LMFDB - Embedded newform 312.2.bt.c.115.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$312 = 2^{3} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [48,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.12
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.c.19.12

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38063 + 0.306387i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.81225 + 0.846013i) q^{4} +(0.728760 - 0.728760i) q^{5} +(-0.424973 - 1.34885i) q^{6} +(0.0829661 - 0.0222307i) q^{7} +(2.24284 + 1.72328i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.22943 - 0.782862i) q^{10} +(3.93572 + 1.05457i) q^{11} +(-0.173458 - 1.99246i) q^{12} +(-3.02219 - 1.96630i) q^{13} +(0.121356 - 0.00527250i) q^{14} +(-0.995505 - 0.266745i) q^{15} +(2.56853 + 3.06638i) q^{16} +(-5.42413 - 3.13162i) q^{17} +(-0.955652 + 1.04246i) q^{18} +(7.27452 - 1.94920i) q^{19} +(1.93724 - 0.704158i) q^{20} +(-0.0607354 - 0.0607354i) q^{21} +(5.11065 + 2.66182i) q^{22} +(-0.980110 - 1.69760i) q^{23} +(0.370985 - 2.80399i) q^{24} +3.93782i q^{25} +(-3.57007 - 3.64069i) q^{26} +1.00000 q^{27} +(0.169163 + 0.0299027i) q^{28} +(-6.96312 + 4.02016i) q^{29} +(-1.29269 - 0.673285i) q^{30} +(-5.86935 + 5.86935i) q^{31} +(2.60667 + 5.02048i) q^{32} +(-1.05457 - 3.93572i) q^{33} +(-6.52920 - 5.98548i) q^{34} +(0.0442616 - 0.0766633i) q^{35} +(-1.63880 + 1.14645i) q^{36} +(-1.12904 + 4.21362i) q^{37} +(10.6406 - 0.462296i) q^{38} +(-0.191769 + 3.60045i) q^{39} +(2.89035 - 0.378633i) q^{40} +(0.550066 - 2.05287i) q^{41} +(-0.0652443 - 0.102461i) q^{42} +(-1.15816 - 0.668666i) q^{43} +(6.24034 + 5.24082i) q^{44} +(0.266745 + 0.995505i) q^{45} +(-0.833042 - 2.64404i) q^{46} +(-6.28717 - 6.28717i) q^{47} +(1.37130 - 3.75760i) q^{48} +(-6.05579 + 3.49631i) q^{49} +(-1.20650 + 5.43665i) q^{50} +6.26324i q^{51} +(-3.81347 - 6.12025i) q^{52} -11.6396i q^{53} +(1.38063 + 0.306387i) q^{54} +(3.63673 - 2.09967i) q^{55} +(0.224389 + 0.0931139i) q^{56} +(-5.32532 - 5.32532i) q^{57} +(-10.8452 + 3.41692i) q^{58} +(0.424780 + 1.58530i) q^{59} +(-1.57844 - 1.32562i) q^{60} +(8.29736 + 4.79048i) q^{61} +(-9.90168 + 6.30508i) q^{62} +(-0.0222307 + 0.0829661i) q^{63} +(2.06062 + 7.73006i) q^{64} +(-3.63542 + 0.769494i) q^{65} +(-0.250115 - 5.75686i) q^{66} +(-0.699814 + 2.61174i) q^{67} +(-7.18050 - 10.2642i) q^{68} +(-0.980110 + 1.69760i) q^{69} +(0.0845973 - 0.0922821i) q^{70} +(0.590920 + 2.20535i) q^{71} +(-2.61382 + 1.08071i) q^{72} +(-4.92594 + 4.92594i) q^{73} +(-2.84977 + 5.47150i) q^{74} +(3.41025 - 1.96891i) q^{75} +(14.8323 + 2.62189i) q^{76} +0.349975 q^{77} +(-1.36789 + 4.91211i) q^{78} -4.54871i q^{79} +(4.10650 + 0.362816i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.38841 - 2.66572i) q^{82} +(-1.80840 - 1.80840i) q^{83} +(-0.0586851 - 0.161451i) q^{84} +(-6.23509 + 1.67069i) q^{85} +(-1.39412 - 1.27802i) q^{86} +(6.96312 + 4.02016i) q^{87} +(7.00985 + 9.14757i) q^{88} +(-6.18251 - 1.65660i) q^{89} +(0.0632644 + 1.45615i) q^{90} +(-0.294452 - 0.0959509i) q^{91} +(-0.340017 - 3.90567i) q^{92} +(8.01769 + 2.14833i) q^{93} +(-6.75392 - 10.6065i) q^{94} +(3.88088 - 6.72189i) q^{95} +(3.04453 - 4.76769i) q^{96} +(8.21652 - 2.20161i) q^{97} +(-9.43200 + 2.97168i) q^{98} +(-2.88115 + 2.88115i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100})$ 48 * q + 2 * q^2 - 24 * q^3 + 2 * q^6 - 4 * q^8 - 24 * q^9 - 6 * q^10 + 20 * q^11 - 28 * q^14 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 20 * q^19 + 4 * q^20 + 14 * q^22 + 2 * q^24 - 12 * q^26 + 48 * q^27 - 2 * q^28 + 6 * q^30 - 18 * q^32 - 28 * q^33 + 12 * q^35 + 52 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 + 12 * q^44 - 14 * q^46 + 4 * q^48 + 24 * q^49 - 32 * q^50 + 24 * q^52 + 2 * q^54 - 54 * q^56 - 40 * q^57 - 22 * q^58 + 96 * q^59 - 56 * q^60 - 108 * q^62 - 52 * q^65 - 28 * q^66 - 12 * q^67 - 6 * q^68 - 52 * q^70 + 2 * q^72 - 48 * q^73 + 114 * q^76 + 36 * q^78 - 16 * q^80 - 24 * q^81 - 60 * q^82 + 48 * q^83 + 10 * q^84 + 24 * q^86 + 102 * q^88 + 80 * q^89 - 152 * q^91 - 100 * q^92 - 10 * q^94 - 24 * q^96 - 64 * q^97 - 6 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$ .

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.38063	+	0.306387i	0.976250	+	0.216649i
$2$	1.38063	+	0.306387i	0.976250	+	0.216649i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.81225	+	0.846013i	0.906127	+	0.423006i
$5$	0.728760	−	0.728760i	0.325912	−	0.325912i	−0.525118	−	0.851029i	$-0.675979\pi$
$5$	0.728760	−	0.728760i	0.325912	−	0.325912i	0.851029	+	0.525118i	$0.175979\pi$
$6$	−0.424973	−	1.34885i	−0.173495	−	0.550666i
$7$	0.0829661	−	0.0222307i	0.0313583	−	0.00840242i	−0.243106	−	0.970000i	$-0.578166\pi$
$7$	0.0829661	−	0.0222307i	0.0313583	−	0.00840242i	0.274464	+	0.961597i	$0.411500\pi$
$8$	2.24284	+	1.72328i	0.792962	+	0.609271i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.22943	−	0.782862i	0.388779	−	0.247563i
$11$	3.93572	+	1.05457i	1.18666	+	0.317966i	0.797567	−	0.603231i	$-0.206120\pi$
$11$	3.93572	+	1.05457i	1.18666	+	0.317966i	0.389097	+	0.921197i	$0.372787\pi$
$12$	−0.173458	−	1.99246i	−0.0500731	−	0.575175i
$13$	−3.02219	−	1.96630i	−0.838206	−	0.545354i
$13$	−3.02219	−	1.96630i	−0.838206	−	0.545354i
$14$	0.121356	−	0.00527250i	0.0324339	−	0.00140914i
$15$	−0.995505	−	0.266745i	−0.257038	−	0.0688732i
$16$	2.56853	+	3.06638i	0.642131	+	0.766595i
$17$	−5.42413	−	3.13162i	−1.31554	−	0.759530i	−0.332536	−	0.943091i	$-0.607904\pi$
$17$	−5.42413	−	3.13162i	−1.31554	−	0.759530i	−0.983008	+	0.183561i	$0.941238\pi$
$18$	−0.955652	+	1.04246i	−0.225249	+	0.245711i
$19$	7.27452	−	1.94920i	1.66889	−	0.447178i	0.704079	−	0.710122i	$-0.251360\pi$
$19$	7.27452	−	1.94920i	1.66889	−	0.447178i	0.964811	+	0.262944i	$0.0846935\pi$
$20$	1.93724	−	0.704158i	0.433180	−	0.157455i
$21$	−0.0607354	−	0.0607354i	−0.0132536	−	0.0132536i
$22$	5.11065	+	2.66182i	1.08959	+	0.567503i
$23$	−0.980110	−	1.69760i	−0.204367	−	0.353974i	0.745564	−	0.666434i	$-0.232180\pi$
$23$	−0.980110	−	1.69760i	−0.204367	−	0.353974i	−0.949931	+	0.312460i	$0.898847\pi$
$24$	0.370985	−	2.80399i	0.0757270	−	0.572362i
$25$			3.93782i			0.787563i
$26$	−3.57007	−	3.64069i	−0.700148	−	0.713998i
$27$	1.00000			0.192450
$28$	0.169163	+	0.0299027i	0.0319688	+	0.00565108i
$29$	−6.96312	+	4.02016i	−1.29302	+	0.746525i	−0.979188	−	0.202954i	$-0.934946\pi$
$29$	−6.96312	+	4.02016i	−1.29302	+	0.746525i	−0.313831	+	0.949479i	$0.601612\pi$
$30$	−1.29269	−	0.673285i	−0.236012	−	0.122924i
$31$	−5.86935	+	5.86935i	−1.05417	+	1.05417i	−0.0557208	+	0.998446i	$0.517746\pi$
$31$	−5.86935	+	5.86935i	−1.05417	+	1.05417i	−0.998446	+	0.0557208i	$0.982254\pi$
$32$	2.60667	+	5.02048i	0.460799	+	0.887505i
$33$	−1.05457	−	3.93572i	−0.183578	−	0.685121i
$34$	−6.52920	−	5.98548i	−1.11975	−	1.02650i
$35$	0.0442616	−	0.0766633i	0.00748157	−	0.0129585i
$36$	−1.63880	+	1.14645i	−0.273133	+	0.191075i
$37$	−1.12904	+	4.21362i	−0.185612	+	0.692714i	0.808886	+	0.587965i	$0.200071\pi$
$37$	−1.12904	+	4.21362i	−0.185612	+	0.692714i	−0.994499	+	0.104749i	$0.966596\pi$
$38$	10.6406	−	0.462296i	1.72613	−	0.0749944i
$39$	−0.191769	+	3.60045i	−0.0307076	+	0.576533i
$40$	2.89035	−	0.378633i	0.457004	−	0.0598671i
$41$	0.550066	−	2.05287i	0.0859058	−	0.320605i	−0.909578	−	0.415532i	$-0.863595\pi$
$41$	0.550066	−	2.05287i	0.0859058	−	0.320605i	0.995484	+	0.0949275i	$0.0302619\pi$
$42$	−0.0652443	−	0.102461i	−0.0100674	−	0.0158101i
$43$	−1.15816	−	0.668666i	−0.176618	−	0.101971i	0.409085	−	0.912496i	$-0.365848\pi$
$43$	−1.15816	−	0.668666i	−0.176618	−	0.101971i	−0.585703	+	0.810526i	$0.699181\pi$
$44$	6.24034	+	5.24082i	0.940766	+	0.790083i
$45$	0.266745	+	0.995505i	0.0397640	+	0.148401i
$46$	−0.833042	−	2.64404i	−0.122825	−	0.389843i
$47$	−6.28717	−	6.28717i	−0.917078	−	0.917078i	0.0797379	−	0.996816i	$-0.474592\pi$
$47$	−6.28717	−	6.28717i	−0.917078	−	0.917078i	−0.996816	+	0.0797379i	$0.974592\pi$
$48$	1.37130	−	3.75760i	0.197930	−	0.542362i
$49$	−6.05579	+	3.49631i	−0.865113	+	0.499473i
$50$	−1.20650	+	5.43665i	−0.170625	+	0.768858i
$51$			6.26324i			0.877029i
$52$	−3.81347	−	6.12025i	−0.528833	−	0.848726i
$53$		−	11.6396i		−	1.59882i	−0.600785	−	0.799411i	$-0.705145\pi$
$53$		−	11.6396i		−	1.59882i	0.600785	−	0.799411i	$-0.294855\pi$
$54$	1.38063	+	0.306387i	0.187879	+	0.0416940i
$55$	3.63673	−	2.09967i	0.490376	−	0.283119i
$56$	0.224389	+	0.0931139i	0.0299853	+	0.0124429i
$57$	−5.32532	−	5.32532i	−0.705356	−	0.705356i
$58$	−10.8452	+	3.41692i	−1.42404	+	0.448664i
$59$	0.424780	+	1.58530i	0.0553016	+	0.206388i	0.988048	−	0.154144i	$-0.0492618\pi$
$59$	0.424780	+	1.58530i	0.0553016	+	0.206388i	−0.932747	+	0.360532i	$0.882595\pi$
$60$	−1.57844	−	1.32562i	−0.203776	−	0.171137i
$61$	8.29736	+	4.79048i	1.06237	+	0.613358i	0.926086	−	0.377312i	$-0.123151\pi$
$61$	8.29736	+	4.79048i	1.06237	+	0.613358i	0.136282	+	0.990670i	$0.456485\pi$
$62$	−9.90168	+	6.30508i	−1.25751	+	0.800746i
