LMFDB - Embedded newform 20.7.b.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,7,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, 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:	$4.60108167240$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 18 x^{10} - 30 x^{9} + 174 x^{8} + 1853 x^{7} + 10388 x^{6} - 17262 x^{5} + \cdots + 7603655 $ x^12 - x^11 - 18x^10 - 30x^9 + 174x^8 + 1853x^7 + 10388x^6 - 17262x^5 - 88626x^4 - 240665x^3 - 173034x^2 + 3703420x + 7603655
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{33}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.1
Root			$-2.35434 + 0.469325i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.7.b.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.94474 - 0.938649i) q^{2} -50.7798i q^{3} +(62.2379 + 14.9147i) q^{4} -55.9017 q^{5} +(-47.6645 + 403.433i) q^{6} -91.7717i q^{7} +(-480.464 - 176.913i) q^{8} -1849.59 q^{9} +O(q^{10})$	\(q+(-7.94474 - 0.938649i) q^{2} -50.7798i q^{3} +(62.2379 + 14.9147i) q^{4} -55.9017 q^{5} +(-47.6645 + 403.433i) q^{6} -91.7717i q^{7} +(-480.464 - 176.913i) q^{8} -1849.59 q^{9} +(444.125 + 52.4721i) q^{10} +1264.47i q^{11} +(757.364 - 3160.43i) q^{12} +802.924 q^{13} +(-86.1415 + 729.103i) q^{14} +2838.68i q^{15} +(3651.11 + 1856.51i) q^{16} -3535.66 q^{17} +(14694.5 + 1736.12i) q^{18} -9426.47i q^{19} +(-3479.20 - 833.754i) q^{20} -4660.16 q^{21} +(1186.89 - 10045.9i) q^{22} -15966.1i q^{23} +(-8983.59 + 24397.9i) q^{24} +3125.00 q^{25} +(-6379.03 - 753.664i) q^{26} +56903.5i q^{27} +(1368.74 - 5711.68i) q^{28} -19762.9 q^{29} +(2664.52 - 22552.6i) q^{30} -25954.8i q^{31} +(-27264.5 - 18176.6i) q^{32} +64209.4 q^{33} +(28089.9 + 3318.75i) q^{34} +5130.20i q^{35} +(-115115. - 27586.0i) q^{36} -8267.10 q^{37} +(-8848.15 + 74890.9i) q^{38} -40772.4i q^{39} +(26858.8 + 9889.71i) q^{40} +1555.31 q^{41} +(37023.7 + 4374.25i) q^{42} -5738.36i q^{43} +(-18859.1 + 78697.7i) q^{44} +103395. q^{45} +(-14986.6 + 126847. i) q^{46} -115524. i q^{47} +(94273.4 - 185403. i) q^{48} +109227. q^{49} +(-24827.3 - 2933.28i) q^{50} +179540. i q^{51} +(49972.3 + 11975.3i) q^{52} -76765.7 q^{53} +(53412.5 - 452084. i) q^{54} -70685.8i q^{55} +(-16235.6 + 44093.0i) q^{56} -478675. q^{57} +(157011. + 18550.5i) q^{58} +277315. i q^{59} +(-42337.9 + 176673. i) q^{60} +143837. q^{61} +(-24362.5 + 206205. i) q^{62} +169740. i q^{63} +(199548. + 170000. i) q^{64} -44884.8 q^{65} +(-510127. - 60270.1i) q^{66} -332157. i q^{67} +(-220052. - 52733.2i) q^{68} -810757. q^{69} +(4815.45 - 40758.1i) q^{70} -472120. i q^{71} +(888663. + 327216. i) q^{72} +168409. q^{73} +(65680.0 + 7759.91i) q^{74} -158687. i q^{75} +(140593. - 586684. i) q^{76} +116042. q^{77} +(-38271.0 + 323926. i) q^{78} +439200. i q^{79} +(-204103. - 103782. i) q^{80} +1.54120e6 q^{81} +(-12356.5 - 1459.89i) q^{82} -99226.2i q^{83} +(-290038. - 69504.6i) q^{84} +197650. q^{85} +(-5386.31 + 45589.8i) q^{86} +1.00356e6i q^{87} +(223700. - 607531. i) q^{88} +901678. q^{89} +(-821450. - 97052.0i) q^{90} -73685.8i q^{91} +(238129. - 993697. i) q^{92} -1.31798e6 q^{93} +(-108436. + 917806. i) q^{94} +526956. i q^{95} +(-923006. + 1.38449e6i) q^{96} -540145. q^{97} +(-867780. - 102526. i) q^{98} -2.33875e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9}+O(q^{10}) $ 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9} + 750 q^{10} - 440 q^{12} - 5040 q^{13} + 6248 q^{14} + 3312 q^{16} + 6840 q^{17} + 15790 q^{18} - 3500 q^{20} - 27464 q^{21} - 26160 q^{22} + 28528 q^{24} + 37500 q^{25} - 18684 q^{26} + 19320 q^{28} - 74968 q^{29} - 13000 q^{30} - 60800 q^{32} + 112880 q^{33} + 48204 q^{34} - 128580 q^{36} + 62640 q^{37} + 74800 q^{38} + 57000 q^{40} - 16976 q^{41} - 138360 q^{42} - 222160 q^{44} + 77000 q^{45} - 144792 q^{46} + 297600 q^{48} + 72564 q^{49} - 31250 q^{50} + 548280 q^{52} + 322160 q^{53} + 150416 q^{54} - 246512 q^{56} - 1213440 q^{57} + 350700 q^{58} + 157000 q^{60} + 46464 q^{61} - 7120 q^{62} - 542784 q^{64} - 133000 q^{65} - 65200 q^{66} - 1678280 q^{68} + 41256 q^{69} - 360000 q^{70} + 2317560 q^{72} - 415080 q^{73} + 1581924 q^{74} + 208320 q^{76} + 75600 q^{77} + 473200 q^{78} + 734000 q^{80} + 2287428 q^{81} - 3169500 q^{82} - 2256224 q^{84} + 372000 q^{85} - 62512 q^{86} - 278880 q^{88} + 278392 q^{89} - 2162250 q^{90} + 4095720 q^{92} - 3646000 q^{93} + 4706568 q^{94} - 2641152 q^{96} + 2344680 q^{97} + 1050270 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9 + 750 * q^10 - 440 * q^12 - 5040 * q^13 + 6248 * q^14 + 3312 * q^16 + 6840 * q^17 + 15790 * q^18 - 3500 * q^20 - 27464 * q^21 - 26160 * q^22 + 28528 * q^24 + 37500 * q^25 - 18684 * q^26 + 19320 * q^28 - 74968 * q^29 - 13000 * q^30 - 60800 * q^32 + 112880 * q^33 + 48204 * q^34 - 128580 * q^36 + 62640 * q^37 + 74800 * q^38 + 57000 * q^40 - 16976 * q^41 - 138360 * q^42 - 222160 * q^44 + 77000 * q^45 - 144792 * q^46 + 297600 * q^48 + 72564 * q^49 - 31250 * q^50 + 548280 * q^52 + 322160 * q^53 + 150416 * q^54 - 246512 * q^56 - 1213440 * q^57 + 350700 * q^58 + 157000 * q^60 + 46464 * q^61 - 7120 * q^62 - 542784 * q^64 - 133000 * q^65 - 65200 * q^66 - 1678280 * q^68 + 41256 * q^69 - 360000 * q^70 + 2317560 * q^72 - 415080 * q^73 + 1581924 * q^74 + 208320 * q^76 + 75600 * q^77 + 473200 * q^78 + 734000 * q^80 + 2287428 * q^81 - 3169500 * q^82 - 2256224 * q^84 + 372000 * q^85 - 62512 * q^86 - 278880 * q^88 + 278392 * q^89 - 2162250 * q^90 + 4095720 * q^92 - 3646000 * q^93 + 4706568 * q^94 - 2641152 * q^96 + 2344680 * q^97 + 1050270 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.94474	−	0.938649i	−0.993093	−	0.117331i
$2$	−7.94474	−	0.938649i	−0.993093	−	0.117331i
$3$		−	50.7798i		−	1.88074i	−0.340160	−	0.940368i	$-0.610481\pi$
$3$		−	50.7798i		−	1.88074i	0.340160	−	0.940368i	$-0.389519\pi$
$4$	62.2379	+	14.9147i	0.972467	+	0.233041i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	−47.6645	+	403.433i	−0.220669	+	1.86774i
$7$		−	91.7717i		−	0.267556i	−0.991011	−	0.133778i	$-0.957289\pi$
$7$		−	91.7717i		−	0.267556i	0.991011	−	0.133778i	$-0.0427109\pi$
$8$	−480.464	−	176.913i	−0.938407	−	0.345532i
$9$	−1849.59			−2.53716
$10$	444.125	+	52.4721i	0.444125	+	0.0524721i
$11$			1264.47i			0.950012i	0.879982	+	0.475006i	$0.157554\pi$
$11$			1264.47i			0.950012i	−0.879982	+	0.475006i	$0.842446\pi$
$12$	757.364	−	3160.43i	0.438289	−	1.82895i
$13$	802.924			0.365464			0.182732	−	0.983163i	$-0.441506\pi$
$13$	802.924			0.365464			0.182732	+	0.983163i	$0.441506\pi$
$14$	−86.1415	+	729.103i	−0.0313927	+	0.265708i
$15$			2838.68i			0.841090i
$16$	3651.11	+	1856.51i	0.891383	+	0.453250i
$17$	−3535.66			−0.719655			−0.359827	−	0.933019i	$-0.617164\pi$
$17$	−3535.66			−0.719655			−0.359827	+	0.933019i	$0.617164\pi$
$18$	14694.5	+	1736.12i	2.51964	+	0.297688i
$19$		−	9426.47i		−	1.37432i	−0.726505	−	0.687161i	$-0.758857\pi$
$19$		−	9426.47i		−	1.37432i	0.726505	−	0.687161i	$-0.241143\pi$
$20$	−3479.20	−	833.754i	−0.434900	−	0.104219i
$21$	−4660.16			−0.503202
$22$	1186.89	−	10045.9i	0.111466	−	0.943451i
$23$		−	15966.1i		−	1.31225i	−0.754653	−	0.656124i	$-0.772195\pi$
$23$		−	15966.1i		−	1.31225i	0.754653	−	0.656124i	$-0.227805\pi$
$24$	−8983.59	+	24397.9i	−0.649855	+	1.76489i
$25$	3125.00			0.200000
$26$	−6379.03	−	753.664i	−0.362940	−	0.0428803i
$27$			56903.5i			2.89100i
$28$	1368.74	−	5711.68i	0.0623517	−	0.260189i
$29$	−19762.9			−0.810321			−0.405161	−	0.914246i	$-0.632784\pi$
$29$	−19762.9			−0.810321			−0.405161	+	0.914246i	$0.632784\pi$
$30$	2664.52	−	22552.6i	0.0986861	−	0.835281i
$31$		−	25954.8i		−	0.871231i	−0.900133	−	0.435615i	$-0.856531\pi$
