	13.6779	+	3.66497i	0.606261	+	0.162447i	0.548874	−	0.835905i	$-0.315057\pi$
$509$	13.6779	+	3.66497i	0.606261	+	0.162447i	0.0573867	+	0.998352i	$0.481723\pi$
$510$	−11.4012	−	10.5407i	−0.504854	−	0.466750i
$511$	5.66381	+	3.27000i	0.250552	+	0.144656i
$512$		−	1.00000i		−	0.0441942i
$513$	2.35942	−	4.08663i	0.104171	−	0.180429i
$514$	−6.00363	+	1.60867i	−0.264809	+	0.0709554i
$515$	0.624879	+	0.328822i	0.0275355	+	0.0144896i
$516$	0.403007	−	0.698028i	0.0177414	−	0.0307290i
$517$	−26.5084	−	7.10289i	−1.16584	−	0.312385i
$518$	−3.63525	+	2.09881i	−0.159724	+	0.0922166i
$519$	−8.89076			−0.390261
$520$	−5.13467	+	6.21572i	−0.225170	+	0.272577i
$521$	−4.48877			−0.196657			−0.0983284	−	0.995154i	$-0.531350\pi$
$521$	−4.48877			−0.196657			−0.0983284	+	0.995154i	$0.531350\pi$
$522$	−5.49047	+	3.16993i	−0.240311	+	0.138744i
$523$	−7.21056	−	1.93207i	−0.315296	−	0.0844833i	0.0977007	−	0.995216i	$-0.468851\pi$
$523$	−7.21056	−	1.93207i	−0.315296	−	0.0844833i	−0.412997	+	0.910733i	$0.635518\pi$
$524$	−6.50417	+	11.2655i	−0.284136	+	0.492138i
$525$	−1.18275	+	6.37640i	−0.0516193	+	0.278289i
$526$	−12.4555	+	3.33744i	−0.543085	+	0.145519i
$527$	−30.6713	+	53.1242i	−1.33606	+	2.31413i
$528$			2.36388i			0.102875i
$529$	−2.49206	−	1.43879i	−0.108350	−	0.0625560i
$530$	−1.09019	−	27.7983i	−0.0473549	−	1.20748i
$531$	5.81956	+	1.55935i	0.252547	+	0.0676698i
$532$	4.32783	−	4.32783i	0.187635	−	0.187635i
$533$	28.9908	−	9.52872i	1.25573	−	0.412735i
$534$		−	4.48635i		−	0.194143i
$535$	−1.17724	−	30.0178i	−0.0508963	−	1.29778i
$536$	0.331346	+	0.573907i	0.0143120	+	0.0247890i
$537$	0.743239	+	2.77380i	0.0320731	+	0.119698i
$538$	−0.213349			−0.00919813
$539$	3.25347	+	12.1421i	0.140137	+	0.522997i
$540$	1.89119	−	1.19306i	0.0813839	−	0.0513412i
$541$	8.66329	−	8.66329i	0.372464	−	0.372464i	−0.495910	−	0.868374i	$-0.665165\pi$
$541$	8.66329	−	8.66329i	0.372464	−	0.372464i	0.868374	+	0.495910i	$0.165165\pi$
$542$	−1.83744	+	0.492340i	−0.0789247	+	0.0211478i
$543$	3.95528	−	14.7613i	0.169737	−	0.633468i
$544$	−1.79723	+	6.70736i	−0.0770557	+	0.287576i
$545$	3.24975	−	6.17568i	0.139204	−	0.264537i
$546$	−4.44270	+	1.46023i	−0.190130	+	0.0624921i
$547$	−3.33496	−	3.33496i	−0.142592	−	0.142592i	0.632207	−	0.774800i	$-0.282149\pi$
$547$	−3.33496	−	3.33496i	−0.142592	−	0.142592i	−0.774800	+	0.632207i	$0.782149\pi$
$548$	−1.36061	−	2.35665i	−0.0581226	−	0.100671i
$549$	3.64147	−	2.10240i	0.155414	−	0.0897284i
$550$	−7.67739	+	8.98645i	−0.327365	+	0.383183i
$551$	21.1543	+	21.1543i	0.901204	+	0.901204i
$552$	4.40547	+	2.54350i	0.187509	+	0.108259i
$553$	−14.9265	−	8.61780i	−0.634738	−	0.366466i
$554$	17.0063	+	17.0063i	0.722528	+	0.722528i
$555$	3.86115	+	6.12052i	0.163896	+	0.259802i
$556$	1.84444	−	1.06489i	0.0782216	−	0.0451613i
$557$	−13.1129	−	22.7122i	−0.555612	−	0.962348i	−0.997856	−	0.0654529i	$-0.979151\pi$
$557$	−13.1129	−	22.7122i	−0.555612	−	0.962348i	0.442244	−	0.896895i	$-0.354183\pi$
$558$	−6.24653	−	6.24653i	−0.264437	−	0.264437i
$559$	2.16627	+	1.93722i	0.0916233	+	0.0819358i
$560$	2.76986	−	0.859846i	0.117048	−	0.0363351i
$561$	4.24845	−	15.8554i	0.179370	−	0.669416i
$562$	2.46292	−	9.19174i	0.103892	−	0.387730i
$563$	−1.03619	+	0.277646i	−0.0436701	+	0.0117014i	−0.280588	−	0.959828i	$-0.590529\pi$
$563$	−1.03619	+	0.277646i	−0.0436701	+	0.0117014i	0.236918	+	0.971530i	$0.423863\pi$
$564$	8.20915	−	8.20915i	0.345667	−	0.345667i
$565$	12.1181	+	19.2090i	0.509811	+	0.808131i
$566$	−3.36636	−	12.5634i	−0.141499	−	0.528080i
$567$	1.29703			0.0544703
$568$	−3.28208	−	12.2489i	−0.137713	−	0.513951i
$569$	1.22207	+	2.11668i	0.0512316	+	0.0887358i	0.890504	−	0.454975i	$-0.150352\pi$
$569$	1.22207	+	2.11668i	0.0512316	+	0.0887358i	−0.839272	+	0.543711i	$0.817019\pi$
$570$	−7.74778	−	7.16301i	−0.324519	−	0.300026i
$571$			20.9592i			0.877117i	0.898703	+	0.438558i	$0.144511\pi$
$571$			20.9592i			0.877117i	−0.898703	+	0.438558i	$0.855489\pi$
$572$	−8.34282	−	1.74371i	−0.348831	−	0.0729082i
$573$	4.02486	−	4.02486i	0.168141	−	0.168141i
$574$	−10.6037	−	2.84126i	−0.442591	−	0.118592i
$575$	8.48692	+	23.9773i	0.353929	+	0.999923i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$		−	27.7348i		−	1.15462i	−0.816527	−	0.577308i	$-0.804103\pi$
$577$		−	27.7348i		−	1.15462i	0.816527	−	0.577308i	$-0.195897\pi$