$63$	−0.0222307	+	0.0829661i	−0.00280081	+	0.0104528i
$64$	2.06062	+	7.73006i	0.257578	+	0.966257i
$65$	−3.63542	+	0.769494i	−0.450918	+	0.0954439i
$66$	−0.250115	−	5.75686i	−0.0307870	−	0.708621i
$67$	−0.699814	+	2.61174i	−0.0854959	+	0.319075i	−0.995408	−	0.0957269i	$-0.969482\pi$
$67$	−0.699814	+	2.61174i	−0.0854959	+	0.319075i	0.909912	+	0.414802i	$0.136149\pi$
$68$	−7.18050	−	10.2642i	−0.870764	−	1.24471i
$69$	−0.980110	+	1.69760i	−0.117991	+	0.204367i
$70$	0.0845973	−	0.0922821i	0.0101113	−	0.0110298i
$71$	0.590920	+	2.20535i	0.0701294	+	0.261726i	0.992085	−	0.125570i	$-0.0400758\pi$
$71$	0.590920	+	2.20535i	0.0701294	+	0.261726i	−0.921955	+	0.387296i	$0.873409\pi$
$72$	−2.61382	+	1.08071i	−0.308042	+	0.127363i
$73$	−4.92594	+	4.92594i	−0.576538	+	0.576538i	−0.933948	−	0.357410i	$-0.883660\pi$
$73$	−4.92594	+	4.92594i	−0.576538	+	0.576538i	0.357410	+	0.933948i	$0.383660\pi$
$74$	−2.84977	+	5.47150i	−0.331279	+	0.636049i
$75$	3.41025	−	1.96891i	0.393782	−	0.227350i
$76$	14.8323	+	2.62189i	1.70138	+	0.300751i
$77$	0.349975			0.0398834
$78$	−1.36789	+	4.91211i	−0.154883	+	0.556187i
$79$		−	4.54871i		−	0.511770i	−0.966707	−	0.255885i	$-0.917633\pi$
$79$		−	4.54871i		−	0.511770i	0.966707	−	0.255885i	$-0.0823668\pi$
$80$	4.10650	+	0.362816i	0.459120	+	0.0405640i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.38841	−	2.66572i	0.153324	−	0.294379i
$83$	−1.80840	−	1.80840i	−0.198497	−	0.198497i	0.600858	−	0.799356i	$-0.294826\pi$
$83$	−1.80840	−	1.80840i	−0.198497	−	0.198497i	−0.799356	+	0.600858i	$0.794826\pi$
$84$	−0.0586851	−	0.161451i	−0.00640306	−	0.0176157i
$85$	−6.23509	+	1.67069i	−0.676291	+	0.181212i
$86$	−1.39412	−	1.27802i	−0.150332	−	0.137813i
$87$	6.96312	+	4.02016i	0.746525	+	0.431006i
$88$	7.00985	+	9.14757i	0.747252	+	0.975134i
$89$	−6.18251	−	1.65660i	−0.655345	−	0.175599i	−0.0842007	−	0.996449i	$-0.526834\pi$
$89$	−6.18251	−	1.65660i	−0.655345	−	0.175599i	−0.571144	+	0.820850i	$0.693500\pi$
$90$	0.0632644	+	1.45615i	0.00666866	+	0.153491i
$91$	−0.294452	−	0.0959509i	−0.0308670	−	0.0100584i
$92$	−0.340017	−	3.90567i	−0.0354492	−	0.407194i
$93$	8.01769	+	2.14833i	0.831395	+	0.222772i
$94$	−6.75392	−	10.6065i	−0.696613	−	1.09398i
$95$	3.88088	−	6.72189i	0.398170	−	0.689651i
$96$	3.04453	−	4.76769i	0.310731	−	0.486600i
$97$	8.21652	−	2.20161i	0.834261	−	0.223540i	0.183689	−	0.982984i	$-0.441196\pi$
$97$	8.21652	−	2.20161i	0.834261	−	0.223540i	0.650572	+	0.759445i	$0.274529\pi$
$98$	−9.43200	+	2.97168i	−0.952776	+	0.300185i
$99$	−2.88115	+	2.88115i	−0.289566	+	0.289566i
$100$	−3.33144	+	7.13632i	−0.333144	+	0.713632i
$101$	−3.16660	−	5.48472i	−0.315089	−	0.545750i	0.664367	−	0.747406i	$-0.268701\pi$
$101$	−3.16660	−	5.48472i	−0.315089	−	0.545750i	−0.979456	+	0.201656i	$0.935368\pi$
$102$	−1.91898	+	8.64719i	−0.190007	+	0.856200i
$103$	7.06035			0.695677			0.347839	−	0.937554i	$-0.386916\pi$
$103$	7.06035			0.695677			0.347839	+	0.937554i	$0.386916\pi$
$104$	−3.38980	−	9.61817i	−0.332398	−	0.943139i
$105$	−0.0885232			−0.00863898
$106$	3.56622	−	16.0699i	0.346382	−	1.56085i
$107$	4.60675	+	7.97913i	0.445352	+	0.771372i	0.998077	−	0.0619920i	$-0.0197453\pi$
$107$	4.60675	+	7.97913i	0.445352	+	0.771372i	−0.552725	+	0.833364i	$0.686412\pi$
$108$	1.81225	+	0.846013i	0.174384	+	0.0814076i
$109$	11.5447	−	11.5447i	1.10578	−	1.10578i	0.112084	−	0.993699i	$-0.464247\pi$
$109$	11.5447	−	11.5447i	1.10578	−	1.10578i	0.993699	−	0.112084i	$-0.0357526\pi$
$110$	5.66427	−	1.78460i	0.540067	−	0.170155i
$111$	4.21362	−	1.12904i	0.399939	−	0.107163i
$112$	0.281268	+	0.197305i	0.0265774	+	0.0186436i
$113$	4.97539	−	8.61764i	0.468046	−	0.810679i	−0.531287	−	0.847192i	$-0.678292\pi$
$113$	4.97539	−	8.61764i	0.468046	−	0.810679i	0.999333	+	0.0365126i	$0.0116249\pi$
$114$	−5.72066	−	8.98388i	−0.535789	−	0.841418i
$115$	−1.95141	−	0.522879i	−0.181970	−	0.0487587i
$116$	−16.0200	+	1.39466i	−1.48742	+	0.129491i
$117$	3.21396	−	1.63415i	0.297131	−	0.151077i
$118$	0.100746	+	2.31885i	0.00927441	+	0.213468i
$119$	−0.519637	−	0.139236i	−0.0476350	−	0.0127638i
$120$	−1.77308	−	2.31380i	−0.161859	−	0.211220i
$121$	4.85148	+	2.80100i	0.441044	+	0.254637i
$122$	9.98780	+	9.15607i	0.904253	+	0.828952i
$123$	−2.05287	+	0.550066i	−0.185101	+	0.0495977i
$124$	−15.6023	+	5.67121i	−1.40113	+	0.509290i
$125$	6.51353	+	6.51353i	0.582588	+	0.582588i
$126$	−0.0561121	+	0.107734i	−0.00499886	+	0.00959770i
$127$	7.95743	+	13.7827i	0.706108	+	1.22302i	0.966290	+	0.257456i	$0.0828841\pi$
$127$	7.95743	+	13.7827i	0.706108	+	1.22302i	−0.260182	+	0.965560i	$0.583783\pi$
$128$	0.476557	+	11.3037i	0.0421221	+	0.999112i
$129$			1.33733i			0.117745i
$130$	−5.25491	−	0.0514639i	−0.460886	−	0.00451368i
$131$	11.3789			0.994179			0.497090	−	0.867699i	$-0.334402\pi$
$131$	11.3789			0.994179			0.497090	+	0.867699i	$0.334402\pi$
$132$	1.41851	−	8.02470i	0.123466	−	0.698461i
$133$	0.560207	−	0.323436i	0.0485761	−	0.0280454i
$134$	−1.76639	+	3.39142i	−0.152593	+	0.292974i
$135$	0.728760	−	0.728760i	0.0627217	−	0.0627217i
$136$	−6.76877	−	16.3710i	−0.580417	−	1.40380i
$137$	−1.72703	−	6.44535i	−0.147550	−	0.550664i	−0.999629	−	0.0272501i	$-0.991325\pi$
$137$	−1.72703	−	6.44535i	−0.147550	−	0.550664i	0.852079	−	0.523414i	$-0.175342\pi$
$138$	−1.87329	+	2.04346i	−0.159465	+	0.173951i
$139$	5.99886	−	10.3903i	0.508817	−	0.881297i	−0.491131	−	0.871086i	$-0.663416\pi$
$139$	5.99886	−	10.3903i	0.508817	−	0.881297i	0.999948	−	0.0102111i	$-0.00325034\pi$
$140$	0.145071	−	0.101487i	0.0122608	−	0.00857726i
$141$	−2.30126	+	8.58843i	−0.193801	+	0.723277i
$142$	0.140150	+	3.22581i	0.0117611	+	0.270704i
$143$	−9.82090	−	10.9259i	−0.821265	−	0.913672i
$144$	−3.93982	+	0.691219i	−0.328319	+	0.0576016i
$145$	−2.14471	+	8.00418i	−0.178109	+	0.664711i
$146$	−8.31013	+	5.29163i	−0.687751	+	0.437939i
$147$	6.05579	+	3.49631i	0.499473	+	0.288371i
$148$	−5.61087	+	6.68096i	−0.461211	+	0.549172i
$149$	−4.44315	−	16.5821i	−0.363997	−	1.35846i	−0.868775	−	0.495207i	$-0.835092\pi$
$149$	−4.44315	−	16.5821i	−0.363997	−	1.35846i	0.504778	−	0.863249i	$-0.331574\pi$
$150$	5.31153	−	1.67347i	0.433684	−	0.136638i
$151$	4.24129	+	4.24129i	0.345151	+	0.345151i	0.858300	−	0.513149i	$-0.171521\pi$
$151$	4.24129	+	4.24129i	0.345151	+	0.345151i	−0.513149	+	0.858300i	$0.671521\pi$
$152$	19.6746	+	8.16429i	1.59582	+	0.662211i
$153$	5.42413	−	3.13162i	0.438515	−	0.253177i
$154$	0.483185	+	0.107228i	0.0389361	+	0.00864068i
$155$			8.55471i			0.687131i
$156$	−3.39356	+	6.36269i	−0.271702	+	0.509423i
$157$			20.1215i			1.60587i	0.596068	+	0.802934i	$0.296729\pi$
$157$			20.1215i			1.60587i	−0.596068	+	0.802934i	$0.703271\pi$
$158$	1.39367	−	6.28006i	0.110874	−	0.499615i
$159$	−10.0802	+	5.81980i	−0.799411	+	0.461540i
$160$	5.55837	+	1.75909i	0.439428	+	0.139068i
$161$	−0.119055	−	0.119055i	−0.00938284	−	0.00938284i
$162$	−0.424973	−	1.34885i	−0.0333891	−	0.105976i
$163$	−4.43341	−	16.5457i	−0.347252	−	1.29596i	−0.889960	−	0.456039i	$-0.849268\pi$
$163$	−4.43341	−	16.5457i	−0.347252	−	1.29596i	0.542708	−	0.839921i	$-0.317399\pi$
$164$	2.73361	−	3.25496i	0.213459	−	0.254170i
$165$	−3.63673	−	2.09967i	−0.283119	−	0.163459i
$166$	−1.94265	−	3.05079i	−0.150779	−	0.236787i
$167$	−2.73628	+	10.2119i	−0.211740	+	0.790223i	0.775549	+	0.631287i	$0.217473\pi$
$167$	−2.73628	+	10.2119i	−0.211740	+	0.790223i	−0.987289	+	0.158936i	$0.949194\pi$
$168$	−0.0315555	−	0.240884i	−0.00243456	−	0.0185846i
$169$	5.26732	+	11.8851i	0.405179	+	0.914238i
$170$	−9.12020	+	0.396240i	−0.699488	+	0.0303902i
$171$	−1.94920	+	7.27452i	−0.149059	+	0.556297i
$172$	−1.53319	−	2.19161i	−0.116904	−	0.167109i
$173$	1.59423	−	2.76129i	0.121207	−	0.209937i	−0.799037	−	0.601282i	$-0.794657\pi$
$173$	1.59423	−	2.76129i	0.121207	−	0.209937i	0.920244	+	0.391345i	$0.127990\pi$
$174$	8.38173	+	7.68375i	0.635418	+	0.582503i
$175$	0.0875405	+	0.326705i	0.00661744	+	0.0246966i
$176$	6.87527	+	14.7771i	0.518243	+	1.11387i
$177$	1.16052	−	1.16052i	0.0872300	−	0.0872300i
$178$	−8.02817	−	4.18139i	−0.601737	−	0.313408i
$179$	−13.8112	+	7.97389i	−1.03230	+	0.595996i	−0.917641	−	0.397409i	$-0.869909\pi$
$179$	−13.8112	+	7.97389i	−1.03230	+	0.595996i	−0.114654	+	0.993405i	$0.536576\pi$
$180$	−0.358801	+	2.02978i	−0.0267434	+	0.151291i
$181$	0.979166			0.0727808			0.0363904	−	0.999338i	$-0.488414\pi$
$181$	0.979166			0.0727808			0.0363904	+	0.999338i	$0.488414\pi$
$182$	−0.377130	−	0.222689i	−0.0279547	−	0.0165068i
$183$		−	9.58097i		−	0.708245i
$184$	0.727212	−	5.49644i	0.0536108	−	0.405203i
$185$	2.24792	+	3.89351i	0.165270	+	0.286257i
$186$	10.4112	+	5.42256i	0.763386	+	0.397602i
$187$	−18.0453	−	18.0453i	−1.31960	−	1.31960i
$188$	−6.07492	−	16.7130i	−0.443059	−	1.21892i
$189$	0.0829661	−	0.0222307i	0.00603490	−	0.00161705i
$190$	7.41755	−	8.09135i	0.538125	−	0.587008i
$191$	18.7111	+	10.8029i	1.35389	+	0.781669i	0.988792	−	0.149299i	$-0.0477018\pi$
$191$	18.7111	+	10.8029i	1.35389	+	0.781669i	0.365099	+	0.930969i	$0.381035\pi$
