LMFDB - Embedded newform 37.6.e.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,6,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	37.e (of order $6$, degree $2$, 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:	$5.93420133308$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	37.11
Dual form			37.6.e.a.27.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.35252 - 5.39968i) q^{2} +(-9.83385 + 17.0327i) q^{3} +(42.3131 - 73.2884i) q^{4} +(68.3185 + 39.4437i) q^{5} +212.399i q^{6} +(50.6016 - 87.6446i) q^{7} -568.329i q^{8} +(-71.9093 - 124.551i) q^{9} +O(q^{10})$	\(q+(9.35252 - 5.39968i) q^{2} +(-9.83385 + 17.0327i) q^{3} +(42.3131 - 73.2884i) q^{4} +(68.3185 + 39.4437i) q^{5} +212.399i q^{6} +(50.6016 - 87.6446i) q^{7} -568.329i q^{8} +(-71.9093 - 124.551i) q^{9} +851.933 q^{10} -592.274 q^{11} +(832.201 + 1441.41i) q^{12} +(458.144 + 264.509i) q^{13} -1092.93i q^{14} +(-1343.67 + 775.767i) q^{15} +(-1714.77 - 2970.08i) q^{16} +(-1626.52 + 939.070i) q^{17} +(-1345.07 - 776.574i) q^{18} +(0.268250 + 0.154874i) q^{19} +(5781.53 - 3337.97i) q^{20} +(995.218 + 1723.77i) q^{21} +(-5539.26 + 3198.09i) q^{22} -4.30819i q^{23} +(9680.19 + 5588.86i) q^{24} +(1549.11 + 2683.14i) q^{25} +5713.06 q^{26} -1950.67 q^{27} +(-4282.22 - 7417.02i) q^{28} -4684.57i q^{29} +(-8377.79 + 14510.7i) q^{30} -1652.15i q^{31} +(-16324.9 - 9425.21i) q^{32} +(5824.34 - 10088.0i) q^{33} +(-10141.4 + 17565.3i) q^{34} +(6914.05 - 3991.83i) q^{35} -12170.8 q^{36} +(-2780.33 + 7849.44i) q^{37} +3.34508 q^{38} +(-9010.63 + 5202.29i) q^{39} +(22417.0 - 38827.4i) q^{40} +(624.931 - 1082.41i) q^{41} +(18615.6 + 10747.7i) q^{42} -5792.36i q^{43} +(-25060.9 + 43406.8i) q^{44} -11345.5i q^{45} +(-23.2629 - 40.2925i) q^{46} +998.865 q^{47} +67451.3 q^{48} +(3282.45 + 5685.38i) q^{49} +(28976.2 + 16729.4i) q^{50} -36938.7i q^{51} +(38770.9 - 22384.4i) q^{52} +(518.744 + 898.490i) q^{53} +(-18243.7 + 10533.0i) q^{54} +(-40463.3 - 23361.5i) q^{55} +(-49810.9 - 28758.4i) q^{56} +(-5.27586 + 3.04602i) q^{57} +(-25295.2 - 43812.5i) q^{58} +(30400.4 - 17551.7i) q^{59} +131300. i q^{60} +(38693.7 + 22339.8i) q^{61} +(-8921.08 - 15451.8i) q^{62} -14554.9 q^{63} -93826.8 q^{64} +(20866.5 + 36141.8i) q^{65} -125798. i q^{66} +(14265.2 - 24708.1i) q^{67} +158940. i q^{68} +(73.3803 + 42.3661i) q^{69} +(43109.2 - 74667.3i) q^{70} +(-445.361 + 771.389i) q^{71} +(-70785.6 + 40868.1i) q^{72} +4973.52 q^{73} +(16381.4 + 88424.9i) q^{74} -60934.9 q^{75} +(22.7009 - 13.1064i) q^{76} +(-29970.0 + 51909.6i) q^{77} +(-56181.4 + 97309.1i) q^{78} +(47316.5 + 27318.2i) q^{79} -270548. i q^{80} +(36656.6 - 63491.0i) q^{81} -13497.7i q^{82} +(-47235.7 - 81814.6i) q^{83} +168443. q^{84} -148162. q^{85} +(-31276.9 - 54173.1i) q^{86} +(79791.0 + 46067.4i) q^{87} +336606. i q^{88} +(-6614.02 + 3818.60i) q^{89} +(-61261.9 - 106109. i) q^{90} +(46365.6 - 26769.2i) q^{91} +(-315.741 - 182.293i) q^{92} +(28140.6 + 16247.0i) q^{93} +(9341.90 - 5393.55i) q^{94} +(12.2176 + 21.1615i) q^{95} +(321074. - 185372. i) q^{96} +148523. i q^{97} +(61398.4 + 35448.4i) q^{98} +(42590.0 + 73768.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{2} + 18 q^{3} + 298 q^{4} + 144 q^{5} - 52 q^{7} - 1490 q^{9}+O(q^{10}) $ 32 * q - 6 * q^2 + 18 * q^3 + 298 * q^4 + 144 * q^5 - 52 * q^7 - 1490 * q^9	\( 32 q - 6 q^{2} + 18 q^{3} + 298 q^{4} + 144 q^{5} - 52 q^{7} - 1490 q^{9} + 668 q^{10} - 348 q^{11} + 134 q^{12} + 222 q^{13} - 4134 q^{15} - 6998 q^{16} - 624 q^{17} + 7632 q^{18} + 2154 q^{19} + 4806 q^{20} - 130 q^{21} - 8214 q^{22} + 24642 q^{24} + 15808 q^{25} + 4332 q^{26} - 30384 q^{27} - 9048 q^{28} + 7780 q^{30} + 35088 q^{32} - 924 q^{33} - 5982 q^{34} + 27072 q^{35} - 57468 q^{36} - 46062 q^{37} - 48048 q^{38} - 31896 q^{39} + 57956 q^{40} - 11136 q^{41} + 50886 q^{42} - 43686 q^{44} + 42866 q^{46} + 63708 q^{47} - 39260 q^{48} - 52426 q^{49} - 29292 q^{50} + 132684 q^{52} - 85398 q^{53} + 235314 q^{54} - 65346 q^{55} + 121836 q^{56} - 96270 q^{57} - 121896 q^{58} + 40980 q^{59} - 74616 q^{61} + 89346 q^{62} + 232304 q^{63} - 321132 q^{64} + 24066 q^{65} + 68018 q^{67} - 11052 q^{69} - 230194 q^{70} - 32544 q^{71} + 117876 q^{72} - 179176 q^{73} - 89166 q^{74} - 379288 q^{75} + 196110 q^{76} + 22428 q^{77} - 288138 q^{78} + 217218 q^{79} - 6200 q^{81} - 127434 q^{83} + 1109800 q^{84} + 218576 q^{85} - 80364 q^{86} + 457230 q^{87} - 164844 q^{89} - 360436 q^{90} + 167160 q^{91} - 984606 q^{92} + 532392 q^{93} - 369822 q^{94} + 187398 q^{95} + 1476018 q^{96} - 174684 q^{98} + 194298 q^{99}+O(q^{100}) \) 32 * q - 6 * q^2 + 18 * q^3 + 298 * q^4 + 144 * q^5 - 52 * q^7 - 1490 * q^9 + 668 * q^10 - 348 * q^11 + 134 * q^12 + 222 * q^13 - 4134 * q^15 - 6998 * q^16 - 624 * q^17 + 7632 * q^18 + 2154 * q^19 + 4806 * q^20 - 130 * q^21 - 8214 * q^22 + 24642 * q^24 + 15808 * q^25 + 4332 * q^26 - 30384 * q^27 - 9048 * q^28 + 7780 * q^30 + 35088 * q^32 - 924 * q^33 - 5982 * q^34 + 27072 * q^35 - 57468 * q^36 - 46062 * q^37 - 48048 * q^38 - 31896 * q^39 + 57956 * q^40 - 11136 * q^41 + 50886 * q^42 - 43686 * q^44 + 42866 * q^46 + 63708 * q^47 - 39260 * q^48 - 52426 * q^49 - 29292 * q^50 + 132684 * q^52 - 85398 * q^53 + 235314 * q^54 - 65346 * q^55 + 121836 * q^56 - 96270 * q^57 - 121896 * q^58 + 40980 * q^59 - 74616 * q^61 + 89346 * q^62 + 232304 * q^63 - 321132 * q^64 + 24066 * q^65 + 68018 * q^67 - 11052 * q^69 - 230194 * q^70 - 32544 * q^71 + 117876 * q^72 - 179176 * q^73 - 89166 * q^74 - 379288 * q^75 + 196110 * q^76 + 22428 * q^77 - 288138 * q^78 + 217218 * q^79 - 6200 * q^81 - 127434 * q^83 + 1109800 * q^84 + 218576 * q^85 - 80364 * q^86 + 457230 * q^87 - 164844 * q^89 - 360436 * q^90 + 167160 * q^91 - 984606 * q^92 + 532392 * q^93 - 369822 * q^94 + 187398 * q^95 + 1476018 * q^96 - 174684 * q^98 + 194298 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	9.35252	−	5.39968i	1.65331	−	0.954537i	0.677608	−	0.735423i	$-0.263017\pi$
$2$	9.35252	−	5.39968i	1.65331	−	0.954537i	0.975699	−	0.219114i	$-0.0703168\pi$
$3$	−9.83385	+	17.0327i	−0.630842	+	1.09265i	0.356538	+	0.934281i	$0.383957\pi$
$3$	−9.83385	+	17.0327i	−0.630842	+	1.09265i	−0.987380	+	0.158369i	$0.949376\pi$
$4$	42.3131	−	73.2884i	1.32228	−	2.29026i
$5$	68.3185	+	39.4437i	1.22212	+	0.705590i	0.965369	−	0.260888i	$-0.0840153\pi$
$5$	68.3185	+	39.4437i	1.22212	+	0.705590i	0.256749	+	0.966478i	$0.417349\pi$
$6$			212.399i			2.40865i
$7$	50.6016	−	87.6446i	0.390319	−	0.676052i	−0.602173	−	0.798366i	$-0.705698\pi$
$7$	50.6016	−	87.6446i	0.390319	−	0.676052i	0.992491	+	0.122314i	$0.0390315\pi$
$8$		−	568.329i		−	3.13960i
$9$	−71.9093	−	124.551i	−0.295923	−	0.512554i
$10$	851.933			2.69405
$11$	−592.274			−1.47585			−0.737923	−	0.674885i	$-0.764193\pi$
$11$	−592.274			−1.47585			−0.737923	+	0.674885i	$0.764193\pi$
$12$	832.201	+	1441.41i	1.66830	+	2.88959i
$13$	458.144	+	264.509i	0.751871	+	0.434093i	0.826370	−	0.563128i	$-0.190402\pi$
$13$	458.144	+	264.509i	0.751871	+	0.434093i	−0.0744986	+	0.997221i	$0.523736\pi$
$14$		−	1092.93i		−	1.49030i
$15$	−1343.67	+	775.767i	−1.54193	+	0.890232i
$16$	−1714.77	−	2970.08i	−1.67458	−	2.90047i
$17$	−1626.52	+	939.070i	−1.36501	+	0.788090i	−0.990286	−	0.139046i	$-0.955596\pi$
$17$	−1626.52	+	939.070i	−1.36501	+	0.788090i	−0.374725	+	0.927136i	$0.622263\pi$
$18$	−1345.07	−	776.574i	−0.978503	−	0.564939i
$19$	0.268250	+	0.154874i	0.000170473	+	9.84226e-5i	0.500085	−	0.865976i	$-0.333302\pi$
$19$	0.268250	+	0.154874i	0.000170473	+	9.84226e-5i	−0.499915	+	0.866075i	$0.666635\pi$
$20$	5781.53	−	3337.97i	3.23197	−	1.86598i
$21$	995.218	+	1723.77i	0.492459	+	0.852963i
$22$	−5539.26	+	3198.09i	−2.44003	+	1.40875i
$23$		−	4.30819i		−	0.00169815i	−1.00000		0.000849074i	$-0.999730\pi$
$23$		−	4.30819i		−	0.00169815i	1.00000		0.000849074i	$-0.000270269\pi$
$24$	9680.19	+	5588.86i	3.43049	+	1.98059i
$25$	1549.11	+	2683.14i	0.495715	+	0.858604i
$26$	5713.06			1.65743
$27$	−1950.67			−0.514961
$28$	−4282.22	−	7417.02i	−1.03222	−	1.78786i
$29$		−	4684.57i		−	1.03437i	−0.855874	−	0.517184i	$-0.826980\pi$
$29$		−	4684.57i		−	1.03437i	0.855874	−	0.517184i	$-0.173020\pi$
$30$	−8377.79	+	14510.7i	−1.69952	+	2.94365i
$31$		−	1652.15i		−	0.308777i	−0.988010	−	0.154389i	$-0.950659\pi$
$31$		−	1652.15i		−	0.308777i	0.988010	−	0.154389i	$-0.0493408\pi$
$32$	−16324.9	−	9425.21i	−2.81823	−	1.62711i
$33$	5824.34	−	10088.0i	0.931025	−	1.61258i
$34$	−10141.4	+	17565.3i	−1.50452	+	2.60591i
$35$	6914.05	−	3991.83i	0.954031	−	0.550810i
$36$	−12170.8			−1.56518
$37$	−2780.33	+	7849.44i	−0.333881	+	0.942615i
$37$	−2780.33	+	7849.44i	−0.333881	+	0.942615i
$38$	3.34508			0.000375792
$39$	−9010.63	+	5202.29i	−0.948623	+	0.547688i
$40$	22417.0	−	38827.4i	2.21527	−	3.83697i
$41$	624.931	−	1082.41i	0.0580594	−	0.100562i	−0.835535	−	0.549437i	$-0.814842\pi$
$41$	624.931	−	1082.41i	0.0580594	−	0.100562i	0.893594	+	0.448876i	$0.148175\pi$
$42$	18615.6	+	10747.7i	1.62837	+	0.940141i
$43$		−	5792.36i		−	0.477732i	−0.971053	−	0.238866i	$-0.923224\pi$
$43$		−	5792.36i		−	0.477732i	0.971053	−	0.238866i	$-0.0767757\pi$
$44$	−25060.9	+	43406.8i	−1.95149	+	3.38007i
$45$		−	11345.5i		−	0.835201i
$46$	−23.2629	−	40.2925i	−0.00162095	−	0.00280756i
$47$	998.865			0.0659572			0.0329786	−	0.999456i	$-0.489501\pi$
