LMFDB - Embedded newform 74.6.e.a.11.13

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			11.13
Character	$\chi$	$=$	74.11
Dual form			74.6.e.a.27.13

$q$-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} +(7.72221 - 13.3753i) q^{3} +(8.00000 - 13.8564i) q^{4} +(53.6293 + 30.9629i) q^{5} -61.7777i q^{6} +(57.7242 - 99.9812i) q^{7} -64.0000i q^{8} +(2.23485 + 3.87087i) q^{9} +247.703 q^{10} +60.8054 q^{11} +(-123.555 - 214.004i) q^{12} +(190.071 + 109.737i) q^{13} -461.793i q^{14} +(828.273 - 478.204i) q^{15} +(-128.000 - 221.703i) q^{16} +(-384.866 + 222.203i) q^{17} +(15.4835 + 8.93939i) q^{18} +(-2240.93 - 1293.80i) q^{19} +(858.068 - 495.406i) q^{20} +(-891.517 - 1544.15i) q^{21} +(210.636 - 121.611i) q^{22} -1199.63i q^{23} +(-856.017 - 494.222i) q^{24} +(354.898 + 614.701i) q^{25} +877.900 q^{26} +3822.03 q^{27} +(-923.587 - 1599.70i) q^{28} +6308.54i q^{29} +(1912.81 - 3313.09i) q^{30} +672.092i q^{31} +(-886.810 - 512.000i) q^{32} +(469.552 - 813.289i) q^{33} +(-888.810 + 1539.46i) q^{34} +(6191.41 - 3574.61i) q^{35} +71.5151 q^{36} +(4486.09 - 7015.62i) q^{37} -10350.4 q^{38} +(2935.54 - 1694.83i) q^{39} +(1981.62 - 3432.27i) q^{40} +(-10399.7 + 18012.8i) q^{41} +(-6176.61 - 3566.07i) q^{42} +2379.72i q^{43} +(486.443 - 842.544i) q^{44} +276.789i q^{45} +(-2399.26 - 4155.64i) q^{46} +4071.54 q^{47} -3953.77 q^{48} +(1739.34 + 3012.62i) q^{49} +(2458.81 + 1419.59i) q^{50} +6863.58i q^{51} +(3041.13 - 1755.80i) q^{52} +(11885.4 + 20586.2i) q^{53} +(13239.9 - 7644.05i) q^{54} +(3260.95 + 1882.71i) q^{55} +(-6398.80 - 3694.35i) q^{56} +(-34609.9 + 19982.0i) q^{57} +(12617.1 + 21853.4i) q^{58} +(-20029.3 + 11563.9i) q^{59} -15302.5i q^{60} +(19953.8 + 11520.4i) q^{61} +(1344.18 + 2328.19i) q^{62} +516.019 q^{63} -4096.00 q^{64} +(6795.57 + 11770.3i) q^{65} -3756.42i q^{66} +(-15175.3 + 26284.4i) q^{67} +7110.48i q^{68} +(-16045.4 - 9263.79i) q^{69} +(14298.4 - 24765.6i) q^{70} +(4491.46 - 7779.44i) q^{71} +(247.736 - 143.030i) q^{72} -11342.9 q^{73} +(1509.03 - 33275.0i) q^{74} +10962.4 q^{75} +(-35854.9 + 20700.8i) q^{76} +(3509.94 - 6079.40i) q^{77} +(6779.33 - 11742.1i) q^{78} +(-9393.05 - 5423.08i) q^{79} -15853.0i q^{80} +(28971.4 - 50180.0i) q^{81} +83197.8i q^{82} +(-6064.10 - 10503.3i) q^{83} -28528.5 q^{84} -27520.1 q^{85} +(4759.44 + 8243.59i) q^{86} +(84378.5 + 48715.9i) q^{87} -3891.55i q^{88} +(17964.9 - 10372.0i) q^{89} +(553.578 + 958.825i) q^{90} +(21943.4 - 12669.0i) q^{91} +(-16622.5 - 9597.03i) q^{92} +(8989.41 + 5190.04i) q^{93} +(14104.2 - 8143.08i) q^{94} +(-80119.6 - 138771. i) q^{95} +(-13696.3 + 7907.55i) q^{96} -56422.7i q^{97} +(12050.5 + 6957.35i) q^{98} +(135.891 + 235.370i) 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
$3$	7.72221	−	13.3753i	0.495380	−	0.858024i	−0.504606	−	0.863350i	$-0.668362\pi$
$3$	7.72221	−	13.3753i	0.495380	−	0.858024i	0.999986	+	0.00532629i	$0.00169542\pi$
$4$	8.00000	−	13.8564i	0.250000	−	0.433013i
$5$	53.6293	+	30.9629i	0.959349	+	0.553881i	0.895973	−	0.444109i	$-0.146480\pi$
$5$	53.6293	+	30.9629i	0.959349	+	0.553881i	0.0633766	+	0.997990i	$0.479813\pi$
$6$		−	61.7777i		−	0.700573i
$7$	57.7242	−	99.9812i	0.445259	−	0.771211i	−0.552811	−	0.833307i	$-0.686445\pi$
$7$	57.7242	−	99.9812i	0.445259	−	0.771211i	0.998070	+	0.0620953i	$0.0197783\pi$
$8$		−	64.0000i		−	0.353553i
$9$	2.23485	+	3.87087i	0.00919690	+	0.0159295i
$10$	247.703			0.783305
$11$	60.8054			0.151517			0.0757584	−	0.997126i	$-0.475862\pi$
$11$	60.8054			0.151517			0.0757584	+	0.997126i	$0.475862\pi$
$12$	−123.555	−	214.004i	−0.247690	−	0.429012i
$13$	190.071	+	109.737i	0.311930	+	0.180093i	0.647790	−	0.761819i	$-0.275693\pi$
$13$	190.071	+	109.737i	0.311930	+	0.180093i	−0.335860	+	0.941912i	$0.609027\pi$
$14$		−	461.793i		−	0.629691i
$15$	828.273	−	478.204i	0.950485	−	0.548763i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−384.866	+	222.203i	−0.322989	+	0.186478i	−0.652724	−	0.757596i	$-0.726374\pi$
$17$	−384.866	+	222.203i	−0.322989	+	0.186478i	0.329735	+	0.944073i	$0.393041\pi$
$18$	15.4835	+	8.93939i	0.0112639	+	0.00650319i
$19$	−2240.93	−	1293.80i	−1.42411	−	0.822212i	−0.427465	−	0.904032i	$-0.640593\pi$
$19$	−2240.93	−	1293.80i	−1.42411	−	0.822212i	−0.996647	+	0.0818204i	$0.973927\pi$
$20$	858.068	−	495.406i	0.479675	−	0.276940i
$21$	−891.517	−	1544.15i	−0.441145	−	0.764086i
$22$	210.636	−	121.611i	0.0927847	−	0.0535692i
$23$		−	1199.63i		−	0.472854i	−0.971649	−	0.236427i	$-0.924024\pi$
$23$		−	1199.63i		−	0.472854i	0.971649	−	0.236427i	$-0.0759765\pi$
$24$	−856.017	−	494.222i	−0.303357	−	0.175143i
$25$	354.898	+	614.701i	0.113567	+	0.196704i
$26$	877.900			0.254690
$27$	3822.03			1.00898
$28$	−923.587	−	1599.70i	−0.222629	−	0.385606i
$29$			6308.54i			1.39295i	0.717583	+	0.696473i	$0.245248\pi$
$29$			6308.54i			1.39295i	−0.717583	+	0.696473i	$0.754752\pi$
$30$	1912.81	−	3313.09i	0.388034	−	0.672095i
$31$			672.092i			0.125610i	0.998026	+	0.0628050i	$0.0200046\pi$
$31$			672.092i			0.125610i	−0.998026	+	0.0628050i	$0.979995\pi$
$32$	−886.810	−	512.000i	−0.153093	−	0.0883883i
$33$	469.552	−	813.289i	0.0750584	−	0.130005i
$34$	−888.810	+	1539.46i	−0.131860	+	0.228388i
$35$	6191.41	−	3574.61i	0.854318	−	0.493241i
$36$	71.5151			0.00919690
$37$	4486.09	−	7015.62i	0.538721	−	0.842484i
$37$	4486.09	−	7015.62i	0.538721	−	0.842484i
$38$	−10350.4			−1.16278
$39$	2935.54	−	1694.83i	0.309048	−	0.178429i
$40$	1981.62	−	3432.27i	0.195826	−	0.339181i
$41$	−10399.7	+	18012.8i	−0.966189	+	1.67349i	−0.259802	+	0.965662i	$0.583657\pi$
$41$	−10399.7	+	18012.8i	−0.966189	+	1.67349i	−0.706387	+	0.707826i	$0.749676\pi$
$42$	−6176.61	−	3566.07i	−0.540290	−	0.311937i
$43$			2379.72i			0.196270i	0.995173	+	0.0981352i	$0.0312878\pi$
$43$			2379.72i			0.196270i	−0.995173	+	0.0981352i	$0.968712\pi$
$44$	486.443	−	842.544i	0.0378792	−	0.0656087i
$45$			276.789i			0.0203759i
$46$	−2399.26	−	4155.64i	−0.167179	−	0.289563i
$47$	4071.54			0.268852			0.134426	−	0.990924i	$-0.457081\pi$
$47$	4071.54			0.268852			0.134426	+	0.990924i	$0.457081\pi$
$48$	−3953.77			−0.247690
$49$	1739.34	+	3012.62i	0.103489	+	0.179248i
$50$	2458.81	+	1419.59i	0.139091	+	0.0803042i
$51$			6863.58i			0.369509i
$52$	3041.13	−	1755.80i	0.155965	−	0.0900465i
$53$	11885.4	+	20586.2i	0.581200	+	1.00667i	0.995337	+	0.0964539i	$0.0307500\pi$
$53$	11885.4	+	20586.2i	0.581200	+	1.00667i	−0.414137	+	0.910214i	$0.635917\pi$
$54$	13239.9	−	7644.05i	0.617874	−	0.356730i
$55$	3260.95	+	1882.71i	0.145357	+	0.0839222i
$56$	−6398.80	−	3694.35i	−0.272664	−	0.157423i
$57$	−34609.9	+	19982.0i	−1.41095	+	0.814615i
$58$	12617.1	+	21853.4i	0.492481	+	0.853002i
$59$	−20029.3	+	11563.9i	−0.749092	+	0.432489i	−0.825366	−	0.564598i	$-0.809031\pi$
$59$	−20029.3	+	11563.9i	−0.749092	+	0.432489i	0.0762734	+	0.997087i	$0.475698\pi$
$60$		−	15302.5i		−	0.548763i
$61$	19953.8	+	11520.4i	0.686597	+	0.396407i	0.802336	−	0.596873i	$-0.203590\pi$
$61$	19953.8	+	11520.4i	0.686597	+	0.396407i	−0.115739	+	0.993280i	$0.536924\pi$
$62$	1344.18	+	2328.19i	0.0444099	+	0.0769201i
$63$	516.019			0.0163800
$64$	−4096.00			−0.125000
$65$	6795.57	+	11770.3i	0.199500	+	0.345544i
$66$		−	3756.42i		−	0.106149i
$67$	−15175.3	+	26284.4i	−0.413000	+	0.715338i	−0.995216	−	0.0976966i	$-0.968853\pi$
$67$	−15175.3	+	26284.4i	−0.413000	+	0.715338i	0.582216	+	0.813034i	$0.302186\pi$
$68$			7110.48i			0.186478i
$69$	−16045.4	−	9263.79i	−0.405720	−	0.234243i
$70$	14298.4	−	24765.6i	0.348774	−	0.604094i
$71$	4491.46	−	7779.44i	0.105741	−	0.183148i	−0.808300	−	0.588771i	$-0.799612\pi$
$71$	4491.46	−	7779.44i	0.105741	−	0.183148i	0.914041	+	0.405623i	$0.132945\pi$
$72$	247.736	−	143.030i	0.00563193	−	0.00325160i
$73$	−11342.9			−0.249126			−0.124563	−	0.992212i	$-0.539753\pi$
$73$	−11342.9			−0.249126			−0.124563	+	0.992212i	$0.539753\pi$
$74$	1509.03	−	33275.0i	0.0320345	−	0.706381i
$75$	10962.4			0.225036
$76$	−35854.9	+	20700.8i	−0.712056	+	0.411106i
$77$	3509.94	−	6079.40i	0.0674642	−	0.116851i
$78$	6779.33	−	11742.1i	0.126168	−	0.218530i
$79$	−9393.05	−	5423.08i	−0.169332	−	0.0977639i	0.412939	−	0.910759i	$-0.364502\pi$
$79$	−9393.05	−	5423.08i	−0.169332	−	0.0977639i	−0.582271	+	0.812995i	$0.697836\pi$
$80$		−	15853.0i		−	0.276940i
$81$	28971.4	−	50180.0i	0.490634	−	0.849803i
$82$			83197.8i			1.36640i
$83$	−6064.10	−	10503.3i	−0.0966209	−	0.167352i	0.813663	−	0.581337i	$-0.197470\pi$
$83$	−6064.10	−	10503.3i	−0.0966209	−	0.167352i	−0.910284	+	0.413984i	$0.864137\pi$
$84$	−28528.5			−0.441145
$85$	−27520.1			−0.413145
