LMFDB - Embedded newform 80.6.q.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.64889 + 0.300072i) q^{2} +(-16.1243 + 16.1243i) q^{3} +(31.8199 - 3.39015i) q^{4} +(33.0407 + 45.0922i) q^{5} +(86.2458 - 95.9226i) q^{6} +106.654 q^{7} +(-178.730 + 28.6988i) q^{8} -276.984i q^{9} +O(q^{10})$	\(q+(-5.64889 + 0.300072i) q^{2} +(-16.1243 + 16.1243i) q^{3} +(31.8199 - 3.39015i) q^{4} +(33.0407 + 45.0922i) q^{5} +(86.2458 - 95.9226i) q^{6} +106.654 q^{7} +(-178.730 + 28.6988i) q^{8} -276.984i q^{9} +(-200.174 - 244.806i) q^{10} +(507.841 - 507.841i) q^{11} +(-458.409 + 567.736i) q^{12} +(478.170 - 478.170i) q^{13} +(-602.476 + 32.0039i) q^{14} +(-1259.84 - 194.321i) q^{15} +(1001.01 - 215.748i) q^{16} +345.388i q^{17} +(83.1151 + 1564.65i) q^{18} +(1702.33 + 1702.33i) q^{19} +(1204.22 + 1322.82i) q^{20} +(-1719.72 + 1719.72i) q^{21} +(-2716.35 + 3021.12i) q^{22} +1767.61 q^{23} +(2419.14 - 3344.64i) q^{24} +(-941.619 + 2979.76i) q^{25} +(-2557.64 + 2844.61i) q^{26} +(547.964 + 547.964i) q^{27} +(3393.72 - 361.573i) q^{28} +(-3730.61 - 3730.61i) q^{29} +(7174.99 + 719.659i) q^{30} +9851.28 q^{31} +(-5589.88 + 1519.12i) q^{32} +16377.1i q^{33} +(-103.641 - 1951.06i) q^{34} +(3523.93 + 4809.26i) q^{35} +(-939.016 - 8813.60i) q^{36} +(-4215.21 - 4215.21i) q^{37} +(-10127.1 - 9105.43i) q^{38} +15420.3i q^{39} +(-7199.46 - 7111.10i) q^{40} +2726.90i q^{41} +(9198.45 - 10230.5i) q^{42} +(-1660.98 - 1660.98i) q^{43} +(14437.8 - 17881.1i) q^{44} +(12489.8 - 9151.75i) q^{45} +(-9985.04 + 530.411i) q^{46} +9102.04i q^{47} +(-12661.8 + 19619.4i) q^{48} -5431.94 q^{49} +(4424.96 - 17114.9i) q^{50} +(-5569.12 - 5569.12i) q^{51} +(13594.2 - 16836.4i) q^{52} +(-9650.20 - 9650.20i) q^{53} +(-3259.82 - 2930.96i) q^{54} +(39679.1 + 6120.24i) q^{55} +(-19062.2 + 3060.84i) q^{56} -54897.5 q^{57} +(22193.3 + 19954.4i) q^{58} +(-23709.2 + 23709.2i) q^{59} +(-40746.7 - 1912.26i) q^{60} +(20219.1 + 20219.1i) q^{61} +(-55648.8 + 2956.09i) q^{62} -29541.4i q^{63} +(31120.8 - 10258.7i) q^{64} +(37360.8 + 5762.66i) q^{65} +(-4914.31 - 92512.5i) q^{66} +(35679.2 - 35679.2i) q^{67} +(1170.92 + 10990.2i) q^{68} +(-28501.4 + 28501.4i) q^{69} +(-21349.4 - 26109.6i) q^{70} -29193.4i q^{71} +(7949.11 + 49505.3i) q^{72} +11534.8 q^{73} +(25076.1 + 22546.4i) q^{74} +(-32863.6 - 63229.4i) q^{75} +(59939.0 + 48396.7i) q^{76} +(54163.2 - 54163.2i) q^{77} +(-4627.19 - 87107.4i) q^{78} -41167.8 q^{79} +(42802.8 + 38009.5i) q^{80} +49636.0 q^{81} +(-818.266 - 15403.9i) q^{82} +(-17752.6 + 17752.6i) q^{83} +(-48891.1 + 60551.3i) q^{84} +(-15574.3 + 11411.9i) q^{85} +(9881.08 + 8884.25i) q^{86} +120307. q^{87} +(-76191.9 + 105341. i) q^{88} +90461.0i q^{89} +(-67807.4 + 55445.1i) q^{90} +(50998.7 - 50998.7i) q^{91} +(56245.2 - 5992.46i) q^{92} +(-158845. + 158845. i) q^{93} +(-2731.27 - 51416.4i) q^{94} +(-20515.6 + 133008. i) q^{95} +(65638.0 - 114627. i) q^{96} +65282.8i q^{97} +(30684.4 - 1629.97i) q^{98} +(-140664. - 140664. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.64889	+	0.300072i	−0.998592	+	0.0530457i
$2$	−5.64889	+	0.300072i	−0.998592	+	0.0530457i
$3$	−16.1243	+	16.1243i	−1.03437	+	1.03437i	−0.0349842	+	0.999388i	$0.511138\pi$
$3$	−16.1243	+	16.1243i	−1.03437	+	1.03437i	−0.999388	+	0.0349842i	$0.988862\pi$
$4$	31.8199	−	3.39015i	0.994372	−	0.105942i
$5$	33.0407	+	45.0922i	0.591051	+	0.806634i
$5$	33.0407	+	45.0922i	0.591051	+	0.806634i
$6$	86.2458	−	95.9226i	0.978047	−	1.08778i
$7$	106.654			0.822682			0.411341	−	0.911482i	$-0.365061\pi$
$7$	106.654			0.822682			0.411341	+	0.911482i	$0.365061\pi$
$8$	−178.730	+	28.6988i	−0.987353	+	0.158540i
$9$		−	276.984i		−	1.13985i
$10$	−200.174	−	244.806i	−0.633007	−	0.774146i
$11$	507.841	−	507.841i	1.26545	−	1.26545i	0.317040	−	0.948412i	$-0.397311\pi$
$11$	507.841	−	507.841i	1.26545	−	1.26545i	0.948412	−	0.317040i	$-0.102689\pi$
$12$	−458.409	+	567.736i	−0.918967	+	1.13813i
$13$	478.170	−	478.170i	0.784736	−	0.784736i	−0.195890	−	0.980626i	$-0.562760\pi$
$13$	478.170	−	478.170i	0.784736	−	0.784736i	0.980626	+	0.195890i	$0.0627595\pi$
$14$	−602.476	+	32.0039i	−0.821523	+	0.0436398i
$15$	−1259.84	−	194.321i	−1.44573	−	0.222994i
$16$	1001.01	−	215.748i	0.977553	−	0.210692i
$17$			345.388i			0.289858i	0.989442	+	0.144929i	$0.0462953\pi$
$17$			345.388i			0.289858i	−0.989442	+	0.144929i	$0.953705\pi$
$18$	83.1151	+	1564.65i	0.0604643	+	1.13825i
$19$	1702.33	+	1702.33i	1.08183	+	1.08183i	0.996339	+	0.0854897i	$0.0272455\pi$
$19$	1702.33	+	1702.33i	1.08183	+	1.08183i	0.0854897	+	0.996339i	$0.472755\pi$
$20$	1204.22	+	1322.82i	0.673181	+	0.739478i
$21$	−1719.72	+	1719.72i	−0.850959	+	0.850959i
$22$	−2716.35	+	3021.12i	−1.19654	+	1.33080i
$23$	1767.61			0.696734			0.348367	−	0.937358i	$-0.386736\pi$
$23$	1767.61			0.696734			0.348367	+	0.937358i	$0.386736\pi$
$24$	2419.14	−	3344.64i	0.857300	−	1.18528i
$25$	−941.619	+	2979.76i	−0.301318	+	0.953524i
$26$	−2557.64	+	2844.61i	−0.742004	+	0.825258i
$27$	547.964	+	547.964i	0.144658	+	0.144658i
$28$	3393.72	−	361.573i	0.818052	−	0.0871567i
$29$	−3730.61	−	3730.61i	−0.823730	−	0.823730i	0.162911	−	0.986641i	$-0.447912\pi$
$29$	−3730.61	−	3730.61i	−0.823730	−	0.823730i	−0.986641	+	0.162911i	$0.947912\pi$
$30$	7174.99	+	719.659i	1.45552	+	0.145990i
$31$	9851.28			1.84115			0.920574	−	0.390569i	$-0.127722\pi$
$31$	9851.28			1.84115			0.920574	+	0.390569i	$0.127722\pi$
$32$	−5589.88	+	1519.12i	−0.965000	+	0.262250i
$33$			16377.1i			2.61790i
$34$	−103.641	−	1951.06i	−0.0153757	−	0.289449i
$35$	3523.93	+	4809.26i	0.486247	+	0.663603i
$36$	−939.016	−	8813.60i	−0.120758	−	1.13344i
$37$	−4215.21	−	4215.21i	−0.506191	−	0.506191i	0.407164	−	0.913355i	$-0.366518\pi$
$37$	−4215.21	−	4215.21i	−0.506191	−	0.506191i	−0.913355	+	0.407164i	$0.866518\pi$
$38$	−10127.1	−	9105.43i	−1.13769	−	1.02292i
$39$			15420.3i			1.62342i
$40$	−7199.46	−	7111.10i	−0.711459	−	0.702727i
$41$			2726.90i			0.253343i	0.991945	+	0.126672i	$0.0404294\pi$
$41$			2726.90i			0.253343i	−0.991945	+	0.126672i	$0.959571\pi$
$42$	9198.45	−	10230.5i	0.804621	−	0.894901i
$43$	−1660.98	−	1660.98i	−0.136991	−	0.136991i	0.635286	−	0.772277i	$-0.280882\pi$
$43$	−1660.98	−	1660.98i	−0.136991	−	0.136991i	−0.772277	+	0.635286i	$0.780882\pi$
$44$	14437.8	−	17881.1i	1.12427	−	1.39240i
$45$	12489.8	−	9151.75i	0.919443	−	0.673710i
$46$	−9985.04	+	530.411i	−0.695753	+	0.0369588i
$47$			9102.04i			0.601027i	0.953778	+	0.300513i	$0.0971580\pi$
$47$			9102.04i			0.601027i	−0.953778	+	0.300513i	$0.902842\pi$
$48$	−12661.8	+	19619.4i	−0.793219	+	1.22909i
$49$	−5431.94			−0.323195
$50$	4424.96	−	17114.9i	0.250313	−	0.968165i
$51$	−5569.12	−	5569.12i	−0.299821	−	0.299821i
$52$	13594.2	−	16836.4i	0.697183	−	0.863456i
$53$	−9650.20	−	9650.20i	−0.471896	−	0.471896i	0.430632	−	0.902528i	$-0.358291\pi$
$53$	−9650.20	−	9650.20i	−0.471896	−	0.471896i	−0.902528	+	0.430632i	$0.858291\pi$
$54$	−3259.82	−	2930.96i	−0.152128	−	0.136781i
$55$	39679.1	+	6120.24i	1.76870	+	0.272811i
$56$	−19062.2	+	3060.84i	−0.812277	+	0.130428i
$57$	−54897.5			−2.23803
$58$	22193.3	+	19954.4i	0.866266	+	0.778875i
$59$	−23709.2	+	23709.2i	−0.886720	+	0.886720i	−0.994207	−	0.107487i	$-0.965720\pi$
$59$	−23709.2	+	23709.2i	−0.886720	+	0.886720i	0.107487	+	0.994207i	$0.465720\pi$
$60$	−40746.7	−	1912.26i	−1.46121	−	0.0685754i
$61$	20219.1	+	20219.1i	0.695724	+	0.695724i	0.963485	−	0.267761i	$-0.0862839\pi$
$61$	20219.1	+	20219.1i	0.695724	+	0.695724i	−0.267761	+	0.963485i	$0.586284\pi$
$62$	−55648.8	+	2956.09i	−1.83856	+	0.0976650i
$63$		−	29541.4i		−	0.937735i
$64$	31120.8	−	10258.7i	0.949730	−	0.313070i
$65$	37360.8	+	5762.66i	1.09681	+	0.169176i
$66$	−4914.31	−	92512.5i	−0.138868	−	2.61421i
$67$	35679.2	−	35679.2i	0.971019	−	0.971019i	−0.0285729	−	0.999592i	$-0.509096\pi$
$67$	35679.2	−	35679.2i	0.971019	−	0.971019i	0.999592	+	0.0285729i	$0.00909628\pi$
$68$	1170.92	+	10990.2i	0.0307081	+	0.288226i
$69$	−28501.4	+	28501.4i	−0.720682	+	0.720682i
$70$	−21349.4	−	26109.6i	−0.520763	−	0.636876i
$71$		−	29193.4i		−	0.687289i	−0.939100	−	0.343644i	$-0.888338\pi$
$71$		−	29193.4i		−	0.687289i	0.939100	−	0.343644i	$-0.111662\pi$
$72$	7949.11	+	49505.3i	0.180712	+	1.12543i
$73$	11534.8			0.253339			0.126669	−	0.991945i	$-0.459571\pi$
$73$	11534.8			0.253339			0.126669	+	0.991945i	$0.459571\pi$
$74$	25076.1	+	22546.4i	0.532330	+	0.478627i
$75$	−32863.6	−	63229.4i	−0.674623	−	1.29797i
$76$	59939.0	+	48396.7i	1.19035	+	0.961129i
$77$	54163.2	−	54163.2i	1.04106	−	1.04106i
$78$	−4627.19	−	87107.4i	−0.0861154	−	1.62113i
$79$	−41167.8			−0.742146			−0.371073	−	0.928604i	$-0.621010\pi$
$79$	−41167.8			−0.742146			−0.371073	+	0.928604i	$0.621010\pi$
$80$	42802.8	+	38009.5i	0.747734	+	0.663998i
$81$	49636.0			0.840591
$82$	−818.266	−	15403.9i	−0.0134388	−	0.252987i
$83$	−17752.6	+	17752.6i	−0.282857	+	0.282857i	−0.834247	−	0.551391i	$-0.814097\pi$
