LMFDB - Embedded newform 55.6.e.b.32.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,6,Mod(32,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			32.8
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.43002 + 4.43002i) q^{2} +(16.3501 - 16.3501i) q^{3} -7.25019i q^{4} +(27.0484 - 48.9222i) q^{5} +144.862i q^{6} +(30.3495 - 30.3495i) q^{7} +(-109.642 - 109.642i) q^{8} -291.649i q^{9} +(96.9014 + 336.552i) q^{10} +(-376.818 + 138.055i) q^{11} +(-118.541 - 118.541i) q^{12} +(-654.367 - 654.367i) q^{13} +268.898i q^{14} +(-357.638 - 1242.12i) q^{15} +1203.44 q^{16} +(607.375 - 607.375i) q^{17} +(1292.01 + 1292.01i) q^{18} +2325.76 q^{19} +(-354.695 - 196.106i) q^{20} -992.433i q^{21} +(1057.73 - 2280.90i) q^{22} +(1241.10 - 1241.10i) q^{23} -3585.31 q^{24} +(-1661.77 - 2646.54i) q^{25} +5797.72 q^{26} +(-795.419 - 795.419i) q^{27} +(-220.040 - 220.040i) q^{28} -5394.40 q^{29} +(7086.98 + 3918.30i) q^{30} +588.113 q^{31} +(-1822.72 + 1822.72i) q^{32} +(-3903.79 + 8418.21i) q^{33} +5381.37i q^{34} +(-663.859 - 2305.67i) q^{35} -2114.51 q^{36} +(1220.18 + 1220.18i) q^{37} +(-10303.1 + 10303.1i) q^{38} -21397.9 q^{39} +(-8329.59 + 2398.29i) q^{40} -12220.9i q^{41} +(4396.50 + 4396.50i) q^{42} +(6029.47 + 6029.47i) q^{43} +(1000.93 + 2732.00i) q^{44} +(-14268.1 - 7888.65i) q^{45} +10996.2i q^{46} +(14862.7 + 14862.7i) q^{47} +(19676.3 - 19676.3i) q^{48} +14964.8i q^{49} +(19085.9 + 4362.56i) q^{50} -19861.2i q^{51} +(-4744.29 + 4744.29i) q^{52} +(11271.3 - 11271.3i) q^{53} +7047.44 q^{54} +(-3438.37 + 22168.9i) q^{55} -6655.17 q^{56} +(38026.3 - 38026.3i) q^{57} +(23897.3 - 23897.3i) q^{58} -15392.8i q^{59} +(-9005.64 + 2592.94i) q^{60} +38610.3i q^{61} +(-2605.35 + 2605.35i) q^{62} +(-8851.41 - 8851.41i) q^{63} +22360.7i q^{64} +(-49712.7 + 14313.5i) q^{65} +(-19999.0 - 54586.7i) q^{66} +(-1883.61 - 1883.61i) q^{67} +(-4403.59 - 4403.59i) q^{68} -40584.2i q^{69} +(13155.1 + 7273.27i) q^{70} -78215.6 q^{71} +(-31977.1 + 31977.1i) q^{72} +(54512.2 + 54512.2i) q^{73} -10810.9 q^{74} +(-70441.0 - 16101.1i) q^{75} -16862.2i q^{76} +(-7246.34 + 15626.1i) q^{77} +(94793.2 - 94793.2i) q^{78} +61884.5 q^{79} +(32551.2 - 58875.0i) q^{80} +44860.5 q^{81} +(54138.7 + 54138.7i) q^{82} +(144.379 + 144.379i) q^{83} -7195.33 q^{84} +(-13285.6 - 46142.7i) q^{85} -53421.4 q^{86} +(-88198.8 + 88198.8i) q^{87} +(56451.8 + 26178.5i) q^{88} -4731.93i q^{89} +(98155.0 - 28261.2i) q^{90} -39719.4 q^{91} +(-8998.22 - 8998.22i) q^{92} +(9615.69 - 9615.69i) q^{93} -131684. q^{94} +(62908.0 - 113781. i) q^{95} +59603.2i q^{96} +(-14811.0 - 14811.0i) q^{97} +(-66294.5 - 66294.5i) q^{98} +(40263.7 + 109899. 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 $

$2$	−4.43002	+	4.43002i	−0.783125	+	0.783125i	−0.980357	−	0.197232i	$-0.936805\pi$
$2$	−4.43002	+	4.43002i	−0.783125	+	0.783125i	0.197232	+	0.980357i	$0.436805\pi$
$3$	16.3501	−	16.3501i	1.04886	−	1.04886i	0.0501137	−	0.998744i	$-0.484042\pi$
$3$	16.3501	−	16.3501i	1.04886	−	1.04886i	0.998744	−	0.0501137i	$-0.0159584\pi$
$4$		−	7.25019i		−	0.226568i
$5$	27.0484	−	48.9222i	0.483857	−	0.875147i
$5$	27.0484	−	48.9222i	0.483857	−	0.875147i
$6$			144.862i			1.64277i
$7$	30.3495	−	30.3495i	0.234103	−	0.234103i	−0.580300	−	0.814403i	$-0.697065\pi$
$7$	30.3495	−	30.3495i	0.234103	−	0.234103i	0.814403	+	0.580300i	$0.197065\pi$
$8$	−109.642	−	109.642i	−0.605693	−	0.605693i
$9$		−	291.649i		−	1.20020i
$10$	96.9014	+	336.552i	0.306429	+	1.06427i
$11$	−376.818	+	138.055i	−0.938966	+	0.344010i
$11$	−376.818	+	138.055i	−0.938966	+	0.344010i
$12$	−118.541	−	118.541i	−0.237638	−	0.237638i
$13$	−654.367	−	654.367i	−1.07390	−	1.07390i	−0.997042	−	0.0768562i	$-0.975512\pi$
$13$	−654.367	−	654.367i	−1.07390	−	1.07390i	−0.0768562	−	0.997042i	$-0.524488\pi$
$14$			268.898i			0.366663i
$15$	−357.638	−	1242.12i	−0.410408	−	1.42540i
$16$	1203.44			1.17524
$17$	607.375	−	607.375i	0.509724	−	0.509724i	−0.404718	−	0.914442i	$-0.632630\pi$
$17$	607.375	−	607.375i	0.509724	−	0.509724i	0.914442	+	0.404718i	$0.132630\pi$
$18$	1292.01	+	1292.01i	0.939908	+	0.939908i
$19$	2325.76			1.47802			0.739010	−	0.673695i	$-0.235294\pi$
$19$	2325.76			1.47802			0.739010	+	0.673695i	$0.235294\pi$
$20$	−354.695	−	196.106i	−0.198281	−	0.109627i
$21$		−	992.433i		−	0.491081i
$22$	1057.73	−	2280.90i	0.465925	−	1.00473i
$23$	1241.10	−	1241.10i	0.489201	−	0.489201i	−0.418853	−	0.908054i	$-0.637568\pi$
$23$	1241.10	−	1241.10i	0.489201	−	0.489201i	0.908054	+	0.418853i	$0.137568\pi$
$24$	−3585.31			−1.27057
$25$	−1661.77	−	2646.54i	−0.531765	−	0.846892i
$26$	5797.72			1.68199
$27$	−795.419	−	795.419i	−0.209984	−	0.209984i
$28$	−220.040	−	220.040i	−0.0530403	−	0.0530403i
$29$	−5394.40			−1.19110			−0.595550	−	0.803318i	$-0.703066\pi$
$29$	−5394.40			−1.19110			−0.595550	+	0.803318i	$0.703066\pi$
$30$	7086.98	+	3918.30i	1.43767	+	0.794866i
$31$	588.113			0.109915			0.0549575	−	0.998489i	$-0.482498\pi$
$31$	588.113			0.109915			0.0549575	+	0.998489i	$0.482498\pi$
$32$	−1822.72	+	1822.72i	−0.314662	+	0.314662i
$33$	−3903.79	+	8418.21i	−0.624024	+	1.34566i
$34$			5381.37i			0.798354i
$35$	−663.859	−	2305.67i	−0.0916021	−	0.318147i
$36$	−2114.51			−0.271928
$37$	1220.18	+	1220.18i	0.146528	+	0.146528i	0.776565	−	0.630037i	$-0.216960\pi$
$37$	1220.18	+	1220.18i	0.146528	+	0.146528i	−0.630037	+	0.776565i	$0.716960\pi$
$38$	−10303.1	+	10303.1i	−1.15747	+	1.15747i
$39$	−21397.9			−2.25273
$40$	−8329.59	+	2398.29i	−0.823140	+	0.237002i
$41$		−	12220.9i		−	1.13538i	−0.823242	−	0.567691i	$-0.807837\pi$
$41$		−	12220.9i		−	1.13538i	0.823242	−	0.567691i	$-0.192163\pi$
$42$	4396.50	+	4396.50i	0.384577	+	0.384577i
$43$	6029.47	+	6029.47i	0.497288	+	0.497288i	0.910593	−	0.413305i	$-0.135626\pi$
$43$	6029.47	+	6029.47i	0.497288	+	0.497288i	−0.413305	+	0.910593i	$0.635626\pi$
$44$	1000.93	+	2732.00i	0.0779417	+	0.212740i
$45$	−14268.1	−	7888.65i	−1.05035	−	0.580726i
$46$			10996.2i			0.766211i
$47$	14862.7	+	14862.7i	0.981415	+	0.981415i	0.999830	−	0.0184150i	$-0.00586202\pi$
$47$	14862.7	+	14862.7i	0.981415	+	0.981415i	−0.0184150	+	0.999830i	$0.505862\pi$
$48$	19676.3	−	19676.3i	1.23265	−	1.23265i
$49$			14964.8i			0.890392i
$50$	19085.9	+	4362.56i	1.07966	+	0.246784i
$51$		−	19861.2i		−	1.06925i
$52$	−4744.29	+	4744.29i	−0.243312	+	0.243312i
$53$	11271.3	−	11271.3i	0.551166	−	0.551166i	−0.375611	−	0.926777i	$-0.622567\pi$
$53$	11271.3	−	11271.3i	0.551166	−	0.551166i	0.926777	+	0.375611i	$0.122567\pi$
$54$	7047.44			0.328887
$55$	−3438.37	+	22168.9i	−0.153266	+	0.988185i
$56$	−6655.17			−0.283589
$57$	38026.3	−	38026.3i	1.55023	−	1.55023i
$58$	23897.3	−	23897.3i	0.932780	−	0.932780i
$59$		−	15392.8i		−	0.575690i	−0.957677	−	0.287845i	$-0.907061\pi$
$59$		−	15392.8i		−	0.575690i	0.957677	−	0.287845i	$-0.0929388\pi$
$60$	−9005.64	+	2592.94i	−0.322951	+	0.0929854i
$61$			38610.3i			1.32855i	0.747487	+	0.664277i	$0.231260\pi$
$61$			38610.3i			1.32855i	−0.747487	+	0.664277i	$0.768740\pi$
$62$	−2605.35	+	2605.35i	−0.0860771	+	0.0860771i
$63$	−8851.41	−	8851.41i	−0.280971	−	0.280971i
$64$			22360.7i			0.682395i
$65$	−49712.7	+	14313.5i	−1.45943	+	0.420206i
$66$	−19999.0	−	54586.7i	−0.565129	−	1.54251i
$67$	−1883.61	−	1883.61i	−0.0512630	−	0.0512630i	0.681011	−	0.732274i	$-0.261541\pi$
$67$	−1883.61	−	1883.61i	−0.0512630	−	0.0512630i	−0.732274	+	0.681011i	$0.761541\pi$
$68$	−4403.59	−	4403.59i	−0.115487	−	0.115487i
$69$		−	40584.2i		−	1.02620i
$70$	13155.1	+	7273.27i	0.320884	+	0.177413i
$71$	−78215.6			−1.84140			−0.920699	−	0.390273i	$-0.872381\pi$
$71$	−78215.6			−1.84140			−0.920699	+	0.390273i	$0.872381\pi$
$72$	−31977.1	+	31977.1i	−0.726955	+	0.726955i
$73$	54512.2	+	54512.2i	1.19726	+	1.19726i	0.974985	+	0.222270i	$0.0713466\pi$
$73$	54512.2	+	54512.2i	1.19726	+	1.19726i	0.222270	+	0.974985i	$0.428653\pi$
$74$	−10810.9			−0.229499
$75$	−70441.0	−	16101.1i	−1.44601	−	0.330523i
$76$		−	16862.2i		−	0.334873i
$77$	−7246.34	+	15626.1i	−0.139281	+	0.300348i
$78$	94793.2	−	94793.2i	1.76417	−	1.76417i
$79$	61884.5			1.11561			0.557807	−	0.829970i	$-0.311643\pi$
$79$	61884.5			1.11561			0.557807	+	0.829970i	$0.311643\pi$
$80$	32551.2	−	58875.0i	0.568646	−	1.02850i
$81$	44860.5			0.759716
$82$	54138.7	+	54138.7i	0.889146	+	0.889146i
$83$	144.379	+	144.379i	0.00230043	+	0.00230043i	0.708256	−	0.705956i	$-0.249482\pi$
$83$	144.379	+	144.379i	0.00230043	+	0.00230043i	−0.705956	+	0.708256i	$0.749482\pi$
