LMFDB - Embedded newform 990.2.n.a.361.1

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			361.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	990.361
Dual form			990.2.n.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.92705 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.92705 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.00000 q^{10} +(-2.80902 + 1.76336i) q^{11} +(0.190983 - 0.587785i) q^{13} +(-2.92705 + 2.12663i) q^{14} +(0.309017 + 0.951057i) q^{16} +(2.00000 + 6.15537i) q^{17} +(0.500000 - 0.363271i) q^{19} +(0.309017 - 0.951057i) q^{20} +(0.809017 + 3.21644i) q^{22} -4.85410 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-0.500000 - 0.363271i) q^{26} +(1.11803 + 3.44095i) q^{28} +(3.00000 + 2.17963i) q^{29} +(-2.85410 + 8.78402i) q^{31} +1.00000 q^{32} +6.47214 q^{34} +(1.11803 - 3.44095i) q^{35} +(0.500000 + 0.363271i) q^{37} +(-0.190983 - 0.587785i) q^{38} +(-0.809017 - 0.587785i) q^{40} +(-7.54508 + 5.48183i) q^{41} +0.763932 q^{43} +(3.30902 + 0.224514i) q^{44} +(-1.50000 + 4.61653i) q^{46} +(-2.11803 + 1.53884i) q^{47} +(1.88197 + 5.79210i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{52} +(1.88197 - 5.79210i) q^{53} +(-2.54508 - 2.12663i) q^{55} +3.61803 q^{56} +(3.00000 - 2.17963i) q^{58} +(-11.8262 - 8.59226i) q^{59} +(3.47214 + 10.6861i) q^{61} +(7.47214 + 5.42882i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.618034 q^{65} -8.18034 q^{67} +(2.00000 - 6.15537i) q^{68} +(-2.92705 - 2.12663i) q^{70} +(0.0901699 + 0.277515i) q^{71} +(-8.85410 - 6.43288i) q^{73} +(0.500000 - 0.363271i) q^{74} -0.618034 q^{76} +(11.9721 + 0.812299i) q^{77} +(-1.38197 + 4.25325i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(2.88197 + 8.86978i) q^{82} +(1.52786 + 4.70228i) q^{83} +(-5.23607 + 3.80423i) q^{85} +(0.236068 - 0.726543i) q^{86} +(1.23607 - 3.07768i) q^{88} +5.14590 q^{89} +(-1.80902 + 1.31433i) q^{91} +(3.92705 + 2.85317i) q^{92} +(0.809017 + 2.48990i) q^{94} +(0.500000 + 0.363271i) q^{95} +(4.61803 - 14.2128i) q^{97} +6.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	−2.92705	−	2.12663i	−1.10632	−	0.803789i	−0.124241	−	0.992252i	$-0.539650\pi$
$7$	−2.92705	−	2.12663i	−1.10632	−	0.803789i	−0.982080	+	0.188463i	$0.939650\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$	1.00000			0.316228
$11$	−2.80902	+	1.76336i	−0.846950	+	0.531672i
$11$	−2.80902	+	1.76336i	−0.846950	+	0.531672i
$12$		0			0
$13$	0.190983	−	0.587785i	0.0529692	−	0.163022i	−0.921073	−	0.389391i	$-0.872685\pi$
$13$	0.190983	−	0.587785i	0.0529692	−	0.163022i	0.974042	+	0.226369i	$0.0726855\pi$
$14$	−2.92705	+	2.12663i	−0.782287	+	0.568365i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.00000	+	6.15537i	0.485071	+	1.49290i	0.831878	+	0.554959i	$0.187266\pi$
$17$	2.00000	+	6.15537i	0.485071	+	1.49290i	−0.346806	+	0.937937i	$0.612734\pi$
$18$		0			0
$19$	0.500000	−	0.363271i	0.114708	−	0.0833401i	−0.528952	−	0.848651i	$-0.677415\pi$
$19$	0.500000	−	0.363271i	0.114708	−	0.0833401i	0.643660	+	0.765311i	$0.277415\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$		0			0
$22$	0.809017	+	3.21644i	0.172483	+	0.685747i
$23$	−4.85410			−1.01215			−0.506075	−	0.862489i	$-0.668904\pi$
$23$	−4.85410			−1.01215			−0.506075	+	0.862489i	$0.668904\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−0.500000	−	0.363271i	−0.0980581	−	0.0712434i
$27$		0			0
$28$	1.11803	+	3.44095i	0.211289	+	0.650279i
$29$	3.00000	+	2.17963i	0.557086	+	0.404747i	0.830391	−	0.557181i	$-0.188117\pi$
$29$	3.00000	+	2.17963i	0.557086	+	0.404747i	−0.273305	+	0.961927i	$0.588117\pi$
$30$		0			0
$31$	−2.85410	+	8.78402i	−0.512612	+	1.57766i	0.274974	+	0.961452i	$0.411331\pi$
$31$	−2.85410	+	8.78402i	−0.512612	+	1.57766i	−0.787586	+	0.616205i	$0.788669\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	6.47214			1.10996
$35$	1.11803	−	3.44095i	0.188982	−	0.581628i
$36$		0			0
$37$	0.500000	+	0.363271i	0.0821995	+	0.0597214i	0.628126	−	0.778112i	$-0.283822\pi$
$37$	0.500000	+	0.363271i	0.0821995	+	0.0597214i	−0.545927	+	0.837833i	$0.683822\pi$
$38$	−0.190983	−	0.587785i	−0.0309815	−	0.0953514i
$39$		0			0
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	−7.54508	+	5.48183i	−1.17834	+	0.856117i	−0.991984	−	0.126364i	$-0.959669\pi$
$41$	−7.54508	+	5.48183i	−1.17834	+	0.856117i	−0.186360	+	0.982481i	$0.559669\pi$
$42$		0			0
$43$	0.763932			0.116499			0.0582493	−	0.998302i	$-0.481448\pi$
$43$	0.763932			0.116499			0.0582493	+	0.998302i	$0.481448\pi$
$44$	3.30902	+	0.224514i	0.498853	+	0.0338468i
$45$		0			0
$46$	−1.50000	+	4.61653i	−0.221163	+	0.680670i
$47$	−2.11803	+	1.53884i	−0.308947	+	0.224463i	−0.731445	−	0.681901i	$-0.761154\pi$
$47$	−2.11803	+	1.53884i	−0.308947	+	0.224463i	0.422498	+	0.906364i	$0.361154\pi$
$48$		0			0
$49$	1.88197	+	5.79210i	0.268852	+	0.827442i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$		0			0
$52$	−0.500000	+	0.363271i	−0.0693375	+	0.0503767i
$53$	1.88197	−	5.79210i	0.258508	−	0.795606i	−0.734610	−	0.678489i	$-0.762635\pi$
$53$	1.88197	−	5.79210i	0.258508	−	0.795606i	0.993118	−	0.117116i	$-0.0373650\pi$
$54$		0			0
$55$	−2.54508	−	2.12663i	−0.343179	−	0.286754i
$56$	3.61803			0.483480
$57$		0			0
$58$	3.00000	−	2.17963i	0.393919	−	0.286199i
$59$	−11.8262	−	8.59226i	−1.53965	−	1.11862i	−0.950558	−	0.310548i	$-0.899487\pi$
$59$	−11.8262	−	8.59226i	−1.53965	−	1.11862i	−0.589087	−	0.808069i	$-0.700513\pi$
$60$		0			0
$61$	3.47214	+	10.6861i	0.444561	+	1.36822i	0.882964	+	0.469441i	$0.155544\pi$
$61$	3.47214	+	10.6861i	0.444561	+	1.36822i	−0.438403	+	0.898779i	$0.644456\pi$
$62$	7.47214	+	5.42882i	0.948962	+	0.689461i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.618034			0.0766577
$66$		0			0
$67$	−8.18034			−0.999388			−0.499694	−	0.866202i	$-0.666554\pi$
$67$	−8.18034			−0.999388			−0.499694	+	0.866202i	$0.666554\pi$
$68$	2.00000	−	6.15537i	0.242536	−	0.746448i
$69$		0			0
$70$	−2.92705	−	2.12663i	−0.349850	−	0.254181i
$71$	0.0901699	+	0.277515i	0.0107012	+	0.0329349i	0.956265	−	0.292503i	$-0.0944882\pi$
$71$	0.0901699	+	0.277515i	0.0107012	+	0.0329349i	−0.945563	+	0.325438i	$0.894488\pi$
$72$		0			0
$73$	−8.85410	−	6.43288i	−1.03629	−	0.752912i	−0.0667355	−	0.997771i	$-0.521258\pi$
$73$	−8.85410	−	6.43288i	−1.03629	−	0.752912i	−0.969559	+	0.244859i	$0.921258\pi$
$74$	0.500000	−	0.363271i	0.0581238	−	0.0422294i
$75$		0			0
$76$	−0.618034			−0.0708934
$77$	11.9721	+	0.812299i	1.36435	+	0.0925701i
$78$		0			0
$79$	−1.38197	+	4.25325i	−0.155483	+	0.478528i	−0.998210	−	0.0598139i	$-0.980949\pi$
$79$	−1.38197	+	4.25325i	−0.155483	+	0.478528i	0.842726	+	0.538342i	$0.180949\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$		0			0
$82$	2.88197	+	8.86978i	0.318260	+	0.979503i
$83$	1.52786	+	4.70228i	0.167705	+	0.516143i	0.999225	−	0.0393515i	$-0.0125292\pi$
$83$	1.52786	+	4.70228i	0.167705	+	0.516143i	−0.831521	+	0.555494i	$0.812529\pi$
$84$		0			0
$85$	−5.23607	+	3.80423i	−0.567931	+	0.412626i
$86$	0.236068	−	0.726543i	0.0254559	−	0.0783451i
$87$		0			0
$88$	1.23607	−	3.07768i	0.131765	−	0.328082i
$89$	5.14590			0.545464			0.272732	−	0.962090i	$-0.412073\pi$