$83$	−17752.6	+	17752.6i	−0.282857	+	0.282857i	0.551391	+	0.834247i	$0.314097\pi$
$84$	−48891.1	+	60551.3i	−0.756018	+	0.936322i
$85$	−15574.3	+	11411.9i	−0.233809	+	0.171321i
$86$	9881.08	+	8884.25i	0.144065	+	0.129531i
$87$	120307.			1.70409
$88$	−76191.9	+	105341.i	−1.04882	+	1.45007i
$89$			90461.0i			1.21056i	0.796013	+	0.605280i	$0.206939\pi$
$89$			90461.0i			1.21056i	−0.796013	+	0.605280i	$0.793061\pi$
$90$	−67807.4	+	55445.1i	−0.882411	+	0.721534i
$91$	50998.7	−	50998.7i	0.645588	−	0.645588i
$92$	56245.2	−	5992.46i	0.692813	−	0.0738135i
$93$	−158845.	+	158845.i	−1.90443	+	1.90443i
$94$	−2731.27	−	51416.4i	−0.0318819	−	0.600181i
$95$	−20515.6	+	133008.i	−0.233225	+	1.51206i
$96$	65638.0	−	114627.i	0.726905	−	1.26943i
$97$			65282.8i			0.704481i	0.935909	+	0.352241i	$0.114580\pi$
$97$			65282.8i			0.704481i	−0.935909	+	0.352241i	$0.885420\pi$
$98$	30684.4	−	1629.97i	0.322740	−	0.0171441i
$99$	−140664.	−	140664.i	−1.44243	−	1.44243i
$100$	−19860.4	+	98008.0i	−0.198604	+	0.980080i
$101$	19875.6	−	19875.6i	0.193872	−	0.193872i	−0.603495	−	0.797367i	$-0.706226\pi$
$101$	19875.6	−	19875.6i	0.193872	−	0.193872i	0.797367	+	0.603495i	$0.206226\pi$
$102$	33130.5	+	29788.2i	0.315303	+	0.283494i
$103$	92076.8			0.855179			0.427590	−	0.903973i	$-0.359363\pi$
$103$	92076.8			0.855179			0.427590	+	0.903973i	$0.359363\pi$
$104$	−71740.3	+	99186.1i	−0.650399	+	0.899223i
$105$	−134367.	−	20725.1i	−1.18937	−	0.183453i
$106$	57408.7	+	51617.2i	0.496264	+	0.446200i
$107$	77619.1	+	77619.1i	0.655404	+	0.655404i	0.954289	−	0.298885i	$-0.0966147\pi$
$107$	77619.1	+	77619.1i	0.655404	+	0.655404i	−0.298885	+	0.954289i	$0.596615\pi$
$108$	19293.8	+	15578.5i	0.159169	+	0.128519i
$109$	−58363.6	−	58363.6i	−0.470518	−	0.470518i	0.431564	−	0.902082i	$-0.357962\pi$
$109$	−58363.6	−	58363.6i	−0.470518	−	0.470518i	−0.902082	+	0.431564i	$0.857962\pi$
$110$	−225979.	−	22666.0i	−1.78068	−	0.178604i
$111$	135934.			1.04718
$112$	106762.	−	23010.4i	0.804215	−	0.173332i
$113$			27760.2i			0.204516i	0.994758	+	0.102258i	$0.0326067\pi$
$113$			27760.2i			0.204516i	−0.994758	+	0.102258i	$0.967393\pi$
$114$	310110.	−	16473.2i	2.23488	−	0.118718i
$115$	58403.2	+	79705.5i	0.411805	+	0.562010i
$116$	−131355.	−	106060.i	−0.906362	−	0.731827i
$117$	−132445.	−	132445.i	−0.894482	−	0.894482i
$118$	126816.	−	141045.i	0.838435	−	0.932508i
$119$			36837.0i			0.238461i
$120$	230747.	−	1424.80i	1.46280	−	0.00903237i
$121$		−	354753.i		−	2.20274i
$122$	−120283.	−	108148.i	−0.731649	−	0.657839i
$123$	−43969.2	−	43969.2i	−0.262051	−	0.262051i
$124$	313467.	−	33397.3i	1.83079	−	0.195055i
$125$	−165476.	+	55993.8i	−0.947239	+	0.320527i
$126$	8864.55	+	166876.i	0.0497428	+	0.936414i
$127$		−	106682.i		−	0.586925i	−0.955971	−	0.293463i	$-0.905192\pi$
$127$		−	106682.i		−	0.586925i	0.955971	−	0.293463i	$-0.0948077\pi$
$128$	−172719.	+	67288.6i	−0.931786	+	0.363008i
$129$	53564.0			0.283399
$130$	−212776.	−	21341.7i	−1.10424	−	0.110757i
$131$	−177951.	−	177951.i	−0.905985	−	0.905985i	0.0899603	−	0.995945i	$-0.471326\pi$
$131$	−177951.	−	177951.i	−0.905985	−	0.905985i	−0.995945	+	0.0899603i	$0.971326\pi$
$132$	55520.8	+	521118.i	0.277346	+	2.60316i
$133$	181560.	+	181560.i	0.890001	+	0.890001i
$134$	−190841.	+	212254.i	−0.918143	+	1.02116i
$135$	−6603.78	+	42814.1i	−0.0311859	+	0.202186i
$136$	−9912.23	−	61731.1i	−0.0459541	−	0.286192i
$137$	−42919.9			−0.195370			−0.0976848	−	0.995217i	$-0.531144\pi$
$137$	−42919.9			−0.195370			−0.0976848	+	0.995217i	$0.531144\pi$
$138$	152449.	−	169554.i	0.681438	−	0.757897i
$139$	67513.6	−	67513.6i	0.296384	−	0.296384i	−0.543212	−	0.839596i	$-0.682792\pi$
$139$	67513.6	−	67513.6i	0.296384	−	0.296384i	0.839596	+	0.543212i	$0.182792\pi$
$140$	128435.	+	141084.i	0.553814	+	0.608355i
$141$	−146764.	−	146764.i	−0.621685	−	0.621685i
$142$	8760.13	+	164911.i	0.0364578	+	0.686321i
$143$		−	485668.i		−	1.98609i
$144$	−59758.8	−	277265.i	−0.240157	−	1.11426i
$145$	44959.4	−	291484.i	0.177583	−	1.15132i
$146$	−65158.6	+	3461.26i	−0.252982	+	0.0134385i
$147$	87586.0	−	87586.0i	0.334304	−	0.334304i
$148$	−148418.	−	119837.i	−0.556970	−	0.449716i
$149$	−111062.	+	111062.i	−0.409826	+	0.409826i	−0.881678	−	0.471852i	$-0.843586\pi$
$149$	−111062.	+	111062.i	−0.409826	+	0.409826i	0.471852	+	0.881678i	$0.343586\pi$
$150$	204616.	+	347314.i	0.742525	+	1.26036i
$151$			450545.i			1.60804i	0.594605	+	0.804018i	$0.297309\pi$
$151$			450545.i			1.60804i	−0.594605	+	0.804018i	$0.702691\pi$
$152$	−353111.	−	255402.i	−1.23966	−	0.896633i
$153$	95666.8			0.330394
$154$	−289709.	+	322215.i	−0.984375	+	1.09482i
$155$	325494.	+	444216.i	1.08821	+	1.48513i
$156$	52277.0	+	490672.i	0.171988	+	1.61428i
$157$	44772.2	−	44772.2i	0.144964	−	0.144964i	−0.630900	−	0.775864i	$-0.717314\pi$
$157$	44772.2	−	44772.2i	0.144964	−	0.144964i	0.775864	+	0.630900i	$0.217314\pi$
$158$	232552.	−	12353.3i	0.741102	−	0.0393677i
$159$	311205.			0.976233
$160$	−253194.	−	201867.i	−0.781904	−	0.623399i
$161$	188523.			0.573190
$162$	−280388.	+	14894.4i	−0.839407	+	0.0445898i
$163$	360485.	−	360485.i	1.06272	−	1.06272i	0.0648203	−	0.997897i	$-0.479353\pi$
$163$	360485.	−	360485.i	1.06272	−	1.06272i	0.997897	−	0.0648203i	$-0.0206474\pi$
$164$	9244.59	+	86769.7i	0.0268397	+	0.251917i
$165$	−738481.	+	541112.i	−2.11169	+	1.54731i
$166$	94955.3	−	105609.i	0.267454	−	0.297463i
$167$	−446604.			−1.23917			−0.619586	−	0.784929i	$-0.712700\pi$
$167$	−446604.			−1.23917			−0.619586	+	0.784929i	$0.712700\pi$
$168$	258011.	−	356719.i	0.705285	−	0.975108i
$169$		−	85999.4i		−	0.231621i
$170$	84553.2	−	69137.8i	0.224392	−	0.183482i
$171$	471517.	−	471517.i	1.23312	−	1.23312i
$172$	−58483.0	−	47221.1i	−0.150733	−	0.121707i
$173$	−125328.	+	125328.i	−0.318370	+	0.318370i	−0.848141	−	0.529771i	$-0.822278\pi$
$173$	−125328.	+	125328.i	−0.318370	+	0.318370i	0.529771	+	0.848141i	$0.322278\pi$
$174$	−679599.	+	36100.7i	−1.70169	+	0.0903945i
$175$	−100427.	+	317803.i	−0.247889	+	0.784446i
$176$	398790.	−	617921.i	0.970426	−	1.50367i
$177$		−	764586.i		−	1.83440i
$178$	−27144.8	−	511004.i	−0.0642151	−	1.20886i
$179$	−141618.	−	141618.i	−0.330359	−	0.330359i	0.522364	−	0.852723i	$-0.325050\pi$
$179$	−141618.	−	141618.i	−0.330359	−	0.330359i	−0.852723	+	0.522364i	$0.825050\pi$
$180$	366399.	−	333550.i	0.842894	−	0.767326i
$181$	140546.	−	140546.i	0.318877	−	0.318877i	−0.529459	−	0.848336i	$-0.677605\pi$
$181$	140546.	−	140546.i	0.318877	−	0.318877i	0.848336	+	0.529459i	$0.177605\pi$
$182$	−272783.	+	303389.i	−0.610433	+	0.678925i
$183$	−652036.			−1.43927
$184$	−315925.	+	50728.4i	−0.687922	+	0.110460i
$185$	50799.5	−	329347.i	0.109127	−	0.707496i
$186$	849631.	−	944961.i	1.80073	−	2.00277i
$187$	175402.	+	175402.i	0.366801	+	0.366801i
$188$	30857.3	+	289626.i	0.0636741	+	0.597645i
$189$	58442.5	+	58442.5i	0.119008	+	0.119008i
$190$	75978.2	−	757502.i	0.152688	−	1.52230i
$191$	−188620.			−0.374114			−0.187057	−	0.982349i	$-0.559895\pi$
$191$	−188620.			−0.374114			−0.187057	+	0.982349i	$0.559895\pi$
$192$	−336386.	+	667213.i	−0.658543	+	1.30621i
$193$			545101.i			1.05338i	0.850058	+	0.526688i	$0.176567\pi$
$193$			545101.i			1.05338i	−0.850058	+	0.526688i	$0.823433\pi$
$194$	−19589.5	−	368775.i	−0.0373697	−	0.703489i
$195$	−695334.	+	509497.i	−1.30950	+	0.959522i
$196$	−172844.	+	18415.1i	−0.321376	+	0.0342399i
$197$	321818.	+	321818.i	0.590806	+	0.590806i	0.937849	−	0.347043i	$-0.112814\pi$
$197$	321818.	+	321818.i	0.590806	+	0.590806i	−0.347043	+	0.937849i	$0.612814\pi$
$198$	836803.	+	752384.i	1.51691	+	1.36388i
$199$			848271.i			1.51846i	0.650825	+	0.759228i	$0.274423\pi$
$199$			848271.i			1.51846i	−0.650825	+	0.759228i	$0.725577\pi$
$200$	82779.7	−	559596.i	0.146335	−	0.989235i
$201$			1.15060e6i			2.00879i
$202$	−106311.	+	118239.i	−0.183315	+	0.203884i
$203$	−397884.	−	397884.i	−0.677668	−	0.677668i
$204$	−196089.	−	158329.i	−0.329897	−	0.266370i
$205$	−122962.	+	90098.7i	−0.204355	+	0.149739i
$206$	−520132.	+	27629.7i	−0.853975	+	0.0453636i
$207$		−	489600.i		−	0.794173i
$208$	375490.	−	581819.i	0.601783	−	0.932458i
$209$	1.72902e6			2.73801
$210$	765241.	+	76754.4i	1.19743	+	0.120103i
$211$	−656915.	−	656915.i	−1.01579	−	1.01579i	−0.999873	−	0.0159151i	$-0.994934\pi$
$211$	−656915.	−	656915.i	−1.01579	−	1.01579i	−0.0159151	−	0.999873i	$-0.505066\pi$
$212$	−339784.	−	274353.i	−0.519234	−	0.419247i
$213$	470723.	+	470723.i	0.710912	+	0.710912i
$214$	−461753.	−	415170.i	−0.689248	−	0.619715i
$215$	20017.2	−	129777.i	0.0295330	−	0.191470i
$216$	−113663.	−	82211.6i	−0.165763	−	0.119894i
$217$	1.05068e6			1.51468
$218$	347203.	+	312176.i	0.494814	+	0.444896i
$219$	−185989.	+	185989.i	−0.262046	+	0.262046i
$220$	1.28333e6	+	60227.4i	1.78765	+	0.0838953i
$221$	165154.	+	165154.i	0.227462	+	0.227462i
$222$	−767878.	+	40790.1i	−1.04571	+	0.0555485i
$223$			1.29876e6i			1.74891i	0.485105	+	0.874456i	$0.338781\pi$
