LMFDB - Embedded newform 375.2.i.b.199.2

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			199.2
Root			$-0.462894 - 1.33631i$ of defining polynomial
Character	$\chi$	$=$	375.199
Dual form			375.2.i.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00297 - 1.38048i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.281722 + 0.867051i) q^{4} +(-0.527295 - 1.62285i) q^{6} +3.94243i q^{7} +(-1.76619 + 0.573870i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(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	$-0.993856\pi$
$2$	−1.00297	−	1.38048i	−0.709210	−	0.976144i	0.290604	−	0.956844i	$-0.406144\pi$
$3$	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	$0.267574\pi$
$7$			3.94243i			1.49010i	−0.667009	+	0.745049i	$0.732426\pi$
$8$	−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	−0.451646	−	0.892197i	$-0.649163\pi$
$13$	1.93420	−	2.66220i	0.536451	−	0.738361i	0.988096	+	0.153836i	$0.0491629\pi$
$14$	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	0.0202310	−	0.999795i	$-0.493560\pi$
$17$	2.57390	−	0.836312i	0.624263	−	0.202835i	0.604032	+	0.796960i	$0.293560\pi$
$18$		−	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	0.843321	−	0.537411i	$-0.180597\pi$
$23$	0.343440	+	0.472705i	0.0716123	+	0.0985658i	−0.771708	+	0.635977i	$0.780597\pi$
$24$	−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	−0.808008	−	0.589171i	$-0.799454\pi$
$37$	0.0122562	−	0.0168692i	0.00201490	−	0.00277328i	0.810023	+	0.586398i	$0.199454\pi$
$38$	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	$0.0309404\pi$
$43$			1.27279i			0.194098i	−0.995280	+	0.0970491i	$0.969060\pi$
$44$	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	−0.0931716	−	0.995650i	$-0.529701\pi$
$47$	−5.16764	−	1.67907i	−0.753777	−	0.244917i	−0.660606	+	0.750733i	$0.729701\pi$
$48$	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	0.487092	−	0.873350i	$-0.338058\pi$
$53$	2.67774	+	0.870050i	0.367816	+	0.119511i	−0.119277	+	0.992861i	$0.538058\pi$
$54$	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	0.0630725	−	0.998009i	$-0.479910\pi$
$67$	5.73559	−	1.86361i	0.700714	−	0.227676i	0.637642	+	0.770333i	$0.279910\pi$
$68$			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	$-0.915578\pi$
$73$	−7.82730	−	10.7734i	−0.916116	−	1.26093i	0.0489187	−	0.998803i	$-0.484422\pi$
$74$	−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	−0.349531	−	0.936925i	$-0.613659\pi$
$83$	−0.743385	+	0.241540i	−0.0815971	+	0.0265125i	0.267934	+	0.963437i	$0.413659\pi$
$84$	−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	0.425115	−	0.905139i	$-0.360234\pi$
$97$	2.33430	+	0.758460i	0.237012	+	0.0770099i	−0.188103	+	0.982149i	$0.560234\pi$
$98$	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	0.802638	−	0.596466i	$-0.203429\pi$
$103$	11.1779	+	3.63192i	1.10139	+	0.357864i	0.298754	+	0.954330i	$0.403429\pi$
$104$	−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	$-0.911665\pi$
$107$		−	5.66780i		−	0.547927i	0.961740	−	0.273964i	$-0.0883348\pi$
$108$	−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	−0.994833	−	0.101526i	$-0.967627\pi$
$113$	−6.28088	+	8.64489i	−0.590856	+	0.813243i	0.403977	+	0.914769i	$0.367627\pi$
$114$	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	$-0.994824\pi$
$127$	−7.96023	−	10.9563i	−0.706356	−	0.972216i	0.293511	−	0.955956i	$-0.405176\pi$
