LMFDB - Embedded newform 45.3.h.a.14.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(14,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.14"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.10
Root			$-1.44078 - 0.961330i$ of defining polynomial
Character	$\chi$	$=$	45.14
Dual form			45.3.h.a.29.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.84364 + 3.19328i) q^{2} +(1.66507 - 2.49550i) q^{3} +(-4.79800 + 8.31039i) q^{4} +(-3.30943 - 3.74802i) q^{5} +(11.0386 + 0.716233i) q^{6} +(2.22343 - 1.28370i) q^{7} -20.6340 q^{8} +(-3.45506 - 8.31039i) q^{9} +(5.86709 - 17.4779i) q^{10} +(-8.51311 + 4.91505i) q^{11} +(12.7496 + 25.8108i) q^{12} +(10.4471 + 6.03166i) q^{13} +(8.19840 + 4.73335i) q^{14} +(-14.8636 + 2.01795i) q^{15} +(-18.8497 - 32.6486i) q^{16} +4.28451 q^{17} +(20.1675 - 26.3543i) q^{18} +7.16698 q^{19} +(47.0262 - 9.51959i) q^{20} +(0.498702 - 7.68602i) q^{21} +(-31.3902 - 18.1231i) q^{22} +(-0.255270 + 0.442140i) q^{23} +(-34.3572 + 51.4923i) q^{24} +(-3.09537 + 24.8076i) q^{25} +44.4808i q^{26} +(-26.4915 - 5.21528i) q^{27} +24.6367i q^{28} +(-26.4589 + 15.2761i) q^{29} +(-33.8471 - 43.7433i) q^{30} +(9.61361 - 16.6513i) q^{31} +(28.2359 - 48.9060i) q^{32} +(-1.90944 + 29.4284i) q^{33} +(7.89910 + 13.6816i) q^{34} +(-12.1696 - 4.08516i) q^{35} +(85.6399 + 11.1604i) q^{36} -1.31851i q^{37} +(13.2133 + 22.8862i) q^{38} +(32.4473 - 16.0277i) q^{39} +(68.2868 + 77.3369i) q^{40} +(-29.9735 - 17.3052i) q^{41} +(25.4630 - 12.5778i) q^{42} +(44.9872 - 25.9734i) q^{43} -94.3297i q^{44} +(-19.7133 + 40.4523i) q^{45} -1.88250 q^{46} +(-25.4656 - 44.1078i) q^{47} +(-112.861 - 7.32289i) q^{48} +(-21.2042 + 36.7268i) q^{49} +(-84.9243 + 35.8519i) q^{50} +(7.13403 - 10.6920i) q^{51} +(-100.251 + 57.8799i) q^{52} +86.6349 q^{53} +(-32.1870 - 94.2098i) q^{54} +(46.5953 + 15.6414i) q^{55} +(-45.8783 + 26.4879i) q^{56} +(11.9336 - 17.8852i) q^{57} +(-97.5613 - 56.3270i) q^{58} +(91.7656 + 52.9809i) q^{59} +(54.5459 - 133.205i) q^{60} +(-15.6600 - 27.1239i) q^{61} +70.8961 q^{62} +(-18.3501 - 14.0423i) q^{63} +57.4297 q^{64} +(-11.9673 - 59.1175i) q^{65} +(-97.4933 + 48.1580i) q^{66} +(67.5968 + 39.0271i) q^{67} +(-20.5571 + 35.6060i) q^{68} +(0.678318 + 1.37322i) q^{69} +(-9.39131 - 46.3925i) q^{70} -72.6762i q^{71} +(71.2919 + 171.477i) q^{72} +30.3097i q^{73} +(4.21037 - 2.43086i) q^{74} +(56.7535 + 49.0310i) q^{75} +(-34.3872 + 59.5604i) q^{76} +(-12.6189 + 21.8565i) q^{77} +(111.002 + 74.0638i) q^{78} +(-57.6398 - 99.8350i) q^{79} +(-59.9861 + 178.697i) q^{80} +(-57.1251 + 57.4258i) q^{81} -127.618i q^{82} +(-30.0069 - 51.9734i) q^{83} +(61.4810 + 41.0220i) q^{84} +(-14.1793 - 16.0585i) q^{85} +(165.880 + 95.7710i) q^{86} +(-5.93457 + 91.4640i) q^{87} +(175.660 - 101.417i) q^{88} +71.2992i q^{89} +(-165.519 + 11.6296i) q^{90} +30.9713 q^{91} +(-2.44957 - 4.24278i) q^{92} +(-25.5459 - 51.7163i) q^{93} +(93.8989 - 162.638i) q^{94} +(-23.7186 - 26.8620i) q^{95} +(-75.0302 - 151.895i) q^{96} +(-110.820 + 63.9819i) q^{97} -156.372 q^{98} +(70.2593 + 53.7655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31}+ \cdots - 468 q^{99}+O(q^{100}) $ 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.84364	+	3.19328i	0.921819	+	1.59664i	0.796599	+	0.604509i	$0.206631\pi$
$2$	1.84364	+	3.19328i	0.921819	+	1.59664i	0.125221	+	0.992129i	$0.460036\pi$
$3$	1.66507	−	2.49550i	0.555024	−	0.831834i
$3$	1.66507	−	2.49550i	0.555024	−	0.831834i
$4$	−4.79800	+	8.31039i	−1.19950	+	2.07760i
$5$	−3.30943	−	3.74802i	−0.661886	−	0.749605i
$5$	−3.30943	−	3.74802i	−0.661886	−	0.749605i
$6$	11.0386	+	0.716233i	1.83977	+	0.119372i
$7$	2.22343	−	1.28370i	0.317633	−	0.183385i	−0.332704	−	0.943031i	$-0.607961\pi$
$7$	2.22343	−	1.28370i	0.317633	−	0.183385i	0.650337	+	0.759646i	$0.274628\pi$
$8$	−20.6340			−2.57925
$9$	−3.45506	−	8.31039i	−0.383896	−	0.923376i
$10$	5.86709	−	17.4779i	0.586709	−	1.74779i
$11$	−8.51311	+	4.91505i	−0.773919	+	0.446823i	−0.834271	−	0.551355i	$-0.814111\pi$
$11$	−8.51311	+	4.91505i	−0.773919	+	0.446823i	0.0603516	+	0.998177i	$0.480778\pi$
$12$	12.7496	+	25.8108i	1.06246	+	2.15090i
$13$	10.4471	+	6.03166i	0.803626	+	0.463974i	0.844738	−	0.535181i	$-0.179757\pi$
$13$	10.4471	+	6.03166i	0.803626	+	0.463974i	−0.0411114	+	0.999155i	$0.513090\pi$
$14$	8.19840	+	4.73335i	0.585600	+	0.338096i
$15$	−14.8636	+	2.01795i	−0.990910	+	0.134530i
$16$	−18.8497	−	32.6486i	−1.17810	−	2.04054i
$17$	4.28451			0.252030			0.126015	−	0.992028i	$-0.459781\pi$
$17$	4.28451			0.252030			0.126015	+	0.992028i	$0.459781\pi$
$18$	20.1675	−	26.3543i	1.12041	−	1.46413i
$19$	7.16698			0.377210			0.188605	−	0.982053i	$-0.439603\pi$
$19$	7.16698			0.377210			0.188605	+	0.982053i	$0.439603\pi$
$20$	47.0262	−	9.51959i	2.35131	−	0.475979i
$21$	0.498702	−	7.68602i	0.0237477	−	0.366001i
$22$	−31.3902	−	18.1231i	−1.42683	−	0.823779i
$23$	−0.255270	+	0.442140i	−0.0110987	+	0.0192235i	−0.871521	−	0.490357i	$-0.836866\pi$
$23$	−0.255270	+	0.442140i	−0.0110987	+	0.0192235i	0.860423	+	0.509581i	$0.170200\pi$
$24$	−34.3572	+	51.4923i	−1.43155	+	2.14551i
$25$	−3.09537	+	24.8076i	−0.123815	+	0.992305i
$26$			44.4808i			1.71080i
$27$	−26.4915	−	5.21528i	−0.981168	−	0.193159i
$28$			24.6367i			0.879884i
$29$	−26.4589	+	15.2761i	−0.912376	+	0.526760i	−0.881195	−	0.472753i	$-0.843260\pi$
$29$	−26.4589	+	15.2761i	−0.912376	+	0.526760i	−0.0311810	+	0.999514i	$0.509927\pi$
$30$	−33.8471	−	43.7433i	−1.12824	−	1.45811i
$31$	9.61361	−	16.6513i	0.310116	−	0.537137i	−0.668271	−	0.743918i	$-0.732965\pi$
$31$	9.61361	−	16.6513i	0.310116	−	0.537137i	0.978387	+	0.206781i	$0.0662986\pi$
$32$	28.2359	−	48.9060i	0.882372	−	1.52831i
$33$	−1.90944	+	29.4284i	−0.0578618	+	0.891770i
$34$	7.89910	+	13.6816i	0.232326	+	0.402401i
$35$	−12.1696	−	4.08516i	−0.347703	−	0.116719i
$36$	85.6399	+	11.1604i	2.37889	+	0.310010i
$37$		−	1.31851i		−	0.0356355i	−0.999841	−	0.0178177i	$-0.994328\pi$
$37$		−	1.31851i		−	0.0356355i	0.999841	−	0.0178177i	$-0.00567186\pi$
$38$	13.2133	+	22.8862i	0.347719	+	0.602267i
$39$	32.4473	−	16.0277i	0.831981	−	0.410967i
$40$	68.2868	+	77.3369i	1.70717	+	1.93342i
$41$	−29.9735	−	17.3052i	−0.731061	−	0.422078i	0.0877493	−	0.996143i	$-0.472033\pi$
$41$	−29.9735	−	17.3052i	−0.731061	−	0.422078i	−0.818810	+	0.574064i	$0.805366\pi$
$42$	25.4630	−	12.5778i	0.606262	−	0.299470i
$43$	44.9872	−	25.9734i	1.04621	−	0.604032i	0.124627	−	0.992204i	$-0.460227\pi$
$43$	44.9872	−	25.9734i	1.04621	−	0.604032i	0.921587	+	0.388172i	$0.126893\pi$
$44$		−	94.3297i		−	2.14386i
$45$	−19.7133	+	40.4523i	−0.438072	+	0.898940i
$46$	−1.88250			−0.0409239
$47$	−25.4656	−	44.1078i	−0.541822	−	0.938463i	−0.998800	−	0.0489851i	$-0.984401\pi$
$47$	−25.4656	−	44.1078i	−0.541822	−	0.938463i	0.456977	−	0.889478i	$-0.348932\pi$
$48$	−112.861	−	7.32289i	−2.35126	−	0.152560i
$49$	−21.2042	+	36.7268i	−0.432740	+	0.749527i
$50$	−84.9243	+	35.8519i	−1.69849	+	0.717038i
$51$	7.13403	−	10.6920i	0.139883	−	0.209647i
$52$	−100.251	+	57.8799i	−1.92790	+	1.11307i
$53$	86.6349			1.63462			0.817311	−	0.576197i	$-0.195464\pi$
$53$	86.6349			1.63462			0.817311	+	0.576197i	$0.195464\pi$
$54$	−32.1870	−	94.2098i	−0.596055	−	1.74463i
$55$	46.5953	+	15.6414i	0.847186	+	0.284388i
$56$	−45.8783	+	26.4879i	−0.819255	+	0.472997i
$57$	11.9336	−	17.8852i	0.209361	−	0.313776i
$58$	−97.5613	−	56.3270i	−1.68209	−	0.971156i
$59$	91.7656	+	52.9809i	1.55535	+	0.897982i	0.997691	+	0.0679111i	$0.0216334\pi$
$59$	91.7656	+	52.9809i	1.55535	+	0.897982i	0.557658	+	0.830071i	$0.311700\pi$
$60$	54.5459	−	133.205i	0.909098	−	2.22008i
$61$	−15.6600	−	27.1239i	−0.256721	−	0.444655i	0.708640	−	0.705570i	$-0.249309\pi$
$61$	−15.6600	−	27.1239i	−0.256721	−	0.444655i	−0.965362	+	0.260915i	$0.915976\pi$
$62$	70.8961			1.14348
$63$	−18.3501	−	14.0423i	−0.291272	−	0.222894i
$64$	57.4297			0.897339
$65$	−11.9673	−	59.1175i	−0.184112	−	0.909500i
$66$	−97.4933	+	48.1580i	−1.47717	+	0.729666i
$67$	67.5968	+	39.0271i	1.00891	+	0.582493i	0.910872	−	0.412689i	$-0.135411\pi$
$67$	67.5968	+	39.0271i	1.00891	+	0.582493i	0.0980363	+	0.995183i	$0.468744\pi$
$68$	−20.5571	+	35.6060i	−0.302311	+	0.523617i
$69$	0.678318	+	1.37322i	0.00983070	+	0.0199017i
$70$	−9.39131	−	46.3925i	−0.134162	−	0.662750i
$71$		−	72.6762i		−	1.02361i	−0.859102	−	0.511804i	$-0.828977\pi$
$71$		−	72.6762i		−	1.02361i	0.859102	−	0.511804i	$-0.171023\pi$
$72$	71.2919	+	171.477i	0.990165	+	2.38162i
$73$			30.3097i			0.415201i	0.978214	+	0.207601i	$0.0665654\pi$
$73$			30.3097i			0.415201i	−0.978214	+	0.207601i	$0.933435\pi$
$74$	4.21037	−	2.43086i	0.0568969	−	0.0328494i
$75$	56.7535	+	49.0310i	0.756713	+	0.653747i
$76$	−34.3872	+	59.5604i	−0.452463	+	0.783690i
$77$	−12.6189	+	21.8565i	−0.163881	+	0.283851i
$78$	111.002	+	74.0638i	1.42310	+	0.949535i
$79$	−57.6398	−	99.8350i	−0.729617	−	1.26373i	−0.957045	−	0.289940i	$-0.906365\pi$
