LMFDB - Embedded newform 725.2.q.d.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(51,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("725.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.q (of order $14$, degree $6$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			51.4
Character	$\chi$	$=$	725.51
Dual form			725.2.q.d.526.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.714081 + 0.162984i) q^{2} +(-0.656356 + 1.36294i) q^{3} +(-1.31859 + 0.635000i) q^{4} +(0.246554 - 1.08022i) q^{6} +(-0.573111 - 0.275996i) q^{7} +(1.98338 - 1.58169i) q^{8} +(0.443675 + 0.556351i) q^{9} +(4.91460 + 3.91926i) q^{11} -2.21394i q^{12} +(-2.02594 + 2.54045i) q^{13} +(0.454230 + 0.103675i) q^{14} +(0.666483 - 0.835743i) q^{16} +2.20509i q^{17} +(-0.407496 - 0.324967i) q^{18} +(-0.336649 - 0.699059i) q^{19} +(0.752330 - 0.599963i) q^{21} +(-4.14820 - 1.99767i) q^{22} +(0.369157 - 1.61738i) q^{23} +(0.853945 + 3.74138i) q^{24} +(1.03263 - 2.14428i) q^{26} +(-5.47393 + 1.24939i) q^{27} +0.930956 q^{28} +(-1.78713 + 5.07998i) q^{29} +(3.41700 - 0.779907i) q^{31} +(-2.54110 + 5.27664i) q^{32} +(-8.56744 + 4.12586i) q^{33} +(-0.359395 - 1.57461i) q^{34} +(-0.938308 - 0.451865i) q^{36} +(-3.14062 + 2.50456i) q^{37} +(0.354330 + 0.444316i) q^{38} +(-2.13273 - 4.42867i) q^{39} -5.53164i q^{41} +(-0.439440 + 0.551040i) q^{42} +(-7.71324 - 1.76050i) q^{43} +(-8.96907 - 2.04713i) q^{44} +1.21511i q^{46} +(2.98310 + 2.37895i) q^{47} +(0.701615 + 1.45692i) q^{48} +(-4.11215 - 5.15647i) q^{49} +(-3.00540 - 1.44732i) q^{51} +(1.05820 - 4.63628i) q^{52} +(-2.04205 - 8.94680i) q^{53} +(3.70520 - 1.78433i) q^{54} +(-1.57324 + 0.359081i) q^{56} +1.17374 q^{57} +(0.448197 - 3.91879i) q^{58} -2.82948 q^{59} +(-3.19314 + 6.63062i) q^{61} +(-2.31290 + 1.11383i) q^{62} +(-0.100725 - 0.441303i) q^{63} +(0.478809 - 2.09780i) q^{64} +(5.44539 - 4.34255i) q^{66} +(-2.46120 - 3.08625i) q^{67} +(-1.40023 - 2.90761i) q^{68} +(1.96209 + 1.56472i) q^{69} +(-7.88704 + 9.89003i) q^{71} +(1.75995 + 0.401698i) q^{72} +(16.0089 + 3.65392i) q^{73} +(1.83445 - 2.30033i) q^{74} +(0.887805 + 0.708001i) q^{76} +(-1.73491 - 3.60258i) q^{77} +(2.24475 + 2.81482i) q^{78} +(-6.83798 + 5.45310i) q^{79} +(1.41497 - 6.19940i) q^{81} +(0.901570 + 3.95004i) q^{82} +(-9.86210 + 4.74934i) q^{83} +(-0.611038 + 1.26883i) q^{84} +5.79481 q^{86} +(-5.75070 - 5.77002i) q^{87} +15.9466 q^{88} +(9.99577 - 2.28147i) q^{89} +(1.86224 - 0.896808i) q^{91} +(0.540270 + 2.36708i) q^{92} +(-1.17980 + 5.16905i) q^{93} +(-2.51791 - 1.21256i) q^{94} +(-5.52387 - 6.92671i) q^{96} +(0.683669 + 1.41965i) q^{97} +(3.77683 + 3.01192i) q^{98} +4.47312i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{4} - 16 q^{6} - 4 q^{7} - 21 q^{8} + 10 q^{9} + 14 q^{11} + 4 q^{13} + 10 q^{16} + 35 q^{22} - 37 q^{23} + 48 q^{24} + 21 q^{27} + 44 q^{28} - 4 q^{29} + 14 q^{31} + 98 q^{32} - 41 q^{33} + 10 q^{34}+ \cdots + 91 q^{98}+O(q^{100}) $ 60 * q + 12 * q^4 - 16 * q^6 - 4 * q^7 - 21 * q^8 + 10 * q^9 + 14 * q^11 + 4 * q^13 + 10 * q^16 + 35 * q^22 - 37 * q^23 + 48 * q^24 + 21 * q^27 + 44 * q^28 - 4 * q^29 + 14 * q^31 + 98 * q^32 - 41 * q^33 + 10 * q^34 + 32 * q^36 + 7 * q^37 - 14 * q^38 + 56 * q^39 - 45 * q^42 - 63 * q^44 - 42 * q^47 - 21 * q^48 - 72 * q^49 - 32 * q^51 - 80 * q^52 - 20 * q^53 - 65 * q^54 - 63 * q^56 - 28 * q^57 - 2 * q^58 - 16 * q^59 - 28 * q^61 - 70 * q^62 + 42 * q^63 + 37 * q^64 - 140 * q^66 - 24 * q^67 - 42 * q^68 - 84 * q^69 + 9 * q^71 - 105 * q^72 + 14 * q^73 - 85 * q^74 + 70 * q^76 + 21 * q^77 + 102 * q^78 + 56 * q^79 - 72 * q^81 + 36 * q^82 + 6 * q^83 - 84 * q^84 + 86 * q^86 + 5 * q^87 + 102 * q^88 + 14 * q^89 - 60 * q^91 + 91 * q^92 - 62 * q^93 - 44 * q^94 + 25 * q^96 + 14 * q^97 + 91 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$1$

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 $

$2$	−0.714081	+	0.162984i	−0.504931	+	0.115247i	−0.467396	−	0.884048i	$-0.654808\pi$
$2$	−0.714081	+	0.162984i	−0.504931	+	0.115247i	−0.0375352	+	0.999295i	$0.511951\pi$
$3$	−0.656356	+	1.36294i	−0.378947	+	0.786892i	0.621048	+	0.783773i	$0.286707\pi$
$3$	−0.656356	+	1.36294i	−0.378947	+	0.786892i	−0.999995	+	0.00311951i	$0.999007\pi$
$4$	−1.31859	+	0.635000i	−0.659295	+	0.317500i
$5$		0			0
$5$		0			0
$6$	0.246554	−	1.08022i	0.100655	−	0.440999i
$7$	−0.573111	−	0.275996i	−0.216616	−	0.104317i	0.322430	−	0.946593i	$-0.395500\pi$
$7$	−0.573111	−	0.275996i	−0.216616	−	0.104317i	−0.539045	+	0.842277i	$0.681215\pi$
$8$	1.98338	−	1.58169i	0.701231	−	0.559213i
$9$	0.443675	+	0.556351i	0.147892	+	0.185450i
$10$		0			0
$11$	4.91460	+	3.91926i	1.48181	+	1.18170i	0.939988	+	0.341207i	$0.110836\pi$
$11$	4.91460	+	3.91926i	1.48181	+	1.18170i	0.541819	+	0.840495i	$0.317736\pi$
$12$		−	2.21394i		−	0.639110i
$13$	−2.02594	+	2.54045i	−0.561894	+	0.704593i	−0.978907	−	0.204308i	$-0.934506\pi$
$13$	−2.02594	+	2.54045i	−0.561894	+	0.704593i	0.417012	+	0.908901i	$0.363077\pi$
$14$	0.454230	+	0.103675i	0.121398	+	0.0277083i
$15$		0			0
$16$	0.666483	−	0.835743i	0.166621	−	0.208936i
$17$			2.20509i			0.534812i	0.963584	+	0.267406i	$0.0861665\pi$
$17$			2.20509i			0.534812i	−0.963584	+	0.267406i	$0.913833\pi$
$18$	−0.407496	−	0.324967i	−0.0960477	−	0.0765955i
$19$	−0.336649	−	0.699059i	−0.0772326	−	0.160375i	0.858777	−	0.512349i	$-0.171225\pi$
$19$	−0.336649	−	0.699059i	−0.0772326	−	0.160375i	−0.936010	+	0.351974i	$0.885510\pi$
$20$		0			0
$21$	0.752330	−	0.599963i	0.164172	−	0.130923i
$22$	−4.14820	−	1.99767i	−0.884399	−	0.425904i
$23$	0.369157	−	1.61738i	0.0769745	−	0.337247i	−0.921747	−	0.387791i	$-0.873238\pi$
$23$	0.369157	−	1.61738i	0.0769745	−	0.337247i	0.998722	+	0.0505436i	$0.0160954\pi$
$24$	0.853945	+	3.74138i	0.174311	+	0.763706i
$25$		0			0
$26$	1.03263	−	2.14428i	0.202516	−	0.420528i
$27$	−5.47393	+	1.24939i	−1.05346	+	0.240445i
$28$	0.930956			0.175934
$29$	−1.78713	+	5.07998i	−0.331861	+	0.943328i
$29$	−1.78713	+	5.07998i	−0.331861	+	0.943328i
$30$		0			0
$31$	3.41700	−	0.779907i	0.613711	−	0.140075i	0.0956439	−	0.995416i	$-0.469509\pi$
$31$	3.41700	−	0.779907i	0.613711	−	0.140075i	0.518067	+	0.855340i	$0.326652\pi$
$32$	−2.54110	+	5.27664i	−0.449207	+	0.932787i
$33$	−8.56744	+	4.12586i	−1.49140	+	0.718220i
$34$	−0.359395	−	1.57461i	−0.0616357	−	0.270043i
$35$		0			0
$36$	−0.938308	−	0.451865i	−0.156385	−	0.0753109i
$37$	−3.14062	+	2.50456i	−0.516315	+	0.411748i	−0.846677	−	0.532106i	$-0.821401\pi$
$37$	−3.14062	+	2.50456i	−0.516315	+	0.411748i	0.330362	+	0.943854i	$0.392829\pi$
$38$	0.354330	+	0.444316i	0.0574800	+	0.0720776i
$39$	−2.13273	−	4.42867i	−0.341511	−	0.709154i
$40$		0			0
$41$		−	5.53164i		−	0.863897i	−0.901898	−	0.431948i	$-0.857826\pi$
$41$		−	5.53164i		−	0.863897i	0.901898	−	0.431948i	$-0.142174\pi$
$42$	−0.439440	+	0.551040i	−0.0678070	+	0.0850273i
$43$	−7.71324	−	1.76050i	−1.17626	−	0.268473i	−0.410658	−	0.911789i	$-0.634701\pi$
$43$	−7.71324	−	1.76050i	−1.17626	−	0.268473i	−0.765601	+	0.643316i	$0.777558\pi$
$44$	−8.96907	−	2.04713i	−1.35214	−	0.308617i
$45$		0			0
$46$			1.21511i			0.179158i
$47$	2.98310	+	2.37895i	0.435130	+	0.347005i	0.816428	−	0.577448i	$-0.195951\pi$
$47$	2.98310	+	2.37895i	0.435130	+	0.347005i	−0.381298	+	0.924452i	$0.624523\pi$
$48$	0.701615	+	1.45692i	0.101269	+	0.210288i
$49$	−4.11215	−	5.15647i	−0.587449	−	0.736638i
$50$		0			0
$51$	−3.00540	−	1.44732i	−0.420840	−	0.202666i
$52$	1.05820	−	4.63628i	0.146746	−	0.642936i
$53$	−2.04205	−	8.94680i	−0.280497	−	1.22894i	−0.897158	−	0.441709i	$-0.854372\pi$
$53$	−2.04205	−	8.94680i	−0.280497	−	1.22894i	0.616661	−	0.787229i	$-0.288485\pi$
$54$	3.70520	−	1.78433i	0.504214	−	0.242817i
$55$		0			0
$56$	−1.57324	+	0.359081i	−0.210233	+	0.0479843i
$57$	1.17374			0.155465
$58$	0.448197	−	3.91879i	0.0588512	−	0.514562i
$59$	−2.82948			−0.368367			−0.184184	−	0.982892i	$-0.558964\pi$
$59$	−2.82948			−0.368367			−0.184184	+	0.982892i	$0.558964\pi$
$60$		0			0
$61$	−3.19314	+	6.63062i	−0.408840	+	0.848964i	0.590288	+	0.807193i	$0.299014\pi$
$61$	−3.19314	+	6.63062i	−0.408840	+	0.848964i	−0.999127	+	0.0417712i	$0.986700\pi$
$62$	−2.31290	+	1.11383i	−0.293738	+	0.141457i
$63$	−0.100725	−	0.441303i	−0.0126901	−	0.0555989i
$64$	0.478809	−	2.09780i	0.0598511	−	0.262225i
$65$		0			0
$66$	5.44539	−	4.34255i	0.670281	−	0.534531i
