LMFDB - Embedded newform 80.2.s.b.27.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 3]))

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

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

chi := DirichletCharacter("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (of order $4$, degree $2$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.7
Root			$-0.635486 + 1.26339i$ of defining polynomial
Character	$\chi$	$=$	80.27
Dual form			80.2.s.b.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.828280 - 1.14628i) q^{2} +0.692712 q^{3} +(-0.627905 - 1.89888i) q^{4} +(-0.245325 + 2.22257i) q^{5} +(0.573759 - 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(-2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +O(q^{10})$	\(q+(0.828280 - 1.14628i) q^{2} +0.692712 q^{3} +(-0.627905 - 1.89888i) q^{4} +(-0.245325 + 2.22257i) q^{5} +(0.573759 - 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(-2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +(2.34448 + 2.12212i) q^{10} +(0.843672 - 0.843672i) q^{11} +(-0.434957 - 1.31538i) q^{12} +3.68390i q^{13} +(-0.678995 + 0.109350i) q^{14} +(-0.169939 + 1.53960i) q^{15} +(-3.21147 + 2.38463i) q^{16} +(0.412137 + 0.412137i) q^{17} +(-2.08739 + 2.88879i) q^{18} +(5.37721 - 5.37721i) q^{19} +(4.37443 - 0.929720i) q^{20} +(-0.238204 - 0.238204i) q^{21} +(-0.268286 - 1.66588i) q^{22} +(-3.08788 + 3.08788i) q^{23} +(-1.86805 - 0.590917i) q^{24} +(-4.87963 - 1.09050i) q^{25} +(4.22278 + 3.05130i) q^{26} -3.82387 q^{27} +(-0.437052 + 0.868890i) q^{28} +(4.22969 + 4.22969i) q^{29} +(1.62405 + 1.47002i) q^{30} -8.75966i q^{31} +(0.0734474 + 5.65638i) q^{32} +(0.584422 - 0.584422i) q^{33} +(0.813788 - 0.131059i) q^{34} +(0.848640 - 0.679919i) q^{35} +(1.58241 + 4.78546i) q^{36} -5.41752i q^{37} +(-1.70994 - 10.6176i) q^{38} +2.55188i q^{39} +(2.55753 - 5.78438i) q^{40} -2.54777i q^{41} +(-0.470348 + 0.0757484i) q^{42} -4.30732i q^{43} +(-2.13178 - 1.07228i) q^{44} +(0.618255 - 5.60121i) q^{45} +(0.981939 + 6.09720i) q^{46} +(-4.56972 + 4.56972i) q^{47} +(-2.22462 + 1.65186i) q^{48} -6.76350i q^{49} +(-5.29172 + 4.69017i) q^{50} +(0.285492 + 0.285492i) q^{51} +(6.99528 - 2.31314i) q^{52} +6.07536 q^{53} +(-3.16724 + 4.38322i) q^{54} +(1.66815 + 2.08209i) q^{55} +(0.633987 + 1.22067i) q^{56} +(3.72486 - 3.72486i) q^{57} +(8.35177 - 1.34503i) q^{58} +(7.33694 + 7.33694i) q^{59} +(3.03022 - 0.644028i) q^{60} +(-4.81576 + 4.81576i) q^{61} +(-10.0410 - 7.25545i) q^{62} +(0.866609 + 0.866609i) q^{63} +(6.54461 + 4.60087i) q^{64} +(-8.18773 - 0.903753i) q^{65} +(-0.185845 - 1.15397i) q^{66} +14.3626i q^{67} +(0.523815 - 1.04138i) q^{68} +(-2.13901 + 2.13901i) q^{69} +(-0.0764647 - 1.53594i) q^{70} -2.97605 q^{71} +(6.79614 + 2.14981i) q^{72} +(6.87152 + 6.87152i) q^{73} +(-6.20998 - 4.48722i) q^{74} +(-3.38018 - 0.755404i) q^{75} +(-13.5870 - 6.83429i) q^{76} -0.580231 q^{77} +(2.92517 + 2.11367i) q^{78} -10.1654 q^{79} +(-4.51215 - 7.72273i) q^{80} +4.91161 q^{81} +(-2.92046 - 2.11027i) q^{82} -7.15276 q^{83} +(-0.302751 + 0.601890i) q^{84} +(-1.01711 + 0.814896i) q^{85} +(-4.93739 - 3.56767i) q^{86} +(2.92996 + 2.92996i) q^{87} +(-2.99484 + 1.55545i) q^{88} -1.10953 q^{89} +(-5.90845 - 5.34806i) q^{90} +(1.26679 - 1.26679i) q^{91} +(7.80240 + 3.92461i) q^{92} -6.06792i q^{93} +(1.45316 + 9.02318i) q^{94} +(10.6321 + 13.2704i) q^{95} +(0.0508779 + 3.91824i) q^{96} +(7.15920 + 7.15920i) q^{97} +(-7.75285 - 5.60207i) q^{98} +(-2.12618 + 2.12618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.828280	−	1.14628i	0.585682	−	0.810541i
$2$	0.828280	−	1.14628i	0.585682	−	0.810541i
$3$	0.692712			0.399937			0.199969	−	0.979802i	$-0.435916\pi$
$3$	0.692712			0.399937			0.199969	+	0.979802i	$0.435916\pi$
$4$	−0.627905	−	1.89888i	−0.313952	−	0.949439i
$5$	−0.245325	+	2.22257i	−0.109713	+	0.993963i
$5$	−0.245325	+	2.22257i	−0.109713	+	0.993963i
$6$	0.573759	−	0.794040i	0.234236	−	0.324166i
$7$	−0.343872	−	0.343872i	−0.129971	−	0.129971i	0.639129	−	0.769100i	$-0.279295\pi$
$7$	−0.343872	−	0.343872i	−0.129971	−	0.129971i	−0.769100	+	0.639129i	$0.779295\pi$
$8$	−2.69672	−	0.853049i	−0.953435	−	0.301598i
$9$	−2.52015			−0.840050
$10$	2.34448	+	2.12212i	0.741391	+	0.671073i
$11$	0.843672	−	0.843672i	0.254377	−	0.254377i	−0.568386	−	0.822762i	$-0.692432\pi$
$11$	0.843672	−	0.843672i	0.254377	−	0.254377i	0.822762	+	0.568386i	$0.192432\pi$
$12$	−0.434957	−	1.31538i	−0.125561	−	0.379716i
$13$			3.68390i			1.02173i	0.859661	+	0.510865i	$0.170675\pi$
$13$			3.68390i			1.02173i	−0.859661	+	0.510865i	$0.829325\pi$
$14$	−0.678995	+	0.109350i	−0.181469	+	0.0292251i
$15$	−0.169939	+	1.53960i	−0.0438782	+	0.397523i
$16$	−3.21147	+	2.38463i	−0.802868	+	0.596157i
$17$	0.412137	+	0.412137i	0.0999579	+	0.0999579i	0.755317	−	0.655359i	$-0.227483\pi$
$17$	0.412137	+	0.412137i	0.0999579	+	0.0999579i	−0.655359	+	0.755317i	$0.727483\pi$
$18$	−2.08739	+	2.88879i	−0.492003	+	0.680895i
$19$	5.37721	−	5.37721i	1.23362	−	1.23362i	0.271052	−	0.962565i	$-0.412629\pi$
$19$	5.37721	−	5.37721i	1.23362	−	1.23362i	0.962565	−	0.271052i	$-0.0873714\pi$
$20$	4.37443	−	0.929720i	0.978152	−	0.207892i
$21$	−0.238204	−	0.238204i	−0.0519804	−	0.0519804i
$22$	−0.268286	−	1.66588i	−0.0571987	−	0.355167i
$23$	−3.08788	+	3.08788i	−0.643868	+	0.643868i	−0.951504	−	0.307636i	$-0.900462\pi$
$23$	−3.08788	+	3.08788i	−0.643868	+	0.643868i	0.307636	+	0.951504i	$0.400462\pi$
$24$	−1.86805	−	0.590917i	−0.381314	−	0.120621i
$25$	−4.87963	−	1.09050i	−0.975926	−	0.218101i
$26$	4.22278	+	3.05130i	0.828154	+	0.598410i
$27$	−3.82387			−0.735905
$28$	−0.437052	+	0.868890i	−0.0825951	+	0.164205i
$29$	4.22969	+	4.22969i	0.785434	+	0.785434i	0.980742	−	0.195308i	$-0.0625707\pi$
$29$	4.22969	+	4.22969i	0.785434	+	0.785434i	−0.195308	+	0.980742i	$0.562571\pi$
$30$	1.62405	+	1.47002i	0.296510	+	0.268387i
$31$		−	8.75966i		−	1.57328i	−0.617411	−	0.786641i	$-0.711818\pi$
$31$		−	8.75966i		−	1.57328i	0.617411	−	0.786641i	$-0.288182\pi$
$32$	0.0734474	+	5.65638i	0.0129838	+	0.999916i
$33$	0.584422	−	0.584422i	0.101735	−	0.101735i
$34$	0.813788	−	0.131059i	0.139564	−	0.0224764i
$35$	0.848640	−	0.679919i	0.143446	−	0.114927i
$36$	1.58241	+	4.78546i	0.263736	+	0.797576i
$37$		−	5.41752i		−	0.890634i	−0.895373	−	0.445317i	$-0.853091\pi$
$37$		−	5.41752i		−	0.890634i	0.895373	−	0.445317i	$-0.146909\pi$
$38$	−1.70994	−	10.6176i	−0.277389	−	1.72240i
$39$			2.55188i			0.408628i
$40$	2.55753	−	5.78438i	0.404382	−	0.914590i
$41$		−	2.54777i		−	0.397895i	−0.980010	−	0.198948i	$-0.936248\pi$
$41$		−	2.54777i		−	0.397895i	0.980010	−	0.198948i	$-0.0637524\pi$
$42$	−0.470348	+	0.0757484i	−0.0725763	+	0.0116882i
$43$		−	4.30732i		−	0.656861i	−0.944528	−	0.328430i	$-0.893480\pi$
$43$		−	4.30732i		−	0.656861i	0.944528	−	0.328430i	$-0.106520\pi$
$44$	−2.13178	−	1.07228i	−0.321377	−	0.161653i
$45$	0.618255	−	5.60121i	0.0921641	−	0.834979i
$46$	0.981939	+	6.09720i	0.144779	+	0.898983i
$47$	−4.56972	+	4.56972i	−0.666562	+	0.666562i	−0.956919	−	0.290356i	$-0.906226\pi$
$47$	−4.56972	+	4.56972i	−0.666562	+	0.666562i	0.290356	+	0.956919i	$0.406226\pi$
$48$	−2.22462	+	1.65186i	−0.321097	+	0.238425i
$49$		−	6.76350i		−	0.966215i
$50$	−5.29172	+	4.69017i	−0.748362	+	0.663290i
$51$	0.285492	+	0.285492i	0.0399769	+	0.0399769i
$52$	6.99528	−	2.31314i	0.970071	−	0.320775i
$53$	6.07536			0.834515			0.417257	−	0.908788i	$-0.362991\pi$
$53$	6.07536			0.834515			0.417257	+	0.908788i	$0.362991\pi$
$54$	−3.16724	+	4.38322i	−0.431007	+	0.596481i
$55$	1.66815	+	2.08209i	0.224933	+	0.280749i
$56$	0.633987	+	1.22067i	0.0847201	+	0.163118i
$57$	3.72486	−	3.72486i	0.493369	−	0.493369i
$58$	8.35177	−	1.34503i	1.09664	−	0.176611i
$59$	7.33694	+	7.33694i	0.955189	+	0.955189i	0.999038	−	0.0438495i	$-0.0139622\pi$
$59$	7.33694	+	7.33694i	0.955189	+	0.955189i	−0.0438495	+	0.999038i	$0.513962\pi$
$60$	3.03022	−	0.644028i	0.391200	−	0.0831437i
$61$	−4.81576	+	4.81576i	−0.616595	+	0.616595i	−0.944656	−	0.328062i	$-0.893605\pi$
$61$	−4.81576	+	4.81576i	−0.616595	+	0.616595i	0.328062	+	0.944656i	$0.393605\pi$
$62$	−10.0410	−	7.25545i	−1.27521	−	0.921444i
$63$	0.866609	+	0.866609i	0.109183	+	0.109183i
$64$	6.54461	+	4.60087i	0.818077	+	0.575109i
$65$	−8.18773	−	0.903753i	−1.01556	−	0.112097i
$66$	−0.185845	−	1.15397i	−0.0228759	−	0.142044i
$67$			14.3626i			1.75467i	0.479880	+	0.877334i	$0.340680\pi$
$67$			14.3626i			1.75467i	−0.479880	+	0.877334i	$0.659320\pi$
$68$	0.523815	−	1.04138i	0.0635219	−	0.126286i
$69$	−2.13901	+	2.13901i	−0.257507	+	0.257507i
$70$	−0.0764647	−	1.53594i	−0.00913928	−	0.183580i
$71$	−2.97605			−0.353193			−0.176596	−	0.984283i	$-0.556509\pi$
$71$	−2.97605			−0.353193			−0.176596	+	0.984283i	$0.556509\pi$
$72$	6.79614	+	2.14981i	0.800933	+	0.253358i
$73$	6.87152	+	6.87152i	0.804250	+	0.804250i	0.983757	−	0.179507i	$-0.0574501\pi$
$73$	6.87152	+	6.87152i	0.804250	+	0.804250i	−0.179507	+	0.983757i	$0.557450\pi$