$79$	−57.6398	−	99.8350i	−0.729617	−	1.26373i	0.227428	−	0.973795i	$-0.426969\pi$
$80$	−59.9861	+	178.697i	−0.749826	+	2.23371i
$81$	−57.1251	+	57.4258i	−0.705248	+	0.708961i
$82$		−	127.618i		−	1.55632i
$83$	−30.0069	−	51.9734i	−0.361529	−	0.626186i	0.626684	−	0.779274i	$-0.284412\pi$
$83$	−30.0069	−	51.9734i	−0.361529	−	0.626186i	−0.988213	+	0.153087i	$0.951078\pi$
$84$	61.4810	+	41.0220i	0.731917	+	0.488357i
$85$	−14.1793	−	16.0585i	−0.166815	−	0.188923i
$86$	165.880	+	95.7710i	1.92884	+	1.11362i
$87$	−5.93457	+	91.4640i	−0.0682135	+	1.05131i
$88$	175.660	−	101.417i	1.99613	−	1.15247i
$89$			71.2992i			0.801115i	0.916272	+	0.400558i	$0.131184\pi$
$89$			71.2992i			0.801115i	−0.916272	+	0.400558i	$0.868816\pi$
$90$	−165.519	+	11.6296i	−1.83910	+	0.129217i
$91$	30.9713			0.340344
$92$	−2.44957	−	4.24278i	−0.0266257	−	0.0461171i
$93$	−25.5459	−	51.7163i	−0.274687	−	0.556090i
$94$	93.8989	−	162.638i	0.998924	−	1.73019i
$95$	−23.7186	−	26.8620i	−0.249670	−	0.282758i
$96$	−75.0302	−	151.895i	−0.781565	−	1.58224i
$97$	−110.820	+	63.9819i	−1.14247	+	0.659607i	−0.947042	−	0.321111i	$-0.895944\pi$
$97$	−110.820	+	63.9819i	−1.14247	+	0.659607i	−0.195431	+	0.980717i	$0.562611\pi$
$98$	−156.372			−1.59563
$99$	70.2593	+	53.7655i	0.709690	+	0.543085i
$100$	−191.309	−	144.751i	−1.91309	−	1.44751i
$101$	74.5445	−	43.0383i	0.738065	−	0.426122i	−0.0833005	−	0.996524i	$-0.526546\pi$
$101$	74.5445	−	43.0383i	0.738065	−	0.426122i	0.821365	+	0.570403i	$0.193213\pi$
$102$	47.2951	+	3.06871i	0.463678	+	0.0300854i
$103$	−35.4060	−	20.4416i	−0.343747	−	0.198463i	0.318181	−	0.948030i	$-0.396928\pi$
$103$	−35.4060	−	20.4416i	−0.343747	−	0.198463i	−0.661928	+	0.749568i	$0.730261\pi$
$104$	−215.567	−	124.457i	−2.07276	−	1.19671i
$105$	−30.4578	+	23.5672i	−0.290074	+	0.224449i
$106$	159.723	+	276.649i	1.50683	+	2.60990i
$107$	1.66026			0.0155165			0.00775823	−	0.999970i	$-0.497530\pi$
$107$	1.66026			0.0155165			0.00775823	+	0.999970i	$0.497530\pi$
$108$	170.447	−	195.132i	1.57822	−	1.80678i
$109$	−148.641			−1.36368			−0.681839	−	0.731502i	$-0.738820\pi$
$109$	−148.641			−1.36368			−0.681839	+	0.731502i	$0.738820\pi$
$110$	35.9576	+	177.628i	0.326888	+	1.61480i
$111$	−3.29035	−	2.19542i	−0.0296428	−	0.0197785i
$112$	−83.8218	−	48.3946i	−0.748409	−	0.432094i
$113$	−65.7284	+	113.845i	−0.581667	+	1.00748i	0.413615	+	0.910452i	$0.364266\pi$
$113$	−65.7284	+	113.845i	−0.581667	+	1.00748i	−0.995282	+	0.0970249i	$0.969067\pi$
$114$	79.1136	+	5.13323i	0.693979	+	0.0450283i
$115$	2.50195	−	0.506473i	0.0217561	−	0.00440412i
$116$		−	293.178i		−	2.52740i
$117$	14.0299	−	107.660i	0.119914	−	0.920167i
$118$			390.711i			3.31111i
$119$	9.52631	−	5.50002i	0.0800531	−	0.0462187i
$120$	306.697	−	41.6385i	2.55581	−	0.346987i
$121$	−12.1846	+	21.1044i	−0.100699	+	0.174416i
$122$	57.7428	−	100.013i	0.473301	−	0.819782i
$123$	−93.0932	+	45.9845i	−0.756856	+	0.373858i
$124$	92.2523	+	159.786i	0.743970	+	1.28859i
$125$	103.224	−	70.4975i	0.825788	−	0.563980i
$126$	11.0100	−	84.4859i	0.0873806	−	0.670523i
$127$		−	101.150i		−	0.796460i	−0.917286	−	0.398230i	$-0.869625\pi$
$127$		−	101.150i		−	0.796460i	0.917286	−	0.398230i	$-0.130375\pi$
$128$	−7.06394	−	12.2351i	−0.0551870	−	0.0955867i
$129$	10.0904	−	155.513i	0.0782198	−	1.20553i
$130$	166.715	−	147.206i	1.28242	−	1.13235i
$131$	−74.3023	−	42.8985i	−0.567193	−	0.327469i	0.188834	−	0.982009i	$-0.439529\pi$
$131$	−74.3023	−	42.8985i	−0.567193	−	0.327469i	−0.756028	+	0.654540i	$0.772862\pi$
$132$	−235.400	−	157.066i	−1.78333	−	1.18989i
$133$	15.9353	−	9.20024i	0.119814	−	0.0691747i
$134$			287.807i			2.14781i
$135$	68.1248	+	116.550i	0.504628	+	0.863337i
$136$	−88.4068			−0.650050
$137$	34.8631	+	60.3847i	0.254475	+	0.440764i	0.964753	−	0.263158i	$-0.0847639\pi$
$137$	34.8631	+	60.3847i	0.254475	+	0.440764i	−0.710278	+	0.703922i	$0.751431\pi$
$138$	−3.13450	+	4.69778i	−0.0227138	+	0.0340419i
$139$	−69.4587	+	120.306i	−0.499703	+	0.865511i	−1.00000		0.000342926i	$-0.999891\pi$
$139$	−69.4587	+	120.306i	−0.499703	+	0.865511i	0.500297	+	0.865854i	$0.333224\pi$
$140$	92.3391	−	81.5335i	0.659565	−	0.582382i
$141$	−152.473	−	9.89312i	−1.08137	−	0.0701639i
$142$	232.075	−	133.989i	1.63433	−	0.943582i
$143$	−118.584			−0.829256
$144$	−206.196	+	269.451i	−1.43191	+	1.87119i
$145$	144.819	+	48.6136i	0.998751	+	0.335266i
$146$	−96.7872	+	55.8801i	−0.662926	+	0.382740i
$147$	56.3453	+	114.068i	0.383301	+	0.775973i
$148$	10.9573	+	6.32622i	0.0740361	+	0.0427448i
$149$	41.3586	+	23.8784i	0.277574	+	0.160258i	0.632325	−	0.774703i	$-0.282101\pi$
$149$	41.3586	+	23.8784i	0.277574	+	0.160258i	−0.354750	+	0.934961i	$0.615434\pi$
$150$	−51.9367	+	271.625i	−0.346245	+	1.81083i
$151$	−27.7457	−	48.0569i	−0.183746	−	0.318258i	0.759407	−	0.650616i	$-0.225489\pi$
$151$	−27.7457	−	48.0569i	−0.183746	−	0.318258i	−0.943153	+	0.332358i	$0.892156\pi$
$152$	−147.884			−0.972920
$153$	−14.8033	−	35.6060i	−0.0967534	−	0.232719i
$154$	−93.0585			−0.604276
$155$	−94.2249	+	19.0741i	−0.607902	+	0.123059i
$156$	−22.4857	+	346.550i	−0.144139	+	2.22148i
$157$	9.58875	+	5.53607i	0.0610749	+	0.0352616i	0.530226	−	0.847856i	$-0.322107\pi$
$157$	9.58875	+	5.53607i	0.0610749	+	0.0352616i	−0.469152	+	0.883118i	$0.655440\pi$
$158$	212.534	−	368.119i	1.34515	−	2.32987i
$159$	144.254	−	216.198i	0.907255	−	1.35973i
$160$	−276.746	+	56.0221i	−1.72966	+	0.350138i
$161$			1.31076i			0.00814134i
$162$	−288.694	−	76.5436i	−1.78206	−	0.472491i
$163$		−	216.230i		−	1.32656i	−0.748370	−	0.663282i	$-0.769163\pi$
$163$		−	216.230i		−	1.32656i	0.748370	−	0.663282i	$-0.230837\pi$
$164$	287.626	−	166.061i	1.75382	−	1.01257i
$165$	116.618	−	90.2346i	0.706773	−	0.546876i
$166$	110.644	−	191.640i	0.666528	−	1.15446i
$167$	30.9734	−	53.6475i	0.185469	−	0.321242i	−0.758265	−	0.651946i	$-0.773953\pi$
$167$	30.9734	−	53.6475i	0.185469	−	0.321242i	0.943735	+	0.330704i	$0.107286\pi$
$168$	−10.2902	+	158.594i	−0.0612514	+	0.944010i
$169$	−11.7382	−	20.3311i	−0.0694567	−	0.120302i
$170$	25.1376	−	74.8844i	0.147868	−	0.440496i
$171$	−24.7624	−	59.5604i	−0.144809	−	0.348307i
$172$			498.481i			2.89815i
$173$	166.735	+	288.794i	0.963788	+	1.66933i	0.712837	+	0.701330i	$0.247410\pi$
$173$	166.735	+	288.794i	0.963788	+	1.66933i	0.250951	+	0.968000i	$0.419257\pi$
$174$	−303.011	+	149.676i	−1.74144	+	0.860206i
$175$	24.9631	+	59.1315i	0.142647	+	0.337894i
$176$	320.939	+	185.294i	1.82352	+	1.05281i
$177$	285.010	−	140.784i	1.61023	−	0.795391i
$178$	−227.678	+	131.450i	−1.27909	+	0.738483i
$179$			193.521i			1.08112i	0.841304	+	0.540562i	$0.181788\pi$
$179$			193.521i			1.08112i	−0.841304	+	0.540562i	$0.818212\pi$
$180$	−241.590	−	357.915i	−1.34217	−	1.98842i
$181$	243.865			1.34732			0.673661	−	0.739041i	$-0.264721\pi$
$181$	243.865			1.34732			0.673661	+	0.739041i	$0.264721\pi$
$182$	57.0999	+	98.8999i	0.313736	+	0.543406i
$183$	−93.7629	−	6.08374i	−0.512365	−	0.0332445i
$184$	5.26724	−	9.12313i	0.0286263	−	0.0495822i
$185$	−4.94181	+	4.36352i	−0.0267125	+	0.0235866i
$186$	118.047	−	176.921i	0.634662	−	0.951190i
$187$	−36.4746	+	21.0586i	−0.195051	+	0.112613i
$188$	488.737			2.59966
$189$	−65.5969	+	22.4113i	−0.347073	+	0.118578i
$190$	42.0493	−	125.264i	0.221312	−	0.659284i
$191$	−122.599	+	70.7825i	−0.641879	+	0.370589i	−0.785338	−	0.619067i	$-0.787511\pi$
$191$	−122.599	+	70.7825i	−0.641879	+	0.370589i	0.143459	+	0.989656i	$0.454177\pi$
$192$	95.6247	−	143.316i	0.498045	−	0.746438i
$193$	−191.757	−	110.711i	−0.993561	−	0.573633i	−0.0872244	−	0.996189i	$-0.527800\pi$
$193$	−191.757	−	110.711i	−0.993561	−	0.573633i	−0.906337	+	0.422556i	$0.861133\pi$
$194$	−408.623	−	235.919i	−2.10631	−	1.21608i
$195$	−167.454	−	68.5706i	−0.858739	−	0.351644i
$196$	−203.476	−	352.431i	−1.03814	−	1.79812i
$197$	−28.4424			−0.144378			−0.0721889	−	0.997391i	$-0.522998\pi$
$197$	−28.4424			−0.144378			−0.0721889	+	0.997391i	$0.522998\pi$
$198$	−42.1552	+	323.481i	−0.212905	+	1.63374i
$199$	153.875			0.773244			0.386622	−	0.922238i	$-0.373642\pi$
$199$	153.875			0.773244			0.386622	+	0.922238i	$0.373642\pi$
$200$	63.8701	−	511.881i	0.319350	−	2.55941i
$201$	209.946	−	103.705i	1.04451	−	0.515946i
$202$	274.866	+	158.694i	1.36072	+	0.785615i
$203$	−39.2197	+	67.9304i	−0.193200	+	0.334633i
$204$	54.6257	+	110.587i	0.267773	+	0.542093i
$205$	34.3348	+	169.612i	0.167487	+	0.827374i
$206$		−	150.748i		−	0.731786i
$207$	4.55632	+	0.593767i	0.0220112	+	0.00286844i
$208$		−	454.779i		−	2.18644i
$209$	−61.0133	+	35.2261i	−0.291930	+	0.168546i
$210$	−131.410	−	53.8108i	−0.625761	−	0.256242i
$211$	−90.0891	+	156.039i	−0.426962	+	0.739521i	−0.996601	−	0.0823744i	$-0.973750\pi$
$211$	−90.0891	+	156.039i	−0.426962	+	0.739521i	0.569639	+	0.821895i	$0.307083\pi$
$212$	−415.675	+	719.970i	−1.96073	+	3.39608i
$213$	−181.364	−	121.011i	−0.851472	−	0.568127i