$89$	5.14590			0.545464			0.272732	+	0.962090i	$0.412073\pi$
$90$		0			0
$91$	−1.80902	+	1.31433i	−0.189637	+	0.137779i
$92$	3.92705	+	2.85317i	0.409423	+	0.297463i
$93$		0			0
$94$	0.809017	+	2.48990i	0.0834437	+	0.256813i
$95$	0.500000	+	0.363271i	0.0512989	+	0.0372708i
$96$		0			0
$97$	4.61803	−	14.2128i	0.468890	−	1.44310i	−0.385133	−	0.922861i	$-0.625844\pi$
$97$	4.61803	−	14.2128i	0.468890	−	1.44310i	0.854023	−	0.520235i	$-0.174156\pi$
$98$	6.09017			0.615200
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.23607	+	3.80423i	−0.122993	+	0.378535i	−0.993530	−	0.113569i	$-0.963772\pi$
$101$	−1.23607	+	3.80423i	−0.122993	+	0.378535i	0.870537	+	0.492103i	$0.163772\pi$
$102$		0			0
$103$	7.97214	+	5.79210i	0.785518	+	0.570712i	0.906630	−	0.421927i	$-0.138646\pi$
$103$	7.97214	+	5.79210i	0.785518	+	0.570712i	−0.121112	+	0.992639i	$0.538646\pi$
$104$	0.190983	+	0.587785i	0.0187274	+	0.0576371i
$105$		0			0
$106$	−4.92705	−	3.57971i	−0.478557	−	0.347692i
$107$	14.4721	−	10.5146i	1.39907	−	1.01649i	0.404274	−	0.914638i	$-0.367524\pi$
$107$	14.4721	−	10.5146i	1.39907	−	1.01649i	0.994800	−	0.101849i	$-0.0324759\pi$
$108$		0			0
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	−2.80902	+	1.76336i	−0.267829	+	0.168129i
$111$		0			0
$112$	1.11803	−	3.44095i	0.105644	−	0.325140i
$113$	−10.0902	+	7.33094i	−0.949203	+	0.689637i	−0.950618	−	0.310362i	$-0.899550\pi$
$113$	−10.0902	+	7.33094i	−0.949203	+	0.689637i	0.00141497	+	0.999999i	$0.499550\pi$
$114$		0			0
$115$	−1.50000	−	4.61653i	−0.139876	−	0.430493i
$116$	−1.14590	−	3.52671i	−0.106394	−	0.327447i
$117$		0			0
$118$	−11.8262	+	8.59226i	−1.08869	+	0.790982i
$119$	7.23607	−	22.2703i	0.663329	−	2.04152i
$120$		0			0
$121$	4.78115	−	9.90659i	0.434650	−	0.900599i
$122$	11.2361			1.01727
$123$		0			0
$124$	7.47214	−	5.42882i	0.671018	−	0.487523i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	3.89919	+	12.0005i	0.345997	+	1.06487i	0.961048	+	0.276382i	$0.0891354\pi$
$127$	3.89919	+	12.0005i	0.345997	+	1.06487i	−0.615051	+	0.788487i	$0.710865\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	0.190983	−	0.587785i	0.0167503	−	0.0515522i
$131$	−20.9443			−1.82991			−0.914955	−	0.403556i	$-0.867774\pi$
$131$	−20.9443			−1.82991			−0.914955	+	0.403556i	$0.867774\pi$
$132$		0			0
$133$	−2.23607			−0.193892
$134$	−2.52786	+	7.77997i	−0.218374	+	0.672087i
$135$		0			0
$136$	−5.23607	−	3.80423i	−0.448989	−	0.326210i
$137$	−4.76393	−	14.6619i	−0.407010	−	1.25265i	−0.919205	−	0.393779i	$-0.871167\pi$
$137$	−4.76393	−	14.6619i	−0.407010	−	1.25265i	0.512195	−	0.858869i	$-0.328833\pi$
$138$		0			0
$139$	6.16312	+	4.47777i	0.522749	+	0.379799i	0.817638	−	0.575732i	$-0.195283\pi$
$139$	6.16312	+	4.47777i	0.522749	+	0.379799i	−0.294890	+	0.955531i	$0.595283\pi$
$140$	−2.92705	+	2.12663i	−0.247381	+	0.179733i
$141$		0			0
$142$	0.291796			0.0244870
$143$	0.500000	+	1.98787i	0.0418121	+	0.166234i
$144$		0			0
$145$	−1.14590	+	3.52671i	−0.0951617	+	0.292877i
$146$	−8.85410	+	6.43288i	−0.732771	+	0.532389i
$147$		0			0
$148$	−0.190983	−	0.587785i	−0.0156987	−	0.0483157i
$149$	2.76393	+	8.50651i	0.226430	+	0.696880i	0.998143	+	0.0609095i	$0.0194001\pi$
$149$	2.76393	+	8.50651i	0.226430	+	0.696880i	−0.771713	+	0.635971i	$0.780600\pi$
$150$		0			0
$151$	10.0902	−	7.33094i	0.821126	−	0.596583i	−0.0959085	−	0.995390i	$-0.530576\pi$
$151$	10.0902	−	7.33094i	0.821126	−	0.596583i	0.917035	+	0.398807i	$0.130576\pi$
$152$	−0.190983	+	0.587785i	−0.0154908	+	0.0476757i
$153$		0			0
$154$	4.47214	−	11.1352i	0.360375	−	0.897297i
$155$	−9.23607			−0.741859
$156$		0			0
$157$	4.54508	−	3.30220i	0.362737	−	0.263544i	−0.391456	−	0.920197i	$-0.628028\pi$
$157$	4.54508	−	3.30220i	0.362737	−	0.263544i	0.754193	+	0.656653i	$0.228028\pi$
$158$	3.61803	+	2.62866i	0.287835	+	0.209125i
$159$		0			0
$160$	0.309017	+	0.951057i	0.0244299	+	0.0751876i
$161$	14.2082	+	10.3229i	1.11976	+	0.813556i
$162$		0			0
$163$	5.52786	−	17.0130i	0.432976	−	1.33256i	−0.462171	−	0.886791i	$-0.652929\pi$
$163$	5.52786	−	17.0130i	0.432976	−	1.33256i	0.895147	−	0.445771i	$-0.147071\pi$
$164$	9.32624			0.728257
$165$		0			0
$166$	4.94427			0.383750
$167$	3.57295	−	10.9964i	0.276483	−	0.850927i	−0.712340	−	0.701834i	$-0.752365\pi$
$167$	3.57295	−	10.9964i	0.276483	−	0.850927i	0.988823	−	0.149093i	$-0.0476354\pi$
$168$		0			0
$169$	10.2082	+	7.41669i	0.785246	+	0.570515i
$170$	2.00000	+	6.15537i	0.153393	+	0.472095i
$171$		0			0
$172$	−0.618034	−	0.449028i	−0.0471246	−	0.0342381i
$173$	−19.8713	+	14.4374i	−1.51079	+	1.09765i	−0.544963	+	0.838460i	$0.683456\pi$
$173$	−19.8713	+	14.4374i	−1.51079	+	1.09765i	−0.965826	+	0.259192i	$0.916544\pi$
$174$		0			0
$175$	3.61803			0.273498
$176$	−2.54508	−	2.12663i	−0.191843	−	0.160301i
$177$		0			0
$178$	1.59017	−	4.89404i	0.119188	−	0.366824i
$179$	−9.01722	+	6.55139i	−0.673979	+	0.489674i	−0.871355	−	0.490654i	$-0.836758\pi$
$179$	−9.01722	+	6.55139i	−0.673979	+	0.489674i	0.197376	+	0.980328i	$0.436758\pi$
$180$		0			0
$181$	−7.52786	−	23.1684i	−0.559542	−	1.72209i	−0.683637	−	0.729822i	$-0.739603\pi$
$181$	−7.52786	−	23.1684i	−0.559542	−	1.72209i	0.124095	−	0.992270i	$-0.460397\pi$
$182$	0.690983	+	2.12663i	0.0512191	+	0.157636i
$183$		0			0
$184$	3.92705	−	2.85317i	0.289506	−	0.210338i
$185$	−0.190983	+	0.587785i	−0.0140413	+	0.0432148i
$186$		0			0
$187$	−16.4721	−	13.7638i	−1.20456	−	1.00651i
$188$	2.61803			0.190940
$189$		0			0
$190$	0.500000	−	0.363271i	0.0362738	−	0.0263545i
$191$	−11.0902	−	8.05748i	−0.802457	−	0.583019i	0.109177	−	0.994022i	$-0.465178\pi$
$191$	−11.0902	−	8.05748i	−0.802457	−	0.583019i	−0.911634	+	0.411004i	$0.865178\pi$
$192$		0			0
$193$	−1.14590	−	3.52671i	−0.0824835	−	0.253858i	0.901307	−	0.433182i	$-0.142609\pi$
$193$	−1.14590	−	3.52671i	−0.0824835	−	0.253858i	−0.983790	+	0.179323i	$0.942609\pi$
$194$	−12.0902	−	8.78402i	−0.868024	−	0.630656i
$195$		0			0
$196$	1.88197	−	5.79210i	0.134426	−	0.413721i
$197$	−3.61803			−0.257774			−0.128887	−	0.991659i	$-0.541140\pi$
$197$	−3.61803			−0.257774			−0.128887	+	0.991659i	$0.541140\pi$
$198$		0			0
$199$	−12.9443			−0.917595			−0.458798	−	0.888541i	$-0.651720\pi$
$199$	−12.9443			−0.917595			−0.458798	+	0.888541i	$0.651720\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$		0			0
$202$	3.23607	+	2.35114i	0.227689	+	0.165426i
$203$	−4.14590	−	12.7598i	−0.290985	−	0.895560i
$204$		0			0
$205$	−7.54508	−	5.48183i	−0.526972	−	0.382867i
$206$	7.97214	−	5.79210i	0.555445	−	0.403554i
$207$		0			0
$208$	0.618034			0.0428529
$209$	−0.763932	+	1.90211i	−0.0528423	+	0.131572i
$210$		0			0
$211$	−7.23607	+	22.2703i	−0.498151	+	1.53315i	0.313836	+	0.949477i	$0.398386\pi$
$211$	−7.23607	+	22.2703i	−0.498151	+	1.53315i	−0.811987	+	0.583675i	$0.801614\pi$
$212$	−4.92705	+	3.57971i	−0.338391	+	0.245856i
$213$		0			0
$214$	−5.52786	−	17.0130i	−0.377877	−	1.16299i
$215$	0.236068	+	0.726543i	0.0160997	+	0.0495498i
$216$		0			0
$217$	27.0344	−	19.6417i	1.83522	−	1.33336i
$218$	1.23607	−	3.80423i	0.0837171	−	0.257655i
$219$		0			0
$220$	0.809017	+	3.21644i	0.0545439	+	0.216852i
$221$	4.00000			0.269069
$222$		0			0
$223$	−6.16312	+	4.47777i	−0.412713	+	0.299854i	−0.774699	−	0.632330i	$-0.782099\pi$