$47$	998.865			0.0659572			0.0329786	+	0.999456i	$0.489501\pi$
$48$	67451.3			4.22559
$49$	3282.45	+	5685.38i	0.195303	+	0.338274i
$50$	28976.2	+	16729.4i	1.63914	+	0.946358i
$51$		−	36938.7i		−	1.98864i
$52$	38770.9	−	22384.4i	1.98837	−	1.14799i
$53$	518.744	+	898.490i	0.0253667	+	0.0439363i	0.878430	−	0.477871i	$-0.158591\pi$
$53$	518.744	+	898.490i	0.0253667	+	0.0439363i	−0.853063	+	0.521807i	$0.825258\pi$
$54$	−18243.7	+	10533.0i	−0.851390	+	0.491550i
$55$	−40463.3	−	23361.5i	−1.80366	−	1.04134i
$56$	−49810.9	−	28758.4i	−2.12253	−	1.22545i
$57$	−5.27586	+	3.04602i	−0.000215083	+	0.000124178i
$58$	−25295.2	−	43812.5i	−0.987342	−	1.71013i
$59$	30400.4	−	17551.7i	1.13697	−	0.656431i	0.191292	−	0.981533i	$-0.438732\pi$
$59$	30400.4	−	17551.7i	1.13697	−	0.656431i	0.945679	+	0.325102i	$0.105399\pi$
$60$			131300.i			4.70856i
$61$	38693.7	+	22339.8i	1.33142	+	0.768698i	0.985518	−	0.169572i	$-0.0542384\pi$
$61$	38693.7	+	22339.8i	1.33142	+	0.768698i	0.345906	+	0.938269i	$0.387572\pi$
$62$	−8921.08	−	15451.8i	−0.294739	−	0.510504i
$63$	−14554.9			−0.462017
$64$	−93826.8			−2.86337
$65$	20866.5	+	36141.8i	0.612584	+	1.06103i
$66$		−	125798.i		−	3.55479i
$67$	14265.2	−	24708.1i	0.388232	−	0.672437i	−0.603980	−	0.796999i	$-0.706419\pi$
$67$	14265.2	−	24708.1i	0.388232	−	0.672437i	0.992212	+	0.124562i	$0.0397527\pi$
$68$			158940.i			4.16831i
$69$	73.3803	+	42.3661i	0.00185548	+	0.00107126i
$70$	43109.2	−	74667.3i	1.05154	−	1.82132i
$71$	−445.361	+	771.389i	−0.0104850	+	0.0181605i	−0.871220	−	0.490892i	$-0.836671\pi$
$71$	−445.361	+	771.389i	−0.0104850	+	0.0181605i	0.860735	+	0.509053i	$0.170004\pi$
$72$	−70785.6	+	40868.1i	−1.60921	+	0.929080i
$73$	4973.52			0.109234			0.0546169	−	0.998507i	$-0.482606\pi$
$73$	4973.52			0.109234			0.0546169	+	0.998507i	$0.482606\pi$
$74$	16381.4	+	88424.9i	0.347754	+	1.87713i
$75$	−60934.9			−1.25087
$76$	22.7009	−	13.1064i	0.000450827	−	0.000260285i
$77$	−29970.0	+	51909.6i	−0.576050	+	0.997748i
$78$	−56181.4	+	97309.1i	−1.04558	+	1.81099i
$79$	47316.5	+	27318.2i	0.852992	+	0.492475i	0.861659	−	0.507487i	$-0.169426\pi$
$79$	47316.5	+	27318.2i	0.852992	+	0.492475i	−0.00866731	+	0.999962i	$0.502759\pi$
$80$		−	270548.i		−	4.72628i
$81$	36656.6	−	63491.0i	0.620782	−	1.07523i
$82$		−	13497.7i		−	0.221679i
$83$	−47235.7	−	81814.6i	−0.752618	−	1.30357i	−0.946550	−	0.322558i	$-0.895457\pi$
$83$	−47235.7	−	81814.6i	−0.752618	−	1.30357i	0.193932	−	0.981015i	$-0.437876\pi$
$84$	168443.			2.60468
$85$	−148162.			−2.22427
$86$	−31276.9	−	54173.1i	−0.456013	−	0.789838i
$87$	79791.0	+	46067.4i	1.13020	+	0.652522i
$88$			336606.i			4.63357i
$89$	−6614.02	+	3818.60i	−0.0885096	+	0.0511010i	−0.543602	−	0.839343i	$-0.682940\pi$
$89$	−6614.02	+	3818.60i	−0.0885096	+	0.0511010i	0.455092	+	0.890444i	$0.349606\pi$
$90$	−61261.9	−	106109.i	−0.797231	−	1.38084i
$91$	46365.6	−	26769.2i	0.586939	−	0.338869i
$92$	−315.741	−	182.293i	−0.00388921	−	0.00224543i
$93$	28140.6	+	16247.0i	0.337385	+	0.194790i
$94$	9341.90	−	5393.55i	0.109047	−	0.0629586i
$95$	12.2176	+	21.1615i	0.000138892	+	0.000240568i
$96$	321074.	−	185372.i	3.55572	−	2.05289i
$97$			148523.i			1.60274i	0.598169	+	0.801370i	$0.295895\pi$
$97$			148523.i			1.60274i	−0.598169	+	0.801370i	$0.704105\pi$
$98$	61398.4	+	35448.4i	0.645791	+	0.372848i
$99$	42590.0	+	73768.0i	0.436737	+	0.756450i
$100$	262190.			2.62190
$101$	−156843.			−1.52990			−0.764948	−	0.644092i	$-0.777236\pi$
$101$	−156843.			−1.52990			−0.764948	+	0.644092i	$0.777236\pi$
$102$	−199457.	−	345470.i	−1.89823	−	3.28783i
$103$			149827.i			1.39155i	0.718261	+	0.695774i	$0.244938\pi$
$103$			149827.i			1.39155i	−0.718261	+	0.695774i	$0.755062\pi$
$104$	150328.	−	260376.i	1.36288	−	2.36058i
$105$			157020.i			1.38990i
$106$	9703.12	+	5602.10i	0.0838777	+	0.0484268i
$107$	−37235.5	+	64493.7i	−0.314411	+	0.544575i	−0.979312	−	0.202356i	$-0.935140\pi$
$107$	−37235.5	+	64493.7i	−0.314411	+	0.544575i	0.664901	+	0.746931i	$0.268474\pi$
$108$	−82538.9	+	142962.i	−0.680925	+	1.17940i
$109$	75405.1	−	43535.2i	0.607904	−	0.350973i	−0.164241	−	0.986420i	$-0.552517\pi$
$109$	75405.1	−	43535.2i	0.607904	−	0.350973i	0.772145	+	0.635447i	$0.219184\pi$
$110$	−504578.			−3.97600
$111$	−106356.	−	124547.i	−0.819323	−	0.959456i
$112$	−347081.			−2.61449
$113$	169073.	−	97614.3i	1.24560	−	0.719146i	0.275369	−	0.961339i	$-0.411200\pi$
$113$	169073.	−	97614.3i	1.24560	−	0.719146i	0.970228	+	0.242192i	$0.0778665\pi$
$114$	−32.8950	+	56.9759i	−0.000237065	+	0.000410609i
$115$	169.931	−	294.329i	0.00119820	−	0.00207534i
$116$	−343325.	−	198219.i	−2.36897	−	1.36773i
$117$		−	76082.7i		−	0.513832i
$118$	189547.	−	328305.i	1.25318	−	2.17056i
$119$			190074.i			1.23042i
$120$	440891.	+	763645.i	2.79497	+	4.84104i
$121$	189738.			1.17812
$122$	482512.			2.93500
$123$	12291.0	+	21288.6i	0.0732525	+	0.126877i
$124$	−121083.	−	69907.5i	−0.707181	−	0.408291i
$125$		−	2112.55i		−	0.0120929i
$126$	−136125.	+	78591.8i	−0.763856	+	0.441012i
$127$	−10441.6	−	18085.3i	−0.0574456	−	0.0994986i	0.835873	−	0.548924i	$-0.184962\pi$
$127$	−10441.6	−	18085.3i	−0.0574456	−	0.0994986i	−0.893318	+	0.449425i	$0.851629\pi$
$128$	−355119.	+	205028.i	−1.91579	+	1.10608i
$129$	98659.7	+	56961.2i	0.521994	+	0.301373i
$130$	390308.	+	225344.i	2.02558	+	1.16947i
$131$	−122824.	+	70912.3i	−0.625323	+	0.361030i	−0.778938	−	0.627100i	$-0.784242\pi$
$131$	−122824.	+	70912.3i	−0.625323	+	0.361030i	0.153616	+	0.988131i	$0.450908\pi$
$132$	−492891.	−	853713.i	−2.46216	−	4.26459i
$133$	27.1477	−	15.6738i	0.000133078	−	7.68323e-5i
$134$		−	308110.i		−	1.48233i
$135$	−133267.	−	76941.7i	−0.629344	−	0.363352i
$136$	533700.	+	924396.i	2.47429	+	4.28559i
$137$	119483.			0.543881			0.271941	−	0.962314i	$-0.412335\pi$
$137$	119483.			0.543881			0.271941	+	0.962314i	$0.412335\pi$
$138$	915.054			0.00409024
$139$	−120278.	−	208327.i	−0.528017	−	0.914552i	−0.999467	−	0.0326590i	$-0.989602\pi$
$139$	−120278.	−	208327.i	−0.528017	−	0.914552i	0.471450	−	0.881893i	$-0.343731\pi$
$140$		−	675626.i		−	2.91331i
$141$	−9822.69	+	17013.4i	−0.0416086	+	0.0720681i
$142$			9619.24i			0.0400332i
$143$	−271347.	−	156662.i	−1.10965	−	0.640654i
$144$	−246616.	+	427152.i	−0.991096	+	1.71663i
$145$	184777.	−	320043.i	0.729840	−	1.26412i
$146$	46514.9	−	26855.4i	0.180597	−	0.104268i
$147$	−129117.			−0.492821
$148$	457629.	+	535900.i	1.71735	+	2.01108i
$149$	−185277.			−0.683686			−0.341843	−	0.939757i	$-0.611051\pi$
$149$	−185277.			−0.683686			−0.341843	+	0.939757i	$0.611051\pi$
$150$	−569895.	+	329029.i	−2.06808	+	1.19400i
$151$	−176719.	+	306086.i	−0.630726	+	1.09245i	0.356677	+	0.934228i	$0.383910\pi$
$151$	−176719.	+	306086.i	−0.630726	+	1.09245i	−0.987403	+	0.158222i	$0.949424\pi$
$152$	88.0194	−	152.454i	0.000309008	−	0.000535217i
$153$	233923.	+	135056.i	0.807876	+	0.466428i
$154$			647314.i			2.19945i
$155$	65166.9	−	112872.i	0.217870	−	0.377362i
$156$			880500.i			2.89680i
$157$	−111831.	−	193697.i	−0.362088	−	0.627154i	0.626217	−	0.779649i	$-0.284603\pi$
$157$	−111831.	−	193697.i	−0.362088	−	0.627154i	−0.988304	+	0.152495i	$0.951269\pi$
$158$	590038.			1.88034
$159$	−20405.0			−0.0640094
$160$	−743530.	−	1.28783e6i	−2.29614	−	3.97703i
$161$	−377.590	−	218.002i	−0.00114804	−	0.000662819i
$162$		−	791735.i		−	2.37024i
$163$	71214.5	−	41115.7i	0.209942	−	0.121210i	−0.391342	−	0.920245i	$-0.627989\pi$
$163$	71214.5	−	41115.7i	0.209942	−	0.121210i	0.601284	+	0.799035i	$0.294656\pi$
$164$	−52885.5	−	91600.3i	−0.153542	−	0.265942i
$165$	795820.	−	459467.i	2.27565	−	1.31385i
$166$	−883545.	−	510115.i	−2.48862	−	1.43680i
$167$	−38385.2	−	22161.7i	−0.106506	−	0.0614911i	0.445801	−	0.895132i	$-0.352919\pi$
$167$	−38385.2	−	22161.7i	−0.106506	−	0.0614911i	−0.552307	+	0.833641i	$0.686252\pi$
$168$	979666.	−	565611.i	2.67797	−	1.54612i
$169$	−45716.1	−	79182.6i	−0.123127	−	0.213262i
$170$	−1.38568e6	+	800025.i	−3.67741	+	2.12315i
$171$		−	44.5475i		−	0.000116502i
$172$	−424513.	−	245093.i	−1.09413	−	0.631697i
$173$	106825.	+	185027.i	0.271368	+	0.470023i	0.969212	−	0.246226i	$-0.0791906\pi$
$173$	106825.	+	185027.i	0.271368	+	0.470023i	−0.697844	+	0.716249i	$0.745857\pi$
$174$	994996.			2.49143
$175$	313550.			0.773948
$176$	1.01562e6	+	1.75910e6i	2.47143	+	4.28064i
$177$			690403.i			1.65642i
$178$	−41238.5	+	71427.1i	−0.0975557	+	0.168971i
$179$		−	355365.i		−	0.828977i	−0.910055	−	0.414488i	$-0.863961\pi$
$179$		−	355365.i		−	0.828977i	0.910055	−	0.414488i	$-0.136039\pi$
$180$	−831491.	−	480062.i	−1.91283	−	1.10437i
$181$	308039.	−	533539.i	0.698890	−	1.21051i	−0.269962	−	0.962871i	$-0.587011\pi$
$181$	308039.	−	533539.i	0.698890	−	1.21051i	0.968852	−	0.247642i	$-0.0796557\pi$
$182$	289090.	−	500719.i	0.646927	−	1.12051i
$183$	−761017.	+	439373.i	−1.67984	+	0.969853i
$184$	−2448.47			−0.00533151
$185$	−499559.	+	426596.i	−1.07314	+	0.916404i
$186$	350914.			0.743736
$187$	963344.	−	556187.i	2.01455	−	1.16310i
$188$	42265.0	−	73205.2i	0.0872141	−	0.151059i
$189$	−98707.1	+	170966.i	−0.200999	+	0.348141i
$190$	228.531	+	131.942i	0.000459262	+	0.000265155i
$191$		−	705358.i		−	1.39903i	−0.714619	−	0.699514i	$-0.753400\pi$
$191$		−	705358.i		−	1.39903i	0.714619	−	0.699514i	$-0.246600\pi$
$192$	922679.	−	1.59813e6i	1.80633	−	3.12866i
$193$		−	379796.i		−	0.733934i	−0.930234	−	0.366967i	$-0.880396\pi$