$214$	3.06092	+	5.30167i	0.0143034	+	0.0247742i
$215$	−246.231	−	82.6561i	−1.14526	−	0.384447i
$216$	546.627	+	107.612i	2.53068	+	0.498205i
$217$		−	49.3638i		−	0.227483i
$218$	−274.040	−	474.651i	−1.25706	−	2.17730i
$219$	75.6379	+	50.4679i	0.345379	+	0.230447i
$220$	−353.550	+	312.177i	−1.60705	+	1.41899i
$221$	44.7609	+	25.8427i	0.202538	+	0.116935i
$222$	0.944361	−	14.5545i	0.00425388	−	0.0655610i
$223$	186.544	−	107.701i	0.836521	−	0.482966i	−0.0195592	−	0.999809i	$-0.506226\pi$
$223$	186.544	−	107.701i	0.836521	−	0.482966i	0.856080	+	0.516843i	$0.172893\pi$
$224$		−	144.985i		−	0.647256i
$225$	216.856	−	59.9882i	0.963803	−	0.266614i
$226$	−484.717			−2.14477
$227$	−25.2080	−	43.6615i	−0.111048	−	0.192341i	0.805145	−	0.593078i	$-0.202088\pi$
$227$	−25.2080	−	43.6615i	−0.111048	−	0.192341i	−0.916193	+	0.400737i	$0.868754\pi$
$228$	91.3759	+	184.986i	0.400772	+	0.811341i
$229$	3.08352	−	5.34081i	0.0134652	−	0.0233223i	−0.859214	−	0.511616i	$-0.829047\pi$
$229$	3.08352	−	5.34081i	0.0134652	−	0.0233223i	0.872679	+	0.488294i	$0.162380\pi$
$230$	6.22999	+	7.05565i	0.0270869	+	0.0306767i
$231$	33.5317	+	67.8831i	0.145159	+	0.293866i
$232$	545.954	−	315.207i	2.35325	−	1.35865i
$233$	52.5336			0.225466			0.112733	−	0.993625i	$-0.464040\pi$
$233$	52.5336			0.225466			0.112733	+	0.993625i	$0.464040\pi$
$234$	369.653	−	153.684i	1.57971	−	0.656769i
$235$	−81.0403	+	241.417i	−0.344853	+	1.02731i
$236$	−880.584	+	508.405i	−3.73129	+	2.15426i
$237$	−345.113	−	22.3924i	−1.45617	−	0.0944827i
$238$	35.1262	+	20.2801i	0.147589	+	0.0852105i
$239$	84.5102	+	48.7920i	0.353599	+	0.204151i	0.666269	−	0.745711i	$-0.267890\pi$
$239$	84.5102	+	48.7920i	0.353599	+	0.204151i	−0.312670	+	0.949862i	$0.601223\pi$
$240$	346.058	+	447.239i	1.44191	+	1.86350i
$241$	71.3647	+	123.607i	0.296119	+	0.512893i	0.975245	−	0.221129i	$-0.0709742\pi$
$241$	71.3647	+	123.607i	0.296119	+	0.512893i	−0.679126	+	0.734022i	$0.737641\pi$
$242$	−89.8560			−0.371306
$243$	48.1889	+	238.174i	0.198308	+	0.980140i
$244$	300.547			1.23175
$245$	207.827	−	42.0708i	0.848273	−	0.171717i
$246$	−318.471	−	212.494i	−1.29460	−	0.863795i
$247$	74.8745	+	43.2288i	0.303136	+	0.175015i
$248$	−198.367	+	343.583i	−0.799869	+	1.38541i
$249$	−179.663	−	11.6573i	−0.721540	−	0.0468166i
$250$	415.425	+	199.649i	1.66170	+	0.798597i
$251$			254.631i			1.01447i	0.861809	+	0.507233i	$0.169332\pi$
$251$			254.631i			1.01447i	−0.861809	+	0.507233i	$0.830668\pi$
$252$	204.741	−	85.1215i	0.812464	−	0.337784i
$253$		−	5.01865i		−	0.0198366i
$254$	323.001	−	186.485i	1.27166	−	0.734192i
$255$	−63.6835	+	8.64594i	−0.249739	+	0.0339056i
$256$	140.906	−	244.057i	0.550415	−	0.953346i
$257$	71.3682	−	123.613i	0.277697	−	0.480986i	−0.693115	−	0.720827i	$-0.743762\pi$
$257$	71.3682	−	123.613i	0.277697	−	0.480986i	0.970812	+	0.239841i	$0.0770955\pi$
$258$	515.199	−	254.489i	1.99690	−	0.986390i
$259$	−1.69257	−	2.93162i	−0.00653502	−	0.0113190i
$260$	548.708	+	184.193i	2.11042	+	0.708436i
$261$	218.367	+	167.104i	0.836656	+	0.640245i
$262$		−	316.357i		−	1.20747i
$263$	126.234	+	218.644i	0.479979	+	0.831347i	0.999736	−	0.0229665i	$-0.00731110\pi$
$263$	126.234	+	218.644i	0.479979	+	0.831347i	−0.519758	+	0.854314i	$0.673978\pi$
$264$	39.3995	−	607.227i	0.149240	−	2.30010i
$265$	−286.712	−	324.710i	−1.08193	−	1.22532i
$266$	58.7578	+	33.9238i	0.220894	+	0.127533i
$267$	177.927	+	118.718i	0.666395	+	0.444638i
$268$	−648.660	+	374.504i	−2.42037	+	1.39740i
$269$		−	388.672i		−	1.44488i	−0.691435	−	0.722439i	$-0.743021\pi$
$269$		−	388.672i		−	1.44488i	0.691435	−	0.722439i	$-0.256979\pi$
$270$	−246.580	+	432.418i	−0.913260	+	1.60155i
$271$	−163.253			−0.602410			−0.301205	−	0.953559i	$-0.597389\pi$
$271$	−163.253			−0.602410			−0.301205	+	0.953559i	$0.597389\pi$
$272$	−80.7617	−	139.883i	−0.296918	−	0.514277i
$273$	51.5695	−	77.2889i	0.188899	−	0.283110i
$274$	−128.550	+	222.655i	−0.469160	+	0.812610i
$275$	−95.5794	−	226.404i	−0.347562	−	0.823288i
$276$	−14.6666	−	0.951630i	−0.0531397	−	0.00344793i
$277$	−419.003	+	241.912i	−1.51265	+	0.873328i	−0.512757	+	0.858534i	$0.671376\pi$
$277$	−419.003	+	241.912i	−1.51265	+	0.873328i	−0.999891	+	0.0147939i	$0.995291\pi$
$278$	−512.227			−1.84254
$279$	−171.594	−	22.3616i	−0.615032	−	0.0801493i
$280$	251.108	+	84.2934i	0.896814	+	0.301048i
$281$	231.798	−	133.829i	0.824906	−	0.476260i	−0.0271995	−	0.999630i	$-0.508659\pi$
$281$	231.798	−	133.829i	0.824906	−	0.476260i	0.852105	+	0.523371i	$0.175326\pi$
$282$	−249.514	−	505.128i	−0.884802	−	1.79124i
$283$	425.908	+	245.898i	1.50498	+	0.868898i	0.999983	+	0.00577475i	$0.00183817\pi$
$283$	425.908	+	245.898i	1.50498	+	0.868898i	0.504993	+	0.863124i	$0.331495\pi$
$284$	603.967	+	348.701i	2.12664	+	1.22782i
$285$	−106.527	+	14.4626i	−0.373781	+	0.0507460i
$286$	−218.625	−	378.670i	−0.764424	−	1.32402i
$287$	−88.8586			−0.309612
$288$	−503.985	−	65.6779i	−1.74995	−	0.228048i
$289$	−270.643			−0.936481
$290$	111.757	+	552.072i	0.385369	+	1.90370i
$291$	−24.8562	+	383.086i	−0.0854166	+	1.31645i
$292$	−251.885	−	145.426i	−0.862621	−	0.498034i
$293$	161.073	−	278.986i	0.549737	−	0.952172i	−0.448555	−	0.893755i	$-0.648061\pi$
$293$	161.073	−	278.986i	0.549737	−	0.952172i	0.998292	−	0.0584171i	$-0.0186053\pi$
$294$	−260.370	+	390.226i	−0.885614	+	1.32730i
$295$	−105.118	−	519.276i	−0.356332	−	1.76026i
$296$			27.2062i			0.0919129i
$297$	251.159	−	85.8088i	0.845652	−	0.288919i
$298$			176.092i			0.590914i
$299$	−5.33367	+	3.07940i	−0.0178384	+	0.0102990i
$300$	−679.770	+	236.392i	−2.26590	+	0.787974i
$301$	66.6839	−	115.500i	0.221541	−	0.383720i
$302$	102.306	−	177.199i	0.338762	−	0.586752i
$303$	16.7199	−	257.688i	0.0551812	−	0.850455i
$304$	−135.095	−	233.992i	−0.444392	−	0.769710i
$305$	−49.8355	+	148.459i	−0.163395	+	0.486750i
$306$	86.4078	−	112.915i	0.282378	−	0.369005i
$307$		−	426.031i		−	1.38772i	−0.720109	−	0.693861i	$-0.755908\pi$
$307$		−	426.031i		−	1.38772i	0.720109	−	0.693861i	$-0.244092\pi$
$308$	−121.091	−	209.735i	−0.393152	−	0.680959i
$309$	−109.966	+	54.3188i	−0.355876	+	0.175789i
$310$	−234.625	−	265.720i	−0.756856	−	0.857162i
$311$	−1.01150	−	0.583987i	−0.00325240	−	0.00187777i	0.498373	−	0.866963i	$-0.333931\pi$
$311$	−1.01150	−	0.583987i	−0.00325240	−	0.00187777i	−0.501625	+	0.865085i	$0.667264\pi$
$312$	−669.518	+	330.716i	−2.14589	+	1.05999i
$313$	225.989	−	130.475i	0.722009	−	0.416852i	−0.0934824	−	0.995621i	$-0.529800\pi$
$313$	225.989	−	130.475i	0.722009	−	0.416852i	0.815492	+	0.578769i	$0.196467\pi$
$314$			40.8260i			0.130019i
$315$	8.09748	+	115.249i	0.0257063	+	0.365869i
$316$	1106.22			3.50071
$317$	−65.5178	−	113.480i	−0.206681	−	0.357981i	0.743986	−	0.668195i	$-0.232933\pi$
$317$	−65.5178	−	113.480i	−0.206681	−	0.357981i	−0.950667	+	0.310213i	$0.899599\pi$
$318$	956.330	+	62.0508i	3.00733	+	0.195128i
$319$	150.165	−	260.094i	0.470737	−	0.815340i
$320$	−190.060	−	215.248i	−0.593936	−	0.672650i
$321$	2.76446	−	4.14318i	0.00861201	−	0.0129071i
$322$	−4.18560	+	2.41656i	−0.0129988	+	0.00750484i
$323$	30.7071			0.0950683
$324$	−203.145	−	750.261i	−0.626989	−	2.31562i
$325$	−181.969	+	240.499i	−0.559905	+	0.739996i
$326$	690.482	−	398.650i	2.11804	−	1.22285i
$327$	−247.498	+	370.934i	−0.756874	+	1.13435i
$328$	618.474	+	357.076i	1.88559	+	1.08865i
$329$	−113.242	−	65.3803i	−0.344201	−	0.198724i
$330$	503.144	+	206.032i	1.52468	+	0.624339i
$331$	−96.7419	−	167.562i	−0.292272	−	0.506229i	0.682075	−	0.731282i	$-0.261078\pi$
$331$	−96.7419	−	167.562i	−0.292272	−	0.506229i	−0.974347	+	0.225053i	$0.927745\pi$
$332$	575.893			1.73462
$333$	−10.9573	+	4.55554i	−0.0329049	+	0.0136803i
$334$	228.415			0.683877
$335$	−77.4325	−	382.512i	−0.231142	−	1.14183i
$336$	−260.338	+	128.597i	−0.774816	+	0.382729i
$337$	401.485	+	231.798i	1.19135	+	0.687827i	0.958613	−	0.284712i	$-0.0918980\pi$
$337$	401.485	+	231.798i	1.19135	+	0.687827i	0.232738	+	0.972539i	$0.425231\pi$
$338$	43.2819	−	74.9664i	0.128053	−	0.221794i
$339$	174.658	+	353.585i	0.515214	+	1.04302i
$340$	201.484	−	40.7868i	0.592601	−	0.119961i
$341$			189.005i			0.554268i
$342$	144.540	−	188.881i	0.422631	−	0.552284i
$343$			234.682i			0.684203i
$344$	−928.267	+	535.935i	−2.69845	+	1.55795i
$345$	2.90202	−	7.08693i	0.00841165	−	0.0205418i
$346$	−614.799	+	1064.86i	−1.77688	+	3.07764i
$347$	4.85934	−	8.41662i	0.0140039	−	0.0242554i	−0.858939	−	0.512079i	$-0.828876\pi$
$347$	4.85934	−	8.41662i	0.0140039	−	0.0242554i	0.872942	+	0.487823i	$0.162209\pi$
$348$	−731.627	−	488.163i	−2.10238	−	1.40277i
$349$	24.6679	+	42.7260i	0.0706816	+	0.122424i	0.899200	−	0.437537i	$-0.144149\pi$
$349$	24.6679	+	42.7260i	0.0706816	+	0.122424i	−0.828519	+	0.559962i	$0.810816\pi$
$350$	−142.800	+	188.731i	−0.408001	+	0.539232i
$351$	−245.304	−	214.273i	−0.698871	−	0.610463i
$352$			555.123i			1.57705i
