LMFDB - Embedded newform 80.2.l.a.61.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(21,80)]

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([0, 1, 0]))

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.l (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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.5
Root			$-1.39563 - 0.228522i$ of defining polynomial
Character	$\chi$	$=$	80.61
Dual form			80.2.l.a.21.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.114638 - 1.40956i) q^{2} +(1.42313 + 1.42313i) q^{3} +(-1.97372 - 0.323179i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.16913 - 1.84284i) q^{6} -0.690576i q^{7} +(-0.681804 + 2.74502i) q^{8} +1.05061i q^{9} +O(q^{10})$	\(q+(0.114638 - 1.40956i) q^{2} +(1.42313 + 1.42313i) q^{3} +(-1.97372 - 0.323179i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.16913 - 1.84284i) q^{6} -0.690576i q^{7} +(-0.681804 + 2.74502i) q^{8} +1.05061i q^{9} +(-0.915648 - 1.07777i) q^{10} +(-3.06057 + 3.06057i) q^{11} +(-2.34893 - 3.26878i) q^{12} +(-2.33686 - 2.33686i) q^{13} +(-0.973408 - 0.0791665i) q^{14} +2.01261 q^{15} +(3.79111 + 1.27573i) q^{16} -5.28770 q^{17} +(1.48089 + 0.120440i) q^{18} +(5.38887 + 5.38887i) q^{19} +(-1.62415 + 1.16711i) q^{20} +(0.982780 - 0.982780i) q^{21} +(3.96320 + 4.66492i) q^{22} -1.60841i q^{23} +(-4.87682 + 2.93623i) q^{24} -1.00000i q^{25} +(-3.56183 + 3.02605i) q^{26} +(2.77424 - 2.77424i) q^{27} +(-0.223180 + 1.36300i) q^{28} +(1.70319 + 1.70319i) q^{29} +(0.230722 - 2.83690i) q^{30} -4.69807 q^{31} +(2.23282 - 5.19755i) q^{32} -8.71119 q^{33} +(-0.606174 + 7.45333i) q^{34} +(-0.488311 - 0.488311i) q^{35} +(0.339534 - 2.07360i) q^{36} +(7.89871 - 7.89871i) q^{37} +(8.21371 - 6.97817i) q^{38} -6.65131i q^{39} +(1.45892 + 2.42313i) q^{40} -5.49891i q^{41} +(-1.27262 - 1.49795i) q^{42} +(-0.256166 + 0.256166i) q^{43} +(7.02981 - 5.05159i) q^{44} +(0.742891 + 0.742891i) q^{45} +(-2.26715 - 0.184385i) q^{46} -4.60743 q^{47} +(3.57972 + 7.21078i) q^{48} +6.52310 q^{49} +(-1.40956 - 0.114638i) q^{50} +(-7.52510 - 7.52510i) q^{51} +(3.85707 + 5.36752i) q^{52} +(-4.99318 + 4.99318i) q^{53} +(-3.59243 - 4.22850i) q^{54} +4.32830i q^{55} +(1.89565 + 0.470837i) q^{56} +15.3382i q^{57} +(2.59600 - 2.20549i) q^{58} +(1.46478 - 1.46478i) q^{59} +(-3.97232 - 0.650434i) q^{60} +(9.33004 + 9.33004i) q^{61} +(-0.538579 + 6.62221i) q^{62} +0.725523 q^{63} +(-7.07029 - 3.74313i) q^{64} -3.30482 q^{65} +(-0.998637 + 12.2789i) q^{66} +(-1.94797 - 1.94797i) q^{67} +(10.4364 + 1.70888i) q^{68} +(2.28897 - 2.28897i) q^{69} +(-0.744283 + 0.632324i) q^{70} -2.32246i q^{71} +(-2.88394 - 0.716307i) q^{72} -1.29733i q^{73} +(-10.2282 - 12.0392i) q^{74} +(1.42313 - 1.42313i) q^{75} +(-8.89454 - 12.3777i) q^{76} +(2.11356 + 2.11356i) q^{77} +(-9.37542 - 0.762495i) q^{78} -5.01968 q^{79} +(3.58280 - 1.77864i) q^{80} +11.0480 q^{81} +(-7.75103 - 0.630385i) q^{82} +(7.30477 + 7.30477i) q^{83} +(-2.25734 + 1.62212i) q^{84} +(-3.73897 + 3.73897i) q^{85} +(0.331715 + 0.390448i) q^{86} +4.84772i q^{87} +(-6.31463 - 10.4880i) q^{88} +1.81564i q^{89} +(1.13231 - 0.961985i) q^{90} +(-1.61378 + 1.61378i) q^{91} +(-0.519803 + 3.17454i) q^{92} +(-6.68597 - 6.68597i) q^{93} +(-0.528188 + 6.49445i) q^{94} +7.62102 q^{95} +(10.5744 - 4.21920i) q^{96} +5.27038 q^{97} +(0.747798 - 9.19470i) q^{98} +(-3.21546 - 3.21546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 12 * q^6	$ 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.114638	−	1.40956i	0.0810615	−	0.996709i
$2$	0.114638	−	1.40956i	0.0810615	−	0.996709i
$3$	1.42313	+	1.42313i	0.821645	+	0.821645i	0.986344	−	0.164699i	$-0.0526652\pi$
$3$	1.42313	+	1.42313i	0.821645	+	0.821645i	−0.164699	+	0.986344i	$0.552665\pi$
$4$	−1.97372	−	0.323179i	−0.986858	−	0.161590i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	2.16913	−	1.84284i	0.885545	−	0.752338i
$7$		−	0.690576i		−	0.261013i	−0.991447	−	0.130507i	$-0.958340\pi$
$7$		−	0.690576i		−	0.261013i	0.991447	−	0.130507i	$-0.0416604\pi$
$8$	−0.681804	+	2.74502i	−0.241054	+	0.970512i
$9$			1.05061i			0.350202i
$10$	−0.915648	−	1.07777i	−0.289553	−	0.340821i
$11$	−3.06057	+	3.06057i	−0.922797	+	0.922797i	−0.997226	−	0.0744292i	$-0.976287\pi$
$11$	−3.06057	+	3.06057i	−0.922797	+	0.922797i	0.0744292	+	0.997226i	$0.476287\pi$
$12$	−2.34893	−	3.26878i	−0.678078	−	0.943617i
$13$	−2.33686	−	2.33686i	−0.648128	−	0.648128i	0.304413	−	0.952540i	$-0.401540\pi$
$13$	−2.33686	−	2.33686i	−0.648128	−	0.648128i	−0.952540	+	0.304413i	$0.901540\pi$
$14$	−0.973408	−	0.0791665i	−0.260154	−	0.0211581i
$15$	2.01261			0.519654
$16$	3.79111	+	1.27573i	0.947778	+	0.318932i
$17$	−5.28770			−1.28246			−0.641228	−	0.767350i	$-0.721575\pi$
$17$	−5.28770			−1.28246			−0.641228	+	0.767350i	$0.721575\pi$
$18$	1.48089	+	0.120440i	0.349050	+	0.0283879i
$19$	5.38887	+	5.38887i	1.23629	+	1.23629i	0.961505	+	0.274787i	$0.0886075\pi$
$19$	5.38887	+	5.38887i	1.23629	+	1.23629i	0.274787	+	0.961505i	$0.411393\pi$
$20$	−1.62415	+	1.16711i	−0.363171	+	0.260973i
$21$	0.982780	−	0.982780i	0.214460	−	0.214460i
$22$	3.96320	+	4.66492i	0.844957	+	0.994564i
$23$		−	1.60841i		−	0.335376i	−0.985840	−	0.167688i	$-0.946370\pi$
$23$		−	1.60841i		−	0.335376i	0.985840	−	0.167688i	$-0.0536301\pi$
$24$	−4.87682	+	2.93623i	−0.995477	+	0.599355i
$25$		−	1.00000i		−	0.200000i
$26$	−3.56183	+	3.02605i	−0.698533	+	0.593457i
$27$	2.77424	−	2.77424i	0.533903	−	0.533903i
$28$	−0.223180	+	1.36300i	−0.0421770	+	0.257583i
$29$	1.70319	+	1.70319i	0.316274	+	0.316274i	0.847334	−	0.531060i	$-0.178206\pi$
$29$	1.70319	+	1.70319i	0.316274	+	0.316274i	−0.531060	+	0.847334i	$0.678206\pi$
$30$	0.230722	−	2.83690i	0.0421240	−	0.517944i
$31$	−4.69807			−0.843798			−0.421899	−	0.906643i	$-0.638636\pi$
$31$	−4.69807			−0.843798			−0.421899	+	0.906643i	$0.638636\pi$
$32$	2.23282	−	5.19755i	0.394711	−	0.918805i
$33$	−8.71119			−1.51642
$34$	−0.606174	+	7.45333i	−0.103958	+	1.27824i
$35$	−0.488311	−	0.488311i	−0.0825396	−	0.0825396i
$36$	0.339534	−	2.07360i	0.0565890	−	0.345600i
$37$	7.89871	−	7.89871i	1.29854	−	1.29854i	0.369185	−	0.929356i	$-0.379637\pi$
$37$	7.89871	−	7.89871i	1.29854	−	1.29854i	0.929356	−	0.369185i	$-0.120363\pi$
$38$	8.21371	−	6.97817i	1.33244	−	1.13201i
$39$		−	6.65131i		−	1.06506i
$40$	1.45892	+	2.42313i	0.230675	+	0.383131i
$41$		−	5.49891i		−	0.858785i	−0.903118	−	0.429392i	$-0.858728\pi$
$41$		−	5.49891i		−	0.858785i	0.903118	−	0.429392i	$-0.141272\pi$
$42$	−1.27262	−	1.49795i	−0.196370	−	0.231139i
$43$	−0.256166	+	0.256166i	−0.0390650	+	0.0390650i	−0.726369	−	0.687304i	$-0.758794\pi$
$43$	−0.256166	+	0.256166i	−0.0390650	+	0.0390650i	0.687304	+	0.726369i	$0.258794\pi$
$44$	7.02981	−	5.05159i	1.05978	−	0.761555i
$45$	0.742891	+	0.742891i	0.110744	+	0.110744i
$46$	−2.26715	−	0.184385i	−0.334272	−	0.0271861i
$47$	−4.60743			−0.672063			−0.336032	−	0.941851i	$-0.609085\pi$
$47$	−4.60743			−0.672063			−0.336032	+	0.941851i	$0.609085\pi$
$48$	3.57972	+	7.21078i	0.516688	+	1.04079i
$49$	6.52310			0.931872
$50$	−1.40956	−	0.114638i	−0.199342	−	0.0162123i
$51$	−7.52510	−	7.52510i	−1.05372	−	1.05372i
$52$	3.85707	+	5.36752i	0.534879	+	0.744341i
$53$	−4.99318	+	4.99318i	−0.685866	+	0.685866i	−0.961316	−	0.275449i	$-0.911173\pi$
$53$	−4.99318	+	4.99318i	−0.685866	+	0.685866i	0.275449	+	0.961316i	$0.411173\pi$
$54$	−3.59243	−	4.22850i	−0.488867	−	0.575425i
$55$			4.32830i			0.583628i
$56$	1.89565	+	0.470837i	0.253316	+	0.0629183i
$57$			15.3382i			2.03159i
$58$	2.59600	−	2.20549i	0.340871	−	0.289596i
$59$	1.46478	−	1.46478i	0.190698	−	0.190698i	−0.605300	−	0.795998i	$-0.706947\pi$
$59$	1.46478	−	1.46478i	0.190698	−	0.190698i	0.795998	+	0.605300i	$0.206947\pi$
$60$	−3.97232	−	0.650434i	−0.512825	−	0.0839707i
$61$	9.33004	+	9.33004i	1.19459	+	1.19459i	0.975764	+	0.218825i	$0.0702224\pi$
$61$	9.33004	+	9.33004i	1.19459	+	1.19459i	0.218825	+	0.975764i	$0.429778\pi$
$62$	−0.538579	+	6.62221i	−0.0683996	+	0.841021i
$63$	0.725523			0.0914074
$64$	−7.07029	−	3.74313i	−0.883786	−	0.467891i
$65$	−3.30482			−0.409912
$66$	−0.998637	+	12.2789i	−0.122924	+	1.51143i
$67$	−1.94797	−	1.94797i	−0.237982	−	0.237982i	0.578032	−	0.816014i	$-0.303821\pi$
$67$	−1.94797	−	1.94797i	−0.237982	−	0.237982i	−0.816014	+	0.578032i	$0.803821\pi$
$68$	10.4364	+	1.70888i	1.26560	+	0.207232i
$69$	2.28897	−	2.28897i	0.275560	−	0.275560i
$70$	−0.744283	+	0.632324i	−0.0889588	+	0.0755772i
$71$		−	2.32246i		−	0.275625i	−0.990458	−	0.137813i	$-0.955993\pi$
$71$		−	2.32246i		−	0.275625i	0.990458	−	0.137813i	$-0.0440072\pi$
$72$	−2.88394	−	0.716307i	−0.339875	−	0.0844176i
$73$		−	1.29733i		−	0.151841i	−0.997114	−	0.0759206i	$-0.975810\pi$
$73$		−	1.29733i		−	0.151841i	0.997114	−	0.0759206i	$-0.0241896\pi$
$74$	−10.2282	−	12.0392i	−1.18901	−	1.39953i
