LMFDB - Embedded newform 29.7.c.a.12.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, 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:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.7
Character	$\chi$	$=$	29.12
Dual form			29.7.c.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624225 - 0.624225i) q^{2} +(1.83796 + 1.83796i) q^{3} -63.2207i q^{4} +41.8066i q^{5} -2.29460i q^{6} -304.112 q^{7} +(-79.4144 + 79.4144i) q^{8} -722.244i q^{9} +O(q^{10})$	\(q+(-0.624225 - 0.624225i) q^{2} +(1.83796 + 1.83796i) q^{3} -63.2207i q^{4} +41.8066i q^{5} -2.29460i q^{6} -304.112 q^{7} +(-79.4144 + 79.4144i) q^{8} -722.244i q^{9} +(26.0967 - 26.0967i) q^{10} +(-1224.69 - 1224.69i) q^{11} +(116.197 - 116.197i) q^{12} -606.965i q^{13} +(189.834 + 189.834i) q^{14} +(-76.8390 + 76.8390i) q^{15} -3946.98 q^{16} +(-4147.47 - 4147.47i) q^{17} +(-450.843 + 450.843i) q^{18} +(6484.79 + 6484.79i) q^{19} +2643.04 q^{20} +(-558.946 - 558.946i) q^{21} +1528.96i q^{22} +9537.06 q^{23} -291.921 q^{24} +13877.2 q^{25} +(-378.883 + 378.883i) q^{26} +(2667.33 - 2667.33i) q^{27} +19226.1i q^{28} +(-19970.1 + 14000.7i) q^{29} +95.9296 q^{30} +(13880.8 + 13880.8i) q^{31} +(7546.32 + 7546.32i) q^{32} -4501.85i q^{33} +5177.92i q^{34} -12713.9i q^{35} -45660.7 q^{36} +(57213.1 - 57213.1i) q^{37} -8095.94i q^{38} +(1115.58 - 1115.58i) q^{39} +(-3320.04 - 3320.04i) q^{40} +(-3635.79 + 3635.79i) q^{41} +697.816i q^{42} +(-87198.3 - 87198.3i) q^{43} +(-77425.5 + 77425.5i) q^{44} +30194.6 q^{45} +(-5953.28 - 5953.28i) q^{46} +(40295.8 - 40295.8i) q^{47} +(-7254.40 - 7254.40i) q^{48} -25165.1 q^{49} +(-8662.50 - 8662.50i) q^{50} -15245.8i q^{51} -38372.7 q^{52} -96211.6 q^{53} -3330.03 q^{54} +(51200.0 - 51200.0i) q^{55} +(24150.8 - 24150.8i) q^{56} +23837.6i q^{57} +(21205.4 + 3726.21i) q^{58} +311418. q^{59} +(4857.81 + 4857.81i) q^{60} +(33936.8 + 33936.8i) q^{61} -17329.5i q^{62} +219643. i q^{63} +243185. i q^{64} +25375.1 q^{65} +(-2810.17 + 2810.17i) q^{66} -231415. i q^{67} +(-262206. + 262206. i) q^{68} +(17528.8 + 17528.8i) q^{69} +(-7936.32 + 7936.32i) q^{70} +358931. i q^{71} +(57356.5 + 57356.5i) q^{72} +(337335. - 337335. i) q^{73} -71427.7 q^{74} +(25505.8 + 25505.8i) q^{75} +(409973. - 409973. i) q^{76} +(372441. + 372441. i) q^{77} -1392.74 q^{78} +(-172965. - 172965. i) q^{79} -165010. i q^{80} -516711. q^{81} +4539.11 q^{82} -606502. q^{83} +(-35336.9 + 35336.9i) q^{84} +(173392. - 173392. i) q^{85} +108863. i q^{86} +(-62437.0 - 10971.4i) q^{87} +194515. q^{88} +(-697037. - 697037. i) q^{89} +(-18848.2 - 18848.2i) q^{90} +184585. i q^{91} -602940. i q^{92} +51024.9i q^{93} -50307.3 q^{94} +(-271107. + 271107. i) q^{95} +27739.7i q^{96} +(-38880.4 + 38880.4i) q^{97} +(15708.7 + 15708.7i) q^{98} +(-884522. + 884522. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.624225	−	0.624225i	−0.0780281	−	0.0780281i	0.667016	−	0.745044i	$-0.267571\pi$
$2$	−0.624225	−	0.624225i	−0.0780281	−	0.0780281i	−0.745044	+	0.667016i	$0.767571\pi$
$3$	1.83796	+	1.83796i	0.0680727	+	0.0680727i	0.740323	−	0.672251i	$-0.234672\pi$
$3$	1.83796	+	1.83796i	0.0680727	+	0.0680727i	−0.672251	+	0.740323i	$0.734672\pi$
$4$		−	63.2207i		−	0.987823i
$5$			41.8066i			0.334453i	0.985919	+	0.167226i	$0.0534811\pi$
$5$			41.8066i			0.334453i	−0.985919	+	0.167226i	$0.946519\pi$
$6$		−	2.29460i		−	0.0106232i
$7$	−304.112			−0.886623			−0.443311	−	0.896368i	$-0.646196\pi$
$7$	−304.112			−0.886623			−0.443311	+	0.896368i	$0.646196\pi$
$8$	−79.4144	+	79.4144i	−0.155106	+	0.155106i
$9$		−	722.244i		−	0.990732i
$10$	26.0967	−	26.0967i	0.0260967	−	0.0260967i
$11$	−1224.69	−	1224.69i	−0.920124	−	0.920124i	0.0769133	−	0.997038i	$-0.475494\pi$
$11$	−1224.69	−	1224.69i	−0.920124	−	0.920124i	−0.997038	+	0.0769133i	$0.975494\pi$
$12$	116.197	−	116.197i	0.0672438	−	0.0672438i
$13$		−	606.965i		−	0.276270i	−0.990413	−	0.138135i	$-0.955889\pi$
$13$		−	606.965i		−	0.276270i	0.990413	−	0.138135i	$-0.0441108\pi$
$14$	189.834	+	189.834i	0.0691815	+	0.0691815i
$15$	−76.8390	+	76.8390i	−0.0227671	+	0.0227671i
$16$	−3946.98			−0.963618
$17$	−4147.47	−	4147.47i	−0.844184	−	0.844184i	0.145216	−	0.989400i	$-0.453612\pi$
$17$	−4147.47	−	4147.47i	−0.844184	−	0.844184i	−0.989400	+	0.145216i	$0.953612\pi$
$18$	−450.843	+	450.843i	−0.0773050	+	0.0773050i
$19$	6484.79	+	6484.79i	0.945443	+	0.945443i	0.998587	−	0.0531440i	$-0.0169242\pi$
$19$	6484.79	+	6484.79i	0.945443	+	0.945443i	−0.0531440	+	0.998587i	$0.516924\pi$
$20$	2643.04			0.330380
$21$	−558.946	−	558.946i	−0.0603548	−	0.0603548i
$22$			1528.96i			0.143591i
$23$	9537.06			0.783847			0.391923	−	0.919998i	$-0.371810\pi$
$23$	9537.06			0.783847			0.391923	+	0.919998i	$0.371810\pi$
$24$	−291.921			−0.0211170
$25$	13877.2			0.888141
$26$	−378.883	+	378.883i	−0.0215568	+	0.0215568i
$27$	2667.33	−	2667.33i	0.135514	−	0.135514i
$28$			19226.1i			0.875827i
$29$	−19970.1	+	14000.7i	−0.818814	+	0.574059i
$29$	−19970.1	+	14000.7i	−0.818814	+	0.574059i
$30$	95.9296			0.00355295
$31$	13880.8	+	13880.8i	0.465941	+	0.465941i	0.900597	−	0.434656i	$-0.143130\pi$
$31$	13880.8	+	13880.8i	0.465941	+	0.465941i	−0.434656	+	0.900597i	$0.643130\pi$
$32$	7546.32	+	7546.32i	0.230295	+	0.230295i
$33$		−	4501.85i		−	0.125271i
$34$			5177.92i			0.131740i
$35$		−	12713.9i		−	0.296533i
$36$	−45660.7			−0.978668
$37$	57213.1	−	57213.1i	1.12951	−	1.12951i	0.139253	−	0.990257i	$-0.455530\pi$
$37$	57213.1	−	57213.1i	1.12951	−	1.12951i	0.990257	−	0.139253i	$-0.0444702\pi$
$38$		−	8095.94i		−	0.147542i
$39$	1115.58	−	1115.58i	0.0188064	−	0.0188064i
$40$	−3320.04	−	3320.04i	−0.0518757	−	0.0518757i
$41$	−3635.79	+	3635.79i	−0.0527530	+	0.0527530i	−0.732991	−	0.680238i	$-0.761876\pi$
$41$	−3635.79	+	3635.79i	−0.0527530	+	0.0527530i	0.680238	+	0.732991i	$0.261876\pi$
$42$			697.816i			0.00941875i
$43$	−87198.3	−	87198.3i	−1.09674	−	1.09674i	−0.994790	−	0.101947i	$-0.967493\pi$
$43$	−87198.3	−	87198.3i	−1.09674	−	1.09674i	−0.101947	−	0.994790i	$-0.532507\pi$
$44$	−77425.5	+	77425.5i	−0.908920	+	0.908920i
$45$	30194.6			0.331353
$46$	−5953.28	−	5953.28i	−0.0611621	−	0.0611621i
$47$	40295.8	−	40295.8i	0.388120	−	0.388120i	−0.485896	−	0.874016i	$-0.661507\pi$
$47$	40295.8	−	40295.8i	0.388120	−	0.388120i	0.874016	+	0.485896i	$0.161507\pi$
$48$	−7254.40	−	7254.40i	−0.0655961	−	0.0655961i
$49$	−25165.1			−0.213900
$50$	−8662.50	−	8662.50i	−0.0693000	−	0.0693000i
$51$		−	15245.8i		−	0.114932i
$52$	−38372.7			−0.272906
$53$	−96211.6			−0.646249			−0.323124	−	0.946357i	$-0.604733\pi$
$53$	−96211.6			−0.646249			−0.323124	+	0.946357i	$0.604733\pi$
$54$	−3330.03			−0.0211479
$55$	51200.0	−	51200.0i	0.307738	−	0.307738i
$56$	24150.8	−	24150.8i	0.137521	−	0.137521i
$57$			23837.6i			0.128718i
$58$	21205.4	+	3726.21i	0.108683	+	0.0190978i
$59$	311418.			1.51631			0.758156	−	0.652074i	$-0.226101\pi$
$59$	311418.			1.51631			0.758156	+	0.652074i	$0.226101\pi$
$60$	4857.81	+	4857.81i	0.0224899	+	0.0224899i
$61$	33936.8	+	33936.8i	0.149514	+	0.149514i	0.777901	−	0.628387i	$-0.216285\pi$
$61$	33936.8	+	33936.8i	0.149514	+	0.149514i	−0.628387	+	0.777901i	$0.716285\pi$
$62$		−	17329.5i		−	0.0727130i
$63$			219643.i			0.878406i
$64$			243185.i			0.927679i
$65$	25375.1			0.0923992
$66$	−2810.17	+	2810.17i	−0.00977464	+	0.00977464i
$67$		−	231415.i		−	0.769425i	−0.923036	−	0.384713i	$-0.874301\pi$
$67$		−	231415.i		−	0.769425i	0.923036	−	0.384713i	$-0.125699\pi$
$68$	−262206.	+	262206.i	−0.833904	+	0.833904i
$69$	17528.8	+	17528.8i	0.0533586	+	0.0533586i
$70$	−7936.32	+	7936.32i	−0.0231380	+	0.0231380i
$71$			358931.i			1.00285i	0.865201	+	0.501424i	$0.167190\pi$
$71$			358931.i			1.00285i	−0.865201	+	0.501424i	$0.832810\pi$
$72$	57356.5	+	57356.5i	0.153669	+	0.153669i
$73$	337335.	−	337335.i	0.867148	−	0.867148i	−0.125008	−	0.992156i	$-0.539896\pi$
$73$	337335.	−	337335.i	0.867148	−	0.867148i	0.992156	+	0.125008i	$0.0398956\pi$
$74$	−71427.7			−0.176267
$75$	25505.8	+	25505.8i	0.0604582	+	0.0604582i
$76$	409973.	−	409973.i	0.933930	−	0.933930i
$77$	372441.	+	372441.i	0.815803	+	0.815803i
$78$	−1392.74			−0.00293486
$79$	−172965.	−	172965.i	−0.350815	−	0.350815i	0.509598	−	0.860413i	$-0.329794\pi$
$79$	−172965.	−	172965.i	−0.350815	−	0.350815i	−0.860413	+	0.509598i	$0.829794\pi$
