LMFDB - Embedded newform 231.2.j.g.148.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.1
Root			$0.739775 - 2.27679i$ of defining polynomial
Character	$\chi$	$=$	231.148
Dual form			231.2.j.g.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.739775 - 2.27679i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.01849 + 2.19306i) q^{4} +(-1.21700 + 3.74554i) q^{5} +(-0.739775 + 2.27679i) q^{6} +(0.809017 - 0.587785i) q^{7} +(3.35264 + 2.43583i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.739775 - 2.27679i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.01849 + 2.19306i) q^{4} +(-1.21700 + 3.74554i) q^{5} +(-0.739775 + 2.27679i) q^{6} +(0.809017 - 0.587785i) q^{7} +(3.35264 + 2.43583i) q^{8} +(0.309017 + 0.951057i) q^{9} +9.42812 q^{10} +(2.04163 + 2.61376i) q^{11} +3.73106 q^{12} +(-0.926710 - 2.85212i) q^{13} +(-1.93676 - 1.40714i) q^{14} +(3.18614 - 2.31487i) q^{15} +(0.759773 - 2.33834i) q^{16} +(-2.04092 + 6.28132i) q^{17} +(1.93676 - 1.40714i) q^{18} +(4.77571 + 3.46976i) q^{19} +(-4.54069 - 13.9748i) q^{20} -1.00000 q^{21} +(4.44064 - 6.58197i) q^{22} -6.02551 q^{23} +(-1.28059 - 3.94126i) q^{24} +(-8.50288 - 6.17770i) q^{25} +(-5.80813 + 4.21986i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-1.15296 + 3.54845i) q^{28} +(1.23031 - 0.893876i) q^{29} +(-7.62751 - 5.54171i) q^{30} +(2.61707 + 8.05452i) q^{31} +2.40219 q^{32} +(-0.115389 - 3.31462i) q^{33} +15.8111 q^{34} +(1.21700 + 3.74554i) q^{35} +(-3.01849 - 2.19306i) q^{36} +(0.491753 - 0.357279i) q^{37} +(4.36697 - 13.4401i) q^{38} +(-0.926710 + 2.85212i) q^{39} +(-13.2037 + 9.59302i) q^{40} +(1.37802 + 1.00119i) q^{41} +(0.739775 + 2.27679i) q^{42} -3.23364 q^{43} +(-11.8948 - 3.41217i) q^{44} -3.93829 q^{45} +(4.45752 + 13.7188i) q^{46} +(3.88520 + 2.82276i) q^{47} +(-1.98911 + 1.44517i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-7.77514 + 23.9294i) q^{50} +(5.34321 - 3.88207i) q^{51} +(9.05214 + 6.57676i) q^{52} +(-1.89376 - 5.82840i) q^{53} -2.39396 q^{54} +(-12.2746 + 4.46608i) q^{55} +4.14409 q^{56} +(-1.82416 - 5.61418i) q^{57} +(-2.94533 - 2.13990i) q^{58} +(-5.04732 + 3.66709i) q^{59} +(-4.54069 + 13.9748i) q^{60} +(-0.645533 + 1.98674i) q^{61} +(16.4024 - 11.9171i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-3.29663 - 10.1460i) q^{64} +11.8105 q^{65} +(-7.46134 + 2.71479i) q^{66} -0.599719 q^{67} +(-7.61481 - 23.4360i) q^{68} +(4.87474 + 3.54171i) q^{69} +(7.62751 - 5.54171i) q^{70} +(0.435614 - 1.34068i) q^{71} +(-1.28059 + 3.94126i) q^{72} +(-5.73473 + 4.16652i) q^{73} +(-1.17724 - 0.855314i) q^{74} +(3.24781 + 9.99573i) q^{75} -22.0248 q^{76} +(3.18805 + 0.914531i) q^{77} +7.17925 q^{78} +(-0.316207 - 0.973184i) q^{79} +(7.83370 + 5.69152i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.26008 - 3.87812i) q^{82} +(0.954026 - 2.93619i) q^{83} +(3.01849 - 2.19306i) q^{84} +(-21.0431 - 15.2887i) q^{85} +(2.39216 + 7.36232i) q^{86} -1.52075 q^{87} +(0.478184 + 13.7361i) q^{88} -2.48531 q^{89} +(2.91345 + 8.96668i) q^{90} +(-2.42616 - 1.76271i) q^{91} +(18.1879 - 13.2143i) q^{92} +(2.61707 - 8.05452i) q^{93} +(3.55268 - 10.9340i) q^{94} +(-18.8081 + 13.6649i) q^{95} +(-1.94342 - 1.41197i) q^{96} +(0.788908 + 2.42801i) q^{97} -2.39396 q^{98} +(-1.85493 + 2.74941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.739775	−	2.27679i	−0.523100	−	1.60994i	−0.768043	−	0.640399i	$-0.778769\pi$
$2$	−0.739775	−	2.27679i	−0.523100	−	1.60994i	0.244942	−	0.969538i	$-0.421231\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−3.01849	+	2.19306i	−1.50924	+	1.09653i
$5$	−1.21700	+	3.74554i	−0.544258	+	1.67506i	0.178488	+	0.983942i	$0.442879\pi$
$5$	−1.21700	+	3.74554i	−0.544258	+	1.67506i	−0.722747	+	0.691113i	$0.757121\pi$
$6$	−0.739775	+	2.27679i	−0.302012	+	0.929497i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	3.35264	+	2.43583i	1.18534	+	0.861197i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	9.42812			2.98143
$11$	2.04163	+	2.61376i	0.615576	+	0.788077i
$11$	2.04163	+	2.61376i	0.615576	+	0.788077i
$12$	3.73106			1.07706
$13$	−0.926710	−	2.85212i	−0.257023	−	0.791036i	−0.993424	−	0.114491i	$-0.963476\pi$
$13$	−0.926710	−	2.85212i	−0.257023	−	0.791036i	0.736401	−	0.676545i	$-0.236524\pi$
$14$	−1.93676	−	1.40714i	−0.517620	−	0.376073i
$15$	3.18614	−	2.31487i	0.822659	−	0.597697i
$16$	0.759773	−	2.33834i	0.189943	−	0.584585i
$17$	−2.04092	+	6.28132i	−0.494997	+	1.52344i	0.321965	+	0.946752i	$0.395657\pi$
$17$	−2.04092	+	6.28132i	−0.494997	+	1.52344i	−0.816961	+	0.576692i	$0.804343\pi$
$18$	1.93676	−	1.40714i	0.456498	−	0.331665i
$19$	4.77571	+	3.46976i	1.09562	+	0.796017i	0.980340	−	0.197316i	$-0.0632225\pi$
$19$	4.77571	+	3.46976i	1.09562	+	0.796017i	0.115283	+	0.993333i	$0.463222\pi$
$20$	−4.54069	−	13.9748i	−1.01533	−	3.12486i
$21$	−1.00000			−0.218218
$22$	4.44064	−	6.58197i	0.946747	−	1.40328i
$23$	−6.02551			−1.25641			−0.628203	−	0.778049i	$-0.716209\pi$
$23$	−6.02551			−1.25641			−0.628203	+	0.778049i	$0.716209\pi$
$24$	−1.28059	−	3.94126i	−0.261400	−	0.804507i
$25$	−8.50288	−	6.17770i	−1.70058	−	1.23554i
$26$	−5.80813	+	4.21986i	−1.13907	+	0.827582i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−1.15296	+	3.54845i	−0.217889	+	0.670593i
$29$	1.23031	−	0.893876i	0.228464	−	0.165989i	−0.467665	−	0.883906i	$-0.654904\pi$
$29$	1.23031	−	0.893876i	0.228464	−	0.165989i	0.696128	+	0.717917i	$0.254904\pi$
$30$	−7.62751	−	5.54171i	−1.39259	−	1.01177i
$31$	2.61707	+	8.05452i	0.470040	+	1.44663i	0.852532	+	0.522675i	$0.175066\pi$
$31$	2.61707	+	8.05452i	0.470040	+	1.44663i	−0.382492	+	0.923959i	$0.624934\pi$
$32$	2.40219			0.424652
$33$	−0.115389	−	3.31462i	−0.0200867	−	0.577001i
$34$	15.8111			2.71158
$35$	1.21700	+	3.74554i	0.205710	+	0.633111i
$36$	−3.01849	−	2.19306i	−0.503082	−	0.365510i
$37$	0.491753	−	0.357279i	0.0808437	−	0.0587364i	−0.546629	−	0.837375i	$-0.684089\pi$
$37$	0.491753	−	0.357279i	0.0808437	−	0.0587364i	0.627473	+	0.778638i	$0.284089\pi$
$38$	4.36697	−	13.4401i	0.708416	−	2.18028i
$39$	−0.926710	+	2.85212i	−0.148392	+	0.456705i
$40$	−13.2037	+	9.59302i	−2.08768	+	1.51679i
$41$	1.37802	+	1.00119i	0.215211	+	0.156360i	0.690168	−	0.723649i	$-0.257537\pi$
$41$	1.37802	+	1.00119i	0.215211	+	0.156360i	−0.474958	+	0.880009i	$0.657537\pi$
$42$	0.739775	+	2.27679i	0.114150	+	0.351317i
$43$	−3.23364			−0.493125			−0.246562	−	0.969127i	$-0.579301\pi$
$43$	−3.23364			−0.493125			−0.246562	+	0.969127i	$0.579301\pi$
$44$	−11.8948	−	3.41217i	−1.79321	−	0.514404i
$45$	−3.93829			−0.587086
$46$	4.45752	+	13.7188i	0.657226	+	2.02273i
$47$	3.88520	+	2.82276i	0.566715	+	0.411742i	0.833910	−	0.551900i	$-0.186097\pi$
$47$	3.88520	+	2.82276i	0.566715	+	0.411742i	−0.267196	+	0.963642i	$0.586097\pi$
$48$	−1.98911	+	1.44517i	−0.287104	+	0.208593i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−7.77514	+	23.9294i	−1.09957	+	3.38413i
$51$	5.34321	−	3.88207i	0.748199	−	0.543598i
$52$	9.05214	+	6.57676i	1.25531	+	0.912033i
$53$	−1.89376	−	5.82840i	−0.260128	−	0.800593i	−0.992776	−	0.119984i	$-0.961716\pi$
$53$	−1.89376	−	5.82840i	−0.260128	−	0.800593i	0.732647	−	0.680608i	$-0.238284\pi$
$54$	−2.39396			−0.325777
$55$	−12.2746	+	4.46608i	−1.65511	+	0.602206i
$56$	4.14409			0.553777
$57$	−1.82416	−	5.61418i	−0.241616	−	0.743617i
$58$	−2.94533	−	2.13990i	−0.386740	−	0.280983i
$59$	−5.04732	+	3.66709i	−0.657105	+	0.477415i	−0.865684	−	0.500591i	$-0.833116\pi$
$59$	−5.04732	+	3.66709i	−0.657105	+	0.477415i	0.208579	+	0.978006i	$0.433116\pi$
$60$	−4.54069	+	13.9748i	−0.586201	+	1.80414i
$61$	−0.645533	+	1.98674i	−0.0826520	+	0.254377i	−0.983839	−	0.179053i	$-0.942697\pi$
$61$	−0.645533	+	1.98674i	−0.0826520	+	0.254377i	0.901187	+	0.433429i	$0.142697\pi$
$62$	16.4024	−	11.9171i	2.08311	−	1.51347i
$63$	0.809017	+	0.587785i	0.101927	+	0.0740540i
$64$	−3.29663	−	10.1460i	−0.412079	−	1.26825i
$65$	11.8105			1.46492
$66$	−7.46134	+	2.71479i	−0.918427	+	0.334167i
$67$	−0.599719			−0.0732673			−0.0366337	−	0.999329i	$-0.511663\pi$
$67$	−0.599719			−0.0732673			−0.0366337	+	0.999329i	$0.511663\pi$
$68$	−7.61481	−	23.4360i	−0.923431	−	2.84203i
$69$	4.87474	+	3.54171i	0.586850	+	0.426371i
$70$	7.62751	−	5.54171i	0.911662	−	0.662361i
$71$	0.435614	−	1.34068i	0.0516978	−	0.159110i	−0.921874	−	0.387489i	$-0.873343\pi$
$71$	0.435614	−	1.34068i	0.0516978	−	0.159110i	0.973572	+	0.228379i	$0.0733426\pi$
$72$	−1.28059	+	3.94126i	−0.150919	+	0.464482i
$73$	−5.73473	+	4.16652i	−0.671199	+	0.487655i	−0.870426	−	0.492299i	$-0.836157\pi$
$73$	−5.73473	+	4.16652i	−0.671199	+	0.487655i	0.199227	+	0.979953i	$0.436157\pi$
$74$	−1.17724	−	0.855314i	−0.136851	−	0.0994282i
$75$	3.24781	+	9.99573i	0.375025	+	1.15421i
$76$	−22.0248			−2.52642
$77$	3.18805	+	0.914531i	0.363311	+	0.104220i
$78$	7.17925			0.812890
