LMFDB - Embedded newform 950.2.n.a.39.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.5
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.812784 - 0.264090i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.775807 + 2.09717i) q^{5} +(0.264090 + 0.812784i) q^{6} +3.74573i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.83618 - 1.33406i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.812784 - 0.264090i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.775807 + 2.09717i) q^{5} +(0.264090 + 0.812784i) q^{6} +3.74573i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.83618 - 1.33406i) q^{9} +(1.24064 - 1.86033i) q^{10} +(1.20043 - 0.872166i) q^{11} +(0.502328 - 0.691395i) q^{12} +(3.51617 - 4.83959i) q^{13} +(3.03036 - 2.20168i) q^{14} +(-0.0767231 - 1.90943i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.10979 - 0.360591i) q^{17} +2.26964i q^{18} +(0.309017 + 0.951057i) q^{19} +(-2.23427 + 0.0897754i) q^{20} +(0.989207 - 3.04447i) q^{21} +(-1.41119 - 0.458525i) q^{22} +(-0.147282 - 0.202717i) q^{23} -0.854612 q^{24} +(-3.79625 + 3.25400i) q^{25} -5.98206 q^{26} +(2.64709 + 3.64340i) q^{27} +(-3.56240 - 1.15749i) q^{28} +(-2.68251 + 8.25590i) q^{29} +(-1.49966 + 1.18440i) q^{30} +(2.50689 + 7.71541i) q^{31} +1.00000i q^{32} +(-1.20602 + 0.391861i) q^{33} +(-0.944041 - 0.685886i) q^{34} +(-7.85542 + 2.90596i) q^{35} +(1.83618 - 1.33406i) q^{36} +(-1.65380 + 2.27626i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-4.13597 + 3.00496i) q^{39} +(1.38590 + 1.75479i) q^{40} +(7.13922 + 5.18695i) q^{41} +(-3.04447 + 0.989207i) q^{42} +6.73362i q^{43} +(0.458525 + 1.41119i) q^{44} +(1.37323 - 4.88575i) q^{45} +(-0.0774309 + 0.238308i) q^{46} +(-0.781275 - 0.253852i) q^{47} +(0.502328 + 0.691395i) q^{48} -7.03046 q^{49} +(4.86392 + 1.15857i) q^{50} -0.997245 q^{51} +(3.51617 + 4.83959i) q^{52} +(-12.0850 - 3.92664i) q^{53} +(1.39166 - 4.28308i) q^{54} +(2.76039 + 1.84088i) q^{55} +(1.15749 + 3.56240i) q^{56} -0.854612i q^{57} +(8.25590 - 2.68251i) q^{58} +(-5.98878 - 4.35111i) q^{59} +(1.83968 + 0.517078i) q^{60} +(-5.77693 + 4.19719i) q^{61} +(4.76838 - 6.56312i) q^{62} +(4.99702 - 6.87781i) q^{63} +(0.809017 - 0.587785i) q^{64} +(12.8773 + 3.61941i) q^{65} +(1.02590 + 0.745364i) q^{66} +(10.2778 - 3.33946i) q^{67} +1.16690i q^{68} +(0.0661734 + 0.203661i) q^{69} +(6.96827 + 4.64709i) q^{70} +(-4.43893 + 13.6616i) q^{71} +(-2.15855 - 0.701357i) q^{72} +(-6.25438 - 8.60842i) q^{73} +2.81361 q^{74} +(3.94488 - 1.64225i) q^{75} -1.00000 q^{76} +(3.26690 + 4.49650i) q^{77} +(4.86212 + 1.57980i) q^{78} +(-1.86688 + 5.74568i) q^{79} +(0.605044 - 2.15265i) q^{80} +(0.914745 + 2.81530i) q^{81} -8.82457i q^{82} +(0.115896 - 0.0376569i) q^{83} +(2.58978 + 1.88158i) q^{84} +(1.61720 + 2.04766i) q^{85} +(5.44761 - 3.95792i) q^{86} +(4.36059 - 6.00184i) q^{87} +(0.872166 - 1.20043i) q^{88} +(10.6793 - 7.75900i) q^{89} +(-4.75982 + 1.76080i) q^{90} +(18.1278 + 13.1706i) q^{91} +(0.238308 - 0.0774309i) q^{92} -6.93300i q^{93} +(0.253852 + 0.781275i) q^{94} +(-1.75479 + 1.38590i) q^{95} +(0.264090 - 0.812784i) q^{96} +(-6.84839 - 2.22518i) q^{97} +(4.13240 + 5.68776i) q^{98} -3.36773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−0.812784	−	0.264090i	−0.469261	−	0.152472i	0.0648349	−	0.997896i	$-0.479348\pi$
$3$	−0.812784	−	0.264090i	−0.469261	−	0.152472i	−0.534096	+	0.845424i	$0.679348\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.775807	+	2.09717i	0.346952	+	0.937883i
$5$	0.775807	+	2.09717i	0.346952	+	0.937883i
$6$	0.264090	+	0.812784i	0.107814	+	0.331818i
$7$			3.74573i			1.41575i	0.706337	+	0.707876i	$0.250346\pi$
$7$			3.74573i			1.41575i	−0.706337	+	0.707876i	$0.749654\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−1.83618	−	1.33406i	−0.612059	−	0.444687i
$10$	1.24064	−	1.86033i	0.392324	−	0.588287i
$11$	1.20043	−	0.872166i	0.361944	−	0.262968i	−0.391918	−	0.920000i	$-0.628188\pi$
$11$	1.20043	−	0.872166i	0.361944	−	0.262968i	0.753863	+	0.657032i	$0.228188\pi$
$12$	0.502328	−	0.691395i	0.145010	−	0.199589i
$13$	3.51617	−	4.83959i	0.975209	−	1.34226i	0.0358384	−	0.999358i	$-0.488590\pi$
$13$	3.51617	−	4.83959i	0.975209	−	1.34226i	0.939371	−	0.342903i	$-0.111410\pi$
$14$	3.03036	−	2.20168i	0.809897	−	0.588424i
$15$	−0.0767231	−	1.90943i	−0.0198098	−	0.493012i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.10979	−	0.360591i	0.269163	−	0.0874563i	−0.171326	−	0.985214i	$-0.554805\pi$
$17$	1.10979	−	0.360591i	0.269163	−	0.0874563i	0.440489	+	0.897758i	$0.354805\pi$
$18$			2.26964i			0.534959i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	−2.23427	+	0.0897754i	−0.499597	+	0.0200744i
$21$	0.989207	−	3.04447i	0.215863	−	0.664357i
$22$	−1.41119	−	0.458525i	−0.300868	−	0.0977579i
$23$	−0.147282	−	0.202717i	−0.0307105	−	0.0422694i	0.793386	−	0.608719i	$-0.208316\pi$
$23$	−0.147282	−	0.202717i	−0.0307105	−	0.0422694i	−0.824096	+	0.566450i	$0.808316\pi$
$24$	−0.854612			−0.174447
$25$	−3.79625	+	3.25400i	−0.759249	+	0.650800i
$26$	−5.98206			−1.17318
$27$	2.64709	+	3.64340i	0.509432	+	0.701173i
$28$	−3.56240	−	1.15749i	−0.673230	−	0.218746i
$29$	−2.68251	+	8.25590i	−0.498129	+	1.53308i	0.313895	+	0.949458i	$0.398366\pi$
$29$	−2.68251	+	8.25590i	−0.498129	+	1.53308i	−0.812024	+	0.583625i	$0.801634\pi$
$30$	−1.49966	+	1.18440i	−0.273800	+	0.216242i
$31$	2.50689	+	7.71541i	0.450250	+	1.38573i	0.876622	+	0.481180i	$0.159792\pi$
$31$	2.50689	+	7.71541i	0.450250	+	1.38573i	−0.426372	+	0.904548i	$0.640208\pi$
$32$			1.00000i			0.176777i
$33$	−1.20602	+	0.391861i	−0.209942	+	0.0682142i
$34$	−0.944041	−	0.685886i	−0.161902	−	0.117628i
$35$	−7.85542	+	2.90596i	−1.32781	+	0.491197i
$36$	1.83618	−	1.33406i	0.306029	−	0.222343i
$37$	−1.65380	+	2.27626i	−0.271883	+	0.374214i	−0.923024	−	0.384742i	$-0.874290\pi$
$37$	−1.65380	+	2.27626i	−0.271883	+	0.374214i	0.651142	+	0.758956i	$0.274290\pi$
$38$	0.587785	−	0.809017i	0.0953514	−	0.131240i
$39$	−4.13597	+	3.00496i	−0.662285	+	0.481178i
$40$	1.38590	+	1.75479i	0.219130	+	0.277457i
$41$	7.13922	+	5.18695i	1.11496	+	0.810066i	0.983437	−	0.181248i	$-0.0580136\pi$
$41$	7.13922	+	5.18695i	1.11496	+	0.810066i	0.131522	+	0.991313i	$0.458014\pi$
$42$	−3.04447	+	0.989207i	−0.469771	+	0.152638i
$43$			6.73362i			1.02687i	0.858129	+	0.513433i	$0.171627\pi$
$43$			6.73362i			1.02687i	−0.858129	+	0.513433i	$0.828373\pi$
$44$	0.458525	+	1.41119i	0.0691252	+	0.212746i
$45$	1.37323	−	4.88575i	0.204709	−	0.728324i
$46$	−0.0774309	+	0.238308i	−0.0114166	+	0.0351366i
$47$	−0.781275	−	0.253852i	−0.113961	−	0.0370281i	0.251482	−	0.967862i	$-0.419082\pi$
$47$	−0.781275	−	0.253852i	−0.113961	−	0.0370281i	−0.365442	+	0.930834i	$0.619082\pi$
$48$	0.502328	+	0.691395i	0.0725048	+	0.0997943i
$49$	−7.03046			−1.00435
$50$	4.86392	+	1.15857i	0.687862	+	0.163847i
$51$	−0.997245			−0.139642
$52$	3.51617	+	4.83959i	0.487605	+	0.671130i
$53$	−12.0850	−	3.92664i	−1.66000	−	0.539366i	−0.679126	−	0.734022i	$-0.737641\pi$
$53$	−12.0850	−	3.92664i	−1.66000	−	0.539366i	−0.980872	+	0.194656i	$0.937641\pi$
$54$	1.39166	−	4.28308i	0.189380	−	0.582853i
$55$	2.76039	+	1.84088i	0.372210	+	0.248224i
$56$	1.15749	+	3.56240i	0.154676	+	0.476045i
$57$		−	0.854612i		−	0.113196i
$58$	8.25590	−	2.68251i	1.08405	−	0.352230i
$59$	−5.98878	−	4.35111i	−0.779673	−	0.566466i	0.125208	−	0.992131i	$-0.460040\pi$
$59$	−5.98878	−	4.35111i	−0.779673	−	0.566466i	−0.904881	+	0.425665i	$0.860040\pi$
$60$	1.83968	+	0.517078i	0.237502	+	0.0667545i
$61$	−5.77693	+	4.19719i	−0.739661	+	0.537395i	−0.892605	−	0.450840i	$-0.851125\pi$
$61$	−5.77693	+	4.19719i	−0.739661	+	0.537395i	0.152944	+	0.988235i	$0.451125\pi$
$62$	4.76838	−	6.56312i	0.605585	−	0.833517i
$63$	4.99702	−	6.87781i	0.629566	−	0.866523i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	12.8773	+	3.61941i	1.59723	+	0.448933i
$66$	1.02590	+	0.745364i	0.126280	+	0.0917479i
$67$	10.2778	−	3.33946i	1.25563	−	0.407980i	0.395697	−	0.918381i	$-0.370503\pi$
$67$	10.2778	−	3.33946i	1.25563	−	0.407980i	0.859936	+	0.510401i	$0.170503\pi$
$68$			1.16690i			0.141507i
$69$	0.0661734	+	0.203661i	0.00796634	+	0.0245179i
$70$	6.96827	+	4.64709i	0.832868	+	0.555433i
$71$	−4.43893	+	13.6616i	−0.526804	+	1.62134i	0.233916	+	0.972257i	$0.424846\pi$
$71$	−4.43893	+	13.6616i	−0.526804	+	1.62134i	−0.760720	+	0.649080i	$0.775154\pi$
$72$	−2.15855	−	0.701357i	−0.254388	−	0.0826557i
$73$	−6.25438	−	8.60842i	−0.732020	−	1.00754i	−0.999038	−	0.0438480i	$-0.986038\pi$
$73$	−6.25438	−	8.60842i	−0.732020	−	1.00754i	0.267018	−	0.963692i	$-0.413962\pi$
$74$	2.81361			0.327075
$75$	3.94488	−	1.64225i	0.455515	−	0.189631i
$76$	−1.00000			−0.114708
$77$	3.26690	+	4.49650i	0.372297	+	0.512423i
$78$	4.86212	+	1.57980i	0.550527	+	0.178877i
$79$	−1.86688	+	5.74568i	−0.210041	+	0.646439i	0.789428	+	0.613843i	$0.210377\pi$
$79$	−1.86688	+	5.74568i	−0.210041	+	0.646439i	−0.999469	+	0.0325958i	$0.989623\pi$
