LMFDB - Embedded newform 55.6.e.b.32.1

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			32.1
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.70910 + 7.70910i) q^{2} +(-16.8901 + 16.8901i) q^{3} -86.8603i q^{4} +(-34.5372 + 43.9566i) q^{5} -260.415i q^{6} +(97.1832 - 97.1832i) q^{7} +(422.923 + 422.923i) q^{8} -327.553i q^{9} +(-72.6145 - 605.116i) q^{10} +(-365.732 - 165.200i) q^{11} +(1467.08 + 1467.08i) q^{12} +(-254.945 - 254.945i) q^{13} +1498.39i q^{14} +(-159.094 - 1325.77i) q^{15} -3741.18 q^{16} +(-887.978 + 887.978i) q^{17} +(2525.14 + 2525.14i) q^{18} +1413.54 q^{19} +(3818.08 + 2999.92i) q^{20} +3282.88i q^{21} +(4093.01 - 1545.92i) q^{22} +(-183.003 + 183.003i) q^{23} -14286.5 q^{24} +(-739.358 - 3036.28i) q^{25} +3930.79 q^{26} +(1428.12 + 1428.12i) q^{27} +(-8441.36 - 8441.36i) q^{28} +3114.96 q^{29} +(11447.0 + 8994.03i) q^{30} -580.366 q^{31} +(15307.6 - 15307.6i) q^{32} +(8967.51 - 3387.02i) q^{33} -13691.0i q^{34} +(915.400 + 7628.28i) q^{35} -28451.4 q^{36} +(5540.44 + 5540.44i) q^{37} +(-10897.1 + 10897.1i) q^{38} +8612.10 q^{39} +(-33196.9 + 3983.65i) q^{40} -14044.6i q^{41} +(-25308.0 - 25308.0i) q^{42} +(6588.81 + 6588.81i) q^{43} +(-14349.3 + 31767.6i) q^{44} +(14398.1 + 11312.8i) q^{45} -2821.57i q^{46} +(-4056.05 - 4056.05i) q^{47} +(63189.1 - 63189.1i) q^{48} -2082.15i q^{49} +(29106.7 + 17707.2i) q^{50} -29996.1i q^{51} +(-22144.6 + 22144.6i) q^{52} +(3315.55 - 3315.55i) q^{53} -22019.0 q^{54} +(19893.0 - 10370.8i) q^{55} +82202.1 q^{56} +(-23874.8 + 23874.8i) q^{57} +(-24013.5 + 24013.5i) q^{58} +12144.8i q^{59} +(-115157. + 13818.9i) q^{60} -18245.4i q^{61} +(4474.10 - 4474.10i) q^{62} +(-31832.7 - 31832.7i) q^{63} +116297. i q^{64} +(20011.6 - 2401.41i) q^{65} +(-43020.6 + 95242.3i) q^{66} +(20241.4 + 20241.4i) q^{67} +(77130.0 + 77130.0i) q^{68} -6181.88i q^{69} +(-65864.0 - 51750.2i) q^{70} +71.7463 q^{71} +(138530. - 138530. i) q^{72} +(-8005.94 - 8005.94i) q^{73} -85423.6 q^{74} +(63771.0 + 38795.3i) q^{75} -122780. i q^{76} +(-51597.7 + 19488.4i) q^{77} +(-66391.5 + 66391.5i) q^{78} +40465.6 q^{79} +(129210. - 164450. i) q^{80} +31353.2 q^{81} +(108271. + 108271. i) q^{82} +(-16732.7 - 16732.7i) q^{83} +285152. q^{84} +(-8364.15 - 69700.7i) q^{85} -101588. q^{86} +(-52612.1 + 52612.1i) q^{87} +(-84809.8 - 224544. i) q^{88} -94643.8i q^{89} +(-198208. + 23785.1i) q^{90} -49552.7 q^{91} +(15895.7 + 15895.7i) q^{92} +(9802.47 - 9802.47i) q^{93} +62537.0 q^{94} +(-48819.6 + 62134.2i) q^{95} +517095. i q^{96} +(-62574.3 - 62574.3i) q^{97} +(16051.5 + 16051.5i) q^{98} +(-54111.8 + 119797. i) 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 $

$2$	−7.70910	+	7.70910i	−1.36279	+	1.36279i	−0.492445	+	0.870344i	$0.663897\pi$
$2$	−7.70910	+	7.70910i	−1.36279	+	1.36279i	−0.870344	+	0.492445i	$0.836103\pi$
$3$	−16.8901	+	16.8901i	−1.08350	+	1.08350i	−0.0873227	+	0.996180i	$0.527831\pi$
$3$	−16.8901	+	16.8901i	−1.08350	+	1.08350i	−0.996180	+	0.0873227i	$0.972169\pi$
$4$		−	86.8603i		−	2.71438i
$5$	−34.5372	+	43.9566i	−0.617821	+	0.786319i
$5$	−34.5372	+	43.9566i	−0.617821	+	0.786319i
$6$		−	260.415i		−	2.95317i
$7$	97.1832	−	97.1832i	0.749629	−	0.749629i	−0.224781	−	0.974409i	$-0.572167\pi$
$7$	97.1832	−	97.1832i	0.749629	−	0.749629i	0.974409	+	0.224781i	$0.0721666\pi$
$8$	422.923	+	422.923i	2.33634	+	2.33634i
$9$		−	327.553i		−	1.34796i
$10$	−72.6145	−	605.116i	−0.229627	−	1.91355i
$11$	−365.732	−	165.200i	−0.911342	−	0.411650i
$11$	−365.732	−	165.200i	−0.911342	−	0.411650i
$12$	1467.08	+	1467.08i	2.94104	+	2.94104i
$13$	−254.945	−	254.945i	−0.418396	−	0.418396i	0.466255	−	0.884651i	$-0.345603\pi$
$13$	−254.945	−	254.945i	−0.418396	−	0.418396i	−0.884651	+	0.466255i	$0.845603\pi$
$14$			1498.39i			2.04317i
$15$	−159.094	−	1325.77i	−0.182568	−	1.52139i
$16$	−3741.18			−3.65350
$17$	−887.978	+	887.978i	−0.745212	+	0.745212i	−0.973576	−	0.228364i	$-0.926662\pi$
$17$	−887.978	+	887.978i	−0.745212	+	0.745212i	0.228364	+	0.973576i	$0.426662\pi$
$18$	2525.14	+	2525.14i	1.83698	+	1.83698i
$19$	1413.54			0.898303			0.449152	−	0.893456i	$-0.351726\pi$
$19$	1413.54			0.898303			0.449152	+	0.893456i	$0.351726\pi$
$20$	3818.08	+	2999.92i	2.13437	+	1.67700i
$21$			3282.88i			1.62445i
$22$	4093.01	−	1545.92i	1.80296	−	0.680975i
$23$	−183.003	+	183.003i	−0.0721336	+	0.0721336i	−0.742253	−	0.670120i	$-0.766243\pi$
$23$	−183.003	+	183.003i	−0.0721336	+	0.0721336i	0.670120	+	0.742253i	$0.266243\pi$
$24$	−14286.5			−5.06287
$25$	−739.358	−	3036.28i	−0.236595	−	0.971608i
$26$	3930.79			1.14037
$27$	1428.12	+	1428.12i	0.377012	+	0.377012i
$28$	−8441.36	−	8441.36i	−2.03478	−	2.03478i
$29$	3114.96			0.687793			0.343897	−	0.939008i	$-0.388253\pi$
$29$	3114.96			0.687793			0.343897	+	0.939008i	$0.388253\pi$
$30$	11447.0	+	8994.03i	2.32213	+	1.82453i
$31$	−580.366			−0.108467			−0.0542335	−	0.998528i	$-0.517272\pi$
$31$	−580.366			−0.108467			−0.0542335	+	0.998528i	$0.517272\pi$
$32$	15307.6	−	15307.6i	2.64260	−	2.64260i
$33$	8967.51	−	3387.02i	1.43347	−	0.541418i
$34$		−	13691.0i		−	2.03113i
$35$	915.400	+	7628.28i	0.126311	+	1.05258i
$36$	−28451.4			−3.65887
$37$	5540.44	+	5540.44i	0.665335	+	0.665335i	0.956632	−	0.291298i	$-0.0940870\pi$
$37$	5540.44	+	5540.44i	0.665335	+	0.665335i	−0.291298	+	0.956632i	$0.594087\pi$
$38$	−10897.1	+	10897.1i	−1.22420	+	1.22420i
$39$	8612.10			0.906667
$40$	−33196.9	+	3983.65i	−3.28055	+	0.393669i
$41$		−	14044.6i		−	1.30481i	−0.757869	−	0.652407i	$-0.773759\pi$
$41$		−	14044.6i		−	1.30481i	0.757869	−	0.652407i	$-0.226241\pi$
$42$	−25308.0	−	25308.0i	−2.21378	−	2.21378i
$43$	6588.81	+	6588.81i	0.543421	+	0.543421i	0.924530	−	0.381109i	$-0.124458\pi$
$43$	6588.81	+	6588.81i	0.543421	+	0.543421i	−0.381109	+	0.924530i	$0.624458\pi$
$44$	−14349.3	+	31767.6i	−1.11738	+	2.47373i
$45$	14398.1	+	11312.8i	1.05992	+	0.832796i
$46$		−	2821.57i		−	0.196606i
$47$	−4056.05	−	4056.05i	−0.267830	−	0.267830i	0.560395	−	0.828225i	$-0.310649\pi$
$47$	−4056.05	−	4056.05i	−0.267830	−	0.267830i	−0.828225	+	0.560395i	$0.810649\pi$
$48$	63189.1	−	63189.1i	3.95858	−	3.95858i
$49$		−	2082.15i		−	0.123886i
$50$	29106.7	+	17707.2i	1.64653	+	1.00167i
$51$		−	29996.1i		−	1.61488i
$52$	−22144.6	+	22144.6i	−1.13569	+	1.13569i
$53$	3315.55	−	3315.55i	0.162131	−	0.162131i	−0.621379	−	0.783510i	$-0.713427\pi$
$53$	3315.55	−	3315.55i	0.162131	−	0.162131i	0.783510	+	0.621379i	$0.213427\pi$
$54$	−22019.0			−1.02757
$55$	19893.0	−	10370.8i	0.886734	−	0.462280i
$56$	82202.1			3.50278
$57$	−23874.8	+	23874.8i	−0.973314	+	0.973314i
$58$	−24013.5	+	24013.5i	−0.937317	+	0.937317i
$59$			12144.8i			0.454214i	0.973870	+	0.227107i	$0.0729267\pi$
$59$			12144.8i			0.454214i	−0.973870	+	0.227107i	$0.927073\pi$
$60$	−115157.	+	13818.9i	−4.12964	+	0.495560i
$61$		−	18245.4i		−	0.627812i	−0.949454	−	0.313906i	$-0.898362\pi$
$61$		−	18245.4i		−	0.627812i	0.949454	−	0.313906i	$-0.101638\pi$
$62$	4474.10	−	4474.10i	0.147818	−	0.147818i
$63$	−31832.7	−	31832.7i	−1.01047	−	1.01047i
$64$			116297.i			3.54912i
$65$	20011.6	−	2401.41i	0.587487	−	0.0704989i
$66$	−43020.6	+	95242.3i	−1.21567	+	2.69135i
$67$	20241.4	+	20241.4i	0.550876	+	0.550876i	0.926694	−	0.375817i	$-0.122638\pi$
$67$	20241.4	+	20241.4i	0.550876	+	0.550876i	−0.375817	+	0.926694i	$0.622638\pi$
$68$	77130.0	+	77130.0i	2.02279	+	2.02279i
$69$		−	6181.88i		−	0.156314i
$70$	−65864.0	−	51750.2i	−1.60658	−	1.26231i
$71$	71.7463			0.00168909			0.000844547	−	1.00000i	$-0.499731\pi$
$71$	71.7463			0.00168909			0.000844547		1.00000i	$0.499731\pi$
$72$	138530.	−	138530.i	3.14929	−	3.14929i
$73$	−8005.94	−	8005.94i	−0.175835	−	0.175835i	0.613702	−	0.789537i	$-0.289679\pi$
$73$	−8005.94	−	8005.94i	−0.175835	−	0.175835i	−0.789537	+	0.613702i	$0.789679\pi$
$74$	−85423.6			−1.81342
$75$	63771.0	+	38795.3i	1.30909	+	0.796389i
$76$		−	122780.i		−	2.43834i
$77$	−51597.7	+	19488.4i	−0.991753	+	0.374584i
$78$	−66391.5	+	66391.5i	−1.23559	+	1.23559i
$79$	40465.6			0.729489			0.364744	−	0.931108i	$-0.381156\pi$
$79$	40465.6			0.729489			0.364744	+	0.931108i	$0.381156\pi$
$80$	129210.	−	164450.i	2.25721	−	2.87282i
$81$	31353.2			0.530970
$82$	108271.	+	108271.i	1.77819	+	1.77819i
$83$	−16732.7	−	16732.7i	−0.266606	−	0.266606i	0.561125	−	0.827731i	$-0.310369\pi$
$83$	−16732.7	−	16732.7i	−0.266606	−	0.266606i	−0.827731	+	0.561125i	$0.810369\pi$
$84$	285152.			4.40938
