LMFDB - Embedded newform 60.7.f.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.65640 + 2.31937i) q^{2} -15.5885 q^{3} +(53.2410 - 35.5161i) q^{4} +(87.3911 - 89.3745i) q^{5} +(119.352 - 36.1554i) q^{6} -36.3122 q^{7} +(-325.260 + 395.411i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(-7.65640 + 2.31937i) q^{2} -15.5885 q^{3} +(53.2410 - 35.5161i) q^{4} +(87.3911 - 89.3745i) q^{5} +(119.352 - 36.1554i) q^{6} -36.3122 q^{7} +(-325.260 + 395.411i) q^{8} +243.000 q^{9} +(-461.809 + 886.980i) q^{10} +995.783i q^{11} +(-829.945 + 553.641i) q^{12} +105.943i q^{13} +(278.021 - 84.2215i) q^{14} +(-1362.29 + 1393.21i) q^{15} +(1573.21 - 3781.83i) q^{16} -1286.27i q^{17} +(-1860.51 + 563.607i) q^{18} -9085.22i q^{19} +(1478.56 - 7862.18i) q^{20} +566.051 q^{21} +(-2309.59 - 7624.12i) q^{22} -1331.63 q^{23} +(5070.30 - 6163.85i) q^{24} +(-350.602 - 15621.1i) q^{25} +(-245.722 - 811.144i) q^{26} -3788.00 q^{27} +(-1933.30 + 1289.67i) q^{28} -14223.4 q^{29} +(7198.88 - 13826.6i) q^{30} -40502.0i q^{31} +(-3273.70 + 32604.1i) q^{32} -15522.7i q^{33} +(2983.33 + 9848.19i) q^{34} +(-3173.36 + 3245.39i) q^{35} +(12937.6 - 8630.41i) q^{36} -71359.6i q^{37} +(21072.0 + 69560.1i) q^{38} -1651.49i q^{39} +(6914.89 + 63625.3i) q^{40} -68453.6 q^{41} +(-4333.92 + 1312.88i) q^{42} -6391.48 q^{43} +(35366.3 + 53016.5i) q^{44} +(21236.0 - 21718.0i) q^{45} +(10195.5 - 3088.55i) q^{46} +56471.4 q^{47} +(-24524.0 + 58952.8i) q^{48} -116330. q^{49} +(38915.4 + 118788. i) q^{50} +20050.9i q^{51} +(3762.69 + 5640.53i) q^{52} -62845.9i q^{53} +(29002.4 - 8785.77i) q^{54} +(88997.6 + 87022.5i) q^{55} +(11810.9 - 14358.3i) q^{56} +141624. i q^{57} +(108900. - 32989.3i) q^{58} +132995. i q^{59} +(-23048.4 + 122559. i) q^{60} -387193. q^{61} +(93939.2 + 310100. i) q^{62} -8823.87 q^{63} +(-50556.2 - 257223. i) q^{64} +(9468.63 + 9258.50i) q^{65} +(36003.0 + 118848. i) q^{66} +476348. q^{67} +(-45683.2 - 68482.2i) q^{68} +20758.1 q^{69} +(16769.3 - 32208.2i) q^{70} -483101. i q^{71} +(-79038.1 + 96084.9i) q^{72} -654838. i q^{73} +(165509. + 546358. i) q^{74} +(5465.35 + 243508. i) q^{75} +(-322671. - 483706. i) q^{76} -36159.1i q^{77} +(3830.42 + 12644.5i) q^{78} -80187.9i q^{79} +(-200514. - 471103. i) q^{80} +59049.0 q^{81} +(524108. - 158769. i) q^{82} -1.03615e6 q^{83} +(30137.2 - 20103.9i) q^{84} +(-114960. - 112408. i) q^{85} +(48935.8 - 14824.2i) q^{86} +221721. q^{87} +(-393744. - 323888. i) q^{88} +1.20220e6 q^{89} +(-112219. + 215536. i) q^{90} -3847.03i q^{91} +(-70897.4 + 47294.4i) q^{92} +631363. i q^{93} +(-432368. + 130978. i) q^{94} +(-811987. - 793967. i) q^{95} +(51031.9 - 508247. i) q^{96} +1.45683e6i q^{97} +(890673. - 269814. i) q^{98} +241975. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−7.65640	+	2.31937i	−0.957050	+	0.289921i
$2$	−7.65640	+	2.31937i	−0.957050	+	0.289921i
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	53.2410	−	35.5161i	0.831891	−	0.554939i
$5$	87.3911	−	89.3745i	0.699129	−	0.714996i
$5$	87.3911	−	89.3745i	0.699129	−	0.714996i
$6$	119.352	−	36.1554i	0.552553	−	0.167386i
$7$	−36.3122			−0.105866			−0.0529332	−	0.998598i	$-0.516857\pi$
$7$	−36.3122			−0.105866			−0.0529332	+	0.998598i	$0.516857\pi$
$8$	−325.260	+	395.411i	−0.635273	+	0.772288i
$9$	243.000			0.333333
$10$	−461.809	+	886.980i	−0.461809	+	0.886980i
$11$			995.783i			0.748146i	0.927399	+	0.374073i	$0.122039\pi$
$11$			995.783i			0.748146i	−0.927399	+	0.374073i	$0.877961\pi$
$12$	−829.945	+	553.641i	−0.480293	+	0.320394i
$13$			105.943i			0.0482218i	0.999709	+	0.0241109i	$0.00767548\pi$
$13$			105.943i			0.0482218i	−0.999709	+	0.0241109i	$0.992325\pi$
$14$	278.021	−	84.2215i	0.101320	−	0.0306930i
$15$	−1362.29	+	1393.21i	−0.403642	+	0.412803i
$16$	1573.21	−	3781.83i	0.384085	−	0.923298i
$17$		−	1286.27i		−	0.261809i	−0.991395	−	0.130905i	$-0.958212\pi$
$17$		−	1286.27i		−	0.261809i	0.991395	−	0.130905i	$-0.0417881\pi$
$18$	−1860.51	+	563.607i	−0.319017	+	0.0966405i
$19$		−	9085.22i		−	1.32457i	−0.749253	−	0.662284i	$-0.769587\pi$
$19$		−	9085.22i		−	1.32457i	0.749253	−	0.662284i	$-0.230413\pi$
$20$	1478.56	−	7862.18i	0.184820	−	0.982772i
$21$	566.051			0.0611221
$22$	−2309.59	−	7624.12i	−0.216904	−	0.716014i
$23$	−1331.63			−0.109446			−0.0547231	−	0.998502i	$-0.517428\pi$
$23$	−1331.63			−0.109446			−0.0547231	+	0.998502i	$0.517428\pi$
$24$	5070.30	−	6163.85i	0.366775	−	0.445880i
$25$	−350.602	−	15621.1i	−0.0224386	−	0.999748i
$26$	−245.722	−	811.144i	−0.0139805	−	0.0461507i
$27$	−3788.00			−0.192450
$28$	−1933.30	+	1289.67i	−0.0880694	+	0.0587494i
$29$	−14223.4			−0.583188			−0.291594	−	0.956542i	$-0.594186\pi$
$29$	−14223.4			−0.583188			−0.291594	+	0.956542i	$0.594186\pi$
$30$	7198.88	−	13826.6i	0.266625	−	0.512098i
$31$		−	40502.0i		−	1.35954i	−0.733426	−	0.679769i	$-0.762080\pi$
$31$		−	40502.0i		−	1.35954i	0.733426	−	0.679769i	$-0.237920\pi$
$32$	−3273.70	+	32604.1i	−0.0999054	+	0.994997i
$33$		−	15522.7i		−	0.431943i
$34$	2983.33	+	9848.19i	0.0759041	+	0.250565i
$35$	−3173.36	+	3245.39i	−0.0740143	+	0.0756941i
$36$	12937.6	−	8630.41i	0.277297	−	0.184980i
$37$		−	71359.6i		−	1.40879i	−0.709807	−	0.704396i	$-0.751218\pi$
$37$		−	71359.6i		−	1.40879i	0.709807	−	0.704396i	$-0.248782\pi$
$38$	21072.0	+	69560.1i	0.384021	+	1.26768i
$39$		−	1651.49i		−	0.0278409i
$40$	6914.89	+	63625.3i	0.108045	+	0.994146i
$41$	−68453.6			−0.993218			−0.496609	−	0.867974i	$-0.665422\pi$
$41$	−68453.6			−0.993218			−0.496609	+	0.867974i	$0.665422\pi$
$42$	−4333.92	+	1312.88i	−0.0584969	+	0.0177206i
$43$	−6391.48			−0.0803889			−0.0401945	−	0.999192i	$-0.512798\pi$
$43$	−6391.48			−0.0803889			−0.0401945	+	0.999192i	$0.512798\pi$
$44$	35366.3	+	53016.5i	0.415176	+	0.622376i
$45$	21236.0	−	21718.0i	0.233043	−	0.238332i
$46$	10195.5	−	3088.55i	0.104746	−	0.0317308i
$47$	56471.4			0.543920			0.271960	−	0.962309i	$-0.412328\pi$
$47$	56471.4			0.543920			0.271960	+	0.962309i	$0.412328\pi$
$48$	−24524.0	+	58952.8i	−0.221752	+	0.533066i
$49$	−116330.			−0.988792
$50$	38915.4	+	118788.i	0.311323	+	0.950304i
$51$			20050.9i			0.151156i
$52$	3762.69	+	5640.53i	0.0267601	+	0.0401153i
$53$		−	62845.9i		−	0.422133i	−0.977472	−	0.211066i	$-0.932306\pi$
$53$		−	62845.9i		−	0.422133i	0.977472	−	0.211066i	$-0.0676936\pi$
$54$	29002.4	−	8785.77i	0.184184	−	0.0557954i
$55$	88997.6	+	87022.5i	0.534922	+	0.523051i
$56$	11810.9	−	14358.3i	0.0672541	−	0.0817594i
$57$			141624.i			0.764740i
$58$	108900.	−	32989.3i	0.558141	−	0.169079i
$59$			132995.i			0.647561i	0.946132	+	0.323780i	$0.104954\pi$
$59$			132995.i			0.647561i	−0.946132	+	0.323780i	$0.895046\pi$
$60$	−23048.4	+	122559.i	−0.106706	+	0.567404i
$61$	−387193.			−1.70584			−0.852920	−	0.522042i	$-0.825171\pi$
$61$	−387193.			−1.70584			−0.852920	+	0.522042i	$0.825171\pi$
$62$	93939.2	+	310100.i	0.394159	+	1.30115i
$63$	−8823.87			−0.0352888
$64$	−50556.2	−	257223.i	−0.192857	−	0.981227i
$65$	9468.63	+	9258.50i	0.0344784	+	0.0337132i
$66$	36003.0	+	118848.i	0.125229	+	0.413391i
$67$	476348.			1.58380			0.791899	−	0.610653i	$-0.209093\pi$
$67$	476348.			1.58380			0.791899	+	0.610653i	$0.209093\pi$
$68$	−45683.2	−	68482.2i	−0.145288	−	0.217797i
$69$	20758.1			0.0631888
$70$	16769.3	−	32208.2i	0.0488901	−	0.0939014i
$71$		−	483101.i		−	1.34978i	−0.737919	−	0.674889i	$-0.764191\pi$
$71$		−	483101.i		−	1.34978i	0.737919	−	0.674889i	$-0.235809\pi$
$72$	−79038.1	+	96084.9i	−0.211758	+	0.257429i
$73$		−	654838.i		−	1.68331i	−0.540012	−	0.841657i	$-0.681580\pi$
$73$		−	654838.i		−	1.68331i	0.540012	−	0.841657i	$-0.318420\pi$
$74$	165509.	+	546358.i	0.408439	+	1.34829i
$75$	5465.35	+	243508.i	0.0129549	+	0.577205i
$76$	−322671.	−	483706.i	−0.735055	−	1.10190i
$77$		−	36159.1i		−	0.0792036i
$78$	3830.42	+	12644.5i	0.00807166	+	0.0266451i
$79$		−	80187.9i		−	0.162640i	−0.996688	−	0.0813200i	$-0.974086\pi$
$79$		−	80187.9i		−	0.162640i	0.996688	−	0.0813200i	$-0.0259136\pi$
$80$	−200514.	−	471103.i	−0.391629	−	0.920123i
$81$	59049.0			0.111111
$82$	524108.	−	158769.i	0.950559	−	0.287955i
$83$	−1.03615e6			−1.81213			−0.906066	−	0.423137i	$-0.860929\pi$
$83$	−1.03615e6			−1.81213			−0.906066	+	0.423137i	$0.860929\pi$
$84$	30137.2	−	20103.9i	0.0508469	−	0.0339190i
$85$	−114960.	−	112408.i	−0.187192	−	0.183038i
$86$	48935.8	−	14824.2i	0.0769362	−	0.0233065i