$74$	−6.20998	−	4.48722i	−0.721895	−	0.521629i
$75$	−3.38018	−	0.755404i	−0.390309	−	0.0872266i
$76$	−13.5870	−	6.83429i	−1.55854	−	0.783947i
$77$	−0.580231			−0.0661234
$78$	2.92517	+	2.11367i	0.331210	+	0.239326i
$79$	−10.1654			−1.14369			−0.571847	−	0.820360i	$-0.693773\pi$
$79$	−10.1654			−1.14369			−0.571847	+	0.820360i	$0.693773\pi$
$80$	−4.51215	−	7.72273i	−0.504473	−	0.863427i
$81$	4.91161			0.545734
$82$	−2.92046	−	2.11027i	−0.322510	−	0.233040i
$83$	−7.15276			−0.785118			−0.392559	−	0.919727i	$-0.628410\pi$
$83$	−7.15276			−0.785118			−0.392559	+	0.919727i	$0.628410\pi$
$84$	−0.302751	+	0.601890i	−0.0330329	+	0.0656716i
$85$	−1.01711	+	0.814896i	−0.110321	+	0.0883878i
$86$	−4.93739	−	3.56767i	−0.532412	−	0.384712i
$87$	2.92996	+	2.92996i	0.314124	+	0.314124i
$88$	−2.99484	+	1.55545i	−0.319251	+	0.165812i
$89$	−1.10953			−0.117610			−0.0588050	−	0.998269i	$-0.518729\pi$
$89$	−1.10953			−0.117610			−0.0588050	+	0.998269i	$0.518729\pi$
$90$	−5.90845	−	5.34806i	−0.622806	−	0.563735i
$91$	1.26679	−	1.26679i	0.132796	−	0.132796i
$92$	7.80240	+	3.92461i	0.813457	+	0.409169i
$93$		−	6.06792i		−	0.629214i
$94$	1.45316	+	9.02318i	0.149882	+	0.930670i
$95$	10.6321	+	13.2704i	1.09083	+	1.36151i
$96$	0.0508779	+	3.91824i	0.00519270	+	0.399904i
$97$	7.15920	+	7.15920i	0.726906	+	0.726906i	0.970002	−	0.243096i	$-0.0781630\pi$
$97$	7.15920	+	7.15920i	0.726906	+	0.726906i	−0.243096	+	0.970002i	$0.578163\pi$
$98$	−7.75285	−	5.60207i	−0.783156	−	0.565895i
$99$	−2.12618	+	2.12618i	−0.213689	+	0.213689i
$100$	0.993211	+	9.95055i	0.0993211	+	0.995055i
$101$	0.953394	+	0.953394i	0.0948663	+	0.0948663i	0.752947	−	0.658081i	$-0.228632\pi$
$101$	0.953394	+	0.953394i	0.0948663	+	0.0948663i	−0.658081	+	0.752947i	$0.728632\pi$
$102$	0.563721	−	0.0907858i	0.0558167	−	0.00898914i
$103$	9.59425	−	9.59425i	0.945350	−	0.945350i	−0.0532322	−	0.998582i	$-0.516952\pi$
$103$	9.59425	−	9.59425i	0.945350	−	0.945350i	0.998582	+	0.0532322i	$0.0169524\pi$
$104$	3.14255	−	9.93446i	0.308152	−	0.974154i
$105$	0.587863	−	0.470988i	0.0573696	−	0.0459637i
$106$	5.03210	−	6.96405i	0.488761	−	0.676408i
$107$	−5.28201			−0.510631			−0.255316	−	0.966858i	$-0.582179\pi$
$107$	−5.28201			−0.510631			−0.255316	+	0.966858i	$0.582179\pi$
$108$	2.40103	+	7.26107i	0.231039	+	0.698697i
$109$	−1.53980	−	1.53980i	−0.147486	−	0.147486i	0.629508	−	0.776994i	$-0.283256\pi$
$109$	−1.53980	−	1.53980i	−0.147486	−	0.147486i	−0.776994	+	0.629508i	$0.783256\pi$
$110$	3.76835	−	0.187602i	0.359298	−	0.0178872i
$111$		−	3.75278i		−	0.356198i
$112$	1.92434	+	0.284329i	0.181833	+	0.0268665i
$113$	−2.99656	+	2.99656i	−0.281893	+	0.281893i	−0.833863	−	0.551971i	$-0.813876\pi$
$113$	−2.99656	+	2.99656i	−0.281893	+	0.281893i	0.551971	+	0.833863i	$0.313876\pi$
$114$	−1.18450	−	7.35494i	−0.110938	−	0.688854i
$115$	−6.10550	−	7.62056i	−0.569340	−	0.710621i
$116$	5.37582	−	10.6875i	0.499133	−	0.992310i
$117$		−	9.28399i		−	0.858305i
$118$	14.4872	−	2.33313i	1.33366	−	0.214782i
$119$		−	0.283445i		−	0.0259833i
$120$	1.77163	−	4.00691i	0.161727	−	0.365779i
$121$			9.57643i			0.870585i
$122$	1.53140	+	9.50899i	0.138646	+	0.860904i
$123$		−	1.76487i		−	0.159133i
$124$	−16.6335	+	5.50023i	−1.49373	+	0.493935i
$125$	3.62081	−	10.5778i	0.323855	−	0.946107i
$126$	1.71117	−	0.275580i	0.152443	−	0.0245506i
$127$	10.5522	−	10.5522i	0.936360	−	0.936360i	−0.0617330	−	0.998093i	$-0.519663\pi$
$127$	10.5522	−	10.5522i	0.936360	−	0.936360i	0.998093	+	0.0617330i	$0.0196627\pi$
$128$	10.6947	−	3.69113i	0.945282	−	0.326253i
$129$		−	2.98373i		−	0.262703i
$130$	−7.81769	+	8.63685i	−0.685656	+	0.757502i
$131$	−0.850513	−	0.850513i	−0.0743096	−	0.0743096i	0.668975	−	0.743285i	$-0.266733\pi$
$131$	−0.850513	−	0.850513i	−0.0743096	−	0.0743096i	−0.743285	+	0.668975i	$0.766733\pi$
$132$	−1.47671	−	0.742784i	−0.128531	−	0.0646511i
$133$	−3.69814			−0.320670
$134$	16.4635	+	11.8962i	1.42223	+	1.02768i
$135$	0.938091	−	8.49883i	0.0807380	−	0.731463i
$136$	−0.759845	−	1.46299i	−0.0651562	−	0.125451i
$137$	5.50145	−	5.50145i	0.470021	−	0.470021i	−0.431901	−	0.901921i	$-0.642157\pi$
$137$	5.50145	−	5.50145i	0.470021	−	0.470021i	0.901921	+	0.431901i	$0.142157\pi$
$138$	0.680201	+	4.22360i	0.0579025	+	0.359537i
$139$	−3.03517	−	3.03517i	−0.257440	−	0.257440i	0.566572	−	0.824012i	$-0.308269\pi$
$139$	−3.03517	−	3.03517i	−0.257440	−	0.257440i	−0.824012	+	0.566572i	$0.808269\pi$
$140$	−1.82395	−	1.18454i	−0.154152	−	0.100112i
$141$	−3.16550	+	3.16550i	−0.266583	+	0.266583i
$142$	−2.46501	+	3.41138i	−0.206859	+	0.286277i
$143$	3.10801	+	3.10801i	0.259905	+	0.259905i
$144$	8.09339	−	6.00962i	0.674449	−	0.500802i
$145$	−10.4384	+	8.36313i	−0.866864	+	0.694520i
$146$	13.5682	−	2.18513i	1.12291	−	0.180842i
$147$		−	4.68516i		−	0.386425i
$148$	−10.2872	+	3.40168i	−0.845603	+	0.279617i
$149$	−11.1571	+	11.1571i	−0.914023	+	0.914023i	−0.996586	−	0.0825625i	$-0.973690\pi$
$149$	−11.1571	+	11.1571i	−0.914023	+	0.914023i	0.0825625	+	0.996586i	$0.473690\pi$
$150$	−3.66564	+	3.24894i	−0.299298	+	0.265275i
$151$	3.18265			0.259000			0.129500	−	0.991579i	$-0.458663\pi$
$151$	3.18265			0.259000			0.129500	+	0.991579i	$0.458663\pi$
$152$	−19.0879	+	9.91381i	−1.54823	+	0.804116i
$153$	−1.03865	−	1.03865i	−0.0839696	−	0.0839696i
$154$	−0.480593	+	0.665105i	−0.0387273	+	0.0535957i
$155$	19.4690	+	2.14896i	1.56378	+	0.172609i
$156$	4.84571	−	1.60234i	0.387968	−	0.128290i
$157$	−7.05454			−0.563014			−0.281507	−	0.959559i	$-0.590834\pi$
$157$	−7.05454			−0.563014			−0.281507	+	0.959559i	$0.590834\pi$
$158$	−8.41978	+	11.6523i	−0.669842	+	0.927011i
$159$	4.20847			0.333754
$160$	−12.5897	−	1.22441i	−0.995304	−	0.0967979i
$161$	2.12367			0.167369
$162$	4.06819	−	5.63007i	0.319627	−	0.442340i
$163$	−16.0208			−1.25484			−0.627422	−	0.778680i	$-0.715890\pi$
$163$	−16.0208			−1.25484			−0.627422	+	0.778680i	$0.715890\pi$
$164$	−4.83791	+	1.59976i	−0.377777	+	0.124920i
$165$	1.15554	+	1.44229i	0.0899591	+	0.112282i
$166$	−5.92449	+	8.19905i	−0.459830	+	0.636370i
$167$	−16.6023	−	16.6023i	−1.28473	−	1.28473i	−0.937946	−	0.346780i	$-0.887275\pi$
$167$	−16.6023	−	16.6023i	−1.28473	−	1.28473i	−0.346780	−	0.937946i	$-0.612725\pi$
$168$	0.439171	+	0.845571i	0.0338827	+	0.0652372i
$169$	−0.571141			−0.0439339
$170$	0.0916444	+	1.84085i	0.00702880	+	0.141187i
$171$	−13.5514	+	13.5514i	−1.03630	+	1.03630i
$172$	−8.17908	+	2.70459i	−0.623649	+	0.206223i
$173$		−	14.9958i		−	1.14011i	−0.821607	−	0.570054i	$-0.806922\pi$
$173$		−	14.9958i		−	1.14011i	0.821607	−	0.570054i	$-0.193078\pi$
$174$	5.78537	−	0.931719i	0.438588	−	0.0706335i
$175$	1.30298	+	2.05296i	0.0984957	+	0.155189i
$176$	−0.697585	+	4.72127i	−0.0525825	+	0.355879i
$177$	5.08239	+	5.08239i	0.382016	+	0.382016i
$178$	−0.919002	+	1.27183i	−0.0688821	+	0.0953277i
$179$	9.91310	−	9.91310i	0.740940	−	0.740940i	−0.231819	−	0.972759i	$-0.574468\pi$
$179$	9.91310	−	9.91310i	0.740940	−	0.740940i	0.972759	+	0.231819i	$0.0744678\pi$
$180$	−11.0242	+	2.34303i	−0.821697	+	0.174639i
$181$	1.04015	+	1.04015i	0.0773139	+	0.0773139i	0.744706	−	0.667392i	$-0.232590\pi$
$181$	1.04015	+	1.04015i	0.0773139	+	0.0773139i	−0.667392	+	0.744706i	$0.732590\pi$
$182$	−0.402837	−	2.50135i	−0.0298602	−	0.185413i
$183$	−3.33593	+	3.33593i	−0.246599	+	0.246599i
$184$	10.9613	−	5.69304i	0.808075	−	0.419696i
$185$	12.0408	+	1.32905i	0.885258	+	0.0977138i
$186$	−6.95552	−	5.02594i	−0.510004	−	0.368520i
$187$	0.695417			0.0508539
$188$	11.5467	+	5.80799i	0.842129	+	0.423591i
$189$	1.31492	+	1.31492i	0.0956466	+	0.0956466i
$190$	24.0179	−	1.19570i	1.74244	−	0.0867450i
$191$			3.08419i			0.223164i	0.993755	+	0.111582i	$0.0355918\pi$
$191$			3.08419i			0.223164i	−0.993755	+	0.111582i	$0.964408\pi$
$192$	4.53353	+	3.18708i	0.327179	+	0.230008i
$193$	−12.0915	+	12.0915i	−0.870368	+	0.870368i	−0.992512	−	0.122144i	$-0.961023\pi$
$193$	−12.0915	+	12.0915i	−0.870368	+	0.870368i	0.122144	+	0.992512i	$0.461023\pi$
$194$	14.1362	−	2.27661i	1.01492	−	0.163451i
$195$	−5.67174	−	0.626040i	−0.406162	−	0.0448317i
$196$	−12.8431	+	4.24683i	−0.917362	+	0.303345i
$197$			13.0186i			0.927540i	0.885956	+	0.463770i	$0.153504\pi$
$197$			13.0186i			0.927540i	−0.885956	+	0.463770i	$0.846496\pi$
$198$	0.676120	+	4.19827i	0.0480498	+	0.298358i
$199$		−	10.6279i		−	0.753395i	−0.926336	−	0.376697i	$-0.877060\pi$
$199$		−	10.6279i		−	0.753395i	0.926336	−	0.376697i	$-0.122940\pi$
$200$	12.2288	+	7.10335i	0.864704	+	0.502283i
$201$			9.94913i			0.701758i
$202$	1.88253	−	0.303177i	0.132455	−	0.0213315i
$203$		−	2.90894i		−	0.204168i
$204$	0.362853	−	0.721377i	0.0254048	−	0.0505065i
$205$	5.66260	+	0.625032i	0.395493	+	0.0436541i
$206$	−3.05095	−	18.9444i	−0.212570	−	1.31992i
$207$	7.78192	−	7.78192i	0.540881	−	0.540881i
$208$	−8.78474	−	11.8308i	−0.609112	−	0.820315i
$209$		−	9.07320i		−	0.627607i
$210$	−0.0529680	−	1.06396i	−0.00365514	−	0.0734205i