$80$		−	165010.i		−	0.322285i
$81$	−516711.			−0.972283
$82$	4539.11			0.00823244
$83$	−606502.			−1.06071			−0.530357	−	0.847775i	$-0.677942\pi$
$83$	−606502.			−1.06071			−0.530357	+	0.847775i	$0.677942\pi$
$84$	−35336.9	+	35336.9i	−0.0596199	+	0.0596199i
$85$	173392.	−	173392.i	0.282340	−	0.282340i
$86$			108863.i			0.171153i
$87$	−62437.0	−	10971.4i	−0.0948166	−	0.0166611i
$88$	194515.			0.285434
$89$	−697037.	−	697037.i	−0.988748	−	0.988748i	0.0111895	−	0.999937i	$-0.496438\pi$
$89$	−697037.	−	697037.i	−0.988748	−	0.988748i	−0.999937	+	0.0111895i	$0.996438\pi$
$90$	−18848.2	−	18848.2i	−0.0258549	−	0.0258549i
$91$			184585.i			0.244947i
$92$		−	602940.i		−	0.774302i
$93$			51024.9i			0.0634356i
$94$	−50307.3			−0.0605686
$95$	−271107.	+	271107.i	−0.316206	+	0.316206i
$96$			27739.7i			0.0313537i
$97$	−38880.4	+	38880.4i	−0.0426006	+	0.0426006i	−0.728086	−	0.685486i	$-0.759590\pi$
$97$	−38880.4	+	38880.4i	−0.0426006	+	0.0426006i	0.685486	+	0.728086i	$0.259590\pi$
$98$	15708.7	+	15708.7i	0.0166902	+	0.0166902i
$99$	−884522.	+	884522.i	−0.911597	+	0.911597i
$100$		−	877327.i		−	0.877327i
$101$	−633624.	−	633624.i	−0.614989	−	0.614989i	0.329253	−	0.944242i	$-0.393203\pi$
$101$	−633624.	−	633624.i	−0.614989	−	0.614989i	−0.944242	+	0.329253i	$0.893203\pi$
$102$	−9516.82	+	9516.82i	−0.00896791	+	0.00896791i
$103$	1.86030e6			1.70243			0.851217	−	0.524813i	$-0.175865\pi$
$103$	1.86030e6			1.70243			0.851217	+	0.524813i	$0.175865\pi$
$104$	48201.7	+	48201.7i	0.0428512	+	0.0428512i
$105$	23367.6	−	23367.6i	0.0201858	−	0.0201858i
$106$	60057.7	+	60057.7i	0.0504256	+	0.0504256i
$107$	207531.			0.169407			0.0847035	−	0.996406i	$-0.473006\pi$
$107$	207531.			0.169407			0.0847035	+	0.996406i	$0.473006\pi$
$108$	−168631.	−	168631.i	−0.133864	−	0.133864i
$109$		−	285579.i		−	0.220520i	−0.993903	−	0.110260i	$-0.964832\pi$
$109$		−	285579.i		−	0.220520i	0.993903	−	0.110260i	$-0.0351683\pi$
$110$	−63920.6			−0.0480245
$111$	210311.			0.153778
$112$	1.20032e6			0.854366
$113$	−994220.	+	994220.i	−0.689044	+	0.689044i	−0.962021	−	0.272976i	$-0.911992\pi$
$113$	−994220.	+	994220.i	−0.689044	+	0.689044i	0.272976	+	0.962021i	$0.411992\pi$
$114$	14880.0	−	14880.0i	0.0100436	−	0.0100436i
$115$			398712.i			0.262160i
$116$	885135.	+	1.26252e6i	0.567069	+	0.808843i
$117$	−438377.			−0.273709
$118$	−194395.	−	194395.i	−0.118315	−	0.118315i
$119$	1.26130e6	+	1.26130e6i	0.748472	+	0.748472i
$120$		−	12204.2i		−	0.00706264i
$121$			1.22815e6i			0.693258i
$122$		−	42368.4i		−	0.0233326i
$123$	−13364.9			−0.00718208
$124$	877556.	−	877556.i	0.460267	−	0.460267i
$125$			1.23339e6i			0.631494i
$126$	137107.	−	137107.i	0.0685404	−	0.0685404i
$127$	295289.	+	295289.i	0.144157	+	0.144157i	0.775502	−	0.631345i	$-0.217497\pi$
$127$	295289.	+	295289.i	0.144157	+	0.144157i	−0.631345	+	0.775502i	$0.717497\pi$
$128$	634767.	−	634767.i	0.302681	−	0.302681i
$129$		−	320534.i		−	0.149316i
$130$	−15839.8	−	15839.8i	−0.00720974	−	0.00720974i
$131$	10706.5	−	10706.5i	0.00476251	−	0.00476251i	−0.704722	−	0.709484i	$-0.748928\pi$
$131$	10706.5	−	10706.5i	0.00476251	−	0.00476251i	0.709484	+	0.704722i	$0.248928\pi$
$132$	−284610.			−0.123745
$133$	−1.97210e6	−	1.97210e6i	−0.838251	−	0.838251i
$134$	−144455.	+	144455.i	−0.0600368	+	0.0600368i
$135$	111512.	+	111512.i	0.0453232	+	0.0453232i
$136$	658738.			0.261876
$137$	−230399.	−	230399.i	−0.0896021	−	0.0896021i	0.660885	−	0.750487i	$-0.270181\pi$
$137$	−230399.	−	230399.i	−0.0896021	−	0.0896021i	−0.750487	+	0.660885i	$0.770181\pi$
$138$		−	21883.8i		−	0.00832694i
$139$	1.98010e6			0.737296			0.368648	−	0.929569i	$-0.379821\pi$
$139$	1.98010e6			0.737296			0.368648	+	0.929569i	$0.379821\pi$
$140$	−803780.			−0.292923
$141$	148124.			0.0528407
$142$	224054.	−	224054.i	0.0782504	−	0.0782504i
$143$	−743341.	+	743341.i	−0.254203	+	0.254203i
$144$			2.85068e6i			0.954687i
$145$	−585323.	−	834880.i	−0.191996	−	0.273855i
$146$	−421146.			−0.135324
$147$	−46252.6	−	46252.6i	−0.0145608	−	0.0145608i
$148$	−3.61705e6	−	3.61705e6i	−1.11576	−	1.11576i
$149$		−	4.41175e6i		−	1.33368i	−0.745200	−	0.666841i	$-0.767646\pi$
$149$		−	4.41175e6i		−	1.33368i	0.745200	−	0.666841i	$-0.232354\pi$
$150$		−	31842.7i		−	0.00943488i
$151$		−	973976.i		−	0.282890i	−0.989946	−	0.141445i	$-0.954825\pi$
$151$		−	973976.i		−	0.282890i	0.989946	−	0.141445i	$-0.0451748\pi$
$152$	−1.02997e6			−0.293288
$153$	−2.99549e6	+	2.99549e6i	−0.836360	+	0.836360i
$154$		−	464974.i		−	0.127311i
$155$	−580311.	+	580311.i	−0.155835	+	0.155835i
$156$	−70527.6	−	70527.6i	−0.0185774	−	0.0185774i
$157$	2.07812e6	−	2.07812e6i	0.536996	−	0.536996i	−0.385650	−	0.922645i	$-0.626023\pi$
$157$	2.07812e6	−	2.07812e6i	0.536996	−	0.536996i	0.922645	+	0.385650i	$0.126023\pi$
$158$			215939.i			0.0547469i
$159$	−176833.	−	176833.i	−0.0439919	−	0.0439919i
$160$	−315486.	+	315486.i	−0.0770230	+	0.0770230i
$161$	−2.90033e6			−0.694976
$162$	322544.	+	322544.i	0.0758654	+	0.0758654i
$163$	2.27318e6	−	2.27318e6i	0.524893	−	0.524893i	−0.394152	−	0.919045i	$-0.628962\pi$
$163$	2.27318e6	−	2.27318e6i	0.524893	−	0.524893i	0.919045	+	0.394152i	$0.128962\pi$
$164$	229857.	+	229857.i	0.0521107	+	0.0521107i
$165$	188207.			0.0418971
$166$	378594.	+	378594.i	0.0827655	+	0.0827655i
$167$			3.62462e6i			0.778239i	0.921187	+	0.389119i	$0.127221\pi$
$167$			3.62462e6i			0.778239i	−0.921187	+	0.389119i	$0.872779\pi$
$168$	88776.6			0.0187228
$169$	4.45840e6			0.923675
$170$	−216471.			−0.0440609
$171$	4.68360e6	−	4.68360e6i	0.936681	−	0.936681i
$172$	−5.51273e6	+	5.51273e6i	−1.08338	+	1.08338i
$173$		−	8.60281e6i		−	1.66151i	−0.556641	−	0.830753i	$-0.687910\pi$
$173$		−	8.60281e6i		−	1.66151i	0.556641	−	0.830753i	$-0.312090\pi$
$174$	32126.1	+	45823.4i	0.00609833	+	0.00869840i
$175$	−4.22022e6			−0.787446
$176$	4.83381e6	+	4.83381e6i	0.886648	+	0.886648i
$177$	572375.	+	572375.i	0.103219	+	0.103219i
$178$			870216.i			0.154300i
$179$			2.41092e6i			0.420363i	0.977662	+	0.210182i	$0.0674055\pi$
$179$			2.41092e6i			0.420363i	−0.977662	+	0.210182i	$0.932595\pi$
$180$		−	1.90892e6i		−	0.327318i
$181$	1.34840e6			0.227397			0.113698	−	0.993515i	$-0.463730\pi$
$181$	1.34840e6			0.227397			0.113698	+	0.993515i	$0.463730\pi$
$182$	115223.	−	115223.i	0.0191128	−	0.0191128i
$183$			124749.i			0.0203556i
$184$	−757380.	+	757380.i	−0.121579	+	0.121579i
$185$	2.39188e6	+	2.39188e6i	0.377768	+	0.377768i
$186$	31851.0	−	31851.0i	0.00494977	−	0.00494977i
$187$			1.01587e7i			1.55351i
$188$	−2.54753e6	−	2.54753e6i	−0.383394	−	0.383394i
$189$	−811167.	+	811167.i	−0.120150	+	0.120150i
$190$	338464.			0.0493459
$191$	6.96124e6	+	6.96124e6i	0.999048	+	0.999048i	1.00000		0.000951164i	$-0.000302765\pi$
$191$	6.96124e6	+	6.96124e6i	0.999048	+	0.999048i	−0.000951164		1.00000i	$0.500303\pi$
$192$	−446966.	+	446966.i	−0.0631496	+	0.0631496i
$193$	−2.70963e6	−	2.70963e6i	−0.376910	−	0.376910i	0.493076	−	0.869986i	$-0.335872\pi$
$193$	−2.70963e6	−	2.70963e6i	−0.376910	−	0.376910i	−0.869986	+	0.493076i	$0.835872\pi$
$194$	48540.2			0.00664809
$195$	46638.5	+	46638.5i	0.00628986	+	0.00628986i
$196$			1.59096e6i			0.211295i
$197$	−4.85046e6			−0.634431			−0.317216	−	0.948353i	$-0.602748\pi$
$197$	−4.85046e6			−0.634431			−0.317216	+	0.948353i	$0.602748\pi$
$198$	1.10428e6			0.142260
$199$	1.31919e7			1.67398			0.836989	−	0.547220i	$-0.184314\pi$
$199$	1.31919e7			1.67398			0.836989	+	0.547220i	$0.184314\pi$
$200$	−1.10205e6	+	1.10205e6i	−0.137756	+	0.137756i
$201$	425331.	−	425331.i	0.0523768	−	0.0523768i
$202$			791048.i			0.0959729i
$203$	6.07313e6	−	4.25778e6i	0.725979	−	0.508974i
$204$	−963850.			−0.113532
$205$	−152000.	−	152000.i	−0.0176434	−	0.0176434i
$206$	−1.16124e6	−	1.16124e6i	−0.132838	−	0.132838i
$207$		−	6.88808e6i		−	0.776582i
$208$			2.39568e6i			0.266219i
$209$		−	1.58837e7i		−	1.73985i
$210$	−29173.3			−0.00315013
$211$	−9.99184e6	+	9.99184e6i	−1.06365	+	1.06365i	−0.0658168	+	0.997832i	$0.520965\pi$
$211$	−9.99184e6	+	9.99184e6i	−1.06365	+	1.06365i	−0.997832	+	0.0658168i	$0.979035\pi$
$212$			6.08256e6i			0.638380i
$213$	−659701.	+	659701.i	−0.0682666	+	0.0682666i
$214$	−129546.	−	129546.i	−0.0132185	−	0.0132185i
$215$	3.64546e6	−	3.64546e6i	0.366807	−	0.366807i
$216$			423649.i			0.0420383i
