LMFDB - Embedded newform 418.2.f.h.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + \cdots + 1936 $ x^20 - x^19 + 11x^18 - 3x^17 + 103x^16 + 50x^15 + 1002x^14 + 1120x^13 + 7288x^12 + 5704x^11 + 24392x^10 + 10376x^9 + 48880x^8 + 21224x^7 + 77528x^6 + 44616x^5 + 147848x^4 + 67728x^3 + 115472x^2 - 24464x + 1936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			115.2
Root			$-0.649220 + 1.99809i$ of defining polynomial
Character	$\chi$	$=$	418.115
Dual form			418.2.f.h.229.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-1.69968 - 1.23489i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.760196 - 2.33964i) q^{5} +(-0.649220 + 1.99809i) q^{6} +(2.50791 - 1.82211i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.436908 + 1.34467i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.69968 - 1.23489i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.760196 - 2.33964i) q^{5} +(-0.649220 + 1.99809i) q^{6} +(2.50791 - 1.82211i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.436908 + 1.34467i) q^{9} -2.46005 q^{10} +(3.02483 - 1.36030i) q^{11} +2.10092 q^{12} +(-1.22937 - 3.78361i) q^{13} +(-2.50791 - 1.82211i) q^{14} +(-4.18129 + 3.03789i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.663077 + 2.04074i) q^{17} +(1.14384 - 0.831049i) q^{18} +(0.809017 + 0.587785i) q^{19} +(0.760196 + 2.33964i) q^{20} -6.51275 q^{21} +(-2.22845 - 2.45643i) q^{22} -2.55940 q^{23} +(-0.649220 - 1.99809i) q^{24} +(-0.850949 - 0.618250i) q^{25} +(-3.21853 + 2.33840i) q^{26} +(-1.02975 + 3.16925i) q^{27} +(-0.957938 + 2.94823i) q^{28} +(-5.26156 + 3.82275i) q^{29} +(4.18129 + 3.03789i) q^{30} +(0.459307 + 1.41360i) q^{31} -1.00000 q^{32} +(-6.82106 - 1.42325i) q^{33} +2.14576 q^{34} +(-2.35657 - 7.25278i) q^{35} +(-1.14384 - 0.831049i) q^{36} +(1.41514 - 1.02816i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-2.58281 + 7.94906i) q^{39} +(1.99022 - 1.44598i) q^{40} +(-4.43769 - 3.22417i) q^{41} +(2.01255 + 6.19400i) q^{42} +4.59472 q^{43} +(-1.64757 + 2.87846i) q^{44} +3.47817 q^{45} +(0.790899 + 2.43414i) q^{46} +(2.75579 + 2.00220i) q^{47} +(-1.69968 + 1.23489i) q^{48} +(0.806443 - 2.48198i) q^{49} +(-0.325033 + 1.00035i) q^{50} +(3.64711 - 2.64978i) q^{51} +(3.21853 + 2.33840i) q^{52} +(-3.63432 - 11.1853i) q^{53} +3.33234 q^{54} +(-0.883158 - 8.11111i) q^{55} +3.09995 q^{56} +(-0.649220 - 1.99809i) q^{57} +(5.26156 + 3.82275i) q^{58} +(5.38019 - 3.90894i) q^{59} +(1.59711 - 4.91540i) q^{60} +(-1.95935 + 6.03026i) q^{61} +(1.20248 - 0.873654i) q^{62} +(3.54585 + 2.57621i) q^{63} +(0.309017 + 0.951057i) q^{64} -9.78686 q^{65} +(0.754232 + 6.92702i) q^{66} +14.1154 q^{67} +(-0.663077 - 2.04074i) q^{68} +(4.35016 + 3.16058i) q^{69} +(-6.16959 + 4.48247i) q^{70} +(-4.93486 + 15.1879i) q^{71} +(-0.436908 + 1.34467i) q^{72} +(2.56962 - 1.86694i) q^{73} +(-1.41514 - 1.02816i) q^{74} +(0.682869 + 2.10166i) q^{75} -1.00000 q^{76} +(5.10739 - 8.92308i) q^{77} +8.35814 q^{78} +(2.24244 + 6.90153i) q^{79} +(-1.99022 - 1.44598i) q^{80} +(9.09544 - 6.60822i) q^{81} +(-1.69505 + 5.21682i) q^{82} +(3.46611 - 10.6676i) q^{83} +(5.26893 - 3.82810i) q^{84} +(4.27054 + 3.10273i) q^{85} +(-1.41985 - 4.36984i) q^{86} +13.6636 q^{87} +(3.24670 + 0.677442i) q^{88} -4.63686 q^{89} +(-1.07481 - 3.30794i) q^{90} +(-9.97729 - 7.24893i) q^{91} +(2.07060 - 1.50438i) q^{92} +(0.964967 - 2.96986i) q^{93} +(1.05262 - 3.23963i) q^{94} +(1.99022 - 1.44598i) q^{95} +(1.69968 + 1.23489i) q^{96} +(-1.69057 - 5.20305i) q^{97} -2.60971 q^{98} +(3.15072 + 3.47305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−1.69968	−	1.23489i	−0.981311	−	0.712964i	−0.0233095	−	0.999728i	$-0.507420\pi$
$3$	−1.69968	−	1.23489i	−0.981311	−	0.712964i	−0.958001	+	0.286764i	$0.907420\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.760196	−	2.33964i	0.339970	−	1.04632i	−0.624252	−	0.781223i	$-0.714596\pi$
$5$	0.760196	−	2.33964i	0.339970	−	1.04632i	0.964222	−	0.265097i	$-0.0854040\pi$
$6$	−0.649220	+	1.99809i	−0.265043	+	0.815718i
$7$	2.50791	−	1.82211i	0.947903	−	0.688691i	−0.00240735	−	0.999997i	$-0.500766\pi$
$7$	2.50791	−	1.82211i	0.947903	−	0.688691i	0.950310	+	0.311306i	$0.100766\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.436908	+	1.34467i	0.145636	+	0.448222i
$10$	−2.46005			−0.777935
$11$	3.02483	−	1.36030i	0.912020	−	0.410146i
$11$	3.02483	−	1.36030i	0.912020	−	0.410146i
$12$	2.10092			0.606483
$13$	−1.22937	−	3.78361i	−0.340966	−	1.04938i	−0.963708	−	0.266958i	$-0.913982\pi$
$13$	−1.22937	−	3.78361i	−0.340966	−	1.04938i	0.622743	−	0.782427i	$-0.286018\pi$
$14$	−2.50791	−	1.82211i	−0.670268	−	0.486978i
$15$	−4.18129	+	3.03789i	−1.07960	+	0.784379i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.663077	+	2.04074i	−0.160820	+	0.494953i	−0.998704	−	0.0508954i	$-0.983792\pi$
$17$	−0.663077	+	2.04074i	−0.160820	+	0.494953i	0.837884	+	0.545848i	$0.183792\pi$
$18$	1.14384	−	0.831049i	0.269606	−	0.195880i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	0.760196	+	2.33964i	0.169985	+	0.523160i
$21$	−6.51275			−1.42120
$22$	−2.22845	−	2.45643i	−0.475106	−	0.523712i
$23$	−2.55940			−0.533672			−0.266836	−	0.963742i	$-0.585978\pi$
$23$	−2.55940			−0.533672			−0.266836	+	0.963742i	$0.585978\pi$
$24$	−0.649220	−	1.99809i	−0.132521	−	0.407859i
$25$	−0.850949	−	0.618250i	−0.170190	−	0.123650i
$26$	−3.21853	+	2.33840i	−0.631206	+	0.458598i
$27$	−1.02975	+	3.16925i	−0.198176	+	0.609922i
$28$	−0.957938	+	2.94823i	−0.181033	+	0.557163i
$29$	−5.26156	+	3.82275i	−0.977048	+	0.709867i	−0.957047	−	0.289933i	$-0.906367\pi$
$29$	−5.26156	+	3.82275i	−0.977048	+	0.709867i	−0.0200009	+	0.999800i	$0.506367\pi$
$30$	4.18129	+	3.03789i	0.763396	+	0.554640i
$31$	0.459307	+	1.41360i	0.0824940	+	0.253890i	0.983793	−	0.179307i	$-0.0573854\pi$
$31$	0.459307	+	1.41360i	0.0824940	+	0.253890i	−0.901299	+	0.433197i	$0.857385\pi$
$32$	−1.00000			−0.176777
$33$	−6.82106	−	1.42325i	−1.18739	−	0.247756i
$34$	2.14576			0.367995
$35$	−2.35657	−	7.25278i	−0.398333	−	1.22594i
$36$	−1.14384	−	0.831049i	−0.190640	−	0.138508i
$37$	1.41514	−	1.02816i	0.232648	−	0.169029i	−0.465354	−	0.885125i	$-0.654073\pi$
$37$	1.41514	−	1.02816i	0.232648	−	0.169029i	0.698002	+	0.716096i	$0.254073\pi$
$38$	0.309017	−	0.951057i	0.0501292	−	0.154282i
$39$	−2.58281	+	7.94906i	−0.413580	+	1.27287i
$40$	1.99022	−	1.44598i	0.314681	−	0.228629i
$41$	−4.43769	−	3.22417i	−0.693051	−	0.503531i	0.184610	−	0.982812i	$-0.440898\pi$
$41$	−4.43769	−	3.22417i	−0.693051	−	0.503531i	−0.877662	+	0.479281i	$0.840898\pi$
$42$	2.01255	+	6.19400i	0.310543	+	0.955754i
$43$	4.59472			0.700689			0.350344	−	0.936621i	$-0.386065\pi$
$43$	4.59472			0.700689			0.350344	+	0.936621i	$0.386065\pi$
$44$	−1.64757	+	2.87846i	−0.248381	+	0.433944i
$45$	3.47817			0.518495
$46$	0.790899	+	2.43414i	0.116612	+	0.358894i
$47$	2.75579	+	2.00220i	0.401973	+	0.292051i	0.770344	−	0.637628i	$-0.220084\pi$
$47$	2.75579	+	2.00220i	0.401973	+	0.292051i	−0.368371	+	0.929679i	$0.620084\pi$
$48$	−1.69968	+	1.23489i	−0.245328	+	0.178241i
$49$	0.806443	−	2.48198i	0.115206	−	0.354568i
$50$	−0.325033	+	1.00035i	−0.0459667	+	0.141471i
$51$	3.64711	−	2.64978i	0.510698	−	0.371044i
$52$	3.21853	+	2.33840i	0.446330	+	0.324278i
$53$	−3.63432	−	11.1853i	−0.499212	−	1.53642i	−0.810288	−	0.586032i	$-0.800689\pi$
$53$	−3.63432	−	11.1853i	−0.499212	−	1.53642i	0.311076	−	0.950385i	$-0.399311\pi$
$54$	3.33234			0.453475
$55$	−0.883158	−	8.11111i	−0.119085	−	1.09370i
$56$	3.09995			0.414249
$57$	−0.649220	−	1.99809i	−0.0859913	−	0.264654i
$58$	5.26156	+	3.82275i	0.690877	+	0.501952i
$59$	5.38019	−	3.90894i	0.700441	−	0.508900i	−0.179635	−	0.983733i	$-0.557492\pi$
$59$	5.38019	−	3.90894i	0.700441	−	0.508900i	0.880076	+	0.474833i	$0.157492\pi$
$60$	1.59711	−	4.91540i	0.206186	−	0.634576i
$61$	−1.95935	+	6.03026i	−0.250869	+	0.772096i	0.743746	+	0.668462i	$0.233047\pi$
$61$	−1.95935	+	6.03026i	−0.250869	+	0.772096i	−0.994616	+	0.103634i	$0.966953\pi$
$62$	1.20248	−	0.873654i	0.152715	−	0.110954i
$63$	3.54585	+	2.57621i	0.446735	+	0.324572i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−9.78686			−1.21391
$66$	0.754232	+	6.92702i	0.0928395	+	0.852658i
$67$	14.1154			1.72447			0.862236	−	0.506506i	$-0.169063\pi$
$67$	14.1154			1.72447			0.862236	+	0.506506i	$0.169063\pi$
$68$	−0.663077	−	2.04074i	−0.0804099	−	0.247476i
$69$	4.35016	+	3.16058i	0.523698	+	0.380489i
$70$	−6.16959	+	4.48247i	−0.737407	+	0.535757i
$71$	−4.93486	+	15.1879i	−0.585661	+	1.80248i	0.0109410	+	0.999940i	$0.496517\pi$
$71$	−4.93486	+	15.1879i	−0.585661	+	1.80248i	−0.596602	+	0.802538i	$0.703483\pi$
$72$	−0.436908	+	1.34467i	−0.0514901	+	0.158470i
$73$	2.56962	−	1.86694i	0.300752	−	0.218509i	−0.427166	−	0.904173i	$-0.640488\pi$
$73$	2.56962	−	1.86694i	0.300752	−	0.218509i	0.727918	+	0.685664i	$0.240488\pi$
