LMFDB - Embedded newform 961.2.d.l.374.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.1
Root			$0.437016 - 1.34500i$ of defining polynomial
Character	$\chi$	$=$	961.374
Dual form			961.2.d.l.388.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.335106 - 0.243469i) q^{2} +(-0.335106 + 0.243469i) q^{3} +(-0.565015 - 1.73894i) q^{4} +1.00000 q^{5} +0.171573 q^{6} +(-0.127999 - 0.393941i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(-0.874032 + 2.68999i) q^{9} +O(q^{10})$	\(q+(-0.335106 - 0.243469i) q^{2} +(-0.335106 + 0.243469i) q^{3} +(-0.565015 - 1.73894i) q^{4} +1.00000 q^{5} +0.171573 q^{6} +(-0.127999 - 0.393941i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(-0.874032 + 2.68999i) q^{9} +(-0.335106 - 0.243469i) q^{10} +(1.00203 + 3.08393i) q^{11} +(0.612717 + 0.445165i) q^{12} +(3.09726 - 2.25029i) q^{13} +(-0.0530189 + 0.163176i) q^{14} +(-0.335106 + 0.243469i) q^{15} +(-2.42705 + 1.76336i) q^{16} +(-1.80108 + 5.54316i) q^{17} +(0.947822 - 0.688633i) q^{18} +(-3.57117 - 2.59461i) q^{19} +(-0.565015 - 1.73894i) q^{20} +(0.138805 + 0.100848i) q^{21} +(0.415055 - 1.27741i) q^{22} +(-1.23607 + 3.80423i) q^{23} +(-0.202979 - 0.624706i) q^{24} -4.00000 q^{25} -1.58579 q^{26} +(-0.746033 - 2.29605i) q^{27} +(-0.612717 + 0.445165i) q^{28} +(5.52431 + 4.01365i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(-1.08663 - 0.789481i) q^{33} +(1.95314 - 1.41904i) q^{34} +(-0.127999 - 0.393941i) q^{35} +5.17157 q^{36} +1.00000 q^{37} +(0.565015 + 1.73894i) q^{38} +(-0.490035 + 1.50817i) q^{39} +(-0.490035 + 1.50817i) q^{40} +(6.05572 + 4.39974i) q^{41} +(-0.0219612 - 0.0675895i) q^{42} +(8.81788 + 6.40656i) q^{43} +(4.79661 - 3.48494i) q^{44} +(-0.874032 + 2.68999i) q^{45} +(1.34042 - 0.973874i) q^{46} +(-7.81256 + 5.67616i) q^{47} +(0.383997 - 1.18182i) q^{48} +(5.52431 - 4.01365i) q^{49} +(1.34042 + 0.973874i) q^{50} +(-0.746033 - 2.29605i) q^{51} +(-5.66312 - 4.11450i) q^{52} +(1.80108 - 5.54316i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.00203 + 3.08393i) q^{55} +0.656854 q^{56} +1.82843 q^{57} +(-0.874032 - 2.68999i) q^{58} +(-3.29356 + 2.39291i) q^{59} +(0.612717 + 0.445165i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(3.37487 + 2.45199i) q^{64} +(3.09726 - 2.25029i) q^{65} +(0.171921 + 0.529120i) q^{66} +3.24264 q^{67} +10.6569 q^{68} +(-0.511996 - 1.57576i) q^{69} +(-0.0530189 + 0.163176i) q^{70} +(0.0219612 - 0.0675895i) q^{71} +(-3.62867 - 2.63638i) q^{72} +(-0.565015 - 1.73894i) q^{73} +(-0.335106 - 0.243469i) q^{74} +(1.34042 - 0.973874i) q^{75} +(-2.49410 + 7.67604i) q^{76} +(1.08663 - 0.789481i) q^{77} +(0.531406 - 0.386089i) q^{78} +(-2.08814 + 6.42663i) q^{79} +(-2.42705 + 1.76336i) q^{80} +(-6.05572 - 4.39974i) q^{81} +(-0.958109 - 2.94876i) q^{82} +(8.14767 + 5.91963i) q^{83} +(0.0969413 - 0.298355i) q^{84} +(-1.80108 + 5.54316i) q^{85} +(-1.39512 - 4.29375i) q^{86} -2.82843 q^{87} -5.14214 q^{88} +(1.38603 + 4.26576i) q^{89} +(0.947822 - 0.688633i) q^{90} +(-1.28293 - 0.932102i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(-3.57117 - 2.59461i) q^{95} +(-1.47923 + 1.07472i) q^{96} +(1.59810 + 4.91846i) q^{97} -2.82843 q^{98} -9.17157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} + 24 q^{6} - 2 q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 + 24 * q^6 - 2 * q^7 + 6 * q^8	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} + 24 q^{6} - 2 q^{7} + 6 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} + 2 q^{15} - 6 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21} - 14 q^{22} + 8 q^{23} - 10 q^{24} - 32 q^{25} - 24 q^{26} + 2 q^{27} - 10 q^{28} + 8 q^{29} + 24 q^{30} + 24 q^{32} - 14 q^{33} + 2 q^{34} - 2 q^{35} + 64 q^{36} + 8 q^{37} + 2 q^{38} + 6 q^{39} + 6 q^{40} - 2 q^{41} - 14 q^{42} + 2 q^{43} + 26 q^{44} - 8 q^{46} - 8 q^{47} + 6 q^{48} + 8 q^{49} - 8 q^{50} + 2 q^{51} - 14 q^{52} - 6 q^{53} + 2 q^{54} + 2 q^{55} - 40 q^{56} - 8 q^{57} + 6 q^{59} + 10 q^{60} + 32 q^{63} + 14 q^{64} + 2 q^{65} + 30 q^{66} - 8 q^{67} + 40 q^{68} - 8 q^{69} + 6 q^{70} + 14 q^{71} + 8 q^{72} - 2 q^{73} + 2 q^{74} - 8 q^{75} + 2 q^{76} + 14 q^{77} - 10 q^{78} + 22 q^{79} - 6 q^{80} + 2 q^{81} + 26 q^{82} + 6 q^{83} + 22 q^{84} + 6 q^{85} + 26 q^{86} + 72 q^{88} + 8 q^{89} + 8 q^{90} - 6 q^{91} - 32 q^{92} + 32 q^{94} - 6 q^{95} + 2 q^{96} - 16 q^{97} - 96 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 + 24 * q^6 - 2 * q^7 + 6 * q^8 + 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 + 6 * q^14 + 2 * q^15 - 6 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 + 6 * q^21 - 14 * q^22 + 8 * q^23 - 10 * q^24 - 32 * q^25 - 24 * q^26 + 2 * q^27 - 10 * q^28 + 8 * q^29 + 24 * q^30 + 24 * q^32 - 14 * q^33 + 2 * q^34 - 2 * q^35 + 64 * q^36 + 8 * q^37 + 2 * q^38 + 6 * q^39 + 6 * q^40 - 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 - 8 * q^46 - 8 * q^47 + 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 - 14 * q^52 - 6 * q^53 + 2 * q^54 + 2 * q^55 - 40 * q^56 - 8 * q^57 + 6 * q^59 + 10 * q^60 + 32 * q^63 + 14 * q^64 + 2 * q^65 + 30 * q^66 - 8 * q^67 + 40 * q^68 - 8 * q^69 + 6 * q^70 + 14 * q^71 + 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 + 2 * q^76 + 14 * q^77 - 10 * q^78 + 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 + 6 * q^83 + 22 * q^84 + 6 * q^85 + 26 * q^86 + 72 * q^88 + 8 * q^89 + 8 * q^90 - 6 * q^91 - 32 * q^92 + 32 * q^94 - 6 * q^95 + 2 * q^96 - 16 * q^97 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.335106	−	0.243469i	−0.236956	−	0.172158i	0.462970	−	0.886374i	$-0.346784\pi$
$2$	−0.335106	−	0.243469i	−0.236956	−	0.172158i	−0.699926	+	0.714215i	$0.746784\pi$
$3$	−0.335106	+	0.243469i	−0.193473	+	0.140567i	−0.680305	−	0.732929i	$-0.738153\pi$
$3$	−0.335106	+	0.243469i	−0.193473	+	0.140567i	0.486831	+	0.873496i	$0.338153\pi$
$4$	−0.565015	−	1.73894i	−0.282508	−	0.869469i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	0.171573			0.0700443
$7$	−0.127999	−	0.393941i	−0.0483791	−	0.148896i	0.923949	−	0.382517i	$-0.124942\pi$
$7$	−0.127999	−	0.393941i	−0.0483791	−	0.148896i	−0.972328	+	0.233621i	$0.924942\pi$
$8$	−0.490035	+	1.50817i	−0.173254	+	0.533220i
$9$	−0.874032	+	2.68999i	−0.291344	+	0.896665i
$10$	−0.335106	−	0.243469i	−0.105970	−	0.0769915i
$11$	1.00203	+	3.08393i	0.302124	+	0.929841i	0.980735	+	0.195344i	$0.0625822\pi$
$11$	1.00203	+	3.08393i	0.302124	+	0.929841i	−0.678611	+	0.734498i	$0.737418\pi$
$12$	0.612717	+	0.445165i	0.176876	+	0.128508i
$13$	3.09726	−	2.25029i	0.859026	−	0.624119i	−0.0685937	−	0.997645i	$-0.521851\pi$
$13$	3.09726	−	2.25029i	0.859026	−	0.624119i	0.927620	+	0.373526i	$0.121851\pi$
$14$	−0.0530189	+	0.163176i	−0.0141699	+	0.0436105i
$15$	−0.335106	+	0.243469i	−0.0865239	+	0.0628633i
$16$	−2.42705	+	1.76336i	−0.606763	+	0.440839i
$17$	−1.80108	+	5.54316i	−0.436827	+	1.34441i	0.454376	+	0.890810i	$0.349862\pi$
$17$	−1.80108	+	5.54316i	−0.436827	+	1.34441i	−0.891203	+	0.453605i	$0.850138\pi$
$18$	0.947822	−	0.688633i	0.223404	−	0.162312i
$19$	−3.57117	−	2.59461i	−0.819283	−	0.595244i	0.0972237	−	0.995263i	$-0.469004\pi$
$19$	−3.57117	−	2.59461i	−0.819283	−	0.595244i	−0.916507	+	0.400018i	$0.869004\pi$
$20$	−0.565015	−	1.73894i	−0.126341	−	0.388838i
$21$	0.138805	+	0.100848i	0.0302898	+	0.0220068i
$22$	0.415055	−	1.27741i	0.0884900	−	0.272344i
$23$	−1.23607	+	3.80423i	−0.257738	+	0.793236i	0.735540	+	0.677481i	$0.236929\pi$
$23$	−1.23607	+	3.80423i	−0.257738	+	0.793236i	−0.993278	+	0.115755i	$0.963071\pi$
$24$	−0.202979	−	0.624706i	−0.0414329	−	0.127517i
$25$	−4.00000			−0.800000
$26$	−1.58579			−0.310998
$27$	−0.746033	−	2.29605i	−0.143574	−	0.441876i
$28$	−0.612717	+	0.445165i	−0.115793	+	0.0841282i
$29$	5.52431	+	4.01365i	1.02584	+	0.745316i	0.967472	−	0.252979i	$-0.0814105\pi$
$29$	5.52431	+	4.01365i	1.02584	+	0.745316i	0.0583676	+	0.998295i	$0.481410\pi$
$30$	0.171573			0.0313248
$31$		0			0
$31$		0			0
$32$	4.41421			0.780330
$33$	−1.08663	−	0.789481i	−0.189158	−	0.137431i
$34$	1.95314	−	1.41904i	0.334961	−	0.243363i
$35$	−0.127999	−	0.393941i	−0.0216358	−	0.0665881i
$36$	5.17157			0.861929
$37$	1.00000			0.164399			0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000			0.164399			0.0821995	+	0.996616i	$0.473806\pi$
$38$	0.565015	+	1.73894i	0.0916575	+	0.282093i
$39$	−0.490035	+	1.50817i	−0.0784684	+	0.241501i
$40$	−0.490035	+	1.50817i	−0.0774813	+	0.238463i
$41$	6.05572	+	4.39974i	0.945745	+	0.687124i	0.949797	−	0.312868i	$-0.101290\pi$
$41$	6.05572	+	4.39974i	0.945745	+	0.687124i	−0.00405202	+	0.999992i	$0.501290\pi$
$42$	−0.0219612	−	0.0675895i	−0.00338868	−	0.0104293i
$43$	8.81788	+	6.40656i	1.34471	+	0.976992i	0.999256	+	0.0385571i	$0.0122761\pi$
$43$	8.81788	+	6.40656i	1.34471	+	0.976992i	0.345457	+	0.938435i	$0.387724\pi$
$44$	4.79661	−	3.48494i	0.723116	−	0.525374i
$45$	−0.874032	+	2.68999i	−0.130293	+	0.401001i
$46$	1.34042	−	0.973874i	0.197635	−	0.143590i
$47$	−7.81256	+	5.67616i	−1.13958	+	0.827953i	−0.987061	−	0.160348i	$-0.948738\pi$
$47$	−7.81256	+	5.67616i	−1.13958	+	0.827953i	−0.152518	+	0.988301i	$0.548738\pi$
$48$	0.383997	−	1.18182i	0.0554252	−	0.170581i
$49$	5.52431	−	4.01365i	0.789188	−	0.573378i
$50$	1.34042	+	0.973874i	0.189564	+	0.137727i
$51$	−0.746033	−	2.29605i	−0.104466	−	0.321512i
$52$	−5.66312	−	4.11450i	−0.785333	−	0.570578i
$53$	1.80108	−	5.54316i	0.247398	−	0.761412i	−0.747835	−	0.663885i	$-0.768907\pi$
$53$	1.80108	−	5.54316i	0.247398	−	0.761412i	0.995233	−	0.0975275i	$-0.0310934\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	1.00203	+	3.08393i	0.135114	+	0.415838i
