LMFDB - Embedded newform 845.2.e.o.146.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 17 x^{16} - 18 x^{15} + 230 x^{14} - 185 x^{13} + 996 x^{12} - 534 x^{11} + 3020 x^{10} + \cdots + 1 $ x^18 + 17x^16 - 18x^15 + 230x^14 - 185x^13 + 996x^12 - 534x^11 + 3020x^10 - 1485x^9 + 3379x^8 - 1280x^7 + 2595x^6 - 1007x^5 + 541x^4 - 65x^3 + 24*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.3
Root			$-0.880259 + 1.52465i$ of defining polynomial
Character	$\chi$	$=$	845.146
Dual form			845.2.e.o.191.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10278 - 1.91007i) q^{2} +(0.00652833 + 0.0113074i) q^{3} +(-1.43225 + 2.48072i) q^{4} +1.00000 q^{5} +(0.0143986 - 0.0249391i) q^{6} +(-2.30448 + 3.99148i) q^{7} +1.90669 q^{8} +(1.49991 - 2.59793i) q^{9} +(-1.10278 - 1.91007i) q^{10} +(-1.46616 - 2.53946i) q^{11} -0.0374007 q^{12} +10.1654 q^{14} +(0.00652833 + 0.0113074i) q^{15} +(0.761834 + 1.31954i) q^{16} +(1.67603 - 2.90297i) q^{17} -6.61630 q^{18} +(1.23010 - 2.13060i) q^{19} +(-1.43225 + 2.48072i) q^{20} -0.0601778 q^{21} +(-3.23370 + 5.60094i) q^{22} +(0.791645 + 1.37117i) q^{23} +(0.0124475 + 0.0215597i) q^{24} +1.00000 q^{25} +0.0783378 q^{27} +(-6.60118 - 11.4336i) q^{28} +(-4.13161 - 7.15616i) q^{29} +(0.0143986 - 0.0249391i) q^{30} -9.77959 q^{31} +(3.58696 - 6.21280i) q^{32} +(0.0191432 - 0.0331569i) q^{33} -7.39317 q^{34} +(-2.30448 + 3.99148i) q^{35} +(4.29649 + 7.44175i) q^{36} +(-2.06458 - 3.57597i) q^{37} -5.42613 q^{38} +1.90669 q^{40} +(-3.63254 - 6.29175i) q^{41} +(0.0663628 + 0.114944i) q^{42} +(0.352665 - 0.610833i) q^{43} +8.39961 q^{44} +(1.49991 - 2.59793i) q^{45} +(1.74602 - 3.02419i) q^{46} +8.57322 q^{47} +(-0.00994701 + 0.0172287i) q^{48} +(-7.12130 - 12.3344i) q^{49} +(-1.10278 - 1.91007i) q^{50} +0.0437667 q^{51} -12.4639 q^{53} +(-0.0863893 - 0.149631i) q^{54} +(-1.46616 - 2.53946i) q^{55} +(-4.39394 + 7.61052i) q^{56} +0.0321221 q^{57} +(-9.11251 + 15.7833i) q^{58} +(2.66723 - 4.61977i) q^{59} -0.0374007 q^{60} +(-0.960460 + 1.66357i) q^{61} +(10.7847 + 18.6797i) q^{62} +(6.91306 + 11.9738i) q^{63} -12.7752 q^{64} -0.0844427 q^{66} +(3.64896 + 6.32019i) q^{67} +(4.80097 + 8.31553i) q^{68} +(-0.0103362 + 0.0179029i) q^{69} +10.1654 q^{70} +(3.34041 - 5.78577i) q^{71} +(2.85987 - 4.95344i) q^{72} -12.4541 q^{73} +(-4.55356 + 7.88700i) q^{74} +(0.00652833 + 0.0113074i) q^{75} +(3.52362 + 6.10309i) q^{76} +13.5150 q^{77} +0.984840 q^{79} +(0.761834 + 1.31954i) q^{80} +(-4.49923 - 7.79290i) q^{81} +(-8.01179 + 13.8768i) q^{82} -7.84405 q^{83} +(0.0861894 - 0.149284i) q^{84} +(1.67603 - 2.90297i) q^{85} -1.55565 q^{86} +(0.0539450 - 0.0934356i) q^{87} +(-2.79551 - 4.84197i) q^{88} +(0.206417 + 0.357525i) q^{89} -6.61630 q^{90} -4.53532 q^{92} +(-0.0638444 - 0.110582i) q^{93} +(-9.45437 - 16.3755i) q^{94} +(1.23010 - 2.13060i) q^{95} +0.0936675 q^{96} +(1.69208 - 2.93077i) q^{97} +(-15.7064 + 27.2044i) q^{98} -8.79646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 7 q^{3} - 17 q^{4} + 18 q^{5} + 2 q^{6} - 7 q^{7} + 24 q^{8} - 16 q^{9} - 3 q^{10} + 9 q^{11} + 24 q^{12} - 4 q^{14} - 7 q^{15} - 37 q^{16} + q^{17} - 20 q^{18} + 4 q^{19} - 17 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) $ 18 * q - 3 * q^2 - 7 * q^3 - 17 * q^4 + 18 * q^5 + 2 * q^6 - 7 * q^7 + 24 * q^8 - 16 * q^9 - 3 * q^10 + 9 * q^11 + 24 * q^12 - 4 * q^14 - 7 * q^15 - 37 * q^16 + q^17 - 20 * q^18 + 4 * q^19 - 17 * q^20 - 2 * q^21 - 12 * q^22 - 14 * q^23 + 35 * q^24 + 18 * q^25 + 44 * q^27 - 18 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 22 * q^32 + 8 * q^33 - 60 * q^34 - 7 * q^35 - 3 * q^36 + 5 * q^37 - 94 * q^38 + 24 * q^40 + 10 * q^41 + 11 * q^42 - 39 * q^43 - 50 * q^44 - 16 * q^45 - 6 * q^46 + 72 * q^47 + 3 * q^48 - 16 * q^49 - 3 * q^50 + 86 * q^51 - 16 * q^53 + 2 * q^54 + 9 * q^55 + 29 * q^56 - 64 * q^57 - 21 * q^58 + 21 * q^59 + 24 * q^60 + 3 * q^61 + 10 * q^62 - 35 * q^63 + 68 * q^64 - 98 * q^66 - q^67 + 20 * q^68 + 13 * q^69 - 4 * q^70 + q^71 + 3 * q^72 + 15 * q^74 - 7 * q^75 + 5 * q^76 - 8 * q^77 + 78 * q^79 - 37 * q^80 - 29 * q^81 + 4 * q^82 + 14 * q^83 - 12 * q^84 + q^85 - 48 * q^86 - 16 * q^87 - 42 * q^88 + 19 * q^89 - 20 * q^90 - 54 * q^92 - 31 * q^93 - 16 * q^94 + 4 * q^95 - 14 * q^96 + 34 * q^97 - 48 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.10278	−	1.91007i	−0.779783	−	1.35062i	−0.932067	−	0.362287i	$-0.881996\pi$
$2$	−1.10278	−	1.91007i	−0.779783	−	1.35062i	0.152284	−	0.988337i	$-0.451337\pi$
$3$	0.00652833	+	0.0113074i	0.00376913	+	0.00652833i	0.867904	−	0.496732i	$-0.165467\pi$
$3$	0.00652833	+	0.0113074i	0.00376913	+	0.00652833i	−0.864135	+	0.503261i	$0.832134\pi$
$4$	−1.43225	+	2.48072i	−0.716123	+	1.24036i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.0143986	−	0.0249391i	0.00587821	−	0.0101814i
$7$	−2.30448	+	3.99148i	−0.871013	+	1.50864i	−0.0100635	+	0.999949i	$0.503203\pi$
$7$	−2.30448	+	3.99148i	−0.871013	+	1.50864i	−0.860950	+	0.508690i	$0.830130\pi$
$8$	1.90669			0.674116
$9$	1.49991	−	2.59793i	0.499972	−	0.865976i
$10$	−1.10278	−	1.91007i	−0.348730	−	0.604017i
$11$	−1.46616	−	2.53946i	−0.442064	−	0.765677i	0.555779	−	0.831330i	$-0.312420\pi$
$11$	−1.46616	−	2.53946i	−0.442064	−	0.765677i	−0.997842	+	0.0656533i	$0.979087\pi$
$12$	−0.0374007			−0.0107967
$13$		0			0
$13$		0			0
$14$	10.1654			2.71681
$15$	0.00652833	+	0.0113074i	0.00168561	+	0.00291956i
$16$	0.761834	+	1.31954i	0.190459	+	0.329884i
$17$	1.67603	−	2.90297i	0.406497	−	0.704073i	−0.587997	−	0.808863i	$-0.700084\pi$
$17$	1.67603	−	2.90297i	0.406497	−	0.704073i	0.994494	+	0.104789i	$0.0334169\pi$
$18$	−6.61630			−1.55948
$19$	1.23010	−	2.13060i	0.282205	−	0.488793i	−0.689723	−	0.724074i	$-0.742267\pi$
$19$	1.23010	−	2.13060i	0.282205	−	0.488793i	0.971928	+	0.235280i	$0.0756008\pi$
$20$	−1.43225	+	2.48072i	−0.320260	+	0.554707i
$21$	−0.0601778			−0.0131319
$22$	−3.23370	+	5.60094i	−0.689428	+	1.19412i
$23$	0.791645	+	1.37117i	0.165069	+	0.285908i	0.936680	−	0.350187i	$-0.113882\pi$
$23$	0.791645	+	1.37117i	0.165069	+	0.285908i	−0.771611	+	0.636095i	$0.780549\pi$
$24$	0.0124475	+	0.0215597i	0.00254083	+	0.00440085i
$25$	1.00000			0.200000
$26$		0			0
$27$	0.0783378			0.0150761
$28$	−6.60118	−	11.4336i	−1.24751	−	2.16074i
$29$	−4.13161	−	7.15616i	−0.767221	−	1.32887i	−0.939064	−	0.343741i	$-0.888306\pi$
$29$	−4.13161	−	7.15616i	−0.767221	−	1.32887i	0.171844	−	0.985124i	$-0.445028\pi$
$30$	0.0143986	−	0.0249391i	0.00262882	−	0.00455324i
$31$	−9.77959			−1.75647			−0.878233	−	0.478233i	$-0.841277\pi$
$31$	−9.77959			−1.75647			−0.878233	+	0.478233i	$0.841277\pi$
$32$	3.58696	−	6.21280i	0.634091	−	1.09828i
$33$	0.0191432	−	0.0331569i	0.00333240	−	0.00577188i
$34$	−7.39317			−1.26792
$35$	−2.30448	+	3.99148i	−0.389529	+	0.674684i
$36$	4.29649	+	7.44175i	0.716082	+	1.24029i
$37$	−2.06458	−	3.57597i	−0.339416	−	0.587885i	0.644907	−	0.764261i	$-0.276896\pi$
$37$	−2.06458	−	3.57597i	−0.339416	−	0.587885i	−0.984323	+	0.176376i	$0.943563\pi$
$38$	−5.42613			−0.880235
$39$		0			0
$40$	1.90669			0.301474
$41$	−3.63254	−	6.29175i	−0.567308	−	0.982606i	−0.996831	−	0.0795500i	$-0.974652\pi$
$41$	−3.63254	−	6.29175i	−0.567308	−	0.982606i	0.429523	−	0.903056i	$-0.358682\pi$
$42$	0.0663628	+	0.114944i	0.0102400	+	0.0177362i
$43$	0.352665	−	0.610833i	0.0537809	−	0.0931512i	−0.837882	−	0.545852i	$-0.816206\pi$
$43$	0.352665	−	0.610833i	0.0537809	−	0.0931512i	0.891662	+	0.452701i	$0.149539\pi$
$44$	8.39961			1.26629
$45$	1.49991	−	2.59793i	0.223594	−	0.387276i
$46$	1.74602	−	3.02419i	0.257437	−	0.445893i
$47$	8.57322			1.25053			0.625266	−	0.780411i	$-0.284990\pi$
$47$	8.57322			1.25053			0.625266	+	0.780411i	$0.284990\pi$
$48$	−0.00994701	+	0.0172287i	−0.00143573	+	0.00248675i
$49$	−7.12130	−	12.3344i	−1.01733	−	1.76206i
$50$	−1.10278	−	1.91007i	−0.155957	−	0.270125i
$51$	0.0437667			0.00612857
$52$		0			0
$53$	−12.4639			−1.71204			−0.856022	−	0.516940i	$-0.827071\pi$
$53$	−12.4639			−1.71204			−0.856022	+	0.516940i	$0.827071\pi$
$54$	−0.0863893	−	0.149631i	−0.0117561	−	0.0203621i
$55$	−1.46616	−	2.53946i	−0.197697	−	0.342421i
$56$	−4.39394	+	7.61052i	−0.587164	+	1.01700i
$57$	0.0321221			0.00425467
$58$	−9.11251	+	15.7833i	−1.19653	+	2.07245i
$59$	2.66723	−	4.61977i	0.347243	−	0.601443i	−0.638515	−	0.769609i	$-0.720451\pi$
$59$	2.66723	−	4.61977i	0.347243	−	0.601443i	0.985759	+	0.168166i	$0.0537845\pi$
$60$	−0.0374007			−0.00482841
$61$	−0.960460	+	1.66357i	−0.122974	+	0.212998i	−0.920939	−	0.389706i	$-0.872577\pi$
