LMFDB - Embedded newform 17.6.c.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,6,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	17.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:	$2.72652493682$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 248x^{10} + 21830x^{8} + 802540x^{6} + 10668257x^{4} + 7196228x^{2} + 1183744 $ x^12 + 248x^10 + 21830x^8 + 802540x^6 + 10668257x^4 + 7196228*x^2 + 1183744
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Root			$-5.80736i$ of defining polynomial
Character	$\chi$	$=$	17.13
Dual form			17.6.c.a.4.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.80736i q^{2} +(15.6906 + 15.6906i) q^{3} +8.88927 q^{4} +(-8.57737 - 8.57737i) q^{5} +(75.4302 - 75.4302i) q^{6} +(38.9646 - 38.9646i) q^{7} -196.570i q^{8} +249.387i q^{9} +O(q^{10})$	\(q-4.80736i q^{2} +(15.6906 + 15.6906i) q^{3} +8.88927 q^{4} +(-8.57737 - 8.57737i) q^{5} +(75.4302 - 75.4302i) q^{6} +(38.9646 - 38.9646i) q^{7} -196.570i q^{8} +249.387i q^{9} +(-41.2345 + 41.2345i) q^{10} +(-492.638 + 492.638i) q^{11} +(139.478 + 139.478i) q^{12} -46.9188 q^{13} +(-187.317 - 187.317i) q^{14} -269.167i q^{15} -660.524 q^{16} +(-322.100 - 1147.22i) q^{17} +1198.89 q^{18} +67.9322i q^{19} +(-76.2465 - 76.2465i) q^{20} +1222.75 q^{21} +(2368.29 + 2368.29i) q^{22} +(-2885.49 + 2885.49i) q^{23} +(3084.29 - 3084.29i) q^{24} -2977.86i q^{25} +225.556i q^{26} +(-100.217 + 100.217i) q^{27} +(346.366 - 346.366i) q^{28} +(-1174.76 - 1174.76i) q^{29} -1293.99 q^{30} +(4296.46 + 4296.46i) q^{31} -3114.84i q^{32} -15459.5 q^{33} +(-5515.09 + 1548.45i) q^{34} -668.427 q^{35} +2216.87i q^{36} +(9246.68 + 9246.68i) q^{37} +326.575 q^{38} +(-736.182 - 736.182i) q^{39} +(-1686.05 + 1686.05i) q^{40} +(11354.6 - 11354.6i) q^{41} -5878.21i q^{42} -5387.60i q^{43} +(-4379.20 + 4379.20i) q^{44} +(2139.09 - 2139.09i) q^{45} +(13871.6 + 13871.6i) q^{46} +11163.1 q^{47} +(-10364.0 - 10364.0i) q^{48} +13770.5i q^{49} -14315.6 q^{50} +(12946.6 - 23054.4i) q^{51} -417.073 q^{52} -668.427i q^{53} +(481.781 + 481.781i) q^{54} +8451.08 q^{55} +(-7659.24 - 7659.24i) q^{56} +(-1065.89 + 1065.89i) q^{57} +(-5647.49 + 5647.49i) q^{58} +968.713i q^{59} -2392.70i q^{60} +(-29807.9 + 29807.9i) q^{61} +(20654.6 - 20654.6i) q^{62} +(9717.26 + 9717.26i) q^{63} -36111.0 q^{64} +(402.440 + 402.440i) q^{65} +74319.6i q^{66} +30216.5 q^{67} +(-2863.23 - 10197.9i) q^{68} -90550.0 q^{69} +3213.37i q^{70} +(-28905.1 - 28905.1i) q^{71} +49021.9 q^{72} +(-15901.1 - 15901.1i) q^{73} +(44452.1 - 44452.1i) q^{74} +(46724.2 - 46724.2i) q^{75} +603.867i q^{76} +38390.9i q^{77} +(-3539.09 + 3539.09i) q^{78} +(57468.4 - 57468.4i) q^{79} +(5665.56 + 5665.56i) q^{80} +57456.1 q^{81} +(-54585.8 - 54585.8i) q^{82} +93023.1i q^{83} +10869.4 q^{84} +(-7077.34 + 12602.9i) q^{85} -25900.1 q^{86} -36865.2i q^{87} +(96837.7 + 96837.7i) q^{88} -65835.9 q^{89} +(-10283.4 - 10283.4i) q^{90} +(-1828.17 + 1828.17i) q^{91} +(-25649.9 + 25649.9i) q^{92} +134828. i q^{93} -53664.9i q^{94} +(582.679 - 582.679i) q^{95} +(48873.6 - 48873.6i) q^{96} +(-27624.2 - 27624.2i) q^{97} +66199.9 q^{98} +(-122858. - 122858. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7}+O(q^{10}) $ 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7} - 334 q^{10} - 504 q^{11} + 1722 q^{12} + 1600 q^{13} - 2364 q^{14} + 2564 q^{16} + 2432 q^{17} - 6052 q^{18} - 4218 q^{20} + 7144 q^{21} - 2590 q^{22} - 2728 q^{23} - 7246 q^{24} - 3024 q^{27} + 26164 q^{28} - 992 q^{29} + 18072 q^{30} - 14680 q^{31} - 96 q^{33} - 20962 q^{34} - 43744 q^{35} + 33552 q^{37} + 9024 q^{38} + 2720 q^{39} + 30922 q^{40} + 20716 q^{41} - 13682 q^{44} + 44848 q^{45} + 4416 q^{46} + 32032 q^{47} - 144770 q^{48} - 42636 q^{50} - 83368 q^{51} - 132556 q^{52} + 80728 q^{54} + 81040 q^{55} + 122460 q^{56} + 36840 q^{57} + 165766 q^{58} - 143200 q^{61} + 222580 q^{62} + 7592 q^{63} + 18428 q^{64} - 175016 q^{65} - 83648 q^{67} - 231150 q^{68} - 341160 q^{69} + 116088 q^{71} + 347100 q^{72} + 83892 q^{73} - 79282 q^{74} + 245864 q^{75} - 128572 q^{78} + 291672 q^{79} + 195426 q^{80} + 387028 q^{81} - 452240 q^{82} - 798600 q^{84} - 200704 q^{85} - 736076 q^{86} + 431258 q^{88} + 456424 q^{89} - 65406 q^{90} + 36224 q^{91} + 476504 q^{92} - 413488 q^{95} + 884318 q^{96} + 356284 q^{97} + 444704 q^{98} - 640440 q^{99}+O(q^{100}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7 - 334 * q^10 - 504 * q^11 + 1722 * q^12 + 1600 * q^13 - 2364 * q^14 + 2564 * q^16 + 2432 * q^17 - 6052 * q^18 - 4218 * q^20 + 7144 * q^21 - 2590 * q^22 - 2728 * q^23 - 7246 * q^24 - 3024 * q^27 + 26164 * q^28 - 992 * q^29 + 18072 * q^30 - 14680 * q^31 - 96 * q^33 - 20962 * q^34 - 43744 * q^35 + 33552 * q^37 + 9024 * q^38 + 2720 * q^39 + 30922 * q^40 + 20716 * q^41 - 13682 * q^44 + 44848 * q^45 + 4416 * q^46 + 32032 * q^47 - 144770 * q^48 - 42636 * q^50 - 83368 * q^51 - 132556 * q^52 + 80728 * q^54 + 81040 * q^55 + 122460 * q^56 + 36840 * q^57 + 165766 * q^58 - 143200 * q^61 + 222580 * q^62 + 7592 * q^63 + 18428 * q^64 - 175016 * q^65 - 83648 * q^67 - 231150 * q^68 - 341160 * q^69 + 116088 * q^71 + 347100 * q^72 + 83892 * q^73 - 79282 * q^74 + 245864 * q^75 - 128572 * q^78 + 291672 * q^79 + 195426 * q^80 + 387028 * q^81 - 452240 * q^82 - 798600 * q^84 - 200704 * q^85 - 736076 * q^86 + 431258 * q^88 + 456424 * q^89 - 65406 * q^90 + 36224 * q^91 + 476504 * q^92 - 413488 * q^95 + 884318 * q^96 + 356284 * q^97 + 444704 * q^98 - 640440 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	4.80736i		−	0.849830i	−0.905233	−	0.424915i	$-0.860304\pi$
$2$		−	4.80736i		−	0.849830i	0.905233	−	0.424915i	$-0.139696\pi$
$3$	15.6906	+	15.6906i	1.00655	+	1.00655i	0.999978	+	0.00657124i	$0.00209171\pi$
$3$	15.6906	+	15.6906i	1.00655	+	1.00655i	0.00657124	+	0.999978i	$0.497908\pi$
$4$	8.88927			0.277790
$5$	−8.57737	−	8.57737i	−0.153437	−	0.153437i	0.626214	−	0.779651i	$-0.284603\pi$
$5$	−8.57737	−	8.57737i	−0.153437	−	0.153437i	−0.779651	+	0.626214i	$0.784603\pi$
$6$	75.4302	−	75.4302i	0.855396	−	0.855396i
$7$	38.9646	−	38.9646i	0.300555	−	0.300555i	−0.540676	−	0.841231i	$-0.681831\pi$
$7$	38.9646	−	38.9646i	0.300555	−	0.300555i	0.841231	+	0.540676i	$0.181831\pi$
$8$		−	196.570i		−	1.08590i
$9$			249.387i			1.02628i
$10$	−41.2345	+	41.2345i	−0.130395	+	0.130395i
$11$	−492.638	+	492.638i	−1.22757	+	1.22757i	−0.262691	+	0.964880i	$0.584610\pi$
$11$	−492.638	+	492.638i	−1.22757	+	1.22757i	−0.964880	+	0.262691i	$0.915390\pi$
$12$	139.478	+	139.478i	0.279609	+	0.279609i
$13$	−46.9188			−0.0769996			−0.0384998	−	0.999259i	$-0.512258\pi$
$13$	−46.9188			−0.0769996			−0.0384998	+	0.999259i	$0.512258\pi$
$14$	−187.317	−	187.317i	−0.255421	−	0.255421i
$15$		−	269.167i		−	0.308883i
$16$	−660.524			−0.645043
$17$	−322.100	−	1147.22i	−0.270314	−	0.962772i
$17$	−322.100	−	1147.22i	−0.270314	−	0.962772i
$18$	1198.89			0.872167
$19$			67.9322i			0.0431710i	0.999767	+	0.0215855i	$0.00687140\pi$
$19$			67.9322i			0.0431710i	−0.999767	+	0.0215855i	$0.993129\pi$
$20$	−76.2465	−	76.2465i	−0.0426231	−	0.0426231i
$21$	1222.75			0.605048
$22$	2368.29	+	2368.29i	1.04323	+	1.04323i
$23$	−2885.49	+	2885.49i	−1.13737	+	1.13737i	−0.148446	+	0.988920i	$0.547427\pi$
$23$	−2885.49	+	2885.49i	−1.13737	+	1.13737i	−0.988920	+	0.148446i	$0.952573\pi$
$24$	3084.29	−	3084.29i	1.09302	−	1.09302i
$25$		−	2977.86i		−	0.952914i
$26$			225.556i			0.0654365i
$27$	−100.217	+	100.217i	−0.0264566	+	0.0264566i
$28$	346.366	−	346.366i	0.0834912	−	0.0834912i
$29$	−1174.76	−	1174.76i	−0.259390	−	0.259390i	0.565416	−	0.824806i	$-0.308716\pi$
$29$	−1174.76	−	1174.76i	−0.259390	−	0.259390i	−0.824806	+	0.565416i	$0.808716\pi$
$30$	−1293.99			−0.262498
$31$	4296.46	+	4296.46i	0.802983	+	0.802983i	0.983561	−	0.180578i	$-0.0577969\pi$
$31$	4296.46	+	4296.46i	0.802983	+	0.802983i	−0.180578	+	0.983561i	$0.557797\pi$
$32$		−	3114.84i		−	0.537727i
$33$	−15459.5			−2.47122
$34$	−5515.09	+	1548.45i	−0.818192	+	0.229721i
$35$	−668.427			−0.0922324
$36$			2216.87i			0.285091i
$37$	9246.68	+	9246.68i	1.11041	+	1.11041i	0.993095	+	0.117310i	$0.0374272\pi$
$37$	9246.68	+	9246.68i	1.11041	+	1.11041i	0.117310	+	0.993095i	$0.462573\pi$
$38$	326.575			0.0366880
$39$	−736.182	−	736.182i	−0.0775039	−	0.0775039i
$40$	−1686.05	+	1686.05i	−0.166617	+	0.166617i
$41$	11354.6	−	11354.6i	1.05491	−	1.05491i	0.0565028	−	0.998402i	$-0.482005\pi$
$41$	11354.6	−	11354.6i	1.05491	−	1.05491i	0.998402	−	0.0565028i	$-0.0179950\pi$
$42$		−	5878.21i		−	0.514188i
$43$		−	5387.60i		−	0.444349i	−0.975007	−	0.222174i	$-0.928685\pi$
$43$		−	5387.60i		−	0.444349i	0.975007	−	0.222174i	$-0.0713155\pi$
$44$	−4379.20	+	4379.20i	−0.341006	+	0.341006i
$45$	2139.09	−	2139.09i	0.157470	−	0.157470i
$46$	13871.6	+	13871.6i	0.966568	+	0.966568i
$47$	11163.1			0.737121			0.368561	−	0.929604i	$-0.379851\pi$
