LMFDB - Embedded newform 74.6.e.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(11,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	74.11
Dual form			74.6.e.a.27.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.46410 + 2.00000i) q^{2} +(-5.84366 + 10.1215i) q^{3} +(8.00000 - 13.8564i) q^{4} +(5.13154 + 2.96270i) q^{5} -46.7492i q^{6} +(-44.9330 + 77.8262i) q^{7} +64.0000i q^{8} +(53.2034 + 92.1510i) q^{9} -23.7016 q^{10} -576.224 q^{11} +(93.4985 + 161.944i) q^{12} +(-69.5059 - 40.1292i) q^{13} -359.464i q^{14} +(-59.9739 + 34.6260i) q^{15} +(-128.000 - 221.703i) q^{16} +(1172.24 - 676.792i) q^{17} +(-368.604 - 212.814i) q^{18} +(-670.030 - 386.842i) q^{19} +(82.1047 - 47.4032i) q^{20} +(-525.146 - 909.579i) q^{21} +(1996.10 - 1152.45i) q^{22} -4118.27i q^{23} +(-647.777 - 373.994i) q^{24} +(-1544.94 - 2675.92i) q^{25} +321.034 q^{26} -4083.63 q^{27} +(718.928 + 1245.22i) q^{28} +1379.08i q^{29} +(138.504 - 239.896i) q^{30} -2419.24i q^{31} +(886.810 + 512.000i) q^{32} +(3367.25 - 5832.26i) q^{33} +(-2707.17 + 4688.95i) q^{34} +(-461.151 + 266.246i) q^{35} +1702.51 q^{36} +(-7620.79 + 3356.70i) q^{37} +3094.74 q^{38} +(812.337 - 469.003i) q^{39} +(-189.613 + 328.419i) q^{40} +(-887.105 + 1536.51i) q^{41} +(3638.32 + 2100.58i) q^{42} -12284.4i q^{43} +(-4609.79 + 7984.40i) q^{44} +630.502i q^{45} +(8236.54 + 14266.1i) q^{46} -12539.8 q^{47} +2991.95 q^{48} +(4365.55 + 7561.36i) q^{49} +(10703.7 + 6179.78i) q^{50} +15819.7i q^{51} +(-1112.09 + 642.068i) q^{52} +(12102.8 + 20962.7i) q^{53} +(14146.1 - 8167.25i) q^{54} +(-2956.92 - 1707.18i) q^{55} +(-4980.88 - 2875.71i) q^{56} +(7830.85 - 4521.14i) q^{57} +(-2758.16 - 4777.27i) q^{58} +(5242.38 - 3026.69i) q^{59} +1108.03i q^{60} +(-5518.55 - 3186.14i) q^{61} +(4838.47 + 8380.48i) q^{62} -9562.35 q^{63} -4096.00 q^{64} +(-237.782 - 411.850i) q^{65} +26938.0i q^{66} +(-28619.3 + 49570.2i) q^{67} -21657.3i q^{68} +(41683.1 + 24065.7i) q^{69} +(1064.98 - 1844.60i) q^{70} +(3494.50 - 6052.65i) q^{71} +(-5897.66 + 3405.02i) q^{72} -81174.1 q^{73} +(19685.8 - 26869.5i) q^{74} +36112.5 q^{75} +(-10720.5 + 6189.47i) q^{76} +(25891.5 - 44845.3i) q^{77} +(-1876.01 + 3249.35i) q^{78} +(-38920.3 - 22470.6i) q^{79} -1516.90i q^{80} +(10934.9 - 18939.8i) q^{81} -7096.84i q^{82} +(-33154.9 - 57426.0i) q^{83} -16804.7 q^{84} +8020.51 q^{85} +(24568.8 + 42554.5i) q^{86} +(-13958.4 - 8058.86i) q^{87} -36878.3i q^{88} +(124231. - 71724.9i) q^{89} +(-1261.00 - 2184.12i) q^{90} +(6246.22 - 3606.25i) q^{91} +(-57064.4 - 32946.2i) q^{92} +(24486.3 + 14137.2i) q^{93} +(43439.3 - 25079.7i) q^{94} +(-2292.19 - 3970.19i) q^{95} +(-10364.4 + 5983.90i) q^{96} +16176.1i q^{97} +(-30245.4 - 17462.2i) q^{98} +(-30657.1 - 53099.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} - 736 q^{10} + 464 q^{11} + 320 q^{12} + 72 q^{13} + 3960 q^{15} - 3584 q^{16} + 1530 q^{17} - 1944 q^{19} - 1440 q^{20} - 192 q^{21} - 3028 q^{25}+ \cdots - 401224 q^{99}+O(q^{100}) $ 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9 - 736 * q^10 + 464 * q^11 + 320 * q^12 + 72 * q^13 + 3960 * q^15 - 3584 * q^16 + 1530 * q^17 - 1944 * q^19 - 1440 * q^20 - 192 * q^21 - 3028 * q^25 - 5280 * q^26 + 36400 * q^27 + 2496 * q^28 - 4368 * q^30 - 2996 * q^33 + 1360 * q^34 - 21636 * q^35 - 18752 * q^36 + 45178 * q^37 - 14304 * q^38 + 14592 * q^39 - 5888 * q^40 + 12894 * q^41 - 26832 * q^42 + 3712 * q^44 - 22080 * q^46 - 39512 * q^47 + 10240 * q^48 + 8262 * q^49 - 44640 * q^50 + 1152 * q^52 + 47912 * q^53 - 101520 * q^54 + 70236 * q^55 + 99984 * q^57 + 51968 * q^58 - 74568 * q^59 - 8274 * q^61 - 22768 * q^62 - 137048 * q^63 - 114688 * q^64 + 33104 * q^65 - 7904 * q^67 - 69096 * q^69 + 65056 * q^70 + 9788 * q^71 + 256784 * q^73 - 8480 * q^74 + 518544 * q^75 - 31104 * q^76 - 86340 * q^77 + 89776 * q^78 - 82740 * q^79 - 174814 * q^81 + 19892 * q^83 - 6144 * q^84 - 167972 * q^85 + 119536 * q^86 - 200424 * q^87 - 223482 * q^89 + 59504 * q^90 - 53016 * q^91 + 198912 * q^92 - 227844 * q^93 + 158736 * q^94 - 140012 * q^95 - 168864 * q^98 - 401224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−3.46410	+	2.00000i	−0.612372	+	0.353553i
$2$	−3.46410	+	2.00000i	−0.612372	+	0.353553i
$3$	−5.84366	+	10.1215i	−0.374871	+	0.649295i	−0.990308	−	0.138891i	$-0.955646\pi$
$3$	−5.84366	+	10.1215i	−0.374871	+	0.649295i	0.615437	+	0.788186i	$0.288980\pi$
$4$	8.00000	−	13.8564i	0.250000	−	0.433013i
$5$	5.13154	+	2.96270i	0.0917958	+	0.0529983i	0.545195	−	0.838309i	$-0.316456\pi$
$5$	5.13154	+	2.96270i	0.0917958	+	0.0529983i	−0.453399	+	0.891307i	$0.649789\pi$
$6$		−	46.7492i		−	0.530147i
$7$	−44.9330	+	77.8262i	−0.346593	+	0.600317i	−0.985642	−	0.168849i	$-0.945995\pi$
$7$	−44.9330	+	77.8262i	−0.346593	+	0.600317i	0.639049	+	0.769166i	$0.279328\pi$
$8$			64.0000i			0.353553i
$9$	53.2034	+	92.1510i	0.218944	+	0.379222i
$10$	−23.7016			−0.0749510
$11$	−576.224			−1.43585			−0.717926	−	0.696119i	$-0.754908\pi$
$11$	−576.224			−1.43585			−0.717926	+	0.696119i	$0.754908\pi$
$12$	93.4985	+	161.944i	0.187435	+	0.324648i
$13$	−69.5059	−	40.1292i	−0.114068	−	0.0658571i	0.441881	−	0.897074i	$-0.354311\pi$
$13$	−69.5059	−	40.1292i	−0.114068	−	0.0658571i	−0.555948	+	0.831217i	$0.687645\pi$
$14$		−	359.464i		−	0.490157i
$15$	−59.9739	+	34.6260i	−0.0688231	+	0.0397350i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	1172.24	−	676.792i	0.983769	−	0.567979i	0.0803633	−	0.996766i	$-0.474392\pi$
$17$	1172.24	−	676.792i	0.983769	−	0.567979i	0.903406	+	0.428786i	$0.141059\pi$
$18$	−368.604	−	212.814i	−0.268150	−	0.154817i
$19$	−670.030	−	386.842i	−0.425805	−	0.245838i	0.271753	−	0.962367i	$-0.412397\pi$
$19$	−670.030	−	386.842i	−0.425805	−	0.245838i	−0.697558	+	0.716529i	$0.745730\pi$
$20$	82.1047	−	47.4032i	0.0458979	−	0.0264992i
$21$	−525.146	−	909.579i	−0.259855	−	0.450083i
$22$	1996.10	−	1152.45i	0.879276	−	0.507650i
$23$		−	4118.27i		−	1.62329i	−0.584154	−	0.811643i	$-0.698573\pi$
$23$		−	4118.27i		−	1.62329i	0.584154	−	0.811643i	$-0.301427\pi$
$24$	−647.777	−	373.994i	−0.229560	−	0.132537i
$25$	−1544.94	−	2675.92i	−0.494382	−	0.856295i
$26$	321.034			0.0931360
$27$	−4083.63			−1.07804
$28$	718.928	+	1245.22i	0.173297	+	0.300159i
$29$			1379.08i			0.304505i	0.988342	+	0.152252i	$0.0486526\pi$
$29$			1379.08i			0.304505i	−0.988342	+	0.152252i	$0.951347\pi$
$30$	138.504	−	239.896i	0.0280969	−	0.0486653i
$31$		−	2419.24i		−	0.452141i	−0.974111	−	0.226071i	$-0.927412\pi$
$31$		−	2419.24i		−	0.452141i	0.974111	−	0.226071i	$-0.0725880\pi$
$32$	886.810	+	512.000i	0.153093	+	0.0883883i
$33$	3367.25	−	5832.26i	0.538259	−	0.932292i
$34$	−2707.17	+	4688.95i	−0.401622	+	0.695630i
$35$	−461.151	+	266.246i	−0.0636316	+	0.0367377i
$36$	1702.51			0.218944
$37$	−7620.79	+	3356.70i	−0.915158	+	0.403096i
$37$	−7620.79	+	3356.70i	−0.915158	+	0.403096i
$38$	3094.74			0.347668
$39$	812.337	−	469.003i	0.0855214	−	0.0493758i
$40$	−189.613	+	328.419i	−0.0187377	+	0.0324547i
$41$	−887.105	+	1536.51i	−0.0824167	+	0.142750i	−0.904288	−	0.426924i	$-0.859597\pi$
$41$	−887.105	+	1536.51i	−0.0824167	+	0.142750i	0.821871	+	0.569674i	$0.192931\pi$
$42$	3638.32	+	2100.58i	0.318257	+	0.183745i
$43$		−	12284.4i		−	1.01317i	−0.862189	−	0.506586i	$-0.830907\pi$
$43$		−	12284.4i		−	1.01317i	0.862189	−	0.506586i	$-0.169093\pi$
$44$	−4609.79	+	7984.40i	−0.358963	+	0.621742i
$45$			630.502i			0.0464147i
$46$	8236.54	+	14266.1i	0.573918	+	0.994056i
$47$	−12539.8			−0.828033			−0.414016	−	0.910269i	$-0.635874\pi$
$47$	−12539.8			−0.828033			−0.414016	+	0.910269i	$0.635874\pi$
$48$	2991.95			0.187435
$49$	4365.55	+	7561.36i	0.259746	+	0.449893i
$50$	10703.7	+	6179.78i	0.605492	+	0.349581i
$51$			15819.7i			0.851675i
$52$	−1112.09	+	642.068i	−0.0570339	+	0.0329285i
$53$	12102.8	+	20962.7i	0.591830	+	1.02508i	0.993986	+	0.109508i	$0.0349275\pi$
$53$	12102.8	+	20962.7i	0.591830	+	1.02508i	−0.402156	+	0.915571i	$0.631739\pi$
$54$	14146.1	−	8167.25i	0.660164	−	0.381146i
$55$	−2956.92	−	1707.18i	−0.131805	−	0.0760978i
$56$	−4980.88	−	2875.71i	−0.212244	−	0.122539i
$57$	7830.85	−	4521.14i	0.319243	−	0.184315i
$58$	−2758.16	−	4777.27i	−0.107659	−	0.186470i
$59$	5242.38	−	3026.69i	0.196064	−	0.113198i	−0.398754	−	0.917058i	$-0.630557\pi$
$59$	5242.38	−	3026.69i	0.196064	−	0.113198i	0.594818	+	0.803860i	$0.297224\pi$
$60$			1108.03i			0.0397350i
$61$	−5518.55	−	3186.14i	−0.189889	−	0.109633i	0.402041	−	0.915621i	$-0.368301\pi$
$61$	−5518.55	−	3186.14i	−0.189889	−	0.109633i	−0.591931	+	0.805989i	$0.701634\pi$
$62$	4838.47	+	8380.48i	0.159856	+	0.276879i
$63$	−9562.35			−0.303538
$64$	−4096.00			−0.125000
$65$	−237.782	−	411.850i	−0.00698063	−	0.0120908i
$66$			26938.0i			0.761213i
$67$	−28619.3	+	49570.2i	−0.778884	+	1.34907i	0.153702	+	0.988117i	$0.450881\pi$
$67$	−28619.3	+	49570.2i	−0.778884	+	1.34907i	−0.932585	+	0.360949i	$0.882453\pi$
$68$		−	21657.3i		−	0.567979i