$192$	5.66412	−	5.64958i	0.408772	−	0.407724i
$193$	2.99346	+	0.802096i	0.215474	+	0.0577361i	0.364941	−	0.931031i	$-0.381089\pi$
$193$	2.99346	+	0.802096i	0.215474	+	0.0577361i	−0.149467	+	0.988767i	$0.547756\pi$
$194$	12.0185	−	0.522160i	0.862876	−	0.0374889i
$195$	2.48411	+	2.76362i	0.177891	+	0.197907i
$196$	−13.9325	+	1.21293i	−0.995182	+	0.0866378i
$197$	7.77756	+	2.08399i	0.554128	+	0.148478i	0.525007	−	0.851098i	$-0.324063\pi$
$197$	7.77756	+	2.08399i	0.554128	+	0.148478i	0.0291209	+	0.999576i	$0.490729\pi$
$198$	−4.86053	+	3.09504i	−0.345423	+	0.219955i
$199$	9.76600	−	16.9152i	0.692293	−	1.19909i	−0.278791	−	0.960352i	$-0.589934\pi$
$199$	9.76600	−	16.9152i	0.692293	−	1.19909i	0.971085	−	0.238736i	$-0.0767330\pi$
$200$	−6.78595	+	8.83188i	−0.479839	+	0.624508i
$201$	2.61174	−	0.699814i	0.184218	−	0.0493611i
$202$	−2.69145	−	8.54255i	−0.189369	−	0.601052i
$203$	−0.488332	+	0.488332i	−0.0342742	+	0.0342742i
$204$	−5.29878	+	11.3506i	−0.370989	+	0.794700i
$205$	−1.09519	−	1.89692i	−0.0764911	−	0.132487i
$206$	9.74770	+	2.16320i	0.679155	+	0.150718i
$207$	1.96022			0.136245
$208$	−1.73316	−	14.3177i	−0.120173	−	0.992753i
$209$	30.6861			2.12260
$210$	−0.122217	−	0.0271224i	−0.00843380	−	0.00187162i
$211$	−8.41848	−	14.5812i	−0.579552	−	1.00381i	−0.995531	−	0.0944389i	$-0.969894\pi$
$211$	−8.41848	−	14.5812i	−0.579552	−	1.00381i	0.415979	−	0.909374i	$-0.363439\pi$
$212$	9.84724	−	21.0939i	0.676311	−	1.44873i
$213$	1.61442	−	1.61442i	0.110619	−	0.110619i
$214$	3.91550	+	12.4276i	0.267658	+	0.849536i
$215$	−1.33132	+	0.356726i	−0.0907953	+	0.0243285i
$216$	2.24284	+	1.72328i	0.152606	+	0.117254i
$217$	−0.356478	+	0.617438i	−0.0241993	+	0.0419144i
$218$	19.4761	−	12.4018i	1.31909	−	0.839954i
$219$	6.72896	+	1.80302i	0.454701	+	0.121837i
$220$	8.36701	−	0.728409i	0.564104	−	0.0491093i
$221$	10.2351	+	20.1298i	0.688484	+	1.35408i
$222$	6.16335	−	0.267776i	0.413657	−	0.0179719i
$223$	−5.19416	−	1.39177i	−0.347826	−	0.0931998i	0.0806761	−	0.996740i	$-0.474292\pi$
$223$	−5.19416	−	1.39177i	−0.347826	−	0.0931998i	−0.428503	+	0.903541i	$0.640959\pi$
$224$	0.327874	+	0.358582i	0.0219070	+	0.0239588i
$225$	−3.41025	−	1.96891i	−0.227350	−	0.131261i
$226$	9.50949	−	10.3733i	0.632562	−	0.690024i
$227$	22.1030	−	5.92248i	1.46703	−	0.393089i	0.565117	−	0.825011i	$-0.308831\pi$
$227$	22.1030	−	5.92248i	1.46703	−	0.393089i	0.901911	+	0.431922i	$0.142164\pi$
$228$	−5.14554	−	14.1561i	−0.340772	−	0.937512i
$229$	−10.6918	−	10.6918i	−0.706533	−	0.706533i	0.259272	−	0.965804i	$-0.416517\pi$
$229$	−10.6918	−	10.6918i	−0.706533	−	0.706533i	−0.965804	+	0.259272i	$0.916517\pi$
$230$	−2.53396	−	1.31979i	−0.167085	−	0.0870242i
$231$	−0.174988	−	0.303087i	−0.0115133	−	0.0199417i
$232$	−22.5450	−	2.98284i	−1.48015	−	0.195833i
$233$			4.54765i			0.297926i	0.988843	+	0.148963i	$0.0475936\pi$
$233$			4.54765i			0.297926i	−0.988843	+	0.148963i	$0.952406\pi$
$234$	4.93796	−	1.27143i	0.322805	−	0.0831158i
$235$	−9.16368			−0.597773
$236$	−0.571375	+	3.23233i	−0.0371933	+	0.210407i
$237$	−3.93930	+	2.27435i	−0.255885	+	0.147735i
$238$	−0.674764	−	0.351443i	−0.0437384	−	0.0227807i
$239$	−5.72060	+	5.72060i	−0.370035	+	0.370035i	−0.867490	−	0.497455i	$-0.834268\pi$
$239$	−5.72060	+	5.72060i	−0.370035	+	0.370035i	0.497455	+	0.867490i	$0.334268\pi$
$240$	−1.73904	−	3.73774i	−0.112255	−	0.241270i
$241$	−1.14943	−	4.28973i	−0.0740412	−	0.276326i	0.918973	−	0.394321i	$-0.129020\pi$
$241$	−1.14943	−	4.28973i	−0.0740412	−	0.276326i	−0.993014	+	0.117995i	$0.962353\pi$
$242$	5.83988	+	5.35357i	0.375402	+	0.344140i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	10.9841	+	15.7012i	0.703186	+	1.00517i
$245$	−1.86525	+	6.96119i	−0.119166	+	0.444734i
$246$	−3.00278	+	0.130460i	−0.191450	+	0.00831784i
$247$	−25.8177	−	8.41303i	−1.64274	−	0.535308i
$248$	−23.2785	+	3.04947i	−1.47819	+	0.193641i
$249$	−0.661919	+	2.47031i	−0.0419474	+	0.156550i
$250$	6.99708	+	10.9884i	0.442534	+	0.694968i
$251$	−18.5859	−	10.7306i	−1.17313	−	0.677307i	−0.218715	−	0.975789i	$-0.570186\pi$
$251$	−18.5859	−	10.7306i	−1.17313	−	0.677307i	−0.954415	+	0.298482i	$0.903520\pi$
$252$	−0.110478	+	0.131548i	−0.00695946	+	0.00828676i
$253$	−2.06720	−	7.71488i	−0.129963	−	0.485030i
$254$	6.76340	+	21.4668i	0.424373	+	1.34695i
$255$	4.56440	+	4.56440i	0.285834	+	0.285834i
$256$	−2.80535	+	15.7521i	−0.175335	+	0.984509i
$257$	−19.8687	+	11.4712i	−1.23937	+	0.715553i	−0.968966	−	0.247193i	$-0.920492\pi$
$257$	−19.8687	+	11.4712i	−1.23937	+	0.715553i	−0.270408	+	0.962746i	$0.587159\pi$
$258$	−0.409742	+	1.84635i	−0.0255094	+	0.114949i
$259$			0.374687i			0.0232819i
$260$	−7.23930	−	1.68109i	−0.448962	−	0.104257i
$261$		−	8.04032i		−	0.497683i
$262$	15.7100	+	3.48635i	0.970567	+	0.215388i
$263$	8.11601	−	4.68578i	0.500455	−	0.288938i	−0.228446	−	0.973556i	$-0.573365\pi$
$263$	8.11601	−	4.68578i	0.500455	−	0.288938i	0.728901	+	0.684619i	$0.240031\pi$
$264$	4.41711	−	10.6445i	0.271854	−	0.655123i
$265$	−8.48248	−	8.48248i	−0.521074	−	0.521074i
$266$	0.872533	−	0.274903i	0.0534984	−	0.0168554i
$267$	1.65660	+	6.18251i	0.101382	+	0.378364i
$268$	−3.47781	+	4.14109i	−0.212441	+	0.252957i
$269$	−0.237969	−	0.137391i	−0.0145092	−	0.00837689i	0.492728	−	0.870183i	$-0.336000\pi$
$269$	−0.237969	−	0.137391i	−0.0145092	−	0.00837689i	−0.507237	+	0.861807i	$0.669333\pi$
$270$	1.22943	−	0.782862i	0.0748206	−	0.0476435i
$271$	1.04029	−	3.88242i	0.0631933	−	0.235840i	−0.927104	−	0.374803i	$-0.877710\pi$
$271$	1.04029	−	3.88242i	0.0631933	−	0.235840i	0.990298	+	0.138963i	$0.0443769\pi$
$272$	−4.32927	−	24.6761i	−0.262501	−	1.49621i
$273$	0.0641302	+	0.302978i	0.00388133	+	0.0183371i
$274$	−0.409603	−	9.42776i	−0.0247450	−	0.569552i
$275$	−4.15271	+	15.4981i	−0.250418	+	0.934573i
$276$	−3.21240	+	2.24730i	−0.193364	+	0.135271i
$277$	0.223922	−	0.387844i	0.0134542	−	0.0233033i	−0.859220	−	0.511606i	$-0.829051\pi$
$277$	0.223922	−	0.387844i	0.0134542	−	0.0233033i	0.872674	+	0.488303i	$0.162384\pi$
$278$	11.4657	−	12.5072i	0.687664	−	0.750131i
$279$	−2.14833	−	8.01769i	−0.128617	−	0.480006i
$280$	0.231384	−	0.0956682i	0.0138278	−	0.00571727i
$281$	−2.22917	+	2.22917i	−0.132981	+	0.132981i	−0.770464	−	0.637483i	$-0.779976\pi$
$281$	−2.22917	+	2.22917i	−0.132981	+	0.132981i	0.637483	+	0.770464i	$0.279976\pi$
$282$	−5.80857	+	11.1523i	−0.345895	+	0.664112i
$283$	6.22131	−	3.59188i	0.369819	−	0.213515i	−0.303561	−	0.952812i	$-0.598175\pi$
$283$	6.22131	−	3.59188i	0.369819	−	0.213515i	0.673379	+	0.739297i	$0.264842\pi$
$284$	−0.794852	+	4.49657i	−0.0471658	+	0.266822i
$285$	−7.76177			−0.459767
$286$	−10.2114	−	18.0936i	−0.603814	−	1.06990i
$287$		−	0.182547i		−	0.0107754i
$288$	−5.65120	−	0.252798i	−0.333000	−	0.0148963i
$289$	11.1141	+	19.2502i	0.653771	+	1.13236i
$290$	−5.41343	+	10.3937i	−0.317887	+	0.610337i
$291$	−6.01491	−	6.01491i	−0.352600	−	0.352600i
$292$	−13.0945	+	4.75965i	−0.766296	+	0.278537i
$293$	−12.6276	+	3.38355i	−0.737712	+	0.197669i	−0.608061	−	0.793890i	$-0.708052\pi$
$293$	−12.6276	+	3.38355i	−0.737712	+	0.197669i	−0.129651	+	0.991560i	$0.541386\pi$
$294$	7.28955	+	6.68251i	0.425135	+	0.389732i
$295$	1.46487	+	0.845741i	0.0852878	+	0.0492410i
$296$	−9.79347	+	7.50481i	−0.569234	+	0.436208i
$297$	3.93572	+	1.05457i	0.228374	+	0.0611925i
$298$	−1.05379	−	24.2549i	−0.0610445	−	1.40505i
$299$	−0.375910	+	7.05767i	−0.0217394	+	0.408156i
$300$	7.84596	−	0.683047i	0.452987	−	0.0394357i
$301$	−0.110953	−	0.0297298i	−0.00639524	−	0.00171360i
$302$	4.55615	+	7.15510i	0.262177	+	0.411730i
$303$	−3.16660	+	5.48472i	−0.181917	+	0.315089i
$304$	24.6618	+	17.2999i	1.41445	+	0.992215i
$305$	9.53790	−	2.55567i	0.546139	−	0.146337i
$306$	8.44818	−	2.66171i	0.482950	−	0.152160i
$307$	−16.7079	+	16.7079i	−0.953568	+	0.953568i	−0.998969	−	0.0454012i	$-0.985543\pi$
$307$	−16.7079	+	16.7079i	−0.953568	+	0.953568i	0.0454012	+	0.998969i	$0.485543\pi$
$308$	0.634244	+	0.296083i	0.0361394	+	0.0168709i
$309$	−3.53018	−	6.11445i	−0.200825	−	0.347839i
$310$	−2.62105	+	11.8108i	−0.148866	+	0.670811i
$311$	−10.0436			−0.569522			−0.284761	−	0.958599i	$-0.591914\pi$
$311$	−10.0436			−0.569522			−0.284761	+	0.958599i	$0.591914\pi$
$312$	−6.63468	+	7.74474i	−0.375615	+	0.438460i
$313$	2.62007			0.148095			0.0740476	−	0.997255i	$-0.476408\pi$
$313$	2.62007			0.148095			0.0740476	+	0.997255i	$0.476408\pi$
$314$	−6.16496	+	27.7802i	−0.347909	+	1.56773i
$315$	0.0442616	+	0.0766633i	0.00249386	+	0.00431949i
$316$	3.84827	−	8.24341i	0.216482	−	0.463728i
$317$	12.0017	−	12.0017i	0.674083	−	0.674083i	−0.284572	−	0.958655i	$-0.591851\pi$
$317$	12.0017	−	12.0017i	0.674083	−	0.674083i	0.958655	+	0.284572i	$0.0918514\pi$
$318$	−15.7001	+	4.94652i	−0.880416	+	0.277387i
$319$	−31.6444	+	8.47910i	−1.77175	+	0.474738i
$320$	7.13506	+	4.13166i	0.398862	+	0.230967i
$321$	4.60675	−	7.97913i	0.257124	−	0.445352i
$322$	−0.127893	−	0.200847i	−0.00712721	−	0.0111928i
$323$	−45.5621	−	12.2083i	−2.53514	−	0.679289i
