LMFDB - Embedded newform 55.6.e.b.43.19

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			43.19
Character	$\chi$	$=$	55.43
Dual form			55.6.e.b.32.19

$q$-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} +(-2280.90 - 1057.73i) 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} +(-8418.21 - 3903.79i) 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} +(-16946.3 - 14700.6i) 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} +(15626.1 + 7246.34i) 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} +(-26178.5 + 56451.8i) 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 $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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	$-0.0631953\pi$
$2$	4.43002	+	4.43002i	0.783125	+	0.783125i	−0.197232	+	0.980357i	$0.563195\pi$
$3$	16.3501	+	16.3501i	1.04886	+	1.04886i	0.998744	+	0.0501137i	$0.0159584\pi$
$3$	16.3501	+	16.3501i	1.04886	+	1.04886i	0.0501137	+	0.998744i	$0.484042\pi$
$4$			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	$-0.302935\pi$
$7$	−30.3495	−	30.3495i	−0.234103	−	0.234103i	−0.814403	+	0.580300i	$0.802935\pi$
$8$	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	0.0768562	−	0.997042i	$-0.475512\pi$
$13$	654.367	−	654.367i	1.07390	−	1.07390i	0.997042	−	0.0768562i	$-0.0244882\pi$
$14$		−	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	$-0.367370\pi$
$17$	−607.375	−	607.375i	−0.509724	−	0.509724i	−0.914442	+	0.404718i	$0.867370\pi$
$18$	−1292.01	+	1292.01i	−0.939908	+	0.939908i
$19$	−2325.76			−1.47802			−0.739010	−	0.673695i	$-0.764706\pi$
$19$	−2325.76			−1.47802			−0.739010	+	0.673695i	$0.764706\pi$
$20$	−354.695	+	196.106i	−0.198281	+	0.109627i
$21$		−	992.433i		−	0.491081i
$22$	−2280.90	−	1057.73i	−1.00473	−	0.465925i
$23$	1241.10	+	1241.10i	0.489201	+	0.489201i	0.908054	−	0.418853i	$-0.137568\pi$
$23$	1241.10	+	1241.10i	0.489201	+	0.489201i	−0.418853	+	0.908054i	$0.637568\pi$
$24$	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	$-0.296934\pi$
$29$	5394.40			1.19110			0.595550	+	0.803318i	$0.296934\pi$
$30$	−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
$33$	−8418.21	−	3903.79i	−1.34566	−	0.624024i
$34$		−	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	−0.630037	−	0.776565i	$-0.716960\pi$
$37$	1220.18	−	1220.18i	0.146528	−	0.146528i	0.776565	+	0.630037i	$0.216960\pi$
$38$	−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	$-0.864374\pi$
$43$	−6029.47	+	6029.47i	−0.497288	+	0.497288i	0.413305	+	0.910593i	$0.364374\pi$
$44$	−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	−0.0184150	−	0.999830i	$-0.505862\pi$
$47$	14862.7	−	14862.7i	0.981415	−	0.981415i	0.999830	+	0.0184150i	$0.00586202\pi$
$48$	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	0.926777	−	0.375611i	$-0.122567\pi$
$53$	11271.3	+	11271.3i	0.551166	+	0.551166i	−0.375611	+	0.926777i	$0.622567\pi$
$54$	−7047.44			−0.328887
$55$	−16946.3	−	14700.6i	−0.755384	−	0.655282i
$56$	−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	$0.0929388\pi$
$59$			15392.8i			0.575690i	−0.957677	+	0.287845i	$0.907061\pi$
$60$	−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	−0.732274	−	0.681011i	$-0.761541\pi$
$67$	−1883.61	+	1883.61i	−0.0512630	+	0.0512630i	0.681011	+	0.732274i	$0.261541\pi$
$68$	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	−0.222270	+	0.974985i	$0.571347\pi$
$73$	−54512.2	+	54512.2i	−1.19726	+	1.19726i	−0.974985	+	0.222270i	$0.928653\pi$
$74$	10810.9			0.229499
$75$	−70441.0	+	16101.1i	−1.44601	+	0.330523i
$76$		−	16862.2i		−	0.334873i
$77$	15626.1	+	7246.34i	0.300348	+	0.139281i
$78$	94793.2	+	94793.2i	1.76417	+	1.76417i