$31$		−	25954.8i		−	0.871231i	0.900133	−	0.435615i	$-0.143469\pi$
$32$	−27264.5	−	18176.6i	−0.832046	−	0.554706i
$33$	64209.4			1.78672
$34$	28089.9	+	3318.75i	0.714684	+	0.0844379i
$35$			5130.20i			0.119655i
$36$	−115115.	−	27586.0i	−2.46731	−	0.591264i
$37$	−8267.10			−0.163210			−0.0816052	−	0.996665i	$-0.526005\pi$
$37$	−8267.10			−0.163210			−0.0816052	+	0.996665i	$0.526005\pi$
$38$	−8848.15	+	74890.9i	−0.161251	+	1.36483i
$39$		−	40772.4i		−	0.687341i
$40$	26858.8	+	9889.71i	0.419668	+	0.154527i
$41$	1555.31			0.0225666			0.0112833	−	0.999936i	$-0.496408\pi$
$41$	1555.31			0.0225666			0.0112833	+	0.999936i	$0.496408\pi$
$42$	37023.7	+	4374.25i	0.499726	+	0.0590413i
$43$		−	5738.36i		−	0.0721743i	−0.999349	−	0.0360871i	$-0.988511\pi$
$43$		−	5738.36i		−	0.0721743i	0.999349	−	0.0360871i	$-0.0114894\pi$
$44$	−18859.1	+	78697.7i	−0.221392	+	0.923856i
$45$	103395.			1.13465
$46$	−14986.6	+	126847.i	−0.153968	+	1.30318i
$47$		−	115524.i		−	1.11270i	−0.830949	−	0.556349i	$-0.812202\pi$
$47$		−	115524.i		−	1.11270i	0.830949	−	0.556349i	$-0.187798\pi$
$48$	94273.4	−	185403.i	0.852443	−	1.67646i
$49$	109227.			0.928414
$50$	−24827.3	−	2933.28i	−0.198619	−	0.0234662i
$51$			179540.i			1.35348i
$52$	49972.3	+	11975.3i	0.355402	+	0.0851683i
$53$	−76765.7			−0.515631			−0.257816	−	0.966194i	$-0.583003\pi$
$53$	−76765.7			−0.515631			−0.257816	+	0.966194i	$0.583003\pi$
$54$	53412.5	−	452084.i	0.339204	−	2.87103i
$55$		−	70685.8i		−	0.424858i
$56$	−16235.6	+	44093.0i	−0.0924493	+	0.251076i
$57$	−478675.			−2.58474
$58$	157011.	+	18550.5i	0.804724	+	0.0950759i
$59$			277315.i			1.35026i	0.737699	+	0.675130i	$0.235913\pi$
$59$			277315.i			1.35026i	−0.737699	+	0.675130i	$0.764087\pi$
$60$	−42337.9	+	176673.i	−0.196009	+	0.817932i
$61$	143837.			0.633695			0.316848	−	0.948476i	$-0.397376\pi$
$61$	143837.			0.633695			0.316848	+	0.948476i	$0.397376\pi$
$62$	−24362.5	+	206205.i	−0.102223	+	0.865213i
$63$			169740.i			0.678834i
$64$	199548.	+	170000.i	0.761215	+	0.648500i
$65$	−44884.8			−0.163440
$66$	−510127.	−	60270.1i	−1.77438	−	0.209638i
$67$		−	332157.i		−	1.10438i	−0.833718	−	0.552190i	$-0.813792\pi$
$67$		−	332157.i		−	1.10438i	0.833718	−	0.552190i	$-0.186208\pi$
$68$	−220052.	−	52733.2i	−0.699840	−	0.167709i
$69$	−810757.			−2.46799
$70$	4815.45	−	40758.1i	0.0140392	−	0.118828i
$71$		−	472120.i		−	1.31910i	−0.751661	−	0.659549i	$-0.770747\pi$
$71$		−	472120.i		−	1.31910i	0.751661	−	0.659549i	$-0.229253\pi$
$72$	888663.	+	327216.i	2.38089	+	0.876673i
$73$	168409.			0.432910			0.216455	−	0.976293i	$-0.430551\pi$
$73$	168409.			0.432910			0.216455	+	0.976293i	$0.430551\pi$
$74$	65680.0	+	7759.91i	0.162083	+	0.0191497i
$75$		−	158687.i		−	0.376147i
$76$	140593.	−	586684.i	0.320274	−	1.33648i
$77$	116042.			0.254182
$78$	−38271.0	+	323926.i	−0.0806465	+	0.682593i
$79$			439200.i			0.890802i	0.895331	+	0.445401i	$0.146939\pi$
$79$			439200.i			0.890802i	−0.895331	+	0.445401i	$0.853061\pi$
$80$	−204103.	−	103782.i	−0.398639	−	0.202700i
$81$	1.54120e6			2.90004
$82$	−12356.5	−	1459.89i	−0.0224107	−	0.00264776i
$83$		−	99226.2i		−	0.173537i	−0.996229	−	0.0867685i	$-0.972346\pi$
$83$		−	99226.2i		−	0.173537i	0.996229	−	0.0867685i	$-0.0276540\pi$
$84$	−290038.	−	69504.6i	−0.489347	−	0.117267i
$85$	197650.			0.321839
$86$	−5386.31	+	45589.8i	−0.00846829	+	0.0716758i
$87$			1.00356e6i			1.52400i
$88$	223700.	−	607531.i	0.328260	−	0.891498i
$89$	901678.			1.27903			0.639516	−	0.768778i	$-0.279135\pi$
$89$	901678.			1.27903			0.639516	+	0.768778i	$0.279135\pi$
$90$	−821450.	−	97052.0i	−1.12682	−	0.133130i
$91$		−	73685.8i		−	0.0977821i
$92$	238129.	−	993697.i	0.305808	−	1.27612i
$93$	−1.31798e6			−1.63855
$94$	−108436.	+	917806.i	−0.130554	+	1.10501i
$95$			526956.i			0.614615i
$96$	−923006.	+	1.38449e6i	−1.04326	+	1.56486i
$97$	−540145.			−0.591827			−0.295914	−	0.955215i	$-0.595624\pi$
$97$	−540145.			−0.591827			−0.295914	+	0.955215i	$0.595624\pi$
$98$	−867780.	−	102526.i	−0.922001	−	0.108932i
$99$		−	2.33875e6i		−	2.41034i
$100$	194493.	+	46608.3i	0.194493	+	0.0466083i
$101$	1.13625e6			1.10283			0.551417	−	0.834230i	$-0.314087\pi$
$101$	1.13625e6			1.10283			0.551417	+	0.834230i	$0.314087\pi$
$102$	168526.	−	1.42640e6i	0.158805	−	1.34413i
$103$		−	269341.i		−	0.246485i	−0.992377	−	0.123243i	$-0.960671\pi$
$103$		−	269341.i		−	0.246485i	0.992377	−	0.123243i	$-0.0393293\pi$
$104$	−385777.	−	142047.i	−0.342954	−	0.126280i
$105$	260511.			0.225039
$106$	609883.	+	72056.0i	0.512070	+	0.0604996i
$107$			165120.i			0.134788i	0.997726	+	0.0673938i	$0.0214684\pi$
$107$			165120.i			0.134788i	−0.997726	+	0.0673938i	$0.978532\pi$
$108$	−848696.	+	3.54155e6i	−0.673723	+	2.81140i
$109$	−1.17772e6			−0.909414			−0.454707	−	0.890641i	$-0.650256\pi$
$109$	−1.17772e6			−0.909414			−0.454707	+	0.890641i	$0.650256\pi$
$110$	−66349.2	+	561581.i	−0.0498491	+	0.421924i
$111$			419802.i			0.306956i
$112$	170375.	−	335068.i	0.121270	−	0.238495i
$113$	−99285.5			−0.0688098			−0.0344049	−	0.999408i	$-0.510954\pi$
$113$	−99285.5			−0.0688098			−0.0344049	+	0.999408i	$0.510954\pi$
$114$	3.80295e6	+	449308.i	2.56688	+	0.303270i
$115$			892533.i			0.586855i
$116$	−1.23000e6	−	294757.i	−0.788010	−	0.188838i
$117$	−1.48508e6			−0.927242
$118$	260302.	−	2.20320e6i	0.158428	−	1.34093i
$119$			324474.i			0.192548i
$120$	502198.	−	1.36388e6i	0.290624	−	0.789285i
$121$	172685.			0.0974764
$122$	−1.14275e6	−	135012.i	−0.629318	−	0.0743522i
$123$		−	78978.5i		−	0.0424418i
$124$	387107.	−	1.61537e6i	0.203033	−	0.847243i
$125$	−174693.			−0.0894427
$126$	159327.	−	1.34854e6i	0.0796483	−	0.674145i
$127$			1.67222e6i			0.816361i	0.912901	+	0.408181i	$0.133837\pi$
$127$			1.67222e6i			0.816361i	−0.912901	+	0.408181i	$0.866163\pi$
$128$	−1.42579e6	−	1.53791e6i	−0.679868	−	0.733335i
$129$	−291393.			−0.135741
$130$	356599.	+	42131.1i	0.162312	+	0.0191767i
$131$			407808.i			0.181402i	0.995878	+	0.0907009i	$0.0289107\pi$
$131$			407808.i			0.181402i	−0.995878	+	0.0907009i	$0.971089\pi$
$132$	3.99626e6	+	957661.i	1.73753	+	0.416380i
$133$	−865084.			−0.367708
$134$	−311778.	+	2.63890e6i	−0.129578	+	1.09675i
$135$		−	3.18100e6i		−	1.29289i
$136$	1.69876e6	+	625503.i	0.675329	+	0.248664i
$137$	2.98134e6			1.15944			0.579722	−	0.814814i	$-0.303161\pi$
$137$	2.98134e6			1.15944			0.579722	+	0.814814i	$0.303161\pi$
$138$	6.44126e6	+	761016.i	2.45094	+	0.289572i
$139$			3.28457e6i			1.22302i	0.791236	+	0.611511i	$0.209438\pi$
$139$			3.28457e6i			1.22302i	−0.791236	+	0.611511i	$0.790562\pi$
$140$	−76515.1	+	319293.i	−0.0278845	+	0.116360i
$141$	−5.86627e6			−2.09269
$142$	−443155.	+	3.75087e6i	−0.154771	+	1.30999i
$143$			1.01527e6i			0.347195i
$144$	−6.75306e6	−	3.43379e6i	−2.26159	−	1.14997i
$145$	1.10478e6			0.362387
$146$	−1.33797e6	−	158077.i	−0.429919	−	0.0507938i
$147$		−	5.54653e6i		−	1.74610i
$148$	−514527.	−	123301.i	−0.158717	−	0.0380348i
$149$	3.38045e6			1.02192			0.510959	−	0.859605i	$-0.329290\pi$
$149$	3.38045e6			1.02192			0.510959	+	0.859605i	$0.329290\pi$
$150$	−148951.	+	1.26073e6i	−0.0441338	+	0.373549i
$151$		−	5.74152e6i		−	1.66762i	−0.552054	−	0.833808i	$-0.686156\pi$
$151$		−	5.74152e6i		−	1.66762i	0.552054	−	0.833808i	$-0.313844\pi$
$152$	−1.66766e6	+	4.52908e6i	−0.474873	+	1.28967i
$153$	6.53954e6			1.82588
$154$	−921926.	−	108923.i	−0.252426	−	0.0298234i
$155$			1.45092e6i			0.389626i
$156$	608106.	−	2.53759e6i	0.160179	−	0.668416i
$157$	−4.78431e6			−1.23629			−0.618145	−	0.786064i	$-0.712116\pi$
$157$	−4.78431e6			−1.23629			−0.618145	+	0.786064i	$0.712116\pi$
$158$	412255.	−	3.48933e6i	0.104519	−	0.884649i
$159$			3.89815e6i			0.969766i
