LMFDB - Embedded newform 961.2.d.g.531.1

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:	$4$
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 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.g.628.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 1.53884i) q^{2} +(1.00000 - 3.07768i) q^{3} +(-0.500000 + 0.363271i) q^{4} +1.00000 q^{5} +5.23607 q^{6} +(-0.190983 + 0.138757i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-6.04508 - 4.39201i) q^{9} +(0.500000 + 1.53884i) q^{10} +(1.61803 - 1.17557i) q^{11} +(0.618034 + 1.90211i) q^{12} +(1.00000 - 3.07768i) q^{13} +(-0.309017 - 0.224514i) q^{14} +(1.00000 - 3.07768i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(0.618034 + 0.449028i) q^{17} +(3.73607 - 11.4984i) q^{18} +(-0.690983 - 2.12663i) q^{19} +(-0.500000 + 0.363271i) q^{20} +(0.236068 + 0.726543i) q^{21} +(2.61803 + 1.90211i) q^{22} +(4.61803 + 3.35520i) q^{23} +(5.85410 - 4.25325i) q^{24} -4.00000 q^{25} +5.23607 q^{26} +(-11.7082 + 8.50651i) q^{27} +(0.0450850 - 0.138757i) q^{28} +(-0.854102 - 2.62866i) q^{29} +5.23607 q^{30} -3.38197 q^{32} +(-2.00000 - 6.15537i) q^{33} +(-0.381966 + 1.17557i) q^{34} +(-0.190983 + 0.138757i) q^{35} +4.61803 q^{36} +2.00000 q^{37} +(2.92705 - 2.12663i) q^{38} +(-8.47214 - 6.15537i) q^{39} +(1.80902 + 1.31433i) q^{40} +(2.16312 + 6.65740i) q^{41} +(-1.00000 + 0.726543i) q^{42} +(-0.381966 - 1.17557i) q^{43} +(-0.381966 + 1.17557i) q^{44} +(-6.04508 - 4.39201i) q^{45} +(-2.85410 + 8.78402i) q^{46} +(0.763932 - 2.35114i) q^{47} +(12.7082 + 9.23305i) q^{48} +(-2.14590 + 6.60440i) q^{49} +(-2.00000 - 6.15537i) q^{50} +(2.00000 - 1.45309i) q^{51} +(0.618034 + 1.90211i) q^{52} +(-8.47214 - 6.15537i) q^{53} +(-18.9443 - 13.7638i) q^{54} +(1.61803 - 1.17557i) q^{55} -0.527864 q^{56} -7.23607 q^{57} +(3.61803 - 2.62866i) q^{58} +(0.690983 - 2.12663i) q^{59} +(0.618034 + 1.90211i) q^{60} -8.18034 q^{61} +1.76393 q^{63} +(1.30902 + 4.02874i) q^{64} +(1.00000 - 3.07768i) q^{65} +(8.47214 - 6.15537i) q^{66} +8.00000 q^{67} -0.472136 q^{68} +(14.9443 - 10.8576i) q^{69} +(-0.309017 - 0.224514i) q^{70} +(7.42705 + 5.39607i) q^{71} +(-5.16312 - 15.8904i) q^{72} +(6.85410 - 4.97980i) q^{73} +(1.00000 + 3.07768i) q^{74} +(-4.00000 + 12.3107i) q^{75} +(1.11803 + 0.812299i) q^{76} +(-0.145898 + 0.449028i) q^{77} +(5.23607 - 16.1150i) q^{78} +(-9.47214 - 6.88191i) q^{79} +(-1.50000 + 4.61653i) q^{80} +(7.54508 + 23.2214i) q^{81} +(-9.16312 + 6.65740i) q^{82} +(4.61803 + 14.2128i) q^{83} +(-0.381966 - 0.277515i) q^{84} +(0.618034 + 0.449028i) q^{85} +(1.61803 - 1.17557i) q^{86} -8.94427 q^{87} +4.47214 q^{88} +(9.47214 - 6.88191i) q^{89} +(3.73607 - 11.4984i) q^{90} +(0.236068 + 0.726543i) q^{91} -3.52786 q^{92} +4.00000 q^{94} +(-0.690983 - 2.12663i) q^{95} +(-3.38197 + 10.4086i) q^{96} +(12.8992 - 9.37181i) q^{97} -11.2361 q^{98} -14.9443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 4 q^{5} + 12 q^{6} - 3 q^{7} + 5 q^{8} - 13 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} - 2 q^{17} + 6 q^{18} - 5 q^{19} - 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 4 * q^5 + 12 * q^6 - 3 * q^7 + 5 * q^8 - 13 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 + q^14 + 4 * q^15 - 6 * q^16 - 2 * q^17 + 6 * q^18 - 5 * q^19 - 2 * q^20 - 8 * q^21 + 6 * q^22 + 14 * q^23 + 10 * q^24 - 16 * q^25 + 12 * q^26 - 20 * q^27 - 11 * q^28 + 10 * q^29 + 12 * q^30 - 18 * q^32 - 8 * q^33 - 6 * q^34 - 3 * q^35 + 14 * q^36 + 8 * q^37 + 5 * q^38 - 16 * q^39 + 5 * q^40 - 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 - 13 * q^45 + 2 * q^46 + 12 * q^47 + 24 * q^48 - 22 * q^49 - 8 * q^50 + 8 * q^51 - 2 * q^52 - 16 * q^53 - 40 * q^54 + 2 * q^55 - 20 * q^56 - 20 * q^57 + 10 * q^58 + 5 * q^59 - 2 * q^60 + 12 * q^61 + 16 * q^63 + 3 * q^64 + 4 * q^65 + 16 * q^66 + 32 * q^67 + 16 * q^68 + 24 * q^69 + q^70 + 23 * q^71 - 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 - 14 * q^77 + 12 * q^78 - 20 * q^79 - 6 * q^80 + 19 * q^81 - 21 * q^82 + 14 * q^83 - 6 * q^84 - 2 * q^85 + 2 * q^86 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 32 * q^92 + 16 * q^94 - 5 * q^95 - 18 * q^96 + 27 * q^97 - 36 * q^98 - 24 * q^99

Character values

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

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

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 $

$2$	0.500000	+	1.53884i	0.353553	+	1.08813i	0.956844	+	0.290604i	$0.0938561\pi$
$2$	0.500000	+	1.53884i	0.353553	+	1.08813i	−0.603290	+	0.797522i	$0.706144\pi$
$3$	1.00000	−	3.07768i	0.577350	−	1.77690i	−0.0506828	−	0.998715i	$-0.516140\pi$
$3$	1.00000	−	3.07768i	0.577350	−	1.77690i	0.628033	−	0.778187i	$-0.283860\pi$
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	5.23607			2.13762
$7$	−0.190983	+	0.138757i	−0.0721848	+	0.0524453i	−0.623292	−	0.781989i	$-0.714205\pi$
$7$	−0.190983	+	0.138757i	−0.0721848	+	0.0524453i	0.551108	+	0.834434i	$0.314205\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$	−6.04508	−	4.39201i	−2.01503	−	1.46400i
$10$	0.500000	+	1.53884i	0.158114	+	0.486624i
$11$	1.61803	−	1.17557i	0.487856	−	0.354448i	−0.316503	−	0.948591i	$-0.602509\pi$
$11$	1.61803	−	1.17557i	0.487856	−	0.354448i	0.804359	+	0.594144i	$0.202509\pi$
$12$	0.618034	+	1.90211i	0.178411	+	0.549093i
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	−0.711238	−	0.702951i	$-0.751865\pi$
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	0.988588	−	0.150644i	$-0.0481349\pi$
$14$	−0.309017	−	0.224514i	−0.0825883	−	0.0600039i
$15$	1.00000	−	3.07768i	0.258199	−	0.794654i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	0.618034	+	0.449028i	0.149895	+	0.108905i	0.660205	−	0.751085i	$-0.270469\pi$
$17$	0.618034	+	0.449028i	0.149895	+	0.108905i	−0.510310	+	0.859991i	$0.670469\pi$
$18$	3.73607	−	11.4984i	0.880600	−	2.71021i
$19$	−0.690983	−	2.12663i	−0.158522	−	0.487882i	0.839978	−	0.542620i	$-0.182568\pi$
$19$	−0.690983	−	2.12663i	−0.158522	−	0.487882i	−0.998501	+	0.0547382i	$0.982568\pi$
$20$	−0.500000	+	0.363271i	−0.111803	+	0.0812299i
$21$	0.236068	+	0.726543i	0.0515143	+	0.158545i
$22$	2.61803	+	1.90211i	0.558167	+	0.405532i
$23$	4.61803	+	3.35520i	0.962927	+	0.699607i	0.953829	−	0.300351i	$-0.0971040\pi$
$23$	4.61803	+	3.35520i	0.962927	+	0.699607i	0.00909805	+	0.999959i	$0.497104\pi$
$24$	5.85410	−	4.25325i	1.19496	−	0.868192i
$25$	−4.00000			−0.800000
$26$	5.23607			1.02688
$27$	−11.7082	+	8.50651i	−2.25324	+	1.63708i
$28$	0.0450850	−	0.138757i	0.00852026	−	0.0262227i
$29$	−0.854102	−	2.62866i	−0.158603	−	0.488129i	0.839905	−	0.542733i	$-0.182610\pi$
$29$	−0.854102	−	2.62866i	−0.158603	−	0.488129i	−0.998508	+	0.0546038i	$0.982610\pi$
$30$	5.23607			0.955971
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	−2.00000	−	6.15537i	−0.348155	−	1.07151i
$34$	−0.381966	+	1.17557i	−0.0655066	+	0.201609i
$35$	−0.190983	+	0.138757i	−0.0322820	+	0.0234543i
$36$	4.61803			0.769672
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	2.92705	−	2.12663i	0.474830	−	0.344984i
$39$	−8.47214	−	6.15537i	−1.35663	−	0.985648i
$40$	1.80902	+	1.31433i	0.286031	+	0.207813i
$41$	2.16312	+	6.65740i	0.337822	+	1.03971i	0.965315	+	0.261088i	$0.0840813\pi$
$41$	2.16312	+	6.65740i	0.337822	+	1.03971i	−0.627493	+	0.778623i	$0.715919\pi$
$42$	−1.00000	+	0.726543i	−0.154303	+	0.112108i
$43$	−0.381966	−	1.17557i	−0.0582493	−	0.179273i	0.917698	−	0.397278i	$-0.130045\pi$
$43$	−0.381966	−	1.17557i	−0.0582493	−	0.179273i	−0.975948	+	0.218005i	$0.930045\pi$
$44$	−0.381966	+	1.17557i	−0.0575835	+	0.177224i
$45$	−6.04508	−	4.39201i	−0.901148	−	0.654722i
$46$	−2.85410	+	8.78402i	−0.420814	+	1.29513i
$47$	0.763932	−	2.35114i	0.111431	−	0.342949i	−0.879755	−	0.475427i	$-0.842293\pi$
$47$	0.763932	−	2.35114i	0.111431	−	0.342949i	0.991186	+	0.132478i	$0.0422935\pi$
$48$	12.7082	+	9.23305i	1.83427	+	1.33268i
$49$	−2.14590	+	6.60440i	−0.306557	+	0.943485i
$50$	−2.00000	−	6.15537i	−0.282843	−	0.870500i
$51$	2.00000	−	1.45309i	0.280056	−	0.203473i
$52$	0.618034	+	1.90211i	0.0857059	+	0.263776i
$53$	−8.47214	−	6.15537i	−1.16374	−	0.845505i	−0.173491	−	0.984835i	$-0.555505\pi$
$53$	−8.47214	−	6.15537i	−1.16374	−	0.845505i	−0.990246	+	0.139331i	$0.955505\pi$
$54$	−18.9443	−	13.7638i	−2.57799	−	1.87302i
$55$	1.61803	−	1.17557i	0.218176	−	0.158514i
$56$	−0.527864			−0.0705388
$57$	−7.23607			−0.958441
$58$	3.61803	−	2.62866i	0.475071	−	0.345159i
$59$	0.690983	−	2.12663i	0.0899583	−	0.276863i	−0.895949	−	0.444158i	$-0.853503\pi$
$59$	0.690983	−	2.12663i	0.0899583	−	0.276863i	0.985907	+	0.167294i	$0.0535030\pi$
$60$	0.618034	+	1.90211i	0.0797878	+	0.245562i
$61$	−8.18034			−1.04739			−0.523693	−	0.851907i	$-0.675446\pi$
$61$	−8.18034			−1.04739			−0.523693	+	0.851907i	$0.675446\pi$
$62$		0			0
$63$	1.76393			0.222235
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	1.00000	−	3.07768i	0.124035	−	0.381740i
$66$	8.47214	−	6.15537i	1.04285	−	0.757673i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	−0.472136			−0.0572549
$69$	14.9443	−	10.8576i	1.79908	−	1.30711i
$70$	−0.309017	−	0.224514i	−0.0369346	−	0.0268346i
