LMFDB - Embedded newform 350.2.h.c.141.4

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 241x^{12} + 1145x^{10} + 2841x^{8} + 3600x^{6} + 2156x^{4} + 480x^{2} + 16 $ x^16 + 25x^14 + 241x^12 + 1145x^10 + 2841x^8 + 3600x^6 + 2156x^4 + 480*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.4
Root			$1.08645i$ of defining polynomial
Character	$\chi$	$=$	350.141
Dual form			350.2.h.c.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(1.01530 + 3.12476i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.0943702 + 2.23408i) q^{5} +(1.01530 - 3.12476i) q^{6} -1.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.30625 + 4.58176i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(1.01530 + 3.12476i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.0943702 + 2.23408i) q^{5} +(1.01530 - 3.12476i) q^{6} -1.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.30625 + 4.58176i) q^{9} +(1.38950 - 1.75194i) q^{10} +(2.00120 + 1.45396i) q^{11} +(-2.65808 + 1.93121i) q^{12} +(2.82834 - 2.05491i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-7.07676 + 1.97336i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.14955 - 3.53796i) q^{17} +7.79495 q^{18} +(0.409074 - 1.25900i) q^{19} +(-2.15389 + 0.600616i) q^{20} +(-1.01530 - 3.12476i) q^{21} +(-0.764390 - 2.35255i) q^{22} +(-4.30061 - 3.12458i) q^{23} +3.28557 q^{24} +(-4.98219 - 0.421660i) q^{25} -3.49602 q^{26} +(-12.7454 - 9.26005i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(3.17864 + 9.78286i) q^{29} +(6.88514 + 2.56313i) q^{30} +(-0.999624 + 3.07653i) q^{31} +1.00000 q^{32} +(-2.51146 + 7.72947i) q^{33} +(-3.00957 + 2.18658i) q^{34} +(0.0943702 - 2.23408i) q^{35} +(-6.30625 - 4.58176i) q^{36} +(8.08738 - 5.87582i) q^{37} +(-1.07097 + 0.778104i) q^{38} +(9.29271 + 6.75155i) q^{39} +(2.09557 + 0.780119i) q^{40} +(1.85833 - 1.35015i) q^{41} +(-1.01530 + 3.12476i) q^{42} -1.26901 q^{43} +(-0.764390 + 2.35255i) q^{44} +(-9.64087 - 14.5210i) q^{45} +(1.64269 + 5.05567i) q^{46} +(3.76119 + 11.5757i) q^{47} +(-2.65808 - 1.93121i) q^{48} +1.00000 q^{49} +(3.78283 + 3.26959i) q^{50} +12.2224 q^{51} +(2.82834 + 2.05491i) q^{52} +(1.79150 + 5.51366i) q^{53} +(4.86830 + 14.9831i) q^{54} +(-3.43710 + 4.33362i) q^{55} +(-0.309017 + 0.951057i) q^{56} +4.34940 q^{57} +(3.17864 - 9.78286i) q^{58} +(2.11540 - 1.53693i) q^{59} +(-4.06362 - 6.12060i) q^{60} +(-5.13244 - 3.72894i) q^{61} +(2.61705 - 1.90140i) q^{62} +(6.30625 - 4.58176i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.32392 + 6.51265i) q^{65} +(6.57508 - 4.77707i) q^{66} +(0.483607 - 1.48839i) q^{67} +3.72003 q^{68} +(5.39716 - 16.6107i) q^{69} +(-1.38950 + 1.75194i) q^{70} +(2.38655 + 7.34506i) q^{71} +(2.40877 + 7.41344i) q^{72} +(-5.68610 - 4.13120i) q^{73} -9.99655 q^{74} +(-3.74081 - 15.9963i) q^{75} +1.32379 q^{76} +(-2.00120 - 1.45396i) q^{77} +(-3.54950 - 10.9242i) q^{78} +(2.30913 + 7.10678i) q^{79} +(-1.23681 - 1.86287i) q^{80} +(8.76880 - 26.9876i) q^{81} -2.29702 q^{82} +(-1.61338 + 4.96547i) q^{83} +(2.65808 - 1.93121i) q^{84} +(7.79559 + 2.90207i) q^{85} +(1.02665 + 0.745904i) q^{86} +(-27.3418 + 19.8650i) q^{87} +(2.00120 - 1.45396i) q^{88} +(-0.787001 - 0.571789i) q^{89} +(-0.735611 + 17.4145i) q^{90} +(-2.82834 + 2.05491i) q^{91} +(1.64269 - 5.05567i) q^{92} -10.6283 q^{93} +(3.76119 - 11.5757i) q^{94} +(2.77410 + 1.03271i) q^{95} +(1.01530 + 3.12476i) q^{96} +(-3.61395 - 11.1226i) q^{97} +(-0.809017 - 0.587785i) q^{98} -19.2817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.01530	+	3.12476i	0.586181	+	1.80408i	0.594473	+	0.804116i	$0.297361\pi$
$3$	1.01530	+	3.12476i	0.586181	+	1.80408i	−0.00829157	+	0.999966i	$0.502639\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.0943702	+	2.23408i	−0.0422036	+	0.999109i
$5$	−0.0943702	+	2.23408i	−0.0422036	+	0.999109i
$6$	1.01530	−	3.12476i	0.414493	−	1.27568i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−6.30625	+	4.58176i	−2.10208	+	1.52725i
$10$	1.38950	−	1.75194i	0.439400	−	0.554011i
$11$	2.00120	+	1.45396i	0.603385	+	0.438385i	0.847079	−	0.531468i	$-0.178359\pi$
$11$	2.00120	+	1.45396i	0.603385	+	0.438385i	−0.243694	+	0.969852i	$0.578359\pi$
$12$	−2.65808	+	1.93121i	−0.767322	+	0.557492i
$13$	2.82834	−	2.05491i	0.784441	−	0.569930i	−0.121867	−	0.992546i	$-0.538888\pi$
$13$	2.82834	−	2.05491i	0.784441	−	0.569930i	0.906309	+	0.422617i	$0.138888\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	−7.07676	+	1.97336i	−1.82721	+	0.509520i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.14955	−	3.53796i	0.278808	−	0.858082i	−0.709379	−	0.704827i	$-0.751024\pi$
$17$	1.14955	−	3.53796i	0.278808	−	0.858082i	0.988187	−	0.153255i	$-0.0489755\pi$
$18$	7.79495			1.83729
$19$	0.409074	−	1.25900i	0.0938479	−	0.288834i	−0.893104	−	0.449851i	$-0.851477\pi$
$19$	0.409074	−	1.25900i	0.0938479	−	0.288834i	0.986952	+	0.161016i	$0.0514772\pi$
$20$	−2.15389	+	0.600616i	−0.481625	+	0.134302i
$21$	−1.01530	−	3.12476i	−0.221556	−	0.681879i
$22$	−0.764390	−	2.35255i	−0.162969	−	0.501566i
$23$	−4.30061	−	3.12458i	−0.896739	−	0.651519i	0.0408871	−	0.999164i	$-0.486982\pi$
$23$	−4.30061	−	3.12458i	−0.896739	−	0.651519i	−0.937626	+	0.347644i	$0.886982\pi$
$24$	3.28557			0.670664
$25$	−4.98219	−	0.421660i	−0.996438	−	0.0843320i
$26$	−3.49602			−0.685627
$27$	−12.7454	−	9.26005i	−2.45285	−	1.78210i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	3.17864	+	9.78286i	0.590259	+	1.81663i	0.577036	+	0.816719i	$0.304209\pi$
$29$	3.17864	+	9.78286i	0.590259	+	1.81663i	0.0132237	+	0.999913i	$0.495791\pi$
$30$	6.88514	+	2.56313i	1.25705	+	0.467962i
$31$	−0.999624	+	3.07653i	−0.179538	+	0.552561i	−0.999812	−	0.0194105i	$-0.993821\pi$
$31$	−0.999624	+	3.07653i	−0.179538	+	0.552561i	0.820274	+	0.571971i	$0.193821\pi$
$32$	1.00000			0.176777
$33$	−2.51146	+	7.72947i	−0.437188	+	1.34553i
$34$	−3.00957	+	2.18658i	−0.516137	+	0.374996i
$35$	0.0943702	−	2.23408i	0.0159515	−	0.377628i
$36$	−6.30625	−	4.58176i	−1.05104	−	0.763626i
$37$	8.08738	−	5.87582i	1.32956	−	0.965980i	0.329797	−	0.944052i	$-0.393020\pi$
$37$	8.08738	−	5.87582i	1.32956	−	0.965980i	0.999760	−	0.0219278i	$-0.00698039\pi$
$38$	−1.07097	+	0.778104i	−0.173734	+	0.126225i
$39$	9.29271	+	6.75155i	1.48802	+	1.08111i
$40$	2.09557	+	0.780119i	0.331339	+	0.123348i
$41$	1.85833	−	1.35015i	0.290222	−	0.210859i	−0.433142	−	0.901326i	$-0.642595\pi$
$41$	1.85833	−	1.35015i	0.290222	−	0.210859i	0.723364	+	0.690467i	$0.242595\pi$
$42$	−1.01530	+	3.12476i	−0.156664	+	0.482161i
$43$	−1.26901			−0.193522			−0.0967610	−	0.995308i	$-0.530848\pi$
$43$	−1.26901			−0.193522			−0.0967610	+	0.995308i	$0.530848\pi$
$44$	−0.764390	+	2.35255i	−0.115236	+	0.354661i
$45$	−9.64087	−	14.5210i	−1.43718	−	2.16467i
$46$	1.64269	+	5.05567i	0.242201	+	0.745418i
$47$	3.76119	+	11.5757i	0.548626	+	1.68850i	0.712210	+	0.701967i	$0.247694\pi$
$47$	3.76119	+	11.5757i	0.548626	+	1.68850i	−0.163584	+	0.986529i	$0.552306\pi$
$48$	−2.65808	−	1.93121i	−0.383661	−	0.278746i
$49$	1.00000			0.142857
$50$	3.78283	+	3.26959i	0.534973	+	0.462389i
$51$	12.2224			1.71148
$52$	2.82834	+	2.05491i	0.392221	+	0.284965i
$53$	1.79150	+	5.51366i	0.246081	+	0.757360i	0.995457	+	0.0952148i	$0.0303538\pi$
$53$	1.79150	+	5.51366i	0.246081	+	0.757360i	−0.749376	+	0.662145i	$0.769646\pi$
$54$	4.86830	+	14.9831i	0.662491	+	2.03894i
$55$	−3.43710	+	4.33362i	−0.463459	+	0.584346i
$56$	−0.309017	+	0.951057i	−0.0412941	+	0.127090i
$57$	4.34940			0.576092
$58$	3.17864	−	9.78286i	0.417376	−	1.28455i
$59$	2.11540	−	1.53693i	0.275401	−	0.200091i	−0.441508	−	0.897257i	$-0.645556\pi$
$59$	2.11540	−	1.53693i	0.275401	−	0.200091i	0.716909	+	0.697167i	$0.245556\pi$
$60$	−4.06362	−	6.12060i	−0.524611	−	0.790166i
$61$	−5.13244	−	3.72894i	−0.657142	−	0.477442i	0.208554	−	0.978011i	$-0.433124\pi$
$61$	−5.13244	−	3.72894i	−0.657142	−	0.477442i	−0.865697	+	0.500569i	$0.833124\pi$
$62$	2.61705	−	1.90140i	0.332366	−	0.241478i
$63$	6.30625	−	4.58176i	0.794513	−	0.577247i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.32392	+	6.51265i	0.536316	+	0.807795i
$66$	6.57508	−	4.77707i	0.809336	−	0.588017i
$67$	0.483607	−	1.48839i	0.0590820	−	0.181836i	−0.917160	−	0.398520i	$-0.869524\pi$
$67$	0.483607	−	1.48839i	0.0590820	−	0.181836i	0.976242	+	0.216684i	$0.0695241\pi$
$68$	3.72003			0.451120
$69$	5.39716	−	16.6107i	0.649742	−	1.99970i
$70$	−1.38950	+	1.75194i	−0.166077	+	0.209396i
$71$	2.38655	+	7.34506i	0.283232	+	0.871698i	0.986923	+	0.161192i	$0.0515338\pi$
$71$	2.38655	+	7.34506i	0.283232	+	0.871698i	−0.703691	+	0.710506i	$0.748466\pi$
$72$	2.40877	+	7.41344i	0.283877	+	0.873682i
$73$	−5.68610	−	4.13120i	−0.665508	−	0.483520i	0.203010	−	0.979177i	$-0.434927\pi$
$73$	−5.68610	−	4.13120i	−0.665508	−	0.483520i	−0.868519	+	0.495657i	$0.834927\pi$
$74$	−9.99655			−1.16208
$75$	−3.74081	−	15.9963i	−0.431951	−	1.84709i
