LMFDB - Embedded newform 950.2.h.b.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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([2, 0]))

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Character	$\chi$	$=$	950.191
Dual form			950.2.h.b.761.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.01321 - 3.11835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.01188 - 0.975874i) q^{5} +(-1.01321 + 3.11835i) q^{6} -3.17274 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.27043 + 4.55573i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.01321 - 3.11835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.01188 - 0.975874i) q^{5} +(-1.01321 + 3.11835i) q^{6} -3.17274 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.27043 + 4.55573i) q^{9} +(1.05404 + 1.97205i) q^{10} +(-3.43270 - 2.49400i) q^{11} +(2.65262 - 1.92724i) q^{12} +(-0.742313 + 0.539322i) q^{13} +(2.56680 + 1.86489i) q^{14} +(-1.00465 + 7.26251i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.27802 - 7.01102i) q^{17} +7.75067 q^{18} +(0.309017 - 0.951057i) q^{19} +(0.306406 - 2.21498i) q^{20} +(3.21466 + 9.89370i) q^{21} +(1.31117 + 4.03538i) q^{22} +(-5.17525 - 3.76004i) q^{23} -3.27882 q^{24} +(3.09534 + 3.92669i) q^{25} +0.917549 q^{26} +(12.6017 + 9.15570i) q^{27} +(-0.980431 - 3.01746i) q^{28} +(1.29878 + 3.99724i) q^{29} +(5.08157 - 5.28498i) q^{30} +(0.0610229 - 0.187809i) q^{31} +1.00000 q^{32} +(-4.29910 + 13.2313i) q^{33} +(-5.96393 + 4.33305i) q^{34} +(6.38318 + 3.09619i) q^{35} +(-6.27043 - 4.55573i) q^{36} +(9.45910 - 6.87243i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(2.43391 + 1.76834i) q^{39} +(-1.54982 + 1.61185i) q^{40} +(-0.353735 + 0.257003i) q^{41} +(3.21466 - 9.89370i) q^{42} -4.77706 q^{43} +(1.31117 - 4.03538i) q^{44} +(17.0612 - 3.04645i) q^{45} +(1.97677 + 6.08388i) q^{46} +(-0.948701 - 2.91980i) q^{47} +(2.65262 + 1.92724i) q^{48} +3.06628 q^{49} +(-0.196134 - 4.99615i) q^{50} -24.1709 q^{51} +(-0.742313 - 0.539322i) q^{52} +(-1.96796 - 6.05677i) q^{53} +(-4.81344 - 14.8142i) q^{54} +(4.47235 + 8.36751i) q^{55} +(-0.980431 + 3.01746i) q^{56} -3.27882 q^{57} +(1.29878 - 3.99724i) q^{58} +(2.18239 - 1.58560i) q^{59} +(-7.21751 + 1.28876i) q^{60} +(-0.438838 - 0.318835i) q^{61} +(-0.159760 + 0.116072i) q^{62} +(19.8944 - 14.4542i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.01976 - 0.360648i) q^{65} +(11.2552 - 8.17738i) q^{66} +(-3.37777 + 10.3957i) q^{67} +7.37182 q^{68} +(-6.48148 + 19.9479i) q^{69} +(-3.34420 - 6.25681i) q^{70} +(-3.74607 - 11.5292i) q^{71} +(2.39509 + 7.37133i) q^{72} +(3.06421 + 2.22628i) q^{73} -11.6921 q^{74} +(9.10853 - 13.6309i) q^{75} +1.00000 q^{76} +(10.8911 + 7.91281i) q^{77} +(-0.929671 - 2.86123i) q^{78} +(-4.09648 - 12.6077i) q^{79} +(2.20125 - 0.393056i) q^{80} +(8.59714 - 26.4593i) q^{81} +0.437240 q^{82} +(-3.90676 + 12.0238i) q^{83} +(-8.41608 + 6.11464i) q^{84} +(-11.4250 + 11.8823i) q^{85} +(3.86472 + 2.80788i) q^{86} +(11.1488 - 8.10010i) q^{87} +(-3.43270 + 2.49400i) q^{88} +(3.41386 + 2.48032i) q^{89} +(-15.5934 - 7.56368i) q^{90} +(2.35516 - 1.71113i) q^{91} +(1.97677 - 6.08388i) q^{92} -0.647483 q^{93} +(-0.948701 + 2.91980i) q^{94} +(-1.54982 + 1.61185i) q^{95} +(-1.01321 - 3.11835i) q^{96} +(1.84303 + 5.67227i) q^{97} +(-2.48067 - 1.80232i) q^{98} +32.8865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) $ 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9} - 6 q^{11} + 16 q^{13} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{17} + 22 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 14 q^{22} + 4 q^{23} - 10 q^{24} - 2 q^{25} - 34 q^{26} + 29 q^{27} + 8 q^{28} + 16 q^{30} + 19 q^{31} + 40 q^{32} - 16 q^{33} + 3 q^{34} - 24 q^{35} - 3 q^{36} + q^{37} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 20 q^{41} + 3 q^{42} - 48 q^{43} + 14 q^{44} + 53 q^{45} + 4 q^{46} + 29 q^{47} + 28 q^{49} + 3 q^{50} - 122 q^{51} + 16 q^{52} - 5 q^{53} - 6 q^{54} + 56 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{59} - 19 q^{60} + 42 q^{61} - 21 q^{62} + 9 q^{63} - 10 q^{64} + 35 q^{65} + 24 q^{66} - 3 q^{67} - 2 q^{68} - 9 q^{69} - 19 q^{70} + 18 q^{71} - 8 q^{72} + 8 q^{73} - 64 q^{74} + 7 q^{75} + 40 q^{76} + 35 q^{77} - 2 q^{78} + q^{79} + 59 q^{81} - 30 q^{82} + 11 q^{83} - 7 q^{84} - 125 q^{85} + 32 q^{86} - 31 q^{87} - 6 q^{88} - 34 q^{89} - 7 q^{90} + 10 q^{91} + 4 q^{92} + 24 q^{93} + 29 q^{94} + 5 q^{95} + 5 q^{96} + 90 q^{97} - 12 q^{98} + 10 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9 - 6 * q^11 + 16 * q^13 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^17 + 22 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 14 * q^22 + 4 * q^23 - 10 * q^24 - 2 * q^25 - 34 * q^26 + 29 * q^27 + 8 * q^28 + 16 * q^30 + 19 * q^31 + 40 * q^32 - 16 * q^33 + 3 * q^34 - 24 * q^35 - 3 * q^36 + q^37 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 20 * q^41 + 3 * q^42 - 48 * q^43 + 14 * q^44 + 53 * q^45 + 4 * q^46 + 29 * q^47 + 28 * q^49 + 3 * q^50 - 122 * q^51 + 16 * q^52 - 5 * q^53 - 6 * q^54 + 56 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^59 - 19 * q^60 + 42 * q^61 - 21 * q^62 + 9 * q^63 - 10 * q^64 + 35 * q^65 + 24 * q^66 - 3 * q^67 - 2 * q^68 - 9 * q^69 - 19 * q^70 + 18 * q^71 - 8 * q^72 + 8 * q^73 - 64 * q^74 + 7 * q^75 + 40 * q^76 + 35 * q^77 - 2 * q^78 + q^79 + 59 * q^81 - 30 * q^82 + 11 * q^83 - 7 * q^84 - 125 * q^85 + 32 * q^86 - 31 * q^87 - 6 * q^88 - 34 * q^89 - 7 * q^90 + 10 * q^91 + 4 * q^92 + 24 * q^93 + 29 * q^94 + 5 * q^95 + 5 * q^96 + 90 * q^97 - 12 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.01321	−	3.11835i	−0.584978	−	1.80038i	−0.599358	−	0.800481i	$-0.704578\pi$
$3$	−1.01321	−	3.11835i	−0.584978	−	1.80038i	0.0143804	−	0.999897i	$-0.495422\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.01188	−	0.975874i	−0.899741	−	0.436424i
$5$	−2.01188	−	0.975874i	−0.899741	−	0.436424i
$6$	−1.01321	+	3.11835i	−0.413642	+	1.27306i
$7$	−3.17274			−1.19918			−0.599592	−	0.800306i	$-0.704670\pi$
$7$	−3.17274			−1.19918			−0.599592	+	0.800306i	$0.704670\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−6.27043	+	4.55573i	−2.09014	+	1.51858i
$10$	1.05404	+	1.97205i	0.333318	+	0.623618i
$11$	−3.43270	−	2.49400i	−1.03500	−	0.751969i	−0.0656940	−	0.997840i	$-0.520926\pi$
$11$	−3.43270	−	2.49400i	−1.03500	−	0.751969i	−0.969303	+	0.245871i	$0.920926\pi$
$12$	2.65262	−	1.92724i	0.765746	−	0.556347i
$13$	−0.742313	+	0.539322i	−0.205880	+	0.149581i	−0.685948	−	0.727651i	$-0.740612\pi$
$13$	−0.742313	+	0.539322i	−0.205880	+	0.149581i	0.480067	+	0.877232i	$0.340612\pi$
$14$	2.56680	+	1.86489i	0.686006	+	0.498413i
$15$	−1.00465	+	7.26251i	−0.259399	+	1.87517i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.27802	−	7.01102i	0.552500	−	1.70042i	−0.149954	−	0.988693i	$-0.547913\pi$
$17$	2.27802	−	7.01102i	0.552500	−	1.70042i	0.702455	−	0.711728i	$-0.252087\pi$
$18$	7.75067			1.82685
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	0.306406	−	2.21498i	0.0685144	−	0.495284i
$21$	3.21466	+	9.89370i	0.701496	+	2.15898i
$22$	1.31117	+	4.03538i	0.279543	+	0.860345i
$23$	−5.17525	−	3.76004i	−1.07911	−	0.784023i	−0.101587	−	0.994827i	$-0.532392\pi$
$23$	−5.17525	−	3.76004i	−1.07911	−	0.784023i	−0.977528	+	0.210804i	$0.932392\pi$
$24$	−3.27882			−0.669287
$25$	3.09534	+	3.92669i	0.619068	+	0.785337i
$26$	0.917549			0.179946
$27$	12.6017	+	9.15570i	2.42521	+	1.76202i
$28$	−0.980431	−	3.01746i	−0.185284	−	0.570245i
$29$	1.29878	+	3.99724i	0.241178	+	0.742269i	0.996242	+	0.0866177i	$0.0276059\pi$
$29$	1.29878	+	3.99724i	0.241178	+	0.742269i	−0.755064	+	0.655651i	$0.772394\pi$
$30$	5.08157	−	5.28498i	0.927764	−	0.964900i
$31$	0.0610229	−	0.187809i	0.0109600	−	0.0337315i	−0.945427	−	0.325834i	$-0.894355\pi$
$31$	0.0610229	−	0.187809i	0.0109600	−	0.0337315i	0.956387	+	0.292103i	$0.0943549\pi$
$32$	1.00000			0.176777
$33$	−4.29910	+	13.2313i	−0.748378	+	2.30327i
$34$	−5.96393	+	4.33305i	−1.02281	+	0.743111i
$35$	6.38318	+	3.09619i	1.07895	+	0.523352i
$36$	−6.27043	−	4.55573i	−1.04507	−	0.759289i
$37$	9.45910	−	6.87243i	1.55507	−	1.12982i	0.615152	−	0.788408i	$-0.289095\pi$
$37$	9.45910	−	6.87243i	1.55507	−	1.12982i	0.939913	−	0.341413i	$-0.110905\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	2.43391	+	1.76834i	0.389738	+	0.283161i
$40$	−1.54982	+	1.61185i	−0.245048	+	0.254856i
$41$	−0.353735	+	0.257003i	−0.0552441	+	0.0401372i	−0.615065	−	0.788477i	$-0.710870\pi$
$41$	−0.353735	+	0.257003i	−0.0552441	+	0.0401372i	0.559821	+	0.828614i	$0.310870\pi$
$42$	3.21466	−	9.89370i	0.496032	−	1.52663i
$43$	−4.77706			−0.728495			−0.364247	−	0.931302i	$-0.618674\pi$
$43$	−4.77706			−0.728495			−0.364247	+	0.931302i	$0.618674\pi$
$44$	1.31117	−	4.03538i	0.197667	−	0.608356i
$45$	17.0612	−	3.04645i	2.54333	−	0.454138i
$46$	1.97677	+	6.08388i	0.291459	+	0.897018i
$47$	−0.948701	−	2.91980i	−0.138382	−	0.425897i	0.857718	−	0.514120i	$-0.171881\pi$
$47$	−0.948701	−	2.91980i	−0.138382	−	0.425897i	−0.996101	+	0.0882227i	$0.971881\pi$
$48$	2.65262	+	1.92724i	0.382873	+	0.278174i
$49$	3.06628			0.438040
$50$	−0.196134	−	4.99615i	−0.0277375	−	0.706563i
$51$	−24.1709			−3.38460
$52$	−0.742313	−	0.539322i	−0.102940	−	0.0747905i
$53$	−1.96796	−	6.05677i	−0.270321	−	0.831961i	−0.990420	−	0.138090i	$-0.955904\pi$