$69$	41683.1	+	24065.7i	1.05399	+	0.608522i
$70$	1064.98	−	1844.60i	0.0259775	−	0.0449944i
$71$	3494.50	−	6052.65i	0.0822696	−	0.142495i	−0.821955	−	0.569553i	$-0.807116\pi$
$71$	3494.50	−	6052.65i	0.0822696	−	0.142495i	0.904224	+	0.427058i	$0.140450\pi$
$72$	−5897.66	+	3405.02i	−0.134075	+	0.0774084i
$73$	−81174.1			−1.78283			−0.891416	−	0.453187i	$-0.850287\pi$
$73$	−81174.1			−1.78283			−0.891416	+	0.453187i	$0.850287\pi$
$74$	19685.8	−	26869.5i	0.417901	−	0.570402i
$75$	36112.5			0.741318
$76$	−10720.5	+	6189.47i	−0.212902	+	0.122919i
$77$	25891.5	−	44845.3i	0.497657	−	0.861967i
$78$	−1876.01	+	3249.35i	−0.0349140	+	0.0604727i
$79$	−38920.3	−	22470.6i	−0.701630	−	0.405086i	0.106324	−	0.994332i	$-0.466092\pi$
$79$	−38920.3	−	22470.6i	−0.701630	−	0.405086i	−0.807954	+	0.589245i	$0.799425\pi$
$80$		−	1516.90i		−	0.0264992i
$81$	10934.9	−	18939.8i	0.185183	−	0.320747i
$82$		−	7096.84i		−	0.116555i
$83$	−33154.9	−	57426.0i	−0.528266	−	0.914983i	−0.999457	−	0.0329523i	$-0.989509\pi$
$83$	−33154.9	−	57426.0i	−0.528266	−	0.914983i	0.471191	−	0.882031i	$-0.343824\pi$
$84$	−16804.7			−0.259855
$85$	8020.51			0.120408
$86$	24568.8	+	42554.5i	0.358211	+	0.620439i
$87$	−13958.4	−	8058.86i	−0.197713	−	0.114150i
$88$		−	36878.3i		−	0.507650i
$89$	124231.	−	71724.9i	1.66248	−	0.959832i	0.690950	−	0.722902i	$-0.257192\pi$
$89$	124231.	−	71724.9i	1.66248	−	0.959832i	0.971527	−	0.236929i	$-0.0761410\pi$
$90$	−1261.00	−	2184.12i	−0.0164101	−	0.0284231i
$91$	6246.22	−	3606.25i	0.0790703	−	0.0456513i
$92$	−57064.4	−	32946.2i	−0.702904	−	0.405822i
$93$	24486.3	+	14137.2i	0.293573	+	0.169495i
$94$	43439.3	−	25079.7i	0.507064	−	0.292754i
$95$	−2292.19	−	3970.19i	−0.0260581	−	0.0451339i
$96$	−10364.4	+	5983.90i	−0.114780	+	0.0662684i
$97$			16176.1i			0.174560i	0.996184	+	0.0872798i	$0.0278174\pi$
$97$			16176.1i			0.174560i	−0.996184	+	0.0872798i	$0.972183\pi$
$98$	−30245.4	−	17462.2i	−0.318123	−	0.183668i
$99$	−30657.1	−	53099.6i	−0.314371	−	0.544507i
$100$	−49438.2			−0.494382
$101$	59131.8			0.576790			0.288395	−	0.957512i	$-0.406878\pi$
$101$	59131.8			0.576790			0.288395	+	0.957512i	$0.406878\pi$
$102$	−31639.5	−	54801.2i	−0.301113	−	0.521543i
$103$			100413.i			0.932606i	0.884625	+	0.466303i	$0.154414\pi$
$103$			100413.i			0.932606i	−0.884625	+	0.466303i	$0.845586\pi$
$104$	2568.27	−	4448.38i	0.0232840	−	0.0403291i
$105$		−	6223.39i		−	0.0550876i
$106$	−83850.8	−	48411.3i	−0.724840	−	0.418487i
$107$	−29314.9	+	50774.9i	−0.247530	+	0.428735i	−0.962840	−	0.270072i	$-0.912952\pi$
$107$	−29314.9	+	50774.9i	−0.247530	+	0.428735i	0.715310	+	0.698808i	$0.246286\pi$
$108$	−32669.0	+	56584.4i	−0.269511	+	0.466807i
$109$	−126544.	+	73060.1i	−1.02017	+	0.588998i	−0.914154	−	0.405366i	$-0.867144\pi$
$109$	−126544.	+	73060.1i	−1.02017	+	0.588998i	−0.106020	+	0.994364i	$0.533811\pi$
$110$	13657.4			0.107619
$111$	10558.4	−	96749.3i	0.0813374	−	0.745316i
$112$	23005.7			0.173297
$113$	−72325.2	+	41757.0i	−0.532836	+	0.307633i	−0.742170	−	0.670211i	$-0.766204\pi$
$113$	−72325.2	+	41757.0i	−0.532836	+	0.307633i	0.209335	+	0.977844i	$0.432870\pi$
$114$	−18084.6	+	31323.4i	−0.130331	+	0.225739i
$115$	12201.2	−	21133.1i	0.0860315	−	0.149011i
$116$	19109.1	+	11032.6i	0.131854	+	0.0761262i
$117$		−	8540.05i		−	0.0576761i
$118$	−12106.8	+	20969.5i	−0.0800429	+	0.138638i
$119$			121641.i			0.787432i
$120$	−2216.06	−	3838.33i	−0.0140485	−	0.0243326i
$121$	170983.			1.06167
$122$	25489.1			0.155044
$123$	−10367.9	−	17957.7i	−0.0617912	−	0.107026i
$124$	−33521.9	−	19353.9i	−0.195783	−	0.113035i
$125$		−	36825.7i		−	0.210802i
$126$	33124.9	−	19124.7i	0.185878	−	0.107317i
$127$	31079.0	+	53830.5i	0.170985	+	0.296155i	0.938765	−	0.344559i	$-0.111972\pi$
$127$	31079.0	+	53830.5i	0.170985	+	0.296155i	−0.767779	+	0.640714i	$0.778638\pi$
$128$	14189.0	−	8192.00i	0.0765466	−	0.0441942i
$129$	124337.	+	71785.9i	0.657848	+	0.379809i
$130$	1647.40	+	951.126i	0.00854950	+	0.00493605i
$131$	16590.0	−	9578.22i	0.0844631	−	0.0487648i	−0.457174	−	0.889377i	$-0.651138\pi$
$131$	16590.0	−	9578.22i	0.0844631	−	0.0487648i	0.541637	+	0.840613i	$0.317805\pi$
$132$	−53876.1	−	93316.1i	−0.269129	−	0.466146i
$133$	60212.9	−	34763.9i	0.295162	−	0.170412i
$134$		−	228955.i		−	1.10151i
$135$	−20955.3	−	12098.5i	−0.0989599	−	0.0571345i
$136$	43314.7	+	75023.2i	0.200811	+	0.347815i
$137$	−44900.6			−0.204386			−0.102193	−	0.994765i	$-0.532586\pi$
$137$	−44900.6			−0.204386			−0.102193	+	0.994765i	$0.532586\pi$
$138$	−192526.			−0.860581
$139$	147124.	+	254827.i	0.645873	+	1.11869i	0.984099	+	0.177621i	$0.0568400\pi$
$139$	147124.	+	254827.i	0.645873	+	1.11869i	−0.338226	+	0.941065i	$0.609827\pi$
$140$			8519.86i			0.0367377i
$141$	73278.5	−	126922.i	0.310405	−	0.537638i
$142$			27956.0i			0.116347i
$143$	40051.0	+	23123.4i	0.163785	+	0.0945611i
$144$	13620.1	−	23590.6i	0.0547360	−	0.0948055i
$145$	−4085.79	+	7076.80i	−0.0161382	+	0.0279523i
$146$	281195.	−	162348.i	1.09176	−	0.630326i
$147$	−102043.			−0.389485
$148$	−14454.5	+	132450.i	−0.0542437	+	0.497049i
$149$	233084.			0.860097			0.430049	−	0.902806i	$-0.358496\pi$
$149$	233084.			0.860097			0.430049	+	0.902806i	$0.358496\pi$
$150$	−125097.	+	72225.0i	−0.453963	+	0.262095i
$151$	−228743.	+	396195.i	−0.816406	+	1.41406i	0.0919078	+	0.995768i	$0.470704\pi$
$151$	−228743.	+	396195.i	−0.816406	+	1.41406i	−0.908314	+	0.418289i	$0.862630\pi$
$152$	24757.9	−	42881.9i	0.0869170	−	0.150545i
$153$	124734.	+	72015.2i	0.430781	+	0.248711i
$154$			207132.i			0.703793i
$155$	7167.47	−	12414.4i	0.0239627	−	0.0415047i
$156$		−	15008.1i		−	0.0493758i
$157$	−105172.	−	182163.i	−0.340527	−	0.589810i	0.644004	−	0.765022i	$-0.277272\pi$
$157$	−105172.	−	182163.i	−0.340527	−	0.589810i	−0.984531	+	0.175213i	$0.943939\pi$
$158$	179765.			0.572879
$159$	−282899.			−0.887438
$160$	3033.80	+	5254.70i	0.00936887	+	0.0162274i
$161$	320509.	+	185046.i	0.974487	+	0.562620i
$162$			87479.0i			0.261888i
$163$	−241513.	+	139438.i	−0.711986	+	0.411065i	−0.811796	−	0.583941i	$-0.801510\pi$
$163$	−241513.	+	139438.i	−0.711986	+	0.411065i	0.0998100	+	0.995007i	$0.468176\pi$
$164$	14193.7	+	24584.2i	0.0412084	+	0.0713750i
$165$	34558.4	−	19952.3i	0.0988198	−	0.0570537i
$166$	229704.	+	132620.i	0.646991	+	0.373540i
$167$	−112491.	−	64946.7i	−0.312124	−	0.180205i	0.335753	−	0.941950i	$-0.391009\pi$
$167$	−112491.	−	64946.7i	−0.312124	−	0.180205i	−0.647876	+	0.761745i	$0.724343\pi$
$168$	58213.1	−	33609.3i	0.159128	−	0.0918727i
$169$	−182426.	−	315971.i	−0.491326	−	0.851001i
$170$	−27783.9	+	16041.0i	−0.0737345	+	0.0425706i
$171$		−	82325.2i		−	0.215299i
$172$	−170218.	−	98275.3i	−0.438716	−	0.253293i
$173$	−26975.6	−	46723.2i	−0.0685261	−	0.118691i	0.829727	−	0.558170i	$-0.188496\pi$
$173$	−26975.6	−	46723.2i	−0.0685261	−	0.118691i	−0.898253	+	0.439479i	$0.855163\pi$
$174$	64470.9			0.161432
$175$	277676.			0.685399
$176$	73756.7	+	127750.i	0.179482	+	0.310871i
$177$			70747.7i			0.169738i
$178$	−286900.	+	496925.i	−0.678703	+	1.17555i
$179$			271967.i			0.634429i	0.948354	+	0.317214i	$0.102748\pi$
$179$			271967.i			0.634429i	−0.948354	+	0.317214i	$0.897252\pi$
$180$	8736.49	+	5044.02i	0.0200981	+	0.0116037i
$181$	−111837.	+	193708.i	−0.253740	+	0.439491i	−0.964553	−	0.263891i	$-0.914994\pi$
$181$	−111837.	+	193708.i	−0.253740	+	0.439491i	0.710812	+	0.703382i	$0.248328\pi$
$182$	−14425.0	+	24984.9i	−0.0322803	+	0.0559112i
$183$	64497.0	−	37237.4i	0.142368	−	0.0821961i
$184$	263569.			0.573918
$185$	−49051.3	−	5353.04i	−0.105371	−	0.0114993i
$186$	−113098.			−0.239701
$187$	−675471.	+	389984.i	−1.41255	+	0.815534i
$188$	−100319.	+	173757.i	−0.207008	+	0.358549i
$189$	183490.	−	317813.i	0.373643	−	0.647168i
$190$	15880.8	+	9168.77i	0.0319145	+	0.0184258i
$191$		−	400875.i		−	0.795108i	−0.917579	−	0.397554i	$-0.869859\pi$
$191$		−	400875.i		−	0.795108i	0.917579	−	0.397554i	$-0.130141\pi$
$192$	23935.6	−	41457.7i	0.0468588	−	0.0811619i
$193$		−	388307.i		−	0.750381i	−0.926948	−	0.375190i	$-0.877577\pi$
$193$		−	388307.i		−	0.750381i	0.926948	−	0.375190i	$-0.122423\pi$
$194$	−32352.1	−	56035.5i	−0.0617161	−	0.106895i
$195$	5558.06			0.0104673
$196$	139698.			0.259746
$197$	−412272.	−	714076.i	−0.756865	−	1.31093i	−0.944442	−	0.328678i	$-0.893397\pi$
$197$	−412272.	−	714076.i	−0.756865	−	1.31093i	0.187577	−	0.982250i	$-0.439936\pi$
$198$	212398.	+	122628.i	0.385024	+	0.222294i
$199$		−	700991.i		−	1.25482i	−0.778691	−	0.627408i	$-0.784116\pi$
$199$		−	700991.i		−	1.25482i	0.778691	−	0.627408i	$-0.215884\pi$
$200$	171259.	−	98876.5i	0.302746	−	0.174791i
$201$	−334483.	−	579342.i	−0.583961	−	1.01145i
$202$	−204839.	+	118264.i	−0.353210	+	0.203926i
$203$	−107328.	−	61966.1i	−0.182799	−	0.105539i
$204$	219205.	+	126558.i	0.368786	+	0.212919i
$205$	−9104.43	+	5256.45i	−0.0151310	+	0.00873590i
$206$	−200827.	−	347842.i	−0.329726	−	0.571102i
$207$	379502.	−	219106.i	0.615586	−	0.355409i