$56$	0.656854			0.0877758
$57$	1.82843			0.242181
$58$	−0.874032	−	2.68999i	−0.114766	−	0.353214i
$59$	−3.29356	+	2.39291i	−0.428785	+	0.311531i	−0.781163	−	0.624327i	$-0.785373\pi$
$59$	−3.29356	+	2.39291i	−0.428785	+	0.311531i	0.352378	+	0.935858i	$0.385373\pi$
$60$	0.612717	+	0.445165i	0.0791014	+	0.0574705i
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$		0			0
$63$	1.17157			0.147604
$64$	3.37487	+	2.45199i	0.421859	+	0.306499i
$65$	3.09726	−	2.25029i	0.384168	−	0.279114i
$66$	0.171921	+	0.529120i	0.0211621	+	0.0651301i
$67$	3.24264			0.396152			0.198076	−	0.980187i	$-0.436531\pi$
$67$	3.24264			0.396152			0.198076	+	0.980187i	$0.436531\pi$
$68$	10.6569			1.29233
$69$	−0.511996	−	1.57576i	−0.0616371	−	0.189699i
$70$	−0.0530189	+	0.163176i	−0.00633697	+	0.0195032i
$71$	0.0219612	−	0.0675895i	0.00260631	−	0.00802140i	−0.949745	−	0.313025i	$-0.898658\pi$
$71$	0.0219612	−	0.0675895i	0.00260631	−	0.00802140i	0.952351	+	0.305004i	$0.0986577\pi$
$72$	−3.62867	−	2.63638i	−0.427643	−	0.310701i
$73$	−0.565015	−	1.73894i	−0.0661300	−	0.203527i	0.912531	−	0.409007i	$-0.134125\pi$
$73$	−0.565015	−	1.73894i	−0.0661300	−	0.203527i	−0.978661	+	0.205479i	$0.934125\pi$
$74$	−0.335106	−	0.243469i	−0.0389553	−	0.0283027i
$75$	1.34042	−	0.973874i	0.154779	−	0.112453i
$76$	−2.49410	+	7.67604i	−0.286093	+	0.880502i
$77$	1.08663	−	0.789481i	0.123833	−	0.0899697i
$78$	0.531406	−	0.386089i	0.0601699	−	0.0437160i
$79$	−2.08814	+	6.42663i	−0.234934	+	0.723052i	0.762196	+	0.647346i	$0.224121\pi$
$79$	−2.08814	+	6.42663i	−0.234934	+	0.723052i	−0.997130	+	0.0757063i	$0.975879\pi$
$80$	−2.42705	+	1.76336i	−0.271353	+	0.197149i
$81$	−6.05572	−	4.39974i	−0.672858	−	0.488860i
$82$	−0.958109	−	2.94876i	−0.105805	−	0.325636i
$83$	8.14767	+	5.91963i	0.894322	+	0.649763i	0.937001	−	0.349326i	$-0.113589\pi$
$83$	8.14767	+	5.91963i	0.894322	+	0.649763i	−0.0426790	+	0.999089i	$0.513589\pi$
$84$	0.0969413	−	0.298355i	0.0105772	−	0.0325531i
$85$	−1.80108	+	5.54316i	−0.195355	+	0.601241i
$86$	−1.39512	−	4.29375i	−0.150440	−	0.463007i
$87$	−2.82843			−0.303239
$88$	−5.14214			−0.548153
$89$	1.38603	+	4.26576i	0.146919	+	0.452169i	0.997253	−	0.0740741i	$-0.0236001\pi$
$89$	1.38603	+	4.26576i	0.146919	+	0.452169i	−0.850334	+	0.526243i	$0.823600\pi$
$90$	0.947822	−	0.688633i	0.0999092	−	0.0725883i
$91$	−1.28293	−	0.932102i	−0.134487	−	0.0977108i
$92$	7.31371			0.762507
$93$		0			0
$94$	4.00000			0.412568
$95$	−3.57117	−	2.59461i	−0.366395	−	0.266201i
$96$	−1.47923	+	1.07472i	−0.150973	+	0.109688i
$97$	1.59810	+	4.91846i	0.162263	+	0.499394i	0.998824	−	0.0484796i	$-0.0154376\pi$
$97$	1.59810	+	4.91846i	0.162263	+	0.499394i	−0.836561	+	0.547873i	$0.815438\pi$
$98$	−2.82843			−0.285714
$99$	−9.17157			−0.921778
$100$	2.26006	+	6.95575i	0.226006	+	0.695575i
$101$	−2.62210	+	8.06998i	−0.260908	+	0.802993i	0.731700	+	0.681627i	$0.238727\pi$
$101$	−2.62210	+	8.06998i	−0.260908	+	0.802993i	−0.992608	+	0.121366i	$0.961273\pi$
$102$	−0.309017	+	0.951057i	−0.0305972	+	0.0941686i
$103$	−1.67553	−	1.21734i	−0.165095	−	0.119948i	0.502170	−	0.864769i	$-0.332535\pi$
$103$	−1.67553	−	1.21734i	−0.165095	−	0.119948i	−0.667265	+	0.744820i	$0.732535\pi$
$104$	1.87606	+	5.77393i	0.183963	+	0.566180i
$105$	0.138805	+	0.100848i	0.0135460	+	0.00984176i
$106$	−1.95314	+	1.41904i	−0.189706	+	0.137829i
$107$	3.83620	−	11.8066i	0.370860	−	1.14139i	−0.575370	−	0.817893i	$-0.695142\pi$
$107$	3.83620	−	11.8066i	0.370860	−	1.14139i	0.946230	−	0.323496i	$-0.104858\pi$
$108$	−3.57117	+	2.59461i	−0.343636	+	0.249666i
$109$	8.76038	−	6.36479i	0.839092	−	0.609636i	−0.0830246	−	0.996547i	$-0.526458\pi$
$109$	8.76038	−	6.36479i	0.839092	−	0.609636i	0.922117	+	0.386911i	$0.126458\pi$
$110$	0.415055	−	1.27741i	0.0395739	−	0.121796i
$111$	−0.335106	+	0.243469i	−0.0318068	+	0.0231090i
$112$	1.00532	+	0.730406i	0.0949936	+	0.0690169i
$113$	5.14725	+	15.8416i	0.484213	+	1.49025i	0.833118	+	0.553095i	$0.186553\pi$
$113$	5.14725	+	15.8416i	0.484213	+	1.49025i	−0.348905	+	0.937158i	$0.613447\pi$
$114$	−0.612717	−	0.445165i	−0.0573862	−	0.0416935i
$115$	−1.23607	+	3.80423i	−0.115264	+	0.354746i
$116$	3.85816	−	11.8742i	0.358222	−	1.10249i
$117$	3.34617	+	10.2984i	0.309353	+	0.952092i
$118$	1.68629			0.155236
$119$	2.41421			0.221311
$120$	−0.202979	−	0.624706i	−0.0185294	−	0.0570276i
$121$	0.392601	−	0.285241i	0.0356910	−	0.0259310i
$122$	0.947822	+	0.688633i	0.0858118	+	0.0623459i
$123$	−3.10051			−0.279563
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−0.392601	−	0.285241i	−0.0349757	−	0.0254113i
$127$	−7.19984	+	5.23099i	−0.638883	+	0.464175i	−0.859466	−	0.511193i	$-0.829204\pi$
$127$	−7.19984	+	5.23099i	−0.638883	+	0.464175i	0.220583	+	0.975368i	$0.429204\pi$
$128$	−3.26209	−	10.0397i	−0.288331	−	0.887391i
$129$	−4.51472			−0.397499
$130$	−1.58579			−0.139083
$131$	−4.09220	−	12.5945i	−0.357537	−	1.10039i	−0.954524	−	0.298135i	$-0.903635\pi$
$131$	−4.09220	−	12.5945i	−0.357537	−	1.10039i	0.596986	−	0.802251i	$-0.296365\pi$
$132$	−0.758898	+	2.33565i	−0.0660536	+	0.203292i
$133$	−0.565015	+	1.73894i	−0.0489930	+	0.150785i
$134$	−1.08663	−	0.789481i	−0.0938703	−	0.0682008i
$135$	−0.746033	−	2.29605i	−0.0642083	−	0.197613i
$136$	−7.47745	−	5.43269i	−0.641186	−	0.465849i
$137$	−7.67375	+	5.57531i	−0.655613	+	0.476331i	−0.865179	−	0.501464i	$-0.832795\pi$
$137$	−7.67375	+	5.57531i	−0.655613	+	0.476331i	0.209566	+	0.977795i	$0.432795\pi$
$138$	−0.212076	+	0.652702i	−0.0180531	+	0.0555617i
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	−0.612717	+	0.445165i	−0.0517840	+	0.0376233i
$141$	1.23607	−	3.80423i	0.104096	−	0.320374i
$142$	−0.0238152	+	0.0173028i	−0.00199853	+	0.00145202i
$143$	10.0433	+	7.29689i	0.839864	+	0.610197i
$144$	−2.62210	−	8.06998i	−0.218508	−	0.672499i
$145$	5.52431	+	4.01365i	0.458769	+	0.333315i
$146$	−0.234037	+	0.720292i	−0.0193690	+	0.0596117i
$147$	−0.874032	+	2.68999i	−0.0720889	+	0.221867i
$148$	−0.565015	−	1.73894i	−0.0464440	−	0.142940i
$149$	1.00000			0.0819232			0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000			0.0819232			0.0409616	+	0.999161i	$0.486958\pi$
$150$	−0.686292			−0.0560355
$151$	1.64203	+	5.05364i	0.133626	+	0.411259i	0.995374	−	0.0960781i	$-0.0306299\pi$
$151$	1.64203	+	5.05364i	0.133626	+	0.411259i	−0.861748	+	0.507337i	$0.830630\pi$
$152$	5.66312	−	4.11450i	0.459340	−	0.333730i
$153$	−13.3369	−	9.68981i	−1.07822	−	0.783374i
$154$	−0.556349			−0.0448319
$155$		0			0
$156$	2.89949			0.232145
$157$	−7.41996	−	5.39092i	−0.592177	−	0.430242i	0.250916	−	0.968009i	$-0.419268\pi$
$157$	−7.41996	−	5.39092i	−0.592177	−	0.430242i	−0.843094	+	0.537767i	$0.819268\pi$
$158$	2.26443	−	1.64520i	0.180148	−	0.130885i
$159$	0.746033	+	2.29605i	0.0591643	+	0.182089i
$160$	4.41421			0.348974
$161$	1.65685			0.130578
$162$	0.958109	+	2.94876i	0.0752761	+	0.231676i
$163$	6.48026	−	19.9442i	0.507573	−	1.56215i	−0.288828	−	0.957381i	$-0.593266\pi$
$163$	6.48026	−	19.9442i	0.507573	−	1.56215i	0.796401	−	0.604769i	$-0.206734\pi$
$164$	4.22930	−	13.0164i	0.330253	−	1.01641i
$165$	−1.08663	−	0.789481i	−0.0845939	−	0.0614610i
$166$	−1.28909	−	3.96740i	−0.100053	−	0.307930i
$167$	−18.2485	−	13.2583i	−1.41211	−	1.02596i	−0.993012	−	0.118016i	$-0.962347\pi$
$167$	−18.2485	−	13.2583i	−1.41211	−	1.02596i	−0.419097	−	0.907941i	$-0.637653\pi$
$168$	−0.220116	+	0.159923i	−0.0169823	+	0.0123384i
$169$	0.511996	−	1.57576i	0.0393843	−	0.121212i
$170$	1.95314	−	1.41904i	0.149799	−	0.108835i
$171$	10.1008	−	7.33866i	0.772428	−	0.561202i
$172$	6.15838	−	18.9535i	0.469572	−	1.44519i
$173$	−6.72593	+	4.88668i	−0.511363	+	0.371527i	−0.813340	−	0.581788i	$-0.802353\pi$
$173$	−6.72593	+	4.88668i	−0.511363	+	0.371527i	0.301977	+	0.953315i	$0.402353\pi$
$174$	0.947822	+	0.688633i	0.0718542	+	0.0522052i
$175$	0.511996	+	1.57576i	0.0387033	+	0.119116i
$176$	−7.87005	−	5.71793i	−0.593228	−	0.431005i
$177$	0.521093	−	1.60376i	0.0391677	−	0.120546i
$178$	0.574112	−	1.76693i	0.0430315	−	0.132437i
$179$	−4.71024	−	14.4966i	−0.352059	−	1.08353i	−0.957695	−	0.287785i	$-0.907081\pi$
$179$	−4.71024	−	14.4966i	−0.352059	−	1.08353i	0.605635	−	0.795742i	$-0.292919\pi$
$180$	5.17157			0.385466
$181$	12.3137			0.915271			0.457635	−	0.889140i	$-0.348697\pi$
$181$	12.3137			0.915271			0.457635	+	0.889140i	$0.348697\pi$
$182$	0.202979	+	0.624706i	0.0150458	+	0.0463063i
$183$	0.947822	−	0.688633i	0.0700650	−	0.0509052i
$184$	−5.13171	−	3.72841i	−0.378315	−	0.274862i
$185$	1.00000			0.0735215
$186$		0			0
$187$	−18.8995			−1.38207
$188$	14.2847	+	10.3784i	1.04182	+	0.756925i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	0.565015	+	1.73894i	0.0409905	+	0.126156i
$191$	−20.8995			−1.51223			−0.756117	−	0.654436i	$-0.772906\pi$
$191$	−20.8995			−1.51223			−0.756117	+	0.654436i	$0.772906\pi$
$192$	−1.72792			−0.124702
$193$	2.20704	+	6.79257i	0.158866	+	0.488940i	0.998532	−	0.0541632i	$-0.0172491\pi$
$193$	2.20704	+	6.79257i	0.158866	+	0.488940i	−0.839666	+	0.543103i	$0.817249\pi$
$194$	0.661956	−	2.03729i	0.0475257	−	0.146269i
$195$	−0.490035	+	1.50817i	−0.0350921	+	0.108002i
$196$	−10.1008	−	7.33866i	−0.721486	−	0.524190i
$197$	−4.16718	−	12.8253i	−0.296899	−	0.913762i	−0.982577	−	0.185857i	$-0.940494\pi$
$197$	−4.16718	−	12.8253i	−0.296899	−	0.913762i	0.685677	−	0.727905i	$-0.259506\pi$
$198$	3.07345	+	2.23299i	0.218420	+	0.158692i
$199$	−14.8974	+	10.8236i	−1.05605	+	0.767265i	−0.973353	−	0.229310i	$-0.926353\pi$