$87$	221721.			0.336704
$88$	−393744.	−	323888.i	−0.577784	−	0.475277i
$89$	1.20220e6			1.70532			0.852662	−	0.522463i	$-0.174987\pi$
$89$	1.20220e6			1.70532			0.852662	+	0.522463i	$0.174987\pi$
$90$	−112219.	+	215536.i	−0.153936	+	0.295660i
$91$		−	3847.03i		−	0.00510507i
$92$	−70897.4	+	47294.4i	−0.0910473	+	0.0607360i
$93$			631363.i			0.784929i
$94$	−432368.	+	130978.i	−0.520559	+	0.157694i
$95$	−811987.	−	793967.i	−0.947061	−	0.926044i
$96$	51031.9	−	508247.i	0.0576804	−	0.574462i
$97$			1.45683e6i			1.59622i	0.602511	+	0.798111i	$0.294167\pi$
$97$			1.45683e6i			1.59622i	−0.602511	+	0.798111i	$0.705833\pi$
$98$	890673.	−	269814.i	0.946324	−	0.286672i
$99$			241975.i			0.249382i
$100$	−573466.	−	819230.i	−0.573466	−	0.819230i
$101$	796216.			0.772800			0.386400	−	0.922331i	$-0.373718\pi$
$101$	796216.			0.772800			0.386400	+	0.922331i	$0.373718\pi$
$102$	−46505.6	−	153518.i	−0.0438232	−	0.144664i
$103$	−747900.			−0.684435			−0.342217	−	0.939621i	$-0.611178\pi$
$103$	−747900.			−0.684435			−0.342217	+	0.939621i	$0.611178\pi$
$104$	−41891.2	−	34459.1i	−0.0372411	−	0.0306340i
$105$	49467.8	−	50590.6i	0.0427322	−	0.0437020i
$106$	145763.	+	481173.i	0.122385	+	0.404002i
$107$	−75240.9			−0.0614190			−0.0307095	−	0.999528i	$-0.509777\pi$
$107$	−75240.9			−0.0614190			−0.0307095	+	0.999528i	$0.509777\pi$
$108$	−201677.	+	134535.i	−0.160098	+	0.106798i
$109$	905540.			0.699243			0.349622	−	0.936891i	$-0.386310\pi$
$109$	905540.			0.699243			0.349622	+	0.936891i	$0.386310\pi$
$110$	−883239.	−	459861.i	−0.663591	−	0.345500i
$111$			1.11239e6i			0.813367i
$112$	−57126.9	+	137326.i	−0.0406618	+	0.0977463i
$113$			799166.i			0.553862i	0.960890	+	0.276931i	$0.0893173\pi$
$113$			799166.i			0.553862i	−0.960890	+	0.276931i	$0.910683\pi$
$114$	−328480.	−	1.08433e6i	−0.221715	−	0.731895i
$115$	−116373.	+	119014.i	−0.0765170	+	0.0782536i
$116$	−757267.	+	505159.i	−0.485149	+	0.323634i
$117$			25744.2i			0.0160739i
$118$	−308466.	−	1.01827e6i	−0.187742	−	0.619748i
$119$			46707.2i			0.0277168i
$120$	−107792.	−	991821.i	−0.0623799	−	0.573970i
$121$	779977.			0.440277
$122$	2.96451e6	−	898045.i	1.63258	−	0.494560i
$123$	1.06709e6			0.573434
$124$	−1.43847e6	−	2.15637e6i	−0.754460	−	1.13099i
$125$	−1.42676e6	−	1.33381e6i	−0.730503	−	0.682909i
$126$	67559.1	−	20465.8i	0.0337732	−	0.0102310i
$127$	3.25779e6			1.59042			0.795209	−	0.606335i	$-0.207361\pi$
$127$	3.25779e6			1.59042			0.795209	+	0.606335i	$0.207361\pi$
$128$	983674.	+	1.85214e6i	0.469052	+	0.883170i
$129$	99633.3			0.0464126
$130$	−93969.5	−	48925.5i	−0.0427717	−	0.0222692i
$131$		−	208824.i		−	0.0928893i	−0.998921	−	0.0464446i	$-0.985211\pi$
$131$		−	208824.i		−	0.0928893i	0.998921	−	0.0464446i	$-0.0147891\pi$
$132$	−551306.	−	826446.i	−0.239702	−	0.359329i
$133$			329904.i			0.140227i
$134$	−3.64711e6	+	1.10483e6i	−1.51577	+	0.459177i
$135$	−331037.	+	338550.i	−0.134547	+	0.137601i
$136$	508605.	+	418371.i	0.202192	+	0.166320i
$137$			2.47104e6i			0.960987i	0.876998	+	0.480493i	$0.159542\pi$
$137$			2.47104e6i			0.960987i	−0.876998	+	0.480493i	$0.840458\pi$
$138$	−158932.	+	48145.7i	−0.0604749	+	0.0183198i
$139$			1.93989e6i			0.722327i	0.932503	+	0.361163i	$0.117620\pi$
$139$			1.93989e6i			0.722327i	−0.932503	+	0.361163i	$0.882380\pi$
$140$	−53689.7	+	285493.i	−0.0195662	+	0.104043i
$141$	−880303.			−0.314033
$142$	1.12049e6	+	3.69881e6i	0.391330	+	1.29181i
$143$	−105496.			−0.0360770
$144$	382291.	−	918984.i	0.128028	−	0.307766i
$145$	−1.24300e6	+	1.27121e6i	−0.407724	+	0.416977i
$146$	1.51881e6	+	5.01370e6i	0.488029	+	1.61102i
$147$	1.81341e6			0.570879
$148$	−2.53441e6	−	3.79926e6i	−0.781794	−	1.17196i
$149$	502061.			0.151774			0.0758870	−	0.997116i	$-0.475821\pi$
$149$	502061.			0.151774			0.0758870	+	0.997116i	$0.475821\pi$
$150$	−606631.	−	1.85172e6i	−0.179743	−	0.548658i
$151$			3.91206e6i			1.13625i	0.822941	+	0.568127i	$0.192332\pi$
$151$			3.91206e6i			1.13625i	−0.822941	+	0.568127i	$0.807668\pi$
$152$	3.59240e6	+	2.95505e6i	1.02295	+	0.841463i
$153$		−	312563.i		−	0.0872697i
$154$	83866.3	+	276848.i	0.0229628	+	0.0758019i
$155$	−3.61984e6	−	3.53951e6i	−0.972064	−	0.950492i
$156$	−58654.5	−	87927.1i	−0.0154500	−	0.0231606i
$157$			1.57181e6i			0.406163i	0.979162	+	0.203081i	$0.0650956\pi$
$157$			1.57181e6i			0.406163i	−0.979162	+	0.203081i	$0.934904\pi$
$158$	185986.	+	613951.i	0.0471528	+	0.155655i
$159$			979670.i			0.243719i
$160$	2.62788e6	+	3.14189e6i	0.641572	+	0.767063i
$161$	48354.5			0.0115867
$162$	−452103.	+	136957.i	−0.106339	+	0.0322135i
$163$	−3.02276e6			−0.697977			−0.348989	−	0.937127i	$-0.613475\pi$
$163$	−3.02276e6			−0.697977			−0.348989	+	0.937127i	$0.613475\pi$
$164$	−3.64454e6	+	2.43120e6i	−0.826249	+	0.551175i
$165$	−1.38734e6	−	1.35655e6i	−0.308837	−	0.301983i
$166$	7.93321e6	−	2.40323e6i	1.73430	−	0.525376i
$167$	−1.71951e6			−0.369194			−0.184597	−	0.982814i	$-0.559098\pi$
$167$	−1.71951e6			−0.369194			−0.184597	+	0.982814i	$0.559098\pi$
$168$	−184114.	+	223823.i	−0.0388292	+	0.0472038i
$169$	4.81559e6			0.997675
$170$	1.14089e6	+	594010.i	0.232219	+	0.120906i
$171$		−	2.20771e6i		−	0.441523i
$172$	−340289.	+	227000.i	−0.0668748	+	0.0446109i
$173$		−	6.03741e6i		−	1.16604i	−0.812459	−	0.583019i	$-0.801871\pi$
$173$		−	6.03741e6i		−	1.16604i	0.812459	−	0.583019i	$-0.198129\pi$
$174$	−1.69758e6	+	514252.i	−0.322243	+	0.0976177i
$175$	12731.2	+	567235.i	0.00237549	+	0.105840i
$176$	3.76588e6	+	1.56658e6i	0.690762	+	0.287352i
$177$		−	2.07319e6i		−	0.373869i
$178$	−9.20453e6	+	2.78835e6i	−1.63208	+	0.494410i
$179$		−	1.11888e7i		−	1.95086i	−0.220311	−	0.975430i	$-0.570707\pi$
$179$		−	1.11888e7i		−	1.95086i	0.220311	−	0.975430i	$-0.429293\pi$
$180$	359289.	−	1.91051e6i	0.0616065	−	0.327591i
$181$	−5.54253e6			−0.934700			−0.467350	−	0.884072i	$-0.654791\pi$
$181$	−5.54253e6			−0.934700			−0.467350	+	0.884072i	$0.654791\pi$
$182$	8922.70	+	29454.4i	0.00148007	+	0.00488581i
$183$	6.03575e6			0.984867
$184$	433126.	−	526542.i	0.0695282	−	0.0845239i
$185$	−6.37773e6	−	6.23619e6i	−1.00728	−	0.984927i
$186$	−1.46437e6	−	4.83397e6i	−0.227568	−	0.751217i
$187$	1.28084e6			0.195872
$188$	3.00660e6	−	2.00565e6i	0.452483	−	0.301843i
$189$	137550.			0.0203740
$190$	8.05840e6	+	4.19563e6i	1.17487	+	0.611697i
$191$		−	4.62646e6i		−	0.663970i	−0.943285	−	0.331985i	$-0.892282\pi$
$191$		−	4.62646e6i		−	0.663970i	0.943285	−	0.331985i	$-0.107718\pi$
$192$	788093.	+	4.00971e6i	0.111346	+	0.566512i
$193$		−	7.66995e6i		−	1.06689i	−0.845834	−	0.533446i	$-0.820897\pi$
$193$		−	7.66995e6i		−	1.06689i	0.845834	−	0.533446i	$-0.179103\pi$
$194$	−3.37893e6	−	1.11541e7i	−0.462779	−	1.52766i
$195$	−147601.	−	144326.i	−0.0199061	−	0.0194643i
$196$	−6.19355e6	+	4.13160e6i	−0.822567	+	0.548719i
$197$		−	1.07837e7i		−	1.41049i	−0.708963	−	0.705246i	$-0.750837\pi$
$197$		−	1.07837e7i		−	1.41049i	0.708963	−	0.705246i	$-0.249163\pi$
$198$	−561231.	−	1.85266e6i	−0.0723012	−	0.238671i
$199$			9.05284e6i			1.14875i	0.818592	+	0.574375i	$0.194755\pi$
$199$			9.05284e6i			1.14875i	−0.818592	+	0.574375i	$0.805245\pi$
$200$	6.29078e6	+	4.94227e6i	0.786348	+	0.617784i
$201$	−7.42552e6			−0.914406
$202$	−6.09615e6	+	1.84672e6i	−0.739608	+	0.224051i
$203$	516482.			0.0617401
$204$	712131.	+	1.06753e6i	0.0838821	+	0.125745i
$205$	−5.98223e6	+	6.11800e6i	−0.694387	+	0.710147i
$206$	5.72623e6	−	1.73466e6i	0.655038	−	0.198432i
$207$	−323587.			−0.0364821
$208$	400659.	+	166671.i	0.0445231	+	0.0185213i
$209$	9.04690e6			0.990971
$210$	−261407.	+	502076.i	−0.0282267	+	0.0542140i
$211$		−	1.08423e7i		−	1.15418i	−0.816680	−	0.577090i	$-0.804188\pi$
$211$		−	1.08423e7i		−	1.15418i	0.816680	−	0.577090i	$-0.195812\pi$
$212$	−2.23204e6	−	3.34598e6i	−0.234258	−	0.351169i
$213$			7.53079e6i			0.779295i
$214$	576075.	−	174512.i	0.0587811	−	0.0178067i
$215$	−558558.	+	571235.i	−0.0562022	+	0.0574777i
$216$	1.23208e6	−	1.49782e6i	0.122258	−	0.148627i
$217$			1.47072e6i			0.143929i
$218$	−6.93318e6	+	2.10028e6i	−0.669211	+	0.202726i
$219$			1.02079e7i			0.971862i
$220$	7.82902e6	+	1.47232e6i	0.735258	+	0.138272i
$221$	136271.			0.0126249
$222$	−2.58004e6	−	8.51688e6i	−0.235813	−	0.778433i
$223$	6.18382e6			0.557625			0.278813	−	0.960345i	$-0.410059\pi$
$223$	6.18382e6			0.557625			0.278813	+	0.960345i	$0.410059\pi$