$79$	−0.316207	−	0.973184i	−0.0355760	−	0.109492i	0.931692	−	0.363250i	$-0.118333\pi$
$79$	−0.316207	−	0.973184i	−0.0355760	−	0.109492i	−0.967268	+	0.253759i	$0.918333\pi$
$80$	7.83370	+	5.69152i	0.875834	+	0.636331i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	1.26008	−	3.87812i	0.139152	−	0.428267i
$83$	0.954026	−	2.93619i	0.104718	−	0.322289i	−0.884946	−	0.465693i	$-0.845805\pi$
$83$	0.954026	−	2.93619i	0.104718	−	0.322289i	0.989664	+	0.143405i	$0.0458050\pi$
$84$	3.01849	−	2.19306i	0.329344	−	0.239283i
$85$	−21.0431	−	15.2887i	−2.28245	−	1.65829i
$86$	2.39216	+	7.36232i	0.257954	+	0.793900i
$87$	−1.52075			−0.163042
$88$	0.478184	+	13.7361i	0.0509746	+	1.46427i
$89$	−2.48531			−0.263442			−0.131721	−	0.991287i	$-0.542050\pi$
$89$	−2.48531			−0.263442			−0.131721	+	0.991287i	$0.542050\pi$
$90$	2.91345	+	8.96668i	0.307105	+	0.945171i
$91$	−2.42616	−	1.76271i	−0.254331	−	0.184782i
$92$	18.1879	−	13.2143i	1.89622	−	1.37769i
$93$	2.61707	−	8.05452i	0.271378	−	0.835215i
$94$	3.55268	−	10.9340i	0.366430	−	1.12776i
$95$	−18.8081	+	13.6649i	−1.92967	+	1.40199i
$96$	−1.94342	−	1.41197i	−0.198349	−	0.144109i
$97$	0.788908	+	2.42801i	0.0801015	+	0.246527i	0.983086	−	0.183147i	$-0.0586284\pi$
$97$	0.788908	+	2.42801i	0.0801015	+	0.246527i	−0.902984	+	0.429674i	$0.858628\pi$
$98$	−2.39396			−0.241827
$99$	−1.85493	+	2.74941i	−0.186428	+	0.276326i
$100$	39.2139			3.92139
$101$	−4.68387	−	14.4155i	−0.466063	−	1.43439i	−0.857641	−	0.514249i	$-0.828071\pi$
$101$	−4.68387	−	14.4155i	−0.466063	−	1.43439i	0.391578	−	0.920145i	$-0.371929\pi$
$102$	−12.7914	−	9.29353i	−1.26654	−	0.920197i
$103$	11.1939	−	8.13282i	1.10296	−	0.801351i	0.121423	−	0.992601i	$-0.461254\pi$
$103$	11.1939	−	8.13282i	1.10296	−	0.801351i	0.981541	+	0.191250i	$0.0612542\pi$
$104$	3.84037	−	11.8194i	0.376579	−	1.15899i
$105$	1.21700	−	3.74554i	0.118767	−	0.365527i
$106$	−11.8691	+	8.62341i	−1.15283	+	0.837580i
$107$	−0.360539	−	0.261947i	−0.0348546	−	0.0253234i	0.570222	−	0.821491i	$-0.306857\pi$
$107$	−0.360539	−	0.261947i	−0.0348546	−	0.0253234i	−0.605076	+	0.796168i	$0.706857\pi$
$108$	1.15296	+	3.54845i	0.110944	+	0.341449i
$109$	11.0988			1.06307			0.531536	−	0.847036i	$-0.321615\pi$
$109$	11.0988			1.06307			0.531536	+	0.847036i	$0.321615\pi$
$110$	19.2488	+	24.6428i	1.83530	+	2.34960i
$111$	−0.607840			−0.0576936
$112$	−0.759773	−	2.33834i	−0.0717918	−	0.220952i
$113$	6.54445	+	4.75482i	0.615650	+	0.447296i	0.851399	−	0.524518i	$-0.175755\pi$
$113$	6.54445	+	4.75482i	0.615650	+	0.447296i	−0.235750	+	0.971814i	$0.575755\pi$
$114$	−11.4329	+	8.30647i	−1.07079	+	0.777972i
$115$	7.33304	−	22.5688i	0.683810	−	2.10455i
$116$	−1.75337	+	5.39631i	−0.162796	+	0.501035i
$117$	2.42616	−	1.76271i	0.224298	−	0.162962i
$118$	12.0831	+	8.77889i	1.11234	+	0.808162i
$119$	2.04092	+	6.28132i	0.187091	+	0.575808i
$120$	16.3206			1.48986
$121$	−2.66345	+	10.6727i	−0.242132	+	0.970243i
$122$	5.00096			0.452765
$123$	−0.526357	−	1.61996i	−0.0474600	−	0.146067i
$124$	−25.5637	−	18.5731i	−2.29568	−	1.66791i
$125$	17.5561	−	12.7552i	1.57026	−	1.14086i
$126$	0.739775	−	2.27679i	0.0659044	−	0.202833i
$127$	0.0555178	−	0.170866i	0.00492640	−	0.0151619i	−0.948563	−	0.316588i	$-0.897463\pi$
$127$	0.0555178	−	0.170866i	0.00492640	−	0.0151619i	0.953490	+	0.301426i	$0.0974627\pi$
$128$	−16.7747	+	12.1875i	−1.48269	+	1.07724i
$129$	2.61607	+	1.90068i	0.230332	+	0.167346i
$130$	−8.73714	−	26.8901i	−0.766298	−	2.35842i
$131$	9.38232			0.819737			0.409868	−	0.912145i	$-0.365575\pi$
$131$	9.38232			0.819737			0.409868	+	0.912145i	$0.365575\pi$
$132$	7.61746	+	9.75208i	0.663015	+	0.848810i
$133$	5.90310			0.511864
$134$	0.443657	+	1.36544i	0.0383261	+	0.117956i
$135$	3.18614	+	2.31487i	0.274220	+	0.199232i
$136$	−22.1427	+	16.0876i	−1.89872	+	1.37950i
$137$	0.276143	−	0.849880i	0.0235925	−	0.0726102i	−0.938567	−	0.345097i	$-0.887846\pi$
$137$	0.276143	−	0.849880i	0.0235925	−	0.0726102i	0.962160	+	0.272487i	$0.0878461\pi$
$138$	4.45752	−	13.7188i	0.379450	−	1.16783i
$139$	−1.71739	+	1.24775i	−0.145667	+	0.105833i	−0.658232	−	0.752815i	$-0.728695\pi$
$139$	−1.71739	+	1.24775i	−0.145667	+	0.105833i	0.512565	+	0.858648i	$0.328695\pi$
$140$	−11.8877	−	8.63691i	−1.00469	−	0.729952i
$141$	−1.48401	−	4.56733i	−0.124977	−	0.384638i
$142$	−3.37471			−0.283199
$143$	5.56275	−	8.24518i	0.465180	−	0.689497i
$144$	2.45868			0.204890
$145$	1.85075	+	5.69603i	0.153697	+	0.473030i
$146$	13.7287	+	9.97450i	1.13620	+	0.825496i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	−0.700815	+	2.15689i	−0.0576067	+	0.177295i
$149$	4.42575	−	13.6211i	0.362572	−	1.11588i	−0.588916	−	0.808194i	$-0.700445\pi$
$149$	4.42575	−	13.6211i	0.362572	−	1.11588i	0.951488	−	0.307687i	$-0.0995549\pi$
$150$	20.3556	−	14.7892i	1.66203	−	1.20753i
$151$	11.1512	+	8.10184i	0.907474	+	0.659318i	0.940375	−	0.340140i	$-0.110475\pi$
$151$	11.1512	+	8.10184i	0.907474	+	0.659318i	−0.0329007	+	0.999459i	$0.510475\pi$
$152$	7.55948	+	23.2657i	0.613154	+	1.88710i
$153$	−6.60457			−0.533948
$154$	−0.276238	−	7.93507i	−0.0222599	−	0.639426i
$155$	−33.3535			−2.67902
$156$	−3.45761	−	10.6414i	−0.276830	−	0.851996i
$157$	9.27195	+	6.73647i	0.739982	+	0.537628i	0.892706	−	0.450641i	$-0.148804\pi$
$157$	9.27195	+	6.73647i	0.739982	+	0.537628i	−0.152723	+	0.988269i	$0.548804\pi$
$158$	−1.98182	+	1.43987i	−0.157665	+	0.114550i
$159$	−1.89376	+	5.82840i	−0.150185	+	0.462222i
$160$	−2.92347	+	8.99751i	−0.231120	+	0.711316i
$161$	−4.87474	+	3.54171i	−0.384183	+	0.279126i
$162$	1.93676	+	1.40714i	0.152166	+	0.110555i
$163$	1.52735	+	4.70071i	0.119632	+	0.368188i	0.992885	−	0.119079i	$-0.0379940\pi$
$163$	1.52735	+	4.70071i	0.119632	+	0.368188i	−0.873253	+	0.487266i	$0.837994\pi$
$164$	−6.35521			−0.496258
$165$	12.5555	+	3.60169i	0.977440	+	0.280391i
$166$	−7.39086			−0.573642
$167$	2.63722	+	8.11651i	0.204074	+	0.628075i	0.999750	+	0.0223527i	$0.00711566\pi$
$167$	2.63722	+	8.11651i	0.204074	+	0.628075i	−0.795676	+	0.605722i	$0.792884\pi$
$168$	−3.35264	−	2.43583i	−0.258662	−	0.187929i
$169$	3.24142	−	2.35503i	0.249340	−	0.181156i
$170$	−19.2421	+	59.2211i	−1.47580	+	4.54205i
$171$	−1.82416	+	5.61418i	−0.139497	+	0.429327i
$172$	9.76069	−	7.09156i	0.744246	−	0.540726i
$173$	−10.5881	−	7.69269i	−0.804997	−	0.584864i	0.107379	−	0.994218i	$-0.465754\pi$
$173$	−10.5881	−	7.69269i	−0.804997	−	0.584864i	−0.912376	+	0.409354i	$0.865754\pi$
$174$	1.12501	+	3.46244i	0.0852871	+	0.262487i
$175$	−10.5101			−0.794492
$176$	7.66303	−	2.78818i	0.577623	−	0.210167i
$177$	6.23883			0.468939
$178$	1.83857	+	5.65853i	0.137807	+	0.424125i
$179$	−20.9229	−	15.2014i	−1.56385	−	1.13621i	−0.932759	−	0.360499i	$-0.882606\pi$
$179$	−20.9229	−	15.2014i	−1.56385	−	1.13621i	−0.631094	−	0.775707i	$-0.717394\pi$
$180$	11.8877	−	8.63691i	0.886056	−	0.643757i
$181$	6.61922	−	20.3719i	0.492003	−	1.51423i	−0.329574	−	0.944130i	$-0.606905\pi$
$181$	6.61922	−	20.3719i	0.492003	−	1.51423i	0.821576	−	0.570099i	$-0.193095\pi$
$182$	−2.21851	+	6.82787i	−0.164447	+	0.506115i
$183$	1.69003	−	1.22788i	0.124930	−	0.0907672i
$184$	−20.2014	−	14.6771i	−1.48926	−	1.08201i
$185$	0.739741	+	2.27669i	0.0543868	+	0.167385i
$186$	−20.2745			−1.48660
$187$	−20.5847	+	7.48968i	−1.50530	+	0.547700i
$188$	−17.9179			−1.30680
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	45.0260	+	32.7133i	3.26653	+	2.37327i
$191$	3.02562	−	2.19825i	0.218927	−	0.159059i	−0.472917	−	0.881107i	$-0.656799\pi$
$191$	3.02562	−	2.19825i	0.218927	−	0.159059i	0.691843	+	0.722048i	$0.256799\pi$
$192$	−3.29663	+	10.1460i	−0.237914	+	0.732223i
$193$	1.87861	−	5.78178i	0.135225	−	0.416181i	−0.860400	−	0.509620i	$-0.829786\pi$
$193$	1.87861	−	5.78178i	0.135225	−	0.416181i	0.995625	+	0.0934388i	$0.0297860\pi$
$194$	4.94446	−	3.59236i	0.354992	−	0.257917i
$195$	−9.55492	−	6.94205i	−0.684242	−	0.497131i
$196$	1.15296	+	3.54845i	0.0823543	+	0.253460i
$197$	21.5458			1.53508			0.767538	−	0.641003i	$-0.221482\pi$
$197$	21.5458			1.53508			0.767538	+	0.641003i	$0.221482\pi$
$198$	7.63206	+	2.18935i	0.542387	+	0.155591i
$199$	−14.8965			−1.05598			−0.527992	−	0.849249i	$-0.677055\pi$
$199$	−14.8965			−1.05598			−0.527992	+	0.849249i	$0.677055\pi$
$200$	−13.4592	−	41.4232i	−0.951710	−	2.92906i
$201$	0.485183	+	0.352506i	0.0342221	+	0.0248638i
$202$	−29.3561	+	21.3284i	−2.06549	+	1.50066i
$203$	0.469938	−	1.44632i	0.0329832	−	0.101512i
$204$	−7.61481	+	23.4360i	−0.533143	+	1.64085i
$205$	−5.42704	+	3.94298i	−0.379041	+	0.275389i
$206$	−26.7977	−	19.4697i	−1.86708	−	1.35652i
$207$	−1.86199	−	5.73060i	−0.129417	−	0.398304i
$208$	−7.37332			−0.511248
$209$	0.681155	+	19.5665i	0.0471165	+	1.35344i
$210$	−9.42812			−0.650602
$211$	5.24074	+	16.1293i	0.360787	+	1.11039i	0.952577	+	0.304296i	$0.0984214\pi$