$211$	11.4801	+	11.4801i	0.790321	+	0.790321i	0.981546	−	0.191225i	$-0.0612460\pi$
$211$	11.4801	+	11.4801i	0.790321	+	0.790321i	−0.191225	+	0.981546i	$0.561246\pi$
$212$	−3.81475	−	11.5364i	−0.261998	−	0.792321i
$213$	−2.06155			−0.141255
$214$	−4.37499	+	6.05465i	−0.299068	+	0.413888i
$215$	9.57332	+	1.05669i	0.652895	+	0.0720659i
$216$	10.3119	+	3.26195i	0.701638	+	0.221948i
$217$	−3.01220	+	3.01220i	−0.204482	+	0.204482i
$218$	−3.04042	+	0.489652i	−0.205923	+	0.0331634i
$219$	4.75998	+	4.75998i	0.321650	+	0.321650i
$220$	2.90620	−	4.47496i	0.195936	−	0.301702i
$221$	−1.51827	+	1.51827i	−0.102130	+	0.102130i
$222$	−4.30173	−	3.10835i	−0.288713	−	0.208619i
$223$	−2.17863	−	2.17863i	−0.145892	−	0.145892i	0.630388	−	0.776280i	$-0.282896\pi$
$223$	−2.17863	−	2.17863i	−0.145892	−	0.145892i	−0.776280	+	0.630388i	$0.782896\pi$
$224$	1.91981	−	1.97033i	0.128273	−	0.131648i
$225$	12.2974	+	2.74823i	0.819827	+	0.183215i
$226$	0.952898	+	5.91688i	0.0633859	+	0.393585i
$227$			9.32318i			0.618801i	0.950932	+	0.309401i	$0.100128\pi$
$227$			9.32318i			0.618801i	−0.950932	+	0.309401i	$0.899872\pi$
$228$	−9.41190	−	4.73419i	−0.623318	−	0.313530i
$229$	2.72259	−	2.72259i	0.179914	−	0.179914i	−0.611404	−	0.791318i	$-0.709395\pi$
$229$	2.72259	−	2.72259i	0.179914	−	0.179914i	0.791318	+	0.611404i	$0.209395\pi$
$230$	−13.7923	+	0.686633i	−0.909440	+	0.0452752i
$231$	−0.401933			−0.0264452
$232$	−7.79816	−	15.0144i	−0.511974	−	0.985746i
$233$	−12.3897	−	12.3897i	−0.811679	−	0.811679i	0.173206	−	0.984886i	$-0.444587\pi$
$233$	−12.3897	−	12.3897i	−0.811679	−	0.811679i	−0.984886	+	0.173206i	$0.944587\pi$
$234$	−10.6420	−	7.68974i	−0.695691	−	0.502694i
$235$	−9.03546	−	11.2776i	−0.589408	−	0.735669i
$236$	9.32506	−	18.5389i	0.607010	−	1.20678i
$237$	−7.04168			−0.457406
$238$	−0.324906	−	0.234772i	−0.0210606	−	0.0152180i
$239$	−25.2180			−1.63122			−0.815609	−	0.578604i	$-0.803598\pi$
$239$	−25.2180			−1.63122			−0.815609	+	0.578604i	$0.803598\pi$
$240$	−3.12562	−	5.34963i	−0.201758	−	0.345317i
$241$	12.0218			0.774391			0.387195	−	0.921998i	$-0.373444\pi$
$241$	12.0218			0.774391			0.387195	+	0.921998i	$0.373444\pi$
$242$	10.9773	+	7.93197i	0.705645	+	0.509886i
$243$	14.8740			0.954164
$244$	12.1684	+	6.12070i	0.779000	+	0.391838i
$245$	15.0324	+	1.65926i	0.960382	+	0.106006i
$246$	−2.02303	−	1.46181i	−0.128984	−	0.0932015i
$247$	19.8091	+	19.8091i	1.26042	+	1.26042i
$248$	−7.47242	+	23.6224i	−0.474499	+	1.50002i
$249$	−4.95480			−0.313998
$250$	−9.12604	−	12.9118i	−0.577181	−	0.816616i
$251$	7.48911	−	7.48911i	0.472709	−	0.472709i	−0.430081	−	0.902790i	$-0.641515\pi$
$251$	7.48911	−	7.48911i	0.472709	−	0.472709i	0.902790	+	0.430081i	$0.141515\pi$
$252$	1.10144	−	2.18973i	0.0693840	−	0.137940i
$253$			5.21032i			0.327570i
$254$	−3.35559	−	20.8360i	−0.210548	−	1.30737i
$255$	−0.704565	+	0.564488i	−0.0441215	+	0.0353496i
$256$	4.62710	−	15.3163i	0.289194	−	0.957271i
$257$	−10.0809	−	10.0809i	−0.628832	−	0.628832i	0.318942	−	0.947774i	$-0.396672\pi$
$257$	−10.0809	−	10.0809i	−0.628832	−	0.628832i	−0.947774	+	0.318942i	$0.896672\pi$
$258$	−3.42019	−	2.47137i	−0.212932	−	0.153861i
$259$	−1.86293	+	1.86293i	−0.115757	+	0.115757i
$260$	3.42500	+	16.1150i	0.212409	+	0.999408i
$261$	−10.6595	−	10.6595i	−0.659804	−	0.659804i
$262$	−1.67939	+	0.270461i	−0.103753	+	0.0167091i
$263$	−3.83599	+	3.83599i	−0.236537	+	0.236537i	−0.815415	−	0.578877i	$-0.803491\pi$
$263$	−3.83599	+	3.83599i	−0.236537	+	0.236537i	0.578877	+	0.815415i	$0.303491\pi$
$264$	−2.07456	+	1.07748i	−0.127681	+	0.0663144i
$265$	−1.49044	+	13.5029i	−0.0915568	+	0.829477i
$266$	−3.06310	+	4.23910i	−0.187811	+	0.259916i
$267$	−0.768585			−0.0470367
$268$	27.2728	−	9.01833i	1.66595	−	0.550882i
$269$	13.4250	+	13.4250i	0.818539	+	0.818539i	0.985896	−	0.167357i	$-0.0535233\pi$
$269$	13.4250	+	13.4250i	0.818539	+	0.818539i	−0.167357	+	0.985896i	$0.553523\pi$
$270$	−8.96501	−	8.11472i	−0.545593	−	0.493846i
$271$			12.3519i			0.750326i	0.926959	+	0.375163i	$0.122413\pi$
$271$			12.3519i			0.750326i	−0.926959	+	0.375163i	$0.877587\pi$
$272$	−2.30636	−	0.340773i	−0.139844	−	0.0206624i
$273$	0.877522	−	0.877522i	0.0531100	−	0.0531100i
$274$	−1.74945	−	10.8629i	−0.105688	−	0.656253i
$275$	−5.03684	+	3.19678i	−0.303733	+	0.192773i
$276$	5.40482	+	2.71863i	0.325332	+	0.163642i
$277$		−	6.78804i		−	0.407854i	−0.978986	−	0.203927i	$-0.934630\pi$
$277$		−	6.78804i		−	0.407854i	0.978986	−	0.203927i	$-0.0653705\pi$
$278$	−5.99312	+	0.965177i	−0.359443	+	0.0578875i
$279$			22.0757i			1.32164i
$280$	−2.86855	+	1.10962i	−0.171429	+	0.0663125i
$281$		−	21.5509i		−	1.28562i	−0.766026	−	0.642810i	$-0.777768\pi$
$281$		−	21.5509i		−	1.28562i	0.766026	−	0.642810i	$-0.222232\pi$
$282$	1.00662	+	6.25046i	0.0599434	+	0.372210i
$283$			9.86809i			0.586597i	0.956021	+	0.293299i	$0.0947530\pi$
$283$			9.86809i			0.586597i	−0.956021	+	0.293299i	$0.905247\pi$
$284$	1.86868	+	5.65116i	0.110886	+	0.335335i
$285$	7.36495	+	9.19255i	0.436262	+	0.544520i
$286$	6.13694	−	0.988339i	0.362885	−	0.0584417i
$287$	−0.876108	+	0.876108i	−0.0517150	+	0.0517150i
$288$	−0.185099	−	14.2549i	−0.0109070	−	0.839979i
$289$		−	16.6603i		−	0.980017i
$290$	0.940530	+	18.8924i	0.0552298	+	1.10940i
$291$	4.95926	+	4.95926i	0.290717	+	0.290717i
$292$	8.73351	−	17.3628i	0.511090	−	1.01608i
$293$	14.1972			0.829410			0.414705	−	0.909956i	$-0.363885\pi$
$293$	14.1972			0.829410			0.414705	+	0.909956i	$0.363885\pi$
$294$	−5.37049	−	3.88062i	−0.313214	−	0.226323i
$295$	−18.1068	+	14.5069i	−1.05422	+	0.844626i
$296$	−4.62141	+	14.6095i	−0.268614	+	0.849162i
$297$	−3.22610	+	3.22610i	−0.187197	+	0.187197i
$298$	3.54792	+	22.0303i	0.205526	+	1.27618i
$299$	−11.3755	−	11.3755i	−0.657859	−	0.657859i
$300$	0.688009	+	6.89287i	0.0397222	+	0.397960i
$301$	−1.48117	+	1.48117i	−0.0853731	+	0.0853731i
$302$	2.63612	−	3.64820i	0.151692	−	0.209930i
$303$	0.660428	+	0.660428i	0.0379406	+	0.0379406i
$304$	−4.44611	+	30.0914i	−0.255002	+	1.72586i
$305$	−9.52194	−	11.8848i	−0.545224	−	0.680521i
$306$	−2.05087	+	0.330287i	−0.117240	+	0.0188813i
$307$		−	20.4161i		−	1.16521i	−0.812756	−	0.582604i	$-0.802034\pi$
$307$		−	20.4161i		−	1.16521i	0.812756	−	0.582604i	$-0.197966\pi$
$308$	0.364329	+	1.10179i	0.0207596	+	0.0627801i
$309$	6.64605	−	6.64605i	0.378081	−	0.378081i
$310$	18.5891	−	20.5369i	1.05579	−	1.16642i
$311$	−6.81074			−0.386202			−0.193101	−	0.981179i	$-0.561854\pi$
$311$	−6.81074			−0.386202			−0.193101	+	0.981179i	$0.561854\pi$
$312$	2.17688	−	6.88172i	0.123242	−	0.389601i
$313$	1.20933	+	1.20933i	0.0683555	+	0.0683555i	0.740458	−	0.672103i	$-0.234609\pi$
$313$	1.20933	+	1.20933i	0.0683555	+	0.0683555i	−0.672103	+	0.740458i	$0.734609\pi$
$314$	−5.84314	+	8.08646i	−0.329747	+	0.456345i
$315$	−2.13870	+	1.71350i	−0.120502	+	0.0965447i
$316$	6.38289	+	19.3028i	0.359065	+	1.08587i
$317$	−3.44178			−0.193310			−0.0966548	−	0.995318i	$-0.530814\pi$
$317$	−3.44178			−0.193310			−0.0966548	+	0.995318i	$0.530814\pi$
$318$	3.48580	−	4.82408i	0.195474	−	0.270521i
$319$	7.13694			0.399592
$320$	−11.8313	+	13.4172i	−0.661391	+	0.750042i
$321$	−3.65891			−0.204221
$322$	1.75899	−	2.43432i	0.0980249	−	0.135659i
$323$	4.43229			0.246619
$324$	−3.08402	−	9.32654i	−0.171334	−	0.518141i
$325$	4.01731	−	17.9761i	0.222840	−	0.997134i
$326$	−13.2697	+	18.3643i	−0.734940	+	1.01710i
$327$	−1.06664	−	1.06664i	−0.0589852	−	0.0589852i
$328$	−2.17338	+	6.87063i	−0.120005	+	0.379367i
$329$	3.14280			0.173268
$330$	2.61038	−	0.129954i	0.143697	−	0.00715375i
$331$	−1.48462	+	1.48462i	−0.0816019	+	0.0816019i	−0.746730	−	0.665128i	$-0.768377\pi$
$331$	−1.48462	+	1.48462i	−0.0816019	+	0.0816019i	0.665128	+	0.746730i	$0.268377\pi$
$332$	4.49125	+	13.5822i	0.246489	+	0.745421i
$333$			13.6530i			0.748177i
$334$	−32.7822	+	5.27950i	−1.79376	+	0.288881i
$335$	−31.9218	−	3.52350i	−1.74408	−	0.192509i
$336$	1.33301	+	0.196958i	0.0727219	+	0.0107449i
$337$	6.21211	+	6.21211i	0.338395	+	0.338395i	0.855763	−	0.517368i	$-0.173088\pi$
$337$	6.21211	+	6.21211i	0.338395	+	0.338395i	−0.517368	+	0.855763i	$0.673088\pi$
$338$	−0.473065	+	0.654686i	−0.0257313	+	0.0356102i
$339$	−2.07575	+	2.07575i	−0.112739	+	0.112739i
$340$	2.18604	+	1.41969i	0.118554	+	0.0769936i
$341$	−7.39028	−	7.39028i	−0.400206	−	0.400206i
$342$	4.30930	+	26.7580i	0.233020	+	1.44691i
$343$	−4.73288	+	4.73288i	−0.255552	+	0.255552i
$344$	−3.67436	+	11.6156i	−0.198108	+	0.626274i
$345$	−4.22935	−	5.27886i	−0.227701	−	0.284204i
$346$	−17.1893	−	12.4207i	−0.924104	−	0.667741i
$347$	10.1502			0.544889			0.272445	−	0.962171i	$-0.412168\pi$
$347$	10.1502			0.544889			0.272445	+	0.962171i	$0.412168\pi$
$348$	3.72390	−	7.40336i	0.199622	−	0.396862i
$349$	3.99595	+	3.99595i	0.213898	+	0.213898i	0.805921	−	0.592023i	$-0.201671\pi$
$349$	3.99595	+	3.99595i	0.213898	+	0.213898i	−0.592023	+	0.805921i	$0.701671\pi$
$350$	3.43249	+	0.206856i	0.183474	+	0.0110569i
$351$		−	14.0868i		−	0.751897i