$324$	−0.173458	−	1.99246i	−0.00963658	−	0.110692i
$325$	7.74293	−	11.9008i	0.429501	−	0.660140i
$326$	−1.05148	−	24.2018i	−0.0582362	−	1.34041i
$327$	−15.7704	−	4.22566i	−0.872103	−	0.233679i
$328$	4.77138	−	3.65634i	0.263455	−	0.201888i
$329$	−0.661390	−	0.381854i	−0.0364636	−	0.0210523i
$330$	−4.37765	−	4.01310i	−0.240982	−	0.220914i
$331$	−15.7904	+	4.23102i	−0.867917	+	0.232558i	−0.665187	−	0.746677i	$-0.731648\pi$
$331$	−15.7904	+	4.23102i	−0.867917	+	0.232558i	−0.202730	+	0.979235i	$0.564981\pi$
$332$	−1.74735	−	4.80720i	−0.0958980	−	0.263829i
$333$	−3.08458	−	3.08458i	−0.169034	−	0.169034i
$334$	−6.90658	+	13.2605i	−0.377911	+	0.725582i
$335$	1.39334	+	2.41333i	0.0761262	+	0.131854i
$336$	0.0302373	−	0.342238i	0.00164958	−	0.0186706i
$337$			15.2823i			0.832478i	0.909255	+	0.416239i	$0.136652\pi$
$337$			15.2823i			0.832478i	−0.909255	+	0.416239i	$0.863348\pi$
$338$	3.63076	+	18.0227i	0.197487	+	0.980305i
$339$	−9.95079			−0.540453
$340$	−12.7130	−	2.24726i	−0.689459	−	0.121875i
$341$	−29.2898	+	16.9105i	−1.58613	+	0.915753i
$342$	−4.91994	+	9.44618i	−0.266040	+	0.510791i
$343$	−0.849848	+	0.849848i	−0.0458875	+	0.0458875i
$344$	−1.44527	−	3.49555i	−0.0779239	−	0.188467i
$345$	0.522879	+	1.95141i	0.0281508	+	0.105060i
$346$	3.04707	−	3.32386i	0.163811	−	0.178692i
$347$	6.73675	−	11.6684i	0.361648	−	0.626393i	−0.626584	−	0.779354i	$-0.715548\pi$
$347$	6.73675	−	11.6684i	0.361648	−	0.626393i	0.988232	+	0.152961i	$0.0488809\pi$
$348$	9.21783	+	13.1764i	0.494128	+	0.706331i
$349$	−7.93909	+	29.6291i	−0.424970	+	1.58601i	0.339019	+	0.940779i	$0.389905\pi$
$349$	−7.93909	+	29.6291i	−0.424970	+	1.58601i	−0.763989	+	0.645229i	$0.776762\pi$
$350$	0.0207621	+	0.477879i	0.00110978	+	0.0255437i
$351$	−3.02219	−	1.96630i	−0.161313	−	0.104953i
$352$	4.96466	+	22.5081i	0.264617	+	1.19969i
$353$	3.00660	−	11.2208i	0.160025	−	0.597221i	−0.838598	−	0.544751i	$-0.816624\pi$
$353$	3.00660	−	11.2208i	0.160025	−	0.597221i	0.998623	−	0.0524698i	$-0.0167093\pi$
$354$	1.95781	−	1.24667i	0.104057	−	0.0662600i
$355$	2.03781	+	1.17653i	0.108156	+	0.0624437i
$356$	−9.80278	−	8.23266i	−0.519546	−	0.436330i
$357$	0.139236	+	0.519637i	0.00736917	+	0.0275021i
$358$	−21.5112	+	6.77738i	−1.13690	+	0.358196i
$359$	12.0541	+	12.0541i	0.636194	+	0.636194i	0.949614	−	0.313421i	$-0.101475\pi$
$359$	12.0541	+	12.0541i	0.636194	+	0.636194i	−0.313421	+	0.949614i	$0.601475\pi$
$360$	−1.11727	+	2.69243i	−0.0588852	+	0.141904i
$361$	32.6648	−	18.8590i	1.71920	−	0.992581i
$362$	1.35186	+	0.300004i	0.0710522	+	0.0157679i
$363$		−	5.60201i		−	0.294029i
$364$	−0.452446	−	0.422997i	−0.0237146	−	0.0221711i
$365$			7.17966i			0.375801i
$366$	2.93549	−	13.2277i	0.153440	−	0.691424i
$367$	28.2435	−	16.3064i	1.47430	−	0.851186i	0.474716	−	0.880139i	$-0.342551\pi$
$367$	28.2435	−	16.3064i	1.47430	−	0.851186i	0.999581	+	0.0289535i	$0.00921748\pi$
$368$	2.68805	−	7.36572i	0.140124	−	0.383965i
$369$	1.50281	+	1.50281i	0.0782330	+	0.0782330i
$370$	1.91061	+	6.06422i	0.0993281	+	0.315264i
$371$	−0.258756	−	0.965692i	−0.0134340	−	0.0501362i
$372$	12.7126	+	10.6764i	0.659116	+	0.553545i
$373$	−28.3185	−	16.3497i	−1.46628	−	0.846556i	−0.466989	−	0.884263i	$-0.654661\pi$
$373$	−28.3185	−	16.3497i	−1.46628	−	0.846556i	−0.999289	+	0.0377071i	$0.987995\pi$
$374$	−19.3850	−	30.4427i	−1.00237	−	1.57415i
$375$	2.38412	−	8.89764i	0.123115	−	0.459472i
$376$	−3.26655	−	24.9356i	−0.168459	−	1.28596i
$377$	28.9487	+	1.54188i	1.49094	+	0.0794111i
$378$	0.121356	−	0.00527250i	0.00624190	−	0.000271188i
$379$	−0.242189	+	0.903862i	−0.0124404	+	0.0464283i	−0.971867	−	0.235530i	$-0.924317\pi$
$379$	−0.242189	+	0.903862i	−0.0124404	+	0.0464283i	0.959427	+	0.281958i	$0.0909840\pi$
$380$	12.7199	−	8.89849i	0.652519	−	0.456483i
$381$	7.95743	−	13.7827i	0.407672	−	0.706108i
$382$	22.5232	+	20.6476i	1.15239	+	1.05642i
$383$	0.0915839	+	0.341796i	0.00467972	+	0.0174649i	0.968226	−	0.250076i	$-0.0804556\pi$
$383$	0.0915839	+	0.341796i	0.00467972	+	0.0174649i	−0.963546	+	0.267541i	$0.913789\pi$
$384$	9.55098	−	6.06454i	0.487397	−	0.309480i
$385$	0.255048	−	0.255048i	0.0129985	−	0.0129985i
$386$	3.88710	+	2.02455i	0.197848	+	0.103047i
$387$	1.15816	−	0.668666i	0.0588727	−	0.0339902i
$388$	16.7530	+	2.96140i	0.850505	+	0.150342i
$389$	15.6727			0.794637			0.397319	−	0.917681i	$-0.369941\pi$
$389$	15.6727			0.794637			0.397319	+	0.917681i	$0.369941\pi$
$390$	2.58289	+	4.57662i	0.130790	+	0.231746i
$391$			12.2773i			0.620892i
$392$	−19.6073	−	2.59416i	−0.990316	−	0.131025i
$393$	−5.68945	−	9.85442i	−0.286995	−	0.497090i
$394$	10.0994	+	5.26016i	0.508800	+	0.265003i
$395$	−3.31492	−	3.31492i	−0.166792	−	0.166792i
$396$	−7.65885	+	2.78388i	−0.384872	+	0.139895i
$397$	−13.5353	+	3.62679i	−0.679320	+	0.182023i	−0.581949	−	0.813225i	$-0.697710\pi$
$397$	−13.5353	+	3.62679i	−0.679320	+	0.182023i	−0.0973703	+	0.995248i	$0.531043\pi$
$398$	18.6658	−	20.3614i	0.935632	−	1.02062i
$399$	−0.560207	−	0.323436i	−0.0280454	−	0.0161920i
$400$	−12.0748	+	10.1144i	−0.603742	+	0.505719i
$401$	−38.2049	−	10.2370i	−1.90786	−	0.511210i	−0.994593	−	0.103848i	$-0.966884\pi$
$401$	−38.2049	−	10.2370i	−1.90786	−	0.511210i	−0.913267	−	0.407362i	$-0.866449\pi$
$402$	3.82025	−	0.165976i	0.190537	−	0.00827815i
$403$	29.2792	−	6.19742i	1.45850	−	0.308715i
$404$	−1.09855	−	12.6187i	−0.0546548	−	0.627803i
$405$	−0.995505	−	0.266745i	−0.0494671	−	0.0132547i
$406$	−0.823823	+	0.524585i	−0.0408856	+	0.0260347i
$407$	−8.88713	+	15.3930i	−0.440519	+	0.763001i
$408$	−10.7933	+	14.0474i	−0.534348	+	0.695451i
$409$	−0.565036	+	0.151401i	−0.0279392	+	0.00748629i	−0.272762	−	0.962082i	$-0.587937\pi$
$409$	−0.565036	+	0.151401i	−0.0279392	+	0.00748629i	0.244822	+	0.969568i	$0.421270\pi$
$410$	−0.930850	−	2.95449i	−0.0459714	−	0.145912i
$411$	−4.71833	+	4.71833i	−0.232738	+	0.232738i
$412$	12.7951	+	5.97315i	0.630372	+	0.294276i
$413$	0.0704847	+	0.122083i	0.00346832	+	0.00600731i
$414$	2.70633	+	0.600587i	0.133009	+	0.0295172i
$415$	−2.63577			−0.129385
$416$	1.99391	−	20.2984i	0.0977596	−	0.995210i
$417$	−11.9977			−0.587531
$418$	42.3659	+	9.40182i	2.07219	+	0.459858i
$419$	11.0772	+	19.1862i	0.541155	+	0.937308i	0.998838	+	0.0481924i	$0.0153460\pi$
$419$	11.0772	+	19.1862i	0.541155	+	0.937308i	−0.457683	+	0.889115i	$0.651321\pi$
$420$	−0.160426	−	0.0748917i	−0.00782801	−	0.00365434i
$421$	17.8761	−	17.8761i	0.871228	−	0.871228i	−0.121379	−	0.992606i	$-0.538732\pi$
$421$	17.8761	−	17.8761i	0.871228	−	0.871228i	0.992606	+	0.121379i	$0.0387315\pi$
$422$	−7.15526	−	22.7105i	−0.348312	−	1.10553i
$423$	8.58843	−	2.30126i	0.417584	−	0.111891i
$424$	20.0583	−	26.1057i	0.974115	−	1.26780i
$425$	12.3317	−	21.3592i	0.598178	−	1.03607i
$426$	2.72356	−	1.73428i	0.131957	−	0.0840260i
$427$	0.794896	+	0.212992i	0.0384677	+	0.0103074i
$428$	1.59816	+	18.3576i	0.0772500	+	0.887347i
$429$	−4.55168	+	13.9681i	−0.219757	+	0.674387i
$430$	−1.94735	+	0.0846055i	−0.0939096	+	0.00408004i
$431$	−15.3613	−	4.11605i	−0.739928	−	0.198263i	−0.130882	−	0.991398i	$-0.541781\pi$
$431$	−15.3613	−	4.11605i	−0.739928	−	0.198263i	−0.609046	+	0.793135i	$0.708448\pi$
$432$	2.56853	+	3.06638i	0.123578	+	0.147531i
$433$	−6.25685	−	3.61239i	−0.300685	−	0.173601i	0.342066	−	0.939676i	$-0.388873\pi$
$433$	−6.25685	−	3.61239i	−0.300685	−	0.173601i	−0.642751	+	0.766076i	$0.722207\pi$
$434$	−0.681337	+	0.743230i	−0.0327052	+	0.0356762i
$435$	8.00418	−	2.14471i	0.383771	−	0.102831i
$436$	30.6889	−	11.1550i	1.46973	−	0.534226i
$437$	−10.4388	−	10.4388i	−0.499356	−	0.499356i
$438$	8.73775	+	4.55096i	0.417506	+	0.217453i
$439$	10.9665	+	18.9945i	0.523402	+	0.906558i	0.999629	+	0.0272362i	$0.00867062\pi$
$439$	10.9665	+	18.9945i	0.523402	+	0.906558i	−0.476227	+	0.879322i	$0.657996\pi$
$440$	11.7749	+	1.55789i	0.561346	+	0.0742694i
$441$		−	6.99262i		−	0.332982i
$442$	7.96325	+	30.9277i	0.378773	+	1.47108i
$443$	28.2046			1.34004			0.670021	−	0.742342i	$-0.266285\pi$
$443$	28.2046			1.34004			0.670021	+	0.742342i	$0.266285\pi$
$444$	8.59132	+	1.51867i	0.407726	+	0.0720731i
$445$	−5.71283	+	3.29831i	−0.270814	+	0.156355i
$446$	−6.74476	−	3.51294i	−0.319374	−	0.166342i
$447$	−12.1389	+	12.1389i	−0.574151	+	0.574151i
$448$	0.342807	+	0.595524i	0.0161961	+	0.0281359i
$449$	7.74268	+	28.8961i	0.365400	+	1.36369i	0.866878	+	0.498520i	$0.166123\pi$
$449$	7.74268	+	28.8961i	0.365400	+	1.36369i	−0.501478	+	0.865170i	$0.667210\pi$
$450$	−4.10503	−	3.76318i	−0.193513	−	0.177398i
$451$	4.32981	−	7.49945i	0.203883	−	0.353135i
$452$	16.3073	−	11.4081i	0.767031	−	0.536592i
$453$	1.55242	−	5.79370i	0.0729390	−	0.272212i
$454$	32.3305	−	1.40465i	1.51735	−	0.0659233i
$455$	−0.284510	+	0.144660i	−0.0133380	+	0.00678176i
$456$	−2.76681	−	21.1208i	−0.129568	−	0.989073i
$457$	−8.83944	+	32.9893i	−0.413492	+	1.54317i	0.374346	+	0.927289i	$0.377867\pi$
$457$	−8.83944	+	32.9893i	−0.413492	+	1.54317i	−0.787838	+	0.615883i	$0.788799\pi$
$458$	−11.4855	−	18.0372i	−0.536683	−	0.842821i