$47$	11163.1			0.737121			0.368561	+	0.929604i	$0.379851\pi$
$48$	−10364.0	−	10364.0i	−0.649268	−	0.649268i
$49$			13770.5i			0.819333i
$50$	−14315.6			−0.809815
$51$	12946.6	−	23054.4i	0.696994	−	1.24116i
$52$	−417.073			−0.0213897
$53$		−	668.427i		−	0.0326862i	−0.999866	−	0.0163431i	$-0.994798\pi$
$53$		−	668.427i		−	0.0326862i	0.999866	−	0.0163431i	$-0.00520240\pi$
$54$	481.781	+	481.781i	0.0224836	+	0.0224836i
$55$	8451.08			0.376709
$56$	−7659.24	−	7659.24i	−0.326374	−	0.326374i
$57$	−1065.89	+	1065.89i	−0.0434537	+	0.0434537i
$58$	−5647.49	+	5647.49i	−0.220437	+	0.220437i
$59$			968.713i			0.0362297i	0.999836	+	0.0181149i	$0.00576646\pi$
$59$			968.713i			0.0362297i	−0.999836	+	0.0181149i	$0.994234\pi$
$60$		−	2392.70i		−	0.0858045i
$61$	−29807.9	+	29807.9i	−1.02567	+	1.02567i	−0.0260045	+	0.999662i	$0.508278\pi$
$61$	−29807.9	+	29807.9i	−1.02567	+	1.02567i	−0.999662	+	0.0260045i	$0.991722\pi$
$62$	20654.6	−	20654.6i	0.682398	−	0.682398i
$63$	9717.26	+	9717.26i	0.308455	+	0.308455i
$64$	−36111.0			−1.10202
$65$	402.440	+	402.440i	0.0118146	+	0.0118146i
$66$			74319.6i			2.10012i
$67$	30216.5			0.822350			0.411175	−	0.911556i	$-0.365118\pi$
$67$	30216.5			0.822350			0.411175	+	0.911556i	$0.365118\pi$
$68$	−2863.23	−	10197.9i	−0.0750904	−	0.267448i
$69$	−90550.0			−2.28963
$70$			3213.37i			0.0783819i
$71$	−28905.1	−	28905.1i	−0.680501	−	0.680501i	0.279612	−	0.960113i	$-0.409794\pi$
$71$	−28905.1	−	28905.1i	−0.680501	−	0.680501i	−0.960113	+	0.279612i	$0.909794\pi$
$72$	49021.9			1.11445
$73$	−15901.1	−	15901.1i	−0.349238	−	0.349238i	0.510588	−	0.859826i	$-0.329428\pi$
$73$	−15901.1	−	15901.1i	−0.349238	−	0.349238i	−0.859826	+	0.510588i	$0.829428\pi$
$74$	44452.1	−	44452.1i	0.943655	−	0.943655i
$75$	46724.2	−	46724.2i	0.959156	−	0.959156i
$76$			603.867i			0.0119924i
$77$			38390.9i			0.737906i
$78$	−3539.09	+	3539.09i	−0.0658651	+	0.0658651i
$79$	57468.4	−	57468.4i	1.03600	−	1.03600i	0.0366766	−	0.999327i	$-0.488323\pi$
$79$	57468.4	−	57468.4i	1.03600	−	1.03600i	0.999327	−	0.0366766i	$-0.0116771\pi$
$80$	5665.56	+	5665.56i	0.0989733	+	0.0989733i
$81$	57456.1			0.973025
$82$	−54585.8	−	54585.8i	−0.896490	−	0.896490i
$83$			93023.1i			1.48216i	0.671416	+	0.741081i	$0.265687\pi$
$83$			93023.1i			1.48216i	−0.671416	+	0.741081i	$0.734313\pi$
$84$	10869.4			0.168076
$85$	−7077.34	+	12602.9i	−0.106248	+	0.189201i
$86$	−25900.1			−0.377621
$87$		−	36865.2i		−	0.522178i
$88$	96837.7	+	96837.7i	1.33302	+	1.33302i
$89$	−65835.9			−0.881023			−0.440512	−	0.897747i	$-0.645203\pi$
$89$	−65835.9			−0.881023			−0.440512	+	0.897747i	$0.645203\pi$
$90$	−10283.4	−	10283.4i	−0.133822	−	0.133822i
$91$	−1828.17	+	1828.17i	−0.0231426	+	0.0231426i
$92$	−25649.9	+	25649.9i	−0.315949	+	0.315949i
$93$			134828.i			1.61648i
$94$		−	53664.9i		−	0.626428i
$95$	582.679	−	582.679i	0.00662401	−	0.00662401i
$96$	48873.6	−	48873.6i	0.541248	−	0.541248i
$97$	−27624.2	−	27624.2i	−0.298099	−	0.298099i	0.542170	−	0.840269i	$-0.317603\pi$
$97$	−27624.2	−	27624.2i	−0.298099	−	0.298099i	−0.840269	+	0.542170i	$0.817603\pi$
$98$	66199.9			0.696293
$99$	−122858.	−	122858.i	−1.25984	−	1.25984i
$100$		−	26471.0i		−	0.264710i
$101$	−98573.6			−0.961518			−0.480759	−	0.876853i	$-0.659639\pi$
$101$	−98573.6			−0.961518			−0.480759	+	0.876853i	$0.659639\pi$
$102$	−110831.	−	62238.8i	−1.05478	−	0.592326i
$103$	−46662.6			−0.433387			−0.216694	−	0.976240i	$-0.569527\pi$
$103$	−46662.6			−0.433387			−0.216694	+	0.976240i	$0.569527\pi$
$104$			9222.80i			0.0836141i
$105$	−10488.0	−	10488.0i	−0.0928365	−	0.0928365i
$106$	−3213.37			−0.0277777
$107$	140067.	+	140067.i	1.18270	+	1.18270i	0.979041	+	0.203662i	$0.0652844\pi$
$107$	140067.	+	140067.i	1.18270	+	1.18270i	0.203662	+	0.979041i	$0.434716\pi$
$108$	−890.859	+	890.859i	−0.00734936	+	0.00734936i
$109$	18188.5	−	18188.5i	0.146633	−	0.146633i	−0.629979	−	0.776612i	$-0.716937\pi$
$109$	18188.5	−	18188.5i	0.146633	−	0.146633i	0.776612	+	0.629979i	$0.216937\pi$
$110$		−	40627.4i		−	0.320138i
$111$			290171.i			2.23536i
$112$	−25737.0	+	25737.0i	−0.193871	+	0.193871i
$113$	37245.3	−	37245.3i	0.274395	−	0.274395i	−0.556472	−	0.830867i	$-0.687845\pi$
$113$	37245.3	−	37245.3i	0.274395	−	0.274395i	0.830867	+	0.556472i	$0.187845\pi$
$114$	5124.14	+	5124.14i	0.0369282	+	0.0369282i
$115$	49499.9			0.349028
$116$	−10442.7	−	10442.7i	−0.0720559	−	0.0720559i
$117$		−	11700.9i		−	0.0790234i
$118$	4656.96			0.0307891
$119$	−57251.3	−	32150.3i	−0.370611	−	0.208122i
$120$	−52910.1			−0.335417
$121$		−	324334.i		−	2.01386i
$122$	143297.	+	143297.i	0.871642	+	0.871642i
$123$	356321.			2.12363
$124$	38192.3	+	38192.3i	0.223060	+	0.223060i
$125$	−52346.5	+	52346.5i	−0.299649	+	0.299649i
$126$	46714.4	−	46714.4i	0.262135	−	0.262135i
$127$		−	209432.i		−	1.15222i	−0.817373	−	0.576108i	$-0.804571\pi$
$127$		−	209432.i		−	1.15222i	0.817373	−	0.576108i	$-0.195429\pi$
$128$			73923.5i			0.398802i
$129$	84534.4	−	84534.4i	0.447259	−	0.447259i
$130$	1934.67	−	1934.67i	0.0100404	−	0.0100404i
$131$	−84233.2	−	84233.2i	−0.428850	−	0.428850i	0.459387	−	0.888236i	$-0.348069\pi$
$131$	−84233.2	−	84233.2i	−0.428850	−	0.428850i	−0.888236	+	0.459387i	$0.848069\pi$
$132$	−137424.			−0.686480
$133$	2646.95	+	2646.95i	0.0129753	+	0.0129753i
$134$		−	145262.i		−	0.698858i
$135$	1719.20			0.00811881
$136$	−225508.	+	63315.0i	−1.04548	+	0.293535i
$137$	25046.4			0.114010			0.0570052	−	0.998374i	$-0.481845\pi$
$137$	25046.4			0.114010			0.0570052	+	0.998374i	$0.481845\pi$
$138$			435307.i			1.94580i
$139$	−190086.	−	190086.i	−0.834474	−	0.834474i	0.153651	−	0.988125i	$-0.450897\pi$
$139$	−190086.	−	190086.i	−0.834474	−	0.834474i	−0.988125	+	0.153651i	$0.950897\pi$
$140$	−5941.82			−0.0256212
$141$	175155.	+	175155.i	0.741949	+	0.741949i
$142$	−138957.	+	138957.i	−0.578310	+	0.578310i
$143$	23114.0	−	23114.0i	0.0945224	−	0.0945224i
$144$		−	164726.i		−	0.661998i
$145$			20152.7i			0.0795999i
$146$	−76442.5	+	76442.5i	−0.296792	+	0.296792i
$147$	−216067.	+	216067.i	−0.824699	+	0.824699i
$148$	82196.2	+	82196.2i	0.308459	+	0.308459i
$149$	111556.			0.411650			0.205825	−	0.978589i	$-0.434012\pi$
$149$	111556.			0.411650			0.205825	+	0.978589i	$0.434012\pi$
$150$	−224620.	−	224620.i	−0.815119	−	0.815119i
$151$			224529.i			0.801366i	0.916217	+	0.400683i	$0.131227\pi$
$151$			224529.i			0.801366i	−0.916217	+	0.400683i	$0.868773\pi$
$152$	13353.4			0.0468795
$153$	286101.	−	80327.6i	0.988078	−	0.277419i
$154$	184559.			0.627095
$155$		−	73704.6i		−	0.246414i
$156$	−6544.11	−	6544.11i	−0.0215298	−	0.0215298i
$157$	−349036.			−1.13011			−0.565056	−	0.825053i	$-0.691145\pi$
$157$	−349036.			−1.13011			−0.565056	+	0.825053i	$0.691145\pi$
$158$	−276271.	−	276271.i	−0.880427	−	0.880427i
$159$	10488.0	−	10488.0i	0.0329003	−	0.0329003i
$160$	−26717.2	+	26717.2i	−0.0825070	+	0.0825070i
$161$			224864.i			0.683684i
$162$		−	276212.i		−	0.826905i
$163$	31891.4	−	31891.4i	0.0940165	−	0.0940165i	−0.658534	−	0.752551i	$-0.728823\pi$
$163$	31891.4	−	31891.4i	0.0940165	−	0.0940165i	0.752551	+	0.658534i	$0.228823\pi$
$164$	100934.	−	100934.i	0.293042	−	0.293042i
$165$	132602.	+	132602.i	0.379176	+	0.379176i
$166$	447196.			1.25959
$167$	354061.	+	354061.i	0.982396	+	0.982396i	0.999848	−	0.0174516i	$-0.00555529\pi$
$167$	354061.	+	354061.i	0.982396	+	0.982396i	−0.0174516	+	0.999848i	$0.505555\pi$
$168$		−	240356.i		−	0.657024i
$169$	−369092.			−0.994071
$170$	60586.6	+	34023.3i	0.160788	+	0.0902931i
$171$	−16941.4			−0.0443057
$172$		−	47891.8i		−	0.123436i
$173$	95401.2	+	95401.2i	0.242348	+	0.242348i	0.817821	−	0.575473i	$-0.195182\pi$
$173$	95401.2	+	95401.2i	0.242348	+	0.242348i	−0.575473	+	0.817821i	$0.695182\pi$
$174$	−177224.			−0.443762
$175$	−116031.	−	116031.i	−0.286404	−	0.286404i
$176$	325400.	−	325400.i	0.791836	−	0.791836i
$177$	−15199.7	+	15199.7i	−0.0364670	+	0.0364670i
$178$			316497.i			0.748720i
$179$		−	626720.i		−	1.46198i	−0.682389	−	0.730989i	$-0.739059\pi$
$179$		−	626720.i		−	1.46198i	0.682389	−	0.730989i	$-0.260941\pi$
$180$	19014.9	−	19014.9i	0.0437434	−	0.0437434i
$181$	184240.	−	184240.i	0.418011	−	0.418011i	−0.466507	−	0.884518i	$-0.654488\pi$
$181$	184240.	−	184240.i	0.418011	−	0.418011i	0.884518	+	0.466507i	$0.154488\pi$
$182$	8788.67	+	8788.67i	0.0196673	+	0.0196673i
$183$	−935404.			−2.06477
$184$	567200.	+	567200.i	1.23507	+	1.23507i
$185$		−	158624.i		−	0.340754i
$186$	648165.			1.37374
$187$	723842.	+	406485.i	1.51370	+	0.850042i
$188$	99231.5			0.204765
$189$			7809.85i			0.0159033i
$190$	−2801.15	−	2801.15i	−0.00562928	−	0.00562928i
$191$	−349834.			−0.693870			−0.346935	−	0.937889i	$-0.612778\pi$
$191$	−349834.			−0.693870			−0.346935	+	0.937889i	$0.612778\pi$
$192$	−566601.	−	566601.i	−1.10924	−	1.10924i
$193$	36212.0	−	36212.0i	0.0699776	−	0.0699776i	−0.671252	−	0.741229i	$-0.734243\pi$