$71$	7.42705	+	5.39607i	0.881429	+	0.640395i	0.933629	−	0.358241i	$-0.116623\pi$
$71$	7.42705	+	5.39607i	0.881429	+	0.640395i	−0.0522003	+	0.998637i	$0.516623\pi$
$72$	−5.16312	−	15.8904i	−0.608479	−	1.87271i
$73$	6.85410	−	4.97980i	0.802212	−	0.582841i	−0.109350	−	0.994003i	$-0.534877\pi$
$73$	6.85410	−	4.97980i	0.802212	−	0.582841i	0.911562	+	0.411162i	$0.134877\pi$
$74$	1.00000	+	3.07768i	0.116248	+	0.357773i
$75$	−4.00000	+	12.3107i	−0.461880	+	1.42152i
$76$	1.11803	+	0.812299i	0.128247	+	0.0931771i
$77$	−0.145898	+	0.449028i	−0.0166266	+	0.0511715i
$78$	5.23607	−	16.1150i	0.592868	−	1.82466i
$79$	−9.47214	−	6.88191i	−1.06570	−	0.774275i	−0.0905644	−	0.995891i	$-0.528867\pi$
$79$	−9.47214	−	6.88191i	−1.06570	−	0.774275i	−0.975134	+	0.221615i	$0.928867\pi$
$80$	−1.50000	+	4.61653i	−0.167705	+	0.516143i
$81$	7.54508	+	23.2214i	0.838343	+	2.58015i
$82$	−9.16312	+	6.65740i	−1.01190	+	0.735186i
$83$	4.61803	+	14.2128i	0.506895	+	1.56006i	0.797561	+	0.603238i	$0.206123\pi$
$83$	4.61803	+	14.2128i	0.506895	+	1.56006i	−0.290666	+	0.956825i	$0.593877\pi$
$84$	−0.381966	−	0.277515i	−0.0416759	−	0.0302793i
$85$	0.618034	+	0.449028i	0.0670352	+	0.0487039i
$86$	1.61803	−	1.17557i	0.174477	−	0.126765i
$87$	−8.94427			−0.958927
$88$	4.47214			0.476731
$89$	9.47214	−	6.88191i	1.00404	−	0.729481i	0.0410928	−	0.999155i	$-0.486916\pi$
$89$	9.47214	−	6.88191i	1.00404	−	0.729481i	0.962952	+	0.269674i	$0.0869161\pi$
$90$	3.73607	−	11.4984i	0.393816	−	1.21204i
$91$	0.236068	+	0.726543i	0.0247466	+	0.0761624i
$92$	−3.52786			−0.367805
$93$		0			0
$94$	4.00000			0.412568
$95$	−0.690983	−	2.12663i	−0.0708934	−	0.218187i
$96$	−3.38197	+	10.4086i	−0.345170	+	1.06233i
$97$	12.8992	−	9.37181i	1.30971	−	0.951563i	0.309714	−	0.950830i	$-0.399767\pi$
$97$	12.8992	−	9.37181i	1.30971	−	0.951563i	1.00000		0.000733244i	$-0.000233399\pi$
$98$	−11.2361			−1.13501
$99$	−14.9443			−1.50196
$100$	2.00000	−	1.45309i	0.200000	−	0.145309i
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	0.701952	−	0.712225i	$-0.252312\pi$
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	−0.460451	+	0.887685i	$0.652312\pi$
$102$	3.23607	+	2.35114i	0.320418	+	0.232798i
$103$	1.92705	+	5.93085i	0.189878	+	0.584384i	0.999998	−	0.00187942i	$-0.000598237\pi$
$103$	1.92705	+	5.93085i	0.189878	+	0.584384i	−0.810120	+	0.586264i	$0.800598\pi$
$104$	5.85410	−	4.25325i	0.574042	−	0.417066i
$105$	0.236068	+	0.726543i	0.0230379	+	0.0709033i
$106$	5.23607	−	16.1150i	0.508572	−	1.56522i
$107$	−4.66312	−	3.38795i	−0.450801	−	0.327526i	0.339111	−	0.940746i	$-0.389874\pi$
$107$	−4.66312	−	3.38795i	−0.450801	−	0.327526i	−0.789912	+	0.613220i	$0.789874\pi$
$108$	2.76393	−	8.50651i	0.265959	−	0.818539i
$109$	−4.30902	+	13.2618i	−0.412729	+	1.27025i	0.501538	+	0.865136i	$0.332768\pi$
$109$	−4.30902	+	13.2618i	−0.412729	+	1.27025i	−0.914266	+	0.405113i	$0.867232\pi$
$110$	2.61803	+	1.90211i	0.249620	+	0.181359i
$111$	2.00000	−	6.15537i	0.189832	−	0.584242i
$112$	−0.354102	−	1.08981i	−0.0334595	−	0.102978i
$113$	−2.80902	+	2.04087i	−0.264250	+	0.191989i	−0.712019	−	0.702161i	$-0.752219\pi$
$113$	−2.80902	+	2.04087i	−0.264250	+	0.191989i	0.447769	+	0.894150i	$0.352219\pi$
$114$	−3.61803	−	11.1352i	−0.338860	−	1.04290i
$115$	4.61803	+	3.35520i	0.430634	+	0.312874i
$116$	1.38197	+	1.00406i	0.128312	+	0.0932244i
$117$	−19.5623	+	14.2128i	−1.80854	+	1.31398i
$118$	3.61803			0.333067
$119$	−0.180340			−0.0165317
$120$	5.85410	−	4.25325i	0.534404	−	0.388267i
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	−4.09017	−	12.5882i	−0.370307	−	1.13969i
$123$	22.6525			2.04250
$124$		0			0
$125$	−9.00000			−0.804984
$126$	0.881966	+	2.71441i	0.0785718	+	0.241819i
$127$	−3.85410	+	11.8617i	−0.341996	+	1.05256i	0.621176	+	0.783671i	$0.286655\pi$
$127$	−3.85410	+	11.8617i	−0.341996	+	1.05256i	−0.963172	+	0.268885i	$0.913345\pi$
$128$	−11.0172	+	8.00448i	−0.973794	+	0.707503i
$129$	−4.00000			−0.352180
$130$	5.23607			0.459234
$131$	−9.70820	+	7.05342i	−0.848210	+	0.616260i	−0.924652	−	0.380814i	$-0.875644\pi$
$131$	−9.70820	+	7.05342i	−0.848210	+	0.616260i	0.0764421	+	0.997074i	$0.475644\pi$
$132$	3.23607	+	2.35114i	0.281664	+	0.204641i
$133$	0.427051	+	0.310271i	0.0370300	+	0.0269039i
$134$	4.00000	+	12.3107i	0.345547	+	1.06349i
$135$	−11.7082	+	8.50651i	−1.00768	+	0.732124i
$136$	0.527864	+	1.62460i	0.0452640	+	0.139308i
$137$	−1.94427	+	5.98385i	−0.166110	+	0.511235i	−0.999116	−	0.0420288i	$-0.986618\pi$
$137$	−1.94427	+	5.98385i	−0.166110	+	0.511235i	0.833006	+	0.553264i	$0.186618\pi$
$138$	24.1803	+	17.5680i	2.05837	+	1.49549i
$139$	−4.14590	+	12.7598i	−0.351650	+	1.08227i	0.606276	+	0.795254i	$0.292663\pi$
$139$	−4.14590	+	12.7598i	−0.351650	+	1.08227i	−0.957926	+	0.287014i	$0.907337\pi$
$140$	0.0450850	−	0.138757i	0.00381038	−	0.0117271i
$141$	−6.47214	−	4.70228i	−0.545052	−	0.396004i
$142$	−4.59017	+	14.1271i	−0.385199	+	1.18552i
$143$	−2.00000	−	6.15537i	−0.167248	−	0.514738i
$144$	29.3435	−	21.3193i	2.44529	−	1.77661i
$145$	−0.854102	−	2.62866i	−0.0709293	−	0.218298i
$146$	11.0902	+	8.05748i	0.917829	+	0.666842i
$147$	18.1803	+	13.2088i	1.49949	+	1.08944i
$148$	−1.00000	+	0.726543i	−0.0821995	+	0.0597214i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	−20.9443			−1.71009
$151$	−11.4721	+	8.33499i	−0.933589	+	0.678292i	−0.946869	−	0.321620i	$-0.895773\pi$
$151$	−11.4721	+	8.33499i	−0.933589	+	0.678292i	0.0132798	+	0.999912i	$0.495773\pi$
$152$	1.54508	−	4.75528i	0.125323	−	0.385704i
$153$	−1.76393	−	5.42882i	−0.142605	−	0.438894i
$154$	−0.763932			−0.0615594
$155$		0			0
$156$	6.47214			0.518186
$157$	6.45492	+	19.8662i	0.515158	+	1.58549i	0.782994	+	0.622030i	$0.213692\pi$
$157$	6.45492	+	19.8662i	0.515158	+	1.58549i	−0.267835	+	0.963465i	$0.586308\pi$
$158$	5.85410	−	18.0171i	0.465727	−	1.43336i
$159$	−27.4164	+	19.9192i	−2.17426	+	1.57969i
$160$	−3.38197			−0.267368
$161$	−1.34752			−0.106200
$162$	−31.9615	+	23.2214i	−2.51113	+	1.82444i
$163$	−8.66312	−	6.29412i	−0.678548	−	0.492994i	0.194328	−	0.980937i	$-0.437747\pi$
$163$	−8.66312	−	6.29412i	−0.678548	−	0.492994i	−0.872876	+	0.487943i	$0.837747\pi$
$164$	−3.50000	−	2.54290i	−0.273304	−	0.198567i
$165$	−2.00000	−	6.15537i	−0.155700	−	0.479195i
$166$	−19.5623	+	14.2128i	−1.51833	+	1.10313i
$167$	2.00000	+	6.15537i	0.154765	+	0.476317i	0.998137	−	0.0610130i	$-0.0194331\pi$
$167$	2.00000	+	6.15537i	0.154765	+	0.476317i	−0.843372	+	0.537330i	$0.819433\pi$
$168$	−0.527864	+	1.62460i	−0.0407256	+	0.125340i
$169$	2.04508	+	1.48584i	0.157314	+	0.114295i
$170$	−0.381966	+	1.17557i	−0.0292955	+	0.0901621i
$171$	−5.16312	+	15.8904i	−0.394834	+	1.21517i
$172$	0.618034	+	0.449028i	0.0471246	+	0.0342381i
$173$	0.909830	−	2.80017i	0.0691731	−	0.212893i	−0.910494	−	0.413522i	$-0.864299\pi$
$173$	0.909830	−	2.80017i	0.0691731	−	0.212893i	0.979667	+	0.200629i	$0.0642985\pi$
$174$	−4.47214	−	13.7638i	−0.339032	−	1.04343i
$175$	0.763932	−	0.555029i	0.0577478	−	0.0419563i
$176$	3.00000	+	9.23305i	0.226134	+	0.695967i
$177$	−5.85410	−	4.25325i	−0.440021	−	0.319694i
$178$	15.3262	+	11.1352i	1.14875	+	0.834616i
$179$	1.38197	−	1.00406i	0.103293	−	0.0750467i	−0.534940	−	0.844890i	$-0.679666\pi$
$179$	1.38197	−	1.00406i	0.103293	−	0.0750467i	0.638233	+	0.769843i	$0.279666\pi$
$180$	4.61803			0.344208
$181$	4.18034			0.310722			0.155361	−	0.987858i	$-0.450346\pi$
$181$	4.18034			0.310722			0.155361	+	0.987858i	$0.450346\pi$
$182$	−1.00000	+	0.726543i	−0.0741249	+	0.0538549i
$183$	−8.18034	+	25.1765i	−0.604708	+	1.86110i
$184$	3.94427	+	12.1392i	0.290776	+	0.894915i
$185$	2.00000			0.147043
$186$		0			0
$187$	1.52786			0.111728
$188$	0.472136	+	1.45309i	0.0344341	+	0.105977i
$189$	1.05573	−	3.24920i	0.0767929	−	0.236344i
$190$	2.92705	−	2.12663i	0.212351	−	0.154282i
$191$	−19.1803			−1.38784			−0.693920	−	0.720052i	$-0.744118\pi$
$191$	−19.1803			−1.38784			−0.693920	+	0.720052i	$0.744118\pi$
$192$	13.7082			0.989304
$193$	−2.80902	+	2.04087i	−0.202197	+	0.146905i	−0.684276	−	0.729223i	$-0.739882\pi$
$193$	−2.80902	+	2.04087i	−0.202197	+	0.146905i	0.482079	+	0.876128i	$0.339882\pi$
$194$	20.8713	+	15.1639i	1.49847	+	1.08870i
$195$	−8.47214	−	6.15537i	−0.606702	−	0.440795i
$196$	−1.32624	−	4.08174i	−0.0947313	−	0.291553i
$197$	9.23607	−	6.71040i	0.658043	−	0.478096i	−0.207959	−	0.978138i	$-0.566682\pi$
$197$	9.23607	−	6.71040i	0.658043	−	0.478096i	0.866001	+	0.500042i	$0.166682\pi$
$198$	−7.47214	−	22.9969i	−0.531022	−	1.63432i
$199$	5.85410	−	18.0171i	0.414986	−	1.27720i	−0.497277	−	0.867592i	$-0.665667\pi$
$199$	5.85410	−	18.0171i	0.414986	−	1.27720i	0.912263	−	0.409605i	$-0.134333\pi$
$200$	−7.23607	−	5.25731i	−0.511667	−	0.371748i
$201$	8.00000	−	24.6215i	0.564276	−	1.73666i
$202$	−1.50000	+	4.61653i	−0.105540	+	0.324818i
$203$	0.527864	+	0.383516i	0.0370488	+	0.0269175i
$204$	−0.472136	+	1.45309i	−0.0330561	+	0.101736i
$205$	2.16312	+	6.65740i	0.151079	+	0.464973i
$206$	−8.16312	+	5.93085i	−0.568751	+	0.413222i
$207$	−13.1803	−	40.5649i	−0.916097	−	2.81946i
$208$	12.7082	+	9.23305i	0.881155	+	0.640197i