$67$	−2.46120	−	3.08625i	−0.300683	−	0.377045i	0.608420	−	0.793615i	$-0.291804\pi$
$67$	−2.46120	−	3.08625i	−0.300683	−	0.377045i	−0.909104	+	0.416570i	$0.863232\pi$
$68$	−1.40023	−	2.90761i	−0.169803	−	0.352599i
$69$	1.96209	+	1.56472i	0.236208	+	0.188370i
$70$		0			0
$71$	−7.88704	+	9.89003i	−0.936019	+	1.17373i	0.0485653	+	0.998820i	$0.484535\pi$
$71$	−7.88704	+	9.89003i	−0.936019	+	1.17373i	−0.984584	+	0.174911i	$0.944036\pi$
$72$	1.75995	+	0.401698i	0.207412	+	0.0473405i
$73$	16.0089	+	3.65392i	1.87370	+	0.427659i	0.998432	−	0.0559827i	$-0.0178292\pi$
$73$	16.0089	+	3.65392i	1.87370	+	0.427659i	0.875266	+	0.483642i	$0.160686\pi$
$74$	1.83445	−	2.30033i	0.213251	−	0.267408i
$75$		0			0
$76$	0.887805	+	0.708001i	0.101838	+	0.0812132i
$77$	−1.73491	−	3.60258i	−0.197711	−	0.410552i
$78$	2.24475	+	2.81482i	0.254167	+	0.318716i
$79$	−6.83798	+	5.45310i	−0.769332	+	0.613522i	−0.927471	−	0.373895i	$-0.878022\pi$
$79$	−6.83798	+	5.45310i	−0.769332	+	0.613522i	0.158139	+	0.987417i	$0.449451\pi$
$80$		0			0
$81$	1.41497	−	6.19940i	0.157219	−	0.688822i
$82$	0.901570	+	3.95004i	0.0995618	+	0.436209i
$83$	−9.86210	+	4.74934i	−1.08251	+	0.521308i	−0.888117	−	0.459617i	$-0.847987\pi$
$83$	−9.86210	+	4.74934i	−1.08251	+	0.521308i	−0.194389	+	0.980925i	$0.562272\pi$
$84$	−0.611038	+	1.26883i	−0.0666698	+	0.138441i
$85$		0			0
$86$	5.79481			0.624871
$87$	−5.75070	−	5.77002i	−0.616540	−	0.618611i
$88$	15.9466			1.69991
$89$	9.99577	−	2.28147i	1.05955	−	0.241835i	0.342974	−	0.939345i	$-0.388566\pi$
$89$	9.99577	−	2.28147i	1.05955	−	0.241835i	0.716576	+	0.697509i	$0.245709\pi$
$90$		0			0
$91$	1.86224	−	0.896808i	0.195216	−	0.0940110i
$92$	0.540270	+	2.36708i	0.0563271	+	0.246785i
$93$	−1.17980	+	5.16905i	−0.122340	+	0.536005i
$94$	−2.51791	−	1.21256i	−0.259702	−	0.125066i
$95$		0			0
$96$	−5.52387	−	6.92671i	−0.563777	−	0.706954i
$97$	0.683669	+	1.41965i	0.0694161	+	0.144144i	0.932790	−	0.360421i	$-0.117367\pi$
$97$	0.683669	+	1.41965i	0.0694161	+	0.144144i	−0.863374	+	0.504565i	$0.831653\pi$
$98$	3.77683	+	3.01192i	0.381517	+	0.304250i
$99$			4.47312i			0.449565i
$100$		0			0
$101$	−8.27123	−	1.88785i	−0.823018	−	0.187849i	−0.209782	−	0.977748i	$-0.567275\pi$
$101$	−8.27123	−	1.88785i	−0.823018	−	0.187849i	−0.613236	+	0.789900i	$0.710133\pi$
$102$	2.38199	+	0.543673i	0.235852	+	0.0538316i
$103$	−3.26058	+	4.08864i	−0.321275	+	0.402866i	−0.916074	−	0.401008i	$-0.868660\pi$
$103$	−3.26058	+	4.08864i	−0.321275	+	0.402866i	0.594800	+	0.803874i	$0.297231\pi$
$104$			8.24309i			0.808302i
$105$		0			0
$106$	2.91638	+	6.05592i	0.283264	+	0.588203i
$107$	3.90452	+	4.89611i	0.377464	+	0.473325i	0.933884	−	0.357577i	$-0.116397\pi$
$107$	3.90452	+	4.89611i	0.377464	+	0.473325i	−0.556420	+	0.830901i	$0.687825\pi$
$108$	6.42452	−	5.12338i	0.618199	−	0.492997i
$109$	7.43403	+	3.58004i	0.712051	+	0.342906i	0.754597	−	0.656189i	$-0.227833\pi$
$109$	7.43403	+	3.58004i	0.712051	+	0.342906i	−0.0425458	+	0.999095i	$0.513547\pi$
$110$		0			0
$111$	−1.35220	−	5.92436i	−0.128345	−	0.562315i
$112$	−0.612630	+	0.295027i	−0.0578881	+	0.0278774i
$113$	−0.0264300	+	0.0548825i	−0.00248633	+	0.00516292i	−0.902208	−	0.431301i	$-0.858055\pi$
$113$	−0.0264300	+	0.0548825i	−0.00248633	+	0.00516292i	0.899722	+	0.436463i	$0.143769\pi$
$114$	−0.838142	+	0.191300i	−0.0784992	+	0.0179169i
$115$		0			0
$116$	−0.869294	−	7.83324i	−0.0807120	−	0.727298i
$117$	−2.31224			−0.213766
$118$	2.02048	−	0.461161i	0.186000	−	0.0424533i
$119$	0.608595	−	1.26376i	0.0557898	−	0.115849i
$120$		0			0
$121$	6.34494	+	27.7990i	0.576813	+	2.52718i
$122$	1.19947	−	5.25523i	0.108595	−	0.475786i
$123$	7.53928	+	3.63072i	0.679794	+	0.327371i
$124$	−4.01038	+	3.19817i	−0.360143	+	0.287204i
$125$		0			0
$126$	0.143851	+	0.298709i	0.0128153	+	0.0266111i
$127$	16.6640	+	13.2891i	1.47869	+	1.17921i	0.942083	+	0.335379i	$0.108864\pi$
$127$	16.6640	+	13.2891i	1.47869	+	1.17921i	0.536604	+	0.843834i	$0.319707\pi$
$128$		−	10.1372i		−	0.896013i
$129$	7.46208	−	9.35715i	0.657000	−	0.823851i
$130$		0			0
$131$	−17.1649	−	3.91778i	−1.49971	−	0.342298i	−0.607644	−	0.794210i	$-0.707885\pi$
$131$	−17.1649	−	3.91778i	−1.49971	−	0.342298i	−0.892063	+	0.451911i	$0.850742\pi$
$132$	8.67702	−	10.8806i	0.755238	−	0.947038i
$133$			0.493552i			0.0427964i
$134$	2.26051	+	1.80269i	0.195278	+	0.155729i
$135$		0			0
$136$	3.48777	+	4.37353i	0.299074	+	0.375027i
$137$	7.74934	−	6.17989i	0.662071	−	0.527984i	−0.233808	−	0.972283i	$-0.575119\pi$
$137$	7.74934	−	6.17989i	0.662071	−	0.527984i	0.895879	+	0.444299i	$0.146547\pi$
$138$	−1.65612	−	0.797543i	−0.140978	−	0.0678914i
$139$	1.02705	−	4.49980i	0.0871133	−	0.381668i	−0.912512	−	0.409051i	$-0.865860\pi$
$139$	1.02705	−	4.49980i	0.0871133	−	0.381668i	0.999625	+	0.0273821i	$0.00871709\pi$
$140$		0			0
$141$	−5.20033	+	2.50435i	−0.437947	+	0.210904i
$142$	4.02006	−	8.34774i	0.337356	−	0.700527i
$143$	−19.9134	+	4.54509i	−1.66524	+	0.380080i
$144$	0.760667			0.0633889
$145$		0			0
$146$	−12.0272			−0.995375
$147$	9.72697	−	2.22012i	0.802267	−	0.183112i
$148$	2.55080	−	5.29679i	0.209674	−	0.435393i
$149$	15.8559	−	7.63578i	1.29896	−	0.625548i	0.348770	−	0.937208i	$-0.386600\pi$
$149$	15.8559	−	7.63578i	1.29896	−	0.625548i	0.950193	+	0.311661i	$0.100885\pi$
$150$		0			0
$151$	0.882594	−	3.86690i	0.0718245	−	0.314684i	−0.926235	−	0.376946i	$-0.876974\pi$
$151$	0.882594	−	3.86690i	0.0718245	−	0.314684i	0.998060	+	0.0622620i	$0.0198314\pi$
$152$	−1.77340	−	0.854025i	−0.143842	−	0.0692706i
$153$	−1.22680	+	0.978342i	−0.0991810	+	0.0790942i
$154$	1.82603	+	2.28977i	0.147146	+	0.184515i
$155$		0			0
$156$	5.62440	+	4.48531i	0.450313	+	0.359112i
$157$		−	9.88964i		−	0.789279i	−0.918836	−	0.394639i	$-0.870870\pi$
$157$		−	9.88964i		−	0.789279i	0.918836	−	0.394639i	$-0.129130\pi$
$158$	3.99410	−	5.00844i	0.317753	−	0.398450i
$159$	13.5342	+	3.08910i	1.07334	+	0.244982i
$160$		0			0
$161$	−0.657958	+	0.825053i	−0.0518544	+	0.0650233i
$162$			4.65749i			0.365927i
$163$	15.1351	+	12.0698i	1.18547	+	0.945382i	0.999310	−	0.0371377i	$-0.0118240\pi$
$163$	15.1351	+	12.0698i	1.18547	+	0.945382i	0.186161	+	0.982519i	$0.440395\pi$
$164$	3.51259	+	7.29397i	0.274287	+	0.569563i
$165$		0			0
$166$	6.26827	−	4.99878i	0.486512	−	0.387980i
$167$	−5.22177	−	2.51467i	−0.404073	−	0.194591i	0.220798	−	0.975320i	$-0.429134\pi$
$167$	−5.22177	−	2.51467i	−0.404073	−	0.194591i	−0.624871	+	0.780728i	$0.714848\pi$
$168$	0.543199	−	2.37991i	0.0419087	−	0.183614i
$169$	0.543329	+	2.38048i	0.0417946	+	0.183114i
$170$		0			0
$171$	0.239559	−	0.497450i	0.0183196	−	0.0380409i
$172$	11.2885	−	2.57653i	0.860742	−	0.196459i
$173$	−3.07510			−0.233796			−0.116898	−	0.993144i	$-0.537295\pi$
$173$	−3.07510			−0.233796			−0.116898	+	0.993144i	$0.537295\pi$
$174$	5.04688	+	3.18298i	0.382603	+	0.241301i
$175$		0			0
$176$	6.55099	−	1.49522i	0.493799	−	0.112707i
$177$	1.85715	−	3.85641i	0.139592	−	0.289865i
$178$	−6.76594	+	3.25831i	−0.507129	+	0.244220i
$179$	−2.06263	−	9.03695i	−0.154168	−	0.675454i	−0.991647	−	0.128984i	$-0.958828\pi$
$179$	−2.06263	−	9.03695i	−0.154168	−	0.675454i	0.837479	−	0.546470i	$-0.184029\pi$
$180$		0			0
$181$	−14.4413	−	6.95458i	−1.07342	−	0.516930i	−0.188210	−	0.982129i	$-0.560269\pi$
$181$	−14.4413	−	6.95458i	−1.07342	−	0.516930i	−0.885206	+	0.465199i	$0.845983\pi$
$182$	−1.18362	+	0.943909i	−0.0877361	+	0.0699672i
$183$	−6.94129	−	8.70410i	−0.513115	−	0.643425i
$184$	−1.82602	−	3.79178i	−0.134616	−	0.279534i
$185$		0			0
$186$		−	3.88341i		−	0.284745i
$187$	−8.64232	+	10.8371i	−0.631989	+	0.792489i
$188$	−5.44412	−	1.24258i	−0.397053	−	0.0906248i
$189$	3.48200	+	0.794743i	0.253278	+	0.0578091i
$190$		0			0
$191$		−	1.76027i		−	0.127369i	−0.997970	−	0.0636844i	$-0.979715\pi$
$191$		−	1.76027i		−	0.127369i	0.997970	−	0.0636844i	$-0.0202851\pi$
$192$	2.54490	+	2.02949i	0.183662	+	0.146466i
$193$	2.57012	+	5.33692i	0.185002	+	0.384160i	0.972757	−	0.231829i	$-0.0744710\pi$
$193$	2.57012	+	5.33692i	0.185002	+	0.384160i	−0.787755	+	0.615989i	$0.788757\pi$
$194$	−0.719576	−	0.902320i	−0.0516626	−	0.0647828i
$195$		0			0
$196$	8.69659	+	4.18806i	0.621185	+	0.299147i
$197$	1.01670	−	4.45443i	0.0724366	−	0.317365i	−0.925709	−	0.378236i	$-0.876531\pi$
$197$	1.01670	−	4.45443i	0.0724366	−	0.317365i	0.998146	+	0.0608710i	$0.0193878\pi$
$198$	−0.729048	−	3.19417i	−0.0518112	−	0.227000i