$193$	36212.0	−	36212.0i	0.0699776	−	0.0699776i	0.741229	+	0.671252i	$0.234243\pi$
$194$	−132800.	+	132800.i	−0.253334	+	0.253334i
$195$			12629.0i			0.0237839i
$196$			122410.i			0.227602i
$197$	−270990.	+	270990.i	−0.497494	+	0.497494i	−0.910657	−	0.413163i	$-0.864424\pi$
$197$	−270990.	+	270990.i	−0.497494	+	0.497494i	0.413163	+	0.910657i	$0.364424\pi$
$198$	−590621.	+	590621.i	−1.07065	+	1.07065i
$199$	−174718.	−	174718.i	−0.312756	−	0.312756i	0.533220	−	0.845976i	$-0.320982\pi$
$199$	−174718.	−	174718.i	−0.312756	−	0.312756i	−0.845976	+	0.533220i	$0.820982\pi$
$200$	−585356.			−1.03477
$201$	474113.	+	474113.i	0.827736	+	0.827736i
$202$			473879.i			0.817126i
$203$	−91547.8			−0.155922
$204$	115085.	−	204937.i	0.193618	−	0.344782i
$205$	−194786.			−0.323722
$206$			224324.i			0.368305i
$207$	−719605.	−	719605.i	−1.16726	−	1.16726i
$208$	30991.0			0.0496680
$209$	−33466.0	−	33466.0i	−0.0529954	−	0.0529954i
$210$	−50419.6	+	50419.6i	−0.0788952	+	0.0788952i
$211$	−364764.	+	364764.i	−0.564034	+	0.564034i	−0.930451	−	0.366417i	$-0.880585\pi$
$211$	−364764.	+	364764.i	−0.564034	+	0.564034i	0.366417	+	0.930451i	$0.380585\pi$
$212$		−	5941.83i		−	0.00907989i
$213$		−	907074.i		−	1.36992i
$214$	673352.	−	673352.i	1.00510	−	1.00510i
$215$	−46211.4	+	46211.4i	−0.0681794	+	0.0681794i
$216$	19699.7	+	19699.7i	0.0287293	+	0.0287293i
$217$	334819.			0.482682
$218$	−87438.7	−	87438.7i	−0.124613	−	0.124613i
$219$		−	498995.i		−	0.703050i
$220$	75123.9			0.104646
$221$	15112.5	+	53826.0i	0.0208141	+	0.0741330i
$222$	1.39496e6			1.89967
$223$			876348.i			1.18009i	0.807371	+	0.590044i	$0.200890\pi$
$223$			876348.i			1.18009i	−0.807371	+	0.590044i	$0.799110\pi$
$224$	−121369.	−	121369.i	−0.161617	−	0.161617i
$225$	742639.			0.977961
$226$	−179052.	−	179052.i	−0.233189	−	0.233189i
$227$	−157045.	+	157045.i	−0.202283	+	0.202283i	−0.800978	−	0.598694i	$-0.795686\pi$
$227$	−157045.	+	157045.i	−0.202283	+	0.202283i	0.598694	+	0.800978i	$0.295686\pi$
$228$	−9475.02	+	9475.02i	−0.0120710	+	0.0120710i
$229$		−	16822.9i		−	0.0211989i	−0.999944	−	0.0105994i	$-0.996626\pi$
$229$		−	16822.9i		−	0.0211989i	0.999944	−	0.0105994i	$-0.00337397\pi$
$230$		−	237964.i		−	0.296614i
$231$	−602374.	+	602374.i	−0.742739	+	0.742739i
$232$	−230922.	+	230922.i	−0.281673	+	0.281673i
$233$	29783.0	+	29783.0i	0.0359400	+	0.0359400i	0.724848	−	0.688908i	$-0.241910\pi$
$233$	29783.0	+	29783.0i	0.0359400	+	0.0359400i	−0.688908	+	0.724848i	$0.741910\pi$
$234$	−56250.6			−0.0671565
$235$	−95749.8	−	95749.8i	−0.113101	−	0.113101i
$236$			8611.15i			0.0100642i
$237$	1.80342e6			2.08558
$238$	−154558.	+	275228.i	−0.176868	+	0.314956i
$239$	847625.			0.959862			0.479931	−	0.877306i	$-0.340662\pi$
$239$	847625.			0.959862			0.479931	+	0.877306i	$0.340662\pi$
$240$			177792.i			0.199243i
$241$	27119.6	+	27119.6i	0.0300774	+	0.0300774i	0.721986	−	0.691908i	$-0.243230\pi$
$241$	27119.6	+	27119.6i	0.0300774	+	0.0300774i	−0.691908	+	0.721986i	$0.743230\pi$
$242$	−1.55919e6			−1.71144
$243$	925872.	+	925872.i	1.00585	+	1.00585i
$244$	−264970.	+	264970.i	−0.284919	+	0.284919i
$245$	118115.	−	118115.i	0.125716	−	0.125716i
$246$		−	1.71296e6i		−	1.80472i
$247$		−	3187.29i		−	0.00332414i
$248$	844552.	−	844552.i	0.871962	−	0.871962i
$249$	−1.45958e6	+	1.45958e6i	−1.49187	+	1.49187i
$250$	251648.	+	251648.i	0.254650	+	0.254650i
$251$	208980.			0.209373			0.104686	−	0.994505i	$-0.466616\pi$
$251$	208980.			0.209373			0.104686	+	0.994505i	$0.466616\pi$
$252$	86379.3	+	86379.3i	0.0856857	+	0.0856857i
$253$		−	2.84301e6i		−	2.79240i
$254$	−1.00682e6			−0.979188
$255$	−308794.	+	86698.8i	−0.297384	+	0.0834954i
$256$	−800174.			−0.763105
$257$		−	1.32448e6i		−	1.25087i	−0.780276	−	0.625436i	$-0.784921\pi$
$257$		−	1.32448e6i		−	1.25087i	0.780276	−	0.625436i	$-0.215079\pi$
$258$	−406388.	−	406388.i	−0.380094	−	0.380094i
$259$	720586.			0.667477
$260$	3577.39	+	3577.39i	0.00328196	+	0.00328196i
$261$	292969.	−	292969.i	0.266208	−	0.266208i
$262$	−404940.	+	404940.i	−0.364449	+	0.364449i
$263$			1.16536e6i			1.03889i	0.854503	+	0.519446i	$0.173862\pi$
$263$			1.16536e6i			1.03889i	−0.854503	+	0.519446i	$0.826138\pi$
$264$			3.03888e6i			2.68351i
$265$	−5733.35	+	5733.35i	−0.00501526	+	0.00501526i
$266$	12724.8	−	12724.8i	0.0110268	−	0.0110268i
$267$	−1.03300e6	−	1.03300e6i	−0.886794	−	0.886794i
$268$	268602.			0.228440
$269$	427171.	+	427171.i	0.359933	+	0.359933i	0.863788	−	0.503855i	$-0.168086\pi$
$269$	427171.	+	427171.i	0.359933	+	0.359933i	−0.503855	+	0.863788i	$0.668086\pi$
$270$		−	8264.83i		−	0.00689961i
$271$	−1.98276e6			−1.64001			−0.820006	−	0.572355i	$-0.806030\pi$
$271$	−1.98276e6			−1.64001			−0.820006	+	0.572355i	$0.806030\pi$
$272$	212755.	+	757765.i	0.174364	+	0.621030i
$273$	−57370.0			−0.0465884
$274$		−	120407.i		−	0.0968893i
$275$	1.46701e6	+	1.46701e6i	1.16977	+	1.16977i
$276$	−804923.			−0.636036
$277$	390194.	+	390194.i	0.305549	+	0.305549i	0.843180	−	0.537631i	$-0.180681\pi$
$277$	390194.	+	390194.i	0.305549	+	0.305549i	−0.537631	+	0.843180i	$0.680681\pi$
$278$	−913812.	+	913812.i	−0.709161	+	0.709161i
$279$	−1.07148e6	+	1.07148e6i	−0.824088	+	0.824088i
$280$			131392.i			0.100156i
$281$		−	422124.i		−	0.318915i	−0.987205	−	0.159457i	$-0.949026\pi$
$281$		−	422124.i		−	0.318915i	0.987205	−	0.159457i	$-0.0509744\pi$
$282$	842033.	−	842033.i	0.630531	−	0.630531i
$283$	1.66198e6	−	1.66198e6i	1.23356	−	1.23356i	0.270975	−	0.962586i	$-0.412654\pi$
$283$	1.66198e6	−	1.66198e6i	1.23356	−	1.23356i	0.962586	−	0.270975i	$-0.0873462\pi$
$284$	−256945.	−	256945.i	−0.189036	−	0.189036i
$285$	18285.1			0.0133348
$286$	−111117.	−	111117.i	−0.0803280	−	0.0803280i
$287$		−	884856.i		−	0.634115i
$288$	776802.			0.551860
$289$	−1.21236e6	+	739038.i	−0.853861	+	0.520501i
$290$	96881.1			0.0676463
$291$		−	866879.i		−	0.600103i
$292$	−141349.	−	141349.i	−0.0970146	−	0.0970146i
$293$	1.58405e6			1.07795			0.538976	−	0.842321i	$-0.318811\pi$
$293$	1.58405e6			1.07795			0.538976	+	0.842321i	$0.318811\pi$
$294$	1.03871e6	+	1.03871e6i	0.700854	+	0.700854i
$295$	8309.01	−	8309.01i	0.00555897	−	0.00555897i
$296$	1.81762e6	−	1.81762e6i	1.20579	−	1.20579i
$297$		−	98741.8i		−	0.0649546i
$298$		−	536291.i		−	0.349832i
$299$	135384.	−	135384.i	0.0875767	−	0.0875767i
$300$	415344.	−	415344.i	0.266443	−	0.266443i
$301$	−209925.	−	209925.i	−0.133551	−	0.133551i
$302$	1.07939e6			0.681025
$303$	−1.54667e6	−	1.54667e6i	−0.967815	−	0.967815i
$304$		−	44870.9i		−	0.0278471i
$305$	511346.			0.314750
$306$	−386164.	−	1.37539e6i	−0.235759	−	0.839698i
$307$	649873.			0.393534			0.196767	−	0.980450i	$-0.436956\pi$
$307$	649873.			0.393534			0.196767	+	0.980450i	$0.436956\pi$
$308$			341267.i			0.204983i
$309$	−732163.	−	732163.i	−0.436226	−	0.436226i
$310$	−354325.			−0.209410
$311$	89736.8	+	89736.8i	0.0526102	+	0.0526102i	0.732922	−	0.680312i	$-0.238156\pi$
$311$	89736.8	+	89736.8i	0.0526102	+	0.0526102i	−0.680312	+	0.732922i	$0.738156\pi$
$312$	−144711.	+	144711.i	−0.0841617	+	0.0841617i
$313$	−1.92953e6	+	1.92953e6i	−1.11325	+	1.11325i	−0.120538	+	0.992709i	$0.538462\pi$
$313$	−1.92953e6	+	1.92953e6i	−1.11325	+	1.11325i	−0.992709	+	0.120538i	$0.961538\pi$
$314$			1.67794e6i			0.960402i
$315$		−	166697.i		−	0.0946567i
$316$	510852.	−	510852.i	0.287791	−	0.287791i
$317$	−1.19663e6	+	1.19663e6i	−0.668824	+	0.668824i	−0.957444	−	0.288620i	$-0.906804\pi$
$317$	−1.19663e6	+	1.19663e6i	−0.668824	+	0.668824i	0.288620	+	0.957444i	$0.406804\pi$
$318$	−50419.6	−	50419.6i	−0.0279596	−	0.0279596i
$319$	1.15746e6			0.636839
$320$	309737.	+	309737.i	0.169090	+	0.169090i
$321$			4.39545e6i			2.38090i
$322$	1.08100e6			0.581015
$323$	77933.0	−	21881.0i	0.0415638	−	0.0116697i
$324$	510743.			0.270296
$325$			139717.i			0.0733740i
$326$	−153313.	−	153313.i	−0.0798980	−	0.0798980i
$327$	570775.			0.295186
$328$	−2.23197e6	−	2.23197e6i	−1.14553	−	1.14553i
$329$	434964.	−	434964.i	0.221546	−	0.221546i
$330$	637467.	−	637467.i	0.322235	−	0.322235i
$331$		−	973578.i		−	0.488428i	−0.969721	−	0.244214i	$-0.921470\pi$
$331$		−	973578.i		−	0.488428i	0.969721	−	0.244214i	$-0.0785300\pi$
$332$			826908.i			0.411729i
$333$	−2.30600e6	+	2.30600e6i	−1.13959	+	1.13959i
$334$	1.70210e6	−	1.70210e6i	0.834869	−	0.834869i
$335$	−259178.	−	259178.i	−0.126179	−	0.126179i
$336$	−807657.			−0.390282
$337$	−2.03395e6	−	2.03395e6i	−0.975587	−	0.975587i	0.0241218	−	0.999709i	$-0.492321\pi$
$337$	−2.03395e6	−	2.03395e6i	−0.975587	−	0.975587i	−0.999709	+	0.0241218i	$0.992321\pi$
$338$			1.77436e6i			0.844791i
$339$	1.16880e6			0.552384
$340$	−62912.4	+	112030.i	−0.0295147	+	0.0525580i
$341$	−4.23320e6			−1.97144
$342$			81443.5i			0.0376523i
$343$	1.19144e6	+	1.19144e6i	0.546810	+	0.546810i
$344$	−1.05904e6			−0.482520
$345$	776681.	+	776681.i	0.351314	+	0.351314i