$193$		−	379796.i		−	0.733934i	0.930234	−	0.366967i	$-0.119604\pi$
$194$	801974.	+	1.38906e6i	1.52988	+	2.64982i
$195$	−820791.			−1.54577
$196$	555563.			1.03298
$197$	254858.	+	441427.i	0.467878	+	0.810388i	0.999326	−	0.0367026i	$-0.0116854\pi$
$197$	254858.	+	441427.i	0.467878	+	0.810388i	−0.531449	+	0.847091i	$0.678352\pi$
$198$	796648.	+	459945.i	1.44412	+	0.833763i
$199$			709953.i			1.27086i	0.772160	+	0.635428i	$0.219177\pi$
$199$			709953.i			1.27086i	−0.772160	+	0.635428i	$0.780823\pi$
$200$	1.52490e6	−	880404.i	2.69568	−	1.55635i
$201$	280564.	+	485951.i	0.489826	+	0.848403i
$202$	−1.46688e6	+	846903.i	−2.52939	+	1.46034i
$203$	−410577.	−	237047.i	−0.699286	−	0.403733i
$204$	−2.70718e6	−	1.56299e6i	−4.55451	−	2.62955i
$205$	85388.6	−	49299.2i	0.141911	−	0.0819322i
$206$	809020.	+	1.40126e6i	1.32828	+	2.30066i
$207$	−536.588	+	309.799i	−0.000870392	+	0.000502521i
$208$		−	1.81430e6i		−	2.90770i
$209$	−158.877	−	91.7279i	−0.000251592	−	0.000145257i
$210$	847859.	+	1.46853e6i	1.32671	+	2.29793i
$211$	−740480.			−1.14500			−0.572502	−	0.819903i	$-0.694027\pi$
$211$	−740480.			−1.14500			−0.572502	+	0.819903i	$0.694027\pi$
$212$	87798.6			0.134168
$213$	−8759.24	−	15171.4i	−0.0132287	−	0.0229128i
$214$			804238.i			1.20047i
$215$	228472.	−	395725.i	0.337083	−	0.583845i
$216$			1.10862e6i			1.61677i
$217$	−144802.	−	83601.4i	−0.208749	−	0.120521i
$218$	470152.	−	814327.i	0.670034	−	1.16053i
$219$	−48908.9	+	84712.6i	−0.0689092	+	0.119354i
$220$	−3.42425e6	+	1.97699e6i	−4.76990	+	2.75390i
$221$	−993571.			−1.36842
$222$	−1.66721e6	−	590538.i	−2.27043	−	0.804202i
$223$	384270.			0.517457			0.258729	−	0.965950i	$-0.416696\pi$
$223$	384270.			0.517457			0.258729	+	0.965950i	$0.416696\pi$
$224$	−1.65214e6	+	953861.i	−2.20002	+	1.27018i
$225$	222791.	−	385885.i	0.293387	−	0.508161i
$226$	1.05417e6	−	1.82588e6i	1.37290	−	2.37794i
$227$	594293.	+	343115.i	0.765484	+	0.441952i	0.831261	−	0.555882i	$-0.187619\pi$
$227$	594293.	+	343115.i	0.765484	+	0.441952i	−0.0657776	+	0.997834i	$0.520953\pi$
$228$			515.545i			0.000656795i
$229$	261646.	−	453184.i	0.329705	−	0.571066i	−0.652748	−	0.757575i	$-0.726384\pi$
$229$	261646.	−	453184.i	0.329705	−	0.571066i	0.982453	+	0.186509i	$0.0597174\pi$
$230$		−	3670.29i		−	0.00457490i
$231$	−589442.	−	1.02094e6i	−0.726793	−	1.25884i
$232$	−2.66238e6			−3.24750
$233$	−937202.			−1.13095			−0.565475	−	0.824766i	$-0.691307\pi$
$233$	−937202.			−1.13095			−0.565475	+	0.824766i	$0.691307\pi$
$234$	−410822.	−	711565.i	−0.490472	−	0.849523i
$235$	68240.9	+	39398.9i	0.0806075	+	0.0465387i
$236$		−	2.97066e6i		−	3.47195i
$237$	−930607.	+	537286.i	−1.07621	+	0.621348i
$238$	1.02634e6	+	1.77767e6i	1.17449	+	2.03427i
$239$	−1.29315e6	+	746603.i	−1.46439	+	0.845464i	−0.999209	−	0.0397543i	$-0.987342\pi$
$239$	−1.29315e6	+	746603.i	−1.46439	+	0.845464i	−0.465177	+	0.885218i	$0.654009\pi$
$240$	4.60817e6	+	2.66053e6i	5.16417	+	2.98154i
$241$	1.10863e6	+	640065.i	1.22954	+	0.709874i	0.966933	−	0.255029i	$-0.0820850\pi$
$241$	1.10863e6	+	640065.i	1.22954	+	0.709874i	0.262605	+	0.964903i	$0.415418\pi$
$242$	1.77453e6	−	1.02452e6i	1.94780	−	1.12456i
$243$	483944.	+	838215.i	0.525750	+	0.910626i
$244$	3.27450e6	−	1.89054e6i	3.52104	−	2.03287i
$245$			517888.i			0.551215i
$246$	229903.	+	132734.i	0.242218	+	0.139845i
$247$	81.9313	+	141.909i	8.54491e−5	+	0.000148002i
$248$	−938964.			−0.969437
$249$	1.85803e6			1.89913
$250$	−11407.1	−	19757.7i	−0.0115432	−	0.0199934i
$251$			474898.i			0.475790i	0.971291	+	0.237895i	$0.0764575\pi$
$251$			474898.i			0.475790i	−0.971291	+	0.237895i	$0.923543\pi$
$252$	−615863.	+	1.06671e6i	−0.610917	+	1.05814i
$253$			2551.63i			0.00250621i
$254$	−195310.	−	112762.i	−0.189950	−	0.109668i
$255$	1.45700e6	−	2.52360e6i	1.40316	−	2.43035i
$256$	−712942.	+	1.23485e6i	−0.679915	+	1.17765i
$257$	801308.	−	462636.i	0.756775	−	0.436924i	−0.0713616	−	0.997451i	$-0.522734\pi$
$257$	801308.	−	462636.i	0.756775	−	0.436924i	0.828137	+	0.560526i	$0.189401\pi$
$258$	1.23029e6			1.15069
$259$	547272.	+	640875.i	0.506937	+	0.593641i
$260$	3.53170e6			3.24004
$261$	−583466.	+	336864.i	−0.530169	+	0.306093i
$262$	−765808.	+	1.32642e6i	−0.689234	+	1.19379i
$263$	−103980.	+	180098.i	−0.0926957	+	0.160554i	−0.908645	−	0.417570i	$-0.862882\pi$
$263$	−103980.	+	180098.i	−0.0926957	+	0.160554i	0.815949	+	0.578124i	$0.196215\pi$
$264$	−5.73333e6	−	3.31014e6i	−5.06287	−	2.92305i
$265$			81844.7i			0.0715938i
$266$	169.267	−	293.178i	0.000146679	−	0.000254055i
$267$		−	150206.i		−	0.128947i
$268$	−1.20721e6	−	2.09095e6i	−1.02670	−	1.77830i
$269$	−783662.			−0.660310			−0.330155	−	0.943927i	$-0.607101\pi$
$269$	−783662.			−0.660310			−0.330155	+	0.943927i	$0.607101\pi$
$270$	−1.66184e6			−1.38733
$271$	23809.7	+	41239.7i	0.0196939	+	0.0341108i	0.875704	−	0.482848i	$-0.160398\pi$
$271$	23809.7	+	41239.7i	0.0196939	+	0.0341108i	−0.856011	+	0.516958i	$0.827064\pi$
$272$	5.57822e6	+	3.22059e6i	4.57165	+	2.63944i
$273$			1.05298e6i			0.855091i
$274$	1.11747e6	−	645169.i	0.899203	−	0.519155i
$275$	−917498.	−	1.58915e6i	−0.731599	−	1.26717i
$276$	6209.89	−	3585.28i	0.00490695	−	0.00283303i
$277$	1.54207e6	+	890313.i	1.20755	+	0.697178i	0.962223	−	0.272263i	$-0.0877722\pi$
$277$	1.54207e6	+	890313.i	1.20755	+	0.697178i	0.245324	+	0.969441i	$0.421106\pi$
$278$	−2.24980e6	−	1.29892e6i	−1.74595	−	1.00802i
$279$	−205776.	+	118805.i	−0.158265	+	0.0913742i
$280$	−2.26867e6	−	3.92945e6i	−1.72932	−	2.99528i
$281$	−1.54113e6	+	889770.i	−1.16432	+	0.672221i	−0.952336	−	0.305052i	$-0.901326\pi$
$281$	−1.54113e6	+	889770.i	−1.16432	+	0.672221i	−0.211985	+	0.977273i	$0.567993\pi$
$282$			212157.i			0.158868i
$283$	−21038.7	−	12146.7i	−0.0156154	−	0.00901557i	0.492172	−	0.870498i	$-0.336203\pi$
$283$	−21038.7	−	12146.7i	−0.0156154	−	0.00901557i	−0.507787	+	0.861482i	$0.669536\pi$
$284$	37689.2	+	65279.7i	0.0277282	+	0.0480266i
$285$	−480.585			−0.000350476
$286$	−3.38370e6			−2.44611
$287$	−63245.0	−	109544.i	−0.0453233	−	0.0785023i
$288$			2.71104e6i			1.92599i
$289$	1.05378e6	−	1.82519e6i	0.742170	−	1.28548i
$290$		−	3.99094e6i		−	2.78664i
$291$	−2.52974e6	−	1.46055e6i	−1.75123	−	1.01108i
$292$	210445.	−	364501.i	0.144438	−	0.250174i
$293$	−196543.	+	340423.i	−0.133748	+	0.231659i	−0.925119	−	0.379678i	$-0.876035\pi$
$293$	−196543.	+	340423.i	−0.133748	+	0.231659i	0.791370	+	0.611337i	$0.209368\pi$
$294$	−1.20757e6	+	697188.i	−0.814784	+	0.470416i
$295$	2.76921e6			1.85268
$296$	4.46106e6	+	1.58014e6i	2.95944	+	1.04825i
$297$	1.15533e6			0.760004
$298$	−1.73281e6	+	1.00044e6i	−1.13034	+	0.652604i
$299$	1139.56	−	1973.77i	0.000737154	−	0.00127679i
$300$	−2.57834e6	+	4.46582e6i	−1.65401	+	2.86482i
$301$	−507669.	−	293103.i	−0.322972	−	0.186468i
$302$			3.81691e6i			2.40821i
$303$	1.54237e6	−	2.67147e6i	0.965123	−	1.67164i
$304$		−	1062.30i		−	0.000659268i
$305$	1.76233e6	+	3.05245e6i	1.08477	+	1.87888i
$306$	2.91703e6			1.78089
$307$	−1.06115e6			−0.642587			−0.321293	−	0.946980i	$-0.604118\pi$
$307$	−1.06115e6			−0.642587			−0.321293	+	0.946980i	$0.604118\pi$
$308$	2.53625e6	+	4.39291e6i	1.52340	+	2.63861i
$309$	−2.55197e6	−	1.47338e6i	−1.52047	−	0.877846i
$310$		−	1.40752e6i		−	0.831861i
$311$	−1.49298e6	+	861970.i	−0.875290	+	0.505349i	−0.869103	−	0.494632i	$-0.835303\pi$
$311$	−1.49298e6	+	861970.i	−0.875290	+	0.505349i	−0.00618751	+	0.999981i	$0.501970\pi$
$312$	2.95661e6	+	5.12100e6i	1.71952	+	2.97830i
$313$	1.66591e6	−	961813.i	0.961148	−	0.554919i	0.0646220	−	0.997910i	$-0.479416\pi$
$313$	1.66591e6	−	961813.i	0.961148	−	0.554919i	0.896526	+	0.442991i	$0.146083\pi$
$314$	−2.09181e6	−	1.20771e6i	−1.19728	−	0.691253i
$315$	−994369.	−	574099.i	−0.564639	−	0.325995i
$316$	4.00421e6	−	2.31183e6i	2.25579	−	1.30238i
$317$	269575.	+	466917.i	0.150672	+	0.260971i	0.931475	−	0.363807i	$-0.118523\pi$
$317$	269575.	+	466917.i	0.150672	+	0.260971i	−0.780803	+	0.624777i	$0.785190\pi$
$318$	−190838.	+	110180.i	−0.105827	+	0.0610994i
$319$			2.77455e6i			1.52657i
$320$	−6.41010e6	−	3.70088e6i	−3.49937	−	2.02036i
$321$	−732336.	−	1.26844e6i	−0.396687	−	0.687082i
$322$	−4708.56			−0.00253074
$323$	−581.750			−0.000310263
$324$	−3.10210e6	−	5.37300e6i	−1.64170	−	2.84351i
$325$			1.63902e6i			0.860746i
$326$	444023.	−	769071.i	0.231399	−	0.400795i
$327$			1.71247e6i			0.885635i
$328$	−615166.	−	355166.i	−0.315724	−	0.182283i
$329$	50544.2	−	87545.1i	0.0257443	−	0.0445905i
$330$	4.96195e6	−	8.59434e6i	2.50823	−	4.34438i
$331$	−96111.5	+	55490.0i	−0.0482176	+	0.0278384i	−0.523915	−	0.851771i	$-0.675529\pi$
$331$	−96111.5	+	55490.0i	−0.0482176	+	0.0278384i	0.475697	+	0.879609i	$0.342196\pi$
$332$	−7.99474e6			−3.98070
$333$	1.17758e6	−	218156.i	0.581944	−	0.107810i
$334$	−478665.			−0.234782
$335$	1.94915e6	−	1.12534e6i	0.948930	−	0.547865i
$336$	3.41315e6	−	5.91174e6i	1.64933	−	2.85672i
$337$	−1.77583e6	+	3.07582e6i	−0.851778	+	1.47532i	0.0278251	+	0.999613i	$0.491142\pi$
$337$	−1.77583e6	+	3.07582e6i	−0.851778	+	1.47532i	−0.879603	+	0.475709i	$0.842191\pi$
$338$	−855121.	−	493704.i	−0.407132	−	0.235058i
$339$			3.83970e6i			1.81467i
$340$	−6.26917e6	+	1.08585e7i	−2.94112	+	5.09417i
$341$			978525.i			0.455708i
$342$	−240.542	−	416.632i	−0.000111206	−	0.000192614i
$343$	2.36531e6			1.08556
$344$	−3.29196e6			−1.49989