$86$	4759.44	+	8243.59i	0.0693920	+	0.120191i
$87$	84378.5	+	48715.9i	1.19518	+	0.690038i
$88$		−	3891.55i		−	0.0535692i
$89$	17964.9	−	10372.0i	0.240409	−	0.138800i	−0.374956	−	0.927043i	$-0.622342\pi$
$89$	17964.9	−	10372.0i	0.240409	−	0.138800i	0.615365	+	0.788243i	$0.289009\pi$
$90$	553.578	+	958.825i	0.00720398	+	0.0124777i
$91$	21943.4	−	12669.0i	0.277779	−	0.160376i
$92$	−16622.5	−	9597.03i	−0.204752	−	0.118214i
$93$	8989.41	+	5190.04i	0.107776	+	0.0622247i
$94$	14104.2	−	8143.08i	0.164638	−	0.0950537i
$95$	−80119.6	−	138771.i	−0.910814	−	1.57758i
$96$	−13696.3	+	7907.55i	−0.151679	+	0.0875717i
$97$		−	56422.7i		−	0.608870i	−0.952533	−	0.304435i	$-0.901532\pi$
$97$		−	56422.7i		−	0.608870i	0.952533	−	0.304435i	$-0.0984677\pi$
$98$	12050.5	+	6957.35i	0.126747	+	0.0731777i
$99$	135.891	+	235.370i	0.00139348	+	0.00241358i
$100$	11356.7			0.113567
$101$	−15047.7			−0.146780			−0.0733898	−	0.997303i	$-0.523382\pi$
$101$	−15047.7			−0.146780			−0.0733898	+	0.997303i	$0.523382\pi$
$102$	13727.2	+	23776.1i	0.130641	+	0.226277i
$103$		−	157223.i		−	1.46023i	−0.683322	−	0.730117i	$-0.739466\pi$
$103$		−	157223.i		−	1.46023i	0.683322	−	0.730117i	$-0.260534\pi$
$104$	7023.20	−	12164.5i	0.0636725	−	0.110284i
$105$		−	110416.i		−	0.977367i
$106$	82344.8	+	47541.8i	0.711822	+	0.410971i
$107$	25232.5	−	43703.9i	0.213059	−	0.369029i	−0.739611	−	0.673034i	$-0.764991\pi$
$107$	25232.5	−	43703.9i	0.213059	−	0.369029i	0.952670	+	0.304005i	$0.0983239\pi$
$108$	30576.2	−	52959.6i	0.252246	−	0.436903i
$109$	−31062.8	+	17934.1i	−0.250423	+	0.144582i	−0.619958	−	0.784635i	$-0.712850\pi$
$109$	−31062.8	+	17934.1i	−0.250423	+	0.144582i	0.369535	+	0.929217i	$0.379517\pi$
$110$	15061.7			0.118684
$111$	−59193.3	−	114179.i	−0.456000	−	0.879585i
$112$	−29554.8			−0.222629
$113$	145363.	−	83925.2i	1.07092	−	0.618296i	0.142487	−	0.989797i	$-0.454490\pi$
$113$	145363.	−	83925.2i	1.07092	−	0.618296i	0.928433	+	0.371501i	$0.121157\pi$
$114$	−79928.1	+	138439.i	−0.576020	+	0.997695i
$115$	37143.9	−	64335.2i	0.261905	−	0.453632i
$116$	87413.8	+	50468.4i	0.603163	+	0.348236i
$117$			980.986i			0.00662519i
$118$	−46255.7	+	80117.1i	−0.305816	+	0.529688i
$119$			51305.8i			0.332123i
$120$	−30605.0	−	53009.5i	−0.194017	−	0.336047i
$121$	−157354.			−0.977043
$122$	92162.9			0.560604
$123$	160618.	+	278198.i	0.957262	+	1.65803i
$124$	9312.78	+	5376.74i	0.0543908	+	0.0314025i
$125$		−	149563.i		−	0.856150i
$126$	1787.54	−	1032.04i	0.0100307	−	0.00579121i
$127$	53421.3	+	92528.5i	0.293904	+	0.509057i	0.974729	−	0.223389i	$-0.0717121\pi$
$127$	53421.3	+	92528.5i	0.293904	+	0.509057i	−0.680825	+	0.732446i	$0.738379\pi$
$128$	−14189.0	+	8192.00i	−0.0765466	+	0.0441942i
$129$	31829.4	+	18376.7i	0.168405	+	0.0972284i
$130$	47081.1	+	27182.3i	0.244337	+	0.141068i
$131$	−77380.7	+	44675.8i	−0.393962	+	0.227454i	−0.683875	−	0.729599i	$-0.739707\pi$
$131$	−77380.7	+	44675.8i	−0.393962	+	0.227454i	0.289913	+	0.957053i	$0.406373\pi$
$132$	−7512.84	−	13012.6i	−0.0375292	−	0.0650025i
$133$	−258712.	+	149367.i	−1.26820	+	0.732194i
$134$			121402.i			0.584071i
$135$	204972.	+	118341.i	0.967968	+	0.558857i
$136$	14221.0	+	24631.4i	0.0659298	+	0.114194i
$137$	−250847.			−1.14185			−0.570923	−	0.821004i	$-0.693414\pi$
$137$	−250847.			−1.14185			−0.570923	+	0.821004i	$0.693414\pi$
$138$	−74110.3			−0.331269
$139$	88471.8	+	153238.i	0.388390	+	0.672711i	0.992233	−	0.124392i	$-0.0396981\pi$
$139$	88471.8	+	153238.i	0.388390	+	0.672711i	−0.603843	+	0.797103i	$0.706365\pi$
$140$		−	114388.i		−	0.493241i
$141$	31441.3	−	54457.9i	0.133184	−	0.230682i
$142$		−	35931.7i		−	0.149540i
$143$	11557.3	+	6672.63i	0.0472626	+	0.0272871i
$144$	572.121	−	990.942i	0.00229922	−	0.00398237i
$145$	−195331.	+	338323.i	−0.771526	+	1.33632i
$146$	−39293.1	+	22685.9i	−0.152558	+	0.0880792i
$147$	53726.1			0.205065
$148$	−61322.6	−	118286.i	−0.230126	−	0.443894i
$149$	−438017.			−1.61631			−0.808156	−	0.588969i	$-0.799534\pi$
$149$	−438017.			−1.61631			−0.808156	+	0.588969i	$0.799534\pi$
$150$	37974.8	−	21924.8i	0.137806	−	0.0795623i
$151$	−186335.	+	322742.i	−0.665047	+	1.15190i	0.314225	+	0.949349i	$0.398255\pi$
$151$	−186335.	+	322742.i	−0.665047	+	1.15190i	−0.979272	+	0.202547i	$0.935078\pi$
$152$	−82803.3	+	143419.i	−0.290696	+	0.503500i
$153$	−1720.23	−	993.177i	−0.00594099	−	0.00343003i
$154$		−	28079.5i		−	0.0954088i
$155$	−20809.9	+	36043.8i	−0.0695730	+	0.120504i
$156$		−	54234.6i		−	0.178429i
$157$	−130596.	−	226198.i	−0.422843	−	0.732386i	0.573373	−	0.819294i	$-0.305635\pi$
$157$	−130596.	−	226198.i	−0.422843	−	0.732386i	−0.996216	+	0.0869087i	$0.972301\pi$
$158$	−43384.7			−0.138259
$159$	367128.			1.15166
$160$	−31706.0	−	54916.4i	−0.0979132	−	0.169591i
$161$	−119940.	−	69247.6i	−0.364671	−	0.210543i
$162$		−	231772.i		−	0.693861i
$163$	26297.1	−	15182.6i	0.0775245	−	0.0447588i	−0.460737	−	0.887537i	$-0.652415\pi$
$163$	26297.1	−	15182.6i	0.0775245	−	0.0447588i	0.538261	+	0.842778i	$0.319081\pi$
$164$	166396.	+	288205.i	0.483094	+	0.836744i
$165$	50363.5	−	29077.4i	0.144014	−	0.0831468i
$166$	−42013.3	−	24256.4i	−0.118336	−	0.0683213i
$167$	603057.	+	348175.i	1.67327	+	0.966066i	0.965786	+	0.259341i	$0.0835054\pi$
$167$	603057.	+	348175.i	1.67327	+	0.966066i	0.707489	+	0.706724i	$0.249828\pi$
$168$	−98825.8	+	57057.1i	−0.270145	+	0.155968i
$169$	−161562.	−	279833.i	−0.435133	−	0.753673i
$170$	−95332.5	+	55040.2i	−0.252999	+	0.146069i
$171$		−	11565.8i		−	0.0302472i
$172$	32974.4	+	19037.8i	0.0849876	+	0.0490676i
$173$	54956.6	+	95187.6i	0.139606	+	0.241805i	0.927348	−	0.374201i	$-0.122083\pi$
$173$	54956.6	+	95187.6i	0.139606	+	0.241805i	−0.787741	+	0.616006i	$0.788750\pi$
$174$	389727.			0.975861
$175$	81944.8			0.202268
$176$	−7783.09	−	13480.7i	−0.0189396	−	0.0328043i
$177$			357196.i			0.856985i
$178$	41488.2	−	71859.7i	0.0981464	−	0.169995i
$179$			270679.i			0.631426i	0.948855	+	0.315713i	$0.102244\pi$
$179$			270679.i			0.631426i	−0.948855	+	0.315713i	$0.897756\pi$
$180$	3835.30	+	2214.31i	0.00882304	+	0.00509398i
$181$	248777.	−	430895.i	0.564435	−	0.977630i	−0.432667	−	0.901554i	$-0.642427\pi$
$181$	248777.	−	430895.i	0.564435	−	0.977630i	0.997102	−	0.0760764i	$-0.0242393\pi$
$182$	50676.1	−	87773.5i	0.113403	−	0.196420i
$183$	308176.	−	177925.i	0.680253	−	0.392744i
$184$	−76776.3			−0.167179
$185$	457809.	−	237340.i	0.983457	−	0.509850i
$186$	41520.3			0.0879991
$187$	−23401.9	+	13511.1i	−0.0489382	+	0.0282545i
$188$	32572.3	−	56416.9i	0.0672131	−	0.116417i
$189$	220623.	−	382131.i	0.449259	−	0.778140i
$190$	−555085.	−	320478.i	−1.11551	−	0.644043i
$191$		−	793056.i		−	1.57297i	−0.617609	−	0.786485i	$-0.711899\pi$
$191$		−	793056.i		−	1.57297i	0.617609	−	0.786485i	$-0.288101\pi$
$192$	−31630.2	+	54785.1i	−0.0619225	+	0.107253i
$193$			177344.i			0.342707i	0.985210	+	0.171353i	$0.0548140\pi$
$193$			177344.i			0.342707i	−0.985210	+	0.171353i	$0.945186\pi$
$194$	−112845.	−	195454.i	−0.215268	−	0.372855i
$195$	209907.			0.395313
$196$	55658.8			0.103489
$197$	−367251.	−	636097.i	−0.674214	−	1.16777i	−0.976698	−	0.214618i	$-0.931149\pi$
$197$	−367251.	−	636097.i	−0.674214	−	1.16777i	0.302485	−	0.953154i	$-0.402184\pi$
$198$	941.479	+	543.563i	0.00170666	+	0.000985342i
$199$		−	93343.2i		−	0.167090i	−0.996504	−	0.0835449i	$-0.973376\pi$
$199$		−	93343.2i		−	0.167090i	0.996504	−	0.0835449i	$-0.0266242\pi$
$200$	39340.9	−	22713.5i	0.0695455	−	0.0401521i
$201$	234374.	+	405947.i	0.409184	+	0.708728i
$202$	−52126.7	+	30095.3i	−0.0898838	+	0.0518945i
$203$	630736.	+	364156.i	1.07426	+	0.620222i
$204$	95104.6	+	54908.7i	0.160002	+	0.0923773i
$205$	−1.11546e6	+	644010.i	−1.85382	+	1.07031i
$206$	−314446.	−	544636.i	−0.516271	−	0.894207i
$207$	4643.61	−	2680.99i	0.00753233	−	0.00434879i
$208$		−	56185.6i		−	0.0900465i
$209$	−136261.	−	78670.1i	−0.215777	−	0.124579i
$210$	−220831.	−	382491.i	−0.345551	−	0.598512i
$211$	−379709.			−0.587144			−0.293572	−	0.955937i	$-0.594844\pi$
$211$	−379709.			−0.587144			−0.293572	+	0.955937i	$0.594844\pi$
$212$	380334.			0.581200
$213$	−69368.0	−	120149.i	−0.104764	−	0.181456i
$214$		−	201860.i		−	0.301311i
$215$	−73682.9	+	127623.i	−0.108710	+	0.188292i
$216$		−	244610.i		−	0.356730i
$217$	67196.6	+	38796.0i	0.0968719	+	0.0559290i
$218$	−71736.4	+	124251.i	−0.102235	+	0.177076i
$219$	−87592.6	+	151715.i	−0.123412	+	0.213756i
$220$	52175.2	−	30123.4i	0.0726787	−	0.0419611i
$221$	−97535.8			−0.134333
$222$	−433409.	−	277140.i	−0.590222	−	0.377413i
$223$	−1.41970e6			−1.91177			−0.955886	−	0.293739i	$-0.905100\pi$
