LMFDB - Embedded newform 375.2.i.b.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			199.3
Root			$0.462894 + 1.33631i$ of defining polynomial
Character	$\chi$	$=$	375.199
Dual form			375.2.i.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00297 + 1.38048i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.281722 + 0.867051i) q^{4} +(-0.527295 - 1.62285i) q^{6} -3.94243i q^{7} +(1.76619 - 0.573870i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.00297 + 1.38048i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.281722 + 0.867051i) q^{4} +(-0.527295 - 1.62285i) q^{6} -3.94243i q^{7} +(1.76619 - 0.573870i) q^{8} +(0.809017 + 0.587785i) q^{9} +(4.78023 - 3.47304i) q^{11} +(0.535867 - 0.737558i) q^{12} +(-1.93420 + 2.66220i) q^{13} +(5.44243 - 3.95416i) q^{14} +(4.03877 + 2.93434i) q^{16} +(-2.57390 + 0.836312i) q^{17} +1.70636i q^{18} +(0.728704 + 2.24272i) q^{19} +(-1.21828 + 3.74947i) q^{21} +(9.58890 + 3.11562i) q^{22} +(-0.343440 - 0.472705i) q^{23} -1.85708 q^{24} -5.61505 q^{26} +(-0.587785 - 0.809017i) q^{27} +(3.41829 + 1.11067i) q^{28} +(1.20877 - 3.72022i) q^{29} +(0.837233 + 2.57674i) q^{31} +4.80433i q^{32} +(-5.61950 + 1.82589i) q^{33} +(-3.73607 - 2.71441i) q^{34} +(-0.737558 + 0.535867i) q^{36} +(-0.0122562 + 0.0168692i) q^{37} +(-2.36515 + 3.25535i) q^{38} +(2.66220 - 1.93420i) q^{39} +(-1.19098 - 0.865300i) q^{41} +(-6.39796 + 2.07882i) q^{42} -1.27279i q^{43} +(1.66461 + 5.12314i) q^{44} +(0.308096 - 0.948222i) q^{46} +(5.16764 + 1.67907i) q^{47} +(-2.93434 - 4.03877i) q^{48} -8.54276 q^{49} +2.70636 q^{51} +(-1.76336 - 2.42705i) q^{52} +(-2.67774 - 0.870050i) q^{53} +(0.527295 - 1.62285i) q^{54} +(-2.26244 - 6.96308i) q^{56} -2.35813i q^{57} +(6.34804 - 2.06260i) q^{58} +(-3.79456 - 2.75691i) q^{59} +(-4.51538 + 3.28061i) q^{61} +(-2.71740 + 3.74018i) q^{62} +(2.31730 - 3.18949i) q^{63} +(1.44528 - 1.05006i) q^{64} +(-8.15681 - 5.92627i) q^{66} +(-5.73559 + 1.86361i) q^{67} -2.46731i q^{68} +(0.180557 + 0.555698i) q^{69} +(-2.50346 + 7.70487i) q^{71} +(1.76619 + 0.573870i) q^{72} +(7.82730 + 10.7734i) q^{73} -0.0355801 q^{74} -2.14984 q^{76} +(-13.6922 - 18.8457i) q^{77} +(5.34023 + 1.73515i) q^{78} +(-5.14971 + 15.8492i) q^{79} +(0.309017 + 0.951057i) q^{81} -2.51200i q^{82} +(0.743385 - 0.241540i) q^{83} +(-2.90777 - 2.11262i) q^{84} +(1.75705 - 1.27657i) q^{86} +(-2.29922 + 3.16461i) q^{87} +(6.44972 - 8.87728i) q^{88} +(-2.80994 + 2.04154i) q^{89} +(10.4955 + 7.62545i) q^{91} +(0.506614 - 0.164609i) q^{92} -2.70934i q^{93} +(2.86510 + 8.81786i) q^{94} +(1.48462 - 4.56919i) q^{96} +(-2.33430 - 0.758460i) q^{97} +(-8.56817 - 11.7931i) q^{98} +5.90869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	1.00297	+	1.38048i	0.709210	+	0.976144i	0.999814	+	0.0193004i	$0.00614389\pi$
$2$	1.00297	+	1.38048i	0.709210	+	0.976144i	−0.290604	+	0.956844i	$0.593856\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.281722	+	0.867051i	−0.140861	+	0.433526i
$5$		0			0
$5$		0			0
$6$	−0.527295	−	1.62285i	−0.215267	−	0.662524i
$7$		−	3.94243i		−	1.49010i	−0.667009	−	0.745049i	$-0.732426\pi$
$7$		−	3.94243i		−	1.49010i	0.667009	−	0.745049i	$-0.267574\pi$
$8$	1.76619	−	0.573870i	0.624442	−	0.202894i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	4.78023	−	3.47304i	1.44129	−	1.04716i	0.453524	−	0.891244i	$-0.350167\pi$
$11$	4.78023	−	3.47304i	1.44129	−	1.04716i	0.987770	−	0.155918i	$-0.0498334\pi$
$12$	0.535867	−	0.737558i	0.154692	−	0.212915i
$13$	−1.93420	+	2.66220i	−0.536451	+	0.738361i	−0.988096	−	0.153836i	$-0.950837\pi$
$13$	−1.93420	+	2.66220i	−0.536451	+	0.738361i	0.451646	+	0.892197i	$0.350837\pi$
$14$	5.44243	−	3.95416i	1.45455	−	1.05679i
$15$		0			0
$16$	4.03877	+	2.93434i	1.00969	+	0.733585i
$17$	−2.57390	+	0.836312i	−0.624263	+	0.202835i	−0.604032	−	0.796960i	$-0.706440\pi$
$17$	−2.57390	+	0.836312i	−0.624263	+	0.202835i	−0.0202310	+	0.999795i	$0.506440\pi$
$18$			1.70636i			0.402193i
$19$	0.728704	+	2.24272i	0.167176	+	0.514515i	0.999190	−	0.0402396i	$-0.0128121\pi$
$19$	0.728704	+	2.24272i	0.167176	+	0.514515i	−0.832014	+	0.554755i	$0.812812\pi$
$20$		0			0
$21$	−1.21828	+	3.74947i	−0.265850	+	0.818202i
$22$	9.58890	+	3.11562i	2.04436	+	0.664253i
$23$	−0.343440	−	0.472705i	−0.0716123	−	0.0985658i	0.771708	−	0.635977i	$-0.219403\pi$
$23$	−0.343440	−	0.472705i	−0.0716123	−	0.0985658i	−0.843321	+	0.537411i	$0.819403\pi$
$24$	−1.85708			−0.379075
$25$		0			0
$26$	−5.61505			−1.10120
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	3.41829	+	1.11067i	0.645996	+	0.209897i
$29$	1.20877	−	3.72022i	0.224464	−	0.690828i	−0.773882	−	0.633330i	$-0.781688\pi$
$29$	1.20877	−	3.72022i	0.224464	−	0.690828i	0.998346	−	0.0574980i	$-0.0183123\pi$
$30$		0			0
$31$	0.837233	+	2.57674i	0.150371	+	0.462796i	0.997663	−	0.0683330i	$-0.0217680\pi$
$31$	0.837233	+	2.57674i	0.150371	+	0.462796i	−0.847291	+	0.531129i	$0.821768\pi$
$32$			4.80433i			0.849294i
$33$	−5.61950	+	1.82589i	−0.978229	+	0.317846i
$34$	−3.73607	−	2.71441i	−0.640730	−	0.465518i
$35$		0			0
$36$	−0.737558	+	0.535867i	−0.122926	+	0.0893112i
$37$	−0.0122562	+	0.0168692i	−0.00201490	+	0.00277328i	−0.810023	−	0.586398i	$-0.800546\pi$
$37$	−0.0122562	+	0.0168692i	−0.00201490	+	0.00277328i	0.808008	+	0.589171i	$0.200546\pi$
$38$	−2.36515	+	3.25535i	−0.383678	+	0.528087i
$39$	2.66220	−	1.93420i	0.426293	−	0.309720i
$40$		0			0
$41$	−1.19098	−	0.865300i	−0.186000	−	0.135137i	0.490889	−	0.871222i	$-0.336672\pi$
$41$	−1.19098	−	0.865300i	−0.186000	−	0.135137i	−0.676889	+	0.736085i	$0.736672\pi$
$42$	−6.39796	+	2.07882i	−0.987227	+	0.320769i
$43$		−	1.27279i		−	0.194098i	−0.995280	−	0.0970491i	$-0.969060\pi$
$43$		−	1.27279i		−	0.194098i	0.995280	−	0.0970491i	$-0.0309404\pi$
$44$	1.66461	+	5.12314i	0.250949	+	0.772342i
$45$		0			0
$46$	0.308096	−	0.948222i	0.0454263	−	0.139808i
$47$	5.16764	+	1.67907i	0.753777	+	0.244917i	0.660606	−	0.750733i	$-0.270299\pi$
$47$	5.16764	+	1.67907i	0.753777	+	0.244917i	0.0931716	+	0.995650i	$0.470299\pi$
$48$	−2.93434	−	4.03877i	−0.423536	−	0.582947i
$49$	−8.54276			−1.22039
$50$		0			0
$51$	2.70636			0.378967
$52$	−1.76336	−	2.42705i	−0.244533	−	0.336571i
$53$	−2.67774	−	0.870050i	−0.367816	−	0.119511i	0.119277	−	0.992861i	$-0.461942\pi$
$53$	−2.67774	−	0.870050i	−0.367816	−	0.119511i	−0.487092	+	0.873350i	$0.661942\pi$
$54$	0.527295	−	1.62285i	0.0717557	−	0.220841i
$55$		0			0
$56$	−2.26244	−	6.96308i	−0.302332	−	0.930481i
$57$		−	2.35813i		−	0.312343i
$58$	6.34804	−	2.06260i	0.833539	−	0.270833i
$59$	−3.79456	−	2.75691i	−0.494009	−	0.358919i	0.312715	−	0.949847i	$-0.398762\pi$
$59$	−3.79456	−	2.75691i	−0.494009	−	0.358919i	−0.806724	+	0.590928i	$0.798762\pi$
$60$		0			0
$61$	−4.51538	+	3.28061i	−0.578135	+	0.420040i	−0.838051	−	0.545591i	$-0.816305\pi$
$61$	−4.51538	+	3.28061i	−0.578135	+	0.420040i	0.259916	+	0.965631i	$0.416305\pi$
$62$	−2.71740	+	3.74018i	−0.345110	+	0.475004i
$63$	2.31730	−	3.18949i	0.291953	−	0.401838i
$64$	1.44528	−	1.05006i	0.180660	−	0.131257i
$65$		0			0
$66$	−8.15681	−	5.92627i	−1.00403	−	0.729473i
$67$	−5.73559	+	1.86361i	−0.700714	+	0.227676i	−0.637642	−	0.770333i	$-0.720090\pi$
$67$	−5.73559	+	1.86361i	−0.700714	+	0.227676i	−0.0630725	+	0.998009i	$0.520090\pi$
$68$		−	2.46731i		−	0.299206i
$69$	0.180557	+	0.555698i	0.0217365	+	0.0668982i
$70$		0			0
$71$	−2.50346	+	7.70487i	−0.297106	+	0.914400i	0.685399	+	0.728167i	$0.259628\pi$
$71$	−2.50346	+	7.70487i	−0.297106	+	0.914400i	−0.982506	+	0.186232i	$0.940372\pi$
$72$	1.76619	+	0.573870i	0.208147	+	0.0676312i
$73$	7.82730	+	10.7734i	0.916116	+	1.26093i	0.965035	+	0.262123i	$0.0844225\pi$
$73$	7.82730	+	10.7734i	0.916116	+	1.26093i	−0.0489187	+	0.998803i	$0.515578\pi$
$74$	−0.0355801			−0.00413611
$75$		0			0
$76$	−2.14984			−0.246604
$77$	−13.6922	−	18.8457i	−1.56037	−	2.14767i
$78$	5.34023	+	1.73515i	0.604662	+	0.196467i
$79$	−5.14971	+	15.8492i	−0.579388	+	1.78317i	0.0413379	+	0.999145i	$0.486838\pi$