$345$	3342.16	+	5788.78i	0.00151175	+	0.00261842i
$346$	1.99817e6	+	1.15364e6i	0.897310	+	0.518062i
$347$			3.04178e6i			1.35614i	0.734998	+	0.678070i	$0.237183\pi$
$347$			3.04178e6i			1.35614i	−0.734998	+	0.678070i	$0.762817\pi$
$348$	6.75241e6	−	3.89850e6i	2.98889	−	1.72564i
$349$	−1.36961e6	−	2.37224e6i	−0.601914	−	1.04255i	−0.992531	−	0.121992i	$-0.961072\pi$
$349$	−1.36961e6	−	2.37224e6i	−0.601914	−	1.04255i	0.390617	−	0.920553i	$-0.372262\pi$
$350$	2.93248e6	−	1.69307e6i	1.27957	−	0.738762i
$351$	−893688.	−	515971.i	−0.387185	−	0.223541i
$352$	9.66884e6	+	5.58231e6i	4.15927	+	2.40136i
$353$	2.47849e6	−	1.43096e6i	1.05865	−	0.611209i	0.133588	−	0.991037i	$-0.457350\pi$
$353$	2.47849e6	−	1.43096e6i	1.05865	−	0.611209i	0.925057	+	0.379828i	$0.124017\pi$
$354$	3.72795e6	+	6.45700e6i	1.58111	+	2.73856i
$355$	−60852.8	+	35133.4i	−0.0256277	+	0.0147962i
$356$			646307.i			0.270280i
$357$	−3.23748e6	−	1.86916e6i	−1.34442	−	0.776203i
$358$	−1.91886e6	−	3.32356e6i	−0.791289	−	1.37055i
$359$	240346.			0.0984240			0.0492120	−	0.998788i	$-0.484329\pi$
$359$	240346.			0.0984240			0.0492120	+	0.998788i	$0.484329\pi$
$360$	−6.44796e6			−2.62220
$361$	−1.23805e6	−	2.14436e6i	−0.500000	−	0.866025i
$362$		−	6.65324e6i		−	2.66847i
$363$	−1.86585e6	+	3.23175e6i	−0.743208	+	1.28727i
$364$		−	4.53075e6i		−	1.79232i
$365$	339783.	+	196174.i	0.133497	+	0.0770743i
$366$	−4.74495e6	+	8.21850e6i	−1.85152	+	3.20693i
$367$	−589290.	+	1.02068e6i	−0.228383	+	0.395571i	−0.957329	−	0.289000i	$-0.906677\pi$
$367$	−589290.	+	1.02068e6i	−0.228383	+	0.395571i	0.728946	+	0.684571i	$0.240011\pi$
$368$	−12795.7	+	7387.58i	−0.00492542	+	0.00284369i
$369$	−179753.			−0.0687244
$370$	−2.36865e6	+	6.68720e6i	−0.899492	+	2.53945i
$371$	104997.			0.0396043
$372$	2.38143e6	−	1.37492e6i	0.892238	−	0.515134i
$373$	−446835.	+	773941.i	−0.166294	+	0.288029i	−0.937114	−	0.349024i	$-0.886513\pi$
$373$	−446835.	+	773941.i	−0.166294	+	0.288029i	0.770820	+	0.637053i	$0.219847\pi$
$374$	6.00646e6	−	1.04035e7i	2.22044	−	3.84592i
$375$	35982.5	+	20774.5i	0.0132134	+	0.00762874i
$376$		−	567684.i		−	0.207079i
$377$	1.23911e6	−	2.14621e6i	0.449012	−	0.777711i
$378$			2.13195e6i			0.767444i
$379$	350961.	+	607881.i	0.125505	+	0.217381i	0.921930	−	0.387356i	$-0.126612\pi$
$379$	350961.	+	607881.i	0.125505	+	0.217381i	−0.796425	+	0.604737i	$0.793278\pi$
$380$	2067.86			0.000734619
$381$	410723.			0.144956
$382$	−3.80871e6	−	6.59688e6i	−1.33542	−	2.31302i
$383$	−2.76695e6	−	1.59750e6i	−0.963839	−	0.556473i	−0.0664868	−	0.997787i	$-0.521179\pi$
$383$	−2.76695e6	−	1.59750e6i	−0.963839	−	0.556473i	−0.897353	+	0.441314i	$0.854512\pi$
$384$		−	8.06486e6i		−	2.79106i
$385$	−4.09501e6	+	2.36426e6i	−1.40800	+	0.812911i
$386$	−2.05078e6	−	3.55205e6i	−0.700567	−	1.21342i
$387$	−721441.	+	416524.i	−0.244863	+	0.141372i
$388$	1.08850e7	+	6.28445e6i	3.67070	+	2.11928i
$389$	−2.50985e6	−	1.44906e6i	−0.840958	−	0.485527i	0.0166316	−	0.999862i	$-0.494706\pi$
$389$	−2.50985e6	−	1.44906e6i	−0.840958	−	0.485527i	−0.857590	+	0.514334i	$0.828039\pi$
$390$	−7.67646e6	+	4.43201e6i	−2.55564	+	1.47550i
$391$	4045.70	+	7007.35i	0.00133829	+	0.00231799i
$392$	3.23116e6	−	1.86551e6i	1.06205	−	0.613173i
$393$		−	2.78937e6i		−	0.911012i
$394$	4.76713e6	+	2.75230e6i	1.54709	+	0.893214i
$395$	2.15506e6	+	3.73268e6i	0.694971	+	1.20373i
$396$	7.20846e6			2.30996
$397$	−2.10417e6			−0.670045			−0.335023	−	0.942210i	$-0.608744\pi$
$397$	−2.10417e6			−0.670045			−0.335023	+	0.942210i	$0.608744\pi$
$398$	3.83352e6	+	6.63985e6i	1.21308	+	2.10112i
$399$			616.534i			0.000193876i
$400$	5.31275e6	−	9.20195e6i	1.66023	−	2.87561i
$401$			2.56816e6i			0.797557i	0.917047	+	0.398779i	$0.130566\pi$
$401$			2.56816e6i			0.797557i	−0.917047	+	0.398779i	$0.869434\pi$
$402$	5.24796e6	+	3.02991e6i	1.61966	+	0.935114i
$403$	437009.	−	756922.i	0.134038	−	0.232161i
$404$	−6.63652e6	+	1.14948e7i	−2.02296	+	3.50387i
$405$	5.00864e6	−	2.89174e6i	1.51734	−	0.876036i
$406$	−5.11991e6			−1.54151
$407$	1.64672e6	−	4.64902e6i	0.492757	−	1.39115i
$408$	−2.09933e7			−6.24354
$409$	614882.	−	355002.i	0.181754	−	0.104936i	−0.406363	−	0.913712i	$-0.633203\pi$
$409$	614882.	−	355002.i	0.181754	−	0.104936i	0.588116	+	0.808776i	$0.299870\pi$
$410$	532399.	−	922143.i	0.156415	−	0.270918i
$411$	−1.17498e6	+	2.03512e6i	−0.343103	+	0.594272i
$412$	1.09806e7	+	6.33966e6i	3.18701	+	1.84002i
$413$		−	3.55257e6i		−	1.02487i
$414$	−3345.63	+	5794.81i	−0.000959351	+	0.00166164i
$415$		−	7.45260e6i		−	2.12416i
$416$	−4.98611e6	−	8.63620e6i	−1.41263	−	2.44675i
$417$	4.73117e6			1.33238
$418$	−1981.21			−0.000554611
$419$	−1.75142e6	−	3.03355e6i	−0.487366	−	0.844142i	0.512529	−	0.858670i	$-0.328709\pi$
$419$	−1.75142e6	−	3.03355e6i	−0.487366	−	0.844142i	−0.999894	+	0.0145281i	$0.995375\pi$
$420$	1.15078e7	+	6.64401e6i	3.18323	+	1.83784i
$421$		−	127118.i		−	0.0349544i	−0.999847	−	0.0174772i	$-0.994437\pi$
$421$		−	127118.i		−	0.0349544i	0.999847	−	0.0174772i	$-0.00556346\pi$
$422$	−6.92535e6	+	3.99835e6i	−1.89304	+	1.09295i
$423$	−71827.6	−	124409.i	−0.0195182	−	0.0338066i
$424$	510638.	−	294817.i	0.137943	−	0.0796412i
$425$	−5.03931e6	−	2.90945e6i	−1.35331	−	0.781336i
$426$	−163842.	−	94594.2i	−0.0437422	−	0.0252546i
$427$	3.91593e6	−	2.26086e6i	1.03936	−	0.600074i
$428$	3.15109e6	+	5.45785e6i	0.831480	+	1.44017i
$429$	5.33677e6	−	3.08118e6i	1.40002	−	0.808303i
$430$		−	4.93470e6i		−	1.28703i
$431$	6.24341e6	+	3.60464e6i	1.61893	+	0.934691i	0.987197	+	0.159508i	$0.0509908\pi$
$431$	6.24341e6	+	3.60464e6i	1.61893	+	0.934691i	0.631736	+	0.775183i	$0.282343\pi$
$432$	3.34496e6	+	5.79364e6i	0.862346	+	1.49363i
$433$	−4.63027e6			−1.18683			−0.593413	−	0.804898i	$-0.702220\pi$
$433$	−4.63027e6			−1.18683			−0.593413	+	0.804898i	$0.702220\pi$
$434$	−1.80568e6			−0.460169
$435$	3.63413e6	+	6.29451e6i	0.920827	+	1.59492i
$436$		−	7.36843e6i		−	1.85634i
$437$	0.667228	−	1.15567i	1.67136e−7	−	2.89488e-7i
$438$			1.05637e6i			0.263106i
$439$	1.97721e6	+	1.14154e6i	0.489657	+	0.282704i	0.724432	−	0.689346i	$-0.242102\pi$
$439$	1.97721e6	+	1.14154e6i	0.489657	+	0.282704i	−0.234775	+	0.972050i	$0.575435\pi$
$440$	−1.32770e7	+	2.29964e7i	−3.26940	+	5.66277i
$441$	472078.	−	817662.i	0.115589	−	0.200206i
$442$	−9.29239e6	+	5.36497e6i	−2.26241	+	1.30620i
$443$	2.49135e6			0.603150			0.301575	−	0.953442i	$-0.402488\pi$
$443$	2.49135e6			0.603150			0.301575	+	0.953442i	$0.402488\pi$
$444$	−1.36281e7	+	2.52471e6i	−3.28078	+	0.607790i
$445$	−602479.			−0.144226
$446$	3.59389e6	−	2.07494e6i	0.855516	−	0.493932i
$447$	1.82199e6	−	3.15578e6i	0.431297	−	0.747029i
$448$	−4.74779e6	+	8.22341e6i	−1.11763	+	1.93578i
$449$	−5.61562e6	−	3.24218e6i	−1.31456	−	0.758964i	−0.331716	−	0.943379i	$-0.607628\pi$
$449$	−5.61562e6	−	3.24218e6i	−1.31456	−	0.758964i	−0.982848	+	0.184415i	$0.940961\pi$
$450$		−	4.81200e6i		−	1.12020i
$451$	−370130.	+	641084.i	−0.0856867	+	0.148414i
$452$		−	1.65214e7i		−	3.80366i
$453$	−3.47566e6	−	6.02002e6i	−0.795777	−	1.37833i
$454$	7.41085e6			1.68744
$455$	4.22351e6			0.956411
$456$	1731.14	+	2998.42i	0.000389870	+	0.000675275i
$457$	−7.15861e6	−	4.13303e6i	−1.60339	−	0.925716i	−0.990803	−	0.135310i	$-0.956797\pi$
$457$	−7.15861e6	−	4.13303e6i	−1.60339	−	0.925716i	−0.612584	−	0.790406i	$-0.709870\pi$
$458$		−	5.65122e6i		−	1.25886i
$459$	3.17280e6	−	1.83182e6i	0.702928	−	0.405836i
$460$	−14380.6	−	24908.0i	−0.00316871	−	0.00548837i
$461$	3.64393e6	−	2.10382e6i	0.798578	−	0.461059i	−0.0443956	−	0.999014i	$-0.514136\pi$
$461$	3.64393e6	−	2.10382e6i	0.798578	−	0.461059i	0.842974	+	0.537955i	$0.180803\pi$
$462$	−1.10255e7	−	6.36559e6i	−2.40323	−	1.38750i
$463$	6.49842e6	+	3.75187e6i	1.40882	+	0.813383i	0.995275	−	0.0971010i	$-0.0309570\pi$
$463$	6.49842e6	+	3.75187e6i	1.40882	+	0.813383i	0.413545	+	0.910484i	$0.364290\pi$
$464$	−1.39135e7	+	8.03298e6i	−3.00015	+	1.73214i
$465$	1.28168e6	+	2.21994e6i	0.274883	+	0.476112i
$466$	−8.76520e6	+	5.06059e6i	−1.86981	+	1.07953i
$467$			3.48430e6i			0.739304i	0.929170	+	0.369652i	$0.120523\pi$
$467$			3.48430e6i			0.739304i	−0.929170	+	0.369652i	$0.879477\pi$
$468$	−5.57598e6	−	3.21929e6i	−1.17681	−	0.679432i
$469$	−1.44368e6	−	2.50054e6i	−0.303068	−	0.524929i
$470$	850966.			0.177692
$471$	4.39892e6			0.913680
$472$	−9.97513e6	−	1.72774e7i	−2.06093	−	3.56964i
$473$			3.43066e6i			0.705059i
$474$	−5.80235e6	+	1.00500e7i	−1.18620	+	2.05456i
$475$			959.668i			0.000195158i
$476$	1.39302e7	+	8.04261e6i	2.81799	+	1.62697i
$477$	74605.0	−	129220.i	0.0150131	−	0.0260035i
$478$	−8.06283e6	+	1.39652e7i	−1.61405	+	2.79562i
$479$	−5.88470e6	+	3.39753e6i	−1.17189	+	0.676589i	−0.954124	−	0.299413i	$-0.903209\pi$
$479$	−5.88470e6	+	3.39753e6i	−1.17189	+	0.676589i	−0.217762	+	0.976002i	$0.569876\pi$
$480$	2.92470e7			5.79401
$481$	−3.35004e6	+	2.86075e6i	−0.660218	+	0.563790i
$482$	1.38246e7			2.71041
$483$	7426.33	−	4287.59i	0.00144846	−	0.000836268i
$484$	8.02838e6	−	1.39056e7i	1.55781	−	2.69821i
$485$	−5.85828e6	+	1.01468e7i	−1.13088	+	1.95874i
$486$	9.05219e6	+	5.22628e6i	1.73845	+	1.00370i
$487$		−	8.40728e6i		−	1.60632i	−0.595760	−	0.803162i	$-0.703149\pi$
$487$		−	8.40728e6i		−	1.60632i	0.595760	−	0.803162i	$-0.296851\pi$
$488$	1.26964e7	−	2.19908e7i	2.41341	−	4.18014i
$489$			1.61730e6i			0.305858i
$490$	2.79643e6	+	4.84356e6i	0.526155	+	0.911328i