$353$	47.6810	+	82.5859i	0.135074	+	0.233954i	0.925626	−	0.378441i	$-0.123540\pi$
$353$	47.6810	+	82.5859i	0.135074	+	0.233954i	−0.790552	+	0.612395i	$0.790206\pi$
$354$	975.019	+	650.562i	2.75429	+	1.83774i
$355$	−272.392	+	240.517i	−0.767302	+	0.677511i
$356$	−592.524	−	342.094i	−1.66439	−	0.960938i
$357$	2.13670	−	32.9309i	0.00598514	−	0.0922433i
$358$	−617.966	+	356.783i	−1.72616	+	0.996600i
$359$		−	539.284i		−	1.50219i	−0.660197	−	0.751093i	$-0.729527\pi$
$359$		−	539.284i		−	1.50219i	0.660197	−	0.751093i	$-0.270473\pi$
$360$	406.764	−	834.694i	1.12990	−	2.31859i
$361$	−309.634			−0.857713
$362$	449.599	+	778.729i	1.24199	+	2.15118i
$363$	32.3777	+	65.5470i	0.0891948	+	0.180570i
$364$	−148.600	+	257.383i	−0.408243	+	0.707098i
$365$	113.601	−	100.308i	0.311237	−	0.274816i
$366$	−153.438	−	310.627i	−0.419229	−	0.848707i
$367$	−262.482	+	151.544i	−0.715211	+	0.412927i	−0.812987	−	0.582281i	$-0.802160\pi$
$367$	−262.482	+	151.544i	−0.715211	+	0.412927i	0.0977766	+	0.995208i	$0.468827\pi$
$368$	19.2470			0.0523016
$369$	−40.2526	+	308.882i	−0.109086	+	0.837078i
$370$	−23.0448	−	7.73582i	−0.0622833	−	0.0209076i
$371$	192.627	−	111.213i	0.519209	−	0.299766i
$372$	552.352	+	35.8390i	1.48482	+	0.0963413i
$373$	−113.159	−	65.3325i	−0.303376	−	0.175154i	0.340582	−	0.940215i	$-0.389376\pi$
$373$	−113.159	−	65.3325i	−0.303376	−	0.175154i	−0.643959	+	0.765060i	$0.722709\pi$
$374$	−134.492	−	77.6489i	−0.359604	−	0.207617i
$375$	−4.05204	−	374.978i	−0.0108054	−	0.999942i
$376$	525.459	+	910.121i	1.39750	+	2.42054i
$377$	−368.560			−0.977612
$378$	−192.502	−	168.151i	−0.509265	−	0.444843i
$379$	545.141			1.43837			0.719183	−	0.694821i	$-0.244516\pi$
$379$	545.141			1.43837			0.719183	+	0.694821i	$0.244516\pi$
$380$	337.036	−	68.2268i	0.886937	−	0.179544i
$381$	−252.421	−	168.423i	−0.662522	−	0.442054i
$382$	−452.056	−	260.995i	−1.18339	−	0.683232i
$383$	−0.623248	+	1.07950i	−0.00162728	+	0.00281853i	−0.866838	−	0.498590i	$-0.833851\pi$
$383$	−0.623248	+	1.07950i	−0.00162728	+	0.00281853i	0.865211	+	0.501409i	$0.167185\pi$
$384$	−42.2947	−	2.74426i	−0.110142	−	0.00714651i
$385$	123.680	−	25.0368i	0.321247	−	0.0650305i
$386$		−	816.445i		−	2.11514i
$387$	−371.282	−	284.121i	−0.959386	−	0.734163i
$388$		−	1227.94i		−	3.16480i
$389$	−345.001	+	199.187i	−0.886893	+	0.512048i	−0.872925	−	0.487855i	$-0.837780\pi$
$389$	−345.001	+	199.187i	−0.886893	+	0.512048i	−0.0139679	+	0.999902i	$0.504446\pi$
$390$	−89.7600	−	661.147i	−0.230154	−	1.69525i
$391$	−1.09371	+	1.89435i	−0.00279720	+	0.00484490i
$392$	437.529	−	757.822i	1.11615	−	1.93322i
$393$	−230.772	+	113.993i	−0.587206	+	0.290057i
$394$	−52.4376	−	90.8245i	−0.133090	−	0.230519i
$395$	−183.429	+	546.432i	−0.464378	+	1.38337i
$396$	−783.916	+	325.915i	−1.97959	+	0.823018i
$397$			685.998i			1.72795i	0.503531	+	0.863977i	$0.332034\pi$
$397$			685.998i			1.72795i	−0.503531	+	0.863977i	$0.667966\pi$
$398$	283.691	+	491.367i	0.712791	+	1.23459i
$399$	3.57419	−	55.0856i	0.00895787	−	0.138059i
$400$	868.281	−	366.556i	2.17070	−	0.916390i
$401$	44.9212	+	25.9353i	0.112023	+	0.0646764i	0.554965	−	0.831874i	$-0.312732\pi$
$401$	44.9212	+	25.9353i	0.112023	+	0.0646764i	−0.442942	+	0.896550i	$0.646065\pi$
$402$	718.223	+	479.220i	1.78663	+	1.19209i
$403$	200.869	−	115.972i	0.498435	−	0.287772i
$404$			825.992i			2.04453i
$405$	404.285	+	24.0595i	0.998234	+	0.0594062i
$406$	−289.227			−0.712383
$407$	6.48055	+	11.2246i	0.0159227	+	0.0275790i
$408$	−147.204	+	220.619i	−0.360794	+	0.540734i
$409$	135.648	−	234.950i	0.331658	−	0.574449i	−0.651179	−	0.758924i	$-0.725725\pi$
$409$	135.648	−	234.950i	0.331658	−	0.574449i	0.982837	+	0.184475i	$0.0590586\pi$
$410$	−478.316	+	422.343i	−1.16662	+	1.03011i
$411$	208.740	+	13.5439i	0.507883	+	0.0329536i
$412$	339.756	−	196.158i	0.824650	−	0.476112i
$413$	272.046			0.658707
$414$	6.50415	+	15.6443i	0.0157105	+	0.0377881i
$415$	−95.4921	+	284.469i	−0.230101	+	0.685467i
$416$	589.969	−	340.619i	1.41819	−	0.818795i
$417$	184.570	+	373.653i	0.442614	+	0.896050i
$418$	−224.973	−	129.888i	−0.538213	−	0.310738i
$419$	23.9467	+	13.8256i	0.0571520	+	0.0329967i	0.528304	−	0.849055i	$-0.322828\pi$
$419$	23.9467	+	13.8256i	0.0571520	+	0.0329967i	−0.471152	+	0.882052i	$0.656162\pi$
$420$	−49.7157	−	366.192i	−0.118371	−	0.871885i
$421$	218.613	+	378.649i	0.519271	+	0.899403i	0.999749	+	0.0223967i	$0.00712970\pi$
$421$	218.613	+	378.649i	0.519271	+	0.899403i	−0.480478	+	0.877007i	$0.659537\pi$
$422$	−664.367			−1.57433
$423$	−278.567	+	364.025i	−0.658552	+	0.860578i
$424$	−1787.63			−4.21610
$425$	−13.2622	+	106.289i	−0.0312051	+	0.250091i
$426$	52.0531	−	802.245i	0.122190	−	1.88320i
$427$	−69.6378	−	40.2054i	−0.163086	−	0.0941579i
$428$	−7.96594	+	13.7974i	−0.0186120	+	0.0322369i
$429$	−197.450	+	295.926i	−0.460257	+	0.689803i
$430$	−190.017	−	938.670i	−0.441899	−	2.18295i
$431$			54.3602i			0.126126i	0.998010	+	0.0630629i	$0.0200869\pi$
$431$			54.3602i			0.126126i	−0.998010	+	0.0630629i	$0.979913\pi$
$432$	329.085	+	963.217i	0.761771	+	2.22967i
$433$		−	526.426i		−	1.21576i	−0.794028	−	0.607882i	$-0.792019\pi$
$433$		−	526.426i		−	1.21576i	0.794028	−	0.607882i	$-0.207981\pi$
$434$	157.632	−	91.0091i	0.363208	−	0.209698i
$435$	362.449	−	280.451i	0.833217	−	0.644714i
$436$	713.180	−	1235.26i	1.63573	−	2.83317i
$437$	−1.82951	+	3.16881i	−0.00418653	+	0.00725128i
$438$	−21.7088	+	334.577i	−0.0495635	+	0.763875i
$439$	208.124	+	360.481i	0.474087	+	0.821142i	0.999560	−	0.0296681i	$-0.00944503\pi$
$439$	208.124	+	360.481i	0.474087	+	0.821142i	−0.525473	+	0.850810i	$0.676112\pi$
$440$	−961.448	−	322.744i	−2.18511	−	0.733510i
$441$	378.476	+	49.3219i	0.858223	+	0.111841i
$442$			190.579i			0.431173i
$443$	−213.582	−	369.935i	−0.482127	−	0.835069i	0.517662	−	0.855585i	$-0.326802\pi$
$443$	−213.582	−	369.935i	−0.482127	−	0.835069i	−0.999790	+	0.0205163i	$0.993469\pi$
$444$	34.0319	−	16.8104i	0.0766484	−	0.0378614i
$445$	267.231	−	235.960i	0.600520	−	0.530247i
$446$	687.840	+	397.125i	1.54224	+	0.890414i
$447$	128.454	−	63.4512i	0.287368	−	0.141949i
$448$	127.691	−	73.7224i	0.285024	−	0.164559i
$449$		−	236.730i		−	0.527239i	−0.964627	−	0.263620i	$-0.915084\pi$
$449$		−	236.730i		−	0.527239i	0.964627	−	0.263620i	$-0.0849164\pi$
$450$	591.362	+	581.884i	1.31414	+	1.29307i
$451$	340.224			0.754376
$452$	−630.730	−	1092.46i	−1.39542	−	2.41694i
$453$	−166.125	−	10.7789i	−0.366721	−	0.0237945i
$454$	92.9488	−	160.992i	0.204733	−	0.354608i
$455$	−102.497	−	116.081i	−0.225269	−	0.255123i
$456$	−246.237	+	369.044i	−0.539994	+	0.809308i
$457$	604.296	−	348.891i	1.32231	−	0.763437i	0.338214	−	0.941069i	$-0.390177\pi$
$457$	604.296	−	348.891i	1.32231	−	0.763437i	0.984097	+	0.177633i	$0.0568439\pi$
$458$	22.7396			0.0496497
$459$	−113.503	−	22.3450i	−0.247284	−	0.0486818i
$460$	−7.79536	+	23.2222i	−0.0169464	+	0.0504831i
$461$	−332.339	+	191.876i	−0.720910	+	0.416217i	−0.815087	−	0.579338i	$-0.803311\pi$
$461$	−332.339	+	191.876i	−0.720910	+	0.416217i	0.0941777	+	0.995555i	$0.469978\pi$
$462$	−154.949	+	232.228i	−0.335388	+	0.502657i
$463$	−233.924	−	135.056i	−0.505235	−	0.291698i	0.225638	−	0.974211i	$-0.427553\pi$
$463$	−233.924	−	135.056i	−0.505235	−	0.291698i	−0.730873	+	0.682514i	$0.760887\pi$
$464$	997.483	+	575.897i	2.14975	+	1.24116i
$465$	−109.292	+	266.898i	−0.235036	+	0.573974i
$466$	96.8529	+	167.754i	0.207839	+	0.359987i
$467$	777.952			1.66585			0.832926	−	0.553385i	$-0.186664\pi$
$467$	777.952			1.66585			0.832926	+	0.553385i	$0.186664\pi$
$468$	827.377	+	633.145i	1.76790	+	1.35287i
$469$	200.396			0.427283
$470$	−920.321	+	186.302i	−1.95813	+	0.396388i
$471$	29.7812	−	14.7108i	0.0632298	−	0.0312331i
$472$	−1893.50	−	1093.21i	−4.01164	−	2.31612i
$473$	−255.321	+	442.228i	−0.539790	+	0.934943i
$474$	−564.758	−	1143.32i	−1.19147	−	2.41208i
$475$	−22.1845	+	177.796i	−0.0467042	+	0.374307i
$476$			105.556i			0.221757i
$477$	−299.329	−	719.970i	−0.627525	−	1.50937i
$478$			359.819i			0.752760i
$479$	62.8429	−	36.2824i	0.131196	−	0.0757460i	−0.432966	−	0.901410i	$-0.642533\pi$
$479$	62.8429	−	36.2824i	0.131196	−	0.0757460i	0.564162	+	0.825664i	$0.309200\pi$
$480$	−320.998	+	783.900i	−0.668747	+	1.63313i
$481$	7.95281	−	13.7747i	0.0165339	−	0.0286376i
$482$	−263.141	+	455.774i	−0.545936	+	0.945590i
$483$	3.27099	+	2.18250i	0.00677224	+	0.00451864i
$484$	−116.924	−	202.518i	−0.241578	−	0.418425i
$485$	606.556	+	203.612i	1.25063	+	0.419819i
$486$	−671.712	+	592.987i	−1.38212	+	1.22014i
$487$		−	729.487i		−	1.49792i	−0.662616	−	0.748959i	$-0.730554\pi$
$487$		−	729.487i		−	1.49792i	0.662616	−	0.748959i	$-0.269446\pi$
$488$	323.129	+	559.676i	0.662150	+	1.14688i
$489$	−539.602	−	360.039i	−1.10348	−	0.736275i
$490$	517.501	+	586.085i	1.05612	+	1.19609i
$491$	3.30449	+	1.90785i	0.00673012	+	0.00388564i	0.503361	−	0.864076i	$-0.332096\pi$