$79$	−61884.5			−1.11561			−0.557807	−	0.829970i	$-0.688357\pi$
$79$	−61884.5			−1.11561			−0.557807	+	0.829970i	$0.688357\pi$
$80$	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	$-0.750518\pi$
$83$	−144.379	+	144.379i	−0.00230043	+	0.00230043i	0.705956	+	0.708256i	$0.250518\pi$
$84$	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
$88$	−26178.5	+	56451.8i	−0.360361	+	0.777090i
$89$			4731.93i			0.0633233i	0.999499	+	0.0316617i	$0.0100799\pi$
$89$			4731.93i			0.0633233i	−0.999499	+	0.0316617i	$0.989920\pi$
$90$	−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	−0.782491	−	0.622662i	$-0.786051\pi$
$97$	−14811.0	+	14811.0i	−0.159829	+	0.159829i	0.622662	+	0.782491i	$0.286051\pi$
$98$	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	0.424395	−	0.905477i	$-0.360487\pi$
$103$	−51797.9	−	51797.9i	−0.481082	−	0.481082i	−0.905477	+	0.424395i	$0.860487\pi$
$104$		−	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	$-0.470784\pi$
$107$	−107076.	−	107076.i	−0.904134	−	0.904134i	−0.995791	+	0.0916569i	$0.970784\pi$
$108$	−5766.94	−	5766.94i	−0.0475758	−	0.0475758i
$109$	−138211.			−1.11423			−0.557117	−	0.830434i	$-0.688092\pi$
$109$	−138211.			−1.11423			−0.557117	+	0.830434i	$0.688092\pi$
$110$	−9948.46	−	140196.i	−0.0783924	−	1.10473i
$111$	39900.1			0.307374
$112$	−36523.8	−	36523.8i	−0.275126	−	0.275126i
$113$	−23783.4	−	23783.4i	−0.175218	−	0.175218i	0.614050	−	0.789267i	$-0.289539\pi$
$113$	−23783.4	−	23783.4i	−0.175218	−	0.175218i	−0.789267	+	0.614050i	$0.789539\pi$
$114$		−	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	$-0.0859853\pi$
$127$	126668.	+	126668.i	0.696878	+	0.696878i	−0.266858	+	0.963736i	$0.585985\pi$
$128$	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	$0.732174\pi$
$132$	28303.2	−	61033.6i	0.141384	−	0.304884i
$133$	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	−0.722366	−	0.691511i	$-0.756946\pi$
$137$	−6778.53	+	6778.53i	−0.0308556	+	0.0308556i	0.691511	+	0.722366i	$0.256946\pi$
$138$	−179789.	+	179789.i	−0.803646	+	0.803646i
$139$	269841.			1.18460			0.592299	−	0.805718i	$-0.298220\pi$
$139$	269841.			1.18460			0.592299	+	0.805718i	$0.298220\pi$
$140$	16716.6	+	4813.10i	0.0720820	+	0.0207542i
$141$	486012.			2.05873
$142$	−346497.	−	346497.i	−1.44204	−	1.44204i
$143$	−156239.	+	336916.i	−0.638923	+	1.37779i
$144$			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	$-0.483687\pi$
$149$	27764.6			0.102453			0.0512267	+	0.998687i	$0.483687\pi$
$150$	−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	−0.747592	−	0.664159i	$-0.768790\pi$
$157$	−25768.4	+	25768.4i	−0.0834332	+	0.0834332i	0.664159	+	0.747592i	$0.268790\pi$
$158$	−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	0.883548	−	0.468341i	$-0.155148\pi$
$163$	140842.	+	140842.i	0.415207	+	0.415207i	−0.468341	+	0.883548i	$0.655148\pi$
$164$	88603.5			0.257242
$165$	−36717.2	−	517429.i	−0.104993	−	1.47959i
$166$	−1279.21			−0.00360305
$167$	−284367.	−	284367.i	−0.789020	−	0.789020i	0.192314	−	0.981334i	$-0.438401\pi$
$167$	−284367.	−	284367.i	−0.789020	−	0.789020i	−0.981334	+	0.192314i	$0.938401\pi$
$168$	−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	$-0.772389\pi$
$173$	−39124.7	+	39124.7i	−0.0993885	+	0.0993885i	0.655664	+	0.755053i	$0.272389\pi$
$174$			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	$0.0661728\pi$
$179$			176953.i			0.412787i	−0.978469	+	0.206394i	$0.933827\pi$
$180$	−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
$187$	312721.	+	145019.i	0.653963	+	0.303263i
$188$	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	$-0.824946\pi$
$193$	−170722.	+	170722.i	−0.329910	+	0.329910i	0.522642	+	0.852552i	$0.324946\pi$