$61$	−0.960460	+	1.66357i	−0.122974	+	0.212998i	0.797965	+	0.602704i	$0.205910\pi$
$62$	10.7847	+	18.6797i	1.36966	+	2.37232i
$63$	6.91306	+	11.9738i	0.870964	+	1.50855i
$64$	−12.7752			−1.59690
$65$		0			0
$66$	−0.0844427			−0.0103942
$67$	3.64896	+	6.32019i	0.445792	+	0.772134i	0.998107	−	0.0615011i	$-0.0195888\pi$
$67$	3.64896	+	6.32019i	0.445792	+	0.772134i	−0.552315	+	0.833635i	$0.686255\pi$
$68$	4.80097	+	8.31553i	0.582204	+	1.00841i
$69$	−0.0103362	+	0.0179029i	−0.00124434	+	0.00215525i
$70$	10.1654			1.21499
$71$	3.34041	−	5.78577i	0.396434	−	0.686644i	−0.596849	−	0.802354i	$-0.703581\pi$
$71$	3.34041	−	5.78577i	0.396434	−	0.686644i	0.993283	+	0.115710i	$0.0369142\pi$
$72$	2.85987	−	4.95344i	0.337039	−	0.583769i
$73$	−12.4541			−1.45765			−0.728824	−	0.684702i	$-0.759933\pi$
$73$	−12.4541			−1.45765			−0.728824	+	0.684702i	$0.759933\pi$
$74$	−4.55356	+	7.88700i	−0.529341	+	0.916846i
$75$	0.00652833	+	0.0113074i	0.000753827	+	0.00130567i
$76$	3.52362	+	6.10309i	0.404187	+	0.700073i
$77$	13.5150			1.54017
$78$		0			0
$79$	0.984840			0.110803			0.0554016	−	0.998464i	$-0.482356\pi$
$79$	0.984840			0.110803			0.0554016	+	0.998464i	$0.482356\pi$
$80$	0.761834	+	1.31954i	0.0851757	+	0.147529i
$81$	−4.49923	−	7.79290i	−0.499915	−	0.865878i
$82$	−8.01179	+	13.8768i	−0.884754	+	1.53244i
$83$	−7.84405			−0.860997			−0.430498	−	0.902591i	$-0.641662\pi$
$83$	−7.84405			−0.860997			−0.430498	+	0.902591i	$0.641662\pi$
$84$	0.0861894	−	0.149284i	0.00940403	−	0.0162883i
$85$	1.67603	−	2.90297i	0.181791	−	0.314871i
$86$	−1.55565			−0.167750
$87$	0.0539450	−	0.0934356i	0.00578352	−	0.0100173i
$88$	−2.79551	−	4.84197i	−0.298002	−	0.516155i
$89$	0.206417	+	0.357525i	0.0218802	+	0.0378976i	0.876758	−	0.480932i	$-0.159701\pi$
$89$	0.206417	+	0.357525i	0.0218802	+	0.0378976i	−0.854878	+	0.518829i	$0.826368\pi$
$90$	−6.61630			−0.697419
$91$		0			0
$92$	−4.53532			−0.472840
$93$	−0.0638444	−	0.110582i	−0.00662035	−	0.0114668i
$94$	−9.45437	−	16.3755i	−0.975144	−	1.68900i
$95$	1.23010	−	2.13060i	0.126206	−	0.218595i
$96$	0.0936675			0.00955989
$97$	1.69208	−	2.93077i	0.171805	−	0.297574i	−0.767246	−	0.641353i	$-0.778374\pi$
$97$	1.69208	−	2.93077i	0.171805	−	0.297574i	0.939051	+	0.343778i	$0.111707\pi$
$98$	−15.7064	+	27.2044i	−1.58659	+	2.74806i
$99$	−8.79646			−0.884077
$100$	−1.43225	+	2.48072i	−0.143225	+	0.248072i
$101$	5.27162	+	9.13071i	0.524545	+	0.908539i	0.999592	+	0.0285783i	$0.00909800\pi$
$101$	5.27162	+	9.13071i	0.524545	+	0.908539i	−0.475046	+	0.879961i	$0.657569\pi$
$102$	−0.0482650	−	0.0835975i	−0.00477895	−	0.00827739i
$103$	14.1152			1.39081			0.695404	−	0.718619i	$-0.255226\pi$
$103$	14.1152			1.39081			0.695404	+	0.718619i	$0.255226\pi$
$104$		0			0
$105$	−0.0601778			−0.00587275
$106$	13.7449	+	23.8069i	1.33502	+	2.31233i
$107$	1.98582	+	3.43955i	0.191977	+	0.332514i	0.945905	−	0.324443i	$-0.105177\pi$
$107$	1.98582	+	3.43955i	0.191977	+	0.332514i	−0.753928	+	0.656957i	$0.771844\pi$
$108$	−0.112199	+	0.194334i	−0.0107963	+	0.0186998i
$109$	10.1737			0.974460			0.487230	−	0.873274i	$-0.338007\pi$
$109$	10.1737			0.974460			0.487230	+	0.873274i	$0.338007\pi$
$110$	−3.23370	+	5.60094i	−0.308321	+	0.534028i
$111$	0.0269566	−	0.0466902i	0.00255861	−	0.00443164i
$112$	−7.02254			−0.663568
$113$	1.29992	−	2.25152i	0.122286	−	0.211806i	−0.798383	−	0.602150i	$-0.794311\pi$
$113$	1.29992	−	2.25152i	0.122286	−	0.211806i	0.920669	+	0.390345i	$0.127644\pi$
$114$	−0.0354236	−	0.0613555i	−0.00331772	−	0.00574646i
$115$	0.791645	+	1.37117i	0.0738212	+	0.127862i
$116$	23.6699			2.19770
$117$		0			0
$118$	−11.7655			−1.08310
$119$	7.72477	+	13.3797i	0.708128	+	1.22651i
$120$	0.0124475	+	0.0215597i	0.00113630	+	0.00196812i
$121$	1.20075	−	2.07976i	0.109159	−	0.189069i
$122$	4.23670			0.383573
$123$	0.0474289	−	0.0821492i	0.00427652	−	0.00740715i
$124$	14.0068	−	24.2604i	1.25785	−	2.17865i
$125$	1.00000			0.0894427
$126$	15.2472	−	26.4089i	1.35833	−	2.35269i
$127$	−9.98595	−	17.2962i	−0.886109	−	1.53479i	−0.844437	−	0.535655i	$-0.820065\pi$
$127$	−9.98595	−	17.2962i	−0.886109	−	1.53479i	−0.0416726	−	0.999131i	$-0.513269\pi$
$128$	6.91428	+	11.9759i	0.611142	+	1.05853i
$129$	0.00920925			0.000810829
$130$		0			0
$131$	−11.4400			−0.999514			−0.499757	−	0.866166i	$-0.666577\pi$
$131$	−11.4400			−0.999514			−0.499757	+	0.866166i	$0.666577\pi$
$132$	0.0548354	+	0.0949777i	0.00477281	+	0.00826675i
$133$	5.66951	+	9.81988i	0.491609	+	0.851491i
$134$	8.04801	−	13.9396i	0.695242	−	1.20419i
$135$	0.0783378			0.00674224
$136$	3.19567	−	5.53506i	0.274026	−	0.474627i
$137$	−1.56260	+	2.70650i	−0.133502	+	0.231232i	−0.925024	−	0.379908i	$-0.875956\pi$
$137$	−1.56260	+	2.70650i	−0.133502	+	0.231232i	0.791522	+	0.611140i	$0.209289\pi$
$138$	0.0455944			0.00388125
$139$	−3.04763	+	5.27865i	−0.258497	+	0.447729i	−0.965839	−	0.259142i	$-0.916560\pi$
$139$	−3.04763	+	5.27865i	−0.258497	+	0.447729i	0.707343	+	0.706871i	$0.249894\pi$
$140$	−6.60118	−	11.4336i	−0.557901	−	0.966314i
$141$	0.0559688	+	0.0969409i	0.00471343	+	0.00816389i
$142$	−14.7350			−1.23653
$143$		0			0
$144$	4.57075			0.380896
$145$	−4.13161	−	7.15616i	−0.343112	−	0.594287i
$146$	13.7342	+	23.7883i	1.13665	+	1.96873i
$147$	0.0929804	−	0.161047i	0.00766889	−	0.0132829i
$148$	11.8280			0.972253
$149$	7.30982	−	12.6610i	0.598844	−	1.03723i	−0.394148	−	0.919047i	$-0.628960\pi$
$149$	7.30982	−	12.6610i	0.598844	−	1.03723i	0.992992	−	0.118181i	$-0.0377063\pi$
$150$	0.0143986	−	0.0249391i	0.00117564	−	0.00203627i
$151$	12.2510			0.996973			0.498487	−	0.866897i	$-0.333889\pi$
$151$	12.2510			0.996973			0.498487	+	0.866897i	$0.333889\pi$
$152$	2.34542	−	4.06239i	0.190239	−	0.329504i
$153$	−5.02780	−	8.70841i	−0.406474	−	0.704033i
$154$	−14.9040	−	25.8145i	−1.20100	−	2.08020i
$155$	−9.77959			−0.785515
$156$		0			0
$157$	7.13991			0.569827			0.284914	−	0.958553i	$-0.408035\pi$
$157$	7.13991			0.569827			0.284914	+	0.958553i	$0.408035\pi$
$158$	−1.08606	−	1.88111i	−0.0864024	−	0.149653i
$159$	−0.0813682	−	0.140934i	−0.00645292	−	0.0111768i
$160$	3.58696	−	6.21280i	0.283574	−	0.491165i
$161$	−7.29733			−0.575110
$162$	−9.92333	+	17.1877i	−0.779650	+	1.35039i
$163$	−1.19501	+	2.06982i	−0.0936004	+	0.162121i	−0.909024	−	0.416745i	$-0.863171\pi$
$163$	−1.19501	+	2.06982i	−0.0936004	+	0.162121i	0.815423	+	0.578865i	$0.196504\pi$
$164$	20.8108			1.62505
$165$	0.0191432	−	0.0331569i	0.00149029	−	0.00258126i
$166$	8.65026	+	14.9827i	0.671391	+	1.16288i
$167$	3.71920	+	6.44185i	0.287801	+	0.498485i	0.973284	−	0.229603i	$-0.0737426\pi$
$167$	3.71920	+	6.44185i	0.287801	+	0.498485i	−0.685484	+	0.728088i	$0.740409\pi$
$168$	−0.114740			−0.00885240
$169$		0			0
$170$	−7.39317			−0.567030
$171$	−3.69010	−	6.39144i	−0.282189	−	0.488766i
$172$	1.01021	+	1.74973i	0.0770274	+	0.133415i
$173$	−1.27059	+	2.20073i	−0.0966015	+	0.167319i	−0.910276	−	0.414002i	$-0.864131\pi$
$173$	−1.27059	+	2.20073i	−0.0966015	+	0.167319i	0.813674	+	0.581321i	$0.197464\pi$
$174$	−0.237958			−0.0180396
$175$	−2.30448	+	3.99148i	−0.174203	+	0.301728i
$176$	2.23394	−	3.86930i	0.168390	−	0.291660i
$177$	0.0696502			0.00523523
$178$	0.455265	−	0.788543i	0.0341236	−	0.0591038i
$179$	5.34565	+	9.25894i	0.399553	+	0.692045i	0.993671	−	0.112332i	$-0.0358322\pi$
$179$	5.34565	+	9.25894i	0.399553	+	0.692045i	−0.594118	+	0.804378i	$0.702499\pi$
$180$	4.29649	+	7.44175i	0.320242	+	0.554675i
$181$	−11.7908			−0.876402			−0.438201	−	0.898877i	$-0.644384\pi$
$181$	−11.7908			−0.876402			−0.438201	+	0.898877i	$0.644384\pi$
$182$		0			0
$183$	−0.0250808			−0.00185403
$184$	1.50942	+	2.61439i	0.111276	+	0.192736i
$185$	−2.06458	−	3.57597i	−0.151791	−	0.262910i
$186$	−0.140813	+	0.243895i	−0.0103249	+	0.0178832i
$187$	−9.82931			−0.718790
$188$	−12.2790	+	21.2678i	−0.895535	+	1.55111i
$189$	−0.180528	+	0.312684i	−0.0131315	+	0.0227444i
$190$	−5.42613			−0.393653
$191$	−6.73731	+	11.6694i	−0.487495	+	0.844366i	−0.999897	−	0.0143798i	$-0.995423\pi$
$191$	−6.73731	+	11.6694i	−0.487495	+	0.844366i	0.512402	+	0.858746i	$0.328756\pi$
$192$	−0.0834005	−	0.144454i	−0.00601892	−	0.0104251i
$193$	−3.49368	−	6.05124i	−0.251481	−	0.435578i	0.712453	−	0.701720i	$-0.247584\pi$
$193$	−3.49368	−	6.05124i	−0.251481	−	0.435578i	−0.963934	+	0.266142i	$0.914251\pi$
$194$	−7.46397			−0.535882
$195$		0			0
$196$	40.7978			2.91413
$197$	−0.718974	−	1.24530i	−0.0512248	−	0.0887240i	0.839276	−	0.543706i	$-0.182979\pi$
$197$	−0.718974	−	1.24530i	−0.0512248	−	0.0887240i	−0.890501	+	0.454982i	$0.849646\pi$