$208$			20546.2i			0.0329285i
$209$	386088.	+	222908.i	0.611392	+	0.352988i
$210$	12446.8	+	21558.5i	0.0194764	+	0.0337341i
$211$	−497685.			−0.769571			−0.384785	−	0.923006i	$-0.625724\pi$
$211$	−497685.			−0.769571			−0.384785	+	0.923006i	$0.625724\pi$
$212$	387290.			0.591830
$213$	40841.3	+	70739.2i	0.0616809	+	0.106834i
$214$		−	234519.i		−	0.350061i
$215$	36395.0	−	63038.0i	0.0536965	−	0.0930050i
$216$		−	261352.i		−	0.381146i
$217$	188280.	+	108704.i	0.271428	+	0.156709i
$218$	292240.	−	506175.i	0.416484	−	0.721372i
$219$	474353.	−	821604.i	0.668331	−	1.15758i
$220$	−47310.7	+	27314.8i	−0.0659026	+	0.0380489i
$221$	−108637.			−0.149622
$222$	156923.	+	356266.i	0.213700	+	0.485168i
$223$	−877507.			−1.18165			−0.590825	−	0.806800i	$-0.701197\pi$
$223$	−877507.			−1.18165			−0.590825	+	0.806800i	$0.701197\pi$
$224$	−79694.1	+	46011.4i	−0.106122	+	0.0612696i
$225$	164393.	−	284736.i	0.216484	−	0.374961i
$226$	167028.	−	289301.i	0.217529	−	0.376772i
$227$	−853490.	−	492763.i	−1.09935	−	0.634707i	−0.163296	−	0.986577i	$-0.552213\pi$
$227$	−853490.	−	492763.i	−1.09935	−	0.634707i	−0.936049	+	0.351870i	$0.885546\pi$
$228$		−	144677.i		−	0.184315i
$229$	−332554.	+	576001.i	−0.419058	+	0.725829i	−0.995845	−	0.0910651i	$-0.970973\pi$
$229$	−332554.	+	576001.i	−0.419058	+	0.725829i	0.576787	+	0.816894i	$0.304306\pi$
$230$			97609.5i			0.121667i
$231$	302602.	+	524121.i	0.373114	+	0.646252i
$232$	−88261.0			−0.107659
$233$	1.11449e6			1.34489			0.672443	−	0.740149i	$-0.265245\pi$
$233$	1.11449e6			1.34489			0.672443	+	0.740149i	$0.265245\pi$
$234$	17080.1	+	29583.6i	0.0203916	+	0.0353192i
$235$	−64348.8	−	37151.8i	−0.0760100	−	0.0438844i
$236$		−	96854.1i		−	0.113198i
$237$	454874.	−	262621.i	0.526041	−	0.303710i
$238$	−243282.	−	421377.i	−0.278399	−	0.482201i
$239$	−1.36742e6	+	789480.i	−1.54849	+	0.894018i	−0.550227	+	0.835015i	$0.685459\pi$
$239$	−1.36742e6	+	789480.i	−1.54849	+	0.894018i	−0.998258	+	0.0590036i	$0.981208\pi$
$240$	15353.3	+	8864.25i	0.0172058	+	0.00993376i
$241$	446155.	+	257588.i	0.494815	+	0.285682i	0.726570	−	0.687093i	$-0.241113\pi$
$241$	446155.	+	257588.i	0.494815	+	0.285682i	−0.231755	+	0.972774i	$0.574447\pi$
$242$	−592303.	+	341966.i	−0.650138	+	0.375357i
$243$	−368361.	−	638020.i	−0.400183	−	0.693137i
$244$	−88296.8	+	50978.2i	−0.0949446	+	0.0548163i
$245$			51735.2i			0.0550645i
$246$	71830.7	+	41471.5i	0.0756785	+	0.0436930i
$247$	31047.4	+	53775.6i	0.0323804	+	0.0560845i
$248$	154831.			0.159856
$249$	774983.			0.792126
$250$	73651.4	+	127568.i	0.0745299	+	0.129090i
$251$			824997.i			0.826548i	0.910607	+	0.413274i	$0.135615\pi$
$251$			824997.i			0.826548i	−0.910607	+	0.413274i	$0.864385\pi$
$252$	−76498.8	+	132500.i	−0.0758845	+	0.131436i
$253$			2.37305e6i			2.33080i
$254$	−215322.	−	124316.i	−0.209413	−	0.120905i
$255$	−46869.1	+	81179.7i	−0.0451374	+	0.0781802i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	793348.	−	458040.i	0.749258	−	0.432584i	−0.0761680	−	0.997095i	$-0.524269\pi$
$257$	793348.	−	458040.i	0.749258	−	0.432584i	0.825426	+	0.564511i	$0.190935\pi$
$258$	−574287.			−0.537130
$259$	81185.5	−	743924.i	0.0752020	−	0.689095i
$260$	−7609.01			−0.00698063
$261$	−127083.	+	73371.6i	−0.115475	+	0.0666695i
$262$	−38312.9	+	66359.8i	−0.0344819	+	0.0597244i
$263$	−16911.0	+	29290.8i	−0.0150758	+	0.0261121i	−0.873465	−	0.486887i	$-0.838132\pi$
$263$	−16911.0	+	29290.8i	−0.0150758	+	0.0261121i	0.858389	+	0.512999i	$0.171466\pi$
$264$	373264.	+	215504.i	0.329615	+	0.190303i
$265$			143428.i			0.125464i
$266$	−139056.	+	240852.i	−0.120499	+	0.208711i
$267$			1.67654e6i			1.43925i
$268$	457910.	+	793123.i	0.389442	+	0.674533i
$269$	82755.1			0.0697291			0.0348646	−	0.999392i	$-0.488900\pi$
$269$	82755.1			0.0697291			0.0348646	+	0.999392i	$0.488900\pi$
$270$	96788.4			0.0808005
$271$	85579.9	+	148229.i	0.0707862	+	0.122605i	0.899246	−	0.437443i	$-0.144116\pi$
$271$	85579.9	+	148229.i	0.0707862	+	0.122605i	−0.828460	+	0.560048i	$0.810783\pi$
$272$	−300093.	−	173259.i	−0.245942	−	0.141995i
$273$			84294.8i			0.0684533i
$274$	155540.	−	89801.3i	0.125160	−	0.0722614i
$275$	890234.	+	1.54193e6i	0.709860	+	1.22951i
$276$	666930.	−	385052.i	0.526996	−	0.304261i
$277$	−5208.27	−	3007.00i	−0.00407844	−	0.00235469i	0.497959	−	0.867200i	$-0.334083\pi$
$277$	−5208.27	−	3007.00i	−0.00407844	−	0.00235469i	−0.502038	+	0.864846i	$0.667416\pi$
$278$	−1.01931e6	−	588497.i	−0.791030	−	0.456701i
$279$	222935.	−	128712.i	0.171462	−	0.0989936i
$280$	−17039.7	−	29513.7i	−0.0129888	−	0.0224972i
$281$	501116.	−	289320.i	0.378593	−	0.218581i	−0.298613	−	0.954374i	$-0.596524\pi$
$281$	501116.	−	289320.i	0.378593	−	0.218581i	0.677206	+	0.735794i	$0.263191\pi$
$282$			586228.i			0.438979i
$283$	−185307.	−	106987.i	−0.137539	−	0.0794081i	0.429652	−	0.902995i	$-0.358636\pi$
$283$	−185307.	−	106987.i	−0.137539	−	0.0794081i	−0.567191	+	0.823587i	$0.691970\pi$
$284$	−55912.0	−	96842.4i	−0.0411348	−	0.0712475i
$285$	53579.1			0.0390736
$286$	−184987.			−0.133730
$287$	−79720.5	−	138080.i	−0.0571302	−	0.0989524i
$288$			108961.i			0.0774084i
$289$	206165.	−	357088.i	0.145201	−	0.251496i
$290$		−	32686.3i		−	0.0228229i
$291$	−163726.	−	94527.4i	−0.113341	−	0.0654373i
$292$	−649393.	+	1.12478e6i	−0.445708	+	0.771989i
$293$	−1.23724e6	+	2.14296e6i	−0.841948	+	1.45830i	0.0462972	+	0.998928i	$0.485258\pi$
$293$	−1.23724e6	+	2.14296e6i	−0.841948	+	1.45830i	−0.888245	+	0.459369i	$0.848075\pi$
$294$	353488.	−	204086.i	0.238510	−	0.137704i
$295$	35868.7			0.0239972
$296$	−214829.	−	487731.i	−0.142516	−	0.323557i
$297$	2.35308e6			1.54791
$298$	−807428.	+	466169.i	−0.526700	+	0.304090i
$299$	−165263.	+	286244.i	−0.106905	+	0.185165i
$300$	288900.	−	500389.i	0.185329	−	0.321000i
$301$	956050.	+	551975.i	0.608225	+	0.351159i
$302$		−	1.82995e6i		−	1.15457i
$303$	−345546.	+	598503.i	−0.216222	+	0.374507i
$304$			198063.i			0.122919i
$305$	−18879.1	−	32699.6i	−0.0116207	−	0.0201276i
$306$	−576122.			−0.351731
$307$	2.30636e6			1.39663			0.698313	−	0.715792i	$-0.253934\pi$
$307$	2.30636e6			1.39663			0.698313	+	0.715792i	$0.253934\pi$
$308$	−414264.	−	717526.i	−0.248828	−	0.430983i
$309$	−1.01633e6	−	586781.i	−0.605536	−	0.349606i
$310$			57339.8i			0.0338884i
$311$	1.99298e6	−	1.15065e6i	1.16843	−	0.674592i	0.215118	−	0.976588i	$-0.430986\pi$
$311$	1.99298e6	−	1.15065e6i	1.16843	−	0.674592i	0.953309	+	0.301996i	$0.0976530\pi$
$312$	30016.2	+	51989.6i	0.0174570	+	0.0302364i
$313$	−1.43387e6	+	827846.i	−0.827274	+	0.477627i	−0.852918	−	0.522044i	$-0.825170\pi$
$313$	−1.43387e6	+	827846.i	−0.827274	+	0.477627i	0.0256445	+	0.999671i	$0.491836\pi$
$314$	728653.	+	420688.i	0.417058	+	0.240789i
$315$	−49069.6	−	28330.3i	−0.0278635	−	0.0160870i
$316$	−622725.	+	359530.i	−0.350815	+	0.202543i
$317$	−1.33919e6	−	2.31955e6i	−0.748506	−	1.29645i	−0.948539	−	0.316661i	$-0.897438\pi$
$317$	−1.33919e6	−	2.31955e6i	−0.748506	−	1.29645i	0.200033	−	0.979789i	$-0.435895\pi$
$318$	979990.	−	565797.i	0.543443	−	0.313757i
$319$		−	794658.i		−	0.437224i
$320$	−21018.8	−	12135.2i	−0.0114745	−	0.00662479i
$321$	−342612.	−	593422.i	−0.185584	−	0.321441i
$322$	−1.48037e6			−0.795665
$323$	−1.04725e6			−0.558525
$324$	−174958.	−	303036.i	−0.0925916	−	0.160373i
$325$			247990.i			0.130234i
$326$	557750.	−	966052.i	0.290667	−	0.503450i
$327$		−	1.70775e6i		−	0.883192i
$328$	−98336.7	−	56774.7i	−0.0504697	−	0.0291387i
$329$	563453.	−	975929.i	0.286991	−	0.497082i
$330$	−79809.3	+	138234.i	−0.0403430	+	0.0698762i
$331$	1.91245e6	−	1.10415e6i	0.959445	−	0.553936i	0.0634428	−	0.997985i	$-0.479792\pi$
$331$	1.91245e6	−	1.10415e6i	0.959445	−	0.553936i	0.896002	+	0.444050i	$0.146459\pi$
$332$	−1.06096e6			−0.528266
$333$	−714775.	−	523676.i	−0.353231	−	0.258793i
$334$	519574.			0.254848
$335$	−293723.	+	169581.i	−0.142997	+	0.0825591i
$336$	−134437.	+	232852.i	−0.0649638	+	0.112521i
$337$	937543.	−	1.62387e6i	0.449693	−	0.778891i	−0.548673	−	0.836037i	$-0.684867\pi$
$337$	937543.	−	1.62387e6i	0.449693	−	0.778891i	0.998366	+	0.0571458i	$0.0182000\pi$
$338$	1.26388e6	+	729703.i	0.601749	+	0.347420i
$339$		−	976053.i		−	0.461290i
$340$	64164.1	−	111136.i	0.0301020	−	0.0521381i
$341$			1.39402e6i			0.649208i
$342$	164650.	+	285183.i	0.0761198	+	0.131843i
$343$	−2.29501e6			−1.05329
$344$	786203.			0.358211
$345$	142599.	+	246989.i	0.0645014	+	0.111720i
$346$	186893.	+	107902.i	0.0839270	+	0.0484553i
$347$			3.74737e6i			1.67072i	0.549705	+	0.835359i	$0.314740\pi$
$347$			3.74737e6i			1.67072i	−0.549705	+	0.835359i	$0.685260\pi$
$348$	−223334.	+	128942.i	−0.0988567	+	0.0570749i
$349$	−517588.	−	896489.i	−0.227468	−	0.393986i	0.729589	−	0.683886i	$-0.239711\pi$
$349$	−517588.	−	896489.i	−0.227468	−	0.393986i	−0.957057	+	0.289900i	$0.906378\pi$
$350$	−961898.	+	555352.i	−0.419719	+	0.242325i
$351$	283836.	+	163873.i	0.122970	+	0.0709969i