$80$	0.605044	−	2.15265i	0.0676460	−	0.240674i
$81$	0.914745	+	2.81530i	0.101638	+	0.312811i
$82$		−	8.82457i		−	0.974510i
$83$	0.115896	−	0.0376569i	0.0127212	−	0.00413338i	−0.302649	−	0.953102i	$-0.597871\pi$
$83$	0.115896	−	0.0376569i	0.0127212	−	0.00413338i	0.315371	+	0.948969i	$0.397871\pi$
$84$	2.58978	+	1.88158i	0.282568	+	0.205298i
$85$	1.61720	+	2.04766i	0.175410	+	0.222100i
$86$	5.44761	−	3.95792i	0.587431	−	0.426794i
$87$	4.36059	−	6.00184i	0.467505	−	0.643465i
$88$	0.872166	−	1.20043i	0.0929732	−	0.127967i
$89$	10.6793	−	7.75900i	1.13201	−	0.822452i	0.146022	−	0.989281i	$-0.453353\pi$
$89$	10.6793	−	7.75900i	1.13201	−	0.822452i	0.985986	+	0.166829i	$0.0533528\pi$
$90$	−4.75982	+	1.76080i	−0.501729	+	0.185605i
$91$	18.1278	+	13.1706i	1.90031	+	1.38065i
$92$	0.238308	−	0.0774309i	0.0248453	−	0.00807273i
$93$		−	6.93300i		−	0.718919i
$94$	0.253852	+	0.781275i	0.0261828	+	0.0805824i
$95$	−1.75479	+	1.38590i	−0.180038	+	0.142190i
$96$	0.264090	−	0.812784i	0.0269535	−	0.0829544i
$97$	−6.84839	−	2.22518i	−0.695349	−	0.225933i	−0.0600459	−	0.998196i	$-0.519125\pi$
$97$	−6.84839	−	2.22518i	−0.695349	−	0.225933i	−0.635303	+	0.772263i	$0.719125\pi$
$98$	4.13240	+	5.68776i	0.417435	+	0.574550i
$99$	−3.36773			−0.338470
$100$	−1.92163	−	4.61599i	−0.192163	−	0.461599i
$101$	−14.2191			−1.41486			−0.707428	−	0.706786i	$-0.750144\pi$
$101$	−14.2191			−1.41486			−0.707428	+	0.706786i	$0.750144\pi$
$102$	0.586166	+	0.806788i	0.0580391	+	0.0798839i
$103$	11.3760	+	3.69630i	1.12091	+	0.364207i	0.810117	−	0.586269i	$-0.199404\pi$
$103$	11.3760	+	3.69630i	1.12091	+	0.364207i	0.310798	+	0.950476i	$0.399404\pi$
$104$	1.84856	−	5.68928i	0.181266	−	0.557880i
$105$	7.15220	−	0.287384i	0.697983	−	0.0280458i
$106$	3.92664	+	12.0850i	0.381389	+	1.17380i
$107$		−	5.83215i		−	0.563815i	−0.959442	−	0.281908i	$-0.909033\pi$
$107$		−	5.83215i		−	0.563815i	0.959442	−	0.281908i	$-0.0909672\pi$
$108$	−4.28308	+	1.39166i	−0.412139	+	0.133912i
$109$	14.2613	+	10.3615i	1.36599	+	0.992447i	0.998039	+	0.0626004i	$0.0199394\pi$
$109$	14.2613	+	10.3615i	1.36599	+	0.992447i	0.367947	+	0.929847i	$0.380061\pi$
$110$	−0.133210	−	3.31524i	−0.0127011	−	0.316096i
$111$	1.94532	−	1.41335i	0.184641	−	0.134150i
$112$	2.20168	−	3.03036i	0.208039	−	0.286342i
$113$	−5.93783	+	8.17272i	−0.558584	+	0.768825i	−0.991146	−	0.132779i	$-0.957610\pi$
$113$	−5.93783	+	8.17272i	−0.558584	+	0.768825i	0.432561	+	0.901604i	$0.357610\pi$
$114$	−0.691395	+	0.502328i	−0.0647551	+	0.0470473i
$115$	0.310869	−	0.466146i	0.0289887	−	0.0434683i
$116$	−7.02289	−	5.10243i	−0.652059	−	0.473749i
$117$	−12.9126	+	4.19556i	−1.19377	+	0.387880i
$118$			7.40254i			0.681459i
$119$	1.35068	+	4.15695i	0.123816	+	0.381067i
$120$	−0.663014	−	1.79227i	−0.0605246	−	0.163611i
$121$	−2.71882	+	8.36767i	−0.247165	+	0.760697i
$122$	6.79119	+	2.20659i	0.614846	+	0.199775i
$123$	−4.43283	−	6.10126i	−0.399695	−	0.550132i
$124$	−8.11246			−0.728520
$125$	−9.76935	−	5.43690i	−0.873797	−	0.486291i
$126$	−8.50144			−0.757369
$127$	2.03843	+	2.80565i	0.180881	+	0.248962i	0.889823	−	0.456305i	$-0.150827\pi$
$127$	2.03843	+	2.80565i	0.180881	+	0.248962i	−0.708942	+	0.705266i	$0.750827\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	1.77828	−	5.47298i	0.156569	−	0.481869i
$130$	−4.64093	−	12.5454i	−0.407036	−	1.10030i
$131$	−0.489896	−	1.50774i	−0.0428024	−	0.131732i	0.927372	−	0.374141i	$-0.122062\pi$
$131$	−0.489896	−	1.50774i	−0.0428024	−	0.131732i	−0.970174	+	0.242409i	$0.922062\pi$
$132$		−	1.26809i		−	0.110373i
$133$	−3.56240	+	1.15749i	−0.308899	+	0.100367i
$134$	−8.74282	−	6.35203i	−0.755265	−	0.548732i
$135$	−5.58721	+	8.37797i	−0.480870	+	0.721061i
$136$	0.944041	−	0.685886i	0.0809508	−	0.0588142i
$137$	12.4469	−	17.1317i	1.06341	−	1.46366i	0.186836	−	0.982391i	$-0.440177\pi$
$137$	12.4469	−	17.1317i	1.06341	−	1.46366i	0.876574	−	0.481267i	$-0.159823\pi$
$138$	0.125869	−	0.173244i	0.0107147	−	0.0147475i
$139$	−3.12211	+	2.26834i	−0.264814	+	0.192398i	−0.712266	−	0.701909i	$-0.752331\pi$
$139$	−3.12211	+	2.26834i	−0.264814	+	0.192398i	0.447453	+	0.894308i	$0.352331\pi$
$140$	−0.336274	−	8.36894i	−0.0284203	−	0.707305i
$141$	0.567968	+	0.412653i	0.0478316	+	0.0347517i
$142$	13.6616	−	4.43893i	1.14646	−	0.372507i
$143$		−	8.87629i		−	0.742273i
$144$	0.701357	+	2.15855i	0.0584464	+	0.179880i
$145$	−19.3951	+	0.779320i	−1.61068	+	0.0647190i
$146$	−3.28812	+	10.1198i	−0.272127	+	0.837521i
$147$	5.71424	+	1.85667i	0.471303	+	0.153136i
$148$	−1.65380	−	2.27626i	−0.135941	−	0.187107i
$149$	6.52658			0.534678			0.267339	−	0.963603i	$-0.413856\pi$
$149$	6.52658			0.534678			0.267339	+	0.963603i	$0.413856\pi$
$150$	−3.64735	−	2.22618i	−0.297805	−	0.181767i
$151$	−2.89168			−0.235322			−0.117661	−	0.993054i	$-0.537540\pi$
$151$	−2.89168			−0.235322			−0.117661	+	0.993054i	$0.537540\pi$
$152$	0.587785	+	0.809017i	0.0476757	+	0.0656199i
$153$	−2.51881	−	0.818412i	−0.203634	−	0.0661647i
$154$	1.71751	−	5.28595i	0.138401	−	0.425954i
$155$	−14.2357	+	11.2430i	−1.14344	+	0.903063i
$156$	−1.57980	−	4.86212i	−0.126485	−	0.389281i
$157$			6.47187i			0.516511i	0.966077	+	0.258256i	$0.0831477\pi$
$157$			6.47187i			0.516511i	−0.966077	+	0.258256i	$0.916852\pi$
$158$	5.74568	−	1.86688i	0.457102	−	0.148521i
$159$	8.78548	+	6.38303i	0.696734	+	0.506207i
$160$	−2.09717	+	0.775807i	−0.165796	+	0.0613330i
$161$	0.759322	−	0.551679i	0.0598429	−	0.0434784i
$162$	1.73995	−	2.39483i	0.136703	−	0.188156i
$163$	8.87615	−	12.2170i	0.695234	−	0.956907i	−0.304756	−	0.952430i	$-0.598575\pi$
$163$	8.87615	−	12.2170i	0.695234	−	0.956907i	0.999990	−	0.00447683i	$-0.00142502\pi$
$164$	−7.13922	+	5.18695i	−0.557480	+	0.405033i
$165$	−1.75744	−	2.22523i	−0.136817	−	0.173234i
$166$	−0.0985870	−	0.0716277i	−0.00765184	−	0.00555938i
$167$	22.3901	−	7.27497i	1.73259	−	0.562954i	0.738774	−	0.673953i	$-0.235405\pi$
$167$	22.3901	−	7.27497i	1.73259	−	0.562954i	0.993821	+	0.110999i	$0.0354050\pi$
$168$		−	3.20114i		−	0.246973i
$169$	−7.04097	−	21.6699i	−0.541613	−	1.66691i
$170$	0.706025	−	2.51193i	0.0541497	−	0.192656i
$171$	0.701357	−	2.15855i	0.0536341	−	0.165069i
$172$	−6.40405	−	2.08080i	−0.488304	−	0.158660i
$173$	−9.46921	−	13.0333i	−0.719931	−	0.990900i	−0.999526	−	0.0307818i	$-0.990200\pi$
$173$	−9.46921	−	13.0333i	−0.719931	−	0.990900i	0.279595	−	0.960118i	$-0.409800\pi$
$174$	−7.41869			−0.562409
$175$	−12.1886	−	14.2197i	−0.921371	−	1.07491i
$176$	−1.48382			−0.111847
$177$	3.71851	+	5.11808i	0.279500	+	0.384699i
$178$	−12.5543	−	4.07915i	−0.940986	−	0.305745i
$179$	3.33131	−	10.2527i	0.248994	−	0.766324i	−0.745960	−	0.665990i	$-0.768009\pi$
$179$	3.33131	−	10.2527i	0.248994	−	0.766324i	0.994954	−	0.100333i	$-0.0319909\pi$
$180$	4.22227	+	2.81580i	0.314709	+	0.209877i
$181$	3.86009	+	11.8801i	0.286918	+	0.883044i	0.985817	+	0.167823i	$0.0536739\pi$
$181$	3.86009	+	11.8801i	0.286918	+	0.883044i	−0.698899	+	0.715221i	$0.746326\pi$
$182$		−	22.4072i		−	1.66093i
$183$	5.80383	−	1.88578i	0.429032	−	0.139401i
$184$	−0.202717	−	0.147282i	−0.0149445	−	0.0108578i
$185$	−6.05673	−	1.70236i	−0.445299	−	0.125160i
$186$	−5.60892	+	4.07512i	−0.411266	+	0.298802i
$187$	1.01773	−	1.40078i	0.0744237	−	0.102435i
$188$	0.482855	−	0.664592i	0.0352158	−	0.0484704i
$189$	−13.6472	+	9.91526i	−0.992687	+	0.721229i
$190$	2.15265	+	0.605044i	0.156170	+	0.0438945i
$191$	12.7851	+	9.28890i	0.925096	+	0.672121i	0.944787	−	0.327685i	$-0.106268\pi$
$191$	12.7851	+	9.28890i	0.925096	+	0.672121i	−0.0196915	+	0.999806i	$0.506268\pi$
$192$	−0.812784	+	0.264090i	−0.0586576	+	0.0190590i
$193$			7.40038i			0.532691i	0.963878	+	0.266345i	$0.0858162\pi$
$193$			7.40038i			0.532691i	−0.963878	+	0.266345i	$0.914184\pi$
$194$	2.22518	+	6.84839i	0.159758	+	0.491686i
$195$	−9.51062	−	6.34256i	−0.681070	−	0.454200i
$196$	2.17253	−	6.68636i	0.155181	−	0.477597i
$197$	−6.77374	−	2.20092i	−0.482609	−	0.156809i	0.0576004	−	0.998340i	$-0.481655\pi$
$197$	−6.77374	−	2.20092i	−0.482609	−	0.156809i	−0.540210	+	0.841530i	$0.681655\pi$
$198$	1.97950	+	2.72455i	0.140677	+	0.193625i
$199$	2.04906			0.145254			0.0726271	−	0.997359i	$-0.476862\pi$
$199$	2.04906			0.145254			0.0726271	+	0.997359i	$0.476862\pi$
$200$	−2.60490	+	4.26784i	−0.184194	+	0.301782i
$201$	−9.23555			−0.651425
$202$	8.35779	+	11.5035i	0.588052	+	0.809384i
$203$	−30.9243	−	10.0479i	−2.17046	−	0.705226i
$204$	0.308166	−	0.948436i	0.0215759	−	0.0664038i
$205$	−5.33925	+	18.9962i	−0.372910	+	1.32676i
$206$	−3.69630	−	11.3760i	−0.257533	−	0.792607i
$207$			0.568708i			0.0395279i
$208$	−5.68928	+	1.84856i	−0.394480	+	0.128174i
$209$	1.20043	+	0.872166i	0.0830358	+	0.0603290i
$210$	−4.43645	−	5.61733i	−0.306144	−	0.387632i
$211$	8.57707	−	6.23161i	0.590470	−	0.429002i	−0.252013	−	0.967724i	$-0.581093\pi$
$211$	8.57707	−	6.23161i	0.590470	−	0.429002i	0.842484	+	0.538722i	$0.181093\pi$
