LMFDB - Embedded newform 418.2.f.a.191.1

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:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.a.267.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.00000 + 3.07768i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.11803 + 2.26538i) q^{5} +(2.61803 - 1.90211i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.00000 + 3.07768i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.11803 + 2.26538i) q^{5} +(2.61803 - 1.90211i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +3.85410 q^{10} +(-0.309017 + 3.30220i) q^{11} -3.23607 q^{12} +(3.23607 + 2.35114i) q^{13} +(-1.19098 + 3.66547i) q^{14} +(-3.85410 - 11.8617i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.30902 + 0.951057i) q^{17} +(2.30902 + 7.10642i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-3.11803 - 2.26538i) q^{20} +12.4721 q^{21} +(2.19098 - 2.48990i) q^{22} +0.854102 q^{23} +(2.61803 + 1.90211i) q^{24} +(3.04508 - 9.37181i) q^{25} +(-1.23607 - 3.80423i) q^{26} +(11.7082 - 8.50651i) q^{27} +(3.11803 - 2.26538i) q^{28} +(-1.76393 - 5.42882i) q^{29} +(-3.85410 + 11.8617i) q^{30} +(2.23607 + 1.62460i) q^{31} +1.00000 q^{32} +(-9.85410 - 4.25325i) q^{33} +1.61803 q^{34} +(12.0172 + 8.73102i) q^{35} +(2.30902 - 7.10642i) q^{36} +(-1.00000 - 3.07768i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-10.4721 + 7.60845i) q^{39} +(1.19098 + 3.66547i) q^{40} +(0.145898 - 0.449028i) q^{41} +(-10.0902 - 7.33094i) q^{42} -7.61803 q^{43} +(-3.23607 + 0.726543i) q^{44} +28.7984 q^{45} +(-0.690983 - 0.502029i) q^{46} +(-0.263932 + 0.812299i) q^{47} +(-1.00000 - 3.07768i) q^{48} +(-6.35410 + 4.61653i) q^{49} +(-7.97214 + 5.79210i) q^{50} +(-1.61803 - 4.97980i) q^{51} +(-1.23607 + 3.80423i) q^{52} +(-9.09017 - 6.60440i) q^{53} -14.4721 q^{54} +(-6.51722 - 10.9964i) q^{55} -3.85410 q^{56} +(2.61803 + 1.90211i) q^{57} +(-1.76393 + 5.42882i) q^{58} +(2.14590 + 6.60440i) q^{59} +(10.0902 - 7.33094i) q^{60} +(0.927051 - 0.673542i) q^{61} +(-0.854102 - 2.62866i) q^{62} +(-8.89919 + 27.3889i) q^{63} +(-0.809017 - 0.587785i) q^{64} -15.4164 q^{65} +(5.47214 + 9.23305i) q^{66} -9.23607 q^{67} +(-1.30902 - 0.951057i) q^{68} +(-0.854102 + 2.62866i) q^{69} +(-4.59017 - 14.1271i) q^{70} +(2.23607 - 1.62460i) q^{71} +(-6.04508 + 4.39201i) q^{72} +(-3.38197 - 10.4086i) q^{73} +(-1.00000 + 3.07768i) q^{74} +(25.7984 + 18.7436i) q^{75} +1.00000 q^{76} +(12.4721 - 2.80017i) q^{77} +12.9443 q^{78} +(7.47214 + 5.42882i) q^{79} +(1.19098 - 3.66547i) q^{80} +(7.54508 + 23.2214i) q^{81} +(-0.381966 + 0.277515i) q^{82} +(-1.73607 + 1.26133i) q^{83} +(3.85410 + 11.8617i) q^{84} +(1.92705 - 5.93085i) q^{85} +(6.16312 + 4.47777i) q^{86} +18.4721 q^{87} +(3.04508 + 1.31433i) q^{88} -14.1803 q^{89} +(-23.2984 - 16.9273i) q^{90} +(4.76393 - 14.6619i) q^{91} +(0.263932 + 0.812299i) q^{92} +(-7.23607 + 5.25731i) q^{93} +(0.690983 - 0.502029i) q^{94} +(1.19098 + 3.66547i) q^{95} +(-1.00000 + 3.07768i) q^{96} +(-13.7082 - 9.95959i) q^{97} +7.85410 q^{98} +(16.3713 - 18.6049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} - q^{4} - 8 q^{5} + 6 q^{6} - 7 q^{7} - q^{8} - 13 q^{9}+O(q^{10}) $ 4 * q - q^2 - 4 * q^3 - q^4 - 8 * q^5 + 6 * q^6 - 7 * q^7 - q^8 - 13 * q^9	\( 4 q - q^{2} - 4 q^{3} - q^{4} - 8 q^{5} + 6 q^{6} - 7 q^{7} - q^{8} - 13 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 4 q^{13} - 7 q^{14} - 2 q^{15} - q^{16} - 3 q^{17} + 7 q^{18} - q^{19} - 8 q^{20} + 32 q^{21} + 11 q^{22} - 10 q^{23} + 6 q^{24} + q^{25} + 4 q^{26} + 20 q^{27} + 8 q^{28} - 16 q^{29} - 2 q^{30} + 4 q^{32} - 26 q^{33} + 2 q^{34} + 19 q^{35} + 7 q^{36} - 4 q^{37} - q^{38} - 24 q^{39} + 7 q^{40} + 14 q^{41} - 18 q^{42} - 26 q^{43} - 4 q^{44} + 66 q^{45} - 5 q^{46} - 10 q^{47} - 4 q^{48} - 12 q^{49} - 14 q^{50} - 2 q^{51} + 4 q^{52} - 14 q^{53} - 40 q^{54} + 3 q^{55} - 2 q^{56} + 6 q^{57} - 16 q^{58} + 22 q^{59} + 18 q^{60} - 3 q^{61} + 10 q^{62} - 11 q^{63} - q^{64} - 8 q^{65} + 4 q^{66} - 28 q^{67} - 3 q^{68} + 10 q^{69} + 4 q^{70} - 13 q^{72} - 18 q^{73} - 4 q^{74} + 54 q^{75} + 4 q^{76} + 32 q^{77} + 16 q^{78} + 12 q^{79} + 7 q^{80} + 19 q^{81} - 6 q^{82} + 2 q^{83} + 2 q^{84} + q^{85} + 9 q^{86} + 56 q^{87} + q^{88} - 12 q^{89} - 44 q^{90} + 28 q^{91} + 10 q^{92} - 20 q^{93} + 5 q^{94} + 7 q^{95} - 4 q^{96} - 28 q^{97} + 18 q^{98} + 23 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 - q^4 - 8 * q^5 + 6 * q^6 - 7 * q^7 - q^8 - 13 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 4 * q^13 - 7 * q^14 - 2 * q^15 - q^16 - 3 * q^17 + 7 * q^18 - q^19 - 8 * q^20 + 32 * q^21 + 11 * q^22 - 10 * q^23 + 6 * q^24 + q^25 + 4 * q^26 + 20 * q^27 + 8 * q^28 - 16 * q^29 - 2 * q^30 + 4 * q^32 - 26 * q^33 + 2 * q^34 + 19 * q^35 + 7 * q^36 - 4 * q^37 - q^38 - 24 * q^39 + 7 * q^40 + 14 * q^41 - 18 * q^42 - 26 * q^43 - 4 * q^44 + 66 * q^45 - 5 * q^46 - 10 * q^47 - 4 * q^48 - 12 * q^49 - 14 * q^50 - 2 * q^51 + 4 * q^52 - 14 * q^53 - 40 * q^54 + 3 * q^55 - 2 * q^56 + 6 * q^57 - 16 * q^58 + 22 * q^59 + 18 * q^60 - 3 * q^61 + 10 * q^62 - 11 * q^63 - q^64 - 8 * q^65 + 4 * q^66 - 28 * q^67 - 3 * q^68 + 10 * q^69 + 4 * q^70 - 13 * q^72 - 18 * q^73 - 4 * q^74 + 54 * q^75 + 4 * q^76 + 32 * q^77 + 16 * q^78 + 12 * q^79 + 7 * q^80 + 19 * q^81 - 6 * q^82 + 2 * q^83 + 2 * q^84 + q^85 + 9 * q^86 + 56 * q^87 + q^88 - 12 * q^89 - 44 * q^90 + 28 * q^91 + 10 * q^92 - 20 * q^93 + 5 * q^94 + 7 * q^95 - 4 * q^96 - 28 * q^97 + 18 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.00000	+	3.07768i	−0.577350	+	1.77690i	0.0506828	+	0.998715i	$0.483860\pi$
$3$	−1.00000	+	3.07768i	−0.577350	+	1.77690i	−0.628033	+	0.778187i	$0.716140\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−3.11803	+	2.26538i	−1.39443	+	1.01311i	−0.399064	+	0.916923i	$0.630665\pi$
$5$	−3.11803	+	2.26538i	−1.39443	+	1.01311i	−0.995363	+	0.0961876i	$0.969335\pi$
$6$	2.61803	−	1.90211i	1.06881	−	0.776534i
$7$	−1.19098	−	3.66547i	−0.450149	−	1.38542i	−0.876737	−	0.480971i	$-0.840284\pi$
$7$	−1.19098	−	3.66547i	−0.450149	−	1.38542i	0.426587	−	0.904446i	$-0.359716\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−6.04508	−	4.39201i	−2.01503	−	1.46400i
$10$	3.85410			1.21877
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$12$	−3.23607			−0.934172
$13$	3.23607	+	2.35114i	0.897524	+	0.652089i	0.937829	−	0.347098i	$-0.112833\pi$
$13$	3.23607	+	2.35114i	0.897524	+	0.652089i	−0.0403050	+	0.999187i	$0.512833\pi$
$14$	−1.19098	+	3.66547i	−0.318304	+	0.979638i
$15$	−3.85410	−	11.8617i	−0.995125	−	3.06268i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.30902	+	0.951057i	−0.317483	+	0.230665i	−0.735101	−	0.677958i	$-0.762865\pi$
$17$	−1.30902	+	0.951057i	−0.317483	+	0.230665i	0.417618	+	0.908623i	$0.362865\pi$
$18$	2.30902	+	7.10642i	0.544241	+	1.67500i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−3.11803	−	2.26538i	−0.697214	−	0.506555i
$21$	12.4721			2.72164
$22$	2.19098	−	2.48990i	0.467119	−	0.530848i
$23$	0.854102			0.178093			0.0890463	−	0.996027i	$-0.471618\pi$
$23$	0.854102			0.178093			0.0890463	+	0.996027i	$0.471618\pi$
$24$	2.61803	+	1.90211i	0.534404	+	0.388267i
$25$	3.04508	−	9.37181i	0.609017	−	1.87436i
$26$	−1.23607	−	3.80423i	−0.242413	−	0.746070i
$27$	11.7082	−	8.50651i	2.25324	−	1.63708i
$28$	3.11803	−	2.26538i	0.589253	−	0.428117i
$29$	−1.76393	−	5.42882i	−0.327554	−	1.00811i	−0.970275	−	0.242007i	$-0.922194\pi$
$29$	−1.76393	−	5.42882i	−0.327554	−	1.00811i	0.642721	−	0.766101i	$-0.277806\pi$
$30$	−3.85410	+	11.8617i	−0.703660	+	2.16564i
$31$	2.23607	+	1.62460i	0.401610	+	0.291787i	0.770196	−	0.637807i	$-0.220158\pi$
$31$	2.23607	+	1.62460i	0.401610	+	0.291787i	−0.368587	+	0.929593i	$0.620158\pi$
$32$	1.00000			0.176777
$33$	−9.85410	−	4.25325i	−1.71538	−	0.740396i
$34$	1.61803			0.277491
$35$	12.0172	+	8.73102i	2.03128	+	1.47581i
$36$	2.30902	−	7.10642i	0.384836	−	1.18440i
$37$	−1.00000	−	3.07768i	−0.164399	−	0.505968i	0.834593	−	0.550868i	$-0.185703\pi$
$37$	−1.00000	−	3.07768i	−0.164399	−	0.505968i	−0.998991	+	0.0448998i	$0.985703\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	−10.4721	+	7.60845i	−1.67688	+	1.21833i
$40$	1.19098	+	3.66547i	0.188311	+	0.579562i
$41$	0.145898	−	0.449028i	0.0227854	−	0.0701264i	−0.939017	−	0.343870i	$-0.888262\pi$
$41$	0.145898	−	0.449028i	0.0227854	−	0.0701264i	0.961803	+	0.273744i	$0.0882620\pi$
$42$	−10.0902	−	7.33094i	−1.55695	−	1.13119i
$43$	−7.61803			−1.16174			−0.580870	−	0.813997i	$-0.697287\pi$
$43$	−7.61803			−1.16174			−0.580870	+	0.813997i	$0.697287\pi$
$44$	−3.23607	+	0.726543i	−0.487856	+	0.109530i
$45$	28.7984			4.29301
$46$	−0.690983	−	0.502029i	−0.101880	−	0.0740201i
$47$	−0.263932	+	0.812299i	−0.0384984	+	0.118486i	−0.968459	−	0.249174i	$-0.919841\pi$
$47$	−0.263932	+	0.812299i	−0.0384984	+	0.118486i	0.929960	+	0.367660i	$0.119841\pi$
$48$	−1.00000	−	3.07768i	−0.144338	−	0.444225i
$49$	−6.35410	+	4.61653i	−0.907729	+	0.659504i
$50$	−7.97214	+	5.79210i	−1.12743	+	0.819126i
$51$	−1.61803	−	4.97980i	−0.226570	−	0.697311i
$52$	−1.23607	+	3.80423i	−0.171412	+	0.527551i
$53$	−9.09017	−	6.60440i	−1.24863	−	0.907183i	−0.250489	−	0.968119i	$-0.580591\pi$
$53$	−9.09017	−	6.60440i	−1.24863	−	0.907183i	−0.998142	+	0.0609360i	$0.980591\pi$
$54$	−14.4721			−1.96941