$209$	−3.61803	−	2.62866i	−0.250265	−	0.181828i
$210$	−1.00000	+	0.726543i	−0.0690066	+	0.0501362i
$211$	23.1803			1.59580			0.797900	−	0.602790i	$-0.205944\pi$
$211$	23.1803			1.59580			0.797900	+	0.602790i	$0.205944\pi$
$212$	6.47214			0.444508
$213$	24.0344	−	17.4620i	1.64681	−	1.19648i
$214$	2.88197	−	8.86978i	0.197007	−	0.606326i
$215$	−0.381966	−	1.17557i	−0.0260499	−	0.0801732i
$216$	−32.3607			−2.20187
$217$		0			0
$218$	−22.5623			−1.52811
$219$	−8.47214	−	26.0746i	−0.572494	−	1.76196i
$220$	−0.381966	+	1.17557i	−0.0257521	+	0.0792569i
$221$	2.00000	−	1.45309i	0.134535	−	0.0977451i
$222$	10.4721			0.702844
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	0.645898	−	0.469272i	0.0431559	−	0.0313546i
$225$	24.1803	+	17.5680i	1.61202	+	1.17120i
$226$	−4.54508	−	3.30220i	−0.302335	−	0.219659i
$227$	−2.00000	−	6.15537i	−0.132745	−	0.408546i	0.862488	−	0.506078i	$-0.168905\pi$
$227$	−2.00000	−	6.15537i	−0.132745	−	0.408546i	−0.995232	+	0.0975319i	$0.968905\pi$
$228$	3.61803	−	2.62866i	0.239610	−	0.174087i
$229$	4.14590	+	12.7598i	0.273969	+	0.843189i	0.989490	+	0.144598i	$0.0461890\pi$
$229$	4.14590	+	12.7598i	0.273969	+	0.843189i	−0.715522	+	0.698590i	$0.753811\pi$
$230$	−2.85410	+	8.78402i	−0.188194	+	0.579201i
$231$	1.23607	+	0.898056i	0.0813273	+	0.0590877i
$232$	1.90983	−	5.87785i	0.125386	−	0.385900i
$233$	5.54508	−	17.0660i	0.363271	−	1.11803i	−0.587786	−	0.809016i	$-0.700000\pi$
$233$	5.54508	−	17.0660i	0.363271	−	1.11803i	0.951057	−	0.309016i	$-0.0999996\pi$
$234$	−31.6525	−	22.9969i	−2.06919	−	1.50335i
$235$	0.763932	−	2.35114i	0.0498334	−	0.153372i
$236$	0.427051	+	1.31433i	0.0277987	+	0.0855555i
$237$	−30.6525	+	22.2703i	−1.99109	+	1.44661i
$238$	−0.0901699	−	0.277515i	−0.00584485	−	0.0179886i
$239$	−9.47214	−	6.88191i	−0.612702	−	0.445154i	0.237663	−	0.971348i	$-0.423619\pi$
$239$	−9.47214	−	6.88191i	−0.612702	−	0.445154i	−0.850365	+	0.526194i	$0.823619\pi$
$240$	12.7082	+	9.23305i	0.820311	+	0.595991i
$241$	11.6180	−	8.44100i	0.748383	−	0.543732i	−0.146942	−	0.989145i	$-0.546943\pi$
$241$	11.6180	−	8.44100i	0.748383	−	0.543732i	0.895325	+	0.445413i	$0.146943\pi$
$242$	−11.3262			−0.728078
$243$	35.5967			2.28353
$244$	4.09017	−	2.97168i	0.261846	−	0.190242i
$245$	−2.14590	+	6.60440i	−0.137096	+	0.421939i
$246$	11.3262	+	34.8586i	0.722135	+	2.22250i
$247$	−7.23607			−0.460420
$248$		0			0
$249$	48.3607			3.06473
$250$	−4.50000	−	13.8496i	−0.284605	−	0.875924i
$251$	0.562306	−	1.73060i	0.0354924	−	0.109234i	−0.931741	−	0.363124i	$-0.881710\pi$
$251$	0.562306	−	1.73060i	0.0354924	−	0.109234i	0.967233	+	0.253890i	$0.0817100\pi$
$252$	−0.881966	+	0.640786i	−0.0555586	+	0.0403657i
$253$	11.4164			0.717743
$254$	−20.1803			−1.26623
$255$	2.00000	−	1.45309i	0.125245	−	0.0909957i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	−1.57295	−	1.14281i	−0.0981179	−	0.0712868i	0.537645	−	0.843172i	$-0.319314\pi$
$257$	−1.57295	−	1.14281i	−0.0981179	−	0.0712868i	−0.635762	+	0.771885i	$0.719314\pi$
$258$	−2.00000	−	6.15537i	−0.124515	−	0.383216i
$259$	−0.381966	+	0.277515i	−0.0237342	+	0.0172439i
$260$	0.618034	+	1.90211i	0.0383288	+	0.117964i
$261$	−6.38197	+	19.6417i	−0.395034	+	1.21579i
$262$	−15.7082	−	11.4127i	−0.970456	−	0.705078i
$263$	7.18034	−	22.0988i	0.442759	−	1.36267i	−0.442164	−	0.896934i	$-0.645789\pi$
$263$	7.18034	−	22.0988i	0.442759	−	1.36267i	0.884923	−	0.465737i	$-0.154211\pi$
$264$	4.47214	−	13.7638i	0.275241	−	0.847105i
$265$	−8.47214	−	6.15537i	−0.520439	−	0.378121i
$266$	−0.263932	+	0.812299i	−0.0161827	+	0.0498053i
$267$	−11.7082	−	36.0341i	−0.716530	−	2.20525i
$268$	−4.00000	+	2.90617i	−0.244339	+	0.177523i
$269$	3.41641	+	10.5146i	0.208302	+	0.641088i	0.999562	+	0.0296074i	$0.00942570\pi$
$269$	3.41641	+	10.5146i	0.208302	+	0.641088i	−0.791260	+	0.611480i	$0.790574\pi$
$270$	−18.9443	−	13.7638i	−1.15291	−	0.837639i
$271$	−11.4721	−	8.33499i	−0.696883	−	0.506315i	0.182033	−	0.983292i	$-0.441732\pi$
$271$	−11.4721	−	8.33499i	−0.696883	−	0.506315i	−0.878915	+	0.476978i	$0.841732\pi$
$272$	−3.00000	+	2.17963i	−0.181902	+	0.132159i
$273$	2.47214			0.149620
$274$	−10.1803			−0.615017
$275$	−6.47214	+	4.70228i	−0.390284	+	0.283558i
$276$	−3.52786	+	10.8576i	−0.212352	+	0.653554i
$277$	3.90983	+	12.0332i	0.234919	+	0.723006i	0.997132	+	0.0756801i	$0.0241128\pi$
$277$	3.90983	+	12.0332i	0.234919	+	0.723006i	−0.762213	+	0.647326i	$0.775887\pi$
$278$	−21.7082			−1.30197
$279$		0			0
$280$	−0.527864			−0.0315459
$281$	5.25329	+	16.1680i	0.313385	+	0.964500i	0.976414	+	0.215906i	$0.0692705\pi$
$281$	5.25329	+	16.1680i	0.313385	+	0.964500i	−0.663029	+	0.748594i	$0.730729\pi$
$282$	4.00000	−	12.3107i	0.238197	−	0.733094i
$283$	11.2361	−	8.16348i	0.667915	−	0.485269i	−0.201412	−	0.979507i	$-0.564553\pi$
$283$	11.2361	−	8.16348i	0.667915	−	0.485269i	0.869327	+	0.494238i	$0.164553\pi$
$284$	−5.67376			−0.336676
$285$	−7.23607			−0.428628
$286$	8.47214	−	6.15537i	0.500968	−	0.363974i
$287$	−1.33688	−	0.971301i	−0.0789136	−	0.0573341i
$288$	20.4443	+	14.8536i	1.20469	+	0.875259i
$289$	−5.07295	−	15.6129i	−0.298409	−	0.918408i
$290$	3.61803	−	2.62866i	0.212458	−	0.154360i
$291$	−15.9443	−	49.0714i	−0.934670	−	2.87662i
$292$	−1.61803	+	4.97980i	−0.0946883	+	0.291421i
$293$	0.381966	+	0.277515i	0.0223147	+	0.0162126i	0.598887	−	0.800834i	$-0.295610\pi$
$293$	0.381966	+	0.277515i	0.0223147	+	0.0162126i	−0.576572	+	0.817046i	$0.695610\pi$
$294$	−11.2361	+	34.5811i	−0.655301	+	2.01681i
$295$	0.690983	−	2.12663i	0.0402306	−	0.123817i
$296$	3.61803	+	2.62866i	0.210294	+	0.152788i
$297$	−8.94427	+	27.5276i	−0.518999	+	1.59732i
$298$	5.00000	+	15.3884i	0.289642	+	0.891427i
$299$	14.9443	−	10.8576i	0.864250	−	0.627914i
$300$	−2.47214	−	7.60845i	−0.142729	−	0.439274i
$301$	0.236068	+	0.171513i	0.0136067	+	0.00988587i
$302$	−18.5623	−	13.4863i	−1.06814	−	0.776050i
$303$	7.85410	−	5.70634i	0.451206	−	0.327821i
$304$	10.8541			0.622525
$305$	−8.18034			−0.468405
$306$	7.47214	−	5.42882i	0.427154	−	0.310345i
$307$	−8.87132	+	27.3031i	−0.506313	+	1.55827i	0.292239	+	0.956345i	$0.405600\pi$
$307$	−8.87132	+	27.3031i	−0.506313	+	1.55827i	−0.798552	+	0.601926i	$0.794400\pi$
$308$	−0.0901699	−	0.277515i	−0.00513791	−	0.0158129i
$309$	20.1803			1.14802
$310$		0			0
$311$	−29.1803			−1.65467			−0.827333	−	0.561712i	$-0.810143\pi$
$311$	−29.1803			−1.65467			−0.827333	+	0.561712i	$0.810143\pi$
$312$	−7.23607	−	22.2703i	−0.409662	−	1.26081i
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	0.691138	+	0.722723i	$0.257110\pi$
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	−0.983948	+	0.178454i	$0.942890\pi$
$314$	−27.3435	+	19.8662i	−1.54308	+	1.12111i
$315$	1.76393			0.0993863
$316$	7.23607			0.407061
$317$	−3.28115	+	2.38390i	−0.184288	+	0.133893i	−0.676104	−	0.736806i	$-0.736333\pi$
$317$	−3.28115	+	2.38390i	−0.184288	+	0.133893i	0.491816	+	0.870699i	$0.336333\pi$
$318$	−44.3607	−	32.2299i	−2.48762	−	1.80736i
$319$	−4.47214	−	3.24920i	−0.250392	−	0.181920i
$320$	1.30902	+	4.02874i	0.0731763	+	0.225213i
$321$	−15.0902	+	10.9637i	−0.842251	+	0.611931i
$322$	−0.673762	−	2.07363i	−0.0375473	−	0.115559i
$323$	0.527864	−	1.62460i	0.0293711	−	0.0903951i
$324$	−12.2082	−	8.86978i	−0.678234	−	0.492766i
$325$	−4.00000	+	12.3107i	−0.221880	+	0.682877i
$326$	5.35410	−	16.4782i	0.296536	−	0.912645i
$327$	36.5066	+	26.5236i	2.01882	+	1.46676i
$328$	−4.83688	+	14.8864i	−0.267072	+	0.821963i
$329$	0.180340	+	0.555029i	0.00994246	+	0.0305997i
$330$	8.47214	−	6.15537i	0.466376	−	0.338842i
$331$	−0.618034	−	1.90211i	−0.0339702	−	0.104550i	0.932634	−	0.360825i	$-0.117505\pi$
$331$	−0.618034	−	1.90211i	−0.0339702	−	0.104550i	−0.966604	+	0.256275i	$0.917505\pi$
$332$	−7.47214	−	5.42882i	−0.410087	−	0.297945i
$333$	−12.0902	−	8.78402i	−0.662537	−	0.481361i
$334$	−8.47214	+	6.15537i	−0.463575	+	0.336807i
$335$	8.00000			0.437087
$336$	−3.70820			−0.202299
$337$	−11.9443	+	8.67802i	−0.650646	+	0.472722i	−0.863491	−	0.504364i	$-0.831727\pi$
$337$	−11.9443	+	8.67802i	−0.650646	+	0.472722i	0.212845	+	0.977086i	$0.431727\pi$
$338$	−1.26393	+	3.88998i	−0.0687488	+	0.211587i
$339$	3.47214	+	10.6861i	0.188581	+	0.580391i
$340$	−0.472136			−0.0256052
$341$		0			0
$342$	−27.0344			−1.46186
$343$	−1.01722	−	3.13068i	−0.0549248	−	0.169041i
$344$	0.854102	−	2.62866i	0.0460501	−	0.141728i
$345$	14.9443	−	10.8576i	0.804573	−	0.584556i
$346$	4.76393			0.256111
$347$	−24.1803			−1.29807			−0.649034	−	0.760759i	$-0.724827\pi$
$347$	−24.1803			−1.29807			−0.649034	+	0.760759i	$0.724827\pi$
$348$	4.47214	−	3.24920i	0.239732	−	0.174175i
$349$	6.38197	+	4.63677i	0.341619	+	0.248201i	0.745345	−	0.666679i	$-0.232285\pi$
$349$	6.38197	+	4.63677i	0.341619	+	0.248201i	−0.403726	+	0.914880i	$0.632285\pi$
$350$	1.23607	+	0.898056i	0.0660706	+	0.0480031i
$351$	14.4721	+	44.5407i	0.772465	+	2.37740i
$352$	−5.47214	+	3.97574i	−0.291666	+	0.211908i
$353$	−2.29180	−	7.05342i	−0.121980	−	0.375416i	0.871359	−	0.490646i	$-0.163239\pi$
$353$	−2.29180	−	7.05342i	−0.121980	−	0.375416i	−0.993339	+	0.115231i	$0.963239\pi$