$79$	−5.14971	+	15.8492i	−0.579388	+	1.78317i	−0.620726	+	0.784028i	$0.713162\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	2.51200i		−	0.277404i
$83$	0.743385	−	0.241540i	0.0815971	−	0.0265125i	−0.267934	−	0.963437i	$-0.586341\pi$
$83$	0.743385	−	0.241540i	0.0815971	−	0.0265125i	0.349531	+	0.936925i	$0.386341\pi$
$84$	−2.90777	−	2.11262i	−0.317264	−	0.230506i
$85$		0			0
$86$	1.75705	−	1.27657i	0.189468	−	0.137656i
$87$	−2.29922	+	3.16461i	−0.246503	+	0.339282i
$88$	6.44972	−	8.87728i	0.687543	−	0.946322i
$89$	−2.80994	+	2.04154i	−0.297853	+	0.216403i	−0.726667	−	0.686990i	$-0.758932\pi$
$89$	−2.80994	+	2.04154i	−0.297853	+	0.216403i	0.428814	+	0.903393i	$0.358932\pi$
$90$		0			0
$91$	10.4955	+	7.62545i	1.10023	+	0.799364i
$92$	0.506614	−	0.164609i	0.0528182	−	0.0171617i
$93$		−	2.70934i		−	0.280946i
$94$	2.86510	+	8.81786i	0.295512	+	0.909493i
$95$		0			0
$96$	1.48462	−	4.56919i	0.151523	−	0.466341i
$97$	−2.33430	−	0.758460i	−0.237012	−	0.0770099i	0.188103	−	0.982149i	$-0.439766\pi$
$97$	−2.33430	−	0.758460i	−0.237012	−	0.0770099i	−0.425115	+	0.905139i	$0.639766\pi$
$98$	−8.56817	−	11.7931i	−0.865515	−	1.19128i
$99$	5.90869			0.593846
$100$		0			0
$101$	−6.87495			−0.684083			−0.342042	−	0.939685i	$-0.611118\pi$
$101$	−6.87495			−0.684083			−0.342042	+	0.939685i	$0.611118\pi$
$102$	2.71441	+	3.73607i	0.268767	+	0.369926i
$103$	−11.1779	−	3.63192i	−1.10139	−	0.357864i	−0.298754	−	0.954330i	$-0.596571\pi$
$103$	−11.1779	−	3.63192i	−1.10139	−	0.357864i	−0.802638	+	0.596466i	$0.796571\pi$
$104$	−1.88841	+	5.81193i	−0.185174	+	0.569906i
$105$		0			0
$106$	−1.48462	−	4.56919i	−0.144199	−	0.443799i
$107$			5.66780i			0.547927i	0.961740	+	0.273964i	$0.0883348\pi$
$107$			5.66780i			0.547927i	−0.961740	+	0.273964i	$0.911665\pi$
$108$	0.867051	−	0.281722i	0.0834321	−	0.0271087i
$109$	−1.10130	−	0.800139i	−0.105485	−	0.0766394i	0.533792	−	0.845616i	$-0.320766\pi$
$109$	−1.10130	−	0.800139i	−0.105485	−	0.0766394i	−0.639277	+	0.768976i	$0.720766\pi$
$110$		0			0
$111$	0.0168692	−	0.0122562i	0.00160115	−	0.00116330i
$112$	11.5684	−	15.9226i	1.09311	−	1.50454i
$113$	6.28088	−	8.64489i	0.590856	−	0.813243i	−0.403977	−	0.914769i	$-0.632373\pi$
$113$	6.28088	−	8.64489i	0.590856	−	0.813243i	0.994833	+	0.101526i	$0.0323725\pi$
$114$	3.25535	−	2.36515i	0.304891	−	0.221516i
$115$		0			0
$116$	2.88508	+	2.09614i	0.267873	+	0.194621i
$117$	−3.12960	+	1.01687i	−0.289332	+	0.0940096i
$118$		−	8.00341i		−	0.736773i
$119$	3.29710	+	10.1474i	0.302245	+	0.930214i
$120$		0			0
$121$	7.38941	−	22.7423i	0.671765	−	2.06748i
$122$	−9.05762	−	2.94300i	−0.820038	−	0.266447i
$123$	0.865300	+	1.19098i	0.0780215	+	0.107387i
$124$	−2.47003			−0.221815
$125$		0			0
$126$	6.72721			0.599308
$127$	7.96023	+	10.9563i	0.706356	+	0.972216i	0.999868	+	0.0162606i	$0.00517612\pi$
$127$	7.96023	+	10.9563i	0.706356	+	0.972216i	−0.293511	+	0.955956i	$0.594824\pi$
$128$	12.0375	+	3.91123i	1.06398	+	0.345708i
$129$	−0.393313	+	1.21049i	−0.0346292	+	0.106578i
$130$		0			0
$131$	1.41912	+	4.36759i	0.123989	+	0.381599i	0.993716	−	0.111935i	$-0.0357049\pi$
$131$	1.41912	+	4.36759i	0.123989	+	0.381599i	−0.869727	+	0.493534i	$0.835705\pi$
$132$		−	5.38679i		−	0.468860i
$133$	8.84176	−	2.87286i	0.766678	−	0.249109i
$134$	−8.32532	−	6.04870i	−0.719198	−	0.522528i
$135$		0			0
$136$	−4.06607	+	2.95417i	−0.348662	+	0.253318i
$137$	8.97078	−	12.3472i	0.766426	−	1.05489i	−0.230227	−	0.973137i	$-0.573947\pi$
$137$	8.97078	−	12.3472i	0.766426	−	1.05489i	0.996652	−	0.0817573i	$-0.0260532\pi$
$138$	−0.586034	+	0.806606i	−0.0498865	+	0.0686629i
$139$	14.7550	−	10.7201i	1.25150	−	0.909269i	0.253194	−	0.967416i	$-0.418519\pi$
$139$	14.7550	−	10.7201i	1.25150	−	0.909269i	0.998308	+	0.0581460i	$0.0185189\pi$
$140$		0			0
$141$	−4.39586	−	3.19378i	−0.370198	−	0.268964i
$142$	−13.1473	+	4.27182i	−1.10330	+	0.358483i
$143$			19.4435i			1.62595i
$144$	1.54267	+	4.74786i	0.128556	+	0.395655i
$145$		0			0
$146$	−7.02177	+	21.6108i	−0.581126	+	1.78852i
$147$	8.12464	+	2.63986i	0.670109	+	0.217732i
$148$	−0.0111736	−	0.0153792i	−0.000918465	−	0.00126416i
$149$	−14.7323			−1.20692			−0.603458	−	0.797394i	$-0.706211\pi$
$149$	−14.7323			−1.20692			−0.603458	+	0.797394i	$0.706211\pi$
$150$		0			0
$151$	−17.4354			−1.41887			−0.709437	−	0.704769i	$-0.751051\pi$
$151$	−17.4354			−1.41887			−0.709437	+	0.704769i	$0.751051\pi$
$152$	2.57406	+	3.54289i	0.208784	+	0.287366i
$153$	−2.57390	−	0.836312i	−0.208088	−	0.0676118i
$154$	12.2831	−	37.8036i	0.989803	−	3.04630i
$155$		0			0
$156$	0.927051	+	2.85317i	0.0742235	+	0.228436i
$157$			17.9105i			1.42942i	0.699423	+	0.714708i	$0.253440\pi$
$157$			17.9105i			1.42942i	−0.699423	+	0.714708i	$0.746560\pi$
$158$	−27.0445	+	8.78728i	−2.15154	+	0.699078i
$159$	2.27782	+	1.65493i	0.180643	+	0.131245i
$160$		0			0
$161$	−1.86361	+	1.35399i	−0.146873	+	0.106709i
$162$	−1.00297	+	1.38048i	−0.0788011	+	0.108460i
$163$	−12.7901	+	17.6041i	−1.00180	+	1.37886i	−0.0775819	+	0.996986i	$0.524720\pi$
$163$	−12.7901	+	17.6041i	−1.00180	+	1.37886i	−0.924216	+	0.381870i	$0.875280\pi$
$164$	1.08579	−	0.788869i	0.0847856	−	0.0616004i
$165$		0			0
$166$	1.07904	+	0.783966i	0.0837495	+	0.0608475i
$167$	21.4967	−	6.98470i	1.66346	−	0.540492i	0.681871	−	0.731473i	$-0.261167\pi$
$167$	21.4967	−	6.98470i	1.66346	−	0.540492i	0.981594	+	0.190980i	$0.0611666\pi$
$168$			7.32142i			0.564860i
$169$	0.671052	+	2.06529i	0.0516194	+	0.158868i
$170$		0			0
$171$	−0.728704	+	2.24272i	−0.0557254	+	0.171505i
$172$	1.10357	+	0.358572i	0.0841465	+	0.0273409i
$173$	7.58929	+	10.4458i	0.577003	+	0.794177i	0.993363	−	0.115023i	$-0.0366943\pi$
$173$	7.58929	+	10.4458i	0.577003	+	0.794177i	−0.416360	+	0.909200i	$0.636694\pi$
$174$	−6.67473			−0.506010
$175$		0			0
$176$	29.4974			2.22345
$177$	2.75691	+	3.79456i	0.207222	+	0.285216i
$178$	−5.63659	−	1.83144i	−0.422480	−	0.137272i
$179$	1.98716	−	6.11586i	0.148528	−	0.457121i	−0.848920	−	0.528521i	$-0.822747\pi$
$179$	1.98716	−	6.11586i	0.148528	−	0.457121i	0.997448	+	0.0714002i	$0.0227468\pi$
$180$		0			0
$181$	4.54473	+	13.9873i	0.337807	+	1.03966i	0.965323	+	0.261060i	$0.0840720\pi$
$181$	4.54473	+	13.9873i	0.337807	+	1.03966i	−0.627515	+	0.778604i	$0.715928\pi$
$182$			22.1370i			1.64090i
$183$	5.30815	−	1.72472i	0.392389	−	0.127495i
$184$	−0.877852	−	0.637797i	−0.0647161	−	0.0470190i
$185$		0			0
$186$	3.74018	−	2.71740i	0.274243	−	0.199250i
$187$	−9.39931	+	12.9370i	−0.687346	+	0.946050i
$188$	−2.91168	+	4.00758i	−0.212356	+	0.292283i
$189$	−3.18949	+	2.31730i	−0.232001	+	0.168559i
$190$		0			0
$191$	−5.43095	−	3.94582i	−0.392970	−	0.285509i	0.373702	−	0.927549i	$-0.378088\pi$
$191$	−5.43095	−	3.94582i	−0.392970	−	0.285509i	−0.766671	+	0.642040i	$0.778088\pi$
$192$	−1.69903	+	0.552047i	−0.122617	+	0.0398406i
$193$		−	4.82817i		−	0.347539i	−0.984786	−	0.173769i	$-0.944405\pi$
$193$		−	4.82817i		−	0.347539i	0.984786	−	0.173769i	$-0.0555948\pi$
$194$	−1.29421	−	3.98316i	−0.0929186	−	0.285974i
$195$		0			0
$196$	2.40668	−	7.40701i	0.171906	−	0.529072i
$197$	−13.6801	−	4.44492i	−0.974664	−	0.316688i	−0.221967	−	0.975054i	$-0.571248\pi$
$197$	−13.6801	−	4.44492i	−0.974664	−	0.316688i	−0.752697	+	0.658367i	$0.771248\pi$
$198$	5.92627	+	8.15681i	0.421161	+	0.579679i
$199$	8.72608			0.618575			0.309288	−	0.950969i	$-0.399909\pi$
$199$	8.72608			0.618575			0.309288	+	0.950969i	$0.399909\pi$
$200$		0			0
$201$	6.03076			0.425377
$202$	−6.89540	−	9.49071i	−0.485159	−	0.667764i
$203$	−14.6667	−	4.76550i	−1.02940	−	0.334473i
$204$	−0.762442	+	2.34656i	−0.0533816	+	0.164292i
$205$		0			0
$206$	−6.19738	−	19.0736i	−0.431792	−	1.32892i
$207$		−	0.584296i		−	0.0406114i
$208$	−15.6236	+	5.07641i	−1.08330	+	0.351986i
$209$	11.2724	+	8.18990i	0.779730	+	0.566507i
$210$		0			0
$211$	−2.40777	+	1.74935i	−0.165758	+	0.120430i	−0.667572	−	0.744546i	$-0.732666\pi$
$211$	−2.40777	+	1.74935i	−0.165758	+	0.120430i	0.501814	+	0.864976i	$0.332666\pi$
$212$	1.50876	−	2.07663i	0.103622	−	0.142623i
$213$	4.76187	−	6.55415i	0.326278	−	0.449083i