$352$	−511001.	−	295027.i	−0.219819	−	0.126913i
$353$	−3.77851e6	+	2.18152e6i	−1.61392	+	0.931800i	−0.625476	+	0.780243i	$0.715095\pi$
$353$	−3.77851e6	+	2.18152e6i	−1.61392	+	0.931800i	−0.988449	+	0.151557i	$0.951571\pi$
$354$	−141495.	−	245077.i	−0.0600115	−	0.103943i
$355$	35864.4	−	20706.3i	0.0151040	−	0.00872030i
$356$		−	2.29520e6i		−	0.959832i
$357$	−1.23119e6	−	710829.i	−0.511275	−	0.295185i
$358$	−543933.	−	942120.i	−0.224305	−	0.388507i
$359$	4.39221e6			1.79865			0.899325	−	0.437280i	$-0.144058\pi$
$359$	4.39221e6			1.79865			0.899325	+	0.437280i	$0.144058\pi$
$360$	−40352.1			−0.0164101
$361$	−938756.	−	1.62597e6i	−0.379127	−	0.656667i
$362$		−	894697.i		−	0.358843i
$363$	−999167.	+	1.73061e6i	−0.397989	+	0.689338i
$364$		−	115400.i		−	0.0456513i
$365$	−416548.	−	240494.i	−0.163656	−	0.0944871i
$366$	−148949.	+	257988.i	−0.0581214	+	0.100669i
$367$	826379.	−	1.43133e6i	0.320269	−	0.554721i	−0.660275	−	0.751024i	$-0.729560\pi$
$367$	826379.	−	1.43133e6i	0.320269	−	0.554721i	0.980543	+	0.196303i	$0.0628935\pi$
$368$	−913031.	+	527138.i	−0.351452	+	0.202911i
$369$	−188788.			−0.0721786
$370$	180625.	−	79559.2i	0.0685920	−	0.0302124i
$371$	−2.17526e6			−0.820497
$372$	391781.	−	226195.i	0.146787	−	0.0847473i
$373$	98318.2	−	170292.i	0.0365900	−	0.0633757i	−0.847151	−	0.531353i	$-0.821684\pi$
$373$	98318.2	−	170292.i	0.0365900	−	0.0633757i	0.883740	+	0.467977i	$0.155017\pi$
$374$	1.55993e6	−	2.70189e6i	0.576670	−	0.998822i
$375$	372731.	+	215197.i	0.136873	+	0.0790237i
$376$		−	802550.i		−	0.292754i
$377$	55341.4	−	95854.1i	0.0200538	−	0.0347342i
$378$			1.46792e6i			0.528411i
$379$	763019.	+	1.32159e6i	0.272859	+	0.472605i	0.969593	−	0.244725i	$-0.0786976\pi$
$379$	763019.	+	1.32159e6i	0.272859	+	0.472605i	−0.696734	+	0.717330i	$0.745364\pi$
$380$	−73350.2			−0.0260581
$381$	−726461.			−0.256389
$382$	801751.	+	1.38867e6i	0.281113	+	0.486902i
$383$	−3.01012e6	−	1.73790e6i	−1.04855	−	0.605378i	−0.126304	−	0.991992i	$-0.540311\pi$
$383$	−3.01012e6	−	1.73790e6i	−1.04855	−	0.605378i	−0.922242	+	0.386614i	$0.873645\pi$
$384$			191485.i			0.0662684i
$385$	265726.	−	153417.i	0.0913656	−	0.0527500i
$386$	776613.	+	1.34513e6i	0.265300	+	0.459512i
$387$	1.13202e6	−	653572.i	0.384217	−	0.221828i
$388$	224142.	+	129409.i	0.0755865	+	0.0436399i
$389$	884837.	+	510861.i	0.296476	+	0.171170i	0.640859	−	0.767659i	$-0.278578\pi$
$389$	884837.	+	510861.i	0.296476	+	0.171170i	−0.344383	+	0.938829i	$0.611912\pi$
$390$	−19253.7	+	11116.1i	−0.00640991	+	0.00370076i
$391$	−2.78721e6	−	4.82759e6i	−0.921993	−	1.59694i
$392$	−483927.	+	279395.i	−0.159061	+	0.0918341i
$393$			223887.i			0.0731220i
$394$	2.85630e6	+	1.64909e6i	0.926966	+	0.535184i
$395$	−133147.	−	230618.i	−0.0429378	−	0.0743705i
$396$	−981026.			−0.314371
$397$	5.05124e6			1.60850			0.804252	−	0.594289i	$-0.202566\pi$
$397$	5.05124e6			1.60850			0.804252	+	0.594289i	$0.202566\pi$
$398$	1.40198e6	+	2.42830e6i	0.443644	+	0.768414i
$399$			812594.i			0.255530i
$400$	−395506.	+	685036.i	−0.123596	+	0.214074i
$401$			1.84898e6i			0.574210i	0.957899	+	0.287105i	$0.0926928\pi$
$401$			1.84898e6i			0.574210i	−0.957899	+	0.287105i	$0.907307\pi$
$402$	2.31737e6	+	1.33793e6i	0.715204	+	0.412923i
$403$	−97082.2	+	168151.i	−0.0297767	+	0.0515748i
$404$	473054.	−	819354.i	0.144197	−	0.249757i
$405$	112226.	−	64793.5i	0.0339981	−	0.0196288i
$406$	495729.			0.149255
$407$	4.39128e6	−	1.93421e6i	1.31403	−	0.578786i
$408$	−1.01246e6			−0.301113
$409$	−4.83373e6	+	2.79075e6i	−1.42881	+	0.824923i	−0.997027	−	0.0770553i	$-0.975448\pi$
$409$	−4.83373e6	+	2.79075e6i	−1.42881	+	0.824923i	−0.431782	+	0.901978i	$0.642115\pi$
$410$	21025.8	−	36417.7i	0.00617721	−	0.0106992i
$411$	262384.	−	454462.i	0.0766183	−	0.132707i
$412$	1.39137e6	+	803306.i	0.403830	+	0.233151i
$413$			543993.i			0.156934i
$414$	−876423.	+	1.51801e6i	−0.251312	+	0.435285i
$415$		−	392912.i		−	0.111989i
$416$	−41092.3	−	71174.0i	−0.0116420	−	0.0201645i
$417$	−3.43897e6			−0.968476
$418$	−1.78326e6			−0.499200
$419$	707792.	+	1.22593e6i	0.196956	+	0.341139i	0.947540	−	0.319637i	$-0.103561\pi$
$419$	707792.	+	1.22593e6i	0.196956	+	0.341139i	−0.750584	+	0.660775i	$0.770228\pi$
$420$	−86233.9	−	49787.1i	−0.0238536	−	0.0137719i
$421$		−	3.77034e6i		−	1.03675i	−0.855152	−	0.518377i	$-0.826536\pi$
$421$		−	3.77034e6i		−	1.03675i	0.855152	−	0.518377i	$-0.173464\pi$
$422$	1.72403e6	−	995370.i	0.471264	−	0.272084i
$423$	−667162.	−	1.15556e6i	−0.181293	−	0.314008i
$424$	−1.34161e6	+	774580.i	−0.362420	+	0.209243i
$425$	−3.62208e6	−	2.09121e6i	−0.972716	−	0.561598i
$426$	−282957.	−	163365.i	−0.0755434	−	0.0436150i
$427$	495930.	−	286325.i	0.131629	−	0.0759959i
$428$	469038.	+	812398.i	0.123765	+	0.214368i
$429$	−468088.	+	270251.i	−0.122796	+	0.0708963i
$430$			291160.i			0.0759383i
$431$	2.76338e6	+	1.59544e6i	0.716552	+	0.413702i	0.813482	−	0.581589i	$-0.197569\pi$
$431$	2.76338e6	+	1.59544e6i	0.716552	+	0.413702i	−0.0969300	+	0.995291i	$0.530902\pi$
$432$	522704.	+	905350.i	0.134756	+	0.233403i
$433$	−2.56752e6			−0.658104			−0.329052	−	0.944312i	$-0.606729\pi$
$433$	−2.56752e6			−0.658104			−0.329052	+	0.944312i	$0.606729\pi$
$434$	−869629.			−0.221620
$435$	−47751.9	−	82708.8i	−0.0120995	−	0.0209570i
$436$			2.33792e6i			0.588998i
$437$	−1.59312e6	+	2.75936e6i	−0.399066	+	0.691203i
$438$			3.79483e6i			0.945163i
$439$	4.08951e6	+	2.36108e6i	1.01277	+	0.584722i	0.912001	−	0.410188i	$-0.134537\pi$
$439$	4.08951e6	+	2.36108e6i	1.01277	+	0.584722i	0.100767	+	0.994910i	$0.467870\pi$
$440$	109259.	−	189243.i	0.0269046	−	0.0466002i
$441$	−464524.	+	804580.i	−0.113740	+	0.197003i
$442$	376328.	−	217273.i	0.0916243	−	0.0528993i
$443$	5.38159e6			1.30287			0.651436	−	0.758704i	$-0.274167\pi$
$443$	5.38159e6			1.30287			0.651436	+	0.758704i	$0.274167\pi$
$444$	−1.25613e6	−	920296.i	−0.302397	−	0.221549i
$445$	849997.			0.203478
$446$	3.03977e6	−	1.75501e6i	0.723609	−	0.417776i
$447$	−1.36206e6	+	2.35917e6i	−0.322425	+	0.558457i
$448$	184046.	−	318776.i	0.0433242	−	0.0750397i
$449$	1.70090e6	+	982017.i	0.398166	+	0.229881i	0.685692	−	0.727892i	$-0.259500\pi$
$449$	1.70090e6	+	982017.i	0.398166	+	0.229881i	−0.287527	+	0.957773i	$0.592833\pi$
$450$			1.31514e6i			0.306155i
$451$	511171.	−	885374.i	0.118338	−	0.204968i
$452$			1.33622e6i			0.307633i
$453$	−2.67340e6	−	4.63046e6i	−0.612093	−	1.06018i
$454$	3.94210e6			0.897611
$455$	42737.0			0.00967777
$456$	289353.	+	501174.i	0.0651653	+	0.112870i
$457$	3.06506e6	+	1.76961e6i	0.686512	+	0.396358i	0.802304	−	0.596916i	$-0.203607\pi$
$457$	3.06506e6	+	1.76961e6i	0.686512	+	0.396358i	−0.115792	+	0.993273i	$0.536941\pi$
$458$		−	2.66043e6i		−	0.592637i
$459$	−4.78698e6	+	2.76376e6i	−1.06055	+	0.612307i
$460$	−195219.	−	338129.i	−0.0430157	−	0.0745055i
$461$	−3.61540e6	+	2.08735e6i	−0.792327	+	0.457450i	−0.840781	−	0.541375i	$-0.817904\pi$
$461$	−3.61540e6	+	2.08735e6i	−0.792327	+	0.457450i	0.0484540	+	0.998825i	$0.484571\pi$
$462$	−2.09649e6	−	1.21041e6i	−0.456969	−	0.263831i
$463$	1.53965e6	+	888917.i	0.333787	+	0.192712i	0.657521	−	0.753436i	$-0.271605\pi$
$463$	1.53965e6	+	888917.i	0.333787	+	0.192712i	−0.323734	+	0.946148i	$0.604938\pi$
$464$	305745.	−	176522.i	0.0659272	−	0.0380631i
$465$	83768.4	+	145091.i	0.0179659	+	0.0311178i
$466$	−3.86070e6	+	2.22897e6i	−0.823571	+	0.475489i
$467$		−	1.41188e6i		−	0.299576i	−0.988718	−	0.149788i	$-0.952141\pi$
$467$		−	1.41188e6i		−	0.299576i	0.988718	−	0.149788i	$-0.0478591\pi$
$468$	−118334.	−	68320.4i	−0.0249745	−	0.0144190i
$469$	−2.57191e6	−	4.45467e6i	−0.539912	−	0.935155i
$470$	297214.			0.0620619
$471$	2.45836e6			0.510614
$472$	193708.	+	335512.i	0.0400215	+	0.0693192i
$473$			7.07858e6i			1.45477i
$474$	−1.05049e6	+	1.81949e6i	−0.214755	+	0.371967i
$475$			2.39060e6i			0.486153i
$476$	1.68551e6	+	973129.i	0.340968	+	0.196858i
$477$	−1.28782e6	+	2.23057e6i	−0.259155	+	0.448870i
$478$	3.15792e6	−	5.46968e6i	0.632166	−	1.09494i
$479$	6.15356e6	−	3.55276e6i	1.22543	−	0.707501i	0.259358	−	0.965781i	$-0.416489\pi$
$479$	6.15356e6	−	3.55276e6i	1.22543	−	0.707501i	0.966070	+	0.258280i	$0.0831556\pi$
$480$	−70914.0			−0.0140485
$481$	664392.	+	72506.1i	0.130937	+	0.0142893i
$482$	−2.06070e6			−0.404015
$483$	−3.74589e6	+	2.16269e6i	−0.730613	+	0.421820i
$484$	1.36787e6	−	2.36921e6i	0.265418	−	0.459717i
$485$	−47924.8	+	83008.2i	−0.00925137	+	0.0160238i
$486$	2.55208e6	+	1.47344e6i	0.490122	+	0.282972i
$487$		−	8.46037e6i		−	1.61647i	−0.588861	−	0.808234i	$-0.700424\pi$
$487$		−	8.46037e6i		−	1.61647i	0.588861	−	0.808234i	$-0.299576\pi$
$488$	203913.	−	353187.i	0.0387610	−	0.0671360i
$489$		−	3.25930e6i		−	0.616385i
$490$	−103470.	−	179216.i	−0.0194682	−	0.0337200i
$491$	835724.			0.156444			0.0782221	−	0.996936i	$-0.475076\pi$
$491$	835724.			0.156444			0.0782221	+	0.996936i	$0.475076\pi$
$492$	−331772.			−0.0617912
$493$	933349.	+	1.61661e6i	0.172952	+	0.299562i