$76$	1.32379			0.151849
$77$	−2.00120	−	1.45396i	−0.228058	−	0.165694i
$78$	−3.54950	−	10.9242i	−0.401902	−	1.23693i
$79$	2.30913	+	7.10678i	0.259798	+	0.799575i	0.992846	+	0.119399i	$0.0380968\pi$
$79$	2.30913	+	7.10678i	0.259798	+	0.799575i	−0.733049	+	0.680176i	$0.761903\pi$
$80$	−1.23681	−	1.86287i	−0.138280	−	0.208276i
$81$	8.76880	−	26.9876i	0.974311	−	2.99862i
$82$	−2.29702			−0.253663
$83$	−1.61338	+	4.96547i	−0.177091	+	0.545031i	−0.999723	−	0.0235439i	$-0.992505\pi$
$83$	−1.61338	+	4.96547i	−0.177091	+	0.545031i	0.822632	+	0.568575i	$0.192505\pi$
$84$	2.65808	−	1.93121i	0.290020	−	0.210712i
$85$	7.79559	+	2.90207i	0.845551	+	0.314774i
$86$	1.02665	+	0.745904i	0.110706	+	0.0804329i
$87$	−27.3418	+	19.8650i	−2.93135	+	2.12975i
$88$	2.00120	−	1.45396i	0.213329	−	0.154992i
$89$	−0.787001	−	0.571789i	−0.0834219	−	0.0606096i	0.545293	−	0.838246i	$-0.316419\pi$
$89$	−0.787001	−	0.571789i	−0.0834219	−	0.0606096i	−0.628714	+	0.777636i	$0.716419\pi$
$90$	−0.735611	+	17.4145i	−0.0775402	+	1.83565i
$91$	−2.82834	+	2.05491i	−0.296491	+	0.215413i
$92$	1.64269	−	5.05567i	0.171262	−	0.527090i
$93$	−10.6283			−1.10211
$94$	3.76119	−	11.5757i	0.387937	−	1.19395i
$95$	2.77410	+	1.03271i	0.284616	+	0.105954i
$96$	1.01530	+	3.12476i	0.103623	+	0.318920i
$97$	−3.61395	−	11.1226i	−0.366941	−	1.12933i	−0.948757	−	0.316007i	$-0.897658\pi$
$97$	−3.61395	−	11.1226i	−0.366941	−	1.12933i	0.581816	−	0.813320i	$-0.302342\pi$
$98$	−0.809017	−	0.587785i	−0.0817231	−	0.0593753i
$99$	−19.2817			−1.93789
$100$	−1.13856	−	4.86864i	−0.113856	−	0.486864i
$101$	18.9346			1.88407			0.942033	−	0.335521i	$-0.108912\pi$
$101$	18.9346			1.88407			0.942033	+	0.335521i	$0.108912\pi$
$102$	−9.88815	−	7.18416i	−0.979073	−	0.711338i
$103$	−4.44187	−	13.6707i	−0.437671	−	1.34701i	−0.890325	−	0.455325i	$-0.849523\pi$
$103$	−4.44187	−	13.6707i	−0.437671	−	1.34701i	0.452655	−	0.891686i	$-0.350477\pi$
$104$	−1.08033	−	3.32492i	−0.105935	−	0.326035i
$105$	7.07676	−	1.97336i	0.690622	−	0.192581i
$106$	1.79150	−	5.51366i	0.174006	−	0.535534i
$107$	1.96689			0.190147			0.0950734	−	0.995470i	$-0.469691\pi$
$107$	1.96689			0.190147			0.0950734	+	0.995470i	$0.469691\pi$
$108$	4.86830	−	14.9831i	0.468452	−	1.44175i
$109$	9.00561	−	6.54296i	0.862581	−	0.626702i	−0.0660050	−	0.997819i	$-0.521025\pi$
$109$	9.00561	−	6.54296i	0.862581	−	0.626702i	0.928586	+	0.371118i	$0.121025\pi$
$110$	5.32791	−	1.48570i	0.507997	−	0.141655i
$111$	26.5716	+	19.3054i	2.52207	+	1.83239i
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	9.30029	−	6.75706i	0.874898	−	0.635650i	−0.0569990	−	0.998374i	$-0.518153\pi$
$113$	9.30029	−	6.75706i	0.874898	−	0.635650i	0.931897	+	0.362724i	$0.118153\pi$
$114$	−3.51874	−	2.55651i	−0.329560	−	0.239439i
$115$	7.38639	−	9.31302i	0.688784	−	0.868444i
$116$	−8.32180	+	6.04614i	−0.772660	+	0.561370i
$117$	−8.42113	+	25.9176i	−0.778533	+	2.39608i
$118$	−2.61477			−0.240709
$119$	−1.14955	+	3.53796i	−0.105379	+	0.324325i
$120$	−0.310060	+	7.34021i	−0.0283044	+	0.670066i
$121$	−1.50838	−	4.64230i	−0.137125	−	0.422028i
$122$	1.96042	+	6.03355i	0.177488	+	0.546252i
$123$	6.10566	+	4.43602i	0.550529	+	0.399983i
$124$	−3.23485			−0.290498
$125$	1.41219	−	11.0908i	0.126310	−	0.991991i
$126$	−7.79495			−0.694430
$127$	9.41662	+	6.84158i	0.835590	+	0.607092i	0.921135	−	0.389242i	$-0.127263\pi$
$127$	9.41662	+	6.84158i	0.835590	+	0.607092i	−0.0855451	+	0.996334i	$0.527263\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−1.28842	−	3.96535i	−0.113439	−	0.349129i
$130$	0.329920	−	7.81038i	0.0289359	−	0.685016i
$131$	−1.08511	+	3.33963i	−0.0948066	+	0.291785i	−0.987203	−	0.159467i	$-0.949022\pi$
$131$	−1.08511	+	3.33963i	−0.0948066	+	0.291785i	0.892397	+	0.451252i	$0.149022\pi$
$132$	−8.12724			−0.707386
$133$	−0.409074	+	1.25900i	−0.0354712	+	0.109169i
$134$	−1.26610	+	0.919875i	−0.109374	+	0.0794651i
$135$	21.8904	−	27.6002i	1.88403	−	2.37545i
$136$	−3.00957	−	2.18658i	−0.258069	−	0.187498i
$137$	−1.80528	+	1.31161i	−0.154235	+	0.112059i	−0.662226	−	0.749304i	$-0.730388\pi$
$137$	−1.80528	+	1.31161i	−0.154235	+	0.112059i	0.507991	+	0.861362i	$0.330388\pi$
$138$	−14.1299	+	10.2660i	−1.20282	+	0.873901i
$139$	3.62423	+	2.63316i	0.307403	+	0.223342i	0.730781	−	0.682611i	$-0.239156\pi$
$139$	3.62423	+	2.63316i	0.307403	+	0.223342i	−0.423378	+	0.905953i	$0.639156\pi$
$140$	2.15389	−	0.600616i	0.182037	−	0.0507613i
$141$	−32.3527	+	23.5056i	−2.72459	+	1.97953i
$142$	2.38655	−	7.34506i	0.200275	−	0.616383i
$143$	8.64783			0.723168
$144$	2.40877	−	7.41344i	0.200731	−	0.617787i
$145$	−22.1556	+	6.17812i	−1.83992	+	0.513065i
$146$	2.17190	+	6.68442i	0.179748	+	0.553206i
$147$	1.01530	+	3.12476i	0.0837402	+	0.257726i
$148$	8.08738	+	5.87582i	0.664778	+	0.482990i
$149$	−19.9327			−1.63295			−0.816477	−	0.577378i	$-0.804076\pi$
$149$	−19.9327			−1.63295			−0.816477	+	0.577378i	$0.804076\pi$
$150$	−6.37598	+	15.1400i	−0.520597	+	1.23618i
$151$	10.8787			0.885299			0.442649	−	0.896695i	$-0.354039\pi$
$151$	10.8787			0.885299			0.442649	+	0.896695i	$0.354039\pi$
$152$	−1.07097	−	0.778104i	−0.0868670	−	0.0631126i
$153$	8.96072	+	27.5783i	0.724431	+	2.22957i
$154$	0.764390	+	2.35255i	0.0615963	+	0.189574i
$155$	−6.77886	−	2.52357i	−0.544491	−	0.202698i
$156$	−3.54950	+	10.9242i	−0.284187	+	0.874639i
$157$	13.3531			1.06569			0.532845	−	0.846213i	$-0.321123\pi$
$157$	13.3531			1.06569			0.532845	+	0.846213i	$0.321123\pi$
$158$	2.30913	−	7.10678i	0.183705	−	0.565385i
$159$	−15.4100	+	11.1960i	−1.22209	+	0.887901i
$160$	−0.0943702	+	2.23408i	−0.00746062	+	0.176619i
$161$	4.30061	+	3.12458i	0.338936	+	0.246251i
$162$	−22.9570	+	16.6792i	−1.80367	+	1.31045i
$163$	−7.39731	+	5.37446i	−0.579402	+	0.420960i	−0.838509	−	0.544889i	$-0.816572\pi$
$163$	−7.39731	+	5.37446i	−0.579402	+	0.420960i	0.259106	+	0.965849i	$0.416572\pi$
$164$	1.85833	+	1.35015i	0.145111	+	0.105429i
$165$	−17.0312	−	6.34021i	−1.32588	−	0.493585i
$166$	4.22388	−	3.06883i	0.327837	−	0.238187i
$167$	1.51081	−	4.64979i	0.116910	−	0.359812i	−0.875431	−	0.483344i	$-0.839422\pi$
$167$	1.51081	−	4.64979i	0.116910	−	0.359812i	0.992341	+	0.123532i	$0.0394222\pi$
$168$	−3.28557			−0.253487
$169$	−0.240359	+	0.739749i	−0.0184892	+	0.0569038i
$170$	−4.60097	−	6.92996i	−0.352879	−	0.531504i
$171$	3.18871	+	9.81384i	0.243847	+	0.750483i
$172$	−0.392145	−	1.20690i	−0.0299008	−	0.0920252i
$173$	−11.3027	−	8.21186i	−0.859325	−	0.624336i	0.0683760	−	0.997660i	$-0.478218\pi$
$173$	−11.3027	−	8.21186i	−0.859325	−	0.624336i	−0.927701	+	0.373323i	$0.878218\pi$
$174$	33.7964			2.56210
$175$	4.98219	+	0.421660i	0.376618	+	0.0318745i
$176$	−2.47362			−0.186456
$177$	6.95028	+	5.04967i	0.522415	+	0.379557i
$178$	0.300607	+	0.925175i	0.0225315	+	0.0693448i
$179$	−2.73434	−	8.41543i	−0.204374	−	0.628999i	−0.999739	−	0.0228673i	$-0.992720\pi$
$179$	−2.73434	−	8.41543i	−0.204374	−	0.628999i	0.795364	−	0.606132i	$-0.207280\pi$
$180$	10.8311	−	13.6563i	0.807304	−	1.01788i
$181$	1.52782	−	4.70216i	0.113562	−	0.349508i	−0.878082	−	0.478510i	$-0.841177\pi$
$181$	1.52782	−	4.70216i	0.113562	−	0.349508i	0.991644	+	0.129001i	$0.0411771\pi$
$182$	3.49602			0.259143
$183$	6.44109	−	19.8236i	0.476139	−	1.46541i
$184$	−4.30061	+	3.12458i	−0.317045	+	0.230347i
$185$	12.3638	+	18.6223i	0.909007	+	1.36914i
$186$	8.59850	+	6.24717i	0.630472	+	0.458065i
$187$	7.44453	−	5.40877i	0.544398	−	0.395528i
$188$	−9.84692	+	7.15420i	−0.718160	+	0.521774i
$189$	12.7454	+	9.26005i	0.927089	+	0.673570i
$190$	−1.63728	−	2.46606i	−0.118781	−	0.178906i
$191$	−8.92782	+	6.48644i	−0.645994	+	0.469342i	−0.861904	−	0.507071i	$-0.830728\pi$
$191$	−8.92782	+	6.48644i	−0.645994	+	0.469342i	0.215910	+	0.976413i	$0.430728\pi$
$192$	1.01530	−	3.12476i	0.0732727	−	0.225510i
$193$	−26.5489			−1.91103			−0.955516	−	0.294939i	$-0.904701\pi$
$193$	−26.5489			−1.91103			−0.955516	+	0.294939i	$0.904701\pi$
$194$	−3.61395	+	11.1226i	−0.259466	+	0.798555i
$195$	−15.9604	+	20.1235i	−1.14295	+	1.44107i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	3.89945	+	12.0013i	0.277824	+	0.855054i	0.988458	+	0.151493i	$0.0484080\pi$
$197$	3.89945	+	12.0013i	0.277824	+	0.855054i	−0.710634	+	0.703561i	$0.751592\pi$
$198$	15.5993	+	11.3335i	1.10859	+	0.805439i
$199$	−17.4148			−1.23451			−0.617253	−	0.786765i	$-0.711754\pi$
$199$	−17.4148			−1.23451			−0.617253	+	0.786765i	$0.711754\pi$
$200$	−1.94060	+	4.60804i	−0.137221	+	0.325838i
$201$	5.14186			0.362679
$202$	−15.3184	−	11.1295i	−1.07780	−	0.783068i
$203$	−3.17864	−	9.78286i	−0.223097	−	0.686622i
$204$	3.77694	+	11.6242i	0.264438	+	0.813858i
$205$	2.84098	+	4.27906i	0.198422	+	0.298863i
$206$	−4.44187	+	13.6707i	−0.309480	+	0.952481i
$207$	41.4368			2.88006
$208$	−1.08033	+	3.32492i	−0.0749075	+	0.230541i
$209$	2.64917	−	1.92473i	0.183247	−	0.133137i
$210$	−6.88514	−	2.56313i	−0.475120	−	0.176873i