$214$	−7.82426	+	5.68466i	−0.534856	+	0.388595i
$215$		0			0
$216$	−1.50241	−	1.09157i	−0.102226	−	0.0742716i
$217$	10.1586	−	3.30073i	0.689611	−	0.224068i
$218$		−	2.32283i		−	0.157322i
$219$	−4.11505	−	12.6648i	−0.278070	−	0.855810i
$220$		0			0
$221$	2.75202	−	8.46984i	0.185121	−	0.569743i
$222$	0.0338387	+	0.0109949i	0.00227111	+	0.000737927i
$223$	−0.179088	−	0.246494i	−0.0119926	−	0.0165064i	0.802979	−	0.596008i	$-0.203247\pi$
$223$	−0.179088	−	0.246494i	−0.0119926	−	0.0165064i	−0.814971	+	0.579501i	$0.803247\pi$
$224$	18.9408			1.26553
$225$		0			0
$226$	18.2336			1.21288
$227$	5.62641	+	7.74408i	0.373438	+	0.513993i	0.953831	−	0.300343i	$-0.0971013\pi$
$227$	5.62641	+	7.74408i	0.373438	+	0.513993i	−0.580394	+	0.814336i	$0.697101\pi$
$228$	2.04462	+	0.664339i	0.135409	+	0.0439969i
$229$	−3.74812	+	11.5355i	−0.247682	+	0.762288i	0.747501	+	0.664260i	$0.231253\pi$
$229$	−3.74812	+	11.5355i	−0.247682	+	0.762288i	−0.995184	+	0.0980277i	$0.968747\pi$
$230$		0			0
$231$	7.19843	+	22.1545i	0.473622	+	1.45766i
$232$		−	7.26430i		−	0.476924i
$233$	19.1165	−	6.21132i	1.25236	−	0.406917i	0.393595	−	0.919284i	$-0.371231\pi$
$233$	19.1165	−	6.21132i	1.25236	−	0.406917i	0.858766	+	0.512367i	$0.171231\pi$
$234$	−4.54267	−	3.30045i	−0.296964	−	0.215757i
$235$		0			0
$236$	3.45939	−	2.51340i	0.225187	−	0.163608i
$237$	9.79534	−	13.4821i	0.636275	−	0.875758i
$238$	−10.7014	+	14.7292i	−0.693667	+	0.954751i
$239$	14.2902	−	10.3825i	0.924358	−	0.671585i	−0.0202473	−	0.999795i	$-0.506445\pi$
$239$	14.2902	−	10.3825i	0.924358	−	0.671585i	0.944605	+	0.328210i	$0.106445\pi$
$240$		0			0
$241$	−23.8973	−	17.3624i	−1.53936	−	1.11841i	−0.950733	−	0.310010i	$-0.899668\pi$
$241$	−23.8973	−	17.3624i	−1.53936	−	1.11841i	−0.588630	−	0.808403i	$-0.700332\pi$
$242$	38.8066	−	12.6090i	2.49458	−	0.810538i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.57238	−	4.83929i	−0.100661	−	0.309804i
$245$		0			0
$246$	−0.776250	+	2.38905i	−0.0494919	+	0.152320i
$247$	−7.38002	−	2.39791i	−0.469580	−	0.152576i
$248$	2.95742	+	4.07055i	0.187797	+	0.258480i
$249$	−0.781641			−0.0495345
$250$		0			0
$251$	1.89396			0.119546			0.0597729	−	0.998212i	$-0.480962\pi$
$251$	1.89396			0.119546			0.0597729	+	0.998212i	$0.480962\pi$
$252$	2.11262	+	2.90777i	0.133083	+	0.183172i
$253$	−3.28345	−	1.06686i	−0.206429	−	0.0670727i
$254$	−7.14103	+	21.9778i	−0.448068	+	1.37901i
$255$		0			0
$256$	5.56989	+	17.1424i	0.348118	+	1.07140i
$257$			22.1211i			1.37988i	0.723869	+	0.689938i	$0.242362\pi$
$257$			22.1211i			1.37988i	−0.723869	+	0.689938i	$0.757638\pi$
$258$	−2.06554	+	0.671134i	−0.128595	+	0.0417830i
$259$	0.0665056	+	0.0483191i	0.00413245	+	0.00300240i
$260$		0			0
$261$	3.16461	−	2.29922i	0.195884	−	0.142318i
$262$	−4.60602	+	6.33964i	−0.284561	+	0.391664i
$263$	11.5884	−	15.9500i	0.714569	−	0.983520i	−0.285118	−	0.958492i	$-0.592033\pi$
$263$	11.5884	−	15.9500i	0.714569	−	0.983520i	0.999687	−	0.0250272i	$-0.00796722\pi$
$264$	−8.87728	+	6.44972i	−0.546359	+	0.396953i
$265$		0			0
$266$	12.8340	+	9.32443i	0.786902	+	0.571718i
$267$	3.30328	−	1.07330i	0.202157	−	0.0656849i
$268$		−	5.49807i		−	0.335848i
$269$	−5.61321	−	17.2757i	−0.342244	−	1.05332i	−0.963043	−	0.269348i	$-0.913192\pi$
$269$	−5.61321	−	17.2757i	−0.342244	−	1.05332i	0.620799	−	0.783970i	$-0.286808\pi$
$270$		0			0
$271$	6.97436	−	21.4649i	0.423662	−	1.30390i	−0.480608	−	0.876936i	$-0.659584\pi$
$271$	6.97436	−	21.4649i	0.423662	−	1.30390i	0.904270	−	0.426962i	$-0.140416\pi$
$272$	−12.8494	−	4.17503i	−0.779111	−	0.253149i
$273$	−7.62545	−	10.4955i	−0.461513	−	0.635218i
$274$	26.0425			1.57329
$275$		0			0
$276$	−0.532686			−0.0320639
$277$	−4.85212	−	6.67837i	−0.291535	−	0.401264i	0.637977	−	0.770056i	$-0.279772\pi$
$277$	−4.85212	−	6.67837i	−0.291535	−	0.401264i	−0.929512	+	0.368792i	$0.879772\pi$
$278$	29.5978	+	9.61690i	1.77516	+	0.576783i
$279$	−0.837233	+	2.57674i	−0.0501238	+	0.154265i
$280$		0			0
$281$	0.395941	+	1.21858i	0.0236199	+	0.0726944i	0.962172	−	0.272444i	$-0.0878320\pi$
$281$	0.395941	+	1.21858i	0.0236199	+	0.0726944i	−0.938552	+	0.345138i	$0.887832\pi$
$282$		−	9.27165i		−	0.552119i
$283$	2.54058	−	0.825484i	0.151022	−	0.0490699i	−0.232531	−	0.972589i	$-0.574701\pi$
$283$	2.54058	−	0.825484i	0.151022	−	0.0490699i	0.383552	+	0.923519i	$0.374701\pi$
$284$	−5.97524	−	4.34126i	−0.354565	−	0.257607i
$285$		0			0
$286$	−26.8413	+	19.5013i	−1.58716	+	1.15314i
$287$	−3.41138	+	4.69537i	−0.201368	+	0.277159i
$288$	−2.82392	+	3.88679i	−0.166401	+	0.229031i
$289$	−7.82773	+	5.68718i	−0.460455	+	0.334540i
$290$		0			0
$291$	1.98567	+	1.44268i	0.116402	+	0.0845712i
$292$	−11.5462	+	3.75158i	−0.675689	+	0.219545i
$293$		−	17.6605i		−	1.03174i	−0.856667	−	0.515870i	$-0.827469\pi$
$293$		−	17.6605i		−	1.03174i	0.856667	−	0.515870i	$-0.172531\pi$
$294$	4.50455	+	13.8636i	0.262711	+	0.808541i
$295$		0			0
$296$	−0.0119660	+	0.0368276i	−0.000695511	+	0.00214056i
$297$	−5.61950	−	1.82589i	−0.326076	−	0.105949i
$298$	−14.7761	−	20.3376i	−0.855958	−	1.17812i
$299$	1.92272			0.111194
$300$		0			0
$301$	−5.01787			−0.289225
$302$	−17.4873	−	24.0692i	−1.00628	−	1.38503i
$303$	6.53847	+	2.12448i	0.375625	+	0.122048i
$304$	−3.63783	+	11.1961i	−0.208644	+	0.642140i
$305$		0			0
$306$	−1.42705	−	4.39201i	−0.0815791	−	0.251075i
$307$		−	28.5593i		−	1.62997i	−0.579484	−	0.814983i	$-0.696746\pi$
$307$		−	28.5593i		−	1.62997i	0.579484	−	0.814983i	$-0.303254\pi$
$308$	20.1976	−	6.56260i	1.15087	−	0.373939i
$309$	9.50850	+	6.90833i	0.540920	+	0.393001i
$310$		0			0
$311$	23.7271	−	17.2388i	1.34544	−	0.977521i	0.346217	−	0.938154i	$-0.387466\pi$
$311$	23.7271	−	17.2388i	1.34544	−	0.977521i	0.999225	−	0.0393664i	$-0.0125340\pi$
$312$	3.59197	−	4.94392i	0.203355	−	0.279894i
$313$	10.2823	−	14.1523i	0.581189	−	0.799937i	−0.412637	−	0.910896i	$-0.635392\pi$
$313$	10.2823	−	14.1523i	0.581189	−	0.799937i	0.993825	+	0.110958i	$0.0353920\pi$
$314$	−24.7251	+	17.9638i	−1.39532	+	1.01376i
$315$		0			0
$316$	−12.2913	−	8.93013i	−0.691438	−	0.502359i
$317$	−3.72589	+	1.21061i	−0.209267	+	0.0679949i	−0.411775	−	0.911286i	$-0.635091\pi$
$317$	−3.72589	+	1.21061i	−0.209267	+	0.0679949i	0.202508	+	0.979281i	$0.435091\pi$
$318$			4.80433i			0.269414i
$319$	−7.14227	−	21.9816i	−0.399890	−	1.23074i
$320$		0			0
$321$	1.75145	−	5.39040i	0.0977562	−	0.300863i
$322$	−3.73830	−	1.21465i	−0.208327	−	0.0676897i
$323$	−3.75123	−	5.16312i	−0.208724	−	0.287284i
$324$	−0.911672			−0.0506484
$325$		0			0
$326$	−37.1301			−2.05645
$327$	0.800139	+	1.10130i	0.0442478	+	0.0609018i
$328$	−2.60007	−	0.844815i	−0.143565	−	0.0466471i
$329$	6.61961	−	20.3731i	0.364951	−	1.12320i
$330$		0			0
$331$	−5.42429	−	16.6942i	−0.298146	−	0.917599i	−0.982147	−	0.188117i	$-0.939762\pi$
$331$	−5.42429	−	16.6942i	−0.298146	−	0.917599i	0.684001	−	0.729481i	$-0.260238\pi$
$332$			0.712600i			0.0391090i
$333$	−0.0198309	+	0.00644345i	−0.00108673	+	0.000353099i
$334$	31.2029	+	22.6702i	1.70734	+	1.24046i
$335$		0			0
$336$	−15.9226	+	11.5684i	−0.868648	+	0.631110i
$337$	−8.25697	+	11.3647i	−0.449786	+	0.619077i	−0.972352	−	0.233522i	$-0.924975\pi$
$337$	−8.25697	+	11.3647i	−0.449786	+	0.619077i	0.522566	+	0.852599i	$0.324975\pi$
$338$	−2.17803	+	2.99780i	−0.118469	+	0.163059i
$339$	−8.64489	+	6.28088i	−0.469526	+	0.341131i
$340$		0			0
$341$	12.9513	+	9.40966i	0.701351	+	0.509562i
$342$	−3.82689	+	1.24343i	−0.206935	+	0.0672371i
$343$			6.08221i			0.328408i
$344$	−0.730414	−	2.24798i	−0.0393813	−	0.121203i
$345$		0			0
$346$	−6.80826	+	20.9537i	−0.366014	+	1.12648i
$347$	−0.980059	−	0.318440i	−0.0526123	−	0.0170948i	0.282593	−	0.959240i	$-0.408806\pi$
$347$	−0.980059	−	0.318440i	−0.0526123	−	0.0170948i	−0.335205	+	0.942145i	$0.608806\pi$
$348$	−2.09614	−	2.88508i	−0.112365	−	0.154657i
$349$	−21.5626			−1.15422			−0.577109	−	0.816667i	$-0.695819\pi$
$349$	−21.5626			−1.15422			−0.577109	+	0.816667i	$0.695819\pi$
$350$		0			0
$351$	3.29066			0.175642