$354$	3.61803	−	11.1352i	0.192296	−	0.591827i
$355$	7.42705	+	5.39607i	0.394187	+	0.286394i
$356$	−2.23607	+	6.88191i	−0.118511	+	0.364740i
$357$	−0.180340	+	0.555029i	−0.00954460	+	0.0293753i
$358$	2.23607	+	1.62460i	0.118180	+	0.0858627i
$359$	6.87132	−	21.1478i	0.362655	−	1.11614i	−0.588782	−	0.808292i	$-0.700392\pi$
$359$	6.87132	−	21.1478i	0.362655	−	1.11614i	0.951437	−	0.307844i	$-0.0996076\pi$
$360$	−5.16312	−	15.8904i	−0.272120	−	0.837500i
$361$	11.3262	−	8.22899i	0.596118	−	0.433105i
$362$	2.09017	+	6.43288i	0.109857	+	0.338105i
$363$	18.3262	+	13.3148i	0.961878	+	0.698845i
$364$	−0.381966	−	0.277515i	−0.0200205	−	0.0145457i
$365$	6.85410	−	4.97980i	0.358760	−	0.260654i
$366$	−42.8328			−2.23891
$367$	−18.0000			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$	−22.4164	+	16.2865i	−1.16854	+	0.848991i
$369$	16.1631	−	49.7450i	0.841418	−	2.58962i
$370$	1.00000	+	3.07768i	0.0519875	+	0.160001i
$371$	2.47214			0.128347
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	0.763932	+	2.35114i	0.0395020	+	0.121575i
$375$	−9.00000	+	27.6992i	−0.464758	+	1.43038i
$376$	4.47214	−	3.24920i	0.230633	−	0.167565i
$377$	−8.94427			−0.460653
$378$	5.52786			0.284323
$379$	1.70820	−	1.24108i	0.0877445	−	0.0637501i	−0.543048	−	0.839702i	$-0.682730\pi$
$379$	1.70820	−	1.24108i	0.0877445	−	0.0637501i	0.630793	+	0.775951i	$0.282730\pi$
$380$	1.11803	+	0.812299i	0.0573539	+	0.0416701i
$381$	32.6525	+	23.7234i	1.67284	+	1.21539i
$382$	−9.59017	−	29.5155i	−0.490676	−	1.51014i
$383$	−19.3262	+	14.0413i	−0.987525	+	0.717479i	−0.959378	−	0.282125i	$-0.908961\pi$
$383$	−19.3262	+	14.0413i	−0.987525	+	0.717479i	−0.0281470	+	0.999604i	$0.508961\pi$
$384$	13.6180	+	41.9120i	0.694942	+	2.13881i
$385$	−0.145898	+	0.449028i	−0.00743565	+	0.0228846i
$386$	−4.54508	−	3.30220i	−0.231339	−	0.168077i
$387$	−2.85410	+	8.78402i	−0.145082	+	0.446517i
$388$	−3.04508	+	9.37181i	−0.154591	+	0.475781i
$389$	−14.4721	−	10.5146i	−0.733766	−	0.533113i	0.156986	−	0.987601i	$-0.449822\pi$
$389$	−14.4721	−	10.5146i	−0.733766	−	0.533113i	−0.890753	+	0.454488i	$0.849822\pi$
$390$	5.23607	−	16.1150i	0.265139	−	0.816013i
$391$	1.34752	+	4.14725i	0.0681472	+	0.209736i
$392$	−12.5623	+	9.12705i	−0.634492	+	0.460986i
$393$	12.0000	+	36.9322i	0.605320	+	1.86298i
$394$	14.9443	+	10.8576i	0.752882	+	0.547000i
$395$	−9.47214	−	6.88191i	−0.476595	−	0.346266i
$396$	7.47214	−	5.42882i	0.375489	−	0.272809i
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$	30.6525			1.53647
$399$	1.38197	−	1.00406i	0.0691848	−	0.0502657i
$400$	6.00000	−	18.4661i	0.300000	−	0.923305i
$401$	−11.7984	−	36.3117i	−0.589183	−	1.81332i	−0.581781	−	0.813345i	$-0.697644\pi$
$401$	−11.7984	−	36.3117i	−0.589183	−	1.81332i	−0.00740130	−	0.999973i	$-0.502356\pi$
$402$	41.8885			2.08921
$403$		0			0
$404$	−1.85410			−0.0922450
$405$	7.54508	+	23.2214i	0.374918	+	1.15388i
$406$	−0.326238	+	1.00406i	−0.0161909	+	0.0498305i
$407$	3.23607	−	2.35114i	0.160406	−	0.116542i
$408$	5.52786			0.273670
$409$	3.81966			0.188870			0.0944350	−	0.995531i	$-0.469896\pi$
$409$	3.81966			0.188870			0.0944350	+	0.995531i	$0.469896\pi$
$410$	−9.16312	+	6.65740i	−0.452534	+	0.328785i
$411$	16.4721	+	11.9677i	0.812511	+	0.590323i
$412$	−3.11803	−	2.26538i	−0.153615	−	0.111607i
$413$	0.163119	+	0.502029i	0.00802656	+	0.0247032i
$414$	55.8328	−	40.5649i	2.74403	−	1.99366i
$415$	4.61803	+	14.2128i	0.226690	+	0.697681i
$416$	−3.38197	+	10.4086i	−0.165815	+	0.510325i
$417$	35.1246	+	25.5195i	1.72006	+	1.24970i
$418$	2.23607	−	6.88191i	0.109370	−	0.336605i
$419$	−3.12868	+	9.62908i	−0.152846	+	0.470411i	−0.997936	−	0.0642122i	$-0.979547\pi$
$419$	−3.12868	+	9.62908i	−0.152846	+	0.470411i	0.845090	+	0.534623i	$0.179547\pi$
$420$	−0.381966	−	0.277515i	−0.0186380	−	0.0135413i
$421$	9.07295	−	27.9237i	0.442188	−	1.36092i	−0.443349	−	0.896349i	$-0.646210\pi$
$421$	9.07295	−	27.9237i	0.442188	−	1.36092i	0.885538	−	0.464567i	$-0.153790\pi$
$422$	11.5902	+	35.6709i	0.564201	+	1.73643i
$423$	−14.9443	+	10.8576i	−0.726615	+	0.527917i
$424$	−7.23607	−	22.2703i	−0.351415	−	1.08154i
$425$	−2.47214	−	1.79611i	−0.119916	−	0.0871242i
$426$	38.8885	+	28.2542i	1.88416	+	1.36892i
$427$	1.56231	−	1.13508i	0.0756053	−	0.0549305i
$428$	3.56231			0.172191
$429$	−20.9443			−1.01120
$430$	1.61803	−	1.17557i	0.0780285	−	0.0566910i
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	−0.821162	−	0.570695i	$-0.806674\pi$
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	0.999780	+	0.0209654i	$0.00667397\pi$
$432$	−21.7082	−	66.8110i	−1.04444	−	3.21444i
$433$	−10.1803			−0.489236			−0.244618	−	0.969620i	$-0.578663\pi$
$433$	−10.1803			−0.489236			−0.244618	+	0.969620i	$0.578663\pi$
$434$		0			0
$435$	−8.94427			−0.428845
$436$	−2.66312	−	8.19624i	−0.127540	−	0.392529i
$437$	3.94427	−	12.1392i	0.188680	−	0.580698i
$438$	35.8885	−	26.0746i	1.71482	−	1.24589i
$439$	−1.18034			−0.0563345			−0.0281673	−	0.999603i	$-0.508967\pi$
$439$	−1.18034			−0.0563345			−0.0281673	+	0.999603i	$0.508967\pi$
$440$	4.47214			0.213201
$441$	41.9787	−	30.4993i	1.99899	−	1.45235i
$442$	3.23607	+	2.35114i	0.153924	+	0.111832i
$443$	−24.8435	−	18.0498i	−1.18035	−	0.857573i	−0.188137	−	0.982143i	$-0.560245\pi$
$443$	−24.8435	−	18.0498i	−1.18035	−	0.857573i	−0.992211	+	0.124569i	$0.960245\pi$
$444$	1.23607	+	3.80423i	0.0586612	+	0.180541i
$445$	9.47214	−	6.88191i	0.449022	−	0.326234i
$446$	−2.00000	−	6.15537i	−0.0947027	−	0.291465i
$447$	10.0000	−	30.7768i	0.472984	−	1.45569i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	9.67376	−	29.7728i	0.456533	−	1.40506i	−0.412793	−	0.910825i	$-0.635447\pi$
$449$	9.67376	−	29.7728i	0.456533	−	1.40506i	0.869326	−	0.494239i	$-0.164553\pi$
$450$	−14.9443	+	45.9937i	−0.704480	+	2.16817i
$451$	11.3262	+	8.22899i	0.533332	+	0.387488i
$452$	0.663119	−	2.04087i	0.0311905	−	0.0959945i
$453$	14.1803	+	43.6426i	0.666250	+	2.05051i
$454$	8.47214	−	6.15537i	0.397617	−	0.288886i
$455$	0.236068	+	0.726543i	0.0110670	+	0.0340608i
$456$	−13.0902	−	9.51057i	−0.613003	−	0.445373i
$457$	−2.47214	−	1.79611i	−0.115642	−	0.0840186i	0.528461	−	0.848957i	$-0.322769\pi$
$457$	−2.47214	−	1.79611i	−0.115642	−	0.0840186i	−0.644103	+	0.764939i	$0.722769\pi$
$458$	−17.5623	+	12.7598i	−0.820633	+	0.596225i
$459$	−11.0557			−0.516037
$460$	−3.52786			−0.164488
$461$	27.7984	−	20.1967i	1.29470	−	0.940654i	0.294810	−	0.955556i	$-0.404744\pi$
$461$	27.7984	−	20.1967i	1.29470	−	0.940654i	0.999889	+	0.0149016i	$0.00474351\pi$
$462$	−0.763932	+	2.35114i	−0.0355413	+	0.109385i
$463$	0.798374	+	2.45714i	0.0371036	+	0.114193i	0.967893	−	0.251363i	$-0.0808788\pi$
$463$	0.798374	+	2.45714i	0.0371036	+	0.114193i	−0.930789	+	0.365556i	$0.880879\pi$
$464$	13.4164			0.622841
$465$		0			0
$466$	29.0344			1.34499
$467$	1.45492	+	4.47777i	0.0673254	+	0.207206i	0.979059	−	0.203575i	$-0.0652560\pi$
$467$	1.45492	+	4.47777i	0.0673254	+	0.207206i	−0.911734	+	0.410781i	$0.865256\pi$
$468$	4.61803	−	14.2128i	0.213469	−	0.656989i
$469$	−1.52786	+	1.11006i	−0.0705502	+	0.0512577i
$470$	4.00000			0.184506
$471$	67.5967			3.11469
$472$	4.04508	−	2.93893i	0.186190	−	0.135275i
$473$	−2.00000	−	1.45309i	−0.0919601	−	0.0668129i
$474$	−49.5967	−	36.0341i	−2.27805	−	1.65510i
$475$	2.76393	+	8.50651i	0.126818	+	0.390305i
$476$	0.0901699	−	0.0655123i	0.00413293	−	0.00300275i
$477$	24.1803	+	74.4194i	1.10714	+	3.40743i
$478$	5.85410	−	18.0171i	0.267760	−	0.824082i
$479$	−18.8435	−	13.6906i	−0.860980	−	0.625538i	0.0671717	−	0.997741i	$-0.478602\pi$
$479$	−18.8435	−	13.6906i	−0.860980	−	0.625538i	−0.928151	+	0.372203i	$0.878602\pi$
$480$	−3.38197	+	10.4086i	−0.154365	+	0.475086i
$481$	2.00000	−	6.15537i	0.0911922	−	0.280661i
$482$	18.7984	+	13.6578i	0.856242	+	0.622097i
$483$	−1.34752	+	4.14725i	−0.0613145	+	0.188707i
$484$	−1.33688	−	4.11450i	−0.0607673	−	0.187023i
$485$	12.8992	−	9.37181i	0.585722	−	0.425552i
$486$	17.7984	+	54.7778i	0.807351	+	2.48477i
$487$	−15.5623	−	11.3067i	−0.705195	−	0.512354i	0.176425	−	0.984314i	$-0.443547\pi$
$487$	−15.5623	−	11.3067i	−0.705195	−	0.512354i	−0.881620	+	0.471960i	$0.843547\pi$
$488$	−14.7984	−	10.7516i	−0.669891	−	0.486704i
$489$	−28.0344	+	20.3682i	−1.26776	+	0.921082i
$490$	−11.2361			−0.507594
$491$	−4.36068			−0.196795			−0.0983974	−	0.995147i	$-0.531372\pi$
$491$	−4.36068			−0.196795			−0.0983974	+	0.995147i	$0.531372\pi$
$492$	−11.3262	+	8.22899i	−0.510626	+	0.370992i
$493$	0.652476	−	2.00811i	0.0293860	−	0.0904409i
$494$	−3.61803	−	11.1352i	−0.162783	−	0.500995i
$495$	−14.9443			−0.671695
$496$		0			0
$497$	−2.16718			−0.0972115
$498$	24.1803	+	74.4194i	1.08355	+	3.33481i
$499$	2.03444	−	6.26137i	0.0910741	−	0.280297i	−0.895137	−	0.445792i	$-0.852922\pi$
$499$	2.03444	−	6.26137i	0.0910741	−	0.280297i	0.986211	+	0.165495i	$0.0529221\pi$
$500$	4.50000	−	3.26944i	0.201246	−	0.146214i
$501$	20.9443			0.935721
$502$	2.94427			0.131409
$503$	−23.9894	+	17.4293i	−1.06963	+	0.777134i	−0.975846	−	0.218459i	$-0.929897\pi$
$503$	−23.9894	+	17.4293i	−1.06963	+	0.777134i	−0.0937864	+	0.995592i	$0.529897\pi$
$504$	3.19098	+	2.31838i	0.142138	+	0.103269i