$211$	5.24074	+	16.1293i	0.360787	+	1.11039i	−0.591790	+	0.806092i	$0.701579\pi$
$212$	18.4983	+	13.4398i	1.27047	+	0.923051i
$213$	−1.14045	+	0.828587i	−0.0781425	+	0.0567738i
$214$	−0.329681	+	1.01465i	−0.0225365	+	0.0693604i
$215$	3.93533	−	12.1117i	0.268387	−	0.826011i
$216$	3.35264	−	2.43583i	0.228118	−	0.165738i
$217$	6.85158	+	4.97797i	0.465116	+	0.337926i
$218$	−8.21061	−	25.2697i	−0.556093	−	1.71148i
$219$	7.08851			0.478997
$220$	27.2563	−	40.3997i	1.83762	−	2.72375i
$221$	19.8064			1.33232
$222$	0.449665	+	1.38393i	0.0301795	+	0.0928831i
$223$	11.1746	+	8.11879i	0.748304	+	0.543675i	0.895301	−	0.445462i	$-0.146961\pi$
$223$	11.1746	+	8.11879i	0.748304	+	0.543675i	−0.146997	+	0.989137i	$0.546961\pi$
$224$	1.94342	−	1.41197i	0.129850	−	0.0943415i
$225$	3.24781	−	9.99573i	0.216521	−	0.666382i
$226$	5.98432	−	18.4179i	0.398071	−	1.22514i
$227$	5.86816	−	4.26347i	0.389484	−	0.282976i	−0.375760	−	0.926717i	$-0.622618\pi$
$227$	5.86816	−	4.26347i	0.389484	−	0.282976i	0.765244	+	0.643740i	$0.222618\pi$
$228$	17.8185	+	12.9459i	1.18006	+	0.857361i
$229$	−0.101091	−	0.311125i	−0.00668026	−	0.0205597i	0.947661	−	0.319279i	$-0.103441\pi$
$229$	−0.101091	−	0.311125i	−0.00668026	−	0.0205597i	−0.954341	+	0.298719i	$0.903441\pi$
$230$	−56.8093			−3.74589
$231$	−2.04163	−	2.61376i	−0.134330	−	0.171973i
$232$	6.30213			0.413755
$233$	5.02003	+	15.4501i	0.328873	+	1.01217i	0.969662	+	0.244450i	$0.0786074\pi$
$233$	5.02003	+	15.4501i	0.328873	+	1.01217i	−0.640789	+	0.767717i	$0.721393\pi$
$234$	−5.80813	−	4.21986i	−0.379690	−	0.275861i
$235$	−15.3010	+	11.1169i	−0.998130	+	0.725184i
$236$	7.19313	−	22.1382i	0.468233	−	1.44107i
$237$	−0.316207	+	0.973184i	−0.0205398	+	0.0632151i
$238$	12.7914	−	9.29353i	0.829146	−	0.602410i
$239$	23.4622	+	17.0463i	1.51764	+	1.10263i	0.962640	+	0.270785i	$0.0872833\pi$
$239$	23.4622	+	17.0463i	1.51764	+	1.10263i	0.555004	+	0.831848i	$0.312717\pi$
$240$	−2.99221	−	9.20907i	−0.193146	−	0.594443i
$241$	−29.3358			−1.88968			−0.944841	−	0.327530i	$-0.893784\pi$
$241$	−29.3358			−1.88968			−0.944841	+	0.327530i	$0.893784\pi$
$242$	26.2698	−	1.83125i	1.68869	−	0.117717i
$243$	1.00000			0.0641500
$244$	−2.40852	−	7.41266i	−0.154190	−	0.474547i
$245$	3.18614	+	2.31487i	0.203555	+	0.147892i
$246$	−3.29893	+	2.39681i	−0.210332	+	0.152815i
$247$	5.47046	−	16.8364i	0.348077	−	1.07127i
$248$	−10.8454	+	33.3786i	−0.688682	+	2.11955i
$249$	−2.49767	+	1.81467i	−0.158284	+	0.115000i
$250$	−42.0286	−	30.5356i	−2.65812	−	1.93124i
$251$	3.96519	+	12.2036i	0.250281	+	0.770285i	0.994723	+	0.102598i	$0.0327155\pi$
$251$	3.96519	+	12.2036i	0.250281	+	0.770285i	−0.744442	+	0.667687i	$0.767285\pi$
$252$	−3.73106			−0.235035
$253$	−12.3019	−	15.7492i	−0.773413	−	0.990145i
$254$	−0.430097			−0.0269867
$255$	8.03776	+	24.7377i	0.503344	+	1.54913i
$256$	22.8967	+	16.6354i	1.43104	+	1.03971i
$257$	−15.7928	+	11.4742i	−0.985131	+	0.715739i	−0.958849	−	0.283915i	$-0.908367\pi$
$257$	−15.7928	+	11.4742i	−0.985131	+	0.715739i	−0.0262812	+	0.999655i	$0.508367\pi$
$258$	2.39216	−	7.36232i	0.148930	−	0.458358i
$259$	0.187833	−	0.578090i	0.0116714	−	0.0359208i
$260$	−35.6500	+	25.9012i	−2.21092	+	1.60632i
$261$	1.23031	+	0.893876i	0.0761545	+	0.0553295i
$262$	−6.94081	−	21.3616i	−0.428804	−	1.31972i
$263$	23.9606			1.47747			0.738736	−	0.673995i	$-0.235423\pi$
$263$	23.9606			1.47747			0.738736	+	0.673995i	$0.235423\pi$
$264$	7.68700	−	11.3938i	0.473102	−	0.701239i
$265$	24.1352			1.48261
$266$	−4.36697	−	13.4401i	−0.267756	−	0.824068i
$267$	2.01066	+	1.46083i	0.123050	+	0.0894011i
$268$	1.81024	−	1.31522i	0.110578	−	0.0803398i
$269$	3.49993	−	10.7717i	0.213394	−	0.656760i	−0.785869	−	0.618393i	$-0.787784\pi$
$269$	3.49993	−	10.7717i	0.213394	−	0.656760i	0.999264	−	0.0383676i	$-0.0122158\pi$
$270$	2.91345	−	8.96668i	0.177307	−	0.545695i
$271$	−4.95343	+	3.59888i	−0.300900	+	0.218616i	−0.727982	−	0.685596i	$-0.759541\pi$
$271$	−4.95343	+	3.59888i	−0.300900	+	0.218616i	0.427082	+	0.904213i	$0.359541\pi$
$272$	13.1372	+	9.54476i	0.796561	+	0.578736i
$273$	0.926710	+	2.85212i	0.0560870	+	0.172618i
$274$	−2.13929			−0.129239
$275$	−1.21276	−	34.8371i	−0.0731321	−	2.10075i
$276$	−22.4815			−1.35323
$277$	0.185461	+	0.570791i	0.0111433	+	0.0342955i	0.956474	−	0.291819i	$-0.0942605\pi$
$277$	0.185461	+	0.570791i	0.0111433	+	0.0342955i	−0.945330	+	0.326115i	$0.894260\pi$
$278$	4.11136	+	2.98708i	0.246583	+	0.179153i
$279$	−6.85158	+	4.97797i	−0.410194	+	0.298023i
$280$	−5.04335	+	15.5218i	−0.301398	+	0.927607i
$281$	7.35528	−	22.6372i	0.438779	−	1.35042i	−0.450385	−	0.892835i	$-0.648713\pi$
$281$	7.35528	−	22.6372i	0.438779	−	1.35042i	0.889164	−	0.457589i	$-0.151287\pi$
$282$	−9.30102	+	6.75759i	−0.553868	+	0.402409i
$283$	14.0284	+	10.1922i	0.833901	+	0.605864i	0.920660	−	0.390365i	$-0.127651\pi$
$283$	14.0284	+	10.1922i	0.833901	+	0.605864i	−0.0867595	+	0.996229i	$0.527651\pi$
$284$	1.62530	+	5.00216i	0.0964438	+	0.296824i
$285$	23.2481			1.37710
$286$	−22.8878	−	6.56565i	−1.35338	−	0.388235i
$287$	1.70333			0.100544
$288$	0.742319	+	2.28462i	0.0437416	+	0.134623i
$289$	−21.5363	−	15.6471i	−1.26684	−	0.920415i
$290$	11.5996	−	8.42757i	0.681149	−	0.494884i
$291$	0.788908	−	2.42801i	0.0462466	−	0.142332i
$292$	8.17278	−	25.1532i	0.478276	−	1.47198i
$293$	12.0642	−	8.76516i	0.704799	−	0.512066i	−0.176693	−	0.984266i	$-0.556540\pi$
$293$	12.0642	−	8.76516i	0.704799	−	0.512066i	0.881491	+	0.472200i	$0.156540\pi$
$294$	1.93676	+	1.40714i	0.112954	+	0.0820658i
$295$	−7.59265	−	23.3678i	−0.442061	−	1.36052i
$296$	2.51894			0.146411
$297$	3.11673	−	1.13401i	0.180851	−	0.0658022i
$298$	−34.2864			−1.98616
$299$	5.58390	+	17.1855i	0.322925	+	0.993862i
$300$	−31.7247	−	23.0494i	−1.83163	−	1.33076i
$301$	−2.61607	+	1.90068i	−0.150788	+	0.109554i
$302$	10.1968	−	31.3826i	0.586761	−	1.80587i
$303$	−4.68387	+	14.4155i	−0.269082	+	0.828148i
$304$	11.7419	−	8.53101i	0.673446	−	0.489287i
$305$	−6.65581	−	4.83573i	−0.381111	−	0.276893i
$306$	4.88590	+	15.0372i	0.279308	+	0.859622i
$307$	29.0453			1.65771			0.828853	−	0.559467i	$-0.188994\pi$
$307$	29.0453			1.65771			0.828853	+	0.559467i	$0.188994\pi$
$308$	−11.6287	+	4.23107i	−0.662607	+	0.241088i
$309$	−13.8364			−0.787124
$310$	24.6741	+	75.9390i	1.40139	+	4.31304i
$311$	16.4757	+	11.9703i	0.934251	+	0.678773i	0.947030	−	0.321145i	$-0.104068\pi$
$311$	16.4757	+	11.9703i	0.934251	+	0.678773i	−0.0127790	+	0.999918i	$0.504068\pi$
$312$	−10.0542	+	7.30481i	−0.569208	+	0.413554i
$313$	−9.11004	+	28.0378i	−0.514930	+	1.58479i	0.268479	+	0.963286i	$0.413479\pi$
$313$	−9.11004	+	28.0378i	−0.514930	+	1.58479i	−0.783409	+	0.621506i	$0.786521\pi$
$314$	8.47839	−	26.0938i	0.478463	−	1.47256i
$315$	−3.18614	+	2.31487i	−0.179519	+	0.130428i
$316$	3.08872	+	2.24408i	0.173754	+	0.126240i
$317$	2.35635	+	7.25210i	0.132346	+	0.407318i	0.995168	−	0.0981896i	$-0.0313052\pi$
$317$	2.35635	+	7.25210i	0.132346	+	0.407318i	−0.862822	+	0.505508i	$0.831305\pi$
$318$	14.6710			0.822710
$319$	4.84823	+	1.39077i	0.271449	+	0.0778684i
$320$	42.0142			2.34866
$321$	0.137714	+	0.423839i	0.00768642	+	0.0236564i
$322$	11.6699	+	8.47871i	0.650341	+	0.472500i
$323$	−31.5415	+	22.9163i	−1.75502	+	1.27509i
$324$	1.15296	−	3.54845i	0.0640533	−	0.197136i
$325$	−9.73985	+	29.9762i	−0.540270	+	1.66278i
$326$	9.57265	−	6.95494i	0.530180	−	0.385198i
$327$	−8.97911	−	6.52370i	−0.496546	−	0.360762i
$328$	2.18127	+	6.71325i	0.120440	+	0.370677i
$329$	4.80237			0.264763
$330$	−1.08791	−	31.2506i	−0.0598872	−	1.72029i
$331$	20.6731			1.13630			0.568148	−	0.822926i	$-0.307660\pi$
$331$	20.6731			1.13630			0.568148	+	0.822926i	$0.307660\pi$
$332$	3.55953	+	10.9551i	0.195354	+	0.601239i
$333$	0.491753	+	0.357279i	0.0269479	+	0.0195788i
$334$	16.5287	−	12.0088i	0.904409	−	0.657092i
$335$	0.729857	−	2.24627i	0.0398764	−	0.122727i
$336$	−0.759773	+	2.33834i	−0.0414490	+	0.127567i
$337$	4.41929	−	3.21080i	0.240734	−	0.174904i	−0.460876	−	0.887464i	$-0.652465\pi$
$337$	4.41929	−	3.21080i	0.240734	−	0.174904i	0.701610	+	0.712561i	$0.252465\pi$
$338$	−7.75984	−	5.63785i	−0.422080	−	0.306659i
$339$	−2.49976	−	7.69346i	−0.135768	−	0.417851i
$340$	97.0475			5.26314
$341$	−15.7095	+	23.2848i	−0.850714	+	1.26094i
$342$	14.1318			0.764161
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−10.8412	−	7.87660i	−0.584519	−	0.424678i
$345$	−19.1981	+	13.9483i	−1.03359	+	0.750950i
$346$	−9.68187	+	29.7977i	−0.520501	+	1.60194i
$347$	2.96072	−	9.11217i	0.158940	−	0.489167i	−0.839599	−	0.543207i	$-0.817210\pi$
$347$	2.96072	−	9.11217i	0.158940	−	0.489167i	0.998539	+	0.0540400i	$0.0172099\pi$
$348$	4.59037	−	3.33510i	0.246070	−	0.178780i
$349$	−7.57277	−	5.50194i	−0.405361	−	0.294512i	0.366360	−	0.930473i	$-0.380604\pi$
