LMFDB - Embedded newform 990.2.n.a.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(91,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("990.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	990.631
Dual form			990.2.n.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.427051 + 1.31433i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.427051 + 1.31433i) q^{7} +(0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(-1.69098 - 2.85317i) q^{11} +(1.30902 + 0.951057i) q^{13} +(0.427051 - 1.31433i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.00000 - 1.45309i) q^{17} +(0.500000 - 1.53884i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(-0.309017 + 3.30220i) q^{22} +1.85410 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.500000 - 1.53884i) q^{26} +(-1.11803 + 0.812299i) q^{28} +(3.00000 + 9.23305i) q^{29} +(3.85410 + 2.80017i) q^{31} +1.00000 q^{32} -2.47214 q^{34} +(-1.11803 - 0.812299i) q^{35} +(0.500000 + 1.53884i) q^{37} +(-1.30902 + 0.951057i) q^{38} +(0.309017 + 0.951057i) q^{40} +(-1.95492 + 6.01661i) q^{41} +5.23607 q^{43} +(2.19098 - 2.48990i) q^{44} +(-1.50000 - 1.08981i) q^{46} +(0.118034 - 0.363271i) q^{47} +(4.11803 - 2.99193i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.500000 + 1.53884i) q^{52} +(4.11803 + 2.99193i) q^{53} +(3.04508 + 1.31433i) q^{55} +1.38197 q^{56} +(3.00000 - 9.23305i) q^{58} +(3.82624 + 11.7759i) q^{59} +(-5.47214 + 3.97574i) q^{61} +(-1.47214 - 4.53077i) q^{62} +(-0.809017 - 0.587785i) q^{64} -1.61803 q^{65} +14.1803 q^{67} +(2.00000 + 1.45309i) q^{68} +(0.427051 + 1.31433i) q^{70} +(-11.0902 + 8.05748i) q^{71} +(-2.14590 - 6.60440i) q^{73} +(0.500000 - 1.53884i) q^{74} +1.61803 q^{76} +(3.02786 - 3.44095i) q^{77} +(-3.61803 - 2.62866i) q^{79} +(0.309017 - 0.951057i) q^{80} +(5.11803 - 3.71847i) q^{82} +(10.4721 - 7.60845i) q^{83} +(-0.763932 + 2.35114i) q^{85} +(-4.23607 - 3.07768i) q^{86} +(-3.23607 + 0.726543i) q^{88} +11.8541 q^{89} +(-0.690983 + 2.12663i) q^{91} +(0.572949 + 1.76336i) q^{92} +(-0.309017 + 0.224514i) q^{94} +(0.500000 + 1.53884i) q^{95} +(2.38197 + 1.73060i) q^{97} -5.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - q^{5} - 5 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 - q^5 - 5 * q^7 - q^8	$ 4 q - q^{2} - q^{4} - q^{5} - 5 q^{7} - q^{8} + 4 q^{10} - 9 q^{11} + 3 q^{13} - 5 q^{14} - q^{16} + 8 q^{17} + 2 q^{19} - q^{20} + q^{22} - 6 q^{23} - q^{25} - 2 q^{26} + 12 q^{29} + 2 q^{31} + 4 q^{32} + 8 q^{34} + 2 q^{37} - 3 q^{38} - q^{40} - 19 q^{41} + 12 q^{43} + 11 q^{44} - 6 q^{46} - 4 q^{47} + 12 q^{49} - q^{50} - 2 q^{52} + 12 q^{53} + q^{55} + 10 q^{56} + 12 q^{58} - 16 q^{59} - 4 q^{61} + 12 q^{62} - q^{64} - 2 q^{65} + 12 q^{67} + 8 q^{68} - 5 q^{70} - 22 q^{71} - 22 q^{73} + 2 q^{74} + 2 q^{76} + 30 q^{77} - 10 q^{79} - q^{80} + 16 q^{82} + 24 q^{83} - 12 q^{85} - 8 q^{86} - 4 q^{88} + 34 q^{89} - 5 q^{91} + 9 q^{92} + q^{94} + 2 q^{95} + 14 q^{97} + 2 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - q^5 - 5 * q^7 - q^8 + 4 * q^10 - 9 * q^11 + 3 * q^13 - 5 * q^14 - q^16 + 8 * q^17 + 2 * q^19 - q^20 + q^22 - 6 * q^23 - q^25 - 2 * q^26 + 12 * q^29 + 2 * q^31 + 4 * q^32 + 8 * q^34 + 2 * q^37 - 3 * q^38 - q^40 - 19 * q^41 + 12 * q^43 + 11 * q^44 - 6 * q^46 - 4 * q^47 + 12 * q^49 - q^50 - 2 * q^52 + 12 * q^53 + q^55 + 10 * q^56 + 12 * q^58 - 16 * q^59 - 4 * q^61 + 12 * q^62 - q^64 - 2 * q^65 + 12 * q^67 + 8 * q^68 - 5 * q^70 - 22 * q^71 - 22 * q^73 + 2 * q^74 + 2 * q^76 + 30 * q^77 - 10 * q^79 - q^80 + 16 * q^82 + 24 * q^83 - 12 * q^85 - 8 * q^86 - 4 * q^88 + 34 * q^89 - 5 * q^91 + 9 * q^92 + q^94 + 2 * q^95 + 14 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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			0
$3$		0			0
$4$	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
$6$		0			0
$7$	0.427051	+	1.31433i	0.161410	+	0.496769i	0.998754	−	0.0499075i	$-0.0158927\pi$
$7$	0.427051	+	1.31433i	0.161410	+	0.496769i	−0.837344	+	0.546677i	$0.815893\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	1.00000			0.316228
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$12$		0			0
$13$	1.30902	+	0.951057i	0.363056	+	0.263776i	0.754326	−	0.656500i	$-0.227964\pi$
$13$	1.30902	+	0.951057i	0.363056	+	0.263776i	−0.391270	+	0.920276i	$0.627964\pi$
$14$	0.427051	−	1.31433i	0.114134	−	0.351269i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.00000	−	1.45309i	0.485071	−	0.352425i	−0.318214	−	0.948019i	$-0.603083\pi$
$17$	2.00000	−	1.45309i	0.485071	−	0.352425i	0.803286	+	0.595594i	$0.203083\pi$
$18$		0			0
$19$	0.500000	−	1.53884i	0.114708	−	0.353035i	−0.877178	−	0.480165i	$-0.840577\pi$
$19$	0.500000	−	1.53884i	0.114708	−	0.353035i	0.991886	+	0.127131i	$0.0405767\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$		0			0
$22$	−0.309017	+	3.30220i	−0.0658826	+	0.704031i
$23$	1.85410			0.386607			0.193303	−	0.981139i	$-0.438080\pi$
$23$	1.85410			0.386607			0.193303	+	0.981139i	$0.438080\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.500000	−	1.53884i	−0.0980581	−	0.301792i
$27$		0			0
$28$	−1.11803	+	0.812299i	−0.211289	+	0.153510i
$29$	3.00000	+	9.23305i	0.557086	+	1.71453i	0.690370	+	0.723457i	$0.257448\pi$
$29$	3.00000	+	9.23305i	0.557086	+	1.71453i	−0.133284	+	0.991078i	$0.542552\pi$
$30$		0			0
$31$	3.85410	+	2.80017i	0.692217	+	0.502925i	0.877388	−	0.479781i	$-0.159284\pi$
$31$	3.85410	+	2.80017i	0.692217	+	0.502925i	−0.185171	+	0.982706i	$0.559284\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.47214			−0.423968
$35$	−1.11803	−	0.812299i	−0.188982	−	0.137304i
$36$		0			0
$37$	0.500000	+	1.53884i	0.0821995	+	0.252984i	0.983707	−	0.179780i	$-0.0575385\pi$
$37$	0.500000	+	1.53884i	0.0821995	+	0.252984i	−0.901507	+	0.432764i	$0.857538\pi$
$38$	−1.30902	+	0.951057i	−0.212351	+	0.154282i
$39$		0			0
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	−1.95492	+	6.01661i	−0.305306	+	0.939637i	0.674256	+	0.738497i	$0.264464\pi$
$41$	−1.95492	+	6.01661i	−0.305306	+	0.939637i	−0.979563	+	0.201139i	$0.935536\pi$
$42$		0			0
$43$	5.23607			0.798493			0.399246	−	0.916844i	$-0.369272\pi$
$43$	5.23607			0.798493			0.399246	+	0.916844i	$0.369272\pi$
$44$	2.19098	−	2.48990i	0.330303	−	0.375366i
$45$		0			0
$46$	−1.50000	−	1.08981i	−0.221163	−	0.160684i
$47$	0.118034	−	0.363271i	0.0172170	−	0.0529886i	−0.942079	−	0.335391i	$-0.891131\pi$
$47$	0.118034	−	0.363271i	0.0172170	−	0.0529886i	0.959296	+	0.282403i	$0.0911315\pi$
$48$		0			0
$49$	4.11803	−	2.99193i	0.588291	−	0.427418i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$		0			0
$52$	−0.500000	+	1.53884i	−0.0693375	+	0.213399i
$53$	4.11803	+	2.99193i	0.565655	+	0.410973i	0.833524	−	0.552483i	$-0.186319\pi$
$53$	4.11803	+	2.99193i	0.565655	+	0.410973i	−0.267869	+	0.963455i	$0.586319\pi$
$54$		0			0
$55$	3.04508	+	1.31433i	0.410599	+	0.177224i
$56$	1.38197			0.184673
$57$		0			0
$58$	3.00000	−	9.23305i	0.393919	−	1.21236i
$59$	3.82624	+	11.7759i	0.498134	+	1.53310i	0.812015	+	0.583636i	$0.198370\pi$
$59$	3.82624	+	11.7759i	0.498134	+	1.53310i	−0.313882	+	0.949462i	$0.601630\pi$
$60$		0			0
$61$	−5.47214	+	3.97574i	−0.700635	+	0.509041i	−0.880139	−	0.474716i	$-0.842551\pi$
$61$	−5.47214	+	3.97574i	−0.700635	+	0.509041i	0.179504	+	0.983757i	$0.442551\pi$
$62$	−1.47214	−	4.53077i	−0.186961	−	0.575408i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.61803			−0.200692
$66$		0			0
$67$	14.1803			1.73240			0.866202	−	0.499694i	$-0.166554\pi$
$67$	14.1803			1.73240			0.866202	+	0.499694i	$0.166554\pi$
$68$	2.00000	+	1.45309i	0.242536	+	0.176212i