$211$	18.1212	+	13.1658i	1.24752	+	0.906374i	0.998075	−	0.0620152i	$-0.0197527\pi$
$211$	18.1212	+	13.1658i	1.24752	+	0.906374i	0.249442	+	0.968390i	$0.419753\pi$
$212$	−4.69020	+	3.40763i	−0.322124	+	0.234037i
$213$	−20.5285	+	14.9148i	−1.40659	+	1.02195i
$214$	−1.59125	−	1.15611i	−0.108776	−	0.0790302i
$215$	0.119757	−	2.83506i	0.00816733	−	0.193350i
$216$	−12.7454	+	9.26005i	−0.867212	+	0.630067i
$217$	0.999624	−	3.07653i	0.0678589	−	0.208848i
$218$	−11.1315			−0.753923
$219$	7.13592	−	21.9621i	0.482201	−	1.48406i
$220$	−5.18364	−	1.92972i	−0.349481	−	0.130101i
$221$	−4.01887	−	12.3688i	−0.270338	−	0.832016i
$222$	−10.1495	−	31.2368i	−0.681187	−	2.09648i
$223$	14.4922	+	10.5292i	0.970469	+	0.705087i	0.955558	−	0.294802i	$-0.0952536\pi$
$223$	14.4922	+	10.5292i	0.970469	+	0.705087i	0.0149106	+	0.999889i	$0.495254\pi$
$224$	−1.00000			−0.0668153
$225$	33.3509	−	20.1681i	2.22339	−	1.34454i
$226$	−11.4958			−0.764689
$227$	−4.45619	−	3.23761i	−0.295768	−	0.214888i	0.429998	−	0.902830i	$-0.358514\pi$
$227$	−4.45619	−	3.23761i	−0.295768	−	0.214888i	−0.725766	+	0.687942i	$0.758514\pi$
$228$	1.34404	+	4.13653i	0.0890112	+	0.273948i
$229$	−2.97868	−	9.16743i	−0.196837	−	0.605801i	−0.999950	−	0.00997495i	$-0.996825\pi$
$229$	−2.97868	−	9.16743i	−0.196837	−	0.605801i	0.803114	−	0.595826i	$-0.203175\pi$
$230$	−11.4498	+	3.19278i	−0.754976	+	0.210526i
$231$	2.51146	−	7.72947i	0.165242	−	0.508562i
$232$	10.2863			0.675329
$233$	7.94640	−	24.4565i	0.520586	−	1.60220i	−0.252296	−	0.967650i	$-0.581186\pi$
$233$	7.94640	−	24.4565i	0.520586	−	1.60220i	0.772882	−	0.634549i	$-0.218814\pi$
$234$	22.0468	−	16.0179i	1.44124	−	1.04713i
$235$	−26.2160	+	7.31037i	−1.71015	+	0.476876i
$236$	2.11540	+	1.53693i	0.137701	+	0.100045i
$237$	−19.8625	+	14.4310i	−1.29021	+	0.937393i
$238$	3.00957	−	2.18658i	0.195082	−	0.141735i
$239$	3.85682	+	2.80214i	0.249477	+	0.181255i	0.705495	−	0.708715i	$-0.250725\pi$
$239$	3.85682	+	2.80214i	0.249477	+	0.181255i	−0.456018	+	0.889970i	$0.650725\pi$
$240$	4.56531	−	5.75610i	0.294689	−	0.371555i
$241$	6.78755	−	4.93144i	0.437224	−	0.317662i	−0.347307	−	0.937752i	$-0.612904\pi$
$241$	6.78755	−	4.93144i	0.437224	−	0.317662i	0.784531	+	0.620090i	$0.212904\pi$
$242$	−1.50838	+	4.64230i	−0.0969621	+	0.298419i
$243$	45.9702			2.94899
$244$	1.96042	−	6.03355i	0.125503	−	0.386258i
$245$	−0.0943702	+	2.23408i	−0.00602909	+	0.142730i
$246$	−2.33216	−	7.17764i	−0.148693	−	0.457629i
$247$	−1.43013	−	4.40149i	−0.0909971	−	0.280060i
$248$	2.61705	+	1.90140i	0.166183	+	0.120739i
$249$	−17.1540			−1.08709
$250$	−7.66149	+	8.14258i	−0.484555	+	0.514982i
$251$	−17.2187			−1.08684			−0.543418	−	0.839463i	$-0.682870\pi$
$251$	−17.2187			−1.08684			−0.543418	+	0.839463i	$0.682870\pi$
$252$	6.30625	+	4.58176i	0.397256	+	0.288624i
$253$	−4.06338	−	12.5058i	−0.255463	−	0.786233i
$254$	−3.59683	−	11.0699i	−0.225685	−	0.694588i
$255$	−1.15343	+	27.3058i	−0.0722307	+	1.70996i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	18.1079			1.12954			0.564771	−	0.825248i	$-0.308965\pi$
$257$	18.1079			1.12954			0.564771	+	0.825248i	$0.308965\pi$
$258$	−1.28842	+	3.96535i	−0.0802135	+	0.246872i
$259$	−8.08738	+	5.87582i	−0.502525	+	0.365106i
$260$	−4.85774	+	6.12481i	−0.301264	+	0.379845i
$261$	−64.8680	−	47.1294i	−4.01523	−	2.91724i
$262$	2.84086	−	2.06400i	0.175509	−	0.127515i
$263$	14.2629	−	10.3626i	0.879488	−	0.638985i	−0.0536282	−	0.998561i	$-0.517079\pi$
$263$	14.2629	−	10.3626i	0.879488	−	0.638985i	0.933116	+	0.359576i	$0.117079\pi$
$264$	6.57508	+	4.77707i	0.404668	+	0.294009i
$265$	−12.4870	+	3.48202i	−0.767071	+	0.213899i
$266$	1.07097	−	0.778104i	0.0656653	−	0.0477086i
$267$	0.987666	−	3.03972i	0.0604442	−	0.186028i
$268$	1.56498			0.0955966
$269$	−2.49081	+	7.66594i	−0.151868	+	0.467401i	−0.997830	−	0.0658420i	$-0.979027\pi$
$269$	−2.49081	+	7.66594i	−0.151868	+	0.467401i	0.845962	+	0.533243i	$0.179027\pi$
$270$	−33.9328	+	9.46219i	−2.06508	+	0.575850i
$271$	−2.97393	−	9.15283i	−0.180654	−	0.555995i	0.819193	−	0.573518i	$-0.194422\pi$
$271$	−2.97393	−	9.15283i	−0.180654	−	0.555995i	−0.999846	+	0.0175234i	$0.994422\pi$
$272$	1.14955	+	3.53796i	0.0697019	+	0.214521i
$273$	−9.29271	−	6.75155i	−0.562420	−	0.408622i
$274$	2.23145			0.134807
$275$	−9.35728	−	8.08771i	−0.564265	−	0.487708i
$276$	17.4656			1.05130
$277$	−5.54453	−	4.02834i	−0.333139	−	0.242040i	0.408622	−	0.912703i	$-0.366009\pi$
$277$	−5.54453	−	4.02834i	−0.333139	−	0.242040i	−0.741761	+	0.670664i	$0.766009\pi$
$278$	−1.38433	−	4.26054i	−0.0830268	−	0.255530i
$279$	−7.79202	−	23.9814i	−0.466496	−	1.43573i
$280$	−2.09557	−	0.780119i	−0.125234	−	0.0466210i
$281$	4.43999	−	13.6649i	0.264868	−	0.815179i	−0.726856	−	0.686790i	$-0.759019\pi$
$281$	4.43999	−	13.6649i	0.264868	−	0.815179i	0.991724	−	0.128389i	$-0.0409807\pi$
$282$	39.9901			2.38138
$283$	4.36960	−	13.4482i	0.259746	−	0.799415i	−0.733112	−	0.680108i	$-0.761933\pi$
$283$	4.36960	−	13.4482i	0.259746	−	0.799415i	0.992857	−	0.119307i	$-0.0380672\pi$
$284$	−6.24808	+	4.53949i	−0.370755	+	0.269369i
$285$	−0.410454	+	9.71689i	−0.0243132	+	0.575579i
$286$	−6.99624	−	5.08307i	−0.413697	−	0.300568i
$287$	−1.85833	+	1.35015i	−0.109694	+	0.0796971i
$288$	−6.30625	+	4.58176i	−0.371599	+	0.269983i
$289$	2.55758	+	1.85819i	0.150446	+	0.109305i
$290$	21.5557	+	8.02454i	1.26579	+	0.471217i
$291$	31.0862	−	22.5854i	1.82230	−	1.32398i
$292$	2.17190	−	6.68442i	0.127101	−	0.391176i
$293$	0.183696			0.0107316			0.00536580	−	0.999986i	$-0.498292\pi$
$293$	0.183696			0.0107316			0.00536580	+	0.999986i	$0.498292\pi$
$294$	1.01530	−	3.12476i	0.0592133	−	0.182240i
$295$	3.23398	+	4.87099i	0.188289	+	0.283600i
$296$	−3.08910	−	9.50728i	−0.179551	−	0.552600i
$297$	−12.0423	−	37.0624i	−0.698766	−	2.15058i
$298$	16.1259	+	11.7162i	0.934150	+	0.678699i
$299$	−18.5843			−1.07476
$300$	14.0574	−	8.50084i	0.811603	−	0.490796i
$301$	1.26901			0.0731444
$302$	−8.80108	−	6.39436i	−0.506445	−	0.367954i
$303$	19.2242	+	59.1662i	1.10440	+	3.39901i
$304$	0.409074	+	1.25900i	0.0234620	+	0.0722086i
$305$	8.81508	−	11.1144i	0.504750	−	0.636407i
$306$	8.96072	−	27.5783i	0.512250	−	1.57654i
$307$	−12.0856			−0.689761			−0.344880	−	0.938647i	$-0.612081\pi$
$307$	−12.0856			−0.689761			−0.344880	+	0.938647i	$0.612081\pi$
$308$	0.764390	−	2.35255i	0.0435552	−	0.134049i
$309$	38.2078	−	27.7596i	2.17356	−	1.57919i
$310$	4.00090	+	6.02612i	0.227236	+	0.342261i
$311$	−25.0777	−	18.2200i	−1.42202	−	1.03316i	−0.991433	−	0.130615i	$-0.958305\pi$
$311$	−25.0777	−	18.2200i	−1.42202	−	1.03316i	−0.430592	−	0.902547i	$-0.641695\pi$
$312$	9.29271	−	6.75155i	0.526096	−	0.382231i
$313$	1.83399	−	1.33247i	0.103663	−	0.0753159i	−0.534746	−	0.845013i	$-0.679593\pi$
$313$	1.83399	−	1.33247i	0.103663	−	0.0753159i	0.638409	+	0.769697i	$0.279593\pi$
$314$	−10.8029	−	7.84873i	−0.609640	−	0.442930i
$315$	9.64087	+	14.5210i	0.543202	+	0.818167i
$316$	−6.04539	+	4.39223i	−0.340080	+	0.247082i
$317$	−8.38101	+	25.7941i	−0.470724	+	1.44874i	0.380914	+	0.924610i	$0.375609\pi$
$317$	−8.38101	+	25.7941i	−0.470724	+	1.44874i	−0.851639	+	0.524130i	$0.824391\pi$
$318$	19.0478			1.06815
$319$	−7.86276	+	24.1991i	−0.440230	+	1.35489i
$320$	1.38950	−	1.75194i	0.0776756	−	0.0979362i
$321$	1.99698	+	6.14607i	0.111461	+	0.343040i
$322$	−1.64269	−	5.05567i	−0.0915434	−	0.281742i
$323$	−3.98404	−	2.89458i	−0.221678	−	0.161058i
$324$	28.3764			1.57647
$325$	−14.9578	+	9.04536i	−0.829710	+	0.501746i
$326$	9.14358			0.506416
$327$	29.5885	+	21.4973i	1.63625	+	1.18880i
$328$	−0.709818	−	2.18460i	−0.0391932	−	0.120624i
$329$	−3.76119	−	11.5757i	−0.207361	−	0.638192i
$330$	10.0519	+	15.1400i	0.553336	+	0.833431i
$331$	1.72855	−	5.31994i	0.0950098	−	0.292410i	−0.892246	−	0.451549i	$-0.850872\pi$
$331$	1.72855	−	5.31994i	0.0950098	−	0.292410i	0.987256	+	0.159139i	$0.0508717\pi$
$332$	−5.22100			−0.286540
$333$	−24.0794	+	74.1088i	−1.31954	+	4.06114i
$334$	−3.95535	+	2.87373i	−0.216427	+	0.157243i
$335$	3.27954	+	1.22087i	0.179180	+	0.0667035i
$336$	2.65808	+	1.93121i	0.145010	+	0.105356i
$337$	23.1935	−	16.8511i	1.26343	−	0.917936i	0.264509	−	0.964383i	$-0.414790\pi$
$337$	23.1935	−	16.8511i	1.26343	−	0.917936i	0.998921	+	0.0464473i	$0.0147900\pi$
$338$	0.629268	−	0.457190i	0.0342277	−	0.0248679i
$339$	30.5567	+	22.2008i	1.65961	+	1.20578i
$340$	−0.351060	+	8.31084i	−0.0190389	+	0.450719i
$341$	−6.47359	+	4.70334i	−0.350564	+	0.254700i
$342$	3.18871	−	9.81384i	0.172426	−	0.530672i
$343$	−1.00000			−0.0539949
$344$	−0.392145	+	1.20690i	−0.0211430	+	0.0650716i
$345$	36.6003	+	13.6252i	1.97050	+	0.733557i
$346$	4.31723	+	13.2871i	0.232096	+	0.714318i
$347$	−5.99973	−	18.4653i	−0.322082	−	0.991267i	−0.972740	−	0.231896i	$-0.925507\pi$
$347$	−5.99973	−	18.4653i	−0.322082	−	0.991267i	0.650658	−	0.759371i	$-0.274493\pi$