$349$	−7.57277	−	5.50194i	−0.405361	−	0.294512i	−0.771721	+	0.635961i	$0.780604\pi$
$350$	7.77514	+	23.9294i	0.415599	+	1.27908i
$351$	−2.99890			−0.160069
$352$	4.90440	+	6.27875i	0.261406	+	0.334659i
$353$	−27.6629			−1.47235			−0.736173	−	0.676794i	$-0.763369\pi$
$353$	−27.6629			−1.47235			−0.736173	+	0.676794i	$0.763369\pi$
$354$	−4.61533	−	14.2045i	−0.245302	−	0.754963i
$355$	4.49143	+	3.26322i	0.238380	+	0.173193i
$356$	7.50187	−	5.45043i	0.397598	−	0.288872i
$357$	2.04092	−	6.28132i	0.108017	−	0.332443i
$358$	−19.1322	+	58.8828i	−1.01117	+	3.11205i
$359$	2.10554	−	1.52976i	0.111126	−	0.0807377i	−0.530834	−	0.847476i	$-0.678121\pi$
$359$	2.10554	−	1.52976i	0.111126	−	0.0807377i	0.641960	+	0.766738i	$0.278121\pi$
$360$	−13.2037	−	9.59302i	−0.695894	−	0.505597i
$361$	4.89687	+	15.0710i	0.257730	+	0.793212i
$362$	−51.2793			−2.69518
$363$	8.42802	−	7.06884i	0.442356	−	0.371018i
$364$	11.1891			0.586466
$365$	−8.62671	−	26.5503i	−0.451543	−	1.38971i
$366$	−4.04586	−	2.93949i	−0.211480	−	0.153650i
$367$	8.36472	−	6.07732i	0.436635	−	0.317234i	−0.347662	−	0.937620i	$-0.613024\pi$
$367$	8.36472	−	6.07732i	0.436635	−	0.317234i	0.784296	+	0.620386i	$0.213024\pi$
$368$	−4.57802	+	14.0897i	−0.238646	+	0.734476i
$369$	−0.526357	+	1.61996i	−0.0274010	+	0.0843317i
$370$	4.63631	−	3.36847i	0.241030	−	0.175119i
$371$	−4.95793	−	3.60215i	−0.257403	−	0.187014i
$372$	9.76445	+	30.0519i	0.506263	+	1.55812i
$373$	−5.15587			−0.266961			−0.133480	−	0.991051i	$-0.542615\pi$
$373$	−5.15587			−0.266961			−0.133480	+	0.991051i	$0.542615\pi$
$374$	32.2805	+	41.3264i	1.66918	+	2.13694i
$375$	−21.7005			−1.12061
$376$	6.14989	+	18.9274i	0.317156	+	0.976106i
$377$	−3.68959	−	2.68064i	−0.190023	−	0.138060i
$378$	−1.93676	+	1.40714i	−0.0996160	+	0.0723753i
$379$	−10.9461	+	33.6886i	−0.562263	+	1.73047i	0.113683	+	0.993517i	$0.463735\pi$
$379$	−10.9461	+	33.6886i	−0.562263	+	1.73047i	−0.675946	+	0.736951i	$0.736265\pi$
$380$	26.8042	−	82.4948i	1.37503	−	4.23189i
$381$	−0.145347	+	0.105601i	−0.00744637	+	0.00541011i
$382$	−7.24323	−	5.26252i	−0.370596	−	0.269254i
$383$	−9.70549	−	29.8704i	−0.495927	−	1.52631i	−0.815506	−	0.578748i	$-0.803541\pi$
$383$	−9.70549	−	29.8704i	−0.495927	−	1.52631i	0.319579	−	0.947560i	$-0.396459\pi$
$384$	20.7347			1.05811
$385$	−7.30526	+	10.8280i	−0.372310	+	0.551844i
$386$	−14.5537			−0.740762
$387$	−0.999248	−	3.07537i	−0.0507946	−	0.156330i
$388$	−7.70608	−	5.59880i	−0.391217	−	0.284236i
$389$	−16.2441	+	11.8021i	−0.823611	+	0.598388i	−0.917745	−	0.397171i	$-0.869992\pi$
$389$	−16.2441	+	11.8021i	−0.823611	+	0.598388i	0.0941336	+	0.995560i	$0.469992\pi$
$390$	−8.73714	+	26.8901i	−0.442422	+	1.36164i
$391$	12.2976	−	37.8482i	0.621917	−	1.91406i
$392$	3.35264	−	2.43583i	0.169334	−	0.123028i
$393$	−7.59045	−	5.51479i	−0.382888	−	0.278184i
$394$	−15.9391	−	49.0554i	−0.802998	−	2.47137i
$395$	4.02992			0.202767
$396$	−0.430524	−	12.3670i	−0.0216347	−	0.621467i
$397$	3.63351			0.182361			0.0911804	−	0.995834i	$-0.470936\pi$
$397$	3.63351			0.182361			0.0911804	+	0.995834i	$0.470936\pi$
$398$	11.0201	+	33.9162i	0.552385	+	1.70007i
$399$	−4.77571	−	3.46976i	−0.239085	−	0.173705i
$400$	−20.9058	+	15.1890i	−1.04529	+	0.759449i
$401$	11.6286	−	35.7891i	0.580704	−	1.78722i	−0.0351753	−	0.999381i	$-0.511199\pi$
$401$	11.6286	−	35.7891i	0.580704	−	1.78722i	0.615879	−	0.787841i	$-0.288801\pi$
$402$	0.443657	−	1.36544i	0.0221276	−	0.0681018i
$403$	20.5472	−	14.9284i	1.02353	−	0.743637i
$404$	45.7523	+	33.2410i	2.27626	+	1.65380i
$405$	−1.21700	−	3.74554i	−0.0604732	−	0.186117i
$406$	−3.64062			−0.180681
$407$	1.93782	+	0.555889i	0.0960542	+	0.0275544i
$408$	27.3699			1.35501
$409$	4.97700	+	15.3176i	0.246097	+	0.757409i	0.995454	+	0.0952425i	$0.0303627\pi$
$409$	4.97700	+	15.3176i	0.246097	+	0.757409i	−0.749357	+	0.662166i	$0.769637\pi$
$410$	12.9921	+	9.43934i	0.641636	+	0.466176i
$411$	−0.722951	+	0.525255i	−0.0356606	+	0.0259089i
$412$	−15.9528	+	49.0977i	−0.785938	+	2.41887i
$413$	−1.92791	+	5.93348i	−0.0948660	+	0.291968i
$414$	−11.6699	+	8.47871i	−0.573547	+	0.416706i
$415$	9.83656	+	7.14668i	0.482858	+	0.350817i
$416$	−2.22614	−	6.85135i	−0.109145	−	0.335915i
$417$	2.12281			0.103954
$418$	44.0450	−	16.0257i	2.15431	−	0.783842i
$419$	−17.7128			−0.865325			−0.432662	−	0.901556i	$-0.642426\pi$
$419$	−17.7128			−0.865325			−0.432662	+	0.901556i	$0.642426\pi$
$420$	4.54069	+	13.9748i	0.221563	+	0.681901i
$421$	−24.4906	−	17.7935i	−1.19360	−	0.867202i	−0.199961	−	0.979804i	$-0.564081\pi$
$421$	−24.4906	−	17.7935i	−1.19360	−	0.867202i	−0.993640	+	0.112602i	$0.964081\pi$
$422$	32.8462	−	23.8641i	1.59893	−	1.16169i
$423$	−1.48401	+	4.56733i	−0.0721553	+	0.222071i
$424$	7.84792	−	24.1534i	0.381129	−	1.17299i
$425$	56.1579	−	40.8011i	2.72406	−	1.97914i
$426$	2.73020	+	1.98361i	0.132279	+	0.0961060i
$427$	0.645533	+	1.98674i	0.0312395	+	0.0961453i
$428$	1.66275			0.0803720
$429$	−9.34675	+	3.40079i	−0.451266	+	0.164192i
$430$	−30.4871			−1.47022
$431$	5.93060	+	18.2525i	0.285667	+	0.879193i	0.986198	+	0.165571i	$0.0529466\pi$
$431$	5.93060	+	18.2525i	0.285667	+	0.879193i	−0.700531	+	0.713622i	$0.747053\pi$
$432$	−1.98911	−	1.44517i	−0.0957012	−	0.0695310i
$433$	−17.5992	+	12.7866i	−0.845765	+	0.614484i	−0.923975	−	0.382453i	$-0.875079\pi$
$433$	−17.5992	+	12.7866i	−0.845765	+	0.614484i	0.0782102	+	0.996937i	$0.475079\pi$
$434$	6.26517	−	19.2822i	0.300738	−	0.925576i
$435$	1.85075	−	5.69603i	0.0887368	−	0.273104i
$436$	−33.5016	+	24.3403i	−1.60443	+	1.16569i
$437$	−28.7761	−	20.9071i	−1.37655	−	1.00012i
$438$	−5.24391	−	16.1391i	−0.250564	−	0.771155i
$439$	2.70519			0.129112			0.0645558	−	0.997914i	$-0.479437\pi$
$439$	2.70519			0.129112			0.0645558	+	0.997914i	$0.479437\pi$
$440$	−52.0309	−	14.9257i	−2.48048	−	0.711556i
$441$	1.00000			0.0476190
$442$	−14.6523	−	45.0952i	−0.696939	−	2.14496i
$443$	−30.9266	−	22.4695i	−1.46937	−	1.06756i	−0.980797	−	0.195032i	$-0.937519\pi$
$443$	−30.9266	−	22.4695i	−1.46937	−	1.06756i	−0.488570	−	0.872525i	$-0.662481\pi$
$444$	1.83476	−	1.33303i	0.0870738	−	0.0632628i
$445$	3.02462	−	9.30881i	0.143381	−	0.441280i
$446$	10.2182	−	31.4482i	0.483844	−	1.48912i
$447$	−11.5868	+	8.41828i	−0.548035	+	0.398171i
$448$	−8.63069	−	6.27056i	−0.407762	−	0.296256i
$449$	7.01814	+	21.5996i	0.331207	+	1.01935i	0.968561	+	0.248778i	$0.0800289\pi$
$449$	7.01814	+	21.5996i	0.331207	+	1.01935i	−0.637354	+	0.770571i	$0.719971\pi$
$450$	−25.1609			−1.18610
$451$	0.196546	+	5.64587i	0.00925498	+	0.265854i
$452$	−30.1819			−1.41964
$453$	−4.25939	−	13.1091i	−0.200124	−	0.615917i
$454$	−14.0482	−	10.2066i	−0.659313	−	0.479019i
$455$	9.55492	−	6.94205i	0.447942	−	0.325449i
$456$	7.55948	−	23.2657i	0.354005	−	1.08951i
$457$	−0.485722	+	1.49490i	−0.0227211	+	0.0699285i	−0.961774	−	0.273844i	$-0.911705\pi$
$457$	−0.485722	+	1.49490i	−0.0227211	+	0.0699285i	0.939053	+	0.343772i	$0.111705\pi$
$458$	−0.633583	+	0.460325i	−0.0296054	+	0.0215096i
$459$	5.34321	+	3.88207i	0.249400	+	0.181199i
$460$	27.3600	+	84.2054i	1.27567	+	3.92610i
$461$	−28.1276			−1.31003			−0.655017	−	0.755614i	$-0.727339\pi$
$461$	−28.1276			−1.31003			−0.655017	+	0.755614i	$0.727339\pi$
$462$	−4.44064	+	6.58197i	−0.206597	+	0.306221i
$463$	−4.69202			−0.218057			−0.109028	−	0.994039i	$-0.534774\pi$
$463$	−4.69202			−0.218057			−0.109028	+	0.994039i	$0.534774\pi$
$464$	−1.15543	−	3.55604i	−0.0536393	−	0.165085i
$465$	26.9835	+	19.6047i	1.25133	+	0.909145i
$466$	31.4629	−	22.8591i	1.45749	−	1.05893i
$467$	−5.44286	+	16.7514i	−0.251866	+	0.775163i	0.742565	+	0.669773i	$0.233609\pi$
$467$	−5.44286	+	16.7514i	−0.251866	+	0.775163i	−0.994431	+	0.105389i	$0.966391\pi$
$468$	−3.45761	+	10.6414i	−0.159828	+	0.491900i
$469$	−0.485183	+	0.352506i	−0.0224037	+	0.0162772i
$470$	36.6301	+	26.6134i	1.68962	+	1.22758i
$471$	−3.54157	−	10.8998i	−0.163187	−	0.502238i
$472$	−25.8543			−1.19004
$473$	−6.60190	−	8.45194i	−0.303556	−	0.388621i
$474$	2.44966			0.112517
$475$	−19.1722	−	59.0058i	−0.879679	−	2.70737i
$476$	−19.9358	−	14.4842i	−0.913757	−	0.663883i
$477$	4.95793	−	3.60215i	0.227008	−	0.164931i
$478$	21.4541	−	66.0290i	0.981289	−	3.02010i
$479$	−3.30865	+	10.1830i	−0.151176	+	0.465271i	−0.997753	−	0.0669940i	$-0.978659\pi$
$479$	−3.30865	+	10.1830i	−0.151176	+	0.465271i	0.846578	+	0.532265i	$0.178659\pi$
$480$	7.65374	−	5.56077i	0.349344	−	0.253813i
$481$	−1.47472	−	1.07144i	−0.0672413	−	0.0488536i
$482$	21.7019	+	66.7915i	0.988493	+	3.04227i
$483$	6.02551			0.274170
$484$	−15.3662	−	38.0565i	−0.698465	−	1.72984i
$485$	−10.0543			−0.456542
$486$	−0.739775	−	2.27679i	−0.0335569	−	0.103277i
$487$	−31.3577	−	22.7827i	−1.42095	−	1.03238i	−0.991613	−	0.129239i	$-0.958746\pi$
$487$	−31.3577	−	22.7827i	−1.42095	−	1.03238i	−0.429339	−	0.903143i	$-0.641254\pi$
