LMFDB - Embedded newform 33.4.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, 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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$0.581882 - 1.79085i$ of defining polynomial
Character	$\chi$	$=$	33.25
Dual form			33.4.e.b.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02339 + 1.47008i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-0.539165 + 1.65938i) q^{4} +(-8.44146 - 6.13308i) q^{5} +(-6.07016 - 4.41023i) q^{6} +(-10.1220 + 31.1524i) q^{7} +(-7.53140 - 23.1793i) q^{8} +(-7.28115 + 5.29007i) q^{9} +O(q^{10})$	\(q+(-2.02339 + 1.47008i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-0.539165 + 1.65938i) q^{4} +(-8.44146 - 6.13308i) q^{5} +(-6.07016 - 4.41023i) q^{6} +(-10.1220 + 31.1524i) q^{7} +(-7.53140 - 23.1793i) q^{8} +(-7.28115 + 5.29007i) q^{9} +26.0964 q^{10} +(12.6666 + 34.2134i) q^{11} -5.23432 q^{12} +(59.2672 - 43.0601i) q^{13} +(-25.3157 - 77.9137i) q^{14} +(9.67305 - 29.7706i) q^{15} +(38.0218 + 27.6245i) q^{16} +(44.7200 + 32.4909i) q^{17} +(6.95579 - 21.4077i) q^{18} +(27.9834 + 86.1240i) q^{19} +(14.7284 - 10.7008i) q^{20} -98.2669 q^{21} +(-75.9259 - 50.6060i) q^{22} -91.1987 q^{23} +(59.1524 - 42.9767i) q^{24} +(-4.98357 - 15.3379i) q^{25} +(-56.6188 + 174.255i) q^{26} +(-21.8435 - 15.8702i) q^{27} +(-46.2362 - 33.5926i) q^{28} +(-23.7073 + 72.9635i) q^{29} +(24.1927 + 74.4576i) q^{30} +(-18.6296 + 13.5352i) q^{31} +77.4339 q^{32} +(-85.8740 + 67.8576i) q^{33} -138.250 q^{34} +(276.505 - 200.893i) q^{35} +(-4.85248 - 14.9344i) q^{36} +(38.8841 - 119.673i) q^{37} +(-183.230 - 133.124i) q^{38} +(177.802 + 129.180i) q^{39} +(-78.5842 + 241.857i) q^{40} +(43.2807 + 133.204i) q^{41} +(198.832 - 144.460i) q^{42} +146.015 q^{43} +(-63.6024 + 2.57208i) q^{44} +93.9079 q^{45} +(184.530 - 134.069i) q^{46} +(-68.4490 - 210.664i) q^{47} +(-43.5692 + 134.092i) q^{48} +(-590.526 - 429.042i) q^{49} +(32.6315 + 23.7082i) q^{50} +(-51.2445 + 157.714i) q^{51} +(39.4983 + 121.563i) q^{52} +(35.5597 - 25.8356i) q^{53} +67.5282 q^{54} +(102.909 - 366.496i) q^{55} +798.324 q^{56} +(-219.784 + 159.683i) q^{57} +(-59.2930 - 182.485i) q^{58} +(-124.159 + 382.121i) q^{59} +(44.1853 + 32.1025i) q^{60} +(328.861 + 238.932i) q^{61} +(17.7972 - 54.7740i) q^{62} +(-91.0984 - 280.372i) q^{63} +(-460.853 + 334.830i) q^{64} -764.393 q^{65} +(74.0005 - 263.544i) q^{66} +221.234 q^{67} +(-78.0262 + 56.6893i) q^{68} +(-84.5459 - 260.205i) q^{69} +(-264.149 + 812.968i) q^{70} +(606.376 + 440.558i) q^{71} +(177.457 + 128.930i) q^{72} +(-68.6023 + 211.136i) q^{73} +(97.2508 + 299.307i) q^{74} +(39.1415 - 28.4379i) q^{75} -158.000 q^{76} +(-1194.04 + 48.2871i) q^{77} -549.667 q^{78} +(954.850 - 693.739i) q^{79} +(-151.537 - 466.382i) q^{80} +(25.0304 - 77.0356i) q^{81} +(-283.394 - 205.898i) q^{82} +(-547.425 - 397.728i) q^{83} +(52.9820 - 163.062i) q^{84} +(-178.232 - 548.542i) q^{85} +(-295.444 + 214.653i) q^{86} -230.155 q^{87} +(697.644 - 551.278i) q^{88} +1054.06 q^{89} +(-190.012 + 138.052i) q^{90} +(741.524 + 2282.17i) q^{91} +(49.1711 - 151.333i) q^{92} +(-55.8889 - 40.6057i) q^{93} +(448.192 + 325.630i) q^{94} +(291.985 - 898.636i) q^{95} +(71.7852 + 220.932i) q^{96} +(198.573 - 144.272i) q^{97} +1825.59 q^{98} +(-273.219 - 182.106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.02339	+	1.47008i	−0.715376	+	0.519751i	−0.884903	−	0.465775i	$-0.845776\pi$
$2$	−2.02339	+	1.47008i	−0.715376	+	0.519751i	0.169528	+	0.985525i	$0.445776\pi$
$3$	0.927051	+	2.85317i	0.178411	+	0.549093i
$3$	0.927051	+	2.85317i	0.178411	+	0.549093i
$4$	−0.539165	+	1.65938i	−0.0673956	+	0.207422i
$5$	−8.44146	−	6.13308i	−0.755027	−	0.548559i	0.142354	−	0.989816i	$-0.454533\pi$
$5$	−8.44146	−	6.13308i	−0.755027	−	0.548559i	−0.897381	+	0.441257i	$0.854533\pi$
$6$	−6.07016	−	4.41023i	−0.413022	−	0.300078i
$7$	−10.1220	+	31.1524i	−0.546539	+	1.68207i	0.170763	+	0.985312i	$0.445377\pi$
$7$	−10.1220	+	31.1524i	−0.546539	+	1.68207i	−0.717302	+	0.696762i	$0.754623\pi$
$8$	−7.53140	−	23.1793i	−0.332844	−	1.02439i
$9$	−7.28115	+	5.29007i	−0.269672	+	0.195928i
$10$	26.0964			0.825242
$11$	12.6666	+	34.2134i	0.347194	+	0.937793i
$11$	12.6666	+	34.2134i	0.347194	+	0.937793i
$12$	−5.23432			−0.125918
$13$	59.2672	−	43.0601i	1.26444	−	0.918672i	0.265477	−	0.964117i	$-0.414471\pi$
$13$	59.2672	−	43.0601i	1.26444	−	0.918672i	0.998967	+	0.0454454i	$0.0144707\pi$
$14$	−25.3157	−	77.9137i	−0.483279	−	1.48738i
$15$	9.67305	−	29.7706i	0.166505	−	0.512449i
$16$	38.0218	+	27.6245i	0.594091	+	0.431633i
$17$	44.7200	+	32.4909i	0.638011	+	0.463542i	0.859166	−	0.511697i	$-0.170983\pi$
$17$	44.7200	+	32.4909i	0.638011	+	0.463542i	−0.221155	+	0.975239i	$0.570983\pi$
$18$	6.95579	−	21.4077i	0.0910831	−	0.280325i
$19$	27.9834	+	86.1240i	0.337886	+	1.03990i	0.965283	+	0.261206i	$0.0841201\pi$
$19$	27.9834	+	86.1240i	0.337886	+	1.03990i	−0.627398	+	0.778699i	$0.715880\pi$
$20$	14.7284	−	10.7008i	0.164669	−	0.119639i
$21$	−98.2669			−1.02112
$22$	−75.9259	−	50.6060i	−0.735793	−	0.490420i
$23$	−91.1987			−0.826793			−0.413397	−	0.910551i	$-0.635658\pi$
$23$	−91.1987			−0.826793			−0.413397	+	0.910551i	$0.635658\pi$
$24$	59.1524	−	42.9767i	0.503101	−	0.365524i
$25$	−4.98357	−	15.3379i	−0.0398686	−	0.122703i
$26$	−56.6188	+	174.255i	−0.427072	+	1.31439i
$27$	−21.8435	−	15.8702i	−0.155695	−	0.113119i
$28$	−46.2362	−	33.5926i	−0.312065	−	0.226729i
$29$	−23.7073	+	72.9635i	−0.151805	+	0.467206i	−0.997823	−	0.0659470i	$-0.978993\pi$
$29$	−23.7073	+	72.9635i	−0.151805	+	0.467206i	0.846019	+	0.533153i	$0.178993\pi$
$30$	24.1927	+	74.4576i	0.147232	+	0.453134i
$31$	−18.6296	+	13.5352i	−0.107935	+	0.0784193i	−0.640443	−	0.768005i	$-0.721249\pi$
$31$	−18.6296	+	13.5352i	−0.107935	+	0.0784193i	0.532509	+	0.846425i	$0.321249\pi$
$32$	77.4339			0.427766
$33$	−85.8740	+	67.8576i	−0.452992	+	0.357954i
$34$	−138.250			−0.697344
$35$	276.505	−	200.893i	1.33537	−	0.970202i
$36$	−4.85248	−	14.9344i	−0.0224652	−	0.0691408i
$37$	38.8841	−	119.673i	0.172770	−	0.531732i	−0.826754	−	0.562563i	$-0.809815\pi$
$37$	38.8841	−	119.673i	0.172770	−	0.531732i	0.999525	+	0.0308308i	$0.00981532\pi$
$38$	−183.230	−	133.124i	−0.782207	−	0.568306i
$39$	177.802	+	129.180i	0.730027	+	0.530395i
$40$	−78.5842	+	241.857i	−0.310631	+	0.956025i
$41$	43.2807	+	133.204i	0.164861	+	0.507391i	0.999026	−	0.0441244i	$-0.0140498\pi$
$41$	43.2807	+	133.204i	0.164861	+	0.507391i	−0.834165	+	0.551515i	$0.814050\pi$
$42$	198.832	−	144.460i	0.730487	−	0.530730i
$43$	146.015			0.517838			0.258919	−	0.965899i	$-0.416634\pi$
$43$	146.015			0.517838			0.258919	+	0.965899i	$0.416634\pi$
$44$	−63.6024	+	2.57208i	−0.217919	+	0.00881262i
$45$	93.9079			0.311088
$46$	184.530	−	134.069i	0.591468	−	0.429727i
$47$	−68.4490	−	210.664i	−0.212432	−	0.653799i	−0.999326	−	0.0367105i	$-0.988312\pi$
$47$	−68.4490	−	210.664i	−0.212432	−	0.653799i	0.786894	−	0.617088i	$-0.211688\pi$
$48$	−43.5692	+	134.092i	−0.131014	+	0.403219i
$49$	−590.526	−	429.042i	−1.72165	−	1.25085i
$50$	32.6315	+	23.7082i	0.0922959	+	0.0670569i
$51$	−51.2445	+	157.714i	−0.140699	+	0.433028i
$52$	39.4983	+	121.563i	0.105335	+	0.324188i
$53$	35.5597	−	25.8356i	0.0921604	−	0.0669585i	−0.540751	−	0.841183i	$-0.681860\pi$
$53$	35.5597	−	25.8356i	0.0921604	−	0.0669585i	0.632911	+	0.774224i	$0.281860\pi$
$54$	67.5282			0.170175
$55$	102.909	−	366.496i	0.252294	−	0.898516i
$56$	798.324			1.90501
$57$	−219.784	+	159.683i	−0.510722	+	0.371061i
$58$	−59.2930	−	182.485i	−0.134234	−	0.413129i
$59$	−124.159	+	382.121i	−0.273967	+	0.843184i	0.715524	+	0.698589i	$0.246188\pi$
$59$	−124.159	+	382.121i	−0.273967	+	0.843184i	−0.989491	+	0.144596i	$0.953812\pi$
$60$	44.1853	+	32.1025i	0.0950716	+	0.0690736i
$61$	328.861	+	238.932i	0.690269	+	0.501509i	0.876748	−	0.480949i	$-0.159708\pi$
$61$	328.861	+	238.932i	0.690269	+	0.501509i	−0.186480	+	0.982459i	$0.559708\pi$
$62$	17.7972	−	54.7740i	0.0364555	−	0.112199i
$63$	−91.0984	−	280.372i	−0.182180	−	0.560691i
$64$	−460.853	+	334.830i	−0.900104	+	0.653964i
$65$	−764.393			−1.45863
$66$	74.0005	−	263.544i	0.138013	−	0.491515i
$67$	221.234			0.403404			0.201702	−	0.979447i	$-0.435353\pi$
$67$	221.234			0.403404			0.201702	+	0.979447i	$0.435353\pi$
$68$	−78.0262	+	56.6893i	−0.139148	+	0.101097i
$69$	−84.5459	−	260.205i	−0.147509	−	0.453986i
$70$	−264.149	+	812.968i	−0.451027	+	1.38812i
$71$	606.376	+	440.558i	1.01357	+	0.736403i	0.964955	−	0.262415i	$-0.0845188\pi$
$71$	606.376	+	440.558i	1.01357	+	0.736403i	0.0486165	+	0.998818i	$0.484519\pi$
$72$	177.457	+	128.930i	0.290466	+	0.211036i
$73$	−68.6023	+	211.136i	−0.109990	+	0.338516i	−0.990869	−	0.134826i	$-0.956952\pi$
$73$	−68.6023	+	211.136i	−0.109990	+	0.338516i	0.880879	+	0.473342i	$0.156952\pi$
$74$	97.2508	+	299.307i	0.152773	+	0.470186i