$348$	−27.3418	−	19.8650i	−1.46568	−	1.06488i
$349$	16.8501			0.901966			0.450983	−	0.892532i	$-0.351073\pi$
$349$	16.8501			0.901966			0.450983	+	0.892532i	$0.351073\pi$
$350$	−3.78283	−	3.26959i	−0.202201	−	0.174767i
$351$	−55.0768			−2.93978
$352$	2.00120	+	1.45396i	0.106664	+	0.0774962i
$353$	−4.29170	−	13.2085i	−0.228424	−	0.703017i	−0.997926	−	0.0643723i	$-0.979495\pi$
$353$	−4.29170	−	13.2085i	−0.228424	−	0.703017i	0.769502	−	0.638644i	$-0.220505\pi$
$354$	−2.65477	−	8.17054i	−0.141099	−	0.434259i
$355$	−16.6346	+	4.63859i	−0.882875	+	0.246191i
$356$	0.300607	−	0.925175i	0.0159322	−	0.0490342i
$357$	−12.2224			−0.646879
$358$	−2.73434	+	8.41543i	−0.144514	+	0.444769i
$359$	−26.8318	+	19.4944i	−1.41613	+	1.02888i	−0.423733	+	0.905787i	$0.639280\pi$
$359$	−26.8318	+	19.4944i	−1.41613	+	1.02888i	−0.992396	+	0.123090i	$0.960720\pi$
$360$	−16.7895	+	4.68177i	−0.884885	+	0.246751i
$361$	13.9536	+	10.1379i	0.734399	+	0.533572i
$362$	−3.99989	+	2.90609i	−0.210230	+	0.152741i
$363$	12.9746	−	9.42663i	0.680992	−	0.494770i
$364$	−2.82834	−	2.05491i	−0.148245	−	0.107707i
$365$	9.76600	−	12.3133i	0.511176	−	0.644509i
$366$	−16.8630	+	12.2517i	−0.881443	+	0.640406i
$367$	3.67940	−	11.3240i	0.192063	−	0.591109i	−0.807935	−	0.589271i	$-0.799415\pi$
$367$	3.67940	−	11.3240i	0.192063	−	0.591109i	0.999998	−	0.00183779i	$-0.000584986\pi$
$368$	5.31585			0.277108
$369$	−5.53300	+	17.0288i	−0.288036	+	0.886485i
$370$	0.943376	−	22.3330i	0.0490438	−	1.16104i
$371$	−1.79150	−	5.51366i	−0.0930099	−	0.286255i
$372$	−3.28433	−	10.1081i	−0.170285	−	0.524083i
$373$	16.0257	+	11.6433i	0.829779	+	0.602869i	0.919497	−	0.393098i	$-0.128597\pi$
$373$	16.0257	+	11.6433i	0.829779	+	0.602869i	−0.0897181	+	0.995967i	$0.528597\pi$
$374$	−9.20195			−0.475821
$375$	36.0899	−	6.84768i	1.86367	−	0.353613i
$376$	12.1715			0.627695
$377$	29.0932	+	21.1374i	1.49838	+	1.08863i
$378$	−4.86830	−	14.9831i	−0.250398	−	0.770646i
$379$	2.05236	+	6.31653i	0.105423	+	0.324458i	0.989829	−	0.142259i	$-0.0454366\pi$
$379$	2.05236	+	6.31653i	0.105423	+	0.324458i	−0.884407	+	0.466717i	$0.845437\pi$
$380$	−0.124926	+	2.95745i	−0.00640858	+	0.151714i
$381$	−11.8176	+	36.3709i	−0.605435	+	1.86334i
$382$	11.0354			0.564620
$383$	1.14706	−	3.53030i	0.0586123	−	0.180390i	−0.917464	−	0.397819i	$-0.869767\pi$
$383$	1.14706	−	3.53030i	0.0586123	−	0.180390i	0.976076	+	0.217429i	$0.0697671\pi$
$384$	−2.65808	+	1.93121i	−0.135645	+	0.0985515i
$385$	3.43710	−	4.33362i	0.175171	−	0.220862i
$386$	21.4785	+	15.6051i	1.09323	+	0.794276i
$387$	8.00268	−	5.81429i	0.406799	−	0.295557i
$388$	9.46144	−	6.87414i	0.480332	−	0.348981i
$389$	−4.03933	−	2.93475i	−0.204802	−	0.148798i	0.480657	−	0.876909i	$-0.340398\pi$
$389$	−4.03933	−	2.93475i	−0.204802	−	0.148798i	−0.685459	+	0.728111i	$0.740398\pi$
$390$	24.7405	−	6.89893i	1.25279	−	0.349341i
$391$	−15.9984	+	11.6235i	−0.809075	+	0.587827i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−11.5372			−0.581977
$394$	3.89945	−	12.0013i	0.196451	−	0.604615i
$395$	−16.0950	+	4.48811i	−0.809827	+	0.225821i
$396$	−5.95839	−	18.3380i	−0.299420	−	0.921521i
$397$	−4.75468	−	14.6334i	−0.238630	−	0.734429i	−0.996619	−	0.0821612i	$-0.973818\pi$
$397$	−4.75468	−	14.6334i	−0.238630	−	0.734429i	0.757989	−	0.652268i	$-0.226182\pi$
$398$	14.0889	+	10.2362i	0.706213	+	0.513094i
$399$	−4.34940			−0.217742
$400$	4.27852	−	2.58733i	0.213926	−	0.129366i
$401$	0.271846			0.0135753			0.00678767	−	0.999977i	$-0.497839\pi$
$401$	0.271846			0.0135753			0.00678767	+	0.999977i	$0.497839\pi$
$402$	−4.15985	−	3.02231i	−0.207475	−	0.150739i
$403$	3.49471	+	10.7556i	0.174084	+	0.535775i
$404$	5.85112	+	18.0079i	0.291104	+	0.895926i
$405$	59.4648	+	22.1370i	2.95483	+	1.10000i
$406$	−3.17864	+	9.78286i	−0.157753	+	0.485515i
$407$	24.7277			1.22570
$408$	3.77694	−	11.6242i	0.186986	−	0.575484i
$409$	15.3744	−	11.1702i	0.760215	−	0.552329i	−0.138761	−	0.990326i	$-0.544312\pi$
$409$	15.3744	−	11.1702i	0.760215	−	0.552329i	0.898976	+	0.437997i	$0.144312\pi$
$410$	0.216770	−	5.13172i	0.0107055	−	0.253437i
$411$	−5.93136	−	4.30939i	−0.292573	−	0.212566i
$412$	11.6290	−	8.44894i	0.572918	−	0.416249i
$413$	−2.11540	+	1.53693i	−0.104092	+	0.0756271i
$414$	−33.5231	−	24.3559i	−1.64757	−	1.19703i
$415$	−10.9410	−	4.07300i	−0.537071	−	0.199936i
$416$	2.82834	−	2.05491i	0.138671	−	0.100750i
$417$	−4.54832	+	13.9983i	−0.222732	+	0.685499i
$418$	−3.27455			−0.160164
$419$	9.06195	−	27.8898i	0.442705	−	1.36251i	−0.442275	−	0.896879i	$-0.645829\pi$
$419$	9.06195	−	27.8898i	0.442705	−	1.36251i	0.884981	−	0.465628i	$-0.154171\pi$
$420$	4.06362	+	6.12060i	0.198284	+	0.298655i
$421$	−2.11180	−	6.49944i	−0.102923	−	0.316764i	0.886315	−	0.463084i	$-0.153257\pi$
$421$	−2.11180	−	6.49944i	−0.102923	−	0.316764i	−0.989237	+	0.146320i	$0.953257\pi$
$422$	−6.92170	−	21.3028i	−0.336943	−	1.03700i
$423$	−76.7563	−	55.7667i	−3.73202	−	2.71147i
$424$	5.79741			0.281547
$425$	−7.21911	+	17.1421i	−0.350178	+	0.831513i
$426$	25.3746			1.22940
$427$	5.13244	+	3.72894i	0.248376	+	0.180456i
$428$	0.607804	+	1.87063i	0.0293793	+	0.0904202i
$429$	8.78011	+	27.0224i	0.423908	+	1.30465i
$430$	−1.76329	+	2.22322i	−0.0850335	+	0.107213i
$431$	−1.40083	+	4.31130i	−0.0674755	+	0.207668i	−0.979109	−	0.203336i	$-0.934822\pi$
$431$	−1.40083	+	4.31130i	−0.0674755	+	0.207668i	0.911634	+	0.411004i	$0.134822\pi$
$432$	15.7541			0.757971
$433$	0.283308	−	0.871933i	0.0136149	−	0.0419024i	−0.944018	−	0.329893i	$-0.892987\pi$
$433$	0.283308	−	0.871933i	0.0136149	−	0.0419024i	0.957633	+	0.287991i	$0.0929873\pi$
$434$	−2.61705	+	1.90140i	−0.125622	+	0.0912700i
$435$	−41.7997	−	62.9584i	−2.00414	−	3.01862i
$436$	9.00561	+	6.54296i	0.431290	+	0.313351i
$437$	−5.69311	+	4.13628i	−0.272338	+	0.197865i
$438$	−18.6821	+	13.5733i	−0.892664	+	0.648558i
$439$	−4.04848	−	2.94140i	−0.193224	−	0.140385i	0.486967	−	0.873420i	$-0.338103\pi$
$439$	−4.04848	−	2.94140i	−0.193224	−	0.140385i	−0.680191	+	0.733035i	$0.738103\pi$
$440$	3.05940	+	4.60804i	0.145851	+	0.219680i
$441$	−6.30625	+	4.58176i	−0.300298	+	0.218179i
$442$	−4.01887	+	12.3688i	−0.191158	+	0.588324i
$443$	−14.7334			−0.700006			−0.350003	−	0.936749i	$-0.613819\pi$
$443$	−14.7334			−0.700006			−0.350003	+	0.936749i	$0.613819\pi$
$444$	−10.1495	+	31.2368i	−0.481672	+	1.48243i
$445$	1.35169	−	1.70426i	0.0640763	−	0.0807896i
$446$	−5.53553	−	17.0366i	−0.262115	−	0.806706i
$447$	−20.2376	−	62.2850i	−0.957207	−	2.94598i
$448$	0.809017	+	0.587785i	0.0382225	+	0.0277702i
$449$	−17.4267			−0.822416			−0.411208	−	0.911542i	$-0.634893\pi$
$449$	−17.4267			−0.822416			−0.411208	+	0.911542i	$0.634893\pi$
$450$	−38.8359	−	3.28682i	−1.83074	−	0.154942i
$451$	5.68195			0.267553
$452$	9.30029	+	6.75706i	0.437449	+	0.317825i
$453$	11.0451	+	33.9934i	0.518946	+	1.59715i
$454$	1.70211	+	5.23857i	0.0798842	+	0.245858i
$455$	−4.32392	−	6.51265i	−0.202708	−	0.305318i
$456$	1.34404	−	4.13653i	0.0629404	−	0.193711i
$457$	−24.8559			−1.16271			−0.581355	−	0.813650i	$-0.697477\pi$
$457$	−24.8559			−1.16271			−0.581355	+	0.813650i	$0.697477\pi$
$458$	−2.97868	+	9.16743i	−0.139185	+	0.428366i
$459$	−47.4132	+	34.4477i	−2.21306	+	1.60788i
$460$	11.1397	+	4.14699i	0.519393	+	0.193355i
$461$	−1.68435	−	1.22375i	−0.0784481	−	0.0569959i	0.547870	−	0.836564i	$-0.315439\pi$
$461$	−1.68435	−	1.22375i	−0.0784481	−	0.0569959i	−0.626318	+	0.779568i	$0.715439\pi$
$462$	−6.57508	+	4.77707i	−0.305900	+	0.222250i
$463$	−27.1614	+	19.7339i	−1.26230	+	0.917113i	−0.998868	−	0.0475651i	$-0.984854\pi$
$463$	−27.1614	+	19.7339i	−1.26230	+	0.917113i	−0.263430	+	0.964678i	$0.584854\pi$
$464$	−8.32180	−	6.04614i	−0.386330	−	0.280685i
$465$	1.00300	−	23.7445i	0.0465129	−	1.10112i
$466$	−20.8040	+	15.1150i	−0.963725	+	0.700187i
$467$	−3.10459	+	9.55496i	−0.143663	+	0.442151i	−0.996837	−	0.0794770i	$-0.974675\pi$
$467$	−3.10459	+	9.55496i	−0.143663	+	0.442151i	0.853173	+	0.521628i	$0.174675\pi$
$468$	−27.2513			−1.25969
$469$	−0.483607	+	1.48839i	−0.0223309	+	0.0687274i
$470$	25.5061	+	9.49518i	1.17651	+	0.437980i
$471$	13.5573	+	41.7251i	0.624688	+	1.92259i
$472$	−0.808009	−	2.48680i	−0.0371916	−	0.114464i
$473$	−2.53954	−	1.84508i	−0.116768	−	0.0848370i
$474$	24.5514			1.12769
$475$	−2.56895	+	6.10008i	−0.117872	+	0.279891i
$476$	−3.72003			−0.170508
$477$	−36.5599	−	26.5623i	−1.67396	−	1.21621i
$478$	−1.47317	−	4.53396i	−0.0673813	−	0.207378i
$479$	2.27069	+	6.98848i	0.103751	+	0.319312i	0.989435	−	0.144976i	$-0.0463105\pi$
$479$	2.27069	+	6.98848i	0.103751	+	0.319312i	−0.885685	+	0.464287i	$0.846310\pi$
$480$	−7.07676	+	1.97336i	−0.323009	+	0.0900713i
$481$	10.7996	−	33.2377i	0.492418	−	1.51551i
$482$	−8.38987			−0.382148
$483$	−5.39716	+	16.6107i	−0.245579	+	0.755815i
$484$	3.94898	−	2.86910i	0.179499	−	0.130414i
$485$	25.1898	−	7.02419i	1.14381	−	0.318952i
