LMFDB - Embedded newform 80.2.l.a.21.4

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			21.4
Root			$1.32070 + 0.505727i$ of defining polynomial
Character	$\chi$	$=$	80.21
Dual form			80.2.l.a.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.257150 + 1.39064i) q^{2} +(-1.66366 + 1.66366i) q^{3} +(-1.86775 - 0.715205i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.88574 - 2.74137i) q^{6} +2.89402i q^{7} +(1.47488 - 2.41345i) q^{8} -2.53555i q^{9} +O(q^{10})$	\(q+(-0.257150 + 1.39064i) q^{2} +(-1.66366 + 1.66366i) q^{3} +(-1.86775 - 0.715205i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.88574 - 2.74137i) q^{6} +2.89402i q^{7} +(1.47488 - 2.41345i) q^{8} -2.53555i q^{9} +(1.16516 - 0.801497i) q^{10} +(1.84462 + 1.84462i) q^{11} +(4.29717 - 1.91744i) q^{12} +(-3.08011 + 3.08011i) q^{13} +(-4.02454 - 0.744198i) q^{14} +2.35278 q^{15} +(2.97696 + 2.67165i) q^{16} +7.29875 q^{17} +(3.52604 + 0.652018i) q^{18} +(-1.23593 + 1.23593i) q^{19} +(0.814970 + 1.82642i) q^{20} +(-4.81468 - 4.81468i) q^{21} +(-3.03955 + 2.09086i) q^{22} -4.60490i q^{23} +(1.56145 + 6.46887i) q^{24} +1.00000i q^{25} +(-3.49126 - 5.07536i) q^{26} +(-0.772683 - 0.772683i) q^{27} +(2.06982 - 5.40530i) q^{28} +(4.24680 - 4.24680i) q^{29} +(-0.605017 + 3.27186i) q^{30} +2.06299 q^{31} +(-4.48082 + 3.45286i) q^{32} -6.13767 q^{33} +(-1.87688 + 10.1499i) q^{34} +(2.04638 - 2.04638i) q^{35} +(-1.81344 + 4.73577i) q^{36} +(-1.17899 - 1.17899i) q^{37} +(-1.40091 - 2.03655i) q^{38} -10.2485i q^{39} +(-2.74946 + 0.663664i) q^{40} +4.61484i q^{41} +(7.93357 - 5.45738i) q^{42} +(3.03019 + 3.03019i) q^{43} +(-2.12601 - 4.76458i) q^{44} +(-1.79291 + 1.79291i) q^{45} +(6.40375 + 1.18415i) q^{46} -11.7111 q^{47} +(-9.39739 + 0.507943i) q^{48} -1.37537 q^{49} +(-1.39064 - 0.257150i) q^{50} +(-12.1427 + 12.1427i) q^{51} +(7.95577 - 3.54995i) q^{52} +(2.73048 + 2.73048i) q^{53} +(1.27322 - 0.875827i) q^{54} -2.60869i q^{55} +(6.98457 + 4.26835i) q^{56} -4.11235i q^{57} +(4.81369 + 6.99782i) q^{58} +(3.11306 + 3.11306i) q^{59} +(-4.39439 - 1.68272i) q^{60} +(2.34962 - 2.34962i) q^{61} +(-0.530498 + 2.86887i) q^{62} +7.33795 q^{63} +(-3.64944 - 7.11910i) q^{64} +4.35593 q^{65} +(1.57830 - 8.53528i) q^{66} +(8.24311 - 8.24311i) q^{67} +(-13.6322 - 5.22011i) q^{68} +(7.66101 + 7.66101i) q^{69} +(2.31955 + 3.37201i) q^{70} -3.25937i q^{71} +(-6.11942 - 3.73965i) q^{72} +12.6877i q^{73} +(1.94272 - 1.33637i) q^{74} +(-1.66366 - 1.66366i) q^{75} +(3.19235 - 1.42446i) q^{76} +(-5.33839 + 5.33839i) q^{77} +(14.2520 + 2.63541i) q^{78} -0.113885 q^{79} +(-0.215891 - 3.99417i) q^{80} +10.1776 q^{81} +(-6.41758 - 1.18671i) q^{82} +(9.76813 - 9.76813i) q^{83} +(5.54912 + 12.4361i) q^{84} +(-5.16100 - 5.16100i) q^{85} +(-4.99310 + 3.43468i) q^{86} +14.1305i q^{87} +(7.17251 - 1.73129i) q^{88} -3.74593i q^{89} +(-2.03224 - 2.95433i) q^{90} +(-8.91390 - 8.91390i) q^{91} +(-3.29345 + 8.60080i) q^{92} +(-3.43212 + 3.43212i) q^{93} +(3.01150 - 16.2858i) q^{94} +1.74787 q^{95} +(1.71017 - 13.1990i) q^{96} -13.9853 q^{97} +(0.353676 - 1.91264i) q^{98} +(4.67714 - 4.67714i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.257150	+	1.39064i	−0.181833	+	0.983329i
$2$	−0.257150	+	1.39064i	−0.181833	+	0.983329i
$3$	−1.66366	+	1.66366i	−0.960517	+	0.960517i	−0.999250	−	0.0387330i	$-0.987668\pi$
$3$	−1.66366	+	1.66366i	−0.960517	+	0.960517i	0.0387330	+	0.999250i	$0.487668\pi$
$4$	−1.86775	−	0.715205i	−0.933874	−	0.357603i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−1.88574	−	2.74137i	−0.769851	−	1.11916i
$7$			2.89402i			1.09384i	0.837186	+	0.546919i	$0.184199\pi$
$7$			2.89402i			1.09384i	−0.837186	+	0.546919i	$0.815801\pi$
$8$	1.47488	−	2.41345i	0.521450	−	0.853282i
$9$		−	2.53555i		−	0.845184i
$10$	1.16516	−	0.801497i	0.368457	−	0.253456i
$11$	1.84462	+	1.84462i	0.556175	+	0.556175i	0.928216	−	0.372041i	$-0.121342\pi$
$11$	1.84462	+	1.84462i	0.556175	+	0.556175i	−0.372041	+	0.928216i	$0.621342\pi$
$12$	4.29717	−	1.91744i	1.24048	−	0.553518i
$13$	−3.08011	+	3.08011i	−0.854268	+	0.854268i	−0.990656	−	0.136388i	$-0.956451\pi$
$13$	−3.08011	+	3.08011i	−0.854268	+	0.854268i	0.136388	+	0.990656i	$0.456451\pi$
$14$	−4.02454	−	0.744198i	−1.07560	−	0.198895i
$15$	2.35278			0.607484
$16$	2.97696	+	2.67165i	0.744241	+	0.667912i
$17$	7.29875			1.77021			0.885104	−	0.465393i	$-0.154087\pi$
$17$	7.29875			1.77021			0.885104	+	0.465393i	$0.154087\pi$
$18$	3.52604	+	0.652018i	0.831095	+	0.153682i
$19$	−1.23593	+	1.23593i	−0.283542	+	0.283542i	−0.834520	−	0.550978i	$-0.814255\pi$
$19$	−1.23593	+	1.23593i	−0.283542	+	0.283542i	0.550978	+	0.834520i	$0.314255\pi$
$20$	0.814970	+	1.82642i	0.182233	+	0.408401i
$21$	−4.81468	−	4.81468i	−1.05065	−	1.05065i
$22$	−3.03955	+	2.09086i	−0.648034	+	0.445773i
$23$		−	4.60490i		−	0.960189i	−0.877217	−	0.480094i	$-0.840602\pi$
$23$		−	4.60490i		−	0.960189i	0.877217	−	0.480094i	$-0.159398\pi$
$24$	1.56145	+	6.46887i	0.318730	+	1.32045i
$25$			1.00000i			0.200000i
$26$	−3.49126	−	5.07536i	−0.684693	−	0.995360i
$27$	−0.772683	−	0.772683i	−0.148703	−	0.148703i
$28$	2.06982	−	5.40530i	0.391159	−	1.02151i
$29$	4.24680	−	4.24680i	0.788611	−	0.788611i	−0.192656	−	0.981266i	$-0.561710\pi$
$29$	4.24680	−	4.24680i	0.788611	−	0.788611i	0.981266	+	0.192656i	$0.0617101\pi$
$30$	−0.605017	+	3.27186i	−0.110460	+	0.597357i
$31$	2.06299			0.370524			0.185262	−	0.982689i	$-0.440687\pi$
$31$	2.06299			0.370524			0.185262	+	0.982689i	$0.440687\pi$
$32$	−4.48082	+	3.45286i	−0.792104	+	0.610386i
$33$	−6.13767			−1.06843
$34$	−1.87688	+	10.1499i	−0.321882	+	1.74070i
$35$	2.04638	−	2.04638i	0.345902	−	0.345902i
$36$	−1.81344	+	4.73577i	−0.302240	+	0.789296i
$37$	−1.17899	−	1.17899i	−0.193825	−	0.193825i	0.603522	−	0.797346i	$-0.293764\pi$
$37$	−1.17899	−	1.17899i	−0.193825	−	0.193825i	−0.797346	+	0.603522i	$0.793764\pi$
$38$	−1.40091	−	2.03655i	−0.227258	−	0.330373i
$39$		−	10.2485i		−	1.64108i
$40$	−2.74946	+	0.663664i	−0.434728	+	0.104934i
$41$			4.61484i			0.720717i	0.932814	+	0.360359i	$0.117346\pi$
$41$			4.61484i			0.720717i	−0.932814	+	0.360359i	$0.882654\pi$
$42$	7.93357	−	5.45738i	1.22418	−	0.842092i
$43$	3.03019	+	3.03019i	0.462099	+	0.462099i	0.899343	−	0.437244i	$-0.144045\pi$
$43$	3.03019	+	3.03019i	0.462099	+	0.462099i	−0.437244	+	0.899343i	$0.644045\pi$
$44$	−2.12601	−	4.76458i	−0.320508	−	0.718287i
$45$	−1.79291	+	1.79291i	−0.267271	+	0.267271i
$46$	6.40375	+	1.18415i	0.944182	+	0.174594i
$47$	−11.7111			−1.70823			−0.854117	−	0.520081i	$-0.825902\pi$
$47$	−11.7111			−1.70823			−0.854117	+	0.520081i	$0.825902\pi$
$48$	−9.39739	+	0.507943i	−1.35640	+	0.0733152i
$49$	−1.37537			−0.196481
$50$	−1.39064	−	0.257150i	−0.196666	−	0.0363665i
$51$	−12.1427	+	12.1427i	−1.70031	+	1.70031i
$52$	7.95577	−	3.54995i	1.10327	−	0.492290i
$53$	2.73048	+	2.73048i	0.375061	+	0.375061i	0.869316	−	0.494256i	$-0.164559\pi$
$53$	2.73048	+	2.73048i	0.375061	+	0.375061i	−0.494256	+	0.869316i	$0.664559\pi$
$54$	1.27322	−	0.875827i	0.173263	−	0.119185i
$55$		−	2.60869i		−	0.351756i
$56$	6.98457	+	4.26835i	0.933352	+	0.570382i
$57$		−	4.11235i		−	0.544694i
$58$	4.81369	+	6.99782i	0.632069	+	0.918859i
$59$	3.11306	+	3.11306i	0.405285	+	0.405285i	0.880091	−	0.474805i	$-0.157482\pi$
$59$	3.11306	+	3.11306i	0.405285	+	0.405285i	−0.474805	+	0.880091i	$0.657482\pi$
$60$	−4.39439	−	1.68272i	−0.567313	−	0.217238i
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	−0.540503	−	0.841342i	$-0.681766\pi$
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	0.841342	+	0.540503i	$0.181766\pi$
$62$	−0.530498	+	2.86887i	−0.0673733	+	0.364347i
$63$	7.33795			0.924495
$64$	−3.64944	−	7.11910i	−0.456180	−	0.889888i
$65$	4.35593			0.540286
$66$	1.57830	−	8.53528i	0.194276	−	1.05062i
$67$	8.24311	−	8.24311i	1.00706	−	1.00706i	0.00708173	−	0.999975i	$-0.497746\pi$
$67$	8.24311	−	8.24311i	1.00706	−	1.00706i	0.999975	−	0.00708173i	$-0.00225420\pi$
$68$	−13.6322	−	5.22011i	−1.65315	−	0.633031i
$69$	7.66101	+	7.66101i	0.922277	+	0.922277i
$70$	2.31955	+	3.37201i	0.277239	+	0.403032i
$71$		−	3.25937i		−	0.386816i	−0.981118	−	0.193408i	$-0.938046\pi$
$71$		−	3.25937i		−	0.386816i	0.981118	−	0.193408i	$-0.0619541\pi$
$72$	−6.11942	−	3.73965i	−0.721180	−	0.440721i
$73$			12.6877i			1.48499i	0.669853	+	0.742494i	$0.266357\pi$
$73$			12.6877i			1.48499i	−0.669853	+	0.742494i	$0.733643\pi$
$74$	1.94272	−	1.33637i	0.225837	−	0.155350i
$75$	−1.66366	−	1.66366i	−0.192103	−	0.192103i
$76$	3.19235	−	1.42446i	0.366188	−	0.163397i
$77$	−5.33839	+	5.33839i	−0.608365	+	0.608365i
$78$	14.2520	+	2.63541i	1.61372	+	0.298401i
$79$	−0.113885			−0.0128130			−0.00640652	−	0.999979i	$-0.502039\pi$
