LMFDB - Embedded newform 55.6.e.b.32.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,6,Mod(32,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("55.32");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	55.e (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:	$8.82111008971$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.11
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.33566 + 2.33566i) q^{2} +(11.4271 - 11.4271i) q^{3} +21.0894i q^{4} +(53.4426 + 16.3977i) q^{5} +53.3797i q^{6} +(-37.7988 + 37.7988i) q^{7} +(-123.999 - 123.999i) q^{8} -18.1587i q^{9} +(-163.123 + 86.5243i) q^{10} +(300.188 - 266.342i) q^{11} +(240.991 + 240.991i) q^{12} +(675.535 + 675.535i) q^{13} -176.570i q^{14} +(798.075 - 423.317i) q^{15} -95.6239 q^{16} +(-1484.44 + 1484.44i) q^{17} +(42.4126 + 42.4126i) q^{18} +2107.75 q^{19} +(-345.818 + 1127.07i) q^{20} +863.864i q^{21} +(-79.0518 + 1323.22i) q^{22} +(676.189 - 676.189i) q^{23} -2833.90 q^{24} +(2587.23 + 1752.67i) q^{25} -3155.64 q^{26} +(2569.29 + 2569.29i) q^{27} +(-797.155 - 797.155i) q^{28} +2654.36 q^{29} +(-875.305 + 2852.75i) q^{30} -4292.79 q^{31} +(4191.30 - 4191.30i) q^{32} +(386.759 - 6473.82i) q^{33} -6934.28i q^{34} +(-2639.88 + 1400.25i) q^{35} +382.957 q^{36} +(-9037.50 - 9037.50i) q^{37} +(-4922.98 + 4922.98i) q^{38} +15438.9 q^{39} +(-4593.52 - 8660.11i) q^{40} -19153.7i q^{41} +(-2017.69 - 2017.69i) q^{42} +(-3487.98 - 3487.98i) q^{43} +(5617.00 + 6330.78i) q^{44} +(297.762 - 970.451i) q^{45} +3158.69i q^{46} +(-8253.73 - 8253.73i) q^{47} +(-1092.71 + 1092.71i) q^{48} +13949.5i q^{49} +(-10136.5 + 1949.24i) q^{50} +33925.7i q^{51} +(-14246.6 + 14246.6i) q^{52} +(-12477.4 + 12477.4i) q^{53} -12002.0 q^{54} +(20410.2 - 9311.64i) q^{55} +9374.01 q^{56} +(24085.5 - 24085.5i) q^{57} +(-6199.67 + 6199.67i) q^{58} -34119.2i q^{59} +(8927.51 + 16830.9i) q^{60} +13118.4i q^{61} +(10026.5 - 10026.5i) q^{62} +(686.379 + 686.379i) q^{63} +16518.9i q^{64} +(25025.2 + 47179.6i) q^{65} +(14217.3 + 16024.0i) q^{66} +(-31408.1 - 31408.1i) q^{67} +(-31305.9 - 31305.9i) q^{68} -15453.8i q^{69} +(2895.34 - 9436.38i) q^{70} +48681.9 q^{71} +(-2251.66 + 2251.66i) q^{72} +(-32510.6 - 32510.6i) q^{73} +42217.0 q^{74} +(49592.7 - 9536.61i) q^{75} +44451.2i q^{76} +(-1279.33 + 21414.2i) q^{77} +(-36059.9 + 36059.9i) q^{78} -20639.0 q^{79} +(-5110.39 - 1568.01i) q^{80} +63131.8 q^{81} +(44736.4 + 44736.4i) q^{82} +(31405.7 + 31405.7i) q^{83} -18218.4 q^{84} +(-103674. + 54990.9i) q^{85} +16293.4 q^{86} +(30331.7 - 30331.7i) q^{87} +(-70249.0 - 4196.82i) q^{88} -52283.1i q^{89} +(1571.17 + 2962.11i) q^{90} -51068.9 q^{91} +(14260.4 + 14260.4i) q^{92} +(-49054.3 + 49054.3i) q^{93} +38555.8 q^{94} +(112644. + 34562.2i) q^{95} -95789.1i q^{96} +(-39366.2 - 39366.2i) q^{97} +(-32581.3 - 32581.3i) q^{98} +(-4836.44 - 5451.03i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) $ 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.33566	+	2.33566i	−0.412890	+	0.412890i	−0.882744	−	0.469854i	$-0.844306\pi$
$2$	−2.33566	+	2.33566i	−0.412890	+	0.412890i	0.469854	+	0.882744i	$0.344306\pi$
$3$	11.4271	−	11.4271i	0.733051	−	0.733051i	−0.238172	−	0.971223i	$-0.576548\pi$
$3$	11.4271	−	11.4271i	0.733051	−	0.733051i	0.971223	+	0.238172i	$0.0765482\pi$
$4$			21.0894i			0.659044i
$5$	53.4426	+	16.3977i	0.956011	+	0.293331i
$5$	53.4426	+	16.3977i	0.956011	+	0.293331i
$6$			53.3797i			0.605339i
$7$	−37.7988	+	37.7988i	−0.291563	+	0.291563i	−0.837698	−	0.546134i	$-0.816099\pi$
$7$	−37.7988	+	37.7988i	−0.291563	+	0.291563i	0.546134	+	0.837698i	$0.316099\pi$
$8$	−123.999	−	123.999i	−0.685002	−	0.685002i
$9$		−	18.1587i		−	0.0747273i
$10$	−163.123	+	86.5243i	−0.515841	+	0.273614i
$11$	300.188	−	266.342i	0.748017	−	0.663679i
$11$	300.188	−	266.342i	0.748017	−	0.663679i
$12$	240.991	+	240.991i	0.483113	+	0.483113i
$13$	675.535	+	675.535i	1.10864	+	1.10864i	0.993330	+	0.115308i	$0.0367854\pi$
$13$	675.535	+	675.535i	1.10864	+	1.10864i	0.115308	+	0.993330i	$0.463215\pi$
$14$		−	176.570i		−	0.240767i
$15$	798.075	−	423.317i	0.915831	−	0.485778i
$16$	−95.6239			−0.0933827
$17$	−1484.44	+	1484.44i	−1.24578	+	1.24578i	−0.288207	+	0.957568i	$0.593059\pi$
$17$	−1484.44	+	1484.44i	−1.24578	+	1.24578i	−0.957568	+	0.288207i	$0.906941\pi$
$18$	42.4126	+	42.4126i	0.0308542	+	0.0308542i
$19$	2107.75			1.33948			0.669738	−	0.742598i	$-0.266407\pi$
$19$	2107.75			1.33948			0.669738	+	0.742598i	$0.266407\pi$
$20$	−345.818	+	1127.07i	−0.193318	+	0.630053i
$21$			863.864i			0.427462i
$22$	−79.0518	+	1323.22i	−0.0348221	+	0.582875i
$23$	676.189	−	676.189i	0.266532	−	0.266532i	−0.561169	−	0.827701i	$-0.689648\pi$
$23$	676.189	−	676.189i	0.266532	−	0.266532i	0.827701	+	0.561169i	$0.189648\pi$
$24$	−2833.90			−1.00428
$25$	2587.23	+	1752.67i	0.827914	+	0.560855i
$26$	−3155.64			−0.915490
$27$	2569.29	+	2569.29i	0.678272	+	0.678272i
$28$	−797.155	−	797.155i	−0.192153	−	0.192153i
$29$	2654.36			0.586090			0.293045	−	0.956099i	$-0.405331\pi$
$29$	2654.36			0.586090			0.293045	+	0.956099i	$0.405331\pi$
$30$	−875.305	+	2852.75i	−0.177565	+	0.578710i
$31$	−4292.79			−0.802297			−0.401149	−	0.916013i	$-0.631389\pi$
$31$	−4292.79			−0.802297			−0.401149	+	0.916013i	$0.631389\pi$
$32$	4191.30	−	4191.30i	0.723559	−	0.723559i
$33$	386.759	−	6473.82i	0.0618237	−	1.03485i
$34$		−	6934.28i		−	1.02874i
$35$	−2639.88	+	1400.25i	−0.364262	+	0.193213i
$36$	382.957			0.0492486
$37$	−9037.50	−	9037.50i	−1.08529	−	1.08529i	−0.996007	−	0.0892791i	$-0.971544\pi$
$37$	−9037.50	−	9037.50i	−1.08529	−	1.08529i	−0.0892791	−	0.996007i	$-0.528456\pi$
$38$	−4922.98	+	4922.98i	−0.553056	+	0.553056i
$39$	15438.9			1.62538
$40$	−4593.52	−	8660.11i	−0.453937	−	0.855802i
$41$		−	19153.7i		−	1.77948i	−0.456470	−	0.889739i	$-0.650887\pi$
$41$		−	19153.7i		−	1.77948i	0.456470	−	0.889739i	$-0.349113\pi$
$42$	−2017.69	−	2017.69i	−0.176495	−	0.176495i
$43$	−3487.98	−	3487.98i	−0.287675	−	0.287675i	0.548485	−	0.836160i	$-0.315205\pi$
$43$	−3487.98	−	3487.98i	−0.287675	−	0.287675i	−0.836160	+	0.548485i	$0.815205\pi$
$44$	5617.00	+	6330.78i	0.437394	+	0.492976i
$45$	297.762	−	970.451i	0.0219198	−	0.0714401i
$46$			3158.69i			0.220096i
$47$	−8253.73	−	8253.73i	−0.545011	−	0.545011i	0.379982	−	0.924994i	$-0.375930\pi$
$47$	−8253.73	−	8253.73i	−0.545011	−	0.545011i	−0.924994	+	0.379982i	$0.875930\pi$
$48$	−1092.71	+	1092.71i	−0.0684543	+	0.0684543i
$49$			13949.5i			0.829981i
$50$	−10136.5	+	1949.24i	−0.573409	+	0.110266i
$51$			33925.7i			1.82643i
$52$	−14246.6	+	14246.6i	−0.730641	+	0.730641i
$53$	−12477.4	+	12477.4i	−0.610146	+	0.610146i	−0.942984	−	0.332838i	$-0.891994\pi$
$53$	−12477.4	+	12477.4i	−0.610146	+	0.610146i	0.332838	+	0.942984i	$0.391994\pi$
$54$	−12002.0			−0.560103
$55$	20410.2	−	9311.64i	0.909790	−	0.415068i
$56$	9374.01			0.399443
$57$	24085.5	−	24085.5i	0.981904	−	0.981904i
$58$	−6199.67	+	6199.67i	−0.241991	+	0.241991i
$59$		−	34119.2i		−	1.27605i	−0.770015	−	0.638026i	$-0.779751\pi$
$59$		−	34119.2i		−	1.27605i	0.770015	−	0.638026i	$-0.220249\pi$
$60$	8927.51	+	16830.9i	0.320149	+	0.603573i
$61$			13118.4i			0.451395i	0.974197	+	0.225697i	$0.0724661\pi$
$61$			13118.4i			0.451395i	−0.974197	+	0.225697i	$0.927534\pi$
$62$	10026.5	−	10026.5i	0.331260	−	0.331260i
$63$	686.379	+	686.379i	0.0217878	+	0.0217878i
$64$			16518.9i			0.504118i
$65$	25025.2	+	47179.6i	0.734672	+	1.38507i
$66$	14217.3	+	16024.0i	0.401751	+	0.452804i
$67$	−31408.1	−	31408.1i	−0.854781	−	0.854781i	0.135937	−	0.990718i	$-0.456596\pi$
$67$	−31408.1	−	31408.1i	−0.854781	−	0.854781i	−0.990718	+	0.135937i	$0.956596\pi$
$68$	−31305.9	−	31305.9i	−0.821021	−	0.821021i
$69$		−	15453.8i		−	0.390762i
$70$	2895.34	−	9436.38i	0.0706245	−	0.230176i
$71$	48681.9			1.14610			0.573049	−	0.819521i	$-0.305761\pi$
$71$	48681.9			1.14610			0.573049	+	0.819521i	$0.305761\pi$
$72$	−2251.66	+	2251.66i	−0.0511884	+	0.0511884i
$73$	−32510.6	−	32510.6i	−0.714031	−	0.714031i	0.253345	−	0.967376i	$-0.418469\pi$
$73$	−32510.6	−	32510.6i	−0.714031	−	0.714031i	−0.967376	+	0.253345i	$0.918469\pi$
$74$	42217.0			0.896207
$75$	49592.7	−	9536.61i	1.01804	−	0.195768i
$76$			44451.2i			0.882773i
$77$	−1279.33	+	21414.2i	−0.0245898	+	0.411599i
$78$	−36059.9	+	36059.9i	−0.671101	+	0.671101i
$79$	−20639.0			−0.372066			−0.186033	−	0.982543i	$-0.559563\pi$
$79$	−20639.0			−0.372066			−0.186033	+	0.982543i	$0.559563\pi$
$80$	−5110.39	−	1568.01i	−0.0892749	−	0.0273920i
