LMFDB - Embedded newform 10.7.c.b.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,7,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	10.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:	$2.30054083620$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{129})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 65x^{2} + 1024 $ x^4 + 65*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.2
Root			$-5.17891i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.7.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 4.00000i) q^{2} +(23.8945 + 23.8945i) q^{3} -32.0000i q^{4} +(54.1055 - 112.684i) q^{5} +191.156 q^{6} +(-362.840 + 362.840i) q^{7} +(-128.000 - 128.000i) q^{8} +412.898i q^{9} +(-234.313 - 667.156i) q^{10} -1321.26 q^{11} +(764.625 - 764.625i) q^{12} +(254.789 + 254.789i) q^{13} +2902.72i q^{14} +(3985.35 - 1399.70i) q^{15} -1024.00 q^{16} +(4398.15 - 4398.15i) q^{17} +(1651.59 + 1651.59i) q^{18} +819.171i q^{19} +(-3605.88 - 1731.37i) q^{20} -17339.8 q^{21} +(-5285.03 + 5285.03i) q^{22} +(11135.5 + 11135.5i) q^{23} -6117.00i q^{24} +(-9770.20 - 12193.6i) q^{25} +2038.31 q^{26} +(7553.11 - 7553.11i) q^{27} +(11610.9 + 11610.9i) q^{28} +27495.1i q^{29} +(10342.6 - 21540.2i) q^{30} +15086.4 q^{31} +(-4096.00 + 4096.00i) q^{32} +(-31570.9 - 31570.9i) q^{33} -35185.2i q^{34} +(21254.5 + 60517.7i) q^{35} +13212.7 q^{36} +(21550.0 - 21550.0i) q^{37} +(3276.68 + 3276.68i) q^{38} +12176.1i q^{39} +(-21349.0 + 7498.01i) q^{40} -45644.1 q^{41} +(-69359.2 + 69359.2i) q^{42} +(-78126.4 - 78126.4i) q^{43} +42280.3i q^{44} +(46526.9 + 22340.0i) q^{45} +89083.7 q^{46} +(-1995.12 + 1995.12i) q^{47} +(-24468.0 - 24468.0i) q^{48} -145657. i q^{49} +(-87855.2 - 9693.60i) q^{50} +210184. q^{51} +(8153.25 - 8153.25i) q^{52} +(106138. + 106138. i) q^{53} -60424.9i q^{54} +(-71487.3 + 148884. i) q^{55} +92887.0 q^{56} +(-19573.7 + 19573.7i) q^{57} +(109980. + 109980. i) q^{58} -64466.6i q^{59} +(-44790.4 - 127531. i) q^{60} -320767. q^{61} +(60345.6 - 60345.6i) q^{62} +(-149816. - 149816. i) q^{63} +32768.0i q^{64} +(42496.0 - 14925.1i) q^{65} -252567. q^{66} +(-35044.1 + 35044.1i) q^{67} +(-140741. - 140741. i) q^{68} +532153. i q^{69} +(327089. + 157053. i) q^{70} -251708. q^{71} +(52851.0 - 52851.0i) q^{72} +(326907. + 326907. i) q^{73} -172400. i q^{74} +(57906.0 - 524815. i) q^{75} +26213.5 q^{76} +(479405. - 479405. i) q^{77} +(48704.5 + 48704.5i) q^{78} +25722.3i q^{79} +(-55404.0 + 115388. i) q^{80} +661959. q^{81} +(-182577. + 182577. i) q^{82} +(-123104. - 123104. i) q^{83} +554873. i q^{84} +(-257636. - 733563. i) q^{85} -625011. q^{86} +(-656982. + 656982. i) q^{87} +(169121. + 169121. i) q^{88} -198715. i q^{89} +(275468. - 96747.3i) q^{90} -184895. q^{91} +(356335. - 356335. i) q^{92} +(360482. + 360482. i) q^{93} +15961.0i q^{94} +(92307.2 + 44321.6i) q^{95} -195744. q^{96} +(-738798. + 738798. i) q^{97} +(-582627. - 582627. i) q^{98} -545545. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 18 q^{3} + 330 q^{5} - 144 q^{6} - 202 q^{7} - 512 q^{8} + 880 q^{10} - 2332 q^{11} - 576 q^{12} + 792 q^{13} + 4470 q^{15} - 4096 q^{16} + 12368 q^{17} + 14784 q^{18} - 3520 q^{20} - 69132 q^{21}+ \cdots - 1321024 q^{98}+O(q^{100}) $ 4 * q + 16 * q^2 - 18 * q^3 + 330 * q^5 - 144 * q^6 - 202 * q^7 - 512 * q^8 + 880 * q^10 - 2332 * q^11 - 576 * q^12 + 792 * q^13 + 4470 * q^15 - 4096 * q^16 + 12368 * q^17 + 14784 * q^18 - 3520 * q^20 - 69132 * q^21 - 9328 * q^22 + 35342 * q^23 - 1600 * q^25 + 6336 * q^26 + 61560 * q^27 + 6464 * q^28 - 37680 * q^30 - 18932 * q^31 - 16384 * q^32 - 73356 * q^33 + 130790 * q^35 + 118272 * q^36 - 67812 * q^37 + 44000 * q^38 - 56320 * q^40 + 110228 * q^41 - 276528 * q^42 - 293538 * q^43 - 72510 * q^45 + 282736 * q^46 + 195438 * q^47 + 18432 * q^48 - 1600 * q^50 + 185388 * q^51 + 25344 * q^52 - 121988 * q^53 - 108540 * q^55 + 51712 * q^56 + 268800 * q^57 + 229120 * q^58 - 444480 * q^60 - 243372 * q^61 - 75728 * q^62 + 451902 * q^63 + 100020 * q^65 - 586848 * q^66 - 773602 * q^67 - 395776 * q^68 + 895840 * q^70 - 1046132 * q^71 + 473088 * q^72 + 922372 * q^73 + 367350 * q^75 + 352000 * q^76 + 1040116 * q^77 + 23088 * q^78 - 337920 * q^80 + 360144 * q^81 + 440912 * q^82 - 1238058 * q^83 + 86840 * q^85 - 2348304 * q^86 - 1238640 * q^87 + 298496 * q^88 + 1161840 * q^90 - 221892 * q^91 + 1130944 * q^92 + 2336244 * q^93 - 355400 * q^95 + 147456 * q^96 - 1937532 * q^97 - 1321024 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	4.00000	−	4.00000i	0.500000	−	0.500000i
$2$	4.00000	−	4.00000i	0.500000	−	0.500000i
$3$	23.8945	+	23.8945i	0.884983	+	0.884983i	0.994036	−	0.109053i	$-0.0347818\pi$
$3$	23.8945	+	23.8945i	0.884983	+	0.884983i	−0.109053	+	0.994036i	$0.534782\pi$
$4$		−	32.0000i		−	0.500000i
$5$	54.1055	−	112.684i	0.432844	−	0.901469i
$5$	54.1055	−	112.684i	0.432844	−	0.901469i
$6$	191.156			0.884983
$7$	−362.840	+	362.840i	−1.05784	+	1.05784i	−0.0596214	+	0.998221i	$0.518989\pi$
$7$	−362.840	+	362.840i	−1.05784	+	1.05784i	−0.998221	+	0.0596214i	$0.981011\pi$
$8$	−128.000	−	128.000i	−0.250000	−	0.250000i
$9$			412.898i			0.566390i
$10$	−234.313	−	667.156i	−0.234313	−	0.667156i
$11$	−1321.26			−0.992681			−0.496340	−	0.868128i	$-0.665323\pi$
$11$	−1321.26			−0.992681			−0.496340	+	0.868128i	$0.665323\pi$
$12$	764.625	−	764.625i	0.442492	−	0.442492i
$13$	254.789	+	254.789i	0.115971	+	0.115971i	0.762711	−	0.646740i	$-0.223868\pi$
$13$	254.789	+	254.789i	0.115971	+	0.115971i	−0.646740	+	0.762711i	$0.723868\pi$
$14$			2902.72i			1.05784i
$15$	3985.35	−	1399.70i	1.18084	−	0.414725i
$16$	−1024.00			−0.250000
$17$	4398.15	−	4398.15i	0.895206	−	0.895206i	−0.0998010	−	0.995007i	$-0.531821\pi$
$17$	4398.15	−	4398.15i	0.895206	−	0.895206i	0.995007	+	0.0998010i	$0.0318206\pi$
$18$	1651.59	+	1651.59i	0.283195	+	0.283195i
$19$			819.171i			0.119430i	0.998215	+	0.0597151i	$0.0190192\pi$
$19$			819.171i			0.119430i	−0.998215	+	0.0597151i	$0.980981\pi$
$20$	−3605.88	−	1731.37i	−0.450735	−	0.216422i
$21$	−17339.8			−1.87235
$22$	−5285.03	+	5285.03i	−0.496340	+	0.496340i
$23$	11135.5	+	11135.5i	0.915218	+	0.915218i	0.996677	−	0.0814587i	$-0.0259579\pi$
$23$	11135.5	+	11135.5i	0.915218	+	0.915218i	−0.0814587	+	0.996677i	$0.525958\pi$
$24$		−	6117.00i		−	0.442492i
$25$	−9770.20	−	12193.6i	−0.625293	−	0.780390i
$26$	2038.31			0.115971
$27$	7553.11	−	7553.11i	0.383738	−	0.383738i
$28$	11610.9	+	11610.9i	0.528921	+	0.528921i
$29$			27495.1i			1.12736i	0.825995	+	0.563678i	$0.190614\pi$
$29$			27495.1i			1.12736i	−0.825995	+	0.563678i	$0.809386\pi$
$30$	10342.6	−	21540.2i	0.383059	−	0.797785i
$31$	15086.4			0.506408			0.253204	−	0.967413i	$-0.418516\pi$
$31$	15086.4			0.506408			0.253204	+	0.967413i	$0.418516\pi$
$32$	−4096.00	+	4096.00i	−0.125000	+	0.125000i
$33$	−31570.9	−	31570.9i	−0.878506	−	0.878506i
$34$		−	35185.2i		−	0.895206i
$35$	21254.5	+	60517.7i	0.495732	+	1.41149i
$36$	13212.7			0.283195
$37$	21550.0	−	21550.0i	0.425444	−	0.425444i	−0.461629	−	0.887073i	$-0.652735\pi$
$37$	21550.0	−	21550.0i	0.425444	−	0.425444i	0.887073	+	0.461629i	$0.152735\pi$
$38$	3276.68	+	3276.68i	0.0597151	+	0.0597151i
$39$			12176.1i			0.205265i
$40$	−21349.0	+	7498.01i	−0.333578	+	0.117156i
$41$	−45644.1			−0.662267			−0.331134	−	0.943584i	$-0.607431\pi$
$41$	−45644.1			−0.662267			−0.331134	+	0.943584i	$0.607431\pi$
$42$	−69359.2	+	69359.2i	−0.936173	+	0.936173i
$43$	−78126.4	−	78126.4i	−0.982635	−	0.982635i	0.0172164	−	0.999852i	$-0.494520\pi$
$43$	−78126.4	−	78126.4i	−0.982635	−	0.982635i	−0.999852	+	0.0172164i	$0.994520\pi$
$44$			42280.3i			0.496340i
$45$	46526.9	+	22340.0i	0.510583	+	0.245158i
$46$	89083.7			0.915218
$47$	−1995.12	+	1995.12i	−0.0192166	+	0.0192166i	−0.716650	−	0.697433i	$-0.754325\pi$
$47$	−1995.12	+	1995.12i	−0.0192166	+	0.0192166i	0.697433	+	0.716650i	$0.254325\pi$
$48$	−24468.0	−	24468.0i	−0.221246	−	0.221246i
$49$		−	145657.i		−	1.23806i
$50$	−87855.2	−	9693.60i	−0.702842	−	0.0775488i
$51$	210184.			1.58448
$52$	8153.25	−	8153.25i	0.0579857	−	0.0579857i
$53$	106138.	+	106138.i	0.712921	+	0.712921i	0.967145	−	0.254224i	$-0.0818202\pi$
$53$	106138.	+	106138.i	0.712921	+	0.712921i	−0.254224	+	0.967145i	$0.581820\pi$
$54$		−	60424.9i		−	0.383738i
$55$	−71487.3	+	148884.i	−0.429676	+	0.894871i
$56$	92887.0			0.528921
$57$	−19573.7	+	19573.7i	−0.105694	+	0.105694i
$58$	109980.	+	109980.i	0.563678	+	0.563678i
$59$		−	64466.6i		−	0.313891i	−0.987607	−	0.156945i	$-0.949835\pi$
$59$		−	64466.6i		−	0.313891i	0.987607	−	0.156945i	$-0.0501647\pi$
$60$	−44790.4	−	127531.i	−0.207363	−	0.590422i
$61$	−320767.			−1.41319			−0.706594	−	0.707620i	$-0.749769\pi$
$61$	−320767.			−1.41319			−0.706594	+	0.707620i	$0.749769\pi$
$62$	60345.6	−	60345.6i	0.253204	−	0.253204i
$63$	−149816.	−	149816.i	−0.599151	−	0.599151i
$64$			32768.0i			0.125000i
$65$	42496.0	−	14925.1i	0.154742	−	0.0543471i