$53$	−1.96796	−	6.05677i	−0.270321	−	0.831961i	0.720099	−	0.693871i	$-0.244096\pi$
$54$	−4.81344	−	14.8142i	−0.655026	−	2.01596i
$55$	4.47235	+	8.36751i	0.603051	+	1.12827i
$56$	−0.980431	+	3.01746i	−0.131016	+	0.403224i
$57$	−3.27882			−0.434291
$58$	1.29878	−	3.99724i	0.170538	−	0.524863i
$59$	2.18239	−	1.58560i	0.284123	−	0.206428i	−0.436591	−	0.899660i	$-0.643814\pi$
$59$	2.18239	−	1.58560i	0.284123	−	0.206428i	0.720714	+	0.693233i	$0.243814\pi$
$60$	−7.21751	+	1.28876i	−0.931777	+	0.166378i
$61$	−0.438838	−	0.318835i	−0.0561875	−	0.0408226i	0.559337	−	0.828940i	$-0.311056\pi$
$61$	−0.438838	−	0.318835i	−0.0561875	−	0.0408226i	−0.615524	+	0.788118i	$0.711056\pi$
$62$	−0.159760	+	0.116072i	−0.0202895	+	0.0147412i
$63$	19.8944	−	14.4542i	2.50646	−	1.82105i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	2.01976	−	0.360648i	0.250520	−	0.0447329i
$66$	11.2552	−	8.17738i	1.38542	−	1.00657i
$67$	−3.37777	+	10.3957i	−0.412661	+	1.27004i	0.501666	+	0.865061i	$0.332721\pi$
$67$	−3.37777	+	10.3957i	−0.412661	+	1.27004i	−0.914327	+	0.404978i	$0.867279\pi$
$68$	7.37182			0.893964
$69$	−6.48148	+	19.9479i	−0.780278	+	2.40145i
$70$	−3.34420	−	6.25681i	−0.399709	−	0.747832i
$71$	−3.74607	−	11.5292i	−0.444577	−	1.36827i	−0.882947	−	0.469472i	$-0.844444\pi$
$71$	−3.74607	−	11.5292i	−0.444577	−	1.36827i	0.438371	−	0.898794i	$-0.355556\pi$
$72$	2.39509	+	7.37133i	0.282264	+	0.868719i
$73$	3.06421	+	2.22628i	0.358638	+	0.260566i	0.752484	−	0.658611i	$-0.228856\pi$
$73$	3.06421	+	2.22628i	0.358638	+	0.260566i	−0.393846	+	0.919177i	$0.628856\pi$
$74$	−11.6921			−1.35918
$75$	9.10853	−	13.6309i	1.05176	−	1.57396i
$76$	1.00000			0.114708
$77$	10.8911	+	7.91281i	1.24115	+	0.901749i
$78$	−0.929671	−	2.86123i	−0.105265	−	0.323971i
$79$	−4.09648	−	12.6077i	−0.460890	−	1.41847i	−0.864078	−	0.503357i	$-0.832098\pi$
$79$	−4.09648	−	12.6077i	−0.460890	−	1.41847i	0.403188	−	0.915117i	$-0.367902\pi$
$80$	2.20125	−	0.393056i	0.246107	−	0.0439450i
$81$	8.59714	−	26.4593i	0.955237	−	2.93992i
$82$	0.437240			0.0482851
$83$	−3.90676	+	12.0238i	−0.428823	+	1.31978i	0.470463	+	0.882420i	$0.344087\pi$
$83$	−3.90676	+	12.0238i	−0.428823	+	1.31978i	−0.899286	+	0.437361i	$0.855913\pi$
$84$	−8.41608	+	6.11464i	−0.918270	+	0.667162i
$85$	−11.4250	+	11.8823i	−1.23921	+	1.28881i
$86$	3.86472	+	2.80788i	0.416744	+	0.302782i
$87$	11.1488	−	8.10010i	1.19528	−	0.868422i
$88$	−3.43270	+	2.49400i	−0.365927	+	0.265861i
$89$	3.41386	+	2.48032i	0.361869	+	0.262913i	0.753831	−	0.657068i	$-0.228204\pi$
$89$	3.41386	+	2.48032i	0.361869	+	0.262913i	−0.391962	+	0.919981i	$0.628204\pi$
$90$	−15.5934	−	7.56368i	−1.64369	−	0.797282i
$91$	2.35516	−	1.71113i	0.246888	−	0.179375i
$92$	1.97677	−	6.08388i	0.206093	−	0.634288i
$93$	−0.647483			−0.0671409
$94$	−0.948701	+	2.91980i	−0.0978511	+	0.301155i
$95$	−1.54982	+	1.61185i	−0.159008	+	0.165373i
$96$	−1.01321	−	3.11835i	−0.103410	−	0.318265i
$97$	1.84303	+	5.67227i	0.187132	+	0.575932i	0.999979	−	0.00654558i	$-0.00208354\pi$
$97$	1.84303	+	5.67227i	0.187132	+	0.575932i	−0.812847	+	0.582477i	$0.802084\pi$
$98$	−2.48067	−	1.80232i	−0.250586	−	0.182061i
$99$	32.8865			3.30521
$100$	−2.77799	+	4.15726i	−0.277799	+	0.415726i
$101$	14.2201			1.41495			0.707474	−	0.706739i	$-0.249834\pi$
$101$	14.2201			1.41495			0.707474	+	0.706739i	$0.249834\pi$
$102$	19.5547	+	14.2073i	1.93620	+	1.40673i
$103$	−1.83065	−	5.63417i	−0.180380	−	0.555151i	0.819459	−	0.573138i	$-0.194274\pi$
$103$	−1.83065	−	5.63417i	−0.180380	−	0.555151i	−0.999838	+	0.0179870i	$0.994274\pi$
$104$	0.283538	+	0.872641i	0.0278032	+	0.0855695i
$105$	3.18749	−	23.0421i	0.311067	−	2.24867i
$106$	−1.96796	+	6.05677i	−0.191146	+	0.588286i
$107$	11.9635			1.15655			0.578276	−	0.815841i	$-0.303726\pi$
$107$	11.9635			1.15655			0.578276	+	0.815841i	$0.303726\pi$
$108$	−4.81344	+	14.8142i	−0.463173	+	1.42550i
$109$	−5.80879	+	4.22034i	−0.556381	+	0.404235i	−0.830133	−	0.557566i	$-0.811735\pi$
$109$	−5.80879	+	4.22034i	−0.556381	+	0.404235i	0.273751	+	0.961801i	$0.411735\pi$
$110$	1.30009	−	9.39824i	0.123959	−	0.896087i
$111$	−31.0147	−	22.5335i	−2.94378	−	2.13878i
$112$	2.56680	−	1.86489i	0.242540	−	0.176216i
$113$	1.52491	−	1.10791i	0.143452	−	0.104224i	−0.513745	−	0.857943i	$-0.671742\pi$
$113$	1.52491	−	1.10791i	0.143452	−	0.104224i	0.657196	+	0.753719i	$0.271742\pi$
$114$	2.65262	+	1.92724i	0.248441	+	0.180503i
$115$	6.74267	+	12.6152i	0.628758	+	1.17637i
$116$	−3.40026	+	2.47043i	−0.315706	+	0.229374i
$117$	2.19761	−	6.76355i	0.203169	−	0.625291i
$118$	−2.69759			−0.248333
$119$	−7.22756	+	22.2441i	−0.662549	+	2.03912i
$120$	6.59660	+	3.19972i	0.602185	+	0.292093i
$121$	2.16418	+	6.66066i	0.196743	+	0.605514i
$122$	0.167621	+	0.515885i	0.0151757	+	0.0467061i
$123$	1.15983	+	0.842668i	0.104579	+	0.0759808i
$124$	0.197474			0.0177337
$125$	−2.39551	−	10.9207i	−0.214261	−	0.976777i
$126$	−24.5909			−2.19073
$127$	2.73415	+	1.98648i	0.242617	+	0.176272i	0.702448	−	0.711735i	$-0.252090\pi$
$127$	2.73415	+	1.98648i	0.242617	+	0.176272i	−0.459831	+	0.888006i	$0.652090\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	4.84017	+	14.8965i	0.426153	+	1.31157i
$130$	−1.84600	−	0.895412i	−0.161905	−	0.0785328i
$131$	−6.51286	+	20.0445i	−0.569031	+	1.75130i	0.0866269	+	0.996241i	$0.472391\pi$
$131$	−6.51286	+	20.0445i	−0.569031	+	1.75130i	−0.655658	+	0.755058i	$0.727609\pi$
$132$	−13.9122			−1.21090
$133$	−0.980431	+	3.01746i	−0.0850141	+	0.261647i
$134$	8.84313	−	6.42491i	0.763930	−	0.555027i
$135$	−16.4184	−	30.7179i	−1.41307	−	2.64378i
$136$	−5.96393	−	4.33305i	−0.511403	−	0.371556i
$137$	−4.59400	+	3.33774i	−0.392492	+	0.285162i	−0.766476	−	0.642273i	$-0.777992\pi$
$137$	−4.59400	+	3.33774i	−0.392492	+	0.285162i	0.373984	+	0.927435i	$0.377992\pi$
$138$	16.9687	−	12.3285i	1.44447	−	1.04947i
$139$	−13.5156	−	9.81969i	−1.14638	−	0.832895i	−0.158386	−	0.987377i	$-0.550629\pi$
$139$	−13.5156	−	9.81969i	−1.14638	−	0.832895i	−0.987996	+	0.154482i	$0.950629\pi$
$140$	−0.972145	+	7.02754i	−0.0821613	+	0.593936i
$141$	−8.14372	+	5.91676i	−0.685825	+	0.498281i
$142$	−3.74607	+	11.5292i	−0.314363	+	0.967510i
$143$	3.89320			0.325566
$144$	2.39509	−	7.37133i	0.199591	−	0.614277i
$145$	1.28781	−	9.30943i	0.106947	−	0.773106i
$146$	−1.17042	−	3.60219i	−0.0968648	−	0.298119i
$147$	−3.10679	−	9.56172i	−0.256244	−	0.788638i
$148$	9.45910	+	6.87243i	0.777533	+	0.564911i
$149$	4.30742			0.352877			0.176439	−	0.984312i	$-0.443542\pi$
$149$	4.30742			0.352877			0.176439	+	0.984312i	$0.443542\pi$
$150$	−15.3810	+	5.67377i	−1.25585	+	0.463262i
$151$	5.32879			0.433650			0.216825	−	0.976210i	$-0.430430\pi$
$151$	5.32879			0.433650			0.216825	+	0.976210i	$0.430430\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	17.6562	+	54.3401i	1.42742	+	4.39314i
$154$	−4.16001	−	12.8032i	−0.335223	−	1.03171i
$155$	−0.306049	+	0.318299i	−0.0245824	+	0.0255664i
$156$	−0.929671	+	2.86123i	−0.0744333	+	0.229082i
$157$	2.90553			0.231886			0.115943	−	0.993256i	$-0.463011\pi$
$157$	2.90553			0.231886			0.115943	+	0.993256i	$0.463011\pi$
$158$	−4.09648	+	12.6077i	−0.325899	+	1.00301i
$159$	−16.8931	+	12.2736i	−1.33971	+	0.973358i
$160$	−2.01188	−	0.975874i	−0.159053	−	0.0771496i
$161$	16.4197	+	11.9296i	1.29406	+	0.940187i
$162$	−22.5076	+	16.3527i	−1.76836	+	1.28479i
$163$	−1.39442	+	1.01310i	−0.109219	+	0.0793523i	−0.641054	−	0.767496i	$-0.721503\pi$
$163$	−1.39442	+	1.01310i	−0.109219	+	0.0793523i	0.531835	+	0.846848i	$0.321503\pi$
$164$	−0.353735	−	0.257003i	−0.0276220	−	0.0200686i
$165$	21.5613	−	22.4244i	1.67855	−	1.74574i
$166$	10.2280	−	7.43110i	0.793849	−	0.576765i
$167$	2.78196	−	8.56199i	0.215275	−	0.662547i	−0.783859	−	0.620938i	$-0.786752\pi$
$167$	2.78196	−	8.56199i	0.215275	−	0.662547i	0.999134	−	0.0416086i	$-0.0132483\pi$
$168$	10.4029			0.802597
$169$	−3.75706	+	11.5630i	−0.289005	+	0.889465i
$170$	16.2272	−	2.89754i	1.24457	−	0.222231i
$171$	2.39509	+	7.37133i	0.183157	+	0.563700i
$172$	−1.47619	−	4.54325i	−0.112559	−	0.346420i
$173$	−2.48998	−	1.80907i	−0.189309	−	0.137541i	0.489094	−	0.872231i	$-0.337328\pi$
$173$	−2.48998	−	1.80907i	−0.189309	−	0.137541i	−0.678403	+	0.734690i	$0.737328\pi$
$174$	−13.7807			−1.04471
$175$	−9.82071	−	12.4584i	−0.742376	−	0.941763i
$176$	4.24304			0.319832
$177$	−7.15568	−	5.19890i	−0.537854	−	0.390774i
$178$	−1.30398	−	4.01324i	−0.0977375	−	0.300805i
$179$	1.72522	+	5.30968i	0.128949	+	0.396864i	0.994600	−	0.103784i	$-0.0330951\pi$
$179$	1.72522	+	5.30968i	0.128949	+	0.396864i	−0.865651	+	0.500648i	$0.833095\pi$
$180$	8.16954	+	15.2847i	0.608922	+	1.13926i
$181$	−5.68689	+	17.5025i	−0.422703	+	1.30095i	0.482473	+	0.875911i	$0.339739\pi$
$181$	−5.68689	+	17.5025i	−0.422703	+	1.30095i	−0.905176	+	0.425036i	$0.860261\pi$
$182$	−2.91114			−0.215788
$183$	−0.549601	+	1.69150i	−0.0406276	+	0.125039i
$184$	−5.17525	+	3.76004i	−0.381525	+	0.277194i
$185$	−25.7372	+	4.59564i	−1.89224	+	0.337878i
$186$	0.523825	+	0.380581i	0.0384087	+	0.0279055i
$187$	−25.3052	+	18.3853i	−1.85050	+	1.34447i
$188$	2.48373	−	1.80454i	0.181145	−	0.131609i
$189$	−39.9821	−	29.0487i	−2.90827	−	2.11298i
$190$	2.20125	−	0.393056i	0.159696	−	0.0285153i
$191$	12.7371	−	9.25405i	0.921625	−	0.669600i	−0.0223031	−	0.999751i	$-0.507100\pi$
$191$	12.7371	−	9.25405i	0.921625	−	0.669600i	0.943928	+	0.330152i	$0.107100\pi$
$192$	−1.01321	+	3.11835i	−0.0731223	+	0.225047i