$160$	1.52413e6	+	1.01610e6i	0.372102	+	0.248072i
$161$	−1.46524e6			−0.351100
$162$	−1.22444e7	−	1.44665e6i	−2.88001	−	0.340265i
$163$			1.51835e6i			0.350597i	0.984515	+	0.175298i	$0.0560890\pi$
$163$			1.51835e6i			0.350597i	−0.984515	+	0.175298i	$0.943911\pi$
$164$	96799.3	+	23196.9i	0.0219453	+	0.00525895i
$165$	−3.58942e6			−0.799046
$166$	−93138.5	+	788326.i	−0.0203613	+	0.172338i
$167$		−	2.52461e6i		−	0.542057i	−0.962571	−	0.271029i	$-0.912636\pi$
$167$		−	2.52461e6i		−	0.542057i	0.962571	−	0.271029i	$-0.0873638\pi$
$168$	2.23904e6	+	824440.i	0.472208	+	0.173873i
$169$	−4.18212e6			−0.866436
$170$	−1.57028e6	−	185524.i	−0.319616	−	0.0377618i
$171$			1.74351e7i			3.48688i
$172$	85585.6	−	357143.i	0.0168196	−	0.0701871i
$173$	9.08999e6			1.75560			0.877799	−	0.479029i	$-0.159011\pi$
$173$	9.08999e6			1.75560			0.877799	+	0.479029i	$0.159011\pi$
$174$	941989.	−	7.97301e6i	0.178813	−	1.51347i
$175$		−	286787.i		−	0.0535112i
$176$	−2.34750e6	+	4.61670e6i	−0.430593	+	0.846825i
$177$	1.40820e7			2.53948
$178$	−7.16360e6	−	846360.i	−1.27020	−	0.150070i
$179$		−	5.12142e6i		−	0.892959i	−0.894794	−	0.446480i	$-0.852678\pi$
$179$		−	5.12142e6i		−	0.892959i	0.894794	−	0.446480i	$-0.147322\pi$
$180$	6.43511e6	+	1.54211e6i	1.10341	+	0.264421i
$181$	−1.09895e6			−0.185329			−0.0926644	−	0.995697i	$-0.529538\pi$
$181$	−1.09895e6			−0.185329			−0.0926644	+	0.995697i	$0.529538\pi$
$182$	−69165.1	+	585415.i	−0.0114729	+	0.0971067i
$183$		−	7.30401e6i		−	1.19181i
$184$	−2.82461e6	+	7.67115e6i	−0.453424	+	1.23142i
$185$	462145.			0.0729899
$186$	1.04710e7	+	1.23712e6i	1.62724	+	0.192253i
$187$		−	4.47073e6i		−	0.683681i
$188$	1.72299e6	−	7.18995e6i	0.259305	−	1.08206i
$189$	5.22214e6			0.773504
$190$	494627.	−	4.18653e6i	0.0721135	−	0.610370i
$191$		−	1.22866e7i		−	1.76332i	−0.471889	−	0.881658i	$-0.656428\pi$
$191$		−	1.22866e7i		−	1.76332i	0.471889	−	0.881658i	$-0.343572\pi$
$192$	8.63259e6	−	1.01330e7i	1.21966	−	1.43164i
$193$	−1.00370e7			−1.39615			−0.698077	−	0.716023i	$-0.745961\pi$
$193$	−1.00370e7			−1.39615			−0.698077	+	0.716023i	$0.745961\pi$
$194$	4.29131e6	+	507006.i	0.587740	+	0.0694398i
$195$			2.27925e6i			0.307388i
$196$	6.79805e6	+	1.62908e6i	0.902852	+	0.216359i
$197$	653955.			0.0855361			0.0427680	−	0.999085i	$-0.486382\pi$
$197$	653955.			0.0855361			0.0427680	+	0.999085i	$0.486382\pi$
$198$	−2.19526e6	+	1.85808e7i	−0.282808	+	2.39369i
$199$		−	5.68141e6i		−	0.720936i	−0.932772	−	0.360468i	$-0.882617\pi$
$199$		−	5.68141e6i		−	0.720936i	0.932772	−	0.360468i	$-0.117383\pi$
$200$	−1.50145e6	−	552852.i	−0.187681	−	0.0691065i
$201$	−1.68669e7			−2.07705
$202$	−9.02722e6	−	1.06654e6i	−1.09522	−	0.129397i
$203$			1.81368e6i			0.216806i
$204$	−2.67778e6	+	1.11742e7i	−0.315417	+	1.31621i
$205$	−86944.6			−0.0100921
$206$	−252817.	+	2.13984e6i	−0.0289204	+	0.244783i
$207$			2.95308e7i			3.32939i
$208$	2.93156e6	+	1.49064e6i	0.325769	+	0.165647i
$209$	1.19195e7			1.30562
$210$	−2.06969e6	−	244528.i	−0.223484	−	0.0264041i
$211$		−	3.37548e6i		−	0.359326i	−0.983728	−	0.179663i	$-0.942499\pi$
$211$		−	3.37548e6i		−	0.359326i	0.983728	−	0.179663i	$-0.0575007\pi$
$212$	−4.77773e6	−	1.14493e6i	−0.501435	−	0.120164i
$213$	−2.39742e7			−2.48087
$214$	154990.	−	1.31184e6i	0.0158148	−	0.133857i
$215$			320784.i			0.0322773i
$216$	1.00670e7	−	2.73401e7i	0.998934	−	2.71293i
$217$	−2.38192e6			−0.233103
$218$	9.35666e6	+	1.10546e6i	0.903132	+	0.106703i
$219$		−	8.55179e6i		−	0.814188i
$220$	1.05425e6	−	4.39934e6i	0.0990096	−	0.413161i
$221$	−2.83887e6			−0.263008
$222$	394047.	−	3.33522e6i	0.0360155	−	0.304835i
$223$			1.75521e7i			1.58276i	0.611326	+	0.791379i	$0.290636\pi$
$223$			1.75521e7i			1.58276i	−0.611326	+	0.791379i	$0.709364\pi$
$224$	−1.66810e6	+	2.50211e6i	−0.148415	+	0.222619i
$225$	−5.77998e6			−0.507433
$226$	788798.	+	93194.2i	0.0683345	+	0.00807353i
$227$		−	4.35329e6i		−	0.372169i	−0.982534	−	0.186084i	$-0.940420\pi$
$227$		−	4.35329e6i		−	0.372169i	0.982534	−	0.186084i	$-0.0595798\pi$
$228$	−2.97917e7	−	7.13927e6i	−2.51357	−	0.602350i
$229$	−1.03201e7			−0.859368			−0.429684	−	0.902979i	$-0.641375\pi$
$229$	−1.03201e7			−0.859368			−0.429684	+	0.902979i	$0.641375\pi$
$230$	837775.	−	7.09095e6i	0.0688564	−	0.582802i
$231$		−	5.89261e6i		−	0.478048i
$232$	9.49538e6	+	3.49631e6i	0.760411	+	0.279992i
$233$	8.14616e6			0.643999			0.322000	−	0.946740i	$-0.395645\pi$
$233$	8.14616e6			0.643999			0.322000	+	0.946740i	$0.395645\pi$
$234$	1.17986e7	+	1.39397e6i	0.920838	+	0.108794i
$235$			6.45797e6i			0.497614i
$236$	−4.13606e6	+	1.72595e7i	−0.314667	+	1.31308i
$237$	2.23025e7			1.67536
$238$	304567.	−	2.57786e6i	0.0225919	−	0.191218i
$239$			5.74017e6i			0.420466i	0.977651	+	0.210233i	$0.0674223\pi$
$239$			5.74017e6i			0.420466i	−0.977651	+	0.210233i	$0.932578\pi$
$240$	−5.27004e6	+	1.03643e7i	−0.381224	+	0.749734i
$241$	2.32809e7			1.66322			0.831608	−	0.555362i	$-0.187420\pi$
$241$	2.32809e7			1.66322			0.831608	+	0.555362i	$0.187420\pi$
$242$	−1.37194e6	−	162091.i	−0.0968031	−	0.0114370i
$243$		−	3.67792e7i		−	2.56321i
$244$	8.95210e6	+	2.14528e6i	0.616248	+	0.147677i
$245$	−6.10597e6			−0.415199
$246$	−74133.1	+	627464.i	−0.00497974	+	0.0421486i
$247$		−	7.56875e6i		−	0.502265i
$248$	−4.59174e6	+	1.24704e7i	−0.301038	+	0.817569i
$249$	−5.03869e6			−0.326377
$250$	1.38789e6	+	163975.i	0.0888249	+	0.0104944i
$251$			1.91423e7i			1.21052i	0.796027	+	0.605261i	$0.206931\pi$
$251$			1.91423e7i			1.21052i	−0.796027	+	0.605261i	$0.793069\pi$
$252$	−2.53162e6	+	1.05643e7i	−0.158196	+	0.660143i
$253$	2.01886e7			1.24665
$254$	1.56963e6	−	1.32854e7i	0.0957846	−	0.810722i
$255$		−	1.00366e7i		−	0.605295i
$256$	9.88394e6	+	1.35566e7i	0.589129	+	0.808039i
$257$	−3.16403e7			−1.86398			−0.931990	−	0.362484i	$-0.881929\pi$
$257$	−3.16403e7			−1.86398			−0.931990	+	0.362484i	$0.881929\pi$
$258$	2.31504e6	+	273516.i	0.134803	+	0.0159266i
$259$			758686.i			0.0436680i
$260$	−2.79354e6	−	669442.i	−0.158940	−	0.0380884i
$261$	3.65534e7			2.05592
$262$	382788.	−	3.23993e6i	0.0212841	−	0.180149i
$263$			2.83432e7i			1.55805i	0.626994	+	0.779024i	$0.284285\pi$
$263$			2.83432e7i			1.55805i	−0.626994	+	0.779024i	$0.715715\pi$
$264$	−3.08503e7	−	1.13595e7i	−1.67667	−	0.617370i
$265$	4.29133e6			0.230597
$266$	6.87287e6	+	812010.i	0.365168	+	0.0431436i
$267$		−	4.57871e7i		−	2.40552i
$268$	4.95400e6	−	2.06727e7i	0.257366	−	1.07397i
$269$	4.95398e6			0.254505			0.127253	−	0.991870i	$-0.459384\pi$
$269$	4.95398e6			0.254505			0.127253	+	0.991870i	$0.459384\pi$
$270$	−2.98585e6	+	2.52723e7i	−0.151697	+	1.28396i
$271$		−	1.31809e7i		−	0.662275i	−0.943583	−	0.331137i	$-0.892568\pi$
$271$		−	1.31809e7i		−	0.662275i	0.943583	−	0.331137i	$-0.107432\pi$
$272$	−1.29091e7	−	6.56400e6i	−0.641488	−	0.326184i
$273$	−3.74175e6			−0.183902
$274$	−2.36860e7	−	2.79843e6i	−1.15144	−	0.136039i
$275$			3.95146e6i			0.190002i
$276$	−5.04598e7	−	1.20922e7i	−2.40004	−	0.575144i
$277$	2.91094e7			1.36960			0.684801	−	0.728730i	$-0.259889\pi$
$277$	2.91094e7			1.36960			0.684801	+	0.728730i	$0.259889\pi$
$278$	3.08306e6	−	2.60951e7i	0.143499	−	1.21457i
$279$			4.80059e7i			2.21046i
$280$	907596.	−	2.46488e6i	0.0413446	−	0.112285i
$281$	−2.32202e7			−1.04652			−0.523259	−	0.852173i	$-0.675284\pi$
$281$	−2.32202e7			−1.04652			−0.523259	+	0.852173i	$0.675284\pi$
$282$	4.66060e7	+	5.50637e6i	2.07824	+	0.245538i
$283$			3.03875e7i			1.34071i	0.742040	+	0.670356i	$0.233859\pi$
$283$			3.03875e7i			1.34071i	−0.742040	+	0.670356i	$0.766141\pi$
$284$	7.04150e6	−	2.93837e7i	0.307405	−	1.28278i
$285$	2.67587e7			1.15593
$286$	952983.	−	8.06607e6i	0.0407368	−	0.344797i
