LMFDB - Embedded newform 375.2.g.b.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			76.1
Root			$-0.0272949 - 1.41395i$ of defining polynomial
Character	$\chi$	$=$	375.76
Dual form			375.2.g.b.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38048 - 1.00297i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.281722 + 0.867051i) q^{4} +(-0.527295 + 1.62285i) q^{6} +3.94243 q^{7} +(-0.573870 + 1.76619i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.38048 - 1.00297i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.281722 + 0.867051i) q^{4} +(-0.527295 + 1.62285i) q^{6} +3.94243 q^{7} +(-0.573870 + 1.76619i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(4.78023 + 3.47304i) q^{11} +(0.737558 - 0.535867i) q^{12} +(2.66220 - 1.93420i) q^{13} +(-5.44243 - 3.95416i) q^{14} +(4.03877 - 2.93434i) q^{16} +(-0.836312 + 2.57390i) q^{17} +1.70636 q^{18} +(-0.728704 + 2.24272i) q^{19} +(-1.21828 - 3.74947i) q^{21} +(-3.11562 - 9.58890i) q^{22} +(-0.472705 - 0.343440i) q^{23} +1.85708 q^{24} -5.61505 q^{26} +(0.809017 + 0.587785i) q^{27} +(1.11067 + 3.41829i) q^{28} +(-1.20877 - 3.72022i) q^{29} +(0.837233 - 2.57674i) q^{31} -4.80433 q^{32} +(1.82589 - 5.61950i) q^{33} +(3.73607 - 2.71441i) q^{34} +(-0.737558 - 0.535867i) q^{36} +(-0.0168692 + 0.0122562i) q^{37} +(3.25535 - 2.36515i) q^{38} +(-2.66220 - 1.93420i) q^{39} +(-1.19098 + 0.865300i) q^{41} +(-2.07882 + 6.39796i) q^{42} -1.27279 q^{43} +(-1.66461 + 5.12314i) q^{44} +(0.308096 + 0.948222i) q^{46} +(-1.67907 - 5.16764i) q^{47} +(-4.03877 - 2.93434i) q^{48} +8.54276 q^{49} +2.70636 q^{51} +(2.42705 + 1.76336i) q^{52} +(-0.870050 - 2.67774i) q^{53} +(-0.527295 - 1.62285i) q^{54} +(-2.26244 + 6.96308i) q^{56} +2.35813 q^{57} +(-2.06260 + 6.34804i) q^{58} +(3.79456 - 2.75691i) q^{59} +(-4.51538 - 3.28061i) q^{61} +(-3.74018 + 2.71740i) q^{62} +(-3.18949 + 2.31730i) q^{63} +(-1.44528 - 1.05006i) q^{64} +(-8.15681 + 5.92627i) q^{66} +(-1.86361 + 5.73559i) q^{67} -2.46731 q^{68} +(-0.180557 + 0.555698i) q^{69} +(-2.50346 - 7.70487i) q^{71} +(-0.573870 - 1.76619i) q^{72} +(10.7734 + 7.82730i) q^{73} +0.0355801 q^{74} -2.14984 q^{76} +(18.8457 + 13.6922i) q^{77} +(1.73515 + 5.34023i) q^{78} +(5.14971 + 15.8492i) q^{79} +(0.309017 - 0.951057i) q^{81} +2.51200 q^{82} +(-0.241540 + 0.743385i) q^{83} +(2.90777 - 2.11262i) q^{84} +(1.75705 + 1.27657i) q^{86} +(-3.16461 + 2.29922i) q^{87} +(-8.87728 + 6.44972i) q^{88} +(2.80994 + 2.04154i) q^{89} +(10.4955 - 7.62545i) q^{91} +(0.164609 - 0.506614i) q^{92} -2.70934 q^{93} +(-2.86510 + 8.81786i) q^{94} +(1.48462 + 4.56919i) q^{96} +(0.758460 + 2.33430i) q^{97} +(-11.7931 - 8.56817i) q^{98} -5.90869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9	$ 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9} + 16 q^{11} + 9 q^{12} + 8 q^{13} - 8 q^{14} - 17 q^{16} + q^{17} - 4 q^{18} - 5 q^{19} - 11 q^{21} - 13 q^{22} - 7 q^{23} + 30 q^{24} + 6 q^{26} + 2 q^{27} + 17 q^{28} + 5 q^{29} - 19 q^{31} - 24 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} + q^{37} + 10 q^{38} - 8 q^{39} - 14 q^{41} + 8 q^{42} - 32 q^{43} - 3 q^{44} + 16 q^{46} + q^{47} + 17 q^{48} + 16 q^{49} + 4 q^{51} + 6 q^{52} + 3 q^{53} - q^{54} - 15 q^{56} - 10 q^{57} - 5 q^{58} + 30 q^{59} - 14 q^{61} + 17 q^{62} - 9 q^{63} - 44 q^{64} - 7 q^{66} - 4 q^{67} + 22 q^{68} - 8 q^{69} + 21 q^{71} - 2 q^{73} - 38 q^{74} + 80 q^{76} + 37 q^{77} + 14 q^{78} - 30 q^{79} - 2 q^{81} + 12 q^{82} - 2 q^{83} + 8 q^{84} - 34 q^{86} - 15 q^{87} - 70 q^{88} + 21 q^{91} - 9 q^{92} - 46 q^{93} - 33 q^{94} + 34 q^{96} + 6 q^{97} - 73 q^{98} - 14 q^{99}+O(q^{100}) $ 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9 + 16 * q^11 + 9 * q^12 + 8 * q^13 - 8 * q^14 - 17 * q^16 + q^17 - 4 * q^18 - 5 * q^19 - 11 * q^21 - 13 * q^22 - 7 * q^23 + 30 * q^24 + 6 * q^26 + 2 * q^27 + 17 * q^28 + 5 * q^29 - 19 * q^31 - 24 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 + q^37 + 10 * q^38 - 8 * q^39 - 14 * q^41 + 8 * q^42 - 32 * q^43 - 3 * q^44 + 16 * q^46 + q^47 + 17 * q^48 + 16 * q^49 + 4 * q^51 + 6 * q^52 + 3 * q^53 - q^54 - 15 * q^56 - 10 * q^57 - 5 * q^58 + 30 * q^59 - 14 * q^61 + 17 * q^62 - 9 * q^63 - 44 * q^64 - 7 * q^66 - 4 * q^67 + 22 * q^68 - 8 * q^69 + 21 * q^71 - 2 * q^73 - 38 * q^74 + 80 * q^76 + 37 * q^77 + 14 * q^78 - 30 * q^79 - 2 * q^81 + 12 * q^82 - 2 * q^83 + 8 * q^84 - 34 * q^86 - 15 * q^87 - 70 * q^88 + 21 * q^91 - 9 * q^92 - 46 * q^93 - 33 * q^94 + 34 * q^96 + 6 * q^97 - 73 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−1.38048	−	1.00297i	−0.976144	−	0.709210i	−0.0193004	−	0.999814i	$-0.506144\pi$
$2$	−1.38048	−	1.00297i	−0.976144	−	0.709210i	−0.956844	+	0.290604i	$0.906144\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.281722	+	0.867051i	0.140861	+	0.433526i
$5$		0			0
$5$		0			0
$6$	−0.527295	+	1.62285i	−0.215267	+	0.662524i
$7$	3.94243			1.49010			0.745049	−	0.667009i	$-0.232426\pi$
$7$	3.94243			1.49010			0.745049	+	0.667009i	$0.232426\pi$
$8$	−0.573870	+	1.76619i	−0.202894	+	0.624442i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	4.78023	+	3.47304i	1.44129	+	1.04716i	0.987770	+	0.155918i	$0.0498334\pi$
$11$	4.78023	+	3.47304i	1.44129	+	1.04716i	0.453524	+	0.891244i	$0.350167\pi$
$12$	0.737558	−	0.535867i	0.212915	−	0.154692i
$13$	2.66220	−	1.93420i	0.738361	−	0.536451i	−0.153836	−	0.988096i	$-0.549163\pi$
$13$	2.66220	−	1.93420i	0.738361	−	0.536451i	0.892197	+	0.451646i	$0.149163\pi$
$14$	−5.44243	−	3.95416i	−1.45455	−	1.05679i
$15$		0			0
$16$	4.03877	−	2.93434i	1.00969	−	0.733585i
$17$	−0.836312	+	2.57390i	−0.202835	+	0.624263i	0.796960	+	0.604032i	$0.206440\pi$
$17$	−0.836312	+	2.57390i	−0.202835	+	0.624263i	−0.999795	+	0.0202310i	$0.993560\pi$
$18$	1.70636			0.402193
$19$	−0.728704	+	2.24272i	−0.167176	+	0.514515i	−0.999190	−	0.0402396i	$-0.987188\pi$
$19$	−0.728704	+	2.24272i	−0.167176	+	0.514515i	0.832014	+	0.554755i	$0.187188\pi$
$20$		0			0
$21$	−1.21828	−	3.74947i	−0.265850	−	0.818202i
$22$	−3.11562	−	9.58890i	−0.664253	−	2.04436i
$23$	−0.472705	−	0.343440i	−0.0985658	−	0.0716123i	0.537411	−	0.843321i	$-0.319403\pi$
$23$	−0.472705	−	0.343440i	−0.0985658	−	0.0716123i	−0.635977	+	0.771708i	$0.719403\pi$
$24$	1.85708			0.379075
$25$		0			0
$26$	−5.61505			−1.10120
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	1.11067	+	3.41829i	0.209897	+	0.645996i
$29$	−1.20877	−	3.72022i	−0.224464	−	0.690828i	−0.998346	−	0.0574980i	$-0.981688\pi$
$29$	−1.20877	−	3.72022i	−0.224464	−	0.690828i	0.773882	−	0.633330i	$-0.218312\pi$
$30$		0			0
$31$	0.837233	−	2.57674i	0.150371	−	0.462796i	−0.847291	−	0.531129i	$-0.821768\pi$
$31$	0.837233	−	2.57674i	0.150371	−	0.462796i	0.997663	+	0.0683330i	$0.0217680\pi$
$32$	−4.80433			−0.849294
$33$	1.82589	−	5.61950i	0.317846	−	0.978229i
$34$	3.73607	−	2.71441i	0.640730	−	0.465518i
$35$		0			0
$36$	−0.737558	−	0.535867i	−0.122926	−	0.0893112i
$37$	−0.0168692	+	0.0122562i	−0.00277328	+	0.00201490i	−0.589171	−	0.808008i	$-0.700546\pi$
$37$	−0.0168692	+	0.0122562i	−0.00277328	+	0.00201490i	0.586398	+	0.810023i	$0.300546\pi$
$38$	3.25535	−	2.36515i	0.528087	−	0.383678i
$39$	−2.66220	−	1.93420i	−0.426293	−	0.309720i
$40$		0			0
$41$	−1.19098	+	0.865300i	−0.186000	+	0.135137i	−0.676889	−	0.736085i	$-0.736672\pi$
$41$	−1.19098	+	0.865300i	−0.186000	+	0.135137i	0.490889	+	0.871222i	$0.336672\pi$
$42$	−2.07882	+	6.39796i	−0.320769	+	0.987227i
$43$	−1.27279			−0.194098			−0.0970491	−	0.995280i	$-0.530940\pi$
$43$	−1.27279			−0.194098			−0.0970491	+	0.995280i	$0.530940\pi$
$44$	−1.66461	+	5.12314i	−0.250949	+	0.772342i
$45$		0			0
$46$	0.308096	+	0.948222i	0.0454263	+	0.139808i
$47$	−1.67907	−	5.16764i	−0.244917	−	0.753777i	−0.995650	−	0.0931716i	$-0.970299\pi$
$47$	−1.67907	−	5.16764i	−0.244917	−	0.753777i	0.750733	−	0.660606i	$-0.229701\pi$
$48$	−4.03877	−	2.93434i	−0.582947	−	0.423536i
$49$	8.54276			1.22039
$50$		0			0
$51$	2.70636			0.378967
$52$	2.42705	+	1.76336i	0.336571	+	0.244533i
$53$	−0.870050	−	2.67774i	−0.119511	−	0.367816i	0.873350	−	0.487092i	$-0.161942\pi$
$53$	−0.870050	−	2.67774i	−0.119511	−	0.367816i	−0.992861	+	0.119277i	$0.961942\pi$
$54$	−0.527295	−	1.62285i	−0.0717557	−	0.220841i
$55$		0			0
$56$	−2.26244	+	6.96308i	−0.302332	+	0.930481i
$57$	2.35813			0.312343
$58$	−2.06260	+	6.34804i	−0.270833	+	0.833539i
