LMFDB - Embedded newform 350.2.h.a.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(71,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			211.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	350.211
Dual form			350.2.h.a.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.413545 + 1.27276i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-0.413545 - 1.27276i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.978148 + 0.710666i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.413545 + 1.27276i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-0.413545 - 1.27276i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.978148 + 0.710666i) q^{9} +(2.04275 + 0.909491i) q^{10} +(-3.33448 + 2.42264i) q^{11} +(1.08268 + 0.786610i) q^{12} +(3.59618 + 2.61278i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(2.92705 - 0.622164i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.06460 + 6.35419i) q^{17} -1.20906 q^{18} +(-0.290943 - 0.895431i) q^{19} +(-2.18720 + 0.464905i) q^{20} +(-0.413545 + 1.27276i) q^{21} +(1.27366 - 3.91992i) q^{22} +(2.44890 - 1.77923i) q^{23} -1.33826 q^{24} +(-2.50000 + 4.33013i) q^{25} -4.44512 q^{26} +(-4.55705 + 3.31089i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-2.64728 + 8.14748i) q^{29} +(-2.00234 + 2.22382i) q^{30} +(-2.36702 - 7.28493i) q^{31} +1.00000 q^{32} +(-1.70449 - 5.24588i) q^{33} +(-5.40520 - 3.92711i) q^{34} +(-1.11803 - 1.93649i) q^{35} +(0.978148 - 0.710666i) q^{36} +(8.85772 + 6.43551i) q^{37} +(0.761699 + 0.553407i) q^{38} +(-4.81263 + 3.49658i) q^{39} +(1.49622 - 1.66172i) q^{40} +(-4.23735 - 3.07861i) q^{41} +(-0.413545 - 1.27276i) q^{42} +1.11600 q^{43} +(1.27366 + 3.91992i) q^{44} +(0.282596 - 2.68872i) q^{45} +(-0.935398 + 2.87886i) q^{46} +(0.997966 - 3.07143i) q^{47} +(1.08268 - 0.786610i) q^{48} +1.00000 q^{49} +(-0.522642 - 4.97261i) q^{50} -8.94118 q^{51} +(3.59618 - 2.61278i) q^{52} +(-1.59161 + 4.89848i) q^{53} +(1.74064 - 5.35713i) q^{54} +(8.41949 + 3.74860i) q^{55} +(0.309017 + 0.951057i) q^{56} +1.25999 q^{57} +(-2.64728 - 8.14748i) q^{58} +(7.03519 + 5.11137i) q^{59} +(0.312795 - 2.97605i) q^{60} +(5.77504 - 4.19581i) q^{61} +(6.19693 + 4.50233i) q^{62} +(0.978148 + 0.710666i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.03897 - 9.88515i) q^{65} +(4.46241 + 3.24213i) q^{66} +(2.10910 + 6.49113i) q^{67} +6.68119 q^{68} +(1.25181 + 3.85266i) q^{69} +(2.04275 + 0.909491i) q^{70} +(3.73781 - 11.5038i) q^{71} +(-0.373619 + 1.14988i) q^{72} +(-4.76765 + 3.46390i) q^{73} -10.9487 q^{74} +(-4.47736 - 4.97261i) q^{75} -0.941512 q^{76} +(-3.33448 + 2.42264i) q^{77} +(1.83826 - 5.65759i) q^{78} +(-1.96038 + 6.03342i) q^{79} +(-0.233733 + 2.22382i) q^{80} +(-1.20857 - 3.71959i) q^{81} +5.23765 q^{82} +(-3.15611 - 9.71352i) q^{83} +(1.08268 + 0.786610i) q^{84} +(9.99654 - 11.1023i) q^{85} +(-0.902863 + 0.655969i) q^{86} +(-9.27504 - 6.73871i) q^{87} +(-3.33448 - 2.42264i) q^{88} +(9.43050 - 6.85166i) q^{89} +(1.35177 + 2.34133i) q^{90} +(3.59618 + 2.61278i) q^{91} +(-0.935398 - 2.87886i) q^{92} +10.2509 q^{93} +(0.997966 + 3.07143i) q^{94} +(-1.40871 + 1.56453i) q^{95} +(-0.413545 + 1.27276i) q^{96} +(5.62920 - 17.3249i) q^{97} +(-0.809017 + 0.587785i) q^{98} -4.98331 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + 3 * q^6 + 8 * q^7 - 2 * q^8 - q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} - q^{9} + 5 q^{10} - q^{11} - 2 q^{12} + 11 q^{13} - 2 q^{14} + 10 q^{15} - 2 q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 5 q^{20} + 3 q^{21} + 4 q^{22} + 15 q^{23} - 2 q^{24} - 20 q^{25} - 14 q^{26} - 2 q^{28} - 8 q^{29} - 5 q^{30} - 7 q^{31} + 8 q^{32} - 11 q^{33} - 21 q^{34} - q^{36} + 14 q^{37} + 14 q^{38} - 4 q^{39} - 5 q^{40} + 3 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 10 q^{45} - 10 q^{46} + 2 q^{47} - 2 q^{48} + 8 q^{49} + 5 q^{50} + 14 q^{51} + 11 q^{52} + 4 q^{53} - 5 q^{54} + 20 q^{55} - 2 q^{56} - 36 q^{57} - 8 q^{58} + 11 q^{59} + 15 q^{60} + 13 q^{62} - q^{63} - 2 q^{64} - 20 q^{65} + 24 q^{66} + 14 q^{67} + 14 q^{68} - 5 q^{69} + 5 q^{70} + 23 q^{71} + 4 q^{72} - 5 q^{73} - 36 q^{74} - 45 q^{75} - 16 q^{76} - q^{77} + 6 q^{78} + 2 q^{79} + 5 q^{80} - 7 q^{81} - 12 q^{82} - 27 q^{83} - 2 q^{84} + 15 q^{85} + 4 q^{86} - 28 q^{87} - q^{88} - 15 q^{89} - 5 q^{90} + 11 q^{91} - 10 q^{92} + 38 q^{93} + 2 q^{94} + 20 q^{95} + 3 q^{96} + 40 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + 3 * q^6 + 8 * q^7 - 2 * q^8 - q^9 + 5 * q^10 - q^11 - 2 * q^12 + 11 * q^13 - 2 * q^14 + 10 * q^15 - 2 * q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 5 * q^20 + 3 * q^21 + 4 * q^22 + 15 * q^23 - 2 * q^24 - 20 * q^25 - 14 * q^26 - 2 * q^28 - 8 * q^29 - 5 * q^30 - 7 * q^31 + 8 * q^32 - 11 * q^33 - 21 * q^34 - q^36 + 14 * q^37 + 14 * q^38 - 4 * q^39 - 5 * q^40 + 3 * q^41 + 3 * q^42 - 6 * q^43 + 4 * q^44 - 10 * q^45 - 10 * q^46 + 2 * q^47 - 2 * q^48 + 8 * q^49 + 5 * q^50 + 14 * q^51 + 11 * q^52 + 4 * q^53 - 5 * q^54 + 20 * q^55 - 2 * q^56 - 36 * q^57 - 8 * q^58 + 11 * q^59 + 15 * q^60 + 13 * q^62 - q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 14 * q^67 + 14 * q^68 - 5 * q^69 + 5 * q^70 + 23 * q^71 + 4 * q^72 - 5 * q^73 - 36 * q^74 - 45 * q^75 - 16 * q^76 - q^77 + 6 * q^78 + 2 * q^79 + 5 * q^80 - 7 * q^81 - 12 * q^82 - 27 * q^83 - 2 * q^84 + 15 * q^85 + 4 * q^86 - 28 * q^87 - q^88 - 15 * q^89 - 5 * q^90 + 11 * q^91 - 10 * q^92 + 38 * q^93 + 2 * q^94 + 20 * q^95 + 3 * q^96 + 40 * q^97 - 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.413545	+	1.27276i	−0.238761	+	0.734830i	0.757840	+	0.652441i	$0.226255\pi$
$3$	−0.413545	+	1.27276i	−0.238761	+	0.734830i	−0.996600	+	0.0823887i	$0.973745\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i
$6$	−0.413545	−	1.27276i	−0.168829	−	0.519603i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.978148	+	0.710666i	0.326049	+	0.236889i
$10$	2.04275	+	0.909491i	0.645974	+	0.287606i
$11$	−3.33448	+	2.42264i	−1.00538	+	0.730455i	−0.963236	−	0.268657i	$-0.913420\pi$
$11$	−3.33448	+	2.42264i	−1.00538	+	0.730455i	−0.0421484	+	0.999111i	$0.513420\pi$
$12$	1.08268	+	0.786610i	0.312542	+	0.227075i
$13$	3.59618	+	2.61278i	0.997401	+	0.724654i	0.961529	−	0.274702i	$-0.0885792\pi$
$13$	3.59618	+	2.61278i	0.997401	+	0.724654i	0.0358719	+	0.999356i	$0.488579\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	2.92705	−	0.622164i	0.755761	−	0.160642i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.06460	+	6.35419i	0.500740	+	1.54112i	0.807817	+	0.589433i	$0.200649\pi$
$17$	2.06460	+	6.35419i	0.500740	+	1.54112i	−0.307077	+	0.951685i	$0.599351\pi$
$18$	−1.20906			−0.284977
$19$	−0.290943	−	0.895431i	−0.0667469	−	0.205426i	0.912120	−	0.409923i	$-0.134444\pi$
$19$	−0.290943	−	0.895431i	−0.0667469	−	0.205426i	−0.978867	+	0.204497i	$0.934444\pi$
$20$	−2.18720	+	0.464905i	−0.489074	+	0.103956i
$21$	−0.413545	+	1.27276i	−0.0902430	+	0.277739i
$22$	1.27366	−	3.91992i	0.271545	−	0.835730i
$23$	2.44890	−	1.77923i	0.510632	−	0.370996i	−0.302431	−	0.953171i	$-0.597798\pi$
$23$	2.44890	−	1.77923i	0.510632	−	0.370996i	0.813063	+	0.582176i	$0.197798\pi$
$24$	−1.33826			−0.273171
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$	−4.44512			−0.871761
$27$	−4.55705	+	3.31089i	−0.877004	+	0.637181i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	−2.64728	+	8.14748i	−0.491587	+	1.51295i	0.330621	+	0.943764i	$0.392742\pi$
$29$	−2.64728	+	8.14748i	−0.491587	+	1.51295i	−0.822209	+	0.569186i	$0.807258\pi$
$30$	−2.00234	+	2.22382i	−0.365575	+	0.406012i
$31$	−2.36702	−	7.28493i	−0.425129	−	1.30841i	−0.902871	−	0.429912i	$-0.858545\pi$
$31$	−2.36702	−	7.28493i	−0.425129	−	1.30841i	0.477742	−	0.878500i	$-0.341455\pi$
$32$	1.00000			0.176777
$33$	−1.70449	−	5.24588i	−0.296713	−	0.913190i
$34$	−5.40520	−	3.92711i	−0.926984	−	0.673493i
$35$	−1.11803	−	1.93649i	−0.188982	−	0.327327i
$36$	0.978148	−	0.710666i	0.163025	−	0.118444i
$37$	8.85772	+	6.43551i	1.45620	+	1.05799i	0.984333	+	0.176321i	$0.0564196\pi$
$37$	8.85772	+	6.43551i	1.45620	+	1.05799i	0.471867	+	0.881670i	$0.343580\pi$
$38$	0.761699	+	0.553407i	0.123564	+	0.0897744i
$39$	−4.81263	+	3.49658i	−0.770638	+	0.559901i
$40$	1.49622	−	1.66172i	0.236573	−	0.262741i
$41$	−4.23735	−	3.07861i	−0.661762	−	0.480798i	0.205495	−	0.978658i	$-0.434119\pi$
$41$	−4.23735	−	3.07861i	−0.661762	−	0.480798i	−0.867258	+	0.497860i	$0.834119\pi$
$42$	−0.413545	−	1.27276i	−0.0638114	−	0.196391i
$43$	1.11600			0.170188			0.0850942	−	0.996373i	$-0.472881\pi$
$43$	1.11600			0.170188			0.0850942	+	0.996373i	$0.472881\pi$
$44$	1.27366	+	3.91992i	0.192011	+	0.590950i
$45$	0.282596	−	2.68872i	0.0421270	−	0.400811i
$46$	−0.935398	+	2.87886i	−0.137917	+	0.424465i
$47$	0.997966	−	3.07143i	0.145568	−	0.448013i	−0.851515	−	0.524330i	$-0.824316\pi$
$47$	0.997966	−	3.07143i	0.145568	−	0.448013i	0.997084	+	0.0763164i	$0.0243159\pi$
$48$	1.08268	−	0.786610i	0.156271	−	0.113537i
$49$	1.00000			0.142857
$50$	−0.522642	−	4.97261i	−0.0739128	−	0.703233i
$51$	−8.94118			−1.25202
$52$	3.59618	−	2.61278i	0.498701	−	0.362327i
$53$	−1.59161	+	4.89848i	−0.218625	+	0.672858i	0.780251	+	0.625466i	$0.215091\pi$
$53$	−1.59161	+	4.89848i	−0.218625	+	0.672858i	−0.998876	+	0.0473923i	$0.984909\pi$
$54$	1.74064	−	5.35713i	0.236871	−	0.729013i
$55$	8.41949	+	3.74860i	1.13528	+	0.505461i