$194$	−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	$-0.240643\pi$
$197$	22640.8	+	22640.8i	0.0415648	+	0.0415648i	−0.686019	+	0.727584i	$0.740643\pi$
$198$	308485.	−	665223.i	0.559205	−	1.20588i
$199$			1.05473e6i			1.88804i	0.329892	+	0.944019i	$0.392988\pi$
$199$			1.05473e6i			1.88804i	−0.329892	+	0.944019i	$0.607012\pi$
$200$	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
$220$	106582.	−	122864.i	0.148466	−	0.171146i
$221$	−794893.			−1.09478
$222$	176758.	+	176758.i	0.240712	+	0.240712i
$223$	701805.	+	701805.i	0.945049	+	0.945049i	0.998567	−	0.0535179i	$-0.0170434\pi$
$223$	701805.	+	701805.i	0.945049	+	0.945049i	−0.0535179	+	0.998567i	$0.517043\pi$
$224$		−	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	$-0.382651\pi$
$227$	−444421.	−	444421.i	−0.572440	−	0.572440i	−0.932810	+	0.360370i	$0.882651\pi$
$228$	275698.	−	275698.i	0.351233	−	0.351233i
$229$		−	1.28545e6i		−	1.61982i	−0.586557	−	0.809908i	$-0.699517\pi$
$229$		−	1.28545e6i		−	1.61982i	0.586557	−	0.809908i	$-0.300483\pi$
$230$	−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	$-0.671599\pi$
$233$	285742.	−	285742.i	0.344813	−	0.344813i	0.858173	+	0.513360i	$0.171599\pi$
$234$			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	$-0.437720\pi$
$239$	343357.			0.388822			0.194411	+	0.980920i	$0.437720\pi$
$240$	−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	$0.948001\pi$
$242$	1.00551e6	+	83680.3i	1.10369	+	0.0918512i
$243$	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
$253$	−639009.	−	296329.i	−0.627633	−	0.291053i
$254$			1.12228e6i			1.09149i
$255$	971656.	−	537215.i	0.935755	−	0.517366i
$256$	678900.			0.647449
$257$	−919414.	+	919414.i	−0.868317	+	0.868317i	−0.992286	−	0.123969i	$-0.960438\pi$
$257$	−919414.	+	919414.i	−0.868317	+	0.868317i	0.123969	+	0.992286i	$0.460438\pi$
$258$	−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	$-0.769462\pi$
$263$	−96932.5	+	96932.5i	−0.0864132	+	0.0864132i	0.662579	+	0.748992i	$0.269462\pi$
$264$	−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	$-0.806824\pi$
$269$		−	1.35369e6i		−	1.14062i	0.821431	−	0.570308i	$-0.193176\pi$
$270$	−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
$275$	260815.	−	1.22668e6i	0.207970	−	0.978135i
$276$	−294243.			−0.232506
$277$	1.34318e6	+	1.34318e6i	1.05180	+	1.05180i	0.998583	+	0.0532211i	$0.0169488\pi$
$277$	1.34318e6	+	1.34318e6i	1.05180	+	1.05180i	0.0532211	+	0.998583i	$0.483051\pi$
$278$	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	$-0.929104\pi$
$283$	−1.01642e6	+	1.01642e6i	−0.754408	+	0.754408i	0.220890	+	0.975299i	$0.429104\pi$
$284$		−	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	0.297950	−	0.954582i	$-0.403697\pi$
$293$	1.84059e6	−	1.84059e6i	1.25253	−	1.25253i	0.954582	−	0.297950i	$-0.0963028\pi$
$294$	2.16784e6			1.46271
$295$	−753052.	+	416352.i	−0.503813	+	0.278552i
$296$		−	267567.i		−	0.177502i
$297$	189917.	−	409540.i	0.124931	−	0.269404i
$298$	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	$-0.126046\pi$
$307$	886625.	+	886625.i	0.536901	+	0.536901i	−0.385717	+	0.922617i	$0.626046\pi$
$308$	−52537.3	+	113293.i	−0.0315567	+	0.0680494i
$309$		−	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	0.983869	−	0.178888i	$-0.0572500\pi$
$313$	1.39523e6	+	1.39523e6i	0.804981	+	0.804981i	−0.178888	+	0.983869i	$0.557250\pi$
$314$	−228310.			−0.130677
$315$	672447.	+	193614.i	0.381840	+	0.109941i
$316$		−	448675.i		−	0.252763i
$317$	148983.	−	148983.i	0.0832699	−	0.0832699i	−0.664245	−	0.747515i	$-0.731247\pi$
$317$	148983.	−	148983.i	0.0832699	−	0.0832699i	0.747515	+	0.664245i	$0.231247\pi$