$578$	15.6094	−	27.0362i	0.649265	−	1.12456i
$579$	−4.18624	+	1.12170i	−0.173974	+	0.0466162i
$580$	4.20290	+	13.5390i	0.174516	+	0.562176i
$581$	−1.32636	+	2.29732i	−0.0550266	+	0.0953090i
$582$	5.79483	+	1.55272i	0.240204	+	0.0643624i
$583$	25.4697	−	14.7049i	1.05485	−	0.609016i
$584$	−5.04229			−0.208651
$585$	2.81563	+	7.55462i	0.116412	+	0.312345i
$586$	−7.02915			−0.290371
$587$	−0.408623	+	0.235919i	−0.0168657	+	0.00973741i	−0.508409	−	0.861116i	$-0.669766\pi$
$587$	−0.408623	+	0.235919i	−0.0168657	+	0.00973741i	0.491543	+	0.870853i	$0.336433\pi$
$588$	−5.13651	−	1.37632i	−0.211826	−	0.0567586i
$589$	−20.8429	+	36.1010i	−0.858817	+	1.48751i
$590$	6.27360	−	11.9221i	0.258280	−	0.490824i
$591$	−0.399504	+	0.107047i	−0.0164334	+	0.00440332i
$592$	1.61817	−	2.80275i	0.0665062	−	0.115192i
$593$		−	30.9039i		−	1.26907i	−0.772893	−	0.634536i	$-0.781191\pi$
$593$		−	30.9039i		−	1.26907i	0.772893	−	0.634536i	$-0.218809\pi$
$594$	2.04718	+	1.18194i	0.0839969	+	0.0484956i
$595$	−20.1238	+	0.789214i	−0.824996	+	0.0323546i
$596$	−4.41052	−	1.18180i	−0.180662	−	0.0484082i
$597$	12.0325	−	12.0325i	0.492456	−	0.492456i
$598$	−12.2264	+	13.6720i	−0.499976	+	0.559089i
$599$		−	18.6640i		−	0.762592i	−0.924453	−	0.381296i	$-0.875478\pi$
$599$		−	18.6640i		−	0.762592i	0.924453	−	0.381296i	$-0.124522\pi$
$600$	−1.66835	−	4.71345i	−0.0681103	−	0.192426i
$601$	6.45779	+	11.1852i	0.263419	+	0.456255i	0.967148	−	0.254213i	$-0.0818166\pi$
$601$	6.45779	+	11.1852i	0.263419	+	0.456255i	−0.703729	+	0.710468i	$0.748483\pi$
$602$	−0.270576	−	1.00980i	−0.0110279	−	0.0411565i
$603$	0.662691			0.0269869
$604$	4.87341	+	18.1878i	0.198296	+	0.740051i
$605$	11.8031	+	2.67167i	0.479866	+	0.108619i
$606$	9.98401	−	9.98401i	0.405573	−	0.405573i
$607$	−3.69210	+	0.989296i	−0.149858	+	0.0401543i	−0.332968	−	0.942938i	$-0.608050\pi$
$607$	−3.69210	+	0.989296i	−0.149858	+	0.0401543i	0.183110	+	0.983092i	$0.441383\pi$
$608$	−1.22132	+	4.55804i	−0.0495312	+	0.184853i
$609$	−2.12827	+	7.94280i	−0.0862418	+	0.321859i
$610$	−2.78751	−	8.97952i	−0.112863	−	0.363570i
$611$	22.9170	+	35.0279i	0.927123	+	1.41708i
$612$	4.91013	+	4.91013i	0.198480	+	0.198480i
$613$	−12.1389	−	21.0252i	−0.490285	−	0.849199i	0.509652	−	0.860381i	$-0.329774\pi$
$613$	−12.1389	−	21.0252i	−0.490285	−	0.849199i	−0.999937	+	0.0111815i	$0.996441\pi$
$614$	11.7367	−	6.77616i	0.473653	−	0.273464i
$615$	−4.17816	+	18.4586i	−0.168480	+	0.744323i
$616$	2.16801	+	2.16801i	0.0873517	+	0.0873517i
$617$	16.1362	+	9.31625i	0.649620	+	0.375058i	0.788311	−	0.615278i	$-0.210956\pi$
$617$	16.1362	+	9.31625i	0.649620	+	0.375058i	−0.138691	+	0.990336i	$0.544289\pi$
$618$	−0.273477	−	0.157892i	−0.0110009	−	0.00635135i
$619$	−16.3696	−	16.3696i	−0.657949	−	0.657949i	0.296946	−	0.954894i	$-0.404032\pi$
$619$	−16.3696	−	16.3696i	−0.657949	−	0.657949i	−0.954894	+	0.296946i	$0.904032\pi$
$620$	−16.7066	+	10.5394i	−0.670955	+	0.423273i
$621$	4.40547	−	2.54350i	0.176786	−	0.102067i
$622$	15.1333	+	26.2116i	0.606789	+	1.05099i
$623$	−4.11461	−	4.11461i	−0.164848	−	0.164848i
$624$	2.40346	−	2.68763i	0.0962156	−	0.107591i
$625$	8.96593	−	23.3369i	0.358637	−	0.933477i
$626$	−6.01958	+	22.4654i	−0.240591	+	0.897897i
$627$	2.88707	−	10.7747i	0.115298	−	0.430299i
$628$	14.4157	−	3.86268i	0.575250	−	0.154138i
$629$	−15.8908	+	15.8908i	−0.633608	+	0.633608i
$630$	0.640282	−	2.82869i	0.0255095	−	0.112698i
$631$	−12.6935	−	47.3728i	−0.505321	−	1.88588i	−0.462121	−	0.886817i	$-0.652912\pi$
$631$	−12.6935	−	47.3728i	−0.505321	−	1.88588i	−0.0431996	−	0.999066i	$-0.513755\pi$
$632$	13.2885			0.528587
$633$	−2.85666	−	10.6612i	−0.113542	−	0.423745i
$634$	7.46982	+	12.9381i	0.296664	+	0.513838i
$635$	−29.9392	+	1.17415i	−1.18810	+	0.0465949i
$636$			12.4413i			0.493331i
$637$	8.64637	−	17.1130i	0.342582	−	0.678041i
$638$	−10.5972	+	10.5972i	−0.419546	+	0.419546i
$639$	−12.2489	−	3.28208i	−0.484558	−	0.129837i
$640$	−1.51796	+	1.64189i	−0.0600028	+	0.0649012i
$641$	30.5023	+	17.6105i	1.20477	+	0.695572i	0.961611	−	0.274415i	$-0.0884842\pi$
$641$	30.5023	+	17.6105i	1.20477	+	0.695572i	0.243155	+	0.969987i	$0.421817\pi$
$642$			13.4347i			0.530225i
$643$	8.61155	−	14.9156i	0.339606	−	0.588215i	−0.644752	−	0.764392i	$-0.723039\pi$