$85$	−8364.15	−	69700.7i	−0.125567	−	1.04638i
$86$	−101588.			−1.48113
$87$	−52612.1	+	52612.1i	−0.745226	+	0.745226i
$88$	−84809.8	−	224544.i	−1.16745	−	3.09096i
$89$		−	94643.8i		−	1.26653i	−0.773933	−	0.633267i	$-0.781713\pi$
$89$		−	94643.8i		−	1.26653i	0.773933	−	0.633267i	$-0.218287\pi$
$90$	−198208.	+	23785.1i	−2.57938	+	0.309527i
$91$	−49552.7			−0.627283
$92$	15895.7	+	15895.7i	0.195798	+	0.195798i
$93$	9802.47	−	9802.47i	0.117524	−	0.117524i
$94$	62537.0			0.729990
$95$	−48819.6	+	62134.2i	−0.554991	+	0.706353i
$96$			517095.i			5.72653i
$97$	−62574.3	−	62574.3i	−0.675254	−	0.675254i	0.283669	−	0.958922i	$-0.408448\pi$
$97$	−62574.3	−	62574.3i	−0.675254	−	0.675254i	−0.958922	+	0.283669i	$0.908448\pi$
$98$	16051.5	+	16051.5i	0.168830	+	0.168830i
$99$	−54111.8	+	119797.i	−0.554886	+	1.22845i
$100$	−263732.	+	64220.9i	−2.63732	+	0.642209i
$101$		−	163803.i		−	1.59778i	−0.601474	−	0.798892i	$-0.705420\pi$
$101$		−	163803.i		−	1.59778i	0.601474	−	0.798892i	$-0.294580\pi$
$102$	231243.	+	231243.i	2.20074	+	2.20074i
$103$	−99500.5	+	99500.5i	−0.924129	+	0.924129i	−0.997318	−	0.0731895i	$-0.976682\pi$
$103$	−99500.5	+	99500.5i	−0.924129	+	0.924129i	0.0731895	+	0.997318i	$0.476682\pi$
$104$		−	215644.i		−	1.95503i
$105$	−144304.	−	113381.i	−1.27734	−	1.00362i
$106$			51119.8i			0.441901i
$107$	147085.	−	147085.i	1.24196	−	1.24196i	0.282775	−	0.959186i	$-0.408745\pi$
$107$	147085.	−	147085.i	1.24196	−	1.24196i	0.959186	−	0.282775i	$-0.0912551\pi$
$108$	124047.	−	124047.i	1.02335	−	1.02335i
$109$	127251.			1.02588			0.512939	−	0.858425i	$-0.328557\pi$
$109$	127251.			1.02588			0.512939	+	0.858425i	$0.328557\pi$
$110$	−73407.7	+	233306.i	−0.578442	+	1.83842i
$111$	−187158.			−1.44178
$112$	−363580.	+	363580.i	−2.73877	+	2.73877i
$113$	161049.	−	161049.i	1.18648	−	1.18648i	0.208450	−	0.978033i	$-0.433158\pi$
$113$	161049.	−	161049.i	1.18648	−	1.18648i	0.978033	−	0.208450i	$-0.0668420\pi$
$114$		−	368107.i		−	2.65284i
$115$	−1723.76	−	14364.6i	−0.0121544	−	0.101286i
$116$		−	270567.i		−	1.86694i
$117$	−83508.0	+	83508.0i	−0.563980	+	0.563980i
$118$	−93625.4	−	93625.4i	−0.618997	−	0.618997i
$119$			172593.i			1.11726i
$120$	493415.	−	627984.i	3.12795	−	3.98103i
$121$	106469.	+	120838.i	0.661089	+	0.750308i
$122$	140656.	+	140656.i	0.855575	+	0.855575i
$123$	237215.	+	237215.i	1.41377	+	1.41377i
$124$			50410.8i			0.294421i
$125$	159000.	+	72364.9i	0.910167	+	0.414241i
$126$	490803.			2.75410
$127$	10135.2	−	10135.2i	0.0557601	−	0.0557601i	−0.678677	−	0.734437i	$-0.737446\pi$
$127$	10135.2	−	10135.2i	0.0557601	−	0.0557601i	0.734437	+	0.678677i	$0.237446\pi$
$128$	−406706.	−	406706.i	−2.19409	−	2.19409i
$129$	−222572.			−1.17760
$130$	−135758.	+	172784.i	−0.704545	+	0.896695i
$131$			293178.i			1.49264i	0.665590	+	0.746318i	$0.268180\pi$
$131$			293178.i			1.49264i	−0.665590	+	0.746318i	$0.731820\pi$
$132$	−294197.	−	778921.i	−1.46962	−	3.89098i
$133$	137372.	−	137372.i	0.673394	−	0.673394i
$134$	−312086.			−1.50146
$135$	−112098.	+	13451.9i	−0.529377	+	0.0635257i
$136$	−751093.			−3.48214
$137$	−292638.	−	292638.i	−1.33208	−	1.33208i	−0.903509	−	0.428569i	$-0.859018\pi$
$137$	−292638.	−	292638.i	−1.33208	−	1.33208i	−0.428569	−	0.903509i	$-0.640982\pi$
$138$	47656.7	+	47656.7i	0.213023	+	0.213023i
$139$	215305.			0.945185			0.472593	−	0.881281i	$-0.343318\pi$
$139$	215305.			0.945185			0.472593	+	0.881281i	$0.343318\pi$
$140$	662595.	−	79511.9i	2.85712	−	0.342856i
$141$	137015.			0.580388
$142$	−553.099	+	553.099i	−0.00230188	+	0.00230188i
$143$	51124.7	+	135358.i	0.209069	+	0.553535i
$144$			1.22544e6i			4.92476i
$145$	−107582.	+	136923.i	−0.424933	+	0.540825i
$146$	123437.			0.479252
$147$	35167.8	+	35167.8i	0.134231	+	0.134231i
$148$	481245.	−	481245.i	1.80597	−	1.80597i
$149$	493846.			1.82232			0.911162	−	0.412049i	$-0.135187\pi$
$149$	493846.			1.82232			0.911162	+	0.412049i	$0.135187\pi$
$150$	−790693.	+	192540.i	−2.86932	+	0.698704i
$151$		−	248572.i		−	0.887174i	−0.896231	−	0.443587i	$-0.853706\pi$
$151$		−	248572.i		−	0.887174i	0.896231	−	0.443587i	$-0.146294\pi$
$152$	597818.	+	597818.i	2.09874	+	2.09874i
$153$	290860.	+	290860.i	1.00451	+	1.00451i
$154$	247534.	−	548009.i	0.841071	−	1.86203i
$155$	20044.3	−	25510.9i	0.0670132	−	0.0852897i
$156$		−	748050.i		−	2.46104i
$157$	64199.8	+	64199.8i	0.207866	+	0.207866i	0.803360	−	0.595494i	$-0.203043\pi$
$157$	64199.8	+	64199.8i	0.207866	+	0.207866i	−0.595494	+	0.803360i	$0.703043\pi$
$158$	−311953.	+	311953.i	−0.994139	+	0.994139i
$159$			112000.i			0.351339i
$160$	144187.	+	1.20155e6i	0.445273	+	3.71058i
$161$			35569.5i			0.108147i
$162$	−241705.	+	241705.i	−0.723600	+	0.723600i
$163$	159667.	−	159667.i	0.470703	−	0.470703i	−0.431439	−	0.902142i	$-0.641994\pi$
$163$	159667.	−	159667.i	0.470703	−	0.470703i	0.902142	+	0.431439i	$0.141994\pi$
$164$	−1.21992e6			−3.54177
$165$	−160831.	+	511159.i	−0.459898	+	1.46166i
$166$	257988.			0.726656
$167$	−78175.6	+	78175.6i	−0.216910	+	0.216910i	−0.807195	−	0.590285i	$-0.799015\pi$
$167$	−78175.6	+	78175.6i	−0.216910	+	0.216910i	0.590285	+	0.807195i	$0.299015\pi$
$168$	−1.38840e6	+	1.38840e6i	−3.79527	+	3.79527i
$169$		−	241299.i		−	0.649889i
$170$	601810.	+	472850.i	1.59712	+	1.25488i
$171$		−	463009.i		−	1.21087i
$172$	572306.	−	572306.i	1.47505	−	1.47505i
$173$	−270580.	−	270580.i	−0.687353	−	0.687353i	0.274293	−	0.961646i	$-0.411556\pi$
$173$	−270580.	−	270580.i	−0.687353	−	0.687353i	−0.961646	+	0.274293i	$0.911556\pi$
$174$		−	811184.i		−	2.03117i
$175$	−366928.	−	223222.i	−0.905704	−	0.550987i
$176$	1.36827e6	+	618043.i	3.32959	+	1.50396i
$177$	−205127.	−	205127.i	−0.492142	−	0.492142i
$178$	729618.	+	729618.i	1.72602	+	1.72602i
$179$			215896.i			0.503632i	0.967775	+	0.251816i	$0.0810277\pi$
$179$			215896.i			0.503632i	−0.967775	+	0.251816i	$0.918972\pi$
$180$	982632.	−	1.25063e6i	2.26053	−	2.87704i
$181$	−813692.			−1.84614			−0.923068	−	0.384638i	$-0.874326\pi$
$181$	−813692.			−1.84614			−0.923068	+	0.384638i	$0.874326\pi$
$182$	382006.	−	382006.i	0.854854	−	0.854854i
$183$	308168.	+	308168.i	0.680236	+	0.680236i
$184$	−154792.			−0.337058
$185$	−434891.	+	52187.2i	−0.934223	+	0.112108i
$186$			151136.i			0.320322i
$187$	471456.	−	178068.i	0.985909	−	0.372377i
$188$	−352310.	+	352310.i	−0.726993	+	0.726993i
$189$	277578.			0.565238
$190$	−102643.	−	855354.i	−0.206275	−	1.71894i
$191$	−250706.			−0.497257			−0.248628	−	0.968599i	$-0.579980\pi$
$191$	−250706.			−0.497257			−0.248628	+	0.968599i	$0.579980\pi$
$192$	−1.96428e6	−	1.96428e6i	−3.84548	−	3.84548i
$193$	−273659.	−	273659.i	−0.528831	−	0.528831i	0.391393	−	0.920224i	$-0.371993\pi$
$193$	−273659.	−	273659.i	−0.528831	−	0.528831i	−0.920224	+	0.391393i	$0.871993\pi$
$194$	964783.			1.84046
$195$	−297438.	+	378558.i	−0.560158	+	0.712929i
$196$	−180856.			−0.336274
$197$	−651222.	+	651222.i	−1.19554	+	1.19554i	−0.220050	+	0.975489i	$0.570622\pi$
$197$	−651222.	+	651222.i	−1.19554	+	1.19554i	−0.975489	+	0.220050i	$0.929378\pi$
$198$	−506372.	−	1.34068e6i	−0.917924	−	2.43031i
$199$			81978.1i			0.146746i	0.997305	+	0.0733728i	$0.0233763\pi$
$199$			81978.1i			0.146746i	−0.997305	+	0.0733728i	$0.976624\pi$
$200$	971420.	−	1.59680e6i	1.71724	−	2.82278i
$201$	−683761.			−1.19375
$202$	1.26277e6	+	1.26277e6i	2.17744	+	2.17744i
$203$	302722.	−	302722.i	0.515589	−	0.515589i
$204$	−2.60547e6			−4.38340
$205$	617351.	+	485061.i	1.02600	+	0.806142i
$206$		−	1.53412e6i		−	2.51878i
$207$	59943.1	+	59943.1i	0.0972329	+	0.0972329i
$208$	953795.	+	953795.i	1.52861	+	1.52861i
$209$	−516976.	−	233516.i	−0.818662	−	0.369786i
$210$	1.98652e6	−	238384.i	3.10846	−	0.373018i
$211$		−	514957.i		−	0.796278i	−0.917325	−	0.398139i	$-0.869656\pi$
$211$		−	514957.i		−	0.796278i	0.917325	−	0.398139i	$-0.130344\pi$
$212$	−287990.	−	287990.i	−0.440086	−	0.440086i
$213$	−1211.80	+	1211.80i	−0.00183014	+	0.00183014i
$214$			2.26778e6i			3.38506i
$215$	−517181.	+	62062.2i	−0.763039	+	0.0915653i
$216$			1.20797e6i			1.76166i
$217$	−56401.9	+	56401.9i	−0.0813100	+	0.0813100i
$218$	−980992.	+	980992.i	−1.39805	+	1.39805i
$219$	270443.			0.381035
$220$	−900809.	−	1.72791e6i	−1.25480	−	2.40694i
$221$	452770.			0.623587
$222$	1.44282e6	−	1.44282e6i	1.96485	−	1.96485i
$223$	274116.	−	274116.i	0.369123	−	0.369123i	−0.498034	−	0.867157i	$-0.665945\pi$