$318$	−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
$330$	2.12956e6	−	2.45488e6i	1.07648	−	1.24092i
$331$	−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	$-0.461483\pi$
$337$	−1.81794e6	−	1.81794e6i	−0.871977	−	0.871977i	−0.992688	+	0.120711i	$0.961483\pi$
$338$	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	$-0.0694414\pi$
$347$	1.70436e6	+	1.70436e6i	0.759868	+	0.759868i	−0.216430	+	0.976298i	$0.569441\pi$
$348$	−639458.	+	639458.i	−0.283051	+	0.283051i
$349$	4.38477e6			1.92701			0.963503	−	0.267696i	$-0.0862623\pi$
$349$	4.38477e6			1.92701			0.963503	+	0.267696i	$0.0862623\pi$
$350$	711648.	+	446845.i	0.310524	+	0.194979i
$351$			1.04099e6i			0.451003i
$352$	−938469.	−	435198.i	−0.403704	−	0.187210i
$353$	1.23660e6	+	1.23660e6i	0.528191	+	0.528191i	0.920033	−	0.391842i	$-0.128162\pi$
$353$	1.23660e6	+	1.23660e6i	0.528191	+	0.528191i	−0.391842	+	0.920033i	$0.628162\pi$
$354$	−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	$-0.437300\pi$
$359$	955811.			0.391413			0.195707	+	0.980662i	$0.437300\pi$
$360$	−699460.	+	2.42932e6i	−0.284450	+	0.987934i
$361$	2.93304e6			1.18454
$362$	2.10342e6	+	2.10342e6i	0.843636	+	0.843636i
$363$	3.71107e6	+	308842.i	1.47820	+	0.123018i
$364$		−	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	−0.0166052	+	0.999862i	$0.505286\pi$
$367$	−2.62276e6	+	2.62276e6i	−1.01647	+	1.01647i	−0.999862	+	0.0166052i	$0.994714\pi$
$368$	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	$-0.839376\pi$
$373$	−1.05302e6	+	1.05302e6i	−0.391890	+	0.391890i	0.483471	+	0.875361i	$0.339376\pi$
$374$	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	$-0.986008\pi$
$379$		−	245756.i		−	0.0878832i	0.999034	−	0.0439416i	$-0.0139916\pi$
$380$	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	0.839960	−	0.542649i	$-0.182579\pi$
$383$	853507.	+	853507.i	0.297310	+	0.297310i	−0.542649	+	0.839960i	$0.682579\pi$
$384$	5.14653e6			1.78109
$385$	68155.6	+	960467.i	0.0234342	+	0.330241i
$386$	−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	$-0.977133\pi$
$389$		−	428449.i		−	0.143557i	0.997421	−	0.0717786i	$-0.0228675\pi$
$390$	−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	−0.918318	−	0.395843i	$-0.870453\pi$
$397$	−1.64075e6	+	1.64075e6i	−0.522476	+	0.522476i	0.395843	+	0.918318i	$0.370453\pi$
$398$	−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
$407$	−291334.	+	628239.i	−0.0871778	+	0.187992i
$408$	−2.17763e6	−	2.17763e6i	−0.647640	−	0.647640i
$409$	1.12188e6			0.331618			0.165809	−	0.986158i	$-0.446976\pi$
$409$	1.12188e6			0.331618			0.165809	+	0.986158i	$0.446976\pi$
$410$	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
$418$	5.30481e6	+	2.46001e6i	1.48501	+	0.688646i
$419$		−	3.38369e6i		−	0.941576i	−0.882246	−	0.470788i	$-0.843970\pi$
$419$		−	3.38369e6i		−	0.941576i	0.882246	−	0.470788i	$-0.156030\pi$
$420$	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	−0.989618	−	0.143719i	$-0.954094\pi$
$433$	−4.42160e6	−	4.42160e6i	−1.13334	−	1.13334i	−0.143719	−	0.989618i	$-0.545906\pi$
$434$		−	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	$-0.517677\pi$
$439$	−448248.			−0.111009			−0.0555043	+	0.998458i	$0.517677\pi$
$440$	−3.46983e6	+	246223.i	−0.854431	+	0.0606312i
$441$	4.36448e6			1.06865
$442$	−3.52139e6	−	3.52139e6i	−0.857351	−	0.857351i
$443$	−3.27800e6	−	3.27800e6i	−0.793597	−	0.793597i	0.188480	−	0.982077i	$-0.439644\pi$
$443$	−3.27800e6	−	3.27800e6i	−0.793597	−	0.793597i	−0.982077	+	0.188480i	$0.939644\pi$
$444$			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	$-0.789559\pi$
$449$		−	5.24584e6i		−	1.22800i	0.789305	−	0.614001i	$-0.210441\pi$