$217$	−4.22132e6	−	4.22132e6i	−0.413113	−	0.413113i
$218$	−178266.	+	178266.i	−0.0172067	+	0.0172067i
$219$	1.24002e6			0.118058
$220$	−3.23690e6	−	3.23690e6i	−0.303991	−	0.303991i
$221$	−2.51737e6	+	2.51737e6i	−0.233222	+	0.233222i
$222$	−131281.	−	131281.i	−0.0119990	−	0.0119990i
$223$	−5.89210e6			−0.531319			−0.265660	−	0.964067i	$-0.585590\pi$
$223$	−5.89210e6			−0.531319			−0.265660	+	0.964067i	$0.585590\pi$
$224$	−2.29492e6	−	2.29492e6i	−0.204185	−	0.204185i
$225$		−	1.00227e7i		−	0.879910i
$226$	1.24123e6			0.107530
$227$	6.65270e6			0.568749			0.284374	−	0.958713i	$-0.408214\pi$
$227$	6.65270e6			0.568749			0.284374	+	0.958713i	$0.408214\pi$
$228$	1.50703e6			0.127150
$229$	−1.46703e7	+	1.46703e7i	−1.22161	+	1.22161i	−0.254545	+	0.967061i	$0.581926\pi$
$229$	−1.46703e7	+	1.46703e7i	−1.22161	+	1.22161i	−0.967061	+	0.254545i	$0.918074\pi$
$230$	248886.	−	248886.i	0.0204558	−	0.0204558i
$231$			1.36907e6i			0.111068i
$232$	474051.	−	2.69777e6i	0.0379630	−	0.216043i
$233$	−1.29680e7			−1.02519			−0.512595	−	0.858631i	$-0.671316\pi$
$233$	−1.29680e7			−1.02519			−0.512595	+	0.858631i	$0.671316\pi$
$234$	273646.	+	273646.i	0.0213570	+	0.0213570i
$235$	1.68463e6	+	1.68463e6i	0.129808	+	0.129808i
$236$		−	1.96881e7i		−	1.49785i
$237$		−	635808.i		−	0.0477618i
$238$		−	1.57466e6i		−	0.116804i
$239$	−6.58953e6			−0.482682			−0.241341	−	0.970440i	$-0.577587\pi$
$239$	−6.58953e6			−0.482682			−0.241341	+	0.970440i	$0.577587\pi$
$240$	303282.	−	303282.i	0.0219388	−	0.0219388i
$241$		−	22395.7i		−	0.00159998i	−1.00000		0.000799989i	$-0.999745\pi$
$241$		−	22395.7i		−	0.00159998i	1.00000		0.000799989i	$-0.000254644\pi$
$242$	766642.	−	766642.i	0.0540937	−	0.0540937i
$243$	−2.89418e6	−	2.89418e6i	−0.201700	−	0.201700i
$244$	2.14551e6	−	2.14551e6i	0.147693	−	0.147693i
$245$		−	1.05207e6i		−	0.0715395i
$246$	8342.71	+	8342.71i	0.000560404	+	0.000560404i
$247$	3.93604e6	−	3.93604e6i	0.261197	−	0.261197i
$248$	−2.20468e6			−0.144540
$249$	−1.11473e6	−	1.11473e6i	−0.0722056	−	0.0722056i
$250$	769911.	−	769911.i	0.0492743	−	0.0492743i
$251$	2.20218e7	+	2.20218e7i	1.39262	+	1.39262i	0.819411	+	0.573207i	$0.194301\pi$
$251$	2.20218e7	+	2.20218e7i	1.39262	+	1.39262i	0.573207	+	0.819411i	$0.305699\pi$
$252$	1.38860e7			0.867710
$253$	−1.16799e7	−	1.16799e7i	−0.721237	−	0.721237i
$254$		−	368654.i		−	0.0224967i
$255$	637375.			0.0384392
$256$	1.47714e7			0.880444
$257$	1.65694e7			0.976128			0.488064	−	0.872808i	$-0.337703\pi$
$257$	1.65694e7			0.976128			0.488064	+	0.872808i	$0.337703\pi$
$258$	−200086.	+	200086.i	−0.0116508	+	0.0116508i
$259$	−1.73992e7	+	1.73992e7i	−1.00145	+	1.00145i
$260$		−	1.60423e6i		−	0.0912741i
$261$	1.01119e7	+	1.44232e7i	0.568739	+	0.811225i
$262$	−13366.6			−0.000743219
$263$	−1.95300e6	−	1.95300e6i	−0.107358	−	0.107358i	0.651387	−	0.758746i	$-0.274187\pi$
$263$	−1.95300e6	−	1.95300e6i	−0.107358	−	0.107358i	−0.758746	+	0.651387i	$0.774187\pi$
$264$	357512.	+	357512.i	0.0194303	+	0.0194303i
$265$		−	4.02228e6i		−	0.216140i
$266$			2.46207e6i			0.130814i
$267$		−	2.56225e6i		−	0.134613i
$268$	−1.46302e7			−0.760056
$269$	−1.73386e7	+	1.73386e7i	−0.890751	+	0.890751i	−0.994594	−	0.103843i	$-0.966886\pi$
$269$	−1.73386e7	+	1.73386e7i	−0.890751	+	0.890751i	0.103843	+	0.994594i	$0.466886\pi$
$270$		−	139217.i		−	0.00707297i
$271$	−1.69492e7	+	1.69492e7i	−0.851610	+	0.851610i	−0.990331	−	0.138722i	$-0.955701\pi$
$271$	−1.69492e7	+	1.69492e7i	−0.851610	+	0.851610i	0.138722	+	0.990331i	$0.455701\pi$
$272$	1.63700e7	+	1.63700e7i	0.813471	+	0.813471i
$273$	−339260.	+	339260.i	−0.0166742	+	0.0166742i
$274$			287641.i			0.0139830i
$275$	−1.69952e7	−	1.69952e7i	−0.817201	−	0.817201i
$276$	1.10818e6	−	1.10818e6i	0.0527088	−	0.0527088i
$277$	3.20123e7			1.50618			0.753092	−	0.657915i	$-0.228561\pi$
$277$	3.20123e7			1.50618			0.753092	+	0.657915i	$0.228561\pi$
$278$	−1.23603e6	−	1.23603e6i	−0.0575298	−	0.0575298i
$279$	1.00253e7	−	1.00253e7i	0.461622	−	0.461622i
$280$	1.00966e6	+	1.00966e6i	0.0459942	+	0.0459942i
$281$	3.35844e7			1.51363			0.756813	−	0.653632i	$-0.226755\pi$
$281$	3.35844e7			1.51363			0.756813	+	0.653632i	$0.226755\pi$
$282$	−92462.9	−	92462.9i	−0.00412306	−	0.00412306i
$283$			1.85857e7i			0.820011i	0.912083	+	0.410005i	$0.134473\pi$
$283$			1.85857e7i			0.820011i	−0.912083	+	0.410005i	$0.865527\pi$
$284$	2.26918e7			0.990637
$285$	−996570.			−0.0430500
$286$	928024.			0.0396699
$287$	1.10569e6	−	1.10569e6i	0.0467720	−	0.0467720i
$288$	5.45028e6	−	5.45028e6i	0.228161	−	0.228161i
$289$			1.02655e7i			0.425292i
$290$	−155780.	+	886526.i	−0.00638731	+	0.0363494i
$291$	−142921.			−0.00579987
$292$	−2.13266e7	−	2.13266e7i	−0.856589	−	0.856589i
$293$	−3.18077e7	−	3.18077e7i	−1.26453	−	1.26453i	−0.948873	−	0.315659i	$-0.897774\pi$
$293$	−3.18077e7	−	3.18077e7i	−1.26453	−	1.26453i	−0.315659	−	0.948873i	$-0.602226\pi$
$294$			57744.0i			0.00227230i
$295$			1.30193e7i			0.507135i
$296$			9.08708e6i			0.350388i
$297$	−6.53329e6			−0.249380
$298$	−2.75393e6	+	2.75393e6i	−0.104065	+	0.104065i
$299$		−	5.78866e6i		−	0.216553i
$300$	1.61249e6	−	1.61249e6i	0.0597220	−	0.0597220i
$301$	2.65180e7	+	2.65180e7i	0.972392	+	0.972392i
$302$	−607980.	+	607980.i	−0.0220734	+	0.0220734i
$303$		−	2.32915e6i		−	0.0837279i
$304$	−2.55953e7	−	2.55953e7i	−0.911046	−	0.911046i
$305$	−1.41878e6	+	1.41878e6i	−0.0500053	+	0.0500053i
$306$	3.73972e6			0.130519
$307$	−1.43585e7	−	1.43585e7i	−0.496243	−	0.496243i	0.414024	−	0.910266i	$-0.364123\pi$
$307$	−1.43585e7	−	1.43585e7i	−0.496243	−	0.496243i	−0.910266	+	0.414024i	$0.864123\pi$
$308$	2.35460e7	−	2.35460e7i	0.805869	−	0.805869i
$309$	3.41915e6	+	3.41915e6i	0.115889	+	0.115889i
$310$	724489.			0.0243191
$311$	−1.46836e7	−	1.46836e7i	−0.488147	−	0.488147i	0.419574	−	0.907721i	$-0.362179\pi$
$311$	−1.46836e7	−	1.46836e7i	−0.488147	−	0.488147i	−0.907721	+	0.419574i	$0.862179\pi$
$312$			177186.i			0.00583399i
$313$	−5.90454e7			−1.92554			−0.962772	−	0.270316i	$-0.912872\pi$
$313$	−5.90454e7			−1.92554			−0.962772	+	0.270316i	$0.912872\pi$
$314$	−2.59442e6			−0.0838016
$315$	−9.18252e6			−0.293785
$316$	−1.09350e7	+	1.09350e7i	−0.346543	+	0.346543i
$317$	−1.86473e7	+	1.86473e7i	−0.585380	+	0.585380i	−0.936377	−	0.350997i	$-0.885843\pi$
$317$	−1.86473e7	+	1.86473e7i	−0.585380	+	0.585380i	0.350997	+	0.936377i	$0.385843\pi$
$318$			220768.i			0.00686521i
$319$	4.16035e7	+	7.31056e6i	1.28162	+	0.225205i
$320$	−1.01668e7			−0.310265
$321$	381434.	+	381434.i	0.0115320	+	0.0115320i
$322$	1.81046e6	+	1.81046e6i	0.0542277	+	0.0542277i
$323$		−	5.37910e7i		−	1.59625i
$324$			3.26668e7i			0.960443i
$325$		−	8.42298e6i		−	0.245367i
$326$	−2.83795e6			−0.0819128
$327$	524884.	−	524884.i	0.0150114	−	0.0150114i
$328$		−	577468.i		−	0.0163646i
$329$	−1.22544e7	+	1.22544e7i	−0.344116	+	0.344116i
$330$	−117484.	−	117484.i	−0.00326916	−	0.00326916i
$331$	1.80357e7	−	1.80357e7i	0.497336	−	0.497336i	−0.413272	−	0.910608i	$-0.635614\pi$
$331$	1.80357e7	−	1.80357e7i	0.497336	−	0.497336i	0.910608	+	0.413272i	$0.135614\pi$
$332$			3.83435e7i			1.04780i
$333$	−4.13218e7	−	4.13218e7i	−1.11904	−	1.11904i
$334$	2.26258e6	−	2.26258e6i	0.0607245	−	0.0607245i
$335$	9.67466e6			0.257336
$336$	2.20615e6	+	2.20615e6i	0.0581590	+	0.0581590i
$337$	3.92558e7	−	3.92558e7i	1.02568	−	1.02568i	0.0260233	−	0.999661i	$-0.491716\pi$
$337$	3.92558e7	−	3.92558e7i	1.02568	−	1.02568i	0.999661	−	0.0260233i	$-0.00828441\pi$
$338$	−2.78305e6	−	2.78305e6i	−0.0720727	−	0.0720727i
$339$	−3.65468e6			−0.0938102
$340$	−1.09620e7	−	1.09620e7i	−0.278902	−	0.278902i
$341$		−	3.39993e7i		−	0.857447i
$342$	−5.84724e6			−0.146175
$343$	4.34314e7			1.07627
$344$	1.38496e7			0.340221
$345$	−732818.	+	732818.i	−0.0178459	+	0.0178459i
$346$	−5.37009e6	+	5.37009e6i	−0.129644	+	0.129644i
$347$			4.53577e7i			1.08558i	0.839868	+	0.542791i	$0.182632\pi$
$347$			4.53577e7i			1.08558i	−0.839868	+	0.542791i	$0.817368\pi$
$348$	−693620.	+	3.94731e6i	−0.0164583	+	0.0936620i
$349$	4.29971e7			1.01149			0.505747	−	0.862682i	$-0.331217\pi$
$349$	4.29971e7			1.01149			0.505747	+	0.862682i	$0.331217\pi$
$350$	2.63437e6	+	2.63437e6i	0.0614430	+	0.0614430i
$351$	−1.61898e6	−	1.61898e6i	−0.0374386	−	0.0374386i
$352$		−	1.84837e7i		−	0.423801i