$79$	−0.113885			−0.0128130			−0.00640652	+	0.999979i	$0.502039\pi$
$80$	−0.215891	−	3.99417i	−0.0241373	−	0.446562i
$81$	10.1776			1.13085
$82$	−6.41758	−	1.18671i	−0.708703	−	0.131050i
$83$	9.76813	−	9.76813i	1.07219	−	1.07219i	0.0750089	−	0.997183i	$-0.476101\pi$
$83$	9.76813	−	9.76813i	1.07219	−	1.07219i	0.997183	−	0.0750089i	$-0.0238985\pi$
$84$	5.54912	+	12.4361i	0.605459	+	1.35689i
$85$	−5.16100	−	5.16100i	−0.559789	−	0.559789i
$86$	−4.99310	+	3.43468i	−0.538420	+	0.370371i
$87$			14.1305i			1.51495i
$88$	7.17251	−	1.73129i	0.764592	−	0.184557i
$89$		−	3.74593i		−	0.397068i	−0.980094	−	0.198534i	$-0.936382\pi$
$89$		−	3.74593i		−	0.397068i	0.980094	−	0.198534i	$-0.0636180\pi$
$90$	−2.03224	−	2.95433i	−0.214217	−	0.311414i
$91$	−8.91390	−	8.91390i	−0.934430	−	0.934430i
$92$	−3.29345	+	8.60080i	−0.343366	+	0.896695i
$93$	−3.43212	+	3.43212i	−0.355894	+	0.355894i
$94$	3.01150	−	16.2858i	0.310613	−	1.67976i
$95$	1.74787			0.179328
$96$	1.71017	−	13.1990i	0.174544	−	1.34711i
$97$	−13.9853			−1.41999			−0.709995	−	0.704206i	$-0.751303\pi$
$97$	−13.9853			−1.41999			−0.709995	+	0.704206i	$0.751303\pi$
$98$	0.353676	−	1.91264i	0.0357267	−	0.193206i
$99$	4.67714	−	4.67714i	0.470071	−	0.470071i
$100$	0.715205	−	1.86775i	0.0715205	−	0.186775i
$101$	3.52228	+	3.52228i	0.350480	+	0.350480i	0.860288	−	0.509808i	$-0.170284\pi$
$101$	3.52228	+	3.52228i	0.350480	+	0.350480i	−0.509808	+	0.860288i	$0.670284\pi$
$102$	−13.7636	−	20.0085i	−1.36280	−	1.98114i
$103$			0.150216i			0.0148013i	0.999973	+	0.00740063i	$0.00235572\pi$
$103$			0.150216i			0.0148013i	−0.999973	+	0.00740063i	$0.997644\pi$
$104$	2.89087	+	11.9765i	0.283473	+	1.17439i
$105$			6.80899i			0.664489i
$106$	−4.49926	+	3.09497i	−0.437006	+	0.300610i
$107$	−2.75062	−	2.75062i	−0.265912	−	0.265912i	0.561539	−	0.827451i	$-0.310210\pi$
$107$	−2.75062	−	2.75062i	−0.265912	−	0.265912i	−0.827451	+	0.561539i	$0.810210\pi$
$108$	0.890550	+	1.99580i	0.0856932	+	0.192046i
$109$	−6.90778	+	6.90778i	−0.661646	+	0.661646i	−0.955768	−	0.294122i	$-0.904973\pi$
$109$	−6.90778	+	6.90778i	−0.661646	+	0.661646i	0.294122	+	0.955768i	$0.404973\pi$
$110$	3.62775	+	0.670826i	0.345892	+	0.0639607i
$111$	3.92288			0.372344
$112$	−7.73181	+	8.61540i	−0.730587	+	0.814078i
$113$	−3.49507			−0.328788			−0.164394	−	0.986395i	$-0.552567\pi$
$113$	−3.49507			−0.328788			−0.164394	+	0.986395i	$0.552567\pi$
$114$	5.71879	+	1.05749i	0.535614	+	0.0990431i
$115$	−3.25616	+	3.25616i	−0.303638	+	0.303638i
$116$	−10.9693	+	4.89461i	−1.01847	+	0.454454i
$117$	7.80977	+	7.80977i	0.722014	+	0.722014i
$118$	−5.12966	+	3.52861i	−0.472223	+	0.324835i
$119$			21.1228i			1.93632i
$120$	3.47007	−	5.67830i	0.316773	−	0.518355i
$121$		−	4.19472i		−	0.381338i
$122$	2.66327	+	3.87168i	0.241121	+	0.350526i
$123$	−7.67755	−	7.67755i	−0.692261	−	0.692261i
$124$	−3.85314	−	1.47546i	−0.346022	−	0.132500i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−1.88695	+	10.2044i	−0.168103	+	0.909083i
$127$	6.25357			0.554915			0.277458	−	0.960738i	$-0.410508\pi$
$127$	6.25357			0.554915			0.277458	+	0.960738i	$0.410508\pi$
$128$	10.8385	−	3.24437i	0.958001	−	0.286764i
$129$	−10.0824			−0.887708
$130$	−1.12013	+	6.05752i	−0.0982417	+	0.531280i
$131$	−5.16490	+	5.16490i	−0.451259	+	0.451259i	−0.895772	−	0.444513i	$-0.853377\pi$
$131$	−5.16490	+	5.16490i	−0.451259	+	0.451259i	0.444513	+	0.895772i	$0.353377\pi$
$132$	11.4636	+	4.38969i	0.997780	+	0.382074i
$133$	−3.57681	−	3.57681i	−0.310149	−	0.310149i
$134$	9.34347	+	13.5829i	0.807153	+	1.17338i
$135$			1.09274i			0.0940480i
$136$	10.7648	−	17.6151i	0.923075	−	1.51049i
$137$		−	18.9408i		−	1.61823i	−0.587654	−	0.809113i	$-0.699948\pi$
$137$		−	18.9408i		−	1.61823i	0.587654	−	0.809113i	$-0.300052\pi$
$138$	−12.6237	+	8.68366i	−1.07460	+	0.739203i
$139$	2.79057	+	2.79057i	0.236693	+	0.236693i	0.815479	−	0.578786i	$-0.196473\pi$
$139$	2.79057	+	2.79057i	0.236693	+	0.236693i	−0.578786	+	0.815479i	$0.696473\pi$
$140$	−5.28571	+	2.35854i	−0.446724	+	0.199333i
$141$	19.4833	−	19.4833i	1.64079	−	1.64079i
$142$	4.53260	+	0.838147i	0.380367	+	0.0703357i
$143$	−11.3633			−0.950245
$144$	6.77410	−	7.54825i	0.564509	−	0.629021i
$145$	−6.00588			−0.498761
$146$	−17.6441	−	3.26265i	−1.46023	−	0.270019i
$147$	2.28815	−	2.28815i	0.188723	−	0.188723i
$148$	1.35883	+	3.04527i	0.111696	+	0.250320i
$149$	−1.60372	−	1.60372i	−0.131382	−	0.131382i	0.638358	−	0.769740i	$-0.279614\pi$
$149$	−1.60372	−	1.60372i	−0.131382	−	0.131382i	−0.769740	+	0.638358i	$0.779614\pi$
$150$	2.74137	−	1.88574i	0.223832	−	0.153970i
$151$			2.53754i			0.206502i	0.994655	+	0.103251i	$0.0329245\pi$
$151$			2.53754i			0.206502i	−0.994655	+	0.103251i	$0.967076\pi$
$152$	1.16000	+	4.80571i	0.0940883	+	0.389794i
$153$		−	18.5064i		−	1.49615i
$154$	−6.05099	−	8.79653i	−0.487603	−	0.708844i
$155$	−1.45875	−	1.45875i	−0.117170	−	0.117170i
$156$	−7.32980	+	19.1417i	−0.586854	+	1.53256i
$157$	10.2405	−	10.2405i	0.817278	−	0.817278i	−0.168435	−	0.985713i	$-0.553871\pi$
$157$	10.2405	−	10.2405i	0.817278	−	0.817278i	0.985713	+	0.168435i	$0.0538712\pi$
$158$	0.0292855	−	0.158373i	0.00232983	−	0.0125994i
$159$	−9.08521			−0.720504
$160$	5.60996	+	0.726875i	0.443506	+	0.0574645i
$161$	13.3267			1.05029
$162$	−2.61718	+	14.1534i	−0.205625	+	1.11200i
$163$	8.02607	−	8.02607i	0.628650	−	0.628650i	−0.319078	−	0.947728i	$-0.603373\pi$
$163$	8.02607	−	8.02607i	0.628650	−	0.628650i	0.947728	+	0.319078i	$0.103373\pi$
$164$	3.30056	−	8.61936i	0.257731	−	0.673059i
$165$	4.33999	+	4.33999i	0.337868	+	0.337868i
$166$	11.0721	+	16.0958i	0.859358	+	1.24928i
$167$		−	6.82611i		−	0.528221i	−0.964492	−	0.264110i	$-0.914922\pi$
$167$		−	6.82611i		−	0.528221i	0.964492	−	0.264110i	$-0.0850783\pi$
$168$	−18.7211	+	4.51888i	−1.44436	+	0.348639i
$169$		−	5.97411i		−	0.459547i
$170$	8.50423	−	5.84993i	0.652245	−	0.448669i
$171$	3.13377	+	3.13377i	0.239645	+	0.239645i
$172$	−3.49242	−	7.82683i	−0.266294	−	0.596790i
$173$	5.08901	−	5.08901i	0.386910	−	0.386910i	−0.486674	−	0.873584i	$-0.661790\pi$
$173$	5.08901	−	5.08901i	0.386910	−	0.386910i	0.873584	+	0.486674i	$0.161790\pi$
$174$	−19.6504	−	3.63366i	−1.48969	−	0.275467i
$175$	−2.89402			−0.218768
$176$	0.563193	+	10.4196i	0.0424523	+	0.785404i
$177$	−10.3582			−0.778567
$178$	5.20924	+	0.963267i	0.390449	+	0.0721999i
$179$	1.63797	−	1.63797i	0.122428	−	0.122428i	−0.643238	−	0.765666i	$-0.722410\pi$
$179$	1.63797	−	1.63797i	0.122428	−	0.122428i	0.765666	+	0.643238i	$0.222410\pi$
$180$	4.63099	−	2.06640i	0.345174	−	0.154020i
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.957071	−	0.289855i	$-0.906393\pi$
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.289855	−	0.957071i	$-0.593607\pi$
$182$	14.6882	−	10.1038i	1.08876	−	0.748943i
$183$			7.81797i			0.577921i
$184$	−11.1137	−	6.79170i	−0.819312	−	0.500691i
$185$			1.66734i			0.122585i
$186$	−3.89026	−	5.65540i	−0.285248	−	0.414674i
$187$	13.4635	+	13.4635i	0.984546	+	0.984546i
$188$	21.8733	+	8.37582i	1.59527	+	0.610869i
$189$	2.23616	−	2.23616i	0.162657	−	0.162657i
$190$	−0.449465	+	2.43066i	−0.0326076	+	0.176338i
$191$	5.85815			0.423881			0.211940	−	0.977283i	$-0.432022\pi$
$191$	5.85815			0.423881			0.211940	+	0.977283i	$0.432022\pi$
$192$	17.9152	+	5.77235i	1.29292	+	0.416584i
$193$	−0.0241155			−0.00173587			−0.000867935	−	1.00000i	$-0.500276\pi$
$193$	−0.0241155			−0.00173587			−0.000867935		1.00000i	$0.500276\pi$
$194$	3.59632	−	19.4485i	0.258201	−	1.39632i
$195$	−7.24680	+	7.24680i	−0.518954	+	0.518954i
$196$	2.56884	+	0.983671i	0.183489	+	0.0702622i
$197$	14.9086	+	14.9086i	1.06219	+	1.06219i	0.997933	+	0.0642576i	$0.0204679\pi$
$197$	14.9086	+	14.9086i	1.06219	+	1.06219i	0.0642576	+	0.997933i	$0.479532\pi$
$198$	5.30149	+	7.70694i	0.376760	+	0.547708i
$199$			13.6525i			0.967801i	0.875123	+	0.483900i	$0.160780\pi$
$199$			13.6525i			0.967801i	−0.875123	+	0.483900i	$0.839220\pi$
$200$	2.41345	+	1.47488i	0.170656	+	0.104290i
$201$			27.4275i			1.93459i
$202$	−5.80397	+	3.99246i	−0.408366	+	0.280909i
$203$	12.2903	+	12.2903i	0.862612	+	0.862612i
$204$	31.3640	−	13.9949i	2.19592	−	0.979842i
$205$	3.26319	−	3.26319i	0.227911	−	0.227911i
$206$	−0.208897	−	0.0386282i	−0.0145545	−	0.00269135i
$207$	−11.6760			−0.811537
$208$	−17.3983	+	0.940405i	−1.20636	+	0.0652053i
$209$	−4.55966			−0.315398
$210$	−9.46883	−	1.75093i	−0.653412	−	0.120826i
$211$	−2.45103	+	2.45103i	−0.168736	+	0.168736i	−0.786424	−	0.617688i	$-0.788070\pi$
$211$	−2.45103	+	2.45103i	−0.168736	+	0.168736i	0.617688	+	0.786424i	$0.288070\pi$
$212$	−3.14700	−	7.05271i	−0.216137	−	0.484382i
$213$	5.42249	+	5.42249i	0.371543	+	0.371543i
$214$	4.53243	−	3.11779i	0.309831	−	0.213128i
$215$		−	4.28533i		−	0.292257i