$199$	−14.8974	+	10.8236i	−1.05605	+	0.767265i	−0.0826961	+	0.996575i	$0.526353\pi$
$200$	1.96014	−	6.03269i	0.138603	−	0.426576i
$201$	−1.08663	+	0.789481i	−0.0766448	+	0.0556857i
$202$	2.84347	−	2.06590i	0.200066	−	0.145356i
$203$	0.874032	−	2.68999i	0.0613450	−	0.188801i
$204$	−3.57117	+	2.59461i	−0.250032	+	0.181659i
$205$	6.05572	+	4.39974i	0.422950	+	0.307291i
$206$	0.265095	+	0.815878i	0.0184700	+	0.0568449i
$207$	−9.15298	−	6.65003i	−0.636176	−	0.462209i
$208$	−3.54915	+	10.9232i	−0.246089	+	0.757384i
$209$	4.42318	−	13.6131i	0.305958	−	0.941641i
$210$	−0.0219612	−	0.0675895i	−0.00151546	−	0.00466412i
$211$	10.4142			0.716944			0.358472	−	0.933540i	$-0.383298\pi$
$211$	10.4142			0.716944			0.358472	+	0.933540i	$0.383298\pi$
$212$	−10.6569			−0.731916
$213$	0.00909661	+	0.0279965i	0.000623290	+	0.00191829i
$214$	−4.16008	+	3.02247i	−0.284377	+	0.206612i
$215$	8.81788	+	6.40656i	0.601374	+	0.436924i
$216$	3.82843			0.260491
$217$		0			0
$218$	−4.48528			−0.303782
$219$	0.612717	+	0.445165i	0.0414035	+	0.0300814i
$220$	4.79661	−	3.48494i	0.323387	−	0.234955i
$221$	6.89532	+	21.2216i	0.463829	+	1.42752i
$222$	0.171573			0.0115152
$223$	−23.7279			−1.58894			−0.794470	−	0.607304i	$-0.792251\pi$
$223$	−23.7279			−1.58894			−0.794470	+	0.607304i	$0.792251\pi$
$224$	−0.565015	−	1.73894i	−0.0377517	−	0.116188i
$225$	3.49613	−	10.7600i	0.233075	−	0.717332i
$226$	2.13206	−	6.56181i	0.141823	−	0.436485i
$227$	14.8974	+	10.8236i	0.988776	+	0.718388i	0.959653	−	0.281188i	$-0.0907285\pi$
$227$	14.8974	+	10.8236i	0.988776	+	0.718388i	0.0291233	+	0.999576i	$0.490728\pi$
$228$	−1.03309	−	3.17952i	−0.0684180	−	0.210569i
$229$	4.43769	+	3.22417i	0.293251	+	0.213059i	0.724676	−	0.689089i	$-0.241989\pi$
$229$	4.43769	+	3.22417i	0.293251	+	0.213059i	−0.431426	+	0.902148i	$0.641989\pi$
$230$	1.34042	−	0.973874i	0.0883849	−	0.0642154i
$231$	−0.171921	+	0.529120i	−0.0113116	+	0.0348135i
$232$	−8.76038	+	6.36479i	−0.575147	+	0.417869i
$233$	7.41996	−	5.39092i	0.486098	−	0.353171i	−0.317584	−	0.948230i	$-0.602872\pi$
$233$	7.41996	−	5.39092i	0.486098	−	0.353171i	0.803682	+	0.595060i	$0.202872\pi$
$234$	1.38603	−	4.26576i	0.0906075	−	0.278861i
$235$	−7.81256	+	5.67616i	−0.509635	+	0.370272i
$236$	6.02204	+	4.37527i	0.392001	+	0.284806i
$237$	−0.864935	−	2.66200i	−0.0561836	−	0.172915i
$238$	−0.809017	−	0.587785i	−0.0524408	−	0.0381005i
$239$	−6.56434	+	20.2030i	−0.424612	+	1.30682i	0.478754	+	0.877949i	$0.341089\pi$
$239$	−6.56434	+	20.2030i	−0.424612	+	1.30682i	−0.903366	+	0.428871i	$0.858911\pi$
$240$	0.383997	−	1.18182i	0.0247869	−	0.0762863i
$241$	4.12326	+	12.6901i	0.265602	+	0.817440i	0.991554	+	0.129694i	$0.0413996\pi$
$241$	4.12326	+	12.6901i	0.265602	+	0.817440i	−0.725952	+	0.687746i	$0.758600\pi$
$242$	−0.201010			−0.0129214
$243$	10.3431			0.663513
$244$	1.59810	+	4.91846i	0.102308	+	0.314872i
$245$	5.52431	−	4.01365i	0.352935	−	0.256423i
$246$	1.03900	+	0.754876i	0.0662440	+	0.0481291i
$247$	−16.8995			−1.07529
$248$		0			0
$249$	−4.17157			−0.264363
$250$	3.01595	+	2.19122i	0.190746	+	0.138585i
$251$	−5.18921	+	3.77018i	−0.327540	+	0.237972i	−0.739386	−	0.673282i	$-0.764884\pi$
$251$	−5.18921	+	3.77018i	−0.327540	+	0.237972i	0.411846	+	0.911253i	$0.364884\pi$
$252$	−0.661956	−	2.03729i	−0.0416993	−	0.128337i
$253$	−12.9706			−0.815452
$254$	3.68629			0.231299
$255$	−0.746033	−	2.29605i	−0.0467184	−	0.143784i
$256$	1.22697	−	3.77623i	0.0766857	−	0.236014i
$257$	6.89532	−	21.2216i	0.430118	−	1.32377i	−0.467890	−	0.883787i	$-0.654986\pi$
$257$	6.89532	−	21.2216i	0.430118	−	1.32377i	0.898008	−	0.439980i	$-0.145014\pi$
$258$	1.51291	+	1.09919i	0.0941896	+	0.0684327i
$259$	−0.127999	−	0.393941i	−0.00795347	−	0.0244783i
$260$	−5.66312	−	4.11450i	−0.351212	−	0.255170i
$261$	−15.6251	+	11.3523i	−0.967171	+	0.702691i
$262$	−1.69505	+	5.21681i	−0.104720	+	0.322296i
$263$	18.8612	−	13.7035i	1.16303	−	0.844991i	0.172872	−	0.984944i	$-0.444695\pi$
$263$	18.8612	−	13.7035i	1.16303	−	0.844991i	0.990158	+	0.139953i	$0.0446952\pi$
$264$	1.72316	−	1.25195i	0.106053	−	0.0770521i
$265$	1.80108	−	5.54316i	0.110640	−	0.340514i
$266$	0.612717	−	0.445165i	0.0375681	−	0.0272948i
$267$	−1.50304	−	1.09203i	−0.0919848	−	0.0668309i
$268$	−1.83214	−	5.63875i	−0.111916	−	0.344441i
$269$	21.1732	+	15.3833i	1.29096	+	0.937934i	0.999824	−	0.0187489i	$-0.00596830\pi$
$269$	21.1732	+	15.3833i	1.29096	+	0.937934i	0.291131	+	0.956683i	$0.405968\pi$
$270$	−0.309017	+	0.951057i	−0.0188062	+	0.0578795i
$271$	−0.212076	+	0.652702i	−0.0128827	+	0.0396488i	−0.957291	−	0.289125i	$-0.906636\pi$
$271$	−0.212076	+	0.652702i	−0.0128827	+	0.0396488i	0.944409	+	0.328774i	$0.106636\pi$
$272$	−5.40325	−	16.6295i	−0.327620	−	1.00831i
$273$	0.656854			0.0397546
$274$	3.92893			0.237355
$275$	−4.00812	−	12.3357i	−0.241699	−	0.743873i
$276$	−2.45087	+	1.78066i	−0.147525	+	0.107183i
$277$	−11.4412	−	8.31254i	−0.687437	−	0.499452i	0.188380	−	0.982096i	$-0.439676\pi$
$277$	−11.4412	−	8.31254i	−0.687437	−	0.499452i	−0.875817	+	0.482644i	$0.839676\pi$
$278$		0			0
$279$		0			0
$280$	0.656854			0.0392545
$281$	−1.61803	−	1.17557i	−0.0965238	−	0.0701287i	0.538477	−	0.842641i	$-0.319000\pi$
$281$	−1.61803	−	1.17557i	−0.0965238	−	0.0701287i	−0.635000	+	0.772512i	$0.719000\pi$
$282$	−1.34042	+	0.973874i	−0.0798210	+	0.0579934i
$283$	−4.22020	−	12.9884i	−0.250865	−	0.772083i	−0.994616	−	0.103626i	$-0.966955\pi$
$283$	−4.22020	−	12.9884i	−0.250865	−	0.772083i	0.743751	−	0.668456i	$-0.233045\pi$
$284$	−0.129942			−0.00771066
$285$	1.82843			0.108307
$286$	−1.58901	−	4.89046i	−0.0939600	−	0.289179i
$287$	0.958109	−	2.94876i	0.0565554	−	0.174060i
$288$	−3.85816	+	11.8742i	−0.227345	+	0.699694i
$289$	−13.7295	−	9.97505i	−0.807616	−	0.586767i
$290$	−0.874032	−	2.68999i	−0.0513249	−	0.157962i
$291$	−1.73302	−	1.25912i	−0.101592	−	0.0738107i
$292$	−2.70466	+	1.96505i	−0.158278	+	0.114996i
$293$	4.57314	−	14.0747i	0.267166	−	0.822251i	−0.724021	−	0.689778i	$-0.757708\pi$
$293$	4.57314	−	14.0747i	0.267166	−	0.822251i	0.991187	−	0.132473i	$-0.0422919\pi$
$294$	0.947822	−	0.688633i	0.0552781	−	0.0401619i
$295$	−3.29356	+	2.39291i	−0.191759	+	0.139321i
$296$	−0.490035	+	1.50817i	−0.0284827	+	0.0876607i
$297$	6.33333	−	4.60143i	0.367497	−	0.267002i
$298$	−0.335106	−	0.243469i	−0.0194122	−	0.0141038i
$299$	4.73220	+	14.5642i	0.273670	+	0.842270i
$300$	−2.45087	−	1.78066i	−0.141501	−	0.102806i
$301$	1.39512	−	4.29375i	0.0804137	−	0.247488i
$302$	0.680150	−	2.09329i	0.0391382	−	0.120455i
$303$	−1.08611	−	3.34270i	−0.0623953	−	0.192033i
$304$	13.2426			0.759518
$305$	−2.82843			−0.161955
$306$	2.11010	+	6.49422i	0.120626	+	0.371250i
$307$	9.09549	−	6.60826i	0.519107	−	0.377153i	−0.297160	−	0.954828i	$-0.596040\pi$
$307$	9.09549	−	6.60826i	0.519107	−	0.377153i	0.816267	+	0.577674i	$0.196040\pi$
$308$	−1.98682	−	1.44351i	−0.113210	−	0.0822516i
$309$	0.857864			0.0488022
$310$		0			0
$311$	11.3137			0.641542			0.320771	−	0.947157i	$-0.396058\pi$
$311$	11.3137			0.641542			0.320771	+	0.947157i	$0.396058\pi$
$312$	−2.03445	−	1.47811i	−0.115178	−	0.0836818i
$313$	1.47923	−	1.07472i	0.0836109	−	0.0607469i	−0.545194	−	0.838310i	$-0.683544\pi$
$313$	1.47923	−	1.07472i	0.0836109	−	0.0607469i	0.628805	+	0.777563i	$0.283544\pi$
$314$	1.17395	+	3.61305i	0.0662500	+	0.203896i
$315$	1.17157			0.0660107
$316$	12.3553			0.695042
$317$	−2.41912	−	7.44528i	−0.135871	−	0.418168i	0.859853	−	0.510541i	$-0.170555\pi$
$317$	−2.41912	−	7.44528i	−0.135871	−	0.418168i	−0.995725	+	0.0923727i	$0.970555\pi$
$318$	0.309017	−	0.951057i	0.0173288	−	0.0533326i
$319$	−6.84230	+	21.0584i	−0.383095	+	1.17905i
$320$	3.37487	+	2.45199i	0.188661	+	0.137070i
$321$	1.58901	+	4.89046i	0.0886897	+	0.272959i
$322$	−0.555221	−	0.403392i	−0.0309413	−	0.0224802i
$323$	20.8143	−	15.1225i	1.15814	−	0.841438i
$324$	−4.22930	+	13.0164i	−0.234961	+	0.723135i
$325$	−12.3891	+	9.00117i	−0.687221	+	0.499295i
$326$	−7.02736	+	5.10567i	−0.389209	+	0.282777i
$327$	−1.38603	+	4.26576i	−0.0766475	+	0.235897i
$328$	−9.60308	+	6.97704i	−0.530241	+	0.385243i
$329$	3.23607	+	2.35114i	0.178410	+	0.129623i
$330$	0.171921	+	0.529120i	0.00946396	+	0.0291271i
$331$	−7.47745	−	5.43269i	−0.410998	−	0.298608i	0.363008	−	0.931786i	$-0.381750\pi$
$331$	−7.47745	−	5.43269i	−0.410998	−	0.298608i	−0.774006	+	0.633179i	$0.781750\pi$
$332$	5.69030	−	17.5130i	0.312296	−	0.961148i
$333$	−0.874032	+	2.68999i	−0.0478967	+	0.147411i
$334$	2.88719	+	8.88586i	0.157980	+	0.486213i
$335$	3.24264			0.177164
$336$	−0.514719			−0.0280802
$337$	2.87809	+	8.85786i	0.156780	+	0.482519i	0.998337	−	0.0576496i	$-0.0183606\pi$
$337$	2.87809	+	8.85786i	0.156780	+	0.482519i	−0.841557	+	0.540168i	$0.818361\pi$
$338$	−0.555221	+	0.403392i	−0.0302001	+	0.0219416i
$339$	−5.58181	−	4.05542i	−0.303162	−	0.220260i
$340$	10.6569			0.577949
$341$		0			0
$342$	−5.17157			−0.279647
$343$	−4.63399	−	3.36679i	−0.250212	−	0.181789i
$344$	−13.9833	+	10.1594i	−0.753927	+	0.547760i
$345$	−0.511996	−	1.57576i	−0.0275649	−	0.0848362i
$346$	3.44365			0.185132
$347$	−8.55635			−0.459329			−0.229664	−	0.973270i	$-0.573763\pi$
$347$	−8.55635			−0.459329			−0.229664	+	0.973270i	$0.573763\pi$
$348$	1.59810	+	4.91846i	0.0856674	+	0.263657i
$349$	−8.37828	+	25.7857i	−0.448479	+	1.38028i	0.430143	+	0.902761i	$0.358463\pi$
$349$	−8.37828	+	25.7857i	−0.448479	+	1.38028i	−0.878623	+	0.477517i	$0.841537\pi$
$350$	0.212076	−	0.652702i	0.0113359	−	0.0348884i
$351$	−7.47745	−	5.43269i	−0.399117	−	0.289975i