$352$	16.6857	+	22.9658i	0.889348	+	1.22408i
$353$	−6.80599	−	2.21140i	−0.362246	−	0.117701i	0.122238	−	0.992501i	$-0.460993\pi$
$353$	−6.80599	−	2.21140i	−0.362246	−	0.117701i	−0.484485	+	0.874800i	$0.660993\pi$
$354$	−2.47319	+	7.61169i	−0.131448	+	0.404557i
$355$		0			0
$356$	−0.978498	−	3.01151i	−0.0518603	−	0.159610i
$357$		−	10.6696i		−	0.564697i
$358$	10.4359	−	3.39082i	0.551553	−	0.179210i
$359$	21.9663	+	15.9595i	1.15934	+	0.842308i	0.989694	−	0.143198i	$-0.0457385\pi$
$359$	21.9663	+	15.9595i	1.15934	+	0.842308i	0.169643	+	0.985506i	$0.445738\pi$
$360$		0			0
$361$	10.8725	−	7.89936i	0.572239	−	0.415756i
$362$	−14.7508	+	20.3028i	−0.775285	+	1.06709i
$363$	−14.0555	+	19.3457i	−0.737722	+	1.01539i
$364$	−9.56848	+	6.95191i	−0.501525	+	0.364379i
$365$		0			0
$366$	7.70487	+	5.59792i	0.402740	+	0.292608i
$367$	−20.3929	+	6.62605i	−1.06450	+	0.345877i	−0.788343	−	0.615236i	$-0.789061\pi$
$367$	−20.3929	+	6.62605i	−1.06450	+	0.345877i	−0.276157	+	0.961113i	$0.589061\pi$
$368$		−	2.91692i		−	0.152055i
$369$	−0.454915	−	1.40008i	−0.0236819	−	0.0728855i
$370$		0			0
$371$	−3.43011	+	10.5568i	−0.178083	+	0.548082i
$372$	2.34914	+	0.763282i	0.121797	+	0.0395743i
$373$	3.75638	+	5.17021i	0.194498	+	0.267703i	0.895116	−	0.445833i	$-0.147092\pi$
$373$	3.75638	+	5.17021i	0.194498	+	0.267703i	−0.700618	+	0.713536i	$0.747092\pi$
$374$	−27.2865			−1.41095
$375$		0			0
$376$	10.0906			0.520383
$377$	7.56596	+	10.4136i	0.389667	+	0.536330i
$378$	−6.39796	−	2.07882i	−0.329076	−	0.106923i
$379$	0.0477946	−	0.147097i	0.00245504	−	0.00755585i	−0.949821	−	0.312792i	$-0.898736\pi$
$379$	0.0477946	−	0.147097i	0.00245504	−	0.00755585i	0.952277	+	0.305237i	$0.0987356\pi$
$380$		0			0
$381$	−4.18494	−	12.8799i	−0.214401	−	0.659859i
$382$		−	11.4549i		−	0.586081i
$383$	−4.04682	+	1.31489i	−0.206783	+	0.0671878i	−0.410577	−	0.911826i	$-0.634673\pi$
$383$	−4.04682	+	1.31489i	−0.206783	+	0.0671878i	0.203794	+	0.979014i	$0.434673\pi$
$384$	−10.2397	−	7.43961i	−0.522545	−	0.379651i
$385$		0			0
$386$	6.66517	−	4.84253i	0.339248	−	0.246478i
$387$	0.748125	−	1.02971i	0.0380293	−	0.0523429i
$388$	1.31525	−	1.81028i	0.0667716	−	0.0919032i
$389$	−16.4782	+	11.9721i	−0.835479	+	0.607011i	−0.921104	−	0.389316i	$-0.872711\pi$
$389$	−16.4782	+	11.9721i	−0.835479	+	0.607011i	0.0856250	+	0.996327i	$0.472711\pi$
$390$		0			0
$391$	1.27931	+	0.929474i	0.0646975	+	0.0470055i
$392$	−15.0881	+	4.90243i	−0.762066	+	0.247610i
$393$		−	4.59236i		−	0.231654i
$394$	−7.58465	−	23.3431i	−0.382109	−	1.17601i
$395$		0			0
$396$	−1.66461	+	5.12314i	−0.0836497	+	0.257447i
$397$	−1.86137	−	0.604795i	−0.0934194	−	0.0303538i	0.261934	−	0.965086i	$-0.415640\pi$
$397$	−1.86137	−	0.604795i	−0.0934194	−	0.0303538i	−0.355354	+	0.934732i	$0.615640\pi$
$398$	8.75203	+	12.0461i	0.438700	+	0.603818i
$399$	−9.29678			−0.465421
$400$		0			0
$401$	−32.8337			−1.63964			−0.819818	−	0.572624i	$-0.805925\pi$
$401$	−32.8337			−1.63964			−0.819818	+	0.572624i	$0.805925\pi$
$402$	6.04870	+	8.32532i	0.301682	+	0.415229i
$403$	−8.47916	−	2.75505i	−0.422377	−	0.137239i
$404$	1.93683	−	5.96094i	0.0963607	−	0.296568i
$405$		0			0
$406$	−8.13167	−	25.0267i	−0.403568	−	1.24206i
$407$			0.123205i			0.00610704i
$408$	4.77995	−	1.55310i	0.236643	−	0.0768899i
$409$	−32.0180	−	23.2624i	−1.58319	−	1.15025i	−0.912923	−	0.408132i	$-0.866180\pi$
$409$	−32.0180	−	23.2624i	−1.58319	−	1.15025i	−0.670265	−	0.742122i	$-0.733820\pi$
$410$		0			0
$411$	−12.3472	+	8.97078i	−0.609043	+	0.442496i
$412$	6.29813	−	8.66863i	0.310287	−	0.427073i
$413$	−10.8689	+	14.9598i	−0.534825	+	0.736123i
$414$	0.806606	−	0.586034i	0.0396425	−	0.0288020i
$415$		0			0
$416$	−12.7901	−	9.29254i	−0.627086	−	0.455604i
$417$	−17.3455	+	5.63591i	−0.849414	+	0.275991i
$418$			23.7756i			1.16290i
$419$	−6.04421	−	18.6022i	−0.295279	−	0.908776i	−0.983128	−	0.182921i	$-0.941445\pi$
$419$	−6.04421	−	18.6022i	−0.295279	−	0.908776i	0.687848	−	0.725854i	$-0.258555\pi$
$420$		0			0
$421$	−12.4634	+	38.3584i	−0.607430	+	1.86948i	−0.128292	+	0.991736i	$0.540949\pi$
$421$	−12.4634	+	38.3584i	−0.607430	+	1.86948i	−0.479138	+	0.877740i	$0.659051\pi$
$422$	−4.82987	−	1.56932i	−0.235114	−	0.0763932i
$423$	3.19378	+	4.39586i	0.155287	+	0.213734i
$424$	−5.22869			−0.253928
$425$		0			0
$426$	13.8239			0.669769
$427$	12.9336	+	17.8016i	0.625901	+	0.861478i
$428$	−4.91428	−	1.59675i	−0.237540	−	0.0771816i
$429$	6.00837	−	18.4919i	0.290087	−	0.892795i
$430$		0			0
$431$	4.24497	+	13.0647i	0.204473	+	0.629304i	0.999735	+	0.0230370i	$0.00733356\pi$
$431$	4.24497	+	13.0647i	0.204473	+	0.629304i	−0.795261	+	0.606267i	$0.792666\pi$
$432$		−	4.99220i		−	0.240187i
$433$	−11.8172	+	3.83964i	−0.567899	+	0.184522i	−0.578872	−	0.815418i	$-0.696507\pi$
$433$	−11.8172	+	3.83964i	−0.567899	+	0.184522i	0.0109734	+	0.999940i	$0.496507\pi$
$434$	14.7454	+	10.7132i	0.707802	+	0.514248i
$435$		0			0
$436$	1.00402	−	0.729464i	0.0480839	−	0.0349350i
$437$	0.809879	−	1.11470i	0.0387417	−	0.0533234i
$438$	13.3562	−	18.3832i	0.638184	−	0.878385i
$439$	8.87118	−	6.44529i	0.423399	−	0.307617i	−0.355605	−	0.934636i	$-0.615725\pi$
$439$	8.87118	−	6.44529i	0.423399	−	0.307617i	0.779004	+	0.627019i	$0.215725\pi$
$440$		0			0
$441$	−6.91123	−	5.02131i	−0.329106	−	0.239110i
$442$	14.4526	−	4.69594i	0.687440	−	0.223363i
$443$		−	8.13187i		−	0.386357i	−0.981164	−	0.193178i	$-0.938120\pi$
$443$		−	8.13187i		−	0.386357i	0.981164	−	0.193178i	$-0.0618796\pi$
$444$	0.00587431	+	0.0180793i	0.000278783	+	0.000858005i
$445$		0			0
$446$	0.160658	−	0.494454i	0.00760737	−	0.0234131i
$447$	14.0112	+	4.55253i	0.662709	+	0.215327i
$448$	−4.13977	−	5.69791i	−0.195586	−	0.269201i
$449$	32.9503			1.55502			0.777511	−	0.628869i	$-0.216482\pi$
$449$	32.9503			1.55502			0.777511	+	0.628869i	$0.216482\pi$
$450$		0			0
$451$	−8.69840			−0.409592
$452$	5.72610	+	7.88130i	0.269333	+	0.370705i
$453$	16.5821	+	5.38784i	0.779093	+	0.253143i
$454$	−5.04738	+	15.5342i	−0.236885	+	0.729058i
$455$		0			0
$456$	−1.35326	−	4.16491i	−0.0633723	−	0.195040i
$457$		−	22.8800i		−	1.07028i	−0.844762	−	0.535142i	$-0.820258\pi$
$457$		−	22.8800i		−	1.07028i	0.844762	−	0.535142i	$-0.179742\pi$
$458$	−19.6838	+	6.39564i	−0.919762	+	0.298849i
$459$	2.18949	+	1.59076i	0.102197	+	0.0742503i
$460$		0			0
$461$	−9.74259	+	7.07841i	−0.453758	+	0.329674i	−0.791078	−	0.611716i	$-0.790480\pi$
$461$	−9.74259	+	7.07841i	−0.453758	+	0.329674i	0.337320	+	0.941390i	$0.390480\pi$
$462$	−23.3639	+	32.1576i	−1.08699	+	1.49611i
$463$	15.9878	−	22.0054i	0.743018	−	1.02268i	−0.255421	−	0.966830i	$-0.582214\pi$
$463$	15.9878	−	22.0054i	0.743018	−	1.02268i	0.998439	−	0.0558471i	$-0.0177859\pi$
$464$	15.7984	−	11.4782i	0.733420	−	0.532861i
$465$		0			0
$466$	27.7479	+	20.1600i	1.28540	+	0.933895i
$467$	3.74947	−	1.21828i	0.173505	−	0.0563752i	−0.220976	−	0.975279i	$-0.570924\pi$
$467$	3.74947	−	1.21828i	0.173505	−	0.0563752i	0.394481	+	0.918904i	$0.370924\pi$
$468$		−	3.00000i		−	0.138675i
$469$	7.34714	+	22.6122i	0.339259	+	1.04413i
$470$		0			0
$471$	5.53466	−	17.0339i	0.255024	−	0.784882i
$472$	−8.28402	−	2.69164i	−0.381303	−	0.123893i
$473$	−4.42044	−	6.08421i	−0.203252	−	0.279752i
$474$	28.4362			1.30612
$475$		0			0
$476$	−9.72721			−0.445846
$477$	−1.65493	−	2.27782i	−0.0757742	−	0.104294i
$478$	28.6655	+	9.31397i	1.31113	+	0.426011i
$479$	−6.16466	+	18.9729i	−0.281670	+	0.866893i	0.705706	+	0.708504i	$0.250630\pi$
$479$	−6.16466	+	18.9729i	−0.281670	+	0.866893i	−0.987377	+	0.158388i	$0.949370\pi$
$480$		0			0
$481$	−0.0212032	−	0.0652567i	−0.000966783	−	0.00297545i
$482$		−	50.4038i		−	2.29583i
$483$	2.19080	−	0.711834i	0.0996849	−	0.0323896i
$484$	17.6370	+	12.8140i	0.801680	+	0.582455i
$485$		0			0
$486$	1.38048	−	1.00297i	0.0626197	−	0.0454958i
$487$	−6.46697	+	8.90102i	−0.293046	+	0.403344i	−0.930001	−	0.367558i	$-0.880194\pi$
$487$	−6.46697	+	8.90102i	−0.293046	+	0.403344i	0.636954	+	0.770902i	$0.280194\pi$
$488$	−6.09237	+	8.38543i	−0.275789	+	0.379591i