$56$	0.309017	+	0.951057i	0.0412941	+	0.127090i
$57$	1.25999			0.166890
$58$	−2.64728	−	8.14748i	−0.347605	−	1.06982i
$59$	7.03519	+	5.11137i	0.915904	+	0.665443i	0.942501	−	0.334203i	$-0.108467\pi$
$59$	7.03519	+	5.11137i	0.915904	+	0.665443i	−0.0265970	+	0.999646i	$0.508467\pi$
$60$	0.312795	−	2.97605i	0.0403817	−	0.384206i
$61$	5.77504	−	4.19581i	0.739418	−	0.537219i	−0.153111	−	0.988209i	$-0.548929\pi$
$61$	5.77504	−	4.19581i	0.739418	−	0.537219i	0.892529	+	0.450990i	$0.148929\pi$
$62$	6.19693	+	4.50233i	0.787011	+	0.571797i
$63$	0.978148	+	0.710666i	0.123235	+	0.0895355i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.03897	−	9.88515i	0.128869	−	1.22610i
$66$	4.46241	+	3.24213i	0.549285	+	0.399079i
$67$	2.10910	+	6.49113i	0.257667	+	0.793018i	0.993292	+	0.115629i	$0.0368885\pi$
$67$	2.10910	+	6.49113i	0.257667	+	0.793018i	−0.735625	+	0.677389i	$0.763112\pi$
$68$	6.68119			0.810214
$69$	1.25181	+	3.85266i	0.150700	+	0.463806i
$70$	2.04275	+	0.909491i	0.244155	+	0.108705i
$71$	3.73781	−	11.5038i	0.443597	−	1.36525i	−0.440419	−	0.897793i	$-0.645170\pi$
$71$	3.73781	−	11.5038i	0.443597	−	1.36525i	0.884015	−	0.467458i	$-0.154830\pi$
$72$	−0.373619	+	1.14988i	−0.0440314	+	0.135515i
$73$	−4.76765	+	3.46390i	−0.558011	+	0.405419i	−0.830730	−	0.556675i	$-0.812077\pi$
$73$	−4.76765	+	3.46390i	−0.558011	+	0.405419i	0.272719	+	0.962094i	$0.412077\pi$
$74$	−10.9487			−1.27276
$75$	−4.47736	−	4.97261i	−0.517001	−	0.574187i
$76$	−0.941512			−0.107999
$77$	−3.33448	+	2.42264i	−0.380000	+	0.276086i
$78$	1.83826	−	5.65759i	0.208142	−	0.640596i
$79$	−1.96038	+	6.03342i	−0.220559	+	0.678812i	0.778153	+	0.628075i	$0.216157\pi$
$79$	−1.96038	+	6.03342i	−0.220559	+	0.678812i	−0.998712	+	0.0507370i	$0.983843\pi$
$80$	−0.233733	+	2.22382i	−0.0261321	+	0.248630i
$81$	−1.20857	−	3.71959i	−0.134285	−	0.413288i
$82$	5.23765			0.578401
$83$	−3.15611	−	9.71352i	−0.346428	−	1.06620i	−0.960815	−	0.277192i	$-0.910596\pi$
$83$	−3.15611	−	9.71352i	−0.346428	−	1.06620i	0.614386	−	0.789005i	$-0.289404\pi$
$84$	1.08268	+	0.786610i	0.118130	+	0.0858262i
$85$	9.99654	−	11.1023i	1.08428	−	1.20421i
$86$	−0.902863	+	0.655969i	−0.0973583	+	0.0707349i
$87$	−9.27504	−	6.73871i	−0.994389	−	0.722466i
$88$	−3.33448	−	2.42264i	−0.355457	−	0.258255i
$89$	9.43050	−	6.85166i	0.999631	−	0.726274i	0.0376219	−	0.999292i	$-0.488022\pi$
$89$	9.43050	−	6.85166i	0.999631	−	0.726274i	0.962009	+	0.273018i	$0.0880218\pi$
$90$	1.35177	+	2.34133i	0.142489	+	0.246798i
$91$	3.59618	+	2.61278i	0.376982	+	0.273894i
$92$	−0.935398	−	2.87886i	−0.0975220	−	0.300142i
$93$	10.2509			1.06296
$94$	0.997966	+	3.07143i	0.102932	+	0.316793i
$95$	−1.40871	+	1.56453i	−0.144531	+	0.160517i
$96$	−0.413545	+	1.27276i	−0.0422073	+	0.129901i
$97$	5.62920	−	17.3249i	0.571559	−	1.75908i	−0.0760486	−	0.997104i	$-0.524230\pi$
$97$	5.62920	−	17.3249i	0.571559	−	1.75908i	0.647608	−	0.761974i	$-0.275770\pi$
$98$	−0.809017	+	0.587785i	−0.0817231	+	0.0593753i
$99$	−4.98331			−0.500841
$100$	3.34565	+	3.71572i	0.334565	+	0.371572i
$101$	−4.96097			−0.493635			−0.246817	−	0.969062i	$-0.579385\pi$
$101$	−4.96097			−0.493635			−0.246817	+	0.969062i	$0.579385\pi$
$102$	7.23357	−	5.25549i	0.716230	−	0.520371i
$103$	3.58755	−	11.0413i	0.353491	−	1.08793i	−0.603388	−	0.797448i	$-0.706183\pi$
$103$	3.58755	−	11.0413i	0.353491	−	1.08793i	0.956879	−	0.290487i	$-0.0938172\pi$
$104$	−1.37362	+	4.22757i	−0.134694	+	0.414547i
$105$	2.92705	−	0.622164i	0.285651	−	0.0607170i
$106$	−1.59161	−	4.89848i	−0.154591	−	0.475783i
$107$	−17.2417			−1.66682			−0.833410	−	0.552656i	$-0.813615\pi$
$107$	−17.2417			−1.66682			−0.833410	+	0.552656i	$0.813615\pi$
$108$	1.74064	+	5.35713i	0.167493	+	0.515490i
$109$	1.53818	+	1.11755i	0.147331	+	0.107042i	0.659009	−	0.752135i	$-0.270976\pi$
$109$	1.53818	+	1.11755i	0.147331	+	0.107042i	−0.511678	+	0.859177i	$0.670976\pi$
$110$	−9.01489	+	1.91617i	−0.859536	+	0.182700i
$111$	−11.8539	+	8.61239i	−1.12513	+	0.817452i
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	−9.87139	−	7.17198i	−0.928622	−	0.674683i	0.0170331	−	0.999855i	$-0.494578\pi$
$113$	−9.87139	−	7.17198i	−0.928622	−	0.674683i	−0.945655	+	0.325172i	$0.894578\pi$
$114$	−1.01935	+	0.740603i	−0.0954711	+	0.0693638i
$115$	−6.18343	−	2.75304i	−0.576607	−	0.256722i
$116$	6.93066	+	5.03542i	0.643496	+	0.467527i
$117$	1.66078	+	5.11137i	0.153540	+	0.472546i
$118$	−8.69598			−0.800530
$119$	2.06460	+	6.35419i	0.189262	+	0.582488i
$120$	1.49622	+	2.59153i	0.136586	+	0.236573i
$121$	1.85039	−	5.69490i	0.168217	−	0.517719i
$122$	−2.20587	+	6.78897i	−0.199710	+	0.614644i
$123$	5.67068	−	4.11999i	0.511308	−	0.371487i
$124$	−7.65983			−0.687873
$125$	11.1803			1.00000
$126$	−1.20906			−0.107711
$127$	−5.38712	+	3.91398i	−0.478030	+	0.347309i	−0.800563	−	0.599249i	$-0.795466\pi$
$127$	−5.38712	+	3.91398i	−0.478030	+	0.347309i	0.322532	+	0.946558i	$0.395466\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.461517	+	1.42040i	−0.0406343	+	0.125060i
$130$	4.96980	+	8.60795i	0.435880	+	0.754967i
$131$	1.13893	+	3.50527i	0.0995089	+	0.306257i	0.988403	−	0.151857i	$-0.0485253\pi$
$131$	1.13893	+	3.50527i	0.0995089	+	0.306257i	−0.888894	+	0.458114i	$0.848525\pi$
$132$	−5.51584			−0.480092
$133$	−0.290943	−	0.895431i	−0.0252280	−	0.0776437i
$134$	−5.52169	−	4.01174i	−0.477001	−	0.346562i
$135$	11.5064	+	5.12300i	0.990316	+	0.440917i
$136$	−5.40520	+	3.92711i	−0.463492	+	0.336747i
$137$	15.3456	+	11.1492i	1.31106	+	0.952542i	0.999998	+	0.00215368i	$0.000685538\pi$
$137$	15.3456	+	11.1492i	1.31106	+	0.952542i	0.311065	+	0.950389i	$0.399314\pi$
$138$	−3.27727	−	2.38108i	−0.278980	−	0.202691i
$139$	1.04715	−	0.760801i	0.0888184	−	0.0645303i	−0.542490	−	0.840062i	$-0.682518\pi$
$139$	1.04715	−	0.760801i	0.0888184	−	0.0645303i	0.631308	+	0.775532i	$0.282518\pi$
$140$	−2.18720	+	0.464905i	−0.184853	+	0.0392916i
$141$	3.49649	+	2.54035i	0.294457	+	0.213936i
$142$	3.73781	+	11.5038i	0.313670	+	0.965378i
$143$	−18.3212			−1.53210
$144$	−0.373619	−	1.14988i	−0.0311349	−	0.0958235i
$145$	18.7373	−	3.98273i	1.55605	−	0.330748i
$146$	1.82108	−	5.60471i	0.150714	−	0.463849i
$147$	−0.413545	+	1.27276i	−0.0341087	+	0.104976i
$148$	8.85772	−	6.43551i	0.728100	−	0.528995i
$149$	−19.0811			−1.56318			−0.781592	−	0.623789i	$-0.785592\pi$
$149$	−19.0811			−1.56318			−0.781592	+	0.623789i	$0.785592\pi$
$150$	6.54508	+	1.39120i	0.534404	+	0.113591i
$151$	1.71207			0.139326			0.0696630	−	0.997571i	$-0.477808\pi$
$151$	1.71207			0.139326			0.0696630	+	0.997571i	$0.477808\pi$
$152$	0.761699	−	0.553407i	0.0617819	−	0.0448872i
$153$	−2.49622	+	7.68258i	−0.201808	+	0.621100i
$154$	1.27366	−	3.91992i	0.102634	−	0.315876i
$155$	−11.4608	+	12.7285i	−0.920554	+	1.02238i
$156$	1.83826	+	5.65759i	0.147179	+	0.452969i
$157$	−3.20499			−0.255786			−0.127893	−	0.991788i	$-0.540821\pi$
$157$	−3.20499			−0.255786			−0.127893	+	0.991788i	$0.540821\pi$
$158$	−1.96038	−	6.03342i	−0.155959	−	0.479993i
$159$	−5.57640	−	4.05149i	−0.442237	−	0.321304i
$160$	−1.11803	−	1.93649i	−0.0883883	−	0.153093i
$161$	2.44890	−	1.77923i	0.193001	−	0.140223i
$162$	3.16407	+	2.29883i	0.248593	+	0.180613i
$163$	7.71198	+	5.60308i	0.604049	+	0.438867i	0.847314	−	0.531093i	$-0.178218\pi$
$163$	7.71198	+	5.60308i	0.604049	+	0.438867i	−0.243265	+	0.969960i	$0.578218\pi$
$164$	−4.23735	+	3.07861i	−0.330881	+	0.240399i
$165$	−8.25292	+	9.16580i	−0.642489	+	0.713556i
$166$	8.26281	+	6.00328i	0.641319	+	0.465945i
$167$	3.64543	+	11.2195i	0.282092	+	0.868190i	0.987255	+	0.159145i	$0.0508737\pi$
$167$	3.64543	+	11.2195i	0.282092	+	0.868190i	−0.705163	+	0.709045i	$0.749126\pi$
$168$	−1.33826			−0.103249
$169$	2.08869	+	6.42832i	0.160668	+	0.494486i
$170$	−1.56161	+	14.8578i	−0.119770	+	1.13954i
$171$	0.351767	−	1.08263i	0.0269003	−	0.0827905i
$172$	0.344863	−	1.06138i	0.0262956	−	0.0809294i
$173$	5.55753	−	4.03778i	0.422531	−	0.306987i	−0.356124	−	0.934439i	$-0.615902\pi$
$173$	5.55753	−	4.03778i	0.422531	−	0.306987i	0.778656	+	0.627452i	$0.215902\pi$
$174$	11.4646			0.869127
$175$	−2.50000	+	4.33013i	−0.188982	+	0.327327i
$176$	4.12165			0.310681
$177$	−9.41493	+	6.84034i	−0.707669	+	0.514152i
$178$	−3.60213	+	11.0862i	−0.269991	+	0.830947i
$179$	4.33040	−	13.3276i	0.323669	−	0.996152i	−0.648368	−	0.761327i	$-0.724548\pi$
$179$	4.33040	−	13.3276i	0.323669	−	0.996152i	0.972038	−	0.234825i	$-0.0754518\pi$
$180$	−2.46980	−	1.09963i	−0.184088	−	0.0819613i
$181$	−5.84714	−	17.9956i	−0.434614	−	1.33760i	−0.893481	−	0.449100i	$-0.851745\pi$
$181$	−5.84714	−	17.9956i	−0.434614	−	1.33760i	0.458867	−	0.888505i	$-0.348255\pi$
$182$	−4.44512			−0.329495
$183$	2.95203	+	9.08541i	0.218220	+	0.671613i
$184$	2.44890	+	1.77923i	0.180536	+	0.131167i
$185$	2.55908	−	24.3480i	0.188147	−	1.79010i
$186$	−8.29311	+	6.02530i	−0.608081	+	0.441796i
$187$	−22.2783	−	16.1861i	−1.62915	−	1.18365i
$188$	−2.61271	−	1.89825i	−0.190551	−	0.138444i
$189$	−4.55705	+	3.31089i	−0.331476	+	0.240832i
$190$	0.220062	−	2.09375i	0.0159650	−	0.151897i
$191$	4.30757	+	3.12964i	0.311685	+	0.226452i	0.732619	−	0.680639i	$-0.238298\pi$
$191$	4.30757	+	3.12964i	0.311685	+	0.226452i	−0.420934	+	0.907091i	$0.638298\pi$
$192$	−0.413545	−	1.27276i	−0.0298451	−	0.0918537i
$193$	−3.02977			−0.218088			−0.109044	−	0.994037i	$-0.534779\pi$
$193$	−3.02977			−0.218088			−0.109044	+	0.994037i	$0.534779\pi$