$128$	−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	$0.426053\pi$
$137$	−8.97078	+	12.3472i	−0.766426	+	1.05489i	−0.996652	+	0.0817573i	$0.973947\pi$
$138$	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	$-0.746560\pi$
$157$		−	17.9105i		−	1.42942i	0.699423	−	0.714708i	$-0.253440\pi$
$158$	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	$-0.475280\pi$
$163$	12.7901	−	17.6041i	1.00180	−	1.37886i	0.924216	−	0.381870i	$-0.124720\pi$
$164$	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	−0.981594	−	0.190980i	$-0.938833\pi$
$167$	−21.4967	+	6.98470i	−1.66346	+	0.540492i	−0.681871	+	0.731473i	$0.738833\pi$
$168$		−	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	0.416360	−	0.909200i	$-0.363306\pi$
$173$	−7.58929	−	10.4458i	−0.577003	−	0.794177i	−0.993363	+	0.115023i	$0.963306\pi$
$174$	−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	$0.0555948\pi$
$193$			4.82817i			0.347539i	−0.984786	+	0.173769i	$0.944405\pi$
$194$	−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	0.752697	−	0.658367i	$-0.228752\pi$
$197$	13.6801	+	4.44492i	0.974664	+	0.316688i	0.221967	+	0.975054i	$0.428752\pi$
$198$	−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	0.814971	−	0.579501i	$-0.196753\pi$
$223$	0.179088	+	0.246494i	0.0119926	+	0.0165064i	−0.802979	+	0.596008i	$0.796753\pi$
$224$	18.9408			1.26553
$225$		0			0
$226$	18.2336			1.21288
$227$	−5.62641	−	7.74408i	−0.373438	−	0.513993i	0.580394	−	0.814336i	$-0.302899\pi$
$227$	−5.62641	−	7.74408i	−0.373438	−	0.513993i	−0.953831	+	0.300343i	$0.902899\pi$
$228$	−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	−0.858766	−	0.512367i	$-0.828769\pi$
$233$	−19.1165	+	6.21132i	−1.25236	+	0.406917i	−0.393595	+	0.919284i	$0.628769\pi$
$234$	−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	$-0.757638\pi$
$257$		−	22.1211i		−	1.37988i	0.723869	−	0.689938i	$-0.242362\pi$
$258$	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	$0.407967\pi$
$263$	−11.5884	+	15.9500i	−0.714569	+	0.983520i	−0.999687	+	0.0250272i	$0.992033\pi$
$264$	−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	0.929512	−	0.368792i	$-0.120228\pi$
$277$	4.85212	+	6.67837i	0.291535	+	0.401264i	−0.637977	+	0.770056i	$0.720228\pi$
$278$	−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	−0.383552	−	0.923519i	$-0.625299\pi$
$283$	−2.54058	+	0.825484i	−0.151022	+	0.0490699i	0.232531	+	0.972589i	$0.425299\pi$
$284$	−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	$0.172531\pi$
$293$			17.6605i			1.03174i	−0.856667	+	0.515870i	$0.827469\pi$
$294$	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	$0.303254\pi$
$307$			28.5593i			1.62997i	−0.579484	+	0.814983i	$0.696746\pi$
$308$	−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	−0.993825	−	0.110958i	$-0.964608\pi$
$313$	−10.2823	+	14.1523i	−0.581189	+	0.799937i	0.412637	+	0.910896i	$0.364608\pi$
$314$	−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	−0.202508	−	0.979281i	$-0.564909\pi$
$317$	3.72589	−	1.21061i	0.209267	−	0.0679949i	0.411775	+	0.911286i	$0.364909\pi$
$318$		−	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	−0.522566	−	0.852599i	$-0.675025\pi$
$337$	8.25697	−	11.3647i	0.449786	−	0.619077i	0.972352	+	0.233522i	$0.0750251\pi$
$338$	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	0.335205	−	0.942145i	$-0.391194\pi$