$352$	4.83409	+	4.71016i	0.257658	+	0.251053i
$353$	22.6637	−	22.6637i	1.20627	−	1.20627i	0.234043	−	0.972226i	$-0.424804\pi$
$353$	22.6637	−	22.6637i	1.20627	−	1.20627i	0.972226	−	0.234043i	$-0.0751957\pi$
$354$	10.0355	−	1.61619i	0.533379	−	0.0858994i
$355$	0.730100	−	6.61449i	0.0387497	−	0.351061i
$356$	0.696680	+	2.10686i	0.0369239	+	0.111664i
$357$		−	0.196346i		−	0.0103917i
$358$	−3.15234	−	19.5740i	−0.166606	−	1.03452i
$359$			4.31874i			0.227934i	0.993485	+	0.113967i	$0.0363559\pi$
$359$			4.31874i			0.227934i	−0.993485	+	0.113967i	$0.963644\pi$
$360$	−6.44537	+	14.5775i	−0.339701	+	0.768302i
$361$		−	38.8288i		−	2.04362i
$362$	2.05384	−	0.330766i	0.107947	−	0.0173847i
$363$			6.63371i			0.348180i
$364$	−3.20091	−	1.61006i	−0.167773	−	0.0843899i
$365$	−16.9582	+	13.5867i	−0.887632	+	0.711159i
$366$	1.06082	+	6.58699i	0.0554499	+	0.344308i
$367$	6.46940	−	6.46940i	0.337700	−	0.337700i	−0.517801	−	0.855501i	$-0.673249\pi$
$367$	6.46940	−	6.46940i	0.337700	−	0.337700i	0.855501	+	0.517801i	$0.173249\pi$
$368$	2.55320	−	17.2801i	0.133095	−	0.900787i
$369$			6.42077i			0.334252i
$370$	11.4966	−	12.7013i	0.597681	−	0.660308i
$371$	−2.08915	−	2.08915i	−0.108463	−	0.108463i
$372$	−11.5222	+	3.81008i	−0.597400	+	0.197543i
$373$	−16.7831			−0.868995			−0.434497	−	0.900673i	$-0.643074\pi$
$373$	−16.7831			−0.868995			−0.434497	+	0.900673i	$0.643074\pi$
$374$	0.576000	−	0.797141i	0.0297842	−	0.0412192i
$375$	2.50818	−	7.32736i	0.129522	−	0.378383i
$376$	16.2215	−	8.42507i	0.836558	−	0.434490i
$377$	−15.5818	+	15.5818i	−0.802502	+	0.802502i
$378$	2.59639	−	0.418142i	0.133544	−	0.0215069i
$379$	7.31046	+	7.31046i	0.375513	+	0.375513i	0.869480	−	0.493967i	$-0.164454\pi$
$379$	7.31046	+	7.31046i	0.375513	+	0.375513i	−0.493967	+	0.869480i	$0.664454\pi$
$380$	18.5229	−	28.5215i	0.950206	−	1.46312i
$381$	7.30966	−	7.30966i	0.374485	−	0.374485i
$382$	3.53533	+	2.55457i	0.180883	+	0.130703i
$383$	5.31492	+	5.31492i	0.271580	+	0.271580i	0.829736	−	0.558156i	$-0.188491\pi$
$383$	5.31492	+	5.31492i	0.271580	+	0.271580i	−0.558156	+	0.829736i	$0.688491\pi$
$384$	7.40831	−	2.55689i	0.378054	−	0.130481i
$385$	0.142345	−	1.28960i	0.00725457	−	0.0657242i
$386$	3.84508	+	23.8754i	0.195710	+	1.21523i
$387$			10.8551i			0.551796i
$388$	9.09915	−	18.0897i	0.461939	−	0.918367i
$389$	1.28845	−	1.28845i	0.0653271	−	0.0653271i	−0.673688	−	0.739016i	$-0.735291\pi$
$389$	1.28845	−	1.28845i	0.0653271	−	0.0653271i	0.739016	+	0.673688i	$0.235291\pi$
$390$	−5.41540	+	5.98285i	−0.274220	+	0.302953i
$391$	−2.54526			−0.128719
$392$	−5.76960	+	18.2393i	−0.291409	+	0.921223i
$393$	−0.589160	−	0.589160i	−0.0297192	−	0.0297192i
$394$	14.9230	+	10.7831i	0.751809	+	0.543244i
$395$	2.49382	−	22.5933i	0.125478	−	1.13679i
$396$	5.37239	+	2.70232i	0.269973	+	0.135797i
$397$	9.53832			0.478715			0.239357	−	0.970932i	$-0.423063\pi$
$397$	9.53832			0.478715			0.239357	+	0.970932i	$0.423063\pi$
$398$	−12.1826	−	8.80291i	−0.610657	−	0.441250i
$399$	−2.56175			−0.128248
$400$	18.2712	−	8.13399i	0.913562	−	0.406699i
$401$	−24.6103			−1.22898			−0.614491	−	0.788924i	$-0.710638\pi$
$401$	−24.6103			−1.22898			−0.614491	+	0.788924i	$0.710638\pi$
$402$	11.4045	+	8.24067i	0.568803	+	0.411007i
$403$	32.2697			1.60747
$404$	1.21174	−	2.40902i	0.0602862	−	0.119853i
$405$	−1.20494	+	10.9164i	−0.0598739	+	0.542440i
$406$	−3.33446	−	2.40942i	−0.165486	−	0.119578i
$407$	−4.57061	−	4.57061i	−0.226557	−	0.226557i
$408$	−0.526354	−	1.01343i	−0.0260584	−	0.0501724i
$409$	16.9457			0.837911			0.418955	−	0.908007i	$-0.362396\pi$
$409$	16.9457			0.837911			0.418955	+	0.908007i	$0.362396\pi$
$410$	5.40668	−	5.97321i	0.267017	−	0.294996i
$411$	3.81092	−	3.81092i	0.187979	−	0.187979i
$412$	−24.2426	−	12.1940i	−1.19435	−	0.600757i
$413$		−	5.04594i		−	0.248294i
$414$	−2.47463	−	15.3659i	−0.121622	−	0.755190i
$415$	1.75475	−	15.8975i	0.0861373	−	0.780378i
$416$	−20.8375	+	0.270573i	−1.02164	+	0.0132659i
$417$	−2.10250	−	2.10250i	−0.102960	−	0.102960i
$418$	−10.4004	−	7.51515i	−0.508701	−	0.367578i
$419$	6.56956	−	6.56956i	0.320944	−	0.320944i	−0.528185	−	0.849129i	$-0.677127\pi$
$419$	6.56956	−	6.56956i	0.320944	−	0.320944i	0.849129	+	0.528185i	$0.177127\pi$
$420$	−1.26347	−	0.820544i	−0.0616511	−	0.0400385i
$421$	13.8805	+	13.8805i	0.676493	+	0.676493i	0.959205	−	0.282712i	$-0.0912341\pi$
$421$	13.8805	+	13.8805i	0.676493	+	0.676493i	−0.282712	+	0.959205i	$0.591234\pi$
$422$	22.6681	−	3.65064i	1.10346	−	0.177710i
$423$	11.5164	−	11.5164i	0.559946	−	0.559946i
$424$	−16.3836	−	5.18258i	−0.795656	−	0.251688i
$425$	−1.56164	−	2.46051i	−0.0757507	−	0.119352i
$426$	−1.70754	+	2.36311i	−0.0827305	+	0.114493i
$427$	3.31201			0.160279
$428$	3.31660	+	10.0299i	0.160314	+	0.484813i
$429$	2.15295	+	2.15295i	0.103946	+	0.103946i
$430$	9.14066	−	10.0984i	0.440802	−	0.486990i
$431$			12.3740i			0.596035i	0.954560	+	0.298017i	$0.0963254\pi$
$431$			12.3740i			0.596035i	−0.954560	+	0.298017i	$0.903675\pi$
$432$	12.2803	−	9.11852i	0.590834	−	0.438715i
$433$	−0.145326	+	0.145326i	−0.00698392	+	0.00698392i	−0.710590	−	0.703606i	$-0.751572\pi$
$433$	−0.145326	+	0.145326i	−0.00698392	+	0.00698392i	0.703606	+	0.710590i	$0.251572\pi$
$434$	0.957873	+	5.94777i	0.0459794	+	0.285502i
$435$	−7.23082	+	5.79324i	−0.346691	+	0.277765i
$436$	−1.95704	+	3.89074i	−0.0937253	+	0.186332i
$437$			33.2084i			1.58857i
$438$	9.39886	−	1.51366i	0.449095	−	0.0723256i
$439$		−	3.65842i		−	0.174607i	−0.996182	−	0.0873035i	$-0.972175\pi$
$439$		−	3.65842i		−	0.174607i	0.996182	−	0.0873035i	$-0.0278250\pi$
$440$	−2.72240	−	7.03784i	−0.129785	−	0.335516i
$441$			17.0450i			0.811669i
$442$	0.482807	+	2.99792i	0.0229648	+	0.142596i
$443$		−	3.94027i		−	0.187208i	−0.995610	−	0.0936039i	$-0.970161\pi$
$443$		−	3.94027i		−	0.187208i	0.995610	−	0.0936039i	$-0.0298387\pi$
$444$	−7.12607	+	2.35639i	−0.338188	+	0.111829i
$445$	0.272195	−	2.46601i	0.0129033	−	0.116900i
$446$	−4.30184	+	0.692800i	−0.203698	+	0.0328050i
$447$	−7.72864	+	7.72864i	−0.365552	+	0.365552i
$448$	−0.668398	−	3.83262i	−0.0315788	−	0.181074i
$449$			38.0014i			1.79340i	0.442642	+	0.896698i	$0.354041\pi$
$449$			38.0014i			1.79340i	−0.442642	+	0.896698i	$0.645959\pi$
$450$	13.3359	−	11.8199i	0.628662	−	0.557197i
$451$	−2.14949	−	2.14949i	−0.101215	−	0.101215i
$452$	7.57165	+	3.80855i	0.356140	+	0.179139i
$453$	2.20466			0.103584
$454$	10.6870	+	7.72221i	0.501564	+	0.362421i
$455$	2.50476	+	3.12631i	0.117425	+	0.146564i
$456$	−13.2224	+	6.86742i	−0.619195	+	0.321596i
$457$	−18.1142	+	18.1142i	−0.847348	+	0.847348i	−0.989801	−	0.142454i	$-0.954501\pi$
$457$	−18.1142	+	18.1142i	−0.847348	+	0.847348i	0.142454	+	0.989801i	$0.454501\pi$
$458$	−0.865778	−	5.37592i	−0.0404551	−	0.251200i
$459$	−1.57596	−	1.57596i	−0.0735595	−	0.0735595i
$460$	−10.6368	+	16.3786i	−0.495946	+	0.763655i
$461$	12.4144	−	12.4144i	0.578197	−	0.578197i	−0.356209	−	0.934406i	$-0.615931\pi$
$461$	12.4144	−	12.4144i	0.578197	−	0.578197i	0.934406	+	0.356209i	$0.115931\pi$
$462$	−0.332913	+	0.460726i	−0.0154885	+	0.0214349i
$463$	8.56578	+	8.56578i	0.398085	+	0.398085i	0.877557	−	0.479472i	$-0.159172\pi$
$463$	8.56578	+	8.56578i	0.398085	+	0.398085i	−0.479472	+	0.877557i	$0.659172\pi$
$464$	−23.6698	−	3.49729i	−1.09884	−	0.162358i
$465$	13.4864	+	1.48861i	0.625416	+	0.0690327i
$466$	−24.4643	+	3.93991i	−1.13329	+	0.182513i
$467$		−	34.3465i		−	1.58937i	−0.607023	−	0.794684i	$-0.707636\pi$
$467$		−	34.3465i		−	1.58937i	0.607023	−	0.794684i	$-0.292364\pi$
$468$	−17.6292	+	5.82946i	−0.814908	+	0.269467i
$469$	4.93889	−	4.93889i	0.228057	−	0.228057i
$470$	−20.4111	+	1.01614i	−0.941495	+	0.0468711i
$471$	−4.88677			−0.225170
$472$	−13.5269	−	26.0445i	−0.622627	−	1.19879i
$473$	−3.63397	−	3.63397i	−0.167090	−	0.167090i
$474$	−5.83248	+	8.07172i	−0.267895	+	0.370746i
$475$	−32.1027	+	20.3749i	−1.47297	+	0.934866i
$476$	−0.538227	+	0.177976i	−0.0246696	+	0.00815753i
$477$	−15.3108			−0.701034
$478$	−20.8876	+	28.9068i	−0.955375	+	1.32217i
$479$	23.4504			1.07148			0.535738	−	0.844384i	$-0.320034\pi$
$479$	23.4504			1.07148			0.535738	+	0.844384i	$0.320034\pi$
$480$	−8.72104	−	0.848162i	−0.398059	−	0.0387131i
$481$	19.9576			0.909988
$482$	9.95740	−	13.7803i	0.453547	−	0.627675i
$483$	1.47109			0.0669370
$484$	18.1845	−	6.01309i	0.826567	−	0.273322i
$485$	−17.6681	+	14.1555i	−0.802269	+	0.642767i
$486$	12.3198	−	17.0497i	0.558837	−	0.773389i
$487$	−5.31215	−	5.31215i	−0.240716	−	0.240716i	0.576430	−	0.817146i	$-0.304445\pi$
$487$	−5.31215	−	5.31215i	−0.240716	−	0.240716i	−0.817146	+	0.576430i	$0.804445\pi$
$488$	17.0948	−	8.87868i	0.773847	−	0.401919i
$489$	−11.0978			−0.501859
$490$	14.3530	−	15.8569i	0.648401	−	0.716343i
$491$	−3.71980	+	3.71980i	−0.167872	+	0.167872i	−0.786044	−	0.618171i	$-0.787874\pi$
$491$	−3.71980	+	3.71980i	−0.167872	+	0.167872i	0.618171	+	0.786044i	$0.287874\pi$
$492$	−3.35128	+	1.10817i	−0.151087	+	0.0499602i
$493$			3.48642i			0.157021i