$84$	−7195.33			−0.111263
$85$	−13285.6	−	46142.7i	−0.199450	−	0.692716i
$86$	−53421.4			−0.778877
$87$	−88198.8	+	88198.8i	−1.24929	+	1.24929i
$88$	56451.8	+	26178.5i	0.777090	+	0.360361i
$89$		−	4731.93i		−	0.0633233i	−0.999499	−	0.0316617i	$-0.989920\pi$
$89$		−	4731.93i		−	0.0633233i	0.999499	−	0.0316617i	$-0.0100799\pi$
$90$	98155.0	−	28261.2i	1.27734	−	0.367777i
$91$	−39719.4			−0.502805
$92$	−8998.22	−	8998.22i	−0.110838	−	0.110838i
$93$	9615.69	−	9615.69i	0.115285	−	0.115285i
$94$	−131684.			−1.53714
$95$	62908.0	−	113781.i	0.715150	−	1.29348i
$96$			59603.2i			0.660072i
$97$	−14811.0	−	14811.0i	−0.159829	−	0.159829i	0.622662	−	0.782491i	$-0.286051\pi$
$97$	−14811.0	−	14811.0i	−0.159829	−	0.159829i	−0.782491	+	0.622662i	$0.786051\pi$
$98$	−66294.5	−	66294.5i	−0.697288	−	0.697288i
$99$	40263.7	+	109899.i	0.412881	+	1.12695i
$100$	−19187.9	+	12048.1i	−0.191879	+	0.120481i
$101$		−	32088.4i		−	0.313001i	−0.987678	−	0.156500i	$-0.949979\pi$
$101$		−	32088.4i		−	0.313001i	0.987678	−	0.156500i	$-0.0500212\pi$
$102$	87985.8	+	87985.8i	0.837359	+	0.837359i
$103$	−51797.9	+	51797.9i	−0.481082	+	0.481082i	−0.905477	−	0.424395i	$-0.860487\pi$
$103$	−51797.9	+	51797.9i	−0.481082	+	0.481082i	0.424395	+	0.905477i	$0.360487\pi$
$104$			143493.i			1.30091i
$105$	−48552.0	−	26843.7i	−0.429768	−	0.237613i
$106$			99863.8i			0.863263i
$107$	107076.	−	107076.i	0.904134	−	0.904134i	−0.0916569	−	0.995791i	$-0.529216\pi$
$107$	107076.	−	107076.i	0.904134	−	0.904134i	0.995791	+	0.0916569i	$0.0292163\pi$
$108$	−5766.94	+	5766.94i	−0.0475758	+	0.0475758i
$109$	138211.			1.11423			0.557117	−	0.830434i	$-0.311908\pi$
$109$	138211.			1.11423			0.557117	+	0.830434i	$0.311908\pi$
$110$	−82976.8	−	113441.i	−0.653845	−	0.893899i
$111$	39900.1			0.307374
$112$	36523.8	−	36523.8i	0.275126	−	0.275126i
$113$	−23783.4	+	23783.4i	−0.175218	+	0.175218i	−0.789267	−	0.614050i	$-0.789539\pi$
$113$	−23783.4	+	23783.4i	−0.175218	+	0.175218i	0.614050	+	0.789267i	$0.289539\pi$
$114$			336914.i			2.42805i
$115$	−27147.6	−	94287.2i	−0.191420	−	0.664826i
$116$			39110.4i			0.269866i
$117$	−190846.	+	190846.i	−1.28890	+	1.28890i
$118$	68190.6	+	68190.6i	0.450837	+	0.450837i
$119$		−	36867.1i		−	0.238655i
$120$	−96977.1	+	175402.i	−0.614775	+	1.11194i
$121$	122933.	−	104043.i	0.763315	−	0.646027i
$122$	−171045.	−	171045.i	−1.04042	−	1.04042i
$123$	−199812.	−	199812.i	−1.19085	−	1.19085i
$124$		−	4263.93i		−	0.0249033i
$125$	−174423.	+	9712.59i	−0.998453	+	0.0555981i
$126$	78423.9			0.440070
$127$	−126668.	+	126668.i	−0.696878	+	0.696878i	−0.963736	−	0.266858i	$-0.914015\pi$
$127$	−126668.	+	126668.i	−0.696878	+	0.696878i	0.266858	+	0.963736i	$0.414015\pi$
$128$	−157386.	−	157386.i	−0.849063	−	0.849063i
$129$	197164.			1.04317
$130$	156819.	−	283637.i	0.813844	−	1.47199i
$131$			292887.i			1.49115i	0.666420	+	0.745577i	$0.267826\pi$
$131$			292887.i			1.49115i	−0.666420	+	0.745577i	$0.732174\pi$
$132$	61033.6	+	28303.2i	0.304884	+	0.141384i
$133$	70585.5	−	70585.5i	0.346008	−	0.346008i
$134$	16688.9			0.0802906
$135$	−60428.5	+	17398.8i	−0.285369	+	0.0821647i
$136$	−133188.			−0.617472
$137$	−6778.53	−	6778.53i	−0.0308556	−	0.0308556i	0.691511	−	0.722366i	$-0.256946\pi$
$137$	−6778.53	−	6778.53i	−0.0308556	−	0.0308556i	−0.722366	+	0.691511i	$0.756946\pi$
$138$	179789.	+	179789.i	0.803646	+	0.803646i
$139$	−269841.			−1.18460			−0.592299	−	0.805718i	$-0.701780\pi$
$139$	−269841.			−1.18460			−0.592299	+	0.805718i	$0.701780\pi$
$140$	−16716.6	+	4813.10i	−0.0720820	+	0.0207542i
$141$	486012.			2.05873
$142$	346497.	−	346497.i	1.44204	−	1.44204i
$143$	336916.	+	156239.i	1.37779	+	0.638923i
$144$		−	350983.i		−	1.41052i
$145$	−145910.	+	263906.i	−0.576322	+	1.04239i
$146$	−482981.			−1.87520
$147$	244676.	+	244676.i	0.933894	+	0.933894i
$148$	8846.56	−	8846.56i	0.0331986	−	0.0331986i
$149$	−27764.6			−0.102453			−0.0512267	−	0.998687i	$-0.516313\pi$
$149$	−27764.6			−0.102453			−0.0512267	+	0.998687i	$0.516313\pi$
$150$	383383.	−	240727.i	1.39125	−	0.873569i
$151$		−	356781.i		−	1.27338i	−0.771119	−	0.636692i	$-0.780302\pi$
$151$		−	356781.i		−	1.27338i	0.771119	−	0.636692i	$-0.219698\pi$
$152$	−255001.	−	255001.i	−0.895226	−	0.895226i
$153$	−177141.	−	177141.i	−0.611772	−	0.611772i
$154$	−37122.7	−	101326.i	−0.126136	−	0.344284i
$155$	15907.5	−	28771.8i	0.0531831	−	0.0961917i
$156$			155139.i			0.510398i
$157$	−25768.4	−	25768.4i	−0.0834332	−	0.0834332i	0.664159	−	0.747592i	$-0.268790\pi$
$157$	−25768.4	−	25768.4i	−0.0834332	−	0.0834332i	−0.747592	+	0.664159i	$0.768790\pi$
$158$	−274150.	+	274150.i	−0.873665	+	0.873665i
$159$		−	368571.i		−	1.15619i
$160$	39869.8	+	138473.i	0.123124	+	0.427627i
$161$		−	75333.6i		−	0.229047i
$162$	−198733.	+	198733.i	−0.594952	+	0.594952i
$163$	140842.	−	140842.i	0.415207	−	0.415207i	−0.468341	−	0.883548i	$-0.655148\pi$
$163$	140842.	−	140842.i	0.415207	−	0.415207i	0.883548	+	0.468341i	$0.155148\pi$
$164$	−88603.5			−0.257242
$165$	306246.	+	418681.i	0.875710	+	1.19722i
$166$	−1279.21			−0.00360305
$167$	284367.	−	284367.i	0.789020	−	0.789020i	−0.192314	−	0.981334i	$-0.561599\pi$
$167$	284367.	−	284367.i	0.789020	−	0.789020i	0.981334	+	0.192314i	$0.0615991\pi$
$168$	−108813.	+	108813.i	−0.297444	+	0.297444i
$169$			485100.i			1.30652i
$170$	263269.	+	145558.i	0.698677	+	0.386289i
$171$		−	678305.i		−	1.77392i
$172$	43714.8	−	43714.8i	0.112670	−	0.112670i
$173$	39124.7	+	39124.7i	0.0993885	+	0.0993885i	0.755053	−	0.655664i	$-0.227611\pi$
$173$	39124.7	+	39124.7i	0.0993885	+	0.0993885i	−0.655664	+	0.755053i	$0.727611\pi$
$174$		−	781445.i		−	1.95671i
$175$	−130755.	−	29887.3i	−0.322747	−	0.0737721i
$176$	−453478.	+	166141.i	−1.10351	+	0.404292i
$177$	−251674.	−	251674.i	−0.603817	−	0.603817i
$178$	20962.6	+	20962.6i	0.0495901	+	0.0495901i
$179$		−	176953.i		−	0.412787i	−0.978469	−	0.206394i	$-0.933827\pi$
$179$		−	176953.i		−	0.412787i	0.978469	−	0.206394i	$-0.0661728\pi$
$180$	−57194.2	+	103447.i	−0.131574	+	0.237977i
$181$	474811.			1.07727			0.538635	−	0.842539i	$-0.318940\pi$
$181$	474811.			1.07727			0.538635	+	0.842539i	$0.318940\pi$
$182$	175958.	−	175958.i	0.393759	−	0.393759i
$183$	631281.	+	631281.i	1.39346	+	1.39346i
$184$	−272154.			−0.592612
$185$	92698.0	−	26690.0i	0.199132	−	0.0573349i
$186$			85195.4i			0.180565i
$187$	−145019.	+	312721.i	−0.303263	+	0.653963i
$188$	107757.	−	107757.i	0.222358	−	0.222358i
$189$	−48281.1			−0.0983157
$190$	225369.	+	782737.i	0.452908	+	1.57301i
$191$	134555.			0.266879			0.133440	−	0.991057i	$-0.457398\pi$
$191$	134555.			0.266879			0.133440	+	0.991057i	$0.457398\pi$
$192$	365599.	+	365599.i	0.715735	+	0.715735i
$193$	170722.	+	170722.i	0.329910	+	0.329910i	0.852552	−	0.522642i	$-0.175054\pi$
$193$	170722.	+	170722.i	0.329910	+	0.329910i	−0.522642	+	0.852552i	$0.675054\pi$
$194$	131226.			0.250332
$195$	−578779.	+	1.04683e6i	−1.09000	+	1.97147i
$196$	108498.			0.201735
$197$	−22640.8	+	22640.8i	−0.0415648	+	0.0415648i	−0.727584	−	0.686019i	$-0.759357\pi$
$197$	−22640.8	+	22640.8i	−0.0415648	+	0.0415648i	0.686019	+	0.727584i	$0.259357\pi$
$198$	−665223.	−	308485.i	−1.20588	−	0.559205i
$199$		−	1.05473e6i		−	1.88804i	−0.329892	−	0.944019i	$-0.607012\pi$
$199$		−	1.05473e6i		−	1.88804i	0.329892	−	0.944019i	$-0.392988\pi$
$200$	−107973.	+	472372.i	−0.190870	+	0.835043i
$201$	−61594.3			−0.107535
$202$	142153.	+	142153.i	0.245119	+	0.245119i
$203$	−163717.	+	163717.i	−0.278840	+	0.278840i
$204$	−143998.			−0.242259
$205$	−597871.	−	330555.i	−0.993626	−	0.549362i
$206$		−	458932.i		−	0.753494i
$207$	−361966.	−	361966.i	−0.587141	−	0.587141i
$208$	−787492.	−	787492.i	−1.26208	−	1.26208i
$209$	−876386.	+	321082.i	−1.38781	+	0.508453i
$210$	334005.	−	96168.1i	0.522642	−	0.150481i
$211$			446832.i			0.690937i	0.938430	+	0.345468i	$0.112280\pi$
$211$			446832.i			0.690937i	−0.938430	+	0.345468i	$0.887720\pi$
$212$	−81718.7	−	81718.7i	−0.124877	−	0.124877i
$213$	−1.27883e6	+	1.27883e6i	−1.93136	+	1.93136i
$214$			948698.i			1.41610i
$215$	458063.	−	131887.i	0.675816	−	0.194584i
$216$			174423.i			0.254372i
$217$	17848.9	−	17848.9i	0.0257314	−	0.0257314i
$218$	−612278.	+	612278.i	−0.872584	+	0.872584i
$219$	1.78256e6			2.51150
$220$	160729.	+	24928.9i	0.223892	+	0.0347253i
$221$	−794893.			−1.09478
$222$	−176758.	+	176758.i	−0.240712	+	0.240712i