$55$	−6.51722	−	10.9964i	−0.878782	−	1.48276i
$56$	−3.85410			−0.515026
$57$	2.61803	+	1.90211i	0.346767	+	0.251941i
$58$	−1.76393	+	5.42882i	−0.231616	+	0.712840i
$59$	2.14590	+	6.60440i	0.279372	+	0.859819i	0.988029	+	0.154266i	$0.0493013\pi$
$59$	2.14590	+	6.60440i	0.279372	+	0.859819i	−0.708657	+	0.705553i	$0.750699\pi$
$60$	10.0902	−	7.33094i	1.30264	−	0.946420i
$61$	0.927051	−	0.673542i	0.118697	−	0.0862382i	−0.526853	−	0.849956i	$-0.676628\pi$
$61$	0.927051	−	0.673542i	0.118697	−	0.0862382i	0.645550	+	0.763718i	$0.276628\pi$
$62$	−0.854102	−	2.62866i	−0.108471	−	0.333840i
$63$	−8.89919	+	27.3889i	−1.12119	+	3.45067i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−15.4164			−1.91217
$66$	5.47214	+	9.23305i	0.673573	+	1.13651i
$67$	−9.23607			−1.12837			−0.564183	−	0.825650i	$-0.690809\pi$
$67$	−9.23607			−1.12837			−0.564183	+	0.825650i	$0.690809\pi$
$68$	−1.30902	−	0.951057i	−0.158742	−	0.115333i
$69$	−0.854102	+	2.62866i	−0.102822	+	0.316453i
$70$	−4.59017	−	14.1271i	−0.548630	−	1.68851i
$71$	2.23607	−	1.62460i	0.265372	−	0.192804i	−0.447140	−	0.894464i	$-0.647557\pi$
$71$	2.23607	−	1.62460i	0.265372	−	0.192804i	0.712512	+	0.701660i	$0.247557\pi$
$72$	−6.04508	+	4.39201i	−0.712420	+	0.517603i
$73$	−3.38197	−	10.4086i	−0.395829	−	1.21824i	−0.928314	−	0.371797i	$-0.878742\pi$
$73$	−3.38197	−	10.4086i	−0.395829	−	1.21824i	0.532485	−	0.846440i	$-0.321258\pi$
$74$	−1.00000	+	3.07768i	−0.116248	+	0.357773i
$75$	25.7984	+	18.7436i	2.97894	+	2.16433i
$76$	1.00000			0.114708
$77$	12.4721	−	2.80017i	1.42133	−	0.319109i
$78$	12.9443			1.46565
$79$	7.47214	+	5.42882i	0.840681	+	0.610790i	0.922561	−	0.385852i	$-0.126092\pi$
$79$	7.47214	+	5.42882i	0.840681	+	0.610790i	−0.0818798	+	0.996642i	$0.526092\pi$
$80$	1.19098	−	3.66547i	0.133156	−	0.409812i
$81$	7.54508	+	23.2214i	0.838343	+	2.58015i
$82$	−0.381966	+	0.277515i	−0.0421811	+	0.0306464i
$83$	−1.73607	+	1.26133i	−0.190558	+	0.138449i	−0.678974	−	0.734162i	$-0.737575\pi$
$83$	−1.73607	+	1.26133i	−0.190558	+	0.138449i	0.488416	+	0.872611i	$0.337575\pi$
$84$	3.85410	+	11.8617i	0.420517	+	1.29422i
$85$	1.92705	−	5.93085i	0.209018	−	0.643291i
$86$	6.16312	+	4.47777i	0.664586	+	0.482850i
$87$	18.4721			1.98042
$88$	3.04508	+	1.31433i	0.324607	+	0.140108i
$89$	−14.1803			−1.50311			−0.751557	−	0.659669i	$-0.770697\pi$
$89$	−14.1803			−1.50311			−0.751557	+	0.659669i	$0.770697\pi$
$90$	−23.2984	−	16.9273i	−2.45586	−	1.78429i
$91$	4.76393	−	14.6619i	0.499396	−	1.53698i
$92$	0.263932	+	0.812299i	0.0275168	+	0.0846881i
$93$	−7.23607	+	5.25731i	−0.750345	+	0.545158i
$94$	0.690983	−	0.502029i	0.0712695	−	0.0517803i
$95$	1.19098	+	3.66547i	0.122192	+	0.376069i
$96$	−1.00000	+	3.07768i	−0.102062	+	0.314115i
$97$	−13.7082	−	9.95959i	−1.39186	−	1.01124i	−0.995659	−	0.0930786i	$-0.970329\pi$
$97$	−13.7082	−	9.95959i	−1.39186	−	1.01124i	−0.396198	−	0.918165i	$-0.629671\pi$
$98$	7.85410			0.793384
$99$	16.3713	−	18.6049i	1.64538	−	1.86986i
$100$	9.85410			0.985410
$101$	−2.88197	−	2.09387i	−0.286766	−	0.208348i	0.435097	−	0.900384i	$-0.356714\pi$
$101$	−2.88197	−	2.09387i	−0.286766	−	0.208348i	−0.721863	+	0.692036i	$0.756714\pi$
$102$	−1.61803	+	4.97980i	−0.160209	+	0.493073i
$103$	−2.14590	−	6.60440i	−0.211442	−	0.650750i	−0.999387	−	0.0350054i	$-0.988855\pi$
$103$	−2.14590	−	6.60440i	−0.211442	−	0.650750i	0.787946	−	0.615745i	$-0.211145\pi$
$104$	3.23607	−	2.35114i	0.317323	−	0.230548i
$105$	−38.8885	+	28.2542i	−3.79513	+	2.75733i
$106$	3.47214	+	10.6861i	0.337244	+	1.03793i
$107$	−0.763932	+	2.35114i	−0.0738521	+	0.227293i	−0.981168	−	0.193156i	$-0.938128\pi$
$107$	−0.763932	+	2.35114i	−0.0738521	+	0.227293i	0.907316	+	0.420450i	$0.138128\pi$
$108$	11.7082	+	8.50651i	1.12662	+	0.818539i
$109$	0.944272			0.0904448			0.0452224	−	0.998977i	$-0.485600\pi$
$109$	0.944272			0.0904448			0.0452224	+	0.998977i	$0.485600\pi$
$110$	−1.19098	+	12.7270i	−0.113556	+	1.21347i
$111$	10.4721			0.993971
$112$	3.11803	+	2.26538i	0.294627	+	0.214059i
$113$	−2.32624	+	7.15942i	−0.218834	+	0.673502i	0.780025	+	0.625748i	$0.215206\pi$
$113$	−2.32624	+	7.15942i	−0.218834	+	0.673502i	−0.998859	+	0.0477537i	$0.984794\pi$
$114$	−1.00000	−	3.07768i	−0.0936586	−	0.288251i
$115$	−2.66312	+	1.93487i	−0.248337	+	0.180427i
$116$	4.61803	−	3.35520i	0.428774	−	0.311522i
$117$	−9.23607	−	28.4257i	−0.853875	−	2.62796i
$118$	2.14590	−	6.60440i	0.197546	−	0.607984i
$119$	5.04508	+	3.66547i	0.462482	+	0.336013i
$120$	−12.4721			−1.13855
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	−1.14590			−0.103745
$123$	1.23607	+	0.898056i	0.111452	+	0.0809750i
$124$	−0.854102	+	2.62866i	−0.0767006	+	0.236060i
$125$	5.78115	+	17.7926i	0.517082	+	1.59141i
$126$	23.2984	−	16.9273i	2.07558	−	1.50800i
$127$	1.85410	−	1.34708i	0.164525	−	0.119534i	−0.502476	−	0.864591i	$-0.667578\pi$
$127$	1.85410	−	1.34708i	0.164525	−	0.119534i	0.667001	+	0.745057i	$0.267578\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	7.61803	−	23.4459i	0.670730	−	2.06430i
$130$	12.4721	+	9.06154i	1.09388	+	0.794749i
$131$	13.8541			1.21044			0.605219	−	0.796059i	$-0.293085\pi$
$131$	13.8541			1.21044			0.605219	+	0.796059i	$0.293085\pi$
$132$	1.00000	−	10.6861i	0.0870388	−	0.930109i
$133$	−3.85410			−0.334193
$134$	7.47214	+	5.42882i	0.645494	+	0.468979i
$135$	−17.2361	+	53.0472i	−1.48344	+	4.56557i
$136$	0.500000	+	1.53884i	0.0428746	+	0.131955i
$137$	7.73607	−	5.62058i	0.660937	−	0.480199i	−0.206042	−	0.978543i	$-0.566058\pi$
$137$	7.73607	−	5.62058i	0.660937	−	0.480199i	0.866979	+	0.498344i	$0.166058\pi$
$138$	2.23607	−	1.62460i	0.190347	−	0.138295i
$139$	4.35410	+	13.4005i	0.369310	+	1.13662i	0.947238	+	0.320532i	$0.103862\pi$
$139$	4.35410	+	13.4005i	0.369310	+	1.13662i	−0.577928	+	0.816088i	$0.696138\pi$
$140$	−4.59017	+	14.1271i	−0.387940	+	1.19396i
$141$	−2.23607	−	1.62460i	−0.188311	−	0.136816i
$142$	−2.76393			−0.231944
$143$	−8.76393	+	9.95959i	−0.732877	+	0.832863i
$144$	7.47214			0.622678
$145$	17.7984	+	12.9313i	1.47807	+	1.07388i
$146$	−3.38197	+	10.4086i	−0.279893	+	0.861424i
$147$	−7.85410	−	24.1724i	−0.647795	−	1.99371i
$148$	2.61803	−	1.90211i	0.215201	−	0.156353i
$149$	2.85410	−	2.07363i	0.233817	−	0.169878i	−0.464707	−	0.885464i	$-0.653840\pi$
$149$	2.85410	−	2.07363i	0.233817	−	0.169878i	0.698524	+	0.715586i	$0.253840\pi$
$150$	−9.85410	−	30.3278i	−0.804584	−	2.47626i
$151$	−3.32624	+	10.2371i	−0.270685	+	0.833084i	0.719643	+	0.694344i	$0.244305\pi$
$151$	−3.32624	+	10.2371i	−0.270685	+	0.833084i	−0.990329	+	0.138740i	$0.955695\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	12.0902			0.977432
$154$	−11.7361	−	5.06555i	−0.945719	−	0.408194i
$155$	−10.6525			−0.855627
$156$	−10.4721	−	7.60845i	−0.838442	−	0.609164i
$157$	−6.89919	+	21.2335i	−0.550615	+	1.69462i	0.156636	+	0.987656i	$0.449935\pi$
$157$	−6.89919	+	21.2335i	−0.550615	+	1.69462i	−0.707251	+	0.706963i	$0.750065\pi$
$158$	−2.85410	−	8.78402i	−0.227060	−	0.698819i
$159$	29.4164	−	21.3723i	2.33287	−	1.69493i
$160$	−3.11803	+	2.26538i	−0.246502	+	0.179094i
$161$	−1.01722	−	3.13068i	−0.0801682	−	0.246732i
$162$	7.54508	−	23.2214i	0.592798	−	1.82444i
$163$	−13.9721	−	10.1514i	−1.09438	−	0.795115i	−0.114248	−	0.993452i	$-0.536446\pi$
$163$	−13.9721	−	10.1514i	−1.09438	−	0.795115i	−0.980134	+	0.198337i	$0.936446\pi$
$164$	0.472136			0.0368676
$165$	40.3607	−	9.06154i	3.14207	−	0.705440i
$166$	2.14590			0.166554
$167$	−5.09017	−	3.69822i	−0.393889	−	0.286177i	0.373158	−	0.927768i	$-0.378275\pi$
$167$	−5.09017	−	3.69822i	−0.393889	−	0.286177i	−0.767047	+	0.641591i	$0.778275\pi$
$168$	3.85410	−	11.8617i	0.297350	−	0.915150i
$169$	0.927051	+	2.85317i	0.0713116	+	0.219475i
$170$	−5.04508	+	3.66547i	−0.386940	+	0.281129i
$171$	−6.04508	+	4.39201i	−0.462279	+	0.335865i
$172$	−2.35410	−	7.24518i	−0.179499	−	0.552440i
$173$	1.23607	−	3.80423i	0.0939765	−	0.289230i	−0.893009	−	0.450039i	$-0.851410\pi$
$173$	1.23607	−	3.80423i	0.0939765	−	0.289230i	0.986986	+	0.160809i	$0.0514102\pi$
$174$	−14.9443	−	10.8576i	−1.13292	−	0.823116i
$175$	−37.9787			−2.87092
$176$	−1.69098	−	2.85317i	−0.127463	−	0.215066i
$177$	−22.4721			−1.68911
$178$	11.4721	+	8.33499i	0.859873	+	0.624734i
$179$	−6.52786	+	20.0907i	−0.487915	+	1.50165i	0.339798	+	0.940498i	$0.389641\pi$
$179$	−6.52786	+	20.0907i	−0.487915	+	1.50165i	−0.827713	+	0.561151i	$0.810359\pi$
$180$	8.89919	+	27.3889i	0.663306	+	2.04145i
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	−0.412899	−	0.910777i	$-0.635484\pi$
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	0.738608	+	0.674136i	$0.235484\pi$
$182$	−12.4721	+	9.06154i	−0.924496	+	0.671686i
$183$	1.14590	+	3.52671i	0.0847072	+	0.260702i
$184$	0.263932	−	0.812299i	0.0194573	−	0.0598835i
$185$	10.0902	+	7.33094i	0.741844	+	0.538981i
$186$	8.94427			0.655826
$187$	−2.73607	−	4.61653i	−0.200081	−	0.337594i
$188$	−0.854102			−0.0622918
$189$	−45.1246	−	32.7849i	−3.28233	−	2.38475i
$190$	1.19098	−	3.66547i	0.0864030	−	0.265921i
$191$	−4.13525	−	12.7270i	−0.299217	−	0.920894i	−0.981772	−	0.190060i	$-0.939132\pi$
$191$	−4.13525	−	12.7270i	−0.299217	−	0.920894i	0.682556	−	0.730833i	$-0.260868\pi$
$192$	2.61803	−	1.90211i	0.188940	−	0.137273i
$193$	14.9443	−	10.8576i	1.07571	−	0.781551i	0.0987819	−	0.995109i	$-0.468505\pi$