$194$	5.62920	+	17.3249i	0.404153	+	1.24386i
$195$	12.1518	+	5.41032i	0.870207	+	0.387441i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−1.74977	+	5.38525i	−0.124666	+	0.383683i	−0.993840	−	0.110823i	$-0.964651\pi$
$197$	−1.74977	+	5.38525i	−0.124666	+	0.383683i	0.869174	+	0.494506i	$0.164651\pi$
$198$	4.03158	−	2.92911i	0.286512	−	0.208163i
$199$	8.09273			0.573678			0.286839	−	0.957979i	$-0.407395\pi$
$199$	8.09273			0.573678			0.286839	+	0.957979i	$0.407395\pi$
$200$	−4.89074	−	1.03956i	−0.345827	−	0.0735079i
$201$	−9.13387			−0.644254
$202$	4.01351	−	2.91598i	0.282389	−	0.205168i
$203$	−2.64728	+	8.14748i	−0.185803	+	0.571841i
$204$	−2.76298	+	8.50357i	−0.193447	+	0.595369i
$205$	−1.22421	+	11.6476i	−0.0855025	+	0.813502i
$206$	3.58755	+	11.0413i	0.249956	+	0.769286i
$207$	3.65983			0.254376
$208$	−1.37362	−	4.22757i	−0.0952434	−	0.293129i
$209$	3.13945	+	2.28095i	0.217161	+	0.157776i
$210$	−2.00234	+	2.22382i	−0.138174	+	0.153458i
$211$	2.64834	−	1.92413i	0.182319	−	0.132462i	−0.492882	−	0.870096i	$-0.664057\pi$
$211$	2.64834	−	1.92413i	0.182319	−	0.132462i	0.675201	+	0.737633i	$0.264057\pi$
$212$	4.16690	+	3.02743i	0.286184	+	0.207925i
$213$	13.0959	+	9.51469i	0.897313	+	0.651936i
$214$	13.9488	−	10.1344i	0.953523	−	0.692775i
$215$	−1.24773	−	2.16113i	−0.0850942	−	0.147388i
$216$	−4.55705	−	3.31089i	−0.310068	−	0.225277i
$217$	−2.36702	−	7.28493i	−0.160684	−	0.494533i
$218$	−1.90130			−0.128772
$219$	−2.43708	−	7.50056i	−0.164683	−	0.506841i
$220$	6.16690	−	6.84903i	0.415772	−	0.461762i
$221$	−9.17741	+	28.2452i	−0.617340	+	1.89998i
$222$	4.52780	−	13.9351i	0.303886	−	0.935265i
$223$	−22.2137	+	16.1392i	−1.48754	+	1.08076i	−0.512510	+	0.858681i	$0.671284\pi$
$223$	−22.2137	+	16.1392i	−1.48754	+	1.08076i	−0.975029	+	0.222078i	$0.928716\pi$
$224$	1.00000			0.0668153
$225$	−5.52264	+	2.45884i	−0.368176	+	0.163923i
$226$	12.2017			0.811645
$227$	2.25947	−	1.64160i	0.149966	−	0.108957i	−0.510272	−	0.860013i	$-0.670455\pi$
$227$	2.25947	−	1.64160i	0.149966	−	0.108957i	0.660238	+	0.751056i	$0.270455\pi$
$228$	0.389358	−	1.19832i	0.0257859	−	0.0793607i
$229$	2.52149	−	7.76034i	0.166625	−	0.512818i	−0.832528	−	0.553983i	$-0.813107\pi$
$229$	2.52149	−	7.76034i	0.166625	−	0.512818i	0.999152	+	0.0411656i	$0.0131071\pi$
$230$	6.62069	−	1.40727i	0.436556	−	0.0927927i
$231$	−1.70449	−	5.24588i	−0.112147	−	0.345153i
$232$	−8.56677			−0.562436
$233$	−6.74888	−	20.7709i	−0.442134	−	1.36075i	−0.885597	−	0.464455i	$-0.846250\pi$
$233$	−6.74888	−	20.7709i	−0.442134	−	1.36075i	0.443463	−	0.896293i	$-0.353750\pi$
$234$	−4.34799	−	3.15900i	−0.284237	−	0.206510i
$235$	−7.06355	+	1.50140i	−0.460775	+	0.0979408i
$236$	7.03519	−	5.11137i	0.457952	−	0.332722i
$237$	−6.86840	−	4.99018i	−0.446150	−	0.324147i
$238$	−5.40520	−	3.92711i	−0.350367	−	0.254557i
$239$	23.9526	−	17.4026i	1.54937	−	1.12568i	0.605264	−	0.796025i	$-0.293067\pi$
$239$	23.9526	−	17.4026i	1.54937	−	1.12568i	0.944101	−	0.329655i	$-0.106933\pi$
$240$	−2.73373	−	1.21714i	−0.176462	−	0.0785658i
$241$	−8.41466	−	6.11361i	−0.542036	−	0.393812i	0.282805	−	0.959178i	$-0.408735\pi$
$241$	−8.41466	−	6.11361i	−0.542036	−	0.393812i	−0.824841	+	0.565365i	$0.808735\pi$
$242$	1.85039	+	5.69490i	0.118947	+	0.366082i
$243$	−11.6645			−0.748278
$244$	−2.20587	−	6.78897i	−0.141216	−	0.434619i
$245$	−1.11803	−	1.93649i	−0.0714286	−	0.123718i
$246$	−2.16601	+	6.66628i	−0.138099	+	0.425026i
$247$	1.29328	−	3.98030i	0.0822893	−	0.253261i
$248$	6.19693	−	4.50233i	0.393506	−	0.285899i
$249$	13.6682			0.866187
$250$	−9.04508	+	6.57164i	−0.572061	+	0.415627i
$251$	−6.93900			−0.437986			−0.218993	−	0.975726i	$-0.570277\pi$
$251$	−6.93900			−0.437986			−0.218993	+	0.975726i	$0.570277\pi$
$252$	0.978148	−	0.710666i	0.0616175	−	0.0447677i
$253$	−3.85538	+	11.8656i	−0.242386	+	0.745986i
$254$	2.05770	−	6.33294i	0.129111	−	0.397364i
$255$	9.99654	+	17.3145i	0.626008	+	1.08428i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.36316			0.147410			0.0737049	−	0.997280i	$-0.476518\pi$
$257$	2.36316			0.147410			0.0737049	+	0.997280i	$0.476518\pi$
$258$	−0.461517	−	1.42040i	−0.0287328	−	0.0884304i
$259$	8.85772	+	6.43551i	0.550392	+	0.399883i
$260$	−9.08028	−	4.04280i	−0.563135	−	0.250724i
$261$	−8.37957	+	6.08811i	−0.518682	+	0.376845i
$262$	−2.98176	−	2.16638i	−0.184214	−	0.133839i
$263$	9.37845	+	6.81385i	0.578300	+	0.420160i	0.838111	−	0.545500i	$-0.183660\pi$
$263$	9.37845	+	6.81385i	0.578300	+	0.420160i	−0.259811	+	0.965660i	$0.583660\pi$
$264$	4.46241	−	3.24213i	0.274642	−	0.199539i
$265$	11.2653	−	2.39452i	0.692025	−	0.147094i
$266$	0.761699	+	0.553407i	0.0467028	+	0.0339315i
$267$	4.82059	+	14.8363i	0.295015	+	0.907964i
$268$	6.82518			0.416914
$269$	−3.42008	−	10.5259i	−0.208526	−	0.641778i	−0.999550	−	0.0299925i	$-0.990452\pi$
$269$	−3.42008	−	10.5259i	−0.208526	−	0.641778i	0.791024	−	0.611785i	$-0.209548\pi$
$270$	−12.3201	+	2.61872i	−0.749779	+	0.159370i
$271$	−7.93300	+	24.4153i	−0.481895	+	1.48312i	0.354532	+	0.935044i	$0.384640\pi$
$271$	−7.93300	+	24.4153i	−0.481895	+	1.48312i	−0.836427	+	0.548078i	$0.815360\pi$
$272$	2.06460	−	6.35419i	0.125185	−	0.385279i
$273$	−4.81263	+	3.49658i	−0.291274	+	0.211623i
$274$	−18.9682			−1.14591
$275$	−2.15415	−	20.4953i	−0.129900	−	1.23592i
$276$	4.05093			0.243837
$277$	17.5562	−	12.7553i	1.05485	−	0.766394i	0.0817225	−	0.996655i	$-0.473958\pi$
$277$	17.5562	−	12.7553i	1.05485	−	0.766394i	0.973129	+	0.230261i	$0.0739579\pi$
$278$	−0.399977	+	1.23100i	−0.0239890	+	0.0738306i
$279$	2.86186	−	8.80790i	0.171335	−	0.527315i
$280$	1.49622	−	1.66172i	0.0894163	−	0.0993069i
$281$	−3.40384	−	10.4759i	−0.203056	−	0.624942i	−0.999788	−	0.0206089i	$-0.993440\pi$
$281$	−3.40384	−	10.4759i	−0.203056	−	0.624942i	0.796732	−	0.604333i	$-0.206560\pi$
$282$	−4.32190			−0.257365
$283$	3.75312	+	11.5509i	0.223100	+	0.686631i	0.998479	+	0.0551350i	$0.0175589\pi$
$283$	3.75312	+	11.5509i	0.223100	+	0.686631i	−0.775379	+	0.631496i	$0.782441\pi$
$284$	−9.78572	−	7.10974i	−0.580676	−	0.421886i
$285$	−1.40871	−	2.43996i	−0.0834448	−	0.144531i
$286$	14.8222	−	10.7690i	0.876455	−	0.636782i
$287$	−4.23735	−	3.07861i	−0.250123	−	0.181725i
$288$	0.978148	+	0.710666i	0.0576379	+	0.0418764i
$289$	−22.3599	+	16.2454i	−1.31529	+	0.955612i
$290$	−12.8178	+	14.2356i	−0.752686	+	0.835943i
$291$	19.7226	+	14.3293i	1.15616	+	0.839997i
$292$	1.82108	+	5.60471i	0.106571	+	0.327991i
$293$	11.9284			0.696862			0.348431	−	0.937334i	$-0.386715\pi$
$293$	11.9284			0.696862			0.348431	+	0.937334i	$0.386715\pi$
$294$	−0.413545	−	1.27276i	−0.0241185	−	0.0742290i
$295$	2.03253	−	19.3383i	0.118339	−	1.12592i
$296$	−3.38335	+	10.4129i	−0.196653	+	0.605236i
$297$	7.17429	−	22.0802i	0.416294	−	1.28122i
$298$	15.4369	−	11.2156i	0.894238	−	0.649702i
$299$	13.4554			0.778148
$300$	−6.11281	+	2.72160i	−0.352923	+	0.157132i
$301$	1.11600			0.0643252
$302$	−1.38509	+	1.00633i	−0.0797030	+	0.0579076i
$303$	2.05158	−	6.31413i	0.117860	−	0.362737i
$304$	−0.290943	+	0.895431i	−0.0166867	+	0.0513565i
$305$	−14.5818	−	6.49226i	−0.834954	−	0.371745i
$306$	−2.49622	−	7.68258i	−0.142699	−	0.439184i
$307$	−7.47469			−0.426603			−0.213302	−	0.976986i	$-0.568422\pi$
$307$	−7.47469			−0.426603			−0.213302	+	0.976986i	$0.568422\pi$
$308$	1.27366	+	3.91992i	0.0725735	+	0.223358i
$309$	12.5694	+	9.13219i	0.715047	+	0.519512i
$310$	1.79035	−	17.0341i	0.101685	−	0.967470i
$311$	18.9168	−	13.7439i	1.07267	−	0.779344i	0.0962838	−	0.995354i	$-0.469304\pi$
$311$	18.9168	−	13.7439i	1.07267	−	0.779344i	0.976391	+	0.216010i	$0.0693044\pi$
$312$	−4.81263	−	3.49658i	−0.272462	−	0.197955i
$313$	10.9094	+	7.92617i	0.616638	+	0.448014i	0.851745	−	0.523956i	$-0.175544\pi$
$313$	10.9094	+	7.92617i	0.616638	+	0.448014i	−0.235108	+	0.971969i	$0.575544\pi$
$314$	2.59289	−	1.88385i	0.146325	−	0.106312i
$315$	0.282596	−	2.68872i	0.0159225	−	0.151492i
$316$	5.13233	+	3.72886i	0.288716	+	0.209765i
$317$	1.76657	+	5.43694i	0.0992204	+	0.305369i	0.988331	−	0.152324i	$-0.0486758\pi$
$317$	1.76657	+	5.43694i	0.0992204	+	0.305369i	−0.889110	+	0.457693i	$0.848676\pi$
$318$	6.89281			0.386529
$319$	−10.9111	−	33.5811i	−0.610907	−	1.88018i
$320$	2.04275	+	0.909491i	0.114193	+	0.0508421i
$321$	7.13023	−	21.9446i	0.397971	−	1.22483i
$322$	−0.935398	+	2.87886i	−0.0521277	+	0.160433i
$323$	5.08906	−	3.69742i	0.283163	−	0.205730i
$324$	−3.91101			−0.217278
$325$	−20.3041	+	9.03998i	−1.12627	+	0.501448i
$326$	−9.53253			−0.527958
$327$	−2.05849	+	1.49558i	−0.113835	+	0.0827057i
$328$	1.61852	−	4.98130i	0.0893679	−	0.275046i
$329$	0.997966	−	3.07143i	0.0550197	−	0.169333i
$330$	1.28923	−	12.2662i	0.0709699	−	0.675234i
$331$	−4.96590	−	15.2835i	−0.272950	−	0.840055i	−0.989754	−	0.142780i	$-0.954396\pi$
$331$	−4.96590	−	15.2835i	−0.272950	−	0.840055i	0.716804	−	0.697275i	$-0.245604\pi$
$332$	−10.2134			−0.560533
$333$	4.09066	+	12.5898i	0.224167	+	0.689914i
$334$	−9.54386	−	6.93402i	−0.522217	−	0.379413i
$335$	10.2120	−	11.3416i	0.557940	−	0.619655i
$336$	1.08268	−	0.786610i	0.0590648	−	0.0429131i
$337$	15.8847	+	11.5409i	0.865296	+	0.628674i	0.929321	−	0.369274i	$-0.120394\pi$
$337$	15.8847	+	11.5409i	0.865296	+	0.628674i	−0.0640244	+	0.997948i	$0.520394\pi$
$338$	−5.46826	−	3.97292i	−0.297434	−	0.216098i
$339$	13.2105	−	9.59798i	0.717495	−	0.521291i
$340$	−7.46980	−	12.9381i	−0.405107	−	0.701666i