$59$	3.79456	−	2.75691i	0.494009	−	0.358919i	−0.312715	−	0.949847i	$-0.601238\pi$
$59$	3.79456	−	2.75691i	0.494009	−	0.358919i	0.806724	+	0.590928i	$0.201238\pi$
$60$		0			0
$61$	−4.51538	−	3.28061i	−0.578135	−	0.420040i	0.259916	−	0.965631i	$-0.416305\pi$
$61$	−4.51538	−	3.28061i	−0.578135	−	0.420040i	−0.838051	+	0.545591i	$0.816305\pi$
$62$	−3.74018	+	2.71740i	−0.475004	+	0.345110i
$63$	−3.18949	+	2.31730i	−0.401838	+	0.291953i
$64$	−1.44528	−	1.05006i	−0.180660	−	0.131257i
$65$		0			0
$66$	−8.15681	+	5.92627i	−1.00403	+	0.729473i
$67$	−1.86361	+	5.73559i	−0.227676	+	0.700714i	0.770333	+	0.637642i	$0.220090\pi$
$67$	−1.86361	+	5.73559i	−0.227676	+	0.700714i	−0.998009	+	0.0630725i	$0.979910\pi$
$68$	−2.46731			−0.299206
$69$	−0.180557	+	0.555698i	−0.0217365	+	0.0668982i
$70$		0			0
$71$	−2.50346	−	7.70487i	−0.297106	−	0.914400i	−0.982506	−	0.186232i	$-0.940372\pi$
$71$	−2.50346	−	7.70487i	−0.297106	−	0.914400i	0.685399	−	0.728167i	$-0.259628\pi$
$72$	−0.573870	−	1.76619i	−0.0676312	−	0.208147i
$73$	10.7734	+	7.82730i	1.26093	+	0.916116i	0.998803	−	0.0489187i	$-0.0155775\pi$
$73$	10.7734	+	7.82730i	1.26093	+	0.916116i	0.262123	+	0.965035i	$0.415578\pi$
$74$	0.0355801			0.00413611
$75$		0			0
$76$	−2.14984			−0.246604
$77$	18.8457	+	13.6922i	2.14767	+	1.56037i
$78$	1.73515	+	5.34023i	0.196467	+	0.604662i
$79$	5.14971	+	15.8492i	0.579388	+	1.78317i	0.620726	+	0.784028i	$0.286838\pi$
$79$	5.14971	+	15.8492i	0.579388	+	1.78317i	−0.0413379	+	0.999145i	$0.513162\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.51200			0.277404
$83$	−0.241540	+	0.743385i	−0.0265125	+	0.0815971i	−0.963437	−	0.267934i	$-0.913659\pi$
$83$	−0.241540	+	0.743385i	−0.0265125	+	0.0815971i	0.936925	+	0.349531i	$0.113659\pi$
$84$	2.90777	−	2.11262i	0.317264	−	0.230506i
$85$		0			0
$86$	1.75705	+	1.27657i	0.189468	+	0.137656i
$87$	−3.16461	+	2.29922i	−0.339282	+	0.246503i
$88$	−8.87728	+	6.44972i	−0.946322	+	0.687543i
$89$	2.80994	+	2.04154i	0.297853	+	0.216403i	0.726667	−	0.686990i	$-0.241068\pi$
$89$	2.80994	+	2.04154i	0.297853	+	0.216403i	−0.428814	+	0.903393i	$0.641068\pi$
$90$		0			0
$91$	10.4955	−	7.62545i	1.10023	−	0.799364i
$92$	0.164609	−	0.506614i	0.0171617	−	0.0528182i
$93$	−2.70934			−0.280946
$94$	−2.86510	+	8.81786i	−0.295512	+	0.909493i
$95$		0			0
$96$	1.48462	+	4.56919i	0.151523	+	0.466341i
$97$	0.758460	+	2.33430i	0.0770099	+	0.237012i	0.982149	−	0.188103i	$-0.0602337\pi$
$97$	0.758460	+	2.33430i	0.0770099	+	0.237012i	−0.905139	+	0.425115i	$0.860234\pi$
$98$	−11.7931	−	8.56817i	−1.19128	−	0.865515i
$99$	−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	$0.611118\pi$
$102$	−3.73607	−	2.71441i	−0.369926	−	0.268767i
$103$	−3.63192	−	11.1779i	−0.357864	−	1.10139i	−0.954330	−	0.298754i	$-0.903429\pi$
$103$	−3.63192	−	11.1779i	−0.357864	−	1.10139i	0.596466	−	0.802638i	$-0.296571\pi$
$104$	1.88841	+	5.81193i	0.185174	+	0.569906i
$105$		0			0
$106$	−1.48462	+	4.56919i	−0.144199	+	0.443799i
$107$	−5.66780			−0.547927			−0.273964	−	0.961740i	$-0.588335\pi$
$107$	−5.66780			−0.547927			−0.273964	+	0.961740i	$0.588335\pi$
$108$	−0.281722	+	0.867051i	−0.0271087	+	0.0834321i
$109$	1.10130	−	0.800139i	0.105485	−	0.0766394i	−0.533792	−	0.845616i	$-0.679234\pi$
$109$	1.10130	−	0.800139i	0.105485	−	0.0766394i	0.639277	+	0.768976i	$0.279234\pi$
$110$		0			0
$111$	0.0168692	+	0.0122562i	0.00160115	+	0.00116330i
$112$	15.9226	−	11.5684i	1.50454	−	1.09311i
$113$	−8.64489	+	6.28088i	−0.813243	+	0.590856i	−0.914769	−	0.403977i	$-0.867627\pi$
$113$	−8.64489	+	6.28088i	−0.813243	+	0.590856i	0.101526	+	0.994833i	$0.467627\pi$
$114$	−3.25535	−	2.36515i	−0.304891	−	0.221516i
$115$		0			0
$116$	2.88508	−	2.09614i	0.267873	−	0.194621i
$117$	−1.01687	+	3.12960i	−0.0940096	+	0.289332i
$118$	−8.00341			−0.736773
$119$	−3.29710	+	10.1474i	−0.302245	+	0.930214i
$120$		0			0
$121$	7.38941	+	22.7423i	0.671765	+	2.06748i
$122$	2.94300	+	9.05762i	0.266447	+	0.820038i
$123$	1.19098	+	0.865300i	0.107387	+	0.0780215i
$124$	2.47003			0.221815
$125$		0			0
$126$	6.72721			0.599308
$127$	−10.9563	−	7.96023i	−0.972216	−	0.706356i	−0.0162606	−	0.999868i	$-0.505176\pi$
$127$	−10.9563	−	7.96023i	−0.972216	−	0.706356i	−0.955956	+	0.293511i	$0.905176\pi$
$128$	3.91123	+	12.0375i	0.345708	+	1.06398i
$129$	0.393313	+	1.21049i	0.0346292	+	0.106578i
$130$		0			0
$131$	1.41912	−	4.36759i	0.123989	−	0.381599i	−0.869727	−	0.493534i	$-0.835705\pi$
$131$	1.41912	−	4.36759i	0.123989	−	0.381599i	0.993716	+	0.111935i	$0.0357049\pi$
$132$	5.38679			0.468860
$133$	−2.87286	+	8.84176i	−0.249109	+	0.766678i
$134$	8.32532	−	6.04870i	0.719198	−	0.522528i
$135$		0			0
$136$	−4.06607	−	2.95417i	−0.348662	−	0.253318i
$137$	12.3472	−	8.97078i	1.05489	−	0.766426i	0.0817573	−	0.996652i	$-0.473947\pi$
$137$	12.3472	−	8.97078i	1.05489	−	0.766426i	0.973137	+	0.230227i	$0.0739468\pi$
$138$	0.806606	−	0.586034i	0.0686629	−	0.0498865i
$139$	−14.7550	−	10.7201i	−1.25150	−	0.909269i	−0.253194	−	0.967416i	$-0.581481\pi$
$139$	−14.7550	−	10.7201i	−1.25150	−	0.909269i	−0.998308	+	0.0581460i	$0.981481\pi$
$140$		0			0
$141$	−4.39586	+	3.19378i	−0.370198	+	0.268964i
$142$	−4.27182	+	13.1473i	−0.358483	+	1.10330i
$143$	19.4435			1.62595
$144$	−1.54267	+	4.74786i	−0.128556	+	0.395655i
$145$		0			0
$146$	−7.02177	−	21.6108i	−0.581126	−	1.78852i
$147$	−2.63986	−	8.12464i	−0.217732	−	0.670109i
$148$	−0.0153792	−	0.0111736i	−0.00126416	−	0.000918465i
$149$	14.7323			1.20692			0.603458	−	0.797394i	$-0.293789\pi$
$149$	14.7323			1.20692			0.603458	+	0.797394i	$0.293789\pi$
$150$		0			0
$151$	−17.4354			−1.41887			−0.709437	−	0.704769i	$-0.751051\pi$
$151$	−17.4354			−1.41887			−0.709437	+	0.704769i	$0.751051\pi$
$152$	−3.54289	−	2.57406i	−0.287366	−	0.208784i
$153$	−0.836312	−	2.57390i	−0.0676118	−	0.208088i
$154$	−12.2831	−	37.8036i	−0.989803	−	3.04630i
$155$		0			0
$156$	0.927051	−	2.85317i	0.0742235	−	0.228436i
$157$	−17.9105			−1.42942			−0.714708	−	0.699423i	$-0.753440\pi$
$157$	−17.9105			−1.42942			−0.714708	+	0.699423i	$0.753440\pi$
$158$	8.78728	−	27.0445i	0.699078	−	2.15154i
$159$	−2.27782	+	1.65493i	−0.180643	+	0.131245i
$160$		0			0
$161$	−1.86361	−	1.35399i	−0.146873	−	0.106709i
$162$	−1.38048	+	1.00297i	−0.108460	+	0.0788011i
$163$	17.6041	−	12.7901i	1.37886	−	1.00180i	0.381870	−	0.924216i	$-0.375280\pi$
$163$	17.6041	−	12.7901i	1.37886	−	1.00180i	0.996986	−	0.0775819i	$-0.0247199\pi$
$164$	−1.08579	−	0.788869i	−0.0847856	−	0.0616004i
$165$		0			0
$166$	1.07904	−	0.783966i	0.0837495	−	0.0608475i
$167$	6.98470	−	21.4967i	0.540492	−	1.66346i	−0.190980	−	0.981594i	$-0.561167\pi$
$167$	6.98470	−	21.4967i	0.540492	−	1.66346i	0.731473	−	0.681871i	$-0.238833\pi$
$168$	7.32142			0.564860
$169$	−0.671052	+	2.06529i	−0.0516194	+	0.158868i
$170$		0			0
$171$	−0.728704	−	2.24272i	−0.0557254	−	0.171505i
$172$	−0.358572	−	1.10357i	−0.0273409	−	0.0841465i
$173$	10.4458	+	7.58929i	0.794177	+	0.577003i	0.909200	−	0.416360i	$-0.136694\pi$
$173$	10.4458	+	7.58929i	0.794177	+	0.577003i	−0.115023	+	0.993363i	$0.536694\pi$
$174$	6.67473			0.506010
$175$		0			0
$176$	29.4974			2.22345
$177$	−3.79456	−	2.75691i	−0.285216	−	0.207222i
$178$	−1.83144	−	5.63659i	−0.137272	−	0.422480i
$179$	−1.98716	−	6.11586i	−0.148528	−	0.457121i	0.848920	−	0.528521i	$-0.177253\pi$
$179$	−1.98716	−	6.11586i	−0.148528	−	0.457121i	−0.997448	+	0.0714002i	$0.977253\pi$
$180$		0			0
$181$	4.54473	−	13.9873i	0.337807	−	1.03966i	−0.627515	−	0.778604i	$-0.715928\pi$
$181$	4.54473	−	13.9873i	0.337807	−	1.03966i	0.965323	−	0.261060i	$-0.0840720\pi$
$182$	−22.1370			−1.64090
$183$	−1.72472	+	5.30815i	−0.127495	+	0.392389i
$184$	0.877852	−	0.637797i	0.0647161	−	0.0470190i
$185$		0			0
$186$	3.74018	+	2.71740i	0.274243	+	0.199250i
$187$	−12.9370	+	9.39931i	−0.946050	+	0.687346i
$188$	4.00758	−	2.91168i	0.292283	−	0.212356i
$189$	3.18949	+	2.31730i	0.232001	+	0.168559i
$190$		0			0
$191$	−5.43095	+	3.94582i	−0.392970	+	0.285509i	−0.766671	−	0.642040i	$-0.778088\pi$
$191$	−5.43095	+	3.94582i	−0.392970	+	0.285509i	0.373702	+	0.927549i	$0.378088\pi$
$192$	−0.552047	+	1.69903i	−0.0398406	+	0.122617i
$193$	−4.82817			−0.347539			−0.173769	−	0.984786i	$-0.555595\pi$
$193$	−4.82817			−0.347539			−0.173769	+	0.984786i	$0.555595\pi$
$194$	1.29421	−	3.98316i	0.0929186	−	0.285974i
$195$		0			0
$196$	2.40668	+	7.40701i	0.171906	+	0.529072i