$75$	1.42313	−	1.42313i	0.164329	−	0.164329i
$76$	−8.89454	−	12.3777i	−1.02027	−	1.41982i
$77$	2.11356	+	2.11356i	0.240862	+	0.240862i
$78$	−9.37542	−	0.762495i	−1.06156	−	0.0863356i
$79$	−5.01968			−0.564758			−0.282379	−	0.959303i	$-0.591124\pi$
$79$	−5.01968			−0.564758			−0.282379	+	0.959303i	$0.591124\pi$
$80$	3.58280	−	1.77864i	0.400569	−	0.198858i
$81$	11.0480			1.22756
$82$	−7.75103	−	0.630385i	−0.855959	−	0.0696144i
$83$	7.30477	+	7.30477i	0.801802	+	0.801802i	0.983377	−	0.181575i	$-0.0581194\pi$
$83$	7.30477	+	7.30477i	0.801802	+	0.801802i	−0.181575	+	0.983377i	$0.558119\pi$
$84$	−2.25734	+	1.62212i	−0.246296	+	0.176987i
$85$	−3.73897	+	3.73897i	−0.405548	+	0.405548i
$86$	0.331715	+	0.390448i	0.0357698	+	0.0421031i
$87$			4.84772i			0.519730i
$88$	−6.31463	−	10.4880i	−0.673141	−	1.11803i
$89$			1.81564i			0.192458i	0.995359	+	0.0962290i	$0.0306781\pi$
$89$			1.81564i			0.192458i	−0.995359	+	0.0962290i	$0.969322\pi$
$90$	1.13231	−	0.961985i	0.119356	−	0.101402i
$91$	−1.61378	+	1.61378i	−0.169170	+	0.169170i
$92$	−0.519803	+	3.17454i	−0.0541933	+	0.330969i
$93$	−6.68597	−	6.68597i	−0.693303	−	0.693303i
$94$	−0.528188	+	6.49445i	−0.0544785	+	0.669851i
$95$	7.62102			0.781900
$96$	10.5744	−	4.21920i	1.07924	−	0.430620i
$97$	5.27038			0.535126			0.267563	−	0.963540i	$-0.413782\pi$
$97$	5.27038			0.535126			0.267563	+	0.963540i	$0.413782\pi$
$98$	0.747798	−	9.19470i	0.0755390	−	0.928805i
$99$	−3.21546	−	3.21546i	−0.323165	−	0.323165i
$100$	−0.323179	+	1.97372i	−0.0323179	+	0.197372i
$101$	−13.4502	+	13.4502i	−1.33834	+	1.33834i	−0.440675	+	0.897667i	$0.645261\pi$
$101$	−13.4502	+	13.4502i	−1.33834	+	1.33834i	−0.897667	+	0.440675i	$0.854739\pi$
$102$	−11.4697	+	9.74441i	−1.13567	+	0.964840i
$103$		−	2.64310i		−	0.260432i	−0.991486	−	0.130216i	$-0.958433\pi$
$103$		−	2.64310i		−	0.260432i	0.991486	−	0.130216i	$-0.0415671\pi$
$104$	8.00800	−	4.82145i	0.785249	−	0.472782i
$105$		−	1.38986i		−	0.135637i
$106$	6.46578	+	7.61060i	0.628012	+	0.739207i
$107$	−6.28120	+	6.28120i	−0.607227	+	0.607227i	−0.942220	−	0.334994i	$-0.891266\pi$
$107$	−6.28120	+	6.28120i	−0.607227	+	0.607227i	0.334994	+	0.942220i	$0.391266\pi$
$108$	−6.37215	+	4.57899i	−0.613160	+	0.440614i
$109$	−6.89216	−	6.89216i	−0.660149	−	0.660149i	0.295266	−	0.955415i	$-0.404592\pi$
$109$	−6.89216	−	6.89216i	−0.660149	−	0.660149i	−0.955415	+	0.295266i	$0.904592\pi$
$110$	6.10100	+	0.496189i	0.581707	+	0.0473098i
$111$	22.4818			2.13388
$112$	0.880987	−	2.61805i	0.0832454	−	0.247382i
$113$	6.46108			0.607807			0.303904	−	0.952703i	$-0.401710\pi$
$113$	6.46108			0.607807			0.303904	+	0.952703i	$0.401710\pi$
$114$	21.6200	+	1.75834i	2.02490	+	0.164684i
$115$	−1.13732	−	1.13732i	−0.106055	−	0.106055i
$116$	−2.81117	−	3.91204i	−0.261011	−	0.363224i
$117$	2.45512	−	2.45512i	0.226976	−	0.226976i
$118$	−1.89677	−	2.23261i	−0.174612	−	0.205528i
$119$			3.65156i			0.334738i
$120$	−1.37221	+	5.52466i	−0.125265	+	0.504330i
$121$		−	7.73420i		−	0.703109i
$122$	14.2208	−	12.0817i	1.28749	−	1.09382i
$123$	7.82566	−	7.82566i	0.705616	−	0.705616i
$124$	9.27265	+	1.51832i	0.832709	+	0.136349i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	0.0831728	−	1.02267i	0.00740962	−	0.0911065i
$127$	−16.6123			−1.47411			−0.737054	−	0.675834i	$-0.763784\pi$
$127$	−16.6123			−1.47411			−0.737054	+	0.675834i	$0.763784\pi$
$128$	−6.08669	+	9.53688i	−0.537993	+	0.842949i
$129$	−0.729117			−0.0641951
$130$	−0.378859	+	4.65834i	−0.0332281	+	0.408563i
$131$	−11.7719	−	11.7719i	−1.02851	−	1.02851i	−0.999581	−	0.0289318i	$-0.990789\pi$
$131$	−11.7719	−	11.7719i	−1.02851	−	1.02851i	−0.0289318	−	0.999581i	$-0.509211\pi$
$132$	17.1934	+	2.81528i	1.49650	+	0.245038i
$133$	3.72143	−	3.72143i	0.322689	−	0.322689i
$134$	−2.96909	+	2.52247i	−0.256490	+	0.217908i
$135$		−	3.92337i		−	0.337670i
$136$	3.60518	−	14.5149i	0.309141	−	1.24464i
$137$		−	8.41495i		−	0.718937i	−0.933157	−	0.359469i	$-0.882958\pi$
$137$		−	8.41495i		−	0.718937i	0.933157	−	0.359469i	$-0.117042\pi$
$138$	−2.96404	−	3.48885i	−0.252316	−	0.296991i
$139$	−1.51845	+	1.51845i	−0.128793	+	0.128793i	−0.768565	−	0.639772i	$-0.779029\pi$
$139$	−1.51845	+	1.51845i	−0.128793	+	0.128793i	0.639772	+	0.768565i	$0.279029\pi$
$140$	0.805975	+	1.12160i	0.0681174	+	0.0947924i
$141$	−6.55698	−	6.55698i	−0.552198	−	0.552198i
$142$	−3.27364	−	0.266243i	−0.274718	−	0.0223426i
$143$	14.3042			1.19618
$144$	−1.34029	+	3.98296i	−0.111691	+	0.331914i
$145$	2.40867			0.200029
$146$	−1.82867	−	0.148724i	−0.151342	−	0.0123085i
$147$	9.28324	+	9.28324i	0.765668	+	0.765668i
$148$	−18.1425	+	13.0371i	−1.49131	+	1.07164i
$149$	−2.61440	+	2.61440i	−0.214180	+	0.214180i	−0.806040	−	0.591860i	$-0.798394\pi$
$149$	−2.61440	+	2.61440i	−0.214180	+	0.214180i	0.591860	+	0.806040i	$0.298394\pi$
$150$	−1.84284	−	2.16913i	−0.150468	−	0.177109i
$151$			12.7143i			1.03467i	0.855782	+	0.517337i	$0.173077\pi$
$151$			12.7143i			1.03467i	−0.855782	+	0.517337i	$0.826923\pi$
$152$	−18.4667	+	11.1184i	−1.49785	+	0.901823i
$153$		−	5.55529i		−	0.449119i
$154$	3.22148	−	2.73689i	0.259594	−	0.220545i
$155$	−3.32204	+	3.32204i	−0.266832	+	0.266832i
$156$	−2.14957	+	13.1278i	−0.172103	+	1.05107i
$157$	−7.17831	−	7.17831i	−0.572891	−	0.572891i	0.360044	−	0.932935i	$-0.382762\pi$
$157$	−7.17831	−	7.17831i	−0.572891	−	0.572891i	−0.932935	+	0.360044i	$0.882762\pi$
$158$	−0.575448	+	7.07554i	−0.0457802	+	0.562900i
$159$	−14.2119			−1.12708
$160$	−2.09638	−	5.25406i	−0.165733	−	0.415370i
$161$	−1.11073			−0.0875376
$162$	1.26653	−	15.5729i	0.0995080	−	1.22352i
$163$	−7.05476	−	7.05476i	−0.552572	−	0.552572i	0.374611	−	0.927182i	$-0.377776\pi$
$163$	−7.05476	−	7.05476i	−0.552572	−	0.552572i	−0.927182	+	0.374611i	$0.877776\pi$
$164$	−1.77713	+	10.8533i	−0.138771	+	0.847499i
$165$	−6.15974	+	6.15974i	−0.479535	+	0.479535i
$166$	11.1339	−	9.45910i	0.864159	−	0.734168i
$167$		−	3.90586i		−	0.302244i	−0.988515	−	0.151122i	$-0.951711\pi$
$167$		−	3.90586i		−	0.302244i	0.988515	−	0.151122i	$-0.0482887\pi$
$168$	2.02769	+	3.36782i	0.156440	+	0.259833i
$169$		−	2.07819i		−	0.159861i
$170$	4.84167	+	5.69893i	0.371339	+	0.437088i
$171$	−5.66158	+	5.66158i	−0.432952	+	0.432952i
$172$	0.588387	−	0.422812i	0.0448641	−	0.0322391i
$173$	8.20139	+	8.20139i	0.623540	+	0.623540i	0.946435	−	0.322895i	$-0.104656\pi$
$173$	8.20139	+	8.20139i	0.623540	+	0.623540i	−0.322895	+	0.946435i	$0.604656\pi$
$174$	6.83315	+	0.555735i	0.518020	+	0.0421301i
$175$	−0.690576			−0.0522026
$176$	−15.5074	+	7.69851i	−1.16892	+	0.580297i
$177$	4.16914			0.313372
$178$	2.55926	+	0.208142i	0.191825	+	0.0156009i
$179$	−3.10363	−	3.10363i	−0.231976	−	0.231976i	0.581541	−	0.813517i	$-0.302450\pi$
$179$	−3.10363	−	3.10363i	−0.231976	−	0.231976i	−0.813517	+	0.581541i	$0.802450\pi$
$180$	−1.22617	−	1.70634i	−0.0913932	−	0.127183i
$181$	−1.91041	+	1.91041i	−0.141999	+	0.141999i	−0.774533	−	0.632534i	$-0.782015\pi$
$181$	−1.91041	+	1.91041i	−0.141999	+	0.141999i	0.632534	+	0.774533i	$0.282015\pi$
$182$	2.08972	+	2.45972i	0.154900	+	0.182326i
$183$			26.5557i			1.96306i
$184$	4.41511	+	1.09662i	0.325486	+	0.0808437i
$185$		−	11.1705i		−	0.821269i
$186$	−10.1907	+	8.65780i	−0.747221	+	0.634821i
$187$	16.1834	−	16.1834i	1.18345	−	1.18345i
$188$	9.09376	+	1.48903i	0.663231	+	0.108598i
$189$	−1.91583	−	1.91583i	−0.139356	−	0.139356i
$190$	0.873661	−	10.7423i	0.0633820	−	0.779327i
$191$	5.61041			0.405955			0.202977	−	0.979183i	$-0.434938\pi$
$191$	5.61041			0.405955			0.202977	+	0.979183i	$0.434938\pi$
$192$	−4.73498	−	15.3889i	−0.341718	−	1.11060i
$193$	3.90696			0.281229			0.140615	−	0.990064i	$-0.455092\pi$
$193$	3.90696			0.281229			0.140615	+	0.990064i	$0.455092\pi$
$194$	0.604187	−	7.42891i	0.0433781	−	0.533365i
$195$	−4.70319	−	4.70319i	−0.336802	−	0.336802i
$196$	−12.8748	−	2.10813i	−0.919625	−	0.150581i
$197$	0.608436	−	0.608436i	0.0433493	−	0.0433493i	−0.685100	−	0.728449i	$-0.740241\pi$
$197$	0.608436	−	0.608436i	0.0433493	−	0.0433493i	0.728449	+	0.685100i	$0.240241\pi$
$198$	−4.90099	+	4.16376i	−0.348298	+	0.295906i
$199$			15.5282i			1.10076i	0.834913	+	0.550382i	$0.185518\pi$
$199$			15.5282i			1.10076i	−0.834913	+	0.550382i	$0.814482\pi$
$200$	2.74502	+	0.681804i	0.194102	+	0.0482108i
$201$		−	5.54443i		−	0.391074i
$202$	17.4169	+	20.5007i	1.22545	+	1.44243i
$203$	1.17618	−	1.17618i	0.0825517	−	0.0825517i
$204$	12.4205	+	17.2844i	0.869606	+	1.21015i
$205$	−3.88831	−	3.88831i	−0.271572	−	0.271572i
$206$	−3.72560	−	0.303000i	−0.259575	−	0.0211110i
$207$	1.68980			0.117449
$208$	−5.87809	−	11.8405i	−0.407572	−	0.820990i
$209$	−32.9861			−2.28169
$210$	−1.95909	−	0.159331i	−0.135190	−	0.0109949i
$211$	2.14501	+	2.14501i	0.147669	+	0.147669i	0.777076	−	0.629407i	$-0.216702\pi$