$347$	0.980059	+	0.318440i	0.0526123	+	0.0170948i	−0.282593	+	0.959240i	$0.591194\pi$
$348$	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	0.484485	−	0.874800i	$-0.339007\pi$
$353$	6.80599	+	2.21140i	0.362246	+	0.117701i	−0.122238	+	0.992501i	$0.539007\pi$
$354$	−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	0.276157	−	0.961113i	$-0.410939\pi$
$367$	20.3929	−	6.62605i	1.06450	−	0.345877i	0.788343	+	0.615236i	$0.210939\pi$
$368$			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	0.700618	−	0.713536i	$-0.252908\pi$
$373$	−3.75638	−	5.17021i	−0.194498	−	0.267703i	−0.895116	+	0.445833i	$0.852908\pi$
$374$	−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	−0.203794	−	0.979014i	$-0.565327\pi$
$383$	4.04682	−	1.31489i	0.206783	−	0.0671878i	0.410577	+	0.911826i	$0.365327\pi$
$384$	−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	0.355354	−	0.934732i	$-0.384360\pi$
$397$	1.86137	+	0.604795i	0.0934194	+	0.0303538i	−0.261934	+	0.965086i	$0.584360\pi$
$398$	−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	−0.0109734	−	0.999940i	$-0.503493\pi$
$433$	11.8172	−	3.83964i	0.567899	−	0.184522i	0.578872	+	0.815418i	$0.303493\pi$
$434$	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	$0.0618796\pi$
$443$			8.13187i			0.386357i	−0.981164	+	0.193178i	$0.938120\pi$
$444$	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	$0.179742\pi$
$457$			22.8800i			1.07028i	−0.844762	+	0.535142i	$0.820258\pi$
$458$	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	$0.417786\pi$
$463$	−15.9878	+	22.0054i	−0.743018	+	1.02268i	−0.998439	+	0.0558471i	$0.982214\pi$
$464$	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	−0.394481	−	0.918904i	$-0.629076\pi$
$467$	−3.74947	+	1.21828i	−0.173505	+	0.0563752i	0.220976	+	0.975279i	$0.429076\pi$
$468$			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	−0.636954	−	0.770902i	$-0.719806\pi$
$487$	6.46697	−	8.90102i	0.293046	−	0.403344i	0.930001	+	0.367558i	$0.119806\pi$
$488$	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	0.896112	−	0.443829i	$-0.146380\pi$
$503$	30.5062	+	9.91207i	1.36021	+	0.441958i	0.464094	+	0.885786i	$0.346380\pi$
$504$	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	0.831447	−	0.555604i	$-0.187513\pi$
$523$	1.05438	+	1.45123i	0.0461047	+	0.0634577i	−0.785342	+	0.619062i	$0.787513\pi$
$524$	−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	−0.115283	−	0.993333i	$-0.536777\pi$
$547$	−18.5330	−	6.02174i	−0.792414	−	0.257471i	−0.677132	+	0.735862i	$0.736777\pi$
$548$	−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	$0.188350\pi$
$557$			26.3285i			1.11557i	−0.829984	+	0.557787i	$0.811650\pi$
$558$	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	$-0.517824\pi$
$563$	21.6134	−	29.7482i	0.910895	−	1.25374i	0.966860	−	0.255306i	$-0.0821763\pi$
$564$	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	0.716437	−	0.697652i	$-0.245772\pi$
$577$	−4.04656	−	5.56961i	−0.168461	−	0.231866i	−0.884898	+	0.465786i	$0.845772\pi$
$578$	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	−0.591919	−	0.805997i	$-0.701630\pi$
$587$	8.66258	−	11.9230i	0.357543	−	0.492116i	0.949462	+	0.313882i	$0.101630\pi$
$588$	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	$0.0381659\pi$
$593$			5.82561i			0.239229i	−0.992820	+	0.119615i	$0.961834\pi$
$594$	−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	$-0.990540\pi$