$197$	4.44492	+	13.6801i	0.316688	+	0.974664i	0.975054	+	0.221967i	$0.0712477\pi$
$197$	4.44492	+	13.6801i	0.316688	+	0.974664i	−0.658367	+	0.752697i	$0.728752\pi$
$198$	8.15681	+	5.92627i	0.579679	+	0.421161i
$199$	−8.72608			−0.618575			−0.309288	−	0.950969i	$-0.600091\pi$
$199$	−8.72608			−0.618575			−0.309288	+	0.950969i	$0.600091\pi$
$200$		0			0
$201$	6.03076			0.425377
$202$	9.49071	+	6.89540i	0.667764	+	0.485159i
$203$	−4.76550	−	14.6667i	−0.334473	−	1.02940i
$204$	0.762442	+	2.34656i	0.0533816	+	0.164292i
$205$		0			0
$206$	−6.19738	+	19.0736i	−0.431792	+	1.32892i
$207$	0.584296			0.0406114
$208$	5.07641	−	15.6236i	0.351986	−	1.08330i
$209$	−11.2724	+	8.18990i	−0.779730	+	0.566507i
$210$		0			0
$211$	−2.40777	−	1.74935i	−0.165758	−	0.120430i	0.501814	−	0.864976i	$-0.332666\pi$
$211$	−2.40777	−	1.74935i	−0.165758	−	0.120430i	−0.667572	+	0.744546i	$0.732666\pi$
$212$	2.07663	−	1.50876i	0.142623	−	0.103622i
$213$	−6.55415	+	4.76187i	−0.449083	+	0.326278i
$214$	7.82426	+	5.68466i	0.534856	+	0.388595i
$215$		0			0
$216$	−1.50241	+	1.09157i	−0.102226	+	0.0742716i
$217$	3.30073	−	10.1586i	0.224068	−	0.689611i
$218$	−2.32283			−0.157322
$219$	4.11505	−	12.6648i	0.278070	−	0.855810i
$220$		0			0
$221$	2.75202	+	8.46984i	0.185121	+	0.569743i
$222$	−0.0109949	−	0.0338387i	−0.000737927	−	0.00227111i
$223$	−0.246494	−	0.179088i	−0.0165064	−	0.0119926i	0.579501	−	0.814971i	$-0.303247\pi$
$223$	−0.246494	−	0.179088i	−0.0165064	−	0.0119926i	−0.596008	+	0.802979i	$0.703247\pi$
$224$	−18.9408			−1.26553
$225$		0			0
$226$	18.2336			1.21288
$227$	−7.74408	−	5.62641i	−0.513993	−	0.373438i	0.300343	−	0.953831i	$-0.402899\pi$
$227$	−7.74408	−	5.62641i	−0.513993	−	0.373438i	−0.814336	+	0.580394i	$0.802899\pi$
$228$	0.664339	+	2.04462i	0.0439969	+	0.135409i
$229$	3.74812	+	11.5355i	0.247682	+	0.762288i	0.995184	+	0.0980277i	$0.0312534\pi$
$229$	3.74812	+	11.5355i	0.247682	+	0.762288i	−0.747501	+	0.664260i	$0.768747\pi$
$230$		0			0
$231$	7.19843	−	22.1545i	0.473622	−	1.45766i
$232$	7.26430			0.476924
$233$	−6.21132	+	19.1165i	−0.406917	+	1.25236i	0.512367	+	0.858766i	$0.328769\pi$
$233$	−6.21132	+	19.1165i	−0.406917	+	1.25236i	−0.919284	+	0.393595i	$0.871231\pi$
$234$	4.54267	−	3.30045i	0.296964	−	0.215757i
$235$		0			0
$236$	3.45939	+	2.51340i	0.225187	+	0.163608i
$237$	13.4821	−	9.79534i	0.875758	−	0.636275i
$238$	14.7292	−	10.7014i	0.954751	−	0.693667i
$239$	−14.2902	−	10.3825i	−0.924358	−	0.671585i	0.0202473	−	0.999795i	$-0.493555\pi$
$239$	−14.2902	−	10.3825i	−0.924358	−	0.671585i	−0.944605	+	0.328210i	$0.893555\pi$
$240$		0			0
$241$	−23.8973	+	17.3624i	−1.53936	+	1.11841i	−0.588630	+	0.808403i	$0.700332\pi$
$241$	−23.8973	+	17.3624i	−1.53936	+	1.11841i	−0.950733	+	0.310010i	$0.899668\pi$
$242$	12.6090	−	38.8066i	0.810538	−	2.49458i
$243$	−1.00000			−0.0641500
$244$	1.57238	−	4.83929i	0.100661	−	0.309804i
$245$		0			0
$246$	−0.776250	−	2.38905i	−0.0494919	−	0.152320i
$247$	2.39791	+	7.38002i	0.152576	+	0.469580i
$248$	4.07055	+	2.95742i	0.258480	+	0.187797i
$249$	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	$0.480962\pi$
$252$	−2.90777	−	2.11262i	−0.183172	−	0.133083i
$253$	−1.06686	−	3.28345i	−0.0670727	−	0.206429i
$254$	7.14103	+	21.9778i	0.448068	+	1.37901i
$255$		0			0
$256$	5.56989	−	17.1424i	0.348118	−	1.07140i
$257$	−22.1211			−1.37988			−0.689938	−	0.723869i	$-0.742362\pi$
$257$	−22.1211			−1.37988			−0.689938	+	0.723869i	$0.742362\pi$
$258$	0.671134	−	2.06554i	0.0417830	−	0.128595i
$259$	−0.0665056	+	0.0483191i	−0.00413245	+	0.00300240i
$260$		0			0
$261$	3.16461	+	2.29922i	0.195884	+	0.142318i
$262$	−6.33964	+	4.60602i	−0.391664	+	0.284561i
$263$	−15.9500	+	11.5884i	−0.983520	+	0.714569i	−0.958492	−	0.285118i	$-0.907967\pi$
$263$	−15.9500	+	11.5884i	−0.983520	+	0.714569i	−0.0250272	+	0.999687i	$0.507967\pi$
$264$	8.87728	+	6.44972i	0.546359	+	0.396953i
$265$		0			0
$266$	12.8340	−	9.32443i	0.786902	−	0.571718i
$267$	1.07330	−	3.30328i	0.0656849	−	0.202157i
$268$	−5.49807			−0.335848
$269$	5.61321	−	17.2757i	0.342244	−	1.05332i	−0.620799	−	0.783970i	$-0.713192\pi$
$269$	5.61321	−	17.2757i	0.342244	−	1.05332i	0.963043	−	0.269348i	$-0.0868082\pi$
$270$		0			0
$271$	6.97436	+	21.4649i	0.423662	+	1.30390i	0.904270	+	0.426962i	$0.140416\pi$
$271$	6.97436	+	21.4649i	0.423662	+	1.30390i	−0.480608	+	0.876936i	$0.659584\pi$
$272$	4.17503	+	12.8494i	0.253149	+	0.779111i
$273$	−10.4955	−	7.62545i	−0.635218	−	0.461513i
$274$	−26.0425			−1.57329
$275$		0			0
$276$	−0.532686			−0.0320639
$277$	6.67837	+	4.85212i	0.401264	+	0.291535i	0.770056	−	0.637977i	$-0.220228\pi$
$277$	6.67837	+	4.85212i	0.401264	+	0.291535i	−0.368792	+	0.929512i	$0.620228\pi$
$278$	9.61690	+	29.5978i	0.576783	+	1.77516i
$279$	0.837233	+	2.57674i	0.0501238	+	0.154265i
$280$		0			0
$281$	0.395941	−	1.21858i	0.0236199	−	0.0726944i	−0.938552	−	0.345138i	$-0.887832\pi$
$281$	0.395941	−	1.21858i	0.0236199	−	0.0726944i	0.962172	+	0.272444i	$0.0878320\pi$
$282$	9.27165			0.552119
$283$	−0.825484	+	2.54058i	−0.0490699	+	0.151022i	−0.972589	−	0.232531i	$-0.925299\pi$
$283$	−0.825484	+	2.54058i	−0.0490699	+	0.151022i	0.923519	+	0.383552i	$0.125299\pi$
$284$	5.97524	−	4.34126i	0.354565	−	0.257607i
$285$		0			0
$286$	−26.8413	−	19.5013i	−1.58716	−	1.15314i
$287$	−4.69537	+	3.41138i	−0.277159	+	0.201368i
$288$	3.88679	−	2.82392i	0.229031	−	0.166401i
$289$	7.82773	+	5.68718i	0.460455	+	0.334540i
$290$		0			0
$291$	1.98567	−	1.44268i	0.116402	−	0.0845712i
$292$	−3.75158	+	11.5462i	−0.219545	+	0.675689i
$293$	−17.6605			−1.03174			−0.515870	−	0.856667i	$-0.672531\pi$
$293$	−17.6605			−1.03174			−0.515870	+	0.856667i	$0.672531\pi$
$294$	−4.50455	+	13.8636i	−0.262711	+	0.808541i
$295$		0			0
$296$	−0.0119660	−	0.0368276i	−0.000695511	−	0.00214056i
$297$	1.82589	+	5.61950i	0.105949	+	0.326076i
$298$	−20.3376	−	14.7761i	−1.17812	−	0.855958i
$299$	−1.92272			−0.111194
$300$		0			0
$301$	−5.01787			−0.289225
$302$	24.0692	+	17.4873i	1.38503	+	1.00628i
$303$	2.12448	+	6.53847i	0.122048	+	0.375625i
$304$	3.63783	+	11.1961i	0.208644	+	0.642140i
$305$		0			0
$306$	−1.42705	+	4.39201i	−0.0815791	+	0.251075i
$307$	28.5593			1.62997			0.814983	−	0.579484i	$-0.196746\pi$
$307$	28.5593			1.62997			0.814983	+	0.579484i	$0.196746\pi$
$308$	−6.56260	+	20.1976i	−0.373939	+	1.15087i
$309$	−9.50850	+	6.90833i	−0.540920	+	0.393001i
$310$		0			0
$311$	23.7271	+	17.2388i	1.34544	+	0.977521i	0.999225	+	0.0393664i	$0.0125340\pi$
$311$	23.7271	+	17.2388i	1.34544	+	0.977521i	0.346217	+	0.938154i	$0.387466\pi$
$312$	4.94392	−	3.59197i	0.279894	−	0.203355i
$313$	−14.1523	+	10.2823i	−0.799937	+	0.581189i	−0.910896	−	0.412637i	$-0.864608\pi$
$313$	−14.1523	+	10.2823i	−0.799937	+	0.581189i	0.110958	+	0.993825i	$0.464608\pi$
$314$	24.7251	+	17.9638i	1.39532	+	1.01376i
$315$		0			0
$316$	−12.2913	+	8.93013i	−0.691438	+	0.502359i
$317$	−1.21061	+	3.72589i	−0.0679949	+	0.209267i	−0.979281	−	0.202508i	$-0.935091\pi$
$317$	−1.21061	+	3.72589i	−0.0679949	+	0.209267i	0.911286	+	0.411775i	$0.135091\pi$
$318$	4.80433			0.269414
$319$	7.14227	−	21.9816i	0.399890	−	1.23074i
$320$		0			0
$321$	1.75145	+	5.39040i	0.0977562	+	0.300863i
$322$	1.21465	+	3.73830i	0.0676897	+	0.208327i
$323$	−5.16312	−	3.75123i	−0.287284	−	0.208724i
$324$	0.911672			0.0506484
$325$		0			0
$326$	−37.1301			−2.05645
$327$	−1.10130	−	0.800139i	−0.0609018	−	0.0442478i
$328$	−0.844815	−	2.60007i	−0.0466471	−	0.143565i
$329$	−6.61961	−	20.3731i	−0.364951	−	1.12320i
$330$		0			0
$331$	−5.42429	+	16.6942i	−0.298146	+	0.917599i	0.684001	+	0.729481i	$0.260238\pi$
$331$	−5.42429	+	16.6942i	−0.298146	+	0.917599i	−0.982147	+	0.188117i	$0.939762\pi$
$332$	−0.712600			−0.0391090
$333$	0.00644345	−	0.0198309i	0.000353099	−	0.00108673i
$334$	−31.2029	+	22.6702i	−1.70734	+	1.24046i
$335$		0			0
$336$	−15.9226	−	11.5684i	−0.868648	−	0.631110i
$337$	−11.3647	+	8.25697i	−0.619077	+	0.449786i	−0.852599	−	0.522566i	$-0.824975\pi$
$337$	−11.3647	+	8.25697i	−0.619077	+	0.449786i	0.233522	+	0.972352i	$0.424975\pi$
$338$	2.99780	−	2.17803i	0.163059	−	0.118469i
$339$	8.64489	+	6.28088i	0.469526	+	0.341131i
$340$		0			0
$341$	12.9513	−	9.40966i	0.701351	−	0.509562i
$342$	−1.24343	+	3.82689i	−0.0672371	+	0.206935i
$343$	6.08221			0.328408
$344$	0.730414	−	2.24798i	0.0393813	−	0.121203i
$345$		0			0