$223$	701805.	−	701805.i	0.945049	−	0.945049i	−0.0535179	−	0.998567i	$-0.517043\pi$
$223$	701805.	−	701805.i	0.945049	−	0.945049i	0.998567	+	0.0535179i	$0.0170434\pi$
$224$			110637.i			0.147327i
$225$	−771861.	+	484653.i	−1.01644	+	0.638226i
$226$		−	210722.i		−	0.274435i
$227$	444421.	−	444421.i	0.572440	−	0.572440i	−0.360370	−	0.932810i	$-0.617349\pi$
$227$	444421.	−	444421.i	0.572440	−	0.572440i	0.932810	+	0.360370i	$0.117349\pi$
$228$	−275698.	−	275698.i	−0.351233	−	0.351233i
$229$			1.28545e6i			1.61982i	0.586557	+	0.809908i	$0.300483\pi$
$229$			1.28545e6i			1.61982i	−0.586557	+	0.809908i	$0.699517\pi$
$230$	537959.	+	297430.i	0.670547	+	0.370737i
$231$	137010.	+	373967.i	0.168936	+	0.461108i
$232$	591454.	+	591454.i	0.721441	+	0.721441i
$233$	−285742.	−	285742.i	−0.344813	−	0.344813i	0.513360	−	0.858173i	$-0.328401\pi$
$233$	−285742.	−	285742.i	−0.344813	−	0.344813i	−0.858173	+	0.513360i	$0.828401\pi$
$234$		−	1.69090e6i		−	2.01873i
$235$	1.12913e6	−	325103.i	1.33375	−	0.384018i
$236$	−111601.			−0.130433
$237$	1.01182e6	−	1.01182e6i	1.17012	−	1.17012i
$238$	163322.	+	163322.i	0.186897	+	0.186897i
$239$	−343357.			−0.388822			−0.194411	−	0.980920i	$-0.562280\pi$
$239$	−343357.			−0.388822			−0.194411	+	0.980920i	$0.562280\pi$
$240$	−430396.	−	1.49482e6i	−0.482325	−	1.67518i
$241$			293283.i			0.325270i	0.986686	+	0.162635i	$0.0519993\pi$
$241$			293283.i			0.325270i	−0.986686	+	0.162635i	$0.948001\pi$
$242$	−83680.3	+	1.00551e6i	−0.0918512	+	1.10369i
$243$	926758.	−	926758.i	1.00682	−	1.00682i
$244$	279932.			0.301008
$245$	732112.	+	404775.i	0.779224	+	0.430822i
$246$	1.77034e6			1.86517
$247$	−1.52190e6	−	1.52190e6i	−1.58724	−	1.58724i
$248$	−64482.0	−	64482.0i	−0.0665747	−	0.0665747i
$249$	4721.22			0.00482565
$250$	729669.	−	815723.i	0.738373	−	0.825454i
$251$	1.55758e6			1.56051			0.780253	−	0.625464i	$-0.215090\pi$
$251$	1.55758e6			1.56051			0.780253	+	0.625464i	$0.215090\pi$
$252$	−64174.4	+	64174.4i	−0.0636591	+	0.0636591i
$253$	−296329.	+	639009.i	−0.291053	+	0.627633i
$254$		−	1.12228e6i		−	1.09149i
$255$	−971656.	−	537215.i	−0.935755	−	0.517366i
$256$	678900.			0.647449
$257$	−919414.	−	919414.i	−0.868317	−	0.868317i	0.123969	−	0.992286i	$-0.460438\pi$
$257$	−919414.	−	919414.i	−0.868317	−	0.868317i	−0.992286	+	0.123969i	$0.960438\pi$
$258$	−873443.	+	873443.i	−0.816931	+	0.816931i
$259$	74063.9			0.0686052
$260$	103776.	+	360427.i	0.0952054	+	0.330661i
$261$			1.57327e6i			1.42956i
$262$	−1.29750e6	−	1.29750e6i	−1.16776	−	1.16776i
$263$	96932.5	+	96932.5i	0.0864132	+	0.0864132i	0.748992	−	0.662579i	$-0.230538\pi$
$263$	96932.5	+	96932.5i	0.0864132	+	0.0864132i	−0.662579	+	0.748992i	$0.730538\pi$
$264$	1.35101e6	−	494971.i	1.19302	−	0.437089i
$265$	−246545.	−	856284.i	−0.215666	−	0.749037i
$266$			625391.i			0.541935i
$267$	−77367.4	−	77367.4i	−0.0664171	−	0.0664171i
$268$	−13656.5	+	13656.5i	−0.0116146	+	0.0116146i
$269$			1.35369e6i			1.14062i	0.821431	+	0.570308i	$0.193176\pi$
$269$			1.35369e6i			1.14062i	−0.821431	+	0.570308i	$0.806824\pi$
$270$	190622.	−	344777.i	0.159134	−	0.287825i
$271$		−	1.49834e6i		−	1.23933i	−0.784866	−	0.619666i	$-0.787268\pi$
$271$		−	1.49834e6i		−	1.23933i	0.784866	−	0.619666i	$-0.212732\pi$
$272$	730940.	−	730940.i	0.599045	−	0.599045i
$273$	−649416.	+	649416.i	−0.527371	+	0.527371i
$274$	60058.1			0.0483276
$275$	991551.	+	767848.i	0.790648	+	0.612271i
$276$	−294243.			−0.232506
$277$	−1.34318e6	+	1.34318e6i	−1.05180	+	1.05180i	−0.0532211	+	0.998583i	$0.516949\pi$
$277$	−1.34318e6	+	1.34318e6i	−1.05180	+	1.05180i	−0.998583	+	0.0532211i	$0.983051\pi$
$278$	1.19540e6	−	1.19540e6i	0.927688	−	0.927688i
$279$		−	171523.i		−	0.131920i
$280$	−180012.	+	325586.i	−0.137216	+	0.248182i
$281$			845773.i			0.638981i	0.947589	+	0.319491i	$0.103512\pi$
$281$			845773.i			0.638981i	−0.947589	+	0.319491i	$0.896488\pi$
$282$	−2.15304e6	+	2.15304e6i	−1.61224	+	1.61224i
$283$	1.01642e6	+	1.01642e6i	0.754408	+	0.754408i	0.975299	−	0.220890i	$-0.0708963\pi$
$283$	1.01642e6	+	1.01642e6i	0.754408	+	0.754408i	−0.220890	+	0.975299i	$0.570896\pi$
$284$			567078.i			0.417203i
$285$	−831778.	−	2.88888e6i	−0.606590	−	2.10677i
$286$	−2.18469e6	+	800405.i	−1.57933	+	0.578622i
$287$	−370897.	−	370897.i	−0.265796	−	0.265796i
$288$	531595.	+	531595.i	0.377659	+	0.377659i
$289$			682048.i			0.480364i
$290$	−522725.	−	1.81549e6i	−0.364988	−	1.26765i
$291$	−484322.			−0.335276
$292$	395224.	−	395224.i	0.271260	−	0.271260i
$293$	−1.84059e6	−	1.84059e6i	−1.25253	−	1.25253i	−0.954582	−	0.297950i	$-0.903697\pi$
$293$	−1.84059e6	−	1.84059e6i	−1.25253	−	1.25253i	−0.297950	−	0.954582i	$-0.596303\pi$
$294$	−2.16784e6			−1.46271
$295$	−753052.	−	416352.i	−0.503813	−	0.278552i
$296$		−	267567.i		−	0.177502i
$297$	409540.	+	189917.i	0.269404	+	0.124931i
$298$	122998.	−	122998.i	0.0802338	−	0.0802338i
$299$	−1.62427e6			−1.05070
$300$	−116736.	+	510711.i	−0.0748861	+	0.327621i
$301$	365983.			0.232833
$302$	1.58055e6	+	1.58055e6i	0.997218	+	0.997218i
$303$	−524648.	−	524648.i	−0.328293	−	0.328293i
$304$	2.79891e6			1.73702
$305$	1.88890e6	+	1.04435e6i	1.16268	+	0.642830i
$306$	1.56947e6			0.958187
$307$	−886625.	+	886625.i	−0.536901	+	0.536901i	−0.922617	−	0.385717i	$-0.873954\pi$
$307$	−886625.	+	886625.i	−0.536901	+	0.536901i	0.385717	+	0.922617i	$0.373954\pi$
$308$	113293.	+	52537.3i	0.0680494	+	0.0315567i
$309$			1.69380e6i			1.00917i
$310$	56989.0	+	197930.i	0.0336811	+	0.116979i
$311$	−2.98006e6			−1.74712			−0.873562	−	0.486713i	$-0.838196\pi$
$311$	−2.98006e6			−1.74712			−0.873562	+	0.486713i	$0.838196\pi$
$312$	2.34611e6	+	2.34611e6i	1.36446	+	1.36446i
$313$	1.39523e6	−	1.39523e6i	0.804981	−	0.804981i	−0.178888	−	0.983869i	$-0.557250\pi$
$313$	1.39523e6	−	1.39523e6i	0.804981	−	0.804981i	0.983869	+	0.178888i	$0.0572500\pi$
$314$	228310.			0.130677
$315$	−672447.	+	193614.i	−0.381840	+	0.109941i
$316$		−	448675.i		−	0.252763i
$317$	148983.	+	148983.i	0.0832699	+	0.0832699i	0.747515	−	0.664245i	$-0.231247\pi$
$317$	148983.	+	148983.i	0.0832699	+	0.0832699i	−0.664245	+	0.747515i	$0.731247\pi$
$318$	1.63278e6	+	1.63278e6i	0.905440	+	0.905440i
$319$	2.03271e6	−	744724.i	1.11840	−	0.409750i
$320$	1.09394e6	+	604823.i	0.597196	+	0.330182i
$321$		−	3.50140e6i		−	1.89661i
$322$	333730.	+	333730.i	0.179372	+	0.179372i
$323$	1.41261e6	−	1.41261e6i	0.753381	−	0.753381i
$324$		−	325247.i		−	0.172128i
$325$	−644402.	+	2.81921e6i	−0.338414	+	1.48054i
$326$			1.24787e6i			0.650318i
$327$	2.25976e6	−	2.25976e6i	1.16867	−	1.16867i
$328$	−1.33992e6	+	1.33992e6i	−0.687693	+	0.687693i
$329$	902151.			0.459504
$330$	−3.21144e6	−	498091.i	−1.62336	−	0.251781i
$331$	−2.44804e6			−1.22814			−0.614072	−	0.789250i	$-0.710470\pi$
$331$	−2.44804e6			−1.22814			−0.614072	+	0.789250i	$0.710470\pi$
$332$	1046.78	−	1046.78i	0.000521206	−	0.000521206i
$333$	355865.	−	355865.i	0.175863	−	0.175863i
$334$			2.51950e6i			1.23580i
$335$	−143099.	+	41201.7i	−0.0696666	+	0.0200587i
$336$		−	1.19433e6i		−	0.577135i
$337$	1.81794e6	−	1.81794e6i	0.871977	−	0.871977i	−0.120711	−	0.992688i	$-0.538517\pi$
$337$	1.81794e6	−	1.81794e6i	0.871977	−	0.871977i	0.992688	+	0.120711i	$0.0385174\pi$
$338$	−2.14900e6	−	2.14900e6i	−1.02316	−	1.02316i
$339$			777721.i			0.367557i
$340$	−334543.	+	96323.1i	−0.156948	+	0.0451890i
$341$	−221612.	+	81192.0i	−0.103206	+	0.0378118i
$342$	3.00491e6	+	3.00491e6i	1.38920	+	1.38920i
$343$	964259.	+	964259.i	0.442546	+	0.442546i
$344$		−	1.32217e6i		−	0.602408i
$345$	−1.98547e6	−	1.09774e6i	−0.898080	−	0.496536i
$346$	−346647.			−0.155667
$347$	−1.70436e6	+	1.70436e6i	−0.759868	+	0.759868i	−0.976298	−	0.216430i	$-0.930559\pi$
$347$	−1.70436e6	+	1.70436e6i	−0.759868	+	0.759868i	0.216430	+	0.976298i	$0.430559\pi$
$348$	639458.	+	639458.i	0.283051	+	0.283051i
$349$	−4.38477e6			−1.92701			−0.963503	−	0.267696i	$-0.913738\pi$
$349$	−4.38477e6			−1.92701			−0.963503	+	0.267696i	$0.913738\pi$
$350$	711648.	−	446845.i	0.310524	−	0.194979i
$351$			1.04099e6i			0.451003i
$352$	435198.	−	938469.i	0.187210	−	0.403704i
$353$	1.23660e6	−	1.23660e6i	0.528191	−	0.528191i	−0.391842	−	0.920033i	$-0.628162\pi$
$353$	1.23660e6	−	1.23660e6i	0.528191	−	0.528191i	0.920033	+	0.391842i	$0.128162\pi$
$354$	2.22984e6			0.945727
$355$	−2.11561e6	+	3.82648e6i	−0.890973	+	1.61149i
$356$	−34307.4			−0.0143471
$357$	−602779.	−	602779.i	−0.250315	−	0.250315i