$211$	2.14501	+	2.14501i	0.147669	+	0.147669i	−0.629407	+	0.777076i	$0.716702\pi$
$212$	11.4688	−	8.24143i	0.787681	−	0.566024i
$213$	3.30516	−	3.30516i	0.226466	−	0.226466i
$214$	8.13366	+	9.57380i	0.556006	+	0.654451i
$215$			0.362274i			0.0247069i
$216$	5.72387	+	9.50685i	0.389460	+	0.646859i
$217$			3.24437i			0.220242i
$218$	−10.5050	+	8.92480i	−0.711489	+	0.604464i
$219$	1.84627	−	1.84627i	0.124760	−	0.124760i
$220$	1.39882	−	8.54284i	0.0943082	−	0.575958i
$221$	12.3566	+	12.3566i	0.831196	+	0.831196i
$222$	2.57728	−	31.6895i	0.172976	−	2.12686i
$223$	−2.34794			−0.157230			−0.0786148	−	0.996905i	$-0.525050\pi$
$223$	−2.34794			−0.157230			−0.0786148	+	0.996905i	$0.525050\pi$
$224$	−3.58930	−	1.54193i	−0.239820	−	0.103025i
$225$	1.05061			0.0700404
$226$	0.740688	−	9.10728i	0.0492698	−	0.605807i
$227$	13.1881	+	13.1881i	0.875325	+	0.875325i	0.993047	−	0.117722i	$-0.0375591\pi$
$227$	13.1881	+	13.1881i	0.875325	+	0.875325i	−0.117722	+	0.993047i	$0.537559\pi$
$228$	4.95697	−	30.2732i	0.328283	−	2.00489i
$229$	9.37860	−	9.37860i	0.619755	−	0.619755i	−0.325713	−	0.945469i	$-0.605604\pi$
$229$	9.37860	−	9.37860i	0.619755	−	0.619755i	0.945469	+	0.325713i	$0.105604\pi$
$230$	−1.73349	+	1.47273i	−0.114303	+	0.0971092i
$231$			6.01574i			0.395807i
$232$	−5.83653	+	3.51405i	−0.383187	+	0.230709i
$233$			16.3435i			1.07070i	0.844630	+	0.535350i	$0.179820\pi$
$233$			16.3435i			1.07070i	−0.844630	+	0.535350i	$0.820180\pi$
$234$	−3.17918	−	3.74208i	−0.207830	−	0.244628i
$235$	−3.25795	+	3.25795i	−0.212525	+	0.212525i
$236$	−3.36444	+	2.41767i	−0.219006	+	0.157377i
$237$	−7.14367	−	7.14367i	−0.464031	−	0.464031i
$238$	5.14709	+	0.418609i	0.333637	+	0.0271344i
$239$	19.3818			1.25371			0.626854	−	0.779137i	$-0.284342\pi$
$239$	19.3818			1.25371			0.626854	+	0.779137i	$0.284342\pi$
$240$	7.63003	+	2.56754i	0.492517	+	0.165734i
$241$	7.15965			0.461193			0.230597	−	0.973049i	$-0.425932\pi$
$241$	7.15965			0.461193			0.230597	+	0.973049i	$0.425932\pi$
$242$	−10.9018	−	0.886636i	−0.700795	−	0.0569951i
$243$	7.40009	+	7.40009i	0.474716	+	0.474716i
$244$	−15.3996	−	21.4301i	−0.985857	−	1.37192i
$245$	4.61253	−	4.61253i	0.294684	−	0.294684i
$246$	−10.1336	−	11.9279i	−0.646096	−	0.760493i
$247$		−	25.1861i		−	1.60255i
$248$	3.20316	−	12.8963i	0.203401	−	0.818916i
$249$			20.7913i			1.31759i
$250$	−1.07777	+	0.915648i	−0.0681642	+	0.0579106i
$251$	10.4372	−	10.4372i	0.658787	−	0.658787i	−0.296306	−	0.955093i	$-0.595755\pi$
$251$	10.4372	−	10.4372i	0.658787	−	0.658787i	0.955093	+	0.296306i	$0.0957548\pi$
$252$	−1.43198	−	0.234474i	−0.0902061	−	0.0147705i
$253$	4.92264	+	4.92264i	0.309484	+	0.309484i
$254$	−1.90441	+	23.4161i	−0.119493	+	1.46926i
$255$	−10.6421			−0.666434
$256$	12.7450	+	9.67285i	0.796565	+	0.604553i
$257$	5.72152			0.356899			0.178449	−	0.983949i	$-0.442892\pi$
$257$	5.72152			0.356899			0.178449	+	0.983949i	$0.442892\pi$
$258$	−0.0835847	+	1.02773i	−0.00520376	+	0.0639839i
$259$	−5.45466	−	5.45466i	−0.338936	−	0.338936i
$260$	6.52277	+	1.06805i	0.404525	+	0.0662375i
$261$	−1.78938	+	1.78938i	−0.110760	+	0.110760i
$262$	−17.9427	+	15.2436i	−1.10850	+	0.941756i
$263$		−	27.1378i		−	1.67339i	−0.547669	−	0.836695i	$-0.684485\pi$
$263$		−	27.1378i		−	1.67339i	0.547669	−	0.836695i	$-0.315515\pi$
$264$	5.93932	−	23.9124i	0.365540	−	1.47171i
$265$			7.06143i			0.433780i
$266$	−4.81895	−	5.67219i	−0.295469	−	0.347784i
$267$	−2.58390	+	2.58390i	−0.158132	+	0.158132i
$268$	3.21519	+	4.47428i	0.196399	+	0.273310i
$269$	13.0770	+	13.0770i	0.797320	+	0.797320i	0.982672	−	0.185352i	$-0.0593426\pi$
$269$	13.0770	+	13.0770i	0.797320	+	0.797320i	−0.185352	+	0.982672i	$0.559343\pi$
$270$	−5.53023	−	0.449769i	−0.336559	−	0.0273721i
$271$	6.55264			0.398044			0.199022	−	0.979995i	$-0.436223\pi$
$271$	6.55264			0.398044			0.199022	+	0.979995i	$0.436223\pi$
$272$	−20.0463	−	6.74567i	−1.21548	−	0.409016i
$273$	−4.59324			−0.277995
$274$	−11.8614	−	0.964675i	−0.716571	−	0.0582782i
$275$	3.06057	+	3.06057i	0.184559	+	0.184559i
$276$	−5.25753	+	3.77804i	−0.316466	+	0.227411i
$277$	−10.2851	+	10.2851i	−0.617973	+	0.617973i	−0.945011	−	0.327038i	$-0.893949\pi$
$277$	−10.2851	+	10.2851i	−0.617973	+	0.617973i	0.327038	+	0.945011i	$0.393949\pi$
$278$	1.96627	+	2.31442i	0.117929	+	0.138809i
$279$		−	4.93582i		−	0.295500i
$280$	1.67336	−	1.00749i	0.100002	−	0.0602092i
$281$		−	29.9714i		−	1.78794i	−0.448124	−	0.893971i	$-0.647908\pi$
$281$		−	29.9714i		−	1.78794i	0.448124	−	0.893971i	$-0.352092\pi$
$282$	−9.99414	+	8.49078i	−0.595142	+	0.505618i
$283$	−19.1176	+	19.1176i	−1.13642	+	1.13642i	−0.147334	+	0.989087i	$0.547069\pi$
$283$	−19.1176	+	19.1176i	−1.13642	+	1.13642i	−0.989087	+	0.147334i	$0.952931\pi$
$284$	−0.750570	+	4.58387i	−0.0445381	+	0.272003i
$285$	10.8457	+	10.8457i	0.642444	+	0.642444i
$286$	1.63981	−	20.1627i	0.0969643	−	1.19224i
$287$	−3.79741			−0.224154
$288$	5.46058	+	2.34582i	0.321768	+	0.138228i
$289$	10.9598			0.644695
$290$	0.276126	−	3.39517i	0.0162147	−	0.199371i
$291$	7.50044	+	7.50044i	0.439684	+	0.439684i
$292$	−0.419271	+	2.56056i	−0.0245360	+	0.149846i
$293$	7.27952	−	7.27952i	0.425274	−	0.425274i	−0.461741	−	0.887015i	$-0.652775\pi$
$293$	7.27952	−	7.27952i	0.425274	−	0.425274i	0.887015	+	0.461741i	$0.152775\pi$
$294$	14.1495	−	12.0211i	0.825215	−	0.701082i
$295$		−	2.07151i		−	0.120608i
$296$	16.2968	+	27.0675i	0.947230	+	1.57327i
$297$			16.9815i			0.985369i
$298$	3.38544	+	3.98486i	0.196113	+	0.230837i
$299$	−3.75862	+	3.75862i	−0.217366	+	0.217366i
$300$	−3.26878	+	2.34893i	−0.188723	+	0.135616i
$301$	0.176902	+	0.176902i	0.0101965	+	0.0101965i
$302$	17.9216	+	1.45755i	1.03127	+	0.0838723i
$303$	−38.2827			−2.19928
$304$	13.5551	+	27.3046i	0.777437	+	1.56602i
$305$	13.1947			0.755525
$306$	−7.83052	−	0.636850i	−0.447641	−	0.0364063i
$307$	7.03304	+	7.03304i	0.401397	+	0.401397i	0.878725	−	0.477328i	$-0.158395\pi$
$307$	7.03304	+	7.03304i	0.401397	+	0.401397i	−0.477328	+	0.878725i	$0.658395\pi$
$308$	−3.48850	−	4.85462i	−0.198776	−	0.276618i
$309$	3.76147	−	3.76147i	0.213983	−	0.213983i
$310$	4.30177	+	5.06344i	0.244324	+	0.287584i
$311$		−	14.2833i		−	0.809929i	−0.914332	−	0.404964i	$-0.867284\pi$
$311$		−	14.2833i		−	0.809929i	0.914332	−	0.404964i	$-0.132716\pi$
$312$	18.2580	+	4.53489i	1.03366	+	0.256738i
$313$			18.4579i			1.04330i	0.853158	+	0.521652i	$0.174684\pi$
$313$			18.4579i			1.04330i	−0.853158	+	0.521652i	$0.825316\pi$
$314$	−10.9412	+	9.29534i	−0.617445	+	0.524567i
$315$	0.513023	−	0.513023i	0.0289055	−	0.0289055i
$316$	9.90743	+	1.62226i	0.557336	+	0.0912590i
$317$	−7.21807	−	7.21807i	−0.405407	−	0.405407i	0.474726	−	0.880133i	$-0.342547\pi$
$317$	−7.21807	−	7.21807i	−0.405407	−	0.405407i	−0.880133	+	0.474726i	$0.842547\pi$
$318$	−1.62923	+	20.0325i	−0.0913626	+	1.12337i
$319$	−10.4255			−0.583714
$320$	−7.64624	+	2.35265i	−0.427438	+	0.131517i
$321$	−17.8780			−0.997850
$322$	−0.127332	+	1.56564i	−0.00709593	+	0.0872495i
$323$	−28.4948	−	28.4948i	−1.58549	−	1.58549i
$324$	−21.8057	−	3.57050i	−1.21143	−	0.198361i
$325$	−2.33686	+	2.33686i	−0.129626	+	0.129626i
$326$	−10.7529	+	9.13536i	−0.595545	+	0.505961i
$327$		−	19.6169i		−	1.08482i
$328$	15.0946	+	3.74917i	0.833461	+	0.207014i
$329$			3.18178i			0.175417i
$330$	7.97638	+	9.38867i	0.439085	+	0.516829i
$331$	−15.4847	+	15.4847i	−0.851116	+	0.851116i	−0.990271	−	0.139155i	$-0.955561\pi$
$331$	−15.4847	+	15.4847i	−0.851116	+	0.851116i	0.139155	+	0.990271i	$0.455561\pi$
$332$	−12.0568	−	16.7783i	−0.661702	−	0.920828i
$333$	8.29844	+	8.29844i	0.454752	+	0.454752i
$334$	−5.50554	−	0.447761i	−0.301250	−	0.0245004i
$335$	−2.75484			−0.150513
$336$	4.97959	−	2.47207i	0.271659	−	0.134862i
$337$	−26.0210			−1.41746			−0.708728	−	0.705482i	$-0.750731\pi$
$337$	−26.0210			−1.41746			−0.708728	+	0.705482i	$0.750731\pi$
$338$	−2.92933	−	0.238240i	−0.159335	−	0.0129586i
$339$	9.19497	+	9.19497i	0.499402	+	0.499402i
$340$	8.58803	−	6.17131i	0.465751	−	0.334686i
$341$	14.3788	−	14.3788i	0.778654	−	0.778654i
$342$	7.33131	+	8.62937i	0.396432	+	0.466623i
$343$		−	9.33873i		−	0.504244i
$344$	−0.528527	−	0.877837i	−0.0284963	−	0.0473298i
$345$		−	3.23710i		−	0.174280i
$346$	12.5005	−	10.6202i	0.672034	−	0.570943i
$347$	−12.8554	+	12.8554i	−0.690115	+	0.690115i	−0.962257	−	0.272142i	$-0.912268\pi$
$347$	−12.8554	+	12.8554i	−0.690115	+	0.690115i	0.272142	+	0.962257i	$0.412268\pi$
$348$	1.56668	−	9.56802i	0.0839830	−	0.512900i
$349$	−20.0227	−	20.0227i	−1.07179	−	1.07179i	−0.997216	−	0.0745736i	$-0.976240\pi$
$349$	−20.0227	−	20.0227i	−1.07179	−	1.07179i	−0.0745736	−	0.997216i	$-0.523760\pi$
$350$	−0.0791665	+	0.973408i	−0.00423163	+	0.0520308i
$351$	−12.9660			−0.692075
$352$	9.07376	+	22.7412i	0.483633	+	1.21211i
$353$	13.7062			0.729510			0.364755	−	0.931104i	$-0.381153\pi$