$450$	−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	$-0.413733\pi$
$457$	−3.10648e6	−	3.10648e6i	−0.695789	−	0.695789i	−0.963499	+	0.267710i	$0.913733\pi$
$458$	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	$0.576219\pi$
$462$	−1.04972e6	+	2.26364e6i	−0.228807	+	0.493403i
$463$	2.15799e6	+	2.15799e6i	0.467840	+	0.467840i	0.901214	−	0.433374i	$-0.142677\pi$
$463$	2.15799e6	+	2.15799e6i	0.467840	+	0.467840i	−0.433374	+	0.901214i	$0.642677\pi$
$464$	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	0.612317	−	0.790612i	$-0.290237\pi$
$467$	6.61193e6	−	6.61193e6i	1.40293	−	1.40293i	0.790612	−	0.612317i	$-0.209763\pi$
$468$	−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
$473$	1.43961e6	−	3.10441e6i	0.295865	−	0.638008i
$474$		−	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	$-0.386392\pi$
$479$	3.50888e6			0.698763			0.349381	+	0.936981i	$0.386392\pi$
$480$	−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	−0.912791	−	0.408427i	$-0.866078\pi$
$487$	−2.63978e6	+	2.63978e6i	−0.504365	+	0.504365i	0.408427	+	0.912791i	$0.366078\pi$
$488$	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
$495$	4.28742e6	−	4.94237e6i	0.786471	−	0.906614i
$496$	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	$0.202497\pi$
$499$			6.60922e6i			1.18823i	−0.804382	+	0.594113i	$0.797503\pi$
$500$	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	$-0.915263\pi$
$503$	−3.98172e6	+	3.98172e6i	−0.701699	+	0.701699i	0.263076	+	0.964775i	$0.415263\pi$
$504$		−	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	$0.198460\pi$
$509$			6.82553e6i			1.16773i	−0.811851	+	0.583864i	$0.801540\pi$
$510$	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
$517$	−3.54866e6	+	7.65240e6i	−0.583900	+	1.25913i
$518$	−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	$-0.803458\pi$
$523$	−1.47874e6	+	1.47874e6i	−0.236394	+	0.236394i	0.578961	+	0.815355i	$0.303458\pi$
$524$	−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
$528$	−1.01308e7	−	4.69798e6i	−1.58146	−	0.733376i
$529$		−	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	$-0.294070\pi$
$547$	−1.36581e6	−	1.36581e6i	−0.195175	−	0.195175i	−0.797928	+	0.602753i	$0.794070\pi$
$548$	−49145.6	−	49145.6i	−0.00699091	−	0.00699091i
$549$	−1.12607e7			−1.59453
$550$	6.58963e6	−	4.27879e6i	0.928868	−	0.603135i
$551$	−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	$-0.417758\pi$
$557$	−5.20826e6	−	5.20826e6i	−0.711303	−	0.711303i	−0.966808	+	0.255505i	$0.917758\pi$
$558$	−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	$-0.742573\pi$
$563$	248163.	−	248163.i	0.0329963	−	0.0329963i	0.723412	+	0.690416i	$0.242573\pi$
$564$			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	$-0.210008\pi$
$569$	1.22043e7			1.58028			0.790140	+	0.612927i	$0.210008\pi$
$570$	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	$-0.0373320\pi$
$572$	−2.44271e6	−	1.13276e6i	−0.312163	−	0.144760i
$573$	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	−0.319235	−	0.947676i	$-0.603426\pi$
$577$	5.02579e6	−	5.02579e6i	0.628441	−	0.628441i	0.947676	+	0.319235i	$0.103426\pi$
$578$	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
$583$	−5.80326e6	−	2.69116e6i	−0.707133	−	0.327920i
$584$			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	−0.870624	−	0.491949i	$-0.836285\pi$
$587$	−3.16128e6	+	3.16128e6i	−0.378676	+	0.378676i	0.491949	+	0.870624i	$0.336285\pi$
$588$	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	$-0.731330\pi$
$593$	709909.	−	709909.i	0.0829022	−	0.0829022i	0.747342	+	0.664440i	$0.231330\pi$
$594$	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	$-0.933789\pi$
$599$		−	3.62696e6i		−	0.413024i	0.978444	−	0.206512i	$-0.0662113\pi$