$489$	17.6041	−	12.7901i	0.796083	−	0.578388i
$490$		0			0
$491$	26.9348	+	19.5693i	1.21555	+	0.883151i	0.995723	−	0.0923876i	$-0.0294499\pi$
$491$	26.9348	+	19.5693i	1.21555	+	0.883151i	0.219830	+	0.975538i	$0.429450\pi$
$492$	−1.27642	+	0.414733i	−0.0575453	+	0.0186976i
$493$			10.5864i			0.476788i
$494$	−4.09171	−	12.5930i	−0.184095	−	0.566585i
$495$		0			0
$496$	−4.17963	+	12.8636i	−0.187671	+	0.577592i
$497$	30.3759	+	9.86973i	1.36255	+	0.442718i
$498$	−0.783966	−	1.07904i	−0.0351303	−	0.0483528i
$499$	41.1448			1.84189			0.920946	−	0.389690i	$-0.127418\pi$
$499$	41.1448			1.84189			0.920946	+	0.389690i	$0.127418\pi$
$500$		0			0
$501$	−22.6030			−1.00983
$502$	1.89960	+	2.61457i	0.0847832	+	0.116694i
$503$	−30.5062	−	9.91207i	−1.36021	−	0.441958i	−0.464094	−	0.885786i	$-0.653620\pi$
$503$	−30.5062	−	9.91207i	−1.36021	−	0.441958i	−0.896112	+	0.443829i	$0.853620\pi$
$504$	2.26244	−	6.96308i	0.100777	−	0.310160i
$505$		0			0
$506$	−1.82044	−	5.60275i	−0.0809286	−	0.249073i
$507$		−	2.17157i		−	0.0964429i
$508$	−11.7423	+	3.81529i	−0.520979	+	0.169276i
$509$	−21.9206	−	15.9262i	−0.971612	−	0.705918i	−0.0157938	−	0.999875i	$-0.505028\pi$
$509$	−21.9206	−	15.9262i	−0.971612	−	0.705918i	−0.955818	+	0.293958i	$0.905028\pi$
$510$		0			0
$511$	42.4732	−	30.8586i	1.87890	−	1.36510i
$512$	−3.19893	+	4.40295i	−0.141374	+	0.194585i
$513$	1.38608	−	1.90777i	0.0611968	−	0.0842301i
$514$	−30.5376	+	22.1869i	−1.34696	+	0.978622i
$515$		0			0
$516$	−0.938754	−	0.682045i	−0.0413263	−	0.0300253i
$517$	30.5340	−	9.92109i	1.34288	−	0.436329i
$518$			0.140272i			0.00616321i
$519$	−3.98993	−	12.2797i	−0.175138	−	0.539020i
$520$		0			0
$521$	8.02073	−	24.6853i	0.351395	−	1.08148i	−0.606676	−	0.794949i	$-0.707497\pi$
$521$	8.02073	−	24.6853i	0.351395	−	1.08148i	0.958071	−	0.286532i	$-0.0925026\pi$
$522$	6.34804	+	2.06260i	0.277846	+	0.0902778i
$523$	−1.05438	−	1.45123i	−0.0461047	−	0.0634577i	0.785342	−	0.619062i	$-0.212487\pi$
$523$	−1.05438	−	1.45123i	−0.0461047	−	0.0634577i	−0.831447	+	0.555604i	$0.812487\pi$
$524$	−4.18673			−0.182898
$525$		0			0
$526$	33.6414			1.46684
$527$	−4.30991	−	5.93209i	−0.187743	−	0.258406i
$528$	−28.0537	−	9.11519i	−1.22088	−	0.396688i
$529$	7.00189	−	21.5496i	0.304430	−	0.936939i
$530$		0			0
$531$	−1.44939	−	4.46077i	−0.0628983	−	0.193581i
$532$			8.47561i			0.367464i
$533$	4.60720	−	1.49697i	0.199560	−	0.0648410i
$534$	4.79477	+	3.48361i	0.207490	+	0.150750i
$535$		0			0
$536$	−9.06068	+	6.58297i	−0.391362	+	0.284341i
$537$	−3.77981	+	5.20246i	−0.163111	+	0.224503i
$538$	18.2188	−	25.0760i	0.785467	−	1.08110i
$539$	−40.8364	+	29.6693i	−1.75895	+	1.27795i
$540$		0			0
$541$	6.01538	+	4.37043i	0.258621	+	0.187899i	0.709539	−	0.704666i	$-0.248903\pi$
$541$	6.01538	+	4.37043i	0.258621	+	0.187899i	−0.450918	+	0.892566i	$0.648903\pi$
$542$	36.6268	−	11.9008i	1.57326	−	0.511182i
$543$		−	14.7071i		−	0.631141i
$544$	−4.01792	−	12.3659i	−0.172267	−	0.530183i
$545$		0			0
$546$	6.84070	−	21.0535i	0.292755	−	0.901007i
$547$	18.5330	+	6.02174i	0.792414	+	0.257471i	0.677132	−	0.735862i	$-0.263223\pi$
$547$	18.5330	+	6.02174i	0.792414	+	0.257471i	0.115283	+	0.993333i	$0.463223\pi$
$548$	8.17841	+	11.2566i	0.349364	+	0.480859i
$549$	−5.58132			−0.238205
$550$		0			0
$551$	9.22425			0.392966
$552$	0.637797	+	0.877852i	0.0271464	+	0.0373639i
$553$	62.4843	+	20.3024i	2.65710	+	0.863345i
$554$	4.35277	−	13.3965i	0.184932	−	0.569161i
$555$		0			0
$556$	5.13810	+	15.8134i	0.217904	+	0.670639i
$557$		−	26.3285i		−	1.11557i	−0.829984	−	0.557787i	$-0.811650\pi$
$557$		−	26.3285i		−	1.11557i	0.829984	−	0.557787i	$-0.188350\pi$
$558$	−4.39685	+	1.42862i	−0.186133	+	0.0604784i
$559$	3.38841	+	2.46182i	0.143314	+	0.104124i
$560$		0			0
$561$	12.9370	−	9.39931i	0.546202	−	0.396839i
$562$	−1.28510	+	1.76879i	−0.0542088	+	0.0746120i
$563$	−21.6134	+	29.7482i	−0.910895	+	1.25374i	0.0559656	+	0.998433i	$0.482176\pi$
$563$	−21.6134	+	29.7482i	−0.910895	+	1.25374i	−0.966860	+	0.255306i	$0.917824\pi$
$564$	4.00758	−	2.91168i	0.168749	−	0.122604i
$565$		0			0
$566$	3.68770	+	2.67927i	0.155005	+	0.112618i
$567$	3.74947	−	1.21828i	0.157463	−	0.0511629i
$568$			15.0449i			0.631271i
$569$	11.2118	+	34.5065i	0.470025	+	1.44659i	0.852552	+	0.522643i	$0.175054\pi$
$569$	11.2118	+	34.5065i	0.470025	+	1.44659i	−0.382527	+	0.923944i	$0.624946\pi$
$570$		0			0
$571$	−1.03966	+	3.19975i	−0.0435085	+	0.133906i	−0.970451	−	0.241298i	$-0.922427\pi$
$571$	−1.03966	+	3.19975i	−0.0435085	+	0.133906i	0.926943	+	0.375203i	$0.122427\pi$
$572$	−16.8585	−	5.47766i	−0.704889	−	0.229032i
$573$	3.94582	+	5.43095i	0.164839	+	0.226881i
$574$	−9.90337			−0.413359
$575$		0			0
$576$	1.78646			0.0744359
$577$	4.04656	+	5.56961i	0.168461	+	0.231866i	0.884898	−	0.465786i	$-0.154228\pi$
$577$	4.04656	+	5.56961i	0.168461	+	0.231866i	−0.716437	+	0.697652i	$0.754228\pi$
$578$	−15.7020	−	5.10190i	−0.653118	−	0.212211i
$579$	−1.49199	+	4.59186i	−0.0620048	+	0.190831i
$580$		0			0
$581$	−0.952256	−	2.93074i	−0.0395062	−	0.121588i
$582$			4.18814i			0.173604i
$583$	−15.8219	+	5.14086i	−0.655278	+	0.212913i
$584$	20.0070	+	14.5359i	0.827895	+	0.601501i
$585$		0			0
$586$	24.3800	−	17.7131i	1.00713	−	0.731720i
$587$	−8.66258	+	11.9230i	−0.357543	+	0.492116i	−0.949462	−	0.313882i	$-0.898370\pi$
$587$	−8.66258	+	11.9230i	−0.357543	+	0.492116i	0.591919	+	0.805997i	$0.298370\pi$
$588$	−4.57778	+	6.30078i	−0.188785	+	0.259840i
$589$	−5.16880	+	3.75536i	−0.212977	+	0.154737i
$590$		0			0
$591$	11.6370	+	8.45474i	0.478680	+	0.347782i
$592$	−0.0989998	+	0.0321670i	−0.00406887	+	0.00132206i
$593$		−	5.82561i		−	0.239229i	−0.992820	−	0.119615i	$-0.961834\pi$
$593$		−	5.82561i		−	0.239229i	0.992820	−	0.119615i	$-0.0381659\pi$
$594$	−3.11562	−	9.58890i	−0.127836	−	0.393437i
$595$		0			0
$596$	4.15041	−	12.7737i	0.170008	−	0.523230i
$597$	−8.29899	−	2.69651i	−0.339655	−	0.110361i
$598$	1.92844	+	2.65426i	0.0788596	+	0.108541i
$599$	27.1527			1.10943			0.554715	−	0.832040i	$-0.312827\pi$
$599$	27.1527			1.10943			0.554715	+	0.832040i	$0.312827\pi$
$600$		0			0
$601$	20.9140			0.853101			0.426551	−	0.904464i	$-0.359729\pi$
$601$	20.9140			0.853101			0.426551	+	0.904464i	$0.359729\pi$
$602$	−5.03280	−	6.92705i	−0.205121	−	0.282326i
$603$	−5.73559	−	1.86361i	−0.233571	−	0.0758919i
$604$	4.91194	−	15.1174i	0.199864	−	0.615118i
$605$		0			0
$606$	3.62513	+	11.1570i	0.147261	+	0.453222i
$607$			1.46424i			0.0594318i	0.999558	+	0.0297159i	$0.00946025\pi$
$607$			1.46424i			0.0594318i	−0.999558	+	0.0297159i	$0.990540\pi$
$608$	−10.7748	+	3.50094i	−0.436975	+	0.141982i
$609$	12.4762	+	9.06453i	0.505563	+	0.367313i
$610$		0			0
$611$	−14.4653	+	10.5096i	−0.585202	+	0.425174i
$612$	1.45025	−	1.99610i	0.0586229	−	0.0806875i
$613$	−20.4023	+	28.0814i	−0.824041	+	1.13420i	0.164962	+	0.986300i	$0.447250\pi$
$613$	−20.4023	+	28.0814i	−0.824041	+	1.13420i	−0.989003	+	0.147896i	$0.952750\pi$
$614$	39.4255	−	28.6443i	1.59108	−	1.15599i
$615$		0			0
$616$	−34.9981	−	25.4276i	−1.41011	−	1.02451i
$617$	−39.8529	+	12.9490i	−1.60442	+	0.521307i	−0.968194	−	0.250199i	$-0.919504\pi$
$617$	−39.8529	+	12.9490i	−1.60442	+	0.521307i	−0.636222	+	0.771506i	$0.719504\pi$
$618$			20.0551i			0.806736i
$619$	5.79758	+	17.8431i	0.233025	+	0.717176i	0.997377	+	0.0723776i	$0.0230587\pi$
$619$	5.79758	+	17.8431i	0.233025	+	0.717176i	−0.764353	+	0.644798i	$0.776941\pi$
$620$		0			0
$621$	−0.180557	+	0.555698i	−0.00724551	+	0.0222994i
$622$	47.5954	+	15.4647i	1.90840	+	0.620077i
$623$	8.04863	+	11.0780i	0.322461	+	0.443830i
$624$	16.4276			0.657631
$625$		0			0
$626$	29.8498			1.19304
$627$	−8.18990	−	11.2724i	−0.327073	−	0.450177i
$628$	−15.5294	−	5.04579i	−0.619689	−	0.201349i
$629$	0.0174383	−	0.0536696i	0.000695311	−	0.00213995i
$630$		0			0
$631$	3.05583	+	9.40488i	0.121651	+	0.374402i	0.993276	−	0.115770i	$-0.0369337\pi$
$631$	3.05583	+	9.40488i	0.121651	+	0.374402i	−0.871625	+	0.490173i	$0.836934\pi$
$632$			30.9479i			1.23104i
$633$	2.83050	−	0.919687i	0.112502	−	0.0365543i