$346$	458628.	−	458628.i	0.205954	−	0.205954i
$347$	1.33613e6	−	1.33613e6i	0.595696	−	0.595696i	−0.343469	−	0.939164i	$-0.611602\pi$
$347$	1.33613e6	−	1.33613e6i	0.595696	−	0.595696i	0.939164	+	0.343469i	$0.111602\pi$
$348$		−	327705.i		−	0.145056i
$349$		−	1.91712e6i		−	0.842529i	−0.906938	−	0.421265i	$-0.861586\pi$
$349$		−	1.91712e6i		−	0.842529i	0.906938	−	0.421265i	$-0.138414\pi$
$350$	−557803.	+	557803.i	−0.243394	+	0.243394i
$351$	4702.07	−	4702.07i	0.00203714	−	0.00203714i
$352$	1.53449e6	+	1.53449e6i	0.660098	+	0.660098i
$353$	−2.44274e6			−1.04338			−0.521688	−	0.853136i	$-0.674698\pi$
$353$	−2.44274e6			−1.04338			−0.521688	+	0.853136i	$0.674698\pi$
$354$	73070.2	+	73070.2i	0.0309908	+	0.0309908i
$355$			495860.i			0.208828i
$356$	−585233.			−0.244739
$357$	−393848.	−	1.40276e6i	−0.163553	−	0.582523i
$358$	−3.01287e6			−1.24243
$359$			2.54283e6i			1.04131i	0.853766	+	0.520656i	$0.174313\pi$
$359$			2.54283e6i			1.04131i	−0.853766	+	0.520656i	$0.825687\pi$
$360$	−420479.	−	420479.i	−0.170997	−	0.170997i
$361$	2.47148e6			0.998136
$362$	−885708.	−	885708.i	−0.355238	−	0.355238i
$363$	5.08899e6	−	5.08899e6i	2.02705	−	2.02705i
$364$	−16251.1	+	16251.1i	−0.00642878	+	0.00642878i
$365$			272780.i			0.107172i
$366$			4.49682e6i			1.75470i
$367$	−1.51718e6	+	1.51718e6i	−0.587994	+	0.587994i	−0.937088	−	0.349094i	$-0.886489\pi$
$367$	−1.51718e6	+	1.51718e6i	−0.587994	+	0.587994i	0.349094	+	0.937088i	$0.386489\pi$
$368$	1.90594e6	−	1.90594e6i	0.733651	−	0.733651i
$369$	2.83170e6	+	2.83170e6i	1.08263	+	1.08263i
$370$	−762565.			−0.289583
$371$	−26045.0	−	26045.0i	−0.00982402	−	0.00982402i
$372$			1.19852e6i			0.449042i
$373$	−71827.4			−0.0267312			−0.0133656	−	0.999911i	$-0.504255\pi$
$373$	−71827.4			−0.0267312			−0.0133656	+	0.999911i	$0.504255\pi$
$374$	1.95412e6	−	3.47977e6i	0.722391	−	1.28639i
$375$	−1.64269e6			−0.603222
$376$		−	2.19432e6i		−	0.800443i
$377$	55118.2	+	55118.2i	0.0199729	+	0.0199729i
$378$	37544.8			0.0135151
$379$	227499.	+	227499.i	0.0813544	+	0.0813544i	0.746613	−	0.665259i	$-0.231679\pi$
$379$	227499.	+	227499.i	0.0813544	+	0.0813544i	−0.665259	+	0.746613i	$0.731679\pi$
$380$	5179.59	−	5179.59i	0.00184008	−	0.00184008i
$381$	3.28611e6	−	3.28611e6i	1.15976	−	1.15976i
$382$			1.68178e6i			0.589671i
$383$		−	4.17122e6i		−	1.45300i	−0.687166	−	0.726501i	$-0.741145\pi$
$383$		−	4.17122e6i		−	1.45300i	0.687166	−	0.726501i	$-0.258855\pi$
$384$	−1.15990e6	+	1.15990e6i	−0.401414	+	0.401414i
$385$	329293.	−	329293.i	0.113222	−	0.113222i
$386$	−174084.	−	174084.i	−0.0594691	−	0.0594691i
$387$	1.34360e6			0.456028
$388$	−245559.	−	245559.i	−0.0828089	−	0.0828089i
$389$			3.66845e6i			1.22916i	0.788854	+	0.614580i	$0.210675\pi$
$389$			3.66845e6i			1.22916i	−0.788854	+	0.614580i	$0.789325\pi$
$390$	60712.2			0.0202122
$391$	4.23971e6	+	2.38087e6i	1.40247	+	0.787579i
$392$	2.70687e6			0.889716
$393$		−	2.64333e6i		−	0.863317i
$394$	1.30275e6	+	1.30275e6i	0.422785	+	0.422785i
$395$	−985855.			−0.317922
$396$	−1.09211e6	−	1.09211e6i	−0.349970	−	0.349970i
$397$	−4.40840e6	+	4.40840e6i	−1.40380	+	1.40380i	−0.616239	+	0.787559i	$0.711345\pi$
$397$	−4.40840e6	+	4.40840e6i	−1.40380	+	1.40380i	−0.787559	+	0.616239i	$0.788655\pi$
$398$	−839934.	+	839934.i	−0.265789	+	0.265789i
$399$			83064.2i			0.0261205i
$400$			1.96695e6i			0.614671i
$401$	411424.	−	411424.i	0.127770	−	0.127770i	−0.640330	−	0.768100i	$-0.721202\pi$
$401$	411424.	−	411424.i	0.127770	−	0.127770i	0.768100	+	0.640330i	$0.221202\pi$
$402$	2.27923e6	−	2.27923e6i	0.703435	−	0.703435i
$403$	−201584.	−	201584.i	−0.0618293	−	0.0618293i
$404$	−876247.			−0.267100
$405$	−492822.	−	492822.i	−0.149298	−	0.149298i
$406$			440104.i			0.132507i
$407$	−9.11054e6			−2.72620
$408$	−4.53179e6	−	2.54490e6i	−1.34778	−	0.756868i
$409$	−556731.			−0.164565			−0.0822825	−	0.996609i	$-0.526221\pi$
$409$	−556731.			−0.164565			−0.0822825	+	0.996609i	$0.526221\pi$
$410$			936406.i			0.275109i
$411$	392992.	+	392992.i	0.114757	+	0.114757i
$412$	−414797.			−0.120390
$413$	37745.5	+	37745.5i	0.0108890	+	0.0108890i
$414$	−3.45940e6	+	3.45940e6i	−0.991974	+	0.991974i
$415$	797894.	−	797894.i	0.227418	−	0.227418i
$416$			146145.i			0.0414047i
$417$		−	5.96511e6i		−	1.67988i
$418$	−160883.	+	160883.i	−0.0450371	+	0.0450371i
$419$	1.12153e6	−	1.12153e6i	0.312088	−	0.312088i	−0.533630	−	0.845718i	$-0.679173\pi$
$419$	1.12153e6	−	1.12153e6i	0.312088	−	0.312088i	0.845718	+	0.533630i	$0.179173\pi$
$420$	−93230.5	−	93230.5i	−0.0257890	−	0.0257890i
$421$	6.81156e6			1.87301			0.936507	−	0.350648i	$-0.114039\pi$
$421$	6.81156e6			1.87301			0.936507	+	0.350648i	$0.114039\pi$
$422$	1.75355e6	+	1.75355e6i	0.479333	+	0.479333i
$423$			2.78393e6i			0.756496i
$424$	−131392.			−0.0354941
$425$	−3.41625e6	+	959168.i	−0.917440	+	0.257586i
$426$	−4.36064e6			−1.16420
$427$			2.32290e6i			0.616539i
$428$	1.24509e6	+	1.24509e6i	0.328543	+	0.328543i
$429$	725343.			0.190283
$430$	222155.	+	222155.i	0.0579409	+	0.0579409i
$431$	1.66700e6	−	1.66700e6i	0.432257	−	0.432257i	−0.457139	−	0.889396i	$-0.651126\pi$
$431$	1.66700e6	−	1.66700e6i	0.432257	−	0.432257i	0.889396	+	0.457139i	$0.151126\pi$
$432$	66196.0	−	66196.0i	0.0170656	−	0.0170656i
$433$		−	2.90831e6i		−	0.745453i	−0.927941	−	0.372727i	$-0.878423\pi$
$433$		−	2.90831e6i		−	0.745453i	0.927941	−	0.372727i	$-0.121577\pi$
$434$		−	1.60960e6i		−	0.410197i
$435$	−316206.	+	316206.i	−0.0801212	+	0.0801212i
$436$	161682.	−	161682.i	0.0407330	−	0.0407330i
$437$	−196018.	−	196018.i	−0.0491012	−	0.0491012i
$438$	−2.39885e6			−0.597473
$439$	−1.55784e6	−	1.55784e6i	−0.385800	−	0.385800i	0.487386	−	0.873187i	$-0.337950\pi$
$439$	−1.55784e6	−	1.55784e6i	−0.385800	−	0.385800i	−0.873187	+	0.487386i	$0.837950\pi$
$440$		−	1.66123e6i		−	0.409069i
$441$	−3.43419e6			−0.840869
$442$	258761.	−	72651.4i	0.0630004	−	0.0176884i
$443$	5.81938e6			1.40886			0.704429	−	0.709775i	$-0.251203\pi$
$443$	5.81938e6			1.40886			0.704429	+	0.709775i	$0.251203\pi$
$444$			2.57941e6i			0.620959i
$445$	564698.	+	564698.i	0.135181	+	0.135181i
$446$	4.21292e6			1.00287
$447$	1.75038e6	+	1.75038e6i	0.414346	+	0.414346i
$448$	−1.40705e6	+	1.40705e6i	−0.331218	+	0.331218i
$449$	5.08223e6	−	5.08223e6i	1.18970	−	1.18970i	0.212554	−	0.977149i	$-0.431822\pi$
$449$	5.08223e6	−	5.08223e6i	1.18970	−	1.18970i	0.977149	−	0.212554i	$-0.0681782\pi$
$450$		−	3.57014e6i		−	0.831100i
$451$			1.11875e7i			2.58994i
$452$	331084.	−	331084.i	0.0762240	−	0.0762240i
$453$	−3.52299e6	+	3.52299e6i	−0.806615	+	0.806615i
$454$	754972.	+	754972.i	0.171906	+	0.171906i
$455$	31361.8			0.00710186
$456$	209522.	+	209522.i	0.0471865	+	0.0471865i
$457$		−	1.27698e6i		−	0.286019i	−0.989721	−	0.143009i	$-0.954322\pi$
$457$		−	1.27698e6i		−	0.286019i	0.989721	−	0.143009i	$-0.0456779\pi$
$458$	−80874.0			−0.0180155
$459$	147251.	+	82691.1i	0.0326232	+	0.0183201i
$460$	440018.			0.0969562
$461$		−	2.73008e6i		−	0.598305i	−0.954205	−	0.299153i	$-0.903296\pi$
$461$		−	2.73008e6i		−	0.598305i	0.954205	−	0.299153i	$-0.0967040\pi$
$462$	2.89583e6	+	2.89583e6i	0.631202	+	0.631202i
$463$	1.92692e6			0.417746			0.208873	−	0.977943i	$-0.433021\pi$
$463$	1.92692e6			0.417746			0.208873	+	0.977943i	$0.433021\pi$
$464$	775956.	+	775956.i	0.167318	+	0.167318i
$465$	1.15647e6	−	1.15647e6i	0.248028	−	0.248028i
$466$	143178.	−	143178.i	0.0305429	−	0.0305429i
$467$		−	3.27830e6i		−	0.695595i	−0.937570	−	0.347798i	$-0.886930\pi$
$467$		−	3.27830e6i		−	0.695595i	0.937570	−	0.347798i	$-0.113070\pi$
$468$		−	104013.i		−	0.0219519i
$469$	1.17737e6	−	1.17737e6i	0.247162	−	0.247162i
$470$	−460304.	+	460304.i	−0.0961170	+	0.0961170i
$471$	−5.47657e6	−	5.47657e6i	−1.13751	−	1.13751i
$472$	190420.			0.0393420
$473$	2.65414e6	+	2.65414e6i	0.545470	+	0.545470i
$474$		−	8.66970e6i		−	1.77239i
$475$	202292.			0.0411382
$476$	−508922.	−	285793.i	−0.102952	−	0.0578142i
$477$	166697.			0.0335453
$478$		−	4.07484e6i		−	0.815719i
$479$	−2.67634e6	−	2.67634e6i	−0.532969	−	0.532969i	0.388486	−	0.921455i	$-0.372998\pi$
$479$	−2.67634e6	−	2.67634e6i	−0.532969	−	0.532969i	−0.921455	+	0.388486i	$0.872998\pi$
$480$	−838415.			−0.166095
$481$	−433843.	−	433843.i	−0.0855007	−	0.0855007i
$482$	130374.	−	130374.i	0.0255607	−	0.0255607i
$483$	−3.52824e6	+	3.52824e6i	−0.688162	+	0.688162i
$484$		−	2.88310e6i		−	0.559430i
$485$			473886.i			0.0914787i
$486$	4.45100e6	−	4.45100e6i	0.854805	−	0.854805i
$487$	−3.87692e6	+	3.87692e6i	−0.740738	+	0.740738i	−0.972720	−	0.231982i	$-0.925479\pi$
$487$	−3.87692e6	+	3.87692e6i	−0.740738	+	0.740738i	0.231982	+	0.972720i	$0.425479\pi$
$488$	5.85932e6	+	5.85932e6i	1.11377	+	1.11377i
$489$	1.00079e6			0.189265
$490$	−567821.	−	567821.i	−0.106837	−	0.106837i
$491$		−	2.98285e6i		−	0.558377i	−0.960236	−	0.279189i	$-0.909935\pi$