$346$	−6.80826	−	20.9537i	−0.366014	−	1.12648i
$347$	0.318440	+	0.980059i	0.0170948	+	0.0526123i	0.959240	−	0.282593i	$-0.0911944\pi$
$347$	0.318440	+	0.980059i	0.0170948	+	0.0526123i	−0.942145	+	0.335205i	$0.891194\pi$
$348$	−2.88508	−	2.09614i	−0.154657	−	0.112365i
$349$	21.5626			1.15422			0.577109	−	0.816667i	$-0.304181\pi$
$349$	21.5626			1.15422			0.577109	+	0.816667i	$0.304181\pi$
$350$		0			0
$351$	3.29066			0.175642
$352$	−22.9658	−	16.6857i	−1.22408	−	0.889348i
$353$	−2.21140	−	6.80599i	−0.117701	−	0.362246i	0.874800	−	0.484485i	$-0.160993\pi$
$353$	−2.21140	−	6.80599i	−0.117701	−	0.362246i	−0.992501	+	0.122238i	$0.960993\pi$
$354$	2.47319	+	7.61169i	0.131448	+	0.404557i
$355$		0			0
$356$	−0.978498	+	3.01151i	−0.0518603	+	0.159610i
$357$	10.6696			0.564697
$358$	−3.39082	+	10.4359i	−0.179210	+	0.551553i
$359$	−21.9663	+	15.9595i	−1.15934	+	0.842308i	−0.989694	−	0.143198i	$-0.954262\pi$
$359$	−21.9663	+	15.9595i	−1.15934	+	0.842308i	−0.169643	+	0.985506i	$0.554262\pi$
$360$		0			0
$361$	10.8725	+	7.89936i	0.572239	+	0.415756i
$362$	−20.3028	+	14.7508i	−1.06709	+	0.775285i
$363$	19.3457	−	14.0555i	1.01539	−	0.737722i
$364$	9.56848	+	6.95191i	0.501525	+	0.364379i
$365$		0			0
$366$	7.70487	−	5.59792i	0.402740	−	0.292608i
$367$	−6.62605	+	20.3929i	−0.345877	+	1.06450i	0.615236	+	0.788343i	$0.289061\pi$
$367$	−6.62605	+	20.3929i	−0.345877	+	1.06450i	−0.961113	+	0.276157i	$0.910939\pi$
$368$	−2.91692			−0.152055
$369$	0.454915	−	1.40008i	0.0236819	−	0.0728855i
$370$		0			0
$371$	−3.43011	−	10.5568i	−0.178083	−	0.548082i
$372$	−0.763282	−	2.34914i	−0.0395743	−	0.121797i
$373$	5.17021	+	3.75638i	0.267703	+	0.194498i	0.713536	−	0.700618i	$-0.247092\pi$
$373$	5.17021	+	3.75638i	0.267703	+	0.194498i	−0.445833	+	0.895116i	$0.647092\pi$
$374$	27.2865			1.41095
$375$		0			0
$376$	10.0906			0.520383
$377$	−10.4136	−	7.56596i	−0.536330	−	0.389667i
$378$	−2.07882	−	6.39796i	−0.106923	−	0.329076i
$379$	−0.0477946	−	0.147097i	−0.00245504	−	0.00755585i	0.949821	−	0.312792i	$-0.101264\pi$
$379$	−0.0477946	−	0.147097i	−0.00245504	−	0.00755585i	−0.952277	+	0.305237i	$0.901264\pi$
$380$		0			0
$381$	−4.18494	+	12.8799i	−0.214401	+	0.659859i
$382$	11.4549			0.586081
$383$	1.31489	−	4.04682i	0.0671878	−	0.206783i	−0.911826	−	0.410577i	$-0.865327\pi$
$383$	1.31489	−	4.04682i	0.0671878	−	0.206783i	0.979014	+	0.203794i	$0.0653273\pi$
$384$	10.2397	−	7.43961i	0.522545	−	0.379651i
$385$		0			0
$386$	6.66517	+	4.84253i	0.339248	+	0.246478i
$387$	1.02971	−	0.748125i	0.0523429	−	0.0380293i
$388$	−1.81028	+	1.31525i	−0.0919032	+	0.0667716i
$389$	16.4782	+	11.9721i	0.835479	+	0.607011i	0.921104	−	0.389316i	$-0.127289\pi$
$389$	16.4782	+	11.9721i	0.835479	+	0.607011i	−0.0856250	+	0.996327i	$0.527289\pi$
$390$		0			0
$391$	1.27931	−	0.929474i	0.0646975	−	0.0470055i
$392$	−4.90243	+	15.0881i	−0.247610	+	0.762066i
$393$	−4.59236			−0.231654
$394$	7.58465	−	23.3431i	0.382109	−	1.17601i
$395$		0			0
$396$	−1.66461	−	5.12314i	−0.0836497	−	0.257447i
$397$	0.604795	+	1.86137i	0.0303538	+	0.0934194i	0.965086	−	0.261934i	$-0.0843604\pi$
$397$	0.604795	+	1.86137i	0.0303538	+	0.0934194i	−0.934732	+	0.355354i	$0.884360\pi$
$398$	12.0461	+	8.75203i	0.603818	+	0.438700i
$399$	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	$0.805925\pi$
$402$	−8.32532	−	6.04870i	−0.415229	−	0.301682i
$403$	−2.75505	−	8.47916i	−0.137239	−	0.422377i
$404$	−1.93683	−	5.96094i	−0.0963607	−	0.296568i
$405$		0			0
$406$	−8.13167	+	25.0267i	−0.403568	+	1.24206i
$407$	−0.123205			−0.00610704
$408$	−1.55310	+	4.77995i	−0.0768899	+	0.236643i
$409$	32.0180	−	23.2624i	1.58319	−	1.15025i	0.670265	−	0.742122i	$-0.266180\pi$
$409$	32.0180	−	23.2624i	1.58319	−	1.15025i	0.912923	−	0.408132i	$-0.133820\pi$
$410$		0			0
$411$	−12.3472	−	8.97078i	−0.609043	−	0.442496i
$412$	8.66863	−	6.29813i	0.427073	−	0.310287i
$413$	14.9598	−	10.8689i	0.736123	−	0.534825i
$414$	−0.806606	−	0.586034i	−0.0396425	−	0.0288020i
$415$		0			0
$416$	−12.7901	+	9.29254i	−0.627086	+	0.455604i
$417$	−5.63591	+	17.3455i	−0.275991	+	0.849414i
$418$	23.7756			1.16290
$419$	6.04421	−	18.6022i	0.295279	−	0.908776i	−0.687848	−	0.725854i	$-0.741445\pi$
$419$	6.04421	−	18.6022i	0.295279	−	0.908776i	0.983128	−	0.182921i	$-0.0585554\pi$
$420$		0			0
$421$	−12.4634	−	38.3584i	−0.607430	−	1.86948i	−0.479138	−	0.877740i	$-0.659051\pi$
$421$	−12.4634	−	38.3584i	−0.607430	−	1.86948i	−0.128292	−	0.991736i	$-0.540949\pi$
$422$	1.56932	+	4.82987i	0.0763932	+	0.235114i
$423$	4.39586	+	3.19378i	0.213734	+	0.155287i
$424$	5.22869			0.253928
$425$		0			0
$426$	13.8239			0.669769
$427$	−17.8016	−	12.9336i	−0.861478	−	0.625901i
$428$	−1.59675	−	4.91428i	−0.0771816	−	0.237540i
$429$	−6.00837	−	18.4919i	−0.290087	−	0.892795i
$430$		0			0
$431$	4.24497	−	13.0647i	0.204473	−	0.629304i	−0.795261	−	0.606267i	$-0.792666\pi$
$431$	4.24497	−	13.0647i	0.204473	−	0.629304i	0.999735	−	0.0230370i	$-0.00733356\pi$
$432$	4.99220			0.240187
$433$	3.83964	−	11.8172i	0.184522	−	0.567899i	−0.815418	−	0.578872i	$-0.803493\pi$
$433$	3.83964	−	11.8172i	0.184522	−	0.567899i	0.999940	+	0.0109734i	$0.00349301\pi$
$434$	−14.7454	+	10.7132i	−0.707802	+	0.514248i
$435$		0			0
$436$	1.00402	+	0.729464i	0.0480839	+	0.0349350i
$437$	1.11470	−	0.809879i	0.0533234	−	0.0387417i
$438$	−18.3832	+	13.3562i	−0.878385	+	0.638184i
$439$	−8.87118	−	6.44529i	−0.423399	−	0.307617i	0.355605	−	0.934636i	$-0.384275\pi$
$439$	−8.87118	−	6.44529i	−0.423399	−	0.307617i	−0.779004	+	0.627019i	$0.784275\pi$
$440$		0			0
$441$	−6.91123	+	5.02131i	−0.329106	+	0.239110i
$442$	4.69594	−	14.4526i	0.223363	−	0.687440i
$443$	−8.13187			−0.386357			−0.193178	−	0.981164i	$-0.561880\pi$
$443$	−8.13187			−0.386357			−0.193178	+	0.981164i	$0.561880\pi$
$444$	−0.00587431	+	0.0180793i	−0.000278783	+	0.000858005i
$445$		0			0
$446$	0.160658	+	0.494454i	0.00760737	+	0.0234131i
$447$	−4.55253	−	14.0112i	−0.215327	−	0.662709i
$448$	−5.69791	−	4.13977i	−0.269201	−	0.195586i
$449$	−32.9503			−1.55502			−0.777511	−	0.628869i	$-0.783518\pi$
$449$	−32.9503			−1.55502			−0.777511	+	0.628869i	$0.783518\pi$
$450$		0			0
$451$	−8.69840			−0.409592
$452$	−7.88130	−	5.72610i	−0.370705	−	0.269333i
$453$	5.38784	+	16.5821i	0.253143	+	0.779093i
$454$	5.04738	+	15.5342i	0.236885	+	0.729058i
$455$		0			0
$456$	−1.35326	+	4.16491i	−0.0633723	+	0.195040i
$457$	22.8800			1.07028			0.535142	−	0.844762i	$-0.320258\pi$
$457$	22.8800			1.07028			0.535142	+	0.844762i	$0.320258\pi$
$458$	6.39564	−	19.6838i	0.298849	−	0.919762i
$459$	−2.18949	+	1.59076i	−0.102197	+	0.0742503i
$460$		0			0
$461$	−9.74259	−	7.07841i	−0.453758	−	0.329674i	0.337320	−	0.941390i	$-0.390480\pi$
$461$	−9.74259	−	7.07841i	−0.453758	−	0.329674i	−0.791078	+	0.611716i	$0.790480\pi$
$462$	−32.1576	+	23.3639i	−1.49611	+	1.08699i
$463$	−22.0054	+	15.9878i	−1.02268	+	0.743018i	−0.966830	−	0.255421i	$-0.917786\pi$
$463$	−22.0054	+	15.9878i	−1.02268	+	0.743018i	−0.0558471	+	0.998439i	$0.517786\pi$
$464$	−15.7984	−	11.4782i	−0.733420	−	0.532861i
$465$		0			0
$466$	27.7479	−	20.1600i	1.28540	−	0.933895i
$467$	1.21828	−	3.74947i	0.0563752	−	0.173505i	−0.918904	−	0.394481i	$-0.870924\pi$
$467$	1.21828	−	3.74947i	0.0563752	−	0.173505i	0.975279	+	0.220976i	$0.0709243\pi$
$468$	−3.00000			−0.138675
$469$	−7.34714	+	22.6122i	−0.339259	+	1.04413i
$470$		0			0
$471$	5.53466	+	17.0339i	0.255024	+	0.784882i
$472$	2.69164	+	8.28402i	0.123893	+	0.381303i
$473$	−6.08421	−	4.42044i	−0.279752	−	0.203252i
$474$	−28.4362			−1.30612
$475$		0			0
$476$	−9.72721			−0.445846
$477$	2.27782	+	1.65493i	0.104294	+	0.0757742i
$478$	9.31397	+	28.6655i	0.426011	+	1.31113i
$479$	6.16466	+	18.9729i	0.281670	+	0.866893i	0.987377	+	0.158388i	$0.0506298\pi$
$479$	6.16466	+	18.9729i	0.281670	+	0.866893i	−0.705706	+	0.708504i	$0.749370\pi$
$480$		0			0
$481$	−0.0212032	+	0.0652567i	−0.000966783	+	0.00297545i
$482$	50.4038			2.29583
$483$	−0.711834	+	2.19080i	−0.0323896	+	0.0996849i
$484$	−17.6370	+	12.8140i	−0.801680	+	0.582455i
$485$		0			0
$486$	1.38048	+	1.00297i	0.0626197	+	0.0454958i
$487$	−8.90102	+	6.46697i	−0.403344	+	0.293046i	−0.770902	−	0.636954i	$-0.780194\pi$
$487$	−8.90102	+	6.46697i	−0.403344	+	0.293046i	0.367558	+	0.930001i	$0.380194\pi$
$488$	8.38543	−	6.09237i	0.379591	−	0.275789i
$489$	−17.6041	−	12.7901i	−0.796083	−	0.578388i