$491$	3.30449	+	1.90785i	0.00673012	+	0.00388564i	−0.496631	+	0.867962i	$0.665430\pi$
$492$	64.5128	−	994.275i	0.131124	−	2.02088i
$493$	−113.364	+	65.4505i	−0.229946	+	0.132760i
$494$			318.793i			0.645330i
$495$	−31.0038	−	441.266i	−0.0626340	−	0.891447i
$496$	−724.853			−1.46140
$497$	−93.2942	−	161.590i	−0.187715	−	0.325131i
$498$	−294.009	−	595.207i	−0.590380	−	1.19519i
$499$	−102.651	+	177.797i	−0.205714	+	0.356307i	−0.950360	−	0.311152i	$-0.899285\pi$
$499$	−102.651	+	177.797i	−0.205714	+	0.356307i	0.744646	+	0.667460i	$0.232618\pi$
$500$	90.5948	+	1196.07i	0.181190	+	2.39215i
$501$	−82.3044	−	166.621i	−0.164280	−	0.332577i
$502$	−813.107	+	469.448i	−1.61974	+	0.935155i
$503$	224.016			0.445360			0.222680	−	0.974892i	$-0.428519\pi$
$503$	224.016			0.445360			0.222680	+	0.974892i	$0.428519\pi$
$504$	378.637	+	289.749i	0.751263	+	0.574899i
$505$	−408.008	−	136.963i	−0.807937	−	0.271213i
$506$	16.0259	−	9.25257i	0.0316718	−	0.0182857i
$507$	−70.2813	−	4.56015i	−0.138622	−	0.00899438i
$508$	840.599	+	485.320i	1.65472	+	0.955354i
$509$	−399.073	−	230.405i	−0.784033	−	0.452662i	0.0538245	−	0.998550i	$-0.482859\pi$
$509$	−399.073	−	230.405i	−0.784033	−	0.452662i	−0.837858	+	0.545889i	$0.816192\pi$
$510$	−145.018	−	187.419i	−0.284349	−	0.367488i
$511$	38.9085	+	67.3915i	0.0761418	+	0.131882i
$512$	982.608			1.91916
$513$	−189.864	−	37.3778i	−0.370106	−	0.0728613i
$514$	526.309			1.02395
$515$	40.5577	+	200.353i	0.0787528	+	0.389034i
$516$	1243.96	+	830.007i	2.41078	+	1.60854i
$517$	433.584	+	250.330i	0.838653	+	0.484197i
$518$	6.24097	−	10.8097i	0.0120482	−	0.0208681i
$519$	998.313	+	64.7748i	1.92353	+	0.124807i
$520$	246.933	+	1219.83i	0.474870	+	2.34583i
$521$			182.438i			0.350168i	0.984554	+	0.175084i	$0.0560197\pi$
$521$			182.438i			0.350168i	−0.984554	+	0.175084i	$0.943980\pi$
$522$	−131.019	+	1005.39i	−0.250994	+	1.92603i
$523$			431.339i			0.824741i	0.911016	+	0.412370i	$0.135299\pi$
$523$			431.339i			0.824741i	−0.911016	+	0.412370i	$0.864701\pi$
$524$	713.006	−	411.654i	1.36070	−	0.785599i
$525$	189.128	+	36.1627i	0.360244	+	0.0688814i
$526$	−465.461	+	806.202i	−0.884907	+	1.53270i
$527$	41.1896	−	71.3426i	0.0781587	−	0.135375i
$528$	996.788	−	492.375i	1.88786	−	0.932529i
$529$	264.370	+	457.902i	0.499754	+	0.865599i
$530$	508.295	−	1514.20i	0.959046	−	2.85698i
$531$	123.236	−	945.660i	0.232083	−	1.78090i
$532$			176.571i			0.331901i
$533$	−208.758	−	361.580i	−0.391666	−	0.678386i
$534$	−51.0669	+	787.045i	−0.0956308	+	1.47387i
$535$	−5.49451	−	6.22270i	−0.0102701	−	0.0116312i
$536$	−1394.80	−	805.285i	−2.60223	−	1.50240i
$537$	482.932	+	322.227i	0.899315	+	0.600050i
$538$	1241.14	−	716.571i	2.30695	−	1.33192i
$539$		−	416.879i		−	0.773431i
$540$	−1295.44	+	6.93361i	−2.39897	+	0.0128400i
$541$	−649.924			−1.20134			−0.600669	−	0.799498i	$-0.705099\pi$
$541$	−649.924			−1.20134			−0.600669	+	0.799498i	$0.705099\pi$
$542$	−300.980	−	521.312i	−0.555313	−	0.961830i
$543$	406.053	−	608.566i	0.747796	−	1.12075i
$544$	120.977	−	209.539i	0.222384	−	0.385181i
$545$	491.916	+	557.110i	0.902599	+	1.02222i
$546$	341.880	+	22.1827i	0.626154	+	0.0406276i
$547$	−368.334	+	212.658i	−0.673371	+	0.388771i	−0.797353	−	0.603513i	$-0.793767\pi$
$547$	−368.334	+	212.658i	−0.673371	+	0.388771i	0.123982	+	0.992285i	$0.460434\pi$
$548$	−669.094			−1.22097
$549$	−171.304	+	223.856i	−0.312029	+	0.407752i
$550$	546.757	−	722.619i	0.994103	−	1.31385i
$551$	−189.631	+	109.483i	−0.344157	+	0.198699i
$552$	−13.9964	−	28.3351i	−0.0253559	−	0.0513317i
$553$	−256.316	−	147.984i	−0.463501	−	0.267602i
$554$	−1544.98	−	891.995i	−2.78878	−	1.61010i
$555$	2.66069	+	19.5979i	0.00479404	+	0.0353115i
$556$	−666.526	−	1154.46i	−1.19879	−	2.07636i
$557$	−325.885			−0.585073			−0.292536	−	0.956254i	$-0.594499\pi$
$557$	−325.885			−0.585073			−0.292536	+	0.956254i	$0.594499\pi$
$558$	−244.950	−	589.174i	−0.438979	−	1.05587i
$559$	626.650			1.12102
$560$	96.0183	+	474.325i	0.171461	+	0.847008i
$561$	−8.18103	+	126.086i	−0.0145829	+	0.224753i
$562$	854.705	+	493.464i	1.52083	+	0.878050i
$563$	−353.382	+	612.075i	−0.627676	+	1.08717i	0.360341	+	0.932821i	$0.382660\pi$
$563$	−353.382	+	612.075i	−0.627676	+	1.08717i	−0.988017	+	0.154346i	$0.950673\pi$
$564$	813.783	−	1219.64i	1.44288	−	2.16249i
$565$	644.217	−	130.410i	1.14021	−	0.230814i
$566$			1813.39i			3.20387i
$567$	−53.2962	+	201.014i	−0.0939967	+	0.354521i
$568$			1499.60i			2.64015i
$569$	−485.178	+	280.118i	−0.852686	+	0.492299i	−0.861556	−	0.507662i	$-0.830510\pi$
$569$	−485.178	+	280.118i	−0.852686	+	0.492299i	0.00887015	+	0.999961i	$0.497177\pi$
$570$	−242.581	−	313.508i	−0.425581	−	0.550014i
$571$	105.346	−	182.465i	0.184494	−	0.319553i	−0.758912	−	0.651193i	$-0.774269\pi$
$571$	105.346	−	182.465i	0.184494	−	0.319553i	0.943406	+	0.331640i	$0.107602\pi$
$572$	568.965	−	985.475i	0.994693	−	1.72286i
$573$	−27.4982	+	423.804i	−0.0479899	+	0.739623i
$574$	−163.823	−	283.750i	−0.285406	−	0.494338i
$575$	−10.1783	−	7.70122i	−0.0177014	−	0.0133934i
$576$	−198.423	−	477.263i	−0.344485	−	0.828582i
$577$		−	502.258i		−	0.870464i	−0.900318	−	0.435232i	$-0.856666\pi$
$577$		−	502.258i		−	0.870464i	0.900318	−	0.435232i	$-0.143334\pi$
$578$	−498.968	−	864.237i	−0.863266	−	1.49522i
$579$	−595.570	+	294.189i	−1.02862	+	0.508098i
$580$	−1098.84	+	970.252i	−1.89455	+	1.67285i
$581$	−133.436	−	77.0395i	−0.229667	−	0.132598i
$582$	−1269.12	+	626.899i	−2.18063	+	1.07715i
$583$	−737.533	+	425.815i	−1.26507	+	0.730386i
$584$		−	625.411i		−	1.07091i
$585$	−449.942	+	303.707i	−0.769131	+	0.519157i
$586$	1187.84			2.02703
$587$	204.886	+	354.873i	0.349040	+	0.604554i	0.986079	−	0.166277i	$-0.0531746\pi$
$587$	204.886	+	354.873i	0.349040	+	0.604554i	−0.637040	+	0.770831i	$0.719841\pi$
$588$	−1218.29	−	79.0482i	−2.07193	−	0.134436i
$589$	68.9006	−	119.339i	0.116979	−	0.202613i
$590$	1464.39	−	1293.03i	2.48202	−	2.19157i
$591$	−47.3587	+	70.9782i	−0.0801332	+	0.120098i
$592$	−43.0476	+	24.8535i	−0.0727155	+	0.0419823i
$593$	−944.139			−1.59214			−0.796070	−	0.605204i	$-0.793092\pi$
$593$	−944.139			−1.59214			−0.796070	+	0.605204i	$0.793092\pi$
$594$	737.057	+	643.818i	1.24084	+	1.08387i
$595$	−52.1409	−	17.5029i	−0.0876317	−	0.0294167i
$596$	−396.877	+	229.137i	−0.665902	+	0.384458i
$597$	256.214	−	383.997i	0.429169	−	0.643210i
$598$	−19.6667	−	11.3546i	−0.0328875	−	0.0189876i
$599$	461.021	+	266.171i	0.769652	+	0.444359i	0.832750	−	0.553649i	$-0.186765\pi$
$599$	461.021	+	266.171i	0.769652	+	0.444359i	−0.0630986	+	0.998007i	$0.520098\pi$
$600$	−1171.05	−	1011.71i	−1.95176	−	1.68618i
$601$	−257.783	−	446.493i	−0.428923	−	0.742917i	0.567855	−	0.823129i	$-0.307774\pi$
$601$	−257.783	−	446.493i	−0.428923	−	0.742917i	−0.996778	+	0.0802121i	$0.974440\pi$
$602$	491.764			0.816883
$603$	90.7785	−	696.597i	0.150545	−	1.15522i
$604$	532.496			0.881615
$605$	119.424	−	24.1751i	0.197395	−	0.0399589i
$606$	853.694	−	421.692i	1.40874	−	0.695862i
$607$	−148.223	−	85.5764i	−0.244189	−	0.140983i	0.372912	−	0.927867i	$-0.378360\pi$
$607$	−148.223	−	85.5764i	−0.244189	−	0.140983i	−0.617101	+	0.786884i	$0.711693\pi$
$608$	202.366	−	350.509i	0.332839	−	0.576494i
$609$	104.217	+	210.982i	0.171128	+	0.346440i
$610$	−565.948	+	114.566i	−0.927784	+	0.187813i
$611$		−	614.400i		−	1.00557i
$612$	366.926	+	47.8167i	0.599552	+	0.0781319i
$613$			875.826i			1.42875i	0.699761	+	0.714377i	$0.253290\pi$
$613$			875.826i			1.42875i	−0.699761	+	0.714377i	$0.746710\pi$
$614$	1360.43	−	785.447i	2.21569	−	1.27923i
$615$	480.436	+	196.733i	0.781197	+	0.319892i
$616$	260.378	−	450.988i	0.422692	−	0.732124i
$617$	−565.874	+	980.122i	−0.917137	+	1.58853i	−0.113396	+	0.993550i	$0.536173\pi$
$617$	−565.874	+	980.122i	−0.917137	+	1.58853i	−0.803742	+	0.594978i	$0.797161\pi$
$618$	−376.192	−	251.006i	−0.608725	−	0.406159i
$619$	−260.187	−	450.658i	−0.420335	−	0.728042i	0.575637	−	0.817705i	$-0.304754\pi$
$619$	−260.187	−	450.658i	−0.420335	−	0.728042i	−0.995972	+	0.0896637i	$0.971421\pi$
$620$	293.578	−	874.563i	0.473513	−	1.41058i
$621$	9.06836	−	10.3817i	0.0146028	−	0.0167176i
$622$		−	4.30664i		−	0.00692386i
$623$	91.5266	+	158.529i	0.146913	+	0.254460i
$624$	−1134.90	−	757.241i	−1.81875	−	1.21353i
$625$	−605.837	−	153.578i	−0.969340	−	0.245725i
$626$	833.284	+	481.097i	1.33112	+	0.768525i
$627$	−13.6849	+	210.913i	−0.0218261	+	0.336384i
$628$	−92.0138	+	53.1242i	−0.146519	+	0.0845926i
$629$		−	5.64918i		−	0.00898121i
$630$	−353.092	+	238.334i	−0.560463	+	0.378308i
$631$	−607.475			−0.962718			−0.481359	−	0.876523i	$-0.659857\pi$
$631$	−607.475			−0.962718			−0.481359	+	0.876523i	$0.659857\pi$
$632$	1189.34	+	2060.00i	1.88187	+	3.25949i
$633$	239.390	+	484.633i	0.378184	+	0.765614i
$634$	241.582	−	418.433i	0.381044	−	0.659988i
$635$	−379.114	+	334.750i	−0.597030	+	0.527165i