$223$			1.29876e6i			1.74891i	−0.485105	+	0.874456i	$0.661219\pi$
$224$	−596182.	+	162020.i	−0.793888	+	0.215748i
$225$	825346.	+	260813.i	1.08688	+	0.343458i
$226$	−8330.06	−	156814.i	−0.0108487	−	0.204228i
$227$	−165088.	+	165088.i	−0.212643	+	0.212643i	−0.805389	−	0.592746i	$-0.798044\pi$
$227$	−165088.	+	165088.i	−0.212643	+	0.212643i	0.592746	+	0.805389i	$0.298044\pi$
$228$	−1.74683e6	+	186111.i	−2.22543	+	0.237101i
$229$	−128962.	+	128962.i	−0.162508	+	0.162508i	−0.783677	−	0.621169i	$-0.786658\pi$
$229$	−128962.	+	128962.i	−0.162508	+	0.162508i	0.621169	+	0.783677i	$0.286658\pi$
$230$	−353830.	−	432723.i	−0.441038	−	0.539374i
$231$			1.74668e6i			2.15370i
$232$	773836.	+	559707.i	0.943906	+	0.682718i
$233$	−157099.			−0.189576			−0.0947882	−	0.995497i	$-0.530217\pi$
$233$	−157099.			−0.189576			−0.0947882	+	0.995497i	$0.530217\pi$
$234$	787912.	+	708425.i	0.940671	+	0.845774i
$235$	−410431.	+	300738.i	−0.484809	+	0.355237i
$236$	−674046.	+	834802.i	−0.787789	+	0.975671i
$237$	663800.	−	663800.i	0.767656	−	0.767656i
$238$	−11053.7	−	208088.i	−0.0126493	−	0.238125i
$239$	108661.			0.123049			0.0615245	−	0.998106i	$-0.480404\pi$
$239$	108661.			0.123049			0.0615245	+	0.998106i	$0.480404\pi$
$240$	−1.30304e6	+	77289.4i	−1.46026	+	0.0866147i
$241$	−1.27264e6			−1.41145			−0.705724	−	0.708487i	$-0.749378\pi$
$241$	−1.27264e6			−1.41145			−0.705724	+	0.708487i	$0.749378\pi$
$242$	106452.	+	2.00396e6i	0.116846	+	2.19964i
$243$	−933500.	+	933500.i	−1.01414	+	1.01414i
$244$	711915.	+	574824.i	0.765515	+	0.618102i
$245$	−179475.	−	244938.i	−0.191025	−	0.260700i
$246$	261571.	+	235183.i	0.275583	+	0.247781i
$247$	1.62800e6			1.69790
$248$	−1.76072e6	+	282720.i	−1.81786	+	0.291896i
$249$		−	572495.i		−	0.585158i
$250$	917953.	−	365958.i	0.928903	−	0.370323i
$251$	−66016.5	+	66016.5i	−0.0661406	+	0.0661406i	−0.739403	−	0.673263i	$-0.764892\pi$
$251$	−66016.5	+	66016.5i	−0.0661406	+	0.0661406i	0.673263	+	0.739403i	$0.264892\pi$
$252$	−100150.	−	940005.i	−0.0993456	−	0.932457i
$253$	897665.	−	897665.i	0.881684	−	0.881684i
$254$	32012.4	+	602636.i	0.0311339	+	0.586099i
$255$	67116.2	−	435132.i	0.0646364	−	0.419055i
$256$	955481.	−	431934.i	0.911218	−	0.411925i
$257$		−	1.74381e6i		−	1.64690i	−0.567390	−	0.823449i	$-0.692047\pi$
$257$		−	1.74381e6i		−	1.64690i	0.567390	−	0.823449i	$-0.307953\pi$
$258$	−302577.	+	16073.1i	−0.283000	+	0.0150331i
$259$	−449569.	−	449569.i	−0.416434	−	0.416434i
$260$	1.20835e6	+	56708.6i	1.10856	+	0.0520254i
$261$	−1.03332e6	+	1.03332e6i	−0.938930	+	0.938930i
$262$	1.05862e6	+	951825.i	0.952768	+	0.856651i
$263$	724361.			0.645752			0.322876	−	0.946441i	$-0.395350\pi$
$263$	724361.			0.645752			0.322876	+	0.946441i	$0.395350\pi$
$264$	−470004.	−	2.92708e6i	−0.415042	−	2.58479i
$265$	116299.	−	753999.i	0.101733	−	0.659562i
$266$	−1.08009e6	−	971130.i	−0.935958	−	0.841537i
$267$	−1.45862e6	−	1.45862e6i	−1.25217	−	1.25217i
$268$	1.01435e6	−	1.25627e6i	0.862682	−	1.06843i
$269$	352734.	+	352734.i	0.297213	+	0.297213i	0.839921	−	0.542709i	$-0.182601\pi$
$269$	352734.	+	352734.i	0.297213	+	0.297213i	−0.542709	+	0.839921i	$0.682601\pi$
$270$	24456.7	−	243834.i	0.0204169	−	0.203556i
$271$	1.98947e6			1.64556			0.822779	−	0.568361i	$-0.192422\pi$
$271$	1.98947e6			1.64556			0.822779	+	0.568361i	$0.192422\pi$
$272$	74516.9	+	345738.i	0.0610706	+	0.283351i
$273$			1.64463e6i			1.33556i
$274$	242450.	−	12879.1i	0.195095	−	0.0103635i
$275$	1.03505e6	+	1.99144e6i	0.825335	+	1.58794i
$276$	−810289.	+	1.00354e6i	−0.640276	+	0.792977i
$277$	−307696.	−	307696.i	−0.240948	−	0.240948i	0.576294	−	0.817242i	$-0.304498\pi$
$277$	−307696.	−	307696.i	−0.240948	−	0.240948i	−0.817242	+	0.576294i	$0.804498\pi$
$278$	−361118.	+	401636.i	−0.280245	+	0.311688i
$279$		−	2.72865e6i		−	2.09863i
$280$	−767851.	−	758427.i	−0.585305	−	0.578121i
$281$		−	1.74500e6i		−	1.31834i	−0.751992	−	0.659172i	$-0.770907\pi$
$281$		−	1.74500e6i		−	1.31834i	0.751992	−	0.659172i	$-0.229093\pi$
$282$	873091.	+	785012.i	0.653788	+	0.587832i
$283$	−1.53254e6	−	1.53254e6i	−1.13748	−	1.13748i	−0.988900	−	0.148582i	$-0.952529\pi$
$283$	−1.53254e6	−	1.53254e6i	−1.13748	−	1.13748i	−0.148582	−	0.988900i	$-0.547471\pi$
$284$	−98970.1	−	928933.i	−0.0728129	−	0.683421i
$285$	−1.81385e6	−	2.47545e6i	−1.32279	−	1.80527i
$286$	145735.	+	2.74348e6i	0.105354	+	1.98330i
$287$			290834.i			0.208421i
$288$	420770.	+	1.54831e6i	0.298926	+	1.09996i
$289$	1.30056e6			0.915983
$290$	−166505.	+	1.66005e6i	−0.116260	+	1.15911i
$291$	−1.05264e6	−	1.05264e6i	−0.728696	−	0.728696i
$292$	367035.	−	39104.5i	0.251913	−	0.0268392i
$293$	−539237.	−	539237.i	−0.366953	−	0.366953i	0.499412	−	0.866365i	$-0.333550\pi$
$293$	−539237.	−	539237.i	−0.366953	−	0.366953i	−0.866365	+	0.499412i	$0.833550\pi$
$294$	−468481.	+	521046.i	−0.316100	+	0.351566i
$295$	−1.85247e6	−	285731.i	−1.23936	−	0.191162i
$296$	874355.	+	632412.i	0.580041	+	0.419538i
$297$	556557.			0.366116
$298$	594049.	−	660702.i	0.387509	−	0.430988i
$299$	845218.	−	845218.i	0.546752	−	0.546752i
$300$	−1.26007e6	−	1.90054e6i	−0.808337	−	1.21920i
$301$	−177150.	−	177150.i	−0.112700	−	0.112700i
$302$	−135196.	−	2.54508e6i	−0.0852995	−	1.60577i
$303$			640958.i			0.401072i
$304$	2.07132e6	+	1.33678e6i	1.28548	+	0.829612i
$305$	−243670.	+	1.57978e6i	−0.149987	+	0.972403i
$306$	−540411.	+	28706.9i	−0.329929	+	0.0175260i
$307$	859969.	−	859969.i	0.520759	−	0.520759i	−0.397041	−	0.917801i	$-0.629963\pi$
$307$	859969.	−	859969.i	0.520759	−	0.520759i	0.917801	+	0.397041i	$0.129963\pi$
$308$	1.53985e6	−	1.90709e6i	0.924913	−	1.14550i
$309$	−1.48467e6	+	1.48467e6i	−0.884573	+	0.884573i
$310$	−1.97197e6	−	2.41166e6i	−1.16546	−	1.42532i
$311$			2.83767e6i			1.66364i	0.555043	+	0.831822i	$0.312702\pi$
$311$			2.83767e6i			1.66364i	−0.555043	+	0.831822i	$0.687298\pi$
$312$	−442544.	−	2.75606e6i	−0.257377	−	1.60289i
$313$	−944802.			−0.545104			−0.272552	−	0.962141i	$-0.587868\pi$
$313$	−944802.			−0.545104			−0.272552	+	0.962141i	$0.587868\pi$
$314$	−239478.	+	266348.i	−0.137070	+	0.152449i
$315$	1.33209e6	−	976070.i	0.756409	−	0.554249i
$316$	−1.30995e6	+	139565.i	−0.737970	+	0.0786246i
$317$	785638.	−	785638.i	0.439111	−	0.439111i	−0.452602	−	0.891713i	$-0.649504\pi$
$317$	785638.	−	785638.i	0.439111	−	0.439111i	0.891713	+	0.452602i	$0.149504\pi$
$318$	−1.75796e6	+	93383.8i	−0.974858	+	0.0517850i
$319$	−3.78911e6			−2.08478
$320$	1.49084e6	+	1.06435e6i	0.813872	+	0.581045i
$321$	−2.50310e6			−1.35586
$322$	−1.06494e6	+	56570.4i	−0.572383	+	0.0304053i
$323$	−587962.	+	587962.i	−0.313576	+	0.313576i
$324$	1.57941e6	−	168274.i	0.835860	−	0.0890540i
$325$	974578.	+	1.87508e6i	0.511809	+	0.984720i
$326$	−1.92817e6	+	2.14451e6i	−1.00485	+	1.11759i
$327$	1.88214e6			0.973381
$328$	−78258.8	−	487378.i	−0.0401651	−	0.250139i
$329$			970768.i			0.494454i
$330$	4.00922e6	−	3.27828e6i	2.02663	−	1.65715i
$331$	49123.4	−	49123.4i	0.0246444	−	0.0246444i	−0.694677	−	0.719322i	$-0.744453\pi$
$331$	49123.4	−	49123.4i	0.0246444	−	0.0246444i	0.719322	+	0.694677i	$0.244453\pi$
$332$	−504702.	+	625070.i	−0.251298	+	0.311231i
$333$	−1.16754e6	+	1.16754e6i	−0.576983	+	0.576983i
$334$	2.52282e6	−	134013.i	1.23743	−	0.0657328i
$335$	2.78772e6	+	429987.i	1.35718	+	0.209336i
$336$	−1.35043e6	+	2.09249e6i	−0.652567	+	1.01115i
$337$			1.86908e6i			0.896507i	0.893906	+	0.448254i	$0.147954\pi$
$337$			1.86908e6i			0.896507i	−0.893906	+	0.448254i	$0.852046\pi$
$338$	25806.0	+	485801.i	0.0122865	+	0.231295i
$339$	−447613.	−	447613.i	−0.211545	−	0.211545i
$340$	−456885.	+	415924.i	−0.214343	+	0.195127i
$341$	5.00288e6	−	5.00288e6i	2.32988	−	2.32988i
$342$	−2.52206e6	+	2.80503e6i	−1.16598	+	1.29680i
$343$	−2.37187e6			−1.08857
$344$	344534.	+	249198.i	0.156977	+	0.113540i
$345$	−2.22690e6	−	343485.i	−1.00729	−	0.155367i
$346$	670356.	−	745571.i	0.301034	−	0.334810i
$347$	283389.	+	283389.i	0.126346	+	0.126346i	0.767452	−	0.641106i	$-0.221524\pi$
$347$	283389.	+	283389.i	0.126346	+	0.126346i	−0.641106	+	0.767452i	$0.721524\pi$
$348$	3.82815e6	−	407858.i	1.69450	−	0.180535i
$349$	−921238.	−	921238.i	−0.404863	−	0.404863i	0.475080	−	0.879943i	$-0.342419\pi$
$349$	−921238.	−	921238.i	−0.404863	−	0.404863i	−0.879943	+	0.475080i	$0.842419\pi$
$350$	471939.	−	1.82537e6i	0.205928	−	0.796491i
$351$	524040.			0.227037
$352$	−2.06730e6	+	3.61024e6i	−0.889296	+	1.55303i
$353$		−	3.61698e6i		−	1.54493i	−0.635057	−	0.772465i	$-0.719023\pi$
$353$		−	3.61698e6i		−	1.54493i	0.635057	−	0.772465i	$-0.280977\pi$
$354$	229431.	+	4.31906e6i	0.0973069	+	1.83181i
$355$	1.31640e6	−	964573.i	0.554391	−	0.406223i
$356$	306676.	+	2.87846e6i	0.128249	+	1.20375i
$357$	−593969.	−	593969.i	−0.246657	−	0.246657i
$358$	842481.	+	757490.i	0.347418	+	0.312370i
$359$		−	897162.i		−	0.367396i	−0.982983	−	0.183698i	$-0.941193\pi$
$359$		−	897162.i		−	0.367396i	0.982983	−	0.183698i	$-0.0588069\pi$
