LMFDB - Embedded newform 825.2.n.j.676.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.2
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.j.526.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0646021 + 0.198825i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.58268 - 1.14988i) q^{4} +(0.0646021 - 0.198825i) q^{6} +(0.395472 - 0.287327i) q^{7} +(0.669131 + 0.486152i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.0646021 + 0.198825i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.58268 - 1.14988i) q^{4} +(0.0646021 - 0.198825i) q^{6} +(0.395472 - 0.287327i) q^{7} +(0.669131 + 0.486152i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-2.66078 - 1.97996i) q^{11} -1.95630 q^{12} +(-1.00973 - 3.10762i) q^{13} +(0.0826761 + 0.0600677i) q^{14} +(1.15563 - 3.55665i) q^{16} +(1.02924 - 3.16769i) q^{17} +(-0.169131 + 0.122881i) q^{18} +(3.12999 + 2.27407i) q^{19} -0.488830 q^{21} +(0.221773 - 0.656940i) q^{22} +0.267545 q^{23} +(-0.255585 - 0.786610i) q^{24} +(0.552642 - 0.401518i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.295511 - 0.909491i) q^{28} +(-5.10969 + 3.71240i) q^{29} +(-1.80242 - 5.54726i) q^{31} +2.43599 q^{32} +(0.988830 + 3.16579i) q^{33} +0.696307 q^{34} +(1.58268 + 1.14988i) q^{36} +(6.07055 - 4.41051i) q^{37} +(-0.249938 + 0.769231i) q^{38} +(-1.00973 + 3.10762i) q^{39} +(-3.38791 - 2.46146i) q^{41} +(-0.0315794 - 0.0971915i) q^{42} +2.26657 q^{43} +(-6.48787 - 0.0740447i) q^{44} +(0.0172840 + 0.0531947i) q^{46} +(-4.51712 - 3.28188i) q^{47} +(-3.02547 + 2.19813i) q^{48} +(-2.08928 + 6.43014i) q^{49} +(-2.69460 + 1.95774i) q^{51} +(-5.17147 - 3.75729i) q^{52} +(0.353210 + 1.08707i) q^{53} +0.209057 q^{54} +0.404307 q^{56} +(-1.19555 - 3.67953i) q^{57} +(-1.06822 - 0.776104i) q^{58} +(3.65467 - 2.65527i) q^{59} +(3.88568 - 11.9589i) q^{61} +(0.986494 - 0.716730i) q^{62} +(0.395472 + 0.287327i) q^{63} +(-2.15388 - 6.62896i) q^{64} +(-0.565557 + 0.401121i) q^{66} -8.97575 q^{67} +(-2.01351 - 6.19693i) q^{68} +(-0.216449 - 0.157259i) q^{69} +(1.64271 - 5.05574i) q^{71} +(-0.255585 + 0.786610i) q^{72} +(7.81418 - 5.67733i) q^{73} +(1.26909 + 0.922048i) q^{74} +7.56868 q^{76} +(-1.62116 - 0.0185019i) q^{77} -0.683103 q^{78} +(-0.466085 - 1.43446i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.270534 - 0.832618i) q^{82} +(-5.45193 + 16.7793i) q^{83} +(-0.773659 + 0.562096i) q^{84} +(0.146425 + 0.450650i) q^{86} +6.31592 q^{87} +(-0.817852 - 2.61839i) q^{88} +15.9226 q^{89} +(-1.29222 - 0.938854i) q^{91} +(0.423438 - 0.307645i) q^{92} +(-1.80242 + 5.54726i) q^{93} +(0.360704 - 1.11013i) q^{94} +(-1.97076 - 1.43184i) q^{96} +(5.04821 + 15.5368i) q^{97} -1.41344 q^{98} +(1.06082 - 3.14240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 5 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 5 * q^7 + q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 5 q^{7} + q^{8} - 2 q^{9} - q^{11} + 2 q^{12} + 16 q^{13} - 10 q^{14} + 12 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 9 q^{22} - 10 q^{23} - 4 q^{24} + 16 q^{26} - 2 q^{27} + 5 q^{28} - 16 q^{29} - 5 q^{31} + 4 q^{33} + 34 q^{34} + 2 q^{36} + 5 q^{37} - 28 q^{38} + 16 q^{39} + 5 q^{41} + 15 q^{42} + 8 q^{43} - 19 q^{44} + 10 q^{46} + q^{47} - 3 q^{48} - 11 q^{49} + 4 q^{51} - 26 q^{52} + 15 q^{53} - 2 q^{54} + 20 q^{56} - 13 q^{57} + 24 q^{58} + 3 q^{59} - 11 q^{61} + 15 q^{62} + 5 q^{63} - 9 q^{64} - 31 q^{66} - 6 q^{67} - 9 q^{68} + 15 q^{69} + q^{71} - 4 q^{72} + 35 q^{73} + 5 q^{74} + 58 q^{76} + 25 q^{77} - 24 q^{78} - 30 q^{79} - 2 q^{81} + 25 q^{82} - 31 q^{83} - 62 q^{86} + 34 q^{87} - 17 q^{88} - 48 q^{89} + 5 q^{91} + 20 q^{92} - 5 q^{93} - 19 q^{94} - 20 q^{96} - 11 q^{97} - 26 q^{98} - 11 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 5 * q^7 + q^8 - 2 * q^9 - q^11 + 2 * q^12 + 16 * q^13 - 10 * q^14 + 12 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 9 * q^22 - 10 * q^23 - 4 * q^24 + 16 * q^26 - 2 * q^27 + 5 * q^28 - 16 * q^29 - 5 * q^31 + 4 * q^33 + 34 * q^34 + 2 * q^36 + 5 * q^37 - 28 * q^38 + 16 * q^39 + 5 * q^41 + 15 * q^42 + 8 * q^43 - 19 * q^44 + 10 * q^46 + q^47 - 3 * q^48 - 11 * q^49 + 4 * q^51 - 26 * q^52 + 15 * q^53 - 2 * q^54 + 20 * q^56 - 13 * q^57 + 24 * q^58 + 3 * q^59 - 11 * q^61 + 15 * q^62 + 5 * q^63 - 9 * q^64 - 31 * q^66 - 6 * q^67 - 9 * q^68 + 15 * q^69 + q^71 - 4 * q^72 + 35 * q^73 + 5 * q^74 + 58 * q^76 + 25 * q^77 - 24 * q^78 - 30 * q^79 - 2 * q^81 + 25 * q^82 - 31 * q^83 - 62 * q^86 + 34 * q^87 - 17 * q^88 - 48 * q^89 + 5 * q^91 + 20 * q^92 - 5 * q^93 - 19 * q^94 - 20 * q^96 - 11 * q^97 - 26 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	0.0646021	+	0.198825i	0.0456806	+	0.140590i	0.971295	−	0.237877i	$-0.0764514\pi$
$2$	0.0646021	+	0.198825i	0.0456806	+	0.140590i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	1.58268	−	1.14988i	0.791338	−	0.574941i
$5$		0			0
$5$		0			0
$6$	0.0646021	−	0.198825i	0.0263737	−	0.0811699i
$7$	0.395472	−	0.287327i	0.149474	−	0.108599i	−0.510535	−	0.859857i	$-0.670553\pi$
$7$	0.395472	−	0.287327i	0.149474	−	0.108599i	0.660009	+	0.751258i	$0.270553\pi$
$8$	0.669131	+	0.486152i	0.236573	+	0.171881i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−2.66078	−	1.97996i	−0.802256	−	0.596980i
$11$	−2.66078	−	1.97996i	−0.802256	−	0.596980i
$12$	−1.95630			−0.564734
$13$	−1.00973	−	3.10762i	−0.280048	−	0.861899i	−0.987839	−	0.155477i	$-0.950308\pi$
$13$	−1.00973	−	3.10762i	−0.280048	−	0.861899i	0.707792	−	0.706421i	$-0.249692\pi$
$14$	0.0826761	+	0.0600677i	0.0220961	+	0.0160538i
$15$		0			0
$16$	1.15563	−	3.55665i	0.288906	−	0.889162i
$17$	1.02924	−	3.16769i	0.249628	−	0.768277i	−0.745212	−	0.666827i	$-0.767652\pi$
$17$	1.02924	−	3.16769i	0.249628	−	0.768277i	0.994841	−	0.101450i	$-0.0323481\pi$
$18$	−0.169131	+	0.122881i	−0.0398645	+	0.0289632i
$19$	3.12999	+	2.27407i	0.718070	+	0.521708i	0.885767	−	0.464130i	$-0.153633\pi$
$19$	3.12999	+	2.27407i	0.718070	+	0.521708i	−0.167697	+	0.985839i	$0.553633\pi$
$20$		0			0
$21$	−0.488830			−0.106671
$22$	0.221773	−	0.656940i	0.0472821	−	0.140060i
$23$	0.267545			0.0557871			0.0278935	−	0.999611i	$-0.491120\pi$
$23$	0.267545			0.0557871			0.0278935	+	0.999611i	$0.491120\pi$
$24$	−0.255585	−	0.786610i	−0.0521711	−	0.160566i
$25$		0			0
$26$	0.552642	−	0.401518i	0.108382	−	0.0787441i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.295511	−	0.909491i	0.0558464	−	0.171878i
$29$	−5.10969	+	3.71240i	−0.948845	+	0.689376i	−0.950533	−	0.310622i	$-0.899463\pi$
$29$	−5.10969	+	3.71240i	−0.948845	+	0.689376i	0.00168835	+	0.999999i	$0.499463\pi$
$30$		0			0
$31$	−1.80242	−	5.54726i	−0.323723	−	0.996318i	−0.972014	−	0.234925i	$-0.924516\pi$
$31$	−1.80242	−	5.54726i	−0.323723	−	0.996318i	0.648290	−	0.761393i	$-0.275484\pi$
$32$	2.43599			0.430626
$33$	0.988830	+	3.16579i	0.172133	+	0.551093i
$34$	0.696307			0.119416
$35$		0			0
$36$	1.58268	+	1.14988i	0.263779	+	0.191647i
$37$	6.07055	−	4.41051i	0.997992	−	0.725084i	0.0363356	−	0.999340i	$-0.488431\pi$
$37$	6.07055	−	4.41051i	0.997992	−	0.725084i	0.961657	+	0.274256i	$0.0884315\pi$
$38$	−0.249938	+	0.769231i	−0.0405453	+	0.124786i
$39$	−1.00973	+	3.10762i	−0.161686	+	0.497618i
$40$		0			0
$41$	−3.38791	−	2.46146i	−0.529103	−	0.384416i	0.290919	−	0.956748i	$-0.406039\pi$
$41$	−3.38791	−	2.46146i	−0.529103	−	0.384416i	−0.820022	+	0.572332i	$0.806039\pi$
$42$	−0.0315794	−	0.0971915i	−0.00487281	−	0.0149970i
$43$	2.26657			0.345649			0.172824	−	0.984953i	$-0.444711\pi$
$43$	2.26657			0.345649			0.172824	+	0.984953i	$0.444711\pi$
$44$	−6.48787	−	0.0740447i	−0.978084	−	0.0111627i
$45$		0			0
$46$	0.0172840	+	0.0531947i	0.00254839	+	0.00784313i
$47$	−4.51712	−	3.28188i	−0.658890	−	0.478711i	0.207398	−	0.978257i	$-0.433500\pi$
$47$	−4.51712	−	3.28188i	−0.658890	−	0.478711i	−0.866288	+	0.499545i	$0.833500\pi$
$48$	−3.02547	+	2.19813i	−0.436688	+	0.317273i
$49$	−2.08928	+	6.43014i	−0.298468	+	0.918591i
$50$		0			0
$51$	−2.69460	+	1.95774i	−0.377319	+	0.274138i
$52$	−5.17147	−	3.75729i	−0.717153	−	0.521042i
$53$	0.353210	+	1.08707i	0.0485171	+	0.149320i	0.972380	−	0.233403i	$-0.0749862\pi$
$53$	0.353210	+	1.08707i	0.0485171	+	0.149320i	−0.923863	+	0.382724i	$0.874986\pi$
$54$	0.209057			0.0284490
$55$		0			0
$56$	0.404307			0.0540277
$57$	−1.19555	−	3.67953i	−0.158355	−	0.487366i
$58$	−1.06822	−	0.776104i	−0.140264	−	0.101907i
$59$	3.65467	−	2.65527i	0.475798	−	0.345687i	−0.323899	−	0.946092i	$-0.604994\pi$
$59$	3.65467	−	2.65527i	0.475798	−	0.345687i	0.799696	+	0.600405i	$0.204994\pi$