$491$		−	2.98285e6i		−	0.558377i	0.960236	−	0.279189i	$-0.0900654\pi$
$492$	3.16743e6			0.589922
$493$	−969314.	+	1.72609e6i	−0.179617	+	0.319850i
$494$	−15322.5			−0.00282496
$495$			2.10759e6i			0.386610i
$496$	−2.83791e6	−	2.83791e6i	−0.517959	−	0.517959i
$497$	−2.25255e6			−0.409057
$498$	7.01675e6	+	7.01675e6i	1.26784	+	1.26784i
$499$	−1.77591e6	+	1.77591e6i	−0.319279	+	0.319279i	−0.848490	−	0.529211i	$-0.822488\pi$
$499$	−1.77591e6	+	1.77591e6i	−0.319279	+	0.319279i	0.529211	+	0.848490i	$0.322488\pi$
$500$	−465322.	+	465322.i	−0.0832393	+	0.0832393i
$501$			1.11108e7i			1.97766i
$502$		−	1.00464e6i		−	0.177931i
$503$	−7.26730e6	+	7.26730e6i	−1.28072	+	1.28072i	−0.340456	+	0.940260i	$0.610582\pi$
$503$	−7.26730e6	+	7.26730e6i	−1.28072	+	1.28072i	−0.940260	+	0.340456i	$0.889418\pi$
$504$	1.91012e6	−	1.91012e6i	0.334953	−	0.334953i
$505$	845502.	+	845502.i	0.147532	+	0.147532i
$506$	−1.36674e7			−2.37306
$507$	−5.79125e6	−	5.79125e6i	−1.00058	−	1.00058i
$508$		−	1.86170e6i		−	0.320074i
$509$	5.97499e6			1.02222			0.511108	−	0.859517i	$-0.329235\pi$
$509$	5.97499e6			1.02222			0.511108	+	0.859517i	$0.329235\pi$
$510$	416793.	+	1.48448e6i	0.0709569	+	0.252726i
$511$	−1.23916e6			−0.209931
$512$			6.21228e6i			1.04731i
$513$	−6807.98	−	6807.98i	−0.00114216	−	0.00114216i
$514$	−6.36726e6			−1.06303
$515$	400243.	+	400243.i	0.0664975	+	0.0664975i
$516$	751449.	−	751449.i	0.124244	−	0.124244i
$517$	−5.49936e6	+	5.49936e6i	−0.904869	+	0.904869i
$518$		−	3.46412e6i		−	0.567242i
$519$			2.99380e6i			0.487870i
$520$	79107.4	−	79107.4i	0.0128295	−	0.0128295i
$521$	−5.54411e6	+	5.54411e6i	−0.894823	+	0.894823i	−0.994972	−	0.100149i	$-0.968068\pi$
$521$	−5.54411e6	+	5.54411e6i	−0.894823	+	0.894823i	0.100149	+	0.994972i	$0.468068\pi$
$522$	−1.40841e6	−	1.40841e6i	−0.226231	−	0.226231i
$523$	8.55850e6			1.36818			0.684090	−	0.729397i	$-0.260199\pi$
$523$	8.55850e6			1.36818			0.684090	+	0.729397i	$0.260199\pi$
$524$	−748772.	−	748772.i	−0.119130	−	0.119130i
$525$		−	3.64118e6i		−	0.576559i
$526$	5.60230e6			0.882881
$527$	3.54508e6	−	6.31286e6i	0.556032	−	0.990147i
$528$	1.02114e7			1.59405
$529$		−	1.02158e7i		−	1.58721i
$530$	27562.3	+	27562.3i	0.00426212	+	0.00426212i
$531$	−241585.			−0.0371820
$532$	23529.4	+	23529.4i	0.00360439	+	0.00360439i
$533$	−532745.	+	532745.i	−0.0812272	+	0.0812272i
$534$	−4.96601e6	+	4.96601e6i	−0.753624	+	0.753624i
$535$		−	2.40281e6i		−	0.362940i
$536$		−	5.93964e6i		−	0.892993i
$537$	9.83359e6	−	9.83359e6i	1.47155	−	1.47155i
$538$	2.05357e6	−	2.05357e6i	0.305881	−	0.305881i
$539$	−6.78389e6	−	6.78389e6i	−1.00579	−	1.00579i
$540$	15282.4			0.00225532
$541$	4.24626e6	+	4.24626e6i	0.623754	+	0.623754i	0.946489	−	0.322735i	$-0.104602\pi$
$541$	4.24626e6	+	4.24626e6i	0.623754	+	0.623754i	−0.322735	+	0.946489i	$0.604602\pi$
$542$			9.53185e6i			1.39373i
$543$	5.78166e6			0.841497
$544$	−3.57341e6	+	1.00329e6i	−0.517708	+	0.145355i
$545$	−312019.			−0.0449976
$546$			275798.i			0.0395922i
$547$	−8.61227e6	−	8.61227e6i	−1.23069	−	1.23069i	−0.963698	−	0.266994i	$-0.913970\pi$
$547$	−8.61227e6	−	8.61227e6i	−1.23069	−	1.23069i	−0.266994	−	0.963698i	$-0.586030\pi$
$548$	222644.			0.0316709
$549$	−7.43369e6	−	7.43369e6i	−1.05263	−	1.05263i
$550$	7.05244e6	−	7.05244e6i	0.994105	−	0.994105i
$551$	79803.9	−	79803.9i	0.0111981	−	0.0111981i
$552$			1.77994e7i			2.48632i
$553$		−	4.47846e6i		−	0.622753i
$554$	1.87580e6	−	1.87580e6i	0.259665	−	0.259665i
$555$	2.48891e6	−	2.48891e6i	0.342986	−	0.342986i
$556$	−1.68972e6	−	1.68972e6i	−0.231808	−	0.231808i
$557$	8.48293e6			1.15853			0.579266	−	0.815139i	$-0.303339\pi$
$557$	8.48293e6			1.15853			0.579266	+	0.815139i	$0.303339\pi$
$558$	5.15100e6	+	5.15100e6i	0.700335	+	0.700335i
$559$			252779.i			0.0342147i
$560$	441512.			0.0594939
$561$	4.97952e6	+	1.77355e7i	0.668006	+	2.37922i
$562$	−2.02930e6			−0.271023
$563$			9.24589e6i			1.22936i	0.788778	+	0.614678i	$0.210714\pi$
$563$			9.24589e6i			1.22936i	−0.788778	+	0.614678i	$0.789286\pi$
$564$	1.55700e6	+	1.55700e6i	0.206106	+	0.206106i
$565$	−638934.			−0.0842044
$566$	−7.98976e6	−	7.98976e6i	−1.04832	−	1.04832i
$567$	2.23875e6	−	2.23875e6i	0.292448	−	0.292448i
$568$	−5.68186e6	+	5.68186e6i	−0.738958	+	0.738958i
$569$			13772.5i			0.00178333i	1.00000		0.000891667i	$0.000283827\pi$
$569$			13772.5i			0.00178333i	−1.00000		0.000891667i	$0.999716\pi$
$570$		−	87903.2i		−	0.0113323i
$571$	2.64411e6	−	2.64411e6i	0.339383	−	0.339383i	−0.516752	−	0.856135i	$-0.672859\pi$
$571$	2.64411e6	−	2.64411e6i	0.339383	−	0.339383i	0.856135	+	0.516752i	$0.172859\pi$
$572$	205466.	−	205466.i	0.0262573	−	0.0262573i
$573$	−5.48908e6	−	5.48908e6i	−0.698415	−	0.698415i
$574$	−4.25383e6			−0.538890
$575$	8.59259e6	+	8.59259e6i	1.08381	+	1.08381i
$576$		−	9.00561e6i		−	1.13099i
$577$	1.10934e7			1.38716			0.693578	−	0.720382i	$-0.256033\pi$
$577$	1.10934e7			1.38716			0.693578	+	0.720382i	$0.256033\pi$
$578$	3.55282e6	+	5.82825e6i	0.442338	+	0.725636i
$579$	1.13637e6			0.140872
$580$			179142.i			0.0221120i
$581$	3.62460e6	+	3.62460e6i	0.445472	+	0.445472i
$582$	−4.16740e6			−0.509986
$583$	329293.	+	329293.i	0.0401246	+	0.0401246i
$584$	−3.12568e6	+	3.12568e6i	−0.379238	+	0.379238i
$585$	−100363.	+	100363.i	−0.0121251	+	0.0121251i
$586$		−	7.61510e6i		−	0.916076i
$587$		−	3.73101e6i		−	0.446922i	−0.974713	−	0.223461i	$-0.928264\pi$
$587$		−	3.73101e6i		−	0.446922i	0.974713	−	0.223461i	$-0.0717355\pi$
$588$	−1.92068e6	+	1.92068e6i	−0.229093	+	0.229093i
$589$	−291868.	+	291868.i	−0.0346655	+	0.0346655i
$590$	−39944.4	−	39944.4i	−0.00472418	−	0.00472418i
$591$	−8.50397e6			−1.00151
$592$	−6.10766e6	−	6.10766e6i	−0.716260	−	0.716260i
$593$			860883.i			0.100533i	0.998736	+	0.0502664i	$0.0160070\pi$
$593$			860883.i			0.100533i	−0.998736	+	0.0502664i	$0.983993\pi$
$594$	−474688.			−0.0552004
$595$	215300.	+	766831.i	0.0249317	+	0.0887988i
$596$	991653.			0.114352
$597$		−	5.48285e6i		−	0.629609i
$598$	−650839.	−	650839.i	−0.0744253	−	0.0744253i
$599$	−7.04065e6			−0.801763			−0.400881	−	0.916130i	$-0.631296\pi$
$599$	−7.04065e6			−0.801763			−0.400881	+	0.916130i	$0.631296\pi$
$600$	−9.18456e6	−	9.18456e6i	−1.04155	−	1.04155i
$601$	5.12244e6	−	5.12244e6i	0.578484	−	0.578484i	−0.356002	−	0.934485i	$-0.615860\pi$
$601$	5.12244e6	−	5.12244e6i	0.578484	−	0.578484i	0.934485	+	0.356002i	$0.115860\pi$
$602$	−1.00919e6	+	1.00919e6i	−0.113496	+	0.113496i
$603$			7.53560e6i			0.843965i
$604$			1.99590e6i			0.222611i
$605$	−2.78194e6	+	2.78194e6i	−0.309000	+	0.309000i
$606$	−7.43543e6	+	7.43543e6i	−0.822478	+	0.822478i
$607$	3.27813e6	+	3.27813e6i	0.361122	+	0.361122i	0.864226	−	0.503104i	$-0.167809\pi$
$607$	3.27813e6	+	3.27813e6i	0.361122	+	0.361122i	−0.503104	+	0.864226i	$0.667809\pi$
$608$	211598.			0.0232142
$609$	−1.43644e6	−	1.43644e6i	−0.156943	−	0.156943i
$610$		−	2.45823e6i		−	0.267484i
$611$	−523758.			−0.0567580
$612$	2.54323e6	−	714053.i	0.274478	−	0.0770641i
$613$	−4.87765e6			−0.524275			−0.262138	−	0.965030i	$-0.584427\pi$
$613$	−4.87765e6			−0.524275			−0.262138	+	0.965030i	$0.584427\pi$
$614$		−	3.12418e6i		−	0.334437i
$615$	−3.05630e6	−	3.05630e6i	−0.325843	−	0.325843i
$616$	7.54648e6			0.801295
$617$	5.67870e6	+	5.67870e6i	0.600532	+	0.600532i	0.940454	−	0.339922i	$-0.110401\pi$
$617$	5.67870e6	+	5.67870e6i	0.600532	+	0.600532i	−0.339922	+	0.940454i	$0.610401\pi$
$618$	−3.51977e6	+	3.51977e6i	−0.370718	+	0.370718i
$619$	−6.79892e6	+	6.79892e6i	−0.713204	+	0.713204i	−0.967204	−	0.254001i	$-0.918254\pi$
$619$	−6.79892e6	+	6.79892e6i	−0.713204	+	0.713204i	0.254001	+	0.967204i	$0.418254\pi$
$620$		−	655180.i		−	0.0684512i
$621$		−	578353.i		−	0.0601816i
$622$	431398.	−	431398.i	0.0447097	−	0.0447097i
$623$	−2.56526e6	+	2.56526e6i	−0.264796	+	0.264796i
$624$	486266.	+	486266.i	0.0499934	+	0.0499934i
$625$	−8.40781e6			−0.860960
$626$	9.27596e6	+	9.27596e6i	0.946070	+	0.946070i
$627$		−	1.05020e6i		−	0.106685i
$628$	−3.10268e6			−0.313933
$629$	7.62960e6	−	1.35863e7i	0.768910	−	1.36923i
$630$	−801373.			−0.0804421
$631$			1.30622e7i			1.30600i	0.757359	+	0.652999i	$0.226489\pi$
$631$			1.30622e7i			1.30600i	−0.757359	+	0.652999i	$0.773511\pi$
$632$	−1.12965e7	−	1.12965e7i	−1.12500	−	1.12500i
$633$	−1.14467e7			−1.13546
$634$	5.75264e6	+	5.75264e6i	0.568387	+	0.568387i
$635$	−1.79638e6	+	1.79638e6i	−0.176792	+	0.176792i
$636$	93230.6	−	93230.6i	0.00913936	−	0.00913936i
$637$		−	646096.i		−	0.0630883i
$638$		−	5.56434e6i		−	0.541205i
$639$	7.20856e6	−	7.20856e6i	0.698388	−	0.698388i
$640$	634069.	−	634069.i	0.0611908	−	0.0611908i
$641$	1.34909e7	+	1.34909e7i	1.29686	+	1.29686i	0.930453	+	0.366412i	$0.119414\pi$
$641$	1.34909e7	+	1.34909e7i	1.29686	+	1.29686i	0.366412	+	0.930453i	$0.380586\pi$
$642$	2.11305e7			2.02336
$643$	−1.49019e6	−	1.49019e6i	−0.142140	−	0.142140i	0.632456	−	0.774596i	$-0.282047\pi$