$353$	13.7062			0.729510			0.364755	+	0.931104i	$0.381153\pi$
$354$	0.477943	−	5.87665i	0.0254024	−	0.312340i
$355$	−1.64223	−	1.64223i	−0.0871603	−	0.0871603i
$356$	0.586778	−	3.58357i	0.0310992	−	0.189929i
$357$	−5.19665	+	5.19665i	−0.275036	+	0.275036i
$358$	−4.73055	+	4.01896i	−0.250017	+	0.212409i
$359$		−	32.3506i		−	1.70740i	−0.520764	−	0.853700i	$-0.674353\pi$
$359$		−	32.3506i		−	1.70740i	0.520764	−	0.853700i	$-0.325647\pi$
$360$	−2.54576	+	1.53275i	−0.134173	+	0.0807828i
$361$			39.0799i			2.05684i
$362$	2.47383	+	2.91184i	0.130021	+	0.153043i
$363$	11.0068	−	11.0068i	0.577706	−	0.577706i
$364$	3.70668	−	2.66360i	0.194283	−	0.139611i
$365$	−0.917352	−	0.917352i	−0.0480164	−	0.0480164i
$366$	37.4319	+	3.04431i	1.95660	+	0.159128i
$367$	16.3714			0.854582			0.427291	−	0.904114i	$-0.359468\pi$
$367$	16.3714			0.854582			0.427291	+	0.904114i	$0.359468\pi$
$368$	2.05189	−	6.09765i	0.106962	−	0.317862i
$369$	5.77718			0.300748
$370$	−15.7454	−	1.28056i	−0.818567	−	0.0665734i
$371$	3.44817	+	3.44817i	0.179020	+	0.179020i
$372$	11.0354	+	15.3570i	0.572161	+	0.796222i
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	−0.179530	−	0.983752i	$-0.557458\pi$
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	0.983752	+	0.179530i	$0.0574578\pi$
$374$	−20.9562	−	24.6667i	−1.08362	−	1.27548i
$375$		−	2.01261i		−	0.103931i
$376$	3.14136	−	12.6475i	0.162004	−	0.652245i
$377$		−	7.96022i		−	0.409972i
$378$	−2.92010	+	2.48084i	−0.150194	+	0.127601i
$379$	24.9538	−	24.9538i	1.28179	−	1.28179i	0.342145	−	0.939647i	$-0.388847\pi$
$379$	24.9538	−	24.9538i	1.28179	−	1.28179i	0.939647	−	0.342145i	$-0.111153\pi$
$380$	−15.0417	−	2.46295i	−0.771624	−	0.126347i
$381$	−23.6416	−	23.6416i	−1.21119	−	1.21119i
$382$	0.643168	−	7.90820i	0.0329073	−	0.404619i
$383$	6.24887			0.319302			0.159651	−	0.987174i	$-0.448963\pi$
$383$	6.24887			0.319302			0.159651	+	0.987174i	$0.448963\pi$
$384$	−22.2344	+	4.91008i	−1.13464	+	0.250566i
$385$	2.98902			0.152335
$386$	0.447888	−	5.50710i	0.0227969	−	0.280304i
$387$	−0.269130	−	0.269130i	−0.0136806	−	0.0136806i
$388$	−10.4022	−	1.70328i	−0.528093	−	0.0864707i
$389$	2.10802	−	2.10802i	0.106881	−	0.106881i	−0.651644	−	0.758525i	$-0.725920\pi$
$389$	2.10802	−	2.10802i	0.106881	−	0.106881i	0.758525	+	0.651644i	$0.225920\pi$
$390$	−7.16859	+	6.09026i	−0.362996	+	0.308392i
$391$			8.50478i			0.430105i
$392$	−4.44748	+	17.9061i	−0.224632	+	0.904393i
$393$		−	33.5058i		−	1.69015i
$394$	−0.787876	−	0.927377i	−0.0396926	−	0.0467206i
$395$	−3.54945	+	3.54945i	−0.178592	+	0.178592i
$396$	5.30723	+	7.38556i	0.266698	+	0.371139i
$397$	23.4977	+	23.4977i	1.17932	+	1.17932i	0.979919	+	0.199397i	$0.0638983\pi$
$397$	23.4977	+	23.4977i	1.17932	+	1.17932i	0.199397	+	0.979919i	$0.436102\pi$
$398$	21.8879	+	1.78013i	1.09714	+	0.0892296i
$399$	10.5922			0.530271
$400$	1.27573	−	3.79111i	0.0637864	−	0.189556i
$401$	−20.9893			−1.04816			−0.524078	−	0.851670i	$-0.675590\pi$
$401$	−20.9893			−1.04816			−0.524078	+	0.851670i	$0.675590\pi$
$402$	−7.81520	−	0.635604i	−0.389787	−	0.0317011i
$403$	10.9787	+	10.9787i	0.546889	+	0.546889i
$404$	30.8936	−	22.2000i	1.53702	−	1.10449i
$405$	7.81215	−	7.81215i	0.388189	−	0.388189i
$406$	−1.52306	−	1.79273i	−0.0755883	−	0.0889718i
$407$			48.3492i			2.39658i
$408$	25.7872	−	15.5259i	1.27666	−	0.768647i
$409$		−	18.4025i		−	0.909944i	−0.890506	−	0.454972i	$-0.849649\pi$
$409$		−	18.4025i		−	0.909944i	0.890506	−	0.454972i	$-0.150351\pi$
$410$	−5.92656	+	5.03506i	−0.292692	+	0.248664i
$411$	11.9756	−	11.9756i	0.590711	−	0.590711i
$412$	−0.854193	+	5.21672i	−0.0420831	+	0.257009i
$413$	−1.01154	−	1.01154i	−0.0497746	−	0.0497746i
$414$	0.193716	−	2.38188i	0.00952063	−	0.117063i
$415$	10.3305			0.507104
$416$	−17.3637	+	6.92815i	−0.851326	+	0.339680i
$417$	−4.32190			−0.211644
$418$	−3.78147	+	46.4958i	−0.184958	+	2.27419i
$419$	14.9331	+	14.9331i	0.729530	+	0.729530i	0.970526	−	0.240996i	$-0.0774740\pi$
$419$	14.9331	+	14.9331i	0.729530	+	0.729530i	−0.240996	+	0.970526i	$0.577474\pi$
$420$	−0.449174	+	2.74319i	−0.0219175	+	0.133854i
$421$	−16.2680	+	16.2680i	−0.792854	+	0.792854i	−0.981957	−	0.189103i	$-0.939442\pi$
$421$	−16.2680	+	16.2680i	−0.792854	+	0.792854i	0.189103	+	0.981957i	$0.439442\pi$
$422$	3.26942	−	2.77762i	0.159153	−	0.135212i
$423$		−	4.84060i		−	0.235358i
$424$	−10.3020	−	17.1108i	−0.500310	−	0.830972i
$425$			5.28770i			0.256491i
$426$	−4.27993	−	5.03772i	−0.207363	−	0.244078i
$427$	6.44310	−	6.44310i	0.311804	−	0.311804i
$428$	14.4273	−	10.3674i	0.697368	−	0.501125i
$429$	20.3568	+	20.3568i	0.982836	+	0.982836i
$430$	0.510647	+	0.0415305i	0.0246256	+	0.00200278i
$431$	7.05425			0.339791			0.169896	−	0.985462i	$-0.445657\pi$
$431$	7.05425			0.339791			0.169896	+	0.985462i	$0.445657\pi$
$432$	14.0566	−	6.97829i	0.676301	−	0.335743i
$433$	−14.3192			−0.688139			−0.344069	−	0.938944i	$-0.611806\pi$
$433$	−14.3192			−0.688139			−0.344069	+	0.938944i	$0.611806\pi$
$434$	4.57314	+	0.371930i	0.219518	+	0.0178532i
$435$	3.42786	+	3.42786i	0.164353	+	0.164353i
$436$	11.3758	+	15.8306i	0.544800	+	0.758146i
$437$	8.66750	−	8.66750i	0.414623	−	0.414623i
$438$	−2.39078	−	2.81409i	−0.114236	−	0.134462i
$439$			25.9047i			1.23637i	0.786034	+	0.618183i	$0.212131\pi$
$439$			25.9047i			1.23637i	−0.786034	+	0.618183i	$0.787869\pi$
$440$	−11.8813	−	2.95105i	−0.566418	−	0.140686i
$441$			6.85321i			0.326344i
$442$	18.8339	−	16.0008i	0.895838	−	0.761082i
$443$	−11.1389	+	11.1389i	−0.529224	+	0.529224i	−0.920341	−	0.391117i	$-0.872089\pi$
$443$	−11.1389	+	11.1389i	−0.529224	+	0.529224i	0.391117	+	0.920341i	$0.372089\pi$
$444$	−44.3727	−	7.26565i	−2.10584	−	0.344813i
$445$	1.28385	+	1.28385i	0.0608605	+	0.0608605i
$446$	−0.269164	+	3.30956i	−0.0127453	+	0.156712i
$447$	−7.44127			−0.351960
$448$	−2.58492	+	4.88257i	−0.122126	+	0.230680i
$449$	12.6659			0.597740			0.298870	−	0.954294i	$-0.403390\pi$
$449$	12.6659			0.597740			0.298870	+	0.954294i	$0.403390\pi$
$450$	0.120440	−	1.48089i	0.00567758	−	0.0698099i
$451$	16.8298	+	16.8298i	0.792484	+	0.792484i
$452$	−12.7523	−	2.08809i	−0.599820	−	0.0982153i
$453$	−18.0941	+	18.0941i	−0.850135	+	0.850135i
$454$	20.1013	−	17.0775i	0.943399	−	0.801489i
$455$			2.28223i			0.106992i
$456$	−42.1036	−	10.4576i	−1.97168	−	0.489722i
$457$		−	16.9442i		−	0.792617i	−0.918117	−	0.396308i	$-0.870291\pi$
$457$		−	16.9442i		−	0.792617i	0.918117	−	0.396308i	$-0.129709\pi$
$458$	−12.1446	−	14.2948i	−0.567478	−	0.667954i
$459$	−14.6694	+	14.6694i	−0.684708	+	0.684708i
$460$	1.87718	+	2.61229i	0.0875240	+	0.121799i
$461$	−13.1888	−	13.1888i	−0.614264	−	0.614264i	0.329790	−	0.944054i	$-0.393022\pi$
$461$	−13.1888	−	13.1888i	−0.614264	−	0.614264i	−0.944054	+	0.329790i	$0.893022\pi$
$462$	8.47954	+	0.689634i	0.394504	+	0.0320847i
$463$	−14.0955			−0.655074			−0.327537	−	0.944838i	$-0.606219\pi$
$463$	−14.0955			−0.655074			−0.327537	+	0.944838i	$0.606219\pi$
$464$	4.28417	+	8.62978i	0.198888	+	0.400627i
$465$	−9.45539			−0.438483
$466$	23.0372	+	1.87360i	1.06718	+	0.0867927i
$467$	−12.0918	−	12.0918i	−0.559540	−	0.559540i	0.369636	−	0.929177i	$-0.379482\pi$
$467$	−12.0918	−	12.0918i	−0.559540	−	0.559540i	−0.929177	+	0.369636i	$0.879482\pi$
$468$	−5.63915	+	4.05226i	−0.260670	+	0.187316i
$469$	−1.34522	+	1.34522i	−0.0621165	+	0.0621165i
$470$	4.21878	+	4.96576i	0.194598	+	0.229053i
$471$		−	20.4313i		−	0.941427i
$472$	3.02215	+	5.01953i	0.139106	+	0.231043i
$473$		−	1.56803i		−	0.0720981i
$474$	−10.8884	+	9.25048i	−0.500119	+	0.424889i
$475$	5.38887	−	5.38887i	0.247258	−	0.247258i
$476$	1.18011	−	7.20715i	0.0540902	−	0.330339i
$477$	−5.24587	−	5.24587i	−0.240192	−	0.240192i
$478$	2.22190	−	27.3199i	0.101627	−	1.24958i
$479$	14.2523			0.651202			0.325601	−	0.945507i	$-0.394433\pi$
$479$	14.2523			0.651202			0.325601	+	0.945507i	$0.394433\pi$
$480$	4.49380	−	10.4606i	0.205113	−	0.477461i
$481$	−36.9163			−1.68324
$482$	0.820770	−	10.0919i	0.0373850	−	0.459676i
$483$	−1.58071	−	1.58071i	−0.0719248	−	0.0719248i
$484$	−2.49953	+	15.2651i	−0.113615	+	0.693869i
$485$	3.72672	−	3.72672i	0.169222	−	0.169222i
$486$	11.2792	−	9.58253i	0.511635	−	0.434672i
$487$			26.0424i			1.18010i	0.807368	+	0.590048i	$0.200891\pi$
$487$			26.0424i			1.18010i	−0.807368	+	0.590048i	$0.799109\pi$
$488$	−31.9724	+	19.2499i	−1.44732	+	0.871402i
$489$		−	20.0797i		−	0.908036i
$490$	−5.97286	−	7.03041i	−0.269827	−	0.317602i
$491$	3.46798	−	3.46798i	0.156508	−	0.156508i	−0.624509	−	0.781017i	$-0.714701\pi$
$491$	3.46798	−	3.46798i	0.156508	−	0.156508i	0.781017	+	0.624509i	$0.214701\pi$
$492$	−17.9747	+	12.9165i	−0.810364	+	0.582323i
$493$	−9.00595	−	9.00595i	−0.405608	−	0.405608i
$494$	−35.5013	−	2.88729i	−1.59728	−	0.129905i
$495$	−4.54734			−0.204388