$643$	8.61155	−	14.9156i	0.339606	−	0.588215i	0.984359	+	0.176176i	$0.0563728\pi$
$644$	6.37319	−	1.70769i	0.251139	−	0.0672924i
$645$	−1.72127	+	0.534333i	−0.0677750	+	0.0210393i
$646$	16.3837	−	28.3774i	0.644609	−	1.11650i
$647$	17.2315	+	4.61717i	0.677441	+	0.181520i	0.581104	−	0.813829i	$-0.302621\pi$
$647$	17.2315	+	4.61717i	0.677441	+	0.181520i	0.0963367	+	0.995349i	$0.469287\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	14.2420			0.559049
$650$	17.8658	−	2.41125i	0.700753	−	0.0945769i
$651$	−11.4579			−0.449070
$652$	−1.52221	+	0.878849i	−0.0596144	+	0.0344184i
$653$	15.0392	+	4.02975i	0.588531	+	0.157696i	0.540782	−	0.841163i	$-0.318129\pi$
$653$	15.0392	+	4.02975i	0.588531	+	0.157696i	0.0477492	+	0.998859i	$0.484795\pi$
$654$	−1.56045	+	2.70278i	−0.0610183	+	0.105687i
$655$	27.7798	−	8.62366i	1.08545	−	0.336954i
$656$	8.17538	−	2.19059i	0.319195	−	0.0855280i
$657$	−2.52114	+	4.36675i	−0.0983591	+	0.170363i
$658$		−	15.0579i		−	0.587018i
$659$	−15.1800	−	8.76418i	−0.591329	−	0.341404i	0.174294	−	0.984694i	$-0.444236\pi$
$659$	−15.1800	−	8.76418i	−0.591329	−	0.341404i	−0.765623	+	0.643290i	$0.777569\pi$
$660$	3.58829	−	3.88122i	0.139674	−	0.151076i
$661$	−37.7494	−	10.1149i	−1.46828	−	0.393425i	−0.565940	−	0.824447i	$-0.691486\pi$
$661$	−37.7494	−	10.1149i	−1.46828	−	0.393425i	−0.902341	+	0.431022i	$0.858153\pi$
$662$	−8.08599	+	8.08599i	−0.314271	+	0.314271i
$663$	−20.9512	+	13.7073i	−0.813678	+	0.532349i
$664$		−	2.04522i		−	0.0793699i
$665$	−13.6753	+	0.536317i	−0.530305	+	0.0207975i
$666$	−1.61817	−	2.80275i	−0.0627027	−	0.108604i
$667$	8.34713	+	31.1519i	0.323202	+	1.20621i
$668$	13.7480			0.531926
$669$	−3.10252	−	11.5788i	−0.119950	−	0.447661i
$670$	0.327139	−	1.44526i	0.0126385	−	0.0558353i
$671$	7.02841	−	7.02841i	0.271329	−	0.271329i
$672$	−1.25284	+	0.335697i	−0.0483293	+	0.0129498i
$673$	−13.2880	+	49.5916i	−0.512216	+	1.91162i	−0.116670	+	0.993171i	$0.537222\pi$
$673$	−13.2880	+	49.5916i	−0.512216	+	1.91162i	−0.395546	+	0.918446i	$0.629445\pi$
$674$	−7.44066	+	27.7689i	−0.286604	+	1.06962i
$675$	−4.91614	−	0.911886i	−0.189222	−	0.0350985i
$676$	7.71252	+	10.4650i	0.296635	+	0.402502i
$677$	8.54818	+	8.54818i	0.328533	+	0.328533i	0.852029	−	0.523495i	$-0.175372\pi$
$677$	8.54818	+	8.54818i	0.328533	+	0.328533i	−0.523495	+	0.852029i	$0.675372\pi$
$678$	−5.07856	−	8.79632i	−0.195041	−	0.337821i
$679$	6.73874	−	3.89061i	0.258609	−	0.149308i
$680$	13.1324	−	8.28459i	0.503604	−	0.317700i
$681$	7.41292	+	7.41292i	0.284064	+	0.284064i
$682$	−18.0847	−	10.4412i	−0.692497	−	0.399813i
$683$	10.7933	+	6.23153i	0.412995	+	0.238443i	0.692076	−	0.721825i	$-0.256696\pi$
$683$	10.7933	+	6.23153i	0.412995	+	0.238443i	−0.279081	+	0.960268i	$0.590030\pi$
$684$	3.33672	+	3.33672i	0.127583	+	0.127583i
$685$	−1.34334	+	5.93472i	−0.0513263	+	0.226754i
$686$	−13.8360	+	7.98823i	−0.528262	+	0.304992i
$687$	6.15514	+	10.6610i	0.234833	+	0.406743i
$688$	0.569937	+	0.569937i	0.0217287	+	0.0217287i
$689$	−43.9091	−	9.17731i	−1.67280	−	0.349628i
$690$	−3.37234	−	10.8635i	−0.128383	−	0.413566i
$691$	8.78573	−	32.7888i	0.334225	−	1.24734i	−0.570482	−	0.821310i	$-0.693244\pi$
$691$	8.78573	−	32.7888i	0.334225	−	1.24734i	0.904707	−	0.426034i	$-0.140090\pi$
$692$	2.30110	−	8.58782i	0.0874746	−	0.326460i
$693$	2.96156	−	0.793548i	0.112500	−	0.0301444i
$694$	−9.84122	+	9.84122i	−0.373568	+	0.373568i
$695$	−4.64482	−	1.05137i	−0.176188	−	0.0398806i
$696$	−1.64087	−	6.12383i	−0.0621972	−	0.232123i
$697$	−58.7722			−2.22616
$698$	7.74172	+	28.8925i	0.293028	+	1.09360i
$699$	12.7767	+	22.1299i	0.483260	+	0.837031i
$700$	−5.85301	−	2.79278i	−0.221223	−	0.105557i
$701$			39.3497i			1.48622i	0.669170	+	0.743109i	$0.266650\pi$
$701$			39.3497i			1.48622i	−0.669170	+	0.743109i	$0.733350\pi$
$702$	−1.12582	−	3.42528i	−0.0424915	−	0.129279i
$703$	−10.7987	+	10.7987i	−0.407282	+	0.407282i
$704$	−2.28334	−	0.611818i	−0.0860564	−	0.0230588i
$705$	−25.9397	+	1.01730i	−0.976944	+	0.0383137i
$706$	−23.2525	−	13.4248i	−0.875119	−	0.505250i
$707$		−	18.3135i		−	0.688750i
$708$	−3.01242	+	5.21767i	−0.113214	+	0.196092i
$709$	14.0918	−	3.77590i	0.529230	−	0.141807i	0.0156976	−	0.999877i	$-0.495003\pi$
$709$	14.0918	−	3.77590i	0.529230	−	0.141807i	0.513533	+	0.858070i	$0.328336\pi$
$710$	−13.2045	+	25.0933i	−0.495558	+	0.941736i
