LMFDB - Embedded newform 975.2.v.b.196.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(196,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("975.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.v (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.11
Character	$\chi$	$=$	975.196
Dual form			975.2.v.b.781.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.650087 - 2.00076i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.96240 - 1.42577i) q^{4} +(1.87342 - 1.22077i) q^{5} +(-1.70195 + 1.23654i) q^{6} +1.15752 q^{7} +(-0.724458 + 0.526350i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.650087 - 2.00076i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.96240 - 1.42577i) q^{4} +(1.87342 - 1.22077i) q^{5} +(-1.70195 + 1.23654i) q^{6} +1.15752 q^{7} +(-0.724458 + 0.526350i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.22459 - 4.54188i) q^{10} +(0.623427 - 1.91871i) q^{11} +(0.749571 + 2.30694i) q^{12} +(0.309017 + 0.951057i) q^{13} +(0.752487 - 2.31592i) q^{14} +(-2.23318 - 0.113544i) q^{15} +(-0.917003 - 2.82224i) q^{16} +(2.54812 - 1.85132i) q^{17} +2.10373 q^{18} +(3.57706 - 2.59889i) q^{19} +(-5.41695 - 0.275420i) q^{20} +(-0.936451 - 0.680372i) q^{21} +(-3.43360 - 2.49466i) q^{22} +(-2.34106 + 7.20505i) q^{23} +0.895480 q^{24} +(2.01943 - 4.57405i) q^{25} +2.10373 q^{26} +(0.309017 - 0.951057i) q^{27} +(-2.27152 - 1.65035i) q^{28} +(-1.72189 - 1.25102i) q^{29} +(-1.67894 + 4.39426i) q^{30} +(-1.65867 + 1.20509i) q^{31} -8.03373 q^{32} +(-1.63215 + 1.18583i) q^{33} +(-2.04755 - 6.30170i) q^{34} +(2.16852 - 1.41307i) q^{35} +(0.749571 - 2.30694i) q^{36} +(-2.96514 - 9.12576i) q^{37} +(-2.87435 - 8.84635i) q^{38} +(0.309017 - 0.951057i) q^{39} +(-0.714663 + 1.87047i) q^{40} +(2.38225 + 7.33181i) q^{41} +(-1.97004 + 1.43132i) q^{42} -2.51123 q^{43} +(-3.95905 + 2.87642i) q^{44} +(1.73994 + 1.40449i) q^{45} +(12.8937 + 9.36782i) q^{46} +(4.83543 + 3.51315i) q^{47} +(-0.917003 + 2.82224i) q^{48} -5.66015 q^{49} +(-7.83878 - 7.01392i) q^{50} -3.14965 q^{51} +(0.749571 - 2.30694i) q^{52} +(-3.74517 - 2.72103i) q^{53} +(-1.70195 - 1.23654i) q^{54} +(-1.17437 - 4.35562i) q^{55} +(-0.838573 + 0.609259i) q^{56} -4.42149 q^{57} +(-3.62238 + 2.63181i) q^{58} +(0.438326 + 1.34903i) q^{59} +(4.22052 + 3.40682i) q^{60} +(-4.16216 + 12.8098i) q^{61} +(1.33283 + 4.10202i) q^{62} +(0.357693 + 1.10086i) q^{63} +(-3.38862 + 10.4291i) q^{64} +(1.73994 + 1.40449i) q^{65} +(1.31152 + 4.03644i) q^{66} +(-1.04244 + 0.757380i) q^{67} -7.63999 q^{68} +(6.12898 - 4.45297i) q^{69} +(-1.41748 - 5.25731i) q^{70} +(12.5715 + 9.13373i) q^{71} +(-0.724458 - 0.526350i) q^{72} +(3.43326 - 10.5665i) q^{73} -20.1861 q^{74} +(-4.32231 + 2.51349i) q^{75} -10.7250 q^{76} +(0.721628 - 2.22094i) q^{77} +(-1.70195 - 1.23654i) q^{78} +(7.14059 + 5.18794i) q^{79} +(-5.16325 - 4.16781i) q^{80} +(-0.809017 + 0.587785i) q^{81} +16.2179 q^{82} +(-13.5119 + 9.81698i) q^{83} +(0.867642 + 2.67033i) q^{84} +(2.51367 - 6.57897i) q^{85} +(-1.63252 + 5.02438i) q^{86} +(0.657702 + 2.02420i) q^{87} +(0.558266 + 1.71817i) q^{88} +(-1.04591 + 3.21899i) q^{89} +(3.94117 - 2.56817i) q^{90} +(0.357693 + 1.10086i) q^{91} +(14.8668 - 10.8014i) q^{92} +2.05023 q^{93} +(10.1724 - 7.39070i) q^{94} +(3.52870 - 9.23559i) q^{95} +(6.49943 + 4.72211i) q^{96} +(1.93450 + 1.40550i) q^{97} +(-3.67959 + 11.3246i) q^{98} +2.01745 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + q^{2} - 13 q^{3} - 17 q^{4} + 3 q^{5} + q^{6} - 20 q^{7} - 6 q^{8} - 13 q^{9}+O(q^{10}) $ 52 * q + q^2 - 13 * q^3 - 17 * q^4 + 3 * q^5 + q^6 - 20 * q^7 - 6 * q^8 - 13 * q^9	\( 52 q + q^{2} - 13 q^{3} - 17 q^{4} + 3 q^{5} + q^{6} - 20 q^{7} - 6 q^{8} - 13 q^{9} + 4 q^{10} - 8 q^{11} - 7 q^{12} - 13 q^{13} - 10 q^{14} + 3 q^{15} - 9 q^{16} + q^{17} - 4 q^{18} + 20 q^{19} - 11 q^{20} + 5 q^{21} + 4 q^{22} - 15 q^{23} - 6 q^{24} + 23 q^{25} - 4 q^{26} - 13 q^{27} + 37 q^{28} - 5 q^{29} - 26 q^{30} + 26 q^{31} - 156 q^{32} + 12 q^{33} + 34 q^{34} - 12 q^{35} - 7 q^{36} + 32 q^{37} + 18 q^{38} - 13 q^{39} - 18 q^{40} + 49 q^{41} + 10 q^{42} - 76 q^{43} + 47 q^{44} - 2 q^{45} + 24 q^{46} + 22 q^{47} - 9 q^{48} - 52 q^{49} + 39 q^{50} + 6 q^{51} - 7 q^{52} + 25 q^{53} + q^{54} + 11 q^{55} + 45 q^{56} - 40 q^{57} - 13 q^{58} - 15 q^{59} + 19 q^{60} + 26 q^{61} + 62 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} - 11 q^{66} + 8 q^{67} + 62 q^{68} + 10 q^{69} + q^{70} + 9 q^{71} - 6 q^{72} + 46 q^{73} + 56 q^{74} + 18 q^{75} - 82 q^{76} + 49 q^{77} + q^{78} + 26 q^{79} + 60 q^{80} - 13 q^{81} - 126 q^{82} - 50 q^{83} - 8 q^{84} + 48 q^{85} + 24 q^{86} + 20 q^{87} - 62 q^{88} + 34 q^{89} - q^{90} + 5 q^{91} - 10 q^{92} - 104 q^{93} + q^{94} - 53 q^{95} + 24 q^{96} + 6 q^{97} - 47 q^{98} - 8 q^{99}+O(q^{100}) \) 52 * q + q^2 - 13 * q^3 - 17 * q^4 + 3 * q^5 + q^6 - 20 * q^7 - 6 * q^8 - 13 * q^9 + 4 * q^10 - 8 * q^11 - 7 * q^12 - 13 * q^13 - 10 * q^14 + 3 * q^15 - 9 * q^16 + q^17 - 4 * q^18 + 20 * q^19 - 11 * q^20 + 5 * q^21 + 4 * q^22 - 15 * q^23 - 6 * q^24 + 23 * q^25 - 4 * q^26 - 13 * q^27 + 37 * q^28 - 5 * q^29 - 26 * q^30 + 26 * q^31 - 156 * q^32 + 12 * q^33 + 34 * q^34 - 12 * q^35 - 7 * q^36 + 32 * q^37 + 18 * q^38 - 13 * q^39 - 18 * q^40 + 49 * q^41 + 10 * q^42 - 76 * q^43 + 47 * q^44 - 2 * q^45 + 24 * q^46 + 22 * q^47 - 9 * q^48 - 52 * q^49 + 39 * q^50 + 6 * q^51 - 7 * q^52 + 25 * q^53 + q^54 + 11 * q^55 + 45 * q^56 - 40 * q^57 - 13 * q^58 - 15 * q^59 + 19 * q^60 + 26 * q^61 + 62 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 - 11 * q^66 + 8 * q^67 + 62 * q^68 + 10 * q^69 + q^70 + 9 * q^71 - 6 * q^72 + 46 * q^73 + 56 * q^74 + 18 * q^75 - 82 * q^76 + 49 * q^77 + q^78 + 26 * q^79 + 60 * q^80 - 13 * q^81 - 126 * q^82 - 50 * q^83 - 8 * q^84 + 48 * q^85 + 24 * q^86 + 20 * q^87 - 62 * q^88 + 34 * q^89 - q^90 + 5 * q^91 - 10 * q^92 - 104 * q^93 + q^94 - 53 * q^95 + 24 * q^96 + 6 * q^97 - 47 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.650087	−	2.00076i	0.459681	−	1.41475i	−0.405870	−	0.913931i	$-0.633031\pi$
$2$	0.650087	−	2.00076i	0.459681	−	1.41475i	0.865551	−	0.500822i	$-0.166969\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−1.96240	−	1.42577i	−0.981202	−	0.712885i
$5$	1.87342	−	1.22077i	0.837820	−	0.545946i
$5$	1.87342	−	1.22077i	0.837820	−	0.545946i
$6$	−1.70195	+	1.23654i	−0.694818	+	0.504815i
$7$	1.15752			0.437501			0.218750	−	0.975781i	$-0.429802\pi$
$7$	1.15752			0.437501			0.218750	+	0.975781i	$0.429802\pi$
$8$	−0.724458	+	0.526350i	−0.256135	+	0.186093i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.22459	−	4.54188i	−0.387249	−	1.43627i
$11$	0.623427	−	1.91871i	0.187970	−	0.578513i	−0.812017	−	0.583634i	$-0.801630\pi$
$11$	0.623427	−	1.91871i	0.187970	−	0.578513i	0.999987	+	0.00512123i	$0.00163014\pi$
$12$	0.749571	+	2.30694i	0.216383	+	0.665957i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	0.752487	−	2.31592i	0.201111	−	0.618955i
$15$	−2.23318	−	0.113544i	−0.576605	−	0.0293170i
$16$	−0.917003	−	2.82224i	−0.229251	−	0.705561i
$17$	2.54812	−	1.85132i	0.618010	−	0.449010i	−0.234216	−	0.972185i	$-0.575252\pi$
$17$	2.54812	−	1.85132i	0.618010	−	0.449010i	0.852226	+	0.523174i	$0.175252\pi$
$18$	2.10373			0.495853
$19$	3.57706	−	2.59889i	0.820634	−	0.596225i	−0.0962602	−	0.995356i	$-0.530688\pi$
$19$	3.57706	−	2.59889i	0.820634	−	0.596225i	0.916894	+	0.399131i	$0.130688\pi$
$20$	−5.41695	−	0.275420i	−1.21127	−	0.0615859i
$21$	−0.936451	−	0.680372i	−0.204350	−	0.148469i
$22$	−3.43360	−	2.49466i	−0.732047	−	0.531863i
$23$	−2.34106	+	7.20505i	−0.488145	+	1.50236i	0.339228	+	0.940704i	$0.389834\pi$
$23$	−2.34106	+	7.20505i	−0.488145	+	1.50236i	−0.827373	+	0.561652i	$0.810166\pi$
$24$	0.895480			0.182789
$25$	2.01943	−	4.57405i	0.403885	−	0.914810i
$26$	2.10373			0.412575
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−2.27152	−	1.65035i	−0.429276	−	0.311887i
$29$	−1.72189	−	1.25102i	−0.319746	−	0.232309i	0.416321	−	0.909218i	$-0.363319\pi$
$29$	−1.72189	−	1.25102i	−0.319746	−	0.232309i	−0.736067	+	0.676908i	$0.763319\pi$
$30$	−1.67894	+	4.39426i	−0.306531	+	0.802278i
$31$	−1.65867	+	1.20509i	−0.297906	+	0.216441i	−0.726690	−	0.686966i	$-0.758942\pi$
$31$	−1.65867	+	1.20509i	−0.297906	+	0.216441i	0.428784	+	0.903407i	$0.358942\pi$
$32$	−8.03373			−1.42018
$33$	−1.63215	+	1.18583i	−0.284121	+	0.206426i
$34$	−2.04755	−	6.30170i	−0.351151	−	1.08073i
$35$	2.16852	−	1.41307i	0.366547	−	0.238852i
$36$	0.749571	−	2.30694i	0.124929	−	0.384491i
$37$	−2.96514	−	9.12576i	−0.487466	−	1.50027i	−0.828377	−	0.560171i	$-0.810736\pi$
$37$	−2.96514	−	9.12576i	−0.487466	−	1.50027i	0.340911	−	0.940096i	$-0.389264\pi$
$38$	−2.87435	−	8.84635i	−0.466282	−	1.43507i
$39$	0.309017	−	0.951057i	0.0494823	−	0.152291i
$40$	−0.714663	+	1.87047i	−0.112998	+	0.295748i
$41$	2.38225	+	7.33181i	0.372045	+	1.14504i	0.945451	+	0.325765i	$0.105622\pi$
$41$	2.38225	+	7.33181i	0.372045	+	1.14504i	−0.573406	+	0.819271i	$0.694378\pi$
$42$	−1.97004	+	1.43132i	−0.303983	+	0.220857i
$43$	−2.51123			−0.382959			−0.191480	−	0.981497i	$-0.561329\pi$
$43$	−2.51123			−0.382959			−0.191480	+	0.981497i	$0.561329\pi$
$44$	−3.95905	+	2.87642i	−0.596850	+	0.433637i
$45$	1.73994	+	1.40449i	0.259375	+	0.209369i
$46$	12.8937	+	9.36782i	1.90107	+	1.38121i
$47$	4.83543	+	3.51315i	0.705320	+	0.512445i	0.881661	−	0.471884i	$-0.156426\pi$
$47$	4.83543	+	3.51315i	0.705320	+	0.512445i	−0.176341	+	0.984329i	$0.556426\pi$
