LMFDB - Embedded newform 55.6.e.b.32.4

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			32.4
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.66565 + 6.66565i) q^{2} +(19.1413 - 19.1413i) q^{3} -56.8618i q^{4} +(-13.1183 + 54.3407i) q^{5} +255.179i q^{6} +(17.8098 - 17.8098i) q^{7} +(165.720 + 165.720i) q^{8} -489.780i q^{9} +(-274.774 - 449.658i) q^{10} +(220.830 - 335.090i) q^{11} +(-1088.41 - 1088.41i) q^{12} +(18.9054 + 18.9054i) q^{13} +237.428i q^{14} +(789.050 + 1291.25i) q^{15} -389.691 q^{16} +(1295.57 - 1295.57i) q^{17} +(3264.70 + 3264.70i) q^{18} -1194.22 q^{19} +(3089.91 + 745.933i) q^{20} -681.806i q^{21} +(761.618 + 3705.57i) q^{22} +(1756.89 - 1756.89i) q^{23} +6344.22 q^{24} +(-2780.82 - 1425.72i) q^{25} -252.034 q^{26} +(-4723.70 - 4723.70i) q^{27} +(-1012.70 - 1012.70i) q^{28} +8883.33 q^{29} +(-13866.6 - 3347.52i) q^{30} +3325.35 q^{31} +(-2705.51 + 2705.51i) q^{32} +(-2187.09 - 10641.0i) q^{33} +17271.7i q^{34} +(734.161 + 1201.43i) q^{35} -27849.8 q^{36} +(-2146.50 - 2146.50i) q^{37} +(7960.25 - 7960.25i) q^{38} +723.748 q^{39} +(-11179.3 + 6831.39i) q^{40} +5592.49i q^{41} +(4544.68 + 4544.68i) q^{42} +(-13040.1 - 13040.1i) q^{43} +(-19053.8 - 12556.8i) q^{44} +(26615.0 + 6425.10i) q^{45} +23421.6i q^{46} +(-8033.21 - 8033.21i) q^{47} +(-7459.20 + 7459.20i) q^{48} +16172.6i q^{49} +(28039.3 - 9032.63i) q^{50} -49597.9i q^{51} +(1075.00 - 1075.00i) q^{52} +(1956.61 - 1956.61i) q^{53} +62973.0 q^{54} +(15312.1 + 16395.9i) q^{55} +5902.89 q^{56} +(-22858.9 + 22858.9i) q^{57} +(-59213.2 + 59213.2i) q^{58} +40026.2i q^{59} +(73423.1 - 44866.8i) q^{60} +20424.6i q^{61} +(-22165.6 + 22165.6i) q^{62} +(-8722.88 - 8722.88i) q^{63} -48538.1i q^{64} +(-1275.34 + 779.324i) q^{65} +(85507.8 + 56351.1i) q^{66} +(-34207.4 - 34207.4i) q^{67} +(-73668.6 - 73668.6i) q^{68} -67258.2i q^{69} +(-12902.0 - 3114.66i) q^{70} -31324.3 q^{71} +(81166.6 - 81166.6i) q^{72} +(29501.7 + 29501.7i) q^{73} +28615.6 q^{74} +(-80518.7 + 25938.4i) q^{75} +67905.5i q^{76} +(-2034.95 - 9900.81i) q^{77} +(-4824.25 + 4824.25i) q^{78} -56304.2 q^{79} +(5112.09 - 21176.1i) q^{80} -61819.0 q^{81} +(-37277.6 - 37277.6i) q^{82} +(12612.1 + 12612.1i) q^{83} -38768.7 q^{84} +(53406.5 + 87398.0i) q^{85} +173842. q^{86} +(170039. - 170039. i) q^{87} +(92127.3 - 18935.2i) q^{88} +92755.4i q^{89} +(-220234. + 134579. i) q^{90} +673.402 q^{91} +(-99899.7 - 99899.7i) q^{92} +(63651.5 - 63651.5i) q^{93} +107093. q^{94} +(15666.2 - 64894.7i) q^{95} +103574. i q^{96} +(54386.7 + 54386.7i) q^{97} +(-107801. - 107801. i) q^{98} +(-164120. - 108158. 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 $

$2$	−6.66565	+	6.66565i	−1.17833	+	1.17833i	−0.198163	+	0.980169i	$0.563498\pi$
$2$	−6.66565	+	6.66565i	−1.17833	+	1.17833i	−0.980169	+	0.198163i	$0.936502\pi$
$3$	19.1413	−	19.1413i	1.22792	−	1.22792i	0.263165	−	0.964751i	$-0.415233\pi$
$3$	19.1413	−	19.1413i	1.22792	−	1.22792i	0.964751	−	0.263165i	$-0.0847665\pi$
$4$		−	56.8618i		−	1.77693i
$5$	−13.1183	+	54.3407i	−0.234668	+	0.972076i
$5$	−13.1183	+	54.3407i	−0.234668	+	0.972076i
$6$			255.179i			2.89379i
$7$	17.8098	−	17.8098i	0.137377	−	0.137377i	−0.635074	−	0.772451i	$-0.719030\pi$
$7$	17.8098	−	17.8098i	0.137377	−	0.137377i	0.772451	+	0.635074i	$0.219030\pi$
$8$	165.720	+	165.720i	0.915485	+	0.915485i
$9$		−	489.780i		−	2.01556i
$10$	−274.774	−	449.658i	−0.868911	−	1.42194i
$11$	220.830	−	335.090i	0.550270	−	0.834987i
$11$	220.830	−	335.090i	0.550270	−	0.834987i
$12$	−1088.41	−	1088.41i	−2.18192	−	2.18192i
$13$	18.9054	+	18.9054i	0.0310261	+	0.0310261i	0.722450	−	0.691424i	$-0.243016\pi$
$13$	18.9054	+	18.9054i	0.0310261	+	0.0310261i	−0.691424	+	0.722450i	$0.743016\pi$
$14$			237.428i			0.323751i
$15$	789.050	+	1291.25i	0.905475	+	1.48178i
$16$	−389.691			−0.380557
$17$	1295.57	−	1295.57i	1.08727	−	1.08727i	0.0914665	−	0.995808i	$-0.470845\pi$
$17$	1295.57	−	1295.57i	1.08727	−	1.08727i	0.995808	−	0.0914665i	$-0.0291554\pi$
$18$	3264.70	+	3264.70i	2.37499	+	2.37499i
$19$	−1194.22			−0.758927			−0.379463	−	0.925207i	$-0.623891\pi$
$19$	−1194.22			−0.758927			−0.379463	+	0.925207i	$0.623891\pi$
$20$	3089.91	+	745.933i	1.72731	+	0.416989i
$21$		−	681.806i		−	0.337375i
$22$	761.618	+	3705.57i	0.335491	+	1.63229i
$23$	1756.89	−	1756.89i	0.692506	−	0.692506i	−0.270276	−	0.962783i	$-0.587115\pi$
$23$	1756.89	−	1756.89i	0.692506	−	0.692506i	0.962783	+	0.270276i	$0.0871151\pi$
$24$	6344.22			2.24828
$25$	−2780.82	−	1425.72i	−0.889862	−	0.456230i
$26$	−252.034			−0.0731181
$27$	−4723.70	−	4723.70i	−1.24702	−	1.24702i
$28$	−1012.70	−	1012.70i	−0.244110	−	0.244110i
$29$	8883.33			1.96147			0.980733	−	0.195354i	$-0.0625856\pi$
$29$	8883.33			1.96147			0.980733	+	0.195354i	$0.0625856\pi$
$30$	−13866.6	−	3347.52i	−2.81298	−	0.679079i
$31$	3325.35			0.621488			0.310744	−	0.950494i	$-0.399422\pi$
$31$	3325.35			0.621488			0.310744	+	0.950494i	$0.399422\pi$
$32$	−2705.51	+	2705.51i	−0.467062	+	0.467062i
$33$	−2187.09	−	10641.0i	−0.349608	−	1.70098i
$34$			17271.7i			2.56234i
$35$	734.161	+	1201.43i	0.101303	+	0.165779i
$36$	−27849.8			−3.58151
$37$	−2146.50	−	2146.50i	−0.257766	−	0.257766i	0.566379	−	0.824145i	$-0.308344\pi$
$37$	−2146.50	−	2146.50i	−0.257766	−	0.257766i	−0.824145	+	0.566379i	$0.808344\pi$
$38$	7960.25	−	7960.25i	0.894268	−	0.894268i
$39$	723.748			0.0761949
$40$	−11179.3	+	6831.39i	−1.10476	+	0.675086i
$41$			5592.49i			0.519572i	0.965666	+	0.259786i	$0.0836520\pi$
$41$			5592.49i			0.519572i	−0.965666	+	0.259786i	$0.916348\pi$
$42$	4544.68	+	4544.68i	0.397539	+	0.397539i
$43$	−13040.1	−	13040.1i	−1.07550	−	1.07550i	−0.996907	−	0.0785912i	$-0.974958\pi$
$43$	−13040.1	−	13040.1i	−1.07550	−	1.07550i	−0.0785912	−	0.996907i	$-0.525042\pi$
$44$	−19053.8	−	12556.8i	−1.48372	−	0.977793i
$45$	26615.0	+	6425.10i	1.95927	+	0.472986i
$46$			23421.6i			1.63200i
$47$	−8033.21	−	8033.21i	−0.530450	−	0.530450i	0.390256	−	0.920706i	$-0.372386\pi$
$47$	−8033.21	−	8033.21i	−0.530450	−	0.530450i	−0.920706	+	0.390256i	$0.872386\pi$
$48$	−7459.20	+	7459.20i	−0.467293	+	0.467293i
$49$			16172.6i			0.962255i
$50$	28039.3	−	9032.63i	1.58614	−	0.510963i
$51$		−	49597.9i		−	2.67016i
$52$	1075.00	−	1075.00i	0.0551313	−	0.0551313i
$53$	1956.61	−	1956.61i	0.0956786	−	0.0956786i	−0.657647	−	0.753326i	$-0.728448\pi$
$53$	1956.61	−	1956.61i	0.0956786	−	0.0956786i	0.753326	+	0.657647i	$0.228448\pi$
$54$	62973.0			2.93880
$55$	15312.1	+	16395.9i	0.682539	+	0.730849i
$56$	5902.89			0.251533
$57$	−22858.9	+	22858.9i	−0.931899	+	0.931899i
$58$	−59213.2	+	59213.2i	−2.31126	+	2.31126i
$59$			40026.2i			1.49697i	0.663150	+	0.748487i	$0.269219\pi$
$59$			40026.2i			1.49697i	−0.663150	+	0.748487i	$0.730781\pi$
$60$	73423.1	−	44866.8i	2.63302	−	1.60897i
$61$			20424.6i			0.702795i	0.936226	+	0.351398i	$0.114293\pi$
$61$			20424.6i			0.702795i	−0.936226	+	0.351398i	$0.885707\pi$
$62$	−22165.6	+	22165.6i	−0.732319	+	0.732319i
$63$	−8722.88	−	8722.88i	−0.276891	−	0.276891i
$64$		−	48538.1i		−	1.48127i
$65$	−1275.34	+	779.324i	−0.0374405	+	0.0228789i
$66$	85507.8	+	56351.1i	2.41627	+	1.59236i
$67$	−34207.4	−	34207.4i	−0.930965	−	0.930965i	0.0668011	−	0.997766i	$-0.478721\pi$
$67$	−34207.4	−	34207.4i	−0.930965	−	0.930965i	−0.997766	+	0.0668011i	$0.978721\pi$
$68$	−73668.6	−	73668.6i	−1.93201	−	1.93201i
$69$		−	67258.2i		−	1.70068i
$70$	−12902.0	−	3114.66i	−0.314711	−	0.0759740i
$71$	−31324.3			−0.737454			−0.368727	−	0.929538i	$-0.620206\pi$
$71$	−31324.3			−0.737454			−0.368727	+	0.929538i	$0.620206\pi$
$72$	81166.6	−	81166.6i	1.84521	−	1.84521i
$73$	29501.7	+	29501.7i	0.647948	+	0.647948i	0.952497	−	0.304549i	$-0.0985057\pi$
$73$	29501.7	+	29501.7i	0.647948	+	0.647948i	−0.304549	+	0.952497i	$0.598506\pi$
$74$	28615.6			0.607468
$75$	−80518.7	+	25938.4i	−1.65289	+	0.532464i
$76$			67905.5i			1.34856i
$77$	−2034.95	−	9900.81i	−0.0391135	−	0.190302i
$78$	−4824.25	+	4824.25i	−0.0897829	+	0.0897829i
$79$	−56304.2			−1.01502			−0.507508	−	0.861647i	$-0.669433\pi$
$79$	−56304.2			−1.01502			−0.507508	+	0.861647i	$0.669433\pi$
$80$	5112.09	−	21176.1i	0.0893046	−	0.369931i
$81$	−61819.0			−1.04691
$82$	−37277.6	−	37277.6i	−0.612228	−	0.612228i
$83$	12612.1	+	12612.1i	0.200951	+	0.200951i	0.800408	−	0.599456i	$-0.204616\pi$
$83$	12612.1	+	12612.1i	0.200951	+	0.200951i	−0.599456	+	0.800408i	$0.704616\pi$