$193$	−21.6595			−1.55908			−0.779541	−	0.626351i	$-0.784548\pi$
$193$	−21.6595			−1.55908			−0.779541	+	0.626351i	$0.784548\pi$
$194$	1.84303	−	5.67227i	0.132322	−	0.407245i
$195$	−3.17106	−	5.93288i	−0.227085	−	0.424862i
$196$	0.947533	+	2.91621i	0.0676809	+	0.208301i
$197$	−7.09647	−	21.8407i	−0.505603	−	1.55608i	−0.799755	−	0.600326i	$-0.795037\pi$
$197$	−7.09647	−	21.8407i	−0.505603	−	1.55608i	0.294153	−	0.955758i	$-0.404963\pi$
$198$	−26.6057	−	19.3302i	−1.89078	−	1.37374i
$199$	−7.84903			−0.556403			−0.278201	−	0.960523i	$-0.589738\pi$
$199$	−7.84903			−0.556403			−0.278201	+	0.960523i	$0.589738\pi$
$200$	4.69101	−	1.73043i	0.331705	−	0.122360i
$201$	35.8398			2.52795
$202$	−11.5043	−	8.35834i	−0.809438	−	0.588091i
$203$	−4.12070	−	12.6822i	−0.289216	−	0.890117i
$204$	−7.46921	−	22.9879i	−0.522950	−	1.60947i
$205$	0.962475	−	0.171860i	0.0672222	−	0.0120032i
$206$	−1.83065	+	5.63417i	−0.127548	+	0.392551i
$207$	49.5808			3.44610
$208$	0.283538	−	0.872641i	0.0196598	−	0.0605067i
$209$	−3.43270	+	2.49400i	−0.237444	+	0.172514i
$210$	−16.1225	+	16.7679i	−1.11256	+	1.15709i
$211$	19.2412	+	13.9796i	1.32462	+	0.962393i	0.999862	+	0.0165955i	$0.00528277\pi$
$211$	19.2412	+	13.9796i	1.32462	+	0.962393i	0.324758	+	0.945797i	$0.394717\pi$
$212$	5.15220	−	3.74329i	0.353854	−	0.257090i
$213$	−32.1565	+	23.3631i	−2.20333	+	1.60081i
$214$	−9.67865	−	7.03195i	−0.661619	−	0.480694i
$215$	9.61088	+	4.66181i	0.655457	+	0.317933i
$216$	12.6017	−	9.15570i	0.857440	−	0.622967i
$217$	−0.193610	+	0.595870i	−0.0131431	+	0.0404503i
$218$	7.18006			0.486295
$219$	3.83761	−	11.8109i	0.259321	−	0.798109i
$220$	−6.57594	+	6.83916i	−0.443350	+	0.461096i
$221$	2.09019	+	6.43295i	0.140602	+	0.432727i
$222$	11.8466	+	36.4600i	0.795089	+	2.44703i
$223$	11.9066	+	8.65065i	0.797324	+	0.579290i	0.910128	−	0.414327i	$-0.135983\pi$
$223$	11.9066	+	8.65065i	0.797324	+	0.579290i	−0.112804	+	0.993617i	$0.535983\pi$
$224$	−3.17274			−0.211988
$225$	−37.2980	−	10.5205i	−2.48654	−	0.701364i
$226$	−1.88489			−0.125381
$227$	−23.5627	−	17.1193i	−1.56391	−	1.13625i	−0.932711	−	0.360625i	$-0.882563\pi$
$227$	−23.5627	−	17.1193i	−1.56391	−	1.13625i	−0.631198	−	0.775622i	$-0.717437\pi$
$228$	−1.01321	−	3.11835i	−0.0671016	−	0.206517i
$229$	6.34211	+	19.5190i	0.419098	+	1.28985i	0.908533	+	0.417812i	$0.137203\pi$
$229$	6.34211	+	19.5190i	0.419098	+	1.28985i	−0.489435	+	0.872040i	$0.662797\pi$
$230$	1.96007	−	14.1691i	0.129243	−	0.934284i
$231$	13.6399	−	41.9794i	0.897442	−	2.76204i
$232$	4.20295			0.275937
$233$	−3.38549	+	10.4195i	−0.221791	+	0.682602i	0.776811	+	0.629734i	$0.216836\pi$
$233$	−3.38549	+	10.4195i	−0.221791	+	0.682602i	−0.998602	+	0.0528679i	$0.983164\pi$
$234$	−5.75342	+	4.18011i	−0.376113	+	0.273262i
$235$	−0.940684	+	6.80011i	−0.0613635	+	0.443590i
$236$	2.18239	+	1.58560i	0.142062	+	0.103214i
$237$	−35.1645	+	25.5485i	−2.28418	+	1.65955i
$238$	18.9220	−	13.7476i	1.22653	−	0.891127i
$239$	0.0779857	+	0.0566599i	0.00504447	+	0.00366503i	0.590305	−	0.807181i	$-0.299008\pi$
$239$	0.0779857	+	0.0566599i	0.00504447	+	0.00366503i	−0.585260	+	0.810846i	$0.699008\pi$
$240$	−3.45602	−	6.46601i	−0.223085	−	0.417379i
$241$	−12.9758	+	9.42751i	−0.835848	+	0.607279i	−0.921208	−	0.389071i	$-0.872796\pi$
$241$	−12.9758	+	9.42751i	−0.835848	+	0.607279i	0.0853598	+	0.996350i	$0.472796\pi$
$242$	2.16418	−	6.66066i	0.139119	−	0.428163i
$243$	−44.4900			−2.85404
$244$	0.167621	−	0.515885i	0.0107309	−	0.0330262i
$245$	−6.16900	−	2.99230i	−0.394123	−	0.191171i
$246$	−0.443017	−	1.36346i	−0.0282457	−	0.0869313i
$247$	0.283538	+	0.872641i	0.0180411	+	0.0555248i
$248$	−0.159760	−	0.116072i	−0.0101448	−	0.00737061i
$249$	41.4527			2.62696
$250$	−4.48102	+	10.2431i	−0.283404	+	0.647829i
$251$	14.8934			0.940066			0.470033	−	0.882649i	$-0.344242\pi$
$251$	14.8934			0.940066			0.470033	+	0.882649i	$0.344242\pi$
$252$	19.8944	+	14.4542i	1.25323	+	0.910526i
$253$	8.38753	+	25.8142i	0.527319	+	1.62292i
$254$	−1.04435	−	3.21419i	−0.0655286	−	0.201676i
$255$	48.6290	+	23.5877i	3.04526	+	1.47712i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−11.4572			−0.714681			−0.357340	−	0.933974i	$-0.616316\pi$
$257$	−11.4572			−0.714681			−0.357340	+	0.933974i	$0.616316\pi$
$258$	4.84017	−	14.8965i	0.301336	−	0.927417i
$259$	−30.0113	+	21.8045i	−1.86481	+	1.35486i
$260$	0.967135	+	1.80946i	0.0599792	+	0.112218i
$261$	−26.3543	−	19.1475i	−1.63129	−	1.18520i
$262$	17.0509	−	12.3882i	1.05341	−	0.765346i
$263$	6.27421	−	4.55848i	0.386885	−	0.281088i	−0.377293	−	0.926094i	$-0.623145\pi$
$263$	6.27421	−	4.55848i	0.386885	−	0.281088i	0.764178	+	0.645006i	$0.223145\pi$
$264$	11.2552	+	8.17738i	0.692709	+	0.503283i
$265$	−1.95133	+	14.1060i	−0.119869	+	0.866524i
$266$	2.56680	−	1.86489i	0.157381	−	0.114344i
$267$	4.27552	−	13.1587i	0.261658	−	0.805299i
$268$	−10.9307			−0.667699
$269$	1.73577	−	5.34216i	0.105832	−	0.325717i	−0.884093	−	0.467311i	$-0.845223\pi$
$269$	1.73577	−	5.34216i	0.105832	−	0.325717i	0.989925	+	0.141594i	$0.0452228\pi$
$270$	−4.77276	+	34.5018i	−0.290461	+	2.09971i
$271$	−6.37784	−	19.6290i	−0.387426	−	1.19238i	−0.934705	−	0.355425i	$-0.884336\pi$
$271$	−6.37784	−	19.6290i	−0.387426	−	1.19238i	0.547279	−	0.836950i	$-0.315664\pi$
$272$	2.27802	+	7.01102i	0.138125	+	0.425105i
$273$	−7.72217	−	5.61048i	−0.467367	−	0.339562i
$274$	5.67850			0.343051
$275$	−0.832204	−	21.1989i	−0.0501838	−	1.27834i
$276$	−20.9745			−1.26252
$277$	−1.13847	−	0.827145i	−0.0684039	−	0.0496983i	0.553058	−	0.833143i	$-0.313461\pi$
$277$	−1.13847	−	0.827145i	−0.0684039	−	0.0496983i	−0.621462	+	0.783445i	$0.713461\pi$
$278$	5.16252	+	15.8886i	0.309627	+	0.952934i
$279$	0.472969	+	1.45565i	0.0283159	+	0.0871473i
$280$	4.91717	−	5.11399i	0.293857	−	0.305619i
$281$	−0.938509	+	2.88843i	−0.0559868	+	0.172310i	−0.975140	−	0.221592i	$-0.928875\pi$
$281$	−0.938509	+	2.88843i	−0.0559868	+	0.172310i	0.919153	+	0.393901i	$0.128875\pi$
$282$	10.0662			0.599433
$283$	2.60243	−	8.00945i	0.154698	−	0.476113i	−0.843432	−	0.537236i	$-0.819468\pi$
$283$	2.60243	−	8.00945i	0.154698	−	0.476113i	0.998130	+	0.0611236i	$0.0194684\pi$
$284$	9.80734	−	7.12545i	0.581958	−	0.422818i
$285$	6.59660	+	3.19972i	0.390749	+	0.189535i
$286$	−3.14967	−	2.28837i	−0.186244	−	0.135314i
$287$	1.12231	−	0.815404i	0.0662477	−	0.0481318i
$288$	−6.27043	+	4.55573i	−0.369488	+	0.268449i
$289$	−30.2117	−	21.9501i	−1.77716	−	1.29118i
$290$	−6.51380	+	6.77453i	−0.382504	+	0.397814i
$291$	15.8207	−	11.4944i	0.927426	−	0.673815i
$292$	−1.17042	+	3.60219i	−0.0684938	+	0.210802i
$293$	−16.7447			−0.978237			−0.489118	−	0.872217i	$-0.662681\pi$
$293$	−16.7447			−0.978237			−0.489118	+	0.872217i	$0.662681\pi$
$294$	−3.10679	+	9.56172i	−0.181192	+	0.557651i
$295$	−5.93806	+	1.06030i	−0.345727	+	0.0617332i
$296$	−3.61305	−	11.1198i	−0.210004	−	0.646327i
$297$	−20.4236	−	62.8575i	−1.18510	−	3.64736i
$298$	−3.48477	−	2.53184i	−0.201867	−	0.146665i
$299$	5.86953			0.339444
$300$	15.7784	+	4.45055i	0.910969	+	0.256952i
$301$	15.1564			0.873599
$302$	−4.31108	−	3.13218i	−0.248075	−	0.180237i
$303$	−14.4079	−	44.3431i	−0.827714	−	2.54744i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	0.571749	+	1.06971i	0.0327382	+	0.0612514i
$306$	17.6562	−	54.3401i	1.00934	−	3.10642i
$307$	−18.9003			−1.07870			−0.539348	−	0.842083i	$-0.681329\pi$
$307$	−18.9003			−1.07870			−0.539348	+	0.842083i	$0.681329\pi$
$308$	−4.16001	+	12.8032i	−0.237039	+	0.729530i
$309$	−15.7144	+	11.4172i	−0.893964	+	0.649503i
$310$	0.434690	−	0.0776184i	0.0246888	−	0.00440843i
$311$	22.6555	+	16.4602i	1.28468	+	0.933371i	0.999683	−	0.0251587i	$-0.00800912\pi$
$311$	22.6555	+	16.4602i	1.28468	+	0.933371i	0.284992	+	0.958530i	$0.408009\pi$
$312$	2.43391	−	1.76834i	0.137793	−	0.100113i
$313$	19.6712	−	14.2919i	1.11188	−	0.807828i	0.128922	−	0.991655i	$-0.458848\pi$
$313$	19.6712	−	14.2919i	1.11188	−	0.807828i	0.982959	+	0.183826i	$0.0588484\pi$
$314$	−2.35062	−	1.70783i	−0.132653	−	0.0963782i
$315$	−54.1307	+	9.66559i	−3.04992	+	0.544594i
$316$	10.7247	−	7.79197i	0.603313	−	0.438333i
$317$	1.54791	−	4.76396i	0.0869390	−	0.267571i	−0.898130	−	0.439730i	$-0.855074\pi$
$317$	1.54791	−	4.76396i	0.0869390	−	0.267571i	0.985069	+	0.172159i	$0.0550743\pi$
$318$	20.8811			1.17095
$319$	5.51079	−	16.9605i	0.308545	−	0.949604i
$320$	1.05404	+	1.97205i	0.0589228	+	0.110241i
$321$	−12.1215	−	37.3062i	−0.676558	−	2.08223i
$322$	−6.27178	−	19.3026i	−0.349513	−	1.07569i
$323$	−5.96393	−	4.33305i	−0.331842	−	0.241097i
$324$	27.8209			1.54561
$325$	−4.41546	−	1.24545i	−0.244925	−	0.0690849i
$326$	1.72359			0.0954610
$327$	19.0460	+	13.8377i	1.05325	+	0.765228i
$328$	0.135115	+	0.415840i	0.00746045	+	0.0229609i
$329$	3.00998	+	9.26378i	0.165946	+	0.510729i
$330$	−30.6242	+	5.46827i	−1.68581	+	0.301018i
$331$	−7.46935	+	22.9883i	−0.410553	+	1.26355i	0.505616	+	0.862759i	$0.331265\pi$
$331$	−7.46935	+	22.9883i	−0.410553	+	1.26355i	−0.916169	+	0.400793i	$0.868735\pi$
$332$	−12.6425			−0.693850
$333$	−28.0036	+	86.1862i	−1.53459	+	4.72297i
$334$	−7.28327	+	5.29160i	−0.398523	+	0.289544i
$335$	16.9406	−	17.6187i	0.925563	−	0.962611i
$336$	−8.41608	−	6.11464i	−0.459135	−	0.333581i
$337$	25.0580	−	18.2057i	1.36499	−	0.991727i	0.366885	−	0.930266i	$-0.380424\pi$
$337$	25.0580	−	18.2057i	1.36499	−	0.991727i	0.998110	−	0.0614603i	$-0.0195758\pi$
$338$	9.83611	−	7.14635i	0.535014	−	0.388710i