$212$	7.46892	−	10.2801i	0.512967	−	0.706039i
$213$	7.21579	−	9.93168i	0.494418	−	0.680507i
$214$	−4.71831	+	3.42805i	−0.322537	+	0.234337i
$215$	−14.1215	+	5.22399i	−0.963081	+	0.356273i
$216$	3.64340	+	2.64709i	0.247902	+	0.180112i
$217$	−28.8998	+	9.39011i	−1.96185	+	0.637442i
$218$		−	17.6280i		−	1.19392i
$219$	2.81007	+	8.64850i	0.189887	+	0.584412i
$220$	−2.60379	+	2.05642i	−0.175547	+	0.138644i
$221$	2.15708	−	6.63881i	0.145101	−	0.446575i
$222$	−2.28686	−	0.743044i	−0.153484	−	0.0498699i
$223$	14.3096	+	19.6955i	0.958242	+	1.31891i	0.947768	+	0.318962i	$0.103334\pi$
$223$	14.3096	+	19.6955i	0.958242	+	1.31891i	0.0104742	+	0.999945i	$0.496666\pi$
$224$	−3.74573			−0.250272
$225$	11.3116	−	0.910498i	0.754107	−	0.0606999i
$226$	10.1020			0.671978
$227$	8.57439	+	11.8016i	0.569102	+	0.783302i	0.992448	−	0.122666i	$-0.0391445\pi$
$227$	8.57439	+	11.8016i	0.569102	+	0.783302i	−0.423346	+	0.905968i	$0.639145\pi$
$228$	0.812784	+	0.264090i	0.0538279	+	0.0174898i
$229$	4.99166	−	15.3627i	0.329858	−	1.01520i	−0.639342	−	0.768923i	$-0.720793\pi$
$229$	4.99166	−	15.3627i	0.329858	−	1.01520i	0.969200	−	0.246276i	$-0.0792068\pi$
$230$	−0.559844	+	0.0224952i	−0.0369150	+	0.00148329i
$231$	−1.46780	−	4.51743i	−0.0965743	−	0.297225i
$232$			8.68077i			0.569920i
$233$	−2.55581	+	0.830432i	−0.167436	+	0.0544034i	−0.391536	−	0.920163i	$-0.628056\pi$
$233$	−2.55581	+	0.830432i	−0.167436	+	0.0544034i	0.224099	+	0.974566i	$0.428056\pi$
$234$	10.9841	+	7.98043i	0.718054	+	0.521697i
$235$	−0.0737488	−	1.83541i	−0.00481084	−	0.119729i
$236$	5.98878	−	4.35111i	0.389837	−	0.283233i
$237$	3.03475	−	4.17697i	0.197128	−	0.271323i
$238$	2.56914	−	3.53612i	0.166533	−	0.229212i
$239$	−14.3041	+	10.3926i	−0.925258	+	0.672239i	−0.944827	−	0.327569i	$-0.893771\pi$
$239$	−14.3041	+	10.3926i	−0.925258	+	0.672239i	0.0195691	+	0.999809i	$0.493771\pi$
$240$	−1.06026	+	1.58986i	−0.0684397	+	0.102625i
$241$	4.14551	+	3.01189i	0.267036	+	0.194013i	0.713243	−	0.700917i	$-0.247226\pi$
$241$	4.14551	+	3.01189i	0.267036	+	0.194013i	−0.446207	+	0.894930i	$0.647226\pi$
$242$	8.36767	−	2.71882i	0.537894	−	0.174772i
$243$		−	16.0403i		−	1.02898i
$244$	−2.20659	−	6.79119i	−0.141263	−	0.434762i
$245$	−5.45428	−	14.7441i	−0.348461	−	0.941964i
$246$	−2.33048	+	7.17247i	−0.148586	+	0.457300i
$247$	5.68928	+	1.84856i	0.362000	+	0.117621i
$248$	4.76838	+	6.56312i	0.302793	+	0.416758i
$249$	−0.104143			−0.00659981
$250$	1.34374	+	11.0993i	0.0849854	+	0.701981i
$251$	16.3572			1.03246			0.516228	−	0.856451i	$-0.327336\pi$
$251$	16.3572			1.03246			0.516228	+	0.856451i	$0.327336\pi$
$252$	4.99702	+	6.87781i	0.314783	+	0.433261i
$253$	−0.353606	−	0.114893i	−0.0222310	−	0.00722329i
$254$	1.07166	−	3.29824i	0.0672422	−	0.206950i
$255$	−0.773670	−	2.09139i	−0.0484491	−	0.130968i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	21.5196i		−	1.34235i	−0.741297	−	0.671177i	$-0.765789\pi$
$257$		−	21.5196i		−	1.34235i	0.741297	−	0.671177i	$-0.234211\pi$
$258$	−5.47298	+	1.77828i	−0.340733	+	0.110711i
$259$	−8.52623	−	6.19467i	−0.529794	−	0.384918i
$260$	−7.42157	+	11.1286i	−0.460266	+	0.690166i
$261$	15.9394	−	11.5807i	0.986626	−	0.716825i
$262$	−0.931837	+	1.28256i	−0.0575691	+	0.0792371i
$263$	−1.30731	+	1.79936i	−0.0806124	+	0.110953i	−0.847419	−	0.530925i	$-0.821845\pi$
$263$	−1.30731	+	1.79936i	−0.0806124	+	0.110953i	0.766806	+	0.641878i	$0.221845\pi$
$264$	−1.02590	+	0.745364i	−0.0631401	+	0.0458740i
$265$	−1.14077	−	28.3905i	−0.0700767	−	1.74402i
$266$	3.03036	+	2.20168i	0.185803	+	0.134994i
$267$	−10.7291	+	3.48609i	−0.656608	+	0.213345i
$268$			10.8067i			0.660125i
$269$	−3.46132	−	10.6529i	−0.211041	−	0.649516i	−0.999411	−	0.0343154i	$-0.989075\pi$
$269$	−3.46132	−	10.6529i	−0.211041	−	0.649516i	0.788370	−	0.615201i	$-0.210925\pi$
$270$	10.0620	−	0.404303i	0.612354	−	0.0246051i
$271$	−4.86234	+	14.9647i	−0.295366	+	0.909044i	0.687732	+	0.725965i	$0.258606\pi$
$271$	−4.86234	+	14.9647i	−0.295366	+	0.909044i	−0.983098	+	0.183079i	$0.941394\pi$
$272$	−1.10979	−	0.360591i	−0.0672907	−	0.0218641i
$273$	−11.2557	−	15.4922i	−0.681229	−	0.937631i
$274$	−21.1759			−1.27928
$275$	−1.71911	+	7.21717i	−0.103666	+	0.435212i
$276$	−0.214142			−0.0128898
$277$	1.70590	+	2.34797i	0.102498	+	0.141076i	0.857185	−	0.515009i	$-0.172211\pi$
$277$	1.70590	+	2.34797i	0.102498	+	0.141076i	−0.754687	+	0.656085i	$0.772211\pi$
$278$	3.67026	+	1.19254i	0.220127	+	0.0715237i
$279$	5.68973	−	17.5112i	0.340635	−	1.04837i
$280$	−6.57296	+	5.19119i	−0.392809	+	0.310233i
$281$	−9.01377	−	27.7415i	−0.537716	−	1.65492i	−0.737706	−	0.675123i	$-0.764091\pi$
$281$	−9.01377	−	27.7415i	−0.537716	−	1.65492i	0.199989	−	0.979798i	$-0.435909\pi$
$282$		−	0.702048i		−	0.0418063i
$283$	18.9854	−	6.16873i	1.12857	−	0.366693i	0.315535	−	0.948914i	$-0.397816\pi$
$283$	18.9854	−	6.16873i	1.12857	−	0.366693i	0.813031	+	0.582221i	$0.197816\pi$
$284$	−11.6213	−	8.44335i	−0.689596	−	0.501021i
$285$	1.79227	−	0.663014i	0.106165	−	0.0392736i
$286$	−7.18107	+	5.21735i	−0.424625	+	0.308508i
$287$	−19.4289	+	26.7416i	−1.14685	+	1.57851i
$288$	1.33406	−	1.83618i	0.0786103	−	0.108198i
$289$	−12.6517	+	9.19199i	−0.744217	+	0.540705i
$290$	12.0307	+	15.2329i	0.706465	+	0.894508i
$291$	4.97862	+	3.61718i	0.291852	+	0.212043i
$292$	10.1198	−	3.28812i	0.592217	−	0.192423i
$293$			6.21956i			0.363351i	0.983359	+	0.181675i	$0.0581520\pi$
$293$			6.21956i			0.363351i	−0.983359	+	0.181675i	$0.941848\pi$
$294$	−1.85667	−	5.71424i	−0.108283	−	0.333261i
$295$	4.47887	−	15.9351i	0.260770	−	0.927778i
$296$	−0.869453	+	2.67590i	−0.0505359	+	0.155534i
$297$	6.35531	+	2.06496i	0.368772	+	0.119821i
$298$	−3.83623	−	5.28011i	−0.222227	−	0.305869i
$299$	−1.49894			−0.0866857
$300$	0.342840	+	4.25928i	0.0197939	+	0.245910i
$301$	−25.2223			−1.45379
$302$	1.69969	+	2.33942i	0.0978062	+	0.134619i
$303$	11.5571	+	3.75512i	0.663936	+	0.215726i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	−13.2840	−	8.85900i	−0.760640	−	0.507265i
$306$	0.818412	+	2.51881i	0.0467855	+	0.143991i
$307$			18.4201i			1.05129i	0.850705	+	0.525644i	$0.176176\pi$
$307$			18.4201i			1.05129i	−0.850705	+	0.525644i	$0.823824\pi$
$308$	−5.28595	+	1.71751i	−0.301195	+	0.0978641i
$309$	−8.27011	−	6.00859i	−0.470470	−	0.341817i
$310$	17.4633	+	4.90840i	0.991850	+	0.278778i
$311$	−2.44678	+	1.77769i	−0.138744	+	0.100804i	−0.654992	−	0.755635i	$-0.727328\pi$
$311$	−2.44678	+	1.77769i	−0.138744	+	0.100804i	0.516248	+	0.856439i	$0.327328\pi$
$312$	−3.00496	+	4.13597i	−0.170122	+	0.234153i
$313$	−0.0321910	+	0.0443070i	−0.00181954	+	0.00250438i	−0.809926	−	0.586532i	$-0.800493\pi$
$313$	−0.0321910	+	0.0443070i	−0.00181954	+	0.00250438i	0.808106	+	0.589037i	$0.200493\pi$
$314$	5.23585	−	3.80407i	0.295476	−	0.214676i
$315$	18.3007	+	5.14375i	1.03113	+	0.289818i
$316$	−4.88757	−	3.55102i	−0.274947	−	0.199761i
$317$	23.9517	−	7.78238i	1.34526	−	0.437102i	0.454166	−	0.890917i	$-0.349937\pi$
$317$	23.9517	−	7.78238i	1.34526	−	0.437102i	0.891096	+	0.453815i	$0.149937\pi$
$318$		−	10.8595i		−	0.608968i
$319$	3.98035	+	12.2503i	0.222857	+	0.685883i
$320$	1.86033	+	1.24064i	0.103995	+	0.0693538i
$321$	−1.54021	+	4.74028i	−0.0859661	+	0.264577i
$322$	−0.892636	−	0.290035i	−0.0497447	−	0.0161630i
$323$	0.685886	+	0.944041i	0.0381637	+	0.0525278i
$324$	−2.96018			−0.164454
$325$	2.39979	+	29.8139i	0.133116	+	1.65378i
$326$	−15.1010			−0.836368
$327$	−8.85502	−	12.1879i	−0.489684	−	0.673992i
$328$	8.39266	+	2.72694i	0.463407	+	0.150570i
$329$	0.950859	−	2.92644i	0.0524225	−	0.161340i
$330$	−0.767250	+	2.72976i	−0.0422357	+	0.150268i
$331$	−9.15078	−	28.1632i	−0.502972	−	1.54799i	−0.804153	−	0.594422i	$-0.797381\pi$
$331$	−9.15078	−	28.1632i	−0.502972	−	1.54799i	0.301181	−	0.953567i	$-0.402619\pi$
$332$			0.121860i			0.00668795i
$333$	6.07333	−	1.97334i	0.332816	−	0.108139i
$334$	−19.0461	−	13.8378i	−1.04216	−	0.757172i
$335$	14.9770	+	18.9635i	0.818281	+	1.03609i
$336$	−2.58978	+	1.88158i	−0.141284	+	0.102649i
$337$	−6.65262	+	9.15654i	−0.362391	+	0.498789i	−0.950813	−	0.309765i	$-0.899749\pi$
$337$	−6.65262	+	9.15654i	−0.362391	+	0.498789i	0.588422	+	0.808554i	$0.299749\pi$
$338$	−13.3927	+	18.4335i	−0.728468	+	1.00265i
$339$	6.98451	−	5.07454i	0.379346	−	0.275611i
$340$	−2.44718	+	0.905288i	−0.132717	+	0.0490962i
$341$	9.73847	+	7.07541i	0.527368	+	0.383155i
$342$	−2.15855	+	0.701357i	−0.116721	+	0.0379250i
$343$		−	0.114083i		−	0.00615989i
$344$	2.08080	+	6.40405i	0.112189	+	0.345283i
$345$	−0.375773	+	0.296778i	−0.0202310	+	0.0159780i
$346$	−4.97826	+	15.3215i	−0.267633	+	0.823689i
$347$	21.3718	+	6.94410i	1.14730	+	0.372779i	0.820124	−	0.572186i	$-0.193904\pi$
$347$	21.3718	+	6.94410i	1.14730	+	0.372779i	0.327172	+	0.944965i	$0.393904\pi$
$348$	4.36059	+	6.00184i	0.233752	+	0.321733i
$349$	34.0398			1.82211			0.911053	−	0.412288i	$-0.135270\pi$