$223$	−6.16312	+	4.47777i	−0.412713	+	0.299854i	0.361986	+	0.932183i	$0.382099\pi$
$224$	−2.92705	−	2.12663i	−0.195572	−	0.142091i
$225$		0			0
$226$	3.85410	+	11.8617i	0.256371	+	0.789029i
$227$	−3.38197	−	2.45714i	−0.224469	−	0.163086i	0.469867	−	0.882737i	$-0.344302\pi$
$227$	−3.38197	−	2.45714i	−0.224469	−	0.163086i	−0.694336	+	0.719651i	$0.744302\pi$
$228$		0			0
$229$	−3.56231	+	10.9637i	−0.235404	+	0.724498i	0.761664	+	0.647972i	$0.224383\pi$
$229$	−3.56231	+	10.9637i	−0.235404	+	0.724498i	−0.997068	+	0.0765260i	$0.975617\pi$
$230$	−4.85410			−0.320070
$231$		0			0
$232$	−3.70820			−0.243456
$233$	5.03444	−	15.4944i	0.329817	−	1.01507i	−0.639402	−	0.768873i	$-0.720818\pi$
$233$	5.03444	−	15.4944i	0.329817	−	1.01507i	0.969219	−	0.246200i	$-0.0791821\pi$
$234$		0			0
$235$	−2.11803	−	1.53884i	−0.138165	−	0.100383i
$236$	4.51722	+	13.9026i	0.294046	+	0.904981i
$237$		0			0
$238$	−18.9443	−	13.7638i	−1.22797	−	0.892176i
$239$	17.9443	−	13.0373i	1.16072	−	0.843311i	0.170850	−	0.985297i	$-0.445349\pi$
$239$	17.9443	−	13.0373i	1.16072	−	0.843311i	0.989869	+	0.141986i	$0.0453487\pi$
$240$		0			0
$241$	−25.6180			−1.65020			−0.825101	−	0.564985i	$-0.808882\pi$
$241$	−25.6180			−1.65020			−0.825101	+	0.564985i	$0.808882\pi$
$242$	−7.94427	−	7.60845i	−0.510677	−	0.489090i
$243$		0			0
$244$	3.47214	−	10.6861i	0.222281	−	0.684110i
$245$	−4.92705	+	3.57971i	−0.314778	+	0.228699i
$246$		0			0
$247$	−0.118034	−	0.363271i	−0.00751032	−	0.0231144i
$248$	−2.85410	−	8.78402i	−0.181236	−	0.557786i
$249$		0			0
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−3.55573	+	10.9434i	−0.224436	+	0.690742i	0.773913	+	0.633292i	$0.218297\pi$
$251$	−3.55573	+	10.9434i	−0.224436	+	0.690742i	−0.998348	+	0.0574495i	$0.981703\pi$
$252$		0			0
$253$	13.6353	−	8.55951i	0.857241	−	0.538132i
$254$	12.6180			0.791726
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−4.09017	−	2.97168i	−0.255138	−	0.185368i	0.452863	−	0.891580i	$-0.350403\pi$
$257$	−4.09017	−	2.97168i	−0.255138	−	0.185368i	−0.708001	+	0.706212i	$0.750403\pi$
$258$		0			0
$259$	−0.690983	−	2.12663i	−0.0429356	−	0.132142i
$260$	−0.500000	−	0.363271i	−0.0310087	−	0.0225291i
$261$		0			0
$262$	−6.47214	+	19.9192i	−0.399850	+	1.23061i
$263$	8.14590			0.502298			0.251149	−	0.967948i	$-0.419192\pi$
$263$	8.14590			0.502298			0.251149	+	0.967948i	$0.419192\pi$
$264$		0			0
$265$	6.09017			0.374116
$266$	−0.690983	+	2.12663i	−0.0423669	+	0.130392i
$267$		0			0
$268$	6.61803	+	4.80828i	0.404261	+	0.293713i
$269$	7.65248	+	23.5519i	0.466580	+	1.43598i	0.856985	+	0.515341i	$0.172335\pi$
$269$	7.65248	+	23.5519i	0.466580	+	1.43598i	−0.390405	+	0.920643i	$0.627665\pi$
$270$		0			0
$271$	−0.527864	−	0.383516i	−0.0320655	−	0.0232969i	0.571637	−	0.820507i	$-0.306309\pi$
$271$	−0.527864	−	0.383516i	−0.0320655	−	0.0232969i	−0.603703	+	0.797210i	$0.706309\pi$
$272$	−5.23607	+	3.80423i	−0.317483	+	0.230665i
$273$		0			0
$274$	−15.4164			−0.931339
$275$	1.23607	−	3.07768i	0.0745377	−	0.185591i
$276$		0			0
$277$	−2.55573	+	7.86572i	−0.153559	+	0.472605i	−0.998012	−	0.0630239i	$-0.979926\pi$
$277$	−2.55573	+	7.86572i	−0.153559	+	0.472605i	0.844453	+	0.535629i	$0.179926\pi$
$278$	6.16312	−	4.47777i	0.369639	−	0.268559i
$279$		0			0
$280$	1.11803	+	3.44095i	0.0668153	+	0.205636i
$281$	−2.43769	−	7.50245i	−0.145421	−	0.447559i	0.851644	−	0.524120i	$-0.175606\pi$
$281$	−2.43769	−	7.50245i	−0.145421	−	0.447559i	−0.997065	+	0.0765616i	$0.975606\pi$
$282$		0			0
$283$	−3.00000	+	2.17963i	−0.178331	+	0.129565i	−0.673370	−	0.739306i	$-0.735154\pi$
$283$	−3.00000	+	2.17963i	−0.178331	+	0.129565i	0.495039	+	0.868871i	$0.335154\pi$
$284$	0.0901699	−	0.277515i	0.00535060	−	0.0164675i
$285$		0			0
$286$	2.04508	+	0.138757i	0.120928	+	0.00820489i
$287$	33.7426			1.99177
$288$		0			0
$289$	−20.1353	+	14.6291i	−1.18443	+	0.860536i
$290$	3.00000	+	2.17963i	0.176166	+	0.127992i
$291$		0			0
$292$	3.38197	+	10.4086i	0.197915	+	0.609118i
$293$	8.92705	+	6.48588i	0.521524	+	0.378909i	0.817178	−	0.576386i	$-0.195537\pi$
$293$	8.92705	+	6.48588i	0.521524	+	0.378909i	−0.295654	+	0.955295i	$0.595537\pi$
$294$		0			0
$295$	4.51722	−	13.9026i	0.263003	−	0.809439i
$296$	−0.618034			−0.0359225
$297$		0			0
$298$	8.94427			0.518128
$299$	−0.927051	+	2.85317i	−0.0536127	+	0.165003i
$300$		0			0
$301$	−2.23607	−	1.62460i	−0.128885	−	0.0936403i
$302$	−3.85410	−	11.8617i	−0.221779	−	0.682564i
$303$		0			0
$304$	0.500000	+	0.363271i	0.0286770	+	0.0208350i
$305$	−9.09017	+	6.60440i	−0.520502	+	0.378167i
$306$		0			0
$307$	26.8328			1.53143			0.765715	−	0.643180i	$-0.222385\pi$
$307$	26.8328			1.53143			0.765715	+	0.643180i	$0.222385\pi$
$308$	−9.20820	−	7.69421i	−0.524686	−	0.438418i
$309$		0			0
$310$	−2.85410	+	8.78402i	−0.162102	+	0.498899i
$311$	−22.5623	+	16.3925i	−1.27939	+	0.929532i	−0.999534	−	0.0305099i	$-0.990287\pi$
$311$	−22.5623	+	16.3925i	−1.27939	+	0.929532i	−0.279857	+	0.960042i	$0.590287\pi$
$312$		0			0
$313$	1.76393	+	5.42882i	0.0997033	+	0.306855i	0.988451	−	0.151542i	$-0.0484238\pi$
$313$	1.76393	+	5.42882i	0.0997033	+	0.306855i	−0.888748	+	0.458397i	$0.848424\pi$
$314$	−1.73607	−	5.34307i	−0.0979720	−	0.301527i
$315$		0			0
$316$	3.61803	−	2.62866i	0.203530	−	0.147873i
$317$	−3.37132	+	10.3759i	−0.189352	+	0.582767i	−0.999996	−	0.00277297i	$-0.999117\pi$
$317$	−3.37132	+	10.3759i	−0.189352	+	0.582767i	0.810644	+	0.585540i	$0.199117\pi$
$318$		0			0
$319$	−12.2705	−	0.832544i	−0.687017	−	0.0466135i
$320$	1.00000			0.0559017
$321$		0			0
$322$	14.2082	−	10.3229i	0.791792	−	0.575271i
$323$	3.23607	+	2.35114i	0.180060	+	0.130821i
$324$		0			0
$325$	0.190983	+	0.587785i	0.0105938	+	0.0326045i
$326$	−14.4721	−	10.5146i	−0.801537	−	0.582351i
$327$		0			0
$328$	2.88197	−	8.86978i	0.159130	−	0.489752i
$329$	9.47214			0.522216
$330$		0			0
$331$	7.67376			0.421788			0.210894	−	0.977509i	$-0.432362\pi$
$331$	7.67376			0.421788			0.210894	+	0.977509i	$0.432362\pi$
$332$	1.52786	−	4.70228i	0.0838524	−	0.258071i
$333$		0			0
$334$	−9.35410	−	6.79615i	−0.511834	−	0.371869i
$335$	−2.52786	−	7.77997i	−0.138112	−	0.425065i
$336$		0			0
$337$	16.1803	+	11.7557i	0.881399	+	0.640374i	0.933621	−	0.358261i	$-0.116630\pi$
$337$	16.1803	+	11.7557i	0.881399	+	0.640374i	−0.0522220	+	0.998635i	$0.516630\pi$
$338$	10.2082	−	7.41669i	0.555253	−	0.403415i
$339$		0			0
$340$	6.47214			0.351001
$341$	−7.47214	−	29.7073i	−0.404639	−	1.60874i
$342$		0			0
$343$	−1.01722	+	3.13068i	−0.0549248	+	0.169041i
$344$	−0.618034	+	0.449028i	−0.0333222	+	0.0242100i
$345$		0			0
$346$	7.59017	+	23.3601i	0.408050	+	1.25585i
$347$	−1.18034	−	3.63271i	−0.0633640	−	0.195014i	0.914363	−	0.404896i	$-0.132692\pi$
$347$	−1.18034	−	3.63271i	−0.0633640	−	0.195014i	−0.977727	+	0.209881i	$0.932692\pi$
$348$		0			0
$349$	−8.09017	+	5.87785i	−0.433057	+	0.314634i	−0.782870	−	0.622185i	$-0.786245\pi$
$349$	−8.09017	+	5.87785i	−0.433057	+	0.314634i	0.349813	+	0.936819i	$0.386245\pi$
$350$	1.11803	−	3.44095i	0.0597614	−	0.183927i
$351$		0			0
$352$	−2.80902	+	1.76336i	−0.149721	+	0.0939872i
$353$	24.6525			1.31212			0.656059	−	0.754709i	$-0.272222\pi$