$75$	39.1415	−	28.4379i	0.0602622	−	0.0437831i
$76$	−158.000			−0.238471
$77$	−1194.04	+	48.2871i	−1.76719	+	0.0714652i
$78$	−549.667			−0.797917
$79$	954.850	−	693.739i	1.35986	−	0.987997i	0.361407	−	0.932408i	$-0.382296\pi$
$79$	954.850	−	693.739i	1.35986	−	0.987997i	0.998454	−	0.0555887i	$-0.0177036\pi$
$80$	−151.537	−	466.382i	−0.211779	−	0.651788i
$81$	25.0304	−	77.0356i	0.0343352	−	0.105673i
$82$	−283.394	−	205.898i	−0.381655	−	0.277288i
$83$	−547.425	−	397.728i	−0.723948	−	0.525979i	0.163695	−	0.986511i	$-0.447659\pi$
$83$	−547.425	−	397.728i	−0.723948	−	0.525979i	−0.887643	+	0.460532i	$0.847659\pi$
$84$	52.9820	−	163.062i	0.0688192	−	0.211804i
$85$	−178.232	−	548.542i	−0.227435	−	0.699973i
$86$	−295.444	+	214.653i	−0.370449	+	0.269147i
$87$	−230.155			−0.283623
$88$	697.644	−	551.278i	0.845103	−	0.667800i
$89$	1054.06			1.25539			0.627695	−	0.778460i	$-0.283999\pi$
$89$	1054.06			1.25539			0.627695	+	0.778460i	$0.283999\pi$
$90$	−190.012	+	138.052i	−0.222545	+	0.161688i
$91$	741.524	+	2282.17i	0.854207	+	2.62898i
$92$	49.1711	−	151.333i	0.0557222	−	0.171495i
$93$	−55.8889	−	40.6057i	−0.0623162	−	0.0452754i
$94$	448.192	+	325.630i	0.491781	+	0.357300i
$95$	291.985	−	898.636i	0.315337	−	0.970506i
$96$	71.7852	+	220.932i	0.0763181	+	0.234883i
$97$	198.573	−	144.272i	0.207857	−	0.151017i	−0.478987	−	0.877822i	$-0.658996\pi$
$97$	198.573	−	144.272i	0.207857	−	0.151017i	0.686843	+	0.726805i	$0.258996\pi$
$98$	1825.59			1.88176
$99$	−273.219	−	182.106i	−0.277369	−	0.184872i
$100$	28.1383			0.0281383
$101$	−18.3580	+	13.3379i	−0.0180860	+	0.0131403i	−0.596792	−	0.802396i	$-0.703558\pi$
$101$	−18.3580	+	13.3379i	−0.0180860	+	0.0131403i	0.578706	+	0.815537i	$0.303558\pi$
$102$	−128.165	−	394.451i	−0.124414	−	0.382906i
$103$	303.269	−	933.366i	0.290116	−	0.892886i	−0.694702	−	0.719298i	$-0.744464\pi$
$103$	303.269	−	933.366i	0.290116	−	0.892886i	0.984818	−	0.173588i	$-0.0555363\pi$
$104$	−1444.47	−	1049.47i	−1.36194	−	0.989507i
$105$	829.515	+	602.678i	0.770975	+	0.560146i
$106$	−33.9707	+	104.551i	−0.0311276	+	0.0958009i
$107$	−205.796	−	633.375i	−0.185935	−	0.572249i	0.814028	−	0.580825i	$-0.197270\pi$
$107$	−205.796	−	633.375i	−0.185935	−	0.572249i	−0.999963	+	0.00857617i	$0.997270\pi$
$108$	38.1119	−	27.6899i	0.0339566	−	0.0246709i
$109$	85.6516			0.0752654			0.0376327	−	0.999292i	$-0.488018\pi$
$109$	85.6516			0.0752654			0.0376327	+	0.999292i	$0.488018\pi$
$110$	330.554	+	892.848i	0.286519	+	0.773906i
$111$	377.494			0.322794
$112$	−1245.43	+	904.857i	−1.05073	+	0.763401i
$113$	−136.056	−	418.736i	−0.113266	−	0.348597i	0.878315	−	0.478081i	$-0.158668\pi$
$113$	−136.056	−	418.736i	−0.113266	−	0.348597i	−0.991581	+	0.129485i	$0.958668\pi$
$114$	209.963	−	646.200i	0.172499	−	0.530896i
$115$	769.850	+	559.329i	0.624251	+	0.453545i
$116$	−108.292	−	78.6787i	−0.0866780	−	0.0629753i
$117$	−203.743	+	627.055i	−0.160991	+	0.495481i
$118$	−310.526	−	955.701i	−0.242256	−	0.745588i
$119$	−1464.83	+	1064.26i	−1.12841	+	0.819838i
$120$	−762.912			−0.580367
$121$	−1010.11	+	866.737i	−0.758913	+	0.651192i
$122$	−1016.66			−0.754461
$123$	−339.931	+	246.974i	−0.249192	+	0.181048i
$124$	−12.4156	−	38.2113i	−0.00899157	−	0.0276732i
$125$	−455.043	+	1400.48i	−0.325603	+	1.00210i
$126$	596.496	+	433.380i	0.421747	+	0.306417i
$127$	−1314.97	−	955.382i	−0.918778	−	0.667531i	0.0244418	−	0.999701i	$-0.492219\pi$
$127$	−1314.97	−	955.382i	−0.918778	−	0.667531i	−0.943219	+	0.332170i	$0.892219\pi$
$128$	248.833	−	765.829i	0.171828	−	0.528831i
$129$	135.363	+	416.605i	0.0923880	+	0.284341i
$130$	1546.66	−	1123.72i	1.04347	−	0.758127i
$131$	1049.60			0.700030			0.350015	−	0.936744i	$-0.386177\pi$
$131$	1049.60			0.700030			0.350015	+	0.936744i	$0.386177\pi$
$132$	−66.3012	−	179.084i	−0.0437180	−	0.118085i
$133$	−2966.22			−1.93386
$134$	−447.642	+	325.231i	−0.288585	+	0.209669i
$135$	87.0574	+	267.935i	0.0555016	+	0.170816i
$136$	416.312	−	1281.28i	0.262489	−	0.807858i
$137$	2486.37	+	1806.45i	1.55055	+	1.12654i	0.943260	+	0.332055i	$0.107742\pi$
$137$	2486.37	+	1806.45i	1.55055	+	1.12654i	0.607287	+	0.794483i	$0.292258\pi$
$138$	553.591	+	402.208i	0.341484	+	0.248103i
$139$	−329.681	+	1014.65i	−0.201174	+	0.619149i	0.798675	+	0.601762i	$0.205535\pi$
$139$	−329.681	+	1014.65i	−0.201174	+	0.619149i	−0.999849	+	0.0173866i	$0.994465\pi$
$140$	184.275	+	567.141i	0.111244	+	0.342372i
$141$	537.605	−	390.593i	0.321096	−	0.233290i
$142$	−1874.59			−1.10783
$143$	2223.95	+	1482.31i	1.30053	+	0.866829i
$144$	−422.978			−0.244779
$145$	647.615	−	470.520i	0.370907	−	0.269480i
$146$	−171.578	−	528.061i	−0.0972593	−	0.299333i
$147$	676.683	−	2082.62i	0.379673	−	1.16851i
$148$	177.618	+	129.047i	0.0986492	+	0.0716728i
$149$	−1706.92	−	1240.15i	−0.938501	−	0.681861i	0.00955863	−	0.999954i	$-0.496957\pi$
$149$	−1706.92	−	1240.15i	−0.938501	−	0.681861i	−0.948059	+	0.318094i	$0.896957\pi$
$150$	−37.3924	+	115.082i	−0.0203538	+	0.0626427i
$151$	366.835	+	1129.00i	0.197699	+	0.608456i	0.999934	+	0.0114476i	$0.00364398\pi$
$151$	366.835	+	1129.00i	0.197699	+	0.608456i	−0.802235	+	0.597008i	$0.796356\pi$
$152$	1785.54	−	1297.27i	0.952803	−	0.692252i
$153$	−497.492			−0.262875
$154$	2345.03	−	1853.04i	1.22706	−	0.969624i
$155$	240.274			0.124511
$156$	−310.223	+	225.391i	−0.159216	+	0.115677i
$157$	−571.355	−	1758.45i	−0.290440	−	0.893882i	−0.984715	−	0.174173i	$-0.944275\pi$
$157$	−571.355	−	1758.45i	−0.290440	−	0.893882i	0.694275	−	0.719710i	$-0.255725\pi$
$158$	−912.182	+	2807.41i	−0.459299	+	1.41358i
$159$	106.679	+	77.5069i	0.0532088	+	0.0386585i
$160$	−653.655	−	474.908i	−0.322975	−	0.234655i
$161$	923.117	−	2841.06i	0.451875	−	1.39073i
$162$	62.6021	+	192.669i	0.0303610	+	0.0934416i
$163$	−1466.71	+	1065.63i	−0.704796	+	0.512064i	−0.881491	−	0.472202i	$-0.843459\pi$
$163$	−1466.71	+	1065.63i	−0.704796	+	0.512064i	0.176695	+	0.984266i	$0.443459\pi$
$164$	−244.372			−0.116355
$165$	1141.08	−	46.1452i	0.538380	−	0.0217721i
$166$	1692.34			0.791273
$167$	−213.891	+	155.401i	−0.0991100	+	0.0720076i	−0.636237	−	0.771494i	$-0.719510\pi$
$167$	−213.891	+	155.401i	−0.0991100	+	0.0720076i	0.537127	+	0.843502i	$0.319510\pi$
$168$	740.087	+	2277.75i	0.339875	+	1.04603i
$169$	979.515	−	3014.64i	0.445842	−	1.37216i
$170$	1167.03	+	847.898i	0.526513	+	0.382534i
$171$	−659.353	−	479.048i	−0.294865	−	0.214232i
$172$	−78.7260	+	242.294i	−0.0349000	+	0.107411i
$173$	−205.545	−	632.602i	−0.0903311	−	0.278011i	0.895678	−	0.444704i	$-0.146691\pi$
$173$	−205.545	−	632.602i	−0.0903311	−	0.278011i	−0.986009	+	0.166693i	$0.946691\pi$
$174$	465.693	−	338.346i	0.202897	−	0.147413i
$175$	528.256			0.228185
$176$	−463.519	+	1650.77i	−0.198517	+	0.706995i
$177$	−1205.36			−0.511865
$178$	−2132.76	+	1549.54i	−0.898075	+	0.652490i
$179$	−20.1093	−	61.8901i	−0.00839688	−	0.0258429i	0.946770	−	0.321910i	$-0.104325\pi$
$179$	−20.1093	−	61.8901i	−0.00839688	−	0.0258429i	−0.955167	+	0.296067i	$0.904325\pi$
$180$	−50.6318	+	155.829i	−0.0209660	+	0.0645266i
$181$	33.1354	+	24.0743i	0.0136074	+	0.00988634i	0.594568	−	0.804045i	$-0.297323\pi$
$181$	33.1354	+	24.0743i	0.0136074	+	0.00988634i	−0.580961	+	0.813932i	$0.697323\pi$
$182$	−4855.36	−	3527.63i	−1.97749	−	1.43673i
$183$	−376.842	+	1159.80i	−0.152224	+	0.468496i
$184$	686.854	+	2113.92i	0.275193	+	0.846958i
$185$	−1062.20	+	771.734i	−0.422133	+	0.306697i
$186$	172.778			0.0681114
$187$	−545.175	+	1941.57i	−0.213193	+	0.759261i
$188$	386.477			0.149929
$189$	715.496	−	519.838i	0.275369	−	0.200067i
$190$	730.266	+	2247.53i	0.278837	+	0.858173i
$191$	1415.27	−	4355.76i	0.536155	−	1.65012i	−0.204985	−	0.978765i	$-0.565715\pi$
$191$	1415.27	−	4355.76i	0.536155	−	1.65012i	0.741140	−	0.671351i	$-0.234285\pi$
$192$	−1382.56	−	1004.49i	−0.519676	−	0.377566i
$193$	4081.18	+	2965.15i	1.52212	+	1.10589i	0.960422	+	0.278550i	$0.0898536\pi$
$193$	4081.18	+	2965.15i	1.52212	+	1.10589i	0.561703	+	0.827339i	$0.310146\pi$
$194$	−189.700	+	583.837i	−0.0702045	+	0.216067i
$195$	−708.631	−	2180.94i	−0.260237	−	0.800926i
$196$	1030.33	−	748.582i	0.375486	−	0.272807i
$197$	1703.26			0.616001			0.308000	−	0.951386i	$-0.400340\pi$
$197$	1703.26			0.616001			0.308000	+	0.951386i	$0.400340\pi$
$198$	820.537	−	33.1825i	0.294510	−	0.0119100i
$199$	−3326.11			−1.18483			−0.592416	−	0.805632i	$-0.701826\pi$
$199$	−3326.11			−1.18483			−0.592416	+	0.805632i	$0.701826\pi$
$200$	−317.987	+	231.031i	−0.112425	+	0.0816818i
$201$	205.095	+	631.218i	0.0719716	+	0.221506i
$202$	17.5376	−	53.9753i	0.00610863	−	0.0188004i
$203$	−2033.03	−	1477.08i	−0.702909	−	0.510693i
$204$	−234.079	−	170.068i	−0.0803371	−	0.0583684i
$205$	451.600	−	1389.88i	0.153859	−	0.473530i
$206$	758.489	+	2334.39i	0.256536	+	0.789537i
$207$	664.032	−	482.447i	0.222963	−	0.161992i
$208$	3442.96			1.14772