$339$	−4.99991	−	3.63265i	−0.271558	−	0.197298i
$340$	−14.8312	−	7.19397i	−0.804336	−	0.390148i
$341$	−0.677869	+	0.492501i	−0.0367087	+	0.0266704i
$342$	2.39509	−	7.37133i	0.129512	−	0.398596i
$343$	12.4807			0.673893
$344$	−1.47619	+	4.54325i	−0.0795910	+	0.244956i
$345$	32.5067	−	33.8078i	1.75010	−	1.82015i
$346$	0.951086	+	2.92714i	0.0511307	+	0.157364i
$347$	0.856584	+	2.63629i	0.0459838	+	0.141524i	0.971412	−	0.237399i	$-0.0762947\pi$
$347$	0.856584	+	2.63629i	0.0459838	+	0.141524i	−0.925428	+	0.378922i	$0.876295\pi$
$348$	11.1488	+	8.10010i	0.597640	+	0.434211i
$349$	26.0390			1.39384			0.696919	−	0.717150i	$-0.254554\pi$
$349$	26.0390			1.39384			0.696919	+	0.717150i	$0.254554\pi$
$350$	0.622282	+	15.8515i	0.0332623	+	0.847298i
$351$	−14.2923			−0.762867
$352$	−3.43270	−	2.49400i	−0.182963	−	0.132931i
$353$	−1.16699	−	3.59164i	−0.0621128	−	0.191164i	0.915185	−	0.403034i	$-0.132044\pi$
$353$	−1.16699	−	3.59164i	−0.0621128	−	0.191164i	−0.977298	+	0.211871i	$0.932044\pi$
$354$	2.73323	+	8.41200i	0.145269	+	0.447093i
$355$	−3.71441	+	26.8511i	−0.197141	+	1.42511i
$356$	−1.30398	+	4.01324i	−0.0691108	+	0.212701i
$357$	76.6879			4.05876
$358$	1.72522	−	5.30968i	0.0911806	−	0.280625i
$359$	2.46897	−	1.79381i	0.130307	−	0.0946736i	−0.520723	−	0.853726i	$-0.674337\pi$
$359$	2.46897	−	1.79381i	0.130307	−	0.0946736i	0.651030	+	0.759052i	$0.274337\pi$
$360$	2.37485	−	17.1676i	0.125166	−	0.904809i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	14.8885	−	10.8171i	0.782521	−	0.568535i
$363$	18.5775	−	13.4973i	0.975063	−	0.708425i
$364$	2.35516	+	1.71113i	0.123444	+	0.0896875i
$365$	−3.99226	−	7.46928i	−0.208964	−	0.390960i
$366$	1.43887	−	1.04540i	0.0752111	−	0.0546441i
$367$	7.25614	−	22.3321i	0.378767	−	1.16573i	−0.562134	−	0.827046i	$-0.690020\pi$
$367$	7.25614	−	22.3321i	0.378767	−	1.16573i	0.940902	−	0.338680i	$-0.109980\pi$
$368$	6.39696			0.333465
$369$	1.04723	−	3.22304i	0.0545166	−	0.167785i
$370$	23.5231	+	11.4100i	1.22291	+	0.593178i
$371$	6.24384	+	19.2166i	0.324164	+	0.997674i
$372$	−0.200083	−	0.615793i	−0.0103738	−	0.0319274i
$373$	−3.80333	−	2.76328i	−0.196929	−	0.143077i	0.484951	−	0.874541i	$-0.338837\pi$
$373$	−3.80333	−	2.76328i	−0.196929	−	0.143077i	−0.681880	+	0.731464i	$0.738837\pi$
$374$	31.2790			1.61740
$375$	−31.6273	+	18.5350i	−1.63323	+	0.957143i
$376$	−3.07006			−0.158326
$377$	−3.11990	−	2.26674i	−0.160683	−	0.116743i
$378$	15.2718	+	47.0017i	0.785496	+	2.41751i
$379$	−0.611950	−	1.88339i	−0.0314338	−	0.0967432i	0.934109	−	0.356989i	$-0.116197\pi$
$379$	−0.611950	−	1.88339i	−0.0314338	−	0.0967432i	−0.965542	+	0.260245i	$0.916197\pi$
$380$	−2.01188	−	0.975874i	−0.103207	−	0.0500613i
$381$	3.42425	−	10.5388i	0.175430	−	0.539917i
$382$	−15.7439			−0.805530
$383$	−10.1308	+	31.1794i	−0.517660	+	1.59319i	0.260729	+	0.965412i	$0.416037\pi$
$383$	−10.1308	+	31.1794i	−0.517660	+	1.59319i	−0.778389	+	0.627782i	$0.783963\pi$
$384$	2.65262	−	1.92724i	0.135366	−	0.0983492i
$385$	−14.1896	−	26.5479i	−0.723169	−	1.35301i
$386$	17.5229	+	12.7311i	0.891891	+	0.647997i
$387$	29.9542	−	21.7630i	1.52266	−	1.10628i
$388$	−4.82512	+	3.50565i	−0.244958	+	0.177973i
$389$	−0.627017	−	0.455555i	−0.0317910	−	0.0230975i	0.571776	−	0.820410i	$-0.306255\pi$
$389$	−0.627017	−	0.455555i	−0.0317910	−	0.0230975i	−0.603567	+	0.797312i	$0.706255\pi$
$390$	−0.921815	+	6.66371i	−0.0466779	+	0.337430i
$391$	−38.1510	+	27.7183i	−1.92938	+	1.40178i
$392$	0.947533	−	2.91621i	0.0478577	−	0.147291i
$393$	69.1047			3.48587
$394$	−7.09647	+	21.8407i	−0.357515	+	1.10032i
$395$	−4.06186	+	29.3628i	−0.204375	+	1.47740i
$396$	10.1625	+	31.2769i	0.510684	+	1.57172i
$397$	1.52570	+	4.69561i	0.0765724	+	0.235666i	0.982015	−	0.188803i	$-0.0604608\pi$
$397$	1.52570	+	4.69561i	0.0765724	+	0.235666i	−0.905443	+	0.424469i	$0.860461\pi$
$398$	6.35000	+	4.61354i	0.318297	+	0.231256i
$399$	10.4029			0.520794
$400$	−4.81223	−	1.35736i	−0.240612	−	0.0678681i
$401$	−2.88017			−0.143829			−0.0719143	−	0.997411i	$-0.522911\pi$
$401$	−2.88017			−0.143829			−0.0719143	+	0.997411i	$0.522911\pi$
$402$	−28.9950	−	21.0661i	−1.44614	−	1.05068i
$403$	0.0559915	+	0.172324i	0.00278913	+	0.00858407i
$404$	4.39424	+	13.5241i	0.218622	+	0.672848i
$405$	−43.1173	+	44.8432i	−2.14252	+	2.22828i
$406$	−4.12070	+	12.6822i	−0.204507	+	0.629407i
$407$	−49.6100			−2.45908
$408$	−7.46921	+	22.9879i	−0.369781	+	1.13807i
$409$	11.9416	−	8.67610i	0.590476	−	0.429006i	−0.252010	−	0.967725i	$-0.581092\pi$
$409$	11.9416	−	8.67610i	0.590476	−	0.429006i	0.842486	+	0.538719i	$0.181092\pi$
$410$	−0.879675	−	0.426691i	−0.0434441	−	0.0210728i
$411$	15.0629	+	10.9438i	0.742999	+	0.539820i
$412$	4.79271	−	3.48211i	0.236120	−	0.171551i
$413$	−6.92417	+	5.03070i	−0.340716	+	0.247545i
$414$	−40.1117	−	29.1429i	−1.97138	−	1.43229i
$415$	19.5936	−	20.3779i	0.961814	−	1.00031i
$416$	−0.742313	+	0.539322i	−0.0363949	+	0.0264424i
$417$	−16.9270	+	52.0959i	−0.828917	+	2.55115i
$418$	4.24304			0.207534
$419$	−9.28050	+	28.5624i	−0.453382	+	1.39537i	0.419642	+	0.907690i	$0.362156\pi$
$419$	−9.28050	+	28.5624i	−0.453382	+	1.39537i	−0.873024	+	0.487677i	$0.837844\pi$
$420$	22.8993	−	4.08890i	1.11737	−	0.199518i
$421$	−0.755991	−	2.32670i	−0.0368448	−	0.113397i	0.930943	−	0.365166i	$-0.118988\pi$
$421$	−0.755991	−	2.32670i	−0.0368448	−	0.113397i	−0.967787	+	0.251769i	$0.918988\pi$
$422$	−7.34949	−	22.6194i	−0.357768	−	1.10110i
$423$	19.2506	+	13.9864i	0.935996	+	0.680041i
$424$	−6.36847			−0.309280
$425$	34.5813	−	12.7564i	1.67744	−	0.618777i
$426$	39.7476			1.92578
$427$	1.39232	+	1.01158i	0.0673791	+	0.0489538i
$428$	3.69692	+	11.3779i	0.178697	+	0.549973i
$429$	−3.94464	−	12.1403i	−0.190449	−	0.586141i
$430$	−5.03522	−	9.42062i	−0.242820	−	0.454302i
$431$	11.2195	−	34.5300i	0.540424	−	1.66325i	−0.191205	−	0.981550i	$-0.561240\pi$
$431$	11.2195	−	34.5300i	0.540424	−	1.66325i	0.731629	−	0.681703i	$-0.238760\pi$
$432$	−15.5766			−0.749430
$433$	−3.44943	+	10.6162i	−0.165769	+	0.510184i	−0.999092	−	0.0426017i	$-0.986435\pi$
$433$	−3.44943	+	10.6162i	−0.165769	+	0.510184i	0.833323	+	0.552786i	$0.186435\pi$
$434$	0.506877	−	0.368268i	0.0243309	−	0.0176774i
$435$	−30.3348	+	5.41659i	−1.45444	+	0.259706i
$436$	−5.80879	−	4.22034i	−0.278191	−	0.202117i
$437$	−5.17525	+	3.76004i	−0.247566	+	0.179867i
$438$	−10.0470	+	7.29956i	−0.480063	+	0.348787i
$439$	15.0211	+	10.9135i	0.716919	+	0.520872i	0.885398	−	0.464833i	$-0.153886\pi$
$439$	15.0211	+	10.9135i	0.716919	+	0.520872i	−0.168479	+	0.985705i	$0.553886\pi$
$440$	9.34001	−	1.66775i	0.445267	−	0.0795071i
$441$	−19.2269	+	13.9692i	−0.915566	+	0.665198i
$442$	2.09019	−	6.43295i	0.0994203	−	0.305984i
$443$	−6.97592			−0.331436			−0.165718	−	0.986173i	$-0.552994\pi$
$443$	−6.97592			−0.331436			−0.165718	+	0.986173i	$0.552994\pi$
$444$	11.8466	−	36.4600i	0.562213	−	1.73031i
$445$	−4.44782	−	8.32161i	−0.210847	−	0.394482i
$446$	−4.54791	−	13.9970i	−0.215350	−	0.662779i
$447$	−4.36433	−	13.4320i	−0.206425	−	0.635312i
$448$	2.56680	+	1.86489i	0.121270	+	0.0881078i
$449$	−17.8004			−0.840051			−0.420025	−	0.907512i	$-0.637979\pi$
$449$	−17.8004			−0.840051			−0.420025	+	0.907512i	$0.637979\pi$
$450$	23.9910	+	30.4345i	1.13095	+	1.43469i
$451$	1.85523			0.0873593
$452$	1.52491	+	1.10791i	0.0717258	+	0.0521119i
$453$	−5.39919	−	16.6170i	−0.253676	−	0.780734i
$454$	9.00014	+	27.6996i	0.422397	+	1.30001i
$455$	−6.40816	+	1.14424i	−0.300419	+	0.0536429i
$456$	−1.01321	+	3.11835i	−0.0474480	+	0.146030i
$457$	−34.9797			−1.63628			−0.818141	−	0.575018i	$-0.804995\pi$
$457$	−34.9797			−1.63628			−0.818141	+	0.575018i	$0.804995\pi$
$458$	6.34211	−	19.5190i	0.296347	−	0.912063i
$459$	92.8978	−	67.4942i	4.33610	−	3.15036i
$460$	−9.91413	+	10.3110i	−0.462249	+	0.480751i
$461$	10.7809	+	7.83280i	0.502118	+	0.364810i	0.809825	−	0.586671i	$-0.199562\pi$
$461$	10.7809	+	7.83280i	0.502118	+	0.364810i	−0.307707	+	0.951481i	$0.599562\pi$
$462$	−35.7098	+	25.9447i	−1.66137	+	1.20706i
$463$	−14.9499	+	10.8617i	−0.694781	+	0.504788i	−0.878228	−	0.478242i	$-0.841274\pi$
$463$	−14.9499	+	10.8617i	−0.694781	+	0.504788i	0.183447	+	0.983030i	$0.441274\pi$
$464$	−3.40026	−	2.47043i	−0.157853	−	0.114687i
$465$	1.30266	+	0.631862i	0.0604094	+	0.0293019i
$466$	8.86333	−	6.43959i	0.410586	−	0.298308i
$467$	−1.36836	+	4.21139i	−0.0633203	+	0.194880i	−0.977712	−	0.209951i	$-0.932670\pi$
$467$	−1.36836	+	4.21139i	−0.0633203	+	0.194880i	0.914392	+	0.404831i	$0.132670\pi$
$468$	7.11162			0.328735
$469$	10.7168	−	32.9829i	0.494856	−	1.52301i
$470$	4.75803	−	4.94849i	0.219472	−	0.228257i
$471$	−2.94391	−	9.06044i	−0.135648	−	0.417483i
$472$	−0.833600	−	2.56556i	−0.0383695	−	0.118089i
$473$	16.3982	+	11.9140i	0.753990	+	0.547805i
$474$	43.4657			1.99645
$475$	4.69101	−	1.73043i	0.215238	−	0.0793976i
$476$	−23.3889			−1.07203
$477$	39.9330	+	29.0130i	1.82841	+	1.32842i
$478$	−0.0297879	−	0.0916777i	−0.00136247	−	0.00419324i
$479$	1.76177	+	5.42217i	0.0804973	+	0.247745i	0.983204	−	0.182512i	$-0.0584228\pi$
$479$	1.76177	+	5.42217i	0.0804973	+	0.247745i	−0.902706	+	0.430257i	$0.858423\pi$
$480$	−1.00465	+	7.26251i	−0.0458558	+	0.331487i
$481$	−3.31515	+	10.2030i	−0.151158	+	0.465216i
$482$	16.0390			0.730558
$483$	20.5641	−	63.2896i	0.935697	−	2.87978i
$484$	−5.66589	+	4.11651i	−0.257541	+	0.187114i
$485$	1.82746	−	13.2105i	0.0829805	−	0.599858i