$353$	24.6525			1.31212			0.656059	+	0.754709i	$0.272222\pi$
$354$		0			0
$355$	−0.236068	+	0.171513i	−0.0125292	+	0.00910299i
$356$	−4.16312	−	3.02468i	−0.220645	−	0.160308i
$357$		0			0
$358$	3.44427	+	10.6004i	0.182035	+	0.560247i
$359$	20.4164	+	14.8334i	1.07754	+	0.782876i	0.977252	−	0.212082i	$-0.0680245\pi$
$359$	20.4164	+	14.8334i	1.07754	+	0.782876i	0.100285	+	0.994959i	$0.468025\pi$
$360$		0			0
$361$	−5.75329	+	17.7068i	−0.302805	+	0.931937i
$362$	−24.3607			−1.28037
$363$		0			0
$364$	2.23607			0.117202
$365$	3.38197	−	10.4086i	0.177020	−	0.544812i
$366$		0			0
$367$	−6.76393	−	4.91428i	−0.353074	−	0.256524i	0.397083	−	0.917783i	$-0.370022\pi$
$367$	−6.76393	−	4.91428i	−0.353074	−	0.256524i	−0.750158	+	0.661259i	$0.770022\pi$
$368$	−1.50000	−	4.61653i	−0.0781929	−	0.240653i
$369$		0			0
$370$	0.500000	+	0.363271i	0.0259938	+	0.0188856i
$371$	−17.8262	+	12.9515i	−0.925492	+	0.672409i
$372$		0			0
$373$	−13.8541			−0.717338			−0.358669	−	0.933465i	$-0.616769\pi$
$373$	−13.8541			−0.717338			−0.358669	+	0.933465i	$0.616769\pi$
$374$	−18.1803	+	11.4127i	−0.940083	+	0.590136i
$375$		0			0
$376$	0.809017	−	2.48990i	0.0417219	−	0.128407i
$377$	1.85410	−	1.34708i	0.0954911	−	0.0693784i
$378$		0			0
$379$	−10.1180	−	31.1401i	−0.519728	−	1.59956i	−0.774510	−	0.632561i	$-0.782004\pi$
$379$	−10.1180	−	31.1401i	−0.519728	−	1.59956i	0.254782	−	0.966999i	$-0.417996\pi$
$380$	−0.190983	−	0.587785i	−0.00979722	−	0.0301527i
$381$		0			0
$382$	−11.0902	+	8.05748i	−0.567422	+	0.412257i
$383$	8.79180	−	27.0584i	0.449240	−	1.38262i	−0.428527	−	0.903529i	$-0.640967\pi$
$383$	8.79180	−	27.0584i	0.449240	−	1.38262i	0.877766	−	0.479089i	$-0.159033\pi$
$384$		0			0
$385$	2.92705	+	11.6372i	0.149176	+	0.593086i
$386$	−3.70820			−0.188743
$387$		0			0
$388$	−12.0902	+	8.78402i	−0.613785	+	0.445941i
$389$	2.85410	+	2.07363i	0.144709	+	0.105137i	0.657784	−	0.753206i	$-0.271494\pi$
$389$	2.85410	+	2.07363i	0.144709	+	0.105137i	−0.513075	+	0.858344i	$0.671494\pi$
$390$		0			0
$391$	−9.70820	−	29.8788i	−0.490965	−	1.51103i
$392$	−4.92705	−	3.57971i	−0.248854	−	0.180803i
$393$		0			0
$394$	−1.11803	+	3.44095i	−0.0563257	+	0.173353i
$395$	−4.47214			−0.225018
$396$		0			0
$397$	12.6738			0.636078			0.318039	−	0.948078i	$-0.396976\pi$
$397$	12.6738			0.636078			0.318039	+	0.948078i	$0.396976\pi$
$398$	−4.00000	+	12.3107i	−0.200502	+	0.617081i
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	0.517221	+	1.59184i	0.0258288	+	0.0794928i	0.963140	−	0.269001i	$-0.0866934\pi$
$401$	0.517221	+	1.59184i	0.0258288	+	0.0794928i	−0.937311	+	0.348493i	$0.886693\pi$
$402$		0			0
$403$	4.61803	+	3.35520i	0.230041	+	0.167134i
$404$	3.23607	−	2.35114i	0.161000	−	0.116974i
$405$		0			0
$406$	−13.4164			−0.665845
$407$	−2.04508	−	0.138757i	−0.101371	−	0.00687794i
$408$		0			0
$409$	4.39261	−	13.5191i	0.217201	−	0.668475i	−0.781790	−	0.623542i	$-0.785693\pi$
$409$	4.39261	−	13.5191i	0.217201	−	0.668475i	0.998990	−	0.0449321i	$-0.0143071\pi$
$410$	−7.54508	+	5.48183i	−0.372625	+	0.270728i
$411$		0			0
$412$	−3.04508	−	9.37181i	−0.150021	−	0.461716i
$413$	16.3435	+	50.3000i	0.804209	+	2.47510i
$414$		0			0
$415$	−4.00000	+	2.90617i	−0.196352	+	0.142658i
$416$	0.190983	−	0.587785i	0.00936371	−	0.0288185i
$417$		0			0
$418$	1.57295	+	1.31433i	0.0769355	+	0.0642859i
$419$	11.2016			0.547235			0.273618	−	0.961839i	$-0.411780\pi$
$419$	11.2016			0.547235			0.273618	+	0.961839i	$0.411780\pi$
$420$		0			0
$421$	−21.7984	+	15.8374i	−1.06239	+	0.771870i	−0.974529	−	0.224263i	$-0.928003\pi$
$421$	−21.7984	+	15.8374i	−1.06239	+	0.771870i	−0.0878591	+	0.996133i	$0.528003\pi$
$422$	18.9443	+	13.7638i	0.922193	+	0.670012i
$423$		0			0
$424$	1.88197	+	5.79210i	0.0913963	+	0.281289i
$425$	−5.23607	−	3.80423i	−0.253987	−	0.184532i
$426$		0			0
$427$	12.5623	−	38.6628i	0.607933	−	1.87102i
$428$	−17.8885			−0.864675
$429$		0			0
$430$	0.763932			0.0368401
$431$	−0.673762	+	2.07363i	−0.0324540	+	0.0998831i	−0.965971	−	0.258649i	$-0.916723\pi$
$431$	−0.673762	+	2.07363i	−0.0324540	+	0.0998831i	0.933517	+	0.358532i	$0.116723\pi$
$432$		0			0
$433$	26.7984	+	19.4702i	1.28785	+	0.935676i	0.999760	−	0.0219278i	$-0.00698040\pi$
$433$	26.7984	+	19.4702i	1.28785	+	0.935676i	0.288088	+	0.957604i	$0.406980\pi$
$434$	−10.3262	−	31.7809i	−0.495675	−	1.52553i
$435$		0			0
$436$	−3.23607	−	2.35114i	−0.154980	−	0.112599i
$437$	−2.42705	+	1.76336i	−0.116102	+	0.0843527i
$438$		0			0
$439$	20.1803			0.963155			0.481578	−	0.876403i	$-0.340064\pi$
$439$	20.1803			0.963155			0.481578	+	0.876403i	$0.340064\pi$
$440$	3.30902	+	0.224514i	0.157751	+	0.0107033i
$441$		0			0
$442$	1.23607	−	3.80423i	0.0587938	−	0.180949i
$443$	23.3262	−	16.9475i	1.10826	−	0.805200i	0.125874	−	0.992046i	$-0.459827\pi$
$443$	23.3262	−	16.9475i	1.10826	−	0.805200i	0.982389	+	0.186846i	$0.0598266\pi$
$444$		0			0
$445$	1.59017	+	4.89404i	0.0753813	+	0.232000i
$446$	2.35410	+	7.24518i	0.111470	+	0.343069i
$447$		0			0
$448$	−2.92705	+	2.12663i	−0.138290	+	0.100474i
$449$	5.75329	−	17.7068i	0.271514	−	0.835636i	−0.718606	−	0.695417i	$-0.755220\pi$
$449$	5.75329	−	17.7068i	0.271514	−	0.835636i	0.990121	−	0.140218i	$-0.0447805\pi$
$450$		0			0
$451$	11.5279	−	28.7032i	0.542826	−	1.35158i
$452$	12.4721			0.586640
$453$		0			0
$454$	−3.38197	+	2.45714i	−0.158724	+	0.115319i
$455$	−1.80902	−	1.31433i	−0.0848080	−	0.0616166i
$456$		0			0
$457$	3.05573	+	9.40456i	0.142941	+	0.439927i	0.996740	−	0.0806750i	$-0.0257076\pi$
$457$	3.05573	+	9.40456i	0.142941	+	0.439927i	−0.853800	+	0.520602i	$0.825708\pi$
$458$	9.32624	+	6.77591i	0.435786	+	0.316617i
$459$		0			0
$460$	−1.50000	+	4.61653i	−0.0699379	+	0.215247i
$461$	24.7639			1.15337			0.576686	−	0.816966i	$-0.304346\pi$
$461$	24.7639			1.15337			0.576686	+	0.816966i	$0.304346\pi$
$462$		0			0
$463$	−3.38197			−0.157173			−0.0785866	−	0.996907i	$-0.525041\pi$
$463$	−3.38197			−0.157173			−0.0785866	+	0.996907i	$0.525041\pi$
$464$	−1.14590	+	3.52671i	−0.0531970	+	0.163723i
$465$		0			0
$466$	−13.1803	−	9.57608i	−0.610567	−	0.443603i
$467$	−2.18034	−	6.71040i	−0.100894	−	0.310520i	0.887851	−	0.460131i	$-0.152198\pi$
$467$	−2.18034	−	6.71040i	−0.100894	−	0.310520i	−0.988745	+	0.149611i	$0.952198\pi$
$468$		0			0
$469$	23.9443	+	17.3965i	1.10564	+	0.803297i
$470$	−2.11803	+	1.53884i	−0.0976976	+	0.0709815i
$471$		0			0
$472$	14.6180			0.672850
$473$	−2.14590	+	1.34708i	−0.0986685	+	0.0619390i
$474$		0			0
$475$	−0.190983	+	0.587785i	−0.00876290	+	0.0269694i
$476$	−18.9443	+	13.7638i	−0.868309	+	0.630864i
$477$		0			0
$478$	−6.85410	−	21.0948i	−0.313499	−	0.964852i
$479$	12.0557	+	37.1037i	0.550840	+	1.69531i	0.706683	+	0.707530i	$0.250191\pi$
$479$	12.0557	+	37.1037i	0.550840	+	1.69531i	−0.155843	+	0.987782i	$0.549809\pi$
$480$		0			0
$481$	0.309017	−	0.224514i	0.0140900	−	0.0102370i
$482$	−7.91641	+	24.3642i	−0.360582	+	1.10976i
$483$		0			0
$484$	−9.69098	+	5.20431i	−0.440499	+	0.236560i
$485$	14.9443			0.678584
$486$		0			0
$487$	−32.6525	+	23.7234i	−1.47962	+	1.07501i	−0.501948	+	0.864898i	$0.667383\pi$
$487$	−32.6525	+	23.7234i	−1.47962	+	1.07501i	−0.977677	+	0.210112i	$0.932617\pi$
$488$	−9.09017	−	6.60440i	−0.411493	−	0.298967i