$494$	−215102.	−	124189.i	−0.0396577	−	0.0228964i
$495$		−	363310.i		−	0.0666446i
$496$	−536351.	+	309662.i	−0.0978915	+	0.0565177i
$497$	314037.	+	543928.i	0.0570282	+	0.0987757i
$498$	−2.68462e6	+	1.54997e6i	−0.485076	+	0.280059i
$499$	1.96990e6	+	1.13732e6i	0.354155	+	0.204471i	0.666514	−	0.745493i	$-0.267786\pi$
$499$	1.96990e6	+	1.13732e6i	0.354155	+	0.204471i	−0.312359	+	0.949964i	$0.601119\pi$
$500$	−510272.	−	294605.i	−0.0912801	−	0.0527006i
$501$	1.31472e6	−	759053.i	0.234012	−	0.135107i
$502$	−1.64999e6	−	2.85787e6i	−0.292229	−	0.506155i
$503$	−7.95893e6	+	4.59509e6i	−1.40260	+	0.809793i	−0.994659	−	0.103214i	$-0.967087\pi$
$503$	−7.95893e6	+	4.59509e6i	−1.40260	+	0.809793i	−0.407944	+	0.913007i	$0.633754\pi$
$504$		−	611990.i		−	0.107317i
$505$	303437.	+	175190.i	0.0529469	+	0.0305689i
$506$	−4.74609e6	−	8.22047e6i	−0.824062	−	1.42732i
$507$	4.26413e6			0.736734
$508$	994530.			0.170985
$509$	−622863.	−	1.07883e6i	−0.106561	−	0.184569i	0.807814	−	0.589438i	$-0.200651\pi$
$509$	−622863.	−	1.07883e6i	−0.106561	−	0.184569i	−0.914375	+	0.404869i	$0.867317\pi$
$510$		−	374953.i		−	0.0638339i
$511$	3.64739e6	−	6.31747e6i	0.617917	−	1.07026i
$512$		−	262144.i		−	0.0441942i
$513$	2.73615e6	+	1.57972e6i	0.459036	+	0.265025i
$514$	−1.83216e6	+	3.17339e6i	−0.305883	+	0.529805i
$515$	−297494.	+	515275.i	−0.0494266	+	0.0856093i
$516$	1.98939e6	−	1.14857e6i	0.328924	−	0.189904i
$517$	7.22576e6			1.18893
$518$	1.20661e6	+	2.73940e6i	0.197580	+	0.448571i
$519$	630545.			0.102754
$520$	26358.4	−	15218.0i	0.00427475	−	0.00246803i
$521$	−3.93402e6	+	6.81393e6i	−0.634955	+	1.09977i	0.351570	+	0.936162i	$0.385648\pi$
$521$	−3.93402e6	+	6.81393e6i	−0.634955	+	1.09977i	−0.986525	+	0.163612i	$0.947685\pi$
$522$	293487.	−	508334.i	0.0471424	−	0.0816531i
$523$	4.38673e6	+	2.53268e6i	0.701273	+	0.404880i	0.807821	−	0.589428i	$-0.200647\pi$
$523$	4.38673e6	+	2.53268e6i	0.701273	+	0.404880i	−0.106549	+	0.994307i	$0.533980\pi$
$524$		−	306503.i		−	0.0487648i
$525$	−1.62264e6	+	2.81050e6i	−0.256936	+	0.445026i
$526$		−	135288.i		−	0.0213204i
$527$	−1.63732e6	−	2.83592e6i	−0.256807	−	0.444803i
$528$	−1.72403e6			−0.269129
$529$	−1.05238e7			−1.63506
$530$	−286856.	−	496849.i	−0.0443582	−	0.0768307i
$531$	557825.	+	322060.i	0.0858542	+	0.0495679i
$532$		−	1.11245e6i		−	0.170412i
$533$	123318.	−	71197.7i	0.0188022	−	0.0108555i
$534$	−3.35309e6	−	5.80771e6i	−0.508852	−	0.881358i
$535$	−300861.	+	173702.i	−0.0454445	+	0.0262374i
$536$	−3.17249e6	−	1.83164e6i	−0.476967	−	0.275377i
$537$	−2.75271e6	−	1.58928e6i	−0.411932	−	0.237829i
$538$	−286672.	+	165510.i	−0.0427002	+	0.0246530i
$539$	−2.51554e6	−	4.35704e6i	−0.372957	−	0.645980i
$540$	−335285.	+	193577.i	−0.0494800	+	0.0285673i
$541$		−	3.74360e6i		−	0.549916i	−0.961456	−	0.274958i	$-0.911336\pi$
$541$		−	3.74360e6i		−	0.549916i	0.961456	−	0.274958i	$-0.0886639\pi$
$542$	−592915.	−	342320.i	−0.0866951	−	0.0500534i
$543$	−1.30708e6	−	2.26392e6i	−0.190240	−	0.329505i
$544$	1.38607e6			0.200811
$545$	−865819.			−0.124864
$546$	−168590.	−	292006.i	−0.0242019	−	0.0419189i
$547$			4.09706e6i			0.585469i	0.956194	+	0.292735i	$0.0945653\pi$
$547$			4.09706e6i			0.585469i	−0.956194	+	0.292735i	$0.905435\pi$
$548$	−359205.	+	622161.i	−0.0510965	+	0.0885017i
$549$		−	678053.i		−	0.0960136i
$550$	−6.16772e6	−	3.56094e6i	−0.869397	−	0.501947i
$551$	533486.	−	924024.i	0.0748590	−	0.129660i
$552$	−1.54021e6	+	2.66772e6i	−0.215145	+	0.372642i
$553$	3.49761e6	−	2.01935e6i	0.486361	−	0.280801i
$554$	24056.0			0.00333003
$555$	340820.	−	465192.i	0.0469670	−	0.0641062i
$556$	4.70798e6			0.645873
$557$	3.21791e6	−	1.85786e6i	0.439477	−	0.253732i	−0.263899	−	0.964550i	$-0.585008\pi$
$557$	3.21791e6	−	1.85786e6i	0.439477	−	0.253732i	0.703376	+	0.710818i	$0.251675\pi$
$558$	−514846.	+	891740.i	−0.0699991	+	0.121242i
$559$	−492964.	+	853839.i	−0.0667246	+	0.115570i
$560$	118055.	+	68158.9i	0.0159079	+	0.00918444i
$561$		−	9.11572e6i		−	1.22288i
$562$	−1.15728e6	+	2.00446e6i	−0.154560	+	0.267706i
$563$			1.04053e7i			1.38351i	0.722132	+	0.691755i	$0.243162\pi$
$563$			1.04053e7i			1.38351i	−0.722132	+	0.691755i	$0.756838\pi$
$564$	−1.17246e6	−	2.03075e6i	−0.155203	−	0.268819i
$565$	−494853.			−0.0652161
$566$	855896.			0.112300
$567$	982674.	+	1.70204e6i	0.128366	+	0.222337i
$568$	387370.	+	223648.i	0.0503796	+	0.0290867i
$569$			6.45205e6i			0.835443i	0.908575	+	0.417721i	$0.137171\pi$
$569$			6.45205e6i			0.835443i	−0.908575	+	0.417721i	$0.862829\pi$
$570$	−185604.	+	107158.i	−0.0239276	+	0.0138146i
$571$	−5.76801e6	−	9.99049e6i	−0.740348	−	1.28232i	−0.952337	−	0.305049i	$-0.901327\pi$
$571$	−5.76801e6	−	9.99049e6i	−0.740348	−	1.28232i	0.211988	−	0.977272i	$-0.432006\pi$
$572$	640815.	−	369975.i	0.0818923	−	0.0472805i
$573$	4.05746e6	+	2.34258e6i	0.516259	+	0.298063i
$574$	552320.	+	318882.i	0.0699699	+	0.0403971i
$575$	−1.10202e7	+	6.36250e6i	−1.39001	+	0.802524i
$576$	−217921.	−	377450.i	−0.0273680	−	0.0474028i
$577$	7.49392e6	−	4.32662e6i	0.937064	−	0.541014i	0.0480255	−	0.998846i	$-0.484707\pi$
$577$	7.49392e6	−	4.32662e6i	0.937064	−	0.541014i	0.889039	+	0.457832i	$0.151374\pi$
$578$			1.64932e6i			0.205346i
$579$	3.93025e6	+	2.26913e6i	0.487218	+	0.281296i
$580$	65372.7	+	113229.i	0.00806912	+	0.0139761i
$581$	5.95900e6			0.732374
$582$	756219.			0.0925423
$583$	−6.97393e6	−	1.20792e7i	−0.849780	−	1.47186i
$584$		−	5.19514e6i		−	0.630326i
$585$	25301.6	−	43823.6i	0.00305674	−	0.00529442i
$586$		−	9.89793e6i		−	1.19069i
$587$	65021.3	+	37540.1i	0.00778862	+	0.00449676i	0.503889	−	0.863768i	$-0.331902\pi$
$587$	65021.3	+	37540.1i	0.00778862	+	0.00449676i	−0.496101	+	0.868265i	$0.665235\pi$
$588$	−816345.	+	1.41395e6i	−0.0973712	+	0.168652i
$589$	−935863.	+	1.62096e6i	−0.111154	+	0.192524i
$590$	−124253.	+	71737.3i	−0.0146952	+	0.00848428i
$591$	9.63670e6			1.13491
$592$	1.71965e6	+	1.25989e6i	0.201668	+	0.147750i
$593$	7.07484e6			0.826190			0.413095	−	0.910688i	$-0.364448\pi$
$593$	7.07484e6			0.826190			0.413095	+	0.910688i	$0.364448\pi$
$594$	−8.15132e6	+	4.70617e6i	−0.947898	+	0.547269i
$595$	−360386.	+	624206.i	−0.0417326	+	0.0722829i
$596$	1.86467e6	−	3.22971e6i	0.215024	−	0.372433i
$597$	7.09509e6	+	4.09635e6i	0.814745	+	0.470393i
$598$		−	1.32210e6i		−	0.151186i
$599$	6.92158e6	−	1.19885e7i	0.788204	−	1.36521i	−0.138863	−	0.990312i	$-0.544345\pi$
$599$	6.92158e6	−	1.19885e7i	0.788204	−	1.36521i	0.927066	−	0.374897i	$-0.122322\pi$
$600$			2.31120e6i			0.262095i
$601$	−5.26126e6	−	9.11278e6i	−0.594161	−	1.02912i	−0.993665	−	0.112385i	$-0.964151\pi$
$601$	−5.26126e6	−	9.11278e6i	−0.594161	−	1.02912i	0.399504	−	0.916731i	$-0.369182\pi$
$602$	−4.41580e6			−0.496614
$603$	−6.09058e6			−0.682128
$604$	3.65989e6	+	6.33912e6i	0.408203	+	0.707028i
$605$	877408.	+	506571.i	0.0974570	+	0.0562668i
$606$		−	2.76437e6i		−	0.305783i
$607$	1.09721e7	−	6.33476e6i	1.20870	−	0.697845i	0.246227	−	0.969212i	$-0.420809\pi$
$607$	1.09721e7	−	6.33476e6i	1.20870	−	0.697845i	0.962476	+	0.271368i	$0.0874759\pi$
$608$	−396126.	−	686111.i	−0.0434585	−	0.0752723i
$609$	1.25438e6	−	724217.i	0.137052	−	0.0791272i
$610$	130798.	+	75516.5i	0.0142324	+	0.00821707i
$611$	871593.	+	503215.i	0.0944519	+	0.0545318i
$612$	1.99574e6	−	1.15224e6i	0.215390	−	0.124356i
$613$	4.97114e6	+	8.61027e6i	0.534325	+	0.925477i	0.999196	+	0.0400989i	$0.0127673\pi$
$613$	4.97114e6	+	8.61027e6i	0.534325	+	0.925477i	−0.464871	+	0.885378i	$0.653899\pi$
$614$	−7.98945e6	+	4.61271e6i	−0.855256	+	0.493782i
$615$		−	122867.i		−	0.0130993i
$616$	2.87010e6	+	1.65705e6i	0.304751	+	0.175948i
$617$	−5.51389e6	−	9.55033e6i	−0.583103	−	1.00996i	−0.995109	−	0.0987825i	$-0.968505\pi$
$617$	−5.51389e6	−	9.55033e6i	−0.583103	−	1.00996i	0.412006	−	0.911181i	$-0.364828\pi$
$618$	4.69424e6			0.494418
$619$	−1.75050e6			−0.183626			−0.0918132	−	0.995776i	$-0.529266\pi$
$619$	−1.75050e6			−0.183626			−0.0918132	+	0.995776i	$0.529266\pi$
$620$	−114680.	−	198631.i	−0.0119814	−	0.0207523i
$621$			1.68175e7i			1.74997i
$622$	−4.60259e6	+	7.97191e6i	−0.477008	+	0.826203i
$623$			1.28913e7i			1.33069i
$624$	−207958.	−	120065.i	−0.0213803	−	0.0123439i
$625$	−4.71885e6	+	8.17329e6i	−0.483210	+	0.836945i
$626$	3.31138e6	−	5.73548e6i	0.337733	−	0.584971i
$627$	−4.51233e6	+	2.60519e6i	−0.458386	+	0.264649i
$628$	−3.36551e6			−0.340527
$629$	−6.66159e6	+	9.09254e6i	−0.671354	+	0.916344i
$630$	226643.			0.0227505
$631$	3.69434e6	−	2.13293e6i	0.369372	−	0.213257i	−0.303812	−	0.952732i	$-0.598260\pi$
$631$	3.69434e6	−	2.13293e6i	0.369372	−	0.213257i	0.673184	+	0.739475i	$0.264926\pi$
$632$	1.43812e6	−	2.49090e6i	0.143220	−	0.248064i
$633$	2.90830e6	−	5.03732e6i	0.288489	−	0.499678i
$634$	9.27820e6	+	5.35677e6i	0.916729	+	0.529273i
$635$			368311.i			0.0362477i
$636$	−2.26319e6	+	3.91996e6i	−0.221860	+	0.384272i
$637$		−	700745.i		−	0.0684245i