$69$		0			0
$70$	0.427051	+	1.31433i	0.0510424	+	0.157092i
$71$	−11.0902	+	8.05748i	−1.31616	+	0.956247i	−0.316190	+	0.948696i	$0.602404\pi$
$71$	−11.0902	+	8.05748i	−1.31616	+	0.956247i	−0.999971	+	0.00755092i	$0.997596\pi$
$72$		0			0
$73$	−2.14590	−	6.60440i	−0.251158	−	0.772986i	−0.994562	−	0.104143i	$-0.966790\pi$
$73$	−2.14590	−	6.60440i	−0.251158	−	0.772986i	0.743404	−	0.668843i	$-0.233210\pi$
$74$	0.500000	−	1.53884i	0.0581238	−	0.178887i
$75$		0			0
$76$	1.61803			0.185601
$77$	3.02786	−	3.44095i	0.345057	−	0.392133i
$78$		0			0
$79$	−3.61803	−	2.62866i	−0.407061	−	0.295747i	0.365350	−	0.930870i	$-0.380949\pi$
$79$	−3.61803	−	2.62866i	−0.407061	−	0.295747i	−0.772411	+	0.635123i	$0.780949\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$		0			0
$82$	5.11803	−	3.71847i	0.565192	−	0.410636i
$83$	10.4721	−	7.60845i	1.14947	−	0.835136i	0.161056	−	0.986945i	$-0.448510\pi$
$83$	10.4721	−	7.60845i	1.14947	−	0.835136i	0.988410	+	0.151809i	$0.0485099\pi$
$84$		0			0
$85$	−0.763932	+	2.35114i	−0.0828601	+	0.255017i
$86$	−4.23607	−	3.07768i	−0.456787	−	0.331875i
$87$		0			0
$88$	−3.23607	+	0.726543i	−0.344966	+	0.0774497i
$89$	11.8541			1.25653			0.628266	−	0.777998i	$-0.283765\pi$
$89$	11.8541			1.25653			0.628266	+	0.777998i	$0.283765\pi$
$90$		0			0
$91$	−0.690983	+	2.12663i	−0.0724347	+	0.222931i
$92$	0.572949	+	1.76336i	0.0597341	+	0.183843i
$93$		0			0
$94$	−0.309017	+	0.224514i	−0.0318727	+	0.0231568i
$95$	0.500000	+	1.53884i	0.0512989	+	0.157882i
$96$		0			0
$97$	2.38197	+	1.73060i	0.241852	+	0.175716i	0.702108	−	0.712070i	$-0.252242\pi$
$97$	2.38197	+	1.73060i	0.241852	+	0.175716i	−0.460256	+	0.887786i	$0.652242\pi$
$98$	−5.09017			−0.514185
$99$		0			0
$100$	1.00000			0.100000
$101$	3.23607	+	2.35114i	0.322001	+	0.233947i	0.737029	−	0.675861i	$-0.236228\pi$
$101$	3.23607	+	2.35114i	0.322001	+	0.233947i	−0.415028	+	0.909809i	$0.636228\pi$
$102$		0			0
$103$	−0.972136	−	2.99193i	−0.0957874	−	0.294803i	0.891671	−	0.452685i	$-0.149534\pi$
$103$	−0.972136	−	2.99193i	−0.0957874	−	0.294803i	−0.987458	+	0.157881i	$0.949534\pi$
$104$	1.30902	−	0.951057i	0.128360	−	0.0932588i
$105$		0			0
$106$	−1.57295	−	4.84104i	−0.152778	−	0.470203i
$107$	5.52786	−	17.0130i	0.534399	−	1.64471i	−0.210546	−	0.977584i	$-0.567524\pi$
$107$	5.52786	−	17.0130i	0.534399	−	1.64471i	0.744945	−	0.667126i	$-0.232476\pi$
$108$		0			0
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	−1.69098	−	2.85317i	−0.161229	−	0.272039i
$111$		0			0
$112$	−1.11803	−	0.812299i	−0.105644	−	0.0767551i
$113$	1.09017	−	3.35520i	0.102555	−	0.315630i	−0.886594	−	0.462548i	$-0.846935\pi$
$113$	1.09017	−	3.35520i	0.102555	−	0.315630i	0.989149	+	0.146918i	$0.0469352\pi$
$114$		0			0
$115$	−1.50000	+	1.08981i	−0.139876	+	0.101626i
$116$	−7.85410	+	5.70634i	−0.729235	+	0.529820i
$117$		0			0
$118$	3.82624	−	11.7759i	0.352234	−	1.08406i
$119$	2.76393	+	2.00811i	0.253369	+	0.184084i
$120$		0			0
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$	6.76393			0.612378
$123$		0			0
$124$	−1.47214	+	4.53077i	−0.132202	+	0.406875i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	−8.39919	+	6.10237i	−0.745307	+	0.541497i	−0.894369	−	0.447330i	$-0.852375\pi$
$127$	−8.39919	+	6.10237i	−0.745307	+	0.541497i	0.149061	+	0.988828i	$0.452375\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	1.30902	+	0.951057i	0.114808	+	0.0834132i
$131$	−3.05573			−0.266980			−0.133490	−	0.991050i	$-0.542618\pi$
$131$	−3.05573			−0.266980			−0.133490	+	0.991050i	$0.542618\pi$
$132$		0			0
$133$	2.23607			0.193892
$134$	−11.4721	−	8.33499i	−0.991042	−	0.720034i
$135$		0			0
$136$	−0.763932	−	2.35114i	−0.0655066	−	0.201609i
$137$	−9.23607	+	6.71040i	−0.789091	+	0.573308i	−0.907693	−	0.419634i	$-0.862158\pi$
$137$	−9.23607	+	6.71040i	−0.789091	+	0.573308i	0.118603	+	0.992942i	$0.462158\pi$
$138$		0			0
$139$	−1.66312	−	5.11855i	−0.141064	−	0.434150i	0.855420	−	0.517935i	$-0.173299\pi$
$139$	−1.66312	−	5.11855i	−0.141064	−	0.434150i	−0.996484	+	0.0837850i	$0.973299\pi$
$140$	0.427051	−	1.31433i	0.0360924	−	0.111081i
$141$		0			0
$142$	13.7082			1.15037
$143$	0.500000	−	5.34307i	0.0418121	−	0.446810i
$144$		0			0
$145$	−7.85410	−	5.70634i	−0.652248	−	0.473886i
$146$	−2.14590	+	6.60440i	−0.177596	+	0.546584i
$147$		0			0
$148$	−1.30902	+	0.951057i	−0.107601	+	0.0781764i
$149$	7.23607	−	5.25731i	0.592802	−	0.430696i	−0.250515	−	0.968113i	$-0.580600\pi$
$149$	7.23607	−	5.25731i	0.592802	−	0.430696i	0.843317	+	0.537417i	$0.180600\pi$
$150$		0			0
$151$	−1.09017	+	3.35520i	−0.0887168	+	0.273042i	−0.985565	−	0.169296i	$-0.945851\pi$
$151$	−1.09017	+	3.35520i	−0.0887168	+	0.273042i	0.896849	+	0.442338i	$0.145851\pi$
$152$	−1.30902	−	0.951057i	−0.106175	−	0.0771409i
$153$		0			0
$154$	−4.47214	+	1.00406i	−0.360375	+	0.0809092i
$155$	−4.76393			−0.382648
$156$		0			0
$157$	−1.04508	+	3.21644i	−0.0834069	+	0.256700i	−0.984059	−	0.177840i	$-0.943089\pi$
$157$	−1.04508	+	3.21644i	−0.0834069	+	0.256700i	0.900653	+	0.434540i	$0.143089\pi$
$158$	1.38197	+	4.25325i	0.109943	+	0.338371i
$159$		0			0
$160$	−0.809017	+	0.587785i	−0.0639584	+	0.0464685i
$161$	0.791796	+	2.43690i	0.0624023	+	0.192054i
$162$		0			0
$163$	14.4721	+	10.5146i	1.13355	+	0.823569i	0.986207	−	0.165517i	$-0.0529294\pi$
$163$	14.4721	+	10.5146i	1.13355	+	0.823569i	0.147338	+	0.989086i	$0.452929\pi$
$164$	−6.32624			−0.493996
$165$		0			0
$166$	−12.9443			−1.00467
$167$	6.92705	+	5.03280i	0.536031	+	0.389450i	0.822609	−	0.568607i	$-0.192518\pi$
$167$	6.92705	+	5.03280i	0.536031	+	0.389450i	−0.286578	+	0.958057i	$0.592518\pi$
$168$		0			0
$169$	−3.20820	−	9.87384i	−0.246785	−	0.759526i
$170$	2.00000	−	1.45309i	0.153393	−	0.111447i
$171$		0			0
$172$	1.61803	+	4.97980i	0.123374	+	0.379706i
$173$	1.37132	−	4.22050i	0.104260	−	0.320879i	−0.885296	−	0.465027i	$-0.846044\pi$
$173$	1.37132	−	4.22050i	0.104260	−	0.320879i	0.989556	+	0.144149i	$0.0460444\pi$
$174$		0			0
$175$	1.38197			0.104467
$176$	3.04508	+	1.31433i	0.229532	+	0.0990712i
$177$		0			0
$178$	−9.59017	−	6.96767i	−0.718814	−	0.522249i
$179$	5.51722	−	16.9803i	0.412376	−	1.26916i	−0.502200	−	0.864751i	$-0.667476\pi$
$179$	5.51722	−	16.9803i	0.412376	−	1.26916i	0.914577	−	0.404413i	$-0.132524\pi$
$180$		0			0
$181$	−16.4721	+	11.9677i	−1.22436	+	0.889553i	−0.996455	−	0.0841297i	$-0.973189\pi$
$181$	−16.4721	+	11.9677i	−1.22436	+	0.889553i	−0.227909	+	0.973682i	$0.573189\pi$
$182$	1.80902	−	1.31433i	0.134093	−	0.0974245i
$183$		0			0
$184$	0.572949	−	1.76336i	0.0422384	−	0.129996i
$185$	−1.30902	−	0.951057i	−0.0962408	−	0.0699231i
$186$		0			0
$187$	−7.52786	−	3.24920i	−0.550492	−	0.237605i
$188$	0.381966			0.0278577
$189$		0			0
$190$	0.500000	−	1.53884i	0.0362738	−	0.111639i
$191$	0.0901699	+	0.277515i	0.00652447	+	0.0200802i	0.954266	−	0.298960i	$-0.0966396\pi$
$191$	0.0901699	+	0.277515i	0.00652447	+	0.0200802i	−0.947741	+	0.319040i	$0.896640\pi$
$192$		0			0
$193$	−7.85410	+	5.70634i	−0.565351	+	0.410751i	−0.833413	−	0.552650i	$-0.813617\pi$
$193$	−7.85410	+	5.70634i	−0.565351	+	0.410751i	0.268063	+	0.963401i	$0.413617\pi$
$194$	−0.909830	−	2.80017i	−0.0653220	−	0.201040i
$195$		0			0
$196$	4.11803	+	2.99193i	0.294145	+	0.213709i
$197$	−1.38197			−0.0984610			−0.0492305	−	0.998787i	$-0.515677\pi$
$197$	−1.38197			−0.0984610			−0.0492305	+	0.998787i	$0.515677\pi$
$198$		0			0
$199$	4.94427			0.350490			0.175245	−	0.984525i	$-0.443928\pi$
$199$	4.94427			0.350490			0.175245	+	0.984525i	$0.443928\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$		0			0