$489$		0			0
$490$	1.88197	+	5.79210i	0.0850186	+	0.261660i
$491$	−1.88197	−	1.36733i	−0.0849319	−	0.0617067i	0.544509	−	0.838755i	$-0.316716\pi$
$491$	−1.88197	−	1.36733i	−0.0849319	−	0.0617067i	−0.629441	+	0.777048i	$0.716716\pi$
$492$		0			0
$493$	−7.41641	+	22.8254i	−0.334018	+	1.02800i
$494$	−0.381966			−0.0171855
$495$		0			0
$496$	−9.23607			−0.414712
$497$	0.326238	−	1.00406i	0.0146338	−	0.0450381i
$498$		0			0
$499$	27.2533	+	19.8007i	1.22002	+	0.886400i	0.996102	−	0.0882071i	$-0.0281137\pi$
$499$	27.2533	+	19.8007i	1.22002	+	0.886400i	0.223923	+	0.974607i	$0.428114\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$		0			0
$502$	9.30902	+	6.76340i	0.415482	+	0.301865i
$503$	−3.88197	+	2.82041i	−0.173088	+	0.125756i	−0.670957	−	0.741497i	$-0.734116\pi$
$503$	−3.88197	+	2.82041i	−0.173088	+	0.125756i	0.497868	+	0.867253i	$0.334116\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$	−3.92705	−	15.6129i	−0.174579	−	0.694079i
$507$		0			0
$508$	3.89919	−	12.0005i	0.172998	−	0.532434i
$509$	−20.5623	+	14.9394i	−0.911408	+	0.662177i	−0.941371	−	0.337374i	$-0.890461\pi$
$509$	−20.5623	+	14.9394i	−0.911408	+	0.662177i	0.0299624	+	0.999551i	$0.490461\pi$
$510$		0			0
$511$	12.2361	+	37.6587i	0.541292	+	1.66592i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−4.09017	+	2.97168i	−0.180410	+	0.131075i
$515$	−3.04508	+	9.37181i	−0.134182	+	0.412971i
$516$		0			0
$517$	3.23607	−	8.05748i	0.142322	−	0.354368i
$518$	−2.23607			−0.0982472
$519$		0			0
$520$	−0.500000	+	0.363271i	−0.0219265	+	0.0159305i
$521$	30.1976	+	21.9398i	1.32298	+	0.961201i	0.999890	+	0.0148321i	$0.00472138\pi$
$521$	30.1976	+	21.9398i	1.32298	+	0.961201i	0.323089	+	0.946369i	$0.395279\pi$
$522$		0			0
$523$	0.708204	+	2.17963i	0.0309676	+	0.0953085i	0.965346	−	0.260975i	$-0.0840439\pi$
$523$	0.708204	+	2.17963i	0.0309676	+	0.0953085i	−0.934378	+	0.356283i	$0.884044\pi$
$524$	16.9443	+	12.3107i	0.740214	+	0.537797i
$525$		0			0
$526$	2.51722	−	7.74721i	0.109756	−	0.337794i
$527$	−59.7771			−2.60393
$528$		0			0
$529$	0.562306			0.0244481
$530$	1.88197	−	5.79210i	0.0817474	−	0.251593i
$531$		0			0
$532$	1.80902	+	1.31433i	0.0784308	+	0.0569833i
$533$	1.78115	+	5.48183i	0.0771503	+	0.237444i
$534$		0			0
$535$	14.4721	+	10.5146i	0.625685	+	0.454587i
$536$	6.61803	−	4.80828i	0.285856	−	0.207686i
$537$		0			0
$538$	24.7639			1.06765
$539$	−15.5000	−	12.9515i	−0.667632	−	0.557861i
$540$		0			0
$541$	−4.65248	+	14.3188i	−0.200026	+	0.615615i	0.799856	+	0.600193i	$0.204909\pi$
$541$	−4.65248	+	14.3188i	−0.200026	+	0.615615i	−0.999881	+	0.0154228i	$0.995091\pi$
$542$	−0.527864	+	0.383516i	−0.0226737	+	0.0164734i
$543$		0			0
$544$	2.00000	+	6.15537i	0.0857493	+	0.263909i
$545$	1.23607	+	3.80423i	0.0529473	+	0.162955i
$546$		0			0
$547$	15.5623	−	11.3067i	0.665396	−	0.483439i	−0.203085	−	0.979161i	$-0.565097\pi$
$547$	15.5623	−	11.3067i	0.665396	−	0.483439i	0.868481	+	0.495723i	$0.165097\pi$
$548$	−4.76393	+	14.6619i	−0.203505	+	0.626324i
$549$		0			0
$550$	−2.54508	−	2.12663i	−0.108523	−	0.0906797i
$551$	2.29180			0.0976338
$552$		0			0
$553$	13.0902	−	9.51057i	0.556651	−	0.404430i
$554$	6.69098	+	4.86128i	0.284273	+	0.206536i
$555$		0			0
$556$	−2.35410	−	7.24518i	−0.0998362	−	0.307264i
$557$	11.0623	+	8.03724i	0.468725	+	0.340549i	0.796944	−	0.604053i	$-0.206448\pi$
$557$	11.0623	+	8.03724i	0.468725	+	0.340549i	−0.328219	+	0.944602i	$0.606448\pi$
$558$		0			0
$559$	0.145898	−	0.449028i	0.00617083	−	0.0189919i
$560$	3.61803			0.152890
$561$		0			0
$562$	−7.88854			−0.332758
$563$	−14.0000	+	43.0876i	−0.590030	+	1.81592i	−0.0119724	+	0.999928i	$0.503811\pi$
$563$	−14.0000	+	43.0876i	−0.590030	+	1.81592i	−0.578057	+	0.815996i	$0.696189\pi$
$564$		0			0
$565$	−10.0902	−	7.33094i	−0.424497	−	0.308415i
$566$	1.14590	+	3.52671i	0.0481657	+	0.148239i
$567$		0			0
$568$	−0.236068	−	0.171513i	−0.00990519	−	0.00719654i
$569$	12.0172	−	8.73102i	0.503788	−	0.366023i	−0.306674	−	0.951815i	$-0.599216\pi$
$569$	12.0172	−	8.73102i	0.503788	−	0.366023i	0.810462	+	0.585791i	$0.199216\pi$
$570$		0			0
$571$	−21.5066			−0.900022			−0.450011	−	0.893023i	$-0.648580\pi$
$571$	−21.5066			−0.900022			−0.450011	+	0.893023i	$0.648580\pi$
$572$	0.763932	−	1.90211i	0.0319416	−	0.0795313i
$573$		0			0
$574$	10.4271	−	32.0912i	0.435217	−	1.33946i
$575$	3.92705	−	2.85317i	0.163769	−	0.118985i
$576$		0			0
$577$	−2.20163	−	6.77591i	−0.0916549	−	0.282085i	0.894713	−	0.446642i	$-0.147380\pi$
$577$	−2.20163	−	6.77591i	−0.0916549	−	0.282085i	−0.986367	+	0.164558i	$0.947380\pi$
$578$	7.69098	+	23.6704i	0.319903	+	0.984559i
$579$		0			0
$580$	3.00000	−	2.17963i	0.124568	−	0.0905041i
$581$	5.52786	−	17.0130i	0.229334	−	0.705819i
$582$		0			0
$583$	4.92705	+	19.5887i	0.204058	+	0.811280i
$584$	10.9443			0.452877
$585$		0			0
$586$	8.92705	−	6.48588i	0.368773	−	0.267929i
$587$	28.1803	+	20.4742i	1.16313	+	0.845061i	0.990170	−	0.139868i	$-0.0446678\pi$
$587$	28.1803	+	20.4742i	1.16313	+	0.845061i	0.172957	+	0.984929i	$0.444668\pi$
$588$		0			0
$589$	1.76393	+	5.42882i	0.0726816	+	0.223691i
$590$	−11.8262	−	8.59226i	−0.486879	−	0.353738i
$591$		0			0
$592$	−0.190983	+	0.587785i	−0.00784935	+	0.0241578i
$593$	2.58359			0.106095			0.0530477	−	0.998592i	$-0.483106\pi$
$593$	2.58359			0.106095			0.0530477	+	0.998592i	$0.483106\pi$
$594$		0			0
$595$	23.4164			0.959979
$596$	2.76393	−	8.50651i	0.113215	−	0.348440i
$597$		0			0
$598$	2.42705	+	1.76336i	0.0992495	+	0.0721090i
$599$	1.32624	+	4.08174i	0.0541886	+	0.166775i	0.974488	−	0.224439i	$-0.0720550\pi$
$599$	1.32624	+	4.08174i	0.0541886	+	0.166775i	−0.920299	+	0.391215i	$0.872055\pi$
$600$		0			0
$601$	28.3885	+	20.6255i	1.15799	+	0.841331i	0.989523	−	0.144376i	$-0.0461174\pi$
$601$	28.3885	+	20.6255i	1.15799	+	0.841331i	0.168470	+	0.985707i	$0.446117\pi$
$602$	−2.23607	+	1.62460i	−0.0911353	+	0.0662137i
$603$		0			0
$604$	−12.4721			−0.507484
$605$	10.8992	+	1.48584i	0.443115	+	0.0604080i
$606$		0			0
$607$	−5.05573	+	15.5599i	−0.205206	+	0.631558i	0.794499	+	0.607265i	$0.207733\pi$
$607$	−5.05573	+	15.5599i	−0.205206	+	0.631558i	−0.999705	+	0.0242929i	$0.992267\pi$
$608$	0.500000	−	0.363271i	0.0202777	−	0.0147326i
$609$		0			0
$610$	3.47214	+	10.6861i	0.140583	+	0.432669i
$611$	0.500000	+	1.53884i	0.0202278	+	0.0622549i
$612$		0			0
$613$	−36.7426	+	26.6951i	−1.48402	+	1.07820i	−0.507788	+	0.861482i	$0.669537\pi$
$613$	−36.7426	+	26.6951i	−1.48402	+	1.07820i	−0.976233	+	0.216723i	$0.930463\pi$
$614$	8.29180	−	25.5195i	0.334630	−	1.02988i
$615$		0			0
$616$	−10.1631	+	6.37988i	−0.409484	+	0.257053i
$617$	−23.0557			−0.928189			−0.464094	−	0.885786i	$-0.653620\pi$
$617$	−23.0557			−0.928189			−0.464094	+	0.885786i	$0.653620\pi$
$618$		0			0
$619$	−19.2082	+	13.9556i	−0.772043	+	0.560922i	−0.902580	−	0.430521i	$-0.858330\pi$
$619$	−19.2082	+	13.9556i	−0.772043	+	0.560922i	0.130537	+	0.991443i	$0.458330\pi$
$620$	7.47214	+	5.42882i	0.300088	+	0.218027i
$621$		0			0
$622$	8.61803	+	26.5236i	0.345552	+	1.06350i
$623$	−15.0623	−	10.9434i	−0.603459	−	0.438438i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	5.70820			0.228146
$627$		0			0