$81$	63131.8			1.06914
$82$	44736.4	+	44736.4i	0.734728	+	0.734728i
$83$	31405.7	+	31405.7i	0.500396	+	0.500396i	0.911561	−	0.411165i	$-0.134878\pi$
$83$	31405.7	+	31405.7i	0.500396	+	0.500396i	−0.411165	+	0.911561i	$0.634878\pi$
$84$	−18218.4			−0.281716
$85$	−103674.	+	54990.9i	−1.55640	+	0.825550i
$86$	16293.4			0.237556
$87$	30331.7	−	30331.7i	0.429634	−	0.429634i
$88$	−70249.0	−	4196.82i	−0.967016	−	0.0577714i
$89$		−	52283.1i		−	0.699659i	−0.936813	−	0.349829i	$-0.886240\pi$
$89$		−	52283.1i		−	0.699659i	0.936813	−	0.349829i	$-0.113760\pi$
$90$	1571.17	+	2962.11i	0.0204464	+	0.0385474i
$91$	−51068.9			−0.646476
$92$	14260.4	+	14260.4i	0.175656	+	0.175656i
$93$	−49054.3	+	49054.3i	−0.588125	+	0.588125i
$94$	38555.8			0.450059
$95$	112644.	+	34562.2i	1.28055	+	0.392910i
$96$		−	95789.1i		−	1.06081i
$97$	−39366.2	−	39366.2i	−0.424809	−	0.424809i	0.462046	−	0.886856i	$-0.347115\pi$
$97$	−39366.2	−	39366.2i	−0.424809	−	0.424809i	−0.886856	+	0.462046i	$0.847115\pi$
$98$	−32581.3	−	32581.3i	−0.342691	−	0.342691i
$99$	−4836.44	−	5451.03i	−0.0495950	−	0.0558973i
$100$	−36962.8	+	54563.2i	−0.369628	+	0.545632i
$101$			21466.7i			0.209392i	0.994504	+	0.104696i	$0.0333870\pi$
$101$			21466.7i			0.209392i	−0.994504	+	0.104696i	$0.966613\pi$
$102$	−79238.9	−	79238.9i	−0.754116	−	0.754116i
$103$	17481.7	−	17481.7i	0.162364	−	0.162364i	−0.621249	−	0.783613i	$-0.713374\pi$
$103$	17481.7	−	17481.7i	0.162364	−	0.162364i	0.783613	+	0.621249i	$0.213374\pi$
$104$		−	167531.i		−	1.51884i
$105$	−14165.4	+	46167.2i	−0.125388	+	0.408658i
$106$		−	58285.8i		−	0.503846i
$107$	100603.	−	100603.i	0.849478	−	0.849478i	−0.140590	−	0.990068i	$-0.544900\pi$
$107$	100603.	−	100603.i	0.849478	−	0.849478i	0.990068	+	0.140590i	$0.0448998\pi$
$108$	−54184.8	+	54184.8i	−0.447011	+	0.447011i
$109$	138971.			1.12036			0.560181	−	0.828370i	$-0.310732\pi$
$109$	138971.			1.12036			0.560181	+	0.828370i	$0.310732\pi$
$110$	−25922.5	+	69420.1i	−0.204266	+	0.547021i
$111$	−206545.			−1.59114
$112$	3614.47	−	3614.47i	0.0272270	−	0.0272270i
$113$	13473.7	−	13473.7i	0.0992641	−	0.0992641i	−0.655731	−	0.754995i	$-0.727639\pi$
$113$	13473.7	−	13473.7i	0.0992641	−	0.0992641i	0.754995	+	0.655731i	$0.227639\pi$
$114$			112511.i			0.810836i
$115$	47225.3	−	25049.4i	0.332989	−	0.176625i
$116$			55978.8i			0.386259i
$117$	12266.9	−	12266.9i	0.0828455	−	0.0828455i
$118$	79690.7	+	79690.7i	0.526869	+	0.526869i
$119$		−	112220.i		−	0.726445i
$120$	−151451.	−	46469.4i	−0.960106	−	0.294587i
$121$	19174.6	−	159905.i	0.119059	−	0.992887i
$122$	−30640.1	−	30640.1i	−0.186376	−	0.186376i
$123$	−218872.	−	218872.i	−1.30445	−	1.30445i
$124$		−	90532.4i		−	0.528749i
$125$	109529.	+	136092.i	0.626979	+	0.779036i
$126$	−3206.29			−0.0179919
$127$	−44801.0	+	44801.0i	−0.246478	+	0.246478i	−0.819524	−	0.573046i	$-0.805762\pi$
$127$	−44801.0	+	44801.0i	−0.246478	+	0.246478i	0.573046	+	0.819524i	$0.305762\pi$
$128$	95539.1	+	95539.1i	0.515414	+	0.515414i
$129$	−79715.1			−0.421761
$130$	−168646.	−	51745.2i	−0.875219	−	0.268542i
$131$			54647.0i			0.278220i	0.990277	+	0.139110i	$0.0444242\pi$
$131$			54647.0i			0.278220i	−0.990277	+	0.139110i	$0.955576\pi$
$132$	136529.	+	8156.51i	0.682009	+	0.0407446i
$133$	−79670.4	+	79670.4i	−0.390542	+	0.390542i
$134$	146717.			0.705861
$135$	95179.2	+	179440.i	0.449477	+	0.847394i
$136$	368137.			1.70672
$137$	−10416.5	−	10416.5i	−0.0474154	−	0.0474154i	0.683002	−	0.730417i	$-0.260674\pi$
$137$	−10416.5	−	10416.5i	−0.0474154	−	0.0474154i	−0.730417	+	0.683002i	$0.760674\pi$
$138$	36094.8	+	36094.8i	0.161342	+	0.161342i
$139$	−321360.			−1.41077			−0.705383	−	0.708827i	$-0.749225\pi$
$139$	−321360.			−1.41077			−0.705383	+	0.708827i	$0.749225\pi$
$140$	−29530.5	−	55673.5i	−0.127336	−	0.240065i
$141$	−188633.			−0.799042
$142$	−113704.	+	113704.i	−0.473212	+	0.473212i
$143$	382711.	+	22863.9i	1.56506	+	0.0934998i
$144$			1736.41i			0.00697824i
$145$	141856.	+	43525.4i	0.560309	+	0.171918i
$146$	151867.			0.589633
$147$	159403.	+	159403.i	0.608419	+	0.608419i
$148$	190596.	−	190596.i	0.715251	−	0.715251i
$149$	−56643.8			−0.209020			−0.104510	−	0.994524i	$-0.533327\pi$
$149$	−56643.8			−0.209020			−0.104510	+	0.994524i	$0.533327\pi$
$150$	−93557.2	+	138106.i	−0.339507	+	0.501168i
$151$			63866.1i			0.227944i	0.993484	+	0.113972i	$0.0363574\pi$
$151$			63866.1i			0.227944i	−0.993484	+	0.113972i	$0.963643\pi$
$152$	−261358.	−	261358.i	−0.917544	−	0.917544i
$153$	26955.5	+	26955.5i	0.0930935	+	0.0930935i
$154$	−47028.1	−	53004.2i	−0.159792	−	0.180098i
$155$	−229418.	−	70391.9i	−0.767005	−	0.235339i
$156$			325596.i			1.07119i
$157$	272571.	+	272571.i	0.882534	+	0.882534i	0.993792	−	0.111258i	$-0.0354880\pi$
$157$	272571.	+	272571.i	0.882534	+	0.882534i	−0.111258	+	0.993792i	$0.535488\pi$
$158$	48205.5	−	48205.5i	0.153622	−	0.153622i
$159$			285161.i			0.894536i
$160$	292722.	−	155267.i	0.903973	−	0.479488i
$161$			51118.3i			0.155422i
$162$	−147454.	+	147454.i	−0.441438	+	0.441438i
$163$	−245748.	+	245748.i	−0.724471	+	0.724471i	−0.969512	−	0.245042i	$-0.921198\pi$
$163$	−245748.	+	245748.i	−0.724471	+	0.724471i	0.245042	+	0.969512i	$0.421198\pi$
$164$	403940.			1.17275
$165$	126825.	−	339636.i	0.362656	−	0.971189i
$166$	−146706.			−0.413217
$167$	−77657.0	+	77657.0i	−0.215471	+	0.215471i	−0.806587	−	0.591116i	$-0.798688\pi$
$167$	−77657.0	+	77657.0i	−0.215471	+	0.215471i	0.591116	+	0.806587i	$0.298688\pi$
$168$	107118.	−	107118.i	0.292812	−	0.292812i
$169$			541403.i			1.45815i
$170$	113706.	−	370586.i	0.301760	−	0.983483i
$171$		−	38274.1i		−	0.100095i
$172$	73559.3	−	73559.3i	0.189591	−	0.189591i
$173$	−246843.	−	246843.i	−0.627056	−	0.627056i	0.320270	−	0.947326i	$-0.396226\pi$
$173$	−246843.	−	246843.i	−0.627056	−	0.627056i	−0.947326	+	0.320270i	$0.896226\pi$
$174$			141689.i			0.354783i
$175$	−164043.	+	31545.3i	−0.404914	+	0.0778646i
$176$	−28705.1	+	25468.7i	−0.0698519	+	0.0619762i
$177$	−389884.	−	389884.i	−0.935411	−	0.935411i
$178$	122115.	+	122115.i	0.288882	+	0.288882i
$179$			213845.i			0.498846i	0.968395	+	0.249423i	$0.0802409\pi$
$179$			213845.i			0.498846i	−0.968395	+	0.249423i	$0.919759\pi$
$180$	20466.2	+	6279.61i	0.0470822	+	0.0144461i
$181$	−223999.			−0.508216			−0.254108	−	0.967176i	$-0.581782\pi$
$181$	−223999.			−0.508216			−0.254108	+	0.967176i	$0.581782\pi$
$182$	119279.	−	119279.i	0.266924	−	0.266924i
$183$	149906.	+	149906.i	0.330895	+	0.330895i
$184$	−167693.			−0.365150
$185$	−334794.	−	631182.i	−0.719197	−	1.35589i
$186$		−	229148.i		−	0.485662i
$187$	−50241.8	+	840979.i	−0.105066	+	1.75866i
$188$	174066.	−	174066.i	0.359186	−	0.359186i
$189$	−194232.			−0.395519
$190$	−343823.	+	182371.i	−0.690956	+	0.366499i
$191$	853622.			1.69310			0.846549	−	0.532310i	$-0.178676\pi$
$191$	853622.			1.69310			0.846549	+	0.532310i	$0.178676\pi$
$192$	188764.	+	188764.i	0.369544	+	0.369544i
$193$	−306095.	−	306095.i	−0.591511	−	0.591511i	0.346529	−	0.938039i	$-0.387360\pi$
$193$	−306095.	−	306095.i	−0.591511	−	0.591511i	−0.938039	+	0.346529i	$0.887360\pi$
$194$	183892.			0.350799
$195$	825093.	+	253162.i	1.55388	+	0.476773i
$196$	−294187.			−0.546994
$197$	82012.0	−	82012.0i	0.150561	−	0.150561i	−0.627808	−	0.778368i	$-0.716048\pi$
$197$	82012.0	−	82012.0i	0.150561	−	0.150561i	0.778368	+	0.627808i	$0.216048\pi$
$198$	24028.0	+	1435.48i	0.0435567	+	0.00260216i
$199$		−	66576.2i		−	0.119175i	−0.998223	−	0.0595876i	$-0.981021\pi$
$199$		−	66576.2i		−	0.119175i	0.998223	−	0.0595876i	$-0.0189786\pi$
$200$	−103484.	−	538142.i	−0.182936	−	0.951310i
$201$	−717809.			−1.25320
$202$	−50138.8	−	50138.8i	−0.0864560	−	0.0864560i
$203$	−100332.	+	100332.i	−0.170883	+	0.170883i
$204$	−715474.			−1.20370
$205$	314076.	−	1.02362e6i	0.521976	−	1.70120i
$206$			81662.4i			0.134077i
$207$	−12278.7	−	12278.7i	−0.0199172	−	0.0199172i
$208$	−64597.3	−	64597.3i	−0.103528	−	0.103528i
$209$	632721.	−	561383.i	1.00195	−	0.888982i
$210$	−74745.3	−	140916.i	−0.116959	−	0.220502i
$211$		−	182773.i		−	0.282622i	−0.989965	−	0.141311i	$-0.954868\pi$
$211$		−	182773.i		−	0.282622i	0.989965	−	0.141311i	$-0.0451318\pi$
$212$	−263140.	−	263140.i	−0.402113	−	0.402113i
$213$	556295.	−	556295.i	0.840148	−	0.840148i
$214$			469949.i			0.701482i
$215$	−129212.	−	243601.i	−0.190637	−	0.359405i
$216$		−	637177.i		−	0.929236i
$217$	162262.	−	162262.i	0.233921	−	0.233921i
$218$	−324589.	+	324589.i	−0.462586	+	0.462586i