$84$	−38768.7			−0.599492
$85$	53406.5	+	87398.0i	0.801765	+	1.31206i
$86$	173842.			2.53459
$87$	170039.	−	170039.i	2.40852	−	2.40852i
$88$	92127.3	−	18935.2i	1.26818	−	0.260654i
$89$			92755.4i			1.24126i	0.784102	+	0.620632i	$0.213124\pi$
$89$			92755.4i			1.24126i	−0.784102	+	0.620632i	$0.786876\pi$
$90$	−220234.	+	134579.i	−2.86601	+	1.75134i
$91$	673.402			0.00852454
$92$	−99899.7	−	99899.7i	−1.23054	−	1.23054i
$93$	63651.5	−	63651.5i	0.763135	−	0.763135i
$94$	107093.			1.25009
$95$	15666.2	−	64894.7i	0.178096	−	0.737734i
$96$			103574.i			1.14703i
$97$	54386.7	+	54386.7i	0.586899	+	0.586899i	0.936790	−	0.349891i	$-0.113781\pi$
$97$	54386.7	+	54386.7i	0.586899	+	0.586899i	−0.349891	+	0.936790i	$0.613781\pi$
$98$	−107801.	−	107801.i	−1.13386	−	1.13386i
$99$	−164120.	−	108158.i	−1.68296	−	1.10910i
$100$	−81069.0	+	158122.i	−0.810690	+	1.58122i
$101$		−	33025.9i		−	0.322145i	−0.986943	−	0.161072i	$-0.948505\pi$
$101$		−	33025.9i		−	0.322145i	0.986943	−	0.161072i	$-0.0514952\pi$
$102$	330602.	+	330602.i	3.14634	+	3.14634i
$103$	−36841.5	+	36841.5i	−0.342171	+	0.342171i	−0.857183	−	0.515012i	$-0.827788\pi$
$103$	−36841.5	+	36841.5i	−0.342171	+	0.342171i	0.515012	+	0.857183i	$0.327788\pi$
$104$			6266.02i			0.0568079i
$105$	37049.8	+	8944.15i	0.327954	+	0.0791710i
$106$			26084.2i			0.225482i
$107$	−30240.0	+	30240.0i	−0.255342	+	0.255342i	−0.823157	−	0.567815i	$-0.807789\pi$
$107$	−30240.0	+	30240.0i	−0.255342	+	0.255342i	0.567815	+	0.823157i	$0.307789\pi$
$108$	−268598.	+	268598.i	−2.21587	+	2.21587i
$109$	204623.			1.64964			0.824818	−	0.565398i	$-0.191277\pi$
$109$	204623.			1.64964			0.824818	+	0.565398i	$0.191277\pi$
$110$	−211354.	−	7224.04i	−1.66544	−	0.0569244i
$111$	−82173.5			−0.633030
$112$	−6940.31	+	6940.31i	−0.0522798	+	0.0522798i
$113$	−4740.45	+	4740.45i	−0.0349240	+	0.0349240i	−0.724353	−	0.689429i	$-0.757861\pi$
$113$	−4740.45	+	4740.45i	−0.0349240	+	0.0349240i	0.689429	+	0.724353i	$0.257861\pi$
$114$		−	304739.i		−	2.19617i
$115$	72422.9	+	118518.i	0.510660	+	0.835678i
$116$		−	505122.i		−	3.48539i
$117$	9259.48	−	9259.48i	0.0625349	−	0.0625349i
$118$	−266801.	−	266801.i	−1.76393	−	1.76393i
$119$		−	46147.7i		−	0.298733i
$120$	−83225.5	+	344749.i	−0.527598	+	2.18550i
$121$	−63519.4	−	147996.i	−0.394406	−	0.918936i
$122$	−136143.	−	136143.i	−0.828126	−	0.828126i
$123$	107048.	+	107048.i	0.637991	+	0.637991i
$124$		−	189085.i		−	1.10434i
$125$	113954.	−	132409.i	0.652312	−	0.757951i
$126$	116287.			0.652539
$127$	−110537.	+	110537.i	−0.608133	+	0.608133i	−0.942458	−	0.334325i	$-0.891492\pi$
$127$	−110537.	+	110537.i	−0.608133	+	0.608133i	0.334325	+	0.942458i	$0.391492\pi$
$128$	236962.	+	236962.i	1.27836	+	1.27836i
$129$	−499209.			−2.64124
$130$	3306.26	−	13695.7i	0.0171585	−	0.0710763i
$131$			63669.7i			0.324156i	0.986778	+	0.162078i	$0.0518197\pi$
$131$			63669.7i			0.324156i	−0.986778	+	0.162078i	$0.948180\pi$
$132$	−605069.	+	124362.i	−3.02253	+	0.621230i
$133$	−21268.8	+	21268.8i	−0.104259	+	0.104259i
$134$	456030.			2.19397
$135$	318656.	−	194722.i	1.50483	−	0.919561i
$136$	429406.			1.99077
$137$	64966.4	+	64966.4i	0.295724	+	0.295724i	0.839337	−	0.543612i	$-0.182944\pi$
$137$	64966.4	+	64966.4i	0.295724	+	0.295724i	−0.543612	+	0.839337i	$0.682944\pi$
$138$	448320.	+	448320.i	2.00397	+	2.00397i
$139$	−32530.0			−0.142806			−0.0714032	−	0.997448i	$-0.522748\pi$
$139$	−32530.0			−0.142806			−0.0714032	+	0.997448i	$0.522748\pi$
$140$	68315.6	−	41745.8i	0.294578	−	0.180008i
$141$	−307533.			−1.30270
$142$	208797.	−	208797.i	0.868966	−	0.868966i
$143$	10509.9	−	2160.13i	0.0429791	−	0.00883364i
$144$			190863.i			0.767035i
$145$	−116534.	+	482726.i	−0.460293	+	1.90669i
$146$	−393296.			−1.52700
$147$	309565.	+	309565.i	1.18157	+	1.18157i
$148$	−122054.	+	122054.i	−0.458033	+	0.458033i
$149$	120324.			0.444005			0.222003	−	0.975046i	$-0.428741\pi$
$149$	120324.			0.444005			0.222003	+	0.975046i	$0.428741\pi$
$150$	363813.	−	709606.i	1.32023	−	2.57507i
$151$			272381.i			0.972152i	0.873917	+	0.486076i	$0.161572\pi$
$151$			272381.i			0.972152i	−0.873917	+	0.486076i	$0.838428\pi$
$152$	−197907.	−	197907.i	−0.694786	−	0.694786i
$153$	−634545.	−	634545.i	−2.19146	−	2.19146i
$154$	79559.6	+	52431.1i	0.270328	+	0.178151i
$155$	−43623.0	+	180702.i	−0.145843	+	0.604133i
$156$		−	41153.7i		−	0.135393i
$157$	−64655.1	−	64655.1i	−0.209341	−	0.209341i	0.594647	−	0.803987i	$-0.297292\pi$
$157$	−64655.1	−	64655.1i	−0.209341	−	0.209341i	−0.803987	+	0.594647i	$0.797292\pi$
$158$	375304.	−	375304.i	1.19603	−	1.19603i
$159$		−	74904.2i		−	0.234971i
$160$	−111528.	−	182511.i	−0.344415	−	0.563624i
$161$		−	62579.5i		−	0.190269i
$162$	412064.	−	412064.i	1.23361	−	1.23361i
$163$	392709.	−	392709.i	1.15772	−	1.15772i	0.172751	−	0.984966i	$-0.444734\pi$
$163$	392709.	−	392709.i	1.15772	−	1.15772i	0.984966	−	0.172751i	$-0.0552655\pi$
$164$	317999.			0.923244
$165$	606932.	+	20744.8i	1.73552	+	0.0593197i
$166$	−168135.			−0.473575
$167$	280875.	−	280875.i	0.779331	−	0.779331i	−0.200386	−	0.979717i	$-0.564220\pi$
$167$	280875.	−	280875.i	0.779331	−	0.779331i	0.979717	+	0.200386i	$0.0642197\pi$
$168$	112989.	−	112989.i	0.308861	−	0.308861i
$169$		−	370578.i		−	0.998075i
$170$	−938554.	−	226575.i	−2.49079	−	0.601299i
$171$			584905.i			1.52966i
$172$	−741484.	+	741484.i	−1.91109	+	1.91109i
$173$	264767.	+	264767.i	0.672588	+	0.672588i	0.958312	−	0.285724i	$-0.0922339\pi$
$173$	264767.	+	264767.i	0.672588	+	0.672588i	−0.285724	+	0.958312i	$0.592234\pi$
$174$			2.26684e6i			5.67606i
$175$	−74917.5	+	24134.1i	−0.184922	+	0.0595710i
$176$	−86055.3	+	130581.i	−0.209409	+	0.317760i
$177$	766154.	+	766154.i	1.83816	+	1.83816i
$178$	−618275.	−	618275.i	−1.46262	−	1.46262i
$179$		−	16411.8i		−	0.0382845i	−0.999817	−	0.0191423i	$-0.993906\pi$
$179$		−	16411.8i		−	0.0382845i	0.999817	−	0.0191423i	$-0.00609354\pi$
$180$	365343.	−	1.51338e6i	0.840465	−	3.48150i
$181$	184629.			0.418893			0.209447	−	0.977820i	$-0.432834\pi$
$181$	184629.			0.418893			0.209447	+	0.977820i	$0.432834\pi$
$182$	−4488.66	+	4488.66i	−0.0100447	+	0.0100447i
$183$	390954.	+	390954.i	0.862974	+	0.862974i
$184$	582304.			1.26796
$185$	144801.	−	88483.6i	0.311058	−	0.190079i
$186$			848557.i			1.79845i
$187$	−148032.	−	720234.i	−0.309565	−	1.50615i
$188$	−456783.	+	456783.i	−0.942574	+	0.942574i
$189$	−168256.			−0.342623
$190$	328140.	+	536990.i	0.659440	+	1.07915i
$191$	24052.6			0.0477067			0.0238533	−	0.999715i	$-0.492407\pi$
$191$	24052.6			0.0477067			0.0238533	+	0.999715i	$0.492407\pi$
$192$	−929083.	−	929083.i	−1.81887	−	1.81887i
$193$	−357727.	−	357727.i	−0.691288	−	0.691288i	0.271227	−	0.962515i	$-0.412570\pi$
$193$	−357727.	−	357727.i	−0.691288	−	0.691288i	−0.962515	+	0.271227i	$0.912570\pi$
$194$	−725046.			−1.38312
$195$	−9494.37	+	39329.0i	−0.0178805	+	0.0740672i
$196$	919605.			1.70986
$197$	−575228.	+	575228.i	−1.05603	+	1.05603i	−0.0576916	+	0.998334i	$0.518374\pi$
$197$	−575228.	+	575228.i	−1.05603	+	1.05603i	−0.998334	+	0.0576916i	$0.981626\pi$
$198$	1.81491e6	−	373025.i	3.28998	−	0.676200i
$199$			322373.i			0.577066i	0.957470	+	0.288533i	$0.0931676\pi$
$199$			322373.i			0.577066i	−0.957470	+	0.288533i	$0.906832\pi$
$200$	−224568.	−	697109.i	−0.396984	−	1.23233i
$201$	−1.30955e6			−2.28629
$202$	220139.	+	220139.i	0.379593	+	0.379593i
$203$	158210.	−	158210.i	0.269460	−	0.269460i
$204$	−2.82023e6			−4.74470
$205$	−303900.	−	73364.1i	−0.505063	−	0.121927i
$206$		−	491145.i		−	0.806383i
$207$	−860487.	−	860487.i	−1.39579	−	1.39579i
$208$	−7367.26	−	7367.26i	−0.0118072	−	0.0118072i
$209$	−263719.	+	400171.i	−0.417615	+	0.633694i
$210$	−306580.	+	187342.i	−0.479728	+	0.293149i
$211$			302403.i			0.467607i	0.972284	+	0.233803i	$0.0751172\pi$
$211$			302403.i			0.467607i	−0.972284	+	0.233803i	$0.924883\pi$
$212$	−111257.	−	111257.i	−0.170014	−	0.170014i
$213$	−599588.	+	599588.i	−0.905532	+	0.905532i
$214$		−	403139.i		−	0.601755i
$215$	879672.	−	537543.i	1.29785	−	0.793081i
$216$		−	1.56563e6i		−	2.28325i
$217$	59223.7	−	59223.7i	0.0853780	−	0.0853780i
$218$	−1.36395e6	+	1.36395e6i	−1.94382	+	1.94382i
$219$	1.12940e6			1.59125
$220$	932299.	−	870674.i	1.29867	−	1.21283i
$221$	48986.6			0.0674678
$222$	547740.	−	547740.i	0.745920	−	0.745920i
$223$	349644.	−	349644.i	0.470829	−	0.470829i	−0.431354	−	0.902183i	$-0.641964\pi$