$223$	−1.41970e6			−1.91177			−0.955886	+	0.293739i	$0.905100\pi$
$224$	−102381.	+	59109.6i	−0.136332	+	0.0787114i
$225$	−1586.28	+	2747.53i	−0.00208893	+	0.00361814i
$226$	335701.	−	581451.i	0.437201	−	0.757255i
$227$	1.12314e6	+	648445.i	1.44667	+	0.835235i	0.998281	−	0.0586045i	$-0.0186651\pi$
$227$	1.12314e6	+	648445.i	1.44667	+	0.835235i	0.448388	+	0.893839i	$0.351998\pi$
$228$			639425.i			0.814615i
$229$	−613230.	+	1.06214e6i	−0.772742	+	1.33843i	0.163313	+	0.986574i	$0.447782\pi$
$229$	−613230.	+	1.06214e6i	−0.772742	+	1.33843i	−0.936055	+	0.351854i	$0.885551\pi$
$230$		−	297152.i		−	0.370389i
$231$	−54209.1	−	93892.8i	−0.0668408	−	0.115772i
$232$	403747.			0.492481
$233$	1.07564e6			1.29800			0.649001	−	0.760787i	$-0.275187\pi$
$233$	1.07564e6			1.29800			0.649001	+	0.760787i	$0.275187\pi$
$234$	1961.97	+	3398.23i	0.00234236	+	0.00405708i
$235$	218354.	+	126067.i	0.257923	+	0.148912i
$236$			370045.i			0.432489i
$237$	−145070.	+	83756.4i	−0.167767	+	0.0968606i
$238$	102612.	+	177729.i	0.117423	+	0.203383i
$239$	748590.	−	432199.i	0.847714	−	0.489428i	−0.0121652	−	0.999926i	$-0.503872\pi$
$239$	748590.	−	432199.i	0.847714	−	0.489428i	0.859879	+	0.510498i	$0.170539\pi$
$240$	−212038.	−	122420.i	−0.237621	−	0.137191i
$241$	−473035.	−	273107.i	−0.524627	−	0.302893i	0.214199	−	0.976790i	$-0.431286\pi$
$241$	−473035.	−	273107.i	−0.524627	−	0.302893i	−0.738826	+	0.673897i	$0.764619\pi$
$242$	−545089.	+	314707.i	−0.598314	+	0.345437i
$243$	16929.0	+	29321.9i	0.0183915	+	0.0318549i
$244$	319262.	−	184326.i	0.343299	−	0.198204i
$245$			215419.i			0.229282i
$246$	1.11279e6	+	642471.i	1.17240	+	0.676886i
$247$	−283957.	−	491828.i	−0.296149	−	0.512945i
$248$	43013.9			0.0444099
$249$	−187313.			−0.191456
$250$	−299127.	−	518102.i	−0.302695	−	0.524283i
$251$		−	1.21695e6i		−	1.21923i	−0.792697	−	0.609616i	$-0.791323\pi$
$251$		−	1.21695e6i		−	1.21923i	0.792697	−	0.609616i	$-0.208677\pi$
$252$	4128.15	−	7150.17i	0.00409500	−	0.00709275i
$253$		−	72943.9i		−	0.0716453i
$254$	370114.	+	213685.i	0.359957	+	0.207821i
$255$	−212516.	+	368089.i	−0.204664	+	0.354488i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	1.24865e6	−	720906.i	1.17925	−	0.680841i	0.223411	−	0.974724i	$-0.428281\pi$
$257$	1.24865e6	−	720906.i	1.17925	−	0.680841i	0.955841	+	0.293883i	$0.0949476\pi$
$258$	147014.			0.137502
$259$	−442475.	−	853496.i	−0.409863	−	0.790591i
$260$	217458.			0.199500
$261$	−24419.5	+	14098.6i	−0.0221889	+	0.0128108i
$262$	−178703.	+	309523.i	−0.160834	+	0.278573i
$263$	−196214.	+	339853.i	−0.174921	+	0.302971i	−0.940134	−	0.340806i	$-0.889300\pi$
$263$	−196214.	+	339853.i	−0.174921	+	0.302971i	0.765213	+	0.643777i	$0.222634\pi$
$264$	−52050.5	−	30051.4i	−0.0459637	−	0.0265371i
$265$			1.47203e6i			1.28766i
$266$	−597469.	+	1.03485e6i	−0.517739	+	0.896751i
$267$		−	320381.i		−	0.275035i
$268$	242805.	+	420550.i	0.206500	+	0.357669i
$269$	−931958.			−0.785264			−0.392632	−	0.919696i	$-0.628435\pi$
$269$	−931958.			−0.785264			−0.392632	+	0.919696i	$0.628435\pi$
$270$	946727.			0.790343
$271$	153267.	+	265467.i	0.126773	+	0.219577i	0.922425	−	0.386177i	$-0.126205\pi$
$271$	153267.	+	265467.i	0.126773	+	0.219577i	−0.795652	+	0.605754i	$0.792871\pi$
$272$	98525.7	+	56883.9i	0.0807472	+	0.0466194i
$273$		−	391331.i		−	0.317788i
$274$	−868959.	+	501694.i	−0.699235	+	0.403703i
$275$	21579.7	+	37377.2i	0.0172073	+	0.0298040i
$276$	−256726.	+	148221.i	−0.202860	+	0.117121i
$277$	1.21724e6	+	702771.i	0.953181	+	0.550319i	0.894068	−	0.447932i	$-0.147839\pi$
$277$	1.21724e6	+	702771.i	0.953181	+	0.550319i	0.0591131	+	0.998251i	$0.481173\pi$
$278$	612950.	+	353887.i	0.475678	+	0.274633i
$279$	−2601.58	+	1502.02i	−0.00200091	+	0.00115522i
$280$	−228775.	−	396250.i	−0.174387	−	0.302047i
$281$	2.09560e6	−	1.20990e6i	1.58323	−	0.914076i	0.588841	−	0.808249i	$-0.299585\pi$
$281$	2.09560e6	−	1.20990e6i	1.58323	−	0.914076i	0.994385	−	0.105827i	$-0.0337488\pi$
$282$		−	251530.i		−	0.188351i
$283$	−1.20456e6	−	695454.i	−0.894053	−	0.516182i	−0.0187868	−	0.999824i	$-0.505980\pi$
$283$	−1.20456e6	−	695454.i	−0.894053	−	0.516182i	−0.875266	+	0.483642i	$0.839314\pi$
$284$	−71863.4	−	124471.i	−0.0528703	−	0.0915740i
$285$	−2.47480e6			−1.80480
$286$	53381.1			0.0385898
$287$	1.20063e6	+	2.07955e6i	0.860408	+	1.49027i
$288$		−	4576.97i		−	0.00325160i
$289$	−611181.	+	1.05860e6i	−0.430452	+	0.745565i
$290$			1.56264e6i			1.09110i
$291$	−754669.	−	435708.i	−0.522425	−	0.301622i
$292$	−90743.5	+	157172.i	−0.0622814	+	0.107875i
$293$	217775.	−	377197.i	0.148197	−	0.256684i	−0.782364	−	0.622821i	$-0.785986\pi$
$293$	217775.	−	377197.i	0.148197	−	0.256684i	0.930561	+	0.366137i	$0.119320\pi$
$294$	186113.	−	107452.i	0.125576	−	0.0725015i
$295$	−1.43221e6			−0.958188
$296$	−449000.	−	287110.i	−0.297863	−	0.190467i
$297$	232400.			0.152878
$298$	−1.51733e6	+	876033.i	−0.989784	+	0.571452i
$299$	131644.	−	228015.i	0.0851577	−	0.147497i
$300$	87699.1	−	151899.i	0.0562590	−	0.0974435i
$301$	237927.	+	137367.i	0.151366	+	0.0873911i
$302$			1.49068e6i			0.940519i
$303$	−116201.	+	201267.i	−0.0727118	+	0.125940i
$304$			662426.i			0.411106i
$305$	713407.	+	1.23566e6i	0.439124	+	0.760586i
$306$	−7945.42			−0.00485080
$307$	586651.			0.355250			0.177625	−	0.984098i	$-0.443159\pi$
$307$	586651.			0.355250			0.177625	+	0.984098i	$0.443159\pi$
$308$	−56159.1	−	97270.4i	−0.0337321	−	0.0584257i
$309$	−2.10290e6	−	1.21411e6i	−1.25292	−	0.723371i
$310$			166479.i			0.0983910i
$311$	1.30999e6	−	756325.i	0.768012	−	0.443412i	−0.0641530	−	0.997940i	$-0.520435\pi$
$311$	1.30999e6	−	756325.i	0.768012	−	0.443412i	0.832165	+	0.554528i	$0.187101\pi$
$312$	−108469.	−	187874.i	−0.0630842	−	0.109265i
$313$	−1.46436e6	+	845446.i	−0.844862	+	0.487781i	−0.858914	−	0.512120i	$-0.828860\pi$
$313$	−1.46436e6	+	845446.i	−0.844862	+	0.487781i	0.0140519	+	0.999901i	$0.495527\pi$
$314$	−904792.	−	522382.i	−0.517875	−	0.298995i
$315$	27673.7	+	15977.4i	0.0157141	+	0.00907257i
$316$	−150289.	+	86769.3i	−0.0846660	+	0.0488819i
$317$	−569190.	−	985866.i	−0.318133	−	0.551023i	0.661965	−	0.749534i	$-0.269723\pi$
$317$	−569190.	−	985866.i	−0.318133	−	0.551023i	−0.980099	+	0.198512i	$0.936389\pi$
$318$	1.27177e6	−	734256.i	0.705245	−	0.407173i
$319$			383594.i			0.211055i
$320$	−219665.	−	126824.i	−0.119919	−	0.0692351i
$321$	−389701.	−	674982.i	−0.211091	−	0.365620i
$322$	−553981.			−0.297752
$323$	1.14994e6			0.613296
$324$	−463543.	−	802880.i	−0.245317	−	0.424901i
$325$			155782.i			0.0818107i
$326$	60730.6	−	105188.i	0.0316492	−	0.0548181i
$327$			553964.i			0.286492i
$328$	1.15282e6	+	665582.i	0.591667	+	0.341599i
$329$	235026.	−	407077.i	0.119709	−	0.207342i
$330$	116309.	−	201454.i	0.0587936	−	0.101834i
$331$	2.96381e6	−	1.71116e6i	1.48690	−	0.858460i	0.487007	−	0.873398i	$-0.338089\pi$
$331$	2.96381e6	−	1.71116e6i	1.48690	−	0.858460i	0.999888	+	0.0149384i	$0.00475523\pi$
$332$	−194051.			−0.0966209
$333$	37182.3	+	1686.22i	0.0183749	+	0.000833305i
$334$	2.78540e6			1.36622
$335$	−1.62768e6	+	939742.i	−0.792423	+	0.457506i
$336$	−228228.	+	395303.i	−0.110286	+	0.191021i
$337$	1.72186e6	−	2.98234e6i	0.825890	−	1.43048i	−0.0753477	−	0.997157i	$-0.524007\pi$
$337$	1.72186e6	−	2.98234e6i	0.825890	−	1.43048i	0.901237	−	0.433326i	$-0.142660\pi$
$338$	−1.11933e6	−	646247.i	−0.532927	−	0.307686i
$339$		−	2.59235e6i		−	1.22517i
$340$	−220161.	+	381330.i	−0.103286	+	0.178897i
$341$			40866.8i			0.0190320i
$342$	−23131.6	−	40065.1i	−0.0106940	−	0.0185225i
$343$	2.34195e6			1.07484
$344$	152302.			0.0693920
$345$	−573667.	−	993620.i	−0.259485	−	0.449441i
$346$	380750.	+	219826.i	0.170982	+	0.0987165i
$347$		−	1.61236e6i		−	0.718851i	−0.933174	−	0.359426i	$-0.882973\pi$
$347$		−	1.61236e6i		−	0.718851i	0.933174	−	0.359426i	$-0.117027\pi$
$348$	1.35006e6	−	779455.i	0.597590	−	0.345019i
$349$	−1.40978e6	−	2.44181e6i	−0.619567	−	1.07312i	−0.989565	−	0.144089i	$-0.953975\pi$
$349$	−1.40978e6	−	2.44181e6i	−0.619567	−	1.07312i	0.369998	−	0.929033i	$-0.379358\pi$
$350$	283865.	−	163890.i	0.123863	−	0.0715124i
$351$	726456.	+	419420.i	0.314733	+	0.181711i
$352$	−53922.8	−	31132.4i	−0.0231962	−	0.0133923i
$353$	−780669.	+	450720.i	−0.333450	+	0.192517i	−0.657372	−	0.753567i	$-0.728332\pi$
$353$	−780669.	+	450720.i	−0.333450	+	0.192517i	0.323922	+	0.946084i	$0.394998\pi$
$354$	714392.	+	1.23736e6i	0.302990	+	0.524794i
$355$	481747.	−	278137.i	0.202884	−	0.117135i
$356$		−	331906.i		−	0.138800i
$357$	686229.	+	396195.i	0.284970	+	0.164527i