$219$	−743005.			−1.04684
$220$	196377.	+	430440.i	0.273548	+	0.599592i
$221$	−2.00558e6			−2.76223
$222$	482420.	−	482420.i	0.656965	−	0.656965i
$223$	394248.	−	394248.i	0.530894	−	0.530894i	−0.389944	−	0.920838i	$-0.627506\pi$
$223$	394248.	−	394248.i	0.530894	−	0.530894i	0.920838	+	0.389944i	$0.127506\pi$
$224$			316853.i			0.421927i
$225$	31826.3	−	46980.9i	0.0419112	−	0.0618678i
$226$			62940.1i			0.0819703i
$227$	−763006.	+	763006.i	−0.982796	+	0.982796i	−0.999854	−	0.0170581i	$-0.994570\pi$
$227$	−763006.	+	763006.i	−0.982796	+	0.982796i	0.0170581	+	0.999854i	$0.494570\pi$
$228$	507949.	+	507949.i	0.647118	+	0.647118i
$229$		−	6772.95i		−	0.00853472i	−0.999991	−	0.00426736i	$-0.998642\pi$
$229$		−	6772.95i		−	0.00853472i	0.999991	−	0.00426736i	$-0.00135835\pi$
$230$	−51795.3	+	168809.i	−0.0645611	+	0.210415i
$231$	230084.	+	259322.i	0.283698	+	0.319749i
$232$	−329137.	−	329137.i	−0.401473	−	0.401473i
$233$	927997.	+	927997.i	1.11984	+	1.11984i	0.991764	+	0.128078i	$0.0408808\pi$
$233$	927997.	+	927997.i	1.11984	+	1.11984i	0.128078	+	0.991764i	$0.459119\pi$
$234$			57302.4i			0.0684122i
$235$	−305759.	−	576443.i	−0.361168	−	0.680906i
$236$	719553.			0.840974
$237$	−235844.	+	235844.i	−0.272743	+	0.272743i
$238$	262108.	+	262108.i	0.299942	+	0.299942i
$239$	−450590.			−0.510254			−0.255127	−	0.966908i	$-0.582117\pi$
$239$	−450590.			−0.510254			−0.255127	+	0.966908i	$0.582117\pi$
$240$	−76315.0	+	40479.3i	−0.0855228	+	0.0453633i
$241$		−	760981.i		−	0.843978i	−0.906601	−	0.421989i	$-0.861332\pi$
$241$		−	760981.i		−	0.843978i	0.906601	−	0.421989i	$-0.138668\pi$
$242$	328699.	+	418270.i	0.360795	+	0.459111i
$243$	97078.2	−	97078.2i	0.105464	−	0.105464i
$244$	−276659.			−0.297489
$245$	−228740.	+	745498.i	−0.243459	+	0.793471i
$246$	1.02242e6			1.07719
$247$	1.42386e6	+	1.42386e6i	1.48499	+	1.48499i
$248$	532300.	+	532300.i	0.549576	+	0.549576i
$249$	717755.			0.733632
$250$	−573686.	−	62043.0i	−0.580529	−	0.0627832i
$251$	1.52197e6			1.52483			0.762413	−	0.647091i	$-0.224014\pi$
$251$	1.52197e6			1.52483			0.762413	+	0.647091i	$0.224014\pi$
$252$	−14475.3	+	14475.3i	−0.0143591	+	0.0143591i
$253$	22886.1	−	383082.i	0.0224786	−	0.376262i
$254$		−	209280.i		−	0.203537i
$255$	−556304.	+	1.81308e6i	−0.535749	+	1.74609i
$256$	−974899.			−0.929736
$257$	135791.	+	135791.i	0.128245	+	0.128245i	0.768316	−	0.640071i	$-0.221095\pi$
$257$	135791.	+	135791.i	0.128245	+	0.128245i	−0.640071	+	0.768316i	$0.721095\pi$
$258$	186187.	−	186187.i	0.174141	−	0.174141i
$259$	683214.			0.632859
$260$	−994990.	+	527766.i	−0.912820	+	0.484181i
$261$		−	48199.8i		−	0.0437970i
$262$	−127637.	−	127637.i	−0.114874	−	0.114874i
$263$	−372624.	−	372624.i	−0.332186	−	0.332186i	0.521230	−	0.853416i	$-0.325473\pi$
$263$	−372624.	−	372624.i	−0.332186	−	0.332186i	−0.853416	+	0.521230i	$0.825473\pi$
$264$	−850702.	+	754787.i	−0.751221	+	0.666522i
$265$	−871424.	+	462224.i	−0.762281	+	0.404331i
$266$		−	372166.i		−	0.322502i
$267$	−597446.	−	597446.i	−0.512885	−	0.512885i
$268$	662378.	−	662378.i	0.563338	−	0.563338i
$269$		−	579966.i		−	0.488677i	−0.969690	−	0.244338i	$-0.921429\pi$
$269$		−	579966.i		−	0.488677i	0.969690	−	0.244338i	$-0.0785707\pi$
$270$	−641417.	−	196805.i	−0.535465	−	0.164296i
$271$			1.38077e6i			1.14209i	0.820920	+	0.571043i	$0.193461\pi$
$271$			1.38077e6i			1.14209i	−0.820920	+	0.571043i	$0.806539\pi$
$272$	141948.	−	141948.i	0.116334	−	0.116334i
$273$	−583571.	+	583571.i	−0.473900	+	0.473900i
$274$	48658.7			0.0391547
$275$	1.24347e6	−	162958.i	0.991522	−	0.129940i
$276$	325912.			0.257530
$277$	−719191.	+	719191.i	−0.563177	+	0.563177i	−0.930209	−	0.367031i	$-0.880374\pi$
$277$	−719191.	+	719191.i	−0.563177	+	0.563177i	0.367031	+	0.930209i	$0.380374\pi$
$278$	750587.	−	750587.i	0.582491	−	0.582491i
$279$			77951.6i			0.0599535i
$280$	500972.	+	153712.i	0.381872	+	0.117169i
$281$		−	2.03334e6i		−	1.53618i	−0.640339	−	0.768092i	$-0.721206\pi$
$281$		−	2.03334e6i		−	1.53618i	0.640339	−	0.768092i	$-0.278794\pi$
$282$	440582.	−	440582.i	0.329916	−	0.329916i
$283$	422949.	+	422949.i	0.313922	+	0.313922i	0.846427	−	0.532505i	$-0.178749\pi$
$283$	422949.	+	422949.i	0.313922	+	0.313922i	−0.532505	+	0.846427i	$0.678749\pi$
$284$			1.02667e6i			0.755329i
$285$	1.68214e6	−	892247.i	1.22673	−	0.650688i
$286$	−947284.	+	840480.i	−0.684802	+	0.607592i
$287$	723986.	+	723986.i	0.518831	+	0.518831i
$288$	−76108.8	−	76108.8i	−0.0540697	−	0.0540697i
$289$		−	2.98725e6i		−	2.10391i
$290$	−432987.	+	229667.i	−0.302329	+	0.160362i
$291$	−899686.			−0.622814
$292$	685628.	−	685628.i	0.470578	−	0.470578i
$293$	−1.14051e6	−	1.14051e6i	−0.776123	−	0.776123i	0.203046	−	0.979169i	$-0.434916\pi$
$293$	−1.14051e6	−	1.14051e6i	−0.776123	−	0.776123i	−0.979169	+	0.203046i	$0.934916\pi$
$294$	−744621.			−0.502420
$295$	559476.	−	1.82342e6i	0.374305	−	1.21992i
$296$			2.24128e6i			1.48685i
$297$	1.45558e6	+	86959.3i	0.957514	+	0.0572038i
$298$	132301.	−	132301.i	0.0863021	−	0.0863021i
$299$	913579.			0.590974
$300$	201121.	+	1.04588e6i	0.129019	+	0.670932i
$301$	263683.			0.167751
$302$	−149169.	−	149169.i	−0.0941157	−	0.0941157i
$303$	245302.	+	245302.i	0.153495	+	0.153495i
$304$	−201551.			−0.125084
$305$	−215112.	+	701082.i	−0.132408	+	0.431538i
$306$	−125918.			−0.0768747
$307$	−338778.	+	338778.i	−0.205149	+	0.205149i	−0.802202	−	0.597053i	$-0.796338\pi$
$307$	−338778.	+	338778.i	−0.205149	+	0.205149i	0.597053	+	0.802202i	$0.296338\pi$
$308$	−451612.	−	26980.2i	−0.271262	−	0.0162057i
$309$		−	399531.i		−	0.238042i
$310$	700253.	−	371431.i	0.413858	−	0.219520i
$311$	892827.			0.523439			0.261720	−	0.965144i	$-0.415710\pi$
$311$	892827.			0.523439			0.261720	+	0.965144i	$0.415710\pi$
$312$	−1.91440e6	−	1.91440e6i	−1.11339	−	1.11339i
$313$	−271738.	+	271738.i	−0.156779	+	0.156779i	−0.781138	−	0.624359i	$-0.785360\pi$
$313$	−271738.	+	271738.i	−0.156779	+	0.156779i	0.624359	+	0.781138i	$0.285360\pi$
$314$	−1.27327e6			−0.728778
$315$	25426.9	+	47936.9i	0.0144383	+	0.0272204i
$316$		−	435263.i		−	0.245208i
$317$	−854577.	−	854577.i	−0.477643	−	0.477643i	0.426734	−	0.904377i	$-0.359664\pi$
$317$	−854577.	−	854577.i	−0.477643	−	0.477643i	−0.904377	+	0.426734i	$0.859664\pi$
$318$	−666039.	−	666039.i	−0.369345	−	0.369345i
$319$	796806.	−	706968.i	0.438406	−	0.388976i
$320$	−270872.	+	882815.i	−0.147873	+	0.481942i
$321$		−	2.29921e6i		−	1.24542i
$322$	−119395.	−	119395.i	−0.0641721	−	0.0641721i
$323$	−3.12882e6	+	3.12882e6i	−1.66869	+	1.66869i
$324$			1.33141e6i			0.704612i
$325$	563774.	+	2.93176e6i	0.296071	+	1.53964i
$326$		−	1.14797e6i		−	0.598253i
$327$	1.58804e6	−	1.58804e6i	0.821283	−	0.821283i
$328$	−2.37503e6	+	2.37503e6i	−1.21895	+	1.21895i
$329$	623962.			0.317811
$330$	497053.	+	1.08949e6i	0.251257	+	0.550731i
$331$	789491.			0.396075			0.198037	−	0.980194i	$-0.436543\pi$
$331$	789491.			0.396075			0.198037	+	0.980194i	$0.436543\pi$
$332$	−662328.	+	662328.i	−0.329783	+	0.329783i
$333$	−164110.	+	164110.i	−0.0811005	+	0.0811005i
$334$		−	362761.i		−	0.177932i
$335$	−1.16351e6	−	2.19355e6i	−0.566446	−	1.06791i
$336$		−	82606.1i		−	0.0399175i
$337$	−495261.	+	495261.i	−0.237553	+	0.237553i	−0.815836	−	0.578283i	$-0.803723\pi$
$337$	−495261.	+	495261.i	−0.237553	+	0.237553i	0.578283	+	0.815836i	$0.303723\pi$
$338$	−1.26453e6	−	1.26453e6i	−0.602057	−	0.602057i
$339$		−	307933.i		−	0.145531i
$340$	−1.15973e6	−	2.18642e6i	−0.544074	−	1.02574i
$341$	−1.28864e6	+	1.14335e6i	−0.600132	+	0.532468i
$342$	89395.1	+	89395.1i	0.0413284	+	0.0413284i
$343$	−1.16256e6	−	1.16256e6i	−0.533556	−	0.533556i
$344$			865009.i			0.394116i
$345$	253407.	−	825892.i	0.114623	−	0.373573i
$346$	1.15308e6			0.517810
$347$	27410.5	−	27410.5i	0.0122206	−	0.0122206i	−0.700970	−	0.713191i	$-0.747249\pi$
$347$	27410.5	−	27410.5i	0.0122206	−	0.0122206i	0.713191	+	0.700970i	$0.247249\pi$
$348$	639678.	+	639678.i	0.283148	+	0.283148i
$349$	955952.			0.420119			0.210060	−	0.977689i	$-0.432634\pi$
$349$	955952.			0.420119			0.210060	+	0.977689i	$0.432634\pi$
$350$	309470.	−	456828.i	0.135036	−	0.199335i
$351$			3.47129e6i			1.50392i
$352$	141857.	−	2.37450e6i	0.0610232	−	1.02145i
$353$	−494139.	+	494139.i	−0.211063	+	0.211063i	−0.804719	−	0.593656i	$-0.797684\pi$
$353$	−494139.	+	494139.i	−0.211063	+	0.211063i	0.593656	+	0.804719i	$0.297684\pi$
$354$	1.82127e6			0.772443
$355$	2.60169e6	+	798271.i	1.09568	+	0.336186i
$356$	1.10262e6			0.461106