$353$			5.98419e7i			1.36045i	0.733005	+	0.680223i	$0.238117\pi$
$353$			5.98419e7i			1.36045i	−0.733005	+	0.680223i	$0.761883\pi$
$354$		−	714582.i		−	0.0161080i
$355$	−1.50057e7			−0.335406
$356$	−4.40671e7	+	4.40671e7i	−0.976708	+	0.976708i
$357$			4.63643e6i			0.101901i
$358$	1.50496e6	−	1.50496e6i	0.0328001	−	0.0328001i
$359$	−1.24809e7	−	1.24809e7i	−0.269751	−	0.269751i	0.559249	−	0.829000i	$-0.311090\pi$
$359$	−1.24809e7	−	1.24809e7i	−0.269751	−	0.269751i	−0.829000	+	0.559249i	$0.811090\pi$
$360$	−2.39788e6	+	2.39788e6i	−0.0513949	+	0.0513949i
$361$			3.70592e7i			0.787724i
$362$	−841707.	−	841707.i	−0.0177433	−	0.0177433i
$363$	−2.25729e6	+	2.25729e6i	−0.0471919	+	0.0471919i
$364$	1.16696e7			0.241964
$365$	1.41028e7	+	1.41028e7i	0.290020	+	0.290020i
$366$	77871.6	−	77871.6i	0.00158831	−	0.00158831i
$367$	4.67799e7	+	4.67799e7i	0.946371	+	0.946371i	0.998633	−	0.0522622i	$-0.0166432\pi$
$367$	4.67799e7	+	4.67799e7i	0.946371	+	0.946371i	−0.0522622	+	0.998633i	$0.516643\pi$
$368$	−3.76426e7			−0.755329
$369$	2.62593e6	+	2.62593e6i	0.0522641	+	0.0522641i
$370$		−	2.98615e6i		−	0.0589530i
$371$	2.92591e7			0.572979
$372$	3.22583e6			0.0626632
$373$	8.49391e7			1.63675			0.818373	−	0.574688i	$-0.194876\pi$
$373$	8.49391e7			1.63675			0.818373	+	0.574688i	$0.194876\pi$
$374$	6.34132e6	−	6.34132e6i	0.121217	−	0.121217i
$375$	−2.26692e6	+	2.26692e6i	−0.0429875	+	0.0429875i
$376$			6.40013e6i			0.120400i
$377$	8.49795e6	+	1.21211e7i	0.158595	+	0.226214i
$378$	1.01270e6			0.0187502
$379$	−4.65324e7	−	4.65324e7i	−0.854748	−	0.854748i	0.135966	−	0.990714i	$-0.456586\pi$
$379$	−4.65324e7	−	4.65324e7i	−0.854748	−	0.854748i	−0.990714	+	0.135966i	$0.956586\pi$
$380$	1.71396e7	+	1.71396e7i	0.312356	+	0.312356i
$381$			1.08546e6i			0.0196264i
$382$		−	8.69076e6i		−	0.155908i
$383$		−	8.47593e7i		−	1.50866i	−0.656496	−	0.754330i	$-0.727962\pi$
$383$		−	8.47593e7i		−	1.50866i	0.656496	−	0.754330i	$-0.272038\pi$
$384$	2.33336e6			0.0412086
$385$	−1.55705e7	+	1.55705e7i	−0.272848	+	0.272848i
$386$			3.38284e6i			0.0588193i
$387$	−6.29784e7	+	6.29784e7i	−1.08657	+	1.08657i
$388$	2.45804e6	+	2.45804e6i	0.0420818	+	0.0420818i
$389$	1.76773e7	−	1.76773e7i	0.300308	−	0.300308i	−0.540827	−	0.841134i	$-0.681888\pi$
$389$	1.76773e7	−	1.76773e7i	0.300308	−	0.300308i	0.841134	+	0.540827i	$0.181888\pi$
$390$		−	58225.9i		−	0.000981573i
$391$	−3.95547e7	−	3.95547e7i	−0.661711	−	0.661711i
$392$	1.99847e6	−	1.99847e6i	0.0331772	−	0.0331772i
$393$	39356.5			0.000648393
$394$	3.02778e6	+	3.02778e6i	0.0495035	+	0.0495035i
$395$	7.23110e6	−	7.23110e6i	0.117331	−	0.117331i
$396$	5.59201e7	+	5.59201e7i	0.900497	+	0.900497i
$397$	6.77085e7			1.08211			0.541055	−	0.840987i	$-0.318025\pi$
$397$	6.77085e7			1.08211			0.541055	+	0.840987i	$0.318025\pi$
$398$	−8.23475e6	−	8.23475e6i	−0.130617	−	0.130617i
$399$		−	7.24929e6i		−	0.114124i
$400$	−5.47730e7			−0.855829
$401$	1.24148e8			1.92534			0.962670	−	0.270679i	$-0.0872481\pi$
$401$	1.24148e8			1.92534			0.962670	+	0.270679i	$0.0872481\pi$
$402$	−531005.			−0.00817374
$403$	8.42518e6	−	8.42518e6i	0.128725	−	0.128725i
$404$	−4.00581e7	+	4.00581e7i	−0.607500	+	0.607500i
$405$		−	2.16019e7i		−	0.325183i
$406$	−6.44881e6	−	1.13318e6i	−0.0963611	−	0.0169325i
$407$	−1.40136e8			−2.07858
$408$	1.21074e6	+	1.21074e6i	0.0178266	+	0.0178266i
$409$	124624.	+	124624.i	0.00182151	+	0.00182151i	0.708017	−	0.706195i	$-0.249590\pi$
$409$	124624.	+	124624.i	0.00182151	+	0.00182151i	−0.706195	+	0.708017i	$0.749590\pi$
$410$			189765.i			0.00275336i
$411$		−	846928.i		−	0.0121989i
$412$		−	1.17609e8i		−	1.68170i
$413$	−9.47060e7			−1.34440
$414$	−4.29972e6	+	4.29972e6i	−0.0605953	+	0.0605953i
$415$		−	2.53558e7i		−	0.354759i
$416$	4.58035e6	−	4.58035e6i	0.0636237	−	0.0636237i
$417$	3.63934e6	+	3.63934e6i	0.0501897	+	0.0501897i
$418$	−9.91498e6	+	9.91498e6i	−0.135757	+	0.135757i
$419$			5.00854e7i			0.680878i	0.940267	+	0.340439i	$0.110576\pi$
$419$			5.00854e7i			0.680878i	−0.940267	+	0.340439i	$0.889424\pi$
$420$	−1.47732e6	−	1.47732e6i	−0.0199400	−	0.0199400i
$421$	−1.40514e6	+	1.40514e6i	−0.0188310	+	0.0188310i	−0.716460	−	0.697629i	$-0.754239\pi$
$421$	−1.40514e6	+	1.40514e6i	−0.0188310	+	0.0188310i	0.697629	+	0.716460i	$0.254239\pi$
$422$	1.24743e7			0.165989
$423$	−2.91034e7	−	2.91034e7i	−0.384523	−	0.384523i
$424$	7.64058e6	−	7.64058e6i	0.100237	−	0.100237i
$425$	−5.75554e7	−	5.75554e7i	−0.749754	−	0.749754i
$426$	823604.			0.0106534
$427$	−1.03206e7	−	1.03206e7i	−0.132562	−	0.132562i
$428$		−	1.31202e7i		−	0.167344i
$429$	−2.73247e6			−0.0346085
$430$	−4.55118e6			−0.0572425
$431$	4.59042e7			0.573351			0.286675	−	0.958028i	$-0.407450\pi$
$431$	4.59042e7			0.573351			0.286675	+	0.958028i	$0.407450\pi$
$432$	−1.05279e7	+	1.05279e7i	−0.130584	+	0.130584i
$433$	−1.21197e7	+	1.21197e7i	−0.149289	+	0.149289i	−0.777800	−	0.628512i	$-0.783664\pi$
$433$	−1.21197e7	+	1.21197e7i	−0.149289	+	0.149289i	0.628512	+	0.777800i	$0.283664\pi$
$434$			5.27011e6i			0.0644690i
$435$	458677.	−	2.61028e6i	0.00557236	−	0.0317117i
$436$	−1.80545e7			−0.217834
$437$	6.18459e7	+	6.18459e7i	0.741082	+	0.741082i
$438$	−774051.	−	774051.i	−0.00921186	−	0.00921186i
$439$		−	1.37425e8i		−	1.62432i	−0.583436	−	0.812159i	$-0.698292\pi$
$439$		−	1.37425e8i		−	1.62432i	0.583436	−	0.812159i	$-0.301708\pi$
$440$			8.13202e6i			0.0954642i
$441$			1.81754e7i			0.211918i
$442$	3.14281e6			0.0363958
$443$	−4.15941e7	+	4.15941e7i	−0.478433	+	0.478433i	−0.904630	−	0.426198i	$-0.859853\pi$
$443$	−4.15941e7	+	4.15941e7i	−0.478433	+	0.478433i	0.426198	+	0.904630i	$0.359853\pi$
$444$		−	1.32960e7i		−	0.151905i
$445$	2.91407e7	−	2.91407e7i	0.330690	−	0.330690i
$446$	3.67800e6	+	3.67800e6i	0.0414579	+	0.0414579i
$447$	8.10864e6	−	8.10864e6i	0.0907873	−	0.0907873i
$448$		−	7.39555e7i		−	0.822501i
$449$	−7.01601e6	−	7.01601e6i	−0.0775088	−	0.0775088i	0.667290	−	0.744798i	$-0.267454\pi$
$449$	−7.01601e6	−	7.01601e6i	−0.0775088	−	0.0775088i	−0.744798	+	0.667290i	$0.767454\pi$
$450$	−6.25644e6	+	6.25644e6i	−0.0686578	+	0.0686578i
$451$	8.90540e6			0.0970787
$452$	6.28553e7	+	6.28553e7i	0.680654	+	0.680654i
$453$	1.79013e6	−	1.79013e6i	0.0192571	−	0.0192571i
$454$	−4.15278e6	−	4.15278e6i	−0.0443784	−	0.0443784i
$455$	−7.71687e6			−0.0819233
$456$	−1.89305e6	−	1.89305e6i	−0.0199649	−	0.0199649i
$457$			9.80787e7i			1.02760i	0.857909	+	0.513802i	$0.171763\pi$
$457$			9.80787e7i			1.02760i	−0.857909	+	0.513802i	$0.828237\pi$
$458$	1.83151e7			0.190639
$459$	−2.21254e7			−0.228798
$460$	2.52069e7			0.258968
$461$	−6.22400e7	+	6.22400e7i	−0.635282	+	0.635282i	−0.949388	−	0.314106i	$-0.898295\pi$
$461$	−6.22400e7	+	6.22400e7i	−0.635282	+	0.635282i	0.314106	+	0.949388i	$0.398295\pi$
$462$	854605.	−	854605.i	0.00866642	−	0.00866642i
$463$		−	3.25537e7i		−	0.327988i	−0.986461	−	0.163994i	$-0.947562\pi$
$463$		−	3.25537e7i		−	0.327988i	0.986461	−	0.163994i	$-0.0524377\pi$
$464$	7.88214e7	−	5.52606e7i	0.789024	−	0.553173i
$465$	−2.13318e6			−0.0212162
$466$	8.09494e6	+	8.09494e6i	0.0799937	+	0.0799937i
$467$	−9.54849e7	−	9.54849e7i	−0.937527	−	0.937527i	0.0606329	−	0.998160i	$-0.480688\pi$
$467$	−9.54849e7	−	9.54849e7i	−0.937527	−	0.937527i	−0.998160	+	0.0606329i	$0.980688\pi$
$468$			2.77145e7i			0.270377i
$469$			7.03759e7i			0.682190i
$470$		−	2.10318e6i		−	0.0202573i
$471$	7.63900e6			0.0731095
$472$	−2.47311e7	+	2.47311e7i	−0.235189	+	0.235189i
$473$			2.13581e8i			2.01827i
$474$	−396887.	+	396887.i	−0.00372677	+	0.00372677i
$475$	8.99908e7	+	8.99908e7i	0.839687	+	0.839687i
$476$	7.97399e7	−	7.97399e7i	0.739358	−	0.739358i
$477$			6.94882e7i			0.640259i
$478$	4.11335e6	+	4.11335e6i	0.0376628	+	0.0376628i
$479$	714820.	−	714820.i	0.00650415	−	0.00650415i	−0.703847	−	0.710351i	$-0.748536\pi$
$479$	714820.	−	714820.i	0.00650415	−	0.00650415i	0.710351	+	0.703847i	$0.248536\pi$
$480$	−1.15970e6			−0.0104863
$481$	−3.47263e7	−	3.47263e7i	−0.312050	−	0.312050i
$482$	−13980.0	+	13980.0i	−0.000124843	+	0.000124843i
$483$	−5.33070e6	−	5.33070e6i	−0.0473089	−	0.0473089i
$484$	7.76444e7			0.684817
$485$	−1.62546e6	−	1.62546e6i	−0.0142479	−	0.0142479i
$486$			3.61324e6i			0.0314766i
$487$	1.43644e8			1.24366			0.621829	−	0.783153i	$-0.286390\pi$