$216$	−3.00445	+	0.725211i	−0.204427	+	0.0493444i
$217$			5.97033i			0.405293i
$218$	−7.82989	−	11.3826i	−0.530307	−	0.770924i
$219$	−21.1081	−	21.1081i	−1.42636	−	1.42636i
$220$	−1.86575	+	4.87238i	−0.125789	+	0.328496i
$221$	−22.4809	+	22.4809i	−1.51223	+	1.51223i
$222$	−1.00877	+	5.45531i	−0.0677042	+	0.366136i
$223$	13.9483			0.934045			0.467023	−	0.884245i	$-0.345327\pi$
$223$	13.9483			0.934045			0.467023	+	0.884245i	$0.345327\pi$
$224$	−9.99266	−	12.9676i	−0.667663	−	0.866434i
$225$	2.53555			0.169037
$226$	0.898758	−	4.86038i	0.0597845	−	0.323307i
$227$	4.43883	−	4.43883i	0.294616	−	0.294616i	−0.544285	−	0.838901i	$-0.683199\pi$
$227$	4.43883	−	4.43883i	0.294616	−	0.294616i	0.838901	+	0.544285i	$0.183199\pi$
$228$	−2.94117	+	7.68083i	−0.194784	+	0.508675i
$229$	−5.35068	−	5.35068i	−0.353583	−	0.353583i	0.507858	−	0.861441i	$-0.330438\pi$
$229$	−5.35068	−	5.35068i	−0.353583	−	0.353583i	−0.861441	+	0.507858i	$0.830438\pi$
$230$	−3.69082	−	5.36546i	−0.243365	−	0.353788i
$231$		−	17.7626i		−	1.16869i
$232$	−3.98588	−	16.5129i	−0.261686	−	1.08413i
$233$		−	11.9370i		−	0.782019i	−0.920387	−	0.391010i	$-0.872126\pi$
$233$		−	11.9370i		−	0.782019i	0.920387	−	0.391010i	$-0.127874\pi$
$234$	−12.8689	+	8.85228i	−0.841263	+	0.578692i
$235$	8.28097	+	8.28097i	0.540191	+	0.540191i
$236$	−3.58793	−	8.04088i	−0.233554	−	0.523416i
$237$	0.189466	−	0.189466i	0.0123071	−	0.0123071i
$238$	−29.3741	−	5.43172i	−1.90404	−	0.352086i
$239$	−16.7720			−1.08489			−0.542445	−	0.840091i	$-0.682501\pi$
$239$	−16.7720			−1.08489			−0.542445	+	0.840091i	$0.682501\pi$
$240$	7.00412	+	6.28579i	0.452114	+	0.405746i
$241$	−22.0294			−1.41904			−0.709519	−	0.704686i	$-0.751088\pi$
$241$	−22.0294			−1.41904			−0.709519	+	0.704686i	$0.751088\pi$
$242$	5.83334	+	1.07867i	0.374981	+	0.0693397i
$243$	−14.6141	+	14.6141i	−0.937495	+	0.937495i
$244$	−6.06897	+	2.70804i	−0.388526	+	0.173365i
$245$	0.972532	+	0.972532i	0.0621328	+	0.0621328i
$246$	12.6510	−	8.70241i	0.806596	−	0.554845i
$247$		−	7.61360i		−	0.484442i
$248$	3.04267	−	4.97891i	0.193210	−	0.316161i
$249$			32.5018i			2.05972i
$250$	0.801497	+	1.16516i	0.0506911	+	0.0736913i
$251$	6.63925	+	6.63925i	0.419066	+	0.419066i	0.884882	−	0.465816i	$-0.154239\pi$
$251$	6.63925	+	6.63925i	0.419066	+	0.419066i	−0.465816	+	0.884882i	$0.654239\pi$
$252$	−13.7054	−	5.24814i	−0.863361	−	0.330602i
$253$	8.49432	−	8.49432i	0.534033	−	0.534033i
$254$	−1.60811	+	8.69646i	−0.100902	+	0.545664i
$255$	17.1723			1.07537
$256$	1.72461	+	15.9068i	0.107788	+	0.994174i
$257$	−7.25821			−0.452755			−0.226377	−	0.974040i	$-0.572688\pi$
$257$	−7.25821			−0.452755			−0.226377	+	0.974040i	$0.572688\pi$
$258$	2.59270	−	14.0210i	0.161414	−	0.872909i
$259$	3.41202	−	3.41202i	0.212013	−	0.212013i
$260$	−8.13577	−	3.11538i	−0.504559	−	0.193208i
$261$	−10.7680	−	10.7680i	−0.666521	−	0.666521i
$262$	−5.85435	−	8.51066i	−0.361683	−	0.525790i
$263$		−	9.27431i		−	0.571878i	−0.958248	−	0.285939i	$-0.907694\pi$
$263$		−	9.27431i		−	0.571878i	0.958248	−	0.285939i	$-0.0923055\pi$
$264$	−9.05235	+	14.8129i	−0.557133	+	0.911673i
$265$		−	3.86149i		−	0.237209i
$266$	5.89383	−	4.05428i	0.361374	−	0.248584i
$267$	6.23197	+	6.23197i	0.381390	+	0.381390i
$268$	−21.2916	+	9.50054i	−1.30059	+	0.580338i
$269$	−13.4195	+	13.4195i	−0.818199	+	0.818199i	−0.985847	−	0.167648i	$-0.946383\pi$
$269$	−13.4195	+	13.4195i	−0.818199	+	0.818199i	0.167648	+	0.985847i	$0.446383\pi$
$270$	−1.51960	−	0.280998i	−0.0924802	−	0.0171010i
$271$	22.5999			1.37285			0.686423	−	0.727202i	$-0.259180\pi$
$271$	22.5999			1.37285			0.686423	+	0.727202i	$0.259180\pi$
$272$	21.7281	+	19.4997i	1.31746	+	1.18234i
$273$	29.6595			1.79507
$274$	26.3399	+	4.87064i	1.59125	+	0.294246i
$275$	−1.84462	+	1.84462i	−0.111235	+	0.111235i
$276$	−8.82964	−	19.7880i	−0.531482	−	1.19110i
$277$	16.2015	+	16.2015i	0.973451	+	0.973451i	0.999657	−	0.0262056i	$-0.00834245\pi$
$277$	16.2015	+	16.2015i	0.973451	+	0.973451i	−0.0262056	+	0.999657i	$0.508342\pi$
$278$	−4.59827	+	3.16308i	−0.275786	+	0.189709i
$279$		−	5.23082i		−	0.313161i
$280$	−1.92066	−	7.95701i	−0.114781	−	0.475522i
$281$		−	8.84793i		−	0.527824i	−0.964547	−	0.263912i	$-0.914987\pi$
$281$		−	8.84793i		−	0.527824i	0.964547	−	0.263912i	$-0.0850128\pi$
$282$	22.0840	+	32.1043i	1.31509	+	1.91178i
$283$	−20.3062	−	20.3062i	−1.20708	−	1.20708i	−0.971969	−	0.235109i	$-0.924455\pi$
$283$	−20.3062	−	20.3062i	−1.20708	−	1.20708i	−0.235109	−	0.971969i	$-0.575545\pi$
$284$	−2.33112	+	6.08768i	−0.138326	+	0.361237i
$285$	−2.90787	+	2.90787i	−0.172247	+	0.172247i
$286$	2.92207	−	15.8022i	0.172786	−	0.934404i
$287$	−13.3555			−0.788348
$288$	8.75492	+	11.3614i	0.515888	+	0.669474i
$289$	36.2718			2.13364
$290$	1.54441	−	8.35200i	0.0906910	−	0.490447i
$291$	23.2668	−	23.2668i	1.36392	−	1.36392i
$292$	9.07434	−	23.6975i	0.531036	−	1.38679i
$293$	−7.16936	−	7.16936i	−0.418839	−	0.418839i	0.465965	−	0.884803i	$-0.345707\pi$
$293$	−7.16936	−	7.16936i	−0.418839	−	0.418839i	−0.884803	+	0.465965i	$0.845707\pi$
$294$	2.59359	+	3.77039i	0.151261	+	0.219893i
$295$		−	4.40253i		−	0.256325i
$296$	−4.58430	+	1.10655i	−0.266457	+	0.0643172i
$297$		−	2.85062i		−	0.165410i
$298$	2.64259	−	1.81779i	0.153081	−	0.105302i
$299$	14.1836	+	14.1836i	0.820258	+	0.820258i
$300$	1.91744	+	4.29717i	0.110704	+	0.248097i
$301$	−8.76943	+	8.76943i	−0.505461	+	0.505461i
$302$	−3.52880	−	0.652528i	−0.203059	−	0.0375488i
$303$	−11.7198			−0.673284
$304$	−6.98129	+	0.377349i	−0.400405	+	0.0216425i
$305$	−3.32287			−0.190267
$306$	25.7357	+	4.75892i	1.47121	+	0.272049i
$307$	−18.4308	+	18.4308i	−1.05190	+	1.05190i	−0.0533241	+	0.998577i	$0.516982\pi$
$307$	−18.4308	+	18.4308i	−1.05190	+	1.05190i	−0.998577	+	0.0533241i	$0.983018\pi$
$308$	13.7888	−	6.15271i	0.785690	−	0.350583i
$309$	−0.249910	−	0.249910i	−0.0142169	−	0.0142169i
$310$	2.40372	−	1.65348i	0.136522	−	0.0939113i
$311$			7.08961i			0.402015i	0.979590	+	0.201007i	$0.0644215\pi$
$311$			7.08961i			0.402015i	−0.979590	+	0.201007i	$0.935578\pi$
$312$	−24.7342	−	15.1154i	−1.40030	−	0.855739i
$313$			22.0477i			1.24621i	0.782139	+	0.623104i	$0.214129\pi$
$313$			22.0477i			1.24621i	−0.782139	+	0.623104i	$0.785871\pi$
$314$	11.6074	+	16.8741i	0.655046	+	0.952262i
$315$	−5.18871	−	5.18871i	−0.292351	−	0.292351i
$316$	0.212708	+	0.0814510i	0.0119658	+	0.00458198i
$317$	−6.19670	+	6.19670i	−0.348042	+	0.348042i	−0.859380	−	0.511338i	$-0.829150\pi$
$317$	−6.19670	+	6.19670i	−0.348042	+	0.348042i	0.511338	+	0.859380i	$0.329150\pi$
$318$	2.33626	−	12.6342i	0.131011	−	0.708493i
$319$	15.6675			0.877211
$320$	−2.45342	+	7.61451i	−0.137150	+	0.425664i
$321$	9.15220			0.510826
$322$	−3.42696	+	18.5326i	−0.190977	+	1.03278i
$323$	−9.02076	+	9.02076i	−0.501929	+	0.501929i
$324$	−19.0092	−	7.27910i	−1.05607	−	0.404394i
$325$	−3.08011	−	3.08011i	−0.170854	−	0.170854i
$326$	9.09745	+	13.2253i	0.503861	+	0.732479i
$327$		−	22.9845i		−	1.27104i
$328$	11.1377	+	6.80636i	0.614975	+	0.375818i
$329$		−	33.8921i		−	1.86853i
$330$	−7.15138	+	4.91932i	−0.393670	+	0.270800i
$331$	−18.6174	−	18.6174i	−1.02330	−	1.02330i	−0.999722	−	0.0235823i	$-0.992493\pi$
$331$	−18.6174	−	18.6174i	−1.02330	−	1.02330i	−0.0235823	−	0.999722i	$-0.507507\pi$
$332$	−25.2306	+	11.2582i	−1.38471	+	0.617873i
$333$	−2.98939	+	2.98939i	−0.163818	+	0.163818i
$334$	9.49265	+	1.75534i	0.519415	+	0.0960477i
$335$	−11.6575			−0.636919
$336$	−1.47000	−	27.1962i	−0.0801949	−	1.48368i
$337$	14.2577			0.776666			0.388333	−	0.921519i	$-0.373051\pi$
$337$	14.2577			0.776666			0.388333	+	0.921519i	$0.373051\pi$
$338$	8.30782	+	1.53624i	0.451886	+	0.0835606i
$339$	5.81462	−	5.81462i	0.315807	−	0.315807i
$340$	5.94827	+	13.3306i	0.322590	+	0.722954i
$341$	3.80544	+	3.80544i	0.206076	+	0.206076i
$342$	−5.16379	+	3.55209i	−0.279226	+	0.192075i
$343$			16.2778i			0.878919i
$344$	11.7824	−	2.84402i	0.635262	−	0.153339i
$345$		−	10.8343i		−	0.583299i
$346$	5.76833	+	8.38561i	0.310107	+	0.450813i
$347$	−23.5395	−	23.5395i	−1.26367	−	1.26367i	−0.949303	−	0.314363i	$-0.898209\pi$
$347$	−23.5395	−	23.5395i	−1.26367	−	1.26367i	−0.314363	−	0.949303i	$-0.601791\pi$
$348$	10.1062	−	26.3922i	0.541749	−	1.41477i
$349$	−1.56682	+	1.56682i	−0.0838701	+	0.0838701i	−0.747797	−	0.663927i	$-0.768888\pi$
$349$	−1.56682	+	1.56682i	−0.0838701	+	0.0838701i	0.663927	+	0.747797i	$0.268888\pi$
$350$	0.744198	−	4.02454i	0.0397791	−	0.215121i
$351$	4.75989			0.254064
$352$	−14.6347	−	1.89619i	−0.780030	−	0.101068i
$353$	9.44678			0.502801			0.251401	−	0.967883i	$-0.419109\pi$
$353$	9.44678			0.502801			0.251401	+	0.967883i	$0.419109\pi$
$354$	2.66360	−	14.4044i	0.141569	−	0.765588i
$355$	−2.30472	+	2.30472i	−0.122322	+	0.122322i