$60$		0			0
$61$	3.88568	−	11.9589i	0.497511	−	1.53118i	−0.315497	−	0.948927i	$-0.602171\pi$
$61$	3.88568	−	11.9589i	0.497511	−	1.53118i	0.813007	−	0.582253i	$-0.197829\pi$
$62$	0.986494	−	0.716730i	0.125285	−	0.0910248i
$63$	0.395472	+	0.287327i	0.0498247	+	0.0361998i
$64$	−2.15388	−	6.62896i	−0.269235	−	0.828620i
$65$		0			0
$66$	−0.565557	+	0.401121i	−0.0696153	+	0.0493745i
$67$	−8.97575			−1.09656			−0.548281	−	0.836294i	$-0.684718\pi$
$67$	−8.97575			−1.09656			−0.548281	+	0.836294i	$0.684718\pi$
$68$	−2.01351	−	6.19693i	−0.244173	−	0.751488i
$69$	−0.216449	−	0.157259i	−0.0260574	−	0.0189318i
$70$		0			0
$71$	1.64271	−	5.05574i	0.194954	−	0.600006i	−0.805023	−	0.593243i	$-0.797847\pi$
$71$	1.64271	−	5.05574i	0.194954	−	0.600006i	0.999977	−	0.00676293i	$-0.00215272\pi$
$72$	−0.255585	+	0.786610i	−0.0301210	+	0.0927029i
$73$	7.81418	−	5.67733i	0.914580	−	0.664481i	−0.0275890	−	0.999619i	$-0.508783\pi$
$73$	7.81418	−	5.67733i	0.914580	−	0.664481i	0.942169	+	0.335138i	$0.108783\pi$
$74$	1.26909	+	0.922048i	0.147529	+	0.107186i
$75$		0			0
$76$	7.56868			0.868187
$77$	−1.62116	−	0.0185019i	−0.184748	−	0.00210849i
$78$	−0.683103			−0.0773462
$79$	−0.466085	−	1.43446i	−0.0524387	−	0.161390i	0.921408	−	0.388598i	$-0.127040\pi$
$79$	−0.466085	−	1.43446i	−0.0524387	−	0.161390i	−0.973846	+	0.227208i	$0.927040\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	0.270534	−	0.832618i	0.0298755	−	0.0919473i
$83$	−5.45193	+	16.7793i	−0.598427	+	1.84177i	−0.0615555	+	0.998104i	$0.519606\pi$
$83$	−5.45193	+	16.7793i	−0.598427	+	1.84177i	−0.536871	+	0.843664i	$0.680394\pi$
$84$	−0.773659	+	0.562096i	−0.0844131	+	0.0613297i
$85$		0			0
$86$	0.146425	+	0.450650i	0.0157894	+	0.0485949i
$87$	6.31592			0.677138
$88$	−0.817852	−	2.61839i	−0.0871833	−	0.279122i
$89$	15.9226			1.68779			0.843895	−	0.536509i	$-0.180257\pi$
$89$	15.9226			1.68779			0.843895	+	0.536509i	$0.180257\pi$
$90$		0			0
$91$	−1.29222	−	0.938854i	−0.135462	−	0.0984186i
$92$	0.423438	−	0.307645i	0.0441464	−	0.0320743i
$93$	−1.80242	+	5.54726i	−0.186902	+	0.575224i
$94$	0.360704	−	1.11013i	0.0372038	−	0.114501i
$95$		0			0
$96$	−1.97076	−	1.43184i	−0.201139	−	0.146136i
$97$	5.04821	+	15.5368i	0.512568	+	1.57752i	0.787664	+	0.616105i	$0.211290\pi$
$97$	5.04821	+	15.5368i	0.512568	+	1.57752i	−0.275096	+	0.961417i	$0.588710\pi$
$98$	−1.41344			−0.142779
$99$	1.06082	−	3.14240i	0.106617	−	0.315823i
$100$		0			0
$101$	5.51663	+	16.9784i	0.548925	+	1.68942i	0.711469	+	0.702717i	$0.248030\pi$
$101$	5.51663	+	16.9784i	0.548925	+	1.68942i	−0.162544	+	0.986701i	$0.551970\pi$
$102$	−0.563324	−	0.409279i	−0.0557774	−	0.0405246i
$103$	12.4079	−	9.01484i	1.22258	−	0.888258i	0.226271	−	0.974064i	$-0.427347\pi$
$103$	12.4079	−	9.01484i	1.22258	−	0.888258i	0.996312	+	0.0858063i	$0.0273466\pi$
$104$	0.835136	−	2.57028i	0.0818918	−	0.252037i
$105$		0			0
$106$	−0.193318	+	0.140454i	−0.0187767	+	0.0136421i
$107$	−4.72411	−	3.43227i	−0.456697	−	0.331810i	0.335537	−	0.942027i	$-0.391082\pi$
$107$	−4.72411	−	3.43227i	−0.456697	−	0.331810i	−0.792234	+	0.610217i	$0.791082\pi$
$108$	−0.604528	−	1.86055i	−0.0581708	−	0.179031i
$109$	7.05284			0.675540			0.337770	−	0.941229i	$-0.390327\pi$
$109$	7.05284			0.675540			0.337770	+	0.941229i	$0.390327\pi$
$110$		0			0
$111$	−7.50361			−0.712211
$112$	−0.564904	−	1.73860i	−0.0533784	−	0.164282i
$113$	−11.0042	−	7.99502i	−1.03519	−	0.752108i	−0.0658479	−	0.997830i	$-0.520975\pi$
$113$	−11.0042	−	7.99502i	−1.03519	−	0.752108i	−0.969341	+	0.245721i	$0.920975\pi$
$114$	0.654347	−	0.475411i	0.0612852	−	0.0445263i
$115$		0			0
$116$	−3.81815	+	11.7511i	−0.354507	+	1.09106i
$117$	2.64350	−	1.92061i	0.244392	−	0.177561i
$118$	0.764034	+	0.555103i	0.0703350	+	0.0511014i
$119$	−0.503125	−	1.54846i	−0.0461214	−	0.141947i
$120$		0			0
$121$	3.15954	+	10.5365i	0.287231	+	0.957861i
$122$	2.62875			0.237996
$123$	1.29407	+	3.98273i	0.116682	+	0.359111i
$124$	−9.23133	−	6.70696i	−0.828998	−	0.602303i
$125$		0			0
$126$	−0.0315794	+	0.0971915i	−0.00281332	+	0.00865851i
$127$	−6.82620	+	21.0089i	−0.605727	+	1.86424i	−0.114015	+	0.993479i	$0.536371\pi$
$127$	−6.82620	+	21.0089i	−0.605727	+	1.86424i	−0.491713	+	0.870758i	$0.663629\pi$
$128$	5.12037	−	3.72017i	0.452581	−	0.328819i
$129$	−1.83369	−	1.33226i	−0.161448	−	0.117299i
$130$		0			0
$131$	3.87993			0.338991			0.169496	−	0.985531i	$-0.445786\pi$
$131$	3.87993			0.338991			0.169496	+	0.985531i	$0.445786\pi$
$132$	5.20528	+	3.87338i	0.453061	+	0.337134i
$133$	1.89123			0.163990
$134$	−0.579853	−	1.78460i	−0.0500916	−	0.154166i
$135$		0			0
$136$	2.22868	−	1.61923i	0.191107	−	0.138848i
$137$	1.65826	−	5.10361i	0.141675	−	0.436030i	−0.854894	−	0.518803i	$-0.826378\pi$
$137$	1.65826	−	5.10361i	0.141675	−	0.436030i	0.996568	+	0.0827730i	$0.0263776\pi$
$138$	0.0172840	−	0.0531947i	0.00147131	−	0.00452823i
$139$	−10.2128	+	7.42001i	−0.866236	+	0.629357i	−0.929574	−	0.368635i	$-0.879825\pi$
$139$	−10.2128	+	7.42001i	−0.866236	+	0.629357i	0.0633383	+	0.997992i	$0.479825\pi$
$140$		0			0
$141$	1.72539	+	5.31019i	0.145304	+	0.447199i
$142$	1.11133			0.0932607
$143$	−3.46629	+	10.2679i	−0.289866	+	0.858647i
$144$	3.73968			0.311640
$145$		0			0
$146$	1.63361	+	1.18689i	0.135198	+	0.0982273i
$147$	5.46980	−	3.97404i	0.451142	−	0.327774i
$148$	4.53615	−	13.9608i	0.372869	−	1.14757i
$149$	−1.45222	+	4.46946i	−0.118970	+	0.366152i	−0.992754	−	0.120161i	$-0.961659\pi$
$149$	−1.45222	+	4.46946i	−0.118970	+	0.366152i	0.873784	+	0.486314i	$0.161659\pi$
$150$		0			0
$151$	−11.7884	−	8.56476i	−0.959325	−	0.696990i	−0.00633091	−	0.999980i	$-0.502015\pi$
$151$	−11.7884	−	8.56476i	−0.959325	−	0.696990i	−0.952994	+	0.302990i	$0.902015\pi$
$152$	0.988830	+	3.04330i	0.0802047	+	0.246845i
$153$	3.33070			0.269271
$154$	−0.101052	−	0.323522i	−0.00814298	−	0.0260702i
$155$		0			0
$156$	1.97532	+	6.07942i	0.158153	+	0.486743i
$157$	0.270369	+	0.196434i	0.0215778	+	0.0156772i	0.598522	−	0.801106i	$-0.295755\pi$
$157$	0.270369	+	0.196434i	0.0215778	+	0.0156772i	−0.576944	+	0.816784i	$0.695755\pi$
$158$	0.255097	−	0.185339i	0.0202944	−	0.0147448i
$159$	0.353210	−	1.08707i	0.0280114	−	0.0862101i
$160$		0			0
$161$	0.105807	−	0.0768730i	0.00833873	−	0.00605844i
$162$	−0.169131	−	0.122881i	−0.0132882	−	0.00965441i
$163$	−0.614744	−	1.89199i	−0.0481504	−	0.148192i	0.924091	−	0.382174i	$-0.124824\pi$
$163$	−0.614744	−	1.89199i	−0.0481504	−	0.148192i	−0.972241	+	0.233982i	$0.924824\pi$
$164$	−8.19236			−0.639716
$165$		0			0
$166$	−3.68835			−0.286272
$167$	5.94309	+	18.2910i	0.459890	+	1.41540i	0.865297	+	0.501260i	$0.167130\pi$
$167$	5.94309	+	18.2910i	0.459890	+	1.41540i	−0.405406	+	0.914137i	$0.632870\pi$
$168$	−0.327091	−	0.237645i	−0.0252356	−	0.0183347i
$169$	1.87947	−	1.36551i	0.144574	−	0.105039i
$170$		0			0
$171$	−1.19555	+	3.67953i	−0.0914261	+	0.281381i
$172$	3.58724	−	2.60629i	0.273525	−	0.198727i
$173$	11.3030	+	8.21211i	0.859352	+	0.624355i	0.927708	−	0.373305i	$-0.121776\pi$
$173$	11.3030	+	8.21211i	0.859352	+	0.624355i	−0.0683569	+	0.997661i	$0.521776\pi$
$174$	0.408022	+	1.25576i	0.0309321	+	0.0951991i
$175$		0			0
$176$	−10.1169	+	7.17538i	−0.762588	+	0.540865i
$177$	−4.51742			−0.339550
$178$	1.02863	+	3.16581i	0.0770993	+	0.237287i
$179$	6.35884	+	4.61996i	0.475282	+	0.345312i	0.799496	−	0.600671i	$-0.205100\pi$
$179$	6.35884	+	4.61996i	0.475282	+	0.345312i	−0.324214	+	0.945984i	$0.605100\pi$
$180$		0			0
$181$	2.28446	−	7.03086i	0.169803	−	0.522600i	−0.829555	−	0.558425i	$-0.811406\pi$
$181$	2.28446	−	7.03086i	0.169803	−	0.522600i	0.999358	+	0.0358251i	$0.0114059\pi$
$182$	0.103187	−	0.317578i	0.00764875	−	0.0235404i
$183$	−10.1728	+	7.39101i	−0.751998	+	0.546359i
$184$	0.179023	+	0.130068i	0.0131977	+	0.00958872i
$185$		0			0
$186$	−1.21937			−0.0894089
$187$	−9.01048	+	6.39067i	−0.658912	+	0.467332i
$188$	−10.9229			−0.796635
$189$	−0.151057	−	0.464905i	−0.0109878	−	0.0338168i
$190$		0			0
$191$	0.347665	−	0.252594i	0.0251562	−	0.0182770i	−0.575136	−	0.818058i	$-0.695051\pi$
$191$	0.347665	−	0.252594i	0.0251562	−	0.0182770i	0.600292	+	0.799781i	$0.295051\pi$
$192$	−2.15388	+	6.62896i	−0.155443	+	0.478404i
$193$	−0.602597	+	1.85460i	−0.0433759	+	0.133497i	−0.970399	−	0.241506i	$-0.922359\pi$
$193$	−0.602597	+	1.85460i	−0.0433759	+	0.133497i	0.927023	+	0.375004i	$0.122359\pi$
$194$	−2.76298	+	2.00742i	−0.198370	+	0.144124i
$195$		0			0
$196$	4.08724	+	12.5792i	0.291946	+	0.898517i
$197$	22.2892			1.58804			0.794018	−	0.607894i	$-0.207985\pi$