$643$	−1.49019e6	−	1.49019e6i	−0.142140	−	0.142140i	−0.774596	+	0.632456i	$0.782047\pi$
$644$			1.99888e6i			0.189920i
$645$	−1.45017e6			−0.137252
$646$	−105190.	−	374652.i	−0.00991726	−	0.0353221i
$647$	1.25071e7			1.17461			0.587306	−	0.809365i	$-0.300189\pi$
$647$	1.25071e7			1.17461			0.587306	+	0.809365i	$0.300189\pi$
$648$		−	1.12941e7i		−	1.05661i
$649$	−477226.	−	477226.i	−0.0444746	−	0.0444746i
$650$	671672.			0.0623554
$651$	5.25350e6	+	5.25350e6i	0.485843	+	0.485843i
$652$	283491.	−	283491.i	0.0261168	−	0.0261168i
$653$	1.17740e7	−	1.17740e7i	1.08054	−	1.08054i	0.0840773	−	0.996459i	$-0.473206\pi$
$653$	1.17740e7	−	1.17740e7i	1.08054	−	1.08054i	0.996459	−	0.0840773i	$-0.0267943\pi$
$654$		−	2.74392e6i		−	0.250858i
$655$			1.44500e6i			0.131603i
$656$	−7.50001e6	+	7.50001e6i	−0.680460	+	0.680460i
$657$	3.96554e6	−	3.96554e6i	0.358417	−	0.358417i
$658$	−2.09103e6	−	2.09103e6i	−0.188276	−	0.188276i
$659$	−1.23002e7			−1.10331			−0.551656	−	0.834072i	$-0.686004\pi$
$659$	−1.23002e7			−1.10331			−0.551656	+	0.834072i	$0.686004\pi$
$660$	1.17874e6	+	1.17874e6i	0.105331	+	0.105331i
$661$		−	1.79409e7i		−	1.59714i	−0.601905	−	0.798568i	$-0.705591\pi$
$661$		−	1.79409e7i		−	1.59714i	0.601905	−	0.798568i	$-0.294409\pi$
$662$	−4.68034e6			−0.415081
$663$	−607436.	+	1.08168e6i	−0.0536682	+	0.0955690i
$664$	1.82855e7			1.60949
$665$		−	45407.7i		−	0.00398176i
$666$	1.10858e7	+	1.10858e7i	0.968459	+	0.968459i
$667$	6.77951e6			0.590043
$668$	3.14734e6	+	3.14734e6i	0.272899	+	0.272899i
$669$	−1.37504e7	+	1.37504e7i	−1.18782	+	1.18782i
$670$	−1.24596e6	+	1.24596e6i	−0.107230	+	0.107230i
$671$		−	2.93690e7i		−	2.51816i
$672$		−	3.80868e6i		−	0.325350i
$673$	−6.27986e6	+	6.27986e6i	−0.534456	+	0.534456i	−0.921895	−	0.387439i	$-0.873360\pi$
$673$	−6.27986e6	+	6.27986e6i	−0.534456	+	0.534456i	0.387439	+	0.921895i	$0.373360\pi$
$674$	−9.77795e6	+	9.77795e6i	−0.829083	+	0.829083i
$675$	298433.	+	298433.i	0.0252108	+	0.0252108i
$676$	−3.28095e6			−0.276143
$677$	−738377.	−	738377.i	−0.0619165	−	0.0619165i	0.675471	−	0.737387i	$-0.263941\pi$
$677$	−738377.	−	738377.i	−0.0619165	−	0.0619165i	−0.737387	+	0.675471i	$0.763941\pi$
$678$		−	5.61884e6i		−	0.469432i
$679$	−2.15273e6			−0.179191
$680$	2.47734e6	+	1.39119e6i	0.205454	+	0.115376i
$681$	−4.92825e6			−0.407216
$682$			2.03505e7i			1.67538i
$683$	−2.02206e6	−	2.02206e6i	−0.165860	−	0.165860i	0.619297	−	0.785157i	$-0.287418\pi$
$683$	−2.02206e6	−	2.02206e6i	−0.165860	−	0.165860i	−0.785157	+	0.619297i	$0.787418\pi$
$684$	−150597.			−0.0123077
$685$	−214832.	−	214832.i	−0.0174934	−	0.0174934i
$686$	5.72768e6	−	5.72768e6i	0.464696	−	0.464696i
$687$	263961.	−	263961.i	0.0213377	−	0.0213377i
$688$			3.55864e6i			0.286624i
$689$			31361.8i			0.00251682i
$690$	3.73379e6	−	3.73379e6i	0.298557	−	0.298557i
$691$	−4.20905e6	+	4.20905e6i	−0.335343	+	0.335343i	−0.854611	−	0.519268i	$-0.826205\pi$
$691$	−4.20905e6	+	4.20905e6i	−0.335343	+	0.335343i	0.519268	+	0.854611i	$0.326205\pi$
$692$	848047.	+	848047.i	0.0673216	+	0.0673216i
$693$	−9.57419e6			−0.757302
$694$	−6.42325e6	−	6.42325e6i	−0.506240	−	0.506240i
$695$			3.26087e6i			0.256078i
$696$	−7.24658e6			−0.567035
$697$	−1.66836e7	−	9.36891e6i	−1.30079	−	0.730478i
$698$	−9.21628e6			−0.716006
$699$			934624.i			0.0723509i
$700$	−1.03143e6	−	1.03143e6i	−0.0795600	−	0.0795600i
$701$	1.26547e7			0.972652			0.486326	−	0.873777i	$-0.338337\pi$
$701$	1.26547e7			0.972652			0.486326	+	0.873777i	$0.338337\pi$
$702$	−22604.6	−	22604.6i	−0.00173122	−	0.00173122i
$703$	−628147.	+	628147.i	−0.0479373	+	0.0479373i
$704$	1.77897e7	−	1.77897e7i	1.35281	−	1.35281i
$705$		−	3.00473e6i		−	0.227684i
$706$			1.17432e7i			0.886692i
$707$	−3.84088e6	+	3.84088e6i	−0.288989	+	0.288989i
$708$	−135114.	+	135114.i	−0.0101302	+	0.0101302i
$709$	4.60411e6	+	4.60411e6i	0.343978	+	0.343978i	0.857860	−	0.513883i	$-0.171793\pi$
$709$	4.60411e6	+	4.60411e6i	0.343978	+	0.343978i	−0.513883	+	0.857860i	$0.671793\pi$
$710$	2.38378e6			0.177468
$711$	1.43319e7	+	1.43319e7i	1.06323	+	1.06323i
$712$			1.29413e7i			0.956706i
$713$	−2.47948e7			−1.82657
$714$	−6.74358e6	+	1.89337e6i	−0.495046	+	0.138992i
$715$	−396514.			−0.0290064
$716$		−	5.57108e6i		−	0.406122i
$717$	1.32997e7	+	1.32997e7i	0.966149	+	0.966149i
$718$	1.22243e7			0.884939
$719$	−1.22767e7	−	1.22767e7i	−0.885645	−	0.885645i	0.108457	−	0.994101i	$-0.465409\pi$
$719$	−1.22767e7	−	1.22767e7i	−0.885645	−	0.885645i	−0.994101	+	0.108457i	$0.965409\pi$
$720$	−1.41292e6	+	1.41292e6i	−0.101575	+	0.101575i
$721$	−1.81819e6	+	1.81819e6i	−0.130257	+	0.130257i
$722$		−	1.18813e7i		−	0.848246i
$723$			851043.i			0.0605488i
$724$	1.63776e6	−	1.63776e6i	0.116119	−	0.116119i
$725$	−3.49826e6	+	3.49826e6i	−0.247177	+	0.247177i
$726$	−2.44646e7	−	2.44646e7i	−1.72265	−	1.72265i
$727$	277677.			0.0194852			0.00974259	−	0.999953i	$-0.496899\pi$
$727$	277677.			0.0194852			0.00974259	+	0.999953i	$0.496899\pi$
$728$	359362.	+	359362.i	0.0251307	+	0.0251307i
$729$			1.50930e7i			1.05186i
$730$	1.31135e6			0.0910777
$731$	−6.18075e6	+	1.73535e6i	−0.427807	+	0.120114i
$732$	−8.31505e6			−0.573571
$733$		−	1.33256e7i		−	0.916069i	−0.888934	−	0.458034i	$-0.848554\pi$
$733$		−	1.33256e7i		−	0.916069i	0.888934	−	0.458034i	$-0.151446\pi$
$734$	7.29365e6	+	7.29365e6i	0.499695	+	0.499695i
$735$	3.70658e6			0.253078
$736$	8.98787e6	+	8.98787e6i	0.611592	+	0.611592i
$737$	−1.48858e7	+	1.48858e7i	−1.00949	+	1.00949i
$738$	1.36130e7	−	1.36130e7i	0.920053	−	0.920053i
$739$			1.94280e7i			1.30863i	0.756221	+	0.654317i	$0.227044\pi$
$739$			1.94280e7i			1.30863i	−0.756221	+	0.654317i	$0.772956\pi$
$740$		−	1.41005e6i		−	0.0946579i
$741$	50010.4	−	50010.4i	0.00334592	−	0.00334592i
$742$	−125208.	+	125208.i	−0.00834874	+	0.00834874i
$743$	7.31998e6	+	7.31998e6i	0.486450	+	0.486450i	0.907184	−	0.420734i	$-0.138228\pi$
$743$	7.31998e6	+	7.31998e6i	0.486450	+	0.486450i	−0.420734	+	0.907184i	$0.638228\pi$
$744$	2.65030e7			1.75535
$745$	−956858.	−	956858.i	−0.0631622	−	0.0631622i
$746$			345300.i			0.0227169i
$747$	−2.31988e7			−1.52112
$748$	6.43443e6	+	3.61335e6i	0.420490	+	0.236133i
$749$	1.09153e7			0.710936
$750$			7.89701e6i			0.512636i
$751$	1.00939e7	+	1.00939e7i	0.653069	+	0.653069i	0.953731	−	0.300662i	$-0.0972075\pi$
$751$	1.00939e7	+	1.00939e7i	0.653069	+	0.653069i	−0.300662	+	0.953731i	$0.597207\pi$
$752$	−7.37348e6			−0.475475
$753$	3.27901e6	+	3.27901e6i	0.210744	+	0.210744i
$754$	264973.	−	264973.i	0.0169736	−	0.0169736i
$755$	1.92587e6	−	1.92587e6i	0.122959	−	0.122959i
$756$			69423.8i			0.00441778i
$757$		−	7.20163e6i		−	0.456763i	−0.973572	−	0.228382i	$-0.926657\pi$
$757$		−	7.20163e6i		−	0.456763i	0.973572	−	0.228382i	$-0.0733434\pi$
$758$	1.09367e6	−	1.09367e6i	0.0691374	−	0.0691374i
$759$	4.46084e7	−	4.46084e7i	2.81069	−	2.81069i
$760$	−114537.	−	114537.i	−0.00719303	−	0.00719303i
$761$	−1.70010e7			−1.06417			−0.532086	−	0.846690i	$-0.678592\pi$
$761$	−1.70010e7			−1.06417			−0.532086	+	0.846690i	$0.678592\pi$
$762$	−1.57975e7	−	1.57975e7i	−0.985601	−	0.985601i
$763$		−	1.41741e6i		−	0.0881425i
$764$	−3.10976e6			−0.192750
$765$	−3.14300e6	−	1.76500e6i	−0.194174	−	0.109041i
$766$	−2.00526e7			−1.23480
$767$		−	45450.8i		−	0.00278967i
$768$	−1.25552e7	−	1.25552e7i	−0.768104	−	0.768104i
$769$	−1.12443e7			−0.685675			−0.342838	−	0.939395i	$-0.611388\pi$
$769$	−1.12443e7			−0.685675			−0.342838	+	0.939395i	$0.611388\pi$
$770$	−1.58303e6	−	1.58303e6i	−0.0962193	−	0.0962193i
$771$	2.07818e7	−	2.07818e7i	1.25906	−	1.25906i
$772$	321898.	−	321898.i	0.0194391	−	0.0194391i
$773$			1.23631e7i			0.744180i	0.928197	+	0.372090i	$0.121359\pi$
$773$			1.23631e7i			0.744180i	−0.928197	+	0.372090i	$0.878641\pi$
$774$		−	6.45916e6i		−	0.387546i
$775$	1.27942e7	−	1.27942e7i	0.765174	−	0.765174i
$776$	−5.43008e6	+	5.43008e6i	−0.323707	+	0.323707i
$777$	1.13064e7	+	1.13064e7i	0.671849	+	0.671849i
$778$	1.76356e7			1.04458
$779$	771345.	+	771345.i	0.0455413	+	0.0455413i
$780$			112263.i			0.00660691i
$781$	2.84795e7			1.67073
$782$	1.14457e7	−	2.03818e7i	0.669308	−	1.19186i
$783$	235462.			0.0137251
$784$		−	9.09577e6i		−	0.528505i
$785$	2.99381e6	+	2.99381e6i	0.173401	+	0.173401i
$786$	−1.27075e7			−0.733673
$787$	1.12105e7	+	1.12105e7i	0.645192	+	0.645192i	0.951827	−	0.306635i	$-0.0992030\pi$
$787$	1.12105e7	+	1.12105e7i	0.645192	+	0.645192i	−0.306635	+	0.951827i	$0.599203\pi$
$788$	−2.40890e6	+	2.40890e6i	−0.138199	+	0.138199i
$789$	−1.82851e7	+	1.82851e7i	−1.04570	+	1.04570i
$790$			4.73936e6i			0.270179i
$791$		−	2.90250e6i		−	0.164942i
$792$	−2.41501e7	+	2.41501e7i	−1.36806	+	1.36806i
$793$	1.39855e6	−	1.39855e6i	0.0789759	−	0.0789759i
$794$	2.11928e7	+	2.11928e7i	1.19299	+	1.19299i
$795$	−179919.			−0.0100962
$796$	−1.55312e6	−	1.55312e6i	−0.0868804	−	0.0868804i