$199$	−7.72249	+	3.71896i	−0.547433	+	0.263630i	−0.687093	−	0.726570i	$-0.741113\pi$
$199$	−7.72249	+	3.71896i	−0.547433	+	0.263630i	0.139660	+	0.990200i	$0.455399\pi$
$200$		0			0
$201$	5.82178	−	1.32878i	0.410637	−	0.0937252i
$202$	6.21402			0.437217
$203$	2.42627	−	2.41815i	0.170291	−	0.169721i
$204$	4.88194			0.341804
$205$		0			0
$206$	1.66193	−	3.45104i	0.115792	−	0.240445i
$207$	1.06362	−	0.512211i	0.0739265	−	0.0356011i
$208$	0.772907	+	3.38633i	0.0535915	+	0.234800i
$209$	1.08530	−	4.75501i	0.0750718	−	0.328911i
$210$		0			0
$211$	−5.15188	+	4.10848i	−0.354670	+	0.282840i	−0.784575	−	0.620035i	$-0.787119\pi$
$211$	−5.15188	+	4.10848i	−0.354670	+	0.282840i	0.429905	+	0.902874i	$0.358547\pi$
$212$	8.37385	+	10.5005i	0.575118	+	0.721175i
$213$	−8.30279	−	17.2409i	−0.568898	−	1.18133i
$214$	−3.58613	−	2.85984i	−0.245143	−	0.195495i
$215$		0			0
$216$	−8.88075	+	11.1361i	−0.604258	+	0.757716i
$217$	−2.17357	−	0.496103i	−0.147551	−	0.0336777i
$218$	−5.89199	−	1.34481i	−0.399056	−	0.0910819i
$219$	−15.4876	+	19.4208i	−1.04655	+	1.31234i
$220$		0			0
$221$	−5.60191	−	4.46737i	−0.376825	−	0.300508i
$222$	1.93115	+	4.01008i	0.129611	+	0.269139i
$223$	5.68711	+	7.13141i	0.380837	+	0.477555i	0.934896	−	0.354923i	$-0.115493\pi$
$223$	5.68711	+	7.13141i	0.380837	+	0.477555i	−0.554058	+	0.832478i	$0.686922\pi$
$224$	2.91266	−	2.32277i	0.194610	−	0.155197i
$225$		0			0
$226$	0.00992819	−	0.0434982i	0.000660413	−	0.00289346i
$227$	4.60216	+	20.1634i	0.305456	+	1.33829i	0.861762	+	0.507314i	$0.169361\pi$
$227$	4.60216	+	20.1634i	0.305456	+	1.33829i	−0.556305	+	0.830978i	$0.687781\pi$
$228$	−1.54768	+	0.745322i	−0.102497	+	0.0493601i
$229$	11.7365	−	24.3711i	0.775569	−	1.61049i	−0.0163556	−	0.999866i	$-0.505206\pi$
$229$	11.7365	−	24.3711i	0.775569	−	1.61049i	0.791924	−	0.610619i	$-0.209079\pi$
$230$		0			0
$231$	6.04881			0.397983
$232$	4.49041	+	12.9022i	0.294810	+	0.847072i
$233$	11.0033			0.720848			0.360424	−	0.932789i	$-0.382632\pi$
$233$	11.0033			0.720848			0.360424	+	0.932789i	$0.382632\pi$
$234$	1.65112	−	0.376858i	0.107937	−	0.0246360i
$235$		0			0
$236$	3.73093	−	1.79672i	0.242863	−	0.116957i
$237$	−2.94409	−	12.8989i	−0.191239	−	0.837874i
$238$	−0.228613	+	1.00162i	−0.0148188	+	0.0649252i
$239$	−4.11405	−	1.98122i	−0.266116	−	0.128155i	0.296068	−	0.955167i	$-0.404324\pi$
$239$	−4.11405	−	1.98122i	−0.266116	−	0.128155i	−0.562184	+	0.827012i	$0.690039\pi$
$240$		0			0
$241$	7.85224	+	9.84639i	0.505807	+	0.634262i	0.967528	−	0.252763i	$-0.0813394\pi$
$241$	7.85224	+	9.84639i	0.505807	+	0.634262i	−0.461721	+	0.887025i	$0.652768\pi$
$242$	−9.06160	−	18.8166i	−0.582502	−	1.20958i
$243$	−5.64860	−	4.50461i	−0.362358	−	0.288971i
$244$		−	10.7707i		−	0.689525i
$245$		0			0
$246$	−5.97540	−	1.36385i	−0.380978	−	0.0869557i
$247$	2.45795	+	0.561012i	0.156396	+	0.0356963i
$248$	5.54363	−	6.95150i	0.352021	−	0.441420i
$249$		−	16.5587i		−	1.04936i
$250$		0			0
$251$	−4.11702	−	8.54909i	−0.259864	−	0.539614i	0.729689	−	0.683779i	$-0.239665\pi$
$251$	−4.11702	−	8.54909i	−0.259864	−	0.539614i	−0.989554	+	0.144165i	$0.953950\pi$
$252$	0.413042	+	0.517938i	0.0260192	+	0.0326270i
$253$	8.15320	−	6.50196i	0.512587	−	0.408775i
$254$	−14.0653	−	6.77350i	−0.882537	−	0.425007i
$255$		0			0
$256$	2.60983	+	11.4344i	0.163114	+	0.714650i
$257$	17.8764	−	8.60883i	1.11510	−	0.537004i	0.216725	−	0.976233i	$-0.430462\pi$
$257$	17.8764	−	8.60883i	1.11510	−	0.537004i	0.898375	+	0.439228i	$0.144748\pi$
$258$	−3.80346	+	7.89796i	−0.236793	+	0.491706i
$259$	2.49118	−	0.568594i	0.154794	−	0.0353307i
$260$		0			0
$261$	−3.61915	+	1.25959i	−0.224020	+	0.0779665i
$262$	12.8957			0.796698
$263$	−19.1524	+	4.37142i	−1.18099	+	0.269553i	−0.767557	−	0.640981i	$-0.778528\pi$
$263$	−19.1524	+	4.37142i	−1.18099	+	0.269553i	−0.413433	+	0.910534i	$0.635671\pi$
$264$	−10.4666	+	21.7342i	−0.644178	+	1.33765i
$265$		0			0
$266$	−0.0804412	−	0.352436i	−0.00493217	−	0.0216092i
$267$	−3.45128	+	15.1211i	−0.211215	+	0.925394i
$268$	5.20508	+	2.50663i	0.317951	+	0.153117i
$269$	−15.5661	+	12.4136i	−0.949084	+	0.756869i	−0.970049	−	0.242911i	$-0.921898\pi$
$269$	−15.5661	+	12.4136i	−0.949084	+	0.756869i	0.0209647	+	0.999780i	$0.493326\pi$
$270$		0			0
$271$	−12.2458	−	25.4287i	−0.743882	−	1.54469i	−0.835871	−	0.548926i	$-0.815037\pi$
$271$	−12.2458	−	25.4287i	−0.743882	−	1.54469i	0.0919894	−	0.995760i	$-0.470677\pi$
$272$	1.84289	+	1.46965i	0.111741	+	0.0891108i
$273$			3.12674i			0.189239i
$274$	−4.52643	+	5.67596i	−0.273452	+	0.342897i
$275$		0			0
$276$	−3.58079	−	0.817292i	−0.215538	−	0.0491952i
$277$	5.44689	−	6.83019i	0.327272	−	0.410386i	−0.590788	−	0.806827i	$-0.701183\pi$
$277$	5.44689	−	6.83019i	0.327272	−	0.410386i	0.918061	+	0.396440i	$0.129755\pi$
$278$			3.38062i			0.202756i
$279$	1.94994	+	1.55502i	0.116740	+	0.0930968i
$280$		0			0
$281$	10.3302	+	12.9536i	0.616245	+	0.772747i	0.987811	−	0.155660i	$-0.0497503\pi$
$281$	10.3302	+	12.9536i	0.616245	+	0.772747i	−0.371566	+	0.928407i	$0.621179\pi$
$282$	3.30529	−	2.63588i	0.196827	−	0.156964i
$283$	23.3919	+	11.2650i	1.39050	+	0.669632i	0.971211	−	0.238219i	$-0.0765636\pi$
$283$	23.3919	+	11.2650i	1.39050	+	0.669632i	0.419293	+	0.907851i	$0.362278\pi$
$284$	4.11960	−	18.0492i	0.244454	−	1.07102i
$285$		0			0
$286$	13.4790	−	6.49113i	0.797028	−	0.383828i
$287$	−1.52671	+	3.17024i	−0.0901188	+	0.187134i
$288$	−4.06308	+	0.927372i	−0.239419	+	0.0546459i
$289$	12.1376			0.713976
$290$		0			0
$291$	−2.38363			−0.139731
$292$	−23.4294	+	5.34761i	−1.37110	+	0.312945i
$293$	13.7872	−	28.6295i	0.805458	−	1.67255i	0.0674860	−	0.997720i	$-0.478502\pi$
$293$	13.7872	−	28.6295i	0.805458	−	1.67255i	0.737972	−	0.674831i	$-0.235784\pi$
$294$	−6.58400	+	3.17069i	−0.383987	+	0.184918i
$295$		0			0
$296$	−2.26760	+	9.93501i	−0.131802	+	0.577461i
$297$	−31.7989	−	15.3135i	−1.84516	−	0.888581i
$298$	−10.0779	+	8.03682i	−0.583794	+	0.465561i
$299$	3.36098	+	4.21454i	0.194371	+	0.243733i
$300$		0			0
$301$	3.93465	+	3.13778i	0.226790	+	0.180859i
$302$			2.90513i			0.167171i
$303$	8.00190	−	10.0341i	0.459697	−	0.576442i
$304$	−0.808604	−	0.184559i	−0.0463766	−	0.0105852i
$305$		0			0
$306$	0.716581	−	0.898564i	0.0409642	−	0.0513675i
$307$			19.6892i			1.12372i	0.827231	+	0.561861i	$0.189915\pi$
$307$			19.6892i			1.12372i	−0.827231	+	0.561861i	$0.810085\pi$
$308$	4.57527	+	3.64866i	0.260700	+	0.207902i
$309$	−3.43246	−	7.12757i	−0.195266	−	0.405473i
$310$		0			0
$311$	24.0528	−	19.1814i	1.36391	−	1.08768i	0.377030	−	0.926201i	$-0.376945\pi$
$311$	24.0528	−	19.1814i	1.36391	−	1.08768i	0.986876	−	0.161478i	$-0.0516262\pi$
$312$	−11.2348	−	5.41040i	−0.636046	−	0.306304i
$313$	−7.80369	+	34.1902i	−0.441091	+	1.93254i	−0.0909201	+	0.995858i	$0.528981\pi$
$313$	−7.80369	+	34.1902i	−0.441091	+	1.93254i	−0.350170	+	0.936686i	$0.613876\pi$
$314$	1.61185	+	7.06200i	0.0909622	+	0.398532i
$315$		0			0
$316$	5.55377	−	11.5325i	0.312424	−	0.648755i
$317$	−26.4632	+	6.04005i	−1.48632	+	0.339243i	−0.887188	−	0.461408i	$-0.847345\pi$
$317$	−26.4632	+	6.04005i	−1.48632	+	0.339243i	−0.599132	+	0.800651i	$0.704487\pi$
$318$	−10.1680			−0.570194
$319$	−28.6928	+	17.9618i	−1.60649	+	1.00567i
$320$		0			0
$321$	−9.23584	+	2.10802i	−0.515494	+	0.117658i
$322$	0.335364	−	0.696391i	0.0186891	−	0.0388084i
$323$	1.54149	−	0.742341i	0.0857706	−	0.0413050i
$324$	2.07085	+	9.07298i	0.115047	+	0.504054i
$325$		0			0
$326$	−12.7749	−	6.15205i	−0.707534	−	0.340730i
$327$	−9.75874	+	7.78233i	−0.539659	+	0.430364i
$328$	−8.74936	−	10.9714i	−0.483103	−	0.605792i
$329$	−1.05307	−	2.18672i	−0.0580576	−	0.120558i
$330$		0			0
$331$			21.5007i			1.18179i	0.806750	+	0.590893i	$0.201224\pi$
$331$			21.5007i			1.18179i	−0.806750	+	0.590893i	$0.798776\pi$
$332$	9.98824	−	12.5249i	0.548176	−	0.687391i
$333$	−2.78683	−	0.636076i	−0.152717	−	0.0348568i
$334$	4.13862	+	0.944613i	0.226455	+	0.0516869i
$335$		0			0
$336$		−	1.02862i		−	0.0561158i
$337$	2.29004	+	1.82625i	0.124747	+	0.0994821i	0.683876	−	0.729598i	$-0.260293\pi$
$337$	2.29004	+	1.82625i	0.124747	+	0.0994821i	−0.559129	+	0.829081i	$0.688864\pi$
$338$	−0.775962	−	1.61130i	−0.0422068	−	0.0876433i
$339$	−0.0574539	−	0.0720450i	−0.00312047	−	0.00391295i
$340$		0			0
$341$	19.8498	+	9.55918i	1.07493	+	0.517658i
$342$	−0.0899881	+	0.394264i	−0.00486600	+	0.0213193i