$66$	−252567.			−0.878506
$67$	−35044.1	+	35044.1i	−0.116517	+	0.116517i	−0.762961	−	0.646444i	$-0.776255\pi$
$67$	−35044.1	+	35044.1i	−0.116517	+	0.116517i	0.646444	+	0.762961i	$0.276255\pi$
$68$	−140741.	−	140741.i	−0.447603	−	0.447603i
$69$			532153.i			1.61990i
$70$	327089.	+	157053.i	0.953612	+	0.457880i
$71$	−251708.			−0.703271			−0.351636	−	0.936137i	$-0.614374\pi$
$71$	−251708.			−0.703271			−0.351636	+	0.936137i	$0.614374\pi$
$72$	52851.0	−	52851.0i	0.141597	−	0.141597i
$73$	326907.	+	326907.i	0.840342	+	0.840342i	0.988903	−	0.148561i	$-0.0474642\pi$
$73$	326907.	+	326907.i	0.840342	+	0.840342i	−0.148561	+	0.988903i	$0.547464\pi$
$74$		−	172400.i		−	0.425444i
$75$	57906.0	−	524815.i	0.137259	−	1.24401i
$76$	26213.5			0.0597151
$77$	479405.	−	479405.i	1.05010	−	1.05010i
$78$	48704.5	+	48704.5i	0.102633	+	0.102633i
$79$			25722.3i			0.0521710i	0.999660	+	0.0260855i	$0.00830421\pi$
$79$			25722.3i			0.0521710i	−0.999660	+	0.0260855i	$0.991696\pi$
$80$	−55404.0	+	115388.i	−0.108211	+	0.225367i
$81$	661959.			1.24559
$82$	−182577.	+	182577.i	−0.331134	+	0.331134i
$83$	−123104.	−	123104.i	−0.215298	−	0.215298i	0.591216	−	0.806513i	$-0.298648\pi$
$83$	−123104.	−	123104.i	−0.215298	−	0.215298i	−0.806513	+	0.591216i	$0.798648\pi$
$84$			554873.i			0.936173i
$85$	−257636.	−	733563.i	−0.419516	−	1.19449i
$86$	−625011.			−0.982635
$87$	−656982.	+	656982.i	−0.997690	+	0.997690i
$88$	169121.	+	169121.i	0.248170	+	0.248170i
$89$		−	198715.i		−	0.281878i	−0.990018	−	0.140939i	$-0.954988\pi$
$89$		−	198715.i		−	0.281878i	0.990018	−	0.140939i	$-0.0450121\pi$
$90$	275468.	−	96747.3i	0.377871	−	0.132712i
$91$	−184895.			−0.245359
$92$	356335.	−	356335.i	0.457609	−	0.457609i
$93$	360482.	+	360482.i	0.448162	+	0.448162i
$94$			15961.0i			0.0192166i
$95$	92307.2	+	44321.6i	0.107663	+	0.0516946i
$96$	−195744.			−0.221246
$97$	−738798.	+	738798.i	−0.809488	+	0.809488i	−0.984556	−	0.175068i	$-0.943985\pi$
$97$	−738798.	+	738798.i	−0.809488	+	0.809488i	0.175068	+	0.984556i	$0.443985\pi$
$98$	−582627.	−	582627.i	−0.619031	−	0.619031i
$99$		−	545545.i		−	0.562244i
$100$	−390195.	+	312646.i	−0.390195	+	0.312646i
$101$	−122972.			−0.119355			−0.0596775	−	0.998218i	$-0.519007\pi$
$101$	−122972.			−0.119355			−0.0596775	+	0.998218i	$0.519007\pi$
$102$	840734.	−	840734.i	0.792242	−	0.792242i
$103$	419455.	+	419455.i	0.383860	+	0.383860i	0.872491	−	0.488631i	$-0.162503\pi$
$103$	419455.	+	419455.i	0.383860	+	0.383860i	−0.488631	+	0.872491i	$0.662503\pi$
$104$		−	65226.0i		−	0.0579857i
$105$	−938177.	+	1.95391e6i	−0.810433	+	1.68786i
$106$	849100.			0.712921
$107$	534643.	−	534643.i	0.436428	−	0.436428i	−0.454380	−	0.890808i	$-0.650139\pi$
$107$	534643.	−	534643.i	0.436428	−	0.436428i	0.890808	+	0.454380i	$0.150139\pi$
$108$	−241699.	−	241699.i	−0.191869	−	0.191869i
$109$		−	1.99464e6i		−	1.54023i	−0.637908	−	0.770113i	$-0.720200\pi$
$109$		−	1.99464e6i		−	1.54023i	0.637908	−	0.770113i	$-0.279800\pi$
$110$	309588.	+	881486.i	0.232598	+	0.662273i
$111$	1.02985e6			0.753021
$112$	371548.	−	371548.i	0.264461	−	0.264461i
$113$	−599768.	−	599768.i	−0.415669	−	0.415669i	0.468039	−	0.883708i	$-0.344961\pi$
$113$	−599768.	−	599768.i	−0.415669	−	0.415669i	−0.883708	+	0.468039i	$0.844961\pi$
$114$			156590.i			0.105694i
$115$	1.85727e6	−	652295.i	1.22119	−	0.428894i
$116$	879842.			0.563678
$117$	−105202.	+	105202.i	−0.0656850	+	0.0656850i
$118$	−257866.	−	257866.i	−0.156945	−	0.156945i
$119$			3.19165e6i			1.89397i
$120$	−689286.	−	330963.i	−0.398892	−	0.191530i
$121$	−25838.1			−0.0145849
$122$	−1.28307e6	+	1.28307e6i	−0.706594	+	0.706594i
$123$	−1.09065e6	−	1.09065e6i	−0.586095	−	0.586095i
$124$		−	482764.i		−	0.253204i
$125$	−1.90264e6	+	441201.i	−0.974152	+	0.225895i
$126$	−1.19853e6			−0.599151
$127$	−1.53367e6	+	1.53367e6i	−0.748724	+	0.748724i	−0.974240	−	0.225516i	$-0.927593\pi$
$127$	−1.53367e6	+	1.53367e6i	−0.748724	+	0.748724i	0.225516	+	0.974240i	$0.427593\pi$
$128$	131072.	+	131072.i	0.0625000	+	0.0625000i
$129$		−	3.73359e6i		−	1.73923i
$130$	110284.	−	229684.i	0.0501975	−	0.104545i
$131$	2.73248e6			1.21547			0.607734	−	0.794141i	$-0.292079\pi$
$131$	2.73248e6			1.21547			0.607734	+	0.794141i	$0.292079\pi$
$132$	−1.01027e6	+	1.01027e6i	−0.439253	+	0.439253i
$133$	−297228.	−	297228.i	−0.126338	−	0.126338i
$134$			280353.i			0.116517i
$135$	−442447.	−	1.25978e6i	−0.179829	−	0.512026i
$136$	−1.12593e6			−0.447603
$137$	1.14362e6	−	1.14362e6i	0.444753	−	0.444753i	−0.448853	−	0.893606i	$-0.648167\pi$
$137$	1.14362e6	−	1.14362e6i	0.444753	−	0.444753i	0.893606	+	0.448853i	$0.148167\pi$
$138$	2.12861e6	+	2.12861e6i	0.809952	+	0.809952i
$139$			1.81621e6i			0.676272i	0.941097	+	0.338136i	$0.109796\pi$
$139$			1.81621e6i			0.676272i	−0.941097	+	0.338136i	$0.890204\pi$
$140$	1.93657e6	−	680144.i	0.705746	−	0.247866i
$141$	−95345.2			−0.0340127
$142$	−1.00683e6	+	1.00683e6i	−0.351636	+	0.351636i
$143$	−336642.	−	336642.i	−0.115123	−	0.115123i
$144$		−	422808.i		−	0.141597i
$145$	3.09824e6	+	1.48763e6i	1.01628	+	0.487969i
$146$	2.61526e6			0.840342
$147$	3.48040e6	−	3.48040e6i	1.09566	−	1.09566i
$148$	−689600.	−	689600.i	−0.212722	−	0.212722i
$149$			4.57708e6i			1.38366i	0.722060	+	0.691830i	$0.243195\pi$
$149$			4.57708e6i			1.38366i	−0.722060	+	0.691830i	$0.756805\pi$
$150$	−1.86764e6	−	2.33088e6i	−0.553373	−	0.690632i
$151$	−6.59081e6			−1.91429			−0.957145	−	0.289608i	$-0.906475\pi$
$151$	−6.59081e6			−1.91429			−0.957145	+	0.289608i	$0.906475\pi$
$152$	104854.	−	104854.i	0.0298575	−	0.0298575i
$153$	1.81599e6	+	1.81599e6i	0.507036	+	0.507036i
$154$		−	3.83524e6i		−	1.05010i
$155$	816256.	−	1.69999e6i	0.219195	−	0.456511i
$156$	389636.			0.102633
$157$	2.59513e6	−	2.59513e6i	0.670594	−	0.670594i	−0.287259	−	0.957853i	$-0.592744\pi$
$157$	2.59513e6	−	2.59513e6i	0.670594	−	0.670594i	0.957853	+	0.287259i	$0.0927439\pi$
$158$	102889.	+	102889.i	0.0260855	+	0.0260855i
$159$			5.07222e6i			1.26185i
$160$	239936.	+	683168.i	0.0585782	+	0.166789i
$161$	−8.08078e6			−1.93631
$162$	2.64784e6	−	2.64784e6i	0.622796	−	0.622796i
$163$	−206143.	−	206143.i	−0.0475999	−	0.0475999i	0.682906	−	0.730506i	$-0.260716\pi$
$163$	−206143.	−	206143.i	−0.0475999	−	0.0475999i	−0.730506	+	0.682906i	$0.760716\pi$
$164$			1.46061e6i			0.331134i
$165$	−5.26567e6	+	1.84936e6i	−1.17220	+	0.411690i
$166$	−984835.			−0.215298
$167$	−2.54852e6	+	2.54852e6i	−0.547191	+	0.547191i	−0.925627	−	0.378436i	$-0.876462\pi$
$167$	−2.54852e6	+	2.54852e6i	−0.547191	+	0.547191i	0.378436	+	0.925627i	$0.376462\pi$
$168$	2.21949e6	+	2.21949e6i	0.468086	+	0.468086i
$169$		−	4.69697e6i		−	0.973101i
$170$	−3.96479e6	−	1.90371e6i	−0.807001	−	0.387484i
$171$	−338234.			−0.0676440
$172$	−2.50004e6	+	2.50004e6i	−0.491318	+	0.491318i
$173$	4.48960e6	+	4.48960e6i	0.867100	+	0.867100i	0.992150	−	0.125050i	$-0.0399092\pi$
$173$	4.48960e6	+	4.48960e6i	0.867100	+	0.867100i	−0.125050	+	0.992150i	$0.539909\pi$
$174$			5.25586e6i			0.997690i
$175$	7.96934e6	+	879306.i	1.48699	+	0.164069i
$176$	1.35297e6			0.248170
$177$	1.54040e6	−	1.54040e6i	0.277788	−	0.277788i
$178$	−794860.	−	794860.i	−0.140939	−	0.140939i
$179$		−	9.36798e6i		−	1.63338i	−0.577078	−	0.816689i	$-0.695807\pi$
$179$		−	9.36798e6i		−	1.63338i	0.577078	−	0.816689i	$-0.304193\pi$
$180$	714882.	−	1.48886e6i	0.122579	−	0.255291i
$181$	7.30958e6			1.23270			0.616349	−	0.787473i	$-0.288611\pi$
$181$	7.30958e6			1.23270			0.616349	+	0.787473i	$0.288611\pi$
$182$	−739581.	+	739581.i	−0.122679	+	0.122679i
$183$	−7.66457e6	−	7.66457e6i	−1.25065	−	1.25065i
$184$		−	2.85068e6i		−	0.457609i
$185$	−1.26236e6	−	3.59430e6i	−0.199374	−	0.567675i
$186$	2.88386e6			0.448162
$187$	−5.81109e6	+	5.81109e6i	−0.888654	+	0.888654i
$188$	63844.0	+	63844.0i	0.00960830	+	0.00960830i
$189$			5.48114e6i			0.811868i
$190$	546515.	−	191942.i	0.0796786	−	0.0279840i
$191$	8.54252e6			1.22599			0.612994	−	0.790088i	$-0.289965\pi$
$191$	8.54252e6			1.22599			0.612994	+	0.790088i	$0.289965\pi$
$192$	−782976.	+	782976.i	−0.110623	+	0.110623i
$193$	7.08708e6	+	7.08708e6i	0.985815	+	0.985815i	0.999901	−	0.0140856i	$-0.00448374\pi$
$193$	7.08708e6	+	7.08708e6i	0.985815	+	0.985815i	−0.0140856	+	0.999901i	$0.504484\pi$
$194$			5.91038e6i			0.809488i
$195$	1.37205e6	+	658795.i	0.185040	+	0.0888478i
$196$	−4.66101e6			−0.619031
$197$	5.09350e6	−	5.09350e6i	0.666220	−	0.666220i	−0.290619	−	0.956839i	$-0.593861\pi$
$197$	5.09350e6	−	5.09350e6i	0.666220	−	0.666220i	0.956839	+	0.290619i	$0.0938611\pi$
$198$	−2.18218e6	−	2.18218e6i	−0.281122	−	0.281122i
$199$		−	2.50957e6i		−	0.318449i	−0.987242	−	0.159224i	$-0.949101\pi$
$199$		−	2.50957e6i		−	0.318449i	0.987242	−	0.159224i	$-0.0508993\pi$
$200$	−310195.	+	2.81137e6i	−0.0387744	+	0.351421i
$201$	−1.67473e6			−0.206232
$202$	−491887.	+	491887.i	−0.0596775	+	0.0596775i
$203$	−9.97631e6	−	9.97631e6i	−1.19256	−	1.19256i