$74$	−1.41514	−	1.02816i	−0.164507	−	0.119521i
$75$	0.682869	+	2.10166i	0.0788509	+	0.242678i
$76$	−1.00000			−0.114708
$77$	5.10739	−	8.92308i	0.582041	−	1.01688i
$78$	8.35814			0.946373
$79$	2.24244	+	6.90153i	0.252294	+	0.776482i	0.994351	+	0.106145i	$0.0338507\pi$
$79$	2.24244	+	6.90153i	0.252294	+	0.776482i	−0.742056	+	0.670338i	$0.766149\pi$
$80$	−1.99022	−	1.44598i	−0.222513	−	0.161665i
$81$	9.09544	−	6.60822i	1.01060	−	0.734247i
$82$	−1.69505	+	5.21682i	−0.187187	+	0.576102i
$83$	3.46611	−	10.6676i	0.380454	−	1.17092i	−0.559270	−	0.828986i	$-0.688918\pi$
$83$	3.46611	−	10.6676i	0.380454	−	1.17092i	0.939724	−	0.341933i	$-0.111082\pi$
$84$	5.26893	−	3.82810i	0.574887	−	0.417680i
$85$	4.27054	+	3.10273i	0.463205	+	0.336538i
$86$	−1.41985	−	4.36984i	−0.153106	−	0.471212i
$87$	13.6636			1.46490
$88$	3.24670	+	0.677442i	0.346100	+	0.0722155i
$89$	−4.63686			−0.491506			−0.245753	−	0.969332i	$-0.579035\pi$
$89$	−4.63686			−0.491506			−0.245753	+	0.969332i	$0.579035\pi$
$90$	−1.07481	−	3.30794i	−0.113295	−	0.348687i
$91$	−9.97729	−	7.24893i	−1.04590	−	0.759894i
$92$	2.07060	−	1.50438i	0.215875	−	0.156842i
$93$	0.964967	−	2.96986i	0.100062	−	0.307960i
$94$	1.05262	−	3.23963i	0.108569	−	0.334142i
$95$	1.99022	−	1.44598i	0.204192	−	0.148354i
$96$	1.69968	+	1.23489i	0.173473	+	0.126035i
$97$	−1.69057	−	5.20305i	−0.171652	−	0.528290i	0.827813	−	0.561004i	$-0.189585\pi$
$97$	−1.69057	−	5.20305i	−0.171652	−	0.528290i	−0.999465	+	0.0327144i	$0.989585\pi$
$98$	−2.60971			−0.263620
$99$	3.15072	+	3.47305i	0.316659	+	0.349055i
$100$	1.05183			0.105183
$101$	−1.79382	−	5.52081i	−0.178492	−	0.549341i	0.821284	−	0.570520i	$-0.193258\pi$
$101$	−1.79382	−	5.52081i	−0.178492	−	0.549341i	−0.999776	+	0.0211787i	$0.993258\pi$
$102$	−3.64711	−	2.64978i	−0.361118	−	0.262367i
$103$	7.73664	−	5.62100i	0.762313	−	0.553853i	−0.137306	−	0.990529i	$-0.543844\pi$
$103$	7.73664	−	5.62100i	0.762313	−	0.553853i	0.899619	+	0.436676i	$0.143844\pi$
$104$	1.22937	−	3.78361i	0.120550	−	0.371013i
$105$	−4.95097	+	15.2375i	−0.483165	+	1.48703i
$106$	−9.51477	+	6.91289i	−0.924156	+	0.671439i
$107$	11.7844	+	8.56187i	1.13924	+	0.827707i	0.987013	−	0.160638i	$-0.0513552\pi$
$107$	11.7844	+	8.56187i	1.13924	+	0.827707i	0.152228	+	0.988345i	$0.451355\pi$
$108$	−1.02975	−	3.16925i	−0.0990878	−	0.304961i
$109$	−3.38080			−0.323822			−0.161911	−	0.986805i	$-0.551766\pi$
$109$	−3.38080			−0.323822			−0.161911	+	0.986805i	$0.551766\pi$
$110$	−7.44122	+	3.34641i	−0.709492	+	0.319067i
$111$	−3.67496			−0.348811
$112$	−0.957938	−	2.94823i	−0.0905166	−	0.278582i
$113$	−9.19594	−	6.68124i	−0.865081	−	0.628518i	0.0641814	−	0.997938i	$-0.479556\pi$
$113$	−9.19594	−	6.68124i	−0.865081	−	0.628518i	−0.929263	+	0.369420i	$0.879556\pi$
$114$	−1.69968	+	1.23489i	−0.159190	+	0.115658i
$115$	−1.94565	+	5.98809i	−0.181433	+	0.558392i
$116$	2.00974	−	6.18534i	0.186600	−	0.574294i
$117$	4.55057	−	3.30618i	0.420700	−	0.305656i
$118$	−5.38019	−	3.90894i	−0.495287	−	0.359847i
$119$	2.05551	+	6.32620i	0.188428	+	0.579922i
$120$	−5.16836			−0.471805
$121$	7.29916	−	8.22935i	0.663560	−	0.748123i
$122$	6.34059			0.574050
$123$	3.56116	+	10.9601i	0.321099	+	0.988241i
$124$	−1.20248	−	0.873654i	−0.107986	−	0.0784564i
$125$	7.85772	−	5.70897i	0.702816	−	0.510626i
$126$	1.35439	−	4.16840i	0.120659	−	0.371350i
$127$	−4.12433	+	12.6934i	−0.365975	+	1.12636i	0.583393	+	0.812190i	$0.301725\pi$
$127$	−4.12433	+	12.6934i	−0.365975	+	1.12636i	−0.949368	+	0.314166i	$0.898275\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−7.80956	−	5.67398i	−0.687593	−	0.499566i
$130$	3.02431	+	9.30786i	0.265249	+	0.816353i
$131$	−4.58757			−0.400818			−0.200409	−	0.979712i	$-0.564227\pi$
$131$	−4.58757			−0.400818			−0.200409	+	0.979712i	$0.564227\pi$
$132$	6.35492	−	2.85788i	0.553125	−	0.248747i
$133$	3.09995			0.268800
$134$	−4.36190	−	13.4246i	−0.376811	−	1.15971i
$135$	6.63210	+	4.81850i	0.570800	+	0.414710i
$136$	−1.73596	+	1.26125i	−0.148857	+	0.108151i
$137$	−4.21408	+	12.9696i	−0.360033	+	1.10807i	0.593000	+	0.805203i	$0.297943\pi$
$137$	−4.21408	+	12.9696i	−0.360033	+	1.10807i	−0.953033	+	0.302866i	$0.902057\pi$
$138$	1.66161	−	5.11392i	0.141446	−	0.435326i
$139$	4.68407	−	3.40317i	0.397297	−	0.288653i	−0.371142	−	0.928576i	$-0.621034\pi$
$139$	4.68407	−	3.40317i	0.397297	−	0.288653i	0.768439	+	0.639923i	$0.221034\pi$
$140$	6.16959	+	4.48247i	0.521425	+	0.378838i
$141$	−2.21147	−	6.80619i	−0.186239	−	0.573185i
$142$	15.9696			1.34014
$143$	−8.86548	−	9.77245i	−0.741369	−	0.817213i
$144$	1.41386			0.117822
$145$	4.94405	+	15.2162i	0.410581	+	1.26364i
$146$	−2.56962	−	1.86694i	−0.212663	−	0.154509i
$147$	−4.43566	+	3.22270i	−0.365847	+	0.265804i
$148$	−0.540537	+	1.66360i	−0.0444318	+	0.136747i
$149$	−3.19841	+	9.84368i	−0.262024	+	0.806426i	0.730340	+	0.683083i	$0.239361\pi$
$149$	−3.19841	+	9.84368i	−0.262024	+	0.806426i	−0.992364	+	0.123343i	$0.960639\pi$
$150$	1.78777	−	1.29889i	0.145971	−	0.106054i
$151$	9.84824	+	7.15517i	0.801438	+	0.582279i	0.911336	−	0.411664i	$-0.135052\pi$
$151$	9.84824	+	7.15517i	0.801438	+	0.582279i	−0.109897	+	0.993943i	$0.535052\pi$
$152$	0.309017	+	0.951057i	0.0250646	+	0.0771409i
$153$	−3.03382			−0.245270
$154$	−10.0646	−	2.10004i	−0.811030	−	0.169226i
$155$	3.65649			0.293696
$156$	−2.58281	−	7.94906i	−0.206790	−	0.636434i
$157$	−3.01269	−	2.18885i	−0.240439	−	0.174689i	0.461040	−	0.887379i	$-0.347476\pi$
$157$	−3.01269	−	2.18885i	−0.240439	−	0.174689i	−0.701479	+	0.712690i	$0.747476\pi$
$158$	5.87079	−	4.26538i	0.467055	−	0.339335i
$159$	−7.63541	+	23.4994i	−0.605528	+	1.86362i
$160$	−0.760196	+	2.33964i	−0.0600988	+	0.184965i
$161$	−6.41876	+	4.66350i	−0.505869	+	0.367535i
$162$	−9.09544	−	6.60822i	−0.714605	−	0.519191i
$163$	−6.14697	−	18.9184i	−0.481468	−	1.48181i	−0.837032	−	0.547155i	$-0.815711\pi$
$163$	−6.14697	−	18.9184i	−0.481468	−	1.48181i	0.355563	−	0.934652i	$-0.384289\pi$
$164$	5.48529			0.428329
$165$	−8.51524	+	14.8769i	−0.662911	+	1.15817i
$166$	−11.2166			−0.870573
$167$	−6.79426	−	20.9106i	−0.525755	−	1.61811i	−0.762817	−	0.646614i	$-0.776184\pi$
$167$	−6.79426	−	20.9106i	−0.525755	−	1.61811i	0.237062	−	0.971495i	$-0.423816\pi$
$168$	−5.26893	−	3.82810i	−0.406507	−	0.295344i
$169$	−2.28713	+	1.66170i	−0.175933	+	0.127823i
$170$	1.63120	−	5.02032i	0.125107	−	0.385041i
$171$	−0.436908	+	1.34467i	−0.0334112	+	0.102829i
$172$	−3.71721	+	2.70071i	−0.283434	+	0.205927i
$173$	20.6153	+	14.9779i	1.56735	+	1.13875i	0.929641	+	0.368467i	$0.120117\pi$
$173$	20.6153	+	14.9779i	1.56735	+	1.13875i	0.637708	+	0.770278i	$0.279883\pi$
$174$	−4.22230	−	12.9949i	−0.320092	−	0.985141i
$175$	−3.26062			−0.246480
$176$	−0.359001	−	3.29714i	−0.0270607	−	0.248531i
$177$	−13.9717			−1.05018
$178$	1.43287	+	4.40992i	0.107398	+	0.330537i
$179$	−18.4362	−	13.3947i	−1.37799	−	1.00117i	−0.997065	−	0.0765594i	$-0.975607\pi$
$179$	−18.4362	−	13.3947i	−1.37799	−	1.00117i	−0.380922	−	0.924607i	$-0.624393\pi$
$180$	−2.81390	+	2.04442i	−0.209736	+	0.152382i
$181$	−0.477575	+	1.46983i	−0.0354979	+	0.109251i	−0.967235	−	0.253881i	$-0.918293\pi$
$181$	−0.477575	+	1.46983i	−0.0354979	+	0.109251i	0.931738	+	0.363132i	$0.118293\pi$
$182$	−3.81099	+	11.7290i	−0.282489	+	0.869412i
$183$	10.7770	−	7.82993i	0.796657	−	0.578805i
$184$	−2.07060	−	1.50438i	−0.152647	−	0.110904i
$185$	−1.32975	−	4.09254i	−0.0977648	−	0.300889i
$186$	−3.12270			−0.228967
$187$	0.770330	+	7.07488i	0.0563321	+	0.517366i
$188$	−3.40634			−0.248433
$189$	3.19218	+	9.82452i	0.232197	+	0.714628i
$190$	−1.99022	−	1.44598i	−0.144386	−	0.104902i
$191$	−5.77965	+	4.19916i	−0.418201	+	0.303841i	−0.776914	−	0.629607i	$-0.783216\pi$
$191$	−5.77965	+	4.19916i	−0.418201	+	0.303841i	0.358713	+	0.933448i	$0.383216\pi$
$192$	0.649220	−	1.99809i	0.0468534	−	0.144200i
$193$	−3.73849	+	11.5059i	−0.269102	+	0.828211i	0.721618	+	0.692292i	$0.243399\pi$
$193$	−3.73849	+	11.5059i	−0.269102	+	0.828211i	−0.990720	+	0.135920i	$0.956601\pi$
$194$	−4.42598	+	3.21566i	−0.317767	+	0.230871i
$195$	16.6345	+	12.0857i	1.19122	+	0.865474i
$196$	0.806443	+	2.48198i	0.0576031	+	0.177284i
$197$	18.2516			1.30037			0.650186	−	0.759775i	$-0.274691\pi$
$197$	18.2516			1.30037			0.650186	+	0.759775i	$0.274691\pi$
$198$	2.32944	−	4.06975i	0.165546	−	0.289224i
$199$	23.9705			1.69923			0.849613	−	0.527406i	$-0.176835\pi$
$199$	23.9705			1.69923			0.849613	+	0.527406i	$0.176835\pi$
$200$	−0.325033	−	1.00035i	−0.0229833	−	0.0707354i
$201$	−23.9917	−	17.4310i	−1.69224	−	1.22949i
$202$	−4.69628	+	3.41205i	−0.330429	+	0.240071i
$203$	−6.23009	+	19.1743i	−0.437267	+	1.34577i
$204$	−1.39307	+	4.28744i	−0.0975346	+	0.300181i
$205$	−10.9169	+	7.93162i	−0.762472	+	0.553968i
$206$	−7.73664	−	5.62100i	−0.539037	−	0.391633i