$486$	−37.1907	−	27.0206i	−1.68700	−	1.22568i
$487$	−1.17221	+	0.851658i	−0.0531178	+	0.0385923i	−0.614027	−	0.789285i	$-0.710452\pi$
$487$	−1.17221	+	0.851658i	−0.0531178	+	0.0385923i	0.560910	+	0.827877i	$0.310452\pi$
$488$	−5.13244	+	3.72894i	−0.232335	+	0.168801i
$489$	−24.3044	−	17.6582i	−1.09908	−	0.798529i
$490$	1.38950	−	1.75194i	0.0627714	−	0.0791444i
$491$	15.4562	−	11.2296i	0.697529	−	0.506784i	−0.181598	−	0.983373i	$-0.558127\pi$
$491$	15.4562	−	11.2296i	0.697529	−	0.506784i	0.879126	+	0.476589i	$0.158127\pi$
$492$	−2.33216	+	7.17764i	−0.105142	+	0.323593i
$493$	38.2654			1.72339
$494$	−1.43013	+	4.40149i	−0.0643446	+	0.198032i
$495$	1.81962	−	43.0769i	0.0817859	−	1.93616i
$496$	−0.999624	−	3.07653i	−0.0448845	−	0.138140i
$497$	−2.38655	−	7.34506i	−0.107052	−	0.329471i
$498$	13.8778	+	10.0828i	0.621881	+	0.451823i
$499$	17.4577			0.781515			0.390757	−	0.920494i	$-0.372213\pi$
$499$	17.4577			0.781515			0.390757	+	0.920494i	$0.372213\pi$
$500$	10.9844	−	2.08417i	0.491236	−	0.0932069i
$501$	16.0634			0.717660
$502$	13.9302	+	10.1209i	0.621736	+	0.451718i
$503$	−10.6243	−	32.6983i	−0.473716	−	1.45795i	−0.847682	−	0.530505i	$-0.822002\pi$
$503$	−10.6243	−	32.6983i	−0.473716	−	1.45795i	0.373966	−	0.927442i	$-0.377998\pi$
$504$	−2.40877	−	7.41344i	−0.107295	−	0.330221i
$505$	−1.78686	+	42.3014i	−0.0795144	+	1.88239i
$506$	−4.06338	+	12.5058i	−0.180639	+	0.555951i
$507$	−2.55557			−0.113497
$508$	−3.59683	+	11.0699i	−0.159584	+	0.491148i
$509$	30.6378	−	22.2597i	1.35800	−	0.986642i	0.359426	−	0.933173i	$-0.382972\pi$
$509$	30.6378	−	22.2597i	1.35800	−	0.986642i	0.998570	−	0.0534683i	$-0.0170276\pi$
$510$	16.9831	−	21.4129i	0.752025	−	0.948179i
$511$	5.68610	+	4.13120i	0.251538	+	0.182753i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−16.8722	+	12.2584i	−0.744925	+	0.541220i
$514$	−14.6496	−	10.6436i	−0.646167	−	0.469468i
$515$	30.9605	−	8.63337i	1.36428	−	0.380432i
$516$	3.37313	−	2.45072i	0.148494	−	0.107887i
$517$	−9.30375	+	28.6340i	−0.409178	+	1.25932i
$518$	9.99655			0.439223
$519$	14.1846	−	43.6556i	0.622633	−	1.91627i
$520$	7.53007	−	2.09977i	0.330215	−	0.0920809i
$521$	−6.33617	−	19.5007i	−0.277593	−	0.854343i	−0.988522	−	0.151079i	$-0.951725\pi$
$521$	−6.33617	−	19.5007i	−0.277593	−	0.854343i	0.710929	−	0.703264i	$-0.248275\pi$
$522$	24.7774	+	76.2569i	1.08448	+	3.33768i
$523$	−3.88188	−	2.82035i	−0.169743	−	0.123325i	0.499670	−	0.866216i	$-0.333454\pi$
$523$	−3.88188	−	2.82035i	−0.169743	−	0.123325i	−0.669413	+	0.742890i	$0.733454\pi$
$524$	−3.51149			−0.153400
$525$	3.74081	+	15.9963i	0.163262	+	0.698134i
$526$	−17.6299			−0.768700
$527$	9.73552	+	7.07327i	0.424086	+	0.308116i
$528$	−2.51146	−	7.72947i	−0.109297	−	0.336382i
$529$	1.62488	+	5.00088i	0.0706471	+	0.217429i
$530$	12.1489	+	4.52267i	0.527714	+	0.196452i
$531$	−6.29840	+	19.3845i	−0.273327	+	0.841214i
$532$	−1.32379			−0.0573936
$533$	2.48154	−	7.63740i	0.107487	−	0.330812i
$534$	−2.58574	+	1.87865i	−0.111896	+	0.0812972i
$535$	−0.185616	+	4.39419i	−0.00802489	+	0.189977i
$536$	−1.26610	−	0.919875i	−0.0546872	−	0.0397325i
$537$	23.5200	−	17.0883i	1.01496	−	0.737415i
$538$	6.52104	−	4.73781i	0.281142	−	0.204262i
$539$	2.00120	+	1.45396i	0.0861978	+	0.0626264i
$540$	33.0139	+	12.2901i	1.42069	+	0.528882i
$541$	11.5228	−	8.37177i	0.495402	−	0.359931i	−0.311856	−	0.950129i	$-0.600951\pi$
$541$	11.5228	−	8.37177i	0.495402	−	0.359931i	0.807258	+	0.590199i	$0.200951\pi$
$542$	−2.97393	+	9.15283i	−0.127741	+	0.393148i
$543$	16.2443			0.697110
$544$	1.14955	−	3.53796i	0.0492867	−	0.151689i
$545$	13.7676	+	20.7367i	0.589739	+	0.888261i
$546$	3.54950	+	10.9242i	0.151905	+	0.467514i
$547$	8.20412	+	25.2497i	0.350783	+	1.07960i	0.958415	+	0.285380i	$0.0921197\pi$
$547$	8.20412	+	25.2497i	0.350783	+	1.07960i	−0.607632	+	0.794219i	$0.707880\pi$
$548$	−1.80528	−	1.31161i	−0.0771177	−	0.0560293i
$549$	49.4516			2.11054
$550$	2.81636	+	12.0432i	0.120090	+	0.513522i
$551$	13.6169			0.580100
$552$	−14.1299	−	10.2660i	−0.601410	−	0.436950i
$553$	−2.30913	−	7.10678i	−0.0981943	−	0.302211i
$554$	2.11782	+	6.51799i	0.0899777	+	0.276923i
$555$	−45.6373	+	57.5412i	−1.93720	+	2.44249i
$556$	−1.38433	+	4.26054i	−0.0587088	+	0.180687i
$557$	0.331500			0.0140461			0.00702305	−	0.999975i	$-0.497764\pi$
$557$	0.331500			0.0140461			0.00702305	+	0.999975i	$0.497764\pi$
$558$	−7.79202	+	23.9814i	−0.329863	+	1.01521i
$559$	−3.58919	+	2.60770i	−0.151807	+	0.110294i
$560$	1.23681	+	1.86287i	0.0522647	+	0.0787208i
$561$	24.4595	+	17.7709i	1.03268	+	0.750287i
$562$	−11.6240	+	8.44537i	−0.490331	+	0.356246i
$563$	18.9957	−	13.8011i	0.800571	−	0.581649i	−0.110510	−	0.993875i	$-0.535249\pi$
$563$	18.9957	−	13.8011i	0.800571	−	0.581649i	0.911082	+	0.412226i	$0.135249\pi$
$564$	−32.3527	−	23.5056i	−1.36229	−	0.989765i
$565$	14.2181	+	21.4152i	0.598160	+	0.900945i
$566$	−11.4398	+	8.31147i	−0.480849	+	0.349357i
$567$	−8.76880	+	26.9876i	−0.368255	+	1.13337i
$568$	7.72305			0.324052
$569$	1.60738	−	4.94702i	0.0673850	−	0.207390i	−0.911694	−	0.410870i	$-0.865225\pi$
$569$	1.60738	−	4.94702i	0.0673850	−	0.207390i	0.979079	+	0.203480i	$0.0652251\pi$
$570$	6.04351	−	7.61987i	0.253135	−	0.319161i
$571$	3.39433	+	10.4467i	0.142048	+	0.437180i	0.996620	−	0.0821543i	$-0.0261800\pi$
$571$	3.39433	+	10.4467i	0.142048	+	0.437180i	−0.854571	+	0.519334i	$0.826180\pi$
$572$	2.67233	+	8.22458i	0.111736	+	0.343887i
$573$	−29.3329	−	21.3116i	−1.22540	−	0.890306i
$574$	2.29702			0.0958758
$575$	20.1089	+	17.3806i	0.838601	+	0.724822i
$576$	7.79495			0.324790
$577$	−19.4588	−	14.1376i	−0.810080	−	0.588558i	0.103774	−	0.994601i	$-0.466908\pi$
$577$	−19.4588	−	14.1376i	−0.810080	−	0.588558i	−0.913854	+	0.406043i	$0.866908\pi$
$578$	−0.976909	−	3.00662i	−0.0406340	−	0.125059i
$579$	−26.9550	−	82.9590i	−1.12021	−	3.44766i
$580$	−12.7222	−	19.1621i	−0.528261	−	0.795663i
$581$	1.61338	−	4.96547i	0.0669342	−	0.206002i
$582$	−38.4246			−1.59275
$583$	−4.43148	+	13.6387i	−0.183533	+	0.564858i
$584$	−5.68610	+	4.13120i	−0.235293	+	0.170950i
$585$	−57.1071	−	21.2593i	−2.36109	−	0.878963i
$586$	−0.148613	−	0.107974i	−0.00613914	−	0.00446035i
$587$	−26.0353	+	18.9158i	−1.07459	+	0.780738i	−0.976732	−	0.214462i	$-0.931200\pi$
$587$	−26.0353	+	18.9158i	−1.07459	+	0.780738i	−0.0978612	+	0.995200i	$0.531200\pi$
$588$	−2.65808	+	1.93121i	−0.109617	+	0.0796417i
$589$	3.46443	+	2.51705i	0.142749	+	0.103713i
$590$	0.246757	−	5.84160i	0.0101588	−	0.240495i
$591$	−33.5420	+	24.3697i	−1.37973	+	1.00243i
$592$	−3.08910	+	9.50728i	−0.126961	+	0.390747i
$593$	18.1206			0.744125			0.372063	−	0.928208i	$-0.378651\pi$
$593$	18.1206			0.744125			0.372063	+	0.928208i	$0.378651\pi$
$594$	−12.0423	+	37.0624i	−0.494102	+	1.52069i
$595$	−7.79559	−	2.90207i	−0.319588	−	0.118973i
$596$	−6.15955	−	18.9572i	−0.252305	−	0.776515i
$597$	−17.6812	−	54.4172i	−0.723644	−	2.22715i
$598$	15.0350	+	10.9236i	0.614828	+	0.446699i
$599$	14.5011			0.592498			0.296249	−	0.955111i	$-0.404264\pi$
$599$	14.5011			0.592498			0.296249	+	0.955111i	$0.404264\pi$
$600$	−16.3693	−	1.38539i	−0.668275	−	0.0565584i
$601$	−2.34186			−0.0955265			−0.0477633	−	0.998859i	$-0.515209\pi$
$601$	−2.34186			−0.0955265			−0.0477633	+	0.998859i	$0.515209\pi$
$602$	−1.02665	−	0.745904i	−0.0418431	−	0.0304008i
$603$	3.76969	+	11.6019i	0.153514	+	0.472467i
$604$	3.36171	+	10.3463i	0.136786	+	0.420985i
$605$	10.5136	−	2.93173i	0.427439	−	0.119192i
$606$	19.2242	−	59.1662i	0.780932	−	2.40346i
$607$	−23.4266			−0.950855			−0.475427	−	0.879755i	$-0.657707\pi$
$607$	−23.4266			−0.950855			−0.475427	+	0.879755i	$0.657707\pi$
$608$	0.409074	−	1.25900i	0.0165901	−	0.0510592i
$609$	27.3418	−	19.8650i	1.10795	−	0.804970i
$610$	−13.6644	+	3.81034i	−0.553256	+	0.154276i
$611$	34.4251	+	25.0113i	1.39269	+	1.01185i
$612$	−23.4595	+	17.0443i	−0.948293	+	0.688975i
$613$	4.48420	−	3.25796i	0.181115	−	0.131588i	−0.493534	−	0.869727i	$-0.664295\pi$
$613$	4.48420	−	3.25796i	0.181115	−	0.131588i	0.674649	+	0.738139i	$0.264295\pi$
$614$	9.77745	+	7.10373i	0.394586	+	0.286683i
$615$	−10.4866	+	13.2219i	−0.422861	+	0.533158i
$616$	−2.00120	+	1.45396i	−0.0806306	+	0.0585816i
$617$	−9.72942	+	29.9441i	−0.391692	+	1.20550i	0.539816	+	0.841783i	$0.318494\pi$
$617$	−9.72942	+	29.9441i	−0.391692	+	1.20550i	−0.931508	+	0.363721i	$0.881506\pi$
$618$	−47.2274			−1.89976
$619$	−2.74283	+	8.44157i	−0.110244	+	0.339295i	−0.990925	−	0.134413i	$-0.957085\pi$
$619$	−2.74283	+	8.44157i	−0.110244	+	0.339295i	0.880682	+	0.473709i	$0.157085\pi$
$620$	0.305274	−	7.22690i	0.0122601	−	0.290239i
$621$	25.8791	+	79.6478i	1.03849	+	3.19615i
$622$	9.57882	+	29.4806i	0.384076	+	1.18206i
$623$	0.787001	+	0.571789i	0.0315305	+	0.0229083i
$624$	−11.4864			−0.459825
$625$	24.6444	+	4.20158i	0.985776	+	0.168063i
$626$	−2.26694			−0.0906052
$627$	8.70402	+	6.32384i	0.347605	+	0.252550i