$358$	783908.	+	783908.i	0.323264	+	0.323264i
$359$	−955811.			−0.391413			−0.195707	−	0.980662i	$-0.562700\pi$
$359$	−955811.			−0.391413			−0.195707	+	0.980662i	$0.562700\pi$
$360$	699460.	+	2.42932e6i	0.284450	+	0.987934i
$361$	2.93304e6			1.18454
$362$	−2.10342e6	+	2.10342e6i	−0.843636	+	0.843636i
$363$	308842.	−	3.71107e6i	0.123018	−	1.47820i
$364$			287974.i			0.113920i
$365$	4.14133e6	−	1.19239e6i	1.62707	−	0.468474i
$366$	−5.59318e6			−2.18251
$367$	−2.62276e6	−	2.62276e6i	−1.01647	−	1.01647i	−0.999862	−	0.0166052i	$-0.994714\pi$
$367$	−2.62276e6	−	2.62276e6i	−1.01647	−	1.01647i	−0.0166052	−	0.999862i	$-0.505286\pi$
$368$	1.49359e6	−	1.49359e6i	0.574927	−	0.574927i
$369$	−3.56420e6			−1.36269
$370$	−292417.	+	528892.i	−0.111045	+	0.200846i
$371$		−	684154.i		−	0.258059i
$372$	−69715.6	−	69715.6i	−0.0261200	−	0.0261200i
$373$	1.05302e6	+	1.05302e6i	0.391890	+	0.391890i	0.875361	−	0.483471i	$-0.160624\pi$
$373$	1.05302e6	+	1.05302e6i	0.391890	+	0.391890i	−0.483471	+	0.875361i	$0.660624\pi$
$374$	−742925.	−	2.02780e6i	−0.274641	−	0.749628i
$375$	−2.69302e6	+	3.01062e6i	−0.988920	+	1.10555i
$376$		−	3.25916e6i		−	1.18887i
$377$	3.52992e6	+	3.52992e6i	1.27912	+	1.27912i
$378$	213886.	−	213886.i	0.0769934	−	0.0769934i
$379$			245756.i			0.0878832i	0.999034	+	0.0439416i	$0.0139916\pi$
$379$			245756.i			0.0878832i	−0.999034	+	0.0439416i	$0.986008\pi$
$380$	−824935.	−	456095.i	−0.293063	−	0.162030i
$381$			4.14205e6i			1.46185i
$382$	−596080.	+	596080.i	−0.209000	+	0.209000i
$383$	853507.	−	853507.i	0.297310	−	0.297310i	−0.542649	−	0.839960i	$-0.682579\pi$
$383$	853507.	−	853507.i	0.297310	−	0.297310i	0.839960	+	0.542649i	$0.182579\pi$
$384$	−5.14653e6			−1.78109
$385$	568463.	+	777169.i	0.195457	+	0.267217i
$386$	−1.51260e6			−0.516721
$387$	1.75849e6	−	1.75849e6i	0.596846	−	0.596846i
$388$	−107383.	+	107383.i	−0.0362122	+	0.0362122i
$389$			428449.i			0.143557i	0.997421	+	0.0717786i	$0.0228675\pi$
$389$			428449.i			0.143557i	−0.997421	+	0.0717786i	$0.977133\pi$
$390$	−2.07349e6	−	7.20150e6i	−0.690303	−	2.39751i
$391$		−	1.50763e6i		−	0.498715i
$392$	1.64078e6	−	1.64078e6i	0.539304	−	0.539304i
$393$	4.78873e6	+	4.78873e6i	1.56401	+	1.56401i
$394$		−	200598.i		−	0.0651008i
$395$	1.67388e6	−	3.02753e6i	0.539798	−	0.976327i
$396$	796787.	−	291919.i	0.255331	−	0.0935459i
$397$	−1.64075e6	−	1.64075e6i	−0.522476	−	0.522476i	0.395843	−	0.918318i	$-0.370453\pi$
$397$	−1.64075e6	−	1.64075e6i	−0.522476	−	0.522476i	−0.918318	+	0.395843i	$0.870453\pi$
$398$	4.67250e6	+	4.67250e6i	1.47857	+	1.47857i
$399$		−	2.30816e6i		−	0.725827i
$400$	−1.99984e6	−	3.18495e6i	−0.624949	−	0.995297i
$401$	4.14380e6			1.28688			0.643440	−	0.765497i	$-0.277507\pi$
$401$	4.14380e6			1.28688			0.643440	+	0.765497i	$0.277507\pi$
$402$	272864.	−	272864.i	0.0842134	−	0.0842134i
$403$	−384842.	−	384842.i	−0.118037	−	0.118037i
$404$	−232647.			−0.0709161
$405$	1.21341e6	−	2.19467e6i	0.367594	−	0.664863i
$406$		−	1.45054e6i		−	0.436733i
$407$	−628239.	−	291334.i	−0.187992	−	0.0871778i
$408$	−2.17763e6	+	2.17763e6i	−0.647640	+	0.647640i
$409$	−1.12188e6			−0.331618			−0.165809	−	0.986158i	$-0.553024\pi$
$409$	−1.12188e6			−0.331618			−0.165809	+	0.986158i	$0.553024\pi$
$410$	4.11295e6	−	1.18422e6i	1.20835	−	0.347914i
$411$	−221659.			−0.0647262
$412$	375545.	+	375545.i	0.108998	+	0.108998i
$413$	−467165.	−	467165.i	−0.134771	−	0.134771i
$414$	3.20704e6			0.919609
$415$	10968.6	−	3158.12i	0.00312630	−	0.000900137i
$416$	2.38546e6			0.675831
$417$	−4.41192e6	+	4.41192e6i	−1.24247	+	1.24247i
$418$	2.46001e6	−	5.30481e6i	0.688646	−	1.48501i
$419$			3.38369e6i			0.941576i	0.882246	+	0.470788i	$0.156030\pi$
$419$			3.38369e6i			0.941576i	−0.882246	+	0.470788i	$0.843970\pi$
$420$	−194622.	+	352011.i	−0.0538356	+	0.0973718i
$421$	3.26329e6			0.897326			0.448663	−	0.893701i	$-0.351900\pi$
$421$	3.26329e6			0.897326			0.448663	+	0.893701i	$0.351900\pi$
$422$	−1.97948e6	−	1.97948e6i	−0.541090	−	0.541090i
$423$	4.33469e6	−	4.33469e6i	1.17790	−	1.17790i
$424$	−2.47161e6			−0.667675
$425$	−2.61676e6	−	598126.i	−0.702734	−	0.160628i
$426$		−	1.13305e7i		−	3.02500i
$427$	1.17180e6	+	1.17180e6i	0.311018	+	0.311018i
$428$	−776322.	−	776322.i	−0.204848	−	0.204848i
$429$	8.06311e6	−	2.95409e6i	2.11524	−	0.774961i
$430$	−1.44496e6	+	2.61349e6i	−0.376865	+	0.681632i
$431$			2.19046e6i			0.567993i	0.958825	+	0.283997i	$0.0916604\pi$
$431$			2.19046e6i			0.567993i	−0.958825	+	0.283997i	$0.908340\pi$
$432$	−957239.	−	957239.i	−0.246781	−	0.246781i
$433$	−4.42160e6	+	4.42160e6i	−1.13334	+	1.13334i	−0.143719	+	0.989618i	$0.545906\pi$
$433$	−4.42160e6	+	4.42160e6i	−1.13334	+	1.13334i	−0.989618	+	0.143719i	$0.954094\pi$
$434$			158142.i			0.0403018i
$435$	1.92924e6	+	6.70052e6i	0.488837	+	1.69780i
$436$		−	1.00206e6i		−	0.252450i
$437$	2.88650e6	−	2.88650e6i	0.723049	−	0.723049i
$438$	−7.89676e6	+	7.89676e6i	−1.96682	+	1.96682i
$439$	448248.			0.111009			0.0555043	−	0.998458i	$-0.482323\pi$
$439$	448248.			0.111009			0.0555043	+	0.998458i	$0.482323\pi$
$440$	2.80764e6	−	2.05366e6i	0.691369	−	0.505705i
$441$	4.36448e6			1.06865
$442$	3.52139e6	−	3.52139e6i	0.857351	−	0.857351i
$443$	−3.27800e6	+	3.27800e6i	−0.793597	+	0.793597i	−0.982077	−	0.188480i	$-0.939644\pi$
$443$	−3.27800e6	+	3.27800e6i	−0.793597	+	0.793597i	0.188480	+	0.982077i	$0.439644\pi$
$444$		−	289284.i		−	0.0696412i
$445$	−231497.	−	127991.i	−0.0554172	−	0.0306394i
$446$			6.21802e6i			1.48018i
$447$	−453954.	+	453954.i	−0.107459	+	0.107459i
$448$	678637.	+	678637.i	0.159751	+	0.159751i
$449$			5.24584e6i			1.22800i	0.789305	+	0.614001i	$0.210441\pi$
$449$			5.24584e6i			1.22800i	−0.789305	+	0.614001i	$0.789559\pi$
$450$	1.27234e6	−	5.56638e6i	0.296190	−	1.29581i
$451$	1.68715e6	+	4.60504e6i	0.390582	+	1.06609i
$452$	172434.	+	172434.i	0.0396988	+	0.0396988i
$453$	−5.83339e6	−	5.83339e6i	−1.33560	−	1.33560i
$454$			3.93759e6i			0.896584i
$455$	−1.07435e6	+	1.94316e6i	−0.243286	+	0.440028i
$456$	−8.33856e6			−1.87793
$457$	3.10648e6	−	3.10648e6i	0.695789	−	0.695789i	−0.267710	−	0.963499i	$-0.586267\pi$
$457$	3.10648e6	−	3.10648e6i	0.695789	−	0.695789i	0.963499	+	0.267710i	$0.0862671\pi$
$458$	−5.69456e6	−	5.69456e6i	−1.26852	−	1.26852i
$459$	−966235.			−0.214068
$460$	−683600.	+	196825.i	−0.150629	+	0.0433697i
$461$			8.86566e6i			1.94294i	0.237168	+	0.971469i	$0.423781\pi$
$461$			8.86566e6i			1.94294i	−0.237168	+	0.971469i	$0.576219\pi$
$462$	−2.26364e6	−	1.04972e6i	−0.493403	−	0.228807i
$463$	2.15799e6	−	2.15799e6i	0.467840	−	0.467840i	−0.433374	−	0.901214i	$-0.642677\pi$
$463$	2.15799e6	−	2.15799e6i	0.467840	−	0.467840i	0.901214	+	0.433374i	$0.142677\pi$
$464$	−6.49184e6			−1.39982
$465$	−210332.	−	730510.i	−0.0451099	−	0.156673i
$466$	2.53168e6			0.540063
$467$	6.61193e6	+	6.61193e6i	1.40293	+	1.40293i	0.790612	+	0.612317i	$0.209763\pi$
$467$	6.61193e6	+	6.61193e6i	1.40293	+	1.40293i	0.612317	+	0.790612i	$0.290237\pi$
$468$	1.38367e6	+	1.38367e6i	0.292023	+	0.292023i
$469$	−114333.			−0.0240016
$470$	−3.56185e6	+	6.44228e6i	−0.743756	+	1.34522i
$471$	−842631.			−0.175019
$472$	−1.68770e6	+	1.68770e6i	−0.348692	+	0.348692i
$473$	−3.10441e6	−	1.43961e6i	−0.638008	−	0.295865i
$474$			8.96473e6i			1.83270i
$475$	−3.86486e6	−	6.15520e6i	−0.785959	−	1.25172i
$476$	−267293.			−0.0540718
$477$	−3.28725e6	−	3.28725e6i	−0.661511	−	0.661511i
$478$	1.52108e6	−	1.52108e6i	0.304496	−	0.304496i
$479$	−3.50888e6			−0.698763			−0.349381	−	0.936981i	$-0.613608\pi$
$479$	−3.50888e6			−0.698763			−0.349381	+	0.936981i	$0.613608\pi$
$480$	2.91592e6	+	1.61217e6i	0.577660	+	0.319380i
$481$		−	1.59689e6i		−	0.314712i
$482$	−1.29925e6	−	1.29925e6i	−0.254727	−	0.254727i
$483$	−1.23171e6	−	1.23171e6i	−0.240237	−	0.240237i
$484$	−754333.	−	891285.i	−0.146369	−	0.172943i
$485$	−1.12520e6	+	323973.i	−0.217208	+	0.0625396i
$486$			8.21112e6i			1.57693i
$487$	−2.63978e6	−	2.63978e6i	−0.504365	−	0.504365i	0.408427	−	0.912791i	$-0.366078\pi$
$487$	−2.63978e6	−	2.63978e6i	−0.504365	−	0.504365i	−0.912791	+	0.408427i	$0.866078\pi$
$488$	4.23332e6	−	4.23332e6i	0.804696	−	0.804696i
$489$		−	4.60557e6i		−	0.870986i
$490$	−5.03643e6	+	1.45011e6i	−0.947617	+	0.272842i
$491$			4.89709e6i			0.916715i	0.888768	+	0.458357i	$0.151562\pi$
$491$			4.89709e6i			0.916715i	−0.888768	+	0.458357i	$0.848438\pi$
$492$	−1.44867e6	+	1.44867e6i	−0.269810	+	0.269810i