$349$	34.0398			1.82211			0.911053	+	0.412288i	$0.135270\pi$
$350$	−4.33970	+	18.2189i	−0.231967	+	0.973841i
$351$	26.9402			1.43796
$352$	0.872166	+	1.20043i	0.0464866	+	0.0639833i
$353$	−18.3768	−	5.97099i	−0.978100	−	0.317804i	−0.224018	−	0.974585i	$-0.571918\pi$
$353$	−18.3768	−	5.97099i	−0.978100	−	0.317804i	−0.754081	+	0.656781i	$0.771918\pi$
$354$	1.95493	−	6.01667i	0.103904	−	0.319782i
$355$	−32.0945	+	1.28960i	−1.70340	+	0.0684446i
$356$	4.07915	+	12.5543i	0.216194	+	0.665378i
$357$		−	3.73541i		−	0.197699i
$358$	−10.2527	+	3.33131i	−0.541873	+	0.176065i
$359$	−25.0278	−	18.1838i	−1.32092	−	0.959702i	−0.999920	−	0.0126220i	$-0.995982\pi$
$359$	−25.0278	−	18.1838i	−1.32092	−	0.959702i	−0.320997	−	0.947080i	$-0.604018\pi$
$360$	−0.203758	−	5.07097i	−0.0107390	−	0.267264i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	7.34233	−	10.1059i	0.385904	−	0.531152i
$363$	4.41963	−	6.08309i	0.231970	−	0.319280i
$364$	−18.1278	+	13.1706i	−0.950153	+	0.690327i
$365$	13.2011	−	19.7950i	0.690979	−	1.03612i
$366$	−4.93704	−	3.58697i	−0.258063	−	0.187494i
$367$	−7.94407	+	2.58118i	−0.414677	+	0.134737i	−0.508923	−	0.860812i	$-0.669956\pi$
$367$	−7.94407	+	2.58118i	−0.414677	+	0.134737i	0.0942457	+	0.995549i	$0.469956\pi$
$368$			0.250572i			0.0130620i
$369$	−6.18917	−	19.0483i	−0.322195	−	0.991615i
$370$	2.18282	+	5.90061i	0.113479	+	0.306758i
$371$	14.7081	−	45.2670i	0.763608	−	2.35014i
$372$	6.59368	+	2.14242i	0.341866	+	0.111079i
$373$	−10.0732	−	13.8646i	−0.521571	−	0.717881i	0.464245	−	0.885707i	$-0.346326\pi$
$373$	−10.0732	−	13.8646i	−0.521571	−	0.717881i	−0.985817	+	0.167825i	$0.946326\pi$
$374$	−1.73146			−0.0895319
$375$	6.50454	+	6.99900i	0.335893	+	0.361427i
$376$	−0.821481			−0.0423647
$377$	30.5230	+	42.0113i	1.57202	+	2.16369i
$378$	16.0432	+	5.21276i	0.825175	+	0.268116i
$379$	−9.43244	+	29.0301i	−0.484512	+	1.49117i	0.348175	+	0.937430i	$0.386802\pi$
$379$	−9.43244	+	29.0301i	−0.484512	+	1.49117i	−0.832686	+	0.553745i	$0.813198\pi$
$380$	−0.775807	−	2.09717i	−0.0397981	−	0.107583i
$381$	−0.915857	−	2.81872i	−0.0469208	−	0.144407i
$382$		−	15.8032i		−	0.808563i
$383$	−10.5673	+	3.43352i	−0.539964	+	0.175445i	−0.566286	−	0.824209i	$-0.691620\pi$
$383$	−10.5673	+	3.43352i	−0.539964	+	0.175445i	0.0263226	+	0.999654i	$0.491620\pi$
$384$	0.691395	+	0.502328i	0.0352826	+	0.0256343i
$385$	−6.89544	+	10.3397i	−0.351424	+	0.526957i
$386$	5.98703	−	4.34983i	0.304732	−	0.221401i
$387$	8.98305	−	12.3641i	0.456634	−	0.628503i
$388$	4.23254	−	5.82559i	0.214875	−	0.295749i
$389$	10.4522	−	7.59395i	0.529946	−	0.385029i	−0.290391	−	0.956908i	$-0.593785\pi$
$389$	10.4522	−	7.59395i	0.529946	−	0.385029i	0.820338	+	0.571879i	$0.193785\pi$
$390$	0.458962	+	11.4223i	0.0232405	+	0.578392i
$391$	−0.236550	−	0.171864i	−0.0119628	−	0.00869152i
$392$	−6.68636	+	2.17253i	−0.337712	+	0.109729i
$393$			1.35485i			0.0683430i
$394$	2.20092	+	6.77374i	0.110881	+	0.341256i
$395$	−13.4980	+	0.542366i	−0.679158	+	0.0272894i
$396$	1.04069	−	3.20290i	0.0522964	−	0.160952i
$397$	16.4701	+	5.35145i	0.826609	+	0.268581i	0.691616	−	0.722265i	$-0.256899\pi$
$397$	16.4701	+	5.35145i	0.826609	+	0.268581i	0.134993	+	0.990847i	$0.456899\pi$
$398$	−1.20441	−	1.65773i	−0.0603715	−	0.0830943i
$399$	3.20114			0.160257
$400$	4.98388	−	0.401164i	0.249194	−	0.0200582i
$401$	24.6110			1.22902			0.614508	−	0.788910i	$-0.289354\pi$
$401$	24.6110			1.22902			0.614508	+	0.788910i	$0.289354\pi$
$402$	5.42852	+	7.47172i	0.270750	+	0.372655i
$403$	46.1540	+	14.9964i	2.29910	+	0.747022i
$404$	4.39395	−	13.5232i	0.218607	−	0.672804i
$405$	−5.19449	+	4.10250i	−0.258116	+	0.203855i
$406$	10.0479	+	30.9243i	0.498670	+	1.53475i
$407$			4.17488i			0.206941i
$408$	−0.948436	+	0.308166i	−0.0469546	+	0.0152565i
$409$	6.45643	+	4.69087i	0.319250	+	0.231949i	0.735855	−	0.677139i	$-0.236780\pi$
$409$	6.45643	+	4.69087i	0.319250	+	0.231949i	−0.416605	+	0.909087i	$0.636780\pi$
$410$	18.5066	−	6.84616i	0.913977	−	0.338108i
$411$	−14.6409	+	10.6373i	−0.722184	+	0.524697i
$412$	−7.03078	+	9.67704i	−0.346382	+	0.476754i
$413$	16.2980	−	22.4323i	0.801974	−	1.10382i
$414$	0.460094	−	0.334278i	0.0226124	−	0.0164289i
$415$	0.168886	+	0.213839i	0.00829028	+	0.0104969i
$416$	4.83959	+	3.51617i	0.237280	+	0.172394i
$417$	3.13664	−	1.01916i	0.153602	−	0.0499084i
$418$		−	1.48382i		−	0.0725759i
$419$	−7.42940	−	22.8653i	−0.362950	−	1.11704i	−0.951255	−	0.308406i	$-0.900205\pi$
$419$	−7.42940	−	22.8653i	−0.362950	−	1.11704i	0.588305	−	0.808639i	$-0.299795\pi$
$420$	−1.93683	+	6.89095i	−0.0945077	+	0.336244i
$421$	0.602189	−	1.85335i	0.0293489	−	0.0903267i	−0.935309	−	0.353832i	$-0.884879\pi$
$421$	0.602189	−	1.85335i	0.0293489	−	0.0903267i	0.964658	+	0.263505i	$0.0848786\pi$
$422$	−10.0830	−	3.27615i	−0.490831	−	0.159481i
$423$	1.09591	+	1.50838i	0.0532848	+	0.0733402i
$424$	−12.7069			−0.617101
$425$	−3.03966	+	4.98014i	−0.147445	+	0.241572i
$426$	−12.2762			−0.594785
$427$	−15.7215	−	21.6388i	−0.760817	−	1.04718i
$428$	5.54670	+	1.80223i	0.268110	+	0.0871142i
$429$	−2.34413	+	7.21451i	−0.113176	+	0.348320i
$430$	12.5267	+	8.35398i	0.604093	+	0.402865i
$431$	−12.8208	−	39.4583i	−0.617556	−	1.90064i	−0.346183	−	0.938167i	$-0.612522\pi$
$431$	−12.8208	−	39.4583i	−0.617556	−	1.90064i	−0.271373	−	0.962474i	$-0.587478\pi$
$432$		−	4.50349i		−	0.216674i
$433$	6.99639	−	2.27327i	0.336225	−	0.109246i	−0.136038	−	0.990704i	$-0.543437\pi$
$433$	6.99639	−	2.27327i	0.336225	−	0.109246i	0.472264	+	0.881457i	$0.343437\pi$
$434$	24.5836	+	17.8611i	1.18005	+	0.857358i
$435$	15.9699	+	4.48863i	0.765697	+	0.215214i
$436$	−14.2613	+	10.3615i	−0.682993	+	0.496224i
$437$	0.147282	−	0.202717i	0.00704547	−	0.00969726i
$438$	5.34507	−	7.35686i	0.255397	−	0.351524i
$439$	−11.6788	+	8.48514i	−0.557399	+	0.404974i	−0.830506	−	0.557010i	$-0.811949\pi$
$439$	−11.6788	+	8.48514i	−0.557399	+	0.404974i	0.273107	+	0.961984i	$0.411949\pi$
$440$	3.19415	+	0.897776i	0.152275	+	0.0427998i
$441$	12.9092	+	9.37905i	0.614722	+	0.446622i
$442$	−6.63881	+	2.15708i	−0.315776	+	0.102602i
$443$			1.29343i			0.0614525i	0.999528	+	0.0307263i	$0.00978201\pi$
$443$			1.29343i			0.0614525i	−0.999528	+	0.0307263i	$0.990218\pi$
$444$	0.743044	+	2.28686i	0.0352633	+	0.108529i
$445$	24.5571	+	16.3769i	1.16412	+	0.776340i
$446$	7.52300	−	23.1534i	0.356225	−	1.09635i
$447$	−5.30470	−	1.72360i	−0.250904	−	0.0815235i
$448$	2.20168	+	3.03036i	0.104020	+	0.143171i
$449$	−11.7506			−0.554544			−0.277272	−	0.960791i	$-0.589430\pi$
$449$	−11.7506			−0.554544			−0.277272	+	0.960791i	$0.589430\pi$
$450$	−7.38541	−	8.61611i	−0.348151	−	0.406167i
$451$	13.0941			0.616575
$452$	−5.93783	−	8.17272i	−0.279292	−	0.384413i
$453$	2.35032	+	0.763664i	0.110427	+	0.0358800i
$454$	4.50782	−	13.8736i	0.211563	−	0.651123i
$455$	−13.5573	+	48.2349i	−0.635577	+	2.26129i
$456$	−0.264090	−	0.812784i	−0.0123671	−	0.0380621i
$457$		−	25.0112i		−	1.16997i	−0.811042	−	0.584987i	$-0.801099\pi$
$457$		−	25.0112i		−	1.16997i	0.811042	−	0.584987i	$-0.198901\pi$
$458$	−15.3627	+	4.99166i	−0.717853	+	0.233245i
$459$	4.25148	+	3.08888i	0.198442	+	0.144177i
$460$	0.347267	+	0.439701i	0.0161914	+	0.0205012i
$461$	−6.57243	+	4.77515i	−0.306109	+	0.222401i	−0.730225	−	0.683207i	$-0.760585\pi$
$461$	−6.57243	+	4.77515i	−0.306109	+	0.222401i	0.424116	+	0.905608i	$0.360585\pi$
$462$	−2.79193	+	3.84276i	−0.129892	+	0.178781i
$463$	−11.6372	+	16.0172i	−0.540827	+	0.744385i	−0.988732	−	0.149697i	$-0.952170\pi$
$463$	−11.6372	+	16.0172i	−0.540827	+	0.744385i	0.447905	+	0.894081i	$0.352170\pi$
$464$	7.02289	−	5.10243i	0.326029	−	0.236874i
$465$	14.5397	−	5.37867i	0.674262	−	0.249430i
$466$	2.17410	+	1.57958i	0.100713	+	0.0731724i
$467$	−24.9356	+	8.10207i	−1.15388	+	0.374919i	−0.822604	−	0.568614i	$-0.807480\pi$
$467$	−24.9356	+	8.10207i	−1.15388	+	0.374919i	−0.331278	+	0.943533i	$0.607480\pi$
$468$		−	13.5771i		−	0.627602i
$469$	12.5087	+	38.4978i	0.577598	+	1.77766i
$470$	−1.44153	+	1.13849i	−0.0664927	+	0.0525146i
$471$	1.70915	−	5.26023i	0.0787536	−	0.242379i
$472$	−7.04024	−	2.28751i	−0.324053	−	0.105291i
$473$	5.87283	+	8.08326i	0.270033	+	0.371669i
$474$	−5.16302			−0.237145
$475$	−4.26784	−	2.60490i	−0.195822	−	0.119521i
$476$	−4.37088			−0.200339
$477$	16.9518	+	23.3321i	0.776167	+	1.06830i
$478$	16.8155	+	5.46370i	0.769124	+	0.249904i
$479$	1.26809	−	3.90277i	0.0579403	−	0.178322i	−0.917898	−	0.396817i	$-0.870115\pi$
$479$	1.26809	−	3.90277i	0.0579403	−	0.178322i	0.975838	+	0.218495i	$0.0701147\pi$
$480$	1.90943	−	0.0767231i	0.0871531	−	0.00350192i
$481$	5.20112	+	16.0074i	0.237151	+	0.729874i
$482$		−	5.12413i		−	0.233398i
$483$	−0.762857	+	0.247867i	−0.0347112	+	0.0112784i
$484$	−7.11796	−	5.17150i	−0.323544	−	0.235068i
$485$	−0.646457	−	16.0886i	−0.0293541	−	0.730543i
$486$	−12.9769	+	9.42824i	−0.588643	+	0.427674i
$487$	−12.2581	+	16.8718i	−0.555466	+	0.764533i	−0.990741	−	0.135764i	$-0.956651\pi$