$207$	−1.11822	−	3.44154i	−0.0777219	−	0.239203i
$208$	−3.97832			−0.275847
$209$	3.24670	+	0.677442i	0.224579	+	0.0468596i
$210$	16.0217			1.10560
$211$	6.41106	+	19.7312i	0.441356	+	1.35835i	0.886431	+	0.462860i	$0.153177\pi$
$211$	6.41106	+	19.7312i	0.441356	+	1.35835i	−0.445076	+	0.895493i	$0.646823\pi$
$212$	9.51477	+	6.91289i	0.653477	+	0.474779i
$213$	27.1431	−	19.7206i	1.85982	−	1.35124i
$214$	4.50124	−	13.8534i	0.307699	−	0.946999i
$215$	3.49289	−	10.7500i	0.238213	−	0.733145i
$216$	−2.69592	+	1.95870i	−0.183434	+	0.133273i
$217$	3.72763	+	2.70828i	0.253048	+	0.183850i
$218$	1.04472	+	3.21533i	0.0707577	+	0.217770i
$219$	−6.67300			−0.450920
$220$	5.48208	+	6.04292i	0.369602	+	0.407414i
$221$	8.53654			0.574230
$222$	1.13562	+	3.49509i	0.0762181	+	0.234575i
$223$	−22.9636	−	16.6840i	−1.53775	−	1.11724i	−0.951725	−	0.306953i	$-0.900691\pi$
$223$	−22.9636	−	16.6840i	−1.53775	−	1.11724i	−0.586028	−	0.810290i	$-0.699309\pi$
$224$	−2.50791	+	1.82211i	−0.167567	+	0.121745i
$225$	0.459553	−	1.41436i	0.0306369	−	0.0942906i
$226$	−3.51254	+	10.8105i	−0.233650	+	0.719102i
$227$	6.88177	−	4.99990i	0.456759	−	0.331855i	−0.335499	−	0.942040i	$-0.608905\pi$
$227$	6.88177	−	4.99990i	0.456759	−	0.331855i	0.792259	+	0.610185i	$0.208905\pi$
$228$	1.69968	+	1.23489i	0.112564	+	0.0817826i
$229$	−0.527586	−	1.62374i	−0.0348638	−	0.107300i	0.932110	−	0.362175i	$-0.117966\pi$
$229$	−0.527586	−	1.62374i	−0.0348638	−	0.107300i	−0.966974	+	0.254875i	$0.917966\pi$
$230$	6.29625			0.415162
$231$	−19.6999	+	8.85931i	−1.29616	+	0.582900i
$232$	−6.50365			−0.426986
$233$	3.07667	+	9.46902i	0.201559	+	0.620336i	0.999837	+	0.0180465i	$0.00574470\pi$
$233$	3.07667	+	9.46902i	0.201559	+	0.620336i	−0.798278	+	0.602289i	$0.794255\pi$
$234$	−4.55057	−	3.30618i	−0.297480	−	0.216132i
$235$	6.77937	−	4.92550i	0.442237	−	0.321304i
$236$	−2.05505	+	6.32479i	−0.133772	+	0.411709i
$237$	4.71119	−	14.4996i	0.306025	−	0.941847i
$238$	5.38139	−	3.90981i	0.348824	−	0.253435i
$239$	−13.1696	−	9.56830i	−0.851873	−	0.618922i	0.0737888	−	0.997274i	$-0.476491\pi$
$239$	−13.1696	−	9.56830i	−0.851873	−	0.618922i	−0.925662	+	0.378352i	$0.876491\pi$
$240$	1.59711	+	4.91540i	0.103093	+	0.317288i
$241$	−5.95144			−0.383366			−0.191683	−	0.981457i	$-0.561395\pi$
$241$	−5.95144			−0.383366			−0.191683	+	0.981457i	$0.561395\pi$
$242$	−10.0821	−	4.39890i	−0.648105	−	0.282772i
$243$	−13.6227			−0.873899
$244$	−1.95935	−	6.03026i	−0.125435	−	0.386048i
$245$	−5.19389	−	3.77358i	−0.331825	−	0.241085i
$246$	9.32324	−	6.77373i	0.594428	−	0.431877i
$247$	1.22937	−	3.78361i	0.0782229	−	0.240745i
$248$	−0.459307	+	1.41360i	−0.0291660	+	0.0897638i
$249$	−19.0645	+	13.8512i	−1.20817	+	0.877784i
$250$	−7.85772	−	5.70897i	−0.496966	−	0.361067i
$251$	−6.50772	−	20.0287i	−0.410764	−	1.26420i	−0.915986	−	0.401211i	$-0.868589\pi$
$251$	−6.50772	−	20.0287i	−0.410764	−	1.26420i	0.505222	−	0.862989i	$-0.331411\pi$
$252$	−4.38291			−0.276098
$253$	−7.74175	+	3.48156i	−0.486719	+	0.218884i
$254$	13.3466			0.837441
$255$	−3.42702	−	10.5473i	−0.214609	−	0.660497i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.03343	+	0.750828i	−0.0644633	+	0.0468353i	−0.619550	−	0.784957i	$-0.712685\pi$
$257$	−1.03343	+	0.750828i	−0.0644633	+	0.0468353i	0.555087	+	0.831792i	$0.312685\pi$
$258$	−2.98299	+	9.18068i	−0.185713	+	0.571564i
$259$	1.67564	−	5.15708i	0.104119	−	0.320446i
$260$	7.91773	−	5.75257i	0.491037	−	0.356759i
$261$	−7.43914	−	5.40485i	−0.460471	−	0.334552i
$262$	1.41764	+	4.36304i	0.0875820	+	0.269550i
$263$	8.85896			0.546267			0.273134	−	0.961976i	$-0.411940\pi$
$263$	8.85896			0.546267			0.273134	+	0.961976i	$0.411940\pi$
$264$	−4.68179	−	5.16075i	−0.288144	−	0.317622i
$265$	−28.9324			−1.77730
$266$	−0.957938	−	2.94823i	−0.0587349	−	0.180768i
$267$	7.88118	+	5.72601i	0.482320	+	0.350426i
$268$	−11.4196	+	8.29684i	−0.697564	+	0.506810i
$269$	8.04167	−	24.7497i	0.490309	−	1.50902i	−0.333832	−	0.942633i	$-0.608342\pi$
$269$	8.04167	−	24.7497i	0.490309	−	1.50902i	0.824141	−	0.566384i	$-0.191658\pi$
$270$	2.53324	−	7.79650i	0.154168	−	0.474480i
$271$	−13.8201	+	10.0409i	−0.839514	+	0.609942i	−0.922235	−	0.386630i	$-0.873639\pi$
$271$	−13.8201	+	10.0409i	−0.839514	+	0.609942i	0.0827211	+	0.996573i	$0.473639\pi$
$272$	1.73596	+	1.26125i	0.105258	+	0.0764744i
$273$	8.00658	+	24.6417i	0.484580	+	1.49138i
$274$	13.6371			0.823845
$275$	−3.41498	−	0.712554i	−0.205931	−	0.0429686i
$276$	−5.37710			−0.323663
$277$	2.62481	+	8.07834i	0.157710	+	0.485380i	0.998425	−	0.0560965i	$-0.0178655\pi$
$277$	2.62481	+	8.07834i	0.157710	+	0.485380i	−0.840716	+	0.541477i	$0.817865\pi$
$278$	−4.68407	−	3.40317i	−0.280932	−	0.204109i
$279$	−1.70015	+	1.23523i	−0.101785	+	0.0739512i
$280$	2.35657	−	7.25278i	0.140832	−	0.433437i
$281$	9.09244	−	27.9837i	0.542410	−	1.66937i	−0.184660	−	0.982802i	$-0.559119\pi$
$281$	9.09244	−	27.9837i	0.542410	−	1.66937i	0.727070	−	0.686563i	$-0.240881\pi$
$282$	−5.78969	+	4.20646i	−0.344771	+	0.250491i
$283$	13.8010	+	10.0270i	0.820382	+	0.596043i	0.916822	−	0.399296i	$-0.130745\pi$
$283$	13.8010	+	10.0270i	0.820382	+	0.596043i	−0.0964396	+	0.995339i	$0.530745\pi$
$284$	−4.93486	−	15.1879i	−0.292830	−	0.901239i
$285$	−5.16836			−0.306147
$286$	−6.55457	+	11.4514i	−0.387580	+	0.677137i
$287$	−17.0041			−1.00372
$288$	−0.436908	−	1.34467i	−0.0257451	−	0.0792351i
$289$	10.0283	+	7.28601i	0.589902	+	0.428589i
$290$	12.9437	−	9.40414i	0.760080	−	0.552230i
$291$	−3.55176	+	10.9312i	−0.208208	+	0.640798i
$292$	−0.981508	+	3.02077i	−0.0574384	+	0.176777i
$293$	−16.5964	+	12.0580i	−0.969569	+	0.704433i	−0.955353	−	0.295466i	$-0.904525\pi$
$293$	−16.5964	+	12.0580i	−0.969569	+	0.704433i	−0.0142160	+	0.999899i	$0.504525\pi$
$294$	4.43566	+	3.22270i	0.258693	+	0.187952i
$295$	−5.05552	−	15.5593i	−0.294344	−	0.905897i
$296$	1.74921			0.101671
$297$	1.19631	+	10.9872i	0.0694171	+	0.637542i
$298$	10.3503			0.599575
$299$	3.14645	+	9.68377i	0.181964	+	0.560027i
$300$	−1.78777	−	1.29889i	−0.103217	−	0.0749917i
$301$	11.5232	−	8.37207i	0.664184	−	0.482558i
$302$	3.76169	−	11.5773i	0.216461	−	0.666199i
$303$	−3.76867	+	11.5988i	−0.216504	+	0.666332i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	12.6192	+	9.16836i	0.722571	+	0.524979i
$306$	0.937502	+	2.88533i	0.0535934	+	0.164944i
$307$	5.64603			0.322236			0.161118	−	0.986935i	$-0.448490\pi$
$307$	5.64603			0.322236			0.161118	+	0.986935i	$0.448490\pi$
$308$	1.11288	+	10.2210i	0.0634125	+	0.582394i
$309$	−20.0911			−1.14294
$310$	−1.12992	−	3.47753i	−0.0641749	−	0.197510i
$311$	−6.80879	−	4.94688i	−0.386091	−	0.280512i	0.377761	−	0.925903i	$-0.376694\pi$
$311$	−6.80879	−	4.94688i	−0.386091	−	0.280512i	−0.763852	+	0.645392i	$0.776694\pi$
$312$	−6.76187	+	4.91279i	−0.382816	+	0.278132i
$313$	9.69591	−	29.8409i	0.548045	−	1.68671i	−0.165593	−	0.986194i	$-0.552954\pi$
$313$	9.69591	−	29.8409i	0.548045	−	1.68671i	0.713638	−	0.700515i	$-0.247046\pi$
$314$	−1.15074	+	3.54163i	−0.0649403	+	0.199866i
$315$	8.72296	−	6.33760i	0.491483	−	0.357083i
$316$	−5.87079	−	4.26538i	−0.330258	−	0.239946i
$317$	2.22582	+	6.85036i	0.125014	+	0.384755i	0.993904	−	0.110252i	$-0.0351657\pi$
$317$	2.22582	+	6.85036i	0.125014	+	0.384755i	−0.868889	+	0.495006i	$0.835166\pi$
$318$	24.7087			1.38560
$319$	−10.7152	+	18.7205i	−0.599938	+	1.04815i
$320$	2.46005			0.137521
$321$	−9.45675	−	29.1049i	−0.527824	−	1.62448i
$322$	6.41876	+	4.66350i	0.357703	+	0.259887i
$323$	−1.73596	+	1.26125i	−0.0965914	+	0.0701777i
$324$	−3.47415	+	10.6923i	−0.193008	+	0.594018i
$325$	−1.29309	+	3.97971i	−0.0717276	+	0.220755i
$326$	−16.0930	+	11.6922i	−0.891308	+	0.647573i
$327$	5.74628	+	4.17492i	0.317770	+	0.230873i
$328$	−1.69505	−	5.21682i	−0.0935934	−	0.288051i
$329$	10.5595			0.582164
$330$	16.7801	+	3.50126i	0.923716	+	0.192738i
$331$	20.4083			1.12174			0.560870	−	0.827904i	$-0.310467\pi$
$331$	20.4083			1.12174			0.560870	+	0.827904i	$0.310467\pi$
$332$	3.46611	+	10.6676i	0.190227	+	0.585459i
$333$	2.00082	+	1.45368i	0.109644	+	0.0796612i
$334$	−17.7876	+	12.9234i	−0.973294	+	0.707139i
$335$	10.7305	−	33.0250i	0.586269	−	1.80435i
$336$	−2.01255	+	6.19400i	−0.109794	+	0.337910i
$337$	25.9791	−	18.8749i	1.41517	−	1.02818i	0.422625	−	0.906305i	$-0.361109\pi$
$337$	25.9791	−	18.8749i	1.41517	−	1.02818i	0.992545	−	0.121877i	$-0.0388912\pi$
$338$	2.28713	+	1.66170i	0.124403	+	0.0903843i
$339$	7.37956	+	22.7119i	0.400803	+	1.23354i
$340$	−5.27868			−0.286277
$341$	3.31225	+	3.65110i	0.179368	+	0.197718i
$342$	1.41386			0.0764530
$343$	4.20563	+	12.9436i	0.227083	+	0.698889i
$344$	3.71721	+	2.70071i	0.200418	+	0.145613i
$345$	10.7016	−	7.77517i	0.576155	−	0.418601i
$346$	7.87433	−	24.2347i	0.423326	−	1.30286i
$347$	0.349090	−	1.07439i	0.0187401	−	0.0576762i	−0.941249	−	0.337713i	$-0.890347\pi$