$494$	39.1142	−	6.29925i	1.75983	−	0.283417i
$495$	−4.20398	−	5.24719i	−0.188955	−	0.235844i
$496$	20.8885	+	28.1314i	0.937923	+	1.26314i
$497$	1.02338	+	1.02338i	0.0459050	+	0.0459050i
$498$	−4.10396	+	5.67958i	−0.183903	+	0.254508i
$499$	−13.6065	+	13.6065i	−0.609111	+	0.609111i	−0.942714	−	0.333603i	$-0.891736\pi$
$499$	−13.6065	+	13.6065i	−0.609111	+	0.609111i	0.333603	+	0.942714i	$0.391736\pi$
$500$	−22.3595	−	0.233636i	−0.999945	−	0.0104485i
$501$	−11.5006	−	11.5006i	−0.513810	−	0.513810i
$502$	−2.38152	−	14.7877i	−0.106292	−	0.660007i
$503$	−9.31208	+	9.31208i	−0.415205	+	0.415205i	−0.883547	−	0.468342i	$-0.844852\pi$
$503$	−9.31208	+	9.31208i	−0.415205	+	0.415205i	0.468342	+	0.883547i	$0.344852\pi$
$504$	−1.59774	−	3.07626i	−0.0711691	−	0.137028i
$505$	−2.35288	+	1.88509i	−0.104702	+	0.0838856i
$506$	5.97247	+	4.31560i	0.265509	+	0.191852i
$507$	−0.395636			−0.0175708
$508$	−26.6632	−	13.4116i	−1.18299	−	0.595044i
$509$	−7.94836	−	7.94836i	−0.352305	−	0.352305i	0.508662	−	0.860966i	$-0.330140\pi$
$509$	−7.94836	−	7.94836i	−0.352305	−	0.352305i	−0.860966	+	0.508662i	$0.830140\pi$
$510$	0.0634831	+	1.27518i	0.00281108	+	0.0564659i
$511$		−	4.72585i		−	0.209059i
$512$	−13.7242	−	17.9902i	−0.606531	−	0.795060i
$513$	−20.5618	+	20.5618i	−0.907824	+	0.907824i
$514$	−19.9054	+	3.20571i	−0.877989	+	0.141398i
$515$	18.9702	+	23.6776i	0.835926	+	1.04336i
$516$	−5.66575	+	1.87350i	−0.249421	+	0.0824762i
$517$			7.71069i			0.339116i
$518$	0.592408	+	3.67847i	0.0260289	+	0.161623i
$519$		−	10.3878i		−	0.455972i
$520$	21.3091	+	9.42171i	0.934465	+	0.413169i
$521$			29.3979i			1.28795i	0.765048	+	0.643974i	$0.222715\pi$
$521$			29.3979i			1.28795i	−0.765048	+	0.643974i	$0.777285\pi$
$522$	−21.0477	+	3.38968i	−0.921233	+	0.148362i
$523$			19.5121i			0.853205i	0.904439	+	0.426602i	$0.140290\pi$
$523$			19.5121i			0.853205i	−0.904439	+	0.426602i	$0.859710\pi$
$524$	−1.08098	+	2.14906i	−0.0472228	+	0.0938821i
$525$	0.902587	+	1.42211i	0.0393921	+	0.0620660i
$526$	1.21984	+	7.57438i	0.0531874	+	0.330259i
$527$	3.61018	−	3.61018i	0.157262	−	0.157262i
$528$	−0.483226	+	3.27048i	−0.0210297	+	0.142329i
$529$			3.92999i			0.170869i
$530$	14.2436	+	12.8926i	0.618702	+	0.560021i
$531$	−18.4902	−	18.4902i	−0.802406	−	0.802406i
$532$	2.32208	+	7.02232i	0.100675	+	0.304456i
$533$	9.38575			0.406542
$534$	−0.636604	+	0.881012i	−0.0275485	+	0.0381251i
$535$	1.29581	−	11.7396i	0.0560227	−	0.507549i
$536$	12.2520	−	38.7319i	0.529205	−	1.67296i
$537$	6.86692	−	6.86692i	0.296329	−	0.296329i
$538$	26.5085	−	4.26913i	1.14286	−	0.184055i
$539$	−5.70618	−	5.70618i	−0.245783	−	0.245783i
$540$	−16.7273	+	3.55513i	−0.719827	+	0.152989i
$541$	8.47183	−	8.47183i	0.364232	−	0.364232i	−0.501136	−	0.865369i	$-0.667084\pi$
$541$	8.47183	−	8.47183i	0.364232	−	0.364232i	0.865369	+	0.501136i	$0.167084\pi$
$542$	14.1587	+	10.2309i	0.608170	+	0.439453i
$543$	0.720526	+	0.720526i	0.0309207	+	0.0309207i
$544$	−2.30093	+	2.36147i	−0.0986516	+	0.101247i
$545$	3.80006	−	3.04456i	0.162777	−	0.130415i
$546$	−0.279050	−	1.73272i	−0.0119422	−	0.0741534i
$547$			9.97988i			0.426709i	0.976975	+	0.213355i	$0.0684389\pi$
$547$			9.97988i			0.426709i	−0.976975	+	0.213355i	$0.931561\pi$
$548$	−13.9010	−	6.99219i	−0.593820	−	0.298692i
$549$	12.1364	−	12.1364i	0.517971	−	0.517971i
$550$	−0.507511	+	8.42144i	−0.0216403	+	0.359092i
$551$	45.4879			1.93785
$552$	7.59300	−	3.94364i	0.323180	−	0.167852i
$553$	3.49559	+	3.49559i	0.148648	+	0.148648i
$554$	−7.78098	−	5.62240i	−0.330582	−	0.238873i
$555$	8.34081	+	0.920650i	0.354048	+	0.0390794i
$556$	−3.85762	+	7.66922i	−0.163600	+	0.325247i
$557$	13.4866			0.571445			0.285722	−	0.958312i	$-0.407766\pi$
$557$	13.4866			0.571445			0.285722	+	0.958312i	$0.407766\pi$
$558$	25.3048	+	18.2848i	1.07124	+	0.774059i
$559$	15.8678			0.671135
$560$	−1.10403	+	4.20723i	−0.0466537	+	0.177788i
$561$	0.481724			0.0203384
$562$	−24.7033	−	17.8502i	−1.04205	−	0.752965i
$563$	−20.3451			−0.857445			−0.428723	−	0.903436i	$-0.641036\pi$
$563$	−20.3451			−0.857445			−0.428723	+	0.903436i	$0.641036\pi$
$564$	7.99853	+	4.02327i	0.336799	+	0.169410i
$565$	−5.92493	−	7.39519i	−0.249264	−	0.311118i
$566$	11.3116	+	8.17354i	0.475461	+	0.343560i
$567$	−1.68896	−	1.68896i	−0.0709298	−	0.0709298i
$568$	8.02559	+	2.53872i	0.336746	+	0.106522i
$569$	17.1460			0.718797			0.359399	−	0.933184i	$-0.382982\pi$
$569$	17.1460			0.718797			0.359399	+	0.933184i	$0.382982\pi$
$570$	16.6375	−	0.828274i	0.696867	−	0.0346926i
$571$	6.24329	−	6.24329i	0.261274	−	0.261274i	−0.564298	−	0.825571i	$-0.690853\pi$
$571$	6.24329	−	6.24329i	0.261274	−	0.261274i	0.825571	+	0.564298i	$0.190853\pi$
$572$	3.95019	−	7.85325i	0.165166	−	0.328361i
$573$			2.13645i			0.0892516i
$574$	0.278600	+	1.72993i	0.0116285	+	0.0722057i
$575$	18.4351	−	11.7004i	0.768795	−	0.487939i
$576$	−16.4934	−	11.5949i	−0.687225	−	0.483120i
$577$	−10.0373	−	10.0373i	−0.417859	−	0.417859i	0.466606	−	0.884465i	$-0.345477\pi$
$577$	−10.0373	−	10.0373i	−0.417859	−	0.417859i	−0.884465	+	0.466606i	$0.845477\pi$
$578$	−19.0973	−	13.7994i	−0.794343	−	0.573979i
$579$	−8.37596	+	8.37596i	−0.348093	+	0.348093i
$580$	22.4349	+	14.5700i	0.931559	+	0.604988i
$581$	2.45963	+	2.45963i	0.102043	+	0.102043i
$582$	9.79235	−	1.57703i	0.405906	−	0.0653701i
$583$	5.12561	−	5.12561i	0.212281	−	0.212281i
$584$	−12.6688	−	24.3923i	−0.524240	−	1.00936i
$585$	20.6343	+	2.27759i	0.853124	+	0.0941669i
$586$	11.7593	−	16.2739i	0.485771	−	0.672270i
$587$	30.6857			1.26654			0.633268	−	0.773933i	$-0.281713\pi$
$587$	30.6857			1.26654			0.633268	+	0.773933i	$0.281713\pi$
$588$	−8.89655	+	2.94183i	−0.366887	+	0.121319i
$589$	−47.1025	−	47.1025i	−1.94083	−	1.94083i
$590$	1.63147	+	32.7712i	0.0671666	+	1.34917i
$591$			9.01817i			0.370958i
$592$	12.9188	+	17.3982i	0.530958	+	0.715062i
$593$	−2.10671	+	2.10671i	−0.0865123	+	0.0865123i	−0.749039	−	0.662526i	$-0.769484\pi$
$593$	−2.10671	+	2.10671i	−0.0865123	+	0.0865123i	0.662526	+	0.749039i	$0.269484\pi$
$594$	1.02589	+	6.37011i	0.0420928	+	0.261369i
$595$	0.629976	+	0.0695360i	0.0258265	+	0.00285070i
$596$	28.1915	+	14.1803i	1.15477	+	0.580850i
$597$		−	7.36210i		−	0.301311i
$598$	−22.4615	+	3.61737i	−0.918518	+	0.147925i
$599$		−	32.1322i		−	1.31289i	−0.754375	−	0.656444i	$-0.772060\pi$
$599$		−	32.1322i		−	1.31289i	0.754375	−	0.656444i	$-0.227940\pi$
$600$	8.47100	+	4.92057i	0.345827	+	0.200882i
$601$		−	14.9811i		−	0.611091i	−0.952177	−	0.305546i	$-0.901161\pi$
$601$		−	14.9811i		−	0.611091i	0.952177	−	0.305546i	$-0.0988388\pi$
$602$	0.471008	+	2.92465i	0.0191968	+	0.119200i
$603$		−	36.1959i		−	1.47401i
$604$	−1.99840	−	6.04345i	−0.0813136	−	0.245905i
$605$	−21.2843	−	2.34934i	−0.865330	−	0.0955141i
$606$	1.30405	−	0.210014i	0.0529735	−	0.00853125i
$607$	−27.3357	+	27.3357i	−1.10952	+	1.10952i	−0.116310	+	0.993213i	$0.537107\pi$
$607$	−27.3357	+	27.3357i	−1.10952	+	1.10952i	−0.993213	+	0.116310i	$0.962893\pi$
$608$	30.8105	+	30.0206i	1.24953	+	1.21750i
$609$		−	2.01506i		−	0.0816544i
$610$	−21.5101	+	1.07085i	−0.870918	+	0.0433575i
$611$	−16.8344	−	16.8344i	−0.681047	−	0.681047i
$612$	−1.32009	+	2.62443i	−0.0533616	+	0.106086i
$613$	−48.3829			−1.95417			−0.977083	−	0.212859i	$-0.931723\pi$
$613$	−48.3829			−1.95417			−0.977083	+	0.212859i	$0.931723\pi$
$614$	−23.4025	−	16.9103i	−0.944449	−	0.682442i
$615$	3.92255	+	0.432967i	0.158173	+	0.0174589i
$616$	1.56472	+	0.494965i	0.0630444	+	0.0199427i
$617$	31.1565	−	31.1565i	1.25432	−	1.25432i	0.300549	−	0.953766i	$-0.402830\pi$
$617$	31.1565	−	31.1565i	1.25432	−	1.25432i	0.953766	−	0.300549i	$-0.0971699\pi$
$618$	−2.11343	−	13.1230i	−0.0850146	−	0.527885i
$619$	−0.198272	−	0.198272i	−0.00796922	−	0.00796922i	0.703111	−	0.711080i	$-0.251794\pi$
$619$	−0.198272	−	0.198272i	−0.00796922	−	0.00796922i	−0.711080	+	0.703111i	$0.751794\pi$
$620$	−8.14403	−	38.3185i	−0.327072	−	1.53891i
$621$	11.8077	−	11.8077i	0.473825	−	0.473825i
$622$	−5.64120	+	7.80700i	−0.226191	+	0.313032i
$623$	0.381537	+	0.381537i	0.0152859	+	0.0152859i
$624$	−6.08529	−	8.19530i	−0.243607	−	0.328075i
$625$	22.6216	+	10.6425i	0.904864	+	0.425700i
$626$	2.38790	−	0.384565i	0.0954395	−	0.0153703i
$627$		−	6.28512i		−	0.251003i
$628$	4.42958	+	13.3957i	0.176759	+	0.534547i
$629$	2.23276	−	2.23276i	0.0890259	−	0.0890259i
$630$	0.192703	+	3.87080i	0.00767745	+	0.154216i
$631$	−32.3314			−1.28709			−0.643547	−	0.765407i	$-0.722538\pi$
$631$	−32.3314			−1.28709			−0.643547	+	0.765407i	$0.722538\pi$
$632$	27.4132	+	8.67157i	1.09044	+	0.344936i
$633$	7.95239	+	7.95239i	0.316079	+	0.316079i
$634$	−2.85076	+	3.94523i	−0.113218	+	0.156685i
$635$	20.8644	+	26.0418i	0.827977	+	1.03344i
$636$	−2.64252	−	7.99138i	−0.104783	−	0.316879i
$637$	24.9161			0.987212
$638$	5.91139	−	8.18092i	0.234034	−	0.323886i
$639$	7.50010			0.296700
$640$	5.58014	+	24.6751i	0.220574	+	0.975370i
$641$	−46.5662			−1.83926			−0.919628	−	0.392790i	$-0.871510\pi$