$628$	4.12632	+	12.6995i	0.164658	+	0.506766i
$629$	−11.4916	−	35.3674i	−0.458199	−	1.41019i
$630$	0.735611	−	17.4145i	0.0293074	−	0.693811i
$631$	1.92857	−	5.93553i	0.0767752	−	0.236290i	−0.905302	−	0.424768i	$-0.860356\pi$
$631$	1.92857	−	5.93553i	0.0767752	−	0.236290i	0.982077	+	0.188478i	$0.0603556\pi$
$632$	7.47251			0.297241
$633$	−22.7417	+	69.9918i	−0.903901	+	2.78192i
$634$	21.9418	−	15.9416i	0.871418	−	0.633123i
$635$	−16.1732	+	20.3918i	−0.641816	+	0.809224i
$636$	−15.4100	−	11.1960i	−0.611045	−	0.443950i
$637$	2.82834	−	2.05491i	0.112063	−	0.0814185i
$638$	20.5850	−	14.9558i	0.814966	−	0.592108i
$639$	−48.7035	−	35.3851i	−1.92668	−	1.39981i
$640$	−2.15389	+	0.600616i	−0.0851401	+	0.0237414i
$641$	6.36054	−	4.62120i	0.251226	−	0.182526i	−0.455044	−	0.890469i	$-0.650376\pi$
$641$	6.36054	−	4.62120i	0.251226	−	0.182526i	0.706270	+	0.707943i	$0.250376\pi$
$642$	1.99698	−	6.14607i	0.0788145	−	0.242566i
$643$	−49.5860			−1.95548			−0.977740	−	0.209819i	$-0.932712\pi$
$643$	−49.5860			−1.95548			−0.977740	+	0.209819i	$0.932712\pi$
$644$	−1.64269	+	5.05567i	−0.0647309	+	0.199221i
$645$	8.98047	−	2.50422i	0.353606	−	0.0986034i
$646$	1.52177	+	4.68352i	0.0598732	+	0.184271i
$647$	4.81469	+	14.8181i	0.189285	+	0.582560i	0.999996	−	0.00288731i	$-0.000919059\pi$
$647$	4.81469	+	14.8181i	0.189285	+	0.582560i	−0.810711	+	0.585447i	$0.800919\pi$
$648$	−22.9570	−	16.6792i	−0.901837	−	0.655223i
$649$	6.46795			0.253889
$650$	17.4178	+	1.47413i	0.683184	+	0.0578203i
$651$	10.6283			0.416557
$652$	−7.39731	−	5.37446i	−0.289701	−	0.210480i
$653$	−6.07013	−	18.6819i	−0.237542	−	0.731080i	−0.996774	−	0.0802598i	$-0.974425\pi$
$653$	−6.07013	−	18.6819i	−0.237542	−	0.731080i	0.759232	−	0.650821i	$-0.225575\pi$
$654$	−11.3018	−	34.7834i	−0.441936	−	1.36014i
$655$	−7.35858	−	2.73938i	−0.287523	−	0.107036i
$656$	−0.709818	+	2.18460i	−0.0277137	+	0.0852941i
$657$	54.7861			2.13741
$658$	−3.76119	+	11.5757i	−0.146626	+	0.451270i
$659$	16.2061	−	11.7744i	0.631299	−	0.458665i	−0.225551	−	0.974231i	$-0.572418\pi$
$659$	16.2061	−	11.7744i	0.631299	−	0.458665i	0.856850	+	0.515566i	$0.172418\pi$
$660$	0.766969	−	18.1569i	0.0298542	−	0.706755i
$661$	−21.0682	−	15.3070i	−0.819460	−	0.595372i	0.0970981	−	0.995275i	$-0.469044\pi$
$661$	−21.0682	−	15.3070i	−0.819460	−	0.595372i	−0.916558	+	0.399903i	$0.869044\pi$
$662$	−4.52541	+	3.28790i	−0.175885	+	0.127788i
$663$	34.5692	−	25.1160i	1.34256	−	0.975424i
$664$	4.22388	+	3.06883i	0.163918	+	0.119094i
$665$	−2.77410	−	1.03271i	−0.107575	−	0.0400469i
$666$	63.0407	−	45.8018i	2.44278	−	1.77478i
$667$	16.8972	−	52.0042i	0.654262	−	2.01361i
$668$	4.88908			0.189164
$669$	−18.1873	+	55.9749i	−0.703163	+	2.16411i
$670$	−1.93559	−	2.91537i	−0.0747783	−	0.112631i
$671$	−4.84933	−	14.9247i	−0.187206	−	0.576162i
$672$	−1.01530	−	3.12476i	−0.0391659	−	0.120540i
$673$	15.5343	+	11.2863i	0.598803	+	0.435056i	0.845454	−	0.534048i	$-0.179330\pi$
$673$	15.5343	+	11.2863i	0.598803	+	0.435056i	−0.246651	+	0.969104i	$0.579330\pi$
$674$	−28.6687			−1.10428
$675$	59.5952	+	51.5095i	2.29382	+	1.98260i
$676$	−0.777818			−0.0299161
$677$	14.4049	+	10.4658i	0.553625	+	0.402232i	0.829120	−	0.559070i	$-0.188842\pi$
$677$	14.4049	+	10.4658i	0.553625	+	0.402232i	−0.275495	+	0.961302i	$0.588842\pi$
$678$	−11.6716	−	35.9216i	−0.448246	−	1.37956i
$679$	3.61395	+	11.1226i	0.138691	+	0.426846i
$680$	5.16900	−	6.51726i	0.198222	−	0.249926i
$681$	5.59241	−	17.2117i	0.214302	−	0.659553i
$682$	8.00179			0.306404
$683$	−7.05675	+	21.7184i	−0.270019	+	0.831033i	0.720476	+	0.693480i	$0.243924\pi$
$683$	−7.05675	+	21.7184i	−0.270019	+	0.831033i	−0.990494	+	0.137552i	$0.956076\pi$
$684$	−8.34815	+	6.06529i	−0.319200	+	0.231912i
$685$	−2.75988	−	4.15691i	−0.105449	−	0.158827i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	25.6218	−	18.6153i	0.977532	−	0.710219i
$688$	1.02665	−	0.745904i	0.0391406	−	0.0284373i
$689$	16.3971	+	11.9132i	0.624678	+	0.453855i
$690$	−21.6016	−	32.5362i	−0.822359	−	1.23863i
$691$	−0.740528	+	0.538025i	−0.0281710	+	0.0204675i	−0.601782	−	0.798661i	$-0.705542\pi$
$691$	−0.740528	+	0.538025i	−0.0281710	+	0.0204675i	0.573611	+	0.819128i	$0.305542\pi$
$692$	4.31723	−	13.2871i	0.164117	−	0.505099i
$693$	19.2817			0.732453
$694$	−5.99973	+	18.4653i	−0.227747	+	0.700932i
$695$	−6.22469	+	7.84832i	−0.236116	+	0.297704i
$696$	10.4436	+	32.1422i	0.395865	+	1.21835i
$697$	−2.64055	−	8.12677i	−0.100018	−	0.307823i
$698$	−13.6320	−	9.90425i	−0.515980	−	0.374882i
$699$	84.4887			3.19566
$700$	1.13856	+	4.86864i	0.0430335	+	0.184017i
$701$	38.5558			1.45623			0.728116	−	0.685454i	$-0.240396\pi$
$701$	38.5558			1.45623			0.728116	+	0.685454i	$0.240396\pi$
$702$	44.5581	+	32.3734i	1.68174	+	1.22185i
$703$	−4.08933	−	12.5856i	−0.154232	−	0.474677i
$704$	−0.764390	−	2.35255i	−0.0288090	−	0.0886651i
$705$	−49.4602	−	74.4966i	−1.86278	−	2.80571i
$706$	−4.29170	+	13.2085i	−0.161520	+	0.497108i
$707$	−18.9346			−0.712110
$708$	−2.65477	+	8.17054i	−0.0997723	+	0.307068i
$709$	−36.6581	+	26.6336i	−1.37672	+	1.00025i	−0.379544	+	0.925174i	$0.623919\pi$
$709$	−36.6581	+	26.6336i	−1.37672	+	1.00025i	−0.997178	+	0.0750738i	$0.976081\pi$
$710$	16.1842	+	6.02490i	0.607382	+	0.226110i
$711$	−47.1235	−	34.2372i	−1.76727	−	1.28400i
$712$	−0.787001	+	0.571789i	−0.0294941	+	0.0214287i
$713$	13.9118	−	10.1075i	0.521003	−	0.378530i
$714$	9.88815	+	7.18416i	0.370055	+	0.268860i
$715$	−0.816097	+	19.3199i	−0.0305203	+	0.722524i
$716$	7.15859	−	5.20102i	0.267529	−	0.194371i
$717$	−4.84021	+	14.8966i	−0.180761	+	0.556325i
$718$	33.1659			1.23774
$719$	−0.761047	+	2.34226i	−0.0283823	+	0.0873517i	−0.964244	−	0.265015i	$-0.914623\pi$
$719$	−0.761047	+	2.34226i	−0.0283823	+	0.0873517i	0.935862	+	0.352367i	$0.114623\pi$
$720$	16.3349	+	6.08099i	0.608765	+	0.226625i
$721$	4.44187	+	13.6707i	0.165424	+	0.509122i
$722$	−5.32980	−	16.4034i	−0.198354	−	0.610472i
$723$	22.3009	+	16.2026i	0.829381	+	0.602581i
$724$	4.94414			0.183747
$725$	−11.7116	−	50.0804i	−0.434956	−	1.85994i
$726$	−16.0375			−0.595209
$727$	17.1131	+	12.4334i	0.634691	+	0.461130i	0.858022	−	0.513613i	$-0.171693\pi$
$727$	17.1131	+	12.4334i	0.634691	+	0.461130i	−0.223331	+	0.974743i	$0.571693\pi$
$728$	1.08033	+	3.32492i	0.0400397	+	0.123230i
$729$	20.3670	+	62.6832i	0.754334	+	2.32160i
$730$	−15.1385	+	4.22138i	−0.560299	+	0.156240i
$731$	−1.45879	+	4.48970i	−0.0539554	+	0.166058i
$732$	20.8438			0.770409
$733$	1.49508	−	4.60139i	0.0552222	−	0.169956i	−0.919641	−	0.392759i	$-0.871521\pi$
$733$	1.49508	−	4.60139i	0.0552222	−	0.169956i	0.974864	+	0.222803i	$0.0715206\pi$
$734$	−9.63278	+	6.99863i	−0.355553	+	0.258324i
$735$	−7.07676	+	1.97336i	−0.261030	+	0.0727886i
$736$	−4.30061	−	3.12458i	−0.158523	−	0.115173i
$737$	3.13185	−	2.27542i	0.115363	−	0.0838162i
$738$	14.4856	−	10.5244i	0.533222	−	0.387408i
$739$	−3.89762	−	2.83179i	−0.143376	−	0.104169i	0.513785	−	0.857919i	$-0.328243\pi$
$739$	−3.89762	−	2.83179i	−0.143376	−	0.104169i	−0.657161	+	0.753750i	$0.728243\pi$
$740$	−13.8902	+	17.5133i	−0.510616	+	0.643802i
$741$	12.3016	−	8.93763i	0.451911	−	0.328332i
$742$	−1.79150	+	5.51366i	−0.0657680	+	0.202413i
$743$	−51.3402			−1.88349			−0.941745	−	0.336328i	$-0.890815\pi$
$743$	−51.3402			−1.88349			−0.941745	+	0.336328i	$0.890815\pi$
$744$	−3.28433	+	10.1081i	−0.120409	+	0.370582i
$745$	1.88106	−	44.5312i	0.0689165	−	1.63150i
$746$	−6.12127	−	18.8393i	−0.224116	−	0.689757i
$747$	−12.5762	−	38.7056i	−0.460139	−	1.41616i
$748$	7.44453	+	5.40877i	0.272199	+	0.197764i
$749$	−1.96689			−0.0718688
$750$	−33.2223	−	15.6732i	−1.21311	−	0.572304i
$751$	31.1079			1.13514			0.567571	−	0.823324i	$-0.307883\pi$
$751$	31.1079			1.13514			0.567571	+	0.823324i	$0.307883\pi$
$752$	−9.84692	−	7.15420i	−0.359080	−	0.260887i
$753$	−17.4821	−	53.8043i	−0.637083	−	1.96074i
$754$	−11.1126	−	34.2011i	−0.404698	−	1.24553i
$755$	−1.02663	+	24.3039i	−0.0373628	+	0.884510i
$756$	−4.86830	+	14.9831i	−0.177058	+	0.544929i
$757$	−18.0392			−0.655647			−0.327824	−	0.944739i	$-0.606315\pi$
$757$	−18.0392			−0.655647			−0.327824	+	0.944739i	$0.606315\pi$
$758$	2.05236	−	6.31653i	0.0745452	−	0.229427i
$759$	34.9521	−	25.3942i	1.26868	−	0.921751i
$760$	1.83941	−	2.31920i	0.0667225	−	0.0841261i
$761$	−31.4898	−	22.8787i	−1.14150	−	0.829351i	−0.154176	−	0.988043i	$-0.549272\pi$
$761$	−31.4898	−	22.8787i	−1.14150	−	0.829351i	−0.987328	+	0.158692i	$0.949272\pi$
$762$	30.9389	−	22.4785i	1.12080	−	0.814309i
$763$	−9.00561	+	6.54296i	−0.326025	+	0.236871i
$764$	−8.92782	−	6.48644i	−0.322997	−	0.234671i
$765$	−62.4575	+	17.4164i	−2.25816	+	0.629690i
$766$	−3.00305	+	2.18185i	−0.108505	+	0.0788333i
$767$	2.82482	−	8.69390i	0.101998	−	0.313919i
$768$	3.28557			0.118558
$769$	−13.6721	+	42.0783i	−0.493028	+	1.51738i	0.326981	+	0.945031i	$0.393969\pi$