$287$		−	142734.i		−	0.00603783i
$288$	5.04282e7	+	3.36193e7i	2.11104	+	1.40738i
$289$	−1.16366e7			−0.482097
$290$	−8.77720e6	−	1.03700e6i	−0.359884	−	0.0425192i
$291$			2.74285e7i			1.11307i
$292$	1.04814e7	+	2.51176e6i	0.420990	+	0.100886i
$293$	−2.38857e7			−0.949588			−0.474794	−	0.880097i	$-0.657477\pi$
$293$	−2.38857e7			−0.949588			−0.474794	+	0.880097i	$0.657477\pi$
$294$	−5.20624e6	+	4.40657e7i	−0.204872	+	1.73404i
$295$		−	1.55024e7i		−	0.603855i
$296$	3.97205e6	+	1.46255e6i	0.153158	+	0.0563945i
$297$	−7.19526e7			−2.74648
$298$	−2.68568e7	−	3.17306e6i	−1.01486	−	0.119903i
$299$		−	1.28196e7i		−	0.479579i
$300$	2.36676e6	−	9.87634e6i	0.0876578	−	0.365790i
$301$	−526619.			−0.0193107
$302$	−5.38928e6	+	4.56149e7i	−0.195663	+	1.65610i
$303$		−	5.76986e7i		−	2.07414i
$304$	1.75004e7	−	3.44171e7i	0.622912	−	1.22505i
$305$	−8.04072e6			−0.283397
$306$	−5.19550e7	−	6.13833e6i	−1.81327	−	0.214233i
$307$			2.22159e7i			0.767801i	0.923374	+	0.383900i	$0.125419\pi$
$307$			2.22159e7i			0.767801i	−0.923374	+	0.383900i	$0.874581\pi$
$308$	7.22223e6	+	1.73073e6i	0.247183	+	0.0592349i
$309$	−1.36771e7			−0.463573
$310$	1.36190e6	−	1.15272e7i	0.0457153	−	0.386935i
$311$		−	4.51336e7i		−	1.50044i	−0.661188	−	0.750220i	$-0.729948\pi$
$311$		−	4.51336e7i		−	1.50044i	0.661188	−	0.750220i	$-0.270052\pi$
$312$	−7.21315e6	+	1.95897e7i	−0.237499	+	0.645005i
$313$	3.95152e7			1.28864			0.644319	−	0.764757i	$-0.277141\pi$
$313$	3.95152e7			1.28864			0.644319	+	0.764757i	$0.277141\pi$
$314$	3.80101e7	+	4.49079e6i	1.22775	+	0.145055i
$315$		−	9.48877e6i		−	0.303584i
$316$	−6.55052e6	+	2.73349e7i	−0.207594	+	0.866275i
$317$	−4.71641e7			−1.48059			−0.740294	−	0.672284i	$-0.765314\pi$
$317$	−4.71641e7			−1.48059			−0.740294	+	0.672284i	$0.765314\pi$
$318$	3.65899e6	−	3.09698e7i	0.113784	−	0.963068i
$319$		−	2.49896e7i		−	0.769815i
$320$	−1.11551e7	−	9.50331e6i	−0.340426	−	0.290018i
$321$	8.38479e6			0.253500
$322$	1.16409e7	+	1.37534e6i	0.348675	+	0.0411950i
$323$			3.33288e7i			0.989037i
$324$	9.59210e7	+	2.29865e7i	2.82019	+	0.675829i
$325$	2.50914e6			0.0730928
$326$	1.42519e6	−	1.20629e7i	0.0411359	−	0.348175i
$327$			5.98043e7i			1.71037i
$328$	−747272.	−	275154.i	−0.0211766	−	0.00779749i
$329$	−1.06018e7			−0.297709
$330$	2.85170e7	+	3.36920e6i	0.793527	+	0.0937530i
$331$		−	1.53303e7i		−	0.422733i	−0.977407	−	0.211367i	$-0.932209\pi$
$331$		−	1.53303e7i		−	0.422733i	0.977407	−	0.211367i	$-0.0677914\pi$
$332$	1.47992e6	−	6.17562e6i	0.0404413	−	0.168759i
$333$	1.52908e7			0.414092
$334$	−2.36972e6	+	2.00574e7i	−0.0636002	+	0.538313i
$335$			1.85681e7i			0.493894i
$336$	−1.70147e7	−	8.65164e6i	−0.448546	−	0.228076i
$337$	2.56029e7			0.668959			0.334480	−	0.942403i	$-0.391439\pi$
$337$	2.56029e7			0.668959			0.334480	+	0.942403i	$0.391439\pi$
$338$	3.32259e7	+	3.92554e6i	0.860451	+	0.101660i
$339$			5.04170e6i			0.129413i
$340$	1.23013e7	+	2.94788e6i	0.312978	+	0.0750019i
$341$	3.28190e7			0.827680
$342$	1.63655e7	−	1.38518e8i	0.409120	−	3.46280i
$343$		−	2.08208e7i		−	0.515959i
$344$	−1.01519e6	+	2.75708e6i	−0.0249386	+	0.0677288i
$345$	4.53227e7			1.10372
$346$	−7.22176e7	−	8.53231e6i	−1.74347	−	0.205986i
$347$			3.72093e7i			0.890560i	0.895391	+	0.445280i	$0.146896\pi$
$347$			3.72093e7i			0.890560i	−0.895391	+	0.445280i	$0.853104\pi$
$348$	−1.49677e7	+	6.24593e7i	−0.355155	+	1.48204i
$349$	5.03804e6			0.118518			0.0592591	−	0.998243i	$-0.481126\pi$
$349$	5.03804e6			0.118518			0.0592591	+	0.998243i	$0.481126\pi$
$350$	−269192.	+	2.27845e6i	−0.00627853	+	0.0531416i
$351$			4.56892e7i			1.05656i
$352$	2.29837e7	−	3.44750e7i	0.526978	−	0.790454i
$353$	−2.74442e7			−0.623916			−0.311958	−	0.950096i	$-0.600985\pi$
$353$	−2.74442e7			−0.623916			−0.311958	+	0.950096i	$0.600985\pi$
$354$	−1.11878e8	−	1.32181e7i	−2.52194	−	0.297960i
$355$			2.63923e7i			0.589919i
$356$	5.61185e7	+	1.34482e7i	1.24382	+	0.298068i
$357$	1.64767e7			0.362132
$358$	−4.80722e6	+	4.06884e7i	−0.104772	+	0.886791i
$359$		−	8.99242e7i		−	1.94354i	−0.235930	−	0.971770i	$-0.575814\pi$
$359$		−	8.99242e7i		−	1.94354i	0.235930	−	0.971770i	$-0.424186\pi$
$360$	−4.96778e7	−	1.82919e7i	−1.06477	−	0.392060i
$361$	−4.18125e7			−0.888761
$362$	8.73089e6	+	1.03153e6i	0.184049	+	0.0217449i
$363$		−	8.76894e6i		−	0.183327i
$364$	1.09900e6	−	4.58605e6i	0.0227873	−	0.0950899i
$365$	−9.41436e6			−0.193603
$366$	−6.85590e6	+	5.80285e7i	−0.139837	+	1.18358i
$367$		−	6.27396e7i		−	1.26924i	−0.772825	−	0.634619i	$-0.781157\pi$
$367$		−	6.27396e7i		−	1.26924i	0.772825	−	0.634619i	$-0.218843\pi$
$368$	2.96413e7	−	5.82940e7i	0.594776	−	1.16972i
$369$	−2.87669e6			−0.0572551
$370$	−3.67162e6	−	433792.i	−0.0724858	−	0.00856399i
$371$			7.04492e6i			0.137960i
$372$	−8.20284e7	−	1.96573e7i	−1.59344	−	0.381851i
$373$	−3.13566e7			−0.604230			−0.302115	−	0.953272i	$-0.597693\pi$
$373$	−3.13566e7			−0.604230			−0.302115	+	0.953272i	$0.597693\pi$
$374$	−4.19645e6	+	3.55188e7i	−0.0802171	+	0.678959i
$375$			8.87087e6i			0.168218i
$376$	−2.04376e7	+	5.55050e7i	−0.384473	+	1.04416i
$377$	−1.58681e7			−0.296143
$378$	−4.14885e7	−	4.90175e6i	−0.768162	−	0.0907562i
$379$			7.54561e6i			0.138604i	0.997596	+	0.0693021i	$0.0220773\pi$
$379$			7.54561e6i			0.138604i	−0.997596	+	0.0693021i	$0.977923\pi$
$380$	−7.85936e6	+	3.27966e7i	−0.143231	+	0.597693i
$381$	8.49151e7			1.53536
$382$	−1.15328e7	+	9.76135e7i	−0.206892	+	1.75114i
$383$		−	3.79673e7i		−	0.675793i	−0.941183	−	0.337897i	$-0.890285\pi$
$383$		−	3.79673e7i		−	0.675793i	0.941183	−	0.337897i	$-0.109715\pi$
$384$	−7.80951e7	+	7.24012e7i	−1.37921	+	1.27865i
$385$	−6.48696e6			−0.113673
$386$	7.97416e7	+	9.42125e6i	1.38651	+	0.163812i
$387$			1.06136e7i			0.183118i
$388$	−3.36175e7	−	8.05607e6i	−0.575532	−	0.137920i
$389$	6.37380e7			1.08280			0.541402	−	0.840764i	$-0.317894\pi$
$389$	6.37380e7			1.08280			0.541402	+	0.840764i	$0.317894\pi$
$390$	2.13941e6	−	1.81080e7i	0.0360662	−	0.305265i
$391$			5.64508e7i			0.944365i
$392$	−5.24796e7	−	1.93236e7i	−0.871230	−	0.320797i
$393$	2.07084e7			0.341169
$394$	−5.19550e6	−	613834.i	−0.0849452	−	0.0100360i
$395$		−	2.45520e7i		−	0.398379i
$396$	3.48816e7	−	1.45559e8i	0.561709	−	2.34397i
$397$	3.64066e7			0.581847			0.290924	−	0.956746i	$-0.406037\pi$
$397$	3.64066e7			0.581847			0.290924	+	0.956746i	$0.406037\pi$
$398$	−5.33285e6	+	4.51373e7i	−0.0845883	+	0.715957i
$399$			4.39288e7i			0.691562i
$400$	1.14097e7	+	5.80160e6i	0.178277	+	0.0906500i
$401$	2.23344e7			0.346370			0.173185	−	0.984889i	$-0.444594\pi$
$401$	2.23344e7			0.346370			0.173185	+	0.984889i	$0.444594\pi$
$402$	1.34003e8	+	1.58321e7i	2.06270	+	0.243702i
$403$		−	2.08398e7i		−	0.318404i
$404$	7.07178e7	+	1.69468e7i	1.07247	+	0.257006i
$405$	−8.61557e7			−1.29694
$406$	1.70241e6	−	1.44092e7i	0.0254381	−	0.215309i
$407$		−	1.04535e7i		−	0.155052i
$408$	3.17630e7	−	8.62628e7i	0.467671	−	1.27011i
$409$	−1.30542e8			−1.90802			−0.954008	−	0.299783i	$-0.903086\pi$
$409$	−1.30542e8			−1.90802			−0.954008	+	0.299783i	$0.903086\pi$
$410$	690752.	+	81610.4i	0.0100224	+	0.00118412i
$411$		−	1.51392e8i		−	2.18061i
$412$	4.01712e6	−	1.67632e7i	0.0574412	−	0.239699i
$413$	2.54497e7			0.361270
$414$	2.77191e7	−	2.34615e8i	0.390641	−	3.30639i
$415$			5.54691e6i			0.0776081i
$416$	−2.18913e7	−	1.45945e7i	−0.304083	−	0.202725i
$417$	1.66790e8			2.30018
$418$	−9.46971e7	−	1.11882e7i	−1.29660	−	0.153190i
$419$			1.13434e8i			1.54206i	0.636799	+	0.771030i	$0.280258\pi$
$419$			1.13434e8i			1.54206i	−0.636799	+	0.771030i	$0.719742\pi$
$420$	1.62136e7	+	3.88542e6i	0.218843	+	0.0524434i