$711$	6.64424	−	11.5082i	0.249179	−	0.431590i
$712$	4.33348	+	1.16115i	0.162404	+	0.0435160i
$713$	−38.9176	+	22.4691i	−1.45748	+	0.841474i
$714$	9.00656			0.337062
$715$	11.0511	+	15.5271i	0.413287	+	0.580679i
$716$	−2.87165			−0.107319
$717$	−11.8640	+	6.84968i	−0.443069	+	0.255806i
$718$	7.94124	+	2.12785i	0.296364	+	0.0794106i
$719$	18.0641	−	31.2880i	0.673678	−	1.16684i	−0.303176	−	0.952935i	$-0.598047\pi$
$719$	18.0641	−	31.2880i	0.673678	−	1.16684i	0.976853	−	0.213909i	$-0.0686198\pi$
$720$	0.662933	+	2.13554i	0.0247061	+	0.0795868i
$721$	−0.395626	+	0.106008i	−0.0147339	+	0.00394793i
$722$	1.63369	−	2.82964i	0.0607997	−	0.105308i
$723$			11.6162i			0.432011i
$724$	13.2346	+	7.64101i	0.491860	+	0.283976i
$725$	13.6510	−	28.6093i	0.506986	−	1.06252i
$726$	−5.22765	−	1.40074i	−0.194016	−	0.0519865i
$727$	−12.0708	+	12.0708i	−0.447682	+	0.447682i	−0.894583	−	0.446901i	$-0.852528\pi$
$727$	−12.0708	+	12.0708i	−0.447682	+	0.447682i	0.446901	+	0.894583i	$0.352528\pi$
$728$	−0.260620	−	4.66925i	−0.00965921	−	0.173054i
$729$			1.00000i			0.0370370i
$730$	8.27886	+	7.65400i	0.306414	+	0.283287i
$731$	−2.79847	−	4.84709i	−0.103505	−	0.179276i
$732$	1.08828	+	4.06153i	0.0402241	+	0.150119i
$733$	7.35261			0.271575			0.135787	−	0.990738i	$-0.456644\pi$
$733$	7.35261			0.271575			0.135787	+	0.990738i	$0.456644\pi$
$734$	7.61596	+	28.4231i	0.281110	+	1.04912i
$735$	6.34435	+	10.0568i	0.234015	+	0.370951i
$736$	−3.59705	+	3.59705i	−0.132589	+	0.132589i
$737$	1.51315	−	0.405446i	0.0557375	−	0.0149348i
$738$	2.19059	−	8.17538i	0.0806366	−	0.300940i
$739$	6.26046	−	23.3644i	0.230295	−	0.859472i	−0.749919	−	0.661530i	$-0.769907\pi$
$739$	6.26046	−	23.3644i	0.230295	−	0.859472i	0.980214	−	0.197942i	$-0.0634258\pi$
$740$	−6.91131	+	2.14547i	−0.254065	+	0.0788691i
$741$	−14.2376	+	9.31492i	−0.523030	+	0.342192i
$742$	11.4105	+	11.4105i	0.418891	+	0.418891i
$743$	−20.1924	−	34.9742i	−0.740786	−	1.28308i	−0.952138	−	0.305669i	$-0.901120\pi$
$743$	−20.1924	−	34.9742i	−0.740786	−	1.28308i	0.211351	−	0.977410i	$-0.432214\pi$
$744$	7.65040	−	4.41696i	0.280477	−	0.161934i
$745$	5.44765	+	8.63538i	0.199586	+	0.316376i
$746$	−7.46697	−	7.46697i	−0.273385	−	0.273385i
$747$	−1.77121	−	1.02261i	−0.0648053	−	0.0374154i
$748$	14.2156	+	8.20737i	0.519773	+	0.300091i
$749$	12.3215	+	12.3215i	0.450218	+	0.450218i
$750$	−4.41559	+	10.2714i	−0.161235	+	0.375060i
$751$	26.0554	−	15.0431i	0.950775	−	0.548930i	0.0574532	−	0.998348i	$-0.481702\pi$
$751$	26.0554	−	15.0431i	0.950775	−	0.548930i	0.893322	+	0.449418i	$0.148369\pi$
$752$	5.80474	+	10.0541i	0.211677	+	0.366636i
$753$	11.9024	+	11.9024i	0.433748	+	0.433748i
$754$	22.8231	−	1.27390i	0.831170	−	0.0463927i
$755$	19.6068	−	37.2599i	0.713565	−	1.35603i
$756$	−0.335697	+	1.25284i	−0.0122092	+	0.0455653i
$757$	7.43615	−	27.7521i	0.270272	−	1.00867i	−0.688673	−	0.725072i	$-0.741806\pi$
$757$	7.43615	−	27.7521i	0.270272	−	1.00867i	0.958944	−	0.283595i	$-0.0915271\pi$
$758$	6.58577	−	1.76465i	0.239206	−	0.0640950i
$759$	8.50301	−	8.50301i	0.308640	−	0.308640i
$760$	8.92421	−	5.62986i	0.323715	−	0.204216i
$761$	5.23591	+	19.5407i	0.189802	+	0.708350i	0.993551	+	0.113382i	$0.0361685\pi$
$761$	5.23591	+	19.5407i	0.189802	+	0.708350i	−0.803750	+	0.594968i	$0.797165\pi$
$762$	13.3995			0.485414
$763$	1.04767	+	3.90998i	0.0379284	+	0.141551i
$764$	2.84601	+	4.92943i	0.102965	+	0.178341i
$765$	−0.608476	−	15.5153i	−0.0219995	−	0.560956i
$766$			19.8357i			0.716692i
$767$	−16.1926	−	14.4805i	−0.584680	−	0.522861i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−1.45984	−	0.391163i	−0.0526431	−	0.0141057i	0.232401	−	0.972620i	$-0.425342\pi$
$769$	−1.45984	−	0.391163i	−0.0526431	−	0.0141057i	−0.285045	+	0.958514i	$0.592008\pi$
$770$	−0.268666	−	6.85059i	−0.00968205	−	0.246878i
$771$	−5.38271	−	3.10771i	−0.193854	−	0.111921i
$772$		−	4.33391i		−	0.155981i
$773$	−19.3363	+	33.4914i	−0.695478	+	1.20460i	0.274541	+	0.961575i	$0.411474\pi$
$773$	−19.3363	+	33.4914i	−0.695478	+	1.20460i	−0.970019	+	0.243028i	$0.921859\pi$
$774$	0.778549	−	0.208612i	0.0279844	−	0.00749839i
$775$	43.4288	+	8.05553i	1.56001	+	0.289363i
$776$	−2.99963	+	5.19551i	−0.107680	+	0.186508i
$777$	−4.05460	−	1.08643i	−0.145458	−	0.0389753i
$778$	23.0286	−	13.2956i	0.825617	−	0.476670i