$341$	25.5416	+	18.5570i	1.38315	+	1.00492i
$342$	0.351767	+	1.08263i	0.0190214	+	0.0585417i
$343$	1.00000			0.0539949
$344$	0.344863	+	1.06138i	0.0185938	+	0.0572257i
$345$	6.06109	−	6.73152i	0.326318	−	0.362413i
$346$	−2.12279	+	6.53327i	−0.114122	+	0.351231i
$347$	4.30942	−	13.2630i	0.231342	−	0.711997i	−0.766244	−	0.642550i	$-0.777877\pi$
$347$	4.30942	−	13.2630i	0.231342	−	0.711997i	0.997586	−	0.0694470i	$-0.0221235\pi$
$348$	−9.27504	+	6.73871i	−0.497194	+	0.361233i
$349$	2.07827			0.111247			0.0556237	−	0.998452i	$-0.482285\pi$
$349$	2.07827			0.111247			0.0556237	+	0.998452i	$0.482285\pi$
$350$	−0.522642	−	4.97261i	−0.0279364	−	0.265797i
$351$	−25.0386			−1.33646
$352$	−3.33448	+	2.42264i	−0.177729	+	0.129127i
$353$	−3.35325	+	10.3202i	−0.178475	+	0.549291i	−0.999775	−	0.0212061i	$-0.993249\pi$
$353$	−3.35325	+	10.3202i	−0.178475	+	0.549291i	0.821300	+	0.570497i	$0.193249\pi$
$354$	3.59618	−	11.0679i	0.191135	−	0.588253i
$355$	−26.4560	+	5.62340i	−1.40414	+	0.298459i
$356$	−3.60213	−	11.0862i	−0.190913	−	0.587568i
$357$	−8.94118			−0.473217
$358$	4.33040	+	13.3276i	0.228869	+	0.704386i
$359$	22.4957	+	16.3441i	1.18728	+	0.862609i	0.992974	−	0.118332i	$-0.0377549\pi$
$359$	22.4957	+	16.3441i	1.18728	+	0.862609i	0.194305	+	0.980941i	$0.437755\pi$
$360$	2.64445	−	0.562096i	0.139375	−	0.0296251i
$361$	14.6542	−	10.6469i	0.771272	−	0.560362i
$362$	15.3080	+	11.1219i	0.804571	+	0.584555i
$363$	6.48304	+	4.71020i	0.340271	+	0.247222i
$364$	3.59618	−	2.61278i	0.188491	−	0.136947i
$365$	12.0382	+	5.35975i	0.630108	+	0.280542i
$366$	−7.72851	−	5.61509i	−0.403976	−	0.293506i
$367$	−6.09865	−	18.7697i	−0.318347	−	0.979772i	−0.974355	−	0.225017i	$-0.927756\pi$
$367$	−6.09865	−	18.7697i	−0.318347	−	0.979772i	0.656008	−	0.754754i	$-0.272244\pi$
$368$	−3.02701			−0.157794
$369$	−1.95689	−	6.02267i	−0.101871	−	0.313528i
$370$	12.2411	+	21.2021i	0.636382	+	1.10225i
$371$	−1.59161	+	4.89848i	−0.0826324	+	0.254316i
$372$	3.16769	−	9.74914i	0.164237	−	0.505469i
$373$	−5.52780	+	4.01618i	−0.286219	+	0.207950i	−0.721625	−	0.692284i	$-0.756605\pi$
$373$	−5.52780	+	4.01618i	−0.286219	+	0.207950i	0.435407	+	0.900234i	$0.356605\pi$
$374$	27.5375			1.42393
$375$	−4.62358	+	14.2299i	−0.238761	+	0.734830i
$376$	3.22949			0.166548
$377$	−30.8077	+	22.3831i	−1.58668	+	1.15279i
$378$	1.74064	−	5.35713i	0.0895287	−	0.275541i
$379$	−1.17015	+	3.60134i	−0.0601064	+	0.184988i	−0.976601	−	0.215058i	$-0.931006\pi$
$379$	−1.17015	+	3.60134i	−0.0601064	+	0.184988i	0.916495	+	0.400046i	$0.131006\pi$
$380$	1.05264	+	1.82323i	0.0539994	+	0.0935297i
$381$	−2.75374	−	8.47513i	−0.141078	−	0.434194i
$382$	−5.32445			−0.272423
$383$	4.62709	+	14.2407i	0.236433	+	0.727667i	0.996928	+	0.0783231i	$0.0249566\pi$
$383$	4.62709	+	14.2407i	0.236433	+	0.727667i	−0.760495	+	0.649344i	$0.775043\pi$
$384$	1.08268	+	0.786610i	0.0552501	+	0.0401415i
$385$	8.41949	+	3.74860i	0.429097	+	0.191046i
$386$	2.45114	−	1.78085i	0.124760	−	0.0906431i
$387$	1.09161	+	0.793103i	0.0554898	+	0.0403157i
$388$	−14.7374	−	10.7074i	−0.748181	−	0.543585i
$389$	−21.7912	+	15.8322i	−1.10486	+	0.802726i	−0.981846	−	0.189679i	$-0.939255\pi$
$389$	−21.7912	+	15.8322i	−1.10486	+	0.802726i	−0.123012	+	0.992405i	$0.539255\pi$
$390$	−13.0111	+	2.76560i	−0.658843	+	0.140041i
$391$	16.3616	+	11.8874i	0.827441	+	0.601171i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	−4.93237			−0.248805
$394$	−1.74977	−	5.38525i	−0.0881523	−	0.271305i
$395$	13.8754	−	2.94931i	0.698148	−	0.148396i
$396$	−1.53993	+	4.73941i	−0.0773842	+	0.238164i
$397$	2.91456	−	8.97010i	0.146278	−	0.450196i	−0.850895	−	0.525335i	$-0.823940\pi$
$397$	2.91456	−	8.97010i	0.146278	−	0.450196i	0.997173	+	0.0751388i	$0.0239400\pi$
$398$	−6.54715	+	4.75679i	−0.328179	+	0.238436i
$399$	1.25999			0.0630783
$400$	4.56773	−	2.03368i	0.228386	−	0.101684i
$401$	17.2398			0.860916			0.430458	−	0.902611i	$-0.358352\pi$
$401$	17.2398			0.860916			0.430458	+	0.902611i	$0.358352\pi$
$402$	7.38946	−	5.36876i	0.368553	−	0.267769i
$403$	10.5217	−	32.3824i	0.524123	−	1.61308i
$404$	−1.53302	+	4.71816i	−0.0762707	+	0.234737i
$405$	−5.85174	+	6.49901i	−0.290775	+	0.322939i
$406$	−2.64728	−	8.14748i	−0.131382	−	0.404353i
$407$	−45.1268			−2.23685
$408$	−2.76298	−	8.50357i	−0.136788	−	0.420989i
$409$	7.51253	+	5.45817i	0.371471	+	0.269889i	0.757821	−	0.652463i	$-0.226264\pi$
$409$	7.51253	+	5.45817i	0.371471	+	0.269889i	−0.386350	+	0.922352i	$0.626264\pi$
$410$	−5.85587	−	10.1427i	−0.289201	−	0.500910i
$411$	−20.5364	+	14.9206i	−1.01299	+	0.735978i
$412$	−9.39232	−	6.82392i	−0.462726	−	0.336190i
$413$	7.03519	+	5.11137i	0.346179	+	0.251514i
$414$	−2.96086	+	2.15119i	−0.145519	+	0.105725i
$415$	−15.2815	+	16.9718i	−0.750140	+	0.833114i
$416$	3.59618	+	2.61278i	0.176317	+	0.128102i
$417$	0.535274	+	1.64740i	0.0262125	+	0.0806736i
$418$	−3.88058			−0.189805
$419$	0.835624	+	2.57179i	0.0408229	+	0.125640i	0.969391	−	0.245522i	$-0.0789594\pi$
$419$	0.835624	+	2.57179i	0.0408229	+	0.125640i	−0.928568	+	0.371162i	$0.878959\pi$
$420$	0.312795	−	2.97605i	0.0152629	−	0.145216i
$421$	−0.649427	+	1.99873i	−0.0316511	+	0.0974122i	−0.965634	−	0.259905i	$-0.916309\pi$
$421$	−0.649427	+	1.99873i	−0.0316511	+	0.0974122i	0.933983	+	0.357318i	$0.116309\pi$
$422$	−1.01157	+	3.11330i	−0.0492427	+	0.151553i
$423$	3.15892	−	2.29509i	0.153592	−	0.111591i
$424$	−5.15057			−0.250134
$425$	−32.6760	−	6.94549i	−1.58502	−	0.336906i
$426$	−16.1874			−0.784280
$427$	5.77504	−	4.19581i	0.279474	−	0.203050i
$428$	−5.32798	+	16.3978i	−0.257538	+	0.792620i
$429$	7.57666	−	23.3186i	0.365805	−	1.12583i
$430$	2.27971	+	1.01499i	0.109937	+	0.0489473i
$431$	−1.55583	−	4.78835i	−0.0749417	−	0.230647i	0.906568	−	0.422060i	$-0.138693\pi$
$431$	−1.55583	−	4.78835i	−0.0749417	−	0.230647i	−0.981510	+	0.191413i	$0.938693\pi$
$432$	5.63282			0.271009
$433$	11.1291	+	34.2518i	0.534829	+	1.64604i	0.744018	+	0.668160i	$0.232918\pi$
$433$	11.1291	+	34.2518i	0.534829	+	1.64604i	−0.209188	+	0.977875i	$0.567082\pi$
$434$	6.19693	+	4.50233i	0.297462	+	0.216119i
$435$	−2.67965	+	25.4951i	−0.128479	+	1.22240i
$436$	1.53818	−	1.11755i	0.0736655	−	0.0535211i
$437$	−2.30567	−	1.67517i	−0.110295	−	0.0801341i
$438$	6.38036	+	4.63560i	0.304865	+	0.221498i
$439$	−18.0791	+	13.1352i	−0.862866	+	0.626909i	−0.928663	−	0.370924i	$-0.879041\pi$
$439$	−18.0791	+	13.1352i	−0.862866	+	0.626909i	0.0657970	+	0.997833i	$0.479041\pi$
$440$	−0.963364	+	9.16580i	−0.0459266	+	0.436962i
$441$	0.978148	+	0.710666i	0.0465785	+	0.0338412i
$442$	−9.17741	−	28.2452i	−0.436525	−	1.34349i
$443$	20.2049			0.959964			0.479982	−	0.877278i	$-0.340643\pi$
$443$	20.2049			0.959964			0.479982	+	0.877278i	$0.340643\pi$
$444$	4.52780	+	13.9351i	0.214880	+	0.661332i
$445$	−23.8118	−	10.6017i	−1.12879	−	0.502569i
$446$	8.48487	−	26.1138i	0.401770	−	1.23652i
$447$	7.89090	−	24.2857i	0.373227	−	1.14867i
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	18.2113			0.859444			0.429722	−	0.902961i	$-0.358612\pi$
$449$	18.2113			0.859444			0.429722	+	0.902961i	$0.358612\pi$
$450$	3.02264	−	5.23537i	0.142489	−	0.246798i
$451$	21.5877			1.01653
$452$	−9.87139	+	7.17198i	−0.464311	+	0.337342i
$453$	−0.708017	+	2.17905i	−0.0332656	+	0.102381i
$454$	−0.863039	+	2.65616i	−0.0405044	+	0.124660i
$455$	1.03897	−	9.88515i	0.0487077	−	0.463423i
$456$	0.389358	+	1.19832i	0.0182334	+	0.0561165i
$457$	9.17063			0.428984			0.214492	−	0.976726i	$-0.431190\pi$
$457$	9.17063			0.428984			0.214492	+	0.976726i	$0.431190\pi$
$458$	2.52149	+	7.76034i	0.117821	+	0.362617i
$459$	−30.4465	−	22.1207i	−1.42112	−	1.03250i
$460$	−4.52908	+	5.03005i	−0.211169	+	0.234527i
$461$	21.3662	−	15.5234i	0.995121	−	0.722998i	0.0340848	−	0.999419i	$-0.489148\pi$
$461$	21.3662	−	15.5234i	0.995121	−	0.722998i	0.961037	+	0.276421i	$0.0891484\pi$
$462$	4.46241	+	3.24213i	0.207610	+	0.150838i
$463$	−1.99563	−	1.44991i	−0.0927449	−	0.0673831i	0.540446	−	0.841378i	$-0.318255\pi$
$463$	−1.99563	−	1.44991i	−0.0927449	−	0.0673831i	−0.633191	+	0.773995i	$0.718255\pi$
$464$	6.93066	−	5.03542i	0.321748	−	0.233764i
$465$	−11.4608	−	19.8507i	−0.531482	−	0.920554i
$466$	17.6688	+	12.8371i	0.818491	+	0.594669i
$467$	4.80152	+	14.7776i	0.222188	+	0.683824i	0.998565	+	0.0535554i	$0.0170554\pi$
$467$	4.80152	+	14.7776i	0.222188	+	0.683824i	−0.776377	+	0.630269i	$0.782945\pi$
$468$	5.37441			0.248432
$469$	2.10910	+	6.49113i	0.0973890	+	0.299733i
$470$	4.83203	−	5.36651i	0.222885	−	0.247539i
$471$	1.32541	−	4.07919i	0.0610716	−	0.187959i
$472$	−2.68720	+	8.27037i	−0.123689	+	0.380674i
$473$	−3.72128	+	2.70367i	−0.171105	+	0.124315i
$474$	8.48981			0.389950
$475$	4.60469	+	0.978756i	0.211278	+	0.0449084i
$476$	6.68119			0.306232
$477$	−5.03802	+	3.66033i	−0.230675	+	0.167595i
$478$	−9.14908	+	28.1580i	−0.418469	+	1.28792i
$479$	−2.03595	+	6.26600i	−0.0930248	+	0.286301i	−0.986734	−	0.162346i	$-0.948094\pi$
$479$	−2.03595	+	6.26600i	−0.0930248	+	0.286301i	0.893709	+	0.448647i	$0.148094\pi$
$480$	2.92705	−	0.622164i	0.133601	−	0.0283978i
$481$	15.0394	+	46.2865i	0.685737	+	2.11048i
$482$	10.4011			0.473757
$483$	1.25181	+	3.85266i	0.0569592	+	0.175302i
$484$	−4.84437	−	3.51964i	−0.220199	−	0.159984i
$485$	−39.8432	+	8.46893i	−1.80919	+	0.384554i
$486$	9.43678	−	6.85622i	0.428061	−	0.311004i
$487$	20.9625	+	15.2302i	0.949902	+	0.690144i	0.950784	−	0.309856i	$-0.100281\pi$