$600$	−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
$605$	8.41516e6	+	3.19993e6i	0.934704	+	0.355428i
$606$	4.64841e6			0.514189
$607$	1.03107e6	+	1.03107e6i	0.113584	+	0.113584i	0.761614	−	0.648030i	$-0.224407\pi$
$607$	1.03107e6	+	1.03107e6i	0.113584	+	0.113584i	−0.648030	+	0.761614i	$0.724407\pi$
$608$	−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	$-0.533236\pi$
$613$	8.28328e6	−	8.28328e6i	0.890331	−	0.890331i	0.994554	+	0.104223i	$0.0332357\pi$
$614$			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	−0.411905	−	0.911227i	$-0.635137\pi$
$617$	4.72164e6	−	4.72164e6i	0.499321	−	0.499321i	0.911227	+	0.411905i	$0.135137\pi$
$618$	7.50356e6	−	7.50356e6i	0.790308	−	0.790308i
$619$		−	4.38237e6i		−	0.459709i	−0.973225	−	0.229854i	$-0.926175\pi$
$619$		−	4.38237e6i		−	0.459709i	0.973225	−	0.229854i	$-0.0738250\pi$
$620$	−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
$627$	1.95787e7	+	9.07926e6i	1.98891	+	0.922320i
$628$	−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
$638$	−1.23041e7	−	5.70579e6i	−1.19673	−	0.554964i
$639$		−	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	0.986556	−	0.163421i	$-0.0522528\pi$
$643$	8.62976e6	+	8.62976e6i	0.823136	+	0.823136i	−0.163421	+	0.986556i	$0.552253\pi$
$644$	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	−0.754798	−	0.655958i	$-0.772265\pi$
$647$	−1.05243e6	+	1.05243e6i	−0.0988397	+	0.0988397i	0.655958	+	0.754798i	$0.272265\pi$
$648$	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	−0.991995	−	0.126281i	$-0.959696\pi$
$653$	−1.21852e7	−	1.21852e7i	−1.11828	−	1.11828i	−0.126281	−	0.991995i	$-0.540304\pi$
$654$		−	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	$-0.633345\pi$
$659$	−9.06968e6			−0.813539			−0.406770	+	0.913531i	$0.633345\pi$
$660$	3.75146e6	−	266207.i	0.335228	−	0.0237881i
$661$	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	$-0.755042\pi$
$673$	−263210.	+	263210.i	−0.0224009	+	0.0224009i	0.695818	+	0.718219i	$0.255042\pi$
$674$		−	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	0.989180	+	0.146706i	$0.0468671\pi$
$677$	1.35459e7	+	1.35459e7i	1.13589	+	1.13589i	0.146706	+	0.989180i	$0.453133\pi$
$678$	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
$682$	−1.34143e6	−	622062.i	−0.110435	−	0.0512121i
$683$	−7.24829e6	−	7.24829e6i	−0.594544	−	0.594544i	0.344311	−	0.938855i	$-0.388112\pi$
$683$	−7.24829e6	−	7.24829e6i	−0.594544	−	0.594544i	−0.938855	+	0.344311i	$0.888112\pi$
$684$	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
$693$	−2.11339e6	+	4.55735e6i	−0.167165	+	0.360479i
$694$			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	$-0.881698\pi$
$709$		−	9.72172e6i		−	0.726319i	0.931727	−	0.363160i	$-0.118302\pi$
$710$	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
$715$	−2.07087e7	+	1.46951e6i	−1.51491	+	0.107500i
$716$	−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	$-0.736571\pi$
$719$		−	2.04130e7i		−	1.47260i	0.676654	−	0.736301i	$-0.263429\pi$
$720$	−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	−0.967156	−	0.254183i	$-0.918193\pi$
$727$	−1.01604e7	+	1.01604e7i	−0.712973	+	0.712973i	0.254183	+	0.967156i	$0.418193\pi$
$728$	−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	−0.295522	+	0.955336i	$0.595494\pi$
$733$	−1.81957e7	+	1.81957e7i	−1.25086	+	1.25086i	−0.955336	+	0.295522i	$0.904506\pi$
$734$	−2.32378e7			−1.59204
$735$	1.85882e7	+	5.35198e6i	1.26917	+	0.365424i
$736$			4.52436e6i			0.307866i
$737$	449736.	−	969819.i	0.0304992	−	0.0657691i
$738$	1.57895e7	+	1.57895e7i	1.06716	+	1.06716i
$739$	5.75813e6			0.387856			0.193928	−	0.981016i	$-0.437877\pi$