$343$	1.92438	+	8.43126i	0.103907	+	0.455245i
$344$	−18.0829	+	8.70825i	−0.974963	+	0.469518i
$345$		0			0
$346$	2.19587	−	0.501193i	0.118051	−	0.0269443i
$347$	−23.7673			−1.27590			−0.637949	−	0.770079i	$-0.720217\pi$
$347$	−23.7673			−1.27590			−0.637949	+	0.770079i	$0.720217\pi$
$348$	11.2468	+	3.95660i	0.602890	+	0.212096i
$349$	−1.84579			−0.0988030			−0.0494015	−	0.998779i	$-0.515731\pi$
$349$	−1.84579			−0.0988030			−0.0494015	+	0.998779i	$0.515731\pi$
$350$		0			0
$351$	7.91585	−	16.4374i	0.422517	−	0.877365i
$352$	−33.1690	+	15.9734i	−1.76791	+	0.851383i
$353$	2.72843	+	11.9540i	0.145220	+	0.636249i	0.994174	+	0.107783i	$0.0343752\pi$
$353$	2.72843	+	11.9540i	0.145220	+	0.636249i	−0.848955	+	0.528465i	$0.822768\pi$
$354$	−0.697620	+	3.05647i	−0.0370781	+	0.162450i
$355$		0			0
$356$	−11.7316	+	9.35564i	−0.621773	+	0.495848i
$357$	1.32297	+	1.65895i	0.0700190	+	0.0878011i
$358$	2.94576	+	6.11694i	0.155688	+	0.323290i
$359$	3.91654	+	3.12334i	0.206707	+	0.164844i	0.721372	−	0.692548i	$-0.243512\pi$
$359$	3.91654	+	3.12334i	0.206707	+	0.164844i	−0.514664	+	0.857392i	$0.672083\pi$
$360$		0			0
$361$	11.4710	−	14.3841i	0.603734	−	0.757059i
$362$	11.4458	+	2.61242i	0.601576	+	0.137306i
$363$	−42.0528	−	9.59829i	−2.20720	−	0.503779i
$364$	−1.88606	+	2.36504i	−0.0988564	+	0.123962i
$365$		0			0
$366$	6.37527	+	5.08411i	0.333241	+	0.265751i
$367$	−13.3120	−	27.6428i	−0.694883	−	1.44294i	−0.887095	−	0.461587i	$-0.847280\pi$
$367$	−13.3120	−	27.6428i	−0.694883	−	1.44294i	0.192212	−	0.981353i	$-0.438434\pi$
$368$	−1.10568	−	1.38648i	−0.0576375	−	0.0722751i
$369$	3.07753	−	2.45425i	0.160210	−	0.127763i
$370$		0			0
$371$	−1.29896	+	5.69111i	−0.0674386	+	0.295468i
$372$	−1.72667	−	7.56503i	−0.0895236	−	0.392229i
$373$	19.2781	−	9.28385i	0.998183	−	0.480700i	0.137862	−	0.990452i	$-0.455977\pi$
$373$	19.2781	−	9.28385i	0.998183	−	0.480700i	0.860321	+	0.509752i	$0.170263\pi$
$374$	4.40503	−	9.14714i	0.227779	−	0.472987i
$375$		0			0
$376$	9.67939			0.499177
$377$	−9.28480	−	14.8318i	−0.478192	−	0.763878i
$378$	−2.61596			−0.134550
$379$	19.1463	−	4.37002i	0.983480	−	0.224473i	0.299598	−	0.954066i	$-0.403147\pi$
$379$	19.1463	−	4.37002i	0.983480	−	0.224473i	0.683882	+	0.729593i	$0.260290\pi$
$380$		0			0
$381$	−29.0496	+	13.9896i	−1.48826	+	0.716707i
$382$	0.286897	+	1.25698i	0.0146789	+	0.0643125i
$383$	−2.08747	+	9.14581i	−0.106665	+	0.467329i	0.893180	+	0.449700i	$0.148469\pi$
$383$	−2.08747	+	9.14581i	−0.106665	+	0.467329i	−0.999845	+	0.0176294i	$0.994388\pi$
$384$	13.8164	+	6.65363i	0.705065	+	0.339542i
$385$		0			0
$386$	−2.70511	−	3.39210i	−0.137686	−	0.172653i
$387$	−2.44272	−	5.07236i	−0.124170	−	0.257842i
$388$	−1.80296	−	1.43781i	−0.0915314	−	0.0729938i
$389$			19.9019i			1.00906i	0.863393	+	0.504532i	$0.168335\pi$
$389$			19.9019i			1.00906i	−0.863393	+	0.504532i	$0.831665\pi$
$390$		0			0
$391$	3.56647	+	0.814023i	0.180364	+	0.0411669i
$392$	−16.3119	−	3.72309i	−0.823876	−	0.188044i
$393$	16.6060	−	20.8233i	0.837662	−	1.05039i
$394$			3.34653i			0.168596i
$395$		0			0
$396$	−2.84043	−	5.89821i	−0.142737	−	0.296396i
$397$	5.99440	+	7.51674i	0.300850	+	0.377254i	0.909161	−	0.416445i	$-0.136724\pi$
$397$	5.99440	+	7.51674i	0.300850	+	0.377254i	−0.608311	+	0.793699i	$0.708153\pi$
$398$	4.90835	−	3.91428i	0.246033	−	0.196205i
$399$	−0.672681	−	0.323946i	−0.0336762	−	0.0162176i
$400$		0			0
$401$	6.17180	+	27.0404i	0.308205	+	1.35033i	0.857404	+	0.514643i	$0.172076\pi$
$401$	6.17180	+	27.0404i	0.308205	+	1.35033i	−0.549199	+	0.835691i	$0.685067\pi$
$402$	−3.94065	+	1.89772i	−0.196542	+	0.0946496i
$403$	−4.94131	+	10.2607i	−0.246144	+	0.511124i
$404$	12.1052	−	2.76292i	0.602254	−	0.137461i
$405$		0			0
$406$	−1.33844	+	2.12220i	−0.0664254	+	0.105323i
$407$	−25.2510			−1.25164
$408$	−8.25007	+	1.88302i	−0.408439	+	0.0932236i
$409$	−2.51532	+	5.22311i	−0.124374	+	0.258266i	−0.953854	−	0.300271i	$-0.902923\pi$
$409$	−2.51532	+	5.22311i	−0.124374	+	0.258266i	0.829480	+	0.558537i	$0.188637\pi$
$410$		0			0
$411$	3.33648	+	14.6181i	0.164576	+	0.721056i
$412$	1.70309	−	7.46171i	0.0839050	−	0.367612i
$413$	1.62161	+	0.780925i	0.0797941	+	0.0384268i
$414$	−0.676026	+	0.539113i	−0.0332249	+	0.0264959i
$415$		0			0
$416$	−8.25692	−	17.1457i	−0.404829	−	0.840636i
$417$	5.45884	+	4.35328i	0.267321	+	0.213181i
$418$			3.57235i			0.174729i
$419$	−11.1079	+	13.9288i	−0.542655	+	0.680468i	−0.975246	−	0.221122i	$-0.929028\pi$
$419$	−11.1079	+	13.9288i	−0.542655	+	0.680468i	0.432591	+	0.901590i	$0.357599\pi$
$420$		0			0
$421$	−18.4825	−	4.21851i	−0.900782	−	0.205598i	−0.253038	−	0.967456i	$-0.581430\pi$
$421$	−18.4825	−	4.21851i	−0.900782	−	0.205598i	−0.647743	+	0.761859i	$0.724287\pi$
$422$	3.00924	−	3.77346i	0.146487	−	0.183689i
$423$			2.71513i			0.132014i
$424$	−18.2013	−	14.5150i	−0.883932	−	0.704912i
$425$		0			0
$426$	8.73886	+	10.9582i	0.423399	+	0.530926i
$427$	3.66005	−	2.91879i	0.177122	−	0.141250i
$428$	−8.25748	−	3.97659i	−0.399140	−	0.192216i
$429$	6.87557	−	30.1239i	0.331956	−	1.45439i
$430$		0			0
$431$	8.23996	−	3.96815i	0.396905	−	0.191139i	−0.224775	−	0.974411i	$-0.572165\pi$
$431$	8.23996	−	3.96815i	0.396905	−	0.191139i	0.621680	+	0.783271i	$0.286450\pi$
$432$	−2.60411	+	5.40750i	−0.125290	+	0.260168i
$433$	−21.0805	+	4.81149i	−1.01306	+	0.231225i	−0.696662	−	0.717400i	$-0.745332\pi$
$433$	−21.0805	+	4.81149i	−1.01306	+	0.231225i	−0.316403	+	0.948625i	$0.602475\pi$
$434$	1.63296			0.0783846
$435$		0			0
$436$	−12.0758			−0.578324
$437$	−1.25492	+	0.286428i	−0.0600310	+	0.0137017i
$438$	7.89410	−	16.3923i	0.377195	−	0.783253i
$439$	−26.2089	+	12.6216i	−1.25088	+	0.602394i	−0.937749	−	0.347315i	$-0.887094\pi$
$439$	−26.2089	+	12.6216i	−1.25088	+	0.602394i	−0.313135	+	0.949709i	$0.601379\pi$
$440$		0			0
$441$	1.04435	−	4.57559i	0.0497309	−	0.217885i
$442$	4.72833	+	2.27704i	0.224904	+	0.108308i
$443$	−20.2859	+	16.1774i	−0.963810	+	0.768613i	−0.972872	−	0.231346i	$-0.925687\pi$
$443$	−20.2859	+	16.1774i	−0.963810	+	0.768613i	0.00906148	+	0.999959i	$0.497116\pi$
$444$	5.54496	+	6.95316i	0.263152	+	0.329982i
$445$		0			0
$446$	−5.22337	−	4.16550i	−0.247334	−	0.197242i
$447$			26.6223i			1.25919i
$448$	−0.853394	+	1.07012i	−0.0403191	+	0.0505585i
$449$	−11.1032	−	2.53422i	−0.523990	−	0.119597i	−0.0476597	−	0.998864i	$-0.515176\pi$
$449$	−11.1032	−	2.53422i	−0.523990	−	0.119597i	−0.476331	+	0.879266i	$0.658033\pi$
$450$		0			0
$451$	21.6799	−	27.1858i	1.02087	−	1.28013i
$452$		−	0.0891507i		−	0.00419329i
$453$	4.69104	+	3.74098i	0.220404	+	0.175767i
$454$	−6.57263	−	13.6482i	−0.308469	−	0.640542i
$455$		0			0
$456$	2.32797	−	1.85649i	0.109017	−	0.0869381i
$457$	34.2758	+	16.5064i	1.60335	+	0.772135i	0.999685	−	0.0250993i	$-0.00799020\pi$
$457$	34.2758	+	16.5064i	1.60335	+	0.772135i	0.603670	+	0.797234i	$0.293704\pi$
$458$	−4.40870	+	19.3158i	−0.206005	+	0.902567i
$459$	−2.75501	−	12.0705i	−0.128593	−	0.563403i
$460$		0			0
$461$	9.61072	−	19.9569i	0.447616	−	0.929484i	−0.548047	−	0.836448i	$-0.684628\pi$
$461$	9.61072	−	19.9569i	0.447616	−	0.929484i	0.995663	−	0.0930362i	$-0.0296572\pi$
$462$	−4.31934	+	0.985861i	−0.200954	+	0.0458664i
$463$	28.4655			1.32290			0.661451	−	0.749988i	$-0.269941\pi$
$463$	28.4655			1.32290			0.661451	+	0.749988i	$0.269941\pi$
$464$	3.05446	+	4.87930i	0.141800	+	0.226516i
$465$		0			0
$466$	−7.85722	+	1.79336i	−0.363979	+	0.0830757i
$467$	0.345383	−	0.717196i	0.0159824	−	0.0331879i	−0.892825	−	0.450404i	$-0.851280\pi$
$467$	0.345383	−	0.717196i	0.0159824	−	0.0331879i	0.908807	+	0.417216i	$0.136994\pi$
$468$	3.04889	−	1.46827i	0.140935	−	0.0678708i
$469$	0.558750	+	2.44804i	0.0258007	+	0.113040i
$470$		0			0
$471$	13.4790	+	6.49112i	0.621077	+	0.299095i
$472$	−5.61194	+	4.47538i	−0.258311	+	0.205996i
$473$	−31.0077	−	38.8824i	−1.42573	−	1.78781i
$474$	4.20464	+	8.73102i	0.193125	+	0.401029i
$475$		0			0
$476$			2.05284i			0.0940917i
$477$	4.07155	−	5.10557i	0.186424	−	0.233768i
$478$	3.26067	+	0.744227i	0.149140	+	0.0340402i
$479$	27.0214	+	6.16747i	1.23464	+	0.281799i	0.789550	−	0.613686i	$-0.210314\pi$
$479$	27.0214	+	6.16747i	1.23464	+	0.281799i	0.445091	+	0.895485i	$0.353171\pi$
$480$		0			0
$481$		−	13.0527i		−	0.595151i
$482$	−7.21194	−	5.75133i	−0.328495	−	0.261966i
$483$	−0.692641	−	1.43828i	−0.0315163	−	0.0654442i
$484$	−26.0187	−	32.6265i	−1.18267	−	1.48302i