$496$	−17.8109	−	5.99346i	−0.799733	−	0.269114i
$497$	−1.60383			−0.0719418
$498$	29.3066	+	2.38348i	1.31326	+	0.106806i
$499$	−5.30274	−	5.30274i	−0.237383	−	0.237383i	0.578383	−	0.815766i	$-0.303684\pi$
$499$	−5.30274	−	5.30274i	−0.237383	−	0.237383i	−0.815766	+	0.578383i	$0.803684\pi$
$500$	1.16711	+	1.62415i	0.0521946	+	0.0726342i
$501$	5.55855	−	5.55855i	0.248338	−	0.248338i
$502$	−13.5153	−	15.9083i	−0.603217	−	0.710021i
$503$			28.8492i			1.28632i	0.765731	+	0.643161i	$0.222378\pi$
$503$			28.8492i			1.28632i	−0.765731	+	0.643161i	$0.777622\pi$
$504$	−0.494665	+	1.99158i	−0.0220341	+	0.0887119i
$505$			19.0214i			0.846442i
$506$	7.50308	−	6.37444i	0.333553	−	0.283378i
$507$	2.95754	−	2.95754i	0.131349	−	0.131349i
$508$	32.7881	+	5.36876i	1.45473	+	0.238200i
$509$	12.9968	+	12.9968i	0.576072	+	0.576072i	0.933819	−	0.357747i	$-0.116455\pi$
$509$	12.9968	+	12.9968i	0.576072	+	0.576072i	−0.357747	+	0.933819i	$0.616455\pi$
$510$	−1.21999	+	15.0007i	−0.0540222	+	0.664241i
$511$	−0.895906			−0.0396326
$512$	15.0955	−	16.8560i	0.667134	−	0.744937i
$513$	29.9001			1.32012
$514$	0.655906	−	8.06482i	0.0289308	−	0.355724i
$515$	−1.86895	−	1.86895i	−0.0823558	−	0.0823558i
$516$	1.43907	+	0.235635i	0.0633515	+	0.0103733i
$517$	14.1014	−	14.1014i	0.620178	−	0.620178i
$518$	−8.31399	+	7.06336i	−0.365296	+	0.310346i
$519$			23.3433i			1.02466i
$520$	2.25324	−	9.07179i	0.0988109	−	0.397824i
$521$			13.9833i			0.612618i	0.951932	+	0.306309i	$0.0990941\pi$
$521$			13.9833i			0.612618i	−0.951932	+	0.306309i	$0.900906\pi$
$522$	2.31711	+	2.72737i	0.101417	+	0.119374i
$523$	−6.30689	+	6.30689i	−0.275781	+	0.275781i	−0.831422	−	0.555641i	$-0.812473\pi$
$523$	−6.30689	+	6.30689i	−0.275781	+	0.275781i	0.555641	+	0.831422i	$0.312473\pi$
$524$	19.4299	+	27.0388i	0.848800	+	1.18119i
$525$	−0.982780	−	0.982780i	−0.0428921	−	0.0428921i
$526$	−38.2524	−	3.11104i	−1.66788	−	0.135648i
$527$	24.8420			1.08213
$528$	−33.0251	−	11.1131i	−1.43723	−	0.483636i
$529$	20.4130			0.887523
$530$	9.95350	+	0.809510i	0.432352	+	0.0351629i
$531$	1.53890	+	1.53890i	0.0667827	+	0.0667827i
$532$	−8.54773	+	6.14235i	−0.370591	+	0.266305i
$533$	−12.8502	+	12.8502i	−0.556602	+	0.556602i
$534$	3.34595	+	3.93838i	0.144793	+	0.170430i
$535$			8.88296i			0.384044i
$536$	6.67535	−	4.01908i	0.288331	−	0.173598i
$537$		−	8.83375i		−	0.381204i
$538$	19.9320	−	16.9337i	0.859328	−	0.730064i
$539$	−19.9644	+	19.9644i	−0.859929	+	0.859929i
$540$	−1.26795	+	7.74362i	−0.0545640	+	0.333233i
$541$	3.89317	+	3.89317i	0.167381	+	0.167381i	0.785827	−	0.618446i	$-0.212238\pi$
$541$	3.89317	+	3.89317i	0.167381	+	0.167381i	−0.618446	+	0.785827i	$0.712238\pi$
$542$	0.751184	−	9.23633i	0.0322661	−	0.396735i
$543$	−5.43752			−0.233346
$544$	−11.8065	+	27.4831i	−0.506199	+	1.17833i
$545$	−9.74698			−0.417515
$546$	−0.526561	+	6.47444i	−0.0225347	+	0.277080i
$547$	−27.8376	−	27.8376i	−1.19025	−	1.19025i	−0.976997	−	0.213251i	$-0.931595\pi$
$547$	−27.8376	−	27.8376i	−1.19025	−	1.19025i	−0.213251	−	0.976997i	$-0.568405\pi$
$548$	−2.71953	+	16.6087i	−0.116173	+	0.709489i
$549$	−9.80220	+	9.80220i	−0.418348	+	0.418348i
$550$	4.66492	−	3.96320i	0.198913	−	0.168991i
$551$			18.3565i			0.782014i
$552$	4.72265	+	7.84391i	0.201009	+	0.333859i
$553$			3.46647i			0.147409i
$554$	13.3184	+	15.6766i	0.565845	+	0.666033i
$555$	15.8970	−	15.8970i	0.674792	−	0.674792i
$556$	3.48772	−	2.50625i	0.147912	−	0.106289i
$557$	1.50454	+	1.50454i	0.0637492	+	0.0637492i	0.738263	−	0.674513i	$-0.235647\pi$
$557$	1.50454	+	1.50454i	0.0637492	+	0.0637492i	−0.674513	+	0.738263i	$0.735647\pi$
$558$	−6.95733	−	0.565834i	−0.294527	−	0.0239537i
$559$	1.19725			0.0506382
$560$	−1.22829	−	2.47419i	−0.0519047	−	0.104554i
$561$	46.0622			1.94475
$562$	−42.2465	−	3.43587i	−1.78206	−	0.144933i
$563$	−6.66663	−	6.66663i	−0.280965	−	0.280965i	0.552529	−	0.833494i	$-0.313663\pi$
$563$	−6.66663	−	6.66663i	−0.280965	−	0.280965i	−0.833494	+	0.552529i	$0.813663\pi$
$564$	10.8225	+	15.0607i	0.455711	+	0.634170i
$565$	4.56867	−	4.56867i	0.192206	−	0.192206i
$566$	24.7557	+	29.1389i	1.04056	+	1.22480i
$567$		−	7.62952i		−	0.320410i
$568$	6.37520	+	1.58346i	0.267497	+	0.0664405i
$569$		−	8.38187i		−	0.351386i	−0.984445	−	0.175693i	$-0.943783\pi$
$569$		−	8.38187i		−	0.351386i	0.984445	−	0.175693i	$-0.0562167\pi$
$570$	16.5310	−	14.0443i	0.692408	−	0.588253i
$571$	28.4129	−	28.4129i	1.18904	−	1.18904i	0.211708	−	0.977333i	$-0.432097\pi$
$571$	28.4129	−	28.4129i	1.18904	−	1.18904i	0.977333	−	0.211708i	$-0.0679027\pi$
$572$	−28.2325	−	4.62283i	−1.18046	−	0.193290i
$573$	7.98435	+	7.98435i	0.333551	+	0.333551i
$574$	−0.435329	+	5.35268i	−0.0181703	+	0.223416i
$575$	−1.60841			−0.0670752
$576$	3.93256	−	7.42809i	0.163857	−	0.309504i
$577$	23.2045			0.966014			0.483007	−	0.875616i	$-0.339545\pi$
$577$	23.2045			0.966014			0.483007	+	0.875616i	$0.339545\pi$
$578$	1.25642	−	15.4485i	0.0522600	−	0.642574i
$579$	5.56012	+	5.56012i	0.231071	+	0.231071i
$580$	−4.75403	−	0.778432i	−0.197400	−	0.0323226i
$581$	5.04450	−	5.04450i	0.209281	−	0.209281i
$582$	11.4322	−	9.71248i	0.473878	−	0.402595i
$583$		−	30.5640i		−	1.26583i
$584$	3.56120	+	0.884526i	0.147364	+	0.0366019i
$585$		−	3.47206i		−	0.143552i
$586$	−9.42640	−	11.0954i	−0.389401	−	0.458348i
$587$	−11.0197	+	11.0197i	−0.454832	+	0.454832i	−0.896955	−	0.442123i	$-0.854226\pi$
$587$	−11.0197	+	11.0197i	−0.454832	+	0.454832i	0.442123	+	0.896955i	$0.354226\pi$
$588$	−15.3223	−	21.3226i	−0.631882	−	0.879330i
$589$	−25.3173	−	25.3173i	−1.04318	−	1.04318i
$590$	−2.91991	−	0.237474i	−0.120211	−	0.00977666i
$591$	1.73177			0.0712354
$592$	40.0215	−	19.8683i	1.64487	−	0.816582i
$593$	−6.98847			−0.286982			−0.143491	−	0.989652i	$-0.545833\pi$
$593$	−6.98847			−0.286982			−0.143491	+	0.989652i	$0.545833\pi$
$594$	23.9365	+	1.94674i	0.982126	+	0.0798755i
$595$	2.58204	+	2.58204i	0.105853	+	0.105853i
$596$	6.00500	−	4.31516i	0.245975	−	0.176756i
$597$	−22.0987	+	22.0987i	−0.904438	+	0.904438i
$598$	4.86711	+	5.72888i	0.199031	+	0.234271i
$599$		−	39.9642i		−	1.63289i	−0.577420	−	0.816447i	$-0.695941\pi$
$599$		−	39.9642i		−	1.63289i	0.577420	−	0.816447i	$-0.304059\pi$
$600$	2.93623	+	4.87682i	0.119871	+	0.199095i
$601$		−	21.0830i		−	0.859993i	−0.902831	−	0.429997i	$-0.858515\pi$
$601$		−	21.0830i		−	0.859993i	0.902831	−	0.429997i	$-0.141485\pi$
$602$	0.269634	−	0.229075i	0.0109895	−	0.00933638i
$603$	2.04655	−	2.04655i	0.0833418	−	0.0833418i
$604$	4.10899	−	25.0944i	0.167193	−	1.02108i
$605$	−5.46890	−	5.46890i	−0.222343	−	0.222343i
$606$	−4.38867	+	53.9618i	−0.178277	+	2.19205i
$607$	22.3189			0.905897			0.452949	−	0.891537i	$-0.350372\pi$
$607$	22.3189			0.905897			0.452949	+	0.891537i	$0.350372\pi$
$608$	40.0413	−	15.9765i	1.62389	−	0.647934i
$609$	3.34772			0.135656
$610$	1.51261	−	18.5987i	0.0612440	−	0.753038i
$611$	10.7669	+	10.7669i	0.435583	+	0.435583i
$612$	−1.79536	+	10.9646i	−0.0725729	+	0.443217i
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	−0.888053	−	0.459741i	$-0.847942\pi$
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	0.459741	+	0.888053i	$0.347942\pi$
$614$	10.7197	−	9.10724i	0.432614	−	0.367538i
$615$		−	11.0672i		−	0.446271i
$616$	−7.24279	+	4.36073i	−0.291820	+	0.175699i
$617$		−	33.7636i		−	1.35927i	−0.733550	−	0.679635i	$-0.762138\pi$
$617$		−	33.7636i		−	1.35927i	0.733550	−	0.679635i	$-0.237862\pi$
$618$	−4.87081	−	5.73323i	−0.195933	−	0.230624i
$619$	4.86777	−	4.86777i	0.195652	−	0.195652i	−0.602481	−	0.798133i	$-0.705821\pi$
$619$	4.86777	−	4.86777i	0.195652	−	0.195652i	0.798133	+	0.602481i	$0.205821\pi$
$620$	7.63037	−	5.48314i	0.306443	−	0.220208i
$621$	−4.46211	−	4.46211i	−0.179058	−	0.179058i
$622$	−20.1331	−	1.63741i	−0.807263	−	0.0656541i
$623$	1.25384			0.0502341
$624$	8.48526	−	25.2159i	0.339682	−	1.00944i
$625$	−1.00000			−0.0400000
$626$	26.0176	+	2.11599i	1.03987	+	0.0845718i
$627$	−46.9435	−	46.9435i	−1.87474	−	1.87474i
$628$	11.8481	+	16.4878i	0.472789	+	0.657936i
$629$	−41.7661	+	41.7661i	−1.66532	+	1.66532i
$630$	−0.664324	−	0.781948i	−0.0264673	−	0.0311535i
$631$		−	16.1348i		−	0.642315i	−0.947026	−	0.321157i	$-0.895928\pi$
$631$		−	16.1348i		−	0.642315i	0.947026	−	0.321157i	$-0.104072\pi$
$632$	3.42244	−	13.7791i	0.136137	−	0.548105i
$633$			6.10526i			0.242662i
$634$	−11.0018	+	9.34683i	−0.436936	+	0.371210i
$635$	−11.7467	+	11.7467i	−0.466154	+	0.466154i
$636$	28.0503	+	4.59299i	1.11227	+	0.182124i
$637$	−15.2436	−	15.2436i	−0.603972	−	0.603972i
$638$	−1.19516	+	14.6953i	−0.0473167	+	0.581793i
$639$	2.43999			0.0965245
$640$	2.43965	+	11.0475i	0.0964358	+	0.436692i
$641$	20.3125			0.802296			0.401148	−	0.916013i	$-0.368611\pi$
$641$	20.3125			0.802296			0.401148	+	0.916013i	$0.368611\pi$
$642$	−2.04950	+	25.2000i	−0.0808873	+	0.994566i