$491$	−9.01955e6			−1.68842			−0.844211	−	0.536011i	$-0.819930\pi$
$491$	−9.01955e6			−1.68842			−0.844211	+	0.536011i	$0.819930\pi$
$492$	2.08027e6			0.387443
$493$	4.39914e6	+	7.61953e6i	0.815174	+	1.41192i
$494$	1532.53	+	884.805i	0.000282547	+	0.000163129i
$495$			6.71963e6i			1.23263i
$496$	−4.90701e6	+	2.83306e6i	−0.895597	+	0.517073i
$497$	45072.0	+	78067.0i	0.00818495	+	0.0141768i
$498$	1.73773e7	−	1.00328e7i	3.13985	−	1.81279i
$499$	−7.16245e6	−	4.13524e6i	−1.28769	−	0.743446i	−0.309446	−	0.950917i	$-0.600143\pi$
$499$	−7.16245e6	−	4.13524e6i	−1.28769	−	0.743446i	−0.978241	+	0.207471i	$0.933477\pi$
$500$	−154825.	−	89388.5i	−0.0276960	−	0.0159903i
$501$	754949.	−	435870.i	0.134377	−	0.0775823i
$502$	2.56429e6	+	4.44149e6i	0.454160	+	0.786628i
$503$	8.18157e6	−	4.72363e6i	1.44184	−	0.832446i	0.443867	−	0.896093i	$-0.353606\pi$
$503$	8.18157e6	−	4.72363e6i	1.44184	−	0.832446i	0.997972	+	0.0636468i	$0.0202731\pi$
$504$			8.27197e6i			1.45055i
$505$	−1.07153e7	−	6.18647e6i	−1.86971	−	1.07948i
$506$	13778.0	+	23864.2i	0.00239227	+	0.00414353i
$507$	1.79826e6			0.310694
$508$	−1.76726e6			−0.303837
$509$	1.04429e6	+	1.80877e6i	0.178661	+	0.309449i	0.941422	−	0.337231i	$-0.109490\pi$
$509$	1.04429e6	+	1.80877e6i	0.178661	+	0.309449i	−0.762761	+	0.646680i	$0.776157\pi$
$510$		−	3.14693e7i		−	5.35749i
$511$	251668.	−	435902.i	0.0426360	−	0.0738476i
$512$			2.27685e6i			0.383848i
$513$	−523.267	−	302.108i	−8.77870e−5	−	5.06838e-5i
$514$	4.99617e6	−	8.65362e6i	0.834121	−	1.44474i
$515$	−5.90974e6	+	1.02360e7i	−0.981862	+	1.70064i
$516$	8.34919e6	−	4.82041e6i	1.38045	−	0.797002i
$517$	−591602.			−0.0973426
$518$	8.57889e6	+	3.03870e6i	1.40477	+	0.497581i
$519$	−4.20202e6			−0.684761
$520$	2.05404e7	−	1.18590e7i	3.33120	−	1.92327i
$521$	−1.26225e6	+	2.18628e6i	−0.203728	+	0.352867i	−0.949727	−	0.313080i	$-0.898639\pi$
$521$	−1.26225e6	+	2.18628e6i	−0.203728	+	0.352867i	0.745999	+	0.665947i	$0.231972\pi$
$522$	−3.63792e6	+	6.30106e6i	−0.584355	+	1.01213i
$523$	−384380.	−	221922.i	−0.0614479	−	0.0354769i	0.468961	−	0.883219i	$-0.344628\pi$
$523$	−384380.	−	221922.i	−0.0614479	−	0.0354769i	−0.530409	+	0.847742i	$0.677962\pi$
$524$			1.20021e7i			1.90954i
$525$	−3.08340e6	+	5.34061e6i	−0.488239	+	0.845654i
$526$			2.24583e6i			0.353926i
$527$	1.55148e6	+	2.68725e6i	0.243344	+	0.421484i
$528$	−3.99497e7			−6.23632
$529$	6.43632e6			0.999997
$530$	441935.	+	765454.i	0.0683390	+	0.118367i
$531$	−4.37214e6	−	2.52426e6i	−0.672912	−	0.388506i
$532$		−	2652.82i		−	0.000406377i
$533$	572616.	−	330600.i	0.0873063	−	0.0504063i
$534$	−811066.	−	1.40481e6i	−0.123084	−	0.213188i
$535$	−5.08774e6	+	2.93741e6i	−0.768494	+	0.443690i
$536$	−1.40423e7	−	8.10732e6i	−2.11118	−	1.21889i
$537$	6.05284e6	+	3.49461e6i	0.905782	+	0.522953i
$538$	−7.32921e6	+	4.23152e6i	−1.09170	+	0.630291i
$539$	−1.94411e6	−	3.36730e6i	−0.288237	−	0.499241i
$540$	−1.12779e7	+	6.51128e6i	−1.66434	+	0.960908i
$541$			8.03942e6i			1.18095i	0.807056	+	0.590475i	$0.201060\pi$
$541$			8.03942e6i			1.18095i	−0.807056	+	0.590475i	$0.798940\pi$
$542$	445362.	+	257130.i	0.0651201	+	0.0375971i
$543$	6.05841e6	+	1.04935e7i	0.881778	+	1.52728i
$544$	3.54037e7			5.12922
$545$	6.86875e6			0.990573
$546$	5.68574e6	+	9.84799e6i	0.816217	+	1.41373i
$547$		−	3.73812e6i		−	0.534177i	−0.963672	−	0.267088i	$-0.913938\pi$
$547$		−	3.73812e6i		−	0.534177i	0.963672	−	0.267088i	$-0.0860616\pi$
$548$	5.05569e6	−	8.75670e6i	0.719165	−	1.24563i
$549$		−	6.42577e6i		−	0.909901i
$550$	−1.71618e7	−	9.90839e6i	−2.41912	−	1.39668i
$551$	725.519	−	1256.64i	0.000101805	−	0.000176332i
$552$	24077.9	−	41704.1i	0.00336334	−	0.00582548i
$553$	4.78858e6	−	2.76469e6i	0.665877	−	0.384444i
$554$	1.92296e7			2.66193
$555$	−2.35350e6	−	1.27039e7i	−0.324326	−	1.75068i
$556$	−2.03573e7			−2.79275
$557$	−1.04982e7	+	6.06113e6i	−1.43376	+	0.827781i	−0.997405	−	0.0719949i	$-0.977063\pi$
$557$	−1.04982e7	+	6.06113e6i	−1.43376	+	0.827781i	−0.436353	+	0.899776i	$0.643730\pi$
$558$	−1.28302e6	+	2.22225e6i	−0.174440	+	0.302139i
$559$	1.53213e6	−	2.65373e6i	0.207380	−	0.359193i
$560$	−2.37121e7	−	1.36902e7i	−3.19521	−	1.84476i
$561$			2.18778e7i			2.93493i
$562$	−9.60895e6	+	1.66432e7i	−1.28332	+	2.22278i
$563$		−	8.94758e6i		−	1.18969i	−0.803839	−	0.594846i	$-0.797213\pi$
$563$		−	8.94758e6i		−	1.18969i	0.803839	−	0.594846i	$-0.202787\pi$
$564$	831256.	+	1.43978e6i	0.110037	+	0.190589i
$565$	1.54011e7			2.02969
$566$	−262354.			−0.0344228
$567$	−3.70976e6	−	6.42550e6i	−0.484606	−	0.839362i
$568$	438402.	+	253112.i	0.0570167	+	0.0329186i
$569$			812835.i			0.105250i	0.998614	+	0.0526249i	$0.0167588\pi$
$569$			812835.i			0.105250i	−0.998614	+	0.0526249i	$0.983241\pi$
$570$	−4494.68	+	2595.00i	−0.000579444	+	0.000334542i
$571$	3.00327e6	+	5.20181e6i	0.385481	+	0.667673i	0.991836	−	0.127521i	$-0.0407020\pi$
$571$	3.00327e6	+	5.20181e6i	0.385481	+	0.667673i	−0.606354	+	0.795195i	$0.707369\pi$
$572$	−2.29630e7	+	1.32577e7i	−2.93453	+	1.69425i
$573$	1.20142e7	+	6.93639e6i	1.52865	+	0.882565i
$574$	−1.18300e6	−	683006.i	−0.149867	−	0.0865256i
$575$	11559.5	−	6673.87i	0.00145804	−	0.000841798i
$576$	6.74702e6	+	1.16862e7i	0.847336	+	1.46763i
$577$	−3.20615e6	+	1.85107e6i	−0.400908	+	0.231464i	−0.686876	−	0.726775i	$-0.741018\pi$
$577$	−3.20615e6	+	1.85107e6i	−0.400908	+	0.231464i	0.285968	+	0.958239i	$0.407685\pi$
$578$		−	2.27602e7i		−	2.83372i
$579$	6.46896e6	+	3.73485e6i	0.801933	+	0.462996i
$580$	−1.56369e7	−	2.70840e7i	−1.93011	−	3.34305i
$581$	−9.56080e6			−1.17504
$582$	−3.15460e7			−3.86044
$583$	−307238.	−	532153.i	−0.0374373	−	0.0648433i
$584$		−	2.82659e6i		−	0.342950i
$585$	3.00098e6	−	5.19786e6i	0.362555	−	0.627964i
$586$			4.24508e6i			0.510672i
$587$	8.21940e6	+	4.74547e6i	0.984566	+	0.568439i	0.903646	−	0.428281i	$-0.140881\pi$
$587$	8.21940e6	+	4.74547e6i	0.984566	+	0.568439i	0.0809205	+	0.996721i	$0.474214\pi$
$588$	−5.46332e6	+	9.46275e6i	−0.651649	+	1.12869i
$589$	255.875	−	443.189i	3.03906e−5	−	5.26381e-5i
$590$	2.58991e7	−	1.49529e7i	3.06306	−	1.76846i
$591$	−1.00249e7			−1.18063
$592$	2.80811e7	−	5.20224e6i	3.29313	−	0.610079i
$593$	4.46687e6			0.521635			0.260817	−	0.965388i	$-0.416008\pi$
$593$	4.46687e6			0.521635			0.260817	+	0.965388i	$0.416008\pi$
$594$	1.08053e7	−	6.23842e6i	1.25652	−	0.725452i
$595$	−7.49721e6	+	1.29856e7i	−0.868175	+	1.50372i
$596$	−7.83965e6	+	1.35787e7i	−0.904026	+	1.56582i
$597$	−1.20924e7	−	6.98157e6i	−1.38860	−	0.801710i
$598$		−	24613.0i		−	0.00281457i
$599$	−80099.6	+	138737.i	−0.00912144	+	0.0157988i	−0.870550	−	0.492080i	$-0.836237\pi$
$599$	−80099.6	+	138737.i	−0.00912144	+	0.0157988i	0.861429	+	0.507879i	$0.169570\pi$
$600$			3.46310e7i			3.92724i
$601$	−7.40551e6	−	1.28267e7i	−0.836313	−	1.44854i	−0.892957	−	0.450143i	$-0.851373\pi$
$601$	−7.40551e6	−	1.28267e7i	−0.836313	−	1.44854i	0.0566434	−	0.998394i	$-0.481960\pi$
$602$	−6.33064e6			−0.711962
$603$	−4.10320e6			−0.459547
$604$	1.49551e7	+	2.59029e7i	1.66800	+	2.88906i
$605$	1.29626e7	+	7.48395e6i	1.43980	+	0.831271i
$606$		−	3.33133e7i		−	3.68498i
$607$	6.12525e6	−	3.53641e6i	0.674764	−	0.389575i	−0.123115	−	0.992392i	$-0.539288\pi$
$607$	6.12525e6	−	3.53641e6i	0.674764	−	0.389575i	0.797879	+	0.602817i	$0.205955\pi$
$608$	−2919.44	−	5056.62i	−0.000320288	−	0.000554755i
$609$	8.07511e6	−	4.66217e6i	0.882278	−	0.509383i
$610$	3.29645e7	+	1.90321e7i	3.58692	+	2.07091i
$611$	457624.	+	264209.i	0.0495913	+	0.0286315i
$612$	1.97960e7	−	1.14292e7i	2.13648	−	1.23350i
$613$	323443.	+	560219.i	0.0347653	+	0.0602153i	0.882885	−	0.469590i	$-0.155598\pi$
$613$	323443.	+	560219.i	0.0347653	+	0.0602153i	−0.848119	+	0.529805i	$0.822265\pi$
$614$	−9.92444e6	+	5.72988e6i	−1.06239	+	0.613373i
$615$			1.93920e6i			0.206745i
$616$	2.95017e7	+	1.70328e7i	3.13253	+	1.80857i
$617$	−5.59982e6	−	9.69917e6i	−0.592190	−	1.02570i	−0.993937	−	0.109953i	$-0.964930\pi$
$617$	−5.59982e6	−	9.69917e6i	−0.592190	−	1.02570i	0.401747	−	0.915751i	$-0.368403\pi$
$618$	−3.18231e7			−3.35175
$619$	−6.35377e6			−0.666507			−0.333253	−	0.942837i	$-0.608146\pi$
$619$	−6.35377e6			−0.666507			−0.333253	+	0.942837i	$0.608146\pi$
$620$	−5.51482e6	−	9.55195e6i	−0.576172	−	0.997960i
$621$			8403.87i			0.000874481i
$622$	−9.30873e6	+	1.61232e7i	−0.964749	+	1.67099i
$623$			772910.i			0.0797827i
$624$	3.09024e7	+	1.78415e7i	3.17710	+	1.83430i
$625$	4.92430e6	−	8.52913e6i	0.504248	−	0.873383i
$626$	1.03870e7	−	1.79907e7i	1.05938	−	1.83490i
$627$	3124.75	−	1804.08i	0.000317429	−	0.000183268i
$628$	−1.89277e7			−1.91513
$629$	−2.84892e6	−	1.53782e7i	−0.287114	−	1.54981i
$630$	−1.23998e7			−1.24470
$631$	7.04852e6	−	4.06947e6i	0.704733	−	0.406878i	−0.104375	−	0.994538i	$-0.533284\pi$
$631$	7.04852e6	−	4.06947e6i	0.704733	−	0.406878i	0.809108	+	0.587660i	$0.199951\pi$
$632$	1.55257e7	−	2.68913e7i	1.54618	−	2.67806i
$633$	7.28177e6	−	1.26124e7i	0.722317	−	1.25109i
$634$	5.04241e6	+	2.91124e6i	0.498213	+	0.287643i
$635$		−	1.64742e6i		−	0.162132i
$636$	−863398.	+	1.49545e6i	−0.0846386	+	0.146598i
$637$			3.47296e6i			0.339118i
$638$	1.49817e7	+	2.59490e7i	1.45717	+	2.52388i
$639$	128102.			0.0124110
$640$	−3.23482e7			−3.12177
$641$	−9.11255e6	−	1.57834e7i	−0.875981	−	1.51724i	−0.855714	−	0.517450i	$-0.826881\pi$