$197$	22.2892			1.58804			0.794018	+	0.607894i	$0.207985\pi$
$198$	0.693318	+	0.00791269i	0.0492720	+	0.000562331i
$199$	6.45077			0.457283			0.228642	−	0.973511i	$-0.426572\pi$
$199$	6.45077			0.457283			0.228642	+	0.973511i	$0.426572\pi$
$200$		0			0
$201$	7.26153	+	5.27581i	0.512189	+	0.372127i
$202$	−3.01935	+	2.19369i	−0.212441	+	0.154347i
$203$	−0.954062	+	2.93630i	−0.0669620	+	0.206088i
$204$	−2.01351	+	6.19693i	−0.140974	+	0.433872i
$205$		0			0
$206$	2.59395	+	1.88461i	0.180729	+	0.131307i
$207$	0.0826761	+	0.254451i	0.00574638	+	0.0176856i
$208$	−12.2196			−0.847275
$209$	−3.82567	−	12.2481i	−0.264627	−	0.847217i
$210$		0			0
$211$	6.87189	+	21.1495i	0.473080	+	1.45599i	0.848529	+	0.529148i	$0.177488\pi$
$211$	6.87189	+	21.1495i	0.473080	+	1.45599i	−0.375449	+	0.926843i	$0.622512\pi$
$212$	1.80902	+	1.31433i	0.124244	+	0.0902684i
$213$	−4.30067	+	3.12462i	−0.294677	+	0.214095i
$214$	0.377232	−	1.16100i	0.0257871	−	0.0793645i
$215$		0			0
$216$	0.669131	−	0.486152i	0.0455286	−	0.0330784i
$217$	−2.30668	−	1.67590i	−0.156588	−	0.113768i
$218$	0.455629	+	1.40228i	0.0308591	+	0.0949744i
$219$	−9.65885			−0.652685
$220$		0			0
$221$	−10.8832			−0.732085
$222$	−0.484750	−	1.49191i	−0.0325343	−	0.100130i
$223$	11.1449	+	8.09725i	0.746319	+	0.542232i	0.894684	−	0.446700i	$-0.147401\pi$
$223$	11.1449	+	8.09725i	0.746319	+	0.542232i	−0.148365	+	0.988933i	$0.547401\pi$
$224$	0.963364	−	0.699925i	0.0643675	−	0.0467657i
$225$		0			0
$226$	0.878715	−	2.70441i	0.0584512	−	0.179894i
$227$	−20.9174	+	15.1974i	−1.38834	+	1.00869i	−0.392292	+	0.919841i	$0.628318\pi$
$227$	−20.9174	+	15.1974i	−1.38834	+	1.00869i	−0.996045	+	0.0888459i	$0.971682\pi$
$228$	−6.12319	−	4.44876i	−0.405518	−	0.294626i
$229$	4.43103	+	13.6373i	0.292811	+	0.901179i	0.983948	+	0.178455i	$0.0571099\pi$
$229$	4.43103	+	13.6373i	0.292811	+	0.901179i	−0.691137	+	0.722723i	$0.742890\pi$
$230$		0			0
$231$	1.30067	+	0.967862i	0.0855778	+	0.0636806i
$232$	−5.22384			−0.342962
$233$	−1.13203	−	3.48402i	−0.0741616	−	0.228246i	0.907104	−	0.420907i	$-0.138288\pi$
$233$	−1.13203	−	3.48402i	−0.0741616	−	0.228246i	−0.981265	+	0.192661i	$0.938288\pi$
$234$	0.552642	+	0.401518i	0.0361273	+	0.0262480i
$235$		0			0
$236$	2.73091	−	8.40487i	0.177767	−	0.547111i
$237$	−0.466085	+	1.43446i	−0.0302755	+	0.0931784i
$238$	0.275370	−	0.200068i	0.0178496	−	0.0129685i
$239$	−0.872074	−	0.633599i	−0.0564098	−	0.0409841i	0.559223	−	0.829017i	$-0.311100\pi$
$239$	−0.872074	−	0.633599i	−0.0564098	−	0.0409841i	−0.615633	+	0.788033i	$0.711100\pi$
$240$		0			0
$241$	27.1803			1.75084			0.875420	−	0.483363i	$-0.160585\pi$
$241$	27.1803			1.75084			0.875420	+	0.483363i	$0.160585\pi$
$242$	−1.89080	+	1.30887i	−0.121545	+	0.0841376i
$243$	1.00000			0.0641500
$244$	−7.60154	−	23.3951i	−0.486639	−	1.49772i
$245$		0			0
$246$	−0.708267	+	0.514586i	−0.0451575	+	0.0328088i
$247$	3.90652	−	12.0230i	0.248566	−	0.765007i
$248$	1.49076	−	4.58809i	0.0946634	−	0.291344i
$249$	14.2733	−	10.3702i	0.904535	−	0.657183i
$250$		0			0
$251$	−0.803494	−	2.47290i	−0.0507161	−	0.156088i	0.922491	−	0.386019i	$-0.126150\pi$
$251$	−0.803494	−	2.47290i	−0.0507161	−	0.156088i	−0.973207	+	0.229931i	$0.926150\pi$
$252$	0.956295			0.0602409
$253$	−0.711880	−	0.529728i	−0.0447555	−	0.0333037i
$254$	−4.61808			−0.289764
$255$		0			0
$256$	−10.2074	−	7.41612i	−0.637963	−	0.463508i
$257$	4.58990	−	3.33476i	0.286310	−	0.208017i	−0.435355	−	0.900259i	$-0.643377\pi$
$257$	4.58990	−	3.33476i	0.286310	−	0.208017i	0.721665	+	0.692242i	$0.243377\pi$
$258$	0.146425	−	0.450650i	0.00911604	−	0.0280563i
$259$	1.13347	−	3.48846i	0.0704305	−	0.216763i
$260$		0			0
$261$	−5.10969	−	3.71240i	−0.316282	−	0.229792i
$262$	0.250652	+	0.771427i	0.0154853	+	0.0476589i
$263$	23.4448			1.44567			0.722834	−	0.691022i	$-0.242839\pi$
$263$	23.4448			1.44567			0.722834	+	0.691022i	$0.242839\pi$
$264$	−0.877398	+	2.59905i	−0.0540001	+	0.159960i
$265$		0			0
$266$	0.122177	+	0.376023i	0.00749117	+	0.0230554i
$267$	−12.8816	−	9.35906i	−0.788343	−	0.572765i
$268$	−14.2057	+	10.3210i	−0.867751	+	0.630458i
$269$	−1.68846	+	5.19655i	−0.102947	+	0.316839i	−0.989243	−	0.146280i	$-0.953270\pi$
$269$	−1.68846	+	5.19655i	−0.102947	+	0.316839i	0.886296	+	0.463119i	$0.153270\pi$
$270$		0			0
$271$	−2.04131	+	1.48310i	−0.124001	+	0.0900917i	−0.648057	−	0.761592i	$-0.724418\pi$
$271$	−2.04131	+	1.48310i	−0.124001	+	0.0900917i	0.524056	+	0.851684i	$0.324418\pi$
$272$	−10.0769	−	7.32132i	−0.611004	−	0.443920i
$273$	0.493585	+	1.51910i	0.0298731	+	0.0919399i
$274$	1.12185			0.0677735
$275$		0			0
$276$	−0.523398			−0.0315048
$277$	6.92406	+	21.3101i	0.416027	+	1.28040i	0.911329	+	0.411678i	$0.135057\pi$
$277$	6.92406	+	21.3101i	0.416027	+	1.28040i	−0.495303	+	0.868720i	$0.664943\pi$
$278$	−2.13505	−	1.55121i	−0.128052	−	0.0930351i
$279$	4.71878	−	3.42840i	0.282506	−	0.205253i
$280$		0			0
$281$	−3.48542	+	10.7270i	−0.207922	+	0.639920i	0.791658	+	0.610964i	$0.209218\pi$
$281$	−3.48542	+	10.7270i	−0.207922	+	0.639920i	−0.999581	+	0.0289554i	$0.990782\pi$
$282$	−0.944335	+	0.686100i	−0.0562343	+	0.0408566i
$283$	−9.45942	−	6.87267i	−0.562304	−	0.408538i	0.269997	−	0.962861i	$-0.412977\pi$
$283$	−9.45942	−	6.87267i	−0.562304	−	0.408538i	−0.832302	+	0.554323i	$0.812977\pi$
$284$	−3.21363	−	9.89052i	−0.190694	−	0.586894i
$285$		0			0
$286$	−2.26545	−	0.0258551i	−0.133959	−	0.00152884i
$287$	−2.04707			−0.120835
$288$	0.752762	+	2.31676i	0.0443569	+	0.136517i
$289$	4.77839	+	3.47170i	0.281081	+	0.204218i
$290$		0			0
$291$	5.04821	−	15.5368i	0.295931	−	0.910783i
$292$	5.83905	−	17.9708i	0.341705	−	1.05166i
$293$	−10.9151	+	7.93028i	−0.637666	+	0.463292i	−0.859048	−	0.511896i	$-0.828943\pi$
$293$	−10.9151	+	7.93028i	−0.637666	+	0.463292i	0.221381	+	0.975187i	$0.428943\pi$
$294$	1.14350	+	0.830801i	0.0666903	+	0.0484533i
$295$		0			0
$296$	6.20617			0.360726
$297$	−2.70528	+	1.91872i	−0.156976	+	0.111335i
$298$	−0.982456			−0.0569121
$299$	−0.270148	−	0.831429i	−0.0156231	−	0.0480828i
$300$		0			0
$301$	0.896364	−	0.651246i	0.0516655	−	0.0375372i
$302$	0.941333	−	2.89713i	0.0541676	−	0.166711i
$303$	5.51663	−	16.9784i	0.316922	−	0.975386i
$304$	11.7052	−	8.50431i	0.671338	−	0.487756i
$305$		0			0
$306$	0.215171	+	0.662227i	0.0123005	+	0.0378570i
$307$	0.364626			0.0208103			0.0104052	−	0.999946i	$-0.496688\pi$
$307$	0.364626			0.0208103			0.0104052	+	0.999946i	$0.496688\pi$
$308$	−2.58704	+	1.83486i	−0.147411	+	0.104551i
$309$	−15.3370			−0.872489
$310$		0			0
$311$	−18.8131	−	13.6685i	−1.06679	−	0.775069i	−0.0914579	−	0.995809i	$-0.529153\pi$
$311$	−18.8131	−	13.6685i	−1.06679	−	0.775069i	−0.975333	+	0.220740i	$0.929153\pi$
$312$	−2.18641	+	1.58852i	−0.123781	+	0.0899324i
$313$	3.78010	−	11.6339i	0.213664	−	0.657589i	−0.785582	−	0.618757i	$-0.787636\pi$
$313$	3.78010	−	11.6339i	0.213664	−	0.657589i	0.999246	−	0.0388317i	$-0.0123636\pi$
$314$	−0.0215897	+	0.0664461i	−0.00121838	+	0.00374977i
$315$		0			0
$316$	−2.38712	−	1.73435i	−0.134286	−	0.0975647i
$317$	−9.89399	−	30.4506i	−0.555702	−	1.71027i	−0.694083	−	0.719895i	$-0.744190\pi$
$317$	−9.89399	−	30.4506i	−0.555702	−	1.71027i	0.138382	−	0.990379i	$-0.455810\pi$
$318$	0.238954			0.0133999
$319$	20.9462	+	0.239054i	1.17276	+	0.0133845i
$320$		0			0
$321$	1.80445	+	5.55352i	0.100714	+	0.309967i
$322$	0.0221196	+	0.0160708i	0.00123268	+	0.000895592i
$323$	10.4251	−	7.57427i	0.580067	−	0.421444i
$324$	−0.604528	+	1.86055i	−0.0335849	+	0.103364i
$325$		0			0
$326$	0.336460	−	0.244453i	0.0186348	−	0.0135390i
$327$	−5.70587	−	4.14556i	−0.315535	−	0.229250i
$328$	−1.07031	−	3.29408i	−0.0590981	−	0.181885i
$329$	−2.72936			−0.150475
$330$		0			0
$331$	−20.5705			−1.13066			−0.565328	−	0.824867i	$-0.691250\pi$
$331$	−20.5705			−1.13066			−0.565328	+	0.824867i	$0.691250\pi$
$332$	10.6656	+	32.8253i	0.585350	+	1.80152i
$333$	6.07055	+	4.41051i	0.332664	+	0.241695i
$334$	−3.25276	+	2.36327i	−0.177983	+	0.129312i
$335$		0			0
$336$	−0.564904	+	1.73860i	−0.0308180	+	0.0948482i
$337$	18.0768	−	13.1336i	0.984707	−	0.715432i	0.0259516	−	0.999663i	$-0.491738\pi$
$337$	18.0768	−	13.1336i	0.984707	−	0.715432i	0.958756	+	0.284231i	$0.0917384\pi$
$338$	0.392915	+	0.285470i	0.0213718	+	0.0155275i
$339$	4.20323	+	12.9362i	0.228288	+	0.702599i
$340$		0			0
$341$	−6.18751	+	18.3288i	−0.335072	+	0.992559i
$342$	−0.808817			−0.0437358
$343$	2.07870	+	6.39757i	0.112239	+	0.345437i
$344$	1.51663	+	1.10190i	0.0817712	+	0.0594103i
$345$		0			0
$346$	−0.902575	+	2.77784i	−0.0485227	+	0.149338i