$628$	−5.61803			−0.224184
$629$	−1.23607	+	3.80423i	−0.0492853	+	0.151684i
$630$		0			0
$631$	−1.38197	−	1.00406i	−0.0550152	−	0.0399709i	0.559938	−	0.828535i	$-0.310825\pi$
$631$	−1.38197	−	1.00406i	−0.0550152	−	0.0399709i	−0.614953	+	0.788564i	$0.710825\pi$
$632$	−1.38197	−	4.25325i	−0.0549717	−	0.169185i
$633$		0			0
$634$	8.82624	+	6.41264i	0.350535	+	0.254678i
$635$	−10.2082	+	7.41669i	−0.405100	+	0.294323i
$636$		0			0
$637$	3.76393			0.149132
$638$	−4.58359	+	11.4127i	−0.181466	+	0.451832i
$639$		0			0
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	30.2984	−	22.0131i	1.19671	−	0.869463i	0.202756	−	0.979229i	$-0.435010\pi$
$641$	30.2984	−	22.0131i	1.19671	−	0.869463i	0.993957	+	0.109766i	$0.0350101\pi$
$642$		0			0
$643$	−1.05573	−	3.24920i	−0.0416339	−	0.128136i	0.928079	−	0.372383i	$-0.121459\pi$
$643$	−1.05573	−	3.24920i	−0.0416339	−	0.128136i	−0.969713	+	0.244247i	$0.921459\pi$
$644$	−5.42705	−	16.7027i	−0.213856	−	0.658180i
$645$		0			0
$646$	3.23607	−	2.35114i	0.127321	−	0.0925044i
$647$	9.52786	−	29.3238i	0.374579	−	1.15284i	−0.569183	−	0.822211i	$-0.692741\pi$
$647$	9.52786	−	29.3238i	0.374579	−	1.15284i	0.943762	−	0.330625i	$-0.107259\pi$
$648$		0			0
$649$	48.3713	+	3.28195i	1.89874	+	0.128828i
$650$	0.618034			0.0242413
$651$		0			0
$652$	−14.4721	+	10.5146i	−0.566773	+	0.411784i
$653$	−12.8262	−	9.31881i	−0.501929	−	0.364673i	0.307824	−	0.951443i	$-0.400399\pi$
$653$	−12.8262	−	9.31881i	−0.501929	−	0.364673i	−0.809754	+	0.586770i	$0.800399\pi$
$654$		0			0
$655$	−6.47214	−	19.9192i	−0.252887	−	0.778307i
$656$	−7.54508	−	5.48183i	−0.294586	−	0.214029i
$657$		0			0
$658$	2.92705	−	9.00854i	0.114108	−	0.351189i
$659$	−28.2705			−1.10126			−0.550631	−	0.834749i	$-0.685613\pi$
$659$	−28.2705			−1.10126			−0.550631	+	0.834749i	$0.685613\pi$
$660$		0			0
$661$	41.4853			1.61359			0.806795	−	0.590831i	$-0.201200\pi$
$661$	41.4853			1.61359			0.806795	+	0.590831i	$0.201200\pi$
$662$	2.37132	−	7.29818i	0.0921641	−	0.283652i
$663$		0			0
$664$	−4.00000	−	2.90617i	−0.155230	−	0.112781i
$665$	−0.690983	−	2.12663i	−0.0267952	−	0.0824671i
$666$		0			0
$667$	−14.5623	−	10.5801i	−0.563855	−	0.409664i
$668$	−9.35410	+	6.79615i	−0.361921	+	0.262951i
$669$		0			0
$670$	−8.18034			−0.316034
$671$	−28.5967	−	23.8949i	−1.10397	−	0.922453i
$672$		0			0
$673$	−14.0902	+	43.3651i	−0.543136	+	1.67160i	0.182245	+	0.983253i	$0.441664\pi$
$673$	−14.0902	+	43.3651i	−0.543136	+	1.67160i	−0.725381	+	0.688348i	$0.758336\pi$
$674$	16.1803	−	11.7557i	0.623243	−	0.452813i
$675$		0			0
$676$	−3.89919	−	12.0005i	−0.149969	−	0.461556i
$677$	−4.43769	−	13.6578i	−0.170554	−	0.524913i	0.828848	−	0.559474i	$-0.188997\pi$
$677$	−4.43769	−	13.6578i	−0.170554	−	0.524913i	−0.999403	+	0.0345610i	$0.988997\pi$
$678$		0			0
$679$	−43.7426	+	31.7809i	−1.67869	+	1.21964i
$680$	2.00000	−	6.15537i	0.0766965	−	0.236048i
$681$		0			0
$682$	−30.5623	−	2.07363i	−1.17029	−	0.0794033i
$683$	−31.1246			−1.19095			−0.595475	−	0.803374i	$-0.703036\pi$
$683$	−31.1246			−1.19095			−0.595475	+	0.803374i	$0.703036\pi$
$684$		0			0
$685$	12.4721	−	9.06154i	0.476536	−	0.346224i
$686$	2.66312	+	1.93487i	0.101678	+	0.0738736i
$687$		0			0
$688$	0.236068	+	0.726543i	0.00900001	+	0.0276992i
$689$	−3.04508	−	2.21238i	−0.116008	−	0.0842851i
$690$		0			0
$691$	−0.465558	+	1.43284i	−0.0177107	+	0.0545078i	−0.959521	−	0.281636i	$-0.909123\pi$
$691$	−0.465558	+	1.43284i	−0.0177107	+	0.0545078i	0.941811	+	0.336144i	$0.109123\pi$
$692$	24.5623			0.933719
$693$		0			0
$694$	−3.81966			−0.144992
$695$	−2.35410	+	7.24518i	−0.0892962	+	0.274825i
$696$		0			0
$697$	−48.8328	−	35.4791i	−1.84967	−	1.34387i
$698$	3.09017	+	9.51057i	0.116965	+	0.359980i
$699$		0			0
$700$	−2.92705	−	2.12663i	−0.110632	−	0.0803789i
$701$	−16.2361	+	11.7962i	−0.613228	+	0.445536i	−0.850549	−	0.525895i	$-0.823730\pi$
$701$	−16.2361	+	11.7962i	−0.613228	+	0.445536i	0.237322	+	0.971431i	$0.423730\pi$
$702$		0			0
$703$	0.381966			0.0144061
$704$	0.809017	+	3.21644i	0.0304910	+	0.121224i
$705$		0			0
$706$	7.61803	−	23.4459i	0.286708	−	0.882398i
$707$	11.7082	−	8.50651i	0.440332	−	0.319920i
$708$		0			0
$709$	−7.61803	−	23.4459i	−0.286101	−	0.880529i	−0.986066	−	0.166352i	$-0.946801\pi$
$709$	−7.61803	−	23.4459i	−0.286101	−	0.880529i	0.699965	−	0.714177i	$-0.253199\pi$
$710$	0.0901699	+	0.277515i	0.00338402	+	0.0104149i
$711$		0			0
$712$	−4.16312	+	3.02468i	−0.156019	+	0.113355i
$713$	13.8541	−	42.6385i	0.518840	−	1.59683i
$714$		0			0
$715$	−1.73607	+	1.08981i	−0.0649253	+	0.0407567i
$716$	11.1459			0.416542
$717$		0			0
$718$	20.4164	−	14.8334i	0.761934	−	0.553577i
$719$	−19.3262	−	14.0413i	−0.720747	−	0.523653i	0.165876	−	0.986147i	$-0.446955\pi$
$719$	−19.3262	−	14.0413i	−0.720747	−	0.523653i	−0.886623	+	0.462493i	$0.846955\pi$
$720$		0			0
$721$	−11.0172	−	33.9075i	−0.410303	−	1.26278i
$722$	15.0623	+	10.9434i	0.560561	+	0.407271i
$723$		0			0
$724$	−7.52786	+	23.1684i	−0.279771	+	0.861046i
$725$	−3.70820			−0.137719
$726$		0			0
$727$	−46.6312			−1.72946			−0.864728	−	0.502241i	$-0.832509\pi$
$727$	−46.6312			−1.72946			−0.864728	+	0.502241i	$0.832509\pi$
$728$	0.690983	−	2.12663i	0.0256095	−	0.0788180i
$729$		0			0
$730$	−8.85410	−	6.43288i	−0.327705	−	0.238092i
$731$	1.52786	+	4.70228i	0.0565101	+	0.173920i
$732$		0			0
$733$	23.0344	+	16.7355i	0.850797	+	0.618140i	0.925366	−	0.379076i	$-0.123758\pi$
$733$	23.0344	+	16.7355i	0.850797	+	0.618140i	−0.0745690	+	0.997216i	$0.523758\pi$
$734$	−6.76393	+	4.91428i	−0.249661	+	0.181390i
$735$		0			0
$736$	−4.85410			−0.178925
$737$	22.9787	−	14.4248i	0.846432	−	0.531346i
$738$		0			0
$739$	8.53444	−	26.2663i	0.313945	−	0.966222i	−0.662242	−	0.749290i	$-0.730395\pi$
$739$	8.53444	−	26.2663i	0.313945	−	0.966222i	0.976187	−	0.216932i	$-0.0696050\pi$
$740$	0.500000	−	0.363271i	0.0183804	−	0.0133541i
$741$		0			0
$742$	6.80902	+	20.9560i	0.249967	+	0.769319i
$743$	2.20820	+	6.79615i	0.0810111	+	0.249327i	0.983356	−	0.181687i	$-0.0581559\pi$
$743$	2.20820	+	6.79615i	0.0810111	+	0.249327i	−0.902345	+	0.431014i	$0.858156\pi$
$744$		0			0
$745$	−7.23607	+	5.25731i	−0.265109	+	0.192613i
$746$	−4.28115	+	13.1760i	−0.156744	+	0.482409i
$747$		0			0
$748$	5.23607	+	20.8172i	0.191450	+	0.761154i
$749$	−64.7214			−2.36487
$750$		0			0
$751$	24.4721	−	17.7800i	0.893001	−	0.648803i	−0.0436578	−	0.999047i	$-0.513901\pi$
$751$	24.4721	−	17.7800i	0.893001	−	0.648803i	0.936659	+	0.350243i	$0.113901\pi$
$752$	−2.11803	−	1.53884i	−0.0772368	−	0.0561158i
$753$		0			0
$754$	−0.708204	−	2.17963i	−0.0257913	−	0.0793774i
$755$	10.0902	+	7.33094i	0.367219	+	0.266800i
$756$		0			0
$757$	0.572949	−	1.76336i	0.0208242	−	0.0640903i	−0.940104	−	0.340887i	$-0.889273\pi$
$757$	0.572949	−	1.76336i	0.0208242	−	0.0640903i	0.960929	+	0.276796i	$0.0892728\pi$
$758$	−32.7426			−1.18927
$759$		0			0
$760$	−0.618034			−0.0224184
$761$	2.43769	−	7.50245i	0.0883663	−	0.271964i	−0.897102	−	0.441824i	$-0.854332\pi$
$761$	2.43769	−	7.50245i	0.0883663	−	0.271964i	0.985468	+	0.169860i	$0.0543316\pi$
$762$		0			0
$763$	−11.7082	−	8.50651i	−0.423865	−	0.307956i
$764$	4.23607	+	13.0373i	0.153256	+	0.471672i
$765$		0			0