$486$	35.9932	+	26.1506i	1.63268	+	1.18621i
$487$	3.96321	−	2.87944i	0.179590	−	0.130480i	−0.494358	−	0.869258i	$-0.664597\pi$
$487$	3.96321	−	2.87944i	0.179590	−	0.130480i	0.673949	+	0.738778i	$0.264597\pi$
$488$	−0.438838	+	0.318835i	−0.0198653	+	0.0144330i
$489$	4.57204	+	3.32178i	0.206755	+	0.150216i
$490$	3.23199	+	6.04687i	0.146006	+	0.273170i
$491$	23.5339	−	17.0984i	1.06207	−	0.771640i	0.0876004	−	0.996156i	$-0.472080\pi$
$491$	23.5339	−	17.0984i	1.06207	−	0.771640i	0.974470	+	0.224516i	$0.0720801\pi$
$492$	−0.443017	+	1.36346i	−0.0199727	+	0.0614697i
$493$	30.9834			1.39542
$494$	0.283538	−	0.872641i	0.0127570	−	0.0392620i
$495$	−66.1637	−	32.0930i	−2.97384	−	1.44247i
$496$	0.0610229	+	0.187809i	0.00274001	+	0.00843288i
$497$	11.8853	+	36.5792i	0.533129	+	1.64080i
$498$	−33.5359	−	24.3653i	−1.50278	−	1.09183i
$499$	0.874799			0.0391614			0.0195807	−	0.999808i	$-0.493767\pi$
$499$	0.874799			0.0391614			0.0195807	+	0.999808i	$0.493767\pi$
$500$	9.64594	−	5.65294i	0.431380	−	0.252807i
$501$	−29.5180			−1.31877
$502$	−12.0490	−	8.75414i	−0.537775	−	0.390717i
$503$	−8.12336	−	25.0011i	−0.362203	−	1.11475i	−0.951714	−	0.306986i	$-0.900680\pi$
$503$	−8.12336	−	25.0011i	−0.362203	−	1.11475i	0.589511	−	0.807760i	$-0.299320\pi$
$504$	−7.59900	−	23.3873i	−0.338486	−	1.04175i
$505$	−28.6091	−	13.8770i	−1.27309	−	0.617518i
$506$	8.38753	−	25.8142i	0.372871	−	1.14758i
$507$	39.8643			1.77043
$508$	−1.04435	+	3.21419i	−0.0463357	+	0.142607i
$509$	−29.7561	+	21.6191i	−1.31892	+	0.958250i	−0.318973	+	0.947764i	$0.603338\pi$
$509$	−29.7561	+	21.6191i	−1.31892	+	0.958250i	−0.999945	+	0.0104862i	$0.996662\pi$
$510$	−25.4771	−	47.6663i	−1.12815	−	2.11070i
$511$	−9.72193	−	7.06339i	−0.430073	−	0.312466i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	12.6017	−	9.15570i	0.556381	−	0.404234i
$514$	9.26907	+	6.73438i	0.408841	+	0.297041i
$515$	−1.81518	+	13.1218i	−0.0799865	+	0.578214i
$516$	−12.6717	+	9.20655i	−0.557842	+	0.405296i
$517$	−4.02538	+	12.3889i	−0.177036	+	0.544861i
$518$	37.0959			1.62990
$519$	−3.11844	+	9.59758i	−0.136884	+	0.421287i
$520$	0.281142	−	2.03235i	0.0123289	−	0.0891243i
$521$	−13.3844	−	41.1928i	−0.586380	−	1.80469i	−0.593658	−	0.804717i	$-0.702317\pi$
$521$	−13.3844	−	41.1928i	−0.586380	−	1.80469i	0.00727851	−	0.999974i	$-0.497683\pi$
$522$	10.0664	+	30.9813i	0.440596	+	1.35602i
$523$	−12.9072	−	9.37763i	−0.564392	−	0.410055i	0.268672	−	0.963232i	$-0.413415\pi$
$523$	−12.9072	−	9.37763i	−0.564392	−	0.410055i	−0.833064	+	0.553177i	$0.813415\pi$
$524$	−21.0761			−0.920712
$525$	−28.8990	+	43.2473i	−1.26126	+	1.88747i
$526$	−7.75535			−0.338149
$527$	−1.17772	−	0.855665i	−0.0513024	−	0.0372734i
$528$	−4.29910	−	13.2313i	−0.187094	−	0.575817i
$529$	5.53794	+	17.0440i	0.240780	+	0.741045i
$530$	9.86996	−	10.2650i	0.428724	−	0.445884i
$531$	−6.46096	+	19.8848i	−0.280382	+	0.862927i
$532$	−3.17274			−0.137556
$533$	0.123974	−	0.381553i	0.00536992	−	0.0165269i
$534$	−11.1935	+	8.13252i	−0.484388	+	0.351929i
$535$	−24.0691	−	11.6748i	−1.04060	−	0.504747i
$536$	8.84313	+	6.42491i	0.381965	+	0.277514i
$537$	14.8094	−	10.7597i	0.639072	−	0.464313i
$538$	−4.54431	+	3.30163i	−0.195919	+	0.142344i
$539$	−10.5256	−	7.64730i	−0.453370	−	0.329393i
$540$	24.1409	−	25.1072i	1.03886	−	1.08044i
$541$	−33.4491	+	24.3022i	−1.43809	+	1.04483i	−0.449652	+	0.893204i	$0.648452\pi$
$541$	−33.4491	+	24.3022i	−1.43809	+	1.04483i	−0.988437	+	0.151630i	$0.951548\pi$
$542$	−6.37784	+	19.6290i	−0.273952	+	0.843136i
$543$	60.3407			2.58947
$544$	2.27802	−	7.01102i	0.0976692	−	0.300595i
$545$	15.8051	−	2.82217i	0.677017	−	0.120888i
$546$	2.94961	+	9.07795i	0.126231	+	0.388500i
$547$	−2.44691	−	7.53081i	−0.104622	−	0.321994i	0.885019	−	0.465554i	$-0.154145\pi$
$547$	−2.44691	−	7.53081i	−0.104622	−	0.321994i	−0.989642	+	0.143560i	$0.954145\pi$
$548$	−4.59400	−	3.33774i	−0.196246	−	0.142581i
$549$	4.20423			0.179432
$550$	−11.7871	+	17.6394i	−0.502605	+	0.752148i
$551$	4.20295			0.179052
$552$	16.9687	+	12.3285i	0.722237	+	0.524736i
$553$	12.9971	+	40.0009i	0.552692	+	1.70101i
$554$	0.434856	+	1.33835i	0.0184753	+	0.0568610i
$555$	40.4081	+	75.6012i	1.71523	+	3.20909i
$556$	5.16252	−	15.8886i	0.218939	−	0.673826i
$557$	13.2882			0.563037			0.281519	−	0.959556i	$-0.409162\pi$
$557$	13.2882			0.563037			0.281519	+	0.959556i	$0.409162\pi$
$558$	0.472969	−	1.45565i	0.0200224	−	0.0616225i
$559$	3.54607	−	2.57637i	0.149983	−	0.108969i
$560$	−6.98400	+	1.24706i	−0.295128	+	0.0526981i
$561$	82.9713	+	60.2822i	3.50305	+	2.54511i
$562$	2.45705	−	1.78515i	0.103644	−	0.0753020i
$563$	−9.10747	+	6.61697i	−0.383834	+	0.278872i	−0.762924	−	0.646488i	$-0.776237\pi$
$563$	−9.10747	+	6.61697i	−0.383834	+	0.278872i	0.379090	+	0.925360i	$0.376237\pi$
$564$	−8.14372	−	5.91676i	−0.342912	−	0.249140i
$565$	−4.14913	+	0.740869i	−0.174555	+	0.0311686i
$566$	−6.81325	+	4.95012i	−0.286382	+	0.208069i
$567$	−27.2765	+	83.9484i	−1.14550	+	3.52550i
$568$	−12.1225			−0.508650
$569$	2.56351	−	7.88966i	0.107468	−	0.330752i	−0.882834	−	0.469685i	$-0.844367\pi$
$569$	2.56351	−	7.88966i	0.107468	−	0.330752i	0.990302	+	0.138934i	$0.0443674\pi$
$570$	−3.45602	−	6.46601i	−0.144757	−	0.270831i
$571$	−4.86977	−	14.9876i	−0.203794	−	0.627212i	−0.999761	−	0.0218724i	$-0.993037\pi$
$571$	−4.86977	−	14.9876i	−0.203794	−	0.627212i	0.795967	−	0.605340i	$-0.206963\pi$
$572$	1.20307	+	3.70265i	0.0503027	+	0.154816i
$573$	−41.7627	−	30.3424i	−1.74466	−	1.26757i
$574$	−1.38725			−0.0579026
$575$	−1.25466	−	31.9602i	−0.0523230	−	1.33283i
$576$	7.75067			0.322945
$577$	2.77393	+	2.01538i	0.115480	+	0.0839014i	0.644026	−	0.765003i	$-0.277263\pi$
$577$	2.77393	+	2.01538i	0.115480	+	0.0839014i	−0.528546	+	0.848905i	$0.677263\pi$
$578$	11.5398	+	35.5160i	0.479994	+	1.47727i
$579$	21.9456	+	67.5417i	0.912029	+	2.80694i
$580$	9.25174	−	1.65199i	0.384158	−	0.0685953i
$581$	12.3951	−	38.1483i	0.514237	−	1.58266i
$582$	−19.5555			−0.810600
$583$	−8.35016	+	25.6992i	−0.345828	+	1.06435i
$584$	3.06421	−	2.22628i	0.126798	−	0.0921239i
$585$	−11.0217	+	11.4629i	−0.455692	+	0.473932i
$586$	13.5468	+	9.84230i	0.559612	+	0.406582i
$587$	−24.3742	+	17.7089i	−1.00603	+	0.730925i	−0.963373	−	0.268165i	$-0.913583\pi$
$587$	−24.3742	+	17.7089i	−1.00603	+	0.730925i	−0.0426588	+	0.999090i	$0.513583\pi$
$588$	8.13369	−	5.90947i	0.335428	−	0.243702i
$589$	−0.159760	−	0.116072i	−0.00658280	−	0.00478268i
$590$	5.42723	+	2.63250i	0.223435	+	0.108378i
$591$	−60.9166	+	44.2585i	−2.50577	+	1.82055i
$592$	−3.61305	+	11.1198i	−0.148496	+	0.457022i
$593$	−10.8837			−0.446940			−0.223470	−	0.974711i	$-0.571738\pi$
$593$	−10.8837			−0.446940			−0.223470	+	0.974711i	$0.571738\pi$
$594$	−20.4236	+	62.8575i	−0.837992	+	2.57907i
$595$	36.2485	−	37.6994i	1.48604	−	1.54552i
$596$	1.33106	+	4.09660i	0.0545225	+	0.167803i
$597$	7.95273	+	24.4760i	0.325483	+	1.00174i
$598$	−4.74855	−	3.45002i	−0.194183	−	0.141082i
$599$	10.7615			0.439704			0.219852	−	0.975533i	$-0.429443\pi$
$599$	10.7615			0.439704			0.219852	+	0.975533i	$0.429443\pi$
$600$	−10.1491	−	12.8749i	−0.414334	−	0.525616i
$601$	31.8025			1.29725			0.648626	−	0.761107i	$-0.275344\pi$
$601$	31.8025			1.29725			0.648626	+	0.761107i	$0.275344\pi$
$602$	−12.2618	−	8.90869i	−0.499752	−	0.363091i
$603$	−26.1800	−	80.5738i	−1.06613	−	3.28122i
$604$	1.64669	+	5.06798i	0.0670027	+	0.206213i
$605$	2.14589	−	15.5124i	0.0872428	−	0.630670i
$606$	−14.4079	+	44.3431i	−0.585282	+	1.80131i
$607$	18.8402			0.764700			0.382350	−	0.924017i	$-0.375115\pi$
$607$	18.8402			0.764700			0.382350	+	0.924017i	$0.375115\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	−35.3724	+	25.6995i	−1.43336	+	1.04140i
$610$	0.166205	−	1.20148i	0.00672944	−	0.0486464i
$611$	2.27895	+	1.65575i	0.0921963	+	0.0669845i
$612$	−46.2245	+	33.5840i	−1.86851	+	1.35755i
$613$	1.01664	−	0.738632i	0.0410617	−	0.0298331i	−0.567065	−	0.823673i	$-0.691921\pi$
$613$	1.01664	−	0.738632i	0.0410617	−	0.0298331i	0.608127	+	0.793840i	$0.291921\pi$
$614$	15.2907	+	11.1093i	0.617081	+	0.448335i
$615$	−1.51111	−	2.82720i	−0.0609338	−	0.114004i
$616$	10.8911	−	7.91281i	0.438813	−	0.318816i
$617$	3.44188	−	10.5930i	0.138565	−	0.426459i	−0.857562	−	0.514380i	$-0.828022\pi$
$617$	3.44188	−	10.5930i	0.138565	−	0.426459i	0.996127	+	0.0879206i	$0.0280222\pi$
$618$	19.4241			0.781353
$619$	5.58520	−	17.1895i	0.224488	−	0.690904i	−0.773855	−	0.633363i	$-0.781674\pi$
$619$	5.58520	−	17.1895i	0.224488	−	0.690904i	0.998343	−	0.0575409i	$-0.0183260\pi$
$620$	−0.397295	−	0.192710i	−0.0159557	−	0.00773942i
$621$	−30.7914	−	94.7662i	−1.23562	−	3.80284i
$622$	−8.65363	−	26.6331i	−0.346979	−	1.06789i
$623$	−10.8313	−	7.86941i	−0.433947	−	0.315281i
$624$	−3.00848			−0.120436
$625$	−5.83774	+	24.3089i	−0.233510	+	0.972354i
$626$	−24.3149			−0.971819
$627$	11.2552	+	8.17738i	0.449489	+	0.326573i
$628$	0.897857	+	2.76332i	0.0358284	+	0.110269i
$629$	−26.6348	−	81.9734i	−1.06200	−	3.26849i
$630$	49.4739	+	23.9976i	1.97109	+	0.956087i
$631$	3.82031	−	11.7577i	0.152084	−	0.468067i	−0.845770	−	0.533548i	$-0.820858\pi$
$631$	3.82031	−	11.7577i	0.152084	−	0.468067i	0.997854	+	0.0654815i	$0.0208583\pi$
$632$	−13.2565			−0.527315
$633$	24.0977	−	74.1650i	0.957796	−	2.94779i
$634$	−4.05247	+	2.94429i	−0.160944	+	0.116933i
$635$	−3.56224	−	6.66475i	−0.141363	−	0.264483i