$224$	118875.	−	1.18393e6i	0.0105766	−	0.105337i
$225$	−85196.4	−	3.79592e6i	−0.00747952	−	0.333249i
$226$	−1.85356e6	−	6.11874e6i	−0.160576	−	0.530074i
$227$	−1.17330e7			−1.00307			−0.501534	−	0.865138i	$-0.667231\pi$
$227$	−1.17330e7			−1.00307			−0.501534	+	0.865138i	$0.667231\pi$
$228$	5.02995e6	+	7.54023e6i	0.424384	+	0.636180i
$229$	1.95291e7			1.62621			0.813105	−	0.582116i	$-0.197775\pi$
$229$	1.95291e7			1.62621			0.813105	+	0.582116i	$0.197775\pi$
$230$	614959.	−	1.18113e6i	0.0505432	−	0.0970765i
$231$			563664.i			0.0457282i
$232$	4.62629e6	−	5.62409e6i	0.370484	−	0.450389i
$233$			2.06220e7i			1.63029i	0.579260	+	0.815143i	$0.303342\pi$
$233$			2.06220e7i			1.63029i	−0.579260	+	0.815143i	$0.696658\pi$
$234$	−59710.4	−	197108.i	−0.00466018	−	0.0153836i
$235$	4.93510e6	−	5.04711e6i	0.380270	−	0.388901i
$236$	4.72348e6	+	7.08081e6i	0.359357	+	0.538700i
$237$			1.25001e6i			0.0939003i
$238$	−108331.	−	357609.i	−0.00803570	−	0.0265264i
$239$			1.82892e7i			1.33968i	0.742506	+	0.669840i	$0.233637\pi$
$239$			1.82892e7i			1.33968i	−0.742506	+	0.669840i	$0.766363\pi$
$240$	3.12570e6	+	7.34377e6i	0.226107	+	0.531233i
$241$	−1.88580e7			−1.34724			−0.673620	−	0.739078i	$-0.735262\pi$
$241$	−1.88580e7			−1.34724			−0.673620	+	0.739078i	$0.735262\pi$
$242$	−5.97182e6	+	1.80906e6i	−0.421367	+	0.127646i
$243$	−920483.			−0.0641500
$244$	−2.06146e7	+	1.37516e7i	−1.41907	+	0.946637i
$245$	−1.01662e7	+	1.03970e7i	−0.691293	+	0.706983i
$246$	−8.17004e6	+	2.47497e6i	−0.548806	+	0.166251i
$247$	962517.			0.0638731
$248$	1.60149e7	+	1.31737e7i	1.04995	+	0.863678i
$249$	1.61520e7			1.04623
$250$	1.40175e7	+	6.90296e6i	0.897119	+	0.441790i
$251$			1.05499e7i			0.667154i	0.942723	+	0.333577i	$0.108256\pi$
$251$			1.05499e7i			0.667154i	−0.942723	+	0.333577i	$0.891744\pi$
$252$	−469792.	+	313389.i	−0.0293565	+	0.0195831i
$253$		−	1.32602e6i		−	0.0818818i
$254$	−2.49429e7	+	7.55602e6i	−1.52211	+	0.461096i
$255$	1.79204e6	+	1.75227e6i	0.108076	+	0.105677i
$256$	−1.18272e7	−	1.18992e7i	−0.704957	−	0.709250i
$257$			343840.i			0.0202562i	0.999949	+	0.0101281i	$0.00322393\pi$
$257$			343840.i			0.0202562i	−0.999949	+	0.0101281i	$0.996776\pi$
$258$	−762833.	+	231087.i	−0.0444192	+	0.0134560i
$259$			2.59122e6i			0.149144i
$260$	832945.	+	156643.i	0.0473910	+	0.00891233i
$261$	−3.45628e6			−0.194396
$262$	484339.	+	1.59884e6i	0.0269306	+	0.0888997i
$263$	1.68620e7			0.926920			0.463460	−	0.886118i	$-0.346608\pi$
$263$	1.68620e7			0.926920			0.463460	+	0.886118i	$0.346608\pi$
$264$	6.13786e6	+	5.04892e6i	0.333584	+	0.274401i
$265$	−5.61682e6	−	5.49217e6i	−0.301823	−	0.295125i
$266$	−765171.	−	2.52588e6i	−0.0406549	−	0.134205i
$267$	−1.87405e7			−0.984569
$268$	2.53612e7	−	1.69180e7i	1.31755	−	0.878911i
$269$	2.06767e7			1.06224			0.531121	−	0.847296i	$-0.321771\pi$
$269$	2.06767e7			1.06224			0.531121	+	0.847296i	$0.321771\pi$
$270$	1.74933e6	−	3.35987e6i	0.0888751	−	0.170699i
$271$		−	1.38151e7i		−	0.694138i	−0.937840	−	0.347069i	$-0.887177\pi$
$271$		−	1.38151e7i		−	0.694138i	0.937840	−	0.347069i	$-0.112823\pi$
$272$	−4.86444e6	−	2.02358e6i	−0.241728	−	0.100557i
$273$			59969.3i			0.00294741i
$274$	−5.73125e6	−	1.89193e7i	−0.278611	−	0.919713i
$275$	1.55552e7	−	349124.i	0.747958	−	0.0167873i
$276$	1.10518e6	−	737246.i	0.0525662	−	0.0350659i
$277$			2.13872e6i			0.100627i	0.998733	+	0.0503134i	$0.0160220\pi$
$277$			2.13872e6i			0.100627i	−0.998733	+	0.0503134i	$0.983978\pi$
$278$	−4.49934e6	−	1.48526e7i	−0.209418	−	0.691303i
$279$		−	9.84198e6i		−	0.453179i
$280$	−251095.	−	2.31038e6i	−0.0114384	−	0.105247i
$281$	1.43930e7			0.648685			0.324342	−	0.945940i	$-0.394857\pi$
$281$	1.43930e7			0.648685			0.324342	+	0.945940i	$0.394857\pi$
$282$	6.73995e6	−	2.04175e6i	0.300545	−	0.0910448i
$283$	−2.56055e7			−1.12973			−0.564865	−	0.825183i	$-0.691072\pi$
$283$	−2.56055e7			−1.12973			−0.564865	+	0.825183i	$0.691072\pi$
$284$	−1.71578e7	−	2.57208e7i	−0.749045	−	1.12287i
$285$	1.26576e7	+	1.23767e7i	0.546786	+	0.534652i
$286$	807724.	−	244686.i	0.0345275	−	0.0104595i
$287$	2.48570e6			0.105148
$288$	−795509.	+	7.92279e6i	−0.0333018	+	0.331666i
$289$	2.24831e7			0.931456
$290$	6.56848e6	−	1.26158e7i	0.269321	−	0.517276i
$291$		−	2.27097e7i		−	0.921579i
$292$	−2.32573e7	−	3.48643e7i	−0.934137	−	1.40033i
$293$			8.11800e6i			0.322735i	0.986894	+	0.161367i	$0.0515904\pi$
$293$			8.11800e6i			0.322735i	−0.986894	+	0.161367i	$0.948410\pi$
$294$	−1.38842e7	+	4.20598e6i	−0.546360	+	0.165510i
$295$	1.18864e7	+	1.16226e7i	0.463003	+	0.452728i
$296$	2.82164e7	+	2.32104e7i	1.08799	+	0.894968i
$297$		−	3.77202e6i		−	0.143981i
$298$	−3.84398e6	+	1.16447e6i	−0.145255	+	0.0440026i
$299$		−	141077.i		−	0.00527769i
$300$	8.93945e6	+	1.27705e7i	0.331091	+	0.472982i
$301$	232089.			0.00851049
$302$	−9.07353e6	−	2.99523e7i	−0.329424	−	1.08745i
$303$	−1.24118e7			−0.446176
$304$	−3.43587e7	−	1.42930e7i	−1.22297	−	0.508748i
$305$	−3.38372e7	+	3.46052e7i	−1.19260	+	1.21967i
$306$	724950.	+	2.39311e6i	0.0253014	+	0.0835215i
$307$	−2.07910e7			−0.718555			−0.359277	−	0.933231i	$-0.616977\pi$
$307$	−2.07910e7			−0.718555			−0.359277	+	0.933231i	$0.616977\pi$
$308$	−1.28423e6	−	1.92515e6i	−0.0439532	−	0.0658888i
$309$	1.16586e7			0.395159
$310$	3.59244e7	+	1.87042e7i	1.20588	+	0.627846i
$311$			5.61955e7i			1.86819i	0.357026	+	0.934094i	$0.383791\pi$
$311$			5.61955e7i			1.86819i	−0.357026	+	0.934094i	$0.616209\pi$
$312$	653019.	+	537164.i	0.0215012	+	0.0176865i
$313$		−	6.05170e6i		−	0.197353i	−0.995120	−	0.0986766i	$-0.968539\pi$
$313$		−	6.05170e6i		−	0.197353i	0.995120	−	0.0986766i	$-0.0314609\pi$
$314$	−3.64560e6	−	1.20344e7i	−0.117755	−	0.388718i
$315$	−771127.	+	788629.i	−0.0246714	+	0.0252314i
$316$	−2.84796e6	−	4.26929e6i	−0.0902553	−	0.135299i
$317$			8.06566e6i			0.253199i	0.991954	+	0.126600i	$0.0404063\pi$
$317$			8.06566e6i			0.253199i	−0.991954	+	0.126600i	$0.959594\pi$
$318$	−2.27222e6	−	7.50075e6i	−0.0706592	−	0.233251i
$319$		−	1.41634e7i		−	0.436310i
$320$	−2.74073e7	−	1.79605e7i	−0.836405	−	0.548112i
$321$	1.17289e6			0.0354603
$322$	−370221.	+	112152.i	−0.0110890	+	0.00335923i
$323$	−1.16860e7			−0.346784
$324$	3.14383e6	−	2.09719e6i	0.0924323	−	0.0616599i
$325$	1.65495e6	−	37144.0i	0.0482096	−	0.00108203i
$326$	2.31435e7	−	7.01091e6i	0.667999	−	0.202359i
$327$	−1.41160e7			−0.403708
$328$	2.22652e7	−	2.70673e7i	0.630964	−	0.767050i
$329$	−2.05060e6			−0.0575829
$330$	1.37683e7	+	7.16852e6i	0.383124	+	0.199475i
$331$		−	6.79995e6i		−	0.187509i	−0.995595	−	0.0937545i	$-0.970113\pi$
$331$		−	6.79995e6i		−	0.187509i	0.995595	−	0.0937545i	$-0.0298869\pi$
$332$	−5.51659e7	+	3.68001e7i	−1.50750	+	1.00562i
$333$		−	1.73404e7i		−	0.469598i
$334$	1.31652e7	−	3.98817e6i	0.353337	−	0.107037i
$335$	4.16285e7	−	4.25733e7i	1.10728	−	1.13241i
$336$	890520.	−	2.14071e6i	0.0234761	−	0.0564338i
$337$		−	4.63328e7i		−	1.21059i	−0.796000	−	0.605297i	$-0.793054\pi$
$337$		−	4.63328e7i		−	1.21059i	0.796000	−	0.605297i	$-0.206946\pi$
$338$	−3.68701e7	+	1.11691e7i	−0.954825	+	0.289247i
$339$		−	1.24578e7i		−	0.319772i
$340$	−1.01129e7	−	1.90182e6i	−0.257299	−	0.0483875i
$341$	4.03312e7			1.01713
$342$	5.12049e6	+	1.69031e7i	0.128007	+	0.422560i
$343$	8.49631e6			0.210546
$344$	2.07889e6	−	2.52726e6i	0.0510689	−	0.0620834i
$345$	1.81407e6	−	1.85524e6i	0.0441771	−	0.0451797i
$346$	1.40030e7	+	4.62249e7i	0.338059	+	1.11596i
$347$	−6.18772e6			−0.148096			−0.0740478	−	0.997255i	$-0.523592\pi$
$347$	−6.18772e6			−0.148096			−0.0740478	+	0.997255i	$0.523592\pi$
$348$	1.18046e7	−	7.87465e6i	0.280101	−	0.186850i
$349$	−9.57198e6			−0.225178			−0.112589	−	0.993642i	$-0.535914\pi$
$349$	−9.57198e6			−0.225178			−0.112589	+	0.993642i	$0.535914\pi$
$350$	−1.41310e6	−	4.31345e6i	−0.0329587	−	0.100605i
$351$		−	401313.i		−	0.00928029i
$352$	−3.24666e7	−	3.25989e6i	−0.744403	−	0.0747439i
$353$		−	4.38759e7i		−	0.997474i	−0.866753	−	0.498737i	$-0.833797\pi$
$353$		−	4.38759e7i		−	0.997474i	0.866753	−	0.498737i	$-0.166203\pi$
$354$	4.80850e6	+	1.58732e7i	0.108393	+	0.357812i
$355$	−4.31769e7	−	4.22187e7i	−0.965086	−	0.943669i
$356$	6.40064e7	−	4.26975e7i	1.41864	−	0.946351i
$357$		−	728094.i		−	0.0160023i
$358$	2.59511e7	+	8.56663e7i	0.565596	+	1.86707i