$204$		−	6.72587e6i		−	0.792242i
$205$	−2.46960e6	+	5.14335e6i	−0.286658	+	0.597013i
$206$	3.35564e6			0.383860
$207$	−4.59781e6	+	4.59781e6i	−0.518370	+	0.518370i
$208$	−260904.	−	260904.i	−0.0289928	−	0.0289928i
$209$		−	1.08234e6i		−	0.118556i
$210$	4.06293e6	+	1.15684e7i	0.438714	+	1.24915i
$211$	1.54519e6			0.164488			0.0822442	−	0.996612i	$-0.473791\pi$
$211$	1.54519e6			0.164488			0.0822442	+	0.996612i	$0.473791\pi$
$212$	3.39640e6	−	3.39640e6i	0.356460	−	0.356460i
$213$	−6.01446e6	−	6.01446e6i	−0.622383	−	0.622383i
$214$		−	4.27714e6i		−	0.436428i
$215$	−1.30306e7	+	4.57650e6i	−1.31114	+	0.460488i
$216$	−1.93360e6			−0.191869
$217$	−5.47395e6	+	5.47395e6i	−0.535700	+	0.535700i
$218$	−7.97855e6	−	7.97855e6i	−0.770113	−	0.770113i
$219$			1.56226e7i			1.48738i
$220$	4.76429e6	+	2.28759e6i	0.447435	+	0.214838i
$221$	2.24120e6			0.207637
$222$	4.11942e6	−	4.11942e6i	0.376510	−	0.376510i
$223$	3.42480e6	+	3.42480e6i	0.308831	+	0.308831i	0.844456	−	0.535625i	$-0.179924\pi$
$223$	3.42480e6	+	3.42480e6i	0.308831	+	0.308831i	−0.535625	+	0.844456i	$0.679924\pi$
$224$		−	2.97238e6i		−	0.264461i
$225$	5.03472e6	−	4.03410e6i	0.442005	−	0.354159i
$226$	−4.79814e6			−0.415669
$227$	1.45900e6	−	1.45900e6i	0.124732	−	0.124732i	−0.641985	−	0.766717i	$-0.721889\pi$
$227$	1.45900e6	−	1.45900e6i	0.124732	−	0.124732i	0.766717	+	0.641985i	$0.221889\pi$
$228$	626359.	+	626359.i	0.0528468	+	0.0528468i
$229$		−	1.46667e7i		−	1.22131i	−0.791895	−	0.610657i	$-0.790905\pi$
$229$		−	1.46667e7i		−	1.22131i	0.791895	−	0.610657i	$-0.209095\pi$
$230$	4.81991e6	−	1.00383e7i	0.396146	−	0.825041i
$231$	2.29103e7			1.85864
$232$	3.51937e6	−	3.51937e6i	0.281839	−	0.281839i
$233$	1.55030e7	+	1.55030e7i	1.22560	+	1.22560i	0.965613	+	0.259982i	$0.0837167\pi$
$233$	1.55030e7	+	1.55030e7i	1.22560	+	1.22560i	0.259982	+	0.965613i	$0.416283\pi$
$234$			841616.i			0.0656850i
$235$	116871.	+	332765.i	0.00900538	+	0.0256409i
$236$	−2.06293e6			−0.156945
$237$	−614623.	+	614623.i	−0.0461704	+	0.0461704i
$238$	1.27666e7	+	1.27666e7i	0.946987	+	0.946987i
$239$		−	1.47874e7i		−	1.08318i	−0.840644	−	0.541588i	$-0.817823\pi$
$239$		−	1.47874e7i		−	1.08318i	0.840644	−	0.541588i	$-0.182177\pi$
$240$	−4.08100e6	+	1.43329e6i	−0.295211	+	0.103681i
$241$	−2.05498e7			−1.46810			−0.734052	−	0.679094i	$-0.762373\pi$
$241$	−2.05498e7			−1.46810			−0.734052	+	0.679094i	$0.762373\pi$
$242$	−103352.	+	103352.i	−0.00729246	+	0.00729246i
$243$	1.03110e7	+	1.03110e7i	0.718591	+	0.718591i
$244$			1.02645e7i			0.706594i
$245$	−1.64131e7	−	7.88082e6i	−1.11607	−	0.535887i
$246$	−8.72516e6			−0.586095
$247$	−208716.	+	208716.i	−0.0138505	+	0.0138505i
$248$	−1.93106e6	−	1.93106e6i	−0.126602	−	0.126602i
$249$		−	5.88304e6i		−	0.381069i
$250$	−5.84576e6	+	9.37536e6i	−0.374128	+	0.600023i
$251$	2.58613e6			0.163542			0.0817709	−	0.996651i	$-0.473942\pi$
$251$	2.58613e6			0.163542			0.0817709	+	0.996651i	$0.473942\pi$
$252$	−4.79411e6	+	4.79411e6i	−0.299576	+	0.299576i
$253$	−1.47128e7	−	1.47128e7i	−0.908519	−	0.908519i
$254$			1.22694e7i			0.748724i
$255$	1.13721e7	−	2.36842e7i	0.685834	−	1.42836i
$256$	1.04858e6			0.0625000
$257$	−8.90392e6	+	8.90392e6i	−0.524544	+	0.524544i	−0.918940	−	0.394397i	$-0.870954\pi$
$257$	−8.90392e6	+	8.90392e6i	−0.524544	+	0.524544i	0.394397	+	0.918940i	$0.370954\pi$
$258$	−1.49344e7	−	1.49344e7i	−0.869616	−	0.869616i
$259$			1.56384e7i			0.900105i
$260$	−477602.	−	1.35987e6i	−0.0271736	−	0.0773710i
$261$	−1.13527e7			−0.638523
$262$	1.09299e7	−	1.09299e7i	0.607734	−	0.607734i
$263$	1.24065e7	+	1.24065e7i	0.681996	+	0.681996i	0.960450	−	0.278454i	$-0.0898219\pi$
$263$	1.24065e7	+	1.24065e7i	0.681996	+	0.681996i	−0.278454	+	0.960450i	$0.589822\pi$
$264$			8.08214e6i			0.439253i
$265$	1.77026e7	−	6.21734e6i	0.951259	−	0.334093i
$266$	−2.37782e6			−0.126338
$267$	4.74820e6	−	4.74820e6i	0.249457	−	0.249457i
$268$	1.12141e6	+	1.12141e6i	0.0582587	+	0.0582587i
$269$			2.06412e7i			1.06042i	0.847866	+	0.530211i	$0.177887\pi$
$269$			2.06412e7i			1.06042i	−0.847866	+	0.530211i	$0.822113\pi$
$270$	−6.80889e6	−	3.26931e6i	−0.345928	−	0.166098i
$271$	−2.50344e7			−1.25785			−0.628926	−	0.777465i	$-0.716505\pi$
$271$	−2.50344e7			−1.25785			−0.628926	+	0.777465i	$0.716505\pi$
$272$	−4.50370e6	+	4.50370e6i	−0.223802	+	0.223802i
$273$	−4.41799e6	−	4.41799e6i	−0.217138	−	0.217138i
$274$		−	9.14894e6i		−	0.444753i
$275$	1.29090e7	+	1.61109e7i	0.620716	+	0.774678i
$276$	1.70289e7			0.809952
$277$	1.30860e7	−	1.30860e7i	0.615699	−	0.615699i	−0.328726	−	0.944425i	$-0.606619\pi$
$277$	1.30860e7	−	1.30860e7i	0.615699	−	0.615699i	0.944425	+	0.328726i	$0.106619\pi$
$278$	7.26483e6	+	7.26483e6i	0.338136	+	0.338136i
$279$			6.22914e6i			0.286824i
$280$	5.02570e6	−	1.04668e7i	0.228940	−	0.476806i
$281$	7.83239e6			0.353001			0.176500	−	0.984301i	$-0.443522\pi$
$281$	7.83239e6			0.353001			0.176500	+	0.984301i	$0.443522\pi$
$282$	−381381.	+	381381.i	−0.0170064	+	0.0170064i
$283$	−3.44660e6	−	3.44660e6i	−0.152066	−	0.152066i	0.626974	−	0.779040i	$-0.284293\pi$
$283$	−3.44660e6	−	3.44660e6i	−0.152066	−	0.152066i	−0.779040	+	0.626974i	$0.784293\pi$
$284$			8.05467e6i			0.351636i
$285$	1.14659e6	+	3.26468e6i	0.0495307	+	0.141028i
$286$	−2.69314e6			−0.115123
$287$	1.65615e7	−	1.65615e7i	0.700575	−	0.700575i
$288$	−1.69123e6	−	1.69123e6i	−0.0707987	−	0.0707987i
$289$		−	1.45499e7i		−	0.602789i
$290$	1.83435e7	−	6.44244e6i	0.752122	−	0.264154i
$291$	−3.53065e7			−1.43277
$292$	1.04610e7	−	1.04610e7i	0.420171	−	0.420171i
$293$	2.34676e6	+	2.34676e6i	0.0932965	+	0.0932965i	0.752215	−	0.658918i	$-0.228986\pi$
$293$	2.34676e6	+	2.34676e6i	0.0932965	+	0.0932965i	−0.658918	+	0.752215i	$0.728986\pi$
$294$		−	2.78432e7i		−	1.09566i
$295$	−7.26433e6	−	3.48799e6i	−0.282963	−	0.135866i
$296$	−5.51680e6			−0.212722
$297$	−9.97960e6	+	9.97960e6i	−0.380929	+	0.380929i
$298$	1.83083e7	+	1.83083e7i	0.691830	+	0.691830i
$299$			5.67439e6i			0.212278i
$300$	−1.67941e7	−	1.85299e6i	−0.622003	−	0.0686294i
$301$	5.66948e7			2.07895
$302$	−2.63632e7	+	2.63632e7i	−0.957145	+	0.957145i
$303$	−2.93835e6	−	2.93835e6i	−0.105627	−	0.105627i
$304$		−	838831.i		−	0.0298575i
$305$	−1.73552e7	+	3.61451e7i	−0.611689	+	1.27394i
$306$	1.45279e7			0.507036
$307$	−3.16294e7	+	3.16294e7i	−1.09314	+	1.09314i	−0.0979492	+	0.995191i	$0.531228\pi$
$307$	−3.16294e7	+	3.16294e7i	−1.09314	+	1.09314i	−0.995191	+	0.0979492i	$0.968772\pi$
$308$	−1.53410e7	−	1.53410e7i	−0.525050	−	0.525050i
$309$			2.00453e7i			0.679420i
$310$	−3.53493e6	−	1.00650e7i	−0.118658	−	0.337853i
$311$	2.07488e6			0.0689781			0.0344891	−	0.999405i	$-0.489020\pi$
$311$	2.07488e6			0.0689781			0.0344891	+	0.999405i	$0.489020\pi$
$312$	1.55855e6	−	1.55855e6i	0.0513163	−	0.0513163i
$313$	−3.33290e7	−	3.33290e7i	−1.08690	−	1.08690i	−0.995846	−	0.0910547i	$-0.970976\pi$
$313$	−3.33290e7	−	3.33290e7i	−1.08690	−	1.08690i	−0.0910547	−	0.995846i	$-0.529024\pi$
$314$		−	2.07610e7i		−	0.670594i
$315$	−2.49877e7	+	8.77595e6i	−0.799455	+	0.280777i
$316$	823114.			0.0260855
$317$	4.17645e6	−	4.17645e6i	0.131108	−	0.131108i	−0.638507	−	0.769616i	$-0.720448\pi$
$317$	4.17645e6	−	4.17645e6i	0.131108	−	0.131108i	0.769616	+	0.638507i	$0.220448\pi$
$318$	2.02889e7	+	2.02889e7i	0.630923	+	0.630923i
$319$		−	3.63281e7i		−	1.11910i
$320$	3.69242e6	+	1.77293e6i	0.112684	+	0.0541055i
$321$	2.55501e7			0.772462
$322$	−3.23231e7	+	3.23231e7i	−0.968156	+	0.968156i
$323$	3.60284e6	+	3.60284e6i	0.106915	+	0.106915i
$324$		−	2.11827e7i		−	0.622796i
$325$	617456.	−	5.59614e6i	0.0179869	−	0.163019i
$326$	−1.64914e6			−0.0475999
$327$	4.76609e7	−	4.76609e7i	1.36307	−	1.36307i
$328$	5.84245e6	+	5.84245e6i	0.165567	+	0.165567i
$329$		−	1.44782e6i		−	0.0406563i
$330$	−1.36652e7	+	2.84601e7i	−0.380256	+	0.791946i
$331$	−1.41314e7			−0.389673			−0.194837	−	0.980836i	$-0.562418\pi$
$331$	−1.41314e7			−0.389673			−0.194837	+	0.980836i	$0.562418\pi$
$332$	−3.93934e6	+	3.93934e6i	−0.107649	+	0.107649i
$333$	8.89796e6	+	8.89796e6i	0.240967	+	0.240967i
$334$			2.03882e7i			0.547191i
$335$	2.05282e6	+	5.84498e6i	0.0546030	+	0.155471i
$336$	1.77559e7			0.468086
$337$	2.19464e7	−	2.19464e7i	0.573420	−	0.573420i	−0.359662	−	0.933083i	$-0.617108\pi$
$337$	2.19464e7	−	2.19464e7i	0.573420	−	0.573420i	0.933083	+	0.359662i	$0.117108\pi$
$338$	−1.87879e7	−	1.87879e7i	−0.486551	−	0.486551i
$339$		−	2.86623e7i		−	0.735720i
$340$	−2.34740e7	+	8.24434e6i	−0.597243	+	0.209758i
$341$	−1.99330e7			−0.502701
$342$	−1.35294e6	+	1.35294e6i	−0.0338220	+	0.0338220i
$343$	1.01623e7	+	1.01623e7i	0.251831	+	0.251831i
$344$			2.00004e7i			0.491318i
$345$	5.99650e7	+	2.87924e7i	1.46029	+	0.701166i
$346$	3.59168e7			0.867100
$347$	3.70959e7	−	3.70959e7i	0.887846	−	0.887846i	−0.106470	−	0.994316i	$-0.533955\pi$
$347$	3.70959e7	−	3.70959e7i	0.887846	−	0.887846i	0.994316	+	0.106470i	$0.0339549\pi$