$636$	−16.8931	−	12.2736i	−0.669856	−	0.486679i
$637$	−2.27614	+	1.65371i	−0.0901839	+	0.0655225i
$638$	−14.4274	+	10.4821i	−0.571188	+	0.414992i
$639$	76.0135	+	55.2270i	3.00705	+	2.18475i
$640$	0.306406	−	2.21498i	0.0121117	−	0.0875546i
$641$	33.9598	−	24.6733i	1.34133	−	0.974535i	0.341939	−	0.939722i	$-0.388916\pi$
$641$	33.9598	−	24.6733i	1.34133	−	0.974535i	0.999394	−	0.0348132i	$-0.0110836\pi$
$642$	−12.1215	+	37.3062i	−0.478399	+	1.47236i
$643$	31.8228			1.25497			0.627484	−	0.778630i	$-0.284085\pi$
$643$	31.8228			1.25497			0.627484	+	0.778630i	$0.284085\pi$
$644$	−6.27178	+	19.3026i	−0.247143	+	0.760627i
$645$	4.79927	−	34.6934i	0.188971	−	1.36605i
$646$	2.27802	+	7.01102i	0.0896274	+	0.275845i
$647$	0.518470	+	1.59569i	0.0203832	+	0.0627329i	0.960731	−	0.277482i	$-0.0895000\pi$
$647$	0.518470	+	1.59569i	0.0203832	+	0.0627329i	−0.940348	+	0.340215i	$0.889500\pi$
$648$	−22.5076	−	16.3527i	−0.884182	−	0.642396i
$649$	−11.4460			−0.449294
$650$	2.84013	+	3.60293i	0.111399	+	0.141318i
$651$	2.05430			0.0805142
$652$	−1.39442	−	1.01310i	−0.0546095	−	0.0396761i
$653$	−2.60254	−	8.00979i	−0.101845	−	0.313447i	0.887132	−	0.461516i	$-0.152694\pi$
$653$	−2.60254	−	8.00979i	−0.101845	−	0.313447i	−0.988977	+	0.148069i	$0.952694\pi$
$654$	−7.27492	−	22.3899i	−0.284472	−	0.875515i
$655$	32.6640	−	33.9715i	1.27629	−	1.32738i
$656$	0.135115	−	0.415840i	0.00527534	−	0.0162358i
$657$	−29.3562			−1.14529
$658$	3.00998	−	9.26378i	0.117341	−	0.361140i
$659$	16.0742	−	11.6786i	0.626163	−	0.454934i	−0.228906	−	0.973449i	$-0.573515\pi$
$659$	16.0742	−	11.6786i	0.626163	−	0.454934i	0.855069	+	0.518514i	$0.173515\pi$
$660$	27.9897	+	13.5765i	1.08950	+	0.528466i
$661$	−15.7471	−	11.4409i	−0.612491	−	0.445001i	0.237799	−	0.971314i	$-0.423574\pi$
$661$	−15.7471	−	11.4409i	−0.612491	−	0.445001i	−0.850291	+	0.526313i	$0.823574\pi$
$662$	19.5550	−	14.2076i	0.760028	−	0.552192i
$663$	17.9423	−	13.0359i	0.696823	−	0.506272i
$664$	10.2280	+	7.43110i	0.396925	+	0.288383i
$665$	4.91717	−	5.11399i	0.190680	−	0.198312i
$666$	73.3144	−	53.2660i	2.84087	−	2.06402i
$667$	8.30827	−	25.5702i	0.321697	−	0.990083i
$668$	9.00261			0.348322
$669$	14.9118	−	45.8938i	0.576523	−	1.77436i
$670$	−24.0612	+	4.29638i	−0.929566	+	0.165984i
$671$	0.711225	+	2.18893i	0.0274565	+	0.0845025i
$672$	3.21466	+	9.89370i	0.124008	+	0.381658i
$673$	−26.0354	−	18.9159i	−1.00359	−	0.729153i	−0.0407370	−	0.999170i	$-0.512971\pi$
$673$	−26.0354	−	18.9159i	−1.00359	−	0.729153i	−0.962855	+	0.270017i	$0.912971\pi$
$674$	−30.9734			−1.19305
$675$	3.05510	+	77.8231i	0.117591	+	2.99541i
$676$	−12.1581			−0.467619
$677$	−6.25080	−	4.54147i	−0.240238	−	0.174543i	0.461151	−	0.887321i	$-0.347436\pi$
$677$	−6.25080	−	4.54147i	−0.240238	−	0.174543i	−0.701389	+	0.712778i	$0.747436\pi$
$678$	1.90980	+	5.87775i	0.0733453	+	0.225734i
$679$	−5.84746	−	17.9966i	−0.224405	−	0.690647i
$680$	7.77021	+	14.5376i	0.297974	+	0.557492i
$681$	−29.5099	+	90.8220i	−1.13082	+	3.48031i
$682$	0.837892			0.0320845
$683$	−1.17925	+	3.62935i	−0.0451226	+	0.138873i	−0.971080	−	0.238756i	$-0.923260\pi$
$683$	−1.17925	+	3.62935i	−0.0451226	+	0.138873i	0.925957	+	0.377629i	$0.123260\pi$
$684$	−6.27043	+	4.55573i	−0.239756	+	0.174193i
$685$	12.4998	−	2.23197i	0.477593	−	0.0852791i
$686$	−10.0971	−	7.33595i	−0.385508	−	0.280088i
$687$	54.4411	−	39.5538i	2.07706	−	1.50907i
$688$	3.86472	−	2.80788i	0.147341	−	0.107050i
$689$	4.72739	+	3.43465i	0.180099	+	0.130850i
$690$	−46.1702	+	8.24416i	−1.75767	+	0.313850i
$691$	6.86196	−	4.98550i	0.261041	−	0.189658i	−0.449565	−	0.893248i	$-0.648421\pi$
$691$	6.86196	−	4.98550i	0.261041	−	0.189658i	0.710606	+	0.703590i	$0.248421\pi$
$692$	0.951086	−	2.92714i	0.0361549	−	0.111273i
$693$	−104.340			−3.96356
$694$	0.856584	−	2.63629i	0.0325155	−	0.100072i
$695$	17.6091	+	32.9456i	0.667951	+	1.24970i
$696$	−4.25848	−	13.1062i	−0.161417	−	0.496791i
$697$	0.996040	+	3.06550i	0.0377277	+	0.116114i
$698$	−21.0660	−	15.3054i	−0.797361	−	0.579317i
$699$	35.9217			1.35868
$700$	8.81384	−	13.1899i	0.333132	−	0.498531i
$701$	−12.2625			−0.463149			−0.231575	−	0.972817i	$-0.574388\pi$
$701$	−12.2625			−0.463149			−0.231575	+	0.972817i	$0.574388\pi$
$702$	11.5627	+	8.40080i	0.436407	+	0.317068i
$703$	−3.61305	−	11.1198i	−0.136269	−	0.419392i
$704$	1.31117	+	4.03538i	0.0494167	+	0.152089i
$705$	22.1582	−	3.95658i	0.834526	−	0.149013i
$706$	−1.16699	+	3.59164i	−0.0439204	+	0.135173i
$707$	−45.1166			−1.69678
$708$	2.73323	−	8.41200i	0.102721	−	0.316142i
$709$	13.3572	−	9.70455i	0.501639	−	0.364462i	−0.308004	−	0.951385i	$-0.599661\pi$
$709$	13.3572	−	9.70455i	0.501639	−	0.364462i	0.809643	+	0.586923i	$0.199661\pi$
$710$	18.7877	−	19.5397i	0.705090	−	0.733313i
$711$	83.1239	+	60.3930i	3.11739	+	2.26492i
$712$	3.41386	−	2.48032i	0.127940	−	0.0929538i
$713$	−1.02198	+	0.742511i	−0.0382734	+	0.0278073i
$714$	−62.0418	−	45.0760i	−2.32186	−	1.68693i
$715$	−7.83266	−	3.79927i	−0.292925	−	0.142085i
$716$	−4.51668	+	3.28156i	−0.168796	+	0.122638i
$717$	0.0976692	−	0.300595i	0.00364752	−	0.0112259i
$718$	−3.05181			−0.113893
$719$	−4.79846	+	14.7681i	−0.178952	+	0.550759i	−0.999792	−	0.0204001i	$-0.993506\pi$
$719$	−4.79846	+	14.7681i	−0.178952	+	0.550759i	0.820840	+	0.571159i	$0.193506\pi$
$720$	−12.0121	+	12.4929i	−0.447666	+	0.465584i
$721$	5.80819	+	17.8758i	0.216308	+	0.665728i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	42.5455	+	30.9111i	1.58228	+	1.14960i
$724$	−18.4032			−0.683949
$725$	−11.6757	+	17.4727i	−0.433626	+	0.648921i
$726$	−22.9630			−0.852237
$727$	−39.2569	−	28.5218i	−1.45596	−	1.05781i	−0.984393	−	0.175983i	$-0.943690\pi$
$727$	−39.2569	−	28.5218i	−1.45596	−	1.05781i	−0.471564	−	0.881832i	$-0.656310\pi$
$728$	−0.899593	−	2.76866i	−0.0333411	−	0.102613i
$729$	19.2864	+	59.3574i	0.714311	+	2.19842i
$730$	−1.16053	+	8.38937i	−0.0429532	+	0.310504i
$731$	−10.8822	+	33.4920i	−0.402494	+	1.23875i
$732$	−1.77854			−0.0657369
$733$	8.25734	−	25.4135i	0.304992	−	0.938669i	−0.674688	−	0.738103i	$-0.735722\pi$
$733$	8.25734	−	25.4135i	0.304992	−	0.938669i	0.979680	−	0.200566i	$-0.0642780\pi$
$734$	−18.9968	+	13.8020i	−0.701185	+	0.509441i
$735$	−3.08054	+	22.2689i	−0.113627	+	0.821401i
$736$	−5.17525	−	3.76004i	−0.190762	−	0.138597i
$737$	37.5218	−	27.2612i	1.38213	−	1.00418i
$738$	−2.74168	+	1.99195i	−0.100923	+	0.0733246i
$739$	−28.3484	−	20.5963i	−1.04281	−	0.757647i	−0.0719788	−	0.997406i	$-0.522931\pi$
$739$	−28.3484	−	20.5963i	−1.04281	−	0.757647i	−0.970832	+	0.239760i	$0.922931\pi$
$740$	−12.3240	−	23.0574i	−0.453038	−	0.847607i
$741$	2.43391	−	1.76834i	0.0894119	−	0.0649616i
$742$	6.24384	−	19.2166i	0.229219	−	0.705462i
$743$	−17.4253			−0.639271			−0.319635	−	0.947541i	$-0.603560\pi$
$743$	−17.4253			−0.639271			−0.319635	+	0.947541i	$0.603560\pi$
$744$	−0.200083	+	0.615793i	−0.00733541	+	0.0225761i
$745$	−8.66601	−	4.20350i	−0.317498	−	0.154004i
$746$	1.45274	+	4.47109i	0.0531887	+	0.163698i
$747$	−30.2800	−	93.1924i	−1.10789	−	3.40973i
$748$	−25.3052	−	18.3853i	−0.925250	−	0.672234i
$749$	−37.9570			−1.38692
$750$	36.4816	+	3.59496i	1.33212	+	0.131269i
$751$	7.96397			0.290610			0.145305	−	0.989387i	$-0.453584\pi$
$751$	7.96397			0.290610			0.145305	+	0.989387i	$0.453584\pi$
$752$	2.48373	+	1.80454i	0.0905724	+	0.0658047i
$753$	−15.0902	−	46.4429i	−0.549918	−	1.69247i
$754$	1.19170	+	3.66766i	0.0433990	+	0.133568i
$755$	−10.7209	−	5.20022i	−0.390173	−	0.189256i
$756$	15.2718	−	47.0017i	0.555430	−	1.70944i
$757$	12.4102			0.451056			0.225528	−	0.974237i	$-0.427589\pi$
$757$	12.4102			0.451056			0.225528	+	0.974237i	$0.427589\pi$
$758$	−0.611950	+	1.88339i	−0.0222270	+	0.0684078i
$759$	71.9991	−	52.3104i	2.61340	−	1.89875i
$760$	1.05404	+	1.97205i	0.0382341	+	0.0715339i
$761$	−2.35291	−	1.70949i	−0.0852928	−	0.0619688i	0.544322	−	0.838877i	$-0.316787\pi$
$761$	−2.35291	−	1.70949i	−0.0852928	−	0.0619688i	−0.629614	+	0.776908i	$0.716787\pi$
$762$	−8.96481	+	6.51331i	−0.324761	+	0.235952i
$763$	18.4298	−	13.3900i	0.667203	−	0.484752i
$764$	12.7371	+	9.25405i	0.460812	+	0.334800i
$765$	17.5070	−	126.556i	0.632965	−	4.57564i
$766$	26.5228	−	19.2699i	0.958308	−	0.696251i
$767$	−0.764869	+	2.35402i	−0.0276178	+	0.0849989i
$768$	−3.27882			−0.118314
$769$	−0.437141	+	1.34538i	−0.0157637	+	0.0485157i	−0.958629	−	0.284659i	$-0.908120\pi$
$769$	−0.437141	+	1.34538i	−0.0157637	+	0.0485157i	0.942865	+	0.333174i	$0.108120\pi$
$770$	−4.12486	+	29.8182i	−0.148649	+	1.07457i
$771$	11.6086	+	35.7275i	0.418073	+	1.28670i
$772$	−6.69315	−	20.5994i	−0.240892	−	0.741388i
$773$	−36.6402	−	26.6206i	−1.31786	−	0.957478i	−0.999956	−	0.00935339i	$-0.997023\pi$
$773$	−36.6402	−	26.6206i	−1.31786	−	0.957478i	−0.317899	−	0.948125i	$-0.602977\pi$
$774$	−37.0254			−1.33085
$775$	0.926354	−	0.341715i	0.0332756	−	0.0122748i
$776$	5.96418			0.214101
$777$	98.4016	+	71.4929i	3.53014	+	2.56479i
$778$	0.239499	+	0.737103i	0.00858647	+	0.0264264i
$779$	0.135115	+	0.415840i	0.00484098	+	0.0148990i
$780$	4.66259	−	4.84922i	0.166948	−	0.173630i
$781$	−15.8947	+	48.9190i	−0.568759	+	1.75046i
$782$	47.1573			1.68634
$783$	−20.2306	+	62.2635i	−0.722984	+	2.22512i
$784$	−2.48067	+	1.80232i	−0.0885955	+	0.0643684i
$785$	−5.84558	−	2.83543i	−0.208638	−	0.101201i
$786$	−55.9068	−	40.6187i	−1.99413	−	1.44882i
$787$	−13.8668	+	10.0748i	−0.494297	+	0.359128i	−0.806835	−	0.590777i	$-0.798821\pi$