$352$	4.42318	+	13.6131i	0.235756	+	0.725583i
$353$	−2.42705	−	1.76336i	−0.129179	−	0.0938540i	0.521320	−	0.853362i	$-0.325440\pi$
$353$	−2.42705	−	1.76336i	−0.129179	−	0.0938540i	−0.650498	+	0.759508i	$0.725440\pi$
$354$	−0.565086	+	0.410559i	−0.0300340	+	0.0218210i
$355$	0.0219612	−	0.0675895i	0.00116558	−	0.00358728i
$356$	6.63476	−	4.82043i	0.351641	−	0.255482i
$357$	−0.809017	+	0.587785i	−0.0428177	+	0.0311089i
$358$	−1.95104	+	6.00469i	−0.103116	+	0.317358i
$359$	−5.74443	+	4.17357i	−0.303179	+	0.220273i	−0.728964	−	0.684552i	$-0.759998\pi$
$359$	−5.74443	+	4.17357i	−0.303179	+	0.220273i	0.425785	+	0.904824i	$0.359998\pi$
$360$	−3.62867	−	2.63638i	−0.191248	−	0.138950i
$361$	0.149960	+	0.461530i	0.00789264	+	0.0242911i
$362$	−4.12640	−	2.99800i	−0.216879	−	0.157571i
$363$	−0.0621155	+	0.191172i	−0.00326022	+	0.0100339i
$364$	−0.895993	+	2.75758i	−0.0469628	+	0.144537i
$365$	−0.565015	−	1.73894i	−0.0295742	−	0.0910202i
$366$	−0.485281			−0.0253661
$367$	−24.2132			−1.26392			−0.631959	−	0.775001i	$-0.717749\pi$
$367$	−24.2132			−1.26392			−0.631959	+	0.775001i	$0.717749\pi$
$368$	−3.70820	−	11.4127i	−0.193303	−	0.594927i
$369$	−17.1282	+	12.4443i	−0.891657	+	0.647826i
$370$	−0.335106	−	0.243469i	−0.0174213	−	0.0126573i
$371$	−2.41421			−0.125340
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	6.33333	+	4.60143i	0.327489	+	0.237934i
$375$	3.01595	−	2.19122i	0.155743	−	0.113154i
$376$	−4.73220	−	14.5642i	−0.244044	−	0.751091i
$377$	26.1421			1.34639
$378$	0.414214			0.0213048
$379$	2.28202	+	7.02334i	0.117220	+	0.360765i	0.992403	−	0.123026i	$-0.0392597\pi$
$379$	2.28202	+	7.02334i	0.117220	+	0.360765i	−0.875184	+	0.483790i	$0.839260\pi$
$380$	−2.49410	+	7.67604i	−0.127944	+	0.393773i
$381$	1.13913	−	3.50587i	0.0583592	−	0.179611i
$382$	7.00354	+	5.08837i	0.358332	+	0.260344i
$383$	1.57614	+	4.85087i	0.0805371	+	0.247868i	0.983215	−	0.182448i	$-0.0584022\pi$
$383$	1.57614	+	4.85087i	0.0805371	+	0.247868i	−0.902678	+	0.430316i	$0.858402\pi$
$384$	3.53749	+	2.57014i	0.180522	+	0.131157i
$385$	1.08663	−	0.789481i	0.0553797	−	0.0402357i
$386$	0.914186	−	2.81358i	0.0465309	−	0.143207i
$387$	−24.9407	+	18.1205i	−1.26781	+	0.921117i
$388$	7.64994	−	5.55801i	0.388367	−	0.282165i
$389$	−3.44311	+	10.5968i	−0.174573	+	0.537279i	−0.999614	−	0.0277936i	$-0.991152\pi$
$389$	−3.44311	+	10.5968i	−0.174573	+	0.537279i	0.825041	+	0.565073i	$0.191152\pi$
$390$	0.531406	−	0.386089i	0.0269088	−	0.0195504i
$391$	−18.8612	−	13.7035i	−0.953851	−	0.693013i
$392$	3.34617	+	10.2984i	0.169007	+	0.520150i
$393$	4.43769	+	3.22417i	0.223852	+	0.162638i
$394$	−1.72610	+	5.31240i	−0.0869598	+	0.267635i
$395$	−2.08814	+	6.42663i	−0.105066	+	0.323359i
$396$	5.18208	+	15.9488i	0.260409	+	0.801457i
$397$	−33.4853			−1.68058			−0.840289	−	0.542139i	$-0.817615\pi$
$397$	−33.4853			−1.68058			−0.840289	+	0.542139i	$0.817615\pi$
$398$	7.62742			0.382328
$399$	−0.234037	−	0.720292i	−0.0117165	−	0.0360597i
$400$	9.70820	−	7.05342i	0.485410	−	0.352671i
$401$	21.7047	+	15.7694i	1.08388	+	0.787484i	0.978355	−	0.206933i	$-0.0663482\pi$
$401$	21.7047	+	15.7694i	1.08388	+	0.787484i	0.105524	+	0.994417i	$0.466348\pi$
$402$	0.556349			0.0277482
$403$		0			0
$404$	15.5147			0.771886
$405$	−6.05572	−	4.39974i	−0.300911	−	0.218625i
$406$	−0.947822	+	0.688633i	−0.0470396	+	0.0341763i
$407$	1.00203	+	3.08393i	0.0496688	+	0.152865i
$408$	3.82843			0.189535
$409$	20.6569			1.02142			0.510708	−	0.859754i	$-0.329383\pi$
$409$	20.6569			1.02142			0.510708	+	0.859754i	$0.329383\pi$
$410$	−0.958109	−	2.94876i	−0.0473176	−	0.145629i
$411$	1.21411	−	3.73664i	0.0598875	−	0.184315i
$412$	−1.17018	+	3.60146i	−0.0576509	+	0.177431i
$413$	1.36424	+	0.991177i	0.0671298	+	0.0487726i
$414$	1.44814	+	4.45693i	0.0711724	+	0.219046i
$415$	8.14767	+	5.91963i	0.399953	+	0.290583i
$416$	13.6720	−	9.93327i	0.670324	−	0.487019i
$417$		0			0
$418$	−4.79661	+	3.48494i	−0.234610	+	0.170454i
$419$	−22.6525	+	16.4580i	−1.10665	+	0.804025i	−0.982132	−	0.188193i	$-0.939737\pi$
$419$	−22.6525	+	16.4580i	−1.10665	+	0.804025i	−0.124514	+	0.992218i	$0.539737\pi$
$420$	0.0969413	−	0.298355i	0.00473025	−	0.0145582i
$421$	25.1945	−	18.3049i	1.22791	−	0.892126i	0.231174	−	0.972912i	$-0.425743\pi$
$421$	25.1945	−	18.3049i	1.22791	−	0.892126i	0.996731	+	0.0807867i	$0.0257433\pi$
$422$	−3.48986	−	2.53553i	−0.169884	−	0.123428i
$423$	−8.44040	−	25.9769i	−0.410386	−	1.26304i
$424$	7.47745	+	5.43269i	0.363137	+	0.263835i
$425$	7.20433	−	22.1727i	0.349461	−	1.07553i
$426$	0.00376794	−	0.0115965i	0.000182557	−	0.000561854i
$427$	0.362036	+	1.11423i	0.0175201	+	0.0539215i
$428$	−22.6985			−1.09717
$429$	−5.14214			−0.248265
$430$	−1.39512	−	4.29375i	−0.0672789	−	0.207063i
$431$	13.5570	−	9.84973i	0.653017	−	0.474445i	−0.211280	−	0.977425i	$-0.567763\pi$
$431$	13.5570	−	9.84973i	0.653017	−	0.474445i	0.864298	+	0.502981i	$0.167763\pi$
$432$	5.85942	+	4.25712i	0.281911	+	0.204821i
$433$	27.1127			1.30295			0.651477	−	0.758669i	$-0.274150\pi$
$433$	27.1127			1.30295			0.651477	+	0.758669i	$0.274150\pi$
$434$		0			0
$435$	−2.82843			−0.135613
$436$	−16.0177	−	11.6376i	−0.767110	−	0.557338i
$437$	14.2847	−	10.3784i	0.683330	−	0.496468i
$438$	−0.0969413	−	0.298355i	−0.00463203	−	0.0142559i
$439$	2.07107			0.0988467			0.0494233	−	0.998778i	$-0.484262\pi$
$439$	2.07107			0.0988467			0.0494233	+	0.998778i	$0.484262\pi$
$440$	−5.14214			−0.245142
$441$	5.96826	+	18.3684i	0.284203	+	0.874687i
$442$	2.85613	−	8.79027i	0.135852	−	0.418111i
$443$	−1.47010	+	4.52452i	−0.0698468	+	0.214966i	−0.979887	−	0.199554i	$-0.936051\pi$
$443$	−1.47010	+	4.52452i	−0.0698468	+	0.214966i	0.910040	+	0.414520i	$0.136051\pi$
$444$	0.612717	+	0.445165i	0.0290782	+	0.0211266i
$445$	1.38603	+	4.26576i	0.0657040	+	0.202216i
$446$	7.95136	+	5.77700i	0.376508	+	0.273549i
$447$	−0.335106	+	0.243469i	−0.0158500	+	0.0115157i
$448$	0.533957	−	1.64335i	0.0252271	−	0.0776411i
$449$	32.8683	−	23.8802i	1.55115	−	1.12698i	0.608324	−	0.793688i	$-0.291842\pi$
$449$	32.8683	−	23.8802i	1.55115	−	1.12698i	0.942825	−	0.333288i	$-0.108158\pi$
$450$	−3.79129	+	2.75453i	−0.178723	+	0.129850i
$451$	−7.50048	+	23.0841i	−0.353184	+	1.08699i
$452$	24.6393	−	17.9015i	1.15893	−	0.842016i
$453$	−1.78065	−	1.29372i	−0.0836625	−	0.0607843i
$454$	−2.35700	−	7.25410i	−0.110620	−	0.340452i
$455$	−1.28293	−	0.932102i	−0.0601446	−	0.0436976i
$456$	−0.895993	+	2.75758i	−0.0419587	+	0.129136i
$457$	−9.61435	+	29.5899i	−0.449740	+	1.38416i	0.427460	+	0.904034i	$0.359409\pi$
$457$	−9.61435	+	29.5899i	−0.449740	+	1.38416i	−0.877200	+	0.480124i	$0.840591\pi$
$458$	−0.702111	−	2.16087i	−0.0328075	−	0.100971i
$459$	14.0711			0.656781
$460$	7.31371			0.341003
$461$	−0.661956	−	2.03729i	−0.0308304	−	0.0948862i	0.934457	−	0.356075i	$-0.115885\pi$
$461$	−0.661956	−	2.03729i	−0.0308304	−	0.0948862i	−0.965288	+	0.261189i	$0.915885\pi$
$462$	0.186436	−	0.135454i	0.00867378	−	0.00630187i
$463$	7.25734	+	5.27276i	0.337277	+	0.245046i	0.743512	−	0.668722i	$-0.233159\pi$
$463$	7.25734	+	5.27276i	0.337277	+	0.245046i	−0.406235	+	0.913769i	$0.633159\pi$
$464$	−20.4853			−0.951005
$465$		0			0
$466$	−3.79899			−0.175985
$467$	6.47214	+	4.70228i	0.299495	+	0.217596i	0.727376	−	0.686239i	$-0.240740\pi$
$467$	6.47214	+	4.70228i	0.299495	+	0.217596i	−0.427881	+	0.903835i	$0.640740\pi$
$468$	16.0177	−	11.6376i	0.740419	−	0.537946i
$469$	−0.415055	−	1.27741i	−0.0191655	−	0.0589852i
$470$	4.00000			0.184506
$471$	3.79899			0.175048
$472$	−1.99497	−	6.13987i	−0.0918257	−	0.282611i
$473$	−10.9216	+	33.6133i	−0.502177	+	1.54554i
$474$	−0.358268	+	1.10264i	−0.0164558	+	0.0506457i
$475$	14.2847	+	10.3784i	0.655427	+	0.476195i
$476$	−1.36407	−	4.19817i	−0.0625219	−	0.192423i
$477$	13.3369	+	9.68981i	0.610653	+	0.443666i
$478$	7.11853	−	5.17192i	0.325594	−	0.236558i
$479$	−4.86020	+	14.9581i	−0.222068	+	0.683455i	0.776508	+	0.630107i	$0.216989\pi$
$479$	−4.86020	+	14.9581i	−0.222068	+	0.683455i	−0.998576	+	0.0533476i	$0.983011\pi$
$480$	−1.47923	+	1.07472i	−0.0675172	+	0.0490541i
$481$	3.09726	−	2.25029i	0.141223	−	0.102605i
$482$	1.70791	−	5.25641i	0.0777932	−	0.239423i
$483$	−0.555221	+	0.403392i	−0.0252635	+	0.0183550i
$484$	−0.717842	−	0.521543i	−0.0326292	−	0.0237065i
$485$	1.59810	+	4.91846i	0.0725662	+	0.223336i
$486$	−3.46605	−	2.51823i	−0.157223	−	0.114229i
$487$	5.99023	−	18.4360i	0.271443	−	0.835416i	−0.718696	−	0.695325i	$-0.755261\pi$
$487$	5.99023	−	18.4360i	0.271443	−	0.835416i	0.990139	−	0.140091i	$-0.0447395\pi$
$488$	1.38603	−	4.26576i	0.0627425	−	0.193102i
$489$	2.68421	+	8.26115i	0.121384	+	0.373582i
$490$	−2.82843			−0.127775
$491$	1.58579			0.0715655			0.0357828	−	0.999360i	$-0.488608\pi$
$491$	1.58579			0.0715655			0.0357828	+	0.999360i	$0.488608\pi$
$492$	1.75183	+	5.39158i	0.0789787	+	0.243071i
$493$	−32.1981	+	23.3933i	−1.45013	+	1.05358i
$494$	5.66312	+	4.11450i	0.254796	+	0.185120i
$495$	−9.17157			−0.412232
$496$		0			0
$497$	−0.0294373			−0.00132044
$498$	1.39792	+	1.01565i	0.0626422	+	0.0455122i
$499$	1.79052	−	1.30089i	0.0801546	−	0.0582358i	−0.546986	−	0.837142i	$-0.684225\pi$
$499$	1.79052	−	1.30089i	0.0801546	−	0.0582358i	0.627141	+	0.778906i	$0.284225\pi$
$500$	5.08514	+	15.6504i	0.227414	+	0.699909i
$501$	9.34315			0.417421
$502$	2.65685			0.118581
$503$	−4.13612	−	12.7297i	−0.184421	−	0.567588i	0.815517	−	0.578733i	$-0.196453\pi$
$503$	−4.13612	−	12.7297i	−0.184421	−	0.567588i	−0.999938	+	0.0111444i	$0.996453\pi$
$504$	−0.574112	+	1.76693i	−0.0255730	+	0.0787055i