$359$			6.69337e7i			1.44664i	0.690511	+	0.723322i	$0.257386\pi$
$359$			6.69337e7i			1.44664i	−0.690511	+	0.723322i	$0.742614\pi$
$360$	1.68032e6	+	1.54610e7i	0.0360150	+	0.331382i
$361$	−3.54953e7			−0.754482
$362$	4.24359e7	−	1.28552e7i	0.894555	−	0.270990i
$363$	−1.21586e7			−0.254194
$364$	−136632.	−	204820.i	−0.00283300	−	0.00424686i
$365$	−5.85258e7	−	5.72270e7i	−1.20356	−	1.17685i
$366$	−4.62121e7	+	1.39991e7i	−0.942568	+	0.285534i
$367$	5.48058e7			1.10874			0.554369	−	0.832271i	$-0.312960\pi$
$367$	5.48058e7			1.10874			0.554369	+	0.832271i	$0.312960\pi$
$368$	−2.09494e6	+	5.03600e6i	−0.0420367	+	0.101051i
$369$	−1.66342e7			−0.331073
$370$	6.32945e7	+	3.29545e7i	1.24957	+	0.650593i
$371$			2.28207e6i			0.0446897i
$372$	2.24236e7	+	3.36144e7i	0.435588	+	0.652976i
$373$			3.78565e7i			0.729482i	0.931109	+	0.364741i	$0.118842\pi$
$373$			3.78565e7i			0.729482i	−0.931109	+	0.364741i	$0.881158\pi$
$374$	−9.80666e6	+	2.97075e6i	−0.187459	+	0.0567874i
$375$	2.22411e7	+	2.07920e7i	0.421756	+	0.394278i
$376$	−1.83679e7	+	2.23294e7i	−0.345538	+	0.420063i
$377$		−	1.50687e6i		−	0.0281224i
$378$	−1.05314e6	+	319031.i	−0.0194990	+	0.00590687i
$379$		−	3.60927e7i		−	0.662982i	−0.943458	−	0.331491i	$-0.892448\pi$
$379$		−	3.60927e7i		−	0.662982i	0.943458	−	0.331491i	$-0.107552\pi$
$380$	−7.14296e7	−	1.34330e7i	−1.30175	−	0.244806i
$381$	−5.07839e7			−0.918229
$382$	1.07305e7	+	3.54220e7i	0.192499	+	0.635453i
$383$	5.97603e7			1.06369			0.531847	−	0.846841i	$-0.321498\pi$
$383$	5.97603e7			1.06369			0.531847	+	0.846841i	$0.321498\pi$
$384$	−1.53340e7	−	2.88720e7i	−0.270807	−	0.509899i
$385$	−3.23170e6	−	3.15998e6i	−0.0566303	−	0.0553735i
$386$	1.77895e7	+	5.87243e7i	0.309315	+	1.02107i
$387$	−1.55313e6			−0.0267963
$388$	5.17409e7	+	7.75630e7i	0.885806	+	1.32788i
$389$	−6.96398e7			−1.18306			−0.591532	−	0.806281i	$-0.701477\pi$
$389$	−6.96398e7			−1.18306			−0.591532	+	0.806281i	$0.701477\pi$
$390$	1.46484e6	+	762673.i	0.0246943	+	0.0128571i
$391$			1.71284e6i			0.0286540i
$392$	3.78376e7	−	4.59984e7i	0.628153	−	0.763632i
$393$			3.25524e6i			0.0536297i
$394$	2.50115e7	+	8.25646e7i	0.408932	+	1.34991i
$395$	−7.16675e6	−	7.00770e6i	−0.116287	−	0.113706i
$396$	8.59402e6	+	1.28830e7i	0.138392	+	0.207459i
$397$			2.84760e7i			0.455101i	0.973766	+	0.227551i	$0.0730717\pi$
$397$			2.84760e7i			0.455101i	−0.973766	+	0.227551i	$0.926928\pi$
$398$	−2.09969e7	−	6.93122e7i	−0.333047	−	1.09941i
$399$		−	5.14270e6i		−	0.0809603i
$400$	−5.96277e7	−	2.32494e7i	−0.931683	−	0.363271i
$401$	−1.00700e6			−0.0156170			−0.00780848	−	0.999970i	$-0.502486\pi$
$401$	−1.00700e6			−0.0156170			−0.00780848	+	0.999970i	$0.502486\pi$
$402$	5.68528e7	−	1.72226e7i	0.875132	−	0.265106i
$403$	4.29091e6			0.0655593
$404$	4.23914e7	−	2.82785e7i	0.642885	−	0.428857i
$405$	5.16036e6	−	5.27747e6i	0.0776809	−	0.0794440i
$406$	−3.95440e6	+	1.19791e6i	−0.0590884	+	0.0178998i
$407$	7.10587e7			1.05398
$408$	−7.92837e6	−	6.52176e6i	−0.116736	−	0.0960251i
$409$	3.61611e7			0.528532			0.264266	−	0.964450i	$-0.414870\pi$
$409$	3.61611e7			0.528532			0.264266	+	0.964450i	$0.414870\pi$
$410$	3.16124e7	−	6.07169e7i	0.458676	−	0.880964i
$411$		−	3.85196e7i		−	0.554826i
$412$	−3.98190e7	+	2.65625e7i	−0.569375	+	0.379819i
$413$		−	4.82936e6i		−	0.0685550i
$414$	2.47751e6	−	750517.i	0.0349152	−	0.0105769i
$415$	−9.05505e7	+	9.26057e7i	−1.26691	+	1.29567i
$416$	−3.45418e6	−	346826.i	−0.0479805	−	0.00481762i
$417$		−	3.02400e7i		−	0.417036i
$418$	−6.92667e7	+	2.09831e7i	−0.948409	+	0.287304i
$419$		−	7.71961e7i		−	1.04943i	−0.851278	−	0.524715i	$-0.824172\pi$
$419$		−	7.71961e7i		−	1.04943i	0.851278	−	0.524715i	$-0.175828\pi$
$420$	836939.	−	4.45040e6i	0.0112966	−	0.0600691i
$421$	1.80523e6			0.0241928			0.0120964	−	0.999927i	$-0.496150\pi$
$421$	1.80523e6			0.0241928			0.0120964	+	0.999927i	$0.496150\pi$
$422$	2.51473e7	+	8.30130e7i	0.334622	+	1.10461i
$423$	1.37226e7			0.181307
$424$	2.48500e7	+	2.04412e7i	0.326008	+	0.268170i
$425$	−2.00929e7	+	450969.i	−0.261743	+	0.00587462i
$426$	−1.74667e7	−	5.76588e7i	−0.225934	−	0.745825i
$427$	1.40598e7			0.180591
$428$	−4.00590e6	+	2.67226e6i	−0.0510939	+	0.0340838i
$429$	1.64453e6			0.0208290
$430$	2.95164e6	−	5.66911e6i	0.0371243	−	0.0713033i
$431$			8.38390e7i			1.04716i	0.851976	+	0.523581i	$0.175404\pi$
$431$			8.38390e7i			1.04716i	−0.851976	+	0.523581i	$0.824596\pi$
$432$	−5.95933e6	+	1.43255e7i	−0.0739173	+	0.177689i
$433$			3.21731e7i			0.396305i	0.980171	+	0.198153i	$0.0634942\pi$
$433$			3.21731e7i			0.396305i	−0.980171	+	0.198153i	$0.936506\pi$
$434$	−3.41114e6	−	1.12604e7i	−0.0417283	−	0.137748i
$435$	1.93764e7	−	1.98162e7i	0.235399	−	0.240742i
$436$	4.82119e7	−	3.21613e7i	0.581694	−	0.388037i
$437$			1.20982e7i			0.144969i
$438$	−2.36760e7	−	7.81559e7i	−0.281764	−	0.930121i
$439$			1.14441e8i			1.35266i	0.736597	+	0.676332i	$0.236431\pi$
$439$			1.14441e8i			1.35266i	−0.736597	+	0.676332i	$0.763569\pi$
$440$	−6.33570e7	+	6.88573e6i	−0.743767	+	0.0808336i
$441$	−2.82683e7			−0.329597
$442$	−1.04335e6	+	316064.i	−0.0120827	+	0.00366023i
$443$	−3.67575e7			−0.422799			−0.211400	−	0.977400i	$-0.567802\pi$
$443$	−3.67575e7			−0.422799			−0.211400	+	0.977400i	$0.567802\pi$
$444$	3.95076e7	+	5.92246e7i	0.451369	+	0.676633i
$445$	1.05062e8	−	1.07446e8i	1.19224	−	1.21930i
$446$	−4.73459e7	+	1.43426e7i	−0.533676	+	0.161668i
$447$	−7.82636e6			−0.0876268
$448$	1.83581e6	+	9.34033e6i	0.0204170	+	0.103879i
$449$	4.64770e6			0.0513451			0.0256725	−	0.999670i	$-0.491827\pi$
$449$	4.64770e6			0.0513451			0.0256725	+	0.999670i	$0.491827\pi$
$450$	9.45645e6	+	2.88655e7i	0.103774	+	0.316768i
$451$		−	6.81649e7i		−	0.743072i
$452$	2.83832e7	+	4.25484e7i	0.307360	+	0.460753i
$453$		−	6.09830e7i		−	0.656016i
$454$	8.98323e7	−	2.72131e7i	0.959987	−	0.290811i
$455$	−343827.	−	336196.i	−0.00365011	−	0.00356910i
$456$	−5.59999e7	−	4.60647e7i	−0.590599	−	0.485819i
$457$			1.37829e8i			1.44408i	0.691851	+	0.722040i	$0.256795\pi$
$457$			1.37829e8i			1.44408i	−0.691851	+	0.722040i	$0.743205\pi$
$458$	−1.49523e8	+	4.52954e7i	−1.55637	+	0.471474i
$459$			4.87238e6i			0.0503852i
$460$	−1.96889e6	+	1.04695e7i	−0.0202278	+	0.107561i
$461$	6.11454e7			0.624110			0.312055	−	0.950064i	$-0.398983\pi$
$461$	6.11454e7			0.624110			0.312055	+	0.950064i	$0.398983\pi$
$462$	−1.30735e6	−	4.31564e6i	−0.0132576	−	0.0437642i
$463$	−8.92817e6			−0.0899538			−0.0449769	−	0.998988i	$-0.514321\pi$
$463$	−8.92817e6			−0.0899538			−0.0449769	+	0.998988i	$0.514321\pi$
$464$	−2.23764e7	+	5.37904e7i	−0.223994	+	0.538456i
$465$	5.64278e7	+	5.51755e7i	0.561221	+	0.548767i
$466$	−4.78302e7	−	1.57891e8i	−0.472655	−	1.56027i
$467$	−9.31715e7			−0.914814			−0.457407	−	0.889258i	$-0.651222\pi$
$467$	−9.31715e7			−0.914814			−0.457407	+	0.889258i	$0.651222\pi$
$468$	914334.	+	1.37065e6i	0.00892005	+	0.0133718i
$469$	−1.72972e7			−0.167671
$470$	−2.60790e7	+	5.00890e7i	−0.251187	+	0.482446i
$471$		−	2.45020e7i		−	0.234498i
$472$	−5.25879e7	−	4.32580e7i	−0.500103	−	0.411378i
$473$		−	6.36453e6i		−	0.0601427i
$474$	−2.89923e6	−	9.57055e6i	−0.0272237	−	0.0898673i
$475$	−1.41921e8	+	3.18530e6i	−1.32424	+	0.0297214i
$476$	1.65886e6	+	2.48674e6i	0.0153811	+	0.0230574i
$477$		−	1.52715e7i		−	0.140711i
$478$	−4.24195e7	−	1.40030e8i	−0.388402	−	1.28214i
$479$		−	7.79984e7i		−	0.709707i	−0.934922	−	0.354854i	$-0.884531\pi$
$479$		−	7.79984e7i		−	0.709707i	0.934922	−	0.354854i	$-0.115469\pi$
$480$	−4.09646e7	−	4.89772e7i	−0.370412	−	0.442864i
$481$	7.56007e6			0.0679345
$482$	1.44385e8	−	4.37388e7i	1.28938	−	0.390594i
$483$	−753772.			−0.00668958
$484$	4.15268e7	−	2.77018e7i	0.366262	−	0.244327i
$485$	1.30203e8	+	1.27314e8i	1.14129	+	1.11596i
$486$	7.04759e6	−	2.13494e6i	0.0613948	−	0.0185985i
$487$	1.84100e8			1.59392			0.796962	−	0.604030i	$-0.206439\pi$
$487$	1.84100e8			1.59392			0.796962	+	0.604030i	$0.206439\pi$
$488$	1.25938e8	−	1.53101e8i	1.08367	−	1.31740i
$489$	4.71202e7			0.402977
$490$	5.37224e7	−	1.03183e8i	0.456633	−	0.877039i
$491$		−	1.36182e8i		−	1.15047i	−0.817987	−	0.575236i	$-0.804910\pi$
$491$		−	1.36182e8i		−	1.15047i	0.817987	−	0.575236i	$-0.195090\pi$
$492$	5.68127e7	−	3.78987e7i	0.477035	−	0.318221i
$493$			1.82951e7i			0.152684i
$494$	−7.36942e6	+	2.23244e6i	−0.0611297	+	0.0185182i