$347$	0.349090	−	1.07439i	0.0187401	−	0.0576762i	0.959989	+	0.280037i	$0.0903467\pi$
$348$	−11.0541	+	8.03129i	−0.592563	+	0.430522i
$349$	17.1155	+	12.4351i	0.916171	+	0.665637i	0.942568	−	0.334015i	$-0.108403\pi$
$349$	17.1155	+	12.4351i	0.916171	+	0.665637i	−0.0263972	+	0.999652i	$0.508403\pi$
$350$	1.00759	+	3.10104i	0.0538579	+	0.165757i
$351$	13.2571			0.707614
$352$	−3.02483	+	1.36030i	−0.161224	+	0.0725043i
$353$	−0.0272714			−0.00145151			−0.000725755	−	1.00000i	$-0.500231\pi$
$353$	−0.0272714			−0.00145151			−0.000725755		1.00000i	$0.500231\pi$
$354$	4.31749	+	13.2879i	0.229472	+	0.706243i
$355$	31.7829	+	23.0916i	1.68686	+	1.22558i
$356$	3.75130	−	2.72548i	0.198818	−	0.144450i
$357$	4.31846	−	13.2908i	0.228557	−	0.703426i
$358$	−7.04201	+	21.6731i	−0.372182	+	1.14546i
$359$	−12.2286	+	8.88459i	−0.645400	+	0.468911i	−0.861701	−	0.507416i	$-0.830601\pi$
$359$	−12.2286	+	8.88459i	−0.645400	+	0.468911i	0.216301	+	0.976327i	$0.430601\pi$
$360$	2.81390	+	2.04442i	0.148306	+	0.107750i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	1.54547			0.0812279
$363$	−22.5686	+	4.97361i	−1.18454	+	0.261047i
$364$	12.3326			0.646404
$365$	−2.41456	−	7.43124i	−0.126384	−	0.388969i
$366$	−10.7770	−	7.82993i	−0.563322	−	0.409277i
$367$	−17.3707	+	12.6206i	−0.906744	+	0.658788i	−0.940189	−	0.340652i	$-0.889352\pi$
$367$	−17.3707	+	12.6206i	−0.906744	+	0.658788i	0.0334451	+	0.999441i	$0.489352\pi$
$368$	−0.790899	+	2.43414i	−0.0412284	+	0.126888i
$369$	2.39657	−	7.37588i	0.124760	−	0.383973i
$370$	−3.48132	+	2.52933i	−0.180985	+	0.131493i
$371$	−29.4953	−	21.4296i	−1.53132	−	1.11257i
$372$	0.964967	+	2.96986i	0.0500312	+	0.153980i
$373$	−18.3417			−0.949697			−0.474848	−	0.880068i	$-0.657497\pi$
$373$	−18.3417			−0.949697			−0.474848	+	0.880068i	$0.657497\pi$
$374$	6.49056	−	2.91889i	0.335619	−	0.150932i
$375$	−20.4056			−1.05374
$376$	1.05262	+	3.23963i	0.0542846	+	0.167071i
$377$	20.9322	+	15.2081i	1.07806	+	0.783258i
$378$	8.35723	−	6.07188i	0.429850	−	0.312304i
$379$	3.80809	−	11.7201i	0.195609	−	0.602021i	−0.804360	−	0.594142i	$-0.797492\pi$
$379$	3.80809	−	11.7201i	0.195609	−	0.602021i	0.999969	−	0.00787967i	$-0.00250820\pi$
$380$	−0.760196	+	2.33964i	−0.0389972	+	0.120021i
$381$	22.6850	−	16.4816i	1.16219	−	0.844378i
$382$	5.77965	+	4.19916i	0.295713	+	0.214848i
$383$	8.88446	+	27.3436i	0.453975	+	1.39719i	0.872335	+	0.488909i	$0.162605\pi$
$383$	8.88446	+	27.3436i	0.453975	+	1.39719i	−0.418360	+	0.908281i	$0.637395\pi$
$384$	−2.10092			−0.107212
$385$	−16.9942	−	18.7328i	−0.866104	−	0.954710i
$386$	12.0980			0.615772
$387$	2.00747	+	6.17836i	0.102046	+	0.314064i
$388$	4.42598	+	3.21566i	0.224695	+	0.163251i
$389$	−2.20852	+	1.60458i	−0.111976	+	0.0813556i	−0.642364	−	0.766400i	$-0.722046\pi$
$389$	−2.20852	+	1.60458i	−0.111976	+	0.0813556i	0.530388	+	0.847755i	$0.322046\pi$
$390$	6.35382	−	19.5551i	0.321738	−	0.990209i
$391$	1.69708	−	5.22308i	0.0858251	−	0.264142i
$392$	2.11130	−	1.53395i	0.106637	−	0.0774760i
$393$	7.79741	+	5.66515i	0.393327	+	0.285769i
$394$	−5.64005	−	17.3583i	−0.284142	−	0.874498i
$395$	17.8518			0.898222
$396$	−4.59040	−	0.957811i	−0.230676	−	0.0481318i
$397$	7.21330			0.362025			0.181013	−	0.983481i	$-0.442062\pi$
$397$	7.21330			0.362025			0.181013	+	0.983481i	$0.442062\pi$
$398$	−7.40730	−	22.7973i	−0.371295	−	1.14273i
$399$	−5.26893	−	3.82810i	−0.263776	−	0.191645i
$400$	−0.850949	+	0.618250i	−0.0425474	+	0.0309125i
$401$	−0.367672	+	1.13158i	−0.0183607	+	0.0565083i	−0.959817	−	0.280626i	$-0.909458\pi$
$401$	−0.367672	+	1.13158i	−0.0183607	+	0.0565083i	0.941456	+	0.337135i	$0.109458\pi$
$402$	−9.16401	+	28.2039i	−0.457059	+	1.40668i
$403$	4.78386	−	3.47568i	0.238301	−	0.173136i
$404$	4.69628	+	3.41205i	0.233649	+	0.169756i
$405$	−8.54657	−	26.3036i	−0.424682	−	1.30704i
$406$	20.1610			1.00057
$407$	2.88195	−	5.03503i	0.142853	−	0.249577i
$408$	4.50808			0.223183
$409$	3.63996	+	11.2026i	0.179984	+	0.553935i	0.999826	−	0.0186553i	$-0.00593851\pi$
$409$	3.63996	+	11.2026i	0.179984	+	0.553935i	−0.819842	+	0.572591i	$0.805939\pi$
$410$	10.9169	+	7.93162i	0.539149	+	0.391715i
$411$	23.1786	−	16.8403i	1.14332	−	0.830669i
$412$	−2.95513	+	9.09496i	−0.145589	+	0.448077i
$413$	6.37056	−	19.6066i	0.313475	−	0.964776i
$414$	−2.92755	+	2.12699i	−0.143881	+	0.104536i
$415$	−22.3234	−	16.2189i	−1.09581	−	0.796155i
$416$	1.22937	+	3.78361i	0.0602748	+	0.185507i
$417$	−12.1640			−0.595672
$418$	−0.359001	−	3.29714i	−0.0175593	−	0.161268i
$419$	20.0798			0.980963			0.490482	−	0.871452i	$-0.336821\pi$
$419$	20.0798			0.980963			0.490482	+	0.871452i	$0.336821\pi$
$420$	−4.95097	−	15.2375i	−0.241583	−	0.743515i
$421$	−0.716128	−	0.520297i	−0.0349019	−	0.0253577i	0.570198	−	0.821508i	$-0.306867\pi$
$421$	−0.716128	−	0.520297i	−0.0349019	−	0.0253577i	−0.605099	+	0.796150i	$0.706867\pi$
$422$	16.7844	−	12.1946i	0.817051	−	0.593622i
$423$	−1.48826	+	4.58039i	−0.0723616	+	0.222706i
$424$	3.63432	−	11.1853i	0.176498	−	0.543206i
$425$	1.82593	−	1.32662i	0.0885708	−	0.0643505i
$426$	−27.1431	−	19.7206i	−1.31509	−	0.955468i
$427$	6.07389	+	18.6935i	0.293936	+	0.904643i
$428$	−14.5663			−0.704090
$429$	3.00058	+	27.5579i	0.144869	+	1.33051i
$430$	−11.3032			−0.545090
$431$	−6.27447	−	19.3108i	−0.302230	−	0.930169i	−0.980696	−	0.195538i	$-0.937355\pi$
$431$	−6.27447	−	19.3108i	−0.302230	−	0.930169i	0.678466	−	0.734632i	$-0.262645\pi$
$432$	2.69592	+	1.95870i	0.129708	+	0.0942381i
$433$	29.2632	−	21.2609i	1.40630	−	1.02174i	0.412451	−	0.910980i	$-0.364673\pi$
$433$	29.2632	−	21.2609i	1.40630	−	1.02174i	0.993848	−	0.110756i	$-0.0353271\pi$
$434$	1.42383	−	4.38210i	0.0683460	−	0.210347i
$435$	10.3871	−	31.9681i	0.498021	−	1.53275i
$436$	2.73512	−	1.98718i	0.130989	−	0.0951689i
$437$	−2.07060	−	1.50438i	−0.0990502	−	0.0719642i
$438$	2.06207	+	6.34640i	0.0985295	+	0.303243i
$439$	21.4914			1.02573			0.512864	−	0.858470i	$-0.328584\pi$
$439$	21.4914			1.02573			0.512864	+	0.858470i	$0.328584\pi$
$440$	4.05310	−	7.08114i	0.193224	−	0.337580i
$441$	3.68977			0.175703
$442$	−2.63794	−	8.11873i	−0.125474	−	0.386169i
$443$	19.9014	+	14.4592i	0.945546	+	0.686979i	0.949749	−	0.313012i	$-0.101338\pi$
$443$	19.9014	+	14.4592i	0.945546	+	0.686979i	−0.00420349	+	0.999991i	$0.501338\pi$
$444$	2.97310	−	2.16009i	0.141097	−	0.102513i
$445$	−3.52492	+	10.8486i	−0.167097	+	0.514273i
$446$	−8.77130	+	26.9953i	−0.415333	+	1.27826i
$447$	17.5921	−	12.7814i	0.832079	−	0.604541i
$448$	2.50791	+	1.82211i	0.118488	+	0.0860864i
$449$	10.8991	+	33.5439i	0.514359	+	1.58303i	0.784445	+	0.620198i	$0.212948\pi$
$449$	10.8991	+	33.5439i	0.514359	+	1.58303i	−0.270086	+	0.962836i	$0.587052\pi$
$450$	−1.48715			−0.0701047
$451$	−17.8091	−	3.71597i	−0.838598	−	0.174978i
$452$	11.3668			0.534650
$453$	−7.90302	−	24.3230i	−0.371316	−	1.14279i
$454$	−6.88177	−	4.99990i	−0.322977	−	0.234657i
$455$	−24.5446	+	17.8327i	−1.15067	+	0.836010i
$456$	0.649220	−	1.99809i	0.0304025	−	0.0935693i
$457$	−2.27762	+	7.00981i	−0.106543	+	0.327905i	−0.990089	−	0.140438i	$-0.955149\pi$
$457$	−2.27762	+	7.00981i	−0.106543	+	0.327905i	0.883547	+	0.468343i	$0.155149\pi$
$458$	−1.38124	+	1.00353i	−0.0645410	+	0.0468918i
$459$	−5.78481	−	4.20291i	−0.270012	−	0.196175i
$460$	−1.94565	−	5.98809i	−0.0907163	−	0.279196i
$461$	−36.4875			−1.69939			−0.849696	−	0.527272i	$-0.823215\pi$
$461$	−36.4875			−1.69939			−0.849696	+	0.527272i	$0.823215\pi$
$462$	14.5133	+	15.9981i	0.675221	+	0.744298i
$463$	−16.2208			−0.753844			−0.376922	−	0.926245i	$-0.623018\pi$
$463$	−16.2208			−0.753844			−0.376922	+	0.926245i	$0.623018\pi$
$464$	2.00974	+	6.18534i	0.0932998	+	0.287147i
$465$	−6.21486	−	4.51536i	−0.288207	−	0.209395i
$466$	8.05483	−	5.85218i	0.373133	−	0.271097i
$467$	1.32060	−	4.06438i	0.0611099	−	0.188077i	−0.915841	−	0.401541i	$-0.868475\pi$
$467$	1.32060	−	4.06438i	0.0611099	−	0.188077i	0.976951	+	0.213464i	$0.0684747\pi$
$468$	−1.73816	+	5.34951i	−0.0803465	+	0.247281i
$469$	35.4003	−	25.7198i	1.63463	−	1.18763i
$470$	−6.77937	−	4.92550i	−0.312709	−	0.227196i
$471$	2.41762	+	7.44068i	0.111398	+	0.342848i
$472$	6.65028			0.306104
$473$	13.8982	−	6.25021i	0.639042	−	0.287385i
$474$	−15.2457			−0.700260
$475$	−0.325033	−	1.00035i	−0.0149136	−	0.0458992i
$476$	−5.38139	−	3.90981i	−0.246656	−	0.179206i
$477$	13.4526	−	9.77389i	0.615952	−	0.447515i
$478$	−5.03035	+	15.4818i	−0.230083	+	0.708123i
$479$	−12.1115	+	37.2754i	−0.553389	+	1.70315i	0.146773	+	0.989170i	$0.453111\pi$
$479$	−12.1115	+	37.2754i	−0.553389	+	1.70315i	−0.700161	+	0.713985i	$0.746889\pi$
$480$	4.18129	−	3.03789i	0.190849	−	0.138660i
$481$	−5.62990	−	4.09036i	−0.256701	−	0.186504i
$482$	1.83910	+	5.66016i	0.0837686	+	0.257813i
$483$	16.6687			0.758454
$484$	−1.06805	+	10.9480i	−0.0485478	+	0.497638i