$202$	−1.23607	−	3.80423i	−0.0869694	−	0.267664i
$203$	−10.8541	+	7.88597i	−0.761809	+	0.553486i
$204$		0			0
$205$	−1.95492	−	6.01661i	−0.136537	−	0.420218i
$206$	−0.972136	+	2.99193i	−0.0677319	+	0.208457i
$207$		0			0
$208$	−1.61803			−0.112190
$209$	−5.23607	+	1.17557i	−0.362186	+	0.0813159i
$210$		0			0
$211$	−2.76393	−	2.00811i	−0.190277	−	0.138244i	0.488568	−	0.872526i	$-0.337519\pi$
$211$	−2.76393	−	2.00811i	−0.190277	−	0.138244i	−0.678845	+	0.734281i	$0.737519\pi$
$212$	−1.57295	+	4.84104i	−0.108031	+	0.332484i
$213$		0			0
$214$	−14.4721	+	10.5146i	−0.989295	+	0.718765i
$215$	−4.23607	+	3.07768i	−0.288897	+	0.209896i
$216$		0			0
$217$	−2.03444	+	6.26137i	−0.138107	+	0.425049i
$218$	−3.23607	−	2.35114i	−0.219174	−	0.159239i
$219$		0			0
$220$	−0.309017	+	3.30220i	−0.0208339	+	0.222634i
$221$	4.00000			0.269069
$222$		0			0
$223$	1.66312	−	5.11855i	0.111371	−	0.342764i	−0.879802	−	0.475340i	$-0.842325\pi$
$223$	1.66312	−	5.11855i	0.111371	−	0.342764i	0.991173	+	0.132576i	$0.0423250\pi$
$224$	0.427051	+	1.31433i	0.0285335	+	0.0878172i
$225$		0			0
$226$	−2.85410	+	2.07363i	−0.189852	+	0.137936i
$227$	−5.61803	−	17.2905i	−0.372882	−	1.14761i	−0.944896	−	0.327369i	$-0.893838\pi$
$227$	−5.61803	−	17.2905i	−0.372882	−	1.14761i	0.572014	−	0.820244i	$-0.306162\pi$
$228$		0			0
$229$	16.5623	+	12.0332i	1.09447	+	0.795178i	0.980148	−	0.198266i	$-0.0635311\pi$
$229$	16.5623	+	12.0332i	1.09447	+	0.795178i	0.114320	+	0.993444i	$0.463531\pi$
$230$	1.85410			0.122256
$231$		0			0
$232$	9.70820			0.637375
$233$	−24.0344	−	17.4620i	−1.57455	−	1.14398i	−0.922629	−	0.385688i	$-0.873964\pi$
$233$	−24.0344	−	17.4620i	−1.57455	−	1.14398i	−0.651920	−	0.758288i	$-0.726036\pi$
$234$		0			0
$235$	0.118034	+	0.363271i	0.00769969	+	0.0236972i
$236$	−10.0172	+	7.27794i	−0.652066	+	0.473753i
$237$		0			0
$238$	−1.05573	−	3.24920i	−0.0684327	−	0.210614i
$239$	0.0557281	−	0.171513i	0.00360475	−	0.0110943i	−0.949238	−	0.314559i	$-0.898143\pi$
$239$	0.0557281	−	0.171513i	0.00360475	−	0.0110943i	0.952843	+	0.303465i	$0.0981434\pi$
$240$		0			0
$241$	−23.3820			−1.50616			−0.753082	−	0.657926i	$-0.771434\pi$
$241$	−23.3820			−1.50616			−0.753082	+	0.657926i	$0.771434\pi$
$242$	9.94427	−	4.70228i	0.639242	−	0.302274i
$243$		0			0
$244$	−5.47214	−	3.97574i	−0.350318	−	0.254521i
$245$	−1.57295	+	4.84104i	−0.100492	+	0.309283i
$246$		0			0
$247$	2.11803	−	1.53884i	0.134767	−	0.0979142i
$248$	3.85410	−	2.80017i	0.244736	−	0.177811i
$249$		0			0
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−21.4443	−	15.5802i	−1.35355	−	0.983412i	−0.998826	−	0.0484410i	$-0.984575\pi$
$251$	−21.4443	−	15.5802i	−1.35355	−	0.983412i	−0.354724	−	0.934971i	$-0.615425\pi$
$252$		0			0
$253$	−3.13525	−	5.29007i	−0.197112	−	0.332584i
$254$	10.3820			0.651422
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	7.09017	+	21.8213i	0.442273	+	1.36118i	0.885447	+	0.464740i	$0.153852\pi$
$257$	7.09017	+	21.8213i	0.442273	+	1.36118i	−0.443175	+	0.896435i	$0.646148\pi$
$258$		0			0
$259$	−1.80902	+	1.31433i	−0.112407	+	0.0816684i
$260$	−0.500000	−	1.53884i	−0.0310087	−	0.0954349i
$261$		0			0
$262$	2.47214	+	1.79611i	0.152729	+	0.110964i
$263$	14.8541			0.915943			0.457972	−	0.888967i	$-0.348576\pi$
$263$	14.8541			0.915943			0.457972	+	0.888967i	$0.348576\pi$
$264$		0			0
$265$	−5.09017			−0.312687
$266$	−1.80902	−	1.31433i	−0.110918	−	0.0805866i
$267$		0			0
$268$	4.38197	+	13.4863i	0.267671	+	0.823807i
$269$	−23.6525	+	17.1845i	−1.44212	+	1.04776i	−0.454522	+	0.890735i	$0.650190\pi$
$269$	−23.6525	+	17.1845i	−1.44212	+	1.04776i	−0.987595	+	0.157024i	$0.949810\pi$
$270$		0			0
$271$	−9.47214	−	29.1522i	−0.575391	−	1.77087i	−0.634843	−	0.772641i	$-0.718935\pi$
$271$	−9.47214	−	29.1522i	−0.575391	−	1.77087i	0.0594518	−	0.998231i	$-0.481065\pi$
$272$	−0.763932	+	2.35114i	−0.0463202	+	0.142559i
$273$		0			0
$274$	11.4164			0.689690
$275$	−3.23607	+	0.726543i	−0.195142	+	0.0438122i
$276$		0			0
$277$	−20.4443	−	14.8536i	−1.22838	−	0.892468i	−0.231610	−	0.972809i	$-0.574399\pi$
$277$	−20.4443	−	14.8536i	−1.22838	−	0.892468i	−0.996767	+	0.0803405i	$0.974399\pi$
$278$	−1.66312	+	5.11855i	−0.0997472	+	0.306990i
$279$		0			0
$280$	−1.11803	+	0.812299i	−0.0668153	+	0.0485442i
$281$	−22.5623	+	16.3925i	−1.34595	+	0.977893i	−0.346752	+	0.937957i	$0.612715\pi$
$281$	−22.5623	+	16.3925i	−1.34595	+	0.977893i	−0.999202	+	0.0399362i	$0.987285\pi$
$282$		0			0
$283$	−3.00000	+	9.23305i	−0.178331	+	0.548848i	−0.999770	−	0.0214493i	$-0.993172\pi$
$283$	−3.00000	+	9.23305i	−0.178331	+	0.548848i	0.821438	+	0.570297i	$0.193172\pi$
$284$	−11.0902	−	8.05748i	−0.658081	−	0.478123i
$285$		0			0
$286$	−3.54508	+	4.02874i	−0.209625	+	0.238224i
$287$	−8.74265			−0.516062
$288$		0			0
$289$	−3.36475	+	10.3556i	−0.197926	+	0.609154i
$290$	3.00000	+	9.23305i	0.176166	+	0.542183i
$291$		0			0
$292$	5.61803	−	4.08174i	0.328771	−	0.238866i
$293$	5.57295	+	17.1518i	0.325575	+	1.00202i	0.971180	+	0.238346i	$0.0766052\pi$
$293$	5.57295	+	17.1518i	0.325575	+	1.00202i	−0.645605	+	0.763671i	$0.723395\pi$
$294$		0			0
$295$	−10.0172	−	7.27794i	−0.583225	−	0.423738i
$296$	1.61803			0.0940463
$297$		0			0
$298$	−8.94427			−0.518128
$299$	2.42705	+	1.76336i	0.140360	+	0.101977i
$300$		0			0
$301$	2.23607	+	6.88191i	0.128885	+	0.396667i
$302$	2.85410	−	2.07363i	0.164235	−	0.119324i
$303$		0			0
$304$	0.500000	+	1.53884i	0.0286770	+	0.0882586i
$305$	2.09017	−	6.43288i	0.119683	−	0.368346i
$306$		0			0
$307$	−26.8328			−1.53143			−0.765715	−	0.643180i	$-0.777615\pi$
$307$	−26.8328			−1.53143			−0.765715	+	0.643180i	$0.777615\pi$
$308$	4.20820	+	1.81636i	0.239785	+	0.103497i
$309$		0			0
$310$	3.85410	+	2.80017i	0.218898	+	0.159039i
$311$	−2.43769	+	7.50245i	−0.138229	+	0.425425i	−0.996078	−	0.0884763i	$-0.971800\pi$
$311$	−2.43769	+	7.50245i	−0.138229	+	0.425425i	0.857849	+	0.513901i	$0.171800\pi$
$312$		0			0
$313$	6.23607	−	4.53077i	0.352483	−	0.256094i	−0.397427	−	0.917634i	$-0.630097\pi$
$313$	6.23607	−	4.53077i	0.352483	−	0.256094i	0.749910	+	0.661540i	$0.230097\pi$
$314$	2.73607	−	1.98787i	0.154405	−	0.112182i
$315$		0			0
$316$	1.38197	−	4.25325i	0.0777417	−	0.239264i
$317$	17.8713	+	12.9843i	1.00375	+	0.729270i	0.962890	−	0.269895i	$-0.0869890\pi$
$317$	17.8713	+	12.9843i	1.00375	+	0.729270i	0.0408638	+	0.999165i	$0.486989\pi$
$318$		0			0
$319$	21.2705	−	24.1724i	1.19092	−	1.35340i
$320$	1.00000			0.0559017
$321$		0			0
$322$	0.791796	−	2.43690i	0.0441251	−	0.135803i
$323$	−1.23607	−	3.80423i	−0.0687767	−	0.211673i
$324$		0			0
$325$	1.30902	−	0.951057i	0.0726112	−	0.0527551i
$326$	−5.52786	−	17.0130i	−0.306160	−	0.942264i
$327$		0			0
$328$	5.11803	+	3.71847i	0.282596	+	0.205318i
$329$	0.527864			0.0291021
$330$		0			0
$331$	23.3262			1.28213			0.641063	−	0.767488i	$-0.278494\pi$
$331$	23.3262			1.28213			0.641063	+	0.767488i	$0.278494\pi$
$332$	10.4721	+	7.60845i	0.574733	+	0.417568i
$333$		0			0
$334$	−2.64590	−	8.14324i	−0.144777	−	0.445578i
$335$	−11.4721	+	8.33499i	−0.626790	+	0.455389i
$336$		0			0
$337$	−6.18034	−	19.0211i	−0.336665	−	1.03615i	−0.965896	−	0.258929i	$-0.916630\pi$
$337$	−6.18034	−	19.0211i	−0.336665	−	1.03615i	0.629232	−	0.777218i	$-0.283370\pi$
$338$	−3.20820	+	9.87384i	−0.174503	+	0.537066i
$339$		0			0
$340$	−2.47214			−0.134070
$341$	1.47214	−	15.7314i	0.0797206	−	0.851905i
$342$		0			0
$343$	13.5172	+	9.82084i	0.729861	+	0.530275i
$344$	1.61803	−	4.97980i	0.0872385	−	0.268493i
$345$		0			0
$346$	−3.59017	+	2.60841i	−0.193009	+	0.140229i
$347$	21.1803	−	15.3884i	1.13702	−	0.826094i	0.150319	−	0.988638i	$-0.451970\pi$