$495$	2.16264e7	+	2.11465e7i	0.178307	+	0.174350i
$496$	−1.53171e8	−	6.37183e7i	−1.25526	−	0.522179i
$497$			1.75424e7i			0.142896i
$498$	−1.23666e8	+	3.74626e7i	−1.00130	+	0.303326i
$499$		−	5.25199e7i		−	0.422690i	−0.977412	−	0.211345i	$-0.932216\pi$
$499$		−	5.25199e7i		−	0.422690i	0.977412	−	0.211345i	$-0.0677844\pi$
$500$	−1.23334e8	−	2.03401e7i	−0.986672	−	0.162721i
$501$	2.68044e7			0.213154
$502$	−2.44691e7	−	8.07741e7i	−0.193422	−	0.638500i
$503$	−7.30908e7			−0.574326			−0.287163	−	0.957882i	$-0.592712\pi$
$503$	−7.30908e7			−0.574326			−0.287163	+	0.957882i	$0.592712\pi$
$504$	2.87005e6	−	3.48906e6i	0.0224180	−	0.0272531i
$505$	6.95822e7	−	7.11614e7i	0.540286	−	0.552549i
$506$	3.07552e6	+	1.01525e7i	0.0237393	+	0.0783650i
$507$	−7.50675e7			−0.576008
$508$	1.73448e8	−	1.15704e8i	1.32305	−	0.882585i
$509$	−1.93773e8			−1.46940			−0.734699	−	0.678393i	$-0.762677\pi$
$509$	−1.93773e8			−1.46940			−0.734699	+	0.678393i	$0.762677\pi$
$510$	−1.77848e7	−	9.25970e6i	−0.134072	−	0.0698049i
$511$			2.37786e7i			0.178207i
$512$	1.18153e8	+	6.36737e7i	0.880306	+	0.474406i
$513$			3.44148e7i			0.254913i
$514$	−797494.	−	2.63258e6i	−0.00587270	−	0.0193862i
$515$	−6.53598e7	+	6.68432e7i	−0.478508	+	0.489368i
$516$	5.30458e6	−	3.53859e6i	0.0386102	−	0.0257561i
$517$			5.62333e7i			0.406932i
$518$	−6.01001e6	−	1.98395e7i	−0.0432400	−	0.142738i
$519$			9.41139e7i			0.673212i
$520$	−6.74068e6	+	732586.i	−0.0479395	+	0.00521013i
$521$	2.38564e8			1.68691			0.843453	−	0.537203i	$-0.180519\pi$
$521$	2.38564e8			1.68691			0.843453	+	0.537203i	$0.180519\pi$
$522$	2.64627e7	−	8.01640e6i	0.186047	−	0.0563596i
$523$	−4.75494e7			−0.332384			−0.166192	−	0.986093i	$-0.553147\pi$
$523$	−4.75494e7			−0.332384			−0.166192	+	0.986093i	$0.553147\pi$
$524$	−7.41660e6	−	1.11180e7i	−0.0515479	−	0.0772738i
$525$	−198459.	−	8.84233e6i	−0.00137149	−	0.0611067i
$526$	−1.29102e8	+	3.91093e7i	−0.887109	+	0.268734i
$527$	−5.20964e7			−0.355939
$528$	−5.87042e7	−	2.44206e7i	−0.398811	−	0.165903i
$529$	−1.46263e8			−0.988022
$530$	5.57430e7	+	2.90228e7i	0.374423	+	0.194945i
$531$			3.23179e7i			0.215854i
$532$	1.17169e7	+	1.75644e7i	0.0778177	+	0.116654i
$533$		−	7.25219e6i		−	0.0478947i
$534$	1.43484e8	−	4.34661e7i	0.942282	−	0.285448i
$535$	−6.57539e6	+	6.72462e6i	−0.0429398	+	0.0439144i
$536$	−1.54937e8	+	1.88353e8i	−1.00614	+	1.22315i
$537$			1.74417e8i			1.12633i
$538$	−1.58309e8	+	4.79568e7i	−1.01662	+	0.307967i
$539$		−	1.15840e8i		−	0.739761i
$540$	−5.60077e6	+	2.97819e7i	−0.0355686	+	0.189135i
$541$	7.93945e6			0.0501417			0.0250708	−	0.999686i	$-0.492019\pi$
$541$	7.93945e6			0.0501417			0.0250708	+	0.999686i	$0.492019\pi$
$542$	3.20423e7	+	1.05774e8i	0.201246	+	0.664325i
$543$	8.63995e7			0.539649
$544$	4.19376e7	+	4.21086e6i	0.260499	+	0.0261561i
$545$	7.91361e7	−	8.09322e7i	0.488861	−	0.499956i
$546$	−139091.	−	459149.i	−0.000854519	−	0.00282082i
$547$	2.71214e8			1.65711			0.828554	−	0.559909i	$-0.189164\pi$
$547$	2.71214e8			1.65711			0.828554	+	0.559909i	$0.189164\pi$
$548$	8.77616e7	+	1.31561e8i	0.533289	+	0.799436i
$549$	−9.40880e7			−0.568613
$550$	−1.18287e8	+	3.87513e7i	−0.710967	+	0.232915i
$551$			1.29222e8i			0.772473i
$552$	−6.75177e6	+	8.20798e6i	−0.0401421	+	0.0487999i
$553$			2.91180e6i			0.0172181i
$554$	−4.96048e6	−	1.63749e7i	−0.0291739	−	0.0963049i
$555$	9.94189e7	+	9.72126e7i	0.581554	+	0.568648i
$556$	6.88975e7	+	1.03282e8i	0.400847	+	0.600897i
$557$			2.95321e7i			0.170895i	0.996343	+	0.0854474i	$0.0272320\pi$
$557$			2.95321e7i			0.170895i	−0.996343	+	0.0854474i	$0.972768\pi$
$558$	2.28272e7	+	7.53542e7i	0.131386	+	0.433715i
$559$		−	677134.i		−	0.00387650i
$560$	7.28111e6	+	1.71068e7i	0.0414604	+	0.0974102i
$561$	−1.99664e7			−0.113087
$562$	−1.10199e8	+	3.33828e7i	−0.620824	+	0.188068i
$563$	−3.69382e7			−0.206991			−0.103495	−	0.994630i	$-0.533003\pi$
$563$	−3.69382e7			−0.206991			−0.103495	+	0.994630i	$0.533003\pi$
$564$	−4.68682e7	+	3.12649e7i	−0.261241	+	0.174269i
$565$	7.14250e7	+	6.98399e7i	0.396009	+	0.387221i
$566$	1.96046e8	−	5.93888e7i	1.08121	−	0.327533i
$567$	−2.14420e6			−0.0117629
$568$	1.91023e8	+	1.57133e8i	1.04242	+	0.857478i
$569$	−4.40705e7			−0.239227			−0.119614	−	0.992821i	$-0.538166\pi$
$569$	−4.40705e7			−0.239227			−0.119614	+	0.992821i	$0.538166\pi$
$570$	−1.25618e8	−	6.54034e7i	−0.678309	−	0.353163i
$571$			1.86429e8i			1.00139i	0.865623	+	0.500697i	$0.166923\pi$
$571$			1.86429e8i			1.00139i	−0.865623	+	0.500697i	$0.833077\pi$
$572$	−5.61674e6	+	3.74682e6i	−0.0300121	+	0.0200205i
$573$			7.21193e7i			0.383343i
$574$	−1.90315e7	+	5.76526e6i	−0.100632	+	0.0304848i
$575$	466873.	+	2.08015e7i	0.00245581	+	0.109419i
$576$	−1.22852e7	−	6.25051e7i	−0.0642855	−	0.327076i
$577$		−	9.75841e7i		−	0.507986i	−0.967206	−	0.253993i	$-0.918256\pi$
$577$		−	9.75841e7i		−	0.507986i	0.967206	−	0.253993i	$-0.0817440\pi$
$578$	−1.72140e8	+	5.21466e7i	−0.891450	+	0.270049i
$579$			1.19563e8i			0.615971i
$580$	−2.10301e7	+	1.11827e8i	−0.107785	+	0.573141i
$581$	3.76250e7			0.191844
$582$	5.26723e7	+	1.73875e8i	0.267186	+	0.881998i
$583$	6.25808e7			0.315817
$584$	2.58930e8	+	2.12992e8i	1.30000	+	1.06936i
$585$	2.30088e6	+	2.24981e6i	0.0114928	+	0.0112377i
$586$	−1.88287e7	−	6.21547e7i	−0.0935678	−	0.308874i
$587$	−2.62750e8			−1.29906			−0.649529	−	0.760337i	$-0.725034\pi$
$587$	−2.62750e8			−1.29906			−0.649529	+	0.760337i	$0.725034\pi$
$588$	9.65479e7	−	6.44053e7i	0.474910	−	0.316803i
$589$	−3.67969e8			−1.80080
$590$	−1.17964e8	−	6.14184e7i	−0.574373	−	0.299049i
$591$			1.68102e8i			0.814347i
$592$	−2.69870e8	−	1.12264e8i	−1.30074	−	0.541097i
$593$			1.29038e8i			0.618806i	0.950931	+	0.309403i	$0.100129\pi$
$593$			1.29038e8i			0.618806i	−0.950931	+	0.309403i	$0.899871\pi$
$594$	8.74872e6	+	2.88801e7i	0.0417431	+	0.137797i
$595$	4.17444e6	+	4.08180e6i	0.0198174	+	0.0193776i
$596$	2.67302e7	−	1.78312e7i	0.126260	−	0.0842254i
$597$		−	1.41120e8i		−	0.663231i
$598$	327211.	+	1.08015e6i	0.00153012	+	0.00505102i
$599$		−	3.16683e8i		−	1.47348i	−0.676176	−	0.736740i	$-0.736364\pi$
$599$		−	3.16683e8i		−	1.47348i	0.676176	−	0.736740i	$-0.263636\pi$
$600$	−9.80636e7	−	7.70424e7i	−0.453998	−	0.356678i
$601$	−6.91171e7			−0.318392			−0.159196	−	0.987247i	$-0.550890\pi$
$601$	−6.91171e7			−0.318392			−0.159196	+	0.987247i	$0.550890\pi$
$602$	−1.77697e6	+	538300.i	−0.00814497	+	0.00246737i
$603$	1.15752e8			0.527932
$604$	1.38941e8	+	2.08282e8i	0.630551	+	0.945239i
$605$	6.81631e7	−	6.97101e7i	0.307810	−	0.314796i
$606$	9.50296e7	−	2.87875e7i	0.427013	−	0.129356i
$607$	3.08877e8			1.38108			0.690542	−	0.723292i	$-0.257372\pi$
$607$	3.08877e8			1.38108			0.690542	+	0.723292i	$0.257372\pi$
$608$	2.96215e8	+	2.97423e7i	1.31794	+	0.132332i
$609$	−8.05116e6			−0.0356457
$610$	1.78809e8	−	3.43433e8i	0.787772	−	1.51305i
$611$			5.98277e6i			0.0262288i
$612$	−1.11010e7	−	1.66412e7i	−0.0484294	−	0.0725989i
$613$		−	2.65213e8i		−	1.15137i	−0.817673	−	0.575683i	$-0.804736\pi$
$613$		−	2.65213e8i		−	1.15137i	0.817673	−	0.575683i	$-0.195264\pi$
$614$	1.59184e8	−	4.82220e7i	0.687693	−	0.208324i
$615$	9.32537e7	−	9.53702e7i	0.400904	−	0.410003i
$616$	1.42977e7	+	1.17611e7i	0.0611680	+	0.0503159i
$617$		−	3.68044e8i		−	1.56691i	−0.621449	−	0.783455i	$-0.713456\pi$
$617$		−	3.68044e8i		−	1.56691i	0.621449	−	0.783455i	$-0.286544\pi$
$618$	−8.92630e7	+	2.70407e7i	−0.378187	+	0.114565i
$619$		−	9.59461e7i		−	0.404534i	−0.979330	−	0.202267i	$-0.935169\pi$
$619$		−	9.59461e7i		−	0.404534i	0.979330	−	0.202267i	$-0.0648309\pi$
$620$	−3.18434e8	−	5.98845e7i	−1.33612	−	0.251269i
$621$	5.04421e6			0.0210629
$622$	−1.30338e8	−	4.30256e8i	−0.541628	−	1.78795i
$623$	−4.36546e7			−0.180537
$624$	−6.24566e6	−	2.59815e6i	−0.0257054	−	0.0106933i
$625$	−2.43895e8	+	1.09536e7i	−0.998993	+	0.0448658i
$626$	1.40361e7	+	4.63342e7i	0.0572169	+	0.188877i
$627$	−1.41027e8			−0.572137
$628$	5.58244e7	+	8.36846e7i	0.225396	+	0.337883i
$629$	−9.17876e7			−0.368835
$630$	4.07494e6	−	7.82659e6i	0.0162967	−	0.0313005i
$631$		−	2.46173e8i		−	0.979832i	−0.871770	−	0.489916i	$-0.837027\pi$
$631$		−	2.46173e8i		−	0.979832i	0.871770	−	0.489916i	$-0.162973\pi$
$632$	3.17072e7	+	2.60819e7i	0.125605	+	0.103321i
$633$			1.69015e8i			0.666367i
$634$	−1.87073e7	−	6.17539e7i	−0.0734078	−	0.242324i