$348$	2.10234e7	+	2.10234e7i	0.498845	+	0.498845i
$349$			5.75499e7i			1.35384i	0.736056	+	0.676921i	$0.236686\pi$
$349$			5.75499e7i			1.35384i	−0.736056	+	0.676921i	$0.763314\pi$
$350$	3.53946e7	−	2.83601e7i	0.825530	−	0.661461i
$351$	3.84890e6			0.0890051
$352$	5.41187e6	−	5.41187e6i	0.124085	−	0.124085i
$353$	−5.20285e7	−	5.20285e7i	−1.18282	−	1.18282i	−0.979011	−	0.203805i	$-0.934669\pi$
$353$	−5.20285e7	−	5.20285e7i	−1.18282	−	1.18282i	−0.203805	−	0.979011i	$-0.565331\pi$
$354$		−	1.23232e7i		−	0.277788i
$355$	−1.36188e7	+	2.83634e7i	−0.304406	+	0.633977i
$356$	−6.35888e6			−0.140939
$357$	−7.62630e7	+	7.62630e7i	−1.67614	+	1.67614i
$358$	−3.74719e7	−	3.74719e7i	−0.816689	−	0.816689i
$359$		−	3.95295e7i		−	0.854354i	−0.904168	−	0.427177i	$-0.859508\pi$
$359$		−	3.95295e7i		−	0.854354i	0.904168	−	0.427177i	$-0.140492\pi$
$360$	−3.09591e6	−	8.81497e6i	−0.0663562	−	0.188935i
$361$	4.63748e7			0.985736
$362$	2.92383e7	−	2.92383e7i	0.616349	−	0.616349i
$363$	−617389.	−	617389.i	−0.0129074	−	0.0129074i
$364$			5.91665e6i			0.122679i
$365$	5.45246e7	−	1.91496e7i	1.12128	−	0.393806i
$366$	−6.13166e7			−1.25065
$367$	−6.40678e7	+	6.40678e7i	−1.29611	+	1.29611i	−0.365168	+	0.930941i	$0.618989\pi$
$367$	−6.40678e7	+	6.40678e7i	−1.29611	+	1.29611i	−0.930941	+	0.365168i	$0.881011\pi$
$368$	−1.14027e7	−	1.14027e7i	−0.228805	−	0.228805i
$369$		−	1.88464e7i		−	0.375102i
$370$	−1.94267e7	−	9.32778e6i	−0.383524	−	0.184151i
$371$	−7.70219e7			−1.50832
$372$	1.15354e7	−	1.15354e7i	0.224081	−	0.224081i
$373$	1.23271e7	+	1.23271e7i	0.237539	+	0.237539i	0.815830	−	0.578291i	$-0.196280\pi$
$373$	1.23271e7	+	1.23271e7i	0.237539	+	0.237539i	−0.578291	+	0.815830i	$0.696280\pi$
$374$			4.64887e7i			0.888654i
$375$	−5.60050e7	−	3.49204e7i	−1.06202	−	0.662194i
$376$	510752.			0.00960830
$377$	−7.00544e6	+	7.00544e6i	−0.130741	+	0.130741i
$378$	2.19246e7	+	2.19246e7i	0.405934	+	0.405934i
$379$			1.03307e8i			1.89764i	0.315817	+	0.948820i	$0.397721\pi$
$379$			1.03307e8i			1.89764i	−0.315817	+	0.948820i	$0.602279\pi$
$380$	1.41829e6	−	2.95383e6i	0.0258473	−	0.0538313i
$381$	−7.32928e7			−1.32522
$382$	3.41701e7	−	3.41701e7i	0.612994	−	0.612994i
$383$	4.46875e7	+	4.46875e7i	0.795408	+	0.795408i	0.982368	−	0.186959i	$-0.0598632\pi$
$383$	4.46875e7	+	4.46875e7i	0.795408	+	0.795408i	−0.186959	+	0.982368i	$0.559863\pi$
$384$			6.26381e6i			0.110623i
$385$	−2.80827e7	−	7.99596e7i	−0.492103	−	1.40116i
$386$	5.66967e7			0.985815
$387$	3.22582e7	−	3.22582e7i	0.556555	−	0.556555i
$388$	2.36415e7	+	2.36415e7i	0.404744	+	0.404744i
$389$		−	6.33567e7i		−	1.07633i	−0.842841	−	0.538163i	$-0.819118\pi$
$389$		−	6.33567e7i		−	1.07633i	0.842841	−	0.538163i	$-0.180882\pi$
$390$	8.12339e6	−	2.85302e6i	0.136944	−	0.0480963i
$391$	9.79508e7			1.63862
$392$	−1.86441e7	+	1.86441e7i	−0.309515	+	0.309515i
$393$	6.52914e7	+	6.52914e7i	1.07567	+	1.07567i
$394$		−	4.07480e7i		−	0.666220i
$395$	2.89848e6	+	1.39172e6i	0.0470305	+	0.0225819i
$396$	−1.74574e7			−0.281122
$397$	5.75784e7	−	5.75784e7i	0.920213	−	0.920213i	−0.0768313	−	0.997044i	$-0.524480\pi$
$397$	5.75784e7	−	5.75784e7i	0.920213	−	0.920213i	0.997044	+	0.0768313i	$0.0244803\pi$
$398$	−1.00383e7	−	1.00383e7i	−0.159224	−	0.159224i
$399$		−	1.42043e7i		−	0.223614i
$400$	1.00047e7	+	1.24862e7i	0.156323	+	0.195098i
$401$	−3.99773e7			−0.619984			−0.309992	−	0.950739i	$-0.600326\pi$
$401$	−3.99773e7			−0.619984			−0.309992	+	0.950739i	$0.600326\pi$
$402$	−6.69891e6	+	6.69891e6i	−0.103116	+	0.103116i
$403$	3.84385e6	+	3.84385e6i	0.0587288	+	0.0587288i
$404$			3.93509e6i			0.0596775i
$405$	3.58156e7	−	7.45919e7i	0.539147	−	1.12286i
$406$	−7.98105e7			−1.19256
$407$	−2.84731e7	+	2.84731e7i	−0.422330	+	0.422330i
$408$	−2.69035e7	−	2.69035e7i	−0.396121	−	0.396121i
$409$			1.10793e8i			1.61936i	0.586870	+	0.809681i	$0.300360\pi$
$409$			1.10793e8i			1.61936i	−0.586870	+	0.809681i	$0.699640\pi$
$410$	1.06950e7	+	3.04518e7i	0.155178	+	0.441836i
$411$	5.46524e7			0.787198
$412$	1.34225e7	−	1.34225e7i	0.191930	−	0.191930i
$413$	2.33910e7	+	2.33910e7i	0.332047	+	0.332047i
$414$			3.67825e7i			0.518370i
$415$	−2.05325e7	+	7.21123e6i	−0.287274	+	0.100894i
$416$	−2.08723e6			−0.0289928
$417$	−4.33975e7	+	4.33975e7i	−0.598489	+	0.598489i
$418$	−4.32935e6	−	4.32935e6i	−0.0592780	−	0.0592780i
$419$		−	1.22089e8i		−	1.65972i	−0.557973	−	0.829859i	$-0.688421\pi$
$419$		−	1.22089e8i		−	1.65972i	0.557973	−	0.829859i	$-0.311579\pi$
$420$	6.25251e7	+	3.00217e7i	0.843931	+	0.405216i
$421$	−4.21420e7			−0.564766			−0.282383	−	0.959302i	$-0.591125\pi$
$421$	−4.21420e7			−0.564766			−0.282383	+	0.959302i	$0.591125\pi$
$422$	6.18077e6	−	6.18077e6i	0.0822442	−	0.0822442i
$423$	−823783.	−	823783.i	−0.0108841	−	0.0108841i
$424$		−	2.71712e7i		−	0.356460i
$425$	−9.66001e7	−	1.06585e7i	−1.25838	−	0.138844i
$426$	−4.81157e7			−0.622383
$427$	1.16387e8	−	1.16387e8i	1.49493	−	1.49493i
$428$	−1.71086e7	−	1.71086e7i	−0.218214	−	0.218214i
$429$		−	1.60878e7i		−	0.203763i
$430$	−3.38165e7	+	7.04285e7i	−0.425327	+	0.885815i
$431$	−3.91762e7			−0.489317			−0.244658	−	0.969609i	$-0.578676\pi$
$431$	−3.91762e7			−0.489317			−0.244658	+	0.969609i	$0.578676\pi$
$432$	−7.73438e6	+	7.73438e6i	−0.0959344	+	0.0959344i
$433$	−9.67310e7	−	9.67310e7i	−1.19152	−	1.19152i	−0.976640	−	0.214882i	$-0.931063\pi$
$433$	−9.67310e7	−	9.67310e7i	−1.19152	−	1.19152i	−0.214882	−	0.976640i	$-0.568937\pi$
$434$			4.37916e7i			0.535700i
$435$	3.84848e7	+	1.09577e8i	0.467543	+	1.33123i
$436$	−6.38284e7			−0.770113
$437$	−9.12185e6	+	9.12185e6i	−0.109305	+	0.109305i
$438$	6.24904e7	+	6.24904e7i	0.743688	+	0.743688i
$439$			7.95720e6i			0.0940517i	0.998894	+	0.0470258i	$0.0149743\pi$
$439$			7.95720e6i			0.0940517i	−0.998894	+	0.0470258i	$0.985026\pi$
$440$	2.82075e7	−	9.90680e6i	0.331137	−	0.116299i
$441$	6.01414e7			0.701225
$442$	8.96480e6	−	8.96480e6i	0.103818	−	0.103818i
$443$	8.63738e7	+	8.63738e7i	0.993507	+	0.993507i	0.999979	−	0.00647172i	$-0.00206003\pi$
$443$	8.63738e7	+	8.63738e7i	0.993507	+	0.993507i	−0.00647172	+	0.999979i	$0.502060\pi$
$444$		−	3.29553e7i		−	0.376510i
$445$	−2.23919e7	−	1.07516e7i	−0.254104	−	0.122009i
$446$	2.73984e7			0.308831
$447$	−1.09367e8	+	1.09367e8i	−1.22452	+	1.22452i
$448$	−1.18895e7	−	1.18895e7i	−0.132230	−	0.132230i
$449$			8.43204e7i			0.931523i	0.884910	+	0.465762i	$0.154220\pi$
$449$			8.43204e7i			0.931523i	−0.884910	+	0.465762i	$0.845780\pi$
$450$	4.00247e6	−	3.62753e7i	0.0439229	−	0.398082i
$451$	6.03077e7			0.657420
$452$	−1.91926e7	+	1.91926e7i	−0.207835	+	0.207835i
$453$	−1.57484e8	−	1.57484e8i	−1.69411	−	1.69411i
$454$		−	1.16720e7i		−	0.124732i
$455$	−1.00038e7	+	2.08347e7i	−0.106202	+	0.221183i
$456$	5.01087e6			0.0528468
$457$	−1.32039e7	+	1.32039e7i	−0.138341	+	0.138341i	−0.772886	−	0.634545i	$-0.781188\pi$
$457$	−1.32039e7	+	1.32039e7i	−0.138341	+	0.138341i	0.634545	+	0.772886i	$0.281188\pi$
$458$	−5.86670e7	−	5.86670e7i	−0.610657	−	0.610657i
$459$		−	6.64394e7i		−	0.687049i
$460$	−2.08734e7	−	5.94327e7i	−0.214447	−	0.610594i
$461$	9.28082e7			0.947291			0.473645	−	0.880716i	$-0.342938\pi$
$461$	9.28082e7			0.947291			0.473645	+	0.880716i	$0.342938\pi$
$462$	9.16413e7	−	9.16413e7i	0.929321	−	0.929321i
$463$	4.15624e7	+	4.15624e7i	0.418753	+	0.418753i	0.884774	−	0.466021i	$-0.154313\pi$
$463$	4.15624e7	+	4.15624e7i	0.418753	+	0.418753i	−0.466021	+	0.884774i	$0.654313\pi$
$464$		−	2.81549e7i		−	0.281839i
$465$	6.01245e7	−	2.11164e7i	0.597988	−	0.210020i
$466$	1.24024e8			1.22560
$467$	−5.74249e7	+	5.74249e7i	−0.563832	+	0.563832i	−0.930394	−	0.366562i	$-0.880535\pi$
$467$	−5.74249e7	+	5.74249e7i	−0.563832	+	0.563832i	0.366562	+	0.930394i	$0.380535\pi$
$468$	3.36646e6	+	3.36646e6i	0.0328425	+	0.0328425i
$469$		−	2.54308e7i		−	0.246514i
$470$	1.79854e6	+	863577.i	0.0173232	+	0.00831778i
$471$	1.24019e8			1.18693
$472$	−8.25172e6	+	8.25172e6i	−0.0784727	+	0.0784727i
$473$	1.03225e8	+	1.03225e8i	0.975443	+	0.975443i
$474$			4.91698e6i			0.0461704i
$475$	9.98864e6	−	8.00347e6i	0.0932021	−	0.0746788i
$476$	1.02133e8			0.946987
$477$	−4.38240e7	+	4.38240e7i	−0.403791	+	0.403791i
$478$	−5.91498e7	−	5.91498e7i	−0.541588	−	0.541588i
$479$		−	1.99190e7i		−	0.181243i	−0.995885	−	0.0906215i	$-0.971115\pi$
$479$		−	1.99190e7i		−	0.181243i	0.995885	−	0.0906215i	$-0.0288854\pi$
$480$	−1.05908e7	+	2.20572e7i	−0.0957648	+	0.199446i
$481$	1.09814e7			0.0986786
$482$	−8.21992e7	+	8.21992e7i	−0.734052	+	0.734052i
$483$	−1.93086e8	−	1.93086e8i	−1.71360	−	1.71360i
$484$			826818.i			0.00729246i
$485$	4.32774e7	+	1.23223e8i	0.379347	+	1.08011i
$486$	8.24879e7			0.718591
$487$	−4.50108e7	+	4.50108e7i	−0.389700	+	0.389700i	−0.874580	−	0.484881i	$-0.838863\pi$
$487$	−4.50108e7	+	4.50108e7i	−0.389700	+	0.389700i	0.484881	+	0.874580i	$0.338863\pi$
$488$	4.10581e7	+	4.10581e7i	0.353297	+	0.353297i
$489$		−	9.85139e6i		−	0.0842502i