$459$	−5.42413	−	3.13162i	−0.253177	−	0.146172i
$460$	−3.09409	−	2.59851i	−0.144263	−	0.121156i
$461$	9.07345	+	33.8626i	0.422593	+	1.57714i	0.769124	+	0.639099i	$0.220693\pi$
$461$	9.07345	+	33.8626i	0.422593	+	1.57714i	−0.346532	+	0.938038i	$0.612641\pi$
$462$	−0.148730	−	0.472064i	−0.00691956	−	0.0219624i
$463$	−21.3597	−	21.3597i	−0.992671	−	0.992671i	0.00730232	−	0.999973i	$-0.497676\pi$
$463$	−21.3597	−	21.3597i	−0.992671	−	0.992671i	−0.999973	+	0.00730232i	$0.997676\pi$
$464$	−30.2123	−	11.0257i	−1.40257	−	0.511854i
$465$	7.40859	−	4.27735i	0.343565	−	0.198358i
$466$	−1.39334	+	6.27860i	−0.0645453	+	0.290850i
$467$		−	13.3077i		−	0.615805i	−0.951418	−	0.307903i	$-0.900373\pi$
$467$		−	13.3077i		−	0.615805i	0.951418	−	0.307903i	$-0.0996271\pi$
$468$	7.20703	−	0.242435i	0.333145	−	0.0112065i
$469$			0.232244i			0.0107240i
$470$	−12.6516	−	2.80764i	−0.583575	−	0.129507i
$471$	17.4257	−	10.0607i	0.802934	−	0.463574i
$472$	−1.77920	+	4.28758i	−0.0818944	+	0.197352i
$473$	−3.85305	−	3.85305i	−0.177163	−	0.177163i
$474$	−6.13553	+	1.93308i	−0.281814	+	0.0887893i
$475$	7.67560	+	28.6457i	0.352181	+	1.31436i
$476$	−0.823918	−	0.691951i	−0.0377642	−	0.0317155i
$477$	10.0802	+	5.81980i	0.461540	+	0.266470i
$478$	−9.65073	+	6.14529i	−0.441414	+	0.281079i
$479$	7.65555	−	28.5709i	0.349791	−	1.30544i	−0.537124	−	0.843503i	$-0.680489\pi$
$479$	7.65555	−	28.5709i	0.349791	−	1.30544i	0.886915	−	0.461934i	$-0.152844\pi$
$480$	−1.25577	−	5.69323i	−0.0573177	−	0.259859i
$481$	11.6974	−	10.5143i	0.533356	−	0.479413i
$482$	−0.272612	−	6.27468i	−0.0124172	−	0.285804i
$483$	−0.0435771	+	0.162632i	−0.00198283	+	0.00740001i
$484$	6.42243	+	9.18054i	0.291929	+	0.417297i
$485$	4.38343	−	7.59232i	0.199041	−	0.344749i
$486$	−0.955652	+	1.04246i	−0.0433493	+	0.0472871i
$487$	3.40192	+	12.6961i	0.154156	+	0.575317i	0.999176	+	0.0405831i	$0.0129216\pi$
$487$	3.40192	+	12.6961i	0.154156	+	0.575317i	−0.845020	+	0.534734i	$0.820412\pi$
$488$	10.3543	+	25.0429i	0.468716	+	1.13364i
$489$	−12.1123	+	12.1123i	−0.547737	+	0.547737i
$490$	−4.70803	+	9.03931i	−0.212687	+	0.408354i
$491$	1.27462	−	0.735902i	0.0575228	−	0.0332108i	−0.470963	−	0.882153i	$-0.656093\pi$
$491$	1.27462	−	0.735902i	0.0575228	−	0.0332108i	0.528486	+	0.848942i	$0.322760\pi$
$492$	−4.18569	−	0.739898i	−0.188705	−	0.0333572i
$493$	50.3585			2.26803
$494$	−33.0670	−	19.5255i	−1.48775	−	0.878493i
$495$			4.19933i			0.188746i
$496$	−33.0732	−	2.92208i	−1.48503	−	0.131205i
$497$	0.0980528	+	0.169832i	0.00439827	+	0.00761802i
$498$	−1.67073	+	3.20777i	−0.0748674	+	0.143744i
$499$	1.31248	+	1.31248i	0.0587548	+	0.0587548i	0.735874	−	0.677119i	$-0.236772\pi$
$499$	1.31248	+	1.31248i	0.0587548	+	0.0587548i	−0.677119	+	0.735874i	$0.736772\pi$
$500$	6.29364	+	17.3147i	0.281460	+	0.774336i
$501$	10.2119	−	2.73628i	0.456235	−	0.122248i
$502$	−22.3724	−	20.5094i	−0.998530	−	0.915378i
$503$	16.2345	+	9.37300i	0.723861	+	0.417921i	0.816172	−	0.577809i	$-0.196092\pi$
$503$	16.2345	+	9.37300i	0.723861	+	0.417921i	−0.0923112	+	0.995730i	$0.529425\pi$
$504$	−0.192834	+	0.147770i	−0.00858949	+	0.00658219i
$505$	−6.30474	−	1.68935i	−0.280557	−	0.0751751i
$506$	−0.490281	−	11.2847i	−0.0217956	−	0.501667i
$507$	7.65913	−	10.5042i	0.340154	−	0.466507i
$508$	2.76057	+	31.7098i	0.122480	+	1.40689i
$509$	23.8548	+	6.39186i	1.05734	+	0.283314i	0.745283	−	0.666748i	$-0.232314\pi$
$509$	23.8548	+	6.39186i	1.05734	+	0.283314i	0.312060	+	0.950062i	$0.398981\pi$
$510$	4.90326	+	7.70021i	0.217120	+	0.340971i
$511$	−0.299179	+	0.518194i	−0.0132349	+	0.0229235i
$512$	−8.69940	+	20.8883i	−0.384463	+	0.923140i
$513$	7.27452	−	1.94920i	0.321178	−	0.0860594i
$514$	−30.9458	+	9.74990i	−1.36496	+	0.430050i
$515$	5.14531	−	5.14531i	0.226729	−	0.226729i
$516$	−1.13140	+	2.42358i	−0.0498071	+	0.106692i
$517$	−18.1143	−	31.3748i	−0.796664	−	1.37986i
$518$	−0.114799	+	0.517302i	−0.00504399	+	0.0227289i
$519$	−3.18847			−0.139958
$520$	−9.47970	−	4.53899i	−0.415712	−	0.199048i
$521$	−4.97602			−0.218003			−0.109002	−	0.994042i	$-0.534765\pi$
$521$	−4.97602			−0.218003			−0.109002	+	0.994042i	$0.534765\pi$
$522$	2.46345	−	11.1007i	0.107822	−	0.485863i
$523$	8.52634	+	14.7681i	0.372831	+	0.645762i	0.990000	−	0.141069i	$-0.0450538\pi$
$523$	8.52634	+	14.7681i	0.372831	+	0.645762i	−0.617169	+	0.786831i	$0.711720\pi$
$524$	20.6215	+	9.62670i	0.900853	+	0.420544i
$525$	0.239165	−	0.239165i	0.0104380	−	0.0104380i
$526$	12.6408	−	3.98267i	0.551167	−	0.173653i
$527$	50.2167	−	13.4555i	2.18747	−	0.586132i
$528$	9.35971	−	13.3427i	0.407329	−	0.580667i
$529$	9.57877	−	16.5909i	0.416468	−	0.721344i
$530$	−9.11220	−	14.3100i	−0.395809	−	0.621589i
$531$	−1.58530	−	0.424780i	−0.0687962	−	0.0184339i
$532$	1.28887	−	0.112205i	0.0558795	−	0.00486471i
$533$	−5.69897	+	5.12259i	−0.246850	+	0.221884i
$534$	0.392899	+	9.04330i	0.0170024	+	0.391342i
$535$	9.17210	+	2.45766i	0.396544	+	0.106254i
$536$	−6.07033	+	4.65173i	−0.262198	+	0.200924i
$537$	13.8112	+	7.97389i	0.595996	+	0.344099i
$538$	−0.286450	−	0.262596i	−0.0123498	−	0.0113213i
$539$	−27.5210	+	7.37423i	−1.18541	+	0.317631i
$540$	1.93724	−	0.704158i	0.0833655	−	0.0303021i
$541$	10.7178	+	10.7178i	0.460796	+	0.460796i	0.898916	−	0.438120i	$-0.144356\pi$
$541$	10.7178	+	10.7178i	0.460796	+	0.460796i	−0.438120	+	0.898916i	$0.644356\pi$
$542$	2.62578	−	5.04144i	0.112787	−	0.216548i
$543$	−0.489583	−	0.847982i	−0.0210100	−	0.0363904i
$544$	1.58334	−	35.3949i	0.0678849	−	1.51754i
$545$		−	16.8267i		−	0.720775i
$546$	−0.00428904	+	0.437948i	−0.000183554	+	0.0187425i
$547$	26.0014			1.11174			0.555870	−	0.831270i	$-0.312385\pi$
$547$	26.0014			1.11174			0.555870	+	0.831270i	$0.312385\pi$
$548$	2.32304	−	13.1417i	0.0992353	−	0.561386i
$549$	−8.29736	+	4.79048i	−0.354123	+	0.204453i
$550$	−10.4818	+	20.1248i	−0.446944	+	0.858124i
$551$	−42.8173	+	42.8173i	−1.82408	+	1.82408i
$552$	−5.12366	+	2.11844i	−0.218078	+	0.0901667i
$553$	−0.101121	−	0.377389i	−0.00430010	−	0.0160482i
$554$	0.427983	−	0.466860i	0.0181832	−	0.0198350i
$555$	2.24792	−	3.89351i	0.0954189	−	0.165270i
$556$	19.6618	−	13.7548i	0.833847	−	0.583334i
$557$	−1.74322	+	6.50580i	−0.0738627	+	0.275659i	−0.992973	−	0.118341i	$-0.962242\pi$
$557$	−1.74322	+	6.50580i	−0.0738627	+	0.275659i	0.919110	+	0.394000i	$0.128909\pi$
$558$	−0.509525	−	11.7276i	−0.0215699	−	0.496471i
$559$	2.18540	+	4.29814i	0.0924324	+	0.181792i
$560$	0.348766	−	0.0611889i	0.0147380	−	0.00258570i
$561$	−6.60504	+	24.6504i	−0.278865	+	1.04074i
$562$	−3.76063	+	2.39466i	−0.158633	+	0.101012i
$563$	10.2085	+	5.89390i	0.430238	+	0.248398i	0.699448	−	0.714683i	$-0.253429\pi$
$563$	10.2085	+	5.89390i	0.430238	+	0.248398i	−0.269210	+	0.963082i	$0.586763\pi$
$564$	−11.4364	+	13.6175i	−0.481559	+	0.573401i
$565$	−2.65432	−	9.90606i	−0.111668	−	0.416751i
$566$	9.68981	−	3.05290i	0.407293	−	0.128323i
$567$	−0.0607354	−	0.0607354i	−0.00255065	−	0.00255065i
$568$	−2.47509	+	5.96455i	−0.103852	+	0.250267i
$569$	−21.1218	+	12.1947i	−0.885474	+	0.511229i	−0.872459	−	0.488687i	$-0.837476\pi$
$569$	−21.1218	+	12.1947i	−0.885474	+	0.511229i	−0.0130145	+	0.999915i	$0.504143\pi$
$570$	−10.7161	−	2.37811i	−0.448848	−	0.0996080i
$571$			34.3265i			1.43652i	0.695774	+	0.718261i	$0.255061\pi$
$571$			34.3265i			1.43652i	−0.695774	+	0.718261i	$0.744939\pi$
$572$	−8.55449	−	28.1092i	−0.357681	−	1.17530i
$573$		−	21.6058i		−	0.902594i
$574$	0.0559302	−	0.252029i	0.00233448	−	0.0105195i
$575$	6.68484	−	3.85949i	0.278777	−	0.160952i
$576$	−7.72474	−	2.08048i	−0.321864	−	0.0866865i
$577$	−21.6148	−	21.6148i	−0.899836	−	0.899836i	0.0955855	−	0.995421i	$-0.469528\pi$
$577$	−21.6148	−	21.6148i	−0.899836	−	0.899836i	−0.995421	+	0.0955855i	$0.969528\pi$
$578$	9.44639	+	29.9825i	0.392918	+	1.24711i
$579$	−0.802096	−	2.99346i	−0.0333340	−	0.124404i
$580$	−10.6584	+	12.6911i	−0.442566	+	0.526971i
$581$	−0.190237	−	0.109834i	−0.00789238	−	0.00455667i
$582$	−6.46144	−	10.1472i	−0.267835	−	0.420616i
$583$	12.2748	−	45.8102i	0.508370	−	1.89726i
$584$	−19.5368	+	2.55931i	−0.808440	+	0.105905i
$585$	1.15131	−	3.53311i	0.0476007	−	0.146076i
$586$	−18.4706	+	0.802484i	−0.763015	+	0.0331503i
$587$	9.59127	−	35.7951i	0.395874	−	1.47742i	−0.424412	−	0.905469i	$-0.639519\pi$
$587$	9.59127	−	35.7951i	0.395874	−	1.47742i	0.820286	−	0.571953i	$-0.193814\pi$
$588$	8.01670	+	11.4595i	0.330603	+	0.472581i
$589$	−31.2562	+	54.1373i	−1.28789	+	2.23069i
$590$	1.76331	+	1.61647i	0.0725942	+	0.0665490i
$591$	−2.08399	−	7.77756i	−0.0857240	−	0.319926i
$592$	−15.8205	+	7.36073i	−0.650218	+	0.302524i
$593$	−5.11162	+	5.11162i	−0.209909	+	0.209909i	−0.804229	−	0.594320i	$-0.797421\pi$
$593$	−5.11162	+	5.11162i	−0.209909	+	0.209909i	0.594320	+	0.804229i	$0.297421\pi$
$594$	5.11065	+	2.66182i	0.209692	+	0.109216i
$595$	−0.480161	+	0.277221i	−0.0196847	+	0.0113650i
$596$	5.97652	−	33.8099i	0.244808	−	1.38491i
$597$	−19.5320			−0.799392
$598$	−2.68137	+	9.62883i	−0.109649	+	0.393752i