$493$	−3.27643e6	+	3.27643e6i	−0.607132	+	0.607132i
$494$	1.34841e7			2.48602
$495$	6.46556e6	+	1.00280e6i	1.18602	+	0.183951i
$496$	707759.			0.129176
$497$	−2.37381e6	+	2.37381e6i	−0.431076	+	0.431076i
$498$	−20915.1	+	20915.1i	−0.00377909	+	0.00377909i
$499$		−	6.60922e6i		−	1.18823i	−0.804382	−	0.594113i	$-0.797503\pi$
$499$		−	6.60922e6i		−	1.18823i	0.804382	−	0.594113i	$-0.202497\pi$
$500$	70418.2	+	1.26460e6i	0.0125968	+	0.226218i
$501$		−	9.29884e6i		−	1.65514i
$502$	−6.90011e6	+	6.90011e6i	−1.22207	+	1.22207i
$503$	3.98172e6	+	3.98172e6i	0.701699	+	0.701699i	0.964775	−	0.263076i	$-0.0847370\pi$
$503$	3.98172e6	+	3.98172e6i	0.701699	+	0.701699i	−0.263076	+	0.964775i	$0.584737\pi$
$504$			1.94098e6i			0.340364i
$505$	−1.56984e6	−	867942.i	−0.273922	−	0.151448i
$506$	−1.51808e6	−	4.14357e6i	−0.263584	−	0.719446i
$507$	7.93142e6	+	7.93142e6i	1.37035	+	1.37035i
$508$	918366.	+	918366.i	0.157891	+	0.157891i
$509$		−	6.82553e6i		−	1.16773i	−0.811851	−	0.583864i	$-0.801540\pi$
$509$		−	6.82553e6i		−	1.16773i	0.811851	−	0.583864i	$-0.198460\pi$
$510$	6.68433e6	−	1.92458e6i	1.13797	−	0.327651i
$511$	3.30884e6			0.560561
$512$	2.02880e6	−	2.02880e6i	0.342030	−	0.342030i
$513$	−1.84995e6	−	1.84995e6i	−0.310360	−	0.310360i
$514$	8.14605e6			1.36000
$515$	1.13302e6	+	3.93512e6i	0.188243	+	0.653792i
$516$		−	1.42948e6i		−	0.236349i
$517$	−7.65240e6	−	3.54866e6i	−1.25913	−	0.583900i
$518$	−328105.	+	328105.i	−0.0537264	+	0.0537264i
$519$	1.27938e6			0.208489
$520$	7.01997e6	+	3.88125e6i	1.13848	+	0.629452i
$521$	1.15925e6			0.187104			0.0935522	−	0.995614i	$-0.470178\pi$
$521$	1.15925e6			0.187104			0.0935522	+	0.995614i	$0.470178\pi$
$522$	−6.96964e6	−	6.96964e6i	−1.11953	−	1.11953i
$523$	1.47874e6	+	1.47874e6i	0.236394	+	0.236394i	0.815355	−	0.578961i	$-0.196542\pi$
$523$	1.47874e6	+	1.47874e6i	0.236394	+	0.236394i	−0.578961	+	0.815355i	$0.696542\pi$
$524$	2.12349e6			0.337848
$525$	−2.62651e6	+	1.64919e6i	−0.415892	+	0.261140i
$526$	−858826.			−0.135345
$527$	357205.	−	357205.i	0.0560262	−	0.0560262i
$528$	−4.69798e6	+	1.01308e7i	−0.733376	+	1.58146i
$529$			3.35568e6i			0.521364i
$530$	4.88556e6	+	2.70116e6i	0.755482	+	0.417696i
$531$	−4.48931e6			−0.690945
$532$	−511759.	−	511759.i	−0.0783946	−	0.0783946i
$533$	−7.99693e6	+	7.99693e6i	−1.21928	+	1.21928i
$534$	685479.			0.104026
$535$	−2.34216e6	−	8.13463e6i	−0.353779	−	1.22872i
$536$			413046.i			0.0620993i
$537$	−2.89320e6	−	2.89320e6i	−0.432955	−	0.432955i
$538$	−5.99689e6	−	5.99689e6i	−0.893244	−	0.893244i
$539$	−2.06597e6	−	5.63901e6i	−0.306303	−	0.836048i
$540$	126145.	+	438118.i	0.0186159	+	0.0646557i
$541$		−	3.88433e6i		−	0.570589i	−0.958440	−	0.285295i	$-0.907909\pi$
$541$		−	3.88433e6i		−	0.570589i	0.958440	−	0.285295i	$-0.0920914\pi$
$542$	6.63769e6	+	6.63769e6i	0.970551	+	0.970551i
$543$	7.76319e6	−	7.76319e6i	1.12990	−	1.12990i
$544$			2.21415e6i			0.320782i
$545$	3.73839e6	−	6.76159e6i	0.539130	−	0.975119i
$546$		−	5.75385e6i		−	0.825994i
$547$	1.36581e6	−	1.36581e6i	0.195175	−	0.195175i	−0.602753	−	0.797928i	$-0.705930\pi$
$547$	1.36581e6	−	1.36581e6i	0.195175	−	0.195175i	0.797928	+	0.602753i	$0.205930\pi$
$548$	−49145.6	+	49145.6i	−0.00699091	+	0.00699091i
$549$	1.12607e7			1.59453
$550$	−7.79418e6	+	991010.i	−1.09866	+	0.139692i
$551$	−1.25461e7			−1.76047
$552$	−4.44974e6	+	4.44974e6i	−0.621565	+	0.621565i
$553$	1.87816e6	−	1.87816e6i	0.261168	−	0.261168i
$554$		−	1.19006e7i		−	1.64739i
$555$	1.07924e6	−	1.95200e6i	0.148725	−	0.268997i
$556$			1.95640e6i			0.268393i
$557$	5.20826e6	−	5.20826e6i	0.711303	−	0.711303i	−0.255505	−	0.966808i	$-0.582242\pi$
$557$	5.20826e6	−	5.20826e6i	0.711303	−	0.711303i	0.966808	+	0.255505i	$0.0822417\pi$
$558$	759850.	+	759850.i	0.103310	+	0.103310i
$559$		−	7.89097e6i		−	1.06807i
$560$	−798915.	−	2.77474e6i	−0.107654	−	0.373897i
$561$	2.74194e6	+	7.48407e6i	0.367834	+	1.00399i
$562$	−3.74679e6	−	3.74679e6i	−0.500402	−	0.500402i
$563$	−248163.	−	248163.i	−0.0329963	−	0.0329963i	0.690416	−	0.723412i	$-0.257427\pi$
$563$	−248163.	−	248163.i	−0.0329963	−	0.0329963i	−0.723412	+	0.690416i	$0.757427\pi$
$564$		−	3.52368e6i		−	0.466443i
$565$	520233.	+	1.80684e6i	0.0685610	+	0.238122i
$566$	−9.00551e6			−1.18159
$567$	1.36149e6	−	1.36149e6i	0.177852	−	0.177852i
$568$	8.57573e6	+	8.57573e6i	1.11532	+	1.11532i
$569$	−1.22043e7			−1.58028			−0.790140	−	0.612927i	$-0.789992\pi$
$569$	−1.22043e7			−1.58028			−0.790140	+	0.612927i	$0.789992\pi$
$570$	1.64826e7	+	9.11300e6i	2.12490	+	1.17483i
$571$		−	1.82329e6i		−	0.234026i	−0.993130	−	0.117013i	$-0.962668\pi$
$571$		−	1.82329e6i		−	0.234026i	0.993130	−	0.117013i	$-0.0373320\pi$
$572$	1.13276e6	−	2.44271e6i	0.144760	−	0.312163i
$573$	2.19998e6	−	2.19998e6i	0.279918	−	0.279918i
$574$	3.28616e6			0.416303
$575$	−5.34704e6	−	1.22220e6i	−0.674441	−	0.154160i
$576$	6.52149e6			0.819013
$577$	5.02579e6	+	5.02579e6i	0.628441	+	0.628441i	0.947676	−	0.319235i	$-0.103426\pi$
$577$	5.02579e6	+	5.02579e6i	0.628441	+	0.628441i	−0.319235	+	0.947676i	$0.603426\pi$
$578$	−3.02149e6	−	3.02149e6i	−0.376185	−	0.376185i
$579$	5.58262e6			0.692056
$580$	1.91337e6	+	1.05788e6i	0.236172	+	0.130576i
$581$	8763.68			0.00107708
$582$	2.14556e6	−	2.14556e6i	0.262563	−	0.262563i
$583$	−2.69116e6	+	5.80326e6i	−0.327920	+	0.707133i
$584$		−	1.19537e7i		−	1.45034i
$585$	4.17452e6	+	1.44987e7i	0.504332	+	1.75161i
$586$	1.63077e7			1.96178
$587$	−3.16128e6	−	3.16128e6i	−0.378676	−	0.378676i	0.491949	−	0.870624i	$-0.336285\pi$
$587$	−3.16128e6	−	3.16128e6i	−0.378676	−	0.378676i	−0.870624	+	0.491949i	$0.836285\pi$
$588$	1.77395e6	−	1.77395e6i	0.211591	−	0.211591i
$589$	1.36781e6			0.162456
$590$	5.18048e6	−	1.49159e6i	0.612689	−	0.176408i
$591$			740356.i			0.0871910i
$592$	1.46842e6	+	1.46842e6i	0.172205	+	0.172205i
$593$	−709909.	−	709909.i	−0.0829022	−	0.0829022i	0.664440	−	0.747342i	$-0.268670\pi$
$593$	−709909.	−	709909.i	−0.0829022	−	0.0829022i	−0.747342	+	0.664440i	$0.768670\pi$
$594$	−2.65560e6	+	972935.i	−0.308814	+	0.113140i
$595$	−1.80362e6	−	997196.i	−0.208859	−	0.115475i
$596$			201299.i			0.0232127i
$597$	−1.72450e7	−	1.72450e7i	−1.98028	−	1.98028i
$598$	7.19556e6	−	7.19556e6i	0.822833	−	0.822833i
$599$			3.62696e6i			0.413024i	0.978444	+	0.206512i	$0.0662113\pi$
$599$			3.62696e6i			0.413024i	−0.978444	+	0.206512i	$0.933789\pi$
$600$	5.95795e6	+	9.48867e6i	0.675645	+	1.07604i
$601$			1.56987e7i			1.77287i	0.462849	+	0.886437i	$0.346827\pi$
$601$			1.56987e7i			1.77287i	−0.462849	+	0.886437i	$0.653173\pi$
$602$	−1.62131e6	+	1.62131e6i	−0.182337	+	0.182337i
$603$	−549353.	+	549353.i	−0.0615260	+	0.0615260i
$604$	−2.58673e6			−0.288508
$605$	−1.76489e6	−	8.82834e6i	−0.196033	−	0.980597i
$606$	4.64841e6			0.514189
$607$	−1.03107e6	+	1.03107e6i	−0.113584	+	0.113584i	−0.761614	−	0.648030i	$-0.775593\pi$
$607$	−1.03107e6	+	1.03107e6i	−0.113584	+	0.113584i	0.648030	+	0.761614i	$0.275593\pi$
$608$	−4.23920e6	+	4.23920e6i	−0.465077	+	0.465077i
$609$			5.35358e6i			0.584926i
$610$	−1.29944e7	+	3.74139e6i	−1.41394	+	0.407107i
$611$		−	1.94513e7i		−	2.10788i
$612$	−1.28430e6	+	1.28430e6i	−0.138608	+	0.138608i
$613$	−8.28328e6	−	8.28328e6i	−0.890331	−	0.890331i	0.104223	−	0.994554i	$-0.466764\pi$
$613$	−8.28328e6	−	8.28328e6i	−0.890331	−	0.890331i	−0.994554	+	0.104223i	$0.966764\pi$
$614$		−	7.85553e6i		−	0.840920i
$615$	−1.51798e7	+	4.37064e6i	−1.61837	+	0.465969i
$616$	2.50779e6	−	918780.i	0.266280	−	0.0975573i
$617$	4.72164e6	+	4.72164e6i	0.499321	+	0.499321i	0.911227	−	0.411905i	$-0.135137\pi$
$617$	4.72164e6	+	4.72164e6i	0.499321	+	0.499321i	−0.411905	+	0.911227i	$0.635137\pi$
$618$	−7.50356e6	−	7.50356e6i	−0.790308	−	0.790308i
$619$			4.38237e6i			0.459709i	0.973225	+	0.229854i	$0.0738250\pi$
$619$			4.38237e6i			0.459709i	−0.973225	+	0.229854i	$0.926175\pi$
$620$	−208601.	−	115333.i	−0.0217940	−	0.0120496i
$621$	−1.97439e6			−0.205449
$622$	1.32017e7	−	1.32017e7i	1.36822	−	1.36822i
$623$	−143612.	−	143612.i	−0.0148242	−	0.0148242i
$624$	−2.57511e7			−2.64749
$625$	−4.24269e6	+	8.79585e6i	−0.434452	+	0.900695i
$626$			1.23618e7i			1.26080i
$627$	−9.07926e6	+	1.95787e7i	−0.922320	+	1.98891i
$628$	−186826.	+	186826.i	−0.0189033	+	0.0189033i
$629$	1.48222e6			0.149377
$630$	2.12124e6	−	3.83667e6i	0.212931	−	0.385126i
$631$	−3.69524e6			−0.369461			−0.184731	−	0.982789i	$-0.559141\pi$
$631$	−3.69524e6			−0.369461			−0.184731	+	0.982789i	$0.559141\pi$