$357$	−1.28235e6	−	1.28235e6i	−0.532521	−	0.532521i
$358$	−499469.	−	499469.i	−0.205968	−	0.205968i
$359$	2.48156e6			1.01622			0.508111	−	0.861291i	$-0.330344\pi$
$359$	2.48156e6			1.01622			0.508111	+	0.861291i	$0.330344\pi$
$360$	−157257.	+	83412.6i	−0.0639518	+	0.0339215i
$361$	1.96650e6			0.794195
$362$	523184.	−	523184.i	0.209837	−	0.209837i
$363$	−1.60815e6	−	2.04637e6i	−0.640561	−	0.815113i
$364$		−	1.07701e6i		−	0.426056i
$365$	−1.20435e6	−	2.27055e6i	−0.473174	−	0.892069i
$366$	−700257.			−0.273247
$367$	−709818.	−	709818.i	−0.275095	−	0.275095i	0.556053	−	0.831147i	$-0.312315\pi$
$367$	−709818.	−	709818.i	−0.275095	−	0.275095i	−0.831147	+	0.556053i	$0.812315\pi$
$368$	−64659.8	+	64659.8i	−0.0248894	+	0.0248894i
$369$	−347807.			−0.132976
$370$	2.25619e6	+	692262.i	0.856784	+	0.262885i
$371$		−	943260.i		−	0.355792i
$372$	−1.03453e6	−	1.03453e6i	−0.387600	−	0.387600i
$373$	6789.72	+	6789.72i	0.00252685	+	0.00252685i	0.708369	−	0.705842i	$-0.249431\pi$
$373$	6789.72	+	6789.72i	0.00252685	+	0.00252685i	−0.705842	+	0.708369i	$0.749431\pi$
$374$	−1.84689e6	−	2.08159e6i	−0.682751	−	0.769512i
$375$	2.80674e6	+	303544.i	1.03068	+	0.111466i
$376$			2.04690e6i			0.746668i
$377$	1.79311e6	+	1.79311e6i	0.649762	+	0.649762i
$378$	453660.	−	453660.i	0.163306	−	0.163306i
$379$		−	2.79388e6i		−	0.999101i	−0.866285	−	0.499550i	$-0.833499\pi$
$379$		−	2.79388e6i		−	0.999101i	0.866285	−	0.499550i	$-0.166501\pi$
$380$	−728897.	+	2.37559e6i	−0.258945	+	0.843941i
$381$			1.02389e6i			0.361362i
$382$	−1.99377e6	+	1.99377e6i	−0.699063	+	0.699063i
$383$	−164292.	+	164292.i	−0.0572295	+	0.0572295i	−0.735142	−	0.677913i	$-0.762885\pi$
$383$	−164292.	+	164292.i	−0.0572295	+	0.0572295i	0.677913	+	0.735142i	$0.262885\pi$
$384$	2.18348e6			0.755649
$385$	−419514.	+	1.12345e6i	−0.144243	+	0.386280i
$386$	1.42987e6			0.488458
$387$	−63337.3	+	63337.3i	−0.0214972	+	0.0214972i
$388$	830210.	−	830210.i	0.279968	−	0.279968i
$389$			4.34588e6i			1.45614i	0.685501	+	0.728071i	$0.259583\pi$
$389$			4.34588e6i			1.45614i	−0.685501	+	0.728071i	$0.740417\pi$
$390$	−2.51844e6	+	1.33584e6i	−0.838435	+	0.444725i
$391$			2.00752e6i			0.664077i
$392$	1.72972e6	−	1.72972e6i	0.568539	−	0.568539i
$393$	624459.	+	624459.i	0.203949	+	0.203949i
$394$			383104.i			0.124330i
$395$	−1.10300e6	−	338431.i	−0.355699	−	0.109138i
$396$	114959.	−	101998.i	0.0368388	−	0.0326853i
$397$	2.94858e6	+	2.94858e6i	0.938936	+	0.938936i	0.998240	−	0.0593036i	$-0.0188880\pi$
$397$	2.94858e6	+	2.94858e6i	0.938936	+	0.938936i	−0.0593036	+	0.998240i	$0.518888\pi$
$398$	155499.	+	155499.i	0.0492063	+	0.0492063i
$399$			1.82081e6i			0.572575i
$400$	−247401.	−	167597.i	−0.0773128	−	0.0523742i
$401$	−2.08805e6			−0.648455			−0.324228	−	0.945979i	$-0.605104\pi$
$401$	−2.08805e6			−0.648455			−0.324228	+	0.945979i	$0.605104\pi$
$402$	1.67656e6	−	1.67656e6i	0.517432	−	0.517432i
$403$	−2.89993e6	−	2.89993e6i	−0.889457	−	0.889457i
$404$	−452719.			−0.137999
$405$	3.37393e6	+	1.03522e6i	1.02211	+	0.313613i
$406$		−	468681.i		−	0.141111i
$407$	−5.12002e6	−	305880.i	−1.53209	−	0.0915304i
$408$	4.20675e6	−	4.20675e6i	1.25111	−	1.25111i
$409$	−5.19259e6			−1.53488			−0.767442	−	0.641118i	$-0.778471\pi$
$409$	−5.19259e6			−1.53488			−0.767442	+	0.641118i	$0.778471\pi$
$410$	1.65726e6	+	3.12441e6i	0.486890	+	0.917927i
$411$	−238061.			−0.0695159
$412$	368678.	+	368678.i	0.107005	+	0.107005i
$413$	1.28966e6	+	1.28966e6i	0.372050	+	0.372050i
$414$	57357.9			0.0164472
$415$	1.16342e6	+	2.19339e6i	0.331602	+	0.625166i
$416$	5.66274e6			1.60433
$417$	−3.67222e6	+	3.67222e6i	−1.03416	+	1.03416i
$418$	−166621.	+	2.78902e6i	−0.0466434	+	0.780747i
$419$			4.12215e6i			1.14707i	0.819183	+	0.573533i	$0.194428\pi$
$419$			4.12215e6i			1.14707i	−0.819183	+	0.573533i	$0.805572\pi$
$420$	−973638.	−	298740.i	−0.269324	−	0.0826360i
$421$	−3.44985e6			−0.948627			−0.474313	−	0.880356i	$-0.657304\pi$
$421$	−3.44985e6			−0.948627			−0.474313	+	0.880356i	$0.657304\pi$
$422$	426895.	+	426895.i	0.116692	+	0.116692i
$423$	−149877.	+	149877.i	−0.0407272	+	0.0407272i
$424$	3.09436e6			0.835903
$425$	−6.44232e6	+	1.23885e6i	−1.73009	+	0.332695i
$426$			2.59863e6i			0.693777i
$427$	−495860.	−	495860.i	−0.131610	−	0.131610i
$428$	2.12166e6	+	2.12166e6i	0.559844	+	0.559844i
$429$	4.63456e6	−	4.11202e6i	1.21581	−	1.07873i
$430$	870764.	+	267175.i	0.227106	+	0.0696826i
$431$		−	828271.i		−	0.214773i	−0.994217	−	0.107386i	$-0.965752\pi$
$431$		−	828271.i		−	0.214773i	0.994217	−	0.107386i	$-0.0342482\pi$
$432$	−245686.	−	245686.i	−0.0633389	−	0.0633389i
$433$	−1.92345e6	+	1.92345e6i	−0.493016	+	0.493016i	−0.909255	−	0.416239i	$-0.863348\pi$
$433$	−1.92345e6	+	1.92345e6i	−0.493016	+	0.493016i	0.416239	+	0.909255i	$0.363348\pi$
$434$			757979.i			0.193167i
$435$	2.11838e6	−	1.12364e6i	0.536760	−	0.284710i
$436$			2.93082e6i			0.738368i
$437$	1.42524e6	−	1.42524e6i	0.357013	−	0.357013i
$438$	1.73541e6	−	1.73541e6i	0.432231	−	0.432231i
$439$	6.55022e6			1.62216			0.811082	−	0.584932i	$-0.198879\pi$
$439$	6.55022e6			1.62216			0.811082	+	0.584932i	$0.198879\pi$
$440$	−3.68547e6	−	1.37621e6i	−0.907531	−	0.338886i
$441$	253305.			0.0620223
$442$	4.68435e6	−	4.68435e6i	1.14050	−	1.14050i
$443$	−2.62287e6	+	2.62287e6i	−0.634991	+	0.634991i	−0.949316	−	0.314324i	$-0.898222\pi$
$443$	−2.62287e6	+	2.62287e6i	−0.634991	+	0.634991i	0.314324	+	0.949316i	$0.398222\pi$
$444$		−	4.35592e6i		−	1.04863i
$445$	857322.	−	2.79415e6i	0.205232	−	0.668881i
$446$			1.84166e6i			0.438402i
$447$	−647277.	+	647277.i	−0.153222	+	0.153222i
$448$	−624396.	−	624396.i	−0.146982	−	0.146982i
$449$		−	583517.i		−	0.136596i	−0.997665	−	0.0682979i	$-0.978243\pi$
$449$		−	583517.i		−	0.136596i	0.997665	−	0.0682979i	$-0.0217568\pi$
$450$	35395.8	+	184067.i	0.00823987	+	0.0428493i
$451$	−5.10143e6	−	5.74970e6i	−1.18100	−	1.33108i
$452$	284153.	+	284153.i	0.0654194	+	0.0654194i
$453$	729806.	+	729806.i	0.167094	+	0.167094i
$454$		−	3.56424e6i		−	0.811573i
$455$	−2.72925e6	−	837412.i	−0.618039	−	0.189632i
$456$	−5.97315e6			−1.34521
$457$	1.19257e6	−	1.19257e6i	0.267112	−	0.267112i	−0.560824	−	0.827935i	$-0.689515\pi$
$457$	1.19257e6	−	1.19257e6i	0.267112	−	0.267112i	0.827935	+	0.560824i	$0.189515\pi$
$458$	15819.3	+	15819.3i	0.00352390	+	0.00352390i
$459$	−7.62791e6			−1.68995
$460$	528277.	+	995953.i	0.116404	+	0.219454i
$461$		−	8.52604e6i		−	1.86851i	−0.356609	−	0.934254i	$-0.616067\pi$
$461$		−	8.52604e6i		−	1.86851i	0.356609	−	0.934254i	$-0.383933\pi$
$462$	−1.14308e6	−	68290.1i	−0.249157	−	0.0148851i
$463$	3.27818e6	−	3.27818e6i	0.710690	−	0.710690i	−0.255989	−	0.966680i	$-0.582401\pi$
$463$	3.27818e6	−	3.27818e6i	0.710690	−	0.710690i	0.966680	+	0.255989i	$0.0824012\pi$
$464$	−253820.			−0.0547307
$465$	−3.42597e6	+	1.81721e6i	−0.734769	+	0.389739i
$466$	−4.33497e6			−0.924743
$467$	−2.48639e6	−	2.48639e6i	−0.527566	−	0.527566i	0.392280	−	0.919846i	$-0.371686\pi$
$467$	−2.48639e6	−	2.48639e6i	−0.527566	−	0.527566i	−0.919846	+	0.392280i	$0.871686\pi$
$468$	258701.	+	258701.i	0.0545988	+	0.0545988i
$469$	2.37438e6			0.498446
$470$	2.06052e6	+	632226.i	0.430262	+	0.132016i
$471$	6.22942e6			1.29388
$472$	−4.23073e6	+	4.23073e6i	−0.874099	+	0.874099i
$473$	−1.97604e6	−	118053.i	−0.406110	−	0.0242618i
$474$		−	1.10170e6i		−	0.225226i
$475$	5.45323e6	+	3.69419e6i	1.10897	+	0.751252i
$476$	2.36665e6			0.478759
$477$	226573.	+	226573.i	0.0455946	+	0.0455946i
$478$	1.05242e6	−	1.05242e6i	0.210679	−	0.210679i
$479$	−8.00469e6			−1.59406			−0.797032	−	0.603937i	$-0.793598\pi$
$479$	−8.00469e6			−1.59406			−0.797032	+	0.603937i	$0.793598\pi$
$480$	1.57072e6	−	5.11922e6i	0.311169	−	1.01415i
$481$		−	1.22103e7i		−	2.40638i
$482$	1.77739e6	+	1.77739e6i	0.348470	+	0.348470i
$483$	584136.	+	584136.i	0.113932	+	0.113932i
$484$	3.37231e6	+	404380.i	0.654356	+	0.0784651i
$485$	−1.45832e6	−	2.74935e6i	−0.281513	−	0.530732i
$486$			453483.i			0.0870904i
$487$	3.41872e6	+	3.41872e6i	0.653193	+	0.653193i	0.953760	−	0.300568i	$-0.0971761\pi$
$487$	3.41872e6	+	3.41872e6i	0.653193	+	0.653193i	−0.300568	+	0.953760i	$0.597176\pi$
$488$	1.62667e6	−	1.62667e6i	0.309207	−	0.309207i
$489$			5.61639e6i			1.06215i
$490$	−1.20697e6	−	2.27549e6i	−0.227094	−	0.428138i
$491$			2.26836e6i			0.424628i	0.977202	+	0.212314i	$0.0680999\pi$
$491$			2.26836e6i			0.424628i	−0.977202	+	0.212314i	$0.931900\pi$
$492$	4.61587e6	−	4.61587e6i	0.859688	−	0.859688i