$485$	−13.4585			−0.611117
$486$	4.20966	+	12.9560i	0.190954	+	0.587696i
$487$	−2.64903	−	1.92463i	−0.120039	−	0.0872134i	0.526146	−	0.850394i	$-0.323637\pi$
$487$	−2.64903	−	1.92463i	−0.120039	−	0.0872134i	−0.646185	+	0.763181i	$0.723637\pi$
$488$	−5.12965	+	3.72691i	−0.232208	+	0.168709i
$489$	−12.9143	+	39.7461i	−0.584005	+	1.79738i
$490$	−1.98389	+	6.10578i	−0.0896229	+	0.275831i
$491$	−32.8868	+	23.8936i	−1.48416	+	1.07830i	−0.507971	+	0.861374i	$0.669604\pi$
$491$	−32.8868	+	23.8936i	−1.48416	+	1.07830i	−0.976187	+	0.216930i	$0.930396\pi$
$492$	−9.32324	−	6.77373i	−0.420324	−	0.305383i
$493$	−4.31242	−	13.2723i	−0.194222	−	0.597753i
$494$	−3.97832			−0.178993
$495$	10.5209	−	4.73136i	0.472878	−	0.212659i
$496$	1.48635			0.0667390
$497$	15.2978	+	47.0819i	0.686202	+	2.11191i
$498$	19.0645	+	13.8512i	0.854303	+	0.620687i
$499$	11.4431	−	8.31393i	0.512266	−	0.372183i	−0.301417	−	0.953492i	$-0.597460\pi$
$499$	11.4431	−	8.31393i	0.512266	−	0.372183i	0.813682	+	0.581310i	$0.197460\pi$
$500$	−3.00138	+	9.23731i	−0.134226	+	0.413105i
$501$	−14.2742	+	43.9314i	−0.637724	+	1.96271i
$502$	−17.0374	+	12.3784i	−0.760418	+	0.552476i
$503$	22.4423	+	16.3053i	1.00065	+	0.727017i	0.962228	−	0.272244i	$-0.0877658\pi$
$503$	22.4423	+	16.3053i	1.00065	+	0.727017i	0.0384254	+	0.999261i	$0.487766\pi$
$504$	1.35439	+	4.16840i	0.0603295	+	0.185675i
$505$	−14.2804			−0.635468
$506$	5.70349	+	6.28698i	0.253551	+	0.279490i
$507$	5.93940			0.263778
$508$	−4.12433	−	12.6934i	−0.182988	−	0.563178i
$509$	−3.93843	−	2.86144i	−0.174568	−	0.126831i	0.497070	−	0.867710i	$-0.334409\pi$
$509$	−3.93843	−	2.86144i	−0.174568	−	0.126831i	−0.671638	+	0.740879i	$0.734409\pi$
$510$	−8.97206	+	6.51859i	−0.397290	+	0.288648i
$511$	3.04263	−	9.36425i	0.134598	−	0.414250i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−2.69592	+	1.95870i	−0.119028	+	0.0864788i
$514$	1.03343	+	0.750828i	0.0455825	+	0.0331176i
$515$	−7.26976	−	22.3740i	−0.320344	−	0.985918i
$516$	9.65314			0.424956
$517$	11.0594	+	2.30760i	0.486391	+	0.101488i
$518$	−5.42248			−0.238250
$519$	−16.5433	−	50.9151i	−0.726171	−	2.23493i
$520$	−7.91773	−	5.75257i	−0.347216	−	0.252267i
$521$	−15.0920	+	10.9650i	−0.661195	+	0.480386i	−0.867066	−	0.498193i	$-0.833997\pi$
$521$	−15.0920	+	10.9650i	−0.661195	+	0.480386i	0.205872	+	0.978579i	$0.433997\pi$
$522$	−2.84150	+	8.74523i	−0.124369	+	0.382768i
$523$	−2.59339	+	7.98164i	−0.113401	+	0.349013i	−0.991610	−	0.129264i	$-0.958738\pi$
$523$	−2.59339	+	7.98164i	−0.113401	+	0.349013i	0.878209	+	0.478277i	$0.158738\pi$
$524$	3.71142	−	2.69651i	0.162134	−	0.117798i
$525$	5.54202	+	4.02651i	0.241873	+	0.175731i
$526$	−2.73757	−	8.42537i	−0.119364	−	0.367364i
$527$	−3.18935			−0.138930
$528$	−3.46142	+	6.04741i	−0.150639	+	0.263180i
$529$	−16.4495			−0.715194
$530$	8.94060	+	27.5163i	0.388355	+	1.19523i
$531$	7.60686	+	5.52671i	0.330110	+	0.239839i
$532$	−2.50791	+	1.82211i	−0.108732	+	0.0789983i
$533$	−6.74345	+	20.7542i	−0.292091	+	0.898964i
$534$	3.01034	−	9.26488i	0.130270	−	0.400931i
$535$	28.9902	−	21.0626i	1.25336	−	0.910616i
$536$	11.4196	+	8.29684i	0.493252	+	0.358369i
$537$	14.7947	+	45.5334i	0.638438	+	1.96491i
$538$	−26.0234			−1.12195
$539$	−0.936886	−	8.60456i	−0.0403545	−	0.370625i
$540$	−8.19772			−0.352774
$541$	−9.89470	−	30.4528i	−0.425407	−	1.30927i	−0.902604	−	0.430471i	$-0.858347\pi$
$541$	−9.89470	−	30.4528i	−0.425407	−	1.30927i	0.477198	−	0.878796i	$-0.341653\pi$
$542$	13.8201	+	10.0409i	0.593626	+	0.431294i
$543$	2.62680	−	1.90848i	0.112727	−	0.0819007i
$544$	0.663077	−	2.04074i	0.0284292	−	0.0874961i
$545$	−2.57007	+	7.90987i	−0.110090	+	0.338821i
$546$	20.9615	−	15.2294i	0.897069	−	0.651759i
$547$	−20.8060	−	15.1164i	−0.889599	−	0.646332i	0.0461743	−	0.998933i	$-0.485297\pi$
$547$	−20.8060	−	15.1164i	−0.889599	−	0.646332i	−0.935773	+	0.352602i	$0.885297\pi$
$548$	−4.21408	−	12.9696i	−0.180017	−	0.554034i
$549$	−8.96474			−0.382606
$550$	0.377608	+	3.46803i	0.0161012	+	0.147877i
$551$	−6.50365			−0.277065
$552$	1.66161	+	5.11392i	0.0707230	+	0.217663i
$553$	18.1992	+	13.2225i	0.773907	+	0.562277i
$554$	6.87184	−	4.99269i	0.291957	−	0.212119i
$555$	−2.79369	+	8.59809i	−0.118585	+	0.364969i
$556$	−1.78915	+	5.50645i	−0.0758770	+	0.233525i
$557$	−30.1853	+	21.9309i	−1.27899	+	0.929243i	−0.999522	−	0.0309112i	$-0.990159\pi$
$557$	−30.1853	+	21.9309i	−1.27899	+	0.929243i	−0.279471	+	0.960154i	$0.590159\pi$
$558$	1.70015	+	1.23523i	0.0719729	+	0.0522914i
$559$	−5.64861	−	17.3846i	−0.238911	−	0.735292i
$560$	−7.62603			−0.322259
$561$	7.42738	−	12.9763i	0.313584	−	0.547860i
$562$	−29.4238			−1.24117
$563$	0.234541	+	0.721842i	0.00988472	+	0.0304220i	0.955877	−	0.293766i	$-0.0949088\pi$
$563$	0.234541	+	0.721842i	0.00988472	+	0.0304220i	−0.945993	+	0.324188i	$0.894909\pi$
$564$	5.78969	+	4.20646i	0.243790	+	0.177124i
$565$	−22.6224	+	16.4362i	−0.951733	+	0.691475i
$566$	5.27150	−	16.2240i	0.221578	−	0.681946i
$567$	10.7697	−	33.1457i	0.452285	−	1.39199i
$568$	−12.9196	+	9.38667i	−0.542096	+	0.393856i
$569$	25.2807	+	18.3675i	1.05982	+	0.770007i	0.974056	−	0.226309i	$-0.0726658\pi$
$569$	25.2807	+	18.3675i	1.05982	+	0.770007i	0.0857675	+	0.996315i	$0.472666\pi$
$570$	1.59711	+	4.91540i	0.0668956	+	0.205884i
$571$	−20.5848			−0.861445			−0.430723	−	0.902484i	$-0.641741\pi$
$571$	−20.5848			−0.861445			−0.430723	+	0.902484i	$0.641741\pi$
$572$	12.9164	+	2.69508i	0.540063	+	0.112687i
$573$	15.0091			0.627012
$574$	5.25457	+	16.1719i	0.219321	+	0.675002i
$575$	2.17792	+	1.58235i	0.0908255	+	0.0659886i
$576$	−1.14384	+	0.831049i	−0.0476600	+	0.0346270i
$577$	3.86681	−	11.9008i	0.160977	−	0.495437i	−0.837740	−	0.546069i	$-0.816124\pi$
$577$	3.86681	−	11.9008i	0.160977	−	0.495437i	0.998717	+	0.0506319i	$0.0161235\pi$
$578$	3.83048	−	11.7890i	0.159327	−	0.490358i
$579$	20.5627	−	14.9397i	0.854558	−	0.620873i
$580$	−12.9437	−	9.40414i	−0.537458	−	0.390486i
$581$	−10.7448	−	33.0690i	−0.445768	−	1.37193i
$582$	11.4937			0.476431
$583$	−26.2086	−	28.8898i	−1.08545	−	1.19649i
$584$	3.17623			0.131433
$585$	−4.27596	−	13.1600i	−0.176789	−	0.544101i
$586$	16.5964	+	12.0580i	0.685589	+	0.498110i
$587$	−9.72555	+	7.06602i	−0.401416	+	0.291646i	−0.770118	−	0.637902i	$-0.779803\pi$
$587$	−9.72555	+	7.06602i	−0.401416	+	0.291646i	0.368701	+	0.929548i	$0.379803\pi$
$588$	1.69427	−	5.21444i	0.0698706	−	0.215040i
$589$	−0.459307	+	1.41360i	−0.0189254	+	0.0582464i
$590$	−13.2355	+	9.61617i	−0.544898	+	0.395891i
$591$	−31.0219	−	22.5387i	−1.27607	−	0.927118i
$592$	−0.540537	−	1.66360i	−0.0222159	−	0.0683736i
$593$	−33.2839			−1.36680			−0.683402	−	0.730042i	$-0.739500\pi$
$593$	−33.2839			−1.36680			−0.683402	+	0.730042i	$0.739500\pi$
$594$	10.0798	−	4.53299i	0.413578	−	0.185991i
$595$	16.3637			0.670844
$596$	−3.19841	−	9.84368i	−0.131012	−	0.403213i
$597$	−40.7422	−	29.6010i	−1.66747	−	1.21149i
$598$	8.23751	−	5.98490i	0.336857	−	0.244741i
$599$	−4.59137	+	14.1308i	−0.187598	+	0.577368i	−0.999983	−	0.00575289i	$-0.998169\pi$
$599$	−4.59137	+	14.1308i	−0.187598	+	0.577368i	0.812385	+	0.583121i	$0.198169\pi$
$600$	−0.682869	+	2.10166i	−0.0278780	+	0.0857997i
$601$	−25.0415	+	18.1937i	−1.02147	+	0.742138i	−0.966583	−	0.256354i	$-0.917479\pi$
$601$	−25.0415	+	18.1937i	−1.02147	+	0.742138i	−0.0548831	+	0.998493i	$0.517479\pi$
$602$	−11.5232	−	8.37207i	−0.469649	−	0.341220i
$603$	6.16714	+	18.9805i	0.251145	+	0.772946i
$604$	−12.1731			−0.495316
$605$	−13.7050	−	23.3334i	−0.557186	−	0.948636i
$606$	12.1957			0.495415
$607$	9.09384	+	27.9880i	0.369108	+	1.13600i	0.947369	+	0.320145i	$0.103732\pi$
$607$	9.09384	+	27.9880i	0.369108	+	1.13600i	−0.578261	+	0.815852i	$0.696268\pi$
$608$	−0.809017	−	0.587785i	−0.0328100	−	0.0238378i
$609$	34.2673	−	24.8966i	1.38858	−	1.00886i
$610$	4.82009	−	14.8347i	0.195160	−	0.600640i
$611$	4.18765	−	12.8883i	0.169414	−	0.521404i
$612$	2.45441	−	1.78323i	0.0992137	−	0.0720830i
$613$	−17.4575	−	12.6836i	−0.705102	−	0.512287i	0.176488	−	0.984303i	$-0.443526\pi$
$613$	−17.4575	−	12.6836i	−0.705102	−	0.512287i	−0.881590	+	0.472016i	$0.843526\pi$
$614$	−1.74472	−	5.36969i	−0.0704111	−	0.216703i
$615$	28.3500			1.14318
$616$	9.37682	−	4.21687i	0.377803	−	0.169903i
$617$	−21.8270			−0.878721			−0.439360	−	0.898311i	$-0.644795\pi$
$617$	−21.8270			−0.878721			−0.439360	+	0.898311i	$0.644795\pi$
$618$	6.20850	+	19.1078i	0.249742	+	0.768628i
$619$	−33.6049	−	24.4154i	−1.35069	−	0.981336i	−0.998977	−	0.0452299i	$-0.985598\pi$
$619$	−33.6049	−	24.4154i	−1.35069	−	0.981336i	−0.351717	−	0.936106i	$-0.614402\pi$
$620$	−2.95816	+	2.14923i	−0.118803	+	0.0863151i
$621$	2.63555	−	8.11138i	0.105761	−	0.325498i
$622$	−2.60073	+	8.00422i	−0.104280	+	0.320940i
$623$	−11.6288	+	8.44885i	−0.465900	+	0.338496i
$624$	6.76187	+	4.91279i	0.270692	+	0.196669i