$787$	−13.8668	+	10.0748i	−0.494297	+	0.359128i	0.312537	+	0.949906i	$0.398821\pi$
$788$	18.5788	−	13.4983i	0.661842	−	0.480857i
$789$	−20.5720	−	14.9465i	−0.732384	−	0.532108i
$790$	20.5451	−	21.3675i	0.730963	−	0.760222i
$791$	−4.83815	+	3.51512i	−0.172025	+	0.124983i
$792$	10.1625	−	31.2769i	0.361108	−	1.11138i
$793$	0.497710			0.0176742
$794$	1.52570	−	4.69561i	0.0541449	−	0.166641i
$795$	45.9645	−	8.20743i	1.63019	−	0.291088i
$796$	−2.42548	−	7.46487i	−0.0859690	−	0.264585i
$797$	−1.30189	−	4.00680i	−0.0461152	−	0.141928i	0.925348	−	0.379120i	$-0.123773\pi$
$797$	−1.30189	−	4.00680i	−0.0461152	−	0.141928i	−0.971463	+	0.237192i	$0.923773\pi$
$798$	−8.41608	−	6.11464i	−0.297926	−	0.216456i
$799$	−22.6319			−0.800661
$800$	3.09534	+	3.92669i	0.109437	+	0.138829i
$801$	−32.7061			−1.15561
$802$	2.33010	+	1.69292i	0.0822788	+	0.0597790i
$803$	−4.96615	−	15.2843i	−0.175252	−	0.539370i
$804$	11.0751	+	34.0857i	0.390589	+	1.20211i
$805$	−21.3928	−	40.0246i	−0.753995	−	1.41068i
$806$	0.0559915	−	0.172324i	0.00197222	−	0.00606986i
$807$	−18.4174			−0.648323
$808$	4.39424	−	13.5241i	0.154589	−	0.475775i
$809$	−38.9267	+	28.2819i	−1.36859	+	0.994338i	−0.370743	+	0.928735i	$0.620897\pi$
$809$	−38.9267	+	28.2819i	−1.36859	+	0.994338i	−0.997846	+	0.0656025i	$0.979103\pi$
$810$	61.2408	−	10.9352i	2.15178	−	0.384223i
$811$	23.9922	+	17.4314i	0.842482	+	0.612099i	0.923063	−	0.384649i	$-0.125678\pi$
$811$	23.9922	+	17.4314i	0.842482	+	0.612099i	−0.0805812	+	0.996748i	$0.525678\pi$
$812$	10.7881	−	7.83804i	0.378589	−	0.275061i
$813$	−54.7478	+	39.7766i	−1.92009	+	1.39503i
$814$	40.1354	+	29.1600i	1.40674	+	1.02206i
$815$	3.79406	−	0.677468i	0.132900	−	0.0237307i
$816$	19.5547	−	14.2073i	0.684550	−	0.497355i
$817$	−1.47619	+	4.54325i	−0.0516454	+	0.158948i
$818$	−14.7607			−0.516095
$819$	−6.97245	+	21.4590i	−0.243637	+	0.749838i
$820$	0.460869	+	0.862260i	0.0160943	+	0.0301114i
$821$	8.17154	+	25.1494i	0.285189	+	0.877721i	0.986342	+	0.164710i	$0.0526689\pi$
$821$	8.17154	+	25.1494i	0.285189	+	0.877721i	−0.701153	+	0.713011i	$0.747331\pi$
$822$	−5.75352	−	17.7075i	−0.200677	−	0.617621i
$823$	−43.0602	−	31.2851i	−1.50098	−	1.09053i	−0.969987	−	0.243155i	$-0.921818\pi$
$823$	−43.0602	−	31.2851i	−1.50098	−	1.09053i	−0.530997	−	0.847374i	$-0.678182\pi$
$824$	−5.92412			−0.206376
$825$	−65.2623	+	24.0741i	−2.27214	+	0.838152i
$826$	8.55874			0.297797
$827$	26.4007	+	19.1812i	0.918042	+	0.666997i	0.943036	−	0.332691i	$-0.107957\pi$
$827$	26.4007	+	19.1812i	0.918042	+	0.666997i	−0.0249936	+	0.999688i	$0.507957\pi$
$828$	15.3213	+	47.1541i	0.532452	+	1.63872i
$829$	−3.64919	−	11.2311i	−0.126742	−	0.390071i	0.867473	−	0.497485i	$-0.165743\pi$
$829$	−3.64919	−	11.2311i	−0.126742	−	0.390071i	−0.994214	+	0.107414i	$0.965743\pi$
$830$	−27.8294	+	4.96923i	−0.965973	+	0.172484i
$831$	−1.42582	+	4.38821i	−0.0494610	+	0.152225i
$832$	0.917549			0.0318103
$833$	6.98504	−	21.4978i	0.242017	−	0.744853i
$834$	44.3154	−	32.1970i	1.53452	−	1.11489i
$835$	−13.9524	+	14.5109i	−0.482843	+	0.502170i
$836$	−3.43270	−	2.49400i	−0.118722	−	0.0862568i
$837$	2.48852	−	1.80802i	0.0860158	−	0.0624942i
$838$	24.2967	−	17.6526i	0.839314	−	0.609798i
$839$	−27.5095	−	19.9868i	−0.949734	−	0.690022i	0.00101016	−	0.999999i	$-0.499678\pi$
$839$	−27.5095	−	19.9868i	−0.949734	−	0.690022i	−0.950744	+	0.309978i	$0.899678\pi$
$840$	−20.9293	−	10.1519i	−0.722130	−	0.350273i
$841$	9.17039	−	6.66268i	0.316220	−	0.229748i
$842$	−0.755991	+	2.32670i	−0.0260532	+	0.0801835i
$843$	9.95804			0.342973
$844$	−7.34949	+	22.6194i	−0.252980	+	0.778592i
$845$	18.8428	−	19.5971i	0.648213	−	0.674160i
$846$	−7.35307	−	22.6304i	−0.252804	−	0.778050i
$847$	−6.86638	−	21.1325i	−0.235931	−	0.726122i
$848$	5.15220	+	3.74329i	0.176927	+	0.128545i
$849$	−27.6131			−0.947678
$850$	−35.4749	−	10.0062i	−1.21678	−	0.343211i
$851$	−74.7939			−2.56390
$852$	−32.1565	−	23.3631i	−1.10166	−	0.800406i
$853$	10.1762	+	31.3190i	0.348425	+	1.07234i	0.959724	+	0.280943i	$0.0906473\pi$
$853$	10.1762	+	31.3190i	0.348425	+	1.07234i	−0.611299	+	0.791400i	$0.709353\pi$
$854$	−0.531819	−	1.63677i	−0.0181985	−	0.0560091i
$855$	2.37485	−	17.1676i	0.0812181	−	0.587118i
$856$	3.69692	−	11.3779i	0.126358	−	0.388890i
$857$	−22.3723			−0.764223			−0.382112	−	0.924116i	$-0.624803\pi$
$857$	−22.3723			−0.764223			−0.382112	+	0.924116i	$0.624803\pi$
$858$	−3.94464	+	12.1403i	−0.134668	+	0.414464i
$859$	19.7033	−	14.3153i	0.672268	−	0.488431i	−0.198516	−	0.980098i	$-0.563612\pi$
$859$	19.7033	−	14.3153i	0.672268	−	0.488431i	0.870784	+	0.491666i	$0.163612\pi$
$860$	−1.46372	+	10.5811i	−0.0499124	+	0.360811i
$861$	−3.67985	−	2.67357i	−0.125409	−	0.0911149i
$862$	−29.3730	+	21.3407i	−1.00045	+	0.726868i
$863$	18.9333	−	13.7559i	0.644498	−	0.468255i	−0.216894	−	0.976195i	$-0.569593\pi$
$863$	18.9333	−	13.7559i	0.644498	−	0.468255i	0.861393	+	0.507940i	$0.169593\pi$
$864$	12.6017	+	9.15570i	0.428720	+	0.311483i
$865$	3.24411	+	6.06955i	0.110303	+	0.206371i
$866$	9.03072	−	6.56120i	0.306876	−	0.222959i
$867$	−37.8371	+	116.451i	−1.28501	+	3.95487i
$868$	−0.626535			−0.0212660
$869$	−17.3816	+	53.4949i	−0.589629	+	1.81469i
$870$	27.7252	+	13.4482i	0.939972	+	0.455938i
$871$	−3.09927	−	9.53858i	−0.105015	−	0.323202i
$872$	2.21876	+	6.82865i	0.0751367	+	0.231247i
$873$	−37.3979	−	27.1712i	−1.26573	−	0.919605i
$874$	6.39696			0.216381
$875$	7.60032	+	34.6485i	0.256938	+	1.17133i
$876$	12.4188			0.419591
$877$	34.2602	+	24.8915i	1.15688	+	0.840526i	0.989381	−	0.145346i	$-0.0464294\pi$
$877$	34.2602	+	24.8915i	1.15688	+	0.840526i	0.167504	+	0.985871i	$0.446429\pi$
$878$	−5.73756	−	17.6584i	−0.193633	−	0.595942i
$879$	16.9659	+	52.2158i	0.572247	+	1.76120i
$880$	−8.53651	−	4.14068i	−0.287766	−	0.139582i
$881$	−17.7281	+	54.5614i	−0.597274	+	1.83822i	−0.0542108	+	0.998530i	$0.517264\pi$
$881$	−17.7281	+	54.5614i	−0.597274	+	1.83822i	−0.543063	+	0.839692i	$0.682736\pi$
$882$	23.7658			0.800234
$883$	−7.64787	+	23.5377i	−0.257371	+	0.792107i	0.735982	+	0.677001i	$0.236721\pi$
$883$	−7.64787	+	23.5377i	−0.257371	+	0.792107i	−0.993353	+	0.115106i	$0.963279\pi$
$884$	−5.47219	+	3.97578i	−0.184050	+	0.133720i
$885$	9.32291	+	17.4426i	0.313386	+	0.586327i
$886$	5.64364	+	4.10034i	0.189602	+	0.137754i
$887$	−46.7983	+	34.0009i	−1.57133	+	1.14164i	−0.645467	+	0.763789i	$0.723337\pi$
$887$	−46.7983	+	34.0009i	−1.57133	+	1.14164i	−0.925866	+	0.377852i	$0.876663\pi$
$888$	−31.0147	+	22.5335i	−1.04078	+	0.756174i
$889$	−8.67476	−	6.30259i	−0.290942	−	0.211382i
$890$	−1.29296	+	9.34668i	−0.0433401	+	0.313302i
$891$	−95.5007	+	69.3854i	−3.19940	+	2.32450i
$892$	−4.54791	+	13.9970i	−0.152275	+	0.468656i
$893$	−3.07006			−0.102736
$894$	−4.36433	+	13.4320i	−0.145965	+	0.449234i
$895$	1.71064	−	12.3660i	0.0571804	−	0.413351i
$896$	−0.980431	−	3.01746i	−0.0327539	−	0.100806i
$897$	−5.94707	−	18.3032i	−0.198567	−	0.611126i
$898$	14.4008	+	10.4628i	0.480560	+	0.349148i
$899$	0.829974			0.0276812
$900$	−1.52017	−	38.7235i	−0.0506723	−	1.29078i
$901$	−46.9472			−1.56404
$902$	−1.50091	−	1.09048i	−0.0499749	−	0.0363089i
$903$	−15.3566	−	47.2628i	−0.511036	−	1.57281i
$904$	−0.582464	−	1.79264i	−0.0193725	−	0.0596224i
$905$	28.5216	−	29.6632i	0.948088	−	0.986038i
$906$	−5.39919	+	16.6170i	−0.179376	+	0.552063i
$907$	24.7413			0.821520			0.410760	−	0.911743i	$-0.365263\pi$
$907$	24.7413			0.821520			0.410760	+	0.911743i	$0.365263\pi$
$908$	9.00014	−	27.6996i	0.298680	−	0.919243i
$909$	−89.1658	+	64.7828i	−2.95744	+	2.14871i
$910$	5.85688	+	2.84091i	0.194154	+	0.0941752i
$911$	5.00319	+	3.63503i	0.165763	+	0.120434i	0.667574	−	0.744543i	$-0.267333\pi$
$911$	5.00319	+	3.63503i	0.165763	+	0.120434i	−0.501811	+	0.864977i	$0.667333\pi$
$912$	2.65262	−	1.92724i	0.0878371	−	0.0638174i
$913$	43.3980	−	31.5305i	1.43626	−	1.04351i
$914$	28.2992	+	20.5606i	0.936054	+	0.680083i
$915$	2.75642	−	2.86675i	0.0911244	−	0.0947719i
$916$	−16.6039	+	12.0634i	−0.548607	+	0.398586i
$917$	20.6636	−	63.5961i	0.682373	−	2.10013i
$918$	−114.828			−3.78989
$919$	−0.889581	+	2.73785i	−0.0293446	+	0.0903133i	−0.964656	−	0.263512i	$-0.915119\pi$
$919$	−0.889581	+	2.73785i	−0.0293446	+	0.0903133i	0.935312	+	0.353825i	$0.115119\pi$
$920$	14.0813	−	2.51437i	0.464248	−	0.0828962i
$921$	19.1500	+	58.9376i	0.631014	+	1.94206i
$922$	−4.11795	−	12.6737i	−0.135617	−	0.417387i
$923$	8.99871	+	6.53795i	0.296196	+	0.215199i
$924$	44.1398			1.45209
$925$	56.2650	+	15.8704i	1.84998	+	0.521815i
$926$	18.4791			0.607261
$927$	37.1467	+	26.9887i	1.22006	+	0.886425i
$928$	1.29878	+	3.99724i	0.0426346	+	0.131216i
$929$	−11.3464	−	34.9207i	−0.372265	−	1.14571i	−0.945306	−	0.326186i	$-0.894236\pi$
$929$	−11.3464	−	34.9207i	−0.372265	−	1.14571i	0.573041	−	0.819527i	$-0.305764\pi$
$930$	−0.682475	−	1.27687i	−0.0223792	−	0.0418702i
$931$	0.947533	−	2.91621i	0.0310541	−	0.0955748i
$932$	−10.9557			−0.358865
$933$	28.3737	−	87.3253i	0.928914	−	2.85890i
$934$	3.58242	−	2.60278i	0.117220	−	0.0851656i
$935$	68.8528	−	12.2944i	2.25173	−	0.402069i
$936$	−5.75342	−	4.18011i	−0.188056	−	0.136631i
$937$	0.728824	−	0.529521i	0.0238096	−	0.0172987i	−0.575817	−	0.817579i	$-0.695316\pi$
$937$	0.728824	−	0.529521i	0.0238096	−	0.0172987i	0.599626	+	0.800280i	$0.295316\pi$
$938$	−28.0569	+	20.3846i	−0.916092	+	0.665580i
$939$	−64.4983	−	46.8607i	−2.10482	−	1.52924i