$493$	−3.94023e6	+	3.94023e6i	−0.730137	+	0.730137i
$494$	−6.65129e6			−1.22628
$495$	−169088.	−	370624.i	−0.0310169	−	0.0679862i
$496$	410493.			0.0749207
$497$	−1.84012e6	+	1.84012e6i	−0.334160	+	0.334160i
$498$	−1.67643e6	+	1.67643e6i	−0.302909	+	0.302909i
$499$			268610.i			0.0482915i	0.999708	+	0.0241458i	$0.00768658\pi$
$499$			268610.i			0.0482915i	−0.999708	+	0.0241458i	$0.992313\pi$
$500$	−2.87010e6	+	2.30989e6i	−0.513419	+	0.413206i
$501$			1.77479e6i			0.315903i
$502$	−3.55479e6	+	3.55479e6i	−0.629585	+	0.629585i
$503$	3.66441e6	+	3.66441e6i	0.645779	+	0.645779i	0.951970	−	0.306191i	$-0.0990547\pi$
$503$	3.66441e6	+	3.66441e6i	0.645779	+	0.645779i	−0.306191	+	0.951970i	$0.599055\pi$
$504$		−	170220.i		−	0.0298493i
$505$	−352004.	+	1.14723e6i	−0.0614213	+	0.200181i
$506$	841294.	+	948202.i	0.146073	+	0.164636i
$507$	6.18668e6	+	6.18668e6i	1.06890	+	1.06890i
$508$	−944826.	−	944826.i	−0.162440	−	0.162440i
$509$		−	3.26221e6i		−	0.558107i	−0.960276	−	0.279054i	$-0.909979\pi$
$509$		−	3.26221e6i		−	0.558107i	0.960276	−	0.279054i	$-0.0900207\pi$
$510$	−2.93540e6	−	5.53407e6i	−0.499738	−	0.942149i
$511$	2.45772e6			0.416371
$512$	−780220.	+	780220.i	−0.131535	+	0.131535i
$513$	5.41542e6	+	5.41542e6i	0.908529	+	0.908529i
$514$	−634324.			−0.105902
$515$	1.22093e6	−	647608.i	0.202848	−	0.107595i
$516$		−	1.68114e6i		−	0.277959i
$517$	−4.67599e6	−	279353.i	−0.769391	−	0.0459649i
$518$	−1.59575e6	+	1.59575e6i	−0.261301	+	0.261301i
$519$	−5.64142e6			−0.919328
$520$	2.74712e6	−	8.95330e6i	0.445522	−	1.45203i
$521$	−9.41585e6			−1.51973			−0.759863	−	0.650083i	$-0.774734\pi$
$521$	−9.41585e6			−1.51973			−0.759863	+	0.650083i	$0.774734\pi$
$522$	112578.	+	112578.i	0.0180833	+	0.0180833i
$523$	−4.26644e6	−	4.26644e6i	−0.682042	−	0.682042i	0.278418	−	0.960460i	$-0.410190\pi$
$523$	−4.26644e6	−	4.26644e6i	−0.682042	−	0.682042i	−0.960460	+	0.278418i	$0.910190\pi$
$524$	−1.15247e6			−0.183359
$525$	−1.51407e6	+	2.23502e6i	−0.239744	+	0.353902i
$526$	1.74064e6			0.274312
$527$	6.37238e6	−	6.37238e6i	0.999482	−	0.999482i
$528$	−36983.4	+	619051.i	−0.00577327	+	0.0966367i
$529$			5.52188e6i			0.857922i
$530$	955753.	−	3.11495e6i	0.147794	−	0.481682i
$531$	−619561.			−0.0953559
$532$	−1.68020e6	−	1.68020e6i	−0.257384	−	0.257384i
$533$	1.29390e7	−	1.29390e7i	1.97280	−	1.97280i
$534$	2.79086e6			0.423530
$535$	7.02616e6	−	3.72684e6i	1.06129	−	0.562932i
$536$			7.78913e6i			1.17105i
$537$	2.44363e6	+	2.44363e6i	0.365679	+	0.365679i
$538$	1.35460e6	+	1.35460e6i	0.201770	+	0.201770i
$539$	3.71534e6	+	4.18747e6i	0.550842	+	0.620840i
$540$	−3.78429e6	+	2.00727e6i	−0.558470	+	0.296225i
$541$			6.06617e6i			0.891089i	0.895260	+	0.445545i	$0.146990\pi$
$541$			6.06617e6i			0.891089i	−0.895260	+	0.445545i	$0.853010\pi$
$542$	−3.22501e6	−	3.22501e6i	−0.471556	−	0.471556i
$543$	−2.55966e6	+	2.55966e6i	−0.372549	+	0.372549i
$544$			1.24435e7i			1.80278i
$545$	7.42699e6	+	2.27881e6i	1.07108	+	0.328637i
$546$		−	2.72604e6i		−	0.391337i
$547$	−1.63355e6	+	1.63355e6i	−0.233435	+	0.233435i	−0.814125	−	0.580690i	$-0.802783\pi$
$547$	−1.63355e6	+	1.63355e6i	−0.233435	+	0.233435i	0.580690	+	0.814125i	$0.302783\pi$
$548$	219677.	−	219677.i	0.0312489	−	0.0312489i
$549$	238214.			0.0337315
$550$	−2.52370e6	+	3.28493e6i	−0.355738	+	0.463040i
$551$	5.59472e6			0.785054
$552$	−1.91625e6	+	1.91625e6i	−0.267673	+	0.267673i
$553$	780128.	−	780128.i	0.108481	−	0.108481i
$554$		−	3.35957e6i		−	0.465060i
$555$	−1.10383e7	−	3.38687e6i	−1.52115	−	0.466730i
$556$		−	6.77729e6i		−	0.929757i
$557$	1.50145e6	−	1.50145e6i	0.205056	−	0.205056i	−0.597106	−	0.802162i	$-0.703683\pi$
$557$	1.50145e6	−	1.50145e6i	0.205056	−	0.205056i	0.802162	+	0.597106i	$0.203683\pi$
$558$	−182068.	−	182068.i	−0.0247542	−	0.0247542i
$559$		−	4.71250e6i		−	0.637855i
$560$	252436.	−	133898.i	0.0340158	−	0.0180428i
$561$	9.03586e6	+	1.01841e7i	1.21217	+	1.36620i
$562$	4.74918e6	+	4.74918e6i	0.634275	+	0.634275i
$563$	1.19240e6	+	1.19240e6i	0.158545	+	0.158545i	0.781922	−	0.623377i	$-0.214240\pi$
$563$	1.19240e6	+	1.19240e6i	0.158545	+	0.158545i	−0.623377	+	0.781922i	$0.714240\pi$
$564$		−	3.97816e6i		−	0.526604i
$565$	941011.	−	499134.i	0.124015	−	0.0657803i
$566$	−1.97573e6			−0.259231
$567$	−2.38631e6	+	2.38631e6i	−0.311723	+	0.311723i
$568$	−6.03649e6	−	6.03649e6i	−0.785080	−	0.785080i
$569$	−467215.			−0.0604973			−0.0302487	−	0.999542i	$-0.509630\pi$
$569$	−467215.			−0.0604973			−0.0302487	+	0.999542i	$0.509630\pi$
$570$	−1.84492e6	+	6.01289e6i	−0.237843	+	0.775168i
$571$			1.13148e7i			1.45230i	0.687537	+	0.726149i	$0.258692\pi$
$571$			1.13148e7i			1.45230i	−0.687537	+	0.726149i	$0.741308\pi$
$572$	−482186.	+	8.07115e6i	−0.0616205	+	1.03144i
$573$	9.75445e6	−	9.75445e6i	1.24113	−	1.24113i
$574$	−3.38197e6			−0.428440
$575$	2.93460e6	−	564320.i	0.370151	−	0.0711796i
$576$	299963.			0.0376714
$577$	7.19072e6	+	7.19072e6i	0.899152	+	0.899152i	0.995361	−	0.0962092i	$-0.0306718\pi$
$577$	7.19072e6	+	7.19072e6i	0.899152	+	0.899152i	−0.0962092	+	0.995361i	$0.530672\pi$
$578$	6.97721e6	+	6.97721e6i	0.868684	+	0.868684i
$579$	−6.99557e6			−0.867215
$580$	−917924.	+	2.99166e6i	−0.113302	+	0.369268i
$581$	−2.37420e6			−0.291794
$582$	2.10136e6	−	2.10136e6i	0.257154	−	0.257154i
$583$	−422305.	+	7.06881e6i	−0.0514582	+	0.861341i
$584$			8.06253e6i			0.978226i
$585$	856722.	−	454425.i	0.103502	−	0.0549001i
$586$	5.32769e6			0.640907
$587$	−3.69416e6	−	3.69416e6i	−0.442507	−	0.442507i	0.450346	−	0.892854i	$-0.351300\pi$
$587$	−3.69416e6	−	3.69416e6i	−0.442507	−	0.442507i	−0.892854	+	0.450346i	$0.851300\pi$
$588$	−3.36171e6	+	3.36171e6i	−0.400975	+	0.400975i
$589$	−9.04812e6			−1.07466
$590$	2.95214e6	+	5.56562e6i	0.349145	+	0.658239i
$591$		−	1.87432e6i		−	0.220737i
$592$	864201.	+	864201.i	0.101347	+	0.101347i
$593$	−2.28441e6	−	2.28441e6i	−0.266771	−	0.266771i	0.561027	−	0.827798i	$-0.310406\pi$
$593$	−2.28441e6	−	2.28441e6i	−0.266771	−	0.266771i	−0.827798	+	0.561027i	$0.810406\pi$
$594$	−3.60285e6	+	3.19663e6i	−0.418967	+	0.371729i
$595$	1.84015e6	−	5.99733e6i	0.213089	−	0.694490i
$596$		−	1.19458e6i		−	0.137753i
$597$	−760775.	−	760775.i	−0.0873615	−	0.0873615i
$598$	−2.13381e6	+	2.13381e6i	−0.244007	+	0.244007i
$599$		−	260972.i		−	0.0297185i	−0.999890	−	0.0148592i	$-0.995270\pi$
$599$		−	260972.i		−	0.0297185i	0.999890	−	0.0148592i	$-0.00473002\pi$
$600$	−7.33195e6	−	4.96690e6i	−0.831460	−	0.563258i
$601$		−	5.43065e6i		−	0.613290i	−0.951824	−	0.306645i	$-0.900794\pi$
$601$		−	5.43065e6i		−	0.613290i	0.951824	−	0.306645i	$-0.0992065\pi$
$602$	−615873.	+	615873.i	−0.0692628	+	0.0692628i
$603$	−570332.	+	570332.i	−0.0638755	+	0.0638755i
$604$	−1.34690e6			−0.150225
$605$	3.64682e6	−	8.23135e6i	0.405066	−	0.914287i
$606$	−1.14588e6			−0.126753
$607$	−115508.	+	115508.i	−0.0127245	+	0.0127245i	−0.713440	−	0.700716i	$-0.752864\pi$
$607$	−115508.	+	115508.i	−0.0127245	+	0.0127245i	0.700716	+	0.713440i	$0.252864\pi$
$608$	8.83421e6	−	8.83421e6i	0.969190	−	0.969190i
$609$			2.29301e6i			0.250531i
$610$	−1.13506e6	−	2.13992e6i	−0.123508	−	0.232848i
$611$		−	1.11514e7i		−	1.20844i
$612$	−568476.	+	568476.i	−0.0613527	+	0.0613527i
$613$	1.07878e7	+	1.07878e7i	1.15953	+	1.15953i	0.984576	+	0.174955i	$0.0559780\pi$
$613$	1.07878e7	+	1.07878e7i	1.15953	+	1.15953i	0.174955	+	0.984576i	$0.444022\pi$
$614$		−	1.58254e6i		−	0.169408i
$615$	−8.10808e6	−	1.52861e7i	−0.864431	−	1.62970i
$616$	2.81396e6	−	2.49669e6i	0.298790	−	0.265102i
$617$	−6.88556e6	−	6.88556e6i	−0.728159	−	0.728159i	0.242094	−	0.970253i	$-0.422166\pi$
$617$	−6.88556e6	−	6.88556e6i	−0.728159	−	0.728159i	−0.970253	+	0.242094i	$0.922166\pi$
$618$	933168.	+	933168.i	0.0982853	+	0.0982853i
$619$			5.02860e6i			0.527498i	0.964591	+	0.263749i	$0.0849590\pi$
$619$			5.02860e6i			0.527498i	−0.964591	+	0.263749i	$0.915041\pi$
$620$	1.48452e6	−	4.83829e6i	0.155098	−	0.505490i
$621$	3.47465e6			0.361562
$622$	−2.08534e6	+	2.08534e6i	−0.216123	+	0.216123i
$623$	1.97624e6	+	1.97624e6i	0.203995	+	0.203995i
$624$	−1.47632e6			−0.151782
$625$	3.62190e6	+	9.06914e6i	0.370883	+	0.928680i
$626$		−	1.26937e6i		−	0.129465i
$627$	815190.	−	1.36452e7i	0.0828114	−	1.38615i
$628$	−5.74837e6	+	5.74837e6i	−0.581628	+	0.581628i
$629$	2.68312e7			2.70404
$630$	−171353.	−	52575.8i	−0.0172004	−	0.00527758i
$631$	−1.62505e7			−1.62477			−0.812386	−	0.583120i	$-0.801832\pi$
$631$	−1.62505e7			−1.62477			−0.812386	+	0.583120i	$0.801832\pi$