$209$	−2592.14	+	2048.31i	−0.857904	+	0.677915i
$210$	−2564.42			−0.842674
$211$	−4013.48	+	2915.96i	−1.30947	+	0.951389i	−0.309475	+	0.950908i	$0.600153\pi$
$211$	−4013.48	+	2915.96i	−1.30947	+	0.951389i	−1.00000		0.000481181i	$0.999847\pi$
$212$	23.6986	+	72.9367i	0.00767747	+	0.0236288i
$213$	−694.845	+	2138.51i	−0.223521	+	0.687927i
$214$	1347.52	+	979.027i	0.430440	+	0.312733i
$215$	−1232.58	−	895.520i	−0.390982	−	0.284065i
$216$	−203.348	+	625.840i	−0.0640558	+	0.197144i
$217$	−233.085	−	717.363i	−0.0729164	−	0.224414i
$218$	−173.306	+	125.914i	−0.0538431	+	0.0391193i
$219$	−666.006			−0.205500
$220$	552.671	+	368.366i	0.169369	+	0.112887i
$221$	4049.49			1.23257
$222$	−763.818	+	554.946i	−0.230919	+	0.167773i
$223$	−1136.92	−	3499.07i	−0.341406	−	1.05074i	−0.963480	−	0.267781i	$-0.913710\pi$
$223$	−1136.92	−	3499.07i	−0.341406	−	1.05074i	0.622074	−	0.782959i	$-0.286290\pi$
$224$	−783.789	+	2412.25i	−0.233791	+	0.719534i
$225$	117.424	+	85.3138i	0.0347924	+	0.0252782i
$226$	890.869	+	647.254i	0.262211	+	0.190507i
$227$	124.139	−	382.062i	0.0362970	−	0.111711i	−0.931266	−	0.364339i	$-0.881295\pi$
$227$	124.139	−	382.062i	0.0362970	−	0.111711i	0.967563	+	0.252628i	$0.0812950\pi$
$228$	−146.474	−	450.800i	−0.0425459	−	0.130943i
$229$	2388.11	−	1735.06i	0.689129	−	0.500681i	−0.187245	−	0.982313i	$-0.559956\pi$
$229$	2388.11	−	1735.06i	0.689129	−	0.500681i	0.876374	+	0.481632i	$0.159956\pi$
$230$	−2379.96			−0.682305
$231$	−1244.71	−	3362.04i	−0.354528	−	0.957603i
$232$	1869.79			0.529128
$233$	1994.88	−	1449.36i	0.560896	−	0.407515i	−0.270891	−	0.962610i	$-0.587318\pi$
$233$	1994.88	−	1449.36i	0.560896	−	0.407515i	0.831787	+	0.555095i	$0.187318\pi$
$234$	−509.569	−	1568.29i	−0.142357	−	0.438130i
$235$	−714.211	+	2198.12i	−0.198255	+	0.610167i
$236$	−567.141	−	412.052i	−0.156431	−	0.113654i
$237$	2864.55	+	2081.22i	0.785116	+	0.570420i
$238$	1399.37	−	4306.83i	0.381125	−	1.17298i
$239$	−1311.91	−	4037.64i	−0.355064	−	1.09278i	−0.955972	−	0.293457i	$-0.905194\pi$
$239$	−1311.91	−	4037.64i	−0.355064	−	1.09278i	0.600908	−	0.799318i	$-0.294806\pi$
$240$	1190.18	−	864.719i	0.320109	−	0.232572i
$241$	−2686.25			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$241$	−2686.25			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$242$	769.680	−	3238.69i	0.204450	−	0.860293i
$243$	243.000			0.0641500
$244$	−573.789	+	416.882i	−0.150545	+	0.109378i
$245$	2353.55	+	7243.49i	0.613726	+	1.88885i
$246$	324.741	−	999.450i	0.0841656	−	0.259035i
$247$	5367.01	+	3899.36i	1.38257	+	1.00449i
$248$	454.044	+	329.882i	0.116257	+	0.0844659i
$249$	627.293	−	1930.61i	0.159651	−	0.491355i
$250$	−1138.08	−	3502.66i	−0.287915	−	0.886111i
$251$	−5951.11	+	4323.74i	−1.49654	+	1.08730i	−0.524802	+	0.851224i	$0.675861\pi$
$251$	−5951.11	+	4323.74i	−1.49654	+	1.08730i	−0.971735	+	0.236074i	$0.924139\pi$
$252$	514.360			0.128578
$253$	−1155.18	−	3120.22i	−0.287058	−	0.775361i
$254$	4065.18			1.00422
$255$	1399.85	−	1017.05i	0.343773	−	0.249766i
$256$	−785.901	−	2418.75i	−0.191870	−	0.590516i
$257$	−147.792	+	454.856i	−0.0358716	+	0.110401i	−0.967389	−	0.253295i	$-0.918486\pi$
$257$	−147.792	+	454.856i	−0.0358716	+	0.110401i	0.931517	+	0.363697i	$0.118486\pi$
$258$	−886.333	−	643.959i	−0.213879	−	0.155392i
$259$	3334.52	+	2422.67i	0.799987	+	0.581225i
$260$	412.133	−	1268.42i	0.0983055	−	0.302553i
$261$	−213.366	−	656.672i	−0.0506015	−	0.155735i
$262$	−2123.75	+	1542.99i	−0.500784	+	0.363841i
$263$	3955.38			0.927373			0.463686	−	0.885999i	$-0.346526\pi$
$263$	3955.38			0.927373			0.463686	+	0.885999i	$0.346526\pi$
$264$	2219.64	+	1479.43i	0.517460	+	0.344897i
$265$	−458.628			−0.106314
$266$	6001.82	−	4360.57i	1.38344	−	1.00513i
$267$	977.163	+	3007.40i	0.223975	+	0.689325i
$268$	−119.282	+	367.111i	−0.0271876	+	0.0836749i
$269$	1059.90	+	770.065i	0.240236	+	0.174542i	0.701388	−	0.712779i	$-0.252564\pi$
$269$	1059.90	+	770.065i	0.240236	+	0.174542i	−0.461153	+	0.887321i	$0.652564\pi$
$270$	−570.037	−	414.156i	−0.128486	−	0.0933508i
$271$	−1685.61	+	5187.78i	−0.377836	+	1.16286i	0.563709	+	0.825974i	$0.309374\pi$
$271$	−1685.61	+	5187.78i	−0.377836	+	1.16286i	−0.941545	+	0.336887i	$0.890626\pi$
$272$	802.789	+	2470.73i	0.178957	+	0.550772i
$273$	−5824.00	+	4231.38i	−1.29115	+	0.938077i
$274$	−7686.52			−1.69474
$275$	461.635	−	364.784i	0.101228	−	0.0799901i
$276$	477.363			0.104108
$277$	3852.71	−	2799.16i	0.835693	−	0.607167i	−0.0854711	−	0.996341i	$-0.527240\pi$
$277$	3852.71	−	2799.16i	0.835693	−	0.607167i	0.921164	+	0.389174i	$0.127240\pi$
$278$	−824.546	−	2537.69i	−0.177888	−	0.547484i
$279$	64.0430	−	197.104i	0.0137425	−	0.0422950i
$280$	−6739.02	−	4896.18i	−1.43833	−	1.04501i
$281$	451.960	+	328.368i	0.0959490	+	0.0697110i	0.634725	−	0.772738i	$-0.281113\pi$
$281$	451.960	+	328.368i	0.0959490	+	0.0697110i	−0.538776	+	0.842449i	$0.681113\pi$
$282$	−513.582	+	1580.64i	−0.108452	+	0.333780i
$283$	−638.145	−	1964.01i	−0.134042	−	0.412538i	0.861398	−	0.507930i	$-0.169589\pi$
$283$	−638.145	−	1964.01i	−0.134042	−	0.412538i	−0.995440	+	0.0953928i	$0.969589\pi$
$284$	−1057.99	+	768.674i	−0.221057	+	0.160607i
$285$	2834.65			0.589157
$286$	−6679.02	+	270.099i	−1.38090	+	0.0558437i
$287$	−4587.73			−0.943572
$288$	−563.808	+	409.630i	−0.115357	+	0.0838115i
$289$	−573.988	−	1766.55i	−0.116830	−	0.359567i
$290$	−618.676	+	1904.09i	−0.125275	+	0.385558i
$291$	595.720	+	432.816i	0.120006	+	0.0871895i
$292$	−313.367	−	227.674i	−0.0628028	−	0.0456289i
$293$	−2316.44	+	7129.26i	−0.461869	+	1.42149i	0.401008	+	0.916074i	$0.368660\pi$
$293$	−2316.44	+	7129.26i	−0.461869	+	1.42149i	−0.862877	+	0.505413i	$0.831340\pi$
$294$	1692.41	+	5208.72i	0.335727	+	1.03326i
$295$	3391.65	−	2464.18i	0.669389	−	0.486340i
$296$	−3066.78			−0.602206
$297$	266.290	−	948.361i	0.0520261	−	0.185284i
$298$	5276.89			1.02578
$299$	−5405.09	+	3927.03i	−1.04543	+	0.759552i
$300$	26.0856	+	80.2832i	0.00502018	+	0.0154505i
$301$	−1477.97	+	4548.72i	−0.283019	+	0.871042i
$302$	−2401.97	−	1745.13i	−0.457675	−	0.332520i
$303$	−55.0739	−	40.0136i	−0.0104420	−	0.00758653i
$304$	−1315.15	+	4047.62i	−0.248122	+	0.763641i
$305$	−1310.68	−	4033.86i	−0.246064	−	0.757306i
$306$	1006.62	−	731.352i	0.188054	−	0.136629i
$307$	1036.23			0.192640			0.0963201	−	0.995350i	$-0.469293\pi$
$307$	1036.23			0.192640			0.0963201	+	0.995350i	$0.469293\pi$
$308$	563.659	−	2007.40i	0.104277	−	0.371372i
$309$	2944.20			0.542037
$310$	−486.167	+	353.221i	−0.0890724	+	0.0647149i
$311$	−3193.59	−	9828.85i	−0.582288	−	1.79210i	−0.609897	−	0.792481i	$-0.708789\pi$
$311$	−3193.59	−	9828.85i	−0.582288	−	1.79210i	0.0276089	−	0.999619i	$-0.491211\pi$
$312$	1655.21	−	5094.22i	0.300346	−	0.924370i
$313$	−5769.05	−	4191.46i	−1.04181	−	0.756918i	−0.0711707	−	0.997464i	$-0.522674\pi$
$313$	−5769.05	−	4191.46i	−1.04181	−	0.756918i	−0.970638	+	0.240546i	$0.922674\pi$
$314$	3741.13	+	2718.09i	0.672370	+	0.488505i
$315$	−950.540	+	2925.46i	−0.170022	+	0.523273i
$316$	636.354	+	1958.50i	0.113284	+	0.348652i
$317$	5215.16	−	3789.04i	0.924014	−	0.671336i	−0.0205056	−	0.999790i	$-0.506528\pi$
$317$	5215.16	−	3789.04i	0.924014	−	0.671336i	0.944520	+	0.328454i	$0.106528\pi$
$318$	−329.794			−0.0581571
$319$	−2796.62	+	113.095i	−0.490849	+	0.0198499i
$320$	5943.81			1.03834
$321$	1616.34	−	1174.34i	0.281045	−	0.204191i
$322$	2308.76	+	7105.63i	0.399572	+	1.22976i
$323$	−1546.83	+	4760.67i	−0.266465	+	0.820095i
$324$	114.336	+	83.0697i	0.0196049	+	0.0142438i
$325$	−955.812	−	694.438i	−0.163135	−	0.118525i
$326$	1401.17	−	4312.36i	0.238048	−	0.732636i
$327$	79.4034	+	244.378i	0.0134282	+	0.0413277i
$328$	2761.61	−	2006.43i	0.464892	−	0.337764i
$329$	7255.55			1.21584
$330$	−2241.01	+	1770.84i	−0.373828	+	0.295399i
$331$	5634.51			0.935652			0.467826	−	0.883821i	$-0.345037\pi$
$331$	5634.51			0.935652			0.467826	+	0.883821i	$0.345037\pi$
$332$	955.133	−	693.945i	0.157891	−	0.114714i
$333$	349.957	+	1077.06i	0.0575901	+	0.177244i
$334$	204.333	−	628.872i	0.0334749	−	0.103025i
$335$	−1867.54	−	1356.85i	−0.304580	−	0.221291i
$336$	−3736.29	−	2714.57i	−0.606640	−	0.440750i
$337$	945.112	−	2908.76i	0.152770	−	0.470178i	−0.845158	−	0.534517i	$-0.820494\pi$
$337$	945.112	−	2908.76i	0.152770	−	0.470178i	0.997928	+	0.0643383i	$0.0204937\pi$
$338$	2449.81	+	7539.74i	0.394237	+	1.21334i
$339$	1068.60	−	776.380i	0.171204	−	0.124387i
$340$	1006.33			0.160518
$341$	−699.061	−	465.937i	−0.111015	−	0.0739939i
$342$	2038.36			0.322287
$343$	10253.6	−	7449.68i	1.61412	−	1.17273i
$344$	−1099.70	−	3384.51i	−0.172359	−	0.530467i
$345$	−882.170	+	2715.04i	−0.137665	+	0.423689i
$346$	1345.87	+	977.832i	0.209117	+	0.151932i
$347$	8507.85	+	6181.32i	1.31621	+	0.956284i	0.999971	+	0.00760501i	$0.00242077\pi$
$347$	8507.85	+	6181.32i	1.31621	+	0.956284i	0.316241	+	0.948679i	$0.397579\pi$