$505$	−2.62210	+	8.06998i	−0.116682	+	0.359109i
$506$	4.34651	+	3.15793i	0.193226	+	0.140387i
$507$	0.212076	+	0.652702i	0.00941861	+	0.0289875i
$508$	13.1644	+	9.56449i	0.584075	+	0.424356i
$509$	26.5349	−	19.2788i	1.17614	−	0.854516i	0.184409	−	0.982850i	$-0.440963\pi$
$509$	26.5349	−	19.2788i	1.17614	−	0.854516i	0.991731	+	0.128333i	$0.0409628\pi$
$510$	−0.309017	+	0.951057i	−0.0136835	+	0.0421135i
$511$	−0.612717	+	0.445165i	−0.0271050	+	0.0196929i
$512$	−18.4111	+	13.3764i	−0.813663	+	0.591161i
$513$	−3.29315	+	10.1353i	−0.145396	+	0.447483i
$514$	−7.47745	+	5.43269i	−0.329816	+	0.239626i
$515$	−1.67553	−	1.21734i	−0.0738326	−	0.0536425i
$516$	2.55088	+	7.85081i	0.112296	+	0.345613i
$517$	−25.3333	−	18.4057i	−1.11416	−	0.809483i
$518$	−0.0530189	+	0.163176i	−0.00232952	+	0.00716952i
$519$	1.06415	−	3.27511i	0.0467109	−	0.143761i
$520$	1.87606	+	5.77393i	0.0822708	+	0.253204i
$521$	−20.4558			−0.896187			−0.448093	−	0.893987i	$-0.647897\pi$
$521$	−20.4558			−0.896187			−0.448093	+	0.893987i	$0.647897\pi$
$522$	8.00000			0.350150
$523$	−2.47214	−	7.60845i	−0.108099	−	0.332694i	0.882346	−	0.470601i	$-0.155963\pi$
$523$	−2.47214	−	7.60845i	−0.108099	−	0.332694i	−0.990445	+	0.137906i	$0.955963\pi$
$524$	−19.5889	+	14.2322i	−0.855745	+	0.621735i
$525$	−0.555221	−	0.403392i	−0.0242319	−	0.0176055i
$526$	−9.65685			−0.421059
$527$		0			0
$528$	4.02944			0.175359
$529$	5.66312	+	4.11450i	0.246223	+	0.178891i
$530$	−1.95314	+	1.41904i	−0.0848390	+	0.0616391i
$531$	−3.55824	−	10.9511i	−0.154415	−	0.475239i
$532$	3.34315			0.144944
$533$	28.6569			1.24127
$534$	0.237805	+	0.731888i	0.0102908	+	0.0316719i
$535$	3.83620	−	11.8066i	0.165854	−	0.510445i
$536$	−1.58901	+	4.89046i	−0.0686347	+	0.211236i
$537$	5.10790	+	3.71110i	0.220422	+	0.160146i
$538$	−3.34994	−	10.3100i	−0.144426	−	0.444498i
$539$	17.9134	+	13.0148i	0.771583	+	0.560588i
$540$	−3.57117	+	2.59461i	−0.153679	+	0.111654i
$541$	−9.66737	+	29.7531i	−0.415633	+	1.27919i	0.496051	+	0.868293i	$0.334783\pi$
$541$	−9.66737	+	29.7531i	−0.415633	+	1.27919i	−0.911684	+	0.410893i	$0.865217\pi$
$542$	0.229980	−	0.167090i	0.00987850	−	0.00717715i
$543$	−4.12640	+	2.99800i	−0.177081	+	0.128657i
$544$	−7.95037	+	24.4687i	−0.340869	+	1.04909i
$545$	8.76038	−	6.36479i	0.375254	−	0.272638i
$546$	−0.220116	−	0.159923i	−0.00942008	−	0.00684409i
$547$	−6.09626	−	18.7624i	−0.260657	−	0.802221i	−0.992662	−	0.120921i	$-0.961415\pi$
$547$	−6.09626	−	18.7624i	−0.260657	−	0.802221i	0.732005	−	0.681300i	$-0.238585\pi$
$548$	14.0309	+	10.1940i	0.599370	+	0.435468i
$549$	2.47214	−	7.60845i	0.105508	−	0.324721i
$550$	−1.66022	+	5.10963i	−0.0707920	+	0.217875i
$551$	−9.31443	−	28.6669i	−0.396808	−	1.22125i
$552$	2.62742			0.111830
$553$	2.79899			0.119025
$554$	1.81018	+	5.57116i	0.0769072	+	0.236696i
$555$	−0.335106	+	0.243469i	−0.0142244	+	0.0103347i
$556$		0			0
$557$	27.5147			1.16584			0.582918	−	0.812531i	$-0.301911\pi$
$557$	27.5147			1.16584			0.582918	+	0.812531i	$0.301911\pi$
$558$		0			0
$559$	41.7279			1.76490
$560$	1.00532	+	0.730406i	0.0424824	+	0.0308653i
$561$	6.33333	−	4.60143i	0.267393	−	0.194273i
$562$	0.255998	+	0.787881i	0.0107986	+	0.0332348i
$563$	13.2426			0.558111			0.279055	−	0.960275i	$-0.409979\pi$
$563$	13.2426			0.558111			0.279055	+	0.960275i	$0.409979\pi$
$564$	−7.31371			−0.307963
$565$	5.14725	+	15.8416i	0.216546	+	0.666462i
$566$	−1.74806	+	5.37999i	−0.0734766	+	0.226138i
$567$	−0.958109	+	2.94876i	−0.0402368	+	0.123836i
$568$	0.0911749	+	0.0662424i	0.00382561	+	0.00277947i
$569$	−4.06114	−	12.4989i	−0.170252	−	0.523982i	0.829133	−	0.559052i	$-0.188835\pi$
$569$	−4.06114	−	12.4989i	−0.170252	−	0.523982i	−0.999385	+	0.0350699i	$0.988835\pi$
$570$	−0.612717	−	0.445165i	−0.0256639	−	0.0186459i
$571$	17.0707	−	12.4026i	0.714385	−	0.519031i	−0.170200	−	0.985410i	$-0.554441\pi$
$571$	17.0707	−	12.4026i	0.714385	−	0.519031i	0.884585	+	0.466378i	$0.154441\pi$
$572$	7.01422	−	21.5875i	0.293279	−	0.902620i
$573$	7.00354	−	5.08837i	0.292577	−	0.212570i
$574$	−1.03900	+	0.754876i	−0.0433669	+	0.0315079i
$575$	4.94427	−	15.2169i	0.206190	−	0.634589i
$576$	−9.54558	+	6.93527i	−0.397733	+	0.288970i
$577$	0.0238152	+	0.0173028i	0.000991441	+	0.000720324i	0.588281	−	0.808657i	$-0.299805\pi$
$577$	0.0238152	+	0.0173028i	0.000991441	+	0.000720324i	−0.587289	+	0.809377i	$0.699805\pi$
$578$	2.17222	+	6.68539i	0.0903523	+	0.278076i
$579$	−2.39337	−	1.73889i	−0.0994651	−	0.0722656i
$580$	3.85816	−	11.8742i	0.160202	−	0.493050i
$581$	1.28909	−	3.96740i	0.0534803	−	0.164596i
$582$	0.274191	+	0.843874i	0.0113656	+	0.0349797i
$583$	18.8995			0.782737
$584$	2.89949			0.119982
$585$	3.34617	+	10.2984i	0.138347	+	0.425788i
$586$	−4.95923	+	3.60309i	−0.204864	+	0.148842i
$587$	25.6109	+	18.6074i	1.05708	+	0.768011i	0.973545	−	0.228494i	$-0.0733802\pi$
$587$	25.6109	+	18.6074i	1.05708	+	0.768011i	0.0835311	+	0.996505i	$0.473380\pi$
$588$	5.17157			0.213272
$589$		0			0
$590$	1.68629			0.0694235
$591$	4.51900	+	3.28324i	0.185887	+	0.135055i
$592$	−2.42705	+	1.76336i	−0.0997512	+	0.0724735i
$593$	−0.405958	−	1.24941i	−0.0166707	−	0.0513072i	0.942375	−	0.334558i	$-0.108587\pi$
$593$	−0.405958	−	1.24941i	−0.0166707	−	0.0513072i	−0.959046	+	0.283251i	$0.908587\pi$
$594$	−3.24264			−0.133047
$595$	2.41421			0.0989731
$596$	−0.565015	−	1.73894i	−0.0231439	−	0.0712297i
$597$	2.35700	−	7.25410i	0.0964656	−	0.296891i
$598$	1.96014	−	6.03269i	0.0801561	−	0.246695i
$599$	−12.2166	−	8.87585i	−0.499155	−	0.362658i	0.309539	−	0.950887i	$-0.399825\pi$
$599$	−12.2166	−	8.87585i	−0.499155	−	0.362658i	−0.808694	+	0.588229i	$0.799825\pi$
$600$	0.811917	+	2.49882i	0.0331464	+	0.102014i
$601$	5.27052	+	3.82926i	0.214989	+	0.156199i	0.690068	−	0.723744i	$-0.257581\pi$
$601$	5.27052	+	3.82926i	0.214989	+	0.156199i	−0.475079	+	0.879943i	$0.657581\pi$
$602$	−1.51291	+	1.09919i	−0.0616615	+	0.0447997i
$603$	−2.83417	+	8.72268i	−0.115416	+	0.355215i
$604$	7.86019	−	5.71076i	0.319827	−	0.232368i
$605$	0.392601	−	0.285241i	0.0159615	−	0.0115967i
$606$	−0.449881	+	1.38459i	−0.0182751	+	0.0562451i
$607$	1.28293	−	0.932102i	0.0520724	−	0.0378328i	−0.561445	−	0.827514i	$-0.689754\pi$
$607$	1.28293	−	0.932102i	0.0520724	−	0.0378328i	0.613517	+	0.789682i	$0.289754\pi$
$608$	−15.7639	−	11.4532i	−0.639312	−	0.464487i
$609$	0.362036	+	1.11423i	0.0146704	+	0.0451510i
$610$	0.947822	+	0.688633i	0.0383762	+	0.0278819i
$611$	−11.4245	+	35.1611i	−0.462187	+	1.42247i
$612$	−9.31443	+	28.6669i	−0.376514	+	1.15879i
$613$	3.80515	+	11.7110i	0.153688	+	0.473004i	0.998026	−	0.0628079i	$-0.0200055\pi$
$613$	3.80515	+	11.7110i	0.153688	+	0.473004i	−0.844337	+	0.535812i	$0.820006\pi$
$614$	−4.65685			−0.187935
$615$	−3.10051			−0.125024
$616$	0.658188	+	2.02570i	0.0265192	+	0.0816176i
$617$	26.9275	−	19.5640i	1.08406	−	0.787617i	0.105675	−	0.994401i	$-0.466300\pi$
$617$	26.9275	−	19.5640i	1.08406	−	0.787617i	0.978387	+	0.206784i	$0.0662996\pi$
$618$	−0.287475	−	0.208863i	−0.0115640	−	0.00840170i
$619$	−20.3431			−0.817660			−0.408830	−	0.912611i	$-0.634063\pi$
$619$	−20.3431			−0.817660			−0.408830	+	0.912611i	$0.634063\pi$
$620$		0			0
$621$	9.65685			0.387516
$622$	−3.79129	−	2.75453i	−0.152017	−	0.110447i
$623$	1.50304	−	1.09203i	0.0602182	−	0.0437511i
$624$	−1.47010	−	4.52452i	−0.0588513	−	0.181126i
$625$	11.0000			0.440000
$626$	−0.757359			−0.0302702
$627$	1.83214	+	5.63875i	0.0731687	+	0.225190i
$628$	−5.18208	+	15.9488i	−0.206787	+	0.636426i
$629$	−1.80108	+	5.54316i	−0.0718139	+	0.221020i
$630$	−0.392601	−	0.285241i	−0.0156416	−	0.0113643i
$631$	15.4546	+	47.5644i	0.615239	+	1.89351i	0.397972	+	0.917397i	$0.369714\pi$
$631$	15.4546	+	47.5644i	0.615239	+	1.89351i	0.217266	+	0.976112i	$0.430286\pi$
$632$	−8.66921	−	6.29855i	−0.344843	−	0.250543i
$633$	−3.48986	+	2.53553i	−0.138710	+	0.100778i
$634$	−1.00203	+	3.08393i	−0.0397957	+	0.122479i
$635$	−7.19984	+	5.23099i	−0.285717	+	0.207586i
$636$	3.57117	−	2.59461i	0.141606	−	0.102883i
$637$	8.07836	−	24.8626i	0.320076	−	0.985094i
$638$	7.41996	−	5.39092i	0.293759	−	0.213428i
$639$	0.162621	+	0.118151i	0.00643317	+	0.00467397i
$640$	−3.26209	−	10.0397i	−0.128945	−	0.396853i
$641$	11.3024	+	8.21169i	0.446419	+	0.324342i	0.788180	−	0.615444i	$-0.211023\pi$
$641$	11.3024	+	8.21169i	0.446419	+	0.324342i	−0.341761	+	0.939787i	$0.611023\pi$
$642$	0.658188	−	2.02570i	0.0259766	−	0.0799478i
$643$	10.9125	−	33.5853i	0.430348	−	1.32448i	−0.467430	−	0.884030i	$-0.654820\pi$
$643$	10.9125	−	33.5853i	0.430348	−	1.32448i	0.897779	−	0.440446i	$-0.145180\pi$
$644$	−0.936148	−	2.88117i	−0.0368894	−	0.113534i
$645$	−4.51472			−0.177767
$646$	−10.6569			−0.419288
$647$	−14.0027	−	43.0959i	−0.550503	−	1.69427i	−0.707533	−	0.706681i	$-0.750192\pi$
$647$	−14.0027	−	43.0959i	−0.550503	−	1.69427i	0.157029	−	0.987594i	$-0.449808\pi$
$648$	9.60308	−	6.97704i	0.377245	−	0.274084i
$649$	−10.6798	−	7.75936i	−0.419220	−	0.304581i
$650$	6.34315			0.248799
$651$		0			0
$652$	−38.3431			−1.50163
$653$	4.96909	+	3.61026i	0.194456	+	0.141280i	0.680753	−	0.732513i	$-0.261653\pi$
$653$	4.96909	+	3.61026i	0.194456	+	0.141280i	−0.486297	+	0.873793i	$0.661653\pi$
$654$	1.50304	−	1.09203i	0.0587737	−	0.0427016i
$655$	−4.09220	−	12.5945i	−0.159896	−	0.492108i
$656$	−22.4558			−0.876753
$657$	5.17157			0.201762
$658$	−0.511996	−	1.57576i	−0.0199597	−	0.0614296i
$659$	−0.511996	+	1.57576i	−0.0199445	+	0.0613830i	−0.960533	−	0.278165i	$-0.910274\pi$
$659$	−0.511996	+	1.57576i	−0.0199445	+	0.0613830i	0.940589	+	0.339548i	$0.110274\pi$