$766$	−23.0172	−	16.7230i	−0.831646	−	0.604226i
$767$	−7.30902	+	5.31031i	−0.263913	+	0.191744i
$768$		0			0
$769$	−34.7984			−1.25486			−0.627431	−	0.778672i	$-0.715893\pi$
$769$	−34.7984			−1.25486			−0.627431	+	0.778672i	$0.715893\pi$
$770$	11.9721	+	0.812299i	0.431446	+	0.0292732i
$771$		0			0
$772$	−1.14590	+	3.52671i	−0.0412418	+	0.126929i
$773$	3.07295	−	2.23263i	0.110526	−	0.0803021i	−0.531149	−	0.847278i	$-0.678240\pi$
$773$	3.07295	−	2.23263i	0.110526	−	0.0803021i	0.641675	+	0.766976i	$0.278240\pi$
$774$		0			0
$775$	−2.85410	−	8.78402i	−0.102522	−	0.315531i
$776$	4.61803	+	14.2128i	0.165778	+	0.510211i
$777$		0			0
$778$	2.85410	−	2.07363i	0.102325	−	0.0743431i
$779$	−1.78115	+	5.48183i	−0.0638164	+	0.196407i
$780$		0			0
$781$	−0.742646	−	0.620541i	−0.0265740	−	0.0222047i
$782$	−31.4164			−1.12345
$783$		0			0
$784$	−4.92705	+	3.57971i	−0.175966	+	0.127847i
$785$	4.54508	+	3.30220i	0.162221	+	0.117860i
$786$		0			0
$787$	−5.61803	−	17.2905i	−0.200261	−	0.616341i	−0.999875	−	0.0158258i	$-0.994962\pi$
$787$	−5.61803	−	17.2905i	−0.200261	−	0.616341i	0.799613	−	0.600515i	$-0.205038\pi$
$788$	2.92705	+	2.12663i	0.104272	+	0.0757580i
$789$		0			0
$790$	−1.38197	+	4.25325i	−0.0491681	+	0.151324i
$791$	45.1246			1.60445
$792$		0			0
$793$	6.94427			0.246598
$794$	3.91641	−	12.0535i	0.138988	−	0.427761i
$795$		0			0
$796$	10.4721	+	7.60845i	0.371175	+	0.269674i
$797$	−4.24671	−	13.0700i	−0.150426	−	0.462964i	0.847243	−	0.531206i	$-0.178261\pi$
$797$	−4.24671	−	13.0700i	−0.150426	−	0.462964i	−0.997669	+	0.0682419i	$0.978261\pi$
$798$		0			0
$799$	−13.7082	−	9.95959i	−0.484961	−	0.352345i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$		0			0
$802$	1.67376			0.0591026
$803$	36.2148	+	2.45714i	1.27799	+	0.0867107i
$804$		0			0
$805$	−5.42705	+	16.7027i	−0.191278	+	0.588694i
$806$	4.61803	−	3.35520i	0.162663	−	0.118182i
$807$		0			0
$808$	−1.23607	−	3.80423i	−0.0434847	−	0.133832i
$809$	1.07953	+	3.32244i	0.0379541	+	0.116811i	0.968239	−	0.250028i	$-0.0804399\pi$
$809$	1.07953	+	3.32244i	0.0379541	+	0.116811i	−0.930284	+	0.366839i	$0.880440\pi$
$810$		0			0
$811$	−21.2533	+	15.4414i	−0.746304	+	0.542222i	−0.894679	−	0.446710i	$-0.852596\pi$
$811$	−21.2533	+	15.4414i	−0.746304	+	0.542222i	0.148375	+	0.988931i	$0.452596\pi$
$812$	−4.14590	+	12.7598i	−0.145492	+	0.447780i
$813$		0			0
$814$	−0.763932	+	1.90211i	−0.0267758	+	0.0666690i
$815$	17.8885			0.626608
$816$		0			0
$817$	0.381966	−	0.277515i	0.0133633	−	0.00970901i
$818$	−11.5000	−	8.35524i	−0.402088	−	0.292134i
$819$		0			0
$820$	2.88197	+	8.86978i	0.100643	+	0.309746i
$821$	10.3262	+	7.50245i	0.360388	+	0.261837i	0.753214	−	0.657776i	$-0.228502\pi$
$821$	10.3262	+	7.50245i	0.360388	+	0.261837i	−0.392826	+	0.919613i	$0.628502\pi$
$822$		0			0
$823$	10.1697	−	31.2991i	0.354493	−	1.09102i	−0.601809	−	0.798640i	$-0.705553\pi$
$823$	10.1697	−	31.2991i	0.354493	−	1.09102i	0.956303	−	0.292379i	$-0.0944467\pi$
$824$	−9.85410			−0.343284
$825$		0			0
$826$	52.8885			1.84023
$827$	3.00000	−	9.23305i	0.104320	−	0.321065i	−0.885250	−	0.465115i	$-0.846013\pi$
$827$	3.00000	−	9.23305i	0.104320	−	0.321065i	0.989570	+	0.144051i	$0.0460128\pi$
$828$		0			0
$829$	18.8541	+	13.6983i	0.654830	+	0.475762i	0.864913	−	0.501922i	$-0.167373\pi$
$829$	18.8541	+	13.6983i	0.654830	+	0.475762i	−0.210083	+	0.977684i	$0.567373\pi$
$830$	1.52786	+	4.70228i	0.0530329	+	0.163219i
$831$		0			0
$832$	−0.500000	−	0.363271i	−0.0173344	−	0.0125942i
$833$	−31.8885	+	23.1684i	−1.10487	+	0.802737i
$834$		0			0
$835$	11.5623			0.400130
$836$	1.73607	−	1.08981i	0.0600432	−	0.0376920i
$837$		0			0
$838$	3.46149	−	10.6534i	0.119575	−	0.368015i
$839$	26.7984	−	19.4702i	0.925183	−	0.672185i	−0.0196260	−	0.999807i	$-0.506248\pi$
$839$	26.7984	−	19.4702i	0.925183	−	0.672185i	0.944809	+	0.327623i	$0.106248\pi$
$840$		0			0
$841$	−4.71227	−	14.5029i	−0.162492	−	0.500099i
$842$	8.32624	+	25.6255i	0.286941	+	0.883114i
$843$		0			0
$844$	18.9443	−	13.7638i	0.652089	−	0.473770i
$845$	−3.89919	+	12.0005i	−0.134136	+	0.412828i
$846$		0			0
$847$	−35.0623	+	18.8294i	−1.20476	+	0.646985i
$848$	6.09017			0.209137
$849$		0			0
$850$	−5.23607	+	3.80423i	−0.179596	+	0.130484i
$851$	−2.42705	−	1.76336i	−0.0831982	−	0.0604471i
$852$		0			0
$853$	15.0836	+	46.4225i	0.516452	+	1.58948i	0.780624	+	0.625001i	$0.214902\pi$
$853$	15.0836	+	46.4225i	0.516452	+	1.58948i	−0.264171	+	0.964476i	$0.585098\pi$
$854$	−32.8885	−	23.8949i	−1.12542	−	0.817668i
$855$		0			0
$856$	−5.52786	+	17.0130i	−0.188939	+	0.581493i
$857$	−55.2361			−1.88683			−0.943414	−	0.331617i	$-0.892406\pi$
$857$	−55.2361			−1.88683			−0.943414	+	0.331617i	$0.892406\pi$
$858$		0			0
$859$	51.0344			1.74127			0.870636	−	0.491927i	$-0.163707\pi$
$859$	51.0344			1.74127			0.870636	+	0.491927i	$0.163707\pi$
$860$	0.236068	−	0.726543i	0.00804985	−	0.0247749i
$861$		0			0
$862$	1.76393	+	1.28157i	0.0600798	+	0.0436505i
$863$	0.0450850	+	0.138757i	0.00153471	+	0.00472335i	0.951821	−	0.306654i	$-0.0992096\pi$
$863$	0.0450850	+	0.138757i	0.00153471	+	0.00472335i	−0.950286	+	0.311378i	$0.899210\pi$
$864$		0			0
$865$	−19.8713	−	14.4374i	−0.675645	−	0.490885i
$866$	26.7984	−	19.4702i	0.910646	−	0.661623i
$867$		0			0
$868$	−33.4164			−1.13423
$869$	−3.61803	−	14.3844i	−0.122733	−	0.487956i
$870$		0			0
$871$	−1.56231	+	4.80828i	−0.0529367	+	0.162922i
$872$	−3.23607	+	2.35114i	−0.109587	+	0.0796197i
$873$		0			0
$874$	0.927051	+	2.85317i	0.0313580	+	0.0965099i
$875$	1.11803	+	3.44095i	0.0377964	+	0.116326i
$876$		0			0
$877$	18.9164	−	13.7436i	0.638762	−	0.464088i	−0.220663	−	0.975350i	$-0.570822\pi$
$877$	18.9164	−	13.7436i	0.638762	−	0.464088i	0.859425	+	0.511263i	$0.170822\pi$
$878$	6.23607	−	19.1926i	0.210457	−	0.647720i
$879$		0			0
$880$	1.23607	−	3.07768i	0.0416678	−	0.103749i
$881$	−7.79837			−0.262734			−0.131367	−	0.991334i	$-0.541937\pi$
$881$	−7.79837			−0.262734			−0.131367	+	0.991334i	$0.541937\pi$
$882$		0			0
$883$	−20.4721	+	14.8739i	−0.688942	+	0.500546i	−0.876312	−	0.481744i	$-0.840004\pi$
$883$	−20.4721	+	14.8739i	−0.688942	+	0.500546i	0.187370	+	0.982289i	$0.440004\pi$
$884$	−3.23607	−	2.35114i	−0.108841	−	0.0790774i
$885$		0			0
$886$	−8.90983	−	27.4216i	−0.299332	−	0.921248i
$887$	1.01722	+	0.739054i	0.0341549	+	0.0248150i	0.604732	−	0.796429i	$-0.293280\pi$
$887$	1.01722	+	0.739054i	0.0341549	+	0.0248150i	−0.570577	+	0.821244i	$0.693280\pi$
$888$		0			0
$889$	14.1074	−	43.4181i	0.473147	−	1.45620i
$890$	5.14590			0.172491
$891$		0			0
$892$	7.61803			0.255071
$893$	−0.500000	+	1.53884i	−0.0167319	+	0.0514954i
$894$		0			0
$895$	−9.01722	−	6.55139i	−0.301412	−	0.218989i
$896$	1.11803	+	3.44095i	0.0373509	+	0.114954i
$897$		0			0
$898$	−15.0623	−	10.9434i	−0.502636	−	0.365186i
$899$	−27.7082	+	20.1312i	−0.924120	+	0.671413i
$900$		0			0
$901$	39.4164			1.31315
$902$	−23.7361	−	19.8334i	−0.790325	−	0.660381i
$903$		0			0
$904$	3.85410	−	11.8617i	0.128186	−	0.394514i
$905$	19.7082	−	14.3188i	0.655123	−	0.475975i
$906$		0			0
$907$	9.23607	+	28.4257i	0.306679	+	0.943860i	0.979045	+	0.203642i	$0.0652777\pi$
$907$	9.23607	+	28.4257i	0.306679	+	0.943860i	−0.672367	+	0.740218i	$0.734722\pi$