$421$	−2.39723e7			−0.321264			−0.160632	−	0.987014i	$-0.551353\pi$
$421$	−2.39723e7			−0.321264			−0.160632	+	0.987014i	$0.551353\pi$
$422$	−3.16839e6	+	2.68173e7i	−0.0421601	+	0.356844i
$423$			2.13672e8i			2.82310i
$424$	3.68832e7	+	1.35808e7i	0.483872	+	0.178167i
$425$	−1.10489e7			−0.143931
$426$	1.90469e8	+	2.25033e7i	2.46374	+	0.291084i
$427$		−	1.32002e7i		−	0.169549i
$428$	−2.46271e6	+	1.02767e7i	−0.0314111	+	0.131076i
$429$	5.15553e7			0.652982
$430$	301104.	−	2.54855e6i	0.00378713	−	0.0320544i
$431$		−	1.75148e7i		−	0.218762i	−0.994000	−	0.109381i	$-0.965113\pi$
$431$		−	1.75148e7i		−	0.218762i	0.994000	−	0.109381i	$-0.0348869\pi$
$432$	−1.05642e8	+	2.07761e8i	−1.31035	+	2.57699i
$433$	3.93936e7			0.485246			0.242623	−	0.970121i	$-0.421992\pi$
$433$	3.93936e7			0.485246			0.242623	+	0.970121i	$0.421992\pi$
$434$	1.89237e7	+	2.23579e6i	0.231493	+	0.0273503i
$435$		−	5.61006e7i		−	0.681553i
$436$	−7.32986e7	−	1.75652e7i	−0.884375	−	0.211931i
$437$	−1.50504e8			−1.80345
$438$	−8.02713e6	+	6.79418e7i	−0.0955296	+	0.808565i
$439$			1.08998e8i			1.28833i	0.764887	+	0.644164i	$0.222795\pi$
$439$			1.08998e8i			1.28833i	−0.764887	+	0.644164i	$0.777205\pi$
$440$	−1.25052e7	+	3.39620e7i	−0.146802	+	0.398690i
$441$	−2.02025e8			−2.35554
$442$	2.25541e7	+	2.66470e6i	0.261191	+	0.0308590i
$443$		−	4.41906e7i		−	0.508299i	−0.967165	−	0.254149i	$-0.918204\pi$
$443$		−	4.41906e7i		−	0.508299i	0.967165	−	0.254149i	$-0.0817955\pi$
$444$	−6.26120e6	+	2.61276e7i	−0.0715334	+	0.298504i
$445$	−5.04054e7			−0.572001
$446$	1.64753e7	−	1.39447e8i	0.185707	−	1.57183i
$447$		−	1.71659e8i		−	1.92196i
$448$	1.56012e7	−	1.83129e7i	0.173510	−	0.203668i
$449$	1.69223e8			1.86947			0.934737	−	0.355340i	$-0.115635\pi$
$449$	1.69223e8			1.86947			0.934737	+	0.355340i	$0.115635\pi$
$450$	4.59204e7	+	5.42537e6i	0.503928	+	0.0595377i
$451$			1.96664e6i			0.0214385i
$452$	−6.17932e6	−	1.48081e6i	−0.0669153	−	0.0160355i
$453$	−2.91554e8			−3.13635
$454$	−4.08621e6	+	3.45858e7i	−0.0436670	+	0.369598i
$455$			4.11916e6i			0.0437295i
$456$	2.29986e8	+	8.46836e7i	2.42553	+	0.893110i
$457$	7.83820e7			0.821236			0.410618	−	0.911808i	$-0.365313\pi$
$457$	7.83820e7			0.821236			0.410618	+	0.911808i	$0.365313\pi$
$458$	8.19909e7	+	9.68699e6i	0.853432	+	0.100831i
$459$		−	2.01192e8i		−	2.08052i
$460$	−1.33118e7	+	5.55494e7i	−0.136762	+	0.570697i
$461$	−5.73198e7			−0.585062			−0.292531	−	0.956256i	$-0.594497\pi$
$461$	−5.73198e7			−0.585062			−0.292531	+	0.956256i	$0.594497\pi$
$462$	−5.53109e6	+	4.68153e7i	−0.0560900	+	0.474746i
$463$		−	7.77769e7i		−	0.783624i	−0.920045	−	0.391812i	$-0.871848\pi$
$463$		−	7.77769e7i		−	0.783624i	0.920045	−	0.391812i	$-0.128152\pi$
$464$	−7.21565e7	−	3.66901e7i	−0.722307	−	0.367278i
$465$	7.36775e7			0.732784
$466$	−6.47192e7	−	7.64639e6i	−0.639551	−	0.0755612i
$467$			1.72752e7i			0.169618i	0.996397	+	0.0848089i	$0.0270280\pi$
$467$			1.72752e7i			0.169618i	−0.996397	+	0.0848089i	$0.972972\pi$
$468$	−9.24284e7	−	2.21495e7i	−0.901712	−	0.216086i
$469$	−3.04826e7			−0.295484
$470$	6.06177e6	−	5.13069e7i	0.0583856	−	0.494177i
$471$			2.42947e8i			2.32514i
$472$	4.90605e7	−	1.33240e8i	0.466559	−	1.26709i
$473$	7.25596e6			0.0685665
$474$	−1.77188e8	−	2.09342e7i	−1.66379	−	0.196572i
$475$		−	2.94577e7i		−	0.274864i
$476$	−4.83942e6	+	2.01946e7i	−0.0448717	+	0.187247i
$477$	1.41985e8			1.30824
$478$	5.38801e6	−	4.56042e7i	0.0493338	−	0.417562i
$479$			3.06358e7i			0.278755i	0.990239	+	0.139377i	$0.0445101\pi$
$479$			3.06358e7i			0.278755i	−0.990239	+	0.139377i	$0.955490\pi$
$480$	5.15976e7	−	7.73951e7i	0.466558	−	0.699826i
$481$	−6.63786e6			−0.0596475
$482$	−1.84961e8	−	2.18526e7i	−1.65173	−	0.195147i
$483$			7.44046e7i			0.660326i
$484$	1.07476e7	+	2.57554e6i	0.0947926	+	0.0227160i
$485$	3.01950e7			0.264673
$486$	−3.45228e7	+	2.92201e8i	−0.300744	+	2.54550i
$487$		−	3.94222e7i		−	0.341314i	−0.985330	−	0.170657i	$-0.945411\pi$
$487$		−	3.94222e7i		−	0.341314i	0.985330	−	0.170657i	$-0.0545890\pi$
$488$	−6.91085e7	−	2.54465e7i	−0.594664	−	0.218962i
$489$	7.71013e7			0.659379
$490$	4.85104e7	+	5.73137e6i	0.412331	+	0.0487158i
$491$			6.86050e7i			0.579577i	0.957091	+	0.289789i	$0.0935850\pi$
$491$			6.86050e7i			0.579577i	−0.957091	+	0.289789i	$0.906415\pi$
$492$	1.17794e6	−	4.91545e6i	0.00989069	−	0.0412732i
$493$	6.98751e7			0.583152
$494$	−7.10440e6	+	6.01317e7i	−0.0589314	+	0.498796i
$495$			1.30740e8i			1.07794i
$496$	4.81855e7	−	9.47639e7i	0.394885	−	0.776601i
$497$	−4.33273e7			−0.352933
$498$	4.00311e7	+	4.72956e6i	0.324123	+	0.0382942i
$499$			9.61683e7i			0.773981i	0.922084	+	0.386991i	$0.126485\pi$
$499$			9.61683e7i			0.773981i	−0.922084	+	0.386991i	$0.873515\pi$
$500$	−1.08725e7	−	2.60548e6i	−0.0869801	−	0.0208439i
$501$	−1.28199e8			−1.01947
$502$	1.79679e7	−	1.52081e8i	0.142032	−	1.20216i
$503$		−	1.42087e8i		−	1.11648i	−0.829681	−	0.558238i	$-0.811478\pi$
$503$		−	1.42087e8i		−	1.11648i	0.829681	−	0.558238i	$-0.188522\pi$
$504$	3.00292e7	−	8.15542e7i	0.234559	−	0.637022i
$505$	−6.35183e7			−0.493202
$506$	−1.60393e8	−	1.89500e7i	−1.23804	−	0.146271i
$507$			2.12367e8i			1.62954i
$508$	−2.49406e7	+	1.04075e8i	−0.190246	+	0.793884i
$509$	2.00915e7			0.152356			0.0761779	−	0.997094i	$-0.475728\pi$
$509$	2.00915e7			0.152356			0.0761779	+	0.997094i	$0.475728\pi$
$510$	−9.42086e6	+	7.97383e7i	−0.0710199	+	0.601114i
$511$		−	1.54552e7i		−	0.115828i
$512$	−6.58004e7	−	1.16982e8i	−0.490251	−	0.871581i
$513$	5.36400e8			3.97316
$514$	2.51374e8	+	2.96991e7i	1.85111	+	0.218703i
$515$			1.50566e7i			0.110231i
$516$	−1.81357e7	−	4.34603e6i	−0.132003	−	0.0316332i
$517$	1.46076e8			1.05708
$518$	712140.	−	6.02757e6i	0.00512361	−	0.0433663i
$519$		−	4.61588e8i		−	3.30181i
$520$	2.15656e7	+	7.94069e6i	0.153374	+	0.0564740i
$521$	6.06060e7			0.428551			0.214275	−	0.976773i	$-0.431261\pi$
$521$	6.06060e7			0.428551			0.214275	+	0.976773i	$0.431261\pi$
$522$	−2.90407e8	−	3.43108e7i	−2.04172	−	0.241223i
$523$		−	6.53123e7i		−	0.456551i	−0.973597	−	0.228276i	$-0.926691\pi$
$523$		−	6.53123e7i		−	0.456551i	0.973597	−	0.228276i	$-0.0733087\pi$
$524$	−6.08231e6	+	2.53811e7i	−0.0422741	+	0.176407i
$525$	−1.45630e7			−0.100640
$526$	2.66043e7	−	2.25179e8i	0.182808	−	1.54729i
$527$			9.17676e7i			0.626985i
$528$	2.34435e8	+	1.19206e8i	1.59265	+	0.809832i
$529$	−1.06881e8			−0.721994
$530$	−3.40935e7	−	4.02805e6i	−0.229005	−	0.0270563i
$531$		−	5.12920e8i		−	3.42583i
$532$	−5.38410e7	−	1.29024e7i	−0.357584	−	0.0856913i
$533$	1.24880e6			0.00824727
$534$	−4.29780e7	+	3.63767e8i	−0.282243	+	2.38891i
$535$		−	9.23052e6i		−	0.0602788i
$536$	−5.87627e7	+	1.59589e8i	−0.381599	+	1.03636i
$537$	−2.60065e8			−1.67942
$538$	−3.93581e7	−	4.65004e6i	−0.252747	−	0.0298614i
$539$			1.38114e8i			0.882005i
$540$	4.74436e7	−	1.97979e8i	0.301298	−	1.25730i
$541$	1.05565e8			0.666698			0.333349	−	0.942803i	$-0.391821\pi$
$541$	1.05565e8			0.666698			0.333349	+	0.942803i	$0.391821\pi$
$542$	−1.23723e7	+	1.04719e8i	−0.0777055	+	0.657700i
$543$			5.58046e7i			0.348555i
$544$	9.63981e7	+	6.42664e7i	0.598786	+	0.399197i
$545$	6.58364e7			0.406702
$546$	2.97273e7	+	3.51219e6i	0.182632	+	0.0215775i
$547$			3.04052e8i			1.85774i	0.370402	+	0.928872i	$0.379220\pi$
$547$			3.04052e8i			1.85774i	−0.370402	+	0.928872i	$0.620780\pi$
$548$	1.85552e8	+	4.44657e7i	1.12752	+	0.270199i
$549$	−2.66040e8			−1.60779
$550$	3.70903e6	−	3.13933e7i	0.0222932	−	0.188690i
$551$			1.86295e8i			1.11364i
$552$	3.89540e8	+	1.43433e8i	2.31598	+	0.852771i
$553$	4.03062e7			0.238339
$554$	−2.31267e8	−	2.73235e7i	−1.36014	−	0.160697i
$555$		−	2.34676e7i		−	0.137275i