$660$	−0.758898	+	2.33565i	−0.0295400	+	0.0909149i
$661$	−3.93009	−	2.85538i	−0.152863	−	0.111061i	0.508725	−	0.860929i	$-0.330117\pi$
$661$	−3.93009	−	2.85538i	−0.152863	−	0.111061i	−0.661588	+	0.749868i	$0.730117\pi$
$662$	1.18305	+	3.64105i	0.0459805	+	0.141513i
$663$	−7.47745	−	5.43269i	−0.290400	−	0.210988i
$664$	−12.9205	+	9.38726i	−0.501411	+	0.364296i
$665$	−0.565015	+	1.73894i	−0.0219103	+	0.0674331i
$666$	0.947822	−	0.688633i	0.0367274	−	0.0266840i
$667$	−22.0973	+	16.0546i	−0.855609	+	0.621636i
$668$	−12.7447	+	39.2241i	−0.493106	+	1.51763i
$669$	7.95136	−	5.77700i	0.307418	−	0.223352i
$670$	−1.08663	−	0.789481i	−0.0419801	−	0.0305003i
$671$	−2.83417	−	8.72268i	−0.109412	−	0.336735i
$672$	0.612717	+	0.445165i	0.0236361	+	0.0171726i
$673$	2.88719	−	8.88586i	0.111293	−	0.342525i	−0.879863	−	0.475228i	$-0.842366\pi$
$673$	2.88719	−	8.88586i	0.111293	−	0.342525i	0.991156	+	0.132703i	$0.0423657\pi$
$674$	1.19215	−	3.66905i	0.0459197	−	0.141326i
$675$	2.98413	+	9.18421i	0.114859	+	0.353501i
$676$	−3.02944			−0.116517
$677$	−38.5980			−1.48344			−0.741720	−	0.670709i	$-0.765990\pi$
$677$	−38.5980			−1.48344			−0.741720	+	0.670709i	$0.765990\pi$
$678$	0.883129	+	2.71799i	0.0339164	+	0.104384i
$679$	1.73302	−	1.25912i	0.0665074	−	0.0483204i
$680$	−7.47745	−	5.43269i	−0.286747	−	0.208334i
$681$	−7.62742			−0.292283
$682$		0			0
$683$	−1.37258			−0.0525204			−0.0262602	−	0.999655i	$-0.508360\pi$
$683$	−1.37258			−0.0525204			−0.0262602	+	0.999655i	$0.508360\pi$
$684$	−18.4686	−	13.4182i	−0.706164	−	0.513058i
$685$	−7.67375	+	5.57531i	−0.293199	+	0.213022i
$686$	0.733168	+	2.25646i	0.0279925	+	0.0861521i
$687$	−2.27208			−0.0866852
$688$	−32.6985			−1.24662
$689$	−6.89532	−	21.2216i	−0.262691	−	0.808478i
$690$	−0.212076	+	0.652702i	−0.00807359	+	0.0248479i
$691$	−0.0219612	+	0.0675895i	−0.000835442	+	0.00257123i	−0.951473	−	0.307731i	$-0.900430\pi$
$691$	−0.0219612	+	0.0675895i	−0.000835442	+	0.00257123i	0.950638	+	0.310302i	$0.100430\pi$
$692$	12.2979	+	8.93493i	0.467495	+	0.339655i
$693$	1.17395	+	3.61305i	0.0445948	+	0.137249i
$694$	2.86728	+	2.08320i	0.108841	+	0.0790773i
$695$		0			0
$696$	1.38603	−	4.26576i	0.0525373	−	0.161693i
$697$	−35.2953	+	25.6436i	−1.33691	+	0.971319i
$698$	9.08562	−	6.60109i	0.343896	−	0.249855i
$699$	−1.17395	+	3.61305i	−0.0444030	+	0.136658i
$700$	2.45087	−	1.78066i	0.0926340	−	0.0673026i
$701$	10.9098	+	7.92645i	0.412058	+	0.299378i	0.774435	−	0.632654i	$-0.218034\pi$
$701$	10.9098	+	7.92645i	0.412058	+	0.299378i	−0.362376	+	0.932032i	$0.618034\pi$
$702$	1.18305	+	3.64105i	0.0446513	+	0.137423i
$703$	−3.57117	−	2.59461i	−0.134689	−	0.0978576i
$704$	−4.18005	+	12.8649i	−0.157541	+	0.484863i
$705$	1.23607	−	3.80423i	0.0465530	−	0.143275i
$706$	0.383997	+	1.18182i	0.0144519	+	0.0444784i
$707$	3.51472			0.132185
$708$	−3.08326			−0.115876
$709$	5.35023	+	16.4663i	0.200932	+	0.618405i	0.999856	+	0.0169732i	$0.00540301\pi$
$709$	5.35023	+	16.4663i	0.200932	+	0.618405i	−0.798924	+	0.601432i	$0.794597\pi$
$710$	−0.0238152	+	0.0173028i	−0.000893770	+	0.000649362i
$711$	−15.4625	−	11.2342i	−0.579889	−	0.421314i
$712$	−7.11270			−0.266560
$713$		0			0
$714$	0.414214			0.0155016
$715$	10.0433	+	7.29689i	0.375598	+	0.272888i
$716$	−22.5474	+	16.3816i	−0.842634	+	0.612209i
$717$	−2.71904	−	8.36834i	−0.101544	−	0.312521i
$718$	2.94113			0.109762
$719$	−8.07107			−0.301000			−0.150500	−	0.988610i	$-0.548088\pi$
$719$	−8.07107			−0.301000			−0.150500	+	0.988610i	$0.548088\pi$
$720$	−2.62210	−	8.06998i	−0.0977198	−	0.300750i
$721$	−0.265095	+	0.815878i	−0.00987264	+	0.0303849i
$722$	0.0621155	−	0.191172i	0.00231170	−	0.00711468i
$723$	−4.47137	−	3.24864i	−0.166292	−	0.120818i
$724$	−6.95743	−	21.4128i	−0.258571	−	0.795799i
$725$	−22.0973	−	16.0546i	−0.820671	−	0.596253i
$726$	0.0673597	−	0.0489397i	0.00249995	−	0.00181632i
$727$	12.6204	−	38.8417i	0.468066	−	1.44056i	−0.387018	−	0.922072i	$-0.626495\pi$
$727$	12.6204	−	38.8417i	0.468066	−	1.44056i	0.855085	−	0.518488i	$-0.173505\pi$
$728$	2.03445	−	1.47811i	0.0754017	−	0.0547826i
$729$	14.7011	−	10.6810i	0.544486	−	0.395592i
$730$	−0.234037	+	0.720292i	−0.00866209	+	0.0266592i
$731$	−51.3944	+	37.3402i	−1.90089	+	1.38108i
$732$	−1.73302	−	1.25912i	−0.0640544	−	0.0465383i
$733$	4.82914	+	14.8626i	0.178368	+	0.548961i	0.999771	−	0.0213872i	$-0.00680827\pi$
$733$	4.82914	+	14.8626i	0.178368	+	0.548961i	−0.821403	+	0.570348i	$0.806808\pi$
$734$	8.11399	+	5.89516i	0.299493	+	0.217594i
$735$	−0.874032	+	2.68999i	−0.0322392	+	0.0992219i
$736$	−5.45627	+	16.7927i	−0.201121	+	0.618986i
$737$	3.24923	+	10.0001i	0.119687	+	0.368358i
$738$	8.76955			0.322812
$739$	45.8701			1.68736			0.843679	−	0.536848i	$-0.180385\pi$
$739$	45.8701			1.68736			0.843679	+	0.536848i	$0.180385\pi$
$740$	−0.565015	−	1.73894i	−0.0207704	−	0.0639246i
$741$	5.66312	−	4.11450i	0.208040	−	0.151150i
$742$	0.809017	+	0.587785i	0.0296999	+	0.0215783i
$743$	5.65685			0.207530			0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685			0.207530			0.103765	+	0.994602i	$0.466911\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	−3.35106	−	2.43469i	−0.122691	−	0.0891402i
$747$	−23.0451	+	16.7432i	−0.843175	+	0.612603i
$748$	10.6785	+	32.8650i	0.390445	+	1.20166i
$749$	−5.14214			−0.187890
$750$	−1.54416			−0.0563846
$751$	2.23810	+	6.88816i	0.0816694	+	0.251353i	0.983551	−	0.180631i	$-0.0578139\pi$
$751$	2.23810	+	6.88816i	0.0816694	+	0.251353i	−0.901882	+	0.431983i	$0.857814\pi$
$752$	8.95240	−	27.5526i	0.326460	−	1.00474i
$753$	0.821013	−	2.52682i	0.0299194	−	0.0920824i
$754$	−8.76038	−	6.36479i	−0.319034	−	0.231792i
$755$	1.64203	+	5.05364i	0.0597595	+	0.183921i
$756$	1.47923	+	1.07472i	0.0537990	+	0.0390873i
$757$	−18.8850	+	13.7208i	−0.686387	+	0.498689i	−0.875470	−	0.483272i	$-0.839448\pi$
$757$	−18.8850	+	13.7208i	−0.686387	+	0.498689i	0.189083	+	0.981961i	$0.439448\pi$
$758$	0.945244	−	2.90916i	0.0343328	−	0.105666i
$759$	4.34651	−	3.15793i	0.157768	−	0.114625i
$760$	5.66312	−	4.11450i	0.205423	−	0.149248i
$761$	9.41137	−	28.9652i	0.341162	−	1.04999i	−0.622444	−	0.782664i	$-0.713860\pi$
$761$	9.41137	−	28.9652i	0.341162	−	1.04999i	0.963606	−	0.267325i	$-0.0861396\pi$
$762$	−1.23530	+	0.897496i	−0.0447501	+	0.0325129i
$763$	−3.62867	−	2.63638i	−0.131367	−	0.0954434i
$764$	11.8085	+	36.3429i	0.427218	+	1.31484i
$765$	−13.3369	−	9.68981i	−0.482196	−	0.350336i
$766$	0.652860	−	2.00930i	0.0235888	−	0.0725988i
$767$	−4.81627	+	14.8230i	−0.173906	+	0.535226i
$768$	0.508228	+	1.56417i	0.0183391	+	0.0564420i
$769$	36.1127			1.30226			0.651129	−	0.758967i	$-0.274296\pi$
$769$	36.1127			1.30226			0.651129	+	0.758967i	$0.274296\pi$
$770$	−0.556349			−0.0200494
$771$	2.85613	+	8.79027i	0.102861	+	0.316574i
$772$	10.5649	−	7.67581i	0.380237	−	0.276259i
$773$	−14.5623	−	10.5801i	−0.523770	−	0.380541i	0.294252	−	0.955728i	$-0.404929\pi$
$773$	−14.5623	−	10.5801i	−0.523770	−	0.380541i	−0.818022	+	0.575187i	$0.804929\pi$
$774$	12.7696			0.458992
$775$		0			0
$776$	−8.20101			−0.294399
$777$	0.138805	+	0.100848i	0.00497961	+	0.00361790i
$778$	3.73379	−	2.71276i	0.133863	−	0.0972572i
$779$	−10.2104	−	31.4245i	−0.365826	−	1.12590i
$780$	2.89949			0.103819
$781$	0.230447			0.00824606
$782$	2.98413	+	9.18421i	0.106712	+	0.328427i
$783$	5.09423	−	15.6784i	0.182053	−	0.560302i
$784$	−6.33030	+	19.4827i	−0.226082	+	0.695809i
$785$	−7.41996	−	5.39092i	−0.264830	−	0.192410i
$786$	−0.702111	−	2.16087i	−0.0250435	−	0.0770758i
$787$	−34.3138	−	24.9304i	−1.22316	−	0.888675i	−0.226797	−	0.973942i	$-0.572826\pi$
$787$	−34.3138	−	24.9304i	−1.22316	−	0.888675i	−0.996358	+	0.0852674i	$0.972826\pi$
$788$	−19.9478	+	14.4929i	−0.710611	+	0.516289i
$789$	−2.98413	+	9.18421i	−0.106238	+	0.326967i
$790$	2.26443	−	1.64520i	0.0805648	−	0.0585338i
$791$	5.58181	−	4.05542i	0.198466	−	0.144194i
$792$	4.49439	−	13.8323i	0.159701	−	0.491510i
$793$	−8.76038	+	6.36479i	−0.311090	+	0.226020i
$794$	11.2211	+	8.15262i	0.398222	+	0.289325i
$795$	0.746033	+	2.29605i	0.0264591	+	0.0814326i
$796$	27.2388	+	19.7902i	0.965455	+	0.701444i
$797$	8.79334	−	27.0631i	0.311476	−	0.958625i	−0.665705	−	0.746215i	$-0.731869\pi$
$797$	8.79334	−	27.0631i	0.311476	−	0.958625i	0.977181	−	0.212409i	$-0.0681311\pi$
$798$	−0.0969413	+	0.298355i	−0.00343168	+	0.0105616i
$799$	−17.3928	−	53.5295i	−0.615313	−	1.89374i
$800$	−17.6569			−0.624264
$801$	−12.6863			−0.448248
$802$	−3.43401	−	10.5688i	−0.121259	−	0.373197i
$803$	4.79661	−	3.48494i	0.169269	−	0.122981i
$804$	1.98682	+	1.44351i	0.0700697	+	0.0509086i
$805$	1.65685			0.0583964
$806$		0			0
$807$	−10.8406			−0.381608
$808$	−10.8860	−	7.90915i	−0.382968	−	0.278243i
$809$	9.73202	−	7.07073i	0.342160	−	0.248593i	−0.403413	−	0.915018i	$-0.632176\pi$
$809$	9.73202	−	7.07073i	0.342160	−	0.248593i	0.745572	+	0.666425i	$0.232176\pi$
$810$	0.958109	+	2.94876i	0.0336645	+	0.103609i
$811$	−13.7279			−0.482053			−0.241026	−	0.970519i	$-0.577484\pi$
$811$	−13.7279			−0.482053			−0.241026	+	0.970519i	$0.577484\pi$
$812$	−5.17157			−0.181487
$813$	−0.0878446	−	0.270358i	−0.00308085	−	0.00948187i
$814$	0.415055	−	1.27741i	0.0145477	−	0.0447731i
$815$	6.48026	−	19.9442i	0.226994	−	0.698615i
$816$	5.85942	+	4.25712i	0.205121	+	0.149029i
$817$	−14.8676	−	45.7579i	−0.520153	−	1.60087i
$818$	−6.92223	−	5.02930i	−0.242030	−	0.175845i
$819$	3.62867	−	2.63638i	0.126796	−	0.0921227i
$820$	4.22930	−	13.0164i	0.147693	−	0.454554i