$356$	−2.67911	+	6.99646i	−0.141993	+	0.370811i
$357$	−35.1412	−	35.1412i	−1.85987	−	1.85987i
$358$	1.85662	+	2.69903i	0.0981256	+	0.142648i
$359$		−	18.0452i		−	0.952392i	−0.879339	−	0.476196i	$-0.842015\pi$
$359$		−	18.0452i		−	0.952392i	0.879339	−	0.476196i	$-0.157985\pi$
$360$	1.68275	+	6.97141i	0.0886889	+	0.367426i
$361$			15.9449i			0.839208i
$362$	27.6427	−	19.0150i	1.45287	−	0.999407i
$363$	6.97860	+	6.97860i	0.366282	+	0.366282i
$364$	10.2736	+	23.0242i	0.538485	+	1.20679i
$365$	8.97159	−	8.97159i	0.469594	−	0.469594i
$366$	−10.8720	−	2.01039i	−0.568286	−	0.105085i
$367$	29.1329			1.52073			0.760363	−	0.649498i	$-0.225021\pi$
$367$	29.1329			1.52073			0.760363	+	0.649498i	$0.225021\pi$
$368$	12.3027	−	13.7086i	0.641321	−	0.714612i
$369$	11.7012			0.609139
$370$	−2.31867	−	0.428757i	−0.120542	−	0.0222900i
$371$	−7.90208	+	7.90208i	−0.410255	+	0.410255i
$372$	8.86500	−	3.95566i	0.459629	−	0.205091i
$373$	3.35598	+	3.35598i	0.173766	+	0.173766i	0.788632	−	0.614866i	$-0.210790\pi$
$373$	3.35598	+	3.35598i	0.173766	+	0.173766i	−0.614866	+	0.788632i	$0.710790\pi$
$374$	−22.1849	+	15.2607i	−1.14716	+	0.789110i
$375$			2.35278i			0.121497i
$376$	−17.2725	+	28.2640i	−0.890759	+	1.45760i
$377$			26.1612i			1.34737i
$378$	2.53466	+	3.68472i	0.130369	+	0.189522i
$379$	11.6507	+	11.6507i	0.598457	+	0.598457i	0.939902	−	0.341445i	$-0.110916\pi$
$379$	11.6507	+	11.6507i	0.598457	+	0.598457i	−0.341445	+	0.939902i	$0.610916\pi$
$380$	−3.26458	−	1.25009i	−0.167470	−	0.0641281i
$381$	−10.4038	+	10.4038i	−0.533005	+	0.533005i
$382$	−1.50642	+	8.14656i	−0.0770753	+	0.416814i
$383$	−21.8044			−1.11415			−0.557077	−	0.830461i	$-0.688077\pi$
$383$	−21.8044			−1.11415			−0.557077	+	0.830461i	$0.688077\pi$
$384$	−12.6342	+	23.4292i	−0.644734	+	1.19562i
$385$	7.54962			0.384764
$386$	0.00620130	−	0.0335359i	0.000315638	−	0.00170693i
$387$	7.68320	−	7.68320i	0.390559	−	0.390559i
$388$	26.1210	+	10.0024i	1.32609	+	0.507793i
$389$	−11.8899	−	11.8899i	−0.602842	−	0.602842i	0.338224	−	0.941066i	$-0.390174\pi$
$389$	−11.8899	−	11.8899i	−0.602842	−	0.602842i	−0.941066	+	0.338224i	$0.890174\pi$
$390$	−8.21416	−	11.9412i	−0.415940	−	0.604666i
$391$		−	33.6101i		−	1.69973i
$392$	−2.02851	+	3.31938i	−0.102455	+	0.167654i
$393$		−	17.1853i		−	0.866884i
$394$	−24.5661	+	16.8987i	−1.23762	+	0.851343i
$395$	0.0805287	+	0.0805287i	0.00405184	+	0.00405184i
$396$	−12.0808	+	5.39061i	−0.607085	+	0.270888i
$397$	−9.23905	+	9.23905i	−0.463694	+	0.463694i	−0.899864	−	0.436170i	$-0.856335\pi$
$397$	−9.23905	+	9.23905i	−0.463694	+	0.463694i	0.436170	+	0.899864i	$0.356335\pi$
$398$	−18.9857	−	3.51074i	−0.951667	−	0.175978i
$399$	11.9012			0.595807
$400$	−2.67165	+	2.97696i	−0.133582	+	0.148848i
$401$	−14.4744			−0.722818			−0.361409	−	0.932407i	$-0.617704\pi$
$401$	−14.4744			−0.722818			−0.361409	+	0.932407i	$0.617704\pi$
$402$	−38.1418	−	7.05300i	−1.90234	−	0.351771i
$403$	−6.35422	+	6.35422i	−0.316526	+	0.316526i
$404$	−4.05958	−	9.09789i	−0.201972	−	0.452637i
$405$	−7.19667	−	7.19667i	−0.357605	−	0.357605i
$406$	−20.2519	+	13.9309i	−1.00508	+	0.691381i
$407$		−	4.34958i		−	0.215601i
$408$	11.3967	+	47.2147i	0.564218	+	2.33748i
$409$		−	9.54117i		−	0.471781i	−0.971780	−	0.235890i	$-0.924199\pi$
$409$		−	9.54117i		−	0.471781i	0.971780	−	0.235890i	$-0.0758006\pi$
$410$	3.69878	+	5.37704i	0.182670	+	0.265553i
$411$	31.5112	+	31.5112i	1.55433	+	1.55433i
$412$	0.107436	−	0.280566i	0.00529297	−	0.0138225i
$413$	−9.00925	+	9.00925i	−0.443316	+	0.443316i
$414$	3.00248	−	16.2371i	0.147564	−	0.798008i
$415$	−13.8142			−0.678114
$416$	3.16622	−	24.4366i	0.155237	−	1.19810i
$417$	−9.28514			−0.454695
$418$	1.17252	−	6.34083i	0.0573497	−	0.310140i
$419$	0.837667	−	0.837667i	0.0409227	−	0.0409227i	−0.686349	−	0.727272i	$-0.740788\pi$
$419$	0.837667	−	0.837667i	0.0409227	−	0.0409227i	0.727272	+	0.686349i	$0.240788\pi$
$420$	4.86982	−	12.7175i	0.237623	−	0.620549i
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	0.993087	−	0.117385i	$-0.0374511\pi$
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	−0.117385	+	0.993087i	$0.537451\pi$
$422$	−2.77822	−	4.03878i	−0.135241	−	0.196605i
$423$			29.6940i			1.44377i
$424$	10.6170	−	2.56273i	0.515608	−	0.124457i
$425$			7.29875i			0.354042i
$426$	−8.93512	+	6.14633i	−0.432908	+	0.297791i
$427$	6.79986	+	6.79986i	0.329068	+	0.329068i
$428$	3.17020	+	7.10471i	0.153237	+	0.343419i
$429$	18.9047	−	18.9047i	0.912726	−	0.912726i
$430$	5.95934	+	1.10197i	0.287385	+	0.0531419i
$431$	−3.85473			−0.185676			−0.0928380	−	0.995681i	$-0.529594\pi$
$431$	−3.85473			−0.185676			−0.0928380	+	0.995681i	$0.529594\pi$
$432$	−0.235912	−	4.36459i	−0.0113503	−	0.209991i
$433$	−25.5651			−1.22858			−0.614289	−	0.789081i	$-0.710557\pi$
$433$	−25.5651			−1.22858			−0.614289	+	0.789081i	$0.710557\pi$
$434$	−8.30257	−	1.53527i	−0.398536	−	0.0736954i
$435$	9.99176	−	9.99176i	0.479068	−	0.479068i
$436$	17.8425	−	7.96151i	0.854500	−	0.381287i
$437$	5.69135	+	5.69135i	0.272254	+	0.272254i
$438$	34.7817	−	23.9258i	1.66194	−	1.14322i
$439$		−	30.1311i		−	1.43808i	−0.694970	−	0.719039i	$-0.744582\pi$
$439$		−	30.1311i		−	1.43808i	0.694970	−	0.719039i	$-0.255418\pi$
$440$	−6.29594	−	3.84752i	−0.300147	−	0.183423i
$441$			3.48732i			0.166063i
$442$	−25.4819	−	37.0438i	−1.21205	−	1.76199i
$443$	20.1625	+	20.1625i	0.957948	+	0.957948i	0.999151	−	0.0412027i	$-0.0131189\pi$
$443$	20.1625	+	20.1625i	0.957948	+	0.957948i	−0.0412027	+	0.999151i	$0.513119\pi$
$444$	−7.32695	−	2.80567i	−0.347722	−	0.133151i
$445$	−2.64877	+	2.64877i	−0.125564	+	0.125564i
$446$	−3.58680	+	19.3970i	−0.169840	+	0.918474i
$447$	5.33610			0.252389
$448$	20.6028	−	10.5616i	0.973393	−	0.498987i
$449$	−36.5827			−1.72644			−0.863221	−	0.504826i	$-0.831557\pi$
$449$	−36.5827			−1.72644			−0.863221	+	0.504826i	$0.831557\pi$
$450$	−0.652018	+	3.52604i	−0.0307364	+	0.166219i
$451$	−8.51265	+	8.51265i	−0.400845	+	0.400845i
$452$	6.52791	+	2.49969i	0.307047	+	0.117576i
$453$	−4.22161	−	4.22161i	−0.198349	−	0.198349i
$454$	5.03136	+	7.31426i	0.236134	+	0.343275i
$455$			12.6062i			0.590986i
$456$	−9.92493	−	6.06523i	−0.464777	−	0.284031i
$457$		−	16.7340i		−	0.782785i	−0.920224	−	0.391392i	$-0.871994\pi$
$457$		−	16.7340i		−	0.782785i	0.920224	−	0.391392i	$-0.128006\pi$
$458$	8.81679	−	6.06493i	0.411982	−	0.283396i
$459$	−5.63962	−	5.63962i	−0.263235	−	0.263235i
$460$	8.41051	−	3.75286i	0.392142	−	0.174978i
$461$	11.8377	−	11.8377i	0.551335	−	0.551335i	−0.375491	−	0.926826i	$-0.622526\pi$
$461$	11.8377	−	11.8377i	0.551335	−	0.551335i	0.926826	+	0.375491i	$0.122526\pi$
$462$	24.7013	+	4.56764i	1.14921	+	0.212506i
$463$	−32.2711			−1.49976			−0.749882	−	0.661572i	$-0.769890\pi$
$463$	−32.2711			−1.49976			−0.749882	+	0.661572i	$0.769890\pi$
$464$	23.9885	−	1.29661i	1.11364	−	0.0601938i
$465$	4.85375			0.225087
$466$	16.6000	+	3.06960i	0.768982	+	0.142197i
$467$	1.22565	−	1.22565i	0.0567163	−	0.0567163i	−0.678180	−	0.734896i	$-0.737231\pi$
$467$	1.22565	−	1.22565i	0.0567163	−	0.0567163i	0.734896	+	0.678180i	$0.237231\pi$
$468$	−9.00109	−	20.1723i	−0.416076	−	0.932464i
$469$	23.8558	+	23.8558i	1.10156	+	1.10156i
$470$	−13.6453	+	9.38638i	−0.629410	+	0.432961i
$471$			34.0734i			1.57002i
$472$	12.1046	−	2.92180i	0.557159	−	0.134487i
$473$			11.1791i			0.514016i
$474$	0.214757	+	0.312200i	0.00986413	+	0.0143398i
$475$	−1.23593	−	1.23593i	−0.0567084	−	0.0567084i
$476$	15.1071	−	39.4520i	0.692433	−	1.80828i
$477$	6.92328	−	6.92328i	0.316995	−	0.316995i
$478$	4.31292	−	23.3238i	0.197268	−	1.06680i
$479$	28.8399			1.31773			0.658865	−	0.752261i	$-0.271037\pi$
$479$	28.8399			1.31773			0.658865	+	0.752261i	$0.271037\pi$
$480$	−10.5424	+	8.12381i	−0.481191	+	0.370800i
$481$	7.26282			0.331156
$482$	5.66486	−	30.6349i	0.258027	−	1.39538i
$483$	−22.1711	+	22.1711i	−1.00882	+	1.00882i
$484$	−3.00009	+	7.83468i	−0.136368	+	0.356122i
$485$	9.88909	+	9.88909i	0.449041	+	0.449041i
$486$	−16.5649	−	24.0809i	−0.751399	−	1.09233i
$487$			32.1668i			1.45762i	0.684718	+	0.728808i	$0.259925\pi$
$487$			32.1668i			1.45762i	−0.684718	+	0.728808i	$0.740075\pi$
$488$	−2.20527	−	9.13611i	−0.0998278	−	0.413572i
$489$			26.7054i			1.20766i
$490$	−1.60253	+	1.10235i	−0.0723948	+	0.0497993i
$491$	−5.43607	−	5.43607i	−0.245326	−	0.245326i	0.573723	−	0.819049i	$-0.305499\pi$
$491$	−5.43607	−	5.43607i	−0.245326	−	0.245326i	−0.819049	+	0.573723i	$0.805499\pi$
$492$	8.84870	+	19.8307i	0.398930	+	0.894039i
$493$	30.9963	−	30.9963i	1.39600	−	1.39600i
$494$	10.5878	+	1.95784i	0.476366	+	0.0880873i
$495$	−6.61448			−0.297299
$496$	6.14144	+	5.51157i	0.275759	+	0.247477i
$497$	9.43268			0.423114
$498$	−45.1982	−	8.35783i	−2.02538	−	0.374524i