$908$	1.29180	+	3.97574i	0.0428698	+	0.131940i
$909$		0			0
$910$	−1.80902	+	1.31433i	−0.0599683	+	0.0435695i
$911$	3.29180	−	10.1311i	0.109062	−	0.335659i	−0.881600	−	0.471997i	$-0.843533\pi$
$911$	3.29180	−	10.1311i	0.109062	−	0.335659i	0.990662	+	0.136338i	$0.0435334\pi$
$912$		0			0
$913$	−12.5836	−	10.5146i	−0.416456	−	0.347983i
$914$	9.88854			0.327084
$915$		0			0
$916$	9.32624	−	6.77591i	0.308148	−	0.223882i
$917$	61.3050	+	44.5407i	2.02447	+	1.47086i
$918$		0			0
$919$	−5.58359	−	17.1845i	−0.184186	−	0.566865i	0.815748	−	0.578408i	$-0.196326\pi$
$919$	−5.58359	−	17.1845i	−0.184186	−	0.566865i	−0.999933	+	0.0115426i	$0.996326\pi$
$920$	3.92705	+	2.85317i	0.129471	+	0.0940662i
$921$		0			0
$922$	7.65248	−	23.5519i	0.252021	−	0.775640i
$923$	0.180340			0.00593596
$924$		0			0
$925$	−0.618034			−0.0203208
$926$	−1.04508	+	3.21644i	−0.0343436	+	0.105699i
$927$		0			0
$928$	3.00000	+	2.17963i	0.0984798	+	0.0715498i
$929$	2.17376	+	6.69015i	0.0713188	+	0.219497i	0.980362	−	0.197204i	$-0.0631862\pi$
$929$	2.17376	+	6.69015i	0.0713188	+	0.219497i	−0.909044	+	0.416701i	$0.863186\pi$
$930$		0			0
$931$	3.04508	+	2.21238i	0.0997986	+	0.0725079i
$932$	−13.1803	+	9.57608i	−0.431736	+	0.313675i
$933$		0			0
$934$	−7.05573			−0.230870
$935$	8.00000	−	19.9192i	0.261628	−	0.651427i
$936$		0			0
$937$	14.9443	−	45.9937i	0.488208	−	1.50255i	−0.339072	−	0.940760i	$-0.610113\pi$
$937$	14.9443	−	45.9937i	0.488208	−	1.50255i	0.827280	−	0.561790i	$-0.189887\pi$
$938$	23.9443	−	17.3965i	0.781808	−	0.568017i
$939$		0			0
$940$	0.809017	+	2.48990i	0.0263872	+	0.0812115i
$941$	−3.41641	−	10.5146i	−0.111372	−	0.342767i	0.879801	−	0.475342i	$-0.157676\pi$
$941$	−3.41641	−	10.5146i	−0.111372	−	0.342767i	−0.991173	+	0.132575i	$0.957676\pi$
$942$		0			0
$943$	36.6246	−	26.6093i	1.19266	−	0.866519i
$944$	4.51722	−	13.9026i	0.147023	−	0.452490i
$945$		0			0
$946$	0.618034	+	2.45714i	0.0200940	+	0.0798886i
$947$	3.30495			0.107396			0.0536982	−	0.998557i	$-0.482899\pi$
$947$	3.30495			0.107396			0.0536982	+	0.998557i	$0.482899\pi$
$948$		0			0
$949$	−5.47214	+	3.97574i	−0.177633	+	0.129058i
$950$	0.500000	+	0.363271i	0.0162221	+	0.0117861i
$951$		0			0
$952$	7.23607	+	22.2703i	0.234522	+	0.721785i
$953$	−36.2148	−	26.3116i	−1.17311	−	0.852316i	−0.181734	−	0.983348i	$-0.558171\pi$
$953$	−36.2148	−	26.3116i	−1.17311	−	0.852316i	−0.991378	+	0.131032i	$0.958171\pi$
$954$		0			0
$955$	4.23607	−	13.0373i	0.137076	−	0.421876i
$956$	−22.1803			−0.717363
$957$		0			0
$958$	39.0132			1.26046
$959$	−17.2361	+	53.0472i	−0.556582	+	1.71298i
$960$		0			0
$961$	−43.9336	−	31.9196i	−1.41721	−	1.02967i
$962$	−0.118034	−	0.363271i	−0.00380557	−	0.0117123i
$963$		0			0
$964$	20.7254	+	15.0579i	0.667521	+	0.484982i
$965$	3.00000	−	2.17963i	0.0965734	−	0.0701647i
$966$		0			0
$967$	−4.25735			−0.136907			−0.0684536	−	0.997654i	$-0.521807\pi$
$967$	−4.25735			−0.136907			−0.0684536	+	0.997654i	$0.521807\pi$
$968$	1.95492	+	10.8249i	0.0628333	+	0.347925i
$969$		0			0
$970$	4.61803	−	14.2128i	0.148276	−	0.456347i
$971$	4.69098	−	3.40820i	0.150541	−	0.109374i	−0.509965	−	0.860195i	$-0.670342\pi$
$971$	4.69098	−	3.40820i	0.150541	−	0.109374i	0.660506	+	0.750821i	$0.270342\pi$
$972$		0			0
$973$	−8.51722	−	26.2133i	−0.273050	−	0.840360i
$974$	12.4721	+	38.3853i	0.399633	+	1.22994i
$975$		0			0
$976$	−9.09017	+	6.60440i	−0.290969	+	0.211402i
$977$	7.67376	−	23.6174i	0.245505	−	0.755588i	−0.750048	−	0.661384i	$-0.769969\pi$
$977$	7.67376	−	23.6174i	0.245505	−	0.755588i	0.995553	−	0.0942040i	$-0.0300306\pi$
$978$		0			0
$979$	−14.4549	+	9.07405i	−0.461981	+	0.290008i
$980$	6.09017			0.194543
$981$		0			0
$982$	−1.88197	+	1.36733i	−0.0600559	+	0.0436332i
$983$	−26.7254	−	19.4172i	−0.852409	−	0.619311i	0.0734004	−	0.997303i	$-0.476615\pi$
$983$	−26.7254	−	19.4172i	−0.852409	−	0.619311i	−0.925809	+	0.377991i	$0.876615\pi$
$984$		0			0
$985$	−1.11803	−	3.44095i	−0.0356235	−	0.109638i
$986$	19.4164	+	14.1068i	0.618344	+	0.449254i
$987$		0			0
$988$	−0.118034	+	0.363271i	−0.00375516	+	0.0115572i
$989$	−3.70820			−0.117914
$990$		0			0
$991$	8.94427			0.284124			0.142062	−	0.989858i	$-0.454627\pi$
$991$	8.94427			0.284124			0.142062	+	0.989858i	$0.454627\pi$
$992$	−2.85410	+	8.78402i	−0.0906178	+	0.278893i
$993$		0			0
$994$	−0.854102	−	0.620541i	−0.0270905	−	0.0196824i
$995$	−4.00000	−	12.3107i	−0.126809	−	0.390277i
$996$		0			0
$997$	11.1459	+	8.09797i	0.352994	+	0.256465i	0.750124	−	0.661297i	$-0.229994\pi$
$997$	11.1459	+	8.09797i	0.352994	+	0.256465i	−0.397130	+	0.917762i	$0.629994\pi$
$998$	27.2533	−	19.8007i	0.862688	−	0.626779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.a.361.1		4
3.2	odd	2		330.2.m.d.31.1	✓	4
11.5	even	5	inner	990.2.n.a.181.1		4
33.5	odd	10		330.2.m.d.181.1	yes	4
33.26	odd	10		3630.2.a.bc.1.2		2
33.29	even	10		3630.2.a.bi.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.d.31.1	✓	4	3.2	odd	2
330.2.m.d.181.1	yes	4	33.5	odd	10
990.2.n.a.181.1		4	11.5	even	5	inner
990.2.n.a.361.1		4	1.1	even	1	trivial
3630.2.a.bc.1.2		2	33.26	odd	10
3630.2.a.bi.1.1		2	33.29	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.92705 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.92705 - 2.12663i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.00000 q^{10} +(-2.80902 + 1.76336i) q^{11} +(0.190983 - 0.587785i) q^{13} +(-2.92705 + 2.12663i) q^{14} +(0.309017 + 0.951057i) q^{16} +(2.00000 + 6.15537i) q^{17} +(0.500000 - 0.363271i) q^{19} +(0.309017 - 0.951057i) q^{20} +(0.809017 + 3.21644i) q^{22} -4.85410 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-0.500000 - 0.363271i) q^{26} +(1.11803 + 3.44095i) q^{28} +(3.00000 + 2.17963i) q^{29} +(-2.85410 + 8.78402i) q^{31} +1.00000 q^{32} +6.47214 q^{34} +(1.11803 - 3.44095i) q^{35} +(0.500000 + 0.363271i) q^{37} +(-0.190983 - 0.587785i) q^{38} +(-0.809017 - 0.587785i) q^{40} +(-7.54508 + 5.48183i) q^{41} +0.763932 q^{43} +(3.30902 + 0.224514i) q^{44} +(-1.50000 + 4.61653i) q^{46} +(-2.11803 + 1.53884i) q^{47} +(1.88197 + 5.79210i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{52} +(1.88197 - 5.79210i) q^{53} +(-2.54508 - 2.12663i) q^{55} +3.61803 q^{56} +(3.00000 - 2.17963i) q^{58} +(-11.8262 - 8.59226i) q^{59} +(3.47214 + 10.6861i) q^{61} +(7.47214 + 5.42882i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.618034 q^{65} -8.18034 q^{67} +(2.00000 - 6.15537i) q^{68} +(-2.92705 - 2.12663i) q^{70} +(0.0901699 + 0.277515i) q^{71} +(-8.85410 - 6.43288i) q^{73} +(0.500000 - 0.363271i) q^{74} -0.618034 q^{76} +(11.9721 + 0.812299i) q^{77} +(-1.38197 + 4.25325i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(2.88197 + 8.86978i) q^{82} +(1.52786 + 4.70228i) q^{83} +(-5.23607 + 3.80423i) q^{85} +(0.236068 - 0.726543i) q^{86} +(1.23607 - 3.07768i) q^{88} +5.14590 q^{89} +(-1.80902 + 1.31433i) q^{91} +(3.92705 + 2.85317i) q^{92} +(0.809017 + 2.48990i) q^{94} +(0.500000 + 0.363271i) q^{95} +(4.61803 - 14.2128i) q^{97} +6.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - q^{5} - 5 q^{7} - q^{8}+O(q^{10}) \) 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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