$779$	−39.9391			−1.43097
$780$	−8.02594	+	0.764411i	−0.287375	+	0.0273703i
$781$	−29.9763			−1.07264
$782$	30.5915	−	17.6620i	1.09395	−	0.631592i
$783$	−6.12383	−	1.64087i	−0.218848	−	0.0586401i
$784$	2.65885	−	4.60527i	0.0949590	−	0.164474i
$785$	−29.5324	−	15.5404i	−1.05406	−	0.554662i
$786$	−12.5651	+	3.36680i	−0.448182	+	0.120090i
$787$	−16.9665	+	29.3868i	−0.604790	+	1.04753i	0.387295	+	0.921956i	$0.373410\pi$
$787$	−16.9665	+	29.3868i	−0.604790	+	1.04753i	−0.992085	+	0.125571i	$0.959924\pi$
$788$		−	0.413597i		−	0.0147338i
$789$	−11.1673	−	6.44744i	−0.397566	−	0.229535i
$790$	−21.8182	−	20.1714i	−0.776256	−	0.717667i
$791$	−12.7252	−	3.40971i	−0.452457	−	0.121235i
$792$	−1.67152	+	1.67152i	−0.0593948	+	0.0593948i
$793$	−15.1371	+	0.844895i	−0.537534	+	0.0300031i
$794$		−	9.97014i		−	0.353827i
$795$	18.8855	−	20.4273i	0.669800	−	0.724480i
$796$	8.50824	+	14.7367i	0.301567	+	0.522329i
$797$	−3.60129	−	13.4402i	−0.127564	−	0.476076i	0.872354	−	0.488875i	$-0.162593\pi$
$797$	−3.60129	−	13.4402i	−0.127564	−	0.476076i	−0.999918	+	0.0127987i	$0.995926\pi$
$798$	6.12048			0.216663
$799$	−20.8650	−	77.8691i	−0.738149	−	2.75481i
$800$	4.98464	−	0.391577i	0.176234	−	0.0138443i
$801$	3.17233	−	3.17233i	0.112089	−	0.112089i
$802$	−17.9265	+	4.80339i	−0.633006	+	0.169614i
$803$	−3.08496	+	11.5132i	−0.108866	+	0.406293i
$804$	−0.171517	+	0.640111i	−0.00604894	+	0.0225750i
$805$	−13.0563	−	6.87043i	−0.460172	−	0.242151i
$806$	9.94544	+	30.2586i	0.350313	+	1.06581i
$807$	−0.150861	−	0.150861i	−0.00531055	−	0.00531055i
$808$	7.05976	+	12.2279i	0.248362	+	0.430175i
$809$	22.1451	−	12.7855i	0.778581	−	0.449514i	−0.0573465	−	0.998354i	$-0.518264\pi$
$809$	22.1451	−	12.7855i	0.778581	−	0.449514i	0.835927	+	0.548841i	$0.184931\pi$
$810$	2.18090	+	0.493652i	0.0766289	+	0.0173452i
$811$	3.84049	+	3.84049i	0.134858	+	0.134858i	0.771313	−	0.636455i	$-0.219600\pi$
$811$	3.84049	+	3.84049i	0.134858	+	0.134858i	−0.636455	+	0.771313i	$0.719600\pi$
$812$	−7.12132	−	4.11150i	−0.249909	−	0.144285i
$813$	−1.64740	−	0.951128i	−0.0577769	−	0.0333575i
$814$	−5.40959	−	5.40959i	−0.189606	−	0.189606i
$815$	3.83336	+	0.867691i	0.134277	+	0.0303939i
$816$	−6.01366	+	3.47199i	−0.210520	+	0.121544i
$817$	−1.90172	−	3.29388i	−0.0665328	−	0.115238i
$818$	−6.93387	−	6.93387i	−0.242437	−	0.242437i
$819$	−4.17400	−	2.10892i	−0.145851	−	0.0736917i
$820$	−16.7483	−	8.81323i	−0.584875	−	0.307771i
$821$	−12.9245	+	48.2351i	−0.451070	+	1.68342i	0.248322	+	0.968677i	$0.420121\pi$
$821$	−12.9245	+	48.2351i	−0.451070	+	1.68342i	−0.699392	+	0.714738i	$0.746546\pi$
$822$	0.704306	−	2.62850i	0.0245655	−	0.0916796i
$823$	17.0463	−	4.56756i	0.594198	−	0.159215i	0.0508271	−	0.998707i	$-0.483814\pi$
$823$	17.0463	−	4.56756i	0.594198	−	0.159215i	0.543371	+	0.839492i	$0.317148\pi$
$824$	0.223293	−	0.223293i	0.00777878	−	0.00777878i
$825$	−11.7831	+	0.925642i	−0.410235	+	0.0322267i
$826$	2.02252	+	7.54816i	0.0703726	+	0.262634i
$827$	7.73011			0.268802			0.134401	−	0.990927i	$-0.457089\pi$
$827$	7.73011			0.268802			0.134401	+	0.990927i	$0.457089\pi$
$828$	1.31661	+	4.91367i	0.0457555	+	0.170762i
$829$	−8.72754	−	15.1165i	−0.303120	−	0.525019i	0.673721	−	0.738986i	$-0.264695\pi$
$829$	−8.72754	−	15.1165i	−0.303120	−	0.525019i	−0.976841	+	0.213966i	$0.931362\pi$
$830$	−3.10457	+	3.35802i	−0.107761	+	0.116559i
$831$			24.0505i			0.834303i
$832$	1.97399	+	3.01718i	0.0684358	+	0.104602i
$833$	−26.1106	+	26.1106i	−0.904680	+	0.904680i
$834$	2.05720	+	0.551226i	0.0712351	+	0.0190874i
$835$	−22.5727	−	20.8690i	−0.781159	−	0.722200i
$836$	9.66031	+	5.57738i	0.334109	+	0.192898i
$837$		−	8.83392i		−	0.305345i
$838$	3.46276	−	5.99767i	0.119619	−	0.207186i
$839$	24.2794	−	6.50564i	0.838217	−	0.224599i	0.185922	−	0.982565i	$-0.440473\pi$
$839$	24.2794	−	6.50564i	0.838217	−	0.224599i	0.652295	+	0.757965i	$0.273806\pi$
$840$	2.56659	+	1.35059i	0.0885558	+	0.0465996i
$841$	5.59686	−	9.69405i	0.192995	−	0.334277i
$842$	26.6562	+	7.14252i	0.918635	+	0.246147i
$843$	8.24109	−	4.75799i	0.283838	−	0.163874i
$844$	11.0373			0.379919
$845$	3.22248	−	28.8897i	0.110857	−	0.993836i
$846$	11.6095			0.399142
$847$	−6.07917	+	3.50981i	−0.208883	+	0.120598i
$848$	−12.0174	−	3.22006i	−0.412680	−	0.110577i
$849$	6.50331	−	11.2641i	0.223193	−	0.386582i