$499$	−17.1282	+	17.1282i	−0.766762	+	0.766762i	−0.977535	−	0.210773i	$-0.932402\pi$
$499$	−17.1282	+	17.1282i	−0.766762	+	0.766762i	0.210773	+	0.977535i	$0.432402\pi$
$500$	−1.82642	+	0.814970i	−0.0816801	+	0.0364466i
$501$	11.3564	+	11.3564i	0.507365	+	0.507365i
$502$	−10.9401	+	7.52551i	−0.488280	+	0.335880i
$503$		−	23.5180i		−	1.04862i	−0.851529	−	0.524308i	$-0.824324\pi$
$503$		−	23.5180i		−	1.04862i	0.851529	−	0.524308i	$-0.175676\pi$
$504$	10.8226	−	17.7097i	0.482078	−	0.788855i
$505$		−	4.98126i		−	0.221663i
$506$	9.62821	+	13.9968i	0.428026	+	0.622235i
$507$	9.93890	+	9.93890i	0.441402	+	0.441402i
$508$	−11.6801	−	4.47259i	−0.518221	−	0.198439i
$509$	20.3147	−	20.3147i	0.900434	−	0.900434i	−0.0950391	−	0.995474i	$-0.530298\pi$
$509$	20.3147	−	20.3147i	0.900434	−	0.900434i	0.995474	+	0.0950391i	$0.0302976\pi$
$510$	−4.41587	+	23.8805i	−0.195538	+	1.05745i
$511$	−36.7186			−1.62434
$512$	−22.5641	−	1.69212i	−0.997200	−	0.0747820i
$513$	1.90997			0.0843271
$514$	1.86645	−	10.0935i	0.0823256	−	0.445207i
$515$	0.106219	−	0.106219i	0.00468057	−	0.00468057i
$516$	18.8314	+	7.21100i	0.829007	+	0.317447i
$517$	−21.6025	−	21.6025i	−0.950077	−	0.950077i
$518$	3.86748	+	5.62229i	0.169928	+	0.247029i
$519$			16.9328i			0.743268i
$520$	6.42449	−	10.5128i	0.281732	−	0.461017i
$521$		−	35.5082i		−	1.55564i	−0.628487	−	0.777820i	$-0.716325\pi$
$521$		−	35.5082i		−	1.55564i	0.628487	−	0.777820i	$-0.283675\pi$
$522$	17.7434	−	12.2054i	0.776606	−	0.534215i
$523$	0.677766	+	0.677766i	0.0296366	+	0.0296366i	0.721770	−	0.692133i	$-0.243329\pi$
$523$	0.677766	+	0.677766i	0.0296366	+	0.0296366i	−0.692133	+	0.721770i	$0.743329\pi$
$524$	13.3407	−	5.95276i	0.582791	−	0.260048i
$525$	4.81468	−	4.81468i	0.210130	−	0.210130i
$526$	12.8972	+	2.38489i	0.562345	+	0.103986i
$527$	15.0572			0.655904
$528$	−18.2716	−	16.3977i	−0.795170	−	0.713618i
$529$	1.79485			0.0780371
$530$	5.36993	+	0.992982i	0.233255	+	0.0431324i
$531$	7.89332	−	7.89332i	0.342541	−	0.342541i
$532$	4.12243	+	9.23874i	0.178730	+	0.400550i
$533$	−14.2142	−	14.2142i	−0.615686	−	0.615686i
$534$	−10.2690	+	7.06386i	−0.444382	+	0.305683i
$535$			3.88996i			0.168178i
$536$	−7.73667	−	32.0519i	−0.334173	−	1.38443i
$537$			5.45007i			0.235188i
$538$	−15.2108	−	22.1124i	−0.655784	−	0.953334i
$539$	−2.53704	−	2.53704i	−0.109278	−	0.109278i
$540$	0.781533	−	2.04096i	0.0336318	−	0.0878290i
$541$	5.37099	−	5.37099i	0.230917	−	0.230917i	−0.582158	−	0.813075i	$-0.697792\pi$
$541$	5.37099	−	5.37099i	0.230917	−	0.230917i	0.813075	+	0.582158i	$0.197792\pi$
$542$	−5.81157	+	31.4283i	−0.249628	+	1.34996i
$543$	55.8181			2.39539
$544$	−32.7044	+	25.2016i	−1.40219	+	1.08051i
$545$	9.76908			0.418461
$546$	−7.62693	+	41.2456i	−0.326403	+	1.76515i
$547$	8.86782	−	8.86782i	0.379161	−	0.379161i	−0.491639	−	0.870799i	$-0.663602\pi$
$547$	8.86782	−	8.86782i	0.379161	−	0.379161i	0.870799	+	0.491639i	$0.163602\pi$
$548$	−13.5466	+	35.3767i	−0.578682	+	1.51122i
$549$	−5.95760	−	5.95760i	−0.254264	−	0.254264i
$550$	−2.09086	−	3.03955i	−0.0891545	−	0.129607i
$551$			10.4975i			0.447209i
$552$	29.7885	−	7.19034i	1.26788	−	0.306041i
$553$		−	0.329585i		−	0.0140154i
$554$	−26.6966	+	18.3641i	−1.13423	+	0.780218i
$555$	−2.77390	−	2.77390i	−0.117745	−	0.117745i
$556$	−3.21625	−	7.20791i	−0.136399	−	0.305684i
$557$	−22.8089	+	22.8089i	−0.966446	+	0.966446i	−0.999455	−	0.0330091i	$-0.989491\pi$
$557$	−22.8089	+	22.8089i	−0.966446	+	0.966446i	0.0330091	+	0.999455i	$0.489491\pi$
$558$	7.27417	+	1.34510i	0.307940	+	0.0569428i
$559$	−18.6666			−0.789513
$560$	11.5592	−	0.624793i	0.488466	−	0.0264023i
$561$	−44.7973			−1.89135
$562$	12.3043	+	2.27525i	0.519024	+	0.0959755i
$563$	20.9711	−	20.9711i	0.883826	−	0.883826i	−0.110095	−	0.993921i	$-0.535116\pi$
$563$	20.9711	−	20.9711i	0.883826	−	0.883826i	0.993921	+	0.110095i	$0.0351156\pi$
$564$	−50.3244	+	22.4553i	−2.11904	+	0.945538i
$565$	2.47139	+	2.47139i	0.103972	+	0.103972i
$566$	33.4603	−	23.0168i	1.40644	−	0.967469i
$567$			29.4543i			1.23696i
$568$	−7.86630	−	4.80719i	−0.330063	−	0.201705i
$569$		−	8.05295i		−	0.337597i	−0.985651	−	0.168799i	$-0.946011\pi$
$569$		−	8.05295i		−	0.337597i	0.985651	−	0.168799i	$-0.0539888\pi$
$570$	−3.29603	−	4.79155i	−0.138056	−	0.200696i
$571$	−22.5040	−	22.5040i	−0.941762	−	0.941762i	0.0566333	−	0.998395i	$-0.481963\pi$
$571$	−22.5040	−	22.5040i	−0.941762	−	0.941762i	−0.998395	+	0.0566333i	$0.981963\pi$
$572$	21.2237	+	8.12708i	0.887409	+	0.339810i
$573$	−9.74599	+	9.74599i	−0.407144	+	0.407144i
$574$	3.43436	−	18.5726i	0.143347	−	0.775206i
$575$	4.60490			0.192038
$576$	−18.0509	+	9.25334i	−0.752119	+	0.385556i
$577$	15.9819			0.665334			0.332667	−	0.943044i	$-0.392051\pi$
$577$	15.9819			0.665334			0.332667	+	0.943044i	$0.392051\pi$
$578$	−9.32730	+	50.4410i	−0.387965	+	2.09807i
$579$	0.0401200	−	0.0401200i	0.00166733	−	0.00166733i
$580$	11.2175	+	4.29544i	0.465780	+	0.178358i
$581$	28.2692	+	28.2692i	1.17280	+	1.17280i
$582$	26.3727	+	38.3388i	1.09318	+	1.58919i
$583$			10.0734i			0.417199i
$584$	30.6212	+	18.7129i	1.26711	+	0.774347i
$585$		−	11.0447i		−	0.456642i
$586$	11.8136	−	8.12638i	0.488015	−	0.335698i
$587$	−5.25752	−	5.25752i	−0.217001	−	0.217001i	0.590232	−	0.807233i	$-0.299036\pi$
$587$	−5.25752	−	5.25752i	−0.217001	−	0.217001i	−0.807233	+	0.590232i	$0.799036\pi$
$588$	−5.91018	+	2.63719i	−0.243732	+	0.108756i
$589$	−2.54971	+	2.54971i	−0.105059	+	0.105059i
$590$	6.12232	+	1.13211i	0.252052	+	0.0466082i
$591$	−49.6057			−2.04050
$592$	−0.359964	−	6.65965i	−0.0147944	−	0.273710i
$593$	3.96571			0.162852			0.0814260	−	0.996679i	$-0.474053\pi$
$593$	3.96571			0.162852			0.0814260	+	0.996679i	$0.474053\pi$
$594$	3.96418	+	0.733038i	0.162652	+	0.0300769i
$595$	14.9360	−	14.9360i	0.612318	−	0.612318i
$596$	1.84835	+	4.14233i	0.0757115	+	0.169676i
$597$	−22.7132	−	22.7132i	−0.929589	−	0.929589i
$598$	−23.3716	+	16.0769i	−0.955734	+	0.657435i
$599$			8.31600i			0.339783i	0.985463	+	0.169891i	$0.0543417\pi$
$599$			8.31600i			0.339783i	−0.985463	+	0.169891i	$0.945658\pi$
$600$	−6.46887	+	1.56145i	−0.264091	+	0.0637460i
$601$		−	46.0550i		−	1.87862i	−0.343068	−	0.939310i	$-0.611466\pi$
$601$		−	46.0550i		−	1.87862i	0.343068	−	0.939310i	$-0.388534\pi$
$602$	−9.94004	−	14.4502i	−0.405126	−	0.588944i
$603$	−20.9009	−	20.9009i	−0.851149	−	0.851149i
$604$	1.81486	−	4.73948i	0.0738456	−	0.192847i
$605$	−2.96612	+	2.96612i	−0.120590	+	0.120590i
$606$	3.01374	−	16.2980i	0.122425	−	0.662060i
$607$	−5.05760			−0.205282			−0.102641	−	0.994718i	$-0.532729\pi$
$607$	−5.05760			−0.205282			−0.102641	+	0.994718i	$0.532729\pi$
$608$	1.27048	−	9.80549i	0.0515249	−	0.397665i
$609$	−40.8940			−1.65711
$610$	0.854476	−	4.62091i	0.0345967	−	0.187095i
$611$	36.0713	−	36.0713i	1.45929	−	1.45929i
$612$	−13.2359	+	34.5652i	−0.535028	+	1.39722i
$613$	31.2000	+	31.2000i	1.26016	+	1.26016i	0.951016	+	0.309141i	$0.100042\pi$
$613$	31.2000	+	31.2000i	1.26016	+	1.26016i	0.309141	+	0.951016i	$0.399958\pi$
$614$	−20.8911	−	30.3701i	−0.843096	−	1.22564i
$615$			10.8577i			0.437824i
$616$	5.01041	+	20.7574i	0.201875	+	0.836339i
$617$			30.7412i			1.23759i	0.785551	+	0.618796i	$0.212379\pi$
$617$			30.7412i			1.23759i	−0.785551	+	0.618796i	$0.787621\pi$
$618$	0.411798	−	0.283269i	0.0165649	−	0.0113948i
$619$	−16.8766	−	16.8766i	−0.678329	−	0.678329i	0.281293	−	0.959622i	$-0.409237\pi$
$619$	−16.8766	−	16.8766i	−0.678329	−	0.678329i	−0.959622	+	0.281293i	$0.909237\pi$
$620$	1.68127	+	3.76789i	0.0675216	+	0.151322i
$621$	−3.55813	+	3.55813i	−0.142783	+	0.142783i
$622$	−9.85908	−	1.82309i	−0.395313	−	0.0730994i
$623$	10.8408			0.434328
$624$	27.3804	−	30.5095i	1.09609	−	1.22136i
$625$	−1.00000			−0.0400000
$626$	−30.6603	−	5.66956i	−1.22543	−	0.226601i
$627$	7.58574	−	7.58574i	0.302945	−	0.302945i
$628$	−26.4506	+	11.8026i	−1.05550	+	0.470974i
$629$	−8.60515	−	8.60515i	−0.343110	−	0.343110i
$630$	8.54990	−	5.88134i	0.340636	−	0.234318i
$631$			30.7318i			1.22342i	0.791084	+	0.611708i	$0.209517\pi$
$631$			30.7318i			1.22342i	−0.791084	+	0.611708i	$0.790483\pi$
$632$	−0.167967	+	0.274855i	−0.00668136	+	0.0109331i
$633$		−	8.15539i		−	0.324147i
$634$	−7.02389	−	10.2109i	−0.278954	−	0.405525i
$635$	−4.42195	−	4.42195i	−0.175480	−	0.175480i
$636$	16.9689	+	6.49779i	0.672860	+	0.257654i
$637$	4.23628	−	4.23628i	0.167848	−	0.167848i
$638$	−4.02890	+	21.7878i	−0.159506	+	0.862588i
$639$	−8.26430			−0.326931
$640$	−9.95812	−	5.36989i	−0.393629	−	0.212264i
$641$	22.1658			0.875496			0.437748	−	0.899098i	$-0.355776\pi$
$641$	22.1658			0.875496			0.437748	+	0.899098i	$0.355776\pi$
$642$	−2.35349	+	12.7274i	−0.0928848	+	0.502310i