$487$	20.9625	+	15.2302i	0.949902	+	0.690144i	−0.000881906		1.00000i	$0.500281\pi$
$488$	5.77504	+	4.19581i	0.261424	+	0.189935i
$489$	−10.3206	+	7.49839i	−0.466716	+	0.339089i
$490$	2.04275	+	0.909491i	0.0922820	+	0.0410866i
$491$	19.2107	+	13.9574i	0.866967	+	0.629888i	0.929771	−	0.368138i	$-0.120005\pi$
$491$	19.2107	+	13.9574i	0.866967	+	0.629888i	−0.0628047	+	0.998026i	$0.520005\pi$
$492$	−2.16601	−	6.66628i	−0.0976511	−	0.300539i
$493$	−57.2363			−2.57779
$494$	1.29328	+	3.98030i	0.0581873	+	0.179082i
$495$	5.57151	+	9.65013i	0.250421	+	0.433741i
$496$	−2.36702	+	7.28493i	−0.106282	+	0.327103i
$497$	3.73781	−	11.5038i	0.167664	−	0.516016i
$498$	−11.0578	+	8.03396i	−0.495512	+	0.360010i
$499$	−24.2119			−1.08387			−0.541936	−	0.840419i	$-0.682309\pi$
$499$	−24.2119			−1.08387			−0.541936	+	0.840419i	$0.682309\pi$
$500$	3.45492	−	10.6331i	0.154508	−	0.475528i
$501$	−15.7873			−0.705324
$502$	5.61377	−	4.07864i	0.250555	−	0.182039i
$503$	−2.75987	+	8.49399i	−0.123056	+	0.378728i	−0.993542	−	0.113465i	$-0.963805\pi$
$503$	−2.75987	+	8.49399i	−0.123056	+	0.378728i	0.870486	+	0.492194i	$0.163805\pi$
$504$	−0.373619	+	1.14988i	−0.0166423	+	0.0512198i
$505$	5.54653	+	9.60687i	0.246817	+	0.427500i
$506$	−3.85538	−	11.8656i	−0.171393	−	0.527492i
$507$	−9.04549			−0.401724
$508$	2.05770	+	6.33294i	0.0912956	+	0.280979i
$509$	−11.2071	−	8.14245i	−0.496747	−	0.360908i	0.311026	−	0.950401i	$-0.399327\pi$
$509$	−11.2071	−	8.14245i	−0.496747	−	0.360908i	−0.807773	+	0.589494i	$0.799327\pi$
$510$	−18.2646	−	8.13192i	−0.808770	−	0.360088i
$511$	−4.76765	+	3.46390i	−0.210908	+	0.153234i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	4.29051	+	3.11724i	0.189431	+	0.137629i
$514$	−1.91184	+	1.38903i	−0.0843274	+	0.0612675i
$515$	−25.3924	+	5.39733i	−1.11892	+	0.237835i
$516$	1.20827	+	0.877857i	0.0531910	+	0.0386455i
$517$	4.11327	+	12.6593i	0.180901	+	0.556757i
$518$	−10.9487			−0.481060
$519$	2.84085	+	8.74322i	0.124699	+	0.383785i
$520$	9.72240	−	2.06656i	0.426355	−	0.0906246i
$521$	11.9820	−	36.8768i	0.524941	−	1.61560i	−0.239492	−	0.970898i	$-0.576981\pi$
$521$	11.9820	−	36.8768i	0.524941	−	1.61560i	0.764433	−	0.644704i	$-0.223019\pi$
$522$	3.20071	−	9.85077i	0.140091	−	0.431157i
$523$	8.79817	−	6.39224i	0.384717	−	0.279513i	−0.378570	−	0.925573i	$-0.623584\pi$
$523$	8.79817	−	6.39224i	0.384717	−	0.279513i	0.763287	+	0.646059i	$0.223584\pi$
$524$	3.68566			0.161009
$525$	−4.47736	−	4.97261i	−0.195408	−	0.217022i
$526$	−11.5924			−0.505453
$527$	41.4029	−	30.0810i	1.80354	−	1.31035i
$528$	−1.70449	+	5.24588i	−0.0741783	+	0.228297i
$529$	−4.27593	+	13.1600i	−0.185910	+	0.572172i
$530$	−7.70639	+	8.55881i	−0.334744	+	0.371771i
$531$	3.24898	+	9.99934i	0.140994	+	0.433934i
$532$	−0.941512			−0.0408197
$533$	−7.19453	−	22.1425i	−0.311630	−	0.959098i
$534$	−12.6205	−	9.16931i	−0.546141	−	0.396795i
$535$	19.2768	+	33.3884i	0.833410	+	1.44351i
$536$	−5.52169	+	4.01174i	−0.238501	+	0.173281i
$537$	15.1721	+	11.0231i	0.654723	+	0.475684i
$538$	8.95390	+	6.50539i	0.386030	+	0.280467i
$539$	−3.33448	+	2.42264i	−0.143626	+	0.104351i
$540$	8.42794	−	9.36018i	0.362681	−	0.402798i
$541$	4.41976	+	3.21114i	0.190020	+	0.138058i	0.678728	−	0.734390i	$-0.262532\pi$
$541$	4.41976	+	3.21114i	0.190020	+	0.138058i	−0.488708	+	0.872448i	$0.662532\pi$
$542$	−7.93300	−	24.4153i	−0.340752	−	1.04873i
$543$	25.3222			1.08668
$544$	2.06460	+	6.35419i	0.0885191	+	0.272434i
$545$	0.444395	−	4.22814i	0.0190358	−	0.181114i
$546$	1.83826	−	5.65759i	0.0786703	−	0.242122i
$547$	6.40424	−	19.7102i	0.273826	−	0.842749i	−0.715702	−	0.698406i	$-0.753893\pi$
$547$	6.40424	−	19.7102i	0.273826	−	0.842749i	0.989528	−	0.144343i	$-0.0461069\pi$
$548$	15.3456	−	11.1492i	0.655531	−	0.476271i
$549$	8.63066			0.368348
$550$	13.7896	+	15.3149i	0.587991	+	0.653030i
$551$	8.06572			0.343611
$552$	−3.27727	+	2.38108i	−0.139490	+	0.101345i
$553$	−1.96038	+	6.03342i	−0.0833636	+	0.256567i
$554$	−6.70588	+	20.6386i	−0.284906	+	0.876849i
$555$	29.9309	+	13.3261i	1.27050	+	0.565662i
$556$	−0.399977	−	1.23100i	−0.0169628	−	0.0522061i
$557$	7.81705			0.331219			0.165609	−	0.986191i	$-0.447041\pi$
$557$	7.81705			0.331219			0.165609	+	0.986191i	$0.447041\pi$
$558$	2.86186	+	8.80790i	0.121152	+	0.372868i
$559$	4.01334	+	2.91586i	0.169746	+	0.123328i
$560$	−0.233733	+	2.22382i	−0.00987701	+	0.0939735i
$561$	29.8142	−	21.6613i	1.25876	−	0.914541i
$562$	8.91137	+	6.47449i	0.375903	+	0.273110i
$563$	−16.5790	−	12.0453i	−0.698722	−	0.507651i	0.180794	−	0.983521i	$-0.442133\pi$
$563$	−16.5790	−	12.0453i	−0.698722	−	0.507651i	−0.879516	+	0.475870i	$0.842133\pi$
$564$	3.49649	−	2.54035i	0.147229	−	0.106968i
$565$	−2.85194	+	27.1344i	−0.119982	+	1.14155i
$566$	−9.82581	−	7.13887i	−0.413009	−	0.300069i
$567$	−1.20857	−	3.71959i	−0.0507551	−	0.156208i
$568$	12.0958			0.507529
$569$	−6.75987	−	20.8048i	−0.283389	−	0.872181i	−0.986877	−	0.161474i	$-0.948375\pi$
$569$	−6.75987	−	20.8048i	−0.283389	−	0.872181i	0.703488	−	0.710707i	$-0.251625\pi$
$570$	2.57384	+	1.14595i	0.107806	+	0.0479985i
$571$	−8.98789	+	27.6619i	−0.376131	+	1.15761i	0.566581	+	0.824006i	$0.308266\pi$
$571$	−8.98789	+	27.6619i	−0.376131	+	1.15761i	−0.942712	+	0.333607i	$0.891734\pi$
$572$	−5.66157	+	17.4245i	−0.236722	+	0.728556i
$573$	−5.76466	+	4.18827i	−0.240822	+	0.174967i
$574$	5.23765			0.218615
$575$	1.58204	+	15.0521i	0.0659758	+	0.627718i
$576$	−1.20906			−0.0503774
$577$	9.12079	−	6.62664i	0.379704	−	0.275871i	−0.381520	−	0.924361i	$-0.624599\pi$
$577$	9.12079	−	6.62664i	0.379704	−	0.275871i	0.761223	+	0.648490i	$0.224599\pi$
$578$	8.54072	−	26.2856i	0.355247	−	1.09334i
$579$	1.25295	−	3.85618i	0.0520708	−	0.160257i
$580$	2.00234	−	19.0509i	0.0831424	−	0.791048i
$581$	−3.15611	−	9.71352i	−0.130938	−	0.402985i
$582$	−24.3784			−1.01052
$583$	−6.56007	−	20.1898i	−0.271690	−	0.836177i
$584$	−4.76765	−	3.46390i	−0.197287	−	0.143337i
$585$	8.04131	−	8.93078i	0.332467	−	0.369242i
$586$	−9.65024	+	7.01131i	−0.398648	+	0.289634i
$587$	−13.0811	−	9.50397i	−0.539914	−	0.392271i	0.284139	−	0.958783i	$-0.408292\pi$
$587$	−13.0811	−	9.50397i	−0.539914	−	0.392271i	−0.824053	+	0.566512i	$0.808292\pi$
$588$	1.08268	+	0.786610i	0.0446488	+	0.0324393i
$589$	−5.83448	+	4.23900i	−0.240406	+	0.174665i
$590$	9.72240	+	16.8397i	0.400265	+	0.693279i
$591$	−6.13053	−	4.45409i	−0.252176	−	0.183217i
$592$	−3.38335	−	10.4129i	−0.139055	−	0.427966i
$593$	22.9056			0.940621			0.470310	−	0.882501i	$-0.344142\pi$
$593$	22.9056			0.940621			0.470310	+	0.882501i	$0.344142\pi$
$594$	7.17429	+	22.0802i	0.294365	+	0.905961i
$595$	9.99654	−	11.1023i	0.409818	−	0.455149i
$596$	−5.89638	+	18.1472i	−0.241525	+	0.743339i
$597$	−3.34671	+	10.3001i	−0.136972	+	0.421556i
$598$	−10.8857	+	7.90891i	−0.445149	+	0.323419i
$599$	47.1703			1.92733			0.963664	−	0.267117i	$-0.0860711\pi$
$599$	47.1703			1.92733			0.963664	+	0.267117i	$0.0860711\pi$
$600$	3.34565	−	5.79484i	0.136586	−	0.236573i
$601$	−16.3476			−0.666834			−0.333417	−	0.942779i	$-0.608202\pi$
$601$	−16.3476			−0.666834			−0.333417	+	0.942779i	$0.608202\pi$
$602$	−0.902863	+	0.655969i	−0.0367980	+	0.0267353i
$603$	−2.55002	+	7.84815i	−0.103845	+	0.319601i
$604$	0.529058	−	1.62827i	0.0215271	−	0.0662535i
$605$	−13.0969	+	2.78384i	−0.532466	+	0.113179i
$606$	2.05158	+	6.31413i	0.0833399	+	0.256494i
$607$	−28.3450			−1.15049			−0.575245	−	0.817981i	$-0.695093\pi$
$607$	−28.3450			−1.15049			−0.575245	+	0.817981i	$0.695093\pi$
$608$	−0.290943	−	0.895431i	−0.0117993	−	0.0363145i
$609$	−9.27504	−	6.73871i	−0.375844	−	0.273066i
$610$	15.6130	−	3.31865i	0.632152	−	0.134368i
$611$	11.6138	−	8.43794i	0.469845	−	0.341362i
$612$	6.53519	+	4.74810i	0.264170	+	0.191930i
$613$	−7.02250	−	5.10214i	−0.283636	−	0.206074i	0.436866	−	0.899527i	$-0.356088\pi$
$613$	−7.02250	−	5.10214i	−0.283636	−	0.206074i	−0.720502	+	0.693453i	$0.756088\pi$
$614$	6.04715	−	4.39351i	0.244043	−	0.177308i
$615$	−14.3183	−	6.37493i	−0.577371	−	0.257062i
$616$	−3.33448	−	2.42264i	−0.134350	−	0.0976111i
$617$	−3.85428	−	11.8623i	−0.155167	−	0.477556i	0.843010	−	0.537897i	$-0.180781\pi$
$617$	−3.85428	−	11.8623i	−0.155167	−	0.477556i	−0.998178	+	0.0603409i	$0.980781\pi$
$618$	−15.5366			−0.624974
$619$	6.84923	+	21.0798i	0.275294	+	0.847267i	0.989141	+	0.146966i	$0.0469509\pi$
$619$	6.84923	+	21.0798i	0.275294	+	0.847267i	−0.713848	+	0.700301i	$0.753049\pi$
$620$	8.56395	+	14.8332i	0.343936	+	0.595715i
$621$	−5.26893	+	16.2161i	−0.211435	+	0.650729i
$622$	−7.22559	+	22.2381i	−0.289720	+	0.891665i
$623$	9.43050	−	6.85166i	0.377825	−	0.274506i
$624$	5.94874			0.238140
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−13.4848			−0.538961
$627$	−4.20141	+	3.05250i	−0.167788	+	0.121905i
$628$	−0.990396	+	3.04813i	−0.0395211	+	0.121633i
$629$	−22.6048	+	69.5704i	−0.901312	+	2.77395i
$630$	1.35177	+	2.34133i	0.0538557	+	0.0932808i
$631$	−13.9137	−	42.8221i	−0.553897	−	1.70472i	−0.698837	−	0.715281i	$-0.746299\pi$
$631$	−13.9137	−	42.8221i	−0.553897	−	1.70472i	0.144940	−	0.989440i	$-0.453701\pi$
$632$	−6.34391			−0.252347
$633$	1.35375	+	4.16642i	0.0538067	+	0.165600i
$634$	−4.62494	−	3.36021i	−0.183680	−	0.133451i
$635$	13.6024	+	6.05616i	0.539794	+	0.240332i
$636$	−5.57640	+	4.05149i	−0.221119	+	0.160652i
$637$	3.59618	+	2.61278i	0.142486	+	0.103522i
$638$	28.5658	+	20.7542i	1.13093	+	0.821668i