$360$	−1.96966e6	+	1.99413e6i	−0.801004	+	0.810958i
$361$			3.31972e6i			1.34071i
$362$	−751757.	+	836105.i	−0.301513	+	0.335343i
$363$	5.72013e6	+	5.72013e6i	2.27845	+	2.27845i
$364$	1.44988e6	−	1.79567e6i	0.573560	−	0.710350i
$365$	381117.	+	520128.i	0.149736	+	0.204352i
$366$	3.68328e6	−	195658.i	1.43725	−	0.0763474i
$367$		−	2.06490e6i		−	0.800264i	−0.916458	−	0.400132i	$-0.868964\pi$
$367$		−	2.06490e6i		−	0.800264i	0.916458	−	0.400132i	$-0.131036\pi$
$368$	1.76940e6	−	381359.i	0.681094	−	0.146796i
$369$	755307.			0.288774
$370$	−188133.	+	1.87569e6i	−0.0714433	+	0.712289i
$371$	−1.02923e6	−	1.02923e6i	−0.388220	−	0.388220i
$372$	−4.51592e6	+	5.59293e6i	−1.69195	+	2.09547i
$373$	−2.11086e6	−	2.11086e6i	−0.785575	−	0.785575i	0.195191	−	0.980765i	$-0.437467\pi$
$373$	−2.11086e6	−	2.11086e6i	−0.785575	−	0.785575i	−0.980765	+	0.195191i	$0.937467\pi$
$374$	−1.04346e6	−	938193.i	−0.385742	−	0.346827i
$375$	1.76532e6	−	3.57104e6i	0.648253	−	1.31134i
$376$	−261218.	−	1.62681e6i	−0.0952869	−	0.593425i
$377$	−3.56773e6			−1.29282
$378$	−347672.	−	312598.i	−0.125153	−	0.112527i
$379$	−3.32981e6	+	3.32981e6i	−1.19075	+	1.19075i	−0.213896	+	0.976857i	$0.568615\pi$
$379$	−3.32981e6	+	3.32981e6i	−1.19075	+	1.19075i	−0.976857	+	0.213896i	$0.931385\pi$
$380$	−201887.	+	4.30185e6i	−0.0717216	+	1.52825i
$381$	1.72017e6	+	1.72017e6i	0.607099	+	0.607099i
$382$	1.06549e6	−	56599.5i	0.373587	−	0.0198451i
$383$		−	1.03056e6i		−	0.358984i	−0.983759	−	0.179492i	$-0.942555\pi$
$383$		−	1.03056e6i		−	0.358984i	0.983759	−	0.179492i	$-0.0574454\pi$
$384$	1.69999e6	−	3.86995e6i	0.588327	−	1.33930i
$385$	4.23193e6	+	652747.i	1.45508	+	0.224436i
$386$	−163570.	−	3.07922e6i	−0.0558772	−	1.05189i
$387$	−460063.	+	460063.i	−0.156149	+	0.156149i
$388$	221318.	+	2.07729e6i	0.0746342	+	0.700517i
$389$	139295.	−	139295.i	0.0466726	−	0.0466726i	−0.683385	−	0.730058i	$-0.739493\pi$
$389$	139295.	−	139295.i	0.0466726	−	0.0466726i	0.730058	+	0.683385i	$0.239493\pi$
$390$	3.77498e6	−	3.08674e6i	1.25676	−	1.02764i
$391$			610511.i			0.201954i
$392$	970849.	−	155890.i	0.319107	−	0.0512394i
$393$	5.73864e6			1.87425
$394$	−1.91448e6	−	1.72135e6i	−0.621314	−	0.558634i
$395$	−1.36021e6	−	1.85635e6i	−0.438646	−	0.598641i
$396$	−4.95278e6	−	3.99903e6i	−1.58712	−	1.28150i
$397$	−1.40764e6	+	1.40764e6i	−0.448244	+	0.448244i	−0.894770	−	0.446527i	$-0.852661\pi$
$397$	−1.40764e6	+	1.40764e6i	−0.448244	+	0.448244i	0.446527	+	0.894770i	$0.352661\pi$
$398$	−254543.	−	4.79179e6i	−0.0805476	−	1.51632i
$399$	−5.85503e6			−1.84118
$400$	−299695.	+	3.18594e6i	−0.0936546	+	0.995605i
$401$	−5.37790e6			−1.67014			−0.835068	−	0.550147i	$-0.814572\pi$
$401$	−5.37790e6			−1.67014			−0.835068	+	0.550147i	$0.814572\pi$
$402$	−345263.	−	6.49962e6i	−0.106558	−	2.00596i
$403$	4.71058e6	−	4.71058e6i	1.44481	−	1.44481i
$404$	565057.	−	699820.i	0.172242	−	0.213321i
$405$	1.64001e6	+	2.23820e6i	0.496832	+	0.678049i
$406$	2.36700e6	+	2.12821e6i	0.712661	+	0.640766i
$407$	−4.28131e6			−1.28112
$408$	1.15520e6	+	835542.i	0.343562	+	0.248495i
$409$		−	1.76714e6i		−	0.522353i	−0.965291	−	0.261176i	$-0.915890\pi$
$409$		−	1.76714e6i		−	0.522353i	0.965291	−	0.261176i	$-0.0841104\pi$
$410$	667562.	−	545855.i	0.196125	−	0.160368i
$411$	692051.	−	692051.i	0.202085	−	0.202085i
$412$	2.92988e6	−	312154.i	0.850367	−	0.0905995i
$413$	−2.52868e6	+	2.52868e6i	−0.729488	+	0.729488i
$414$	146915.	+	2.76569e6i	0.0421275	+	0.793055i
$415$	−1.38706e6	−	213945.i	−0.395345	−	0.0609793i
$416$	−1.94651e6	+	3.39930e6i	−0.551473	+	0.963067i
$417$			2.17722e6i			0.613142i
$418$	−9.76704e6	+	518831.i	−2.73415	+	0.145240i
$419$	1.53830e6	+	1.53830e6i	0.428061	+	0.428061i	0.887968	−	0.459906i	$-0.152117\pi$
$419$	1.53830e6	+	1.53830e6i	0.428061	+	0.428061i	−0.459906	+	0.887968i	$0.652117\pi$
$420$	−4.34579e6	−	203950.i	−1.20211	−	0.0564157i
$421$	−1.46939e6	+	1.46939e6i	−0.404047	+	0.404047i	−0.879657	−	0.475609i	$-0.842228\pi$
$421$	−1.46939e6	+	1.46939e6i	−0.404047	+	0.404047i	0.475609	+	0.879657i	$0.342228\pi$
$422$	3.90796e6	+	3.51372e6i	1.06824	+	0.960475i
$423$	2.52112e6			0.685081
$424$	2.00173e6	+	1.44783e6i	0.540743	+	0.391113i
$425$	−1.02917e6	−	325224.i	−0.276386	−	0.0873393i
$426$	−2.80031e6	−	2.51781e6i	−0.747622	−	0.672201i
$427$	2.15644e6	+	2.15644e6i	0.572359	+	0.572359i
$428$	2.73297e6	+	2.20669e6i	0.721151	+	0.582281i
$429$	7.83104e6	+	7.83104e6i	2.05436	+	2.05436i
$430$	−74132.7	+	739102.i	−0.0193348	+	0.192767i
$431$	1.73678e6			0.450350			0.225175	−	0.974318i	$-0.427705\pi$
$431$	1.73678e6			0.450350			0.225175	+	0.974318i	$0.427705\pi$
$432$	666742.	+	430297.i	0.171889	+	0.110933i
$433$		−	3.15065e6i		−	0.807572i	−0.914854	−	0.403786i	$-0.867694\pi$
$433$		−	3.15065e6i		−	0.807572i	0.914854	−	0.403786i	$-0.132306\pi$
$434$	−5.93516e6	+	315279.i	−1.51255	+	0.0803472i
$435$	3.97502e6	+	5.42490e6i	1.00720	+	1.37457i
$436$	−2.05499e6	−	1.65926e6i	−0.517717	−	0.418022i
$437$	3.00905e6	+	3.00905e6i	0.753747	+	0.753747i
$438$	994824.	−	1.10644e6i	0.247777	−	0.275578i
$439$		−	5.85460e6i		−	1.44989i	−0.688806	−	0.724946i	$-0.741865\pi$
$439$		−	5.85460e6i		−	1.44989i	0.688806	−	0.724946i	$-0.258135\pi$
$440$	−7.26749e6	+	44874.8i	−1.78959	+	0.0110502i
$441$			1.50456e6i			0.368394i
$442$	−982494.	−	883378.i	−0.239207	−	0.215076i
$443$	1.99689e6	+	1.99689e6i	0.483443	+	0.483443i	0.906229	−	0.422787i	$-0.138948\pi$
$443$	1.99689e6	+	1.99689e6i	0.483443	+	0.483443i	−0.422787	+	0.906229i	$0.638948\pi$
$444$	4.32542e6	−	460837.i	1.04129	−	0.110941i
$445$	−4.07909e6	+	2.98890e6i	−0.976479	+	0.715502i
$446$	−389723.	−	7.33657e6i	−0.0927723	−	1.74645i
$447$		−	3.58158e6i		−	0.847824i
$448$	3.31915e6	−	1.09413e6i	0.781325	−	0.257557i
$449$	3.70028e6			0.866201			0.433101	−	0.901346i	$-0.357419\pi$
$449$	3.70028e6			0.866201			0.433101	+	0.901346i	$0.357419\pi$
$450$	−4.74055e6	−	1.22564e6i	−1.10356	−	0.285320i
$451$	1.38483e6	+	1.38483e6i	0.320594	+	0.320594i
$452$	94111.2	+	883327.i	0.0216668	+	0.203365i
$453$	−7.26471e6	−	7.26471e6i	−1.66331	−	1.66331i
$454$	883026.	−	982103.i	0.201064	−	0.223623i
$455$	3.98468e6	+	614610.i	0.902329	+	0.139178i
$456$	9.81182e6	−	1.57549e6i	2.20972	−	0.354817i
$457$	−1.17955e6			−0.264196			−0.132098	−	0.991237i	$-0.542171\pi$
$457$	−1.17955e6			−0.264196			−0.132098	+	0.991237i	$0.542171\pi$
$458$	689796.	−	767192.i	0.153659	−	0.170899i
$459$	−189260.	+	189260.i	−0.0419302	+	0.0419302i
$460$	2.12860e6	+	2.33823e6i	0.469028	+	0.515219i
$461$	2.05756e6	+	2.05756e6i	0.450920	+	0.450920i	0.895660	−	0.444740i	$-0.146704\pi$
$461$	2.05756e6	+	2.05756e6i	0.450920	+	0.450920i	−0.444740	+	0.895660i	$0.646704\pi$
$462$	−524131.	−	9.86682e6i	−0.114244	−	2.15066i
$463$			7.30819e6i			1.58437i	0.610279	+	0.792187i	$0.291057\pi$
$463$			7.30819e6i			1.58437i	−0.610279	+	0.792187i	$0.708943\pi$
$464$	−4.53927e6	−	2.92952e6i	−0.978793	−	0.631686i
$465$	−1.24110e7	−	1.91432e6i	−2.66180	−	0.410564i
$466$	887436.	−	47141.1i	0.189310	−	0.0100562i
$467$	3.80558e6	−	3.80558e6i	0.807473	−	0.807473i	−0.176778	−	0.984251i	$-0.556567\pi$
$467$	3.80558e6	−	3.80558e6i	0.807473	−	0.807473i	0.984251	+	0.176778i	$0.0565673\pi$
$468$	−4.66341e6	−	3.76539e6i	−0.984212	−	0.794685i
$469$	3.80532e6	−	3.80532e6i	0.798839	−	0.798839i
$470$	2.22824e6	−	1.82199e6i	0.465283	−	0.380454i
$471$			1.44384e6i			0.299893i
$472$	3.55711e6	−	4.91796e6i	0.734924	−	1.01609i
$473$	−1.68702e6			−0.346711
$474$	−3.55055e6	+	3.94892e6i	−0.725854	+	0.807296i
$475$	−6.67546e6	+	3.46958e6i	−1.35752	+	0.705575i
$476$	124883.	+	1.17215e6i	0.0252630	+	0.237119i
$477$	−2.67295e6	+	2.67295e6i	−0.537892	+	0.537892i
$478$	−613812.	+	32606.0i	−0.122876	+	0.00652722i
$479$	2.15210e6			0.428571			0.214286	−	0.976771i	$-0.431258\pi$
$479$	2.15210e6			0.428571			0.214286	+	0.976771i	$0.431258\pi$
$480$	7.33753e6	−	827605.i	1.45361	−	0.163953i
$481$	−4.03117e6			−0.794453
$482$	7.18903e6	−	381885.i	1.40946	−	0.0748713i
$483$	−3.03979e6	+	3.03979e6i	−0.592892	+	0.592892i
$484$	−1.20267e6	−	1.12882e7i	−0.233363	−	2.19034i
$485$	−2.94375e6	+	2.15699e6i	−0.568259	+	0.416384i
$486$	4.99312e6	−	5.55335e6i	0.958918	−	1.06651i
$487$	−3.58426e6			−0.684821			−0.342410	−	0.939551i	$-0.611243\pi$
$487$	−3.58426e6			−0.684821			−0.342410	+	0.939551i	$0.611243\pi$
$488$	−4.19402e6	−	3.03349e6i	−0.797225	−	0.576624i
$489$			1.16251e7i			2.19849i
$490$	1.08733e6	+	1.32977e6i	0.204585	+	0.250200i
$491$	2.36369e6	−	2.36369e6i	0.442473	−	0.442473i	−0.450369	−	0.892842i	$-0.648708\pi$
$491$	2.36369e6	−	2.36369e6i	0.442473	−	0.442473i	0.892842	+	0.450369i	$0.148708\pi$
$492$	−1.54816e6	−	1.25003e6i	−0.288339	−	0.232814i
$493$	1.28851e6	−	1.28851e6i	0.238764	−	0.238764i
$494$	−9.19639e6	+	488517.i	−1.69551	+	0.0900664i
$495$	1.69521e6	−	1.09905e7i	0.310964	−	2.01606i
$496$	9.86127e6	−	2.12540e6i	1.79982	−	0.387915i
$497$		−	3.11360e6i		−	0.565420i