$769$	−13.6721	+	42.0783i	−0.493028	+	1.51738i	−0.820008	+	0.572352i	$0.806031\pi$
$770$	−5.32791	+	1.48570i	−0.192005	+	0.0535407i
$771$	18.3849	+	56.5829i	0.662116	+	2.03778i
$772$	−8.20406	−	25.2495i	−0.295271	−	0.908750i
$773$	24.2800	+	17.6405i	0.873291	+	0.634483i	0.931468	−	0.363823i	$-0.118529\pi$
$773$	24.2800	+	17.6405i	0.873291	+	0.634483i	−0.0581771	+	0.998306i	$0.518529\pi$
$774$	−9.89186			−0.355556
$775$	6.27757	−	14.9063i	0.225497	−	0.535451i
$776$	−11.6950			−0.419825
$777$	−26.5716	−	19.3054i	−0.953252	−	0.692578i
$778$	1.54289	+	4.74852i	0.0553152	+	0.170243i
$779$	−0.939650	−	2.89195i	−0.0336665	−	0.103615i
$780$	−24.0706	−	8.96077i	−0.861866	−	0.320847i
$781$	−5.90342	+	18.1689i	−0.211241	+	0.650133i
$782$	19.7751			0.707157
$783$	50.0768	−	154.121i	1.78960	−	5.50782i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−1.26013	+	29.8318i	−0.0449760	+	1.06474i
$786$	9.33383	+	6.78142i	0.332927	+	0.241885i
$787$	−3.88716	+	2.82419i	−0.138562	+	0.100671i	−0.654907	−	0.755709i	$-0.727292\pi$
$787$	−3.88716	+	2.82419i	−0.138562	+	0.100671i	0.516345	+	0.856381i	$0.327292\pi$
$788$	−10.2089	+	7.41719i	−0.363676	+	0.264226i
$789$	46.8617	+	34.0470i	1.66832	+	1.21211i
$790$	15.6592	+	5.82945i	0.557128	+	0.207402i
$791$	−9.30029	+	6.75706i	−0.330680	+	0.240253i
$792$	−5.95839	+	18.3380i	−0.211722	+	0.651614i
$793$	−22.1789			−0.787598
$794$	−4.75468	+	14.6334i	−0.168737	+	0.519320i
$795$	−23.5585	−	35.4836i	−0.835533	−	1.25847i
$796$	−5.38148	−	16.5625i	−0.190742	−	0.587042i
$797$	14.3793	+	44.2549i	0.509341	+	1.56759i	0.793349	+	0.608768i	$0.208336\pi$
$797$	14.3793	+	44.2549i	0.509341	+	1.56759i	−0.284008	+	0.958822i	$0.591664\pi$
$798$	3.51874	+	2.55651i	0.124562	+	0.0904996i
$799$	45.2783			1.60183
$800$	−4.98219	−	0.421660i	−0.176147	−	0.0149079i
$801$	7.58282			0.267926
$802$	−0.219928	−	0.159787i	−0.00776593	−	0.00564228i
$803$	−5.37245	−	16.5347i	−0.189590	−	0.583497i
$804$	1.58892	+	4.89020i	0.0560370	+	0.172464i
$805$	−7.38639	+	9.31302i	−0.260336	+	0.328241i
$806$	3.49471	−	10.7556i	0.123096	−	0.378850i
$807$	−26.4831			−0.932250
$808$	5.85112	−	18.0079i	0.205842	−	0.633516i
$809$	−14.3388	+	10.4177i	−0.504124	+	0.366268i	−0.810590	−	0.585614i	$-0.800853\pi$
$809$	−14.3388	+	10.4177i	−0.504124	+	0.366268i	0.306466	+	0.951882i	$0.400853\pi$
$810$	−35.0962	−	52.8617i	−1.23316	−	1.85737i
$811$	−2.27718	−	1.65447i	−0.0799627	−	0.0580963i	0.547086	−	0.837077i	$-0.315737\pi$
$811$	−2.27718	−	1.65447i	−0.0799627	−	0.0580963i	−0.627048	+	0.778980i	$0.715737\pi$
$812$	8.32180	−	6.04614i	0.292038	−	0.212178i
$813$	25.5810	−	18.5857i	0.897164	−	0.651828i
$814$	−20.0051	−	14.5346i	−0.701178	−	0.509436i
$815$	−11.3089	−	17.0333i	−0.396132	−	0.596652i
$816$	−9.88815	+	7.18416i	−0.346154	+	0.251496i
$817$	−0.519118	+	1.59768i	−0.0181616	+	0.0558958i
$818$	−19.0038			−0.664452
$819$	8.42113	−	25.9176i	0.294258	−	0.905633i
$820$	−3.19172	+	4.02423i	−0.111460	+	0.140532i
$821$	−1.99385	−	6.13645i	−0.0695859	−	0.214163i	0.910216	−	0.414134i	$-0.135915\pi$
$821$	−1.99385	−	6.13645i	−0.0695859	−	0.214163i	−0.979802	+	0.199970i	$0.935915\pi$
$822$	2.26558	+	6.97274i	0.0790212	+	0.243202i
$823$	42.8580	+	31.1381i	1.49394	+	1.08541i	0.972720	+	0.231982i	$0.0745211\pi$
$823$	42.8580	+	31.1381i	1.49394	+	1.08541i	0.521215	+	0.853425i	$0.325479\pi$
$824$	−14.3742			−0.500749
$825$	15.7718	−	37.4507i	0.549102	−	1.30387i
$826$	2.61477			0.0909796
$827$	−23.2668	−	16.9044i	−0.809067	−	0.587822i	0.104493	−	0.994526i	$-0.466678\pi$
$827$	−23.2668	−	16.9044i	−0.809067	−	0.587822i	−0.913560	+	0.406704i	$0.866678\pi$
$828$	12.8047	+	39.4087i	0.444993	+	1.36955i
$829$	4.31884	+	13.2920i	0.149999	+	0.461651i	0.997620	−	0.0689523i	$-0.0219656\pi$
$829$	4.31884	+	13.2920i	0.149999	+	0.461651i	−0.847621	+	0.530603i	$0.821966\pi$
$830$	6.45739	+	9.72607i	0.224139	+	0.337597i
$831$	6.95825	−	21.4153i	0.241379	−	0.742889i
$832$	−3.49602			−0.121203
$833$	1.14955	−	3.53796i	0.0398297	−	0.122583i
$834$	11.9077	−	8.65142i	0.412328	−	0.299574i
$835$	10.2454	+	3.81406i	0.354557	+	0.131991i
$836$	2.64917	+	1.92473i	0.0916234	+	0.0665683i
$837$	41.2294	−	29.9549i	1.42510	−	1.03539i
$838$	−23.7245	+	17.2369i	−0.819549	+	0.595437i
$839$	29.1376	+	21.1697i	1.00594	+	0.730860i	0.963354	−	0.268232i	$-0.0864395\pi$
$839$	29.1376	+	21.1697i	1.00594	+	0.730860i	0.0425888	+	0.999093i	$0.486439\pi$
$840$	0.310060	−	7.34021i	0.0106981	−	0.253261i
$841$	−62.1391	+	45.1467i	−2.14273	+	1.55678i
$842$	−2.11180	+	6.49944i	−0.0727773	+	0.223986i
$843$	47.2074			1.62591
$844$	−6.92170	+	21.3028i	−0.238255	+	0.733272i
$845$	−1.62997	−	0.606791i	−0.0560728	−	0.0208742i
$846$	29.3183	+	90.2324i	1.00798	+	3.10225i
$847$	1.50838	+	4.64230i	0.0518284	+	0.159511i
$848$	−4.69020	−	3.40763i	−0.161062	−	0.117019i
$849$	46.4590			1.59447
$850$	15.9162	−	9.62494i	0.545923	−	0.330133i
$851$	−53.1401			−1.82162
$852$	−20.5285	−	14.9148i	−0.703294	−	0.510973i
$853$	8.50056	+	26.1620i	0.291054	+	0.895771i	0.984518	+	0.175281i	$0.0560833\pi$
$853$	8.50056	+	26.1620i	0.291054	+	0.895771i	−0.693465	+	0.720491i	$0.743917\pi$
$854$	−1.96042	−	6.03355i	−0.0670842	−	0.206464i
$855$	−22.2258	+	6.19769i	−0.760106	+	0.211956i
$856$	0.607804	−	1.87063i	0.0207743	−	0.0639367i
$857$	−35.7941			−1.22270			−0.611352	−	0.791359i	$-0.709374\pi$
$857$	−35.7941			−1.22270			−0.611352	+	0.791359i	$0.709374\pi$
$858$	8.78011	−	27.0224i	0.299748	−	0.922530i
$859$	26.3461	−	19.1415i	0.898916	−	0.653101i	−0.0392715	−	0.999229i	$-0.512504\pi$
$859$	26.3461	−	19.1415i	0.898916	−	0.653101i	0.938187	+	0.346128i	$0.112504\pi$
$860$	2.73331	−	0.762187i	0.0932051	−	0.0259903i
$861$	−6.10566	−	4.43602i	−0.208080	−	0.151179i
$862$	3.66741	−	2.66453i	0.124913	−	0.0907543i
$863$	20.9161	−	15.1964i	0.711993	−	0.517293i	−0.171823	−	0.985128i	$-0.554966\pi$
$863$	20.9161	−	15.1964i	0.711993	−	0.517293i	0.883816	+	0.467835i	$0.154966\pi$
$864$	−12.7454	−	9.26005i	−0.433606	−	0.315033i
$865$	19.4126	−	24.4760i	0.660047	−	0.832210i
$866$	−0.741711	+	0.538884i	−0.0252044	+	0.0183120i
$867$	−3.20970	+	9.87844i	−0.109007	+	0.335489i
$868$	3.23485			0.109798
$869$	−5.71192	+	17.5795i	−0.193764	+	0.596343i
$870$	−3.18937	+	75.5036i	−0.108130	+	2.55981i
$871$	−1.69070	−	5.20344i	−0.0572872	−	0.176312i
$872$	−3.43984	−	10.5867i	−0.116488	−	0.358512i
$873$	73.7515	+	53.5836i	2.49611	+	1.81353i
$874$	7.03707			0.238032
$875$	−1.41219	+	11.0908i	−0.0477408	+	0.374937i
$876$	23.0923			0.780217
$877$	−27.5864	−	20.0427i	−0.931527	−	0.676794i	0.0148392	−	0.999890i	$-0.495276\pi$
$877$	−27.5864	−	20.0427i	−0.931527	−	0.676794i	−0.946366	+	0.323096i	$0.895276\pi$
$878$	1.54638	+	4.75928i	0.0521879	+	0.160618i
$879$	0.186505	+	0.574004i	0.00629067	+	0.0193607i
$880$	0.233436	−	5.52625i	0.00786912	−	0.186290i
$881$	10.2750	−	31.6231i	0.346172	−	1.06541i	−0.614781	−	0.788698i	$-0.710756\pi$
$881$	10.2750	−	31.6231i	0.346172	−	1.06541i	0.960953	−	0.276711i	$-0.0892444\pi$
$882$	7.79495			0.262470
$883$	6.77059	−	20.8377i	0.227848	−	0.701245i	−0.770141	−	0.637873i	$-0.779814\pi$
$883$	6.77059	−	20.8377i	0.227848	−	0.701245i	0.997990	−	0.0633724i	$-0.0201856\pi$
$884$	10.5215	−	7.64434i	0.353877	−	0.257107i
$885$	−11.9372	+	15.0509i	−0.401266	+	0.505931i
$886$	11.9196	+	8.66009i	0.400447	+	0.290941i
$887$	−18.5205	+	13.4560i	−0.621859	+	0.451807i	−0.853570	−	0.520978i	$-0.825568\pi$
$887$	−18.5205	+	13.4560i	−0.621859	+	0.451807i	0.231711	+	0.972785i	$0.425568\pi$
$888$	26.5716	−	19.3054i	0.891685	−	0.647847i
$889$	−9.41662	−	6.84158i	−0.315823	−	0.229459i
$890$	−2.09528	+	0.584271i	−0.0702339	+	0.0195848i
$891$	56.7869	−	41.2581i	1.90243	−	1.38220i
$892$	−5.53553	+	17.0366i	−0.185343	+	0.570427i
$893$	16.1125			0.539183
$894$	−20.2376	+	62.2850i	−0.676848	+	2.08312i
$895$	19.0587	−	5.31456i	0.637064	−	0.177646i
$896$	−0.309017	−	0.951057i	−0.0103235	−	0.0317726i
$897$	−18.8686	−	58.0716i	−0.630004	−	1.93895i
$898$	14.0985	+	10.2431i	0.470472	+	0.341818i
$899$	−33.2747			−1.10977
$900$	29.4870	+	25.4863i	0.982899	+	0.849543i
$901$	21.5666			0.718486
$902$	−4.59680	−	3.33977i	−0.153057	−	0.111202i
$903$	1.28842	+	3.96535i	0.0428759	+	0.131958i
$904$	−3.55239	−	10.9331i	−0.118151	−	0.363631i
$905$	10.3608	+	3.85702i	0.344404	+	0.128212i
$906$	11.0451	−	33.9934i	0.366950	−	1.12936i
$907$	−20.3487			−0.675666			−0.337833	−	0.941206i	$-0.609694\pi$
$907$	−20.3487			−0.675666			−0.337833	+	0.941206i	$0.609694\pi$
$908$	1.70211	−	5.23857i	0.0564867	−	0.173848i
$909$	−119.406	+	86.7539i	−3.96046	+	2.87744i
$910$	−0.329920	+	7.81038i	−0.0109368	+	0.258912i
$911$	−39.2410	−	28.5102i	−1.30011	−	0.944587i	−0.300155	−	0.953890i	$-0.597038\pi$
$911$	−39.2410	−	28.5102i	−1.30011	−	0.944587i	−0.999957	+	0.00930384i	$0.997038\pi$
$912$	−3.51874	+	2.55651i	−0.116517	+	0.0846546i