$639$	11.8315	−	8.59608i	0.468047	−	0.340056i
$640$	−2.18720	+	0.464905i	−0.0864569	+	0.0183770i
$641$	−10.4135	−	7.56588i	−0.411310	−	0.298834i	0.362822	−	0.931858i	$-0.381813\pi$
$641$	−10.4135	−	7.56588i	−0.411310	−	0.298834i	−0.774132	+	0.633024i	$0.781813\pi$
$642$	7.13023	+	21.9446i	0.281408	+	0.866084i
$643$	−0.757886			−0.0298881			−0.0149441	−	0.999888i	$-0.504757\pi$
$643$	−0.757886			−0.0298881			−0.0149441	+	0.999888i	$0.504757\pi$
$644$	−0.935398	−	2.87886i	−0.0368598	−	0.113443i
$645$	3.26659	−	0.694335i	0.128622	−	0.0273394i
$646$	−1.94385	+	5.98255i	−0.0764796	+	0.235380i
$647$	−4.24125	+	13.0532i	−0.166741	+	0.513175i	−0.999160	−	0.0409707i	$-0.986955\pi$
$647$	−4.24125	+	13.0532i	−0.166741	+	0.513175i	0.832420	+	0.554146i	$0.186955\pi$
$648$	3.16407	−	2.29883i	0.124297	−	0.0903067i
$649$	−35.8417			−1.40691
$650$	11.1128	−	19.2480i	0.435880	−	0.754967i
$651$	10.2509			0.401763
$652$	7.71198	−	5.60308i	0.302025	−	0.219434i
$653$	6.58205	−	20.2575i	0.257575	−	0.792736i	−0.735736	−	0.677269i	$-0.763164\pi$
$653$	6.58205	−	20.2575i	0.257575	−	0.792736i	0.993311	−	0.115467i	$-0.0368365\pi$
$654$	0.786273	−	2.41990i	0.0307457	−	0.0946255i
$655$	5.51456	−	6.12454i	0.215472	−	0.239306i
$656$	1.61852	+	4.98130i	0.0631927	+	0.194487i
$657$	−7.12514			−0.277978
$658$	0.997966	+	3.07143i	0.0389048	+	0.119737i
$659$	16.1805	+	11.7558i	0.630303	+	0.457942i	0.856505	−	0.516138i	$-0.172631\pi$
$659$	16.1805	+	11.7558i	0.630303	+	0.457942i	−0.226202	+	0.974080i	$0.572631\pi$
$660$	6.16690	+	10.6814i	0.240046	+	0.415772i
$661$	−22.7875	+	16.5561i	−0.886329	+	0.643956i	−0.934918	−	0.354863i	$-0.884528\pi$
$661$	−22.7875	+	16.5561i	−0.886329	+	0.643956i	0.0485889	+	0.998819i	$0.484528\pi$
$662$	13.0009	+	9.44570i	0.505294	+	0.367118i
$663$	−32.1541	−	23.3613i	−1.24876	−	0.907279i
$664$	8.26281	−	6.00328i	0.320659	−	0.232973i
$665$	−1.40871	+	1.56453i	−0.0546274	+	0.0606699i
$666$	−10.7095	−	7.78089i	−0.414984	−	0.301504i
$667$	8.01334	+	24.6625i	0.310278	+	0.954937i
$668$	11.7969			0.456434
$669$	−11.3550	−	34.9470i	−0.439009	−	1.35113i
$670$	−1.59527	+	15.1780i	−0.0616306	+	0.586376i
$671$	−9.09181	+	27.9817i	−0.350986	+	1.08022i
$672$	−0.413545	+	1.27276i	−0.0159529	+	0.0490979i
$673$	−33.3135	+	24.2037i	−1.28414	+	0.932983i	−0.999670	−	0.0257022i	$-0.991818\pi$
$673$	−33.3135	+	24.2037i	−1.28414	+	0.932983i	−0.284471	+	0.958685i	$0.591818\pi$
$674$	−19.6346			−0.756297
$675$	−2.94395	−	28.0098i	−0.113313	−	1.07810i
$676$	6.75914			0.259967
$677$	24.1724	−	17.5623i	0.929021	−	0.674974i	−0.0167317	−	0.999860i	$-0.505326\pi$
$677$	24.1724	−	17.5623i	0.929021	−	0.674974i	0.945753	+	0.324887i	$0.105326\pi$
$678$	−5.04596	+	15.5299i	−0.193789	+	0.596421i
$679$	5.62920	−	17.3249i	0.216029	−	0.664869i
$680$	13.6480	+	6.07648i	0.523377	+	0.233022i
$681$	1.15497	+	3.55464i	0.0442586	+	0.136214i
$682$	−31.5711			−1.20892
$683$	−15.8660	−	48.8306i	−0.607096	−	1.86845i	−0.481684	−	0.876345i	$-0.659975\pi$
$683$	−15.8660	−	48.8306i	−0.607096	−	1.86845i	−0.125412	−	0.992105i	$-0.540025\pi$
$684$	−0.920937	−	0.669100i	−0.0352129	−	0.0255837i
$685$	4.43349	−	42.1818i	0.169395	−	1.61168i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	8.83432	+	6.41851i	0.337050	+	0.244881i
$688$	−0.902863	−	0.655969i	−0.0344213	−	0.0250086i
$689$	−18.5224	+	13.4573i	−0.705646	+	0.512682i
$690$	−0.946835	+	9.00854i	−0.0360454	+	0.342949i
$691$	−32.1016	−	23.3232i	−1.22120	−	0.887256i	−0.225004	−	0.974358i	$-0.572240\pi$
$691$	−32.1016	−	23.3232i	−1.22120	−	0.887256i	−0.996199	+	0.0871013i	$0.972240\pi$
$692$	−2.12279	−	6.53327i	−0.0806963	−	0.248358i
$693$	−4.98331			−0.189300
$694$	4.30942	+	13.2630i	0.163583	+	0.503458i
$695$	−2.64404	−	1.17720i	−0.100294	−	0.0446538i
$696$	3.54275	−	10.9035i	0.134288	−	0.413295i
$697$	10.8137	−	33.2810i	0.409597	−	1.26061i
$698$	−1.68136	+	1.22158i	−0.0636403	+	0.0462374i
$699$	29.2274			1.10548
$700$	3.34565	+	3.71572i	0.126454	+	0.140441i
$701$	10.6224			0.401202			0.200601	−	0.979673i	$-0.435711\pi$
$701$	10.6224			0.401202			0.200601	+	0.979673i	$0.435711\pi$
$702$	20.2566	−	14.7173i	0.764537	−	0.555469i
$703$	3.18546	−	9.80384i	0.120142	−	0.369759i
$704$	1.27366	−	3.91992i	0.0480028	−	0.147738i
$705$	1.01017	−	9.61112i	0.0380452	−	0.361976i
$706$	−3.35325	−	10.3202i	−0.126201	−	0.388407i
$707$	−4.96097			−0.186576
$708$	3.59618	+	11.0679i	0.135153	+	0.415957i
$709$	3.09444	+	2.24824i	0.116214	+	0.0844344i	0.644374	−	0.764710i	$-0.277118\pi$
$709$	3.09444	+	2.24824i	0.116214	+	0.0844344i	−0.528160	+	0.849145i	$0.677118\pi$
$710$	18.0980	−	20.0999i	0.679207	−	0.754335i
$711$	−6.20528	+	4.50840i	−0.232716	+	0.169078i
$712$	9.43050	+	6.85166i	0.353423	+	0.256777i
$713$	−18.7582	−	13.6286i	−0.702499	−	0.510396i
$714$	7.23357	−	5.25549i	0.270709	−	0.196682i
$715$	20.4838	+	35.4789i	0.766049	+	1.32684i
$716$	−11.3371	−	8.23692i	−0.423689	−	0.307828i
$717$	12.2439	+	37.6827i	0.457255	+	1.40729i
$718$	−27.8062			−1.03772
$719$	−10.5002	−	32.3163i	−0.391591	−	1.20519i	−0.931585	−	0.363524i	$-0.881573\pi$
$719$	−10.5002	−	32.3163i	−0.391591	−	1.20519i	0.539994	−	0.841669i	$-0.318427\pi$
$720$	−1.80902	+	2.00912i	−0.0674181	+	0.0748754i
$721$	3.58755	−	11.0413i	0.133607	−	0.411201i
$722$	−5.59740	+	17.2270i	−0.208314	+	0.641123i
$723$	11.2610	−	8.18160i	0.418802	−	0.304277i
$724$	−18.9217			−0.703220
$725$	−28.6614	−	31.8318i	−1.06446	−	1.18220i
$726$	−8.01348			−0.297408
$727$	−9.36052	+	6.80081i	−0.347162	+	0.252228i	−0.747678	−	0.664062i	$-0.768831\pi$
$727$	−9.36052	+	6.80081i	−0.347162	+	0.252228i	0.400515	+	0.916290i	$0.368831\pi$
$728$	−1.37362	+	4.22757i	−0.0509097	+	0.156684i
$729$	8.44951	−	26.0049i	0.312945	−	0.963145i
$730$	−12.8895	+	2.73975i	−0.477062	+	0.101403i
$731$	2.30410	+	7.09128i	0.0852201	+	0.262281i
$732$	9.55296			0.353088
$733$	11.8522	+	36.4773i	0.437771	+	1.34732i	0.890221	+	0.455530i	$0.150550\pi$
$733$	11.8522	+	36.4773i	0.437771	+	1.34732i	−0.452450	+	0.891790i	$0.649450\pi$
$734$	15.9665	+	11.6003i	0.589334	+	0.428176i
$735$	2.92705	−	0.622164i	0.107966	−	0.0229489i
$736$	2.44890	−	1.77923i	0.0902678	−	0.0655834i
$737$	−22.7584	−	16.5350i	−0.838318	−	0.609074i
$738$	5.12319	+	3.72222i	0.188587	+	0.137017i
$739$	7.47279	−	5.42930i	0.274891	−	0.199720i	−0.441795	−	0.897116i	$-0.645658\pi$
$739$	7.47279	−	5.42930i	0.274891	−	0.199720i	0.716686	+	0.697396i	$0.245658\pi$
$740$	−22.3655	−	9.95778i	−0.822173	−	0.366055i
$741$	4.53115	+	3.29207i	0.166456	+	0.120937i
$742$	−1.59161	−	4.89848i	−0.0584300	−	0.179829i
$743$	−21.7479			−0.797854			−0.398927	−	0.916983i	$-0.630617\pi$
$743$	−21.7479			−0.797854			−0.398927	+	0.916983i	$0.630617\pi$
$744$	3.16769	+	9.74914i	0.116133	+	0.357421i
$745$	21.3333	+	36.9504i	0.781592	+	1.35376i
$746$	2.11143	−	6.49832i	0.0773050	−	0.237920i
$747$	3.81592	−	11.7442i	0.139617	−	0.429698i
$748$	−22.2783	+	16.1861i	−0.814576	+	0.591824i
$749$	−17.2417			−0.629999
$750$	−4.62358	−	14.2299i	−0.168829	−	0.519603i
$751$	−38.8681			−1.41832			−0.709159	−	0.705049i	$-0.750925\pi$
$751$	−38.8681			−1.41832			−0.709159	+	0.705049i	$0.750925\pi$
$752$	−2.61271	+	1.89825i	−0.0952757	+	0.0692219i
$753$	2.86959	−	8.83169i	0.104574	−	0.321845i
$754$	11.7675	−	36.2166i	0.428546	−	1.31893i
$755$	−1.91415	−	3.31540i	−0.0696630	−	0.120660i
$756$	1.74064	+	5.35713i	0.0633063	+	0.194837i
$757$	28.7252			1.04404			0.522018	−	0.852935i	$-0.325179\pi$
$757$	28.7252			1.04404			0.522018	+	0.852935i	$0.325179\pi$
$758$	−1.17015	−	3.60134i	−0.0425016	−	0.130807i
$759$	−13.5078	−	9.81396i	−0.490301	−	0.356224i
$760$	−1.92327	−	0.856296i	−0.0697644	−	0.0310611i
$761$	31.1331	−	22.6195i	1.12857	−	0.819956i	0.143087	−	0.989710i	$-0.454297\pi$
$761$	31.1331	−	22.6195i	1.12857	−	0.819956i	0.985487	+	0.169754i	$0.0542972\pi$
$762$	7.20938	+	5.23792i	0.261168	+	0.189750i
$763$	1.53818	+	1.11755i	0.0556859	+	0.0404582i
$764$	4.30757	−	3.12964i	0.155843	−	0.113226i
$765$	17.6681	−	3.75547i	0.638792	−	0.135779i
$766$	−12.1139	−	8.80126i	−0.437693	−	0.318002i
$767$	11.9450	+	36.7628i	0.431307	+	1.32743i
$768$	−1.33826			−0.0482903
$769$	−13.0252	−	40.0875i	−0.469701	−	1.44559i	−0.852973	−	0.521955i	$-0.825203\pi$
$769$	−13.0252	−	40.0875i	−0.469701	−	1.44559i	0.383272	−	0.923635i	$-0.374797\pi$
$770$	−9.01489	+	1.91617i	−0.324874	+	0.0690541i
$771$	−0.977273	+	3.00774i	−0.0351956	+	0.108321i
$772$	−0.936251	+	2.88148i	−0.0336964	+	0.103707i
$773$	22.8998	−	16.6377i	0.823649	−	0.598416i	−0.0941064	−	0.995562i	$-0.529999\pi$
$773$	22.8998	−	16.6377i	0.823649	−	0.598416i	0.917755	+	0.397146i	$0.129999\pi$
$774$	−1.34931			−0.0484999
$775$	37.4622	+	7.96284i	1.34568	+	0.286034i
$776$	18.2165			0.653934
$777$	−11.8539	+	8.61239i	−0.425258	+	0.308968i
$778$	8.32350	−	25.6171i	0.298412	−	0.918417i
$779$	−1.52386	+	4.68995i	−0.0545979	+	0.168035i
$780$	8.90063	−	9.88515i	0.318694	−	0.353945i
$781$	15.4059	+	47.4146i	0.551268	+	1.69663i
$782$	−20.2240			−0.723210
$783$	−14.9116	−	45.8933i	−0.532898	−	1.64009i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	3.58329	+	6.20644i	0.127893	+	0.221517i
$786$	3.99038	−	2.89918i	0.142332	−	0.103410i
$787$	−26.5029	−	19.2555i	−0.944727	−	0.686384i	0.00482685	−	0.999988i	$-0.498464\pi$
$787$	−26.5029	−	19.2555i	−0.944727	−	0.686384i	−0.949554	+	0.313604i	$0.898464\pi$