$490$	−9.71758e7	+	3.41292e7i	−0.825980	+	0.290093i
$491$	−1.28208e8			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−1.28208e8			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$	−3.49007e7	+	3.49007e7i	−0.293048	+	0.293048i
$493$	1.20927e8	+	1.20927e8i	1.00922	+	1.00922i
$494$			1.66973e6i			0.0138505i
$495$	−6.14740e7	−	2.95170e7i	−0.506846	−	0.243364i
$496$	−1.54485e7			−0.126602
$497$	9.13299e7	−	9.13299e7i	0.743950	−	0.743950i
$498$	−2.35322e7	−	2.35322e7i	−0.190535	−	0.190535i
$499$		−	5.72011e7i		−	0.460366i	−0.973147	−	0.230183i	$-0.926068\pi$
$499$		−	5.72011e7i		−	0.460366i	0.973147	−	0.230183i	$-0.0739324\pi$
$500$	1.41184e7	+	6.08845e7i	0.112948	+	0.487076i
$501$	−1.21792e8			−0.968510
$502$	1.03445e7	−	1.03445e7i	0.0817709	−	0.0817709i
$503$	−6.91106e6	−	6.91106e6i	−0.0543051	−	0.0543051i	0.679433	−	0.733738i	$-0.262226\pi$
$503$	−6.91106e6	−	6.91106e6i	−0.0543051	−	0.0543051i	−0.733738	+	0.679433i	$0.762226\pi$
$504$			3.83529e7i			0.299576i
$505$	−6.65344e6	+	1.38569e7i	−0.0516621	+	0.107595i
$506$	−1.17703e8			−0.908519
$507$	1.12232e8	−	1.12232e8i	0.861178	−	0.861178i
$508$	4.90775e7	+	4.90775e7i	0.374362	+	0.374362i
$509$		−	1.61164e8i		−	1.22213i	−0.791582	−	0.611063i	$-0.790742\pi$
$509$		−	1.61164e8i		−	1.22213i	0.791582	−	0.611063i	$-0.209258\pi$
$510$	−4.92487e7	−	1.40225e8i	−0.371265	−	1.05710i
$511$	−2.37230e8			−1.77790
$512$	4.19430e6	−	4.19430e6i	0.0312500	−	0.0312500i
$513$	6.18729e6	+	6.18729e6i	0.0458298	+	0.0458298i
$514$			7.12313e7i			0.524544i
$515$	6.99604e7	−	2.45709e7i	0.512190	−	0.179887i
$516$	−1.19475e8			−0.869616
$517$	2.63607e6	−	2.63607e6i	0.0190759	−	0.0190759i
$518$	6.25536e7	+	6.25536e7i	0.450052	+	0.450052i
$519$			2.14554e8i			1.53474i
$520$	−7.34990e6	−	3.52908e6i	−0.0522723	−	0.0250987i
$521$	9.62590e7			0.680656			0.340328	−	0.940307i	$-0.389462\pi$
$521$	9.62590e7			0.680656			0.340328	+	0.940307i	$0.389462\pi$
$522$	−4.54107e7	+	4.54107e7i	−0.319261	+	0.319261i
$523$	−1.16479e8	−	1.16479e8i	−0.814221	−	0.814221i	0.171042	−	0.985264i	$-0.445286\pi$
$523$	−1.16479e8	−	1.16479e8i	−0.814221	−	0.814221i	−0.985264	+	0.171042i	$0.945286\pi$
$524$		−	8.74394e7i		−	0.607734i
$525$	1.69413e8	+	2.11434e8i	1.17076	+	1.46116i
$526$	9.92520e7			0.681996
$527$	6.63522e7	−	6.63522e7i	0.453339	−	0.453339i
$528$	3.23286e7	+	3.23286e7i	0.219626	+	0.219626i
$529$			9.99610e7i			0.675248i
$530$	4.59410e7	−	9.56797e7i	0.308583	−	0.642676i
$531$	2.66181e7			0.177785
$532$	−9.51130e6	+	9.51130e6i	−0.0631691	+	0.0631691i
$533$	−1.16296e7	−	1.16296e7i	−0.0768040	−	0.0768040i
$534$		−	3.79856e7i		−	0.249457i
$535$	−3.13184e7	−	8.91726e7i	−0.204521	−	0.582331i
$536$	8.97130e6			0.0582587
$537$	2.23844e8	−	2.23844e8i	1.44551	−	1.44551i
$538$	8.25650e7	+	8.25650e7i	0.530211	+	0.530211i
$539$			1.92450e8i			1.22900i
$540$	−4.03128e7	+	1.41583e7i	−0.256013	+	0.0899146i
$541$	8.42748e7			0.532238			0.266119	−	0.963940i	$-0.414259\pi$
$541$	8.42748e7			0.532238			0.266119	+	0.963940i	$0.414259\pi$
$542$	−1.00138e8	+	1.00138e8i	−0.628926	+	0.628926i
$543$	1.74659e8	+	1.74659e8i	1.09092	+	1.09092i
$544$			3.60296e7i			0.223802i
$545$	−2.24763e8	−	1.07921e8i	−1.38847	−	0.666677i
$546$	−3.53439e7			−0.217138
$547$	1.60144e8	−	1.60144e8i	0.978475	−	0.978475i	−0.0212983	−	0.999773i	$-0.506780\pi$
$547$	1.60144e8	−	1.60144e8i	0.978475	−	0.978475i	0.999773	+	0.0212983i	$0.00677998\pi$
$548$	−3.65958e7	−	3.65958e7i	−0.222377	−	0.222377i
$549$		−	1.32444e8i		−	0.800415i
$550$	1.16079e8	+	1.28077e7i	0.697697	+	0.0769812i
$551$	−2.25232e7			−0.134640
$552$	6.81156e7	−	6.81156e7i	0.404976	−	0.404976i
$553$	−9.33308e6	−	9.33308e6i	−0.0551887	−	0.0551887i
$554$		−	1.04688e8i		−	0.615699i
$555$	5.57208e7	−	1.16048e8i	0.325940	−	0.678825i
$556$	5.81187e7			0.338136
$557$	−1.89112e8	+	1.89112e8i	−1.09434	+	1.09434i	−0.0992858	+	0.995059i	$0.531656\pi$
$557$	−1.89112e8	+	1.89112e8i	−1.09434	+	1.09434i	−0.995059	+	0.0992858i	$0.968344\pi$
$558$	2.49166e7	+	2.49166e7i	0.143412	+	0.143412i
$559$		−	3.98115e7i		−	0.227915i
$560$	−2.17646e7	−	6.19702e7i	−0.123933	−	0.352873i
$561$	−2.77707e8			−1.57289
$562$	3.13296e7	−	3.13296e7i	0.176500	−	0.176500i
$563$	−3.67704e7	−	3.67704e7i	−0.206050	−	0.206050i	0.596536	−	0.802586i	$-0.296543\pi$
$563$	−3.67704e7	−	3.67704e7i	−0.206050	−	0.206050i	−0.802586	+	0.596536i	$0.796543\pi$
$564$			3.05105e6i			0.0170064i
$565$	−1.00035e8	+	3.51333e7i	−0.554632	+	0.194793i
$566$	−2.75728e7			−0.152066
$567$	−2.40185e8	+	2.40185e8i	−1.31764	+	1.31764i
$568$	3.22187e7	+	3.22187e7i	0.175818	+	0.175818i
$569$			1.52471e8i			0.827658i	0.910355	+	0.413829i	$0.135809\pi$
$569$			1.52471e8i			0.827658i	−0.910355	+	0.413829i	$0.864191\pi$
$570$	1.76451e7	+	8.47236e6i	0.0952795	+	0.0457488i
$571$	−1.91478e8			−1.02851			−0.514257	−	0.857636i	$-0.671932\pi$
$571$	−1.91478e8			−1.02851			−0.514257	+	0.857636i	$0.671932\pi$
$572$	−1.07725e7	+	1.07725e7i	−0.0575613	+	0.0575613i
$573$	2.04120e8	+	2.04120e8i	1.08498	+	1.08498i
$574$		−	1.32492e8i		−	0.700575i
$575$	2.69857e7	−	2.44577e8i	0.141948	−	1.28651i
$576$	−1.35298e7			−0.0707987
$577$	−1.09464e8	+	1.09464e8i	−0.569828	+	0.569828i	−0.932080	−	0.362252i	$-0.882008\pi$
$577$	−1.09464e8	+	1.09464e8i	−0.569828	+	0.569828i	0.362252	+	0.932080i	$0.382008\pi$
$578$	−5.81994e7	−	5.81994e7i	−0.301394	−	0.301394i
$579$			3.38685e8i			1.74486i
$580$	4.76043e7	−	9.91438e7i	0.243984	−	0.508138i
$581$	8.93343e7			0.455502
$582$	−1.41226e8	+	1.41226e8i	−0.716383	+	0.716383i
$583$	−1.40235e8	−	1.40235e8i	−0.707703	−	0.707703i
$584$		−	8.36883e7i		−	0.420171i
$585$	6.16254e6	+	1.75465e7i	0.0307817	+	0.0876443i
$586$	1.87741e7			0.0932965
$587$	1.33081e8	−	1.33081e8i	0.657961	−	0.657961i	−0.296936	−	0.954897i	$-0.595965\pi$
$587$	1.33081e8	−	1.33081e8i	0.657961	−	0.657961i	0.954897	+	0.296936i	$0.0959649\pi$
$588$	−1.11373e8	−	1.11373e8i	−0.547832	−	0.547832i
$589$			1.23583e7i			0.0604803i
$590$	−4.30093e7	+	1.51053e7i	−0.209414	+	0.0735486i
$591$	2.43414e8			1.17919
$592$	−2.20672e7	+	2.20672e7i	−0.106361	+	0.106361i
$593$	−1.32615e8	−	1.32615e8i	−0.635956	−	0.635956i	0.313599	−	0.949555i	$-0.398465\pi$
$593$	−1.32615e8	−	1.32615e8i	−0.635956	−	0.635956i	−0.949555	+	0.313599i	$0.898465\pi$
$594$			7.98368e7i			0.380929i
$595$	3.59647e8	+	1.72686e8i	1.70736	+	0.819795i
$596$	1.46466e8			0.691830
$597$	5.99649e7	−	5.99649e7i	0.281822	−	0.281822i
$598$	2.26975e7	+	2.26975e7i	0.106139	+	0.106139i
$599$		−	9.86190e7i		−	0.458860i	−0.973325	−	0.229430i	$-0.926314\pi$
$599$		−	9.86190e7i		−	0.458860i	0.973325	−	0.229430i	$-0.0736862\pi$
$600$	−7.45883e7	+	5.97643e7i	−0.345316	+	0.276687i
$601$	1.55654e6			0.00717031			0.00358515	−	0.999994i	$-0.498859\pi$
$601$	1.55654e6			0.00717031			0.00358515	+	0.999994i	$0.498859\pi$
$602$	2.26779e8	−	2.26779e8i	1.03947	−	1.03947i
$603$	−1.44697e7	−	1.44697e7i	−0.0659943	−	0.0659943i
$604$			2.10906e8i			0.957145i
$605$	−1.39798e6	+	2.91153e6i	−0.00631299	+	0.0131479i
$606$	−2.35068e7			−0.105627
$607$	−1.81568e8	+	1.81568e8i	−0.811847	+	0.811847i	−0.984911	−	0.173063i	$-0.944633\pi$
$607$	−1.81568e8	+	1.81568e8i	−0.811847	+	0.811847i	0.173063	+	0.984911i	$0.444633\pi$
$608$	−3.35533e6	−	3.35533e6i	−0.0149288	−	0.0149288i
$609$		−	4.76759e8i		−	2.11080i
$610$	7.51597e7	+	2.14001e8i	0.331128	+	0.942817i
$611$	−1.01667e6			−0.00445715
$612$	5.81116e7	−	5.81116e7i	0.253518	−	0.253518i
$613$	−8.56979e7	−	8.56979e7i	−0.372039	−	0.372039i	0.496180	−	0.868220i	$-0.334736\pi$
$613$	−8.56979e7	−	8.56979e7i	−0.372039	−	0.372039i	−0.868220	+	0.496180i	$0.834736\pi$
$614$			2.53035e8i			1.09314i
$615$	−1.81908e8	+	6.38880e7i	−0.782034	+	0.274659i
$616$	−1.22728e8			−0.525050
$617$	1.85185e8	−	1.85185e8i	0.788405	−	0.788405i	−0.192827	−	0.981233i	$-0.561766\pi$
$617$	1.85185e8	−	1.85185e8i	0.788405	−	0.788405i	0.981233	+	0.192827i	$0.0617658\pi$
$618$	8.01814e7	+	8.01814e7i	0.339710	+	0.339710i
$619$		−	2.30579e8i		−	0.972185i	−0.873907	−	0.486092i	$-0.838422\pi$
$619$		−	2.30579e8i		−	0.972185i	0.873907	−	0.486092i	$-0.161578\pi$
$620$	−5.43997e7	−	2.61202e7i	−0.228255	−	0.109598i
$621$	1.68215e8			0.702407
$622$	8.29951e6	−	8.29951e6i	0.0344891	−	0.0344891i
$623$	7.21018e7	+	7.21018e7i	0.298182	+	0.298182i
$624$		−	1.24684e7i		−	0.0513163i
$625$	−5.32271e7	+	2.38268e8i	−0.218018	+	0.975945i
$626$	−2.66632e8			−1.08690
$627$	2.58619e7	−	2.58619e7i	0.104920	−	0.104920i
$628$	−8.30441e7	−	8.30441e7i	−0.335297	−	0.335297i
$629$		−	1.89560e8i		−	0.761720i
$630$	−6.48469e7	+	1.35054e8i	−0.259339	+	0.540116i
$631$	4.64011e8			1.84689			0.923444	−	0.383734i	$-0.125362\pi$
$631$	4.64011e8			1.84689			0.923444	+	0.383734i	$0.125362\pi$
$632$	3.29246e6	−	3.29246e6i	0.0130427	−	0.0130427i
$633$	3.69217e7	+	3.69217e7i	0.145569	+	0.145569i
$634$		−	3.34116e7i		−	0.131108i
$635$	8.98397e7	+	2.55800e8i	0.350871	+	0.999032i