$490$		0			0
$491$	26.9348	−	19.5693i	1.21555	−	0.883151i	0.219830	−	0.975538i	$-0.429450\pi$
$491$	26.9348	−	19.5693i	1.21555	−	0.883151i	0.995723	+	0.0923876i	$0.0294499\pi$
$492$	−0.414733	+	1.27642i	−0.0186976	+	0.0575453i
$493$	10.5864			0.476788
$494$	4.09171	−	12.5930i	0.184095	−	0.566585i
$495$		0			0
$496$	−4.17963	−	12.8636i	−0.187671	−	0.577592i
$497$	−9.86973	−	30.3759i	−0.442718	−	1.36255i
$498$	−1.07904	−	0.783966i	−0.0483528	−	0.0351303i
$499$	−41.1448			−1.84189			−0.920946	−	0.389690i	$-0.872582\pi$
$499$	−41.1448			−1.84189			−0.920946	+	0.389690i	$0.872582\pi$
$500$		0			0
$501$	−22.6030			−1.00983
$502$	−2.61457	−	1.89960i	−0.116694	−	0.0847832i
$503$	−9.91207	−	30.5062i	−0.441958	−	1.36021i	−0.885786	−	0.464094i	$-0.846380\pi$
$503$	−9.91207	−	30.5062i	−0.441958	−	1.36021i	0.443829	−	0.896112i	$-0.353620\pi$
$504$	−2.26244	−	6.96308i	−0.100777	−	0.310160i
$505$		0			0
$506$	−1.82044	+	5.60275i	−0.0809286	+	0.249073i
$507$	2.17157			0.0964429
$508$	3.81529	−	11.7423i	0.169276	−	0.520979i
$509$	21.9206	−	15.9262i	0.971612	−	0.705918i	0.0157938	−	0.999875i	$-0.494972\pi$
$509$	21.9206	−	15.9262i	0.971612	−	0.705918i	0.955818	+	0.293958i	$0.0949725\pi$
$510$		0			0
$511$	42.4732	+	30.8586i	1.87890	+	1.36510i
$512$	−4.40295	+	3.19893i	−0.194585	+	0.141374i
$513$	−1.90777	+	1.38608i	−0.0842301	+	0.0611968i
$514$	30.5376	+	22.1869i	1.34696	+	0.978622i
$515$		0			0
$516$	−0.938754	+	0.682045i	−0.0413263	+	0.0300253i
$517$	9.92109	−	30.5340i	0.436329	−	1.34288i
$518$	0.140272			0.00616321
$519$	3.98993	−	12.2797i	0.175138	−	0.539020i
$520$		0			0
$521$	8.02073	+	24.6853i	0.351395	+	1.08148i	0.958071	+	0.286532i	$0.0925026\pi$
$521$	8.02073	+	24.6853i	0.351395	+	1.08148i	−0.606676	+	0.794949i	$0.707497\pi$
$522$	−2.06260	−	6.34804i	−0.0902778	−	0.277846i
$523$	−1.45123	−	1.05438i	−0.0634577	−	0.0461047i	0.555604	−	0.831447i	$-0.312487\pi$
$523$	−1.45123	−	1.05438i	−0.0634577	−	0.0461047i	−0.619062	+	0.785342i	$0.712487\pi$
$524$	4.18673			0.182898
$525$		0			0
$526$	33.6414			1.46684
$527$	5.93209	+	4.30991i	0.258406	+	0.187743i
$528$	−9.11519	−	28.0537i	−0.396688	−	1.22088i
$529$	−7.00189	−	21.5496i	−0.304430	−	0.936939i
$530$		0			0
$531$	−1.44939	+	4.46077i	−0.0628983	+	0.193581i
$532$	−8.47561			−0.367464
$533$	−1.49697	+	4.60720i	−0.0648410	+	0.199560i
$534$	−4.79477	+	3.48361i	−0.207490	+	0.150750i
$535$		0			0
$536$	−9.06068	−	6.58297i	−0.391362	−	0.284341i
$537$	−5.20246	+	3.77981i	−0.224503	+	0.163111i
$538$	−25.0760	+	18.2188i	−1.08110	+	0.785467i
$539$	40.8364	+	29.6693i	1.75895	+	1.27795i
$540$		0			0
$541$	6.01538	−	4.37043i	0.258621	−	0.187899i	−0.450918	−	0.892566i	$-0.648903\pi$
$541$	6.01538	−	4.37043i	0.258621	−	0.187899i	0.709539	+	0.704666i	$0.248903\pi$
$542$	11.9008	−	36.6268i	0.511182	−	1.57326i
$543$	−14.7071			−0.631141
$544$	4.01792	−	12.3659i	0.172267	−	0.530183i
$545$		0			0
$546$	6.84070	+	21.0535i	0.292755	+	0.901007i
$547$	−6.02174	−	18.5330i	−0.257471	−	0.792414i	−0.993333	−	0.115283i	$-0.963223\pi$
$547$	−6.02174	−	18.5330i	−0.257471	−	0.792414i	0.735862	−	0.677132i	$-0.236777\pi$
$548$	11.2566	+	8.17841i	0.480859	+	0.349364i
$549$	5.58132			0.238205
$550$		0			0
$551$	9.22425			0.392966
$552$	−0.877852	−	0.637797i	−0.0373639	−	0.0271464i
$553$	20.3024	+	62.4843i	0.863345	+	2.65710i
$554$	−4.35277	−	13.3965i	−0.184932	−	0.569161i
$555$		0			0
$556$	5.13810	−	15.8134i	0.217904	−	0.670639i
$557$	26.3285			1.11557			0.557787	−	0.829984i	$-0.311650\pi$
$557$	26.3285			1.11557			0.557787	+	0.829984i	$0.311650\pi$
$558$	1.42862	−	4.39685i	0.0604784	−	0.186133i
$559$	−3.38841	+	2.46182i	−0.143314	+	0.104124i
$560$		0			0
$561$	12.9370	+	9.39931i	0.546202	+	0.396839i
$562$	−1.76879	+	1.28510i	−0.0746120	+	0.0542088i
$563$	29.7482	−	21.6134i	1.25374	−	0.910895i	0.255306	−	0.966860i	$-0.417824\pi$
$563$	29.7482	−	21.6134i	1.25374	−	0.910895i	0.998433	+	0.0559656i	$0.0178237\pi$
$564$	−4.00758	−	2.91168i	−0.168749	−	0.122604i
$565$		0			0
$566$	3.68770	−	2.67927i	0.155005	−	0.112618i
$567$	1.21828	−	3.74947i	0.0511629	−	0.157463i
$568$	15.0449			0.631271
$569$	−11.2118	+	34.5065i	−0.470025	+	1.44659i	0.382527	+	0.923944i	$0.375054\pi$
$569$	−11.2118	+	34.5065i	−0.470025	+	1.44659i	−0.852552	+	0.522643i	$0.824946\pi$
$570$		0			0
$571$	−1.03966	−	3.19975i	−0.0435085	−	0.133906i	0.926943	−	0.375203i	$-0.122427\pi$
$571$	−1.03966	−	3.19975i	−0.0435085	−	0.133906i	−0.970451	+	0.241298i	$0.922427\pi$
$572$	5.47766	+	16.8585i	0.229032	+	0.704889i
$573$	5.43095	+	3.94582i	0.226881	+	0.164839i
$574$	9.90337			0.413359
$575$		0			0
$576$	1.78646			0.0744359
$577$	−5.56961	−	4.04656i	−0.231866	−	0.168461i	0.465786	−	0.884898i	$-0.345772\pi$
$577$	−5.56961	−	4.04656i	−0.231866	−	0.168461i	−0.697652	+	0.716437i	$0.745772\pi$
$578$	−5.10190	−	15.7020i	−0.212211	−	0.653118i
$579$	1.49199	+	4.59186i	0.0620048	+	0.190831i
$580$		0			0
$581$	−0.952256	+	2.93074i	−0.0395062	+	0.121588i
$582$	−4.18814			−0.173604
$583$	5.14086	−	15.8219i	0.212913	−	0.655278i
$584$	−20.0070	+	14.5359i	−0.827895	+	0.601501i
$585$		0			0
$586$	24.3800	+	17.7131i	1.00713	+	0.731720i
$587$	−11.9230	+	8.66258i	−0.492116	+	0.357543i	−0.805997	−	0.591919i	$-0.798370\pi$
$587$	−11.9230	+	8.66258i	−0.492116	+	0.357543i	0.313882	+	0.949462i	$0.398370\pi$
$588$	6.30078	−	4.57778i	0.259840	−	0.188785i
$589$	5.16880	+	3.75536i	0.212977	+	0.154737i
$590$		0			0
$591$	11.6370	−	8.45474i	0.478680	−	0.347782i
$592$	−0.0321670	+	0.0989998i	−0.00132206	+	0.00406887i
$593$	−5.82561			−0.239229			−0.119615	−	0.992820i	$-0.538166\pi$
$593$	−5.82561			−0.239229			−0.119615	+	0.992820i	$0.538166\pi$
$594$	3.11562	−	9.58890i	0.127836	−	0.393437i
$595$		0			0
$596$	4.15041	+	12.7737i	0.170008	+	0.523230i
$597$	2.69651	+	8.29899i	0.110361	+	0.339655i
$598$	2.65426	+	1.92844i	0.108541	+	0.0788596i
$599$	−27.1527			−1.10943			−0.554715	−	0.832040i	$-0.687173\pi$
$599$	−27.1527			−1.10943			−0.554715	+	0.832040i	$0.687173\pi$
$600$		0			0
$601$	20.9140			0.853101			0.426551	−	0.904464i	$-0.359729\pi$
$601$	20.9140			0.853101			0.426551	+	0.904464i	$0.359729\pi$
$602$	6.92705	+	5.03280i	0.282326	+	0.205121i
$603$	−1.86361	−	5.73559i	−0.0758919	−	0.233571i
$604$	−4.91194	−	15.1174i	−0.199864	−	0.615118i
$605$		0			0
$606$	3.62513	−	11.1570i	0.147261	−	0.453222i
$607$	−1.46424			−0.0594318			−0.0297159	−	0.999558i	$-0.509460\pi$
$607$	−1.46424			−0.0594318			−0.0297159	+	0.999558i	$0.509460\pi$
$608$	3.50094	−	10.7748i	0.141982	−	0.436975i
$609$	−12.4762	+	9.06453i	−0.505563	+	0.367313i
$610$		0			0
$611$	−14.4653	−	10.5096i	−0.585202	−	0.425174i
$612$	1.99610	−	1.45025i	0.0806875	−	0.0586229i
$613$	28.0814	−	20.4023i	1.13420	−	0.824041i	0.147896	−	0.989003i	$-0.452750\pi$
$613$	28.0814	−	20.4023i	1.13420	−	0.824041i	0.986300	+	0.164962i	$0.0527501\pi$
$614$	−39.4255	−	28.6443i	−1.59108	−	1.15599i
$615$		0			0
$616$	−34.9981	+	25.4276i	−1.41011	+	1.02451i
$617$	−12.9490	+	39.8529i	−0.521307	+	1.60442i	0.250199	+	0.968194i	$0.419504\pi$
$617$	−12.9490	+	39.8529i	−0.521307	+	1.60442i	−0.771506	+	0.636222i	$0.780496\pi$
$618$	20.0551			0.806736
$619$	−5.79758	+	17.8431i	−0.233025	+	0.717176i	0.764353	+	0.644798i	$0.223059\pi$
$619$	−5.79758	+	17.8431i	−0.233025	+	0.717176i	−0.997377	+	0.0723776i	$0.976941\pi$
$620$		0			0
$621$	−0.180557	−	0.555698i	−0.00724551	−	0.0222994i
$622$	−15.4647	−	47.5954i	−0.620077	−	1.90840i
$623$	11.0780	+	8.04863i	0.443830	+	0.322461i
$624$	−16.4276			−0.657631
$625$		0			0
$626$	29.8498			1.19304
$627$	11.2724	+	8.18990i	0.450177	+	0.327073i
$628$	−5.04579	−	15.5294i	−0.201349	−	0.619689i
$629$	−0.0174383	−	0.0536696i	−0.000695311	−	0.00213995i
$630$		0			0
$631$	3.05583	−	9.40488i	0.121651	−	0.374402i	−0.871625	−	0.490173i	$-0.836934\pi$
$631$	3.05583	−	9.40488i	0.121651	−	0.374402i	0.993276	+	0.115770i	$0.0369337\pi$
$632$	−30.9479			−1.23104
$633$	−0.919687	+	2.83050i	−0.0365543	+	0.112502i
$634$	5.40820	−	3.92928i	0.214787	−	0.156052i
$635$		0			0
$636$	−2.07663	−	1.50876i	−0.0823436	−	0.0598261i
$637$	22.7425	−	16.5234i	0.901091	−	0.654681i
$638$	−31.9068	+	23.1816i	−1.26320	+	0.917769i
$639$	6.55415	+	4.76187i	0.259278	+	0.188377i
$640$		0			0
$641$	1.46647	−	1.06546i	0.0579223	−	0.0420830i	−0.558447	−	0.829540i	$-0.688603\pi$