$643$	7.78443	+	7.78443i	0.306988	+	0.306988i	0.843740	−	0.536752i	$-0.180349\pi$
$643$	7.78443	+	7.78443i	0.306988	+	0.306988i	−0.536752	+	0.843740i	$0.680349\pi$
$644$	2.19226	+	0.358964i	0.0863871	+	0.0141452i
$645$	−0.515563	+	0.515563i	−0.0203003	+	0.0203003i
$646$	−43.4317	+	36.8985i	−1.70880	+	1.45175i
$647$			21.7693i			0.855840i	0.903817	+	0.427920i	$0.140754\pi$
$647$			21.7693i			0.855840i	−0.903817	+	0.427920i	$0.859246\pi$
$648$	−7.53260	+	30.3271i	−0.295908	+	1.19136i
$649$			8.96611i			0.351951i
$650$	3.02605	+	3.56183i	0.118691	+	0.139707i
$651$	−4.61717	+	4.61717i	−0.180961	+	0.180961i
$652$	11.6441	+	16.2040i	0.456020	+	0.634600i
$653$	−26.3118	−	26.3118i	−1.02966	−	1.02966i	−0.999546	−	0.0301152i	$-0.990413\pi$
$653$	−26.3118	−	26.3118i	−1.02966	−	1.02966i	−0.0301152	−	0.999546i	$-0.509587\pi$
$654$	−27.6512	−	2.24885i	−1.08125	−	0.0879369i
$655$	−16.6479			−0.650489
$656$	7.01511	−	20.8470i	0.273894	−	0.813937i
$657$	1.36298			0.0531751
$658$	4.48491	+	0.364754i	0.174840	+	0.0142196i
$659$	−20.2389	−	20.2389i	−0.788397	−	0.788397i	0.192835	−	0.981231i	$-0.438232\pi$
$659$	−20.2389	−	20.2389i	−0.788397	−	0.788397i	−0.981231	+	0.192835i	$0.938232\pi$
$660$	14.1483	−	10.1669i	0.550721	−	0.395745i
$661$	6.81905	−	6.81905i	0.265230	−	0.265230i	−0.561945	−	0.827175i	$-0.689947\pi$
$661$	6.81905	−	6.81905i	0.265230	−	0.265230i	0.827175	+	0.561945i	$0.189947\pi$
$662$	20.0515	+	23.6017i	0.779322	+	0.917308i
$663$			35.1702i			1.36590i
$664$	−25.0322	+	15.0713i	−0.971436	+	0.584881i
$665$		−	5.26289i		−	0.204086i
$666$	12.6485	−	10.7458i	0.490118	−	0.416392i
$667$	2.73942	−	2.73942i	0.106071	−	0.106071i
$668$	−1.26229	+	7.70905i	−0.0488395	+	0.298272i
$669$	−3.34143	−	3.34143i	−0.129187	−	0.129187i
$670$	−0.315811	+	3.88311i	−0.0122008	+	0.150018i
$671$	−57.1105			−2.20473
$672$	−2.91368	−	7.30242i	−0.112398	−	0.281697i
$673$	−8.19512			−0.315899			−0.157949	−	0.987447i	$-0.550488\pi$
$673$	−8.19512			−0.315899			−0.157949	+	0.987447i	$0.550488\pi$
$674$	−2.98301	+	36.6782i	−0.114901	+	1.41279i
$675$	−2.77424	−	2.77424i	−0.106781	−	0.106781i
$676$	−0.671628	+	4.10176i	−0.0258318	+	0.157760i
$677$	12.8834	−	12.8834i	0.495151	−	0.495151i	−0.414774	−	0.909925i	$-0.636139\pi$
$677$	12.8834	−	12.8834i	0.495151	−	0.495151i	0.909925	+	0.414774i	$0.136139\pi$
$678$	14.0150	−	11.9068i	0.538241	−	0.457276i
$679$		−	3.63960i		−	0.139675i
$680$	−7.71431	−	12.8128i	−0.295830	−	0.491349i
$681$			37.5368i			1.43841i
$682$	−18.6194	−	21.9161i	−0.712973	−	0.839211i
$683$	15.0673	−	15.0673i	0.576535	−	0.576535i	−0.357412	−	0.933947i	$-0.616341\pi$
$683$	15.0673	−	15.0673i	0.576535	−	0.576535i	0.933947	+	0.357412i	$0.116341\pi$
$684$	13.0041	−	9.34465i	0.497223	−	0.357302i
$685$	−5.95027	−	5.95027i	−0.227348	−	0.227348i
$686$	−13.1635	−	1.07058i	−0.502585	−	0.0408748i
$687$	26.6940			1.01844
$688$	−1.29795	+	0.644356i	−0.0494840	+	0.0245659i
$689$	23.3367			0.889058
$690$	−4.56288	−	0.371096i	−0.173706	−	0.0141274i
$691$	−5.23733	−	5.23733i	−0.199237	−	0.199237i	0.600436	−	0.799673i	$-0.294994\pi$
$691$	−5.23733	−	5.23733i	−0.199237	−	0.199237i	−0.799673	+	0.600436i	$0.794994\pi$
$692$	−13.5367	−	18.8377i	−0.514588	−	0.716104i
$693$	−2.22052	+	2.22052i	−0.0843504	+	0.0843504i
$694$	16.6467	+	19.5942i	0.631902	+	0.743786i
$695$			2.14741i			0.0814559i
$696$	−13.3071	−	3.30519i	−0.504404	−	0.125283i
$697$			29.0766i			1.10135i
$698$	−30.5185	+	25.9278i	−1.15514	+	0.981381i
$699$	−23.2590	+	23.2590i	−0.879736	+	0.879736i
$700$	1.36300	+	0.223180i	0.0515166	+	0.00843540i
$701$	21.7664	+	21.7664i	0.822106	+	0.822106i	0.986410	−	0.164303i	$-0.0525376\pi$
$701$	21.7664	+	21.7664i	0.822106	+	0.822106i	−0.164303	+	0.986410i	$0.552538\pi$
$702$	−1.48640	+	18.2764i	−0.0561007	+	0.689798i
$703$	85.1304			3.21075
$704$	33.0952	−	10.1830i	1.24732	−	0.383786i
$705$	−9.27297			−0.349240
$706$	1.57126	−	19.3198i	0.0591352	−	0.727109i
$707$	9.28836	+	9.28836i	0.349325	+	0.349325i
$708$	−8.22870	−	1.34738i	−0.309253	−	0.0506376i
$709$	−23.9643	+	23.9643i	−0.899997	+	0.899997i	−0.995435	−	0.0954387i	$-0.969575\pi$
$709$	−23.9643	+	23.9643i	−0.899997	+	0.899997i	0.0954387	+	0.995435i	$0.469575\pi$
$710$	−2.50308	+	2.12655i	−0.0939388	+	0.0798081i
$711$		−	5.27371i		−	0.197779i
$712$	−4.98398	−	1.23791i	−0.186783	−	0.0463928i
$713$			7.55640i			0.282990i
$714$	6.72926	+	7.92073i	0.251836	+	0.296426i
$715$	10.1146	−	10.1146i	0.378266	−	0.378266i
$716$	5.12266	+	7.12872i	0.191443	+	0.266413i
$717$	27.5829	+	27.5829i	1.03010	+	1.03010i
$718$	−45.6001	−	3.70862i	−1.70178	−	0.138405i
$719$	−44.4408			−1.65736			−0.828681	−	0.559721i	$-0.810908\pi$
$719$	−44.4408			−1.65736			−0.828681	+	0.559721i	$0.810908\pi$
$720$	1.86865	+	3.76411i	0.0696406	+	0.140280i
$721$	−1.82526			−0.0679762
$722$	55.0855	+	4.48006i	2.05007	+	0.166730i
$723$	10.1891	+	10.1891i	0.378937	+	0.378937i
$724$	4.38800	−	3.15320i	0.163079	−	0.117188i
$725$	1.70319	−	1.70319i	0.0632548	−	0.0632548i
$726$	−14.2529	−	16.7765i	−0.528975	−	0.622635i
$727$		−	46.6543i		−	1.73031i	−0.501504	−	0.865155i	$-0.667220\pi$
$727$		−	46.6543i		−	1.73031i	0.501504	−	0.865155i	$-0.332780\pi$
$728$	−3.32958	−	5.53014i	−0.123402	−	0.204960i
$729$		−	12.0815i		−	0.447464i
$730$	−1.39823	+	1.18790i	−0.0517507	+	0.0439661i
$731$	1.35453	−	1.35453i	0.0500992	−	0.0500992i
$732$	8.58226	−	52.4135i	0.317210	−	1.93726i
$733$	19.4202	+	19.4202i	0.717303	+	0.717303i	0.968052	−	0.250749i	$-0.0806770\pi$
$733$	19.4202	+	19.4202i	0.717303	+	0.717303i	−0.250749	+	0.968052i	$0.580677\pi$
$734$	1.87679	−	23.0765i	0.0692737	−	0.851769i
$735$	13.1285			0.484251
$736$	−8.35977	−	3.59128i	−0.308145	−	0.132376i
$737$	11.9238			0.439219
$738$	0.662287	−	8.14328i	0.0243791	−	0.299758i
$739$	−20.5243	−	20.5243i	−0.754999	−	0.754999i	0.220409	−	0.975408i	$-0.429261\pi$
$739$	−20.5243	−	20.5243i	−0.754999	−	0.754999i	−0.975408	+	0.220409i	$0.929261\pi$
$740$	−3.61006	+	22.0473i	−0.132709	+	0.810476i
$741$	35.8431	−	35.8431i	1.31673	−	1.31673i
$742$	5.25570	−	4.46511i	0.192943	−	0.163919i
$743$			12.9245i			0.474154i	0.971491	+	0.237077i	$0.0761893\pi$
$743$			12.9245i			0.474154i	−0.971491	+	0.237077i	$0.923811\pi$
$744$	22.9116	−	13.7946i	0.839982	−	0.505735i
$745$			3.69732i			0.135459i
$746$	−20.1129	−	23.6740i	−0.736384	−	0.866767i
$747$	−7.67443	+	7.67443i	−0.280793	+	0.280793i
$748$	−37.1716	+	26.7113i	−1.35913	+	0.976662i
$749$	4.33765	+	4.33765i	0.158494	+	0.158494i
$750$	−2.83690	−	0.230722i	−0.103589	−	0.00842479i
$751$	−52.2694			−1.90734			−0.953668	−	0.300861i	$-0.902726\pi$
$751$	−52.2694			−1.90734			−0.953668	+	0.300861i	$0.902726\pi$
$752$	−17.4673	−	5.87783i	−0.636966	−	0.214342i
$753$	29.7069			1.08258
$754$	−11.2204	−	0.912546i	−0.408623	−	0.0332330i
$755$	8.99036	+	8.99036i	0.327193	+	0.327193i
$756$	3.16214	+	4.40045i	0.115006	+	0.160043i
$757$	−34.4514	+	34.4514i	−1.25216	+	1.25216i	−0.297407	+	0.954751i	$0.596122\pi$
$757$	−34.4514	+	34.4514i	−1.25216	+	1.25216i	−0.954751	+	0.297407i	$0.903878\pi$
$758$	−32.3132	−	38.0346i	−1.17367	−	1.38148i
$759$			14.0111i			0.508572i
$760$	−5.19604	+	20.9199i	−0.188480	+	0.758843i
$761$			47.7467i			1.73082i	0.501067	+	0.865408i	$0.332941\pi$
$761$			47.7467i			1.73082i	−0.501067	+	0.865408i	$0.667059\pi$
$762$	−36.0344	+	30.6139i	−1.30539	+	1.10903i
$763$	−4.75956	+	4.75956i	−0.172308	+	0.172308i
$764$	−11.0733	−	1.81317i	−0.400620	−	0.0655980i
$765$	−3.92819	−	3.92819i	−0.142024	−	0.142024i
$766$	0.716360	−	8.80815i	0.0258831	−	0.318251i
$767$	−6.84595			−0.247193
$768$	4.37213	+	31.9036i	0.157766	+	1.15122i
$769$	−17.9108			−0.645882			−0.322941	−	0.946419i	$-0.604671\pi$
$769$	−17.9108			−0.645882			−0.322941	+	0.946419i	$0.604671\pi$
$770$	0.342656	−	4.21320i	0.0123485	−	0.151833i
$771$	8.14247	+	8.14247i	0.293244	+	0.293244i
$772$	−7.71124	−	1.26265i	−0.277534	−	0.0454437i
$773$	3.73170	−	3.73170i	0.134220	−	0.134220i	−0.636805	−	0.771025i	$-0.719744\pi$
$773$	3.73170	−	3.73170i	0.134220	−	0.134220i	0.771025	+	0.636805i	$0.219744\pi$
$774$	−0.410207	+	0.348502i	−0.0147446	+	0.0125266i
$775$			4.69807i			0.168760i
$776$	−3.59336	+	14.4673i	−0.128994	+	0.519346i
$777$		−	15.5254i		−	0.556971i
$778$	−2.72972	−	3.21304i	−0.0978652	−	0.115193i
$779$	29.6329	−	29.6329i	1.06171	−	1.06171i
$780$	7.76279	+	10.8027i	0.277952	+	0.386800i
$781$	7.10805	+	7.10805i	0.254346	+	0.254346i
$782$	11.9880	+	0.974974i	0.428690	+	0.0348650i
$783$	9.45012			0.337720
$784$	24.7298	+	8.32170i	0.883208	+	0.297204i
$785$	−10.1517			−0.362328
$786$	−47.2285	−	3.84105i	−1.68458	−	0.137006i
$787$	2.40160	+	2.40160i	0.0856076	+	0.0856076i	0.748614	−	0.663006i	$-0.230720\pi$
$787$	2.40160	+	2.40160i	0.0856076	+	0.0856076i	−0.663006	+	0.748614i	$0.730720\pi$