$505$	2.42705	+	1.76336i	0.108002	+	0.0784683i
$506$	5.70820	+	17.5680i	0.253761	+	0.780995i
$507$	6.61803	−	4.80828i	0.293917	−	0.213543i
$508$	−2.38197	−	7.33094i	−0.105683	−	0.325258i
$509$	−9.14590	+	28.1482i	−0.405385	+	1.24765i	0.515189	+	0.857077i	$0.327722\pi$
$509$	−9.14590	+	28.1482i	−0.405385	+	1.24765i	−0.920574	+	0.390569i	$0.872278\pi$
$510$	3.23607	+	2.35114i	0.143295	+	0.104110i
$511$	−0.618034	+	1.90211i	−0.0273402	+	0.0841445i
$512$	−1.63525	+	5.03280i	−0.0722687	+	0.222420i
$513$	26.1803	+	19.0211i	1.15589	+	0.839803i
$514$	0.972136	−	2.99193i	0.0428791	−	0.131968i
$515$	1.92705	+	5.93085i	0.0849160	+	0.261345i
$516$	2.00000	−	1.45309i	0.0880451	−	0.0639685i
$517$	−1.52786	−	4.70228i	−0.0671954	−	0.206806i
$518$	−0.618034	−	0.449028i	−0.0271549	−	0.0197292i
$519$	−7.70820	−	5.60034i	−0.338353	−	0.245828i
$520$	5.85410	−	4.25325i	0.256719	−	0.186518i
$521$	2.00000			0.0876216			0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000			0.0876216			0.0438108	+	0.999040i	$0.486050\pi$
$522$	−33.4164			−1.46260
$523$	−14.3262	+	10.4086i	−0.626443	+	0.455137i	−0.855166	−	0.518354i	$-0.826545\pi$
$523$	−14.3262	+	10.4086i	−0.626443	+	0.455137i	0.228723	+	0.973491i	$0.426545\pi$
$524$	2.29180	−	7.05342i	0.100118	−	0.308130i
$525$	−0.944272	−	2.90617i	−0.0412114	−	0.126836i
$526$	37.5967			1.63930
$527$		0			0
$528$	31.4164			1.36722
$529$	2.96149	+	9.11454i	0.128761	+	0.396284i
$530$	5.23607	−	16.1150i	0.227440	−	0.699989i
$531$	−13.5172	+	9.82084i	−0.586597	+	0.426188i
$532$	−0.326238			−0.0141442
$533$	22.6525			0.981188
$534$	49.5967	−	36.0341i	2.14626	−	1.55935i
$535$	−4.66312	−	3.38795i	−0.201604	−	0.146474i
$536$	14.4721	+	10.5146i	0.625101	+	0.454163i
$537$	−1.70820	−	5.25731i	−0.0737144	−	0.226870i
$538$	−14.4721	+	10.5146i	−0.623938	+	0.453318i
$539$	4.29180	+	13.2088i	0.184861	+	0.568943i
$540$	2.76393	−	8.50651i	0.118941	−	0.366062i
$541$	20.5172	+	14.9066i	0.882104	+	0.640886i	0.933807	−	0.357776i	$-0.116465\pi$
$541$	20.5172	+	14.9066i	0.882104	+	0.640886i	−0.0517031	+	0.998662i	$0.516465\pi$
$542$	7.09017	−	21.8213i	0.304549	−	0.937305i
$543$	4.18034	−	12.8658i	0.179396	−	0.552123i
$544$	−2.09017	−	1.51860i	−0.0896153	−	0.0651093i
$545$	−4.30902	+	13.2618i	−0.184578	+	0.568073i
$546$	1.23607	+	3.80423i	0.0528988	+	0.162806i
$547$	9.80902	−	7.12667i	0.419403	−	0.304714i	−0.357994	−	0.933724i	$-0.616539\pi$
$547$	9.80902	−	7.12667i	0.419403	−	0.304714i	0.777398	+	0.629009i	$0.216539\pi$
$548$	−1.20163	−	3.69822i	−0.0513309	−	0.157980i
$549$	49.4508	+	35.9281i	2.11051	+	1.53338i
$550$	−10.4721	−	7.60845i	−0.446533	−	0.324425i
$551$	−5.00000	+	3.63271i	−0.213007	+	0.154759i
$552$	41.3050			1.75806
$553$	2.76393			0.117534
$554$	−16.5623	+	12.0332i	−0.703665	+	0.511243i
$555$	2.00000	−	6.15537i	0.0848953	−	0.261281i
$556$	−2.56231	−	7.88597i	−0.108666	−	0.334439i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	−0.354102	−	1.08981i	−0.0149635	−	0.0460530i
$561$	1.52786	−	4.70228i	0.0645065	−	0.198531i
$562$	−22.2533	+	16.1680i	−0.938698	+	0.682004i
$563$	27.5410			1.16072			0.580358	−	0.814362i	$-0.302913\pi$
$563$	27.5410			1.16072			0.580358	+	0.814362i	$0.302913\pi$
$564$	4.94427			0.208191
$565$	−2.80902	+	2.04087i	−0.118176	+	0.0858601i
$566$	18.1803	+	13.2088i	0.764177	+	0.555207i
$567$	−4.66312	−	3.38795i	−0.195833	−	0.142281i
$568$	6.34346	+	19.5232i	0.266166	+	0.819174i
$569$	4.47214	−	3.24920i	0.187482	−	0.136213i	−0.490085	−	0.871674i	$-0.663034\pi$
$569$	4.47214	−	3.24920i	0.187482	−	0.136213i	0.677567	+	0.735461i	$0.263034\pi$
$570$	−3.61803	−	11.1352i	−0.151543	−	0.466401i
$571$	−8.70820	+	26.8011i	−0.364427	+	1.12159i	0.585912	+	0.810375i	$0.300736\pi$
$571$	−8.70820	+	26.8011i	−0.364427	+	1.12159i	−0.950339	+	0.311216i	$0.899264\pi$
$572$	3.23607	+	2.35114i	0.135307	+	0.0983061i
$573$	−19.1803	+	59.0310i	−0.801270	+	2.46606i
$574$	0.826238	−	2.54290i	0.0344865	−	0.106139i
$575$	−18.4721	−	13.4208i	−0.770341	−	0.559686i
$576$	9.78115	−	30.1033i	0.407548	−	1.25430i
$577$	−8.90983	−	27.4216i	−0.370921	−	1.14158i	−0.946190	−	0.323613i	$-0.895102\pi$
$577$	−8.90983	−	27.4216i	−0.370921	−	1.14158i	0.575268	−	0.817965i	$-0.304898\pi$
$578$	21.4894	−	15.6129i	0.893839	−	0.649412i
$579$	3.47214	+	10.6861i	0.144297	+	0.444101i
$580$	1.38197	+	1.00406i	0.0573830	+	0.0416912i
$581$	−2.85410	−	2.07363i	−0.118408	−	0.0860285i
$582$	67.5410	−	49.0714i	2.79967	−	2.03408i
$583$	−20.9443			−0.867423
$584$	18.9443			0.783920
$585$	−19.5623	+	14.2128i	−0.808802	+	0.587629i
$586$	−0.236068	+	0.726543i	−0.00975188	+	0.0300132i
$587$	2.00000	+	6.15537i	0.0825488	+	0.254059i	0.983809	−	0.179219i	$-0.0573569\pi$
$587$	2.00000	+	6.15537i	0.0825488	+	0.254059i	−0.901260	+	0.433278i	$0.857357\pi$
$588$	−13.8885			−0.572754
$589$		0			0
$590$	3.61803			0.148952
$591$	−11.4164	−	35.1361i	−0.469608	−	1.44531i
$592$	−3.00000	+	9.23305i	−0.123299	+	0.379476i
$593$	5.28115	−	3.83698i	0.216871	−	0.157566i	−0.474046	−	0.880500i	$-0.657207\pi$
$593$	5.28115	−	3.83698i	0.216871	−	0.157566i	0.690917	+	0.722934i	$0.257207\pi$
$594$	−46.8328			−1.92157
$595$	−0.180340			−0.00739321
$596$	−5.00000	+	3.63271i	−0.204808	+	0.148802i
$597$	−49.5967	−	36.0341i	−2.02986	−	1.47478i
$598$	24.1803	+	17.5680i	0.988808	+	0.718411i
$599$	−4.51064	−	13.8823i	−0.184300	−	0.567217i	0.815636	−	0.578566i	$-0.196387\pi$
$599$	−4.51064	−	13.8823i	−0.184300	−	0.567217i	−0.999936	+	0.0113491i	$0.996387\pi$
$600$	−23.4164	+	17.0130i	−0.955971	+	0.694553i
$601$	−9.43769	−	29.0462i	−0.384972	−	1.18482i	−0.936501	−	0.350665i	$-0.885956\pi$
$601$	−9.43769	−	29.0462i	−0.384972	−	1.18482i	0.551529	−	0.834156i	$-0.314044\pi$
$602$	−0.145898	+	0.449028i	−0.00594636	+	0.0183010i
$603$	−48.3607	−	35.1361i	−1.96940	−	1.43085i
$604$	2.70820	−	8.33499i	0.110195	−	0.339146i
$605$	−2.16312	+	6.65740i	−0.0879433	+	0.270662i
$606$	12.7082	+	9.23305i	0.516235	+	0.375067i
$607$	6.94427	−	21.3723i	0.281859	−	0.867474i	−0.705463	−	0.708747i	$-0.749261\pi$
$607$	6.94427	−	21.3723i	0.281859	−	0.867474i	0.987322	−	0.158727i	$-0.0507390\pi$
$608$	2.33688	+	7.19218i	0.0947730	+	0.291681i
$609$	1.70820	−	1.24108i	0.0692199	−	0.0502912i
$610$	−4.09017	−	12.5882i	−0.165606	−	0.509683i
$611$	−6.47214	−	4.70228i	−0.261835	−	0.190234i
$612$	2.85410	+	2.07363i	0.115370	+	0.0838214i
$613$	−35.5066	+	25.7970i	−1.43410	+	1.04193i	−0.444862	+	0.895599i	$0.646747\pi$
$613$	−35.5066	+	25.7970i	−1.43410	+	1.04193i	−0.989235	+	0.146333i	$0.953253\pi$
$614$	−46.4508			−1.87460
$615$	22.6525			0.913436
$616$	−0.854102	+	0.620541i	−0.0344127	+	0.0250023i
$617$	10.0344	−	30.8828i	0.403971	−	1.24330i	−0.517780	−	0.855514i	$-0.673241\pi$
$617$	10.0344	−	30.8828i	0.403971	−	1.24330i	0.921751	−	0.387782i	$-0.126759\pi$
$618$	10.0902	+	31.0543i	0.405886	+	1.24919i
$619$	−6.18034			−0.248409			−0.124204	−	0.992257i	$-0.539638\pi$
$619$	−6.18034			−0.248409			−0.124204	+	0.992257i	$0.539638\pi$
$620$		0			0
$621$	−82.6099			−3.31502
$622$	−14.5902	−	44.9039i	−0.585013	−	1.80048i
$623$	−0.854102	+	2.62866i	−0.0342189	+	0.105315i
$624$	41.1246	−	29.8788i	1.64630	−	1.19611i
$625$	11.0000			0.440000
$626$	−27.1246			−1.08412
$627$	−11.7082	+	8.50651i	−0.467581	+	0.339717i
$628$	−10.4443	−	7.58821i	−0.416772	−	0.302802i
$629$	1.23607	+	0.898056i	0.0492853	+	0.0358078i
$630$	0.881966	+	2.71441i	0.0351384	+	0.108145i
$631$	27.7984	−	20.1967i	1.10664	−	0.804018i	0.124505	−	0.992219i	$-0.460266\pi$
$631$	27.7984	−	20.1967i	1.10664	−	0.804018i	0.982131	+	0.188201i	$0.0602656\pi$
$632$	−8.09017	−	24.8990i	−0.321810	−	0.990428i
$633$	23.1803	−	71.3418i	0.921336	−	2.83558i
$634$	−5.30902	−	3.85723i	−0.210848	−	0.153190i
$635$	−3.85410	+	11.8617i	−0.152945	+	0.470717i
$636$	6.47214	−	19.9192i	0.256637	−	0.789847i
$637$	18.1803	+	13.2088i	0.720331	+	0.523351i
$638$	2.76393	−	8.50651i	0.109425	−	0.336776i
$639$	−21.1976	−	65.2394i	−0.838563	−	2.58083i
$640$	−11.0172	+	8.00448i	−0.435494	+	0.316405i
$641$	−3.70820	−	11.4127i	−0.146465	−	0.450774i	0.850731	−	0.525601i	$-0.176159\pi$
$641$	−3.70820	−	11.4127i	−0.146465	−	0.450774i	−0.997197	+	0.0748272i	$0.976159\pi$
$642$	−24.4164	−	17.7396i	−0.963639	−	0.700125i
$643$	15.7984	+	11.4782i	0.623027	+	0.452656i	0.853978	−	0.520310i	$-0.174184\pi$
$643$	15.7984	+	11.4782i	0.623027	+	0.452656i	−0.230951	+	0.972966i	$0.574184\pi$
$644$	0.673762	−	0.489517i	0.0265499	−	0.0192897i
$645$	−4.00000			−0.157500
$646$	2.76393			0.108745
$647$	−0.763932	+	0.555029i	−0.0300333	+	0.0218204i	−0.602701	−	0.797967i	$-0.705909\pi$
$647$	−0.763932	+	0.555029i	−0.0300333	+	0.0218204i	0.572667	+	0.819788i	$0.305909\pi$
$648$	−16.8713	+	51.9246i	−0.662768	+	2.03979i
$649$	−1.38197	−	4.25325i	−0.0542469	−	0.166955i
$650$	−20.9443			−0.821502
$651$		0			0
$652$	6.61803			0.259182
$653$	−14.6180	−	44.9897i	−0.572048	−	1.76058i	−0.646018	−	0.763322i	$-0.723567\pi$
$653$	−14.6180	−	44.9897i	−0.572048	−	1.76058i	0.0739705	−	0.997260i	$-0.476433\pi$
$654$	−22.5623	+	69.4396i	−0.882256	+	2.71530i
$655$	−9.70820	+	7.05342i	−0.379331	+	0.275600i