$487$	−12.2581	+	16.8718i	−0.555466	+	0.764533i	0.435275	+	0.900297i	$0.356651\pi$
$488$	−4.19719	+	5.77693i	−0.189998	+	0.261510i
$489$	−10.4408	+	7.58566i	−0.472148	+	0.343035i
$490$	−8.72225	+	13.0789i	−0.394031	+	0.590847i
$491$	10.3747	+	7.53769i	0.468205	+	0.340171i	0.796741	−	0.604320i	$-0.206555\pi$
$491$	10.3747	+	7.53769i	0.468205	+	0.340171i	−0.328536	+	0.944491i	$0.606555\pi$
$492$	7.17247	−	2.33048i	0.323360	−	0.105066i
$493$			10.1296i			0.456213i
$494$	−1.84856	−	5.68928i	−0.0831706	−	0.255973i
$495$	−2.61271	−	7.06271i	−0.117433	−	0.317445i
$496$	2.50689	−	7.71541i	0.112563	−	0.346432i
$497$	−51.1727	−	16.6270i	−2.29541	−	0.745824i
$498$	0.0612138	+	0.0842536i	0.00274306	+	0.00377549i
$499$	0.673711			0.0301594			0.0150797	−	0.999886i	$-0.495200\pi$
$499$	0.673711			0.0301594			0.0150797	+	0.999886i	$0.495200\pi$
$500$	8.18969	−	7.61111i	0.366254	−	0.340379i
$501$	−20.1195			−0.898874
$502$	−9.61450	−	13.2332i	−0.429116	−	0.590628i
$503$	−14.3291	−	4.65580i	−0.638903	−	0.207592i	−0.0283880	−	0.999597i	$-0.509037\pi$
$503$	−14.3291	−	4.65580i	−0.638903	−	0.207592i	−0.610515	+	0.792005i	$0.709037\pi$
$504$	2.62709	−	8.08535i	0.117020	−	0.360150i
$505$	−11.0313	−	29.8199i	−0.490886	−	1.32697i
$506$	0.114893	+	0.353606i	0.00510764	+	0.0157197i
$507$			19.4724i			0.864798i
$508$	−3.29824	+	1.07166i	−0.146336	+	0.0475474i
$509$	23.7464	+	17.2528i	1.05254	+	0.764715i	0.972694	−	0.232092i	$-0.0745572\pi$
$509$	23.7464	+	17.2528i	1.05254	+	0.764715i	0.0798459	+	0.996807i	$0.474557\pi$
$510$	−1.23722	+	1.85520i	−0.0547850	+	0.0821497i
$511$	32.2448	−	23.4272i	1.42643	−	1.03636i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−2.64709	+	3.64340i	−0.116872	+	0.160860i
$514$	−17.4097	+	12.6489i	−0.767909	+	0.557919i
$515$	1.07385	+	26.7251i	0.0473194	+	1.17765i
$516$	4.65559	+	3.38249i	0.204951	+	0.148906i
$517$	−1.15927	+	0.376670i	−0.0509846	+	0.0165659i
$518$			10.5390i			0.463057i
$519$	4.25448	+	13.0939i	0.186751	+	0.574760i
$520$	13.3655	−	0.537042i	0.586116	−	0.0235509i
$521$	5.25667	−	16.1784i	0.230299	−	0.708787i	−0.767412	−	0.641155i	$-0.778456\pi$
$521$	5.25667	−	16.1784i	0.230299	−	0.708787i	0.997710	−	0.0676319i	$-0.0215444\pi$
$522$	−18.7379	−	6.08832i	−0.820136	−	0.266478i
$523$	−5.65157	−	7.77872i	−0.247126	−	0.340140i	0.667376	−	0.744721i	$-0.267417\pi$
$523$	−5.65157	−	7.77872i	−0.247126	−	0.340140i	−0.914502	+	0.404581i	$0.867417\pi$
$524$	1.58534			0.0692557
$525$	6.15142	+	14.7764i	0.268470	+	0.644896i
$526$	2.22413			0.0969768
$527$	5.56422	+	7.65849i	0.242381	+	0.333609i
$528$	1.20602	+	0.391861i	0.0524854	+	0.0170536i
$529$	7.08799	−	21.8146i	0.308173	−	0.948460i
$530$	−22.2979	+	17.6104i	−0.968559	+	0.764949i
$531$	5.19182	+	15.9788i	0.225306	+	0.693421i
$532$		−	3.74573i		−	0.162398i
$533$	50.2054	−	16.3127i	2.17464	−	0.706583i
$534$	9.12669	+	6.63093i	0.394951	+	0.286948i
$535$	12.2310	−	4.52463i	0.528793	−	0.195617i
$536$	8.74282	−	6.35203i	0.377632	−	0.274366i
$537$	−5.41527	+	7.45348i	−0.233686	+	0.321641i
$538$	−6.58383	+	9.06186i	−0.283849	+	0.390685i
$539$	−8.43960	+	6.13173i	−0.363519	+	0.264112i
$540$	−6.24138	−	7.90269i	−0.268586	−	0.340077i
$541$	−2.23241	−	1.62194i	−0.0959787	−	0.0697326i	0.538761	−	0.842459i	$-0.318893\pi$
$541$	−2.23241	−	1.62194i	−0.0959787	−	0.0697326i	−0.634740	+	0.772726i	$0.718893\pi$
$542$	14.9647	−	4.86234i	0.642791	−	0.208855i
$543$		−	10.6754i		−	0.458125i
$544$	0.360591	+	1.10979i	0.0154602	+	0.0475817i
$545$	−10.6657	+	37.9469i	−0.456868	+	1.62547i
$546$	−5.91749	+	18.2122i	−0.253245	+	0.779409i
$547$	28.3355	+	9.20677i	1.21154	+	0.393653i	0.843994	−	0.536353i	$-0.180198\pi$
$547$	28.3355	+	9.20677i	1.21154	+	0.393653i	0.367545	+	0.930006i	$0.380198\pi$
$548$	12.4469	+	17.1317i	0.531705	+	0.731829i
$549$	16.2068			0.691688
$550$	6.84928	−	2.85135i	0.292054	−	0.121582i
$551$	−8.68077			−0.369813
$552$	0.125869	+	0.173244i	0.00535735	+	0.00737376i
$553$	−21.5217	−	6.99283i	−0.915197	−	0.297366i
$554$	0.896847	−	2.76021i	0.0381034	−	0.117270i
$555$	4.47323	+	2.98317i	0.189878	+	0.126628i
$556$	−1.19254	−	3.67026i	−0.0505749	−	0.155654i
$557$		−	7.35521i		−	0.311650i	−0.987785	−	0.155825i	$-0.950196\pi$
$557$		−	7.35521i		−	0.311650i	0.987785	−	0.155825i	$-0.0498036\pi$
$558$	−17.5112	+	5.68973i	−0.741308	+	0.240865i
$559$	32.5879	+	23.6765i	1.37832	+	1.00141i
$560$	8.06325	+	2.26633i	0.340735	+	0.0957699i
$561$	−1.19713	+	0.869763i	−0.0505427	+	0.0367214i
$562$	−17.1452	+	23.5984i	−0.723227	+	0.995436i
$563$	12.5234	−	17.2370i	0.527798	−	0.726452i	−0.458995	−	0.888439i	$-0.651790\pi$
$563$	12.5234	−	17.2370i	0.527798	−	0.726452i	0.986793	+	0.161987i	$0.0517903\pi$
$564$	−0.567968	+	0.412653i	−0.0239158	+	0.0173758i
$565$	−21.7462	−	6.11218i	−0.914870	−	0.257142i
$566$	−16.1500	−	11.7336i	−0.678833	−	0.493201i
$567$	−10.5453	+	3.42638i	−0.442862	+	0.143895i
$568$			14.3647i			0.602729i
$569$	0.808729	+	2.48901i	0.0339037	+	0.104345i	0.966576	−	0.256379i	$-0.0825296\pi$
$569$	0.808729	+	2.48901i	0.0339037	+	0.104345i	−0.932673	+	0.360724i	$0.882530\pi$
$570$	−1.58986	−	1.06026i	−0.0665918	−	0.0444096i
$571$	−11.9317	+	36.7221i	−0.499328	+	1.53677i	0.310775	+	0.950484i	$0.399411\pi$
$571$	−11.9317	+	36.7221i	−0.499328	+	1.53677i	−0.810102	+	0.586289i	$0.800589\pi$
$572$	8.44185	+	2.74292i	0.352972	+	0.114687i
$573$	−7.93840	−	10.9263i	−0.331632	−	0.456452i
$574$	33.0544			1.37966
$575$	1.21876	+	0.290306i	0.0508258	+	0.0121066i
$576$	−2.26964			−0.0945683
$577$	−2.71375	−	3.73515i	−0.112975	−	0.155497i	0.748785	−	0.662813i	$-0.230638\pi$
$577$	−2.71375	−	3.73515i	−0.112975	−	0.155497i	−0.861760	+	0.507316i	$0.830638\pi$
$578$	14.8730	+	4.83252i	0.618633	+	0.201006i
$579$	1.95436	−	6.01491i	0.0812205	−	0.249971i
$580$	5.25225	−	18.6867i	0.218088	−	0.775923i
$581$	0.141052	+	0.434115i	0.00585184	+	0.0180101i
$582$		−	6.15391i		−	0.255088i
$583$	−17.9319	+	5.82642i	−0.742663	+	0.241306i
$584$	−8.60842	−	6.25438i	−0.356219	−	0.258808i
$585$	−18.8165	−	23.8250i	−0.777966	−	0.985042i
$586$	5.03173	−	3.65577i	0.207859	−	0.151018i
$587$	4.70915	−	6.48159i	0.194368	−	0.267524i	−0.700699	−	0.713457i	$-0.747128\pi$
$587$	4.70915	−	6.48159i	0.194368	−	0.267524i	0.895066	+	0.445933i	$0.147128\pi$
$588$	−3.53160	+	4.86083i	−0.145641	+	0.200457i
$589$	−6.56312	+	4.76838i	−0.270429	+	0.196478i
$590$	−15.5244	+	5.74295i	−0.639129	+	0.236433i
$591$	4.92435	+	3.57775i	0.202561	+	0.147169i
$592$	2.67590	−	0.869453i	0.109979	−	0.0357343i
$593$		−	5.04234i		−	0.207064i	−0.994626	−	0.103532i	$-0.966986\pi$
$593$		−	5.04234i		−	0.207064i	0.994626	−	0.103532i	$-0.0330144\pi$
$594$	−2.06496	−	6.35531i	−0.0847265	−	0.260761i
$595$	−7.66998	+	6.05759i	−0.314438	+	0.248337i
$596$	−2.01682	+	6.20714i	−0.0826123	+	0.254254i
$597$	−1.66544	−	0.541136i	−0.0681621	−	0.0221472i
$598$	0.881052	+	1.21266i	0.0360289	+	0.0495895i
$599$	−16.4713			−0.672999			−0.336500	−	0.941684i	$-0.609243\pi$
$599$	−16.4713			−0.672999			−0.336500	+	0.941684i	$0.609243\pi$
$600$	3.24432	−	2.78091i	0.132449	−	0.113530i
$601$	40.5611			1.65452			0.827261	−	0.561817i	$-0.189898\pi$
$601$	40.5611			1.65452			0.827261	+	0.561817i	$0.189898\pi$
$602$	14.8253	+	20.4053i	0.604233	+	0.831656i
$603$	−23.3269	−	7.57937i	−0.949945	−	0.308656i
$604$	0.893580	−	2.75016i	0.0363592	−	0.111902i
$605$	−19.6577	+	0.789870i	−0.799199	+	0.0321128i
$606$	−3.75512	−	11.5571i	−0.152541	−	0.469474i
$607$		−	39.2969i		−	1.59501i	−0.603311	−	0.797506i	$-0.706152\pi$
$607$		−	39.2969i		−	1.59501i	0.603311	−	0.797506i	$-0.293848\pi$
$608$	−0.951057	+	0.309017i	−0.0385704	+	0.0125323i
$609$	22.4813	+	16.3336i	0.910986	+	0.661870i
$610$	0.641058	+	15.9542i	0.0259557	+	0.645966i
$611$	−3.97563	+	2.88847i	−0.160837	+	0.116855i
$612$	1.55671	−	2.14263i	0.0629264	−	0.0866107i
$613$	21.4881	−	29.5759i	0.867898	−	1.19456i	−0.111730	−	0.993739i	$-0.535639\pi$
$613$	21.4881	−	29.5759i	0.867898	−	1.19456i	0.979628	−	0.200820i	$-0.0643607\pi$
$614$	14.9021	−	10.8270i	0.601401	−	0.436944i
$615$	9.35637	−	14.0298i	0.377285	−	0.565736i
$616$	4.49650	+	3.26690i	0.181169	+	0.131627i
$617$	14.7570	−	4.79485i	0.594095	−	0.193033i	0.00349013	−	0.999994i	$-0.498889\pi$
$617$	14.7570	−	4.79485i	0.594095	−	0.193033i	0.590605	+	0.806961i	$0.298889\pi$
$618$			10.2224i			0.411206i
$619$	0.240330	+	0.739659i	0.00965967	+	0.0297294i	0.955770	−	0.294115i	$-0.0950247\pi$
$619$	0.240330	+	0.739659i	0.00965967	+	0.0297294i	−0.946111	+	0.323844i	$0.895025\pi$
$620$	−6.29371	−	17.0132i	−0.252761	−	0.683267i
$621$	0.348710	−	1.07322i	0.0139932	−	0.0430668i
$622$	2.87636	+	0.934587i	0.115332	+	0.0374735i
$623$	29.0631	+	40.0019i	1.16439	+	1.60264i
$624$	5.11234			0.204657
$625$	3.82296	−	24.7060i	0.152919	−	0.988239i
$626$	0.0547665			0.00218891
$627$	−0.745364	−	1.02590i	−0.0297670	−	0.0409707i