$487$	1.43644e8			1.24366			0.621829	+	0.783153i	$0.286390\pi$
$488$	−5.39014e6			−0.0463811
$489$	8.35603e6			0.0714617
$490$	−656728.	+	656728.i	−0.00558209	+	0.00558209i
$491$	−9.26930e7	+	9.26930e7i	−0.783074	+	0.783074i	−0.980348	−	0.197275i	$-0.936791\pi$
$491$	−9.26930e7	+	9.26930e7i	−0.783074	+	0.783074i	0.197275	+	0.980348i	$0.436791\pi$
$492$			844938.i			0.00709463i
$493$	1.40893e8	+	2.47577e7i	1.17584	+	0.206618i
$494$	−4.91395e6			−0.0407615
$495$	−3.69788e7	−	3.69788e7i	−0.304886	−	0.304886i
$496$	−5.47874e7	−	5.47874e7i	−0.448989	−	0.448989i
$497$		−	1.09155e8i		−	0.889148i
$498$			1.39168e6i			0.0112681i
$499$			1.43739e8i			1.15684i	0.815738	+	0.578421i	$0.196331\pi$
$499$			1.43739e8i			1.15684i	−0.815738	+	0.578421i	$0.803669\pi$
$500$	7.79756e7			0.623805
$501$	−6.66191e6	+	6.66191e6i	−0.0529768	+	0.0529768i
$502$		−	2.74931e7i		−	0.217327i
$503$	1.11358e8	−	1.11358e8i	0.875017	−	0.875017i	−0.117997	−	0.993014i	$-0.537647\pi$
$503$	1.11358e8	−	1.11358e8i	0.875017	−	0.875017i	0.993014	+	0.117997i	$0.0376474\pi$
$504$	−1.74428e7	−	1.74428e7i	−0.136246	−	0.136246i
$505$	2.64896e7	−	2.64896e7i	0.205685	−	0.205685i
$506$			1.45818e7i			0.112554i
$507$	8.19438e6	+	8.19438e6i	0.0628770	+	0.0628770i
$508$	1.86684e7	−	1.86684e7i	0.142402	−	0.142402i
$509$	−7.38896e7			−0.560312			−0.280156	−	0.959954i	$-0.590386\pi$
$509$	−7.38896e7			−0.560312			−0.280156	+	0.959954i	$0.590386\pi$
$510$	−397866.	−	397866.i	−0.00299934	−	0.00299934i
$511$	−1.02588e8	+	1.02588e8i	−0.768833	+	0.768833i
$512$	−4.98458e7	−	4.98458e7i	−0.371380	−	0.371380i
$513$	3.45942e7			0.256242
$514$	−1.03430e7	−	1.03430e7i	−0.0761655	−	0.0761655i
$515$			7.77727e7i			0.569384i
$516$	−2.02644e7			−0.147497
$517$	−9.86993e7			−0.714237
$518$	2.17220e7			0.156282
$519$	1.58116e7	−	1.58116e7i	0.113103	−	0.113103i
$520$	−2.01515e6	+	2.01515e6i	−0.0143317	+	0.0143317i
$521$		−	9.94073e7i		−	0.702919i	−0.936203	−	0.351459i	$-0.885686\pi$
$521$		−	9.94073e7i		−	0.702919i	0.936203	−	0.351459i	$-0.114314\pi$
$522$	2.69123e6	−	1.53155e7i	0.0189208	−	0.107676i
$523$	−1.16559e8			−0.814778			−0.407389	−	0.913255i	$-0.633561\pi$
$523$	−1.16559e8			−0.814778			−0.407389	+	0.913255i	$0.633561\pi$
$524$	−676875.	−	676875.i	−0.00470451	−	0.00470451i
$525$	−7.75661e6	−	7.75661e6i	−0.0536036	−	0.0536036i
$526$			2.43823e6i			0.0167539i
$527$		−	1.15141e8i		−	0.786679i
$528$			1.77687e7i			0.120713i
$529$	−5.70803e7			−0.385584
$530$	−2.51081e6	+	2.51081e6i	−0.0168650	+	0.0168650i
$531$		−	2.24920e8i		−	1.50226i
$532$	−1.24678e8	+	1.24678e8i	−0.828044	+	0.828044i
$533$	2.20680e6	+	2.20680e6i	0.0145741	+	0.0145741i
$534$	−1.59942e6	+	1.59942e6i	−0.0105036	+	0.0105036i
$535$			8.67616e6i			0.0566586i
$536$	1.83776e7	+	1.83776e7i	0.119343	+	0.119343i
$537$	−4.43119e6	+	4.43119e6i	−0.0286152	+	0.0286152i
$538$	2.16463e7			0.139007
$539$	3.08194e7	+	3.08194e7i	0.196815	+	0.196815i
$540$	7.04987e6	−	7.04987e6i	0.0447713	−	0.0447713i
$541$	3.60878e7	+	3.60878e7i	0.227913	+	0.227913i	0.811820	−	0.583907i	$-0.198477\pi$
$541$	3.60878e7	+	3.60878e7i	0.227913	+	0.227913i	−0.583907	+	0.811820i	$0.698477\pi$
$542$	2.11602e7			0.132899
$543$	2.47831e6	+	2.47831e6i	0.0154795	+	0.0154795i
$544$		−	6.25964e7i		−	0.388823i
$545$	1.19391e7			0.0737534
$546$	423550.			0.00260211
$547$	−1.72258e8			−1.05249			−0.526243	−	0.850334i	$-0.676400\pi$
$547$	−1.72258e8			−1.05249			−0.526243	+	0.850334i	$0.676400\pi$
$548$	−1.45660e7	+	1.45660e7i	−0.0885110	+	0.0885110i
$549$	2.45107e7	−	2.45107e7i	0.148128	−	0.148128i
$550$			2.12177e7i			0.127529i
$551$	−2.20293e8	−	3.87099e7i	−1.31688	−	0.231402i
$552$	−2.78407e6			−0.0165525
$553$	5.26008e7	+	5.26008e7i	0.311040	+	0.311040i
$554$	−1.99829e7	−	1.99829e7i	−0.117525	−	0.117525i
$555$			8.79239e6i			0.0514313i
$556$		−	1.25183e8i		−	0.728318i
$557$		−	2.41388e8i		−	1.39685i	−0.715683	−	0.698425i	$-0.753885\pi$
$557$		−	2.41388e8i		−	1.39685i	0.715683	−	0.698425i	$-0.246115\pi$
$558$	−1.25161e7			−0.0720391
$559$	−5.29263e7	+	5.29263e7i	−0.302995	+	0.302995i
$560$			5.01814e7i			0.285745i
$561$	−1.86713e7	+	1.86713e7i	−0.105751	+	0.105751i
$562$	−2.09642e7	−	2.09642e7i	−0.118105	−	0.118105i
$563$	−1.13086e7	+	1.13086e7i	−0.0633700	+	0.0633700i	−0.738082	−	0.674712i	$-0.764268\pi$
$563$	−1.13086e7	+	1.13086e7i	−0.0633700	+	0.0633700i	0.674712	+	0.738082i	$0.264268\pi$
$564$		−	9.36452e6i		−	0.0521973i
$565$	−4.15650e7	−	4.15650e7i	−0.230453	−	0.230453i
$566$	1.16017e7	−	1.16017e7i	0.0639839	−	0.0639839i
$567$	1.57138e8			0.862048
$568$	−2.85042e7	−	2.85042e7i	−0.155548	−	0.155548i
$569$	3.57421e7	−	3.57421e7i	0.194019	−	0.194019i	−0.603411	−	0.797430i	$-0.706192\pi$
$569$	3.57421e7	−	3.57421e7i	0.194019	−	0.194019i	0.797430	+	0.603411i	$0.206192\pi$
$570$	622084.	+	622084.i	0.00335911	+	0.00335911i
$571$	−1.52313e7			−0.0818143			−0.0409072	−	0.999163i	$-0.513025\pi$
$571$	−1.52313e7			−0.0818143			−0.0409072	+	0.999163i	$0.513025\pi$
$572$	4.69945e7	+	4.69945e7i	0.251107	+	0.251107i
$573$			2.55890e7i			0.136016i
$574$	−1.38039e6			−0.00729907
$575$	1.32348e8			0.696167
$576$	1.75639e8			0.919081
$577$	2.53116e7	−	2.53116e7i	0.131763	−	0.131763i	−0.638150	−	0.769912i	$-0.720300\pi$
$577$	2.53116e7	−	2.53116e7i	0.131763	−	0.131763i	0.769912	+	0.638150i	$0.220300\pi$
$578$	6.40800e6	−	6.40800e6i	0.0331848	−	0.0331848i
$579$		−	9.96040e6i		−	0.0513146i
$580$	−5.27817e7	+	3.70045e7i	−0.270520	+	0.189658i
$581$	1.84444e8			0.940452
$582$	89215.1	+	89215.1i	0.000452553	+	0.000452553i
$583$	1.17829e8	+	1.17829e8i	0.594629	+	0.594629i
$584$			5.35785e7i			0.269000i
$585$		−	1.83270e7i		−	0.0915429i
$586$			3.97104e7i			0.197338i
$587$	7.85511e7			0.388363			0.194182	−	0.980966i	$-0.437795\pi$
$587$	7.85511e7			0.388363			0.194182	+	0.980966i	$0.437795\pi$
$588$	−2.92412e6	+	2.92412e6i	−0.0143835	+	0.0143835i
$589$			1.80029e8i			0.881040i
$590$	8.12701e6	−	8.12701e6i	0.0395708	−	0.0395708i
$591$	−8.91497e6	−	8.91497e6i	−0.0431874	−	0.0431874i
$592$	−2.25819e8	+	2.25819e8i	−1.08842	+	1.08842i
$593$		−	1.36789e8i		−	0.655975i	−0.944682	−	0.327988i	$-0.893630\pi$
$593$		−	1.36789e8i		−	0.655975i	0.944682	−	0.327988i	$-0.106370\pi$
$594$	4.07824e6	+	4.07824e6i	0.0194587	+	0.0194587i
$595$	−5.27305e7	+	5.27305e7i	−0.250329	+	0.250329i
$596$	−2.78914e8			−1.31744
$597$	2.42463e7	+	2.42463e7i	0.113952	+	0.113952i
$598$	−3.61343e6	+	3.61343e6i	−0.0168972	+	0.0168972i
$599$	2.36120e8	+	2.36120e8i	1.09863	+	1.09863i	0.994571	+	0.104060i	$0.0331835\pi$
$599$	2.36120e8	+	2.36120e8i	1.09863	+	1.09863i	0.104060	+	0.994571i	$0.466816\pi$
$600$	−4.05105e6			−0.0187549
$601$	−4.91186e7	−	4.91186e7i	−0.226268	−	0.226268i	0.584864	−	0.811132i	$-0.301148\pi$
$601$	−4.91186e7	−	4.91186e7i	−0.226268	−	0.226268i	−0.811132	+	0.584864i	$0.801148\pi$
$602$		−	3.31064e7i		−	0.151748i
$603$	−1.67138e8			−0.762294
$604$	−6.15754e7			−0.279445
$605$	−5.13447e7			−0.231862
$606$	−1.45392e6	+	1.45392e6i	−0.00653313	+	0.00653313i
$607$	2.45469e8	−	2.45469e8i	1.09757	−	1.09757i	0.102872	−	0.994695i	$-0.467197\pi$
$607$	2.45469e8	−	2.45469e8i	1.09757	−	1.09757i	0.994695	−	0.102872i	$-0.0328032\pi$
$608$			9.78727e7i			0.435462i
$609$	1.89878e7	+	3.33653e6i	0.0840666	+	0.0147721i
$610$	1.77128e6			0.00780365
$611$	−2.44581e7	−	2.44581e7i	−0.107226	−	0.107226i
$612$	1.89377e8	+	1.89377e8i	0.826176	+	0.826176i
$613$			3.68166e8i			1.59831i	0.601122	+	0.799157i	$0.294721\pi$
$613$			3.68166e8i			1.59831i	−0.601122	+	0.799157i	$0.705279\pi$
$614$			1.79259e7i			0.0774418i
$615$		−	558741.i		−	0.00240207i
$616$	−5.91543e7			−0.253072
$617$	3.09191e8	−	3.09191e8i	1.31635	−	1.31635i	0.399706	−	0.916644i	$-0.369112\pi$
$617$	3.09191e8	−	3.09191e8i	1.31635	−	1.31635i	0.916644	−	0.399706i	$-0.130888\pi$
$618$		−	4.26865e6i		−	0.0180853i
$619$	4.06774e7	−	4.06774e7i	0.171507	−	0.171507i	−0.616134	−	0.787641i	$-0.711302\pi$
$619$	4.06774e7	−	4.06774e7i	0.171507	−	0.171507i	0.787641	+	0.616134i	$0.211302\pi$
$620$	3.66876e7	+	3.66876e7i	0.153938	+	0.153938i
$621$	2.54385e7	−	2.54385e7i	0.106223	−	0.106223i
$622$			1.83317e7i			0.0761784i
$623$	2.11977e8	+	2.11977e8i	0.876646	+	0.876646i
$624$	−4.40316e6	+	4.40316e6i	−0.0181222	+	0.0181222i
$625$	1.65268e8			0.676936
$626$	3.68576e7	+	3.68576e7i	0.150247	+	0.150247i