$636$	1.62311e8			0.630923
$637$	3.71117e7	−	3.71117e7i	0.143580	−	0.143580i
$638$	−1.45312e8	−	1.45312e8i	−0.559552	−	0.559552i
$639$		−	1.03930e8i		−	0.398326i
$640$	2.18614e7	−	7.67796e6i	0.0833945	−	0.0292891i
$641$	1.58114e8			0.600337			0.300168	−	0.953886i	$-0.402957\pi$
$641$	1.58114e8			0.600337			0.300168	+	0.953886i	$0.402957\pi$
$642$	1.02200e8	−	1.02200e8i	0.386231	−	0.386231i
$643$	7.86358e7	+	7.86358e7i	0.295793	+	0.295793i	0.839363	−	0.543571i	$-0.182928\pi$
$643$	7.86358e7	+	7.86358e7i	0.295793	+	0.295793i	−0.543571	+	0.839363i	$0.682928\pi$
$644$			2.58585e8i			0.968156i
$645$	−4.20714e8	−	2.02008e8i	−1.56786	−	0.752815i
$646$	2.88227e7			0.106915
$647$	−3.62583e8	+	3.62583e8i	−1.33873	+	1.33873i	−0.441445	+	0.897288i	$0.645534\pi$
$647$	−3.62583e8	+	3.62583e8i	−1.33873	+	1.33873i	−0.897288	+	0.441445i	$0.854466\pi$
$648$	−8.47307e7	−	8.47307e7i	−0.311398	−	0.311398i
$649$			8.51770e7i			0.311593i
$650$	−1.99147e7	−	2.48544e7i	−0.0725160	−	0.0905029i
$651$	−2.61595e8			−0.948170
$652$	−6.59658e6	+	6.59658e6i	−0.0237999	+	0.0237999i
$653$	−2.28612e7	−	2.28612e7i	−0.0821031	−	0.0821031i	0.664863	−	0.746966i	$-0.268490\pi$
$653$	−2.28612e7	−	2.28612e7i	−0.0821031	−	0.0821031i	−0.746966	+	0.664863i	$0.768490\pi$
$654$		−	3.81288e8i		−	1.36307i
$655$	1.47842e8	−	3.07906e8i	0.526107	−	1.09571i
$656$	4.67396e7			0.165567
$657$	−1.34979e8	+	1.34979e8i	−0.475961	+	0.475961i
$658$	−5.79129e6	−	5.79129e6i	−0.0203281	−	0.0203281i
$659$			1.62416e8i			0.567510i	0.958897	+	0.283755i	$0.0915803\pi$
$659$			1.62416e8i			0.567510i	−0.958897	+	0.283755i	$0.908420\pi$
$660$	5.91796e7	+	1.68502e8i	0.205845	+	0.586101i
$661$	−5.53972e8			−1.91815			−0.959076	−	0.283148i	$-0.908621\pi$
$661$	−5.53972e8			−1.91815			−0.959076	+	0.283148i	$0.908621\pi$
$662$	−5.65255e7	+	5.65255e7i	−0.194837	+	0.194837i
$663$	5.35525e7	+	5.35525e7i	0.183755	+	0.183755i
$664$			3.15147e7i			0.107649i
$665$	−4.95744e7	+	1.74111e7i	−0.168575	+	0.0592053i
$666$	7.11837e7			0.240967
$667$	−3.06170e8	+	3.06170e8i	−1.03178	+	1.03178i
$668$	8.15528e7	+	8.15528e7i	0.273596	+	0.273596i
$669$			1.63668e8i			0.546620i
$670$	3.15912e7	+	1.51686e7i	0.105037	+	0.0504338i
$671$	4.23816e8			1.40284
$672$	7.10238e7	−	7.10238e7i	0.234043	−	0.234043i
$673$	2.60781e8	+	2.60781e8i	0.855521	+	0.855521i	0.990807	−	0.135286i	$-0.0431953\pi$
$673$	2.60781e8	+	2.60781e8i	0.855521	+	0.855521i	−0.135286	+	0.990807i	$0.543195\pi$
$674$		−	1.75571e8i		−	0.573420i
$675$	−1.65895e8	−	1.83042e7i	−0.539413	−	0.0595168i
$676$	−1.50303e8			−0.486551
$677$	8.65269e7	−	8.65269e7i	0.278859	−	0.278859i	−0.553794	−	0.832654i	$-0.686821\pi$
$677$	8.65269e7	−	8.65269e7i	0.278859	−	0.278859i	0.832654	+	0.553794i	$0.186821\pi$
$678$	−1.14649e8	−	1.14649e8i	−0.367860	−	0.367860i
$679$		−	5.36131e8i		−	1.71262i
$680$	−6.09187e7	+	1.26873e8i	−0.193742	+	0.403500i
$681$	6.97242e7			0.220771
$682$	−7.97321e7	+	7.97321e7i	−0.251351	+	0.251351i
$683$	−3.62755e8	−	3.62755e8i	−1.13855	−	1.13855i	−0.988710	−	0.149839i	$-0.952125\pi$
$683$	−3.62755e8	−	3.62755e8i	−1.13855	−	1.13855i	−0.149839	−	0.988710i	$-0.547875\pi$
$684$			1.08235e7i			0.0338220i
$685$	−6.69910e7	−	1.90743e8i	−0.208423	−	0.593440i
$686$	8.12984e7			0.251831
$687$	3.50455e8	−	3.50455e8i	1.08084	−	1.08084i
$688$	8.00014e7	+	8.00014e7i	0.245659	+	0.245659i
$689$			5.40854e7i			0.165357i
$690$	3.55029e8	−	1.24690e8i	1.08073	−	0.379564i
$691$	5.53386e8			1.67724			0.838618	−	0.544720i	$-0.183364\pi$
$691$	5.53386e8			1.67724			0.838618	+	0.544720i	$0.183364\pi$
$692$	1.43667e8	−	1.43667e8i	0.433550	−	0.433550i
$693$	1.97946e8	+	1.97946e8i	0.594766	+	0.594766i
$694$		−	2.96767e8i		−	0.887846i
$695$	2.04657e8	+	9.82668e7i	0.609638	+	0.292720i
$696$	1.68187e8			0.498845
$697$	−2.00750e8	+	2.00750e8i	−0.592866	+	0.592866i
$698$	2.30199e8	+	2.30199e8i	0.676921	+	0.676921i
$699$			7.40873e8i			2.16926i
$700$	2.81378e7	−	2.55019e8i	0.0820344	−	0.743496i
$701$	−2.46611e8			−0.715910			−0.357955	−	0.933739i	$-0.616526\pi$
$701$	−2.46611e8			−0.715910			−0.357955	+	0.933739i	$0.616526\pi$
$702$	1.53956e7	−	1.53956e7i	0.0445026	−	0.0445026i
$703$	1.76531e7	+	1.76531e7i	0.0508108	+	0.0508108i
$704$		−	4.32950e7i		−	0.124085i
$705$	−5.15869e6	+	1.07438e7i	−0.0147222	+	0.0306614i
$706$	−4.16228e8			−1.18282
$707$	4.46190e7	−	4.46190e7i	0.126259	−	0.126259i
$708$	−4.92928e7	−	4.92928e7i	−0.138894	−	0.138894i
$709$		−	2.37496e7i		−	0.0666374i	−0.999445	−	0.0333187i	$-0.989392\pi$
$709$		−	2.37496e7i		−	0.0666374i	0.999445	−	0.0333187i	$-0.0106076\pi$
$710$	5.89785e7	+	1.67929e8i	0.164785	+	0.469192i
$711$	−1.06207e7			−0.0295491
$712$	−2.54355e7	+	2.54355e7i	−0.0704694	+	0.0704694i
$713$	1.67994e8	+	1.67994e8i	0.463473	+	0.463473i
$714$			6.10104e8i			1.67614i
$715$	−5.61482e7	+	1.97199e7i	−0.153609	+	0.0539493i
$716$	−2.99775e8			−0.816689
$717$	3.53339e8	−	3.53339e8i	0.958593	−	0.958593i
$718$	−1.58118e8	−	1.58118e8i	−0.427177	−	0.427177i
$719$			5.91472e8i			1.59128i	0.605767	+	0.795642i	$0.292866\pi$
$719$			5.91472e8i			1.59128i	−0.605767	+	0.795642i	$0.707134\pi$
$720$	−4.76435e7	−	2.28762e7i	−0.127646	−	0.0612896i
$721$	−3.04390e8			−0.812127
$722$	1.85499e8	−	1.85499e8i	0.492868	−	0.492868i
$723$	−4.91028e8	−	4.91028e8i	−1.29925	−	1.29925i
$724$		−	2.33906e8i		−	0.616349i
$725$	3.35264e8	−	2.68632e8i	0.879777	−	0.704927i
$726$	−4.93911e6			−0.0129074
$727$	1.16120e8	−	1.16120e8i	0.302207	−	0.302207i	−0.539670	−	0.841877i	$-0.681451\pi$
$727$	1.16120e8	−	1.16120e8i	0.302207	−	0.302207i	0.841877	+	0.539670i	$0.181451\pi$
$728$	2.36666e7	+	2.36666e7i	0.0613397	+	0.0613397i
$729$			1.01847e7i			0.0262885i
$730$	1.41500e8	−	2.94697e8i	0.363737	−	0.757542i
$731$	−6.87223e8			−1.75932
$732$	−2.45266e8	+	2.45266e8i	−0.625323	+	0.625323i
$733$	9.94477e7	+	9.94477e7i	0.252512	+	0.252512i	0.822000	−	0.569488i	$-0.192858\pi$
$733$	9.94477e7	+	9.94477e7i	0.252512	+	0.252512i	−0.569488	+	0.822000i	$0.692858\pi$
$734$			5.12543e8i			1.29611i
$735$	−2.03875e8	−	5.80493e8i	−0.513456	−	1.46196i
$736$	−9.12217e7			−0.228805
$737$	4.63024e7	−	4.63024e7i	0.115665	−	0.115665i
$738$	−7.53855e7	−	7.53855e7i	−0.187551	−	0.187551i
$739$		−	3.16873e8i		−	0.785150i	−0.919720	−	0.392575i	$-0.871584\pi$
$739$		−	3.16873e8i		−	0.785150i	0.919720	−	0.392575i	$-0.128416\pi$
$740$	−1.15018e8	+	4.03955e7i	−0.283837	+	0.0996868i
$741$	−9.97434e6			−0.0245149
$742$	−3.08088e8	+	3.08088e8i	−0.754158	+	0.754158i
$743$	−2.89147e8	−	2.89147e8i	−0.704939	−	0.704939i	0.260527	−	0.965467i	$-0.416104\pi$
$743$	−2.89147e8	−	2.89147e8i	−0.704939	−	0.704939i	−0.965467	+	0.260527i	$0.916104\pi$
$744$		−	9.22835e7i		−	0.224081i
$745$	5.15762e8	+	2.47645e8i	1.24733	+	0.598909i
$746$	9.86170e7			0.237539
$747$	5.08296e7	−	5.08296e7i	0.121942	−	0.121942i
$748$	1.85955e8	+	1.85955e8i	0.444327	+	0.444327i
$749$			3.87980e8i			0.923344i
$750$	−3.63702e8	+	8.43384e7i	−0.862108	+	0.199913i
$751$	−3.85591e8			−0.910346			−0.455173	−	0.890403i	$-0.650423\pi$
$751$	−3.85591e8			−0.910346			−0.455173	+	0.890403i	$0.650423\pi$
$752$	2.04301e6	−	2.04301e6i	0.00480415	−	0.00480415i
$753$	6.17943e7	+	6.17943e7i	0.144732	+	0.144732i
$754$			5.60435e7i			0.130741i
$755$	−3.56599e8	+	7.42676e8i	−0.828588	+	1.72567i
$756$	1.75396e8			0.405934
$757$	2.20526e8	−	2.20526e8i	0.508361	−	0.508361i	−0.405662	−	0.914023i	$-0.632959\pi$
$757$	2.20526e8	−	2.20526e8i	0.508361	−	0.508361i	0.914023	+	0.405662i	$0.132959\pi$
$758$	4.13230e8	+	4.13230e8i	0.948820	+	0.948820i
$759$		−	7.03112e8i		−	1.60805i
$760$	−6.14215e6	−	1.74885e7i	−0.0139920	−	0.0398393i
$761$	2.54649e8			0.577815			0.288907	−	0.957357i	$-0.406708\pi$
$761$	2.54649e8			0.577815			0.288907	+	0.957357i	$0.406708\pi$
$762$	−2.93171e8	+	2.93171e8i	−0.662608	+	0.662608i
$763$	7.23734e8	+	7.23734e8i	1.62932	+	1.62932i
$764$		−	2.73361e8i		−	0.612994i
$765$	3.02887e8	−	1.06377e8i	0.676544	−	0.237610i
$766$	3.57500e8			0.795408
$767$	1.64254e7	−	1.64254e7i	0.0364023	−	0.0364023i
$768$	2.50552e7	+	2.50552e7i	0.0553114	+	0.0553114i
$769$		−	4.95784e8i		−	1.09022i	−0.838365	−	0.545109i	$-0.816488\pi$
$769$		−	4.95784e8i		−	1.09022i	0.838365	−	0.545109i	$-0.183512\pi$
$770$	−4.32169e8	−	2.07508e8i	−0.946632	−	0.454529i
$771$	−4.25510e8			−0.928425
$772$	2.26787e8	−	2.26787e8i	0.492908	−	0.492908i
$773$	1.32543e8	+	1.32543e8i	0.286957	+	0.286957i	0.835876	−	0.548918i	$-0.184960\pi$
$773$	1.32543e8	+	1.32543e8i	0.286957	+	0.286957i	−0.548918	+	0.835876i	$0.684960\pi$
$774$		−	2.58066e8i		−	0.556555i
$775$	−1.47397e8	−	1.83957e8i	−0.316653	−	0.395196i
$776$	1.89132e8			0.404744
$777$	−3.73672e8	+	3.73672e8i	−0.796577	+	0.796577i
$778$	−2.53427e8	−	2.53427e8i	−0.538163	−	0.538163i
$779$		−	3.73904e7i		−	0.0790947i
$780$	2.10815e7	−	4.39056e7i	0.0444239	−	0.0925202i
$781$	3.32572e8			0.698124
$782$	3.91803e8	−	3.91803e8i	0.819309	−	0.819309i