$607$		−	1.46424i		−	0.0594318i	0.999558	−	0.0297159i	$-0.00946025\pi$
$608$	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	$-0.552750\pi$
$613$	20.4023	−	28.0814i	0.824041	−	1.13420i	0.989003	−	0.147896i	$-0.0472499\pi$
$614$	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	0.636222	−	0.771506i	$-0.280496\pi$
$617$	39.8529	−	12.9490i	1.60442	−	0.521307i	0.968194	+	0.250199i	$0.0804961\pi$
$618$		−	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	$0.357817\pi$
$643$			45.7391i			1.80377i	−0.431974	+	0.901886i	$0.642183\pi$
$644$	−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	0.746798	−	0.665050i	$-0.231590\pi$
$647$	24.4204	+	7.93466i	0.960064	+	0.311944i	0.213266	+	0.976994i	$0.431590\pi$
$648$	−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	0.888863	−	0.458173i	$-0.151496\pi$
$653$	34.2079	+	11.1148i	1.33866	+	0.434957i	0.449798	+	0.893130i	$0.351496\pi$
$654$	−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	$-0.971233\pi$
$673$	−20.0792	−	27.6367i	−0.773997	−	1.06531i	0.221922	−	0.975064i	$-0.428767\pi$
$674$	−23.9703			−0.923301
$675$		0			0
$676$	−1.97976			−0.0761446
$677$	5.39301	+	7.42284i	0.207270	+	0.285283i	0.899978	−	0.435935i	$-0.143582\pi$
$677$	5.39301	+	7.42284i	0.207270	+	0.285283i	−0.692708	+	0.721218i	$0.743582\pi$
$678$	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	−0.641531	−	0.767097i	$-0.721701\pi$
$683$	−18.5463	+	6.02604i	−0.709653	+	0.230580i	−0.0681215	+	0.997677i	$0.521701\pi$
$684$	−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	0.798503	−	0.601991i	$-0.205626\pi$
$727$	−0.560188	−	0.771033i	−0.0207762	−	0.0285960i	−0.819279	+	0.573395i	$0.805626\pi$
$728$	−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	−0.0262485	−	0.999655i	$-0.508356\pi$
$733$	14.6226	−	4.75118i	0.540099	−	0.175489i	0.566347	+	0.824167i	$0.308356\pi$
$734$	−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	$-0.716917\pi$
$743$		−	42.3399i		−	1.55330i	0.629932	−	0.776650i	$-0.283083\pi$
$744$	−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	$0.0539199\pi$
$757$			9.27680i			0.337171i	−0.985687	+	0.168585i	$0.946080\pi$
$758$	−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	0.863261	−	0.504758i	$-0.168418\pi$
$773$	3.23751	+	4.45605i	0.116445	+	0.160273i	−0.746816	+	0.665031i	$0.768418\pi$
$774$	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	−0.988686	−	0.149998i	$-0.952073\pi$
$787$	−15.1632	+	20.8703i	−0.540509	+	0.743946i	0.448178	+	0.893944i	$0.352073\pi$
$788$	−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	0.245860	−	0.969305i	$-0.420930\pi$
$797$	−3.52831	−	1.14642i	−0.124979	−	0.0406082i	−0.370839	+	0.928697i	$0.620930\pi$
$798$	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	$0.0570328\pi$
$823$	24.3680	+	33.5397i	0.849415	+	1.16912i	−0.134576	+	0.990903i	$0.542967\pi$
$824$	−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	$-0.965113\pi$
$827$	−22.7434	−	31.3035i	−0.790864	−	1.08853i	0.203136	−	0.979151i	$-0.434887\pi$
$828$	−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	0.510566	−	0.859839i	$-0.329436\pi$
$853$	12.2147	+	3.96878i	0.418222	+	0.135889i	−0.0923439	+	0.995727i	$0.529436\pi$
$854$	−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	$0.0858566\pi$
$857$			15.6015i			0.532936i	−0.963844	+	0.266468i	$0.914143\pi$