$788$	4.58097	+	3.32827i	0.163190	+	0.118565i
$789$	−12.5508	+	9.11871i	−0.446821	+	0.324635i
$790$	−9.49189	+	10.5418i	−0.337706	+	0.375061i
$791$	−9.87139	−	7.17198i	−0.350986	−	0.255006i
$792$	−1.53993	−	4.73941i	−0.0547189	−	0.168407i
$793$	31.7308			1.12679
$794$	2.91456	+	8.97010i	0.103434	+	0.318337i
$795$	−1.61107	+	15.3284i	−0.0571389	+	0.543641i
$796$	2.50079	−	7.69664i	0.0886381	−	0.272800i
$797$	−4.62067	+	14.2210i	−0.163673	+	0.503732i	−0.998936	−	0.0461176i	$-0.985315\pi$
$797$	−4.62067	+	14.2210i	−0.163673	+	0.503732i	0.835263	+	0.549850i	$0.185315\pi$
$798$	−1.01935	+	0.740603i	−0.0360847	+	0.0262170i
$799$	21.5768			0.763333
$800$	−2.50000	+	4.33013i	−0.0883883	+	0.153093i
$801$	14.0937			0.497975
$802$	−13.9473	+	10.1333i	−0.492497	+	0.357820i
$803$	7.50585	−	23.1006i	0.264876	−	0.815203i
$804$	−2.82252	+	8.68683i	−0.0995427	+	0.306361i
$805$	−6.18343	−	2.75304i	−0.217937	−	0.0970319i
$806$	10.5217	+	32.3824i	0.370611	+	1.14062i
$807$	14.8114			0.521385
$808$	−1.53302	−	4.71816i	−0.0539316	−	0.165984i
$809$	−17.5634	−	12.7605i	−0.617495	−	0.448636i	0.234551	−	0.972104i	$-0.424638\pi$
$809$	−17.5634	−	12.7605i	−0.617495	−	0.448636i	−0.852045	+	0.523468i	$0.824638\pi$
$810$	0.914131	−	8.69738i	0.0321193	−	0.305595i
$811$	15.2002	−	11.0436i	0.533752	−	0.387794i	−0.288007	−	0.957628i	$-0.592993\pi$
$811$	15.2002	−	11.0436i	0.533752	−	0.387794i	0.821759	+	0.569835i	$0.192993\pi$
$812$	6.93066	+	5.03542i	0.243219	+	0.176709i
$813$	−27.7942	−	20.1936i	−0.974784	−	0.708222i
$814$	36.5084	−	26.5249i	1.27962	−	0.929697i
$815$	2.22807	−	21.1986i	0.0780457	−	0.742556i
$816$	7.23357	+	5.25549i	0.253226	+	0.183979i
$817$	−0.324693	−	0.999301i	−0.0113596	−	0.0349611i
$818$	−9.28600			−0.324677
$819$	1.66078	+	5.11137i	0.0580325	+	0.178606i
$820$	10.6992	+	4.76359i	0.373632	+	0.166352i
$821$	−5.78983	+	17.8193i	−0.202066	+	0.621896i	0.797755	+	0.602982i	$0.206021\pi$
$821$	−5.78983	+	17.8193i	−0.202066	+	0.621896i	−0.999821	+	0.0189143i	$0.993979\pi$
$822$	7.84421	−	24.1420i	0.273598	−	0.842049i
$823$	41.6507	−	30.2610i	1.45185	−	1.05483i	0.466456	−	0.884544i	$-0.345531\pi$
$823$	41.6507	−	30.2610i	1.45185	−	1.05483i	0.985395	−	0.170287i	$-0.0544694\pi$
$824$	11.6095			0.404438
$825$	26.9765	+	5.73404i	0.939202	+	0.199634i
$826$	−8.69598			−0.302572
$827$	−28.3549	+	20.6011i	−0.985998	+	0.716369i	−0.959041	−	0.283267i	$-0.908582\pi$
$827$	−28.3549	+	20.6011i	−0.985998	+	0.716369i	−0.0269566	+	0.999637i	$0.508582\pi$
$828$	1.13095	−	3.48070i	0.0393032	−	0.120963i
$829$	−2.03761	+	6.27113i	−0.0707692	+	0.217805i	−0.980185	−	0.198082i	$-0.936529\pi$
$829$	−2.03761	+	6.27113i	−0.0707692	+	0.217805i	0.909416	+	0.415887i	$0.136529\pi$
$830$	2.38721	−	22.7127i	0.0828611	−	0.788371i
$831$	8.97422	+	27.6198i	0.311312	+	0.958121i
$832$	−4.44512			−0.154107
$833$	2.06460	+	6.35419i	0.0715342	+	0.220160i
$834$	−1.40136	−	1.01815i	−0.0485253	−	0.0352557i
$835$	17.6507	−	19.6031i	0.610828	−	0.678394i
$836$	3.13945	−	2.28095i	0.108580	−	0.0788882i
$837$	34.9062	+	25.3608i	1.20653	+	0.876598i
$838$	−2.18769	−	1.58945i	−0.0755726	−	0.0549067i
$839$	−41.6784	+	30.2811i	−1.43890	+	1.04542i	−0.450625	+	0.892713i	$0.648799\pi$
$839$	−41.6784	+	30.2811i	−1.43890	+	1.04542i	−0.988272	+	0.152707i	$0.951201\pi$
$840$	1.49622	+	2.59153i	0.0516245	+	0.0894163i
$841$	−35.9119	−	26.0915i	−1.23834	−	0.899708i
$842$	−0.649427	−	1.99873i	−0.0223807	−	0.0688808i
$843$	14.7410			0.507708
$844$	−1.01157	−	3.11330i	−0.0348198	−	0.107164i
$845$	10.1132	−	11.2318i	0.347903	−	0.386386i
$846$	−1.20660	+	3.71353i	−0.0414837	+	0.127674i
$847$	1.85039	−	5.69490i	0.0635800	−	0.195679i
$848$	4.16690	−	3.02743i	0.143092	−	0.103962i
$849$	−16.2537			−0.557824
$850$	30.5179	−	13.5874i	1.04675	−	0.466045i
$851$	33.1420			1.13609
$852$	13.0959	−	9.51469i	0.448656	−	0.325968i
$853$	5.20775	−	16.0278i	0.178310	−	0.548782i	−0.821459	−	0.570268i	$-0.806840\pi$
$853$	5.20775	−	16.0278i	0.178310	−	0.548782i	0.999769	+	0.0214854i	$0.00683954\pi$
$854$	−2.20587	+	6.78897i	−0.0754833	+	0.232314i
$855$	−2.48978	+	0.529220i	−0.0851488	+	0.0180989i
$856$	−5.32798	−	16.3978i	−0.182107	−	0.560467i
$857$	−33.1837			−1.13354			−0.566768	−	0.823878i	$-0.691806\pi$
$857$	−33.1837			−1.13354			−0.566768	+	0.823878i	$0.691806\pi$
$858$	7.57666	+	23.3186i	0.258663	+	0.796083i
$859$	32.1561	+	23.3628i	1.09715	+	0.797127i	0.980593	−	0.196056i	$-0.0628136\pi$
$859$	32.1561	+	23.3628i	1.09715	+	0.797127i	0.116559	+	0.993184i	$0.462814\pi$
$860$	−2.44092	+	0.518834i	−0.0832347	+	0.0176921i
$861$	5.67068	−	4.11999i	0.193256	−	0.140409i
$862$	4.07322	+	2.95936i	0.138734	+	0.100796i
$863$	−1.64557	−	1.19557i	−0.0560158	−	0.0406978i	0.559425	−	0.828881i	$-0.311022\pi$
$863$	−1.64557	−	1.19557i	−0.0560158	−	0.0406978i	−0.615441	+	0.788183i	$0.711022\pi$
$864$	−4.55705	+	3.31089i	−0.155034	+	0.112639i
$865$	−14.0326	−	6.24774i	−0.477124	−	0.212429i
$866$	−29.1363	−	21.1688i	−0.990092	−	0.719344i
$867$	−11.4297	−	35.1770i	−0.388173	−	1.19467i
$868$	−7.65983			−0.259992
$869$	−8.07998	−	24.8676i	−0.274094	−	0.843576i
$870$	−12.8178	−	22.2011i	−0.434564	−	0.752686i
$871$	−9.37520	+	28.8539i	−0.317666	+	0.977677i
$872$	−0.587533	+	1.80824i	−0.0198964	+	0.0612348i
$873$	17.8184	−	12.9458i	0.603062	−	0.438150i
$874$	2.84997			0.0964015
$875$	11.1803			0.377964
$876$	−7.88656			−0.266462
$877$	22.2825	−	16.1892i	0.752427	−	0.546670i	−0.144152	−	0.989556i	$-0.546045\pi$
$877$	22.2825	−	16.1892i	0.752427	−	0.546670i	0.896578	+	0.442886i	$0.146045\pi$
$878$	6.90558	−	21.2532i	0.233052	−	0.717261i
$879$	−4.93292	+	15.1820i	−0.166383	+	0.512075i
$880$	−4.60814	−	7.98154i	−0.155340	−	0.269058i
$881$	−2.74070	−	8.43500i	−0.0923364	−	0.284182i	0.894214	−	0.447640i	$-0.147735\pi$
$881$	−2.74070	−	8.43500i	−0.0923364	−	0.284182i	−0.986550	+	0.163458i	$0.947735\pi$
$882$	−1.20906			−0.0407111
$883$	−10.2622	−	31.5839i	−0.345352	−	1.06288i	−0.961395	−	0.275172i	$-0.911265\pi$
$883$	−10.2622	−	31.5839i	−0.345352	−	1.06288i	0.616043	−	0.787713i	$-0.288735\pi$
$884$	24.0268	+	17.4565i	0.808108	+	0.587125i
$885$	23.7725	+	10.5842i	0.799103	+	0.355784i
$886$	−16.3461	+	11.8761i	−0.549158	+	0.398987i
$887$	43.0985	+	31.3129i	1.44711	+	1.05138i	0.986497	+	0.163780i	$0.0523688\pi$
$887$	43.0985	+	31.3129i	1.44711	+	1.05138i	0.460609	+	0.887603i	$0.347631\pi$
$888$	−11.8539	−	8.61239i	−0.397792	−	0.289013i
$889$	−5.38712	+	3.91398i	−0.180678	+	0.131271i
$890$	25.4957	−	5.41927i	0.854617	−	0.181654i
$891$	13.0412	+	9.47498i	0.436897	+	0.317424i
$892$	8.48487	+	26.1138i	0.284095	+	0.874353i
$893$	−3.04060			−0.101750
$894$	7.89090	+	24.2857i	0.263911	+	0.812235i
$895$	−30.6503	+	6.51493i	−1.02453	+	0.217770i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	−5.56444	+	17.1256i	−0.185791	+	0.571806i
$898$	−14.7332	+	10.7043i	−0.491654	+	0.357208i
$899$	65.6200			2.18855
$900$	0.631904	+	6.01217i	0.0210635	+	0.200406i
$901$	−34.4119			−1.14643
$902$	−17.4648	+	12.6890i	−0.581516	+	0.422496i
$903$	−0.461517	+	1.42040i	−0.0153583	+	0.0472681i
$904$	3.77053	−	11.6045i	0.125406	−	0.385960i
$905$	−28.3111	+	31.4427i	−0.941093	+	1.04519i
$906$	−0.708017	−	2.17905i	−0.0235223	−	0.0723942i
$907$	44.7484			1.48584			0.742922	−	0.669377i	$-0.233439\pi$
$907$	44.7484			1.48584			0.742922	+	0.669377i	$0.233439\pi$
$908$	−0.863039	−	2.65616i	−0.0286410	−	0.0881478i
$909$	−4.85256	−	3.52559i	−0.160949	−	0.116936i
$910$	4.96980	+	8.60795i	0.164747	+	0.285351i
$911$	−29.0615	+	21.1144i	−0.962849	+	0.699551i	−0.953811	−	0.300408i	$-0.902877\pi$
$911$	−29.0615	+	21.1144i	−0.962849	+	0.699551i	−0.00903825	+	0.999959i	$0.502877\pi$
$912$	−1.01935	−	0.740603i	−0.0337541	−	0.0245238i
$913$	34.0564	+	24.7434i	1.12710	+	0.818888i
$914$	−7.41919	+	5.39036i	−0.245405	+	0.178297i
$915$	14.2934	−	15.8744i	0.472524	−	0.524791i
$916$	−6.60134	−	4.79615i	−0.218114	−	0.158469i
$917$	1.13893	+	3.50527i	0.0376108	+	0.115754i
$918$	37.6339			1.24211
$919$	−4.61168	−	14.1933i	−0.152125	−	0.468194i	0.845733	−	0.533606i	$-0.179164\pi$
$919$	−4.61168	−	14.1933i	−0.152125	−	0.468194i	−0.997858	+	0.0654127i	$0.979164\pi$
$920$	0.707512	−	6.73152i	0.0233260	−	0.221932i
$921$	3.09112	−	9.51350i	0.101856	−	0.313481i
$922$	−8.16115	+	25.1174i	−0.268773	+	0.827199i
$923$	43.4988	−	31.6037i	1.43178	−	1.04025i
$924$	−5.51584			−0.181458
$925$	−50.0109	+	22.2663i	−1.64435	+	0.732110i
$926$	2.46674			0.0810620
$927$	11.3558	−	8.25051i	0.372975	−	0.270982i
$928$	−2.64728	+	8.14748i	−0.0869012	+	0.267454i
$929$	1.70278	−	5.24063i	0.0558665	−	0.171939i	−0.919230	−	0.393722i	$-0.871187\pi$
$929$	1.70278	−	5.24063i	0.0558665	−	0.171939i	0.975096	+	0.221782i	$0.0711874\pi$
$930$	20.9399	+	9.32306i	0.686647	+	0.305715i
$931$	−0.290943	−	0.895431i	−0.00953527	−	0.0293466i
$932$	−21.8398			−0.715388
$933$	9.66972	+	29.7603i	0.316572	+	0.974310i
$934$	−12.5706	−	9.13304i	−0.411321	−	0.298842i
$935$	−6.43642	+	61.2384i	−0.210493	+	2.00271i
$936$	−4.34799	+	3.15900i	−0.142118	+	0.103255i
$937$	−28.2148	−	20.4993i	−0.921739	−	0.669682i	0.0222174	−	0.999753i	$-0.492927\pi$
$937$	−28.2148	−	20.4993i	−0.921739	−	0.669682i	−0.943956	+	0.330071i	$0.892927\pi$
$938$	−5.52169	−	4.01174i	−0.180289	−	0.130988i
$939$	−14.5997	+	10.6073i	−0.476442	+	0.346156i
$940$	−0.754837	+	7.18179i	−0.0246201	+	0.234244i
$941$	−13.3723	−	9.71555i	−0.435925	−	0.316718i	0.348089	−	0.937462i	$-0.386831\pi$