$198$	9.70056	+	16.8019i	0.689389	+	1.19406i
$199$	1.21426	−	2.10316i	0.0860765	−	0.149089i	−0.819773	−	0.572689i	$-0.805900\pi$
$199$	1.21426	−	2.10316i	0.0860765	−	0.149089i	0.905849	+	0.423600i	$0.139234\pi$
$200$	1.90669			0.134823
$201$	−0.0476433	+	0.0825206i	−0.00336050	+	0.00582056i
$202$	11.6269	−	20.1383i	0.818063	−	1.41693i
$203$	38.0849			2.67304
$204$	−0.0626847	+	0.108573i	−0.00438881	+	0.00760164i
$205$	−3.63254	−	6.29175i	−0.253708	−	0.439435i
$206$	−15.5659	−	26.9609i	−1.08453	−	1.87846i
$207$	4.74960			0.330120
$208$		0			0
$209$	−7.21411			−0.499011
$210$	0.0663628	+	0.114944i	0.00457947	+	0.00793187i
$211$	−9.13202	−	15.8171i	−0.628674	−	1.08890i	−0.987818	−	0.155613i	$-0.950265\pi$
$211$	−9.13202	−	15.8171i	−0.628674	−	1.08890i	0.359144	−	0.933282i	$-0.383069\pi$
$212$	17.8513	−	30.9194i	1.22603	−	2.12355i
$213$	0.0872293			0.00597685
$214$	4.37985	−	7.58612i	0.299400	−	0.518577i
$215$	0.352665	−	0.610833i	0.0240515	−	0.0416585i
$216$	0.149366			0.0101631
$217$	22.5369	−	39.0351i	1.52990	−	2.64987i
$218$	−11.2193	−	19.4324i	−0.759867	−	1.31613i
$219$	−0.0813048	−	0.140824i	−0.00549407	−	0.00951600i
$220$	8.39961			0.566301
$221$		0			0
$222$	−0.118909			−0.00798063
$223$	−7.79204	−	13.4962i	−0.521793	−	0.903773i	−0.999679	−	0.0253505i	$-0.991930\pi$
$223$	−7.79204	−	13.4962i	−0.521793	−	0.903773i	0.477885	−	0.878422i	$-0.341404\pi$
$224$	16.5322	+	28.6346i	1.10460	+	1.91323i
$225$	1.49991	−	2.59793i	0.0999943	−	0.173195i
$226$	−5.73409			−0.381426
$227$	2.01690	−	3.49338i	0.133866	−	0.231863i	−0.791297	−	0.611431i	$-0.790594\pi$
$227$	2.01690	−	3.49338i	0.133866	−	0.231863i	0.925164	+	0.379568i	$0.123927\pi$
$228$	−0.0460067	+	0.0796860i	−0.00304687	+	0.00527733i
$229$	22.5147			1.48781			0.743906	−	0.668284i	$-0.232971\pi$
$229$	22.5147			1.48781			0.743906	+	0.668284i	$0.232971\pi$
$230$	1.74602	−	3.02419i	0.115129	−	0.199409i
$231$	0.0882302	+	0.152819i	0.00580512	+	0.0100548i
$232$	−7.87770	−	13.6446i	−0.517196	−	0.895810i
$233$	−7.69759			−0.504286			−0.252143	−	0.967690i	$-0.581135\pi$
$233$	−7.69759			−0.504286			−0.252143	+	0.967690i	$0.581135\pi$
$234$		0			0
$235$	8.57322			0.559255
$236$	7.64025	+	13.2333i	0.497338	+	0.861414i
$237$	0.00642936	+	0.0111360i	0.000417632	+	0.000723360i
$238$	17.0374	−	29.5097i	1.10437	−	1.91283i
$239$	18.7203			1.21092			0.605459	−	0.795877i	$-0.292990\pi$
$239$	18.7203			1.21092			0.605459	+	0.795877i	$0.292990\pi$
$240$	−0.00994701	+	0.0172287i	−0.000642077	+	0.00111211i
$241$	11.3091	−	19.5880i	0.728486	−	1.26177i	−0.229037	−	0.973418i	$-0.573558\pi$
$241$	11.3091	−	19.5880i	0.728486	−	1.26177i	0.957523	−	0.288357i	$-0.0931088\pi$
$242$	−5.29665			−0.340482
$243$	0.176252	−	0.305277i	0.0113065	−	0.0195835i
$244$	−2.75123	−	4.76527i	−0.176130	−	0.305065i
$245$	−7.12130	−	12.3344i	−0.454963	−	0.788019i
$246$	−0.209214			−0.0133390
$247$		0			0
$248$	−18.6466			−1.18406
$249$	−0.0512086	−	0.0886959i	−0.00324521	−	0.00562087i
$250$	−1.10278	−	1.91007i	−0.0697459	−	0.120803i
$251$	−0.892059	+	1.54509i	−0.0563062	+	0.0975253i	−0.892805	−	0.450444i	$-0.851266\pi$
$251$	−0.892059	+	1.54509i	−0.0563062	+	0.0975253i	0.836498	+	0.547969i	$0.184599\pi$
$252$	−39.6048			−2.49487
$253$	2.32136	−	4.02071i	0.145942	−	0.252780i
$254$	−22.0246	+	38.1477i	−1.38195	+	2.39360i
$255$	0.0437667			0.00274078
$256$	2.47468	−	4.28627i	0.154667	−	0.267892i
$257$	2.29924	+	3.98240i	0.143422	+	0.248415i	0.928783	−	0.370623i	$-0.120856\pi$
$257$	2.29924	+	3.98240i	0.143422	+	0.248415i	−0.785361	+	0.619038i	$0.787523\pi$
$258$	−0.0101558	−	0.0175903i	−0.000632271	−	0.00109513i
$259$	19.0312			1.18254
$260$		0			0
$261$	−24.7883			−1.53435
$262$	12.6158	+	21.8511i	0.779404	+	1.34997i
$263$	−9.40637	−	16.2923i	−0.580022	−	1.00463i	−0.995476	−	0.0950132i	$-0.969711\pi$
$263$	−9.40637	−	16.2923i	−0.580022	−	1.00463i	0.415454	−	0.909614i	$-0.363623\pi$
$264$	0.0365000	−	0.0632199i	0.00224642	−	0.00389092i
$265$	−12.4639			−0.765649
$266$	12.5044	−	21.6583i	0.766696	−	1.32796i
$267$	−0.00269512	+	0.00466808i	−0.000164939	+	0.000285682i
$268$	−20.9049			−1.27697
$269$	−0.927060	+	1.60571i	−0.0565238	+	0.0979022i	−0.892903	−	0.450250i	$-0.851335\pi$
$269$	−0.927060	+	1.60571i	−0.0565238	+	0.0979022i	0.836379	+	0.548152i	$0.184668\pi$
$270$	−0.0863893	−	0.149631i	−0.00525748	−	0.00910623i
$271$	−0.0748491	−	0.129642i	−0.00454676	−	0.00787522i	0.863743	−	0.503932i	$-0.168114\pi$
$271$	−0.0748491	−	0.129642i	−0.00454676	−	0.00787522i	−0.868290	+	0.496057i	$0.834781\pi$
$272$	5.10743			0.309683
$273$		0			0
$274$	6.89281			0.416410
$275$	−1.46616	−	2.53946i	−0.0884128	−	0.153135i
$276$	−0.0296081	−	0.0512827i	−0.00178220	−	0.00308686i
$277$	−11.0092	+	19.0685i	−0.661478	+	1.14571i	0.318749	+	0.947839i	$0.396737\pi$
$277$	−11.0092	+	19.0685i	−0.661478	+	1.14571i	−0.980227	+	0.197874i	$0.936596\pi$
$278$	13.4435			0.806285
$279$	−14.6685	+	25.4067i	−0.878183	+	1.52106i
$280$	−4.39394	+	7.61052i	−0.262588	+	0.454815i
$281$	−0.438029			−0.0261306			−0.0130653	−	0.999915i	$-0.504159\pi$
$281$	−0.438029			−0.0261306			−0.0130653	+	0.999915i	$0.504159\pi$
$282$	0.123443	−	0.213809i	0.00735090	−	0.0127321i
$283$	−6.91451	−	11.9763i	−0.411025	−	0.711916i	0.583977	−	0.811770i	$-0.301496\pi$
$283$	−6.91451	−	11.9763i	−0.411025	−	0.711916i	−0.995002	+	0.0998543i	$0.968162\pi$
$284$	9.56859	+	16.5733i	0.567791	+	0.983443i
$285$	0.0321221			0.00190275
$286$		0			0
$287$	33.4845			1.97653
$288$	−10.7603	−	18.6373i	−0.634055	−	1.09822i
$289$	2.88185	+	4.99151i	0.169520	+	0.293618i
$290$	−9.11251	+	15.7833i	−0.535105	+	0.926829i
$291$	0.0441858			0.00259022
$292$	17.8374	−	30.8953i	1.04385	−	1.80801i
$293$	−7.28278	+	12.6141i	−0.425464	+	0.736926i	−0.996464	−	0.0840245i	$-0.973223\pi$
$293$	−7.28278	+	12.6141i	−0.425464	+	0.736926i	0.570999	+	0.820951i	$0.306556\pi$
$294$	−0.410148			−0.0239203
$295$	2.66723	−	4.61977i	0.155292	−	0.268974i
$296$	−3.93652	−	6.81825i	−0.228806	−	0.396303i
$297$	−0.114856	−	0.198936i	−0.00666460	−	0.0115434i
$298$	−32.2445			−1.86787
$299$		0			0
$300$	−0.0374007			−0.00215933
$301$	1.62542	+	2.81531i	0.0936877	+	0.162272i
$302$	−13.5102	−	23.4003i	−0.777423	−	1.34654i
$303$	−0.0688297	+	0.119217i	−0.00395416	+	0.00684881i
$304$	3.74854			0.214994
$305$	−0.960460	+	1.66357i	−0.0549958	+	0.0952555i
$306$	−11.0891	+	19.2069i	−0.633923	+	1.09799i
$307$	−9.05062			−0.516546			−0.258273	−	0.966072i	$-0.583153\pi$
$307$	−9.05062			−0.516546			−0.258273	+	0.966072i	$0.583153\pi$
$308$	−19.3568	+	33.5269i	−1.10295	+	1.91037i
$309$	0.0921484	+	0.159606i	0.00524214	+	0.00907965i
$310$	10.7847	+	18.6797i	0.612531	+	1.06094i
$311$	7.28812			0.413272			0.206636	−	0.978418i	$-0.433748\pi$
$311$	7.28812			0.413272			0.206636	+	0.978418i	$0.433748\pi$
$312$		0			0
$313$	12.9725			0.733250			0.366625	−	0.930369i	$-0.380513\pi$
$313$	12.9725			0.733250			0.366625	+	0.930369i	$0.380513\pi$
$314$	−7.87375	−	13.6377i	−0.444342	−	0.769622i
$315$	6.91306	+	11.9738i	0.389507	+	0.674646i
$316$	−1.41053	+	2.44312i	−0.0793487	+	0.137436i
$317$	15.5048			0.870838			0.435419	−	0.900228i	$-0.356600\pi$
$317$	15.5048			0.870838			0.435419	+	0.900228i	$0.356600\pi$
$318$	−0.179462	+	0.310838i	−0.0100638	+	0.0174309i
$319$	−12.1152	+	20.9841i	−0.678321	+	1.17489i
$320$	−12.7752			−0.714154
$321$	−0.0259282	+	0.0449090i	−0.00144717	+	0.00250658i
$322$	8.04735	+	13.9384i	0.448461	+	0.776758i
$323$	−4.12338	−	7.14190i	−0.229431	−	0.397386i
$324$	25.7760			1.43200
$325$		0			0
$326$	5.27133			0.291952
$327$	0.0664170	+	0.115038i	0.00367287	+	0.00636160i
$328$	−6.92613	−	11.9964i	−0.382431	−	0.662391i
$329$	−19.7569	+	34.2199i	−1.08923	+	1.88660i
$330$	−0.0844427			−0.00464842
$331$	−13.0427	+	22.5906i	−0.716890	+	1.24169i	0.245336	+	0.969438i	$0.421102\pi$
$331$	−13.0427	+	22.5906i	−0.716890	+	1.24169i	−0.962226	+	0.272252i	$0.912232\pi$
$332$	11.2346	−	19.4589i	0.616580	−	1.06795i
$333$	−12.3868			−0.678793
$334$	8.20292	−	14.2079i	0.448844	−	0.777420i
$335$	3.64896	+	6.32019i	0.199364	+	0.345309i
$336$	−0.0458455	−	0.0794067i	−0.00250108	−	0.00433199i
$337$	−14.4785			−0.788697			−0.394348	−	0.918961i	$-0.629030\pi$
$337$	−14.4785			−0.788697			−0.394348	+	0.918961i	$0.629030\pi$
$338$		0			0
$339$	0.0339452			0.00184365
$340$	4.80097	+	8.31553i	0.260369	+	0.450973i
$341$	14.3384	+	24.8349i	0.776470	+	1.34489i
$342$	−8.13874	+	14.0967i	−0.440092	+	0.762262i
$343$	33.3809			1.80240
$344$	0.672422	−	1.16467i	0.0362546	−	0.0627947i