$635$	2.84701e8	−	2.91163e8i	1.11191	−	1.13714i
$636$	3.47941e7	+	5.21587e7i	0.135249	+	0.202747i
$637$		−	1.23244e7i		−	0.0476813i
$638$	3.28502e7	+	1.08441e8i	0.126496	+	0.417571i
$639$		−	1.17393e8i		−	0.449926i
$640$	2.51499e8	+	7.39454e7i	0.959391	+	0.282079i
$641$	−1.40284e8			−0.532641			−0.266321	−	0.963884i	$-0.585808\pi$
$641$	−1.40284e8			−0.532641			−0.266321	+	0.963884i	$0.585808\pi$
$642$	−8.98012e6	+	2.72037e6i	−0.0339373	+	0.0102807i
$643$	−1.91656e8			−0.720924			−0.360462	−	0.932774i	$-0.617381\pi$
$643$	−1.91656e8			−0.720924			−0.360462	+	0.932774i	$0.617381\pi$
$644$	2.57444e6	−	1.71736e6i	0.00963886	−	0.00642990i
$645$	8.70706e6	−	8.90468e6i	0.0324483	−	0.0331848i
$646$	8.94729e7	−	2.71042e7i	0.331890	−	0.100540i
$647$	−4.33268e8			−1.59972			−0.799860	−	0.600187i	$-0.795093\pi$
$647$	−4.33268e8			−1.59972			−0.799860	+	0.600187i	$0.795093\pi$
$648$	−1.92063e7	+	2.33486e7i	−0.0705859	+	0.0858097i
$649$	−1.32435e8			−0.484470
$650$	−1.25848e7	+	4.12283e6i	−0.0458254	+	0.0150126i
$651$		−	2.29262e7i		−	0.0830977i
$652$	−1.60935e8	+	1.07357e8i	−0.580641	+	0.387335i
$653$		−	1.61233e8i		−	0.579048i	−0.957171	−	0.289524i	$-0.906503\pi$
$653$		−	1.61233e8i		−	0.579048i	0.957171	−	0.289524i	$-0.0934969\pi$
$654$	1.08078e8	−	3.27402e7i	0.386369	−	0.117044i
$655$	−1.86635e7	−	1.82493e7i	−0.0664155	−	0.0649415i
$656$	−1.07692e8	+	2.58879e8i	−0.381480	+	0.917035i
$657$		−	1.59126e8i		−	0.561105i
$658$	1.57002e7	−	4.75611e6i	0.0551098	−	0.0166945i
$659$			2.39459e8i			0.836711i	0.908283	+	0.418356i	$0.137393\pi$
$659$			2.39459e8i			0.836711i	−0.908283	+	0.418356i	$0.862607\pi$
$660$	−1.22042e8	−	2.29512e7i	−0.424501	−	0.0798315i
$661$	3.06751e8			1.06214			0.531071	−	0.847328i	$-0.321790\pi$
$661$	3.06751e8			1.06214			0.531071	+	0.847328i	$0.321790\pi$
$662$	1.57716e7	+	5.20632e7i	0.0543629	+	0.179456i
$663$	−2.12426e6			−0.00728899
$664$	3.37019e8	−	4.09707e8i	1.15120	−	1.39949i
$665$	2.94850e7	+	2.88307e7i	0.100262	+	0.0980370i
$666$	4.02188e7	+	1.32765e8i	0.136146	+	0.449429i
$667$	1.89403e7			0.0638277
$668$	−9.15483e7	+	6.10701e7i	−0.307129	+	0.204880i
$669$	−9.63963e7			−0.321945
$670$	−2.19981e8	+	4.22511e8i	−0.731411	+	1.40480i
$671$		−	3.85560e8i		−	1.27622i
$672$	−1.85308e6	+	1.84556e7i	−0.00610642	+	0.0608163i
$673$		−	4.75380e8i		−	1.55954i	−0.626068	−	0.779769i	$-0.715337\pi$
$673$		−	4.75380e8i		−	1.55954i	0.626068	−	0.779769i	$-0.284663\pi$
$674$	1.07463e8	+	3.54742e8i	0.350977	+	1.15860i
$675$	1.32808e6	+	5.91725e7i	0.00431830	+	0.192402i
$676$	2.56387e8	−	1.71031e8i	0.829957	−	0.553649i
$677$		−	1.03793e8i		−	0.334505i	−0.985914	−	0.167252i	$-0.946511\pi$
$677$		−	1.03793e8i		−	0.334505i	0.985914	−	0.167252i	$-0.0534895\pi$
$678$	2.88942e7	+	9.53816e7i	0.0927089	+	0.306038i
$679$		−	5.29007e7i		−	0.168986i
$680$	8.18393e7	−	8.89440e6i	0.260276	−	0.0282872i
$681$	1.82899e8			0.579122
$682$	−3.08792e8	+	9.35430e7i	−0.973448	+	0.294889i
$683$	1.94870e8			0.611621			0.305810	−	0.952092i	$-0.401073\pi$
$683$	1.94870e8			0.611621			0.305810	+	0.952092i	$0.401073\pi$
$684$	−7.84091e7	−	1.17541e8i	−0.245018	−	0.367299i
$685$	2.20848e8	+	2.15947e8i	0.687102	+	0.671853i
$686$	−6.50512e7	+	1.97061e7i	−0.201504	+	0.0610419i
$687$	−3.04429e8			−0.938893
$688$	−1.00552e7	+	2.41715e7i	−0.0308762	+	0.0742229i
$689$	6.65810e6			0.0203560
$690$	−9.58626e6	+	1.84120e7i	−0.0291811	+	0.0560472i
$691$			4.76743e8i			1.44494i	0.691402	+	0.722471i	$0.256994\pi$
$691$			4.76743e8i			1.44494i	−0.691402	+	0.722471i	$0.743006\pi$
$692$	−2.14425e8	−	3.21438e8i	−0.647079	−	0.970016i
$693$		−	8.78666e6i		−	0.0264012i
$694$	4.73757e7	−	1.43516e7i	0.141735	−	0.0429361i
$695$	1.73377e8	+	1.69529e8i	0.516461	+	0.504999i
$696$	−7.21168e7	+	8.76708e7i	−0.213899	+	0.260032i
$697$			8.80496e7i			0.260033i
$698$	7.32869e7	−	2.22010e7i	0.215506	−	0.0652838i
$699$		−	3.21466e8i		−	0.941246i
$700$	2.08238e7	+	2.97480e7i	0.0607108	+	0.0867290i
$701$	−1.50161e8			−0.435915			−0.217958	−	0.975958i	$-0.569939\pi$
$701$	−1.50161e8			−0.435915			−0.217958	+	0.975958i	$0.569939\pi$
$702$	930793.	+	3.07261e6i	0.00269055	+	0.00888170i
$703$	−6.48317e8			−1.86604
$704$	2.56138e8	−	5.03430e7i	0.734101	−	0.144285i
$705$	−7.69306e7	+	7.86766e7i	−0.219549	+	0.224532i
$706$	1.01764e8	+	3.35931e8i	0.289189	+	0.954633i
$707$	−2.89124e7			−0.0818136
$708$	−7.36317e7	−	1.10379e8i	−0.207475	−	0.311019i
$709$	2.76865e8			0.776836			0.388418	−	0.921483i	$-0.373022\pi$
$709$	2.76865e8			0.776836			0.388418	+	0.921483i	$0.373022\pi$
$710$	4.28500e8	+	2.23100e8i	1.19723	+	0.623339i
$711$		−	1.94857e7i		−	0.0542133i
$712$	−3.91027e8	+	4.75364e8i	−1.08335	+	1.31700i
$713$			5.39337e7i			0.148796i
$714$	1.68872e6	+	5.57458e6i	0.00463941	+	0.0153150i
$715$	−9.21945e6	+	9.42870e6i	−0.0252224	+	0.0257949i
$716$	−3.97384e8	−	5.95705e8i	−1.08261	−	1.62290i
$717$		−	2.85100e8i		−	0.773465i
$718$	−1.55244e8	−	5.12472e8i	−0.419413	−	1.38451i
$719$			4.05407e8i			1.09070i	0.838209	+	0.545349i	$0.183603\pi$
$719$			4.05407e8i			1.09070i	−0.838209	+	0.545349i	$0.816397\pi$
$720$	−4.87249e7	−	1.14478e8i	−0.130543	−	0.306708i
$721$	2.71579e7			0.0724587
$722$	2.71766e8	−	8.23267e7i	0.722077	−	0.218740i
$723$	2.93967e8			0.777829
$724$	−2.95090e8	+	1.96849e8i	−0.777569	+	0.518702i
$725$	4.98675e6	+	2.22184e8i	0.0130859	+	0.583042i
$726$	9.30915e7	−	2.82004e7i	0.243276	−	0.0736963i
$727$	2.43401e8			0.633460			0.316730	−	0.948516i	$-0.397415\pi$
$727$	2.43401e8			0.633460			0.316730	+	0.948516i	$0.397415\pi$
$728$	1.52116e6	+	1.25129e6i	0.00394258	+	0.00324311i
$729$	1.43489e7			0.0370370
$730$	5.80828e8	+	3.02410e8i	1.49307	+	0.777369i
$731$			8.22116e6i			0.0210465i
$732$	3.21349e8	−	2.14366e8i	0.819302	−	0.546541i
$733$			6.38589e8i			1.62147i	0.585411	+	0.810737i	$0.300933\pi$
$733$			6.38589e8i			1.62147i	−0.585411	+	0.810737i	$0.699067\pi$
$734$	−4.19616e8	+	1.27115e8i	−1.06112	+	0.321447i
$735$	1.58476e8	−	1.62073e8i	0.399118	−	0.408177i
$736$	4.35936e6	−	4.34166e7i	0.0109343	−	0.108899i
$737$			4.74339e8i			1.18491i
$738$	1.27358e8	−	3.85809e7i	0.316853	−	0.0959850i
$739$		−	1.88890e7i		−	0.0468031i	−0.999726	−	0.0234016i	$-0.992550\pi$
$739$		−	1.88890e7i		−	0.0468031i	0.999726	−	0.0234016i	$-0.00744963\pi$
$740$	−5.61042e8	−	1.05509e8i	−1.38452	−	0.260373i
$741$	−1.50042e7			−0.0368771
$742$	−5.29298e6	−	1.74725e7i	−0.0129565	−	0.0427703i
$743$	5.63528e8			1.37388			0.686940	−	0.726714i	$-0.258953\pi$
$743$	5.63528e8			1.37388			0.686940	+	0.726714i	$0.258953\pi$
$744$	−2.49648e8	−	2.05357e8i	−0.606191	−	0.498644i
$745$	4.38756e7	−	4.48714e7i	0.106110	−	0.108518i
$746$	−8.78034e7	−	2.89845e8i	−0.211492	−	0.698151i
$747$	−2.51785e8			−0.604044
$748$	6.81934e7	−	4.54906e7i	0.162944	−	0.108697i
$749$	2.73216e6			0.00650222
$750$	−2.18511e8	−	1.07607e8i	−0.517952	−	0.255067i
$751$			1.95339e8i			0.461178i	0.973051	+	0.230589i	$0.0740652\pi$
$751$			1.95339e8i			0.461178i	−0.973051	+	0.230589i	$0.925935\pi$
$752$	8.88417e7	−	2.13565e8i	0.208912	−	0.502200i
$753$		−	1.64456e8i		−	0.385182i
$754$	3.49500e6	+	1.15372e7i	0.00815328	+	0.0269145i
$755$	3.49639e8	+	3.41879e8i	0.812416	+	0.794387i
$756$	7.32333e6	−	4.88526e6i	0.0169490	−	0.0113063i
$757$			6.04178e8i			1.39276i	0.717671	+	0.696382i	$0.245208\pi$
$757$			6.04178e8i			1.39276i	−0.717671	+	0.696382i	$0.754792\pi$
$758$	8.37123e7	+	2.76340e8i	0.192213	+	0.634507i
$759$			2.06705e7i			0.0472745i
$760$	5.78050e8	−	6.28233e7i	1.31681	−	0.143113i
$761$	−6.11654e8			−1.38788			−0.693940	−	0.720033i	$-0.744127\pi$
$761$	−6.11654e8			−1.38788			−0.693940	+	0.720033i	$0.744127\pi$
$762$	3.88822e8	−	1.17787e8i	0.878791	−	0.266214i
$763$	−3.28822e7			−0.0740264
$764$	−1.64314e8	−	2.46317e8i	−0.368463	−	0.552351i
$765$	−2.79352e7	−	2.73152e7i	−0.0623975	−	0.0610127i
$766$	−4.57549e8	+	1.38606e8i	−1.01801	+	0.308388i
$767$	−1.40900e7			−0.0312265
$768$	1.84368e8	+	1.85491e8i	0.407007	+	0.409486i
$769$	1.56867e8			0.344948			0.172474	−	0.985014i	$-0.444824\pi$
$769$	1.56867e8			0.344948			0.172474	+	0.985014i	$0.444824\pi$
$770$	3.20724e7	+	1.66986e7i	0.0702520	+	0.0365769i
$771$		−	5.35994e6i		−	0.0116949i
$772$	−2.72407e8	−	4.08356e8i	−0.592060	−	0.887539i
$773$			6.26937e8i			1.35733i	0.734448	+	0.678665i	$0.237441\pi$