$48$	−0.917003	+	2.82224i	−0.132358	+	0.407356i
$49$	−5.66015			−0.808593
$50$	−7.83878	−	7.01392i	−1.10857	−	0.991919i
$51$	−3.14965			−0.441039
$52$	0.749571	−	2.30694i	0.103947	−	0.319915i
$53$	−3.74517	−	2.72103i	−0.514439	−	0.373762i	0.300066	−	0.953918i	$-0.402991\pi$
$53$	−3.74517	−	2.72103i	−0.514439	−	0.373762i	−0.814505	+	0.580157i	$0.802991\pi$
$54$	−1.70195	−	1.23654i	−0.231606	−	0.168272i
$55$	−1.17437	−	4.35562i	−0.158352	−	0.587312i
$56$	−0.838573	+	0.609259i	−0.112059	+	0.0814157i
$57$	−4.42149			−0.585640
$58$	−3.62238	+	2.63181i	−0.475641	+	0.345574i
$59$	0.438326	+	1.34903i	0.0570652	+	0.175628i	0.975526	−	0.219883i	$-0.0705675\pi$
$59$	0.438326	+	1.34903i	0.0570652	+	0.175628i	−0.918461	+	0.395511i	$0.870567\pi$
$60$	4.22052	+	3.40682i	0.544866	+	0.439819i
$61$	−4.16216	+	12.8098i	−0.532909	+	1.64013i	0.215214	+	0.976567i	$0.430955\pi$
$61$	−4.16216	+	12.8098i	−0.532909	+	1.64013i	−0.748123	+	0.663560i	$0.769045\pi$
$62$	1.33283	+	4.10202i	0.169269	+	0.520957i
$63$	0.357693	+	1.10086i	0.0450650	+	0.138696i
$64$	−3.38862	+	10.4291i	−0.423577	+	1.30364i
$65$	1.73994	+	1.40449i	0.215813	+	0.174206i
$66$	1.31152	+	4.03644i	0.161437	+	0.496852i
$67$	−1.04244	+	0.757380i	−0.127355	+	0.0925287i	−0.649639	−	0.760243i	$-0.725080\pi$
$67$	−1.04244	+	0.757380i	−0.127355	+	0.0925287i	0.522284	+	0.852771i	$0.325080\pi$
$68$	−7.63999			−0.926485
$69$	6.12898	−	4.45297i	0.737843	−	0.536074i
$70$	−1.41748	−	5.25731i	−0.169422	−	0.628369i
$71$	12.5715	+	9.13373i	1.49196	+	1.08397i	0.973449	+	0.228905i	$0.0735144\pi$
$71$	12.5715	+	9.13373i	1.49196	+	1.08397i	0.518513	+	0.855070i	$0.326486\pi$
$72$	−0.724458	−	0.526350i	−0.0853782	−	0.0620309i
$73$	3.43326	−	10.5665i	0.401833	−	1.23671i	−0.521678	−	0.853142i	$-0.674694\pi$
$73$	3.43326	−	10.5665i	0.401833	−	1.23671i	0.923511	−	0.383572i	$-0.125306\pi$
$74$	−20.1861			−2.34658
$75$	−4.32231	+	2.51349i	−0.499097	+	0.290233i
$76$	−10.7250			−1.23025
$77$	0.721628	−	2.22094i	0.0822371	−	0.253100i
$78$	−1.70195	−	1.23654i	−0.192708	−	0.140010i
$79$	7.14059	+	5.18794i	0.803379	+	0.583689i	0.911904	−	0.410405i	$-0.134613\pi$
$79$	7.14059	+	5.18794i	0.803379	+	0.583689i	−0.108524	+	0.994094i	$0.534613\pi$
$80$	−5.16325	−	4.16781i	−0.577269	−	0.465975i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	16.2179			1.79096
$83$	−13.5119	+	9.81698i	−1.48312	+	1.07755i	−0.506591	+	0.862186i	$0.669095\pi$
$83$	−13.5119	+	9.81698i	−1.48312	+	1.07755i	−0.976533	+	0.215367i	$0.930905\pi$
$84$	0.867642	+	2.67033i	0.0946675	+	0.291357i
$85$	2.51367	−	6.57897i	0.272646	−	0.713590i
$86$	−1.63252	+	5.02438i	−0.176039	+	0.541793i
$87$	0.657702	+	2.02420i	0.0705130	+	0.217017i
$88$	0.558266	+	1.71817i	0.0595114	+	0.183157i
$89$	−1.04591	+	3.21899i	−0.110867	+	0.341213i	−0.991063	−	0.133398i	$-0.957411\pi$
$89$	−1.04591	+	3.21899i	−0.110867	+	0.341213i	0.880196	+	0.474611i	$0.157411\pi$
$90$	3.94117	−	2.56817i	0.415436	−	0.270709i
$91$	0.357693	+	1.10086i	0.0374964	+	0.115402i
$92$	14.8668	−	10.8014i	1.54998	−	1.12612i
$93$	2.05023			0.212599
$94$	10.1724	−	7.39070i	1.04921	−	0.762292i
$95$	3.52870	−	9.23559i	0.362037	−	0.947552i
$96$	6.49943	+	4.72211i	0.663345	+	0.481948i
$97$	1.93450	+	1.40550i	0.196419	+	0.142706i	0.681648	−	0.731681i	$-0.261264\pi$
$97$	1.93450	+	1.40550i	0.196419	+	0.142706i	−0.485229	+	0.874387i	$0.661264\pi$
$98$	−3.67959	+	11.3246i	−0.371695	+	1.14396i
$99$	2.01745			0.202762
$100$	−10.4845	+	6.09689i	−1.04845	+	0.609689i
$101$	−2.81432			−0.280035			−0.140018	−	0.990149i	$-0.544716\pi$
$101$	−2.81432			−0.280035			−0.140018	+	0.990149i	$0.544716\pi$
$102$	−2.04755	+	6.30170i	−0.202737	+	0.623961i
$103$	8.36022	+	6.07406i	0.823757	+	0.598495i	0.917786	−	0.397075i	$-0.129975\pi$
$103$	8.36022	+	6.07406i	0.823757	+	0.598495i	−0.0940292	+	0.995569i	$0.529975\pi$
$104$	−0.724458	−	0.526350i	−0.0710390	−	0.0516128i
$105$	−2.58495	−	0.131430i	−0.252265	−	0.0128262i
$106$	−7.87881	+	5.72429i	−0.765258	+	0.555992i
$107$	−18.4603			−1.78462			−0.892312	−	0.451418i	$-0.850918\pi$
$107$	−18.4603			−1.78462			−0.892312	+	0.451418i	$0.850918\pi$
$108$	−1.96240	+	1.42577i	−0.188832	+	0.137195i
$109$	−0.657896	−	2.02480i	−0.0630150	−	0.193940i	0.914593	−	0.404377i	$-0.132512\pi$
$109$	−0.657896	−	2.02480i	−0.0630150	−	0.193940i	−0.977608	+	0.210436i	$0.932512\pi$
$110$	−9.47800	−	0.481901i	−0.903692	−	0.0459475i
$111$	−2.96514	+	9.12576i	−0.281439	+	0.866179i
$112$	−1.06145	−	3.26680i	−0.100297	−	0.308683i
$113$	−4.57279	−	14.0736i	−0.430172	−	1.32393i	−0.897954	−	0.440090i	$-0.854947\pi$
$113$	−4.57279	−	14.0736i	−0.430172	−	1.32393i	0.467782	−	0.883844i	$-0.345053\pi$
$114$	−2.87435	+	8.84635i	−0.269208	+	0.828536i
$115$	4.40993	+	16.3560i	0.411228	+	1.52521i
$116$	1.59536	+	4.91002i	0.148126	+	0.455884i
$117$	−0.809017	+	0.587785i	−0.0747936	+	0.0543408i
$118$	2.98403			0.274703
$119$	2.94949	−	2.14293i	0.270380	−	0.196442i
$120$	1.67761	−	1.09318i	0.153144	−	0.0997930i
$121$	5.60640	+	4.07329i	0.509672	+	0.370299i
$122$	22.9236	+	16.6550i	2.07541	+	1.50787i
$123$	2.38225	−	7.33181i	0.214800	−	0.661087i
$124$	4.97316			0.446603
$125$	−1.80063	−	11.0344i	−0.161054	−	0.986946i
$126$	2.43510			0.216936
$127$	6.17226	−	18.9963i	0.547700	−	1.68565i	−0.166783	−	0.985994i	$-0.553338\pi$
$127$	6.17226	−	18.9963i	0.547700	−	1.68565i	0.714483	−	0.699653i	$-0.246662\pi$
$128$	5.66440	+	4.11543i	0.500667	+	0.363756i
$129$	2.03163	+	1.47607i	0.178875	+	0.129960i
$130$	3.94117	−	2.56817i	0.345663	−	0.225244i
$131$	9.85414	−	7.15946i	0.860961	−	0.625525i	−0.0671855	−	0.997741i	$-0.521402\pi$
$131$	9.85414	−	7.15946i	0.860961	−	0.625525i	0.928146	+	0.372216i	$0.121402\pi$
$132$	4.89366			0.425938
$133$	4.14051	−	3.00826i	0.359028	−	0.260849i
$134$	0.837658	+	2.57804i	0.0723626	+	0.222709i
$135$	−0.582105	−	2.15897i	−0.0500996	−	0.185815i
$136$	−0.871566	+	2.68240i	−0.0747361	+	0.230014i
$137$	2.68764	+	8.27169i	0.229620	+	0.706698i	0.997790	+	0.0664516i	$0.0211678\pi$
$137$	2.68764	+	8.27169i	0.229620	+	0.706698i	−0.768169	+	0.640247i	$0.778832\pi$
$138$	−4.92495	−	15.1575i	−0.419240	−	1.29029i
$139$	4.58939	−	14.1247i	0.389267	−	1.19804i	−0.544071	−	0.839039i	$-0.683118\pi$
$139$	4.58939	−	14.1247i	0.389267	−	1.19804i	0.933337	−	0.359000i	$-0.116882\pi$
$140$	−6.27022	−	0.318804i	−0.529930	−	0.0269438i
$141$	−1.84697	−	5.68439i	−0.155543	−	0.478712i
$142$	26.4470	−	19.2149i	2.21938	−	1.61248i
$143$	2.01745			0.168708
$144$	2.40074	−	1.74424i	0.200062	−	0.145354i
$145$	−4.75304	−	0.241664i	−0.394718	−	0.0200691i
$146$	−18.9091	−	13.7383i	−1.56493	−	1.13699i
$147$	4.57916	+	3.32695i	0.377683	+	0.274403i
$148$	−7.19243	+	22.1360i	−0.591214	+	1.81957i
$149$	9.09164			0.744816			0.372408	−	0.928069i	$-0.378532\pi$
$149$	9.09164			0.744816			0.372408	+	0.928069i	$0.378532\pi$
$150$	2.21903	+	10.2819i	0.181183	+	0.839514i
$151$	20.3923			1.65950			0.829751	−	0.558134i	$-0.188482\pi$
$151$	20.3923			1.65950			0.829751	+	0.558134i	$0.188482\pi$
$152$	−1.22351	+	3.76557i	−0.0992395	+	0.305428i
$153$	2.54812	+	1.85132i	0.206003	+	0.149670i
$154$	−3.97446	−	2.88761i	−0.320271	−	0.232690i
$155$	−1.63624	+	4.28251i	−0.131426	+	0.343979i
$156$	−1.96240	+	1.42577i	−0.157118	+	0.114153i
$157$	−10.9373			−0.872888			−0.436444	−	0.899731i	$-0.643762\pi$
$157$	−10.9373			−0.872888			−0.436444	+	0.899731i	$0.643762\pi$
$158$	15.0218	−	10.9140i	1.19507	−	0.868272i
$159$	1.43053	+	4.40271i	0.113448	+	0.349158i
$160$	−15.0506	+	9.80736i	−1.18985	+	0.775340i
$161$	−2.70982	+	8.33997i	−0.213564	+	0.657282i
$162$	0.650087	+	2.00076i	0.0510757	+	0.157195i
$163$	3.68539	+	11.3425i	0.288662	+	0.888410i	0.985277	+	0.170965i	$0.0546885\pi$
$163$	3.68539	+	11.3425i	0.288662	+	0.888410i	−0.696615	+	0.717445i	$0.745311\pi$
$164$	5.77853	−	17.7845i	0.451228	−	1.38874i
$165$	−1.61009	+	4.21405i	−0.125345	+	0.328063i
$166$	10.8575	+	33.4160i	0.842707	+	2.59359i
$167$	3.27017	−	2.37592i	0.253053	−	0.183854i	−0.454026	−	0.890989i	$-0.650013\pi$
$167$	3.27017	−	2.37592i	0.253053	−	0.183854i	0.707079	+	0.707135i	$0.250013\pi$
$168$	1.03653			0.0799703
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−11.5289	−	9.30616i	−0.884223	−	0.713750i
$171$	3.57706	+	2.59889i	0.273545	+	0.198742i
$172$	4.92805	+	3.58044i	0.375760	+	0.273006i
$173$	1.85838	−	5.71950i	0.141290	−	0.434845i	−0.855225	−	0.518256i	$-0.826581\pi$
$173$	1.85838	−	5.71950i	0.141290	−	0.434845i	0.996515	+	0.0834109i	$0.0265814\pi$
$174$	4.47750			0.339439
$175$	2.33752	−	5.29454i	0.176700	−	0.400230i
$176$	−5.98676			−0.451269
$177$	0.438326	−	1.34903i	0.0329466	−	0.101399i
$178$	5.76051	+	4.18525i	0.431768	+	0.313698i
$179$	0.267978	+	0.194698i	0.0200297	+	0.0145524i	0.597755	−	0.801679i	$-0.296060\pi$
$179$	0.267978	+	0.194698i	0.0200297	+	0.0145524i	−0.577725	+	0.816231i	$0.696060\pi$
$180$	−1.41199	−	5.23694i	−0.105244	−	0.390338i
$181$	−1.32010	+	0.959108i	−0.0981221	+	0.0712899i	−0.635765	−	0.771883i	$-0.719315\pi$
$181$	−1.32010	+	0.959108i	−0.0981221	+	0.0712899i	0.537642	+	0.843173i	$0.319315\pi$
$182$	2.43510			0.180502
$183$	10.8967	−	7.91689i	0.805505	−	0.585233i
$184$	−2.09637	−	6.45197i	−0.154547	−	0.475646i
$185$	−16.6954	−	13.4767i	−1.22747	−	0.990823i
$186$	1.33283	−	4.10202i	0.0977276	−	0.300775i
$187$	−1.96358	−	6.04327i	−0.143591	−	0.441927i
$188$	−4.48013	−	13.7884i	−0.326747	−	1.00562i
$189$	0.357693	−	1.10086i	0.0260183	−	0.0800761i
$190$	−16.1843	−	13.0640i	−1.17413	−	0.947764i