$641$	−46.5662			−1.83926			−0.919628	+	0.392790i	$0.871510\pi$
$642$	−3.03060	+	4.19413i	−0.119608	+	0.165529i
$643$	−40.2247			−1.58631			−0.793154	−	0.609021i	$-0.791563\pi$
$643$	−40.2247			−1.58631			−0.793154	+	0.609021i	$0.791563\pi$
$644$	−1.33346	−	4.03259i	−0.0525458	−	0.158906i
$645$	6.63156	+	0.731984i	0.261117	+	0.0288218i
$646$	3.67118	−	5.08064i	0.144441	−	0.199895i
$647$	−10.7938	−	10.7938i	−0.424349	−	0.424349i	0.462349	−	0.886698i	$-0.347007\pi$
$647$	−10.7938	−	10.7938i	−0.424349	−	0.424349i	−0.886698	+	0.462349i	$0.847007\pi$
$648$	−13.2452	−	4.18984i	−0.520322	−	0.164593i
$649$	12.3799			0.485956
$650$	−17.2781	−	19.4942i	−0.677704	−	0.764625i
$651$	−2.08659	+	2.08659i	−0.0817799	+	0.0817799i
$652$	10.0595	+	30.4215i	0.393961	+	1.19140i
$653$			3.92443i			0.153575i	0.997047	+	0.0767875i	$0.0244663\pi$
$653$			3.92443i			0.153575i	−0.997047	+	0.0767875i	$0.975534\pi$
$654$	−2.10614	+	0.339188i	−0.0823564	+	0.0132633i
$655$	2.09898	−	1.68167i	0.0820138	−	0.0657084i
$656$	6.07549	+	8.18210i	0.237208	+	0.319457i
$657$	−17.3173	−	17.3173i	−0.675610	−	0.675610i
$658$	2.60312	−	3.60252i	0.101480	−	0.140441i
$659$	−34.6142	+	34.6142i	−1.34838	+	1.34838i	−0.460952	+	0.887425i	$0.652492\pi$
$659$	−34.6142	+	34.6142i	−1.34838	+	1.34838i	−0.887425	+	0.460952i	$0.847508\pi$
$660$	2.01316	−	3.09986i	0.0783622	−	0.120662i
$661$	21.7641	+	21.7641i	0.846525	+	0.846525i	0.989698	−	0.143173i	$-0.0457304\pi$
$661$	21.7641	+	21.7641i	0.846525	+	0.846525i	−0.143173	+	0.989698i	$0.545730\pi$
$662$	0.472104	+	2.93146i	0.0183489	+	0.113934i
$663$	−1.05173	+	1.05173i	−0.0408456	+	0.0408456i
$664$	19.2890	+	6.10166i	0.748559	+	0.236790i
$665$	0.907246	−	8.21938i	0.0351815	−	0.318734i
$666$	15.6501	+	11.3085i	0.606428	+	0.438194i
$667$	−26.1216			−1.01143
$668$	−21.1011	+	41.9505i	−0.816426	+	1.62311i
$669$	−1.50917	−	1.50917i	−0.0583477	−	0.0583477i
$670$	−30.4791	+	33.6728i	−1.17751	+	1.30090i
$671$			8.12584i			0.313695i
$672$	1.32988	−	1.36487i	0.0513012	−	0.0526510i
$673$	29.4450	−	29.4450i	1.13502	−	1.13502i	0.145691	−	0.989330i	$-0.453459\pi$
$673$	29.4450	−	29.4450i	1.13502	−	1.13502i	0.989330	−	0.145691i	$-0.0465405\pi$
$674$	12.2662	−	1.97544i	0.472475	−	0.0760910i
$675$	18.6591	+	4.16995i	0.718189	+	0.160501i
$676$	0.358622	+	1.08453i	0.0137932	+	0.0417126i
$677$		−	34.7351i		−	1.33498i	−0.744619	−	0.667490i	$-0.767369\pi$
$677$		−	34.7351i		−	1.33498i	0.744619	−	0.667490i	$-0.232631\pi$
$678$	0.660084	+	4.09869i	0.0253504	+	0.157409i
$679$		−	4.92370i		−	0.188954i
$680$	3.43801	−	1.32990i	0.131842	−	0.0509994i
$681$			6.45828i			0.247482i
$682$	−14.5925	+	2.35009i	−0.558777	+	0.0899897i
$683$			22.2693i			0.852110i	0.904697	+	0.426055i	$0.140097\pi$
$683$			22.2693i			0.852110i	−0.904697	+	0.426055i	$0.859903\pi$
$684$	34.2414	+	17.2234i	1.30925	+	0.658554i
$685$	10.8777	+	13.5770i	0.415616	+	0.518750i
$686$	1.50505	+	9.34535i	0.0574629	+	0.356807i
$687$	1.88597	−	1.88597i	0.0719543	−	0.0719543i
$688$	10.2714	+	13.8328i	0.391592	+	0.527372i
$689$			22.3810i			0.852650i
$690$	−9.55412	+	0.475639i	−0.363719	+	0.0181073i
$691$	15.7043	+	15.7043i	0.597420	+	0.597420i	0.939625	−	0.342205i	$-0.111174\pi$
$691$	15.7043	+	15.7043i	0.597420	+	0.597420i	−0.342205	+	0.939625i	$0.611174\pi$
$692$	−28.4751	+	9.41591i	−1.08246	+	0.357939i
$693$	1.46227			0.0555470
$694$	8.40717	−	11.6349i	0.319132	−	0.441655i
$695$	7.49048	−	6.00128i	0.284130	−	0.227641i
$696$	−5.40188	−	10.4007i	−0.204758	−	0.394237i
$697$	1.05003	−	1.05003i	0.0397728	−	0.0397728i
$698$	7.89023	−	1.27070i	0.298650	−	0.0480968i
$699$	−8.58253	−	8.58253i	−0.324621	−	0.324621i
$700$	3.08018	−	3.76326i	0.116420	−	0.142238i
$701$	−21.5588	+	21.5588i	−0.814266	+	0.814266i	−0.985270	−	0.171004i	$-0.945299\pi$
$701$	−21.5588	+	21.5588i	−0.814266	+	0.814266i	0.171004	+	0.985270i	$0.445299\pi$
$702$	−16.1474	−	11.6678i	−0.609443	−	0.440373i
$703$	−29.1311	−	29.1311i	−1.09870	−	1.09870i
$704$	9.40314	−	1.63988i	0.354394	−	0.0618053i
$705$	−6.25897	−	7.81212i	−0.235726	−	0.294221i
$706$	−7.20702	−	44.7509i	−0.271240	−	1.68422i
$707$		−	0.655691i		−	0.0246598i
$708$	6.45958	−	12.8421i	0.242766	−	0.482635i
$709$	2.96687	−	2.96687i	0.111423	−	0.111423i	−0.649197	−	0.760620i	$-0.724895\pi$
$709$	2.96687	−	2.96687i	0.111423	−	0.111423i	0.760620	+	0.649197i	$0.224895\pi$
$710$	−6.97731	−	6.31555i	−0.261854	−	0.237018i
$711$	25.6183			0.960760
$712$	2.99210	+	0.946485i	0.112134	+	0.0354710i
$713$	27.0488	+	27.0488i	1.01299	+	1.01299i
$714$	−0.225067	−	0.162629i	−0.00842290	−	0.00608624i
$715$	−7.67023	+	6.14529i	−0.286850	+	0.229821i
$716$	−25.0482	−	12.5993i	−0.936096	−	0.470857i
$717$	−17.4688			−0.652385
$718$	4.95047	+	3.57712i	0.184750	+	0.133497i
$719$	25.8357			0.963509			0.481755	−	0.876306i	$-0.340000\pi$
$719$	25.8357			0.963509			0.481755	+	0.876306i	$0.340000\pi$
$720$	11.3713	+	19.4624i	0.423783	+	0.725322i
$721$	−6.59839			−0.245737
$722$	−44.5085	−	32.1611i	−1.65644	−	1.19691i
$723$	8.32763			0.309708
$724$	1.32201	−	2.62824i	0.0491320	−	0.0976777i
$725$	−16.0268	−	25.2518i	−0.595222	−	0.937829i
$726$	7.60407	+	5.49457i	0.282214	+	0.203923i
$727$	28.9620	+	28.9620i	1.07414	+	1.07414i	0.997022	+	0.0771198i	$0.0245724\pi$
$727$	28.9620	+	28.9620i	1.07414	+	1.07414i	0.0771198	+	0.997022i	$0.475428\pi$
$728$	−4.49682	+	2.33555i	−0.166663	+	0.0865612i
$729$	−4.43146			−0.164128
$730$	1.52798	+	30.6923i	0.0565530	+	1.13597i
$731$	1.77521	−	1.77521i	0.0656584	−	0.0656584i
$732$	8.42918	+	4.23988i	0.311551	+	0.156711i
$733$		−	21.1673i		−	0.781832i	−0.920426	−	0.390916i	$-0.872158\pi$
$733$		−	21.1673i		−	0.781832i	0.920426	−	0.390916i	$-0.127842\pi$
$734$	−2.05725	−	12.7742i	−0.0759346	−	0.471504i
$735$	10.4131	+	1.14939i	0.384093	+	0.0423957i
$736$	−17.6930	−	17.2394i	−0.652173	−	0.635453i
$737$	12.1173	+	12.1173i	0.446347	+	0.446347i
$738$	7.35999	+	5.31820i	0.270925	+	0.195765i
$739$	−2.23302	+	2.23302i	−0.0821431	+	0.0821431i	−0.746985	−	0.664841i	$-0.768499\pi$
$739$	−2.23302	+	2.23302i	−0.0821431	+	0.0821431i	0.664841	+	0.746985i	$0.268499\pi$
$740$	−5.03677	−	23.6985i	−0.185155	−	0.871175i
$741$	13.7220	+	13.7220i	0.504091	+	0.504091i
$742$	−4.12514	+	0.664344i	−0.151439	+	0.0243888i
$743$	−18.4514	+	18.4514i	−0.676915	+	0.676915i	−0.959301	−	0.282386i	$-0.908874\pi$
$743$	−18.4514	+	18.4514i	−0.676915	+	0.676915i	0.282386	+	0.959301i	$0.408874\pi$
$744$	−5.17624	+	16.3635i	−0.189770	+	0.599915i
$745$	−22.0603	−	27.5345i	−0.808226	−	1.00879i
$746$	−13.9011	+	19.2381i	−0.508955	+	0.704356i
$747$	18.0260			0.659538
$748$	−0.436655	−	1.32051i	−0.0159657	−	0.0482827i
$749$	1.81634	+	1.81634i	0.0663675	+	0.0663675i
$750$	−6.32172	−	8.94418i	−0.230836	−	0.326595i
$751$			42.4243i			1.54808i	0.633134	+	0.774042i	$0.281768\pi$
$751$			42.4243i			1.54808i	−0.633134	+	0.774042i	$0.718232\pi$
$752$	3.77845	−	25.5726i	0.137786	−	0.932537i
$753$	5.18780	−	5.18780i	0.189054	−	0.189054i
$754$	4.95496	+	30.7671i	0.180449	+	1.12047i
$755$	−0.780782	+	7.07365i	−0.0284156	+	0.257437i
$756$	1.67123	−	3.32253i	0.0607821	−	0.120839i
$757$		−	19.7595i		−	0.718170i	−0.933305	−	0.359085i	$-0.883089\pi$
$757$		−	19.7595i		−	0.718170i	0.933305	−	0.359085i	$-0.116911\pi$
$758$	14.4349	−	2.32471i	0.524300	−	0.0844372i
$759$			3.60925i			0.131007i
$760$	−17.3514	−	44.8562i	−0.629402	−	1.62711i
$761$			48.0351i			1.74127i	0.491928	+	0.870636i	$0.336292\pi$
$761$			48.0351i			1.74127i	−0.491928	+	0.870636i	$0.663708\pi$
$762$	−2.32445	−	14.4333i	−0.0842061	−	0.522865i
$763$			1.05899i			0.0383379i
$764$	5.85649	−	1.93657i	0.211880	−	0.0700628i
$765$	2.56327	−	2.05366i	0.0926753	−	0.0742502i
$766$	10.4946	−	1.69013i	0.379186	−	0.0610669i
$767$	−27.0286	+	27.0286i	−0.975946	+	0.975946i
$768$	3.20525	−	10.6098i	0.115659	−	0.382848i
$769$			24.0184i			0.866127i	0.901363	+	0.433064i	$0.142567\pi$
$769$			24.0184i			0.866127i	−0.901363	+	0.433064i	$0.857433\pi$
$770$	−1.36034	−	1.23132i	−0.0490233	−	0.0443737i
$771$	−6.98319	−	6.98319i	−0.251493	−	0.251493i
$772$	30.5527	+	15.3680i	1.09962	+	0.553107i
$773$	22.4630			0.807937			0.403969	−	0.914773i	$-0.367630\pi$
$773$	22.4630			0.807937			0.403969	+	0.914773i	$0.367630\pi$
$774$	12.4430	+	8.99106i	0.447253	+	0.323177i
$775$	−9.55244	+	42.7439i	−0.343134	+	1.53541i
$776$	−13.1992	−	25.4135i	−0.473824	−	0.912292i
$777$	−1.29048	+	1.29048i	−0.0462956	+	0.0462956i
$778$	−0.409725	−	2.54412i	−0.0146893	−	0.0912113i
$779$	−13.6999	−	13.6999i	−0.490850	−	0.490850i
$780$	2.37254	+	11.1630i	0.0849504	+	0.399701i
$781$	−2.51081	+	2.51081i	−0.0898440	+	0.0898440i
$782$	−2.10819	+	2.91757i	−0.0753886	+	0.104332i
$783$	−16.1738	−	16.1738i	−0.578005	−	0.578005i
$784$	16.1284	+	21.7208i	0.576016	+	0.775743i
$785$	1.73065	−	15.6792i	0.0617697	−	0.559615i
$786$	−1.16333	+	0.187352i	−0.0414946	+	0.00668261i
$787$			26.1054i			0.930556i	0.885165	+	0.465278i	$0.154046\pi$