$345$	−0.0103362	+	0.0179029i	−0.000556484	+	0.000963859i
$346$	5.60474			0.301313
$347$	−3.40706	+	5.90120i	−0.182901	+	0.316793i	−0.942867	−	0.333169i	$-0.891882\pi$
$347$	−3.40706	+	5.90120i	−0.182901	+	0.316793i	0.759967	+	0.649962i	$0.225215\pi$
$348$	0.154525	+	0.267645i	0.00828342	+	0.0143473i
$349$	16.8679	+	29.2160i	0.902915	+	1.56390i	0.823691	+	0.567039i	$0.191911\pi$
$349$	16.8679	+	29.2160i	0.902915	+	1.56390i	0.0792242	+	0.996857i	$0.474756\pi$
$350$	10.1654			0.543361
$351$		0			0
$352$	−21.0362			−1.12123
$353$	9.36077	+	16.2133i	0.498223	+	0.862948i	0.999998	−	0.00205026i	$-0.000652619\pi$
$353$	9.36077	+	16.2133i	0.498223	+	0.862948i	−0.501775	+	0.864998i	$0.667319\pi$
$354$	−0.0768088	−	0.133037i	−0.00408234	−	0.00707082i
$355$	3.34041	−	5.78577i	0.177291	−	0.307077i
$356$	−1.18256			−0.0626756
$357$	−0.100860	+	0.174694i	−0.00533806	+	0.00924579i
$358$	11.7901	−	20.4211i	0.623129	−	1.07929i
$359$	−27.9262			−1.47389			−0.736945	−	0.675952i	$-0.763732\pi$
$359$	−27.9262			−1.47389			−0.736945	+	0.675952i	$0.763732\pi$
$360$	2.85987	−	4.95344i	0.150728	−	0.261069i
$361$	6.47369	+	11.2128i	0.340721	+	0.590145i
$362$	13.0026	+	22.5212i	0.683404	+	1.18369i
$363$	0.0313556			0.00164574
$364$		0			0
$365$	−12.4541			−0.651880
$366$	0.0276586	+	0.0479061i	0.00144574	+	0.00250409i
$367$	−1.25494	−	2.17362i	−0.0655074	−	0.113462i	0.831412	−	0.555657i	$-0.187533\pi$
$367$	−1.25494	−	2.17362i	−0.0655074	−	0.113462i	−0.896919	+	0.442195i	$0.854200\pi$
$368$	−1.20620	+	2.08921i	−0.0628777	+	0.108907i
$369$	−21.7940			−1.13455
$370$	−4.55356	+	7.88700i	−0.236729	+	0.410026i
$371$	28.7228	−	49.7493i	1.49121	−	2.58286i
$372$	0.365763			0.0189640
$373$	−11.0890	+	19.2067i	−0.574165	+	0.994483i	0.421967	+	0.906611i	$0.361340\pi$
$373$	−11.0890	+	19.2067i	−0.574165	+	0.994483i	−0.996132	+	0.0878719i	$0.971993\pi$
$374$	10.8396	+	18.7747i	0.560501	+	0.970815i
$375$	0.00652833	+	0.0113074i	0.000337122	+	0.000583912i
$376$	16.3465			0.843005
$377$		0			0
$378$	0.796331			0.0409589
$379$	0.710581	+	1.23076i	0.0365001	+	0.0632200i	0.883698	−	0.468057i	$-0.155046\pi$
$379$	0.710581	+	1.23076i	0.0365001	+	0.0632200i	−0.847198	+	0.531277i	$0.821712\pi$
$380$	3.52362	+	6.10309i	0.180758	+	0.313082i
$381$	0.130383	−	0.225830i	0.00667973	−	0.0115696i
$382$	29.7191			1.52056
$383$	−10.5366	+	18.2500i	−0.538397	+	0.932531i	0.460594	+	0.887611i	$0.347637\pi$
$383$	−10.5366	+	18.2500i	−0.538397	+	0.932531i	−0.998991	+	0.0449197i	$0.985697\pi$
$384$	−0.0902774	+	0.156365i	−0.00460695	+	0.00797947i
$385$	13.5150			0.688787
$386$	−7.70553	+	13.3464i	−0.392201	+	0.679312i
$387$	−1.05793	−	1.83240i	−0.0537778	−	0.0931459i
$388$	4.84695	+	8.39516i	0.246067	+	0.426200i
$389$	13.4713			0.683021			0.341511	−	0.939878i	$-0.389061\pi$
$389$	13.4713			0.683021			0.341511	+	0.939878i	$0.389061\pi$
$390$		0			0
$391$	5.30728			0.268401
$392$	−13.5781	−	23.5180i	−0.685798	−	1.18784i
$393$	−0.0746839	−	0.129356i	−0.00376730	−	0.00652516i
$394$	−1.58574	+	2.74658i	−0.0798885	+	0.138371i
$395$	0.984840			0.0495527
$396$	12.5987	−	21.8216i	0.633108	−	1.09658i
$397$	−13.5929	+	23.5437i	−0.682210	+	1.18162i	0.292094	+	0.956390i	$0.405648\pi$
$397$	−13.5929	+	23.5437i	−0.682210	+	1.18162i	−0.974305	+	0.225234i	$0.927685\pi$
$398$	−5.35624			−0.268484
$399$	−0.0740249	+	0.128215i	−0.00370588	+	0.00641877i
$400$	0.761834	+	1.31954i	0.0380917	+	0.0659768i
$401$	1.63760	+	2.83641i	0.0817779	+	0.141643i	0.904014	−	0.427504i	$-0.140607\pi$
$401$	1.63760	+	2.83641i	0.0817779	+	0.141643i	−0.822236	+	0.569147i	$0.807274\pi$
$402$	0.210160			0.0104818
$403$		0			0
$404$	−30.2010			−1.50256
$405$	−4.49923	−	7.79290i	−0.223569	−	0.387232i
$406$	−41.9993	−	72.7449i	−2.08439	−	3.61027i
$407$	−6.05402	+	10.4859i	−0.300087	+	0.519765i
$408$	0.0834495			0.00413137
$409$	9.58386	−	16.5997i	0.473891	−	0.820804i	−0.525662	−	0.850694i	$-0.676182\pi$
$409$	9.58386	−	16.5997i	0.473891	−	0.820804i	0.999553	+	0.0298899i	$0.00951565\pi$
$410$	−8.01179	+	13.8768i	−0.395674	+	0.685327i
$411$	−0.0408047			−0.00201275
$412$	−20.2164	+	35.0158i	−0.995989	+	1.72510i
$413$	12.2932	+	21.2924i	0.604907	+	1.04773i
$414$	−5.23776	−	9.07207i	−0.257422	−	0.445868i
$415$	−7.84405			−0.385049
$416$		0			0
$417$	−0.0795837			−0.00389723
$418$	7.95558	+	13.7795i	0.389120	+	0.673976i
$419$	−0.196231	−	0.339883i	−0.00958653	−	0.0166044i	0.861192	−	0.508279i	$-0.169718\pi$
$419$	−0.196231	−	0.339883i	−0.00958653	−	0.0166044i	−0.870779	+	0.491675i	$0.836385\pi$
$420$	0.0861894	−	0.149284i	0.00420561	−	0.00728433i
$421$	35.1816			1.71465			0.857323	−	0.514779i	$-0.172126\pi$
$421$	35.1816			1.71465			0.857323	+	0.514779i	$0.172126\pi$
$422$	−20.1412	+	34.8856i	−0.980458	+	1.69820i
$423$	12.8591	−	22.2726i	0.625231	−	1.08293i
$424$	−23.7647			−1.15412
$425$	1.67603	−	2.90297i	0.0812994	−	0.140815i
$426$	−0.0961947	−	0.166614i	−0.00466065	−	0.00807248i
$427$	−4.42673	−	7.66732i	−0.214225	−	0.371048i
$428$	−11.3768			−0.549916
$429$		0			0
$430$	−1.55565			−0.0750199
$431$	−1.13727	−	1.96981i	−0.0547803	−	0.0948823i	0.837335	−	0.546690i	$-0.184113\pi$
$431$	−1.13727	−	1.96981i	−0.0547803	−	0.0948823i	−0.892115	+	0.451808i	$0.850779\pi$
$432$	0.0596804	+	0.103369i	0.00287137	+	0.00497337i
$433$	−5.94137	+	10.2908i	−0.285524	+	0.494542i	−0.972736	−	0.231915i	$-0.925501\pi$
$433$	−5.94137	+	10.2908i	−0.285524	+	0.494542i	0.687212	+	0.726457i	$0.258834\pi$
$434$	−99.4130			−4.77197
$435$	0.0539450	−	0.0934356i	0.00258647	−	0.00447989i
$436$	−14.5712	+	25.2380i	−0.697833	+	1.20868i
$437$	3.89522			0.186334
$438$	−0.179322	+	0.310596i	−0.00856836	+	0.0148408i
$439$	17.8636	+	30.9407i	0.852585	+	1.47672i	0.878867	+	0.477067i	$0.158300\pi$
$439$	17.8636	+	30.9407i	0.852585	+	1.47672i	−0.0262818	+	0.999655i	$0.508367\pi$
$440$	−2.79551	−	4.84197i	−0.133271	−	0.230832i
$441$	−42.7254			−2.03454
$442$		0			0
$443$	4.98904			0.237036			0.118518	−	0.992952i	$-0.462186\pi$
$443$	4.98904			0.237036			0.118518	+	0.992952i	$0.462186\pi$
$444$	0.0772169	+	0.133744i	0.00366455	+	0.00634719i
$445$	0.206417	+	0.357525i	0.00978511	+	0.0169483i
$446$	−17.1858	+	29.7667i	−0.813771	+	1.40949i
$447$	0.190884			0.00902849
$448$	29.4402	−	50.9919i	1.39092	−	2.40914i
$449$	11.7443	−	20.3417i	0.554248	−	0.959985i	−0.443714	−	0.896168i	$-0.646339\pi$
$449$	11.7443	−	20.3417i	0.554248	−	0.959985i	0.997962	−	0.0638165i	$-0.0203272\pi$
$450$	−6.61630			−0.311895
$451$	−10.6518	+	18.4494i	−0.501572	+	0.868749i
$452$	3.72361	+	6.44947i	0.175144	+	0.303358i
$453$	0.0799787	+	0.138527i	0.00375773	+	0.00650857i
$454$	−8.89679			−0.417547
$455$		0			0
$456$	0.0612468			0.00286815
$457$	−20.1255	−	34.8584i	−0.941430	−	1.63061i	−0.762746	−	0.646699i	$-0.776149\pi$
$457$	−20.1255	−	34.8584i	−0.941430	−	1.63061i	−0.178685	−	0.983906i	$-0.557184\pi$
$458$	−24.8287	−	43.0046i	−1.16017	−	2.00947i
$459$	0.131296	−	0.227412i	0.00612839	−	0.0106147i
$460$	−4.53532			−0.211460
$461$	15.6070	−	27.0321i	0.726890	−	1.25901i	−0.231302	−	0.972882i	$-0.574298\pi$
$461$	15.6070	−	27.0321i	0.726890	−	1.25901i	0.958191	−	0.286128i	$-0.0923682\pi$
$462$	0.194597	−	0.337052i	0.00905347	−	0.0156811i
$463$	−17.7491			−0.824872			−0.412436	−	0.910987i	$-0.635322\pi$
$463$	−17.7491			−0.824872			−0.412436	+	0.910987i	$0.635322\pi$
$464$	6.29521	−	10.9036i	0.292248	−	0.506188i
$465$	−0.0638444	−	0.110582i	−0.00296071	−	0.00512810i
$466$	8.48875	+	14.7029i	0.393234	+	0.681101i
$467$	26.6645			1.23389			0.616944	−	0.787007i	$-0.288370\pi$
$467$	26.6645			1.23389			0.616944	+	0.787007i	$0.288370\pi$
$468$		0			0
$469$	−33.6359			−1.55316
$470$	−9.45437	−	16.3755i	−0.436098	−	0.755344i
$471$	0.0466117	+	0.0807339i	0.00214775	+	0.00372002i
$472$	5.08557	−	8.80847i	0.234082	−	0.405443i
$473$	−2.06825			−0.0950983
$474$	0.0141803	−	0.0245611i	0.000651325	−	0.00112813i
$475$	1.23010	−	2.13060i	0.0564410	−	0.0977587i
$476$	−44.2551			−2.02843
$477$	−18.6947	+	32.3802i	−0.855973	+	1.48259i
$478$	−20.6444	−	35.7572i	−0.944253	−	1.63549i
$479$	10.2315	+	17.7215i	0.467490	+	0.809716i	0.999310	−	0.0371410i	$-0.0118251\pi$
$479$	10.2315	+	17.7215i	0.467490	+	0.809716i	−0.531820	+	0.846857i	$0.678492\pi$
$480$	0.0936675			0.00427531
$481$		0			0
$482$	−49.8860			−2.27224
$483$	−0.0476394	−	0.0825139i	−0.00216767	−	0.00375451i
$484$	3.43954	+	5.95746i	0.156343	+	0.270794i
$485$	1.69208	−	2.93077i	0.0768334	−	0.133079i
$486$	−0.777467			−0.0352666
$487$	4.05895	−	7.03030i	0.183928	−	0.318573i	−0.759286	−	0.650757i	$-0.774452\pi$