$797$			3.70676e6i			0.206704i	0.994645	+	0.103352i	$0.0329568\pi$
$797$			3.70676e6i			0.206704i	−0.994645	+	0.103352i	$0.967043\pi$
$798$	399320.			0.0221980
$799$	−3.59563e6	−	1.28065e7i	−0.199254	−	0.709680i
$800$	−9.27556e6			−0.512407
$801$		−	1.64186e7i		−	0.904181i
$802$	−1.97786e6	−	1.97786e6i	−0.108583	−	0.108583i
$803$	1.56670e7			0.857428
$804$	4.21452e6	+	4.21452e6i	0.229937	+	0.229937i
$805$	1.92874e6	−	1.92874e6i	0.104902	−	0.104902i
$806$	−969089.	+	969089.i	−0.0525444	+	0.0525444i
$807$			1.34051e7i			0.724580i
$808$			1.93766e7i			1.04412i
$809$	−1.37926e7	+	1.37926e7i	−0.740927	+	0.740927i	−0.972757	−	0.231829i	$-0.925529\pi$
$809$	−1.37926e7	+	1.37926e7i	−0.740927	+	0.740927i	0.231829	+	0.972757i	$0.425529\pi$
$810$	−2.36918e6	+	2.36918e6i	−0.126878	+	0.126878i
$811$	−1.41359e7	−	1.41359e7i	−0.754695	−	0.754695i	0.220656	−	0.975352i	$-0.429180\pi$
$811$	−1.41359e7	−	1.41359e7i	−0.754695	−	0.754695i	−0.975352	+	0.220656i	$0.929180\pi$
$812$	−813793.			−0.0433136
$813$	−3.11106e7	−	3.11106e7i	−1.65075	−	1.65075i
$814$			4.37977e7i			2.31681i
$815$	−547088.			−0.0288512
$816$	−8.55152e6	+	1.52280e7i	−0.449591	+	0.800604i
$817$	365991.			0.0191830
$818$			2.67641e6i			0.139852i
$819$	−455922.	−	455922.i	−0.0237509	−	0.0237509i
$820$	−1.73150e6			−0.0899267
$821$	−1.78516e7	−	1.78516e7i	−0.924315	−	0.924315i	0.0730157	−	0.997331i	$-0.476738\pi$
$821$	−1.78516e7	−	1.78516e7i	−0.924315	−	0.924315i	−0.997331	+	0.0730157i	$0.976738\pi$
$822$	1.88926e6	−	1.88926e6i	0.0975239	−	0.0975239i
$823$	1.00605e7	−	1.00605e7i	0.517748	−	0.517748i	−0.399141	−	0.916889i	$-0.630692\pi$
$823$	1.00605e7	−	1.00605e7i	0.517748	−	0.517748i	0.916889	+	0.399141i	$0.130692\pi$
$824$			9.17245e6i			0.470617i
$825$			4.60363e7i			2.35486i
$826$	181456.	−	181456.i	0.00925384	−	0.00925384i
$827$	1.64639e7	−	1.64639e7i	0.837083	−	0.837083i	−0.151391	−	0.988474i	$-0.548375\pi$
$827$	1.64639e7	−	1.64639e7i	0.837083	−	0.837083i	0.988474	+	0.151391i	$0.0483752\pi$
$828$	−6.39676e6	−	6.39676e6i	−0.324253	−	0.324253i
$829$	−2.08669e7			−1.05456			−0.527280	−	0.849692i	$-0.676788\pi$
$829$	−2.08669e7			−1.05456			−0.527280	+	0.849692i	$0.676788\pi$
$830$	−3.83576e6	−	3.83576e6i	−0.193267	−	0.193267i
$831$			1.22447e7i			0.615100i
$832$	1.69428e6			0.0848550
$833$	1.57978e7	−	4.43549e6i	0.788831	−	0.221477i
$834$	−2.86764e7			−1.42761
$835$		−	6.07382e6i		−	0.301471i
$836$	−297488.	−	297488.i	−0.0147216	−	0.0147216i
$837$	−861159.			−0.0424883
$838$	−5.39161e6	−	5.39161e6i	−0.265221	−	0.265221i
$839$	5.29741e6	−	5.29741e6i	0.259812	−	0.259812i	−0.565166	−	0.824977i	$-0.691188\pi$
$839$	5.29741e6	−	5.29741e6i	0.259812	−	0.259812i	0.824977	+	0.565166i	$0.191188\pi$
$840$	−2.06162e6	+	2.06162e6i	−0.100812	+	0.100812i
$841$		−	1.77510e7i		−	0.865434i
$842$		−	3.27456e7i		−	1.59174i
$843$	6.62337e6	−	6.62337e6i	0.321004	−	0.321004i
$844$	−3.24248e6	+	3.24248e6i	−0.156683	+	0.156683i
$845$	3.16584e6	+	3.16584e6i	0.152527	+	0.152527i
$846$	1.33833e7			0.642893
$847$	−1.26375e7	−	1.26375e7i	−0.605277	−	0.605277i
$848$			441512.i			0.0210840i
$849$	5.21549e7			2.48328
$850$	4.61107e6	+	1.64232e7i	0.218904	+	0.779667i
$851$	−5.33625e7			−2.52588
$852$		−	8.06323e6i		−	0.380548i
$853$	−7.43132e6	−	7.43132e6i	−0.349698	−	0.349698i	0.510299	−	0.859997i	$-0.329535\pi$
$853$	−7.43132e6	−	7.43132e6i	−0.349698	−	0.349698i	−0.859997	+	0.510299i	$0.829535\pi$
$854$	1.11670e7			0.523953
$855$	145313.	+	145313.i	0.00679811	+	0.00679811i
$856$	2.75329e7	−	2.75329e7i	1.28430	−	1.28430i
$857$	2.94702e6	−	2.94702e6i	0.137067	−	0.137067i	−0.635244	−	0.772311i	$-0.719101\pi$
$857$	2.94702e6	−	2.94702e6i	0.137067	−	0.137067i	0.772311	+	0.635244i	$0.219101\pi$
$858$		−	3.48699e6i		−	0.161708i
$859$			2.11309e7i			0.977090i	0.872539	+	0.488545i	$0.162472\pi$
$859$			2.11309e7i			0.977090i	−0.872539	+	0.488545i	$0.837528\pi$
$860$	−410786.	+	410786.i	−0.0189395	+	0.0189395i
$861$	1.38839e7	−	1.38839e7i	0.638268	−	0.638268i
$862$	−8.01387e6	−	8.01387e6i	−0.367345	−	0.367345i
$863$	2.08045e7			0.950889			0.475444	−	0.879746i	$-0.342287\pi$
$863$	2.08045e7			0.950889			0.475444	+	0.879746i	$0.342287\pi$
$864$	312161.	+	312161.i	0.0142264	+	0.0142264i
$865$		−	1.63658e6i		−	0.0743700i
$866$	−1.39813e7			−0.633508
$867$	−3.06185e7	−	7.42669e6i	−1.38336	−	0.335543i
$868$	2.97630e6			0.134084
$869$			5.66223e7i			2.54354i
$870$	1.52012e6	+	1.52012e6i	0.0680894	+	0.0680894i
$871$	−1.41772e6			−0.0633206
$872$	−3.57531e6	−	3.57531e6i	−0.159229	−	0.159229i
$873$	6.88913e6	−	6.88913e6i	0.305935	−	0.305935i
$874$	−942329.	+	942329.i	−0.0417277	+	0.0417277i
$875$			4.07931e6i			0.180122i
$876$		−	4.43570e6i		−	0.195300i
$877$	−170828.	+	170828.i	−0.00749996	+	0.00749996i	−0.710847	−	0.703347i	$-0.751688\pi$
$877$	−170828.	+	170828.i	−0.00749996	+	0.00749996i	0.703347	+	0.710847i	$0.251688\pi$
$878$	−7.48912e6	+	7.48912e6i	−0.327865	+	0.327865i
$879$	2.48546e7	+	2.48546e7i	1.08501	+	1.08501i
$880$	−5.58215e6			−0.242993
$881$	1.28017e7	+	1.28017e7i	0.555685	+	0.555685i	0.928076	−	0.372391i	$-0.121462\pi$
$881$	1.28017e7	+	1.28017e7i	0.555685	+	0.555685i	−0.372391	+	0.928076i	$0.621462\pi$
$882$			1.65094e7i			0.714595i
$883$	2.13775e7			0.922690			0.461345	−	0.887221i	$-0.347367\pi$
$883$	2.13775e7			0.922690			0.461345	+	0.887221i	$0.347367\pi$
$884$	134339.	+	478474.i	0.00578193	+	0.0205934i
$885$	260746.			0.0111908
$886$		−	2.79758e7i		−	1.19729i
$887$	6.42893e6	+	6.42893e6i	0.274365	+	0.274365i	0.830855	−	0.556489i	$-0.187852\pi$
$887$	6.42893e6	+	6.42893e6i	0.274365	+	0.274365i	−0.556489	+	0.830855i	$0.687852\pi$
$888$	5.70388e7			2.42738
$889$	−8.16043e6	−	8.16043e6i	−0.346305	−	0.346305i
$890$	2.71471e6	−	2.71471e6i	0.114881	−	0.114881i
$891$	−2.83051e7	+	2.83051e7i	−1.19446	+	1.19446i
$892$			7.79009e6i			0.327816i
$893$			758332.i			0.0318222i
$894$	8.41470e6	−	8.41470e6i	0.352123	−	0.352123i
$895$	−5.37561e6	+	5.37561e6i	−0.224321	+	0.224321i
$896$	2.88039e6	+	2.88039e6i	0.119862	+	0.119862i
$897$	4.24849e6			0.176301
$898$	−2.44321e7	−	2.44321e7i	−1.01105	−	1.01105i
$899$		−	1.00946e7i		−	0.416571i
$900$	6.60152e6			0.271667
$901$	−766832.	+	215300.i	−0.0314694	+	0.00883554i
$902$	5.37822e7			2.20101
$903$		−	6.58769e6i		−	0.268852i
$904$	−7.32130e6	−	7.32130e6i	−0.297966	−	0.297966i
$905$	−3.16059e6			−0.128276
$906$	1.69363e7	+	1.69363e7i	0.685485	+	0.685485i
$907$	−2.71046e7	+	2.71046e7i	−1.09402	+	1.09402i	−0.0989251	+	0.995095i	$0.531540\pi$
$907$	−2.71046e7	+	2.71046e7i	−1.09402	+	1.09402i	−0.995095	+	0.0989251i	$0.968460\pi$
$908$	−1.39602e6	+	1.39602e6i	−0.0561921	+	0.0561921i
$909$		−	2.45830e7i		−	0.986791i
$910$		−	150767.i		−	0.00603537i
$911$	1.24756e6	−	1.24756e6i	0.0498042	−	0.0498042i	−0.681766	−	0.731570i	$-0.738788\pi$
$911$	1.24756e6	−	1.24756e6i	0.0498042	−	0.0498042i	0.731570	+	0.681766i	$0.238788\pi$
$912$	704049.	−	704049.i	0.0280295	−	0.0280295i
$913$	−4.58268e7	−	4.58268e7i	−1.81946	−	1.81946i
$914$	−6.13892e6			−0.243067
$915$	8.02330e6	+	8.02330e6i	0.316811	+	0.316811i
$916$		−	149544.i		−	0.00588883i
$917$	−6.56422e6			−0.257786
$918$	397526.	−	707889.i	0.0155689	−	0.0277242i
$919$	3.27416e6			0.127883			0.0639413	−	0.997954i	$-0.479633\pi$
$919$	3.27416e6			0.127883			0.0639413	+	0.997954i	$0.479633\pi$
$920$		−	9.73017e6i		−	0.379010i
$921$	1.01969e7	+	1.01969e7i	0.396112	+	0.396112i
$922$	−1.31245e7			−0.508457
$923$	1.35619e6	+	1.35619e6i	0.0523983	+	0.0523983i
$924$	−5.35467e6	+	5.35467e6i	−0.206325	+	0.206325i
$925$	2.75353e7	−	2.75353e7i	1.05812	−	1.05812i
$926$		−	9.26342e6i		−	0.355013i
$927$		−	1.16371e7i		−	0.444779i
$928$	−3.65919e6	+	3.65919e6i	−0.139481	+	0.139481i
$929$	1.81736e7	−	1.81736e7i	0.690880	−	0.690880i	−0.271546	−	0.962425i	$-0.587535\pi$
$929$	1.81736e7	−	1.81736e7i	0.690880	−	0.690880i	0.962425	+	0.271546i	$0.0875349\pi$
$930$	−5.55955e6	−	5.55955e6i	−0.210781	−	0.210781i
$931$	−935462.			−0.0353714
$932$	264749.	+	264749.i	0.00998377	+	0.00998377i
$933$			2.81604e6i			0.105910i
$934$	−1.57600e7			−0.591138
$935$	−2.72209e6	−	9.69523e6i	−0.101830	−	0.362685i
$936$	−2.30005e6			−0.0858118
$937$		−	1.53629e7i		−	0.571644i	−0.958283	−	0.285822i	$-0.907733\pi$
$937$		−	1.53629e7i		−	0.571644i	0.958283	−	0.285822i	$-0.0922666\pi$
$938$	−5.66005e6	−	5.66005e6i	−0.210046	−	0.210046i
$939$	−6.05509e7			−2.24108
$940$	−851145.	−	851145.i	−0.0314184	−	0.0314184i
$941$	−1.86954e7	+	1.86954e7i	−0.688272	+	0.688272i	−0.961850	−	0.273578i	$-0.911793\pi$
$941$	−1.86954e7	+	1.86954e7i	−0.688272	+	0.688272i	0.273578	+	0.961850i	$0.411793\pi$
$942$	−2.63279e7	+	2.63279e7i	−0.966692	+	0.966692i
$943$			6.55275e7i			2.39963i
$944$		−	639859.i		−	0.0233698i
$945$	66987.9	−	66987.9i	0.00244015	−	0.00244015i
$946$	1.27594e7	−	1.27594e7i	0.463556	−	0.463556i