$488$	−7.00362	+	5.08843i	−0.317039	+	0.230342i
$489$	1.52735	−	4.70071i	0.0690693	−	0.212573i
$490$	2.91345	−	8.96668i	0.131616	−	0.405073i
$491$	4.85460	−	3.52707i	0.219085	−	0.159174i	−0.472830	−	0.881154i	$-0.656767\pi$
$491$	4.85460	−	3.52707i	0.219085	−	0.159174i	0.691915	+	0.721979i	$0.256767\pi$
$492$	5.14147	+	3.73550i	0.231795	+	0.168409i
$493$	3.10374	+	9.55233i	0.139785	+	0.430215i
$494$	−42.3798			−1.90676
$495$	−8.04055	−	10.2937i	−0.361396	−	0.462669i
$496$	20.8226			0.934962
$497$	−0.435614	−	1.34068i	−0.0195399	−	0.0601378i
$498$	5.97934	+	4.34424i	0.267940	+	0.194670i
$499$	23.4434	−	17.0326i	1.04947	−	0.762484i	0.0773578	−	0.997003i	$-0.475352\pi$
$499$	23.4434	−	17.0326i	1.04947	−	0.762484i	0.972111	+	0.234519i	$0.0753516\pi$
$500$	−25.0198	+	77.0031i	−1.11892	+	3.44369i
$501$	2.63722	−	8.11651i	0.117822	−	0.362619i
$502$	24.8517	−	18.0559i	1.10919	−	0.805872i
$503$	10.4086	+	7.56227i	0.464095	+	0.337185i	0.795136	−	0.606432i	$-0.207400\pi$
$503$	10.4086	+	7.56227i	0.464095	+	0.337185i	−0.331040	+	0.943617i	$0.607400\pi$
$504$	1.28059	+	3.94126i	0.0570422	+	0.175558i
$505$	59.6940			2.65635
$506$	−26.7571	+	39.6598i	−1.18950	+	1.76309i
$507$	−4.00662			−0.177940
$508$	0.207140	+	0.637511i	0.00919035	+	0.0282850i
$509$	−15.9668	−	11.6006i	−0.707718	−	0.514187i	0.174719	−	0.984618i	$-0.444098\pi$
$509$	−15.9668	−	11.6006i	−0.707718	−	0.514187i	−0.882437	+	0.470431i	$0.844098\pi$
$510$	50.3764	−	36.6006i	2.23071	−	1.62070i
$511$	−2.19047	+	6.74158i	−0.0969008	+	0.298230i
$512$	8.12226	−	24.9977i	0.358956	−	1.10475i
$513$	4.77571	−	3.46976i	0.210853	−	0.153193i
$514$	37.8075	+	27.4687i	1.66762	+	1.21159i
$515$	16.8389	+	51.8247i	0.742009	+	2.28367i
$516$	−12.0649			−0.531127
$517$	0.554143	+	15.9180i	0.0243712	+	0.700074i
$518$	−1.45515			−0.0639355
$519$	4.04429	+	12.4470i	0.177524	+	0.546364i
$520$	39.5964	+	28.7685i	1.73642	+	1.26158i
$521$	18.9250	−	13.7498i	0.829118	−	0.602390i	−0.0901914	−	0.995924i	$-0.528748\pi$
$521$	18.9250	−	13.7498i	0.829118	−	0.602390i	0.919310	+	0.393535i	$0.128748\pi$
$522$	1.12501	−	3.46244i	0.0492405	−	0.151547i
$523$	−3.33109	+	10.2520i	−0.145659	+	0.448291i	−0.997095	−	0.0761668i	$-0.975732\pi$
$523$	−3.33109	+	10.2520i	−0.145659	+	0.448291i	0.851437	+	0.524458i	$0.175732\pi$
$524$	−28.3204	+	20.5760i	−1.23718	+	0.898866i
$525$	8.50288	+	6.17770i	0.371096	+	0.269617i
$526$	−17.7254	−	54.5533i	−0.772866	−	2.37864i
$527$	−55.9343			−2.43653
$528$	−7.83837	−	2.24854i	−0.341121	−	0.0978550i
$529$	13.3068			0.578556
$530$	−17.8546	−	54.9509i	−0.775555	−	2.38691i
$531$	−5.04732	−	3.66709i	−0.219035	−	0.159138i
$532$	−17.8185	+	12.9459i	−0.772528	+	0.561274i
$533$	1.57849	−	4.85809i	0.0683720	−	0.210427i
$534$	1.83857	−	5.65853i	0.0795626	−	0.244869i
$535$	1.41991	−	1.03162i	0.0613879	−	0.0446010i
$536$	−2.01064	−	1.46082i	−0.0868464	−	0.0630976i
$537$	7.99185	+	24.5964i	0.344874	+	1.06141i
$538$	−27.1140			−1.16897
$539$	3.11673	−	1.13401i	0.134247	−	0.0488455i
$540$	−14.6940			−0.632329
$541$	−1.98437	−	6.10725i	−0.0853146	−	0.262571i	0.899294	−	0.437344i	$-0.144081\pi$
$541$	−1.98437	−	6.10725i	−0.0853146	−	0.262571i	−0.984609	+	0.174773i	$0.944081\pi$
$542$	11.8583	+	8.61558i	0.509359	+	0.370071i
$543$	−17.3293	+	12.5905i	−0.743673	+	0.540310i
$544$	−4.90270	+	15.0890i	−0.210201	+	0.646934i
$545$	−13.5072	+	41.5709i	−0.578585	+	1.78070i
$546$	5.80813	−	4.21986i	0.248565	−	0.180593i
$547$	22.6953	+	16.4891i	0.970380	+	0.705022i	0.955538	−	0.294868i	$-0.0952756\pi$
$547$	22.6953	+	16.4891i	0.970380	+	0.705022i	0.0148415	+	0.999890i	$0.495276\pi$
$548$	1.03030	+	3.17095i	0.0440124	+	0.135456i
$549$	−2.08899			−0.0891558
$550$	−78.4197	+	28.5328i	−3.34383	+	1.21664i
$551$	8.97715			0.382440
$552$	7.71623	+	23.7481i	0.328425	+	1.01079i
$553$	−0.827839	−	0.601461i	−0.0352033	−	0.0255767i
$554$	1.16237	−	0.844514i	0.0493846	−	0.0358800i
$555$	0.739741	−	2.27669i	0.0314002	−	0.0966400i
$556$	2.44751	−	7.53267i	0.103798	−	0.319456i
$557$	−18.6966	+	13.5838i	−0.792198	+	0.575566i	−0.908615	−	0.417635i	$-0.862859\pi$
$557$	−18.6966	+	13.5838i	−0.792198	+	0.575566i	0.116417	+	0.993200i	$0.462859\pi$
$558$	16.4024	+	11.9171i	0.694370	+	0.504490i
$559$	2.99664	+	9.22272i	0.126744	+	0.390079i
$560$	9.68299			0.409181
$561$	21.0557	+	6.04009i	0.888971	+	0.255013i
$562$	−56.9815			−2.40362
$563$	−8.91315	−	27.4319i	−0.375644	−	1.15611i	−0.943043	−	0.332671i	$-0.892050\pi$
$563$	−8.91315	−	27.4319i	−0.375644	−	1.15611i	0.567398	−	0.823443i	$-0.307950\pi$
$564$	14.4959	+	10.5319i	0.610388	+	0.443473i
$565$	−25.7739	+	18.7259i	−1.08432	+	0.787803i
$566$	12.8277	−	39.4797i	0.539189	−	1.65945i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	4.72613	−	3.43374i	0.198304	−	0.144076i
$569$	14.3811	+	10.4485i	0.602886	+	0.438022i	0.846902	−	0.531749i	$-0.178465\pi$
$569$	14.3811	+	10.4485i	0.602886	+	0.438022i	−0.244016	+	0.969771i	$0.578465\pi$
$570$	−17.1984	−	52.9312i	−0.720361	−	2.21704i
$571$	17.8981			0.749012			0.374506	−	0.927225i	$-0.377812\pi$
$571$	17.8981			0.749012			0.374506	+	0.927225i	$0.377812\pi$
$572$	1.29110	+	37.0874i	0.0539835	+	1.55070i
$573$	−3.73988			−0.156236
$574$	−1.26008	−	3.87812i	−0.0525947	−	0.161870i
$575$	51.2342	+	37.2238i	2.13661	+	1.55234i
$576$	8.63069	−	6.27056i	0.359612	−	0.261273i
$577$	6.51311	−	20.0453i	0.271144	−	0.834496i	−0.719070	−	0.694938i	$-0.755432\pi$
$577$	6.51311	−	20.0453i	0.271144	−	0.834496i	0.990214	−	0.139558i	$-0.0445682\pi$
$578$	−19.6931	+	60.6091i	−0.819124	+	2.52101i
$579$	−4.91827	+	3.57333i	−0.204396	+	0.148503i
$580$	−18.0782	−	13.1346i	−0.750657	−	0.545385i
$581$	−0.954026	−	2.93619i	−0.0395797	−	0.121814i
$582$	−6.11169			−0.253338
$583$	11.3677	−	16.8493i	0.470800	−	0.697827i
$584$	−29.3754			−1.21556
$585$	3.64965	+	11.2325i	0.150895	+	0.464406i
$586$	−28.8813	−	20.9835i	−1.19307	−	0.866819i
$587$	−14.0070	+	10.1767i	−0.578131	+	0.420037i	−0.838050	−	0.545594i	$-0.816304\pi$
$587$	−14.0070	+	10.1767i	−0.578131	+	0.420037i	0.259919	+	0.965630i	$0.416304\pi$
$588$	1.15296	−	3.54845i	0.0475473	−	0.146335i
$589$	−15.4488	+	47.5466i	−0.636558	+	1.95913i
$590$	−47.5868	+	34.5738i	−1.95912	+	1.42338i
$591$	−17.4309	−	12.6643i	−0.717013	−	0.520940i
$592$	−0.461820	−	1.42134i	−0.0189807	−	0.0584166i
$593$	−26.3881			−1.08363			−0.541814	−	0.840498i	$-0.682262\pi$
$593$	−26.3881			−1.08363			−0.541814	+	0.840498i	$0.682262\pi$
$594$	−4.88760	−	6.25724i	−0.200541	−	0.256738i
$595$	−26.0107			−1.06634
$596$	16.5127	+	50.8210i	0.676388	+	2.08171i
$597$	12.0515	+	8.75594i	0.493236	+	0.358357i
$598$	34.9970	−	25.4268i	1.43113	−	1.03978i
$599$	−8.73262	+	26.8762i	−0.356805	+	1.09813i	0.598150	+	0.801384i	$0.295903\pi$
$599$	−8.73262	+	26.8762i	−0.356805	+	1.09813i	−0.954955	+	0.296749i	$0.904097\pi$
$600$	−13.4592	+	41.4232i	−0.549470	+	1.69110i
$601$	0.356702	−	0.259159i	0.0145502	−	0.0105713i	−0.580486	−	0.814270i	$-0.697138\pi$
$601$	0.356702	−	0.259159i	0.0145502	−	0.0105713i	0.595037	+	0.803699i	$0.297138\pi$
$602$	6.26276	+	4.55016i	0.255251	+	0.185451i
$603$	−0.185323	−	0.570366i	−0.00754695	−	0.0232271i
$604$	−51.4277			−2.09256
$605$	−36.7335	−	22.9647i	−1.49343	−	0.933648i
$606$	36.2861			1.47402
$607$	0.172767	+	0.531721i	0.00701238	+	0.0215819i	0.954501	−	0.298206i	$-0.0963883\pi$
$607$	0.172767	+	0.531721i	0.00701238	+	0.0215819i	−0.947489	+	0.319788i	$0.896388\pi$
$608$	11.4722	+	8.33503i	0.465259	+	0.338030i
$609$	−1.23031	+	0.893876i	−0.0498548	+	0.0362217i
$610$	−6.08616	+	18.7313i	−0.246421	+	0.758407i
$611$	4.45041	−	13.6969i	0.180044	−	0.554119i
$612$	19.9358	−	14.4842i	0.805858	−	0.585490i
$613$	−24.5796	−	17.8581i	−0.992759	−	0.721282i	−0.0322356	−	0.999480i	$-0.510263\pi$
$613$	−24.5796	−	17.8581i	−0.992759	−	0.721282i	−0.960524	+	0.278199i	$0.910263\pi$
$614$	−21.4870	−	66.1303i	−0.867146	−	2.66880i
$615$	6.70819			0.270500
$616$	8.46072	+	10.8316i	0.340892	+	0.436419i
$617$	2.35080			0.0946395			0.0473198	−	0.998880i	$-0.484932\pi$
$617$	2.35080			0.0946395			0.0473198	+	0.998880i	$0.484932\pi$
$618$	10.2358	+	31.5026i	0.411745	+	1.26722i
$619$	−4.94340	−	3.59159i	−0.198692	−	0.144358i	0.483991	−	0.875073i	$-0.339187\pi$
$619$	−4.94340	−	3.59159i	−0.198692	−	0.144358i	−0.682683	+	0.730715i	$0.739187\pi$
$620$	100.677	−	73.1462i	4.04329	−	2.93762i
$621$	−1.86199	+	5.73060i	−0.0747189	+	0.229961i
$622$	15.0656	−	46.3671i	0.604075	−	1.85915i
$623$	−2.01066	+	1.46083i	−0.0805552	+	0.0585268i
$624$	5.96514	+	4.33393i	0.238797	+	0.173496i
$625$	10.1705	+	31.3014i	0.406818	+	1.25206i
$626$	70.5757			2.82077
$627$	10.9498	−	16.2300i	0.437295	−	0.648165i
$628$	−42.7608			−1.70634
$629$	1.24056	+	3.81804i	0.0494642	+	0.152235i
$630$	7.62751	+	5.54171i	0.303887	+	0.220787i