$348$	124.092	−	381.914i	0.0191150	−	0.0588298i
$349$	465.051	+	1431.28i	0.0713283	+	0.219526i	0.980365	−	0.197189i	$-0.0631813\pi$
$349$	465.051	+	1431.28i	0.0713283	+	0.219526i	−0.909037	+	0.416715i	$0.863181\pi$
$350$	−1068.87	+	776.577i	−0.163238	+	0.118599i
$351$	−1977.97			−0.300788
$352$	980.826	+	2649.28i	0.148518	+	0.401156i
$353$	−11810.2			−1.78071			−0.890356	−	0.455264i	$-0.849545\pi$
$353$	−11810.2			−1.78071			−0.890356	+	0.455264i	$0.849545\pi$
$354$	2438.90	−	1771.97i	0.366176	−	0.266042i
$355$	−2416.72	−	7437.90i	−0.361313	−	1.11201i
$356$	−568.309	+	1749.08i	−0.0846077	+	0.260396i
$357$	−4394.49	−	3192.78i	−0.651488	−	0.473333i
$358$	131.672	+	95.6655i	0.0194388	+	0.0141231i
$359$	1021.81	−	3144.82i	0.150221	−	0.462332i	−0.847424	−	0.530916i	$-0.821848\pi$
$359$	1021.81	−	3144.82i	0.150221	−	0.462332i	0.997645	+	0.0685836i	$0.0218480\pi$
$360$	−707.258	−	2176.72i	−0.103544	−	0.318675i
$361$	−1085.22	+	788.459i	−0.158218	+	0.114952i
$362$	−102.437			−0.0148728
$363$	−3409.37	−	2078.51i	−0.492963	−	0.300534i
$364$	−4186.79			−0.602878
$365$	1874.02	−	1361.55i	0.268741	−	0.195252i
$366$	−942.498	−	2900.71i	−0.134604	−	0.414269i
$367$	−1108.64	+	3412.03i	−0.157685	+	0.485304i	−0.998423	−	0.0561380i	$-0.982121\pi$
$367$	−1108.64	+	3412.03i	−0.157685	+	0.485304i	0.840738	+	0.541442i	$0.182121\pi$
$368$	−3467.54	−	2519.32i	−0.491191	−	0.356871i
$369$	−1019.79	−	740.923i	−0.143871	−	0.104528i
$370$	1014.74	−	3123.04i	0.142577	−	0.438808i
$371$	444.906	+	1369.28i	0.0622598	+	0.191616i
$372$	97.5135	−	70.8477i	0.0135910	−	0.00987441i
$373$	−2022.36			−0.280734			−0.140367	−	0.990100i	$-0.544828\pi$
$373$	−2022.36			−0.280734			−0.140367	+	0.990100i	$0.544828\pi$
$374$	−1751.16	−	4730.00i	−0.242113	−	0.653964i
$375$	−4417.65			−0.608338
$376$	−4367.53	+	3173.19i	−0.599037	+	0.435226i
$377$	1736.76	+	5345.18i	0.237261	+	0.730215i
$378$	−683.524	+	2103.67i	−0.0930070	+	0.286246i
$379$	4696.18	+	3411.97i	0.636482	+	0.462431i	0.858640	−	0.512580i	$-0.171310\pi$
$379$	4696.18	+	3411.97i	0.636482	+	0.462431i	−0.222158	+	0.975011i	$0.571310\pi$
$380$	1333.75	+	969.025i	0.180052	+	0.130816i
$381$	1506.82	−	4637.52i	0.202616	−	0.623589i
$382$	3539.66	+	10894.0i	0.474097	+	1.45912i
$383$	4237.83	−	3078.96i	0.565387	−	0.410777i	−0.268040	−	0.963408i	$-0.586376\pi$
$383$	4237.83	−	3078.96i	0.565387	−	0.410777i	0.833426	+	0.552630i	$0.186376\pi$
$384$	2415.72			0.321033
$385$	10375.6	+	6915.55i	1.37348	+	0.915452i
$386$	−12616.8			−1.66368
$387$	−1063.16	+	772.428i	−0.139647	+	0.101459i
$388$	132.338	+	407.295i	0.0173156	+	0.0532919i
$389$	−26.2617	+	80.8251i	−0.00342293	+	0.0105347i	−0.952753	−	0.303745i	$-0.901763\pi$
$389$	−26.2617	+	80.8251i	−0.00342293	+	0.0105347i	0.949330	+	0.314280i	$0.101763\pi$
$390$	4639.99	+	3371.15i	0.602449	+	0.437705i
$391$	−4078.40	−	2963.13i	−0.527503	−	0.383253i
$392$	−5497.40	+	16919.3i	−0.708318	+	2.17998i
$393$	973.032	+	2994.68i	0.124893	+	0.384381i
$394$	−3446.35	+	2503.92i	−0.440672	+	0.320167i
$395$	−12315.1			−1.56871
$396$	449.492	−	355.188i	0.0570400	−	0.0450730i
$397$	−7187.71			−0.908667			−0.454334	−	0.890832i	$-0.650123\pi$
$397$	−7187.71			−0.908667			−0.454334	+	0.890832i	$0.650123\pi$
$398$	6730.01	−	4889.64i	0.847600	−	0.615818i
$399$	−2749.84	−	8463.13i	−0.345023	−	1.06187i
$400$	234.216	−	720.842i	0.0292770	−	0.0901052i
$401$	−1839.76	−	1336.66i	−0.229110	−	0.166458i	0.467308	−	0.884095i	$-0.345224\pi$
$401$	−1839.76	−	1336.66i	−0.229110	−	0.166458i	−0.696418	+	0.717636i	$0.745224\pi$
$402$	−1342.93	−	975.693i	−0.166615	−	0.121053i
$403$	−521.298	+	1604.39i	−0.0644360	+	0.198314i
$404$	−12.2346	−	37.6541i	−0.00150666	−	0.00463704i
$405$	−683.758	+	496.779i	−0.0838919	+	0.0609510i
$406$	6285.02			0.768277
$407$	4586.94	−	185.496i	0.558640	−	0.0225914i
$408$	4041.65			0.490420
$409$	7772.40	−	5646.98i	0.939659	−	0.682702i	−0.00867953	−	0.999962i	$-0.502763\pi$
$409$	7772.40	−	5646.98i	0.939659	−	0.682702i	0.948339	+	0.317260i	$0.102763\pi$
$410$	1129.47	+	3476.16i	0.136050	+	0.418720i
$411$	−2849.13	+	8768.71i	−0.341939	+	1.05238i
$412$	1385.30	+	1006.48i	0.165652	+	0.120353i
$413$	−10647.3	−	7735.68i	−1.26856	−	0.921666i
$414$	−634.359	+	1952.36i	−0.0753069	+	0.231771i
$415$	2181.77	+	6714.80i	0.258070	+	0.794257i
$416$	4589.29	−	3334.31i	0.540886	−	0.392976i
$417$	−3200.61			−0.375862
$418$	2233.73	−	7955.16i	0.261377	−	0.930861i
$419$	10777.3			1.25658			0.628291	−	0.777979i	$-0.283755\pi$
$419$	10777.3			1.25658			0.628291	+	0.777979i	$0.283755\pi$
$420$	−1447.32	+	1051.54i	−0.168147	+	0.122166i
$421$	380.512	+	1171.10i	0.0440500	+	0.135572i	0.970663	−	0.240445i	$-0.0772934\pi$
$421$	380.512	+	1171.10i	0.0440500	+	0.135572i	−0.926613	+	0.376017i	$0.877293\pi$
$422$	3834.13	−	11800.2i	0.442281	−	1.36120i
$423$	1612.82	+	1171.78i	0.185385	+	0.134690i
$424$	−866.665	−	629.669i	−0.0992665	−	0.0721213i
$425$	275.476	−	847.829i	0.0314413	−	0.0967665i
$426$	−1737.84	−	5348.52i	−0.197649	−	0.608302i
$427$	−10772.1	+	7826.36i	−1.22083	+	0.886988i
$428$	1161.97			0.131228
$429$	−2167.55	+	7719.48i	−0.243941	+	0.868764i
$430$	3810.46			0.427342
$431$	−7047.38	+	5120.22i	−0.787611	+	0.572233i	−0.907253	−	0.420584i	$-0.861825\pi$
$431$	−7047.38	+	5120.22i	−0.787611	+	0.572233i	0.119643	+	0.992817i	$0.461825\pi$
$432$	−392.122	−	1206.83i	−0.0436713	−	0.134406i
$433$	2313.66	−	7120.71i	0.256784	−	0.790299i	−0.736689	−	0.676231i	$-0.763612\pi$
$433$	2313.66	−	7120.71i	0.256784	−	0.790299i	0.993473	−	0.114068i	$-0.0363880\pi$
$434$	1526.20	+	1108.85i	0.168802	+	0.122642i
$435$	1942.84	+	1411.56i	0.214143	+	0.155584i
$436$	−46.1803	+	142.128i	−0.00507256	+	0.0156117i
$437$	−2552.05	−	7854.40i	−0.279362	−	0.859787i
$438$	1347.59	−	979.080i	0.147010	−	0.106809i
$439$	9595.95			1.04326			0.521628	−	0.853173i	$-0.325325\pi$
$439$	9595.95			1.04326			0.521628	+	0.853173i	$0.325325\pi$
$440$	−9270.16	+	374.885i	−1.00440	+	0.0406180i
$441$	6569.38			0.709359
$442$	−8193.69	+	5953.07i	−0.881752	+	0.640630i
$443$	2871.05	+	8836.18i	0.307918	+	0.947674i	0.978572	+	0.205904i	$0.0660133\pi$
$443$	2871.05	+	8836.18i	0.307918	+	0.947674i	−0.670654	+	0.741770i	$0.733987\pi$
$444$	−203.532	+	626.406i	−0.0217549	+	0.0669548i
$445$	−8897.76	−	6464.60i	−0.947853	−	0.688655i
$446$	7444.32	+	5408.62i	0.790356	+	0.574227i
$447$	1955.96	−	6019.83i	0.206966	−	0.636975i
$448$	−5765.98	−	17745.9i	−0.608074	−	1.87146i
$449$	5550.31	−	4032.54i	0.583375	−	0.423847i	−0.256564	−	0.966527i	$-0.582591\pi$
$449$	5550.31	−	4032.54i	0.583375	−	0.423847i	0.839939	+	0.542680i	$0.182591\pi$
$450$	−363.013			−0.0380280
$451$	−4009.15	+	3168.03i	−0.418589	+	0.330769i
$452$	768.199			0.0799403
$453$	−2881.16	+	2093.28i	−0.298827	+	0.217110i
$454$	310.478	+	955.553i	0.0320957	+	0.0987805i
$455$	7737.22	−	23812.7i	0.797201	−	2.45353i
$456$	5356.61	+	3891.80i	0.550101	+	0.399672i
$457$	−935.459	−	679.650i	−0.0957525	−	0.0695683i	0.538879	−	0.842383i	$-0.318848\pi$
$457$	−935.459	−	679.650i	−0.0957525	−	0.0695683i	−0.634631	+	0.772815i	$0.718848\pi$
$458$	−2281.39	+	7021.40i	−0.232756	+	0.716351i
$459$	−461.201	−	1419.43i	−0.0468998	−	0.144343i
$460$	−1343.21	+	975.902i	−0.136147	+	0.0989167i
$461$	−8394.87			−0.848131			−0.424065	−	0.905632i	$-0.639397\pi$
$461$	−8394.87			−0.848131			−0.424065	+	0.905632i	$0.639397\pi$
$462$	7460.99	+	4972.90i	0.751335	+	0.500779i
$463$	1801.45			0.180822			0.0904108	−	0.995905i	$-0.471182\pi$
$463$	1801.45			0.180822			0.0904108	+	0.995905i	$0.471182\pi$
$464$	−2916.97	+	2119.31i	−0.291847	+	0.212039i
$465$	222.746	+	685.542i	0.0222142	+	0.0683683i
$466$	−1905.73	+	5865.25i	−0.189445	+	0.583052i
$467$	15389.4	+	11181.0i	1.52492	+	1.10792i	0.958982	+	0.283466i	$0.0914842\pi$
$467$	15389.4	+	11181.0i	1.52492	+	1.10792i	0.565934	+	0.824451i	$0.308516\pi$
$468$	−930.670	−	676.172i	−0.0919236	−	0.0667864i
$469$	−2239.34	+	6891.98i	−0.220476	+	0.678555i
$470$	−1786.27	−	5497.59i	−0.175308	−	0.539542i
$471$	4487.48	−	3260.34i	0.439007	−	0.318957i
$472$	9792.36			0.954936
$473$	1849.51	+	4995.66i	0.179790	+	0.485625i
$474$	−8855.65			−0.858129
$475$	1181.50	−	858.410i	0.114128	−	0.0829190i
$476$	−976.227	−	3004.52i	−0.0940027	−	0.289311i
$477$	−122.243	+	376.226i	−0.0117340	+	0.0361137i
$478$	8590.15	+	6241.11i	0.821976	+	0.597200i
$479$	13686.9	+	9944.13i	1.30558	+	0.948557i	0.999993	−	0.00360855i	$-0.00114864\pi$
$479$	13686.9	+	9944.13i	1.30558	+	0.948557i	0.305583	+	0.952165i	$0.401149\pi$
$480$	749.022	−	2305.25i	0.0712250	−	0.219208i
$481$	−2848.58	−	8767.03i	−0.270029	−	0.831065i
$482$	5435.33	−	3949.00i	0.513636	−	0.373178i
$483$	8961.81			0.844258
$484$	−893.627	−	2143.47i	−0.0839244	−	0.201303i
$485$	−2561.08			−0.239779
$486$	−491.683	+	357.229i	−0.0458914	+	0.0333420i