$191$	−0.443625	−	1.36534i	−0.0320996	−	0.0987923i	0.933723	−	0.357996i	$-0.116540\pi$
$191$	−0.443625	−	1.36534i	−0.0320996	−	0.0987923i	−0.965823	+	0.259204i	$0.916540\pi$
$192$	8.87152	−	6.44554i	0.640247	−	0.465167i
$193$	17.5838			1.26571			0.632857	−	0.774269i	$-0.281882\pi$
$193$	17.5838			1.26571			0.632857	+	0.774269i	$0.281882\pi$
$194$	4.06966	−	2.95678i	0.292184	−	0.212284i
$195$	−0.582105	−	2.15897i	−0.0416854	−	0.154607i
$196$	11.1075	+	8.07007i	0.793393	+	0.576434i
$197$	0.660018	+	0.479531i	0.0470244	+	0.0341652i	0.611049	−	0.791593i	$-0.290748\pi$
$197$	0.660018	+	0.479531i	0.0470244	+	0.0341652i	−0.564025	+	0.825758i	$0.690748\pi$
$198$	1.31152	−	4.03644i	0.0932056	−	0.286857i
$199$	4.55323			0.322770			0.161385	−	0.986892i	$-0.448404\pi$
$199$	4.55323			0.322770			0.161385	+	0.986892i	$0.448404\pi$
$200$	0.944558	+	4.37663i	0.0667904	+	0.309475i
$201$	1.28853			0.0908860
$202$	−1.82955	+	5.63078i	−0.128727	+	0.396180i
$203$	−1.99311	−	1.44808i	−0.139889	−	0.101635i
$204$	6.18088	+	4.49067i	0.432748	+	0.314410i
$205$	13.4134	+	10.8274i	0.936835	+	0.756218i
$206$	17.5876	−	12.7782i	1.22539	−	0.890296i
$207$	−7.57584			−0.526557
$208$	2.40074	−	1.74424i	0.166462	−	0.120941i
$209$	−2.75648	−	8.48356i	−0.190669	−	0.586820i
$210$	−1.94340	+	5.08643i	−0.134107	+	0.350997i
$211$	−7.90490	+	24.3288i	−0.544196	+	1.67486i	0.178699	+	0.983904i	$0.442811\pi$
$211$	−7.90490	+	24.3288i	−0.544196	+	1.67486i	−0.722895	+	0.690958i	$0.757189\pi$
$212$	3.46998	+	10.6795i	0.238319	+	0.733471i
$213$	−4.80188	−	14.7787i	−0.329020	−	1.01262i
$214$	−12.0008	+	36.9347i	−0.820358	+	2.52480i
$215$	−4.70460	+	3.06564i	−0.320851	+	0.209075i
$216$	0.276718	+	0.851652i	0.0188283	+	0.0579476i
$217$	−1.91994	+	1.39492i	−0.130334	+	0.0946931i
$218$	−4.47882			−0.303344
$219$	−8.98839	+	6.53045i	−0.607379	+	0.441287i
$220$	−3.90553	+	10.2219i	−0.263311	+	0.689158i
$221$	2.54812	+	1.85132i	0.171405	+	0.124533i
$222$	16.3309	+	11.8651i	1.09606	+	0.796332i
$223$	3.90316	−	12.0127i	0.261375	−	0.804430i	−0.731131	−	0.682237i	$-0.761007\pi$
$223$	3.90316	−	12.0127i	0.261375	−	0.804430i	0.992506	−	0.122193i	$-0.0389928\pi$
$224$	−9.29919			−0.621328
$225$	4.97422	+	0.507131i	0.331614	+	0.0338087i
$226$	−31.1307			−2.07078
$227$	−7.04858	+	21.6933i	−0.467831	+	1.43983i	0.387557	+	0.921846i	$0.373319\pi$
$227$	−7.04858	+	21.6933i	−0.467831	+	1.43983i	−0.855387	+	0.517989i	$0.826681\pi$
$228$	8.67674	+	6.30402i	0.574631	+	0.417494i
$229$	−3.09001	−	2.24502i	−0.204194	−	0.148355i	0.480989	−	0.876727i	$-0.340278\pi$
$229$	−3.09001	−	2.24502i	−0.204194	−	0.148355i	−0.685183	+	0.728371i	$0.740278\pi$
$230$	35.5913	+	1.80961i	2.34682	+	0.119322i
$231$	−1.88925	+	1.37262i	−0.124303	+	0.0903116i
$232$	1.90591			0.125129
$233$	1.29180	−	0.938545i	0.0846284	−	0.0614861i	−0.544667	−	0.838653i	$-0.683344\pi$
$233$	1.29180	−	0.938545i	0.0846284	−	0.0614861i	0.629295	+	0.777167i	$0.283344\pi$
$234$	0.650087	+	2.00076i	0.0424975	+	0.130794i
$235$	13.3476	+	0.678645i	0.870699	+	0.0442699i
$236$	1.06323	−	3.27229i	0.0692104	−	0.213008i
$237$	−2.72746	−	8.39427i	−0.177168	−	0.545266i
$238$	−2.37007	−	7.29433i	−0.153629	−	0.472821i
$239$	−3.82545	+	11.7735i	−0.247448	+	0.761566i	0.747776	+	0.663951i	$0.231122\pi$
$239$	−3.82545	+	11.7735i	−0.247448	+	0.761566i	−0.995224	+	0.0976155i	$0.968878\pi$
$240$	1.72739	+	6.40671i	0.111502	+	0.413551i
$241$	−3.56971	−	10.9864i	−0.229945	−	0.707698i	−0.997752	−	0.0670167i	$-0.978652\pi$
$241$	−3.56971	−	10.9864i	−0.229945	−	0.707698i	0.767807	−	0.640681i	$-0.221348\pi$
$242$	11.7943	−	8.56908i	0.758168	−	0.550841i
$243$	1.00000			0.0641500
$244$	26.4316	−	19.2037i	1.69211	−	1.22939i
$245$	−10.6039	+	6.90976i	−0.677456	+	0.441448i
$246$	−13.1205	−	9.53263i	−0.836535	−	0.607778i
$247$	3.57706	+	2.59889i	0.227603	+	0.165363i
$248$	0.567336	−	1.74608i	0.0360259	−	0.110876i
$249$	16.7016			1.05842
$250$	−23.2478	−	3.57067i	−1.47032	−	0.225829i
$251$	−7.62233			−0.481117			−0.240559	−	0.970635i	$-0.577331\pi$
$251$	−7.62233			−0.481117			−0.240559	+	0.970635i	$0.577331\pi$
$252$	0.867642	−	2.67033i	0.0546563	−	0.168215i
$253$	12.3649	+	8.98365i	0.777376	+	0.564797i
$254$	−33.9945	−	24.6985i	−2.13301	−	1.54972i
$255$	−5.90062	+	3.84501i	−0.369511	+	0.240784i
$256$	−5.82669	+	4.23334i	−0.364168	+	0.264584i
$257$	10.9935			0.685757			0.342879	−	0.939380i	$-0.388598\pi$
$257$	10.9935			0.685757			0.342879	+	0.939380i	$0.388598\pi$
$258$	4.27399	−	3.10524i	0.266087	−	0.193324i
$259$	−3.43220	−	10.5632i	−0.213267	−	0.656367i
$260$	−1.41199	−	5.23694i	−0.0875679	−	0.324781i
$261$	0.657702	−	2.02420i	0.0407107	−	0.125295i
$262$	−7.91832	−	24.3701i	−0.489195	−	1.50559i
$263$	5.00430	+	15.4017i	0.308579	+	0.949707i	0.978318	+	0.207111i	$0.0664060\pi$
$263$	5.00430	+	15.4017i	0.308579	+	0.949707i	−0.669739	+	0.742597i	$0.733594\pi$
$264$	0.558266	−	1.71817i	0.0343589	−	0.105746i
$265$	−10.3380	−	0.525629i	−0.635061	−	0.0322891i
$266$	−3.32711	−	10.2398i	−0.203998	−	0.627843i
$267$	2.73824	−	1.98945i	0.167578	−	0.121752i
$268$	3.12554			0.190923
$269$	12.6240	−	9.17186i	0.769698	−	0.559218i	−0.132172	−	0.991227i	$-0.542195\pi$
$269$	12.6240	−	9.17186i	0.769698	−	0.559218i	0.901869	+	0.432009i	$0.142195\pi$
$270$	−4.69801	−	0.238866i	−0.285912	−	0.0145369i
$271$	4.67363	+	3.39559i	0.283903	+	0.206268i	0.720618	−	0.693332i	$-0.243858\pi$
$271$	4.67363	+	3.39559i	0.283903	+	0.206268i	−0.436715	+	0.899600i	$0.643858\pi$
$272$	−7.56150	−	5.49375i	−0.458483	−	0.333108i
$273$	0.357693	−	1.10086i	0.0216485	−	0.0666274i
$274$	18.2969			1.10536
$275$	−7.51731	−	6.72628i	−0.453311	−	0.405610i
$276$	−18.3764			−1.10613
$277$	7.51965	−	23.1431i	0.451812	−	1.39053i	−0.423026	−	0.906118i	$-0.639032\pi$
$277$	7.51965	−	23.1431i	0.451812	−	1.39053i	0.874837	−	0.484417i	$-0.160968\pi$
$278$	−25.2766	−	18.3645i	−1.51599	−	1.10143i
$279$	−1.65867	−	1.20509i	−0.0993019	−	0.0721471i
$280$	−0.827235	+	2.16511i	−0.0494368	+	0.129390i
$281$	3.16493	−	2.29946i	0.188804	−	0.137174i	−0.489368	−	0.872077i	$-0.662773\pi$
$281$	3.16493	−	2.29946i	0.188804	−	0.137174i	0.678172	+	0.734903i	$0.262773\pi$
$282$	−12.5738			−0.748759
$283$	−3.28457	+	2.38638i	−0.195247	+	0.141856i	−0.681114	−	0.732178i	$-0.738504\pi$
$283$	−3.28457	+	2.38638i	−0.195247	+	0.141856i	0.485866	+	0.874033i	$0.338504\pi$
$284$	−11.6478	−	35.8481i	−0.691167	−	2.12719i
$285$	−8.28332	+	5.39763i	−0.490661	+	0.319728i
$286$	1.31152	−	4.03644i	0.0775518	−	0.238680i
$287$	2.75749	+	8.48669i	0.162770	+	0.500954i
$288$	−2.48256	−	7.64053i	−0.146286	−	0.450223i
$289$	−2.18775	+	6.73321i	−0.128691	+	0.396071i
$290$	−3.57340	+	9.35259i	−0.209837	+	0.549203i
$291$	−0.738913	−	2.27414i	−0.0433158	−	0.133312i
$292$	−21.8028	+	15.8407i	−1.27591	+	0.927005i
$293$	20.2609			1.18366			0.591828	−	0.806064i	$-0.298406\pi$
$293$	20.2609			1.18366			0.591828	+	0.806064i	$0.298406\pi$
$294$	9.63330	−	6.99900i	0.561825	−	0.408190i
$295$	2.46803	+	1.99220i	0.143694	+	0.115991i
$296$	6.95146	+	5.05053i	0.404046	+	0.293556i
$297$	−1.63215	−	1.18583i	−0.0947071	−	0.0688088i
$298$	5.91036	−	18.1902i	0.342378	−	1.05373i
$299$	−7.57584			−0.438122
$300$	12.0658	+	1.23013i	0.696618	+	0.0710215i
$301$	−2.90680			−0.167545
$302$	13.2568	−	40.8002i	0.762842	−	2.34778i
$303$	2.27683	+	1.65421i	0.130801	+	0.0950321i
$304$	−10.6149	−	7.71215i	−0.608804	−	0.442322i
$305$	7.84038	+	29.0792i	0.448939	+	1.66507i
$306$	5.36055	−	3.89466i	0.306442	−	0.222643i
$307$	−7.20945			−0.411465			−0.205733	−	0.978608i	$-0.565958\pi$
$307$	−7.20945			−0.411465			−0.205733	+	0.978608i	$0.565958\pi$
$308$	−4.58267	+	3.32951i	−0.261122	+	0.189716i
$309$	−3.19332	−	9.82803i	−0.181662	−	0.559097i
$310$	7.50458	+	6.05774i	0.426232	+	0.344056i
$311$	−5.50665	+	16.9477i	−0.312254	+	0.961018i	0.664616	+	0.747185i	$0.268595\pi$
$311$	−5.50665	+	16.9477i	−0.312254	+	0.961018i	−0.976870	+	0.213833i	$0.931405\pi$
$312$	0.276718	+	0.851652i	0.0156661	+	0.0482153i
$313$	−5.92242	−	18.2273i	−0.334755	−	1.03027i	−0.966843	−	0.255373i	$-0.917802\pi$
$313$	−5.92242	−	18.2273i	−0.334755	−	1.03027i	0.632088	−	0.774897i	$-0.282198\pi$
$314$	−7.11017	+	21.8828i	−0.401250	+	1.23492i
$315$	2.01402	+	1.62572i	0.113477	+	0.0915991i
$316$	−6.61591	−	20.3617i	−0.372174	−	1.14543i
$317$	−14.5449	+	10.5675i	−0.816921	+	0.593528i	−0.915829	−	0.401568i	$-0.868465\pi$
$317$	−14.5449	+	10.5675i	−0.816921	+	0.593528i	0.0989076	+	0.995097i	$0.468465\pi$
$318$	9.73875			0.546122
$319$	−3.47382	+	2.52388i	−0.194497	+	0.141310i
$320$	6.38324	+	23.6748i	0.356834	+	1.32346i
$321$	14.9347	+	10.8507i	0.833574	+	0.605627i
$322$	14.9247	+	10.8434i	0.831720	+	0.604280i
$323$	4.30341	−	13.2445i	0.239448	−	0.736946i
$324$	2.42566			0.134759
$325$	4.97422	+	0.507131i	0.275920	+	0.0281305i
$326$	25.0894			1.38957
$327$	−0.657896	+	2.02480i	−0.0363817	+	0.111971i
$328$	−5.58493	−	4.05769i	−0.308376	−	0.224049i
$329$	5.59710	+	4.06653i	0.308578	+	0.224195i
$330$	7.38461	+	5.96090i	0.406509	+	0.328137i
$331$	−17.0637	+	12.3975i	−0.937908	+	0.681430i	−0.947916	−	0.318520i	$-0.896814\pi$
$331$	−17.0637	+	12.3975i	−0.937908	+	0.681430i	0.0100085	+	0.999950i	$0.496814\pi$
$332$	40.5126			2.22342
$333$	7.76284	−	5.64003i	0.425401	−	0.309072i
$334$	−2.62775	−	8.08739i	−0.143784	−	0.442522i
$335$	−1.02835	+	2.69148i	−0.0561847	+	0.147051i
$336$	−1.06145	+	3.26680i	−0.0579067	+	0.178218i
$337$	−5.11746	−	15.7499i	−0.278766	−	0.857954i	−0.988198	−	0.153180i	$-0.951049\pi$