$487$	4.05895	−	7.03030i	0.183928	−	0.318573i	0.943215	+	0.332183i	$0.107785\pi$
$488$	−1.83130	+	3.17190i	−0.0828990	+	0.143585i
$489$	−0.0312057			−0.00141117
$490$	−15.7064	+	27.2044i	−0.709545	+	1.22897i
$491$	−1.63498	−	2.83187i	−0.0737857	−	0.127801i	0.826772	−	0.562537i	$-0.190175\pi$
$491$	−1.63498	−	2.83187i	−0.0737857	−	0.127801i	−0.900558	+	0.434737i	$0.856841\pi$
$492$	0.135860	+	0.235316i	0.00612503	+	0.0106089i
$493$	−27.6988			−1.24749
$494$		0			0
$495$	−8.79646			−0.395371
$496$	−7.45042	−	12.9045i	−0.334534	−	0.579430i
$497$	15.3959	+	26.6664i	0.690599	+	1.19615i
$498$	−0.112944	+	0.195624i	−0.00506112	+	0.00876612i
$499$	−8.89340			−0.398123			−0.199062	−	0.979987i	$-0.563789\pi$
$499$	−8.89340			−0.398123			−0.199062	+	0.979987i	$0.563789\pi$
$500$	−1.43225	+	2.48072i	−0.0640520	+	0.110941i
$501$	−0.0485604	+	0.0841090i	−0.00216952	+	0.00375771i
$502$	3.93498			0.175627
$503$	11.8987	−	20.6092i	0.530537	−	0.918917i	−0.468828	−	0.883289i	$-0.655324\pi$
$503$	11.8987	−	20.6092i	0.530537	−	0.918917i	0.999365	−	0.0356275i	$-0.0113430\pi$
$504$	13.1811	+	22.8303i	0.587131	+	1.01694i
$505$	5.27162	+	9.13071i	0.234584	+	0.406311i
$506$	−10.2398			−0.455213
$507$		0			0
$508$	57.2093			2.53825
$509$	−0.633850	−	1.09786i	−0.0280949	−	0.0486618i	0.851636	−	0.524134i	$-0.175611\pi$
$509$	−0.633850	−	1.09786i	−0.0280949	−	0.0486618i	−0.879731	+	0.475472i	$0.842277\pi$
$510$	−0.0482650	−	0.0835975i	−0.00213721	−	0.00370176i
$511$	28.7004	−	49.7105i	1.26963	−	2.19906i
$512$	16.7410			0.739855
$513$	0.0963635	−	0.166907i	0.00425455	−	0.00736910i
$514$	5.07110	−	8.78341i	0.223677	−	0.387420i
$515$	14.1152			0.621988
$516$	−0.0131899	+	0.0228456i	−0.000580653	+	0.00100572i
$517$	−12.5697	−	21.7714i	−0.552815	−	0.957504i
$518$	−20.9872	−	36.3510i	−0.922126	−	1.59717i
$519$	−0.0331794			−0.00145642
$520$		0			0
$521$	14.3916			0.630506			0.315253	−	0.949008i	$-0.397911\pi$
$521$	14.3916			0.630506			0.315253	+	0.949008i	$0.397911\pi$
$522$	27.3360	+	47.3473i	1.19646	+	2.07234i
$523$	−9.50927	−	16.4705i	−0.415811	−	0.720206i	0.579702	−	0.814829i	$-0.303169\pi$
$523$	−9.50927	−	16.4705i	−0.415811	−	0.720206i	−0.995513	+	0.0946225i	$0.969836\pi$
$524$	16.3848	−	28.3794i	0.715775	−	1.23976i
$525$	−0.0601778			−0.00262637
$526$	−20.7463	+	35.9337i	−0.904582	+	1.56678i
$527$	−16.3909	+	28.3898i	−0.713998	+	1.23668i
$528$	0.0583357			0.00253873
$529$	10.2466	−	17.7476i	0.445504	−	0.771636i
$530$	13.7449	+	23.8069i	0.597040	+	1.03410i
$531$	−8.00122	−	13.8585i	−0.347224	−	0.601409i
$532$	−32.4805			−1.40821
$533$		0			0
$534$	0.0118885			0.000514465
$535$	1.98582	+	3.43955i	0.0858546	+	0.148705i
$536$	6.95744	+	12.0506i	0.300516	+	0.520508i
$537$	−0.0697963	+	0.120891i	−0.00301193	+	0.00521682i
$538$	4.08937			0.176305
$539$	−20.8819	+	36.1685i	−0.899448	+	1.55789i
$540$	−0.112199	+	0.194334i	−0.00482827	+	0.00836282i
$541$	13.8969			0.597475			0.298738	−	0.954335i	$-0.403434\pi$
$541$	13.8969			0.597475			0.298738	+	0.954335i	$0.403434\pi$
$542$	−0.165084	+	0.285934i	−0.00709097	+	0.0122819i
$543$	−0.0769742	−	0.133323i	−0.00330328	−	0.00572145i
$544$	−12.0237	−	20.8257i	−0.515512	−	0.892893i
$545$	10.1737			0.435792
$546$		0			0
$547$	37.0840			1.58560			0.792798	−	0.609484i	$-0.208623\pi$
$547$	37.0840			1.58560			0.792798	+	0.609484i	$0.208623\pi$
$548$	−4.47605	−	7.75275i	−0.191208	−	0.331181i
$549$	2.88122	+	4.99041i	0.122967	+	0.212986i
$550$	−3.23370	+	5.60094i	−0.137886	+	0.238825i
$551$	−20.3292			−0.866054
$552$	−0.0197080	+	0.0341352i	−0.000838828	+	0.00145289i
$553$	−2.26955	+	3.93097i	−0.0965110	+	0.167162i
$554$	48.5628			2.06324
$555$	0.0269566	−	0.0466902i	0.00114424	−	0.00198189i
$556$	−8.72991	−	15.1206i	−0.370231	−	0.641258i
$557$	−15.9033	−	27.5452i	−0.673842	−	1.16713i	−0.976806	−	0.214127i	$-0.931309\pi$
$557$	−15.9033	−	27.5452i	−0.673842	−	1.16713i	0.302963	−	0.953002i	$-0.402024\pi$
$558$	64.7047			2.73917
$559$		0			0
$560$	−7.02254			−0.296757
$561$	−0.0641690	−	0.111144i	−0.00270922	−	0.00469250i
$562$	0.483050	+	0.836667i	0.0203762	+	0.0352927i
$563$	−13.1798	+	22.8280i	−0.555461	+	0.962086i	0.442407	+	0.896814i	$0.354125\pi$
$563$	−13.1798	+	22.8280i	−0.555461	+	0.962086i	−0.997868	+	0.0652715i	$0.979209\pi$
$564$	−0.320645			−0.0135016
$565$	1.29992	−	2.25152i	0.0546880	−	0.0947223i
$566$	−15.2504	+	26.4144i	−0.641020	+	1.11028i
$567$	41.4736			1.74173
$568$	6.36913	−	11.0317i	0.267243	−	0.462878i
$569$	−8.89230	−	15.4019i	−0.372785	−	0.645682i	0.617208	−	0.786800i	$-0.288264\pi$
$569$	−8.89230	−	15.4019i	−0.372785	−	0.645682i	−0.989993	+	0.141118i	$0.954930\pi$
$570$	−0.0354236	−	0.0613555i	−0.00148373	−	0.00256990i
$571$	19.6399			0.821903			0.410952	−	0.911657i	$-0.365196\pi$
$571$	19.6399			0.821903			0.410952	+	0.911657i	$0.365196\pi$
$572$		0			0
$573$	−0.175934			−0.00734974
$574$	−36.9261	−	63.9578i	−1.54126	−	2.66955i
$575$	0.791645	+	1.37117i	0.0330139	+	0.0571817i
$576$	−19.1617	+	33.1890i	−0.798403	+	1.38287i
$577$	18.1454			0.755403			0.377701	−	0.925927i	$-0.376715\pi$
$577$	18.1454			0.755403			0.377701	+	0.925927i	$0.376715\pi$
$578$	6.35609	−	11.0091i	0.264378	−	0.457917i
$579$	0.0456159	−	0.0790090i	0.00189573	−	0.00328350i
$580$	23.6699			0.982840
$581$	18.0765	−	31.3094i	0.749940	−	1.29893i
$582$	−0.0487273	−	0.0843981i	−0.00201981	−	0.00349841i
$583$	18.2740	+	31.6515i	0.756832	+	1.31087i
$584$	−23.7462			−0.982624
$585$		0			0
$586$	32.1252			1.32708
$587$	0.211922	+	0.367059i	0.00874694	+	0.0151501i	0.870366	−	0.492406i	$-0.163882\pi$
$587$	0.211922	+	0.367059i	0.00874694	+	0.0151501i	−0.861619	+	0.507556i	$0.830549\pi$
$588$	0.266342	+	0.461317i	0.0109837	+	0.0190244i
$589$	−12.0299	+	20.8364i	−0.495683	+	0.858549i
$590$	−11.7655			−0.484376
$591$	0.00938741	−	0.0162595i	0.000386146	−	0.000668825i
$592$	3.14574	−	5.44859i	0.129289	−	0.223936i
$593$	−47.5064			−1.95085			−0.975426	−	0.220327i	$-0.929288\pi$
$593$	−47.5064			−1.95085			−0.975426	+	0.220327i	$0.929288\pi$
$594$	−0.253321	+	0.438765i	−0.0103939	+	0.0180027i
$595$	7.72477	+	13.3797i	0.316685	+	0.548514i
$596$	20.9389	+	36.2673i	0.857692	+	1.48557i
$597$	0.0317083			0.00129774
$598$		0			0
$599$	25.7871			1.05363			0.526816	−	0.849979i	$-0.323386\pi$
$599$	25.7871			1.05363			0.526816	+	0.849979i	$0.323386\pi$
$600$	0.0124475	+	0.0215597i	0.000508167	+	0.000880171i
$601$	6.33880	+	10.9791i	0.258565	+	0.447848i	0.965858	−	0.259073i	$-0.0834171\pi$
$601$	6.33880	+	10.9791i	0.258565	+	0.447848i	−0.707293	+	0.706921i	$0.750084\pi$
$602$	3.58496	−	6.20934i	0.146112	−	0.253074i
$603$	21.8925			0.891533
$604$	−17.5465	+	30.3914i	−0.713955	+	1.23661i
$605$	1.20075	−	2.07976i	0.0488175	−	0.0845543i
$606$	0.303616			0.0123336
$607$	2.20224	−	3.81439i	0.0893862	−	0.154821i	−0.817866	−	0.575409i	$-0.804843\pi$
$607$	2.20224	−	3.81439i	0.0893862	−	0.154821i	0.907252	+	0.420588i	$0.138176\pi$
$608$	−8.82466	−	15.2848i	−0.357887	−	0.619879i
$609$	0.248631	+	0.430642i	0.0100750	+	0.0174505i
$610$	4.23670			0.171539
$611$		0			0
$612$	28.8042			1.16434
$613$	16.6799	+	28.8905i	0.673696	+	1.16688i	0.976848	+	0.213934i	$0.0686277\pi$
$613$	16.6799	+	28.8905i	0.673696	+	1.16688i	−0.303152	+	0.952942i	$0.598039\pi$
$614$	9.98084	+	17.2873i	0.402794	+	0.697660i
$615$	0.0474289	−	0.0821492i	0.00191252	−	0.00331258i
$616$	25.7688			1.03826
$617$	16.2767	−	28.1921i	0.655277	−	1.13497i	−0.326547	−	0.945181i	$-0.605885\pi$
$617$	16.2767	−	28.1921i	0.655277	−	1.13497i	0.981824	−	0.189792i	$-0.0607814\pi$
$618$	0.203239	−	0.352020i	0.00817546	−	0.0141603i
$619$	−35.5813			−1.43013			−0.715067	−	0.699056i	$-0.753604\pi$
$619$	−35.5813			−1.43013			−0.715067	+	0.699056i	$0.753604\pi$
$620$	14.0068	−	24.2604i	0.562526	−	0.974323i
$621$	0.0620157	+	0.107414i	0.00248860	+	0.00431039i
$622$	−8.03719	−	13.9208i	−0.322262	−	0.558174i
$623$	−1.90274			−0.0762317
$624$		0			0
$625$	1.00000			0.0400000
$626$	−14.3058	−	24.7784i	−0.571776	−	0.990344i
$627$	−0.0470961	−	0.0815729i	−0.00188084	−	0.00325771i
$628$	−10.2261	+	17.7121i	−0.408066	+	0.706792i
$629$	−13.8412			−0.551886
$630$	15.2472	−	26.4089i	0.607462	−	1.05215i
$631$	−12.7058	+	22.0072i	−0.505812	+	0.876091i	0.494166	+	0.869368i	$0.335474\pi$
$631$	−12.7058	+	22.0072i	−0.505812	+	0.876091i	−0.999977	+	0.00672365i	$0.997860\pi$
$632$	1.87778			0.0746942
$633$	0.119234	−	0.206519i	0.00473911	−	0.00820838i
$634$	−17.0984	−	29.6153i	−0.679064	−	1.17617i
$635$	−9.98595	−	17.2962i	−0.396280	−	0.686377i
$636$	0.466157			0.0184843