$821$	−6.86474	+	4.98752i	−0.239581	+	0.174066i	−0.701097	−	0.713066i	$-0.747306\pi$
$821$	−6.86474	+	4.98752i	−0.239581	+	0.174066i	0.461516	+	0.887132i	$0.347306\pi$
$822$	−1.31661	+	0.956572i	−0.0459220	+	0.0333643i
$823$	11.1905	−	34.4408i	0.390076	−	1.20053i	−0.542654	−	0.839956i	$-0.682581\pi$
$823$	11.1905	−	34.4408i	0.390076	−	1.20053i	0.932730	−	0.360575i	$-0.117419\pi$
$824$	2.65703	−	1.93045i	0.0925621	−	0.0672503i
$825$	4.34651	+	3.15793i	0.151326	+	0.109945i
$826$	−0.215844	−	0.664299i	−0.00751016	−	0.0231139i
$827$	−29.8523	−	21.6890i	−1.03807	−	0.754200i	−0.0681596	−	0.997674i	$-0.521713\pi$
$827$	−29.8523	−	21.6890i	−1.03807	−	0.754200i	−0.969907	+	0.243475i	$0.921713\pi$
$828$	−6.39242	+	19.6738i	−0.222152	+	0.683713i
$829$	11.8744	−	36.5457i	0.412415	−	1.26928i	−0.502127	−	0.864794i	$-0.667449\pi$
$829$	11.8744	−	36.5457i	0.412415	−	1.26928i	0.914542	−	0.404490i	$-0.132551\pi$
$830$	−1.28909	−	3.96740i	−0.0447449	−	0.137711i
$831$	5.85786			0.203207
$832$	15.9706			0.553680
$833$	12.2986	+	37.8511i	0.426120	+	1.31146i
$834$		0			0
$835$	−18.2485	−	13.2583i	−0.631514	−	0.458822i
$836$	−26.1716			−0.905163
$837$		0			0
$838$	11.5980			0.400646
$839$	11.8338	+	8.59778i	0.408549	+	0.296828i	0.773014	−	0.634389i	$-0.218748\pi$
$839$	11.8338	+	8.59778i	0.408549	+	0.296828i	−0.364465	+	0.931217i	$0.618748\pi$
$840$	−0.220116	+	0.159923i	−0.00759471	+	0.00551788i
$841$	5.44717	+	16.7647i	0.187833	+	0.578092i
$842$	−12.8995			−0.444546
$843$	0.828427			0.0285325
$844$	−5.88419	−	18.1097i	−0.202542	−	0.623360i
$845$	0.511996	−	1.57576i	0.0176132	−	0.0542079i
$846$	−3.49613	+	10.7600i	−0.120199	+	0.369936i
$847$	−0.162621	−	0.118151i	−0.00558771	−	0.00405971i
$848$	5.40325	+	16.6295i	0.185548	+	0.571059i
$849$	4.57649	+	3.32502i	0.157065	+	0.114114i
$850$	−7.81256	+	5.67616i	−0.267969	+	0.194691i
$851$	−1.23607	+	3.80423i	−0.0423719	+	0.130407i
$852$	0.0435444	−	0.0316369i	0.00149181	−	0.00108386i
$853$	12.5517	−	9.11932i	0.429761	−	0.312240i	−0.351792	−	0.936078i	$-0.614428\pi$
$853$	12.5517	−	9.11932i	0.429761	−	0.312240i	0.781553	+	0.623838i	$0.214428\pi$
$854$	0.149960	−	0.461530i	0.00513153	−	0.0157932i
$855$	10.1008	−	7.33866i	0.345440	−	0.250977i
$856$	15.9265	+	11.5713i	0.544358	+	0.395499i
$857$	−6.02128	−	18.5316i	−0.205683	−	0.633028i	−0.999685	−	0.0251118i	$-0.992006\pi$
$857$	−6.02128	−	18.5316i	−0.205683	−	0.633028i	0.794002	−	0.607916i	$-0.207994\pi$
$858$	1.72316	+	1.25195i	0.0588277	+	0.0427408i
$859$	−15.2607	+	46.9677i	−0.520690	+	1.60252i	0.251996	+	0.967728i	$0.418913\pi$
$859$	−15.2607	+	46.9677i	−0.520690	+	1.60252i	−0.772685	+	0.634789i	$0.781087\pi$
$860$	6.15838	−	18.9535i	0.209999	−	0.646310i
$861$	0.396862	+	1.22141i	0.0135250	+	0.0416257i
$862$	−6.94113			−0.236416
$863$	−2.61522			−0.0890232			−0.0445116	−	0.999009i	$-0.514173\pi$
$863$	−2.61522			−0.0890232			−0.0445116	+	0.999009i	$0.514173\pi$
$864$	−3.29315	−	10.1353i	−0.112035	−	0.344809i
$865$	−6.72593	+	4.88668i	−0.228689	+	0.166152i
$866$	−9.08562	−	6.60109i	−0.308742	−	0.224314i
$867$	7.02944			0.238732
$868$		0			0
$869$	−21.9117			−0.743303
$870$	0.947822	+	0.688633i	0.0321342	+	0.0233469i
$871$	10.0433	−	7.29689i	0.340305	−	0.247246i
$872$	5.30631	+	16.3311i	0.179694	+	0.553042i
$873$	−14.6274			−0.495063
$874$	−7.31371			−0.247390
$875$	1.15199	+	3.54546i	0.0389444	+	0.119859i
$876$	0.427919	−	1.31700i	0.0144581	−	0.0444973i
$877$	16.6339	−	51.1939i	0.561687	−	1.72869i	−0.115909	−	0.993260i	$-0.536978\pi$
$877$	16.6339	−	51.1939i	0.561687	−	1.72869i	0.677596	−	0.735435i	$-0.263022\pi$
$878$	−0.694027	−	0.504240i	−0.0234223	−	0.0170173i
$879$	1.89426	+	5.82992i	0.0638917	+	0.196638i
$880$	−7.87005	−	5.71793i	−0.265299	−	0.192751i
$881$	−9.45441	+	6.86903i	−0.318527	+	0.231423i	−0.735547	−	0.677474i	$-0.763075\pi$
$881$	−9.45441	+	6.86903i	−0.318527	+	0.231423i	0.417020	+	0.908897i	$0.363075\pi$
$882$	2.47214	−	7.60845i	0.0832411	−	0.256190i
$883$	24.5005	−	17.8006i	0.824507	−	0.599040i	−0.0934928	−	0.995620i	$-0.529803\pi$
$883$	24.5005	−	17.8006i	0.824507	−	0.599040i	0.918000	+	0.396580i	$0.129803\pi$
$884$	33.0071	−	23.9810i	1.11015	−	0.806570i
$885$	0.521093	−	1.60376i	0.0175163	−	0.0539098i
$886$	1.59422	−	1.15827i	0.0535588	−	0.0389128i
$887$	41.5235	+	30.1686i	1.39422	+	1.01296i	0.995387	+	0.0959407i	$0.0305859\pi$
$887$	41.5235	+	30.1686i	1.39422	+	1.01296i	0.398837	+	0.917022i	$0.369414\pi$
$888$	−0.202979	−	0.624706i	−0.00681153	−	0.0209637i
$889$	2.98227	+	2.16675i	0.100022	+	0.0726704i
$890$	0.574112	−	1.76693i	0.0192443	−	0.0592278i
$891$	7.50048	−	23.0841i	0.251276	−	0.773347i
$892$	13.4066	+	41.2614i	0.448887	+	1.38153i
$893$	42.6274			1.42647
$894$	0.171573			0.00573826
$895$	−4.71024	−	14.4966i	−0.157446	−	0.484568i
$896$	−3.53749	+	2.57014i	−0.118179	+	0.0858623i
$897$	−5.13171	−	3.72841i	−0.171343	−	0.124488i
$898$	−16.8284			−0.561572
$899$		0			0
$900$	−20.6863			−0.689543
$901$	27.4828	+	19.9674i	0.915584	+	0.665210i
$902$	8.13371	−	5.90949i	0.270823	−	0.196764i
$903$	0.577880	+	1.77853i	0.0192306	+	0.0591858i
$904$	−26.4142			−0.878524
$905$	12.3137			0.409322
$906$	0.281727	+	0.867067i	0.00935976	+	0.0288064i
$907$	10.1006	−	31.0865i	0.335386	−	1.03221i	−0.631146	−	0.775664i	$-0.717415\pi$
$907$	10.1006	−	31.0865i	0.335386	−	1.03221i	0.966532	−	0.256547i	$-0.0825848\pi$
$908$	10.4043	−	32.0212i	0.345279	−	1.06266i
$909$	−19.4164	−	14.1068i	−0.644002	−	0.467895i
$910$	0.202979	+	0.624706i	0.00672869	+	0.0207088i
$911$	−0.775337	−	0.563315i	−0.0256881	−	0.0186635i	0.574867	−	0.818247i	$-0.305054\pi$
$911$	−0.775337	−	0.563315i	−0.0256881	−	0.0186635i	−0.600555	+	0.799583i	$0.705054\pi$
$912$	−4.43769	+	3.22417i	−0.146946	+	0.106763i
$913$	−10.0915	+	31.0585i	−0.333981	+	1.02789i
$914$	10.4260	−	7.57497i	0.344863	−	0.250558i
$915$	0.947822	−	0.688633i	0.0313340	−	0.0227655i
$916$	3.09927	−	9.53856i	0.102403	−	0.315163i
$917$	−4.43769	+	3.22417i	−0.146545	+	0.106471i
$918$	−4.71530	−	3.42586i	−0.155628	−	0.113070i
$919$	−10.7845	−	33.1914i	−0.355749	−	1.09488i	−0.955574	−	0.294752i	$-0.904763\pi$
$919$	−10.7845	−	33.1914i	−0.355749	−	1.09488i	0.599825	−	0.800131i	$-0.295237\pi$
$920$	−5.13171	−	3.72841i	−0.169188	−	0.122922i
$921$	−1.43905	+	4.42893i	−0.0474182	+	0.145938i
$922$	−0.274191	+	0.843874i	−0.00903001	+	0.0277915i
$923$	−0.0840767	−	0.258761i	−0.00276742	−	0.00851724i
$924$	1.01724			0.0334649
$925$	−4.00000			−0.131519
$926$	−1.14822	−	3.53387i	−0.0377330	−	0.116130i
$927$	4.73911	−	3.44317i	0.155653	−	0.113088i
$928$	24.3855	+	17.7171i	0.800493	+	0.581592i
$929$	7.51472			0.246550			0.123275	−	0.992373i	$-0.460660\pi$
$929$	7.51472			0.246550			0.123275	+	0.992373i	$0.460660\pi$
$930$		0			0
$931$	−30.1421			−0.987869
$932$	−13.5669	−	9.85690i	−0.444397	−	0.322873i
$933$	−3.79129	+	2.75453i	−0.124121	+	0.0901794i
$934$	−1.02399	−	3.15152i	−0.0335060	−	0.103121i
$935$	−18.8995			−0.618080
$936$	−17.1716			−0.561270
$937$	4.84733	+	14.9185i	0.158355	+	0.487368i	0.998485	−	0.0550173i	$-0.0175214\pi$
$937$	4.84733	+	14.9185i	0.158355	+	0.487368i	−0.840130	+	0.542385i	$0.817521\pi$
$938$	−0.171921	+	0.529120i	−0.00561343	+	0.0172764i
$939$	−0.234037	+	0.720292i	−0.00763751	+	0.0235058i
$940$	14.2847	+	10.3784i	0.465915	+	0.338507i
$941$	−10.8156	−	33.2870i	−0.352578	−	1.08512i	−0.957400	−	0.288764i	$-0.906756\pi$
$941$	−10.8156	−	33.2870i	−0.352578	−	1.08512i	0.604822	−	0.796361i	$-0.293244\pi$
$942$	−1.27306	−	0.924935i	−0.0414787	−	0.0301360i
$943$	−24.2229	+	17.5990i	−0.788805	+	0.573101i
$944$	3.77409	−	11.6154i	0.122836	−	0.378051i
$945$	−0.809017	+	0.587785i	−0.0263173	+	0.0191207i
$946$	11.8437	−	8.60495i	0.385072	−	0.279771i
$947$	5.90238	−	18.1657i	0.191802	−	0.590305i	−0.808197	−	0.588912i	$-0.799557\pi$
$947$	5.90238	−	18.1657i	0.191802	−	0.590305i	0.999999	−	0.00139299i	$-0.000443403\pi$
$948$	−4.14035	+	3.00814i	−0.134472	+	0.0976998i
$949$	−5.66312	−	4.11450i	−0.183833	−	0.133562i
$950$	−2.26006	−	6.95575i	−0.0733260	−	0.225674i
$951$	2.62335	+	1.90598i	0.0850680	+	0.0618055i
$952$	−1.18305	+	3.64105i	−0.0383428	+	0.118007i
$953$	1.08611	−	3.34270i	0.0351825	−	0.108281i	−0.931923	−	0.362656i	$-0.881870\pi$
$953$	1.08611	−	3.34270i	0.0351825	−	0.108281i	0.967106	+	0.254376i	$0.0818699\pi$
$954$	−2.11010	−	6.49422i	−0.0683170	−	0.210258i
$955$	−20.8995			−0.676292
$956$	38.8406			1.25620
$957$	−2.83417	−	8.72268i	−0.0916158	−	0.281964i
$958$	5.27052	−	3.82926i	0.170283	−	0.123718i
$959$	3.17857	+	2.30937i	0.102641	+	0.0745734i
$960$	−1.72792			−0.0557684
$961$		0			0
$962$	−1.58579			−0.0511278
$963$	28.4068	+	20.6387i	0.915395	+	0.665074i
$964$	19.7376	−	14.3402i	0.635704	−	0.461866i
$965$	2.20704	+	6.79257i	0.0710472	+	0.218661i
$966$	0.284271			0.00914628
$967$	−15.4437			−0.496634			−0.248317	−	0.968679i	$-0.579878\pi$
$967$	−15.4437			−0.496634			−0.248317	+	0.968679i	$0.579878\pi$
$968$	0.237805	+	0.731888i	0.00764334	+	0.0235238i
$969$	−3.29315	+	10.1353i	−0.105791	+	0.325592i
$970$	0.661956	−	2.03729i	0.0212541	−	0.0654135i
$971$	0.565086	+	0.410559i	0.0181345	+	0.0131755i	0.596816	−	0.802378i	$-0.296432\pi$
$971$	0.565086	+	0.410559i	0.0181345	+	0.0131755i	−0.578681	+	0.815554i	$0.696432\pi$
$972$	−5.84403	−	17.9861i	−0.187447	−	0.576904i
$973$		0			0
$974$	−6.49595	+	4.71958i	−0.208144	+	0.151225i
$975$	1.96014	−	6.03269i	0.0627747	−	0.193201i
$976$	6.86474	−	4.98752i	0.219735	−	0.159647i
$977$	0.392601	−	0.285241i	0.0125604	−	0.00912568i	−0.581487	−	0.813555i	$-0.697529\pi$