$631$	23.3662	−	16.9765i	0.930193	−	0.675824i	−0.0158474	−	0.999874i	$-0.505045\pi$
$631$	23.3662	−	16.9765i	0.930193	−	0.675824i	0.946040	+	0.324050i	$0.105045\pi$
$632$	1.31039	−	4.03296i	0.0521244	−	0.160422i
$633$	5.24074	−	16.1293i	0.208301	−	0.641083i
$634$	14.7684	−	10.7298i	0.586526	−	0.426136i
$635$	0.572420	+	0.415888i	0.0227158	+	0.0165040i
$636$	−7.06574	−	21.7461i	−0.280175	−	0.862289i
$637$	−2.99890			−0.118821
$638$	−0.420089	−	12.0673i	−0.0166315	−	0.477748i
$639$	1.40968			0.0557659
$640$	−25.2341	−	77.6626i	−0.997465	−	3.06988i
$641$	32.2196	+	23.4089i	1.27260	+	0.924596i	0.999303	−	0.0373342i	$-0.0118866\pi$
$641$	32.2196	+	23.4089i	1.27260	+	0.924596i	0.273295	+	0.961930i	$0.411887\pi$
$642$	0.863117	−	0.627091i	0.0340645	−	0.0247493i
$643$	1.80999	−	5.57056i	0.0713788	−	0.219681i	−0.909003	−	0.416790i	$-0.863155\pi$
$643$	1.80999	−	5.57056i	0.0713788	−	0.219681i	0.980382	+	0.197108i	$0.0631551\pi$
$644$	6.94718	−	21.3812i	0.273757	−	0.842538i
$645$	−10.3028	+	7.48544i	−0.405673	+	0.294739i
$646$	75.5092	+	54.8607i	2.97087	+	2.15846i
$647$	6.97929	+	21.4801i	0.274384	+	0.844468i	0.989382	+	0.145341i	$0.0464279\pi$
$647$	6.97929	+	21.4801i	0.274384	+	0.844468i	−0.714997	+	0.699127i	$0.753572\pi$
$648$	−4.14409			−0.162795
$649$	−19.8897	−	5.70561i	−0.780738	−	0.223965i
$650$	75.4549			2.95958
$651$	−2.61707	−	8.05452i	−0.102571	−	0.315681i
$652$	−14.9192	−	10.8395i	−0.584282	−	0.424506i
$653$	33.0377	−	24.0033i	1.29287	−	0.939323i	0.293007	−	0.956110i	$-0.405344\pi$
$653$	33.0377	−	24.0033i	1.29287	−	0.939323i	0.999859	+	0.0167876i	$0.00534391\pi$
$654$	−8.21061	+	25.2697i	−0.321060	+	0.988122i
$655$	−11.4183	+	35.1418i	−0.446149	+	1.37310i
$656$	3.38811	−	2.46160i	0.132283	−	0.0961094i
$657$	−5.73473	−	4.16652i	−0.223733	−	0.162552i
$658$	−3.55268	−	10.9340i	−0.138498	−	0.426252i
$659$	32.5869			1.26941			0.634703	−	0.772756i	$-0.281122\pi$
$659$	32.5869			1.26941			0.634703	+	0.772756i	$0.281122\pi$
$660$	−45.7972	+	16.6632i	−1.78265	+	0.648614i
$661$	43.6393			1.69737			0.848686	−	0.528898i	$-0.177395\pi$
$661$	43.6393			1.69737			0.848686	+	0.528898i	$0.177395\pi$
$662$	−15.2934	−	47.0684i	−0.594397	−	1.82936i
$663$	−16.0237	−	11.6419i	−0.622310	−	0.452135i
$664$	10.3506	−	7.52013i	0.401680	−	0.291838i
$665$	−7.18407	+	22.1103i	−0.278586	+	0.857400i
$666$	0.449665	−	1.38393i	0.0174242	−	0.0536261i
$667$	−7.41327	+	5.38606i	−0.287043	+	0.208549i
$668$	−25.7604	−	18.7160i	−0.996700	−	0.724145i
$669$	−4.26830	−	13.1365i	−0.165022	−	0.507886i
$670$	−5.65422			−0.218442
$671$	−6.51081	+	2.36894i	−0.251347	+	0.0914520i
$672$	−2.40219			−0.0926667
$673$	−7.37679	−	22.7034i	−0.284354	−	0.875153i	−0.986591	−	0.163210i	$-0.947815\pi$
$673$	−7.37679	−	22.7034i	−0.284354	−	0.875153i	0.702237	−	0.711943i	$-0.252185\pi$
$674$	−10.5796	−	7.68655i	−0.407512	−	0.296075i
$675$	−8.50288	+	6.17770i	−0.327276	+	0.237780i
$676$	−4.61947	+	14.2173i	−0.177672	+	0.546818i
$677$	−1.31843	+	4.05770i	−0.0506712	+	0.155950i	−0.973190	−	0.230002i	$-0.926127\pi$
$677$	−1.31843	+	4.05770i	−0.0506712	+	0.155950i	0.922519	+	0.385952i	$0.126127\pi$
$678$	−15.6672	+	11.3829i	−0.601694	+	0.437156i
$679$	2.06539	+	1.50059i	0.0792623	+	0.0575875i
$680$	−33.3092	−	102.515i	−1.27735	−	3.93127i
$681$	−7.25345			−0.277953
$682$	64.6361	+	18.5417i	2.47504	+	0.709998i
$683$	5.88217			0.225075			0.112537	−	0.993647i	$-0.464102\pi$
$683$	5.88217			0.225075			0.112537	+	0.993647i	$0.464102\pi$
$684$	−6.80604	−	20.9468i	−0.260236	−	0.800923i
$685$	2.84719	+	2.06861i	0.108786	+	0.0790374i
$686$	−1.93676	+	1.40714i	−0.0739457	+	0.0537247i
$687$	−0.101091	+	0.311125i	−0.00385685	+	0.0118702i
$688$	−2.45683	+	7.56134i	−0.0936657	+	0.288273i
$689$	−14.8683	+	10.8025i	−0.566438	+	0.411542i
$690$	45.9597	+	33.3916i	1.74965	+	1.27120i
$691$	−0.0734097	−	0.225932i	−0.00279264	−	0.00859485i	0.949650	−	0.313311i	$-0.101438\pi$
$691$	−0.0734097	−	0.225932i	−0.00279264	−	0.00859485i	−0.952443	+	0.304716i	$0.901438\pi$
$692$	48.8305			1.85626
$693$	0.115389	+	3.31462i	0.00438328	+	0.125912i
$694$	−22.9368			−0.870669
$695$	−2.58345	−	7.95105i	−0.0979960	−	0.301601i
$696$	−5.09853	−	3.70430i	−0.193259	−	0.140411i
$697$	−9.10123	+	6.61243i	−0.344734	+	0.250464i
$698$	−6.92463	+	21.3118i	−0.262101	+	0.806664i
$699$	5.02003	−	15.4501i	0.189875	−	0.584375i
$700$	31.7247	−	23.0494i	1.19908	−	0.871184i
$701$	8.57852	+	6.23266i	0.324006	+	0.235404i	0.737883	−	0.674929i	$-0.235826\pi$
$701$	8.57852	+	6.23266i	0.324006	+	0.235404i	−0.413877	+	0.910333i	$0.635826\pi$
$702$	2.21851	+	6.82787i	0.0837322	+	0.257701i
$703$	3.58814			0.135329
$704$	19.7886	−	29.3310i	0.745812	−	1.10545i
$705$	18.9131			0.712310
$706$	20.4643	+	62.9826i	0.770184	+	2.37038i
$707$	−12.2625	−	8.90926i	−0.461180	−	0.335067i
$708$	−18.8318	+	13.6821i	−0.707744	+	0.514206i
$709$	−14.9328	+	45.9585i	−0.560813	+	1.72601i	0.119261	+	0.992863i	$0.461947\pi$
$709$	−14.9328	+	45.9585i	−0.560813	+	1.72601i	−0.680074	+	0.733143i	$0.738053\pi$
$710$	4.10702	−	12.6401i	0.154134	−	0.474375i
$711$	0.827839	−	0.601461i	0.0310464	−	0.0225565i
$712$	−8.33233	−	6.05379i	−0.312267	−	0.226876i
$713$	−15.7692	−	48.5326i	−0.590561	−	1.81756i
$714$	−15.8111			−0.591715
$715$	24.1128	+	30.8699i	0.901767	+	1.15447i
$716$	96.4932			3.60612
$717$	−8.96176	−	27.5815i	−0.334683	−	1.03005i
$718$	−5.04057	−	3.66219i	−0.188113	−	0.136672i
$719$	29.3379	−	21.3152i	1.09412	−	0.794925i	0.114030	−	0.993477i	$-0.463624\pi$
$719$	29.3379	−	21.3152i	1.09412	−	0.794925i	0.980090	+	0.198553i	$0.0636241\pi$
$720$	−2.99221	+	9.20907i	−0.111513	+	0.343202i
$721$	4.27568	−	13.1592i	0.159235	−	0.490073i
$722$	30.6910	−	22.2983i	1.14220	−	0.829859i
$723$	23.7331	+	17.2431i	0.882644	+	0.641279i
$724$	24.6967	+	76.0086i	0.917845	+	2.82484i
$725$	−15.9833			−0.593605
$726$	−22.3291	−	13.9595i	−0.828712	−	0.518086i
$727$	1.15184			0.0427195			0.0213597	−	0.999772i	$-0.493200\pi$
$727$	1.15184			0.0427195			0.0213597	+	0.999772i	$0.493200\pi$
$728$	−3.84037	−	11.8194i	−0.142334	−	0.438058i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−54.0677	+	39.2825i	−2.00114	+	1.45391i
$731$	6.59961	−	20.3115i	0.244095	−	0.751248i
$732$	−2.40852	+	7.41266i	−0.0890214	+	0.273980i
$733$	21.9277	−	15.9314i	0.809919	−	0.588441i	−0.103888	−	0.994589i	$-0.533128\pi$
$733$	21.9277	−	15.9314i	0.809919	−	0.588441i	0.913807	+	0.406148i	$0.133128\pi$
$734$	−20.0248	−	14.5489i	−0.739130	−	0.537009i
$735$	−1.21700	−	3.74554i	−0.0448897	−	0.138156i
$736$	−14.4745			−0.533535
$737$	−1.22441	−	1.56752i	−0.0451016	−	0.0577403i
$738$	4.07770			0.150102
$739$	−7.35516	−	22.6369i	−0.270564	−	0.832710i	−0.990359	−	0.138524i	$-0.955764\pi$
$739$	−7.35516	−	22.6369i	−0.270564	−	0.832710i	0.719795	−	0.694186i	$-0.244236\pi$
$740$	−7.22581	−	5.24986i	−0.265626	−	0.192989i
$741$	−14.3219	+	10.4054i	−0.526127	+	0.382253i
$742$	−4.53360	+	13.9530i	−0.166434	+	0.512230i
$743$	4.65554	−	14.3283i	0.170795	−	0.525653i	−0.828621	−	0.559809i	$-0.810874\pi$
$743$	4.65554	−	14.3283i	0.170795	−	0.525653i	0.999417	+	0.0341562i	$0.0108744\pi$
$744$	28.3936	−	20.6291i	1.04096	−	0.756301i
$745$	45.6321	+	33.1536i	1.67183	+	1.21466i
$746$	3.81418	+	11.7389i	0.139647	+	0.429790i
$747$	3.08729			0.112958
$748$	45.7093	−	67.7510i	1.67130	−	2.47722i
$749$	−0.445651			−0.0162837
$750$	16.0535	+	49.4076i	0.586191	+	1.80411i
$751$	−8.58427	−	6.23684i	−0.313244	−	0.227585i	0.420043	−	0.907504i	$-0.362015\pi$
$751$	−8.58427	−	6.23684i	−0.313244	−	0.227585i	−0.733287	+	0.679919i	$0.762015\pi$
$752$	9.55245	−	6.94026i	0.348342	−	0.253085i
$753$	3.96519	−	12.2036i	0.144500	−	0.444724i
$754$	−3.37380	+	10.3835i	−0.122867	+	0.378145i
$755$	−43.9168	+	31.9074i	−1.59830	+	1.16123i
$756$	3.01849	+	2.19306i	0.109781	+	0.0797608i
$757$	−10.8422	−	33.3690i	−0.394068	−	1.21282i	−0.929685	−	0.368355i	$-0.879921\pi$
$757$	−10.8422	−	33.3690i	−0.394068	−	1.21282i	0.535618	−	0.844461i	$-0.320079\pi$
$758$	84.7997			3.08006
$759$	0.695280	+	19.9723i	0.0252371	+	0.724947i
$760$	−96.3423			−3.49470
$761$	11.5231	+	35.4644i	0.417712	+	1.28558i	0.909803	+	0.415040i	$0.136233\pi$
$761$	11.5231	+	35.4644i	0.417712	+	1.28558i	−0.492091	+	0.870544i	$0.663767\pi$
$762$	0.347956	+	0.252805i	0.0126051	+	0.00915816i
$763$	8.97911	−	6.52370i	0.325066	−	0.236174i
$764$	−4.31193	+	13.2708i	−0.156000	+	0.480119i
$765$	8.03776	−	24.7377i	0.290606	−	0.894392i
$766$	−60.8289	+	44.1948i	−2.19784	+	1.59682i
$767$	15.1364	+	10.9972i	0.546544	+	0.397087i
$768$	−8.74575	−	26.9166i	−0.315585	−	0.971271i
$769$	21.8827			0.789110			0.394555	−	0.918872i	$-0.370899\pi$
$769$	21.8827			0.789110			0.394555	+	0.918872i	$0.370899\pi$
$770$	30.0573	+	8.62231i	1.08319	+	0.310727i
$771$	19.5210			0.703033
$772$	7.00921	+	21.5721i	0.252267	+	0.776398i