$487$	−2844.77	−	8755.32i	−0.264700	−	0.814664i	−0.991762	−	0.128092i	$-0.959115\pi$
$487$	−2844.77	−	8755.32i	−0.264700	−	0.814664i	0.727062	−	0.686572i	$-0.240885\pi$
$488$	3061.48	−	9422.25i	0.283989	−	0.874027i
$489$	−4400.13	−	3196.88i	−0.406914	−	0.295640i
$490$	−15410.6	−	11196.5i	−1.42078	−	1.03226i
$491$	5069.27	−	15601.6i	0.465933	−	1.43399i	−0.391872	−	0.920020i	$-0.628173\pi$
$491$	5069.27	−	15601.6i	0.465933	−	1.43399i	0.857805	−	0.513975i	$-0.171827\pi$
$492$	−226.545	−	697.234i	−0.0207590	−	0.0638897i
$493$	−3430.84	+	2492.65i	−0.313423	+	0.227715i
$494$	−16591.9			−1.51114
$495$	1189.50	+	3212.91i	0.108008	+	0.291736i
$496$	−1082.24			−0.0979715
$497$	−19862.2	+	14430.7i	−1.79264	+	1.30243i
$498$	1568.89	+	4828.54i	0.141172	+	0.434482i
$499$	−1431.17	+	4404.69i	−0.128393	+	0.395152i	−0.994504	−	0.104699i	$-0.966612\pi$
$499$	−1431.17	+	4404.69i	−0.128393	+	0.395152i	0.866111	+	0.499851i	$0.166612\pi$
$500$	−2078.58	−	1510.18i	−0.185914	−	0.135074i
$501$	−641.673	−	466.202i	−0.0572212	−	0.0415736i
$502$	5685.18	−	17497.2i	0.505462	−	1.55565i
$503$	6057.33	+	18642.5i	0.536944	+	1.65255i	0.739410	+	0.673256i	$0.235105\pi$
$503$	6057.33	+	18642.5i	0.536944	+	1.65255i	−0.202465	+	0.979289i	$0.564895\pi$
$504$	−5812.72	+	4223.19i	−0.513728	+	0.373245i
$505$	236.770			0.0208636
$506$	6924.34	+	4615.21i	0.608349	+	0.405476i
$507$	9509.33			0.832987
$508$	2294.33	−	1666.93i	0.200382	−	0.145586i
$509$	5031.84	+	15486.4i	0.438178	+	1.34857i	0.889795	+	0.456360i	$0.150847\pi$
$509$	5031.84	+	15486.4i	0.438178	+	1.34857i	−0.451617	+	0.892212i	$0.649153\pi$
$510$	−1337.30	+	4115.78i	−0.116111	+	0.357353i
$511$	−5883.02	−	4274.26i	−0.509294	−	0.370024i
$512$	10357.6	+	7525.21i	0.894031	+	0.649551i
$513$	755.551	−	2325.35i	0.0650261	−	0.200130i
$514$	−369.634	−	1137.62i	−0.0317196	−	0.0976227i
$515$	−8284.44	+	6019.00i	−0.708846	+	0.515007i
$516$	−764.288			−0.0652052
$517$	6340.52	−	5010.28i	0.539373	−	0.426212i
$518$	−10308.5			−0.874384
$519$	1614.37	−	1172.91i	0.136538	−	0.0992003i
$520$	5756.95	+	17718.1i	0.485498	+	1.49421i
$521$	−3170.21	+	9756.91i	−0.266583	+	0.820457i	0.724742	+	0.689020i	$0.241959\pi$
$521$	−3170.21	+	9756.91i	−0.266583	+	0.820457i	−0.991325	+	0.131436i	$0.958041\pi$
$522$	1397.08	+	1015.04i	0.117143	+	0.0851092i
$523$	−17290.3	−	12562.2i	−1.44561	−	1.05030i	−0.986833	−	0.161744i	$-0.948288\pi$
$523$	−17290.3	−	12562.2i	−1.44561	−	1.05030i	−0.458776	−	0.888552i	$-0.651712\pi$
$524$	−565.907	+	1741.68i	−0.0471789	+	0.145202i
$525$	489.720	+	1507.20i	0.0407107	+	0.125295i
$526$	−8003.27	+	5814.71i	−0.663420	+	0.482003i
$527$	−1272.89			−0.105214
$528$	−5139.62	+	207.846i	−0.423624	+	0.0171313i
$529$	−3849.79			−0.316413
$530$	927.982	−	674.218i	0.0760546	−	0.0552569i
$531$	−1117.43	−	3439.09i	−0.0913224	−	0.281061i
$532$	1599.28	−	4922.08i	0.130334	−	0.401127i
$533$	8300.93	+	6030.98i	0.674584	+	0.490114i
$534$	−6398.29	−	4648.63i	−0.518504	−	0.376715i
$535$	−2147.32	+	6608.77i	−0.173527	+	0.534060i
$536$	−1666.20	−	5128.04i	−0.134270	−	0.413242i
$537$	157.941	−	114.751i	0.0126921	−	0.00922133i
$538$	−3276.65			−0.262577
$539$	7199.02	−	25638.4i	0.575295	−	2.04884i
$540$	−491.544			−0.0391717
$541$	−17097.0	+	12421.7i	−1.35870	+	0.987157i	−0.360179	+	0.932883i	$0.617284\pi$
$541$	−17097.0	+	12421.7i	−1.35870	+	0.987157i	−0.998526	+	0.0542736i	$0.982716\pi$
$542$	−4215.79	−	12974.9i	−0.334103	−	1.02826i
$543$	−37.9698	+	116.859i	−0.00300081	+	0.00923555i
$544$	3462.84	+	2515.90i	0.272919	+	0.198287i
$545$	−723.024	−	525.308i	−0.0568274	−	0.0412875i
$546$	5563.75	−	17123.5i	0.436093	−	1.34216i
$547$	214.684	+	660.729i	0.0167810	+	0.0516467i	0.959096	−	0.283080i	$-0.0913561\pi$
$547$	214.684	+	660.729i	0.0167810	+	0.0516467i	−0.942315	+	0.334726i	$0.891356\pi$
$548$	−4338.15	+	3151.85i	−0.338169	+	0.245694i
$549$	−3658.45			−0.284406
$550$	−397.806	+	1416.74i	−0.0308409	+	0.109836i
$551$	−6947.32			−0.537143
$552$	−5394.62	+	3919.42i	−0.415961	+	0.302213i
$553$	11946.6	+	36768.0i	0.918667	+	2.82737i
$554$	−3680.55	+	11327.6i	−0.282259	+	0.868704i
$555$	−3186.60	−	2315.20i	−0.243718	−	0.177072i
$556$	−1505.94	−	1094.13i	−0.114867	−	0.0834558i
$557$	5531.72	−	17024.9i	0.420801	−	1.29509i	−0.486156	−	0.873872i	$-0.661601\pi$
$557$	5531.72	−	17024.9i	0.420801	−	1.29509i	0.906958	−	0.421222i	$-0.138399\pi$
$558$	160.174	+	492.966i	0.0121518	+	0.0373995i
$559$	8653.88	−	6287.42i	0.654777	−	0.475723i
$560$	16062.8			1.21210
$561$	−6045.04	+	244.461i	−0.454941	+	0.0183978i
$562$	−1397.22			−0.104872
$563$	−12328.2	+	8956.97i	−0.922864	+	0.670500i	−0.944235	−	0.329272i	$-0.893197\pi$
$563$	−12328.2	+	8956.97i	−0.922864	+	0.670500i	0.0213713	+	0.999772i	$0.493197\pi$
$564$	358.284	+	1102.68i	0.0267491	+	0.0823252i
$565$	−1419.63	+	4369.19i	−0.105707	+	0.325333i
$566$	4178.46	+	3035.83i	0.310307	+	0.225451i
$567$	2146.49	+	1559.51i	0.158984	+	0.115509i
$568$	5644.95	−	17373.4i	0.417001	−	1.28340i
$569$	−7618.38	−	23447.0i	−0.561299	−	1.72750i	−0.678700	−	0.734416i	$-0.737456\pi$
$569$	−7618.38	−	23447.0i	−0.561299	−	1.72750i	0.117401	−	0.993085i	$-0.462544\pi$
$570$	−5735.59	+	4167.15i	−0.421469	+	0.306215i
$571$	20893.8			1.53131			0.765656	−	0.643250i	$-0.222415\pi$
$571$	20893.8			1.53131			0.765656	+	0.643250i	$0.222415\pi$
$572$	−3658.78	+	2891.17i	−0.267450	+	0.211339i
$573$	13739.8			1.00172
$574$	9282.76	−	6744.32i	0.675009	−	0.490422i
$575$	454.495	+	1398.79i	0.0329631	+	0.101450i
$576$	1584.27	−	4875.89i	0.114603	−	0.352712i
$577$	11720.4	+	8515.35i	0.845624	+	0.614382i	0.923936	−	0.382547i	$-0.124953\pi$
$577$	11720.4	+	8515.35i	0.845624	+	0.614382i	−0.0783117	+	0.996929i	$0.524953\pi$
$578$	3758.37	+	2730.62i	0.270463	+	0.196503i
$579$	−4676.62	+	14393.2i	−0.335671	+	1.03309i
$580$	431.599	+	1328.33i	0.0308986	+	0.0950961i
$581$	17931.2	−	13027.8i	1.28040	−	0.930266i
$582$	−1841.65			−0.131166
$583$	1334.35	+	889.368i	0.0947907	+	0.0631798i
$584$	5410.65			0.383381
$585$	5565.66	−	4043.69i	0.393353	−	0.285788i
$586$	−5793.51	−	17830.6i	−0.408409	−	1.25695i
$587$	2950.00	−	9079.16i	0.207427	−	0.638394i	−0.792178	−	0.610290i	$-0.791053\pi$
$587$	2950.00	−	9079.16i	0.207427	−	0.638394i	0.999605	−	0.0281041i	$-0.00894698\pi$
$588$	3091.00	+	2245.75i	0.216787	+	0.157505i
$589$	−1687.03	−	1225.70i	−0.118018	−	0.0857453i
$590$	−3240.10	+	9971.99i	−0.226089	+	0.695831i
$591$	1579.01	+	4859.68i	0.109901	+	0.338242i
$592$	4784.34	−	3476.03i	0.332154	−	0.241324i
$593$	−15771.0			−1.09213			−0.546067	−	0.837741i	$-0.683876\pi$
$593$	−15771.0			−1.09213			−0.546067	+	0.837741i	$0.683876\pi$
$594$	855.355	+	2310.37i	0.0590836	+	0.159589i
$595$	18892.5			1.30171
$596$	2978.19	−	2163.78i	0.204684	−	0.148712i
$597$	−3083.47	−	9489.95i	−0.211387	−	0.650583i
$598$	5163.56	−	15891.8i	0.353100	−	1.08673i
$599$	−15970.3	−	11603.1i	−1.08936	−	0.791469i	−0.110072	−	0.993924i	$-0.535108\pi$
$599$	−15970.3	−	11603.1i	−1.08936	−	0.791469i	−0.979292	+	0.202455i	$0.935108\pi$
$600$	−953.961	−	693.093i	−0.0649088	−	0.0471590i
$601$	667.170	−	2053.34i	0.0452819	−	0.139363i	−0.925859	−	0.377868i	$-0.876657\pi$
$601$	667.170	−	2053.34i	0.0452819	−	0.139363i	0.971141	+	0.238505i	$0.0766573\pi$
$602$	−3696.46	−	11376.5i	−0.250260	−	0.770221i
$603$	−1610.84	+	1170.34i	−0.108787	+	0.0790382i
$604$	−2071.22			−0.139531
$605$	13842.6	−	1121.42i	0.930217	−	0.0753591i
$606$	170.259			0.0114130
$607$	−4096.74	+	2976.46i	−0.273940	+	0.199029i	−0.716270	−	0.697823i	$-0.754152\pi$
$607$	−4096.74	+	2976.46i	−0.273940	+	0.199029i	0.442330	+	0.896852i	$0.354152\pi$
$608$	2166.86	+	6668.91i	0.144536	+	0.444836i
$609$	2329.64	−	7169.90i	0.155011	−	0.477075i
$610$	8582.11	+	6235.27i	0.569639	+	0.413867i
$611$	−13128.0	−	9538.06i	−0.869235	−	0.631536i
$612$	268.230	−	825.528i	0.0177166	−	0.0545261i
$613$	7547.95	+	23230.2i	0.497323	+	1.53060i	0.813305	+	0.581837i	$0.197666\pi$
$613$	7547.95	+	23230.2i	0.497323	+	1.53060i	−0.315982	+	0.948765i	$0.602334\pi$
$614$	−2096.69	+	1523.33i	−0.137810	+	0.100125i
$615$	4384.23			0.287462
$616$	10112.1	+	27313.4i	0.661408	+	1.78650i
$617$	−13814.4			−0.901369			−0.450685	−	0.892683i	$-0.648820\pi$
$617$	−13814.4			−0.901369			−0.450685	+	0.892683i	$0.648820\pi$
$618$	−5957.25	+	4328.20i	−0.387760	+	0.281724i
$619$	−1351.02	−	4158.01i	−0.0877255	−	0.269991i	0.897564	−	0.440884i	$-0.145335\pi$
$619$	−1351.02	−	4158.01i	−0.0877255	−	0.269991i	−0.985290	+	0.170892i	$0.945335\pi$
$620$	−129.547	+	398.705i	−0.00839151	+	0.0258264i
$621$	1992.10	+	1447.34i	0.128728	+	0.0935263i
$622$	20911.0	+	15192.8i	1.34800	+	0.979379i
$623$	−10669.2	+	32836.4i	−0.686119	+	2.11166i
$624$	3191.80	+	9823.36i	0.204767	+	0.630207i
$625$	10799.6	−	7846.36i	0.691173	−	0.502167i
$626$	17834.8			1.13869
$627$	−8247.21	−	5496.93i	−0.525298	−	0.350121i
$628$	3225.99			0.204985