$193$	14.9443	−	10.8576i	1.07571	−	0.781551i	0.976930	+	0.213558i	$0.0685054\pi$
$194$	5.23607	+	16.1150i	0.375928	+	1.15699i
$195$	15.4164	−	47.4468i	1.10399	−	3.39774i
$196$	−6.35410	−	4.61653i	−0.453864	−	0.329752i
$197$	−10.9443			−0.779747			−0.389874	−	0.920868i	$-0.627481\pi$
$197$	−10.9443			−0.779747			−0.389874	+	0.920868i	$0.627481\pi$
$198$	−24.1803	+	5.42882i	−1.71842	+	0.385810i
$199$	26.6180			1.88690			0.943451	−	0.331511i	$-0.107559\pi$
$199$	26.6180			1.88690			0.943451	+	0.331511i	$0.107559\pi$
$200$	−7.97214	−	5.79210i	−0.563715	−	0.409563i
$201$	9.23607	−	28.4257i	0.651462	−	2.00499i
$202$	1.10081	+	3.38795i	0.0774529	+	0.238376i
$203$	−17.7984	+	12.9313i	−1.24920	+	0.907598i
$204$	4.23607	−	3.07768i	0.296584	−	0.215481i
$205$	0.562306	+	1.73060i	0.0392731	+	0.120870i
$206$	−2.14590	+	6.60440i	−0.149512	+	0.460150i
$207$	−5.16312	−	3.75123i	−0.358862	−	0.260728i
$208$	−4.00000			−0.277350
$209$	3.04508	+	1.31433i	0.210633	+	0.0909140i
$210$	48.0689			3.31707
$211$	−12.0902	−	8.78402i	−0.832322	−	0.604717i	0.0878936	−	0.996130i	$-0.471986\pi$
$211$	−12.0902	−	8.78402i	−0.832322	−	0.604717i	−0.920215	+	0.391413i	$0.871986\pi$
$212$	3.47214	−	10.6861i	0.238467	−	0.733927i
$213$	2.76393	+	8.50651i	0.189382	+	0.582856i
$214$	2.00000	−	1.45309i	0.136717	−	0.0993308i
$215$	23.7533	−	17.2578i	1.61996	−	1.17697i
$216$	−4.47214	−	13.7638i	−0.304290	−	0.936509i
$217$	3.29180	−	10.1311i	0.223462	−	0.687744i
$218$	−0.763932	−	0.555029i	−0.0517400	−	0.0375913i
$219$	35.4164			2.39322
$220$	8.44427	−	9.59632i	0.569313	−	0.646984i
$221$	−6.47214			−0.435363
$222$	−8.47214	−	6.15537i	−0.568613	−	0.413121i
$223$	−3.29180	+	10.1311i	−0.220435	+	0.678429i	0.778288	+	0.627907i	$0.216088\pi$
$223$	−3.29180	+	10.1311i	−0.220435	+	0.678429i	−0.998723	+	0.0505216i	$0.983912\pi$
$224$	−1.19098	−	3.66547i	−0.0795759	−	0.244909i
$225$	−59.5689	+	43.2793i	−3.97126	+	2.88529i
$226$	6.09017	−	4.42477i	0.405112	−	0.294331i
$227$	−8.09017	−	24.8990i	−0.536963	−	1.65260i	−0.739368	−	0.673302i	$-0.764876\pi$
$227$	−8.09017	−	24.8990i	−0.536963	−	1.65260i	0.202405	−	0.979302i	$-0.435124\pi$
$228$	−1.00000	+	3.07768i	−0.0662266	+	0.203825i
$229$	8.78115	+	6.37988i	0.580275	+	0.421594i	0.838823	−	0.544404i	$-0.183244\pi$
$229$	8.78115	+	6.37988i	0.580275	+	0.421594i	−0.258548	+	0.965998i	$0.583244\pi$
$230$	3.29180			0.217055
$231$	−3.85410	+	41.1855i	−0.253581	+	2.70980i
$232$	−5.70820			−0.374762
$233$	0.263932	+	0.191758i	0.0172908	+	0.0125625i	0.596397	−	0.802690i	$-0.296598\pi$
$233$	0.263932	+	0.191758i	0.0172908	+	0.0125625i	−0.579106	+	0.815252i	$0.696598\pi$
$234$	−9.23607	+	28.4257i	−0.603781	+	1.85825i
$235$	−1.01722	−	3.13068i	−0.0663562	−	0.204223i
$236$	−5.61803	+	4.08174i	−0.365703	+	0.265699i
$237$	−24.1803	+	17.5680i	−1.57068	+	1.14117i
$238$	−1.92705	−	5.93085i	−0.124912	−	0.384440i
$239$	−4.73607	+	14.5761i	−0.306351	+	0.942851i	0.672819	+	0.739807i	$0.265083\pi$
$239$	−4.73607	+	14.5761i	−0.306351	+	0.942851i	−0.979170	+	0.203044i	$0.934917\pi$
$240$	10.0902	+	7.33094i	0.651318	+	0.473210i
$241$	−19.5279			−1.25790			−0.628950	−	0.777446i	$-0.716515\pi$
$241$	−19.5279			−1.25790			−0.628950	+	0.777446i	$0.716515\pi$
$242$	7.54508	+	8.00448i	0.485016	+	0.514547i
$243$	−35.5967			−2.28353
$244$	0.927051	+	0.673542i	0.0593484	+	0.0431191i
$245$	9.35410	−	28.7890i	0.597612	−	1.83926i
$246$	−0.472136	−	1.45309i	−0.0301023	−	0.0926453i
$247$	3.23607	−	2.35114i	0.205906	−	0.149600i
$248$	2.23607	−	1.62460i	0.141990	−	0.103162i
$249$	−2.14590	−	6.60440i	−0.135991	−	0.418537i
$250$	5.78115	−	17.7926i	0.365632	−	1.12530i
$251$	10.0172	+	7.27794i	0.632281	+	0.459379i	0.857190	−	0.515001i	$-0.172208\pi$
$251$	10.0172	+	7.27794i	0.632281	+	0.459379i	−0.224908	+	0.974380i	$0.572208\pi$
$252$	−28.7984			−1.81413
$253$	−0.263932	+	2.82041i	−0.0165933	+	0.177318i
$254$	−2.29180			−0.143800
$255$	16.3262	+	11.8617i	1.02239	+	0.742809i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−5.61803	−	17.2905i	−0.350443	−	1.07855i	−0.958605	−	0.284740i	$-0.908093\pi$
$257$	−5.61803	−	17.2905i	−0.350443	−	1.07855i	0.608161	−	0.793813i	$-0.291907\pi$
$258$	−19.9443	+	14.4904i	−1.24168	+	0.902131i
$259$	−10.0902	+	7.33094i	−0.626973	+	0.455522i
$260$	−4.76393	−	14.6619i	−0.295447	−	0.909291i
$261$	−13.1803	+	40.5649i	−0.815843	+	2.51091i
$262$	−11.2082	−	8.14324i	−0.692445	−	0.503091i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$	−7.09017	+	8.05748i	−0.436370	+	0.495904i
$265$	43.3050			2.66020
$266$	3.11803	+	2.26538i	0.191179	+	0.138900i
$267$	14.1803	−	43.6426i	0.867823	−	2.67088i
$268$	−2.85410	−	8.78402i	−0.174342	−	0.536570i
$269$	−15.9443	+	11.5842i	−0.972139	+	0.706301i	−0.955938	−	0.293568i	$-0.905157\pi$
$269$	−15.9443	+	11.5842i	−0.972139	+	0.706301i	−0.0162013	+	0.999869i	$0.505157\pi$
$270$	45.1246	−	32.7849i	2.74620	−	1.99523i
$271$	8.68034	+	26.7153i	0.527293	+	1.62284i	0.759736	+	0.650231i	$0.225328\pi$
$271$	8.68034	+	26.7153i	0.527293	+	1.62284i	−0.232443	+	0.972610i	$0.574672\pi$
$272$	0.500000	−	1.53884i	0.0303170	−	0.0933060i
$273$	40.3607	+	29.3238i	2.44274	+	1.77475i
$274$	−9.56231			−0.577680
$275$	30.0066	+	12.9515i	1.80946	+	0.781006i
$276$	−2.76393			−0.166369
$277$	16.5623	+	12.0332i	0.995133	+	0.723006i	0.961039	−	0.276413i	$-0.0891456\pi$
$277$	16.5623	+	12.0332i	0.995133	+	0.723006i	0.0340934	+	0.999419i	$0.489146\pi$
$278$	4.35410	−	13.4005i	0.261142	−	0.803711i
$279$	−6.38197	−	19.6417i	−0.382078	−	1.17592i
$280$	12.0172	−	8.73102i	0.718166	−	0.521778i
$281$	3.23607	−	2.35114i	0.193048	−	0.140257i	−0.487063	−	0.873367i	$-0.661932\pi$
$281$	3.23607	−	2.35114i	0.193048	−	0.140257i	0.680111	+	0.733110i	$0.261932\pi$
$282$	0.854102	+	2.62866i	0.0508610	+	0.156534i
$283$	−3.04508	+	9.37181i	−0.181012	+	0.557096i	−0.999857	−	0.0169180i	$-0.994615\pi$
$283$	−3.04508	+	9.37181i	−0.181012	+	0.557096i	0.818845	+	0.574014i	$0.194615\pi$
$284$	2.23607	+	1.62460i	0.132686	+	0.0964022i
$285$	−12.4721			−0.738786
$286$	12.9443	−	2.90617i	0.765411	−	0.171845i
$287$	−1.81966			−0.107411
$288$	−6.04508	−	4.39201i	−0.356210	−	0.258802i
$289$	−4.44427	+	13.6781i	−0.261428	+	0.804592i
$290$	−6.79837	−	20.9232i	−0.399214	−	1.22866i
$291$	44.3607	−	32.2299i	2.60047	−	1.88935i
$292$	8.85410	−	6.43288i	0.518147	−	0.376456i
$293$	−7.41641	−	22.8254i	−0.433271	−	1.33347i	−0.894848	−	0.446371i	$-0.852716\pi$
$293$	−7.41641	−	22.8254i	−0.433271	−	1.33347i	0.461577	−	0.887100i	$-0.347284\pi$
$294$	−7.85410	+	24.1724i	−0.458061	+	1.40977i
$295$	−21.6525	−	15.7314i	−1.26066	−	0.915920i
$296$	−3.23607			−0.188093
$297$	24.4721	+	41.2915i	1.42002	+	2.39597i
$298$	−3.52786			−0.204364
$299$	2.76393	+	2.00811i	0.159842	+	0.116132i
$300$	−9.85410	+	30.3278i	−0.568927	+	1.75098i
$301$	9.07295	+	27.9237i	0.522956	+	1.60949i
$302$	8.70820	−	6.32688i	0.501101	−	0.364071i
$303$	9.32624	−	6.77591i	0.535778	−	0.389266i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	−1.36475	+	4.20025i	−0.0781451	+	0.240506i
$306$	−9.78115	−	7.10642i	−0.559151	−	0.406247i
$307$	−1.52786			−0.0871998			−0.0435999	−	0.999049i	$-0.513883\pi$
$307$	−1.52786			−0.0871998			−0.0435999	+	0.999049i	$0.513883\pi$
$308$	6.51722	+	10.9964i	0.371353	+	0.626578i
$309$	22.4721			1.27840
$310$	8.61803	+	6.26137i	0.489471	+	0.355622i
$311$	1.68034	−	5.17155i	0.0952833	−	0.293252i	−0.892044	−	0.451948i	$-0.850729\pi$
$311$	1.68034	−	5.17155i	0.0952833	−	0.293252i	0.987327	+	0.158696i	$0.0507291\pi$
$312$	4.00000	+	12.3107i	0.226455	+	0.696958i
$313$	12.5451	−	9.11454i	0.709090	−	0.515184i	−0.173790	−	0.984783i	$-0.555601\pi$
$313$	12.5451	−	9.11454i	0.709090	−	0.515184i	0.882880	+	0.469599i	$0.155601\pi$
$314$	18.0623	−	13.1230i	1.01931	−	0.740576i
$315$	−34.2984	−	105.560i	−1.93249	−	5.94761i
$316$	−2.85410	+	8.78402i	−0.160556	+	0.494140i
$317$	6.85410	+	4.97980i	0.384965	+	0.279693i	0.763389	−	0.645939i	$-0.223534\pi$
$317$	6.85410	+	4.97980i	0.384965	+	0.279693i	−0.378424	+	0.925632i	$0.623534\pi$
$318$	−36.3607			−2.03901
$319$	18.4721	−	4.14725i	1.03424	−	0.232202i
$320$	3.85410			0.215451
$321$	−6.47214	−	4.70228i	−0.361239	−	0.262456i
$322$	−1.01722	+	3.13068i	−0.0566875	+	0.174466i
$323$	0.500000	+	1.53884i	0.0278207	+	0.0856234i
$324$	−19.7533	+	14.3516i	−1.09740	+	0.797311i
$325$	31.8885	−	23.1684i	1.76886	−	1.28515i
$326$	5.33688	+	16.4252i	0.295583	+	0.909709i
$327$	−0.944272	+	2.90617i	−0.0522184	+	0.160712i
$328$	−0.381966	−	0.277515i	−0.0210905	−	0.0153232i
$329$	3.29180			0.181483
$330$	−37.9787	−	16.3925i	−2.09066	−	0.902376i
$331$	−10.4721			−0.575601			−0.287800	−	0.957690i	$-0.592924\pi$
$331$	−10.4721			−0.575601			−0.287800	+	0.957690i	$0.592924\pi$
$332$	−1.73607	−	1.26133i	−0.0952791	−	0.0692243i
$333$	−7.47214	+	22.9969i	−0.409471	+	1.26022i
$334$	1.94427	+	5.98385i	0.106386	+	0.327422i
$335$	28.7984	−	20.9232i	1.57342	−	1.14316i
$336$	−10.0902	+	7.33094i	−0.550464	+	0.399935i
$337$	8.09017	+	24.8990i	0.440700	+	1.35633i	0.887132	+	0.461516i	$0.152694\pi$
$337$	8.09017	+	24.8990i	0.440700	+	1.35633i	−0.446432	+	0.894818i	$0.647306\pi$
$338$	0.927051	−	2.85317i	0.0504249	−	0.155192i
$339$	−19.7082	−	14.3188i	−1.07040	−	0.777693i
$340$	6.23607			0.338198
$341$	−6.05573	+	6.88191i	−0.327936	+	0.372676i