$656$	−33.9787			−1.32665
$657$	−63.3050			−2.46976
$658$	−0.763932	+	0.555029i	−0.0297812	+	0.0216373i
$659$	−20.7533	−	15.0781i	−0.808433	−	0.587361i	0.104943	−	0.994478i	$-0.466534\pi$
$659$	−20.7533	−	15.0781i	−0.808433	−	0.587361i	−0.913376	+	0.407117i	$0.866534\pi$
$660$	3.23607	+	2.35114i	0.125964	+	0.0915180i
$661$	−0.197561	−	0.608030i	−0.00768423	−	0.0236496i	0.947141	−	0.320818i	$-0.103958\pi$
$661$	−0.197561	−	0.608030i	−0.00768423	−	0.0236496i	−0.954825	+	0.297168i	$0.903958\pi$
$662$	2.61803	−	1.90211i	0.101753	−	0.0739277i
$663$	−2.47214	−	7.60845i	−0.0960098	−	0.295488i
$664$	−10.3262	+	31.7809i	−0.400736	+	1.23334i
$665$	0.427051	+	0.310271i	0.0165603	+	0.0120318i
$666$	7.47214	−	22.9969i	0.289539	−	0.891111i
$667$	4.87539	−	15.0049i	0.188776	−	0.580992i
$668$	−3.23607	−	2.35114i	−0.125207	−	0.0909684i
$669$	−4.00000	+	12.3107i	−0.154649	+	0.475960i
$670$	4.00000	+	12.3107i	0.154533	+	0.475605i
$671$	−13.2361	+	9.61657i	−0.510973	+	0.371243i
$672$	−0.798374	−	2.45714i	−0.0307979	−	0.0947863i
$673$	−23.4721	−	17.0535i	−0.904784	−	0.657364i	0.0349060	−	0.999391i	$-0.488887\pi$
$673$	−23.4721	−	17.0535i	−0.904784	−	0.657364i	−0.939690	+	0.342026i	$0.888887\pi$
$674$	−19.3262	−	14.0413i	−0.744419	−	0.540852i
$675$	46.8328	−	34.0260i	1.80260	−	1.30966i
$676$	−1.56231			−0.0600887
$677$	46.7214			1.79565			0.897824	−	0.440355i	$-0.145147\pi$
$677$	46.7214			1.79565			0.897824	+	0.440355i	$0.145147\pi$
$678$	−14.7082	+	10.6861i	−0.564865	+	0.410399i
$679$	−1.16312	+	3.57971i	−0.0446364	+	0.137377i
$680$	0.527864	+	1.62460i	0.0202427	+	0.0623005i
$681$	−20.9443			−0.802586
$682$		0			0
$683$	5.18034			0.198220			0.0991101	−	0.995076i	$-0.468400\pi$
$683$	5.18034			0.198220			0.0991101	+	0.995076i	$0.468400\pi$
$684$	−3.19098	−	9.82084i	−0.122010	−	0.375509i
$685$	−1.94427	+	5.98385i	−0.0742868	+	0.228631i
$686$	4.30902	−	3.13068i	0.164519	−	0.119530i
$687$	43.4164			1.65644
$688$	6.00000			0.228748
$689$	−27.4164	+	19.9192i	−1.04448	+	0.758861i
$690$	24.1803	+	17.5680i	0.920530	+	0.668804i
$691$	−2.57295	−	1.86936i	−0.0978796	−	0.0711137i	0.537769	−	0.843092i	$-0.319267\pi$
$691$	−2.57295	−	1.86936i	−0.0978796	−	0.0711137i	−0.635649	+	0.771979i	$0.719267\pi$
$692$	0.562306	+	1.73060i	0.0213757	+	0.0657875i
$693$	2.85410	−	2.07363i	0.108418	−	0.0787706i
$694$	−12.0902	−	37.2097i	−0.458937	−	1.41246i
$695$	−4.14590	+	12.7598i	−0.157263	+	0.484005i
$696$	−16.1803	−	11.7557i	−0.613314	−	0.445599i
$697$	−1.65248	+	5.08580i	−0.0625920	+	0.192638i
$698$	−3.94427	+	12.1392i	−0.149293	+	0.459476i
$699$	−46.9787	−	34.1320i	−1.77690	−	1.29099i
$700$	−0.180340	+	0.555029i	−0.00681621	+	0.0209781i
$701$	2.16312	+	6.65740i	0.0816999	+	0.251446i	0.983560	−	0.180582i	$-0.0577981\pi$
$701$	2.16312	+	6.65740i	0.0816999	+	0.251446i	−0.901860	+	0.432028i	$0.857798\pi$
$702$	−61.3050	+	44.5407i	−2.31381	+	1.68108i
$703$	−1.38197	−	4.25325i	−0.0521218	−	0.160415i
$704$	6.85410	+	4.97980i	0.258324	+	0.187683i
$705$	−6.47214	−	4.70228i	−0.243755	−	0.177098i
$706$	9.70820	−	7.05342i	0.365373	−	0.265459i
$707$	−0.708204			−0.0266348
$708$	4.47214			0.168073
$709$	20.6525	−	15.0049i	0.775620	−	0.563521i	−0.128041	−	0.991769i	$-0.540869\pi$
$709$	20.6525	−	15.0049i	0.775620	−	0.563521i	0.903661	+	0.428248i	$0.140869\pi$
$710$	−4.59017	+	14.1271i	−0.172266	+	0.530180i
$711$	27.0344	+	83.2035i	1.01387	+	3.12037i
$712$	26.1803			0.981150
$713$		0			0
$714$	−0.944272			−0.0353385
$715$	−2.00000	−	6.15537i	−0.0747958	−	0.230198i
$716$	−0.326238	+	1.00406i	−0.0121921	+	0.0375234i
$717$	−30.6525	+	22.2703i	−1.14474	+	0.831701i
$718$	35.9787			1.34271
$719$	13.8197			0.515386			0.257693	−	0.966227i	$-0.417038\pi$
$719$	13.8197			0.515386			0.257693	+	0.966227i	$0.417038\pi$
$720$	29.3435	−	21.3193i	1.09357	−	0.794522i
$721$	−1.19098	−	0.865300i	−0.0443545	−	0.0322254i
$722$	18.3262	+	13.3148i	0.682032	+	0.495525i
$723$	−14.3607	−	44.1976i	−0.534079	−	1.64373i
$724$	−2.09017	+	1.51860i	−0.0776806	+	0.0564382i
$725$	3.41641	+	10.5146i	0.126882	+	0.390503i
$726$	−11.3262	+	34.8586i	−0.420356	+	1.29372i
$727$	35.7877	+	26.0013i	1.32729	+	0.964335i	0.999810	+	0.0194781i	$0.00620048\pi$
$727$	35.7877	+	26.0013i	1.32729	+	0.964335i	0.327483	+	0.944857i	$0.393800\pi$
$728$	−0.527864	+	1.62460i	−0.0195639	+	0.0602116i
$729$	12.9615	−	39.8914i	0.480055	−	1.47746i
$730$	11.0902	+	8.05748i	0.410466	+	0.298221i
$731$	0.291796	−	0.898056i	0.0107925	−	0.0332158i
$732$	−5.05573	−	15.5599i	−0.186865	−	0.575112i
$733$	−2.80902	+	2.04087i	−0.103753	+	0.0753813i	−0.638452	−	0.769661i	$-0.720425\pi$
$733$	−2.80902	+	2.04087i	−0.103753	+	0.0753813i	0.534699	+	0.845043i	$0.320425\pi$
$734$	−9.00000	−	27.6992i	−0.332196	−	1.02239i
$735$	18.1803	+	13.2088i	0.670592	+	0.487214i
$736$	−15.6180	−	11.3472i	−0.575688	−	0.418262i
$737$	12.9443	−	9.40456i	0.476808	−	0.346422i
$738$	84.6312			3.11532
$739$	−6.18034			−0.227347			−0.113674	−	0.993518i	$-0.536262\pi$
$739$	−6.18034			−0.227347			−0.113674	+	0.993518i	$0.536262\pi$
$740$	−1.00000	+	0.726543i	−0.0367607	+	0.0267082i
$741$	−7.23607	+	22.2703i	−0.265824	+	0.818121i
$742$	1.23607	+	3.80423i	0.0453775	+	0.139658i
$743$	−50.1803			−1.84094			−0.920469	−	0.390815i	$-0.872193\pi$
$743$	−50.1803			−1.84094			−0.920469	+	0.390815i	$0.872193\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	9.50000	+	29.2380i	0.347820	+	1.07048i
$747$	34.5066	−	106.200i	1.26253	−	3.88567i
$748$	−0.763932	+	0.555029i	−0.0279321	+	0.0202939i
$749$	1.36068			0.0497182
$750$	−47.1246			−1.72075
$751$	17.4271	−	12.6615i	0.635922	−	0.462024i	−0.222525	−	0.974927i	$-0.571430\pi$
$751$	17.4271	−	12.6615i	0.635922	−	0.462024i	0.858447	+	0.512903i	$0.171430\pi$
$752$	9.70820	+	7.05342i	0.354022	+	0.257212i
$753$	−4.76393	−	3.46120i	−0.173607	−	0.126133i
$754$	−4.47214	−	13.7638i	−0.162866	−	0.501249i
$755$	−11.4721	+	8.33499i	−0.417514	+	0.303342i
$756$	0.652476	+	2.00811i	0.0237303	+	0.0730344i
$757$	−2.67376	+	8.22899i	−0.0971795	+	0.299088i	−0.987816	−	0.155629i	$-0.950260\pi$
$757$	−2.67376	+	8.22899i	−0.0971795	+	0.299088i	0.890636	+	0.454717i	$0.150260\pi$
$758$	2.76393	+	2.00811i	0.100391	+	0.0729380i
$759$	11.4164	−	35.1361i	0.414389	−	1.27536i
$760$	1.54508	−	4.75528i	0.0560461	−	0.172492i
$761$	1.61803	+	1.17557i	0.0586537	+	0.0426144i	0.616726	−	0.787178i	$-0.288459\pi$
$761$	1.61803	+	1.17557i	0.0586537	+	0.0426144i	−0.558072	+	0.829792i	$0.688459\pi$
$762$	−20.1803	+	62.1087i	−0.731057	+	2.24996i
$763$	−1.01722	−	3.13068i	−0.0368259	−	0.113338i
$764$	9.59017	−	6.96767i	0.346960	−	0.252081i
$765$	−1.76393	−	5.42882i	−0.0637751	−	0.196280i
$766$	−31.2705	−	22.7194i	−1.12985	−	0.820884i
$767$	−5.85410	−	4.25325i	−0.211379	−	0.153576i
$768$	−35.5066	+	25.7970i	−1.28123	+	0.930870i
$769$	−47.3607			−1.70787			−0.853935	−	0.520380i	$-0.825790\pi$
$769$	−47.3607			−1.70787			−0.853935	+	0.520380i	$0.825790\pi$
$770$	−0.763932			−0.0275302
$771$	−5.09017	+	3.69822i	−0.183318	+	0.133188i
$772$	0.663119	−	2.04087i	0.0238662	−	0.0734525i
$773$	3.43769	+	10.5801i	0.123645	+	0.380541i	0.993652	−	0.112499i	$-0.0358856\pi$
$773$	3.43769	+	10.5801i	0.123645	+	0.380541i	−0.870007	+	0.493040i	$0.835886\pi$
$774$	−14.9443			−0.537161
$775$		0			0
$776$	35.6525			1.27985
$777$	0.472136	+	1.45309i	0.0169378	+	0.0521291i
$778$	8.94427	−	27.5276i	0.320668	−	0.986914i
$779$	12.6631	−	9.20029i	0.453703	−	0.329635i
$780$	6.47214			0.231740
$781$	18.3607			0.656997
$782$	−5.70820	+	4.14725i	−0.204125	+	0.148305i
$783$	32.3607	+	23.5114i	1.15648	+	0.840229i
$784$	−27.2705	−	19.8132i	−0.973947	−	0.707614i
$785$	6.45492	+	19.8662i	0.230386	+	0.709055i
$786$	−50.8328	+	36.9322i	−1.81315	+	1.31733i
$787$	−2.27051	−	6.98791i	−0.0809349	−	0.249092i	0.902399	−	0.430902i	$-0.141804\pi$
$787$	−2.27051	−	6.98791i	−0.0809349	−	0.249092i	−0.983334	+	0.181810i	$0.941804\pi$
$788$	−2.18034	+	6.71040i	−0.0776714	+	0.239048i
$789$	−60.8328	−	44.1976i	−2.16571	−	1.57348i
$790$	5.85410	−	18.0171i	0.208280	−	0.641019i
$791$	0.253289	−	0.779543i	0.00900592	−	0.0277174i
$792$	−27.0344	−	19.6417i	−0.960627	−	0.697936i
$793$	−8.18034	+	25.1765i	−0.290492	+	0.894044i
$794$	−3.50000	−	10.7719i	−0.124210	−	0.382280i
$795$	−27.4164	+	19.9192i	−0.972360	+	0.706461i
$796$	3.61803	+	11.1352i	0.128238	+	0.394675i
$797$	−44.8328	−	32.5729i	−1.58806	−	1.15379i	−0.906644	−	0.421896i	$-0.861365\pi$
$797$	−44.8328	−	32.5729i	−1.58806	−	1.15379i	−0.681416	−	0.731897i	$-0.738635\pi$
$798$	2.23607	+	1.62460i	0.0791559	+	0.0575102i
$799$	1.52786	−	1.11006i	0.0540519	−	0.0392710i
$800$	13.5279			0.478282
$801$	−87.4853			−3.09114
$802$	49.9787	−	36.3117i	1.76481	−	1.28221i
$803$	5.23607	−	16.1150i	0.184777	−	0.568685i
$804$	4.94427	+	15.2169i	0.174371	+	0.536659i
$805$	−1.34752			−0.0474940
$806$		0			0
$807$	35.7771			1.25941
$808$	2.07295	+	6.37988i	0.0729261	+	0.224443i
$809$	−7.23607	+	22.2703i	−0.254407	+	0.782983i	0.739539	+	0.673113i	$0.235043\pi$
$809$	−7.23607	+	22.2703i	−0.254407	+	0.782983i	−0.993946	+	0.109870i	$0.964957\pi$