$223$	274116.	−	274116.i	0.369123	−	0.369123i	0.867157	+	0.498034i	$0.165945\pi$
$224$		−	2.97528e6i		−	3.96194i
$225$	−994543.	+	242179.i	−1.30969	+	0.318919i
$226$			2.48308e6i			3.23385i
$227$	−689400.	+	689400.i	−0.887987	+	0.887987i	−0.994330	−	0.106343i	$-0.966086\pi$
$227$	−689400.	+	689400.i	−0.887987	+	0.887987i	0.106343	+	0.994330i	$0.466086\pi$
$228$	2.07377e6	+	2.07377e6i	2.64195	+	2.64195i
$229$		−	86699.3i		−	0.109251i	−0.998507	−	0.0546257i	$-0.982603\pi$
$229$		−	86699.3i		−	0.109251i	0.998507	−	0.0546257i	$-0.0173966\pi$
$230$	124026.	+	97449.2i	0.154595	+	0.121467i
$231$	542330.	−	1.20065e6i	0.668704	−	1.48043i
$232$	1.31739e6	+	1.31739e6i	1.60692	+	1.60692i
$233$	163582.	+	163582.i	0.197399	+	0.197399i	0.798884	−	0.601485i	$-0.205424\pi$
$233$	163582.	+	163582.i	0.197399	+	0.197399i	−0.601485	+	0.798884i	$0.705424\pi$
$234$		−	1.28754e6i		−	1.53717i
$235$	318375.	−	38205.3i	0.376070	−	0.0451288i
$236$	1.05490e6			1.23291
$237$	−683470.	+	683470.i	−0.790403	+	0.790403i
$238$	−1.33054e6	−	1.33054e6i	−1.52259	−	1.52259i
$239$	−304570.			−0.344899			−0.172450	−	0.985018i	$-0.555168\pi$
$239$	−304570.			−0.344899			−0.172450	+	0.985018i	$0.555168\pi$
$240$	595198.	+	4.95995e6i	0.667012	+	5.55839i
$241$		−	1.68986e6i		−	1.87416i	−0.349112	−	0.937081i	$-0.613517\pi$
$241$		−	1.68986e6i		−	1.87416i	0.349112	−	0.937081i	$-0.386483\pi$
$242$	−1.75233e6	−	110770.i	−1.92343	−	0.121586i
$243$	−876593.	+	876593.i	−0.952319	+	0.952319i
$244$	−1.58480e6			−1.70412
$245$	91524.2	+	71911.8i	0.0974139	+	0.0765393i
$246$	−3.65742e6			−3.85334
$247$	−360374.	−	360374.i	−0.375847	−	0.375847i
$248$	−245450.	−	245450.i	−0.253416	−	0.253416i
$249$	565235.			0.577737
$250$	−1.78361e6	+	667875.i	−1.80489	+	0.675842i
$251$	1.41172e6			1.41438			0.707188	−	0.707025i	$-0.249963\pi$
$251$	1.41172e6			1.41438			0.707188	+	0.707025i	$0.249963\pi$
$252$	−2.76500e6	+	2.76500e6i	−2.74280	+	2.74280i
$253$	97161.9	−	36697.9i	0.0954322	−	0.0360446i
$254$			156267.i			0.151979i
$255$	1.31853e6	+	1.03598e6i	1.26981	+	0.997705i
$256$	2.54914e6			2.43105
$257$	267880.	+	267880.i	0.252992	+	0.252992i	0.822196	−	0.569204i	$-0.192749\pi$
$257$	267880.	+	267880.i	0.252992	+	0.252992i	−0.569204	+	0.822196i	$0.692749\pi$
$258$	1.71583e6	−	1.71583e6i	1.60481	−	1.60481i
$259$	1.07688e6			0.997508
$260$	−208587.	−	1.73821e6i	−0.191361	−	1.59466i
$261$		−	1.02032e6i		−	0.927115i
$262$	−2.26014e6	−	2.26014e6i	−2.03415	−	2.03415i
$263$	−1.48278e6	−	1.48278e6i	−1.32186	−	1.32186i	−0.912267	−	0.409595i	$-0.865670\pi$
$263$	−1.48278e6	−	1.48278e6i	−1.32186	−	1.32186i	−0.409595	−	0.912267i	$-0.634330\pi$
$264$	5.22502e6	+	2.36012e6i	4.61401	+	2.08413i
$265$	31230.3	+	260250.i	0.0273188	+	0.227655i
$266$			2.11803e6i			1.83539i
$267$	1.59855e6	+	1.59855e6i	1.37229	+	1.37229i
$268$	1.75818e6	−	1.75818e6i	1.49529	−	1.49529i
$269$		−	692482.i		−	0.583483i	−0.956497	−	0.291741i	$-0.905765\pi$
$269$		−	692482.i		−	0.583483i	0.956497	−	0.291741i	$-0.0942346\pi$
$270$	760476.	−	967880.i	0.634857	−	0.808001i
$271$		−	241675.i		−	0.199898i	−0.994993	−	0.0999490i	$-0.968132\pi$
$271$		−	241675.i		−	0.199898i	0.994993	−	0.0999490i	$-0.0318680\pi$
$272$	3.32209e6	−	3.32209e6i	2.72263	−	2.72263i
$273$	836952.	−	836952.i	0.679663	−	0.679663i
$274$	4.51195e6			3.63068
$275$	−231185.	+	1.23261e6i	−0.184344	+	0.982862i
$276$	−536960.			−0.424296
$277$	659834.	−	659834.i	0.516696	−	0.516696i	−0.399874	−	0.916570i	$-0.630946\pi$
$277$	659834.	−	659834.i	0.516696	−	0.516696i	0.916570	+	0.399874i	$0.130946\pi$
$278$	−1.65981e6	+	1.65981e6i	−1.28809	+	1.28809i
$279$			190101.i			0.146209i
$280$	−2.83903e6	+	3.61332e6i	−2.16409	+	2.75430i
$281$			2.08712e6i			1.57682i	0.615150	+	0.788410i	$0.289095\pi$
$281$			2.08712e6i			1.57682i	−0.615150	+	0.788410i	$0.710905\pi$
$282$	−1.05626e6	+	1.05626e6i	−0.790947	+	0.790947i
$283$	−197844.	−	197844.i	−0.146845	−	0.146845i	0.629862	−	0.776707i	$-0.283111\pi$
$283$	−197844.	−	197844.i	−0.146845	−	0.146845i	−0.776707	+	0.629862i	$0.783111\pi$
$284$		−	6231.90i		−	0.00458485i
$285$	−224885.	−	1.87403e6i	−0.164001	−	1.36667i
$286$	−1.43761e6	−	649365.i	−1.03927	−	0.469433i
$287$	−1.36490e6	−	1.36490e6i	−0.978126	−	0.978126i
$288$	−5.01405e6	−	5.01405e6i	−3.56211	−	3.56211i
$289$		−	157152.i		−	0.110681i
$290$	−226191.	−	1.88491e6i	−0.157936	−	1.31612i
$291$	2.11378e6			1.46328
$292$	−695398.	+	695398.i	−0.477284	+	0.477284i
$293$	−786238.	−	786238.i	−0.535038	−	0.535038i	0.387029	−	0.922067i	$-0.373501\pi$
$293$	−786238.	−	786238.i	−0.535038	−	0.535038i	−0.922067	+	0.387029i	$0.873501\pi$
$294$	−542224.			−0.365856
$295$	−533843.	−	419448.i	−0.357157	−	0.280623i
$296$			4.68637e6i			3.10890i
$297$	−286384.	−	758234.i	−0.188390	−	0.498784i
$298$	−3.80710e6	+	3.80710e6i	−2.48344	+	2.48344i
$299$	93311.1			0.0603608
$300$	3.36977e6	−	5.53917e6i	2.16171	−	3.55338i
$301$	1.28064e6			0.814727
$302$	1.91626e6	+	1.91626e6i	1.20903	+	1.20903i
$303$	2.76665e6	+	2.76665e6i	1.73120	+	1.73120i
$304$	−5.28830e6			−3.28195
$305$	802007.	+	630147.i	0.493661	+	0.387875i
$306$	−4.48454e6			−2.73788
$307$	879499.	−	879499.i	0.532586	−	0.532586i	−0.388755	−	0.921341i	$-0.627095\pi$
$307$	879499.	−	879499.i	0.532586	−	0.532586i	0.921341	+	0.388755i	$0.127095\pi$
$308$	1.69277e6	+	4.48179e6i	1.01676	+	2.69200i
$309$		−	3.36116e6i		−	2.00259i
$310$	42143.0	+	351189.i	0.0249070	+	0.207557i
$311$	1.67019e6			0.979184			0.489592	−	0.871952i	$-0.337146\pi$
$311$	1.67019e6			0.979184			0.489592	+	0.871952i	$0.337146\pi$
$312$	3.64226e6	+	3.64226e6i	2.11828	+	2.11828i
$313$	−73261.5	+	73261.5i	−0.0422683	+	0.0422683i	−0.727925	−	0.685657i	$-0.759515\pi$
$313$	−73261.5	+	73261.5i	−0.0422683	+	0.0422683i	0.685657	+	0.727925i	$0.259515\pi$
$314$	−989844.			−0.566556
$315$	2.49867e6	−	299842.i	1.41884	−	0.170262i
$316$		−	3.51486e6i		−	1.98011i
$317$	1.14103e6	+	1.14103e6i	0.637749	+	0.637749i	0.950000	−	0.312251i	$-0.101083\pi$
$317$	1.14103e6	+	1.14103e6i	0.637749	+	0.637749i	−0.312251	+	0.950000i	$0.601083\pi$
$318$	−863421.	−	863421.i	−0.478801	−	0.478801i
$319$	−1.13924e6	−	514591.i	−0.626815	−	0.283130i
$320$	−5.11204e6	−	4.01659e6i	−2.79074	−	2.19272i
$321$			4.96856e6i			2.69134i
$322$	−274209.	−	274209.i	−0.147381	−	0.147381i
$323$	−1.25519e6	+	1.25519e6i	−0.669426	+	0.669426i
$324$		−	2.72335e6i		−	1.44126i
$325$	−585587.	+	962578.i	−0.307527	+	0.505507i
$326$			2.46178e6i			1.28294i
$327$	−2.14929e6	+	2.14929e6i	−1.11154	+	1.11154i
$328$	5.93978e6	−	5.93978e6i	3.04850	−	3.04850i
$329$	−788360.			−0.401546
$330$	−2.70071e6	−	5.18044e6i	−1.36519	−	2.61868i
$331$	−652652.			−0.327425			−0.163712	−	0.986508i	$-0.552347\pi$
$331$	−652652.			−0.327425			−0.163712	+	0.986508i	$0.552347\pi$
$332$	−1.45341e6	+	1.45341e6i	−0.723672	+	0.723672i
$333$	1.81479e6	−	1.81479e6i	0.896842	−	0.896842i
$334$		−	1.20533e6i		−	0.591205i
$335$	−1.58883e6	+	190661.i	−0.773507	+	0.0928216i
$336$		−	1.22818e7i		−	5.93492i
$337$	1.80174e6	−	1.80174e6i	0.864206	−	0.864206i	−0.127617	−	0.991823i	$-0.540733\pi$
$337$	1.80174e6	−	1.80174e6i	0.864206	−	0.864206i	0.991823	+	0.127617i	$0.0407329\pi$
$338$	1.86020e6	+	1.86020e6i	0.885662	+	0.885662i
$339$			5.44028e6i			2.57112i
$340$	−6.05423e6	+	726512.i	−2.84028	+	0.340836i
$341$	212259.	+	95876.4i	0.0988506	+	0.0446505i
$342$	3.56938e6	+	3.56938e6i	1.65016	+	1.65016i
$343$	1.43101e6	+	1.43101e6i	0.656760	+	0.656760i
$344$			5.57313e6i			2.53923i
$345$	271734.	+	213505.i	0.122913	+	0.0965740i
$346$	4.17185e6			1.87343
$347$	1.79709e6	−	1.79709e6i	0.801210	−	0.801210i	−0.182074	−	0.983285i	$-0.558281\pi$
$347$	1.79709e6	−	1.79709e6i	0.801210	−	0.801210i	0.983285	+	0.182074i	$0.0582812\pi$
$348$	4.56991e6	+	4.56991e6i	2.02283	+	2.02283i
$349$	−1.94330e6			−0.854037			−0.427019	−	0.904243i	$-0.640436\pi$
$349$	−1.94330e6			−0.854037			−0.427019	+	0.904243i	$0.640436\pi$
$350$	4.54952e6	−	1.10785e6i	1.98516	−	0.483403i
$351$		−	728183.i		−	0.315480i
$352$	−8.12729e6	+	3.06967e6i	−3.49614	+	1.32049i
$353$	3.19507e6	−	3.19507e6i	1.36472	−	1.36472i	0.496933	−	0.867789i	$-0.334460\pi$
$353$	3.19507e6	−	3.19507e6i	1.36472	−	1.36472i	0.867789	−	0.496933i	$-0.165540\pi$
$354$	3.16269e6			1.34137
$355$	−2477.92	+	3153.72i	−0.00104356	+	0.00132817i
$356$	−8.22079e6			−3.43786
$357$	−2.91512e6	−	2.91512e6i	−1.21056	−	1.21056i
$358$	−1.66437e6	−	1.66437e6i	−0.686343	−	0.686343i