$498$	171790.	+	3.23396e6i	0.0310401	+	0.584334i
$499$	66435.0	+	66435.0i	0.0119439	+	0.0119439i	0.713054	−	0.701110i	$-0.247312\pi$
$499$	66435.0	+	66435.0i	0.0119439	+	0.0119439i	−0.701110	+	0.713054i	$0.747312\pi$
$500$	−5.07560e6	+	2.34271e6i	−0.907951	+	0.419076i
$501$	7.20117e6	−	7.20117e6i	1.28177	−	1.28177i
$502$	353110.	−	392729.i	0.0625390	−	0.0695559i
$503$	3.27183e6			0.576594			0.288297	−	0.957541i	$-0.406911\pi$
$503$	3.27183e6			0.576594			0.288297	+	0.957541i	$0.406911\pi$
$504$	847804.	+	5.27993e6i	0.148669	+	0.925875i
$505$	1.55294e6	+	239530.i	0.270973	+	0.0417957i
$506$	−4.80144e6	+	5.34017e6i	−0.833673	+	0.927212i
$507$	1.38668e6	+	1.38668e6i	0.239583	+	0.239583i
$508$	−361669.	−	3.39462e6i	−0.0621801	−	0.583622i
$509$	−2.09968e6	−	2.09968e6i	−0.359218	−	0.359218i	0.504307	−	0.863525i	$-0.331748\pi$
$509$	−2.09968e6	−	2.09968e6i	−0.359218	−	0.359218i	−0.863525	+	0.504307i	$0.831748\pi$
$510$	−248561.	+	2.47815e6i	−0.0423163	+	0.421893i
$511$	1.23023e6			0.208417
$512$	−5.26780e6	+	2.72666e6i	−0.888084	+	0.459681i
$513$			1.86563e6i			0.312991i
$514$	523269.	+	9.85060e6i	0.0873609	+	1.64458i
$515$	3.04229e6	+	4.15195e6i	0.505454	+	0.689817i
$516$	1.70440e6	−	181590.i	0.281804	−	0.0300239i
$517$	4.62238e6	+	4.62238e6i	0.760571	+	0.760571i
$518$	2.67447e6	+	2.40466e6i	0.437938	+	0.393758i
$519$		−	4.04164e6i		−	0.658627i
$520$	−6.84288e6	+	42252.9i	−1.10976	+	0.00685249i
$521$		−	716199.i		−	0.115595i	−0.998328	−	0.0577975i	$-0.981592\pi$
$521$		−	716199.i		−	0.115595i	0.998328	−	0.0577975i	$-0.0184078\pi$
$522$	5.52703e6	−	6.14717e6i	0.887801	−	0.987414i
$523$	−8.61633e6	−	8.61633e6i	−1.37742	−	1.37742i	−0.848947	−	0.528478i	$-0.822763\pi$
$523$	−8.61633e6	−	8.61633e6i	−1.37742	−	1.37742i	−0.528478	−	0.848947i	$-0.677237\pi$
$524$	−6.26565e6	−	5.05909e6i	−0.996868	−	0.804904i
$525$	−3.50503e6	−	6.74366e6i	−0.555000	−	1.06782i
$526$	−4.09183e6	+	217360.i	−0.644843	+	0.0342544i
$527$			3.40251e6i			0.533670i
$528$	3.53334e6	+	1.63937e7i	0.551569	+	2.55913i
$529$	−3.31190e6			−0.514562
$530$	−430708.	+	4.29415e6i	−0.0666029	+	0.664030i
$531$	6.56706e6	+	6.56706e6i	1.01073	+	1.01073i
$532$	6.39273e6	+	5.16170e6i	0.979281	+	0.790703i
$533$	1.30392e6	+	1.30392e6i	0.198808	+	0.198808i
$534$	8.67726e6	+	7.80188e6i	1.31683	+	1.18398i
$535$	−935426.	+	6.06461e6i	−0.141294	+	0.916049i
$536$	−5.35298e6	+	7.40088e6i	−0.804792	+	1.11268i
$537$	4.56698e6			0.683428
$538$	−2.09840e6	−	1.88671e6i	−0.312560	−	0.281028i
$539$	−2.75856e6	+	2.75856e6i	−0.408988	+	0.408988i
$540$	−64985.8	+	1.38473e6i	−0.00959035	+	0.204352i
$541$	−9.21163e6	−	9.21163e6i	−1.35314	−	1.35314i	−0.882124	−	0.471017i	$-0.843887\pi$
$541$	−9.21163e6	−	9.21163e6i	−1.35314	−	1.35314i	−0.471017	−	0.882124i	$-0.656113\pi$
$542$	−1.12383e7	+	596983.i	−1.64324	+	0.0872899i
$543$			4.53241e6i			0.659675i
$544$	−524684.	−	1.93067e6i	−0.0760152	−	0.279713i
$545$	703369.	−	4.56012e6i	0.101436	−	0.657635i
$546$	−493508.	−	9.29035e6i	−0.0708456	−	1.33368i
$547$	−2.84257e6	+	2.84257e6i	−0.406203	+	0.406203i	−0.880412	−	0.474209i	$-0.842734\pi$
$547$	−2.84257e6	+	2.84257e6i	−0.406203	+	0.406203i	0.474209	+	0.880412i	$0.342734\pi$
$548$	−1.36571e6	+	145505.i	−0.194270	+	0.0206979i
$549$	5.60036e6	−	5.60036e6i	0.793022	−	0.793022i
$550$	−6.44447e6	−	1.09388e7i	−0.908407	−	1.54193i
$551$		−	1.27014e7i		−	1.78227i
$552$	4.27610e6	−	5.91201e6i	0.597310	−	0.825825i
$553$	−4.39071e6			−0.610550
$554$	1.83047e6	+	1.64581e6i	0.253390	+	0.227827i
$555$	4.49137e6	+	6.12958e6i	0.618937	+	0.844692i
$556$	1.91940e6	−	2.37716e6i	0.263316	−	0.326115i
$557$	4.92637e6	−	4.92637e6i	0.672804	−	0.672804i	−0.285557	−	0.958362i	$-0.592179\pi$
$557$	4.92637e6	−	4.92637e6i	0.672804	−	0.672804i	0.958362	+	0.285557i	$0.0921787\pi$
$558$	818790.	+	1.54138e7i	0.111324	+	2.09568i
$559$	−1.58846e6			−0.215004
$560$	4.56509e6	+	4.05386e6i	0.615147	+	0.546259i
$561$	−5.65645e6			−0.758817
$562$	523625.	+	9.85730e6i	0.0699326	+	1.31649i
$563$	8.55023e6	−	8.55023e6i	1.13686	−	1.13686i	0.147850	−	0.989010i	$-0.452765\pi$
$563$	8.55023e6	−	8.55023e6i	1.13686	−	1.13686i	0.989010	−	0.147850i	$-0.0472354\pi$
$564$	−5.16756e6	−	4.17246e6i	−0.684049	−	0.552324i
$565$	−1.25177e6	+	917217.i	−0.164969	+	0.120879i
$566$	9.11700e6	+	8.19726e6i	1.19622	+	1.07554i
$567$	5.29388e6			0.691538
$568$	837818.	+	5.21774e6i	0.108963	+	0.678596i
$569$		−	7.88710e6i		−	1.02126i	−0.859800	−	0.510630i	$-0.829412\pi$
$569$		−	7.88710e6i		−	1.02126i	0.859800	−	0.510630i	$-0.170588\pi$
$570$	1.09891e7	+	1.34393e7i	1.41669	+	1.73256i
$571$	5.49118e6	−	5.49118e6i	0.704816	−	0.704816i	−0.260625	−	0.965440i	$-0.583928\pi$
$571$	5.49118e6	−	5.49118e6i	0.704816	−	0.704816i	0.965440	+	0.260625i	$0.0839285\pi$
$572$	−1.64649e6	−	1.54539e7i	−0.210411	−	1.97491i
$573$	3.04135e6	−	3.04135e6i	0.386973	−	0.386973i
$574$	−87271.3	−	1.64289e6i	−0.0110558	−	0.208127i
$575$	−1.66442e6	+	5.26706e6i	−0.209939	+	0.664352i
$576$	−2.84149e6	−	8.61994e6i	−0.356853	−	1.08255i
$577$			1.57700e7i			1.97193i	0.166959	+	0.985964i	$0.446605\pi$
$577$			1.57700e7i			1.97193i	−0.166959	+	0.985964i	$0.553395\pi$
$578$	−7.34674e6	+	390263.i	−0.914693	+	0.0485890i
$579$	−8.78936e6	−	8.78936e6i	−1.08958	−	1.08958i
$580$	442432.	−	9.42740e6i	0.0546105	−	1.16365i
$581$	−1.89338e6	+	1.89338e6i	−0.232701	+	0.232701i
$582$	6.26210e6	+	5.63036e6i	0.766324	+	0.689016i
$583$	−9.80153e6			−1.19432
$584$	−2.06161e6	+	331034.i	−0.250134	+	0.0401643i
$585$	1.59616e6	−	1.03483e7i	0.192836	−	1.25020i
$586$	3.20790e6	+	2.88428e6i	0.385902	+	0.346971i
$587$	1.56405e6	+	1.56405e6i	0.187351	+	0.187351i	0.794550	−	0.607199i	$-0.207707\pi$
$587$	1.56405e6	+	1.56405e6i	0.187351	+	0.187351i	−0.607199	+	0.794550i	$0.707707\pi$
$588$	2.49005e6	−	3.08391e6i	0.297005	−	0.367839i
$589$	1.67701e7	+	1.67701e7i	1.99181	+	1.99181i
$590$	1.05501e7	+	1.05819e6i	1.24775	+	0.125151i
$591$	−1.03782e7			−1.22223
$592$	−5.12891e6	−	3.31006e6i	−0.601479	−	0.388178i
$593$			1.54632e7i			1.80577i	0.429881	+	0.902886i	$0.358555\pi$
$593$			1.54632e7i			1.80577i	−0.429881	+	0.902886i	$0.641445\pi$
$594$	−3.14393e6	+	167007.i	−0.365600	+	0.0194209i
$595$	−1.66106e6	+	1.21712e6i	−0.192350	+	0.140942i
$596$	−3.15746e6	+	3.91049e6i	−0.364101	+	0.450937i
$597$	−1.36778e7	−	1.36778e7i	−1.57065	−	1.57065i
$598$	−4.52092e6	+	5.02817e6i	−0.516980	+	0.574985i
$599$		−	4.21528e6i		−	0.480020i	−0.970770	−	0.240010i	$-0.922849\pi$
$599$		−	4.21528e6i		−	0.480020i	0.970770	−	0.240010i	$-0.0771508\pi$
$600$	7.68831e6	+	1.03578e7i	0.871872	+	1.17460i
$601$		−	1.05672e7i		−	1.19337i	−0.802476	−	0.596684i	$-0.796485\pi$
$601$		−	1.05672e7i		−	1.19337i	0.802476	−	0.596684i	$-0.203515\pi$
$602$	1.05386e6	+	947541.i	0.118520	+	0.106563i
$603$	−9.88255e6	−	9.88255e6i	−1.10682	−	1.10682i
$604$	1.52741e6	+	1.43363e7i	0.170359	+	1.59899i
$605$	1.59966e7	−	1.17213e7i	1.77680	−	1.30193i
$606$	−192333.	−	3.62070e6i	−0.0212752	−	0.400508i
$607$			8.11448e6i			0.893900i	0.894559	+	0.446950i	$0.147490\pi$
$607$			8.11448e6i			0.893900i	−0.894559	+	0.446950i	$0.852510\pi$
$608$	−1.21018e7	−	6.92976e6i	−1.32767	−	0.760255i
$609$	1.28312e7			1.40192
$610$	902419.	−	8.99711e6i	0.0981937	−	0.978990i
$611$	4.35232e6	+	4.35232e6i	0.471647	+	0.471647i
$612$	3.04411e6	−	324325.i	0.328535	−	0.0350027i
$613$	9.50964e6	+	9.50964e6i	1.02215	+	1.02215i	0.999749	+	0.0223966i	$0.00712966\pi$
$613$	9.50964e6	+	9.50964e6i	1.02215	+	1.02215i	0.0223966	+	0.999749i	$0.492870\pi$
$614$	−4.59982e6	+	5.11592e6i	−0.492402	+	0.547650i
$615$	529895.	−	3.43545e6i	0.0564939	−	0.366265i
$616$	−8.12616e6	+	1.12350e7i	−0.862847	+	1.19295i
$617$	−1.49495e7			−1.58093			−0.790466	−	0.612506i	$-0.790162\pi$
$617$	−1.49495e7			−1.58093			−0.790466	+	0.612506i	$0.790162\pi$
$618$	7.94123e6	−	8.83225e6i	0.836405	−	0.930251i
$619$	−167897.	+	167897.i	−0.0176123	+	0.0176123i	−0.715858	−	0.698246i	$-0.753964\pi$
$619$	−167897.	+	167897.i	−0.0176123	+	0.0176123i	0.698246	+	0.715858i	$0.253964\pi$
$620$	1.18631e7	+	1.30315e7i	1.23943	+	1.36149i
$621$	968587.	+	968587.i	0.100788	+	0.100788i
$622$	−851504.	−	1.60297e7i	−0.0882492	−	1.66130i
$623$			9.64802e6i			0.995905i
$624$	3.32690e6	+	1.54359e7i	0.342041	+	1.58698i
$625$	−7.99233e6	−	5.61160e6i	−0.818415	−	0.574628i
$626$	5.33708e6	−	283509.i	0.544337	−	0.0289155i
$627$	−2.78792e7	+	2.78792e7i	−2.83212	+	2.83212i
$628$	1.27286e6	−	1.57643e6i	0.128790	−	0.159506i
$629$	1.45588e6	−	1.45588e6i	0.146723	−	0.146723i
$630$	−7.23193e6	+	5.91344e6i	−0.725943	+	0.593593i
$631$		−	4.46243e6i		−	0.446168i	−0.974799	−	0.223084i	$-0.928388\pi$
$631$		−	4.46243e6i		−	0.446168i	0.974799	−	0.223084i	$-0.0716123\pi$
$632$	7.35791e6	−	1.18147e6i	0.732760	−	0.117660i
$633$	2.11846e7			2.10141
$634$	−4.20223e6	+	4.67373e6i	−0.415200	+	0.461786i
$635$	4.81054e6	−	3.52486e6i	0.473434	−	0.346903i