$773$	27.8902	+	20.2634i	1.00314	+	0.728824i	0.962759	−	0.270361i	$-0.0871429\pi$
$773$	27.8902	+	20.2634i	1.00314	+	0.728824i	0.0403807	+	0.999184i	$0.487143\pi$
$774$	−6.26276	+	4.55016i	−0.225110	+	0.163552i
$775$	27.5058	−	84.6541i	0.988037	−	3.04086i
$776$	−3.26931	+	10.0619i	−0.117361	+	0.361201i
$777$	−0.491753	+	0.357279i	−0.0176415	+	0.0128173i
$778$	38.8879	+	28.2537i	1.39420	+	1.01294i
$779$	3.10714	+	9.56279i	0.111325	+	0.342622i
$780$	44.0658			1.57781
$781$	4.39358	−	1.59859i	0.157215	−	0.0572022i
$782$	−95.2699			−3.40685
$783$	−0.469938	−	1.44632i	−0.0167942	−	0.0516873i
$784$	−1.98911	−	1.44517i	−0.0710397	−	0.0516134i
$785$	−36.5156	+	26.5302i	−1.30330	+	0.946902i
$786$	−6.94081	+	21.3616i	−0.247570	+	0.761943i
$787$	3.60525	−	11.0958i	0.128513	−	0.395524i	−0.866011	−	0.500024i	$-0.833324\pi$
$787$	3.60525	−	11.0958i	0.128513	−	0.395524i	0.994525	+	0.104501i	$0.0333244\pi$
$788$	−65.0358	+	47.2513i	−2.31681	+	1.68326i
$789$	−19.3845	−	14.0837i	−0.690107	−	0.501392i
$790$	−2.98123	−	9.17529i	−0.106068	−	0.326442i
$791$	8.08938			0.287625
$792$	−12.9160	+	4.69946i	−0.458950	+	0.166988i
$793$	6.26466			0.222464
$794$	−2.68798	−	8.27276i	−0.0953929	−	0.293589i
$795$	−19.5258	−	14.1863i	−0.692508	−	0.503137i
$796$	44.9649	−	32.6689i	1.59374	−	1.15792i
$797$	−10.8564	+	33.4127i	−0.384555	+	1.18354i	0.552248	+	0.833680i	$0.313770\pi$
$797$	−10.8564	+	33.4127i	−0.384555	+	1.18354i	−0.936803	+	0.349858i	$0.886230\pi$
$798$	−4.36697	+	13.4401i	−0.154589	+	0.475776i
$799$	−25.6601	+	18.6431i	−0.907788	+	0.659547i
$800$	−20.4256	−	14.8400i	−0.722153	−	0.524675i
$801$	−0.768002	−	2.36367i	−0.0271360	−	0.0835161i
$802$	−90.0869			−3.18108
$803$	−22.5985	−	6.48267i	−0.797484	−	0.228768i
$804$	−2.23759			−0.0789136
$805$	−7.33304	−	22.5688i	−0.258456	−	0.795445i
$806$	−49.1892	−	35.7381i	−1.73262	−	1.25882i
$807$	−9.16293	+	6.65726i	−0.322550	+	0.234347i
$808$	19.4104	−	59.7390i	0.682855	−	2.10161i
$809$	−4.48802	+	13.8127i	−0.157790	+	0.485629i	−0.998433	−	0.0559616i	$-0.982178\pi$
$809$	−4.48802	+	13.8127i	−0.157790	+	0.485629i	0.840643	+	0.541590i	$0.182178\pi$
$810$	−7.62751	+	5.54171i	−0.268003	+	0.194716i
$811$	−1.42724	−	1.03695i	−0.0501172	−	0.0364123i	0.562445	−	0.826835i	$-0.309861\pi$
$811$	−1.42724	−	1.03695i	−0.0501172	−	0.0364123i	−0.612562	+	0.790423i	$0.709861\pi$
$812$	1.75337	+	5.39631i	0.0615311	+	0.189373i
$813$	6.12278			0.214735
$814$	−0.167908	−	4.82325i	−0.00588519	−	0.169055i
$815$	−19.4655			−0.681846
$816$	−5.01797	−	15.4437i	−0.175664	−	0.540639i
$817$	−15.4429	−	11.2199i	−0.540279	−	0.392536i
$818$	31.1932	−	22.6632i	1.09065	−	0.792401i
$819$	0.926710	−	2.85212i	0.0323819	−	0.0996612i
$820$	7.73428	−	23.8037i	0.270093	−	0.831260i
$821$	7.89660	−	5.73722i	0.275593	−	0.200230i	−0.441400	−	0.897311i	$-0.645518\pi$
$821$	7.89660	−	5.73722i	0.275593	−	0.200230i	0.716993	+	0.697080i	$0.245518\pi$
$822$	1.73072	+	1.25744i	0.0603657	+	0.0438583i
$823$	−14.1011	−	43.3988i	−0.491534	−	1.51279i	−0.822289	−	0.569070i	$-0.807303\pi$
$823$	−14.1011	−	43.3988i	−0.491534	−	1.51279i	0.330755	−	0.943717i	$-0.392697\pi$
$824$	57.3392			1.99750
$825$	−19.4956	+	28.8966i	−0.678749	+	1.00605i
$826$	14.9355			0.519674
$827$	6.41263	+	19.7361i	0.222989	+	0.686290i	0.998490	+	0.0549428i	$0.0174977\pi$
$827$	6.41263	+	19.7361i	0.222989	+	0.686290i	−0.775500	+	0.631347i	$0.782502\pi$
$828$	18.1879	+	13.2143i	0.632075	+	0.459229i
$829$	−13.2572	+	9.63191i	−0.460441	+	0.334530i	−0.793704	−	0.608304i	$-0.791850\pi$
$829$	−13.2572	+	9.63191i	−0.460441	+	0.334530i	0.333263	+	0.942834i	$0.391850\pi$
$830$	8.99467	−	27.6828i	0.312210	−	0.960883i
$831$	0.185461	−	0.570791i	0.00643358	−	0.0198005i
$832$	−25.8825	+	18.8048i	−0.897316	+	0.651938i
$833$	5.34321	+	3.88207i	0.185131	+	0.134506i
$834$	−1.57040	−	4.83319i	−0.0543785	−	0.167360i
$835$	−33.6102			−1.16313
$836$	−44.9666	−	57.5675i	−1.55520	−	1.99101i
$837$	8.46902			0.292732
$838$	13.1035	+	40.3283i	0.452651	+	1.39312i
$839$	−28.3913	−	20.6275i	−0.980176	−	0.712139i	−0.0224277	−	0.999748i	$-0.507140\pi$
$839$	−28.3913	−	20.6275i	−0.980176	−	0.712139i	−0.957748	+	0.287609i	$0.907140\pi$
$840$	13.2037	−	9.59302i	0.455570	−	0.330991i
$841$	−8.24683	+	25.3811i	−0.284374	+	0.875212i
$842$	−22.3945	+	68.9233i	−0.771767	+	2.37525i
$843$	−19.2564	+	13.9906i	−0.663225	+	0.481861i
$844$	−51.1917	−	37.1929i	−1.76209	−	1.28023i
$845$	4.87605	+	15.0069i	0.167741	+	0.516254i
$846$	11.4967			0.395265
$847$	4.11846	+	10.1999i	0.141512	+	0.350473i
$848$	−15.0676			−0.517424
$849$	−5.35836	−	16.4913i	−0.183899	−	0.565982i
$850$	−134.440	−	97.6763i	−4.61125	−	3.35027i
$851$	−2.96306	+	2.15279i	−0.101572	+	0.0737967i
$852$	1.62530	−	5.00216i	0.0556819	−	0.171371i
$853$	−3.49282	+	10.7498i	−0.119592	+	0.368066i	−0.992877	−	0.119144i	$-0.961985\pi$
$853$	−3.49282	+	10.7498i	−0.119592	+	0.368066i	0.873285	+	0.487209i	$0.161985\pi$
$854$	4.04586	−	2.93949i	0.138446	−	0.100587i
$855$	−18.8081	−	13.6649i	−0.643225	−	0.467330i
$856$	−0.570697	−	1.75643i	−0.0195060	−	0.0600334i
$857$	13.8531			0.473214			0.236607	−	0.971605i	$-0.423965\pi$
$857$	13.8531			0.473214			0.236607	+	0.971605i	$0.423965\pi$
$858$	14.6574	+	18.7648i	0.500395	+	0.640620i
$859$	−5.23831			−0.178729			−0.0893645	−	0.995999i	$-0.528484\pi$
$859$	−5.23831			−0.178729			−0.0893645	+	0.995999i	$0.528484\pi$
$860$	14.6829	+	45.1895i	0.500684	+	1.54095i
$861$	−1.37802	−	1.00119i	−0.0469628	−	0.0341205i
$862$	37.1699	−	27.0055i	1.26601	−	0.919812i
$863$	−12.7095	+	39.1159i	−0.432637	+	1.33152i	0.462851	+	0.886436i	$0.346826\pi$
$863$	−12.7095	+	39.1159i	−0.432637	+	1.33152i	−0.895489	+	0.445085i	$0.853174\pi$
$864$	0.742319	−	2.28462i	0.0252542	−	0.0777245i
$865$	41.6989	−	30.2960i	1.41781	−	1.03010i
$866$	42.1319	+	30.6106i	1.43170	+	1.04019i
$867$	8.22614	+	25.3175i	0.279374	+	0.859826i
$868$	−31.5984			−1.07252
$869$	1.89809	−	2.81337i	0.0643882	−	0.0954371i
$870$	−14.3378			−0.486098
$871$	0.555765	+	1.71047i	0.0188314	+	0.0579571i
$872$	37.2102	+	27.0348i	1.26010	+	0.915514i
$873$	−2.06539	+	1.50059i	−0.0699028	+	0.0507874i
$874$	−26.3132	+	80.9838i	−0.890058	+	2.73932i
$875$	6.70583	−	20.6384i	0.226698	−	0.697706i
$876$	−21.3966	+	15.5455i	−0.722924	+	0.525235i
$877$	4.38073	+	3.18279i	0.147927	+	0.107475i	0.659287	−	0.751891i	$-0.270858\pi$
$877$	4.38073	+	3.18279i	0.147927	+	0.107475i	−0.511360	+	0.859366i	$0.670858\pi$
$878$	−2.00123	−	6.15915i	−0.0675382	−	0.207861i
$879$	−14.9122			−0.502975
$880$	1.11731	+	32.0954i	0.0376646	+	1.08194i
$881$	11.0961			0.373837			0.186918	−	0.982375i	$-0.440150\pi$
$881$	11.0961			0.373837			0.186918	+	0.982375i	$0.440150\pi$
$882$	−0.739775	−	2.27679i	−0.0249095	−	0.0766636i
$883$	41.6317	+	30.2472i	1.40102	+	1.01790i	0.994553	+	0.104234i	$0.0332391\pi$
$883$	41.6317	+	30.2472i	1.40102	+	1.01790i	0.406466	+	0.913666i	$0.366761\pi$
$884$	−59.7855	+	43.4367i	−2.01080	+	1.46093i
$885$	−7.59265	+	23.3678i	−0.255224	+	0.785499i
$886$	−28.2797	+	87.0358i	−0.950074	+	2.92403i
$887$	16.1753	−	11.7520i	0.543113	−	0.394595i	−0.282127	−	0.959377i	$-0.591040\pi$
$887$	16.1753	−	11.7520i	0.543113	−	0.394595i	0.825240	+	0.564782i	$0.191040\pi$
$888$	−2.03787	−	1.48060i	−0.0683863	−	0.0496856i
$889$	−0.0555178	−	0.170866i	−0.00186201	−	0.00573066i
$890$	−23.4318			−0.785435
$891$	−3.18805	−	0.914531i	−0.106804	−	0.0306379i
$892$	−51.5353			−1.72553
$893$	8.76029	+	26.9614i	0.293152	+	0.902229i
$894$	27.7383	+	20.1531i	0.927707	+	0.674019i
$895$	82.4006	−	59.8675i	2.75435	−	2.00115i
$896$	−6.40737	+	19.7199i	−0.214055	+	0.658794i
$897$	5.58390	−	17.1855i	0.186441	−	0.573807i
$898$	43.9860	−	31.9577i	1.46783	−	1.06644i
$899$	10.4196	+	7.57025i	0.347512	+	0.252482i
$900$	12.1178	+	37.2947i	0.403926	+	1.24316i
$901$	40.4751			1.34842
$902$	12.7091	−	4.62417i	0.423166	−	0.153968i
$903$	3.23364			0.107609
$904$	10.3592	+	31.8824i	0.344542	+	1.06039i
$905$	68.2480	+	49.5851i	2.26864	+	1.64826i
$906$	−26.6956	+	19.3955i	−0.886903	+	0.644373i
$907$	−1.61880	+	4.98215i	−0.0537514	+	0.165430i	−0.974328	−	0.225131i	$-0.927719\pi$
$907$	−1.61880	+	4.98215i	−0.0537514	+	0.165430i	0.920577	+	0.390561i	$0.127719\pi$
$908$	−8.36294	+	25.7385i	−0.277534	+	0.854161i
$909$	12.2625	−	8.90926i	0.406723	−	0.295501i
$910$	−22.8741	−	16.6190i	−0.758270	−	0.550915i
$911$	−3.40325	−	10.4741i	−0.112755	−	0.347023i	0.878717	−	0.477342i	$-0.158400\pi$
$911$	−3.40325	−	10.4741i	−0.112755	−	0.347023i	−0.991472	+	0.130319i	$0.958400\pi$
$912$	−14.5138			−0.480601
$913$	9.62226	−	3.50104i	0.318450	−	0.115867i
$914$	3.76290			0.124466
$915$	2.54229	+	7.82438i	0.0840457	+	0.258666i
$916$	0.987457	+	0.717430i	0.0326265	+	0.0237045i
$917$	7.59045	−	5.51479i	0.250659	−	0.182114i
$918$	4.88590	−	15.0372i	0.161259	−	0.496303i