$347$	21.1803	−	15.3884i	1.13702	−	0.826094i	0.986701	+	0.162544i	$0.0519699\pi$
$348$		0			0
$349$	3.09017	−	9.51057i	0.165413	−	0.509089i	−0.833653	−	0.552288i	$-0.813755\pi$
$349$	3.09017	−	9.51057i	0.165413	−	0.509089i	0.999066	+	0.0431990i	$0.0137549\pi$
$350$	−1.11803	−	0.812299i	−0.0597614	−	0.0434192i
$351$		0			0
$352$	−1.69098	−	2.85317i	−0.0901297	−	0.152074i
$353$	−6.65248			−0.354076			−0.177038	−	0.984204i	$-0.556651\pi$
$353$	−6.65248			−0.354076			−0.177038	+	0.984204i	$0.556651\pi$
$354$		0			0
$355$	4.23607	−	13.0373i	0.224827	−	0.691947i
$356$	3.66312	+	11.2739i	0.194145	+	0.597517i
$357$		0			0
$358$	−14.4443	+	10.4944i	−0.763403	+	0.554645i
$359$	−6.41641	−	19.7477i	−0.338645	−	1.04224i	−0.964899	−	0.262623i	$-0.915413\pi$
$359$	−6.41641	−	19.7477i	−0.338645	−	1.04224i	0.626254	−	0.779619i	$-0.284587\pi$
$360$		0			0
$361$	13.2533	+	9.62908i	0.697542	+	0.506794i
$362$	20.3607			1.07013
$363$		0			0
$364$	−2.23607			−0.117202
$365$	5.61803	+	4.08174i	0.294061	+	0.213648i
$366$		0			0
$367$	−11.2361	−	34.5811i	−0.586518	−	1.80512i	−0.593087	−	0.805138i	$-0.702091\pi$
$367$	−11.2361	−	34.5811i	−0.586518	−	1.80512i	0.00656915	−	0.999978i	$-0.497909\pi$
$368$	−1.50000	+	1.08981i	−0.0781929	+	0.0568105i
$369$		0			0
$370$	0.500000	+	1.53884i	0.0259938	+	0.0800006i
$371$	−2.17376	+	6.69015i	−0.112856	+	0.347335i
$372$		0			0
$373$	−7.14590			−0.370001			−0.185000	−	0.982738i	$-0.559229\pi$
$373$	−7.14590			−0.370001			−0.185000	+	0.982738i	$0.559229\pi$
$374$	4.18034	+	7.05342i	0.216160	+	0.364724i
$375$		0			0
$376$	−0.309017	−	0.224514i	−0.0159363	−	0.0115784i
$377$	−4.85410	+	14.9394i	−0.249999	+	0.769418i
$378$		0			0
$379$	−7.88197	+	5.72658i	−0.404869	+	0.294155i	−0.771521	−	0.636203i	$-0.780504\pi$
$379$	−7.88197	+	5.72658i	−0.404869	+	0.294155i	0.366652	+	0.930358i	$0.380504\pi$
$380$	−1.30902	+	0.951057i	−0.0671512	+	0.0487882i
$381$		0			0
$382$	0.0901699	−	0.277515i	0.00461350	−	0.0141989i
$383$	22.2082	+	16.1352i	1.13479	+	0.824470i	0.986384	−	0.164457i	$-0.0525871\pi$
$383$	22.2082	+	16.1352i	1.13479	+	0.824470i	0.148402	+	0.988927i	$0.452587\pi$
$384$		0			0
$385$	−0.427051	+	4.56352i	−0.0217645	+	0.232579i
$386$	9.70820			0.494135
$387$		0			0
$388$	−0.909830	+	2.80017i	−0.0461896	+	0.142157i
$389$	−3.85410	−	11.8617i	−0.195411	−	0.601412i	−0.999972	−	0.00754213i	$-0.997599\pi$
$389$	−3.85410	−	11.8617i	−0.195411	−	0.601412i	0.804561	−	0.593870i	$-0.202401\pi$
$390$		0			0
$391$	3.70820	−	2.69417i	0.187532	−	0.136250i
$392$	−1.57295	−	4.84104i	−0.0794459	−	0.244509i
$393$		0			0
$394$	1.11803	+	0.812299i	0.0563257	+	0.0409230i
$395$	4.47214			0.225018
$396$		0			0
$397$	28.3262			1.42165			0.710827	−	0.703367i	$-0.248321\pi$
$397$	28.3262			1.42165			0.710827	+	0.703367i	$0.248321\pi$
$398$	−4.00000	−	2.90617i	−0.200502	−	0.145673i
$399$		0			0
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−14.0172	+	10.1841i	−0.699987	+	0.508570i	−0.879928	−	0.475107i	$-0.842409\pi$
$401$	−14.0172	+	10.1841i	−0.699987	+	0.508570i	0.179941	+	0.983677i	$0.442409\pi$
$402$		0			0
$403$	2.38197	+	7.33094i	0.118654	+	0.365180i
$404$	−1.23607	+	3.80423i	−0.0614967	+	0.189267i
$405$		0			0
$406$	13.4164			0.665845
$407$	3.54508	−	4.02874i	0.175723	−	0.199697i
$408$		0			0
$409$	30.1074	+	21.8743i	1.48871	+	1.08161i	0.974616	+	0.223884i	$0.0718735\pi$
$409$	30.1074	+	21.8743i	1.48871	+	1.08161i	0.514099	+	0.857731i	$0.328126\pi$
$410$	−1.95492	+	6.01661i	−0.0965464	+	0.297139i
$411$		0			0
$412$	2.54508	−	1.84911i	0.125387	−	0.0910992i
$413$	−13.8435	+	10.0579i	−0.681192	+	0.494915i
$414$		0			0
$415$	−4.00000	+	12.3107i	−0.196352	+	0.604310i
$416$	1.30902	+	0.951057i	0.0641798	+	0.0466294i
$417$		0			0
$418$	4.92705	+	2.12663i	0.240990	+	0.104017i
$419$	35.7984			1.74887			0.874433	−	0.485147i	$-0.161234\pi$
$419$	35.7984			1.74887			0.874433	+	0.485147i	$0.161234\pi$
$420$		0			0
$421$	2.79837	−	8.61251i	0.136384	−	0.419748i	−0.859418	−	0.511273i	$-0.829174\pi$
$421$	2.79837	−	8.61251i	0.136384	−	0.419748i	0.995803	+	0.0915249i	$0.0291741\pi$
$422$	1.05573	+	3.24920i	0.0513920	+	0.158168i
$423$		0			0
$424$	4.11803	−	2.99193i	0.199989	−	0.145301i
$425$	−0.763932	−	2.35114i	−0.0370561	−	0.114047i
$426$		0			0
$427$	−7.56231	−	5.49434i	−0.365966	−	0.265890i
$428$	17.8885			0.864675
$429$		0			0
$430$	5.23607			0.252506
$431$	−16.3262	−	11.8617i	−0.786407	−	0.571358i	0.120488	−	0.992715i	$-0.461554\pi$
$431$	−16.3262	−	11.8617i	−0.786407	−	0.571358i	−0.906895	+	0.421357i	$0.861554\pi$
$432$		0			0
$433$	2.20163	+	6.77591i	0.105803	+	0.325629i	0.989918	−	0.141640i	$-0.0452377\pi$
$433$	2.20163	+	6.77591i	0.105803	+	0.325629i	−0.884115	+	0.467270i	$0.845238\pi$
$434$	5.32624	−	3.86974i	0.255668	−	0.185753i
$435$		0			0
$436$	1.23607	+	3.80423i	0.0591969	+	0.182189i
$437$	0.927051	−	2.85317i	0.0443469	−	0.136486i
$438$		0			0
$439$	−2.18034			−0.104062			−0.0520310	−	0.998645i	$-0.516569\pi$
$439$	−2.18034			−0.104062			−0.0520310	+	0.998645i	$0.516569\pi$
$440$	2.19098	−	2.48990i	0.104451	−	0.118701i
$441$		0			0
$442$	−3.23607	−	2.35114i	−0.153924	−	0.111832i
$443$	7.67376	−	23.6174i	0.364591	−	1.12210i	−0.585645	−	0.810568i	$-0.699159\pi$
$443$	7.67376	−	23.6174i	0.364591	−	1.12210i	0.950236	−	0.311529i	$-0.100841\pi$
$444$		0			0
$445$	−9.59017	+	6.96767i	−0.454618	+	0.330299i
$446$	−4.35410	+	3.16344i	−0.206173	+	0.149793i
$447$		0			0
$448$	0.427051	−	1.31433i	0.0201763	−	0.0620962i
$449$	−13.2533	−	9.62908i	−0.625461	−	0.454424i	0.229364	−	0.973341i	$-0.426336\pi$
$449$	−13.2533	−	9.62908i	−0.625461	−	0.454424i	−0.854825	+	0.518917i	$0.826336\pi$
$450$		0			0
$451$	20.4721	−	4.59628i	0.963995	−	0.216430i
$452$	3.52786			0.165937
$453$		0			0
$454$	−5.61803	+	17.2905i	−0.263667	+	0.811485i
$455$	−0.690983	−	2.12663i	−0.0323938	−	0.0996978i
$456$		0			0
$457$	20.9443	−	15.2169i	0.979732	−	0.711817i	0.0220831	−	0.999756i	$-0.492970\pi$
$457$	20.9443	−	15.2169i	0.979732	−	0.711817i	0.957649	+	0.287939i	$0.0929702\pi$
$458$	−6.32624	−	19.4702i	−0.295606	−	0.909781i
$459$		0			0
$460$	−1.50000	−	1.08981i	−0.0699379	−	0.0508128i
$461$	29.2361			1.36166			0.680830	−	0.732442i	$-0.261619\pi$
$461$	29.2361			1.36166			0.680830	+	0.732442i	$0.261619\pi$
$462$		0			0
$463$	−5.61803			−0.261092			−0.130546	−	0.991442i	$-0.541673\pi$
$463$	−5.61803			−0.261092			−0.130546	+	0.991442i	$0.541673\pi$
$464$	−7.85410	−	5.70634i	−0.364618	−	0.264910i
$465$		0			0
$466$	9.18034	+	28.2542i	0.425271	+	1.30885i
$467$	20.1803	−	14.6619i	0.933835	−	0.678471i	−0.0130940	−	0.999914i	$-0.504168\pi$
$467$	20.1803	−	14.6619i	0.933835	−	0.678471i	0.946929	+	0.321444i	$0.104168\pi$
$468$		0			0
$469$	6.05573	+	18.6376i	0.279628	+	0.860605i
$470$	0.118034	−	0.363271i	0.00544450	−	0.0167565i
$471$		0			0
$472$	12.3820			0.569926
$473$	−8.85410	−	14.9394i	−0.407112	−	0.686914i
$474$		0			0
$475$	−1.30902	−	0.951057i	−0.0600618	−	0.0436375i
$476$	−1.05573	+	3.24920i	−0.0483892	+	0.148927i
$477$		0			0
$478$	−0.145898	+	0.106001i	−0.00667322	+	0.00484838i
$479$	29.9443	−	21.7558i	1.36819	−	0.994047i	0.370313	−	0.928907i	$-0.379251\pi$
$479$	29.9443	−	21.7558i	1.36819	−	0.994047i	0.997876	−	0.0651401i	$-0.0207494\pi$
$480$		0			0
$481$	−0.809017	+	2.48990i	−0.0368880	+	0.113530i
$482$	18.9164	+	13.7436i	0.861619	+	0.626003i
$483$		0			0
$484$	−10.8090	−	2.04087i	−0.491319	−	0.0927668i
$485$	−2.94427			−0.133693
$486$		0			0
$487$	−1.34752	+	4.14725i	−0.0610621	+	0.187930i	−0.976934	−	0.213540i	$-0.931501\pi$