$347$	7.41805	−	22.8304i	0.398222	−	1.22560i	−0.528202	−	0.849119i	$-0.677134\pi$
$347$	7.41805	−	22.8304i	0.398222	−	1.22560i	0.926424	−	0.376482i	$-0.122866\pi$
$348$	9.99606	−	7.26256i	0.535845	−	0.389314i
$349$	−11.0256	−	8.01054i	−0.590185	−	0.428795i	0.252196	−	0.967676i	$-0.418847\pi$
$349$	−11.0256	−	8.01054i	−0.590185	−	0.428795i	−0.842382	+	0.538881i	$0.818847\pi$
$350$		0			0
$351$	−3.26755			−0.174409
$352$	−6.48164	−	4.82315i	−0.345472	−	0.257075i
$353$	31.4058			1.67156			0.835780	−	0.549065i	$-0.185016\pi$
$353$	31.4058			1.67156			0.835780	+	0.549065i	$0.185016\pi$
$354$	−0.291835	−	0.898176i	−0.0155109	−	0.0477375i
$355$		0			0
$356$	25.2003	−	18.3091i	1.33561	−	0.970379i
$357$	−0.503125	+	1.54846i	−0.0266282	+	0.0819532i
$358$	−0.507770	+	1.56275i	−0.0268365	+	0.0825942i
$359$	−2.32476	+	1.68903i	−0.122696	+	0.0891438i	−0.647441	−	0.762116i	$-0.724161\pi$
$359$	−2.32476	+	1.68903i	−0.122696	+	0.0891438i	0.524745	+	0.851260i	$0.324161\pi$
$360$		0			0
$361$	−1.24587	−	3.83440i	−0.0655722	−	0.201810i
$362$	1.54549			0.0812292
$363$	3.63706	−	10.3813i	0.190896	−	0.544878i
$364$	−3.12474			−0.163781
$365$		0			0
$366$	−2.12670	−	1.54514i	−0.111165	−	0.0807658i
$367$	19.4659	−	14.1428i	1.01611	−	0.738247i	0.0506278	−	0.998718i	$-0.483878\pi$
$367$	19.4659	−	14.1428i	1.01611	−	0.738247i	0.965482	+	0.260471i	$0.0838778\pi$
$368$	0.309182	−	0.951565i	0.0161172	−	0.0496037i
$369$	1.29407	−	3.98273i	0.0673665	−	0.207333i
$370$		0			0
$371$	0.452029	+	0.328418i	0.0234682	+	0.0170506i
$372$	3.52606	+	10.8521i	0.182817	+	0.562654i
$373$	−17.5348			−0.907915			−0.453958	−	0.891023i	$-0.649988\pi$
$373$	−17.5348			−0.907915			−0.453958	+	0.891023i	$0.649988\pi$
$374$	−1.85272	−	1.37866i	−0.0958020	−	0.0712887i
$375$		0			0
$376$	−1.42705	−	4.39201i	−0.0735945	−	0.226501i
$377$	16.6961	+	12.1305i	0.859895	+	0.624750i
$378$	0.0826761	−	0.0600677i	0.00425240	−	0.00308955i
$379$	−10.0861	+	31.0419i	−0.518089	+	1.59451i	0.259502	+	0.965743i	$0.416442\pi$
$379$	−10.0861	+	31.0419i	−0.518089	+	1.59451i	−0.777591	+	0.628771i	$0.783558\pi$
$380$		0			0
$381$	17.8712	−	12.9842i	0.915570	−	0.665201i
$382$	0.0726818	+	0.0528064i	0.00371873	+	0.00270181i
$383$	−3.24984	−	10.0020i	−0.166059	−	0.511077i	0.833054	−	0.553192i	$-0.186590\pi$
$383$	−3.24984	−	10.0020i	−0.166059	−	0.511077i	−0.999113	+	0.0421152i	$0.986590\pi$
$384$	−6.32912			−0.322982
$385$		0			0
$386$	−0.407670			−0.0207499
$387$	0.700408	+	2.15564i	0.0356038	+	0.109577i
$388$	25.8552	+	18.7849i	1.31260	+	0.953657i
$389$	−18.8879	+	13.7229i	−0.957655	+	0.695777i	−0.952605	−	0.304210i	$-0.901607\pi$
$389$	−18.8879	+	13.7229i	−0.957655	+	0.695777i	−0.00504999	+	0.999987i	$0.501607\pi$
$390$		0			0
$391$	0.275370	−	0.847500i	0.0139260	−	0.0428599i
$392$	−4.52402	+	3.28689i	−0.228498	+	0.166013i
$393$	−3.13893	−	2.28057i	−0.158338	−	0.115039i
$394$	1.43993	+	4.43164i	0.0725425	+	0.223263i
$395$		0			0
$396$	−1.93444	−	6.19322i	−0.0972094	−	0.311221i
$397$	−7.04740			−0.353699			−0.176849	−	0.984238i	$-0.556591\pi$
$397$	−7.04740			−0.353699			−0.176849	+	0.984238i	$0.556591\pi$
$398$	0.416734	+	1.28257i	0.0208890	+	0.0642896i
$399$	−1.53003	−	1.11163i	−0.0765975	−	0.0556514i
$400$		0			0
$401$	6.94190	−	21.3650i	0.346662	−	1.06692i	−0.614026	−	0.789286i	$-0.710451\pi$
$401$	6.94190	−	21.3650i	0.346662	−	1.06692i	0.960688	−	0.277630i	$-0.0895489\pi$
$402$	−0.579853	+	1.78460i	−0.0289204	+	0.0890079i
$403$	−15.4188	+	11.2024i	−0.768067	+	0.558033i
$404$	28.2542	+	20.5279i	1.40570	+	1.02130i
$405$		0			0
$406$	−0.645444			−0.0320329
$407$	−24.8850	−	0.284008i	−1.23351	−	0.0140777i
$408$	−2.75480			−0.136383
$409$	0.314944	+	0.969299i	0.0155730	+	0.0479287i	0.958541	−	0.284955i	$-0.0919785\pi$
$409$	0.314944	+	0.969299i	0.0155730	+	0.0479287i	−0.942968	+	0.332883i	$0.891978\pi$
$410$		0			0
$411$	−4.34139	+	3.15420i	−0.214145	+	0.155585i
$412$	9.27163	−	28.5351i	0.456780	−	1.40582i
$413$	0.682387	−	2.10017i	0.0335780	−	0.103343i
$414$	−0.0452501	+	0.0328761i	−0.00222392	+	0.00161577i
$415$		0			0
$416$	−2.45968	−	7.57013i	−0.120596	−	0.371156i
$417$	12.6237			0.618184
$418$	2.18808	−	1.55189i	0.107022	−	0.0759054i
$419$	7.54074			0.368389			0.184195	−	0.982890i	$-0.441032\pi$
$419$	7.54074			0.368389			0.184195	+	0.982890i	$0.441032\pi$
$420$		0			0
$421$	−9.51285	−	6.91149i	−0.463628	−	0.336845i	0.331325	−	0.943517i	$-0.392504\pi$
$421$	−9.51285	−	6.91149i	−0.463628	−	0.336845i	−0.794953	+	0.606671i	$0.792504\pi$
$422$	−3.76111	+	2.73261i	−0.183088	+	0.133021i
$423$	1.72539	−	5.31019i	0.0838911	−	0.258190i
$424$	−0.292137	+	0.899105i	−0.0141874	+	0.0436644i
$425$		0			0
$426$	−0.899085	−	0.653223i	−0.0435608	−	0.0316488i
$427$	−1.89944	−	5.84586i	−0.0919202	−	0.282901i
$428$	−11.4234			−0.552172
$429$	8.83962	−	6.26949i	0.426781	−	0.302694i
$430$		0			0
$431$	−8.35910	−	25.7267i	−0.402643	−	1.23921i	−0.922847	−	0.385167i	$-0.874144\pi$
$431$	−8.35910	−	25.7267i	−0.402643	−	1.23921i	0.520204	−	0.854042i	$-0.325856\pi$
$432$	−3.02547	−	2.19813i	−0.145563	−	0.105758i
$433$	−20.7678	+	15.0887i	−0.998037	+	0.725116i	−0.961666	−	0.274222i	$-0.911580\pi$
$433$	−20.7678	+	15.0887i	−0.998037	+	0.725116i	−0.0363706	+	0.999338i	$0.511580\pi$
$434$	0.184195	−	0.566893i	0.00884163	−	0.0272117i
$435$		0			0
$436$	11.1624	−	8.10993i	0.534580	−	0.388395i
$437$	0.837415	+	0.608418i	0.0400590	+	0.0291046i
$438$	−0.623983	−	1.92042i	−0.0298150	−	0.0917613i
$439$	0.512954			0.0244820			0.0122410	−	0.999925i	$-0.496103\pi$
$439$	0.512954			0.0244820			0.0122410	+	0.999925i	$0.496103\pi$
$440$		0			0
$441$	−6.76105			−0.321955
$442$	−0.703080	−	2.16386i	−0.0334421	−	0.102924i
$443$	−26.9133	−	19.5537i	−1.27869	−	0.929023i	−0.279178	−	0.960239i	$-0.590062\pi$
$443$	−26.9133	−	19.5537i	−1.27869	−	0.929023i	−0.999513	+	0.0312166i	$0.990062\pi$
$444$	−11.8758	+	8.62827i	−0.563600	+	0.409479i
$445$		0			0
$446$	−0.889951	+	2.73899i	−0.0421404	+	0.129695i
$447$	3.80195	−	2.76228i	0.179826	−	0.130651i
$448$	−2.75648	−	2.00270i	−0.130231	−	0.0946186i
$449$	1.84125	+	5.66678i	0.0868939	+	0.267432i	0.985057	−	0.172231i	$-0.0550977\pi$
$449$	1.84125	+	5.66678i	0.0868939	+	0.267432i	−0.898163	+	0.439664i	$0.855098\pi$
$450$		0			0
$451$	4.14091	+	13.2573i	0.194988	+	0.624264i
$452$	−26.6094			−1.25160
$453$	4.50276	+	13.8581i	0.211558	+	0.651109i
$454$	−4.37293	−	3.17712i	−0.205232	−	0.149110i
$455$		0			0
$456$	0.988830	−	3.04330i	0.0463062	−	0.142516i
$457$	−6.32451	+	19.4648i	−0.295848	+	0.910526i	0.687087	+	0.726575i	$0.258889\pi$
$457$	−6.32451	+	19.4648i	−0.295848	+	0.910526i	−0.982935	+	0.183951i	$0.941111\pi$
$458$	−2.42518	+	1.76200i	−0.113321	+	0.0823328i
$459$	−2.69460	−	1.95774i	−0.125773	−	0.0913794i
$460$		0			0
$461$	31.1778			1.45210			0.726048	−	0.687644i	$-0.241355\pi$
$461$	31.1778			1.45210			0.726048	+	0.687644i	$0.241355\pi$
$462$	−0.108409	+	0.321132i	−0.00504364	+	0.0149404i
$463$	−10.9989			−0.511164			−0.255582	−	0.966787i	$-0.582267\pi$
$463$	−10.9989			−0.511164			−0.255582	+	0.966787i	$0.582267\pi$
$464$	7.29884	+	22.4635i	0.338840	+	1.04284i
$465$		0			0
$466$	0.619579	−	0.450151i	0.0287015	−	0.0208528i
$467$	10.9410	−	33.6731i	0.506291	−	1.55820i	−0.292298	−	0.956327i	$-0.594420\pi$
$467$	10.9410	−	33.6731i	0.506291	−	1.55820i	0.798589	−	0.601877i	$-0.205580\pi$
$468$	1.97532	−	6.07942i	0.0913094	−	0.281021i
$469$	−3.54965	+	2.57897i	−0.163908	+	0.119086i
$470$		0			0
$471$	−0.103272	−	0.317838i	−0.00475851	−	0.0146452i
$472$	3.73632			0.171978
$473$	−6.03085	−	4.48771i	−0.277299	−	0.206345i
$474$	−0.315317			−0.0144830
$475$		0			0
$476$	−2.57683	−	1.87218i	−0.118109	−	0.0858111i
$477$	−0.924716	+	0.671845i	−0.0423398	+	0.0307617i
$478$	0.0696374	−	0.214322i	0.00318514	−	0.00980285i
$479$	5.98925	−	18.4330i	0.273656	−	0.842227i	−0.715916	−	0.698187i	$-0.753991\pi$
$479$	5.98925	−	18.4330i	0.273656	−	0.842227i	0.989572	−	0.144040i	$-0.0460094\pi$
$480$		0			0
$481$	−19.8358	−	14.4116i	−0.904435	−	0.657110i
$482$	1.75591	+	5.40413i	0.0799794	+	0.246151i
$483$	−0.130784			−0.00595088
$484$	17.1162	+	13.0427i	0.778010	+	0.592851i
$485$		0			0
$486$	0.0646021	+	0.198825i	0.00293041	+	0.00901888i
$487$	−13.2275	−	9.61031i	−0.599393	−	0.435485i	0.246270	−	0.969201i	$-0.420795\pi$
$487$	−13.2275	−	9.61031i	−0.599393	−	0.435485i	−0.845663	+	0.533717i	$0.820795\pi$
$488$	8.41387	−	6.11303i	0.380878	−	0.276724i
$489$	−0.614744	+	1.89199i	−0.0277997	+	0.0855586i
$490$		0			0