$223$	349644.	−	349644.i	0.470829	−	0.470829i	0.902183	+	0.431354i	$0.141964\pi$
$224$			96369.2i			0.128327i
$225$	−698288.	+	1.36199e6i	−0.919557	+	1.79357i
$226$		−	63196.4i		−	0.0823041i
$227$	−640332.	+	640332.i	−0.824784	+	0.824784i	−0.986790	−	0.162006i	$-0.948204\pi$
$227$	−640332.	+	640332.i	−0.824784	+	0.824784i	0.162006	+	0.986790i	$0.448204\pi$
$228$	1.29980e6	+	1.29980e6i	1.65592	+	1.65592i
$229$		−	823918.i		−	1.03823i	−0.854703	−	0.519117i	$-0.826261\pi$
$229$		−	823918.i		−	1.03823i	0.854703	−	0.519117i	$-0.173739\pi$
$230$	−1.27274e6	−	307252.i	−1.58643	−	0.382979i
$231$	−228466.	−	150563.i	−0.281703	−	0.185647i
$232$	1.47215e6	+	1.47215e6i	1.79569	+	1.79569i
$233$	−41543.3	−	41543.3i	−0.0501316	−	0.0501316i	0.681597	−	0.731728i	$-0.261286\pi$
$233$	−41543.3	−	41543.3i	−0.0501316	−	0.0501316i	−0.731728	+	0.681597i	$0.761286\pi$
$234$			123441.i			0.147374i
$235$	541913.	−	331148.i	0.640117	−	0.391158i
$236$	2.27596e6			2.66002
$237$	−1.07774e6	+	1.07774e6i	−1.24636	+	1.24636i
$238$	307605.	+	307605.i	0.352006	+	0.352006i
$239$	268053.			0.303547			0.151774	−	0.988415i	$-0.451502\pi$
$239$	268053.			0.303547			0.151774	+	0.988415i	$0.451502\pi$
$240$	−307486.	−	503190.i	−0.344585	−	0.563902i
$241$			513151.i			0.569119i	0.958658	+	0.284559i	$0.0918473\pi$
$241$			513151.i			0.569119i	−0.958658	+	0.284559i	$0.908153\pi$
$242$	1.40989e6	+	563089.i	1.54755	+	0.618072i
$243$	−35438.9	+	35438.9i	−0.0385004	+	0.0385004i
$244$	1.16138e6			1.24882
$245$	−878831.	−	212158.i	−0.935385	−	0.225810i
$246$	−1.42708e6			−1.50353
$247$	−22577.2	−	22577.2i	−0.0235465	−	0.0235465i
$248$	551078.	+	551078.i	0.568963	+	0.568963i
$249$	482823.			0.493503
$250$	123010.	+	1.64217e6i	0.124478	+	1.66176i
$251$	346563.			0.347215			0.173607	−	0.984815i	$-0.444458\pi$
$251$	346563.			0.347215			0.173607	+	0.984815i	$0.444458\pi$
$252$	−495999.	+	495999.i	−0.492016	+	0.492016i
$253$	−200742.	−	976687.i	−0.197168	−	0.959299i
$254$		−	1.47360e6i		−	1.43317i
$255$	2.69518e6	+	650642.i	2.59560	+	0.626602i
$256$	−1.60579e6			−1.53140
$257$	625579.	+	625579.i	0.590812	+	0.590812i	0.937851	−	0.347039i	$-0.112813\pi$
$257$	625579.	+	625579.i	0.590812	+	0.590812i	−0.347039	+	0.937851i	$0.612813\pi$
$258$	3.32756e6	−	3.32756e6i	3.11226	−	3.11226i
$259$	−76457.3			−0.0708222
$260$	44313.8	+	72518.1i	0.0406542	+	0.0665293i
$261$		−	4.35088e6i		−	3.95344i
$262$	−424400.	−	424400.i	−0.381964	−	0.381964i
$263$	−239990.	−	239990.i	−0.213946	−	0.213946i	0.591996	−	0.805941i	$-0.298340\pi$
$263$	−239990.	−	239990.i	−0.213946	−	0.213946i	−0.805941	+	0.591996i	$0.798340\pi$
$264$	1.40099e6	−	2.12588e6i	1.23716	−	1.87728i
$265$	80656.1	+	131991.i	0.0705541	+	0.115460i
$266$		−	283541.i		−	0.245703i
$267$	1.77546e6	+	1.77546e6i	1.52417	+	1.52417i
$268$	−1.94510e6	+	1.94510e6i	−1.65426	+	1.65426i
$269$			997484.i			0.840476i	0.907414	+	0.420238i	$0.138053\pi$
$269$			997484.i			0.840476i	−0.907414	+	0.420238i	$0.861947\pi$
$270$	−826101.	+	3.42200e6i	−0.689642	+	2.85674i
$271$			1.90345e6i			1.57441i	0.616690	+	0.787206i	$0.288473\pi$
$271$			1.90345e6i			1.57441i	−0.616690	+	0.787206i	$0.711527\pi$
$272$	−504872.	+	504872.i	−0.413770	+	0.413770i
$273$	12889.8	−	12889.8i	0.0104674	−	0.0104674i
$274$	−866087.			−0.696923
$275$	−1.09183e6	+	616983.i	−0.870610	+	0.491973i
$276$	−3.82443e6			−3.02199
$277$	302516.	−	302516.i	0.236891	−	0.236891i	−0.578670	−	0.815561i	$-0.696428\pi$
$277$	302516.	−	302516.i	0.236891	−	0.236891i	0.815561	+	0.578670i	$0.196428\pi$
$278$	216834.	−	216834.i	0.168273	−	0.168273i
$279$		−	1.62869e6i		−	1.25264i
$280$	−77436.1	+	320767.i	−0.0590267	+	0.244509i
$281$		−	1.13512e6i		−	0.857582i	−0.903404	−	0.428791i	$-0.858940\pi$
$281$		−	1.13512e6i		−	0.857582i	0.903404	−	0.428791i	$-0.141060\pi$
$282$	2.04991e6	−	2.04991e6i	1.53501	−	1.53501i
$283$	−1.36900e6	−	1.36900e6i	−1.01610	−	1.01610i	−0.999868	−	0.0162319i	$-0.994833\pi$
$283$	−1.36900e6	−	1.36900e6i	−1.01610	−	1.01610i	−0.0162319	−	0.999868i	$-0.505167\pi$
$284$			1.78116e6i			1.31041i
$285$	−942298.	−	1.54204e6i	−0.687189	−	1.12456i
$286$	−55656.5	+	84453.9i	−0.0402347	+	0.0610526i
$287$	99601.1	+	99601.1i	0.0713772	+	0.0713772i
$288$	1.32511e6	+	1.32511e6i	0.941389	+	0.941389i
$289$		−	1.93716e6i		−	1.36433i
$290$	−2.44091e6	−	3.99446e6i	−1.70434	−	2.78910i
$291$	2.08207e6			1.44133
$292$	1.67752e6	−	1.67752e6i	1.15136	−	1.15136i
$293$	404070.	+	404070.i	0.274971	+	0.274971i	0.831098	−	0.556126i	$-0.187713\pi$
$293$	404070.	+	404070.i	0.274971	+	0.274971i	−0.556126	+	0.831098i	$0.687713\pi$
$294$	−4.12691e6			−2.78456
$295$	−2.17505e6	−	525077.i	−1.45517	−	0.351292i
$296$		−	711437.i		−	0.471962i
$297$	−2.62600e6	+	539730.i	−1.72744	+	0.355047i
$298$	−802041.	+	802041.i	−0.523186	+	0.523186i
$299$	66429.2			0.0429715
$300$	1.47491e6	+	4.57844e6i	0.946153	+	2.93707i
$301$	−464483.			−0.295497
$302$	−1.81560e6	−	1.81560e6i	−1.14552	−	1.14552i
$303$	−632159.	−	632159.i	−0.395566	−	0.395566i
$304$	465376.			0.288815
$305$	−1.10989e6	−	267937.i	−0.683170	−	0.164923i
$306$	8.45932e6			5.16454
$307$	−1.69454e6	+	1.69454e6i	−1.02614	+	1.02614i	−0.0264884	+	0.999649i	$0.508433\pi$
$307$	−1.69454e6	+	1.69454e6i	−1.02614	+	1.02614i	−0.999649	+	0.0264884i	$0.991567\pi$
$308$	−562978.	+	115711.i	−0.338154	+	0.0695020i
$309$			1.41039e6i			0.840316i
$310$	−913718.	−	1.49527e6i	−0.540018	−	0.883721i
$311$	1.91546e6			1.12298			0.561489	−	0.827484i	$-0.310229\pi$
$311$	1.91546e6			1.12298			0.561489	+	0.827484i	$0.310229\pi$
$312$	119940.	+	119940.i	0.0697553	+	0.0697553i
$313$	−1.02736e6	+	1.02736e6i	−0.592739	+	0.592739i	−0.938370	−	0.345632i	$-0.887665\pi$
$313$	−1.02736e6	+	1.02736e6i	−0.592739	+	0.592739i	0.345632	+	0.938370i	$0.387665\pi$
$314$	861937.			0.493346
$315$	588437.	−	359578.i	0.334136	−	0.204181i
$316$			3.20156e6i			1.80362i
$317$	590517.	+	590517.i	0.330054	+	0.330054i	0.852607	−	0.522553i	$-0.175020\pi$
$317$	590517.	+	590517.i	0.330054	+	0.330054i	−0.522553	+	0.852607i	$0.675020\pi$
$318$	499286.	+	499286.i	0.276873	+	0.276873i
$319$	1.96170e6	−	2.97671e6i	1.07934	−	1.63780i
$320$	2.63759e6	+	636739.i	1.43990	+	0.347605i
$321$			1.15767e6i			0.627077i
$322$	417133.	+	417133.i	0.224200	+	0.224200i
$323$	−1.54720e6	+	1.54720e6i	−0.825162	+	0.825162i
$324$			3.51514e6i			1.86029i
$325$	−25618.7	−	79526.2i	−0.0134539	−	0.0417640i
$326$			5.23533e6i			2.72835i
$327$	3.91675e6	−	3.91675e6i	2.02561	−	2.02561i
$328$	−926790.	+	926790.i	−0.475660	+	0.475660i
$329$	−286140.			−0.145743
$330$	−4.18388e6	+	3.90732e6i	−2.11492	+	1.97512i
$331$	−3.30683e6			−1.65898			−0.829492	−	0.558519i	$-0.811370\pi$
$331$	−3.30683e6			−1.65898			−0.829492	+	0.558519i	$0.811370\pi$
$332$	717145.	−	717145.i	0.357077	−	0.357077i
$333$	−1.05131e6	+	1.05131e6i	−0.519542	+	0.519542i
$334$			3.74443e6i			1.83662i
$335$	2.30760e6	−	1.41011e6i	1.12344	−	0.686501i
$336$			265693.i			0.128390i
$337$	877971.	−	877971.i	0.421119	−	0.421119i	−0.464470	−	0.885589i	$-0.653755\pi$
$337$	877971.	−	877971.i	0.421119	−	0.421119i	0.885589	+	0.464470i	$0.153755\pi$
$338$	2.47015e6	+	2.47015e6i	1.17606	+	1.17606i
$339$			181477.i			0.0857674i
$340$	4.96961e6	−	3.03679e6i	2.33145	−	1.42468i
$341$	734335.	−	1.11429e6i	0.341986	−	0.518934i
$342$	−3.89877e6	−	3.89877e6i	−1.80245	−	1.80245i
$343$	587360.	+	587360.i	0.269569	+	0.269569i
$344$		−	4.32202e6i		−	1.96920i
$345$	3.65486e6	+	882315.i	1.65319	+	0.399095i
$346$	−3.52970e6			−1.58507
$347$	1.08895e6	−	1.08895e6i	0.485495	−	0.485495i	−0.421387	−	0.906881i	$-0.638456\pi$
$347$	1.08895e6	−	1.08895e6i	0.485495	−	0.485495i	0.906881	+	0.421387i	$0.138456\pi$
$348$	−9.66871e6	−	9.66871e6i	−4.27977	−	4.27977i
$349$	−1.71830e6			−0.755156			−0.377578	−	0.925978i	$-0.623243\pi$
$349$	−1.71830e6			−0.755156			−0.377578	+	0.925978i	$0.623243\pi$
$350$	338505.	−	660244.i	0.147705	−	0.288094i
$351$		−	178607.i		−	0.0773802i
$352$	309132.	+	1.50405e6i	0.132980	+	0.647001i
$353$	2.14036e6	−	2.14036e6i	0.914219	−	0.914219i	−0.0823817	−	0.996601i	$-0.526253\pi$
$353$	2.14036e6	−	2.14036e6i	0.914219	−	0.914219i	0.996601	+	0.0823817i	$0.0262527\pi$
$354$	−1.02138e7			−4.33192
$355$	410922.	−	1.70218e6i	0.173057	−	0.716861i
$356$	5.27424e6			2.20564
$357$	−883328.	−	883328.i	−0.366819	−	0.366819i
$358$	109395.	+	109395.i	0.0451119	+	0.0451119i