$342$	7.47214			0.404047
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$	−2.35410	+	7.24518i	−0.126925	+	0.390634i
$345$	−3.29180	−	10.1311i	−0.177224	−	0.545440i
$346$	−3.23607	+	2.35114i	−0.173972	+	0.126398i
$347$	−3.07295	+	2.23263i	−0.164965	+	0.119854i	−0.667205	−	0.744874i	$-0.732509\pi$
$347$	−3.07295	+	2.23263i	−0.164965	+	0.119854i	0.502240	+	0.864728i	$0.332509\pi$
$348$	5.70820	+	17.5680i	0.305992	+	0.941746i
$349$	2.98936	−	9.20029i	0.160017	−	0.492480i	−0.838618	−	0.544720i	$-0.816636\pi$
$349$	2.98936	−	9.20029i	0.160017	−	0.492480i	0.998635	+	0.0522395i	$0.0166359\pi$
$350$	30.7254	+	22.3233i	1.64234	+	1.19323i
$351$	57.8885			3.08986
$352$	−0.309017	+	3.30220i	−0.0164707	+	0.176008i
$353$	−33.9230			−1.80554			−0.902769	−	0.430125i	$-0.858469\pi$
$353$	−33.9230			−1.80554			−0.902769	+	0.430125i	$0.858469\pi$
$354$	18.1803	+	13.2088i	0.966274	+	0.702039i
$355$	−3.29180	+	10.1311i	−0.174710	+	0.537703i
$356$	−4.38197	−	13.4863i	−0.232244	−	0.714773i
$357$	−16.3262	+	11.8617i	−0.864076	+	0.627788i
$358$	17.0902	−	12.4167i	0.903244	−	0.656245i
$359$	−0.680340	−	2.09387i	−0.0359070	−	0.110510i	0.931497	−	0.363750i	$-0.118504\pi$
$359$	−0.680340	−	2.09387i	−0.0359070	−	0.110510i	−0.967404	+	0.253240i	$0.918504\pi$
$360$	8.89919	−	27.3889i	0.469028	−	1.44352i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−5.41641			−0.284680
$363$	17.0902	−	31.2259i	0.897001	−	1.63893i
$364$	15.4164			0.808039
$365$	34.1246	+	24.7930i	1.78616	+	1.29772i
$366$	1.14590	−	3.52671i	0.0598970	−	0.184344i
$367$	2.80902	+	8.64527i	0.146629	+	0.451279i	0.997217	−	0.0745544i	$-0.0237535\pi$
$367$	2.80902	+	8.64527i	0.146629	+	0.451279i	−0.850587	+	0.525834i	$0.823753\pi$
$368$	−0.690983	+	0.502029i	−0.0360200	+	0.0261700i
$369$	−2.85410	+	2.07363i	−0.148579	+	0.107949i
$370$	−3.85410	−	11.8617i	−0.200365	−	0.616661i
$371$	−13.3820	+	41.1855i	−0.694757	+	2.13824i
$372$	−7.23607	−	5.25731i	−0.375173	−	0.272579i
$373$	−18.4721			−0.956451			−0.478225	−	0.878237i	$-0.658720\pi$
$373$	−18.4721			−0.956451			−0.478225	+	0.878237i	$0.658720\pi$
$374$	−0.500000	+	5.34307i	−0.0258544	+	0.276283i
$375$	−60.5410			−3.12632
$376$	0.690983	+	0.502029i	0.0356347	+	0.0258901i
$377$	7.05573	−	21.7153i	0.363388	−	1.11839i
$378$	17.2361	+	53.0472i	0.886528	+	2.72845i
$379$	−6.38197	+	4.63677i	−0.327820	+	0.238175i	−0.739505	−	0.673151i	$-0.764940\pi$
$379$	−6.38197	+	4.63677i	−0.327820	+	0.238175i	0.411685	+	0.911326i	$0.364940\pi$
$380$	−3.11803	+	2.26538i	−0.159952	+	0.116212i
$381$	2.29180	+	7.05342i	0.117412	+	0.361358i
$382$	−4.13525	+	12.7270i	−0.211578	+	0.651170i
$383$	15.0902	+	10.9637i	0.771072	+	0.560216i	0.902286	−	0.431138i	$-0.141888\pi$
$383$	15.0902	+	10.9637i	0.771072	+	0.560216i	−0.131215	+	0.991354i	$0.541888\pi$
$384$	−3.23607			−0.165140
$385$	−32.5451	+	36.9852i	−1.65865	+	1.88494i
$386$	−18.4721			−0.940207
$387$	46.0517	+	33.4585i	2.34094	+	1.70079i
$388$	5.23607	−	16.1150i	0.265821	−	0.818113i
$389$	0.701626	+	2.15938i	0.0355739	+	0.109485i	0.967267	−	0.253762i	$-0.0816680\pi$
$389$	0.701626	+	2.15938i	0.0355739	+	0.109485i	−0.931693	+	0.363247i	$0.881668\pi$
$390$	−40.3607	+	29.3238i	−2.04374	+	1.48487i
$391$	−1.11803	+	0.812299i	−0.0565414	+	0.0410797i
$392$	2.42705	+	7.46969i	0.122585	+	0.377277i
$393$	−13.8541	+	42.6385i	−0.698847	+	2.15083i
$394$	8.85410	+	6.43288i	0.446063	+	0.324084i
$395$	−35.5967			−1.79107
$396$	22.7533	+	9.82084i	1.14340	+	0.493516i
$397$	16.5623			0.831238			0.415619	−	0.909539i	$-0.363565\pi$
$397$	16.5623			0.831238			0.415619	+	0.909539i	$0.363565\pi$
$398$	−21.5344	−	15.6457i	−1.07942	−	0.784247i
$399$	3.85410	−	11.8617i	0.192946	−	0.593828i
$400$	3.04508	+	9.37181i	0.152254	+	0.468590i
$401$	15.5623	−	11.3067i	0.777144	−	0.564629i	−0.126976	−	0.991906i	$-0.540527\pi$
$401$	15.5623	−	11.3067i	0.777144	−	0.564629i	0.904121	+	0.427277i	$0.140527\pi$
$402$	−24.1803	+	17.5680i	−1.20601	+	0.876214i
$403$	3.41641	+	10.5146i	0.170183	+	0.523771i
$404$	1.10081	−	3.38795i	0.0547675	−	0.168557i
$405$	−76.1312	−	55.3125i	−3.78299	−	2.74850i
$406$	22.0000			1.09184
$407$	10.4721	−	2.35114i	0.519085	−	0.116542i
$408$	−5.23607			−0.259224
$409$	−23.8885	−	17.3560i	−1.18121	−	0.858201i	−0.188905	−	0.981995i	$-0.560494\pi$
$409$	−23.8885	−	17.3560i	−1.18121	−	0.858201i	−0.992308	+	0.123794i	$0.960494\pi$
$410$	0.562306	−	1.73060i	0.0277703	−	0.0854682i
$411$	9.56231	+	29.4298i	0.471674	+	1.45166i
$412$	5.61803	−	4.08174i	0.276781	−	0.201093i
$413$	21.6525	−	15.7314i	1.06545	−	0.774094i
$414$	1.97214	+	6.06961i	0.0969252	+	0.298305i
$415$	2.55573	−	7.86572i	0.125456	−	0.386113i
$416$	3.23607	+	2.35114i	0.158661	+	0.115274i
$417$	−45.5967			−2.23288
$418$	−1.69098	−	2.85317i	−0.0827087	−	0.139553i
$419$	−28.7426			−1.40417			−0.702085	−	0.712093i	$-0.747747\pi$
$419$	−28.7426			−1.40417			−0.702085	+	0.712093i	$0.747747\pi$
$420$	−38.8885	−	28.2542i	−1.89757	−	1.37866i
$421$	7.56231	−	23.2744i	0.368564	−	1.13432i	−0.579155	−	0.815218i	$-0.696617\pi$
$421$	7.56231	−	23.2744i	0.368564	−	1.13432i	0.947719	−	0.319106i	$-0.103383\pi$
$422$	4.61803	+	14.2128i	0.224802	+	0.691871i
$423$	5.16312	−	3.75123i	0.251039	−	0.182391i
$424$	−9.09017	+	6.60440i	−0.441458	+	0.320738i
$425$	4.92705	+	15.1639i	0.238997	+	0.735557i
$426$	2.76393	−	8.50651i	0.133913	−	0.412142i
$427$	−3.57295	−	2.59590i	−0.172907	−	0.125624i
$428$	−2.47214			−0.119495
$429$	−21.8885	−	36.9322i	−1.05679	−	1.78310i
$430$	−29.3607			−1.41590
$431$	−8.56231	−	6.22088i	−0.412432	−	0.299649i	0.362154	−	0.932118i	$-0.382042\pi$
$431$	−8.56231	−	6.22088i	−0.412432	−	0.299649i	−0.774586	+	0.632469i	$0.782042\pi$
$432$	−4.47214	+	13.7638i	−0.215166	+	0.662212i
$433$	3.67376	+	11.3067i	0.176550	+	0.543364i	0.999701	−	0.0244581i	$-0.00778604\pi$
$433$	3.67376	+	11.3067i	0.176550	+	0.543364i	−0.823151	+	0.567822i	$0.807786\pi$
$434$	−8.61803	+	6.26137i	−0.413679	+	0.300555i
$435$	−57.5967	+	41.8465i	−2.76155	+	2.00639i
$436$	0.291796	+	0.898056i	0.0139745	+	0.0430091i
$437$	0.263932	−	0.812299i	0.0126256	−	0.0388575i
$438$	−28.6525	−	20.8172i	−1.36907	−	0.994686i
$439$	18.3607			0.876307			0.438154	−	0.898900i	$-0.355633\pi$
$439$	18.3607			0.876307			0.438154	+	0.898900i	$0.355633\pi$
$440$	−12.4721	+	2.80017i	−0.594586	+	0.133493i
$441$	58.6869			2.79462
$442$	5.23607	+	3.80423i	0.249054	+	0.180949i
$443$	−6.57295	+	20.2295i	−0.312290	+	0.961131i	0.664565	+	0.747230i	$0.268617\pi$
$443$	−6.57295	+	20.2295i	−0.312290	+	0.961131i	−0.976856	+	0.213900i	$0.931383\pi$
$444$	3.23607	+	9.95959i	0.153577	+	0.472661i
$445$	44.2148	−	32.1239i	2.09598	−	1.52282i
$446$	8.61803	−	6.26137i	0.408076	−	0.296484i
$447$	3.52786	+	10.8576i	0.166862	+	0.513549i
$448$	−1.19098	+	3.66547i	−0.0562687	+	0.173177i
$449$	−12.7082	−	9.23305i	−0.599737	−	0.435735i	0.246048	−	0.969258i	$-0.420868\pi$
$449$	−12.7082	−	9.23305i	−0.599737	−	0.435735i	−0.845786	+	0.533523i	$0.820868\pi$
$450$	73.6312			3.47101
$451$	1.43769	+	0.620541i	0.0676984	+	0.0292202i
$452$	−7.52786			−0.354081
$453$	−28.1803	−	20.4742i	−1.32403	−	0.961963i
$454$	−8.09017	+	24.8990i	−0.379690	+	1.16857i
$455$	18.3607	+	56.5084i	0.860762	+	2.64915i
$456$	2.61803	−	1.90211i	0.122601	−	0.0890746i
$457$	−8.97214	+	6.51864i	−0.419699	+	0.304929i	−0.777517	−	0.628862i	$-0.783521\pi$
$457$	−8.97214	+	6.51864i	−0.419699	+	0.304929i	0.357818	+	0.933791i	$0.383521\pi$
$458$	−3.35410	−	10.3229i	−0.156727	−	0.482356i
$459$	−7.23607	+	22.2703i	−0.337751	+	1.03949i
$460$	−2.66312	−	1.93487i	−0.124169	−	0.0902137i
$461$	−30.6869			−1.42923			−0.714616	−	0.699517i	$-0.753399\pi$
$461$	−30.6869			−1.42923			−0.714616	+	0.699517i	$0.753399\pi$
$462$	27.3262	−	31.0543i	1.27133	−	1.44478i
$463$	−12.2148			−0.567669			−0.283835	−	0.958873i	$-0.591607\pi$
$463$	−12.2148			−0.567669			−0.283835	+	0.958873i	$0.591607\pi$
$464$	4.61803	+	3.35520i	0.214387	+	0.155761i
$465$	10.6525	−	32.7849i	0.493997	−	1.52037i
$466$	−0.100813	−	0.310271i	−0.00467007	−	0.0143730i
$467$	−7.50000	+	5.44907i	−0.347059	+	0.252153i	−0.747634	−	0.664111i	$-0.768810\pi$
$467$	−7.50000	+	5.44907i	−0.347059	+	0.252153i	0.400575	+	0.916264i	$0.368810\pi$
$468$	24.1803	−	17.5680i	1.11774	−	0.812083i
$469$	11.0000	+	33.8545i	0.507933	+	1.56326i
$470$	−1.01722	+	3.13068i	−0.0469209	+	0.144408i
$471$	−58.4508	−	42.4670i	−2.69327	−	1.95678i
$472$	6.94427			0.319636
$473$	2.35410	−	25.1563i	0.108242	−	1.15669i
$474$	29.8885			1.37283
$475$	−7.97214	−	5.79210i	−0.365787	−	0.265760i
$476$	−1.92705	+	5.93085i	−0.0883262	+	0.271840i
$477$	25.9443	+	79.8483i	1.18791	+	3.65600i
$478$	12.3992	−	9.00854i	0.567126	−	0.412041i
$479$	−16.1074	+	11.7027i	−0.735965	+	0.534710i	−0.891445	−	0.453129i	$-0.850308\pi$
$479$	−16.1074	+	11.7027i	−0.735965	+	0.534710i	0.155480	+	0.987839i	$0.450308\pi$
$480$	−3.85410	−	11.8617i	−0.175915	−	0.541410i
$481$	4.00000	−	12.3107i	0.182384	−	0.561321i
$482$	15.7984	+	11.4782i	0.719596	+	0.522817i
$483$	10.6525			0.484704
$484$	−1.39919	−	10.9106i	−0.0635994	−	0.495939i
$485$	65.3050			2.96535
$486$	28.7984	+	20.9232i	1.30632	+	0.949098i
$487$	6.61803	−	20.3682i	0.299892	−	0.922972i	−0.681642	−	0.731685i	$-0.738734\pi$
$487$	6.61803	−	20.3682i	0.299892	−	0.922972i	0.981534	−	0.191287i	$-0.0612660\pi$