$627$	2.91936e7	−	2.91936e7i	0.118436	−	0.118436i
$628$	−1.31380e8	−	1.31380e8i	−0.530457	−	0.530457i
$629$	−4.74580e8			−1.90703
$630$	5.73196e6	+	5.73196e6i	0.0229235	+	0.0229235i
$631$		−	3.34720e8i		−	1.33227i	−0.745830	−	0.666136i	$-0.767947\pi$
$631$		−	3.34720e8i		−	1.33227i	0.745830	−	0.666136i	$-0.232053\pi$
$632$	2.74719e7			0.108827
$633$	−3.67293e7			−0.144811
$634$	2.32802e7			0.0913522
$635$	−1.23450e7	+	1.23450e7i	−0.0482138	+	0.0482138i
$636$	−1.11795e7	+	1.11795e7i	−0.0434562	+	0.0434562i
$637$			1.52744e7i			0.0590941i
$638$	−2.14065e7	−	3.05334e7i	−0.0824298	−	0.117575i
$639$	2.59235e8			0.993554
$640$	2.65375e7	+	2.65375e7i	0.101232	+	0.101232i
$641$	1.20236e8	+	1.20236e8i	0.456521	+	0.456521i	0.897512	−	0.440991i	$-0.145373\pi$
$641$	1.20236e8	+	1.20236e8i	0.456521	+	0.456521i	−0.440991	+	0.897512i	$0.645373\pi$
$642$		−	476201.i		−	0.00179964i
$643$			3.85613e8i			1.45051i	0.688483	+	0.725253i	$0.258277\pi$
$643$			3.85613e8i			1.45051i	−0.688483	+	0.725253i	$0.741723\pi$
$644$			1.83361e8i			0.686514i
$645$	1.34005e7			0.0499391
$646$	−3.35777e7	+	3.35777e7i	−0.124553	+	0.124553i
$647$		−	1.69008e8i		−	0.624012i	−0.950080	−	0.312006i	$-0.898999\pi$
$647$		−	1.69008e8i		−	0.624012i	0.950080	−	0.312006i	$-0.101001\pi$
$648$	4.10343e7	−	4.10343e7i	0.150807	−	0.150807i
$649$	−3.81390e8	−	3.81390e8i	−1.39519	−	1.39519i
$650$	−5.25783e6	+	5.25783e6i	−0.0191455	+	0.0191455i
$651$		−	1.55173e7i		−	0.0562435i
$652$	−1.43712e8	−	1.43712e8i	−0.518501	−	0.518501i
$653$	6.79865e7	−	6.79865e7i	0.244165	−	0.244165i	−0.574406	−	0.818571i	$-0.694767\pi$
$653$	6.79865e7	−	6.79865e7i	0.244165	−	0.244165i	0.818571	+	0.574406i	$0.194767\pi$
$654$	−655292.			−0.00234262
$655$	447604.	+	447604.i	0.00159283	+	0.00159283i
$656$	1.43504e7	−	1.43504e7i	0.0508338	−	0.0508338i
$657$	−2.43638e8	−	2.43638e8i	−0.859111	−	0.859111i
$658$	1.52990e7			0.0537015
$659$	−1.06388e8	−	1.06388e8i	−0.371737	−	0.371737i	0.496373	−	0.868110i	$-0.334665\pi$
$659$	−1.06388e8	−	1.06388e8i	−0.371737	−	0.371737i	−0.868110	+	0.496373i	$0.834665\pi$
$660$		−	1.18986e7i		−	0.0413870i
$661$	−2.58567e8			−0.895300			−0.447650	−	0.894209i	$-0.647739\pi$
$661$	−2.58567e8			−0.895300			−0.447650	+	0.894209i	$0.647739\pi$
$662$	−2.25167e7			−0.0776123
$663$	−9.25367e6			−0.0317522
$664$	4.81650e7	−	4.81650e7i	0.164523	−	0.164523i
$665$	8.24468e7	−	8.24468e7i	0.280355	−	0.280355i
$666$			5.15882e7i			0.174634i
$667$	−1.90456e8	+	1.33526e8i	−0.641825	+	0.449974i
$668$	2.29151e8			0.768762
$669$	−1.08295e7	−	1.08295e7i	−0.0361683	−	0.0361683i
$670$	−6.03917e6	−	6.03917e6i	−0.0200795	−	0.0200795i
$671$		−	8.31239e7i		−	0.275143i
$672$		−	8.43597e6i		−	0.0277989i
$673$			3.72225e8i			1.22113i	0.791968	+	0.610563i	$0.209057\pi$
$673$			3.72225e8i			1.22113i	−0.791968	+	0.610563i	$0.790943\pi$
$674$	−4.90089e7			−0.160065
$675$	3.70151e7	−	3.70151e7i	0.120356	−	0.120356i
$676$		−	2.81863e8i		−	0.912428i
$677$	−7.36730e7	+	7.36730e7i	−0.237434	+	0.237434i	−0.815787	−	0.578353i	$-0.803696\pi$
$677$	−7.36730e7	+	7.36730e7i	−0.237434	+	0.237434i	0.578353	+	0.815787i	$0.303696\pi$
$678$	2.28134e6	+	2.28134e6i	0.00731983	+	0.00731983i
$679$	1.18240e7	−	1.18240e7i	0.0377706	−	0.0377706i
$680$			2.75396e7i			0.0875852i
$681$	1.22274e7	+	1.22274e7i	0.0387162	+	0.0387162i
$682$	−2.12232e7	+	2.12232e7i	−0.0669050	+	0.0669050i
$683$	−1.78140e8			−0.559114			−0.279557	−	0.960129i	$-0.590188\pi$
$683$	−1.78140e8			−0.559114			−0.279557	+	0.960129i	$0.590188\pi$
$684$	−2.96100e8	−	2.96100e8i	−0.925275	−	0.925275i
$685$	9.63219e6	−	9.63219e6i	0.0299677	−	0.0299677i
$686$	−2.71110e7	−	2.71110e7i	−0.0839795	−	0.0839795i
$687$	−5.39268e7			−0.166316
$688$	3.44170e8	+	3.44170e8i	1.05684	+	1.05684i
$689$			5.83970e7i			0.178539i
$690$	914887.			0.00278497
$691$	−3.89378e8			−1.18015			−0.590076	−	0.807348i	$-0.700902\pi$
$691$	−3.89378e8			−1.18015			−0.590076	+	0.807348i	$0.700902\pi$
$692$	−5.43875e8			−1.64127
$693$	2.68993e8	−	2.68993e8i	0.808243	−	0.808243i
$694$	2.83134e7	−	2.83134e7i	0.0847059	−	0.0847059i
$695$			8.27811e7i			0.246591i
$696$	5.82968e6	−	4.08711e6i	0.0172909	−	0.0121224i
$697$	3.01587e7			0.0890665
$698$	−2.68399e7	−	2.68399e7i	−0.0789250	−	0.0789250i
$699$	−2.38346e7	−	2.38346e7i	−0.0697874	−	0.0697874i
$700$			2.66805e8i			0.777858i
$701$		−	5.97648e8i		−	1.73497i	−0.497466	−	0.867483i	$-0.665736\pi$
$701$		−	5.97648e8i		−	1.73497i	0.497466	−	0.867483i	$-0.334264\pi$
$702$			2.02121e6i			0.00584252i
$703$	7.42030e8			2.13577
$704$	2.97826e8	−	2.97826e8i	0.853580	−	0.853580i
$705$			6.19257e6i			0.0176727i
$706$	3.73548e7	−	3.73548e7i	0.106153	−	0.106153i
$707$	1.92692e8	+	1.92692e8i	0.545263	+	0.545263i
$708$	3.61860e7	−	3.61860e7i	0.101962	−	0.101962i
$709$		−	2.30053e8i		−	0.645490i	−0.946486	−	0.322745i	$-0.895394\pi$
$709$		−	2.30053e8i		−	0.645490i	0.946486	−	0.322745i	$-0.104606\pi$
$710$	9.36692e6	+	9.36692e6i	0.0261711	+	0.0261711i
$711$	−1.24923e8	+	1.24923e8i	−0.347564	+	0.347564i
$712$	1.10709e8			0.306722
$713$	1.32382e8	+	1.32382e8i	0.365226	+	0.365226i
$714$	2.89417e6	−	2.89417e6i	0.00795115	−	0.00795115i
$715$	−3.10766e7	−	3.10766e7i	−0.0850188	−	0.0850188i
$716$	1.52420e8			0.415244
$717$	−1.21113e7	−	1.21113e7i	−0.0328574	−	0.0328574i
$718$			1.55818e7i			0.0420963i
$719$	6.51238e7			0.175208			0.0876039	−	0.996155i	$-0.472079\pi$
$719$	6.51238e7			0.175208			0.0876039	+	0.996155i	$0.472079\pi$
$720$	−1.19177e8			−0.319298
$721$	−5.65738e8			−1.50942
$722$	2.31333e7	−	2.31333e7i	0.0614647	−	0.0614647i
$723$	41162.5	−	41162.5i	0.000108915	−	0.000108915i
$724$		−	8.52469e7i		−	0.224628i
$725$	−2.77129e8	+	1.94291e8i	−0.727223	+	0.509845i
$726$	2.81812e6			0.00736460
$727$	−8.41475e7	−	8.41475e7i	−0.218997	−	0.218997i	0.589079	−	0.808076i	$-0.299491\pi$
$727$	−8.41475e7	−	8.41475e7i	−0.218997	−	0.218997i	−0.808076	+	0.589079i	$0.799491\pi$
$728$	−1.46587e7	−	1.46587e7i	−0.0379928	−	0.0379928i
$729$			3.66043e8i			0.944822i
$730$		−	1.76067e7i		−	0.0452595i
$731$			7.23305e8i			1.85170i
$732$	7.88673e6			0.0201078
$733$	7.52472e7	−	7.52472e7i	0.191064	−	0.191064i	−0.605092	−	0.796156i	$-0.706864\pi$
$733$	7.52472e7	−	7.52472e7i	0.191064	−	0.191064i	0.796156	+	0.605092i	$0.206864\pi$
$734$		−	5.84024e7i		−	0.147687i
$735$	1.93366e6	−	1.93366e6i	0.00486989	−	0.00486989i
$736$	7.19698e7	+	7.19698e7i	0.180516	+	0.180516i
$737$	−2.83410e8	+	2.83410e8i	−0.707967	+	0.707967i
$738$		−	3.27834e6i		−	0.00815615i
$739$	5.43225e8	+	5.43225e8i	1.34600	+	1.34600i	0.889955	+	0.456048i	$0.150736\pi$
$739$	5.43225e8	+	5.43225e8i	1.34600	+	1.34600i	0.456048	+	0.889955i	$0.349264\pi$
$740$	1.51217e8	−	1.51217e8i	0.373168	−	0.373168i
$741$	1.44686e7			0.0355608
$742$	−1.82642e7	−	1.82642e7i	−0.0447085	−	0.0447085i
$743$	3.57492e7	−	3.57492e7i	0.0871566	−	0.0871566i	−0.662184	−	0.749341i	$-0.730370\pi$
$743$	3.57492e7	−	3.57492e7i	0.0871566	−	0.0871566i	0.749341	+	0.662184i	$0.230370\pi$
$744$	−4.05211e6	−	4.05211e6i	−0.00983926	−	0.00983926i
$745$	1.84440e8			0.446054
$746$	−5.30211e7	−	5.30211e7i	−0.127712	−	0.127712i
$747$			4.38042e8i			1.05088i
$748$	6.42240e8			1.53459
$749$	−6.31125e7			−0.150200
$750$	2.83014e6			0.00670847
$751$	1.08287e8	−	1.08287e8i	0.255657	−	0.255657i	−0.567628	−	0.823285i	$-0.692139\pi$
$751$	1.08287e8	−	1.08287e8i	0.255657	−	0.255657i	0.823285	+	0.567628i	$0.192139\pi$
$752$	−1.59047e8	+	1.59047e8i	−0.373999	+	0.373999i
$753$			8.09505e7i			0.189598i
$754$	2.26168e6	−	1.28709e7i	0.00527614	−	0.0300259i
$755$	4.07186e7			0.0946133
$756$	5.12825e7	+	5.12825e7i	0.118687	+	0.118687i
$757$	−1.65444e8	−	1.65444e8i	−0.381386	−	0.381386i	0.490216	−	0.871601i	$-0.336918\pi$
$757$	−1.65444e8	−	1.65444e8i	−0.381386	−	0.381386i	−0.871601	+	0.490216i	$0.836918\pi$
$758$			5.80934e7i			0.133389i
$759$		−	4.29345e7i		−	0.0981930i
$760$		−	4.30596e7i		−	0.0980910i
$761$	−3.13688e8			−0.711776			−0.355888	−	0.934529i	$-0.615822\pi$
$761$	−3.13688e8			−0.711776			−0.355888	+	0.934529i	$0.615822\pi$
$762$	677573.	−	677573.i	0.00153141	−	0.00153141i
$763$			8.68480e7i			0.195518i
$764$	4.40094e8	−	4.40094e8i	0.986883	−	0.986883i
$765$	−1.25231e8	−	1.25231e8i	−0.279723	−	0.279723i
$766$	−5.29089e7	+	5.29089e7i	−0.117718	+	0.117718i