$641$	1.46647	−	1.06546i	0.0579223	−	0.0420830i	0.616370	+	0.787457i	$0.288603\pi$
$642$	2.98860	−	9.19797i	0.117951	−	0.363015i
$643$	−45.7391			−1.80377			−0.901886	−	0.431974i	$-0.857817\pi$
$643$	−45.7391			−1.80377			−0.901886	+	0.431974i	$0.857817\pi$
$644$	0.648959	−	1.99729i	0.0255726	−	0.0787043i
$645$		0			0
$646$	3.36518	+	10.3570i	0.132401	+	0.407489i
$647$	7.93466	+	24.4204i	0.311944	+	0.960064i	0.976994	+	0.213266i	$0.0684101\pi$
$647$	7.93466	+	24.4204i	0.311944	+	0.960064i	−0.665050	+	0.746798i	$0.731590\pi$
$648$	1.50241	+	1.09157i	0.0590203	+	0.0428807i
$649$	27.7137			1.08786
$650$		0			0
$651$	−10.6814			−0.418637
$652$	16.0491	+	11.6604i	0.628532	+	0.456655i
$653$	−11.1148	−	34.2079i	−0.434957	−	1.33866i	−0.893130	−	0.449798i	$-0.851496\pi$
$653$	−11.1148	−	34.2079i	−0.434957	−	1.33866i	0.458173	−	0.888863i	$-0.348504\pi$
$654$	0.717795	+	2.20914i	0.0280680	+	0.0863844i
$655$		0			0
$656$	−2.27103	+	6.98950i	−0.0886687	+	0.272894i
$657$	−13.3166			−0.519530
$658$	−11.2954	+	34.7638i	−0.440342	+	1.35523i
$659$	25.9633	−	18.8635i	1.01139	−	0.734816i	0.0468880	−	0.998900i	$-0.485070\pi$
$659$	25.9633	−	18.8635i	1.01139	−	0.734816i	0.964500	+	0.264084i	$0.0850696\pi$
$660$		0			0
$661$	−13.1113	−	9.52591i	−0.509970	−	0.370515i	0.302842	−	0.953041i	$-0.402064\pi$
$661$	−13.1113	−	9.52591i	−0.509970	−	0.370515i	−0.812812	+	0.582526i	$0.802064\pi$
$662$	24.2320	−	17.6056i	0.941803	−	0.684260i
$663$	7.20487	−	5.23465i	0.279814	−	0.203297i
$664$	−1.17435	−	0.853212i	−0.0455734	−	0.0331110i
$665$		0			0
$666$	−0.0287849	+	0.0209135i	−0.00111539	+	0.000810381i
$667$	−0.706281	+	2.17371i	−0.0273473	+	0.0841663i
$668$	20.6065			0.797289
$669$	−0.0941522	+	0.289771i	−0.00364014	+	0.0112032i
$670$		0			0
$671$	−10.1908	−	31.3642i	−0.393413	−	1.21080i
$672$	5.85301	+	18.0137i	0.225785	+	0.694895i
$673$	27.6367	+	20.0792i	1.06531	+	0.773997i	0.975064	−	0.221922i	$-0.0712332\pi$
$673$	27.6367	+	20.0792i	1.06531	+	0.773997i	0.0902506	+	0.995919i	$0.471233\pi$
$674$	23.9703			0.923301
$675$		0			0
$676$	−1.97976			−0.0761446
$677$	7.42284	+	5.39301i	0.285283	+	0.207270i	0.721218	−	0.692708i	$-0.243582\pi$
$677$	7.42284	+	5.39301i	0.285283	+	0.207270i	−0.435935	+	0.899978i	$0.643582\pi$
$678$	−5.63450	−	17.3412i	−0.216392	−	0.665985i
$679$	2.99017	+	9.20281i	0.114752	+	0.353171i
$680$		0			0
$681$	−2.95798	+	9.10372i	−0.113350	+	0.348855i
$682$	−27.3166			−1.04601
$683$	−6.02604	+	18.5463i	−0.230580	+	0.709653i	0.767097	+	0.641531i	$0.221701\pi$
$683$	−6.02604	+	18.5463i	−0.230580	+	0.709653i	−0.997677	+	0.0681215i	$0.978299\pi$
$684$	1.73926	−	1.26365i	0.0665023	−	0.0483168i
$685$		0			0
$686$	−8.39634	−	6.10030i	−0.320574	−	0.232910i
$687$	9.81269	−	7.12934i	0.374378	−	0.272001i
$688$	−5.14050	+	3.73479i	−0.195980	+	0.142387i
$689$	−7.49553	−	5.44582i	−0.285557	−	0.207469i
$690$		0			0
$691$	−23.4986	+	17.0727i	−0.893927	+	0.649476i	−0.936899	−	0.349600i	$-0.886317\pi$
$691$	−23.4986	+	17.0727i	−0.893927	+	0.649476i	0.0429718	+	0.999076i	$0.486317\pi$
$692$	−3.63750	+	11.1951i	−0.138277	+	0.425573i
$693$	−23.2946			−0.884889
$694$	0.543375	−	1.67234i	0.0206262	−	0.0634810i
$695$		0			0
$696$	−2.24479	−	6.90876i	−0.0850886	−	0.261876i
$697$	−1.23116	−	3.78914i	−0.0466337	−	0.143524i
$698$	−29.7666	−	21.6267i	−1.12668	−	0.818583i
$699$	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	$0.625940\pi$
$702$	−4.54267	−	3.30045i	−0.171452	−	0.124567i
$703$	−0.0151945	−	0.0467640i	−0.000573073	−	0.00176374i
$704$	−3.26188	−	10.0390i	−0.122937	−	0.378360i
$705$		0			0
$706$	−3.77345	+	11.6135i	−0.142016	+	0.437079i
$707$	−27.1040			−1.01935
$708$	1.32137	−	4.06676i	0.0496601	−	0.152838i
$709$	−13.3334	+	9.68727i	−0.500746	+	0.363813i	−0.809302	−	0.587393i	$-0.800154\pi$
$709$	−13.3334	+	9.68727i	−0.500746	+	0.363813i	0.308556	+	0.951206i	$0.400154\pi$
$710$		0			0
$711$	−13.4821	−	9.79534i	−0.505619	−	0.367354i
$712$	−5.21829	+	3.79131i	−0.195564	+	0.142085i
$713$	−1.28072	+	0.930497i	−0.0479633	+	0.0348474i
$714$	−14.7292	−	10.7014i	−0.551226	−	0.400489i
$715$		0			0
$716$	4.74294	−	3.44595i	0.177252	−	0.128781i
$717$	−5.45838	+	16.7992i	−0.203847	+	0.627376i
$718$	46.3309			1.72905
$719$	9.60466	−	29.5601i	0.358193	−	1.10241i	−0.595941	−	0.803028i	$-0.703221\pi$
$719$	9.60466	−	29.5601i	0.358193	−	1.10241i	0.954135	−	0.299378i	$-0.0967791\pi$
$720$		0			0
$721$	−14.3186	−	44.0681i	−0.533253	−	1.64118i
$722$	−7.08642	−	21.8098i	−0.263729	−	0.811675i
$723$	23.8973	+	17.3624i	0.888752	+	0.645716i
$724$	13.4080			0.498305
$725$		0			0
$726$	−40.8036			−1.51436
$727$	−0.771033	−	0.560188i	−0.0285960	−	0.0207762i	0.573395	−	0.819279i	$-0.305626\pi$
$727$	−0.771033	−	0.560188i	−0.0285960	−	0.0207762i	−0.601991	+	0.798503i	$0.705626\pi$
$728$	7.44492	+	22.9131i	0.275927	+	0.849217i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	1.06445	−	3.27603i	0.0393700	−	0.121168i
$732$	−5.08833			−0.188070
$733$	4.75118	−	14.6226i	0.175489	−	0.540099i	−0.824167	−	0.566347i	$-0.808356\pi$
$733$	4.75118	−	14.6226i	0.175489	−	0.540099i	0.999655	+	0.0262485i	$0.00835612\pi$
$734$	29.6006	−	21.5061i	1.09258	−	0.793806i
$735$		0			0
$736$	2.27103	+	1.65000i	0.0837114	+	0.0608199i
$737$	−28.8284	+	20.9451i	−1.06191	+	0.771522i
$738$	−2.03225	+	1.47651i	−0.0748081	+	0.0543513i
$739$	−4.20110	−	3.05228i	−0.154540	−	0.112280i	0.507828	−	0.861458i	$-0.330449\pi$
$739$	−4.20110	−	3.05228i	−0.154540	−	0.112280i	−0.662368	+	0.749179i	$0.730449\pi$
$740$		0			0
$741$	6.27782	−	4.56110i	0.230622	−	0.167556i
$742$	−5.85301	+	18.0137i	−0.214871	+	0.661305i
$743$	42.3399			1.55330			0.776650	−	0.629932i	$-0.216917\pi$
$743$	42.3399			1.55330			0.776650	+	0.629932i	$0.216917\pi$
$744$	1.55481	−	4.78521i	0.0570021	−	0.175434i
$745$		0			0
$746$	−3.36980	−	10.3712i	−0.123377	−	0.379716i
$747$	−0.241540	−	0.743385i	−0.00883750	−	0.0271990i
$748$	−11.7943	−	8.56909i	−0.431244	−	0.313317i
$749$	−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	$0.366963\pi$
$752$	−21.9450	−	15.9440i	−0.800251	−	0.581416i
$753$	−0.585267	−	1.80127i	−0.0213283	−	0.0656418i
$754$	6.78733	+	20.8892i	0.247180	+	0.760741i
$755$		0			0
$756$	−1.11067	+	3.41829i	−0.0403947	+	0.124322i
$757$	9.27680			0.337171			0.168585	−	0.985687i	$-0.446080\pi$
$757$	9.27680			0.337171			0.168585	+	0.985687i	$0.446080\pi$
$758$	−0.0815549	+	0.251000i	−0.00296221	+	0.00911674i
$759$	−2.79307	+	2.02928i	−0.101382	+	0.0736583i
$760$		0			0
$761$	14.0868	+	10.2346i	0.510644	+	0.371005i	0.813068	−	0.582169i	$-0.197796\pi$
$761$	14.0868	+	10.2346i	0.510644	+	0.371005i	−0.302424	+	0.953174i	$0.597796\pi$
$762$	18.6954	−	13.5830i	0.677265	−	0.492062i
$763$	4.34178	−	3.15449i	0.157183	−	0.114200i
$764$	−4.95125	−	3.59729i	−0.179130	−	0.130145i
$765$		0			0
$766$	−5.87403	+	4.26773i	−0.212237	+	0.154200i
$767$	4.76945	−	14.6789i	0.172215	−	0.530023i
$768$	−18.0245			−0.650404
$769$	−7.16648	+	22.0562i	−0.258430	+	0.795365i	0.734705	+	0.678387i	$0.237321\pi$
$769$	−7.16648	+	22.0562i	−0.258430	+	0.795365i	−0.993134	+	0.116978i	$0.962679\pi$
$770$		0			0
$771$	6.83579	+	21.0384i	0.246185	+	0.757680i
$772$	−1.36020	−	4.18627i	−0.0489547	−	0.150667i
$773$	−4.45605	−	3.23751i	−0.160273	−	0.116445i	0.504758	−	0.863261i	$-0.331582\pi$
$773$	−4.45605	−	3.23751i	−0.160273	−	0.116445i	−0.665031	+	0.746816i	$0.731582\pi$
$774$	−2.17183			−0.0780650
$775$		0			0
$776$	−4.55807			−0.163625
$777$	0.0665056	+	0.0483191i	0.00238587	+	0.00173344i
$778$	−10.7401	−	33.0545i	−0.385049	−	1.18506i
$779$	−1.07275	−	3.30159i	−0.0384353	−	0.118292i
$780$		0			0
$781$	14.7922	−	45.5257i	0.529306	−	1.62904i
$782$	−2.69830			−0.0964909
$783$	1.20877	−	3.72022i	0.0431980	−	0.132950i
$784$	34.5023	−	25.0674i	1.23222	−	0.895263i
$785$		0			0
$786$	6.33964	+	4.60602i	0.226128	+	0.164291i
$787$	20.8703	−	15.1632i	0.743946	−	0.540509i	−0.149998	−	0.988686i	$-0.547927\pi$
$787$	20.8703	−	15.1632i	0.743946	−	0.540509i	0.893944	+	0.448178i	$0.147927\pi$
$788$	−10.6091	+	7.70795i	−0.377933	+	0.274584i
$789$	15.9500	+	11.5884i	0.567835	+	0.412556i
$790$		0			0
$791$	−34.0819	+	24.7619i	−1.21181	+	0.880433i
$792$	3.39082	−	10.4359i	0.120488	−	0.370823i
$793$	−18.3662			−0.652203
$794$	1.03200	−	3.17617i	0.0366243	−	0.112718i
$795$		0			0
$796$	−2.45833	−	7.56596i	−0.0871331	−	0.268168i