$337$	−5.11746	−	15.7499i	−0.278766	−	0.857954i	0.709432	−	0.704774i	$-0.248951\pi$
$338$	0.650087	+	2.00076i	0.0353601	+	0.108827i
$339$	−4.57279	+	14.0736i	−0.248360	+	0.764373i
$340$	−14.3129	+	9.32669i	−0.776228	+	0.505811i
$341$	1.27817	+	3.93379i	0.0692166	+	0.213027i
$342$	7.52515	−	5.46734i	0.406914	−	0.295640i
$343$	−14.6543			−0.791260
$344$	1.81928	−	1.32179i	0.0980891	−	0.0712659i
$345$	6.04611	−	15.8244i	0.325512	−	0.851956i
$346$	−10.2352	−	7.43634i	−0.550250	−	0.399780i
$347$	11.8578	+	8.61523i	0.636562	+	0.462490i	0.858668	−	0.512533i	$-0.171293\pi$
$347$	11.8578	+	8.61523i	0.636562	+	0.462490i	−0.222105	+	0.975023i	$0.571293\pi$
$348$	1.59536	−	4.91002i	0.0855205	−	0.263205i
$349$	20.9610			1.12202			0.561009	−	0.827810i	$-0.310413\pi$
$349$	20.9610			1.12202			0.561009	+	0.827810i	$0.310413\pi$
$350$	−9.07353	−	8.11874i	−0.485000	−	0.433965i
$351$	1.00000			0.0533761
$352$	−5.00845	+	15.4144i	−0.266951	+	0.821591i
$353$	5.27879	+	3.83527i	0.280962	+	0.204131i	0.719337	−	0.694662i	$-0.244446\pi$
$353$	5.27879	+	3.83527i	0.280962	+	0.204131i	−0.438375	+	0.898792i	$0.644446\pi$
$354$	−2.41413	−	1.75397i	−0.128310	−	0.0932225i
$355$	34.7019	+	1.76439i	1.84179	+	0.0936441i
$356$	6.64205	−	4.82573i	0.352028	−	0.255763i
$357$	−3.64577			−0.192955
$358$	0.563753	−	0.409591i	0.0297953	−	0.0216475i
$359$	6.23963	+	19.2036i	0.329315	+	1.01353i	0.969455	+	0.245270i	$0.0788765\pi$
$359$	6.23963	+	19.2036i	0.329315	+	1.01353i	−0.640140	+	0.768259i	$0.721124\pi$
$360$	−1.99977	−	0.101677i	−0.105397	−	0.00535883i
$361$	0.169824	−	0.522665i	0.00893811	−	0.0275087i
$362$	1.06077	+	3.26471i	0.0557527	+	0.171589i
$363$	−2.14145	−	6.59071i	−0.112397	−	0.345923i
$364$	0.867642	−	2.67033i	0.0454768	−	0.139963i
$365$	−6.46734	−	23.9867i	−0.338516	−	1.25552i
$366$	−8.75604	−	26.9483i	−0.457685	−	1.40861i
$367$	−6.12654	+	4.45119i	−0.319803	+	0.232350i	−0.736091	−	0.676882i	$-0.763331\pi$
$367$	−6.12654	+	4.45119i	−0.319803	+	0.232350i	0.416289	+	0.909232i	$0.363331\pi$
$368$	22.4812			1.17191
$369$	−6.23681	+	4.53131i	−0.324675	+	0.235890i
$370$	−37.8171	+	24.6426i	−1.96602	+	1.28111i
$371$	−4.33510	−	3.14963i	−0.225067	−	0.163521i
$372$	−4.02337	−	2.92315i	−0.208602	−	0.151558i
$373$	−7.84229	+	24.1361i	−0.406058	+	1.24972i	0.513950	+	0.857820i	$0.328182\pi$
$373$	−7.84229	+	24.1361i	−0.406058	+	1.24972i	−0.920008	+	0.391899i	$0.871818\pi$
$374$	−13.3676			−0.691224
$375$	−5.02911	+	9.98539i	−0.259702	+	0.515643i
$376$	−5.35221			−0.276019
$377$	0.657702	−	2.02420i	0.0338734	−	0.104252i
$378$	−1.97004	−	1.43132i	−0.101328	−	0.0736189i
$379$	1.39981	+	1.01702i	0.0719033	+	0.0522408i	0.623156	−	0.782097i	$-0.285850\pi$
$379$	1.39981	+	1.01702i	0.0719033	+	0.0522408i	−0.551253	+	0.834338i	$0.685850\pi$
$380$	−20.0925	+	13.0928i	−1.03073	+	0.671649i
$381$	−16.1592	+	11.7403i	−0.827861	+	0.601476i
$382$	−3.02011			−0.154522
$383$	−18.1193	+	13.1645i	−0.925855	+	0.672673i	−0.944975	−	0.327144i	$-0.893914\pi$
$383$	−18.1193	+	13.1645i	−0.925855	+	0.672673i	0.0191191	+	0.999817i	$0.493914\pi$
$384$	−2.16361	−	6.65890i	−0.110411	−	0.339811i
$385$	−1.35935	−	5.04171i	−0.0692790	−	0.256949i
$386$	11.4310	−	35.1811i	0.581824	−	1.79067i
$387$	−0.776013	−	2.38832i	−0.0394470	−	0.121405i
$388$	−1.79235	−	5.51630i	−0.0909930	−	0.280048i
$389$	−10.0831	+	31.0326i	−0.511234	+	1.57342i	0.278797	+	0.960350i	$0.410064\pi$
$389$	−10.0831	+	31.0326i	−0.511234	+	1.57342i	−0.790031	+	0.613066i	$0.789936\pi$
$390$	−4.69801	−	0.238866i	−0.237893	−	0.0120955i
$391$	7.37352	+	22.6934i	0.372895	+	1.14765i
$392$	4.10054	−	2.97922i	0.207109	−	0.150473i
$393$	−12.1804			−0.614420
$394$	1.38850	−	1.00880i	0.0699515	−	0.0508227i
$395$	19.7106	+	1.00217i	0.991750	+	0.0504247i
$396$	−3.95905	−	2.87642i	−0.198950	−	0.144546i
$397$	−16.7051	−	12.1370i	−0.838406	−	0.609138i	0.0835188	−	0.996506i	$-0.473384\pi$
$397$	−16.7051	−	12.1370i	−0.838406	−	0.609138i	−0.921925	+	0.387368i	$0.873384\pi$
$398$	2.96000	−	9.10994i	0.148371	−	0.456640i
$399$	−5.11795			−0.256218
$400$	−14.7609	−	1.50490i	−0.738045	−	0.0752451i
$401$	9.83105			0.490939			0.245470	−	0.969404i	$-0.421058\pi$
$401$	9.83105			0.490939			0.245470	+	0.969404i	$0.421058\pi$
$402$	0.837658	−	2.57804i	0.0417786	−	0.128581i
$403$	−1.65867	−	1.20509i	−0.0826242	−	0.0600300i
$404$	5.52282	+	4.01257i	0.274771	+	0.199633i
$405$	−0.798079	+	2.08880i	−0.0396568	+	0.103793i
$406$	−4.19296	+	3.04637i	−0.208093	+	0.151189i
$407$	−19.3583			−0.959553
$408$	2.28179	−	1.65782i	0.112965	−	0.0820741i
$409$	0.304550	+	0.937309i	0.0150590	+	0.0463469i	0.958304	−	0.285752i	$-0.0922433\pi$
$409$	0.304550	+	0.937309i	0.0150590	+	0.0463469i	−0.943245	+	0.332099i	$0.892243\pi$
$410$	30.3829	−	19.7983i	1.50051	−	0.977770i
$411$	2.68764	−	8.27169i	0.132571	−	0.408012i
$412$	−7.74592	−	23.8395i	−0.381614	−	1.17449i
$413$	0.507370	+	1.56152i	0.0249660	+	0.0768376i
$414$	−4.92495	+	15.1575i	−0.242048	+	0.744948i
$415$	−13.3292	+	34.8863i	−0.654306	+	1.71250i
$416$	−2.48256	−	7.64053i	−0.121717	−	0.374608i
$417$	−12.0152	+	8.72953i	−0.588385	+	0.427487i
$418$	−18.7655			−0.917852
$419$	−0.948231	+	0.688930i	−0.0463241	+	0.0336564i	−0.610706	−	0.791857i	$-0.709114\pi$
$419$	−0.948231	+	0.688930i	−0.0463241	+	0.0336564i	0.564382	+	0.825514i	$0.309114\pi$
$420$	4.88532	+	3.94346i	0.238379	+	0.192421i
$421$	27.1214	+	19.7048i	1.32182	+	0.960355i	0.999908	+	0.0135843i	$0.00432417\pi$
$421$	27.1214	+	19.7048i	1.32182	+	0.960355i	0.321908	+	0.946771i	$0.395676\pi$
$422$	43.5372	+	31.6316i	2.11936	+	1.53980i
$423$	−1.84697	+	5.68439i	−0.0898028	+	0.276384i
$424$	4.14543			0.201320
$425$	−3.32227	−	15.3938i	−0.161154	−	0.746710i
$426$	−32.6903			−1.58385
$427$	−4.81777	+	14.8276i	−0.233148	+	0.717556i
$428$	36.2266	+	26.3201i	1.75108	+	1.27223i
$429$	−1.63215	−	1.18583i	−0.0788011	−	0.0572523i
$430$	3.07523	+	11.4057i	0.148301	+	0.550033i
$431$	20.7732	−	15.0926i	1.00061	−	0.726985i	0.0383904	−	0.999263i	$-0.487777\pi$
$431$	20.7732	−	15.0926i	1.00061	−	0.726985i	0.962219	+	0.272278i	$0.0877769\pi$
$432$	−2.96748			−0.142773
$433$	−1.53850	+	1.11779i	−0.0739357	+	0.0537174i	−0.624139	−	0.781313i	$-0.714550\pi$
$433$	−1.53850	+	1.11779i	−0.0739357	+	0.0537174i	0.550203	+	0.835031i	$0.314550\pi$
$434$	1.54277	+	4.74816i	0.0740553	+	0.227919i
$435$	3.70324	+	2.98927i	0.177557	+	0.143325i
$436$	−1.59583	+	4.91147i	−0.0764266	+	0.235217i
$437$	10.3510	+	31.8570i	0.495155	+	1.52393i
$438$	7.22264	+	22.2290i	0.345111	+	1.06214i
$439$	−2.73602	+	8.42059i	−0.130583	+	0.401893i	−0.994877	−	0.101094i	$-0.967766\pi$
$439$	−2.73602	+	8.42059i	−0.130583	+	0.401893i	0.864294	+	0.502987i	$0.167766\pi$
$440$	3.14336	+	2.53734i	0.149854	+	0.120963i
$441$	−1.74908	−	5.38313i	−0.0832897	−	0.256339i
$442$	5.36055	−	3.89466i	0.254975	−	0.185250i
$443$	4.41491			0.209759			0.104879	−	0.994485i	$-0.466554\pi$
$443$	4.41491			0.209759			0.104879	+	0.994485i	$0.466554\pi$
$444$	18.8300	−	13.6808i	0.893634	−	0.649263i
$445$	1.97022	+	7.30736i	0.0933974	+	0.346402i
$446$	−21.4972	−	15.6186i	−1.01792	−	0.739563i
$447$	−7.35529	−	5.34393i	−0.347893	−	0.252759i
$448$	−3.92239	+	12.0719i	−0.185315	+	0.570342i
$449$	−30.1935			−1.42492			−0.712460	−	0.701712i	$-0.752419\pi$
$449$	−30.1935			−1.42492			−0.712460	+	0.701712i	$0.752419\pi$
$450$	4.24832	−	9.62254i	0.200268	−	0.453611i
$451$	15.5528			0.732352
$452$	−11.0921	+	34.1378i	−0.521726	+	1.60571i
$453$	−16.4977	−	11.9863i	−0.775130	−	0.563165i
$454$	38.8209	+	28.2051i	1.82196	+	1.32373i
$455$	2.01402	+	1.62572i	0.0944185	+	0.0762151i
$456$	3.20318	−	2.32725i	0.150003	−	0.108983i
$457$	−28.8044			−1.34741			−0.673707	−	0.738999i	$-0.735299\pi$
$457$	−28.8044			−1.34741			−0.673707	+	0.738999i	$0.735299\pi$
$458$	−6.50054	+	4.72292i	−0.303750	+	0.220687i
$459$	−0.973295	−	2.99549i	−0.0454295	−	0.139818i
$460$	14.6658	−	38.3846i	0.683798	−	1.78969i
$461$	10.5856	−	32.5792i	0.493022	−	1.51737i	−0.326995	−	0.945026i	$-0.606036\pi$
$461$	10.5856	−	32.5792i	0.493022	−	1.51737i	0.820017	−	0.572339i	$-0.193964\pi$
$462$	1.51811	+	4.67225i	0.0706287	+	0.217373i
$463$	−2.15780	−	6.64101i	−0.100281	−	0.308634i	0.888313	−	0.459239i	$-0.151878\pi$
$463$	−2.15780	−	6.64101i	−0.100281	−	0.308634i	−0.988594	+	0.150605i	$0.951878\pi$
$464$	−1.95172	+	6.00678i	−0.0906063	+	0.278858i
$465$	3.84094	−	2.50286i	0.178119	−	0.116067i
$466$	−1.03803	−	3.19471i	−0.0480856	−	0.147992i
$467$	−2.23260	+	1.62208i	−0.103313	+	0.0750610i	−0.638242	−	0.769836i	$-0.720338\pi$
$467$	−2.23260	+	1.62208i	−0.103313	+	0.0750610i	0.534930	+	0.844897i	$0.320338\pi$
$468$	2.42566			0.112126
$469$	−1.20665	+	0.876680i	−0.0557178	+	0.0404813i
$470$	10.0349	−	26.2641i	0.462875	−	1.21147i
$471$	8.84843	+	6.42876i	0.407714	+	0.296222i
$472$	−1.02761	−	0.746602i	−0.0472995	−	0.0343651i
$473$	−1.56557	+	4.81833i	−0.0719850	+	0.221547i
$474$	−18.5680			−0.852858
$475$	−4.66382	−	21.6099i	−0.213991	−	0.991530i
$476$	−8.84342			−0.405337
$477$	1.43053	−	4.40271i	0.0654994	−	0.201586i
$478$	21.0692	+	15.3076i	0.963681	+	0.700155i
$479$	−29.6608	−	21.5498i	−1.35524	−	0.984637i	−0.998732	−	0.0503428i	$-0.983969\pi$
$479$	−29.6608	−	21.5498i	−1.35524	−	0.984637i	−0.356504	−	0.934294i	$-0.616031\pi$
$480$	17.9408	+	0.912185i	0.818882	+	0.0416353i
$481$	7.76284	−	5.64003i	0.353955	−	0.257163i
$482$	−24.3019			−1.10692
$483$	7.09440	−	5.15439i	0.322807	−	0.234533i
$484$	−5.19444	−	15.9869i	−0.236111	−	0.726675i