$632$	−6.78515e6	−	6.78515e6i	−0.675720	−	0.675720i
$633$	7.30573e6	+	7.30573e6i	0.724694	+	0.724694i
$634$	−1.32000e6			−0.130421
$635$	2.77071e6	+	9.62303e6i	0.272682	+	0.947060i
$636$	−2.67221e6			−0.261956
$637$	9.79249e6	−	9.79249e6i	0.956190	−	0.956190i
$638$	−5.70579e6	+	1.23041e7i	−0.554964	+	1.19673i
$639$			2.28115e7i			2.21005i
$640$	−1.19567e7	+	3.44262e6i	−1.15388	+	0.332230i
$641$	6.56650e6			0.631232			0.315616	−	0.948887i	$-0.397789\pi$
$641$	6.56650e6			0.631232			0.315616	+	0.948887i	$0.397789\pi$
$642$	1.55113e7	+	1.55113e7i	1.48529	+	1.48529i
$643$	8.62976e6	−	8.62976e6i	0.823136	−	0.823136i	−0.163421	−	0.986556i	$-0.552253\pi$
$643$	8.62976e6	−	8.62976e6i	0.823136	−	0.823136i	0.986556	+	0.163421i	$0.0522528\pi$
$644$	−546183.			−0.0518948
$645$	5.33299e6	−	9.64572e6i	0.504744	−	0.912926i
$646$			1.25158e7i			1.17998i
$647$	−1.05243e6	−	1.05243e6i	−0.0988397	−	0.0988397i	0.655958	−	0.754798i	$-0.272265\pi$
$647$	−1.05243e6	−	1.05243e6i	−0.0988397	−	0.0988397i	−0.754798	+	0.655958i	$0.772265\pi$
$648$	−4.91860e6	−	4.91860e6i	−0.460155	−	0.460155i
$649$	2.12506e6	+	5.80030e6i	0.198043	+	0.540553i
$650$	−9.63446e6	−	1.53439e7i	−0.894425	−	1.42447i
$651$		−	583663.i		−	0.0539771i
$652$	−1.02113e6	−	1.02113e6i	−0.0940728	−	0.0940728i
$653$	−1.21852e7	+	1.21852e7i	−1.11828	+	1.11828i	−0.126281	+	0.991995i	$0.540304\pi$
$653$	−1.21852e7	+	1.21852e7i	−1.11828	+	1.11828i	−0.991995	+	0.126281i	$0.959696\pi$
$654$			2.00216e7i			1.83043i
$655$	1.43287e7	+	7.92214e6i	1.30498	+	0.721505i
$656$		−	1.47071e7i		−	1.33434i
$657$	1.58984e7	−	1.58984e7i	1.43695	−	1.43695i
$658$	−3.99655e6	+	3.99655e6i	−0.359849	+	0.359849i
$659$	9.06968e6			0.813539			0.406770	−	0.913531i	$-0.366655\pi$
$659$	9.06968e6			0.813539			0.406770	+	0.913531i	$0.366655\pi$
$660$	3.03552e6	−	2.22034e6i	0.271252	−	0.198408i
$661$	1.40788e7			1.25332			0.626659	−	0.779293i	$-0.284422\pi$
$661$	1.40788e7			1.25332			0.626659	+	0.779293i	$0.284422\pi$
$662$	1.08449e7	−	1.08449e7i	0.961790	−	0.961790i
$663$	−1.29965e7	+	1.29965e7i	−1.14827	+	1.14827i
$664$		−	31660.1i		−	0.00278671i
$665$	−1.54397e6	−	5.36243e6i	−0.135390	−	0.470227i
$666$			3.15298e6i			0.275446i
$667$	−6.69500e6	+	6.69500e6i	−0.582688	+	0.582688i
$668$	−2.06171e6	−	2.06171e6i	−0.178767	−	0.178767i
$669$		−	2.29491e7i		−	1.98244i
$670$	451407.	−	816456.i	0.0388492	−	0.0702661i
$671$	−5.33035e6	−	1.45491e7i	−0.457035	−	1.24747i
$672$	1.80893e6	+	1.80893e6i	0.154525	+	0.154525i
$673$	263210.	+	263210.i	0.0224009	+	0.0224009i	0.718219	−	0.695818i	$-0.244958\pi$
$673$	263210.	+	263210.i	0.0224009	+	0.0224009i	−0.695818	+	0.718219i	$0.744958\pi$
$674$			1.61070e7i			1.36573i
$675$	−783306.	+	3.42690e6i	−0.0661716	+	0.289496i
$676$	3.51707e6			0.296015
$677$	−1.35459e7	+	1.35459e7i	−1.13589	+	1.13589i	−0.146706	+	0.989180i	$0.546867\pi$
$677$	−1.35459e7	+	1.35459e7i	−1.13589	+	1.13589i	−0.989180	+	0.146706i	$0.953133\pi$
$678$	−3.44532e6	−	3.44532e6i	−0.287843	−	0.287843i
$679$	−899014.			−0.0748328
$680$	−3.60252e6	+	6.51585e6i	−0.298768	+	0.540379i
$681$		−	1.45326e7i		−	1.20082i
$682$	622062.	−	1.34143e6i	0.0512121	−	0.110435i
$683$	−7.24829e6	+	7.24829e6i	−0.594544	+	0.594544i	−0.938855	−	0.344311i	$-0.888112\pi$
$683$	−7.24829e6	+	7.24829e6i	−0.594544	+	0.594544i	0.344311	+	0.938855i	$0.388112\pi$
$684$	−4.91784e6			−0.401915
$685$	−514969.	+	148272.i	−0.0419329	+	0.0120735i
$686$	−8.54338e6			−0.693137
$687$	2.10171e7	+	2.10171e7i	1.69896	+	1.69896i
$688$	7.25611e6	+	7.25611e6i	0.584430	+	0.584430i
$689$	−1.47511e7			−1.18379
$690$	1.36587e7	−	3.93266e6i	1.09216	−	0.314459i
$691$	−3.82155e6			−0.304470			−0.152235	−	0.988344i	$-0.548647\pi$
$691$	−3.82155e6			−0.304470			−0.152235	+	0.988344i	$0.548647\pi$
$692$	283662.	−	283662.i	0.0225183	−	0.0225183i
$693$	4.55735e6	+	2.11339e6i	0.360479	+	0.167165i
$694$		−	1.51007e7i		−	1.19014i
$695$	−7.29877e6	+	1.32012e7i	−0.573176	+	1.03670i
$696$	1.93406e7			1.51338
$697$	−7.42264e6	−	7.42264e6i	−0.578731	−	0.578731i
$698$	1.94246e7	−	1.94246e7i	1.50909	−	1.50909i
$699$	−9.34379e6			−0.723319
$700$	−216689.	+	947998.i	−0.0167144	+	0.0731244i
$701$			111901.i			0.00860083i	0.999991	+	0.00430042i	$0.00136887\pi$
$701$			111901.i			0.00860083i	−0.999991	+	0.00430042i	$0.998631\pi$
$702$	−4.61162e6	−	4.61162e6i	−0.353192	−	0.353192i
$703$	2.83785e6	+	2.83785e6i	0.216571	+	0.216571i
$704$	−3.08701e6	−	8.42593e6i	−0.234751	−	0.640746i
$705$	1.31459e7	−	2.37768e7i	0.996130	−	1.80169i
$706$			1.09563e7i			0.827278i
$707$	−973868.	−	973868.i	−0.0732743	−	0.0732743i
$708$	−1.82468e6	+	1.82468e6i	−0.136806	+	0.136806i
$709$			9.72172e6i			0.726319i	0.931727	+	0.363160i	$0.118302\pi$
$709$			9.72172e6i			0.726319i	−0.931727	+	0.363160i	$0.881698\pi$
$710$	−7.57920e6	−	2.63236e7i	−0.564258	−	1.95974i
$711$		−	1.80486e7i		−	1.33896i
$712$	−518820.	+	518820.i	−0.0383545	+	0.0383545i
$713$	729908.	−	729908.i	0.0537705	−	0.0537705i
$714$	5.34065e6			0.392056
$715$	1.67566e7	−	1.22567e7i	1.22580	−	0.896618i
$716$	−1.28295e6			−0.0935246
$717$	−5.61391e6	+	5.61391e6i	−0.407819	+	0.407819i
$718$	4.23426e6	−	4.23426e6i	0.306526	−	0.306526i
$719$			2.04130e7i			1.47260i	0.676654	+	0.736301i	$0.263429\pi$
$719$			2.04130e7i			1.47260i	−0.676654	+	0.736301i	$0.736571\pi$
$720$	−1.71708e7	−	9.49353e6i	−1.23441	−	0.682490i
$721$			3.14408e6i			0.225245i
$722$	−1.29934e7	+	1.29934e7i	−0.927643	+	0.927643i
$723$	4.79519e6	+	4.79519e6i	0.341162	+	0.341162i
$724$		−	3.44247e6i		−	0.244075i
$725$	8.96423e6	+	1.42765e7i	0.633385	+	1.00873i
$726$	1.50719e7	+	1.78083e7i	1.06127	+	1.25395i
$727$	−1.01604e7	−	1.01604e7i	−0.712973	−	0.712973i	0.254183	−	0.967156i	$-0.418193\pi$
$727$	−1.01604e7	−	1.01604e7i	−0.712973	−	0.712973i	−0.967156	+	0.254183i	$0.918193\pi$
$728$	4.35493e6	+	4.35493e6i	0.304546	+	0.304546i
$729$		−	1.94040e7i		−	1.35230i
$730$	−1.30639e7	+	2.36285e7i	−0.907328	+	1.64108i
$731$	7.32430e6			0.506959
$732$	4.57691e6	−	4.57691e6i	0.315715	−	0.315715i
$733$	1.81957e7	+	1.81957e7i	1.25086	+	1.25086i	0.955336	+	0.295522i	$0.0954936\pi$
$733$	1.81957e7	+	1.81957e7i	1.25086	+	1.25086i	0.295522	+	0.955336i	$0.404506\pi$
$734$	2.32378e7			1.59204
$735$	1.85882e7	−	5.35198e6i	1.26917	−	0.365424i
$736$			4.52436e6i			0.307866i
$737$	969819.	+	449736.i	0.0657691	+	0.0304992i
$738$	1.57895e7	−	1.57895e7i	1.06716	−	1.06716i
$739$	−5.75813e6			−0.387856			−0.193928	−	0.981016i	$-0.562123\pi$
$739$	−5.75813e6			−0.387856			−0.193928	+	0.981016i	$0.562123\pi$
$740$	−193508.	−	672078.i	−0.0129903	−	0.0451170i
$741$	−4.97663e7			−3.32958
$742$	3.03082e6	+	3.03082e6i	0.202092	+	0.202092i
$743$	−7.49227e6	−	7.49227e6i	−0.497899	−	0.497899i	0.412884	−	0.910783i	$-0.364521\pi$
$743$	−7.49227e6	−	7.49227e6i	−0.497899	−	0.497899i	−0.910783	+	0.412884i	$0.864521\pi$
$744$	−2.10857e6			−0.139655
$745$	−750989.	+	1.35831e6i	−0.0495728	+	0.0896618i
$746$	−9.32980e6			−0.613798
$747$	42108.1	−	42108.1i	0.00276099	−	0.00276099i
$748$	2.26729e6	+	1.05141e6i	0.148167	+	0.0687099i
$749$		−	6.49941e6i		−	0.423320i
$750$	−1.40699e6	−	2.52673e7i	−0.0913350	−	1.64023i
$751$	7.51983e6			0.486528			0.243264	−	0.969960i	$-0.421782\pi$
$751$	7.51983e6			0.486528			0.243264	+	0.969960i	$0.421782\pi$
$752$	1.78864e7	+	1.78864e7i	1.15339	+	1.15339i
$753$	2.54665e7	−	2.54665e7i	1.63675	−	1.63675i
$754$	−3.12752e7			−2.00342
$755$	−1.74545e7	−	9.65036e6i	−1.11440	−	0.616135i
$756$			350047.i			0.0222752i
$757$	−7.19478e6	−	7.19478e6i	−0.456329	−	0.456329i	0.441120	−	0.897448i	$-0.354581\pi$
$757$	−7.19478e6	−	7.19478e6i	−0.456329	−	0.456329i	−0.897448	+	0.441120i	$0.854581\pi$
$758$	−1.08870e6	−	1.08870e6i	−0.0688235	−	0.0688235i
$759$	5.60285e6	+	1.52928e7i	0.353024	+	0.963571i
$760$	−1.93726e7	+	5.57784e6i	−1.21662	+	0.350293i
$761$		−	7.25575e6i		−	0.454172i	−0.973875	−	0.227086i	$-0.927080\pi$
$761$		−	7.25575e6i		−	0.454172i	0.973875	−	0.227086i	$-0.0729199\pi$
$762$	−1.83494e7	−	1.83494e7i	−1.14481	−	1.14481i
$763$	4.19463e6	−	4.19463e6i	0.260845	−	0.260845i
$764$		−	975546.i		−	0.0604664i
$765$	−1.34575e7	+	3.87473e6i	−0.831400	+	0.239380i
$766$			7.56211e6i			0.465662i
$767$	−1.00726e7	+	1.00726e7i	−0.618233	+	0.618233i
$768$	1.11001e7	−	1.11001e7i	0.679082	−	0.679082i
$769$	697902.			0.0425577			0.0212789	−	0.999774i	$-0.493226\pi$