$773$			6.26937e8i			1.35733i	−0.734448	+	0.678665i	$0.762559\pi$
$774$	1.18914e7	−	3.60229e6i	0.0256454	−	0.00776882i
$775$	−6.32684e8	+	1.42001e7i	−1.35920	+	0.0305061i
$776$	−5.76046e8	−	4.73848e8i	−1.23274	−	1.01404i
$777$		−	4.03932e7i		−	0.0861083i
$778$	5.33190e8	−	1.61520e8i	1.13225	−	0.342996i
$779$			6.21915e8i			1.31558i
$780$	−1.29843e7	−	2.44183e6i	−0.0273612	−	0.00514554i
$781$	4.81063e8			1.00983
$782$	−3.97270e6	−	1.31142e7i	−0.00830741	−	0.0274233i
$783$	5.38781e7			0.112235
$784$	−1.83013e8	+	4.39942e8i	−0.379781	+	0.912949i
$785$	1.40479e8	+	1.37362e8i	0.290405	+	0.283960i
$786$	−7.55011e6	−	2.49234e7i	−0.0155484	−	0.0513263i
$787$	4.20122e8			0.861888			0.430944	−	0.902379i	$-0.358181\pi$
$787$	4.20122e8			0.861888			0.430944	+	0.902379i	$0.358181\pi$
$788$	−3.82996e8	−	5.74137e8i	−0.782736	−	1.17337i
$789$	−2.62853e8			−0.535157
$790$	7.11250e7	+	3.70315e7i	0.144258	+	0.0751086i
$791$		−	2.90195e7i		−	0.0586354i
$792$	−9.56797e7	−	7.87048e7i	−0.192595	−	0.158426i
$793$		−	4.10205e7i		−	0.0822587i
$794$	−6.60465e7	−	2.18024e8i	−0.131944	−	0.435555i
$795$	8.75575e7	+	8.56144e7i	0.174258	+	0.170391i
$796$	3.21522e8	+	4.81983e8i	0.637487	+	0.955635i
$797$		−	8.14269e8i		−	1.60840i	−0.594362	−	0.804198i	$-0.702595\pi$
$797$		−	8.14269e8i		−	1.60840i	0.594362	−	0.804198i	$-0.297405\pi$
$798$	1.19278e7	+	3.93746e7i	0.0234721	+	0.0774831i
$799$		−	7.26374e7i		−	0.142403i
$800$	5.10458e8	+	3.97076e7i	0.996988	+	0.0775539i
$801$	2.92135e8			0.568441
$802$	7.71000e6	−	2.33561e6i	0.0149462	−	0.00452769i
$803$	6.52077e8			1.25937
$804$	−3.95343e8	+	2.63726e8i	−0.760686	+	0.507439i
$805$	4.22575e6	−	4.32166e6i	0.00810058	−	0.00828443i
$806$	−3.28530e7	+	9.95222e6i	−0.0627436	+	0.0190071i
$807$	−3.22317e8			−0.613286
$808$	−2.58977e8	+	3.14833e8i	−0.490939	+	0.596824i
$809$	1.00451e9			1.89719			0.948594	−	0.316496i	$-0.102506\pi$
$809$	1.00451e9			1.89719			0.948594	+	0.316496i	$0.102506\pi$
$810$	−2.72693e7	+	5.23753e7i	−0.0513121	+	0.0985533i
$811$		−	9.40317e8i		−	1.76283i	−0.472338	−	0.881417i	$-0.656590\pi$
$811$		−	9.40317e8i		−	1.76283i	0.472338	−	0.881417i	$-0.343410\pi$
$812$	2.74981e7	−	1.83434e7i	0.0513610	−	0.0342620i
$813$			2.15356e8i			0.400761i
$814$	−5.44054e8	+	1.64811e8i	−1.00872	+	0.305572i
$815$	−2.64162e8	+	2.70158e8i	−0.487976	+	0.499051i
$816$	7.58292e7	+	3.15444e7i	0.139562	+	0.0580567i
$817$			5.80680e7i			0.106481i
$818$	−2.76864e8	+	8.38710e7i	−0.505832	+	0.153233i
$819$		−	934829.i		−	0.00170169i
$820$	−1.01212e8	+	5.38194e8i	−0.183566	+	0.976107i
$821$	−5.07811e8			−0.917640			−0.458820	−	0.888529i	$-0.651728\pi$
$821$	−5.07811e8			−0.917640			−0.458820	+	0.888529i	$0.651728\pi$
$822$	8.93414e7	+	2.94922e8i	0.160856	+	0.530997i
$823$	−3.22556e8			−0.578637			−0.289318	−	0.957233i	$-0.593429\pi$
$823$	−3.22556e8			−0.578637			−0.289318	+	0.957233i	$0.593429\pi$
$824$	2.43262e8	−	2.95728e8i	0.434803	−	0.528580i
$825$	−2.42481e8	+	5.44230e6i	−0.431834	+	0.00969217i
$826$	1.12011e7	+	3.69755e7i	0.0198756	+	0.0656106i
$827$	−4.20915e8			−0.744180			−0.372090	−	0.928197i	$-0.621359\pi$
$827$	−4.20915e8			−0.744180			−0.372090	+	0.928197i	$0.621359\pi$
$828$	−1.72281e7	+	1.14925e7i	−0.0303491	+	0.0202453i
$829$	7.22698e8			1.26851			0.634254	−	0.773125i	$-0.281307\pi$
$829$	7.22698e8			1.26851			0.634254	+	0.773125i	$0.281307\pi$
$830$	4.78505e8	−	9.19047e8i	0.836858	−	1.60732i
$831$		−	3.33393e7i		−	0.0580969i
$832$	2.72510e7	−	5.35609e6i	0.0473165	−	0.00929989i
$833$			1.49632e8i			0.258875i
$834$	7.01377e7	+	2.31529e8i	0.120908	+	0.399124i
$835$	−1.50269e8	+	1.53680e8i	−0.258114	+	0.263972i
$836$	4.81666e8	−	3.21311e8i	0.824380	−	0.549929i
$837$			1.53421e8i			0.261643i
$838$	1.79047e8	+	5.91045e8i	0.304252	+	1.00436i
$839$		−	3.57997e8i		−	0.606168i	−0.952964	−	0.303084i	$-0.901984\pi$
$839$		−	3.57997e8i		−	0.606168i	0.952964	−	0.303084i	$-0.0980163\pi$
$840$	3.91418e6	+	3.60152e7i	0.00660394	+	0.0607642i
$841$	−3.92519e8			−0.659891
$842$	−1.38216e7	+	4.18699e6i	−0.0231537	+	0.00701401i
$843$	−2.24365e8			−0.374518
$844$	−3.85076e8	−	5.77255e8i	−0.640500	−	0.960153i
$845$	4.20839e8	−	4.30391e8i	0.697503	−	0.713333i
$846$	−1.05065e8	+	3.18277e7i	−0.173520	+	0.0525647i
$847$	−2.83227e7			−0.0466106
$848$	−2.37672e8	−	9.88700e7i	−0.389754	−	0.162135i
$849$	3.99151e8			0.652250
$850$	1.52793e8	−	5.00557e7i	0.248798	−	0.0815073i
$851$			9.50247e7i			0.154187i
$852$	2.67464e8	+	4.00947e8i	0.432461	+	0.648289i
$853$		−	1.53019e8i		−	0.246546i	−0.992373	−	0.123273i	$-0.960661\pi$
$853$		−	1.53019e8i		−	0.246546i	0.992373	−	0.123273i	$-0.0393390\pi$
$854$	−1.07648e8	+	3.26100e7i	−0.172835	+	0.0523573i
$855$	−1.97313e8	−	1.92934e8i	−0.315687	−	0.308681i
$856$	2.44728e7	−	2.97511e7i	0.0390178	−	0.0474332i
$857$			2.61817e8i			0.415963i	0.978133	+	0.207982i	$0.0666894\pi$
$857$			2.61817e8i			0.415963i	−0.978133	+	0.207982i	$0.933311\pi$
$858$	−1.25912e7	+	3.81427e6i	−0.0199344	+	0.00603879i
$859$			6.48325e7i			0.102285i	0.998691	+	0.0511426i	$0.0162863\pi$
$859$			6.48325e7i			0.102285i	−0.998691	+	0.0511426i	$0.983714\pi$
$860$	−9.45017e6	+	5.02510e7i	−0.0148574	+	0.0790040i
$861$	−3.87482e7			−0.0607075
$862$	−1.94454e8	−	6.41905e8i	−0.303595	−	1.00219i
$863$	−3.46397e8			−0.538942			−0.269471	−	0.963008i	$-0.586849\pi$
$863$	−3.46397e8			−0.538942			−0.269471	+	0.963008i	$0.586849\pi$
$864$	1.24008e7	−	1.23504e8i	0.0192268	−	0.191487i
$865$	−5.39591e8	−	5.27616e8i	−0.833712	−	0.815210i
$866$	−7.46215e7	−	2.46331e8i	−0.114897	−	0.379284i
$867$	−3.50477e8			−0.537776
$868$	5.22341e7	+	7.83025e7i	0.0798721	+	0.119734i
$869$	7.98497e7			0.121679
$870$	−1.02392e8	+	1.96662e8i	−0.155493	+	0.298650i
$871$			5.04658e7i			0.0763735i
$872$	−2.94536e8	+	3.58061e8i	−0.444210	+	0.540017i
$873$			3.54009e8i			0.532074i
$874$	−2.80601e7	−	9.26284e7i	−0.0420296	−	0.138743i
$875$	5.18090e7	+	4.84335e7i	0.0773358	+	0.0722972i
$876$	3.62545e8	+	5.43480e8i	0.539324	+	0.808484i
$877$			3.86932e8i			0.573635i	0.957985	+	0.286817i	$0.0925973\pi$
$877$			3.86932e8i			0.573635i	−0.957985	+	0.286817i	$0.907403\pi$
$878$	−2.65432e8	−	8.76210e8i	−0.392166	−	1.29457i
$879$		−	1.26547e8i		−	0.186331i
$880$	4.69116e8	−	1.99668e8i	0.688387	−	0.292996i
$881$	−7.55475e7			−0.110482			−0.0552411	−	0.998473i	$-0.517593\pi$
$881$	−7.55475e7			−0.110482			−0.0552411	+	0.998473i	$0.517593\pi$
$882$	2.16433e8	−	6.55647e7i	0.315441	−	0.0955574i
$883$	1.09819e8			0.159513			0.0797563	−	0.996814i	$-0.474586\pi$
$883$	1.09819e8			0.159513			0.0797563	+	0.996814i	$0.474586\pi$
$884$	7.25523e6	−	4.83983e6i	0.0105025	−	0.00700605i
$885$	−1.85291e8	−	1.81179e8i	−0.267315	−	0.261383i
$886$	2.81430e8	−	8.52542e7i	0.404640	−	0.122579i
$887$	4.08975e8			0.586038			0.293019	−	0.956107i	$-0.405340\pi$
$887$	4.08975e8			0.586038			0.293019	+	0.956107i	$0.405340\pi$
$888$	−4.39850e8	−	3.61814e8i	−0.628153	−	0.516710i
$889$	−1.18297e8			−0.168372
$890$	−5.55187e8	+	1.06633e9i	−0.787533	+	1.51259i
$891$			5.88000e7i			0.0831274i
$892$	3.29233e8	−	2.19625e8i	0.463884	−	0.309448i
$893$		−	5.13055e8i		−	0.720460i
$894$	5.99217e7	−	1.81522e7i	0.0838633	−	0.0254049i
$895$	−9.99997e8	−	9.77805e8i	−1.39486	−	1.36390i
$896$	−3.57194e7	−	6.72554e7i	−0.0496569	−	0.0934982i
$897$			2.19918e6i			0.00304708i
$898$	−3.55846e7	+	1.07797e7i	−0.0491398	+	0.0148860i
$899$			5.76075e8i			0.792867i
$900$	−1.39352e8	−	1.99073e8i	−0.191155	−	0.273077i
$901$	−8.08367e7			−0.110518
$902$	1.58100e8	+	5.21898e8i	0.215433	+	0.711158i
$903$	−3.61791e6			−0.00491353
$904$	−3.15999e8	−	2.59936e8i	−0.427741	−	0.351854i
$905$	−4.84368e8	+	4.95361e8i	−0.653476	+	0.668307i
$906$	1.41442e8	+	4.66911e8i	0.190193	+	0.627840i
$907$	1.19298e9			1.59886			0.799429	−	0.600761i	$-0.205136\pi$
$907$	1.19298e9			1.59886			0.799429	+	0.600761i	$0.205136\pi$
$908$	−6.24675e8	+	4.16709e8i	−0.834443	+	0.556641i
$909$	1.93481e8			0.257600
$910$	3.41224e6	+	1.77659e6i	0.00452809	+	0.00235757i
$911$		−	6.51943e8i		−	0.862292i	−0.902282	−	0.431146i	$-0.858109\pi$
$911$		−	6.51943e8i		−	0.862292i	0.902282	−	0.431146i	$-0.141891\pi$
$912$	5.35599e8	+	2.22806e8i	0.706083	+	0.293726i
$913$		−	1.03178e9i		−	1.35574i
$914$	−3.19676e8	−	1.05527e9i	−0.418670	−	1.38206i
$915$	5.27470e8	−	5.39442e8i	0.688549	−	0.704176i
$916$	1.03975e9	−	6.93599e8i	1.35283	−	0.902448i