$637$		0			0
$638$	53.4416			2.11577
$639$	−10.0207	−	17.3563i	−0.396412	−	0.686605i
$640$	6.91428	+	11.9759i	0.273311	+	0.473388i
$641$	5.07393	−	8.78831i	0.200408	−	0.347117i	−0.748252	−	0.663415i	$-0.769106\pi$
$641$	5.07393	−	8.78831i	0.200408	−	0.347117i	0.948660	+	0.316298i	$0.102440\pi$
$642$	0.114372			0.00451392
$643$	−0.927193	+	1.60595i	−0.0365649	+	0.0633323i	−0.883729	−	0.467999i	$-0.844975\pi$
$643$	−0.927193	+	1.60595i	−0.0365649	+	0.0633323i	0.847164	+	0.531332i	$0.178308\pi$
$644$	10.4516	−	18.1027i	0.411850	−	0.713345i
$645$	0.00920925			0.000362614
$646$	−9.09436	+	15.7519i	−0.357813	+	0.619750i
$647$	14.8017	+	25.6373i	0.581914	+	1.00790i	0.995252	+	0.0973272i	$0.0310293\pi$
$647$	14.8017	+	25.6373i	0.581914	+	1.00790i	−0.413338	+	0.910577i	$0.635637\pi$
$648$	−8.57864	−	14.8586i	−0.337001	−	0.583702i
$649$	−15.6423			−0.614015
$650$		0			0
$651$	0.588514			0.0230657
$652$	−3.42310	−	5.92898i	−0.134059	−	0.232197i
$653$	−3.39441	−	5.87929i	−0.132834	−	0.230075i	0.791934	−	0.610606i	$-0.209074\pi$
$653$	−3.39441	−	5.87929i	−0.132834	−	0.230075i	−0.924768	+	0.380532i	$0.875741\pi$
$654$	0.146487	−	0.253722i	0.00572808	−	0.00992133i
$655$	−11.4400			−0.446996
$656$	5.53479	−	9.58654i	0.216097	−	0.374291i
$657$	−18.6802	+	32.3550i	−0.728782	+	1.26229i
$658$	87.1498			3.39745
$659$	−3.97479	+	6.88455i	−0.154836	+	0.268184i	−0.932999	−	0.359878i	$-0.882818\pi$
$659$	−3.97479	+	6.88455i	−0.154836	+	0.268184i	0.778163	+	0.628062i	$0.216152\pi$
$660$	0.0548354	+	0.0949777i	0.00213447	+	0.00369700i
$661$	−20.1916	−	34.9728i	−0.785361	−	1.36029i	−0.928783	−	0.370624i	$-0.879144\pi$
$661$	−20.1916	−	34.9728i	−0.785361	−	1.36029i	0.143422	−	0.989662i	$-0.454189\pi$
$662$	57.5328			2.23607
$663$		0			0
$664$	−14.9562			−0.580412
$665$	5.66951	+	9.81988i	0.219854	+	0.380798i
$666$	13.6599	+	23.6597i	0.529311	+	0.916794i
$667$	6.54154	−	11.3303i	0.253289	−	0.438710i
$668$	−21.3073			−0.824402
$669$	0.101738	−	0.176215i	0.00393342	−	0.00681288i
$670$	8.04801	−	13.9396i	0.310922	−	0.538532i
$671$	5.63275			0.217450
$672$	−0.215855	+	0.373872i	−0.00832680	+	0.0144224i
$673$	−4.81960	−	8.34779i	−0.185782	−	0.321784i	0.758058	−	0.652187i	$-0.226148\pi$
$673$	−4.81960	−	8.34779i	−0.185782	−	0.321784i	−0.943840	+	0.330404i	$0.892815\pi$
$674$	15.9666	+	27.6550i	0.615012	+	1.06523i
$675$	0.0783378			0.00301522
$676$		0			0
$677$	51.1565			1.96610			0.983051	−	0.183330i	$-0.0586878\pi$
$677$	51.1565			1.96610			0.983051	+	0.183330i	$0.0586878\pi$
$678$	−0.0374341	−	0.0648377i	−0.00143765	−	0.00249008i
$679$	7.79875	+	13.5078i	0.299288	+	0.518383i
$680$	3.19567	−	5.53506i	0.122548	−	0.212260i
$681$	0.0526680			0.00201824
$682$	31.6243	−	54.7748i	1.21096	−	2.09744i
$683$	4.17251	−	7.22700i	0.159657	−	0.276533i	−0.775088	−	0.631853i	$-0.782295\pi$
$683$	4.17251	−	7.22700i	0.159657	−	0.276533i	0.934745	+	0.355320i	$0.115628\pi$
$684$	21.1405			0.808328
$685$	−1.56260	+	2.70650i	−0.0597039	+	0.103410i
$686$	−36.8118	−	63.7599i	−1.40548	−	2.43436i
$687$	0.146983	+	0.254583i	0.00560776	+	0.00971293i
$688$	1.07469			0.0409721
$689$		0			0
$690$	0.0455944			0.00173575
$691$	18.0622	+	31.2846i	0.687117	+	1.19012i	0.972766	+	0.231788i	$0.0744574\pi$
$691$	18.0622	+	31.2846i	0.687117	+	1.19012i	−0.285649	+	0.958334i	$0.592209\pi$
$692$	−3.63961	−	6.30398i	−0.138357	−	0.239641i
$693$	20.2713	−	35.1109i	0.770043	−	1.33375i
$694$	15.0289			0.570491
$695$	−3.04763	+	5.27865i	−0.115603	+	0.200231i
$696$	0.102856	−	0.178153i	0.00389876	−	0.00675286i
$697$	−24.3530			−0.922435
$698$	37.2030	−	64.4376i	1.40816	−	2.43900i
$699$	−0.0502524	−	0.0870398i	−0.00190072	−	0.00329215i
$700$	−6.60118	−	11.4336i	−0.249501	−	0.432149i
$701$	−45.9823			−1.73673			−0.868364	−	0.495928i	$-0.834828\pi$
$701$	−45.9823			−1.73673			−0.868364	+	0.495928i	$0.834828\pi$
$702$		0			0
$703$	−10.1586			−0.383139
$704$	18.7304	+	32.4421i	0.705930	+	1.22271i
$705$	0.0559688	+	0.0969409i	0.00210791	+	0.00365100i
$706$	20.6457	−	35.7595i	0.777012	−	1.34582i
$707$	−48.5934			−1.82754
$708$	−0.0997562	+	0.172783i	−0.00374907	+	0.00649357i
$709$	−19.0475	+	32.9912i	−0.715343	+	1.23901i	0.247484	+	0.968892i	$0.420396\pi$
$709$	−19.0475	+	32.9912i	−0.715343	+	1.23901i	−0.962827	+	0.270118i	$0.912937\pi$
$710$	−14.7350			−0.552993
$711$	1.47718	−	2.55854i	0.0553984	−	0.0959529i
$712$	0.393573	+	0.681689i	0.0147498	+	0.0255474i
$713$	−7.74196	−	13.4095i	−0.289939	−	0.502188i
$714$	0.444904			0.0166501
$715$		0			0
$716$	−30.6251			−1.14452
$717$	0.122213	+	0.211678i	0.00456411	+	0.00790527i
$718$	30.7965	+	53.3411i	1.14931	+	1.99067i
$719$	13.9336	−	24.1337i	0.519635	−	0.900035i	−0.480104	−	0.877212i	$-0.659401\pi$
$719$	13.9336	−	24.1337i	0.519635	−	0.900035i	0.999740	−	0.0228234i	$-0.00726554\pi$
$720$	4.57075			0.170342
$721$	−32.5281	+	56.3404i	−1.21141	+	2.09823i
$722$	14.2781	−	24.7304i	0.531376	−	0.920371i
$723$	0.295319			0.0109830
$724$	16.8873	−	29.2497i	0.627612	−	1.08706i
$725$	−4.13161	−	7.15616i	−0.153444	−	0.265773i
$726$	−0.0345783	−	0.0598914i	−0.00128332	−	0.00222278i
$727$	−13.7750			−0.510885			−0.255443	−	0.966824i	$-0.582221\pi$
$727$	−13.7750			−0.510885			−0.255443	+	0.966824i	$0.582221\pi$
$728$		0			0
$729$	−26.9908			−0.999659
$730$	13.7342	+	23.7883i	0.508325	+	0.880444i
$731$	−1.18215	−	2.04755i	−0.0437235	−	0.0757313i
$732$	0.0359219	−	0.0622185i	0.00132771	−	0.00229966i
$733$	−6.58392			−0.243183			−0.121591	−	0.992580i	$-0.538800\pi$
$733$	−6.58392			−0.243183			−0.121591	+	0.992580i	$0.538800\pi$
$734$	−2.76785	+	4.79406i	−0.102163	+	0.176952i
$735$	0.0929804	−	0.161047i	0.00342963	−	0.00594030i
$736$	11.3584			0.418676
$737$	10.6999	−	18.5328i	0.394137	−	0.682665i
$738$	24.0340	+	41.6281i	0.884704	+	1.53235i
$739$	−2.73750	−	4.74150i	−0.100701	−	0.174419i	0.811273	−	0.584668i	$-0.198775\pi$
$739$	−2.73750	−	4.74150i	−0.100701	−	0.174419i	−0.911974	+	0.410249i	$0.865442\pi$
$740$	11.8280			0.434805
$741$		0			0
$742$	−126.700			−4.65129
$743$	13.3357	+	23.0981i	0.489239	+	0.847387i	0.999923	−	0.0123810i	$-0.00394111\pi$
$743$	13.3357	+	23.0981i	0.489239	+	0.847387i	−0.510684	+	0.859769i	$0.670608\pi$
$744$	−0.121731	−	0.210845i	−0.00446289	−	0.00772995i
$745$	7.30982	−	12.6610i	0.267811	−	0.463862i
$746$	48.9148			1.79090
$747$	−11.7654	+	20.3783i	−0.430474	+	0.745603i
$748$	14.0780	−	24.3838i	0.514742	−	0.891560i
$749$	−18.3052			−0.668857
$750$	0.0143986	−	0.0249391i	0.000525763	−	0.000910649i
$751$	−10.9034	−	18.8852i	−0.397870	−	0.689131i	0.595593	−	0.803286i	$-0.296917\pi$
$751$	−10.9034	−	18.8852i	−0.397870	−	0.689131i	−0.993463	+	0.114156i	$0.963584\pi$
$752$	6.53137	+	11.3127i	0.238175	+	0.412531i
$753$	−0.0232946			−0.000848903
$754$		0			0
$755$	12.2510			0.445860
$756$	−0.517121	−	0.895681i	−0.0188075	−	0.0325756i
$757$	4.16711	+	7.21764i	0.151456	+	0.262330i	0.931763	−	0.363067i	$-0.118270\pi$
$757$	4.16711	+	7.21764i	0.151456	+	0.262330i	−0.780307	+	0.625397i	$0.784937\pi$
$758$	1.56723	−	2.71452i	0.0569243	−	0.0985957i
$759$	0.0606183			0.00220031
$760$	2.34542	−	4.06239i	0.0850775	−	0.147359i
$761$	3.66548	−	6.34880i	0.132874	−	0.230144i	−0.791910	−	0.610638i	$-0.790913\pi$
$761$	3.66548	−	6.34880i	0.132874	−	0.230144i	0.924783	+	0.380495i	$0.124246\pi$
$762$	−0.575135			−0.0208350
$763$	−23.4450	+	40.6080i	−0.848767	+	1.47011i
$764$	−19.2990	−	33.4268i	−0.698213	−	1.20934i
$765$	−5.02780	−	8.70841i	−0.181781	−	0.314853i
$766$	46.4783			1.67933
$767$		0			0
$768$	0.0646221			0.00233185
$769$	11.1673	+	19.3423i	0.402703	+	0.697503i	0.994051	−	0.108914i	$-0.0347373\pi$
$769$	11.1673	+	19.3423i	0.402703	+	0.697503i	−0.591348	+	0.806417i	$0.701404\pi$
$770$	−14.9040	−	25.8145i	−0.537104	−	0.930292i
$771$	−0.0300204	+	0.0519968i	−0.00108116	+	0.00187262i
$772$	20.0153			0.720365
$773$	13.5795	−	23.5204i	0.488422	−	0.845971i	−0.511490	−	0.859290i	$-0.670906\pi$
$773$	13.5795	−	23.5204i	0.488422	−	0.845971i	0.999911	+	0.0133182i	$0.00423943\pi$
$774$	−2.33334	+	4.04146i	−0.0838700	+	0.145267i
$775$	−9.77959			−0.351293
$776$	3.22627	−	5.58806i	0.115816	−	0.200600i
$777$	0.124242	+	0.215194i	0.00445716	+	0.00772003i
$778$	−14.8559	−	25.7311i	−0.532608	−	0.922505i
$779$	−17.8736			−0.640388
$780$		0			0
$781$	−19.5903			−0.700997
$782$	−5.85276	−	10.1373i	−0.209294	−	0.362508i
$783$	−0.323661	−	0.560597i	−0.0115667	−	0.0200341i
$784$	10.8505	−	18.7936i	0.387518	−	0.671201i
$785$	7.13991			0.254834
$786$	−0.164720	+	0.285303i	−0.00587536	+	0.0101764i