$556$	−4.89882e7	+	2.04425e8i	−0.285015	+	1.18935i
$557$	2.14782e8			1.24289			0.621445	−	0.783458i	$-0.286546\pi$
$557$	2.14782e8			1.24289			0.621445	+	0.783458i	$0.286546\pi$
$558$	4.50607e7	−	3.81394e8i	0.259355	−	2.19519i
$559$		−	4.60747e6i		−	0.0263771i
$560$	−9.52427e6	+	1.87309e7i	−0.0542335	+	0.106658i
$561$	−2.27023e8			−1.28582
$562$	1.84479e8	+	2.17956e7i	1.03929	+	0.122789i
$563$		−	1.52173e8i		−	0.852733i	−0.904551	−	0.426366i	$-0.859793\pi$
$563$		−	1.52173e8i		−	0.852733i	0.904551	−	0.426366i	$-0.140207\pi$
$564$	−3.65104e8	−	8.74934e7i	−2.03507	−	0.487683i
$565$	5.55023e6			0.0307727
$566$	2.85232e7	−	2.41421e8i	0.157307	−	1.33145i
$567$		−	1.41439e8i		−	0.775923i
$568$	−8.35239e7	+	2.26837e8i	−0.455791	+	1.23785i
$569$	2.25478e8			1.22396			0.611981	−	0.790873i	$-0.290373\pi$
$569$	2.25478e8			1.22396			0.611981	+	0.790873i	$0.290373\pi$
$570$	−2.12591e8	−	2.51171e7i	−1.14794	−	0.135626i
$571$			2.29693e8i			1.23379i	0.787047	+	0.616893i	$0.211609\pi$
$571$			2.29693e8i			1.23379i	−0.787047	+	0.616893i	$0.788391\pi$
$572$	−1.51424e7	+	6.31883e7i	−0.0809109	+	0.337636i
$573$	−6.23909e8			−3.31633
$574$	−133977.	+	1.13398e6i	−0.000708425	+	0.00599612i
$575$		−	4.98941e7i		−	0.262450i
$576$	−3.69082e8	−	3.14431e8i	−1.93133	−	1.64535i
$577$	−3.10445e8			−1.61606			−0.808030	−	0.589141i	$-0.799466\pi$
$577$	−3.10445e8			−1.61606			−0.808030	+	0.589141i	$0.799466\pi$
$578$	9.24502e7	+	1.09227e7i	0.478767	+	0.0565650i
$579$			5.09679e8i			2.62580i
$580$	6.87592e7	+	1.64774e7i	0.352409	+	0.0844511i
$581$	−9.10616e6			−0.0464309
$582$	2.57457e7	−	2.17912e8i	0.130598	−	1.10538i
$583$		−	9.70676e7i		−	0.489856i
$584$	−8.09146e7	−	2.97937e7i	−0.406245	−	0.149584i
$585$	8.30187e7			0.414675
$586$	1.89766e8	+	2.24203e7i	0.943029	+	0.111416i
$587$		−	2.93067e7i		−	0.144895i	−0.997372	−	0.0724474i	$-0.976919\pi$
$587$		−	2.93067e7i		−	0.144895i	0.997372	−	0.0724474i	$-0.0230809\pi$
$588$	8.27245e7	−	3.45204e8i	0.406914	−	1.69802i
$589$	−2.44663e8			−1.19735
$590$	−1.45513e7	+	1.23162e8i	−0.0708510	+	0.599684i
$591$		−	3.32077e7i		−	0.160871i
$592$	−3.01841e7	−	1.53480e7i	−0.145483	−	0.0739752i
$593$	1.44018e8			0.690644			0.345322	−	0.938484i	$-0.387770\pi$
$593$	1.44018e8			0.690644			0.345322	+	0.938484i	$0.387770\pi$
$594$	5.71645e8	+	6.75383e7i	2.72751	+	0.322248i
$595$		−	1.81387e7i		−	0.0861101i
$596$	2.10392e8	+	5.04183e7i	0.993782	+	0.238149i
$597$	−2.88501e8			−1.35589
$598$	−1.20331e7	+	1.01848e8i	−0.0562696	+	0.476267i
$599$		−	2.11564e8i		−	0.984379i	−0.870488	−	0.492189i	$-0.836197\pi$
$599$		−	2.11564e8i		−	0.984379i	0.870488	−	0.492189i	$-0.163803\pi$
$600$	−2.80737e7	+	7.62434e7i	−0.129971	+	0.352979i
$601$	1.12631e8			0.518842			0.259421	−	0.965764i	$-0.416468\pi$
$601$	1.12631e8			0.518842			0.259421	+	0.965764i	$0.416468\pi$
$602$	4.18386e6	+	494311.i	0.0191773	+	0.00226574i
$603$			6.14354e8i			2.80199i
$604$	8.56328e7	−	3.57340e8i	0.388624	−	1.62170i
$605$	−9.65341e6			−0.0435928
$606$	−5.41588e7	+	4.58401e8i	−0.243361	+	2.05981i
$607$		−	3.22477e8i		−	1.44189i	−0.692992	−	0.720946i	$-0.743708\pi$
$607$		−	3.22477e8i		−	1.44189i	0.692992	−	0.720946i	$-0.256292\pi$
$608$	−1.71341e8	+	2.57008e8i	−0.762345	+	1.14350i
$609$	9.20983e7			0.407755
$610$	6.38815e7	+	7.54742e6i	0.281440	+	0.0332513i
$611$		−	9.27568e7i		−	0.406651i
$612$	4.07007e8	+	9.75349e7i	1.77561	+	0.425506i
$613$	1.87346e8			0.813324			0.406662	−	0.913579i	$-0.366693\pi$
$613$	1.87346e8			0.813324			0.406662	+	0.913579i	$0.366693\pi$
$614$	2.08529e7	−	1.76500e8i	0.0900870	−	0.762498i
$615$			4.41503e6i			0.0189805i
$616$	−5.57542e7	−	2.05293e7i	−0.238526	−	0.0878280i
$617$	5.10161e7			0.217196			0.108598	−	0.994086i	$-0.465364\pi$
$617$	5.10161e7			0.217196			0.108598	+	0.994086i	$0.465364\pi$
$618$	1.08661e8	+	1.28380e7i	0.460371	+	0.0543916i
$619$		−	3.83764e8i		−	1.61805i	−0.587774	−	0.809025i	$-0.699996\pi$
$619$		−	3.83764e8i		−	1.61805i	0.587774	−	0.809025i	$-0.300004\pi$
$620$	−2.16400e7	+	9.03021e7i	−0.0907991	+	0.378899i
$621$	9.08529e8			3.79371
$622$	−4.23646e7	+	3.58575e8i	−0.176048	+	1.49008i
$623$		−	8.27486e7i		−	0.342213i
$624$	7.56944e7	−	1.48864e8i	0.311537	−	0.612684i
$625$	9.76562e6			0.0400000
$626$	−3.13938e8	−	3.70909e7i	−1.27974	−	0.151197i
$627$		−	6.05268e8i		−	2.45553i
$628$	−2.97765e8	−	7.13564e7i	−1.20225	−	0.288107i
$629$	2.92297e7			0.117455
$630$	−8.90663e6	+	7.53859e7i	−0.0356198	+	0.301487i
$631$		−	5.24412e6i		−	0.0208730i	−0.999946	−	0.0104365i	$-0.996678\pi$
$631$		−	5.24412e6i		−	0.0208730i	0.999946	−	0.0104365i	$-0.00332210\pi$
$632$	7.77000e7	−	2.11020e8i	0.307801	−	0.835934i
$633$	−1.71406e8			−0.675796
$634$	3.74707e8	+	4.42706e7i	1.47036	+	0.173719i
$635$		−	9.34800e7i		−	0.365088i
$636$	−5.81395e7	+	2.42613e8i	−0.225996	+	0.943065i
$637$	8.77010e7			0.339302
$638$	−2.34564e7	+	1.98536e8i	−0.0903233	+	0.764498i
$639$			8.73229e8i			3.34677i
$640$	7.97038e7	+	8.59720e7i	0.304046	+	0.327957i
$641$	−1.88158e7			−0.0714413			−0.0357206	−	0.999362i	$-0.511373\pi$
$641$	−1.88158e7			−0.0714413			−0.0357206	+	0.999362i	$0.511373\pi$
$642$	−6.66150e7	−	7.87038e6i	−0.251749	−	0.0297434i
$643$		−	2.13902e8i		−	0.804603i	−0.915507	−	0.402302i	$-0.868210\pi$
$643$		−	2.13902e8i		−	0.804603i	0.915507	−	0.402302i	$-0.131790\pi$
$644$	−9.11933e7	−	2.18535e7i	−0.341433	−	0.0818208i
$645$	1.62894e7			0.0607051
$646$	3.12841e7	−	2.64789e8i	0.116045	−	0.982206i
$647$			3.04981e7i			0.112606i	0.998414	+	0.0563029i	$0.0179312\pi$
$647$			3.04981e7i			0.112606i	−0.998414	+	0.0563029i	$0.982069\pi$
$648$	−7.40491e8	−	2.72658e8i	−2.72142	−	1.00206i
$649$	−3.50656e8			−1.28276
$650$	−1.99345e7	−	2.35520e6i	−0.0725879	−	0.00857606i
$651$			1.20954e8i			0.438405i
$652$	−2.26456e7	+	9.44986e7i	−0.0817035	+	0.340944i
$653$	−4.41039e8			−1.58393			−0.791967	−	0.610563i	$-0.790943\pi$
$653$	−4.41039e8			−1.58393			−0.791967	+	0.610563i	$0.790943\pi$
$654$	5.61353e7	−	4.75130e8i	0.200679	−	1.69855i
$655$		−	2.27971e7i		−	0.0811253i
$656$	5.67861e6	+	2.88746e6i	0.0201155	+	0.0102283i
$657$	−3.11488e8			−1.09836
$658$	8.42286e7	+	9.95138e6i	0.295653	+	0.0349306i
$659$		−	3.50023e8i		−	1.22304i	−0.791230	−	0.611519i	$-0.790559\pi$
$659$		−	3.50023e8i		−	1.22304i	0.791230	−	0.611519i	$-0.209441\pi$
$660$	−2.23398e8	−	5.35349e7i	−0.777046	−	0.186211i
$661$	4.28072e8			1.48222			0.741109	−	0.671385i	$-0.234300\pi$
$661$	4.28072e8			1.48222			0.741109	+	0.671385i	$0.234300\pi$
$662$	−1.43898e7	+	1.21795e8i	−0.0495998	+	0.419813i
$663$			1.44157e8i			0.494648i
$664$	−1.75544e7	+	4.76746e7i	−0.0599626	+	0.162848i
$665$	4.83597e7			0.164444
$666$	−1.21481e8	−	1.43527e7i	−0.411232	−	0.0485859i
$667$			3.15537e8i			1.06334i
$668$	3.76537e7	−	1.57126e8i	0.126322	−	0.527133i
$669$	8.91293e8			2.97675
$670$	1.74289e7	−	1.47519e8i	0.0579491	−	0.490482i
$671$			1.81877e8i			0.602019i
$672$	1.27057e8	+	8.47059e7i	0.418687	+	0.279129i
$673$	2.25709e8			0.740464			0.370232	−	0.928939i	$-0.379278\pi$
$673$	2.25709e8			0.740464			0.370232	+	0.928939i	$0.379278\pi$
$674$	−2.03409e8	−	2.40321e7i	−0.664338	−	0.0784897i
$675$			1.77824e8i			0.578200i
$676$	−2.60286e8	−	6.23749e7i	−0.842580	−	0.201915i
$677$	7.81992e7			0.252021			0.126010	−	0.992029i	$-0.459783\pi$
$677$	7.81992e7			0.252021			0.126010	+	0.992029i	$0.459783\pi$
$678$	4.73239e6	−	4.00550e7i	0.0151842	−	0.128519i
$679$			4.95700e7i			0.158347i
$680$	−9.49636e7	−	3.49667e7i	−0.302016	−	0.111206i
$681$	−2.21059e8			−0.699951
$682$	−2.60739e8	−	3.08055e7i	−0.821963	−	0.0971127i
$683$			2.57804e8i			0.809146i	0.914506	+	0.404573i	$0.132580\pi$
$683$			2.57804e8i			0.809146i	−0.914506	+	0.404573i	$0.867420\pi$