$643$	0.975773	−	0.975773i	0.0384807	−	0.0384807i	−0.687605	−	0.726085i	$-0.741338\pi$
$643$	0.975773	−	0.975773i	0.0384807	−	0.0384807i	0.726085	+	0.687605i	$0.241338\pi$
$644$	−24.8909	−	9.53133i	−0.980839	−	0.375587i
$645$	7.12935	+	7.12935i	0.280718	+	0.280718i
$646$	−10.2249	−	14.8643i	−0.402294	−	0.584828i
$647$		−	23.2610i		−	0.914484i	−0.889342	−	0.457242i	$-0.848837\pi$
$647$		−	23.2610i		−	0.914484i	0.889342	−	0.457242i	$-0.151163\pi$
$648$	15.0108	−	24.5632i	0.589681	−	0.964932i
$649$			11.4848i			0.450819i
$650$	5.07536	−	3.49126i	0.199072	−	0.136939i
$651$	−9.93263	−	9.93263i	−0.389290	−	0.389290i
$652$	−20.7310	+	9.25038i	−0.811887	+	0.362273i
$653$	−23.9372	+	23.9372i	−0.936735	+	0.936735i	−0.998115	−	0.0613792i	$-0.980450\pi$
$653$	−23.9372	+	23.9372i	−0.936735	+	0.936735i	0.0613792	+	0.998115i	$0.480450\pi$
$654$	31.9631	+	5.91046i	1.24985	+	0.231117i
$655$	7.30427			0.285401
$656$	−12.3292	+	13.7382i	−0.481376	+	0.536387i
$657$	32.1704			1.25509
$658$	47.1316	+	8.71535i	1.83738	+	0.339760i
$659$	−14.1064	+	14.1064i	−0.549508	+	0.549508i	−0.926299	−	0.376790i	$-0.877028\pi$
$659$	−14.1064	+	14.1064i	−0.549508	+	0.549508i	0.376790	+	0.926299i	$0.377028\pi$
$660$	−5.00202	−	11.2100i	−0.194703	−	0.436348i
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	0.645484	−	0.763774i	$-0.276656\pi$
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	−0.763774	+	0.645484i	$0.776656\pi$
$662$	30.6775	−	21.1026i	1.19232	−	0.820175i
$663$		−	74.8014i		−	2.90505i
$664$	−9.16800	−	37.9817i	−0.355787	−	1.47398i
$665$			5.05838i			0.196156i
$666$	−3.38844	−	4.92588i	−0.131299	−	0.190874i
$667$	−19.5561	−	19.5561i	−0.757215	−	0.757215i
$668$	−4.88207	+	12.7495i	−0.188893	+	0.493291i
$669$	−23.2052	+	23.2052i	−0.897166	+	0.897166i
$670$	2.99773	−	16.2114i	0.115813	−	0.626301i
$671$	8.66835			0.334638
$672$	38.1981	+	4.94928i	1.47353	+	0.190923i
$673$	−25.3628			−0.977662			−0.488831	−	0.872378i	$-0.662577\pi$
$673$	−25.3628			−0.977662			−0.488831	+	0.872378i	$0.662577\pi$
$674$	−3.66637	+	19.8273i	−0.141223	+	0.763719i
$675$	0.772683	−	0.772683i	0.0297406	−	0.0297406i
$676$	−4.27271	+	11.1581i	−0.164335	+	0.429159i
$677$	9.36526	+	9.36526i	0.359936	+	0.359936i	0.863789	−	0.503853i	$-0.168085\pi$
$677$	9.36526	+	9.36526i	0.359936	+	0.359936i	−0.503853	+	0.863789i	$0.668085\pi$
$678$	6.59080	+	9.58126i	0.253118	+	0.367966i
$679$		−	40.4737i		−	1.55324i
$680$	−20.0677	+	4.84392i	−0.769560	+	0.185756i
$681$			14.7695i			0.565967i
$682$	−6.27056	+	4.31342i	−0.240112	+	0.165169i
$683$	4.20530	+	4.20530i	0.160911	+	0.160911i	0.782970	−	0.622059i	$-0.213704\pi$
$683$	4.20530	+	4.20530i	0.160911	+	0.160911i	−0.622059	+	0.782970i	$0.713704\pi$
$684$	−3.61180	−	8.09438i	−0.138101	−	0.309496i
$685$	−13.3932	+	13.3932i	−0.511728	+	0.511728i
$686$	−22.6365	−	4.18584i	−0.864267	−	0.159816i
$687$	17.8035			0.679245
$688$	0.925163	+	17.1163i	0.0352715	+	0.652554i
$689$	−16.8204			−0.640804
$690$	15.0666	+	2.78604i	0.573576	+	0.106063i
$691$	5.79295	−	5.79295i	0.220374	−	0.220374i	−0.588282	−	0.808656i	$-0.700195\pi$
$691$	5.79295	−	5.79295i	0.220374	−	0.220374i	0.808656	+	0.588282i	$0.200195\pi$
$692$	−13.1447	+	5.86530i	−0.499686	+	0.222965i
$693$	13.5358	+	13.5358i	0.514181	+	0.514181i
$694$	38.7881	−	26.6817i	1.47238	−	1.01282i
$695$		−	3.94646i		−	0.149698i
$696$	34.1032	+	20.8408i	1.29268	+	0.789969i
$697$			33.6826i			1.27582i
$698$	−1.77598	−	2.58179i	−0.0672217	−	0.0977223i
$699$	19.8592	+	19.8592i	0.751142	+	0.751142i
$700$	5.40530	+	2.06982i	0.204301	+	0.0782319i
$701$	−0.258991	+	0.258991i	−0.00978196	+	0.00978196i	−0.711981	−	0.702199i	$-0.752202\pi$
$701$	−0.258991	+	0.258991i	−0.00978196	+	0.00978196i	0.702199	+	0.711981i	$0.252202\pi$
$702$	−1.22401	+	6.61929i	−0.0461972	+	0.249829i
$703$	2.91430			0.109915
$704$	6.40023	−	19.8639i	0.241218	−	0.748649i
$705$	−27.5535			−1.03772
$706$	−2.42924	+	13.1370i	−0.0914257	+	0.494419i
$707$	−10.1936	+	10.1936i	−0.383368	+	0.383368i
$708$	19.3464	+	7.40821i	0.727083	+	0.278418i
$709$	−0.751674	−	0.751674i	−0.0282297	−	0.0282297i	0.692851	−	0.721081i	$-0.256354\pi$
$709$	−0.751674	−	0.751674i	−0.0282297	−	0.0282297i	−0.721081	+	0.692851i	$0.756354\pi$
$710$	−2.61237	−	3.79769i	−0.0980406	−	0.142525i
$711$			0.288761i			0.0108294i
$712$	−9.04060	−	5.52481i	−0.338811	−	0.207051i
$713$		−	9.49986i		−	0.355773i
$714$	57.9052	−	39.8321i	2.16705	−	1.49068i
$715$	8.03505	+	8.03505i	0.300494	+	0.300494i
$716$	−4.23081	+	1.88783i	−0.158113	+	0.0705516i
$717$	27.9029	−	27.9029i	1.04205	−	1.04205i
$718$	25.0944	+	4.64034i	0.936515	+	0.173176i
$719$	39.6557			1.47891			0.739455	−	0.673206i	$-0.235083\pi$
$719$	39.6557			1.47891			0.739455	+	0.673206i	$0.235083\pi$
$720$	−10.1274	+	0.547403i	−0.377427	+	0.0204005i
$721$	−0.434730			−0.0161902
$722$	−22.1736	−	4.10025i	−0.825218	−	0.152595i
$723$	36.6495	−	36.6495i	1.36301	−	1.36301i
$724$	19.3347	+	43.3308i	0.718567	+	1.61037i
$725$	4.24680	+	4.24680i	0.157722	+	0.157722i
$726$	−11.4993	+	7.91016i	−0.426778	+	0.293574i
$727$			22.2952i			0.826881i	0.910531	+	0.413441i	$0.135673\pi$
$727$			22.2952i			0.826881i	−0.910531	+	0.413441i	$0.864327\pi$
$728$	−34.6602	+	8.36625i	−1.28459	+	0.310074i
$729$		−	18.0930i		−	0.670112i
$730$	10.1692	+	14.7833i	0.376378	+	0.547154i
$731$	22.1166	+	22.1166i	0.818011	+	0.818011i
$732$	5.59145	−	14.6020i	0.206666	−	0.539705i
$733$	28.2309	−	28.2309i	1.04273	−	1.04273i	0.0436851	−	0.999045i	$-0.486090\pi$
$733$	28.2309	−	28.2309i	1.04273	−	1.04273i	0.999045	−	0.0436851i	$-0.0139098\pi$
$734$	−7.49154	+	40.5134i	−0.276518	+	1.49538i
$735$	−3.23593			−0.119359
$736$	15.9001	+	20.6337i	0.586086	+	0.760570i
$737$	30.4109			1.12020
$738$	−3.00896	+	16.2721i	−0.110761	+	0.598985i
$739$	−5.45140	+	5.45140i	−0.200533	+	0.200533i	−0.800228	−	0.599695i	$-0.795288\pi$
$739$	−5.45140	+	5.45140i	−0.200533	+	0.200533i	0.599695	+	0.800228i	$0.295288\pi$
$740$	1.19249	−	3.11417i	0.0438369	−	0.114479i
$741$	12.6665	+	12.6665i	0.465314	+	0.465314i
$742$	−8.95691	−	13.0210i	−0.328819	−	0.478014i
$743$			52.5667i			1.92849i	0.265020	+	0.964243i	$0.414621\pi$
$743$			52.5667i			1.92849i	−0.265020	+	0.964243i	$0.585379\pi$
$744$	3.22126	+	13.3452i	0.118097	+	0.489259i
$745$			2.26800i			0.0830931i
$746$	−5.52994	+	3.80396i	−0.202466	+	0.139273i
$747$	−24.7676	−	24.7676i	−0.906200	−	0.906200i
$748$	−15.5172	−	34.7755i	−0.567365	−	1.27152i
$749$	7.96035	−	7.96035i	0.290865	−	0.290865i
$750$	−3.27186	−	0.605017i	−0.119471	−	0.0220921i
$751$	31.0189			1.13190			0.565948	−	0.824441i	$-0.308510\pi$
$751$	31.0189			1.13190			0.565948	+	0.824441i	$0.308510\pi$
$752$	−34.8634	−	31.2878i	−1.27134	−	1.14095i
$753$	−22.0910			−0.805040
$754$	−36.3807	−	6.72735i	−1.32491	−	0.244996i
$755$	1.79431	−	1.79431i	0.0653016	−	0.0653016i
$756$	−5.77590	+	2.57727i	−0.210068	+	0.0937345i
$757$	−2.47389	−	2.47389i	−0.0899152	−	0.0899152i	0.660719	−	0.750634i	$-0.270252\pi$
$757$	−2.47389	−	2.47389i	−0.0899152	−	0.0899152i	−0.750634	+	0.660719i	$0.770252\pi$
$758$	−19.1979	+	13.2059i	−0.697300	+	0.479662i
$759$			28.2634i			1.02590i
$760$	2.57791	−	4.21839i	0.0935105	−	0.153017i
$761$		−	2.48375i		−	0.0900358i	−0.998986	−	0.0450179i	$-0.985666\pi$
$761$		−	2.48375i		−	0.0900358i	0.998986	−	0.0450179i	$-0.0143345\pi$
$762$	−11.7926	−	17.1433i	−0.427202	−	0.621037i
$763$	−19.9913	−	19.9913i	−0.723733	−	0.723733i
$764$	−10.9415	−	4.18978i	−0.395851	−	0.151581i
$765$	−13.0860	+	13.0860i	−0.473125	+	0.473125i
$766$	5.60701	−	30.3221i	0.202590	−	1.09558i
$767$	−19.1771			−0.692444
$768$	−29.3327	−	23.5944i	−1.05845	−	0.851388i
$769$	43.4690			1.56753			0.783767	−	0.621055i	$-0.213296\pi$
$769$	43.4690			1.56753			0.783767	+	0.621055i	$0.213296\pi$
$770$	−1.94139	+	10.4988i	−0.0699627	+	0.378350i
$771$	12.0752	−	12.0752i	0.434879	−	0.434879i
$772$	0.0450416	+	0.0172475i	0.00162108	+	0.000620752i
$773$	0.297026	+	0.297026i	0.0106833	+	0.0106833i	0.712428	−	0.701745i	$-0.247595\pi$
$773$	0.297026	+	0.297026i	0.0106833	+	0.0106833i	−0.701745	+	0.712428i	$0.747595\pi$
$774$	8.70881	+	12.6603i	0.313032	+	0.455064i
$775$			2.06299i			0.0741047i
$776$	−20.6267	+	33.7527i	−0.740454	+	1.21165i
$777$			11.3529i			0.407283i
$778$	19.5920	−	13.4771i	0.702409	−	0.483176i
$779$	−5.70363	−	5.70363i	−0.204354	−	0.204354i
$780$	18.7181	−	8.35224i	0.670217	−	0.299058i
$781$	6.01231	−	6.01231i	0.215137	−	0.215137i
$782$	46.7394	+	8.64283i	1.67140	+	0.309067i
$783$	−6.56286			−0.234537
$784$	−4.09442	−	3.67450i	−0.146229	−	0.131232i
$785$	−14.4822			−0.516892
$786$	23.8985	+	4.41920i	0.852433	+	0.157628i
$787$	−23.6931	+	23.6931i	−0.844567	+	0.844567i	−0.989449	−	0.144882i	$-0.953720\pi$