$625$	−9.00871	−	27.7260i	−0.360348	−	1.10904i
$626$	−31.3766			−1.25406
$627$	−4.68179	−	5.16075i	−0.186973	−	0.206101i
$628$	3.72389			0.148599
$629$	1.15986	+	3.56969i	0.0462468	+	0.142333i
$630$	−8.72296	−	6.33760i	−0.347531	−	0.252496i
$631$	−1.13636	+	0.825616i	−0.0452379	+	0.0328672i	−0.610174	−	0.792267i	$-0.708901\pi$
$631$	−1.13636	+	0.825616i	−0.0452379	+	0.0328672i	0.564937	+	0.825134i	$0.308901\pi$
$632$	−2.24244	+	6.90153i	−0.0891996	+	0.274528i
$633$	13.4691	−	41.4537i	0.535350	−	1.64764i
$634$	5.82726	−	4.23375i	0.231430	−	0.168144i
$635$	26.5627	+	19.2989i	1.05411	+	0.765855i
$636$	−7.63541	−	23.4994i	−0.302764	−	0.931811i
$637$	−10.3822			−0.411360
$638$	21.1154	+	4.40584i	0.835967	+	0.174429i
$639$	−22.5788			−0.893203
$640$	−0.760196	−	2.33964i	−0.0300494	−	0.0924825i
$641$	10.2584	+	7.45315i	0.405182	+	0.294382i	0.771648	−	0.636049i	$-0.219433\pi$
$641$	10.2584	+	7.45315i	0.405182	+	0.294382i	−0.366467	+	0.930431i	$0.619433\pi$
$642$	−24.7581	+	17.9878i	−0.977124	+	0.709922i
$643$	1.36681	−	4.20660i	0.0539017	−	0.165892i	−0.920482	−	0.390786i	$-0.872203\pi$
$643$	1.36681	−	4.20660i	0.0539017	−	0.165892i	0.974383	+	0.224893i	$0.0722034\pi$
$644$	2.45175	−	7.54570i	0.0966124	−	0.297342i
$645$	−19.2119	+	13.9582i	−0.756467	+	0.549605i
$646$	1.73596	+	1.26125i	0.0683004	+	0.0496231i
$647$	−7.59875	−	23.3866i	−0.298738	−	0.919421i	−0.981940	−	0.189191i	$-0.939413\pi$
$647$	−7.59875	−	23.3866i	−0.298738	−	0.919421i	0.683202	−	0.730229i	$-0.260587\pi$
$648$	11.2426			0.441650
$649$	10.9568	−	19.1425i	0.430092	−	0.751410i
$650$	4.18452			0.164130
$651$	−2.99135	−	9.20643i	−0.117240	−	0.360829i
$652$	16.0930	+	11.6922i	0.630250	+	0.457903i
$653$	−15.8056	+	11.4834i	−0.618521	+	0.449381i	−0.852404	−	0.522883i	$-0.824856\pi$
$653$	−15.8056	+	11.4834i	−0.618521	+	0.449381i	0.233884	+	0.972265i	$0.424856\pi$
$654$	2.19488	−	6.75516i	0.0858267	−	0.264147i
$655$	−3.48746	+	10.7333i	−0.136266	+	0.419384i
$656$	−4.43769	+	3.22417i	−0.173263	+	0.125883i
$657$	3.63310	+	2.63960i	0.141741	+	0.102981i
$658$	−3.26307	−	10.0427i	−0.127208	−	0.391505i
$659$	35.3980			1.37891			0.689456	−	0.724328i	$-0.257850\pi$
$659$	35.3980			1.37891			0.689456	+	0.724328i	$0.257850\pi$
$660$	−1.85544	−	17.0408i	−0.0722231	−	0.663312i
$661$	−26.3898			−1.02644			−0.513222	−	0.858256i	$-0.671548\pi$
$661$	−26.3898			−1.02644			−0.513222	+	0.858256i	$0.671548\pi$
$662$	−6.30650	−	19.4094i	−0.245109	−	0.754368i
$663$	−14.5094	−	10.5417i	−0.563498	−	0.409405i
$664$	9.07438	−	6.59292i	0.352154	−	0.255855i
$665$	2.35657	−	7.25278i	0.0913840	−	0.281251i
$666$	0.764246	−	2.35211i	0.0296139	−	0.0911423i
$667$	13.4665	−	9.78395i	0.521423	−	0.378836i
$668$	17.7876	+	12.9234i	0.688223	+	0.500023i
$669$	18.4278	+	56.7149i	0.712460	+	2.19273i
$670$	−34.7246			−1.34153
$671$	2.27628	+	20.9058i	0.0878747	+	0.807060i
$672$	6.51275			0.251235
$673$	−1.24471	−	3.83081i	−0.0479799	−	0.147667i	0.924196	−	0.381918i	$-0.124736\pi$
$673$	−1.24471	−	3.83081i	−0.0479799	−	0.147667i	−0.972176	+	0.234251i	$0.924736\pi$
$674$	−25.9791	−	18.8749i	−1.00068	−	0.727034i
$675$	2.83565	−	2.06022i	0.109144	−	0.0792980i
$676$	0.873605	−	2.68868i	0.0336002	−	0.103411i
$677$	6.67689	−	20.5493i	0.256614	−	0.789776i	−0.736894	−	0.676009i	$-0.763708\pi$
$677$	6.67689	−	20.5493i	0.256614	−	0.789776i	0.993507	−	0.113767i	$-0.0362918\pi$
$678$	19.3199	−	14.0368i	0.741977	−	0.539078i
$679$	−13.7203	−	9.96840i	−0.526538	−	0.382552i
$680$	1.63120	+	5.02032i	0.0625537	+	0.192521i
$681$	−17.8711			−0.684823
$682$	2.44887	−	4.27839i	0.0937719	−	0.163828i
$683$	3.73163			0.142787			0.0713935	−	0.997448i	$-0.477255\pi$
$683$	3.73163			0.142787			0.0713935	+	0.997448i	$0.477255\pi$
$684$	−0.436908	−	1.34467i	−0.0167056	−	0.0514146i
$685$	27.1407	+	19.7189i	1.03699	+	0.753420i
$686$	11.0105	−	7.99958i	0.420382	−	0.305426i
$687$	−1.10842	+	3.41135i	−0.0422887	+	0.130151i
$688$	1.41985	−	4.36984i	0.0541312	−	0.166599i
$689$	−37.8528	+	27.5017i	−1.44208	+	1.04773i
$690$	−10.7016	−	7.77517i	−0.407403	−	0.295996i
$691$	13.1069	+	40.3388i	0.498608	+	1.53456i	0.811257	+	0.584690i	$0.198784\pi$
$691$	13.1069	+	40.3388i	0.498608	+	1.53456i	−0.312648	+	0.949869i	$0.601216\pi$
$692$	−25.4819			−0.968675
$693$	14.2300	+	2.96917i	0.540553	+	0.112789i
$694$	−1.12968			−0.0428820
$695$	−4.40140	−	13.5461i	−0.166955	−	0.513834i
$696$	11.0541	+	8.03129i	0.419005	+	0.304425i
$697$	9.52224	−	6.91831i	0.360681	−	0.262050i
$698$	6.53753	−	20.1205i	0.247449	−	0.761570i
$699$	6.46384	−	19.8936i	0.244485	−	0.752447i
$700$	2.63790	−	1.91655i	0.0997033	−	0.0724387i
$701$	41.9946	+	30.5108i	1.58611	+	1.15238i	0.909235	+	0.416284i	$0.136668\pi$
$701$	41.9946	+	30.5108i	1.58611	+	1.15238i	0.676879	+	0.736095i	$0.263332\pi$
$702$	−4.09668	−	12.6083i	−0.154619	−	0.475869i
$703$	1.74921			0.0659728
$704$	2.22845	+	2.45643i	0.0839877	+	0.0925800i
$705$	−17.6052			−0.663051
$706$	0.00842732	+	0.0259366i	0.000317166	+	0.000976138i
$707$	−14.5582	−	10.5772i	−0.547519	−	0.397796i
$708$	11.3033	−	8.21236i	0.424806	−	0.308639i
$709$	−13.0146	+	40.0548i	−0.488773	+	1.50429i	0.337668	+	0.941265i	$0.390362\pi$
$709$	−13.0146	+	40.0548i	−0.488773	+	1.50429i	−0.826441	+	0.563024i	$0.809638\pi$
$710$	12.1400	−	37.3631i	0.455606	−	1.40221i
$711$	−8.30050	+	6.03067i	−0.311293	+	0.226168i
$712$	−3.75130	−	2.72548i	−0.140586	−	0.102142i
$713$	−1.17555	−	3.61797i	−0.0440247	−	0.135494i
$714$	−13.9748			−0.522995
$715$	−29.6036	+	13.3131i	−1.10711	+	0.497881i
$716$	22.7884			0.851643
$717$	10.5684	+	32.5261i	0.394683	+	1.21471i
$718$	12.2286	+	8.88459i	0.456367	+	0.331570i
$719$	5.15475	−	3.74514i	0.192240	−	0.139670i	−0.487502	−	0.873122i	$-0.662092\pi$
$719$	5.15475	−	3.74514i	0.192240	−	0.139670i	0.679742	+	0.733452i	$0.262092\pi$
$720$	1.07481	−	3.30794i	0.0400560	−	0.123280i
$721$	9.16077	−	28.1939i	0.341165	−	1.05000i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	10.1155	+	7.34938i	0.376201	+	0.273326i
$724$	−0.477575	−	1.46983i	−0.0177489	−	0.0546256i
$725$	6.84074			0.254059
$726$	11.7043	+	19.9271i	0.434386	+	0.739563i
$727$	−36.8358			−1.36616			−0.683082	−	0.730342i	$-0.739361\pi$
$727$	−36.8358			−1.36616			−0.683082	+	0.730342i	$0.739361\pi$
$728$	−3.81099	−	11.7290i	−0.141245	−	0.434706i
$729$	−4.13203	−	3.00210i	−0.153038	−	0.111189i
$730$	−6.32139	+	4.59276i	−0.233965	+	0.169986i
$731$	−3.04666	+	9.37664i	−0.112685	+	0.346808i
$732$	−4.11644	+	12.6691i	−0.152148	+	0.468263i
$733$	5.85493	−	4.25386i	0.216257	−	0.157120i	−0.474383	−	0.880318i	$-0.657329\pi$
$733$	5.85493	−	4.25386i	0.216257	−	0.157120i	0.690640	+	0.723199i	$0.257329\pi$
$734$	17.3707	+	12.6206i	0.641165	+	0.465834i
$735$	4.16799	+	12.8278i	0.153739	+	0.473159i
$736$	2.55940			0.0943408
$737$	42.6967	−	19.2012i	1.57275	−	0.707286i
$738$	−7.75546			−0.285482
$739$	6.07208	+	18.6880i	0.223365	+	0.687448i	0.998453	+	0.0555945i	$0.0177054\pi$
$739$	6.07208	+	18.6880i	0.223365	+	0.687448i	−0.775088	+	0.631853i	$0.782295\pi$
$740$	3.48132	+	2.52933i	0.127976	+	0.0929799i
$741$	−6.76187	+	4.91279i	−0.248404	+	0.180476i
$742$	−11.2662	+	34.6739i	−0.413596	+	1.27292i
$743$	2.38663	−	7.34530i	0.0875571	−	0.269473i	−0.897686	−	0.440637i	$-0.854753\pi$
$743$	2.38663	−	7.34530i	0.0875571	−	0.269473i	0.985243	+	0.171164i	$0.0547527\pi$
$744$	2.52632	−	1.83548i	0.0926193	−	0.0672918i
$745$	20.5993	+	14.9663i	0.754700	+	0.548321i
$746$	5.66789	+	17.4440i	0.207516	+	0.638670i
$747$	15.8587			0.580239
$748$	−4.78172	−	5.27091i	−0.174837	−	0.192723i
$749$	45.1549			1.64992
$750$	6.30567	+	19.4068i	0.230250	+	0.708638i
$751$	36.7609	+	26.7084i	1.34142	+	0.974602i	0.999390	+	0.0349139i	$0.0111157\pi$
$751$	36.7609	+	26.7084i	1.34142	+	0.974602i	0.342034	+	0.939688i	$0.388884\pi$
$752$	2.75579	−	2.00220i	0.100493	−	0.0730127i
$753$	−13.6722	+	42.0787i	−0.498243	+	1.53343i
$754$	7.99539	−	24.6073i	0.291175	−	0.896144i
$755$	24.2271	−	17.6020i	0.881716	−	0.640604i
$756$	−8.35723	−	6.07188i	−0.303950	−	0.220832i
$757$	−0.121953	−	0.375334i	−0.00443247	−	0.0136417i	0.948816	−	0.315830i	$-0.102283\pi$
$757$	−0.121953	−	0.375334i	−0.00443247	−	0.0136417i	−0.953248	+	0.302188i	$0.902283\pi$
$758$	−12.3232			−0.447601
$759$	17.4578	+	3.64267i	0.633679	+	0.132221i
$760$	2.46005			0.0892353
$761$	11.5882	+	35.6649i	0.420072	+	1.29285i	0.907634	+	0.419762i	$0.137886\pi$
$761$	11.5882	+	35.6649i	0.420072	+	1.29285i	−0.487562	+	0.873088i	$0.662114\pi$
$762$	−22.6850	−	16.4816i	−0.821790	−	0.597065i
$763$	−8.47876	+	6.16018i	−0.306952	+	0.223013i
$764$	2.20763	−	6.79439i	0.0798692	−	0.245812i
$765$	−2.30630	+	7.09806i	−0.0833844	+	0.256631i
$766$	23.2598	−	16.8992i	0.840411	−	0.610595i
$767$	−21.4041	−	15.5510i	−0.772858	−	0.561514i