$636$	1104.56	+	2236.12i	1.73673	+	3.51591i
$637$	−443.047	+	255.794i	−0.695522	+	0.401560i
$638$	1107.40			1.73574
$639$	−603.967	+	251.101i	−0.945176	+	0.392959i
$640$	−22.4799	+	66.9670i	−0.0351248	+	0.104636i
$641$	161.252	−	93.0990i	0.251564	−	0.145240i	−0.368916	−	0.929463i	$-0.620271\pi$
$641$	161.252	−	93.0990i	0.251564	−	0.145240i	0.620480	+	0.784222i	$0.286938\pi$
$642$	18.3270	+	1.18913i	0.0285467	+	0.00185223i
$643$	−690.674	−	398.761i	−1.07414	−	0.620157i	−0.144833	−	0.989456i	$-0.546264\pi$
$643$	−690.674	−	398.761i	−1.07414	−	0.620157i	−0.929311	+	0.369299i	$0.879598\pi$
$644$	−10.8929	−	6.28901i	−0.0169144	−	0.00976554i
$645$	−616.260	+	476.841i	−0.955442	+	0.739288i
$646$	56.6127	+	98.0561i	0.0876357	+	0.151790i
$647$	849.489			1.31297			0.656483	−	0.754341i	$-0.272043\pi$
$647$	849.489			1.31297			0.656483	+	0.754341i	$0.272043\pi$
$648$	1178.72	−	1184.93i	1.81901	−	1.82859i
$649$	−1041.61			−1.60495
$650$	−1103.46	−	137.685i	−1.69764	−	0.211823i
$651$	−123.188	−	82.1944i	−0.189228	−	0.126259i
$652$	1796.95	+	1037.47i	2.75607	+	1.59122i
$653$	520.594	−	901.696i	0.797235	−	1.38085i	−0.124175	−	0.992260i	$-0.539629\pi$
$653$	520.594	−	901.696i	0.797235	−	1.38085i	0.921410	−	0.388591i	$-0.127038\pi$
$654$	−1640.79	−	106.461i	−2.50885	−	0.162785i
$655$	85.1137	+	420.456i	0.129945	+	0.641918i
$656$			1304.79i			1.98901i
$657$	251.885	−	104.722i	0.383387	−	0.159394i
$658$		−	482.151i		−	0.732752i
$659$	556.318	−	321.190i	0.844185	−	0.487390i	−0.0144997	−	0.999895i	$-0.504616\pi$
$659$	556.318	−	321.190i	0.844185	−	0.487390i	0.858685	+	0.512505i	$0.171282\pi$
$660$	190.353	+	1402.08i	0.288413	+	2.12437i
$661$	394.759	−	683.742i	0.597214	−	1.03441i	−0.396016	−	0.918244i	$-0.629608\pi$
$661$	394.759	−	683.742i	0.597214	−	1.03441i	0.993230	−	0.116162i	$-0.0370591\pi$
$662$	356.714	−	617.847i	0.538843	−	0.933304i
$663$	139.021	−	68.6710i	0.209684	−	0.103576i
$664$	619.163	+	1072.42i	0.932474	+	1.61509i
$665$	−87.2194	−	29.2783i	−0.131157	−	0.0440275i
$666$	−34.7485	−	26.5910i	−0.0521749	−	0.0399265i
$667$		−	15.5980i		−	0.0233854i
$668$	297.221	+	514.802i	0.444941	+	0.770661i
$669$	41.8408	−	644.852i	0.0625422	−	0.963904i
$670$	1078.71	−	952.477i	1.61001	−	1.42161i
$671$	266.631	+	153.939i	0.397363	+	0.229418i
$672$	−361.811	−	241.411i	−0.538410	−	0.359243i
$673$	879.824	−	507.967i	1.30732	−	0.754780i	0.325669	−	0.945484i	$-0.394410\pi$
$673$	879.824	−	507.967i	1.30732	−	0.754780i	0.981648	+	0.190704i	$0.0610771\pi$
$674$			1709.40i			2.53621i
$675$	211.380	−	641.049i	0.313156	−	0.949702i
$676$	225.279			0.333253
$677$	−371.811	−	643.996i	−0.549204	−	0.951249i	−0.998329	−	0.0577802i	$-0.981598\pi$
$677$	−371.811	−	643.996i	−0.549204	−	0.951249i	0.449126	−	0.893469i	$-0.351736\pi$
$678$	−807.090	+	1209.61i	−1.19040	+	1.78409i
$679$	−164.267	+	284.518i	−0.241924	+	0.419025i
$680$	292.576	+	331.351i	0.430259	+	0.487281i
$681$	−150.930	−	9.79301i	−0.221631	−	0.0143803i
$682$	−603.546	+	348.458i	−0.884965	+	0.510935i
$683$	152.482			0.223254			0.111627	−	0.993750i	$-0.464394\pi$
$683$	152.482			0.223254			0.111627	+	0.993750i	$0.464394\pi$
$684$	613.780	+	79.9861i	0.897339	+	0.116939i
$685$	110.946	−	330.507i	0.161965	−	0.482491i
$686$	−749.403	+	432.668i	−1.09242	+	0.630711i
$687$	−8.19373	−	16.5878i	−0.0119268	−	0.0241452i
$688$	−1695.99	−	979.179i	−2.46510	−	1.42322i
$689$	905.087	+	522.552i	1.31362	+	0.758422i
$690$	27.9808	−	3.79879i	0.0405519	−	0.00550549i
$691$	−388.586	−	673.050i	−0.562353	−	0.974023i	−0.997291	−	0.0735628i	$-0.976563\pi$
$691$	−388.586	−	673.050i	−0.562353	−	0.974023i	0.434938	−	0.900460i	$-0.356770\pi$
$692$	−3199.99			−4.62426
$693$	225.235	+	29.3520i	0.325015	+	0.0423550i
$694$	35.8355			0.0516361
$695$	680.779	−	137.811i	0.979537	−	0.198289i
$696$	122.454	−	1887.27i	0.175940	−	2.71160i
$697$	−128.422	−	74.1444i	−0.184249	−	0.106376i
$698$	−90.9573	+	157.543i	−0.130311	+	0.225706i
$699$	87.4722	−	131.098i	0.125139	−	0.187550i
$700$	−611.179	−	76.2599i	−0.873113	−	0.108943i
$701$		−	461.657i		−	0.658569i	−0.944231	−	0.329284i	$-0.893192\pi$
$701$		−	461.657i		−	0.658569i	0.944231	−	0.329284i	$-0.106808\pi$
$702$	231.980	−	1178.36i	0.330456	−	1.67858i
$703$		−	9.44975i		−	0.0134420i
$704$	−488.906	+	282.270i	−0.694468	+	0.400952i
$705$	467.519	+	604.214i	0.663148	+	0.857041i
$706$	−175.813	+	304.517i	−0.249027	+	0.431327i
$707$	110.496	−	191.385i	0.156289	−	0.270701i
$708$	−197.510	+	3044.03i	−0.278969	+	4.29948i
$709$	179.227	+	310.431i	0.252789	+	0.437843i	0.964293	−	0.264839i	$-0.0853189\pi$
$709$	179.227	+	310.431i	0.252789	+	0.437843i	−0.711504	+	0.702682i	$0.751986\pi$
$710$	−1270.23	−	426.397i	−1.78905	−	0.600560i
$711$	−630.519	+	823.945i	−0.886805	+	1.15885i
$712$		−	1471.19i		−	2.06628i
$713$	4.90812	+	8.50112i	0.00688376	+	0.0119230i
$714$	109.097	−	53.8896i	0.152796	−	0.0754756i
$715$	392.444	+	444.454i	0.548872	+	0.621614i
$716$	−1608.24	−	928.515i	−2.24614	−	1.29681i
$717$	262.476	−	129.653i	0.366076	−	0.180827i
$718$	1722.08	−	994.245i	2.39845	−	1.38474i
$719$			283.414i			0.394178i	0.980386	+	0.197089i	$0.0631488\pi$
$719$			283.414i			0.394178i	−0.980386	+	0.197089i	$0.936851\pi$
$720$	1692.30	−	118.903i	2.35041	−	0.165142i
$721$	−104.964			−0.145580
$722$	−570.854	−	988.748i	−0.790656	−	1.36946i
$723$	427.290	+	27.7244i	0.590995	+	0.0383463i
$724$	−1170.07	+	2026.61i	−1.61611	+	2.79919i
$725$	−297.063	−	703.668i	−0.409741	−	0.970576i
$726$	−149.617	+	224.236i	−0.206084	+	0.308865i
$727$	134.545	−	77.6796i	0.185069	−	0.106850i	−0.404603	−	0.914492i	$-0.632590\pi$
$727$	134.545	−	77.6796i	0.185069	−	0.106850i	0.589672	+	0.807643i	$0.299257\pi$
$728$	−639.063			−0.877833
$729$	674.602	+	276.322i	0.925380	+	0.379042i
$730$	529.750	+	177.830i	0.725685	+	0.243602i
$731$	192.748	−	111.283i	0.263677	−	0.152234i
$732$	500.433	−	750.016i	0.683652	−	1.02461i
$733$	90.8735	+	52.4658i	0.123975	+	0.0715768i	0.560705	−	0.828016i	$-0.310530\pi$
$733$	90.8735	+	52.4658i	0.123975	+	0.0715768i	−0.436730	+	0.899593i	$0.643864\pi$
$734$	−967.845	−	558.786i	−1.31859	−	0.761288i
$735$	241.059	−	588.684i	0.327972	−	0.800930i
$736$	14.4155	+	24.9684i	0.0195863	+	0.0339245i
$737$	−767.279			−1.04108
$738$	−1060.56	+	440.929i	−1.43707	+	0.597465i
$739$	−627.375			−0.848951			−0.424476	−	0.905439i	$-0.639542\pi$
$739$	−627.375			−0.848951			−0.424476	+	0.905439i	$0.639542\pi$
$740$	−12.5517	−	62.0046i	−0.0169617	−	0.0837900i
$741$	232.549	−	114.870i	0.313831	−	0.155021i
$742$	710.268	+	410.073i	0.957234	+	0.552659i
$743$	193.295	−	334.797i	0.260155	−	0.450602i	−0.706128	−	0.708084i	$-0.749560\pi$
$743$	193.295	−	334.797i	0.260155	−	0.450602i	0.966283	+	0.257483i	$0.0828930\pi$
$744$	527.115	+	1067.12i	0.708488	+	1.43430i
$745$	−47.3765	−	234.037i	−0.0635926	−	0.314143i
$746$		−	481.798i		−	0.645842i
$747$	−328.244	+	428.940i	−0.439416	+	0.574217i
$748$		−	404.157i		−	0.540317i
$749$	3.69147	−	2.13127i	0.00492853	−	0.00284549i
$750$	1189.94	−	704.263i	1.58658	−	0.939018i
$751$	−452.601	+	783.928i	−0.602665	+	1.04385i	0.389751	+	0.920920i	$0.372561\pi$
$751$	−452.601	+	783.928i	−0.602665	+	1.04385i	−0.992416	+	0.122926i	$0.960772\pi$
$752$	−960.038	+	1662.83i	−1.27665	+	2.21122i
$753$	635.433	+	423.979i	0.843868	+	0.563054i
$754$	−679.491	−	1176.91i	−0.901182	−	1.56089i
$755$	−88.2962	+	263.032i	−0.116949	+	0.348387i
$756$	128.488	−	652.665i	0.169957	−	0.863313i
$757$			332.222i			0.438867i	0.975627	+	0.219433i	$0.0704209\pi$
$757$			332.222i			0.438867i	−0.975627	+	0.219433i	$0.929579\pi$
$758$	1005.04	+	1740.78i	1.32591	+	2.29655i
$759$	−12.5240	−	8.35641i	−0.0165007	−	0.0110098i
$760$	489.411	+	554.272i	0.643961	+	0.729305i
$761$	−396.726	−	229.050i	−0.521322	−	0.300986i	0.216153	−	0.976359i	$-0.430649\pi$
$761$	−396.726	−	229.050i	−0.521322	−	0.300986i	−0.737475	+	0.675374i	$0.763982\pi$
$762$	72.4472	−	1116.56i	0.0950751	−	1.46530i
$763$	−330.492	+	190.810i	−0.433149	+	0.250079i
$764$		−	1358.46i		−	1.77809i
$765$	−84.4617	+	173.318i	−0.110407	+	0.226560i
$766$	−4.59618			−0.00600023
$767$	639.126	+	1107.00i	0.833280	+	1.44328i
$768$	−374.425	−	758.004i	−0.487532	−	0.986984i
$769$	458.196	−	793.618i	0.595833	−	1.03201i	−0.397595	−	0.917561i	$-0.630155\pi$
$769$	458.196	−	793.618i	0.595833	−	1.03201i	0.993429	−	0.114453i	$-0.0365115\pi$
$770$	307.970	+	348.786i	0.399962	+	0.452968i
$771$	−189.644	−	383.925i	−0.245972	−	0.497957i
$772$	1840.11	−	1062.39i	2.38356	−	1.37615i
$773$	1186.06			1.53436			0.767178	−	0.641434i	$-0.221660\pi$
$773$	1186.06			1.53436			0.767178	+	0.641434i	$0.221660\pi$
$774$	222.767	−	1709.42i	0.287813	−	2.20856i
$775$	383.321	+	290.033i	0.494607	+	0.374236i
$776$	2286.66	−	1320.20i	2.94673	−	1.70129i
$777$	−10.1341	−	0.657544i	−0.0130426	−	0.000846261i
$778$	−1272.12	−	734.456i	−1.63511	−	0.944031i