$485$		0			0
$486$	4.76773	+	2.29602i	0.216269	+	0.104150i
$487$	−1.02879	+	4.50745i	−0.0466192	+	0.204252i	−0.992874	−	0.119171i	$-0.961976\pi$
$487$	−1.02879	+	4.50745i	−0.0466192	+	0.204252i	0.946255	+	0.323423i	$0.104834\pi$
$488$	4.15440	+	18.2016i	0.188061	+	0.823949i
$489$	−26.3844	+	12.7061i	−1.19314	+	0.574588i
$490$		0			0
$491$	30.3604	−	6.92956i	1.37015	−	0.312727i	0.526750	−	0.850020i	$-0.323410\pi$
$491$	30.3604	−	6.92956i	1.37015	−	0.312727i	0.843395	+	0.537293i	$0.180553\pi$
$492$	−12.2467			−0.552125
$493$	−11.2018	−	3.94077i	−0.504504	−	0.177484i
$494$	−1.84661			−0.0830831
$495$		0			0
$496$	1.62557	−	3.37552i	0.0729901	−	0.151566i
$497$	7.24975	−	3.49130i	0.325196	−	0.156606i
$498$	2.69880	+	11.8242i	0.120936	+	0.529857i
$499$	−1.08889	+	4.77073i	−0.0487454	+	0.213567i	−0.993435	−	0.114398i	$-0.963506\pi$
$499$	−1.08889	+	4.77073i	−0.0487454	+	0.213567i	0.944690	+	0.327966i	$0.106363\pi$
$500$		0			0
$501$	6.85469	−	5.46643i	0.306245	−	0.244222i
$502$	4.33325	+	5.43373i	0.193403	+	0.242519i
$503$	−15.5451	−	32.2798i	−0.693122	−	1.43928i	−0.888650	−	0.458585i	$-0.848356\pi$
$503$	−15.5451	−	32.2798i	−0.693122	−	1.43928i	0.195528	−	0.980698i	$-0.437358\pi$
$504$	−0.897781	−	0.715957i	−0.0399904	−	0.0318912i
$505$		0			0
$506$	−4.76233	+	5.97177i	−0.211711	+	0.265477i
$507$	−3.60107	−	0.821920i	−0.159929	−	0.0365027i
$508$	−30.4115	−	6.94122i	−1.34929	−	0.307967i
$509$	−16.4331	+	20.6065i	−0.728386	+	0.913367i	−0.998780	−	0.0493830i	$-0.984274\pi$
$509$	−16.4331	+	20.6065i	−0.728386	+	0.913367i	0.270394	+	0.962750i	$0.412846\pi$
$510$		0			0
$511$	−8.16640	−	6.51248i	−0.361260	−	0.288095i
$512$	5.06950	+	10.5269i	0.224042	+	0.465229i
$513$	2.71619	+	3.40600i	0.119923	+	0.150378i
$514$	−11.3621	+	9.06098i	−0.501161	+	0.399663i
$515$		0			0
$516$	−3.89764	+	17.0767i	−0.171584	+	0.751759i
$517$	5.33705	+	23.3831i	0.234723	+	1.02839i
$518$	−1.68623	+	0.812045i	−0.0740886	+	0.0356792i
$519$	2.01836	−	4.19117i	0.0885963	−	0.183972i
$520$		0			0
$521$	−13.8781			−0.608009			−0.304004	−	0.952671i	$-0.598324\pi$
$521$	−13.8781			−0.608009			−0.304004	+	0.952671i	$0.598324\pi$
$522$	2.37907	−	1.48931i	0.104129	−	0.0651854i
$523$	39.9348			1.74623			0.873114	−	0.487516i	$-0.162097\pi$
$523$	39.9348			1.74623			0.873114	+	0.487516i	$0.162097\pi$
$524$	25.1213	−	5.73377i	1.09743	−	0.250481i
$525$		0			0
$526$	12.9639	−	6.24309i	0.565254	−	0.272212i
$527$	1.71976	+	7.53478i	0.0749141	+	0.328220i
$528$	−2.26189	+	9.90999i	−0.0984361	+	0.431277i
$529$	18.2426	+	8.78519i	0.793158	+	0.381965i
$530$		0			0
$531$	−1.25537	−	1.57418i	−0.0544784	−	0.0683138i
$532$	−0.313405	−	0.650793i	−0.0135879	−	0.0282155i
$533$	14.0528	+	11.2068i	0.608696	+	0.485419i
$534$		−	11.3602i		−	0.491602i
$535$		0			0
$536$	−9.76300	−	2.22834i	−0.421697	−	0.0962496i
$537$	13.6706	+	3.12023i	0.589931	+	0.134648i
$538$	9.09226	−	11.4013i	0.391995	−	0.491546i
$539$		−	41.4586i		−	1.78575i
$540$		0			0
$541$	13.8461	+	28.7517i	0.595291	+	1.23613i	0.953189	+	0.302374i	$0.0977791\pi$
$541$	13.8461	+	28.7517i	0.595291	+	1.23613i	−0.357899	+	0.933760i	$0.616507\pi$
$542$	12.8890	+	16.1623i	0.553630	+	0.694230i
$543$	18.9573	−	15.1180i	0.813537	−	0.648774i
$544$	−11.6355	−	5.60334i	−0.498866	−	0.240241i
$545$		0			0
$546$	−0.509610	−	2.23275i	−0.0218093	−	0.0955527i
$547$	30.7402	−	14.8037i	1.31436	−	0.632961i	0.360371	−	0.932809i	$-0.382650\pi$
$547$	30.7402	−	14.8037i	1.31436	−	0.632961i	0.953987	+	0.299848i	$0.0969359\pi$
$548$	−6.29398	+	13.0696i	−0.268865	+	0.558305i
$549$	−5.10567	+	1.16533i	−0.217904	+	0.0497353i
$550$		0			0
$551$	4.15284	−	0.460862i	0.176917	−	0.0196334i
$552$	6.36648			0.270975
$553$	5.42395	−	1.23798i	0.230650	−	0.0526443i
$554$	−2.77631	+	5.76506i	−0.117954	+	0.244934i
$555$		0			0
$556$	1.50311	+	6.58558i	0.0637463	+	0.279291i
$557$	2.62021	−	11.4799i	0.111022	−	0.486419i	−0.888594	−	0.458695i	$-0.848317\pi$
$557$	2.62021	−	11.4799i	0.111022	−	0.486419i	0.999616	−	0.0277240i	$-0.00882594\pi$
$558$	−1.64586	−	0.792603i	−0.0696747	−	0.0335535i
$559$	20.0990	−	16.0284i	0.850098	−	0.677930i
$560$		0			0
$561$	−9.09788	−	18.8919i	−0.384113	−	0.797619i
$562$	−9.48779	−	7.56626i	−0.400218	−	0.319164i
$563$			7.87596i			0.331932i	0.986131	+	0.165966i	$0.0530743\pi$
$563$			7.87596i			0.331932i	−0.986131	+	0.165966i	$0.946926\pi$
$564$	5.26685	−	6.60442i	0.221774	−	0.278096i
$565$		0			0
$566$	−18.5397	−	4.23157i	−0.779283	−	0.177866i
$567$	−2.52194	+	3.16242i	−0.105912	+	0.132809i
$568$			32.0906i			1.34649i
$569$	7.71035	+	6.14880i	0.323235	+	0.257771i	0.771640	−	0.636059i	$-0.219437\pi$
$569$	7.71035	+	6.14880i	0.323235	+	0.257771i	−0.448406	+	0.893830i	$0.648008\pi$
$570$		0			0
$571$	17.3108	+	21.7071i	0.724435	+	0.908413i	0.998580	−	0.0532758i	$-0.0169662\pi$
$571$	17.3108	+	21.7071i	0.724435	+	0.908413i	−0.274145	+	0.961688i	$0.588395\pi$
$572$	23.3714	−	18.6381i	0.977209	−	0.779298i
$573$	2.39914	+	1.15536i	0.100226	+	0.0482661i
$574$	0.573493	−	2.51264i	0.0239372	−	0.104876i
$575$		0			0
$576$	1.37955	−	0.664355i	0.0574811	−	0.0276814i
$577$	16.7201	−	34.7196i	0.696066	−	1.44540i	−0.189976	−	0.981789i	$-0.560841\pi$
$577$	16.7201	−	34.7196i	0.696066	−	1.44540i	0.886041	−	0.463606i	$-0.153445\pi$
$578$	−8.66722	+	1.97824i	−0.360509	+	0.0822838i
$579$	−8.96080			−0.372398
$580$		0			0
$581$	6.96287			0.288869
$582$	1.70210	−	0.388494i	0.0705545	−	0.0161036i
$583$	25.0290	−	51.9733i	1.03660	−	2.15251i
$584$	37.5311	−	18.0740i	1.55305	−	0.747909i
$585$		0			0
$586$	−5.17904	+	22.6908i	−0.213944	+	0.937350i
$587$	−9.26946	−	4.46394i	−0.382592	−	0.184246i	0.232695	−	0.972550i	$-0.425246\pi$
$587$	−9.26946	−	4.46394i	−0.382592	−	0.184246i	−0.615287	+	0.788303i	$0.710960\pi$
$588$	−11.4161	+	9.10405i	−0.470793	+	0.375445i
$589$	−1.69553	−	2.12613i	−0.0698631	−	0.0876056i
$590$		0			0
$591$	5.40380	+	4.30939i	0.222283	+	0.177264i
$592$			4.29400i			0.176482i
$593$	15.5899	−	19.5491i	0.640200	−	0.802786i	−0.350828	−	0.936440i	$-0.614100\pi$
$593$	15.5899	−	19.5491i	0.640200	−	0.802786i	0.991028	+	0.133654i	$0.0426712\pi$
$594$	25.2028	+	5.75238i	1.03408	+	0.236023i
$595$		0			0
$596$	−16.0587	+	20.1369i	−0.657789	+	0.824841i
$597$		−	12.9662i		−	0.530672i
$598$	−3.08692	−	2.46173i	−0.126233	−	0.100668i
$599$	17.1224	+	35.5551i	0.699603	+	1.45274i	0.882841	+	0.469672i	$0.155628\pi$
$599$	17.1224	+	35.5551i	0.699603	+	1.45274i	−0.183238	+	0.983069i	$0.558658\pi$
$600$		0			0
$601$	16.3872	−	13.0684i	0.668448	−	0.533070i	−0.229423	−	0.973327i	$-0.573684\pi$
$601$	16.3872	−	13.0684i	0.668448	−	0.533070i	0.897872	+	0.440257i	$0.145113\pi$
$602$	−3.32107	−	1.59934i	−0.135357	−	0.0651844i
$603$	0.625063	−	2.73858i	0.0254545	−	0.111524i
$604$	1.29170	+	5.65930i	0.0525585	+	0.230274i
$605$		0			0
$606$	−4.07861	+	8.46932i	−0.165682	+	0.344042i
$607$	25.3316	−	5.78176i	1.02818	−	0.234675i	0.325018	−	0.945708i	$-0.394630\pi$
$607$	25.3316	−	5.78176i	1.02818	−	0.234675i	0.703158	+	0.711033i	$0.251773\pi$
$608$	4.54414			0.184289
$609$	1.70329	+	4.89403i	0.0690207	+	0.198316i
$610$		0			0
$611$	−12.0872	+	2.75882i	−0.488994	+	0.111610i
$612$	0.996402	−	2.06905i	0.0402772	−	0.0836364i
$613$	−30.0408	+	14.4669i	−1.21334	+	0.584313i	−0.927449	−	0.373950i	$-0.878003\pi$
$613$	−30.0408	+	14.4669i	−1.21334	+	0.584313i	−0.285889	+	0.958263i	$0.592289\pi$
$614$	−3.20903	−	14.0597i	−0.129506	−	0.567403i
$615$		0			0
$616$	−9.13917	−	4.40119i	−0.368228	−	0.177329i
$617$	28.3577	−	22.6145i	1.14164	−	0.910427i	0.144768	−	0.989466i	$-0.453756\pi$
$617$	28.3577	−	22.6145i	1.14164	−	0.910427i	0.996872	+	0.0790386i	$0.0251850\pi$
$618$	3.61273	+	4.53022i	0.145325	+	0.182232i
$619$	−1.39538	−	2.89753i	−0.0560849	−	0.116462i	0.871043	−	0.491207i	$-0.163444\pi$
$619$	−1.39538	−	2.89753i	−0.0560849	−	0.116462i	−0.927128	+	0.374746i	$0.877730\pi$
$620$		0			0
$621$			9.31466i			0.373785i
$622$	−14.0493	+	17.6173i	−0.563327	+	0.706390i
$623$	−6.35836	−	1.45125i	−0.254742	−	0.0581433i
$624$	−5.12265	−	1.16921i	−0.205070	−	0.0468060i
$625$		0			0
$626$		−	25.6864i		−	1.02664i
$627$	5.76844	+	4.60018i	0.230369	+	0.183713i
$628$	6.27992	+	13.0404i	0.250596	+	0.520368i
$629$	−5.52278	−	6.92535i	−0.220208	−	0.276132i
$630$		0			0
$631$	−2.07770	−	1.00057i	−0.0827119	−	0.0398319i	0.392070	−	0.919935i	$-0.371759\pi$