$638$	1.58932e6	+	2.75278e6i	0.154582	+	0.267744i
$639$	743677.			0.0720497
$640$	97081.7			0.00936887
$641$	8.09882e6	+	1.40276e7i	0.778532	+	1.34846i	0.932788	+	0.360426i	$0.117369\pi$
$641$	8.09882e6	+	1.40276e7i	0.778532	+	1.34846i	−0.154255	+	0.988031i	$0.549298\pi$
$642$	2.37369e6	+	1.37045e6i	0.227293	+	0.131228i
$643$			1.93740e7i			1.84796i	0.382443	+	0.923979i	$0.375083\pi$
$643$			1.93740e7i			1.84796i	−0.382443	+	0.923979i	$0.624917\pi$
$644$	5.12815e6	−	2.96074e6i	0.487243	−	0.281310i
$645$	425360.	+	736745.i	0.0402585	+	0.0697297i
$646$	3.62777e6	−	2.09449e6i	0.342025	−	0.197468i
$647$	−1.36875e7	−	7.90250e6i	−1.28548	−	0.742170i	−0.307633	−	0.951505i	$-0.599537\pi$
$647$	−1.36875e7	−	7.90250e6i	−1.28548	−	0.742170i	−0.977844	+	0.209335i	$0.932870\pi$
$648$	1.21214e6	+	699832.i	0.113401	+	0.0654721i
$649$	−3.02079e6	+	1.74405e6i	−0.281519	+	0.162535i
$650$	−495980.	−	859062.i	−0.0460448	−	0.0797519i
$651$	−2.20049e6	+	1.27045e6i	−0.203501	+	0.117491i
$652$			4.46200e6i			0.411065i
$653$	−1.35436e7	−	7.81943e6i	−1.24295	−	0.717616i	−0.273254	−	0.961942i	$-0.588100\pi$
$653$	−1.35436e7	−	7.81943e6i	−1.24295	−	0.717616i	−0.969693	+	0.244326i	$0.921433\pi$
$654$	3.41550e6	+	5.91582e6i	0.312256	+	0.540843i
$655$	113509.			0.0103378
$656$	454198.			0.0412084
$657$	−4.31874e6	−	7.48027e6i	−0.390340	−	0.676089i
$658$			4.50762e6i			0.405866i
$659$	58474.4	−	101281.i	0.00524508	−	0.00908475i	−0.863391	−	0.504535i	$-0.831664\pi$
$659$	58474.4	−	101281.i	0.00524508	−	0.00908475i	0.868636	+	0.495451i	$0.164997\pi$
$660$		−	638474.i		−	0.0570537i
$661$	1.14749e7	+	6.62502e6i	1.02151	+	0.589772i	0.914542	−	0.404490i	$-0.132551\pi$
$661$	1.14749e7	+	6.62502e6i	1.02151	+	0.589772i	0.106972	+	0.994262i	$0.465884\pi$
$662$	−4.41661e6	+	7.64980e6i	−0.391692	+	0.678430i
$663$	634834.	−	1.09957e6i	0.0560889	−	0.0971488i
$664$	3.67526e6	−	2.12191e6i	0.323496	−	0.186770i
$665$	411980.			0.0361262
$666$	3.52341e6	+	384514.i	0.307806	+	0.0335913i
$667$	5.67942e6			0.494298
$668$	−1.79986e6	+	1.03915e6i	−0.156062	+	0.0901024i
$669$	5.12785e6	−	8.88170e6i	0.442966	−	0.767239i
$670$	678324.	−	1.17489e6i	0.0583781	−	0.101114i
$671$	3.17992e6	+	1.83593e6i	0.272653	+	0.157416i
$672$		−	1.07550e6i		−	0.0918727i
$673$	−6.38051e6	+	1.10514e7i	−0.543022	+	0.940542i	0.455706	+	0.890130i	$0.349387\pi$
$673$	−6.38051e6	+	1.10514e7i	−0.543022	+	0.940542i	−0.998729	+	0.0504117i	$0.983947\pi$
$674$			7.50034e6i			0.635962i
$675$	6.30898e6	+	1.09275e7i	0.532966	+	0.923124i
$676$	−5.83763e6			−0.491326
$677$	−1.57040e7			−1.31686			−0.658429	−	0.752643i	$-0.728779\pi$
$677$	−1.57040e7			−1.31686			−0.658429	+	0.752643i	$0.728779\pi$
$678$	1.95211e6	+	3.38115e6i	0.163091	+	0.282481i
$679$	−1.25892e6	−	726839.i	−0.104791	−	0.0605012i
$680$			513313.i			0.0425706i
$681$	9.97501e6	−	5.75907e6i	0.824224	−	0.475866i
$682$	−2.78805e6	−	4.82904e6i	−0.229530	−	0.397557i
$683$	−1.94946e7	+	1.12552e7i	−1.59905	+	0.923213i	−0.607381	+	0.794410i	$0.707780\pi$
$683$	−1.94946e7	+	1.12552e7i	−1.59905	+	0.923213i	−0.991670	+	0.128802i	$0.958887\pi$
$684$	−1.14073e6	−	658602.i	−0.0932274	−	0.0538248i
$685$	−230410.	−	133027.i	−0.0187618	−	0.0108321i
$686$	7.95014e6	−	4.59001e6i	0.645007	−	0.372395i
$687$	−3.88667e6	−	6.73190e6i	−0.314185	−	0.544184i
$688$	−2.72349e6	+	1.57241e6i	−0.219358	+	0.126647i
$689$		−	1.94271e6i		−	0.155905i
$690$	−987955.	−	570396.i	−0.0789977	−	0.0456094i
$691$	2.41843e6	+	4.18884e6i	0.192681	+	0.333733i	0.946138	−	0.323764i	$-0.104949\pi$
$691$	2.41843e6	+	4.18884e6i	0.192681	+	0.333733i	−0.753457	+	0.657497i	$0.771615\pi$
$692$	−863220.			−0.0685261
$693$	5.51006e6			0.435836
$694$	−7.49475e6	−	1.29813e7i	−0.590688	−	1.02310i
$695$			1.74354e6i			0.136921i
$696$	515767.	−	893335.i	0.0403581	−	0.0699022i
$697$			2.40154e6i			0.187244i
$698$	3.58596e6	+	2.07035e6i	0.278591	+	0.160844i
$699$	−6.51268e6	+	1.12803e7i	−0.504158	+	0.873227i
$700$	2.22141e6	−	3.84759e6i	0.171350	−	0.296786i
$701$	−2.13468e6	+	1.23246e6i	−0.164073	+	0.0947277i	−0.579788	−	0.814767i	$-0.696865\pi$
$701$	−2.13468e6	+	1.23246e6i	−0.164073	+	0.0947277i	0.415715	+	0.909495i	$0.363531\pi$
$702$	−1.31098e6			−0.100405
$703$	6.40468e6	+	698952.i	0.488775	+	0.0533407i
$704$	2.36021e6			0.179482
$705$	752064.	−	434204.i	0.0569878	−	0.0329019i
$706$	8.72609e6	−	1.51140e7i	0.658882	−	1.14122i
$707$	−2.65697e6	+	4.60200e6i	−0.199912	+	0.346257i
$708$	980309.	+	565982.i	0.0734987	+	0.0424345i
$709$		−	2.58092e7i		−	1.92823i	−0.265480	−	0.964116i	$-0.585531\pi$
$709$		−	2.58092e7i		−	1.92823i	0.265480	−	0.964116i	$-0.414469\pi$
$710$	−82825.2	+	143457.i	−0.00616618	+	0.0106801i
$711$		−	4.78206e6i		−	0.354765i
$712$	4.59039e6	+	7.95080e6i	0.339352	+	0.587774i
$713$	−9.96307e6			−0.733955
$714$	5.68663e6			0.417455
$715$	137015.	+	237318.i	0.0100232	+	0.0173606i
$716$	3.76848e6	+	2.17573e6i	0.274716	+	0.158607i
$717$		−	1.84538e7i		−	1.34057i
$718$	−1.52151e7	+	8.78442e6i	−1.10144	+	0.635919i
$719$	2.57359e6	+	4.45758e6i	0.185659	+	0.321571i	0.943798	−	0.330521i	$-0.107225\pi$
$719$	2.57359e6	+	4.45758e6i	0.185659	+	0.321571i	−0.758139	+	0.652093i	$0.773891\pi$
$720$	139784.	−	80704.3i	0.0100491	−	0.00580183i
$721$	−7.81479e6	−	4.51187e6i	−0.559859	−	0.323235i
$722$	6.50389e6	+	3.75502e6i	0.464334	+	0.268083i
$723$	−5.21435e6	+	3.01051e6i	−0.370983	+	0.214187i
$724$	1.78939e6	+	3.09932e6i	0.126870	+	0.219746i
$725$	3.69031e6	−	2.13060e6i	0.260746	−	0.150542i
$726$		−	7.99333e6i		−	0.562842i
$727$	−8.33777e6	−	4.81382e6i	−0.585078	−	0.337795i	0.178071	−	0.984018i	$-0.443014\pi$
$727$	−8.33777e6	−	4.81382e6i	−0.585078	−	0.337795i	−0.763149	+	0.646223i	$0.776348\pi$
$728$	230800.	+	399758.i	0.0161402	+	0.0279556i
$729$	1.39247e7			0.970433
$730$	1.92395e6			0.133625
$731$	−8.31399e6	−	1.44002e7i	−0.575461	−	0.996728i
$732$		−	1.19160e6i		−	0.0821961i
$733$	1.30238e7	−	2.25579e7i	0.895321	−	1.55074i	0.0619135	−	0.998082i	$-0.480280\pi$
$733$	1.30238e7	−	2.25579e7i	0.895321	−	1.55074i	0.833407	−	0.552659i	$-0.186387\pi$
$734$			6.61103e6i			0.452928i
$735$	−523639.	−	302323.i	−0.0357531	−	0.0206420i
$736$	2.10855e6	−	3.65212e6i	0.143480	−	0.248514i
$737$	1.64912e7	−	2.85635e7i	1.11836	−	1.93706i
$738$	653980.	−	377576.i	0.0442002	−	0.0255190i
$739$	−2.69962e6			−0.181841			−0.0909203	−	0.995858i	$-0.528981\pi$
$739$	−2.69962e6			−0.181841			−0.0909203	+	0.995858i	$0.528981\pi$
$740$	−466585.	+	636851.i	−0.0313221	+	0.0427522i
$741$	−725720.			−0.0485539
$742$	7.53533e6	−	4.35053e6i	0.502450	−	0.290089i
$743$	1.40837e7	−	2.43937e7i	0.935934	−	1.62108i	0.162973	−	0.986631i	$-0.447892\pi$
$743$	1.40837e7	−	2.43937e7i	0.935934	−	1.62108i	0.772961	−	0.634454i	$-0.218775\pi$
$744$	−904780.	+	1.56713e6i	−0.0599254	+	0.103794i
$745$	1.19608e6	+	690558.i	0.0789533	+	0.0455837i
$746$			786546.i			0.0517460i
$747$	3.52791e6	−	6.11051e6i	0.231321	−	0.400660i
$748$			1.24795e7i			0.815534i
$749$	−2.63441e6	−	4.56293e6i	−0.171585	−	0.297194i
$750$	−1.72157e6			−0.111756
$751$	2.02407e6			0.130956			0.0654781	−	0.997854i	$-0.479143\pi$
$751$	2.02407e6			0.130956			0.0654781	+	0.997854i	$0.479143\pi$
$752$	1.60510e6	+	2.78012e6i	0.103504	+	0.179274i
$753$	−8.35022e6	−	4.82100e6i	−0.536674	−	0.309849i
$754$			442731.i			0.0283604i
$755$	−2.34761e6	+	1.35540e6i	−0.149885	+	0.0865363i
$756$	−2.93583e6	−	5.08501e6i	−0.186821	−	0.323584i
$757$	−8.95551e6	+	5.17046e6i	−0.568003	+	0.327937i	−0.756351	−	0.654166i	$-0.773020\pi$
$757$	−8.95551e6	+	5.17046e6i	−0.568003	+	0.327937i	0.188349	+	0.982102i	$0.439687\pi$
$758$	−5.28635e6	−	3.05208e6i	−0.334182	−	0.192940i
$759$	−2.40188e7	−	1.38673e7i	−1.51338	−	0.873748i
$760$	254092.	−	146700.i	0.0159572	−	0.00921291i
$761$	−3.60142e6	−	6.23784e6i	−0.225430	−	0.390456i	0.731018	−	0.682358i	$-0.239045\pi$
$761$	−3.60142e6	−	6.23784e6i	−0.225430	−	0.390456i	−0.956448	+	0.291901i	$0.905712\pi$
$762$	2.51653e6	−	1.45292e6i	0.157006	−	0.0906473i
$763$		−	1.31312e7i		−	0.816571i
$764$	−5.55469e6	−	3.20700e6i	−0.344292	−	0.198777i
$765$	426718.	+	739098.i	0.0263626	+	0.0456613i
$766$	1.39032e7			0.856134
$767$	−485835.			−0.0298195
$768$	−382970.	−	663323.i	−0.0234294	−	0.0405809i
$769$			2.89610e7i			1.76603i	0.469345	+	0.883015i	$0.344490\pi$
$769$			2.89610e7i			1.76603i	−0.469345	+	0.883015i	$0.655510\pi$
$770$	−613669.	+	1.06291e6i	−0.0372999	+	0.0646053i
$771$			1.07065e7i			0.648652i
$772$	−5.38054e6	−	3.10645e6i	−0.324924	−	0.187595i
$773$	−618494.	+	1.07126e6i	−0.0372295	+	0.0644833i	−0.884040	−	0.467412i	$-0.845187\pi$
$773$	−618494.	+	1.07126e6i	−0.0372295	+	0.0644833i	0.846810	+	0.531895i	$0.178520\pi$
$774$	−2.61429e6	+	4.52808e6i	−0.156856	+	0.271683i
$775$	−6.47369e6	+	3.73759e6i	−0.387167	+	0.223531i
$776$	−1.03527e6			−0.0617161
$777$	7.05522e6	+	5.16896e6i	0.419235	+	0.307150i
$778$	−4.08689e6			−0.242071
$779$	1.18877e6	−	686339.i	0.0701868	−	0.0405224i