$628$	−6.15511	−	1.99992i	−0.245616	−	0.0798054i
$629$	−1.01456	+	3.12250i	−0.0404533	+	0.124502i
$630$	−6.59548	−	17.8290i	−0.262770	−	0.710323i
$631$	10.4985	+	32.3111i	0.417939	+	1.28628i	0.909596	+	0.415494i	$0.136391\pi$
$631$	10.4985	+	32.3111i	0.417939	+	1.28628i	−0.491657	+	0.870789i	$0.663609\pi$
$632$			6.04136i			0.240313i
$633$	−8.61701	+	2.79984i	−0.342495	+	0.111284i
$634$	−20.3745	−	14.8030i	−0.809176	−	0.587901i
$635$	−4.30251	+	6.45158i	−0.170740	+	0.256023i
$636$	−8.78548	+	6.38303i	−0.348367	+	0.253103i
$637$	−24.7203	+	34.0245i	−0.979452	+	1.34810i
$638$	7.57107	−	10.4207i	0.299742	−	0.412559i
$639$	26.3761	−	19.1634i	1.04342	−	0.758091i
$640$	−0.0897754	−	2.23427i	−0.00354869	−	0.0883171i
$641$	−32.8497	−	23.8667i	−1.29749	−	0.942678i	−0.297558	−	0.954704i	$-0.596172\pi$
$641$	−32.8497	−	23.8667i	−1.29749	−	0.942678i	−0.999928	+	0.0120257i	$0.996172\pi$
$642$	4.74028	−	1.54021i	0.187084	−	0.0607872i
$643$			8.13791i			0.320928i	0.987042	+	0.160464i	$0.0512990\pi$
$643$			8.13791i			0.320928i	−0.987042	+	0.160464i	$0.948701\pi$
$644$	0.290035	+	0.892636i	0.0114290	+	0.0351748i
$645$	12.8574	−	0.516624i	0.506258	−	0.0203421i
$646$	0.360591	−	1.10979i	0.0141873	−	0.0436640i
$647$	−25.9846	−	8.44289i	−1.02156	−	0.331924i	−0.250111	−	0.968217i	$-0.580467\pi$
$647$	−25.9846	−	8.44289i	−1.02156	−	0.331924i	−0.771448	+	0.636293i	$0.780467\pi$
$648$	1.73995	+	2.39483i	0.0683516	+	0.0940780i
$649$	−10.9840			−0.431161
$650$	22.7094	−	19.4656i	0.890735	−	0.763505i
$651$	25.9691			1.01781
$652$	8.87615	+	12.2170i	0.347617	+	0.478454i
$653$	8.84027	+	2.87238i	0.345946	+	0.112405i	0.476836	−	0.878992i	$-0.341783\pi$
$653$	8.84027	+	2.87238i	0.345946	+	0.112405i	−0.130890	+	0.991397i	$0.541783\pi$
$654$	−4.65536	+	14.3277i	−0.182039	+	0.560258i
$655$	2.78193	−	2.19711i	0.108699	−	0.0858484i
$656$	−2.72694	−	8.39266i	−0.106469	−	0.327678i
$657$			24.1503i			0.942193i
$658$	−2.92644	+	0.950859i	−0.114085	+	0.0370683i
$659$	14.2178	+	10.3299i	0.553849	+	0.402395i	0.829202	−	0.558948i	$-0.188795\pi$
$659$	14.2178	+	10.3299i	0.553849	+	0.402395i	−0.275354	+	0.961343i	$0.588795\pi$
$660$	2.65940	−	0.983792i	0.103517	−	0.0382941i
$661$	−11.7908	+	8.56649i	−0.458607	+	0.333198i	−0.792985	−	0.609242i	$-0.791474\pi$
$661$	−11.7908	+	8.56649i	−0.458607	+	0.333198i	0.334377	+	0.942439i	$0.391474\pi$
$662$	−17.4058	+	23.9570i	−0.676496	+	0.931117i
$663$	−3.50648	+	4.82626i	−0.136180	+	0.187436i
$664$	0.0985870	−	0.0716277i	0.00382592	−	0.00277969i
$665$	−5.19119	−	6.57296i	−0.201306	−	0.254888i
$666$	−5.16628	−	3.75352i	−0.200189	−	0.145446i
$667$	2.06870	−	0.672160i	0.0801002	−	0.0260261i
$668$			23.5423i			0.910879i
$669$	−6.42925	−	19.7872i	−0.248569	−	0.765017i
$670$	6.53854	−	23.2631i	0.252606	−	0.898733i
$671$	−3.27418	+	10.0769i	−0.126398	+	0.389014i
$672$	3.04447	+	0.989207i	0.117443	+	0.0381595i
$673$	−2.47444	−	3.40578i	−0.0953828	−	0.131283i	0.758658	−	0.651489i	$-0.225855\pi$
$673$	−2.47444	−	3.40578i	−0.0953828	−	0.131283i	−0.854041	+	0.520206i	$0.825855\pi$
$674$	11.3181			0.435957
$675$	−21.9046	−	5.21763i	−0.843110	−	0.200827i
$676$	22.7850			0.876348
$677$	1.68493	+	2.31910i	0.0647570	+	0.0891304i	0.840167	−	0.542328i	$-0.182457\pi$
$677$	1.68493	+	2.31910i	0.0647570	+	0.0891304i	−0.775410	+	0.631458i	$0.782457\pi$
$678$	−8.21078	−	2.66784i	−0.315333	−	0.102458i
$679$	8.33490	−	25.6522i	0.319864	−	0.984441i
$680$	2.17081	+	1.44770i	0.0832469	+	0.0555167i
$681$	−3.85244	−	11.8566i	−0.147626	−	0.454345i
$682$		−	12.0374i		−	0.460936i
$683$	17.1828	−	5.58302i	0.657480	−	0.213628i	0.0387706	−	0.999248i	$-0.487656\pi$
$683$	17.1828	−	5.58302i	0.657480	−	0.213628i	0.618709	+	0.785620i	$0.287656\pi$
$684$	1.83618	+	1.33406i	0.0702080	+	0.0510091i
$685$	45.5845	+	12.8124i	1.74169	+	0.489536i
$686$	−0.0922948	+	0.0670561i	−0.00352383	+	0.00256021i
$687$	−8.11427	+	11.1683i	−0.309579	+	0.426099i
$688$	3.95792	−	5.44761i	0.150894	−	0.207688i
$689$	−61.4961	+	44.6795i	−2.34281	+	1.70215i
$690$	0.460973	+	0.129565i	0.0175489	+	0.00493246i
$691$	−19.3755	−	14.0771i	−0.737078	−	0.535518i	0.154717	−	0.987959i	$-0.450553\pi$
$691$	−19.3755	−	14.0771i	−0.737078	−	0.535518i	−0.891795	+	0.452441i	$0.850553\pi$
$692$	15.3215	−	4.97826i	0.582436	−	0.189245i
$693$		−	12.6146i		−	0.479189i
$694$	−6.94410	−	21.3718i	−0.263595	−	0.811261i
$695$	−7.17926	−	4.78779i	−0.272325	−	0.181611i
$696$	2.29250	−	7.05559i	0.0868970	−	0.267441i
$697$	9.79338	+	3.18206i	0.370951	+	0.120529i
$698$	−20.0081	−	27.5387i	−0.757317	−	1.04236i
$699$	2.29663			0.0868664
$700$	17.2902	−	7.19791i	0.653509	−	0.272055i
$701$	−20.9471			−0.791160			−0.395580	−	0.918432i	$-0.629456\pi$
$701$	−20.9471			−0.791160			−0.395580	+	0.918432i	$0.629456\pi$
$702$	−15.8350	−	21.7951i	−0.597655	−	0.822602i
$703$	−2.67590	−	0.869453i	−0.100923	−	0.0327920i
$704$	0.458525	−	1.41119i	0.0172813	−	0.0531864i
$705$	−0.424770	+	1.51127i	−0.0159978	+	0.0569176i
$706$	5.97099	+	18.3768i	0.224721	+	0.691621i
$707$		−	53.2609i		−	2.00308i
$708$	−6.01667	+	1.95493i	−0.226120	+	0.0734709i
$709$	−4.41132	−	3.20501i	−0.165671	−	0.120367i	0.501861	−	0.864948i	$-0.332649\pi$
$709$	−4.41132	−	3.20501i	−0.165671	−	0.120367i	−0.667531	+	0.744582i	$0.732649\pi$
$710$	19.9080	+	25.2070i	0.747134	+	0.946002i
$711$	11.0930	−	8.05954i	0.416020	−	0.302256i
$712$	7.75900	−	10.6793i	0.290781	−	0.400225i
$713$	1.19482	−	1.64453i	0.0447465	−	0.0615882i
$714$	−3.02201	+	2.19562i	−0.113096	+	0.0821689i
$715$	18.6151	−	6.88629i	0.696165	−	0.257533i
$716$	8.72148	+	6.33652i	0.325937	+	0.236807i
$717$	14.3707	−	4.66934i	0.536685	−	0.174380i
$718$			30.9361i			1.15452i
$719$	0.291780	+	0.898005i	0.0108815	+	0.0334900i	0.956350	−	0.292224i	$-0.0943953\pi$
$719$	0.291780	+	0.898005i	0.0108815	+	0.0334900i	−0.945468	+	0.325714i	$0.894395\pi$
$720$	−3.98274	+	3.14549i	−0.148428	+	0.117225i
$721$	−13.8453	+	42.6115i	−0.515627	+	1.58694i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	−2.57400	−	3.54280i	−0.0957280	−	0.131758i
$724$	−12.4915			−0.464244
$725$	−16.6813	−	40.0703i	−0.619526	−	1.48817i
$726$	−7.51912			−0.279061
$727$	−5.26390	−	7.24514i	−0.195227	−	0.268707i	0.700169	−	0.713977i	$-0.253108\pi$
$727$	−5.26390	−	7.24514i	−0.195227	−	0.268707i	−0.895397	+	0.445270i	$0.853108\pi$
$728$	21.3105	+	6.92419i	0.789819	+	0.256628i
$729$	−1.49184	+	4.59140i	−0.0552532	+	0.170052i
$730$	−23.7739	+	0.955264i	−0.879912	+	0.0353559i
$731$	2.42808	+	7.47288i	0.0898060	+	0.276394i
$732$			6.10251i			0.225555i
$733$	8.99724	−	2.92338i	0.332321	−	0.107978i	−0.138104	−	0.990418i	$-0.544101\pi$
$733$	8.99724	−	2.92338i	0.332321	−	0.107978i	0.470425	+	0.882440i	$0.344101\pi$
$734$	6.75763	+	4.90970i	0.249429	+	0.181220i
$735$	0.539399	+	13.4242i	0.0198960	+	0.495158i
$736$	0.202717	−	0.147282i	0.00747224	−	0.00542890i
$737$	9.42526	−	12.9728i	0.347184	−	0.477857i
$738$	−11.7725	+	16.2035i	−0.433352	+	0.596458i
$739$	10.4237	−	7.57330i	0.383444	−	0.278588i	−0.379320	−	0.925266i	$-0.623842\pi$
$739$	10.4237	−	7.57330i	0.383444	−	0.278588i	0.762764	+	0.646677i	$0.223842\pi$
$740$	3.49067	−	5.23423i	0.128320	−	0.192414i
$741$	−4.13597	−	3.00496i	−0.151939	−	0.110390i
$742$	−45.2670	+	14.7081i	−1.66180	+	0.539952i
$743$			5.38504i			0.197558i	0.995109	+	0.0987790i	$0.0314937\pi$
$743$			5.38504i			0.197558i	−0.995109	+	0.0987790i	$0.968506\pi$
$744$	−2.14242	−	6.59368i	−0.0785448	−	0.241736i
$745$	5.06337	+	13.6873i	0.185507	+	0.501465i
$746$	−5.29580	+	16.2988i	−0.193893	+	0.596742i
$747$	−0.263042	−	0.0854675i	−0.00962420	−	0.00312709i
$748$	1.01773	+	1.40078i	0.0372119	+	0.0512177i
$749$	21.8456			0.798222
$750$	1.83904	−	9.37620i	0.0671522	−	0.342370i
$751$	29.2829			1.06855			0.534274	−	0.845311i	$-0.320585\pi$
$751$	29.2829			1.06855			0.534274	+	0.845311i	$0.320585\pi$
$752$	0.482855	+	0.664592i	0.0176079	+	0.0242352i
$753$	−13.2948	−	4.31976i	−0.484491	−	0.157421i
$754$	16.0469	−	49.3873i	0.584394	−	1.79858i
$755$	−2.24339	−	6.06436i	−0.0816453	−	0.220704i
$756$	−5.21276	−	16.0432i	−0.189586	−	0.583487i
$757$		−	26.9024i		−	0.977783i	−0.872345	−	0.488891i	$-0.837401\pi$
$757$		−	26.9024i		−	0.977783i	0.872345	−	0.488891i	$-0.162599\pi$
$758$	29.0301	−	9.43244i	1.05442	−	0.342602i
$759$	0.257063	+	0.186767i	0.00933079	+	0.00677922i
$760$	−1.24064	+	1.86033i	−0.0450027	+	0.0674812i
$761$	−18.7916	+	13.6529i	−0.681195	+	0.494917i	−0.873754	−	0.486368i	$-0.838321\pi$
$761$	−18.7916	+	13.6529i	−0.681195	+	0.494917i	0.192559	+	0.981285i	$0.438321\pi$
$762$	−1.74206	+	2.39774i	−0.0631083	+	0.0868611i
$763$	−38.8111	+	53.4190i	−1.40506	+	1.93390i
$764$	−12.7851	+	9.28890i	−0.462548	+	0.336061i
$765$	−0.237765	−	5.91731i	−0.00859640	−	0.213941i
$766$	8.98908	+	6.53095i	0.324789	+	0.235973i
$767$	−42.1151	+	13.6840i	−1.52069	+	0.494102i
$768$		−	0.854612i		−	0.0308381i
$769$	−9.05207	−	27.8594i	−0.326426	−	1.00464i	−0.970793	−	0.239920i	$-0.922879\pi$