$358$	541359.	+	937661.i	0.223243	+	0.386668i
$359$	−2.87536e6			−1.17749			−0.588744	−	0.808320i	$-0.700377\pi$
$359$	−2.87536e6			−1.17749			−0.588744	+	0.808320i	$0.700377\pi$
$360$	17714.5			0.00720398
$361$	2.10979e6	+	3.65427e6i	0.852064	+	1.47582i
$362$		−	1.99022e6i		−	0.798232i
$363$	−1.21512e6	+	2.10465e6i	−0.484008	+	0.838326i
$364$		−	405408.i		−	0.160376i
$365$	−608313.	−	351210.i	−0.238999	−	0.137986i
$366$	711701.	−	1.23270e6i	0.277712	−	0.481012i
$367$	−2.47044e6	+	4.27893e6i	−0.957435	+	1.65833i	−0.228741	+	0.973487i	$0.573461\pi$
$367$	−2.47044e6	+	4.27893e6i	−0.957435	+	1.65833i	−0.728695	+	0.684839i	$0.759873\pi$
$368$	−265961.	+	153553.i	−0.102376	+	0.0591068i
$369$	−92967.1			−0.0355438
$370$	1.11122e6	−	1.73779e6i	0.421983	−	0.659923i
$371$	2.74431e6			1.03514
$372$	143831.	−	83040.6i	0.0538882	−	0.0311124i
$373$	885549.	−	1.53382e6i	0.329564	−	0.570822i	−0.652861	−	0.757478i	$-0.726431\pi$
$373$	885549.	−	1.53382e6i	0.329564	−	0.570822i	0.982425	+	0.186655i	$0.0597648\pi$
$374$	−54044.5	+	93607.8i	−0.0199789	+	0.0346045i
$375$	−2.00045e6	−	1.15496e6i	−0.734597	−	0.424120i
$376$		−	260579.i		−	0.0950537i
$377$	−692284.	+	1.19907e6i	−0.250860	+	0.434502i
$378$		−	1.76499e6i		−	0.635349i
$379$	−1.12209e6	−	1.94351e6i	−0.401262	−	0.695006i	0.592617	−	0.805485i	$-0.298095\pi$
$379$	−1.12209e6	−	1.94351e6i	−0.401262	−	0.695006i	−0.993879	+	0.110479i	$0.964762\pi$
$380$	−2.56383e6			−0.910814
$381$	1.65012e6			0.582377
$382$	−1.58611e6	−	2.74723e6i	−0.556129	−	0.963244i
$383$	−4.53319e6	−	2.61724e6i	−1.57909	−	0.911689i	−0.994986	−	0.100012i	$-0.968112\pi$
$383$	−4.53319e6	−	2.61724e6i	−1.57909	−	0.911689i	−0.584106	−	0.811678i	$-0.698555\pi$
$384$			253041.i			0.0875717i
$385$	376471.	−	217356.i	0.129443	−	0.0747342i
$386$	354687.	+	614337.i	0.121165	+	0.209864i
$387$	−9211.58	+	5318.31i	−0.00312649	+	0.00180508i
$388$	−781816.	−	451382.i	−0.263649	−	0.152218i
$389$	464130.	+	267966.i	0.155513	+	0.0897853i	0.575737	−	0.817635i	$-0.304715\pi$
$389$	464130.	+	267966.i	0.155513	+	0.0897853i	−0.420224	+	0.907420i	$0.638049\pi$
$390$	727141.	−	419815.i	0.242079	−	0.139764i
$391$	266561.	+	461697.i	0.0881768	+	0.152727i
$392$	192808.	−	111318.i	0.0633737	−	0.0365888i
$393$			1.37998e6i			0.450705i
$394$	−2.54439e6	−	1.46900e6i	−0.825740	−	0.476741i
$395$	−335828.	−	581672.i	−0.108299	−	0.187579i
$396$	4348.50			0.00139348
$397$	5.91482e6			1.88350			0.941750	−	0.336315i	$-0.109181\pi$
$397$	5.91482e6			1.88350			0.941750	+	0.336315i	$0.109181\pi$
$398$	−186686.	−	323350.i	−0.0590752	−	0.102321i
$399$			4.61378e6i			1.45086i
$400$	90853.9	−	157364.i	0.0283918	−	0.0491761i
$401$		−	933126.i		−	0.289787i	−0.989447	−	0.144894i	$-0.953716\pi$
$401$		−	933126.i		−	0.289787i	0.989447	−	0.144894i	$-0.0462840\pi$
$402$	1.62379e6	+	937495.i	0.501146	+	0.289337i
$403$	−73753.7	+	127745.i	−0.0226215	+	0.0391816i
$404$	−120381.	+	208507.i	−0.0366949	+	0.0635575i
$405$	3.10743e6	−	1.79408e6i	0.941379	−	0.543505i
$406$	2.91324e6			0.877126
$407$	272779.	−	426588.i	0.0816252	−	0.127650i
$408$	439269.			0.130641
$409$	1.62618e6	−	938877.i	0.480685	−	0.277524i	−0.240017	−	0.970769i	$-0.577153\pi$
$409$	1.62618e6	−	938877.i	0.480685	−	0.277524i	0.720702	+	0.693245i	$0.243820\pi$
$410$	−2.57604e6	+	4.46183e6i	−0.756821	+	1.31085i
$411$	−1.93709e6	+	3.35514e6i	−0.565648	+	0.979730i
$412$	−2.17854e6	−	1.25778e6i	−0.632300	−	0.365059i
$413$			2.67007e6i			0.770278i
$414$	10723.9	−	18574.4i	0.00307506	−	0.00532616i
$415$		−	751047.i		−	0.214066i
$416$	−112371.	−	194633.i	−0.0318362	−	0.0551420i
$417$	2.73279e6			0.769602
$418$	−629361.			−0.176181
$419$	−1.38746e6	−	2.40315e6i	−0.386088	−	0.668723i	0.605832	−	0.795593i	$-0.292840\pi$
$419$	−1.38746e6	−	2.40315e6i	−0.386088	−	0.668723i	−0.991919	+	0.126869i	$0.959507\pi$
$420$	−1.52996e6	−	883325.i	−0.423212	−	0.244342i
$421$			4.92504e6i			1.35427i	0.735859	+	0.677134i	$0.236778\pi$
$421$			4.92504e6i			1.35427i	−0.735859	+	0.677134i	$0.763222\pi$
$422$	−1.31535e6	+	759418.i	−0.359551	+	0.207587i
$423$	9099.27	+	15760.4i	0.00247261	+	0.00428268i
$424$	1.31752e6	−	760669.i	0.355911	−	0.205485i
$425$	−273176.	−	157718.i	−0.0733619	−	0.0423555i
$426$	−480596.	−	277472.i	−0.128309	−	0.0740790i
$427$	2.30364e6	−	1.33001e6i	0.611427	−	0.353008i
$428$	−403720.	−	699263.i	−0.106530	−	0.184515i
$429$	178496.	−	103055.i	0.0468259	−	0.0270350i
$430$			589464.i			0.153740i
$431$	5.53041e6	+	3.19299e6i	1.43405	+	0.827949i	0.997427	−	0.0716949i	$-0.0228408\pi$
$431$	5.53041e6	+	3.19299e6i	1.43405	+	0.827949i	0.436624	+	0.899644i	$0.356174\pi$
$432$	−489220.	−	847353.i	−0.126123	−	0.218452i
$433$	−5.64290e6			−1.44638			−0.723191	−	0.690648i	$-0.757325\pi$
$433$	−5.64290e6			−1.44638			−0.723191	+	0.690648i	$0.757325\pi$
$434$	310368.			0.0790956
$435$	3.01677e6	+	5.22520e6i	0.764397	+	1.32397i
$436$			573891.i			0.144582i
$437$	−1.55208e6	+	2.68828e6i	−0.388786	+	0.673398i
$438$			700741.i			0.174531i
$439$	−408776.	−	236007.i	−0.101233	−	0.0584471i	0.448529	−	0.893768i	$-0.351948\pi$
$439$	−408776.	−	236007.i	−0.101233	−	0.0584471i	−0.549762	+	0.835321i	$0.685282\pi$
$440$	120493.	−	208701.i	0.0296710	−	0.0513916i
$441$	−7774.30	+	13465.5i	−0.00190355	+	0.00329705i
$442$	−337874.	+	195072.i	−0.0822620	+	0.0474940i
$443$	−6.91609e6			−1.67437			−0.837185	−	0.546920i	$-0.815800\pi$
$443$	−6.91609e6			−1.67437			−0.837185	+	0.546920i	$0.815800\pi$
$444$	−2.05565e6	−	93224.2i	−0.494872	−	0.0224425i
$445$	1.28459e6			0.307515
$446$	−4.91800e6	+	2.83941e6i	−1.17072	+	0.675913i
$447$	−3.38246e6	+	5.85859e6i	−0.800689	+	1.38683i
$448$	−236438.	+	409523.i	−0.0556574	+	0.0964014i
$449$	−1.57237e6	−	907809.i	−0.368078	−	0.212510i	0.304541	−	0.952499i	$-0.401497\pi$
$449$	−1.57237e6	−	907809.i	−0.368078	−	0.212510i	−0.672618	+	0.739990i	$0.734830\pi$
$450$			12690.3i			0.00295420i
$451$	−632359.	+	1.09528e6i	−0.146394	+	0.253561i
$452$		−	2.68561e6i		−	0.618296i
$453$	2.87784e6	+	4.98457e6i	0.658903	+	1.14125i
$454$	5.18756e6			1.18120
$455$	1.56908e6			0.355317
$456$	1.27885e6	+	2.21503e6i	0.288010	+	0.498848i
$457$	651185.	+	375962.i	0.145852	+	0.0842079i	0.571150	−	0.820845i	$-0.306497\pi$
$457$	651185.	+	375962.i	0.145852	+	0.0842079i	−0.425298	+	0.905053i	$0.639831\pi$
$458$			4.90584e6i			1.09282i
$459$	−1.47097e6	+	849264.i	−0.325891	+	0.188153i
$460$	−594303.	−	1.02936e6i	−0.130952	−	0.226816i
$461$	2.15979e6	−	1.24695e6i	0.473324	−	0.273274i	−0.244306	−	0.969698i	$-0.578560\pi$
$461$	2.15979e6	−	1.24695e6i	0.473324	−	0.273274i	0.717630	+	0.696424i	$0.245227\pi$
$462$	−375571.	−	216836.i	−0.0818630	−	0.0472636i
$463$	−5.19677e6	−	3.00036e6i	−1.12663	−	0.650459i	−0.183544	−	0.983012i	$-0.558757\pi$
$463$	−5.19677e6	−	3.00036e6i	−1.12663	−	0.650459i	−0.943085	+	0.332552i	$0.892090\pi$
$464$	1.39862e6	−	807494.i	0.301582	−	0.174118i
$465$	321397.	+	556676.i	0.0689301	+	0.119391i
$466$	3.72611e6	−	2.15127e6i	0.794861	−	0.458913i
$467$		−	8.35329e6i		−	1.77241i	−0.463289	−	0.886207i	$-0.653331\pi$
$467$		−	8.35329e6i		−	1.77241i	0.463289	−	0.886207i	$-0.346669\pi$
$468$	13592.9	+	7847.89i	0.00286879	+	0.00165630i
$469$	1.75196e6	+	3.03449e6i	0.367784	+	0.637021i
$470$	1.00853e6			0.210594
$471$	−4.03395e6			−0.837872
$472$	740090.	+	1.28187e6i	0.152908	+	0.264844i
$473$			144700.i			0.0297382i
$474$	−335026.	+	580281.i	−0.0684908	+	0.118629i
$475$		−	1.83667e6i		−	0.373505i
$476$	710915.	+	410447.i	0.143814	+	0.0830308i
$477$	−53124.3	+	92014.0i	−0.0106905	+	0.0185165i
$478$	1.72879e6	−	2.99436e6i	0.346078	−	0.599424i
$479$	−5.66425e6	+	3.27026e6i	−1.12799	+	0.651243i	−0.943428	−	0.331579i	$-0.892419\pi$
$479$	−5.66425e6	+	3.27026e6i	−1.12799	+	0.651243i	−0.184558	+	0.982822i	$0.559085\pi$
$480$	−979361.			−0.194017
$481$	1.62255e6	−	841173.i	0.319769	−	0.165776i
$482$	−2.18485e6			−0.428356
$483$	−1.85241e6	+	1.06949e6i	−0.361301	+	0.208597i
$484$	−1.25883e6	+	2.18036e6i	−0.244261	+	0.423072i
$485$	1.74701e6	−	3.02591e6i	0.337241	−	0.584119i
$486$	117288.	+	67716.1i	0.0225248	+	0.0130047i
$487$		−	595830.i		−	0.113841i	−0.998379	−	0.0569207i	$-0.981872\pi$
$487$		−	595830.i		−	0.113841i	0.998379	−	0.0569207i	$-0.0181282\pi$
$488$	737303.	−	1.27705e6i	0.140151	−	0.242749i
$489$		−	468974.i		−	0.0886905i
$490$	430839.	+	746235.i	0.0810634	+	0.140406i
$491$	9.04220e6			1.69266			0.846331	−	0.532657i	$-0.178806\pi$
$491$	9.04220e6			1.69266			0.846331	+	0.532657i	$0.178806\pi$
$492$	5.13977e6			0.957262
$493$	−1.40177e6	−	2.42795e6i	−0.259753	−	0.449906i