$780$	44464.4	−	77014.7i	0.00261684	−	0.00453249i
$781$	−2.01362e6	+	3.48768e6i	−0.118127	+	0.204602i
$782$	1.93104e7	+	1.11488e7i	1.12921	+	0.651948i
$783$		−	5.63164e6i		−	0.328269i
$784$	1.11758e6	−	1.93571e6i	0.0649365	−	0.112473i
$785$		−	1.24637e6i		−	0.0721894i
$786$	−447774.	−	775568.i	−0.0258525	−	0.0447779i
$787$	−2.92462e7			−1.68319			−0.841594	−	0.540111i	$-0.818382\pi$
$787$	−2.92462e7			−1.68319			−0.841594	+	0.540111i	$0.818382\pi$
$788$	−1.31927e7			−0.756865
$789$	−197644.	−	342330.i	−0.0113030	−	0.0195773i
$790$	922472.	+	532590.i	0.0525879	+	0.0303616i
$791$		−	7.50506e6i		−	0.426494i
$792$	3.39837e6	−	1.96205e6i	0.192512	−	0.111147i
$793$	255715.	+	442911.i	0.0144402	+	0.0250111i
$794$	−1.74980e7	+	1.01025e7i	−0.985003	+	0.568692i
$795$	−1.45171e6	−	838143.i	−0.0814631	−	0.0470328i
$796$	−9.71322e6	−	5.60793e6i	−0.543351	−	0.313704i
$797$	−5.56617e6	+	3.21363e6i	−0.310392	+	0.179205i	−0.647102	−	0.762403i	$-0.724019\pi$
$797$	−5.56617e6	+	3.21363e6i	−0.310392	+	0.179205i	0.336710	+	0.941609i	$0.390686\pi$
$798$	−1.62519e6	−	2.81491e6i	−0.0903434	−	0.156479i
$799$	−1.46997e7	+	8.48686e6i	−0.814593	+	0.470306i
$800$		−	3.16405e6i		−	0.174791i
$801$	1.32190e7	+	7.63202e6i	0.727979	+	0.420299i
$802$	−3.69795e6	−	6.40505e6i	−0.203014	−	0.351630i
$803$	4.67745e7			2.55988
$804$	−1.07035e7			−0.583961
$805$	1.09647e6	+	1.89914e6i	0.0596359	+	0.103292i
$806$		−	776657.i		−	0.0421106i
$807$	−483592.	+	837607.i	−0.0261394	+	0.0452748i
$808$			3.78443e6i			0.203926i
$809$	9.71439e6	+	5.60860e6i	0.521848	+	0.301289i	0.737690	−	0.675139i	$-0.235916\pi$
$809$	9.71439e6	+	5.60860e6i	0.521848	+	0.301289i	−0.215842	+	0.976428i	$0.569250\pi$
$810$	−259174.	+	448902.i	−0.0138797	+	0.0240403i
$811$	−1.84895e7	+	3.20248e7i	−0.987128	+	1.70976i	−0.355060	+	0.934843i	$0.615540\pi$
$811$	−1.84895e7	+	3.20248e7i	−0.987128	+	1.70976i	−0.632068	+	0.774913i	$0.717794\pi$
$812$	−1.71726e6	+	991458.i	−0.0913997	+	0.0527697i
$813$	−2.00040e6			−0.106143
$814$	−1.13434e7	+	1.54829e7i	−0.600044	+	0.819013i
$815$	−1.65245e6			−0.0871431
$816$	3.50728e6	−	2.02493e6i	0.184393	−	0.106459i
$817$	−4.75213e6	+	8.23093e6i	−0.249077	+	0.431413i
$818$	1.11630e7	−	1.93349e7i	0.583309	−	1.01032i
$819$	664640.	+	383730.i	0.0346239	+	0.0199901i
$820$			168206.i			0.00873590i
$821$	1.51163e7	−	2.61822e7i	0.782685	−	1.35565i	−0.147687	−	0.989034i	$-0.547183\pi$
$821$	1.51163e7	−	2.61822e7i	0.782685	−	1.35565i	0.930372	−	0.366617i	$-0.119484\pi$
$822$			2.09907e6i			0.108355i
$823$	6.08953e6	+	1.05474e7i	0.313389	+	0.542806i	0.979094	−	0.203409i	$-0.0652022\pi$
$823$	6.08953e6	+	1.05474e7i	0.313389	+	0.542806i	−0.665704	+	0.746216i	$0.731869\pi$
$824$	−6.42645e6			−0.329726
$825$	−2.08089e7			−1.06442
$826$	−1.08799e6	−	1.88445e6i	−0.0554847	−	0.0961023i
$827$	1.71055e7	+	9.87584e6i	0.869703	+	0.502123i	0.867249	−	0.497874i	$-0.165886\pi$
$827$	1.71055e7	+	9.87584e6i	0.869703	+	0.502123i	0.00245322	+	0.999997i	$0.499219\pi$
$828$		−	7.01139e6i		−	0.355409i
$829$	7.93477e6	−	4.58114e6i	0.401003	−	0.231519i	−0.285914	−	0.958255i	$-0.592297\pi$
$829$	7.93477e6	−	4.58114e6i	0.401003	−	0.231519i	0.686917	+	0.726736i	$0.258964\pi$
$830$	785824.	+	1.36109e6i	0.0395940	+	0.0685789i
$831$	60870.7	−	35143.7i	0.00305778	−	0.00176541i
$832$	284696.	+	164369.i	0.0142585	+	0.00823214i
$833$	1.02349e7	+	5.90914e6i	0.511060	+	0.295061i
$834$	1.19130e7	−	6.87795e6i	0.593068	−	0.342408i
$835$	−384835.	−	666554.i	−0.0191011	−	0.0330841i
$836$	6.17740e6	−	3.56652e6i	0.305696	−	0.176494i
$837$			9.87926e6i			0.487428i
$838$	−4.90372e6	−	2.83117e6i	−0.241221	−	0.139269i
$839$	−6.32023e6	−	1.09470e7i	−0.309976	−	0.536894i	0.668381	−	0.743819i	$-0.266988\pi$
$839$	−6.32023e6	−	1.09470e7i	−0.309976	−	0.536894i	−0.978357	+	0.206925i	$0.933654\pi$
$840$	398297.			0.0194764
$841$	1.86093e7			0.907277
$842$	7.54069e6	+	1.30609e7i	0.366548	+	0.634880i
$843$			6.76273e6i			0.327758i
$844$	−3.98148e6	+	6.89613e6i	−0.192393	+	0.333234i
$845$		−	2.16189e6i		−	0.104158i
$846$	4.62224e6	+	2.66865e6i	0.222037	+	0.128193i
$847$	−7.68279e6	+	1.33070e7i	−0.367968	+	0.637340i
$848$	3.09832e6	−	5.36645e6i	0.147957	−	0.256270i
$849$	2.16574e6	−	1.25039e6i	0.103119	−	0.0595355i
$850$	1.67297e7			0.794220
$851$	1.38238e7	+	3.13845e7i	0.654340	+	1.48556i
$852$	1.30692e6			0.0616809
$853$	−2.14612e7	+	1.23906e7i	−1.00991	+	0.583069i	−0.911164	−	0.412044i	$-0.864815\pi$
$853$	−2.14612e7	+	1.23906e7i	−1.00991	+	0.583069i	−0.0987414	+	0.995113i	$0.531482\pi$
$854$	−1.14530e6	+	1.98372e6i	−0.0537372	+	0.0930756i
$855$	243905.	−	422455.i	0.0114105	−	0.0197636i
$856$	−3.24959e6	−	1.87615e6i	−0.151581	−	0.0875152i
$857$		−	682075.i		−	0.0317234i	−0.999874	−	0.0158617i	$-0.994951\pi$
$857$		−	682075.i		−	0.0317234i	0.999874	−	0.0158617i	$-0.00504915\pi$
$858$	1.08100e6	−	1.87235e6i	0.0501313	−	0.0868299i
$859$			1.92255e7i			0.888987i	0.895782	+	0.444494i	$0.146616\pi$
$859$			1.92255e7i			0.888987i	−0.895782	+	0.444494i	$0.853384\pi$
$860$	−582320.	−	1.00861e6i	−0.0268482	−	0.0465025i
$861$	1.86344e6			0.0856657
$862$	−1.27635e7			−0.585063
$863$	−4.55380e6	−	7.88741e6i	−0.208136	−	0.360502i	0.742991	−	0.669301i	$-0.233406\pi$
$863$	−4.55380e6	−	7.88741e6i	−0.208136	−	0.360502i	−0.951127	+	0.308799i	$0.900073\pi$
$864$	−3.62140e6	−	2.09082e6i	−0.165041	−	0.0952865i
$865$		−	319682.i		−	0.0145271i
$866$	8.89416e6	−	5.13504e6i	0.403005	−	0.232675i
$867$	2.40952e6	+	4.17340e6i	0.108863	+	0.188557i
$868$	3.01248e6	−	1.73926e6i	0.135714	−	0.0783546i
$869$	2.24268e7	+	1.29481e7i	1.00744	+	0.581644i
$870$	330835.	+	191008.i	0.0148188	+	0.00855565i
$871$	3.97843e6	−	2.29695e6i	0.177691	−	0.102590i
$872$	−4.67584e6	−	8.09880e6i	−0.208242	−	0.360686i
$873$	−1.49064e6	+	860621.i	−0.0661968	+	0.0382188i
$874$		−	1.27450e7i		−	0.564365i
$875$	2.86600e6	+	1.65469e6i	0.126548	+	0.0730627i
$876$	−7.58965e6	−	1.31457e7i	−0.334166	−	0.578792i
$877$	2.55808e7			1.12309			0.561547	−	0.827445i	$-0.310207\pi$
$877$	2.55808e7			1.12309			0.561547	+	0.827445i	$0.310207\pi$
$878$	−1.88886e7			−0.826921
$879$	−1.44600e7	−	2.50455e7i	−0.631243	−	1.09335i
$880$			874075.i			0.0380489i
$881$	−410865.	+	711638.i	−0.0178344	+	0.0308901i	−0.874805	−	0.484475i	$-0.839011\pi$
$881$	−410865.	+	711638.i	−0.0178344	+	0.0308901i	0.856970	+	0.515366i	$0.172344\pi$
$882$		−	3.71619e6i		−	0.160852i
$883$	−1.81301e7	−	1.04674e7i	−0.782527	−	0.451792i	0.0547980	−	0.998497i	$-0.482549\pi$
$883$	−1.81301e7	−	1.04674e7i	−0.782527	−	0.451792i	−0.837325	+	0.546705i	$0.815882\pi$
$884$	−869092.	+	1.50531e6i	−0.0374055	+	0.0647882i
$885$	−209604.	+	363045.i	−0.00899584	+	0.0155812i
$886$	−1.86424e7	+	1.07632e7i	−0.797843	+	0.460635i
$887$	3.89955e7			1.66420			0.832100	−	0.554625i	$-0.187138\pi$
$887$	3.89955e7			1.66420			0.832100	+	0.554625i	$0.187138\pi$
$888$	6.19196e6	+	675737.i	0.263509	+	0.0287571i
$889$	−5.58590e6			−0.237049
$890$	−2.94448e6	+	1.69999e6i	−0.124604	+	0.0719403i
$891$	−6.30094e6	+	1.09135e7i	−0.265896	+	0.460545i
$892$	−7.02006e6	+	1.21591e7i	−0.295412	+	0.511669i
$893$	8.40208e6	+	4.85094e6i	0.352580	+	0.203562i
$894$		−	1.08965e7i		−	0.455978i
$895$	−805755.	+	1.39561e6i	−0.0336237	+	0.0582379i
$896$			1.47236e6i			0.0612696i
$897$	−1.93148e6	−	3.34542e6i	−0.0801510	−	0.138826i
$898$	−7.85613e6			−0.325101
$899$	3.33632e6			0.137679
$900$	−2.63028e6	−	4.55578e6i	−0.108242	−	0.187481i
$901$	2.83747e7	+	1.63822e7i	1.16445	+	0.672294i
$902$			4.08937e6i			0.167355i
$903$	−1.11736e7	+	6.45111e6i	−0.456011	+	0.263278i
$904$	−2.67245e6	−	4.62881e6i	−0.108765	−	0.188386i
$905$	−1.14779e6	+	662679.i	−0.0465846	+	0.0268956i
$906$	1.85218e7	+	1.06936e7i	0.749658	+	0.432815i
$907$	−1.06293e7	−	6.13682e6i	−0.429028	−	0.247700i	0.269904	−	0.962887i	$-0.413008\pi$
$907$	−1.06293e7	−	6.13682e6i	−0.429028	−	0.247700i	−0.698933	+	0.715187i	$0.746341\pi$
$908$	−1.36558e7	+	7.88421e6i	−0.549673	+	0.317354i
$909$	3.14601e6	+	5.44905e6i	0.126285	+	0.218731i
$910$	−148045.	+	85473.9i	−0.00592640	+	0.00342161i
$911$			1.44205e6i			0.0575685i	0.999586	+	0.0287843i	$0.00916358\pi$
$911$			1.44205e6i			0.0575685i	−0.999586	+	0.0287843i	$0.990836\pi$
$912$	−2.00470e6	−	1.15741e6i	−0.0798108	−	0.0460788i
$913$	1.91047e7	+	3.30902e7i	0.758512	+	1.31378i
$914$	−1.41569e7			−0.560535
$915$	441292.			0.0174250
$916$	5.32087e6	+	9.21602e6i	0.209529	+	0.362915i
$917$			1.72151e6i			0.0676062i
$918$	1.10551e7	−	1.91479e7i	0.432966	−	0.749920i
$919$		−	1.52705e7i		−	0.596439i	−0.954497	−	0.298219i	$-0.903607\pi$
$919$		−	1.52705e7i		−	0.596439i	0.954497	−	0.298219i	$-0.0963927\pi$
$920$	1.35252e6	+	780876.i	0.0526833	+	0.0304167i
$921$	−1.34775e7	+	2.33438e7i	−0.523554	+	0.906823i
$922$	8.34942e6	−	1.44616e7i	0.323466	−	0.560260i
$923$	−485777.	+	280463.i	−0.0187686	+	0.0108361i
$924$	9.68325e6			0.373114
$925$	2.07560e7	+	1.52067e7i	0.797607	+	0.584362i