$491$	11.1527	−	8.10291i	0.503314	−	0.365679i	−0.306967	−	0.951720i	$-0.599314\pi$
$491$	11.1527	−	8.10291i	0.503314	−	0.365679i	0.810282	+	0.586041i	$0.199314\pi$
$492$	6.62776	+	4.81535i	0.298803	+	0.217093i
$493$	6.50062	+	20.0069i	0.292773	+	0.901064i
$494$	2.64285			0.118907
$495$		0			0
$496$	−21.8126			−0.979414
$497$	−0.803005	−	2.47140i	−0.0360197	−	0.110857i
$498$	2.98394	+	2.16796i	0.133713	+	0.0971485i
$499$	−16.0046	+	11.6280i	−0.716465	+	0.520542i	−0.885253	−	0.465110i	$-0.846015\pi$
$499$	−16.0046	+	11.6280i	−0.716465	+	0.520542i	0.168788	+	0.985652i	$0.446015\pi$
$500$		0			0
$501$	5.94309	−	18.2910i	0.265518	−	0.817180i
$502$	0.439767	−	0.319509i	0.0196277	−	0.0142604i
$503$	−9.71852	−	7.06092i	−0.433327	−	0.314831i	0.349651	−	0.936880i	$-0.386300\pi$
$503$	−9.71852	−	7.06092i	−0.433327	−	0.314831i	−0.782978	+	0.622049i	$0.786300\pi$
$504$	0.124938	+	0.384518i	0.00556516	+	0.0171278i
$505$		0			0
$506$	0.0593342	−	0.175761i	0.00263773	−	0.00781354i
$507$	−2.32315			−0.103175
$508$	13.3541	+	41.0996i	0.592491	+	1.82350i
$509$	6.45678	+	4.69113i	0.286192	+	0.207931i	0.721614	−	0.692296i	$-0.243401\pi$
$509$	6.45678	+	4.69113i	0.286192	+	0.207931i	−0.435422	+	0.900227i	$0.643401\pi$
$510$		0			0
$511$	1.45903	−	4.49045i	0.0645439	−	0.198646i
$512$	4.72670	−	14.5473i	0.208893	−	0.642906i
$513$	3.12999	−	2.27407i	0.138193	−	0.100403i
$514$	0.959551	+	0.697155i	0.0423240	+	0.0307502i
$515$		0			0
$516$	−4.43408			−0.195199
$517$	5.52110	+	17.6761i	0.242818	+	0.777393i
$518$	0.766819			0.0336921
$519$	−4.31736	−	13.2875i	−0.189511	−	0.583256i
$520$		0			0
$521$	35.9546	−	26.1226i	1.57520	−	1.14445i	0.653250	−	0.757142i	$-0.273405\pi$
$521$	35.9546	−	26.1226i	1.57520	−	1.14445i	0.921951	−	0.387308i	$-0.126595\pi$
$522$	0.408022	−	1.25576i	0.0178586	−	0.0549632i
$523$	3.72695	−	11.4704i	0.162968	−	0.501565i	−0.835913	−	0.548863i	$-0.815061\pi$
$523$	3.72695	−	11.4704i	0.162968	−	0.501565i	0.998881	+	0.0472979i	$0.0150610\pi$
$524$	6.14068	−	4.46146i	0.268257	−	0.194900i
$525$		0			0
$526$	1.51458	+	4.66141i	0.0660390	+	0.203247i
$527$	−19.4271			−0.846259
$528$	12.4023	+	0.141545i	0.539741	+	0.00615995i
$529$	−22.9284			−0.996888
$530$		0			0
$531$	3.65467	+	2.65527i	0.158599	+	0.115229i
$532$	2.99320	−	2.17469i	0.129772	−	0.0942846i
$533$	−4.22843	+	13.0138i	−0.183153	+	0.563688i
$534$	1.02863	−	3.16581i	0.0445133	−	0.136998i
$535$		0			0
$536$	−6.00595	−	4.36358i	−0.259417	−	0.188478i
$537$	−2.42886	−	7.47526i	−0.104813	−	0.322581i
$538$	−1.14228			−0.0492473
$539$	18.2905	−	12.9725i	0.787828	−	0.558766i
$540$		0			0
$541$	11.6805	+	35.9490i	0.502185	+	1.54557i	0.805452	+	0.592661i	$0.201923\pi$
$541$	11.6805	+	35.9490i	0.502185	+	1.54557i	−0.303267	+	0.952906i	$0.598077\pi$
$542$	−0.426749	−	0.310051i	−0.0183305	−	0.0133179i
$543$	−5.98081	+	4.34531i	−0.256661	+	0.186475i
$544$	2.50723	−	7.71645i	0.107496	−	0.330840i
$545$		0			0
$546$	−0.270148	+	0.196274i	−0.0115613	+	0.00839975i
$547$	−12.0874	−	8.78201i	−0.516820	−	0.375492i	0.298585	−	0.954383i	$-0.403485\pi$
$547$	−12.0874	−	8.78201i	−0.516820	−	0.375492i	−0.815405	+	0.578891i	$0.803485\pi$
$548$	−3.24405	−	9.98416i	−0.138579	−	0.426502i
$549$	12.5743			0.536659
$550$		0			0
$551$	−24.4356			−1.04099
$552$	−0.0683806	−	0.210454i	−0.00291047	−	0.00895751i
$553$	−0.596483	−	0.433370i	−0.0253651	−	0.0184288i
$554$	−3.78966	+	2.75335i	−0.161007	+	0.116979i
$555$		0			0
$556$	−7.63137	+	23.4870i	−0.323642	+	0.996069i
$557$	5.90631	−	4.29119i	0.250258	−	0.181823i	−0.455583	−	0.890193i	$-0.650569\pi$
$557$	5.90631	−	4.29119i	0.250258	−	0.181823i	0.705841	+	0.708370i	$0.250569\pi$
$558$	0.986494	+	0.716730i	0.0417616	+	0.0303416i
$559$	−2.28862	−	7.04364i	−0.0967981	−	0.297914i
$560$		0			0
$561$	11.0460	+	0.126065i	0.466362	+	0.00532248i
$562$	−2.35796			−0.0994646
$563$	−7.21369	−	22.2015i	−0.304021	−	0.935680i	−0.980041	−	0.198796i	$-0.936297\pi$
$563$	−7.21369	−	22.2015i	−0.304021	−	0.935680i	0.676020	−	0.736883i	$-0.263703\pi$
$564$	8.83682	+	6.42032i	0.372097	+	0.270344i
$565$		0			0
$566$	0.755360	−	2.32476i	0.0317501	−	0.0977169i
$567$	−0.151057	+	0.464905i	−0.00634378	+	0.0195242i
$568$	3.55705	−	2.58434i	0.149250	−	0.108437i
$569$	−35.9382	−	26.1106i	−1.50661	−	1.09461i	−0.967655	−	0.252275i	$-0.918821\pi$
$569$	−35.9382	−	26.1106i	−1.50661	−	1.09461i	−0.538950	−	0.842338i	$-0.681179\pi$
$570$		0			0
$571$	−0.347203			−0.0145300			−0.00726499	−	0.999974i	$-0.502313\pi$
$571$	−0.347203			−0.0145300			−0.00726499	+	0.999974i	$0.502313\pi$
$572$	6.32088	+	20.2366i	0.264289	+	0.846135i
$573$	−0.429738			−0.0179526
$574$	−0.132245	−	0.407008i	−0.00551980	−	0.0169882i
$575$		0			0
$576$	5.63893	−	4.09692i	0.234955	−	0.170705i
$577$	−3.07272	+	9.45687i	−0.127919	+	0.393695i	−0.994422	−	0.105478i	$-0.966363\pi$
$577$	−3.07272	+	9.45687i	−0.127919	+	0.393695i	0.866502	+	0.499173i	$0.166363\pi$
$578$	−0.381567	+	1.17434i	−0.0158711	+	0.0488462i
$579$	1.57762	−	1.14621i	0.0655636	−	0.0476348i
$580$		0			0
$581$	2.66506	+	8.20222i	0.110565	+	0.340286i
$582$	3.41523			0.141566
$583$	1.21253	−	3.59179i	0.0502180	−	0.148757i
$584$	7.98875			0.330577
$585$		0			0
$586$	−2.28188	−	1.65788i	−0.0942634	−	0.0684864i
$587$	−6.53190	+	4.74570i	−0.269600	+	0.195876i	−0.714369	−	0.699769i	$-0.753286\pi$
$587$	−6.53190	+	4.74570i	−0.269600	+	0.195876i	0.444768	+	0.895646i	$0.353286\pi$
$588$	4.08724	−	12.5792i	0.168555	−	0.518759i
$589$	6.97334	−	21.4617i	0.287331	−	0.884315i
$590$		0			0
$591$	−18.0323	−	13.1012i	−0.741750	−	0.538913i
$592$	−8.67136	−	26.6877i	−0.356391	−	1.09686i
$593$	25.5393			1.04877			0.524387	−	0.851480i	$-0.324295\pi$
$593$	25.5393			1.04877			0.524387	+	0.851480i	$0.324295\pi$
$594$	−0.556255	−	0.413924i	−0.0228234	−	0.0169835i
$595$		0			0
$596$	2.84096	+	8.74358i	0.116370	+	0.358151i
$597$	−5.21878	−	3.79167i	−0.213591	−	0.155183i
$598$	0.147857	−	0.107424i	0.00604631	−	0.00439290i
$599$	1.16548	−	3.58696i	0.0476200	−	0.146559i	−0.924419	−	0.381378i	$-0.875450\pi$
$599$	1.16548	−	3.58696i	0.0476200	−	0.146559i	0.972039	+	0.234819i	$0.0754496\pi$
$600$		0			0
$601$	−2.00687	+	1.45808i	−0.0818619	+	0.0594762i	−0.627963	−	0.778243i	$-0.716111\pi$
$601$	−2.00687	+	1.45808i	−0.0818619	+	0.0594762i	0.546102	+	0.837719i	$0.316111\pi$
$602$	0.187391	+	0.136148i	0.00763749	+	0.00554896i
$603$	−2.77366	−	8.53644i	−0.112952	−	0.347631i
$604$	−28.5056			−1.15988
$605$		0			0
$606$	3.73212			0.151607
$607$	2.30075	+	7.08097i	0.0933844	+	0.287408i	0.986829	−	0.161765i	$-0.0517187\pi$
$607$	2.30075	+	7.08097i	0.0933844	+	0.287408i	−0.893445	+	0.449173i	$0.851719\pi$
$608$	7.62463	+	5.53962i	0.309220	+	0.224661i
$609$	2.49777	−	1.81473i	0.101215	−	0.0735367i
$610$		0			0
$611$	−5.63778	+	17.3513i	−0.228080	+	0.701958i
$612$	5.27143	−	3.82992i	0.213085	−	0.154815i
$613$	−23.4182	−	17.0143i	−0.945850	−	0.687200i	0.00397148	−	0.999992i	$-0.498736\pi$
$613$	−23.4182	−	17.0143i	−0.945850	−	0.687200i	−0.949822	+	0.312792i	$0.898736\pi$
$614$	0.0235556	+	0.0724968i	0.000950628	+	0.00292573i
$615$		0			0
$616$	−1.07577	−	0.800510i	−0.0433441	−	0.0322535i
$617$	18.7581			0.755172			0.377586	−	0.925975i	$-0.376754\pi$
$617$	18.7581			0.755172			0.377586	+	0.925975i	$0.376754\pi$
$618$	−0.990800	−	3.04937i	−0.0398558	−	0.122664i
$619$	23.8216	+	17.3074i	0.957469	+	0.695642i	0.952562	−	0.304346i	$-0.0984378\pi$
$619$	23.8216	+	17.3074i	0.957469	+	0.695642i	0.00490772	+	0.999988i	$0.498438\pi$
$620$		0			0
$621$	0.0826761	−	0.254451i	0.00331768	−	0.0102108i
$622$	1.50227	−	4.62352i	0.0602356	−	0.185386i
$623$	6.29693	−	4.57498i	0.252281	−	0.183293i
$624$	9.88585	+	7.18249i	0.395751	+	0.287530i
$625$		0			0
$626$	2.55732			0.102211
$627$	−4.10421	+	12.1576i	−0.163906	+	0.485527i
$628$	0.653783			0.0260888
$629$	−7.72305	−	23.7691i	−0.307938	−	0.947736i
$630$		0			0
$631$	−32.8831	+	23.8909i	−1.30905	+	0.951083i	−0.309054	+	0.951045i	$0.600012\pi$
$631$	−32.8831	+	23.8909i	−1.30905	+	0.951083i	−1.00000		3.86441e-5i	$0.999988\pi$
$632$	0.385495	−	1.18643i	0.0153342	−	0.0471937i
$633$	6.87189	−	21.1495i	0.273133	−	0.840617i
$634$	5.41516	−	3.93434i	0.215063	−	0.156253i
$635$		0			0
$636$	−0.690983	−	2.12663i	−0.0273993	−	0.0843262i
$637$	22.0920			0.875318
$638$	1.30564	+	4.18007i	0.0516907	+	0.165490i
$639$	5.31592			0.210295
$640$		0			0
$641$	−18.5238	−	13.4583i	−0.731647	−	0.531573i	0.158437	−	0.987369i	$-0.449355\pi$
$641$	−18.5238	−	13.4583i	−0.731647	−	0.531573i	−0.890084	+	0.455796i	$0.849355\pi$