$632$	2.55920e6	+	2.55920e6i	0.254866	+	0.254866i
$633$	−2.08857e6	−	2.08857e6i	−0.207176	−	0.207176i
$634$	3.99200e6			0.394428
$635$	−3.12892e6	+	1.65965e6i	−0.307935	+	0.163336i
$636$	−6.01388e6			−0.589538
$637$	−9.42338e6	+	9.42338e6i	−0.920149	+	0.920149i
$638$	−209832.	+	3.51230e6i	−0.0204089	+	0.341618i
$639$		−	884002.i		−	0.0856448i
$640$	3.53924e6	+	6.67248e6i	0.341555	+	0.643928i
$641$	3.71797e6			0.357405			0.178703	−	0.983903i	$-0.442810\pi$
$641$	3.71797e6			0.357405			0.178703	+	0.983903i	$0.442810\pi$
$642$	5.37017e6	+	5.37017e6i	0.514222	+	0.514222i
$643$	1.12376e7	−	1.12376e7i	1.07188	−	1.07188i	0.0746727	−	0.997208i	$-0.476209\pi$
$643$	1.12376e7	−	1.12376e7i	1.07188	−	1.07188i	0.997208	−	0.0746727i	$-0.0237912\pi$
$644$	−1.07805e6			−0.102430
$645$	−4.26019e6	−	1.30714e6i	−0.403208	−	0.123716i
$646$		−	1.46157e7i		−	1.37797i
$647$	−1.26570e7	−	1.26570e7i	−1.18869	−	1.18869i	−0.977429	−	0.211265i	$-0.932242\pi$
$647$	−1.26570e7	−	1.26570e7i	−1.18869	−	1.18869i	−0.211265	−	0.977429i	$-0.567758\pi$
$648$	−7.82826e6	−	7.82826e6i	−0.732366	−	0.732366i
$649$	−9.08737e6	−	1.02422e7i	−0.846889	−	0.954508i
$650$	−8.16436e6	−	5.53080e6i	−0.757947	−	0.513458i
$651$		−	3.70839e6i		−	0.342951i
$652$	−5.18268e6	−	5.18268e6i	−0.477458	−	0.477458i
$653$	9.46648e6	−	9.46648e6i	0.868771	−	0.868771i	−0.123565	−	0.992336i	$-0.539433\pi$
$653$	9.46648e6	−	9.46648e6i	0.868771	−	0.868771i	0.992336	+	0.123565i	$0.0394329\pi$
$654$			7.41825e6i			0.678199i
$655$	−896086.	+	2.92048e6i	−0.0816106	+	0.265981i
$656$			1.83155e6i			0.166172i
$657$	−590351.	+	590351.i	−0.0533577	+	0.0533577i
$658$	−1.45736e6	+	1.45736e6i	−0.131221	+	0.131221i
$659$	1.56974e7			1.40804			0.704019	−	0.710181i	$-0.251387\pi$
$659$	1.56974e7			1.40804			0.704019	+	0.710181i	$0.251387\pi$
$660$	7.16272e6	+	2.67467e6i	0.640056	+	0.239006i
$661$	−1.65290e7			−1.47144			−0.735721	−	0.677285i	$-0.763156\pi$
$661$	−1.65290e7			−1.47144			−0.735721	+	0.677285i	$0.763156\pi$
$662$	−1.84398e6	+	1.84398e6i	−0.163535	+	0.163535i
$663$	−2.29180e7	+	2.29180e7i	−2.02485	+	2.02485i
$664$		−	7.78854e6i		−	0.685545i
$665$	−5.56421e6	+	2.95139e6i	−0.487921	+	0.258804i
$666$		−	766608.i		−	0.0669712i
$667$	1.79485e6	−	1.79485e6i	0.156212	−	0.156212i
$668$	−1.63774e6	−	1.63774e6i	−0.142005	−	0.142005i
$669$		−	9.01026e6i		−	0.778345i
$670$	7.84095e6	+	2.40582e6i	0.674811	+	0.207051i
$671$	3.49399e6	+	3.93799e6i	0.299581	+	0.337651i
$672$	3.62072e6	+	3.62072e6i	0.309294	+	0.309294i
$673$	−5.67914e6	−	5.67914e6i	−0.483332	−	0.483332i	0.422862	−	0.906194i	$-0.361025\pi$
$673$	−5.67914e6	−	5.67914e6i	−0.483332	−	0.483332i	−0.906194	+	0.422862i	$0.861025\pi$
$674$		−	2.31352e6i		−	0.196166i
$675$	2.14422e6	+	1.11505e7i	0.181138	+	0.941963i
$676$	−1.14179e7			−0.960988
$677$	9.14748e6	−	9.14748e6i	0.767061	−	0.767061i	−0.210527	−	0.977588i	$-0.567518\pi$
$677$	9.14748e6	−	9.14748e6i	0.767061	−	0.767061i	0.977588	+	0.210527i	$0.0675181\pi$
$678$	719225.	+	719225.i	0.0600884	+	0.0600884i
$679$	2.97599e6			0.247718
$680$	1.96742e7	+	6.03659e6i	1.63164	+	0.500633i
$681$			1.74380e7i			1.44088i
$682$	339353.	−	5.68031e6i	0.0279377	−	0.467639i
$683$	3.02781e6	−	3.02781e6i	0.248357	−	0.248357i	−0.571939	−	0.820296i	$-0.693809\pi$
$683$	3.02781e6	−	3.02781e6i	0.248357	−	0.248357i	0.820296	+	0.571939i	$0.193809\pi$
$684$	807177.			0.0659673
$685$	−385878.	−	727491.i	−0.0314213	−	0.0592381i
$686$	5.43068e6			0.440600
$687$	−77395.4	−	77395.4i	−0.00625638	−	0.00625638i
$688$	333534.	+	333534.i	0.0268639	+	0.0268639i
$689$	−1.68578e7			−1.35286
$690$	1.33713e6	+	2.52087e6i	0.106918	+	0.201571i
$691$	−1.22272e7			−0.974163			−0.487082	−	0.873356i	$-0.661939\pi$
$691$	−1.22272e7			−0.974163			−0.487082	+	0.873356i	$0.661939\pi$
$692$	5.20578e6	−	5.20578e6i	0.413257	−	0.413257i
$693$	388854.	+	23230.9i	0.0307577	+	0.00183753i
$694$			128043.i			0.0100915i
$695$	−1.71743e7	−	5.26957e6i	−1.34871	−	0.413821i
$696$	−7.52218e6			−0.588601
$697$	2.84324e7	+	2.84324e7i	2.21683	+	2.21683i
$698$	−2.23278e6	+	2.23278e6i	−0.173463	+	0.173463i
$699$	2.12087e7			1.64180
$700$	−665272.	−	3.45957e6i	−0.0513162	−	0.266856i
$701$			1.05357e7i			0.809779i	0.914366	+	0.404890i	$0.132690\pi$
$701$			1.05357e7i			0.809779i	−0.914366	+	0.404890i	$0.867310\pi$
$702$	−8.10775e6	−	8.10775e6i	−0.620952	−	0.620952i
$703$	−1.90488e7	−	1.90488e7i	−1.45371	−	1.45371i
$704$	4.39969e6	+	4.95878e6i	0.334573	+	0.377089i
$705$	−1.00810e7	−	3.09315e6i	−0.763893	−	0.234384i
$706$		−	2.30828e6i		−	0.174292i
$707$	−811414.	−	811414.i	−0.0610512	−	0.0610512i
$708$	8.22242e6	−	8.22242e6i	0.616477	−	0.616477i
$709$		−	1.27616e7i		−	0.953430i	−0.879058	−	0.476715i	$-0.841827\pi$
$709$		−	1.27616e7i		−	0.953430i	0.879058	−	0.476715i	$-0.158173\pi$
$710$	−7.94114e6	+	4.21217e6i	−0.591204	+	0.313588i
$711$			374777.i			0.0278035i
$712$	−6.48304e6	+	6.48304e6i	−0.479268	+	0.479268i
$713$	−2.90274e6	+	2.90274e6i	−0.213838	+	0.213838i
$714$	5.99028e6			0.439745
$715$	2.00782e7	+	7.49749e6i	1.46879	+	0.548467i
$716$	−4.50986e6			−0.328761
$717$	−5.14895e6	+	5.14895e6i	−0.374042	+	0.374042i
$718$	−5.79608e6	+	5.79608e6i	−0.419588	+	0.419588i
$719$			300341.i			0.0216667i	0.999941	+	0.0108334i	$0.00344843\pi$
$719$			300341.i			0.0216667i	−0.999941	+	0.0108334i	$0.996552\pi$
$720$	−28473.1	+	92798.3i	−0.00204693	+	0.00667127i
$721$			1.32157e6i			0.0946789i
$722$	−4.59308e6	+	4.59308e6i	−0.327915	+	0.327915i
$723$	−8.69583e6	−	8.69583e6i	−0.618679	−	0.618679i
$724$		−	4.72400e6i		−	0.334937i
$725$	6.86744e6	+	4.65222e6i	0.485232	+	0.328712i
$726$	8.53571e6	+	1.02353e6i	0.601033	+	0.0720710i
$727$	−5.66577e6	−	5.66577e6i	−0.397579	−	0.397579i	0.479800	−	0.877378i	$-0.340709\pi$
$727$	−5.66577e6	−	5.66577e6i	−0.397579	−	0.397579i	−0.877378	+	0.479800i	$0.840709\pi$
$728$	6.33247e6	+	6.33247e6i	0.442838	+	0.442838i
$729$			1.31224e7i			0.914522i
$730$	8.11618e6	+	2.49027e6i	0.563695	+	0.172958i
$731$	1.03554e7			0.716757
$732$	−3.16142e6	+	3.16142e6i	−0.218075	+	0.218075i
$733$	1.10107e7	+	1.10107e7i	0.756928	+	0.756928i	0.975762	−	0.218834i	$-0.0702253\pi$
$733$	1.10107e7	+	1.10107e7i	0.756928	+	0.756928i	−0.218834	+	0.975762i	$0.570225\pi$
$734$	3.31579e6			0.227168
$735$	5.90507e6	+	1.11327e7i	0.403187	+	0.760123i
$736$		−	5.66823e6i		−	0.385703i
$737$	−1.77936e7	−	1.06303e6i	−1.20669	−	0.0720901i
$738$	812357.	−	812357.i	0.0549043	−	0.0549043i
$739$	−9.06157e6			−0.610369			−0.305184	−	0.952293i	$-0.598718\pi$
$739$	−9.06157e6			−0.610369			−0.305184	+	0.952293i	$0.598718\pi$
$740$	1.33113e7	−	7.06060e6i	0.893593	−	0.473982i
$741$	3.25412e7			2.17715
$742$	2.20313e6	+	2.20313e6i	0.146903	+	0.146903i
$743$	983060.	+	983060.i	0.0653293	+	0.0653293i	0.739017	−	0.673687i	$-0.235291\pi$
$743$	983060.	+	983060.i	0.0653293	+	0.0653293i	−0.673687	+	0.739017i	$0.735291\pi$
$744$	1.21653e7			0.805734
$745$	−3.02720e6	−	928829.i	−0.199825	−	0.0613119i
$746$	−31716.9			−0.00208662
$747$	570289.	−	570289.i	0.0373933	−	0.0373933i
$748$	−1.77357e7	−	1.05957e6i	−1.15903	−	0.0692429i
$749$			7.60536e6i			0.495354i
$750$	−7.26456e6	+	5.84661e6i	−0.471581	+	0.379534i
$751$	2.20552e7			1.42696			0.713479	−	0.700677i	$-0.247119\pi$
$751$	2.20552e7			1.42696			0.713479	+	0.700677i	$0.247119\pi$
$752$	789254.	+	789254.i	0.0508946	+	0.0508946i
$753$	1.73917e7	−	1.73917e7i	1.11778	−	1.11778i
$754$	−8.37620e6			−0.536560
$755$	−1.04726e6	+	3.41317e6i	−0.0668630	+	0.217917i
$756$		−	4.09624e6i		−	0.260664i
$757$	−1.59253e6	−	1.59253e6i	−0.101006	−	0.101006i	0.654798	−	0.755804i	$-0.272754\pi$
$757$	−1.59253e6	−	1.59253e6i	−0.101006	−	0.101006i	−0.755804	+	0.654798i	$0.772754\pi$
$758$	6.52554e6	+	6.52554e6i	0.412519	+	0.412519i
$759$	−4.11600e6	−	4.63905e6i	−0.259341	−	0.292297i
$760$	−9.68199e6	−	1.82533e7i	−0.608038	−	1.14633i
$761$			8.96669e6i			0.561268i	0.959815	+	0.280634i	$0.0905448\pi$
$761$			8.96669e6i			0.561268i	−0.959815	+	0.280634i	$0.909455\pi$
$762$	−2.39146e6	−	2.39146e6i	−0.149203	−	0.149203i
$763$	−5.25295e6	+	5.25295e6i	−0.326657	+	0.326657i
$764$			1.80024e7i			1.11583i
$765$	998566.	+	1.88258e6i	0.0616912	+	0.116306i
$766$		−	767461.i		−	0.0472590i
$767$	2.30487e7	−	2.30487e7i	1.41468	−	1.41468i
$768$	−1.11403e7	+	1.11403e7i	−0.681544	+	0.681544i
$769$	−5.51734e6			−0.336445			−0.168223	−	0.985749i	$-0.553803\pi$
$769$	−5.51734e6			−0.336445			−0.168223	+	0.985749i	$0.553803\pi$