$641$	−9.11255e6	−	1.57834e7i	−0.875981	−	1.51724i	−0.0202678	−	0.999795i	$-0.506452\pi$
$642$	−1.36984e7	−	7.90876e6i	−1.31169	−	0.757305i
$643$			1.24290e7i			1.18552i	0.805379	+	0.592760i	$0.201962\pi$
$643$			1.24290e7i			1.18552i	−0.805379	+	0.592760i	$0.798038\pi$
$644$	−31954.0	+	18448.6i	−0.00303606	+	0.00175287i
$645$	4.49352e6	+	7.78301e6i	0.425292	+	0.736628i
$646$	−5440.83	+	3141.26i	−0.000512960	+	0.000296158i
$647$	1.15993e7	+	6.69688e6i	1.08936	+	0.628944i	0.933407	−	0.358820i	$-0.116821\pi$
$647$	1.15993e7	+	6.69688e6i	1.08936	+	0.628944i	0.155956	+	0.987764i	$0.450154\pi$
$648$	−3.60838e7	−	2.08330e7i	−3.37578	−	1.94901i
$649$	−1.80054e7	+	1.03954e7i	−1.67799	+	0.968791i
$650$	8.85017e6	+	1.53289e7i	0.821614	+	1.42308i
$651$	2.84792e6	−	1.64425e6i	0.263376	−	0.152060i
$652$		−	6.95893e6i		−	0.641097i
$653$	8.87177e6	+	5.12212e6i	0.814193	+	0.470074i	0.848410	−	0.529340i	$-0.177560\pi$
$653$	8.87177e6	+	5.12212e6i	0.814193	+	0.470074i	−0.0342172	+	0.999414i	$0.510894\pi$
$654$	9.24681e6	+	1.60159e7i	0.845371	+	1.46423i
$655$	−1.11882e7			−1.01896
$656$	−4.28646e6			−0.388901
$657$	−357642.	−	619455.i	−0.0323248	−	0.0559881i
$658$		−	1.09169e6i		−	0.0982957i
$659$	1.02927e6	−	1.78274e6i	0.0923239	−	0.159910i	−0.816165	−	0.577819i	$-0.803904\pi$
$659$	1.02927e6	−	1.78274e6i	0.0923239	−	0.159910i	0.908489	+	0.417910i	$0.137237\pi$
$660$		−	7.77658e7i		−	6.94910i
$661$	−7.77306e6	−	4.48778e6i	−0.691972	−	0.399510i	0.112379	−	0.993665i	$-0.464153\pi$
$661$	−7.77306e6	−	4.48778e6i	−0.691972	−	0.399510i	−0.804350	+	0.594155i	$0.797486\pi$
$662$	−599257.	+	1.03794e6i	−0.0531457	+	0.0920510i
$663$	9.77063e6	−	1.69232e7i	0.863254	−	1.49520i
$664$	−4.64976e7	+	2.68454e7i	−4.09270	+	2.36292i
$665$	2472.92			0.000216849
$666$	9.83540e6	−	8.39888e6i	0.859224	−	0.733730i
$667$	−20182.0			−0.00175651
$668$	−3.24839e6	+	1.87546e6i	−0.281662	+	0.162617i
$669$	−3.77886e6	+	6.54517e6i	−0.326434	+	0.565400i
$670$	1.21530e7	−	2.10496e7i	1.04592	−	1.81158i
$671$	−2.29173e7	−	1.32313e7i	−1.96498	−	1.13448i
$672$		−	3.75205e7i		−	3.20513i
$673$	−1.17003e6	+	2.02655e6i	−0.0995770	+	0.172472i	−0.911510	−	0.411279i	$-0.865082\pi$
$673$	−1.17003e6	+	2.02655e6i	−0.0995770	+	0.172472i	0.811933	+	0.583751i	$0.198416\pi$
$674$			3.83556e7i			3.25221i
$675$	−3.02181e6	−	5.23392e6i	−0.255274	−	0.442148i
$676$	−7.73755e6			−0.651234
$677$	9.44742e6			0.792212			0.396106	−	0.918205i	$-0.370361\pi$
$677$	9.44742e6			0.792212			0.396106	+	0.918205i	$0.370361\pi$
$678$	2.07331e7	+	3.59108e7i	1.73217	+	3.00021i
$679$	1.30172e7	+	7.51548e6i	1.08354	+	0.625579i
$680$			8.42045e7i			6.98333i
$681$	−1.16884e7	+	6.74829e6i	−0.965798	+	0.557604i
$682$	5.28372e6	+	9.15168e6i	0.434990	+	0.753425i
$683$	1.04112e7	−	6.01091e6i	0.853982	−	0.493047i	−0.00801013	−	0.999968i	$-0.502550\pi$
$683$	1.04112e7	−	6.01091e6i	0.853982	−	0.493047i	0.861993	+	0.506921i	$0.169216\pi$
$684$	−3264.82	−	1884.94i	−0.000266820	−	0.000154049i
$685$	8.16288e6	+	4.71284e6i	0.664687	+	0.383757i
$686$	2.21216e7	−	1.27719e7i	1.79476	−	1.03621i
$687$	5.14598e6	+	8.91309e6i	0.415983	+	0.720504i
$688$	−1.72037e7	+	9.93259e6i	−1.38565	+	0.800003i
$689$			548850.i			0.0440459i
$690$	62515.1	+	36093.1i	0.00499876	+	0.00288604i
$691$	−5.04651e6	−	8.74081e6i	−0.402065	−	0.696397i	0.591910	−	0.806004i	$-0.298374\pi$
$691$	−5.04651e6	−	8.74081e6i	−0.402065	−	0.696397i	−0.993975	+	0.109607i	$0.965041\pi$
$692$	1.80804e7			1.43530
$693$	8.62049e6			0.681866
$694$	1.64246e7	+	2.84483e7i	1.29449	+	2.24211i
$695$		−	1.89768e7i		−	1.49025i
$696$	2.61814e7	−	4.53475e7i	2.04866	−	3.54838i
$697$			2.34741e6i			0.183024i
$698$	−2.56187e7	−	1.47909e7i	−1.99030	−	1.14910i
$699$	9.21630e6	−	1.59631e7i	0.713450	−	1.23573i
$700$	1.32673e7	−	2.29796e7i	1.02338	−	1.77254i
$701$	−9.03576e6	+	5.21680e6i	−0.694496	+	0.400967i	−0.805294	−	0.592876i	$-0.797993\pi$
$701$	−9.03576e6	+	5.21680e6i	−0.694496	+	0.400967i	0.110798	+	0.993843i	$0.464659\pi$
$702$	−1.11443e7			−0.853513
$703$	−1961.50	+	1675.01i	−0.000149692	+	0.000127829i
$704$	5.55712e7			4.22589
$705$	−1.34214e6	+	774886.i	−0.101701	+	0.0587172i
$706$	1.54534e7	−	2.67661e7i	1.16684	−	2.02103i
$707$	−7.93652e6	+	1.37465e7i	−0.597147	+	1.03429i
$708$	5.05985e7	+	2.92131e7i	3.79363	+	2.19025i
$709$			2.02807e7i			1.51519i	0.652724	+	0.757596i	$0.273626\pi$
$709$			2.02807e7i			1.51519i	−0.652724	+	0.757596i	$0.726374\pi$
$710$	−379418.	+	657172.i	−0.0282470	+	0.0489252i
$711$		−	7.85773e6i		−	0.582939i
$712$	2.17022e6	+	3.75893e6i	0.160437	+	0.277885i
$713$	−7117.78			−0.000524350
$714$	−4.03714e7			−2.96366
$715$	−1.23587e7	−	2.14058e7i	−0.904079	−	1.56591i
$716$	−2.60441e7	−	1.50366e7i	−1.89857	−	1.09614i
$717$		−	2.93679e7i		−	2.13342i
$718$	2.24784e6	−	1.29779e6i	0.162725	−	0.0939494i
$719$	9.10975e6	+	1.57785e7i	0.657180	+	1.13827i	0.981343	+	0.192267i	$0.0615841\pi$
$719$	9.10975e6	+	1.57785e7i	0.657180	+	1.13827i	−0.324163	+	0.946001i	$0.605083\pi$
$720$	−3.36969e7	+	1.94549e7i	−2.42247	+	1.39862i
$721$	1.31316e7	+	7.58151e6i	0.940758	+	0.543147i
$722$	−2.31578e7	−	1.33701e7i	−1.65331	−	0.954537i
$723$	−2.18041e7	+	1.25886e7i	−1.55129	+	0.895637i
$724$	−2.60681e7	−	4.51513e7i	−1.84826	−	3.20128i
$725$	1.25693e7	−	7.25692e6i	0.888112	−	0.512752i
$726$			4.03000e7i			2.83768i
$727$	905397.	+	522731.i	0.0635336	+	0.0366811i	0.531430	−	0.847102i	$-0.321655\pi$
$727$	905397.	+	522731.i	0.0635336	+	0.0366811i	−0.467897	+	0.883783i	$0.654988\pi$
$728$	−1.52137e7	−	2.63509e7i	−1.06391	−	1.84275i
$729$	−1.22104e6			−0.0850963
$730$	4.23711e6			0.294281
$731$	5.43943e6	+	9.42137e6i	0.376496	+	0.652109i
$732$			7.43650e7i			5.12969i
$733$	1.68345e6	−	2.91583e6i	0.115729	−	0.200448i	−0.802342	−	0.596864i	$-0.796413\pi$
$733$	1.68345e6	−	2.91583e6i	0.115729	−	0.200448i	0.918071	+	0.396416i	$0.129746\pi$
$734$			1.27279e7i			0.872001i
$735$	−8.82105e6	−	5.09284e6i	−0.602285	−	0.347729i
$736$	−40605.6	+	70331.0i	−0.00276307	+	0.00478577i
$737$	−8.44891e6	+	1.46339e7i	−0.572970	+	0.992414i
$738$	−1.68115e6	+	970610.i	−0.113623	+	0.0656000i
$739$	777251.			0.0523540			0.0261770	−	0.999657i	$-0.491667\pi$
$739$	777251.			0.0523540			0.0261770	+	0.999657i	$0.491667\pi$
$740$	1.01266e7	+	5.46624e7i	0.679807	+	3.66952i
$741$	−3222.80			−0.000215619
$742$	981987.	−	566951.i	0.0654781	−	0.0378038i
$743$	−9.10408e6	+	1.57687e7i	−0.605012	+	1.04791i	0.387038	+	0.922064i	$0.373498\pi$
$743$	−9.10408e6	+	1.57687e7i	−0.605012	+	1.04791i	−0.992050	+	0.125847i	$0.959835\pi$
$744$	9.23363e6	−	1.59931e7i	0.611562	−	1.05926i
$745$	−1.26579e7	−	7.30802e6i	−0.835545	−	0.482402i
$746$			9.65107e6i			0.634934i
$747$	−6.79336e6	+	1.17665e7i	−0.445434	+	0.771514i
$748$		−	9.41359e7i		−	6.15179i
$749$	3.76835e6	+	6.52697e6i	0.245441	+	0.425116i
$750$	448703.			0.0291277
$751$	1.11249e7			0.719774			0.359887	−	0.932996i	$-0.382815\pi$
$751$	1.11249e7			0.719774			0.359887	+	0.932996i	$0.382815\pi$
$752$	−1.71283e6	−	2.96671e6i	−0.110451	−	0.191307i
$753$	−8.08880e6	−	4.67007e6i	−0.519872	−	0.300149i
$754$		−	2.67632e7i		−	1.71439i
$755$	−2.41464e7	+	1.39409e7i	−1.54164	+	0.890069i
$756$	8.35320e6	+	1.44682e7i	0.531555	+	0.920681i
$757$	2.35444e7	−	1.35934e7i	1.49330	−	0.862159i	0.493332	−	0.869841i	$-0.335779\pi$
$757$	2.35444e7	−	1.35934e7i	1.49330	−	0.862159i	0.999970	+	0.00768257i	$0.00244546\pi$
$758$	6.56473e6	+	3.79015e6i	0.414996	+	0.239598i
$759$	−43461.3	−	25092.4i	−0.00273841	−	0.00158102i
$760$	12026.7	−	6943.62i	0.000755288	−	0.000436066i
$761$	−6.89367e6	−	1.19402e7i	−0.431508	−	0.747394i	0.565496	−	0.824751i	$-0.308685\pi$
$761$	−6.89367e6	−	1.19402e7i	−0.431508	−	0.747394i	−0.997003	+	0.0773578i	$0.975352\pi$
$762$	3.84130e6	−	2.21777e6i	0.239657	−	0.138366i
$763$		−	8.81180e6i		−	0.547966i
$764$	−5.16946e7	−	2.98459e7i	−3.20414	−	1.84991i
$765$	1.06542e7	+	1.84536e7i	0.658213	+	1.14006i
$766$	−3.45040e7			−2.12470
$767$	1.85703e7			1.13981
$768$	−1.40219e7	−	2.42867e7i	−0.857837	−	1.48582i
$769$			4.46807e6i			0.272461i	0.990677	+	0.136230i	$0.0434987\pi$
$769$			4.46807e6i			0.272461i	−0.990677	+	0.136230i	$0.956501\pi$
$770$	−2.55325e7	+	4.42235e7i	−1.55191	+	2.68798i
$771$			1.81980e7i			1.10252i
$772$	−2.78346e7	−	1.60703e7i	−1.68090	−	0.970468i
$773$	9.08454e6	−	1.57349e7i	0.546833	−	0.947142i	−0.451657	−	0.892192i	$-0.649167\pi$
$773$	9.08454e6	−	1.57349e7i	0.546833	−	0.947142i	0.998489	−	0.0549499i	$-0.0174999\pi$
$774$	−4.49820e6	+	7.79110e6i	−0.269889	+	0.467462i
$775$	4.43294e6	−	2.55936e6i	0.265117	−	0.153066i
$776$	8.44096e7			5.03197
$777$	−1.62976e7	+	3.01926e6i	−0.968439	+	0.179411i
$778$	−3.12979e7			−1.85382
$779$	335.275	−	193.571i	1.97951e−5	−	1.14287e-5i
$780$	−3.47302e7	+	6.01544e7i	−2.04395	+	3.54023i
$781$	263776.	−	456874.i	0.0154742	−	0.0268021i
$782$	75674.9	+	43690.9i	0.00442522	+	0.00255490i
$783$			9.13806e6i			0.532659i
$784$	1.12573e7	−	1.94983e7i	0.654102	−	1.13294i
$785$		−	1.76441e7i		−	1.02194i
$786$	−1.50617e7	−	2.60876e7i	−0.869595	−	1.50618i
$787$	−1.48130e7			−0.852522			−0.426261	−	0.904600i	$-0.640170\pi$
$787$	−1.48130e7			−0.852522			−0.426261	+	0.904600i	$0.640170\pi$
$788$	4.31353e7			2.47467
$789$	−2.04504e6	−	3.54212e6i	−0.116953	−	0.202568i
$790$	4.03105e7	+	2.32733e7i	2.29800	+	1.32675i
$791$		−	1.97578e7i		−	1.12278i