$787$	−5.79032	+	10.0291i	−0.206403	+	0.357500i	−0.950579	−	0.310484i	$-0.899509\pi$
$787$	−5.79032	+	10.0291i	−0.206403	+	0.357500i	0.744176	+	0.667983i	$0.232842\pi$
$788$	4.11899			0.146733
$789$	0.122816	−	0.212723i	0.00437236	−	0.00757315i
$790$	−1.08606	−	1.88111i	−0.0386403	−	0.0669270i
$791$	5.99128	+	10.3772i	0.213025	+	0.368971i
$792$	−16.7721			−0.595971
$793$		0			0
$794$	59.9601			2.12790
$795$	−0.0813682	−	0.140934i	−0.00288583	−	0.00499841i
$796$	3.47824	+	6.02448i	0.123283	+	0.213532i
$797$	23.8502	−	41.3097i	0.844817	−	1.46327i	−0.0409626	−	0.999161i	$-0.513042\pi$
$797$	23.8502	−	41.3097i	0.844817	−	1.46327i	0.885780	−	0.464106i	$-0.153624\pi$
$798$	0.326532			0.0115591
$799$	14.3690	−	24.8878i	0.508338	−	0.880467i
$800$	3.58696	−	6.21280i	0.126818	−	0.219656i
$801$	1.23843			0.0437579
$802$	3.61183	−	6.25587i	0.127538	−	0.220902i
$803$	18.2598	+	31.6268i	0.644373	+	1.11609i
$804$	−0.136474	−	0.236380i	−0.00481306	−	0.00833647i
$805$	−7.29733			−0.257197
$806$		0			0
$807$	−0.0242086			−0.000852184
$808$	10.0513	+	17.4094i	0.353605	+	0.612461i
$809$	−18.1955	−	31.5155i	−0.639720	−	1.10803i	−0.985494	−	0.169709i	$-0.945717\pi$
$809$	−18.1955	−	31.5155i	−0.639720	−	1.10803i	0.345774	−	0.938318i	$-0.387616\pi$
$810$	−9.92333	+	17.1877i	−0.348670	+	0.603914i
$811$	−36.8088			−1.29253			−0.646266	−	0.763112i	$-0.723670\pi$
$811$	−36.8088			−1.29253			−0.646266	+	0.763112i	$0.723670\pi$
$812$	−54.5470	+	94.4782i	−1.91422	+	3.31553i
$813$	0.000977280	−	0.00169270i	3.42747e−5	−	5.93655e-5i
$814$	26.7050			0.936010
$815$	−1.19501	+	2.06982i	−0.0418594	+	0.0725026i
$816$	0.0333430	+	0.0577517i	0.00116724	+	0.00202172i
$817$	−0.867628	−	1.50278i	−0.0303545	−	0.0525755i
$818$	−42.2755			−1.47813
$819$		0			0
$820$	20.8108			0.726744
$821$	−16.8334	−	29.1563i	−0.587491	−	1.01756i	−0.994560	−	0.104166i	$-0.966783\pi$
$821$	−16.8334	−	29.1563i	−0.587491	−	1.01756i	0.407069	−	0.913397i	$-0.366551\pi$
$822$	0.0449986	+	0.0779398i	0.00156951	+	0.00271846i
$823$	−15.9404	+	27.6096i	−0.555649	+	0.962412i	0.442204	+	0.896914i	$0.354197\pi$
$823$	−15.9404	+	27.6096i	−0.555649	+	0.962412i	−0.997853	+	0.0654973i	$0.979137\pi$
$824$	26.9132			0.937566
$825$	0.0191432	−	0.0331569i	0.000666479	−	0.00115438i
$826$	27.1133	−	46.9616i	0.943392	−	1.63400i
$827$	−18.4625			−0.642003			−0.321002	−	0.947079i	$-0.604019\pi$
$827$	−18.4625			−0.642003			−0.321002	+	0.947079i	$0.604019\pi$
$828$	−6.80259	+	11.7824i	−0.236406	+	0.409468i
$829$	17.4831	+	30.2817i	0.607214	+	1.05173i	0.991697	+	0.128594i	$0.0410464\pi$
$829$	17.4831	+	30.2817i	0.607214	+	1.05173i	−0.384483	+	0.923132i	$0.625620\pi$
$830$	8.65026	+	14.9827i	0.300255	+	0.520057i
$831$	−0.287487			−0.00997280
$832$		0			0
$833$	−47.7420			−1.65416
$834$	0.0877633	+	0.152011i	0.00303900	+	0.00526369i
$835$	3.71920	+	6.44185i	0.128708	+	0.222929i
$836$	10.3324	−	17.8962i	0.357353	−	0.618954i
$837$	−0.766111			−0.0264807
$838$	−0.432800	+	0.749632i	−0.0149508	+	0.0258956i
$839$	14.3617	−	24.8752i	0.495820	−	0.858786i	−0.504168	−	0.863606i	$-0.668201\pi$
$839$	14.3617	−	24.8752i	0.495820	−	0.858786i	0.999988	+	0.00481947i	$0.00153409\pi$
$840$	−0.114740			−0.00395892
$841$	−19.6404	+	34.0182i	−0.677256	+	1.17304i
$842$	−38.7975	−	67.1993i	−1.33705	−	2.31584i
$843$	−0.00285960	−	0.00495297i	−9.84899e−5	−	0.000170589i
$844$	52.3172			1.80083
$845$		0			0
$846$	−56.7230			−1.95018
$847$	5.53422	+	9.58555i	0.190158	+	0.329364i
$848$	−9.49540	−	16.4465i	−0.326073	−	0.564776i
$849$	0.0902804	−	0.156370i	0.00309841	−	0.00536661i
$850$	−7.39317			−0.253584
$851$	3.26884	−	5.66179i	0.112054	−	0.194084i
$852$	−0.124934	+	0.216392i	−0.00428016	+	0.00741346i
$853$	−13.7453			−0.470629			−0.235315	−	0.971919i	$-0.575612\pi$
$853$	−13.7453			−0.470629			−0.235315	+	0.971919i	$0.575612\pi$
$854$	−9.76342	+	16.9107i	−0.334097	+	0.578674i
$855$	−3.69010	−	6.39144i	−0.126199	−	0.218583i
$856$	3.78635	+	6.55815i	0.129415	+	0.224153i
$857$	−12.6495			−0.432099			−0.216049	−	0.976382i	$-0.569317\pi$
$857$	−12.6495			−0.432099			−0.216049	+	0.976382i	$0.569317\pi$
$858$		0			0
$859$	−11.0929			−0.378485			−0.189243	−	0.981930i	$-0.560603\pi$
$859$	−11.0929			−0.378485			−0.189243	+	0.981930i	$0.560603\pi$
$860$	1.01021	+	1.74973i	0.0344477	+	0.0596652i
$861$	0.218598	+	0.378623i	0.00744981	+	0.0129034i
$862$	−2.50832	+	4.34453i	−0.0854336	+	0.147975i
$863$	−33.0295			−1.12434			−0.562169	−	0.827022i	$-0.690033\pi$
$863$	−33.0295			−1.12434			−0.562169	+	0.827022i	$0.690033\pi$
$864$	0.280994	−	0.486697i	0.00955962	−	0.0165578i
$865$	−1.27059	+	2.20073i	−0.0432015	+	0.0748272i
$866$	26.2081			0.890587
$867$	−0.0376273	+	0.0651724i	−0.00127789	+	0.00221337i
$868$	64.5568	+	111.816i	2.19120	+	3.79527i
$869$	−1.44393	−	2.50096i	−0.0489821	−	0.0848394i
$870$	−0.237958			−0.00806753
$871$		0			0
$872$	19.3980			0.656899
$873$	−5.07595	−	8.79181i	−0.171795	−	0.297558i
$874$	−4.29557	−	7.44014i	−0.145300	−	0.251667i
$875$	−2.30448	+	3.99148i	−0.0779058	+	0.134937i
$876$	0.465794			0.0157377
$877$	−7.71986	+	13.3712i	−0.260681	+	0.451513i	−0.966423	−	0.256956i	$-0.917280\pi$
$877$	−7.71986	+	13.3712i	−0.260681	+	0.451513i	0.705742	+	0.708469i	$0.250614\pi$
$878$	39.3993	−	68.2417i	1.32966	−	2.30304i
$879$	−0.190178			−0.00641453
$880$	2.23394	−	3.86930i	0.0753062	−	0.130434i
$881$	8.31299	+	14.3985i	0.280072	+	0.485098i	0.971402	−	0.237440i	$-0.0763085\pi$
$881$	8.31299	+	14.3985i	0.280072	+	0.485098i	−0.691331	+	0.722539i	$0.742975\pi$
$882$	47.1167	+	81.6084i	1.58650	+	2.74790i
$883$	57.2845			1.92778			0.963888	−	0.266309i	$-0.0858041\pi$
$883$	57.2845			1.92778			0.963888	+	0.266309i	$0.0858041\pi$
$884$		0			0
$885$	0.0696502			0.00234126
$886$	−5.50181	−	9.52942i	−0.184837	−	0.320147i
$887$	−9.23286	−	15.9918i	−0.310009	−	0.536952i	0.668355	−	0.743843i	$-0.266999\pi$
$887$	−9.23286	−	15.9918i	−0.310009	−	0.536952i	−0.978364	+	0.206891i	$0.933665\pi$
$888$	0.0513978	−	0.0890236i	0.00172480	−	0.00298744i
$889$	92.0498			3.08725
$890$	0.455265	−	0.788543i	0.0152605	−	0.0264320i
$891$	−13.1932	+	22.8513i	−0.441988	+	0.765546i
$892$	44.6405			1.49467
$893$	10.5459	−	18.2661i	0.352907	−	0.611252i
$894$	−0.210503	−	0.364601i	−0.00704026	−	0.0121941i
$895$	5.34565	+	9.25894i	0.178685	+	0.309492i
$896$	−63.7354			−2.12925
$897$		0			0
$898$	−51.8055			−1.72877
$899$	40.4054	+	69.9843i	1.34760	+	2.33411i
$900$	4.29649	+	7.44175i	0.143216	+	0.248058i
$901$	−20.8898	+	36.1822i	−0.695940	+	1.20540i
$902$	46.9862			1.56447
$903$	−0.0212226	+	0.0367586i	−0.000706243	+	0.00122325i
$904$	2.47854	−	4.29296i	0.0824350	−	0.142782i
$905$	−11.7908			−0.391939
$906$	0.176398	−	0.305530i	0.00586042	−	0.0101505i
$907$	−22.4744	−	38.9269i	−0.746251	−	1.29255i	−0.949608	−	0.313440i	$-0.898518\pi$
$907$	−22.4744	−	38.9269i	−0.746251	−	1.29255i	0.203357	−	0.979105i	$-0.434815\pi$
$908$	5.77740	+	10.0067i	0.191730	+	0.332086i
$909$	31.6279			1.04903
$910$		0			0
$911$	−44.3728			−1.47014			−0.735069	−	0.677992i	$-0.762850\pi$
$911$	−44.3728			−1.47014			−0.735069	+	0.677992i	$0.762850\pi$
$912$	0.0244717	+	0.0423862i	0.000810339	+	0.00140355i
$913$	11.5006	+	19.9197i	0.380616	+	0.659245i
$914$	−44.3879	+	76.8822i	−1.46822	+	2.54304i
$915$	−0.0250808			−0.000829146
$916$	−32.2466	+	55.8527i	−1.06546	+	1.84542i
$917$	26.3632	−	45.6624i	0.870590	−	1.50791i
$918$	−0.579164			−0.0191153
$919$	−12.5840	+	21.7961i	−0.415108	+	0.718989i	−0.995440	−	0.0953917i	$-0.969590\pi$
$919$	−12.5840	+	21.7961i	−0.415108	+	0.718989i	0.580332	+	0.814380i	$0.302923\pi$
$920$	1.50942	+	2.61439i	0.0497641	+	0.0861940i
$921$	−0.0590855	−	0.102339i	−0.00194693	−	0.00337219i
$922$	−68.8443			−2.26726
$923$		0			0
$924$	−0.505469			−0.0166287
$925$	−2.06458	−	3.57597i	−0.0678831	−	0.117577i
$926$	19.5734	+	33.9021i	0.643221	+	1.11409i
$927$	21.1715	−	36.6702i	0.695364	−	1.20441i
$928$	−59.2797			−1.94595
$929$	18.7800	−	32.5280i	0.616153	−	1.06721i	−0.374028	−	0.927417i	$-0.622024\pi$
$929$	18.7800	−	32.5280i	0.616153	−	1.06721i	0.990181	−	0.139791i	$-0.0446431\pi$
$930$	−0.140813	+	0.243895i	−0.00461743	+	0.00799762i
$931$	−35.0397			−1.14838
$932$	11.0248	−	19.0956i	0.361131	−	0.625497i
$933$	0.0475793	+	0.0824097i	0.00155768	+	0.00269797i
$934$	−29.4051	−	50.9312i	−0.962165	−	1.66652i
$935$	−9.82931			−0.321453
$936$		0			0
$937$	−17.1212			−0.559326			−0.279663	−	0.960098i	$-0.590223\pi$
$937$	−17.1212			−0.559326			−0.279663	+	0.960098i	$0.590223\pi$
$938$	37.0930	+	64.2470i	1.21113	+	2.09774i