$769$	697902.			0.0425577			0.0212789	+	0.999774i	$0.493226\pi$
$770$	−5.96118e6	−	924572.i	−0.362331	−	0.0561971i
$771$	−3.00649e7			−1.82148
$772$	1.23776e6	−	1.23776e6i	0.0747471	−	0.0747471i
$773$	−9.59735e6	+	9.59735e6i	−0.577701	+	0.577701i	−0.934269	−	0.356569i	$-0.883947\pi$
$773$	−9.59735e6	+	9.59735e6i	−0.577701	+	0.577701i	0.356569	+	0.934269i	$0.383947\pi$
$774$			1.55803e7i			0.934810i
$775$	−977306.	−	1.55646e6i	−0.0584489	−	0.0930861i
$776$			3.24783e6i			0.193615i
$777$	1.21095e6	−	1.21095e6i	0.0719570	−	0.0719570i
$778$	−1.89804e6	−	1.89804e6i	−0.112423	−	0.112423i
$779$		−	2.84227e7i		−	1.67812i
$780$	7.58974e6	+	4.19626e6i	0.446673	+	0.246960i
$781$	2.94731e7	−	1.07981e7i	1.72901	−	0.633459i
$782$	6.67882e6	+	6.67882e6i	0.390556	+	0.390556i
$783$	4.29081e6	+	4.29081e6i	0.250112	+	0.250112i
$784$			1.80093e7i			1.04642i
$785$	−1.95764e6	+	563653.i	−0.113386	+	0.0326466i
$786$	−4.24283e7			−2.44963
$787$	−2.64217e6	+	2.64217e6i	−0.152063	+	0.152063i	−0.779039	−	0.626976i	$-0.784293\pi$
$787$	−2.64217e6	+	2.64217e6i	−0.152063	+	0.152063i	0.626976	+	0.779039i	$0.284293\pi$
$788$	164150.	+	164150.i	0.00941726	+	0.00941726i
$789$	3.16971e6			0.181270
$790$	5.99669e6	+	2.08273e7i	0.341857	+	1.18731i
$791$			1.44363e6i			0.0820379i
$792$	7.63494e6	−	1.64641e7i	0.432506	−	0.932665i
$793$	2.52653e7	−	2.52653e7i	1.42673	−	1.42673i
$794$	1.45371e7			0.818327
$795$	−1.80313e7	−	9.96927e6i	−1.01184	−	0.559430i
$796$	−7.64703e6			−0.427770
$797$	8.68725e6	+	8.68725e6i	0.484436	+	0.484436i	0.906545	−	0.422109i	$-0.138710\pi$
$797$	8.68725e6	+	8.68725e6i	0.484436	+	0.484436i	−0.422109	+	0.906545i	$0.638710\pi$
$798$	1.02252e7	+	1.02252e7i	0.568413	+	0.568413i
$799$	1.80545e7			1.00050
$800$	7.85283e6	+	1.79496e6i	0.433811	+	0.0991586i
$801$	−1.38007e6			−0.0760008
$802$	−1.83571e7	+	1.83571e7i	−1.00779	+	1.00779i
$803$	−2.80669e7	−	1.30155e7i	−1.53605	−	0.712315i
$804$			446570.i			0.0243641i
$805$	−3.68549e6	−	2.03766e6i	−0.200450	−	0.110826i
$806$	3.40972e6			0.184876
$807$	2.21330e7	+	2.21330e7i	1.19634	+	1.19634i
$808$	−3.51825e6	+	3.51825e6i	−0.189582	+	0.189582i
$809$	3.49031e7			1.87496			0.937480	−	0.348038i	$-0.113152\pi$
$809$	3.49031e7			1.87496			0.937480	+	0.348038i	$0.113152\pi$
$810$	4.34704e6	+	1.50979e7i	0.232799	+	0.808543i
$811$		−	1.07514e7i		−	0.574001i	−0.957930	−	0.287001i	$-0.907342\pi$
$811$		−	1.07514e7i		−	0.574001i	0.957930	−	0.287001i	$-0.0926582\pi$
$812$	1.18698e6	+	1.18698e6i	0.0631763	+	0.0631763i
$813$	−2.44980e7	−	2.44980e7i	−1.29988	−	1.29988i
$814$	4.07373e6	−	1.49249e6i	0.215492	−	0.0789499i
$815$	−3.08076e6	−	1.06999e7i	−0.162466	−	0.564268i
$816$		−	2.39018e7i		−	1.25663i
$817$	1.40231e7	+	1.40231e7i	0.735001	+	0.735001i
$818$	4.96996e6	−	4.96996e6i	0.259699	−	0.259699i
$819$			1.15841e7i			0.603468i
$820$	−2.39659e6	+	4.33468e6i	−0.124468	+	0.225124i
$821$			2.19747e6i			0.113780i	0.998380	+	0.0568898i	$0.0181184\pi$
$821$			2.19747e6i			0.113780i	−0.998380	+	0.0568898i	$0.981882\pi$
$822$	981953.	−	981953.i	0.0506887	−	0.0506887i
$823$	1.86800e7	−	1.86800e7i	0.961339	−	0.961339i	−0.0379408	−	0.999280i	$-0.512080\pi$
$823$	1.86800e7	−	1.86800e7i	0.961339	−	0.961339i	0.999280	+	0.0379408i	$0.0120798\pi$
$824$	1.13585e7			0.582776
$825$	2.87663e7	−	3.65756e6i	1.47146	−	0.187093i
$826$	4.13910e6			0.211084
$827$	1.68402e7	−	1.68402e7i	0.856214	−	0.856214i	−0.134676	−	0.990890i	$-0.542999\pi$
$827$	1.68402e7	−	1.68402e7i	0.856214	−	0.856214i	0.990890	+	0.134676i	$0.0429992\pi$
$828$	−2.62432e6	+	2.62432e6i	−0.133028	+	0.133028i
$829$			6.63244e6i			0.335187i	0.985856	+	0.167593i	$0.0535996\pi$
$829$			6.63244e6i			0.335187i	−0.985856	+	0.167593i	$0.946400\pi$
$830$	−34600.5	+	62581.6i	−0.00174336	+	0.00315320i
$831$			4.39222e7i			2.20638i
$832$	1.46321e7	−	1.46321e7i	0.732823	−	0.732823i
$833$	9.08926e6	+	9.08926e6i	0.453854	+	0.453854i
$834$		−	3.90898e7i		−	1.94602i
$835$	−6.22018e6	−	2.16035e7i	−0.308736	−	1.07228i
$836$	2.32791e6	+	6.35397e6i	0.115199	+	0.314434i
$837$	−467796.	−	467796.i	−0.0230804	−	0.0230804i
$838$	−1.49898e7	−	1.49898e7i	−0.737372	−	0.737372i
$839$			2.42760e7i			1.19062i	0.803497	+	0.595309i	$0.202970\pi$
$839$			2.42760e7i			1.19062i	−0.803497	+	0.595309i	$0.797030\pi$
$840$	2.38014e6	+	8.26656e6i	0.116387	+	0.404228i
$841$	8.58842e6			0.418720
$842$	−1.44564e7	+	1.44564e7i	−0.702718	+	0.702718i
$843$	1.38284e7	+	1.38284e7i	0.670200	+	0.670200i
$844$	3.23962e6			0.156544
$845$	2.37322e7	+	1.31212e7i	1.14339	+	0.632167i
$846$			3.84056e7i			1.84488i
$847$	573283.	−	6.88860e6i	0.0274575	−	0.329931i
$848$	1.35643e7	−	1.35643e7i	0.647750	−	0.647750i
$849$	3.32370e7			1.58253
$850$	1.42420e7	−	8.94258e6i	0.676120	−	0.424537i
$851$	3.02874e6			0.143363
$852$	9.27177e6	+	9.27177e6i	0.437586	+	0.437586i
$853$	−1.25064e7	−	1.25064e7i	−0.588517	−	0.588517i	0.348713	−	0.937230i	$-0.386619\pi$
$853$	−1.25064e7	−	1.25064e7i	−0.588517	−	0.588517i	−0.937230	+	0.348713i	$0.886619\pi$
$854$	−1.03822e7			−0.487132
$855$	−3.31842e7	−	1.83471e7i	−1.55244	−	0.858325i
$856$	−2.34801e7			−1.09526
$857$	−2.46422e7	+	2.46422e7i	−1.14611	+	1.14611i	−0.158801	+	0.987311i	$0.550763\pi$
$857$	−2.46422e7	+	2.46422e7i	−1.14611	+	1.14611i	−0.987311	+	0.158801i	$0.949237\pi$
$858$	−2.26331e7	+	4.88064e7i	−1.04960	+	2.26339i
$859$			2.75934e7i			1.27592i	0.770071	+	0.637959i	$0.220221\pi$
$859$			2.75934e7i			1.27592i	−0.770071	+	0.637959i	$0.779779\pi$
$860$	−956208.	−	3.32104e6i	−0.0440866	−	0.153119i
$861$	−1.21284e7			−0.557564
$862$	−9.70381e6	−	9.70381e6i	−0.444809	−	0.444809i
$863$	−2.18694e6	+	2.18694e6i	−0.0999564	+	0.0999564i	−0.755317	−	0.655360i	$-0.772517\pi$
$863$	−2.18694e6	+	2.18694e6i	−0.0999564	+	0.0999564i	0.655360	+	0.755317i	$0.272517\pi$
$864$	2.89965e6			0.132148
$865$	2.97233e6	−	855806.i	0.135069	−	0.0388897i
$866$		−	3.91755e7i		−	1.77509i
$867$	1.11515e7	+	1.11515e7i	0.503833	+	0.503833i
$868$	−129408.	−	129408.i	−0.00582992	−	0.00582992i
$869$	−2.33192e7	+	8.54347e6i	−1.04752	+	0.383782i
$870$	−3.82300e7	−	2.11369e7i	−1.71241	−	0.946766i
$871$			2.46514e6i			0.110102i
$872$	−1.51538e7	−	1.51538e7i	−0.674884	−	0.674884i
$873$	−4.31962e6	+	4.31962e6i	−0.191827	+	0.191827i
$874$			2.55745e7i			1.13247i
$875$	−4.99887e6	+	5.58841e6i	−0.220725	+	0.246756i
$876$		−	1.29239e7i		−	0.569027i
$877$	−1.17054e7	+	1.17054e7i	−0.513909	+	0.513909i	−0.915722	−	0.401813i	$-0.868380\pi$
$877$	−1.17054e7	+	1.17054e7i	−0.513909	+	0.513909i	0.401813	+	0.915722i	$0.368380\pi$
$878$	−1.98575e6	+	1.98575e6i	−0.0869336	+	0.0869336i
$879$	−6.01876e7			−2.62745
$880$	−4.13788e6	+	2.66790e7i	−0.180124	+	1.16135i
$881$	8.92860e6			0.387564			0.193782	−	0.981045i	$-0.437925\pi$
$881$	8.92860e6			0.387564			0.193782	+	0.981045i	$0.437925\pi$
$882$	−1.93347e7	+	1.93347e7i	−0.836887	+	0.836887i
$883$	−2.17045e7	+	2.17045e7i	−0.936804	+	0.936804i	−0.998118	−	0.0613145i	$-0.980471\pi$
$883$	−2.17045e7	+	2.17045e7i	−0.936804	+	0.936804i	0.0613145	+	0.998118i	$0.480471\pi$
$884$			5.76313e6i			0.248043i
$885$	−1.91198e7	+	5.50506e6i	−0.820589	+	0.236268i
$886$		−	2.90432e7i		−	1.24297i
$887$	5.45809e6	−	5.45809e6i	0.232933	−	0.232933i	−0.580983	−	0.813916i	$-0.697332\pi$
$887$	5.45809e6	−	5.45809e6i	0.232933	−	0.232933i	0.813916	+	0.580983i	$0.197332\pi$
$888$	−4.37474e6	−	4.37474e6i	−0.186174	−	0.186174i
$889$			7.68861e6i			0.326282i
$890$	1.59254e6	−	458531.i	0.0673931	−	0.0194041i
$891$	−1.69042e7	+	6.19321e6i	−0.713348	+	0.261350i
$892$	−5.08822e6	−	5.08822e6i	−0.214118	−	0.214118i
$893$	3.45670e7	+	3.45670e7i	1.45055	+	1.45055i
$894$		−	4.02205e6i		−	0.168308i
$895$	−8.65695e6	−	4.78631e6i	−0.361250	−	0.199730i
$896$	−9.55315e6			−0.397536
$897$	−2.65570e7	+	2.65570e7i	−1.10204	+	1.10204i
$898$	−2.32392e7	−	2.32392e7i	−0.961679	−	0.961679i
$899$	−3.17252e6			−0.130920
$900$	3.51383e6	+	5.59614e6i	0.144602	+	0.230294i
$901$		−	1.36918e7i		−	0.561885i
$902$	−2.78745e7	−	1.29263e7i	−1.14075	−	0.529003i
$903$	5.98384e6	−	5.98384e6i	0.244208	−	0.244208i
$904$	5.21533e6			0.212256
$905$	1.28429e7	−	2.32288e7i	0.521244	−	0.942769i
$906$	5.16841e7			2.09188
$907$	9.99571e6	+	9.99571e6i	0.403455	+	0.403455i	0.879449	−	0.475993i	$-0.157911\pi$
$907$	9.99571e6	+	9.99571e6i	0.403455	+	0.403455i	−0.475993	+	0.879449i	$0.657911\pi$
$908$	−3.22214e6	−	3.22214e6i	−0.129697	−	0.129697i
$909$	−9.35857e6			−0.375664