$487$	−1.34752	+	4.14725i	−0.0610621	+	0.187930i	0.915872	+	0.401470i	$0.131501\pi$
$488$	2.09017	+	6.43288i	0.0946175	+	0.291203i
$489$		0			0
$490$	4.11803	−	2.99193i	0.186034	−	0.135161i
$491$	−4.11803	−	12.6740i	−0.185844	−	0.571970i	0.814118	−	0.580700i	$-0.197221\pi$
$491$	−4.11803	−	12.6740i	−0.185844	−	0.571970i	−0.999962	+	0.00873015i	$0.997221\pi$
$492$		0			0
$493$	19.4164	+	14.1068i	0.874471	+	0.635340i
$494$	−2.61803			−0.117791
$495$		0			0
$496$	−4.76393			−0.213907
$497$	−15.3262	−	11.1352i	−0.687476	−	0.499480i
$498$		0			0
$499$	8.24671	+	25.3808i	0.369173	+	1.13620i	0.947326	+	0.320271i	$0.103774\pi$
$499$	8.24671	+	25.3808i	0.369173	+	1.13620i	−0.578153	+	0.815929i	$0.696226\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$		0			0
$502$	8.19098	+	25.2093i	0.365581	+	1.12514i
$503$	−6.11803	+	18.8294i	−0.272790	+	0.839560i	0.717006	+	0.697067i	$0.245512\pi$
$503$	−6.11803	+	18.8294i	−0.272790	+	0.839560i	−0.989796	+	0.142493i	$0.954488\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$	−0.572949	+	6.12261i	−0.0254707	+	0.272183i
$507$		0			0
$508$	−8.39919	−	6.10237i	−0.372654	−	0.270749i
$509$	−0.437694	+	1.34708i	−0.0194004	+	0.0597084i	−0.960288	−	0.279010i	$-0.909994\pi$
$509$	−0.437694	+	1.34708i	−0.0194004	+	0.0597084i	0.940888	+	0.338719i	$0.109994\pi$
$510$		0			0
$511$	7.76393	−	5.64083i	0.343456	−	0.249535i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	7.09017	−	21.8213i	0.312734	−	0.962496i
$515$	2.54508	+	1.84911i	0.112150	+	0.0814816i
$516$		0			0
$517$	−1.23607	+	0.277515i	−0.0543622	+	0.0122051i
$518$	2.23607			0.0982472
$519$		0			0
$520$	−0.500000	+	1.53884i	−0.0219265	+	0.0674827i
$521$	−6.69756	−	20.6130i	−0.293425	−	0.903071i	−0.983746	−	0.179567i	$-0.942530\pi$
$521$	−6.69756	−	20.6130i	−0.293425	−	0.903071i	0.690320	−	0.723504i	$-0.257470\pi$
$522$		0			0
$523$	−12.7082	+	9.23305i	−0.555691	+	0.403733i	−0.829879	−	0.557943i	$-0.811591\pi$
$523$	−12.7082	+	9.23305i	−0.555691	+	0.403733i	0.274188	+	0.961676i	$0.411591\pi$
$524$	−0.944272	−	2.90617i	−0.0412507	−	0.126957i
$525$		0			0
$526$	−12.0172	−	8.73102i	−0.523976	−	0.380691i
$527$	11.7771			0.513018
$528$		0			0
$529$	−19.5623			−0.850535
$530$	4.11803	+	2.99193i	0.178876	+	0.129961i
$531$		0			0
$532$	0.690983	+	2.12663i	0.0299579	+	0.0922010i
$533$	−8.28115	+	6.01661i	−0.358697	+	0.260608i
$534$		0			0
$535$	5.52786	+	17.0130i	0.238990	+	0.735537i
$536$	4.38197	−	13.4863i	0.189272	−	0.582520i
$537$		0			0
$538$	29.2361			1.26046
$539$	−15.5000	−	6.69015i	−0.667632	−	0.288165i
$540$		0			0
$541$	26.6525	+	19.3642i	1.14588	+	0.832530i	0.987928	−	0.154917i	$-0.0495109\pi$
$541$	26.6525	+	19.3642i	1.14588	+	0.832530i	0.157952	+	0.987447i	$0.449511\pi$
$542$	−9.47214	+	29.1522i	−0.406863	+	1.25220i
$543$		0			0
$544$	2.00000	−	1.45309i	0.0857493	−	0.0623005i
$545$	−3.23607	+	2.35114i	−0.138618	+	0.100712i
$546$		0			0
$547$	−4.56231	+	14.0413i	−0.195070	+	0.600364i	0.804906	+	0.593403i	$0.202216\pi$
$547$	−4.56231	+	14.0413i	−0.195070	+	0.600364i	−0.999976	+	0.00696128i	$0.997784\pi$
$548$	−9.23607	−	6.71040i	−0.394545	−	0.286654i
$549$		0			0
$550$	3.04508	+	1.31433i	0.129843	+	0.0560431i
$551$	15.7082			0.669192
$552$		0			0
$553$	1.90983	−	5.87785i	0.0812142	−	0.249952i
$554$	7.80902	+	24.0337i	0.331773	+	1.02109i
$555$		0			0
$556$	4.35410	−	3.16344i	0.184655	−	0.134160i
$557$	−9.06231	−	27.8909i	−0.383982	−	1.18178i	−0.937216	−	0.348750i	$-0.886606\pi$
$557$	−9.06231	−	27.8909i	−0.383982	−	1.18178i	0.553234	−	0.833026i	$-0.313394\pi$
$558$		0			0
$559$	6.85410	+	4.97980i	0.289898	+	0.210623i
$560$	1.38197			0.0583987
$561$		0			0
$562$	27.8885			1.17641
$563$	−14.0000	−	10.1716i	−0.590030	−	0.428682i	0.252296	−	0.967650i	$-0.418814\pi$
$563$	−14.0000	−	10.1716i	−0.590030	−	0.428682i	−0.842326	+	0.538968i	$0.818814\pi$
$564$		0			0
$565$	1.09017	+	3.35520i	0.0458638	+	0.141154i
$566$	7.85410	−	5.70634i	0.330133	−	0.239855i
$567$		0			0
$568$	4.23607	+	13.0373i	0.177741	+	0.547032i
$569$	−2.51722	+	7.74721i	−0.105527	+	0.324780i	−0.989854	−	0.142089i	$-0.954618\pi$
$569$	−2.51722	+	7.74721i	−0.105527	+	0.324780i	0.884326	+	0.466869i	$0.154618\pi$
$570$		0			0
$571$	16.5066			0.690779			0.345389	−	0.938459i	$-0.387747\pi$
$571$	16.5066			0.690779			0.345389	+	0.938459i	$0.387747\pi$
$572$	5.23607	−	1.17557i	0.218931	−	0.0491531i
$573$		0			0
$574$	7.07295	+	5.13880i	0.295219	+	0.214489i
$575$	0.572949	−	1.76336i	0.0238936	−	0.0735370i
$576$		0			0
$577$	−26.7984	+	19.4702i	−1.11563	+	0.810553i	−0.983541	−	0.180684i	$-0.942169\pi$
$577$	−26.7984	+	19.4702i	−1.11563	+	0.810553i	−0.132090	+	0.991238i	$0.542169\pi$
$578$	8.80902	−	6.40013i	0.366407	−	0.266210i
$579$		0			0
$580$	3.00000	−	9.23305i	0.124568	−	0.383382i
$581$	14.4721	+	10.5146i	0.600405	+	0.436220i
$582$		0			0
$583$	1.57295	−	16.8087i	0.0651449	−	0.696147i
$584$	−6.94427			−0.287356
$585$		0			0
$586$	5.57295	−	17.1518i	0.230216	−	0.708533i
$587$	5.81966	+	17.9111i	0.240203	+	0.739269i	0.996388	+	0.0849116i	$0.0270608\pi$
$587$	5.81966	+	17.9111i	0.240203	+	0.739269i	−0.756185	+	0.654357i	$0.772939\pi$
$588$		0			0
$589$	6.23607	−	4.53077i	0.256953	−	0.186687i
$590$	3.82624	+	11.7759i	0.157524	+	0.484808i
$591$		0			0
$592$	−1.30902	−	0.951057i	−0.0538003	−	0.0390882i
$593$	29.4164			1.20799			0.603994	−	0.796989i	$-0.293575\pi$
$593$	29.4164			1.20799			0.603994	+	0.796989i	$0.293575\pi$
$594$		0			0
$595$	−3.41641			−0.140059
$596$	7.23607	+	5.25731i	0.296401	+	0.215348i
$597$		0			0
$598$	−0.927051	−	2.85317i	−0.0379099	−	0.116675i
$599$	−14.3262	+	10.4086i	−0.585354	+	0.425285i	−0.840650	−	0.541578i	$-0.817827\pi$
$599$	−14.3262	+	10.4086i	−0.585354	+	0.425285i	0.255296	+	0.966863i	$0.417827\pi$
$600$		0			0
$601$	−7.38854	−	22.7396i	−0.301385	−	0.927568i	−0.981002	−	0.194000i	$-0.937854\pi$
$601$	−7.38854	−	22.7396i	−0.301385	−	0.927568i	0.679617	−	0.733568i	$-0.262146\pi$
$602$	2.23607	−	6.88191i	0.0911353	−	0.280486i
$603$		0			0
$604$	−3.52786			−0.143547
$605$	−1.39919	−	10.9106i	−0.0568850	−	0.443581i
$606$		0			0
$607$	−22.9443	−	16.6700i	−0.931279	−	0.676614i	0.0150264	−	0.999887i	$-0.495217\pi$
$607$	−22.9443	−	16.6700i	−0.931279	−	0.676614i	−0.946306	+	0.323273i	$0.895217\pi$
$608$	0.500000	−	1.53884i	0.0202777	−	0.0624083i
$609$		0			0
$610$	−5.47214	+	3.97574i	−0.221560	+	0.160973i
$611$	0.500000	−	0.363271i	0.0202278	−	0.0146964i
$612$		0			0
$613$	5.74265	−	17.6740i	0.231943	−	0.713848i	−0.765569	−	0.643354i	$-0.777542\pi$
$613$	5.74265	−	17.6740i	0.231943	−	0.713848i	0.997512	−	0.0704941i	$-0.0224576\pi$
$614$	21.7082	+	15.7719i	0.876072	+	0.636503i
$615$		0			0
$616$	−2.33688	−	3.94298i	−0.0941556	−	0.158867i
$617$	−40.9443			−1.64835			−0.824177	−	0.566332i	$-0.808362\pi$
$617$	−40.9443			−1.64835			−0.824177	+	0.566332i	$0.808362\pi$
$618$		0			0
$619$	−5.79180	+	17.8253i	−0.232792	+	0.716460i	0.764615	+	0.644488i	$0.222929\pi$
$619$	−5.79180	+	17.8253i	−0.232792	+	0.716460i	−0.997407	+	0.0719722i	$0.977071\pi$
$620$	−1.47214	−	4.53077i	−0.0591224	−	0.181960i
$621$		0			0
$622$	6.38197	−	4.63677i	0.255894	−	0.185918i
$623$	5.06231	+	15.5802i	0.202817	+	0.624207i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−7.70820			−0.308082
$627$		0			0
$628$	−3.38197			−0.134955
$629$	3.23607	+	2.35114i	0.129030	+	0.0937461i
$630$		0			0
$631$	−3.61803	−	11.1352i	−0.144032	−	0.443284i	0.852854	−	0.522150i	$-0.174870\pi$
$631$	−3.61803	−	11.1352i	−0.144032	−	0.443284i	−0.996885	+	0.0788663i	$0.974870\pi$
$632$	−3.61803	+	2.62866i	−0.143918	+	0.104562i
$633$		0			0