$767$		−	1.89020e8i		−	0.418911i
$768$	2.71493e7	+	2.71493e7i	0.0599342	+	0.0599342i
$769$	1.68996e8	−	1.68996e8i	0.371618	−	0.371618i	−0.496448	−	0.868066i	$-0.665363\pi$
$769$	1.68996e8	−	1.68996e8i	0.371618	−	0.371618i	0.868066	+	0.496448i	$0.165363\pi$
$770$	1.94390e7			0.0425796
$771$	3.04539e7	+	3.04539e7i	0.0664477	+	0.0664477i
$772$	−1.71305e8	+	1.71305e8i	−0.372321	+	0.372321i
$773$	−2.87001e8	−	2.87001e8i	−0.621362	−	0.621362i	0.324518	−	0.945880i	$-0.394798\pi$
$773$	−2.87001e8	−	2.87001e8i	−0.621362	−	0.621362i	−0.945880	+	0.324518i	$0.894798\pi$
$774$	7.86254e7			0.169567
$775$	1.92627e8	+	1.92627e8i	0.413821	+	0.413821i
$776$		−	6.17532e6i		−	0.0132152i
$777$	−6.39580e7			−0.136343
$778$	−2.20692e7			−0.0468649
$779$	−4.71547e7			−0.0997499
$780$	2.94852e6	−	2.94852e6i	0.00621327	−	0.00621327i
$781$	4.39577e8	−	4.39577e8i	0.922746	−	0.922746i
$782$			4.93821e7i			0.103264i
$783$	−1.59222e7	+	9.06113e7i	−0.0331679	+	0.188754i
$784$	9.93263e7			0.206118
$785$	8.68790e7	+	8.68790e7i	0.179600	+	0.179600i
$786$	−24567.3	−	24567.3i	−5.05929e−5	−	5.05929e-5i
$787$			4.91602e8i			1.00853i	0.863548	+	0.504266i	$0.168237\pi$
$787$			4.91602e8i			1.00853i	−0.863548	+	0.504266i	$0.831763\pi$
$788$			3.06650e8i			0.626706i
$789$		−	7.17909e6i		−	0.0146163i
$790$	−9.02766e6			−0.0183102
$791$	3.02354e8	−	3.02354e8i	0.610922	−	0.610922i
$792$		−	1.40487e8i		−	0.282789i
$793$	2.05985e7	−	2.05985e7i	0.0413062	−	0.0413062i
$794$	−4.22654e7	−	4.22654e7i	−0.0844351	−	0.0844351i
$795$	7.39280e6	−	7.39280e6i	0.0147132	−	0.0147132i
$796$		−	8.34004e8i		−	1.65359i
$797$	4.17870e8	+	4.17870e8i	0.825404	+	0.825404i	0.986877	−	0.161473i	$-0.0516245\pi$
$797$	4.17870e8	+	4.17870e8i	0.825404	+	0.825404i	−0.161473	+	0.986877i	$0.551625\pi$
$798$	−4.52519e6	+	4.52519e6i	−0.00890489	+	0.00890489i
$799$	−3.34251e8			−0.655289
$800$	1.04722e8	+	1.04722e8i	0.204535	+	0.204535i
$801$	−5.03430e8	+	5.03430e8i	−0.979584	+	0.979584i
$802$	−7.74964e7	−	7.74964e7i	−0.150231	−	0.150231i
$803$	−8.26259e8			−1.59577
$804$	−2.68897e7	−	2.68897e7i	−0.0517391	−	0.0517391i
$805$		−	1.21253e8i		−	0.232437i
$806$	−1.05184e7			−0.0200884
$807$	−6.37353e7			−0.121272
$808$	1.00638e8			0.190777
$809$	−3.80343e8	+	3.80343e8i	−0.718340	+	0.718340i	−0.968265	−	0.249925i	$-0.919594\pi$
$809$	−3.80343e8	+	3.80343e8i	−0.718340	+	0.718340i	0.249925	+	0.968265i	$0.419594\pi$
$810$	−1.34845e7	+	1.34845e7i	−0.0253734	+	0.0253734i
$811$		−	6.69773e8i		−	1.25564i	−0.778359	−	0.627820i	$-0.783948\pi$
$811$		−	6.69773e8i		−	1.25564i	0.778359	−	0.627820i	$-0.216052\pi$
$812$	−2.69180e8	−	3.83947e8i	−0.502776	−	0.717139i
$813$	−6.23039e7			−0.115943
$814$	8.74765e7	+	8.74765e7i	0.162188	+	0.162188i
$815$	9.50338e7	+	9.50338e7i	0.175552	+	0.175552i
$816$			6.01749e7i			0.110750i
$817$		−	1.13093e9i		−	2.07380i
$818$		−	155587.i		−	0.000284258i
$819$	1.33315e8			0.242677
$820$	−9.60955e6	+	9.60955e6i	−0.0174286	+	0.0174286i
$821$			8.70672e8i			1.57335i	0.617368	+	0.786675i	$0.288199\pi$
$821$			8.70672e8i			1.57335i	−0.617368	+	0.786675i	$0.711801\pi$
$822$	−528674.	+	528674.i	−0.000951859	+	0.000951859i
$823$	−4.06043e8	−	4.06043e8i	−0.728404	−	0.728404i	0.241898	−	0.970302i	$-0.422230\pi$
$823$	−4.06043e8	−	4.06043e8i	−0.728404	−	0.728404i	−0.970302	+	0.241898i	$0.922230\pi$
$824$	−1.47734e8	+	1.47734e8i	−0.264058	+	0.264058i
$825$		−	6.24731e7i		−	0.111258i
$826$	5.91179e7	+	5.91179e7i	0.104901	+	0.104901i
$827$	−3.48226e8	+	3.48226e8i	−0.615666	+	0.615666i	−0.944417	−	0.328751i	$-0.893372\pi$
$827$	−3.48226e8	+	3.48226e8i	−0.615666	+	0.615666i	0.328751	+	0.944417i	$0.393372\pi$
$828$	−4.35469e8			−0.767126
$829$	−5.25519e8	−	5.25519e8i	−0.922411	−	0.922411i	0.0747884	−	0.997199i	$-0.476172\pi$
$829$	−5.25519e8	−	5.25519e8i	−0.922411	−	0.922411i	−0.997199	+	0.0747884i	$0.976172\pi$
$830$	−1.58277e7	+	1.58277e7i	−0.0276812	+	0.0276812i
$831$	5.88375e7	+	5.88375e7i	0.102530	+	0.102530i
$832$	1.47605e8			0.256290
$833$	1.04372e8	+	1.04372e8i	0.180571	+	0.180571i
$834$		−	4.54354e6i		−	0.00783242i
$835$	−1.51533e8			−0.260284
$836$	−1.00418e9			−1.71866
$837$	7.40496e7			0.126283
$838$	3.12646e7	−	3.12646e7i	0.0531276	−	0.0531276i
$839$	7.48029e8	−	7.48029e8i	1.26658	−	1.26658i	0.318736	−	0.947843i	$-0.396742\pi$
$839$	7.48029e8	−	7.48029e8i	1.26658	−	1.26658i	0.947843	−	0.318736i	$-0.103258\pi$
$840$			3.71145e6i			0.00626189i
$841$	2.02783e8	−	5.59190e8i	0.340913	−	0.940095i
$842$	1.75425e6			0.00293870
$843$	6.17268e7	+	6.17268e7i	0.103037	+	0.103037i
$844$	6.31691e8	+	6.31691e8i	1.05070	+	1.05070i
$845$			1.86391e8i			0.308926i
$846$			3.63341e7i			0.0600072i
$847$		−	3.73494e8i		−	0.614658i
$848$	3.79745e8			0.622737
$849$	−3.41598e7	+	3.41598e7i	−0.0558203	+	0.0558203i
$850$			7.18550e7i			0.117004i
$851$	5.45645e8	−	5.45645e8i	0.885363	−	0.885363i
$852$	4.17067e7	+	4.17067e7i	0.0674353	+	0.0674353i
$853$	1.79878e8	−	1.79878e8i	0.289822	−	0.289822i	−0.547188	−	0.837010i	$-0.684302\pi$
$853$	1.79878e8	−	1.79878e8i	0.289822	−	0.289822i	0.837010	+	0.547188i	$0.184302\pi$
$854$			1.28847e7i			0.0206872i
$855$	1.95805e8	+	1.95805e8i	0.313276	+	0.313276i
$856$	−1.64809e7	+	1.64809e7i	−0.0262761	+	0.0262761i
$857$	2.24985e8			0.357446			0.178723	−	0.983899i	$-0.442803\pi$
$857$	2.24985e8			0.357446			0.178723	+	0.983899i	$0.442803\pi$
$858$	1.70567e6	+	1.70567e6i	0.00270044	+	0.00270044i
$859$	−8.07967e8	+	8.07967e8i	−1.27472	+	1.27472i	−0.331135	+	0.943584i	$0.607431\pi$
$859$	−8.07967e8	+	8.07967e8i	−1.27472	+	1.27472i	−0.943584	+	0.331135i	$0.892569\pi$
$860$	−2.30469e8	−	2.30469e8i	−0.362340	−	0.362340i
$861$	4.06442e6			0.00636780
$862$	−2.86546e7	−	2.86546e7i	−0.0447375	−	0.0447375i
$863$		−	5.04863e8i		−	0.785491i	−0.919647	−	0.392745i	$-0.871525\pi$
$863$		−	5.04863e8i		−	0.785491i	0.919647	−	0.392745i	$-0.128475\pi$
$864$	4.02571e7			0.0624168
$865$	3.59654e8			0.555695
$866$	1.51308e7			0.0232974
$867$	−1.88676e7	+	1.88676e7i	−0.0289508	+	0.0289508i
$868$	−2.66875e8	+	2.66875e8i	−0.408083	+	0.408083i
$869$			4.23656e8i			0.645587i
$870$	−1.91572e6	+	1.34308e6i	−0.00290921	+	0.00203960i
$871$	−1.40461e8			−0.212569
$872$	2.26791e7	+	2.26791e7i	0.0342040	+	0.0342040i
$873$	2.80811e7	+	2.80811e7i	0.0422057	+	0.0422057i
$874$		−	7.72115e7i		−	0.115651i
$875$		−	3.75087e8i		−	0.559897i
$876$		−	7.83948e7i		−	0.116621i
$877$	2.91154e8			0.431643			0.215821	−	0.976433i	$-0.430757\pi$
$877$	2.91154e8			0.431643			0.215821	+	0.976433i	$0.430757\pi$
$878$	−8.57840e7	+	8.57840e7i	−0.126743	+	0.126743i
$879$		−	1.16923e8i		−	0.172160i
$880$	−2.02085e8	+	2.02085e8i	−0.296542	+	0.296542i
$881$	−2.94749e8	−	2.94749e8i	−0.431046	−	0.431046i	0.457938	−	0.888984i	$-0.348588\pi$
$881$	−2.94749e8	−	2.94749e8i	−0.431046	−	0.431046i	−0.888984	+	0.457938i	$0.848588\pi$
$882$	1.13455e7	−	1.13455e7i	0.0165355	−	0.0165355i
$883$			7.01799e8i			1.01937i	0.860362	+	0.509684i	$0.170238\pi$
$883$			7.01799e8i			1.01937i	−0.860362	+	0.509684i	$0.829762\pi$
$884$	1.59150e8	+	1.59150e8i	0.230383	+	0.230383i
$885$	−2.39291e7	+	2.39291e7i	−0.0345220	+	0.0345220i
$886$	5.19282e7			0.0746624
$887$	7.52490e8	+	7.52490e8i	1.07828	+	1.07828i	0.996664	+	0.0816114i	$0.0260066\pi$
$887$	7.52490e8	+	7.52490e8i	1.07828	+	1.07828i	0.0816114	+	0.996664i	$0.473993\pi$
$888$	−1.67017e7	+	1.67017e7i	−0.0238518	+	0.0238518i
$889$	−8.98009e7	−	8.98009e7i	−0.127813	−	0.127813i
$890$	−3.63808e7			−0.0516062
$891$	6.32808e8	+	6.32808e8i	0.894621	+	0.894621i
$892$			3.72503e8i			0.524850i
$893$	5.22619e8			0.733890
$894$	−1.01232e7			−0.0141679
$895$	−1.00793e8			−0.140592
$896$	−1.93040e8	+	1.93040e8i	−0.268363	+	0.268363i
$897$	1.06393e7	−	1.06393e7i	0.0147414	−	0.0147414i
$898$			8.75914e6i			0.0120957i
$899$	−4.71543e8	−	8.28593e7i	−0.648996	−	0.114041i
$900$	−6.33644e8			−0.869196
$901$	3.99035e8	+	3.99035e8i	0.545553	+	0.545553i
$902$	−5.55898e6	−	5.55898e6i	−0.00757487	−	0.00757487i
$903$			9.74782e7i			0.132387i
$904$		−	1.57911e8i		−	0.213750i
$905$			5.63721e7i			0.0760534i
$906$	−2.23489e6			−0.00300519
$907$	6.15105e8	−	6.15105e8i	0.824380	−	0.824380i	−0.162353	−	0.986733i	$-0.551908\pi$
$907$	6.15105e8	−	6.15105e8i	0.824380	−	0.824380i	0.986733	+	0.162353i	$0.0519082\pi$