$488$	−0.354102	−	1.08981i	−0.0160294	−	0.0493336i
$489$	45.2148	−	32.8505i	2.04468	−	1.48555i
$490$	−24.4894	+	17.7926i	−1.10632	+	0.803786i
$491$	−7.33688	−	22.5806i	−0.331109	−	1.01905i	−0.968607	−	0.248596i	$-0.920031\pi$
$491$	−7.33688	−	22.5806i	−0.331109	−	1.01905i	0.637498	−	0.770452i	$-0.279969\pi$
$492$	−0.472136	+	1.45309i	−0.0212855	+	0.0655101i
$493$	7.47214	+	5.42882i	0.336528	+	0.244502i
$494$	−4.00000			−0.179969
$495$	−8.89919	+	95.0979i	−0.399989	+	4.27433i
$496$	−2.76393			−0.124104
$497$	−8.61803	−	6.26137i	−0.386572	−	0.280861i
$498$	−2.14590	+	6.60440i	−0.0961600	+	0.295950i
$499$	−6.19098	−	19.0539i	−0.277146	−	0.852969i	−0.988643	−	0.150280i	$-0.951982\pi$
$499$	−6.19098	−	19.0539i	−0.277146	−	0.852969i	0.711497	−	0.702689i	$-0.248018\pi$
$500$	−15.1353	+	10.9964i	−0.676869	+	0.491774i
$501$	16.4721	−	11.9677i	0.735921	−	0.534678i
$502$	−3.82624	−	11.7759i	−0.170773	−	0.525586i
$503$	7.70820	−	23.7234i	0.343692	−	1.05777i	−0.618589	−	0.785715i	$-0.712295\pi$
$503$	7.70820	−	23.7234i	0.343692	−	1.05777i	0.962280	−	0.272060i	$-0.0877048\pi$
$504$	23.2984	+	16.9273i	1.03779	+	0.754000i
$505$	13.7295			0.610954
$506$	1.87132	−	2.12663i	0.0831904	−	0.0945401i
$507$	−9.70820			−0.431156
$508$	1.85410	+	1.34708i	0.0822625	+	0.0597672i
$509$	7.18034	−	22.0988i	0.318263	−	0.979513i	−0.656128	−	0.754650i	$-0.727807\pi$
$509$	7.18034	−	22.0988i	0.318263	−	0.979513i	0.974390	−	0.224863i	$-0.0721933\pi$
$510$	−6.23607	−	19.1926i	−0.276138	−	0.849865i
$511$	−34.1246	+	24.7930i	−1.50958	+	1.09678i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.47214	−	13.7638i	−0.197450	−	0.607687i
$514$	−5.61803	+	17.2905i	−0.247801	+	0.762653i
$515$	21.6525	+	15.7314i	0.954122	+	0.693210i
$516$	24.6525			1.08526
$517$	−2.60081	−	1.12257i	−0.114384	−	0.0493706i
$518$	12.4721			0.547994
$519$	10.4721	+	7.60845i	0.459676	+	0.333974i
$520$	−4.76393	+	14.6619i	−0.208912	+	0.642966i
$521$	−7.23607	−	22.2703i	−0.317018	−	0.975681i	−0.974916	−	0.222574i	$-0.928554\pi$
$521$	−7.23607	−	22.2703i	−0.317018	−	0.975681i	0.657898	−	0.753107i	$-0.271446\pi$
$522$	34.5066	−	25.0705i	1.51031	−	1.09731i
$523$	23.7984	−	17.2905i	1.04063	−	0.756062i	0.0702218	−	0.997531i	$-0.477629\pi$
$523$	23.7984	−	17.2905i	1.04063	−	0.756062i	0.970408	+	0.241469i	$0.0776293\pi$
$524$	4.28115	+	13.1760i	0.187023	+	0.575598i
$525$	37.9787	−	116.886i	1.65753	−	5.10134i
$526$	12.9443	+	9.40456i	0.564397	+	0.410058i
$527$	−4.47214			−0.194809
$528$	10.4721	−	2.35114i	0.455741	−	0.102320i
$529$	−22.2705			−0.968283
$530$	−35.0344	−	25.4540i	−1.52180	−	1.10565i
$531$	16.0344	−	49.3489i	0.695836	−	2.14156i
$532$	−1.19098	−	3.66547i	−0.0516357	−	0.158918i
$533$	1.52786	−	1.11006i	0.0661791	−	0.0480820i
$534$	−37.1246	+	26.9726i	−1.60654	+	1.16722i
$535$	−2.94427	−	9.06154i	−0.127292	−	0.391764i
$536$	−2.85410	+	8.78402i	−0.123278	+	0.379412i
$537$	−55.3050	−	40.1814i	−2.38658	−	1.73396i
$538$	19.7082			0.849681
$539$	−13.2812	−	22.4091i	−0.572060	−	0.965228i
$540$	−55.7771			−2.40026
$541$	−12.0172	−	8.73102i	−0.516661	−	0.375376i	0.298684	−	0.954352i	$-0.403452\pi$
$541$	−12.0172	−	8.73102i	−0.516661	−	0.375376i	−0.815344	+	0.578976i	$0.803452\pi$
$542$	8.68034	−	26.7153i	0.372853	−	1.14752i
$543$	5.41641	+	16.6700i	0.232440	+	0.715378i
$544$	−1.30902	+	0.951057i	−0.0561236	+	0.0407762i
$545$	−2.94427	+	2.13914i	−0.126119	+	0.0916306i
$546$	−15.4164	−	47.4468i	−0.659761	−	2.03054i
$547$	−13.3820	+	41.1855i	−0.572172	+	1.76096i	0.0734429	+	0.997299i	$0.476601\pi$
$547$	−13.3820	+	41.1855i	−0.572172	+	1.76096i	−0.645614	+	0.763664i	$0.723399\pi$
$548$	7.73607	+	5.62058i	0.330468	+	0.240099i
$549$	−8.56231			−0.365430
$550$	−16.6631	−	28.1154i	−0.710518	−	1.19885i
$551$	−5.70820			−0.243178
$552$	2.23607	+	1.62460i	0.0951734	+	0.0691475i
$553$	11.0000	−	33.8545i	0.467768	−	1.43964i
$554$	−6.32624	−	19.4702i	−0.268776	−	0.827208i
$555$	−32.6525	+	23.7234i	−1.38602	+	1.00700i
$556$	−11.3992	+	8.28199i	−0.483433	+	0.351235i
$557$	8.69756	+	26.7683i	0.368527	+	1.13421i	0.947743	+	0.319036i	$0.103359\pi$
$557$	8.69756	+	26.7683i	0.368527	+	1.13421i	−0.579215	+	0.815175i	$0.696641\pi$
$558$	−6.38197	+	19.6417i	−0.270170	+	0.831498i
$559$	−24.6525	−	17.9111i	−1.04269	−	0.757558i
$560$	−14.8541			−0.627700
$561$	16.9443	−	3.80423i	0.715388	−	0.160615i
$562$	−4.00000			−0.168730
$563$	−26.6525	−	19.3642i	−1.12327	−	0.816102i	−0.138567	−	0.990353i	$-0.544250\pi$
$563$	−26.6525	−	19.3642i	−1.12327	−	0.816102i	−0.984701	+	0.174251i	$0.944250\pi$
$564$	0.854102	−	2.62866i	0.0359642	−	0.110686i
$565$	−8.96556	−	27.5932i	−0.377184	−	1.16085i
$566$	7.97214	−	5.79210i	0.335094	−	0.243460i
$567$	76.1312	−	55.3125i	3.19721	−	2.32291i
$568$	−0.854102	−	2.62866i	−0.0358373	−	0.110296i
$569$	4.38197	−	13.4863i	0.183702	−	0.565375i	−0.816222	−	0.577738i	$-0.803935\pi$
$569$	4.38197	−	13.4863i	0.183702	−	0.565375i	0.999924	+	0.0123631i	$0.00393539\pi$
$570$	10.0902	+	7.33094i	0.422631	+	0.307059i
$571$	14.2148			0.594870			0.297435	−	0.954742i	$-0.403869\pi$
$571$	14.2148			0.594870			0.297435	+	0.954742i	$0.403869\pi$
$572$	−12.1803	−	5.25731i	−0.509286	−	0.219819i
$573$	43.3050			1.80909
$574$	1.47214	+	1.06957i	0.0614458	+	0.0446430i
$575$	2.60081	−	8.00448i	0.108461	−	0.333810i
$576$	2.30902	+	7.10642i	0.0962090	+	0.296101i
$577$	−31.7984	+	23.1029i	−1.32378	+	0.961785i	−0.323907	+	0.946089i	$0.604996\pi$
$577$	−31.7984	+	23.1029i	−1.32378	+	0.961785i	−0.999877	+	0.0156961i	$0.995004\pi$
$578$	11.6353	−	8.45351i	0.483963	−	0.351620i
$579$	18.4721	+	56.8514i	0.767676	+	2.36266i
$580$	−6.79837	+	20.9232i	−0.282287	+	0.868790i
$581$	6.69098	+	4.86128i	0.277589	+	0.201680i
$582$	−54.8328			−2.27289
$583$	24.6180	−	27.9767i	1.01957	−	1.15868i
$584$	−10.9443			−0.452877
$585$	93.1935	+	67.7090i	3.85308	+	2.79942i
$586$	−7.41641	+	22.8254i	−0.306369	+	0.942907i
$587$	10.3607	+	31.8869i	0.427631	+	1.31611i	0.900452	+	0.434955i	$0.143236\pi$
$587$	10.3607	+	31.8869i	0.427631	+	1.31611i	−0.472821	+	0.881158i	$0.656764\pi$
$588$	20.5623	−	14.9394i	0.847975	−	0.616090i
$589$	2.23607	−	1.62460i	0.0921356	−	0.0669404i
$590$	8.27051	+	25.4540i	0.340492	+	1.04793i
$591$	10.9443	−	33.6830i	0.450187	−	1.38553i
$592$	2.61803	+	1.90211i	0.107601	+	0.0781764i
$593$	10.7426			0.441148			0.220574	−	0.975370i	$-0.429207\pi$
$593$	10.7426			0.441148			0.220574	+	0.975370i	$0.429207\pi$
$594$	4.47214	−	47.7899i	0.183494	−	1.96084i
$595$	−24.0344			−0.985316
$596$	2.85410	+	2.07363i	0.116909	+	0.0849390i
$597$	−26.6180	+	81.9219i	−1.08940	+	3.35284i
$598$	−1.05573	−	3.24920i	−0.0431719	−	0.132870i
$599$	−23.7984	+	17.2905i	−0.972375	+	0.706472i	−0.955992	−	0.293394i	$-0.905215\pi$
$599$	−23.7984	+	17.2905i	−0.972375	+	0.706472i	−0.0163835	+	0.999866i	$0.505215\pi$
$600$	25.7984	−	18.7436i	1.05321	−	0.765205i
$601$	9.05573	+	27.8707i	0.369391	+	1.13687i	0.947186	+	0.320686i	$0.103913\pi$
$601$	9.05573	+	27.8707i	0.369391	+	1.13687i	−0.577795	+	0.816182i	$0.696087\pi$
$602$	9.07295	−	27.9237i	0.369786	−	1.13808i
$603$	55.8328	+	40.5649i	2.27369	+	1.65193i
$604$	−10.7639			−0.437978
$605$	38.3262	−	18.1231i	1.55818	−	0.736808i
$606$	−11.5279			−0.468287
$607$	7.47214	+	5.42882i	0.303285	+	0.220349i	0.729010	−	0.684503i	$-0.239981\pi$
$607$	7.47214	+	5.42882i	0.303285	+	0.220349i	−0.425725	+	0.904853i	$0.639981\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	−22.0000	−	67.7090i	−0.891485	−	2.74371i
$610$	3.57295	−	2.59590i	0.144664	−	0.105105i
$611$	−2.76393	+	2.00811i	−0.111817	+	0.0812396i
$612$	3.73607	+	11.4984i	0.151022	+	0.464797i
$613$	−0.701626	+	2.15938i	−0.0283384	+	0.0872167i	−0.964225	−	0.265084i	$-0.914600\pi$
$613$	−0.701626	+	2.15938i	−0.0283384	+	0.0872167i	0.935887	+	0.352300i	$0.114600\pi$
$614$	1.23607	+	0.898056i	0.0498836	+	0.0362426i
$615$	−5.88854			−0.237449
$616$	1.19098	−	12.7270i	0.0479861	−	0.512786i
$617$	2.36068			0.0950374			0.0475187	−	0.998870i	$-0.484869\pi$
$617$	2.36068			0.0950374			0.0475187	+	0.998870i	$0.484869\pi$
$618$	−18.1803	−	13.2088i	−0.731321	−	0.531335i
$619$	10.5902	−	32.5932i	0.425655	−	1.31003i	−0.476711	−	0.879060i	$-0.658171\pi$
$619$	10.5902	−	32.5932i	0.425655	−	1.31003i	0.902366	−	0.430971i	$-0.141829\pi$
$620$	−3.29180	−	10.1311i	−0.132202	−	0.406875i
$621$	10.0000	−	7.26543i	0.401286	−	0.291551i
$622$	−4.39919	+	3.19620i	−0.176391	+	0.128156i
$623$	16.8885	+	51.9776i	0.676625	+	2.08244i
$624$	4.00000	−	12.3107i	0.160128	−	0.492824i
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	−15.5066			−0.619767
$627$	−7.09017	+	8.05748i	−0.283154	+	0.321785i
$628$	−22.3262			−0.890914
$629$	4.23607	+	3.07768i	0.168903	+	0.122715i
$630$	−34.2984	+	105.560i	−1.36648	+	4.20559i
$631$	−4.18034	−	12.8658i	−0.166417	−	0.512178i	0.832721	−	0.553693i	$-0.186782\pi$
$631$	−4.18034	−	12.8658i	−0.166417	−	0.512178i	−0.999138	+	0.0415146i	$0.986782\pi$
$632$	7.47214	−	5.42882i	0.297226	−	0.215947i
$633$	39.1246	−	28.4257i	1.55506	−	1.12982i
$634$	−2.61803	−	8.05748i	−0.103975	−	0.320003i
$635$	−2.72949	+	8.40051i	−0.108317	+	0.333364i
$636$	29.4164	+	21.3723i	1.16644	+	0.847466i
$637$	−31.4164			−1.24476
$638$	−17.3820	−	7.50245i	−0.688159	−	0.297025i
$639$	−20.6525			−0.816999