$599$		−	7.10600i		−	0.290343i	−0.989406	−	0.145172i	$-0.953627\pi$
$599$		−	7.10600i		−	0.290343i	0.989406	−	0.145172i	$-0.0463735\pi$
$600$	11.0416	+	1.46087i	0.450772	+	0.0596398i
$601$	−23.3873	−	40.5080i	−0.953988	−	1.65236i	−0.736668	−	0.676255i	$-0.763602\pi$
$601$	−23.3873	−	40.5080i	−0.953988	−	1.65236i	−0.217320	−	0.976100i	$-0.569731\pi$
$602$	−0.144076	−	0.0750404i	−0.00587210	−	0.00305842i
$603$	−1.91193	−	1.91193i	−0.0778597	−	0.0778597i
$604$	4.09810	+	11.2745i	0.166749	+	0.458752i
$605$	5.57683	−	1.49431i	0.226730	−	0.0607522i
$606$	−6.05234	+	6.60214i	−0.245860	+	0.268193i
$607$	−4.20189	−	2.42596i	−0.170549	−	0.0984667i	0.412295	−	0.911050i	$-0.364727\pi$
$607$	−4.20189	−	2.42596i	−0.170549	−	0.0984667i	−0.582845	+	0.812583i	$0.698060\pi$
$608$	28.7482	+	31.4407i	1.16589	+	1.27509i
$609$	0.667074	+	0.178742i	0.0270312	+	0.00724299i
$610$	13.9513	−	0.606134i	0.564871	−	0.0245417i
$611$	6.63858	+	31.3635i	0.268568	+	1.26883i
$612$	12.4793	−	1.08641i	0.504445	−	0.0439156i
$613$	13.6345	+	3.65337i	0.550694	+	0.147558i	0.523428	−	0.852070i	$-0.324653\pi$
$613$	13.6345	+	3.65337i	0.550694	+	0.147558i	0.0272666	+	0.999628i	$0.491320\pi$
$614$	−28.1864	+	17.9482i	−1.13751	+	0.724331i
$615$	−1.09519	+	1.89692i	−0.0441622	+	0.0764911i
$616$	0.784937	+	0.603105i	0.0316260	+	0.0242998i
$617$	−36.6701	+	9.82573i	−1.47628	+	0.395569i	−0.905081	−	0.425240i	$-0.860190\pi$
$617$	−36.6701	+	9.82573i	−1.47628	+	0.395569i	−0.571203	+	0.820809i	$0.693523\pi$
$618$	−3.00046	−	9.52336i	−0.120696	−	0.383086i
$619$	22.2000	−	22.2000i	0.892291	−	0.892291i	−0.102447	−	0.994738i	$-0.532667\pi$
$619$	22.2000	−	22.2000i	0.892291	−	0.892291i	0.994738	+	0.102447i	$0.0326672\pi$
$620$	−7.23739	+	15.5033i	−0.290661	+	0.622627i
$621$	−0.980110	−	1.69760i	−0.0393305	−	0.0681224i
$622$	−13.8665	−	3.07724i	−0.555995	−	0.123386i
$623$	−0.549767			−0.0220259
$624$	−11.5329	+	8.65981i	−0.461685	+	0.346670i
$625$	−10.1955			−0.407819
$626$	3.61734	+	0.802757i	0.144578	+	0.0320846i
$627$	−15.3430	−	26.5749i	−0.612741	−	1.06130i
$628$	−17.0230	+	36.4652i	−0.679292	+	1.45512i
$629$	19.3195	−	19.3195i	0.770318	−	0.770318i
$630$	0.0376200	+	0.119405i	0.00149882	+	0.00475719i
$631$	−0.0274496	+	0.00735510i	−0.00109275	+	0.000292802i	−0.259365	−	0.965779i	$-0.583513\pi$
$631$	−0.0274496	+	0.00735510i	−0.00109275	+	0.000292802i	0.258273	+	0.966072i	$0.416847\pi$
$632$	7.83869	−	10.2020i	0.311806	−	0.405814i
$633$	−8.41848	+	14.5812i	−0.334604	+	0.579552i
$634$	20.2470	−	12.8927i	0.804113	−	0.512034i
$635$	15.8433	+	4.24521i	0.628724	+	0.168466i
$636$	−23.1915	+	2.01898i	−0.919602	+	0.0800580i
$637$	25.1766	+	1.34097i	0.997532	+	0.0531311i
$638$	−46.2870	+	2.01101i	−1.83252	+	0.0796165i
$639$	−2.20535	−	0.590920i	−0.0872421	−	0.0233765i
$640$	8.58496	+	7.89037i	0.339350	+	0.311894i
$641$	−5.53364	−	3.19485i	−0.218566	−	0.126189i	0.386720	−	0.922197i	$-0.373608\pi$
$641$	−5.53364	−	3.19485i	−0.218566	−	0.126189i	−0.605286	+	0.796008i	$0.706941\pi$
$642$	8.80491	−	9.60474i	0.347502	−	0.379069i
$643$	11.2790	−	3.02221i	0.444802	−	0.119184i	−0.0294644	−	0.999566i	$-0.509380\pi$
$643$	11.2790	−	3.02221i	0.444802	−	0.119184i	0.474266	+	0.880382i	$0.342714\pi$
$644$	−0.115036	−	0.316479i	−0.00453304	−	0.0124710i
$645$	0.974594	+	0.974594i	0.0383746	+	0.0383746i
$646$	−59.1637	−	30.8148i	−2.32777	−	1.21239i
$647$	13.7635	+	23.8390i	0.541098	+	0.937209i	0.998841	+	0.0481245i	$0.0153244\pi$
$647$	13.7635	+	23.8390i	0.541098	+	0.937209i	−0.457744	+	0.889084i	$0.651342\pi$
$648$	0.370985	−	2.80399i	0.0145737	−	0.110151i
$649$			6.68726i			0.262498i
$650$	14.3364	−	14.0583i	0.562318	−	0.551411i
$651$	0.712956			0.0279429
$652$	5.96342	−	33.7358i	0.233546	−	1.32119i
$653$	26.8877	−	15.5236i	1.05220	−	0.607486i	0.128933	−	0.991653i	$-0.458845\pi$
$653$	26.8877	−	15.5236i	1.05220	−	0.607486i	0.923264	+	0.384167i	$0.125511\pi$
$654$	−20.4783	−	10.6659i	−0.800764	−	0.417069i
$655$	8.29250	−	8.29250i	0.324015	−	0.324015i
$656$	7.70774	−	3.58615i	0.300937	−	0.140016i
$657$	−1.80302	−	6.72896i	−0.0703425	−	0.262522i
$658$	−0.796137	−	0.729839i	−0.0310367	−	0.0284521i
$659$	9.43933	−	16.3494i	0.367704	−	0.636882i	−0.621502	−	0.783412i	$-0.713477\pi$
$659$	9.43933	−	16.3494i	0.367704	−	0.636882i	0.989206	+	0.146530i	$0.0468106\pi$
$660$	−4.81433	−	6.88184i	−0.187397	−	0.267875i
$661$	4.85362	−	18.1140i	0.188784	−	0.704552i	−0.805005	−	0.593269i	$-0.797837\pi$
$661$	4.85362	−	18.1140i	0.188784	−	0.704552i	0.993789	−	0.111283i	$-0.0354961\pi$
$662$	−23.0969	+	1.00348i	−0.897687	+	0.0390013i
$663$	12.3154	−	18.9287i	0.478291	−	0.735131i
$664$	−0.939565	−	7.17230i	−0.0364622	−	0.278339i
$665$	0.172550	−	0.643964i	0.00669118	−	0.0249718i
$666$	−3.31357	−	5.20373i	−0.128398	−	0.201640i
$667$	13.6492	+	7.88040i	0.528501	+	0.305130i
$668$	−13.5982	+	16.1917i	−0.526132	+	0.626475i
$669$	1.39177	+	5.19416i	0.0538089	+	0.200818i
$670$	1.18426	+	3.75881i	0.0457521	+	0.145215i
$671$	27.6042	+	27.6042i	1.06565	+	1.06565i
$672$	0.146604	−	0.463239i	0.00565537	−	0.0178698i
$673$	−27.7602	+	16.0273i	−1.07008	+	0.617809i	−0.928202	−	0.372076i	$-0.878646\pi$
$673$	−27.7602	+	16.0273i	−1.07008	+	0.617809i	−0.141874	+	0.989885i	$0.545313\pi$
$674$	−4.68229	+	21.0991i	−0.180355	+	0.812706i
$675$			3.93782i			0.151567i
$676$	−0.509212	+	25.9950i	−0.0195851	+	0.999808i
$677$		−	8.81522i		−	0.338797i	−0.985548	−	0.169398i	$-0.945818\pi$
$677$		−	8.81522i		−	0.338797i	0.985548	−	0.169398i	$-0.0541824\pi$
$678$	−13.7383	−	3.04880i	−0.527617	−	0.117088i
$679$	0.632749	−	0.365318i	0.0242827	−	0.0140196i
$680$	−16.8633	−	6.99772i	−0.646680	−	0.268350i
$681$	−16.1805	−	16.1805i	−0.620039	−	0.620039i
$682$	−45.6194	+	14.3730i	−1.74686	+	0.550371i
$683$	−4.93115	−	18.4033i	−0.188685	−	0.704183i	−0.993812	−	0.111079i	$-0.964569\pi$
$683$	−4.93115	−	18.4033i	−0.188685	−	0.704183i	0.805126	−	0.593103i	$-0.202097\pi$
$684$	−9.68679	+	11.5342i	−0.370384	+	0.441022i
$685$	−5.95571	−	3.43853i	−0.227556	−	0.131379i
$686$	−1.43370	+	0.912939i	−0.0547391	+	0.0348562i
$687$	−3.91346	+	14.6052i	−0.149308	+	0.557225i
$688$	−0.924389	−	5.26885i	−0.0352420	−	0.200873i
$689$	−22.8869	+	35.1771i	−0.871923	+	1.34014i
$690$	0.124012	+	2.85437i	0.00472106	+	0.108664i
$691$	−12.5835	+	46.9623i	−0.478699	+	1.78653i	0.128199	+	0.991749i	$0.459080\pi$
$691$	−12.5835	+	46.9623i	−0.478699	+	1.78653i	−0.606898	+	0.794780i	$0.707586\pi$
$692$	5.22525	−	3.65542i	0.198634	−	0.138958i
$693$	−0.174988	+	0.303087i	−0.00664723	+	0.0115133i
$694$	12.8760	−	14.0456i	0.488766	−	0.533165i
$695$	−3.20033	−	11.9438i	−0.121396	−	0.453054i
$696$	8.68928	+	21.0159i	0.329366	+	0.796607i
$697$	−9.41245	+	9.41245i	−0.356522	+	0.356522i
$698$	−20.0389	+	38.4742i	−0.758483	+	1.45627i
$699$	3.93838	−	2.27382i	0.148963	−	0.0860039i
$700$	−0.117751	+	0.666133i	−0.00445058	+	0.0251775i
$701$	−24.5446			−0.927037			−0.463519	−	0.886087i	$-0.653413\pi$
$701$	−24.5446			−0.927037			−0.463519	+	0.886087i	$0.653413\pi$
$702$	−3.57007	−	3.64069i	−0.134744	−	0.137409i
$703$			32.8528i			1.23907i
$704$	−0.0418719	+	32.5964i	−0.00157811	+	1.22852i
$705$	4.58184	+	7.93598i	0.172562	+	0.298886i
$706$	7.58888	−	14.5705i	0.285611	−	0.548368i
$707$	−0.384650	−	0.384650i	−0.0144663	−	0.0144663i
$708$	3.08497	−	1.12134i	0.115940	−	0.0421426i
$709$	7.36268	−	1.97283i	0.276511	−	0.0740910i	−0.117898	−	0.993026i	$-0.537616\pi$
$709$	7.36268	−	1.97283i	0.276511	−	0.0740910i	0.394410	+	0.918935i	$0.370949\pi$
$710$	2.45298	+	2.24870i	0.0920585	+	0.0843924i
$711$	3.93930	+	2.27435i	0.147735	+	0.0852950i
$712$	−11.0116	−	14.3697i	−0.412676	−	0.538526i
$713$	15.7164	+	4.21121i	0.588585	+	0.157711i
$714$	0.0330230	+	0.760084i	0.00123585	+	0.0284454i
$715$	−15.1195	−	0.805302i	−0.565436	−	0.0301166i
$716$	−31.7754	+	2.76627i	−1.18750	+	0.103381i
$717$	7.81449	+	2.09389i	0.291837	+	0.0781976i
$718$	12.9490	+	20.3355i	0.483253	+	0.758914i
$719$	19.7044	−	34.1289i	0.734849	−	1.27280i	−0.219941	−	0.975513i	$-0.570587\pi$
$719$	19.7044	−	34.1289i	0.734849	−	1.27280i	0.954790	−	0.297282i	$-0.0960801\pi$
$720$	−2.36746	+	3.37492i	−0.0882298	+	0.125776i
$721$	0.585770	−	0.156957i	0.0218152	−	0.00584537i
$722$	50.8760	−	16.0292i	1.89341	−	0.596544i
$723$	−3.14030	+	3.14030i	−0.116789	+	0.116789i
$724$	1.77450	+	0.828386i	0.0659486	+	0.0307867i
$725$	−15.8306	−	27.4195i	−0.587935	−	1.01833i
$726$	1.71638	−	7.73427i	0.0637010	−	0.287046i
$727$	−28.8599			−1.07035			−0.535177	−	0.844740i	$-0.679755\pi$
$727$	−28.8599			−1.07035			−0.535177	+	0.844740i	$0.679755\pi$
$728$	−0.495058	−	0.722625i	−0.0183481	−	0.0267823i
$729$	1.00000			0.0370370
$730$	−2.19976	+	9.91243i	−0.0814167	+	0.366875i
$731$	4.18802	+	7.25386i	0.154899	+	0.268294i
$732$	8.10562	−	17.3631i	0.299592	−	0.641760i
$733$	12.0012	−	12.0012i	0.443274	−	0.443274i	−0.449837	−	0.893111i	$-0.648518\pi$
$733$	12.0012	−	12.0012i	0.443274	−	0.443274i	0.893111	+	0.449837i	$0.148518\pi$
$734$	43.9897	−	13.8595i	1.62369	−	0.511565i