$631$	−2.07770	−	1.00057i	−0.0827119	−	0.0398319i	−0.474782	+	0.880103i	$0.657473\pi$
$632$	−4.93717	+	21.6312i	−0.196390	+	0.860442i
$633$	−2.21814	−	9.71831i	−0.0881632	−	0.386268i
$634$	17.9124	−	8.62616i	0.711393	−	0.342589i
$635$		0			0
$636$	−19.8077	+	4.52098i	−0.785427	+	0.179268i
$637$	21.4307			0.849115
$638$	17.5615	−	17.5027i	0.695265	−	0.692937i
$639$	−9.00160			−0.356098
$640$		0			0
$641$	13.5821	−	28.2035i	0.536460	−	1.11397i	−0.439946	−	0.898024i	$-0.645002\pi$
$641$	13.5821	−	28.2035i	0.536460	−	1.11397i	0.976405	−	0.215945i	$-0.0692833\pi$
$642$	6.25156	−	3.01059i	0.246729	−	0.118819i
$643$	3.97257	+	17.4050i	0.156663	+	0.686384i	0.990857	+	0.134914i	$0.0430758\pi$
$643$	3.97257	+	17.4050i	0.156663	+	0.686384i	−0.834195	+	0.551470i	$0.814067\pi$
$644$	0.343669	−	1.50571i	0.0135424	−	0.0593333i
$645$		0			0
$646$	−0.979756	+	0.781329i	−0.0385480	+	0.0307410i
$647$	−16.2401	−	20.3645i	−0.638466	−	0.800611i	0.352344	−	0.935870i	$-0.385385\pi$
$647$	−16.2401	−	20.3645i	−0.638466	−	0.800611i	−0.990810	+	0.135260i	$0.956813\pi$
$648$	−6.99912	−	14.5338i	−0.274952	−	0.570943i
$649$	−13.9058	−	11.0895i	−0.545849	−	0.435300i
$650$		0			0
$651$	2.10279	−	2.63682i	0.0824149	−	0.103345i
$652$	−27.6213	−	6.30438i	−1.08173	−	0.246899i
$653$	−1.88604	−	0.430476i	−0.0738063	−	0.0168458i	0.185458	−	0.982652i	$-0.440623\pi$
$653$	−1.88604	−	0.430476i	−0.0738063	−	0.0168458i	−0.259265	+	0.965806i	$0.583480\pi$
$654$	5.70013	−	7.14774i	0.222893	−	0.279499i
$655$		0			0
$656$	−4.62303	−	3.68674i	−0.180499	−	0.143943i
$657$	5.06987	+	10.5277i	0.197795	+	0.410725i
$658$	1.10838	+	1.38986i	0.0432091	+	0.0541825i
$659$	−5.71996	+	4.56151i	−0.222818	+	0.177691i	−0.728536	−	0.685007i	$-0.759799\pi$
$659$	−5.71996	+	4.56151i	−0.222818	+	0.177691i	0.505718	+	0.862699i	$0.331228\pi$
$660$		0			0
$661$	−7.93742	+	34.7761i	−0.308730	+	1.35263i	0.547831	+	0.836589i	$0.315454\pi$
$661$	−7.93742	+	34.7761i	−0.308730	+	1.35263i	−0.856561	+	0.516045i	$0.827404\pi$
$662$	−3.50428	−	15.3532i	−0.136198	−	0.596721i
$663$	9.76560	−	4.70286i	0.379264	−	0.182644i
$664$	−12.0483	+	25.0186i	−0.467565	+	0.970909i
$665$		0			0
$666$	2.09369			0.0811289
$667$	7.55653	+	4.76578i	0.292590	+	0.184532i
$668$	8.48220			0.328186
$669$	−13.4524	+	3.07043i	−0.520101	+	0.118710i
$670$		0			0
$671$	−41.6802	+	20.0721i	−1.60904	+	0.774875i
$672$	1.25405	+	5.49434i	0.0483759	+	0.211949i
$673$	−5.10438	+	22.3638i	−0.196759	+	0.862060i	0.776090	+	0.630622i	$0.217200\pi$
$673$	−5.10438	+	22.3638i	−0.196759	+	0.862060i	−0.972850	+	0.231438i	$0.925657\pi$
$674$	−1.93293	−	0.930848i	−0.0744535	−	0.0358549i
$675$		0			0
$676$	−2.22803	−	2.79387i	−0.0856936	−	0.107456i
$677$	6.76940	+	14.0568i	0.260169	+	0.540247i	0.989607	−	0.143801i	$-0.0459324\pi$
$677$	6.76940	+	14.0568i	0.260169	+	0.540247i	−0.729437	+	0.684047i	$0.760218\pi$
$678$	0.0527689	+	0.0420818i	0.00202658	+	0.00161614i
$679$		−	1.00231i		−	0.0384651i
$680$		0			0
$681$	−30.5021	−	6.96191i	−1.16884	−	0.266781i
$682$	−15.7324	−	3.59081i	−0.602424	−	0.137499i
$683$	−13.0728	+	16.3928i	−0.500218	+	0.627254i	−0.966279	−	0.257499i	$-0.917102\pi$
$683$	−13.0728	+	16.3928i	−0.500218	+	0.627254i	0.466060	+	0.884753i	$0.345673\pi$
$684$			0.808053i			0.0308967i
$685$		0			0
$686$	−2.74833	−	5.70696i	−0.104932	−	0.217893i
$687$	25.5129	+	31.9922i	0.973379	+	1.22058i
$688$	−6.61207	+	5.27295i	−0.252083	+	0.201029i
$689$	26.8660	+	12.9380i	1.02351	+	0.492897i
$690$		0			0
$691$	−10.5021	−	46.0126i	−0.399518	−	1.75040i	−0.629304	−	0.777160i	$-0.716660\pi$
$691$	−10.5021	−	46.0126i	−0.399518	−	1.75040i	0.229786	−	0.973241i	$-0.426197\pi$
$692$	4.05480	−	1.95269i	0.154140	−	0.0742301i
$693$	1.23456	−	2.56359i	0.0468971	−	0.0973828i
$694$	16.9718	−	3.87370i	0.644241	−	0.147044i
$695$		0			0
$696$	−20.5322	−	2.34830i	−0.778272	−	0.0890121i
$697$	12.1978			0.462023
$698$	1.31804	−	0.300835i	0.0498887	−	0.0113868i
$699$	−7.22206	+	14.9968i	−0.273163	+	0.567229i
$700$		0			0
$701$	3.49249	+	15.3016i	0.131909	+	0.577933i	0.997074	+	0.0764446i	$0.0243568\pi$
$701$	3.49249	+	15.3016i	0.131909	+	0.577933i	−0.865164	+	0.501488i	$0.832786\pi$
$702$	−2.97351	+	13.0278i	−0.112228	+	0.491703i
$703$	2.80813	+	1.35232i	0.105911	+	0.0510038i
$704$	10.5750	−	8.43326i	0.398559	−	0.317841i
$705$		0			0
$706$	−3.89664	−	8.09145i	−0.146652	−	0.304526i
$707$	4.21929	+	3.36477i	0.158683	+	0.126545i
$708$			6.26431i			0.235427i
$709$	0.327267	−	0.410380i	0.0122908	−	0.0154121i	−0.775648	−	0.631166i	$-0.782577\pi$
$709$	0.327267	−	0.410380i	0.0122908	−	0.0154121i	0.787939	+	0.615753i	$0.211148\pi$
$710$		0			0
$711$	−6.06767	−	1.38491i	−0.227556	−	0.0519381i
$712$	16.2168	−	20.3353i	0.607752	−	0.762097i
$713$		−	5.81450i		−	0.217755i
$714$	−1.21509	−	0.969003i	−0.0454736	−	0.0362640i
$715$		0			0
$716$	8.45822	+	10.6063i	0.316099	+	0.396375i
$717$	5.40056	−	4.30681i	0.201688	−	0.160841i
$718$	−3.30578	−	1.59198i	−0.123371	−	0.0594122i
$719$	−6.67556	+	29.2475i	−0.248956	+	1.09075i	0.683637	+	0.729822i	$0.260397\pi$
$719$	−6.67556	+	29.2475i	−0.248956	+	1.09075i	−0.932594	+	0.360928i	$0.882460\pi$
$720$		0			0
$721$	2.99712	−	1.44334i	0.111619	−	0.0537527i
$722$	−5.84680	+	12.1410i	−0.217595	+	0.451842i
$723$	−18.5739	+	4.23937i	−0.690770	+	0.157664i
$724$	23.4584			0.871824
$725$		0			0
$726$	31.5935			1.17254
$727$	−35.3545	+	8.06943i	−1.31122	+	0.299279i	−0.820305	−	0.571926i	$-0.806196\pi$
$727$	−35.3545	+	8.06943i	−1.31122	+	0.299279i	−0.490920	+	0.871205i	$0.663339\pi$
$728$	2.27506	−	4.72421i	0.0843192	−	0.175091i
$729$	27.0343	−	13.0190i	1.00127	−	0.482187i
$730$		0			0
$731$	3.88205	−	17.0084i	0.143583	−	0.629078i
$732$	14.6798	+	7.06942i	0.542581	+	0.261293i
$733$	34.1644	−	27.2452i	1.26189	−	1.00632i	0.262750	−	0.964864i	$-0.415370\pi$
$733$	34.1644	−	27.2452i	1.26189	−	1.00632i	0.999140	−	0.0414602i	$-0.0132010\pi$
$734$	14.0112	+	17.5695i	0.517163	+	0.648502i
$735$		0			0
$736$	7.59628	+	6.05783i	0.280003	+	0.223295i
$737$		−	24.8138i		−	0.914027i
$738$	−1.79760	+	2.25412i	−0.0661706	+	0.0829753i
$739$	14.1653	+	3.23314i	0.521079	+	0.118933i	0.474967	−	0.880003i	$-0.342460\pi$
$739$	14.1653	+	3.23314i	0.521079	+	0.118933i	0.0461117	+	0.998936i	$0.485317\pi$
$740$		0			0
$741$	−2.37792	+	2.98181i	−0.0873549	+	0.109540i
$742$		−	4.27562i		−	0.156963i
$743$	16.1507	+	12.8797i	0.592511	+	0.472511i	0.873250	−	0.487273i	$-0.162008\pi$
$743$	16.1507	+	12.8797i	0.592511	+	0.472511i	−0.280739	+	0.959784i	$0.590580\pi$
$744$	5.83586	+	12.1183i	0.213953	+	0.444278i
$745$		0			0
$746$	−12.2530	+	9.77145i	−0.448615	+	0.357758i
$747$	−7.01786	−	3.37962i	−0.256770	−	0.123654i
$748$	4.51411	−	19.7776i	0.165052	−	0.723141i
$749$	−0.886416	−	3.88364i	−0.0323889	−	0.141905i
$750$		0			0
$751$	0.212351	−	0.440952i	0.00774880	−	0.0160906i	−0.897059	−	0.441912i	$-0.854300\pi$
$751$	0.212351	−	0.440952i	0.00774880	−	0.0160906i	0.904807	+	0.425821i	$0.140015\pi$
$752$	3.97637	−	0.907581i	0.145003	−	0.0330961i
$753$	14.3541			0.523092
$754$	9.04745	+	9.07785i	0.329489	+	0.330596i
$755$		0			0
$756$	−5.09599	+	1.16313i	−0.185339	+	0.0423025i
$757$	12.7817	−	26.5415i	0.464560	−	0.964668i	−0.528706	−	0.848805i	$-0.677322\pi$
$757$	12.7817	−	26.5415i	0.464560	−	0.964668i	0.993265	−	0.115863i	$-0.0369633\pi$
$758$	−12.9598	+	6.24109i	−0.470720	+	0.226687i
$759$	3.51036	+	15.3799i	0.127418	+	0.558255i
$760$		0			0
$761$	23.4314	+	11.2840i	0.849388	+	0.409044i	0.807350	−	0.590072i	$-0.200901\pi$
$761$	23.4314	+	11.2840i	0.849388	+	0.409044i	0.0420377	+	0.999116i	$0.486615\pi$
$762$	18.4637	−	14.7243i	0.668870	−	0.533406i
$763$	−3.27245	−	4.10352i	−0.118471	−	0.148557i
$764$	1.11777	+	2.32108i	0.0404396	+	0.0839736i
$765$		0			0
$766$		−	6.87107i		−	0.248262i
$767$	5.73236	−	7.18815i	0.206983	−	0.259549i
$768$	−17.2973	−	3.94800i	−0.624164	−	0.142461i
$769$	19.0299	+	4.34344i	0.686234	+	0.156629i	0.551402	−	0.834240i	$-0.314093\pi$
$769$	19.0299	+	4.34344i	0.686234	+	0.156629i	0.134833	+	0.990868i	$0.456950\pi$
$770$		0			0
$771$			30.0149i			1.08096i
$772$	−6.77788	−	5.40518i	−0.243941	−	0.194537i
$773$	17.8321	+	37.0287i	0.641376	+	1.33183i	0.927567	+	0.373658i	$0.121897\pi$
$773$	17.8321	+	37.0287i	0.641376	+	1.33183i	−0.286191	+	0.958173i	$0.592389\pi$
$774$	2.57101	+	3.22395i	0.0924131	+	0.115882i