$850$	−34.1376	−	6.33212i	−1.17091	−	0.217190i
$851$	−15.9023	+	4.26100i	−0.545122	+	0.146065i
$852$	6.34049	−	10.9820i	0.217221	−	0.376239i
$853$		−	56.0723i		−	1.91988i	−0.280208	−	0.959939i	$-0.590403\pi$
$853$		−	56.0723i		−	1.91988i	0.280208	−	0.959939i	$-0.409597\pi$
$854$	4.72311	+	2.72689i	0.161621	+	0.0933122i
$855$	−0.413495	−	10.5435i	−0.0141412	−	0.360581i
$856$	−12.9769	−	3.47715i	−0.443542	−	0.118847i
$857$	−5.26394	+	5.26394i	−0.179813	+	0.179813i	−0.791274	−	0.611461i	$-0.790582\pi$
$857$	−5.26394	+	5.26394i	−0.179813	+	0.179813i	0.611461	+	0.791274i	$0.290582\pi$
$858$	−4.66628	−	7.13226i	−0.159304	−	0.243491i
$859$			34.7014i			1.18400i	0.805939	+	0.591998i	$0.201661\pi$
$859$			34.7014i			1.18400i	−0.805939	+	0.591998i	$0.798339\pi$
$860$	−0.0706281	−	1.80092i	−0.00240840	−	0.0614107i
$861$	−5.48890	−	9.50705i	−0.187061	−	0.323999i
$862$	0.563587	+	2.10333i	0.0191958	+	0.0716398i
$863$	−24.1858			−0.823294			−0.411647	−	0.911343i	$-0.635046\pi$
$863$	−24.1858			−0.823294			−0.411647	+	0.911343i	$0.635046\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	−16.8141	+	10.6072i	−0.571698	+	0.360657i
$866$	25.5505	−	25.5505i	0.868242	−	0.868242i
$867$	30.1550	−	8.08001i	1.02412	−	0.274412i
$868$	2.96552	−	11.0675i	0.100656	−	0.375654i
$869$	8.13013	−	30.3421i	0.275796	−	1.02928i
$870$	−6.60161	+	12.5454i	−0.223816	+	0.425329i
$871$	−2.13262	−	1.07751i	−0.0722609	−	0.0365100i
$872$	−2.20681	−	2.20681i	−0.0747319	−	0.0747319i
$873$	2.99963	+	5.19551i	0.101522	+	0.175841i
$874$	20.7887	−	12.0024i	0.703188	−	0.405986i
$875$	5.37064	+	13.4701i	0.181561	+	0.455372i
$876$	−3.56543	−	3.56543i	−0.120465	−	0.120465i
$877$	−27.2208	−	15.7159i	−0.919182	−	0.530690i	−0.0358078	−	0.999359i	$-0.511400\pi$
$877$	−27.2208	−	15.7159i	−0.919182	−	0.530690i	−0.883374	+	0.468669i	$0.844734\pi$
$878$	14.2300	+	8.21571i	0.480240	+	0.277267i
$879$	−4.97036	−	4.97036i	−0.167646	−	0.167646i
$880$	2.82026	+	4.47055i	0.0950709	+	0.150702i
$881$	−3.05134	+	1.76169i	−0.102802	+	0.0593530i	−0.550520	−	0.834822i	$-0.685570\pi$
$881$	−3.05134	+	1.76169i	−0.102802	+	0.0593530i	0.447717	+	0.894175i	$0.352237\pi$
$882$	−2.65885	−	4.60527i	−0.0895282	−	0.155067i
$883$	−4.24181	−	4.24181i	−0.142748	−	0.142748i	0.632121	−	0.774870i	$-0.282184\pi$
$883$	−4.24181	−	4.24181i	−0.142748	−	0.142748i	−0.774870	+	0.632121i	$0.782184\pi$
$884$	−7.81769	−	23.7850i	−0.262937	−	0.799977i
$885$	12.8663	−	3.99407i	0.432496	−	0.134259i
$886$	10.0270	−	37.4212i	0.336863	−	1.25719i
$887$	−1.71855	+	6.41370i	−0.0577031	+	0.215351i	−0.988757	−	0.149530i	$-0.952224\pi$
$887$	−1.71855	+	6.41370i	−0.0577031	+	0.215351i	0.931054	+	0.364881i	$0.118890\pi$
$888$	3.12606	−	0.837624i	0.104904	−	0.0281088i
$889$	12.2893	−	12.2893i	0.412168	−	0.412168i
$890$	−5.35249	−	8.48454i	−0.179416	−	0.284402i
$891$	0.611818	+	2.28334i	0.0204967	+	0.0764946i
$892$	11.9872			0.401362
$893$	−14.1789	−	52.9165i	−0.474480	−	1.77078i
$894$	−2.28305	−	3.95436i	−0.0763567	−	0.132254i
$895$	4.71493	+	4.35906i	0.157603	+	0.145707i
$896$		−	1.29703i		−	0.0433308i
$897$	−18.3129	+	1.02216i	−0.611451	+	0.0341289i
$898$	−28.5529	+	28.5529i	−0.952824	+	0.952824i
$899$	54.0974	+	14.4954i	1.80425	+	0.483447i
$900$	2.15321	−	4.51262i	0.0717735	−	0.150421i
$901$	74.8180	+	43.1962i	2.49255	+	1.43907i
$902$		−	20.0074i		−	0.666173i
$903$	0.522713	−	0.905365i	0.0173948	−	0.0301287i
$904$	9.81102	−	2.62886i	0.326310	−	0.0874344i
$905$	−10.1310	−	32.6353i	−0.336764	−	1.08483i
$906$	−9.41470	+	16.3067i	−0.312782	+	0.541755i
$907$	46.5727	+	12.4791i	1.54642	+	0.414362i	0.928334	−	0.371747i	$-0.121241\pi$
$907$	46.5727	+	12.4791i	1.54642	+	0.414362i	0.618088	+	0.786109i	$0.287908\pi$
$908$	−9.07894	+	5.24173i	−0.301295	+	0.173953i
$909$	14.1195			0.468315
$910$	−6.65984	+	8.06199i	−0.220772	+	0.267252i
$911$	−26.5844			−0.880781			−0.440390	−	0.897806i	$-0.645160\pi$
$911$	−26.5844			−0.880781			−0.440390	+	0.897806i	$0.645160\pi$
$912$	−4.08663	+	2.35942i	−0.135322	+	0.0781281i
$913$	−4.66992	−	1.25130i	−0.154552	−	0.0414121i
$914$	−3.53353	+	6.12025i	−0.116879	+	0.202440i
$915$	4.37842	−	8.32055i	0.144746	−	0.275069i
$916$	−11.8908	+	3.18614i	−0.392884	+	0.105273i
$917$	−8.43612	+	14.6118i	−0.278585	+	0.482524i
$918$			6.94397i			0.229185i