$770$	−1.64416e6	−	3.60384e6i	−0.0999348	−	0.219048i
$771$	3.10341e6			0.188020
$772$	6.45536e6	−	6.45536e6i	0.389832	−	0.389832i
$773$	−2.01629e7	+	2.01629e7i	−1.21368	+	1.21368i	−0.243870	+	0.969808i	$0.578417\pi$
$773$	−2.01629e7	+	2.01629e7i	−1.21368	+	1.21368i	−0.969808	+	0.243870i	$0.921583\pi$
$774$		−	295868.i		−	0.0177520i
$775$	−1.11064e7	−	7.52385e6i	−0.664233	−	0.449973i
$776$			9.76272e6i			0.581991i
$777$	7.80717e6	−	7.80717e6i	0.463918	−	0.463918i
$778$	−1.01505e7	−	1.01505e7i	−0.601227	−	0.601227i
$779$		−	4.03711e7i		−	2.38357i
$780$	−5.33903e6	+	1.74007e7i	−0.314214	+	1.02407i
$781$	1.46137e7	−	1.29660e7i	0.857301	−	0.760642i
$782$	−4.68888e6	−	4.68888e6i	−0.274191	−	0.274191i
$783$	6.81982e6	+	6.81982e6i	0.397529	+	0.397529i
$784$		−	1.33391e6i		−	0.0775059i
$785$	1.00974e7	+	1.90365e7i	0.584837	+	1.10259i
$786$	−2.91705e6			−0.168417
$787$	−6.07156e6	+	6.07156e6i	−0.349433	+	0.349433i	−0.859898	−	0.510466i	$-0.829473\pi$
$787$	−6.07156e6	+	6.07156e6i	−0.349433	+	0.349433i	0.510466	+	0.859898i	$0.329473\pi$
$788$	1.72958e6	+	1.72958e6i	0.0992262	+	0.0992262i
$789$	−8.51604e6			−0.487018
$790$	3.36669e6	−	1.78577e6i	0.191927	−	0.101802i
$791$			1.01858e6i			0.0578836i
$792$	−76208.9	+	1.27563e6i	−0.00431711	+	0.0722625i
$793$	−8.86195e6	+	8.86195e6i	−0.500433	+	0.500433i
$794$	−1.37737e7			−0.775355
$795$	−4.67599e6	+	1.52398e7i	−0.262395	+	0.855186i
$796$	1.40405e6			0.0785417
$797$	1.03854e7	+	1.03854e7i	0.579134	+	0.579134i	0.934665	−	0.355531i	$-0.115700\pi$
$797$	1.03854e7	+	1.03854e7i	0.579134	+	0.579134i	−0.355531	+	0.934665i	$0.615700\pi$
$798$	−4.25279e6	−	4.25279e6i	−0.236410	−	0.236410i
$799$	2.45043e7			1.35792
$800$	1.81898e7	−	3.49789e6i	1.00486	−	0.193233i
$801$	−949395.			−0.0522836
$802$	4.87697e6	−	4.87697e6i	0.267741	−	0.267741i
$803$	−1.84182e7	−	1.10034e6i	−1.00800	−	0.0602197i
$804$		−	1.51382e7i		−	0.825911i
$805$	−838223.	+	2.73190e6i	−0.0455900	+	0.148585i
$806$	1.35465e7			0.734495
$807$	−6.62734e6	−	6.62734e6i	−0.358225	−	0.358225i
$808$	2.66184e6	−	2.66184e6i	0.143434	−	0.143434i
$809$	−3.09183e7			−1.66090			−0.830452	−	0.557091i	$-0.811918\pi$
$809$	−3.09183e7			−1.66090			−0.830452	+	0.557091i	$0.811918\pi$
$810$	−1.02983e7	+	5.46244e6i	−0.551507	+	0.292532i
$811$			3.50965e7i			1.87375i	0.349664	+	0.936875i	$0.386296\pi$
$811$			3.50965e7i			1.87375i	−0.349664	+	0.936875i	$0.613704\pi$
$812$	−2.11593e6	−	2.11593e6i	−0.112619	−	0.112619i
$813$	1.57783e7	+	1.57783e7i	0.837207	+	0.837207i
$814$	1.26730e7	−	1.12442e7i	0.670378	−	0.594794i
$815$	−1.71631e7	+	9.10371e6i	−0.905111	+	0.480092i
$816$		−	3.24411e6i		−	0.170557i
$817$	−7.35178e6	−	7.35178e6i	−0.385334	−	0.385334i
$818$	1.21281e7	−	1.21281e7i	0.633738	−	0.633738i
$819$			927346.i			0.0483095i
$820$	2.15876e7	+	6.62368e6i	1.12117	+	0.344005i
$821$			3.31451e6i			0.171617i	0.996312	+	0.0858086i	$0.0273474\pi$
$821$			3.31451e6i			0.171617i	−0.996312	+	0.0858086i	$0.972653\pi$
$822$	556029.	−	556029.i	0.0287024	−	0.0287024i
$823$	−1.49749e7	+	1.49749e7i	−0.770665	+	0.770665i	−0.978223	−	0.207558i	$-0.933448\pi$
$823$	−1.49749e7	+	1.49749e7i	−0.770665	+	0.770665i	0.207558	+	0.978223i	$0.433448\pi$
$824$	−4.33541e6			−0.222440
$825$	1.23471e7	−	1.60714e7i	0.631583	−	0.822089i
$826$	−6.02443e6			−0.307231
$827$	2.28638e7	−	2.28638e7i	1.16248	−	1.16248i	0.178545	−	0.983932i	$-0.442861\pi$
$827$	2.28638e7	−	2.28638e7i	1.16248	−	1.16248i	0.983932	−	0.178545i	$-0.0571391\pi$
$828$	258951.	−	258951.i	0.0131263	−	0.0131263i
$829$			3.92509e7i			1.98364i	0.127627	+	0.991822i	$0.459264\pi$
$829$			3.92509e7i			1.98364i	−0.127627	+	0.991822i	$0.540736\pi$
$830$	−7.84036e6	−	2.40564e6i	−0.395040	−	0.121209i
$831$			1.64366e7i			0.825675i
$832$	−1.11591e7	+	1.11591e7i	−0.558884	+	0.558884i
$833$	−2.07072e7	−	2.07072e7i	−1.03397	−	1.03397i
$834$		−	1.71541e7i		−	0.853991i
$835$	−5.42359e6	+	2.87680e6i	−0.269197	+	0.142789i
$836$	1.18392e7	+	1.33437e7i	0.585878	+	0.660329i
$837$	−1.10294e7	−	1.10294e7i	−0.544176	−	0.544176i
$838$	−9.62792e6	−	9.62792e6i	−0.473612	−	0.473612i
$839$		−	9.91077e6i		−	0.486074i	−0.970017	−	0.243037i	$-0.921856\pi$
$839$		−	9.91077e6i		−	0.486074i	0.970017	−	0.243037i	$-0.0781436\pi$
$840$	7.48116e6	−	3.96818e6i	0.365823	−	0.194041i
$841$	−1.34655e7			−0.656498
$842$	8.05768e6	−	8.05768e6i	0.391678	−	0.391678i
$843$	−2.32352e7	−	2.32352e7i	−1.12610	−	1.12610i
$844$	3.85458e6			0.186260
$845$	−8.87776e6	+	2.89340e7i	−0.427722	+	1.39401i
$846$		−	700124.i		−	0.0336317i
$847$	5.31946e6	+	6.76901e6i	0.254776	+	0.324203i
$848$	1.19314e6	−	1.19314e6i	0.0569771	−	0.0569771i
$849$	9.66620e6			0.460242
$850$	1.21535e7	−	1.79406e7i	0.576972	−	0.851705i
$851$	−1.22221e7			−0.578526
$852$	1.17319e7	+	1.17319e7i	0.553694	+	0.553694i
$853$	1.56496e7	+	1.56496e7i	0.736428	+	0.736428i	0.971885	−	0.235457i	$-0.0756587\pi$
$853$	1.56496e7	+	1.56496e7i	0.736428	+	0.736428i	−0.235457	+	0.971885i	$0.575659\pi$
$854$	2.31632e6			0.108681
$855$	627606.	−	2.04547e6i	0.0293611	−	0.0956923i
$856$	−2.49493e7			−1.16379
$857$	6.75281e6	−	6.75281e6i	0.314074	−	0.314074i	−0.532411	−	0.846486i	$-0.678714\pi$
$857$	6.75281e6	−	6.75281e6i	0.314074	−	0.314074i	0.846486	+	0.532411i	$0.178714\pi$
$858$	−1.22047e6	+	2.04290e7i	−0.0565990	+	0.947391i
$859$			1.96850e7i			0.910234i	0.890432	+	0.455117i	$0.150403\pi$
$859$			1.96850e7i			0.910234i	−0.890432	+	0.455117i	$0.849597\pi$
$860$	5.13741e6	−	2.72500e6i	0.236863	−	0.125638i
$861$	1.65462e7			0.760658
$862$	1.93456e6	+	1.93456e6i	0.0886775	+	0.0886775i
$863$	1.73258e7	−	1.73258e7i	0.791892	−	0.791892i	−0.189910	−	0.981802i	$-0.560820\pi$
$863$	1.73258e7	−	1.73258e7i	0.791892	−	0.791892i	0.981802	+	0.189910i	$0.0608195\pi$
$864$	2.15374e7			0.981540
$865$	−9.14430e6	−	1.72396e7i	−0.415537	−	0.783407i
$866$		−	8.98504e6i		−	0.407123i
$867$	−3.41358e7	−	3.41358e7i	−1.54228	−	1.54228i
$868$	3.42202e6	+	3.42202e6i	0.154164	+	0.154164i
$869$	−6.19557e6	+	5.49703e6i	−0.278312	+	0.246933i
$870$	−2.32337e6	+	7.57223e6i	−0.104069	+	0.339177i
$871$		−	4.24346e7i		−	1.89528i
$872$	−1.72322e7	−	1.72322e7i	−0.767451	−	0.767451i
$873$	−714841.	+	714841.i	−0.0317449	+	0.0317449i
$874$			6.65773e6i			0.294814i
$875$	−9.28417e6	−	1.00407e6i	−0.409943	−	0.0443345i
$876$		−	1.56695e7i		−	0.689915i
$877$	−1.52535e7	+	1.52535e7i	−0.669687	+	0.669687i	−0.957643	−	0.287957i	$-0.907024\pi$
$877$	−1.52535e7	+	1.52535e7i	−0.669687	+	0.669687i	0.287957	+	0.957643i	$0.407024\pi$
$878$	−1.52991e7	+	1.52991e7i	−0.669775	+	0.669775i
$879$	−2.60656e7			−1.13788
$880$	−1.95171e6	+	890416.i	−0.0849587	+	0.0387602i
$881$	−2.81289e7			−1.22099			−0.610497	−	0.792019i	$-0.709030\pi$
$881$	−2.81289e7			−1.22099			−0.610497	+	0.792019i	$0.709030\pi$
$882$	−591635.	+	591635.i	−0.0256084	+	0.0256084i
$883$	5.35392e6	−	5.35392e6i	0.231084	−	0.231084i	−0.582061	−	0.813145i	$-0.697754\pi$
$883$	5.35392e6	−	5.35392e6i	0.231084	−	0.231084i	0.813145	+	0.582061i	$0.197754\pi$
$884$		−	4.22965e7i		−	1.82043i
$885$	−1.44432e7	−	2.72296e7i	−0.619878	−	1.16865i
$886$		−	1.22523e7i		−	0.524363i
$887$	2.73744e6	−	2.73744e6i	0.116825	−	0.116825i	−0.646277	−	0.763103i	$-0.723675\pi$
$887$	2.73744e6	−	2.73744e6i	0.116825	−	0.116825i	0.763103	+	0.646277i	$0.223675\pi$
$888$	2.56114e7	+	2.56114e7i	1.08993	+	1.08993i
$889$		−	3.38685e6i		−	0.143728i
$890$	4.52376e6	+	8.52858e6i	0.191436	+	0.360912i
$891$	1.89514e7	−	1.68147e7i	0.799737	−	0.709568i
$892$	8.31447e6	+	8.31447e6i	0.349882	+	0.349882i
$893$	−1.73968e7	−	1.73968e7i	−0.730029	−	0.730029i
$894$		−	3.02363e6i		−	0.126528i
$895$	−3.50656e6	+	1.14284e7i	−0.146327	+	0.476902i
$896$	−7.22253e6			−0.300552
$897$	1.04396e7	−	1.04396e7i	0.433214	−	0.433214i
$898$	1.36290e6	+	1.36290e6i	0.0563990	+	0.0563990i
$899$	−1.13946e7			−0.470219
$900$	990798.	+	671198.i	0.0407736	+	0.0276213i
$901$		−	3.70438e7i		−	1.52021i
$902$	2.53445e7	+	1.51413e6i	1.03721	+	0.0619652i
$903$	3.01314e6	−	3.01314e6i	0.122970	−	0.122970i
$904$	−3.34145e6			−0.135992
$905$	−1.19711e7	−	3.67306e6i	−0.485861	−	0.149076i
$906$	−3.40916e6			−0.137983
$907$	2.05162e7	+	2.05162e7i	0.828094	+	0.828094i	0.987253	−	0.159159i	$-0.0508784\pi$
$907$	2.05162e7	+	2.05162e7i	0.828094	+	0.828094i	−0.159159	+	0.987253i	$0.550878\pi$
$908$	−1.60914e7	−	1.60914e7i	−0.647706	−	0.647706i
$909$	389807.			0.0156473
$910$	8.33051e6	−	4.41870e6i	0.333479	−	0.176885i
$911$	−6.36272e6			−0.254008			−0.127004	−	0.991902i	$-0.540536\pi$