$941$	−13.3723	−	9.71555i	−0.435925	−	0.316718i	−0.784014	+	0.620744i	$0.786831\pi$
$942$	1.32541	+	4.07919i	0.0431842	+	0.132907i
$943$	−15.8544			−0.516291
$944$	−2.68720	−	8.27037i	−0.0874611	−	0.269177i
$945$	11.5064	+	5.12300i	0.374304	+	0.166651i
$946$	1.42140	−	4.37463i	0.0462138	−	0.142232i
$947$	−6.94228	+	21.3661i	−0.225594	+	0.694306i	0.772637	+	0.634848i	$0.218937\pi$
$947$	−6.94228	+	21.3661i	−0.225594	+	0.694306i	−0.998231	+	0.0594581i	$0.981063\pi$
$948$	−6.86840	+	4.99018i	−0.223075	+	0.162074i
$949$	−26.1957			−0.850349
$950$	−4.30057	+	1.91474i	−0.139529	+	0.0621222i
$951$	−7.65049			−0.248084
$952$	−5.40520	+	3.92711i	−0.175183	+	0.127278i
$953$	6.25093	−	19.2384i	0.202488	−	0.623193i	−0.797320	−	0.603557i	$-0.793749\pi$
$953$	6.25093	−	19.2384i	0.202488	−	0.623193i	0.999807	−	0.0196354i	$-0.00625053\pi$
$954$	1.92435	−	5.92254i	0.0623032	−	0.191749i
$955$	1.24450	−	11.8406i	0.0402711	−	0.383153i
$956$	−9.14908	−	28.1580i	−0.295903	−	0.910694i
$957$	47.2530			1.52747
$958$	−2.03595	−	6.26600i	−0.0657785	−	0.202445i
$959$	15.3456	+	11.1492i	0.495535	+	0.360027i
$960$	−2.00234	+	2.22382i	−0.0646251	+	0.0717734i
$961$	−22.3879	+	16.2658i	−0.722191	+	0.524702i
$962$	−39.3737	−	28.6066i	−1.26946	−	0.922315i
$963$	−16.8649	−	12.2531i	−0.543465	−	0.394851i
$964$	−8.41466	+	6.11361i	−0.271018	+	0.196906i
$965$	3.38739	+	5.86713i	0.109044	+	0.188870i
$966$	−3.27727	−	2.38108i	−0.105445	−	0.0766099i
$967$	−0.335765	−	1.03338i	−0.0107975	−	0.0332312i	0.945513	−	0.325585i	$-0.105561\pi$
$967$	−0.335765	−	1.03338i	−0.0107975	−	0.0332312i	−0.956310	+	0.292354i	$0.905561\pi$
$968$	5.98798			0.192461
$969$	2.60137	+	8.00621i	0.0835682	+	0.257196i
$970$	27.2559	−	30.2707i	0.875134	−	0.971935i
$971$	−2.04525	+	6.29462i	−0.0656351	+	0.202004i	−0.978496	−	0.206267i	$-0.933868\pi$
$971$	−2.04525	+	6.29462i	−0.0656351	+	0.202004i	0.912861	+	0.408271i	$0.133868\pi$
$972$	−3.60453	+	11.0936i	−0.115615	+	0.355827i
$973$	1.04715	−	0.760801i	0.0335702	−	0.0243902i
$974$	−25.9111			−0.830245
$975$	−3.10906	−	29.5808i	−0.0995697	−	0.947342i
$976$	−7.13834			−0.228493
$977$	−48.2324	+	35.0429i	−1.54309	+	1.12112i	−0.594733	+	0.803923i	$0.702742\pi$
$977$	−48.2324	+	35.0429i	−1.54309	+	1.12112i	−0.948359	+	0.317198i	$0.897258\pi$
$978$	3.94214	−	12.1326i	0.126056	−	0.387959i
$979$	−14.8467	+	45.6935i	−0.474503	+	1.46037i
$980$	−2.18720	+	0.464905i	−0.0698677	+	0.0148508i
$981$	0.710361	+	2.18627i	0.0226801	+	0.0698021i
$982$	−23.7457			−0.757757
$983$	2.22414	+	6.84521i	0.0709391	+	0.218328i	0.980240	−	0.197811i	$-0.0633831\pi$
$983$	2.22414	+	6.84521i	0.0709391	+	0.218328i	−0.909301	+	0.416139i	$0.863383\pi$
$984$	5.67068	+	4.11999i	0.180775	+	0.131340i
$985$	12.3848	−	2.63247i	0.394612	−	0.0838774i
$986$	46.3051	−	33.6426i	1.47465	−	1.07140i
$987$	3.49649	+	2.54035i	0.111294	+	0.0808602i
$988$	−3.38585	−	2.45996i	−0.107718	−	0.0782618i
$989$	2.73298	−	1.98562i	0.0869036	−	0.0631392i
$990$	−10.1796	−	4.53227i	−0.323530	−	0.144045i
$991$	−16.8863	−	12.2686i	−0.536412	−	0.389726i	0.286339	−	0.958128i	$-0.407562\pi$
$991$	−16.8863	−	12.2686i	−0.536412	−	0.389726i	−0.822751	+	0.568402i	$0.807562\pi$
$992$	−2.36702	−	7.28493i	−0.0751529	−	0.231297i
$993$	21.5058			0.682467
$994$	3.73781	+	11.5038i	0.118556	+	0.364879i
$995$	−9.04794	−	15.6715i	−0.286839	−	0.496820i
$996$	4.22370	−	12.9992i	0.133833	−	0.411896i
$997$	−12.1036	+	37.2512i	−0.383326	+	1.17976i	0.554361	+	0.832276i	$0.312963\pi$
$997$	−12.1036	+	37.2512i	−0.383326	+	1.17976i	−0.937687	+	0.347480i	$0.887037\pi$
$998$	19.5878	−	14.2314i	0.620042	−	0.450487i
$999$	−61.6722			−1.95122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.a.211.1	yes	8
25.4	even	10		8750.2.a.e.1.3		4
25.16	even	5	inner	350.2.h.a.141.1	✓	8
25.21	even	5		8750.2.a.j.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.a.141.1	✓	8	25.16	even	5	inner
350.2.h.a.211.1	yes	8	1.1	even	1	trivial
8750.2.a.e.1.3		4	25.4	even	10
8750.2.a.j.1.2		4	25.21	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.413545 + 1.27276i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-0.413545 - 1.27276i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.978148 + 0.710666i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.413545 + 1.27276i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-0.413545 - 1.27276i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.978148 + 0.710666i) q^{9} +(2.04275 + 0.909491i) q^{10} +(-3.33448 + 2.42264i) q^{11} +(1.08268 + 0.786610i) q^{12} +(3.59618 + 2.61278i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(2.92705 - 0.622164i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.06460 + 6.35419i) q^{17} -1.20906 q^{18} +(-0.290943 - 0.895431i) q^{19} +(-2.18720 + 0.464905i) q^{20} +(-0.413545 + 1.27276i) q^{21} +(1.27366 - 3.91992i) q^{22} +(2.44890 - 1.77923i) q^{23} -1.33826 q^{24} +(-2.50000 + 4.33013i) q^{25} -4.44512 q^{26} +(-4.55705 + 3.31089i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-2.64728 + 8.14748i) q^{29} +(-2.00234 + 2.22382i) q^{30} +(-2.36702 - 7.28493i) q^{31} +1.00000 q^{32} +(-1.70449 - 5.24588i) q^{33} +(-5.40520 - 3.92711i) q^{34} +(-1.11803 - 1.93649i) q^{35} +(0.978148 - 0.710666i) q^{36} +(8.85772 + 6.43551i) q^{37} +(0.761699 + 0.553407i) q^{38} +(-4.81263 + 3.49658i) q^{39} +(1.49622 - 1.66172i) q^{40} +(-4.23735 - 3.07861i) q^{41} +(-0.413545 - 1.27276i) q^{42} +1.11600 q^{43} +(1.27366 + 3.91992i) q^{44} +(0.282596 - 2.68872i) q^{45} +(-0.935398 + 2.87886i) q^{46} +(0.997966 - 3.07143i) q^{47} +(1.08268 - 0.786610i) q^{48} +1.00000 q^{49} +(-0.522642 - 4.97261i) q^{50} -8.94118 q^{51} +(3.59618 - 2.61278i) q^{52} +(-1.59161 + 4.89848i) q^{53} +(1.74064 - 5.35713i) q^{54} +(8.41949 + 3.74860i) q^{55} +(0.309017 + 0.951057i) q^{56} +1.25999 q^{57} +(-2.64728 - 8.14748i) q^{58} +(7.03519 + 5.11137i) q^{59} +(0.312795 - 2.97605i) q^{60} +(5.77504 - 4.19581i) q^{61} +(6.19693 + 4.50233i) q^{62} +(0.978148 + 0.710666i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.03897 - 9.88515i) q^{65} +(4.46241 + 3.24213i) q^{66} +(2.10910 + 6.49113i) q^{67} +6.68119 q^{68} +(1.25181 + 3.85266i) q^{69} +(2.04275 + 0.909491i) q^{70} +(3.73781 - 11.5038i) q^{71} +(-0.373619 + 1.14988i) q^{72} +(-4.76765 + 3.46390i) q^{73} -10.9487 q^{74} +(-4.47736 - 4.97261i) q^{75} -0.941512 q^{76} +(-3.33448 + 2.42264i) q^{77} +(1.83826 - 5.65759i) q^{78} +(-1.96038 + 6.03342i) q^{79} +(-0.233733 + 2.22382i) q^{80} +(-1.20857 - 3.71959i) q^{81} +5.23765 q^{82} +(-3.15611 - 9.71352i) q^{83} +(1.08268 + 0.786610i) q^{84} +(9.99654 - 11.1023i) q^{85} +(-0.902863 + 0.655969i) q^{86} +(-9.27504 - 6.73871i) q^{87} +(-3.33448 - 2.42264i) q^{88} +(9.43050 - 6.85166i) q^{89} +(1.35177 + 2.34133i) q^{90} +(3.59618 + 2.61278i) q^{91} +(-0.935398 - 2.87886i) q^{92} +10.2509 q^{93} +(0.997966 + 3.07143i) q^{94} +(-1.40871 + 1.56453i) q^{95} +(-0.413545 + 1.27276i) q^{96} +(5.62920 - 17.3249i) q^{97} +(-0.809017 + 0.587785i) q^{98} -4.98331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + 3 * q^6 + 8 * q^7 - 2 * q^8 - q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} - q^{9} + 5 q^{10} - q^{11} - 2 q^{12} + 11 q^{13} - 2 q^{14} + 10 q^{15} - 2 q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 5 q^{20} + 3 q^{21} + 4 q^{22} + 15 q^{23} - 2 q^{24} - 20 q^{25} - 14 q^{26} - 2 q^{28} - 8 q^{29} - 5 q^{30} - 7 q^{31} + 8 q^{32} - 11 q^{33} - 21 q^{34} - q^{36} + 14 q^{37} + 14 q^{38} - 4 q^{39} - 5 q^{40} + 3 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 10 q^{45} - 10 q^{46} + 2 q^{47} - 2 q^{48} + 8 q^{49} + 5 q^{50} + 14 q^{51} + 11 q^{52} + 4 q^{53} - 5 q^{54} + 20 q^{55} - 2 q^{56} - 36 q^{57} - 8 q^{58} + 11 q^{59} + 15 q^{60} + 13 q^{62} - q^{63} - 2 q^{64} - 20 q^{65} + 24 q^{66} + 14 q^{67} + 14 q^{68} - 5 q^{69} + 5 q^{70} + 23 q^{71} + 4 q^{72} - 5 q^{73} - 36 q^{74} - 45 q^{75} - 16 q^{76} - q^{77} + 6 q^{78} + 2 q^{79} + 5 q^{80} - 7 q^{81} - 12 q^{82} - 27 q^{83} - 2 q^{84} + 15 q^{85} + 4 q^{86} - 28 q^{87} - q^{88} - 15 q^{89} - 5 q^{90} + 11 q^{91} - 10 q^{92} + 38 q^{93} + 2 q^{94} + 20 q^{95} + 3 q^{96} + 40 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + 3 * q^6 + 8 * q^7 - 2 * q^8 - q^9 + 5 * q^10 - q^11 - 2 * q^12 + 11 * q^13 - 2 * q^14 + 10 * q^15 - 2 * q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 5 * q^20 + 3 * q^21 + 4 * q^22 + 15 * q^23 - 2 * q^24 - 20 * q^25 - 14 * q^26 - 2 * q^28 - 8 * q^29 - 5 * q^30 - 7 * q^31 + 8 * q^32 - 11 * q^33 - 21 * q^34 - q^36 + 14 * q^37 + 14 * q^38 - 4 * q^39 - 5 * q^40 + 3 * q^41 + 3 * q^42 - 6 * q^43 + 4 * q^44 - 10 * q^45 - 10 * q^46 + 2 * q^47 - 2 * q^48 + 8 * q^49 + 5 * q^50 + 14 * q^51 + 11 * q^52 + 4 * q^53 - 5 * q^54 + 20 * q^55 - 2 * q^56 - 36 * q^57 - 8 * q^58 + 11 * q^59 + 15 * q^60 + 13 * q^62 - q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 14 * q^67 + 14 * q^68 - 5 * q^69 + 5 * q^70 + 23 * q^71 + 4 * q^72 - 5 * q^73 - 36 * q^74 - 45 * q^75 - 16 * q^76 - q^77 + 6 * q^78 + 2 * q^79 + 5 * q^80 - 7 * q^81 - 12 * q^82 - 27 * q^83 - 2 * q^84 + 15 * q^85 + 4 * q^86 - 28 * q^87 - q^88 - 15 * q^89 - 5 * q^90 + 11 * q^91 - 10 * q^92 + 38 * q^93 + 2 * q^94 + 20 * q^95 + 3 * q^96 + 40 * q^97 - 2 * q^98 - 8 * q^99

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