$735$	6.96119	−	1.86525i	0.256767	−	0.0688006i
$736$	5.96795	−	9.34572i	0.219982	−	0.344488i
$737$	−5.50854	+	9.54108i	−0.202910	+	0.351450i
$738$	1.61437	+	2.53526i	0.0594259	+	0.0933240i
$739$	7.16807	+	1.92068i	0.263682	+	0.0706533i	0.388238	−	0.921559i	$-0.373084\pi$
$739$	7.16807	+	1.92068i	0.263682	+	0.0706533i	−0.124556	+	0.992213i	$0.539751\pi$
$740$	0.779841	+	8.95780i	0.0286675	+	0.329295i
$741$	5.62297	+	26.5653i	0.206565	+	0.975902i
$742$	−0.0613698	−	1.41254i	−0.00225296	−	0.0518559i
$743$	−51.0831	−	13.6877i	−1.87406	−	0.502152i	−0.999863	−	0.0165747i	$-0.994724\pi$
$743$	−51.0831	−	13.6877i	−1.87406	−	0.502152i	−0.874194	−	0.485577i	$-0.838609\pi$
$744$	14.2802	+	18.6351i	0.523537	+	0.683195i
$745$	−15.3223	−	8.84636i	−0.561367	−	0.324106i
$746$	−34.0879	−	31.2493i	−1.24805	−	1.14412i
$747$	2.47031	−	0.661919i	0.0903841	−	0.0242183i
$748$	−17.4361	−	47.9693i	−0.637528	−	1.75393i
$749$	0.559586	+	0.559586i	0.0204468	+	0.0204468i
$750$	6.01770	−	11.5539i	0.219735	−	0.421887i
$751$	17.1644	+	29.7295i	0.626336	+	1.08485i	0.988281	+	0.152647i	$0.0487796\pi$
$751$	17.1644	+	29.7295i	0.626336	+	1.08485i	−0.361945	+	0.932200i	$0.617887\pi$
$752$	3.13009	−	35.4276i	0.114143	−	1.29191i
$753$			21.4611i			0.782087i
$754$	39.4950	+	10.9983i	1.43832	+	0.400534i
$755$	6.18176			0.224977
$756$	0.169163	+	0.0299027i	0.00615240	+	0.00108755i
$757$	−15.2430	+	8.80057i	−0.554018	+	0.319862i	−0.750741	−	0.660597i	$-0.770303\pi$
$757$	−15.2430	+	8.80057i	−0.554018	+	0.319862i	0.196723	+	0.980459i	$0.436970\pi$
$758$	−0.611304	+	1.17369i	−0.0222036	+	0.0426304i
$759$	−5.64768	+	5.64768i	−0.204998	+	0.204998i
$760$	20.2879	−	8.38825i	0.735918	−	0.304274i
$761$	−8.27641	−	30.8880i	−0.300020	−	1.11969i	−0.937148	−	0.348932i	$-0.886545\pi$
$761$	−8.27641	−	30.8880i	−0.300020	−	1.11969i	0.637128	−	0.770758i	$-0.280122\pi$
$762$	15.2091	−	16.5907i	0.550967	−	0.601016i
$763$	0.701173	−	1.21447i	0.0253842	−	0.0439667i
$764$	24.7700	+	35.4074i	0.896146	+	1.28100i
$765$	1.67069	−	6.23509i	0.0604038	−	0.225430i
$766$	0.0217211	+	0.499952i	0.000784817	+	0.0180640i
$767$	1.83341	−	5.62633i	0.0662006	−	0.203155i
$768$	15.0444	−	5.44656i	0.542869	−	0.196536i
$769$	8.56321	−	31.9583i	0.308797	−	1.15245i	−0.620830	−	0.783945i	$-0.713204\pi$
$769$	8.56321	−	31.9583i	0.308797	−	1.15245i	0.929627	−	0.368502i	$-0.120129\pi$
$770$	0.430270	−	0.273982i	0.0155058	−	0.00987364i
$771$	19.8687	+	11.4712i	0.715553	+	0.413125i
$772$	4.74633	+	3.98611i	0.170824	+	0.143463i
$773$	1.28651	+	4.80132i	0.0462725	+	0.172691i	0.985195	−	0.171437i	$-0.0548411\pi$
$773$	1.28651	+	4.80132i	0.0462725	+	0.172691i	−0.938923	+	0.344129i	$0.888174\pi$
$774$	1.80386	−	0.568330i	0.0648384	−	0.0204282i
$775$	−23.1124	−	23.1124i	−0.830223	−	0.830223i
$776$	22.2223	+	9.22150i	0.797733	+	0.331032i
$777$	0.324488	−	0.187343i	0.0116409	−	0.00672091i
$778$	21.6381	+	4.80192i	0.775764	+	0.172157i
$779$		−	16.0059i		−	0.573469i
$780$	2.16378	+	7.10996i	0.0774758	+	0.254578i
$781$			9.30279i			0.332880i
$782$	−3.76162	+	16.9504i	−0.134515	+	0.606145i
$783$	−6.96312	+	4.02016i	−0.248842	+	0.143669i
$784$	−26.2755	−	9.58898i	−0.938409	−	0.342463i
$785$	14.6637	+	14.6637i	0.523371	+	0.523371i
$786$	−4.83573	−	15.3484i	−0.172485	−	0.547461i
$787$	0.743534	+	2.77491i	0.0265041	+	0.0989147i	0.977911	−	0.209022i	$-0.0670281\pi$
$787$	0.743534	+	2.77491i	0.0265041	+	0.0989147i	−0.951407	+	0.307937i	$0.900361\pi$
$788$	12.3318	+	10.3566i	0.439303	+	0.368940i
$789$	−8.11601	−	4.68578i	−0.288938	−	0.166818i
$790$	−3.56101	−	5.59231i	−0.126695	−	0.198966i
$791$	0.221213	−	0.825579i	0.00786543	−	0.0293542i
$792$	−11.4270	+	1.49692i	−0.406039	+	0.0531908i
$793$	−15.6567	−	30.7929i	−0.555986	−	1.09349i
$794$	−19.7984	+	0.860172i	−0.702621	+	0.0305264i
$795$	−3.10480	+	11.5873i	−0.110116	+	0.410958i
$796$	32.0090	−	22.3925i	1.13453	−	0.793681i
$797$	−17.2438	+	29.8672i	−0.610808	+	1.05795i	0.380297	+	0.924865i	$0.375822\pi$
$797$	−17.2438	+	29.8672i	−0.610808	+	1.05795i	−0.991105	+	0.133086i	$0.957511\pi$
$798$	−0.674339	−	0.618184i	−0.0238714	−	0.0218835i
$799$	14.4134	+	53.7914i	0.509908	+	1.90300i
$800$	−19.7697	+	10.2646i	−0.698966	+	0.362908i
$801$	4.52591	−	4.52591i	0.159915	−	0.159915i
$802$	−49.6101	−	25.8389i	−1.75179	−	0.912403i
$803$	−24.5819	+	14.1924i	−0.867476	+	0.500837i
$804$	5.32519	+	0.941326i	0.187805	+	0.0331980i
$805$	−0.173525			−0.00611595
$806$	42.3225	+	0.414484i	1.49075	+	0.0145996i
$807$			0.274782i			0.00967280i
$808$	2.34952	−	17.7583i	0.0826560	−	0.624734i
$809$	8.46711	+	14.6655i	0.297688	+	0.515610i	0.975607	−	0.219526i	$-0.0704512\pi$
$809$	8.46711	+	14.6655i	0.297688	+	0.515610i	−0.677919	+	0.735137i	$0.737118\pi$
$810$	−1.29269	−	0.673285i	−0.0454206	−	0.0236568i
$811$	15.2854	+	15.2854i	0.536743	+	0.536743i	0.922571	−	0.385828i	$-0.126084\pi$
$811$	15.2854	+	15.2854i	0.536743	+	0.536743i	−0.385828	+	0.922571i	$0.626084\pi$
$812$	−1.29812	+	0.471846i	−0.0455550	+	0.0165586i
$813$	−3.88242	+	1.04029i	−0.136163	+	0.0364846i
$814$	−16.9860	+	18.5290i	−0.595359	+	0.649441i
$815$	−15.2888	−	8.82697i	−0.535542	−	0.309195i
$816$	−19.2055	+	16.0873i	−0.672326	+	0.563168i
$817$	−9.72845	−	2.60673i	−0.340355	−	0.0911979i
$818$	−0.826490	+	0.0359081i	−0.0288975	+	0.00125550i
$819$	0.230322	−	0.207028i	0.00804810	−	0.00723413i
$820$	−0.379938	−	4.36424i	−0.0132680	−	0.152406i
$821$	16.3470	+	4.38017i	0.570514	+	0.152869i	0.532532	−	0.846410i	$-0.321240\pi$
$821$	16.3470	+	4.38017i	0.570514	+	0.152869i	0.0379818	+	0.999278i	$0.487907\pi$
$822$	−7.95988	+	5.06861i	−0.277633	+	0.176788i
$823$	27.3031	−	47.2904i	0.951727	−	1.64844i	0.210042	−	0.977692i	$-0.432640\pi$
$823$	27.3031	−	47.2904i	0.951727	−	1.64844i	0.741685	−	0.670748i	$-0.234027\pi$
$824$	15.8352	+	12.1670i	0.551646	+	0.423856i
$825$	15.4981	−	4.15271i	0.539576	−	0.144579i
$826$	0.0599082	+	0.190147i	0.00208447	+	0.00661605i
$827$	−10.6439	+	10.6439i	−0.370126	+	0.370126i	−0.867523	−	0.497397i	$-0.834289\pi$
$827$	−10.6439	+	10.6439i	−0.370126	+	0.370126i	0.497397	+	0.867523i	$0.334289\pi$
$828$	3.55242	+	1.65837i	0.123455	+	0.0576324i
$829$	−12.6298	−	21.8754i	−0.438651	−	0.759765i	0.558935	−	0.829212i	$-0.311210\pi$
$829$	−12.6298	−	21.8754i	−0.438651	−	0.759765i	−0.997586	+	0.0694461i	$0.977877\pi$
$830$	−3.63902	−	0.807568i	−0.126312	−	0.0280311i
$831$	−0.447844			−0.0155355
$832$	8.97202	−	27.4136i	0.311049	−	0.950394i
$833$	43.7965			1.51746
$834$	−16.5644	−	3.67595i	−0.573577	−	0.127288i
$835$	5.44796	+	9.43614i	0.188534	+	0.326551i
$836$	55.6109	+	25.9608i	1.92334	+	0.897873i
$837$	−5.86935	+	5.86935i	−0.202875	+	0.202875i
$838$	9.41500	+	29.8829i	0.325236	+	1.03229i
$839$	4.70293	−	1.26015i	0.162363	−	0.0435051i	−0.176722	−	0.984261i	$-0.556549\pi$
$839$	4.70293	−	1.26015i	0.162363	−	0.0435051i	0.339085	+	0.940756i	$0.389883\pi$
$840$	−0.198543	−	0.152550i	−0.00685038	−	0.00526348i
$841$	17.8234	−	30.8710i	0.614598	−	1.06452i
$842$	30.1572	−	19.2032i	1.03929	−	0.661785i
$843$	3.04510	+	0.815932i	0.104879	+	0.0281022i
$844$	−2.92051	−	33.5470i	−0.100528	−	1.15474i
$845$	12.5000	+	4.82277i	0.430013	+	0.165908i
$846$	12.5625	−	0.545795i	0.431907	−	0.0187648i
$847$	0.464777	+	0.124537i	0.0159699	+	0.00427913i
$848$	35.6914	−	29.8966i	1.22565	−	1.02665i
$849$	−6.22131	−	3.59188i	−0.213515	−	0.123273i
$850$	23.5697	−	25.7108i	0.808435	−	0.881873i
$851$	8.25962	−	2.21316i	0.283136	−	0.0758661i
$852$	4.29157	−	1.55992i	0.147027	−	0.0534421i
$853$	−19.3267	−	19.3267i	−0.661733	−	0.661733i	0.294056	−	0.955788i	$-0.404995\pi$
$853$	−19.3267	−	19.3267i	−0.661733	−	0.661733i	−0.955788	+	0.294056i	$0.904995\pi$
$854$	1.03220	+	0.537608i	0.0353210	+	0.0183966i
$855$	3.88088	+	6.72189i	0.132723	+	0.229884i
$856$	−3.41807	+	25.8346i	−0.116827	+	0.883008i
$857$			28.4852i			0.973035i	0.873671	+	0.486517i	$0.161733\pi$
$857$			28.4852i			0.973035i	−0.873671	+	0.486517i	$0.838267\pi$
$858$	−10.5638	+	17.8902i	−0.360643	+	0.610760i
$859$	−17.0052			−0.580210			−0.290105	−	0.956995i	$-0.593690\pi$
$859$	−17.0052			−0.580210			−0.290105	+	0.956995i	$0.593690\pi$
$860$	−2.71449	−	0.479836i	−0.0925632	−	0.0163623i
$861$	−0.158091	+	0.0912736i	−0.00538771	+	0.00311060i
$862$	−19.9471	−	10.3892i	−0.679401	−	0.353859i
$863$	−3.29699	+	3.29699i	−0.112231	+	0.112231i	−0.760992	−	0.648761i	$-0.775287\pi$
$863$	−3.29699	+	3.29699i	−0.112231	+	0.112231i	0.648761	+	0.760992i	$0.275287\pi$
$864$	2.60667	+	5.02048i	0.0886808	+	0.170800i
$865$	−0.850507	−	3.17414i	−0.0289181	−	0.107924i
$866$	−7.53157	−	6.90438i	−0.255933	−	0.234620i
$867$	11.1141	−	19.2502i	0.377455	−	0.653771i
$868$	−1.16839	+	0.817369i	−0.0396577	+	0.0277433i
$869$	4.79694	−	17.9024i	0.162725	−	0.607299i
$870$	11.7079	−	0.508666i	0.396935	−	0.0172454i
$871$	7.25045	−	6.51715i	0.245672	−	0.220825i
$872$	45.7876	−	5.99814i	1.55057	−	0.203123i
$873$	−2.20161	+	8.21652i	−0.0745132	+	0.278087i