$629$	5627.18	−	4088.38i	0.356710	−	0.259165i
$630$	−2377.34	−	7316.71i	−0.150342	−	0.462706i
$631$	−714.402	+	2198.70i	−0.0450711	+	0.138715i	−0.971060	−	0.238837i	$-0.923234\pi$
$631$	−714.402	+	2198.70i	−0.0450711	+	0.138715i	0.925989	+	0.377552i	$0.123234\pi$
$632$	−23271.7	−	16907.9i	−1.46471	−	1.06418i
$633$	−12040.4	−	8747.88i	−0.756025	−	0.549285i
$634$	−4982.12	+	15333.4i	−0.312090	+	0.960514i
$635$	5240.84	+	16129.6i	0.327522	+	1.00801i
$636$	−186.131	+	135.232i	−0.0116047	+	0.00843129i
$637$	−53473.5			−3.32605
$638$	5492.39	−	4340.09i	0.340824	−	0.269319i
$639$	−6745.70			−0.417615
$640$	−6797.40	+	4938.60i	−0.419829	+	0.305024i
$641$	−5704.03	−	17555.2i	−0.351475	−	1.08173i	−0.958025	−	0.286684i	$-0.907447\pi$
$641$	−5704.03	−	17555.2i	−0.351475	−	1.08173i	0.606550	−	0.795045i	$-0.292553\pi$
$642$	−1544.12	+	4752.30i	−0.0949242	+	0.292147i
$643$	−23792.8	−	17286.4i	−1.45925	−	1.06020i	−0.983559	−	0.180589i	$-0.942200\pi$
$643$	−23792.8	−	17286.4i	−1.45925	−	1.06020i	−0.475686	−	0.879615i	$-0.657800\pi$
$644$	4216.69	+	3063.60i	0.258014	+	0.187458i
$645$	1412.41	−	4346.94i	0.0862225	−	0.265365i
$646$	−3868.70	−	11906.6i	−0.235622	−	0.725171i
$647$	1793.76	−	1303.24i	0.108995	−	0.0791897i	−0.531953	−	0.846774i	$-0.678542\pi$
$647$	1793.76	−	1303.24i	0.108995	−	0.0791897i	0.640948	+	0.767585i	$0.278542\pi$
$648$	−1974.14			−0.119678
$649$	−14646.3	+	592.297i	−0.885852	+	0.0358238i
$650$	2954.86			0.178306
$651$	1830.68	−	1330.06i	0.110215	−	0.0800758i
$652$	−977.481	−	3008.38i	−0.0587134	−	0.180701i
$653$	6953.29	−	21400.0i	0.416697	−	1.28246i	−0.494027	−	0.869447i	$-0.664476\pi$
$653$	6953.29	−	21400.0i	0.416697	−	1.28246i	0.910724	−	0.413015i	$-0.135524\pi$
$654$	−519.919	−	377.743i	−0.0310863	−	0.0225855i
$655$	−8860.14	−	6437.27i	−0.528541	−	0.384008i
$656$	−2034.09	+	6260.28i	−0.121064	+	0.372596i
$657$	−617.421	−	1900.23i	−0.0366635	−	0.112839i
$658$	−14680.8	+	10666.2i	−0.869783	+	0.631934i
$659$	5908.12			0.349238			0.174619	−	0.984636i	$-0.444131\pi$
$659$	5908.12			0.349238			0.174619	+	0.984636i	$0.444131\pi$
$660$	−538.656	+	1918.36i	−0.0317684	+	0.113139i
$661$	22387.2			1.31734			0.658670	−	0.752432i	$-0.271120\pi$
$661$	22387.2			1.31734			0.658670	+	0.752432i	$0.271120\pi$
$662$	−11400.8	+	8283.17i	−0.669343	+	0.486306i
$663$	3754.09	+	11553.9i	0.219904	+	0.676796i
$664$	−5096.16	+	15684.4i	−0.297845	+	0.916673i
$665$	25039.2	+	18192.1i	1.46012	+	1.06084i
$666$	−2291.45	−	1664.84i	−0.133321	−	0.0968636i
$667$	2162.07	−	6654.18i	0.125511	−	0.386283i
$668$	−142.546	−	438.712i	−0.00825641	−	0.0254106i
$669$	8929.45	−	6487.63i	0.516043	−	0.374927i
$670$	5773.42			0.332906
$671$	−4009.10	+	14277.9i	−0.230655	+	0.821450i
$672$	−7609.18			−0.436802
$673$	25692.3	−	18666.6i	1.47157	−	1.06916i	0.491416	−	0.870925i	$-0.336480\pi$
$673$	25692.3	−	18666.6i	1.47157	−	1.06916i	0.980155	−	0.198233i	$-0.0635204\pi$
$674$	2363.77	+	7274.93i	0.135087	+	0.415757i
$675$	−134.556	+	414.122i	−0.00767271	+	0.0236142i
$676$	4474.30	+	3250.77i	0.254569	+	0.184955i
$677$	2970.62	+	2158.28i	0.168641	+	0.122525i	0.668905	−	0.743348i	$-0.266763\pi$
$677$	2970.62	+	2158.28i	0.168641	+	0.122525i	−0.500263	+	0.865873i	$0.666763\pi$
$678$	−1020.84	+	3141.84i	−0.0578249	+	0.177967i
$679$	2484.46	+	7646.38i	0.140419	+	0.432166i
$680$	−11372.5	+	8262.58i	−0.641344	+	0.465964i
$681$	1205.17			0.0678153
$682$	2099.44	−	84.9011i	0.117876	−	0.00476691i
$683$	−11719.2			−0.656549			−0.328274	−	0.944582i	$-0.606467\pi$
$683$	−11719.2			−0.656549			−0.328274	+	0.944582i	$0.606467\pi$
$684$	1150.42	−	835.830i	0.0643091	−	0.0467233i
$685$	−9909.46	−	30498.2i	−0.552732	−	1.70113i
$686$	−9795.42	+	30147.2i	−0.545176	+	1.67788i
$687$	7164.32	+	5205.18i	0.397869	+	0.289069i
$688$	5551.75	+	4033.58i	0.307643	+	0.223516i
$689$	995.038	−	3062.41i	0.0550188	−	0.169330i
$690$	−2206.35	−	6790.44i	−0.121731	−	0.374649i
$691$	−495.853	+	360.259i	−0.0272983	+	0.0198334i	−0.601351	−	0.798985i	$-0.705371\pi$
$691$	−495.853	+	360.259i	−0.0272983	+	0.0198334i	0.574052	+	0.818819i	$0.305371\pi$
$692$	1160.55			0.0637535
$693$	8438.57	−	6668.15i	0.462561	−	0.365515i
$694$	−26301.7			−1.43862
$695$	9005.93	−	6543.19i	0.491531	−	0.357119i
$696$	1733.39	+	5334.83i	0.0944023	+	0.290540i
$697$	−2392.42	+	7363.13i	−0.130014	+	0.400141i
$698$	−3045.07	−	2212.37i	−0.165125	−	0.119971i
$699$	5984.63	+	4348.09i	0.323833	+	0.235279i
$700$	−284.817	+	876.576i	−0.0153787	+	0.0473306i
$701$	8657.42	+	26644.8i	0.466457	+	1.43561i	0.857141	+	0.515082i	$0.172238\pi$
$701$	8657.42	+	26644.8i	0.466457	+	1.43561i	−0.390684	+	0.920525i	$0.627762\pi$
$702$	4002.21	−	2907.77i	0.215176	−	0.156335i
$703$	11394.8			0.611328
$704$	−17293.1	−	11526.2i	−0.925794	−	0.617060i
$705$	−6933.71			−0.370409
$706$	23896.5	−	17361.9i	1.27388	−	0.925527i
$707$	−229.686	−	706.902i	−0.0122182	−	0.0376037i
$708$	649.886	−	2000.14i	0.0344974	−	0.106172i
$709$	−9146.28	−	6645.16i	−0.484479	−	0.351995i	0.318578	−	0.947897i	$-0.396795\pi$
$709$	−9146.28	−	6645.16i	−0.484479	−	0.351995i	−0.803057	+	0.595902i	$0.796795\pi$
$710$	15824.3	+	11497.0i	0.836442	+	0.607711i
$711$	−3282.48	+	10102.4i	−0.173140	+	0.532871i
$712$	−7938.51	−	24432.2i	−0.417849	−	1.28601i
$713$	1699.00	−	1234.40i	0.0892399	−	0.0648366i
$714$	13585.4			0.712074
$715$	−9682.28	−	26152.5i	−0.506429	−	1.36790i
$716$	113.541			0.00592631
$717$	10303.9	−	7486.20i	0.536688	−	0.389927i
$718$	2555.60	+	7865.34i	0.132833	+	0.408819i
$719$	3455.04	−	10633.5i	0.179209	−	0.551549i	−0.820592	−	0.571515i	$-0.806356\pi$
$719$	3455.04	−	10633.5i	0.179209	−	0.551549i	0.999801	+	0.0199662i	$0.00635588\pi$
$720$	3570.55	+	2594.16i	0.184815	+	0.134276i
$721$	26006.9	+	18895.1i	1.34334	+	0.975994i
$722$	1036.73	−	3190.72i	0.0534390	−	0.164468i
$723$	−2490.29	−	7664.33i	−0.128098	−	0.394246i
$724$	−57.8138	+	42.0042i	−0.00296772	+	0.00215618i
$725$	1237.25			0.0633798
$726$	9954.06	−	806.403i	0.508857	−	0.0412237i
$727$	−31428.7			−1.60334			−0.801669	−	0.597769i	$-0.796054\pi$
$727$	−31428.7			−1.60334			−0.801669	+	0.597769i	$0.796054\pi$
$728$	47314.4	−	34375.9i	2.40878	−	1.75008i
$729$	225.273	+	693.320i	0.0114451	+	0.0352243i
$730$	−1790.28	+	5509.91i	−0.0907687	+	0.279357i
$731$	6529.77	+	4744.16i	0.330386	+	0.240040i
$732$	−1721.37	−	1250.65i	−0.0869174	−	0.0631492i
$733$	392.631	−	1208.39i	0.0197847	−	0.0608910i	−0.940677	−	0.339304i	$-0.889808\pi$
$733$	392.631	−	1208.39i	0.0197847	−	0.0608910i	0.960461	+	0.278413i	$0.0898084\pi$
$734$	−2772.75	−	8533.64i	−0.139433	−	0.429131i
$735$	−18485.0	+	13430.2i	−0.927661	+	0.673985i
$736$	−7061.87			−0.353674
$737$	2802.29	+	7569.17i	0.140059	+	0.378309i
$738$	3152.65			0.157250
$739$	−10929.8	+	7940.95i	−0.544057	+	0.395281i	−0.825590	−	0.564271i	$-0.809157\pi$
$739$	−10929.8	+	7940.95i	−0.544057	+	0.395281i	0.281532	+	0.959552i	$0.409157\pi$
$740$	−707.898	−	2178.68i	−0.0351660	−	0.108230i
$741$	−6150.04	+	18927.9i	−0.304895	+	0.938371i
$742$	−2913.17	−	2116.54i	−0.144132	−	0.104718i
$743$	−25972.0	−	18869.8i	−1.28240	−	0.931716i	−0.282775	−	0.959186i	$-0.591255\pi$
$743$	−25972.0	−	18869.8i	−1.28240	−	0.931716i	−0.999623	+	0.0274700i	$0.991255\pi$
$744$	−520.288	+	1601.28i	−0.0256380	+	0.0789057i
$745$	6802.97	+	20937.4i	0.334552	+	1.02965i
$746$	4092.02	−	2973.03i	0.200830	−	0.145912i
$747$	6089.89			0.298283
$748$	−2927.86	−	1951.48i	−0.143119	−	0.0953918i
$749$	21814.3			1.06419
$750$	8938.63	−	6494.29i	0.435190	−	0.316184i
$751$	−7329.02	−	22556.4i	−0.356111	−	1.09600i	−0.955362	−	0.295437i	$-0.904535\pi$
$751$	−7329.02	−	22556.4i	−0.356111	−	1.09600i	0.599251	−	0.800561i	$-0.295465\pi$
$752$	3216.94	−	9900.71i	0.155997	−	0.480109i
$753$	−17853.3	−	12971.2i	−0.864026	−	0.627752i
$754$	−11372.0	−	8262.21i	−0.549260	−	0.399061i
$755$	3827.63	−	11780.2i	0.184506	−	0.567850i
$756$	476.838	+	1467.56i	0.0229397	+	0.0706012i
$757$	18715.6	−	13597.7i	0.898589	−	0.652863i	−0.0395142	−	0.999219i	$-0.512581\pi$
$757$	18715.6	−	13597.7i	0.898589	−	0.652863i	0.938103	+	0.346356i	$0.112581\pi$
$758$	−14518.1			−0.695672
$759$	7831.60	−	6188.53i	0.374531	−	0.295954i
$760$	−23028.8			−1.09913
$761$	−667.872	+	485.238i	−0.0318139	+	0.0231141i	−0.603579	−	0.797304i	$-0.706259\pi$
$761$	−667.872	+	485.238i	−0.0318139	+	0.0231141i	0.571765	+	0.820418i	$0.306259\pi$
$762$	3768.63	+	11598.7i	0.179164	+	0.551410i
$763$	−866.969	+	2668.26i	−0.0411355	+	0.126602i
$764$	6464.80	+	4696.95i	0.306136	+	0.222421i
$765$	4199.56	+	3051.16i	0.198478	+	0.144202i
$766$	−4048.46	+	12459.9i	−0.190962	+	0.587720i
$767$	9095.64	+	27993.5i	0.428194	+	1.31784i
$768$	6172.55	−	4484.62i	0.290016	−	0.210709i
$769$	9591.21			0.449763			0.224882	−	0.974386i	$-0.427800\pi$
$769$	9591.21			0.449763			0.224882	+	0.974386i	$0.427800\pi$
$770$	−31160.3	+	1260.12i	−1.45836	+	0.0589761i