$779$	−214.820	−	124.026i	−0.275763	−	0.159212i
$780$	1373.29	−	1062.61i	1.76063	−	1.36232i
$781$	357.207	+	618.701i	0.457371	+	0.792190i
$782$	−8.06559			−0.0103141
$783$	780.605	−	266.695i	0.996942	−	0.340607i
$784$	1598.77			2.03925
$785$	−10.9840	−	54.2601i	−0.0139923	−	0.0691211i
$786$	−789.470	−	526.757i	−1.00441	−	0.670175i
$787$	−764.249	−	441.240i	−0.971092	−	0.560660i	−0.0715229	−	0.997439i	$-0.522786\pi$
$787$	−764.249	−	441.240i	−0.971092	−	0.560660i	−0.899569	+	0.436779i	$0.856119\pi$
$788$	136.467	−	236.368i	0.173181	−	0.299959i
$789$	755.817	+	49.0406i	0.957943	+	0.0621554i
$790$	−2083.09	+	421.683i	−2.63682	+	0.533775i
$791$			337.501i			0.426677i
$792$	−1449.73	−	1109.40i	−1.83047	−	1.40076i
$793$		−	377.823i		−	0.476448i
$794$	−2190.58	+	1264.73i	−2.75892	+	1.59286i
$795$	−1287.71	+	174.825i	−1.61976	+	0.219906i
$796$	−738.295	+	1278.76i	−0.927507	+	1.60649i
$797$	71.9016	−	124.537i	0.0902153	−	0.156258i	−0.817386	−	0.576090i	$-0.804578\pi$
$797$	71.9016	−	124.537i	0.0902153	−	0.156258i	0.907602	+	0.419832i	$0.137911\pi$
$798$	182.493	−	90.1446i	0.228688	−	0.112963i
$799$	−109.108	−	188.980i	−0.136556	−	0.236521i
$800$	1125.84	+	851.848i	1.40730	+	1.06481i
$801$	592.524	−	246.343i	0.739731	−	0.307545i
$802$			191.261i			0.238480i
$803$	−148.974	−	258.030i	−0.185521	−	0.321332i
$804$	−145.491	+	2242.31i	−0.180958	+	2.78894i
$805$	4.91274	−	4.33785i	0.00610279	−	0.00538863i
$806$	740.661	+	427.621i	0.918934	+	0.530547i
$807$	−969.932	−	647.167i	−1.20190	−	0.801942i
$808$	−1538.15	+	888.054i	−1.90366	+	1.09908i
$809$			52.3078i			0.0646574i	0.999477	+	0.0323287i	$0.0102923\pi$
$809$			52.3078i			0.0646574i	−0.999477	+	0.0323287i	$0.989708\pi$
$810$	668.526	+	1335.35i	0.825341	+	1.64858i
$811$	1518.65			1.87256			0.936281	−	0.351253i	$-0.114244\pi$
$811$	1518.65			1.87256			0.936281	+	0.351253i	$0.114244\pi$
$812$	−376.352	−	651.861i	−0.463488	−	0.802785i
$813$	−271.828	+	407.398i	−0.334352	+	0.501105i
$814$	−23.8956	+	41.3883i	−0.0293557	+	0.0508456i
$815$	−810.435	+	715.597i	−0.994399	+	0.878034i
$816$	−483.553	−	31.3750i	−0.592590	−	0.0384498i
$817$	322.422	−	186.151i	0.394642	−	0.227847i
$818$	1000.35			1.22292
$819$	−107.008	−	257.383i	−0.130657	−	0.314266i
$820$	−1574.28	−	528.462i	−1.91985	−	0.644466i
$821$	950.059	−	548.517i	1.15720	−	0.668108i	0.206567	−	0.978432i	$-0.433771\pi$
$821$	950.059	−	548.517i	1.15720	−	0.668108i	0.950631	+	0.310324i	$0.100438\pi$
$822$	341.591	+	691.534i	0.415561	+	0.841282i
$823$	828.873	+	478.550i	1.00714	+	0.581470i	0.910352	−	0.413835i	$-0.135811\pi$
$823$	828.873	+	478.550i	1.00714	+	0.581470i	0.0967841	+	0.995305i	$0.469144\pi$
$824$	730.568	+	421.793i	0.886611	+	0.511885i
$825$	−724.139	−	138.461i	−0.877744	−	0.167831i
$826$	501.554	+	868.717i	0.607208	+	1.05172i
$827$	−171.626			−0.207529			−0.103764	−	0.994602i	$-0.533089\pi$
$827$	−171.626			−0.207529			−0.103764	+	0.994602i	$0.533089\pi$
$828$	−26.7957	+	35.0159i	−0.0323620	+	0.0422898i
$829$	203.896			0.245954			0.122977	−	0.992410i	$-0.460756\pi$
$829$	203.896			0.245954			0.122977	+	0.992410i	$0.460756\pi$
$830$	−1084.44	+	219.525i	−1.30655	+	0.264488i
$831$	−93.9800	+	1448.42i	−0.113093	+	1.74299i
$832$	599.976	+	346.397i	0.721126	+	0.416342i
$833$	−90.8499	+	157.357i	−0.109063	+	0.188904i
$834$	−852.895	+	1278.26i	−1.02266	+	1.53269i
$835$	−303.576	+	61.4534i	−0.363564	+	0.0735969i
$836$		−	676.059i		−	0.808683i
$837$	−341.520	+	390.979i	−0.408029	+	0.467120i
$838$			101.958i			0.121668i
$839$	−1348.10	+	778.323i	−1.60679	+	0.927680i	−0.616705	+	0.787194i	$0.711533\pi$
$839$	−1348.10	+	778.323i	−1.60679	+	0.927680i	−0.990083	+	0.140486i	$0.955134\pi$
$840$	628.468	−	486.286i	0.748176	−	0.578912i
$841$	46.2156	−	80.0477i	0.0549531	−	0.0951816i
$842$	−806.087	+	1396.18i	−0.957347	+	1.65817i
$843$	51.9910	−	801.289i	0.0616738	−	0.950520i
$844$	−864.495	−	1497.35i	−1.02428	−	1.77411i
$845$	−37.3549	+	111.279i	−0.0442069	+	0.131692i
$846$	−1676.01	−	218.413i	−1.98110	−	0.258171i
$847$			62.5654i			0.0738670i
$848$	−1633.04	−	2828.51i	−1.92576	−	3.33551i
$849$	1322.81	−	653.416i	1.55808	−	0.769631i
$850$	−363.860	+	153.608i	−0.428070	+	0.180715i
$851$	0.582966	+	0.336576i	0.000685037	+	0.000395506i
$852$	1875.83	−	926.589i	2.20168	−	1.08755i
$853$	−488.377	+	281.964i	−0.572540	+	0.330556i	−0.758163	−	0.652065i	$-0.773903\pi$
$853$	−488.377	+	281.964i	−0.572540	+	0.330556i	0.185623	+	0.982621i	$0.440570\pi$
$854$		−	296.497i		−	0.347186i
$855$	−141.285	+	289.921i	−0.165245	+	0.339089i
$856$	−34.2579			−0.0400209
$857$	−476.953	−	826.107i	−0.556538	−	0.963952i	−0.997782	−	0.0665649i	$-0.978796\pi$
$857$	−476.953	−	826.107i	−0.556538	−	0.963952i	0.441244	−	0.897387i	$-0.354537\pi$
$858$	−1309.00	−	84.9334i	−1.52564	−	0.0989900i
$859$	−422.728	+	732.186i	−0.492116	+	0.852371i	−0.999959	−	0.00907936i	$-0.997110\pi$
$859$	−422.728	+	732.186i	−0.492116	+	0.852371i	0.507842	+	0.861450i	$0.330443\pi$
$860$	1868.32	−	1649.69i	2.17246	−	1.91824i
$861$	−147.956	+	221.747i	−0.171842	+	0.257546i
$862$	−173.587	+	100.221i	−0.201377	+	0.116265i
$863$	−1109.42			−1.28554			−0.642768	−	0.766061i	$-0.722214\pi$
$863$	−1109.42			−1.28554			−0.642768	+	0.766061i	$0.722214\pi$
$864$	−1003.07	+	1148.34i	−1.16096	+	1.32909i
$865$	530.609	−	1580.67i	0.613420	−	1.82737i
$866$	1681.02	−	970.538i	1.94113	−	1.12071i
$867$	−450.640	+	675.390i	−0.519770	+	0.778997i
$868$	410.233	+	236.848i	0.472618	+	0.272866i
$869$	981.388	+	566.605i	1.12933	+	0.652019i
$870$	1563.78	+	640.351i	1.79745	+	0.736036i
$871$	470.796	+	815.442i	0.540523	+	0.936214i
$872$	3067.06			3.51727
$873$	914.604	+	699.894i	1.04766	+	0.801712i
$874$	−13.4918			−0.0154369
$875$	139.013	−	289.254i	0.158872	−	0.330576i
$876$	−782.318	+	386.435i	−0.893058	+	0.441136i
$877$	878.724	+	507.331i	1.00197	+	0.578485i	0.908829	−	0.417168i	$-0.136977\pi$
$877$	878.724	+	507.331i	1.00197	+	0.578485i	0.0931364	+	0.995653i	$0.470311\pi$
$878$	−767.411	+	1329.19i	−0.874044	+	1.51389i
$879$	−428.013	−	866.491i	−0.486932	−	0.985769i
$880$	−367.637	−	1816.10i	−0.417769	−	2.06375i
$881$			1226.86i			1.39257i	0.717764	+	0.696287i	$0.245166\pi$
$881$			1226.86i			1.39257i	−0.717764	+	0.696287i	$0.754834\pi$
$882$	540.275	+	1299.51i	0.612556	+	1.47337i
$883$			659.407i			0.746780i	0.927674	+	0.373390i	$0.121805\pi$
$883$			659.407i			0.746780i	−0.927674	+	0.373390i	$0.878195\pi$
$884$	−429.526	+	247.987i	−0.485889	+	0.280528i
$885$	−1470.88	−	602.311i	−1.66202	−	0.680577i
$886$	787.537	−	1364.05i	0.888868	−	1.53956i
$887$	385.984	−	668.543i	0.435156	−	0.753713i	−0.562152	−	0.827034i	$-0.690026\pi$
$887$	385.984	−	668.543i	0.435156	−	0.753713i	0.997308	+	0.0733209i	$0.0233597\pi$
$888$	67.8932	+	45.3003i	0.0764563	+	0.0510139i
$889$	−129.846	−	224.901i	−0.146059	−	0.252982i
$890$	1246.16	+	418.319i	1.40018	+	0.470021i
$891$	204.061	−	769.645i	0.229025	−	0.863799i
$892$			2067.01i			2.31727i
$893$	−182.512	−	316.120i	−0.204381	−	0.353998i
$894$	439.439	+	293.207i	0.491543	+	0.327972i
$895$	725.322	−	640.444i	0.810415	−	0.715580i
$896$	−31.4123	−	18.1359i	−0.0350584	−	0.0202410i
$897$	−1.19631	+	18.4376i	−0.00133368	+	0.0205548i
$898$	755.945	−	436.445i	0.841810	−	0.486019i
$899$			587.432i			0.653428i
$900$	−541.950	+	2089.98i	−0.602166	+	2.32220i
$901$	371.189			0.411974
$902$	627.249	+	1086.43i	0.695398	+	1.20447i
$903$	−177.197	−	358.725i	−0.196231	−	0.397260i
$904$	1356.24	−	2349.08i	1.50027	−	2.59854i
$905$	−807.055	−	914.013i	−0.891773	−	1.00996i
$906$	−271.854	−	550.355i	−0.300060	−	0.607455i
$907$	105.197	−	60.7354i	0.115983	−	0.0669629i	−0.440886	−	0.897563i	$-0.645336\pi$
$907$	105.197	−	60.7354i	0.115983	−	0.0669629i	0.556869	+	0.830600i	$0.312002\pi$
$908$	483.792			0.532810
$909$	−615.221	−	470.794i	−0.676811	−	0.517925i
$910$	181.711	−	541.314i	0.199683	−	0.594850i
$911$	−1000.46	+	577.616i	−1.09820	+	0.634046i	−0.935748	−	0.352670i	$-0.885274\pi$
$911$	−1000.46	+	577.616i	−1.09820	+	0.634046i	−0.162453	+	0.986716i	$0.551940\pi$
$912$	−808.871	−	52.4830i	−0.886920	−	0.0575472i
$913$	510.904	+	294.971i	0.559588	+	0.323078i
$914$	2228.21	+	1286.46i	2.43786	+	1.40750i
$915$	287.499	+	371.559i	0.314207	+	0.406076i
$916$	29.5895	+	51.2505i	0.0323029	+	0.0559503i
$917$	−220.275			−0.240212
$918$	−137.905	−	403.643i	−0.150224	−	0.439699i
$919$	−994.576			−1.08224			−0.541119	−	0.840946i	$-0.681999\pi$
$919$	−994.576			−1.08224			−0.541119	+	0.840946i	$0.681999\pi$
$920$	−51.6252	+	10.4506i	−0.0561144	+	0.0113593i
$921$	−1063.16	−	709.372i	−1.15436	−	0.770220i
$922$	−1225.43	−	707.501i	−1.32910	−	0.767354i
$923$	438.358	−	759.258i	0.474927	−	0.822598i
$924$	−725.020	−	47.0424i	−0.784654	−	0.0509117i
$925$	32.7092	+	4.08129i	0.0353612	+	0.00441220i
$926$		−	995.977i		−	1.07557i
$927$	−47.5481	+	364.864i	−0.0512924	+	0.393597i