$940$	−6.75798	+	1.20671i	−0.220421	+	0.0393584i
$941$	13.8019	−	10.0276i	0.449928	−	0.326892i	−0.339640	−	0.940556i	$-0.610305\pi$
$941$	13.8019	−	10.0276i	0.449928	−	0.326892i	0.789567	+	0.613664i	$0.210305\pi$
$942$	−2.94391	+	9.06044i	−0.0959179	+	0.295205i
$943$	2.79701			0.0910831
$944$	−0.833600	+	2.56556i	−0.0271314	+	0.0835018i
$945$	52.0914	+	97.4600i	1.69453	+	3.17037i
$946$	−6.26355	−	19.2772i	−0.203646	−	0.626757i
$947$	6.66098	+	20.5004i	0.216453	+	0.666173i	0.999047	+	0.0436411i	$0.0138958\pi$
$947$	6.66098	+	20.5004i	0.216453	+	0.666173i	−0.782595	+	0.622532i	$0.786104\pi$
$948$	−35.1645	−	25.5485i	−1.14209	−	0.829776i
$949$	−3.47528			−0.112812
$950$	−4.81223	−	1.35736i	−0.156129	−	0.0440386i
$951$	−16.4240			−0.532586
$952$	18.9220	+	13.7476i	0.613265	+	0.445563i
$953$	4.17068	+	12.8360i	0.135101	+	0.415800i	0.995606	−	0.0936436i	$-0.0298514\pi$
$953$	4.17068	+	12.8360i	0.135101	+	0.415800i	−0.860504	+	0.509443i	$0.829851\pi$
$954$	−15.2530	−	46.9441i	−0.493836	−	1.51987i
$955$	−34.6564	+	6.18825i	−1.12145	+	0.200247i
$956$	−0.0297879	+	0.0916777i	−0.000963409	+	0.00296507i
$957$	−58.4722			−1.89014
$958$	1.76177	−	5.42217i	0.0569202	−	0.175182i
$959$	14.5756	−	10.5898i	0.470670	−	0.341962i
$960$	5.08157	−	5.28498i	0.164007	−	0.170572i
$961$	25.0480	+	18.1984i	0.807999	+	0.587046i
$962$	8.67918	−	6.30579i	0.279828	−	0.203307i
$963$	−75.0161	+	54.5024i	−2.41736	+	1.75631i
$964$	−12.9758	−	9.42751i	−0.417924	−	0.303640i
$965$	43.5763	+	21.1369i	1.40277	+	0.680421i
$966$	−53.8374	+	39.1152i	−1.73219	+	1.25851i
$967$	−12.8240	+	39.4682i	−0.412392	+	1.26921i	0.502171	+	0.864768i	$0.332535\pi$
$967$	−12.8240	+	39.4682i	−0.412392	+	1.26921i	−0.914563	+	0.404444i	$0.867465\pi$
$968$	7.00343			0.225099
$969$	−7.46921	+	22.9879i	−0.239946	+	0.738477i
$970$	−9.24338	+	9.61337i	−0.296787	+	0.308667i
$971$	0.979396	+	3.01427i	0.0314303	+	0.0967325i	0.965541	−	0.260251i	$-0.0838053\pi$
$971$	0.979396	+	3.01427i	0.0314303	+	0.0967325i	−0.934111	+	0.356983i	$0.883805\pi$
$972$	−13.7482	−	42.3125i	−0.440973	−	1.35717i
$973$	42.8816	+	31.1553i	1.37472	+	0.998794i
$974$	−4.89880			−0.156968
$975$	0.590064	+	15.0308i	0.0188972	+	0.481371i
$976$	0.542434			0.0173629
$977$	−30.1388	−	21.8971i	−0.964226	−	0.700551i	−0.0100974	−	0.999949i	$-0.503214\pi$
$977$	−30.1388	−	21.8971i	−0.964226	−	0.700551i	−0.954128	+	0.299398i	$0.903214\pi$
$978$	−1.74636	−	5.37476i	−0.0558426	−	0.171866i
$979$	−5.53285	−	17.0284i	−0.176831	−	0.544228i
$980$	0.939526	−	6.79174i	0.0300121	−	0.216954i
$981$	17.1969	−	52.9266i	0.549055	−	1.68982i
$982$	−29.0895			−0.928284
$983$	−8.90811	+	27.4164i	−0.284125	+	0.874446i	0.702535	+	0.711649i	$0.252051\pi$
$983$	−8.90811	+	27.4164i	−0.284125	+	0.874446i	−0.986660	+	0.162797i	$0.947949\pi$
$984$	1.15983	−	0.842668i	0.0369741	−	0.0268633i
$985$	−7.03650	+	50.8662i	−0.224201	+	1.62073i
$986$	−25.0661	−	18.2116i	−0.798266	−	0.579974i
$987$	25.8379	−	18.7723i	0.822429	−	0.597530i
$988$	−0.742313	+	0.539322i	−0.0236161	+	0.0171581i
$989$	24.7225	+	17.9619i	0.786129	+	0.571157i
$990$	34.6637	+	64.8538i	1.10169	+	2.06119i
$991$	46.5619	−	33.8292i	1.47909	−	1.07462i	0.501237	−	0.865310i	$-0.332878\pi$
$991$	46.5619	−	33.8292i	1.47909	−	1.07462i	0.977849	−	0.209309i	$-0.0671216\pi$
$992$	0.0610229	−	0.187809i	0.00193748	−	0.00596295i
$993$	79.2535			2.51503
$994$	11.8853	−	36.5792i	0.376979	−	1.16022i
$995$	15.7913	+	7.65966i	0.500619	+	0.242828i
$996$	12.8096	+	39.4238i	0.405887	+	1.24919i
$997$	7.17518	+	22.0829i	0.227240	+	0.699374i	0.998056	+	0.0623161i	$0.0198487\pi$
$997$	7.17518	+	22.0829i	0.227240	+	0.699374i	−0.770816	+	0.637058i	$0.780151\pi$
$998$	−0.707727	−	0.514194i	−0.0224027	−	0.0162765i
$999$	182.123			5.76212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.b.191.1	✓	40
25.11	even	5	inner	950.2.h.b.761.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.b.191.1	✓	40	1.1	even	1	trivial
950.2.h.b.761.1	yes	40	25.11	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.01321 - 3.11835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.01188 - 0.975874i) q^{5} +(-1.01321 + 3.11835i) q^{6} -3.17274 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.27043 + 4.55573i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.01321 - 3.11835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.01188 - 0.975874i) q^{5} +(-1.01321 + 3.11835i) q^{6} -3.17274 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.27043 + 4.55573i) q^{9} +(1.05404 + 1.97205i) q^{10} +(-3.43270 - 2.49400i) q^{11} +(2.65262 - 1.92724i) q^{12} +(-0.742313 + 0.539322i) q^{13} +(2.56680 + 1.86489i) q^{14} +(-1.00465 + 7.26251i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.27802 - 7.01102i) q^{17} +7.75067 q^{18} +(0.309017 - 0.951057i) q^{19} +(0.306406 - 2.21498i) q^{20} +(3.21466 + 9.89370i) q^{21} +(1.31117 + 4.03538i) q^{22} +(-5.17525 - 3.76004i) q^{23} -3.27882 q^{24} +(3.09534 + 3.92669i) q^{25} +0.917549 q^{26} +(12.6017 + 9.15570i) q^{27} +(-0.980431 - 3.01746i) q^{28} +(1.29878 + 3.99724i) q^{29} +(5.08157 - 5.28498i) q^{30} +(0.0610229 - 0.187809i) q^{31} +1.00000 q^{32} +(-4.29910 + 13.2313i) q^{33} +(-5.96393 + 4.33305i) q^{34} +(6.38318 + 3.09619i) q^{35} +(-6.27043 - 4.55573i) q^{36} +(9.45910 - 6.87243i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(2.43391 + 1.76834i) q^{39} +(-1.54982 + 1.61185i) q^{40} +(-0.353735 + 0.257003i) q^{41} +(3.21466 - 9.89370i) q^{42} -4.77706 q^{43} +(1.31117 - 4.03538i) q^{44} +(17.0612 - 3.04645i) q^{45} +(1.97677 + 6.08388i) q^{46} +(-0.948701 - 2.91980i) q^{47} +(2.65262 + 1.92724i) q^{48} +3.06628 q^{49} +(-0.196134 - 4.99615i) q^{50} -24.1709 q^{51} +(-0.742313 - 0.539322i) q^{52} +(-1.96796 - 6.05677i) q^{53} +(-4.81344 - 14.8142i) q^{54} +(4.47235 + 8.36751i) q^{55} +(-0.980431 + 3.01746i) q^{56} -3.27882 q^{57} +(1.29878 - 3.99724i) q^{58} +(2.18239 - 1.58560i) q^{59} +(-7.21751 + 1.28876i) q^{60} +(-0.438838 - 0.318835i) q^{61} +(-0.159760 + 0.116072i) q^{62} +(19.8944 - 14.4542i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.01976 - 0.360648i) q^{65} +(11.2552 - 8.17738i) q^{66} +(-3.37777 + 10.3957i) q^{67} +7.37182 q^{68} +(-6.48148 + 19.9479i) q^{69} +(-3.34420 - 6.25681i) q^{70} +(-3.74607 - 11.5292i) q^{71} +(2.39509 + 7.37133i) q^{72} +(3.06421 + 2.22628i) q^{73} -11.6921 q^{74} +(9.10853 - 13.6309i) q^{75} +1.00000 q^{76} +(10.8911 + 7.91281i) q^{77} +(-0.929671 - 2.86123i) q^{78} +(-4.09648 - 12.6077i) q^{79} +(2.20125 - 0.393056i) q^{80} +(8.59714 - 26.4593i) q^{81} +0.437240 q^{82} +(-3.90676 + 12.0238i) q^{83} +(-8.41608 + 6.11464i) q^{84} +(-11.4250 + 11.8823i) q^{85} +(3.86472 + 2.80788i) q^{86} +(11.1488 - 8.10010i) q^{87} +(-3.43270 + 2.49400i) q^{88} +(3.41386 + 2.48032i) q^{89} +(-15.5934 - 7.56368i) q^{90} +(2.35516 - 1.71113i) q^{91} +(1.97677 - 6.08388i) q^{92} -0.647483 q^{93} +(-0.948701 + 2.91980i) q^{94} +(-1.54982 + 1.61185i) q^{95} +(-1.01321 - 3.11835i) q^{96} +(1.84303 + 5.67227i) q^{97} +(-2.48067 - 1.80232i) q^{98} +32.8865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 5 q^{6} - 12 q^{7} - 10 q^{8} - 3 q^{9} - 6 q^{11} + 16 q^{13} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{17} + 22 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 14 q^{22} + 4 q^{23} - 10 q^{24} - 2 q^{25} - 34 q^{26} + 29 q^{27} + 8 q^{28} + 16 q^{30} + 19 q^{31} + 40 q^{32} - 16 q^{33} + 3 q^{34} - 24 q^{35} - 3 q^{36} + q^{37} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 20 q^{41} + 3 q^{42} - 48 q^{43} + 14 q^{44} + 53 q^{45} + 4 q^{46} + 29 q^{47} + 28 q^{49} + 3 q^{50} - 122 q^{51} + 16 q^{52} - 5 q^{53} - 6 q^{54} + 56 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{59} - 19 q^{60} + 42 q^{61} - 21 q^{62} + 9 q^{63} - 10 q^{64} + 35 q^{65} + 24 q^{66} - 3 q^{67} - 2 q^{68} - 9 q^{69} - 19 q^{70} + 18 q^{71} - 8 q^{72} + 8 q^{73} - 64 q^{74} + 7 q^{75} + 40 q^{76} + 35 q^{77} - 2 q^{78} + q^{79} + 59 q^{81} - 30 q^{82} + 11 q^{83} - 7 q^{84} - 125 q^{85} + 32 q^{86} - 31 q^{87} - 6 q^{88} - 34 q^{89} - 7 q^{90} + 10 q^{91} + 4 q^{92} + 24 q^{93} + 29 q^{94} + 5 q^{95} + 5 q^{96} + 90 q^{97} - 12 q^{98} + 10 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 5 * q^6 - 12 * q^7 - 10 * q^8 - 3 * q^9 - 6 * q^11 + 16 * q^13 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^17 + 22 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 14 * q^22 + 4 * q^23 - 10 * q^24 - 2 * q^25 - 34 * q^26 + 29 * q^27 + 8 * q^28 + 16 * q^30 + 19 * q^31 + 40 * q^32 - 16 * q^33 + 3 * q^34 - 24 * q^35 - 3 * q^36 + q^37 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 20 * q^41 + 3 * q^42 - 48 * q^43 + 14 * q^44 + 53 * q^45 + 4 * q^46 + 29 * q^47 + 28 * q^49 + 3 * q^50 - 122 * q^51 + 16 * q^52 - 5 * q^53 - 6 * q^54 + 56 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^59 - 19 * q^60 + 42 * q^61 - 21 * q^62 + 9 * q^63 - 10 * q^64 + 35 * q^65 + 24 * q^66 - 3 * q^67 - 2 * q^68 - 9 * q^69 - 19 * q^70 + 18 * q^71 - 8 * q^72 + 8 * q^73 - 64 * q^74 + 7 * q^75 + 40 * q^76 + 35 * q^77 - 2 * q^78 + q^79 + 59 * q^81 - 30 * q^82 + 11 * q^83 - 7 * q^84 - 125 * q^85 + 32 * q^86 - 31 * q^87 - 6 * q^88 - 34 * q^89 - 7 * q^90 + 10 * q^91 + 4 * q^92 + 24 * q^93 + 29 * q^94 + 5 * q^95 + 5 * q^96 + 90 * q^97 - 12 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more