$642$	−0.987607	+	0.717539i	−0.0389778	+	0.0283190i
$643$	−9.41068	+	28.9631i	−0.371121	+	1.14219i	0.574938	+	0.818197i	$0.305026\pi$
$643$	−9.41068	+	28.9631i	−0.371121	+	1.14219i	−0.946059	+	0.323996i	$0.894974\pi$
$644$	0.0790627	−	0.243330i	0.00311551	−	0.00958855i
$645$		0			0
$646$	2.17944	+	1.58345i	0.0857488	+	0.0623001i
$647$	4.45002	+	13.6958i	0.174948	+	0.538436i	0.999631	−	0.0271599i	$-0.00864632\pi$
$647$	4.45002	+	13.6958i	0.174948	+	0.538436i	−0.824683	+	0.565596i	$0.808646\pi$
$648$	−0.827091			−0.0324912
$649$	−14.9816	−	0.170982i	−0.588080	−	0.00671163i
$650$		0			0
$651$	0.881074	+	2.71167i	0.0345320	+	0.106279i
$652$	−3.14850	−	2.28752i	−0.123305	−	0.0895862i
$653$	24.5284	−	17.8209i	0.959870	−	0.697386i	0.00674955	−	0.999977i	$-0.497852\pi$
$653$	24.5284	−	17.8209i	0.959870	−	0.697386i	0.953121	+	0.302591i	$0.0978515\pi$
$654$	0.455629	−	1.40228i	0.0178165	−	0.0548335i
$655$		0			0
$656$	−12.6697	+	9.20509i	−0.494669	+	0.359398i
$657$	7.81418	+	5.67733i	0.304860	+	0.221494i
$658$	−0.176323	−	0.542666i	−0.00687378	−	0.0211553i
$659$	−25.8802			−1.00815			−0.504076	−	0.863659i	$-0.668167\pi$
$659$	−25.8802			−1.00815			−0.504076	+	0.863659i	$0.668167\pi$
$660$		0			0
$661$	−9.41852			−0.366338			−0.183169	−	0.983081i	$-0.558636\pi$
$661$	−9.41852			−0.366338			−0.183169	+	0.983081i	$0.558636\pi$
$662$	−1.32890	−	4.08992i	−0.0516490	−	0.158959i
$663$	8.80472	+	6.39700i	0.341947	+	0.248439i
$664$	−11.8053	+	8.57708i	−0.458136	+	0.332855i
$665$		0			0
$666$	−0.484750	+	1.49191i	−0.0187837	+	0.0578102i
$667$	−1.36707	+	0.993237i	−0.0529333	+	0.0384583i
$668$	30.4384	+	22.1148i	1.17770	+	0.855648i
$669$	−4.25698	−	13.1016i	−0.164584	−	0.506538i
$670$		0			0
$671$	−34.0171	+	24.1266i	−1.31321	+	0.931395i
$672$	−1.19078			−0.0459355
$673$	−4.11793	−	12.6737i	−0.158735	−	0.488535i	0.839786	−	0.542918i	$-0.182681\pi$
$673$	−4.11793	−	12.6737i	−0.158735	−	0.488535i	−0.998520	+	0.0543834i	$0.982681\pi$
$674$	3.77908	+	2.74567i	0.145565	+	0.105759i
$675$		0			0
$676$	1.40441	−	4.32233i	0.0540157	−	0.166243i
$677$	−1.56990	+	4.83165i	−0.0603361	+	0.185695i	−0.976682	−	0.214693i	$-0.931125\pi$
$677$	−1.56990	+	4.83165i	−0.0603361	+	0.185695i	0.916345	+	0.400389i	$0.131125\pi$
$678$	−2.30050	+	1.67141i	−0.0883504	+	0.0641903i
$679$	6.46056	+	4.69387i	0.247934	+	0.180134i
$680$		0			0
$681$	25.8554			0.990779
$682$	−4.04394	−	0.0461527i	−0.154851	−	0.00176728i
$683$	−19.0765			−0.729942			−0.364971	−	0.931019i	$-0.618921\pi$
$683$	−19.0765			−0.729942			−0.364971	+	0.931019i	$0.618921\pi$
$684$	2.33885	+	7.19824i	0.0894282	+	0.275232i
$685$		0			0
$686$	−1.13771	+	0.826594i	−0.0434379	+	0.0315595i
$687$	4.43103	−	13.6373i	0.169054	−	0.520296i
$688$	2.61930	−	8.06139i	0.0998600	−	0.307338i
$689$	3.02155	−	2.19529i	0.115112	−	0.0836337i
$690$		0			0
$691$	2.68811	+	8.27315i	0.102261	+	0.314725i	0.989078	−	0.147395i	$-0.0470888\pi$
$691$	2.68811	+	8.27315i	0.102261	+	0.314725i	−0.886817	+	0.462120i	$0.847089\pi$
$692$	27.3320			1.03900
$693$	−0.483369	−	1.54753i	−0.0183617	−	0.0587859i
$694$	5.01848			0.190499
$695$		0			0
$696$	4.22618	+	3.07050i	0.160193	+	0.116387i
$697$	−11.2841	+	8.19841i	−0.427417	+	0.310537i
$698$	0.880421	−	2.70966i	0.0333244	−	0.102562i
$699$	−1.13203	+	3.48402i	−0.0428172	+	0.131778i
$700$		0			0
$701$	32.5986	+	23.6843i	1.23123	+	0.894543i	0.996982	−	0.0776334i	$-0.0247364\pi$
$701$	32.5986	+	23.6843i	1.23123	+	0.894543i	0.234251	+	0.972176i	$0.424736\pi$
$702$	−0.211090	−	0.649670i	−0.00796709	−	0.0245202i
$703$	29.0306			1.09491
$704$	−7.39405	+	21.9028i	−0.278674	+	0.825494i
$705$		0			0
$706$	2.02888	+	6.24425i	0.0763579	+	0.235005i
$707$	7.06003	+	5.12941i	0.265520	+	0.192911i
$708$	−7.14961	+	5.19450i	−0.268699	+	0.195221i
$709$	7.32270	−	22.5370i	0.275010	−	0.846393i	−0.714207	−	0.699935i	$-0.753212\pi$
$709$	7.32270	−	22.5370i	0.275010	−	0.846393i	0.989217	−	0.146459i	$-0.0467875\pi$
$710$		0			0
$711$	1.22023	−	0.886547i	0.0457621	−	0.0332481i
$712$	10.6543	+	7.74079i	0.399286	+	0.290098i
$713$	−0.482228	−	1.48414i	−0.0180596	−	0.0555817i
$714$	−0.340375			−0.0127382
$715$		0			0
$716$	15.3764			0.574643
$717$	0.333103	+	1.02518i	0.0124399	+	0.0382862i
$718$	−0.486006	−	0.353104i	−0.0181376	−	0.0131777i
$719$	14.0426	−	10.2026i	0.523701	−	0.380491i	−0.294295	−	0.955715i	$-0.595085\pi$
$719$	14.0426	−	10.2026i	0.523701	−	0.380491i	0.817996	+	0.575223i	$0.195085\pi$
$720$		0			0
$721$	2.31675	−	7.13022i	0.0862803	−	0.265543i
$722$	0.681888	−	0.495421i	0.0253772	−	0.0184376i
$723$	−21.9894	−	15.9762i	−0.817793	−	0.594161i
$724$	−4.46909	−	13.7544i	−0.166092	−	0.511180i
$725$		0			0
$726$	2.29903	+	0.0524834i	0.0853249	+	0.00194784i
$727$	−28.5895			−1.06033			−0.530163	−	0.847896i	$-0.677869\pi$
$727$	−28.5895			−1.06033			−0.530163	+	0.847896i	$0.677869\pi$
$728$	−0.408239	−	1.25643i	−0.0151304	−	0.0465664i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	2.33285	−	7.17978i	0.0862837	−	0.265554i
$732$	−7.60154	+	23.3951i	−0.280961	+	0.864709i
$733$	−26.2169	+	19.0477i	−0.968342	+	0.703542i	−0.955073	−	0.296370i	$-0.904224\pi$
$733$	−26.2169	+	19.0477i	−0.968342	+	0.703542i	−0.0132689	+	0.999912i	$0.504224\pi$
$734$	4.06947	+	2.95664i	0.150207	+	0.109132i
$735$		0			0
$736$	0.651737			0.0240234
$737$	23.8825	+	17.7716i	0.879724	+	0.654625i
$738$	0.875466			0.0322264
$739$	1.28835	+	3.96512i	0.0473925	+	0.145859i	0.971952	−	0.235177i	$-0.0755671\pi$
$739$	1.28835	+	3.96512i	0.0473925	+	0.145859i	−0.924560	+	0.381037i	$0.875567\pi$
$740$		0			0
$741$	−10.2274	+	7.43064i	−0.375713	+	0.272971i
$742$	−0.0360957	+	0.111091i	−0.00132511	+	0.00407828i
$743$	−15.1069	+	46.4942i	−0.554218	+	1.70571i	0.143782	+	0.989609i	$0.454074\pi$
$743$	−15.1069	+	46.4942i	−0.554218	+	1.70571i	−0.698000	+	0.716098i	$0.745926\pi$
$744$	−3.90286	+	2.83560i	−0.143086	+	0.103958i
$745$		0			0
$746$	−1.13278	−	3.48635i	−0.0414741	−	0.127644i
$747$	−17.6428			−0.645516
$748$	−6.91216	+	20.4754i	−0.252734	+	0.748653i
$749$	−2.85443			−0.104299
$750$		0			0
$751$	32.7929	+	23.8254i	1.19663	+	0.869402i	0.993949	−	0.109843i	$-0.0350347\pi$
$751$	32.7929	+	23.8254i	1.19663	+	0.869402i	0.202680	+	0.979245i	$0.435035\pi$
$752$	−16.8926	+	12.2732i	−0.616009	+	0.447557i
$753$	−0.803494	+	2.47290i	−0.0292809	+	0.0901174i
$754$	−1.33323	+	4.10326i	−0.0485534	+	0.149432i
$755$		0			0
$756$	−0.773659	−	0.562096i	−0.0281377	−	0.0204432i
$757$	6.74099	+	20.7466i	0.245005	+	0.754049i	0.995636	+	0.0933264i	$0.0297500\pi$
$757$	6.74099	+	20.7466i	0.245005	+	0.754049i	−0.750630	+	0.660723i	$0.770250\pi$
$758$	−6.82348			−0.247840
$759$	0.264557	+	0.846992i	0.00960280	+	0.0307439i
$760$		0			0
$761$	8.84170	+	27.2119i	0.320511	+	0.986432i	0.973426	+	0.229001i	$0.0735459\pi$
$761$	8.84170	+	27.2119i	0.320511	+	0.986432i	−0.652915	+	0.757431i	$0.726454\pi$
$762$	3.73610	+	2.71444i	0.135345	+	0.0983337i
$763$	2.78920	−	2.02647i	0.100976	−	0.0733632i
$764$	0.259789	−	0.799548i	0.00939883	−	0.0289266i
$765$		0			0
$766$	1.77869	−	1.29230i	0.0642668	−	0.0466926i
$767$	−11.9418	−	8.67623i	−0.431193	−	0.313280i
$768$	3.89889	+	11.9995i	0.140689	+	0.432996i
$769$	−11.2690			−0.406372			−0.203186	−	0.979140i	$-0.565130\pi$
$769$	−11.2690			−0.406372			−0.203186	+	0.979140i	$0.565130\pi$
$770$		0			0
$771$	−5.67343			−0.204324
$772$	1.17886	+	3.62815i	0.0424280	+	0.130580i
$773$	−12.7123	−	9.23602i	−0.457229	−	0.332196i	0.335214	−	0.942142i	$-0.391191\pi$
$773$	−12.7123	−	9.23602i	−0.457229	−	0.332196i	−0.792443	+	0.609946i	$0.791191\pi$
$774$	−0.383346	+	0.278517i	−0.0137791	+	0.0100111i
$775$		0			0
$776$	−4.17533	+	12.8503i	−0.149886	+	0.461300i
$777$	−2.96747	+	2.15599i	−0.106457	+	0.0773457i
$778$	−3.94865	−	2.86886i	−0.141566	−	0.102854i
$779$	−5.00660	−	15.4087i	−0.179380	−	0.552075i
$780$		0			0
$781$	−14.3810	+	10.1997i	−0.514594	+	0.364975i
$782$	0.186294			0.00666185
$783$	1.95173	+	6.00680i	0.0697490	+	0.214665i
$784$	20.4553	+	14.8617i	0.730547	+	0.530773i
$785$		0			0
$786$	0.250652	−	0.771427i	0.00894046	−	0.0275159i
$787$	−5.69048	+	17.5135i	−0.202844	+	0.624288i	0.796951	+	0.604043i	$0.206445\pi$
$787$	−5.69048	+	17.5135i	−0.202844	+	0.624288i	−0.999795	+	0.0202450i	$0.993555\pi$
$788$	35.2765	−	25.6299i	1.25667	−	0.913027i
$789$	−18.9672	−	13.7805i	−0.675252	−	0.490599i
$790$		0			0
$791$	−6.64903			−0.236412
$792$	2.23751	−	1.58695i	0.0795065	−	0.0563899i
$793$	−41.0872			−1.45905
$794$	−0.455277	−	1.40120i	−0.0161572	−	0.0497267i
$795$		0			0