$928$			1725.33i			1.85919i
$929$	140.236	−	80.9655i	0.150954	−	0.0871534i	−0.422620	−	0.906307i	$-0.638890\pi$
$929$	140.236	−	80.9655i	0.150954	−	0.0871534i	0.573575	+	0.819153i	$0.305556\pi$
$930$	−1053.77	+	143.065i	−1.13309	+	0.153833i
$931$	−151.970	+	263.221i	−0.163234	+	0.282729i
$932$	−252.056	+	436.574i	−0.270447	+	0.468427i
$933$	−3.14155	+	1.55181i	−0.00336715	+	0.00166324i
$934$	1434.26	+	2484.22i	1.53561	+	2.65976i
$935$	199.638	+	67.0156i	0.213517	+	0.0716745i
$936$	−289.493	+	2221.45i	−0.309288	+	2.37334i
$937$			660.489i			0.704898i	0.935831	+	0.352449i	$0.114651\pi$
$937$			660.489i			0.704898i	−0.935831	+	0.352449i	$0.885349\pi$
$938$	369.457	+	639.919i	0.393878	+	0.682216i
$939$	50.6880	−	781.206i	0.0539808	−	0.831955i
$940$	−1617.44	−	1831.80i	−1.72068	−	1.94872i
$941$	−1378.06	−	795.624i	−1.46446	−	0.845509i	−0.465252	−	0.885179i	$-0.654036\pi$
$941$	−1378.06	−	795.624i	−1.46446	−	0.845509i	−0.999213	+	0.0396696i	$0.987369\pi$
$942$	101.881	+	67.9783i	0.108154	+	0.0721638i
$943$	15.3026	−	8.83498i	0.0162276	−	0.00936902i
$944$		−	3994.69i		−	4.23167i
$945$	301.086	+	171.690i	0.318610	+	0.181683i
$946$	−1882.88			−1.99035
$947$	781.678	+	1353.91i	0.825426	+	1.42968i	0.901594	+	0.432584i	$0.142398\pi$
$947$	781.678	+	1353.91i	0.825426	+	1.42968i	−0.0761680	+	0.997095i	$0.524269\pi$
$948$	1841.94	−	2760.58i	1.94298	−	2.91201i
$949$	−182.818	+	316.650i	−0.192643	+	0.333667i
$950$	−608.651	+	256.950i	−0.640686	+	0.270474i
$951$	−392.282	−	25.4529i	−0.412494	−	0.0267644i
$952$	−196.566	+	113.488i	−0.206477	+	0.119210i
$953$	−996.612			−1.04576			−0.522881	−	0.852405i	$-0.675143\pi$
$953$	−996.612			−1.04576			−0.522881	+	0.852405i	$0.675143\pi$
$954$	1747.21	−	2283.20i	1.83145	−	2.39330i
$955$	671.027	+	225.254i	0.702646	+	0.235868i
$956$	−810.961	+	468.209i	−0.848285	+	0.489758i
$957$	−399.028	−	807.812i	−0.416957	−	0.844109i
$958$	231.719	+	133.783i	0.241878	+	0.139648i
$959$	155.031	+	89.5074i	0.161659	+	0.0933341i
$960$	−853.615	+	115.890i	−0.889182	+	0.120719i
$961$	295.657	+	512.093i	0.307656	+	0.532875i
$962$	58.6484			0.0609651
$963$	−5.73631	−	13.7974i	−0.00595670	−	0.0143275i
$964$	−1369.63			−1.42078
$965$	219.659	+	1085.10i	0.227626	+	1.12446i
$966$	−0.938806	+	14.4689i	−0.000971849	+	0.0149782i
$967$	−562.916	−	325.000i	−0.582126	−	0.336091i	0.179852	−	0.983694i	$-0.442438\pi$
$967$	−562.916	−	325.000i	−0.582126	−	0.336091i	−0.761978	+	0.647603i	$0.775771\pi$
$968$	251.418	−	435.468i	0.259729	−	0.449864i
$969$	51.1295	−	76.6295i	0.0527652	−	0.0790810i
$970$	468.080	+	2312.29i	0.482557	+	2.38380i
$971$		−	1717.75i		−	1.76905i	−0.466495	−	0.884524i	$-0.654483\pi$
$971$		−	1717.75i		−	1.76905i	0.466495	−	0.884524i	$-0.345517\pi$
$972$	−2210.53	−	742.291i	−2.27421	−	0.763674i
$973$			356.656i			0.366553i
$974$	2329.45	−	1344.91i	2.39163	−	1.38081i
$975$	297.173	+	854.552i	0.304793	+	0.876463i
$976$	−590.372	+	1022.55i	−0.604889	+	1.04770i
$977$	141.061	−	244.324i	0.144381	−	0.250076i	−0.784761	−	0.619799i	$-0.787214\pi$
$977$	141.061	−	244.324i	0.144381	−	0.250076i	0.929142	+	0.369723i	$0.120547\pi$
$978$	154.871	−	2386.88i	0.158355	−	2.44057i
$979$	−350.439	−	606.979i	−0.357956	−	0.619998i
$980$	−647.530	+	1928.98i	−0.660745	+	1.96834i
$981$	513.564	+	1235.26i	0.523510	+	1.25919i
$982$			14.0695i			0.0143274i
$983$	−192.267	−	333.017i	−0.195592	−	0.338776i	0.751502	−	0.659731i	$-0.229330\pi$
$983$	−192.267	−	333.017i	−0.195592	−	0.338776i	−0.947095	+	0.320955i	$0.895996\pi$
$984$	1920.89	−	948.846i	1.95212	−	0.964274i
$985$	94.1282	+	106.603i	0.0955616	+	0.108226i
$986$	−418.003	−	241.334i	−0.423938	−	0.244761i
$987$	−351.713	+	173.733i	−0.356346	+	0.176021i
$988$	−718.496	+	414.824i	−0.727223	+	0.419862i
$989$			26.5208i			0.0268158i
$990$	1351.93	−	912.540i	1.36558	−	0.921757i
$991$	399.250			0.402876			0.201438	−	0.979501i	$-0.435439\pi$
$991$	399.250			0.402876			0.201438	+	0.979501i	$0.435439\pi$
$992$	−542.898	−	940.326i	−0.547276	−	0.947910i
$993$	−579.234	−	37.5832i	−0.583317	−	0.0378481i
$994$	344.002	−	595.828i	0.346078	−	0.599425i
$995$	−509.240	−	576.729i	−0.511799	−	0.579627i
$996$	958.903	−	1437.14i	0.962754	−	1.44291i
$997$	1257.62	−	726.087i	1.26140	−	0.728272i	0.288058	−	0.957613i	$-0.406991\pi$
$997$	1257.62	−	726.087i	1.26140	−	0.728272i	0.973346	+	0.229341i	$0.0736572\pi$
$998$	−757.008			−0.758525
$999$	−6.87641	+	34.9294i	−0.00688329	+	0.0349643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.h.a.14.10	yes	20
3.2	odd	2		135.3.h.a.44.1		20
5.2	odd	4		225.3.j.e.176.1		20
5.3	odd	4		225.3.j.e.176.10		20
5.4	even	2	inner	45.3.h.a.14.1	✓	20
9.2	odd	6	inner	45.3.h.a.29.1	yes	20
9.4	even	3		405.3.d.a.404.2		20
9.5	odd	6		405.3.d.a.404.19		20
9.7	even	3		135.3.h.a.89.10		20
15.2	even	4		675.3.j.e.476.10		20
15.8	even	4		675.3.j.e.476.1		20
15.14	odd	2		135.3.h.a.44.10		20
45.2	even	12		225.3.j.e.101.1		20
45.4	even	6		405.3.d.a.404.20		20
45.7	odd	12		675.3.j.e.251.10		20
45.14	odd	6		405.3.d.a.404.1		20
45.29	odd	6	inner	45.3.h.a.29.10	yes	20
45.34	even	6		135.3.h.a.89.1		20
45.38	even	12		225.3.j.e.101.10		20
45.43	odd	12		675.3.j.e.251.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.1	✓	20	5.4	even	2	inner
45.3.h.a.14.10	yes	20	1.1	even	1	trivial
45.3.h.a.29.1	yes	20	9.2	odd	6	inner
45.3.h.a.29.10	yes	20	45.29	odd	6	inner
135.3.h.a.44.1		20	3.2	odd	2
135.3.h.a.44.10		20	15.14	odd	2
135.3.h.a.89.1		20	45.34	even	6
135.3.h.a.89.10		20	9.7	even	3
225.3.j.e.101.1		20	45.2	even	12
225.3.j.e.101.10		20	45.38	even	12
225.3.j.e.176.1		20	5.2	odd	4
225.3.j.e.176.10		20	5.3	odd	4
405.3.d.a.404.1		20	45.14	odd	6
405.3.d.a.404.2		20	9.4	even	3
405.3.d.a.404.19		20	9.5	odd	6
405.3.d.a.404.20		20	45.4	even	6
675.3.j.e.251.1		20	45.43	odd	12
675.3.j.e.251.10		20	45.7	odd	12
675.3.j.e.476.1		20	15.8	even	4
675.3.j.e.476.10		20	15.2	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84364 + 3.19328i) q^{2} +(1.66507 - 2.49550i) q^{3} +(-4.79800 + 8.31039i) q^{4} +(-3.30943 - 3.74802i) q^{5} +(11.0386 + 0.716233i) q^{6} +(2.22343 - 1.28370i) q^{7} -20.6340 q^{8} +(-3.45506 - 8.31039i) q^{9} +(5.86709 - 17.4779i) q^{10} +(-8.51311 + 4.91505i) q^{11} +(12.7496 + 25.8108i) q^{12} +(10.4471 + 6.03166i) q^{13} +(8.19840 + 4.73335i) q^{14} +(-14.8636 + 2.01795i) q^{15} +(-18.8497 - 32.6486i) q^{16} +4.28451 q^{17} +(20.1675 - 26.3543i) q^{18} +7.16698 q^{19} +(47.0262 - 9.51959i) q^{20} +(0.498702 - 7.68602i) q^{21} +(-31.3902 - 18.1231i) q^{22} +(-0.255270 + 0.442140i) q^{23} +(-34.3572 + 51.4923i) q^{24} +(-3.09537 + 24.8076i) q^{25} +44.4808i q^{26} +(-26.4915 - 5.21528i) q^{27} +24.6367i q^{28} +(-26.4589 + 15.2761i) q^{29} +(-33.8471 - 43.7433i) q^{30} +(9.61361 - 16.6513i) q^{31} +(28.2359 - 48.9060i) q^{32} +(-1.90944 + 29.4284i) q^{33} +(7.89910 + 13.6816i) q^{34} +(-12.1696 - 4.08516i) q^{35} +(85.6399 + 11.1604i) q^{36} -1.31851i q^{37} +(13.2133 + 22.8862i) q^{38} +(32.4473 - 16.0277i) q^{39} +(68.2868 + 77.3369i) q^{40} +(-29.9735 - 17.3052i) q^{41} +(25.4630 - 12.5778i) q^{42} +(44.9872 - 25.9734i) q^{43} -94.3297i q^{44} +(-19.7133 + 40.4523i) q^{45} -1.88250 q^{46} +(-25.4656 - 44.1078i) q^{47} +(-112.861 - 7.32289i) q^{48} +(-21.2042 + 36.7268i) q^{49} +(-84.9243 + 35.8519i) q^{50} +(7.13403 - 10.6920i) q^{51} +(-100.251 + 57.8799i) q^{52} +86.6349 q^{53} +(-32.1870 - 94.2098i) q^{54} +(46.5953 + 15.6414i) q^{55} +(-45.8783 + 26.4879i) q^{56} +(11.9336 - 17.8852i) q^{57} +(-97.5613 - 56.3270i) q^{58} +(91.7656 + 52.9809i) q^{59} +(54.5459 - 133.205i) q^{60} +(-15.6600 - 27.1239i) q^{61} +70.8961 q^{62} +(-18.3501 - 14.0423i) q^{63} +57.4297 q^{64} +(-11.9673 - 59.1175i) q^{65} +(-97.4933 + 48.1580i) q^{66} +(67.5968 + 39.0271i) q^{67} +(-20.5571 + 35.6060i) q^{68} +(0.678318 + 1.37322i) q^{69} +(-9.39131 - 46.3925i) q^{70} -72.6762i q^{71} +(71.2919 + 171.477i) q^{72} +30.3097i q^{73} +(4.21037 - 2.43086i) q^{74} +(56.7535 + 49.0310i) q^{75} +(-34.3872 + 59.5604i) q^{76} +(-12.6189 + 21.8565i) q^{77} +(111.002 + 74.0638i) q^{78} +(-57.6398 - 99.8350i) q^{79} +(-59.9861 + 178.697i) q^{80} +(-57.1251 + 57.4258i) q^{81} -127.618i q^{82} +(-30.0069 - 51.9734i) q^{83} +(61.4810 + 41.0220i) q^{84} +(-14.1793 - 16.0585i) q^{85} +(165.880 + 95.7710i) q^{86} +(-5.93457 + 91.4640i) q^{87} +(175.660 - 101.417i) q^{88} +71.2992i q^{89} +(-165.519 + 11.6296i) q^{90} +30.9713 q^{91} +(-2.44957 - 4.24278i) q^{92} +(-25.5459 - 51.7163i) q^{93} +(93.8989 - 162.638i) q^{94} +(-23.7186 - 26.8620i) q^{95} +(-75.0302 - 151.895i) q^{96} +(-110.820 + 63.9819i) q^{97} -156.372 q^{98} +(70.2593 + 53.7655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31}+ \cdots - 468 q^{99}+O(q^{100}) \) 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Introduction

L-functions

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