$771$	−1434.79			−0.0670205
$772$	−7120.74	+	5173.52i	−0.331970	+	0.241191i
$773$	724.297	+	2229.16i	0.0337014	+	0.103722i	0.966492	−	0.256696i	$-0.0826340\pi$
$773$	724.297	+	2229.16i	0.0337014	+	0.103722i	−0.932791	+	0.360418i	$0.882634\pi$
$774$	1015.65	−	3125.84i	0.0471663	−	0.145163i
$775$	300.443	+	218.285i	0.0139255	+	0.0101175i
$776$	−4839.66	−	3516.22i	−0.223883	−	0.162661i
$777$	−3821.02	+	11759.9i	−0.176420	+	0.542964i
$778$	−65.6816	−	202.147i	−0.00302674	−	0.00931533i
$779$	−10260.9	+	7455.02i	−0.471934	+	0.342880i
$780$	4001.08			0.183669
$781$	−7392.24	+	26326.6i	−0.338688	+	1.20620i
$782$	12608.2			0.576559
$783$	1675.79	−	1217.54i	0.0764853	−	0.0555699i
$784$	−10600.8	−	32626.0i	−0.482909	−	1.48624i
$785$	−5961.64	+	18348.0i	−0.271057	+	0.834229i
$786$	−6371.24	−	4628.98i	−0.289128	−	0.210064i
$787$	21078.8	+	15314.6i	0.954736	+	0.693656i	0.951922	−	0.306340i	$-0.0991044\pi$
$787$	21078.8	+	15314.6i	0.954736	+	0.693656i	0.00281375	+	0.999996i	$0.499104\pi$
$788$	−918.337	+	2826.35i	−0.0415157	+	0.127772i
$789$	3666.84	+	11285.4i	0.165454	+	0.509214i
$790$	24918.2	−	18104.1i	1.12221	−	0.815336i
$791$	14421.8			0.648269
$792$	−2163.35	+	7704.52i	−0.0970599	+	0.345667i
$793$	29779.1			1.33353
$794$	14543.5	−	10566.5i	0.650039	−	0.472281i
$795$	−425.171	−	1308.54i	−0.0189676	−	0.0583764i
$796$	1793.32	−	5519.27i	0.0798525	−	0.245761i
$797$	−35109.5	−	25508.5i	−1.56040	−	1.13370i	−0.935677	−	0.352856i	$-0.885210\pi$
$797$	−35109.5	−	25508.5i	−1.56040	−	1.13370i	−0.624727	−	0.780844i	$-0.714790\pi$
$798$	18005.4	+	13081.7i	0.798729	+	0.580311i
$799$	3783.65	−	11644.9i	0.167529	−	0.515602i
$800$	−385.897	−	1187.67i	−0.0170544	−	0.0524881i
$801$	−7674.74	+	5576.02i	−0.338544	+	0.245966i
$802$	5687.54			0.250417
$803$	−8092.65	+	327.267i	−0.355646	+	0.0143823i
$804$	−1158.01			−0.0507958
$805$	−25216.9	+	18321.2i	−1.10407	+	0.802157i
$806$	−1303.79	−	4012.65i	−0.0569777	−	0.175359i
$807$	−1214.54	+	3737.97i	−0.0529788	+	0.163052i
$808$	447.423	+	325.072i	0.0194805	+	0.0141534i
$809$	6863.36	+	4986.53i	0.298273	+	0.216708i	0.726848	−	0.686798i	$-0.240984\pi$
$809$	6863.36	+	4986.53i	0.298273	+	0.216708i	−0.428575	+	0.903506i	$0.640984\pi$
$810$	653.204	−	2010.35i	0.0283349	−	0.0872057i
$811$	1715.59	+	5280.06i	0.0742820	+	0.228616i	0.981303	−	0.192469i	$-0.0616494\pi$
$811$	1715.59	+	5280.06i	0.0742820	+	0.228616i	−0.907021	+	0.421085i	$0.861649\pi$
$812$	3547.17	−	2577.17i	0.153302	−	0.111380i
$813$	−16364.3			−0.705928
$814$	−9008.48	+	7118.49i	−0.387895	+	0.306515i
$815$	18916.8			0.813037
$816$	−6305.19	+	4580.99i	−0.270497	+	0.196528i
$817$	4085.98	+	12575.4i	0.174970	+	0.538502i
$818$	−7425.09	+	22852.1i	−0.317374	+	0.976777i
$819$	−17472.0	−	12694.2i	−0.745447	−	0.541599i
$820$	2062.85	+	1498.75i	0.0878512	+	0.0638276i
$821$	−32.7348	+	100.748i	−0.00139154	+	0.00428272i	−0.951750	−	0.306875i	$-0.900717\pi$
$821$	−32.7348	+	100.748i	−0.00139154	+	0.00428272i	0.950358	+	0.311158i	$0.100717\pi$
$822$	−7125.79	−	21930.9i	−0.302361	−	0.930571i
$823$	−30200.5	+	21941.9i	−1.27913	+	0.929341i	−0.999526	−	0.0307751i	$-0.990202\pi$
$823$	−30200.5	+	21941.9i	−1.27913	+	0.929341i	−0.279602	+	0.960116i	$0.590202\pi$
$824$	−23918.8			−1.01123
$825$	1468.75	+	978.950i	0.0619822	+	0.0413123i
$826$	32915.6			1.38654
$827$	1408.83	−	1023.58i	0.0592380	−	0.0430389i	−0.557772	−	0.829994i	$-0.688344\pi$
$827$	1408.83	−	1023.58i	0.0592380	−	0.0430389i	0.617010	+	0.786955i	$0.288344\pi$
$828$	442.540	+	1362.00i	0.0185741	+	0.0571651i
$829$	−1629.09	+	5013.82i	−0.0682516	+	0.210057i	−0.979365	−	0.202098i	$-0.935224\pi$
$829$	−1629.09	+	5013.82i	−0.0682516	+	0.210057i	0.911114	+	0.412155i	$0.135224\pi$
$830$	−14285.8	−	10379.3i	−0.597432	−	0.434060i
$831$	11558.1	+	8397.48i	0.482488	+	0.350548i
$832$	−12895.7	+	39688.8i	−0.537353	+	1.65380i
$833$	−12468.3	−	38373.5i	−0.518609	−	1.59611i
$834$	6476.07	−	4705.14i	0.268882	−	0.195355i
$835$	2758.64			0.114331
$836$	−2001.33	−	5405.71i	−0.0827958	−	0.223637i
$837$	621.742			0.0256757
$838$	−21806.7	+	15843.5i	−0.898928	+	0.653109i
$839$	7446.81	+	22918.9i	0.306427	+	0.943086i	0.979141	+	0.203183i	$0.0651286\pi$
$839$	7446.81	+	22918.9i	0.306427	+	0.943086i	−0.672714	+	0.739903i	$0.734871\pi$
$840$	7722.23	−	23766.6i	0.317193	−	0.976220i
$841$	14969.5	+	10876.0i	0.613780	+	0.445937i
$842$	−2491.53	−	1810.20i	−0.101976	−	0.0740898i
$843$	−517.900	+	1593.93i	−0.0211595	+	0.0651221i
$844$	−2674.76	−	8232.06i	−0.109086	−	0.335734i
$845$	−26757.5	+	19440.5i	−1.08933	+	0.791447i
$846$	−4985.96			−0.202625
$847$	−16776.6	−	40240.6i	−0.680578	−	1.63245i
$848$	2065.74			0.0836531
$849$	5012.05	−	3641.47i	0.202607	−	0.147203i
$850$	688.979	+	2120.46i	0.0278021	+	0.0855660i
$851$	−3546.18	+	10914.0i	−0.142845	+	0.439633i
$852$	−3173.97	−	2306.02i	−0.127627	−	0.0927265i
$853$	22983.5	+	16698.5i	0.922555	+	0.670275i	0.944159	−	0.329491i	$-0.106877\pi$
$853$	22983.5	+	16698.5i	0.922555	+	0.670275i	−0.0216040	+	0.999767i	$0.506877\pi$
$854$	10290.7	−	31671.5i	0.412343	−	1.26906i
$855$	2627.86	+	8087.72i	0.105112	+	0.323502i
$856$	−13131.2	+	9540.40i	−0.524318	+	0.380939i
$857$	−6941.16			−0.276669			−0.138335	−	0.990386i	$-0.544175\pi$
$857$	−6941.16			−0.276669			−0.138335	+	0.990386i	$0.544175\pi$
$858$	−6962.43	−	18806.0i	−0.277032	−	0.748281i
$859$	21637.2			0.859430			0.429715	−	0.902965i	$-0.358614\pi$
$859$	21637.2			0.859430			0.429715	+	0.902965i	$0.358614\pi$
$860$	2150.57	−	1562.48i	0.0852718	−	0.0619536i
$861$	−4253.06	−	13089.6i	−0.168344	−	0.518109i
$862$	6732.46	−	20720.4i	0.266019	−	0.818723i
$863$	−6019.83	−	4373.67i	−0.237448	−	0.172516i	0.462698	−	0.886516i	$-0.346882\pi$
$863$	−6019.83	−	4373.67i	−0.237448	−	0.172516i	−0.700146	+	0.714000i	$0.746882\pi$
$864$	−1691.42	−	1228.89i	−0.0666012	−	0.0483886i
$865$	−2144.70	+	6600.70i	−0.0843028	+	0.259457i
$866$	5786.56	+	17809.2i	0.227062	+	0.698824i
$867$	4508.16	−	3275.37i	0.176592	−	0.128301i
$868$	1316.05			0.0514626
$869$	35829.9	+	23881.3i	1.39867	+	0.932242i
$870$	−6006.23			−0.234058
$871$	13111.9	−	9526.37i	0.510081	−	0.370595i
$872$	−645.076	−	1985.34i	−0.0250516	−	0.0771010i
$873$	−682.635	+	2100.93i	−0.0264647	+	0.0814500i
$874$	16710.4	+	12140.8i	0.646723	+	0.469872i
$875$	−39022.4	−	28351.4i	−1.50765	−	1.09537i
$876$	359.087	−	1105.15i	0.0138498	−	0.0426253i
$877$	−9984.83	−	30730.2i	−0.384451	−	1.18322i	−0.936877	−	0.349658i	$-0.886298\pi$
$877$	−9984.83	−	30730.2i	−0.384451	−	1.18322i	0.552426	−	0.833562i	$-0.313702\pi$
$878$	−19416.3	+	14106.8i	−0.746320	+	0.542233i
$879$	−22488.4			−0.862931
$880$	14037.0	−	11092.1i	0.537714	−	0.424902i
$881$	21907.4			0.837774			0.418887	−	0.908038i	$-0.362420\pi$
$881$	21907.4			0.837774			0.418887	+	0.908038i	$0.362420\pi$
$882$	−13292.4	+	9657.49i	−0.507458	+	0.368690i
$883$	−370.914	−	1141.56i	−0.0141362	−	0.0435067i	0.943740	−	0.330689i	$-0.107281\pi$
$883$	−370.914	−	1141.56i	−0.0141362	−	0.0435067i	−0.957876	+	0.287183i	$0.907281\pi$
$884$	−2183.34	+	6719.64i	−0.0830699	+	0.255663i
$885$	10175.0	+	7392.54i	0.386472	+	0.280788i
$886$	−18799.1	−	13658.3i	−0.712831	−	0.517902i
$887$	−7342.41	+	22597.6i	−0.277941	+	0.855415i	0.710485	+	0.703712i	$0.248476\pi$
$887$	−7342.41	+	22597.6i	−0.277941	+	0.855415i	−0.988426	+	0.151703i	$0.951524\pi$
$888$	−2843.06	−	8750.04i	−0.107440	−	0.330667i
$889$	43072.7	−	31294.1i	1.62498	−	1.18062i
$890$	27507.1			1.03600
$891$	2952.70	−	119.407i	0.111020	−	0.00448966i
$892$	6419.26			0.240956
$893$	16227.8	−	11790.2i	0.608111	−	0.441818i
$894$	4891.94	+	15055.9i	0.183010	+	0.563247i
$895$	−209.825	+	645.775i	−0.00783651	+	0.0241183i
$896$	21338.7	+	15503.5i	0.795622	+	0.578053i
$897$	−16215.3	−	11781.1i	−0.603581	−	0.438528i
$898$	−5302.29	+	16318.8i	−0.197038	+	0.606419i
$899$	−545.919	−	1680.17i	−0.0202530	−	0.0623323i
$900$	−204.879	+	148.853i	−0.00758811	+	0.00551308i
$901$	2429.65			0.0898374
$902$	3454.82	−	12303.9i	0.127531	−	0.454186i
$903$	−14348.4			−0.528777
$904$	−8681.31	+	6307.34i	−0.319398	+	0.232057i
$905$	−132.062	−	406.444i	−0.00485069	−	0.0149289i
$906$	2752.41	−	8471.05i	0.100930	−	0.310631i
$907$	10232.4	+	7434.24i	0.374597	+	0.272161i	0.759115	−	0.650957i	$-0.225632\pi$
$907$	10232.4	+	7434.24i	0.374597	+	0.272161i	−0.384517	+	0.923118i	$0.625632\pi$
$908$	567.053	+	411.988i	0.0207250	+	0.0150576i
$909$	63.1091	−	194.230i	0.00230275	−	0.00708713i
$910$	19351.1	+	59556.6i	0.704927	+	2.16954i
$911$	10814.5	−	7857.18i	0.393304	−	0.285752i	−0.373504	−	0.927628i	$-0.621844\pi$
$911$	10814.5	−	7857.18i	0.393304	−	0.285752i	0.766808	+	0.641877i	$0.221844\pi$
$912$	−12767.8			−0.463577
$913$	6673.58	−	23767.1i	0.241909	−	0.861531i
$914$	2891.93			0.104657
$915$	10294.2	−	7479.20i	0.371931	−	0.270224i