$797$	−1.14642	−	3.52831i	−0.0406082	−	0.124979i	0.928697	−	0.370839i	$-0.120930\pi$
$797$	−1.14642	−	3.52831i	−0.0406082	−	0.124979i	−0.969305	+	0.245860i	$0.920930\pi$
$798$	−12.8340	−	9.32443i	−0.454318	−	0.330081i
$799$	14.7052			0.520233
$800$		0			0
$801$	−3.47327			−0.122722
$802$	45.3261	+	32.9313i	1.60052	+	1.16285i
$803$	24.3146	+	74.8326i	0.858043	+	2.64079i
$804$	1.69900	+	5.22898i	0.0599190	+	0.184412i
$805$		0			0
$806$	−4.70111	+	14.4685i	−0.165589	+	0.509632i
$807$	−18.1647			−0.639429
$808$	3.94533	−	12.1425i	0.138796	−	0.427171i
$809$	−30.3414	+	22.0443i	−1.06675	+	0.775037i	−0.975325	−	0.220776i	$-0.929141\pi$
$809$	−30.3414	+	22.0443i	−1.06675	+	0.775037i	−0.0914219	+	0.995812i	$0.529141\pi$
$810$		0			0
$811$	−36.9041	−	26.8124i	−1.29588	−	0.941509i	−0.295970	−	0.955197i	$-0.595643\pi$
$811$	−36.9041	−	26.8124i	−1.29588	−	0.941509i	−0.999906	+	0.0136877i	$0.995643\pi$
$812$	11.3742	−	8.26387i	0.399158	−	0.290005i
$813$	18.2591	−	13.2660i	0.640375	−	0.465260i
$814$	0.170081	+	0.123571i	0.00596135	+	0.00433117i
$815$		0			0
$816$	10.9304	−	7.94139i	0.382640	−	0.278004i
$817$	0.927484	−	2.85450i	0.0324486	−	0.0998664i
$818$	−67.5317			−2.36119
$819$	−4.00894	+	12.3382i	−0.140084	+	0.431133i
$820$		0			0
$821$	13.9216	+	42.8462i	0.485866	+	1.49534i	0.830723	+	0.556686i	$0.187927\pi$
$821$	13.9216	+	42.8462i	0.485866	+	1.49534i	−0.344857	+	0.938655i	$0.612073\pi$
$822$	8.04758	+	24.7679i	0.280691	+	0.863880i
$823$	−33.5397	−	24.3680i	−1.16912	−	0.849415i	−0.178217	−	0.983991i	$-0.557033\pi$
$823$	−33.5397	−	24.3680i	−1.16912	−	0.849415i	−0.990903	+	0.134576i	$0.957033\pi$
$824$	21.8266			0.760364
$825$		0			0
$826$	−31.5529			−1.09786
$827$	−31.3035	−	22.7434i	−1.08853	−	0.790864i	−0.109380	−	0.994000i	$-0.534887\pi$
$827$	−31.3035	−	22.7434i	−1.08853	−	0.790864i	−0.979151	+	0.203136i	$0.934887\pi$
$828$	0.164609	+	0.506614i	0.00572056	+	0.0176061i
$829$	7.45527	+	22.9450i	0.258932	+	0.796911i	0.993029	+	0.117867i	$0.0376056\pi$
$829$	7.45527	+	22.9450i	0.258932	+	0.796911i	−0.734097	+	0.679044i	$0.762394\pi$
$830$		0			0
$831$	2.55091	−	7.85089i	0.0884901	−	0.272344i
$832$	−5.87864			−0.203805
$833$	−7.14441	+	21.9882i	−0.247539	+	0.761847i
$834$	25.1774	−	18.2924i	0.871821	−	0.633415i
$835$		0			0
$836$	−10.2768	−	7.46650i	−0.355429	−	0.258234i
$837$	2.19190	−	1.59251i	0.0757633	−	0.0550452i
$838$	−27.0014	+	19.6177i	−0.932748	+	0.677681i
$839$	14.3890	+	10.4542i	0.496763	+	0.360919i	0.807779	−	0.589485i	$-0.200669\pi$
$839$	14.3890	+	10.4542i	0.496763	+	0.360919i	−0.311016	+	0.950405i	$0.600669\pi$
$840$		0			0
$841$	11.0826	−	8.05197i	0.382158	−	0.277654i
$842$	−21.2671	+	65.4534i	−0.732913	+	2.25567i
$843$	−1.28129			−0.0441300
$844$	0.838452	−	2.58049i	0.0288607	−	0.0888242i
$845$		0			0
$846$	−2.86510	−	8.81786i	−0.0985041	−	0.303164i
$847$	29.1322	+	89.6598i	1.00100	+	3.08075i
$848$	−11.3713	−	8.26176i	−0.390493	−	0.283710i
$849$	2.67132			0.0916796
$850$		0			0
$851$	0.0121834			0.000417642
$852$	−5.97524	−	4.34126i	−0.204708	−	0.148729i
$853$	−3.96878	−	12.2147i	−0.135889	−	0.418222i	0.859839	−	0.510566i	$-0.170564\pi$
$853$	−3.96878	−	12.2147i	−0.135889	−	0.418222i	−0.995727	+	0.0923439i	$0.970564\pi$
$854$	11.6026	+	35.7090i	0.397032	+	1.22194i
$855$		0			0
$856$	3.25258	−	10.0104i	0.111171	−	0.342149i
$857$	15.6015			0.532936			0.266468	−	0.963844i	$-0.414143\pi$
$857$	15.6015			0.532936			0.266468	+	0.963844i	$0.414143\pi$
$858$	−10.2524	+	31.5538i	−0.350013	+	1.07723i
$859$	−3.90628	+	2.83808i	−0.133281	+	0.0968340i	−0.652428	−	0.757851i	$-0.726250\pi$
$859$	−3.90628	+	2.83808i	−0.133281	+	0.0968340i	0.519147	+	0.854685i	$0.326250\pi$
$860$		0			0
$861$	4.69537	+	3.41138i	0.160018	+	0.116260i
$862$	−18.9636	+	13.7779i	−0.645904	+	0.469276i
$863$	−10.6425	+	7.73222i	−0.362274	+	0.263208i	−0.754000	−	0.656874i	$-0.771878\pi$
$863$	−10.6425	+	7.73222i	−0.362274	+	0.263208i	0.391726	+	0.920082i	$0.371878\pi$
$864$	−3.88679	−	2.82392i	−0.132231	−	0.0960716i
$865$		0			0
$866$	−17.1529	+	12.4623i	−0.582879	+	0.423486i
$867$	2.98993	−	9.20205i	0.101543	−	0.312518i
$868$	9.73792			0.330527
$869$	−30.4281	+	93.6480i	−1.03220	+	3.17679i
$870$		0			0
$871$	6.13249	+	18.8739i	0.207792	+	0.639517i
$872$	0.781196	+	2.40427i	0.0264546	+	0.0814190i
$873$	−1.98567	−	1.44268i	−0.0672049	−	0.0488272i
$874$	−2.35111			−0.0795274
$875$		0			0
$876$	12.1404			0.410185
$877$	5.05840	+	3.67515i	0.170810	+	0.124101i	0.669906	−	0.742446i	$-0.266334\pi$
$877$	5.05840	+	3.67515i	0.170810	+	0.124101i	−0.499096	+	0.866547i	$0.666334\pi$
$878$	5.78199	+	17.7951i	0.195133	+	0.600557i
$879$	5.45741	+	16.7962i	0.184074	+	0.566521i
$880$		0			0
$881$	−5.18532	+	15.9588i	−0.174698	+	0.537665i	−0.999620	−	0.0275821i	$-0.991219\pi$
$881$	−5.18532	+	15.9588i	−0.174698	+	0.537665i	0.824922	+	0.565247i	$0.191219\pi$
$882$	14.5770			0.490834
$883$	−5.01740	+	15.4420i	−0.168849	+	0.519664i	−0.999299	−	0.0374289i	$-0.988083\pi$
$883$	−5.01740	+	15.4420i	−0.168849	+	0.519664i	0.830450	+	0.557093i	$0.188083\pi$
$884$	−6.56848	+	4.77228i	−0.220922	+	0.160509i
$885$		0			0
$886$	11.2259	+	8.15606i	0.377140	+	0.274008i
$887$	46.6700	−	33.9078i	1.56703	−	1.13851i	0.637091	−	0.770788i	$-0.280137\pi$
$887$	46.6700	−	33.9078i	1.56703	−	1.13851i	0.929935	−	0.367723i	$-0.119863\pi$
$888$	−0.0313275	+	0.0227607i	−0.00105128	+	0.000763800i
$889$	−43.1945	−	31.3827i	−1.44870	−	1.05254i
$890$		0			0
$891$	4.78023	−	3.47304i	0.160144	−	0.116351i
$892$	0.0858359	−	0.264176i	0.00287400	−	0.00884526i
$893$	12.8131			0.428774
$894$	−7.76827	+	23.9083i	−0.259810	+	0.799612i
$895$		0			0
$896$	15.4198	+	47.4572i	0.515138	+	1.58543i
$897$	0.594152	+	1.82861i	0.0198382	+	0.0610556i
$898$	45.4871	+	33.0483i	1.51793	+	1.10284i
$899$	−10.5981			−0.353465
$900$		0			0
$901$	7.61988			0.253855
$902$	12.0079	+	8.72427i	0.399820	+	0.290486i
$903$	1.55061	+	4.77228i	0.0516010	+	0.158812i
$904$	−6.13219	−	18.8729i	−0.203953	−	0.627704i
$905$		0			0
$906$	9.19361	−	28.2950i	0.305437	−	0.940039i
$907$	−9.00465			−0.298995			−0.149497	−	0.988762i	$-0.547766\pi$
$907$	−9.00465			−0.298995			−0.149497	+	0.988762i	$0.547766\pi$
$908$	2.69670	−	8.29960i	0.0894933	−	0.275432i
$909$	5.56195	−	4.04100i	0.184478	−	0.134031i
$910$		0			0
$911$	−24.2303	−	17.6044i	−0.802786	−	0.583258i	0.108944	−	0.994048i	$-0.465253\pi$
$911$	−24.2303	−	17.6044i	−0.802786	−	0.583258i	−0.911730	+	0.410789i	$0.865253\pi$
$912$	9.52397	−	6.91957i	0.315370	−	0.229130i
$913$	−3.73642	+	2.71467i	−0.123658	+	0.0898425i
$914$	−31.5853	−	22.9481i	−1.04475	−	0.759056i
$915$		0			0
$916$	−8.94596	+	6.49962i	−0.295583	+	0.214753i
$917$	5.59477	−	17.2189i	0.184756	−	0.568619i
$918$	4.61803			0.152418
$919$	2.76125	−	8.49826i	0.0910853	−	0.280332i	−0.895128	−	0.445808i	$-0.852916\pi$
$919$	2.76125	−	8.49826i	0.0910853	−	0.280332i	0.986214	+	0.165477i	$0.0529162\pi$
$920$		0			0
$921$	−8.82532	−	27.1615i	−0.290804	−	0.895003i
$922$	6.34995	+	19.5431i	0.209125	+	0.643619i
$923$	−21.5675	−	15.6697i	−0.709902	−	0.515774i
$924$	21.2370			0.698647
$925$		0			0
$926$	46.4133			1.52524
$927$	9.50850	+	6.90833i	0.312300	+	0.226899i
$928$	5.80735	+	17.8732i	0.190636	+	0.586716i
$929$	−12.8117	−	39.4304i	−0.420339	−	1.29367i	−0.907387	−	0.420296i	$-0.861926\pi$
$929$	−12.8117	−	39.4304i	−0.420339	−	1.29367i	0.487048	−	0.873375i	$-0.338074\pi$
$930$		0			0
$931$	−6.22514	+	19.1590i	−0.204021	+	0.627911i
$932$	−18.3248			−0.600250
$933$	9.06296	−	27.8929i	0.296708	−	0.913173i
$934$	−5.44243	+	3.95416i	−0.178082	+	0.129384i
$935$		0			0
$936$	−4.94392	−	3.59197i	−0.161597	−	0.117407i
$937$	16.8749	−	12.2603i	0.551278	−	0.400527i	−0.276978	−	0.960876i	$-0.589333\pi$
$937$	16.8749	−	12.2603i	0.551278	−	0.400527i	0.828256	+	0.560349i	$0.189333\pi$
$938$	32.8220	−	23.8466i	1.07168	−	0.778618i
$939$	14.1523	+	10.2823i	0.461844	+	0.335549i
$940$		0			0
$941$	−2.97219	+	2.15942i	−0.0968905	+	0.0703951i	−0.635176	−	0.772368i	$-0.719072\pi$
$941$	−2.97219	+	2.15942i	−0.0968905	+	0.0703951i	0.538285	+	0.842763i	$0.319072\pi$
$942$	9.44413	−	29.0661i	0.307706	−	0.947023i
$943$	0.860163			0.0280107
$944$	7.23565	−	22.2691i	0.235500	−	0.724796i
$945$		0			0
$946$	3.96552	+	12.2046i	0.128930	+	0.396807i
$947$	9.79575	+	30.1482i	0.318319	+	0.979685i	0.974367	+	0.224966i	$0.0722270\pi$