$494$	−1.96731e6	−	1.13583e6i	−0.362707	−	0.209409i
$495$			16830.3i			0.00308729i
$496$	149004.	−	86027.8i	0.0271954	−	0.0157013i
$497$	−518532.	−	898123.i	−0.0941639	−	0.163097i
$498$	−648871.	+	374626.i	−0.117243	+	0.0676900i
$499$	−2.84053e6	−	1.63998e6i	−0.510679	−	0.294841i	0.222433	−	0.974948i	$-0.428600\pi$
$499$	−2.84053e6	−	1.63998e6i	−0.510679	−	0.294841i	−0.733113	+	0.680107i	$0.761933\pi$
$500$	−2.07241e6	−	1.19651e6i	−0.370724	−	0.214038i
$501$	9.31387e6	−	5.37737e6i	1.65781	−	0.957140i
$502$	−2.43389e6	−	4.21562e6i	−0.431064	−	0.746625i
$503$	−5.83979e6	+	3.37160e6i	−1.02915	+	0.594178i	−0.916740	−	0.399485i	$-0.869189\pi$
$503$	−5.83979e6	+	3.37160e6i	−1.02915	+	0.594178i	−0.112406	+	0.993662i	$0.535856\pi$
$504$		−	33025.2i		−	0.00579121i
$505$	−806996.	−	465919.i	−0.140813	−	0.0812984i
$506$	−145888.	−	252685.i	−0.0253304	−	0.0438736i
$507$	−4.99046e6			−0.862225
$508$	1.70948e6			0.293904
$509$	1.07294e6	+	1.85839e6i	0.183562	+	0.317938i	0.943091	−	0.332535i	$-0.107904\pi$
$509$	1.07294e6	+	1.85839e6i	0.183562	+	0.317938i	−0.759529	+	0.650473i	$0.774571\pi$
$510$			1.70013e6i			0.289439i
$511$	−654762.	+	1.13408e6i	−0.110925	+	0.192128i
$512$			262144.i			0.0441942i
$513$	−8.56489e6	−	4.94494e6i	−1.43691	−	0.829598i
$514$	2.88362e6	−	4.99458e6i	0.481428	−	0.833857i
$515$	4.86807e6	−	8.43174e6i	0.808795	−	1.40087i
$516$	509270.	−	294027.i	0.0842023	−	0.0486142i
$517$	247572.			0.0407356
$518$	−3.23977e6	−	2.07165e6i	−0.530505	−	0.339228i
$519$	1.69755e6			0.276633
$520$	753298.	−	434917.i	0.122168	−	0.0705339i
$521$	2.22246e6	−	3.84941e6i	0.358706	−	0.621298i	−0.629039	−	0.777374i	$-0.716551\pi$
$521$	2.22246e6	−	3.84941e6i	0.358706	−	0.621298i	0.987745	+	0.156076i	$0.0498846\pi$
$522$	−56394.5	+	97678.2i	−0.00905859	+	0.0156899i
$523$	6.87086e6	+	3.96689e6i	1.09839	+	0.634156i	0.935798	−	0.352537i	$-0.114681\pi$
$523$	6.87086e6	+	3.96689e6i	1.09839	+	0.634156i	0.162592	+	0.986693i	$0.448014\pi$
$524$			1.42962e6i			0.227454i
$525$	632795.	−	1.09603e6i	0.100199	−	0.173550i
$526$			1.56971e6i			0.247375i
$527$	−149341.	−	258665.i	−0.0234235	−	0.0405706i
$528$	−240411.			−0.0375292
$529$	4.99723e6			0.776409
$530$	2.94406e6	+	5.09926e6i	0.455257	+	0.788529i
$531$	−89524.8	−	51687.1i	−0.0137787	−	0.00795511i
$532$			4.77975e6i			0.732194i
$533$	−3.95337e6	+	2.28248e6i	−0.602767	+	0.348008i
$534$	−640761.	−	1.10983e6i	−0.0972396	−	0.168424i
$535$	2.70640e6	−	1.56254e6i	0.408797	−	0.236019i
$536$	1.68220e6	+	971219.i	0.252910	+	0.146018i
$537$	3.62041e6	+	2.09024e6i	0.541778	+	0.312796i
$538$	−3.22840e6	+	1.86392e6i	−0.480874	+	0.277633i
$539$	105761.	+	183184.i	0.0156803	+	0.0271591i
$540$	3.27956e6	−	1.89345e6i	0.483984	−	0.279428i
$541$			5.71112e6i			0.838935i	0.907770	+	0.419468i	$0.137783\pi$
$541$			5.71112e6i			0.838935i	−0.907770	+	0.419468i	$0.862217\pi$
$542$	1.06187e6	+	613069.i	0.155264	+	0.0896419i
$543$	−3.84222e6	−	6.65492e6i	−0.559220	−	0.968597i
$544$	455071.			0.0659298
$545$	−2.22117e6			−0.320324
$546$	−782663.	−	1.35561e6i	−0.112355	−	0.194605i
$547$		−	8.85518e6i		−	1.26540i	−0.774396	−	0.632702i	$-0.781946\pi$
$547$		−	8.85518e6i		−	1.26540i	0.774396	−	0.632702i	$-0.218054\pi$
$548$	−2.00678e6	+	3.47584e6i	−0.285461	+	0.494434i
$549$			102985.i			0.0145829i
$550$	149509.	+	86318.9i	0.0210746	+	0.0121674i
$551$	8.16200e6	−	1.41370e7i	1.14530	−	1.98371i
$552$	−592883.	+	1.02690e6i	−0.0828173	+	0.143444i
$553$	−1.08441e6	+	626086.i	−0.150793	+	0.0870605i
$554$	5.62217e6			0.778269
$555$	360811.	−	7.95612e6i	0.0497219	−	1.09640i
$556$	2.83110e6			0.388390
$557$	1.73605e6	−	1.00231e6i	0.237096	−	0.136887i	−0.376745	−	0.926317i	$-0.622957\pi$
$557$	1.73605e6	−	1.00231e6i	0.237096	−	0.136887i	0.613841	+	0.789429i	$0.289623\pi$
$558$	−6008.09	+	10406.3i	−0.000816866	+	0.00141485i
$559$	−261144.	+	452316.i	−0.0353469	+	0.0612226i
$560$	−1.58500e6	−	915101.i	−0.213579	−	0.123310i
$561$			417343.i			0.0559868i
$562$	4.83958e6	−	8.38240e6i	0.646349	−	1.11951i
$563$		−	593750.i		−	0.0789465i	−0.999221	−	0.0394733i	$-0.987432\pi$
$563$		−	593750.i		−	0.0789465i	0.999221	−	0.0394733i	$-0.0125680\pi$
$564$	−503061.	−	871327.i	−0.0665921	−	0.115341i
$565$	1.03943e7			1.36985
$566$	−5.56363e6			−0.729991
$567$	−3.34471e6	−	5.79320e6i	−0.436918	−	0.756765i
$568$	−497884.	−	287453.i	−0.0647526	−	0.0373849i
$569$			8.59043e6i			1.11233i	0.831071	+	0.556166i	$0.187728\pi$
$569$			8.59043e6i			1.11233i	−0.831071	+	0.556166i	$0.812272\pi$
$570$	−8.57297e6	+	4.94960e6i	−1.10521	+	0.638092i
$571$	333475.	+	577596.i	0.0428029	+	0.0741368i	0.886633	−	0.462473i	$-0.153038\pi$
$571$	333475.	+	577596.i	0.0428029	+	0.0741368i	−0.843830	+	0.536610i	$0.819705\pi$
$572$	184917.	−	106762.i	0.0236313	−	0.0136435i
$573$	−1.06073e7	−	6.12415e6i	−1.34965	−	0.779219i
$574$	8.31821e6	+	4.80252e6i	1.05378	+	0.608401i
$575$	737413.	−	425746.i	0.0930125	−	0.0537008i
$576$	−9153.93	−	15855.1i	−0.00114961	−	0.00199119i
$577$	−8.37940e6	+	4.83785e6i	−1.04779	+	0.604941i	−0.922029	−	0.387120i	$-0.873470\pi$
$577$	−8.37940e6	+	4.83785e6i	−1.04779	+	0.604941i	−0.125759	+	0.992061i	$0.540136\pi$
$578$			4.88944e6i			0.608751i
$579$	2.37202e6	+	1.36949e6i	0.294050	+	0.169770i
$580$	3.12529e6	+	5.41316e6i	0.385763	+	0.668161i
$581$	−1.40018e6			−0.172085
$582$	−3.48567e6			−0.426558
$583$	722699.	+	1.25175e6i	0.0880615	+	0.152527i
$584$			725948.i			0.0880792i
$585$	−30374.1	+	52609.5i	−0.00366956	+	0.00635587i
$586$		−	1.74220e6i		−	0.209582i
$587$	−2.06068e6	−	1.18973e6i	−0.246840	−	0.142513i	0.371477	−	0.928442i	$-0.378852\pi$
$587$	−2.06068e6	−	1.18973e6i	−0.246840	−	0.142513i	−0.618316	+	0.785929i	$0.712185\pi$
$588$	429809.	−	744451.i	0.0512663	−	0.0887959i
$589$	869553.	−	1.50611e6i	0.103278	−	0.178883i
$590$	−4.96131e6	+	2.86442e6i	−0.586768	+	0.338771i
$591$	−1.13440e7			−1.33597
$592$	−2.12960e6	−	96577.7i	−0.249743	−	0.0113259i
$593$	−1.11132e7			−1.29779			−0.648893	−	0.760880i	$-0.724768\pi$
$593$	−1.11132e7			−1.29779			−0.648893	+	0.760880i	$0.724768\pi$
$594$	805057.	−	464800.i	0.0936183	−	0.0540505i
$595$	−1.58858e6	+	2.75149e6i	−0.183957	+	0.318622i
$596$	−3.50413e6	+	6.06934e6i	−0.404078	+	0.699883i
$597$	−1.24849e6	−	720816.i	−0.143367	−	0.0827730i
$598$		−	1.05315e6i		−	0.120431i
$599$	−1.11995e6	+	1.93981e6i	−0.127536	+	0.220898i	−0.922721	−	0.385468i	$-0.874040\pi$
$599$	−1.11995e6	+	1.93981e6i	−0.127536	+	0.220898i	0.795186	+	0.606366i	$0.207373\pi$
$600$		−	701593.i		−	0.0795623i
$601$	−1.15452e6	−	1.99969e6i	−0.130381	−	0.225827i	0.793442	−	0.608645i	$-0.208287\pi$
$601$	−1.15452e6	−	1.99969e6i	−0.130381	−	0.225827i	−0.923824	+	0.382819i	$0.874953\pi$
$602$	1.09894e6			0.123590
$603$	−135658.			−0.0151933
$604$	2.98136e6	+	5.16387e6i	0.332524	+	0.575948i
$605$	−8.43876e6	−	4.87212e6i	−0.937325	−	0.541165i
$606$			929611.i			0.102830i
$607$	−5.46300e6	+	3.15407e6i	−0.601810	+	0.347455i	−0.769753	−	0.638341i	$-0.779621\pi$
$607$	−5.46300e6	+	3.15407e6i	−0.601810	+	0.347455i	0.167943	+	0.985797i	$0.446288\pi$
$608$	1.32485e6	+	2.29471e6i	0.145348	+	0.251750i
$609$	9.74136e6	−	5.62417e6i	1.06433	−	0.614491i
$610$	4.94263e6	+	2.85363e6i	0.537815	+	0.310508i
$611$	773881.	+	446801.i	0.0838632	+	0.0484184i
$612$	−27523.7	+	15890.8i	−0.00297049	+	0.00171502i
$613$	5.24480e6	+	9.08425e6i	0.563738	+	0.976423i	0.997166	+	0.0752348i	$0.0239706\pi$
$613$	5.24480e6	+	9.08425e6i	0.563738	+	0.976423i	−0.433428	+	0.901188i	$0.642696\pi$
$614$	2.03222e6	−	1.17330e6i	0.217545	−	0.125600i
$615$			1.98927e7i			2.12083i
$616$	−389082.	−	224636.i	−0.0413132	−	0.0238522i
$617$	6.42056e6	+	1.11207e7i	0.678984	+	1.17604i	0.975287	+	0.220941i	$0.0709129\pi$
$617$	6.42056e6	+	1.11207e7i	0.678984	+	1.17604i	−0.296303	+	0.955094i	$0.595754\pi$
$618$	−9.71286e6			−1.02300
$619$	9.37982e6			0.983939			0.491969	−	0.870613i	$-0.336277\pi$
$619$	9.37982e6			0.983939			0.491969	+	0.870613i	$0.336277\pi$
$620$	332958.	+	576701.i	0.0347865	+	0.0602520i
$621$		−	4.58501e6i		−	0.477103i
$622$	3.02530e6	−	5.23997e6i	0.313540	−	0.543066i
$623$		−	2.39487e6i		−	0.247208i
$624$	−751497.	−	433877.i	−0.0772620	−	0.0446072i
$625$	5.73996e6	−	9.94191e6i	0.587772	−	1.01805i
$626$	−3.38178e6	+	5.85742e6i	−0.344913	+	0.597408i
$627$	−2.10447e6	+	1.21501e6i	−0.213783	+	0.123428i
$628$	−4.17906e6			−0.422843
$629$	−167655.	+	3.69690e6i	−0.0168962	+	0.372572i
$630$	127819.			0.0128305
$631$	1.27417e7	−	7.35644e6i	1.27396	−	0.735520i	0.298227	−	0.954495i	$-0.403605\pi$
$631$	1.27417e7	−	7.35644e6i	1.27396	−	0.735520i	0.975730	+	0.218975i	$0.0702713\pi$