$775$		0			0
$776$	3.60143	+	1.73436i	0.129284	+	0.0622599i
$777$	−0.860139	+	3.76852i	−0.0308573	+	0.135195i
$778$	−3.24369	−	14.2115i	−0.116292	−	0.509508i
$779$	−3.86694	+	1.86222i	−0.138548	+	0.0667210i
$780$		0			0
$781$	−77.5233	+	17.6942i	−2.77400	+	0.633147i
$782$	−2.67942			−0.0958158
$783$	3.43575	−	30.0403i	0.122784	−	1.07355i
$784$	−7.05015			−0.251791
$785$		0			0
$786$	−8.46416	+	17.5760i	−0.301906	+	0.626915i
$787$	−7.17773	+	3.45661i	−0.255859	+	0.123215i	−0.557417	−	0.830233i	$-0.688207\pi$
$787$	−7.17773	+	3.45661i	−0.255859	+	0.123215i	0.301558	+	0.953448i	$0.402493\pi$
$788$	1.48796	+	6.51918i	0.0530064	+	0.232236i
$789$	6.61285	−	28.9728i	0.235424	−	1.03146i
$790$		0			0
$791$	0.0302947	−	0.0241592i	0.00107716	−	0.000859003i
$792$	7.07510	+	8.87190i	0.251403	+	0.315249i
$793$	−10.3756	−	21.5452i	−0.368450	−	0.765094i
$794$	−5.50559	−	4.39057i	−0.195386	−	0.155815i
$795$		0			0
$796$	7.82127	−	9.80756i	0.277217	−	0.347620i
$797$	0.259286	+	0.0591803i	0.00918438	+	0.00209627i	0.227111	−	0.973869i	$-0.427072\pi$
$797$	0.259286	+	0.0591803i	0.00918438	+	0.00209627i	−0.217926	+	0.975965i	$0.569929\pi$
$798$	0.533146	+	0.121687i	0.0188732	+	0.00430768i
$799$	−5.24578	+	6.57800i	−0.185582	+	0.232713i
$800$		0			0
$801$	5.70417	+	4.54892i	0.201547	+	0.160728i
$802$	−8.81433	−	18.3031i	−0.311245	−	0.646307i
$803$	64.3566	+	80.7006i	2.27109	+	2.84786i
$804$	−6.83277	+	5.44895i	−0.240973	+	0.192170i
$805$		0			0
$806$	1.85616	−	8.13235i	0.0653803	−	0.286450i
$807$	−6.70200	−	29.3634i	−0.235922	−	1.03364i
$808$	−19.3910	+	9.33822i	−0.682174	+	0.328518i
$809$	16.3627	−	33.9775i	0.575282	−	1.19459i	−0.386886	−	0.922128i	$-0.626449\pi$
$809$	16.3627	−	33.9775i	0.575282	−	1.19459i	0.962168	−	0.272458i	$-0.0878365\pi$
$810$		0			0
$811$	−20.6410			−0.724802			−0.362401	−	0.932022i	$-0.618043\pi$
$811$	−20.6410			−0.724802			−0.362401	+	0.932022i	$0.618043\pi$
$812$	−1.66374	+	4.72923i	−0.0583857	+	0.165964i
$813$	42.6954			1.49739
$814$	18.0312	−	4.11551i	0.631994	−	0.144248i
$815$		0			0
$816$	−3.21263	+	1.54712i	−0.112465	+	0.0541601i
$817$	1.36597	+	5.98468i	0.0477891	+	0.209378i
$818$	0.944854	−	4.13968i	0.0330360	−	0.144740i
$819$	1.32517	+	0.638167i	0.0463051	+	0.0222994i
$820$		0			0
$821$	−13.6668	−	17.1376i	−0.476973	−	0.598105i	0.483890	−	0.875129i	$-0.339223\pi$
$821$	−13.6668	−	17.1376i	−0.476973	−	0.598105i	−0.960863	+	0.277024i	$0.910652\pi$
$822$	−4.76503	−	9.89469i	−0.166200	−	0.345117i
$823$	6.73188	+	5.36849i	0.234658	+	0.187134i	0.733758	−	0.679411i	$-0.237764\pi$
$823$	6.73188	+	5.36849i	0.234658	+	0.187134i	−0.499100	+	0.866545i	$0.666336\pi$
$824$			13.2666i			0.462163i
$825$		0			0
$826$	−1.28524	−	0.293347i	−0.0447191	−	0.0102068i
$827$	−15.2842	−	3.48853i	−0.531485	−	0.121308i	−0.0516474	−	0.998665i	$-0.516447\pi$
$827$	−15.2842	−	3.48853i	−0.531485	−	0.121308i	−0.479837	+	0.877357i	$0.659304\pi$
$828$	−1.07722	+	1.35079i	−0.0374360	+	0.0469433i
$829$		−	34.5336i		−	1.19940i	−0.800225	−	0.599700i	$-0.795286\pi$
$829$		−	34.5336i		−	1.19940i	0.800225	−	0.599700i	$-0.204714\pi$
$830$		0			0
$831$	5.73402	+	11.9068i	0.198911	+	0.413043i
$832$	4.35931	+	5.46640i	0.151132	+	0.189513i
$833$	11.3705	−	9.06764i	0.393963	−	0.314175i
$834$	−4.60757	−	2.21889i	−0.159547	−	0.0768338i
$835$		0			0
$836$	1.58836	+	6.95908i	0.0549347	+	0.240685i
$837$	−17.7300	+	8.53832i	−0.612839	+	0.295128i
$838$	5.66174	−	11.7567i	0.195581	−	0.406129i
$839$	−23.8692	+	5.44798i	−0.824055	+	0.188085i	−0.613699	−	0.789540i	$-0.710319\pi$
$839$	−23.8692	+	5.44798i	−0.824055	+	0.188085i	−0.210355	+	0.977625i	$0.567462\pi$
$840$		0			0
$841$	−22.6123	−	18.1571i	−0.779736	−	0.626108i
$842$	13.8855			0.478527
$843$	−24.4352	+	5.57718i	−0.841593	+	0.192088i
$844$	4.18433	−	8.68885i	0.144031	−	0.299082i
$845$		0			0
$846$	−0.442523	−	1.93882i	−0.0152143	−	0.0666580i
$847$	4.03605	−	17.6831i	0.138680	−	0.607598i
$848$	−8.83822	−	4.25626i	−0.303506	−	0.146161i
$849$	−30.7068	+	24.4879i	−1.05386	+	0.840422i
$850$		0			0
$851$	2.89145	+	6.00416i	0.0991177	+	0.205820i
$852$	21.8960	+	17.4614i	0.750143	+	0.598219i
$853$		−	40.1587i		−	1.37501i	−0.726180	−	0.687504i	$-0.758706\pi$
$853$		−	40.1587i		−	1.37501i	0.726180	−	0.687504i	$-0.241294\pi$
$854$	−2.13785	+	2.68078i	−0.0731558	+	0.0917344i
$855$		0			0
$856$	15.4883	+	3.53510i	0.529379	+	0.120827i
$857$	3.15799	−	3.96000i	0.107875	−	0.135271i	−0.724963	−	0.688788i	$-0.758143\pi$
$857$	3.15799	−	3.96000i	0.107875	−	0.135271i	0.832838	+	0.553517i	$0.186715\pi$
$858$			22.6315i			0.772626i
$859$	−12.1082	−	9.65593i	−0.413125	−	0.329456i	0.394773	−	0.918779i	$-0.370823\pi$
$859$	−12.1082	−	9.65593i	−0.413125	−	0.329456i	−0.807898	+	0.589323i	$0.799395\pi$
$860$		0			0
$861$	−3.31878	−	4.16162i	−0.113104	−	0.141827i
$862$	−5.23725	+	4.17657i	−0.178381	+	0.142254i
$863$	9.30326	+	4.48022i	0.316687	+	0.152508i	0.585474	−	0.810691i	$-0.300908\pi$
$863$	9.30326	+	4.48022i	0.316687	+	0.152508i	−0.268787	+	0.963200i	$0.586623\pi$
$864$	7.31721	−	32.0588i	0.248937	−	1.09066i
$865$		0			0
$866$	14.2690	−	6.87158i	0.484880	−	0.233506i
$867$	−7.96658	+	16.5428i	−0.270559	+	0.561822i
$868$	3.18107	−	0.726059i	0.107973	−	0.0246441i
$869$	−54.9781			−1.86500
$870$		0			0
$871$	12.8267			0.434616
$872$	20.4070	−	4.65777i	0.691070	−	0.157732i
$873$	−0.486498	+	1.01022i	−0.0164655	+	0.0341909i
$874$	0.849432	−	0.409065i	0.0287325	−	0.0138368i
$875$		0			0
$876$	8.08957	−	35.4427i	0.273321	−	1.19750i
$877$	12.8036	+	6.16589i	0.432347	+	0.208207i	0.637383	−	0.770547i	$-0.280017\pi$
$877$	12.8036	+	6.16589i	0.432347	+	0.208207i	−0.205036	+	0.978754i	$0.565731\pi$
$878$	16.6582	−	13.2844i	0.562186	−	0.448328i
$879$	29.9708	+	37.5822i	1.01089	+	1.26762i
$880$		0			0
$881$	21.9891	+	17.5357i	0.740830	+	0.590792i	0.919488	−	0.393119i	$-0.128604\pi$
$881$	21.9891	+	17.5357i	0.740830	+	0.590792i	−0.178657	+	0.983911i	$0.557175\pi$
$882$			3.43755i			0.115748i
$883$	−18.9531	+	23.7665i	−0.637823	+	0.799805i	−0.990729	−	0.135854i	$-0.956622\pi$
$883$	−18.9531	+	23.7665i	−0.637823	+	0.799805i	0.352906	+	0.935659i	$0.385194\pi$
$884$	10.2234	+	2.33343i	0.343850	+	0.0784816i
$885$		0			0
$886$	11.8491	−	14.8583i	0.398077	−	0.499173i
$887$			22.0850i			0.741543i	0.928724	+	0.370771i	$0.120907\pi$
$887$			22.0850i			0.741543i	−0.928724	+	0.370771i	$0.879093\pi$
$888$	−12.0524	−	9.61150i	−0.404454	−	0.322541i
$889$	−5.88257	−	12.2153i	−0.197295	−	0.409688i
$890$		0			0
$891$	31.2511	−	24.9219i	1.04695	−	0.834916i
$892$	−12.0274	−	5.79210i	−0.402708	−	0.193934i
$893$	0.658764	−	2.88624i	0.0220447	−	0.0965842i
$894$	−4.33902	−	19.0105i	−0.145119	−	0.635806i
$895$		0			0
$896$	−2.79783	+	5.80975i	−0.0934690	+	0.194090i
$897$	−7.95015	+	1.81457i	−0.265448	+	0.0605868i
$898$	8.34159			0.278362
$899$	−2.14470	+	18.7521i	−0.0715297	+	0.625416i
$900$		0			0
$901$	19.7285	−	4.50290i	0.657251	−	0.150013i
$902$	−11.0504	+	22.9463i	−0.367937	+	0.764030i
$903$	−6.85913	+	3.30319i	−0.228258	+	0.109923i
$904$	0.0343865	+	0.150657i	0.00114368	+	0.00501079i
$905$		0			0
$906$	−3.95951	−	1.90680i	−0.131546	−	0.0633491i
$907$	−27.2865	+	21.7603i	−0.906034	+	0.722538i	−0.961175	−	0.275940i	$-0.911011\pi$
$907$	−27.2865	+	21.7603i	−0.906034	+	0.722538i	0.0551405	+	0.998479i	$0.482439\pi$
$908$	−18.8721	−	23.6649i	−0.626293	−	0.785347i
$909$	−2.61943	−	5.43930i	−0.0868809	−	0.180410i
$910$		0			0
$911$		−	5.90821i		−	0.195748i	−0.995199	−	0.0978739i	$-0.968796\pi$
$911$		−	5.90821i		−	0.195748i	0.995199	−	0.0978739i	$-0.0312042\pi$
$912$	0.782274	−	0.980941i	0.0259037	−	0.0324822i
$913$	−67.0822	−	15.3111i	−2.22010	−	0.506722i
$914$	−27.1660	−	6.20046i	−0.898571	−	0.205093i
$915$		0			0
$916$			39.5881i			1.30803i
$917$	8.75612	+	6.98277i	0.289152	+	0.230591i
$918$	3.93461	+	8.17029i	0.129861	+	0.269660i
$919$	−35.2009	−	44.1406i	−1.16117	−	1.45606i	−0.865595	−	0.500744i	$-0.833060\pi$
$919$	−35.2009	−	44.1406i	−1.16117	−	1.45606i	−0.295577	−	0.955319i	$-0.595512\pi$
$920$		0			0
$921$	−26.8352	−	12.9231i	−0.884249	−	0.425832i
$922$	−3.61017	+	15.8172i	−0.118895	+	0.520912i
$923$	−9.14645	−	40.0732i	−0.301059	−	1.31903i
$924$	−7.97590	+	3.84099i	−0.262388	+	0.126359i
$925$		0			0
$926$	−20.3266	+	4.63942i	−0.667975	+	0.152461i
$927$	−3.72135			−0.122225