$739$	5.75813e6			0.387856			0.193928	+	0.981016i	$0.437877\pi$
$740$	−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	$-0.635479\pi$
$743$	7.49227e6	−	7.49227e6i	0.497899	−	0.497899i	0.910783	+	0.412884i	$0.135479\pi$
$744$	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
$748$	−1.05141e6	+	2.26729e6i	−0.0687099	+	0.148167i
$749$			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	−0.897448	−	0.441120i	$-0.854581\pi$
$757$	−7.19478e6	+	7.19478e6i	−0.456329	+	0.456329i	0.441120	+	0.897448i	$0.354581\pi$
$758$	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	$-0.506774\pi$
$769$	−697902.			−0.0425577			−0.0212789	+	0.999774i	$0.506774\pi$
$770$	−3.95296e6	+	4.55682e6i	−0.240268	+	0.276972i
$771$	−3.00649e7			−1.82148
$772$	−1.23776e6	−	1.23776e6i	−0.0747471	−	0.0747471i
$773$	−9.59735e6	−	9.59735e6i	−0.577701	−	0.577701i	0.356569	−	0.934269i	$-0.383947\pi$
$773$	−9.59735e6	−	9.59735e6i	−0.577701	−	0.577701i	−0.934269	+	0.356569i	$0.883947\pi$
$774$		−	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	$-0.215707\pi$
$787$	2.64217e6	+	2.64217e6i	0.152063	+	0.152063i	−0.626976	+	0.779039i	$0.715707\pi$
$788$	−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
$792$	−1.64641e7	−	7.63494e6i	−0.932665	−	0.432506i
$793$	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	−0.422109	−	0.906545i	$-0.638710\pi$
$797$	8.68725e6	−	8.68725e6i	0.484436	−	0.484436i	0.906545	+	0.422109i	$0.138710\pi$
$798$	−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
$803$	1.30155e7	−	2.80669e7i	0.712315	−	1.53605i
$804$		−	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	$-0.886848\pi$
$809$	−3.49031e7			−1.87496			−0.937480	+	0.348038i	$0.886848\pi$
$810$	−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	0.999280	−	0.0379408i	$-0.0120798\pi$
$823$	1.86800e7	+	1.86800e7i	0.961339	+	0.961339i	−0.0379408	+	0.999280i	$0.512080\pi$
$824$	−1.13585e7			−0.582776
$825$	2.43206e7	−	1.57919e7i	1.24406	−	0.807793i
$826$	4.13910e6			0.211084
$827$	−1.68402e7	−	1.68402e7i	−0.856214	−	0.856214i	0.134676	−	0.990890i	$-0.457001\pi$
$827$	−1.68402e7	−	1.68402e7i	−0.856214	−	0.856214i	−0.990890	+	0.134676i	$0.957001\pi$
$828$	−2.62432e6	−	2.62432e6i	−0.133028	−	0.133028i
$829$		−	6.63244e6i		−	0.335187i	−0.985856	−	0.167593i	$-0.946400\pi$
$829$		−	6.63244e6i		−	0.335187i	0.985856	−	0.167593i	$-0.0535996\pi$
$830$	−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	$-0.797030\pi$
$839$		−	2.42760e7i		−	1.19062i	0.803497	−	0.595309i	$-0.202970\pi$
$840$	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
$847$	−6.88860e6	−	573283.i	−0.329931	−	0.0274575i
$848$	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	$-0.613381\pi$
$853$	1.25064e7	−	1.25064e7i	0.588517	−	0.588517i	0.937230	+	0.348713i	$0.113381\pi$
$854$	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	0.987311	+	0.158801i	$0.0507628\pi$
$857$	2.46422e7	+	2.46422e7i	1.14611	+	1.14611i	0.158801	+	0.987311i	$0.449237\pi$
$858$	−4.88064e7	−	2.26331e7i	−2.26339	−	1.04960i
$859$		−	2.75934e7i		−	1.27592i	−0.770071	−	0.637959i	$-0.779779\pi$
$859$		−	2.75934e7i		−	1.27592i	0.770071	−	0.637959i	$-0.220221\pi$
$860$	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	0.655360	−	0.755317i	$-0.272517\pi$
$863$	−2.18694e6	−	2.18694e6i	−0.0999564	−	0.0999564i	−0.755317	+	0.655360i	$0.772517\pi$
$864$	−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	$-0.131620\pi$
$877$	1.17054e7	+	1.17054e7i	0.513909	+	0.513909i	−0.401813	+	0.915722i	$0.631620\pi$
$878$	−1.98575e6	−	1.98575e6i	−0.0869336	−	0.0869336i
$879$	6.01876e7			2.62745
$880$	−2.03939e7	−	1.76913e7i	−0.887754	−	0.770111i