$359$	3.20323e6			1.31175			0.655877	−	0.754868i	$-0.272299\pi$
$359$	3.20323e6			1.31175			0.655877	+	0.754868i	$0.272299\pi$
$360$	3.34588e6	+	5.47542e6i	1.36067	+	2.22670i
$361$	−1.04994e6			−0.424030
$362$	−1.23067e6	+	1.23067e6i	−0.493595	+	0.493595i
$363$	−4.04868e6	−	1.61699e6i	−1.61267	−	0.644080i
$364$		−	38290.9i		−	0.0151475i
$365$	−1.99016e6	+	1.21613e6i	−0.781907	+	0.477802i
$366$	−5.21192e6			−2.03374
$367$	−221282.	−	221282.i	−0.0857593	−	0.0857593i	0.662926	−	0.748685i	$-0.269314\pi$
$367$	−221282.	−	221282.i	−0.0857593	−	0.0857593i	−0.748685	+	0.662926i	$0.769314\pi$
$368$	−684642.	+	684642.i	−0.263538	+	0.263538i
$369$	2.73909e6			1.04723
$370$	−375389.	+	1.55499e6i	−0.142553	+	0.590505i
$371$		−	69693.7i		−	0.0262881i
$372$	−3.61934e6	−	3.61934e6i	−1.35604	−	1.35604i
$373$	2.49356e6	+	2.49356e6i	0.928001	+	0.928001i	0.997577	−	0.0695757i	$-0.0221645\pi$
$373$	2.49356e6	+	2.49356e6i	0.928001	+	0.928001i	−0.0695757	+	0.997577i	$0.522165\pi$
$374$	5.78756e6	+	3.81410e6i	2.13952	+	1.40998i
$375$	−353240.	−	4.71571e6i	−0.129716	−	1.73168i
$376$		−	2.66254e6i		−	0.971238i
$377$	167943.	+	167943.i	0.0608566	+	0.0608566i
$378$	1.12154e6	−	1.12154e6i	0.403723	−	0.403723i
$379$			3.81946e6i			1.36585i	0.730487	+	0.682926i	$0.239293\pi$
$379$			3.81946e6i			1.36585i	−0.730487	+	0.682926i	$0.760707\pi$
$380$	−3.69003e6	−	890807.i	−1.31090	−	0.316464i
$381$			4.23165e6i			1.49347i
$382$	−160326.	+	160326.i	−0.0562143	+	0.0562143i
$383$	−2.60812e6	+	2.60812e6i	−0.908512	+	0.908512i	−0.996152	−	0.0876406i	$-0.972067\pi$
$383$	−2.60812e6	+	2.60812e6i	−0.908512	+	0.908512i	0.0876406	+	0.996152i	$0.472067\pi$
$384$	9.07152e6			3.13944
$385$	564712.	+	19301.7i	0.194167	+	0.00663658i
$386$	4.76897e6			1.62913
$387$	−6.38678e6	+	6.38678e6i	−2.16773	+	2.16773i
$388$	3.09253e6	−	3.09253e6i	1.04288	−	1.04288i
$389$			1.05098e6i			0.352145i	0.984377	+	0.176072i	$0.0563393\pi$
$389$			1.05098e6i			0.352145i	−0.984377	+	0.176072i	$0.943661\pi$
$390$	−198867.	−	325439.i	−0.0662066	−	0.108345i
$391$		−	4.55234e6i		−	1.50589i
$392$	−2.68013e6	+	2.68013e6i	−0.880930	+	0.880930i
$393$	1.21872e6	+	1.21872e6i	0.398037	+	0.398037i
$394$		−	7.66854e6i		−	2.48870i
$395$	738618.	−	3.05961e6i	0.238192	−	0.986673i
$396$	−6.15007e6	+	9.33219e6i	−1.97080	+	2.99051i
$397$	3.27328e6	+	3.27328e6i	1.04234	+	1.04234i	0.999063	+	0.0432721i	$0.0137782\pi$
$397$	3.27328e6	+	3.27328e6i	1.04234	+	1.04234i	0.0432721	+	0.999063i	$0.486222\pi$
$398$	−2.14883e6	−	2.14883e6i	−0.679976	−	0.679976i
$399$			814225.i			0.256043i
$400$	1.08366e6	+	555589.i	0.338644	+	0.173622i
$401$	−3.67110e6			−1.14008			−0.570039	−	0.821617i	$-0.693072\pi$
$401$	−3.67110e6			−1.14008			−0.570039	+	0.821617i	$0.693072\pi$
$402$	8.72901e6	−	8.72901e6i	2.69401	−	2.69401i
$403$	62866.9	+	62866.9i	0.0192823	+	0.0192823i
$404$	−1.87791e6			−0.572429
$405$	810962.	−	3.35929e6i	0.245676	−	1.01768i
$406$			2.10915e6i			0.635027i
$407$	−1.19328e6	+	245259.i	−0.357072	+	0.0733903i
$408$	8.21939e6	−	8.21939e6i	2.44449	−	2.44449i
$409$	3.09760e6			0.915622			0.457811	−	0.889049i	$-0.348634\pi$
$409$	3.09760e6			0.915622			0.457811	+	0.889049i	$0.348634\pi$
$410$	2.51471e6	−	1.53667e6i	0.738802	−	0.451462i
$411$	2.48708e6			0.726250
$412$	2.09487e6	+	2.09487e6i	0.608016	+	0.608016i
$413$	712858.	+	712858.i	0.205650	+	0.205650i
$414$	1.14714e7			3.28940
$415$	−850797.	+	519899.i	−0.242497	+	0.148183i
$416$	−102297.			−0.0289822
$417$	−622668.	+	622668.i	−0.175354	+	0.175354i
$418$	−909538.	−	4.42526e6i	−0.254613	−	1.23879i
$419$			1.20239e6i			0.334588i	0.985907	+	0.167294i	$0.0535030\pi$
$419$			1.20239e6i			0.334588i	−0.985907	+	0.167294i	$0.946497\pi$
$420$	508581.	−	2.10672e6i	0.140682	−	0.582752i
$421$	−3.68458e6			−1.01317			−0.506586	−	0.862190i	$-0.669093\pi$
$421$	−3.68458e6			−1.01317			−0.506586	+	0.862190i	$0.669093\pi$
$422$	−2.01572e6	−	2.01572e6i	−0.550996	−	0.550996i
$423$	−3.93451e6	+	3.93451e6i	−1.06915	+	1.06915i
$424$	648501.			0.175185
$425$	−5.44987e6	+	1.75563e6i	−1.46357	+	0.471477i
$426$		−	7.99329e6i		−	2.13403i
$427$	363758.	+	363758.i	0.0965478	+	0.0965478i
$428$	1.71950e6	+	1.71950e6i	0.453726	+	0.453726i
$429$	159825.	−	242521.i	0.0419278	−	0.0636217i
$430$	−2.28051e6	+	9.44667e6i	−0.594786	+	2.46381i
$431$		−	122609.i		−	0.0317928i	−0.999874	−	0.0158964i	$-0.994940\pi$
$431$		−	122609.i		−	0.0317928i	0.999874	−	0.0158964i	$-0.00506019\pi$
$432$	1.84078e6	+	1.84078e6i	0.474562	+	0.474562i
$433$	731225.	−	731225.i	0.187427	−	0.187427i	−0.607156	−	0.794583i	$-0.707690\pi$
$433$	731225.	−	731225.i	0.187427	−	0.187427i	0.794583	+	0.607156i	$0.207690\pi$
$434$			789529.i			0.201207i
$435$	7.00939e6	+	1.14706e7i	1.77606	+	2.90646i
$436$		−	1.16352e7i		−	2.93129i
$437$	−2.09811e6	+	2.09811e6i	−0.525562	+	0.525562i
$438$	−7.52821e6	+	7.52821e6i	−1.87502	+	1.87502i
$439$	−2.67323e6			−0.662025			−0.331013	−	0.943626i	$-0.607390\pi$
$439$	−2.67323e6			−0.662025			−0.331013	+	0.943626i	$0.607390\pi$
$440$	−179603.	+	5.25466e6i	−0.0442264	+	1.29394i
$441$	7.92103e6			1.93948
$442$	−326528.	+	326528.i	−0.0794995	+	0.0794995i
$443$	1.02394e6	−	1.02394e6i	0.247893	−	0.247893i	−0.572212	−	0.820105i	$-0.693915\pi$
$443$	1.02394e6	−	1.02394e6i	0.247893	−	0.247893i	0.820105	+	0.572212i	$0.193915\pi$
$444$			4.67254e6i			1.12485i
$445$	−5.04039e6	−	1.21680e6i	−1.20660	−	0.291285i
$446$			4.66121e6i			1.10959i
$447$	2.30317e6	−	2.30317e6i	0.545201	−	0.545201i
$448$	−864453.	−	864453.i	−0.203492	−	0.203492i
$449$			6.99671e6i			1.63787i	0.573889	+	0.818933i	$0.305434\pi$
$449$			6.99671e6i			1.63787i	−0.573889	+	0.818933i	$0.694566\pi$
$450$	−4.42400e6	−	1.37331e7i	−1.02987	−	3.19696i
$451$	1.87399e6	+	1.23499e6i	0.433836	+	0.285905i
$452$	269551.	+	269551.i	0.0620576	+	0.0620576i
$453$	5.21373e6	+	5.21373e6i	1.19372	+	1.19372i
$454$		−	8.53646e6i		−	1.94374i
$455$	−8833.91	+	36593.1i	−0.00200044	+	0.00828650i
$456$	−7.57638e6			−1.70628
$457$	−2.95746e6	+	2.95746e6i	−0.662413	+	0.662413i	−0.955948	−	0.293535i	$-0.905168\pi$
$457$	−2.95746e6	+	2.95746e6i	−0.662413	+	0.662413i	0.293535	+	0.955948i	$0.405168\pi$
$458$	5.49195e6	+	5.49195e6i	1.22338	+	1.22338i
$459$	−1.22398e7			−2.71170
$460$	6.73914e6	−	4.11810e6i	1.48494	−	0.907408i
$461$		−	8.54473e6i		−	1.87260i	−0.351196	−	0.936302i	$-0.614225\pi$
$461$		−	8.54473e6i		−	1.87260i	0.351196	−	0.936302i	$-0.385775\pi$
$462$	2.52648e6	−	519275.i	0.550694	−	0.113186i
$463$	1.48809e6	−	1.48809e6i	0.322609	−	0.322609i	−0.527158	−	0.849767i	$-0.676742\pi$
$463$	1.48809e6	−	1.48809e6i	0.322609	−	0.322609i	0.849767	+	0.527158i	$0.176742\pi$
$464$	−3.46175e6			−0.746450
$465$	2.62386e6	+	4.29387e6i	0.562741	+	0.920908i
$466$	553827.			0.118143
$467$	1.12143e6	+	1.12143e6i	0.237948	+	0.237948i	0.816000	−	0.578052i	$-0.196187\pi$
$467$	1.12143e6	+	1.12143e6i	0.237948	+	0.237948i	−0.578052	+	0.816000i	$0.696187\pi$
$468$	−526511.	−	526511.i	−0.111120	−	0.111120i
$469$	−1.21845e6			−0.255786
$470$	−1.40488e6	+	5.81952e6i	−0.293357	+	1.21518i
$471$	−2.47517e6			−0.514106
$472$	−6.63316e6	+	6.63316e6i	−1.37046	+	1.37046i
$473$	−7.24925e6	+	1.48996e6i	−1.48984	+	0.306212i
$474$		−	1.43676e7i		−	2.93724i
$475$	3.32091e6	+	1.70262e6i	0.675340	+	0.346245i
$476$	−2.62405e6			−0.530828
$477$	−958309.	−	958309.i	−0.192846	−	0.192846i
$478$	−1.78675e6	+	1.78675e6i	−0.357679	+	0.357679i
$479$	−5.13513e6			−1.02262			−0.511308	−	0.859397i	$-0.670839\pi$
$479$	−5.13513e6			−1.02262			−0.511308	+	0.859397i	$0.670839\pi$
$480$	−5.62829e6	−	1.35872e6i	−1.11500	−	0.269170i
$481$		−	81160.7i		−	0.0159950i
$482$	−3.42049e6	−	3.42049e6i	−0.670611	−	0.670611i
$483$	−1.19785e6	−	1.19785e6i	−0.233634	−	0.233634i
$484$	−8.41531e6	+	3.61183e6i	−1.63289	+	0.700832i
$485$	−3.66888e6	+	2.24195e6i	−0.708237	+	0.432784i
$486$		−	472447.i		−	0.0907324i
$487$	−491977.	−	491977.i	−0.0939988	−	0.0939988i	0.658544	−	0.752542i	$-0.271173\pi$
$487$	−491977.	−	491977.i	−0.0939988	−	0.0939988i	−0.752542	+	0.658544i	$0.771173\pi$
$488$	−3.38477e6	+	3.38477e6i	−0.643398	+	0.643398i
$489$		−	1.50339e7i		−	2.84316i
$490$	7.27215e6	−	4.44381e6i	1.36827	−	0.836114i
$491$			4.22441e6i			0.790793i	0.918511	+	0.395396i	$0.129393\pi$
$491$			4.22441e6i			0.790793i	−0.918511	+	0.395396i	$0.870607\pi$
$492$	6.08693e6	−	6.08693e6i	1.13367	−	1.13367i