$768$	0.649220	+	1.99809i	0.0234267	+	0.0721000i
$769$	0.388213			0.0139993			0.00699965	−	0.999976i	$-0.497772\pi$
$769$	0.388213			0.0139993			0.00699965	+	0.999976i	$0.497772\pi$
$770$	−12.5644	+	21.9512i	−0.452791	+	0.791066i
$771$	2.68368			0.0966505
$772$	−3.73849	−	11.5059i	−0.134551	−	0.414106i
$773$	26.2976	+	19.1063i	0.945860	+	0.687208i	0.949824	−	0.312785i	$-0.101262\pi$
$773$	26.2976	+	19.1063i	0.945860	+	0.687208i	−0.00396401	+	0.999992i	$0.501262\pi$
$774$	5.25563	−	3.81844i	0.188910	−	0.137251i
$775$	0.483113	−	1.48687i	0.0173539	−	0.0534099i
$776$	1.69057	−	5.20305i	0.0606881	−	0.186779i
$777$	−9.21648	+	6.69616i	−0.330639	+	0.240223i
$778$	2.20852	+	1.60458i	0.0791792	+	0.0575271i
$779$	−1.69505	−	5.21682i	−0.0607314	−	0.186912i
$780$	−20.5614			−0.736216
$781$	5.73308	+	52.6538i	0.205146	+	1.88410i
$782$	−5.49187			−0.196389
$783$	−6.69714	−	20.6117i	−0.239336	−	0.736601i
$784$	−2.11130	−	1.53395i	−0.0754034	−	0.0547838i
$785$	−7.41136	+	5.38467i	−0.264523	+	0.192187i
$786$	2.97834	−	9.16640i	0.106234	−	0.326955i
$787$	−3.65334	+	11.2438i	−0.130228	+	0.400799i	−0.994817	−	0.101679i	$-0.967578\pi$
$787$	−3.65334	+	11.2438i	−0.130228	+	0.400799i	0.864590	+	0.502479i	$0.167578\pi$
$788$	−14.7658	+	10.7280i	−0.526012	+	0.382170i
$789$	−15.0574	−	10.9398i	−0.536058	−	0.389469i
$790$	−5.51651	−	16.9781i	−0.196269	−	0.604053i
$791$	−35.2366			−1.25287
$792$	0.507578	+	4.66171i	0.0180360	+	0.165647i
$793$	25.2249			0.895763
$794$	−2.22903	−	6.86026i	−0.0791054	−	0.243461i
$795$	49.1758	+	35.7283i	1.74409	+	1.26715i
$796$	−19.3926	+	14.0895i	−0.687352	+	0.499390i
$797$	8.46847	−	26.0633i	0.299969	−	0.923208i	−0.681538	−	0.731782i	$-0.738689\pi$
$797$	8.46847	−	26.0633i	0.299969	−	0.923208i	0.981507	−	0.191426i	$-0.0613112\pi$
$798$	−2.01255	+	6.19400i	−0.0712435	+	0.219265i
$799$	−5.91327	+	4.29624i	−0.209197	+	0.151990i
$800$	0.850949	+	0.618250i	0.0300856	+	0.0218585i
$801$	−2.02588	−	6.23502i	−0.0715810	−	0.220304i
$802$	1.18981			0.0420137
$803$	5.23306	−	9.14263i	0.184671	−	0.322636i
$804$	29.6554			1.04586
$805$	6.03141	+	18.5628i	0.212579	+	0.654252i
$806$	−4.78386	−	3.47568i	−0.168504	−	0.122425i
$807$	−44.2314	+	32.1360i	−1.55702	+	1.13124i
$808$	1.79382	−	5.52081i	0.0631063	−	0.194221i
$809$	2.85290	−	8.78033i	0.100303	−	0.308700i	−0.888297	−	0.459270i	$-0.848111\pi$
$809$	2.85290	−	8.78033i	0.100303	−	0.308700i	0.988599	+	0.150570i	$0.0481110\pi$
$810$	−22.3752	+	16.2565i	−0.786185	+	0.571197i
$811$	22.9620	+	16.6828i	0.806303	+	0.585814i	0.912756	−	0.408504i	$-0.133949\pi$
$811$	22.9620	+	16.6828i	0.806303	+	0.585814i	−0.106453	+	0.994318i	$0.533949\pi$
$812$	−6.23009	−	19.1743i	−0.218633	−	0.672884i
$813$	35.8892			1.25869
$814$	−5.67917	−	1.18499i	−0.199055	−	0.0415339i
$815$	−48.9353			−1.71413
$816$	−1.39307	−	4.28744i	−0.0487673	−	0.150090i
$817$	3.71721	+	2.70071i	0.130049	+	0.0944859i
$818$	9.52954	−	6.92362i	0.333193	−	0.242079i
$819$	5.38822	−	16.5832i	0.188280	−	0.579465i
$820$	4.16990	−	12.8336i	0.145619	−	0.448170i
$821$	−23.7179	+	17.2321i	−0.827761	+	0.601403i	−0.918925	−	0.394432i	$-0.870941\pi$
$821$	−23.7179	+	17.2321i	−0.827761	+	0.601403i	0.0911641	+	0.995836i	$0.470941\pi$
$822$	−23.1786	−	16.8403i	−0.808448	−	0.587372i
$823$	−5.91914	−	18.2172i	−0.206328	−	0.635013i	−0.999656	−	0.0262187i	$-0.991653\pi$
$823$	−5.91914	−	18.2172i	−0.206328	−	0.635013i	0.793328	−	0.608795i	$-0.208347\pi$
$824$	9.56301			0.333143
$825$	4.92445	+	5.42824i	0.171447	+	0.188987i
$826$	−20.6156			−0.717307
$827$	−5.89089	−	18.1303i	−0.204846	−	0.630452i	−0.999720	−	0.0236766i	$-0.992463\pi$
$827$	−5.89089	−	18.1303i	−0.204846	−	0.630452i	0.794873	−	0.606775i	$-0.207537\pi$
$828$	2.92755	+	2.12699i	0.101739	+	0.0739179i
$829$	2.79451	−	2.03033i	0.0970574	−	0.0705163i	−0.538198	−	0.842818i	$-0.680895\pi$
$829$	2.79451	−	2.03033i	0.0970574	−	0.0705163i	0.635256	+	0.772302i	$0.280895\pi$
$830$	−8.52678	+	26.2427i	−0.295969	+	0.910899i
$831$	5.51452	−	16.9719i	0.191296	−	0.588750i
$832$	3.21853	−	2.33840i	0.111582	−	0.0810694i
$833$	4.53034	+	3.29149i	0.156967	+	0.114043i
$834$	3.75887	+	11.5686i	0.130159	+	0.400588i
$835$	−54.0883			−1.87180
$836$	−3.02483	+	1.36030i	−0.104616	+	0.0470470i
$837$	−4.95302			−0.171202
$838$	−6.20500	−	19.0970i	−0.214348	−	0.659696i
$839$	−13.5883	−	9.87248i	−0.469120	−	0.340836i	0.327978	−	0.944685i	$-0.393633\pi$
$839$	−13.5883	−	9.87248i	−0.469120	−	0.340836i	−0.797098	+	0.603849i	$0.793633\pi$
$840$	−12.9618	+	9.41730i	−0.447225	+	0.324928i
$841$	4.10914	−	12.6466i	0.141695	−	0.436091i
$842$	−0.273536	+	0.841859i	−0.00942669	+	0.0290124i
$843$	−50.0110	+	36.3351i	−1.72247	+	1.25145i
$844$	−16.7844	−	12.1946i	−0.577742	−	0.419754i
$845$	2.14911	+	6.61428i	0.0739316	+	0.227538i
$846$	4.81611			0.165581
$847$	3.31091	−	33.9384i	0.113764	−	1.16614i
$848$	−11.7609			−0.403871
$849$	−11.0750	−	34.0853i	−0.380093	−	1.16981i
$850$	−1.82593	−	1.32662i	−0.0626290	−	0.0455027i
$851$	−3.62192	+	2.63148i	−0.124158	+	0.0902059i
$852$	−10.3678	+	31.9087i	−0.355193	+	1.09317i
$853$	−1.71110	+	5.26623i	−0.0585870	+	0.180312i	−0.976067	−	0.217469i	$-0.930220\pi$
$853$	−1.71110	+	5.26623i	−0.0585870	+	0.180312i	0.917480	+	0.397782i	$0.130220\pi$
$854$	15.9017	−	11.5532i	0.544144	−	0.395343i
$855$	2.81390	+	2.04442i	0.0962334	+	0.0699176i
$856$	4.50124	+	13.8534i	0.153849	+	0.473499i
$857$	26.5793			0.907932			0.453966	−	0.891019i	$-0.350009\pi$
$857$	26.5793			0.907932			0.453966	+	0.891019i	$0.350009\pi$
$858$	25.2819	−	11.3696i	0.863110	−	0.388151i
$859$	19.7426			0.673610			0.336805	−	0.941574i	$-0.390654\pi$
$859$	19.7426			0.673610			0.336805	+	0.941574i	$0.390654\pi$
$860$	3.49289	+	10.7500i	0.119107	+	0.366572i
$861$	28.9016	+	20.9982i	0.984964	+	0.715618i
$862$	−16.4268	+	11.9347i	−0.559498	+	0.406499i
$863$	−7.05846	+	21.7237i	−0.240273	+	0.739484i	0.756105	+	0.654450i	$0.227100\pi$
$863$	−7.05846	+	21.7237i	−0.240273	+	0.739484i	−0.996378	+	0.0850337i	$0.972900\pi$
$864$	1.02975	−	3.16925i	0.0350328	−	0.107820i
$865$	50.7145	−	36.8462i	1.72434	−	1.25281i
$866$	−29.2632	−	21.2609i	−0.994403	−	0.722476i
$867$	−8.04753	−	24.7678i	−0.273309	−	0.841157i
$868$	−4.60761			−0.156392
$869$	16.1712	+	17.8255i	0.548569	+	0.604690i
$870$	−33.6132			−1.13959
$871$	−17.3531	−	53.4072i	−0.587986	−	1.80963i
$872$	−2.73512	−	1.98718i	−0.0926230	−	0.0672946i
$873$	6.25774	−	4.54651i	0.211792	−	0.153876i
$874$	−0.790899	+	2.43414i	−0.0267525	+	0.0823359i
$875$	9.30415	−	28.6352i	0.314538	−	0.968047i
$876$	5.39857	−	3.92229i	0.182401	−	0.132522i
$877$	−31.6495	−	22.9947i	−1.06873	−	0.776476i	−0.0930448	−	0.995662i	$-0.529660\pi$
$877$	−31.6495	−	22.9947i	−1.06873	−	0.776476i	−0.975683	+	0.219186i	$0.929660\pi$
$878$	−6.64121	−	20.4395i	−0.224130	−	0.689801i
$879$	43.0987			1.45368
$880$	−7.98704	−	1.66654i	−0.269243	−	0.0561790i
$881$	39.7517			1.33927			0.669635	−	0.742691i	$-0.266451\pi$
$881$	39.7517			1.33927			0.669635	+	0.742691i	$0.266451\pi$
$882$	−1.14020	−	3.50918i	−0.0383926	−	0.118160i
$883$	19.4987	+	14.1667i	0.656184	+	0.476746i	0.865372	−	0.501130i	$-0.167082\pi$
$883$	19.4987	+	14.1667i	0.656184	+	0.476746i	−0.209188	+	0.977875i	$0.567082\pi$
$884$	−6.90620	+	5.01765i	−0.232281	+	0.168762i
$885$	−10.6212	+	32.6888i	−0.357029	+	1.09882i
$886$	7.60167	−	23.3955i	0.255383	−	0.785989i
$887$	33.1280	−	24.0689i	1.11233	−	0.808154i	0.129300	−	0.991606i	$-0.458727\pi$
$887$	33.1280	−	24.0689i	1.11233	−	0.808154i	0.983029	+	0.183452i	$0.0587270\pi$
$888$	−2.97310	−	2.16009i	−0.0997708	−	0.0724877i
$889$	12.7852	+	39.3489i	0.428803	+	1.31972i
$890$	11.4069			0.382360
$891$	18.5230	−	32.3613i	0.620542	−	1.08414i
$892$	28.3845			0.950384
$893$	1.05262	+	3.23963i	0.0352245	+	0.108410i
$894$	−17.5921	−	12.7814i	−0.588369	−	0.427475i
$895$	−45.3540	+	32.9516i	−1.51602	+	1.10145i
$896$	0.957938	−	2.94823i	0.0320025	−	0.0984935i
$897$	6.61044	−	20.3448i	0.220716	−	0.679294i
$898$	28.5341	−	20.7313i	0.952197	−	0.691812i
$899$	−7.82052	−	5.68194i	−0.260829	−	0.189503i
$900$	0.459553	+	1.41436i	0.0153184	+	0.0471453i
$901$	25.2361			0.840737
$902$	1.96922	+	18.0858i	0.0655679	+	0.602190i
$903$	−29.9243			−0.995818
$904$	−3.51254	−	10.8105i	−0.116825	−	0.359551i
$905$	3.07582	+	2.23471i	0.102244	+	0.0742843i
$906$	−20.6904	+	15.0324i	−0.687391	+	0.499419i
$907$	−16.9648	+	52.2122i	−0.563306	+	1.73368i	0.109624	+	0.993973i	$0.465035\pi$
$907$	−16.9648	+	52.2122i	−0.563306	+	1.73368i	−0.672930	+	0.739706i	$0.734965\pi$
$908$	−2.62860	+	8.09001i	−0.0872332	+	0.268476i
$909$	6.63990	−	4.82417i	0.220232	−	0.160008i
$910$	24.5446	+	17.8327i	0.813646	+	0.591148i
$911$	14.4762	+	44.5531i	0.479617	+	1.47611i	0.839628	+	0.543162i	$0.182773\pi$
$911$	14.4762	+	44.5531i	0.479617	+	1.47611i	−0.360011	+	0.932948i	$0.617227\pi$