$634$	−6.82624	−	21.0090i	−0.271105	−	0.834374i
$635$	3.20820	−	9.87384i	0.127314	−	0.391831i
$636$		0			0
$637$	8.23607			0.326325
$638$	−31.4164	+	7.05342i	−1.24379	+	0.279248i
$639$		0			0
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	5.70163	−	17.5478i	0.225201	−	0.693096i	−0.773070	−	0.634320i	$-0.781280\pi$
$641$	5.70163	−	17.5478i	0.225201	−	0.693096i	0.998271	−	0.0587763i	$-0.0187199\pi$
$642$		0			0
$643$	−18.9443	+	13.7638i	−0.747089	+	0.542792i	−0.894923	−	0.446220i	$-0.852770\pi$
$643$	−18.9443	+	13.7638i	−0.747089	+	0.542792i	0.147834	+	0.989012i	$0.452770\pi$
$644$	−2.07295	+	1.50609i	−0.0816856	+	0.0593481i
$645$		0			0
$646$	−1.23607	+	3.80423i	−0.0486324	+	0.149675i
$647$	18.4721	+	13.4208i	0.726215	+	0.527626i	0.888364	−	0.459140i	$-0.151843\pi$
$647$	18.4721	+	13.4208i	0.726215	+	0.527626i	−0.162149	+	0.986766i	$0.551843\pi$
$648$		0			0
$649$	27.1287	−	30.8298i	1.06489	−	1.21018i
$650$	−1.61803			−0.0634645
$651$		0			0
$652$	−5.52786	+	17.0130i	−0.216488	+	0.666281i
$653$	2.82624	+	8.69827i	0.110599	+	0.340389i	0.991004	−	0.133834i	$-0.0427289\pi$
$653$	2.82624	+	8.69827i	0.110599	+	0.340389i	−0.880405	+	0.474223i	$0.842729\pi$
$654$		0			0
$655$	2.47214	−	1.79611i	0.0965943	−	0.0701799i
$656$	−1.95492	−	6.01661i	−0.0763266	−	0.234909i
$657$		0			0
$658$	−0.427051	−	0.310271i	−0.0166482	−	0.0120956i
$659$	5.27051			0.205310			0.102655	−	0.994717i	$-0.467266\pi$
$659$	5.27051			0.205310			0.102655	+	0.994717i	$0.467266\pi$
$660$		0			0
$661$	−43.4853			−1.69138			−0.845691	−	0.533673i	$-0.820811\pi$
$661$	−43.4853			−1.69138			−0.845691	+	0.533673i	$0.820811\pi$
$662$	−18.8713	−	13.7108i	−0.733455	−	0.532886i
$663$		0			0
$664$	−4.00000	−	12.3107i	−0.155230	−	0.477749i
$665$	−1.80902	+	1.31433i	−0.0701507	+	0.0509674i
$666$		0			0
$667$	5.56231	+	17.1190i	0.215373	+	0.662851i
$668$	−2.64590	+	8.14324i	−0.102373	+	0.315071i
$669$		0			0
$670$	14.1803			0.547834
$671$	20.5967	+	8.89002i	0.795129	+	0.343196i
$672$		0			0
$673$	−2.90983	−	2.11412i	−0.112166	−	0.0814932i	0.530288	−	0.847817i	$-0.322084\pi$
$673$	−2.90983	−	2.11412i	−0.112166	−	0.0814932i	−0.642454	+	0.766324i	$0.722084\pi$
$674$	−6.18034	+	19.0211i	−0.238058	+	0.732667i
$675$		0			0
$676$	8.39919	−	6.10237i	0.323046	−	0.234706i
$677$	−24.5623	+	17.8456i	−0.944006	+	0.685861i	−0.949382	−	0.314125i	$-0.898289\pi$
$677$	−24.5623	+	17.8456i	−0.944006	+	0.685861i	0.00537554	+	0.999986i	$0.498289\pi$
$678$		0			0
$679$	−1.25735	+	3.86974i	−0.0482528	+	0.148507i
$680$	2.00000	+	1.45309i	0.0766965	+	0.0557233i
$681$		0			0
$682$	−10.4377	+	11.8617i	−0.399680	+	0.454208i
$683$	9.12461			0.349144			0.174572	−	0.984644i	$-0.444146\pi$
$683$	9.12461			0.349144			0.174572	+	0.984644i	$0.444146\pi$
$684$		0			0
$685$	3.52786	−	10.8576i	0.134793	−	0.414849i
$686$	−5.16312	−	15.8904i	−0.197129	−	0.606700i
$687$		0			0
$688$	−4.23607	+	3.07768i	−0.161499	+	0.117336i
$689$	2.54508	+	7.83297i	0.0969600	+	0.298412i
$690$		0			0
$691$	−29.5344	−	21.4580i	−1.12354	−	0.816302i	−0.138801	−	0.990320i	$-0.544325\pi$
$691$	−29.5344	−	21.4580i	−1.12354	−	0.816302i	−0.984742	+	0.174018i	$0.944325\pi$
$692$	4.43769			0.168696
$693$		0			0
$694$	−26.1803			−0.993792
$695$	4.35410	+	3.16344i	0.165161	+	0.119996i
$696$		0			0
$697$	4.83282	+	14.8739i	0.183056	+	0.563388i
$698$	−8.09017	+	5.87785i	−0.306217	+	0.222480i
$699$		0			0
$700$	0.427051	+	1.31433i	0.0161410	+	0.0496769i
$701$	−11.7639	+	36.2057i	−0.444318	+	1.36747i	0.438913	+	0.898530i	$0.355364\pi$
$701$	−11.7639	+	36.2057i	−0.444318	+	1.36747i	−0.883230	+	0.468939i	$0.844636\pi$
$702$		0			0
$703$	2.61803			0.0987410
$704$	−0.309017	+	3.30220i	−0.0116465	+	0.124456i
$705$		0			0
$706$	5.38197	+	3.91023i	0.202553	+	0.147163i
$707$	−1.70820	+	5.25731i	−0.0642436	+	0.197722i
$708$		0			0
$709$	−5.38197	+	3.91023i	−0.202124	+	0.146852i	−0.684243	−	0.729254i	$-0.739867\pi$
$709$	−5.38197	+	3.91023i	−0.202124	+	0.146852i	0.482119	+	0.876106i	$0.339867\pi$
$710$	−11.0902	+	8.05748i	−0.416207	+	0.302392i
$711$		0			0
$712$	3.66312	−	11.2739i	0.137281	−	0.422508i
$713$	7.14590	+	5.19180i	0.267616	+	0.194434i
$714$		0			0
$715$	2.73607	+	4.61653i	0.102323	+	0.172648i
$716$	17.8541			0.667239
$717$		0			0
$718$	−6.41641	+	19.7477i	−0.239458	+	0.736977i
$719$	−3.67376	−	11.3067i	−0.137008	−	0.421668i	0.858889	−	0.512162i	$-0.171155\pi$
$719$	−3.67376	−	11.3067i	−0.137008	−	0.421668i	−0.995897	+	0.0904943i	$0.971155\pi$
$720$		0			0
$721$	3.51722	−	2.55541i	0.130988	−	0.0951685i
$722$	−5.06231	−	15.5802i	−0.188400	−	0.579834i
$723$		0			0
$724$	−16.4721	−	11.9677i	−0.612182	−	0.444776i
$725$	9.70820			0.360554
$726$		0			0
$727$	31.6312			1.17314			0.586568	−	0.809900i	$-0.300479\pi$
$727$	31.6312			1.17314			0.586568	+	0.809900i	$0.300479\pi$
$728$	1.80902	+	1.31433i	0.0670466	+	0.0487122i
$729$		0			0
$730$	−2.14590	−	6.60440i	−0.0794232	−	0.244440i
$731$	10.4721	−	7.60845i	0.387326	−	0.281409i
$732$		0			0
$733$	−6.03444	−	18.5721i	−0.222887	−	0.685976i	−0.998499	−	0.0547663i	$-0.982559\pi$
$733$	−6.03444	−	18.5721i	−0.222887	−	0.685976i	0.775612	−	0.631210i	$-0.217441\pi$
$734$	−11.2361	+	34.5811i	−0.414731	+	1.27641i
$735$		0			0
$736$	1.85410			0.0683431
$737$	−23.9787	−	40.4589i	−0.883267	−	1.49032i
$738$		0			0
$739$	−20.5344	−	14.9191i	−0.755372	−	0.548810i	0.142116	−	0.989850i	$-0.454610\pi$
$739$	−20.5344	−	14.9191i	−0.755372	−	0.548810i	−0.897487	+	0.441040i	$0.854610\pi$
$740$	0.500000	−	1.53884i	0.0183804	−	0.0565689i
$741$		0			0
$742$	5.69098	−	4.13474i	0.208923	−	0.151791i
$743$	−11.2082	+	8.14324i	−0.411189	+	0.298746i	−0.774083	−	0.633084i	$-0.781789\pi$
$743$	−11.2082	+	8.14324i	−0.411189	+	0.298746i	0.362894	+	0.931830i	$0.381789\pi$
$744$		0			0
$745$	−2.76393	+	8.50651i	−0.101263	+	0.311654i
$746$	5.78115	+	4.20025i	0.211663	+	0.153782i
$747$		0			0
$748$	0.763932	−	8.16348i	0.0279321	−	0.298486i
$749$	24.7214			0.903299
$750$		0			0
$751$	15.5279	−	47.7899i	0.566620	−	1.74388i	−0.0964693	−	0.995336i	$-0.530755\pi$
$751$	15.5279	−	47.7899i	0.566620	−	1.74388i	0.663089	−	0.748540i	$-0.269245\pi$
$752$	0.118034	+	0.363271i	0.00430426	+	0.0132471i
$753$		0			0
$754$	12.7082	−	9.23305i	0.462805	−	0.336248i
$755$	−1.09017	−	3.35520i	−0.0396753	−	0.122108i
$756$		0			0
$757$	3.92705	+	2.85317i	0.142731	+	0.103700i	0.656859	−	0.754013i	$-0.271884\pi$
$757$	3.92705	+	2.85317i	0.142731	+	0.103700i	−0.514128	+	0.857713i	$0.671884\pi$
$758$	9.74265			0.353869
$759$		0			0
$760$	1.61803			0.0586923
$761$	22.5623	+	16.3925i	0.817883	+	0.594227i	0.916105	−	0.400938i	$-0.131316\pi$
$761$	22.5623	+	16.3925i	0.817883	+	0.594227i	−0.0982224	+	0.995164i	$0.531316\pi$
$762$		0			0
$763$	1.70820	+	5.25731i	0.0618411	+	0.190327i
$764$	−0.236068	+	0.171513i	−0.00854064	+	0.00620514i
$765$		0			0
$766$	−8.48278	−	26.1073i	−0.306495	−	0.943295i
$767$	−6.19098	+	19.0539i	−0.223543	+	0.687996i
$768$		0			0
$769$	−10.2016			−0.367880			−0.183940	−	0.982937i	$-0.558885\pi$
$769$	−10.2016			−0.367880			−0.183940	+	0.982937i	$0.558885\pi$
$770$	3.02786	−	3.44095i	0.109117	−	0.124003i
$771$		0			0
$772$	−7.85410	−	5.70634i	−0.282675	−	0.205376i
$773$	6.42705	−	19.7804i	0.231165	−	0.711453i	−0.766442	−	0.642313i	$-0.777975\pi$
$773$	6.42705	−	19.7804i	0.231165	−	0.711453i	0.997607	−	0.0691391i	$-0.0220252\pi$
$774$		0			0
$775$	3.85410	−	2.80017i	0.138443	−	0.100585i
$776$	2.38197	−	1.73060i	0.0855076	−	0.0621249i
$777$		0			0
$778$	−3.85410	+	11.8617i	−0.138176	+	0.425263i
$779$	8.28115	+	6.01661i	0.296703	+	0.215567i
$780$		0			0