$493$	1.15090e7	−	1.15090e7i	2.13265	−	2.13265i
$494$	300983.			0.0554913
$495$	8.03037e6	−	7.49956e6i	1.47307	−	1.37570i
$496$	−1.29586e6			−0.236512
$497$	−557878.	+	557878.i	−0.101309	+	0.101309i
$498$	−3.21833e6	+	3.21833e6i	−0.581510	+	0.581510i
$499$			7.19643e6i			1.29380i	0.762577	+	0.646898i	$0.223934\pi$
$499$			7.19643e6i			1.29380i	−0.762577	+	0.646898i	$0.776066\pi$
$500$	−7.52899e6	−	6.47965e6i	−1.34683	−	1.15911i
$501$		−	1.07526e7i		−	1.91391i
$502$	−2.31007e6	+	2.31007e6i	−0.409134	+	0.409134i
$503$	−301551.	−	301551.i	−0.0531424	−	0.0531424i	0.680036	−	0.733179i	$-0.261964\pi$
$503$	−301551.	−	301551.i	−0.0531424	−	0.0531424i	−0.733179	+	0.680036i	$0.761964\pi$
$504$		−	2.89112e6i		−	0.506979i
$505$	1.79465e6	+	433244.i	0.313149	+	0.0755970i
$506$	7.84833e6	+	5.17218e6i	1.36270	+	0.898044i
$507$	−7.09335e6	−	7.09335e6i	−1.22555	−	1.22555i
$508$	6.28535e6	+	6.28535e6i	1.08061	+	1.08061i
$509$			6.44969e6i			1.10343i	0.834033	+	0.551715i	$0.186026\pi$
$509$			6.44969e6i			1.10343i	−0.834033	+	0.551715i	$0.813974\pi$
$510$	−2.23021e7	+	1.36282e7i	−3.79683	+	2.32014i
$511$	1.05084e6			0.178026
$512$	3.12086e6	−	3.12086e6i	0.526138	−	0.526138i
$513$	5.64113e6	+	5.64113e6i	0.946395	+	0.946395i
$514$	−8.33978e6			−1.39234
$515$	−1.51869e6	−	2.48529e6i	−0.252320	−	0.412913i
$516$			2.83860e7i			4.69331i
$517$	−4.46582e6	+	917875.i	−0.734810	+	0.151028i
$518$	509638.	−	509638.i	0.0834521	−	0.0834521i
$519$	1.01360e7			1.65176
$520$	−340500.	−	82199.7i	−0.0552215	−	0.0133310i
$521$	9.16486e6			1.47922			0.739608	−	0.673038i	$-0.235011\pi$
$521$	9.16486e6			1.47922			0.739608	+	0.673038i	$0.235011\pi$
$522$	2.90014e7	+	2.90014e7i	4.65847	+	4.65847i
$523$	−1.94148e6	−	1.94148e6i	−0.310370	−	0.310370i	0.534683	−	0.845053i	$-0.320431\pi$
$523$	−1.94148e6	−	1.94148e6i	−0.310370	−	0.310370i	−0.845053	+	0.534683i	$0.820431\pi$
$524$	3.62038e6			0.576004
$525$	−972063.	+	1.89598e6i	−0.153920	+	0.300217i
$526$	3.19938e6			0.504198
$527$	4.30822e6	−	4.30822e6i	0.675728	−	0.675728i
$528$	852288.	+	4.14671e6i	0.133046	+	0.647320i
$529$			263052.i			0.0408698i
$530$	−1.41743e6	−	342181.i	−0.219186	−	0.0529135i
$531$	1.96040e7			3.01723
$532$	1.20938e6	+	1.20938e6i	0.185261	+	0.185261i
$533$	−105728.	+	105728.i	−0.0161203	+	0.0161203i
$534$	−2.36692e7			−3.59195
$535$	−1.24656e6	−	2.03996e6i	−0.188291	−	0.308132i
$536$		−	1.13377e7i		−	1.70457i
$537$	−314143.	−	314143.i	−0.0470102	−	0.0470102i
$538$	−6.64888e6	−	6.64888e6i	−0.990359	−	0.990359i
$539$	5.41928e6	+	3.57140e6i	0.803470	+	0.529500i
$540$	−1.10722e7	−	1.81194e7i	−1.63400	−	2.67398i
$541$		−	5.86606e6i		−	0.861695i	−0.902425	−	0.430847i	$-0.858215\pi$
$541$		−	5.86606e6i		−	0.861695i	0.902425	−	0.430847i	$-0.141785\pi$
$542$	−1.26877e7	−	1.26877e7i	−1.85518	−	1.85518i
$543$	3.53404e6	−	3.53404e6i	0.514366	−	0.514366i
$544$			7.01037e6i			1.01565i
$545$	−2.68431e6	+	1.11194e7i	−0.387117	+	1.60357i
$546$			171838.i			0.0246682i
$547$	6.47159e6	−	6.47159e6i	0.924789	−	0.924789i	−0.0725744	−	0.997363i	$-0.523121\pi$
$547$	6.47159e6	−	6.47159e6i	0.924789	−	0.924789i	0.997363	+	0.0725744i	$0.0231215\pi$
$548$	3.69411e6	−	3.69411e6i	0.525483	−	0.525483i
$549$	1.00036e7			1.41652
$550$	3.16517e6	−	1.13904e7i	0.446160	−	1.60558i
$551$	−1.06086e7			−1.48861
$552$	1.11461e7	−	1.11461e7i	1.55695	−	1.55695i
$553$	−1.00277e6	+	1.00277e6i	−0.139440	+	0.139440i
$554$			4.03293e6i			0.558272i
$555$	1.07798e6	−	4.46537e6i	0.148552	−	0.615353i
$556$			1.84972e6i			0.253757i
$557$	4.23770e6	−	4.23770e6i	0.578752	−	0.578752i	−0.355808	−	0.934559i	$-0.615794\pi$
$557$	4.23770e6	−	4.23770e6i	0.578752	−	0.578752i	0.934559	+	0.355808i	$0.115794\pi$
$558$	1.08563e7	+	1.08563e7i	1.47603	+	1.47603i
$559$		−	493056.i		−	0.0667370i
$560$	−286096.	−	468187.i	−0.0385515	−	0.0630883i
$561$	−1.66198e7	−	1.09527e7i	−2.22955	−	1.46931i
$562$	7.56631e6	+	7.56631e6i	1.01052	+	1.01052i
$563$	−5.64702e6	−	5.64702e6i	−0.750842	−	0.750842i	0.223795	−	0.974636i	$-0.428155\pi$
$563$	−5.64702e6	−	5.64702e6i	−0.750842	−	0.750842i	−0.974636	+	0.223795i	$0.928155\pi$
$564$			1.74869e7i			2.31480i
$565$	−195413.	−	319786.i	−0.0257532	−	0.0421443i
$566$	1.82505e7			2.39461
$567$	−1.10098e6	+	1.10098e6i	−0.143821	+	0.143821i
$568$	−5.19107e6	−	5.19107e6i	−0.675128	−	0.675128i
$569$	526765.			0.0682082			0.0341041	−	0.999418i	$-0.489142\pi$
$569$	526765.			0.0682082			0.0341041	+	0.999418i	$0.489142\pi$
$570$	1.65597e7	+	3.99767e6i	2.13485	+	0.515371i
$571$			368729.i			0.0473279i	0.999720	+	0.0236640i	$0.00753317\pi$
$571$			368729.i			0.0473279i	−0.999720	+	0.0236640i	$0.992467\pi$
$572$	−122829.	−	597611.i	−0.0156968	−	0.0763710i
$573$	460399.	−	460399.i	0.0585798	−	0.0585798i
$574$	−1.32781e6			−0.168212
$575$	−7.39040e6	+	2.38076e6i	−0.932177	+	0.300293i
$576$	−2.37730e7			−2.98557
$577$	−593366.	−	593366.i	−0.0741965	−	0.0741965i	0.669035	−	0.743231i	$-0.266708\pi$
$577$	−593366.	−	593366.i	−0.0741965	−	0.0741965i	−0.743231	+	0.669035i	$0.766708\pi$
$578$	1.29124e7	+	1.29124e7i	1.60764	+	1.60764i
$579$	−1.36947e7			−1.69769
$580$	2.74487e7	+	6.62636e6i	3.38807	+	0.817910i
$581$	449236.			0.0552121
$582$	−1.38783e7	+	1.38783e7i	−1.69836	+	1.69836i
$583$	−223562.	−	1.08772e6i	−0.0272413	−	0.132539i
$584$			9.77807e6i			1.18637i
$585$	381698.	+	624636.i	0.0461137	+	0.0754635i
$586$	−5.38678e6			−0.648015
$587$	−7.71643e6	−	7.71643e6i	−0.924318	−	0.924318i	0.0730134	−	0.997331i	$-0.476738\pi$
$587$	−7.71643e6	−	7.71643e6i	−0.924318	−	0.924318i	−0.997331	+	0.0730134i	$0.976738\pi$
$588$	1.76025e7	−	1.76025e7i	2.09957	−	2.09957i
$589$	−3.97119e6			−0.471664
$590$	1.79981e7	−	1.09981e7i	2.12861	−	1.30074i
$591$			2.20213e7i			2.59342i
$592$	836470.	+	836470.i	0.0980948	+	0.0980948i
$593$	−1.09625e7	−	1.09625e7i	−1.28019	−	1.28019i	−0.940561	−	0.339625i	$-0.889700\pi$
$593$	−1.09625e7	−	1.09625e7i	−1.28019	−	1.28019i	−0.339625	−	0.940561i	$-0.610300\pi$
$594$	1.39063e7	−	2.11016e7i	1.61714	−	2.45386i
$595$	2.50770e6	+	605381.i	0.290391	+	0.0701030i
$596$		−	6.84187e6i		−	0.788968i
$597$	6.17064e6	+	6.17064e6i	0.708589	+	0.708589i
$598$	−442794.	+	442794.i	−0.0506348	+	0.0506348i
$599$		−	1.26649e7i		−	1.44223i	−0.692815	−	0.721116i	$-0.743630\pi$
$599$		−	1.26649e7i		−	1.44223i	0.692815	−	0.721116i	$-0.256370\pi$
$600$	−1.76421e7	−	9.04506e6i	−2.00066	−	1.02573i
$601$			2.35725e6i			0.266207i	0.991102	+	0.133104i	$0.0424943\pi$
$601$			2.35725e6i			0.266207i	−0.991102	+	0.133104i	$0.957506\pi$
$602$	3.09608e6	−	3.09608e6i	0.348194	−	0.348194i
$603$	−1.67541e7	+	1.67541e7i	−1.87641	+	1.87641i
$604$	1.54881e7			1.72745
$605$	8.87545e6	−	1.51023e6i	0.985830	−	0.167747i
$606$	8.42750e6			0.932217
$607$	−5.01202e6	+	5.01202e6i	−0.552129	+	0.552129i	−0.927055	−	0.374926i	$-0.877668\pi$
$607$	−5.01202e6	+	5.01202e6i	−0.552129	+	0.552129i	0.374926	+	0.927055i	$0.377668\pi$
$608$	3.23097e6	−	3.23097e6i	0.354466	−	0.354466i
$609$		−	6.05670e6i		−	0.661749i
$610$	9.18409e6	−	5.61214e6i	0.999336	−	0.610667i
$611$		−	303742.i		−	0.0329156i
$612$	−3.60814e7	+	3.60814e7i	−3.89408	+	3.89408i
$613$	1.22413e6	+	1.22413e6i	0.131576	+	0.131576i	0.769828	−	0.638252i	$-0.220342\pi$
$613$	1.22413e6	+	1.22413e6i	0.131576	+	0.131576i	−0.638252	+	0.769828i	$0.720342\pi$
$614$		−	2.25904e7i		−	2.41826i
$615$	−7.22133e6	+	4.41275e6i	−0.769891	+	0.470459i
$616$	1.30353e6	−	1.97800e6i	0.138411	−	0.210027i
$617$	317084.	+	317084.i	0.0335321	+	0.0335321i	0.723674	−	0.690142i	$-0.242452\pi$
$617$	317084.	+	317084.i	0.0335321	+	0.0335321i	−0.690142	+	0.723674i	$0.742452\pi$
$618$	−9.40116e6	−	9.40116e6i	−0.990171	−	0.990171i
$619$		−	6.90745e6i		−	0.724588i	−0.932064	−	0.362294i	$-0.881994\pi$
$619$		−	6.90745e6i		−	0.724588i	0.932064	−	0.362294i	$-0.118006\pi$
$620$	1.02750e7	+	2.48048e6i	1.07350	+	0.259154i
$621$	−1.65980e7			−1.72714
$622$	−1.27678e7	+	1.27678e7i	−1.32324	+	1.32324i
$623$	1.65195e6	+	1.65195e6i	0.170521	+	0.170521i
$624$	−282038.			−0.0289965
$625$	5.70028e6	+	7.92933e6i	0.583709	+	0.811963i
$626$		−	1.36961e7i		−	1.39689i
$627$	2.61186e6	+	1.27077e7i	0.265327	+	1.29092i
$628$	−3.67641e6	+	3.67641e6i	−0.371984	+	0.371984i
$629$	−5.56188e6			−0.560525
$630$	−1.52550e6	+	6.31914e6i	−0.153130	+	0.634317i
$631$	1.09179e7			1.09161			0.545804	−	0.837913i	$-0.316224\pi$
$631$	1.09179e7			1.09161			0.545804	+	0.837913i	$0.316224\pi$