$634$	−5.40820	−	3.92928i	−0.214787	−	0.156052i
$635$		0			0
$636$	−2.07663	+	1.50876i	−0.0823436	+	0.0598261i
$637$	16.5234	−	22.7425i	0.654681	−	0.901091i
$638$	23.1816	−	31.9068i	0.917769	−	1.26320i
$639$	−6.55415	+	4.76187i	−0.259278	+	0.188377i
$640$		0			0
$641$	1.46647	+	1.06546i	0.0579223	+	0.0420830i	0.616370	−	0.787457i	$-0.288603\pi$
$641$	1.46647	+	1.06546i	0.0579223	+	0.0420830i	−0.558447	+	0.829540i	$0.688603\pi$
$642$	9.19797	−	2.98860i	0.363015	−	0.117951i
$643$		−	45.7391i		−	1.80377i	−0.431974	−	0.901886i	$-0.642183\pi$
$643$		−	45.7391i		−	1.80377i	0.431974	−	0.901886i	$-0.357817\pi$
$644$	−0.648959	−	1.99729i	−0.0255726	−	0.0787043i
$645$		0			0
$646$	3.36518	−	10.3570i	0.132401	−	0.407489i
$647$	−24.4204	−	7.93466i	−0.960064	−	0.311944i	−0.213266	−	0.976994i	$-0.568410\pi$
$647$	−24.4204	−	7.93466i	−0.960064	−	0.311944i	−0.746798	+	0.665050i	$0.768410\pi$
$648$	1.09157	+	1.50241i	0.0428807	+	0.0590203i
$649$	−27.7137			−1.08786
$650$		0			0
$651$	−10.6814			−0.418637
$652$	−11.6604	−	16.0491i	−0.456655	−	0.628532i
$653$	−34.2079	−	11.1148i	−1.33866	−	0.434957i	−0.449798	−	0.893130i	$-0.648504\pi$
$653$	−34.2079	−	11.1148i	−1.33866	−	0.434957i	−0.888863	+	0.458173i	$0.848504\pi$
$654$	−0.717795	+	2.20914i	−0.0280680	+	0.0863844i
$655$		0			0
$656$	−2.27103	−	6.98950i	−0.0886687	−	0.272894i
$657$			13.3166i			0.519530i
$658$	34.7638	−	11.2954i	1.35523	−	0.440342i
$659$	−25.9633	−	18.8635i	−1.01139	−	0.734816i	−0.0468880	−	0.998900i	$-0.514930\pi$
$659$	−25.9633	−	18.8635i	−1.01139	−	0.734816i	−0.964500	+	0.264084i	$0.914930\pi$
$660$		0			0
$661$	−13.1113	+	9.52591i	−0.509970	+	0.370515i	−0.812812	−	0.582526i	$-0.802064\pi$
$661$	−13.1113	+	9.52591i	−0.509970	+	0.370515i	0.302842	+	0.953041i	$0.402064\pi$
$662$	17.6056	−	24.2320i	0.684260	−	0.941803i
$663$	−5.23465	+	7.20487i	−0.203297	+	0.279814i
$664$	1.17435	−	0.853212i	0.0455734	−	0.0331110i
$665$		0			0
$666$	−0.0287849	−	0.0209135i	−0.00111539	−	0.000810381i
$667$	−2.17371	+	0.706281i	−0.0841663	+	0.0273473i
$668$			20.6065i			0.797289i
$669$	0.0941522	+	0.289771i	0.00364014	+	0.0112032i
$670$		0			0
$671$	−10.1908	+	31.3642i	−0.393413	+	1.21080i
$672$	−18.0137	−	5.85301i	−0.694895	−	0.225785i
$673$	20.0792	+	27.6367i	0.773997	+	1.06531i	0.995919	+	0.0902506i	$0.0287668\pi$
$673$	20.0792	+	27.6367i	0.773997	+	1.06531i	−0.221922	+	0.975064i	$0.571233\pi$
$674$	−23.9703			−0.923301
$675$		0			0
$676$	−1.97976			−0.0761446
$677$	−5.39301	−	7.42284i	−0.207270	−	0.285283i	0.692708	−	0.721218i	$-0.256418\pi$
$677$	−5.39301	−	7.42284i	−0.207270	−	0.285283i	−0.899978	+	0.435935i	$0.856418\pi$
$678$	−17.3412	−	5.63450i	−0.665985	−	0.216392i
$679$	−2.99017	+	9.20281i	−0.114752	+	0.353171i
$680$		0			0
$681$	−2.95798	−	9.10372i	−0.113350	−	0.348855i
$682$			27.3166i			1.04601i
$683$	18.5463	−	6.02604i	0.709653	−	0.230580i	0.0681215	−	0.997677i	$-0.478299\pi$
$683$	18.5463	−	6.02604i	0.709653	−	0.230580i	0.641531	+	0.767097i	$0.278299\pi$
$684$	−1.73926	−	1.26365i	−0.0665023	−	0.0483168i
$685$		0			0
$686$	−8.39634	+	6.10030i	−0.320574	+	0.232910i
$687$	7.12934	−	9.81269i	0.272001	−	0.374378i
$688$	3.73479	−	5.14050i	0.142387	−	0.195980i
$689$	7.49553	−	5.44582i	0.285557	−	0.207469i
$690$		0			0
$691$	−23.4986	−	17.0727i	−0.893927	−	0.649476i	0.0429718	−	0.999076i	$-0.486317\pi$
$691$	−23.4986	−	17.0727i	−0.893927	−	0.649476i	−0.936899	+	0.349600i	$0.886317\pi$
$692$	−11.1951	+	3.63750i	−0.425573	+	0.138277i
$693$		−	23.2946i		−	0.884889i
$694$	−0.543375	−	1.67234i	−0.0206262	−	0.0634810i
$695$		0			0
$696$	−2.24479	+	6.90876i	−0.0850886	+	0.261876i
$697$	3.78914	+	1.23116i	0.143524	+	0.0466337i
$698$	−21.6267	−	29.7666i	−0.818583	−	1.12668i
$699$	−20.1002			−0.760261
$700$		0			0
$701$	−20.4085			−0.770820			−0.385410	−	0.922745i	$-0.625940\pi$
$701$	−20.4085			−0.770820			−0.385410	+	0.922745i	$0.625940\pi$
$702$	3.30045	+	4.54267i	0.124567	+	0.171452i
$703$	−0.0467640	−	0.0151945i	−0.00176374	−	0.000573073i
$704$	3.26188	−	10.0390i	0.122937	−	0.378360i
$705$		0			0
$706$	−3.77345	−	11.6135i	−0.142016	−	0.437079i
$707$			27.1040i			1.01935i
$708$	−4.06676	+	1.32137i	−0.152838	+	0.0496601i
$709$	13.3334	+	9.68727i	0.500746	+	0.363813i	0.809302	−	0.587393i	$-0.199846\pi$
$709$	13.3334	+	9.68727i	0.500746	+	0.363813i	−0.308556	+	0.951206i	$0.599846\pi$
$710$		0			0
$711$	−13.4821	+	9.79534i	−0.505619	+	0.367354i
$712$	−3.79131	+	5.21829i	−0.142085	+	0.195564i
$713$	0.930497	−	1.28072i	0.0348474	−	0.0479633i
$714$	14.7292	−	10.7014i	0.551226	−	0.400489i
$715$		0			0
$716$	4.74294	+	3.44595i	0.177252	+	0.128781i
$717$	−16.7992	+	5.45838i	−0.627376	+	0.203847i
$718$			46.3309i			1.72905i
$719$	−9.60466	−	29.5601i	−0.358193	−	1.10241i	−0.954135	−	0.299378i	$-0.903221\pi$
$719$	−9.60466	−	29.5601i	−0.358193	−	1.10241i	0.595941	−	0.803028i	$-0.296779\pi$
$720$		0			0
$721$	−14.3186	+	44.0681i	−0.533253	+	1.64118i
$722$	21.8098	+	7.08642i	0.811675	+	0.263729i
$723$	17.3624	+	23.8973i	0.645716	+	0.888752i
$724$	−13.4080			−0.498305
$725$		0			0
$726$	−40.8036			−1.51436
$727$	0.560188	+	0.771033i	0.0207762	+	0.0285960i	0.819279	−	0.573395i	$-0.194374\pi$
$727$	0.560188	+	0.771033i	0.0207762	+	0.0285960i	−0.798503	+	0.601991i	$0.794374\pi$
$728$	22.9131	+	7.44492i	0.849217	+	0.275927i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	1.06445	+	3.27603i	0.0393700	+	0.121168i
$732$			5.08833i			0.188070i
$733$	−14.6226	+	4.75118i	−0.540099	+	0.175489i	−0.566347	−	0.824167i	$-0.691644\pi$
$733$	−14.6226	+	4.75118i	−0.540099	+	0.175489i	0.0262485	+	0.999655i	$0.491644\pi$
$734$	−29.6006	−	21.5061i	−1.09258	−	0.793806i
$735$		0			0
$736$	2.27103	−	1.65000i	0.0837114	−	0.0608199i
$737$	−20.9451	+	28.8284i	−0.771522	+	1.06191i
$738$	1.47651	−	2.03225i	0.0543513	−	0.0748081i
$739$	4.20110	−	3.05228i	0.154540	−	0.112280i	−0.507828	−	0.861458i	$-0.669551\pi$
$739$	4.20110	−	3.05228i	0.154540	−	0.112280i	0.662368	+	0.749179i	$0.269551\pi$
$740$		0			0
$741$	6.27782	+	4.56110i	0.230622	+	0.167556i
$742$	−18.0137	+	5.85301i	−0.661305	+	0.214871i
$743$			42.3399i			1.55330i	0.629932	+	0.776650i	$0.283083\pi$
$743$			42.3399i			1.55330i	−0.629932	+	0.776650i	$0.716917\pi$
$744$	−1.55481	−	4.78521i	−0.0570021	−	0.175434i
$745$		0			0
$746$	−3.36980	+	10.3712i	−0.123377	+	0.379716i
$747$	0.743385	+	0.241540i	0.0271990	+	0.00883750i
$748$	−8.56909	−	11.7943i	−0.313317	−	0.431244i
$749$	22.3449			0.816465
$750$		0			0
$751$	22.2461			0.811773			0.405887	−	0.913923i	$-0.366963\pi$
$751$	22.2461			0.811773			0.405887	+	0.913923i	$0.366963\pi$
$752$	15.9440	+	21.9450i	0.581416	+	0.800251i
$753$	−1.80127	−	0.585267i	−0.0656418	−	0.0213283i
$754$	−6.78733	+	20.8892i	−0.247180	+	0.760741i
$755$		0			0
$756$	−1.11067	−	3.41829i	−0.0403947	−	0.124322i
$757$		−	9.27680i		−	0.337171i	−0.985687	−	0.168585i	$-0.946080\pi$
$757$		−	9.27680i		−	0.337171i	0.985687	−	0.168585i	$-0.0539199\pi$
$758$	0.251000	−	0.0815549i	0.00911674	−	0.00296221i
$759$	2.79307	+	2.02928i	0.101382	+	0.0736583i
$760$		0			0
$761$	14.0868	−	10.2346i	0.510644	−	0.371005i	−0.302424	−	0.953174i	$-0.597796\pi$
$761$	14.0868	−	10.2346i	0.510644	−	0.371005i	0.813068	+	0.582169i	$0.197796\pi$
$762$	13.5830	−	18.6954i	0.492062	−	0.677265i
$763$	−3.15449	+	4.34178i	−0.114200	+	0.157183i
$764$	4.95125	−	3.59729i	0.179130	−	0.130145i
$765$		0			0
$766$	−5.87403	−	4.26773i	−0.212237	−	0.154200i
$767$	14.6789	−	4.76945i	0.530023	−	0.172215i
$768$		−	18.0245i		−	0.650404i
$769$	7.16648	+	22.0562i	0.258430	+	0.795365i	0.993134	+	0.116978i	$0.0373208\pi$
$769$	7.16648	+	22.0562i	0.258430	+	0.795365i	−0.734705	+	0.678387i	$0.762679\pi$
$770$		0			0
$771$	6.83579	−	21.0384i	0.246185	−	0.757680i
$772$	4.18627	+	1.36020i	0.150667	+	0.0489547i
$773$	−3.23751	−	4.45605i	−0.116445	−	0.160273i	0.746816	−	0.665031i	$-0.231582\pi$
$773$	−3.23751	−	4.45605i	−0.116445	−	0.160273i	−0.863261	+	0.504758i	$0.831582\pi$
$774$	2.17183			0.0780650
$775$		0			0