$788$	−1.39751	+	1.00425i	−0.0497843	+	0.0357748i
$789$	38.6207	−	38.6207i	1.37493	−	1.37493i
$790$	4.59626	+	5.41007i	0.163528	+	0.192481i
$791$		−	4.46187i		−	0.158646i
$792$	11.0188	−	6.63419i	0.391536	−	0.235736i
$793$		−	43.6060i		−	1.54849i
$794$	35.8151	−	30.4277i	1.27103	−	1.07984i
$795$	−10.0493	+	10.0493i	−0.356413	+	0.356413i
$796$	5.01839	−	30.6482i	0.177872	−	1.08630i
$797$	35.4972	+	35.4972i	1.25738	+	1.25738i	0.952341	+	0.305035i	$0.0986682\pi$
$797$	35.4972	+	35.4972i	1.25738	+	1.25738i	0.305035	+	0.952341i	$0.401332\pi$
$798$	1.21427	−	14.9303i	0.0429846	−	0.528526i
$799$	24.3627			0.861892
$800$	−5.19755	−	2.23282i	−0.183761	−	0.0789421i
$801$	−1.90753			−0.0673992
$802$	−2.40618	+	29.5857i	−0.0849652	+	1.04471i
$803$	3.97058	+	3.97058i	0.140119	+	0.140119i
$804$	−1.79184	+	10.9431i	−0.0631935	+	0.385934i
$805$	−0.785403	+	0.785403i	−0.0276818	+	0.0276818i
$806$	16.7337	−	14.2166i	0.589421	−	0.500757i
$807$			37.2206i			1.31023i
$808$	−27.7506	−	46.0914i	−0.976264	−	1.62149i
$809$			11.9182i			0.419021i	0.977806	+	0.209510i	$0.0671870\pi$
$809$			11.9182i			0.419021i	−0.977806	+	0.209510i	$0.932813\pi$
$810$	−10.1161	−	11.9073i	−0.355444	−	0.418378i
$811$	−22.1494	+	22.1494i	−0.777772	+	0.777772i	−0.979452	−	0.201680i	$-0.935360\pi$
$811$	−22.1494	+	22.1494i	−0.777772	+	0.777772i	0.201680	+	0.979452i	$0.435360\pi$
$812$	−2.70156	+	1.94133i	−0.0948063	+	0.0681273i
$813$	9.32527	+	9.32527i	0.327051	+	0.327051i
$814$	68.1510	+	5.54267i	2.38869	+	0.194270i
$815$	−9.97694			−0.349477
$816$	−18.9285	−	38.1285i	−0.662630	−	1.33476i
$817$	−2.76090			−0.0965915
$818$	−25.9394	−	2.10963i	−0.906949	−	0.0737615i
$819$	−1.69545	−	1.69545i	−0.0592436	−	0.0592436i
$820$	6.41780	+	8.93105i	0.224119	+	0.311886i
$821$	13.3909	−	13.3909i	0.467344	−	0.467344i	−0.433709	−	0.901053i	$-0.642795\pi$
$821$	13.3909	−	13.3909i	0.467344	−	0.467344i	0.901053	+	0.433709i	$0.142795\pi$
$822$	−15.5074	−	18.2531i	−0.540884	−	0.636652i
$823$		−	43.9496i		−	1.53199i	−0.642848	−	0.765994i	$-0.722247\pi$
$823$		−	43.9496i		−	1.53199i	0.642848	−	0.765994i	$-0.277753\pi$
$824$	7.25536	+	1.80207i	0.252752	+	0.0627782i
$825$			8.71119i			0.303285i
$826$	−1.54179	+	1.30986i	−0.0536456	+	0.0455760i
$827$	1.79096	−	1.79096i	0.0622777	−	0.0622777i	−0.675282	−	0.737560i	$-0.735978\pi$
$827$	1.79096	−	1.79096i	0.0622777	−	0.0622777i	0.737560	+	0.675282i	$0.235978\pi$
$828$	−3.33519	−	0.546109i	−0.115906	−	0.0189786i
$829$	13.4979	+	13.4979i	0.468801	+	0.468801i	0.901526	−	0.432725i	$-0.142448\pi$
$829$	13.4979	+	13.4979i	0.468801	+	0.468801i	−0.432725	+	0.901526i	$0.642448\pi$
$830$	1.18427	−	14.5615i	0.0411067	−	0.505436i
$831$	−29.2742			−1.01551
$832$	7.77509	+	25.2694i	0.269553	+	0.876060i
$833$	−34.4923			−1.19509
$834$	−0.495456	+	6.09198i	−0.0171562	+	0.210948i
$835$	−2.76186	−	2.76186i	−0.0955780	−	0.0955780i
$836$	65.1051	+	10.6604i	2.25171	+	0.368698i
$837$	−13.0336	+	13.0336i	−0.450507	+	0.450507i
$838$	22.7610	−	19.3372i	0.786266	−	0.667993i
$839$			14.5332i			0.501741i	0.968021	+	0.250870i	$0.0807168\pi$
$839$			14.5332i			0.501741i	−0.968021	+	0.250870i	$0.919283\pi$
$840$	3.81520	+	0.947613i	0.131637	+	0.0326957i
$841$		−	23.1983i		−	0.799941i
$842$	21.0658	+	24.7956i	0.725975	+	0.854515i
$843$	42.6532	−	42.6532i	1.46905	−	1.46905i
$844$	−3.54042	−	4.92686i	−0.121866	−	0.169590i
$845$	−1.46950	−	1.46950i	−0.0505524	−	0.0505524i
$846$	−6.82311	−	0.554918i	−0.234583	−	0.0190785i
$847$	−5.34105			−0.183521
$848$	−25.2996	+	12.5598i	−0.868793	+	0.431304i
$849$	−54.4136			−1.86747
$850$	7.45333	+	0.606174i	0.255647	+	0.0207916i
$851$	−12.7043	−	12.7043i	−0.435499	−	0.435499i
$852$	−7.59161	+	5.45529i	−0.260084	+	0.186895i
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	−0.480423	−	0.877037i	$-0.659517\pi$
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	0.877037	+	0.480423i	$0.159517\pi$
$854$	−8.34331	−	9.82056i	−0.285502	−	0.336053i
$855$			8.00669i			0.273823i
$856$	−12.9595	−	21.5246i	−0.442946	−	0.735695i
$857$		−	15.6443i		−	0.534399i	−0.963641	−	0.267200i	$-0.913902\pi$
$857$		−	15.6443i		−	0.534399i	0.963641	−	0.267200i	$-0.0860983\pi$
$858$	31.0278	−	26.3605i	1.05927	−	0.899932i
$859$	12.0947	−	12.0947i	0.412665	−	0.412665i	−0.470001	−	0.882666i	$-0.655746\pi$
$859$	12.0947	−	12.0947i	0.412665	−	0.412665i	0.882666	+	0.470001i	$0.155746\pi$
$860$	0.117079	−	0.715026i	0.00399237	−	0.0243822i
$861$	−5.40422	−	5.40422i	−0.184175	−	0.184175i
$862$	0.808687	−	9.94338i	0.0275440	−	0.338673i
$863$	−9.28120			−0.315936			−0.157968	−	0.987444i	$-0.550494\pi$
$863$	−9.28120			−0.315936			−0.157968	+	0.987444i	$0.550494\pi$
$864$	−8.22488	−	20.6137i	−0.279816	−	0.701291i
$865$	11.5985			0.394362
$866$	−1.64153	+	20.1838i	−0.0557816	+	0.685874i
$867$	15.5973	+	15.5973i	0.529711	+	0.529711i
$868$	1.04851	−	6.40347i	0.0355889	−	0.217348i
$869$	15.3631	−	15.3631i	0.521157	−	0.521157i
$870$	5.22473	−	4.43880i	0.177135	−	0.150490i
$871$			9.10425i			0.308486i
$872$	23.6182	−	14.2200i	0.799814	−	0.481551i
$873$			5.53709i			0.187402i
$874$	−11.2237	−	13.2110i	−0.379648	−	0.446868i
$875$	−0.488311	+	0.488311i	−0.0165079	+	0.0165079i
$876$	−4.24070	+	3.04734i	−0.143280	+	0.102960i
$877$	−2.97610	−	2.97610i	−0.100496	−	0.100496i	0.655071	−	0.755567i	$-0.272639\pi$
$877$	−2.97610	−	2.97610i	−0.100496	−	0.100496i	−0.755567	+	0.655071i	$0.772639\pi$
$878$	36.5143	+	2.96968i	1.23230	+	0.100222i
$879$	20.7194			0.698849
$880$	−5.52173	+	16.4091i	−0.186138	+	0.553150i
$881$	29.3318			0.988214			0.494107	−	0.869401i	$-0.335495\pi$
$881$	29.3318			0.988214			0.494107	+	0.869401i	$0.335495\pi$
$882$	9.66001	+	0.785641i	0.325270	+	0.0264539i
$883$	35.5597	+	35.5597i	1.19668	+	1.19668i	0.975155	+	0.221525i	$0.0711033\pi$
$883$	35.5597	+	35.5597i	1.19668	+	1.19668i	0.221525	+	0.975155i	$0.428897\pi$
$884$	−20.3950	−	28.3818i	−0.685960	−	0.954585i
$885$	2.94803	−	2.94803i	0.0990968	−	0.0990968i
$886$	14.4240	+	16.9778i	0.484583	+	0.570382i
$887$		−	4.51671i		−	0.151656i	−0.997121	−	0.0758282i	$-0.975840\pi$
$887$		−	4.51671i		−	0.151656i	0.997121	−	0.0758282i	$-0.0241601\pi$
$888$	−15.3282	+	61.7131i	−0.514380	+	2.07096i
$889$			11.4721i			0.384762i
$890$	1.95685	−	1.66249i	0.0655937	−	0.0557268i
$891$	−33.8133	+	33.8133i	−1.13279	+	1.13279i
$892$	4.63416	+	0.758805i	0.155163	+	0.0254067i
$893$	−24.8289	−	24.8289i	−0.830867	−	0.830867i
$894$	−0.853055	+	10.4889i	−0.0285304	+	0.350802i
$895$	−4.38920			−0.146715
$896$	6.58594	+	4.20332i	0.220021	+	0.140423i
$897$	−10.6980			−0.357196
$898$	1.45200	−	17.8533i	0.0484537	−	0.595773i
$899$	−8.00169	−	8.00169i	−0.266871	−	0.266871i
$900$	−2.07360	−	0.339534i	−0.0691199	−	0.0113178i
$901$	26.4025	−	26.4025i	0.879594	−	0.879594i
$902$	25.6519	−	21.7933i	0.854116	−	0.725636i
$903$			0.503511i			0.0167558i
$904$	−4.40519	+	17.7358i	−0.146514	+	0.589884i
$905$			2.70172i			0.0898083i
$906$	23.4304	+	27.5790i	0.778424	+	0.916251i
$907$	−5.06769	+	5.06769i	−0.168270	+	0.168270i	−0.786218	−	0.617949i	$-0.787964\pi$
$907$	−5.06769	+	5.06769i	−0.168270	+	0.168270i	0.617949	+	0.786218i	$0.287964\pi$
$908$	−21.7674	−	30.2917i	−0.722378	−	1.00526i
$909$	−14.1308	−	14.1308i	−0.468690	−	0.468690i
$910$	3.21693	+	0.261631i	0.106640	+	0.00867297i
$911$	36.7140			1.21639			0.608194	−	0.793788i	$-0.291894\pi$
$911$	36.7140			1.21639			0.608194	+	0.793788i	$0.291894\pi$
$912$	−19.5673	+	58.1486i	−0.647938	+	1.92549i
$913$	−44.7135			−1.47980
$914$	−23.8839	−	1.94246i	−0.790008	−	0.0642507i
$915$	18.7777	+	18.7777i	0.620773	+	0.620773i
$916$	−21.5417	+	15.4797i	−0.711757	+	0.511465i
$917$	−8.12937	+	8.12937i	−0.268456	+	0.268456i
$918$	18.9957	+	22.3590i	0.626951	+	0.737958i
$919$			21.5651i			0.711365i	0.934607	+	0.355683i	$0.115752\pi$
$919$			21.5651i			0.711365i	−0.934607	+	0.355683i	$0.884248\pi$
$920$	3.89738	−	2.34653i	0.128493	−	0.0773628i
$921$			20.0179i			0.659612i
$922$	−20.1023	+	17.0785i	−0.662035	+	0.562449i
$923$	−5.42725	+	5.42725i	−0.178640	+	0.178640i
$924$	1.94416	−	11.8734i	0.0639582	−	0.390605i
$925$	−7.89871	−	7.89871i	−0.259708	−	0.259708i
$926$	−1.61589	+	19.8685i	−0.0531013	+	0.652918i
$927$	2.77685			0.0912038
$928$	12.6553	−	5.04949i	0.415431	−	0.165758i
$929$	−45.6603			−1.49807			−0.749033	−	0.662532i	$-0.769482\pi$
$929$	−45.6603			−1.49807			−0.749033	+	0.662532i	$0.769482\pi$
$930$	−1.08395	+	13.3279i	−0.0355441	+	0.437040i
$931$	35.1522	+	35.1522i	1.15207	+	1.15207i
$932$	5.28189	−	32.2575i	0.173014	−	1.05663i
$933$	20.3269	−	20.3269i	0.665474	−	0.665474i
$934$	−18.4303	+	15.6579i	−0.603056	+	0.512342i
$935$		−	22.8868i		−	0.748478i
$936$	5.06544	+	8.41326i	0.165569	+	0.274996i
$937$		−	2.29807i		−	0.0750746i	−0.999295	−	0.0375373i	$-0.988049\pi$
$937$		−	2.29807i		−	0.0750746i	0.999295	−	0.0375373i	$-0.0119513\pi$