$632$	−9.33076e6	−	9.33076e6i	−0.929233	−	0.929233i
$633$	5.78840e6	+	5.78840e6i	0.574182	+	0.574182i
$634$	−7.87237e6			−0.777826
$635$	−4.55660e6	−	7.45672e6i	−0.448442	−	0.733861i
$636$	−4.25919e6			−0.417527
$637$	−305750.	+	305750.i	−0.0298550	+	0.0298550i
$638$	6.76570e6	+	3.29178e7i	0.658053	+	3.20169i
$639$			1.53420e7i			1.48638i
$640$	−1.59852e7	+	9.76812e6i	−1.54265	+	0.942673i
$641$	−2.10355e6			−0.202212			−0.101106	−	0.994876i	$-0.532238\pi$
$641$	−2.10355e6			−0.202212			−0.101106	+	0.994876i	$0.532238\pi$
$642$	−7.71660e6	−	7.71660e6i	−0.738905	−	0.738905i
$643$	−1.49776e6	+	1.49776e6i	−0.142861	+	0.142861i	−0.774920	−	0.632059i	$-0.782210\pi$
$643$	−1.49776e6	+	1.49776e6i	−0.142861	+	0.142861i	0.632059	+	0.774920i	$0.282210\pi$
$644$	−3.55839e6			−0.338095
$645$	6.54879e6	−	2.71274e7i	0.619815	−	2.56749i
$646$		−	2.06262e7i		−	1.94463i
$647$	1.09315e7	+	1.09315e7i	1.02664	+	1.02664i	0.999635	+	0.0270041i	$0.00859671\pi$
$647$	1.09315e7	+	1.09315e7i	1.02664	+	1.02664i	0.0270041	+	0.999635i	$0.491403\pi$
$648$	−1.02447e7	−	1.02447e7i	−0.958431	−	0.958431i
$649$	1.34124e7	+	8.83897e6i	1.24995	+	0.823740i
$650$	700859.	+	359329.i	0.0650650	+	0.0333587i
$651$		−	2.26724e6i		−	0.209674i
$652$	−2.23302e7	−	2.23302e7i	−2.05718	−	2.05718i
$653$	440857.	−	440857.i	0.0404589	−	0.0404589i	−0.686588	−	0.727047i	$-0.740892\pi$
$653$	440857.	−	440857.i	0.0404589	−	0.0404589i	0.727047	+	0.686588i	$0.240892\pi$
$654$			5.22154e7i			4.77369i
$655$	−3.45986e6	−	835241.i	−0.315105	−	0.0760691i
$656$		−	2.17934e6i		−	0.197727i
$657$	1.44493e7	−	1.44493e7i	1.30598	−	1.30598i
$658$	1.90731e6	−	1.90731e6i	0.171734	−	0.171734i
$659$	−5.18339e6			−0.464944			−0.232472	−	0.972603i	$-0.574681\pi$
$659$	−5.18339e6			−0.464944			−0.232472	+	0.972603i	$0.574681\pi$
$660$	1.17959e6	−	3.45113e7i	0.105407	−	3.08391i
$661$	−1.81917e7			−1.61946			−0.809729	−	0.586804i	$-0.800386\pi$
$661$	−1.81917e7			−1.61946			−0.809729	+	0.586804i	$0.800386\pi$
$662$	2.20422e7	−	2.20422e7i	1.95483	−	1.95483i
$663$	937668.	−	937668.i	0.0828448	−	0.0828448i
$664$			4.18015e6i			0.367936i
$665$	−876749.	−	1.43477e6i	−0.0768814	−	0.125814i
$666$		−	1.40154e7i		−	1.22439i
$667$	1.56070e7	−	1.56070e7i	1.35833	−	1.35833i
$668$	−1.59711e7	−	1.59711e7i	−1.38482	−	1.38482i
$669$		−	1.33853e7i		−	1.15628i
$670$	−5.98235e6	+	2.47810e7i	−0.514855	+	2.13271i
$671$	6.84407e6	+	4.51036e6i	0.586825	+	0.386727i
$672$	1.84463e6	+	1.84463e6i	0.157575	+	0.157575i
$673$	5.52010e6	+	5.52010e6i	0.469796	+	0.469796i	0.901848	−	0.432053i	$-0.142211\pi$
$673$	5.52010e6	+	5.52010e6i	0.469796	+	0.469796i	−0.432053	+	0.901848i	$0.642211\pi$
$674$			1.17045e7i			0.992437i
$675$	6.40108e6	+	1.98704e7i	0.540747	+	1.67860i
$676$	−2.10718e7			−1.77351
$677$	−1.21877e7	+	1.21877e7i	−1.02200	+	1.02200i	−0.0222432	+	0.999753i	$0.507081\pi$
$677$	−1.21877e7	+	1.21877e7i	−1.02200	+	1.02200i	−0.999753	+	0.0222432i	$0.992919\pi$
$678$	−1.20966e6	−	1.20966e6i	−0.101063	−	0.101063i
$679$	1.93723e6			0.161253
$680$	−5.63309e6	+	2.33342e7i	−0.467169	+	1.93518i
$681$			2.45136e7i			2.02553i
$682$	2.53264e6	+	1.23223e7i	0.208503	+	1.01445i
$683$	1.33578e7	−	1.33578e7i	1.09568	−	1.09568i	0.100767	−	0.994910i	$-0.467870\pi$
$683$	1.33578e7	−	1.33578e7i	1.09568	−	1.09568i	0.994910	−	0.100767i	$-0.0321295\pi$
$684$	3.32588e7			2.71810
$685$	−4.38257e6	+	2.67807e6i	−0.356864	+	0.218070i
$686$	−7.83028e6			−0.635282
$687$	−1.57709e7	−	1.57709e7i	−1.27486	−	1.27486i
$688$	5.08161e6	+	5.08161e6i	0.409289	+	0.409289i
$689$	73981.0			0.00593707
$690$	−3.02432e7	+	1.84808e7i	−2.41827	+	1.47774i
$691$	−1.66024e7			−1.32274			−0.661372	−	0.750058i	$-0.730026\pi$
$691$	−1.66024e7			−1.32274			−0.661372	+	0.750058i	$0.730026\pi$
$692$	1.50552e7	−	1.50552e7i	1.19514	−	1.19514i
$693$	−4.84922e6	+	996677.i	−0.383565	+	0.0788354i
$694$			1.45171e7i			1.14415i
$695$	426740.	−	1.76770e6i	0.0335121	−	0.138819i
$696$	5.63577e7			4.40992
$697$	7.24547e6	+	7.24547e6i	0.564917	+	0.564917i
$698$	1.14536e7	−	1.14536e7i	0.889825	−	0.889825i
$699$	−1.59039e6			−0.123115
$700$	1.37231e6	+	4.25995e6i	0.105854	+	0.328594i
$701$		−	9.23755e6i		−	0.710005i	−0.934865	−	0.355003i	$-0.884480\pi$
$701$		−	9.23755e6i		−	0.710005i	0.934865	−	0.355003i	$-0.115520\pi$
$702$	1.19053e6	+	1.19053e6i	0.0911796	+	0.0911796i
$703$	2.56339e6	+	2.56339e6i	0.195626	+	0.195626i
$704$	−1.62646e7	−	1.07187e7i	−1.23684	−	0.815096i
$705$	4.03431e6	−	1.67115e7i	0.305701	−	1.26632i
$706$			2.85338e7i			2.15451i
$707$	−588184.	−	588184.i	−0.0442552	−	0.0442552i
$708$	4.35649e7	−	4.35649e7i	3.26628	−	3.26628i
$709$		−	4.61830e6i		−	0.345038i	−0.985006	−	0.172519i	$-0.944809\pi$
$709$		−	4.61830e6i		−	0.345038i	0.985006	−	0.172519i	$-0.0551906\pi$
$710$	8.60709e6	+	1.40852e7i	0.640782	+	1.04862i
$711$			2.75767e7i			2.04582i
$712$	−1.53715e7	+	1.53715e7i	−1.13636	+	1.13636i
$713$	5.84225e6	−	5.84225e6i	0.430384	−	0.430384i
$714$	1.17759e7			0.864469
$715$	−20489.1	+	599451.i	−0.00149885	+	0.0438519i
$716$	−933204.			−0.0680290
$717$	5.13089e6	−	5.13089e6i	0.372730	−	0.372730i
$718$	−2.13516e7	+	2.13516e7i	−1.54568	+	1.54568i
$719$			1.20305e7i			0.867884i	0.900941	+	0.433942i	$0.142878\pi$
$719$			1.20305e7i			0.867884i	−0.900941	+	0.433942i	$0.857122\pi$
$720$	−1.03716e7	−	2.50380e6i	−0.745616	−	0.179998i
$721$			1.31228e6i			0.0940129i
$722$	6.99854e6	−	6.99854e6i	0.499648	−	0.499648i
$723$	9.82239e6	+	9.82239e6i	0.698830	+	0.698830i
$724$		−	1.04983e7i		−	0.744345i
$725$	−2.47029e7	−	1.26651e7i	−1.74543	−	0.894879i
$726$	3.77653e7	−	1.62088e7i	2.65921	−	1.14133i
$727$	5.69121e6	+	5.69121e6i	0.399364	+	0.399364i	0.878009	−	0.478645i	$-0.158872\pi$
$727$	5.69121e6	+	5.69121e6i	0.399364	+	0.399364i	−0.478645	+	0.878009i	$0.658872\pi$
$728$	111596.	+	111596.i	0.00780409	+	0.00780409i
$729$		−	1.36653e7i		−	0.952360i
$730$	5.15939e6	−	2.13720e7i	0.358337	−	1.48435i
$731$	−3.37888e7			−2.33872
$732$	2.22303e7	−	2.22303e7i	1.53345	−	1.53345i
$733$	8.42710e6	+	8.42710e6i	0.579320	+	0.579320i	0.934716	−	0.355396i	$-0.115654\pi$
$733$	8.42710e6	+	8.42710e6i	0.579320	+	0.579320i	−0.355396	+	0.934716i	$0.615654\pi$
$734$	2.94998e6			0.202106
$735$	−2.08830e7	+	1.27610e7i	−1.42585	+	0.871298i
$736$			9.50655e6i			0.646887i
$737$	−1.90166e7	+	3.90854e6i	−1.28963	+	0.265061i
$738$	−1.82578e7	+	1.82578e7i	−1.23398	+	1.23398i
$739$	1.53613e7			1.03471			0.517354	−	0.855771i	$-0.326917\pi$
$739$	1.53613e7			1.03471			0.517354	+	0.855771i	$0.326917\pi$
$740$	−5.03134e6	−	8.23363e6i	−0.337757	−	0.552728i
$741$	−864314.			−0.0578264
$742$	464554.	+	464554.i	0.0309761	+	0.0309761i
$743$	−1.36829e7	−	1.36829e7i	−0.909295	−	0.909295i	0.0869200	−	0.996215i	$-0.472298\pi$
$743$	−1.36829e7	−	1.36829e7i	−0.909295	−	0.909295i	−0.996215	+	0.0869200i	$0.972298\pi$
$744$	2.10967e7			1.39728
$745$	−1.57846e6	+	6.53851e6i	−0.104194	+	0.431607i
$746$	−3.32425e7			−2.18699
$747$	6.17714e6	−	6.17714e6i	0.405029	−	0.405029i
$748$	−4.09538e7	+	8.41738e6i	−2.67634	+	0.550076i
$749$			1.07714e6i			0.0701562i
$750$	3.37878e7	+	2.90787e7i	2.19335	+	1.88765i
$751$	1.86724e7			1.20809			0.604045	−	0.796950i	$-0.293555\pi$
$751$	1.86724e7			1.20809			0.604045	+	0.796950i	$0.293555\pi$
$752$	3.13047e6	+	3.13047e6i	0.201867	+	0.201867i
$753$	6.63368e6	−	6.63368e6i	0.426350	−	0.426350i
$754$	−2.23890e6			−0.143419
$755$	−1.48014e7	−	3.57318e6i	−0.945005	−	0.228133i
$756$			9.56735e6i			0.608818i
$757$	4.60837e6	+	4.60837e6i	0.292286	+	0.292286i	0.837983	−	0.545697i	$-0.183735\pi$
$757$	4.60837e6	+	4.60837e6i	0.292286	+	0.292286i	−0.545697	+	0.837983i	$0.683735\pi$
$758$	−2.54592e7	−	2.54592e7i	−1.60943	−	1.60943i
$759$	−2.25375e7	−	1.48526e7i	−1.42004	−	0.935833i
$760$	1.33506e7	−	8.15817e6i	0.838429	−	0.512341i
$761$			6.73616e6i			0.421649i	0.977524	+	0.210824i	$0.0676148\pi$
$761$			6.73616e6i			0.421649i	−0.977524	+	0.210824i	$0.932385\pi$
$762$	−2.82067e7	−	2.82067e7i	−1.75981	−	1.75981i
$763$	3.64429e6	−	3.64429e6i	0.226622	−	0.226622i
$764$		−	1.36768e6i		−	0.0847716i
$765$	4.28058e7	−	2.61575e7i	2.64453	−	1.61600i
$766$		−	3.47696e7i		−	2.14106i
$767$	−756711.	+	756711.i	−0.0464453	+	0.0464453i
$768$	−3.07369e7	+	3.07369e7i	−1.88043	+	1.88043i
$769$	2.17441e7			1.32594			0.662972	−	0.748644i	$-0.269295\pi$
$769$	2.17441e7			1.32594			0.662972	+	0.748644i	$0.269295\pi$