$776$	−4.55807			−0.163625
$777$	−0.0483191	−	0.0665056i	−0.00173344	−	0.00238587i
$778$	−33.0545	−	10.7401i	−1.18506	−	0.385049i
$779$	1.07275	−	3.30159i	0.0384353	−	0.118292i
$780$		0			0
$781$	14.7922	+	45.5257i	0.529306	+	1.62904i
$782$			2.69830i			0.0964909i
$783$	−3.72022	+	1.20877i	−0.132950	+	0.0431980i
$784$	−34.5023	−	25.0674i	−1.23222	−	0.895263i
$785$		0			0
$786$	6.33964	−	4.60602i	0.226128	−	0.164291i
$787$	15.1632	−	20.8703i	0.540509	−	0.743946i	−0.448178	−	0.893944i	$-0.647927\pi$
$787$	15.1632	−	20.8703i	0.540509	−	0.743946i	0.988686	+	0.149998i	$0.0479268\pi$
$788$	7.70795	−	10.6091i	0.274584	−	0.377933i
$789$	−15.9500	+	11.5884i	−0.567835	+	0.412556i
$790$		0			0
$791$	−34.0819	−	24.7619i	−1.21181	−	0.880433i
$792$	10.4359	−	3.39082i	0.370823	−	0.120488i
$793$		−	18.3662i		−	0.652203i
$794$	−1.03200	−	3.17617i	−0.0366243	−	0.112718i
$795$		0			0
$796$	−2.45833	+	7.56596i	−0.0871331	+	0.268168i
$797$	3.52831	+	1.14642i	0.124979	+	0.0406082i	0.370839	−	0.928697i	$-0.379070\pi$
$797$	3.52831	+	1.14642i	0.124979	+	0.0406082i	−0.245860	+	0.969305i	$0.579070\pi$
$798$	−9.32443	−	12.8340i	−0.330081	−	0.454318i
$799$	−14.7052			−0.520233
$800$		0			0
$801$	−3.47327			−0.122722
$802$	−32.9313	−	45.3261i	−1.16285	−	1.60052i
$803$	74.8326	+	24.3146i	2.64079	+	0.858043i
$804$	−1.69900	+	5.22898i	−0.0599190	+	0.184412i
$805$		0			0
$806$	−4.70111	−	14.4685i	−0.165589	−	0.509632i
$807$			18.1647i			0.639429i
$808$	−12.1425	+	3.94533i	−0.427171	+	0.138796i
$809$	30.3414	+	22.0443i	1.06675	+	0.775037i	0.975325	−	0.220776i	$-0.0708588\pi$
$809$	30.3414	+	22.0443i	1.06675	+	0.775037i	0.0914219	+	0.995812i	$0.470859\pi$
$810$		0			0
$811$	−36.9041	+	26.8124i	−1.29588	+	0.941509i	−0.999906	−	0.0136877i	$-0.995643\pi$
$811$	−36.9041	+	26.8124i	−1.29588	+	0.941509i	−0.295970	+	0.955197i	$0.595643\pi$
$812$	8.26387	−	11.3742i	0.290005	−	0.399158i
$813$	−13.2660	+	18.2591i	−0.465260	+	0.640375i
$814$	−0.170081	+	0.123571i	−0.00596135	+	0.00433117i
$815$		0			0
$816$	10.9304	+	7.94139i	0.382640	+	0.278004i
$817$	2.85450	−	0.927484i	0.0998664	−	0.0324486i
$818$		−	67.5317i		−	2.36119i
$819$	4.00894	+	12.3382i	0.140084	+	0.431133i
$820$		0			0
$821$	13.9216	−	42.8462i	0.485866	−	1.49534i	−0.344857	−	0.938655i	$-0.612073\pi$
$821$	13.9216	−	42.8462i	0.485866	−	1.49534i	0.830723	−	0.556686i	$-0.187927\pi$
$822$	−24.7679	−	8.04758i	−0.863880	−	0.280691i
$823$	−24.3680	−	33.5397i	−0.849415	−	1.16912i	−0.983991	−	0.178217i	$-0.942967\pi$
$823$	−24.3680	−	33.5397i	−0.849415	−	1.16912i	0.134576	−	0.990903i	$-0.457033\pi$
$824$	−21.8266			−0.760364
$825$		0			0
$826$	−31.5529			−1.09786
$827$	22.7434	+	31.3035i	0.790864	+	1.08853i	0.994000	+	0.109380i	$0.0348866\pi$
$827$	22.7434	+	31.3035i	0.790864	+	1.08853i	−0.203136	+	0.979151i	$0.565113\pi$
$828$	0.506614	+	0.164609i	0.0176061	+	0.00572056i
$829$	−7.45527	+	22.9450i	−0.258932	+	0.796911i	0.734097	+	0.679044i	$0.237606\pi$
$829$	−7.45527	+	22.9450i	−0.258932	+	0.796911i	−0.993029	+	0.117867i	$0.962394\pi$
$830$		0			0
$831$	2.55091	+	7.85089i	0.0884901	+	0.272344i
$832$			5.87864i			0.203805i
$833$	21.9882	−	7.14441i	0.761847	−	0.247539i
$834$	−25.1774	−	18.2924i	−0.871821	−	0.633415i
$835$		0			0
$836$	−10.2768	+	7.46650i	−0.355429	+	0.258234i
$837$	1.59251	−	2.19190i	0.0550452	−	0.0757633i
$838$	19.6177	−	27.0014i	0.677681	−	0.932748i
$839$	−14.3890	+	10.4542i	−0.496763	+	0.360919i	−0.807779	−	0.589485i	$-0.799331\pi$
$839$	−14.3890	+	10.4542i	−0.496763	+	0.360919i	0.311016	+	0.950405i	$0.399331\pi$
$840$		0			0
$841$	11.0826	+	8.05197i	0.382158	+	0.277654i
$842$	−65.4534	+	21.2671i	−2.25567	+	0.732913i
$843$		−	1.28129i		−	0.0441300i
$844$	−0.838452	−	2.58049i	−0.0288607	−	0.0888242i
$845$		0			0
$846$	−2.86510	+	8.81786i	−0.0985041	+	0.303164i
$847$	−89.6598	−	29.1322i	−3.08075	−	1.00100i
$848$	−8.26176	−	11.3713i	−0.283710	−	0.390493i
$849$	−2.67132			−0.0916796
$850$		0			0
$851$	0.0121834			0.000417642
$852$	4.34126	+	5.97524i	0.148729	+	0.204708i
$853$	−12.2147	−	3.96878i	−0.418222	−	0.135889i	0.0923439	−	0.995727i	$-0.470564\pi$
$853$	−12.2147	−	3.96878i	−0.418222	−	0.135889i	−0.510566	+	0.859839i	$0.670564\pi$
$854$	−11.6026	+	35.7090i	−0.397032	+	1.22194i
$855$		0			0
$856$	3.25258	+	10.0104i	0.111171	+	0.342149i
$857$		−	15.6015i		−	0.532936i	−0.963844	−	0.266468i	$-0.914143\pi$
$857$		−	15.6015i		−	0.532936i	0.963844	−	0.266468i	$-0.0858566\pi$
$858$	31.5538	−	10.2524i	1.07723	−	0.350013i
$859$	3.90628	+	2.83808i	0.133281	+	0.0968340i	0.652428	−	0.757851i	$-0.273750\pi$
$859$	3.90628	+	2.83808i	0.133281	+	0.0968340i	−0.519147	+	0.854685i	$0.673750\pi$
$860$		0			0
$861$	4.69537	−	3.41138i	0.160018	−	0.116260i
$862$	−13.7779	+	18.9636i	−0.469276	+	0.645904i
$863$	7.73222	−	10.6425i	0.263208	−	0.362274i	−0.656874	−	0.754000i	$-0.728122\pi$
$863$	7.73222	−	10.6425i	0.263208	−	0.362274i	0.920082	+	0.391726i	$0.128122\pi$
$864$	3.88679	−	2.82392i	0.132231	−	0.0960716i
$865$		0			0
$866$	−17.1529	−	12.4623i	−0.582879	−	0.423486i
$867$	9.20205	−	2.98993i	0.312518	−	0.101543i
$868$			9.73792i			0.330527i
$869$	30.4281	+	93.6480i	1.03220	+	3.17679i
$870$		0			0
$871$	6.13249	−	18.8739i	0.207792	−	0.639517i
$872$	−2.40427	−	0.781196i	−0.0814190	−	0.0264546i
$873$	−1.44268	−	1.98567i	−0.0488272	−	0.0672049i
$874$	2.35111			0.0795274
$875$		0			0
$876$	12.1404			0.410185
$877$	−3.67515	−	5.05840i	−0.124101	−	0.170810i	0.742446	−	0.669906i	$-0.233666\pi$
$877$	−3.67515	−	5.05840i	−0.124101	−	0.170810i	−0.866547	+	0.499096i	$0.833666\pi$
$878$	17.7951	+	5.78199i	0.600557	+	0.195133i
$879$	−5.45741	+	16.7962i	−0.184074	+	0.566521i
$880$		0			0
$881$	−5.18532	−	15.9588i	−0.174698	−	0.537665i	0.824922	−	0.565247i	$-0.191219\pi$
$881$	−5.18532	−	15.9588i	−0.174698	−	0.537665i	−0.999620	+	0.0275821i	$0.991219\pi$
$882$		−	14.5770i		−	0.490834i
$883$	15.4420	−	5.01740i	0.519664	−	0.168849i	−0.0374289	−	0.999299i	$-0.511917\pi$
$883$	15.4420	−	5.01740i	0.519664	−	0.168849i	0.557093	+	0.830450i	$0.311917\pi$
$884$	6.56848	+	4.77228i	0.220922	+	0.160509i
$885$		0			0
$886$	11.2259	−	8.15606i	0.377140	−	0.274008i
$887$	33.9078	−	46.6700i	1.13851	−	1.56703i	0.367723	−	0.929935i	$-0.380137\pi$
$887$	33.9078	−	46.6700i	1.13851	−	1.56703i	0.770788	−	0.637091i	$-0.219863\pi$
$888$	0.0227607	−	0.0313275i	0.000763800	−	0.00105128i
$889$	43.1945	−	31.3827i	1.44870	−	1.05254i
$890$		0			0
$891$	4.78023	+	3.47304i	0.160144	+	0.116351i
$892$	0.264176	−	0.0858359i	0.00884526	−	0.00287400i
$893$			12.8131i			0.428774i
$894$	7.76827	+	23.9083i	0.259810	+	0.799612i
$895$		0			0
$896$	15.4198	−	47.4572i	0.515138	−	1.58543i
$897$	−1.82861	−	0.594152i	−0.0610556	−	0.0198382i
$898$	33.0483	+	45.4871i	1.10284	+	1.51793i
$899$	10.5981			0.353465
$900$		0			0
$901$	7.61988			0.253855
$902$	−8.72427	−	12.0079i	−0.290486	−	0.399820i
$903$	4.77228	+	1.55061i	0.158812	+	0.0516010i
$904$	6.13219	−	18.8729i	0.203953	−	0.627704i
$905$		0			0
$906$	9.19361	+	28.2950i	0.305437	+	0.940039i
$907$			9.00465i			0.298995i	0.988762	+	0.149497i	$0.0477655\pi$
$907$			9.00465i			0.298995i	−0.988762	+	0.149497i	$0.952234\pi$
$908$	−8.29960	+	2.69670i	−0.275432	+	0.0894933i
$909$	−5.56195	−	4.04100i	−0.184478	−	0.134031i
$910$		0			0
$911$	−24.2303	+	17.6044i	−0.802786	+	0.583258i	−0.911730	−	0.410789i	$-0.865253\pi$
$911$	−24.2303	+	17.6044i	−0.802786	+	0.583258i	0.108944	+	0.994048i	$0.465253\pi$
$912$	6.91957	−	9.52397i	0.229130	−	0.315370i
$913$	2.71467	−	3.73642i	0.0898425	−	0.123658i
$914$	31.5853	−	22.9481i	1.04475	−	0.759056i
$915$		0			0
$916$	−8.94596	−	6.49962i	−0.295583	−	0.214753i
$917$	17.2189	−	5.59477i	0.568619	−	0.184756i
$918$			4.61803i			0.152418i
$919$	−2.76125	−	8.49826i	−0.0910853	−	0.280332i	0.895128	−	0.445808i	$-0.147084\pi$
$919$	−2.76125	−	8.49826i	−0.0910853	−	0.280332i	−0.986214	+	0.165477i	$0.947084\pi$
$920$		0			0
$921$	−8.82532	+	27.1615i	−0.290804	+	0.895003i
$922$	−19.5431	−	6.34995i	−0.643619	−	0.209125i