$781$	41.7426	+	18.0171i	1.49367	+	0.644702i
$782$	−4.58359			−0.163909
$783$		0			0
$784$	−1.57295	+	4.84104i	−0.0561768	+	0.172894i
$785$	−1.04508	−	3.21644i	−0.0373007	−	0.114800i
$786$		0			0
$787$	−3.38197	+	2.45714i	−0.120554	+	0.0875877i	−0.646429	−	0.762975i	$-0.723738\pi$
$787$	−3.38197	+	2.45714i	−0.120554	+	0.0875877i	0.525874	+	0.850562i	$0.323738\pi$
$788$	−0.427051	−	1.31433i	−0.0152131	−	0.0468210i
$789$		0			0
$790$	−3.61803	−	2.62866i	−0.128724	−	0.0935234i
$791$	4.87539			0.173349
$792$		0			0
$793$	−10.9443			−0.388642
$794$	−22.9164	−	16.6497i	−0.813273	−	0.590877i
$795$		0			0
$796$	1.52786	+	4.70228i	0.0541537	+	0.166668i
$797$	−23.2533	+	16.8945i	−0.823674	+	0.598434i	−0.917762	−	0.397130i	$-0.870006\pi$
$797$	−23.2533	+	16.8945i	−0.823674	+	0.598434i	0.0940887	+	0.995564i	$0.470006\pi$
$798$		0			0
$799$	−0.291796	−	0.898056i	−0.0103230	−	0.0317709i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$		0			0
$802$	17.3262			0.611811
$803$	−15.2148	+	17.2905i	−0.536918	+	0.610170i
$804$		0			0
$805$	−2.07295	−	1.50609i	−0.0730619	−	0.0530825i
$806$	2.38197	−	7.33094i	0.0839012	−	0.258221i
$807$		0			0
$808$	3.23607	−	2.35114i	0.113844	−	0.0827129i
$809$	−33.5795	+	24.3970i	−1.18059	+	0.857751i	−0.992238	−	0.124350i	$-0.960316\pi$
$809$	−33.5795	+	24.3970i	−1.18059	+	0.857751i	−0.188355	+	0.982101i	$0.560316\pi$
$810$		0			0
$811$	−2.24671	+	6.91467i	−0.0788927	+	0.242807i	−0.982722	−	0.185086i	$-0.940744\pi$
$811$	−2.24671	+	6.91467i	−0.0788927	+	0.242807i	0.903830	+	0.427892i	$0.140744\pi$
$812$	−10.8541	−	7.88597i	−0.380904	−	0.276743i
$813$		0			0
$814$	−5.23607	+	1.17557i	−0.183524	+	0.0412037i
$815$	−17.8885			−0.626608
$816$		0			0
$817$	2.61803	−	8.05748i	0.0915934	−	0.281896i
$818$	−11.5000	−	35.3934i	−0.402088	−	1.23750i
$819$		0			0
$820$	5.11803	−	3.71847i	0.178729	−	0.129855i
$821$	−5.32624	−	16.3925i	−0.185887	−	0.572101i	0.814076	−	0.580759i	$-0.197244\pi$
$821$	−5.32624	−	16.3925i	−0.185887	−	0.572101i	−0.999963	+	0.00865769i	$0.997244\pi$
$822$		0			0
$823$	−35.6697	−	25.9156i	−1.24337	−	0.903359i	−0.245549	−	0.969384i	$-0.578968\pi$
$823$	−35.6697	−	25.9156i	−1.24337	−	0.903359i	−0.997818	+	0.0660247i	$0.978968\pi$
$824$	−3.14590			−0.109593
$825$		0			0
$826$	17.1115			0.595384
$827$	3.00000	+	2.17963i	0.104320	+	0.0757931i	0.638722	−	0.769437i	$-0.279463\pi$
$827$	3.00000	+	2.17963i	0.104320	+	0.0757931i	−0.534402	+	0.845230i	$0.679463\pi$
$828$		0			0
$829$	12.1459	+	37.3812i	0.421844	+	1.29830i	0.905984	+	0.423313i	$0.139133\pi$
$829$	12.1459	+	37.3812i	0.421844	+	1.29830i	−0.484139	+	0.874991i	$0.660867\pi$
$830$	10.4721	−	7.60845i	0.363493	−	0.264093i
$831$		0			0
$832$	−0.500000	−	1.53884i	−0.0173344	−	0.0533497i
$833$	3.88854	−	11.9677i	0.134730	−	0.414656i
$834$		0			0
$835$	−8.56231			−0.296311
$836$	−2.73607	−	4.61653i	−0.0946289	−	0.159666i
$837$		0			0
$838$	−28.9615	−	21.0418i	−1.00046	−	0.726875i
$839$	2.20163	−	6.77591i	0.0760086	−	0.233930i	−0.905832	−	0.423636i	$-0.860753\pi$
$839$	2.20163	−	6.77591i	0.0760086	−	0.233930i	0.981841	+	0.189706i	$0.0607535\pi$
$840$		0			0
$841$	−52.7877	+	38.3525i	−1.82027	+	1.32250i
$842$	−7.32624	+	5.32282i	−0.252479	+	0.183437i
$843$		0			0
$844$	1.05573	−	3.24920i	0.0363397	−	0.111842i
$845$	8.39919	+	6.10237i	0.288941	+	0.209928i
$846$		0			0
$847$	−14.9377	−	2.82041i	−0.513265	−	0.0969106i
$848$	−5.09017			−0.174797
$849$		0			0
$850$	−0.763932	+	2.35114i	−0.0262027	+	0.0806435i
$851$	0.927051	+	2.85317i	0.0317789	+	0.0978054i
$852$		0			0
$853$	41.9164	−	30.4541i	1.43519	−	1.04273i	0.446170	−	0.894948i	$-0.352788\pi$
$853$	41.9164	−	30.4541i	1.43519	−	1.04273i	0.989020	−	0.147779i	$-0.0472123\pi$
$854$	2.88854	+	8.89002i	0.0988439	+	0.304210i
$855$		0			0
$856$	−14.4721	−	10.5146i	−0.494647	−	0.359382i
$857$	−50.7639			−1.73406			−0.867031	−	0.498253i	$-0.833975\pi$
$857$	−50.7639			−1.73406			−0.867031	+	0.498253i	$0.833975\pi$
$858$		0			0
$859$	21.9656			0.749455			0.374728	−	0.927135i	$-0.377736\pi$
$859$	21.9656			0.749455			0.374728	+	0.927135i	$0.377736\pi$
$860$	−4.23607	−	3.07768i	−0.144449	−	0.104948i
$861$		0			0
$862$	6.23607	+	19.1926i	0.212401	+	0.653704i
$863$	−5.54508	+	4.02874i	−0.188757	+	0.137140i	−0.678150	−	0.734923i	$-0.737218\pi$
$863$	−5.54508	+	4.02874i	−0.188757	+	0.137140i	0.489393	+	0.872063i	$0.337218\pi$
$864$		0			0
$865$	1.37132	+	4.22050i	0.0466264	+	0.143501i
$866$	2.20163	−	6.77591i	0.0748143	−	0.230255i
$867$		0			0
$868$	−6.58359			−0.223462
$869$	−1.38197	+	14.7679i	−0.0468800	+	0.500966i
$870$		0			0
$871$	18.5623	+	13.4863i	0.628960	+	0.456966i
$872$	1.23607	−	3.80423i	0.0418585	−	0.128827i
$873$		0			0
$874$	−2.42705	+	1.76336i	−0.0820962	+	0.0596464i
$875$	−1.11803	+	0.812299i	−0.0377964	+	0.0274607i
$876$		0			0
$877$	−7.91641	+	24.3642i	−0.267318	+	0.822721i	0.723832	+	0.689976i	$0.242379\pi$
$877$	−7.91641	+	24.3642i	−0.267318	+	0.822721i	−0.991150	+	0.132744i	$0.957621\pi$
$878$	1.76393	+	1.28157i	0.0595298	+	0.0432509i
$879$		0			0
$880$	−3.23607	+	0.726543i	−0.109088	+	0.0244917i
$881$	16.7984			0.565952			0.282976	−	0.959127i	$-0.408678\pi$
$881$	16.7984			0.565952			0.282976	+	0.959127i	$0.408678\pi$
$882$		0			0
$883$	−11.5279	+	35.4791i	−0.387944	+	1.19397i	0.546379	+	0.837538i	$0.316006\pi$
$883$	−11.5279	+	35.4791i	−0.387944	+	1.19397i	−0.934322	+	0.356429i	$0.883994\pi$
$884$	1.23607	+	3.80423i	0.0415735	+	0.127950i
$885$		0			0
$886$	−20.0902	+	14.5964i	−0.674942	+	0.490374i
$887$	−13.5172	−	41.6017i	−0.453864	−	1.39685i	−0.872464	−	0.488679i	$-0.837479\pi$
$887$	−13.5172	−	41.6017i	−0.453864	−	1.39685i	0.418600	−	0.908171i	$-0.362521\pi$
$888$		0			0
$889$	−11.6074	−	8.43326i	−0.389299	−	0.282843i
$890$	11.8541			0.397350
$891$		0			0
$892$	5.38197			0.180202
$893$	−0.500000	−	0.363271i	−0.0167319	−	0.0121564i
$894$		0			0
$895$	5.51722	+	16.9803i	0.184420	+	0.567587i
$896$	−1.11803	+	0.812299i	−0.0373509	+	0.0271370i
$897$		0			0
$898$	5.06231	+	15.5802i	0.168931	+	0.519917i
$899$	−14.2918	+	43.9856i	−0.476658	+	1.46700i
$900$		0			0
$901$	12.5836			0.419220
$902$	−19.2639	−	8.31475i	−0.641419	−	0.276851i
$903$		0			0
$904$	−2.85410	−	2.07363i	−0.0949260	−	0.0689678i
$905$	6.29180	−	19.3642i	0.209146	−	0.643686i
$906$		0			0
$907$	4.76393	−	3.46120i	0.158184	−	0.114927i	−0.505878	−	0.862605i	$-0.668831\pi$
$907$	4.76393	−	3.46120i	0.158184	−	0.114927i	0.664061	+	0.747678i	$0.268831\pi$
$908$	14.7082	−	10.6861i	0.488109	−	0.354632i
$909$		0			0
$910$	−0.690983	+	2.12663i	−0.0229059	+	0.0704970i
$911$	16.7082	+	12.1392i	0.553567	+	0.402190i	0.829099	−	0.559102i	$-0.188854\pi$
$911$	16.7082	+	12.1392i	0.553567	+	0.402190i	−0.275532	+	0.961292i	$0.588854\pi$
$912$		0			0
$913$	−39.4164	−	17.0130i	−1.30449	−	0.563049i
$914$	−25.8885			−0.856317
$915$		0			0
$916$	−6.32624	+	19.4702i	−0.209025	+	0.643312i
$917$	−1.30495	−	4.01623i	−0.0430933	−	0.132628i
$918$		0			0
$919$	−32.4164	+	23.5519i	−1.06932	+	0.776905i	−0.975790	−	0.218711i	$-0.929815\pi$
$919$	−32.4164	+	23.5519i	−1.06932	+	0.776905i	−0.0935290	+	0.995617i	$0.529815\pi$
$920$	0.572949	+	1.76336i	0.0188896	+	0.0581361i
$921$		0			0
$922$	−23.6525	−	17.1845i	−0.778953	−	0.565942i
$923$	−22.1803			−0.730075
$924$		0			0
$925$	1.61803			0.0532006
$926$	4.54508	+	3.30220i	0.149361	+	0.108517i
$927$		0			0
$928$	3.00000	+	9.23305i	0.0984798	+	0.303090i
$929$	17.8262	−	12.9515i	0.584860	−	0.424926i	−0.255613	−	0.966779i	$-0.582277\pi$
$929$	17.8262	−	12.9515i	0.584860	−	0.424926i	0.840473	+	0.541854i	$0.182277\pi$
$930$		0			0