$926$	−7.11133e6			−0.272536
$927$	−9.25318e6	+	5.34233e6i	−0.353665	+	0.204188i
$928$	−706088.	+	1.22298e6i	−0.0269147	+	0.0466176i
$929$	1.33659e7	−	2.31504e7i	0.508111	−	0.880074i	−0.491845	−	0.870683i	$-0.663677\pi$
$929$	1.33659e7	−	2.31504e7i	0.508111	−	0.880074i	0.999956	−	0.00939127i	$-0.00298938\pi$
$930$	−580365.	−	335074.i	−0.0220036	−	0.0127038i
$931$		−	6.75512e6i		−	0.255422i
$932$	8.91590e6	−	1.54428e7i	0.336221	−	0.582352i
$933$			2.68959e7i			1.01154i
$934$	2.82377e6	+	4.89091e6i	0.105916	+	0.183452i
$935$	−4.62161e6			−0.172888
$936$	546563.			0.0203916
$937$	−1.45648e7	−	2.52269e7i	−0.541944	−	0.938674i	−0.998792	−	0.0491297i	$-0.984355\pi$
$937$	−1.45648e7	−	2.52269e7i	−0.541944	−	0.938674i	0.456849	−	0.889544i	$-0.348978\pi$
$938$	1.78187e7	+	1.02876e7i	0.661254	+	0.381775i
$939$		−	1.93506e7i		−	0.716193i
$940$	−1.02958e6	+	594428.i	−0.0380050	+	0.0219422i
$941$	−4.84248e6	−	8.38742e6i	−0.178276	−	0.308784i	0.763014	−	0.646382i	$-0.223719\pi$
$941$	−4.84248e6	−	8.38742e6i	−0.178276	−	0.308784i	−0.941290	+	0.337598i	$0.890385\pi$
$942$	−8.51600e6	+	4.91671e6i	−0.312686	+	0.180529i
$943$	6.32776e6	+	3.65334e6i	0.231724	+	0.133786i
$944$	−1.34205e6	−	774833.i	−0.0490161	−	0.0282994i
$945$	1.88317e6	−	1.08725e6i	0.0685977	−	0.0396049i
$946$	−1.41572e7	−	2.45209e7i	−0.514337	−	0.890858i
$947$	−2.51218e7	+	1.45041e7i	−0.910283	+	0.525552i	−0.880522	−	0.474005i	$-0.842808\pi$
$947$	−2.51218e7	+	1.45041e7i	−0.910283	+	0.525552i	−0.0297608	+	0.999557i	$0.509475\pi$
$948$		−	8.40388e6i		−	0.303710i
$949$	5.64208e6	+	3.25745e6i	0.203364	+	0.117412i
$950$	−4.78120e6	−	8.28128e6i	−0.171881	−	0.297707i
$951$	3.13031e7			1.12237
$952$	−7.78503e6			−0.278399
$953$	−2.42068e7	−	4.19275e7i	−0.863387	−	1.49543i	−0.868640	−	0.495444i	$-0.835005\pi$
$953$	−2.42068e7	−	4.19275e7i	−0.863387	−	1.49543i	0.00525252	−	0.999986i	$-0.498328\pi$
$954$		−	1.03026e7i		−	0.366501i
$955$	1.18767e6	−	2.05711e6i	0.0421394	−	0.0729876i
$956$			2.52634e7i			0.894018i
$957$	8.04314e6	+	4.64371e6i	0.283887	+	0.163902i
$958$	−1.42110e7	+	2.46143e7i	−0.500279	+	0.866509i
$959$	2.01752e6	−	3.49445e6i	0.0708388	−	0.122696i
$960$	245653.	−	141828.i	0.00860289	−	0.00496688i
$961$	2.27764e7			0.795568
$962$	−2.44653e6	+	1.07762e6i	−0.0852341	+	0.0375428i
$963$	−6.23860e6			−0.216781
$964$	7.13848e6	−	4.12140e6i	0.247408	−	0.142841i
$965$	1.15044e6	−	1.99261e6i	0.0397689	−	0.0688818i
$966$	8.65077e6	−	1.49836e7i	0.298272	−	0.516621i
$967$	−4.24194e6	−	2.44909e6i	−0.145881	−	0.0842244i	0.425283	−	0.905060i	$-0.360175\pi$
$967$	−4.24194e6	−	2.44909e6i	−0.145881	−	0.0842244i	−0.571164	+	0.820836i	$0.693508\pi$
$968$			1.09429e7i			0.375357i
$969$	6.11974e6	−	1.05997e7i	0.209375	−	0.362647i
$970$		−	383398.i		−	0.0130834i
$971$	−1.49713e7	−	2.59311e7i	−0.509581	−	0.882619i	−0.999938	−	0.0110982i	$-0.996467\pi$
$971$	−1.49713e7	−	2.59311e7i	−0.509581	−	0.882619i	0.490358	−	0.871521i	$-0.336866\pi$
$972$	−1.17876e7			−0.400183
$973$	−2.64429e7			−0.895422
$974$	1.69207e7	+	2.93076e7i	0.571508	+	0.989880i
$975$	−2.51003e6	−	1.44917e6i	−0.0845605	−	0.0488210i
$976$			1.63130e6i			0.0548163i
$977$	4.54756e7	−	2.62553e7i	1.52420	−	0.879997i	0.524610	−	0.851343i	$-0.324211\pi$
$977$	4.54756e7	−	2.62553e7i	1.52420	−	0.879997i	0.999589	−	0.0286537i	$-0.00912200\pi$
$978$	6.51860e6	+	1.12905e7i	0.217925	+	0.377457i
$979$	−7.15850e7	+	4.13296e7i	−2.38707	+	1.37818i
$980$	716865.	+	413882.i	0.0238436	+	0.0137661i
$981$	−1.34651e7	−	7.77408e6i	−0.446722	−	0.257915i
$982$	−2.89503e6	+	1.67145e6i	−0.0958021	+	0.0553114i
$983$	−2.91264e6	−	5.04484e6i	−0.0961398	−	0.166519i	0.813944	−	0.580943i	$-0.197316\pi$
$983$	−2.91264e6	−	5.04484e6i	−0.0961398	−	0.166519i	−0.910084	+	0.414424i	$0.863983\pi$
$984$	1.14929e6	−	663544.i	0.0378392	−	0.0218465i
$985$		−	4.88575e6i		−	0.160450i
$986$	−6.46643e6	−	3.73339e6i	−0.211823	−	0.122296i
$987$	6.58525e6	+	1.14060e7i	0.215169	+	0.372683i
$988$	993516.			0.0323804
$989$	−5.05905e7			−1.64467
$990$	726621.	+	1.25854e6i	0.0235624	+	0.0408113i
$991$		−	4.33939e6i		−	0.140361i	−0.997534	−	0.0701803i	$-0.977643\pi$
$991$		−	4.33939e6i		−	0.140361i	0.997534	−	0.0701803i	$-0.0223574\pi$
$992$	1.23865e6	−	2.14540e6i	0.0399640	−	0.0692197i
$993$			2.58092e7i			0.830617i
$994$	−2.17571e6	−	1.25615e6i	−0.0698450	−	0.0403250i
$995$	2.07682e6	−	3.59717e6i	0.0665031	−	0.115187i
$996$	6.19987e6	−	1.07385e7i	0.198031	−	0.343000i
$997$	−448487.	+	258934.i	−0.0142893	+	0.00824995i	−0.507128	−	0.861871i	$-0.669293\pi$
$997$	−448487.	+	258934.i	−0.0142893	+	0.00824995i	0.492838	+	0.870121i	$0.335959\pi$
$998$	−9.09858e6			−0.289166
$999$	3.11205e7	−	1.37075e7i	0.986580	−	0.434555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.e.a.11.3	✓	28
37.27	even	6	inner	74.6.e.a.27.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.e.a.11.3	✓	28	1.1	even	1	trivial
74.6.e.a.27.3	yes	28	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.46410 + 2.00000i) q^{2} +(-5.84366 + 10.1215i) q^{3} +(8.00000 - 13.8564i) q^{4} +(5.13154 + 2.96270i) q^{5} -46.7492i q^{6} +(-44.9330 + 77.8262i) q^{7} +64.0000i q^{8} +(53.2034 + 92.1510i) q^{9} -23.7016 q^{10} -576.224 q^{11} +(93.4985 + 161.944i) q^{12} +(-69.5059 - 40.1292i) q^{13} -359.464i q^{14} +(-59.9739 + 34.6260i) q^{15} +(-128.000 - 221.703i) q^{16} +(1172.24 - 676.792i) q^{17} +(-368.604 - 212.814i) q^{18} +(-670.030 - 386.842i) q^{19} +(82.1047 - 47.4032i) q^{20} +(-525.146 - 909.579i) q^{21} +(1996.10 - 1152.45i) q^{22} -4118.27i q^{23} +(-647.777 - 373.994i) q^{24} +(-1544.94 - 2675.92i) q^{25} +321.034 q^{26} -4083.63 q^{27} +(718.928 + 1245.22i) q^{28} +1379.08i q^{29} +(138.504 - 239.896i) q^{30} -2419.24i q^{31} +(886.810 + 512.000i) q^{32} +(3367.25 - 5832.26i) q^{33} +(-2707.17 + 4688.95i) q^{34} +(-461.151 + 266.246i) q^{35} +1702.51 q^{36} +(-7620.79 + 3356.70i) q^{37} +3094.74 q^{38} +(812.337 - 469.003i) q^{39} +(-189.613 + 328.419i) q^{40} +(-887.105 + 1536.51i) q^{41} +(3638.32 + 2100.58i) q^{42} -12284.4i q^{43} +(-4609.79 + 7984.40i) q^{44} +630.502i q^{45} +(8236.54 + 14266.1i) q^{46} -12539.8 q^{47} +2991.95 q^{48} +(4365.55 + 7561.36i) q^{49} +(10703.7 + 6179.78i) q^{50} +15819.7i q^{51} +(-1112.09 + 642.068i) q^{52} +(12102.8 + 20962.7i) q^{53} +(14146.1 - 8167.25i) q^{54} +(-2956.92 - 1707.18i) q^{55} +(-4980.88 - 2875.71i) q^{56} +(7830.85 - 4521.14i) q^{57} +(-2758.16 - 4777.27i) q^{58} +(5242.38 - 3026.69i) q^{59} +1108.03i q^{60} +(-5518.55 - 3186.14i) q^{61} +(4838.47 + 8380.48i) q^{62} -9562.35 q^{63} -4096.00 q^{64} +(-237.782 - 411.850i) q^{65} +26938.0i q^{66} +(-28619.3 + 49570.2i) q^{67} -21657.3i q^{68} +(41683.1 + 24065.7i) q^{69} +(1064.98 - 1844.60i) q^{70} +(3494.50 - 6052.65i) q^{71} +(-5897.66 + 3405.02i) q^{72} -81174.1 q^{73} +(19685.8 - 26869.5i) q^{74} +36112.5 q^{75} +(-10720.5 + 6189.47i) q^{76} +(25891.5 - 44845.3i) q^{77} +(-1876.01 + 3249.35i) q^{78} +(-38920.3 - 22470.6i) q^{79} -1516.90i q^{80} +(10934.9 - 18939.8i) q^{81} -7096.84i q^{82} +(-33154.9 - 57426.0i) q^{83} -16804.7 q^{84} +8020.51 q^{85} +(24568.8 + 42554.5i) q^{86} +(-13958.4 - 8058.86i) q^{87} -36878.3i q^{88} +(124231. - 71724.9i) q^{89} +(-1261.00 - 2184.12i) q^{90} +(6246.22 - 3606.25i) q^{91} +(-57064.4 - 32946.2i) q^{92} +(24486.3 + 14137.2i) q^{93} +(43439.3 - 25079.7i) q^{94} +(-2292.19 - 3970.19i) q^{95} +(-10364.4 + 5983.90i) q^{96} +16176.1i q^{97} +(-30245.4 - 17462.2i) q^{98} +(-30657.1 - 53099.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} - 736 q^{10} + 464 q^{11} + 320 q^{12} + 72 q^{13} + 3960 q^{15} - 3584 q^{16} + 1530 q^{17} - 1944 q^{19} - 1440 q^{20} - 192 q^{21} - 3028 q^{25}+ \cdots - 401224 q^{99}+O(q^{100}) \) 28 * q - 20 * q^3 + 224 * q^4 - 90 * q^5 - 156 * q^7 - 586 * q^9 - 736 * q^10 + 464 * q^11 + 320 * q^12 + 72 * q^13 + 3960 * q^15 - 3584 * q^16 + 1530 * q^17 - 1944 * q^19 - 1440 * q^20 - 192 * q^21 - 3028 * q^25 - 5280 * q^26 + 36400 * q^27 + 2496 * q^28 - 4368 * q^30 - 2996 * q^33 + 1360 * q^34 - 21636 * q^35 - 18752 * q^36 + 45178 * q^37 - 14304 * q^38 + 14592 * q^39 - 5888 * q^40 + 12894 * q^41 - 26832 * q^42 + 3712 * q^44 - 22080 * q^46 - 39512 * q^47 + 10240 * q^48 + 8262 * q^49 - 44640 * q^50 + 1152 * q^52 + 47912 * q^53 - 101520 * q^54 + 70236 * q^55 + 99984 * q^57 + 51968 * q^58 - 74568 * q^59 - 8274 * q^61 - 22768 * q^62 - 137048 * q^63 - 114688 * q^64 + 33104 * q^65 - 7904 * q^67 - 69096 * q^69 + 65056 * q^70 + 9788 * q^71 + 256784 * q^73 - 8480 * q^74 + 518544 * q^75 - 31104 * q^76 - 86340 * q^77 + 89776 * q^78 - 82740 * q^79 - 174814 * q^81 + 19892 * q^83 - 6144 * q^84 - 167972 * q^85 + 119536 * q^86 - 200424 * q^87 - 223482 * q^89 + 59504 * q^90 - 53016 * q^91 + 198912 * q^92 - 227844 * q^93 + 158736 * q^94 - 140012 * q^95 - 168864 * q^98 - 401224 * q^99

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