$485$	5.33992	+	0.271504i	0.242473	+	0.0123284i
$486$	0.650087	−	2.00076i	0.0294886	−	0.0907564i
$487$	3.40880	+	10.4912i	0.154468	+	0.475402i	0.998107	−	0.0615086i	$-0.0195912\pi$
$487$	3.40880	+	10.4912i	0.154468	+	0.475402i	−0.843639	+	0.536911i	$0.819591\pi$
$488$	−3.72713	−	11.4709i	−0.168719	−	0.519264i
$489$	3.68539	−	11.3425i	0.166659	−	0.512924i
$490$	6.93136	+	25.7078i	0.313127	+	1.16136i
$491$	6.08879	+	18.7394i	0.274783	+	0.845696i	0.989277	+	0.146054i	$0.0466572\pi$
$491$	6.08879	+	18.7394i	0.274783	+	0.845696i	−0.714494	+	0.699642i	$0.753343\pi$
$492$	−15.1284	+	10.9914i	−0.682041	+	0.495532i
$493$	−6.70361			−0.301915
$494$	7.52515	−	5.46734i	0.338573	−	0.245987i
$495$	3.77954	−	2.46285i	0.169878	−	0.110697i
$496$	4.92207	+	3.57610i	0.221008	+	0.160571i
$497$	14.5517	+	10.5724i	0.652734	+	0.474239i
$498$	10.8575	−	33.4160i	0.486537	−	1.49741i
$499$	−11.4866			−0.514212			−0.257106	−	0.966383i	$-0.582769\pi$
$499$	−11.4866			−0.514212			−0.257106	+	0.966383i	$0.582769\pi$
$500$	−12.1989	+	24.2212i	−0.545552	+	1.08321i
$501$	−4.04215			−0.180590
$502$	−4.95518	+	15.2505i	−0.221161	+	0.680662i
$503$	23.3189	+	16.9422i	1.03974	+	0.755414i	0.970234	−	0.242168i	$-0.0778584\pi$
$503$	23.3189	+	16.9422i	1.03974	+	0.755414i	0.0695038	+	0.997582i	$0.477858\pi$
$504$	−0.838573	−	0.609259i	−0.0373530	−	0.0271386i
$505$	−5.27241	+	3.43564i	−0.234619	+	0.152884i
$506$	26.0124	−	18.8991i	1.15639	−	0.840169i
$507$	1.00000			0.0444116
$508$	−39.1968	+	28.4781i	−1.73908	+	1.26351i
$509$	1.34114	+	4.12761i	0.0594450	+	0.182953i	0.976370	−	0.216108i	$-0.0693363\pi$
$509$	1.34114	+	4.12761i	0.0594450	+	0.182953i	−0.916925	+	0.399061i	$0.869336\pi$
$510$	3.85702	+	14.3053i	0.170792	+	0.633451i
$511$	3.97406	−	12.2309i	0.175802	−	0.541063i
$512$	9.00927	+	27.7277i	0.398157	+	1.22540i
$513$	−1.36632	−	4.20509i	−0.0603243	−	0.185659i
$514$	7.14675	−	21.9954i	0.315230	−	0.970177i
$515$	23.0773	+	1.17334i	1.01691	+	0.0517037i
$516$	−1.88235	−	5.79327i	−0.0828657	−	0.255034i
$517$	9.75525	−	7.08760i	0.429035	−	0.311712i
$518$	−23.3657			−1.02663
$519$	−4.86529	+	3.53484i	−0.213563	+	0.155162i
$520$	−1.99977	−	0.101677i	−0.0876957	−	0.00445881i
$521$	2.50838	+	1.82244i	0.109894	+	0.0798426i	0.641375	−	0.767228i	$-0.278364\pi$
$521$	2.50838	+	1.82244i	0.109894	+	0.0798426i	−0.531481	+	0.847070i	$0.678364\pi$
$522$	−3.62238	−	2.63181i	−0.158547	−	0.115191i
$523$	11.4427	−	35.2170i	0.500355	−	1.53993i	−0.308087	−	0.951358i	$-0.599689\pi$
$523$	11.4427	−	35.2170i	0.500355	−	1.53993i	0.808442	−	0.588576i	$-0.200311\pi$
$524$	−29.5455			−1.29070
$525$	−5.00315	+	2.90941i	−0.218355	+	0.126977i
$526$	34.0683			1.48545
$527$	−1.99548	+	6.14144i	−0.0869243	+	0.267526i
$528$	4.84339	+	3.51893i	0.210781	+	0.153142i
$529$	−27.8248	−	20.2159i	−1.20977	−	0.878951i
$530$	−7.77229	+	20.3423i	−0.337607	+	0.883611i
$531$	−1.14755	+	0.833745i	−0.0497995	+	0.0361815i
$532$	−12.4144			−0.538234
$533$	−6.23681	+	4.53131i	−0.270146	+	0.196273i
$534$	−2.20032	−	6.77188i	−0.0952171	−	0.293048i
$535$	−34.5840	+	22.5358i	−1.49519	+	0.974309i
$536$	0.356560	−	1.09738i	0.0154011	−	0.0473996i
$537$	−0.102359	−	0.315028i	−0.00441710	−	0.0135944i
$538$	−10.1440	−	31.2201i	−0.437340	−	1.34599i
$539$	−3.52869	+	10.8602i	−0.151992	+	0.467782i
$540$	−1.93587	+	5.06672i	−0.0833066	+	0.218037i
$541$	1.91328	+	5.88846i	0.0822581	+	0.253165i	0.983724	−	0.179685i	$-0.0575080\pi$
$541$	1.91328	+	5.88846i	0.0822581	+	0.253165i	−0.901466	+	0.432850i	$0.857508\pi$
$542$	9.83205	−	7.14340i	0.422323	−	0.306835i
$543$	1.63173			0.0700243
$544$	−20.4709	+	14.8730i	−0.877683	+	0.637674i
$545$	−3.70433	−	2.99016i	−0.158676	−	0.128084i
$546$	−1.97004	−	1.43132i	−0.0843098	−	0.0612547i
$547$	20.5736	+	14.9476i	0.879665	+	0.639114i	0.933163	−	0.359454i	$-0.117037\pi$
$547$	20.5736	+	14.9476i	0.879665	+	0.639114i	−0.0534978	+	0.998568i	$0.517037\pi$
$548$	6.51930	−	20.0643i	0.278491	−	0.857106i
$549$	−13.4690			−0.574844
$550$	−18.3446	+	10.6677i	−0.782216	+	0.454872i
$551$	−9.41056			−0.400903
$552$	−2.09637	+	6.45197i	−0.0892276	+	0.274614i
$553$	8.26536	+	6.00513i	0.351479	+	0.255364i
$554$	−41.4154	−	30.0901i	−1.75957	−	1.27840i
$555$	5.58552	+	20.7162i	0.237092	+	0.879353i
$556$	−29.1448	+	21.1749i	−1.23601	+	0.898016i
$557$	−39.7767			−1.68539			−0.842696	−	0.538390i	$-0.819033\pi$
$557$	−39.7767			−1.68539			−0.842696	+	0.538390i	$0.819033\pi$
$558$	−3.48939	+	2.53519i	−0.147717	+	0.107323i
$559$	−0.776013	−	2.38832i	−0.0328219	−	0.101015i
$560$	−5.97656	−	4.82431i	−0.252556	−	0.203864i
$561$	−1.96358	+	6.04327i	−0.0829022	+	0.255147i
$562$	−2.54318	−	7.82712i	−0.107278	−	0.330167i
$563$	11.5036	+	35.4045i	0.484820	+	1.49212i	0.832241	+	0.554414i	$0.187057\pi$
$563$	11.5036	+	35.4045i	0.484820	+	1.49212i	−0.347421	+	0.937709i	$0.612943\pi$
$564$	−4.48013	+	13.7884i	−0.188647	+	0.580597i
$565$	−25.7475	−	20.7835i	−1.08320	−	0.874368i
$566$	2.63932	+	8.12300i	0.110939	+	0.341435i
$567$	−0.936451	+	0.680372i	−0.0393273	+	0.0285729i
$568$	−13.9151			−0.583863
$569$	7.38430	−	5.36501i	0.309566	−	0.224913i	−0.422144	−	0.906529i	$-0.638722\pi$
$569$	7.38430	−	5.36501i	0.309566	−	0.224913i	0.731710	+	0.681616i	$0.238722\pi$
$570$	5.41450	+	20.0819i	0.226789	+	0.841138i
$571$	−10.7717	−	7.82613i	−0.450783	−	0.327513i	0.339122	−	0.940743i	$-0.389870\pi$
$571$	−10.7717	−	7.82613i	−0.450783	−	0.327513i	−0.789905	+	0.613229i	$0.789870\pi$
$572$	−3.95905	−	2.87642i	−0.165536	−	0.120269i
$573$	−0.443625	+	1.36534i	−0.0185327	+	0.0570378i
$574$	18.7725			0.783548
$575$	28.2286	+	25.2582i	1.17722	+	1.05334i
$576$	−10.9658			−0.456908
$577$	−3.29860	+	10.1521i	−0.137323	+	0.422636i	−0.995944	−	0.0899747i	$-0.971321\pi$
$577$	−3.29860	+	10.1521i	−0.137323	+	0.422636i	0.858621	+	0.512610i	$0.171321\pi$
$578$	12.0493	+	8.75434i	0.501186	+	0.364133i
$579$	−14.2256	−	10.3355i	−0.591197	−	0.429530i
$580$	8.98282	+	7.25098i	0.372991	+	0.301080i
$581$	−15.6403	+	11.3633i	−0.648868	+	0.471430i
$582$	−5.03037			−0.208516
$583$	−7.55570	+	5.48954i	−0.312925	+	0.227353i
$584$	3.07442	+	9.46208i	0.127220	+	0.391544i
$585$	−0.798079	+	2.08880i	−0.0329965	+	0.0863611i
$586$	13.1714	−	40.5373i	0.544104	−	1.67458i
$587$	−10.7593	−	33.1139i	−0.444086	−	1.36676i	−0.883483	−	0.468463i	$-0.844808\pi$
$587$	−10.7593	−	33.1139i	−0.444086	−	1.36676i	0.439397	−	0.898293i	$-0.355192\pi$
$588$	−4.24269	−	13.0577i	−0.174966	−	0.538488i
$589$	−2.80126	+	8.62138i	−0.115424	+	0.355238i
$590$	5.59036	−	3.64283i	0.230151	−	0.149973i
$591$	−0.252105	−	0.775898i	−0.0103702	−	0.0319162i
$592$	−23.0361	+	16.7367i	−0.946778	+	0.687874i
$593$	25.6884			1.05490			0.527448	−	0.849587i	$-0.323149\pi$
$593$	25.6884			1.05490			0.527448	+	0.849587i	$0.323149\pi$
$594$	−3.43360	+	2.49466i	−0.140882	+	0.102357i
$595$	2.90961	−	7.61528i	0.119283	−	0.312196i
$596$	−17.8415	−	12.9626i	−0.730815	−	0.530968i
$597$	−3.68364	−	2.67632i	−0.150761	−	0.109535i
$598$	−4.92495	+	15.1575i	−0.201396	+	0.619834i
$599$	20.6866			0.845233			0.422617	−	0.906308i	$-0.361112\pi$
$599$	20.6866			0.845233			0.422617	+	0.906308i	$0.361112\pi$
$600$	1.80836	−	4.09597i	0.0738258	−	0.167217i
$601$	12.8835			0.525530			0.262765	−	0.964860i	$-0.415366\pi$
$601$	12.8835			0.525530			0.262765	+	0.964860i	$0.415366\pi$
$602$	−1.88967	+	5.81581i	−0.0770172	+	0.237035i
$603$	−1.04244	−	0.757380i	−0.0424516	−	0.0308429i
$604$	−40.0179	−	29.0747i	−1.62831	−	1.18303i
$605$	15.4757	+	0.786849i	0.629177	+	0.0319900i
$606$	4.78983	−	3.48001i	0.194573	−	0.141366i
$607$	−19.7465			−0.801484			−0.400742	−	0.916191i	$-0.631248\pi$
$607$	−19.7465			−0.801484			−0.400742	+	0.916191i	$0.631248\pi$
$608$	−28.7371	+	20.8788i	−1.16544	+	0.846745i
$609$	0.761302	+	2.34305i	0.0308495	+	0.0949450i
$610$	63.2775	+	3.21729i	2.56203	+	0.130264i
$611$	−1.84697	+	5.68439i	−0.0747204	+	0.229966i
$612$	−2.36089	−	7.26606i	−0.0954332	−	0.293713i
$613$	−14.3973	−	44.3102i	−0.581500	−	1.78967i	−0.612894	−	0.790165i	$-0.709995\pi$
$613$	−14.3973	−	44.3102i	−0.581500	−	1.78967i	0.0313948	−	0.999507i	$-0.490005\pi$
$614$	−4.68677	+	14.4244i	−0.189143	+	0.582121i
$615$	−4.48751	−	16.6438i	−0.180954	−	0.671141i
$616$	0.646203	+	1.98881i	0.0260363	+	0.0801314i
$617$	−30.9446	+	22.4825i	−1.24578	+	0.905113i	−0.997969	−	0.0636955i	$-0.979711\pi$
$617$	−30.9446	+	22.4825i	−1.24578	+	0.905113i	−0.247811	+	0.968808i	$0.579711\pi$
$618$	−21.7395			−0.874490
$619$	13.6089	−	9.88742i	0.546987	−	0.397409i	−0.279687	−	0.960091i	$-0.590231\pi$
$619$	13.6089	−	9.88742i	0.546987	−	0.397409i	0.826673	+	0.562682i	$0.190231\pi$
$620$	9.31684	−	6.07110i	0.374173	−	0.243821i
$621$	6.12898	+	4.45297i	0.245948	+	0.178691i
$622$	30.3286	+	22.0350i	1.21607	+	0.883524i
$623$	−1.21066	+	3.72604i	−0.0485043	+	0.149281i
$624$	−2.96748			−0.118794
$625$	−16.8438	−	18.4739i	−0.673753	−	0.738956i
$626$	−40.3186			−1.61146
$627$	−2.75648	+	8.48356i	−0.110083	+	0.338801i
$628$	21.4633	+	15.5940i	0.856479	+	0.622268i
$629$	−24.4502	−	17.7641i	−0.974894	−	0.708302i
$630$	4.56197	−	2.97270i	0.181753	−	0.118435i
$631$	−23.9101	+	17.3717i	−0.951845	+	0.691556i	−0.951243	−	0.308444i	$-0.900192\pi$
$631$	−23.9101	+	17.3717i	−0.951845	+	0.691556i	−0.000602485		1.00000i	$0.500192\pi$
$632$	−7.90373			−0.314394
$633$	20.6953	−	15.0360i	0.822564	−	0.597628i
$634$	11.6876	+	35.9706i	0.464172	+	1.42858i
$635$	−11.6269	−	43.1230i	−0.461399	−	1.71128i
$636$	3.46998	−	10.6795i	0.137594	−	0.423470i