$911$	−6.36272e6			−0.254008			−0.127004	+	0.991902i	$0.540536\pi$
$912$	−2.30315e6	+	2.30315e6i	−0.0916928	+	0.0916928i
$913$	1.77923e7	+	1.06295e6i	0.706407	+	0.0422022i
$914$			5.57086e6i			0.220575i
$915$	5.55325e6	+	1.04695e7i	0.219278	+	0.413401i
$916$	142838.			0.00562475
$917$	−2.06559e6	−	2.06559e6i	−0.0811188	−	0.0811188i
$918$	1.78162e7	−	1.78162e7i	0.697763	−	0.697763i
$919$	4.29242e7			1.67654			0.838269	−	0.545256i	$-0.183568\pi$
$919$	4.29242e7			1.67654			0.838269	+	0.545256i	$0.183568\pi$
$920$	−8.96196e6	−	2.74978e6i	−0.349087	−	0.107110i
$921$			7.74253e6i			0.300769i
$922$	1.99139e7	+	1.99139e7i	0.771488	+	0.771488i
$923$	3.28863e7	+	3.28863e7i	1.27061	+	1.27061i
$924$	−5.46894e6	+	4.85233e6i	−0.210728	+	0.186969i
$925$	−7.54232e6	−	3.92219e7i	−0.289835	−	1.50721i
$926$			1.53134e7i			0.586874i
$927$	−317445.	−	317445.i	−0.0121330	−	0.0121330i
$928$	1.11252e7	−	1.11252e7i	0.424071	−	0.424071i
$929$			2.39537e7i			0.910612i	0.890335	+	0.455306i	$0.150470\pi$
$929$			2.39537e7i			0.910612i	−0.890335	+	0.455306i	$0.849530\pi$
$930$	3.75750e6	−	1.22463e7i	0.142460	−	0.464298i
$931$			2.94020e7i			1.11174i
$932$	−1.95709e7	+	1.95709e7i	−0.738025	+	0.738025i
$933$	1.02025e7	−	1.02025e7i	0.383708	−	0.383708i
$934$	1.16147e7			0.435653
$935$	−1.64752e7	+	4.41203e7i	−0.616312	+	1.65048i
$936$	−3.04215e6			−0.113499
$937$	−2.87191e7	+	2.87191e7i	−1.06862	+	1.06862i	−0.0711513	+	0.997466i	$0.522667\pi$
$937$	−2.87191e7	+	2.87191e7i	−1.06862	+	1.06862i	−0.997466	+	0.0711513i	$0.977333\pi$
$938$	−5.54574e6	+	5.54574e6i	−0.205803	+	0.205803i
$939$			6.21036e6i			0.229855i
$940$	1.21568e7	−	6.44827e6i	0.448747	−	0.238026i
$941$			2.55888e7i			0.942055i	0.882119	+	0.471027i	$0.156117\pi$
$941$			2.55888e7i			0.942055i	−0.882119	+	0.471027i	$0.843883\pi$
$942$	−1.45498e7	+	1.45498e7i	−0.534232	+	0.534232i
$943$	−1.29515e7	−	1.29515e7i	−0.474287	−	0.474287i
$944$			3.26261e6i			0.119161i
$945$	−1.03803e7	−	3.18496e6i	−0.378120	−	0.116018i
$946$	4.89109e6	−	4.33963e6i	0.177696	−	0.157661i
$947$	1.40569e7	+	1.40569e7i	0.509347	+	0.509347i	0.914326	−	0.404979i	$-0.132721\pi$
$947$	1.40569e7	+	1.40569e7i	0.509347	+	0.509347i	−0.404979	+	0.914326i	$0.632721\pi$
$948$	−4.97381e6	−	4.97381e6i	−0.179750	−	0.179750i
$949$		−	4.39241e7i		−	1.58320i
$950$	−2.13653e7	+	4.10851e6i	−0.768067	+	0.147698i
$951$	−1.95307e7			−0.700273
$952$	−1.39151e7	+	1.39151e7i	−0.497617	+	0.497617i
$953$	1.86263e7	+	1.86263e7i	0.664345	+	0.664345i	0.956401	−	0.292056i	$-0.0943393\pi$
$953$	1.86263e7	+	1.86263e7i	0.664345	+	0.664345i	−0.292056	+	0.956401i	$0.594339\pi$
$954$	−1.05840e6			−0.0376511
$955$	4.56198e7	+	1.39974e7i	1.61862	+	0.496638i
$956$		−	9.50267e6i		−	0.336280i
$957$	1.02660e6	−	1.71838e7i	0.0362343	−	0.606513i
$958$	1.86962e7	−	1.86962e7i	0.658173	−	0.658173i
$959$	787462.			0.0276492
$960$	6.99275e6	+	1.31833e7i	0.244889	+	0.461687i
$961$	−1.02011e7			−0.356319
$962$	2.85191e7	+	2.85191e7i	0.993569	+	0.993569i
$963$	−1.82683e6	−	1.82683e6i	−0.0634793	−	0.0634793i
$964$	1.60486e7			0.556218
$965$	−1.13393e7	−	2.13778e7i	−0.391982	−	0.738999i
$966$	−2.72868e6			−0.0940828
$967$	−1.93426e7	+	1.93426e7i	−0.665194	+	0.665194i	−0.956600	−	0.291406i	$-0.905877\pi$
$967$	−1.93426e7	+	1.93426e7i	−0.665194	+	0.665194i	0.291406	+	0.956600i	$0.405877\pi$
$968$	−2.22057e7	+	1.74504e7i	−0.761686	+	0.598574i
$969$			7.15069e7i			2.44646i
$970$	9.82767e6	+	3.01540e6i	0.335368	+	0.102900i
$971$	1.25107e7			0.425828			0.212914	−	0.977071i	$-0.431705\pi$
$971$	1.25107e7			0.425828			0.212914	+	0.977071i	$0.431705\pi$
$972$	2.04732e6	+	2.04732e6i	0.0695057	+	0.0695057i
$973$	1.21470e7	−	1.21470e7i	0.411328	−	0.411328i
$974$	−1.59699e7			−0.539393
$975$	3.99439e7	+	2.70593e7i	1.34567	+	0.911600i
$976$		−	1.25443e6i		−	0.0421525i
$977$	9.19541e6	+	9.19541e6i	0.308201	+	0.308201i	0.844212	−	0.536010i	$-0.180069\pi$
$977$	9.19541e6	+	9.19541e6i	0.308201	+	0.308201i	−0.536010	+	0.844212i	$0.680069\pi$
$978$	−1.31180e7	−	1.31180e7i	−0.438550	−	0.438550i
$979$	−1.39252e7	−	1.56948e7i	−0.464349	−	0.523357i
$980$	−1.57221e7	−	4.82398e6i	−0.522932	−	0.160450i
$981$		−	2.52354e6i		−	0.0837217i
$982$	−5.29811e6	−	5.29811e6i	−0.175324	−	0.175324i
$983$	2.75090e7	−	2.75090e7i	0.908011	−	0.908011i	−0.0881006	−	0.996112i	$-0.528080\pi$
$983$	2.75090e7	−	2.75090e7i	0.908011	−	0.908011i	0.996112	+	0.0881006i	$0.0280797\pi$
$984$			5.42796e7i			1.78710i
$985$	5.72775e6	−	3.03813e6i	0.188102	−	0.0997736i
$986$		−	1.84061e7i		−	0.602932i
$987$	7.13010e6	−	7.13010e6i	0.232972	−	0.232972i
$988$	−3.00283e7	+	3.00283e7i	−0.978675	+	0.978675i
$989$	−4.71706e6			−0.153349
$990$	1.26058e6	+	470720.i	0.0408774	+	0.0152642i
$991$	−1.34334e7			−0.434514			−0.217257	−	0.976114i	$-0.569711\pi$
$991$	−1.34334e7			−0.434514			−0.217257	+	0.976114i	$0.569711\pi$
$992$	−1.79924e7	+	1.79924e7i	−0.580510	+	0.580510i
$993$	9.02161e6	−	9.02161e6i	0.290343	−	0.290343i
$994$		−	8.59577e6i		−	0.275943i
$995$	1.09170e6	−	3.55801e6i	0.0349578	−	0.113933i
$996$			1.51370e7i			0.483495i
$997$	1.29267e7	−	1.29267e7i	0.411861	−	0.411861i	−0.470526	−	0.882386i	$-0.655936\pi$
$997$	1.29267e7	−	1.29267e7i	0.411861	−	0.411861i	0.882386	+	0.470526i	$0.155936\pi$
$998$	−627381.	−	627381.i	−0.0199391	−	0.0199391i
$999$		−	4.64399e7i		−	1.47224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.11	✓	52
5.3	odd	4	inner	55.6.e.b.43.16	yes	52
11.10	odd	2	inner	55.6.e.b.32.16	yes	52
55.43	even	4	inner	55.6.e.b.43.11	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.11	✓	52	1.1	even	1	trivial
55.6.e.b.32.16	yes	52	11.10	odd	2	inner
55.6.e.b.43.11	yes	52	55.43	even	4	inner
55.6.e.b.43.16	yes	52	5.3	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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.33566 + 2.33566i) q^{2} +(11.4271 - 11.4271i) q^{3} +21.0894i q^{4} +(53.4426 + 16.3977i) q^{5} +53.3797i q^{6} +(-37.7988 + 37.7988i) q^{7} +(-123.999 - 123.999i) q^{8} -18.1587i q^{9} +(-163.123 + 86.5243i) q^{10} +(300.188 - 266.342i) q^{11} +(240.991 + 240.991i) q^{12} +(675.535 + 675.535i) q^{13} -176.570i q^{14} +(798.075 - 423.317i) q^{15} -95.6239 q^{16} +(-1484.44 + 1484.44i) q^{17} +(42.4126 + 42.4126i) q^{18} +2107.75 q^{19} +(-345.818 + 1127.07i) q^{20} +863.864i q^{21} +(-79.0518 + 1323.22i) q^{22} +(676.189 - 676.189i) q^{23} -2833.90 q^{24} +(2587.23 + 1752.67i) q^{25} -3155.64 q^{26} +(2569.29 + 2569.29i) q^{27} +(-797.155 - 797.155i) q^{28} +2654.36 q^{29} +(-875.305 + 2852.75i) q^{30} -4292.79 q^{31} +(4191.30 - 4191.30i) q^{32} +(386.759 - 6473.82i) q^{33} -6934.28i q^{34} +(-2639.88 + 1400.25i) q^{35} +382.957 q^{36} +(-9037.50 - 9037.50i) q^{37} +(-4922.98 + 4922.98i) q^{38} +15438.9 q^{39} +(-4593.52 - 8660.11i) q^{40} -19153.7i q^{41} +(-2017.69 - 2017.69i) q^{42} +(-3487.98 - 3487.98i) q^{43} +(5617.00 + 6330.78i) q^{44} +(297.762 - 970.451i) q^{45} +3158.69i q^{46} +(-8253.73 - 8253.73i) q^{47} +(-1092.71 + 1092.71i) q^{48} +13949.5i q^{49} +(-10136.5 + 1949.24i) q^{50} +33925.7i q^{51} +(-14246.6 + 14246.6i) q^{52} +(-12477.4 + 12477.4i) q^{53} -12002.0 q^{54} +(20410.2 - 9311.64i) q^{55} +9374.01 q^{56} +(24085.5 - 24085.5i) q^{57} +(-6199.67 + 6199.67i) q^{58} -34119.2i q^{59} +(8927.51 + 16830.9i) q^{60} +13118.4i q^{61} +(10026.5 - 10026.5i) q^{62} +(686.379 + 686.379i) q^{63} +16518.9i q^{64} +(25025.2 + 47179.6i) q^{65} +(14217.3 + 16024.0i) q^{66} +(-31408.1 - 31408.1i) q^{67} +(-31305.9 - 31305.9i) q^{68} -15453.8i q^{69} +(2895.34 - 9436.38i) q^{70} +48681.9 q^{71} +(-2251.66 + 2251.66i) q^{72} +(-32510.6 - 32510.6i) q^{73} +42217.0 q^{74} +(49592.7 - 9536.61i) q^{75} +44451.2i q^{76} +(-1279.33 + 21414.2i) q^{77} +(-36059.9 + 36059.9i) q^{78} -20639.0 q^{79} +(-5110.39 - 1568.01i) q^{80} +63131.8 q^{81} +(44736.4 + 44736.4i) q^{82} +(31405.7 + 31405.7i) q^{83} -18218.4 q^{84} +(-103674. + 54990.9i) q^{85} +16293.4 q^{86} +(30331.7 - 30331.7i) q^{87} +(-70249.0 - 4196.82i) q^{88} -52283.1i q^{89} +(1571.17 + 2962.11i) q^{90} -51068.9 q^{91} +(14260.4 + 14260.4i) q^{92} +(-49054.3 + 49054.3i) q^{93} +38555.8 q^{94} +(112644. + 34562.2i) q^{95} -95789.1i q^{96} +(-39366.2 - 39366.2i) q^{97} +(-32581.3 - 32581.3i) q^{98} +(-4836.44 - 5451.03i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) \) 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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