$787$			26.1054i			0.930556i	−0.885165	+	0.465278i	$0.845954\pi$
$788$	24.7208	−	8.17446i	0.880642	−	0.291203i
$789$	−2.65724	+	2.65724i	−0.0946001	+	0.0946001i
$790$	−23.8326	−	21.5721i	−0.847924	−	0.767503i
$791$	2.06087			0.0732759
$792$	7.54745	−	3.91998i	0.268187	−	0.139290i
$793$	−17.7408	−	17.7408i	−0.629994	−	0.629994i
$794$	7.90040	−	10.9336i	0.280375	−	0.388018i
$795$	−1.03244	+	9.35363i	−0.0366170	+	0.331739i
$796$	−20.1812	+	6.67333i	−0.715302	+	0.236530i
$797$	43.4888			1.54045			0.770227	−	0.637770i	$-0.220143\pi$
$797$	43.4888			1.54045			0.770227	+	0.637770i	$0.220143\pi$
$798$	−2.12185	+	2.93647i	−0.0751125	+	0.103950i
$799$	−3.76670			−0.133256
$800$	5.80990	−	27.6811i	0.205411	−	0.978676i
$801$	2.79618			0.0987983
$802$	−20.3842	+	28.2103i	−0.719793	+	0.996139i
$803$	11.5946			0.409165
$804$	18.8922	−	6.24710i	0.666276	−	0.220318i
$805$	−0.520989	+	4.72001i	−0.0183625	+	0.166358i
$806$	26.7284	−	36.9901i	0.941467	−	1.30292i
$807$	9.29969	+	9.29969i	0.327364	+	0.327364i
$808$	−1.75775	−	3.38433i	−0.0618373	−	0.119060i
$809$	−36.6271			−1.28774			−0.643870	−	0.765135i	$-0.722672\pi$
$809$	−36.6271			−1.28774			−0.643870	+	0.765135i	$0.722672\pi$
$810$	11.5152	+	10.4230i	0.404602	+	0.366228i
$811$	18.7904	−	18.7904i	0.659821	−	0.659821i	−0.295516	−	0.955338i	$-0.595492\pi$
$811$	18.7904	−	18.7904i	0.659821	−	0.659821i	0.955338	+	0.295516i	$0.0954917\pi$
$812$	−5.52373	+	1.82654i	−0.193845	+	0.0640990i
$813$			8.55633i			0.300084i
$814$	−9.02493	+	1.45344i	−0.316324	+	0.0509431i
$815$	3.93029	−	35.6073i	0.137672	−	1.24727i
$816$	−1.59764	−	0.236058i	−0.0559287	−	0.00826367i
$817$	−23.1614	−	23.1614i	−0.810314	−	0.810314i
$818$	14.0358	−	19.4245i	0.490750	−	0.679161i
$819$	−3.19250	+	3.19250i	−0.111555	+	0.111555i
$820$	−2.36872	−	11.1451i	−0.0827191	−	0.389202i
$821$	3.91048	+	3.91048i	0.136477	+	0.136477i	0.772045	−	0.635568i	$-0.219234\pi$
$821$	3.91048	+	3.91048i	0.136477	+	0.136477i	−0.635568	+	0.772045i	$0.719234\pi$
$822$	−1.21186	−	7.52488i	−0.0422686	−	0.262460i
$823$	35.4412	−	35.4412i	1.23540	−	1.23540i	0.273542	−	0.961860i	$-0.411805\pi$
$823$	35.4412	−	35.4412i	1.23540	−	1.23540i	0.961860	−	0.273542i	$-0.0881952\pi$
$824$	−34.0574	+	17.6887i	−1.18645	+	0.616214i
$825$	−3.48908	+	2.21445i	−0.121474	+	0.0770972i
$826$	−5.78405	−	4.17945i	−0.201253	−	0.145422i
$827$	−44.0700			−1.53246			−0.766232	−	0.642565i	$-0.777870\pi$
$827$	−44.0700			−1.53246			−0.766232	+	0.642565i	$0.777870\pi$
$828$	−19.6632	−	9.89061i	−0.683344	−	0.343723i
$829$	−15.1609	−	15.1609i	−0.526561	−	0.526561i	0.392984	−	0.919545i	$-0.371443\pi$
$829$	−15.1609	−	15.1609i	−0.526561	−	0.526561i	−0.919545	+	0.392984i	$0.871443\pi$
$830$	−16.7695	−	15.1790i	−0.582079	−	0.526871i
$831$		−	4.70216i		−	0.163116i
$832$	−16.9492	+	24.1097i	−0.587607	+	0.835854i
$833$	2.78749	−	2.78749i	0.0965808	−	0.0965808i
$834$	−4.15151	+	0.668590i	−0.143755	+	0.0231514i
$835$	40.9728	−	32.8269i	1.41792	−	1.13602i
$836$	−17.2289	+	5.69711i	−0.595874	+	0.197039i
$837$			33.4958i			1.15779i
$838$	−2.08910	−	12.9720i	−0.0721669	−	0.448109i
$839$			40.3143i			1.39180i	0.718137	+	0.695901i	$0.244995\pi$
$839$			40.3143i			1.39180i	−0.718137	+	0.695901i	$0.755005\pi$
$840$	−1.98708	+	0.768648i	−0.0685607	+	0.0265209i
$841$			6.78056i			0.233812i
$842$	27.4078	−	4.41396i	0.944535	−	0.152115i
$843$		−	14.9286i		−	0.514168i
$844$	14.5909	−	29.0077i	0.502238	−	0.998485i
$845$	0.140115	−	1.26940i	0.00482011	−	0.0436687i
$846$	−3.66218	−	22.7398i	−0.125908	−	0.781809i
$847$	3.29307	−	3.29307i	0.113151	−	0.113151i
$848$	−19.5108	+	14.4875i	−0.670005	+	0.497502i
$849$			6.83575i			0.234602i
$850$	−4.11391	−	0.247921i	−0.141106	−	0.00850361i
$851$	16.7286	+	16.7286i	0.573450	+	0.573450i
$852$	1.29446	+	3.91463i	0.0443473	+	0.134113i
$853$	28.6203			0.979941			0.489971	−	0.871739i	$-0.337008\pi$
$853$	28.6203			0.979941			0.489971	+	0.871739i	$0.337008\pi$
$854$	2.74327	−	3.79648i	0.0938728	−	0.129913i
$855$	−26.7944	−	33.4434i	−0.916349	−	1.14374i
$856$	14.2441	+	4.50582i	0.486854	+	0.154006i
$857$	7.19794	−	7.19794i	0.245877	−	0.245877i	−0.573399	−	0.819276i	$-0.694376\pi$
$857$	7.19794	−	7.19794i	0.245877	−	0.245877i	0.819276	+	0.573399i	$0.194376\pi$
$858$	4.25113	−	0.684634i	0.145131	−	0.0233730i
$859$	18.8135	+	18.8135i	0.641910	+	0.641910i	0.951025	−	0.309115i	$-0.100033\pi$
$859$	18.8135	+	18.8135i	0.641910	+	0.641910i	−0.309115	+	0.951025i	$0.600033\pi$
$860$	−4.00460	−	18.8421i	−0.136556	−	0.642509i
$861$	−0.606890	+	0.606890i	−0.0206828	+	0.0206828i
$862$	14.1840	+	10.2491i	0.483110	+	0.349087i
$863$	−19.2328	−	19.2328i	−0.654691	−	0.654691i	0.299428	−	0.954119i	$-0.403204\pi$
$863$	−19.2328	−	19.2328i	−0.654691	−	0.654691i	−0.954119	+	0.299428i	$0.903204\pi$
$864$	−0.280854	−	21.6293i	−0.00955484	−	0.735843i
$865$	33.3292	+	3.67883i	1.13323	+	0.125084i
$866$	0.0462133	+	0.286955i	0.00157039	+	0.00975112i
$867$		−	11.5408i		−	0.391945i
$868$	7.61118	+	3.82843i	0.258340	+	0.129945i
$869$	−8.57624	+	8.57624i	−0.290929	+	0.290929i
$870$	0.651517	+	13.0870i	0.0220885	+	0.443689i
$871$	−52.9103			−1.79280
$872$	2.83888	+	5.46593i	0.0961367	+	0.185100i
$873$	−18.0423	−	18.0423i	−0.610638	−	0.610638i
$874$	38.0660	+	27.5058i	1.28760	+	0.930398i
$875$	−4.88250	+	2.39231i	−0.165059	+	0.0808749i
$876$	6.04981	−	12.0274i	0.204404	−	0.406369i
$877$	35.4397			1.19671			0.598357	−	0.801229i	$-0.295820\pi$
$877$	35.4397			1.19671			0.598357	+	0.801229i	$0.295820\pi$
$878$	−4.19357	−	3.03020i	−0.141526	−	0.102264i
$879$	9.83458			0.331712
$880$	−10.3222	−	2.70868i	−0.347962	−	0.0913095i
$881$	30.2010			1.01750			0.508748	−	0.860915i	$-0.330108\pi$
$881$	30.2010			1.01750			0.508748	+	0.860915i	$0.330108\pi$
$882$	19.5384	+	14.1181i	0.657891	+	0.475380i
$883$	28.9931			0.975696			0.487848	−	0.872928i	$-0.337782\pi$
$883$	28.9931			0.975696			0.487848	+	0.872928i	$0.337782\pi$
$884$	3.83634	+	1.92968i	0.129030	+	0.0649023i
$885$	−12.5428	+	10.0491i	−0.421622	+	0.337798i
$886$	−4.51664	−	3.26364i	−0.151740	−	0.109644i
$887$	5.33418	+	5.33418i	0.179104	+	0.179104i	0.790965	−	0.611861i	$-0.209579\pi$
$887$	5.33418	+	5.33418i	0.179104	+	0.179104i	−0.611861	+	0.790965i	$0.709579\pi$
$888$	−3.20131	+	10.1202i	−0.107429	+	0.339612i
$889$	−7.25724			−0.243400
$890$	−2.60128	−	2.35456i	−0.0871950	−	0.0789250i
$891$	4.14379	−	4.14379i	0.138822	−	0.138822i
$892$	−2.76898	+	5.50493i	−0.0927125	+	0.184319i
$893$			49.1447i			1.64456i
$894$	2.45769	+	15.2606i	0.0821974	+	0.510392i
$895$	19.6006	+	24.4645i	0.655176	+	0.817757i
$896$	−4.94687	−	2.40831i	−0.165263	−	0.0804561i
$897$	−7.87991	−	7.87991i	−0.263103	−	0.263103i
$898$	43.5602	+	31.4758i	1.45362	+	1.05036i
$899$	37.0507	−	37.0507i	1.23571	−	1.23571i
$900$	−2.50304	−	25.0769i	−0.0834347	−	0.835896i
$901$	2.50388	+	2.50388i	0.0834163	+	0.0834163i
$902$	−4.24428	+	0.683531i	−0.141319	+	0.0227591i
$903$	−1.02602	+	1.02602i	−0.0341439	+	0.0341439i
$904$	10.6371	−	5.52467i	0.353785	−	0.183748i
$905$	−2.56699	+	2.05664i	−0.0853295	+	0.0683649i
$906$	1.82607	−	2.52715i	0.0606672	−	0.0839589i
$907$	26.2683			0.872226			0.436113	−	0.899892i	$-0.356355\pi$
$907$	26.2683			0.872226			0.436113	+	0.899892i	$0.356355\pi$
$908$	17.7036	−	5.85407i	0.587514	−	0.194274i
$909$	−2.40270	−	2.40270i	−0.0796924	−	0.0796924i
$910$	5.65826	−	0.281689i	0.187569	−	0.00933789i
$911$		−	33.5196i		−	1.11055i	−0.831665	−	0.555277i	$-0.812612\pi$
$911$		−	33.5196i		−	1.11055i	0.831665	−	0.555277i	$-0.187388\pi$
$912$	−3.07988	+	20.8447i	−0.101985	+	0.690236i
$913$	−6.03459	+	6.03459i	−0.199716	+	0.199716i
$914$	5.76028	+	35.7676i	0.190533	+	1.18309i
$915$	−6.59596	−	8.23273i	−0.218056	−	0.272166i
$916$	−6.87940	−	3.46034i	−0.227302	−	0.114333i
$917$			0.584935i			0.0193163i
$918$	−3.11182	+	0.501151i	−0.102705	+	0.0165405i
$919$		−	25.7545i		−	0.849564i	−0.905296	−	0.424782i	$-0.860351\pi$
$919$		−	25.7545i		−	0.849564i	0.905296	−	0.424782i	$-0.139649\pi$
$920$	9.96411	+	25.7588i	0.328507	+	0.849243i
$921$		−	14.1425i		−	0.466011i
$922$	−3.94775	−	24.5130i	−0.130012	−	0.807292i
$923$		−	10.9635i		−	0.360868i
$924$	0.252375	+	0.763221i	0.00830254	+	0.0251081i
$925$	−5.90782	+	26.4355i	−0.194248	+	0.869193i
$926$	16.9136	−	2.72390i	0.555816	−	0.0895128i
$927$	−24.1790	+	24.1790i	−0.794141	+	0.794141i
$928$	−23.6141	+	24.2354i	−0.775170	+	0.795565i
$929$			9.06425i			0.297388i	0.988883	+	0.148694i	$0.0475070\pi$
$929$			9.06425i			0.297388i	−0.988883	+	0.148694i	$0.952493\pi$
$930$	12.8769	−	14.2261i	0.422249	−	0.466494i
$931$	−36.3688	−	36.3688i	−1.19194	−	1.19194i
$932$	−15.7470	+	31.3062i	−0.515811	+	1.02547i
$933$	−4.71788			−0.154456
$934$	−39.3707	−	28.4486i	−1.28825	−	0.930865i
$935$	−0.170603	+	1.54561i	−0.00557931	+	0.0505469i
$936$	−7.91970	+	25.0363i	−0.258864	+	0.818338i
$937$	3.38621	−	3.38621i	0.110623	−	0.110623i	−0.649629	−	0.760251i	$-0.725076\pi$