$912$	−2.10092			−0.0695684
$913$	−4.02675	−	36.9825i	−0.133266	−	1.22394i
$914$	7.37055			0.243796
$915$	−10.1266	−	31.1666i	−0.334776	−	1.03033i
$916$	1.38124	+	1.00353i	0.0456374	+	0.0331575i
$917$	−11.5052	+	8.35905i	−0.379937	+	0.276040i
$918$	−2.20960	+	6.80046i	−0.0729277	+	0.224448i
$919$	−0.545464	+	1.67876i	−0.0179932	+	0.0553773i	−0.959650	−	0.281197i	$-0.909268\pi$
$919$	−0.545464	+	1.67876i	−0.0179932	+	0.0553773i	0.941657	+	0.336575i	$0.109268\pi$
$920$	−5.09377	+	3.70084i	−0.167937	+	0.122013i
$921$	−9.59644	−	6.97222i	−0.316214	−	0.229743i
$922$	11.2753	+	34.7017i	0.371331	+	1.14284i
$923$	63.5320			2.09118
$924$	10.7302	−	18.7467i	0.352998	−	0.616720i
$925$	−1.83988			−0.0604947
$926$	5.01250	+	15.4269i	0.164721	+	0.506959i
$927$	10.9386	+	7.94733i	0.359269	+	0.261024i
$928$	5.26156	−	3.82275i	0.172719	−	0.125488i
$929$	−8.92707	+	27.4747i	−0.292888	+	0.901416i	0.691035	+	0.722821i	$0.257155\pi$
$929$	−8.92707	+	27.4747i	−0.292888	+	0.901416i	−0.983923	+	0.178595i	$0.942845\pi$
$930$	−2.37386	+	7.30600i	−0.0778421	+	0.239573i
$931$	2.11130	−	1.53395i	0.0691949	−	0.0502731i
$932$	−8.05483	−	5.85218i	−0.263845	−	0.191694i
$933$	5.46392	+	16.8162i	0.178881	+	0.550538i
$934$	−4.27354			−0.139835
$935$	17.1383	+	3.57600i	0.560482	+	0.116948i
$936$	5.62481			0.183853
$937$	7.77009	+	23.9139i	0.253838	+	0.781232i	0.994056	+	0.108866i	$0.0347219\pi$
$937$	7.77009	+	23.9139i	0.253838	+	0.781232i	−0.740219	+	0.672366i	$0.765278\pi$
$938$	−35.4003	−	25.7198i	−1.15586	−	0.839781i
$939$	−53.3302	+	38.7467i	−1.74037	+	1.26445i
$940$	−2.58949	+	7.96963i	−0.0844598	+	0.259941i
$941$	−0.230113	+	0.708216i	−0.00750148	+	0.0230872i	−0.954737	−	0.297451i	$-0.903864\pi$
$941$	−0.230113	+	0.708216i	−0.00750148	+	0.0230872i	0.947236	+	0.320538i	$0.103864\pi$
$942$	6.32942	−	4.59859i	0.206224	−	0.149830i
$943$	11.3578	+	8.25195i	0.369862	+	0.268721i
$944$	−2.05505	−	6.32479i	−0.0668862	−	0.205854i
$945$	25.4125			0.826670
$946$	−10.2391	−	11.2866i	−0.332902	−	0.366959i
$947$	54.6088			1.77455			0.887273	−	0.461244i	$-0.152597\pi$
$947$	54.6088			1.77455			0.887273	+	0.461244i	$0.152597\pi$
$948$	4.71119	+	14.4996i	0.153012	+	0.470924i
$949$	−10.2228	−	7.42729i	−0.331846	−	0.241100i
$950$	−0.850949	+	0.618250i	−0.0276084	+	0.0200587i
$951$	4.67626	−	14.3921i	0.151638	−	0.466694i
$952$	−2.05551	+	6.32620i	−0.0666194	+	0.205033i
$953$	−23.8404	+	17.3211i	−0.772267	+	0.561085i	−0.902648	−	0.430379i	$-0.858380\pi$
$953$	−23.8404	+	17.3211i	−0.772267	+	0.561085i	0.130381	+	0.991464i	$0.458380\pi$
$954$	−13.4526	−	9.77389i	−0.435544	−	0.316441i
$955$	5.43087	+	16.7145i	0.175739	+	0.540869i
$956$	16.2786			0.526487
$957$	41.3302	−	18.5867i	1.33601	−	0.600822i
$958$	39.1936			1.26629
$959$	13.0635	+	40.2052i	0.421841	+	1.29829i
$960$	−4.18129	−	3.03789i	−0.134951	−	0.0980474i
$961$	23.2922	−	16.9228i	0.751362	−	0.545896i
$962$	−2.15043	+	6.61834i	−0.0693326	+	0.213384i
$963$	−6.36415	+	19.5868i	−0.205082	+	0.631177i
$964$	4.81482	−	3.49817i	0.155075	−	0.112668i
$965$	24.0777	+	17.4935i	0.775088	+	0.563134i
$966$	−5.15093	−	15.8529i	−0.165728	−	0.510059i
$967$	−30.8647			−0.992541			−0.496271	−	0.868168i	$-0.665298\pi$
$967$	−30.8647			−0.992541			−0.496271	+	0.868168i	$0.665298\pi$
$968$	10.7422	−	2.36735i	0.345269	−	0.0760895i
$969$	4.50808			0.144820
$970$	4.15889	+	12.7997i	0.133534	+	0.410975i
$971$	8.76140	+	6.36553i	0.281167	+	0.204280i	0.719426	−	0.694569i	$-0.244405\pi$
$971$	8.76140	+	6.36553i	0.281167	+	0.204280i	−0.438259	+	0.898849i	$0.644405\pi$
$972$	11.0210	−	8.00724i	0.353499	−	0.256832i
$973$	5.54629	−	17.0697i	0.177806	−	0.547231i
$974$	−1.01184	+	3.11412i	−0.0324214	+	0.0997829i
$975$	7.11234	−	5.16742i	0.227777	−	0.165490i
$976$	5.12965	+	3.72691i	0.164196	+	0.119295i
$977$	1.70953	+	5.26138i	0.0546926	+	0.168327i	0.974672	−	0.223641i	$-0.0717944\pi$
$977$	1.70953	+	5.26138i	0.0546926	+	0.168327i	−0.919979	+	0.391968i	$0.871794\pi$
$978$	41.7916			1.33635
$979$	−14.0257	+	6.30753i	−0.448263	+	0.201589i
$980$	6.42000			0.205079
$981$	−1.47710	−	4.54604i	−0.0471601	−	0.145144i
$982$	32.8868	+	23.8936i	1.04946	+	0.762476i
$983$	−17.9985	+	13.0767i	−0.574065	+	0.417082i	−0.836579	−	0.547846i	$-0.815448\pi$
$983$	−17.9985	+	13.0767i	−0.574065	+	0.417082i	0.262515	+	0.964928i	$0.415448\pi$
$984$	−3.56116	+	10.9601i	−0.113526	+	0.349396i
$985$	13.8748	−	42.7022i	0.442088	−	1.36061i
$986$	−11.2901	+	8.20272i	−0.359549	+	0.261228i
$987$	−17.9478	−	13.0398i	−0.571284	−	0.415062i
$988$	1.22937	+	3.78361i	0.0391114	+	0.120373i
$989$	−11.7597			−0.373938
$990$	−7.75092	−	8.54387i	−0.246340	−	0.271542i
$991$	−8.28887			−0.263305			−0.131652	−	0.991296i	$-0.542028\pi$
$991$	−8.28887			−0.263305			−0.131652	+	0.991296i	$0.542028\pi$
$992$	−0.459307	−	1.41360i	−0.0145830	−	0.0448819i
$993$	−34.6875	−	25.2020i	−1.10078	−	0.799760i
$994$	40.0503	−	29.0982i	1.27032	−	0.922940i
$995$	18.2223	−	56.0825i	0.577686	−	1.77794i
$996$	7.28201	−	22.4117i	0.230739	−	0.710143i
$997$	22.2912	−	16.1955i	0.705968	−	0.512916i	−0.175903	−	0.984408i	$-0.556284\pi$
$997$	22.2912	−	16.1955i	0.705968	−	0.512916i	0.881870	+	0.471492i	$0.156284\pi$
$998$	−11.4431	−	8.31393i	−0.362226	−	0.263173i
$999$	1.80125	+	5.54369i	0.0569891	+	0.175395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.h.115.2	✓	20
11.3	even	5		4598.2.a.cc.1.8		10
11.8	odd	10		4598.2.a.cd.1.8		10
11.9	even	5	inner	418.2.f.h.229.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.2	✓	20	1.1	even	1	trivial
418.2.f.h.229.2	yes	20	11.9	even	5	inner
4598.2.a.cc.1.8		10	11.3	even	5
4598.2.a.cd.1.8		10	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.69968 - 1.23489i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.760196 - 2.33964i) q^{5} +(-0.649220 + 1.99809i) q^{6} +(2.50791 - 1.82211i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.436908 + 1.34467i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.69968 - 1.23489i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.760196 - 2.33964i) q^{5} +(-0.649220 + 1.99809i) q^{6} +(2.50791 - 1.82211i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.436908 + 1.34467i) q^{9} -2.46005 q^{10} +(3.02483 - 1.36030i) q^{11} +2.10092 q^{12} +(-1.22937 - 3.78361i) q^{13} +(-2.50791 - 1.82211i) q^{14} +(-4.18129 + 3.03789i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.663077 + 2.04074i) q^{17} +(1.14384 - 0.831049i) q^{18} +(0.809017 + 0.587785i) q^{19} +(0.760196 + 2.33964i) q^{20} -6.51275 q^{21} +(-2.22845 - 2.45643i) q^{22} -2.55940 q^{23} +(-0.649220 - 1.99809i) q^{24} +(-0.850949 - 0.618250i) q^{25} +(-3.21853 + 2.33840i) q^{26} +(-1.02975 + 3.16925i) q^{27} +(-0.957938 + 2.94823i) q^{28} +(-5.26156 + 3.82275i) q^{29} +(4.18129 + 3.03789i) q^{30} +(0.459307 + 1.41360i) q^{31} -1.00000 q^{32} +(-6.82106 - 1.42325i) q^{33} +2.14576 q^{34} +(-2.35657 - 7.25278i) q^{35} +(-1.14384 - 0.831049i) q^{36} +(1.41514 - 1.02816i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-2.58281 + 7.94906i) q^{39} +(1.99022 - 1.44598i) q^{40} +(-4.43769 - 3.22417i) q^{41} +(2.01255 + 6.19400i) q^{42} +4.59472 q^{43} +(-1.64757 + 2.87846i) q^{44} +3.47817 q^{45} +(0.790899 + 2.43414i) q^{46} +(2.75579 + 2.00220i) q^{47} +(-1.69968 + 1.23489i) q^{48} +(0.806443 - 2.48198i) q^{49} +(-0.325033 + 1.00035i) q^{50} +(3.64711 - 2.64978i) q^{51} +(3.21853 + 2.33840i) q^{52} +(-3.63432 - 11.1853i) q^{53} +3.33234 q^{54} +(-0.883158 - 8.11111i) q^{55} +3.09995 q^{56} +(-0.649220 - 1.99809i) q^{57} +(5.26156 + 3.82275i) q^{58} +(5.38019 - 3.90894i) q^{59} +(1.59711 - 4.91540i) q^{60} +(-1.95935 + 6.03026i) q^{61} +(1.20248 - 0.873654i) q^{62} +(3.54585 + 2.57621i) q^{63} +(0.309017 + 0.951057i) q^{64} -9.78686 q^{65} +(0.754232 + 6.92702i) q^{66} +14.1154 q^{67} +(-0.663077 - 2.04074i) q^{68} +(4.35016 + 3.16058i) q^{69} +(-6.16959 + 4.48247i) q^{70} +(-4.93486 + 15.1879i) q^{71} +(-0.436908 + 1.34467i) q^{72} +(2.56962 - 1.86694i) q^{73} +(-1.41514 - 1.02816i) q^{74} +(0.682869 + 2.10166i) q^{75} -1.00000 q^{76} +(5.10739 - 8.92308i) q^{77} +8.35814 q^{78} +(2.24244 + 6.90153i) q^{79} +(-1.99022 - 1.44598i) q^{80} +(9.09544 - 6.60822i) q^{81} +(-1.69505 + 5.21682i) q^{82} +(3.46611 - 10.6676i) q^{83} +(5.26893 - 3.82810i) q^{84} +(4.27054 + 3.10273i) q^{85} +(-1.41985 - 4.36984i) q^{86} +13.6636 q^{87} +(3.24670 + 0.677442i) q^{88} -4.63686 q^{89} +(-1.07481 - 3.30794i) q^{90} +(-9.97729 - 7.24893i) q^{91} +(2.07060 - 1.50438i) q^{92} +(0.964967 - 2.96986i) q^{93} +(1.05262 - 3.23963i) q^{94} +(1.99022 - 1.44598i) q^{95} +(1.69968 + 1.23489i) q^{96} +(-1.69057 - 5.20305i) q^{97} -2.60971 q^{98} +(3.15072 + 3.47305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

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