$636$	9.90251e6	−	1.05503e6i	0.970739	−	0.103424i
$637$	−2.59739e6	+	2.59739e6i	−0.253623	+	0.253623i
$638$	2.14043e7	−	1.13701e6i	2.08185	−	0.110589i
$639$	−8.08611e6			−0.783407
$640$	−8.74097e6	−	5.56504e6i	−0.843548	−	0.537054i
$641$	1.53043e7			1.47119			0.735593	−	0.677424i	$-0.236904\pi$
$641$	1.53043e7			1.47119			0.735593	+	0.677424i	$0.236904\pi$
$642$	1.41397e7	−	751111.i	1.35395	−	0.0719228i
$643$	2.54082e6	−	2.54082e6i	0.242352	−	0.242352i	−0.575471	−	0.817822i	$-0.695181\pi$
$643$	2.54082e6	−	2.54082e6i	0.242352	−	0.242352i	0.817822	+	0.575471i	$0.195181\pi$
$644$	5.99878e6	−	639120.i	0.569965	−	0.0607250i
$645$	1.76979e6	+	2.41532e6i	0.167503	+	0.228600i
$646$	3.14490e6	−	3.49777e6i	0.296501	−	0.329769i
$647$	−7.78276e6			−0.730925			−0.365463	−	0.930826i	$-0.619089\pi$
$647$	−7.78276e6			−0.730925			−0.365463	+	0.930826i	$0.619089\pi$
$648$	−8.87144e6	+	1.42450e6i	−0.829959	+	0.133267i
$649$			2.40810e7i			2.24420i
$650$	−6.06794e6	−	1.02997e7i	−0.563324	−	0.956184i
$651$	−1.69414e7	+	1.69414e7i	−1.56674	+	1.56674i
$652$	1.02485e7	−	1.26927e7i	0.944150	−	1.16932i
$653$	9.68542e6	−	9.68542e6i	0.888865	−	0.888865i	−0.105549	−	0.994414i	$-0.533660\pi$
$653$	9.68542e6	−	9.68542e6i	0.888865	−	0.888865i	0.994414	+	0.105549i	$0.0336601\pi$
$654$	−1.06320e7	+	564778.i	−0.972010	+	0.0516337i
$655$	2.14457e6	−	1.39038e7i	0.195316	−	1.26628i
$656$	588324.	+	2.72966e6i	0.0533773	+	0.247656i
$657$		−	3.19494e6i		−	0.288768i
$658$	−291300.	−	5.48376e6i	−0.0262287	−	0.493758i
$659$	−9.93741e6	−	9.93741e6i	−0.891374	−	0.891374i	0.103279	−	0.994652i	$-0.467067\pi$
$659$	−9.93741e6	−	9.93741e6i	−0.891374	−	0.891374i	−0.994652	+	0.103279i	$0.967067\pi$
$660$	−2.16639e7	+	1.97217e7i	−1.93588	+	1.76232i
$661$	−4.73013e6	+	4.73013e6i	−0.421084	+	0.421084i	−0.885577	−	0.464493i	$-0.846237\pi$
$661$	−4.73013e6	+	4.73013e6i	−0.421084	+	0.421084i	0.464493	+	0.885577i	$0.346237\pi$
$662$	−262752.	+	292233.i	−0.0233024	+	0.0259170i
$663$	−5.32597e6			−0.470560
$664$	2.66344e6	−	3.68240e6i	0.234435	−	0.324123i
$665$	−2.18807e6	+	1.41858e7i	−0.191870	+	1.24394i
$666$	6.24498e6	−	6.94568e6i	0.545564	−	0.606777i
$667$	−6.59427e6	−	6.59427e6i	−0.573921	−	0.573921i
$668$	−1.42109e7	+	1.51405e6i	−1.23220	+	0.131281i
$669$	−2.09416e7	−	2.09416e7i	−1.80903	−	1.80903i
$670$	−1.58765e7	−	1.59243e6i	−1.36637	−	0.137048i
$671$	2.05361e7			1.76081
$672$	7.00055e6	−	1.22255e7i	0.598011	−	1.04434i
$673$			7.73701e6i			0.658470i	0.944248	+	0.329235i	$0.106791\pi$
$673$			7.73701e6i			0.658470i	−0.944248	+	0.329235i	$0.893209\pi$
$674$	−560860.	−	1.05582e7i	−0.0475559	−	0.895245i
$675$	−2.14878e6	+	1.11683e6i	−0.181523	+	0.0943468i
$676$	−291551.	−	2.73649e6i	−0.0245385	−	0.230318i
$677$	8.28716e6	+	8.28716e6i	0.694919	+	0.694919i	0.963310	−	0.268391i	$-0.0864919\pi$
$677$	8.28716e6	+	8.28716e6i	0.694919	+	0.694919i	−0.268391	+	0.963310i	$0.586492\pi$
$678$	2.66283e6	+	2.39420e6i	0.222469	+	0.200026i
$679$			6.96267e6i			0.579564i
$680$	2.45609e6	−	2.48661e6i	0.203691	−	0.206222i
$681$		−	5.32385e6i		−	0.439904i
$682$	−2.67595e7	+	2.97620e7i	−2.20301	+	2.45019i
$683$	−2.20912e6	−	2.20912e6i	−0.181204	−	0.181204i	0.610676	−	0.791880i	$-0.290898\pi$
$683$	−2.20912e6	−	2.20912e6i	−0.181204	−	0.181204i	−0.791880	+	0.610676i	$0.790898\pi$
$684$	1.34051e7	−	1.66021e7i	1.09554	−	1.35682i
$685$	−1.41810e6	−	1.93535e6i	−0.115473	−	0.157592i
$686$	1.33984e7	−	711732.i	1.08704	−	0.0577439i
$687$		−	4.15884e6i		−	0.336187i
$688$	−2.02101e6	−	1.30431e6i	−0.162779	−	0.105053i
$689$	−9.22886e6			−0.740628
$690$	1.26826e7	+	1.27208e6i	1.01411	+	0.101716i
$691$	−8.33836e6	−	8.33836e6i	−0.664332	−	0.664332i	0.292066	−	0.956398i	$-0.405657\pi$
$691$	−8.33836e6	−	8.33836e6i	−0.664332	−	0.664332i	−0.956398	+	0.292066i	$0.905657\pi$
$692$	−3.56304e6	+	4.41281e6i	−0.282850	+	0.350308i
$693$	−1.50023e7	−	1.50023e7i	−1.18666	−	1.18666i
$694$	−1.68587e6	−	1.51580e6i	−0.132870	−	0.119466i
$695$	5.27504e6	+	813640.i	0.414251	+	0.0638955i
$696$	−2.15024e7	+	3.45266e6i	−1.68253	+	0.270166i
$697$	−941837.			−0.0734334
$698$	5.48041e6	+	4.92754e6i	0.425770	+	0.382817i
$699$	2.53311e6	−	2.53311e6i	0.196093	−	0.196093i
$700$	−2.11819e6	+	1.04529e7i	−0.163388	+	0.806294i
$701$	6.30948e6	+	6.30948e6i	0.484952	+	0.484952i	0.906709	−	0.421757i	$-0.138587\pi$
$701$	6.30948e6	+	6.30948e6i	0.484952	+	0.484952i	−0.421757	+	0.906709i	$0.638587\pi$
$702$	−2.96024e6	+	157250.i	−0.226717	+	0.0120433i
$703$		−	1.43513e7i		−	1.09522i
$704$	1.05946e7	−	2.10142e7i	0.805663	−	1.59801i
$705$	1.76872e6	−	1.14671e7i	0.134025	−	0.868921i
$706$	1.08535e6	+	2.04319e7i	0.0819520	+	1.54276i
$707$	2.11981e6	−	2.11981e6i	0.159495	−	0.159495i
$708$	−2.59206e6	−	2.43291e7i	−0.194340	−	1.82407i
$709$	5.00389e6	−	5.00389e6i	0.373846	−	0.373846i	−0.495030	−	0.868876i	$-0.664843\pi$
$709$	5.00389e6	−	5.00389e6i	0.373846	−	0.373846i	0.868876	+	0.495030i	$0.164843\pi$
$710$	−7.14674e6	+	5.84378e6i	−0.532062	+	0.435059i
$711$			1.14028e7i			0.845936i
$712$	−2.59613e6	−	1.61681e7i	−0.191922	−	1.19525i
$713$	1.74132e7			1.28279
$714$	3.53350e6	+	3.17703e6i	0.259394	+	0.233226i
$715$	2.18999e7	−	1.60468e7i	1.60205	−	1.17388i
$716$	−4.98638e6	−	4.02617e6i	−0.363499	−	0.293501i
$717$	−1.75207e6	+	1.75207e6i	−0.127278	+	0.127278i
$718$	269213.	+	5.06797e6i	0.0194888	+	0.366879i
$719$	1.73742e6			0.125338			0.0626691	−	0.998034i	$-0.480039\pi$
$719$	1.73742e6			0.125338			0.0626691	+	0.998034i	$0.480039\pi$
$720$	1.05280e7	−	1.18557e7i	0.756859	−	0.852306i
$721$	9.82035e6			0.703540
$722$	−996156.	−	1.87527e7i	−0.0711188	−	1.33882i
$723$	2.05205e7	−	2.05205e7i	1.45996	−	1.45996i
$724$	3.99570e6	−	4.94865e6i	0.283300	−	0.350865i
$725$	1.46291e7	−	7.60352e6i	1.03365	−	0.537241i
$726$	−3.40289e7	−	3.05960e7i	−2.39611	−	2.15438i
$727$	1.99882e7			1.40261			0.701307	−	0.712860i	$-0.252600\pi$
$727$	1.99882e7			1.40261			0.701307	+	0.712860i	$0.252600\pi$
$728$	−7.65139e6	+	1.05786e7i	−0.535071	+	0.739775i
$729$		−	1.80424e7i		−	1.25741i
$730$	−2.30896e6	−	2.82378e6i	−0.160365	−	0.196121i
$731$	573680.	−	573680.i	0.0397079	−	0.0397079i
$732$	−2.07477e7	+	2.21050e6i	−1.43117	+	0.152480i
$733$	−1.06277e7	+	1.06277e7i	−0.730603	+	0.730603i	−0.970739	−	0.240136i	$-0.922808\pi$
$733$	−1.06277e7	+	1.06277e7i	−0.730603	+	0.730603i	0.240136	+	0.970739i	$0.422808\pi$
$734$	619618.	+	1.16644e7i	0.0424506	+	0.799137i
$735$	6.84335e6	+	1.05554e6i	0.467251	+	0.0720704i
$736$	−9.88073e6	+	2.68520e6i	−0.672348	+	0.182719i
$737$		−	3.62387e7i		−	2.45756i
$738$	−4.26664e6	+	226646.i	−0.288367	+	0.0153182i
$739$	6.73131e6	+	6.73131e6i	0.453407	+	0.453407i	0.896484	−	0.443076i	$-0.146113\pi$
$739$	6.73131e6	+	6.73131e6i	0.453407	+	0.453407i	−0.443076	+	0.896484i	$0.646113\pi$
$740$	499903.	−	1.06520e7i	0.0335588	−	0.715076i
$741$	−2.62503e7	+	2.62503e7i	−1.75626	+	1.75626i
$742$	6.12286e6	+	5.50517e6i	0.408267	+	0.367080i
$743$	−1.25304e7			−0.832707			−0.416353	−	0.909203i	$-0.636692\pi$
$743$	−1.25304e7			−0.832707			−0.416353	+	0.909203i	$0.636692\pi$
$744$	2.38316e7	−	3.29490e7i	1.57842	−	2.18227i
$745$	−8.67759e6	−	1.33846e6i	−0.572807	−	0.0883517i
$746$	1.25574e7	+	1.12906e7i	0.826140	+	0.742797i
$747$	4.91718e6	+	4.91718e6i	0.322414	+	0.322414i
$748$	6.17591e6	+	4.98664e6i	0.403596	+	0.325877i
$749$	8.27838e6	+	8.27838e6i	0.539189	+	0.539189i
$750$	−8.90052e6	+	2.07021e7i	−0.577779	+	1.34388i
$751$	−1.63533e7			−1.05805			−0.529025	−	0.848606i	$-0.677442\pi$
$751$	−1.63533e7			−1.05805			−0.529025	+	0.848606i	$0.677442\pi$
$752$	1.96375e6	+	9.11126e6i	0.126631	+	0.587535i
$753$		−	2.12893e6i		−	0.136828i
$754$	2.01537e7	−	1.07058e6i	1.29100	−	0.0685787i
$755$	−2.03161e7	+	1.48863e7i	−1.29710	+	0.950431i
$756$	2.05777e6	+	1.66151e6i	0.130946	+	0.105730i
$757$	2.18368e7	+	2.18368e7i	1.38500	+	1.38500i	0.835487	+	0.549510i	$0.185186\pi$
$757$	2.18368e7	+	2.18368e7i	1.38500	+	1.38500i	0.549510	+	0.835487i	$0.314814\pi$
$758$	1.78105e7	−	1.98089e7i	1.12591	−	1.25224i
$759$			2.89484e7i			1.82398i
$760$	−150424.	−	2.43612e7i	−0.00944677	−	1.52991i
$761$		−	3.37886e6i		−	0.211499i	−0.994393	−	0.105749i	$-0.966276\pi$
$761$		−	3.37886e6i		−	0.211499i	0.994393	−	0.105749i	$-0.0337241\pi$
$762$	−1.02332e7	−	9.20089e6i	−0.638449	−	0.574040i
$763$	−6.22471e6	−	6.22471e6i	−0.387086	−	0.387086i
$764$	−6.00186e6	+	639449.i	−0.372008	+	0.0396344i
$765$	3.16090e6	+	4.31383e6i	0.195280	+	0.266508i
$766$	309241.	+	5.82150e6i	0.0190426	+	0.358479i
$767$			2.26740e7i			1.39168i
$768$	−8.44181e6	+	2.23711e7i	−0.516455	+	1.36862i
$769$	−1.77754e7			−1.08394			−0.541968	−	0.840399i	$-0.682321\pi$
$769$	−1.77754e7			−1.08394			−0.541968	+	0.840399i	$0.682321\pi$
$770$	−2.41016e7	−	2.41741e6i	−1.46494	−	0.146935i
$771$	2.81177e7	+	2.81177e7i	1.70351	+	1.70351i
$772$	1.84797e6	+	1.73451e7i	0.111597	+	1.04745i
$773$	−1.26205e7	−	1.26205e7i	−0.759676	−	0.759676i	0.216588	−	0.976263i	$-0.430507\pi$