$858$	−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	−0.920082	−	0.391726i	$-0.871878\pi$
$863$	−7.73222	+	10.6425i	−0.263208	+	0.362274i	0.656874	+	0.754000i	$0.271878\pi$
$864$	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	0.866547	−	0.499096i	$-0.166334\pi$
$877$	3.67515	+	5.05840i	0.124101	+	0.170810i	−0.742446	+	0.669906i	$0.766334\pi$
$878$	−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	−0.557093	−	0.830450i	$-0.688083\pi$
$883$	−15.4420	+	5.01740i	−0.519664	+	0.168849i	0.0374289	+	0.999299i	$0.488083\pi$
$884$	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	$0.619863\pi$
$887$	−33.9078	+	46.6700i	−1.13851	+	1.56703i	−0.770788	+	0.637091i	$0.780137\pi$
$888$	−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	$-0.952234\pi$
$907$		−	9.00465i		−	0.298995i	0.988762	−	0.149497i	$-0.0477655\pi$
$908$	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	−0.960876	−	0.276978i	$-0.910667\pi$
$937$	−12.2603	+	16.8749i	−0.400527	+	0.551278i	0.560349	+	0.828256i	$0.310667\pi$
$938$	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	0.754719	−	0.656048i	$-0.227773\pi$
$947$	30.1482	+	9.79575i	0.979685	+	0.318319i	0.224966	+	0.974367i	$0.427773\pi$
$948$	−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	0.675822	−	0.737064i	$-0.263789\pi$
$953$	24.3674	+	7.91746i	0.789339	+	0.256472i	0.113516	+	0.993536i	$0.463789\pi$
$954$	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	−0.717044	−	0.697028i	$-0.754505\pi$
$967$	−27.5965	+	8.96663i	−0.887442	+	0.288347i	−0.170398	+	0.985375i	$0.554505\pi$
$968$			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	1.00000		0.000555441i	$-0.000176802\pi$
$977$	21.5815	+	29.7044i	0.690455	+	0.950329i	−0.309545	+	0.950885i	$0.600177\pi$
$978$	−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	−0.643746	−	0.765239i	$-0.722621\pi$
$983$	−22.4095	+	7.28128i	−0.714752	+	0.232237i	−0.0710055	+	0.997476i	$0.522621\pi$
$984$	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	−0.439478	−	0.898254i	$-0.644836\pi$
$997$	−41.7742	−	13.5733i	−1.32300	−	0.429870i	−0.883525	+	0.468384i	$0.844836\pi$
$998$	−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.199.2		16
5.2	odd	4		75.2.g.b.61.2	yes	8
5.3	odd	4		375.2.g.b.301.1		8
5.4	even	2	inner	375.2.i.b.199.3		16
15.2	even	4		225.2.h.c.136.1		8
25.3	odd	20		1875.2.a.e.1.4		4
25.4	even	10		1875.2.b.c.1249.3		8
25.9	even	10	inner	375.2.i.b.49.2		16
25.12	odd	20		75.2.g.b.16.2	✓	8
25.13	odd	20		375.2.g.b.76.1		8
25.16	even	5	inner	375.2.i.b.49.3		16
25.21	even	5		1875.2.b.c.1249.6		8
25.22	odd	20		1875.2.a.h.1.1		4
75.47	even	20		5625.2.a.i.1.4		4
75.53	even	20		5625.2.a.n.1.1		4
75.62	even	20		225.2.h.c.91.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.16.2	✓	8	25.12	odd	20
75.2.g.b.61.2	yes	8	5.2	odd	4
225.2.h.c.91.1		8	75.62	even	20
225.2.h.c.136.1		8	15.2	even	4
375.2.g.b.76.1		8	25.13	odd	20
375.2.g.b.301.1		8	5.3	odd	4
375.2.i.b.49.2		16	25.9	even	10	inner
375.2.i.b.49.3		16	25.16	even	5	inner
375.2.i.b.199.2		16	1.1	even	1	trivial
375.2.i.b.199.3		16	5.4	even	2	inner
1875.2.a.e.1.4		4	25.3	odd	20
1875.2.a.h.1.1		4	25.22	odd	20
1875.2.b.c.1249.3		8	25.4	even	10
1875.2.b.c.1249.6		8	25.21	even	5
5625.2.a.i.1.4		4	75.47	even	20
5625.2.a.n.1.1		4	75.53	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

L-functions

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