$908$		−	4.20588e8i		−	0.561823i
$909$	−4.57631e8	+	4.57631e8i	−0.609289	+	0.609289i
$910$	4.81707e6	+	4.81707e6i	0.00639232	+	0.00639232i
$911$	−1.33569e8	+	1.33569e8i	−0.176665	+	0.176665i	−0.789900	−	0.613235i	$-0.789868\pi$
$911$	−1.33569e8	+	1.33569e8i	−0.176665	+	0.176665i	0.613235	+	0.789900i	$0.289868\pi$
$912$		−	9.40865e7i		−	0.124035i
$913$	7.42774e8	+	7.42774e8i	0.975988	+	0.975988i
$914$	6.12232e7	−	6.12232e7i	0.0801821	−	0.0801821i
$915$	−5.21534e6			−0.00680800
$916$	9.27464e8	+	9.27464e8i	1.20673	+	1.20673i
$917$	−3.25599e6	+	3.25599e6i	−0.00422255	+	0.00422255i
$918$	1.38112e7	+	1.38112e7i	0.0178527	+	0.0178527i
$919$	−3.94946e8			−0.508852			−0.254426	−	0.967092i	$-0.581886\pi$
$919$	−3.94946e8			−0.508852			−0.254426	+	0.967092i	$0.581886\pi$
$920$	−3.16635e7	−	3.16635e7i	−0.0406626	−	0.0406626i
$921$		−	5.27808e7i		−	0.0675611i
$922$	7.77035e7			0.0991398
$923$	2.17858e8			0.277057
$924$	8.65533e7			0.109715
$925$	7.93958e8	−	7.93958e8i	1.00316	−	1.00316i
$926$	−2.03209e7	+	2.03209e7i	−0.0255923	+	0.0255923i
$927$		−	1.34359e9i		−	1.68666i
$928$	−2.56354e8	−	4.50465e7i	−0.320772	−	0.0563660i
$929$	9.38096e8			1.17004			0.585019	−	0.811020i	$-0.301087\pi$
$929$	9.38096e8			1.17004			0.585019	+	0.811020i	$0.301087\pi$
$930$	1.33158e6	+	1.33158e6i	0.00165546	+	0.00165546i
$931$	−1.63191e8	−	1.63191e8i	−0.202230	−	0.202230i
$932$			8.19844e8i			1.01271i
$933$		−	5.39757e7i		−	0.0664589i
$934$			1.19208e8i			0.146307i
$935$	−4.24701e8			−0.519575
$936$	3.48134e7	−	3.48134e7i	0.0424540	−	0.0424540i
$937$		−	7.28634e8i		−	0.885708i	−0.896594	−	0.442854i	$-0.853966\pi$
$937$		−	7.28634e8i		−	0.885708i	0.896594	−	0.442854i	$-0.146034\pi$
$938$	4.39304e7	−	4.39304e7i	0.0532300	−	0.0532300i
$939$	−1.08523e8	−	1.08523e8i	−0.131077	−	0.131077i
$940$	1.06503e8	−	1.06503e8i	0.128227	−	0.128227i
$941$			8.10819e8i			0.973095i	0.873654	+	0.486548i	$0.161744\pi$
$941$			8.10819e8i			0.973095i	−0.873654	+	0.486548i	$0.838256\pi$
$942$	−4.76845e6	−	4.76845e6i	−0.00570460	−	0.00570460i
$943$	−3.46748e7	+	3.46748e7i	−0.0413503	+	0.0413503i
$944$	−1.22916e9			−1.46114
$945$	−3.39121e7	−	3.39121e7i	−0.0401846	−	0.0401846i
$946$	1.33323e8	−	1.33323e8i	0.157482	−	0.157482i
$947$	−8.68764e7	−	8.68764e7i	−0.102294	−	0.102294i	0.654107	−	0.756402i	$-0.273044\pi$
$947$	−8.68764e7	−	8.68764e7i	−0.102294	−	0.102294i	−0.756402	+	0.654107i	$0.773044\pi$
$948$	−4.01962e7			−0.0471802
$949$	−2.04751e8	−	2.04751e8i	−0.239567	−	0.239567i
$950$		−	1.12349e8i		−	0.131038i
$951$	−6.85460e7			−0.0796968
$952$	−2.00330e8			−0.232185
$953$	−1.01866e9			−1.17693			−0.588466	−	0.808522i	$-0.700268\pi$
$953$	−1.01866e9			−1.17693			−0.588466	+	0.808522i	$0.700268\pi$
$954$	4.33763e7	−	4.33763e7i	0.0499583	−	0.0499583i
$955$	−2.91026e8	+	2.91026e8i	−0.334135	+	0.334135i
$956$			4.16595e8i			0.476804i
$957$	6.30292e7	+	8.99022e7i	0.0719128	+	0.102573i
$958$	−892418.			−0.00101501
$959$	7.00669e7	+	7.00669e7i	0.0794433	+	0.0794433i
$960$	−1.86861e7	−	1.86861e7i	−0.0211206	−	0.0211206i
$961$		−	5.02149e8i		−	0.565799i
$962$			4.33541e7i			0.0486973i
$963$		−	1.49888e8i		−	0.167837i
$964$	−1.41587e6			−0.00158050
$965$	1.13280e8	−	1.13280e8i	0.126059	−	0.126059i
$966$			6.65512e6i			0.00738285i
$967$	5.34707e8	−	5.34707e8i	0.591339	−	0.591339i	−0.346654	−	0.937993i	$-0.612682\pi$
$967$	5.34707e8	−	5.34707e8i	0.591339	−	0.591339i	0.937993	+	0.346654i	$0.112682\pi$
$968$	−9.75327e7	−	9.75327e7i	−0.107529	−	0.107529i
$969$	9.88659e7	−	9.88659e7i	0.108661	−	0.108661i
$970$			2.02930e6i			0.00222347i
$971$	−6.30909e8	−	6.30909e8i	−0.689143	−	0.689143i	0.272900	−	0.962043i	$-0.412017\pi$
$971$	−6.30909e8	−	6.30909e8i	−0.689143	−	0.689143i	−0.962043	+	0.272900i	$0.912017\pi$
$972$	−1.82972e8	+	1.82972e8i	−0.199244	+	0.199244i
$973$	−6.02170e8			−0.653703
$974$	−8.96663e7	−	8.96663e7i	−0.0970403	−	0.0970403i
$975$	1.54811e7	−	1.54811e7i	0.0167028	−	0.0167028i
$976$	−1.33948e8	−	1.33948e8i	−0.144074	−	0.144074i
$977$	1.26848e8			0.136019			0.0680094	−	0.997685i	$-0.478335\pi$
$977$	1.26848e8			0.136019			0.0680094	+	0.997685i	$0.478335\pi$
$978$	−5.21604e6	−	5.21604e6i	−0.00557603	−	0.00557603i
$979$			1.70730e9i			1.81954i
$980$	−6.65125e7			−0.0706684
$981$	−2.06258e8			−0.218476
$982$	1.15723e8			0.122204
$983$	6.94135e8	−	6.94135e8i	0.730775	−	0.730775i	−0.239999	−	0.970773i	$-0.577147\pi$
$983$	6.94135e8	−	6.94135e8i	0.730775	−	0.730775i	0.970773	+	0.239999i	$0.0771470\pi$
$984$	1.06136e6	−	1.06136e6i	0.00111399	−	0.00111399i
$985$		−	2.02781e8i		−	0.212187i
$986$	−7.24946e7	−	1.03403e8i	−0.0756266	−	0.107871i
$987$	−4.50463e7			−0.0468498
$988$	−2.48839e8	−	2.48839e8i	−0.258017	−	0.258017i
$989$	−8.31615e8	−	8.31615e8i	−0.859674	−	0.859674i
$990$			4.61663e7i			0.0475794i
$991$			5.37817e8i			0.552603i	0.961071	+	0.276301i	$0.0891088\pi$
$991$			5.37817e8i			0.552603i	−0.961071	+	0.276301i	$0.910891\pi$
$992$			2.09499e8i			0.214608i
$993$	6.62980e7			0.0677099
$994$	−6.81373e7	+	6.81373e7i	−0.0693786	+	0.0693786i
$995$			5.51511e8i			0.559867i
$996$	−7.04739e7	+	7.04739e7i	−0.0713264	+	0.0713264i
$997$	4.30647e8	+	4.30647e8i	0.434546	+	0.434546i	0.890171	−	0.455626i	$-0.150584\pi$
$997$	4.30647e8	+	4.30647e8i	0.434546	+	0.434546i	−0.455626	+	0.890171i	$0.650584\pi$
$998$	8.97257e7	−	8.97257e7i	0.0902662	−	0.0902662i
$999$		−	3.05212e8i		−	0.306130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.12.7	✓	28
29.17	odd	4	inner	29.7.c.a.17.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.7	✓	28	1.1	even	1	trivial
29.7.c.a.17.7	yes	28	29.17	odd	4	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.624225 - 0.624225i) q^{2} +(1.83796 + 1.83796i) q^{3} -63.2207i q^{4} +41.8066i q^{5} -2.29460i q^{6} -304.112 q^{7} +(-79.4144 + 79.4144i) q^{8} -722.244i q^{9} +O(q^{10})\)	\(q+(-0.624225 - 0.624225i) q^{2} +(1.83796 + 1.83796i) q^{3} -63.2207i q^{4} +41.8066i q^{5} -2.29460i q^{6} -304.112 q^{7} +(-79.4144 + 79.4144i) q^{8} -722.244i q^{9} +(26.0967 - 26.0967i) q^{10} +(-1224.69 - 1224.69i) q^{11} +(116.197 - 116.197i) q^{12} -606.965i q^{13} +(189.834 + 189.834i) q^{14} +(-76.8390 + 76.8390i) q^{15} -3946.98 q^{16} +(-4147.47 - 4147.47i) q^{17} +(-450.843 + 450.843i) q^{18} +(6484.79 + 6484.79i) q^{19} +2643.04 q^{20} +(-558.946 - 558.946i) q^{21} +1528.96i q^{22} +9537.06 q^{23} -291.921 q^{24} +13877.2 q^{25} +(-378.883 + 378.883i) q^{26} +(2667.33 - 2667.33i) q^{27} +19226.1i q^{28} +(-19970.1 + 14000.7i) q^{29} +95.9296 q^{30} +(13880.8 + 13880.8i) q^{31} +(7546.32 + 7546.32i) q^{32} -4501.85i q^{33} +5177.92i q^{34} -12713.9i q^{35} -45660.7 q^{36} +(57213.1 - 57213.1i) q^{37} -8095.94i q^{38} +(1115.58 - 1115.58i) q^{39} +(-3320.04 - 3320.04i) q^{40} +(-3635.79 + 3635.79i) q^{41} +697.816i q^{42} +(-87198.3 - 87198.3i) q^{43} +(-77425.5 + 77425.5i) q^{44} +30194.6 q^{45} +(-5953.28 - 5953.28i) q^{46} +(40295.8 - 40295.8i) q^{47} +(-7254.40 - 7254.40i) q^{48} -25165.1 q^{49} +(-8662.50 - 8662.50i) q^{50} -15245.8i q^{51} -38372.7 q^{52} -96211.6 q^{53} -3330.03 q^{54} +(51200.0 - 51200.0i) q^{55} +(24150.8 - 24150.8i) q^{56} +23837.6i q^{57} +(21205.4 + 3726.21i) q^{58} +311418. q^{59} +(4857.81 + 4857.81i) q^{60} +(33936.8 + 33936.8i) q^{61} -17329.5i q^{62} +219643. i q^{63} +243185. i q^{64} +25375.1 q^{65} +(-2810.17 + 2810.17i) q^{66} -231415. i q^{67} +(-262206. + 262206. i) q^{68} +(17528.8 + 17528.8i) q^{69} +(-7936.32 + 7936.32i) q^{70} +358931. i q^{71} +(57356.5 + 57356.5i) q^{72} +(337335. - 337335. i) q^{73} -71427.7 q^{74} +(25505.8 + 25505.8i) q^{75} +(409973. - 409973. i) q^{76} +(372441. + 372441. i) q^{77} -1392.74 q^{78} +(-172965. - 172965. i) q^{79} -165010. i q^{80} -516711. q^{81} +4539.11 q^{82} -606502. q^{83} +(-35336.9 + 35336.9i) q^{84} +(173392. - 173392. i) q^{85} +108863. i q^{86} +(-62437.0 - 10971.4i) q^{87} +194515. q^{88} +(-697037. - 697037. i) q^{89} +(-18848.2 - 18848.2i) q^{90} +184585. i q^{91} -602940. i q^{92} +51024.9i q^{93} -50307.3 q^{94} +(-271107. + 271107. i) q^{95} +27739.7i q^{96} +(-38880.4 + 38880.4i) q^{97} +(15708.7 + 15708.7i) q^{98} +(-884522. + 884522. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

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