$938$	1.74195	+	2.05038i	0.0568768	+	0.0669473i
$939$	−26.2681	+	26.2681i	−0.857226	+	0.857226i
$940$	7.48316	−	5.37736i	0.244074	−	0.175390i
$941$	−24.1999	−	24.1999i	−0.788894	−	0.788894i	0.192419	−	0.981313i	$-0.438367\pi$
$941$	−24.1999	−	24.1999i	−0.788894	−	0.788894i	−0.981313	+	0.192419i	$0.938367\pi$
$942$	−28.7992	−	2.34222i	−0.938329	−	0.0763135i
$943$	−8.84448			−0.288016
$944$	7.42179	−	3.68447i	0.241559	−	0.119919i
$945$	−2.70939			−0.0881364
$946$	−2.21023	−	0.179756i	−0.0718609	−	0.00584439i
$947$	24.5182	+	24.5182i	0.796733	+	0.796733i	0.982579	−	0.185846i	$-0.0595025\pi$
$947$	24.5182	+	24.5182i	0.796733	+	0.796733i	−0.185846	+	0.982579i	$0.559502\pi$
$948$	11.7909	+	16.4083i	0.382950	+	0.532915i
$949$	−3.03168	+	3.03168i	−0.0984125	+	0.0984125i
$950$	−6.97817	−	8.21371i	−0.226402	−	0.266488i
$951$		−	20.5445i		−	0.666202i
$952$	−10.0236	−	2.48965i	−0.324867	−	0.0806900i
$953$			32.3462i			1.04780i	0.851781	+	0.523898i	$0.175523\pi$
$953$			32.3462i			1.04780i	−0.851781	+	0.523898i	$0.824477\pi$
$954$	−7.99574	+	6.79298i	−0.258872	+	0.219931i
$955$	3.96716	−	3.96716i	0.128374	−	0.128374i
$956$	−38.2543	−	6.26381i	−1.23723	−	0.202586i
$957$	−14.8368	−	14.8368i	−0.479605	−	0.479605i
$958$	1.63385	−	20.0894i	0.0527874	−	0.649059i
$959$	−5.81116			−0.187652
$960$	−14.2297	−	7.53347i	−0.459263	−	0.243142i
$961$	−8.92816			−0.288005
$962$	−4.23203	+	52.0358i	−0.136446	+	1.67770i
$963$	−6.59907	−	6.59907i	−0.212652	−	0.212652i
$964$	−14.1311	−	2.31385i	−0.455132	−	0.0745240i
$965$	2.76264	−	2.76264i	0.0889326	−	0.0889326i
$966$	−2.40932	+	2.04690i	−0.0775185	+	0.0658578i
$967$		−	14.6983i		−	0.472665i	−0.971672	−	0.236333i	$-0.924054\pi$
$967$		−	14.6983i		−	0.472665i	0.971672	−	0.236333i	$-0.0759455\pi$
$968$	21.2305	+	5.27321i	0.682376	+	0.169487i
$969$		−	81.1036i		−	2.60542i
$970$	−4.82581	−	5.68026i	−0.154947	−	0.182382i
$971$	29.1065	−	29.1065i	0.934073	−	0.934073i	−0.0638845	−	0.997957i	$-0.520349\pi$
$971$	29.1065	−	29.1065i	0.934073	−	0.934073i	0.997957	+	0.0638845i	$0.0203489\pi$
$972$	−12.2141	−	16.9972i	−0.391768	−	0.545186i
$973$	1.04860	+	1.04860i	0.0336167	+	0.0336167i
$974$	36.7084	+	2.98546i	1.17621	+	0.0956604i
$975$	−6.65131			−0.213012
$976$	23.4686	+	47.2738i	0.751212	+	1.51320i
$977$	17.3533			0.555180			0.277590	−	0.960700i	$-0.410464\pi$
$977$	17.3533			0.555180			0.277590	+	0.960700i	$0.410464\pi$
$978$	−28.3035	−	2.30190i	−0.905048	−	0.0736068i
$979$	−5.55691	−	5.55691i	−0.177600	−	0.177600i
$980$	−10.5945	+	7.61315i	−0.338429	+	0.243193i
$981$	7.24094	−	7.24094i	0.231186	−	0.231186i
$982$	−4.49076	−	5.28589i	−0.143306	−	0.168680i
$983$			27.5174i			0.877668i	0.898568	+	0.438834i	$0.144608\pi$
$983$			27.5174i			0.877668i	−0.898568	+	0.438834i	$0.855392\pi$
$984$	16.1461	+	26.8172i	0.514717	+	0.854901i
$985$		−	0.860458i		−	0.0274165i
$986$	−13.7269	+	11.6620i	−0.437152	+	0.371394i
$987$	−4.52809	+	4.52809i	−0.144131	+	0.144131i
$988$	−8.13961	+	49.7101i	−0.258955	+	1.58149i
$989$	0.412020	+	0.412020i	0.0131015	+	0.0131015i
$990$	−0.521300	+	6.40975i	−0.0165680	+	0.203715i
$991$	6.96363			0.221207			0.110604	−	0.993865i	$-0.464722\pi$
$991$	6.96363			0.221207			0.110604	+	0.993865i	$0.464722\pi$
$992$	−10.4899	+	24.4184i	−0.333056	+	0.775286i
$993$	−44.0735			−1.39863
$994$	−0.183861	+	2.26070i	−0.00583171	+	0.0717050i
$995$	10.9801	+	10.9801i	0.348092	+	0.348092i
$996$	6.71931	−	41.0361i	0.212909	−	1.30028i
$997$	−15.7051	+	15.7051i	−0.497385	+	0.497385i	−0.910623	−	0.413238i	$-0.864398\pi$
$997$	−15.7051	+	15.7051i	−0.497385	+	0.497385i	0.413238	+	0.910623i	$0.364398\pi$
$998$	−8.08242	+	6.86663i	−0.255845	+	0.217359i
$999$		−	43.8259i		−	1.38659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.l.a.61.5	yes	16
3.2	odd	2		720.2.t.c.541.4		16
4.3	odd	2		320.2.l.a.81.2		16
5.2	odd	4		400.2.q.h.349.8		16
5.3	odd	4		400.2.q.g.349.1		16
5.4	even	2		400.2.l.h.301.4		16
8.3	odd	2		640.2.l.a.161.7		16
8.5	even	2		640.2.l.b.161.2		16
12.11	even	2		2880.2.t.c.721.3		16
16.3	odd	4		640.2.l.a.481.7		16
16.5	even	4	inner	80.2.l.a.21.5	✓	16
16.11	odd	4		320.2.l.a.241.2		16
16.13	even	4		640.2.l.b.481.2		16
20.3	even	4		1600.2.q.h.849.7		16
20.7	even	4		1600.2.q.g.849.2		16
20.19	odd	2		1600.2.l.i.401.7		16
32.5	even	8		5120.2.a.v.1.2		8
32.11	odd	8		5120.2.a.u.1.2		8
32.21	even	8		5120.2.a.s.1.7		8
32.27	odd	8		5120.2.a.t.1.7		8
48.5	odd	4		720.2.t.c.181.4		16
48.11	even	4		2880.2.t.c.2161.2		16
80.27	even	4		1600.2.q.h.49.7		16
80.37	odd	4		400.2.q.g.149.1		16
80.43	even	4		1600.2.q.g.49.2		16
80.53	odd	4		400.2.q.h.149.8		16
80.59	odd	4		1600.2.l.i.1201.7		16
80.69	even	4		400.2.l.h.101.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.5	✓	16	16.5	even	4	inner
80.2.l.a.61.5	yes	16	1.1	even	1	trivial
320.2.l.a.81.2		16	4.3	odd	2
320.2.l.a.241.2		16	16.11	odd	4
400.2.l.h.101.4		16	80.69	even	4
400.2.l.h.301.4		16	5.4	even	2
400.2.q.g.149.1		16	80.37	odd	4
400.2.q.g.349.1		16	5.3	odd	4
400.2.q.h.149.8		16	80.53	odd	4
400.2.q.h.349.8		16	5.2	odd	4
640.2.l.a.161.7		16	8.3	odd	2
640.2.l.a.481.7		16	16.3	odd	4
640.2.l.b.161.2		16	8.5	even	2
640.2.l.b.481.2		16	16.13	even	4
720.2.t.c.181.4		16	48.5	odd	4
720.2.t.c.541.4		16	3.2	odd	2
1600.2.l.i.401.7		16	20.19	odd	2
1600.2.l.i.1201.7		16	80.59	odd	4
1600.2.q.g.49.2		16	80.43	even	4
1600.2.q.g.849.2		16	20.7	even	4
1600.2.q.h.49.7		16	80.27	even	4
1600.2.q.h.849.7		16	20.3	even	4
2880.2.t.c.721.3		16	12.11	even	2
2880.2.t.c.2161.2		16	48.11	even	4
5120.2.a.s.1.7		8	32.21	even	8
5120.2.a.t.1.7		8	32.27	odd	8
5120.2.a.u.1.2		8	32.11	odd	8
5120.2.a.v.1.2		8	32.5	even	8

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.114638 - 1.40956i) q^{2} +(1.42313 + 1.42313i) q^{3} +(-1.97372 - 0.323179i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.16913 - 1.84284i) q^{6} -0.690576i q^{7} +(-0.681804 + 2.74502i) q^{8} +1.05061i q^{9} +O(q^{10})\)	\(q+(0.114638 - 1.40956i) q^{2} +(1.42313 + 1.42313i) q^{3} +(-1.97372 - 0.323179i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.16913 - 1.84284i) q^{6} -0.690576i q^{7} +(-0.681804 + 2.74502i) q^{8} +1.05061i q^{9} +(-0.915648 - 1.07777i) q^{10} +(-3.06057 + 3.06057i) q^{11} +(-2.34893 - 3.26878i) q^{12} +(-2.33686 - 2.33686i) q^{13} +(-0.973408 - 0.0791665i) q^{14} +2.01261 q^{15} +(3.79111 + 1.27573i) q^{16} -5.28770 q^{17} +(1.48089 + 0.120440i) q^{18} +(5.38887 + 5.38887i) q^{19} +(-1.62415 + 1.16711i) q^{20} +(0.982780 - 0.982780i) q^{21} +(3.96320 + 4.66492i) q^{22} -1.60841i q^{23} +(-4.87682 + 2.93623i) q^{24} -1.00000i q^{25} +(-3.56183 + 3.02605i) q^{26} +(2.77424 - 2.77424i) q^{27} +(-0.223180 + 1.36300i) q^{28} +(1.70319 + 1.70319i) q^{29} +(0.230722 - 2.83690i) q^{30} -4.69807 q^{31} +(2.23282 - 5.19755i) q^{32} -8.71119 q^{33} +(-0.606174 + 7.45333i) q^{34} +(-0.488311 - 0.488311i) q^{35} +(0.339534 - 2.07360i) q^{36} +(7.89871 - 7.89871i) q^{37} +(8.21371 - 6.97817i) q^{38} -6.65131i q^{39} +(1.45892 + 2.42313i) q^{40} -5.49891i q^{41} +(-1.27262 - 1.49795i) q^{42} +(-0.256166 + 0.256166i) q^{43} +(7.02981 - 5.05159i) q^{44} +(0.742891 + 0.742891i) q^{45} +(-2.26715 - 0.184385i) q^{46} -4.60743 q^{47} +(3.57972 + 7.21078i) q^{48} +6.52310 q^{49} +(-1.40956 - 0.114638i) q^{50} +(-7.52510 - 7.52510i) q^{51} +(3.85707 + 5.36752i) q^{52} +(-4.99318 + 4.99318i) q^{53} +(-3.59243 - 4.22850i) q^{54} +4.32830i q^{55} +(1.89565 + 0.470837i) q^{56} +15.3382i q^{57} +(2.59600 - 2.20549i) q^{58} +(1.46478 - 1.46478i) q^{59} +(-3.97232 - 0.650434i) q^{60} +(9.33004 + 9.33004i) q^{61} +(-0.538579 + 6.62221i) q^{62} +0.725523 q^{63} +(-7.07029 - 3.74313i) q^{64} -3.30482 q^{65} +(-0.998637 + 12.2789i) q^{66} +(-1.94797 - 1.94797i) q^{67} +(10.4364 + 1.70888i) q^{68} +(2.28897 - 2.28897i) q^{69} +(-0.744283 + 0.632324i) q^{70} -2.32246i q^{71} +(-2.88394 - 0.716307i) q^{72} -1.29733i q^{73} +(-10.2282 - 12.0392i) q^{74} +(1.42313 - 1.42313i) q^{75} +(-8.89454 - 12.3777i) q^{76} +(2.11356 + 2.11356i) q^{77} +(-9.37542 - 0.762495i) q^{78} -5.01968 q^{79} +(3.58280 - 1.77864i) q^{80} +11.0480 q^{81} +(-7.75103 - 0.630385i) q^{82} +(7.30477 + 7.30477i) q^{83} +(-2.25734 + 1.62212i) q^{84} +(-3.73897 + 3.73897i) q^{85} +(0.331715 + 0.390448i) q^{86} +4.84772i q^{87} +(-6.31463 - 10.4880i) q^{88} +1.81564i q^{89} +(1.13231 - 0.961985i) q^{90} +(-1.61378 + 1.61378i) q^{91} +(-0.519803 + 3.17454i) q^{92} +(-6.68597 - 6.68597i) q^{93} +(-0.528188 + 6.49445i) q^{94} +7.62102 q^{95} +(10.5744 - 4.21920i) q^{96} +5.27038 q^{97} +(0.747798 - 9.19470i) q^{98} +(-3.21546 - 3.21546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 12 * q^6	\( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Introduction

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