$359$	1.35867e6			0.556387			0.278193	−	0.960525i	$-0.410264\pi$
$359$	1.35867e6			0.556387			0.278193	+	0.960525i	$0.410264\pi$
$360$	1.30486e6	+	1.08737e7i	0.530649	+	4.42204i
$361$	−478014.			−0.193051
$362$	6.27283e6	−	6.27283e6i	2.51589	−	2.51589i
$363$	−3.83924e6	−	242690.i	−1.52925	−	0.0966687i
$364$			4.30416e6i			1.70269i
$365$	628417.	−	75410.5i	0.246897	−	0.0296278i
$366$	−4.75139e6			−1.85404
$367$	−2.47441e6	−	2.47441e6i	−0.958973	−	0.958973i	0.0402183	−	0.999191i	$-0.487195\pi$
$367$	−2.47441e6	−	2.47441e6i	−0.958973	−	0.958973i	−0.999191	+	0.0402183i	$0.987195\pi$
$368$	684646.	−	684646.i	0.263540	−	0.263540i
$369$	−4.60035e6			−1.75883
$370$	2.95030e6	−	3.75493e6i	1.12037	−	1.42593i
$371$		−	644432.i		−	0.243076i
$372$	−851445.	−	851445.i	−0.319006	−	0.319006i
$373$	−1.34191e6	−	1.34191e6i	−0.499403	−	0.499403i	0.411849	−	0.911252i	$-0.364883\pi$
$373$	−1.34191e6	−	1.34191e6i	−0.499403	−	0.499403i	−0.911252	+	0.411849i	$0.864883\pi$
$374$	−2.26175e6	+	5.00724e6i	−0.836115	+	1.85106i
$375$	−3.90778e6	+	1.46327e6i	−1.43500	+	0.537337i
$376$		−	3.43080e6i		−	1.25148i
$377$	−794143.	−	794143.i	−0.287770	−	0.287770i
$378$	−2.13988e6	+	2.13988e6i	−0.770299	+	0.770299i
$379$			1.58935e6i			0.568357i	0.958771	+	0.284178i	$0.0917208\pi$
$379$			1.58935e6i			0.568357i	−0.958771	+	0.284178i	$0.908279\pi$
$380$	5.39700e6	+	4.24049e6i	1.91731	+	1.50646i
$381$			342371.i			0.120833i
$382$	1.93271e6	−	1.93271e6i	0.677656	−	0.677656i
$383$	−309039.	+	309039.i	−0.107651	+	0.107651i	−0.758881	−	0.651230i	$-0.774253\pi$
$383$	−309039.	+	309039.i	−0.107651	+	0.107651i	0.651230	+	0.758881i	$0.274253\pi$
$384$	1.37386e7			4.75461
$385$	925399.	−	2.94113e6i	0.318183	−	1.01126i
$386$	4.21933e6			1.44137
$387$	2.15819e6	−	2.15819e6i	0.732507	−	0.732507i
$388$	−5.43523e6	+	5.43523e6i	−1.83290	+	1.83290i
$389$		−	2.55195e6i		−	0.855064i	−0.904000	−	0.427532i	$-0.859383\pi$
$389$		−	2.55195e6i		−	0.855064i	0.904000	−	0.427532i	$-0.140617\pi$
$390$	−625363.	−	5.21132e6i	−0.208195	−	1.73495i
$391$		−	325004.i		−	0.107510i
$392$	880590.	−	880590.i	0.289440	−	0.289440i
$393$	−4.95182e6	−	4.95182e6i	−1.61727	−	1.61727i
$394$		−	1.00407e7i		−	3.25853i
$395$	−1.39757e6	+	1.77873e6i	−0.450693	+	0.573611i
$396$	1.04056e7	+	4.70017e6i	3.33448	+	1.50617i
$397$	863149.	+	863149.i	0.274859	+	0.274859i	0.831053	−	0.556194i	$-0.187739\pi$
$397$	863149.	+	863149.i	0.274859	+	0.274859i	−0.556194	+	0.831053i	$0.687739\pi$
$398$	−631977.	−	631977.i	−0.199983	−	0.199983i
$399$			4.64046e6i			1.45925i
$400$	2.76608e6	+	1.13593e7i	0.864398	+	3.54977i
$401$	−3.21589e6			−0.998713			−0.499357	−	0.866397i	$-0.666430\pi$
$401$	−3.21589e6			−0.998713			−0.499357	+	0.866397i	$0.666430\pi$
$402$	5.27118e6	−	5.27118e6i	1.62683	−	1.62683i
$403$	147961.	+	147961.i	0.0453822	+	0.0453822i
$404$	−1.42280e7			−4.33700
$405$	−1.08285e6	+	1.37818e6i	−0.328044	+	0.417512i
$406$			4.66743e6i			1.40528i
$407$	−1.11104e6	−	2.94160e6i	−0.332463	−	0.880233i
$408$	1.26861e7	−	1.26861e7i	3.77291	−	3.77291i
$409$	1.19272e6			0.352558			0.176279	−	0.984340i	$-0.443594\pi$
$409$	1.19272e6			0.352558			0.176279	+	0.984340i	$0.443594\pi$
$410$	−8.49860e6	+	1.01984e6i	−2.49682	+	0.299621i
$411$	9.88540e6			2.88662
$412$	8.64265e6	+	8.64265e6i	2.50844	+	2.50844i
$413$	1.18027e6	+	1.18027e6i	0.340492	+	0.340492i
$414$	−924214.			−0.265016
$415$	1.31341e6	−	157611.i	0.374353	−	0.0449226i
$416$	−7.80518e6			−2.21131
$417$	−3.63653e6	+	3.63653e6i	−1.02411	+	1.02411i
$418$	5.78561e6	−	2.18522e6i	1.61960	−	0.611722i
$419$			4.91446e6i			1.36754i	0.729696	+	0.683772i	$0.239662\pi$
$419$			4.91446e6i			1.36754i	−0.729696	+	0.683772i	$0.760338\pi$
$420$	−9.84835e6	+	1.25343e7i	−2.72421	+	3.46718i
$421$	−1.17877e6			−0.324134			−0.162067	−	0.986780i	$-0.551816\pi$
$421$	−1.17877e6			−0.324134			−0.162067	+	0.986780i	$0.551816\pi$
$422$	3.96985e6	+	3.96985e6i	1.08516	+	1.08516i
$423$	−1.32857e6	+	1.32857e6i	−0.361023	+	0.361023i
$424$	2.80445e6			0.757588
$425$	3.35268e6	+	2.03961e6i	0.900367	+	0.547741i
$426$		−	18683.8i		−	0.00498818i
$427$	−1.77315e6	−	1.77315e6i	−0.470626	−	0.470626i
$428$	−1.27758e7	−	1.27758e7i	−3.37116	−	3.37116i
$429$	−3.14972e6	−	1.42272e6i	−0.826283	−	0.373229i
$430$	3.50856e6	−	4.46544e6i	0.915076	−	1.16464i
$431$			4.77313e6i			1.23769i	0.785515	+	0.618843i	$0.212398\pi$
$431$			4.77313e6i			1.23769i	−0.785515	+	0.618843i	$0.787602\pi$
$432$	−5.34285e6	−	5.34285e6i	−1.37741	−	1.37741i
$433$	−2.62325e6	+	2.62325e6i	−0.672388	+	0.672388i	−0.958266	−	0.285878i	$-0.907715\pi$
$433$	−2.62325e6	+	2.62325e6i	−0.672388	+	0.672388i	0.285878	+	0.958266i	$0.407715\pi$
$434$		−	869615.i		−	0.221617i
$435$	−495571.	−	4.12973e6i	−0.125569	−	1.04640i
$436$		−	1.10531e7i		−	2.78463i
$437$	−258681.	+	258681.i	−0.0647978	+	0.0647978i
$438$	−2.08487e6	+	2.08487e6i	−0.519270	+	0.519270i
$439$	5.29240e6			1.31067			0.655333	−	0.755340i	$-0.272529\pi$
$439$	5.29240e6			1.31067			0.655333	+	0.755340i	$0.272529\pi$
$440$	1.27993e7	+	4.02717e6i	3.15176	+	0.991672i
$441$	−682016.			−0.166993
$442$	−3.49045e6	+	3.49045e6i	−0.849818	+	0.849818i
$443$	1.54556e6	−	1.54556e6i	0.374176	−	0.374176i	−0.494820	−	0.868996i	$-0.664766\pi$
$443$	1.54556e6	−	1.54556e6i	0.374176	−	0.374176i	0.868996	+	0.494820i	$0.164766\pi$
$444$			1.62566e7i			3.91356i
$445$	4.16021e6	+	3.26873e6i	0.995900	+	0.782491i
$446$			4.22637e6i			1.00607i
$447$	−8.34112e6	+	8.34112e6i	−1.97449	+	1.97449i
$448$	1.13022e7	+	1.13022e7i	2.66052	+	2.66052i
$449$		−	2.12484e6i		−	0.497405i	−0.968580	−	0.248703i	$-0.919996\pi$
$449$		−	2.12484e6i		−	0.497405i	0.968580	−	0.248703i	$-0.0800042\pi$
$450$	5.80004e6	−	9.53401e6i	1.35021	−	2.21944i
$451$	−2.32016e6	+	5.13655e6i	−0.537127	+	1.18913i
$452$	−1.39888e7	−	1.39888e7i	−3.22057	−	3.22057i
$453$	4.19841e6	+	4.19841e6i	0.961256	+	0.961256i
$454$		−	1.06293e7i		−	2.42028i
$455$	1.71141e6	−	2.17817e6i	0.387549	−	0.493245i
$456$	−2.01944e7			−4.54799
$457$	5.45677e6	−	5.45677e6i	1.22221	−	1.22221i	0.255362	−	0.966846i	$-0.417806\pi$
$457$	5.45677e6	−	5.45677e6i	1.22221	−	1.22221i	0.966846	−	0.255362i	$-0.0821945\pi$
$458$	668373.	+	668373.i	0.148887	+	0.148887i
$459$	−2.53627e6			−0.561907
$460$	−1.24771e6	+	149726.i	−0.274928	+	0.0329916i
$461$		−	1.65802e6i		−	0.363361i	−0.983358	−	0.181681i	$-0.941846\pi$
$461$		−	1.65802e6i		−	0.363361i	0.983358	−	0.181681i	$-0.0581537\pi$
$462$	5.07507e6	+	1.34368e7i	1.10621	+	2.92881i
$463$	−2.98781e6	+	2.98781e6i	−0.647740	+	0.647740i	−0.952446	−	0.304706i	$-0.901442\pi$
$463$	−2.98781e6	+	2.98781e6i	−0.647740	+	0.647740i	0.304706	+	0.952446i	$0.401442\pi$
$464$	−1.16536e7			−2.51285
$465$	92332.6	+	769433.i	0.0198026	+	0.165021i
$466$	−2.52213e6			−0.538025
$467$	−1.93710e6	−	1.93710e6i	−0.411017	−	0.411017i	0.471076	−	0.882093i	$-0.343866\pi$
$467$	−1.93710e6	−	1.93710e6i	−0.411017	−	0.411017i	−0.882093	+	0.471076i	$0.843866\pi$
$468$	7.25353e6	+	7.25353e6i	1.53086	+	1.53086i
$469$	3.93425e6			0.825905
$470$	−2.15985e6	+	2.74891e6i	−0.451003	+	0.574005i
$471$	−2.16869e6			−0.450448
$472$	−5.13632e6	+	5.13632e6i	−1.06120	+	1.06120i
$473$	−1.32127e6	−	3.49821e6i	−0.271543	−	0.718941i
$474$		−	1.05379e7i		−	2.15430i
$475$	−1.04511e6	−	4.29189e6i	−0.212534	−	0.872799i
$476$	1.49915e7			3.03268
$477$	−1.08602e6	−	1.08602e6i	−0.218546	−	0.218546i
$478$	2.34796e6	−	2.34796e6i	0.470024	−	0.470024i
$479$	−3.25019e6			−0.647248			−0.323624	−	0.946186i	$-0.604901\pi$
$479$	−3.25019e6			−0.647248			−0.323624	+	0.946186i	$0.604901\pi$
$480$	−2.27297e7	−	1.78590e7i	−4.50288	−	3.53797i
$481$		−	2.82501e6i		−	0.556747i
$482$	1.30273e7	+	1.30273e7i	2.55409	+	2.55409i
$483$	−600774.	−	600774.i	−0.117177	−	0.117177i
$484$	1.04960e7	−	9.24793e6i	2.03662	−	1.79445i
$485$	4.91170e6	−	589408.i	0.948151	−	0.113779i
$486$		−	1.35155e7i		−	2.59562i
$487$	−1.57167e6	−	1.57167e6i	−0.300288	−	0.300288i	0.540838	−	0.841127i	$-0.318107\pi$
$487$	−1.57167e6	−	1.57167e6i	−0.300288	−	0.300288i	−0.841127	+	0.540838i	$0.818107\pi$
$488$	7.71642e6	−	7.71642e6i	1.46678	−	1.46678i
$489$			5.39361e6i			1.02002i
$490$	−1.25994e6	+	151194.i	−0.237061	+	0.0284476i
$491$		−	558411.i		−	0.104532i	−0.998633	−	0.0522661i	$-0.983356\pi$
$491$		−	558411.i		−	0.104532i	0.998633	−	0.0522661i	$-0.0166444\pi$
$492$	2.06045e7	−	2.06045e7i	3.83752	−	3.83752i