$928$	−22.2640	−	22.3387i	−0.730850	−	0.733305i
$929$	−29.1845			−0.957513			−0.478757	−	0.877948i	$-0.658912\pi$
$929$	−29.1845			−0.957513			−0.478757	+	0.877948i	$0.658912\pi$
$930$		0			0
$931$	−2.22033	+	4.61055i	−0.0727682	+	0.151105i
$932$	−14.5088	+	6.98707i	−0.475251	+	0.228869i
$933$	10.3559	+	45.3722i	0.339038	+	1.48542i
$934$	−0.129740	+	0.568428i	−0.00424522	+	0.0185995i
$935$		0			0
$936$	−4.58605	+	3.65725i	−0.149900	+	0.119541i
$937$	−22.1430	−	27.7664i	−0.723379	−	0.907089i	0.275145	−	0.961403i	$-0.411274\pi$
$937$	−22.1430	−	27.7664i	−0.723379	−	0.907089i	−0.998524	+	0.0543139i	$0.982703\pi$
$938$	−0.797985	−	1.65703i	−0.0260551	−	0.0541040i
$939$	−41.4771	−	33.0769i	−1.35355	−	1.07942i
$940$		0			0
$941$	5.33621	−	6.69140i	0.173956	−	0.218133i	−0.687209	−	0.726460i	$-0.741164\pi$
$941$	5.33621	−	6.69140i	0.173956	−	0.218133i	0.861164	+	0.508326i	$0.169736\pi$
$942$	−10.6830	−	2.43833i	−0.348071	−	0.0794450i
$943$	−8.94677	−	2.04204i	−0.291347	−	0.0664980i
$944$	−1.88580	+	2.36472i	−0.0613776	+	0.0769651i
$945$		0			0
$946$	28.4792	+	22.7114i	0.925938	+	0.738411i
$947$	21.5413	+	44.7310i	0.699999	+	1.45356i	0.882478	+	0.470353i	$0.155874\pi$
$947$	21.5413	+	44.7310i	0.699999	+	1.45356i	−0.182479	+	0.983210i	$0.558412\pi$
$948$	12.0729	+	15.1389i	0.392108	+	0.491688i
$949$	−41.7156	+	33.2671i	−1.35415	+	1.07990i
$950$		0			0
$951$	9.13706	−	40.0321i	0.296289	−	1.29813i
$952$	−0.791806	−	3.46913i	−0.0256626	−	0.112435i
$953$	14.4100	−	6.93947i	0.466784	−	0.224791i	−0.185681	−	0.982610i	$-0.559449\pi$
$953$	14.4100	−	6.93947i	0.466784	−	0.224791i	0.652465	+	0.757819i	$0.273735\pi$
$954$	−2.07529	+	4.30939i	−0.0671900	+	0.139522i
$955$		0			0
$956$	6.68283			0.216138
$957$	−5.64817	−	50.8958i	−0.182579	−	1.64523i
$958$	−20.3007			−0.655886
$959$	−6.14686	+	1.40298i	−0.198492	+	0.0453046i
$960$		0			0
$961$	−16.8624	+	8.12052i	−0.543949	+	0.261952i
$962$	2.12738	+	9.32067i	0.0685895	+	0.300510i
$963$	−0.991617	+	4.34456i	−0.0319544	+	0.140001i
$964$	−16.6063	−	7.99719i	−0.534854	−	0.257572i
$965$		0			0
$966$	0.729019	+	0.914161i	0.0234558	+	0.0294127i
$967$	24.1863	+	50.2234i	0.777779	+	1.61508i	0.788424	+	0.615132i	$0.210897\pi$
$967$	24.1863	+	50.2234i	0.777779	+	1.61508i	−0.0106445	+	0.999943i	$0.503388\pi$
$968$	56.5540	+	45.1003i	1.81771	+	1.44958i
$969$			2.58819i			0.0831446i
$970$		0			0
$971$	1.84897	+	0.422015i	0.0593362	+	0.0135431i	0.252086	−	0.967705i	$-0.418883\pi$
$971$	1.84897	+	0.422015i	0.0593362	+	0.0135431i	−0.192750	+	0.981248i	$0.561741\pi$
$972$	10.3086	+	2.35287i	0.330649	+	0.0754684i
$973$	−1.83054	+	2.29543i	−0.0586844	+	0.0735880i
$974$		−	3.38636i		−	0.108506i
$975$		0			0
$976$	3.41332	+	7.08784i	0.109258	+	0.226876i
$977$	−18.8474	−	23.6339i	−0.602982	−	0.756115i	0.382858	−	0.923807i	$-0.374940\pi$
$977$	−18.8474	−	23.6339i	−0.602982	−	0.756115i	−0.985839	+	0.167692i	$0.946368\pi$
$978$	16.7697	−	13.3734i	0.536236	−	0.427634i
$979$	58.0669	+	27.9635i	1.85583	+	0.893719i
$980$		0			0
$981$	1.30653	+	5.72430i	0.0417144	+	0.182763i
$982$	−20.5504	+	9.89653i	−0.655789	+	0.315811i
$983$	16.8323	−	34.9525i	0.536866	−	1.11481i	−0.439411	−	0.898286i	$-0.644813\pi$
$983$	16.8323	−	34.9525i	0.536866	−	1.11481i	0.976277	−	0.216527i	$-0.0694729\pi$
$984$	20.6960	−	4.72372i	0.659763	−	0.150587i
$985$		0			0
$986$	8.64127	+	0.988314i	0.275194	+	0.0314743i
$987$	3.67155			0.116867
$988$	−3.59728	+	0.821055i	−0.114445	+	0.0261212i
$989$	−5.69479	+	11.8254i	−0.181084	+	0.376025i
$990$		0			0
$991$	−9.22034	−	40.3970i	−0.292894	−	1.28325i	−0.880477	−	0.474088i	$-0.842778\pi$
$991$	−9.22034	−	40.3970i	−0.292894	−	1.28325i	0.587583	−	0.809164i	$-0.300079\pi$
$992$	−4.56763	+	20.0121i	−0.145022	+	0.635384i
$993$	−29.3041	−	14.1121i	−0.929938	−	0.447834i
$994$	−4.60788	+	3.67466i	−0.146153	+	0.116553i
$995$		0			0
$996$	10.5148	+	21.8341i	0.333173	+	0.691840i
$997$	−8.99545	−	7.17364i	−0.284889	−	0.227191i	0.470610	−	0.882341i	$-0.344034\pi$
$997$	−8.99545	−	7.17364i	−0.284889	−	0.227191i	−0.755499	+	0.655150i	$0.772605\pi$
$998$		−	3.58416i		−	0.113455i
$999$	14.0624	−	17.6337i	0.444914	−	0.557905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.q.d.51.4	✓	60
5.2	odd	4		725.2.p.d.399.8		120
5.3	odd	4		725.2.p.d.399.13		120
5.4	even	2		725.2.q.e.51.7	yes	60
29.4	even	14	inner	725.2.q.d.526.4	yes	60
145.4	even	14		725.2.q.e.526.7	yes	60
145.33	odd	28		725.2.p.d.149.8		120
145.62	odd	28		725.2.p.d.149.13		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.p.d.149.8		120	145.33	odd	28
725.2.p.d.149.13		120	145.62	odd	28
725.2.p.d.399.8		120	5.2	odd	4
725.2.p.d.399.13		120	5.3	odd	4
725.2.q.d.51.4	✓	60	1.1	even	1	trivial
725.2.q.d.526.4	yes	60	29.4	even	14	inner
725.2.q.e.51.7	yes	60	5.4	even	2
725.2.q.e.526.7	yes	60	145.4	even	14

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.q (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.714081 + 0.162984i) q^{2} +(-0.656356 + 1.36294i) q^{3} +(-1.31859 + 0.635000i) q^{4} +(0.246554 - 1.08022i) q^{6} +(-0.573111 - 0.275996i) q^{7} +(1.98338 - 1.58169i) q^{8} +(0.443675 + 0.556351i) q^{9} +(4.91460 + 3.91926i) q^{11} -2.21394i q^{12} +(-2.02594 + 2.54045i) q^{13} +(0.454230 + 0.103675i) q^{14} +(0.666483 - 0.835743i) q^{16} +2.20509i q^{17} +(-0.407496 - 0.324967i) q^{18} +(-0.336649 - 0.699059i) q^{19} +(0.752330 - 0.599963i) q^{21} +(-4.14820 - 1.99767i) q^{22} +(0.369157 - 1.61738i) q^{23} +(0.853945 + 3.74138i) q^{24} +(1.03263 - 2.14428i) q^{26} +(-5.47393 + 1.24939i) q^{27} +0.930956 q^{28} +(-1.78713 + 5.07998i) q^{29} +(3.41700 - 0.779907i) q^{31} +(-2.54110 + 5.27664i) q^{32} +(-8.56744 + 4.12586i) q^{33} +(-0.359395 - 1.57461i) q^{34} +(-0.938308 - 0.451865i) q^{36} +(-3.14062 + 2.50456i) q^{37} +(0.354330 + 0.444316i) q^{38} +(-2.13273 - 4.42867i) q^{39} -5.53164i q^{41} +(-0.439440 + 0.551040i) q^{42} +(-7.71324 - 1.76050i) q^{43} +(-8.96907 - 2.04713i) q^{44} +1.21511i q^{46} +(2.98310 + 2.37895i) q^{47} +(0.701615 + 1.45692i) q^{48} +(-4.11215 - 5.15647i) q^{49} +(-3.00540 - 1.44732i) q^{51} +(1.05820 - 4.63628i) q^{52} +(-2.04205 - 8.94680i) q^{53} +(3.70520 - 1.78433i) q^{54} +(-1.57324 + 0.359081i) q^{56} +1.17374 q^{57} +(0.448197 - 3.91879i) q^{58} -2.82948 q^{59} +(-3.19314 + 6.63062i) q^{61} +(-2.31290 + 1.11383i) q^{62} +(-0.100725 - 0.441303i) q^{63} +(0.478809 - 2.09780i) q^{64} +(5.44539 - 4.34255i) q^{66} +(-2.46120 - 3.08625i) q^{67} +(-1.40023 - 2.90761i) q^{68} +(1.96209 + 1.56472i) q^{69} +(-7.88704 + 9.89003i) q^{71} +(1.75995 + 0.401698i) q^{72} +(16.0089 + 3.65392i) q^{73} +(1.83445 - 2.30033i) q^{74} +(0.887805 + 0.708001i) q^{76} +(-1.73491 - 3.60258i) q^{77} +(2.24475 + 2.81482i) q^{78} +(-6.83798 + 5.45310i) q^{79} +(1.41497 - 6.19940i) q^{81} +(0.901570 + 3.95004i) q^{82} +(-9.86210 + 4.74934i) q^{83} +(-0.611038 + 1.26883i) q^{84} +5.79481 q^{86} +(-5.75070 - 5.77002i) q^{87} +15.9466 q^{88} +(9.99577 - 2.28147i) q^{89} +(1.86224 - 0.896808i) q^{91} +(0.540270 + 2.36708i) q^{92} +(-1.17980 + 5.16905i) q^{93} +(-2.51791 - 1.21256i) q^{94} +(-5.52387 - 6.92671i) q^{96} +(0.683669 + 1.41965i) q^{97} +(3.77683 + 3.01192i) q^{98} +4.47312i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{4} - 16 q^{6} - 4 q^{7} - 21 q^{8} + 10 q^{9} + 14 q^{11} + 4 q^{13} + 10 q^{16} + 35 q^{22} - 37 q^{23} + 48 q^{24} + 21 q^{27} + 44 q^{28} - 4 q^{29} + 14 q^{31} + 98 q^{32} - 41 q^{33} + 10 q^{34}+ \cdots + 91 q^{98}+O(q^{100}) \) 60 * q + 12 * q^4 - 16 * q^6 - 4 * q^7 - 21 * q^8 + 10 * q^9 + 14 * q^11 + 4 * q^13 + 10 * q^16 + 35 * q^22 - 37 * q^23 + 48 * q^24 + 21 * q^27 + 44 * q^28 - 4 * q^29 + 14 * q^31 + 98 * q^32 - 41 * q^33 + 10 * q^34 + 32 * q^36 + 7 * q^37 - 14 * q^38 + 56 * q^39 - 45 * q^42 - 63 * q^44 - 42 * q^47 - 21 * q^48 - 72 * q^49 - 32 * q^51 - 80 * q^52 - 20 * q^53 - 65 * q^54 - 63 * q^56 - 28 * q^57 - 2 * q^58 - 16 * q^59 - 28 * q^61 - 70 * q^62 + 42 * q^63 + 37 * q^64 - 140 * q^66 - 24 * q^67 - 42 * q^68 - 84 * q^69 + 9 * q^71 - 105 * q^72 + 14 * q^73 - 85 * q^74 + 70 * q^76 + 21 * q^77 + 102 * q^78 + 56 * q^79 - 72 * q^81 + 36 * q^82 + 6 * q^83 - 84 * q^84 + 86 * q^86 + 5 * q^87 + 102 * q^88 + 14 * q^89 - 60 * q^91 + 91 * q^92 - 62 * q^93 - 44 * q^94 + 25 * q^96 + 14 * q^97 + 91 * q^98

Introduction

L-functions

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