$947$	1.86466e7	+	1.86466e7i	0.675654	+	0.675654i	0.959014	−	0.283359i	$-0.0914489\pi$
$947$	1.86466e7	+	1.86466e7i	0.675654	+	0.675654i	−0.283359	+	0.959014i	$0.591449\pi$
$948$	1.60311e7			0.579352
$949$	746062.	+	746062.i	0.0268911	+	0.0268911i
$950$		−	972493.i		−	0.0349605i
$951$	−3.75516e7			−1.34641
$952$	−6.31978e6	+	1.12539e7i	−0.226001	+	0.402448i
$953$	8.40385e6			0.299741			0.149870	−	0.988706i	$-0.452114\pi$
$953$	8.40385e6			0.299741			0.149870	+	0.988706i	$0.452114\pi$
$954$		−	801374.i		−	0.0285078i
$955$	3.00065e6	+	3.00065e6i	0.106465	+	0.106465i
$956$	7.53476e6			0.266640
$957$	1.81612e7	+	1.81612e7i	0.641011	+	0.641011i
$958$	−1.28661e7	+	1.28661e7i	−0.452933	+	0.452933i
$959$	975922.	−	975922.i	0.0342664	−	0.0342664i
$960$			9.71989e6i			0.340395i
$961$			8.28991e6i			0.289562i
$962$	−2.08564e6	+	2.08564e6i	−0.0726610	+	0.0726610i
$963$	−3.49309e7	+	3.49309e7i	−1.21379	+	1.21379i
$964$	241073.	+	241073.i	0.00835519	+	0.00835519i
$965$	−621207.			−0.0214743
$966$	1.69615e7	+	1.69615e7i	0.584820	+	0.584820i
$967$		−	4.65328e7i		−	1.60027i	−0.599820	−	0.800135i	$-0.704761\pi$
$967$		−	4.65328e7i		−	1.60027i	0.599820	−	0.800135i	$-0.295239\pi$
$968$	−6.37543e7			−2.18686
$969$	1.56614e6	+	879488.i	0.0535822	+	0.0300899i
$970$	2.27814e6			0.0777413
$971$			1.13478e7i			0.386246i	0.981175	+	0.193123i	$0.0618616\pi$
$971$			1.13478e7i			0.386246i	−0.981175	+	0.193123i	$0.938138\pi$
$972$	8.23032e6	+	8.23032e6i	0.279416	+	0.279416i
$973$	−1.48132e7			−0.501611
$974$	1.86378e7	+	1.86378e7i	0.629501	+	0.629501i
$975$	−2.19224e6	+	2.19224e6i	−0.0738546	+	0.0738546i
$976$	1.96888e7	−	1.96888e7i	0.661599	−	0.661599i
$977$		−	4.36607e7i		−	1.46337i	−0.681643	−	0.731685i	$-0.738734\pi$
$977$		−	4.36607e7i		−	1.46337i	0.681643	−	0.731685i	$-0.261266\pi$
$978$		−	4.81114e6i		−	0.160843i
$979$	3.24333e7	−	3.24333e7i	1.08152	−	1.08152i
$980$	1.04995e6	−	1.04995e6i	0.0349225	−	0.0349225i
$981$	4.53598e6	+	4.53598e6i	0.150487	+	0.150487i
$982$	−1.43396e7			−0.474525
$983$	2.11606e7	+	2.11606e7i	0.698464	+	0.698464i	0.964079	−	0.265615i	$-0.0855749\pi$
$983$	2.11606e7	+	2.11606e7i	0.698464	+	0.698464i	−0.265615	+	0.964079i	$0.585575\pi$
$984$		−	7.00419e7i		−	2.30606i
$985$	4.64877e6			0.152668
$986$	8.29795e6	+	4.65984e6i	0.271818	+	0.152644i
$987$	1.36497e7			0.445994
$988$		−	28332.7i		−	0.000923413i
$989$	1.55459e7	+	1.55459e7i	0.505388	+	0.505388i
$990$	1.01320e7			0.328553
$991$	6.45593e6	+	6.45593e6i	0.208821	+	0.208821i	0.803766	−	0.594945i	$-0.202826\pi$
$991$	6.45593e6	+	6.45593e6i	0.208821	+	0.208821i	−0.594945	+	0.803766i	$0.702826\pi$
$992$	1.33828e7	−	1.33828e7i	0.431785	−	0.431785i
$993$	1.52760e7	−	1.52760e7i	0.491627	−	0.491627i
$994$			1.08288e7i			0.347628i
$995$			2.99725e6i			0.0959764i
$996$	−1.29746e7	+	1.29746e7i	−0.414426	+	0.414426i
$997$	−1.08488e7	+	1.08488e7i	−0.345655	+	0.345655i	−0.858488	−	0.512833i	$-0.828596\pi$
$997$	−1.08488e7	+	1.08488e7i	−0.345655	+	0.345655i	0.512833	+	0.858488i	$0.328596\pi$
$998$	8.53745e6	+	8.53745e6i	0.271332	+	0.271332i
$999$	−1.85336e6			−0.0587550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.6.c.a.13.2	yes	12
3.2	odd	2		153.6.f.a.64.5		12
4.3	odd	2		272.6.o.c.81.1		12
17.2	even	8		289.6.a.g.1.10		12
17.4	even	4	inner	17.6.c.a.4.5	✓	12
17.15	even	8		289.6.a.g.1.9		12
51.38	odd	4		153.6.f.a.55.2		12
68.55	odd	4		272.6.o.c.225.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.c.a.4.5	✓	12	17.4	even	4	inner
17.6.c.a.13.2	yes	12	1.1	even	1	trivial
153.6.f.a.55.2		12	51.38	odd	4
153.6.f.a.64.5		12	3.2	odd	2
272.6.o.c.81.1		12	4.3	odd	2
272.6.o.c.225.1		12	68.55	odd	4
289.6.a.g.1.9		12	17.15	even	8
289.6.a.g.1.10		12	17.2	even	8

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-4.80736i q^{2} +(15.6906 + 15.6906i) q^{3} +8.88927 q^{4} +(-8.57737 - 8.57737i) q^{5} +(75.4302 - 75.4302i) q^{6} +(38.9646 - 38.9646i) q^{7} -196.570i q^{8} +249.387i q^{9} +O(q^{10})\)	\(q-4.80736i q^{2} +(15.6906 + 15.6906i) q^{3} +8.88927 q^{4} +(-8.57737 - 8.57737i) q^{5} +(75.4302 - 75.4302i) q^{6} +(38.9646 - 38.9646i) q^{7} -196.570i q^{8} +249.387i q^{9} +(-41.2345 + 41.2345i) q^{10} +(-492.638 + 492.638i) q^{11} +(139.478 + 139.478i) q^{12} -46.9188 q^{13} +(-187.317 - 187.317i) q^{14} -269.167i q^{15} -660.524 q^{16} +(-322.100 - 1147.22i) q^{17} +1198.89 q^{18} +67.9322i q^{19} +(-76.2465 - 76.2465i) q^{20} +1222.75 q^{21} +(2368.29 + 2368.29i) q^{22} +(-2885.49 + 2885.49i) q^{23} +(3084.29 - 3084.29i) q^{24} -2977.86i q^{25} +225.556i q^{26} +(-100.217 + 100.217i) q^{27} +(346.366 - 346.366i) q^{28} +(-1174.76 - 1174.76i) q^{29} -1293.99 q^{30} +(4296.46 + 4296.46i) q^{31} -3114.84i q^{32} -15459.5 q^{33} +(-5515.09 + 1548.45i) q^{34} -668.427 q^{35} +2216.87i q^{36} +(9246.68 + 9246.68i) q^{37} +326.575 q^{38} +(-736.182 - 736.182i) q^{39} +(-1686.05 + 1686.05i) q^{40} +(11354.6 - 11354.6i) q^{41} -5878.21i q^{42} -5387.60i q^{43} +(-4379.20 + 4379.20i) q^{44} +(2139.09 - 2139.09i) q^{45} +(13871.6 + 13871.6i) q^{46} +11163.1 q^{47} +(-10364.0 - 10364.0i) q^{48} +13770.5i q^{49} -14315.6 q^{50} +(12946.6 - 23054.4i) q^{51} -417.073 q^{52} -668.427i q^{53} +(481.781 + 481.781i) q^{54} +8451.08 q^{55} +(-7659.24 - 7659.24i) q^{56} +(-1065.89 + 1065.89i) q^{57} +(-5647.49 + 5647.49i) q^{58} +968.713i q^{59} -2392.70i q^{60} +(-29807.9 + 29807.9i) q^{61} +(20654.6 - 20654.6i) q^{62} +(9717.26 + 9717.26i) q^{63} -36111.0 q^{64} +(402.440 + 402.440i) q^{65} +74319.6i q^{66} +30216.5 q^{67} +(-2863.23 - 10197.9i) q^{68} -90550.0 q^{69} +3213.37i q^{70} +(-28905.1 - 28905.1i) q^{71} +49021.9 q^{72} +(-15901.1 - 15901.1i) q^{73} +(44452.1 - 44452.1i) q^{74} +(46724.2 - 46724.2i) q^{75} +603.867i q^{76} +38390.9i q^{77} +(-3539.09 + 3539.09i) q^{78} +(57468.4 - 57468.4i) q^{79} +(5665.56 + 5665.56i) q^{80} +57456.1 q^{81} +(-54585.8 - 54585.8i) q^{82} +93023.1i q^{83} +10869.4 q^{84} +(-7077.34 + 12602.9i) q^{85} -25900.1 q^{86} -36865.2i q^{87} +(96837.7 + 96837.7i) q^{88} -65835.9 q^{89} +(-10283.4 - 10283.4i) q^{90} +(-1828.17 + 1828.17i) q^{91} +(-25649.9 + 25649.9i) q^{92} +134828. i q^{93} -53664.9i q^{94} +(582.679 - 582.679i) q^{95} +(48873.6 - 48873.6i) q^{96} +(-27624.2 - 27624.2i) q^{97} +66199.9 q^{98} +(-122858. - 122858. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7}+O(q^{10}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7	\( 12 q - 24 q^{3} - 132 q^{4} - 40 q^{5} + 250 q^{6} - 120 q^{7} - 334 q^{10} - 504 q^{11} + 1722 q^{12} + 1600 q^{13} - 2364 q^{14} + 2564 q^{16} + 2432 q^{17} - 6052 q^{18} - 4218 q^{20} + 7144 q^{21} - 2590 q^{22} - 2728 q^{23} - 7246 q^{24} - 3024 q^{27} + 26164 q^{28} - 992 q^{29} + 18072 q^{30} - 14680 q^{31} - 96 q^{33} - 20962 q^{34} - 43744 q^{35} + 33552 q^{37} + 9024 q^{38} + 2720 q^{39} + 30922 q^{40} + 20716 q^{41} - 13682 q^{44} + 44848 q^{45} + 4416 q^{46} + 32032 q^{47} - 144770 q^{48} - 42636 q^{50} - 83368 q^{51} - 132556 q^{52} + 80728 q^{54} + 81040 q^{55} + 122460 q^{56} + 36840 q^{57} + 165766 q^{58} - 143200 q^{61} + 222580 q^{62} + 7592 q^{63} + 18428 q^{64} - 175016 q^{65} - 83648 q^{67} - 231150 q^{68} - 341160 q^{69} + 116088 q^{71} + 347100 q^{72} + 83892 q^{73} - 79282 q^{74} + 245864 q^{75} - 128572 q^{78} + 291672 q^{79} + 195426 q^{80} + 387028 q^{81} - 452240 q^{82} - 798600 q^{84} - 200704 q^{85} - 736076 q^{86} + 431258 q^{88} + 456424 q^{89} - 65406 q^{90} + 36224 q^{91} + 476504 q^{92} - 413488 q^{95} + 884318 q^{96} + 356284 q^{97} + 444704 q^{98} - 640440 q^{99}+O(q^{100}) \) 12 * q - 24 * q^3 - 132 * q^4 - 40 * q^5 + 250 * q^6 - 120 * q^7 - 334 * q^10 - 504 * q^11 + 1722 * q^12 + 1600 * q^13 - 2364 * q^14 + 2564 * q^16 + 2432 * q^17 - 6052 * q^18 - 4218 * q^20 + 7144 * q^21 - 2590 * q^22 - 2728 * q^23 - 7246 * q^24 - 3024 * q^27 + 26164 * q^28 - 992 * q^29 + 18072 * q^30 - 14680 * q^31 - 96 * q^33 - 20962 * q^34 - 43744 * q^35 + 33552 * q^37 + 9024 * q^38 + 2720 * q^39 + 30922 * q^40 + 20716 * q^41 - 13682 * q^44 + 44848 * q^45 + 4416 * q^46 + 32032 * q^47 - 144770 * q^48 - 42636 * q^50 - 83368 * q^51 - 132556 * q^52 + 80728 * q^54 + 81040 * q^55 + 122460 * q^56 + 36840 * q^57 + 165766 * q^58 - 143200 * q^61 + 222580 * q^62 + 7592 * q^63 + 18428 * q^64 - 175016 * q^65 - 83648 * q^67 - 231150 * q^68 - 341160 * q^69 + 116088 * q^71 + 347100 * q^72 + 83892 * q^73 - 79282 * q^74 + 245864 * q^75 - 128572 * q^78 + 291672 * q^79 + 195426 * q^80 + 387028 * q^81 - 452240 * q^82 - 798600 * q^84 - 200704 * q^85 - 736076 * q^86 + 431258 * q^88 + 456424 * q^89 - 65406 * q^90 + 36224 * q^91 + 476504 * q^92 - 413488 * q^95 + 884318 * q^96 + 356284 * q^97 + 444704 * q^98 - 640440 * q^99

Introduction

L-functions

Modular forms

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Database

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