$939$	0.0846889	+	0.146685i	0.00276372	+	0.00478690i
$940$	−12.2790	+	21.2678i	−0.400496	+	0.693679i
$941$	0.208568			0.00679913			0.00339956	−	0.999994i	$-0.498918\pi$
$941$	0.208568			0.00679913			0.00339956	+	0.999994i	$0.498918\pi$
$942$	0.102805	−	0.178063i	0.00334957	−	0.00580162i
$943$	5.75137	−	9.96166i	0.187290	−	0.324396i
$944$	8.12794			0.264542
$945$	−0.180528	+	0.312684i	−0.00587258	+	0.0101716i
$946$	2.28083	+	3.95051i	0.0741560	+	0.128442i
$947$	0.207029	+	0.358585i	0.00672755	+	0.0116525i	0.869370	−	0.494162i	$-0.164525\pi$
$947$	0.207029	+	0.358585i	0.00672755	+	0.0116525i	−0.862642	+	0.505815i	$0.831192\pi$
$948$	−0.0368337			−0.00119630
$949$		0			0
$950$	−5.42613			−0.176047
$951$	0.101221	+	0.175319i	0.00328230	+	0.00568512i
$952$	14.7287	+	25.5109i	0.477361	+	0.826813i
$953$	16.9296	−	29.3230i	0.548404	−	0.949864i	−0.449980	−	0.893039i	$-0.648569\pi$
$953$	16.9296	−	29.3230i	0.548404	−	0.949864i	0.998384	−	0.0568255i	$-0.0180979\pi$
$954$	82.4647			2.66989
$955$	−6.73731	+	11.6694i	−0.218014	+	0.377612i
$956$	−26.8121	+	46.4400i	−0.867166	+	1.50198i
$957$	−0.316368			−0.0102267
$958$	22.5662	−	39.0858i	0.729081	−	1.26281i
$959$	−7.20197	−	12.4742i	−0.232564	−	0.402812i
$960$	−0.0834005	−	0.144454i	−0.00269174	−	0.00466223i
$961$	64.6403			2.08517
$962$		0			0
$963$	11.9143			0.383932
$964$	32.3949	+	56.1097i	1.04337	+	1.80717i
$965$	−3.49368	−	6.05124i	−0.112466	−	0.194796i
$966$	−0.105072	+	0.181989i	−0.00338062	+	0.00585541i
$967$	−13.2125			−0.424885			−0.212442	−	0.977174i	$-0.568142\pi$
$967$	−13.2125			−0.424885			−0.212442	+	0.977174i	$0.568142\pi$
$968$	2.28946	−	3.96546i	0.0735860	−	0.127455i
$969$	0.0538376	−	0.0932494i	0.00172951	−	0.00299560i
$970$	−7.46397			−0.239654
$971$	8.80095	−	15.2437i	0.282436	−	0.489193i	−0.689548	−	0.724240i	$-0.742191\pi$
$971$	8.80095	−	15.2437i	0.282436	−	0.489193i	0.971984	+	0.235046i	$0.0755242\pi$
$972$	0.504871	+	0.874463i	0.0161938	+	0.0280484i
$973$	−14.0464	−	24.3291i	−0.450308	−	0.779956i
$974$	−17.9045			−0.573697
$975$		0			0
$976$	−2.92685			−0.0936861
$977$	−5.89059	−	10.2028i	−0.188457	−	0.326416i	0.756279	−	0.654249i	$-0.227015\pi$
$977$	−5.89059	−	10.2028i	−0.188457	−	0.326416i	−0.944736	+	0.327833i	$0.893682\pi$
$978$	0.0344130	+	0.0596051i	0.00110041	+	0.00190596i
$979$	0.605281	−	1.04838i	0.0193449	−	0.0335063i
$980$	40.7978			1.30324
$981$	15.2596	−	26.4304i	0.487202	−	0.843859i
$982$	−3.60605	+	6.24586i	−0.115074	+	0.199314i
$983$	45.4985			1.45118			0.725589	−	0.688128i	$-0.241567\pi$
$983$	45.4985			1.45118			0.725589	+	0.688128i	$0.241567\pi$
$984$	0.0904321	−	0.156633i	0.00288287	−	0.00499328i
$985$	−0.718974	−	1.24530i	−0.0229084	−	0.0396786i
$986$	30.5457	+	52.9067i	0.972773	+	1.68489i
$987$	−0.515917			−0.0164218
$988$		0			0
$989$	1.11674			0.0355103
$990$	9.70056	+	16.8019i	0.308304	+	0.533998i
$991$	−16.6343	−	28.8114i	−0.528405	−	0.915224i	−0.999452	−	0.0331155i	$-0.989457\pi$
$991$	−16.6343	−	28.8114i	−0.528405	−	0.915224i	0.471047	−	0.882108i	$-0.343876\pi$
$992$	−35.0790	+	60.7586i	−1.11376	+	1.92909i
$993$	−0.340588			−0.0108082
$994$	33.9565	−	58.8144i	1.07703	−	1.86548i
$995$	1.21426	−	2.10316i	0.0384946	−	0.0666746i
$996$	0.293373			0.00929589
$997$	19.8935	−	34.4566i	0.630033	−	1.09125i	−0.357511	−	0.933909i	$-0.616375\pi$
$997$	19.8935	−	34.4566i	0.630033	−	1.09125i	0.987544	−	0.157341i	$-0.0502922\pi$
$998$	9.80746	+	16.9870i	0.310450	+	0.537715i
$999$	−0.161735	−	0.280133i	−0.00511707	−	0.00886302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.o.146.3		18
13.2	odd	12		845.2.c.h.506.5		18
13.3	even	3		845.2.a.o.1.7	yes	9
13.4	even	6		845.2.e.p.191.7		18
13.5	odd	4		845.2.m.j.361.5		36
13.6	odd	12		845.2.m.j.316.14		36
13.7	odd	12		845.2.m.j.316.5		36
13.8	odd	4		845.2.m.j.361.14		36
13.9	even	3	inner	845.2.e.o.191.3		18
13.10	even	6		845.2.a.n.1.3	✓	9
13.11	odd	12		845.2.c.h.506.14		18
13.12	even	2		845.2.e.p.146.7		18
39.23	odd	6		7605.2.a.cs.1.7		9
39.29	odd	6		7605.2.a.cp.1.3		9
65.29	even	6		4225.2.a.bs.1.3		9
65.49	even	6		4225.2.a.bt.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.3	✓	9	13.10	even	6
845.2.a.o.1.7	yes	9	13.3	even	3
845.2.c.h.506.5		18	13.2	odd	12
845.2.c.h.506.14		18	13.11	odd	12
845.2.e.o.146.3		18	1.1	even	1	trivial
845.2.e.o.191.3		18	13.9	even	3	inner
845.2.e.p.146.7		18	13.12	even	2
845.2.e.p.191.7		18	13.4	even	6
845.2.m.j.316.5		36	13.7	odd	12
845.2.m.j.316.14		36	13.6	odd	12
845.2.m.j.361.5		36	13.5	odd	4
845.2.m.j.361.14		36	13.8	odd	4
4225.2.a.bs.1.3		9	65.29	even	6
4225.2.a.bt.1.7		9	65.49	even	6
7605.2.a.cp.1.3		9	39.29	odd	6
7605.2.a.cs.1.7		9	39.23	odd	6

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.10278 - 1.91007i) q^{2} +(0.00652833 + 0.0113074i) q^{3} +(-1.43225 + 2.48072i) q^{4} +1.00000 q^{5} +(0.0143986 - 0.0249391i) q^{6} +(-2.30448 + 3.99148i) q^{7} +1.90669 q^{8} +(1.49991 - 2.59793i) q^{9} +(-1.10278 - 1.91007i) q^{10} +(-1.46616 - 2.53946i) q^{11} -0.0374007 q^{12} +10.1654 q^{14} +(0.00652833 + 0.0113074i) q^{15} +(0.761834 + 1.31954i) q^{16} +(1.67603 - 2.90297i) q^{17} -6.61630 q^{18} +(1.23010 - 2.13060i) q^{19} +(-1.43225 + 2.48072i) q^{20} -0.0601778 q^{21} +(-3.23370 + 5.60094i) q^{22} +(0.791645 + 1.37117i) q^{23} +(0.0124475 + 0.0215597i) q^{24} +1.00000 q^{25} +0.0783378 q^{27} +(-6.60118 - 11.4336i) q^{28} +(-4.13161 - 7.15616i) q^{29} +(0.0143986 - 0.0249391i) q^{30} -9.77959 q^{31} +(3.58696 - 6.21280i) q^{32} +(0.0191432 - 0.0331569i) q^{33} -7.39317 q^{34} +(-2.30448 + 3.99148i) q^{35} +(4.29649 + 7.44175i) q^{36} +(-2.06458 - 3.57597i) q^{37} -5.42613 q^{38} +1.90669 q^{40} +(-3.63254 - 6.29175i) q^{41} +(0.0663628 + 0.114944i) q^{42} +(0.352665 - 0.610833i) q^{43} +8.39961 q^{44} +(1.49991 - 2.59793i) q^{45} +(1.74602 - 3.02419i) q^{46} +8.57322 q^{47} +(-0.00994701 + 0.0172287i) q^{48} +(-7.12130 - 12.3344i) q^{49} +(-1.10278 - 1.91007i) q^{50} +0.0437667 q^{51} -12.4639 q^{53} +(-0.0863893 - 0.149631i) q^{54} +(-1.46616 - 2.53946i) q^{55} +(-4.39394 + 7.61052i) q^{56} +0.0321221 q^{57} +(-9.11251 + 15.7833i) q^{58} +(2.66723 - 4.61977i) q^{59} -0.0374007 q^{60} +(-0.960460 + 1.66357i) q^{61} +(10.7847 + 18.6797i) q^{62} +(6.91306 + 11.9738i) q^{63} -12.7752 q^{64} -0.0844427 q^{66} +(3.64896 + 6.32019i) q^{67} +(4.80097 + 8.31553i) q^{68} +(-0.0103362 + 0.0179029i) q^{69} +10.1654 q^{70} +(3.34041 - 5.78577i) q^{71} +(2.85987 - 4.95344i) q^{72} -12.4541 q^{73} +(-4.55356 + 7.88700i) q^{74} +(0.00652833 + 0.0113074i) q^{75} +(3.52362 + 6.10309i) q^{76} +13.5150 q^{77} +0.984840 q^{79} +(0.761834 + 1.31954i) q^{80} +(-4.49923 - 7.79290i) q^{81} +(-8.01179 + 13.8768i) q^{82} -7.84405 q^{83} +(0.0861894 - 0.149284i) q^{84} +(1.67603 - 2.90297i) q^{85} -1.55565 q^{86} +(0.0539450 - 0.0934356i) q^{87} +(-2.79551 - 4.84197i) q^{88} +(0.206417 + 0.357525i) q^{89} -6.61630 q^{90} -4.53532 q^{92} +(-0.0638444 - 0.110582i) q^{93} +(-9.45437 - 16.3755i) q^{94} +(1.23010 - 2.13060i) q^{95} +0.0936675 q^{96} +(1.69208 - 2.93077i) q^{97} +(-15.7064 + 27.2044i) q^{98} -8.79646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 7 q^{3} - 17 q^{4} + 18 q^{5} + 2 q^{6} - 7 q^{7} + 24 q^{8} - 16 q^{9} - 3 q^{10} + 9 q^{11} + 24 q^{12} - 4 q^{14} - 7 q^{15} - 37 q^{16} + q^{17} - 20 q^{18} + 4 q^{19} - 17 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 7 * q^3 - 17 * q^4 + 18 * q^5 + 2 * q^6 - 7 * q^7 + 24 * q^8 - 16 * q^9 - 3 * q^10 + 9 * q^11 + 24 * q^12 - 4 * q^14 - 7 * q^15 - 37 * q^16 + q^17 - 20 * q^18 + 4 * q^19 - 17 * q^20 - 2 * q^21 - 12 * q^22 - 14 * q^23 + 35 * q^24 + 18 * q^25 + 44 * q^27 - 18 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 22 * q^32 + 8 * q^33 - 60 * q^34 - 7 * q^35 - 3 * q^36 + 5 * q^37 - 94 * q^38 + 24 * q^40 + 10 * q^41 + 11 * q^42 - 39 * q^43 - 50 * q^44 - 16 * q^45 - 6 * q^46 + 72 * q^47 + 3 * q^48 - 16 * q^49 - 3 * q^50 + 86 * q^51 - 16 * q^53 + 2 * q^54 + 9 * q^55 + 29 * q^56 - 64 * q^57 - 21 * q^58 + 21 * q^59 + 24 * q^60 + 3 * q^61 + 10 * q^62 - 35 * q^63 + 68 * q^64 - 98 * q^66 - q^67 + 20 * q^68 + 13 * q^69 - 4 * q^70 + q^71 + 3 * q^72 + 15 * q^74 - 7 * q^75 + 5 * q^76 - 8 * q^77 + 78 * q^79 - 37 * q^80 - 29 * q^81 + 4 * q^82 + 14 * q^83 - 12 * q^84 + q^85 - 48 * q^86 - 16 * q^87 - 42 * q^88 + 19 * q^89 - 20 * q^90 - 54 * q^92 - 31 * q^93 - 16 * q^94 + 4 * q^95 - 14 * q^96 + 34 * q^97 - 48 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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