$787$	−23.6931	+	23.6931i	−0.844567	+	0.844567i	0.144882	+	0.989449i	$0.453720\pi$
$788$	−17.1827	−	38.5081i	−0.612110	−	1.37179i
$789$	15.4293	+	15.4293i	0.549299	+	0.549299i
$790$	−0.132694	+	0.0912783i	−0.00472105	+	0.00324754i
$791$		−	10.1148i		−	0.359641i
$792$	−4.38979	−	18.1863i	−0.155984	−	0.646221i
$793$			14.4742i			0.513993i
$794$	−10.4723	−	15.2240i	−0.371650	−	0.540279i
$795$	6.42421	+	6.42421i	0.227843	+	0.227843i
$796$	9.76435	−	25.4994i	0.346088	−	0.903804i
$797$	38.2292	−	38.2292i	1.35415	−	1.35415i	0.473186	−	0.880963i	$-0.343104\pi$
$797$	38.2292	−	38.2292i	1.35415	−	1.35415i	0.880963	−	0.473186i	$-0.156896\pi$
$798$	−3.06040	+	16.5503i	−0.108337	+	0.585874i
$799$	−85.4762			−3.02393
$800$	−3.45286	−	4.48082i	−0.122077	−	0.158421i
$801$	−9.49801			−0.335596
$802$	3.72210	−	20.1287i	0.131432	−	0.710768i
$803$	−23.4041	+	23.4041i	−0.825913	+	0.825913i
$804$	19.6163	−	51.2277i	0.691814	−	1.80666i
$805$	−9.42340	−	9.42340i	−0.332131	−	0.332131i
$806$	−7.20243	−	10.4704i	−0.253695	−	0.368804i
$807$		−	44.6509i		−	1.57179i
$808$	13.6958	−	3.30588i	0.481816	−	0.116300i
$809$			53.8310i			1.89260i	0.323296	+	0.946298i	$0.395209\pi$
$809$			53.8310i			1.89260i	−0.323296	+	0.946298i	$0.604791\pi$
$810$	11.8586	−	8.15734i	0.416668	−	0.286620i
$811$	27.0549	+	27.0549i	0.950025	+	0.950025i	0.998809	−	0.0487847i	$-0.0155348\pi$
$811$	27.0549	+	27.0549i	0.950025	+	0.950025i	−0.0487847	+	0.998809i	$0.515535\pi$
$812$	−14.1651	−	31.7454i	−0.497098	−	1.11404i
$813$	−37.5986	+	37.5986i	−1.31864	+	1.31864i
$814$	6.04870	+	1.11850i	0.212007	+	0.0392033i
$815$	−11.3506			−0.397593
$816$	−68.5892	+	3.70735i	−2.40110	+	0.129783i
$817$	−7.49020			−0.262049
$818$	13.2683	+	2.45351i	0.463916	+	0.0857851i
$819$	−22.6017	+	22.6017i	−0.789766	+	0.789766i
$820$	−8.42866	+	3.76096i	−0.294342	+	0.131338i
$821$	−24.2170	−	24.2170i	−0.845180	−	0.845180i	0.144347	−	0.989527i	$-0.453892\pi$
$821$	−24.2170	−	24.2170i	−0.845180	−	0.845180i	−0.989527	+	0.144347i	$0.953892\pi$
$822$	−51.9238	+	35.7175i	−1.81105	+	1.24579i
$823$		−	41.3013i		−	1.43967i	−0.694144	−	0.719836i	$-0.744217\pi$
$823$		−	41.3013i		−	1.43967i	0.694144	−	0.719836i	$-0.255783\pi$
$824$	0.362539	+	0.221552i	0.0126296	+	0.00771812i
$825$		−	6.13767i		−	0.213686i
$826$	−10.2119	−	14.8453i	−0.355317	−	0.516535i
$827$	15.7264	+	15.7264i	0.546862	+	0.546862i	0.925532	−	0.378670i	$-0.123618\pi$
$827$	15.7264	+	15.7264i	0.546862	+	0.546862i	−0.378670	+	0.925532i	$0.623618\pi$
$828$	21.8078	+	8.35072i	0.757873	+	0.290208i
$829$	−20.7323	+	20.7323i	−0.720061	+	0.720061i	−0.968618	−	0.248556i	$-0.920044\pi$
$829$	−20.7323	+	20.7323i	−0.720061	+	0.720061i	0.248556	+	0.968618i	$0.420044\pi$
$830$	3.55233	−	19.2106i	0.123303	−	0.666809i
$831$	−53.9075			−1.87003
$832$	33.1682	+	10.6869i	1.14990	+	0.370503i
$833$	−10.0385			−0.347813
$834$	2.38767	−	12.9123i	0.0826784	−	0.447115i
$835$	−4.82679	+	4.82679i	−0.167038	+	0.167038i
$836$	8.51629	+	3.26109i	0.294542	+	0.112787i
$837$	−1.59404	−	1.59404i	−0.0550980	−	0.0550980i
$838$	0.949485	+	1.38030i	0.0327994	+	0.0476816i
$839$			43.6919i			1.50841i	0.656638	+	0.754206i	$0.271978\pi$
$839$			43.6919i			1.50841i	−0.656638	+	0.754206i	$0.728022\pi$
$840$	16.4331	+	10.0425i	0.566996	+	0.346498i
$841$		−	7.07060i		−	0.243814i
$842$	−29.6073	+	20.3664i	−1.02033	+	0.701872i
$843$	14.7200	+	14.7200i	0.506983	+	0.506983i
$844$	6.33090	−	2.82492i	0.217919	−	0.0972377i
$845$	−4.22433	+	4.22433i	−0.145321	+	0.145321i
$846$	−41.2936	−	7.63582i	−1.41970	−	0.262525i
$847$	12.1396			0.417122
$848$	0.833659	+	15.4234i	0.0286280	+	0.529643i
$849$	67.5654			2.31884
$850$	−10.1499	−	1.87688i	−0.348140	−	0.0643763i
$851$	−5.42913	+	5.42913i	−0.186108	+	0.186108i
$852$	−6.24965	−	14.0060i	−0.214109	−	0.479839i
$853$	−35.0610	−	35.0610i	−1.20046	−	1.20046i	−0.974025	−	0.226439i	$-0.927292\pi$
$853$	−35.0610	−	35.0610i	−1.20046	−	1.20046i	−0.226439	−	0.974025i	$-0.572708\pi$
$854$	−11.2047	+	7.70756i	−0.383418	+	0.263747i
$855$		−	4.43182i		−	0.151565i
$856$	−10.6953	+	2.58162i	−0.365558	+	0.0882381i
$857$		−	45.3397i		−	1.54878i	−0.632711	−	0.774388i	$-0.718058\pi$
$857$		−	45.3397i		−	1.54878i	0.632711	−	0.774388i	$-0.281942\pi$
$858$	21.4282	+	31.1509i	0.731547	+	1.06347i
$859$	32.1229	+	32.1229i	1.09602	+	1.09602i	0.994871	+	0.101147i	$0.0322514\pi$
$859$	32.1229	+	32.1229i	1.09602	+	1.09602i	0.101147	+	0.994871i	$0.467749\pi$
$860$	−3.06489	+	8.00391i	−0.104512	+	0.272931i
$861$	22.2190	−	22.2190i	0.757221	−	0.757221i
$862$	0.991245	−	5.36054i	0.0337619	−	0.182581i
$863$	36.9142			1.25657			0.628287	−	0.777981i	$-0.283756\pi$
$863$	36.9142			1.25657			0.628287	+	0.777981i	$0.283756\pi$
$864$	6.13022	+	0.794285i	0.208554	+	0.0270221i
$865$	−7.19695			−0.244704
$866$	6.57406	−	35.5517i	0.223396	−	1.20810i
$867$	−60.3441	+	60.3441i	−2.04939	+	2.04939i
$868$	4.27002	−	11.1511i	0.144934	−	0.378492i
$869$	−0.210075	−	0.210075i	−0.00712630	−	0.00712630i
$870$	11.3255	+	16.4643i	0.383972	+	0.558192i
$871$			50.7793i			1.72059i
$872$	6.48338	+	26.8597i	0.219555	+	0.909585i
$873$			35.4604i			1.20015i
$874$	−9.37813	+	6.45107i	−0.317220	+	0.218211i
$875$	2.04638	+	2.04638i	0.0691804	+	0.0691804i
$876$	24.3280	+	54.5213i	0.821967	+	1.84210i
$877$	−15.7178	+	15.7178i	−0.530753	+	0.530753i	−0.920796	−	0.390044i	$-0.872460\pi$
$877$	−15.7178	+	15.7178i	−0.530753	+	0.530753i	0.390044	+	0.920796i	$0.372460\pi$
$878$	41.9014	+	7.74821i	1.41410	+	0.261490i
$879$	23.8548			0.804603
$880$	6.96951	−	7.76598i	0.234942	−	0.261791i
$881$	1.16748			0.0393335			0.0196667	−	0.999807i	$-0.493739\pi$
$881$	1.16748			0.0393335			0.0196667	+	0.999807i	$0.493739\pi$
$882$	−4.84960	−	0.896765i	−0.163294	−	0.0301956i
$883$	32.2410	−	32.2410i	1.08500	−	1.08500i	0.0889621	−	0.996035i	$-0.471645\pi$
$883$	32.2410	−	32.2410i	1.08500	−	1.08500i	0.996035	−	0.0889621i	$-0.0283550\pi$
$884$	58.0672	−	25.9102i	1.95301	−	0.871455i
$885$	7.32432	+	7.32432i	0.246204	+	0.246204i
$886$	−33.2235	+	22.8539i	−1.11616	+	0.767792i
$887$		−	42.7282i		−	1.43467i	−0.696728	−	0.717336i	$-0.745361\pi$
$887$		−	42.7282i		−	1.43467i	0.696728	−	0.717336i	$-0.254639\pi$
$888$	5.78579	−	9.46766i	0.194159	−	0.317714i
$889$			18.0980i			0.606987i
$890$	−3.00235	−	4.36462i	−0.100639	−	0.146302i
$891$	18.7739	+	18.7739i	0.628949	+	0.628949i
$892$	−26.0518	−	9.97588i	−0.872280	−	0.334017i
$893$	14.4741	−	14.4741i	0.484356	−	0.484356i
$894$	−1.37218	+	7.42058i	−0.0458925	+	0.248181i
$895$	−2.31644			−0.0774302
$896$	9.38928	+	31.3670i	0.313674	+	1.04790i
$897$	−47.1935			−1.57574
$898$	9.40724	−	50.8732i	0.313924	−	1.69766i
$899$	8.76109	−	8.76109i	0.292199	−	0.292199i
$900$	−4.73577	−	1.81344i	−0.157859	−	0.0604481i
$901$	19.9291	+	19.9291i	0.663935	+	0.663935i
$902$	−9.64899	−	14.0270i	−0.321276	−	0.467050i
$903$		−	29.1788i		−	0.971008i
$904$	−5.15482	+	8.43516i	−0.171447	+	0.280549i
$905$			23.7244i			0.788625i
$906$	6.95632	−	4.78514i	0.231108	−	0.158976i
$907$	1.23335	+	1.23335i	0.0409528	+	0.0409528i	0.727287	−	0.686334i	$-0.240781\pi$
$907$	1.23335	+	1.23335i	0.0409528	+	0.0409528i	−0.686334	+	0.727287i	$0.740781\pi$
$908$	−11.4653	+	5.11594i	−0.380489	+	0.169779i
$909$	8.93093	−	8.93093i	0.296220	−	0.296220i
$910$	−17.5306	−	3.24167i	−0.581134	−	0.107460i
$911$	23.9284			0.792785			0.396392	−	0.918081i	$-0.370262\pi$
$911$	23.9284			0.792785			0.396392	+	0.918081i	$0.370262\pi$
$912$	10.9867	−	12.2423i	0.363807	−	0.405383i
$913$	36.0371			1.19265
$914$	23.2710	+	4.30316i	0.769735	+	0.142336i
$915$	5.52814	−	5.52814i	0.182755	−	0.182755i
$916$	6.16689	+	13.8206i	0.203760	+	0.456644i
$917$	−14.9473	−	14.9473i	−0.493605	−	0.493605i
$918$	9.29291	−	6.39245i	0.306712	−	0.210982i
$919$		−	45.3844i		−	1.49709i	−0.663082	−	0.748546i	$-0.730752\pi$
$919$		−	45.3844i		−	1.49709i	0.663082	−	0.748546i	$-0.269248\pi$
$920$	3.05611	+	12.6610i	0.100757	+	0.417421i
$921$		−	61.3253i		−	2.02074i
$922$	13.4179	+	19.5060i	0.441893	+	0.642395i
$923$	10.0392	+	10.0392i	0.330444	+	0.330444i
$924$	−12.7039	+	33.1760i	−0.417927	+	1.09141i
$925$	1.17899	−	1.17899i	0.0387649	−	0.0387649i
$926$	8.29851	−	44.8774i	0.272706	−	1.47476i
$927$	0.380882			0.0125098
$928$	−4.36553	+	33.6927i	−0.143305	+	1.10602i
$929$	−6.51036			−0.213598			−0.106799	−	0.994281i	$-0.534060\pi$
$929$	−6.51036			−0.213598			−0.106799	+	0.994281i	$0.534060\pi$
$930$	−1.24814	+	6.74981i	−0.0409282	+	0.221335i
$931$	1.69986	−	1.69986i	0.0557107	−	0.0557107i
$932$	−8.53741	+	22.2953i	−0.279652	+	0.730307i
$933$	−11.7947	−	11.7947i	−0.386142	−	0.386142i
$934$	1.38926	+	2.01961i	0.0454579	+	0.0660837i
$935$		−	19.0402i		−	0.622681i
$936$	30.3670	−	7.32996i	0.992575	−	0.239587i