$810$	−31.9615	+	23.2214i	−1.12301	+	0.815916i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−0.403252			−0.0141514
$813$	−37.1246	+	26.9726i	−1.30202	+	0.945971i
$814$	5.23607	+	3.80423i	0.183524	+	0.133338i
$815$	−8.66312	−	6.29412i	−0.303456	−	0.220474i
$816$	3.70820	+	11.4127i	0.129813	+	0.399524i
$817$	−2.23607	+	1.62460i	−0.0782301	+	0.0568375i
$818$	1.90983	+	5.87785i	0.0667756	+	0.205514i
$819$	1.76393	−	5.42882i	0.0616368	−	0.189698i
$820$	−3.50000	−	2.54290i	−0.122225	−	0.0888019i
$821$	−9.43769	+	29.0462i	−0.329378	+	1.01372i	0.640048	+	0.768335i	$0.278915\pi$
$821$	−9.43769	+	29.0462i	−0.329378	+	1.01372i	−0.969426	+	0.245386i	$0.921085\pi$
$822$	−10.1803	+	31.3319i	−0.355080	+	1.09282i
$823$	−11.5623	−	8.40051i	−0.403037	−	0.292823i	0.367740	−	0.929929i	$-0.380132\pi$
$823$	−11.5623	−	8.40051i	−0.403037	−	0.292823i	−0.770777	+	0.637105i	$0.780132\pi$
$824$	−4.30902	+	13.2618i	−0.150112	+	0.461996i
$825$	8.00000	+	24.6215i	0.278524	+	0.857209i
$826$	−0.690983	+	0.502029i	−0.0240424	+	0.0174678i
$827$	−5.36068	−	16.4985i	−0.186409	−	0.573708i	0.813561	−	0.581480i	$-0.197526\pi$
$827$	−5.36068	−	16.4985i	−0.186409	−	0.573708i	−0.999970	+	0.00777178i	$0.997526\pi$
$828$	21.3262	+	15.4944i	0.741138	+	0.538468i
$829$	13.6180	+	9.89408i	0.472974	+	0.343636i	0.798599	−	0.601863i	$-0.205575\pi$
$829$	13.6180	+	9.89408i	0.472974	+	0.343636i	−0.325625	+	0.945499i	$0.605575\pi$
$830$	−19.5623	+	14.2128i	−0.679018	+	0.493335i
$831$	40.9443			1.42034
$832$	13.7082			0.475246
$833$	−4.29180	+	3.11817i	−0.148702	+	0.108038i
$834$	−21.7082	+	66.8110i	−0.751694	+	2.31348i
$835$	2.00000	+	6.15537i	0.0692129	+	0.213015i
$836$	2.76393			0.0955926
$837$		0			0
$838$	−16.3820			−0.565906
$839$	8.94427	+	27.5276i	0.308791	+	0.950360i	0.978235	+	0.207498i	$0.0665320\pi$
$839$	8.94427	+	27.5276i	0.308791	+	0.950360i	−0.669445	+	0.742862i	$0.733468\pi$
$840$	−0.527864	+	1.62460i	−0.0182130	+	0.0560540i
$841$	17.2812	−	12.5555i	0.595902	−	0.432948i
$842$	47.5066			1.63718
$843$	55.0132			1.89475
$844$	−11.5902	+	8.42075i	−0.398950	+	0.289854i
$845$	2.04508	+	1.48584i	0.0703531	+	0.0511145i
$846$	−24.1803	−	17.5680i	−0.831337	−	0.604002i
$847$	−0.510643	−	1.57160i	−0.0175459	−	0.0540007i
$848$	41.1246	−	29.8788i	1.41222	−	1.02604i
$849$	−13.8885	−	42.7445i	−0.476654	−	1.46699i
$850$	1.52786	−	4.70228i	0.0524053	−	0.161287i
$851$	9.23607	+	6.71040i	0.316608	+	0.230029i
$852$	−5.67376	+	17.4620i	−0.194380	+	0.598240i
$853$	3.27051	−	10.0656i	0.111980	−	0.344639i	−0.879325	−	0.476222i	$-0.842006\pi$
$853$	3.27051	−	10.0656i	0.111980	−	0.344639i	0.991305	+	0.131583i	$0.0420059\pi$
$854$	2.52786	+	1.83660i	0.0865017	+	0.0628472i
$855$	−5.16312	+	15.8904i	−0.176575	+	0.543442i
$856$	−3.98278	−	12.2577i	−0.136129	−	0.418961i
$857$	45.0344	−	32.7194i	1.53835	−	1.11767i	0.586986	−	0.809597i	$-0.300314\pi$
$857$	45.0344	−	32.7194i	1.53835	−	1.11767i	0.951361	−	0.308078i	$-0.0996856\pi$
$858$	−10.4721	−	32.2299i	−0.357513	−	1.10031i
$859$	1.70820	+	1.24108i	0.0582832	+	0.0423452i	0.616545	−	0.787319i	$-0.288532\pi$
$859$	1.70820	+	1.24108i	0.0582832	+	0.0423452i	−0.558262	+	0.829665i	$0.688532\pi$
$860$	0.618034	+	0.449028i	0.0210748	+	0.0153117i
$861$	−4.32624	+	3.14320i	−0.147438	+	0.107120i
$862$	19.4164			0.661325
$863$	9.81966			0.334265			0.167133	−	0.985934i	$-0.446549\pi$
$863$	9.81966			0.334265			0.167133	+	0.985934i	$0.446549\pi$
$864$	39.5967	−	28.7687i	1.34711	−	0.978732i
$865$	0.909830	−	2.80017i	0.0309351	−	0.0952086i
$866$	−5.09017	−	15.6659i	−0.172971	−	0.532350i
$867$	−53.1246			−1.80421
$868$		0			0
$869$	−23.4164			−0.794347
$870$	−4.47214	−	13.7638i	−0.151620	−	0.466637i
$871$	8.00000	−	24.6215i	0.271070	−	0.834267i
$872$	−25.2254	+	18.3273i	−0.854241	+	0.620642i
$873$	−119.138			−4.03220
$874$	20.6525			0.698580
$875$	1.71885	−	1.24882i	0.0581076	−	0.0422177i
$876$	13.7082	+	9.95959i	0.463157	+	0.336503i
$877$	14.6074	+	10.6129i	0.493257	+	0.358372i	0.806435	−	0.591322i	$-0.201394\pi$
$877$	14.6074	+	10.6129i	0.493257	+	0.358372i	−0.313179	+	0.949694i	$0.601394\pi$
$878$	−0.590170	−	1.81636i	−0.0199173	−	0.0612991i
$879$	1.23607	−	0.898056i	0.0416915	−	0.0302907i
$880$	3.00000	+	9.23305i	0.101130	+	0.311246i
$881$	6.29180	−	19.3642i	0.211976	−	0.652395i	−0.787378	−	0.616470i	$-0.788562\pi$
$881$	6.29180	−	19.3642i	0.211976	−	0.652395i	0.999354	−	0.0359251i	$-0.0114378\pi$
$882$	67.9230	+	49.3489i	2.28709	+	1.66167i
$883$	9.81966	−	30.2218i	0.330458	−	1.01704i	−0.638458	−	0.769656i	$-0.720428\pi$
$883$	9.81966	−	30.2218i	0.330458	−	1.01704i	0.968916	−	0.247389i	$-0.0795724\pi$
$884$	−0.472136	+	1.45309i	−0.0158797	+	0.0488725i
$885$	−5.85410	−	4.25325i	−0.196783	−	0.142972i
$886$	15.3541	−	47.2551i	0.515831	−	1.58757i
$887$	8.36475	+	25.7440i	0.280861	+	0.864400i	0.987609	+	0.156935i	$0.0501613\pi$
$887$	8.36475	+	25.7440i	0.280861	+	0.864400i	−0.706748	+	0.707465i	$0.749839\pi$
$888$	11.7082	−	8.50651i	0.392902	−	0.285460i
$889$	−0.909830	−	2.80017i	−0.0305147	−	0.0939147i
$890$	15.3262	+	11.1352i	0.513737	+	0.373252i
$891$	39.5066	+	28.7032i	1.32352	+	0.961594i
$892$	2.00000	−	1.45309i	0.0669650	−	0.0486529i
$893$	−5.52786			−0.184983
$894$	52.3607			1.75120
$895$	1.38197	−	1.00406i	0.0461940	−	0.0335619i
$896$	0.993422	−	3.05744i	0.0331879	−	0.102142i
$897$	−18.4721	−	56.8514i	−0.616767	−	1.89821i
$898$	50.6525			1.69030
$899$		0			0
$900$	−18.4721			−0.615738
$901$	−2.47214	−	7.60845i	−0.0823588	−	0.253474i
$902$	−7.00000	+	21.5438i	−0.233075	+	0.717330i
$903$	0.763932	−	0.555029i	0.0254221	−	0.0184702i
$904$	−7.76393			−0.258225
$905$	4.18034			0.138959
$906$	−60.0689	+	43.6426i	−1.99565	+	1.44993i
$907$	19.6074	+	14.2456i	0.651053	+	0.473017i	0.863630	−	0.504127i	$-0.168186\pi$
$907$	19.6074	+	14.2456i	0.651053	+	0.473017i	−0.212577	+	0.977144i	$0.568186\pi$
$908$	3.23607	+	2.35114i	0.107393	+	0.0780254i
$909$	−6.92705	−	21.3193i	−0.229756	−	0.707116i
$910$	−1.00000	+	0.726543i	−0.0331497	+	0.0240847i
$911$	−5.61803	−	17.2905i	−0.186134	−	0.572861i	0.813832	−	0.581100i	$-0.197377\pi$
$911$	−5.61803	−	17.2905i	−0.186134	−	0.572861i	−0.999966	+	0.00823898i	$0.997377\pi$
$912$	10.8541	−	33.4055i	0.359415	−	1.10617i
$913$	24.1803	+	17.5680i	0.800252	+	0.581417i
$914$	1.52786	−	4.70228i	0.0505373	−	0.155538i
$915$	−8.18034	+	25.1765i	−0.270434	+	0.832309i
$916$	−6.70820	−	4.87380i	−0.221645	−	0.161035i
$917$	0.875388	−	2.69417i	0.0289079	−	0.0889693i
$918$	−5.52786	−	17.0130i	−0.182447	−	0.561513i
$919$	11.7082	−	8.50651i	0.386218	−	0.280604i	−0.377686	−	0.925934i	$-0.623280\pi$
$919$	11.7082	−	8.50651i	0.386218	−	0.280604i	0.763904	+	0.645330i	$0.223280\pi$
$920$	3.94427	+	12.1392i	0.130039	+	0.400218i
$921$	75.1591	+	54.6062i	2.47658	+	1.79934i
$922$	44.9787	+	32.6789i	1.48130	+	1.07622i
$923$	24.0344	−	17.4620i	0.791103	−	0.574770i
$924$	−0.944272			−0.0310643
$925$	−8.00000			−0.263038
$926$	−3.38197	+	2.45714i	−0.111138	+	0.0807467i
$927$	14.3992	−	44.3161i	0.472931	−	1.45553i
$928$	2.88854	+	8.89002i	0.0948211	+	0.291829i
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		0			0
$931$	15.5279			0.508905
$932$	3.42705	+	10.5474i	0.112257	+	0.345491i
$933$	−29.1803	+	89.8079i	−0.955321	+	2.94018i
$934$	−6.16312	+	4.47777i	−0.201663	+	0.146517i
$935$	1.52786			0.0499665
$936$	−54.0689			−1.76730
$937$	−7.32624	+	5.32282i	−0.239338	+	0.173889i	−0.700988	−	0.713173i	$-0.747257\pi$
$937$	−7.32624	+	5.32282i	−0.239338	+	0.173889i	0.461650	+	0.887062i	$0.347257\pi$
$938$	−2.47214	−	1.79611i	−0.0807181	−	0.0586451i
$939$	43.8885	+	31.8869i	1.43225	+	1.04059i
$940$	0.472136	+	1.45309i	0.0153994	+	0.0473944i
$941$	−30.7426	+	22.3358i	−1.00218	+	0.728128i	−0.962555	−	0.271087i	$-0.912617\pi$
$941$	−30.7426	+	22.3358i	−1.00218	+	0.728128i	−0.0396268	+	0.999215i	$0.512617\pi$
$942$	33.7984	+	104.021i	1.10121	+	3.38918i
$943$	−12.3475	+	38.0018i	−0.402091	+	1.23751i
$944$	8.78115	+	6.37988i	0.285802	+	0.207647i
$945$	1.05573	−	3.24920i	0.0343428	−	0.105696i
$946$	1.23607	−	3.80423i	0.0401880	−	0.123686i
$947$	−10.5623	−	7.67396i	−0.343229	−	0.249370i	0.402794	−	0.915291i	$-0.368039\pi$
$947$	−10.5623	−	7.67396i	−0.343229	−	0.249370i	−0.746023	+	0.665920i	$0.768039\pi$
$948$	7.23607	−	22.2703i	0.235017	−	0.723307i
$949$	−8.47214	−	26.0746i	−0.275017	−	0.846416i
$950$	−11.7082	+	8.50651i	−0.379864	+	0.275988i
$951$	4.05573	+	12.4822i	0.131516	+	0.404765i
$952$	−0.326238	−	0.237026i	−0.0105734	−	0.00768205i
$953$	36.9787	+	26.8666i	1.19786	+	0.870295i	0.994072	−	0.108721i	$-0.0346754\pi$
$953$	36.9787	+	26.8666i	1.19786	+	0.870295i	0.203786	+	0.979016i	$0.434675\pi$
$954$	−102.430	+	74.4194i	−3.31628	+	2.40942i
$955$	−19.1803			−0.620661
$956$	7.23607			0.234031
$957$	−14.4721	+	10.5146i	−0.467818	+	0.339889i
$958$	11.6459	−	35.8424i	0.376262	−	1.15802i
$959$	−0.458980	−	1.41260i	−0.0148212	−	0.0456151i
$960$	13.7082			0.442430
$961$		0			0
$962$	10.4721			0.337635
$963$	13.3090	+	40.9609i	0.428877	+	1.31995i
$964$	−2.74265	+	8.44100i	−0.0883347	+	0.271866i
$965$	−2.80902	+	2.04087i	−0.0904255	+	0.0656979i
$966$	−7.05573			−0.227014