$947$	9.79575	+	30.1482i	0.318319	+	0.979685i	−0.656048	+	0.754719i	$0.727773\pi$
$948$	12.2913	+	8.93013i	0.399202	+	0.290037i
$949$	43.8204			1.42247
$950$		0			0
$951$	3.91763			0.127038
$952$	−16.0302	−	11.6466i	−0.519541	−	0.377469i
$953$	−7.91746	−	24.3674i	−0.256472	−	0.789339i	−0.993536	−	0.113516i	$-0.963789\pi$
$953$	−7.91746	−	24.3674i	−0.256472	−	0.789339i	0.737064	−	0.675822i	$-0.236211\pi$
$954$	−1.48462	−	4.56919i	−0.0480664	−	0.147933i
$955$		0			0
$956$	4.97625	−	15.3153i	0.160943	−	0.495333i
$957$	−23.1129			−0.747133
$958$	10.5191	−	32.3746i	0.339858	−	1.04598i
$959$	48.6781	−	35.3667i	1.57190	−	1.14205i
$960$		0			0
$961$	19.1409	+	13.9067i	0.617449	+	0.448603i
$962$	0.0947214	−	0.0688191i	0.00305394	−	0.00221882i
$963$	4.58535	−	3.33145i	0.147761	−	0.107354i
$964$	−21.7865	−	15.8288i	−0.701697	−	0.509813i
$965$		0			0
$966$	3.17999	−	2.31040i	0.102314	−	0.0743358i
$967$	8.96663	−	27.5965i	0.288347	−	0.887442i	−0.697028	−	0.717044i	$-0.745495\pi$
$967$	8.96663	−	27.5965i	0.288347	−	0.887442i	0.985375	−	0.170398i	$-0.0545054\pi$
$968$	−44.4077			−1.42732
$969$	−1.97214	+	6.06961i	−0.0633541	+	0.194984i
$970$		0			0
$971$	−1.16588	−	3.58821i	−0.0374149	−	0.115151i	0.930605	−	0.366026i	$-0.119282\pi$
$971$	−1.16588	−	3.58821i	−0.0374149	−	0.115151i	−0.968020	+	0.250875i	$0.919282\pi$
$972$	−0.281722	−	0.867051i	−0.00903624	−	0.0278107i
$973$	−58.1705	−	42.2634i	−1.86486	−	1.35490i
$974$	18.7739			0.601553
$975$		0			0
$976$	−27.8630			−0.891874
$977$	29.7044	+	21.5815i	0.950329	+	0.690455i	0.950885	−	0.309545i	$-0.100177\pi$
$977$	29.7044	+	21.5815i	0.950329	+	0.690455i	−0.000555441		1.00000i	$0.500177\pi$
$978$	11.4738	+	35.3128i	0.366893	+	1.12918i
$979$	6.34180	+	19.5181i	0.202685	+	0.623800i
$980$		0			0
$981$	−0.420658	+	1.29465i	−0.0134306	+	0.0413350i
$982$	−56.8104			−1.81289
$983$	−7.28128	+	22.4095i	−0.232237	+	0.714752i	0.765239	+	0.643746i	$0.222621\pi$
$983$	−7.28128	+	22.4095i	−0.232237	+	0.714752i	−0.997476	+	0.0710055i	$0.977379\pi$
$984$	−2.21175	+	1.60693i	−0.0705081	+	0.0512271i
$985$		0			0
$986$	−14.6143	−	10.6179i	−0.465413	−	0.338143i
$987$	−17.3304	+	12.5912i	−0.551631	+	0.400784i
$988$	−5.72331	+	4.15823i	−0.182083	+	0.132291i
$989$	0.601653	+	0.437126i	0.0191314	+	0.0138998i
$990$		0			0
$991$	−23.5727	+	17.1266i	−0.748812	+	0.544044i	−0.895458	−	0.445145i	$-0.853152\pi$
$991$	−23.5727	+	17.1266i	−0.748812	+	0.544044i	0.146646	+	0.989189i	$0.453152\pi$
$992$	−4.02235	+	12.3795i	−0.127710	+	0.393050i
$993$	17.5534			0.557039
$994$	−16.8413	+	51.8323i	−0.534175	+	1.64402i
$995$		0			0
$996$	0.220205	+	0.677723i	0.00697748	+	0.0214745i
$997$	−13.5733	−	41.7742i	−0.429870	−	1.32300i	−0.898254	−	0.439478i	$-0.855164\pi$
$997$	−13.5733	−	41.7742i	−0.429870	−	1.32300i	0.468384	−	0.883525i	$-0.344836\pi$
$998$	56.7993	+	41.2671i	1.79795	+	1.30629i
$999$	−0.0208515			−0.000659711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.b.76.1		8
5.2	odd	4		375.2.i.b.49.3		16
5.3	odd	4		375.2.i.b.49.2		16
5.4	even	2		75.2.g.b.16.2	✓	8
15.14	odd	2		225.2.h.c.91.1		8
25.2	odd	20		375.2.i.b.199.2		16
25.6	even	5		1875.2.a.e.1.4		4
25.8	odd	20		1875.2.b.c.1249.3		8
25.11	even	5	inner	375.2.g.b.301.1		8
25.14	even	10		75.2.g.b.61.2	yes	8
25.17	odd	20		1875.2.b.c.1249.6		8
25.19	even	10		1875.2.a.h.1.1		4
25.23	odd	20		375.2.i.b.199.3		16
75.14	odd	10		225.2.h.c.136.1		8
75.44	odd	10		5625.2.a.i.1.4		4
75.56	odd	10		5625.2.a.n.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.16.2	✓	8	5.4	even	2
75.2.g.b.61.2	yes	8	25.14	even	10
225.2.h.c.91.1		8	15.14	odd	2
225.2.h.c.136.1		8	75.14	odd	10
375.2.g.b.76.1		8	1.1	even	1	trivial
375.2.g.b.301.1		8	25.11	even	5	inner
375.2.i.b.49.2		16	5.3	odd	4
375.2.i.b.49.3		16	5.2	odd	4
375.2.i.b.199.2		16	25.2	odd	20
375.2.i.b.199.3		16	25.23	odd	20
1875.2.a.e.1.4		4	25.6	even	5
1875.2.a.h.1.1		4	25.19	even	10
1875.2.b.c.1249.3		8	25.8	odd	20
1875.2.b.c.1249.6		8	25.17	odd	20
5625.2.a.i.1.4		4	75.44	odd	10
5625.2.a.n.1.1		4	75.56	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.38048 - 1.00297i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.281722 + 0.867051i) q^{4} +(-0.527295 + 1.62285i) q^{6} +3.94243 q^{7} +(-0.573870 + 1.76619i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.38048 - 1.00297i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.281722 + 0.867051i) q^{4} +(-0.527295 + 1.62285i) q^{6} +3.94243 q^{7} +(-0.573870 + 1.76619i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(4.78023 + 3.47304i) q^{11} +(0.737558 - 0.535867i) q^{12} +(2.66220 - 1.93420i) q^{13} +(-5.44243 - 3.95416i) q^{14} +(4.03877 - 2.93434i) q^{16} +(-0.836312 + 2.57390i) q^{17} +1.70636 q^{18} +(-0.728704 + 2.24272i) q^{19} +(-1.21828 - 3.74947i) q^{21} +(-3.11562 - 9.58890i) q^{22} +(-0.472705 - 0.343440i) q^{23} +1.85708 q^{24} -5.61505 q^{26} +(0.809017 + 0.587785i) q^{27} +(1.11067 + 3.41829i) q^{28} +(-1.20877 - 3.72022i) q^{29} +(0.837233 - 2.57674i) q^{31} -4.80433 q^{32} +(1.82589 - 5.61950i) q^{33} +(3.73607 - 2.71441i) q^{34} +(-0.737558 - 0.535867i) q^{36} +(-0.0168692 + 0.0122562i) q^{37} +(3.25535 - 2.36515i) q^{38} +(-2.66220 - 1.93420i) q^{39} +(-1.19098 + 0.865300i) q^{41} +(-2.07882 + 6.39796i) q^{42} -1.27279 q^{43} +(-1.66461 + 5.12314i) q^{44} +(0.308096 + 0.948222i) q^{46} +(-1.67907 - 5.16764i) q^{47} +(-4.03877 - 2.93434i) q^{48} +8.54276 q^{49} +2.70636 q^{51} +(2.42705 + 1.76336i) q^{52} +(-0.870050 - 2.67774i) q^{53} +(-0.527295 - 1.62285i) q^{54} +(-2.26244 + 6.96308i) q^{56} +2.35813 q^{57} +(-2.06260 + 6.34804i) q^{58} +(3.79456 - 2.75691i) q^{59} +(-4.51538 - 3.28061i) q^{61} +(-3.74018 + 2.71740i) q^{62} +(-3.18949 + 2.31730i) q^{63} +(-1.44528 - 1.05006i) q^{64} +(-8.15681 + 5.92627i) q^{66} +(-1.86361 + 5.73559i) q^{67} -2.46731 q^{68} +(-0.180557 + 0.555698i) q^{69} +(-2.50346 - 7.70487i) q^{71} +(-0.573870 - 1.76619i) q^{72} +(10.7734 + 7.82730i) q^{73} +0.0355801 q^{74} -2.14984 q^{76} +(18.8457 + 13.6922i) q^{77} +(1.73515 + 5.34023i) q^{78} +(5.14971 + 15.8492i) q^{79} +(0.309017 - 0.951057i) q^{81} +2.51200 q^{82} +(-0.241540 + 0.743385i) q^{83} +(2.90777 - 2.11262i) q^{84} +(1.75705 + 1.27657i) q^{86} +(-3.16461 + 2.29922i) q^{87} +(-8.87728 + 6.44972i) q^{88} +(2.80994 + 2.04154i) q^{89} +(10.4955 - 7.62545i) q^{91} +(0.164609 - 0.506614i) q^{92} -2.70934 q^{93} +(-2.86510 + 8.81786i) q^{94} +(1.48462 + 4.56919i) q^{96} +(0.758460 + 2.33430i) q^{97} +(-11.7931 - 8.56817i) q^{98} -5.90869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9	\( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9} + 16 q^{11} + 9 q^{12} + 8 q^{13} - 8 q^{14} - 17 q^{16} + q^{17} - 4 q^{18} - 5 q^{19} - 11 q^{21} - 13 q^{22} - 7 q^{23} + 30 q^{24} + 6 q^{26} + 2 q^{27} + 17 q^{28} + 5 q^{29} - 19 q^{31} - 24 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} + q^{37} + 10 q^{38} - 8 q^{39} - 14 q^{41} + 8 q^{42} - 32 q^{43} - 3 q^{44} + 16 q^{46} + q^{47} + 17 q^{48} + 16 q^{49} + 4 q^{51} + 6 q^{52} + 3 q^{53} - q^{54} - 15 q^{56} - 10 q^{57} - 5 q^{58} + 30 q^{59} - 14 q^{61} + 17 q^{62} - 9 q^{63} - 44 q^{64} - 7 q^{66} - 4 q^{67} + 22 q^{68} - 8 q^{69} + 21 q^{71} - 2 q^{73} - 38 q^{74} + 80 q^{76} + 37 q^{77} + 14 q^{78} - 30 q^{79} - 2 q^{81} + 12 q^{82} - 2 q^{83} + 8 q^{84} - 34 q^{86} - 15 q^{87} - 70 q^{88} + 21 q^{91} - 9 q^{92} - 46 q^{93} - 33 q^{94} + 34 q^{96} + 6 q^{97} - 73 q^{98} - 14 q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9 + 16 * q^11 + 9 * q^12 + 8 * q^13 - 8 * q^14 - 17 * q^16 + q^17 - 4 * q^18 - 5 * q^19 - 11 * q^21 - 13 * q^22 - 7 * q^23 + 30 * q^24 + 6 * q^26 + 2 * q^27 + 17 * q^28 + 5 * q^29 - 19 * q^31 - 24 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 + q^37 + 10 * q^38 - 8 * q^39 - 14 * q^41 + 8 * q^42 - 32 * q^43 - 3 * q^44 + 16 * q^46 + q^47 + 17 * q^48 + 16 * q^49 + 4 * q^51 + 6 * q^52 + 3 * q^53 - q^54 - 15 * q^56 - 10 * q^57 - 5 * q^58 + 30 * q^59 - 14 * q^61 + 17 * q^62 - 9 * q^63 - 44 * q^64 - 7 * q^66 - 4 * q^67 + 22 * q^68 - 8 * q^69 + 21 * q^71 - 2 * q^73 - 38 * q^74 + 80 * q^76 + 37 * q^77 + 14 * q^78 - 30 * q^79 - 2 * q^81 + 12 * q^82 - 2 * q^83 + 8 * q^84 - 34 * q^86 - 15 * q^87 - 70 * q^88 + 21 * q^91 - 9 * q^92 - 46 * q^93 - 33 * q^94 + 34 * q^96 + 6 * q^97 - 73 * q^98 - 14 * q^99

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