$913$	−10.4483	+	7.59111i	−0.345787	+	0.251229i
$914$	20.1088	+	14.6099i	0.665141	+	0.483253i
$915$	43.6797	+	16.2606i	1.44400	+	0.537560i
$916$	7.79828	−	5.66578i	0.257662	−	0.187203i
$917$	1.08511	−	3.33963i	0.0358335	−	0.110284i
$918$	58.6059			1.93428
$919$	5.14924	−	15.8477i	0.169858	−	0.522769i	−0.829504	−	0.558502i	$-0.811376\pi$
$919$	5.14924	−	15.8477i	0.169858	−	0.522769i	0.999361	+	0.0357327i	$0.0113765\pi$
$920$	−6.57469	−	9.90276i	−0.216761	−	0.326484i
$921$	−12.2704	−	37.7646i	−0.404325	−	1.24438i
$922$	0.643365	+	1.98007i	0.0211881	+	0.0652103i
$923$	21.8434	+	15.8702i	0.718985	+	0.522373i
$924$	8.12724			0.267367
$925$	−42.7704	+	25.8643i	−1.40628	+	0.850414i
$926$	33.5734			1.10329
$927$	90.6473	+	65.8591i	2.97725	+	2.16310i
$928$	3.17864	+	9.78286i	0.104344	+	0.321138i
$929$	4.23691	+	13.0399i	0.139009	+	0.427825i	0.996192	−	0.0871868i	$-0.0277877\pi$
$929$	4.23691	+	13.0399i	0.139009	+	0.427825i	−0.857183	+	0.515011i	$0.827788\pi$
$930$	−14.7681	+	18.6201i	−0.484265	+	0.610579i
$931$	0.409074	−	1.25900i	0.0134068	−	0.0412620i
$932$	25.7151			0.842326
$933$	31.4719	−	96.8604i	1.03034	−	3.17107i
$934$	8.12793	−	5.90529i	0.265954	−	0.193227i
$935$	11.3811	+	17.1421i	0.372200	+	0.560606i
$936$	22.0468	+	16.0179i	0.720622	+	0.523563i
$937$	−9.51184	+	6.91075i	−0.310738	+	0.225764i	−0.732213	−	0.681076i	$-0.761513\pi$
$937$	−9.51184	+	6.91075i	−0.310738	+	0.225764i	0.421475	+	0.906840i	$0.361513\pi$
$938$	1.26610	−	0.919875i	0.0413396	−	0.0300350i
$939$	6.02571	+	4.37793i	0.196642	+	0.142868i
$940$	−15.0538	−	22.6739i	−0.491000	−	0.739541i
$941$	−32.5177	+	23.6255i	−1.06005	+	0.770170i	−0.974097	−	0.226129i	$-0.927393\pi$
$941$	−32.5177	+	23.6255i	−1.06005	+	0.770170i	−0.0859508	+	0.996299i	$0.527393\pi$
$942$	13.5573	−	41.7251i	0.441721	−	1.35948i
$943$	−12.2106			−0.397632
$944$	−0.808009	+	2.48680i	−0.0262985	+	0.0809384i
$945$	−21.8904	+	27.6002i	−0.712096	+	0.897836i
$946$	0.970018	+	2.98541i	0.0315380	+	0.0970640i
$947$	8.25008	+	25.3911i	0.268092	+	0.825101i	0.990965	+	0.134121i	$0.0428209\pi$
$947$	8.25008	+	25.3911i	0.268092	+	0.825101i	−0.722873	+	0.690980i	$0.757179\pi$
$948$	−19.8625	−	14.4310i	−0.645105	−	0.468696i
$949$	−24.5715			−0.797624
$950$	5.66386	−	3.42508i	0.183760	−	0.111124i
$951$	−89.1095			−2.88957
$952$	3.00957	+	2.18658i	0.0975408	+	0.0708675i
$953$	9.22279	+	28.3848i	0.298755	+	0.919474i	0.981934	+	0.189223i	$0.0605970\pi$
$953$	9.22279	+	28.3848i	0.298755	+	0.919474i	−0.683179	+	0.730251i	$0.739403\pi$
$954$	13.9646	+	42.9788i	0.452122	+	1.39149i
$955$	−13.6487	−	20.5575i	−0.441661	−	0.665227i
$956$	−1.47317	+	4.53396i	−0.0476458	+	0.146639i
$957$	−83.5993			−2.70238
$958$	2.27069	−	6.98848i	0.0733628	−	0.225787i
$959$	1.80528	−	1.31161i	0.0582955	−	0.0423542i
$960$	6.88514	+	2.56313i	0.222217	+	0.0827247i
$961$	16.6138	+	12.0706i	0.535928	+	0.389374i
$962$	−28.2737	+	20.5420i	−0.911580	+	0.662301i
$963$	−12.4037	+	9.01183i	−0.399704	+	0.290402i
$964$	6.78755	+	4.93144i	0.218612	+	0.158831i
$965$	2.50542	−	59.3123i	0.0806525	−	1.90933i
$966$	14.1299	−	10.2660i	0.454624	−	0.330303i
$967$	7.08258	−	21.7979i	0.227760	−	0.700974i	−0.770239	−	0.637755i	$-0.779863\pi$
$967$	7.08258	−	21.7979i	0.227760	−	0.700974i	0.998000	−	0.0632193i	$-0.0201368\pi$
$968$	−4.88121			−0.156888
$969$	4.99987	−	15.3880i	0.160619	−	0.494335i
$970$	−24.5077	−	9.12347i	−0.786893	−	0.292937i
$971$	−12.1581	−	37.4188i	−0.390172	−	1.20083i	−0.932658	−	0.360761i	$-0.882517\pi$
$971$	−12.1581	−	37.4188i	−0.390172	−	1.20083i	0.542486	−	0.840065i	$-0.317483\pi$
$972$	14.2056	+	43.7203i	0.455644	+	1.40233i
$973$	−3.62423	−	2.63316i	−0.116188	−	0.0844152i
$974$	1.44893			0.0464266
$975$	−43.4512	−	37.5559i	−1.39155	−	1.20275i
$976$	6.34405			0.203068
$977$	22.2978	+	16.2003i	0.713371	+	0.518295i	0.884259	−	0.466996i	$-0.154664\pi$
$977$	22.2978	+	16.2003i	0.713371	+	0.518295i	−0.170888	+	0.985290i	$0.554664\pi$
$978$	9.28344	+	28.5715i	0.296852	+	0.913616i
$979$	−0.743588	−	2.28853i	−0.0237652	−	0.0731417i
$980$	−2.15389	+	0.600616i	−0.0688036	+	0.0191860i
$981$	−26.8134	+	82.5230i	−0.856085	+	2.63476i
$982$	−19.1049			−0.609662
$983$	−0.278636	+	0.857555i	−0.00888712	+	0.0273517i	−0.955402	−	0.295309i	$-0.904577\pi$
$983$	−0.278636	+	0.857555i	−0.00888712	+	0.0273517i	0.946515	+	0.322661i	$0.104577\pi$
$984$	6.10566	−	4.43602i	0.194641	−	0.141415i
$985$	−27.1797	+	7.57910i	−0.866018	+	0.241490i
$986$	−30.9574	−	22.4918i	−0.985884	−	0.716286i
$987$	32.3527	−	23.5056i	1.02980	−	0.748192i
$988$	3.74413	−	2.72027i	0.119117	−	0.0865434i
$989$	5.45751	+	3.96511i	0.173539	+	0.126083i
$990$	−26.7921	+	33.7804i	−0.851508	+	1.07361i
$991$	7.06990	−	5.13658i	0.224583	−	0.163169i	−0.469804	−	0.882771i	$-0.655676\pi$
$991$	7.06990	−	5.13658i	0.224583	−	0.163169i	0.694387	+	0.719602i	$0.255676\pi$
$992$	−0.999624	+	3.07653i	−0.0317381	+	0.0976798i
$993$	18.3785			0.583225
$994$	−2.38655	+	7.34506i	−0.0756969	+	0.232971i
$995$	1.64344	−	38.9061i	0.0521006	−	1.23341i
$996$	−5.30086	−	16.3144i	−0.167964	−	0.516941i
$997$	−3.56306	−	10.9660i	−0.112843	−	0.347296i	0.878648	−	0.477470i	$-0.158446\pi$
$997$	−3.56306	−	10.9660i	−0.112843	−	0.347296i	−0.991491	+	0.130175i	$0.958446\pi$
$998$	−14.1236	−	10.2614i	−0.447074	−	0.324819i
$999$	−157.487			−4.98267

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.c.141.4	✓	16
25.6	even	5		8750.2.a.u.1.8		8
25.11	even	5	inner	350.2.h.c.211.4	yes	16
25.19	even	10		8750.2.a.s.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.c.141.4	✓	16	1.1	even	1	trivial
350.2.h.c.211.4	yes	16	25.11	even	5	inner
8750.2.a.s.1.1		8	25.19	even	10
8750.2.a.u.1.8		8	25.6	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.01530 + 3.12476i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.0943702 + 2.23408i) q^{5} +(1.01530 - 3.12476i) q^{6} -1.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.30625 + 4.58176i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.01530 + 3.12476i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.0943702 + 2.23408i) q^{5} +(1.01530 - 3.12476i) q^{6} -1.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(-6.30625 + 4.58176i) q^{9} +(1.38950 - 1.75194i) q^{10} +(2.00120 + 1.45396i) q^{11} +(-2.65808 + 1.93121i) q^{12} +(2.82834 - 2.05491i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-7.07676 + 1.97336i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.14955 - 3.53796i) q^{17} +7.79495 q^{18} +(0.409074 - 1.25900i) q^{19} +(-2.15389 + 0.600616i) q^{20} +(-1.01530 - 3.12476i) q^{21} +(-0.764390 - 2.35255i) q^{22} +(-4.30061 - 3.12458i) q^{23} +3.28557 q^{24} +(-4.98219 - 0.421660i) q^{25} -3.49602 q^{26} +(-12.7454 - 9.26005i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(3.17864 + 9.78286i) q^{29} +(6.88514 + 2.56313i) q^{30} +(-0.999624 + 3.07653i) q^{31} +1.00000 q^{32} +(-2.51146 + 7.72947i) q^{33} +(-3.00957 + 2.18658i) q^{34} +(0.0943702 - 2.23408i) q^{35} +(-6.30625 - 4.58176i) q^{36} +(8.08738 - 5.87582i) q^{37} +(-1.07097 + 0.778104i) q^{38} +(9.29271 + 6.75155i) q^{39} +(2.09557 + 0.780119i) q^{40} +(1.85833 - 1.35015i) q^{41} +(-1.01530 + 3.12476i) q^{42} -1.26901 q^{43} +(-0.764390 + 2.35255i) q^{44} +(-9.64087 - 14.5210i) q^{45} +(1.64269 + 5.05567i) q^{46} +(3.76119 + 11.5757i) q^{47} +(-2.65808 - 1.93121i) q^{48} +1.00000 q^{49} +(3.78283 + 3.26959i) q^{50} +12.2224 q^{51} +(2.82834 + 2.05491i) q^{52} +(1.79150 + 5.51366i) q^{53} +(4.86830 + 14.9831i) q^{54} +(-3.43710 + 4.33362i) q^{55} +(-0.309017 + 0.951057i) q^{56} +4.34940 q^{57} +(3.17864 - 9.78286i) q^{58} +(2.11540 - 1.53693i) q^{59} +(-4.06362 - 6.12060i) q^{60} +(-5.13244 - 3.72894i) q^{61} +(2.61705 - 1.90140i) q^{62} +(6.30625 - 4.58176i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.32392 + 6.51265i) q^{65} +(6.57508 - 4.77707i) q^{66} +(0.483607 - 1.48839i) q^{67} +3.72003 q^{68} +(5.39716 - 16.6107i) q^{69} +(-1.38950 + 1.75194i) q^{70} +(2.38655 + 7.34506i) q^{71} +(2.40877 + 7.41344i) q^{72} +(-5.68610 - 4.13120i) q^{73} -9.99655 q^{74} +(-3.74081 - 15.9963i) q^{75} +1.32379 q^{76} +(-2.00120 - 1.45396i) q^{77} +(-3.54950 - 10.9242i) q^{78} +(2.30913 + 7.10678i) q^{79} +(-1.23681 - 1.86287i) q^{80} +(8.76880 - 26.9876i) q^{81} -2.29702 q^{82} +(-1.61338 + 4.96547i) q^{83} +(2.65808 - 1.93121i) q^{84} +(7.79559 + 2.90207i) q^{85} +(1.02665 + 0.745904i) q^{86} +(-27.3418 + 19.8650i) q^{87} +(2.00120 - 1.45396i) q^{88} +(-0.787001 - 0.571789i) q^{89} +(-0.735611 + 17.4145i) q^{90} +(-2.82834 + 2.05491i) q^{91} +(1.64269 - 5.05567i) q^{92} -10.6283 q^{93} +(3.76119 - 11.5757i) q^{94} +(2.77410 + 1.03271i) q^{95} +(1.01530 + 3.12476i) q^{96} +(-3.61395 - 11.1226i) q^{97} +(-0.809017 - 0.587785i) q^{98} -19.2817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

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