$792$	4.19245e7	−	2.42051e7i	2.37495	−	1.37118i
$793$	1.18182e7	+	2.04697e7i	0.667372	+	1.15592i
$794$	−1.96793e7	+	1.13618e7i	−1.10779	+	0.639583i
$795$	−1.39404e6	−	804848.i	−0.0782270	−	0.0451644i
$796$	5.20313e7	+	3.00403e7i	2.91060	+	1.68043i
$797$	1.07915e7	−	6.23050e6i	0.601780	−	0.347438i	−0.167962	−	0.985794i	$-0.553718\pi$
$797$	1.07915e7	−	6.23050e6i	0.601780	−	0.347438i	0.769742	+	0.638356i	$0.220385\pi$
$798$	3329.08	+	5766.14i	0.000185062	+	0.000320537i
$799$	−1.62467e6	+	938004.i	−0.0900323	+	0.0519802i
$800$		−	5.84027e7i		−	3.22633i
$801$	951218.	+	549186.i	0.0523840	+	0.0302439i
$802$	1.38673e7	+	2.40188e7i	0.761298	+	1.31861i
$803$	−2.94569e6			−0.161212
$804$	4.74861e7			2.59075
$805$	−17197.6	−	29787.1i	−0.000935357	−	0.00162009i
$806$		−	9.43884e6i		−	0.511777i
$807$	7.70642e6	−	1.33479e7i	0.416551	−	0.721488i
$808$			8.91385e7i			4.80327i
$809$	1.58161e7	+	9.13143e6i	0.849626	+	0.490532i	0.860525	−	0.509409i	$-0.170136\pi$
$809$	1.58161e7	+	9.13143e6i	0.849626	+	0.490532i	−0.0108984	+	0.999941i	$0.503469\pi$
$810$	3.12289e7	−	5.40901e7i	1.67242	−	2.89671i
$811$	−8.84936e6	+	1.53275e7i	−0.472454	+	0.818315i	−0.999503	−	0.0315203i	$-0.989965\pi$
$811$	−8.84936e6	+	1.53275e7i	−0.472454	+	0.818315i	0.527049	+	0.849835i	$0.323298\pi$
$812$	−3.47456e7	+	2.00604e7i	−1.84931	+	1.06770i
$813$	−936566.			−0.0496949
$814$	−9.70228e6	−	5.23718e7i	−0.513231	−	2.77036i
$815$	6.48702e6			0.342099
$816$	−1.09711e8	+	6.33415e7i	−5.76798	+	3.33014i
$817$	897.086	−	1553.80i	4.70196e−5	−	8.14404e-5i
$818$	3.83380e6	−	6.64033e6i	0.200330	−	0.346982i
$819$	−6.66824e6	−	3.84991e6i	−0.347377	−	0.200558i
$820$		−	8.34400e6i		−	0.433351i
$821$	−1.05413e7	+	1.82580e7i	−0.545803	+	0.945358i	0.452753	+	0.891636i	$0.350442\pi$
$821$	−1.05413e7	+	1.82580e7i	−0.545803	+	0.945358i	−0.998556	+	0.0537219i	$0.982892\pi$
$822$			2.53780e7i			1.31002i
$823$	2.47587e6	+	4.28833e6i	0.127417	+	0.220693i	0.922675	−	0.385578i	$-0.125998\pi$
$823$	2.47587e6	+	4.28833e6i	0.127417	+	0.220693i	−0.795258	+	0.606271i	$0.792665\pi$
$824$	8.51512e7			4.36891
$825$	3.60902e7			1.84609
$826$	−1.91828e7	−	3.32255e7i	−0.978275	−	1.69442i
$827$	−2.43841e7	−	1.40781e7i	−1.23977	−	0.715783i	−0.270725	−	0.962657i	$-0.587263\pi$
$827$	−2.43841e7	−	1.40781e7i	−1.23977	−	0.715783i	−0.969048	+	0.246873i	$0.920597\pi$
$828$			52434.2i			0.00265790i
$829$	1.88079e7	−	1.08588e7i	0.950505	−	0.548774i	0.0572673	−	0.998359i	$-0.481761\pi$
$829$	1.88079e7	−	1.08588e7i	0.950505	−	0.548774i	0.893238	+	0.449584i	$0.148428\pi$
$830$	−4.02416e7	−	6.97005e7i	−2.02759	−	3.51189i
$831$	−3.03289e7	+	1.75104e7i	−1.52354	+	0.879618i
$832$	−4.29861e7	−	2.48181e7i	−2.15288	−	1.24297i
$833$	−1.06779e7	−	6.16491e6i	−0.533181	−	0.307832i
$834$	4.42483e7	−	2.55468e7i	2.20283	−	1.27181i
$835$	−1.74828e6	−	3.02811e6i	−0.0867751	−	0.150299i
$836$	−13445.2	+	7762.58i	−0.000665351	+	0.000384141i
$837$			3.22280e6i			0.159008i
$838$	−3.27603e7	−	1.89142e7i	−1.61153	−	0.930417i
$839$	9.56300e6	+	1.65636e7i	0.469018	+	0.812363i	0.999373	−	0.0354131i	$-0.0112747\pi$
$839$	9.56300e6	+	1.65636e7i	0.469018	+	0.812363i	−0.530355	+	0.847776i	$0.677941\pi$
$840$	8.92391e7			4.36372
$841$	−1.43405e6			−0.0699158
$842$	−686397.	−	1.18888e6i	−0.0333653	−	0.0577904i
$843$		−	3.49995e7i		−	1.69626i
$844$	−3.13320e7	+	5.42686e7i	−1.51402	+	2.62236i
$845$		−	7.21284e6i		−	0.347508i
$846$	−1.34354e6	−	775693.i	−0.0645393	−	0.0372618i
$847$	9.60103e6	−	1.66295e7i	0.459843	−	0.796471i
$848$	1.77906e6	−	3.08142e6i	0.0849572	−	0.147150i
$849$	413784.	−	238898.i	0.0197017	−	0.0113748i
$850$	−6.28403e7			−2.98326
$851$	33816.9	+	11978.2i	0.00160070	+	0.000566980i
$852$	−1.48252e6			−0.0699684
$853$	−771329.	+	445327.i	−0.0362967	+	0.0209559i	−0.518039	−	0.855357i	$-0.673338\pi$
$853$	−771329.	+	445327.i	−0.0362967	+	0.0209559i	0.481742	+	0.876313i	$0.340004\pi$
$854$	2.44159e7	−	4.22896e7i	1.14559	−	1.98421i
$855$	1757.12	−	3043.42i	8.22027e−5	−	0.000142379i
$856$	3.66536e7	+	2.11620e7i	1.70975	+	0.987124i
$857$			1.69280e7i			0.787325i	0.919255	+	0.393663i	$0.128792\pi$
$857$			1.69280e7i			0.787325i	−0.919255	+	0.393663i	$0.871208\pi$
$858$	3.32748e7	−	5.76336e7i	1.54311	−	2.67275i
$859$			614851.i			0.0284307i	0.999899	+	0.0142153i	$0.00452503\pi$
$859$			614851.i			0.0284307i	−0.999899	+	0.0142153i	$0.995475\pi$
$860$	−1.93347e7	−	3.34887e7i	−0.891439	−	1.54402i
$861$	2.48777e6			0.114367
$862$	7.78555e7			3.56879
$863$	−1.49905e6	−	2.59643e6i	−0.0685154	−	0.118672i	0.829733	−	0.558161i	$-0.188493\pi$
$863$	−1.49905e6	−	2.59643e6i	−0.0685154	−	0.118672i	−0.898248	+	0.439489i	$0.855160\pi$
$864$	3.18446e7	+	1.83855e7i	1.45128	+	0.837897i
$865$			1.68543e7i			0.765899i
$866$	−4.33047e7	+	2.50020e7i	−1.96219	+	1.13287i
$867$	2.07253e7	+	3.58974e7i	0.936384	+	1.62186i
$868$	−1.22540e7	+	7.07487e6i	−0.552052	+	0.318727i
$869$	−2.80243e7	−	1.61799e7i	−1.25888	−	0.726817i
$870$	6.79766e7	+	3.92463e7i	3.04482	+	1.75793i
$871$	1.30710e7	−	7.54656e6i	0.583800	−	0.337057i
$872$	−2.47423e7	−	4.28549e7i	−1.10192	−	1.90858i
$873$	1.84986e7	−	1.06801e7i	0.821490	−	0.474288i
$874$		−	14.4113i		−	6.38151e-7i
$875$	−185154.	−	106898.i	−0.00817546	−	0.00472010i
$876$	4.13897e6	+	7.16890e6i	0.182235	+	0.315640i
$877$	1.34432e7			0.590205			0.295103	−	0.955466i	$-0.404646\pi$
$877$	1.34432e7			0.590205			0.295103	+	0.955466i	$0.404646\pi$
$878$	2.46559e7			1.07941
$879$	−3.86555e6	−	6.69533e6i	−0.168748	−	0.292280i
$880$			1.60239e8i			6.97526i
$881$	−9.14433e6	+	1.58384e7i	−0.396928	+	0.687500i	−0.993345	−	0.115175i	$-0.963257\pi$
$881$	−9.14433e6	+	1.58384e7i	−0.396928	+	0.687500i	0.596417	+	0.802675i	$0.296590\pi$
$882$		−	1.01963e7i		−	0.441337i
$883$	−3.87067e6	−	2.23473e6i	−0.167065	−	0.0964549i	0.414136	−	0.910215i	$-0.364084\pi$
$883$	−3.87067e6	−	2.23473e6i	−0.167065	−	0.0964549i	−0.581201	+	0.813760i	$0.697417\pi$
$884$	−4.20410e7	+	7.28172e7i	−1.80943	+	3.13403i
$885$	−2.72320e7	+	4.71673e7i	−1.16875	+	2.02434i
$886$	2.33004e7	−	1.34525e7i	0.997192	−	0.575729i
$887$	−4.61340e7			−1.96885			−0.984423	−	0.175818i	$-0.943743\pi$
$887$	−4.61340e7			−1.96885			−0.984423	+	0.175818i	$0.943743\pi$
$888$	−7.07835e7	+	6.04452e7i	−3.01231	+	2.57235i
$889$	−2.11344e6			−0.0896883
$890$	−5.63470e6	+	3.25320e6i	−0.238449	+	0.137669i
$891$	−2.17107e7	+	3.76041e7i	−0.916179	+	1.58687i
$892$	1.62597e7	−	2.81625e7i	0.684225	−	1.18511i
$893$	267.945	+	154.698i	1.12439e−5	+	6.49168e-6i
$894$		−	3.93526e7i		−	1.64676i
$895$	1.40169e7	−	2.42780e7i	0.584918	−	1.01311i
$896$			4.14990e7i			1.72690i
$897$	22412.5	+	38819.6i	0.000930056	+	0.00161090i
$898$	−7.00269e7			−2.89784
$899$	−7.73961e6			−0.319389
$900$	−1.88539e7	−	3.26560e7i	−0.775882	−	1.34387i
$901$	−1.68749e6	−	974273.i	−0.0692515	−	0.0399824i
$902$			7.99434e6i			0.327165i
$903$	9.98468e6	−	5.76466e6i	0.407488	−	0.235263i
$904$	−5.54770e7	−	9.60890e7i	−2.25783	−	3.91068i
$905$	4.20895e7	−	2.43004e7i	1.70825	−	0.986260i
$906$	−6.50123e7	−	3.75349e7i	−2.63133	−	1.51920i
$907$	−1.00542e6	−	580482.i	−0.0405818	−	0.0234299i	0.479572	−	0.877503i	$-0.340792\pi$
$907$	−1.00542e6	−	580482.i	−0.0405818	−	0.0234299i	−0.520154	+	0.854073i	$0.674125\pi$
$908$	5.02927e7	−	2.90365e7i	2.02437	−	1.16877i
$909$	1.12785e7	+	1.95349e7i	0.452732	+	0.784154i
$910$	3.95004e7	−	2.28056e7i	1.58124	−	0.912930i
$911$		−	1.95947e7i		−	0.782247i	−0.920338	−	0.391123i	$-0.872087\pi$
$911$		−	1.95947e7i		−	0.782247i	0.920338	−	0.391123i	$-0.127913\pi$
$912$	18093.8	+	10446.5i	0.000720349	+	0.000415894i
$913$	2.79765e7	+	4.84566e7i	1.11075	+	1.92387i
$914$	−8.92681e7			−3.53452
$915$	−6.93221e7			−2.73728
$916$	−2.21421e7	−	3.83512e7i	−0.871927	−	1.51022i
$917$			1.43531e7i			0.563667i
$918$	1.97824e7	−	3.42642e7i	0.774771	−	1.34194i
$919$		−	4.30649e7i		−	1.68203i	−0.541008	−	0.841017i	$-0.681957\pi$
$919$		−	4.30649e7i		−	1.68203i	0.541008	−	0.841017i	$-0.318043\pi$
$920$	−167276.	−	96576.7i	−0.00651574	−	0.00376186i
$921$	1.04352e7	−	1.80743e7i	0.405370	−	0.702122i
$922$	2.27199e7	−	3.93521e7i	0.880197	−	1.52455i
$923$	−408079.	+	235605.i	−0.0157667	+	0.00910289i
$924$	−9.97644e7			−3.84411
$925$	−2.53682e7	+	4.69965e6i	−0.974843	+	0.180597i
$926$	8.10355e7			3.10562
$927$	1.86611e7	−	1.07740e7i	0.713243	−	0.411791i
$928$	−4.41530e7	+	7.64753e7i	−1.68303	+	2.91509i
$929$	5.04772e6	−	8.74291e6i	0.191892	−	0.332366i	−0.753985	−	0.656891i	$-0.771871\pi$
$929$	5.04772e6	−	8.74291e6i	0.191892	−	0.332366i	0.945877	+	0.324525i	$0.105204\pi$
$930$	2.39739e7	+	1.38414e7i	0.908933	+	0.524773i
$931$			2033.47i			7.68888e-5i
$932$	−3.96559e7	+	6.86860e7i	−1.49544	+	2.59017i
$933$		−	3.39060e7i		−	1.27518i
$934$	1.88141e7	+	3.25869e7i	0.705693	+	1.22230i
$935$	8.77522e7			3.28268
$936$	−4.32400e7			−1.61323
$937$	2.42744e7	+	4.20444e7i	0.903231	+	1.56444i	0.823275	+	0.567643i	$0.192145\pi$
$937$	2.42744e7	+	4.20444e7i	0.903231	+	1.56444i	0.0799559	+	0.996798i	$0.474522\pi$
$938$	−2.70042e7	−	1.55909e7i	−1.00213	−	0.578580i
$939$			3.78333e7i			1.40027i
$940$	5.77497e6	−	3.33418e6i	0.213172	−	0.123075i
$941$	−1.33625e7	−	2.31446e7i	−0.491943	−	0.852070i	0.508014	−	0.861349i	$-0.330380\pi$
$941$	−1.33625e7	−	2.31446e7i	−0.491943	−	0.852070i	−0.999957	+	0.00927892i	$0.997046\pi$
$942$	4.11410e7	−	2.37528e7i	1.51059	−	0.872142i