$493$	−2.76602e6	+	2.76602e6i	−0.512552	+	0.512552i
$494$	5.55631e6			1.02440
$495$	−3.39698e6	−	6.51602e6i	−0.623133	−	1.19528i
$496$	2.17126e6			0.396284
$497$	6972.53	−	6972.53i	0.00126619	−	0.00126619i
$498$	−4.35745e6	+	4.35745e6i	−0.787334	+	0.787334i
$499$		−	2.86754e6i		−	0.515535i	−0.966207	−	0.257768i	$-0.917013\pi$
$499$		−	2.86754e6i		−	0.515535i	0.966207	−	0.257768i	$-0.0829869\pi$
$500$	6.28564e6	−	1.38108e7i	1.12441	−	2.47054i
$501$		−	2.64079e6i		−	0.470046i
$502$	−1.08831e7	+	1.08831e7i	−1.92750	+	1.92750i
$503$	−5.54040e6	−	5.54040e6i	−0.976384	−	0.976384i	0.0233432	−	0.999728i	$-0.492569\pi$
$503$	−5.54040e6	−	5.54040e6i	−0.976384	−	0.976384i	−0.999728	+	0.0233432i	$0.992569\pi$
$504$		−	2.69256e7i		−	4.72159i
$505$	7.20021e6	+	5.65730e6i	1.25637	+	0.987145i
$506$	−466123.	+	1.03194e6i	−0.0809327	+	0.179175i
$507$	4.07558e6	+	4.07558e6i	0.704157	+	0.704157i
$508$	−880348.	−	880348.i	−0.151354	−	0.151354i
$509$		−	551216.i		−	0.0943034i	−0.998888	−	0.0471517i	$-0.984986\pi$
$509$		−	551216.i		−	0.0943034i	0.998888	−	0.0471517i	$-0.0150144\pi$
$510$	−1.81511e7	+	2.17815e6i	−3.09014	+	0.370820i
$511$	−1.55609e6			−0.263622
$512$	−6.63702e6	+	6.63702e6i	−1.11892	+	1.11892i
$513$	2.01870e6	+	2.01870e6i	0.338671	+	0.338671i
$514$	−4.13022e6			−0.689550
$515$	−937228.	−	7.81018e6i	−0.155714	−	1.29761i
$516$			1.93327e7i			3.19645i
$517$	813369.	+	2.15349e6i	0.133832	+	0.354337i
$518$	−8.30174e6	+	8.30174e6i	−1.35939	+	1.35939i
$519$	9.14025e6			1.48950
$520$	9.47897e6	+	7.44775e6i	1.53728	+	1.20786i
$521$	−7.85196e6			−1.26731			−0.633657	−	0.773614i	$-0.718447\pi$
$521$	−7.85196e6			−1.26731			−0.633657	+	0.773614i	$0.718447\pi$
$522$	7.86572e6	+	7.86572e6i	1.26346	+	1.26346i
$523$	−1.59606e6	−	1.59606e6i	−0.255150	−	0.255150i	0.567928	−	0.823078i	$-0.307745\pi$
$523$	−1.59606e6	−	1.59606e6i	−0.255150	−	0.255150i	−0.823078	+	0.567928i	$0.807745\pi$
$524$	2.54656e7			4.05159
$525$	9.96772e6	−	2.42722e6i	1.57833	−	0.384336i
$526$	2.28617e7			3.60284
$527$	515352.	−	515352.i	0.0808310	−	0.0808310i
$528$	−3.35491e7	+	1.26715e7i	−5.23716	+	1.97807i
$529$			6.36936e6i			0.989593i
$530$	−2.24705e6	−	1.76554e6i	−0.347475	−	0.273016i
$531$	3.97807e6			0.612260
$532$	−1.19322e7	−	1.19322e7i	−1.82785	−	1.82785i
$533$	−3.58059e6	+	3.58059e6i	−0.545929	+	0.545929i
$534$	−2.46467e7			−3.74029
$535$	1.38544e6	+	1.15452e7i	0.209268	+	1.74389i
$536$			1.71211e7i			2.57407i
$537$	−3.64652e6	−	3.64652e6i	−0.545686	−	0.545686i
$538$	5.33841e6	+	5.33841e6i	0.795163	+	0.795163i
$539$	−343971.	+	761510.i	−0.0509976	+	0.112902i
$540$	1.16844e6	+	9.73691e6i	0.172433	+	1.43693i
$541$			5.55046e6i			0.815334i	0.913131	+	0.407667i	$0.133658\pi$
$541$			5.55046e6i			0.815334i	−0.913131	+	0.407667i	$0.866342\pi$
$542$	1.86310e6	+	1.86310e6i	0.272419	+	0.272419i
$543$	1.37434e7	−	1.37434e7i	2.00029	−	2.00029i
$544$			2.71856e7i			3.93860i
$545$	−4.39491e6	+	5.59353e6i	−0.633809	+	0.806667i
$546$			1.29043e7i			1.85247i
$547$	−5.45372e6	+	5.45372e6i	−0.779336	+	0.779336i	−0.979718	−	0.200382i	$-0.935782\pi$
$547$	−5.45372e6	+	5.45372e6i	−0.779336	+	0.779336i	0.200382	+	0.979718i	$0.435782\pi$
$548$	−2.54186e7	+	2.54186e7i	−3.61577	+	3.61577i
$549$	−5.97636e6			−0.846263
$550$	−7.72005e6	−	1.12845e7i	−1.08821	−	1.59065i
$551$	4.40311e6			0.617847
$552$	2.61446e6	−	2.61446e6i	0.365203	−	0.365203i
$553$	3.93258e6	−	3.93258e6i	0.546845	−	0.546845i
$554$			1.01734e7i			1.40830i
$555$	6.46391e6	−	8.22681e6i	0.890764	−	1.13370i
$556$		−	1.87015e7i		−	2.56560i
$557$	−3.38053e6	+	3.38053e6i	−0.461686	+	0.461686i	−0.899208	−	0.437522i	$-0.855856\pi$
$557$	−3.38053e6	+	3.38053e6i	−0.461686	+	0.461686i	0.437522	+	0.899208i	$0.355856\pi$
$558$	−1.46551e6	−	1.46551e6i	−0.199252	−	0.199252i
$559$		−	3.35957e6i		−	0.454730i
$560$	−3.42468e6	−	2.85388e7i	−0.461477	−	3.84561i
$561$	−4.95536e6	+	1.09705e7i	−0.664764	+	1.47171i
$562$	−1.60898e7	−	1.60898e7i	−2.14887	−	2.14887i
$563$	−922068.	−	922068.i	−0.122600	−	0.122600i	0.643144	−	0.765745i	$-0.277629\pi$
$563$	−922068.	−	922068.i	−0.122600	−	0.122600i	−0.765745	+	0.643144i	$0.777629\pi$
$564$		−	1.19011e7i		−	1.57540i
$565$	1.51697e6	+	1.26413e7i	0.199920	+	1.66599i
$566$	3.05040e6			0.400236
$567$	3.04701e6	−	3.04701e6i	0.398030	−	0.398030i
$568$	30343.2	+	30343.2i	0.00394630	+	0.00394630i
$569$	5.43480e6			0.703725			0.351862	−	0.936052i	$-0.385548\pi$
$569$	5.43480e6			0.703725			0.351862	+	0.936052i	$0.385548\pi$
$570$	1.61807e7	+	1.27134e7i	2.08598	+	1.63898i
$571$			5.73677e6i			0.736338i	0.929759	+	0.368169i	$0.120015\pi$
$571$			5.73677e6i			0.736338i	−0.929759	+	0.368169i	$0.879985\pi$
$572$	1.17573e7	−	4.44070e6i	1.50251	−	0.567494i
$573$	4.23445e6	−	4.23445e6i	0.538779	−	0.538779i
$574$	2.10442e7			2.66596
$575$	690951.	+	420342.i	0.0871520	+	0.0530192i
$576$	3.80936e7			4.78406
$577$	4.09231e6	+	4.09231e6i	0.511716	+	0.511716i	0.915052	−	0.403336i	$-0.132149\pi$
$577$	4.09231e6	+	4.09231e6i	0.511716	+	0.511716i	−0.403336	+	0.915052i	$0.632149\pi$
$578$	1.21150e6	+	1.21150e6i	0.150835	+	0.150835i
$579$	9.24429e6			1.14598
$580$	1.18932e7	+	9.34462e6i	1.46801	+	1.15343i
$581$	−3.25227e6			−0.399712
$582$	−1.62953e7	+	1.62953e7i	−1.99414	+	1.99414i
$583$	−1.76033e6	+	664876.i	−0.214498	+	0.0810157i
$584$		−	6.77180e6i		−	0.821621i
$585$	−786589.	−	6.55486e6i	−0.0950294	−	0.791906i
$586$	1.21224e7			1.45829
$587$	3.02675e6	+	3.02675e6i	0.362561	+	0.362561i	0.864755	−	0.502194i	$-0.167474\pi$
$587$	3.02675e6	+	3.02675e6i	0.362561	+	0.362561i	−0.502194	+	0.864755i	$0.667474\pi$
$588$	3.05469e6	−	3.05469e6i	0.364354	−	0.364354i
$589$	−820369.			−0.0974363
$590$	7.34901e6	−	881888.i	0.869159	−	0.104300i
$591$		−	2.19985e7i		−	2.59074i
$592$	−2.07278e7	−	2.07278e7i	−2.43080	−	2.43080i
$593$	6.04367e6	+	6.04367e6i	0.705771	+	0.705771i	0.965643	−	0.259872i	$-0.0836805\pi$
$593$	6.04367e6	+	6.04367e6i	0.705771	+	0.705771i	−0.259872	+	0.965643i	$0.583680\pi$
$594$	8.05306e6	+	3.63754e6i	0.936472	+	0.423001i
$595$	−7.58660e6	−	5.96089e6i	−0.878526	−	0.690269i
$596$		−	4.28956e7i		−	4.94649i
$597$	−1.38462e6	−	1.38462e6i	−0.158999	−	0.158999i
$598$	−719344.	+	719344.i	−0.0822590	+	0.0822590i
$599$		−	1.14062e7i		−	1.29889i	−0.760408	−	0.649445i	$-0.775001\pi$
$599$		−	1.14062e7i		−	1.29889i	0.760408	−	0.649445i	$-0.224999\pi$
$600$	1.05628e7	+	4.33777e7i	1.19785	+	4.91913i
$601$		−	8.64015e6i		−	0.975742i	−0.872916	−	0.487871i	$-0.837774\pi$
$601$		−	8.64015e6i		−	0.975742i	0.872916	−	0.487871i	$-0.162226\pi$
$602$	−9.87261e6	+	9.87261e6i	−1.11030	+	1.11030i
$603$	6.63015e6	−	6.63015e6i	0.742557	−	0.742557i
$604$	−2.15910e7			−2.40813
$605$	−8.98876e6	+	506609.i	−0.998416	+	0.0562709i
$606$	−4.26568e7			−4.71853
$607$	1.65227e6	−	1.65227e6i	0.182016	−	0.182016i	−0.610218	−	0.792234i	$-0.708918\pi$
$607$	1.65227e6	−	1.65227e6i	0.182016	−	0.182016i	0.792234	+	0.610218i	$0.208918\pi$
$608$	2.16378e7	−	2.16378e7i	2.37386	−	2.37386i
$609$			1.02260e7i			1.11729i
$610$	−1.10406e7	+	1.32488e6i	−1.20135	+	0.144163i
$611$			2.06814e6i			0.224118i
$612$	2.52642e7	−	2.52642e7i	2.72663	−	2.72663i
$613$	−6.75541e6	−	6.75541e6i	−0.726107	−	0.726107i	0.243735	−	0.969842i	$-0.421627\pi$
$613$	−6.75541e6	−	6.75541e6i	−0.726107	−	0.726107i	−0.969842	+	0.243735i	$0.921627\pi$
$614$			1.35603e7i			1.45160i
$615$	−1.86199e7	+	2.23440e6i	−1.98513	+	0.238217i
$616$	−3.00639e7	−	1.35798e7i	−3.19223	−	1.44192i
$617$	5.35467e6	+	5.35467e6i	0.566265	+	0.566265i	0.931080	−	0.364815i	$-0.118868\pi$
$617$	5.35467e6	+	5.35467e6i	0.566265	+	0.566265i	−0.364815	+	0.931080i	$0.618868\pi$
$618$	2.59115e7	+	2.59115e7i	2.72911	+	2.72911i
$619$			3.26169e6i			0.342149i	0.985258	+	0.171075i	$0.0547239\pi$
$619$			3.26169e6i			0.342149i	−0.985258	+	0.171075i	$0.945276\pi$
$620$	−2.21589e6	−	1.74105e6i	−0.231509	−	0.181900i
$621$	−522699.			−0.0543904
$622$	−1.28756e7	+	1.28756e7i	−1.33442	+	1.33442i
$623$	−9.19779e6	−	9.19779e6i	−0.949430	−	0.949430i
$624$	−3.22194e7			−3.31251
$625$	−8.67232e6	+	4.48979e6i	−0.888046	+	0.459755i
$626$		−	1.12956e6i		−	0.115205i
$627$	1.26759e7	−	4.78767e6i	1.28769	−	0.486358i
$628$	5.57641e6	−	5.57641e6i	0.564229	−	0.564229i
$629$	−9.83958e6			−0.991631
$630$	−1.69510e7	+	2.15740e7i	−1.70154	+	2.16560i
$631$	1.50718e7			1.50692			0.753462	−	0.657491i	$-0.228382\pi$