$640$	−3.11803	−	2.26538i	−0.123251	−	0.0895472i
$641$	0.652476	−	2.00811i	0.0257712	−	0.0793157i	−0.937344	−	0.348406i	$-0.886723\pi$
$641$	0.652476	−	2.00811i	0.0257712	−	0.0793157i	0.963115	+	0.269090i	$0.0867230\pi$
$642$	2.47214	+	7.60845i	0.0975674	+	0.300282i
$643$	−23.7254	+	17.2375i	−0.935639	+	0.679782i	−0.947367	−	0.320149i	$-0.896267\pi$
$643$	−23.7254	+	17.2375i	−0.935639	+	0.679782i	0.0117276	+	0.999931i	$0.496267\pi$
$644$	2.66312	−	1.93487i	0.104942	−	0.0762445i
$645$	29.3607	+	90.3629i	1.15608	+	3.55803i
$646$	0.500000	−	1.53884i	0.0196722	−	0.0605449i
$647$	26.9443	+	19.5762i	1.05929	+	0.769618i	0.973957	−	0.226734i	$-0.0728049\pi$
$647$	26.9443	+	19.5762i	1.05929	+	0.769618i	0.0853320	+	0.996353i	$0.472805\pi$
$648$	24.4164			0.959167
$649$	−22.4721	+	5.04531i	−0.882108	+	0.198046i
$650$	−39.4164			−1.54604
$651$	27.8885	+	20.2622i	1.09304	+	0.794139i
$652$	5.33688	−	16.4252i	0.209008	−	0.643262i
$653$	8.53444	+	26.2663i	0.333979	+	1.02788i	0.967223	+	0.253928i	$0.0817228\pi$
$653$	8.53444	+	26.2663i	0.333979	+	1.02788i	−0.633245	+	0.773952i	$0.718277\pi$
$654$	2.47214	−	1.79611i	0.0966682	−	0.0702335i
$655$	−43.1976	+	31.3849i	−1.68787	+	1.22631i
$656$	0.145898	+	0.449028i	0.00569636	+	0.0175316i
$657$	−25.2705	+	77.7746i	−0.985896	+	3.03428i
$658$	−2.66312	−	1.93487i	−0.103819	−	0.0754291i
$659$	29.4164			1.14590			0.572950	−	0.819590i	$-0.305799\pi$
$659$	29.4164			1.14590			0.572950	+	0.819590i	$0.305799\pi$
$660$	21.0902	+	35.5851i	0.820934	+	1.38515i
$661$	−19.4164			−0.755211			−0.377605	−	0.925967i	$-0.623252\pi$
$661$	−19.4164			−0.755211			−0.377605	+	0.925967i	$0.623252\pi$
$662$	8.47214	+	6.15537i	0.329279	+	0.239235i
$663$	6.47214	−	19.9192i	0.251357	−	0.773597i
$664$	0.663119	+	2.04087i	0.0257340	+	0.0792011i
$665$	12.0172	−	8.73102i	0.466008	−	0.338575i
$666$	19.5623	−	14.2128i	0.758024	−	0.550737i
$667$	−1.50658	−	4.63677i	−0.0583349	−	0.179536i
$668$	1.94427	−	5.98385i	0.0752261	−	0.231522i
$669$	−27.8885	−	20.2622i	−1.07823	−	0.783382i
$670$	−35.5967			−1.37522
$671$	1.93769	+	3.26944i	0.0748039	+	0.126215i
$672$	12.4721			0.481123
$673$	19.9443	+	14.4904i	0.768795	+	0.558562i	0.901595	−	0.432580i	$-0.142397\pi$
$673$	19.9443	+	14.4904i	0.768795	+	0.558562i	−0.132800	+	0.991143i	$0.542397\pi$
$674$	8.09017	−	24.8990i	0.311622	−	0.959073i
$675$	−44.0689	−	135.630i	−1.69621	−	5.22040i
$676$	−2.42705	+	1.76336i	−0.0933481	+	0.0678214i
$677$	14.0902	−	10.2371i	0.541529	−	0.393444i	−0.283123	−	0.959083i	$-0.591371\pi$
$677$	14.0902	−	10.2371i	0.541529	−	0.393444i	0.824653	+	0.565639i	$0.191371\pi$
$678$	7.52786	+	23.1684i	0.289106	+	0.889776i
$679$	−20.1803	+	62.1087i	−0.774450	+	2.38351i
$680$	−5.04508	−	3.66547i	−0.193470	−	0.140564i
$681$	84.7214			3.24653
$682$	8.94427	−	2.00811i	0.342494	−	0.0768947i
$683$	−9.70820			−0.371474			−0.185737	−	0.982599i	$-0.559467\pi$
$683$	−9.70820			−0.371474			−0.185737	+	0.982599i	$0.559467\pi$
$684$	−6.04508	−	4.39201i	−0.231140	−	0.167933i
$685$	−11.3885	+	35.0503i	−0.435134	+	1.33920i
$686$	−1.01722	−	3.13068i	−0.0388377	−	0.119530i
$687$	−28.4164	+	20.6457i	−1.08415	+	0.787684i
$688$	6.16312	−	4.47777i	0.234967	−	0.170713i
$689$	−13.8885	−	42.7445i	−0.529111	−	1.62844i
$690$	−3.29180	+	10.1311i	−0.125317	+	0.385685i
$691$	−11.5000	−	8.35524i	−0.437481	−	0.317848i	0.347152	−	0.937809i	$-0.387149\pi$
$691$	−11.5000	−	8.35524i	−0.437481	−	0.317848i	−0.784633	+	0.619960i	$0.787149\pi$
$692$	4.00000			0.152057
$693$	−87.6935	−	37.8505i	−3.33120	−	1.43782i
$694$	3.79837			0.144184
$695$	−43.9336	−	31.9196i	−1.66650	−	1.21078i
$696$	5.70820	−	17.5680i	0.216369	−	0.665915i
$697$	0.236068	+	0.726543i	0.00894171	+	0.0275198i
$698$	−7.82624	+	5.68609i	−0.296227	+	0.215222i
$699$	−0.854102	+	0.620541i	−0.0323051	+	0.0234710i
$700$	−11.7361	−	36.1199i	−0.443582	−	1.36520i
$701$	13.0066	−	40.0301i	0.491252	−	1.51192i	−0.331466	−	0.943467i	$-0.607543\pi$
$701$	13.0066	−	40.0301i	0.491252	−	1.51192i	0.822718	−	0.568450i	$-0.192457\pi$
$702$	−46.8328	−	34.0260i	−1.76759	−	1.28423i
$703$	−3.23607			−0.122051
$704$	2.19098	−	2.48990i	0.0825758	−	0.0938416i
$705$	10.6525			0.401195
$706$	27.4443	+	19.9394i	1.03288	+	0.750430i
$707$	−4.24265	+	13.0575i	−0.159561	+	0.491079i
$708$	−6.94427	−	21.3723i	−0.260982	−	0.803219i
$709$	−37.2426	+	27.0584i	−1.39868	+	1.01620i	−0.403827	+	0.914835i	$0.632320\pi$
$709$	−37.2426	+	27.0584i	−1.39868	+	1.01620i	−0.994849	+	0.101363i	$0.967680\pi$
$710$	8.61803	−	6.26137i	0.323429	−	0.234985i
$711$	−21.3262	−	65.6354i	−0.799796	−	2.46152i
$712$	−4.38197	+	13.4863i	−0.164221	+	0.505421i
$713$	1.90983	+	1.38757i	0.0715237	+	0.0519650i
$714$	20.1803			0.755230
$715$	4.76393	−	50.9080i	0.178161	−	1.90385i
$716$	−21.1246			−0.789464
$717$	−40.1246	−	29.1522i	−1.49848	−	1.08871i
$718$	−0.680340	+	2.09387i	−0.0253901	+	0.0781426i
$719$	−2.69756	−	8.30224i	−0.100602	−	0.309621i	0.888071	−	0.459706i	$-0.152045\pi$
$719$	−2.69756	−	8.30224i	−0.100602	−	0.309621i	−0.988673	+	0.150085i	$0.952045\pi$
$720$	−23.2984	+	16.9273i	−0.868279	+	0.630842i
$721$	−21.6525	+	15.7314i	−0.806380	+	0.585870i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	19.5279	−	60.1006i	0.726249	−	2.23516i
$724$	4.38197	+	3.18368i	0.162854	+	0.118321i
$725$	−56.2492			−2.08904
$726$	−32.1803	+	15.2169i	−1.19432	+	0.564752i
$727$	34.1591			1.26689			0.633445	−	0.773788i	$-0.281640\pi$
$727$	34.1591			1.26689			0.633445	+	0.773788i	$0.281640\pi$
$728$	−12.4721	−	9.06154i	−0.462248	−	0.335843i
$729$	12.9615	−	39.8914i	0.480055	−	1.47746i
$730$	−13.0344	−	40.1159i	−0.482426	−	1.48476i
$731$	9.97214	−	7.24518i	0.368833	−	0.267973i
$732$	−3.00000	+	2.17963i	−0.110883	+	0.0805614i
$733$	6.42705	+	19.7804i	0.237389	+	0.730607i	0.996796	+	0.0799910i	$0.0254892\pi$
$733$	6.42705	+	19.7804i	0.237389	+	0.730607i	−0.759407	+	0.650616i	$0.774511\pi$
$734$	2.80902	−	8.64527i	0.103683	−	0.319103i
$735$	79.2492	+	57.5779i	2.92315	+	2.12379i
$736$	0.854102			0.0314826
$737$	2.85410	−	30.4993i	0.105132	−	1.12346i
$738$	3.52786			0.129862
$739$	37.3885	+	27.1644i	1.37536	+	0.999257i	0.997297	+	0.0734775i	$0.0234097\pi$
$739$	37.3885	+	27.1644i	1.37536	+	0.999257i	0.378063	+	0.925780i	$0.376590\pi$
$740$	−3.85410	+	11.8617i	−0.141680	+	0.436045i
$741$	4.00000	+	12.3107i	0.146944	+	0.452246i
$742$	35.0344	−	25.4540i	1.28615	−	0.934446i
$743$	−2.76393	+	2.00811i	−0.101399	+	0.0736706i	−0.637329	−	0.770592i	$-0.719961\pi$
$743$	−2.76393	+	2.00811i	−0.101399	+	0.0736706i	0.535931	+	0.844262i	$0.319961\pi$
$744$	2.76393	+	8.50651i	0.101331	+	0.311864i
$745$	−4.20163	+	12.9313i	−0.153936	+	0.473765i
$746$	14.9443	+	10.8576i	0.547149	+	0.397527i
$747$	16.0344			0.586670
$748$	3.54508	−	4.02874i	0.129621	−	0.147305i
$749$	9.52786			0.348141
$750$	48.9787	+	35.5851i	1.78845	+	1.29938i
$751$	−11.7082	+	36.0341i	−0.427238	+	1.31490i	0.473596	+	0.880742i	$0.342956\pi$
$751$	−11.7082	+	36.0341i	−0.427238	+	1.31490i	−0.900835	+	0.434163i	$0.857044\pi$
$752$	−0.263932	−	0.812299i	−0.00962461	−	0.0296215i
$753$	−32.4164	+	23.5519i	−1.18132	+	0.858279i
$754$	−18.4721	+	13.4208i	−0.672716	+	0.488756i
$755$	−12.8197	−	39.4549i	−0.466555	−	1.43591i
$756$	17.2361	−	53.0472i	0.626870	−	1.92931i
$757$	−24.5623	−	17.8456i	−0.892732	−	0.648608i	0.0438568	−	0.999038i	$-0.486035\pi$
$757$	−24.5623	−	17.8456i	−0.892732	−	0.648608i	−0.936589	+	0.350430i	$0.886035\pi$
$758$	7.88854			0.286525
$759$	−8.41641	−	3.63271i	−0.305496	−	0.131859i
$760$	3.85410			0.139803
$761$	25.5066	+	18.5316i	0.924613	+	0.671770i	0.944668	−	0.328028i	$-0.106384\pi$
$761$	25.5066	+	18.5316i	0.924613	+	0.671770i	−0.0200551	+	0.999799i	$0.506384\pi$
$762$	2.29180	−	7.05342i	0.0830230	−	0.255519i
$763$	−1.12461	−	3.46120i	−0.0407137	−	0.125304i
$764$	10.8262	−	7.86572i	0.391680	−	0.284572i
$765$	−37.6976	+	27.3889i	−1.36296	+	0.990247i
$766$	−5.76393	−	17.7396i	−0.208259	−	0.640956i
$767$	−8.58359	+	26.4176i	−0.309936	+	0.953884i
$768$	2.61803	+	1.90211i	0.0944702	+	0.0686366i
$769$	−13.2705			−0.478547			−0.239273	−	0.970952i	$-0.576909\pi$
$769$	−13.2705			−0.478547			−0.239273	+	0.970952i	$0.576909\pi$
$770$	48.0689	−	10.7921i	1.73228	−	0.388922i
$771$	58.8328			2.11881
$772$	14.9443	+	10.8576i	0.537856	+	0.390775i
$773$	4.43769	−	13.6578i	0.159613	−	0.491238i	−0.838986	−	0.544153i	$-0.816851\pi$
$773$	4.43769	−	13.6578i	0.159613	−	0.491238i	0.998599	+	0.0529150i	$0.0168512\pi$
$774$	−17.5902	−	54.1370i	−0.632266	−	1.94591i
$775$	22.0344	−	16.0090i	0.791501	−	0.575059i
$776$	−13.7082	+	9.95959i	−0.492096	+	0.357529i
$777$	−12.4721	−	38.3853i	−0.447435	−	1.37706i
$778$	0.701626	−	2.15938i	0.0251545	−	0.0774176i
$779$	−0.381966	−	0.277515i	−0.0136854	−	0.00994299i
$780$	49.8885			1.78630
$781$	4.67376	+	7.88597i	0.167240	+	0.282182i
$782$	1.38197			0.0494190
$783$	−66.8328	−	48.5569i	−2.38841	−	1.73528i
$784$	2.42705	−	7.46969i	0.0866804	−	0.266775i
$785$	−26.5902	−	81.8361i	−0.949044	−	2.92086i
$786$	36.2705	−	26.3521i	1.29373	−	0.939947i
$787$	−14.0902	+	10.2371i	−0.502260	+	0.364913i	−0.809880	−	0.586596i	$-0.800468\pi$
$787$	−14.0902	+	10.2371i	−0.502260	+	0.364913i	0.307619	+	0.951509i	$0.400468\pi$
$788$	−3.38197	−	10.4086i	−0.120478	−	0.370792i