$684$	−2.60039e8	+	1.08513e9i	−0.812588	+	3.39088i
$685$	−1.66662e8			−0.518520
$686$	−1.95434e7	+	1.65416e8i	−0.0605380	+	0.512395i
$687$			5.24055e8i			1.61624i
$688$	1.06533e7	−	2.09514e7i	0.0327130	−	0.0643350i
$689$	−6.16370e7			−0.188445
$690$	−3.60077e8	−	4.25421e7i	−1.09610	−	0.129501i
$691$		−	2.77384e8i		−	0.840713i	−0.907359	−	0.420357i	$-0.861905\pi$
$691$		−	2.77384e8i		−	0.840713i	0.907359	−	0.420357i	$-0.138095\pi$
$692$	5.65742e8	+	1.35574e8i	1.70726	+	0.409127i
$693$	−2.14631e8			−0.644901
$694$	3.49265e7	−	2.95619e8i	0.104490	−	0.884409i
$695$		−	1.83613e8i		−	0.546952i
$696$	1.77542e8	−	4.82174e8i	0.526591	−	1.43013i
$697$	−5.49906e6			−0.0162401
$698$	−4.00259e7	−	4.72895e6i	−0.117700	−	0.0139059i
$699$		−	4.13661e8i		−	1.21119i
$700$	4.27732e6	−	1.78490e7i	0.0124703	−	0.0520379i
$701$	4.72598e7			0.137195			0.0685974	−	0.997644i	$-0.478148\pi$
$701$	4.72598e7			0.137195			0.0685974	+	0.997644i	$0.478148\pi$
$702$	4.28862e7	−	3.62989e8i	0.123967	−	1.04926i
$703$			7.79296e7i			0.224304i
$704$	−2.14960e8	+	2.52322e8i	−0.616083	+	0.723163i
$705$	3.27935e8			0.935879
$706$	2.18037e8	+	2.57605e7i	0.619607	+	0.0732048i
$707$		−	1.04276e8i		−	0.295070i
$708$	8.76435e8	+	2.10028e8i	2.46956	+	0.591805i
$709$	−4.22496e8			−1.18545			−0.592726	−	0.805404i	$-0.701948\pi$
$709$	−4.22496e8			−1.18545			−0.592726	+	0.805404i	$0.701948\pi$
$710$	2.47731e7	−	2.09680e8i	0.0692158	−	0.585844i
$711$		−	8.12341e8i		−	2.26011i
$712$	−4.33224e8	−	1.59518e8i	−1.20025	−	0.441947i
$713$	−4.14398e8			−1.14327
$714$	−1.30903e8	−	1.54659e7i	−0.359631	−	0.0424893i
$715$		−	5.67554e7i		−	0.155270i
$716$	7.63843e7	−	3.18747e8i	0.208096	−	0.868373i
$717$	2.91485e8			0.790785
$718$	−8.44073e7	+	7.14425e8i	−0.228038	+	1.93012i
$719$			9.02589e6i			0.0242831i	0.999926	+	0.0121415i	$0.00386486\pi$
$719$			9.02589e6i			0.0242831i	−0.999926	+	0.0121415i	$0.996135\pi$
$720$	3.77508e8	+	1.91955e8i	1.01141	+	0.514282i
$721$	−2.47179e7			−0.0659486
$722$	3.32190e8	+	3.92473e7i	0.882622	+	0.104279i
$723$		−	1.18220e9i		−	3.12807i
$724$	−6.83965e7	−	1.63905e7i	−0.180226	−	0.0431893i
$725$	−6.17591e7			−0.162064
$726$	−8.23096e6	+	6.96670e7i	−0.0215100	+	0.182061i
$727$			4.91993e8i			1.28043i	0.768196	+	0.640215i	$0.221155\pi$
$727$			4.91993e8i			1.28043i	−0.768196	+	0.640215i	$0.778845\pi$
$728$	−1.30359e7	+	3.54034e7i	−0.0337869	+	0.0917594i
$729$	−7.44108e8			−1.92067
$730$	7.47947e7	+	8.83678e6i	0.192266	+	0.0227157i
$731$			2.02889e7i			0.0519406i
$732$	1.08937e8	−	4.54586e8i	0.277742	−	1.15900i
$733$	5.81009e8			1.47527			0.737634	−	0.675201i	$-0.235943\pi$
$733$	5.81009e8			1.47527			0.737634	+	0.675201i	$0.235943\pi$
$734$	−5.88904e7	+	4.98450e8i	−0.148921	+	1.26047i
$735$			3.10060e8i			0.780880i
$736$	−2.90210e8	+	4.35308e8i	−0.727912	+	1.09185i
$737$	4.20001e8			1.04917
$738$	2.28546e7	+	2.70021e6i	0.0568597	+	0.00671781i
$739$			3.91007e8i			0.968838i	0.874836	+	0.484419i	$0.160969\pi$
$739$			3.91007e8i			0.968838i	−0.874836	+	0.484419i	$0.839031\pi$
$740$	2.87629e7	+	6.89273e6i	0.0709803	+	0.0170097i
$741$	−3.84340e8			−0.944628
$742$	6.61271e6	−	5.59701e7i	0.0161870	−	0.137007i
$743$			6.77953e8i			1.65285i	0.563048	+	0.826424i	$0.309628\pi$
$743$			6.77953e8i			1.65285i	−0.563048	+	0.826424i	$0.690372\pi$
$744$	6.33244e8	+	2.33168e8i	1.53763	+	0.566174i
$745$	−1.88973e8			−0.457016
$746$	2.49120e8	+	2.94328e7i	0.600056	+	0.0708950i
$747$			1.83528e8i			0.440292i
$748$	6.66794e7	−	2.78249e8i	0.159326	−	0.664857i
$749$	1.51534e7			0.0360632
$750$	8.32664e6	−	7.04768e7i	0.0197372	−	0.167056i
$751$			1.34306e8i			0.317085i	0.987352	+	0.158542i	$0.0506794\pi$
$751$			1.34306e8i			0.317085i	−0.987352	+	0.158542i	$0.949321\pi$
$752$	2.14471e8	−	4.21789e8i	0.504330	−	0.991840i
$753$	9.72042e8			2.27667
$754$	1.26068e8	+	1.48946e7i	0.294098	+	0.0347468i
$755$			3.20961e8i			0.745781i
$756$	3.25015e8	+	7.78863e7i	0.752207	+	0.180259i
$757$	−7.87980e8			−1.81647			−0.908234	−	0.418463i	$-0.862569\pi$
$757$	−7.87980e8			−1.81647			−0.908234	+	0.418463i	$0.862569\pi$
$758$	7.08268e6	−	5.99479e7i	0.0162626	−	0.137647i
$759$		−	1.02518e9i		−	2.34462i
$760$	9.32251e7	−	2.53184e8i	0.212370	−	0.576759i
$761$	−5.89265e8			−1.33708			−0.668539	−	0.743677i	$-0.733080\pi$
$761$	−5.89265e8			−1.33708			−0.668539	+	0.743677i	$0.733080\pi$
$762$	−6.74629e8	−	7.97055e7i	−1.52475	−	0.180145i
$763$			1.08081e8i			0.243319i
$764$	1.83250e8	−	7.64689e8i	0.410926	−	1.71477i
$765$	−3.65571e8			−0.816559
$766$	−3.56380e7	+	3.01641e8i	−0.0792916	+	0.671126i
$767$			2.22663e8i			0.493472i
$768$	6.88405e8	−	5.01905e8i	1.51971	−	1.10799i
$769$	−4.75958e8			−1.04662			−0.523310	−	0.852142i	$-0.675303\pi$
$769$	−4.75958e8			−1.04662			−0.523310	+	0.852142i	$0.675303\pi$
$770$	5.15372e7	+	6.08898e6i	0.112888	+	0.0133374i
$771$			1.60669e9i			3.50565i
$772$	−6.24683e8	−	1.49699e8i	−1.35771	−	0.325362i
$773$	−4.75770e7			−0.103005			−0.0515026	−	0.998673i	$-0.516401\pi$
$773$	−4.75770e7			−0.103005			−0.0515026	+	0.998673i	$0.516401\pi$
$774$	9.96247e6	−	8.43226e7i	0.0214854	−	0.181853i
$775$		−	8.11089e7i		−	0.174246i
$776$	2.59520e8	+	9.55584e7i	0.555375	+	0.204496i
$777$	3.85260e7			0.0821279
$778$	−5.06382e8	−	5.98276e7i	−1.07532	−	0.127047i
$779$		−	1.46611e7i		−	0.0310138i
$780$	−3.39942e7	+	1.41855e8i	−0.0716342	+	0.298925i
$781$	5.96980e8			1.25316
$782$	5.29875e7	−	4.48487e8i	0.110803	−	0.937842i
$783$		−	1.12458e9i		−	2.34264i
$784$	3.98799e8	+	2.02781e8i	0.827573	+	0.420804i
$785$	2.67451e8			0.552886
$786$	−1.64523e8	−	1.94379e7i	−0.338812	−	0.0400297i
$787$		−	6.88813e8i		−	1.41311i	−0.707656	−	0.706557i	$-0.750247\pi$
$787$		−	6.88813e8i		−	1.41311i	0.707656	−	0.706557i	$-0.249753\pi$
$788$	4.07008e7	+	9.75351e6i	0.0831810	+	0.0199334i
$789$	1.43926e9			2.93028
$790$	−2.30457e7	+	1.95060e8i	−0.0467422	+	0.395627i
$791$			9.11160e6i			0.0184105i
$792$	−4.13754e8	+	1.12369e9i	−0.832850	+	2.26188i
$793$	1.15490e8			0.231593
$794$	−2.89241e8	−	3.41730e7i	−0.577828	−	0.0682688i
$795$		−	2.17913e8i		−	0.433693i
$796$	8.47363e7	−	3.53599e8i	0.168008	−	0.701087i
$797$	1.93915e8			0.383034			0.191517	−	0.981489i	$-0.438659\pi$
$797$	1.93915e8			0.383034			0.191517	+	0.981489i	$0.438659\pi$
$798$	4.12338e7	−	3.49003e8i	0.0811417	−	0.686785i
$799$			4.08453e8i			0.800758i
$800$	−8.52015e7	−	5.68019e7i	−0.166409	−	0.110941i
$801$	−1.66774e9			−3.24512
$802$	−1.77441e8	−	2.09641e7i	−0.343978	−	0.0406400i
$803$			2.12948e8i			0.411270i
$804$	−1.04976e9	−	2.51563e8i	−2.01986	−	0.484038i
$805$	8.19093e7			0.157017
$806$	−1.95612e7	+	1.65567e8i	−0.0373586	+	0.316204i
$807$		−	2.51562e8i		−	0.478657i
$808$	−5.45928e8	−	2.01017e8i	−1.03491	−	0.381065i
$809$	−2.69550e7			−0.0509090			−0.0254545	−	0.999676i	$-0.508103\pi$
$809$	−2.69550e7			−0.0509090			−0.0254545	+	0.999676i	$0.508103\pi$
$810$	6.84485e8	+	8.08699e7i	1.28798	+	0.152171i
$811$			1.12006e6i			0.00209981i	0.999999	+	0.00104990i	$0.000334195\pi$
$811$			1.12006e6i			0.00209981i	−0.999999	+	0.00104990i	$0.999666\pi$
$812$	−2.70504e7	+	1.12879e8i	−0.0505249	+	0.210837i
$813$	−6.69326e8			−1.24556
$814$	−9.81214e6	+	8.30501e7i	−0.0181924	+	0.153981i
$815$		−	8.48781e7i		−	0.156792i
$816$	−3.33319e8	+	6.55521e8i	−0.613465	+	1.20647i
$817$	−5.40925e7			−0.0991907
$818$	1.03713e9	+	1.22534e8i	1.89484	+	0.223870i
$819$			1.36289e8i			0.248089i
$820$	−5.41124e6	−	1.29675e6i	−0.00981422	−	0.00235187i
$821$	−4.27689e8			−0.772856			−0.386428	−	0.922320i	$-0.626291\pi$
$821$	−4.27689e8			−0.772856			−0.386428	+	0.922320i	$0.626291\pi$