$773$	−1.26205e7	−	1.26205e7i	−0.759676	−	0.759676i	−0.976263	+	0.216588i	$0.930507\pi$
$774$	2.46079e6	−	2.73690e6i	0.147646	−	0.164213i
$775$	−9.27615e6	+	2.93545e7i	−0.554771	+	1.75558i
$776$	−1.87354e6	−	1.16680e7i	−0.111689	−	0.695571i
$777$	1.44979e7			0.861496
$778$	−745065.	+	828662.i	−0.0441311	+	0.0490827i
$779$	−4.64207e6	+	4.64207e6i	−0.274074	+	0.274074i
$780$	−2.03982e7	+	1.85694e7i	−1.20048	+	1.09285i
$781$	−1.48256e7	−	1.48256e7i	−0.869731	−	0.869731i
$782$	−183197.	−	3.44871e6i	−0.0107128	−	0.201669i
$783$		−	4.08848e6i		−	0.238318i
$784$	−5.43744e6	+	1.17193e6i	−0.315940	+	0.0680945i
$785$	3.49819e6	+	539572.i	0.202614	+	0.0312518i
$786$	−3.24170e7	+	1.72201e6i	−1.87161	+	0.0994211i
$787$	1.91780e7	−	1.91780e7i	1.10374	−	1.10374i	0.109787	−	0.993955i	$-0.464983\pi$
$787$	1.91780e7	−	1.91780e7i	1.10374	−	1.10374i	0.993955	−	0.109787i	$-0.0350169\pi$
$788$	1.13312e7	+	9.14921e6i	0.650072	+	0.524890i
$789$	−1.16798e7	+	1.16798e7i	−0.667948	+	0.667948i
$790$	8.24073e6	+	1.00781e7i	0.469784	+	0.574530i
$791$			2.96073e6i			0.168251i
$792$	2.91777e7	+	2.11039e7i	1.65287	+	1.19550i
$793$	1.93363e7			1.09192
$794$	7.52919e6	−	8.37397e6i	0.423835	−	0.471390i
$795$	1.02824e7	+	1.40329e7i	0.577003	+	0.787463i
$796$	2.87577e6	+	2.69919e7i	0.160868	+	1.50991i
$797$	−2.21710e7	+	2.21710e7i	−1.23634	+	1.23634i	−0.274858	+	0.961485i	$0.588631\pi$
$797$	−2.21710e7	+	2.21710e7i	−1.23634	+	1.23634i	−0.961485	+	0.274858i	$0.911369\pi$
$798$	3.30744e7	−	1.75693e6i	1.83859	−	0.0976670i
$799$	−3.14373e6			−0.174212
$800$	736932.	−	1.80869e7i	0.0407101	−	0.999171i
$801$	2.50562e7			1.37986
$802$	3.03792e7	−	1.61376e6i	1.66778	−	0.0885936i
$803$	5.85782e6	−	5.85782e6i	0.320588	−	0.320588i
$804$	3.90071e6	+	3.66120e7i	0.212815	+	1.99748i
$805$	6.22893e6	+	8.50091e6i	0.338785	+	0.462355i
$806$	−2.51961e7	+	2.80231e7i	−1.36614	+	1.51942i
$807$	−1.13752e7			−0.614857
$808$	−2.98195e6	+	4.12276e6i	−0.160684	+	0.222157i
$809$			2.46367e6i			0.132346i	0.997808	+	0.0661731i	$0.0210790\pi$
$809$			2.46367e6i			0.132346i	−0.997808	+	0.0661731i	$0.978921\pi$
$810$	−9.93586e6	−	1.21512e7i	−0.532100	−	0.650740i
$811$	−5.44607e6	+	5.44607e6i	−0.290758	+	0.290758i	−0.837380	−	0.546622i	$-0.815914\pi$
$811$	−5.44607e6	+	5.44607e6i	−0.290758	+	0.290758i	0.546622	+	0.837380i	$0.315914\pi$
$812$	−1.40095e7	−	1.13118e7i	−0.745647	−	0.602060i
$813$	−3.20787e7	+	3.20787e7i	−1.70212	+	1.70212i
$814$	2.41846e7	−	1.28470e6i	1.27932	−	0.0679581i
$815$	2.81657e7	+	4.34438e6i	1.48534	+	0.229104i
$816$	−6.77630e6	−	4.37324e6i	−0.356260	−	0.229921i
$817$		−	5.65504e6i		−	0.296402i
$818$	530271.	+	9.98241e6i	0.0277086	+	0.521617i
$819$	−1.41258e7	−	1.41258e7i	−0.735874	−	0.735874i
$820$	−3.60719e6	+	3.28379e6i	−0.187342	+	0.170546i
$821$	−1.95859e7	+	1.95859e7i	−1.01411	+	1.01411i	−0.0142118	+	0.999899i	$0.504524\pi$
$821$	−1.95859e7	+	1.95859e7i	−1.01411	+	1.01411i	−0.999899	+	0.0142118i	$0.995476\pi$
$822$	−3.70166e6	+	4.11699e6i	−0.191081	+	0.212520i
$823$	−1.02295e7			−0.526448			−0.263224	−	0.964735i	$-0.584786\pi$
$823$	−1.02295e7			−0.526448			−0.263224	+	0.964735i	$0.584786\pi$
$824$	−1.64569e7	+	2.64250e6i	−0.844363	+	0.135580i
$825$	−4.87999e7	−	1.54210e7i	−2.49623	−	0.788820i
$826$	1.35254e7	−	1.50430e7i	0.689765	−	0.767157i
$827$	1.19752e7	+	1.19752e7i	0.608862	+	0.608862i	0.942649	−	0.333787i	$-0.108327\pi$
$827$	1.19752e7	+	1.19752e7i	0.608862	+	0.608862i	−0.333787	+	0.942649i	$0.608327\pi$
$828$	−1.65982e6	−	1.55790e7i	−0.0841364	−	0.789704i
$829$	8.75199e6	+	8.75199e6i	0.442304	+	0.442304i	0.892786	−	0.450482i	$-0.148748\pi$
$829$	8.75199e6	+	8.75199e6i	0.442304	+	0.442304i	−0.450482	+	0.892786i	$0.648748\pi$
$830$	7.89956e6	+	792334.i	0.398023	+	0.0399221i
$831$	9.92275e6			0.498459
$832$	9.97561e6	−	1.97864e7i	0.499610	−	0.990965i
$833$		−	1.87612e6i		−	0.0936805i
$834$	−653322.	−	1.22989e7i	−0.0325246	−	0.612279i
$835$	−1.47561e7	−	2.01384e7i	−0.732414	−	0.999559i
$836$	5.50173e7	−	5.86163e6i	2.72260	−	0.290070i
$837$	5.39815e6	+	5.39815e6i	0.266337	+	0.266337i
$838$	−9.15129e6	−	8.22809e6i	−0.450166	−	0.404752i
$839$			868183.i			0.0425801i	0.999773	+	0.0212900i	$0.00677734\pi$
$839$			868183.i			0.0425801i	−0.999773	+	0.0212900i	$0.993223\pi$
$840$	2.46101e7	−	151961.i	1.20341	−	0.00743076i
$841$			7.32375e6i			0.357062i
$842$	7.85950e6	−	8.74135e6i	0.382045	−	0.424911i
$843$	2.81368e7	+	2.81368e7i	1.36366	+	1.36366i
$844$	−2.31300e7	−	1.86759e7i	−1.11769	−	0.902457i
$845$	3.87790e6	−	2.84148e6i	0.186834	−	0.136900i
$846$	−1.42415e7	+	756517.i	−0.684117	+	0.0363406i
$847$		−	3.78358e7i		−	1.81215i
$848$	−1.17420e7	−	7.57797e6i	−0.560728	−	0.361879i
$849$	4.94220e7			2.35316
$850$	5.91128e6	+	1.52833e6i	0.280630	+	0.0725552i
$851$	−7.45085e6	−	7.45085e6i	−0.352681	−	0.352681i
$852$	1.65742e7	+	1.33825e7i	0.782227	+	0.631596i
$853$	8.34033e6	+	8.34033e6i	0.392474	+	0.392474i	0.875568	−	0.483094i	$-0.160487\pi$
$853$	8.34033e6	+	8.34033e6i	0.392474	+	0.392474i	−0.483094	+	0.875568i	$0.660487\pi$
$854$	−1.28286e7	−	1.15344e7i	−0.601915	−	0.541192i
$855$	3.68410e7	+	5.68248e6i	1.72352	+	0.265841i
$856$	−1.61004e7	−	1.16453e7i	−0.751023	−	0.543207i
$857$	−2.76278e7			−1.28497			−0.642486	−	0.766297i	$-0.722097\pi$
$857$	−2.76278e7			−1.28497			−0.642486	+	0.766297i	$0.722097\pi$
$858$	−4.65865e7	−	4.18868e7i	−2.16044	−	1.94249i
$859$	1.72101e7	−	1.72101e7i	0.795792	−	0.795792i	−0.186637	−	0.982429i	$-0.559759\pi$
$859$	1.72101e7	−	1.72101e7i	0.795792	−	0.795792i	0.982429	+	0.186637i	$0.0597587\pi$
$860$	196983.	−	4.19735e6i	0.00908204	−	0.193522i
$861$	−4.68949e6	−	4.68949e6i	−0.215585	−	0.215585i
$862$	−9.81085e6	+	521158.i	−0.449716	+	0.0238892i
$863$			1.78668e7i			0.816620i	0.912843	+	0.408310i	$0.133882\pi$
$863$			1.78668e7i			0.816620i	−0.912843	+	0.408310i	$0.866118\pi$
$864$	−3.89547e6	−	2.23063e6i	−0.177532	−	0.101658i
$865$	−9.79225e6	−	1.51039e6i	−0.444982	−	0.0686355i
$866$	945424.	+	1.77977e7i	0.0428382	+	0.806435i
$867$	−2.09706e7	+	2.09706e7i	−0.947467	+	0.947467i
$868$	3.34325e7	−	3.56195e6i	1.50615	−	0.160468i
$869$	−2.09067e7	+	2.09067e7i	−0.939151	+	0.939151i
$870$	−2.40823e7	−	2.94519e7i	−1.07870	−	1.31921i
$871$		−	3.41214e7i		−	1.52399i
$872$	1.21063e7	+	8.75635e6i	0.539163	+	0.389971i
$873$	1.80823e7			0.803004
$874$	−1.79007e7	−	1.60949e7i	−0.792669	−	0.712703i
$875$	−1.76487e7	+	5.97196e6i	−0.779276	+	0.263692i
$876$	−5.28764e6	+	6.54870e6i	−0.232810	+	0.288333i
$877$	1.19339e7	−	1.19339e7i	0.523944	−	0.523944i	−0.394816	−	0.918760i	$-0.629192\pi$
$877$	1.19339e7	−	1.19339e7i	0.523944	−	0.523944i	0.918760	+	0.394816i	$0.129192\pi$
$878$	1.75680e6	+	3.30720e7i	0.0769106	+	1.44785i
$879$	1.73896e7			0.759132
$880$	4.10398e7	−	2.43426e6i	1.78648	−	0.105965i
$881$	−5.00773e6			−0.217371			−0.108685	−	0.994076i	$-0.534664\pi$
$881$	−5.00773e6			−0.217371			−0.108685	+	0.994076i	$0.534664\pi$
$882$	−451476.	−	8.49908e6i	−0.0195417	−	0.367875i
$883$	3.25992e6	−	3.25992e6i	0.140704	−	0.140704i	−0.633247	−	0.773950i	$-0.718278\pi$
$883$	3.25992e6	−	3.25992e6i	0.140704	−	0.140704i	0.773950	+	0.633247i	$0.218278\pi$
$884$	5.81508e6	+	4.69529e6i	0.250279	+	0.202084i
$885$	3.44769e7	−	2.52625e7i	1.47969	−	1.08422i
$886$	−1.18794e7	−	1.06810e7i	−0.508407	−	0.457118i
$887$	4.03033e6			0.172001			0.0860007	−	0.996295i	$-0.472591\pi$
$887$	4.03033e6			0.172001			0.0860007	+	0.996295i	$0.472591\pi$
$888$	−2.42955e7	+	3.90116e6i	−1.03394	+	0.166020i
$889$		−	1.13781e7i		−	0.482853i
$890$	2.21454e7	−	1.81080e7i	0.937150	−	0.766293i
$891$	2.52072e7	−	2.52072e7i	1.06373	−	1.06373i
$892$	4.40300e6	+	4.13265e7i	0.185283	+	1.73907i
$893$	−1.54946e7	+	1.54946e7i	−0.650208	+	0.650208i
$894$	1.07473e6	+	2.02320e7i	0.0449735	+	0.846631i
$895$	1.70671e6	−	1.10650e7i	0.0712200	−	0.461738i
$896$	−1.84212e7	+	7.17660e6i	−0.766563	+	0.298640i
$897$			2.72570e7i			1.13109i
$898$	−2.09025e7	+	1.11035e6i	−0.864982	+	0.0459483i
$899$	−3.67513e7	−	3.67513e7i	−1.51661	−	1.51661i
$900$	2.71466e7	+	5.50101e6i	1.11715	+	0.226379i
$901$	3.33306e6	−	3.33306e6i	0.136783	−	0.136783i
$902$	−8.23830e6	−	7.40720e6i	−0.337148	−	0.303136i
$903$	5.71281e6			0.233147
$904$	−796685.	−	4.96158e6i	−0.0324239	−	0.201929i
$905$	1.09813e7	+	1.69379e6i	0.445690	+	0.0687447i
$906$	4.32175e7	+	3.88576e7i	1.74920	+	1.57273i
$907$	−5.05223e6	−	5.05223e6i	−0.203922	−	0.203922i	0.597756	−	0.801678i	$-0.296059\pi$
$907$	−5.05223e6	−	5.05223e6i	−0.203922	−	0.203922i	−0.801678	+	0.597756i	$0.796059\pi$
$908$	−4.69342e6	+	5.81276e6i	−0.188918	+	0.233974i
$909$	−5.50521e6	−	5.50521e6i	−0.220986	−	0.220986i
$910$	−2.26934e7	−	2.27617e6i	−0.908441	−	0.0911176i
$911$	−3.18053e7			−1.26971			−0.634855	−	0.772632i	$-0.718940\pi$
$911$	−3.18053e7			−1.26971			−0.634855	+	0.772632i	$0.718940\pi$
$912$	−5.49531e7	+	1.18440e7i	−2.18779	+	0.471534i