$769$	−9.05207	−	27.8594i	−0.326426	−	1.00464i	0.644367	−	0.764717i	$-0.277121\pi$
$770$	12.4180	−	0.498970i	0.447513	−	0.0179816i
$771$	−5.68309	+	17.4908i	−0.204672	+	0.629915i
$772$	−7.03818	−	2.28684i	−0.253310	−	0.0823053i
$773$	−3.89472	−	5.36062i	−0.140083	−	0.192808i	0.733211	−	0.680001i	$-0.238021\pi$
$773$	−3.89472	−	5.36062i	−0.140083	−	0.192808i	−0.873294	+	0.487193i	$0.838021\pi$
$774$	−15.2829			−0.549332
$775$	−34.6227	−	21.1322i	−1.24368	−	0.759090i
$776$	−7.20082			−0.258495
$777$	5.29404	+	7.28662i	0.189923	+	0.261406i
$778$	−12.2873	−	3.99238i	−0.440520	−	0.143134i
$779$	−2.72694	+	8.39266i	−0.0977028	+	0.300698i
$780$	8.97108	−	7.08518i	0.321216	−	0.253690i
$781$	6.58657	+	20.2714i	0.235686	+	0.725367i
$782$			0.292392i			0.0104559i
$783$	−37.1804	+	12.0806i	−1.32872	+	0.431727i
$784$	5.68776	+	4.13240i	0.203134	+	0.147586i
$785$	−13.5726	+	5.02092i	−0.484427	+	0.179204i
$786$	1.09609	−	0.796359i	0.0390964	−	0.0284052i
$787$	12.1713	−	16.7523i	0.433859	−	0.597156i	−0.534975	−	0.844868i	$-0.679679\pi$
$787$	12.1713	−	16.7523i	0.433859	−	0.597156i	0.968834	+	0.247713i	$0.0796788\pi$
$788$	4.18640	−	5.76209i	0.149134	−	0.205266i
$789$	1.53776	−	1.11724i	0.0547455	−	0.0397750i
$790$	8.37271	+	10.6013i	0.297888	+	0.377178i
$791$	−30.6128	−	22.2415i	−1.08847	−	0.790816i
$792$	−3.20290	+	1.04069i	−0.113810	+	0.0369792i
$793$			42.7160i			1.51689i
$794$	−5.35145	−	16.4701i	−0.189916	−	0.584501i
$795$	−6.57045	+	23.3766i	−0.233030	+	0.829084i
$796$	−0.633195	+	1.94877i	−0.0224430	+	0.0690724i
$797$	−20.4963	−	6.65964i	−0.726015	−	0.235897i	−0.0773859	−	0.997001i	$-0.524657\pi$
$797$	−20.4963	−	6.65964i	−0.726015	−	0.235897i	−0.648629	+	0.761105i	$0.724657\pi$
$798$	−1.88158	−	2.58978i	−0.0666073	−	0.0916771i
$799$	−0.958585			−0.0339123
$800$	−3.25400	−	3.79625i	−0.115046	−	0.134218i
$801$	−29.9601			−1.05859
$802$	−14.4660	−	19.9107i	−0.510812	−	0.703073i
$803$	−15.0160	−	4.87898i	−0.529901	−	0.172175i
$804$	2.85394	−	8.78353i	0.100651	−	0.309771i
$805$	1.74605	+	1.16443i	0.0615403	+	0.0410408i
$806$	−14.9964	−	46.1540i	−0.528224	−	1.62571i
$807$			9.57257i			0.336971i
$808$	−13.5232	+	4.39395i	−0.475744	+	0.154579i
$809$	29.2635	+	21.2612i	1.02885	+	0.747503i	0.968078	−	0.250648i	$-0.0806438\pi$
$809$	29.2635	+	21.2612i	1.02885	+	0.747503i	0.0607719	+	0.998152i	$0.480644\pi$
$810$	6.37224	+	1.79104i	0.223898	+	0.0629307i
$811$	21.0532	−	15.2961i	0.739279	−	0.537117i	−0.153207	−	0.988194i	$-0.548960\pi$
$811$	21.0532	−	15.2961i	0.739279	−	0.537117i	0.892485	+	0.451077i	$0.148960\pi$
$812$	19.1123	−	26.3058i	0.670710	−	0.923153i
$813$	7.90407	−	10.8790i	0.277208	−	0.381544i
$814$	3.37755	−	2.45393i	0.118383	−	0.0860103i
$815$	32.5073	+	9.13678i	1.13868	+	0.320047i
$816$	0.806788	+	0.586166i	0.0282432	+	0.0205199i
$817$	−6.40405	+	2.08080i	−0.224049	+	0.0727981i
$818$		−	7.98059i		−	0.279035i
$819$	−15.7154	−	48.3671i	−0.549141	−	1.69008i
$820$	−16.4166	−	10.9481i	−0.573292	−	0.382324i
$821$	3.82961	−	11.7863i	0.133654	−	0.411346i	−0.861724	−	0.507378i	$-0.830615\pi$
$821$	3.82961	−	11.7863i	0.133654	−	0.411346i	0.995378	+	0.0960315i	$0.0306150\pi$
$822$	17.2115	+	5.59234i	0.600318	+	0.195055i
$823$	−30.6205	−	42.1455i	−1.06736	−	1.46910i	−0.872717	−	0.488226i	$-0.837644\pi$
$823$	−30.6205	−	42.1455i	−1.06736	−	1.46910i	−0.194646	−	0.980874i	$-0.562356\pi$
$824$	11.9615			0.416698
$825$	3.30325	−	5.41200i	0.115004	−	0.188422i
$826$	−27.7279			−0.964777
$827$	−5.69615	−	7.84008i	−0.198075	−	0.272626i	0.698413	−	0.715695i	$-0.253890\pi$
$827$	−5.69615	−	7.84008i	−0.198075	−	0.272626i	−0.896488	+	0.443068i	$0.853890\pi$
$828$	−0.540873	−	0.175740i	−0.0187966	−	0.00610740i
$829$	2.75170	−	8.46885i	0.0955703	−	0.294135i	−0.891832	−	0.452368i	$-0.850580\pi$
$829$	2.75170	−	8.46885i	0.0955703	−	0.294135i	0.987402	+	0.158232i	$0.0505795\pi$
$830$	0.0737309	−	0.262323i	0.00255924	−	0.00910536i
$831$	−0.766456	−	2.35891i	−0.0265880	−	0.0818296i
$832$		−	5.98206i		−	0.207391i
$833$	−7.80230	+	2.53512i	−0.270334	+	0.0878368i
$834$	−2.66819	−	1.93855i	−0.0923918	−	0.0671266i
$835$	32.6272	+	41.3118i	1.12911	+	1.42965i
$836$	−1.20043	+	0.872166i	−0.0415179	+	0.0301645i
$837$	−21.4744	+	29.5570i	−0.742264	+	1.02164i
$838$	−14.1316	+	19.4504i	−0.488166	+	0.671903i
$839$	9.18852	−	6.67585i	0.317223	−	0.230476i	−0.417767	−	0.908554i	$-0.637187\pi$
$839$	9.18852	−	6.67585i	0.317223	−	0.230476i	0.734990	+	0.678078i	$0.237187\pi$
$840$	6.71334	−	2.48347i	0.231632	−	0.0856878i
$841$	−37.5026	−	27.2472i	−1.29319	−	0.939559i
$842$	−1.85335	+	0.602189i	−0.0638706	+	0.0207528i
$843$			24.9283i			0.858577i
$844$	3.27615	+	10.0830i	0.112770	+	0.347070i
$845$	39.9830	−	31.5778i	1.37546	−	1.08631i
$846$	0.576152	−	1.77321i	0.0198085	−	0.0609643i
$847$	−31.3430	−	10.1839i	−1.07696	−	0.349925i
$848$	7.46892	+	10.2801i	0.256484	+	0.353020i
$849$	−17.0601			−0.585502
$850$	5.81568	−	0.468118i	0.199476	−	0.0160563i
$851$	0.705011			0.0241675
$852$	7.21579	+	9.93168i	0.247209	+	0.340254i
$853$	−28.5741	−	9.28430i	−0.978360	−	0.317888i	−0.224174	−	0.974549i	$-0.571968\pi$
$853$	−28.5741	−	9.28430i	−0.978360	−	0.317888i	−0.754186	+	0.656661i	$0.771968\pi$
$854$	−8.26529	+	25.4379i	−0.282832	+	0.870469i
$855$	5.07097	−	0.203758i	0.173424	−	0.00696837i
$856$	−1.80223	−	5.54670i	−0.0615991	−	0.189582i
$857$			49.5114i			1.69128i	0.533756	+	0.845639i	$0.320780\pi$
$857$			49.5114i			1.69128i	−0.533756	+	0.845639i	$0.679220\pi$
$858$	7.21451	−	2.34413i	0.246299	−	0.0800274i
$859$	25.4085	+	18.4603i	0.866926	+	0.629858i	0.929760	−	0.368166i	$-0.120014\pi$
$859$	25.4085	+	18.4603i	0.866926	+	0.629858i	−0.0628346	+	0.998024i	$0.520014\pi$
$860$	−0.604513	−	15.0447i	−0.0206137	−	0.513020i
$861$	22.8537	−	16.6042i	0.778851	−	0.565868i
$862$	−24.3866	+	33.5653i	−0.830611	+	1.14324i
$863$	−3.39745	+	4.67619i	−0.115651	+	0.159179i	−0.862918	−	0.505344i	$-0.831366\pi$
$863$	−3.39745	+	4.67619i	−0.115651	+	0.159179i	0.747267	+	0.664524i	$0.231366\pi$
$864$	−3.64340	+	2.64709i	−0.123951	+	0.0900558i
$865$	19.9867	−	29.9698i	0.679567	−	1.01901i
$866$	−5.95149	−	4.32401i	−0.202240	−	0.146936i
$867$	12.7106	−	4.12992i	0.431675	−	0.140260i
$868$		−	30.3870i		−	1.03140i
$869$	2.77012	+	8.52554i	0.0939698	+	0.289209i
$870$	−5.75547	−	15.5582i	−0.195129	−	0.527474i
$871$	19.9769	−	61.4824i	0.676890	−	2.08325i
$872$	16.7652	+	5.44734i	0.567741	+	0.184470i
$873$	9.60633	+	13.2220i	0.325125	+	0.447496i
$874$	−0.250572			−0.00847572
$875$	20.3651	−	36.5933i	0.688467	−	1.23708i
$876$	−9.09358			−0.307243
$877$	−33.2740	−	45.7978i	−1.12358	−	1.54648i	−0.799715	−	0.600380i	$-0.795016\pi$
$877$	−33.2740	−	45.7978i	−1.12358	−	1.54648i	−0.323870	−	0.946102i	$-0.604984\pi$
$878$	13.7293	+	4.46090i	0.463340	+	0.150548i
$879$	1.64252	−	5.05516i	0.0554008	−	0.170506i
$880$	−1.15116	−	3.11182i	−0.0388055	−	0.104899i
$881$	4.09062	+	12.5896i	0.137816	+	0.424155i	0.996017	−	0.0891584i	$-0.0284177\pi$
$881$	4.09062	+	12.5896i	0.137816	+	0.424155i	−0.858201	+	0.513314i	$0.828418\pi$
$882$		−	15.9566i		−	0.537287i
$883$	54.3787	−	17.6687i	1.82999	−	0.594600i	0.830709	−	0.556707i	$-0.187935\pi$
$883$	54.3787	−	17.6687i	1.82999	−	0.594600i	0.999282	−	0.0378928i	$-0.0120645\pi$
$884$	5.64731	+	4.10301i	0.189940	+	0.137999i
$885$	−7.84865	+	11.7690i	−0.263829	+	0.395610i
$886$	1.04640	−	0.760257i	0.0351546	−	0.0255413i
$887$	−13.1354	+	18.0794i	−0.441045	+	0.607046i	−0.970444	−	0.241327i	$-0.922417\pi$
$887$	−13.1354	+	18.0794i	−0.441045	+	0.607046i	0.529399	+	0.848373i	$0.322417\pi$
$888$	1.41335	−	1.94532i	0.0474291	−	0.0652805i
$889$	−10.5092	+	7.63539i	−0.352468	+	0.256083i
$890$	−1.18507	−	29.4932i	−0.0397237	−	0.988614i
$891$	3.55350	+	2.58177i	0.119047	+	0.0864925i
$892$	−23.1534	+	7.52300i	−0.775234	+	0.251889i
$893$		−	0.821481i		−	0.0274898i
$894$	1.72360	+	5.30470i	0.0576458	+	0.177416i
$895$	24.0861	−	0.967810i	0.805111	−	0.0323503i
$896$	1.15749	−	3.56240i	0.0386691	−	0.119011i
$897$	1.21831	+	0.395853i	0.0406782	+	0.0132172i
$898$	6.90682	+	9.50642i	0.230483	+	0.317233i
$899$	−70.4224			−2.34872
$900$	−2.62954	+	11.0393i	−0.0876515	+	0.367978i
$901$	−14.8276			−0.493980
$902$	−7.69649	−	10.5933i	−0.256265	−	0.352719i
$903$	20.5003	+	6.66094i	0.682206	+	0.221662i
$904$	−3.12170	+	9.60761i	−0.103826	+	0.319544i
$905$	−21.9200	+	17.3120i	−0.728645	+	0.575470i
$906$	−0.763664	−	2.35032i	−0.0253710	−	0.0780840i
$907$		−	37.4701i		−	1.24418i	−0.782948	−	0.622088i	$-0.786285\pi$
$907$		−	37.4701i		−	1.24418i	0.782948	−	0.622088i	$-0.213715\pi$
$908$	−13.8736	+	4.50782i	−0.460413	+	0.149597i
$909$	26.1088	+	18.9692i	0.865975	+	0.629167i
$910$	46.9916	−	17.3836i	1.55776	−	0.576262i
$911$	23.9490	−	17.3999i	0.793465	−	0.576486i	−0.115525	−	0.993305i	$-0.536855\pi$
$911$	23.9490	−	17.3999i	0.793465	−	0.576486i	0.908990	+	0.416819i	$0.136855\pi$