$967$	−60.3607			−1.94107			−0.970534	−	0.240963i	$-0.922537\pi$
$967$	−60.3607			−1.94107			−0.970534	+	0.240963i	$0.922537\pi$
$968$	−12.6631	+	9.20029i	−0.407008	+	0.295709i
$969$	−4.47214	−	3.24920i	−0.143666	−	0.104379i
$970$	20.8713	+	15.1639i	0.670138	+	0.486884i
$971$	−8.65248	−	26.6296i	−0.277671	−	0.854584i	−0.988500	−	0.151219i	$-0.951680\pi$
$971$	−8.65248	−	26.6296i	−0.277671	−	0.854584i	0.710829	−	0.703365i	$-0.248320\pi$
$972$	−17.7984	+	12.9313i	−0.570883	+	0.414771i
$973$	−0.978714	−	3.01217i	−0.0313761	−	0.0965658i
$974$	9.61803	−	29.6013i	0.308182	−	0.948486i
$975$	33.8885	+	24.6215i	1.08530	+	0.788518i
$976$	12.2705	−	37.7647i	0.392769	−	1.20882i
$977$	−14.6008	+	44.9367i	−0.467121	+	1.43765i	0.389173	+	0.921164i	$0.372761\pi$
$977$	−14.6008	+	44.9367i	−0.467121	+	1.43765i	−0.856295	+	0.516487i	$0.827239\pi$
$978$	−45.3607	−	32.9565i	−1.45047	−	1.05383i
$979$	7.23607	−	22.2703i	0.231266	−	0.711763i
$980$	−1.32624	−	4.08174i	−0.0423651	−	0.130386i
$981$	84.2943	−	61.2434i	2.69131	−	1.95535i
$982$	−2.18034	−	6.71040i	−0.0695774	−	0.214137i
$983$	31.9787	+	23.2339i	1.01996	+	0.741046i	0.966275	−	0.257512i	$-0.0829026\pi$
$983$	31.9787	+	23.2339i	1.01996	+	0.741046i	0.0536874	+	0.998558i	$0.482903\pi$
$984$	40.9787	+	29.7728i	1.30635	+	0.949122i
$985$	9.23607	−	6.71040i	0.294286	−	0.213811i
$986$	3.41641			0.108801
$987$	1.88854			0.0601130
$988$	3.61803	−	2.62866i	0.115105	−	0.0836287i
$989$	2.18034	−	6.71040i	0.0693308	−	0.213378i
$990$	−7.47214	−	22.9969i	−0.237480	−	0.730889i
$991$	16.5410			0.525443			0.262721	−	0.964872i	$-0.415380\pi$
$991$	16.5410			0.525443			0.262721	+	0.964872i	$0.415380\pi$
$992$		0			0
$993$	−6.47214			−0.205387
$994$	−1.08359	−	3.33495i	−0.0343695	−	0.105778i
$995$	5.85410	−	18.0171i	0.185588	−	0.571180i
$996$	−24.1803	+	17.5680i	−0.766183	+	0.556665i
$997$	−29.3607			−0.929862			−0.464931	−	0.885347i	$-0.653921\pi$
$997$	−29.3607			−0.929862			−0.464931	+	0.885347i	$0.653921\pi$
$998$	10.6525			0.337198
$999$	−23.4164	+	17.0130i	−0.740862	+	0.538268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.g.531.1		4
31.2	even	5		961.2.d.a.388.1		4
31.3	odd	30		961.2.c.e.439.2		4
31.4	even	5		961.2.d.a.374.1		4
31.5	even	3		961.2.g.e.844.1		8
31.6	odd	6		961.2.g.h.547.1		8
31.7	even	15		961.2.g.d.816.1		8
31.8	even	5	inner	961.2.d.g.628.1		4
31.9	even	15		961.2.g.e.448.1		8
31.10	even	15		961.2.g.d.338.1		8
31.11	odd	30		961.2.g.a.732.1		8
31.12	odd	30		961.2.g.a.235.1		8
31.13	odd	30		961.2.c.e.521.2		4
31.14	even	15		961.2.g.e.846.1		8
31.15	odd	10		31.2.a.a.1.2	✓	2
31.16	even	5		961.2.a.f.1.2		2
31.17	odd	30		961.2.g.h.846.1		8
31.18	even	15		961.2.c.c.521.2		4
31.19	even	15		961.2.g.d.235.1		8
31.20	even	15		961.2.g.d.732.1		8
31.21	odd	30		961.2.g.a.338.1		8
31.22	odd	30		961.2.g.h.448.1		8
31.23	odd	10		961.2.d.d.628.1		4
31.24	odd	30		961.2.g.a.816.1		8
31.25	even	3		961.2.g.e.547.1		8
31.26	odd	6		961.2.g.h.844.1		8
31.27	odd	10		961.2.d.c.374.1		4
31.28	even	15		961.2.c.c.439.2		4
31.29	odd	10		961.2.d.c.388.1		4
31.30	odd	2		961.2.d.d.531.1		4
93.47	odd	10		8649.2.a.c.1.1		2
93.77	even	10		279.2.a.a.1.1		2
124.15	even	10		496.2.a.i.1.2		2
155.77	even	20		775.2.b.d.249.4		4
155.108	even	20		775.2.b.d.249.1		4
155.139	odd	10		775.2.a.d.1.1		2
217.139	even	10		1519.2.a.a.1.2		2
248.77	odd	10		1984.2.a.r.1.2		2
248.139	even	10		1984.2.a.n.1.1		2
341.263	even	10		3751.2.a.b.1.1		2
372.263	odd	10		4464.2.a.bf.1.1		2
403.77	odd	10		5239.2.a.f.1.1		2
465.449	even	10		6975.2.a.y.1.2		2
527.356	odd	10		8959.2.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.2	✓	2	31.15	odd	10
279.2.a.a.1.1		2	93.77	even	10
496.2.a.i.1.2		2	124.15	even	10
775.2.a.d.1.1		2	155.139	odd	10
775.2.b.d.249.1		4	155.108	even	20
775.2.b.d.249.4		4	155.77	even	20
961.2.a.f.1.2		2	31.16	even	5
961.2.c.c.439.2		4	31.28	even	15
961.2.c.c.521.2		4	31.18	even	15
961.2.c.e.439.2		4	31.3	odd	30
961.2.c.e.521.2		4	31.13	odd	30
961.2.d.a.374.1		4	31.4	even	5
961.2.d.a.388.1		4	31.2	even	5
961.2.d.c.374.1		4	31.27	odd	10
961.2.d.c.388.1		4	31.29	odd	10
961.2.d.d.531.1		4	31.30	odd	2
961.2.d.d.628.1		4	31.23	odd	10
961.2.d.g.531.1		4	1.1	even	1	trivial
961.2.d.g.628.1		4	31.8	even	5	inner
961.2.g.a.235.1		8	31.12	odd	30
961.2.g.a.338.1		8	31.21	odd	30
961.2.g.a.732.1		8	31.11	odd	30
961.2.g.a.816.1		8	31.24	odd	30
961.2.g.d.235.1		8	31.19	even	15
961.2.g.d.338.1		8	31.10	even	15
961.2.g.d.732.1		8	31.20	even	15
961.2.g.d.816.1		8	31.7	even	15
961.2.g.e.448.1		8	31.9	even	15
961.2.g.e.547.1		8	31.25	even	3
961.2.g.e.844.1		8	31.5	even	3
961.2.g.e.846.1		8	31.14	even	15
961.2.g.h.448.1		8	31.22	odd	30
961.2.g.h.547.1		8	31.6	odd	6
961.2.g.h.844.1		8	31.26	odd	6
961.2.g.h.846.1		8	31.17	odd	30
1519.2.a.a.1.2		2	217.139	even	10
1984.2.a.n.1.1		2	248.139	even	10
1984.2.a.r.1.2		2	248.77	odd	10
3751.2.a.b.1.1		2	341.263	even	10
4464.2.a.bf.1.1		2	372.263	odd	10
5239.2.a.f.1.1		2	403.77	odd	10
6975.2.a.y.1.2		2	465.449	even	10
8649.2.a.c.1.1		2	93.47	odd	10
8959.2.a.b.1.2		2	527.356	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+(0.500000 + 1.53884i) q^{2} +(1.00000 - 3.07768i) q^{3} +(-0.500000 + 0.363271i) q^{4} +1.00000 q^{5} +5.23607 q^{6} +(-0.190983 + 0.138757i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-6.04508 - 4.39201i) q^{9} +(0.500000 + 1.53884i) q^{10} +(1.61803 - 1.17557i) q^{11} +(0.618034 + 1.90211i) q^{12} +(1.00000 - 3.07768i) q^{13} +(-0.309017 - 0.224514i) q^{14} +(1.00000 - 3.07768i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(0.618034 + 0.449028i) q^{17} +(3.73607 - 11.4984i) q^{18} +(-0.690983 - 2.12663i) q^{19} +(-0.500000 + 0.363271i) q^{20} +(0.236068 + 0.726543i) q^{21} +(2.61803 + 1.90211i) q^{22} +(4.61803 + 3.35520i) q^{23} +(5.85410 - 4.25325i) q^{24} -4.00000 q^{25} +5.23607 q^{26} +(-11.7082 + 8.50651i) q^{27} +(0.0450850 - 0.138757i) q^{28} +(-0.854102 - 2.62866i) q^{29} +5.23607 q^{30} -3.38197 q^{32} +(-2.00000 - 6.15537i) q^{33} +(-0.381966 + 1.17557i) q^{34} +(-0.190983 + 0.138757i) q^{35} +4.61803 q^{36} +2.00000 q^{37} +(2.92705 - 2.12663i) q^{38} +(-8.47214 - 6.15537i) q^{39} +(1.80902 + 1.31433i) q^{40} +(2.16312 + 6.65740i) q^{41} +(-1.00000 + 0.726543i) q^{42} +(-0.381966 - 1.17557i) q^{43} +(-0.381966 + 1.17557i) q^{44} +(-6.04508 - 4.39201i) q^{45} +(-2.85410 + 8.78402i) q^{46} +(0.763932 - 2.35114i) q^{47} +(12.7082 + 9.23305i) q^{48} +(-2.14590 + 6.60440i) q^{49} +(-2.00000 - 6.15537i) q^{50} +(2.00000 - 1.45309i) q^{51} +(0.618034 + 1.90211i) q^{52} +(-8.47214 - 6.15537i) q^{53} +(-18.9443 - 13.7638i) q^{54} +(1.61803 - 1.17557i) q^{55} -0.527864 q^{56} -7.23607 q^{57} +(3.61803 - 2.62866i) q^{58} +(0.690983 - 2.12663i) q^{59} +(0.618034 + 1.90211i) q^{60} -8.18034 q^{61} +1.76393 q^{63} +(1.30902 + 4.02874i) q^{64} +(1.00000 - 3.07768i) q^{65} +(8.47214 - 6.15537i) q^{66} +8.00000 q^{67} -0.472136 q^{68} +(14.9443 - 10.8576i) q^{69} +(-0.309017 - 0.224514i) q^{70} +(7.42705 + 5.39607i) q^{71} +(-5.16312 - 15.8904i) q^{72} +(6.85410 - 4.97980i) q^{73} +(1.00000 + 3.07768i) q^{74} +(-4.00000 + 12.3107i) q^{75} +(1.11803 + 0.812299i) q^{76} +(-0.145898 + 0.449028i) q^{77} +(5.23607 - 16.1150i) q^{78} +(-9.47214 - 6.88191i) q^{79} +(-1.50000 + 4.61653i) q^{80} +(7.54508 + 23.2214i) q^{81} +(-9.16312 + 6.65740i) q^{82} +(4.61803 + 14.2128i) q^{83} +(-0.381966 - 0.277515i) q^{84} +(0.618034 + 0.449028i) q^{85} +(1.61803 - 1.17557i) q^{86} -8.94427 q^{87} +4.47214 q^{88} +(9.47214 - 6.88191i) q^{89} +(3.73607 - 11.4984i) q^{90} +(0.236068 + 0.726543i) q^{91} -3.52786 q^{92} +4.00000 q^{94} +(-0.690983 - 2.12663i) q^{95} +(-3.38197 + 10.4086i) q^{96} +(12.8992 - 9.37181i) q^{97} -11.2361 q^{98} -14.9443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 4 q^{5} + 12 q^{6} - 3 q^{7} + 5 q^{8} - 13 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} - 2 q^{17} + 6 q^{18} - 5 q^{19} - 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 4 * q^5 + 12 * q^6 - 3 * q^7 + 5 * q^8 - 13 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 + q^14 + 4 * q^15 - 6 * q^16 - 2 * q^17 + 6 * q^18 - 5 * q^19 - 2 * q^20 - 8 * q^21 + 6 * q^22 + 14 * q^23 + 10 * q^24 - 16 * q^25 + 12 * q^26 - 20 * q^27 - 11 * q^28 + 10 * q^29 + 12 * q^30 - 18 * q^32 - 8 * q^33 - 6 * q^34 - 3 * q^35 + 14 * q^36 + 8 * q^37 + 5 * q^38 - 16 * q^39 + 5 * q^40 - 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 - 13 * q^45 + 2 * q^46 + 12 * q^47 + 24 * q^48 - 22 * q^49 - 8 * q^50 + 8 * q^51 - 2 * q^52 - 16 * q^53 - 40 * q^54 + 2 * q^55 - 20 * q^56 - 20 * q^57 + 10 * q^58 + 5 * q^59 - 2 * q^60 + 12 * q^61 + 16 * q^63 + 3 * q^64 + 4 * q^65 + 16 * q^66 + 32 * q^67 + 16 * q^68 + 24 * q^69 + q^70 + 23 * q^71 - 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 - 14 * q^77 + 12 * q^78 - 20 * q^79 - 6 * q^80 + 19 * q^81 - 21 * q^82 + 14 * q^83 - 6 * q^84 - 2 * q^85 + 2 * q^86 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 32 * q^92 + 16 * q^94 - 5 * q^95 - 18 * q^96 + 27 * q^97 - 36 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more