$937$		−	40.2986i		−	1.31650i	−0.752801	−	0.658248i	$-0.771298\pi$
$937$		−	40.2986i		−	1.31650i	0.752801	−	0.658248i	$-0.228702\pi$
$938$	−39.3092	+	27.0402i	−1.28349	+	0.882894i
$939$	−36.6799	−	36.6799i	−1.19700	−	1.19700i
$940$	−9.54417	−	21.3894i	−0.311296	−	0.697644i
$941$	1.10649	−	1.10649i	0.0360705	−	0.0360705i	−0.688841	−	0.724912i	$-0.741880\pi$
$941$	1.10649	−	1.10649i	0.0360705	−	0.0360705i	0.724912	+	0.688841i	$0.241880\pi$
$942$	−47.3837	−	8.76198i	−1.54385	−	0.285481i
$943$	21.2509			0.692025
$944$	0.950465	+	17.5844i	0.0309350	+	0.572325i
$945$	−3.16241			−0.102873
$946$	−15.5461	−	2.87471i	−0.505447	−	0.0934649i
$947$	−8.83833	+	8.83833i	−0.287207	+	0.287207i	−0.835975	−	0.548768i	$-0.815097\pi$
$947$	−8.83833	+	8.83833i	−0.287207	+	0.287207i	0.548768	+	0.835975i	$0.315097\pi$
$948$	−0.489382	+	0.218368i	−0.0158944	+	0.00709225i
$949$	−39.0796	−	39.0796i	−1.26858	−	1.26858i
$950$	2.03655	−	1.40091i	0.0660745	−	0.0454516i
$951$		−	20.6185i		−	0.668600i
$952$	50.9786	+	31.1536i	1.65223	+	1.00969i
$953$			14.9610i			0.484636i	0.970197	+	0.242318i	$0.0779077\pi$
$953$			14.9610i			0.484636i	−0.970197	+	0.242318i	$0.922092\pi$
$954$	7.84746	+	11.4081i	0.254071	+	0.369351i
$955$	−4.14234	−	4.14234i	−0.134043	−	0.134043i
$956$	31.3258	+	11.9954i	1.01315	+	0.387959i
$957$	−26.0654	+	26.0654i	−0.842576	+	0.842576i
$958$	−7.41620	+	40.1059i	−0.239606	+	1.29576i
$959$	54.8152			1.77008
$960$	−8.58631	−	16.7496i	−0.277122	−	0.540593i
$961$	−26.7441			−0.862712
$962$	−1.86764	+	10.1000i	−0.0602150	+	0.325636i
$963$	−6.97433	+	6.97433i	−0.224745	+	0.224745i
$964$	41.1453	+	15.7555i	1.32520	+	0.507452i
$965$	0.0170522	+	0.0170522i	0.000548930	+	0.000548930i
$966$	−25.1307	−	36.5333i	−0.808568	−	1.17544i
$967$		−	3.95287i		−	0.127116i	−0.997978	−	0.0635578i	$-0.979755\pi$
$967$		−	3.95287i		−	0.127116i	0.997978	−	0.0635578i	$-0.0202447\pi$
$968$	−10.1237	−	6.18672i	−0.325389	−	0.198849i
$969$		−	30.0150i		−	0.964221i
$970$	−16.2951	+	11.2092i	−0.523205	+	0.359905i
$971$	−29.0538	−	29.0538i	−0.932380	−	0.932380i	0.0654740	−	0.997854i	$-0.479144\pi$
$971$	−29.0538	−	29.0538i	−0.932380	−	0.932380i	−0.997854	+	0.0654740i	$0.979144\pi$
$972$	37.7475	−	16.8434i	1.21075	−	0.540251i
$973$	−8.07597	+	8.07597i	−0.258904	+	0.258904i
$974$	−44.7323	−	8.27169i	−1.43332	−	0.265042i
$975$	10.2485			0.328215
$976$	13.2721	−	0.717377i	0.424830	−	0.0229627i
$977$	25.8962			0.828494			0.414247	−	0.910164i	$-0.364045\pi$
$977$	25.8962			0.828494			0.414247	+	0.910164i	$0.364045\pi$
$978$	−37.1375	−	6.86729i	−1.18753	−	0.219592i
$979$	6.90984	−	6.90984i	0.220839	−	0.220839i
$980$	−1.12088	−	2.51201i	−0.0358053	−	0.0802431i
$981$	17.5151	+	17.5151i	0.559213	+	0.559213i
$982$	8.95749	−	6.16172i	0.285845	−	0.196628i
$983$			22.0151i			0.702173i	0.936343	+	0.351087i	$0.114188\pi$
$983$			22.0151i			0.702173i	−0.936343	+	0.351087i	$0.885812\pi$
$984$	−29.8528	+	7.20585i	−0.951673	+	0.229714i
$985$		−	21.0839i		−	0.671789i
$986$	35.1340	+	51.0754i	1.11889	+	1.62657i
$987$	56.3850	+	56.3850i	1.79476	+	1.79476i
$988$	−5.44529	+	14.2203i	−0.173238	+	0.452407i
$989$	13.9537	−	13.9537i	0.443702	−	0.443702i
$990$	1.70091	−	9.19835i	0.0540586	−	0.292343i
$991$	−54.3207			−1.72556			−0.862778	−	0.505583i	$-0.831277\pi$
$991$	−54.3207			−1.72556			−0.862778	+	0.505583i	$0.831277\pi$
$992$	−9.24388	+	7.12321i	−0.293493	+	0.226162i
$993$	61.9461			1.96580
$994$	−2.42562	+	13.1174i	−0.0769359	+	0.416060i
$995$	9.65378	−	9.65378i	0.306045	−	0.306045i
$996$	23.2454	−	60.7051i	0.736560	−	1.92351i
$997$	8.14405	+	8.14405i	0.257925	+	0.257925i	0.824210	−	0.566285i	$-0.191620\pi$
$997$	8.14405	+	8.14405i	0.257925	+	0.257925i	−0.566285	+	0.824210i	$0.691620\pi$
$998$	−19.4146	−	28.2236i	−0.614557	−	0.893402i
$999$			1.82197i			0.0576446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.l.a.21.4	✓	16
3.2	odd	2		720.2.t.c.181.5		16
4.3	odd	2		320.2.l.a.241.7		16
5.2	odd	4		400.2.q.g.149.2		16
5.3	odd	4		400.2.q.h.149.7		16
5.4	even	2		400.2.l.h.101.5		16
8.3	odd	2		640.2.l.a.481.2		16
8.5	even	2		640.2.l.b.481.7		16
12.11	even	2		2880.2.t.c.2161.6		16
16.3	odd	4		320.2.l.a.81.7		16
16.5	even	4		640.2.l.b.161.7		16
16.11	odd	4		640.2.l.a.161.2		16
16.13	even	4	inner	80.2.l.a.61.4	yes	16
20.3	even	4		1600.2.q.g.49.7		16
20.7	even	4		1600.2.q.h.49.2		16
20.19	odd	2		1600.2.l.i.1201.2		16
32.3	odd	8		5120.2.a.t.1.8		8
32.13	even	8		5120.2.a.s.1.8		8
32.19	odd	8		5120.2.a.u.1.1		8
32.29	even	8		5120.2.a.v.1.1		8
48.29	odd	4		720.2.t.c.541.5		16
48.35	even	4		2880.2.t.c.721.7		16
80.3	even	4		1600.2.q.h.849.2		16
80.13	odd	4		400.2.q.g.349.2		16
80.19	odd	4		1600.2.l.i.401.2		16
80.29	even	4		400.2.l.h.301.5		16
80.67	even	4		1600.2.q.g.849.7		16
80.77	odd	4		400.2.q.h.349.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.4	✓	16	1.1	even	1	trivial
80.2.l.a.61.4	yes	16	16.13	even	4	inner
320.2.l.a.81.7		16	16.3	odd	4
320.2.l.a.241.7		16	4.3	odd	2
400.2.l.h.101.5		16	5.4	even	2
400.2.l.h.301.5		16	80.29	even	4
400.2.q.g.149.2		16	5.2	odd	4
400.2.q.g.349.2		16	80.13	odd	4
400.2.q.h.149.7		16	5.3	odd	4
400.2.q.h.349.7		16	80.77	odd	4
640.2.l.a.161.2		16	16.11	odd	4
640.2.l.a.481.2		16	8.3	odd	2
640.2.l.b.161.7		16	16.5	even	4
640.2.l.b.481.7		16	8.5	even	2
720.2.t.c.181.5		16	3.2	odd	2
720.2.t.c.541.5		16	48.29	odd	4
1600.2.l.i.401.2		16	80.19	odd	4
1600.2.l.i.1201.2		16	20.19	odd	2
1600.2.q.g.49.7		16	20.3	even	4
1600.2.q.g.849.7		16	80.67	even	4
1600.2.q.h.49.2		16	20.7	even	4
1600.2.q.h.849.2		16	80.3	even	4
2880.2.t.c.721.7		16	48.35	even	4
2880.2.t.c.2161.6		16	12.11	even	2
5120.2.a.s.1.8		8	32.13	even	8
5120.2.a.t.1.8		8	32.3	odd	8
5120.2.a.u.1.1		8	32.19	odd	8
5120.2.a.v.1.1		8	32.29	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)

\(f(q)\)	\(=\)	\(q+(-0.257150 + 1.39064i) q^{2} +(-1.66366 + 1.66366i) q^{3} +(-1.86775 - 0.715205i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.88574 - 2.74137i) q^{6} +2.89402i q^{7} +(1.47488 - 2.41345i) q^{8} -2.53555i q^{9} +O(q^{10})\)	\(q+(-0.257150 + 1.39064i) q^{2} +(-1.66366 + 1.66366i) q^{3} +(-1.86775 - 0.715205i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.88574 - 2.74137i) q^{6} +2.89402i q^{7} +(1.47488 - 2.41345i) q^{8} -2.53555i q^{9} +(1.16516 - 0.801497i) q^{10} +(1.84462 + 1.84462i) q^{11} +(4.29717 - 1.91744i) q^{12} +(-3.08011 + 3.08011i) q^{13} +(-4.02454 - 0.744198i) q^{14} +2.35278 q^{15} +(2.97696 + 2.67165i) q^{16} +7.29875 q^{17} +(3.52604 + 0.652018i) q^{18} +(-1.23593 + 1.23593i) q^{19} +(0.814970 + 1.82642i) q^{20} +(-4.81468 - 4.81468i) q^{21} +(-3.03955 + 2.09086i) q^{22} -4.60490i q^{23} +(1.56145 + 6.46887i) q^{24} +1.00000i q^{25} +(-3.49126 - 5.07536i) q^{26} +(-0.772683 - 0.772683i) q^{27} +(2.06982 - 5.40530i) q^{28} +(4.24680 - 4.24680i) q^{29} +(-0.605017 + 3.27186i) q^{30} +2.06299 q^{31} +(-4.48082 + 3.45286i) q^{32} -6.13767 q^{33} +(-1.87688 + 10.1499i) q^{34} +(2.04638 - 2.04638i) q^{35} +(-1.81344 + 4.73577i) q^{36} +(-1.17899 - 1.17899i) q^{37} +(-1.40091 - 2.03655i) q^{38} -10.2485i q^{39} +(-2.74946 + 0.663664i) q^{40} +4.61484i q^{41} +(7.93357 - 5.45738i) q^{42} +(3.03019 + 3.03019i) q^{43} +(-2.12601 - 4.76458i) q^{44} +(-1.79291 + 1.79291i) q^{45} +(6.40375 + 1.18415i) q^{46} -11.7111 q^{47} +(-9.39739 + 0.507943i) q^{48} -1.37537 q^{49} +(-1.39064 - 0.257150i) q^{50} +(-12.1427 + 12.1427i) q^{51} +(7.95577 - 3.54995i) q^{52} +(2.73048 + 2.73048i) q^{53} +(1.27322 - 0.875827i) q^{54} -2.60869i q^{55} +(6.98457 + 4.26835i) q^{56} -4.11235i q^{57} +(4.81369 + 6.99782i) q^{58} +(3.11306 + 3.11306i) q^{59} +(-4.39439 - 1.68272i) q^{60} +(2.34962 - 2.34962i) q^{61} +(-0.530498 + 2.86887i) q^{62} +7.33795 q^{63} +(-3.64944 - 7.11910i) q^{64} +4.35593 q^{65} +(1.57830 - 8.53528i) q^{66} +(8.24311 - 8.24311i) q^{67} +(-13.6322 - 5.22011i) q^{68} +(7.66101 + 7.66101i) q^{69} +(2.31955 + 3.37201i) q^{70} -3.25937i q^{71} +(-6.11942 - 3.73965i) q^{72} +12.6877i q^{73} +(1.94272 - 1.33637i) q^{74} +(-1.66366 - 1.66366i) q^{75} +(3.19235 - 1.42446i) q^{76} +(-5.33839 + 5.33839i) q^{77} +(14.2520 + 2.63541i) q^{78} -0.113885 q^{79} +(-0.215891 - 3.99417i) q^{80} +10.1776 q^{81} +(-6.41758 - 1.18671i) q^{82} +(9.76813 - 9.76813i) q^{83} +(5.54912 + 12.4361i) q^{84} +(-5.16100 - 5.16100i) q^{85} +(-4.99310 + 3.43468i) q^{86} +14.1305i q^{87} +(7.17251 - 1.73129i) q^{88} -3.74593i q^{89} +(-2.03224 - 2.95433i) q^{90} +(-8.91390 - 8.91390i) q^{91} +(-3.29345 + 8.60080i) q^{92} +(-3.43212 + 3.43212i) q^{93} +(3.01150 - 16.2858i) q^{94} +1.74787 q^{95} +(1.71017 - 13.1990i) q^{96} -13.9853 q^{97} +(0.353676 - 1.91264i) q^{98} +(4.67714 - 4.67714i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more