$770$	−3.89283e6	+	3.63552e6i	−0.236613	+	0.220973i
$771$	2.39488e7			1.45093
$772$	−2.03410e7	+	2.03410e7i	−1.22837	+	1.22837i
$773$	1.13205e7	−	1.13205e7i	0.681423	−	0.681423i	−0.278898	−	0.960321i	$-0.589969\pi$
$773$	1.13205e7	−	1.13205e7i	0.681423	−	0.681423i	0.960321	+	0.278898i	$0.0899690\pi$
$774$		−	8.51441e7i		−	5.10860i
$775$	−9.24718e6	−	4.74101e6i	−0.553038	−	0.283541i
$776$			1.80260e7i			1.07460i
$777$	−1.46349e6	+	1.46349e6i	−0.0869637	+	0.0869637i
$778$	−7.00548e6	−	7.00548e6i	−0.414944	−	0.414944i
$779$		−	6.67866e6i		−	0.394317i
$780$	2.23632e6	+	539867.i	0.131612	+	0.0317724i
$781$	−6.91733e6	+	1.04964e7i	−0.405799	+	0.615764i
$782$	3.03443e7	+	3.03443e7i	1.77444	+	1.77444i
$783$	−4.19621e7	−	4.19621e7i	−2.44598	−	2.44598i
$784$		−	6.30232e6i		−	0.366193i
$785$	4.36157e6	−	2.66523e6i	0.252620	−	0.154369i
$786$	−1.62472e7			−0.938039
$787$	813933.	−	813933.i	0.0468438	−	0.0468438i	−0.683297	−	0.730141i	$-0.739455\pi$
$787$	813933.	−	813933.i	0.0468438	−	0.0468438i	0.730141	+	0.683297i	$0.239455\pi$
$788$	3.27085e7	+	3.27085e7i	1.87649	+	1.87649i
$789$	−9.18744e6			−0.525415
$790$	1.54709e7	+	2.53177e7i	0.881960	+	1.44330i
$791$			168853.i			0.00959550i
$792$	−9.27410e6	−	4.51221e7i	−0.525362	−	2.55609i
$793$	−386135.	+	386135.i	−0.0218050	+	0.0218050i
$794$	−4.36372e7			−2.45643
$795$	4.07035e6	+	982619.i	0.228409	+	0.0551400i
$796$	1.83307e7			1.02541
$797$	7.08615e6	+	7.08615e6i	0.395152	+	0.395152i	0.876519	−	0.481367i	$-0.159860\pi$
$797$	7.08615e6	+	7.08615e6i	0.395152	+	0.395152i	−0.481367	+	0.876519i	$0.659860\pi$
$798$	−5.42734e6	−	5.42734e6i	−0.301703	−	0.301703i
$799$	−2.08152e7			−1.15349
$800$	1.13808e7	−	3.66624e6i	0.628708	−	0.202533i
$801$	4.54297e7			2.50184
$802$	2.44703e7	−	2.44703e7i	1.34339	−	1.34339i
$803$	1.64006e7	−	3.37087e6i	0.897574	−	0.184481i
$804$			7.44635e7i			4.06259i
$805$	3.40061e6	+	820939.i	0.184956	+	0.0446500i
$806$	−838098.			−0.0454420
$807$	1.90932e7	+	1.90932e7i	1.03203	+	1.03203i
$808$	5.47306e6	−	5.47306e6i	0.294918	−	0.294918i
$809$	1.72570e7			0.927032			0.463516	−	0.886089i	$-0.346588\pi$
$809$	1.72570e7			0.927032			0.463516	+	0.886089i	$0.346588\pi$
$810$	1.69862e7	+	2.77974e7i	0.909672	+	1.48865i
$811$		−	2.83384e7i		−	1.51295i	−0.654025	−	0.756473i	$-0.726921\pi$
$811$		−	2.83384e7i		−	1.51295i	0.654025	−	0.756473i	$-0.273079\pi$
$812$	−8.99612e6	−	8.99612e6i	−0.478812	−	0.478812i
$813$	3.64346e7	+	3.64346e7i	1.93325	+	1.93325i
$814$	6.31918e6	−	9.58880e6i	0.334272	−	0.507228i
$815$	1.61884e7	+	2.64918e7i	0.853709	+	1.39707i
$816$			1.93278e7i			1.01615i
$817$	1.55727e7	+	1.55727e7i	0.816224	+	0.816224i
$818$	−2.06475e7	+	2.06475e7i	−1.07891	+	1.07891i
$819$		−	329819.i		−	0.0171817i
$820$	−4.17162e6	+	1.72803e7i	−0.216656	+	0.897463i
$821$			2.11808e7i			1.09669i	0.836252	+	0.548346i	$0.184742\pi$
$821$			2.11808e7i			1.09669i	−0.836252	+	0.548346i	$0.815258\pi$
$822$	−1.65780e7	+	1.65780e7i	−0.855763	+	0.855763i
$823$	−2.65918e7	+	2.65918e7i	−1.36851	+	1.36851i	−0.505939	+	0.862569i	$0.668854\pi$
$823$	−2.65918e7	+	2.65918e7i	−1.36851	+	1.36851i	−0.862569	+	0.505939i	$0.831146\pi$
$824$	−1.22108e7			−0.626506
$825$	−9.08922e6	+	3.27090e7i	−0.464935	+	1.67314i
$826$	−9.50333e6			−0.484647
$827$	1.51818e7	−	1.51818e7i	0.771896	−	0.771896i	−0.206542	−	0.978438i	$-0.566221\pi$
$827$	1.51818e7	−	1.51818e7i	0.771896	−	0.771896i	0.978438	+	0.206542i	$0.0662210\pi$
$828$	−4.89289e7	+	4.89289e7i	−2.48022	+	2.48022i
$829$		−	8.94328e6i		−	0.451971i	−0.974131	−	0.225985i	$-0.927440\pi$
$829$		−	8.94328e6i		−	0.451971i	0.974131	−	0.225985i	$-0.0725602\pi$
$830$	2.20565e6	−	9.13658e6i	0.111133	−	0.460350i
$831$		−	1.15811e7i		−	0.581764i
$832$	917632.	−	917632.i	0.0459579	−	0.0459579i
$833$	2.09528e7	+	2.09528e7i	1.04624	+	1.04624i
$834$		−	8.30097e6i		−	0.413251i
$835$	1.15783e7	+	1.89475e7i	0.574685	+	0.940452i
$836$	2.27544e7	+	1.49956e7i	1.12603	+	0.742073i
$837$	−1.57079e7	−	1.57079e7i	−0.775006	−	0.775006i
$838$	−8.01473e6	−	8.01473e6i	−0.394256	−	0.394256i
$839$		−	2.79077e6i		−	0.136873i	−0.997655	−	0.0684367i	$-0.978199\pi$
$839$		−	2.79077e6i		−	0.136873i	0.997655	−	0.0684367i	$-0.0218011\pi$
$840$	4.65768e6	+	7.62214e6i	0.227757	+	0.372716i
$841$	5.84024e7			2.84735
$842$	2.45601e7	−	2.45601e7i	1.19385	−	1.19385i
$843$	−2.17277e7	−	2.17277e7i	−1.05304	−	1.05304i
$844$	1.71952e7			0.830906
$845$	2.01375e7	+	4.86137e6i	0.970204	+	0.234216i
$846$		−	5.24521e7i		−	2.51963i
$847$	−3.76704e6	−	1.50450e6i	−0.180423	−	0.0720584i
$848$	−762473.	+	762473.i	−0.0364112	+	0.0364112i
$849$	−5.24088e7			−2.49537
$850$	2.46245e7	−	4.80294e7i	1.16902	−	2.28013i
$851$	−7.54229e6			−0.357009
$852$	3.40937e7	+	3.40937e7i	1.60907	+	1.60907i
$853$	−2.43113e7	−	2.43113e7i	−1.14402	−	1.14402i	−0.987707	−	0.156316i	$-0.950038\pi$
$853$	−2.43113e7	−	2.43113e7i	−1.14402	−	1.14402i	−0.156316	−	0.987707i	$-0.549962\pi$
$854$	−4.84936e6			−0.227531
$855$	−3.17841e7	−	7.67297e6i	−1.48694	−	0.358962i
$856$	−1.00228e7			−0.467523
$857$	−2.42205e7	+	2.42205e7i	−1.12650	+	1.12650i	−0.135759	+	0.990742i	$0.543347\pi$
$857$	−2.42205e7	+	2.42205e7i	−1.12650	+	1.12650i	−0.990742	+	0.135759i	$0.956653\pi$
$858$	551219.	+	2.68190e6i	0.0255627	+	0.124372i
$859$		−	2.50139e7i		−	1.15664i	−0.815809	−	0.578321i	$-0.803708\pi$
$859$		−	2.50139e7i		−	1.15664i	0.815809	−	0.578321i	$-0.196292\pi$
$860$	−3.05657e7	−	5.00198e7i	−1.40925	−	2.30619i
$861$	3.81299e6			0.175290
$862$	817267.	+	817267.i	0.0374624	+	0.0374624i
$863$	−7.67946e6	+	7.67946e6i	−0.350997	+	0.350997i	−0.860481	−	0.509483i	$-0.829837\pi$
$863$	−7.67946e6	+	7.67946e6i	−0.350997	+	0.350997i	0.509483	+	0.860481i	$0.329837\pi$
$864$	2.55600e7			1.16487
$865$	−1.78610e7	+	1.09143e7i	−0.811642	+	0.495972i
$866$			9.74818e6i			0.441702i
$867$	−3.70797e7	−	3.70797e7i	−1.67529	−	1.67529i
$868$	−3.36757e6	−	3.36757e6i	−0.151711	−	0.151711i
$869$	−1.24337e7	+	1.88670e7i	−0.558534	+	0.847526i
$870$	−1.23181e8	−	2.97371e7i	−5.51756	−	1.33199i
$871$		−	1.29341e6i		−	0.0577684i
$872$	3.39102e7	+	3.39102e7i	1.51022	+	1.51022i
$873$	2.66375e7	−	2.66375e7i	1.18293	−	1.18293i
$874$		−	2.79705e7i		−	1.23857i
$875$	−328668.	−	4.38767e6i	−0.0145123	−	0.193737i
$876$		−	6.42199e7i		−	2.82755i
$877$	3.48820e6	−	3.48820e6i	0.153145	−	0.153145i	−0.626376	−	0.779521i	$-0.715463\pi$
$877$	3.48820e6	−	3.48820e6i	0.153145	−	0.153145i	0.779521	+	0.626376i	$0.215463\pi$
$878$	1.78188e7	−	1.78188e7i	0.780085	−	0.780085i
$879$	1.54689e7			0.675283
$880$	−5.96698e6	−	6.38932e6i	−0.259745	−	0.278130i
$881$	−1.79073e7			−0.777301			−0.388651	−	0.921385i	$-0.627059\pi$
$881$	−1.79073e7			−0.777301			−0.388651	+	0.921385i	$0.627059\pi$
$882$	−5.27988e7	+	5.27988e7i	−2.28535	+	2.28535i
$883$	−2.67403e6	+	2.67403e6i	−0.115415	+	0.115415i	−0.762456	−	0.647040i	$-0.776007\pi$
$883$	−2.67403e6	+	2.67403e6i	−0.115415	+	0.115415i	0.647040	+	0.762456i	$0.276007\pi$
$884$		−	2.78547e6i		−	0.119886i
$885$	−5.16840e7	+	3.15827e7i	−2.21819	+	1.35547i
$886$			1.36504e7i			0.584200i
$887$	8.30487e6	−	8.30487e6i	0.354425	−	0.354425i	−0.507328	−	0.861753i	$-0.669367\pi$
$887$	8.30487e6	−	8.30487e6i	0.354425	−	0.354425i	0.861753	+	0.507328i	$0.169367\pi$
$888$	−1.36178e7	−	1.36178e7i	−0.579530	−	0.579530i
$889$			3.93729e6i			0.167087i
$890$	4.17082e7	−	2.54867e7i	1.76501	−	1.07855i
$891$	−1.36515e7	+	2.07149e7i	−0.576084	+	0.874156i
$892$	−1.98814e7	−	1.98814e7i	−0.836632	−	0.836632i
$893$	9.59341e6	+	9.59341e6i	0.402573	+	0.402573i
$894$			3.07042e7i			1.28486i
$895$	891827.	+	215295.i	0.0372154	+	0.00898415i
$896$	8.44048e6			0.351234
$897$	1.27154e6	−	1.27154e6i	0.0527655	−	0.0527655i
$898$	−4.66377e7	−	4.66377e7i	−1.92995	−	1.92995i
$899$	2.95401e7			1.21903
$900$	7.74453e7	+	3.97060e7i	3.18705	+	1.63399i
$901$		−	5.06986e6i		−	0.208058i
$902$	−2.07233e7	+	4.25934e6i	−0.848093	+	0.174311i
$903$	−8.89081e6	+	8.89081e6i	−0.362846	+	0.362846i
$904$	−1.57118e6			−0.0639447
$905$	−2.42202e6	+	1.00329e7i	−0.0983008	+	0.407196i
$906$	−6.95058e7			−2.81320
$907$	3.78150e6	+	3.78150e6i	0.152632	+	0.152632i	0.779293	−	0.626660i	$-0.215579\pi$
$907$	3.78150e6	+	3.78150e6i	0.152632	+	0.152632i	−0.626660	+	0.779293i	$0.715579\pi$
$908$	3.64104e7	+	3.64104e7i	1.46559	+	1.46559i
$909$	−1.61754e7			−0.649300