$632$	−347077.	+	601155.i	−0.0345647	+	0.0598679i
$633$	−2.93220e6	+	5.07871e6i	−0.290860	+	0.503784i
$634$	−3.94346e6	−	2.27676e6i	−0.389632	−	0.224954i
$635$			6.61631e6i			0.651151i
$636$	2.93702e6	−	5.08707e6i	0.287915	−	0.498684i
$637$			763482.i			0.0745504i
$638$	767187.	+	1.32881e6i	0.0746191	+	0.129244i
$639$	40150.9			0.00388994
$640$	−1.01459e6			−0.0979132
$641$	1.69784e6	+	2.94074e6i	0.163211	+	0.282691i	0.936019	−	0.351950i	$-0.114481\pi$
$641$	1.69784e6	+	2.94074e6i	0.163211	+	0.282691i	−0.772807	+	0.634641i	$0.781148\pi$
$642$	−2.69993e6	−	1.55880e6i	−0.258532	−	0.149264i
$643$			8.49152e6i			0.809949i	0.914328	+	0.404975i	$0.132720\pi$
$643$			8.49152e6i			0.809949i	−0.914328	+	0.404975i	$0.867280\pi$
$644$	−1.91905e6	+	1.10796e6i	−0.182335	+	0.105271i
$645$	1.13799e6	+	1.97106e6i	0.107706	+	0.186552i
$646$	3.98352e6	−	2.29989e6i	0.375566	−	0.216833i
$647$	−1.23799e6	−	714754.i	−0.116267	−	0.0671268i	0.440739	−	0.897635i	$-0.354717\pi$
$647$	−1.23799e6	−	714754.i	−0.116267	−	0.0671268i	−0.557006	+	0.830509i	$0.688050\pi$
$648$	−3.21152e6	−	1.85417e6i	−0.300451	−	0.173465i
$649$	−1.21789e6	+	703149.i	−0.113500	+	0.0655293i
$650$	311565.	+	539646.i	0.0289244	+	0.0500986i
$651$	1.03781e6	−	599181.i	0.0959768	−	0.0554123i
$652$		−	485845.i		−	0.0447588i
$653$	1.74393e7	+	1.00686e7i	1.60047	+	0.924030i	0.991394	+	0.130916i	$0.0417917\pi$
$653$	1.74393e7	+	1.00686e7i	1.60047	+	0.924030i	0.609073	+	0.793114i	$0.291542\pi$
$654$	1.10793e6	+	1.91899e6i	0.101290	+	0.175440i
$655$	−5.53316e6			−0.503929
$656$	5.32466e6			0.483094
$657$	−25349.7	−	43907.0i	−0.00229118	−	0.00396845i
$658$		−	1.88021e6i		−	0.169294i
$659$	4.51085e6	−	7.81302e6i	0.404617	−	0.700818i	−0.589659	−	0.807652i	$-0.700738\pi$
$659$	4.51085e6	−	7.81302e6i	0.404617	−	0.700818i	0.994277	+	0.106834i	$0.0340714\pi$
$660$		−	930476.i		−	0.0831468i
$661$	−1.42710e7	−	8.23934e6i	−1.27043	−	0.733481i	−0.295358	−	0.955387i	$-0.595439\pi$
$661$	−1.42710e7	−	8.23934e6i	−1.27043	−	0.733481i	−0.975068	+	0.221906i	$0.928772\pi$
$662$	6.84463e6	−	1.18552e7i	0.607023	−	1.05139i
$663$	−753192.	+	1.30457e6i	−0.0665460	+	0.115261i
$664$	−672213.	+	388102.i	−0.0591680	+	0.0341606i
$665$	−1.84994e7			−1.62219
$666$	132176.	−	68523.3i	0.0115469	−	0.00598622i
$667$	7.56791e6			0.658660
$668$	9.64891e6	−	5.57080e6i	0.836637	−	0.483033i
$669$	−1.09633e7	+	1.89889e7i	−0.947054	+	1.64034i
$670$	−3.75897e6	+	6.51072e6i	−0.323505	+	0.560328i
$671$	1.21330e6	+	700500.i	0.104031	+	0.0600623i
$672$			1.82583e6i			0.155968i
$673$	−3.63066e6	+	6.28849e6i	−0.308993	+	0.535191i	−0.978142	−	0.207937i	$-0.933325\pi$
$673$	−3.63066e6	+	6.28849e6i	−0.308993	+	0.535191i	0.669150	+	0.743128i	$0.266658\pi$
$674$		−	1.37748e7i		−	1.16798i
$675$	1.35643e6	+	2.34941e6i	0.114588	+	0.198472i
$676$	−5.16998e6			−0.435133
$677$	2.99772e6			0.251373			0.125687	−	0.992070i	$-0.459887\pi$
$677$	2.99772e6			0.251373			0.125687	+	0.992070i	$0.459887\pi$
$678$	−5.18471e6	−	8.98018e6i	−0.433162	−	0.750258i
$679$	−5.64121e6	−	3.25696e6i	−0.469568	−	0.271105i
$680$			1.76129e6i			0.146069i
$681$	1.73462e7	−	1.00149e7i	1.43330	−	0.827517i
$682$	81733.7	+	141567.i	0.00672884	+	0.0116547i
$683$	544403.	−	314311.i	0.0446549	−	0.0257815i	−0.477506	−	0.878628i	$-0.658459\pi$
$683$	544403.	−	314311.i	0.0446549	−	0.0257815i	0.522161	+	0.852847i	$0.325126\pi$
$684$	−160260.	−	92526.3i	−0.0130974	−	0.00756180i
$685$	−1.34527e7	−	7.76694e6i	−1.09543	−	0.632446i
$686$	8.11275e6	−	4.68390e6i	0.658200	−	0.380012i
$687$	9.47098e6	+	1.64042e7i	0.765602	+	1.32606i
$688$	527590.	−	304604.i	0.0424938	−	0.0245338i
$689$			5.21712e6i			0.418680i
$690$	−3.97448e6	−	2.29467e6i	−0.317803	−	0.183484i
$691$	8.69597e6	+	1.50619e7i	0.692824	+	1.20001i	0.970909	+	0.239450i	$0.0769670\pi$
$691$	8.69597e6	+	1.50619e7i	0.692824	+	1.20001i	−0.278085	+	0.960557i	$0.589700\pi$
$692$	1.75861e6			0.139606
$693$	31376.7			0.00248184
$694$	−3.22472e6	−	5.58539e6i	−0.254152	−	0.440205i
$695$			1.09574e7i			0.860486i
$696$	3.11782e6	−	5.40022e6i	0.243965	−	0.422560i
$697$		−	9.24338e6i		−	0.720690i
$698$	−9.76725e6	−	5.63913e6i	−0.758811	−	0.438100i
$699$	8.30629e6	−	1.43869e7i	0.643005	−	1.11372i
$700$	655558.	−	1.13546e6i	0.0505669	−	0.0875844i
$701$	9.86785e6	−	5.69721e6i	0.758451	−	0.437892i	−0.0702882	−	0.997527i	$-0.522392\pi$
$701$	9.86785e6	−	5.69721e6i	0.758451	−	0.437892i	0.828739	+	0.559635i	$0.189059\pi$
$702$	3.35536e6			0.256978
$703$	−1.91298e7	+	9.91741e6i	−1.45990	+	0.756850i
$704$	−249059.			−0.0189396
$705$	3.37235e6	−	1.94703e6i	0.255540	−	0.147536i
$706$	−1.80288e6	+	3.12268e6i	−0.136130	+	0.235784i
$707$	−868615.	+	1.50448e6i	−0.0653550	+	0.113198i
$708$	4.94945e6	+	2.85757e6i	0.371086	+	0.214246i
$709$			1.08192e7i			0.808312i	0.914690	+	0.404156i	$0.132435\pi$
$709$			1.08192e7i			0.808312i	−0.914690	+	0.404156i	$0.867565\pi$
$710$	1.11255e6	−	1.92699e6i	0.0828272	−	0.143461i
$711$		−	48479.0i		−	0.00359650i
$712$	−663811.	−	1.14975e6i	−0.0490732	−	0.0849973i
$713$	806261.			0.0593953
$714$	3.16956e6			0.232677
$715$	413208.	+	715697.i	0.0302276	+	0.0523557i
$716$	3.75064e6	+	2.16543e6i	0.273415	+	0.157857i
$717$		−	1.33501e7i		−	0.969811i
$718$	−9.96054e6	+	5.75072e6i	−0.721061	+	0.416305i
$719$	5.14882e6	+	8.91802e6i	0.371437	+	0.643348i	0.989787	−	0.142555i	$-0.0455318\pi$
$719$	5.14882e6	+	8.91802e6i	0.371437	+	0.643348i	−0.618350	+	0.785903i	$0.712198\pi$
$720$	61364.8	−	35429.0i	0.00441152	−	0.00254699i
$721$	−1.57193e7	−	9.07556e6i	−1.12615	−	0.650182i
$722$	1.46171e7	+	8.43917e6i	1.04356	+	0.602500i
$723$	−7.30575e6	+	4.21798e6i	−0.519779	+	0.300095i
$724$	−3.98043e6	−	6.89431e6i	−0.282218	−	0.488815i
$725$	−3.87787e6	+	2.23889e6i	−0.273999	+	0.158193i
$726$			9.72095e6i			0.684490i
$727$	5.93156e6	+	3.42459e6i	0.416230	+	0.240310i	0.693463	−	0.720492i	$-0.256084\pi$
$727$	5.93156e6	+	3.42459e6i	0.416230	+	0.240310i	−0.277233	+	0.960803i	$0.589417\pi$
$728$	−810817.	−	1.40438e6i	−0.0567015	−	0.0982098i
$729$	1.46030e7			1.01771
$730$	−2.80968e6			−0.195141
$731$	−528780.	−	915874.i	−0.0366000	−	0.0633931i
$732$		−	5.69361e6i		−	0.392744i
$733$	4.00515e6	−	6.93712e6i	0.275333	−	0.476891i	−0.694886	−	0.719120i	$-0.744545\pi$
$733$	4.00515e6	−	6.93712e6i	0.275333	−	0.476891i	0.970219	+	0.242229i	$0.0778785\pi$
$734$			1.97635e7i			1.35402i
$735$	2.88129e6	+	1.66351e6i	0.196729	+	0.113582i
$736$	−614210.	+	1.06384e6i	−0.0417948	+	0.0723907i
$737$	−922741.	+	1.59823e6i	−0.0625765	+	0.108386i
$738$	−322048.	+	185934.i	−0.0217660	+	0.0125666i
$739$	4.40089e6			0.296435			0.148217	−	0.988955i	$-0.452646\pi$
$739$	4.40089e6			0.296435			0.148217	+	0.988955i	$0.452646\pi$
$740$	373790.	−	8.24232e6i	0.0250928	−	0.553312i
$741$	−8.77111e6			−0.586825
$742$	9.50657e6	−	5.48862e6i	0.633890	−	0.365977i
$743$	652517.	−	1.13019e6i	0.0433631	−	0.0751070i	−0.843529	−	0.537083i	$-0.819526\pi$
$743$	652517.	−	1.13019e6i	0.0433631	−	0.0751070i	0.886892	+	0.461976i	$0.152859\pi$
$744$	332162.	−	575322.i	0.0219998	−	0.0381047i
$745$	−2.34905e7	−	1.35623e7i	−1.55061	−	0.895243i
$746$		−	7.08439e6i		−	0.466075i
$747$	27104.7	−	46946.6i	0.00177723	−	0.00307824i
$748$			432356.i			0.0282545i
$749$	−2.91305e6	−	5.04555e6i	−0.189733	−	0.328627i
$750$	−9.23968e6			−0.599796
$751$	3.06692e6			0.198428			0.0992141	−	0.995066i	$-0.468367\pi$
$751$	3.06692e6			0.198428			0.0992141	+	0.995066i	$0.468367\pi$
$752$	−521157.	−	902670.i	−0.0336066	−	0.0582083i
$753$	−1.62770e7	−	9.39751e6i	−1.04613	−	0.603984i
$754$			5.53827e6i			0.354769i
$755$	−1.99860e7	+	1.15389e7i	−1.27603	+	0.736714i
$756$	−3.52997e6	−	6.11410e6i	−0.224630	−	0.389070i
$757$	2.06716e7	−	1.19348e7i	1.31110	−	0.756962i	0.328820	−	0.944393i	$-0.393349\pi$
$757$	2.06716e7	−	1.19348e7i	1.31110	−	0.756962i	0.982278	+	0.187430i	$0.0600159\pi$
$758$	−7.77404e6	−	4.48834e6i	−0.491444	−	0.283735i
$759$	−975644.	−	563289.i	−0.0614734	−	0.0354917i
$760$	−8.88136e6	+	5.12765e6i	−0.557757	+	0.322021i
$761$	1.08542e7	+	1.88001e7i	0.679418	+	1.17679i	0.975156	+	0.221518i	$0.0711011\pi$
$761$	1.08542e7	+	1.88001e7i	0.679418	+	1.17679i	−0.295738	+	0.955269i	$0.595566\pi$
$762$	5.71620e6	−	3.30025e6i	0.356632	−	0.205901i
$763$			4.14093e6i			0.257505i
$764$	−1.09889e7	−	6.34445e6i	−0.681116	−	0.393243i
$765$	−61503.2	−	106527.i	−0.00379966	−	0.00658120i
$766$	−2.09379e7			−1.28932
$767$	−5.07598e6			−0.311553
$768$	506083.	+	876561.i	0.0309613	+	0.0536265i
$769$		−	1.61485e7i		−	0.984731i	−0.870389	−	0.492365i	$-0.836132\pi$