$913$			1.80310e7i			0.715883i
$914$	6.66315e6	−	353950.i	0.263824	−	0.0140145i
$915$	−2.15437e7	−	2.94017e7i	−0.850684	−	1.16097i
$916$	−3.66637e6	+	4.54077e6i	−0.144377	+	0.178810i
$917$	−1.89791e7	−	1.89791e7i	−0.745337	−	0.745337i
$918$	1.01232e6	−	1.12590e6i	0.0396470	−	0.0440954i
$919$		−	2.12511e6i		−	0.0830029i	−0.999138	−	0.0415014i	$-0.986786\pi$
$919$		−	2.12511e6i		−	0.0830029i	0.999138	−	0.0415014i	$-0.0132141\pi$
$920$	−1.27258e7	−	1.25697e7i	−0.495698	−	0.489614i
$921$			2.77327e7i			1.07732i
$922$	−1.22403e7	−	1.10055e7i	−0.474205	−	0.426366i
$923$	−1.39594e7	−	1.39594e7i	−0.539340	−	0.539340i
$924$	5.92152e6	+	5.55793e7i	0.228167	+	2.14158i
$925$	1.65294e7	−	8.59119e6i	0.635190	−	0.330141i
$926$	−2.19298e6	−	4.12832e7i	−0.0840443	−	1.58214i
$927$		−	2.55038e7i		−	0.974777i
$928$	2.65209e7	+	1.51864e7i	1.01092	+	0.578876i
$929$	−2.94416e7			−1.11924			−0.559619	−	0.828750i	$-0.689052\pi$
$929$	−2.94416e7			−1.11924			−0.559619	+	0.828750i	$0.689052\pi$
$930$	7.06828e7	+	7.08956e6i	2.67983	+	0.268789i
$931$	−9.24692e6	−	9.24692e6i	−0.349641	−	0.349641i
$932$	−4.99888e6	+	532590.i	−0.188510	+	0.0200841i
$933$	−4.57553e7	−	4.57553e7i	−1.72083	−	1.72083i
$934$	−2.03553e7	+	2.26392e7i	−0.763503	+	0.849169i
$935$	−2.11386e6	+	1.37047e7i	−0.0790763	+	0.512672i
$936$	2.74729e7	+	1.98709e7i	1.02498	+	0.741358i
$937$	−3.12962e7			−1.16451			−0.582254	−	0.813007i	$-0.697829\pi$
$937$	−3.12962e7			−1.16451			−0.582254	+	0.813007i	$0.697829\pi$
$938$	−2.03540e7	+	2.26377e7i	−0.755340	+	0.840090i
$939$	1.52342e7	−	1.52342e7i	0.563841	−	0.563841i
$940$	−1.20403e7	+	1.09609e7i	−0.444446	+	0.404600i
$941$	−1.47019e7	−	1.47019e7i	−0.541252	−	0.541252i	0.382644	−	0.923896i	$-0.375014\pi$
$941$	−1.47019e7	−	1.47019e7i	−0.541252	−	0.541252i	−0.923896	+	0.382644i	$0.875014\pi$
$942$	−433256.	−	8.15608e6i	−0.0159080	−	0.299471i
$943$			4.82009e6i			0.176513i
$944$	−1.86180e7	+	2.88484e7i	−0.679991	+	1.05364i
$945$	−704320.	+	4.56629e6i	−0.0256561	+	0.166335i
$946$	9.52980e6	−	506228.i	0.346223	−	0.0183915i
$947$	3.08335e7	−	3.08335e7i	1.11724	−	1.11724i	0.125099	−	0.992144i	$-0.460075\pi$
$947$	3.08335e7	−	3.08335e7i	1.11724	−	1.11724i	0.992144	−	0.125099i	$-0.0399248\pi$
$948$	1.88717e7	−	2.33724e7i	0.682008	−	0.844662i
$949$	5.51557e6	−	5.51557e6i	0.198804	−	0.198804i
$950$	3.66678e7	−	2.16024e7i	1.31818	−	0.776592i
$951$			2.53357e7i			0.908408i
$952$	−1.05718e6	−	6.58387e6i	−0.0378056	−	0.235445i
$953$	−1.41803e7			−0.505771			−0.252886	−	0.967496i	$-0.581380\pi$
$953$	−1.41803e7			−0.505771			−0.252886	+	0.967496i	$0.581380\pi$
$954$	1.42971e7	−	1.59013e7i	0.508601	−	0.565667i
$955$	−6.23214e6	−	8.50529e6i	−0.221120	−	0.301773i
$956$	3.45757e6	−	368376.i	0.122356	−	0.0130361i
$957$	6.10966e7	−	6.10966e7i	2.15644	−	2.15644i
$958$	−1.21570e7	+	645784.i	−0.427968	+	0.0227339i
$959$	−4.57757e6			−0.160727
$960$	−4.12005e7	+	6.87683e6i	−1.44286	+	0.240830i
$961$	6.84186e7			2.38982
$962$	2.27716e7	−	1.20964e6i	0.793335	−	0.0421424i
$963$	2.14992e7	−	2.14992e7i	0.747063	−	0.747063i
$964$	−4.04954e7	+	4.31445e6i	−1.40350	+	0.149532i
$965$	−2.45798e7	+	1.80105e7i	−0.849690	+	0.622599i
$966$	1.62593e7	−	1.80836e7i	0.560607	−	0.623508i
$967$	2.22183e7			0.764091			0.382045	−	0.924144i	$-0.375220\pi$
$967$	2.22183e7			0.764091			0.382045	+	0.924144i	$0.375220\pi$
$968$	1.01810e7	+	6.34050e7i	0.349223	+	2.17488i
$969$		−	1.89609e7i		−	0.648709i
$970$	1.59817e7	−	1.30679e7i	0.545371	−	0.445942i
$971$	−2.04474e7	+	2.04474e7i	−0.695971	+	0.695971i	−0.963539	−	0.267568i	$-0.913780\pi$
$971$	−2.04474e7	+	2.04474e7i	−0.695971	+	0.695971i	0.267568	+	0.963539i	$0.413780\pi$
$972$	−2.65392e7	+	3.28686e7i	−0.900994	+	1.11587i
$973$	7.20060e6	−	7.20060e6i	0.243830	−	0.243830i
$974$	2.02471e7	−	1.07554e6i	0.683856	−	0.0363268i
$975$	−4.59487e7	−	1.45200e7i	−1.54797	−	0.489165i
$976$	2.46018e7	+	1.58773e7i	0.826690	+	0.533523i
$977$		−	3.19207e6i		−	0.106988i	−0.998568	−	0.0534941i	$-0.982964\pi$
$977$		−	3.19207e6i		−	0.106988i	0.998568	−	0.0534941i	$-0.0170358\pi$
$978$	−3.48837e6	−	6.56689e7i	−0.116621	−	2.19539i
$979$	4.59398e7	+	4.59398e7i	1.53191	+	1.53191i
$980$	−6.54126e6	−	7.18546e6i	−0.217569	−	0.238995i
$981$	−1.61658e7	+	1.61658e7i	−0.536320	+	0.536320i
$982$	−1.26430e7	+	1.40615e7i	−0.418379	+	0.465322i
$983$	2.73221e7			0.901842			0.450921	−	0.892564i	$-0.351096\pi$
$983$	2.73221e7			0.901842			0.450921	+	0.892564i	$0.351096\pi$
$984$	9.12048e6	+	6.59675e6i	0.300282	+	0.217191i
$985$	−3.87839e6	+	2.51446e7i	−0.127368	+	0.825761i
$986$	−6.89199e6	+	7.66528e6i	−0.225763	+	0.251094i
$987$	−1.56529e7	−	1.56529e7i	−0.511449	−	0.511449i
$988$	5.18028e7	−	5.51916e6i	1.68834	−	0.179879i
$989$	−2.93596e6	−	2.93596e6i	−0.0954463	−	0.0954463i
$990$	−6.27810e6	+	6.25926e7i	−0.203583	+	2.02972i
$991$	−9.35812e6			−0.302695			−0.151347	−	0.988481i	$-0.548361\pi$
$991$	−9.35812e6			−0.302695			−0.151347	+	0.988481i	$0.548361\pi$
$992$	−5.50674e7	+	1.49652e7i	−1.77671	+	0.482841i
$993$			1.58416e6i			0.0509829i
$994$	934303.	+	1.75884e7i	0.0299931	+	0.564624i
$995$	−3.82504e7	+	2.80275e7i	−1.22484	+	0.897484i
$996$	−1.94084e6	−	1.82167e7i	−0.0619929	−	0.581865i
$997$	−8.08977e6	−	8.08977e6i	−0.257750	−	0.257750i	0.566388	−	0.824138i	$-0.308340\pi$
$997$	−8.08977e6	−	8.08977e6i	−0.257750	−	0.257750i	−0.824138	+	0.566388i	$0.808340\pi$
$998$	−395219.	−	355349.i	−0.0125606	−	0.0112935i
$999$		−	4.61956e6i		−	0.146449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.2	✓	116
5.4	even	2	inner	80.6.q.a.29.57	yes	116
16.5	even	4	inner	80.6.q.a.69.57	yes	116
80.69	even	4	inner	80.6.q.a.69.2	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.2	✓	116	1.1	even	1	trivial
80.6.q.a.29.57	yes	116	5.4	even	2	inner
80.6.q.a.69.2	yes	116	80.69	even	4	inner
80.6.q.a.69.57	yes	116	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.64889 + 0.300072i) q^{2} +(-16.1243 + 16.1243i) q^{3} +(31.8199 - 3.39015i) q^{4} +(33.0407 + 45.0922i) q^{5} +(86.2458 - 95.9226i) q^{6} +106.654 q^{7} +(-178.730 + 28.6988i) q^{8} -276.984i q^{9} +O(q^{10})\)	\(q+(-5.64889 + 0.300072i) q^{2} +(-16.1243 + 16.1243i) q^{3} +(31.8199 - 3.39015i) q^{4} +(33.0407 + 45.0922i) q^{5} +(86.2458 - 95.9226i) q^{6} +106.654 q^{7} +(-178.730 + 28.6988i) q^{8} -276.984i q^{9} +(-200.174 - 244.806i) q^{10} +(507.841 - 507.841i) q^{11} +(-458.409 + 567.736i) q^{12} +(478.170 - 478.170i) q^{13} +(-602.476 + 32.0039i) q^{14} +(-1259.84 - 194.321i) q^{15} +(1001.01 - 215.748i) q^{16} +345.388i q^{17} +(83.1151 + 1564.65i) q^{18} +(1702.33 + 1702.33i) q^{19} +(1204.22 + 1322.82i) q^{20} +(-1719.72 + 1719.72i) q^{21} +(-2716.35 + 3021.12i) q^{22} +1767.61 q^{23} +(2419.14 - 3344.64i) q^{24} +(-941.619 + 2979.76i) q^{25} +(-2557.64 + 2844.61i) q^{26} +(547.964 + 547.964i) q^{27} +(3393.72 - 361.573i) q^{28} +(-3730.61 - 3730.61i) q^{29} +(7174.99 + 719.659i) q^{30} +9851.28 q^{31} +(-5589.88 + 1519.12i) q^{32} +16377.1i q^{33} +(-103.641 - 1951.06i) q^{34} +(3523.93 + 4809.26i) q^{35} +(-939.016 - 8813.60i) q^{36} +(-4215.21 - 4215.21i) q^{37} +(-10127.1 - 9105.43i) q^{38} +15420.3i q^{39} +(-7199.46 - 7111.10i) q^{40} +2726.90i q^{41} +(9198.45 - 10230.5i) q^{42} +(-1660.98 - 1660.98i) q^{43} +(14437.8 - 17881.1i) q^{44} +(12489.8 - 9151.75i) q^{45} +(-9985.04 + 530.411i) q^{46} +9102.04i q^{47} +(-12661.8 + 19619.4i) q^{48} -5431.94 q^{49} +(4424.96 - 17114.9i) q^{50} +(-5569.12 - 5569.12i) q^{51} +(13594.2 - 16836.4i) q^{52} +(-9650.20 - 9650.20i) q^{53} +(-3259.82 - 2930.96i) q^{54} +(39679.1 + 6120.24i) q^{55} +(-19062.2 + 3060.84i) q^{56} -54897.5 q^{57} +(22193.3 + 19954.4i) q^{58} +(-23709.2 + 23709.2i) q^{59} +(-40746.7 - 1912.26i) q^{60} +(20219.1 + 20219.1i) q^{61} +(-55648.8 + 2956.09i) q^{62} -29541.4i q^{63} +(31120.8 - 10258.7i) q^{64} +(37360.8 + 5762.66i) q^{65} +(-4914.31 - 92512.5i) q^{66} +(35679.2 - 35679.2i) q^{67} +(1170.92 + 10990.2i) q^{68} +(-28501.4 + 28501.4i) q^{69} +(-21349.4 - 26109.6i) q^{70} -29193.4i q^{71} +(7949.11 + 49505.3i) q^{72} +11534.8 q^{73} +(25076.1 + 22546.4i) q^{74} +(-32863.6 - 63229.4i) q^{75} +(59939.0 + 48396.7i) q^{76} +(54163.2 - 54163.2i) q^{77} +(-4627.19 - 87107.4i) q^{78} -41167.8 q^{79} +(42802.8 + 38009.5i) q^{80} +49636.0 q^{81} +(-818.266 - 15403.9i) q^{82} +(-17752.6 + 17752.6i) q^{83} +(-48891.1 + 60551.3i) q^{84} +(-15574.3 + 11411.9i) q^{85} +(9881.08 + 8884.25i) q^{86} +120307. q^{87} +(-76191.9 + 105341. i) q^{88} +90461.0i q^{89} +(-67807.4 + 55445.1i) q^{90} +(50998.7 - 50998.7i) q^{91} +(56245.2 - 5992.46i) q^{92} +(-158845. + 158845. i) q^{93} +(-2731.27 - 51416.4i) q^{94} +(-20515.6 + 133008. i) q^{95} +(65638.0 - 114627. i) q^{96} +65282.8i q^{97} +(30684.4 - 1629.97i) q^{98} +(-140664. - 140664. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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