$919$	−8.91382	+	27.4339i	−0.294040	+	0.904962i	0.689502	+	0.724283i	$0.257829\pi$
$919$	−8.91382	+	27.4339i	−0.294040	+	0.904962i	−0.983542	+	0.180678i	$0.942171\pi$
$920$	79.5588	−	57.8029i	2.62298	−	1.90570i
$921$	−23.4982	−	17.0724i	−0.774291	−	0.562556i
$922$	20.8081	+	64.0408i	0.685279	+	2.10907i
$923$	−4.22747			−0.139149
$924$	11.8948	+	3.41217i	0.391310	+	0.112252i
$925$	−6.38848			−0.210052
$926$	3.47104	+	10.6828i	0.114065	+	0.351057i
$927$	11.1939	+	8.13282i	0.367655	+	0.267117i
$928$	2.95545	−	2.14726i	0.0970175	−	0.0704874i
$929$	5.01250	−	15.4269i	0.164455	−	0.506139i	−0.834541	−	0.550946i	$-0.814267\pi$
$929$	5.01250	−	15.4269i	0.164455	−	0.506139i	0.998996	+	0.0448064i	$0.0142671\pi$
$930$	24.6741	−	75.9390i	0.809095	−	2.49014i
$931$	4.77571	−	3.46976i	0.156518	−	0.113717i
$932$	−49.0358	−	35.6266i	−1.60622	−	1.16699i
$933$	−6.29316	−	19.3683i	−0.206029	−	0.634091i
$934$	42.1660			1.37971
$935$	−3.00136	−	86.2156i	−0.0981550	−	2.81955i
$936$	12.4277			0.406212
$937$	−8.48784	−	26.1229i	−0.277286	−	0.853397i	−0.988606	−	0.150529i	$-0.951902\pi$
$937$	−8.48784	−	26.1229i	−0.277286	−	0.853397i	0.711320	−	0.702868i	$-0.248098\pi$
$938$	1.16151	+	0.843886i	0.0379246	+	0.0275539i
$939$	23.8504	−	17.3283i	0.778328	−	0.565489i
$940$	21.8061	−	67.1123i	0.711236	−	2.18896i
$941$	15.0560	−	46.3376i	0.490812	−	1.51056i	−0.332572	−	0.943078i	$-0.607916\pi$
$941$	15.0560	−	46.3376i	0.490812	−	1.51056i	0.823384	−	0.567485i	$-0.192084\pi$
$942$	−22.1967	+	16.1268i	−0.723208	+	0.525441i
$943$	−8.30327	−	6.03268i	−0.270392	−	0.196451i
$944$	4.74010	+	14.5885i	0.154277	+	0.474816i
$945$	3.93829			0.128113
$946$	−14.3594	+	21.2837i	−0.466864	+	0.691993i
$947$	21.1998			0.688902			0.344451	−	0.938804i	$-0.388065\pi$
$947$	21.1998			0.688902			0.344451	+	0.938804i	$0.388065\pi$
$948$	−1.17978	−	3.63100i	−0.0383176	−	0.117930i
$949$	17.1979	+	12.4950i	0.558266	+	0.405604i
$950$	−120.161	+	87.3021i	−3.89854	+	2.83245i
$951$	2.35635	−	7.25210i	0.0764098	−	0.235165i
$952$	−8.45777	+	26.0303i	−0.274118	+	0.843648i
$953$	−27.6059	+	20.0569i	−0.894244	+	0.649707i	−0.936981	−	0.349380i	$-0.886392\pi$
$953$	−27.6059	+	20.0569i	−0.894244	+	0.649707i	0.0427369	+	0.999086i	$0.486392\pi$
$954$	−11.8691	−	8.62341i	−0.384277	−	0.279193i
$955$	4.55143	+	14.0079i	0.147281	+	0.453283i
$956$	−108.204			−3.49957
$957$	−3.10482	−	3.97488i	−0.100365	−	0.128490i
$958$	25.6322			0.828138
$959$	−0.276143	−	0.849880i	−0.00891712	−	0.0274441i
$960$	−33.9902	−	24.6953i	−1.09703	−	0.797037i
$961$	−32.9467	+	23.9372i	−1.06280	+	0.772166i
$962$	−1.34850	+	4.15025i	−0.0434773	+	0.133810i
$963$	0.137714	−	0.423839i	0.00443776	−	0.0136580i
$964$	88.5496	−	64.3351i	2.85199	−	2.07209i
$965$	19.3696	+	14.0728i	0.623529	+	0.453020i
$966$	−4.45752	−	13.7188i	−0.143418	−	0.441397i
$967$	−18.8881			−0.607400			−0.303700	−	0.952768i	$-0.598222\pi$
$967$	−18.8881			−0.607400			−0.303700	+	0.952768i	$0.598222\pi$
$968$	−34.9265	+	29.2939i	−1.12258	+	0.941541i
$969$	38.9875			1.25246
$970$	7.43792	+	22.8916i	0.238817	+	0.735004i
$971$	−10.1003	−	7.33830i	−0.324134	−	0.235497i	0.413803	−	0.910366i	$-0.364200\pi$
$971$	−10.1003	−	7.33830i	−0.324134	−	0.235497i	−0.737937	+	0.674869i	$0.764200\pi$
$972$	−3.01849	+	2.19306i	−0.0968181	+	0.0703425i
$973$	−0.655983	+	2.01891i	−0.0210299	+	0.0647233i
$974$	−28.6739	+	88.2491i	−0.918770	+	2.82768i
$975$	25.4993	−	18.5263i	0.816630	−	0.593316i
$976$	4.15523	+	3.01895i	0.133006	+	0.0966342i
$977$	−4.28751	−	13.1956i	−0.137170	−	0.422165i	0.858752	−	0.512392i	$-0.171241\pi$
$977$	−4.28751	−	13.1956i	−0.137170	−	0.422165i	−0.995921	+	0.0902274i	$0.971241\pi$
$978$	−11.8324			−0.378360
$979$	−5.07409	−	6.49599i	−0.162169	−	0.207613i
$980$	−14.6940			−0.469382
$981$	3.42971	+	10.5556i	0.109502	+	0.337014i
$982$	−11.6217	−	8.44367i	−0.370864	−	0.269448i
$983$	−35.4613	+	25.7641i	−1.13104	+	0.821749i	−0.985846	−	0.167655i	$-0.946381\pi$
$983$	−35.4613	+	25.7641i	−1.13104	+	0.821749i	−0.145194	+	0.989403i	$0.546381\pi$
$984$	2.18127	−	6.71325i	0.0695363	−	0.214011i
$985$	−26.2212	+	80.7007i	−0.835478	+	2.57134i
$986$	19.4526	−	14.1332i	0.619498	−	0.450091i
$987$	−3.88520	−	2.82276i	−0.123667	−	0.0898495i
$988$	20.4106	+	62.8174i	0.649348	+	1.99849i
$989$	19.4843			0.619565
$990$	−17.4885	+	25.9217i	−0.555822	+	0.823847i
$991$	42.8926			1.36253			0.681264	−	0.732037i	$-0.261430\pi$
$991$	42.8926			1.36253			0.681264	+	0.732037i	$0.261430\pi$
$992$	6.28672	+	19.3485i	0.199603	+	0.614316i
$993$	−16.7249	−	12.1513i	−0.530748	−	0.385611i
$994$	−2.73020	+	1.98361i	−0.0865967	+	0.0629162i
$995$	18.1290	−	55.7954i	0.574728	−	1.76883i
$996$	3.55953	−	10.9551i	0.112788	−	0.347125i
$997$	22.8940	−	16.6335i	0.725060	−	0.526787i	−0.162937	−	0.986637i	$-0.552097\pi$
$997$	22.8940	−	16.6335i	0.725060	−	0.526787i	0.887997	+	0.459849i	$0.152097\pi$
$998$	−56.1225	−	40.7754i	−1.77653	−	1.29072i
$999$	−0.187833	−	0.578090i	−0.00594277	−	0.0182900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.148.1	yes	20
3.2	odd	2		693.2.m.j.379.5		20
11.3	even	5		2541.2.a.bq.1.2		10
11.8	odd	10		2541.2.a.br.1.9		10
11.9	even	5	inner	231.2.j.g.64.1	✓	20
33.8	even	10		7623.2.a.cy.1.2		10
33.14	odd	10		7623.2.a.cx.1.9		10
33.20	odd	10		693.2.m.j.64.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.1	✓	20	11.9	even	5	inner
231.2.j.g.148.1	yes	20	1.1	even	1	trivial
693.2.m.j.64.5		20	33.20	odd	10
693.2.m.j.379.5		20	3.2	odd	2
2541.2.a.bq.1.2		10	11.3	even	5
2541.2.a.br.1.9		10	11.8	odd	10
7623.2.a.cx.1.9		10	33.14	odd	10
7623.2.a.cy.1.2		10	33.8	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.739775 - 2.27679i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.01849 + 2.19306i) q^{4} +(-1.21700 + 3.74554i) q^{5} +(-0.739775 + 2.27679i) q^{6} +(0.809017 - 0.587785i) q^{7} +(3.35264 + 2.43583i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.739775 - 2.27679i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.01849 + 2.19306i) q^{4} +(-1.21700 + 3.74554i) q^{5} +(-0.739775 + 2.27679i) q^{6} +(0.809017 - 0.587785i) q^{7} +(3.35264 + 2.43583i) q^{8} +(0.309017 + 0.951057i) q^{9} +9.42812 q^{10} +(2.04163 + 2.61376i) q^{11} +3.73106 q^{12} +(-0.926710 - 2.85212i) q^{13} +(-1.93676 - 1.40714i) q^{14} +(3.18614 - 2.31487i) q^{15} +(0.759773 - 2.33834i) q^{16} +(-2.04092 + 6.28132i) q^{17} +(1.93676 - 1.40714i) q^{18} +(4.77571 + 3.46976i) q^{19} +(-4.54069 - 13.9748i) q^{20} -1.00000 q^{21} +(4.44064 - 6.58197i) q^{22} -6.02551 q^{23} +(-1.28059 - 3.94126i) q^{24} +(-8.50288 - 6.17770i) q^{25} +(-5.80813 + 4.21986i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-1.15296 + 3.54845i) q^{28} +(1.23031 - 0.893876i) q^{29} +(-7.62751 - 5.54171i) q^{30} +(2.61707 + 8.05452i) q^{31} +2.40219 q^{32} +(-0.115389 - 3.31462i) q^{33} +15.8111 q^{34} +(1.21700 + 3.74554i) q^{35} +(-3.01849 - 2.19306i) q^{36} +(0.491753 - 0.357279i) q^{37} +(4.36697 - 13.4401i) q^{38} +(-0.926710 + 2.85212i) q^{39} +(-13.2037 + 9.59302i) q^{40} +(1.37802 + 1.00119i) q^{41} +(0.739775 + 2.27679i) q^{42} -3.23364 q^{43} +(-11.8948 - 3.41217i) q^{44} -3.93829 q^{45} +(4.45752 + 13.7188i) q^{46} +(3.88520 + 2.82276i) q^{47} +(-1.98911 + 1.44517i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-7.77514 + 23.9294i) q^{50} +(5.34321 - 3.88207i) q^{51} +(9.05214 + 6.57676i) q^{52} +(-1.89376 - 5.82840i) q^{53} -2.39396 q^{54} +(-12.2746 + 4.46608i) q^{55} +4.14409 q^{56} +(-1.82416 - 5.61418i) q^{57} +(-2.94533 - 2.13990i) q^{58} +(-5.04732 + 3.66709i) q^{59} +(-4.54069 + 13.9748i) q^{60} +(-0.645533 + 1.98674i) q^{61} +(16.4024 - 11.9171i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-3.29663 - 10.1460i) q^{64} +11.8105 q^{65} +(-7.46134 + 2.71479i) q^{66} -0.599719 q^{67} +(-7.61481 - 23.4360i) q^{68} +(4.87474 + 3.54171i) q^{69} +(7.62751 - 5.54171i) q^{70} +(0.435614 - 1.34068i) q^{71} +(-1.28059 + 3.94126i) q^{72} +(-5.73473 + 4.16652i) q^{73} +(-1.17724 - 0.855314i) q^{74} +(3.24781 + 9.99573i) q^{75} -22.0248 q^{76} +(3.18805 + 0.914531i) q^{77} +7.17925 q^{78} +(-0.316207 - 0.973184i) q^{79} +(7.83370 + 5.69152i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.26008 - 3.87812i) q^{82} +(0.954026 - 2.93619i) q^{83} +(3.01849 - 2.19306i) q^{84} +(-21.0431 - 15.2887i) q^{85} +(2.39216 + 7.36232i) q^{86} -1.52075 q^{87} +(0.478184 + 13.7361i) q^{88} -2.48531 q^{89} +(2.91345 + 8.96668i) q^{90} +(-2.42616 - 1.76271i) q^{91} +(18.1879 - 13.2143i) q^{92} +(2.61707 - 8.05452i) q^{93} +(3.55268 - 10.9340i) q^{94} +(-18.8081 + 13.6649i) q^{95} +(-1.94342 - 1.41197i) q^{96} +(0.788908 + 2.42801i) q^{97} -2.39396 q^{98} +(-1.85493 + 2.74941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

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