$631$	1.50718e7			1.50692			0.753462	+	0.657491i	$0.228382\pi$
$632$	1.71139e7	+	1.71139e7i	1.70434	+	1.70434i
$633$	8.69770e6	+	8.69770e6i	0.862770	+	0.862770i
$634$	−1.75926e7			−1.73823
$635$	95466.9	+	795552.i	0.00939547	+	0.0782950i
$636$	9.72838e6			0.953669
$637$	−530833.	+	530833.i	−0.0518334	+	0.0518334i
$638$	1.27496e7	−	4.81549e6i	1.24006	−	0.468370i
$639$		−	23500.7i		−	0.00227682i
$640$	3.19239e7	−	3.83089e6i	3.08081	−	0.369700i
$641$	3.72955e6			0.358519			0.179259	−	0.983802i	$-0.442630\pi$
$641$	3.72955e6			0.358519			0.179259	+	0.983802i	$0.442630\pi$
$642$	−3.83031e7	−	3.83031e7i	−3.66772	−	3.66772i
$643$	−7.18982e6	+	7.18982e6i	−0.685789	+	0.685789i	−0.961298	−	0.275509i	$-0.911154\pi$
$643$	−7.18982e6	+	7.18982e6i	−0.685789	+	0.685789i	0.275509	+	0.961298i	$0.411154\pi$
$644$	3.08958e6			0.293552
$645$	7.68702e6	−	9.78350e6i	0.727543	−	0.925966i
$646$		−	1.93527e7i		−	1.82457i
$647$	−602849.	−	602849.i	−0.0566172	−	0.0566172i	0.678231	−	0.734848i	$-0.262747\pi$
$647$	−602849.	−	602849.i	−0.0566172	−	0.0566172i	−0.734848	+	0.678231i	$0.762747\pi$
$648$	1.32600e7	+	1.32600e7i	1.24053	+	1.24053i
$649$	2.00632e6	−	4.44174e6i	0.186977	−	0.413944i
$650$	−2.90626e6	−	1.19350e7i	−0.269806	−	1.10799i
$651$		−	1.90527e6i		−	0.176199i
$652$	−1.38688e7	−	1.38688e7i	−1.27767	−	1.27767i
$653$	−3.21671e6	+	3.21671e6i	−0.295209	+	0.295209i	−0.839134	−	0.543925i	$-0.816938\pi$
$653$	−3.21671e6	+	3.21671e6i	−0.295209	+	0.295209i	0.543925	+	0.839134i	$0.316938\pi$
$654$		−	3.31382e7i		−	3.02959i
$655$	−1.28871e7	−	1.01256e7i	−1.17369	−	0.922181i
$656$			5.25433e7i			4.76714i
$657$	−2.62237e6	+	2.62237e6i	−0.237018	+	0.237018i
$658$	6.07754e6	−	6.07754e6i	0.547222	−	0.547222i
$659$	−74519.3			−0.00668429			−0.00334214	−	0.999994i	$-0.501064\pi$
$659$	−74519.3			−0.00668429			−0.00334214	+	0.999994i	$0.501064\pi$
$660$	4.43995e7	+	1.39699e7i	3.96751	+	1.24834i
$661$	1.77177e7			1.57726			0.788631	−	0.614867i	$-0.210790\pi$
$661$	1.77177e7			1.57726			0.788631	+	0.614867i	$0.210790\pi$
$662$	5.03135e6	−	5.03135e6i	0.446211	−	0.446211i
$663$	−7.64735e6	+	7.64735e6i	−0.675659	+	0.675659i
$664$		−	1.41533e7i		−	1.24577i
$665$	1.29395e6	+	1.07828e7i	0.113465	+	0.945539i
$666$			2.79808e7i			2.44441i
$667$	−570046.	+	570046.i	−0.0496130	+	0.0496130i
$668$	6.79035e6	+	6.79035e6i	0.588778	+	0.588778i
$669$			9.25970e6i			0.799892i
$670$	1.07786e7	−	1.37182e7i	0.927631	−	1.18062i
$671$	−3.01414e6	+	6.67294e6i	−0.258439	+	0.572152i
$672$	5.02529e7	+	5.02529e7i	4.29277	+	4.29277i
$673$	−3.34528e6	−	3.34528e6i	−0.284705	−	0.284705i	0.550277	−	0.834982i	$-0.314522\pi$
$673$	−3.34528e6	−	3.34528e6i	−0.284705	−	0.284705i	−0.834982	+	0.550277i	$0.814522\pi$
$674$			2.77796e7i			2.35546i
$675$	3.28027e6	−	5.39205e6i	0.277109	−	0.455507i
$676$	−2.09593e7			−1.76405
$677$	1.35920e7	−	1.35920e7i	1.13976	−	1.13976i	0.151266	−	0.988493i	$-0.451665\pi$
$677$	1.35920e7	−	1.35920e7i	1.13976	−	1.13976i	0.988493	−	0.151266i	$-0.0483350\pi$
$678$	−4.19396e7	−	4.19396e7i	−3.50389	−	3.50389i
$679$	−1.21624e7			−1.01238
$680$	2.59407e7	−	3.30155e7i	2.15134	−	2.73807i
$681$		−	2.32881e7i		−	1.92427i
$682$	−2.37544e6	+	897202.i	−0.195562	+	0.0738634i
$683$	766765.	−	766765.i	0.0628942	−	0.0628942i	−0.674960	−	0.737854i	$-0.735839\pi$
$683$	766765.	−	766765.i	0.0628942	−	0.0628942i	0.737854	+	0.674960i	$0.235839\pi$
$684$	−4.02171e7			−3.28678
$685$	2.29703e7	−	2.75645e6i	1.87042	−	0.224452i
$686$	−2.20636e7			−1.79005
$687$	1.46436e6	+	1.46436e6i	0.118374	+	0.118374i
$688$	−2.46500e7	−	2.46500e7i	−1.98539	−	1.98539i
$689$	−1.69057e6			−0.135670
$690$	−3.74075e6	+	448894.i	−0.299114	+	0.0358939i
$691$	−1.97830e7			−1.57615			−0.788073	−	0.615582i	$-0.788921\pi$
$691$	−1.97830e7			−1.57615			−0.788073	+	0.615582i	$0.788921\pi$
$692$	−2.35026e7	+	2.35026e7i	−1.86574	+	1.86574i
$693$	6.38348e6	+	1.69010e7i	0.504922	+	1.33684i
$694$			2.77079e7i			2.18376i
$695$	−7.43604e6	+	9.46406e6i	−0.583955	+	0.743217i
$696$	−4.45018e7			−3.48221
$697$	1.24713e7	+	1.24713e7i	0.972363	+	0.972363i
$698$	1.49811e7	−	1.49811e7i	1.16387	−	1.16387i
$699$	−5.52583e6			−0.427764
$700$	−1.93891e7	+	3.18715e7i	−1.49559	+	2.45843i
$701$			5.18096e6i			0.398213i	0.979978	+	0.199106i	$0.0638039\pi$
$701$			5.18096e6i			0.398213i	−0.979978	+	0.199106i	$0.936196\pi$
$702$	5.61363e6	+	5.61363e6i	0.429933	+	0.429933i
$703$	7.83162e6	+	7.83162e6i	0.597672	+	0.597672i
$704$	1.92123e7	−	4.25337e7i	1.46099	−	3.23446i
$705$	−4.73210e6	+	6.02269e6i	−0.358576	+	0.456370i
$706$			4.92623e7i			3.71965i
$707$	−1.59189e7	−	1.59189e7i	−1.19775	−	1.19775i
$708$	−1.78174e7	+	1.78174e7i	−1.33586	+	1.33586i
$709$		−	7.44439e6i		−	0.556178i	−0.960555	−	0.278089i	$-0.910299\pi$
$709$		−	7.44439e6i		−	0.556178i	0.960555	−	0.278089i	$-0.0897010\pi$
$710$	−5209.82	−	43414.8i	−0.000387862	−	0.00323216i
$711$		−	1.32547e7i		−	0.983319i
$712$	4.00271e7	−	4.00271e7i	2.95906	−	2.95906i
$713$	106209.	−	106209.i	0.00782412	−	0.00782412i
$714$	4.49459e7			3.29947
$715$	−7.71559e6	−	2.42764e6i	−0.564422	−	0.177590i
$716$	1.87528e7			1.36705
$717$	5.14422e6	−	5.14422e6i	0.373699	−	0.373699i
$718$	−1.04741e7	+	1.04741e7i	−0.758237	+	0.758237i
$719$		−	1.67088e7i		−	1.20538i	−0.797977	−	0.602688i	$-0.794096\pi$
$719$		−	1.67088e7i		−	1.20538i	0.797977	−	0.602688i	$-0.205904\pi$
$720$	−5.38660e7	−	4.23232e7i	−3.87243	−	3.04262i
$721$			1.93396e7i			1.38551i
$722$	3.68505e6	−	3.68505e6i	0.263088	−	0.263088i
$723$	2.85419e7	+	2.85419e7i	2.03066	+	2.03066i
$724$			7.06775e7i			5.01112i
$725$	−2.30307e6	−	9.45789e6i	−0.162728	−	0.668266i
$726$	3.14680e7	−	2.77262e7i	2.21579	−	1.95231i
$727$	1.36322e7	+	1.36322e7i	0.956602	+	0.956602i	0.999097	−	0.0424944i	$-0.0135305\pi$
$727$	1.36322e7	+	1.36322e7i	0.956602	+	0.956602i	−0.0424944	+	0.999097i	$0.513530\pi$
$728$	−2.09570e7	−	2.09570e7i	−1.46555	−	1.46555i
$729$		−	2.19927e7i		−	1.53271i
$730$	−4.26318e6	+	5.42587e6i	−0.296092	+	0.376845i
$731$	−1.17014e7			−0.809927
$732$	2.67676e7	−	2.67676e7i	1.84642	−	1.84642i
$733$	−5.72618e6	−	5.72618e6i	−0.393645	−	0.393645i	0.482339	−	0.875984i	$-0.339787\pi$
$733$	−5.72618e6	−	5.72618e6i	−0.393645	−	0.393645i	−0.875984	+	0.482339i	$0.839787\pi$
$734$	3.81509e7			2.61375
$735$	−2.76046e6	+	331257.i	−0.188479	+	0.0226176i
$736$			5.60266e6i			0.381241i
$737$	−4.05906e6	−	1.07468e7i	−0.275269	−	0.728805i
$738$	3.54645e7	−	3.54645e7i	2.39692	−	2.39692i
$739$	−2.36968e7			−1.59617			−0.798083	−	0.602548i	$-0.794152\pi$
$739$	−2.36968e7			−1.59617			−0.798083	+	0.602548i	$0.794152\pi$
$740$	4.53300e6	+	3.77747e7i	0.304303	+	2.53584i
$741$	1.21735e7			0.814462
$742$	4.96799e6	+	4.96799e6i	0.331261	+	0.331261i
$743$	1.55483e7	+	1.55483e7i	1.03326	+	1.03326i	0.999428	+	0.0338329i	$0.0107714\pi$
$743$	1.55483e7	+	1.55483e7i	1.03326	+	1.03326i	0.0338329	+	0.999428i	$0.489229\pi$
$744$	8.29138e6			0.549155
$745$	−1.70561e7	+	2.17078e7i	−1.12587	+	1.43293i
$746$	2.06898e7			1.36116
$747$	−5.48085e6	+	5.48085e6i	−0.359374	+	0.359374i
$748$	−1.54671e7	−	4.09508e7i	−1.01077	−	2.67614i
$749$		−	2.85883e7i		−	1.86202i
$750$	1.88449e7	−	4.14060e7i	1.22332	−	2.68788i
$751$	−2.07258e7			−1.34095			−0.670473	−	0.741934i	$-0.733909\pi$
$751$	−2.07258e7			−1.34095			−0.670473	+	0.741934i	$0.733909\pi$
$752$	1.51744e7	+	1.51744e7i	0.978516	+	0.978516i
$753$	−2.38442e7	+	2.38442e7i	−1.53248	+	1.53248i
$754$	1.22443e7			0.784339
$755$	1.09263e7	+	8.58497e6i	0.697602	+	0.548115i
$756$		−	2.41105e7i		−	1.53427i
$757$	7.92727e6	+	7.92727e6i	0.502787	+	0.502787i	0.912303	−	0.409516i	$-0.134302\pi$
$757$	7.92727e6	+	7.92727e6i	0.502787	+	0.502787i	−0.409516	+	0.912303i	$0.634302\pi$
$758$	−1.22524e7	−	1.22524e7i	−0.774550	−	0.774550i
$759$	−1.02124e6	+	2.26091e6i	−0.0643466	+	0.142455i
$760$	−4.69250e7	+	5.63104e6i	−2.94693	+	0.353634i
$761$		−	1.65648e7i		−	1.03687i	−0.855116	−	0.518437i	$-0.826514\pi$
$761$		−	1.65648e7i		−	1.03687i	0.855116	−	0.518437i	$-0.173486\pi$
$762$	−2.63937e6	−	2.63937e6i	−0.164669	−	0.164669i
$763$	1.23667e7	−	1.23667e7i	0.769028	−	0.769028i
$764$			2.17764e7i			1.34975i
$765$	−2.28307e7	+	2.73971e6i	−1.41048	+	0.169258i
$766$		−	4.76483e6i		−	0.293410i
$767$	3.09625e6	−	3.09625e6i	0.190041	−	0.190041i
$768$	−4.30554e7	+	4.30554e7i	−2.63405	+	2.63405i
$769$	1.78160e7			1.08641			0.543205	−	0.839600i	$-0.317210\pi$