$910$	−185033.	−	302801.i	−0.00740707	−	0.0121214i
$911$	−4.47238e7			−1.78543			−0.892714	−	0.450623i	$-0.851202\pi$
$911$	−4.47238e7			−1.78543			−0.892714	+	0.450623i	$0.851202\pi$
$912$	8.90791e6	−	8.90791e6i	0.354641	−	0.354641i
$913$	7.01129e6	−	1.44105e6i	0.278369	−	0.0572142i
$914$		−	3.94268e7i		−	1.56108i
$915$	−2.63733e7	+	1.61160e7i	−1.04139	+	0.636363i
$916$	−4.68495e7			−1.84487
$917$	1.13394e6	+	1.13394e6i	0.0445316	+	0.0445316i
$918$	8.15861e7	−	8.15861e7i	3.19528	−	3.19528i
$919$	2.91320e7			1.13784			0.568921	−	0.822392i	$-0.307361\pi$
$919$	2.91320e7			1.13784			0.568921	+	0.822392i	$0.307361\pi$
$920$	−7.63885e6	+	3.16428e7i	−0.297549	+	1.23255i
$921$			6.48714e7i			2.52002i
$922$	5.69562e7	+	5.69562e7i	2.20655	+	2.20655i
$923$	−592197.	−	592197.i	−0.0228803	−	0.0228803i
$924$	−8.56129e6	+	1.29910e7i	−0.329883	+	0.500568i
$925$	2.90872e6	+	9.02932e6i	0.111776	+	0.346977i
$926$			1.98382e7i			0.760282i
$927$	1.80442e7	+	1.80442e7i	0.689666	+	0.689666i
$928$	−2.40339e7	+	2.40339e7i	−0.916126	+	0.916126i
$929$			1.95898e7i			0.744715i	0.928089	+	0.372358i	$0.121451\pi$
$929$			1.95898e7i			0.744715i	−0.928089	+	0.372358i	$0.878549\pi$
$930$	−4.61112e7	−	1.11317e7i	−1.74823	−	0.422039i
$931$		−	1.93137e7i		−	0.730281i
$932$	−2.36223e6	+	2.36223e6i	−0.0890805	+	0.0890805i
$933$	3.66644e7	−	3.66644e7i	1.37892	−	1.37892i
$934$	−1.49502e7			−0.560763
$935$	4.10799e7	+	1.40410e6i	1.53674	+	0.0525254i
$936$	3.06897e6			0.114499
$937$	6.21218e6	−	6.21218e6i	0.231150	−	0.231150i	−0.582022	−	0.813173i	$-0.697738\pi$
$937$	6.21218e6	−	6.21218e6i	0.231150	−	0.231150i	0.813173	+	0.582022i	$0.197738\pi$
$938$	8.12179e6	−	8.12179e6i	0.301401	−	0.301401i
$939$			3.93302e7i			1.45567i
$940$	−1.88297e7	−	3.08142e7i	−0.695062	−	1.13745i
$941$			2.33085e7i			0.858105i	0.903279	+	0.429053i	$0.141153\pi$
$941$			2.33085e7i			0.858105i	−0.903279	+	0.429053i	$0.858847\pi$
$942$	1.64986e7	−	1.64986e7i	0.605787	−	0.605787i
$943$	9.82536e6	+	9.82536e6i	0.359807	+	0.359807i
$944$		−	1.55978e7i		−	0.569684i
$945$	2.20724e6	−	9.14315e6i	0.0804026	−	0.333055i
$946$	3.83894e7	−	5.82525e7i	1.39471	−	2.11635i
$947$	−2.19838e7	−	2.19838e7i	−0.796576	−	0.796576i	0.185978	−	0.982554i	$-0.440455\pi$
$947$	−2.19838e7	−	2.19838e7i	−0.796576	−	0.796576i	−0.982554	+	0.185978i	$0.940455\pi$
$948$	6.12821e7	+	6.12821e7i	2.21469	+	2.21469i
$949$			1.11548e6i			0.0402066i
$950$	−3.34851e7	+	1.07869e7i	−1.20377	+	0.387783i
$951$	2.26066e7			0.810557
$952$	7.64762e6	−	7.64762e6i	0.273485	−	0.273485i
$953$	−4.52946e6	−	4.52946e6i	−0.161553	−	0.161553i	0.621702	−	0.783254i	$-0.286442\pi$
$953$	−4.52946e6	−	4.52946e6i	−0.161553	−	0.161553i	−0.783254	+	0.621702i	$0.786442\pi$
$954$	1.27755e7			0.454472
$955$	−315530.	+	1.30704e6i	−0.0111952	+	0.0463745i
$956$		−	1.52420e7i		−	0.539383i
$957$	−1.94286e7	−	9.45278e7i	−0.685744	−	3.33641i
$958$	3.42290e7	−	3.42290e7i	1.20498	−	1.20498i
$959$	2.31408e6			0.0812514
$960$	6.26750e7	−	3.82990e7i	2.19491	−	1.34125i
$961$	−1.75712e7			−0.613753
$962$	540989.	+	540989.i	0.0188474	+	0.0188474i
$963$	1.48109e7	+	1.48109e7i	0.514656	+	0.514656i
$964$	2.91787e7			1.01129
$965$	2.41319e7	−	1.47464e7i	0.834207	−	0.509761i
$966$	1.59690e7			0.550597
$967$	−2.70324e7	+	2.70324e7i	−0.929647	+	0.929647i	−0.997683	−	0.0680357i	$-0.978327\pi$
$967$	−2.70324e7	+	2.70324e7i	−0.929647	+	0.929647i	0.0680357	+	0.997683i	$0.478327\pi$
$968$	1.39994e7	−	3.50524e7i	0.480200	−	1.20234i
$969$			5.92308e7i			2.02646i
$970$	9.51140e6	−	3.93995e7i	0.324575	−	1.34450i
$971$	6.30631e6			0.214648			0.107324	−	0.994224i	$-0.465772\pi$
$971$	6.30631e6			0.214648			0.107324	+	0.994224i	$0.465772\pi$
$972$	2.01512e6	+	2.01512e6i	0.0684126	+	0.0684126i
$973$	−579353.	+	579353.i	−0.0196183	+	0.0196183i
$974$	6.55869e6			0.221523
$975$	−2.01261e6	−	1.03186e6i	−0.0678029	−	0.0347624i
$976$		−	7.95928e6i		−	0.267454i
$977$	−2.75309e7	−	2.75309e7i	−0.922750	−	0.922750i	0.0744730	−	0.997223i	$-0.476273\pi$
$977$	−2.75309e7	−	2.75309e7i	−0.922750	−	0.922750i	−0.997223	+	0.0744730i	$0.976273\pi$
$978$	1.00211e8	+	1.00211e8i	3.35018	+	3.35018i
$979$	3.10814e7	+	2.04831e7i	1.03644	+	0.683030i
$980$	−1.20637e7	+	4.99720e7i	−0.401250	+	1.66212i
$981$		−	1.00220e8i		−	3.32493i
$982$	−2.81585e7	−	2.81585e7i	−0.931816	−	0.931816i
$983$	2.23452e7	−	2.23452e7i	0.737565	−	0.737565i	−0.234542	−	0.972106i	$-0.575359\pi$
$983$	2.23452e7	−	2.23452e7i	0.737565	−	0.737565i	0.972106	+	0.234542i	$0.0753589\pi$
$984$			3.54800e7i			1.16814i
$985$	−2.37123e7	−	3.88043e7i	−0.778722	−	1.27435i
$986$			1.53430e8i			5.02594i
$987$	−5.47709e6	+	5.47709e6i	−0.178960	+	0.178960i
$988$	−1.28378e6	+	1.28378e6i	−0.0418406	+	0.0418406i
$989$	−4.58199e7			−1.48958
$990$	−3.53819e6	+	1.03517e8i	−0.114734	+	3.35679i
$991$	2.14201e7			0.692848			0.346424	−	0.938078i	$-0.387396\pi$
$991$	2.14201e7			0.692848			0.346424	+	0.938078i	$0.387396\pi$
$992$	−8.99676e6	+	8.99676e6i	−0.290273	+	0.290273i
$993$	−6.32971e7	+	6.32971e7i	−2.03709	+	2.03709i
$994$		−	7.43725e6i		−	0.238752i
$995$	−1.75180e7	−	4.22899e6i	−0.560952	−	0.135419i
$996$		−	2.74542e7i		−	0.876921i
$997$	3.34063e7	−	3.34063e7i	1.06437	−	1.06437i	0.0665850	−	0.997781i	$-0.478790\pi$
$997$	3.34063e7	−	3.34063e7i	1.06437	−	1.06437i	0.997781	−	0.0665850i	$-0.0212104\pi$
$998$	−4.79689e7	−	4.79689e7i	−1.52452	−	1.52452i
$999$			2.02788e7i			0.642878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.4	✓	52
5.3	odd	4	inner	55.6.e.b.43.23	yes	52
11.10	odd	2	inner	55.6.e.b.32.23	yes	52
55.43	even	4	inner	55.6.e.b.43.4	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.4	✓	52	1.1	even	1	trivial
55.6.e.b.32.23	yes	52	11.10	odd	2	inner
55.6.e.b.43.4	yes	52	55.43	even	4	inner
55.6.e.b.43.23	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+(-6.66565 + 6.66565i) q^{2} +(19.1413 - 19.1413i) q^{3} -56.8618i q^{4} +(-13.1183 + 54.3407i) q^{5} +255.179i q^{6} +(17.8098 - 17.8098i) q^{7} +(165.720 + 165.720i) q^{8} -489.780i q^{9} +(-274.774 - 449.658i) q^{10} +(220.830 - 335.090i) q^{11} +(-1088.41 - 1088.41i) q^{12} +(18.9054 + 18.9054i) q^{13} +237.428i q^{14} +(789.050 + 1291.25i) q^{15} -389.691 q^{16} +(1295.57 - 1295.57i) q^{17} +(3264.70 + 3264.70i) q^{18} -1194.22 q^{19} +(3089.91 + 745.933i) q^{20} -681.806i q^{21} +(761.618 + 3705.57i) q^{22} +(1756.89 - 1756.89i) q^{23} +6344.22 q^{24} +(-2780.82 - 1425.72i) q^{25} -252.034 q^{26} +(-4723.70 - 4723.70i) q^{27} +(-1012.70 - 1012.70i) q^{28} +8883.33 q^{29} +(-13866.6 - 3347.52i) q^{30} +3325.35 q^{31} +(-2705.51 + 2705.51i) q^{32} +(-2187.09 - 10641.0i) q^{33} +17271.7i q^{34} +(734.161 + 1201.43i) q^{35} -27849.8 q^{36} +(-2146.50 - 2146.50i) q^{37} +(7960.25 - 7960.25i) q^{38} +723.748 q^{39} +(-11179.3 + 6831.39i) q^{40} +5592.49i q^{41} +(4544.68 + 4544.68i) q^{42} +(-13040.1 - 13040.1i) q^{43} +(-19053.8 - 12556.8i) q^{44} +(26615.0 + 6425.10i) q^{45} +23421.6i q^{46} +(-8033.21 - 8033.21i) q^{47} +(-7459.20 + 7459.20i) q^{48} +16172.6i q^{49} +(28039.3 - 9032.63i) q^{50} -49597.9i q^{51} +(1075.00 - 1075.00i) q^{52} +(1956.61 - 1956.61i) q^{53} +62973.0 q^{54} +(15312.1 + 16395.9i) q^{55} +5902.89 q^{56} +(-22858.9 + 22858.9i) q^{57} +(-59213.2 + 59213.2i) q^{58} +40026.2i q^{59} +(73423.1 - 44866.8i) q^{60} +20424.6i q^{61} +(-22165.6 + 22165.6i) q^{62} +(-8722.88 - 8722.88i) q^{63} -48538.1i q^{64} +(-1275.34 + 779.324i) q^{65} +(85507.8 + 56351.1i) q^{66} +(-34207.4 - 34207.4i) q^{67} +(-73668.6 - 73668.6i) q^{68} -67258.2i q^{69} +(-12902.0 - 3114.66i) q^{70} -31324.3 q^{71} +(81166.6 - 81166.6i) q^{72} +(29501.7 + 29501.7i) q^{73} +28615.6 q^{74} +(-80518.7 + 25938.4i) q^{75} +67905.5i q^{76} +(-2034.95 - 9900.81i) q^{77} +(-4824.25 + 4824.25i) q^{78} -56304.2 q^{79} +(5112.09 - 21176.1i) q^{80} -61819.0 q^{81} +(-37277.6 - 37277.6i) q^{82} +(12612.1 + 12612.1i) q^{83} -38768.7 q^{84} +(53406.5 + 87398.0i) q^{85} +173842. q^{86} +(170039. - 170039. i) q^{87} +(92127.3 - 18935.2i) q^{88} +92755.4i q^{89} +(-220234. + 134579. i) q^{90} +673.402 q^{91} +(-99899.7 - 99899.7i) q^{92} +(63651.5 - 63651.5i) q^{93} +107093. q^{94} +(15666.2 - 64894.7i) q^{95} +103574. i q^{96} +(54386.7 + 54386.7i) q^{97} +(-107801. - 107801. i) q^{98} +(-164120. - 108158. 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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