$881$	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	0.0613145	−	0.998118i	$-0.480471\pi$
$883$	−2.17045e7	−	2.17045e7i	−0.936804	−	0.936804i	−0.998118	+	0.0613145i	$0.980471\pi$
$884$		−	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	$-0.302668\pi$
$887$	−5.45809e6	−	5.45809e6i	−0.232933	−	0.232933i	−0.813916	+	0.580983i	$0.802668\pi$
$888$	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
$902$	−1.29263e7	+	2.78745e7i	−0.529003	+	1.14075i
$903$	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	−0.475993	−	0.879449i	$-0.657911\pi$
$907$	9.99571e6	−	9.99571e6i	0.403455	−	0.403455i	0.879449	+	0.475993i	$0.157911\pi$
$908$	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
$913$	34472.4	−	74337.0i	0.00136866	−	0.00295140i
$914$		−	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	$-0.545329\pi$
$919$	−7.26738e6			−0.283850			−0.141925	+	0.989877i	$0.545329\pi$
$920$	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	$0.0336688\pi$
$929$			5.55439e6i			0.211153i	−0.994411	+	0.105577i	$0.966331\pi$
$930$	−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
$935$	1.36398e6	+	1.92215e7i	0.0510244	+	0.719050i
$936$	4.18495e7			1.56135
$937$	−9.21635e6	−	9.21635e6i	−0.342933	−	0.342933i	0.514536	−	0.857469i	$-0.327964\pi$
$937$	−9.21635e6	−	9.21635e6i	−0.342933	−	0.342933i	−0.857469	+	0.514536i	$0.827964\pi$
$938$	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	−0.985399	−	0.170260i	$-0.945539\pi$
$947$	−2.24961e7	+	2.24961e7i	−0.815139	+	0.815139i	0.170260	+	0.985399i	$0.445539\pi$
$948$	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	0.0644176	−	0.997923i	$-0.479481\pi$
$953$	2.97849e7	−	2.97849e7i	1.06234	−	1.06234i	0.997923	−	0.0644176i	$-0.0205190\pi$
$954$	−2.91252e7			−1.03609
$955$	3.63949e6	+	6.58271e6i	0.129131	+	0.233559i
$956$			2.48941e6i			0.0880949i
$957$	−4.54112e7	−	2.10586e7i	−1.60281	−	0.743276i
$958$	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	$-0.368868\pi$
$967$	−1.50022e7	−	1.50022e7i	−0.515928	−	0.515928i	−0.916337	+	0.400409i	$0.868868\pi$
$968$	2.07107e6	−	2.48861e7i	0.0710406	−	0.853629i
$969$			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	−0.409175	−	0.912456i	$-0.634184\pi$
$977$	1.50157e7	−	1.50157e7i	0.503280	−	0.503280i	0.912456	+	0.409175i	$0.134184\pi$
$978$	−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	0.962309	−	0.271959i	$-0.0876714\pi$
$983$	2.09148e7	+	2.09148e7i	0.690350	+	0.690350i	−0.271959	+	0.962309i	$0.587671\pi$
$984$		−	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
$990$	4.08882e7	−	2.90146e6i	1.32590	−	0.0940868i
$991$	−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	−0.999997	−	0.00255114i	$-0.999188\pi$
$997$	−3.14661e7	−	3.14661e7i	−1.00255	−	1.00255i	−0.00255114	−	0.999997i	$-0.500812\pi$
$998$	−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.43.19	yes	52
5.2	odd	4	inner	55.6.e.b.32.8	✓	52
11.10	odd	2	inner	55.6.e.b.43.8	yes	52
55.32	even	4	inner	55.6.e.b.32.19	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.8	✓	52	5.2	odd	4	inner
55.6.e.b.32.19	yes	52	55.32	even	4	inner
55.6.e.b.43.8	yes	52	11.10	odd	2	inner
55.6.e.b.43.19	yes	52	1.1	even	1	trivial

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} +(-2280.90 - 1057.73i) 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} +(-8418.21 - 3903.79i) 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} +(-16946.3 - 14700.6i) 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} +(15626.1 + 7246.34i) 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} +(-26178.5 + 56451.8i) 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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