$919$	23.3323	+	13.4709i	0.769662	+	0.444364i	0.832754	−	0.553643i	$-0.186763\pi$
$919$	23.3323	+	13.4709i	0.769662	+	0.444364i	−0.0630921	+	0.998008i	$0.520096\pi$
$920$	11.3661	−	0.445756i	0.374731	−	0.0146962i
$921$	13.0905	+	3.50760i	0.431348	+	0.115579i
$922$	11.1164	−	11.1164i	0.366099	−	0.366099i
$923$	34.0818	+	30.4783i	1.12181	+	1.00320i
$924$			3.06603i			0.100865i
$925$	14.6043	+	6.96849i	0.480187	+	0.229123i
$926$	−6.64433	−	11.5083i	−0.218346	−	0.378187i
$927$	−0.0817310	−	0.305024i	−0.00268440	−	0.0100183i
$928$	6.33985			0.208116
$929$	−5.88216	−	21.9525i	−0.192987	−	0.720239i	−0.992779	−	0.119960i	$-0.961723\pi$
$929$	−5.88216	−	21.9525i	−0.192987	−	0.720239i	0.799791	−	0.600278i	$-0.204943\pi$
$930$	−19.2659	−	4.36088i	−0.631753	−	0.142999i
$931$	−17.7437	+	17.7437i	−0.581526	+	0.581526i
$932$	−24.6827	+	6.61372i	−0.808510	+	0.216640i
$933$	−7.83356	+	29.2352i	−0.256459	+	0.957119i
$934$	−4.21754	+	15.7401i	−0.138002	+	0.515031i
$935$	−10.8819	−	35.0543i	−0.355875	−	1.14640i
$936$	3.59995	−	0.200935i	0.117668	−	0.00656778i
$937$	8.06909	+	8.06909i	0.263606	+	0.263606i	0.826517	−	0.562911i	$-0.190319\pi$
$937$	8.06909	+	8.06909i	0.263606	+	0.263606i	−0.562911	+	0.826517i	$0.690319\pi$
$938$	0.429766	+	0.744377i	0.0140324	+	0.0243048i
$939$	−20.1419	+	11.6289i	−0.657306	+	0.379496i
$940$	5.73104	−	25.3191i	0.186926	−	0.825818i
$941$	−16.4810	−	16.4810i	−0.537265	−	0.537265i	0.385460	−	0.922725i	$-0.374043\pi$
$941$	−16.4810	−	16.4810i	−0.537265	−	0.537265i	−0.922725	+	0.385460i	$0.874043\pi$
$942$	12.9248	+	7.46212i	0.421112	+	0.243129i
$943$	−37.2869	−	21.5276i	−1.21423	−	0.701036i
$944$	−4.26021	−	4.26021i	−0.138658	−	0.138658i
$945$	2.45294	−	1.54744i	0.0797940	−	0.0503382i
$946$	1.65006	−	0.952660i	0.0536479	−	0.0309737i
$947$	−11.7074	−	20.2779i	−0.380441	−	0.658943i	0.610684	−	0.791874i	$-0.290894\pi$
$947$	−11.7074	−	20.2779i	−0.380441	−	0.658943i	−0.991125	+	0.132931i	$0.957561\pi$
$948$	9.39638	+	9.39638i	0.305180	+	0.305180i
$949$	15.2135	−	9.95342i	0.493850	−	0.323102i
$950$	−23.1985	−	4.30304i	−0.752657	−	0.139609i
$951$	−3.86666	+	14.4306i	−0.125385	+	0.467944i
$952$	−2.33107	+	8.69967i	−0.0755504	+	0.281958i
$953$	−41.0626	+	11.0027i	−1.33015	+	0.356412i	−0.852770	−	0.522287i	$-0.825079\pi$
$953$	−41.0626	+	11.0027i	−1.33015	+	0.356412i	−0.477377	+	0.878698i	$0.658412\pi$
$954$	−8.79736	+	8.79736i	−0.284825	+	0.284825i
$955$	2.80987	−	12.4137i	0.0909254	−	0.401698i
$956$	−3.54566	−	13.2326i	−0.114675	−	0.427972i
$957$	−14.9867			−0.484450
$958$	−8.77511	−	32.7492i	−0.283511	−	1.05808i
$959$	−1.76476	−	3.05666i	−0.0569871	−	0.0987046i
$960$	−2.23435	+	0.0876265i	−0.0721133	+	0.00282813i
$961$			47.0382i			1.51736i
$962$	0.650294	+	11.6506i	0.0209663	+	0.375631i
$963$	−9.49976	+	9.49976i	−0.306125	+	0.306125i
$964$	−11.2204	−	3.00649i	−0.361384	−	0.0968327i
$965$	−6.57872	+	7.11579i	−0.211776	+	0.229065i
$966$	5.71404	+	3.29900i	0.183846	+	0.106144i
$967$		−	20.8344i		−	0.669990i	−0.942220	−	0.334995i	$-0.891265\pi$
$967$		−	20.8344i		−	0.669990i	0.942220	−	0.334995i	$-0.108735\pi$
$968$	2.70603	−	4.68698i	0.0869751	−	0.150645i
$969$	31.6509	−	8.48084i	1.01677	−	0.272444i
$970$	12.8116	−	3.97710i	0.411357	−	0.127697i
$971$	20.8974	−	36.1954i	0.670630	−	1.16157i	−0.307095	−	0.951679i	$-0.599357\pi$
$971$	20.8974	−	36.1954i	0.670630	−	1.16157i	0.977726	−	0.209887i	$-0.0673096\pi$
$972$	−0.965926	−	0.258819i	−0.0309821	−	0.00830162i
$973$	2.39230	−	1.38119i	0.0766935	−	0.0442790i
$974$	−39.2716			−1.25834
$975$	14.3380	+	10.9280i	0.459184	+	0.349976i
$976$	−4.20481			−0.134593
$977$	4.81248	−	2.77849i	0.153965	−	0.0888917i	−0.421038	−	0.907043i	$-0.638334\pi$
$977$	4.81248	−	2.77849i	0.153965	−	0.0888917i	0.575003	+	0.818151i	$0.305001\pi$
$978$	−1.69781	−	0.454926i	−0.0542898	−	0.0145469i
$979$	5.30260	−	9.18437i	0.169472	−	0.293534i
$980$	−11.3562	+	3.52528i	−0.362759	+	0.112611i
$981$	−3.01455	+	0.807747i	−0.0962473	+	0.0257894i
$982$	−20.1369	+	34.8781i	−0.642594	+	1.11301i
$983$			5.70951i			0.182105i	0.995846	+	0.0910526i	$0.0290231\pi$
$983$			5.70951i			0.182105i	−0.995846	+	0.0910526i	$0.970977\pi$
$984$	7.32985	+	4.23189i	0.233667	+	0.134908i
$985$	−0.627826	+	0.679080i	−0.0200042	+	0.0216373i
$986$	−42.5237	−	11.3942i	−1.35423	−	0.362865i