$769$	1.78160e7			1.08641			0.543205	+	0.839600i	$0.317210\pi$
$770$	1.55395e7	+	2.98075e7i	0.944516	+	1.81175i
$771$	−9.04906e6			−0.548236
$772$	−2.37701e7	+	2.37701e7i	−1.43545	+	1.43545i
$773$	9.74783e6	−	9.74783e6i	0.586758	−	0.586758i	−0.349994	−	0.936752i	$-0.613816\pi$
$773$	9.74783e6	−	9.74783e6i	0.586758	−	0.586758i	0.936752	+	0.349994i	$0.113816\pi$
$774$			3.32754e7i			1.99651i
$775$	429099.	+	1.76215e6i	0.0256627	+	0.105388i
$776$		−	5.29283e7i		−	3.15525i
$777$	−1.81886e7	+	1.81886e7i	−1.08080	+	1.08080i
$778$	1.96732e7	+	1.96732e7i	1.16527	+	1.16527i
$779$		−	1.98525e7i		−	1.17212i
$780$	3.28817e7	+	2.58356e7i	1.93516	+	1.52048i
$781$	−26239.9	−	11852.5i	−0.00153934	−	0.000695315i
$782$	2.50549e6	+	2.50549e6i	0.146513	+	0.146513i
$783$	4.44854e6	+	4.44854e6i	0.259306	+	0.259306i
$784$			7.78971e6i			0.452617i
$785$	−5.03928e6	+	604718.i	−0.291874	+	0.0350251i
$786$	7.63481e7			4.40801
$787$	−9.22087e6	+	9.22087e6i	−0.530683	+	0.530683i	−0.920776	−	0.390093i	$-0.872443\pi$
$787$	−9.22087e6	+	9.22087e6i	−0.530683	+	0.530683i	0.390093	+	0.920776i	$0.372443\pi$
$788$	5.65654e7	+	5.65654e7i	3.24515	+	3.24515i
$789$	5.00886e7			2.86448
$790$	−2.93839e6	−	2.44864e7i	−0.167510	−	1.39591i
$791$		−	3.13025e7i		−	1.77884i
$792$	−7.35500e7	+	2.77797e7i	−4.16648	+	1.57368i
$793$	−4.65158e6	+	4.65158e6i	−0.262674	+	0.262674i
$794$	−1.33082e7			−0.749149
$795$	−4.92315e6	−	3.86818e6i	−0.276264	−	0.217065i
$796$	7.12064e6			0.398324
$797$	−1.13231e7	−	1.13231e7i	−0.631420	−	0.631420i	0.317004	−	0.948424i	$-0.397323\pi$
$797$	−1.13231e7	−	1.13231e7i	−0.631420	−	0.631420i	−0.948424	+	0.317004i	$0.897323\pi$
$798$	−3.57738e7	−	3.57738e7i	−1.98865	−	1.98865i
$799$	7.20336e6			0.399180
$800$	−5.77959e7	−	3.51603e7i	−3.19280	−	1.94235i
$801$	−3.10009e7			−1.70723
$802$	2.47916e7	−	2.47916e7i	1.36104	−	1.36104i
$803$	1.60545e6	+	4.25061e6i	0.0878633	+	0.232628i
$804$			5.93917e7i			3.24030i
$805$	−1.56351e6	−	1.22847e6i	−0.0850379	−	0.0668153i
$806$	−2.28130e6			−0.123693
$807$	1.16961e7	+	1.16961e7i	0.632205	+	0.632205i
$808$	6.92761e7	−	6.92761e7i	3.73297	−	3.73297i
$809$	1.76449e6			0.0947870			0.0473935	−	0.998876i	$-0.484909\pi$
$809$	1.76449e6			0.0947870			0.0473935	+	0.998876i	$0.484909\pi$
$810$	−2.27670e6	−	1.89724e7i	−0.121925	−	1.01603i
$811$			2.44196e7i			1.30373i	0.758337	+	0.651863i	$0.226012\pi$
$811$			2.44196e7i			1.30373i	−0.758337	+	0.651863i	$0.773988\pi$
$812$	−2.62945e7	−	2.62945e7i	−1.39951	−	1.39951i
$813$	4.08192e6	+	4.08192e6i	0.216590	+	0.216590i
$814$	3.12422e7	+	1.41120e7i	1.65265	+	0.746495i
$815$	1.50396e6	+	1.25329e7i	0.0793125	+	0.660933i
$816$			1.12221e8i			5.89996i
$817$	9.31353e6	+	9.31353e6i	0.488157	+	0.488157i
$818$	−9.19481e6	+	9.19481e6i	−0.480463	+	0.480463i
$819$			1.62312e7i			0.845551i
$820$	4.21325e7	−	5.36233e7i	2.18818	−	2.78496i
$821$		−	1.74687e6i		−	0.0904487i	−0.998977	−	0.0452244i	$-0.985600\pi$
$821$		−	1.74687e6i		−	0.0904487i	0.998977	−	0.0452244i	$-0.0144003\pi$
$822$	−7.62075e7	+	7.62075e7i	−3.93385	+	3.93385i
$823$	5.08779e6	−	5.08779e6i	0.261836	−	0.261836i	−0.563963	−	0.825800i	$-0.690724\pi$
$823$	5.08779e6	−	5.08779e6i	0.261836	−	0.261836i	0.825800	+	0.563963i	$0.190724\pi$
$824$	−8.41622e7			−4.31816
$825$	−1.69141e7	−	2.47236e7i	−0.865197	−	1.26467i
$826$	−1.81976e7			−0.928036
$827$	5.44128e6	−	5.44128e6i	0.276654	−	0.276654i	−0.555118	−	0.831772i	$-0.687327\pi$
$827$	5.44128e6	−	5.44128e6i	0.276654	−	0.276654i	0.831772	+	0.555118i	$0.187327\pi$
$828$	5.20668e6	−	5.20668e6i	0.263928	−	0.263928i
$829$			1544.29i			7.80445e-5i	1.00000		3.90223e-5i	$1.24212e-5\pi$
$829$			1544.29i			7.80445e-5i	−1.00000		3.90223e-5i	$0.999988\pi$
$830$	−8.91019e6	+	1.13403e7i	−0.448943	+	0.571383i
$831$			2.22894e7i			1.11968i
$832$	2.96494e7	−	2.96494e7i	1.48494	−	1.48494i
$833$	1.84890e6	+	1.84890e6i	0.0923213	+	0.0923213i
$834$		−	5.60687e7i		−	2.79129i
$835$	−736361.	−	6.13630e6i	−0.0365489	−	0.304572i
$836$	−2.02833e7	+	4.49047e7i	−1.00374	+	2.22216i
$837$	−828832.	−	828832.i	−0.0408934	−	0.0408934i
$838$	−3.78861e7	−	3.78861e7i	−1.86367	−	1.86367i
$839$			3.14672e7i			1.54331i	0.636042	+	0.771654i	$0.280570\pi$
$839$			3.14672e7i			1.54331i	−0.636042	+	0.771654i	$0.719430\pi$
$840$	−1.30778e7	−	1.08981e8i	−0.639495	−	5.32909i
$841$	−1.08082e7			−0.526940
$842$	9.08727e6	−	9.08727e6i	0.441726	−	0.441726i
$843$	−3.52518e7	−	3.52518e7i	−1.70849	−	1.70849i
$844$	−4.47293e7			−2.16141
$845$	1.06067e7	+	8.33381e6i	0.511020	+	0.401515i
$846$		−	2.04842e7i		−	0.983995i
$847$	2.20904e7	+	1.39640e6i	1.05802	+	0.0668809i
$848$	−1.24041e7	+	1.24041e7i	−0.592346	+	0.592346i
$849$	6.68324e6			0.318213
$850$	−4.15697e7	+	1.01226e7i	−1.97347	+	0.480555i
$851$	−2.02783e6			−0.0959860
$852$	105258.	+	105258.i	0.00496770	+	0.00496770i
$853$	1.49388e6	+	1.49388e6i	0.0702982	+	0.0702982i	0.741382	−	0.671084i	$-0.234171\pi$
$853$	1.49388e6	+	1.49388e6i	0.0702982	+	0.0702982i	−0.671084	+	0.741382i	$0.734171\pi$
$854$	2.73388e7			1.28273
$855$	2.03523e7	+	1.59910e7i	0.952133	+	0.748103i
$856$	1.24411e8			5.80330
$857$	−4.58618e6	+	4.58618e6i	−0.213304	+	0.213304i	−0.805669	−	0.592366i	$-0.798194\pi$
$857$	−4.58618e6	+	4.58618e6i	−0.213304	+	0.213304i	0.592366	+	0.805669i	$0.298194\pi$
$858$	3.52494e7	−	1.33136e7i	1.63468	−	0.617417i
$859$		−	2.02259e7i		−	0.935244i	−0.883929	−	0.467622i	$-0.845111\pi$
$859$		−	2.02259e7i		−	0.935244i	0.883929	−	0.467622i	$-0.154889\pi$
$860$	5.39074e6	+	4.49225e7i	0.248543	+	2.07118i
$861$	4.61066e7			2.11961
$862$	−3.67965e7	−	3.67965e7i	−1.68670	−	1.68670i
$863$	1.49069e7	−	1.49069e7i	0.681335	−	0.681335i	−0.278966	−	0.960301i	$-0.589992\pi$
$863$	1.49069e7	−	1.49069e7i	0.681335	−	0.681335i	0.960301	+	0.278966i	$0.0899917\pi$
$864$	4.37221e7			1.99258
$865$	2.12388e7	−	2.54868e6i	0.965139	−	0.115818i
$866$		−	4.04458e7i		−	1.83265i
$867$	2.65431e6	+	2.65431e6i	0.119923	+	0.119923i
$868$	4.89908e6	+	4.89908e6i	0.220707	+	0.220707i
$869$	−1.47996e7	−	6.68491e6i	−0.664814	−	0.300294i
$870$	3.56569e7	+	2.80161e7i	1.59715	+	1.25490i
$871$		−	1.03209e7i		−	0.460969i
$872$	5.38175e7	+	5.38175e7i	2.39680	+	2.39680i
$873$	−2.04964e7	+	2.04964e7i	−0.910213	+	0.910213i
$874$		−	3.98839e6i		−	0.176611i
$875$	2.24848e7	−	8.41944e6i	0.992814	−	0.371760i
$876$		−	2.34907e7i		−	1.03428i
$877$	−1.88357e7	+	1.88357e7i	−0.826955	+	0.826955i	−0.987094	−	0.160140i	$-0.948806\pi$
$877$	−1.88357e7	+	1.88357e7i	−0.826955	+	0.826955i	0.160140	+	0.987094i	$0.448806\pi$
$878$	−4.07997e7	+	4.07997e7i	−1.78616	+	1.78616i
$879$	2.65593e7			1.15943
$880$	−7.44233e7	+	3.87990e7i	−3.23968	+	1.68894i
$881$	−1.11198e7			−0.482679			−0.241339	−	0.970441i	$-0.577587\pi$
$881$	−1.11198e7			−0.482679			−0.241339	+	0.970441i	$0.577587\pi$
$882$	5.25773e6	−	5.25773e6i	0.227576	−	0.227576i
$883$	−4.40069e6	+	4.40069e6i	−0.189941	+	0.189941i	−0.795671	−	0.605730i	$-0.792881\pi$
$883$	−4.40069e6	+	4.40069e6i	−0.189941	+	0.189941i	0.605730	+	0.795671i	$0.292881\pi$
$884$		−	3.93278e7i		−	1.69266i
$885$	1.61012e7	−	1.93216e6i	0.691036	−	0.0829249i
$886$			2.38297e7i			1.01985i
$887$	−6.56999e6	+	6.56999e6i	−0.280385	+	0.280385i	−0.833263	−	0.552877i	$-0.813530\pi$
$887$	−6.56999e6	+	6.56999e6i	−0.280385	+	0.280385i	0.552877	+	0.833263i	$0.313530\pi$
$888$	−7.91534e7	−	7.91534e7i	−3.36850	−	3.36850i
$889$		−	1.96995e6i		−	0.0835988i
$890$	−5.72705e7	+	6.87251e6i	−2.42357	+	0.290831i
$891$	−1.14669e7	−	5.17955e6i	−0.483895	−	0.218574i
$892$	−2.38098e7	−	2.38098e7i	−1.00194	−	1.00194i
$893$	−5.73338e6	−	5.73338e6i	−0.240592	−	0.240592i
$894$		−	1.28605e8i		−	5.38163i
$895$	−9.49007e6	−	7.45647e6i	−0.396015	−	0.311154i
$896$	−7.90499e7			−3.28951
$897$	−1.57604e6	+	1.57604e6i	−0.0654011	+	0.0654011i
$898$	1.63806e7	+	1.63806e7i	0.677858	+	0.677858i
$899$	−1.80782e6			−0.0746029
$900$	2.10358e7	+	8.63863e7i	0.865670	+	3.55499i
$901$			5.88827e6i			0.241644i
$902$	−2.17118e7	−	5.74845e7i	−0.888546	−	2.35253i
$903$	−2.16303e7	+	2.16303e7i	−0.882759	+	0.882759i
$904$	1.36223e8			5.54406
$905$	2.81027e7	−	3.57671e7i	1.14058	−	1.45165i
$906$	−6.47318e7			−2.61998
$907$	−1.24260e7	−	1.24260e7i	−0.501549	−	0.501549i	0.410370	−	0.911919i	$-0.365399\pi$
$907$	−1.24260e7	−	1.24260e7i	−0.501549	−	0.501549i	−0.911919	+	0.410370i	$0.865399\pi$
$908$	5.98815e7	+	5.98815e7i	2.41034	+	2.41034i
$909$	−5.36542e7			−2.15374