$769$		−	1.61485e7i		−	0.984731i	0.870389	−	0.492365i	$-0.163868\pi$
$770$	869423.	−	1.50588e6i	0.0528451	−	0.0915303i
$771$		−	2.22680e7i		−	1.34910i
$772$	2.45735e6	+	1.41875e6i	0.148396	+	0.0856767i
$773$	8.51339e6	−	1.47456e7i	0.512452	−	0.887594i	−0.487443	−	0.873155i	$-0.662070\pi$
$773$	8.51339e6	−	1.47456e7i	0.512452	−	0.887594i	0.999896	−	0.0144390i	$-0.00459623\pi$
$774$	−21273.2	+	36846.3i	−0.00127638	+	0.00221076i
$775$	−413136.	+	238524.i	−0.0247081	+	0.0142652i
$776$	−3.61106e6			−0.215268
$777$	−1.48326e7	−	672661.i	−0.881384	−	0.0399709i
$778$	2.14373e6			0.126976
$779$	4.66101e7	−	2.69103e7i	2.75192	−	1.58882i
$780$	1.67926e6	−	2.90856e6i	0.0988283	−	0.171176i
$781$	273105.	−	473032.i	0.0160215	−	0.0277500i
$782$	1.84679e6	+	1.06624e6i	0.107994	+	0.0623504i
$783$			2.41114e7i			1.40546i
$784$	445270.	−	771231.i	0.0258722	−	0.0448120i
$785$		−	1.61744e7i		−	0.936818i
$786$	2.75997e6	+	4.78040e6i	0.159348	+	0.275999i
$787$	1.08602e7			0.625030			0.312515	−	0.949913i	$-0.398829\pi$
$787$	1.08602e7			0.625030			0.312515	+	0.949913i	$0.398829\pi$
$788$	−1.17520e7			−0.674214
$789$	3.03042e6	+	5.24883e6i	0.173304	+	0.300172i
$790$	−2.32669e6	−	1.34331e6i	−0.132639	−	0.0765790i
$791$		−	1.93781e7i		−	1.10121i
$792$	15063.7	−	8697.01i	0.000853331	−	0.000492671i
$793$	2.52843e6	+	4.37937e6i	0.142780	+	0.247303i
$794$	2.04895e7	−	1.18296e7i	1.15340	−	0.665918i
$795$	1.96888e7	+	1.13673e7i	1.10484	+	0.637882i
$796$	−1.29340e6	−	746746.i	−0.0723520	−	0.0417725i
$797$	−1.01129e7	+	5.83869e6i	−0.563936	+	0.325589i	−0.754724	−	0.656043i	$-0.772229\pi$
$797$	−1.01129e7	+	5.83869e6i	−0.563936	+	0.325589i	0.190788	+	0.981631i	$0.438896\pi$
$798$	9.22757e6	+	1.59826e7i	0.512956	+	0.888465i
$799$	−1.56700e6	+	904706.i	−0.0868363	+	0.0501350i
$800$		−	726831.i		−	0.0401521i
$801$	80297.7	+	46359.9i	0.00442203	+	0.00255306i
$802$	−1.86625e6	−	3.23244e6i	−0.102455	−	0.177458i
$803$	−689712.			−0.0377467
$804$	7.49996e6			0.409184
$805$	−4.28821e6	−	7.42739e6i	−0.233231	−	0.403968i
$806$			590029.i			0.0319916i
$807$	−7.19678e6	+	1.24652e7i	−0.389004	+	0.673775i
$808$			963051.i			0.0518945i
$809$	2.33355e6	+	1.34728e6i	0.125356	+	0.0723745i	0.561367	−	0.827567i	$-0.310276\pi$
$809$	2.33355e6	+	1.34728e6i	0.125356	+	0.0723745i	−0.436011	+	0.899942i	$0.643609\pi$
$810$	7.17631e6	−	1.24297e7i	0.384316	−	0.665655i
$811$	1.45738e7	−	2.52426e7i	0.778074	−	1.34766i	−0.154976	−	0.987918i	$-0.549530\pi$
$811$	1.45738e7	−	2.52426e7i	0.778074	−	1.34766i	0.933050	−	0.359746i	$-0.117137\pi$
$812$	1.00918e7	−	5.82649e6i	0.537128	−	0.310111i
$813$	4.73425e6			0.251203
$814$	91757.0	−	2.02330e6i	0.00485376	−	0.107028i
$815$	1.88039e6			0.0991641
$816$	1.52167e6	−	878539.i	0.0800011	−	0.0461887i
$817$	3.07888e6	−	5.33278e6i	0.161376	−	0.279511i
$818$	3.75551e6	−	6.50473e6i	0.196239	−	0.339896i
$819$	98080.2	+	56626.6i	0.00510942	+	0.00294992i
$820$			2.06083e7i			1.07031i
$821$	−734906.	+	1.27289e6i	−0.0380517	+	0.0659075i	−0.884424	−	0.466684i	$-0.845448\pi$
$821$	−734906.	+	1.27289e6i	−0.0380517	+	0.0659075i	0.846372	+	0.532592i	$0.178782\pi$
$822$			1.54967e7i			0.799947i
$823$	7.55204e6	+	1.30805e7i	0.388655	+	0.673171i	0.992269	−	0.124106i	$-0.0396063\pi$
$823$	7.55204e6	+	1.30805e7i	0.388655	+	0.673171i	−0.603613	+	0.797277i	$0.706273\pi$
$824$	−1.00623e7			−0.516271
$825$	666573.			0.0340967
$826$	5.34014e6	+	9.24939e6i	0.272334	+	0.471697i
$827$	8.10947e6	+	4.68201e6i	0.412315	+	0.238050i	0.691784	−	0.722105i	$-0.256825\pi$
$827$	8.10947e6	+	4.68201e6i	0.412315	+	0.238050i	−0.279469	+	0.960155i	$0.590158\pi$
$828$		−	85791.6i		−	0.00434879i
$829$	−2.92610e7	+	1.68938e7i	−1.47878	+	0.853772i	−0.999712	−	0.0240084i	$-0.992357\pi$
$829$	−2.92610e7	+	1.68938e7i	−1.47878	+	0.853772i	−0.479064	+	0.877780i	$0.659024\pi$
$830$	−1.50209e6	−	2.60170e6i	−0.0756837	−	0.131088i
$831$	1.87995e7	−	1.08539e7i	0.944374	−	0.545234i
$832$	−778530.	−	449485.i	−0.0389913	−	0.0225116i
$833$	−1.33882e6	−	772970.i	−0.0668515	−	0.0385967i
$834$	9.46667e6	−	5.46558e6i	0.471283	−	0.272095i
$835$	2.15610e7	+	3.73447e7i	1.07017	+	1.85359i
$836$	−2.18017e6	+	1.25872e6i	−0.107888	+	0.0622894i
$837$			2.56875e6i			0.126739i
$838$	−9.61261e6	−	5.54984e6i	−0.472859	−	0.273005i
$839$	8.77978e6	+	1.52070e7i	0.430605	+	0.745829i	0.996925	−	0.0783559i	$-0.0249670\pi$
$839$	8.77978e6	+	1.52070e7i	0.430605	+	0.745829i	−0.566321	+	0.824185i	$0.691634\pi$
$840$	−7.06660e6			−0.345551
$841$	−1.92866e7			−0.940298
$842$	9.85009e6	+	1.70609e7i	0.478806	+	0.829317i
$843$		−	3.73723e7i		−	1.81126i
$844$	−3.03767e6	+	5.26140e6i	−0.146786	+	0.254241i
$845$		−	2.00097e7i		−	0.964047i
$846$	63041.6	+	36397.1i	0.00302832	+	0.00174840i
$847$	−9.08311e6	+	1.57324e7i	−0.435037	+	0.753506i
$848$	3.04267e6	−	5.27007e6i	0.145300	−	0.251667i
$849$	−1.86038e7	+	1.07409e7i	−0.885792	+	0.511412i
$850$	−1.26175e6			−0.0598998
$851$	−8.41614e6	−	5.38164e6i	−0.398372	−	0.254736i
$852$	−2.21978e6			−0.104764
$853$	−2.32623e7	+	1.34305e7i	−1.09466	+	0.632003i	−0.934813	−	0.355139i	$-0.884433\pi$
$853$	−2.32623e7	+	1.34305e7i	−1.09466	+	0.632003i	−0.159847	+	0.987142i	$0.551100\pi$
$854$	5.32003e6	−	9.21456e6i	0.249614	−	0.432344i
$855$	358110.	−	620265.i	0.0167533	−	0.0290176i
$856$	−2.79705e6	−	1.61488e6i	−0.130472	−	0.0753278i
$857$			3.01565e7i			1.40258i	0.712875	+	0.701291i	$0.247393\pi$
$857$			3.01565e7i			1.40258i	−0.712875	+	0.701291i	$0.752607\pi$
$858$	412220.	−	713986.i	0.0191166	−	0.0331109i
$859$		−	3.04081e7i		−	1.40607i	−0.711156	−	0.703034i	$-0.751828\pi$
$859$		−	3.04081e7i		−	1.40607i	0.711156	−	0.703034i	$-0.248172\pi$
$860$	1.17893e6	+	2.04196e6i	0.0543552	+	0.0941459i
$861$	3.70861e7			1.70492
$862$	2.55439e7			1.17090
$863$	−1.83350e7	−	3.17572e7i	−0.838021	−	1.45150i	−0.891547	−	0.452929i	$-0.850379\pi$
$863$	−1.83350e7	−	3.17572e7i	−0.838021	−	1.45150i	0.0535256	−	0.998566i	$-0.482954\pi$
$864$	−3.38941e6	−	1.95688e6i	−0.154469	−	0.0891825i
$865$			6.80645e6i			0.309301i
$866$	−1.95476e7	+	1.12858e7i	−0.885724	+	0.511373i
$867$	9.43933e6	+	1.63494e7i	0.426475	+	0.738676i
$868$	1.07515e6	−	620735.i	0.0484359	−	0.0279645i
$869$	−571148.	−	329753.i	−0.0256566	−	0.0148129i
$870$	2.09008e7	+	1.20671e7i	0.936191	+	0.540510i
$871$	−5.76877e6	+	3.33060e6i	−0.257654	+	0.148757i
$872$	1.14778e6	+	1.98802e6i	0.0511174	+	0.0885379i
$873$	218405.	−	126096.i	0.00969900	−	0.00559972i
$874$			1.24167e7i			0.549827i
$875$	−1.49535e7	−	8.63342e6i	−0.660273	−	0.381209i
$876$	1.40148e6	+	2.42744e6i	0.0617060	+	0.106878i
$877$	−3.61194e7			−1.58578			−0.792888	−	0.609368i	$-0.791423\pi$
$877$	−3.61194e7			−1.58578			−0.792888	+	0.609368i	$0.791423\pi$
$878$	−1.88805e6			−0.0826567
$879$	−3.36340e6	−	5.82559e6i	−0.146827	−	0.254312i
$880$		−	963947.i		−	0.0419611i
$881$	−1.55987e7	+	2.70178e7i	−0.677095	+	1.17276i	0.298756	+	0.954329i	$0.403428\pi$
$881$	−1.55987e7	+	2.70178e7i	−0.677095	+	1.17276i	−0.975852	+	0.218434i	$0.929905\pi$
$882$			62194.4i			0.00269203i
$883$	−3.07811e7	−	1.77715e7i	−1.32857	−	0.767047i	−0.343487	−	0.939157i	$-0.611608\pi$
$883$	−3.07811e7	−	1.77715e7i	−1.32857	−	0.767047i	−0.985078	+	0.172110i	$0.944942\pi$
$884$	−780286.	+	1.35150e6i	−0.0335833	+	0.0581680i
$885$	−1.10598e7	+	1.91562e7i	−0.474668	+	0.822148i
$886$	−2.39580e7	+	1.38322e7i	−1.02534	+	0.591979i
$887$	−3.10387e7			−1.32463			−0.662315	−	0.749226i	$-0.730426\pi$
$887$	−3.10387e7			−1.32463			−0.662315	+	0.749226i	$0.730426\pi$
$888$	−7.30744e6	+	3.78837e6i	−0.310980	+	0.161220i
$889$	1.23348e7			0.523454
$890$	4.44996e6	−	2.56919e6i	0.188313	−	0.108723i
$891$	1.76162e6	−	3.05122e6i	0.0743392	−	0.128759i
$892$	−1.13576e7	+	1.96720e7i	−0.477943	+	0.827821i
$893$	−9.12403e6	−	5.26776e6i	−0.382876	−	0.221054i
$894$			2.70597e7i			1.13234i
$895$	−8.38101e6	+	1.45163e7i	−0.349735	+	0.605758i
$896$			1.89151e6i			0.0787114i
$897$	−2.03317e6	−	3.52155e6i	−0.0843709	−	0.146135i
$898$	−7.26247e6			−0.300534
$899$	−4.23992e6			−0.174968
$900$	25380.6	+	43960.4i	0.00104447	+	0.00180907i
$901$	−9.14861e6	−	5.28195e6i	−0.375442	−	0.216762i
$902$			5.05887e6i			0.207032i
$903$	3.67465e6	−	2.12156e6i	0.149967	−	0.0865837i
$904$	−5.37122e6	−	9.30322e6i	−0.218601	−	0.378627i
$905$	2.66835e7	−	1.54057e7i	1.08298	−	0.625259i
$906$	1.99383e7	+	1.15114e7i	0.806988	+	0.465915i
$907$	−3.03851e6	−	1.75429e6i	−0.122643	−	0.0708079i	0.437424	−	0.899256i	$-0.355891\pi$
$907$	−3.03851e6	−	1.75429e6i	−0.122643	−	0.0708079i	−0.560066	+	0.828448i	$0.689224\pi$