$987$	10.6475	−	10.6475i	0.338915	−	0.338915i
$988$	−5.31257	−	16.1633i	−0.169015	−	0.514223i
$989$		−	4.10019i		−	0.130378i
$990$	5.28174	−	0.207139i	0.167865	−	0.00658331i
$991$	2.03911	+	3.53185i	0.0647745	+	0.112193i	0.896594	−	0.442854i	$-0.146034\pi$
$991$	2.03911	+	3.53185i	0.0647745	+	0.112193i	−0.831819	+	0.555046i	$0.812701\pi$
$992$	2.28639	+	8.53291i	0.0725929	+	0.270920i
$993$	−11.4353			−0.362889
$994$	−4.25696	−	15.8872i	−0.135023	−	0.503911i
$995$	8.40022	−	37.1112i	0.266305	−	1.17650i
$996$	1.44619	−	1.44619i	0.0458243	−	0.0458243i
$997$	−50.5754	+	13.5516i	−1.60174	+	0.429184i	−0.945567	−	0.325428i	$-0.894492\pi$
$997$	−50.5754	+	13.5516i	−1.60174	+	0.429184i	−0.656171	+	0.754612i	$0.727825\pi$
$998$	5.42650	−	20.2520i	0.171773	−	0.641064i
$999$	0.837624	−	3.12606i	0.0265013	−	0.0989041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.b.37.1	✓	16
5.3	odd	4		390.2.bn.b.193.4	yes	16
13.6	odd	12		390.2.bn.b.97.4	yes	16
65.58	even	12	inner	390.2.bd.b.253.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.37.1	✓	16	1.1	even	1	trivial
390.2.bd.b.253.1	yes	16	65.58	even	12	inner
390.2.bn.b.97.4	yes	16	13.6	odd	12
390.2.bn.b.193.4	yes	16	5.3	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.13554 + 0.662933i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.648516 - 1.12326i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.13554 + 0.662933i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.648516 - 1.12326i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(1.51796 - 1.64189i) q^{10} +(2.28334 + 0.611818i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.97399 - 3.01718i) q^{13} +1.29703i q^{14} +(2.23435 - 0.0876265i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.79723 + 6.70736i) q^{17} -1.00000 q^{18} +(1.22132 + 4.55804i) q^{19} +(-0.493652 + 2.18090i) q^{20} +(-0.917141 + 0.917141i) q^{21} +(-2.28334 + 0.611818i) q^{22} +(-1.31661 + 4.91367i) q^{23} +(0.258819 - 0.965926i) q^{24} +(4.12104 - 2.83144i) q^{25} +(3.21811 + 1.62596i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.648516 - 1.12326i) q^{28} +(5.49047 - 3.16993i) q^{29} +(-1.89119 + 1.19306i) q^{30} +(6.24653 + 6.24653i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.04718 - 1.18194i) q^{33} +(-4.91013 - 4.91013i) q^{34} +(-0.640282 + 2.82869i) q^{35} +(0.866025 - 0.500000i) q^{36} +(1.61817 + 2.80275i) q^{37} +(-3.33672 - 3.33672i) q^{38} +(1.12582 + 3.42528i) q^{39} +(-0.662933 - 2.13554i) q^{40} +(-2.19059 + 8.17538i) q^{41} +(0.335697 - 1.25284i) q^{42} +(-0.778549 + 0.208612i) q^{43} +(1.67152 - 1.67152i) q^{44} +(-2.18090 - 0.493652i) q^{45} +(-1.31661 - 4.91367i) q^{46} -11.6095 q^{47} +(0.258819 + 0.965926i) q^{48} +(2.65885 + 4.60527i) q^{49} +(-2.15321 + 4.51262i) q^{50} -6.94397i q^{51} +(-3.59995 + 0.200935i) q^{52} +(8.79736 - 8.79736i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-5.28174 + 0.207139i) q^{55} +(1.12326 + 0.648516i) q^{56} -4.71883i q^{57} +(-3.16993 + 5.49047i) q^{58} +(5.81956 - 1.55935i) q^{59} +(1.04129 - 1.97882i) q^{60} +(2.10240 - 3.64147i) q^{61} +(-8.53291 - 2.28639i) q^{62} +(1.12326 - 0.648516i) q^{63} -1.00000 q^{64} +(6.21572 + 5.13467i) q^{65} +2.36388 q^{66} +(0.573907 - 0.331346i) q^{67} +(6.70736 + 1.79723i) q^{68} +(2.54350 - 4.40547i) q^{69} +(-0.859846 - 2.76986i) q^{70} +(-12.2489 + 3.28208i) q^{71} +(-0.500000 + 0.866025i) q^{72} +5.04229i q^{73} +(-2.80275 - 1.61817i) q^{74} +(-4.71345 + 1.66835i) q^{75} +(4.55804 + 1.22132i) q^{76} +(2.16801 - 2.16801i) q^{77} +(-2.68763 - 2.40346i) q^{78} -13.2885i q^{79} +(1.64189 + 1.51796i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.19059 - 8.17538i) q^{82} -2.04522 q^{83} +(0.335697 + 1.25284i) q^{84} +(-8.28459 - 13.1324i) q^{85} +(0.569937 - 0.569937i) q^{86} +(-6.12383 + 1.64087i) q^{87} +(-0.611818 + 2.28334i) q^{88} +(1.16115 - 4.33348i) q^{89} +(2.13554 - 0.662933i) q^{90} +(-4.66925 + 0.260620i) q^{91} +(3.59705 + 3.59705i) q^{92} +(-4.41696 - 7.65040i) q^{93} +(10.0541 - 5.80474i) q^{94} +(-5.62986 - 8.92421i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(5.19551 + 2.99963i) q^{97} +(-4.60527 - 2.65885i) q^{98} +(1.67152 + 1.67152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

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