$637$	−1.74908	−	5.38313i	−0.0693012	−	0.213287i
$638$	2.79140	+	8.59104i	0.110512	+	0.340122i
$639$	−4.80188	+	14.7787i	−0.189960	+	0.584636i
$640$	15.6358	+	0.794990i	0.618060	+	0.0314247i
$641$	−3.27000	−	10.0640i	−0.129157	−	0.397505i	0.865478	−	0.500946i	$-0.167015\pi$
$641$	−3.27000	−	10.0640i	−0.129157	−	0.397505i	−0.994636	+	0.103441i	$0.967015\pi$
$642$	31.4185	−	22.8269i	1.23999	−	0.900905i
$643$	8.87372			0.349945			0.174973	−	0.984573i	$-0.444016\pi$
$643$	8.87372			0.349945			0.174973	+	0.984573i	$0.444016\pi$
$644$	17.2086	−	12.5028i	0.678115	−	0.492680i
$645$	5.60804	+	0.285136i	0.220816	+	0.0112272i
$646$	−23.7016	−	17.2202i	−0.932527	−	0.677520i
$647$	−14.8967	−	10.8231i	−0.585649	−	0.425499i	0.255107	−	0.966913i	$-0.417889\pi$
$647$	−14.8967	−	10.8231i	−0.585649	−	0.425499i	−0.840756	+	0.541414i	$0.817889\pi$
$648$	0.276718	−	0.851652i	0.0108705	−	0.0334560i
$649$	2.86166			0.112330
$650$	4.24832	−	9.62254i	0.166633	−	0.377427i
$651$	2.37317			0.0930120
$652$	8.93951	−	27.5130i	0.350098	−	1.07749i
$653$	−13.3718	−	9.71518i	−0.523279	−	0.380184i	0.294559	−	0.955633i	$-0.404827\pi$
$653$	−13.3718	−	9.71518i	−0.523279	−	0.380184i	−0.817838	+	0.575449i	$0.804827\pi$
$654$	3.62345	+	2.63259i	0.141688	+	0.102942i
$655$	9.72091	−	25.4424i	0.379827	−	0.994115i
$656$	18.5076	−	13.4466i	0.722601	−	0.525001i
$657$	11.1103			0.433453
$658$	11.7748	−	8.55486i	0.459028	−	0.333503i
$659$	1.27598	+	3.92705i	0.0497050	+	0.152976i	0.972828	−	0.231528i	$-0.0743725\pi$
$659$	1.27598	+	3.92705i	0.0497050	+	0.152976i	−0.923123	+	0.384504i	$0.874372\pi$
$660$	9.16790	−	5.97405i	0.356860	−	0.232540i
$661$	13.5288	−	41.6374i	0.526209	−	1.61951i	−0.235702	−	0.971825i	$-0.575739\pi$
$661$	13.5288	−	41.6374i	0.526209	−	1.61951i	0.761912	−	0.647681i	$-0.224261\pi$
$662$	13.7116	+	42.1999i	0.532916	+	1.64015i
$663$	−0.973295	−	2.99549i	−0.0377996	−	0.116335i
$664$	4.62165	−	14.2240i	0.179355	−	0.551997i
$665$	4.08453	−	10.6904i	0.158391	−	0.414554i
$666$	−6.23784	−	19.1981i	−0.241711	−	0.743911i
$667$	13.0447	−	9.47755i	0.505094	−	0.366972i
$668$	−9.80490			−0.379363
$669$	−10.2186	+	7.42426i	−0.395075	+	0.287038i
$670$	4.71649	+	3.80718i	0.182214	+	0.147084i
$671$	21.9835	+	15.9719i	0.848664	+	0.616590i
$672$	7.52320	+	5.46592i	0.290214	+	0.210853i
$673$	2.26061	−	6.95745i	0.0871402	−	0.268190i	−0.897986	−	0.440025i	$-0.854970\pi$
$673$	2.26061	−	6.95745i	0.0871402	−	0.268190i	0.985126	+	0.171835i	$0.0549696\pi$
$674$	−34.8387			−1.34194
$675$	−3.72614	−	3.33405i	−0.143419	−	0.128328i
$676$	2.42566			0.0932948
$677$	−14.1793	+	43.6394i	−0.544954	+	1.67720i	0.176144	+	0.984364i	$0.443637\pi$
$677$	−14.1793	+	43.6394i	−0.544954	+	1.67720i	−0.721099	+	0.692832i	$0.756363\pi$
$678$	25.1852	+	18.2981i	0.967233	+	0.702736i
$679$	2.23922	+	1.62689i	0.0859332	+	0.0624341i
$680$	1.64179	+	6.08926i	0.0629599	+	0.233512i
$681$	18.4534	−	13.4072i	0.707137	−	0.513765i
$682$	8.70151			0.333198
$683$	−12.2865	+	8.92664i	−0.470129	+	0.341569i	−0.797491	−	0.603330i	$-0.793840\pi$
$683$	−12.2865	+	8.92664i	−0.470129	+	0.341569i	0.327363	+	0.944899i	$0.393840\pi$
$684$	−3.31422	−	10.2001i	−0.126722	−	0.390011i
$685$	15.1329	+	12.2154i	0.578200	+	0.466726i
$686$	−9.52660	+	29.3199i	−0.363727	+	1.11944i
$687$	1.18028	+	3.63253i	0.0450304	+	0.138589i
$688$	2.30281	+	7.08731i	0.0877937	+	0.270201i
$689$	1.43053	−	4.40271i	0.0544988	−	0.167730i
$690$	−27.7303	−	22.3841i	−1.05568	−	0.852147i
$691$	−7.12477	−	21.9278i	−0.271039	−	0.834172i	−0.990240	−	0.139370i	$-0.955492\pi$
$691$	−7.12477	−	21.9278i	−0.271039	−	0.834172i	0.719201	−	0.694802i	$-0.244508\pi$
$692$	−11.8016	+	8.57434i	−0.448628	+	0.325947i
$693$	2.33524			0.0887083
$694$	24.9457	−	18.1241i	0.946924	−	0.687981i
$695$	−8.64516	−	32.0641i	−0.327930	−	1.21626i
$696$	−1.54191	−	1.12027i	−0.0584461	−	0.0424636i
$697$	19.6438	+	14.2720i	0.744060	+	0.540591i
$698$	13.6265	−	41.9381i	0.515771	−	1.58738i
$699$	−1.59675			−0.0603945
$700$	−12.1360	+	7.05726i	−0.458696	+	0.266739i
$701$	−46.1651			−1.74363			−0.871816	−	0.489833i	$-0.837058\pi$
$701$	−46.1651			−1.74363			−0.871816	+	0.489833i	$0.837058\pi$
$702$	0.650087	−	2.00076i	0.0245360	−	0.0755139i
$703$	−34.3233	−	24.9373i	−1.29453	−	0.940529i
$704$	17.8979	+	13.0036i	0.674551	+	0.490090i
$705$	−10.3995	−	8.39453i	−0.391668	−	0.316156i
$706$	11.1051	−	8.06835i	0.417947	−	0.303656i
$707$	−3.25762			−0.122515
$708$	−2.78357	+	2.02239i	−0.104613	+	0.0760059i
$709$	−14.4166	−	44.3699i	−0.541429	−	1.66635i	−0.729333	−	0.684158i	$-0.760170\pi$
$709$	−14.4166	−	44.3699i	−0.541429	−	1.66635i	0.187905	−	0.982187i	$-0.439830\pi$
$710$	26.0894	−	68.2833i	0.979118	−	2.56263i
$711$	−2.72746	+	8.39427i	−0.102288	+	0.314810i
$712$	−0.936595	−	2.88254i	−0.0351004	−	0.108028i
$713$	−4.79971	−	14.7720i	−0.179751	−	0.553215i
$714$	−2.37007	+	7.29433i	−0.0886977	+	0.272983i
$715$	3.77954	−	2.46285i	0.141347	−	0.0921054i
$716$	−0.248288	−	0.764151i	−0.00927895	−	0.0285577i
$717$	10.0152	−	7.27644i	0.374023	−	0.271744i
$718$	42.4782			1.58527
$719$	12.6634	−	9.20047i	0.472264	−	0.343120i	−0.326059	−	0.945349i	$-0.605721\pi$
$719$	12.6634	−	9.20047i	0.472264	−	0.343120i	0.798323	+	0.602230i	$0.205721\pi$
$720$	2.36829	−	6.19847i	0.0882608	−	0.231003i
$721$	9.67710	+	7.03083i	0.360394	+	0.261842i
$722$	−0.935328	−	0.679555i	−0.0348093	−	0.0252904i
$723$	−3.56971	+	10.9864i	−0.132759	+	0.408590i
$724$	3.95803			0.147099
$725$	−9.19946	+	5.34964i	−0.341660	+	0.198681i
$726$	−14.5786			−0.541062
$727$	4.41673	−	13.5933i	0.163807	−	0.504147i	−0.835139	−	0.550039i	$-0.814613\pi$
$727$	4.41673	−	13.5933i	0.163807	−	0.504147i	0.998946	+	0.0458917i	$0.0146129\pi$
$728$	−0.838573	−	0.609259i	−0.0310796	−	0.0225806i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−52.1961	−	2.65387i	−1.93186	−	0.0982240i
$731$	−6.39892	+	4.64909i	−0.236673	+	0.171953i
$732$	−32.6713			−1.20757
$733$	−14.8207	+	10.7679i	−0.547416	+	0.397721i	−0.826832	−	0.562449i	$-0.809859\pi$
$733$	−14.8207	+	10.7679i	−0.547416	+	0.397721i	0.279416	+	0.960170i	$0.409859\pi$
$734$	4.92299	+	15.1514i	0.181711	+	0.559248i
$735$	12.6402	+	0.642678i	0.466239	+	0.0237055i
$736$	18.8075	−	57.8834i	0.693252	−	2.13361i
$737$	0.803305	+	2.47232i	0.0295901	+	0.0910690i
$738$	5.01160	+	15.4241i	0.184479	+	0.567769i
$739$	5.81545	−	17.8981i	0.213925	−	0.658392i	−0.785304	−	0.619111i	$-0.787493\pi$
$739$	5.81545	−	17.8981i	0.213925	−	0.658392i	0.999228	−	0.0392814i	$-0.0125069\pi$
$740$	13.5486	+	50.2505i	0.498056	+	1.84724i
$741$	−1.36632	−	4.20509i	−0.0501928	−	0.154478i
$742$	−9.11986	+	6.62597i	−0.334801	+	0.243247i
$743$	6.47171			0.237424			0.118712	−	0.992929i	$-0.462123\pi$
$743$	6.47171			0.237424			0.118712	+	0.992929i	$0.462123\pi$
$744$	−1.48530	+	1.07914i	−0.0544539	+	0.0395631i
$745$	17.0325	−	11.0988i	0.624022	−	0.406629i
$746$	43.1924	+	31.3811i	1.58139	+	1.14894i
$747$	−13.5119	−	9.81698i	−0.494375	−	0.359184i
$748$	−4.76298	+	14.6589i	−0.174152	+	0.535984i
$749$	−21.3681			−0.780774
$750$	16.7090	+	16.5534i	0.610128	+	0.604446i
$751$	21.1692			0.772477			0.386238	−	0.922399i	$-0.373774\pi$
$751$	21.1692			0.772477			0.386238	+	0.922399i	$0.373774\pi$
$752$	5.48085	−	16.8683i	0.199866	−	0.615125i
$753$	6.16660	+	4.48029i	0.224723	+	0.163271i
$754$	−3.62238	−	2.63181i	−0.131919	−	0.0958449i
$755$	38.2034	−	24.8944i	1.39036	−	0.905999i
$756$	−2.27152	+	1.65035i	−0.0826142	+	0.0600228i
$757$	24.0384			0.873690			0.436845	−	0.899537i	$-0.356096\pi$
$757$	24.0384			0.873690			0.436845	+	0.899537i	$0.356096\pi$
$758$	2.94481	−	2.13953i	0.106960	−	0.0777113i
$759$	−4.72298	−	14.5358i	−0.171433	−	0.527618i
$760$	2.30476	+	8.54813i	0.0836023	+	0.310073i
$761$	−1.64430	+	5.06064i	−0.0596059	+	0.183448i	−0.976426	−	0.215852i	$-0.930747\pi$
$761$	−1.64430	+	5.06064i	−0.0596059	+	0.183448i	0.916820	+	0.399300i	$0.130747\pi$
$762$	12.9848	+	39.9630i	0.470388	+	1.44771i
$763$	−0.761526	−	2.34374i	−0.0275691	−	0.0848490i
$764$	−1.07609	+	3.31185i	−0.0389314	+	0.119818i
$765$	7.03374	+	0.357625i	0.254306	+	0.0129299i
$766$	14.5598	+	44.8106i	0.526068	+	1.61907i
$767$	−1.14755	+	0.833745i	−0.0414357	+	0.0301048i
$768$	7.20219			0.259887
$769$	12.1696	−	8.84177i	0.438849	−	0.318842i	−0.346329	−	0.938113i	$-0.612572\pi$
$769$	12.1696	−	8.84177i	0.438849	−	0.318842i	0.785177	+	0.619271i	$0.212572\pi$
$770$	−10.9710	−	0.557809i	−0.395366	−	0.0201020i
$771$	−8.89395	−	6.46183i	−0.320308	−	0.232717i
$772$	−34.5066	−	25.0705i	−1.24192	−	0.902307i
$773$	9.43029	−	29.0235i	0.339184	−	1.04390i	−0.625440	−	0.780272i	$-0.715081\pi$
$773$	9.43029	−	29.0235i	0.339184	−	1.04390i	0.964624	−	0.263629i	$-0.0849195\pi$
$774$	−5.28294			−0.189892
$775$	2.16260	+	10.0204i	0.0776827	+	0.359944i
$776$	−2.14125			−0.0768662
$777$	−3.43220	+	10.5632i	−0.123130	+	0.378954i
$778$	55.5340	+	40.3478i	1.99099	+	1.44654i
$779$	27.5760	+	20.0351i	0.988012	+	0.717833i
$780$	−1.93587	+	5.06672i	−0.0693153	+	0.181418i
$781$	25.3624	−	18.4269i	0.907538	−	0.659365i
$782$	50.1975			1.79506
$783$	−1.72189	+	1.25102i	−0.0615352	+	0.0447079i
$784$	5.19038	+	15.9743i	0.185371	+	0.570512i
$785$	−20.4901	+	13.3519i	−0.731323	+	0.476550i
$786$	−7.91832	+	24.3701i	−0.282437	+	0.869252i
$787$	−12.2265	−	37.6292i	−0.435827	−	1.34134i	−0.892237	−	0.451568i	$-0.850865\pi$
$787$	−12.2265	−	37.6292i	−0.435827	−	1.34134i	0.456410	−	0.889770i	$-0.349135\pi$
$788$	−0.611521	−	1.88207i	−0.0217845	−	0.0670459i
$789$	5.00430	−	15.4017i	0.178158	−	0.548314i