$789$	16.0000	−	49.2429i	0.569615	−	1.75309i
$790$	28.7984	+	20.9232i	1.02460	+	0.744416i
$791$	29.0132			1.03159
$792$	−12.6353	−	21.3193i	−0.448974	−	0.757547i
$793$	4.58359			0.162768
$794$	−13.3992	−	9.73508i	−0.475519	−	0.345485i
$795$	−43.3050	+	133.279i	−1.53587	+	4.72692i
$796$	8.22542	+	25.3153i	0.291542	+	0.897275i
$797$	−27.5066	+	19.9847i	−0.974333	+	0.707894i	−0.956435	−	0.291945i	$-0.905697\pi$
$797$	−27.5066	+	19.9847i	−0.974333	+	0.707894i	−0.0178980	+	0.999840i	$0.505697\pi$
$798$	−10.0902	+	7.33094i	−0.357188	+	0.259512i
$799$	−0.427051	−	1.31433i	−0.0151080	−	0.0464976i
$800$	3.04508	−	9.37181i	0.107660	−	0.331343i
$801$	85.7214	+	62.2802i	3.02882	+	2.20056i
$802$	−19.2361			−0.679249
$803$	35.4164	−	7.95148i	1.24982	−	0.280602i
$804$	29.8885			1.05409
$805$	10.2639	+	7.45718i	0.361756	+	0.262831i
$806$	3.41641	−	10.5146i	0.120338	−	0.370362i
$807$	−19.7082	−	60.6556i	−0.693762	−	2.13518i
$808$	−2.88197	+	2.09387i	−0.101387	+	0.0736621i
$809$	−28.3885	+	20.6255i	−0.998088	+	0.725153i	−0.961677	−	0.274183i	$-0.911592\pi$
$809$	−28.3885	+	20.6255i	−0.998088	+	0.725153i	−0.0364107	+	0.999337i	$0.511592\pi$
$810$	29.0795	+	89.4976i	1.02175	+	3.14462i
$811$	−3.94427	+	12.1392i	−0.138502	+	0.426266i	−0.996118	−	0.0880246i	$-0.971945\pi$
$811$	−3.94427	+	12.1392i	−0.138502	+	0.426266i	0.857616	+	0.514290i	$0.171945\pi$
$812$	−17.7984	−	12.9313i	−0.624600	−	0.453799i
$813$	−90.9017			−3.18806
$814$	−9.85410	−	4.25325i	−0.345386	−	0.149076i
$815$	66.5623			2.33158
$816$	4.23607	+	3.07768i	0.148292	+	0.107740i
$817$	−2.35410	+	7.24518i	−0.0823596	+	0.253477i
$818$	9.12461	+	28.0827i	0.319035	+	0.981887i
$819$	−93.1935	+	67.7090i	−3.25644	+	2.36595i
$820$	−1.47214	+	1.06957i	−0.0514092	+	0.0373510i
$821$	14.7148	+	45.2874i	0.513549	+	1.58054i	0.785906	+	0.618346i	$0.212197\pi$
$821$	14.7148	+	45.2874i	0.513549	+	1.58054i	−0.272356	+	0.962196i	$0.587803\pi$
$822$	9.56231	−	29.4298i	0.333524	−	1.02648i
$823$	1.40983	+	1.02430i	0.0491436	+	0.0357049i	0.612086	−	0.790791i	$-0.290331\pi$
$823$	1.40983	+	1.02430i	0.0491436	+	0.0357049i	−0.562942	+	0.826496i	$0.690331\pi$
$824$	−6.94427			−0.241915
$825$	−69.8673	+	79.3992i	−2.43247	+	2.76433i
$826$	−26.7639			−0.931236
$827$	9.76393	+	7.09391i	0.339525	+	0.246679i	0.744461	−	0.667665i	$-0.232706\pi$
$827$	9.76393	+	7.09391i	0.339525	+	0.246679i	−0.404936	+	0.914345i	$0.632706\pi$
$828$	1.97214	−	6.06961i	0.0685365	−	0.210934i
$829$	13.0902	+	40.2874i	0.454640	+	1.39924i	0.871557	+	0.490294i	$0.163111\pi$
$829$	13.0902	+	40.2874i	0.454640	+	1.39924i	−0.416916	+	0.908945i	$0.636889\pi$
$830$	−6.69098	+	4.86128i	−0.232247	+	0.168738i
$831$	−53.5967	+	38.9403i	−1.85925	+	1.35082i
$832$	−1.23607	−	3.80423i	−0.0428529	−	0.131888i
$833$	3.92705	−	12.0862i	0.136064	−	0.418763i
$834$	36.8885	+	26.8011i	1.27735	+	0.928046i
$835$	24.2492			0.839179
$836$	−0.309017	+	3.30220i	−0.0106876	+	0.114209i
$837$	40.0000			1.38260
$838$	23.2533	+	16.8945i	0.803272	+	0.583611i
$839$	7.11146	−	21.8868i	0.245515	−	0.755617i	−0.750037	−	0.661396i	$-0.769964\pi$
$839$	7.11146	−	21.8868i	0.245515	−	0.755617i	0.995551	−	0.0942204i	$-0.0300358\pi$
$840$	14.8541	+	45.7162i	0.512515	+	1.57736i
$841$	−2.89919	+	2.10638i	−0.0999720	+	0.0726339i
$842$	−19.7984	+	14.3844i	−0.682297	+	0.495718i
$843$	4.00000	+	12.3107i	0.137767	+	0.424004i
$844$	4.61803	−	14.2128i	0.158959	−	0.489226i
$845$	−9.35410	−	6.79615i	−0.321791	−	0.233795i
$846$	−6.38197			−0.219417
$847$	5.39261	+	42.0508i	0.185292	+	1.44488i
$848$	11.2361			0.385848
$849$	−25.7984	−	18.7436i	−0.885398	−	0.643279i
$850$	4.92705	−	15.1639i	0.168996	−	0.520118i
$851$	−0.854102	−	2.62866i	−0.0292782	−	0.0901092i
$852$	−7.23607	+	5.25731i	−0.247904	+	0.180113i
$853$	−5.54508	+	4.02874i	−0.189860	+	0.137941i	−0.678655	−	0.734457i	$-0.737437\pi$
$853$	−5.54508	+	4.02874i	−0.189860	+	0.137941i	0.488795	+	0.872399i	$0.337437\pi$
$854$	1.36475	+	4.20025i	0.0467006	+	0.143730i
$855$	8.89919	−	27.3889i	0.304346	−	0.936680i
$856$	2.00000	+	1.45309i	0.0683586	+	0.0496654i
$857$	26.8328			0.916592			0.458296	−	0.888800i	$-0.348460\pi$
$857$	26.8328			0.916592			0.458296	+	0.888800i	$0.348460\pi$
$858$	−4.00000	+	42.7445i	−0.136558	+	1.45927i
$859$	7.03444			0.240012			0.120006	−	0.992773i	$-0.461709\pi$
$859$	7.03444			0.240012			0.120006	+	0.992773i	$0.461709\pi$
$860$	23.7533	+	17.2578i	0.809980	+	0.588485i
$861$	1.81966	−	5.60034i	0.0620139	−	0.190859i
$862$	3.27051	+	10.0656i	0.111394	+	0.342836i
$863$	15.1803	−	11.0292i	0.516745	−	0.375437i	−0.298631	−	0.954369i	$-0.596530\pi$
$863$	15.1803	−	11.0292i	0.516745	−	0.375437i	0.815376	+	0.578931i	$0.196530\pi$
$864$	11.7082	−	8.50651i	0.398321	−	0.289397i
$865$	4.76393	+	14.6619i	0.161979	+	0.498519i
$866$	3.67376	−	11.3067i	0.124840	−	0.384217i
$867$	−37.6525	−	27.3561i	−1.27875	−	0.929063i
$868$	10.6525			0.361569
$869$	−20.2361	+	22.9969i	−0.686462	+	0.780115i
$870$	71.1935			2.41369
$871$	−29.8885	−	21.7153i	−1.01273	−	0.735795i
$872$	0.291796	−	0.898056i	0.00988146	−	0.0304120i
$873$	39.1246	+	120.413i	1.32417	+	4.07537i
$874$	−0.690983	+	0.502029i	−0.0233728	+	0.0169814i
$875$	58.3328	−	42.3813i	1.97201	−	1.43275i
$876$	10.9443	+	33.6830i	0.369773	+	1.13804i
$877$	10.0902	−	31.0543i	0.340721	−	1.04863i	−0.623114	−	0.782131i	$-0.714133\pi$
$877$	10.0902	−	31.0543i	0.340721	−	1.04863i	0.963835	−	0.266500i	$-0.0858672\pi$
$878$	−14.8541	−	10.7921i	−0.501302	−	0.364217i
$879$	77.6656			2.61960
$880$	11.7361	+	5.06555i	0.395623	+	0.170760i
$881$	5.41641			0.182483			0.0912417	−	0.995829i	$-0.470916\pi$
$881$	5.41641			0.182483			0.0912417	+	0.995829i	$0.470916\pi$
$882$	−47.4787	−	34.4953i	−1.59869	−	1.16152i
$883$	8.66312	−	26.6623i	0.291537	−	0.897259i	−0.692825	−	0.721105i	$-0.743634\pi$
$883$	8.66312	−	26.6623i	0.291537	−	0.897259i	0.984363	−	0.176154i	$-0.0563656\pi$
$884$	−2.00000	−	6.15537i	−0.0672673	−	0.207027i
$885$	70.0689	−	50.9080i	2.35534	−	1.71125i
$886$	17.2082	−	12.5025i	0.578121	−	0.420029i
$887$	−10.9098	−	33.5770i	−0.366316	−	1.12741i	−0.949153	−	0.314816i	$-0.898057\pi$
$887$	−10.9098	−	33.5770i	−0.366316	−	1.12741i	0.582836	−	0.812589i	$-0.301943\pi$
$888$	3.23607	−	9.95959i	0.108595	−	0.334222i
$889$	−7.14590	−	5.19180i	−0.239666	−	0.174127i
$890$	−54.6525			−1.83196
$891$	−79.0132	+	17.7396i	−2.64704	+	0.594298i
$892$	−10.6525			−0.356671
$893$	0.690983	+	0.502029i	0.0231229	+	0.0167997i
$894$	3.52786	−	10.8576i	0.117989	−	0.363134i
$895$	−25.1591	−	77.4316i	−0.840974	−	2.58825i
$896$	3.11803	−	2.26538i	0.104166	−	0.0756812i
$897$	−8.94427	+	6.49839i	−0.298641	+	0.216975i
$898$	4.85410	+	14.9394i	0.161983	+	0.498534i
$899$	4.87539	−	15.0049i	0.162603	−	0.500442i
$900$	−59.5689	−	43.2793i	−1.98563	−	1.44264i
$901$	18.1803			0.605675
$902$	−0.798374	−	1.34708i	−0.0265829	−	0.0448530i
$903$	−95.0132			−3.16184
$904$	6.09017	+	4.42477i	0.202556	+	0.147166i
$905$	−6.45085	+	19.8537i	−0.214434	+	0.659958i
$906$	10.7639	+	33.1280i	0.357608	+	1.10060i
$907$	−14.0344	+	10.1966i	−0.466006	+	0.338573i	−0.795883	−	0.605451i	$-0.792993\pi$
$907$	−14.0344	+	10.1966i	−0.466006	+	0.338573i	0.329877	+	0.944024i	$0.392993\pi$
$908$	21.1803	−	15.3884i	0.702894	−	0.510683i
$909$	8.22542	+	25.3153i	0.272820	+	0.839654i
$910$	18.3607	−	56.5084i	0.608651	−	1.87323i
$911$	−19.0902	−	13.8698i	−0.632486	−	0.459528i	0.224775	−	0.974411i	$-0.427835\pi$
$911$	−19.0902	−	13.8698i	−0.632486	−	0.459528i	−0.857260	+	0.514883i	$0.827835\pi$
$912$	−3.23607			−0.107157
$913$	−3.62868	−	6.12261i	−0.120092	−	0.202629i
$914$	11.0902			0.366830
$915$	−11.5623	−	8.40051i	−0.382238	−	0.277712i
$916$	−3.35410	+	10.3229i	−0.110823	+	0.341077i
$917$	−16.5000	−	50.7818i	−0.544878	−	1.67696i
$918$	18.9443	−	13.7638i	0.625254	−	0.454274i
$919$	−32.0623	+	23.2946i	−1.05764	+	0.768419i	−0.973650	−	0.228048i	$-0.926766\pi$
$919$	−32.0623	+	23.2946i	−1.05764	+	0.768419i	−0.0839880	+	0.996467i	$0.526766\pi$
$920$	1.01722	+	3.13068i	0.0335368	+	0.103216i
$921$	1.52786	−	4.70228i	0.0503448	−	0.154945i
$922$	24.8262	+	18.0373i	0.817609	+	0.594027i
$923$	11.0557			0.363904
$924$	−40.3607	+	9.06154i	−1.32777	+	0.298103i
$925$	−31.8885			−1.04849
$926$	9.88197	+	7.17967i	0.324742	+	0.235939i
$927$	−16.0344	+	49.3489i	−0.526640	+	1.62083i
$928$	−1.76393	−	5.42882i	−0.0579039	−	0.178210i
$929$	40.1418	−	29.1647i	1.31701	−	0.956864i	0.317047	−	0.948410i	$-0.397309\pi$
$929$	40.1418	−	29.1647i	1.31701	−	0.956864i	0.999964	−	0.00845439i	$-0.00269115\pi$
$930$	−27.8885	+	20.2622i	−0.914501	+	0.664424i
$931$	2.42705	+	7.46969i	0.0795434	+	0.244809i
$932$	−0.100813	+	0.310271i	−0.00330224	+	0.0101633i
$933$	14.2361	+	10.3431i	0.466068	+	0.338618i
$934$	9.27051			0.303340
$935$	18.9894	+	8.19624i	0.621018	+	0.268046i
$936$	−29.8885			−0.976938
$937$	6.87132	+	4.99231i	0.224476	+	0.163092i	0.694339	−	0.719648i	$-0.255697\pi$
$937$	6.87132	+	4.99231i	0.224476	+	0.163092i	−0.469863	+	0.882739i	$0.655697\pi$
$938$	11.0000	−	33.8545i	0.359163	−	1.10539i
$939$	15.5066	+	47.7243i	0.506038	+	1.55742i
$940$	2.66312	−	1.93487i	0.0868614	−	0.0631085i
$941$	−16.7984	+	12.2047i	−0.547611	+	0.397863i	−0.826904	−	0.562343i	$-0.809900\pi$
$941$	−16.7984	+	12.2047i	−0.547611	+	0.397863i	0.279293	+	0.960206i	$0.409900\pi$