$783$	2.07673e8	+	2.07673e8i	0.432609	+	0.432609i
$784$			1.49152e8i			0.309515i
$785$	−1.52018e8	−	4.32839e8i	−0.314258	−	0.894783i
$786$	5.22331e8			1.07567
$787$	1.81673e8	−	1.81673e8i	0.372705	−	0.372705i	−0.495757	−	0.868462i	$-0.665109\pi$
$787$	1.81673e8	−	1.81673e8i	0.372705	−	0.372705i	0.868462	+	0.495757i	$0.165109\pi$
$788$	−1.62992e8	−	1.62992e8i	−0.333110	−	0.333110i
$789$			5.92895e8i			1.20711i
$790$	1.71608e7	−	6.02707e6i	0.0348062	−	0.0122243i
$791$	4.35239e8			0.879425
$792$	−6.98298e7	+	6.98298e7i	−0.140561	+	0.140561i
$793$	−8.17278e7	−	8.17278e7i	−0.163889	−	0.163889i
$794$		−	4.60627e8i		−	0.920213i
$795$	5.71556e8	+	2.74435e8i	1.13751	+	0.546182i
$796$	−8.03061e7			−0.159224
$797$	−1.28320e7	+	1.28320e7i	−0.0253466	+	0.0253466i	−0.719666	−	0.694320i	$-0.755705\pi$
$797$	−1.28320e7	+	1.28320e7i	−0.0253466	+	0.0253466i	0.694320	+	0.719666i	$0.255705\pi$
$798$	−5.68170e7	−	5.68170e7i	−0.111807	−	0.111807i
$799$			1.75497e7i			0.0344056i
$800$	8.99637e7	+	9.92624e6i	0.175710	+	0.0193872i
$801$	8.20491e7			0.159653
$802$	−1.59909e8	+	1.59909e8i	−0.309992	+	0.309992i
$803$	−4.31929e8	−	4.31929e8i	−0.834191	−	0.834191i
$804$			5.35913e7i			0.103116i
$805$	−4.37214e8	+	9.10571e8i	−0.838121	+	1.74553i
$806$	3.07508e7			0.0587288
$807$	−4.93213e8	+	4.93213e8i	−0.938456	+	0.938456i
$808$	1.57404e7	+	1.57404e7i	0.0298388	+	0.0298388i
$809$		−	2.71170e8i		−	0.512150i	−0.966657	−	0.256075i	$-0.917571\pi$
$809$		−	2.71170e8i		−	0.512150i	0.966657	−	0.256075i	$-0.0824293\pi$
$810$	−1.55105e8	−	4.41630e8i	−0.291858	−	0.831005i
$811$	−5.93403e8			−1.11247			−0.556234	−	0.831026i	$-0.687754\pi$
$811$	−5.93403e8			−1.11247			−0.556234	+	0.831026i	$0.687754\pi$
$812$	−3.19242e8	+	3.19242e8i	−0.596282	+	0.596282i
$813$	−5.98186e8	−	5.98186e8i	−1.11318	−	1.11318i
$814$			2.27785e8i			0.422330i
$815$	−3.43824e7	+	1.20755e7i	−0.0635131	+	0.0223065i
$816$	−2.15228e8			−0.396121
$817$	6.39989e7	−	6.39989e7i	0.117356	−	0.117356i
$818$	4.43174e8	+	4.43174e8i	0.809681	+	0.809681i
$819$		−	7.63430e7i		−	0.138969i
$820$	1.64587e8	+	7.90271e7i	0.298507	+	0.143329i
$821$	−2.50203e7			−0.0452130			−0.0226065	−	0.999744i	$-0.507196\pi$
$821$	−2.50203e7			−0.0452130			−0.0226065	+	0.999744i	$0.507196\pi$
$822$	2.18610e8	−	2.18610e8i	0.393599	−	0.393599i
$823$	−5.91490e6	−	5.91490e6i	−0.0106108	−	0.0106108i	0.701781	−	0.712392i	$-0.252388\pi$
$823$	−5.91490e6	−	5.91490e6i	−0.0106108	−	0.0106108i	−0.712392	+	0.701781i	$0.752388\pi$
$824$		−	1.07380e8i		−	0.191930i
$825$	−7.65088e7	+	6.93416e8i	−0.136254	+	1.23490i
$826$	1.87128e8			0.332047
$827$	3.92300e8	−	3.92300e8i	0.693588	−	0.693588i	−0.269432	−	0.963019i	$-0.586836\pi$
$827$	3.92300e8	−	3.92300e8i	0.693588	−	0.693588i	0.963019	+	0.269432i	$0.0868359\pi$
$828$	1.47130e8	+	1.47130e8i	0.259185	+	0.259185i
$829$			6.16308e8i			1.08177i	0.841097	+	0.540884i	$0.181910\pi$
$829$			6.16308e8i			1.08177i	−0.841097	+	0.540884i	$0.818090\pi$
$830$	−5.32849e7	+	1.10975e8i	−0.0931902	+	0.194084i
$831$	6.25369e8			1.08977
$832$	−8.34893e6	+	8.34893e6i	−0.0144964	+	0.0144964i
$833$	−6.40620e8	−	6.40620e8i	−1.10832	−	1.10832i
$834$			3.47180e8i			0.598489i
$835$	1.49288e8	+	4.25066e8i	0.256428	+	0.730124i
$836$	−3.46348e7			−0.0592780
$837$	1.13949e8	−	1.13949e8i	0.194328	−	0.194328i
$838$	−4.88356e8	−	4.88356e8i	−0.829859	−	0.829859i
$839$		−	5.89741e8i		−	0.998564i	−0.866440	−	0.499282i	$-0.833597\pi$
$839$		−	5.89741e8i		−	0.998564i	0.866440	−	0.499282i	$-0.166403\pi$
$840$	3.70187e8	−	1.30014e8i	0.624573	−	0.219357i
$841$	−1.61155e8			−0.270930
$842$	−1.68568e8	+	1.68568e8i	−0.282383	+	0.282383i
$843$	1.87151e8	+	1.87151e8i	0.312400	+	0.312400i
$844$		−	4.94461e7i		−	0.0822442i
$845$	−5.29272e8	−	2.54132e8i	−0.877221	−	0.421201i
$846$	−6.59027e6			−0.0108841
$847$	9.37509e6	−	9.37509e6i	0.0154285	−	0.0154285i
$848$	−1.08685e8	−	1.08685e8i	−0.178230	−	0.178230i
$849$		−	1.64710e8i		−	0.269151i
$850$	−4.29034e8	+	3.43766e8i	−0.698610	+	0.559766i
$851$	4.79938e8			0.778747
$852$	−1.92463e8	+	1.92463e8i	−0.311192	+	0.311192i
$853$	−5.34794e8	−	5.34794e8i	−0.861666	−	0.861666i	0.129865	−	0.991532i	$-0.458546\pi$
$853$	−5.34794e8	−	5.34794e8i	−0.861666	−	0.861666i	−0.991532	+	0.129865i	$0.958546\pi$
$854$		−	9.31096e8i		−	1.49493i
$855$	−1.83003e7	+	3.81135e7i	−0.0292793	+	0.0609790i
$856$	−1.36869e8			−0.218214
$857$	−3.90046e7	+	3.90046e7i	−0.0619689	+	0.0619689i	−0.737412	−	0.675443i	$-0.763952\pi$
$857$	−3.90046e7	+	3.90046e7i	−0.0619689	+	0.0619689i	0.675443	+	0.737412i	$0.263952\pi$
$858$	−6.43513e7	−	6.43513e7i	−0.101881	−	0.101881i
$859$			8.15365e8i			1.28639i	0.765702	+	0.643195i	$0.222392\pi$
$859$			8.15365e8i			1.28639i	−0.765702	+	0.643195i	$0.777608\pi$
$860$	1.46448e8	+	4.16980e8i	0.230244	+	0.655571i
$861$	7.91460e8			1.23999
$862$	−1.56705e8	+	1.56705e8i	−0.244658	+	0.244658i
$863$	5.03491e8	+	5.03491e8i	0.783357	+	0.783357i	0.980396	−	0.197039i	$-0.0631325\pi$
$863$	5.03491e8	+	5.03491e8i	0.783357	+	0.783357i	−0.197039	+	0.980396i	$0.563132\pi$
$864$			6.18750e7i			0.0959344i
$865$	7.48816e8	−	2.62993e8i	1.15698	−	0.406345i
$866$	−7.73848e8			−1.19152
$867$	3.47662e8	−	3.47662e8i	0.533458	−	0.533458i
$868$	1.75166e8	+	1.75166e8i	0.267850	+	0.267850i
$869$		−	3.39858e7i		−	0.0517891i
$870$	5.92249e8	+	2.84371e8i	0.899387	+	0.431844i
$871$	−1.78577e7			−0.0270254
$872$	−2.55314e8	+	2.55314e8i	−0.385056	+	0.385056i
$873$	−3.05048e8	−	3.05048e8i	−0.458486	−	0.458486i
$874$			7.29748e7i			0.109305i
$875$	5.30268e8	−	8.50439e8i	0.791538	−	1.26946i
$876$	4.99923e8			0.743688
$877$	−4.25203e8	+	4.25203e8i	−0.630373	+	0.630373i	−0.948162	−	0.317788i	$-0.897060\pi$
$877$	−4.25203e8	+	4.25203e8i	−0.630373	+	0.630373i	0.317788	+	0.948162i	$0.397060\pi$
$878$	3.18288e7	+	3.18288e7i	0.0470258	+	0.0470258i
$879$			1.12149e8i			0.165132i
$880$	7.32030e7	−	1.52457e8i	0.107419	−	0.223718i
$881$	4.01941e8			0.587806			0.293903	−	0.955835i	$-0.405046\pi$
$881$	4.01941e8			0.587806			0.293903	+	0.955835i	$0.405046\pi$
$882$	2.40566e8	−	2.40566e8i	0.350613	−	0.350613i
$883$	4.01338e8	+	4.01338e8i	0.582946	+	0.582946i	0.935712	−	0.352766i	$-0.114759\pi$
$883$	4.01338e8	+	4.01338e8i	0.582946	+	0.582946i	−0.352766	+	0.935712i	$0.614759\pi$
$884$		−	7.17184e7i		−	0.103818i
$885$	−9.02338e7	−	2.56922e8i	−0.130178	−	0.370656i
$886$	6.90991e8			0.993507
$887$	5.18983e6	−	5.18983e6i	0.00743674	−	0.00743674i	−0.703379	−	0.710815i	$-0.748326\pi$
$887$	5.18983e6	−	5.18983e6i	0.00743674	−	0.00743674i	0.710815	+	0.703379i	$0.248326\pi$
$888$	−1.31821e8	−	1.31821e8i	−0.188255	−	0.188255i
$889$		−	1.11296e9i		−	1.58406i
$890$	−1.32574e8	+	4.65615e7i	−0.188056	+	0.0660475i
$891$	−8.74618e8			−1.23648
$892$	1.09594e8	−	1.09594e8i	0.154415	−	0.154415i
$893$	−1.63435e6	−	1.63435e6i	−0.00229504	−	0.00229504i
$894$			8.74937e8i			1.22452i
$895$	−1.05562e9	−	5.06859e8i	−1.47244	−	0.706997i
$896$	−9.51163e7			−0.132230
$897$	−1.35587e8	+	1.35587e8i	−0.187863	+	0.187863i
$898$	3.37282e8	+	3.37282e8i	0.465762	+	0.465762i
$899$			4.14801e8i			0.570901i
$900$	−1.29091e8	−	1.61111e8i	−0.177080	−	0.221003i
$901$	9.33617e8			1.27642
$902$	2.41231e8	−	2.41231e8i	0.328710	−	0.328710i
$903$	1.35470e9	+	1.35470e9i	1.83983	+	1.83983i
$904$			1.53541e8i			0.207835i
$905$	3.95488e8	−	8.23670e8i	0.533565	−	1.11124i
$906$	−1.25987e9			−1.69411
$907$	3.76104e8	−	3.76104e8i	0.504065	−	0.504065i	−0.408634	−	0.912698i	$-0.633995\pi$
$907$	3.76104e8	−	3.76104e8i	0.504065	−	0.504065i	0.912698	+	0.408634i	$0.133995\pi$
$908$	−4.66879e7	−	4.66879e7i	−0.0623659	−	0.0623659i
$909$		−	5.07748e7i		−	0.0676015i
$910$	4.33233e7	+	1.23354e8i	0.0574907	+	0.163693i
$911$	−9.07902e8			−1.20084			−0.600418	−	0.799686i	$-0.704999\pi$
$911$	−9.07902e8			−1.20084			−0.600418	+	0.799686i	$0.704999\pi$
$912$	2.00435e7	−	2.00435e7i	0.0264234	−	0.0264234i
$913$	1.62653e8	+	1.62653e8i	0.213722	+	0.213722i
$914$			1.05631e8i			0.138341i
$915$	−1.27837e9	+	4.48977e8i	−1.66875	+	0.586085i
$916$	−4.69336e8			−0.610657
$917$	−9.91453e8	+	9.91453e8i	−1.28577	+	1.28577i
$918$	−2.65757e8	−	2.65757e8i	−0.343524	−	0.343524i
$919$		−	2.04129e8i		−	0.263002i	−0.991316	−	0.131501i	$-0.958020\pi$
$919$		−	2.04129e8i		−	0.263002i	0.991316	−	0.131501i	$-0.0419796\pi$
$920$	−3.21225e8	−	1.54237e8i	−0.412520	−	0.198073i
$921$	−1.51154e9			−1.93482
$922$	3.71233e8	−	3.71233e8i	0.473645	−	0.473645i
$923$	−6.41326e7	−	6.41326e7i	−0.0815593	−	0.0815593i
$924$		−	7.33131e8i		−	0.929321i
$925$	−4.73320e8	−	5.22243e7i	−0.598039	−	0.0659853i
$926$	3.32499e8			0.418753
$927$	−1.73192e8	+	1.73192e8i	−0.217415	+	0.217415i
$928$	−1.12620e8	−	1.12620e8i	−0.140919	−	0.140919i
$929$			1.33077e9i			1.65980i	0.557914	+	0.829898i	$0.311602\pi$
$929$			1.33077e9i			1.65980i	−0.557914	+	0.829898i	$0.688398\pi$
$930$	1.56033e8	−	3.24964e8i	0.193984	−	0.404004i