$790$	14.8187	−	38.7848i	0.527227	−	1.37990i
$791$	−5.29309	−	16.2904i	−0.188201	−	0.579222i
$792$	−1.46156	+	1.06189i	−0.0519343	+	0.0377325i
$793$	−13.4690			−0.478299
$794$	−35.1430	+	25.5329i	−1.24718	+	0.906128i
$795$	8.05470	+	6.50179i	0.285671	+	0.230595i
$796$	−8.93528	−	6.49186i	−0.316703	−	0.230098i
$797$	−21.7697	−	15.8166i	−0.771121	−	0.560252i	0.131180	−	0.991359i	$-0.458123\pi$
$797$	−21.7697	−	15.8166i	−0.771121	−	0.560252i	−0.902301	+	0.431106i	$0.858123\pi$
$798$	−3.32711	+	10.2398i	−0.117779	+	0.362485i
$799$	18.8252			0.665988
$800$	−16.2235	+	36.7467i	−0.573589	+	1.29919i
$801$	−3.38465			−0.119591
$802$	6.39104	−	19.6696i	0.225675	−	0.694558i
$803$	−18.1337	−	13.1749i	−0.639923	−	0.464931i
$804$	−2.52862	−	1.83715i	−0.0891775	−	0.0647912i
$805$	5.10457	+	18.9324i	0.179912	+	0.667278i
$806$	−3.48939	+	2.53519i	−0.122908	+	0.0892982i
$807$	−15.6041			−0.549290
$808$	2.03886	−	1.48132i	0.0717267	−	0.0521125i
$809$	7.53441	+	23.1885i	0.264896	+	0.815265i	0.991717	+	0.128439i	$0.0409966\pi$
$809$	7.53441	+	23.1885i	0.264896	+	0.815265i	−0.726822	+	0.686826i	$0.759003\pi$
$810$	3.66036	+	2.95467i	0.128612	+	0.103816i
$811$	−0.482860	+	1.48609i	−0.0169555	+	0.0521837i	−0.959176	−	0.282809i	$-0.908734\pi$
$811$	−0.482860	+	1.48609i	−0.0169555	+	0.0521837i	0.942221	+	0.334993i	$0.108734\pi$
$812$	1.84666	+	5.68344i	0.0648051	+	0.199450i
$813$	−1.78517	−	5.49419i	−0.0626086	−	0.192690i
$814$	−12.5845	+	38.7313i	−0.441088	+	1.35753i
$815$	20.7509	+	16.7502i	0.726871	+	0.586734i
$816$	2.88824	+	8.88908i	0.101109	+	0.311180i
$817$	−8.98283	+	6.52641i	−0.314269	+	0.228330i
$818$	2.07332			0.0724918
$819$	−0.936451	+	0.680372i	−0.0327223	+	0.0237741i
$820$	−10.8852	−	40.3722i	−0.380128	−	1.40986i
$821$	−19.3002	−	14.0224i	−0.673582	−	0.489386i	0.197641	−	0.980275i	$-0.436672\pi$
$821$	−19.3002	−	14.0224i	−0.673582	−	0.489386i	−0.871222	+	0.490889i	$0.836672\pi$
$822$	−14.8025	−	10.7546i	−0.516296	−	0.375111i
$823$	11.0275	−	33.9392i	0.384395	−	1.18305i	−0.552524	−	0.833497i	$-0.686335\pi$
$823$	11.0275	−	33.9392i	0.384395	−	1.18305i	0.936918	−	0.349548i	$-0.113665\pi$
$824$	−9.25371			−0.322368
$825$	2.12802	+	9.86024i	0.0740883	+	0.343290i
$826$	3.45407			0.120183
$827$	−14.8452	+	45.6887i	−0.516216	+	1.58875i	0.264841	+	0.964292i	$0.414680\pi$
$827$	−14.8452	+	45.6887i	−0.516216	+	1.58875i	−0.781058	+	0.624459i	$0.785320\pi$
$828$	14.8668	+	10.8014i	0.516659	+	0.375374i
$829$	−17.6899	−	12.8525i	−0.614395	−	0.446384i	0.236564	−	0.971616i	$-0.423979\pi$
$829$	−17.6899	−	12.8525i	−0.614395	−	0.446384i	−0.850959	+	0.525232i	$0.823979\pi$
$830$	61.1341	+	49.3477i	2.12199	+	1.71289i
$831$	−19.6867	+	14.3032i	−0.682924	+	0.496173i
$832$	−10.9658			−0.380171
$833$	−14.4227	+	10.4787i	−0.499719	+	0.363067i
$834$	9.65481	+	29.7145i	0.334319	+	1.02893i
$835$	3.22596	−	8.44323i	0.111639	−	0.292190i
$836$	−6.68628	+	20.5783i	−0.231250	+	0.711714i
$837$	0.633555	+	1.94988i	0.0218989	+	0.0673978i
$838$	0.761953	+	2.34505i	0.0263212	+	0.0810084i
$839$	7.28202	−	22.4117i	0.251403	−	0.773739i	−0.743114	−	0.669165i	$-0.766652\pi$
$839$	7.28202	−	22.4117i	0.251403	−	0.773739i	0.994517	−	0.104574i	$-0.0333481\pi$
$840$	1.94187	−	1.26537i	0.0670007	−	0.0436595i
$841$	−7.56166	−	23.2724i	−0.260747	−	0.802497i
$842$	57.0560	−	41.4536i	1.96628	−	1.42859i
$843$	−3.91207			−0.134739
$844$	50.1998	−	36.4723i	1.72795	−	1.25543i
$845$	−0.798079	+	2.08880i	−0.0274547	+	0.0718568i
$846$	10.1724	+	7.39070i	0.349735	+	0.254097i
$847$	6.48950	+	4.71490i	0.222982	+	0.162006i
$848$	−4.24507	+	13.0650i	−0.145776	+	0.448653i
$849$	4.05995			0.139337
$850$	−32.9591	−	3.36025i	−1.13049	−	0.115255i
$851$	72.6932			2.49189
$852$	−11.6478	+	35.8481i	−0.399046	+	1.22814i
$853$	−24.1795	−	17.5675i	−0.827892	−	0.601498i	0.0910704	−	0.995844i	$-0.470971\pi$
$853$	−24.1795	−	17.5675i	−0.827892	−	0.601498i	−0.918962	+	0.394346i	$0.870971\pi$
$854$	26.5345	+	19.2784i	0.907991	+	0.659694i
$855$	9.87399	+	0.502035i	0.337683	+	0.0171692i
$856$	13.3737	−	9.71657i	0.457104	−	0.332106i
$857$	−11.1938			−0.382373			−0.191187	−	0.981554i	$-0.561234\pi$
$857$	−11.1938			−0.382373			−0.191187	+	0.981554i	$0.561234\pi$
$858$	−3.43360	+	2.49466i	−0.117221	+	0.0851662i
$859$	6.08511	+	18.7280i	0.207621	+	0.638992i	0.999596	+	0.0284379i	$0.00905328\pi$
$859$	6.08511	+	18.7280i	0.207621	+	0.638992i	−0.791974	+	0.610554i	$0.790947\pi$
$860$	13.6032	+	0.691644i	0.463866	+	0.0235849i
$861$	2.75749	−	8.48669i	0.0939752	−	0.289226i
$862$	−16.6923	−	51.3737i	−0.568543	−	1.74980i
$863$	8.50661	+	26.1807i	0.289568	+	0.891200i	0.984992	+	0.172600i	$0.0552167\pi$
$863$	8.50661	+	26.1807i	0.289568	+	0.891200i	−0.695424	+	0.718600i	$0.744783\pi$
$864$	−2.48256	+	7.64053i	−0.0844584	+	0.259936i
$865$	−3.50068	−	12.9837i	−0.119027	−	0.441459i
$866$	1.23627	+	3.80484i	0.0420101	+	0.129294i
$867$	5.72761	−	4.16135i	0.194520	−	0.141327i
$868$	5.75652			0.195389
$869$	14.4058	−	10.4664i	0.488683	−	0.355049i
$870$	8.38826	−	5.46602i	0.284389	−	0.185315i
$871$	−1.04244	−	0.757380i	−0.0353219	−	0.0256628i
$872$	1.54237	+	1.12060i	0.0522312	+	0.0379482i
$873$	−0.738913	+	2.27414i	−0.0250084	+	0.0769680i
$874$	70.4674			2.38360
$875$	−2.08426	−	12.7725i	−0.0704610	−	0.431789i
$876$	26.9498			0.910548
$877$	−16.9524	+	52.1740i	−0.572440	+	1.76179i	0.0722933	+	0.997383i	$0.476968\pi$
$877$	−16.9524	+	52.1740i	−0.572440	+	1.76179i	−0.644734	+	0.764407i	$0.723032\pi$
$878$	15.0690	+	10.9482i	0.508553	+	0.369485i
$879$	−16.3914	−	11.9091i	−0.552869	−	0.401683i
$880$	−11.2157	+	7.30847i	−0.378082	+	0.246368i
$881$	−8.99327	+	6.53399i	−0.302991	+	0.220136i	−0.728883	−	0.684638i	$-0.759960\pi$
$881$	−8.99327	+	6.53399i	−0.302991	+	0.220136i	0.425892	+	0.904774i	$0.359960\pi$
$882$	−11.9074			−0.400943
$883$	5.55126	−	4.03322i	0.186815	−	0.135729i	−0.490447	−	0.871471i	$-0.663167\pi$
$883$	5.55126	−	4.03322i	0.186815	−	0.135729i	0.677262	+	0.735742i	$0.263167\pi$
$884$	−2.36089	−	7.26606i	−0.0794052	−	0.244384i
$885$	−0.825687	−	3.06240i	−0.0277552	−	0.102941i
$886$	2.87008	−	8.83319i	0.0964221	−	0.296757i
$887$	−15.9135	−	48.9768i	−0.534324	−	1.64448i	−0.745106	−	0.666947i	$-0.767601\pi$
$887$	−15.9135	−	48.9768i	−0.534324	−	1.64448i	0.210782	−	0.977533i	$-0.432399\pi$
$888$	−2.65522	−	8.17193i	−0.0891034	−	0.274232i
$889$	7.14450	−	21.9885i	0.239619	−	0.737471i
$890$	15.9011	+	0.808479i	0.533006	+	0.0271003i
$891$	0.623427	+	1.91871i	0.0208856	+	0.0642792i
$892$	−24.7869	+	18.0088i	−0.829928	+	0.602978i
$893$	26.4269			0.884342
$894$	−15.4735	+	11.2422i	−0.517512	+	0.375994i
$895$	0.739719	+	0.0376104i	0.0247261	+	0.00125718i
$896$	6.55664	+	4.76368i	0.219042	+	0.159143i
$897$	6.12898	+	4.45297i	0.204641	+	0.148680i
$898$	−19.6284	+	60.4101i	−0.655009	+	2.01591i
$899$	4.36364			0.145536
$900$	−9.03836	−	8.08728i	−0.301279	−	0.269576i
$901$	−14.5806			−0.485751
$902$	10.1107	−	31.1174i	0.336648	−	1.03610i
$903$	2.35165	+	1.70857i	0.0782579	+	0.0568577i
$904$	10.7204	+	7.78885i	0.356556	+	0.259053i
$905$	−1.30225	+	3.40835i	−0.0432883	+	0.113298i
$906$	−34.7067	+	25.2159i	−1.15305	+	0.837742i
$907$	29.7575			0.988080			0.494040	−	0.869439i	$-0.335520\pi$
$907$	29.7575			0.988080			0.494040	+	0.869439i	$0.335520\pi$
$908$	44.7618	−	32.5213i	1.48547	−	1.07926i
$909$	−0.869672	−	2.67657i	−0.0288452	−	0.0887764i
$910$	4.56197	−	2.97270i	0.151228	−	0.0985442i
$911$	−6.77127	+	20.8398i	−0.224342	+	0.690455i	0.774015	+	0.633167i	$0.218245\pi$
$911$	−6.77127	+	20.8398i	−0.224342	+	0.690455i	−0.998358	+	0.0572878i	$0.981755\pi$
$912$	4.05452	+	12.4785i	0.134258	+	0.413205i
$913$	10.4123	+	32.0456i	0.344595	+	1.06056i
$914$	−18.7254	+	57.6308i	−0.619380	+	1.90626i
$915$	10.7493	−	28.1340i	0.355362	−	0.930083i
$916$	2.86296	+	8.81128i	0.0945948	+	0.291133i
$917$	11.4063	−	8.28720i	0.376671	−	0.273667i
$918$	−6.62600			−0.218691
$919$	−9.92821	+	7.21326i	−0.327501	+	0.237944i	−0.739370	−	0.673300i	$-0.764876\pi$
$919$	−9.92821	+	7.21326i	−0.327501	+	0.237944i	0.411868	+	0.911243i	$0.364876\pi$
$920$	−11.8038	−	9.52808i	−0.389159	−	0.314132i
$921$	5.83257	+	4.23761i	0.192190	+	0.139634i
$922$	−58.3017	−	42.3587i	−1.92006	−	1.39501i
$923$	−4.80188	+	14.7787i	−0.158056	+	0.486446i
$924$	5.66450			0.186348
$925$	−47.7296	−	4.86612i	−1.56934	−	0.159997i
$926$	−14.6898			−0.482738
$927$	−3.19332	+	9.82803i	−0.104882	+	0.322795i
$928$	13.8332	+	10.0504i	0.454096	+	0.329920i
$929$	28.7943	+	20.9203i	0.944710	+	0.686372i	0.949550	−	0.313617i	$-0.101541\pi$
$929$	28.7943	+	20.9203i	0.944710	+	0.686372i	−0.00484015	+	0.999988i	$0.501541\pi$
$930$	−2.51069	−	9.31189i	−0.0823286	−	0.305349i
$931$	−20.2467	+	14.7101i	−0.663559	+	0.482104i
$932$	−3.87317			−0.126870
$933$	14.4166	−	10.4743i	0.471979	−	0.342912i
$934$	1.79401	+	5.52140i	0.0587019	+	0.180666i
$935$	−11.0561	−	8.92451i	−0.361572	−	0.291863i
$936$	0.276718	−	0.851652i	0.00904482	−	0.0278371i
$937$	−2.68192	−	8.25409i	−0.0876144	−	0.269649i	0.897644	−	0.440721i	$-0.145277\pi$
$937$	−2.68192	−	8.25409i	−0.0876144	−	0.269649i	−0.985259	+	0.171071i	$0.945277\pi$
$938$	0.969603	+	2.98413i	0.0316587	+	0.0974354i
$939$	−5.92242	+	18.2273i	−0.193271	+	0.594826i
$940$	−25.2257	−	20.3623i	−0.822772	−	0.664146i
$941$	10.6077	+	32.6472i	0.345802	+	1.06427i	0.961153	+	0.276015i	$0.0890141\pi$
$941$	10.6077	+	32.6472i	0.345802	+	1.06427i	−0.615351	+	0.788253i	$0.710986\pi$
$942$	18.6147	−	13.5243i	0.606499	−	0.440647i