$796$	10.2095	−	7.41762i	0.361865	−	0.262911i
$797$	−7.80944	+	24.0350i	−0.276625	+	0.851363i	0.712160	+	0.702017i	$0.247717\pi$
$797$	−7.80944	+	24.0350i	−0.276625	+	0.851363i	−0.988785	+	0.149346i	$0.952283\pi$
$798$	0.122177	−	0.376023i	0.00432503	−	0.0133111i
$799$	−15.0452	+	10.9310i	−0.532260	+	0.386710i
$800$		0			0
$801$	4.92035	+	15.1433i	0.173852	+	0.535061i
$802$	4.69635			0.165834
$803$	−32.0327	−	0.365582i	−1.13041	−	0.0129011i
$804$	17.5592			0.619266
$805$		0			0
$806$	−3.22342	−	2.34195i	−0.113540	−	0.0824916i
$807$	4.42045	−	3.21164i	0.155607	−	0.113055i
$808$	−4.56276	+	14.0427i	−0.160517	+	0.494021i
$809$	−3.48060	+	10.7122i	−0.122371	+	0.376620i	−0.993413	−	0.114589i	$-0.963445\pi$
$809$	−3.48060	+	10.7122i	−0.122371	+	0.376620i	0.871042	+	0.491209i	$0.163445\pi$
$810$		0			0
$811$	19.6919	+	14.3070i	0.691475	+	0.502386i	0.877145	−	0.480226i	$-0.159445\pi$
$811$	19.6919	+	14.3070i	0.691475	+	0.502386i	−0.185670	+	0.982612i	$0.559445\pi$
$812$	1.86643	+	5.74427i	0.0654987	+	0.201584i
$813$	2.52319			0.0884923
$814$	−1.55116	−	4.96612i	−0.0543681	−	0.174062i
$815$		0			0
$816$	3.84905	+	11.8461i	0.134744	+	0.414698i
$817$	7.09435	+	5.15435i	0.248200	+	0.180328i
$818$	−0.172375	+	0.125238i	−0.00602694	+	0.00437883i
$819$	0.493585	−	1.51910i	0.0172472	−	0.0530815i
$820$		0			0
$821$	−2.86011	+	2.07799i	−0.0998187	+	0.0725225i	−0.636575	−	0.771215i	$-0.719649\pi$
$821$	−2.86011	+	2.07799i	−0.0998187	+	0.0725225i	0.536756	+	0.843737i	$0.319649\pi$
$822$	−0.907597	−	0.659408i	−0.0316561	−	0.0229995i
$823$	14.5000	+	44.6265i	0.505439	+	1.55558i	0.800032	+	0.599958i	$0.204816\pi$
$823$	14.5000	+	44.6265i	0.505439	+	1.55558i	−0.294593	+	0.955623i	$0.595184\pi$
$824$	12.6851			0.441905
$825$		0			0
$826$	0.461650			0.0160629
$827$	13.5240	+	41.6227i	0.470276	+	1.44736i	0.852224	+	0.523178i	$0.175254\pi$
$827$	13.5240	+	41.6227i	0.470276	+	1.44736i	−0.381947	+	0.924184i	$0.624746\pi$
$828$	0.423438	+	0.307645i	0.0147155	+	0.0106914i
$829$	16.3783	−	11.8995i	0.568841	−	0.413287i	−0.265843	−	0.964016i	$-0.585650\pi$
$829$	16.3783	−	11.8995i	0.568841	−	0.413287i	0.834684	+	0.550729i	$0.185650\pi$
$830$		0			0
$831$	6.92406	−	21.3101i	0.240193	−	0.739238i
$832$	−18.4255	+	13.3869i	−0.638788	+	0.464107i
$833$	18.2183	+	13.2364i	0.631226	+	0.458613i
$834$	0.815517	+	2.50990i	0.0282390	+	0.0869108i
$835$		0			0
$836$	−20.1386	−	14.9857i	−0.696509	−	0.518290i
$837$	−5.83274			−0.201609
$838$	0.487148	+	1.49929i	0.0168282	+	0.0517920i
$839$	−31.5917	−	22.9527i	−1.09067	−	0.792417i	−0.111156	−	0.993803i	$-0.535455\pi$
$839$	−31.5917	−	22.9527i	−1.09067	−	0.792417i	−0.979512	+	0.201386i	$0.935455\pi$
$840$		0			0
$841$	3.36546	−	10.3578i	0.116050	−	0.357166i
$842$	0.759626	−	2.33789i	0.0261785	−	0.0805690i
$843$	9.12494	−	6.62966i	0.314280	−	0.228337i
$844$	35.1954	+	25.5709i	1.21148	+	0.880188i
$845$		0			0
$846$	1.16726			0.0401313
$847$	4.27692	+	3.25906i	0.146957	+	0.111982i
$848$	4.27450			0.146787
$849$	3.61318	+	11.1202i	0.124004	+	0.381645i
$850$		0			0
$851$	1.62415	−	1.18001i	0.0556751	−	0.0404503i
$852$	−3.21363	+	9.89052i	−0.110097	+	0.338844i
$853$	12.7307	−	39.1810i	0.435890	−	1.34153i	−0.456281	−	0.889836i	$-0.650819\pi$
$853$	12.7307	−	39.1810i	0.435890	−	1.34153i	0.892172	−	0.451697i	$-0.149181\pi$
$854$	1.03960	−	0.755311i	0.0355742	−	0.0258462i
$855$		0			0
$856$	−1.49244	−	4.59327i	−0.0510107	−	0.156995i
$857$	−39.6853			−1.35563			−0.677813	−	0.735235i	$-0.737072\pi$
$857$	−39.6853			−1.35563			−0.677813	+	0.735235i	$0.737072\pi$
$858$	1.81759	+	1.35251i	0.0620515	+	0.0461741i
$859$	22.6446			0.772625			0.386313	−	0.922368i	$-0.373749\pi$
$859$	22.6446			0.772625			0.386313	+	0.922368i	$0.373749\pi$
$860$		0			0
$861$	1.65611	+	1.20324i	0.0564402	+	0.0410062i
$862$	4.57508	−	3.32399i	0.155828	−	0.113216i
$863$	10.5107	−	32.3487i	0.357790	−	1.10116i	−0.596585	−	0.802550i	$-0.703476\pi$
$863$	10.5107	−	32.3487i	0.357790	−	1.10116i	0.954374	−	0.298613i	$-0.0965240\pi$
$864$	0.752762	−	2.31676i	0.0256095	−	0.0788179i
$865$		0			0
$866$	−4.34165	−	3.15440i	−0.147535	−	0.107191i
$867$	−1.82518	−	5.61733i	−0.0619864	−	0.190774i
$868$	−5.57782			−0.189324
$869$	−1.60002	+	4.73963i	−0.0542771	+	0.160781i
$870$		0			0
$871$	9.06306	+	27.8932i	0.307090	+	0.945126i
$872$	4.71927	+	3.42875i	0.159815	+	0.116112i
$873$	−13.2164	+	9.60227i	−0.447307	+	0.324987i
$874$	−0.0668698	+	0.205804i	−0.00226191	+	0.00696143i
$875$		0			0
$876$	−15.2868	+	11.1065i	−0.516494	+	0.375255i
$877$	22.2427	+	16.1603i	0.751083	+	0.545693i	0.896162	−	0.443727i	$-0.146344\pi$
$877$	22.2427	+	16.1603i	0.751083	+	0.545693i	−0.145080	+	0.989420i	$0.546344\pi$
$878$	0.0331379	+	0.101988i	0.00111835	+	0.00344193i
$879$	13.4918			0.455067
$880$		0			0
$881$	41.2585			1.39003			0.695017	−	0.718993i	$-0.255397\pi$
$881$	41.2585			1.39003			0.695017	+	0.718993i	$0.255397\pi$
$882$	−0.436778	−	1.34426i	−0.0147071	−	0.0452637i
$883$	−12.2820	−	8.92340i	−0.413323	−	0.300296i	0.361623	−	0.932324i	$-0.382223\pi$
$883$	−12.2820	−	8.92340i	−0.413323	−	0.300296i	−0.774946	+	0.632028i	$0.782223\pi$
$884$	−17.2246	+	12.5144i	−0.579327	+	0.420906i
$885$		0			0
$886$	2.14910	−	6.61425i	0.0722004	−	0.222210i
$887$	27.5939	−	20.0482i	0.926514	−	0.673152i	−0.0186229	−	0.999827i	$-0.505928\pi$
$887$	27.5939	−	20.0482i	0.926514	−	0.673152i	0.945137	+	0.326675i	$0.105928\pi$
$888$	−5.02090	−	3.64790i	−0.168490	−	0.122415i
$889$	3.33685	+	10.2698i	0.111914	+	0.344437i
$890$		0			0
$891$	3.31641	+	0.0378495i	0.111104	+	0.00126800i
$892$	26.9497			0.902342
$893$	−6.67532	−	20.5445i	−0.223381	−	0.687496i
$894$	0.794824	+	0.577473i	0.0265829	+	0.0193136i
$895$		0			0
$896$	0.956057	−	2.94244i	0.0319396	−	0.0983000i
$897$	−0.270148	+	0.831429i	−0.00901997	+	0.0277606i
$898$	−1.00775	+	0.732173i	−0.0336290	+	0.0244329i
$899$	29.8035	+	21.6535i	0.994001	+	0.722184i
$900$		0			0
$901$	3.80703			0.126831
$902$	−2.36838	+	1.67977i	−0.0788584	+	0.0559302i
$903$	−1.10797			−0.0368708
$904$	−3.47645	−	10.6994i	−0.115625	−	0.355858i
$905$		0			0
$906$	−2.46444	+	1.79052i	−0.0818756	+	0.0594861i
$907$	5.53850	−	17.0458i	0.183903	−	0.565995i	−0.816025	−	0.578017i	$-0.803827\pi$
$907$	5.53850	−	17.0458i	0.183903	−	0.565995i	0.999928	+	0.0120217i	$0.00382672\pi$
$908$	−15.6303	+	48.1051i	−0.518710	+	1.59642i
$909$	−14.4427	+	10.4933i	−0.479035	+	0.348039i
$910$		0			0
$911$	−6.76885	−	20.8324i	−0.224262	−	0.690208i	−0.998366	−	0.0571488i	$-0.981799\pi$
$911$	−6.76885	−	20.8324i	−0.224262	−	0.690208i	0.774104	−	0.633059i	$-0.218201\pi$
$912$	−14.4684			−0.479097
$913$	47.7287	−	33.8515i	1.57959	−	1.12032i
$914$	−4.27867			−0.141526
$915$		0			0
$916$	22.6942	+	16.4883i	0.749836	+	0.544788i
$917$	1.53440	−	1.11481i	0.0506704	−	0.0368142i
$918$	0.215171	−	0.662227i	0.00710169	−	0.0218568i
$919$	1.24957	−	3.84579i	0.0412196	−	0.126861i	−0.928329	−	0.371759i	$-0.878755\pi$
$919$	1.24957	−	3.84579i	0.0412196	−	0.126861i	0.969549	+	0.244898i	$0.0787546\pi$
$920$		0			0
$921$	−0.294989	−	0.214322i	−0.00972021	−	0.00706215i
$922$	2.01415	+	6.19893i	0.0663326	+	0.204151i
$923$	−17.3700			−0.571741
$924$	3.17147	+	0.0361953i	0.104334	+	0.00119074i
$925$		0			0
$926$	−0.710555	−	2.18686i	−0.0233503	−	0.0718648i
$927$	12.4079	+	9.01484i	0.407527	+	0.296086i
$928$	−12.4471	+	9.04337i	−0.408597	+	0.296863i
$929$	−3.19319	+	9.82763i	−0.104765	+	0.322434i	−0.989675	−	0.143328i	$-0.954220\pi$
$929$	−3.19319	+	9.82763i	−0.104765	+	0.322434i	0.884910	+	0.465762i	$0.154220\pi$
$930$		0			0
$931$	−21.1620	+	15.3751i	−0.693558	+	0.503899i
$932$	−5.79785	−	4.21238i	−0.189915	−	0.137981i
$933$	7.18595	+	22.1161i	0.235257	+	0.724048i
$934$	7.40186			0.242196
$935$		0			0
$936$	2.70256			0.0883358
$937$	−10.0570	−	30.9522i	−0.328547	−	1.01116i	−0.969814	−	0.243846i	$-0.921591\pi$
$937$	−10.0570	−	30.9522i	−0.328547	−	1.01116i	0.641267	−	0.767318i	$-0.278409\pi$
$938$	−0.742080	−	0.539152i	−0.0242298	−	0.0176040i
$939$	−9.89642	+	7.19017i	−0.322957	+	0.234642i
$940$		0			0
$941$	−3.83063	+	11.7895i	−0.124875	+	0.384326i	−0.993878	−	0.110481i	$-0.964761\pi$
$941$	−3.83063	+	11.7895i	−0.124875	+	0.384326i	0.869003	+	0.494806i	$0.164761\pi$
$942$	0.0565225	−	0.0410660i	0.00184160	−	0.00133800i
$943$	−0.906421	−	0.658553i	−0.0295171	−	0.0214454i
$944$	−5.22044	−	16.0669i	−0.169911	−	0.522932i
$945$		0			0
$946$	0.502663	−	1.48900i	0.0163430	−	0.0484115i
$947$	−44.7602			−1.45451			−0.727256	−	0.686366i	$-0.759205\pi$