$923$	−15.6697	−	21.5675i	−0.515774	−	0.709902i
$924$	−21.2370			−0.698647
$925$		0			0
$926$	46.4133			1.52524
$927$	−6.90833	−	9.50850i	−0.226899	−	0.312300i
$928$	17.8732	+	5.80735i	0.586716	+	0.190636i
$929$	12.8117	−	39.4304i	0.420339	−	1.29367i	−0.487048	−	0.873375i	$-0.661926\pi$
$929$	12.8117	−	39.4304i	0.420339	−	1.29367i	0.907387	−	0.420296i	$-0.138074\pi$
$930$		0			0
$931$	−6.22514	−	19.1590i	−0.204021	−	0.627911i
$932$			18.3248i			0.600250i
$933$	−27.8929	+	9.06296i	−0.913173	+	0.296708i
$934$	5.44243	+	3.95416i	0.178082	+	0.129384i
$935$		0			0
$936$	−4.94392	+	3.59197i	−0.161597	+	0.117407i
$937$	12.2603	−	16.8749i	0.400527	−	0.551278i	−0.560349	−	0.828256i	$-0.689333\pi$
$937$	12.2603	−	16.8749i	0.400527	−	0.551278i	0.960876	+	0.276978i	$0.0893331\pi$
$938$	−23.8466	+	32.8220i	−0.778618	+	1.07168i
$939$	−14.1523	+	10.2823i	−0.461844	+	0.335549i
$940$		0			0
$941$	−2.97219	−	2.15942i	−0.0968905	−	0.0703951i	0.538285	−	0.842763i	$-0.319072\pi$
$941$	−2.97219	−	2.15942i	−0.0968905	−	0.0703951i	−0.635176	+	0.772368i	$0.719072\pi$
$942$	29.0661	−	9.44413i	0.947023	−	0.307706i
$943$			0.860163i			0.0280107i
$944$	−7.23565	−	22.2691i	−0.235500	−	0.724796i
$945$		0			0
$946$	3.96552	−	12.2046i	0.128930	−	0.396807i
$947$	−30.1482	−	9.79575i	−0.979685	−	0.318319i	−0.224966	−	0.974367i	$-0.572227\pi$
$947$	−30.1482	−	9.79575i	−0.979685	−	0.318319i	−0.754719	+	0.656048i	$0.772227\pi$
$948$	8.93013	+	12.2913i	0.290037	+	0.399202i
$949$	−43.8204			−1.42247
$950$		0			0
$951$	3.91763			0.127038
$952$	11.6466	+	16.0302i	0.377469	+	0.519541i
$953$	−24.3674	−	7.91746i	−0.789339	−	0.256472i	−0.113516	−	0.993536i	$-0.536211\pi$
$953$	−24.3674	−	7.91746i	−0.789339	−	0.256472i	−0.675822	+	0.737064i	$0.736211\pi$
$954$	1.48462	−	4.56919i	0.0480664	−	0.147933i
$955$		0			0
$956$	4.97625	+	15.3153i	0.160943	+	0.495333i
$957$			23.1129i			0.747133i
$958$	−32.3746	+	10.5191i	−1.04598	+	0.339858i
$959$	−48.6781	−	35.3667i	−1.57190	−	1.14205i
$960$		0			0
$961$	19.1409	−	13.9067i	0.617449	−	0.448603i
$962$	0.0688191	−	0.0947214i	0.00221882	−	0.00305394i
$963$	−3.33145	+	4.58535i	−0.107354	+	0.147761i
$964$	21.7865	−	15.8288i	0.701697	−	0.509813i
$965$		0			0
$966$	3.17999	+	2.31040i	0.102314	+	0.0743358i
$967$	27.5965	−	8.96663i	0.887442	−	0.288347i	0.170398	−	0.985375i	$-0.445495\pi$
$967$	27.5965	−	8.96663i	0.887442	−	0.288347i	0.717044	+	0.697028i	$0.245495\pi$
$968$		−	44.4077i		−	1.42732i
$969$	1.97214	+	6.06961i	0.0633541	+	0.194984i
$970$		0			0
$971$	−1.16588	+	3.58821i	−0.0374149	+	0.115151i	−0.968020	−	0.250875i	$-0.919282\pi$
$971$	−1.16588	+	3.58821i	−0.0374149	+	0.115151i	0.930605	+	0.366026i	$0.119282\pi$
$972$	0.867051	+	0.281722i	0.0278107	+	0.00903624i
$973$	−42.2634	−	58.1705i	−1.35490	−	1.86486i
$974$	−18.7739			−0.601553
$975$		0			0
$976$	−27.8630			−0.891874
$977$	−21.5815	−	29.7044i	−0.690455	−	0.950329i	0.309545	−	0.950885i	$-0.399823\pi$
$977$	−21.5815	−	29.7044i	−0.690455	−	0.950329i	−1.00000		0.000555441i	$0.999823\pi$
$978$	35.3128	+	11.4738i	1.12918	+	0.366893i
$979$	−6.34180	+	19.5181i	−0.202685	+	0.623800i
$980$		0			0
$981$	−0.420658	−	1.29465i	−0.0134306	−	0.0413350i
$982$			56.8104i			1.81289i
$983$	22.4095	−	7.28128i	0.714752	−	0.232237i	0.0710055	−	0.997476i	$-0.477379\pi$
$983$	22.4095	−	7.28128i	0.714752	−	0.232237i	0.643746	+	0.765239i	$0.277379\pi$
$984$	2.21175	+	1.60693i	0.0705081	+	0.0512271i
$985$		0			0
$986$	−14.6143	+	10.6179i	−0.465413	+	0.338143i
$987$	−12.5912	+	17.3304i	−0.400784	+	0.551631i
$988$	4.15823	−	5.72331i	0.132291	−	0.182083i
$989$	−0.601653	+	0.437126i	−0.0191314	+	0.0138998i
$990$		0			0
$991$	−23.5727	−	17.1266i	−0.748812	−	0.544044i	0.146646	−	0.989189i	$-0.453152\pi$
$991$	−23.5727	−	17.1266i	−0.748812	−	0.544044i	−0.895458	+	0.445145i	$0.853152\pi$
$992$	−12.3795	+	4.02235i	−0.393050	+	0.127710i
$993$			17.5534i			0.557039i
$994$	16.8413	+	51.8323i	0.534175	+	1.64402i
$995$		0			0
$996$	0.220205	−	0.677723i	0.00697748	−	0.0214745i
$997$	41.7742	+	13.5733i	1.32300	+	0.429870i	0.883525	−	0.468384i	$-0.155164\pi$
$997$	41.7742	+	13.5733i	1.32300	+	0.429870i	0.439478	+	0.898254i	$0.355164\pi$
$998$	41.2671	+	56.7993i	1.30629	+	1.79795i
$999$	0.0208515			0.000659711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.b.199.3		16
5.2	odd	4		375.2.g.b.301.1		8
5.3	odd	4		75.2.g.b.61.2	yes	8
5.4	even	2	inner	375.2.i.b.199.2		16
15.8	even	4		225.2.h.c.136.1		8
25.3	odd	20		1875.2.a.h.1.1		4
25.4	even	10		1875.2.b.c.1249.6		8
25.9	even	10	inner	375.2.i.b.49.3		16
25.12	odd	20		375.2.g.b.76.1		8
25.13	odd	20		75.2.g.b.16.2	✓	8
25.16	even	5	inner	375.2.i.b.49.2		16
25.21	even	5		1875.2.b.c.1249.3		8
25.22	odd	20		1875.2.a.e.1.4		4
75.38	even	20		225.2.h.c.91.1		8
75.47	even	20		5625.2.a.n.1.1		4
75.53	even	20		5625.2.a.i.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.16.2	✓	8	25.13	odd	20
75.2.g.b.61.2	yes	8	5.3	odd	4
225.2.h.c.91.1		8	75.38	even	20
225.2.h.c.136.1		8	15.8	even	4
375.2.g.b.76.1		8	25.12	odd	20
375.2.g.b.301.1		8	5.2	odd	4
375.2.i.b.49.2		16	25.16	even	5	inner
375.2.i.b.49.3		16	25.9	even	10	inner
375.2.i.b.199.2		16	5.4	even	2	inner
375.2.i.b.199.3		16	1.1	even	1	trivial
1875.2.a.e.1.4		4	25.22	odd	20
1875.2.a.h.1.1		4	25.3	odd	20
1875.2.b.c.1249.3		8	25.21	even	5
1875.2.b.c.1249.6		8	25.4	even	10
5625.2.a.i.1.4		4	75.53	even	20
5625.2.a.n.1.1		4	75.47	even	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00297 + 1.38048i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.281722 + 0.867051i) q^{4} +(-0.527295 - 1.62285i) q^{6} -3.94243i q^{7} +(1.76619 - 0.573870i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.00297 + 1.38048i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.281722 + 0.867051i) q^{4} +(-0.527295 - 1.62285i) q^{6} -3.94243i q^{7} +(1.76619 - 0.573870i) q^{8} +(0.809017 + 0.587785i) q^{9} +(4.78023 - 3.47304i) q^{11} +(0.535867 - 0.737558i) q^{12} +(-1.93420 + 2.66220i) q^{13} +(5.44243 - 3.95416i) q^{14} +(4.03877 + 2.93434i) q^{16} +(-2.57390 + 0.836312i) q^{17} +1.70636i q^{18} +(0.728704 + 2.24272i) q^{19} +(-1.21828 + 3.74947i) q^{21} +(9.58890 + 3.11562i) q^{22} +(-0.343440 - 0.472705i) q^{23} -1.85708 q^{24} -5.61505 q^{26} +(-0.587785 - 0.809017i) q^{27} +(3.41829 + 1.11067i) q^{28} +(1.20877 - 3.72022i) q^{29} +(0.837233 + 2.57674i) q^{31} +4.80433i q^{32} +(-5.61950 + 1.82589i) q^{33} +(-3.73607 - 2.71441i) q^{34} +(-0.737558 + 0.535867i) q^{36} +(-0.0122562 + 0.0168692i) q^{37} +(-2.36515 + 3.25535i) q^{38} +(2.66220 - 1.93420i) q^{39} +(-1.19098 - 0.865300i) q^{41} +(-6.39796 + 2.07882i) q^{42} -1.27279i q^{43} +(1.66461 + 5.12314i) q^{44} +(0.308096 - 0.948222i) q^{46} +(5.16764 + 1.67907i) q^{47} +(-2.93434 - 4.03877i) q^{48} -8.54276 q^{49} +2.70636 q^{51} +(-1.76336 - 2.42705i) q^{52} +(-2.67774 - 0.870050i) q^{53} +(0.527295 - 1.62285i) q^{54} +(-2.26244 - 6.96308i) q^{56} -2.35813i q^{57} +(6.34804 - 2.06260i) q^{58} +(-3.79456 - 2.75691i) q^{59} +(-4.51538 + 3.28061i) q^{61} +(-2.71740 + 3.74018i) q^{62} +(2.31730 - 3.18949i) q^{63} +(1.44528 - 1.05006i) q^{64} +(-8.15681 - 5.92627i) q^{66} +(-5.73559 + 1.86361i) q^{67} -2.46731i q^{68} +(0.180557 + 0.555698i) q^{69} +(-2.50346 + 7.70487i) q^{71} +(1.76619 + 0.573870i) q^{72} +(7.82730 + 10.7734i) q^{73} -0.0355801 q^{74} -2.14984 q^{76} +(-13.6922 - 18.8457i) q^{77} +(5.34023 + 1.73515i) q^{78} +(-5.14971 + 15.8492i) q^{79} +(0.309017 + 0.951057i) q^{81} -2.51200i q^{82} +(0.743385 - 0.241540i) q^{83} +(-2.90777 - 2.11262i) q^{84} +(1.75705 - 1.27657i) q^{86} +(-2.29922 + 3.16461i) q^{87} +(6.44972 - 8.87728i) q^{88} +(-2.80994 + 2.04154i) q^{89} +(10.4955 + 7.62545i) q^{91} +(0.506614 - 0.164609i) q^{92} -2.70934i q^{93} +(2.86510 + 8.81786i) q^{94} +(1.48462 - 4.56919i) q^{96} +(-2.33430 - 0.758460i) q^{97} +(-8.56817 - 11.7931i) q^{98} +5.90869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Introduction

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