$942$	22.3262	+	68.7131i	0.727428	+	2.23879i
$943$	0.124612	−	0.383516i	0.00405792	−	0.0124890i
$944$	−5.61803	−	4.08174i	−0.182851	−	0.132849i
$945$	214.971			6.99299
$946$	−16.6910	+	18.9681i	−0.542671	+	0.616707i
$947$	−1.49342			−0.0485297			−0.0242649	−	0.999706i	$-0.507724\pi$
$947$	−1.49342			−0.0485297			−0.0242649	+	0.999706i	$0.507724\pi$
$948$	−24.1803	−	17.5680i	−0.785341	−	0.570584i
$949$	13.5279	−	41.6345i	0.439133	−	1.35151i
$950$	3.04508	+	9.37181i	0.0987956	+	0.304062i
$951$	−22.1803	+	16.1150i	−0.719247	+	0.522563i
$952$	5.04508	−	3.66547i	0.163512	−	0.118799i
$953$	7.11146	+	21.8868i	0.230363	+	0.708983i	0.997703	+	0.0677431i	$0.0215798\pi$
$953$	7.11146	+	21.8868i	0.230363	+	0.708983i	−0.767340	+	0.641240i	$0.778420\pi$
$954$	25.9443	−	79.8483i	0.839977	−	2.58518i
$955$	41.7254	+	30.3153i	1.35020	+	0.980980i
$956$	−15.3262			−0.495686
$957$	−5.70820	+	60.9986i	−0.184520	+	1.97181i
$958$	19.9098			0.643257
$959$	−29.8156	−	21.6623i	−0.962796	−	0.699512i
$960$	−3.85410	+	11.8617i	−0.124391	+	0.382835i
$961$	−7.21885	−	22.2173i	−0.232866	−	0.716688i
$962$	−10.4721	+	7.60845i	−0.337635	+	0.245306i
$963$	14.9443	−	10.8576i	0.481572	−	0.349883i
$964$	−6.03444	−	18.5721i	−0.194356	−	0.598167i
$965$	−22.0000	+	67.7090i	−0.708205	+	2.17963i
$966$	−8.61803	−	6.26137i	−0.277281	−	0.201456i
$967$	−48.8541			−1.57104			−0.785521	−	0.618835i	$-0.787605\pi$
$967$	−48.8541			−1.57104			−0.785521	+	0.618835i	$0.787605\pi$
$968$	−5.28115	+	9.64932i	−0.169743	+	0.310141i
$969$	−5.23607			−0.168207
$970$	−52.8328	−	38.3853i	−1.69636	−	1.23248i
$971$	−10.1803	+	31.3319i	−0.326703	+	1.00549i	0.643964	+	0.765056i	$0.277289\pi$
$971$	−10.1803	+	31.3319i	−0.326703	+	1.00549i	−0.970666	+	0.240431i	$0.922711\pi$
$972$	−11.0000	−	33.8545i	−0.352825	−	1.08588i
$973$	43.9336	−	31.9196i	1.40845	−	1.02330i
$974$	−17.3262	+	12.5882i	−0.555168	+	0.403354i
$975$	39.4164	+	121.311i	1.26234	+	3.88507i
$976$	−0.354102	+	1.08981i	−0.0113345	+	0.0348841i
$977$	−5.52786	−	4.01623i	−0.176852	−	0.128491i	0.495838	−	0.868415i	$-0.334861\pi$
$977$	−5.52786	−	4.01623i	−0.176852	−	0.128491i	−0.672690	+	0.739925i	$0.734861\pi$
$978$	−55.8885			−1.78712
$979$	4.38197	−	46.8263i	0.140048	−	1.49657i
$980$	30.2705			0.966956
$981$	−5.70820	−	4.14725i	−0.182249	−	0.132412i
$982$	−7.33688	+	22.5806i	−0.234129	+	0.720576i
$983$	0.180340	+	0.555029i	0.00575195	+	0.0177027i	0.953891	−	0.300152i	$-0.0970375\pi$
$983$	0.180340	+	0.555029i	0.00575195	+	0.0177027i	−0.948139	+	0.317855i	$0.897037\pi$
$984$	1.23607	−	0.898056i	0.0394044	−	0.0286290i
$985$	34.1246	−	24.7930i	1.08730	−	0.789970i
$986$	−2.85410	−	8.78402i	−0.0908931	−	0.279740i
$987$	−3.29180	+	10.1311i	−0.104779	+	0.322477i
$988$	3.23607	+	2.35114i	0.102953	+	0.0747998i
$989$	−6.50658			−0.206897
$990$	63.0967	−	71.7050i	2.00535	−	2.27894i
$991$	12.9443			0.411188			0.205594	−	0.978637i	$-0.434087\pi$
$991$	12.9443			0.411188			0.205594	+	0.978637i	$0.434087\pi$
$992$	2.23607	+	1.62460i	0.0709952	+	0.0515811i
$993$	10.4721	−	32.2299i	0.332323	−	1.02279i
$994$	3.29180	+	10.1311i	0.104409	+	0.321339i
$995$	−82.9959	+	60.3001i	−2.63115	+	1.91164i
$996$	5.61803	−	4.08174i	0.178014	−	0.129335i
$997$	12.3369	+	37.9690i	0.390713	+	1.20249i	0.932250	+	0.361814i	$0.117842\pi$
$997$	12.3369	+	37.9690i	0.390713	+	1.20249i	−0.541537	+	0.840677i	$0.682158\pi$
$998$	−6.19098	+	19.0539i	−0.195972	+	0.603140i
$999$	−37.8885	−	27.5276i	−1.19874	−	0.870936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.a.191.1	✓	4
11.3	even	5	inner	418.2.f.a.267.1	yes	4
11.5	even	5		4598.2.a.be.1.1		2
11.6	odd	10		4598.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.a.191.1	✓	4	1.1	even	1	trivial
418.2.f.a.267.1	yes	4	11.3	even	5	inner
4598.2.a.v.1.1		2	11.6	odd	10
4598.2.a.be.1.1		2	11.5	even	5

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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.00000 + 3.07768i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.11803 + 2.26538i) q^{5} +(2.61803 - 1.90211i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.00000 + 3.07768i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.11803 + 2.26538i) q^{5} +(2.61803 - 1.90211i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +3.85410 q^{10} +(-0.309017 + 3.30220i) q^{11} -3.23607 q^{12} +(3.23607 + 2.35114i) q^{13} +(-1.19098 + 3.66547i) q^{14} +(-3.85410 - 11.8617i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.30902 + 0.951057i) q^{17} +(2.30902 + 7.10642i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-3.11803 - 2.26538i) q^{20} +12.4721 q^{21} +(2.19098 - 2.48990i) q^{22} +0.854102 q^{23} +(2.61803 + 1.90211i) q^{24} +(3.04508 - 9.37181i) q^{25} +(-1.23607 - 3.80423i) q^{26} +(11.7082 - 8.50651i) q^{27} +(3.11803 - 2.26538i) q^{28} +(-1.76393 - 5.42882i) q^{29} +(-3.85410 + 11.8617i) q^{30} +(2.23607 + 1.62460i) q^{31} +1.00000 q^{32} +(-9.85410 - 4.25325i) q^{33} +1.61803 q^{34} +(12.0172 + 8.73102i) q^{35} +(2.30902 - 7.10642i) q^{36} +(-1.00000 - 3.07768i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-10.4721 + 7.60845i) q^{39} +(1.19098 + 3.66547i) q^{40} +(0.145898 - 0.449028i) q^{41} +(-10.0902 - 7.33094i) q^{42} -7.61803 q^{43} +(-3.23607 + 0.726543i) q^{44} +28.7984 q^{45} +(-0.690983 - 0.502029i) q^{46} +(-0.263932 + 0.812299i) q^{47} +(-1.00000 - 3.07768i) q^{48} +(-6.35410 + 4.61653i) q^{49} +(-7.97214 + 5.79210i) q^{50} +(-1.61803 - 4.97980i) q^{51} +(-1.23607 + 3.80423i) q^{52} +(-9.09017 - 6.60440i) q^{53} -14.4721 q^{54} +(-6.51722 - 10.9964i) q^{55} -3.85410 q^{56} +(2.61803 + 1.90211i) q^{57} +(-1.76393 + 5.42882i) q^{58} +(2.14590 + 6.60440i) q^{59} +(10.0902 - 7.33094i) q^{60} +(0.927051 - 0.673542i) q^{61} +(-0.854102 - 2.62866i) q^{62} +(-8.89919 + 27.3889i) q^{63} +(-0.809017 - 0.587785i) q^{64} -15.4164 q^{65} +(5.47214 + 9.23305i) q^{66} -9.23607 q^{67} +(-1.30902 - 0.951057i) q^{68} +(-0.854102 + 2.62866i) q^{69} +(-4.59017 - 14.1271i) q^{70} +(2.23607 - 1.62460i) q^{71} +(-6.04508 + 4.39201i) q^{72} +(-3.38197 - 10.4086i) q^{73} +(-1.00000 + 3.07768i) q^{74} +(25.7984 + 18.7436i) q^{75} +1.00000 q^{76} +(12.4721 - 2.80017i) q^{77} +12.9443 q^{78} +(7.47214 + 5.42882i) q^{79} +(1.19098 - 3.66547i) q^{80} +(7.54508 + 23.2214i) q^{81} +(-0.381966 + 0.277515i) q^{82} +(-1.73607 + 1.26133i) q^{83} +(3.85410 + 11.8617i) q^{84} +(1.92705 - 5.93085i) q^{85} +(6.16312 + 4.47777i) q^{86} +18.4721 q^{87} +(3.04508 + 1.31433i) q^{88} -14.1803 q^{89} +(-23.2984 - 16.9273i) q^{90} +(4.76393 - 14.6619i) q^{91} +(0.263932 + 0.812299i) q^{92} +(-7.23607 + 5.25731i) q^{93} +(0.690983 - 0.502029i) q^{94} +(1.19098 + 3.66547i) q^{95} +(-1.00000 + 3.07768i) q^{96} +(-13.7082 - 9.95959i) q^{97} +7.85410 q^{98} +(16.3713 - 18.6049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} - q^{4} - 8 q^{5} + 6 q^{6} - 7 q^{7} - q^{8} - 13 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 - q^4 - 8 * q^5 + 6 * q^6 - 7 * q^7 - q^8 - 13 * q^9	\( 4 q - q^{2} - 4 q^{3} - q^{4} - 8 q^{5} + 6 q^{6} - 7 q^{7} - q^{8} - 13 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 4 q^{13} - 7 q^{14} - 2 q^{15} - q^{16} - 3 q^{17} + 7 q^{18} - q^{19} - 8 q^{20} + 32 q^{21} + 11 q^{22} - 10 q^{23} + 6 q^{24} + q^{25} + 4 q^{26} + 20 q^{27} + 8 q^{28} - 16 q^{29} - 2 q^{30} + 4 q^{32} - 26 q^{33} + 2 q^{34} + 19 q^{35} + 7 q^{36} - 4 q^{37} - q^{38} - 24 q^{39} + 7 q^{40} + 14 q^{41} - 18 q^{42} - 26 q^{43} - 4 q^{44} + 66 q^{45} - 5 q^{46} - 10 q^{47} - 4 q^{48} - 12 q^{49} - 14 q^{50} - 2 q^{51} + 4 q^{52} - 14 q^{53} - 40 q^{54} + 3 q^{55} - 2 q^{56} + 6 q^{57} - 16 q^{58} + 22 q^{59} + 18 q^{60} - 3 q^{61} + 10 q^{62} - 11 q^{63} - q^{64} - 8 q^{65} + 4 q^{66} - 28 q^{67} - 3 q^{68} + 10 q^{69} + 4 q^{70} - 13 q^{72} - 18 q^{73} - 4 q^{74} + 54 q^{75} + 4 q^{76} + 32 q^{77} + 16 q^{78} + 12 q^{79} + 7 q^{80} + 19 q^{81} - 6 q^{82} + 2 q^{83} + 2 q^{84} + q^{85} + 9 q^{86} + 56 q^{87} + q^{88} - 12 q^{89} - 44 q^{90} + 28 q^{91} + 10 q^{92} - 20 q^{93} + 5 q^{94} + 7 q^{95} - 4 q^{96} - 28 q^{97} + 18 q^{98} + 23 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 - q^4 - 8 * q^5 + 6 * q^6 - 7 * q^7 - q^8 - 13 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 4 * q^13 - 7 * q^14 - 2 * q^15 - q^16 - 3 * q^17 + 7 * q^18 - q^19 - 8 * q^20 + 32 * q^21 + 11 * q^22 - 10 * q^23 + 6 * q^24 + q^25 + 4 * q^26 + 20 * q^27 + 8 * q^28 - 16 * q^29 - 2 * q^30 + 4 * q^32 - 26 * q^33 + 2 * q^34 + 19 * q^35 + 7 * q^36 - 4 * q^37 - q^38 - 24 * q^39 + 7 * q^40 + 14 * q^41 - 18 * q^42 - 26 * q^43 - 4 * q^44 + 66 * q^45 - 5 * q^46 - 10 * q^47 - 4 * q^48 - 12 * q^49 - 14 * q^50 - 2 * q^51 + 4 * q^52 - 14 * q^53 - 40 * q^54 + 3 * q^55 - 2 * q^56 + 6 * q^57 - 16 * q^58 + 22 * q^59 + 18 * q^60 - 3 * q^61 + 10 * q^62 - 11 * q^63 - q^64 - 8 * q^65 + 4 * q^66 - 28 * q^67 - 3 * q^68 + 10 * q^69 + 4 * q^70 - 13 * q^72 - 18 * q^73 - 4 * q^74 + 54 * q^75 + 4 * q^76 + 32 * q^77 + 16 * q^78 + 12 * q^79 + 7 * q^80 + 19 * q^81 - 6 * q^82 + 2 * q^83 + 2 * q^84 + q^85 + 9 * q^86 + 56 * q^87 + q^88 - 12 * q^89 - 44 * q^90 + 28 * q^91 + 10 * q^92 - 20 * q^93 + 5 * q^94 + 7 * q^95 - 4 * q^96 - 28 * q^97 + 18 * q^98 + 23 * q^99

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