$943$	−58.4030			−1.90186
$944$	3.40534	−	2.47412i	0.110834	−	0.0805259i
$945$	−0.673796	−	2.49905i	−0.0219186	−	0.0812940i
$946$	8.62257	+	6.26467i	0.280344	+	0.203682i
$947$	−27.3501	−	19.8710i	−0.888759	−	0.645721i	0.0467953	−	0.998905i	$-0.485099\pi$
$947$	−27.3501	−	19.8710i	−0.888759	−	0.645721i	−0.935554	+	0.353183i	$0.885099\pi$
$948$	−6.61591	+	20.3617i	−0.214875	+	0.661316i
$949$	11.1103			0.360655
$950$	−46.2682	−	4.71713i	−1.50114	−	0.153044i
$951$	17.9785			0.582991
$952$	−1.00885	+	3.10493i	−0.0326971	+	0.100631i
$953$	18.0812	+	13.1368i	0.585709	+	0.425542i	0.840778	−	0.541381i	$-0.182098\pi$
$953$	18.0812	+	13.1368i	0.585709	+	0.425542i	−0.255069	+	0.966923i	$0.582098\pi$
$954$	−7.87881	−	5.72429i	−0.255086	−	0.185331i
$955$	−2.49786	−	2.01629i	−0.0808290	−	0.0652456i
$956$	24.2934	−	17.6502i	0.785705	−	0.570848i
$957$	4.29388			0.138801
$958$	−62.3982	+	45.3349i	−2.01599	+	1.46470i
$959$	3.11098	+	9.57463i	0.100459	+	0.309181i
$960$	8.75157	−	22.9053i	0.282456	−	0.739266i
$961$	−8.28059	+	25.4850i	−0.267116	+	0.822098i
$962$	−6.23784	−	19.1981i	−0.201116	−	0.618972i
$963$	−5.70455	−	17.5568i	−0.183826	−	0.565760i
$964$	−8.65891	+	26.6494i	−0.278885	+	0.858319i
$965$	32.9420	−	21.4659i	1.06044	−	0.691011i
$966$	−5.70072	−	17.5450i	−0.183418	−	0.564502i
$967$	−9.92859	+	7.21354i	−0.319282	+	0.231972i	−0.735869	−	0.677124i	$-0.763226\pi$
$967$	−9.92859	+	7.21354i	−0.319282	+	0.231972i	0.416587	+	0.909096i	$0.363226\pi$
$968$	−6.20557			−0.199455
$969$	−11.2665	+	8.18558i	−0.361932	+	0.262959i
$970$	4.01463	−	10.5074i	0.128902	−	0.337373i
$971$	−20.4264	−	14.8407i	−0.655515	−	0.476259i	0.209631	−	0.977781i	$-0.432774\pi$
$971$	−20.4264	−	14.8407i	−0.655515	−	0.476259i	−0.865145	+	0.501521i	$0.832774\pi$
$972$	−1.96240	−	1.42577i	−0.0629441	−	0.0457316i
$973$	5.31230	−	16.3496i	0.170304	−	0.524143i
$974$	23.2064			0.743582
$975$	−3.72614	−	3.33405i	−0.119332	−	0.106775i
$976$	39.9691			1.27938
$977$	6.32328	−	19.4610i	0.202300	−	0.622614i	−0.797514	−	0.603300i	$-0.793852\pi$
$977$	6.32328	−	19.4610i	0.202300	−	0.622614i	0.999813	−	0.0193134i	$-0.00614802\pi$
$978$	−20.2977	−	14.7472i	−0.649050	−	0.471563i
$979$	5.52427	+	4.01362i	0.176556	+	0.128276i
$980$	30.6608	+	1.55892i	0.979423	+	0.0497979i
$981$	1.72239	−	1.25139i	0.0549918	−	0.0399539i
$982$	41.4513			1.32276
$983$	−9.93855	+	7.22078i	−0.316991	+	0.230307i	−0.734890	−	0.678186i	$-0.762766\pi$
$983$	−9.93855	+	7.22078i	−0.316991	+	0.230307i	0.417900	+	0.908493i	$0.362766\pi$
$984$	2.13325	+	6.56548i	0.0680057	+	0.209300i
$985$	1.82189	+	0.0926326i	0.0580503	+	0.00295152i
$986$	−4.35793	+	13.4123i	−0.138785	+	0.427136i
$987$	−2.13790	−	6.57978i	−0.0680501	−	0.209437i
$988$	−3.31422	−	10.2001i	−0.105439	−	0.324509i
$989$	5.87895	−	18.0936i	0.186940	−	0.575341i
$990$	−2.47055	−	9.16303i	−0.0785192	−	0.291220i
$991$	7.99804	+	24.6154i	0.254066	+	0.781935i	0.994012	+	0.109269i	$0.0348509\pi$
$991$	7.99804	+	24.6154i	0.254066	+	0.781935i	−0.739946	+	0.672666i	$0.765149\pi$
$992$	13.3253	−	9.68140i	0.423079	−	0.307385i
$993$	21.0919			0.669332
$994$	30.6129	−	22.2415i	0.970981	−	0.705459i
$995$	8.53013	−	5.55846i	0.270423	−	0.176215i
$996$	−32.7753	−	23.8127i	−1.03853	−	0.754534i
$997$	29.0573	+	21.1114i	0.920254	+	0.668604i	0.943587	−	0.331124i	$-0.107428\pi$
$997$	29.0573	+	21.1114i	0.920254	+	0.668604i	−0.0233333	+	0.999728i	$0.507428\pi$
$998$	−7.46731	+	22.9820i	−0.236374	+	0.727483i
$999$	−9.59540			−0.303585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.v.b.196.11	✓	52
25.6	even	5	inner	975.2.v.b.781.11	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.v.b.196.11	✓	52	1.1	even	1	trivial
975.2.v.b.781.11	yes	52	25.6	even	5	inner

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.v (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.650087 - 2.00076i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.96240 - 1.42577i) q^{4} +(1.87342 - 1.22077i) q^{5} +(-1.70195 + 1.23654i) q^{6} +1.15752 q^{7} +(-0.724458 + 0.526350i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.650087 - 2.00076i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.96240 - 1.42577i) q^{4} +(1.87342 - 1.22077i) q^{5} +(-1.70195 + 1.23654i) q^{6} +1.15752 q^{7} +(-0.724458 + 0.526350i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.22459 - 4.54188i) q^{10} +(0.623427 - 1.91871i) q^{11} +(0.749571 + 2.30694i) q^{12} +(0.309017 + 0.951057i) q^{13} +(0.752487 - 2.31592i) q^{14} +(-2.23318 - 0.113544i) q^{15} +(-0.917003 - 2.82224i) q^{16} +(2.54812 - 1.85132i) q^{17} +2.10373 q^{18} +(3.57706 - 2.59889i) q^{19} +(-5.41695 - 0.275420i) q^{20} +(-0.936451 - 0.680372i) q^{21} +(-3.43360 - 2.49466i) q^{22} +(-2.34106 + 7.20505i) q^{23} +0.895480 q^{24} +(2.01943 - 4.57405i) q^{25} +2.10373 q^{26} +(0.309017 - 0.951057i) q^{27} +(-2.27152 - 1.65035i) q^{28} +(-1.72189 - 1.25102i) q^{29} +(-1.67894 + 4.39426i) q^{30} +(-1.65867 + 1.20509i) q^{31} -8.03373 q^{32} +(-1.63215 + 1.18583i) q^{33} +(-2.04755 - 6.30170i) q^{34} +(2.16852 - 1.41307i) q^{35} +(0.749571 - 2.30694i) q^{36} +(-2.96514 - 9.12576i) q^{37} +(-2.87435 - 8.84635i) q^{38} +(0.309017 - 0.951057i) q^{39} +(-0.714663 + 1.87047i) q^{40} +(2.38225 + 7.33181i) q^{41} +(-1.97004 + 1.43132i) q^{42} -2.51123 q^{43} +(-3.95905 + 2.87642i) q^{44} +(1.73994 + 1.40449i) q^{45} +(12.8937 + 9.36782i) q^{46} +(4.83543 + 3.51315i) q^{47} +(-0.917003 + 2.82224i) q^{48} -5.66015 q^{49} +(-7.83878 - 7.01392i) q^{50} -3.14965 q^{51} +(0.749571 - 2.30694i) q^{52} +(-3.74517 - 2.72103i) q^{53} +(-1.70195 - 1.23654i) q^{54} +(-1.17437 - 4.35562i) q^{55} +(-0.838573 + 0.609259i) q^{56} -4.42149 q^{57} +(-3.62238 + 2.63181i) q^{58} +(0.438326 + 1.34903i) q^{59} +(4.22052 + 3.40682i) q^{60} +(-4.16216 + 12.8098i) q^{61} +(1.33283 + 4.10202i) q^{62} +(0.357693 + 1.10086i) q^{63} +(-3.38862 + 10.4291i) q^{64} +(1.73994 + 1.40449i) q^{65} +(1.31152 + 4.03644i) q^{66} +(-1.04244 + 0.757380i) q^{67} -7.63999 q^{68} +(6.12898 - 4.45297i) q^{69} +(-1.41748 - 5.25731i) q^{70} +(12.5715 + 9.13373i) q^{71} +(-0.724458 - 0.526350i) q^{72} +(3.43326 - 10.5665i) q^{73} -20.1861 q^{74} +(-4.32231 + 2.51349i) q^{75} -10.7250 q^{76} +(0.721628 - 2.22094i) q^{77} +(-1.70195 - 1.23654i) q^{78} +(7.14059 + 5.18794i) q^{79} +(-5.16325 - 4.16781i) q^{80} +(-0.809017 + 0.587785i) q^{81} +16.2179 q^{82} +(-13.5119 + 9.81698i) q^{83} +(0.867642 + 2.67033i) q^{84} +(2.51367 - 6.57897i) q^{85} +(-1.63252 + 5.02438i) q^{86} +(0.657702 + 2.02420i) q^{87} +(0.558266 + 1.71817i) q^{88} +(-1.04591 + 3.21899i) q^{89} +(3.94117 - 2.56817i) q^{90} +(0.357693 + 1.10086i) q^{91} +(14.8668 - 10.8014i) q^{92} +2.05023 q^{93} +(10.1724 - 7.39070i) q^{94} +(3.52870 - 9.23559i) q^{95} +(6.49943 + 4.72211i) q^{96} +(1.93450 + 1.40550i) q^{97} +(-3.67959 + 11.3246i) q^{98} +2.01745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + q^{2} - 13 q^{3} - 17 q^{4} + 3 q^{5} + q^{6} - 20 q^{7} - 6 q^{8} - 13 q^{9}+O(q^{10}) \) 52 * q + q^2 - 13 * q^3 - 17 * q^4 + 3 * q^5 + q^6 - 20 * q^7 - 6 * q^8 - 13 * q^9	\( 52 q + q^{2} - 13 q^{3} - 17 q^{4} + 3 q^{5} + q^{6} - 20 q^{7} - 6 q^{8} - 13 q^{9} + 4 q^{10} - 8 q^{11} - 7 q^{12} - 13 q^{13} - 10 q^{14} + 3 q^{15} - 9 q^{16} + q^{17} - 4 q^{18} + 20 q^{19} - 11 q^{20} + 5 q^{21} + 4 q^{22} - 15 q^{23} - 6 q^{24} + 23 q^{25} - 4 q^{26} - 13 q^{27} + 37 q^{28} - 5 q^{29} - 26 q^{30} + 26 q^{31} - 156 q^{32} + 12 q^{33} + 34 q^{34} - 12 q^{35} - 7 q^{36} + 32 q^{37} + 18 q^{38} - 13 q^{39} - 18 q^{40} + 49 q^{41} + 10 q^{42} - 76 q^{43} + 47 q^{44} - 2 q^{45} + 24 q^{46} + 22 q^{47} - 9 q^{48} - 52 q^{49} + 39 q^{50} + 6 q^{51} - 7 q^{52} + 25 q^{53} + q^{54} + 11 q^{55} + 45 q^{56} - 40 q^{57} - 13 q^{58} - 15 q^{59} + 19 q^{60} + 26 q^{61} + 62 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} - 11 q^{66} + 8 q^{67} + 62 q^{68} + 10 q^{69} + q^{70} + 9 q^{71} - 6 q^{72} + 46 q^{73} + 56 q^{74} + 18 q^{75} - 82 q^{76} + 49 q^{77} + q^{78} + 26 q^{79} + 60 q^{80} - 13 q^{81} - 126 q^{82} - 50 q^{83} - 8 q^{84} + 48 q^{85} + 24 q^{86} + 20 q^{87} - 62 q^{88} + 34 q^{89} - q^{90} + 5 q^{91} - 10 q^{92} - 104 q^{93} + q^{94} - 53 q^{95} + 24 q^{96} + 6 q^{97} - 47 q^{98} - 8 q^{99}+O(q^{100}) \) 52 * q + q^2 - 13 * q^3 - 17 * q^4 + 3 * q^5 + q^6 - 20 * q^7 - 6 * q^8 - 13 * q^9 + 4 * q^10 - 8 * q^11 - 7 * q^12 - 13 * q^13 - 10 * q^14 + 3 * q^15 - 9 * q^16 + q^17 - 4 * q^18 + 20 * q^19 - 11 * q^20 + 5 * q^21 + 4 * q^22 - 15 * q^23 - 6 * q^24 + 23 * q^25 - 4 * q^26 - 13 * q^27 + 37 * q^28 - 5 * q^29 - 26 * q^30 + 26 * q^31 - 156 * q^32 + 12 * q^33 + 34 * q^34 - 12 * q^35 - 7 * q^36 + 32 * q^37 + 18 * q^38 - 13 * q^39 - 18 * q^40 + 49 * q^41 + 10 * q^42 - 76 * q^43 + 47 * q^44 - 2 * q^45 + 24 * q^46 + 22 * q^47 - 9 * q^48 - 52 * q^49 + 39 * q^50 + 6 * q^51 - 7 * q^52 + 25 * q^53 + q^54 + 11 * q^55 + 45 * q^56 - 40 * q^57 - 13 * q^58 - 15 * q^59 + 19 * q^60 + 26 * q^61 + 62 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 - 11 * q^66 + 8 * q^67 + 62 * q^68 + 10 * q^69 + q^70 + 9 * q^71 - 6 * q^72 + 46 * q^73 + 56 * q^74 + 18 * q^75 - 82 * q^76 + 49 * q^77 + q^78 + 26 * q^79 + 60 * q^80 - 13 * q^81 - 126 * q^82 - 50 * q^83 - 8 * q^84 + 48 * q^85 + 24 * q^86 + 20 * q^87 - 62 * q^88 + 34 * q^89 - q^90 + 5 * q^91 - 10 * q^92 - 104 * q^93 + q^94 - 53 * q^95 + 24 * q^96 + 6 * q^97 - 47 * q^98 - 8 * q^99

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