$943$	−4663.24	−	2692.32i	−0.000170769	−	9.85934e-5i
$944$	−1.04260e8	−	6.01944e7i	−3.80791	−	2.19850i
$945$	−1.34870e7	+	7.78675e6i	−0.491289	+	0.283646i
$946$	1.85245e7	+	3.20854e7i	0.673005	+	1.16568i
$947$	1.99953e7	−	1.15443e7i	0.724523	−	0.418304i	−0.0918920	−	0.995769i	$-0.529291\pi$
$947$	1.99953e7	−	1.15443e7i	0.724523	−	0.418304i	0.816415	+	0.577465i	$0.195958\pi$
$948$			9.09369e7i			3.28639i
$949$	2.27859e6	+	1.31554e6i	0.0821297	+	0.0474176i
$950$	5181.90	+	8975.31i	0.000186286	+	0.000322657i
$951$	−1.06038e7			−0.380200
$952$	1.08024e8			3.86304
$953$	−3.96370e6	−	6.86534e6i	−0.141374	−	0.244867i	0.786640	−	0.617411i	$-0.211819\pi$
$953$	−3.96370e6	−	6.86534e6i	−0.141374	−	0.244867i	−0.928014	+	0.372545i	$0.878485\pi$
$954$		−	1.61137e6i		−	0.0573224i
$955$	2.78219e7	−	4.81890e7i	0.987140	−	1.70978i
$956$			1.26364e8i			4.47177i
$957$	−4.72582e7	−	2.72845e7i	−1.66800	−	0.963022i
$958$	−3.66912e7	+	6.35510e7i	−1.29166	+	2.23722i
$959$	6.04602e6	−	1.04720e7i	0.212287	−	0.367692i
$960$	1.26072e8	−	7.27877e7i	4.41510	−	2.54906i
$961$	2.58996e7			0.904657
$962$	−1.58842e7	+	4.48444e7i	−0.553385	+	1.56232i
$963$	1.07103e7			0.372165
$964$	9.38187e7	−	5.41662e7i	3.25160	−	1.87731i
$965$	1.49805e7	−	2.59471e7i	0.517856	−	0.896954i
$966$	46303.2	−	80199.6i	0.00159650	−	0.00276522i
$967$	−1.83981e7	−	1.06222e7i	−0.632714	−	0.365298i	0.149088	−	0.988824i	$-0.452366\pi$
$967$	−1.83981e7	−	1.06222e7i	−0.632714	−	0.365298i	−0.781802	+	0.623526i	$0.785699\pi$
$968$		−	1.07833e8i		−	3.69883i
$969$	5720.85	−	9908.80i	0.000195727	−	0.000339009i
$970$			1.26531e8i			4.31786i
$971$	2.69530e7	+	4.66840e7i	0.917401	+	1.58899i	0.803347	+	0.595511i	$0.203050\pi$
$971$	2.69530e7	+	4.66840e7i	0.917401	+	1.58899i	0.114054	+	0.993475i	$0.463616\pi$
$972$	8.19086e7			2.78076
$973$	−2.43450e7			−0.824379
$974$	−4.53966e7	−	7.86293e7i	−1.53330	−	2.65575i
$975$	−2.79169e7	−	1.61178e7i	−0.940494	−	0.542995i
$976$		−	1.53231e8i		−	5.14900i
$977$	3.32181e7	−	1.91785e7i	1.11337	−	0.642804i	0.173669	−	0.984804i	$-0.444438\pi$
$977$	3.32181e7	−	1.91785e7i	1.11337	−	0.642804i	0.939700	+	0.342000i	$0.111104\pi$
$978$	8.73292e6	+	1.51259e7i	0.291953	+	0.505677i
$979$	3.91731e6	−	2.26166e6i	0.130626	−	0.0754172i
$980$	3.79552e7	+	2.19134e7i	1.26243	+	0.728862i
$981$	−1.08447e7	−	6.26117e6i	−0.359785	−	0.207722i
$982$	−8.43555e7	+	4.87027e7i	−2.79148	+	1.61166i
$983$	2.05339e7	+	3.55657e7i	0.677777	+	1.17394i	0.975649	+	0.219338i	$0.0703897\pi$
$983$	2.05339e7	+	3.55657e7i	0.677777	+	1.17394i	−0.297872	+	0.954606i	$0.596277\pi$
$984$	1.20989e7	−	6.98530e6i	0.398344	−	0.229984i
$985$			4.02101e7i			1.32052i
$986$	8.22861e7	+	4.75079e7i	2.69547	+	1.55623i
$987$	994088.	+	1.72181e6i	0.0324812	+	0.0562591i
$988$	13867.1			0.000451952
$989$	−24954.6			−0.000811260
$990$	3.62838e7	+	6.28455e7i	1.17659	+	2.03791i
$991$		−	2.70950e7i		−	0.876406i	−0.898876	−	0.438203i	$-0.855615\pi$
$991$		−	2.70950e7i		−	0.876406i	0.898876	−	0.438203i	$-0.144385\pi$
$992$	−1.55718e7	+	2.69712e7i	−0.502413	+	0.870205i
$993$		−	2.18272e6i		−	0.0702466i
$994$	843074.	+	486749.i	0.0270645	+	0.0156257i
$995$	−2.80032e7	+	4.85029e7i	−0.896704	+	1.55314i
$996$	7.86191e7	−	1.36172e8i	2.51119	−	4.34951i
$997$	−2.14505e7	+	1.23844e7i	−0.683438	+	0.394583i	−0.801149	−	0.598465i	$-0.795778\pi$
$997$	−2.14505e7	+	1.23844e7i	−0.683438	+	0.394583i	0.117711	+	0.993048i	$0.462444\pi$
$998$	−8.93159e7			−2.83859
$999$	5.42351e6	−	1.53117e7i	0.171936	−	0.485410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.e.a.11.16	✓	32
37.27	even	6	inner	37.6.e.a.27.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.e.a.11.16	✓	32	1.1	even	1	trivial
37.6.e.a.27.16	yes	32	37.27	even	6	inner

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(9.35252 - 5.39968i) q^{2} +(-9.83385 + 17.0327i) q^{3} +(42.3131 - 73.2884i) q^{4} +(68.3185 + 39.4437i) q^{5} +212.399i q^{6} +(50.6016 - 87.6446i) q^{7} -568.329i q^{8} +(-71.9093 - 124.551i) q^{9} +O(q^{10})\)	\(q+(9.35252 - 5.39968i) q^{2} +(-9.83385 + 17.0327i) q^{3} +(42.3131 - 73.2884i) q^{4} +(68.3185 + 39.4437i) q^{5} +212.399i q^{6} +(50.6016 - 87.6446i) q^{7} -568.329i q^{8} +(-71.9093 - 124.551i) q^{9} +851.933 q^{10} -592.274 q^{11} +(832.201 + 1441.41i) q^{12} +(458.144 + 264.509i) q^{13} -1092.93i q^{14} +(-1343.67 + 775.767i) q^{15} +(-1714.77 - 2970.08i) q^{16} +(-1626.52 + 939.070i) q^{17} +(-1345.07 - 776.574i) q^{18} +(0.268250 + 0.154874i) q^{19} +(5781.53 - 3337.97i) q^{20} +(995.218 + 1723.77i) q^{21} +(-5539.26 + 3198.09i) q^{22} -4.30819i q^{23} +(9680.19 + 5588.86i) q^{24} +(1549.11 + 2683.14i) q^{25} +5713.06 q^{26} -1950.67 q^{27} +(-4282.22 - 7417.02i) q^{28} -4684.57i q^{29} +(-8377.79 + 14510.7i) q^{30} -1652.15i q^{31} +(-16324.9 - 9425.21i) q^{32} +(5824.34 - 10088.0i) q^{33} +(-10141.4 + 17565.3i) q^{34} +(6914.05 - 3991.83i) q^{35} -12170.8 q^{36} +(-2780.33 + 7849.44i) q^{37} +3.34508 q^{38} +(-9010.63 + 5202.29i) q^{39} +(22417.0 - 38827.4i) q^{40} +(624.931 - 1082.41i) q^{41} +(18615.6 + 10747.7i) q^{42} -5792.36i q^{43} +(-25060.9 + 43406.8i) q^{44} -11345.5i q^{45} +(-23.2629 - 40.2925i) q^{46} +998.865 q^{47} +67451.3 q^{48} +(3282.45 + 5685.38i) q^{49} +(28976.2 + 16729.4i) q^{50} -36938.7i q^{51} +(38770.9 - 22384.4i) q^{52} +(518.744 + 898.490i) q^{53} +(-18243.7 + 10533.0i) q^{54} +(-40463.3 - 23361.5i) q^{55} +(-49810.9 - 28758.4i) q^{56} +(-5.27586 + 3.04602i) q^{57} +(-25295.2 - 43812.5i) q^{58} +(30400.4 - 17551.7i) q^{59} +131300. i q^{60} +(38693.7 + 22339.8i) q^{61} +(-8921.08 - 15451.8i) q^{62} -14554.9 q^{63} -93826.8 q^{64} +(20866.5 + 36141.8i) q^{65} -125798. i q^{66} +(14265.2 - 24708.1i) q^{67} +158940. i q^{68} +(73.3803 + 42.3661i) q^{69} +(43109.2 - 74667.3i) q^{70} +(-445.361 + 771.389i) q^{71} +(-70785.6 + 40868.1i) q^{72} +4973.52 q^{73} +(16381.4 + 88424.9i) q^{74} -60934.9 q^{75} +(22.7009 - 13.1064i) q^{76} +(-29970.0 + 51909.6i) q^{77} +(-56181.4 + 97309.1i) q^{78} +(47316.5 + 27318.2i) q^{79} -270548. i q^{80} +(36656.6 - 63491.0i) q^{81} -13497.7i q^{82} +(-47235.7 - 81814.6i) q^{83} +168443. q^{84} -148162. q^{85} +(-31276.9 - 54173.1i) q^{86} +(79791.0 + 46067.4i) q^{87} +336606. i q^{88} +(-6614.02 + 3818.60i) q^{89} +(-61261.9 - 106109. i) q^{90} +(46365.6 - 26769.2i) q^{91} +(-315.741 - 182.293i) q^{92} +(28140.6 + 16247.0i) q^{93} +(9341.90 - 5393.55i) q^{94} +(12.2176 + 21.1615i) q^{95} +(321074. - 185372. i) q^{96} +148523. i q^{97} +(61398.4 + 35448.4i) q^{98} +(42590.0 + 73768.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{2} + 18 q^{3} + 298 q^{4} + 144 q^{5} - 52 q^{7} - 1490 q^{9}+O(q^{10}) \) 32 * q - 6 * q^2 + 18 * q^3 + 298 * q^4 + 144 * q^5 - 52 * q^7 - 1490 * q^9	\( 32 q - 6 q^{2} + 18 q^{3} + 298 q^{4} + 144 q^{5} - 52 q^{7} - 1490 q^{9} + 668 q^{10} - 348 q^{11} + 134 q^{12} + 222 q^{13} - 4134 q^{15} - 6998 q^{16} - 624 q^{17} + 7632 q^{18} + 2154 q^{19} + 4806 q^{20} - 130 q^{21} - 8214 q^{22} + 24642 q^{24} + 15808 q^{25} + 4332 q^{26} - 30384 q^{27} - 9048 q^{28} + 7780 q^{30} + 35088 q^{32} - 924 q^{33} - 5982 q^{34} + 27072 q^{35} - 57468 q^{36} - 46062 q^{37} - 48048 q^{38} - 31896 q^{39} + 57956 q^{40} - 11136 q^{41} + 50886 q^{42} - 43686 q^{44} + 42866 q^{46} + 63708 q^{47} - 39260 q^{48} - 52426 q^{49} - 29292 q^{50} + 132684 q^{52} - 85398 q^{53} + 235314 q^{54} - 65346 q^{55} + 121836 q^{56} - 96270 q^{57} - 121896 q^{58} + 40980 q^{59} - 74616 q^{61} + 89346 q^{62} + 232304 q^{63} - 321132 q^{64} + 24066 q^{65} + 68018 q^{67} - 11052 q^{69} - 230194 q^{70} - 32544 q^{71} + 117876 q^{72} - 179176 q^{73} - 89166 q^{74} - 379288 q^{75} + 196110 q^{76} + 22428 q^{77} - 288138 q^{78} + 217218 q^{79} - 6200 q^{81} - 127434 q^{83} + 1109800 q^{84} + 218576 q^{85} - 80364 q^{86} + 457230 q^{87} - 164844 q^{89} - 360436 q^{90} + 167160 q^{91} - 984606 q^{92} + 532392 q^{93} - 369822 q^{94} + 187398 q^{95} + 1476018 q^{96} - 174684 q^{98} + 194298 q^{99}+O(q^{100}) \) 32 * q - 6 * q^2 + 18 * q^3 + 298 * q^4 + 144 * q^5 - 52 * q^7 - 1490 * q^9 + 668 * q^10 - 348 * q^11 + 134 * q^12 + 222 * q^13 - 4134 * q^15 - 6998 * q^16 - 624 * q^17 + 7632 * q^18 + 2154 * q^19 + 4806 * q^20 - 130 * q^21 - 8214 * q^22 + 24642 * q^24 + 15808 * q^25 + 4332 * q^26 - 30384 * q^27 - 9048 * q^28 + 7780 * q^30 + 35088 * q^32 - 924 * q^33 - 5982 * q^34 + 27072 * q^35 - 57468 * q^36 - 46062 * q^37 - 48048 * q^38 - 31896 * q^39 + 57956 * q^40 - 11136 * q^41 + 50886 * q^42 - 43686 * q^44 + 42866 * q^46 + 63708 * q^47 - 39260 * q^48 - 52426 * q^49 - 29292 * q^50 + 132684 * q^52 - 85398 * q^53 + 235314 * q^54 - 65346 * q^55 + 121836 * q^56 - 96270 * q^57 - 121896 * q^58 + 40980 * q^59 - 74616 * q^61 + 89346 * q^62 + 232304 * q^63 - 321132 * q^64 + 24066 * q^65 + 68018 * q^67 - 11052 * q^69 - 230194 * q^70 - 32544 * q^71 + 117876 * q^72 - 179176 * q^73 - 89166 * q^74 - 379288 * q^75 + 196110 * q^76 + 22428 * q^77 - 288138 * q^78 + 217218 * q^79 - 6200 * q^81 - 127434 * q^83 + 1109800 * q^84 + 218576 * q^85 - 80364 * q^86 + 457230 * q^87 - 164844 * q^89 - 360436 * q^90 + 167160 * q^91 - 984606 * q^92 + 532392 * q^93 - 369822 * q^94 + 187398 * q^95 + 1476018 * q^96 - 174684 * q^98 + 194298 * q^99

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