$916$	1591.54	+	4898.26i	0.0574082	+	0.176684i
$917$	−10624.1	+	32697.6i	−0.382593	+	1.17750i
$918$	3019.86	+	2194.06i	0.108573	+	0.0788830i
$919$	14994.8	+	10894.4i	0.538230	+	0.391047i	0.823427	−	0.567422i	$-0.192059\pi$
$919$	14994.8	+	10894.4i	0.538230	+	0.391047i	−0.285197	+	0.958469i	$0.592059\pi$
$920$	7166.78	−	22057.1i	0.256828	−	0.790435i
$921$	960.635	+	2956.53i	0.0343692	+	0.105777i
$922$	16986.1	−	12341.1i	0.606732	−	0.440817i
$923$	54908.7			1.95812
$924$	6250.00	−	252.750i	0.222522	−	0.00899877i
$925$	−2029.31			−0.0721332
$926$	−3645.03	+	2648.27i	−0.129355	+	0.0939822i
$927$	2729.42	+	8400.29i	0.0967054	+	0.297629i
$928$	−1835.75	+	5649.85i	−0.0649368	+	0.199855i
$929$	−21222.9	−	15419.3i	−0.749517	−	0.544556i	0.146160	−	0.989261i	$-0.453309\pi$
$929$	−21222.9	−	15419.3i	−0.749517	−	0.544556i	−0.895677	+	0.444705i	$0.853309\pi$
$930$	−1458.50	−	1059.66i	−0.0514260	−	0.0373632i
$931$	20425.9	−	62864.5i	0.719047	−	2.21300i
$932$	1329.47	+	4091.70i	0.0467257	+	0.143807i
$933$	25082.8	−	18223.7i	0.880142	−	0.639461i
$934$	−47575.7			−1.66673
$935$	16509.9	−	13046.1i	0.577466	−	0.456314i
$936$	16069.1			0.561150
$937$	11249.4	−	8173.17i	0.392212	−	0.284958i	−0.374150	−	0.927368i	$-0.622065\pi$
$937$	11249.4	−	8173.17i	0.392212	−	0.284958i	0.766361	+	0.642410i	$0.222065\pi$
$938$	−5600.69	−	17237.2i	−0.194956	−	0.600014i
$939$	6610.74	−	20345.8i	0.229748	−	0.707092i
$940$	−3262.43	−	2370.29i	−0.113201	−	0.0822452i
$941$	−29656.0	−	21546.4i	−1.02737	−	0.746431i	−0.0595926	−	0.998223i	$-0.518980\pi$
$941$	−29656.0	−	21546.4i	−1.02737	−	0.746431i	−0.967781	+	0.251792i	$0.918980\pi$
$942$	−4286.95	+	13193.9i	−0.148276	+	0.456348i
$943$	−3947.15	−	12148.1i	−0.136306	−	0.419508i
$944$	−15276.6	+	11099.1i	−0.526707	+	0.382675i
$945$	−9228.04			−0.317659
$946$	−11086.3	−	7389.23i	−0.381022	−	0.253958i
$947$	−9454.30			−0.324417			−0.162209	−	0.986756i	$-0.551862\pi$
$947$	−9454.30			−0.324417			−0.162209	+	0.986756i	$0.551862\pi$
$948$	−4997.99	+	3631.25i	−0.171231	+	0.124407i
$949$	5025.69	+	15467.5i	0.171908	+	0.529079i
$950$	−1128.70	+	3473.79i	−0.0385473	+	0.118637i
$951$	15645.5	+	11367.1i	0.533480	+	0.387596i
$952$	35701.0	+	25938.3i	1.21542	+	0.883052i
$953$	9444.38	−	29066.8i	0.321022	−	0.988003i	−0.652183	−	0.758062i	$-0.726147\pi$
$953$	9444.38	−	29066.8i	0.321022	−	0.988003i	0.973204	−	0.229941i	$-0.0738534\pi$
$954$	−305.736	−	940.959i	−0.0103759	−	0.0319336i
$955$	−38661.2	+	28089.0i	−1.31000	+	0.951769i
$956$	7407.31			0.250596
$957$	−2915.29	−	7874.39i	−0.0984723	−	0.265980i
$958$	−42312.6			−1.42699
$959$	−81442.6	+	59171.5i	−2.74235	+	1.99244i
$960$	5510.22	+	16958.7i	0.185252	+	0.570146i
$961$	−9042.06	+	27828.6i	−0.303517	+	0.934128i
$962$	18652.0	+	13551.5i	0.625119	+	0.454175i
$963$	4849.03	+	3523.03i	0.162261	+	0.117890i
$964$	1448.33	−	4457.51i	0.0483897	−	0.148928i
$965$	−16265.6	−	50060.4i	−0.542600	−	1.66995i
$966$	−18133.2	+	13174.6i	−0.603962	+	0.438804i
$967$	−30119.6			−1.00164			−0.500818	−	0.865553i	$-0.666967\pi$
$967$	−30119.6			−1.00164			−0.500818	+	0.865553i	$0.666967\pi$
$968$	27697.9	+	16885.9i	0.919673	+	0.560676i
$969$	−15017.0			−0.497848
$970$	5182.06	−	3764.99i	0.171532	−	0.124625i
$971$	−9953.51	−	30633.7i	−0.328963	−	1.01244i	−0.969620	−	0.244617i	$-0.921338\pi$
$971$	−9953.51	−	30633.7i	−0.328963	−	1.01244i	0.640657	−	0.767828i	$-0.278662\pi$
$972$	−131.017	+	403.229i	−0.00432343	+	0.0133061i
$973$	−28271.9	−	20540.7i	−0.931505	−	0.676778i
$974$	18627.1	+	13533.4i	0.612782	+	0.445212i
$975$	1095.26	−	3370.87i	0.0359759	−	0.110722i
$976$	5903.55	+	18169.3i	0.193615	+	0.595885i
$977$	6868.82	−	4990.49i	0.224926	−	0.163419i	−0.469615	−	0.882871i	$-0.655607\pi$
$977$	6868.82	−	4990.49i	0.224926	−	0.163419i	0.694541	+	0.719453i	$0.255607\pi$
$978$	13602.8			0.444756
$979$	13351.3	+	36062.8i	0.435864	+	1.17730i
$980$	−13288.6			−0.433153
$981$	−623.642	+	453.103i	−0.0202970	+	0.0147466i
$982$	12678.5	+	39020.3i	0.412003	+	1.26801i
$983$	−1043.50	+	3211.55i	−0.0338580	+	0.104204i	−0.966557	−	0.256451i	$-0.917447\pi$
$983$	−1043.50	+	3211.55i	−0.0338580	+	0.104204i	0.932699	+	0.360655i	$0.117447\pi$
$984$	8284.84	+	6019.29i	0.268406	+	0.195008i
$985$	−14378.0	−	10446.2i	−0.465097	−	0.337913i
$986$	3277.53	−	10087.2i	0.105860	−	0.325803i
$987$	6726.27	+	20701.3i	0.216919	+	0.667609i
$988$	−9364.21	+	6803.50i	−0.301534	+	0.219077i
$989$	−13316.4			−0.428145
$990$	−7130.04	−	4752.31i	−0.228896	−	0.152564i
$991$	−20081.5			−0.643703			−0.321851	−	0.946790i	$-0.604305\pi$
$991$	−20081.5			−0.643703			−0.321851	+	0.946790i	$0.604305\pi$
$992$	−1442.57	+	1048.08i	−0.0461709	+	0.0335451i
$993$	5223.48	+	16076.2i	0.166931	+	0.513760i
$994$	18974.7	−	58398.0i	0.605473	−	1.86345i
$995$	28077.2	+	20399.3i	0.894580	+	0.649951i
$996$	2865.40	+	2081.83i	0.0911582	+	0.0662303i
$997$	−10625.0	+	32700.4i	−0.337510	+	1.03875i	0.627962	+	0.778244i	$0.283889\pi$
$997$	−10625.0	+	32700.4i	−0.337510	+	1.03875i	−0.965472	+	0.260506i	$0.916111\pi$
$998$	−3579.42	−	11016.3i	−0.113532	−	0.349414i
$999$	−2748.59	+	1996.97i	−0.0870487	+	0.0632446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.e.b.25.1	yes	8
3.2	odd	2		99.4.f.b.91.2		8
11.2	odd	10		363.4.a.t.1.1		4
11.4	even	5	inner	33.4.e.b.4.1	✓	8
11.9	even	5		363.4.a.p.1.4		4
33.2	even	10		1089.4.a.z.1.4		4
33.20	odd	10		1089.4.a.bg.1.1		4
33.26	odd	10		99.4.f.b.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.4.1	✓	8	11.4	even	5	inner
33.4.e.b.25.1	yes	8	1.1	even	1	trivial
99.4.f.b.37.2		8	33.26	odd	10
99.4.f.b.91.2		8	3.2	odd	2
363.4.a.p.1.4		4	11.9	even	5
363.4.a.t.1.1		4	11.2	odd	10
1089.4.a.z.1.4		4	33.2	even	10
1089.4.a.bg.1.1		4	33.20	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02339 + 1.47008i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-0.539165 + 1.65938i) q^{4} +(-8.44146 - 6.13308i) q^{5} +(-6.07016 - 4.41023i) q^{6} +(-10.1220 + 31.1524i) q^{7} +(-7.53140 - 23.1793i) q^{8} +(-7.28115 + 5.29007i) q^{9} +O(q^{10})\)	\(q+(-2.02339 + 1.47008i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-0.539165 + 1.65938i) q^{4} +(-8.44146 - 6.13308i) q^{5} +(-6.07016 - 4.41023i) q^{6} +(-10.1220 + 31.1524i) q^{7} +(-7.53140 - 23.1793i) q^{8} +(-7.28115 + 5.29007i) q^{9} +26.0964 q^{10} +(12.6666 + 34.2134i) q^{11} -5.23432 q^{12} +(59.2672 - 43.0601i) q^{13} +(-25.3157 - 77.9137i) q^{14} +(9.67305 - 29.7706i) q^{15} +(38.0218 + 27.6245i) q^{16} +(44.7200 + 32.4909i) q^{17} +(6.95579 - 21.4077i) q^{18} +(27.9834 + 86.1240i) q^{19} +(14.7284 - 10.7008i) q^{20} -98.2669 q^{21} +(-75.9259 - 50.6060i) q^{22} -91.1987 q^{23} +(59.1524 - 42.9767i) q^{24} +(-4.98357 - 15.3379i) q^{25} +(-56.6188 + 174.255i) q^{26} +(-21.8435 - 15.8702i) q^{27} +(-46.2362 - 33.5926i) q^{28} +(-23.7073 + 72.9635i) q^{29} +(24.1927 + 74.4576i) q^{30} +(-18.6296 + 13.5352i) q^{31} +77.4339 q^{32} +(-85.8740 + 67.8576i) q^{33} -138.250 q^{34} +(276.505 - 200.893i) q^{35} +(-4.85248 - 14.9344i) q^{36} +(38.8841 - 119.673i) q^{37} +(-183.230 - 133.124i) q^{38} +(177.802 + 129.180i) q^{39} +(-78.5842 + 241.857i) q^{40} +(43.2807 + 133.204i) q^{41} +(198.832 - 144.460i) q^{42} +146.015 q^{43} +(-63.6024 + 2.57208i) q^{44} +93.9079 q^{45} +(184.530 - 134.069i) q^{46} +(-68.4490 - 210.664i) q^{47} +(-43.5692 + 134.092i) q^{48} +(-590.526 - 429.042i) q^{49} +(32.6315 + 23.7082i) q^{50} +(-51.2445 + 157.714i) q^{51} +(39.4983 + 121.563i) q^{52} +(35.5597 - 25.8356i) q^{53} +67.5282 q^{54} +(102.909 - 366.496i) q^{55} +798.324 q^{56} +(-219.784 + 159.683i) q^{57} +(-59.2930 - 182.485i) q^{58} +(-124.159 + 382.121i) q^{59} +(44.1853 + 32.1025i) q^{60} +(328.861 + 238.932i) q^{61} +(17.7972 - 54.7740i) q^{62} +(-91.0984 - 280.372i) q^{63} +(-460.853 + 334.830i) q^{64} -764.393 q^{65} +(74.0005 - 263.544i) q^{66} +221.234 q^{67} +(-78.0262 + 56.6893i) q^{68} +(-84.5459 - 260.205i) q^{69} +(-264.149 + 812.968i) q^{70} +(606.376 + 440.558i) q^{71} +(177.457 + 128.930i) q^{72} +(-68.6023 + 211.136i) q^{73} +(97.2508 + 299.307i) q^{74} +(39.1415 - 28.4379i) q^{75} -158.000 q^{76} +(-1194.04 + 48.2871i) q^{77} -549.667 q^{78} +(954.850 - 693.739i) q^{79} +(-151.537 - 466.382i) q^{80} +(25.0304 - 77.0356i) q^{81} +(-283.394 - 205.898i) q^{82} +(-547.425 - 397.728i) q^{83} +(52.9820 - 163.062i) q^{84} +(-178.232 - 548.542i) q^{85} +(-295.444 + 214.653i) q^{86} -230.155 q^{87} +(697.644 - 551.278i) q^{88} +1054.06 q^{89} +(-190.012 + 138.052i) q^{90} +(741.524 + 2282.17i) q^{91} +(49.1711 - 151.333i) q^{92} +(-55.8889 - 40.6057i) q^{93} +(448.192 + 325.630i) q^{94} +(291.985 - 898.636i) q^{95} +(71.7852 + 220.932i) q^{96} +(198.573 - 144.272i) q^{97} +1825.59 q^{98} +(-273.219 - 182.106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Introduction

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