$908$	1.79702e7	−	1.03751e7i	0.723334	−	0.417617i
$909$	−33629.2	−	58247.6i	−0.00134992	−	0.00233813i
$910$	5.43544e6	−	3.13815e6i	0.217586	−	0.125623i
$911$			1.39750e7i			0.557900i	0.960306	+	0.278950i	$0.0899863\pi$
$911$			1.39750e7i			0.557900i	−0.960306	+	0.278950i	$0.910014\pi$
$912$	8.86013e6	+	5.11540e6i	0.352738	+	0.203654i
$913$	−368730.	−	638659.i	−0.0146397	−	0.0253567i
$914$	3.00769e6			0.119088
$915$	2.20363e7			0.870134
$916$	9.81167e6	+	1.69943e7i	0.386371	+	0.669214i
$917$			1.03155e7i			0.405104i
$918$	−3.39706e6	+	5.88388e6i	−0.133044	+	0.230439i
$919$			2.22782e7i			0.870145i	0.900395	+	0.435072i	$0.143277\pi$
$919$			2.22782e7i			0.870145i	−0.900395	+	0.435072i	$0.856723\pi$
$920$	−4.11745e6	−	2.37721e6i	−0.160383	−	0.0925973i
$921$	4.53024e6	−	7.84661e6i	0.175984	−	0.304813i
$922$	4.98782e6	−	8.63915e6i	0.193234	−	0.334691i
$923$	1.70739e6	−	985763.i	0.0659673	−	0.0380863i
$924$	−1.73469e6			−0.0668408
$925$	5.90462e6	+	267775.i	0.226901	+	0.0102900i
$926$	−2.40028e7			−0.919889
$927$	608589.	−	351369.i	0.0232608	−	0.0134296i
$928$	3.22997e6	−	5.59448e6i	0.123120	−	0.213250i
$929$	−2.12396e7	+	3.67881e7i	−0.807434	+	1.39852i	0.107202	+	0.994237i	$0.465811\pi$
$929$	−2.12396e7	+	3.67881e7i	−0.807434	+	1.39852i	−0.914636	+	0.404279i	$0.867522\pi$
$930$	2.22670e6	+	1.28559e6i	0.0844218	+	0.0487410i
$931$		−	9.00143e6i		−	0.340359i
$932$	8.60509e6	−	1.49044e7i	0.324501	−	0.562051i
$933$		−	2.33620e7i		−	0.878630i
$934$	−1.67066e7	−	2.89366e7i	−0.626643	−	1.08538i
$935$	−1.67337e6			−0.0625984
$936$	62783.1			0.00234236
$937$	7.26329e6	+	1.25804e7i	0.270262	+	0.468107i	0.968929	−	0.247340i	$-0.0795564\pi$
$937$	7.26329e6	+	1.25804e7i	0.270262	+	0.468107i	−0.698667	+	0.715447i	$0.746223\pi$
$938$	1.21380e7	+	7.00786e6i	0.450442	+	0.260063i
$939$			2.61149e7i			0.966549i
$940$	3.49366e6	−	2.01706e6i	0.128962	−	0.0744561i
$941$	−2.42573e6	−	4.20149e6i	−0.0893035	−	0.154678i	0.817913	−	0.575341i	$-0.195131\pi$
$941$	−2.42573e6	−	4.20149e6i	−0.0893035	−	0.154678i	−0.907217	+	0.420663i	$0.861797\pi$
$942$	−1.39740e7	+	8.06789e6i	−0.513090	+	0.296233i
$943$	2.16087e7	+	1.24758e7i	0.791316	+	0.456867i
$944$	5.12750e6	+	2.96036e6i	0.187273	+	0.108122i
$945$	2.36637e7	−	1.36623e7i	0.861993	−	0.497672i
$946$	289400.	+	501255.i	0.0105141	+	0.0182109i
$947$	2.95505e7	−	1.70610e7i	1.07075	−	0.618200i	0.142366	−	0.989814i	$-0.454529\pi$
$947$	2.95505e7	−	1.70610e7i	1.07075	−	0.618200i	0.928387	+	0.371614i	$0.121196\pi$
$948$			2.68020e6i			0.0968606i
$949$	−2.15596e6	−	1.24475e6i	−0.0777098	−	0.0448658i
$950$	−3.67334e6	−	6.36241e6i	−0.132054	−	0.228724i
$951$	−1.75816e7			−0.630388
$952$	3.28357e6			0.117423
$953$	1.23010e7	+	2.13060e7i	0.438742	+	0.759923i	0.997593	−	0.0693452i	$-0.0220910\pi$
$953$	1.23010e7	+	2.13060e7i	0.438742	+	0.759923i	−0.558851	+	0.829268i	$0.688758\pi$
$954$			424994.i			0.0151186i
$955$	2.45553e7	−	4.25310e7i	0.871238	−	1.50903i
$956$		−	1.38304e7i		−	0.489428i
$957$	5.13067e6	+	2.96219e6i	0.181090	+	0.104552i
$958$	−1.30810e7	+	2.26570e7i	−0.460498	+	0.797606i
$959$	−1.44799e7	+	2.50800e7i	−0.508417	+	0.880604i
$960$	−3.39261e6	+	1.95872e6i	−0.118811	+	0.0685954i
$961$	2.81774e7			0.984222
$962$	3.93834e6	−	6.15901e6i	0.137207	−	0.214572i
$963$	225563.			0.00783794
$964$	−7.56856e6	+	4.36971e6i	−0.262313	+	0.151447i
$965$	−5.49107e6	+	9.51081e6i	−0.189819	+	0.328775i
$966$	−4.27796e6	+	7.40964e6i	−0.147501	+	0.255478i
$967$	−2.79084e7	−	1.61129e7i	−0.959772	−	0.554125i	−0.0636691	−	0.997971i	$-0.520280\pi$
$967$	−2.79084e7	−	1.61129e7i	−0.959772	−	0.554125i	−0.896103	+	0.443847i	$0.853614\pi$
$968$			1.00706e7i			0.345437i
$969$	8.88011e6	−	1.53808e7i	0.303815	−	0.526223i
$970$		−	1.39761e7i		−	0.476931i
$971$	−6.37455e6	−	1.10410e7i	−0.216971	−	0.375804i	0.736910	−	0.675991i	$-0.236284\pi$
$971$	−6.37455e6	−	1.10410e7i	−0.216971	−	0.375804i	−0.953880	+	0.300187i	$0.902951\pi$
$972$	541728.			0.0183915
$973$	2.04278e7			0.691736
$974$	−1.19166e6	−	2.06402e6i	−0.0402490	−	0.0697133i
$975$	2.08363e6	+	1.20299e6i	0.0701955	+	0.0405274i
$976$		−	5.89842e6i		−	0.198204i
$977$	1.32022e7	−	7.62229e6i	0.442497	−	0.255476i	−0.262159	−	0.965025i	$-0.584435\pi$
$977$	1.32022e7	−	7.62229e6i	0.442497	−	0.255476i	0.704656	+	0.709549i	$0.251101\pi$
$978$	−937949.	−	1.62458e6i	−0.0313568	−	0.0543116i
$979$	1.09236e6	−	630677.i	0.0364259	−	0.0210305i
$980$	2.98494e6	+	1.72336e6i	0.0992820	+	0.0573205i
$981$	−138841.	−	80159.9i	−0.00460623	−	0.00265941i
$982$	3.13231e7	−	1.80844e7i	1.03654	−	0.598447i
$983$	8.97296e6	+	1.55416e7i	0.296177	+	0.512994i	0.975258	−	0.221069i	$-0.0709547\pi$
$983$	8.97296e6	+	1.55416e7i	0.296177	+	0.512994i	−0.679081	+	0.734064i	$0.737621\pi$
$984$	1.78047e7	−	1.02795e7i	0.586201	−	0.338443i
$985$		−	4.54846e7i		−	1.49374i
$986$	−9.71178e6	−	5.60710e6i	−0.318131	−	0.183673i
$987$	−3.62985e6	−	6.28708e6i	−0.118603	−	0.205426i
$988$	−9.08662e6			−0.296149
$989$	2.85478e6			0.0928073
$990$	33660.5	+	58301.8i	0.00109152	+	0.00189057i
$991$		−	1.47566e7i		−	0.477313i	−0.971104	−	0.238657i	$-0.923293\pi$
$991$		−	1.47566e7i		−	0.477313i	0.971104	−	0.238657i	$-0.0767070\pi$
$992$	344111.	−	596018.i	0.0111025	−	0.0192300i
$993$		−	5.28557e7i		−	1.70106i
$994$	−3.59249e6	−	2.07413e6i	−0.115327	−	0.0665839i
$995$	2.89017e6	−	5.00593e6i	0.0925478	−	0.160298i
$996$	−1.49850e6	+	2.59549e6i	−0.0478641	+	0.0829030i
$997$	1.35539e6	−	782535.i	0.0431844	−	0.0249325i	−0.478252	−	0.878222i	$-0.658730\pi$
$997$	1.35539e6	−	782535.i	0.0431844	−	0.0249325i	0.521437	+	0.853290i	$0.325396\pi$
$998$	−1.31199e7			−0.416968
$999$	1.71460e7	−	2.68139e7i	0.543561	−	0.850054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.e.a.11.13	✓	28
37.27	even	6	inner	74.6.e.a.27.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.e.a.11.13	✓	28	1.1	even	1	trivial
74.6.e.a.27.13	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} +(7.72221 - 13.3753i) q^{3} +(8.00000 - 13.8564i) q^{4} +(53.6293 + 30.9629i) q^{5} -61.7777i q^{6} +(57.7242 - 99.9812i) q^{7} -64.0000i q^{8} +(2.23485 + 3.87087i) q^{9} +247.703 q^{10} +60.8054 q^{11} +(-123.555 - 214.004i) q^{12} +(190.071 + 109.737i) q^{13} -461.793i q^{14} +(828.273 - 478.204i) q^{15} +(-128.000 - 221.703i) q^{16} +(-384.866 + 222.203i) q^{17} +(15.4835 + 8.93939i) q^{18} +(-2240.93 - 1293.80i) q^{19} +(858.068 - 495.406i) q^{20} +(-891.517 - 1544.15i) q^{21} +(210.636 - 121.611i) q^{22} -1199.63i q^{23} +(-856.017 - 494.222i) q^{24} +(354.898 + 614.701i) q^{25} +877.900 q^{26} +3822.03 q^{27} +(-923.587 - 1599.70i) q^{28} +6308.54i q^{29} +(1912.81 - 3313.09i) q^{30} +672.092i q^{31} +(-886.810 - 512.000i) q^{32} +(469.552 - 813.289i) q^{33} +(-888.810 + 1539.46i) q^{34} +(6191.41 - 3574.61i) q^{35} +71.5151 q^{36} +(4486.09 - 7015.62i) q^{37} -10350.4 q^{38} +(2935.54 - 1694.83i) q^{39} +(1981.62 - 3432.27i) q^{40} +(-10399.7 + 18012.8i) q^{41} +(-6176.61 - 3566.07i) q^{42} +2379.72i q^{43} +(486.443 - 842.544i) q^{44} +276.789i q^{45} +(-2399.26 - 4155.64i) q^{46} +4071.54 q^{47} -3953.77 q^{48} +(1739.34 + 3012.62i) q^{49} +(2458.81 + 1419.59i) q^{50} +6863.58i q^{51} +(3041.13 - 1755.80i) q^{52} +(11885.4 + 20586.2i) q^{53} +(13239.9 - 7644.05i) q^{54} +(3260.95 + 1882.71i) q^{55} +(-6398.80 - 3694.35i) q^{56} +(-34609.9 + 19982.0i) q^{57} +(12617.1 + 21853.4i) q^{58} +(-20029.3 + 11563.9i) q^{59} -15302.5i q^{60} +(19953.8 + 11520.4i) q^{61} +(1344.18 + 2328.19i) q^{62} +516.019 q^{63} -4096.00 q^{64} +(6795.57 + 11770.3i) q^{65} -3756.42i q^{66} +(-15175.3 + 26284.4i) q^{67} +7110.48i q^{68} +(-16045.4 - 9263.79i) q^{69} +(14298.4 - 24765.6i) q^{70} +(4491.46 - 7779.44i) q^{71} +(247.736 - 143.030i) q^{72} -11342.9 q^{73} +(1509.03 - 33275.0i) q^{74} +10962.4 q^{75} +(-35854.9 + 20700.8i) q^{76} +(3509.94 - 6079.40i) q^{77} +(6779.33 - 11742.1i) q^{78} +(-9393.05 - 5423.08i) q^{79} -15853.0i q^{80} +(28971.4 - 50180.0i) q^{81} +83197.8i q^{82} +(-6064.10 - 10503.3i) q^{83} -28528.5 q^{84} -27520.1 q^{85} +(4759.44 + 8243.59i) q^{86} +(84378.5 + 48715.9i) q^{87} -3891.55i q^{88} +(17964.9 - 10372.0i) q^{89} +(553.578 + 958.825i) q^{90} +(21943.4 - 12669.0i) q^{91} +(-16622.5 - 9597.03i) q^{92} +(8989.41 + 5190.04i) q^{93} +(14104.2 - 8143.08i) q^{94} +(-80119.6 - 138771. i) q^{95} +(-13696.3 + 7907.55i) q^{96} -56422.7i q^{97} +(12050.5 + 6957.35i) q^{98} +(135.891 + 235.370i) 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

Introduction

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