$874$	−11.2138	−	17.6104i	−0.379311	−	0.595680i
$875$	0.685203	+	0.395602i	0.0231641	+	0.0133738i
$876$	10.6692	+	8.96032i	0.360479	+	0.302741i
$877$	1.83642	+	6.85360i	0.0620114	+	0.231430i	0.989975	−	0.141240i	$-0.0451090\pi$
$877$	1.83642	+	6.85360i	0.0620114	+	0.231430i	−0.927964	+	0.372670i	$0.878442\pi$
$878$	9.32093	+	29.5843i	0.314566	+	0.998422i
$879$	9.24404	+	9.24404i	0.311794	+	0.311794i
$880$	15.7794	+	5.75854i	0.531923	+	0.194120i
$881$	42.2977	−	24.4206i	1.42505	−	0.822750i	0.428321	−	0.903626i	$-0.359105\pi$
$881$	42.2977	−	24.4206i	1.42505	−	0.822750i	0.996724	+	0.0808761i	$0.0257718\pi$
$882$	2.14245	−	9.65419i	0.0721401	−	0.325074i
$883$		−	14.5136i		−	0.488421i	−0.969722	−	0.244211i	$-0.921471\pi$
$883$		−	14.5136i		−	0.488421i	0.969722	−	0.244211i	$-0.0785288\pi$
$884$	1.51843	+	45.1393i	0.0510702	+	1.51820i
$885$		−	1.69148i		−	0.0568586i
$886$	38.9400	+	8.64154i	1.30822	+	0.290318i
$887$	−33.8365	+	19.5355i	−1.13612	+	0.655938i	−0.945466	−	0.325720i	$-0.894393\pi$
$887$	−33.8365	+	19.5355i	−1.13612	+	0.655938i	−0.190651	+	0.981658i	$0.561060\pi$
$888$	11.3961	+	4.72899i	0.382428	+	0.158695i
$889$	0.966596	+	0.966596i	0.0324186	+	0.0324186i
$890$	−8.89784	+	2.80339i	−0.298256	+	0.0939697i
$891$	−1.05457	−	3.93572i	−0.0353295	−	0.131852i
$892$	−8.23567	−	6.91656i	−0.275751	−	0.231584i
$893$	−57.9911	−	33.4812i	−1.94060	−	1.12041i
$894$	−20.4785	+	13.0401i	−0.684904	+	0.436126i
$895$	−4.25399	+	15.8761i	−0.142195	+	0.530679i
$896$	0.290827	+	0.927227i	0.00971584	+	0.0309765i
$897$	6.30008	−	3.20329i	0.210353	−	0.106955i
$898$	1.83635	+	42.2669i	0.0612797	+	1.41047i
$899$	17.2733	−	64.4648i	0.576096	−	2.15002i
$900$	−4.51451	−	6.45327i	−0.150484	−	0.215109i
$901$	−36.4508	+	63.1346i	−1.21435	+	2.10332i
$902$	8.27558	−	9.02733i	0.275547	−	0.300577i
$903$	0.0297298	+	0.110953i	0.000989347	+	0.00369229i
$904$	26.0096	−	10.7540i	0.865066	−	0.357671i
$905$	0.713577	−	0.713577i	0.0237201	−	0.0237201i
$906$	3.91843	−	7.52329i	0.130181	−	0.249945i
$907$	−4.33480	+	2.50270i	−0.143935	+	0.0831008i	−0.570238	−	0.821480i	$-0.693149\pi$
$907$	−4.33480	+	2.50270i	−0.143935	+	0.0831008i	0.426303	+	0.904580i	$0.359816\pi$
$908$	45.0667	+	7.96638i	1.49559	+	0.264374i
$909$	6.33321			0.210059
$910$	−0.437124	+	0.112551i	−0.0144905	+	0.00373102i
$911$		−	7.98936i		−	0.264699i	−0.991203	−	0.132350i	$-0.957748\pi$
$911$		−	7.98936i		−	0.264699i	0.991203	−	0.132350i	$-0.0422522\pi$
$912$	2.65123	−	30.0077i	0.0877909	−	0.993653i
$913$	−5.21025	−	9.02442i	−0.172434	−	0.298665i
$914$	−22.3115	+	42.8375i	−0.737997	+	1.41694i
$915$	−6.98223	−	6.98223i	−0.230825	−	0.230825i
$916$	−10.3308	−	28.4216i	−0.341340	−	0.939076i
$917$	0.944064	−	0.252961i	0.0311757	−	0.00835351i
$918$	−6.52920	−	5.98548i	−0.215496	−	0.197550i
$919$	−26.5337	−	15.3192i	−0.875266	−	0.505335i	−0.00617162	−	0.999981i	$-0.501965\pi$
$919$	−26.5337	−	15.3192i	−0.875266	−	0.505335i	−0.869095	+	0.494646i	$0.835298\pi$
$920$	−3.47563	−	4.53555i	−0.114588	−	0.149533i
$921$	22.8234	+	6.11550i	0.752055	+	0.201513i
$922$	2.15197	+	49.5315i	0.0708713	+	1.63123i
$923$	2.55050	−	7.82691i	0.0839506	−	0.257626i
$924$	−0.0607061	−	0.697313i	−0.00199709	−	0.0229399i
$925$	−16.5924	−	4.44593i	−0.545556	−	0.146181i
$926$	−22.9454	−	36.0341i	−0.754034	−	1.18416i
$927$	−3.53018	+	6.11445i	−0.115946	+	0.200825i
$928$	−38.3337	−	24.4790i	−1.25837	−	0.803562i
$929$	−23.2228	+	6.22253i	−0.761915	+	0.204154i	−0.618797	−	0.785551i	$-0.712380\pi$
$929$	−23.2228	+	6.22253i	−0.761915	+	0.204154i	−0.143118	+	0.989706i	$0.545713\pi$
$930$	11.5390	−	3.63552i	0.378379	−	0.119214i
$931$	−37.2380	+	37.2380i	−1.22042	+	1.22042i
$932$	−3.84737	+	8.24149i	−0.126025	+	0.269959i
$933$	5.02181	+	8.69803i	0.164407	+	0.284761i
$934$	4.07730	−	18.3729i	0.133413	−	0.601180i
$935$	−26.3014			−0.860149
$936$	10.0245	+	1.87343i	0.327660	+	0.0612350i
$937$	−29.7170			−0.970811			−0.485406	−	0.874289i	$-0.661328\pi$
$937$	−29.7170			−0.970811			−0.485406	+	0.874289i	$0.661328\pi$
$938$	−0.0711565	+	0.320641i	−0.00232334	+	0.0104693i
$939$	−1.31004	−	2.26905i	−0.0427514	−	0.0740476i
$940$	−16.6069	−	7.75259i	−0.541658	−	0.252862i
$941$	−16.3658	+	16.3658i	−0.533509	+	0.533509i	−0.921615	−	0.388106i	$-0.873130\pi$
$941$	−16.3658	+	16.3658i	−0.533509	+	0.533509i	0.388106	+	0.921615i	$0.373130\pi$
$942$	27.1408	−	8.55109i	0.884297	−	0.278610i
$943$	−4.02408	+	1.07825i	−0.131042	+	0.0351126i
$944$	−3.77007	+	5.37442i	−0.122705	+	0.174922i
$945$	0.0442616	−	0.0766633i	0.00143983	−	0.00249386i
$946$	−4.13909	−	6.50014i	−0.134573	−	0.211338i
$947$	6.10086	+	1.63472i	0.198251	+	0.0531213i	0.356578	−	0.934265i	$-0.383943\pi$
$947$	6.10086	+	1.63472i	0.198251	+	0.0531213i	−0.158327	+	0.987387i	$0.550610\pi$
$948$	−9.06314	+	0.789012i	−0.294357	+	0.0256259i
$949$	24.5730	−	5.20127i	0.797675	−	0.168840i
$950$	1.82044	+	41.9007i	0.0590628	+	1.35944i
$951$	−16.3946	−	4.39293i	−0.531633	−	0.142451i
$952$	−0.925518	−	1.20776i	−0.0299962	−	0.0391438i
$953$	19.8389	+	11.4540i	0.642645	+	0.371031i	0.785633	−	0.618693i	$-0.212338\pi$
$953$	19.8389	+	11.4540i	0.642645	+	0.371031i	−0.142988	+	0.989724i	$0.545671\pi$
$954$	12.1338	+	11.1234i	0.392848	+	0.360133i
$955$	21.5087	−	5.76323i	0.696004	−	0.186494i
$956$	−15.2069	+	5.52748i	−0.491826	+	0.178772i
$957$	23.1653	+	23.1653i	0.748829	+	0.748829i
$958$	19.3232	−	37.1001i	0.624304	−	1.19865i
$959$	−0.286570	−	0.496353i	−0.00925381	−	0.0160281i
$960$	0.0105911	−	8.24498i	0.000341827	−	0.266105i
$961$		−	37.8986i		−	1.22254i
$962$	19.3712	−	10.9324i	0.624552	−	0.352476i
$963$	−9.21351			−0.296901
$964$	1.54611	−	8.74650i	0.0497967	−	0.281706i
$965$	2.76605	−	1.59698i	0.0890424	−	0.0514086i
$966$	−0.109992	+	0.211182i	−0.00353894	+	0.00679468i
$967$	−22.2400	+	22.2400i	−0.715190	+	0.715190i	−0.967616	−	0.252426i	$-0.918772\pi$
$967$	−22.2400	+	22.2400i	−0.715190	+	0.715190i	0.252426	+	0.967616i	$0.418772\pi$
$968$	6.05416	+	14.6426i	0.194588	+	0.470632i
$969$	12.2083	+	45.5621i	0.392188	+	1.46367i
$970$	8.37806	−	9.13912i	0.269003	−	0.293440i
$971$	−28.4656	+	49.3039i	−0.913505	+	1.58224i	−0.104431	+	0.994532i	$0.533302\pi$
$971$	−28.4656	+	49.3039i	−0.913505	+	1.58224i	−0.809075	+	0.587706i	$0.800031\pi$
$972$	−1.63880	+	1.14645i	−0.0525644	+	0.0367724i
$973$	0.266718	−	0.995405i	0.00855059	−	0.0319112i
$974$	0.806841	+	18.5709i	0.0258528	+	0.595051i
$975$	−14.1779	−	0.755152i	−0.454056	−	0.0241842i
$976$	6.62255	+	37.7473i	0.211983	+	1.20826i
$977$	7.98517	−	29.8010i	0.255468	−	0.953420i	−0.712361	−	0.701813i	$-0.752374\pi$
$977$	7.98517	−	29.8010i	0.255468	−	0.953420i	0.967829	−	0.251607i	$-0.0809590\pi$
$978$	−20.4336	+	13.0115i	−0.653395	+	0.416062i
$979$	−22.5856	−	13.0398i	−0.721840	−	0.416754i
$980$	−9.26956	+	11.0374i	−0.296105	+	0.352578i
$981$	4.22566	+	15.7704i	0.134915	+	0.503509i
$982$	1.98524	−	0.625478i	0.0633517	−	0.0199598i
$983$	−7.41337	−	7.41337i	−0.236450	−	0.236450i	0.578929	−	0.815378i	$-0.303471\pi$
$983$	−7.41337	−	7.41337i	−0.236450	−	0.236450i	−0.815378	+	0.578929i	$0.803471\pi$
$984$	−5.55217	−	2.30396i	−0.176997	−	0.0734477i
$985$	7.18671	−	4.14925i	0.228988	−	0.132206i
$986$	69.5262	+	15.4292i	2.21416	+	0.491366i
$987$			0.763708i			0.0243091i
$988$	−39.6708	−	37.0887i	−1.26210	−	1.17995i
$989$			2.62147i			0.0833577i
$990$	−1.28662	+	5.79770i	−0.0408915	+	0.184263i
$991$	17.8332	−	10.2960i	0.566489	−	0.327063i	−0.189257	−	0.981928i	$-0.560608\pi$
$991$	17.8332	−	10.2960i	0.566489	−	0.327063i	0.755746	+	0.654865i	$0.227275\pi$
$992$	−44.7665	−	14.1675i	−1.42134	−	0.449819i
$993$	11.5594	+	11.5594i	0.366825	+	0.366825i
$994$	0.0833396	+	0.264517i	0.00264337	+	0.00838997i
$995$	−5.21006	−	19.4442i	−0.165170	−	0.616423i
$996$	−3.28948	+	3.91684i	−0.104231	+	0.124110i
$997$	25.9036	+	14.9554i	0.820374	+	0.473643i	0.850546	−	0.525901i	$-0.176272\pi$
$997$	25.9036	+	14.9554i	0.820374	+	0.473643i	−0.0301712	+	0.999545i	$0.509605\pi$
$998$	1.40992	+	2.21417i	0.0446302	+	0.0700884i
$999$	−1.12904	+	4.21362i	−0.0357211	+	0.133313i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.c.115.12	yes	48
3.2	odd	2		936.2.ed.c.739.1		48
8.3	odd	2	inner	312.2.bt.c.115.2	yes	48
13.6	odd	12	inner	312.2.bt.c.19.2	✓	48
24.11	even	2		936.2.ed.c.739.11		48
39.32	even	12		936.2.ed.c.19.11		48
104.19	even	12	inner	312.2.bt.c.19.12	yes	48
312.227	odd	12		936.2.ed.c.19.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.c.19.2	✓	48	13.6	odd	12	inner
312.2.bt.c.19.12	yes	48	104.19	even	12	inner
312.2.bt.c.115.2	yes	48	8.3	odd	2	inner
312.2.bt.c.115.12	yes	48	1.1	even	1	trivial
936.2.ed.c.19.1		48	312.227	odd	12
936.2.ed.c.19.11		48	39.32	even	12
936.2.ed.c.739.1		48	3.2	odd	2
936.2.ed.c.739.11		48	24.11	even	2

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

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	312.2.bt.c.115.12

Level	$312$
Weight	$2$
Character	312.115
Analytic conductor	$2.491$
Analytic rank	$0$
Dimension	$48$
Inner twists	$4$