$910$	−3.84887e6	−	1.33676e7i	−0.154074	−	0.535120i
$911$	2.19871e7			0.877753			0.438876	−	0.898547i	$-0.355377\pi$
$911$	2.19871e7			0.877753			0.438876	+	0.898547i	$0.355377\pi$
$912$	4.57623e7	−	4.57623e7i	1.82189	−	1.82189i
$913$	−74337.0	−	34472.4i	−0.00295140	−	0.00136866i
$914$			2.75235e7i			1.08978i
$915$	4.79588e7	−	1.38085e7i	1.89372	−	0.545248i
$916$	9.31974e6			0.366999
$917$	8.88899e6	+	8.88899e6i	0.349083	+	0.349083i
$918$	4.28044e6	−	4.28044e6i	0.167642	−	0.167642i
$919$	7.26738e6			0.283850			0.141925	−	0.989877i	$-0.454671\pi$
$919$	7.26738e6			0.283850			0.141925	+	0.989877i	$0.454671\pi$
$920$	−7.36134e6	+	1.33144e7i	−0.286739	+	0.518623i
$921$			2.89927e7i			1.12626i
$922$	−3.92751e7	−	3.92751e7i	−1.52156	−	1.52156i
$923$	5.11818e7	+	5.11818e7i	1.97747	+	1.97747i
$924$	2.71133e6	−	993351.i	0.104473	−	0.0382757i
$925$	1.20160e6	−	5.25692e6i	0.0461749	−	0.202012i
$926$			1.91199e7i			0.732754i
$927$	1.51068e7	+	1.51068e7i	0.577396	+	0.577396i
$928$	9.83248e6	−	9.83248e6i	0.374794	−	0.374794i
$929$		−	5.55439e6i		−	0.211153i	−0.994411	−	0.105577i	$-0.966331\pi$
$929$		−	5.55439e6i		−	0.211153i	0.994411	−	0.105577i	$-0.0336688\pi$
$930$	4.16795e6	+	2.30440e6i	0.158021	+	0.0873677i
$931$			3.48045e7i			1.31602i
$932$	−2.07168e6	+	2.07168e6i	−0.0781238	+	0.0781238i
$933$	−4.87242e7	+	4.87242e7i	−1.83248	+	1.83248i
$934$	−5.85820e7			−2.19734
$935$	1.13765e7	+	1.55532e7i	0.425578	+	0.581825i
$936$	4.18495e7			1.56135
$937$	9.21635e6	−	9.21635e6i	0.342933	−	0.342933i	−0.514536	−	0.857469i	$-0.672036\pi$
$937$	9.21635e6	−	9.21635e6i	0.342933	−	0.342933i	0.857469	+	0.514536i	$0.172036\pi$
$938$	506499.	−	506499.i	0.0187962	−	0.0187962i
$939$		−	4.56243e7i		−	1.68862i
$940$	−2.35706e6	−	8.18640e6i	−0.0870064	−	0.302185i
$941$		−	5.85310e6i		−	0.215482i	−0.994179	−	0.107741i	$-0.965638\pi$
$941$		−	5.85310e6i		−	0.215482i	0.994179	−	0.107741i	$-0.0343618\pi$
$942$	3.73288e6	−	3.73288e6i	0.137062	−	0.137062i
$943$	−1.51673e7	−	1.51673e7i	−0.555430	−	0.555430i
$944$		−	1.85244e7i		−	0.676571i
$945$	−1.30593e6	+	2.36202e6i	−0.0475707	+	0.0860407i
$946$	2.01301e7	−	7.37509e6i	0.731339	−	0.267941i
$947$	−2.24961e7	−	2.24961e7i	−0.815139	−	0.815139i	0.170260	−	0.985399i	$-0.445539\pi$
$947$	−2.24961e7	−	2.24961e7i	−0.815139	−	0.815139i	−0.985399	+	0.170260i	$0.945539\pi$
$948$	−7.33586e6	−	7.33586e6i	−0.265112	−	0.265112i
$949$		−	7.13420e7i		−	2.57146i
$950$	4.43891e7	+	1.01462e7i	1.59576	+	0.364751i
$951$	4.87176e6			0.174677
$952$	−4.04219e6	+	4.04219e6i	−0.144552	+	0.144552i
$953$	−2.97849e7	−	2.97849e7i	−1.06234	−	1.06234i	−0.997923	−	0.0644176i	$-0.979481\pi$
$953$	−2.97849e7	−	2.97849e7i	−1.06234	−	1.06234i	−0.0644176	−	0.997923i	$-0.520519\pi$
$954$	2.91252e7			1.03609
$955$	3.63949e6	−	6.58271e6i	0.129131	−	0.233559i
$956$			2.48941e6i			0.0880949i
$957$	2.10586e7	−	4.54112e7i	0.743276	−	1.60281i
$958$	1.55444e7	−	1.55444e7i	0.547218	−	0.547218i
$959$	−411450.			−0.0144468
$960$	2.77748e7	−	7.99705e6i	0.972687	−	0.280060i
$961$	−2.82833e7			−0.987919
$962$	7.07428e6	+	7.07428e6i	0.246459	+	0.246459i
$963$	−3.12286e7	−	3.12286e7i	−1.08514	−	1.08514i
$964$	2.12636e6			0.0736959
$965$	1.29698e7	−	3.73433e6i	0.448349	−	0.129090i
$966$	1.09130e7			0.376271
$967$	1.50022e7	−	1.50022e7i	0.515928	−	0.515928i	−0.400409	−	0.916337i	$-0.631132\pi$
$967$	1.50022e7	−	1.50022e7i	0.515928	−	0.515928i	0.916337	+	0.400409i	$0.131132\pi$
$968$	−2.48861e7	−	2.07107e6i	−0.853629	−	0.0710406i
$969$		−	4.61924e7i		−	1.58038i
$970$	3.54947e6	−	6.41988e6i	0.121125	−	0.219077i
$971$	1.73202e7			0.589527			0.294763	−	0.955570i	$-0.404759\pi$
$971$	1.73202e7			0.589527			0.294763	+	0.955570i	$0.404759\pi$
$972$	−6.71918e6	−	6.71918e6i	−0.228113	−	0.228113i
$973$	−8.18954e6	+	8.18954e6i	−0.277318	+	0.277318i
$974$	2.33885e7			0.789961
$975$	3.55583e7	+	5.66303e7i	1.19792	+	1.90782i
$976$			4.64652e7i			1.56136i
$977$	1.50157e7	+	1.50157e7i	0.503280	+	0.503280i	0.912456	−	0.409175i	$-0.134184\pi$
$977$	1.50157e7	+	1.50157e7i	0.503280	+	0.503280i	−0.409175	+	0.912456i	$0.634184\pi$
$978$	2.04028e7	+	2.04028e7i	0.682090	+	0.682090i
$979$	653267.	+	1.78308e6i	0.0217838	+	0.0594585i
$980$	2.93469e6	−	5.30795e6i	0.0976107	−	0.176548i
$981$		−	4.03091e7i		−	1.33731i
$982$	−2.16942e7	−	2.16942e7i	−0.717902	−	0.717902i
$983$	2.09148e7	−	2.09148e7i	0.690350	−	0.690350i	−0.271959	−	0.962309i	$-0.587671\pi$
$983$	2.09148e7	−	2.09148e7i	0.690350	−	0.690350i	0.962309	+	0.271959i	$0.0876714\pi$
$984$			4.38156e7i			1.44258i
$985$	495239.	+	1.72003e6i	0.0162639	+	0.0564867i
$986$		−	2.90293e7i		−	0.950920i
$987$	1.47502e7	−	1.47502e7i	0.481954	−	0.481954i
$988$	−1.10341e7	+	1.10341e7i	−0.359619	+	0.359619i
$989$	1.49664e7			0.486548
$990$	−3.30850e7	+	2.42001e7i	−1.07286	+	0.784747i
$991$	−336168.			−0.0108736			−0.00543678	−	0.999985i	$-0.501731\pi$
$991$	−336168.			−0.0108736			−0.00543678	+	0.999985i	$0.501731\pi$
$992$	−1.07197e6	+	1.07197e6i	−0.0345861	+	0.0345861i
$993$	−4.00257e7	+	4.00257e7i	−1.28815	+	1.28815i
$994$		−	2.10320e7i		−	0.675173i
$995$	−5.16000e7	−	2.85289e7i	−1.65231	−	0.913540i
$996$		−	34229.8i		−	0.00109334i
$997$	3.14661e7	−	3.14661e7i	1.00255	−	1.00255i	0.00255114	−	0.999997i	$-0.499188\pi$
$997$	3.14661e7	−	3.14661e7i	1.00255	−	1.00255i	0.999997	−	0.00255114i	$-0.000812054\pi$
$998$	2.92790e7	+	2.92790e7i	0.930528	+	0.930528i
$999$		−	1.94111e6i		−	0.0615371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.8	✓	52
5.3	odd	4	inner	55.6.e.b.43.19	yes	52
11.10	odd	2	inner	55.6.e.b.32.19	yes	52
55.43	even	4	inner	55.6.e.b.43.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.8	✓	52	1.1	even	1	trivial
55.6.e.b.32.19	yes	52	11.10	odd	2	inner
55.6.e.b.43.8	yes	52	55.43	even	4	inner
55.6.e.b.43.19	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.43002 + 4.43002i) q^{2} +(16.3501 - 16.3501i) q^{3} -7.25019i q^{4} +(27.0484 - 48.9222i) q^{5} +144.862i q^{6} +(30.3495 - 30.3495i) q^{7} +(-109.642 - 109.642i) q^{8} -291.649i q^{9} +(96.9014 + 336.552i) q^{10} +(-376.818 + 138.055i) q^{11} +(-118.541 - 118.541i) q^{12} +(-654.367 - 654.367i) q^{13} +268.898i q^{14} +(-357.638 - 1242.12i) q^{15} +1203.44 q^{16} +(607.375 - 607.375i) q^{17} +(1292.01 + 1292.01i) q^{18} +2325.76 q^{19} +(-354.695 - 196.106i) q^{20} -992.433i q^{21} +(1057.73 - 2280.90i) q^{22} +(1241.10 - 1241.10i) q^{23} -3585.31 q^{24} +(-1661.77 - 2646.54i) q^{25} +5797.72 q^{26} +(-795.419 - 795.419i) q^{27} +(-220.040 - 220.040i) q^{28} -5394.40 q^{29} +(7086.98 + 3918.30i) q^{30} +588.113 q^{31} +(-1822.72 + 1822.72i) q^{32} +(-3903.79 + 8418.21i) q^{33} +5381.37i q^{34} +(-663.859 - 2305.67i) q^{35} -2114.51 q^{36} +(1220.18 + 1220.18i) q^{37} +(-10303.1 + 10303.1i) q^{38} -21397.9 q^{39} +(-8329.59 + 2398.29i) q^{40} -12220.9i q^{41} +(4396.50 + 4396.50i) q^{42} +(6029.47 + 6029.47i) q^{43} +(1000.93 + 2732.00i) q^{44} +(-14268.1 - 7888.65i) q^{45} +10996.2i q^{46} +(14862.7 + 14862.7i) q^{47} +(19676.3 - 19676.3i) q^{48} +14964.8i q^{49} +(19085.9 + 4362.56i) q^{50} -19861.2i q^{51} +(-4744.29 + 4744.29i) q^{52} +(11271.3 - 11271.3i) q^{53} +7047.44 q^{54} +(-3438.37 + 22168.9i) q^{55} -6655.17 q^{56} +(38026.3 - 38026.3i) q^{57} +(23897.3 - 23897.3i) q^{58} -15392.8i q^{59} +(-9005.64 + 2592.94i) q^{60} +38610.3i q^{61} +(-2605.35 + 2605.35i) q^{62} +(-8851.41 - 8851.41i) q^{63} +22360.7i q^{64} +(-49712.7 + 14313.5i) q^{65} +(-19999.0 - 54586.7i) q^{66} +(-1883.61 - 1883.61i) q^{67} +(-4403.59 - 4403.59i) q^{68} -40584.2i q^{69} +(13155.1 + 7273.27i) q^{70} -78215.6 q^{71} +(-31977.1 + 31977.1i) q^{72} +(54512.2 + 54512.2i) q^{73} -10810.9 q^{74} +(-70441.0 - 16101.1i) q^{75} -16862.2i q^{76} +(-7246.34 + 15626.1i) q^{77} +(94793.2 - 94793.2i) q^{78} +61884.5 q^{79} +(32551.2 - 58875.0i) q^{80} +44860.5 q^{81} +(54138.7 + 54138.7i) q^{82} +(144.379 + 144.379i) q^{83} -7195.33 q^{84} +(-13285.6 - 46142.7i) q^{85} -53421.4 q^{86} +(-88198.8 + 88198.8i) q^{87} +(56451.8 + 26178.5i) q^{88} -4731.93i q^{89} +(98155.0 - 28261.2i) q^{90} -39719.4 q^{91} +(-8998.22 - 8998.22i) q^{92} +(9615.69 - 9615.69i) q^{93} -131684. q^{94} +(62908.0 - 113781. i) q^{95} +59603.2i q^{96} +(-14811.0 - 14811.0i) q^{97} +(-66294.5 - 66294.5i) q^{98} +(40263.7 + 109899. 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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