$910$	3.59824e6	+	2.99851e7i	0.144041	+	1.20034i
$911$	2.51510e7			1.00406			0.502030	−	0.864850i	$-0.332587\pi$
$911$	2.51510e7			1.00406			0.502030	+	0.864850i	$0.332587\pi$
$912$	8.93201e7	−	8.93201e7i	3.55600	−	3.55600i
$913$	3.35545e6	+	8.88392e6i	0.133221	+	0.352718i
$914$			8.41335e7i			3.33122i
$915$	−2.41893e7	+	2.90273e6i	−0.955147	+	0.114618i
$916$	−7.53073e6			−0.296550
$917$	2.84920e7	+	2.84920e7i	1.11892	+	1.11892i
$918$	1.95524e7	−	1.95524e7i	0.765761	−	0.765761i
$919$	3.39669e7			1.32668			0.663341	−	0.748317i	$-0.269138\pi$
$919$	3.39669e7			1.32668			0.663341	+	0.748317i	$0.269138\pi$
$920$	5.34609e6	−	6.80413e6i	0.208241	−	0.265035i
$921$			2.97097e7i			1.15412i
$922$	1.27819e7	+	1.27819e7i	0.495184	+	0.495184i
$923$	−18291.3	−	18291.3i	−0.000706710	−	0.000706710i
$924$	−1.04289e8	−	4.71070e7i	−4.01845	−	1.81512i
$925$	1.27259e7	−	2.09187e7i	0.489030	−	0.803860i
$926$		−	4.60667e7i		−	1.76547i
$927$	3.25917e7	+	3.25917e7i	1.24569	+	1.24569i
$928$	4.76826e7	−	4.76826e7i	1.81756	−	1.81756i
$929$			5.20675e7i			1.97937i	0.143259	+	0.989685i	$0.454242\pi$
$929$			5.20675e7i			1.97937i	−0.143259	+	0.989685i	$0.545758\pi$
$930$	−6.64343e6	−	5.21983e6i	−0.251875	−	0.197901i
$931$		−	2.94320e6i		−	0.111287i
$932$	1.42087e7	−	1.42087e7i	0.535816	−	0.535816i
$933$	−2.82097e7	+	2.82097e7i	−1.06095	+	1.06095i
$934$	2.98666e7			1.12026
$935$	−8.45551e6	+	2.68736e7i	−0.316309	+	1.00530i
$936$	−7.06350e7			−2.63530
$937$	−1.61951e7	+	1.61951e7i	−0.602609	+	0.602609i	−0.941004	−	0.338395i	$-0.890116\pi$
$937$	−1.61951e7	+	1.61951e7i	−0.602609	+	0.602609i	0.338395	+	0.941004i	$0.390116\pi$
$938$	−3.03295e7	+	3.03295e7i	−1.12553	+	1.12553i
$939$		−	2.47479e6i		−	0.0915956i
$940$	−3.31852e6	−	2.76541e7i	−0.122497	−	1.02080i
$941$		−	3.55266e7i		−	1.30792i	−0.756531	−	0.653958i	$-0.773107\pi$
$941$		−	3.55266e7i		−	1.30792i	0.756531	−	0.653958i	$-0.226893\pi$
$942$	1.67186e7	−	1.67186e7i	0.613865	−	0.613865i
$943$	2.57019e6	+	2.57019e6i	0.0941210	+	0.0941210i
$944$		−	4.54359e7i		−	1.65947i
$945$	−9.58679e6	+	1.22014e7i	−0.349216	+	0.444457i
$946$	3.71539e7	+	1.67823e7i	1.34982	+	0.609709i
$947$	−2.41415e7	−	2.41415e7i	−0.874761	−	0.874761i	0.118226	−	0.992987i	$-0.462279\pi$
$947$	−2.41415e7	−	2.41415e7i	−0.874761	−	0.874761i	−0.992987	+	0.118226i	$0.962279\pi$
$948$	5.93664e7	+	5.93664e7i	2.14546	+	2.14546i
$949$			4.08214e6i			0.147137i
$950$	4.11434e7	+	2.50297e7i	1.47908	+	0.899802i
$951$	−3.85444e7			−1.38200
$952$	−7.29936e7	+	7.29936e7i	−2.61031	+	2.61031i
$953$	−6.56700e6	−	6.56700e6i	−0.234226	−	0.234226i	0.580228	−	0.814454i	$-0.302963\pi$
$953$	−6.56700e6	−	6.56700e6i	−0.234226	−	0.234226i	−0.814454	+	0.580228i	$0.802963\pi$
$954$	1.67445e7			0.595663
$955$	8.65868e6	−	1.10202e7i	0.307216	−	0.391002i
$956$			2.64550e7i			0.936189i
$957$	2.79335e7	−	1.05504e7i	0.985928	−	0.372384i
$958$	2.50561e7	−	2.50561e7i	0.882062	−	0.882062i
$959$	−5.68790e7			−1.99713
$960$	1.54184e8	−	1.85022e7i	5.39959	−	0.647955i
$961$	−2.82923e7			−0.988235
$962$	2.17783e7	+	2.17783e7i	0.758728	+	0.758728i
$963$	−4.81781e7	−	4.81781e7i	−1.67411	−	1.67411i
$964$	−1.46781e8			−5.08720
$965$	2.14806e7	−	2.57769e6i	0.742553	−	0.0891070i
$966$	9.26286e6			0.319376
$967$	9.06560e6	−	9.06560e6i	0.311767	−	0.311767i	−0.533827	−	0.845594i	$-0.679247\pi$
$967$	9.06560e6	−	9.06560e6i	0.311767	−	0.311767i	0.845594	+	0.533827i	$0.179247\pi$
$968$	−6.07689e6	+	9.61334e7i	−0.208446	+	3.29751i
$969$		−	4.24006e7i		−	1.45065i
$970$	−3.33209e7	+	4.24086e7i	−1.13707	+	1.44719i
$971$	−4.97343e7			−1.69281			−0.846404	−	0.532541i	$-0.821237\pi$
$971$	−4.97343e7			−1.69281			−0.846404	+	0.532541i	$0.821237\pi$
$972$	7.61412e7	+	7.61412e7i	2.58496	+	2.58496i
$973$	2.09240e7	−	2.09240e7i	0.708538	−	0.708538i
$974$	2.42323e7			0.818459
$975$	−6.36743e6	−	2.61487e7i	−0.214513	−	0.880925i
$976$			6.82595e7i			2.29371i
$977$	−2.76919e7	−	2.76919e7i	−0.928146	−	0.928146i	0.0694404	−	0.997586i	$-0.477879\pi$
$977$	−2.76919e7	−	2.76919e7i	−0.928146	−	0.928146i	−0.997586	+	0.0694404i	$0.977879\pi$
$978$	−4.15798e7	−	4.15798e7i	−1.39007	−	1.39007i
$979$	−1.56351e7	+	3.46143e7i	−0.521369	+	1.15425i
$980$	6.24628e6	−	7.94982e6i	0.207757	−	0.264419i
$981$		−	4.16816e7i		−	1.38284i
$982$	4.30484e6	+	4.30484e6i	0.142455	+	0.142455i
$983$	3.04996e7	−	3.04996e7i	1.00672	−	1.00672i	0.00674499	−	0.999977i	$-0.497853\pi$
$983$	3.04996e7	−	3.04996e7i	1.00672	−	1.00672i	0.999977	−	0.00674499i	$-0.00214701\pi$
$984$			2.00647e8i			6.60611i
$985$	−6.13407e6	−	5.11169e7i	−0.201446	−	1.67870i
$986$		−	4.26470e7i		−	1.39700i
$987$	1.33155e7	−	1.33155e7i	0.435076	−	0.435076i
$988$	−3.13022e7	+	3.13022e7i	−1.02019	+	1.02019i
$989$	−2.41154e6			−0.0783978
$990$	7.64203e7	+	2.40449e7i	2.47811	+	0.779714i
$991$	1.24158e7			0.401597			0.200799	−	0.979633i	$-0.435646\pi$
$991$	1.24158e7			0.401597			0.200799	+	0.979633i	$0.435646\pi$
$992$	−8.88401e6	+	8.88401e6i	−0.286635	+	0.286635i
$993$	1.10234e7	−	1.10234e7i	0.354766	−	0.354766i
$994$			107504.i			0.00345110i
$995$	−3.60347e6	−	2.83130e6i	−0.115389	−	0.0906625i
$996$		−	4.90965e7i		−	1.56820i
$997$	1.99214e7	−	1.99214e7i	0.634721	−	0.634721i	−0.314527	−	0.949248i	$-0.601846\pi$
$997$	1.99214e7	−	1.99214e7i	0.634721	−	0.634721i	0.949248	+	0.314527i	$0.101846\pi$
$998$	2.21062e7	+	2.21062e7i	0.702566	+	0.702566i
$999$			1.58248e7i			0.501678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.1	✓	52
5.3	odd	4	inner	55.6.e.b.43.26	yes	52
11.10	odd	2	inner	55.6.e.b.32.26	yes	52
55.43	even	4	inner	55.6.e.b.43.1	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.1	✓	52	1.1	even	1	trivial
55.6.e.b.32.26	yes	52	11.10	odd	2	inner
55.6.e.b.43.1	yes	52	55.43	even	4	inner
55.6.e.b.43.26	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+(-7.70910 + 7.70910i) q^{2} +(-16.8901 + 16.8901i) q^{3} -86.8603i q^{4} +(-34.5372 + 43.9566i) q^{5} -260.415i q^{6} +(97.1832 - 97.1832i) q^{7} +(422.923 + 422.923i) q^{8} -327.553i q^{9} +(-72.6145 - 605.116i) q^{10} +(-365.732 - 165.200i) q^{11} +(1467.08 + 1467.08i) q^{12} +(-254.945 - 254.945i) q^{13} +1498.39i q^{14} +(-159.094 - 1325.77i) q^{15} -3741.18 q^{16} +(-887.978 + 887.978i) q^{17} +(2525.14 + 2525.14i) q^{18} +1413.54 q^{19} +(3818.08 + 2999.92i) q^{20} +3282.88i q^{21} +(4093.01 - 1545.92i) q^{22} +(-183.003 + 183.003i) q^{23} -14286.5 q^{24} +(-739.358 - 3036.28i) q^{25} +3930.79 q^{26} +(1428.12 + 1428.12i) q^{27} +(-8441.36 - 8441.36i) q^{28} +3114.96 q^{29} +(11447.0 + 8994.03i) q^{30} -580.366 q^{31} +(15307.6 - 15307.6i) q^{32} +(8967.51 - 3387.02i) q^{33} -13691.0i q^{34} +(915.400 + 7628.28i) q^{35} -28451.4 q^{36} +(5540.44 + 5540.44i) q^{37} +(-10897.1 + 10897.1i) q^{38} +8612.10 q^{39} +(-33196.9 + 3983.65i) q^{40} -14044.6i q^{41} +(-25308.0 - 25308.0i) q^{42} +(6588.81 + 6588.81i) q^{43} +(-14349.3 + 31767.6i) q^{44} +(14398.1 + 11312.8i) q^{45} -2821.57i q^{46} +(-4056.05 - 4056.05i) q^{47} +(63189.1 - 63189.1i) q^{48} -2082.15i q^{49} +(29106.7 + 17707.2i) q^{50} -29996.1i q^{51} +(-22144.6 + 22144.6i) q^{52} +(3315.55 - 3315.55i) q^{53} -22019.0 q^{54} +(19893.0 - 10370.8i) q^{55} +82202.1 q^{56} +(-23874.8 + 23874.8i) q^{57} +(-24013.5 + 24013.5i) q^{58} +12144.8i q^{59} +(-115157. + 13818.9i) q^{60} -18245.4i q^{61} +(4474.10 - 4474.10i) q^{62} +(-31832.7 - 31832.7i) q^{63} +116297. i q^{64} +(20011.6 - 2401.41i) q^{65} +(-43020.6 + 95242.3i) q^{66} +(20241.4 + 20241.4i) q^{67} +(77130.0 + 77130.0i) q^{68} -6181.88i q^{69} +(-65864.0 - 51750.2i) q^{70} +71.7463 q^{71} +(138530. - 138530. i) q^{72} +(-8005.94 - 8005.94i) q^{73} -85423.6 q^{74} +(63771.0 + 38795.3i) q^{75} -122780. i q^{76} +(-51597.7 + 19488.4i) q^{77} +(-66391.5 + 66391.5i) q^{78} +40465.6 q^{79} +(129210. - 164450. i) q^{80} +31353.2 q^{81} +(108271. + 108271. i) q^{82} +(-16732.7 - 16732.7i) q^{83} +285152. q^{84} +(-8364.15 - 69700.7i) q^{85} -101588. q^{86} +(-52612.1 + 52612.1i) q^{87} +(-84809.8 - 224544. i) q^{88} -94643.8i q^{89} +(-198208. + 23785.1i) q^{90} -49552.7 q^{91} +(15895.7 + 15895.7i) q^{92} +(9802.47 - 9802.47i) q^{93} +62537.0 q^{94} +(-48819.6 + 62134.2i) q^{95} +517095. i q^{96} +(-62574.3 - 62574.3i) q^{97} +(16051.5 + 16051.5i) q^{98} +(-54111.8 + 119797. i) 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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