$977$	0.392601	−	0.285241i	0.0125604	−	0.00912568i	0.594048	+	0.804430i	$0.297529\pi$
$978$	1.11184	−	3.42188i	0.0355526	−	0.109420i
$979$	−11.7665	+	8.54884i	−0.376058	+	0.273222i
$980$	−10.1008	−	7.33866i	−0.322658	−	0.234425i
$981$	9.46439	+	29.1284i	0.302175	+	0.929998i
$982$	−0.531406	−	0.386089i	−0.0169579	−	0.0123206i
$983$	−12.0024	+	36.9396i	−0.382817	+	1.17819i	0.555234	+	0.831694i	$0.312629\pi$
$983$	−12.0024	+	36.9396i	−0.382817	+	1.17819i	−0.938051	+	0.346497i	$0.887371\pi$
$984$	1.51936	−	4.67610i	0.0484353	−	0.149069i
$985$	−4.16718	−	12.8253i	−0.132777	−	0.408647i
$986$	16.4853			0.524998
$987$	−1.65685			−0.0527383
$988$	9.54847	+	29.3872i	0.303777	+	0.934930i
$989$	−35.2715	+	25.6262i	−1.12157	+	0.814867i
$990$	3.07345	+	2.23299i	0.0976806	+	0.0709691i
$991$	47.9411			1.52290			0.761450	−	0.648224i	$-0.224488\pi$
$991$	47.9411			1.52290			0.761450	+	0.648224i	$0.224488\pi$
$992$		0			0
$993$	3.82843			0.121491
$994$	0.00986459	+	0.00716705i	0.000312886	+	0.000227325i
$995$	−14.8974	+	10.8236i	−0.472280	+	0.343131i
$996$	2.35700	+	7.25410i	0.0746844	+	0.229855i
$997$	32.5980			1.03239			0.516194	−	0.856472i	$-0.327348\pi$
$997$	32.5980			1.03239			0.516194	+	0.856472i	$0.327348\pi$
$998$	−0.916739			−0.0290189
$999$	−0.746033	−	2.29605i	−0.0236034	−	0.0726439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.l.374.1		8
31.2	even	5	inner	961.2.d.l.628.2		8
31.3	odd	30		961.2.g.r.235.1		16
31.4	even	5		961.2.a.a.1.2		2
31.5	even	3		961.2.g.o.732.1		16
31.6	odd	6		961.2.g.r.816.1		16
31.7	even	15		31.2.c.a.5.2	✓	4
31.8	even	5	inner	961.2.d.l.531.2		8
31.9	even	15		961.2.g.o.844.2		16
31.10	even	15		961.2.g.o.448.2		16
31.11	odd	30		961.2.c.a.521.2		4
31.12	odd	30		961.2.g.r.846.2		16
31.13	odd	30		961.2.g.r.338.1		16
31.14	even	15		961.2.g.o.547.2		16
31.15	odd	10		961.2.d.i.388.1		8
31.16	even	5	inner	961.2.d.l.388.1		8
31.17	odd	30		961.2.g.r.547.2		16
31.18	even	15		961.2.g.o.338.1		16
31.19	even	15		961.2.g.o.846.2		16
31.20	even	15		31.2.c.a.25.2	yes	4
31.21	odd	30		961.2.g.r.448.2		16
31.22	odd	30		961.2.g.r.844.2		16
31.23	odd	10		961.2.d.i.531.2		8
31.24	odd	30		961.2.c.a.439.2		4
31.25	even	3		961.2.g.o.816.1		16
31.26	odd	6		961.2.g.r.732.1		16
31.27	odd	10		961.2.a.c.1.2		2
31.28	even	15		961.2.g.o.235.1		16
31.29	odd	10		961.2.d.i.628.2		8
31.30	odd	2		961.2.d.i.374.1		8
93.20	odd	30		279.2.h.c.118.1		4
93.35	odd	10		8649.2.a.l.1.1		2
93.38	odd	30		279.2.h.c.253.1		4
93.89	even	10		8649.2.a.k.1.1		2
124.7	odd	30		496.2.i.h.129.2		4
124.51	odd	30		496.2.i.h.273.2		4
155.7	odd	60		775.2.o.d.749.3		8
155.38	odd	60		775.2.o.d.749.2		8
155.69	even	30		775.2.e.e.501.1		4
155.82	odd	60		775.2.o.d.149.3		8
155.113	odd	60		775.2.o.d.149.2		8
155.144	even	30		775.2.e.e.676.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	31.7	even	15
31.2.c.a.25.2	yes	4	31.20	even	15
279.2.h.c.118.1		4	93.20	odd	30
279.2.h.c.253.1		4	93.38	odd	30
496.2.i.h.129.2		4	124.7	odd	30
496.2.i.h.273.2		4	124.51	odd	30
775.2.e.e.501.1		4	155.69	even	30
775.2.e.e.676.1		4	155.144	even	30
775.2.o.d.149.2		8	155.113	odd	60
775.2.o.d.149.3		8	155.82	odd	60
775.2.o.d.749.2		8	155.38	odd	60
775.2.o.d.749.3		8	155.7	odd	60
961.2.a.a.1.2		2	31.4	even	5
961.2.a.c.1.2		2	31.27	odd	10
961.2.c.a.439.2		4	31.24	odd	30
961.2.c.a.521.2		4	31.11	odd	30
961.2.d.i.374.1		8	31.30	odd	2
961.2.d.i.388.1		8	31.15	odd	10
961.2.d.i.531.2		8	31.23	odd	10
961.2.d.i.628.2		8	31.29	odd	10
961.2.d.l.374.1		8	1.1	even	1	trivial
961.2.d.l.388.1		8	31.16	even	5	inner
961.2.d.l.531.2		8	31.8	even	5	inner
961.2.d.l.628.2		8	31.2	even	5	inner
961.2.g.o.235.1		16	31.28	even	15
961.2.g.o.338.1		16	31.18	even	15
961.2.g.o.448.2		16	31.10	even	15
961.2.g.o.547.2		16	31.14	even	15
961.2.g.o.732.1		16	31.5	even	3
961.2.g.o.816.1		16	31.25	even	3
961.2.g.o.844.2		16	31.9	even	15
961.2.g.o.846.2		16	31.19	even	15
961.2.g.r.235.1		16	31.3	odd	30
961.2.g.r.338.1		16	31.13	odd	30
961.2.g.r.448.2		16	31.21	odd	30
961.2.g.r.547.2		16	31.17	odd	30
961.2.g.r.732.1		16	31.26	odd	6
961.2.g.r.816.1		16	31.6	odd	6
961.2.g.r.844.2		16	31.22	odd	30
961.2.g.r.846.2		16	31.12	odd	30
8649.2.a.k.1.1		2	93.89	even	10
8649.2.a.l.1.1		2	93.35	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.335106 - 0.243469i) q^{2} +(-0.335106 + 0.243469i) q^{3} +(-0.565015 - 1.73894i) q^{4} +1.00000 q^{5} +0.171573 q^{6} +(-0.127999 - 0.393941i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(-0.874032 + 2.68999i) q^{9} +O(q^{10})\)	\(q+(-0.335106 - 0.243469i) q^{2} +(-0.335106 + 0.243469i) q^{3} +(-0.565015 - 1.73894i) q^{4} +1.00000 q^{5} +0.171573 q^{6} +(-0.127999 - 0.393941i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(-0.874032 + 2.68999i) q^{9} +(-0.335106 - 0.243469i) q^{10} +(1.00203 + 3.08393i) q^{11} +(0.612717 + 0.445165i) q^{12} +(3.09726 - 2.25029i) q^{13} +(-0.0530189 + 0.163176i) q^{14} +(-0.335106 + 0.243469i) q^{15} +(-2.42705 + 1.76336i) q^{16} +(-1.80108 + 5.54316i) q^{17} +(0.947822 - 0.688633i) q^{18} +(-3.57117 - 2.59461i) q^{19} +(-0.565015 - 1.73894i) q^{20} +(0.138805 + 0.100848i) q^{21} +(0.415055 - 1.27741i) q^{22} +(-1.23607 + 3.80423i) q^{23} +(-0.202979 - 0.624706i) q^{24} -4.00000 q^{25} -1.58579 q^{26} +(-0.746033 - 2.29605i) q^{27} +(-0.612717 + 0.445165i) q^{28} +(5.52431 + 4.01365i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(-1.08663 - 0.789481i) q^{33} +(1.95314 - 1.41904i) q^{34} +(-0.127999 - 0.393941i) q^{35} +5.17157 q^{36} +1.00000 q^{37} +(0.565015 + 1.73894i) q^{38} +(-0.490035 + 1.50817i) q^{39} +(-0.490035 + 1.50817i) q^{40} +(6.05572 + 4.39974i) q^{41} +(-0.0219612 - 0.0675895i) q^{42} +(8.81788 + 6.40656i) q^{43} +(4.79661 - 3.48494i) q^{44} +(-0.874032 + 2.68999i) q^{45} +(1.34042 - 0.973874i) q^{46} +(-7.81256 + 5.67616i) q^{47} +(0.383997 - 1.18182i) q^{48} +(5.52431 - 4.01365i) q^{49} +(1.34042 + 0.973874i) q^{50} +(-0.746033 - 2.29605i) q^{51} +(-5.66312 - 4.11450i) q^{52} +(1.80108 - 5.54316i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.00203 + 3.08393i) q^{55} +0.656854 q^{56} +1.82843 q^{57} +(-0.874032 - 2.68999i) q^{58} +(-3.29356 + 2.39291i) q^{59} +(0.612717 + 0.445165i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(3.37487 + 2.45199i) q^{64} +(3.09726 - 2.25029i) q^{65} +(0.171921 + 0.529120i) q^{66} +3.24264 q^{67} +10.6569 q^{68} +(-0.511996 - 1.57576i) q^{69} +(-0.0530189 + 0.163176i) q^{70} +(0.0219612 - 0.0675895i) q^{71} +(-3.62867 - 2.63638i) q^{72} +(-0.565015 - 1.73894i) q^{73} +(-0.335106 - 0.243469i) q^{74} +(1.34042 - 0.973874i) q^{75} +(-2.49410 + 7.67604i) q^{76} +(1.08663 - 0.789481i) q^{77} +(0.531406 - 0.386089i) q^{78} +(-2.08814 + 6.42663i) q^{79} +(-2.42705 + 1.76336i) q^{80} +(-6.05572 - 4.39974i) q^{81} +(-0.958109 - 2.94876i) q^{82} +(8.14767 + 5.91963i) q^{83} +(0.0969413 - 0.298355i) q^{84} +(-1.80108 + 5.54316i) q^{85} +(-1.39512 - 4.29375i) q^{86} -2.82843 q^{87} -5.14214 q^{88} +(1.38603 + 4.26576i) q^{89} +(0.947822 - 0.688633i) q^{90} +(-1.28293 - 0.932102i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(-3.57117 - 2.59461i) q^{95} +(-1.47923 + 1.07472i) q^{96} +(1.59810 + 4.91846i) q^{97} -2.82843 q^{98} -9.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} + 24 q^{6} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 + 24 * q^6 - 2 * q^7 + 6 * q^8	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} + 24 q^{6} - 2 q^{7} + 6 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} + 2 q^{15} - 6 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21} - 14 q^{22} + 8 q^{23} - 10 q^{24} - 32 q^{25} - 24 q^{26} + 2 q^{27} - 10 q^{28} + 8 q^{29} + 24 q^{30} + 24 q^{32} - 14 q^{33} + 2 q^{34} - 2 q^{35} + 64 q^{36} + 8 q^{37} + 2 q^{38} + 6 q^{39} + 6 q^{40} - 2 q^{41} - 14 q^{42} + 2 q^{43} + 26 q^{44} - 8 q^{46} - 8 q^{47} + 6 q^{48} + 8 q^{49} - 8 q^{50} + 2 q^{51} - 14 q^{52} - 6 q^{53} + 2 q^{54} + 2 q^{55} - 40 q^{56} - 8 q^{57} + 6 q^{59} + 10 q^{60} + 32 q^{63} + 14 q^{64} + 2 q^{65} + 30 q^{66} - 8 q^{67} + 40 q^{68} - 8 q^{69} + 6 q^{70} + 14 q^{71} + 8 q^{72} - 2 q^{73} + 2 q^{74} - 8 q^{75} + 2 q^{76} + 14 q^{77} - 10 q^{78} + 22 q^{79} - 6 q^{80} + 2 q^{81} + 26 q^{82} + 6 q^{83} + 22 q^{84} + 6 q^{85} + 26 q^{86} + 72 q^{88} + 8 q^{89} + 8 q^{90} - 6 q^{91} - 32 q^{92} + 32 q^{94} - 6 q^{95} + 2 q^{96} - 16 q^{97} - 96 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 + 24 * q^6 - 2 * q^7 + 6 * q^8 + 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 + 6 * q^14 + 2 * q^15 - 6 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 + 6 * q^21 - 14 * q^22 + 8 * q^23 - 10 * q^24 - 32 * q^25 - 24 * q^26 + 2 * q^27 - 10 * q^28 + 8 * q^29 + 24 * q^30 + 24 * q^32 - 14 * q^33 + 2 * q^34 - 2 * q^35 + 64 * q^36 + 8 * q^37 + 2 * q^38 + 6 * q^39 + 6 * q^40 - 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 - 8 * q^46 - 8 * q^47 + 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 - 14 * q^52 - 6 * q^53 + 2 * q^54 + 2 * q^55 - 40 * q^56 - 8 * q^57 + 6 * q^59 + 10 * q^60 + 32 * q^63 + 14 * q^64 + 2 * q^65 + 30 * q^66 - 8 * q^67 + 40 * q^68 - 8 * q^69 + 6 * q^70 + 14 * q^71 + 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 + 2 * q^76 + 14 * q^77 - 10 * q^78 + 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 + 6 * q^83 + 22 * q^84 + 6 * q^85 + 26 * q^86 + 72 * q^88 + 8 * q^89 + 8 * q^90 - 6 * q^91 - 32 * q^92 + 32 * q^94 - 6 * q^95 + 2 * q^96 - 16 * q^97 - 96 * q^99

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