$937$	3.38621	−	3.38621i	0.110623	−	0.110623i	0.760251	+	0.649629i	$0.225076\pi$
$938$	−1.57055	−	9.75212i	−0.0512804	−	0.318418i
$939$	0.837719	+	0.837719i	0.0273379	+	0.0273379i
$940$	−15.7414	+	24.2385i	−0.513426	+	0.790572i
$941$	−16.9347	+	16.9347i	−0.552054	+	0.552054i	−0.927033	−	0.374979i	$-0.877650\pi$
$941$	−16.9347	+	16.9347i	−0.552054	+	0.552054i	0.374979	+	0.927033i	$0.377650\pi$
$942$	−4.04761	+	5.60159i	−0.131878	+	0.182510i
$943$	7.86722	+	7.86722i	0.256192	+	0.256192i
$944$	−41.0583	−	6.06651i	−1.33633	−	0.197448i
$945$	−3.24509	+	2.59993i	−0.105563	+	0.0845756i
$946$	−7.17548	+	1.15559i	−0.233295	+	0.0375716i
$947$		−	1.08633i		−	0.0353011i	−0.999844	−	0.0176505i	$-0.994381\pi$
$947$		−	1.08633i		−	0.0353011i	0.999844	−	0.0176505i	$-0.00561863\pi$
$948$	4.42150	+	13.3713i	0.143604	+	0.434279i
$949$	−25.3140	+	25.3140i	−0.821727	+	0.821727i
$950$	−3.23466	+	53.6747i	−0.104946	+	1.74144i
$951$	−2.38416			−0.0773117
$952$	−0.241792	+	0.764372i	−0.00783654	+	0.0247734i
$953$	−10.7914	−	10.7914i	−0.349567	−	0.349567i	0.510381	−	0.859948i	$-0.329504\pi$
$953$	−10.7914	−	10.7914i	−0.349567	−	0.349567i	−0.859948	+	0.510381i	$0.829504\pi$
$954$	−12.6816	+	17.5504i	−0.410583	+	0.568217i
$955$	−6.85482	−	0.756627i	−0.221817	−	0.0244839i
$956$	15.8345	+	47.8859i	0.512124	+	1.54874i
$957$	4.94385			0.159812
$958$	19.4235	−	26.8807i	0.627544	−	0.868475i
$959$	−3.78359			−0.122178
$960$	−8.19569	+	9.29422i	−0.264515	+	0.299970i
$961$	−45.7317			−1.47522
$962$	16.5305	−	22.8770i	0.532964	−	0.737583i
$963$	13.3115			0.428956
$964$	−7.54853	−	22.8279i	−0.243122	−	0.735237i
$965$	−23.9079	−	29.8407i	−0.769624	−	0.960605i
$966$	1.21848	−	1.68628i	0.0392038	−	0.0542552i
$967$	−31.4724	−	31.4724i	−1.01208	−	1.01208i	−0.999926	−	0.0121587i	$-0.996130\pi$
$967$	−31.4724	−	31.4724i	−1.01208	−	1.01208i	−0.0121587	−	0.999926i	$-0.503870\pi$
$968$	8.16917	−	25.8250i	0.262567	−	0.830046i
$969$	3.07030			0.0986323
$970$	1.59195	+	31.9773i	0.0511143	+	1.02673i
$971$	−23.1234	+	23.1234i	−0.742066	+	0.742066i	−0.972975	−	0.230909i	$-0.925830\pi$
$971$	−23.1234	+	23.1234i	−0.742066	+	0.742066i	0.230909	+	0.972975i	$0.425830\pi$
$972$	−9.33942	−	28.2438i	−0.299562	−	0.905921i
$973$			2.08742i			0.0669196i
$974$	−10.4891	+	1.68925i	−0.336094	+	0.0541271i
$975$	2.78284	−	12.4523i	0.0891221	−	0.398791i
$976$	3.98188	−	26.9495i	0.127457	−	0.862632i
$977$	15.3820	+	15.3820i	0.492114	+	0.492114i	0.908972	−	0.416858i	$-0.136869\pi$
$977$	15.3820	+	15.3820i	0.492114	+	0.492114i	−0.416858	+	0.908972i	$0.636869\pi$
$978$	−9.19207	+	12.7211i	−0.293930	+	0.406777i
$979$	−0.936080	+	0.936080i	−0.0299173	+	0.0299173i
$980$	−6.28816	−	29.5865i	−0.200868	−	0.945105i
$981$	3.88052	+	3.88052i	0.123896	+	0.123896i
$982$	1.18289	+	7.34496i	0.0377475	+	0.234387i
$983$	−38.5198	+	38.5198i	−1.22859	+	1.22859i	−0.264093	+	0.964497i	$0.585073\pi$
$983$	−38.5198	+	38.5198i	−1.22859	+	1.22859i	−0.964497	+	0.264093i	$0.914927\pi$
$984$	−1.50552	+	4.75937i	−0.0479943	+	0.151723i
$985$	−28.9348	−	3.19380i	−0.921941	−	0.101763i
$986$	3.99641	+	2.88773i	0.127272	+	0.0919642i
$987$	2.17705			0.0692964
$988$	25.1769	−	50.0533i	0.800982	−	1.59241i
$989$	13.3005	+	13.3005i	0.422931	+	0.422931i
$990$	−9.49681	+	0.472786i	−0.301828	+	0.0150261i
$991$		−	22.0556i		−	0.700619i	−0.936634	−	0.350310i	$-0.886076\pi$
$991$		−	22.0556i		−	0.700619i	0.936634	−	0.350310i	$-0.113924\pi$
$992$	49.5480	−	0.643375i	1.57315	−	0.0204272i
$993$	−1.02841	+	1.02841i	−0.0326356	+	0.0326356i
$994$	2.02073	−	0.325433i	0.0640936	−	0.0103221i
$995$	23.6213	+	2.60730i	0.748847	+	0.0826569i
$996$	3.11114	+	9.40856i	0.0985804	+	0.298122i
$997$			0.840040i			0.0266043i	0.999912	+	0.0133022i	$0.00423434\pi$
$997$			0.840040i			0.0266043i	−0.999912	+	0.0133022i	$0.995766\pi$
$998$	4.32684	+	26.8668i	0.136964	+	0.850455i
$999$			20.7159i			0.655422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.s.b.27.7	yes	18
3.2	odd	2		720.2.z.g.667.3		18
4.3	odd	2		320.2.s.b.207.4		18
5.2	odd	4		400.2.j.d.43.7		18
5.3	odd	4		80.2.j.b.43.3	✓	18
5.4	even	2		400.2.s.d.107.3		18
8.3	odd	2		640.2.s.c.287.6		18
8.5	even	2		640.2.s.d.287.4		18
15.8	even	4		720.2.bd.g.523.7		18
16.3	odd	4		80.2.j.b.67.3	yes	18
16.5	even	4		640.2.j.c.607.4		18
16.11	odd	4		640.2.j.d.607.6		18
16.13	even	4		320.2.j.b.47.6		18
20.3	even	4		320.2.j.b.143.4		18
20.7	even	4		1600.2.j.d.143.6		18
20.19	odd	2		1600.2.s.d.207.6		18
40.3	even	4		640.2.j.c.543.6		18
40.13	odd	4		640.2.j.d.543.4		18
48.35	even	4		720.2.bd.g.307.7		18
80.3	even	4	inner	80.2.s.b.3.7	yes	18
80.13	odd	4		320.2.s.b.303.4		18
80.19	odd	4		400.2.j.d.307.7		18
80.29	even	4		1600.2.j.d.1007.4		18
80.43	even	4		640.2.s.d.223.4		18
80.53	odd	4		640.2.s.c.223.6		18
80.67	even	4		400.2.s.d.243.3		18
80.77	odd	4		1600.2.s.d.943.6		18
240.83	odd	4		720.2.z.g.163.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.3	✓	18	5.3	odd	4
80.2.j.b.67.3	yes	18	16.3	odd	4
80.2.s.b.3.7	yes	18	80.3	even	4	inner
80.2.s.b.27.7	yes	18	1.1	even	1	trivial
320.2.j.b.47.6		18	16.13	even	4
320.2.j.b.143.4		18	20.3	even	4
320.2.s.b.207.4		18	4.3	odd	2
320.2.s.b.303.4		18	80.13	odd	4
400.2.j.d.43.7		18	5.2	odd	4
400.2.j.d.307.7		18	80.19	odd	4
400.2.s.d.107.3		18	5.4	even	2
400.2.s.d.243.3		18	80.67	even	4
640.2.j.c.543.6		18	40.3	even	4
640.2.j.c.607.4		18	16.5	even	4
640.2.j.d.543.4		18	40.13	odd	4
640.2.j.d.607.6		18	16.11	odd	4
640.2.s.c.223.6		18	80.53	odd	4
640.2.s.c.287.6		18	8.3	odd	2
640.2.s.d.223.4		18	80.43	even	4
640.2.s.d.287.4		18	8.5	even	2
720.2.z.g.163.3		18	240.83	odd	4
720.2.z.g.667.3		18	3.2	odd	2
720.2.bd.g.307.7		18	48.35	even	4
720.2.bd.g.523.7		18	15.8	even	4
1600.2.j.d.143.6		18	20.7	even	4
1600.2.j.d.1007.4		18	80.29	even	4
1600.2.s.d.207.6		18	20.19	odd	2
1600.2.s.d.943.6		18	80.77	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.828280 - 1.14628i) q^{2} +0.692712 q^{3} +(-0.627905 - 1.89888i) q^{4} +(-0.245325 + 2.22257i) q^{5} +(0.573759 - 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(-2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +O(q^{10})\)	\(q+(0.828280 - 1.14628i) q^{2} +0.692712 q^{3} +(-0.627905 - 1.89888i) q^{4} +(-0.245325 + 2.22257i) q^{5} +(0.573759 - 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(-2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +(2.34448 + 2.12212i) q^{10} +(0.843672 - 0.843672i) q^{11} +(-0.434957 - 1.31538i) q^{12} +3.68390i q^{13} +(-0.678995 + 0.109350i) q^{14} +(-0.169939 + 1.53960i) q^{15} +(-3.21147 + 2.38463i) q^{16} +(0.412137 + 0.412137i) q^{17} +(-2.08739 + 2.88879i) q^{18} +(5.37721 - 5.37721i) q^{19} +(4.37443 - 0.929720i) q^{20} +(-0.238204 - 0.238204i) q^{21} +(-0.268286 - 1.66588i) q^{22} +(-3.08788 + 3.08788i) q^{23} +(-1.86805 - 0.590917i) q^{24} +(-4.87963 - 1.09050i) q^{25} +(4.22278 + 3.05130i) q^{26} -3.82387 q^{27} +(-0.437052 + 0.868890i) q^{28} +(4.22969 + 4.22969i) q^{29} +(1.62405 + 1.47002i) q^{30} -8.75966i q^{31} +(0.0734474 + 5.65638i) q^{32} +(0.584422 - 0.584422i) q^{33} +(0.813788 - 0.131059i) q^{34} +(0.848640 - 0.679919i) q^{35} +(1.58241 + 4.78546i) q^{36} -5.41752i q^{37} +(-1.70994 - 10.6176i) q^{38} +2.55188i q^{39} +(2.55753 - 5.78438i) q^{40} -2.54777i q^{41} +(-0.470348 + 0.0757484i) q^{42} -4.30732i q^{43} +(-2.13178 - 1.07228i) q^{44} +(0.618255 - 5.60121i) q^{45} +(0.981939 + 6.09720i) q^{46} +(-4.56972 + 4.56972i) q^{47} +(-2.22462 + 1.65186i) q^{48} -6.76350i q^{49} +(-5.29172 + 4.69017i) q^{50} +(0.285492 + 0.285492i) q^{51} +(6.99528 - 2.31314i) q^{52} +6.07536 q^{53} +(-3.16724 + 4.38322i) q^{54} +(1.66815 + 2.08209i) q^{55} +(0.633987 + 1.22067i) q^{56} +(3.72486 - 3.72486i) q^{57} +(8.35177 - 1.34503i) q^{58} +(7.33694 + 7.33694i) q^{59} +(3.03022 - 0.644028i) q^{60} +(-4.81576 + 4.81576i) q^{61} +(-10.0410 - 7.25545i) q^{62} +(0.866609 + 0.866609i) q^{63} +(6.54461 + 4.60087i) q^{64} +(-8.18773 - 0.903753i) q^{65} +(-0.185845 - 1.15397i) q^{66} +14.3626i q^{67} +(0.523815 - 1.04138i) q^{68} +(-2.13901 + 2.13901i) q^{69} +(-0.0764647 - 1.53594i) q^{70} -2.97605 q^{71} +(6.79614 + 2.14981i) q^{72} +(6.87152 + 6.87152i) q^{73} +(-6.20998 - 4.48722i) q^{74} +(-3.38018 - 0.755404i) q^{75} +(-13.5870 - 6.83429i) q^{76} -0.580231 q^{77} +(2.92517 + 2.11367i) q^{78} -10.1654 q^{79} +(-4.51215 - 7.72273i) q^{80} +4.91161 q^{81} +(-2.92046 - 2.11027i) q^{82} -7.15276 q^{83} +(-0.302751 + 0.601890i) q^{84} +(-1.01711 + 0.814896i) q^{85} +(-4.93739 - 3.56767i) q^{86} +(2.92996 + 2.92996i) q^{87} +(-2.99484 + 1.55545i) q^{88} -1.10953 q^{89} +(-5.90845 - 5.34806i) q^{90} +(1.26679 - 1.26679i) q^{91} +(7.80240 + 3.92461i) q^{92} -6.06792i q^{93} +(1.45316 + 9.02318i) q^{94} +(10.6321 + 13.2704i) q^{95} +(0.0508779 + 3.91824i) q^{96} +(7.15920 + 7.15920i) q^{97} +(-7.75285 - 5.60207i) q^{98} +(-2.12618 + 2.12618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

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