$931$	−2.54508	−	7.83297i	−0.0834118	−	0.256715i
$932$	9.18034	−	28.2542i	0.300712	−	0.925496i
$933$		0			0
$934$	−24.9443			−0.816202
$935$	8.00000	−	1.79611i	0.261628	−	0.0587391i
$936$		0			0
$937$	−2.94427	−	2.13914i	−0.0961852	−	0.0698826i	0.538653	−	0.842528i	$-0.318933\pi$
$937$	−2.94427	−	2.13914i	−0.0961852	−	0.0698826i	−0.634838	+	0.772645i	$0.718933\pi$
$938$	6.05573	−	18.6376i	0.197727	−	0.608540i
$939$		0			0
$940$	−0.309017	+	0.224514i	−0.0100790	+	0.00732284i
$941$	23.4164	−	17.0130i	0.763353	−	0.554608i	−0.136584	−	0.990629i	$-0.543612\pi$
$941$	23.4164	−	17.0130i	0.763353	−	0.554608i	0.899937	+	0.436020i	$0.143612\pi$
$942$		0			0
$943$	−3.62461	+	11.1554i	−0.118034	+	0.363270i
$944$	−10.0172	−	7.27794i	−0.326033	−	0.236877i
$945$		0			0
$946$	−1.61803	+	17.2905i	−0.0526068	+	0.562164i
$947$	−59.3050			−1.92715			−0.963576	−	0.267435i	$-0.913824\pi$
$947$	−59.3050			−1.92715			−0.963576	+	0.267435i	$0.913824\pi$
$948$		0			0
$949$	3.47214	−	10.6861i	0.112710	−	0.346887i
$950$	0.500000	+	1.53884i	0.0162221	+	0.0499266i
$951$		0			0
$952$	2.76393	−	2.00811i	0.0895796	−	0.0650834i
$953$	15.2148	+	46.8263i	0.492855	+	1.51685i	0.820273	+	0.571972i	$0.193822\pi$
$953$	15.2148	+	46.8263i	0.492855	+	1.51685i	−0.327418	+	0.944880i	$0.606178\pi$
$954$		0			0
$955$	−0.236068	−	0.171513i	−0.00763898	−	0.00555004i
$956$	0.180340			0.00583261
$957$		0			0
$958$	−37.0132			−1.19584
$959$	−12.7639	−	9.27354i	−0.412169	−	0.299458i
$960$		0			0
$961$	−2.56637	−	7.89848i	−0.0827862	−	0.254790i
$962$	2.11803	−	1.53884i	0.0682882	−	0.0496142i
$963$		0			0
$964$	−7.22542	−	22.2376i	−0.232715	−	0.716224i
$965$	3.00000	−	9.23305i	0.0965734	−	0.297222i
$966$		0			0
$967$	−46.7426			−1.50314			−0.751571	−	0.659652i	$-0.770704\pi$
$967$	−46.7426			−1.50314			−0.751571	+	0.659652i	$0.770704\pi$
$968$	7.54508	+	8.00448i	0.242508	+	0.257274i
$969$		0			0
$970$	2.38197	+	1.73060i	0.0764803	+	0.0555662i
$971$	5.80902	−	17.8783i	0.186420	−	0.573742i	−0.813550	−	0.581495i	$-0.802468\pi$
$971$	5.80902	−	17.8783i	0.186420	−	0.573742i	0.999970	+	0.00775290i	$0.00246785\pi$
$972$		0			0
$973$	6.01722	−	4.37177i	0.192903	−	0.140152i
$974$	3.52786	−	2.56314i	0.113040	−	0.0821284i
$975$		0			0
$976$	2.09017	−	6.43288i	0.0669047	−	0.205912i
$977$	23.3262	+	16.9475i	0.746272	+	0.542199i	0.894669	−	0.446729i	$-0.147411\pi$
$977$	23.3262	+	16.9475i	0.746272	+	0.542199i	−0.148397	+	0.988928i	$0.547411\pi$
$978$		0			0
$979$	−20.0451	−	33.8218i	−0.640644	−	1.08095i
$980$	−5.09017			−0.162600
$981$		0			0
$982$	−4.11803	+	12.6740i	−0.131412	+	0.404444i
$983$	1.22542	+	3.77147i	0.0390850	+	0.120291i	0.968695	−	0.248253i	$-0.0798564\pi$
$983$	1.22542	+	3.77147i	0.0390850	+	0.120291i	−0.929610	+	0.368544i	$0.879856\pi$
$984$		0			0
$985$	1.11803	−	0.812299i	0.0356235	−	0.0258820i
$986$	−7.41641	−	22.8254i	−0.236187	−	0.726907i
$987$		0			0
$988$	2.11803	+	1.53884i	0.0673836	+	0.0489571i
$989$	9.70820			0.308703
$990$		0			0
$991$	−8.94427			−0.284124			−0.142062	−	0.989858i	$-0.545373\pi$
$991$	−8.94427			−0.284124			−0.142062	+	0.989858i	$0.545373\pi$
$992$	3.85410	+	2.80017i	0.122368	+	0.0889055i
$993$		0			0
$994$	5.85410	+	18.0171i	0.185681	+	0.571467i
$995$	−4.00000	+	2.90617i	−0.126809	+	0.0921318i
$996$		0			0
$997$	17.8541	+	54.9493i	0.565445	+	1.74026i	0.666625	+	0.745393i	$0.267738\pi$
$997$	17.8541	+	54.9493i	0.565445	+	1.74026i	−0.101180	+	0.994868i	$0.532262\pi$
$998$	8.24671	−	25.3808i	0.261045	−	0.803414i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.a.631.1		4
3.2	odd	2		330.2.m.d.301.1	yes	4
11.3	even	5	inner	990.2.n.a.91.1		4
33.5	odd	10		3630.2.a.bc.1.1		2
33.14	odd	10		330.2.m.d.91.1	✓	4
33.17	even	10		3630.2.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.d.91.1	✓	4	33.14	odd	10
330.2.m.d.301.1	yes	4	3.2	odd	2
990.2.n.a.91.1		4	11.3	even	5	inner
990.2.n.a.631.1		4	1.1	even	1	trivial
3630.2.a.bc.1.1		2	33.5	odd	10
3630.2.a.bi.1.2		2	33.17	even	10

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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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.427051 + 1.31433i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.427051 + 1.31433i) q^{7} +(0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(-1.69098 - 2.85317i) q^{11} +(1.30902 + 0.951057i) q^{13} +(0.427051 - 1.31433i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.00000 - 1.45309i) q^{17} +(0.500000 - 1.53884i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(-0.309017 + 3.30220i) q^{22} +1.85410 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.500000 - 1.53884i) q^{26} +(-1.11803 + 0.812299i) q^{28} +(3.00000 + 9.23305i) q^{29} +(3.85410 + 2.80017i) q^{31} +1.00000 q^{32} -2.47214 q^{34} +(-1.11803 - 0.812299i) q^{35} +(0.500000 + 1.53884i) q^{37} +(-1.30902 + 0.951057i) q^{38} +(0.309017 + 0.951057i) q^{40} +(-1.95492 + 6.01661i) q^{41} +5.23607 q^{43} +(2.19098 - 2.48990i) q^{44} +(-1.50000 - 1.08981i) q^{46} +(0.118034 - 0.363271i) q^{47} +(4.11803 - 2.99193i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.500000 + 1.53884i) q^{52} +(4.11803 + 2.99193i) q^{53} +(3.04508 + 1.31433i) q^{55} +1.38197 q^{56} +(3.00000 - 9.23305i) q^{58} +(3.82624 + 11.7759i) q^{59} +(-5.47214 + 3.97574i) q^{61} +(-1.47214 - 4.53077i) q^{62} +(-0.809017 - 0.587785i) q^{64} -1.61803 q^{65} +14.1803 q^{67} +(2.00000 + 1.45309i) q^{68} +(0.427051 + 1.31433i) q^{70} +(-11.0902 + 8.05748i) q^{71} +(-2.14590 - 6.60440i) q^{73} +(0.500000 - 1.53884i) q^{74} +1.61803 q^{76} +(3.02786 - 3.44095i) q^{77} +(-3.61803 - 2.62866i) q^{79} +(0.309017 - 0.951057i) q^{80} +(5.11803 - 3.71847i) q^{82} +(10.4721 - 7.60845i) q^{83} +(-0.763932 + 2.35114i) q^{85} +(-4.23607 - 3.07768i) q^{86} +(-3.23607 + 0.726543i) q^{88} +11.8541 q^{89} +(-0.690983 + 2.12663i) q^{91} +(0.572949 + 1.76336i) q^{92} +(-0.309017 + 0.224514i) q^{94} +(0.500000 + 1.53884i) q^{95} +(2.38197 + 1.73060i) q^{97} -5.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - q^{5} - 5 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 - q^5 - 5 * q^7 - q^8	\( 4 q - q^{2} - q^{4} - q^{5} - 5 q^{7} - q^{8} + 4 q^{10} - 9 q^{11} + 3 q^{13} - 5 q^{14} - q^{16} + 8 q^{17} + 2 q^{19} - q^{20} + q^{22} - 6 q^{23} - q^{25} - 2 q^{26} + 12 q^{29} + 2 q^{31} + 4 q^{32} + 8 q^{34} + 2 q^{37} - 3 q^{38} - q^{40} - 19 q^{41} + 12 q^{43} + 11 q^{44} - 6 q^{46} - 4 q^{47} + 12 q^{49} - q^{50} - 2 q^{52} + 12 q^{53} + q^{55} + 10 q^{56} + 12 q^{58} - 16 q^{59} - 4 q^{61} + 12 q^{62} - q^{64} - 2 q^{65} + 12 q^{67} + 8 q^{68} - 5 q^{70} - 22 q^{71} - 22 q^{73} + 2 q^{74} + 2 q^{76} + 30 q^{77} - 10 q^{79} - q^{80} + 16 q^{82} + 24 q^{83} - 12 q^{85} - 8 q^{86} - 4 q^{88} + 34 q^{89} - 5 q^{91} + 9 q^{92} + q^{94} + 2 q^{95} + 14 q^{97} + 2 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - q^5 - 5 * q^7 - q^8 + 4 * q^10 - 9 * q^11 + 3 * q^13 - 5 * q^14 - q^16 + 8 * q^17 + 2 * q^19 - q^20 + q^22 - 6 * q^23 - q^25 - 2 * q^26 + 12 * q^29 + 2 * q^31 + 4 * q^32 + 8 * q^34 + 2 * q^37 - 3 * q^38 - q^40 - 19 * q^41 + 12 * q^43 + 11 * q^44 - 6 * q^46 - 4 * q^47 + 12 * q^49 - q^50 - 2 * q^52 + 12 * q^53 + q^55 + 10 * q^56 + 12 * q^58 - 16 * q^59 - 4 * q^61 + 12 * q^62 - q^64 - 2 * q^65 + 12 * q^67 + 8 * q^68 - 5 * q^70 - 22 * q^71 - 22 * q^73 + 2 * q^74 + 2 * q^76 + 30 * q^77 - 10 * q^79 - q^80 + 16 * q^82 + 24 * q^83 - 12 * q^85 - 8 * q^86 - 4 * q^88 + 34 * q^89 - 5 * q^91 + 9 * q^92 + q^94 + 2 * q^95 + 14 * q^97 + 2 * q^98

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