$931$	1.19318e8			0.147862
$932$	4.96095e8	−	4.96095e8i	0.612798	−	0.612798i
$933$	4.95782e7	+	4.95782e7i	0.0610445	+	0.0610445i
$934$			4.59399e8i			0.563832i
$935$	3.40403e8	+	9.69226e8i	0.416446	+	1.18574i
$936$	2.69317e7			0.0328425
$937$	−9.92661e7	+	9.92661e7i	−0.120665	+	0.120665i	−0.764861	−	0.644196i	$-0.777192\pi$
$937$	−9.92661e7	+	9.92661e7i	−0.120665	+	0.120665i	0.644196	+	0.764861i	$0.277192\pi$
$938$	−1.01723e8	−	1.01723e8i	−0.123257	−	0.123257i
$939$		−	1.59276e9i		−	1.92378i
$940$	1.06485e7	−	3.73986e6i	0.0128205	−	0.00450269i
$941$	−3.77955e7			−0.0453598			−0.0226799	−	0.999743i	$-0.507220\pi$
$941$	−3.77955e7			−0.0453598			−0.0226799	+	0.999743i	$0.507220\pi$
$942$	4.96075e8	−	4.96075e8i	0.593465	−	0.593465i
$943$	−5.08268e8	−	5.08268e8i	−0.606119	−	0.606119i
$944$			6.60138e7i			0.0784727i
$945$	6.17634e8	+	2.96559e8i	0.731874	+	0.351412i
$946$	8.25801e8			0.975443
$947$	−1.09711e7	+	1.09711e7i	−0.0129181	+	0.0129181i	−0.713536	−	0.700618i	$-0.752908\pi$
$947$	−1.09711e7	+	1.09711e7i	−0.0129181	+	0.0129181i	0.700618	+	0.713536i	$0.252908\pi$
$948$	1.96679e7	+	1.96679e7i	0.0230852	+	0.0230852i
$949$			1.66585e8i			0.194911i
$950$	7.94072e6	−	7.19684e7i	0.00926166	−	0.0839404i
$951$	1.99589e8			0.232057
$952$	4.08531e8	−	4.08531e8i	0.473494	−	0.473494i
$953$	1.06083e9	+	1.06083e9i	1.22565	+	1.22565i	0.965593	+	0.260059i	$0.0837420\pi$
$953$	1.06083e9	+	1.06083e9i	1.22565	+	1.22565i	0.260059	+	0.965593i	$0.416258\pi$
$954$			3.50592e8i			0.403791i
$955$	4.62197e8	−	9.62602e8i	0.530661	−	1.10519i
$956$	−4.73198e8			−0.541588
$957$	8.68043e8	−	8.68043e8i	0.990388	−	0.990388i
$958$	−7.96761e7	−	7.96761e7i	−0.0906215	−	0.0906215i
$959$			8.29900e8i			0.940958i
$960$	4.58653e7	+	1.30592e8i	0.0518407	+	0.147606i
$961$	−6.59905e8			−0.743551
$962$	4.39256e7	−	4.39256e7i	0.0493393	−	0.0493393i
$963$	2.20753e8	+	2.20753e8i	0.247188	+	0.247188i
$964$			6.57594e8i			0.734052i
$965$	1.18205e9	−	4.15148e8i	1.31539	−	0.461978i
$966$	−1.54469e9			−1.71360
$967$	3.42662e8	−	3.42662e8i	0.378954	−	0.378954i	−0.491771	−	0.870725i	$-0.663650\pi$
$967$	3.42662e8	−	3.42662e8i	0.378954	−	0.378954i	0.870725	+	0.491771i	$0.163650\pi$
$968$	3.30727e6	+	3.30727e6i	0.00364623	+	0.00364623i
$969$			1.72176e8i			0.189235i
$970$	6.66004e8	+	3.19784e8i	0.729729	+	0.350382i
$971$	3.06097e8			0.334350			0.167175	−	0.985927i	$-0.446536\pi$
$971$	3.06097e8			0.334350			0.167175	+	0.985927i	$0.446536\pi$
$972$	3.29952e8	−	3.29952e8i	0.359295	−	0.359295i
$973$	−6.58993e8	−	6.58993e8i	−0.715389	−	0.715389i
$974$			3.60087e8i			0.389700i
$975$	1.48471e8	−	1.18963e8i	0.160187	−	0.128351i
$976$	3.28465e8			0.353297
$977$	−1.01093e9	+	1.01093e9i	−1.08402	+	1.08402i	−0.0878855	+	0.996131i	$0.528011\pi$
$977$	−1.01093e9	+	1.01093e9i	−1.08402	+	1.08402i	−0.996131	+	0.0878855i	$0.971989\pi$
$978$	−3.94056e7	−	3.94056e7i	−0.0421251	−	0.0421251i
$979$			2.62554e8i			0.279815i
$980$	−2.52186e8	+	5.25220e8i	−0.267943	+	0.558037i
$981$	8.23582e8			0.872368
$982$	−5.12831e8	+	5.12831e8i	−0.541552	+	0.541552i
$983$	3.66759e8	+	3.66759e8i	0.386118	+	0.386118i	0.873300	−	0.487182i	$-0.161975\pi$
$983$	3.66759e8	+	3.66759e8i	0.386118	+	0.386118i	−0.487182	+	0.873300i	$0.661975\pi$
$984$			2.79205e8i			0.293048i
$985$	−2.98368e8	−	8.49541e8i	−0.312208	−	0.888946i
$986$	9.67419e8			1.00922
$987$	3.45950e7	−	3.45950e7i	0.0359801	−	0.0359801i
$988$	6.67891e6	+	6.67891e6i	0.00692524	+	0.00692524i
$989$		−	1.73995e9i		−	1.79865i
$990$	−3.63964e8	+	1.27828e8i	−0.375105	+	0.131741i
$991$	−7.65601e8			−0.786649			−0.393325	−	0.919400i	$-0.628675\pi$
$991$	−7.65601e8			−0.786649			−0.393325	+	0.919400i	$0.628675\pi$
$992$	−6.17939e7	+	6.17939e7i	−0.0633010	+	0.0633010i
$993$	−3.37663e8	−	3.37663e8i	−0.344854	−	0.344854i
$994$		−	7.30639e8i		−	0.743950i
$995$	−2.82787e8	−	1.35781e8i	−0.287072	−	0.137838i
$996$	−1.88257e8			−0.190535
$997$	3.07440e8	−	3.07440e8i	0.310223	−	0.310223i	−0.534773	−	0.844996i	$-0.679603\pi$
$997$	3.07440e8	−	3.07440e8i	0.310223	−	0.310223i	0.844996	+	0.534773i	$0.179603\pi$
$998$	−2.28805e8	−	2.28805e8i	−0.230183	−	0.230183i
$999$		−	3.25539e8i		−	0.326517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.7.c.b.3.2	✓	4
3.2	odd	2		90.7.g.b.73.2		4
4.3	odd	2		80.7.p.c.33.1		4
5.2	odd	4	inner	10.7.c.b.7.2	yes	4
5.3	odd	4		50.7.c.d.7.1		4
5.4	even	2		50.7.c.d.43.1		4
15.2	even	4		90.7.g.b.37.2		4
15.8	even	4		450.7.g.m.307.2		4
15.14	odd	2		450.7.g.m.343.2		4
20.7	even	4		80.7.p.c.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.7.c.b.3.2	✓	4	1.1	even	1	trivial
10.7.c.b.7.2	yes	4	5.2	odd	4	inner
50.7.c.d.7.1		4	5.3	odd	4
50.7.c.d.43.1		4	5.4	even	2
80.7.p.c.17.1		4	20.7	even	4
80.7.p.c.33.1		4	4.3	odd	2
90.7.g.b.37.2		4	15.2	even	4
90.7.g.b.73.2		4	3.2	odd	2
450.7.g.m.307.2		4	15.8	even	4
450.7.g.m.343.2		4	15.14	odd	2

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 4.00000i) q^{2} +(23.8945 + 23.8945i) q^{3} -32.0000i q^{4} +(54.1055 - 112.684i) q^{5} +191.156 q^{6} +(-362.840 + 362.840i) q^{7} +(-128.000 - 128.000i) q^{8} +412.898i q^{9} +(-234.313 - 667.156i) q^{10} -1321.26 q^{11} +(764.625 - 764.625i) q^{12} +(254.789 + 254.789i) q^{13} +2902.72i q^{14} +(3985.35 - 1399.70i) q^{15} -1024.00 q^{16} +(4398.15 - 4398.15i) q^{17} +(1651.59 + 1651.59i) q^{18} +819.171i q^{19} +(-3605.88 - 1731.37i) q^{20} -17339.8 q^{21} +(-5285.03 + 5285.03i) q^{22} +(11135.5 + 11135.5i) q^{23} -6117.00i q^{24} +(-9770.20 - 12193.6i) q^{25} +2038.31 q^{26} +(7553.11 - 7553.11i) q^{27} +(11610.9 + 11610.9i) q^{28} +27495.1i q^{29} +(10342.6 - 21540.2i) q^{30} +15086.4 q^{31} +(-4096.00 + 4096.00i) q^{32} +(-31570.9 - 31570.9i) q^{33} -35185.2i q^{34} +(21254.5 + 60517.7i) q^{35} +13212.7 q^{36} +(21550.0 - 21550.0i) q^{37} +(3276.68 + 3276.68i) q^{38} +12176.1i q^{39} +(-21349.0 + 7498.01i) q^{40} -45644.1 q^{41} +(-69359.2 + 69359.2i) q^{42} +(-78126.4 - 78126.4i) q^{43} +42280.3i q^{44} +(46526.9 + 22340.0i) q^{45} +89083.7 q^{46} +(-1995.12 + 1995.12i) q^{47} +(-24468.0 - 24468.0i) q^{48} -145657. i q^{49} +(-87855.2 - 9693.60i) q^{50} +210184. q^{51} +(8153.25 - 8153.25i) q^{52} +(106138. + 106138. i) q^{53} -60424.9i q^{54} +(-71487.3 + 148884. i) q^{55} +92887.0 q^{56} +(-19573.7 + 19573.7i) q^{57} +(109980. + 109980. i) q^{58} -64466.6i q^{59} +(-44790.4 - 127531. i) q^{60} -320767. q^{61} +(60345.6 - 60345.6i) q^{62} +(-149816. - 149816. i) q^{63} +32768.0i q^{64} +(42496.0 - 14925.1i) q^{65} -252567. q^{66} +(-35044.1 + 35044.1i) q^{67} +(-140741. - 140741. i) q^{68} +532153. i q^{69} +(327089. + 157053. i) q^{70} -251708. q^{71} +(52851.0 - 52851.0i) q^{72} +(326907. + 326907. i) q^{73} -172400. i q^{74} +(57906.0 - 524815. i) q^{75} +26213.5 q^{76} +(479405. - 479405. i) q^{77} +(48704.5 + 48704.5i) q^{78} +25722.3i q^{79} +(-55404.0 + 115388. i) q^{80} +661959. q^{81} +(-182577. + 182577. i) q^{82} +(-123104. - 123104. i) q^{83} +554873. i q^{84} +(-257636. - 733563. i) q^{85} -625011. q^{86} +(-656982. + 656982. i) q^{87} +(169121. + 169121. i) q^{88} -198715. i q^{89} +(275468. - 96747.3i) q^{90} -184895. q^{91} +(356335. - 356335. i) q^{92} +(360482. + 360482. i) q^{93} +15961.0i q^{94} +(92307.2 + 44321.6i) q^{95} -195744. q^{96} +(-738798. + 738798. i) q^{97} +(-582627. - 582627. i) q^{98} -545545. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 18 q^{3} + 330 q^{5} - 144 q^{6} - 202 q^{7} - 512 q^{8} + 880 q^{10} - 2332 q^{11} - 576 q^{12} + 792 q^{13} + 4470 q^{15} - 4096 q^{16} + 12368 q^{17} + 14784 q^{18} - 3520 q^{20} - 69132 q^{21}+ \cdots - 1321024 q^{98}+O(q^{100}) \) 4 * q + 16 * q^2 - 18 * q^3 + 330 * q^5 - 144 * q^6 - 202 * q^7 - 512 * q^8 + 880 * q^10 - 2332 * q^11 - 576 * q^12 + 792 * q^13 + 4470 * q^15 - 4096 * q^16 + 12368 * q^17 + 14784 * q^18 - 3520 * q^20 - 69132 * q^21 - 9328 * q^22 + 35342 * q^23 - 1600 * q^25 + 6336 * q^26 + 61560 * q^27 + 6464 * q^28 - 37680 * q^30 - 18932 * q^31 - 16384 * q^32 - 73356 * q^33 + 130790 * q^35 + 118272 * q^36 - 67812 * q^37 + 44000 * q^38 - 56320 * q^40 + 110228 * q^41 - 276528 * q^42 - 293538 * q^43 - 72510 * q^45 + 282736 * q^46 + 195438 * q^47 + 18432 * q^48 - 1600 * q^50 + 185388 * q^51 + 25344 * q^52 - 121988 * q^53 - 108540 * q^55 + 51712 * q^56 + 268800 * q^57 + 229120 * q^58 - 444480 * q^60 - 243372 * q^61 - 75728 * q^62 + 451902 * q^63 + 100020 * q^65 - 586848 * q^66 - 773602 * q^67 - 395776 * q^68 + 895840 * q^70 - 1046132 * q^71 + 473088 * q^72 + 922372 * q^73 + 367350 * q^75 + 352000 * q^76 + 1040116 * q^77 + 23088 * q^78 - 337920 * q^80 + 360144 * q^81 + 440912 * q^82 - 1238058 * q^83 + 86840 * q^85 - 2348304 * q^86 - 1238640 * q^87 + 298496 * q^88 + 1161840 * q^90 - 221892 * q^91 + 1130944 * q^92 + 2336244 * q^93 - 355400 * q^95 + 147456 * q^96 - 1937532 * q^97 - 1321024 * q^98

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