$947$	−44.7602			−1.45451			−0.727256	+	0.686366i	$0.759205\pi$
$948$	0.911800	+	2.80623i	0.0296139	+	0.0911422i
$949$	−25.5332	−	18.5509i	−0.828842	−	0.602189i
$950$		0			0
$951$	−9.89399	+	30.4506i	−0.320834	+	0.987427i
$952$	0.416130	−	1.28072i	0.0134869	−	0.0415083i
$953$	−17.2775	+	12.5528i	−0.559673	+	0.406626i	−0.831339	−	0.555765i	$-0.812425\pi$
$953$	−17.2775	+	12.5528i	−0.559673	+	0.406626i	0.271666	+	0.962392i	$0.412425\pi$
$954$	−0.193318	−	0.140454i	−0.00625891	−	0.00454736i
$955$		0			0
$956$	−2.10877			−0.0682026
$957$	−16.8053	−	12.5053i	−0.543238	−	0.404237i
$958$	4.05187			0.130910
$959$	−0.810608	−	2.49479i	−0.0261759	−	0.0805611i
$960$		0			0
$961$	−2.44390	+	1.77560i	−0.0788356	+	0.0572774i
$962$	1.58394	−	4.87487i	0.0510683	−	0.157172i
$963$	1.80445	−	5.55352i	0.0581475	−	0.178960i
$964$	43.0177	−	31.2542i	1.38551	−	1.00663i
$965$		0			0
$966$	−0.00844893	−	0.0260031i	−0.000271840	−	0.000836638i
$967$	31.3251			1.00735			0.503674	−	0.863894i	$-0.331981\pi$
$967$	31.3251			1.00735			0.503674	+	0.863894i	$0.331981\pi$
$968$	−3.00818	+	8.58629i	−0.0966866	+	0.275974i
$969$	−12.8861			−0.413962
$970$		0			0
$971$	−12.7117	−	9.23559i	−0.407938	−	0.296384i	0.364829	−	0.931075i	$-0.381128\pi$
$971$	−12.7117	−	9.23559i	−0.407938	−	0.296384i	−0.772766	+	0.634691i	$0.781128\pi$
$972$	1.58268	−	1.14988i	0.0507644	−	0.0368825i
$973$	−1.90689	+	5.86881i	−0.0611321	+	0.188145i
$974$	1.05625	−	3.25079i	0.0338443	−	0.104162i
$975$		0			0
$976$	−38.0432	−	27.6400i	−1.21773	−	0.884735i
$977$	6.97210	+	21.4579i	0.223057	+	0.686499i	0.998483	+	0.0550607i	$0.0175352\pi$
$977$	6.97210	+	21.4579i	0.223057	+	0.686499i	−0.775426	+	0.631439i	$0.782465\pi$
$978$	−0.415888			−0.0132986
$979$	−42.3665	−	31.5260i	−1.35404	−	1.00758i
$980$		0			0
$981$	2.17945	+	6.70765i	0.0695844	+	0.214159i
$982$	2.33155	+	1.69397i	0.0744028	+	0.0540568i
$983$	37.1982	−	27.0261i	1.18644	−	0.861998i	0.193555	−	0.981089i	$-0.437998\pi$
$983$	37.1982	−	27.0261i	1.18644	−	0.861998i	0.992883	+	0.119092i	$0.0379983\pi$
$984$	−1.07031	+	3.29408i	−0.0341203	+	0.105011i
$985$		0			0
$986$	−3.55791	+	2.58497i	−0.113307	+	0.0823223i
$987$	2.20810	+	1.60428i	0.0702847	+	0.0510648i
$988$	−7.64230	−	23.5206i	−0.243134	−	0.748290i
$989$	0.606410			0.0192827
$990$		0			0
$991$	5.48050			0.174094			0.0870469	−	0.996204i	$-0.472257\pi$
$991$	5.48050			0.174094			0.0870469	+	0.996204i	$0.472257\pi$
$992$	−4.39066	−	13.5131i	−0.139404	−	0.429040i
$993$	16.6419	+	12.0910i	0.528113	+	0.383697i
$994$	0.439499	−	0.319315i	0.0139401	−	0.0101281i
$995$		0			0
$996$	10.6656	−	32.8253i	0.337952	−	1.04011i
$997$	14.7692	−	10.7305i	0.467747	−	0.339838i	−0.328816	−	0.944394i	$-0.606650\pi$
$997$	14.7692	−	10.7305i	0.467747	−	0.339838i	0.796563	+	0.604556i	$0.206650\pi$
$998$	−3.34587	−	2.43092i	−0.105912	−	0.0769494i
$999$	−2.31874	−	7.13636i	−0.0733618	−	0.225784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.j.676.2		8
5.2	odd	4		825.2.bx.e.49.2		16
5.3	odd	4		825.2.bx.e.49.3		16
5.4	even	2		165.2.m.c.16.1	✓	8
11.3	even	5		9075.2.a.co.1.3		4
11.8	odd	10		9075.2.a.df.1.2		4
11.9	even	5	inner	825.2.n.j.526.2		8
15.14	odd	2		495.2.n.c.181.2		8
55.9	even	10		165.2.m.c.31.1	yes	8
55.14	even	10		1815.2.a.u.1.2		4
55.19	odd	10		1815.2.a.q.1.3		4
55.42	odd	20		825.2.bx.e.724.3		16
55.53	odd	20		825.2.bx.e.724.2		16
165.14	odd	10		5445.2.a.bj.1.3		4
165.74	even	10		5445.2.a.bq.1.2		4
165.119	odd	10		495.2.n.c.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.c.16.1	✓	8	5.4	even	2
165.2.m.c.31.1	yes	8	55.9	even	10
495.2.n.c.181.2		8	15.14	odd	2
495.2.n.c.361.2		8	165.119	odd	10
825.2.n.j.526.2		8	11.9	even	5	inner
825.2.n.j.676.2		8	1.1	even	1	trivial
825.2.bx.e.49.2		16	5.2	odd	4
825.2.bx.e.49.3		16	5.3	odd	4
825.2.bx.e.724.2		16	55.53	odd	20
825.2.bx.e.724.3		16	55.42	odd	20
1815.2.a.q.1.3		4	55.19	odd	10
1815.2.a.u.1.2		4	55.14	even	10
5445.2.a.bj.1.3		4	165.14	odd	10
5445.2.a.bq.1.2		4	165.74	even	10
9075.2.a.co.1.3		4	11.3	even	5
9075.2.a.df.1.2		4	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0646021 + 0.198825i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.58268 - 1.14988i) q^{4} +(0.0646021 - 0.198825i) q^{6} +(0.395472 - 0.287327i) q^{7} +(0.669131 + 0.486152i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.0646021 + 0.198825i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.58268 - 1.14988i) q^{4} +(0.0646021 - 0.198825i) q^{6} +(0.395472 - 0.287327i) q^{7} +(0.669131 + 0.486152i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-2.66078 - 1.97996i) q^{11} -1.95630 q^{12} +(-1.00973 - 3.10762i) q^{13} +(0.0826761 + 0.0600677i) q^{14} +(1.15563 - 3.55665i) q^{16} +(1.02924 - 3.16769i) q^{17} +(-0.169131 + 0.122881i) q^{18} +(3.12999 + 2.27407i) q^{19} -0.488830 q^{21} +(0.221773 - 0.656940i) q^{22} +0.267545 q^{23} +(-0.255585 - 0.786610i) q^{24} +(0.552642 - 0.401518i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.295511 - 0.909491i) q^{28} +(-5.10969 + 3.71240i) q^{29} +(-1.80242 - 5.54726i) q^{31} +2.43599 q^{32} +(0.988830 + 3.16579i) q^{33} +0.696307 q^{34} +(1.58268 + 1.14988i) q^{36} +(6.07055 - 4.41051i) q^{37} +(-0.249938 + 0.769231i) q^{38} +(-1.00973 + 3.10762i) q^{39} +(-3.38791 - 2.46146i) q^{41} +(-0.0315794 - 0.0971915i) q^{42} +2.26657 q^{43} +(-6.48787 - 0.0740447i) q^{44} +(0.0172840 + 0.0531947i) q^{46} +(-4.51712 - 3.28188i) q^{47} +(-3.02547 + 2.19813i) q^{48} +(-2.08928 + 6.43014i) q^{49} +(-2.69460 + 1.95774i) q^{51} +(-5.17147 - 3.75729i) q^{52} +(0.353210 + 1.08707i) q^{53} +0.209057 q^{54} +0.404307 q^{56} +(-1.19555 - 3.67953i) q^{57} +(-1.06822 - 0.776104i) q^{58} +(3.65467 - 2.65527i) q^{59} +(3.88568 - 11.9589i) q^{61} +(0.986494 - 0.716730i) q^{62} +(0.395472 + 0.287327i) q^{63} +(-2.15388 - 6.62896i) q^{64} +(-0.565557 + 0.401121i) q^{66} -8.97575 q^{67} +(-2.01351 - 6.19693i) q^{68} +(-0.216449 - 0.157259i) q^{69} +(1.64271 - 5.05574i) q^{71} +(-0.255585 + 0.786610i) q^{72} +(7.81418 - 5.67733i) q^{73} +(1.26909 + 0.922048i) q^{74} +7.56868 q^{76} +(-1.62116 - 0.0185019i) q^{77} -0.683103 q^{78} +(-0.466085 - 1.43446i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.270534 - 0.832618i) q^{82} +(-5.45193 + 16.7793i) q^{83} +(-0.773659 + 0.562096i) q^{84} +(0.146425 + 0.450650i) q^{86} +6.31592 q^{87} +(-0.817852 - 2.61839i) q^{88} +15.9226 q^{89} +(-1.29222 - 0.938854i) q^{91} +(0.423438 - 0.307645i) q^{92} +(-1.80242 + 5.54726i) q^{93} +(0.360704 - 1.11013i) q^{94} +(-1.97076 - 1.43184i) q^{96} +(5.04821 + 15.5368i) q^{97} -1.41344 q^{98} +(1.06082 - 3.14240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 5 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 5 * q^7 + q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 5 q^{7} + q^{8} - 2 q^{9} - q^{11} + 2 q^{12} + 16 q^{13} - 10 q^{14} + 12 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 9 q^{22} - 10 q^{23} - 4 q^{24} + 16 q^{26} - 2 q^{27} + 5 q^{28} - 16 q^{29} - 5 q^{31} + 4 q^{33} + 34 q^{34} + 2 q^{36} + 5 q^{37} - 28 q^{38} + 16 q^{39} + 5 q^{41} + 15 q^{42} + 8 q^{43} - 19 q^{44} + 10 q^{46} + q^{47} - 3 q^{48} - 11 q^{49} + 4 q^{51} - 26 q^{52} + 15 q^{53} - 2 q^{54} + 20 q^{56} - 13 q^{57} + 24 q^{58} + 3 q^{59} - 11 q^{61} + 15 q^{62} + 5 q^{63} - 9 q^{64} - 31 q^{66} - 6 q^{67} - 9 q^{68} + 15 q^{69} + q^{71} - 4 q^{72} + 35 q^{73} + 5 q^{74} + 58 q^{76} + 25 q^{77} - 24 q^{78} - 30 q^{79} - 2 q^{81} + 25 q^{82} - 31 q^{83} - 62 q^{86} + 34 q^{87} - 17 q^{88} - 48 q^{89} + 5 q^{91} + 20 q^{92} - 5 q^{93} - 19 q^{94} - 20 q^{96} - 11 q^{97} - 26 q^{98} - 11 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 5 * q^7 + q^8 - 2 * q^9 - q^11 + 2 * q^12 + 16 * q^13 - 10 * q^14 + 12 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 9 * q^22 - 10 * q^23 - 4 * q^24 + 16 * q^26 - 2 * q^27 + 5 * q^28 - 16 * q^29 - 5 * q^31 + 4 * q^33 + 34 * q^34 + 2 * q^36 + 5 * q^37 - 28 * q^38 + 16 * q^39 + 5 * q^41 + 15 * q^42 + 8 * q^43 - 19 * q^44 + 10 * q^46 + q^47 - 3 * q^48 - 11 * q^49 + 4 * q^51 - 26 * q^52 + 15 * q^53 - 2 * q^54 + 20 * q^56 - 13 * q^57 + 24 * q^58 + 3 * q^59 - 11 * q^61 + 15 * q^62 + 5 * q^63 - 9 * q^64 - 31 * q^66 - 6 * q^67 - 9 * q^68 + 15 * q^69 + q^71 - 4 * q^72 + 35 * q^73 + 5 * q^74 + 58 * q^76 + 25 * q^77 - 24 * q^78 - 30 * q^79 - 2 * q^81 + 25 * q^82 - 31 * q^83 - 62 * q^86 + 34 * q^87 - 17 * q^88 - 48 * q^89 + 5 * q^91 + 20 * q^92 - 5 * q^93 - 19 * q^94 - 20 * q^96 - 11 * q^97 - 26 * q^98 - 11 * q^99

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