$912$	−0.502328	+	0.691395i	−0.0166337	+	0.0228944i
$913$	0.106282	−	0.146285i	0.00351743	−	0.00484133i
$914$	−20.2345	+	14.7012i	−0.669298	+	0.486273i
$915$	8.45746	+	10.7086i	0.279595	+	0.354016i
$916$	13.0683	+	9.49469i	0.431790	+	0.313713i
$917$	5.64760	−	1.83502i	0.186500	−	0.0605975i
$918$		−	5.25512i		−	0.173445i
$919$	−10.5590	−	32.4973i	−0.348310	−	1.07199i	−0.959788	−	0.280727i	$-0.909425\pi$
$919$	−10.5590	−	32.4973i	−0.348310	−	1.07199i	0.611478	−	0.791262i	$-0.290575\pi$
$920$	0.151607	−	0.539395i	0.00499834	−	0.0177833i
$921$	4.86454	−	14.9715i	0.160292	−	0.493329i
$922$	7.72636	+	2.51044i	0.254454	+	0.0826771i
$923$	50.5086	+	69.5192i	1.66251	+	2.28825i
$924$	4.74991			0.156261
$925$	−1.12872	−	14.0227i	−0.0371120	−	0.461063i
$926$	19.7984			0.650616
$927$	−15.9573	−	21.9634i	−0.524108	−	0.721372i
$928$	−8.25590	−	2.68251i	−0.271013	−	0.0880575i
$929$	−4.84339	+	14.9064i	−0.158907	+	0.489064i	−0.998536	−	0.0540960i	$-0.982772\pi$
$929$	−4.84339	+	14.9064i	−0.158907	+	0.489064i	0.839629	+	0.543160i	$0.182772\pi$
$930$	−12.8977	−	8.60135i	−0.422931	−	0.282049i
$931$	−2.17253	−	6.68636i	−0.0712018	−	0.219137i
$932$		−	2.68733i		−	0.0880266i
$933$	2.45817	−	0.798709i	0.0804770	−	0.0261486i
$934$	21.2115	+	15.4111i	0.694061	+	0.504265i
$935$	3.72725	+	1.04761i	0.121894	+	0.0342606i
$936$	−10.9841	+	7.98043i	−0.359027	+	0.260848i
$937$	−23.6827	+	32.5965i	−0.773681	+	1.06488i	0.222271	+	0.974985i	$0.428653\pi$
$937$	−23.6827	+	32.5965i	−0.773681	+	1.06488i	−0.995951	+	0.0898949i	$0.971347\pi$
$938$	23.7930	−	32.7482i	0.776868	−	1.06927i
$939$	0.0378653	−	0.0275108i	0.00123569	−	0.000897780i
$940$	1.76837	+	0.497033i	0.0576777	+	0.0162114i
$941$	−6.00986	−	4.36642i	−0.195916	−	0.142341i	0.485503	−	0.874235i	$-0.338637\pi$
$941$	−6.00986	−	4.36642i	−0.195916	−	0.142341i	−0.681418	+	0.731894i	$0.738637\pi$
$942$	−5.26023	+	1.70915i	−0.171388	+	0.0556872i
$943$		−	2.21119i		−	0.0720062i
$944$	2.28751	+	7.04024i	0.0744522	+	0.229140i
$945$	−31.3816	−	20.9281i	−1.02084	−	0.680793i
$946$	3.08753	−	9.50245i	0.100384	−	0.308951i
$947$	29.4866	+	9.58077i	0.958185	+	0.311333i	0.746037	−	0.665905i	$-0.231954\pi$
$947$	29.4866	+	9.58077i	0.958185	+	0.311333i	0.212148	+	0.977238i	$0.431954\pi$
$948$	3.03475	+	4.17697i	0.0985640	+	0.135662i
$949$	−63.6527			−2.06625
$950$	0.401164	+	4.98388i	0.0130155	+	0.161698i
$951$	−21.5228			−0.697925
$952$	2.56914	+	3.53612i	0.0832663	+	0.114606i
$953$	19.8452	+	6.44810i	0.642849	+	0.208874i	0.612259	−	0.790658i	$-0.290261\pi$
$953$	19.8452	+	6.44810i	0.642849	+	0.208874i	0.0305906	+	0.999532i	$0.490261\pi$
$954$	8.91206	−	27.4285i	0.288539	−	0.888031i
$955$	−9.56165	+	34.0189i	−0.309408	+	1.10083i
$956$	−5.46370	−	16.8155i	−0.176709	−	0.543853i
$957$		−	11.0080i		−	0.355837i
$958$	−3.90277	+	1.26809i	−0.126093	+	0.0409700i
$959$	64.1706	+	46.6227i	2.07218	+	1.50552i
$960$	−1.18440	−	1.49966i	−0.0382265	−	0.0484014i
$961$	−28.1635	+	20.4620i	−0.908500	+	0.660064i
$962$	9.89312	−	13.6167i	0.318967	−	0.439020i
$963$	−7.78044	+	10.7089i	−0.250721	+	0.345088i
$964$	−4.14551	+	3.01189i	−0.133518	+	0.0970065i
$965$	−15.5199	+	5.74127i	−0.499602	+	0.184818i
$966$	0.648925	+	0.471472i	0.0208788	+	0.0151694i
$967$	−21.7310	+	7.06085i	−0.698823	+	0.227061i	−0.636818	−	0.771014i	$-0.719750\pi$
$967$	−21.7310	+	7.06085i	−0.698823	+	0.227061i	−0.0620056	+	0.998076i	$0.519750\pi$
$968$			8.79828i			0.282788i
$969$	−0.308166	−	0.948436i	−0.00989971	−	0.0304682i
$970$	−12.6359	+	9.97961i	−0.405715	+	0.320426i
$971$	−4.01412	+	12.3542i	−0.128819	+	0.396465i	−0.994578	−	0.103997i	$-0.966837\pi$
$971$	−4.01412	+	12.3542i	−0.128819	+	0.396465i	0.865758	+	0.500462i	$0.166837\pi$
$972$	15.2552	+	4.95672i	0.489311	+	0.158987i
$973$	−8.49659	−	11.6946i	−0.272388	−	0.374910i
$974$	20.8547			0.668226
$975$	5.92302	−	24.8660i	0.189689	−	0.796349i
$976$	7.14068			0.228568
$977$	33.5698	+	46.2049i	1.07399	+	1.47823i	0.865966	+	0.500103i	$0.166705\pi$
$977$	33.5698	+	46.2049i	1.07399	+	1.47823i	0.208028	+	0.978123i	$0.433295\pi$
$978$	12.2739	+	3.98802i	0.392475	+	0.127523i
$979$	6.05271	−	18.6283i	0.193445	−	0.595364i
$980$	15.7079	−	0.631162i	0.501771	−	0.0201617i
$981$	−12.3635	−	38.0509i	−0.394736	−	1.21487i
$982$		−	12.8239i		−	0.409226i
$983$	15.8735	−	5.15763i	0.506287	−	0.164503i	−0.0447257	−	0.998999i	$-0.514241\pi$
$983$	15.8735	−	5.15763i	0.506287	−	0.164503i	0.551013	+	0.834497i	$0.314241\pi$
$984$	−6.10126	−	4.43283i	−0.194501	−	0.141313i
$985$	−0.639411	−	15.9132i	−0.0203733	−	0.507036i
$986$	8.19500	−	5.95401i	0.260982	−	0.189614i
$987$	−1.54569	+	2.12745i	−0.0491997	+	0.0677176i
$988$	−3.51617	+	4.83959i	−0.111864	+	0.153968i
$989$	1.36502	−	0.991743i	0.0434050	−	0.0315356i
$990$	−4.17814	+	6.26508i	−0.132790	+	0.199117i
$991$	6.00851	+	4.36544i	0.190867	+	0.138673i	0.679115	−	0.734032i	$-0.262364\pi$
$991$	6.00851	+	4.36544i	0.190867	+	0.138673i	−0.488248	+	0.872705i	$0.662364\pi$
$992$	−7.71541	+	2.50689i	−0.244964	+	0.0795938i
$993$			25.3072i			0.803100i
$994$	16.6270	+	51.1727i	0.527377	+	1.62310i
$995$	1.58968	+	4.29723i	0.0503962	+	0.136231i
$996$	0.0321820	−	0.0990461i	0.00101973	−	0.00313839i
$997$	−0.252372	−	0.0820007i	−0.00799271	−	0.00259699i	0.305018	−	0.952347i	$-0.401338\pi$
$997$	−0.252372	−	0.0820007i	−0.00799271	−	0.00259699i	−0.313011	+	0.949750i	$0.601338\pi$
$998$	−0.395997	−	0.545043i	−0.0125351	−	0.0172531i
$999$	−12.6711			−0.400895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.5	✓	88
25.9	even	10	inner	950.2.n.a.609.5	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.5	✓	88	1.1	even	1	trivial
950.2.n.a.609.5	yes	88	25.9	even	10	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.812784 - 0.264090i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.775807 + 2.09717i) q^{5} +(0.264090 + 0.812784i) q^{6} +3.74573i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.83618 - 1.33406i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.812784 - 0.264090i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.775807 + 2.09717i) q^{5} +(0.264090 + 0.812784i) q^{6} +3.74573i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.83618 - 1.33406i) q^{9} +(1.24064 - 1.86033i) q^{10} +(1.20043 - 0.872166i) q^{11} +(0.502328 - 0.691395i) q^{12} +(3.51617 - 4.83959i) q^{13} +(3.03036 - 2.20168i) q^{14} +(-0.0767231 - 1.90943i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.10979 - 0.360591i) q^{17} +2.26964i q^{18} +(0.309017 + 0.951057i) q^{19} +(-2.23427 + 0.0897754i) q^{20} +(0.989207 - 3.04447i) q^{21} +(-1.41119 - 0.458525i) q^{22} +(-0.147282 - 0.202717i) q^{23} -0.854612 q^{24} +(-3.79625 + 3.25400i) q^{25} -5.98206 q^{26} +(2.64709 + 3.64340i) q^{27} +(-3.56240 - 1.15749i) q^{28} +(-2.68251 + 8.25590i) q^{29} +(-1.49966 + 1.18440i) q^{30} +(2.50689 + 7.71541i) q^{31} +1.00000i q^{32} +(-1.20602 + 0.391861i) q^{33} +(-0.944041 - 0.685886i) q^{34} +(-7.85542 + 2.90596i) q^{35} +(1.83618 - 1.33406i) q^{36} +(-1.65380 + 2.27626i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-4.13597 + 3.00496i) q^{39} +(1.38590 + 1.75479i) q^{40} +(7.13922 + 5.18695i) q^{41} +(-3.04447 + 0.989207i) q^{42} +6.73362i q^{43} +(0.458525 + 1.41119i) q^{44} +(1.37323 - 4.88575i) q^{45} +(-0.0774309 + 0.238308i) q^{46} +(-0.781275 - 0.253852i) q^{47} +(0.502328 + 0.691395i) q^{48} -7.03046 q^{49} +(4.86392 + 1.15857i) q^{50} -0.997245 q^{51} +(3.51617 + 4.83959i) q^{52} +(-12.0850 - 3.92664i) q^{53} +(1.39166 - 4.28308i) q^{54} +(2.76039 + 1.84088i) q^{55} +(1.15749 + 3.56240i) q^{56} -0.854612i q^{57} +(8.25590 - 2.68251i) q^{58} +(-5.98878 - 4.35111i) q^{59} +(1.83968 + 0.517078i) q^{60} +(-5.77693 + 4.19719i) q^{61} +(4.76838 - 6.56312i) q^{62} +(4.99702 - 6.87781i) q^{63} +(0.809017 - 0.587785i) q^{64} +(12.8773 + 3.61941i) q^{65} +(1.02590 + 0.745364i) q^{66} +(10.2778 - 3.33946i) q^{67} +1.16690i q^{68} +(0.0661734 + 0.203661i) q^{69} +(6.96827 + 4.64709i) q^{70} +(-4.43893 + 13.6616i) q^{71} +(-2.15855 - 0.701357i) q^{72} +(-6.25438 - 8.60842i) q^{73} +2.81361 q^{74} +(3.94488 - 1.64225i) q^{75} -1.00000 q^{76} +(3.26690 + 4.49650i) q^{77} +(4.86212 + 1.57980i) q^{78} +(-1.86688 + 5.74568i) q^{79} +(0.605044 - 2.15265i) q^{80} +(0.914745 + 2.81530i) q^{81} -8.82457i q^{82} +(0.115896 - 0.0376569i) q^{83} +(2.58978 + 1.88158i) q^{84} +(1.61720 + 2.04766i) q^{85} +(5.44761 - 3.95792i) q^{86} +(4.36059 - 6.00184i) q^{87} +(0.872166 - 1.20043i) q^{88} +(10.6793 - 7.75900i) q^{89} +(-4.75982 + 1.76080i) q^{90} +(18.1278 + 13.1706i) q^{91} +(0.238308 - 0.0774309i) q^{92} -6.93300i q^{93} +(0.253852 + 0.781275i) q^{94} +(-1.75479 + 1.38590i) q^{95} +(0.264090 - 0.812784i) q^{96} +(-6.84839 - 2.22518i) q^{97} +(4.13240 + 5.68776i) q^{98} -3.36773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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