$917$			7.58284e6i			0.00983386i
$918$	−1.13009e7	−	3.73049e7i	−0.0146077	−	0.0482212i
$919$		−	5.07991e7i		−	0.0654500i	−0.999464	−	0.0327250i	$-0.989581\pi$
$919$		−	5.07991e7i		−	0.0654500i	0.999464	−	0.0327250i	$-0.0104185\pi$
$920$	−9.20809e6	−	8.47255e7i	−0.0118251	−	0.108805i
$921$	3.24099e8			0.414858
$922$	−4.68154e8	+	1.41819e8i	−0.597305	+	0.180943i
$923$	5.11813e7			0.0650887
$924$	2.00192e7	+	3.00101e7i	0.0253764	+	0.0380409i
$925$	−1.11471e9	+	2.50188e7i	−1.40844	+	0.0316113i
$926$	6.83577e7	−	2.07077e7i	0.0860903	−	0.0260795i
$927$	−1.81740e8			−0.228145
$928$	4.65631e7	−	4.63740e8i	0.0582637	−	0.580271i
$929$	5.44046e8			0.678560			0.339280	−	0.940685i	$-0.389817\pi$
$929$	5.44046e8			0.678560			0.339280	+	0.940685i	$0.389817\pi$
$930$	−5.60007e8	−	2.91569e8i	−0.696216	−	0.362487i
$931$			1.05689e9i			1.30972i
$932$	7.32414e8	+	1.09794e9i	0.904709	+	1.35622i
$933$		−	8.76002e8i		−	1.07860i
$934$	7.13359e8	−	2.16099e8i	0.875523	−	0.265224i
$935$	1.11934e8	−	1.14475e8i	0.136939	−	0.140047i
$936$	−1.01796e7	−	8.37356e6i	−0.0124137	−	0.0102113i
$937$		−	1.23031e9i		−	1.49553i	−0.663963	−	0.747765i	$-0.731127\pi$
$937$		−	1.23031e9i		−	1.49553i	0.663963	−	0.747765i	$-0.268873\pi$
$938$	1.32435e8	−	4.01187e7i	0.160470	−	0.0486114i
$939$			9.43366e7i			0.113942i
$940$	8.34963e7	−	4.43989e8i	0.100527	−	0.534550i
$941$	−1.04638e9			−1.25580			−0.627901	−	0.778293i	$-0.716086\pi$
$941$	−1.04638e9			−1.25580			−0.627901	+	0.778293i	$0.716086\pi$
$942$	5.68293e7	+	1.87597e8i	0.0679860	+	0.224427i
$943$	9.11549e7			0.108704
$944$	5.02965e8	+	2.09230e8i	0.597891	+	0.248719i
$945$	1.20207e7	−	1.22935e7i	0.0142441	−	0.0145673i
$946$	1.47617e7	+	4.87294e7i	0.0174367	+	0.0575596i
$947$	1.05258e9			1.23938			0.619692	−	0.784845i	$-0.287257\pi$
$947$	1.05258e9			1.23938			0.619692	+	0.784845i	$0.287257\pi$
$948$	4.43953e7	+	6.65516e7i	0.0521089	+	0.0781148i
$949$	6.93757e7			0.0811725
$950$	1.07921e9	−	3.53555e8i	1.25874	−	0.412369i
$951$		−	1.25731e8i		−	0.146185i
$952$	−1.84686e7	−	1.51920e7i	−0.0214054	−	0.0176077i
$953$			1.26282e8i			0.145902i	0.997336	+	0.0729512i	$0.0232417\pi$
$953$			1.26282e8i			0.145902i	−0.997336	+	0.0729512i	$0.976758\pi$
$954$	3.54204e7	+	1.16925e8i	0.0407951	+	0.134667i
$955$	−4.13487e8	−	4.04311e8i	−0.474736	−	0.464200i
$956$	6.49561e8	+	9.73736e8i	0.743441	+	1.11447i
$957$			2.20786e8i			0.251904i
$958$	1.80907e8	+	5.97187e8i	0.205759	+	0.679225i
$959$		−	8.97288e7i		−	0.101736i
$960$	4.27238e8	+	2.79977e8i	0.482899	+	0.316453i
$961$	−7.52907e8			−0.848343
$962$	−5.78829e7	+	1.75346e7i	−0.0650168	+	0.0196957i
$963$	−1.82835e7			−0.0204730
$964$	−1.00402e9	+	6.69763e8i	−1.12076	+	0.747636i
$965$	−6.85498e8	−	6.70285e8i	−0.762824	−	0.745895i
$966$	5.77118e6	−	1.74828e6i	0.00640226	−	0.00193945i
$967$	1.32116e9			1.46108			0.730542	−	0.682868i	$-0.239268\pi$
$967$	1.32116e9			1.46108			0.730542	+	0.682868i	$0.239268\pi$
$968$	−2.53695e8	+	3.08412e8i	−0.279696	+	0.340020i
$969$	1.82167e8			0.200216
$970$	−1.29218e9	−	6.72776e8i	−1.41582	−	0.737149i
$971$			6.03829e8i			0.659563i	0.944057	+	0.329781i	$0.106975\pi$
$971$			6.03829e8i			0.659563i	−0.944057	+	0.329781i	$0.893025\pi$
$972$	−4.90075e7	+	3.26920e7i	−0.0533658	+	0.0355994i
$973$		−	7.04419e7i		−	0.0764702i
$974$	−1.40955e9	+	4.26997e8i	−1.52547	+	0.462113i
$975$	−2.57981e7	+	579017.i	−0.0278339	+	0.000624709i
$976$	−6.09138e8	+	1.46430e9i	−0.655188	+	1.57500i
$977$			9.72123e8i			1.04241i	0.853432	+	0.521204i	$0.174517\pi$
$977$			9.72123e8i			1.04241i	−0.853432	+	0.521204i	$0.825483\pi$
$978$	−3.60771e8	+	1.09289e8i	−0.385670	+	0.116832i
$979$			1.19713e9i			1.27583i
$980$	−1.72001e8	+	9.14611e8i	−0.182748	+	0.971758i
$981$	2.20046e8			0.233081
$982$	3.15858e8	+	1.04267e9i	0.333547	+	1.10106i
$983$	−5.59576e8			−0.589112			−0.294556	−	0.955634i	$-0.595172\pi$
$983$	−5.59576e8			−0.589112			−0.294556	+	0.955634i	$0.595172\pi$
$984$	−3.47080e8	+	4.21938e8i	−0.364287	+	0.442856i
$985$	−9.63791e8	−	9.42402e8i	−1.00850	−	0.986115i
$986$	−4.24331e7	−	1.40075e8i	−0.0442664	−	0.146126i
$987$	3.19657e7			0.0332455
$988$	5.12454e7	−	3.41849e7i	0.0531354	−	0.0354457i
$989$	8.51110e6			0.00879826
$990$	−2.14627e8	−	1.11746e8i	−0.221197	−	0.115167i
$991$		−	1.32095e9i		−	1.35727i	−0.734477	−	0.678634i	$-0.762572\pi$
$991$		−	1.32095e9i		−	1.35727i	0.734477	−	0.678634i	$-0.237428\pi$
$992$	1.32053e9	+	1.32591e8i	1.35274	+	0.135825i
$993$			1.06001e8i			0.108258i
$994$	−4.06875e7	−	1.34312e8i	−0.0414287	−	0.136759i
$995$	8.09093e8	+	7.91138e8i	0.821352	+	0.803124i
$996$	8.59951e8	−	5.73657e8i	0.870353	−	0.580596i
$997$			8.80146e8i			0.888115i	0.895998	+	0.444058i	$0.146461\pi$
$997$			8.80146e8i			0.888115i	−0.895998	+	0.444058i	$0.853539\pi$
$998$	1.21813e8	+	4.02113e8i	0.122547	+	0.404536i
$999$			2.70310e8i			0.271122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.4	yes	36
3.2	odd	2		180.7.f.g.19.33		36
4.3	odd	2	inner	60.7.f.a.19.34	yes	36
5.4	even	2	inner	60.7.f.a.19.33	yes	36
12.11	even	2		180.7.f.g.19.3		36
15.14	odd	2		180.7.f.g.19.4		36
20.19	odd	2	inner	60.7.f.a.19.3	✓	36
60.59	even	2		180.7.f.g.19.34		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.3	✓	36	20.19	odd	2	inner
60.7.f.a.19.4	yes	36	1.1	even	1	trivial
60.7.f.a.19.33	yes	36	5.4	even	2	inner
60.7.f.a.19.34	yes	36	4.3	odd	2	inner
180.7.f.g.19.3		36	12.11	even	2
180.7.f.g.19.4		36	15.14	odd	2
180.7.f.g.19.33		36	3.2	odd	2
180.7.f.g.19.34		36	60.59	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.65640 + 2.31937i) q^{2} -15.5885 q^{3} +(53.2410 - 35.5161i) q^{4} +(87.3911 - 89.3745i) q^{5} +(119.352 - 36.1554i) q^{6} -36.3122 q^{7} +(-325.260 + 395.411i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(-7.65640 + 2.31937i) q^{2} -15.5885 q^{3} +(53.2410 - 35.5161i) q^{4} +(87.3911 - 89.3745i) q^{5} +(119.352 - 36.1554i) q^{6} -36.3122 q^{7} +(-325.260 + 395.411i) q^{8} +243.000 q^{9} +(-461.809 + 886.980i) q^{10} +995.783i q^{11} +(-829.945 + 553.641i) q^{12} +105.943i q^{13} +(278.021 - 84.2215i) q^{14} +(-1362.29 + 1393.21i) q^{15} +(1573.21 - 3781.83i) q^{16} -1286.27i q^{17} +(-1860.51 + 563.607i) q^{18} -9085.22i q^{19} +(1478.56 - 7862.18i) q^{20} +566.051 q^{21} +(-2309.59 - 7624.12i) q^{22} -1331.63 q^{23} +(5070.30 - 6163.85i) q^{24} +(-350.602 - 15621.1i) q^{25} +(-245.722 - 811.144i) q^{26} -3788.00 q^{27} +(-1933.30 + 1289.67i) q^{28} -14223.4 q^{29} +(7198.88 - 13826.6i) q^{30} -40502.0i q^{31} +(-3273.70 + 32604.1i) q^{32} -15522.7i q^{33} +(2983.33 + 9848.19i) q^{34} +(-3173.36 + 3245.39i) q^{35} +(12937.6 - 8630.41i) q^{36} -71359.6i q^{37} +(21072.0 + 69560.1i) q^{38} -1651.49i q^{39} +(6914.89 + 63625.3i) q^{40} -68453.6 q^{41} +(-4333.92 + 1312.88i) q^{42} -6391.48 q^{43} +(35366.3 + 53016.5i) q^{44} +(21236.0 - 21718.0i) q^{45} +(10195.5 - 3088.55i) q^{46} +56471.4 q^{47} +(-24524.0 + 58952.8i) q^{48} -116330. q^{49} +(38915.4 + 118788. i) q^{50} +20050.9i q^{51} +(3762.69 + 5640.53i) q^{52} -62845.9i q^{53} +(29002.4 - 8785.77i) q^{54} +(88997.6 + 87022.5i) q^{55} +(11810.9 - 14358.3i) q^{56} +141624. i q^{57} +(108900. - 32989.3i) q^{58} +132995. i q^{59} +(-23048.4 + 122559. i) q^{60} -387193. q^{61} +(93939.2 + 310100. i) q^{62} -8823.87 q^{63} +(-50556.2 - 257223. i) q^{64} +(9468.63 + 9258.50i) q^{65} +(36003.0 + 118848. i) q^{66} +476348. q^{67} +(-45683.2 - 68482.2i) q^{68} +20758.1 q^{69} +(16769.3 - 32208.2i) q^{70} -483101. i q^{71} +(-79038.1 + 96084.9i) q^{72} -654838. i q^{73} +(165509. + 546358. i) q^{74} +(5465.35 + 243508. i) q^{75} +(-322671. - 483706. i) q^{76} -36159.1i q^{77} +(3830.42 + 12644.5i) q^{78} -80187.9i q^{79} +(-200514. - 471103. i) q^{80} +59049.0 q^{81} +(524108. - 158769. i) q^{82} -1.03615e6 q^{83} +(30137.2 - 20103.9i) q^{84} +(-114960. - 112408. i) q^{85} +(48935.8 - 14824.2i) q^{86} +221721. q^{87} +(-393744. - 323888. i) q^{88} +1.20220e6 q^{89} +(-112219. + 215536. i) q^{90} -3847.03i q^{91} +(-70897.4 + 47294.4i) q^{92} +631363. i q^{93} +(-432368. + 130978. i) q^{94} +(-811987. - 793967. i) q^{95} +(51031.9 - 508247. i) q^{96} +1.45683e6i q^{97} +(890673. - 269814. i) q^{98} +241975. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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