$822$	−1.42104e8	+	1.20277e9i	−0.255853	+	2.16555i
$823$			8.99926e8i			1.61439i	0.590288	+	0.807193i	$0.299014\pi$
$823$			8.99926e8i			1.61439i	−0.590288	+	0.807193i	$0.700986\pi$
$824$	−4.76498e7	+	1.29409e8i	−0.0851686	+	0.231303i
$825$	2.00654e8			0.357344
$826$	−2.02191e8	−	2.38883e7i	−0.358775	−	0.0423883i
$827$		−	9.93270e8i		−	1.75611i	−0.478563	−	0.878053i	$-0.658842\pi$
$827$		−	9.93270e8i		−	1.75611i	0.478563	−	0.878053i	$-0.341158\pi$
$828$	−4.40442e8	+	1.83794e9i	−0.775885	+	3.23772i
$829$	2.24021e8			0.393211			0.196605	−	0.980483i	$-0.437008\pi$
$829$	2.24021e8			0.393211			0.196605	+	0.980483i	$0.437008\pi$
$830$	5.20660e6	−	4.40688e7i	0.00910584	−	0.0770720i
$831$		−	1.47817e9i		−	2.57586i
$832$	1.60222e8	+	1.36497e8i	0.278197	+	0.237003i
$833$	−3.86190e8			−0.668137
$834$	−1.32510e9	−	1.56557e8i	−2.28429	−	0.269883i
$835$			1.41130e8i			0.242415i
$836$	7.41842e8	+	1.77775e8i	1.26968	+	0.304264i
$837$	1.47692e9			2.51873
$838$	1.06475e8	−	9.01204e8i	0.180932	−	1.53141i
$839$			7.36298e8i			1.24672i	0.781937	+	0.623358i	$0.214232\pi$
$839$			7.36298e8i			1.24672i	−0.781937	+	0.623358i	$0.785768\pi$
$840$	−1.25166e8	−	4.60876e7i	−0.211178	−	0.0777582i
$841$	−2.04250e8			−0.343380
$842$	1.90453e8	+	2.25015e7i	0.319045	+	0.0376943i
$843$			1.17912e9i			1.96822i
$844$	5.03441e7	−	2.10083e8i	0.0837378	−	0.349432i
$845$	2.33788e8			0.387482
$846$	2.00563e8	−	1.69757e9i	0.331237	−	2.80360i
$847$		−	1.58476e7i		−	0.0260804i
$848$	−2.80280e8	−	1.42516e8i	−0.459625	−	0.233710i
$849$	1.54307e9			2.52152
$850$	8.77811e7	+	1.03711e7i	0.142937	+	0.0168876i
$851$			1.31993e8i			0.214173i
$852$	−1.49210e9	−	3.57566e8i	−2.41257	−	0.578146i
$853$	9.76087e8			1.57268			0.786342	−	0.617791i	$-0.211972\pi$
$853$	9.76087e8			1.57268			0.786342	+	0.617791i	$0.211972\pi$
$854$	−1.23903e7	+	1.04872e8i	−0.0198934	+	0.168378i
$855$		−	9.74654e8i		−	1.55938i
$856$	2.92119e7	−	7.93345e7i	0.0465735	−	0.126486i
$857$	−3.18267e7			−0.0505649			−0.0252825	−	0.999680i	$-0.508049\pi$
$857$	−3.18267e7			−0.0505649			−0.0252825	+	0.999680i	$0.508049\pi$
$858$	−4.09594e8	−	4.83923e7i	−0.648472	−	0.0766152i
$859$		−	3.51311e8i		−	0.554258i	−0.960833	−	0.277129i	$-0.910617\pi$
$859$		−	3.51311e8i		−	0.554258i	0.960833	−	0.277129i	$-0.0893829\pi$
$860$	−4.78438e6	+	1.99649e7i	−0.00752195	+	0.0313886i
$861$	−7.24799e6			−0.0113556
$862$	−1.64402e7	+	1.39150e8i	−0.0256676	+	0.217251i
$863$		−	7.46593e8i		−	1.16159i	−0.814051	−	0.580793i	$-0.802743\pi$
$863$		−	7.46593e8i		−	1.16159i	0.814051	−	0.580793i	$-0.197257\pi$
$864$	1.03431e9	−	1.55145e9i	1.60366	−	2.40544i
$865$	−5.08146e8			−0.785127
$866$	−3.12972e8	−	3.69768e7i	−0.481894	−	0.0569345i
$867$			5.90907e8i			0.906697i
$868$	−1.48246e8	−	3.55255e7i	−0.226685	−	0.0543227i
$869$	−5.55354e8			−0.846273
$870$	−5.26588e7	+	4.45705e8i	−0.0799674	+	0.676846i
$871$		−	2.66697e8i		−	0.403611i
$872$	5.65851e8	+	2.08353e8i	0.853400	+	0.314232i
$873$	9.99048e8			1.50156
$874$	1.19572e9	+	1.41271e8i	1.79099	+	0.211601i
$875$			1.60319e7i			0.0239309i
$876$	1.27547e8	−	5.32245e8i	0.189740	−	0.791771i
$877$	7.51643e8			1.11433			0.557164	−	0.830403i	$-0.311889\pi$
$877$	7.51643e8			1.11433			0.557164	+	0.830403i	$0.311889\pi$
$878$	1.02311e8	−	8.65964e8i	0.151161	−	1.27943i
$879$			1.21291e9i			1.78592i
$880$	1.31229e8	−	2.58081e8i	0.192567	−	0.378712i
$881$	2.85122e8			0.416968			0.208484	−	0.978026i	$-0.433147\pi$
$881$	2.85122e8			0.416968			0.208484	+	0.978026i	$0.433147\pi$
$882$	1.60504e9	+	1.89631e8i	2.33927	+	0.276378i
$883$		−	3.81100e8i		−	0.553550i	−0.960935	−	0.276775i	$-0.910734\pi$
$883$		−	3.81100e8i		−	0.553550i	0.960935	−	0.276775i	$-0.0892658\pi$
$884$	−1.76685e8	−	4.23408e7i	−0.255766	−	0.0612917i
$885$	−7.87209e8			−1.13569
$886$	−4.14795e7	+	3.51083e8i	−0.0596393	+	0.504788i
$887$			7.23444e7i			0.103665i	0.998656	+	0.0518327i	$0.0165063\pi$
$887$			7.23444e7i			0.103665i	−0.998656	+	0.0518327i	$0.983494\pi$
$888$	7.42683e7	−	2.01700e8i	0.106063	−	0.288049i
$889$	1.53463e8			0.218422
$890$	4.00458e8	+	4.73129e7i	0.568050	+	0.0671135i
$891$			1.94880e9i			2.75507i
$892$	−2.61783e8	+	1.09241e9i	−0.368848	+	1.53918i
$893$	−1.08898e9			−1.52921
$894$	−1.61127e8	+	1.36379e9i	−0.225505	+	1.90868i
$895$			2.86296e8i			0.399343i
$896$	−1.41137e8	+	1.30847e8i	−0.196208	+	0.181903i
$897$	−6.50977e8			−0.901962
$898$	−1.34443e9	−	1.58841e8i	−1.85656	−	0.219348i
$899$			5.12943e8i			0.705977i
$900$	−3.59734e8	−	8.62064e7i	−0.493462	−	0.118253i
$901$	2.71418e8			0.371077
$902$	1.84598e6	−	1.56244e7i	0.00251541	−	0.0212905i
$903$			2.67416e7i			0.0363183i
$904$	4.77031e7	+	1.75649e7i	0.0645716	+	0.0237760i
$905$	6.14333e7			0.0828816
$906$	2.31632e9	+	2.73667e8i	3.11468	+	0.367991i
$907$		−	9.85565e8i		−	1.32088i	−0.750879	−	0.660440i	$-0.770370\pi$
$907$		−	9.85565e8i		−	1.32088i	0.750879	−	0.660440i	$-0.229630\pi$
$908$	6.49278e7	−	2.70939e8i	0.0867308	−	0.361922i
$909$	−2.10160e9			−2.79807
$910$	3.86645e6	−	3.27257e7i	0.00513083	−	0.0434275i
$911$		−	1.17138e9i		−	1.54933i	−0.632371	−	0.774666i	$-0.717918\pi$
$911$		−	1.17138e9i		−	1.54933i	0.632371	−	0.774666i	$-0.282082\pi$
$912$	−1.74769e9	−	8.88666e8i	−2.30399	−	1.17153i
$913$	1.25468e8			0.164862
$914$	−6.22725e8	−	7.35732e7i	−0.815563	−	0.0963565i
$915$			4.08307e8i			0.532995i
$916$	−6.42304e8	−	1.53921e8i	−0.835707	−	0.200268i
$917$	3.74252e7			0.0485352
$918$	−1.88848e8	+	1.59842e9i	−0.244110	+	2.06615i
$919$		−	1.13344e9i		−	1.46034i	−0.683268	−	0.730168i	$-0.739442\pi$
$919$		−	1.13344e9i		−	1.46034i	0.683268	−	0.730168i	$-0.260558\pi$
$920$	1.57900e8	−	4.28830e8i	0.202777	−	0.550709i
$921$	1.12812e9			1.44403
$922$	4.55391e8	+	5.38031e7i	0.581021	+	0.0686460i
$923$		−	3.79076e8i		−	0.482083i
$924$	8.78862e7	−	3.66744e8i	0.111405	−	0.464886i
$925$	−2.58347e7			−0.0326421
$926$	−7.30052e7	+	6.17917e8i	−0.0919435	+	0.778211i
$927$			4.98171e8i			0.625373i
$928$	5.38826e8	+	3.59223e8i	0.674225	+	0.449490i
$929$	−3.91500e8			−0.488298			−0.244149	−	0.969738i	$-0.578509\pi$
$929$	−3.91500e8			−0.488298			−0.244149	+	0.969738i	$0.578509\pi$
$930$	−5.85349e8	−	6.91573e7i	−0.727722	−	0.0859784i
$931$		−	1.02963e9i		−	1.27594i
$932$	5.07000e8	+	1.21497e8i	0.626268	+	0.150078i
$933$	−2.29188e9			−2.82193
$934$	1.62153e7	−	1.37247e8i	0.0199014	−	0.168446i
$935$			2.49921e8i			0.305751i
$936$	7.13530e8	+	2.62730e8i	0.870130	+	0.320392i
$937$	−2.03549e8			−0.247429			−0.123714	−	0.992318i	$-0.539481\pi$
$937$	−2.03549e8			−0.247429			−0.123714	+	0.992318i	$0.539481\pi$
$938$	2.42176e8	+	2.86124e7i	0.293443	+	0.0346694i
$939$		−	2.00657e9i		−	2.42359i
$940$	−9.63183e7	+	4.01930e8i	−0.115965	+	0.483913i
$941$	−1.27603e9			−1.53141			−0.765706	−	0.643191i	$-0.777610\pi$
$941$	−1.27603e9			−1.53141			−0.765706	+	0.643191i	$0.777610\pi$
$942$	2.28042e8	−	1.93015e9i	0.272811	−	2.30908i
$943$		−	2.48323e7i		−	0.0296129i
$944$	−5.14839e8	+	1.01251e9i	−0.612006	+	1.20360i
$945$	−2.91926e8			−0.345922
$946$	−5.76468e7	−	6.81080e6i	−0.0680929	−	0.00804498i
$947$			2.29619e8i			0.270370i	0.990820	+	0.135185i	$0.0431628\pi$
$947$			2.29619e8i			0.270370i	−0.990820	+	0.135185i	$0.956837\pi$
$948$	1.38806e9	+	3.32634e8i	1.62923	+	0.390429i
$949$	1.35220e8			0.158213
$950$	−2.76505e7	+	2.34034e8i	−0.0322502	+	0.272966i
$951$			2.39499e9i			2.78459i
$952$	5.74035e7	−	1.55898e8i	0.0665316	−	0.180688i
$953$	5.00345e8			0.578084			0.289042	−	0.957316i	$-0.406663\pi$
$953$	5.00345e8			0.578084			0.289042	+	0.957316i	$0.406663\pi$
$954$	−1.12804e9	−	1.33274e8i	−1.29921	−	0.153498i
$955$			6.86839e8i			0.788579i
$956$	−8.56126e7	+	3.57256e8i	−0.0979860	+	0.408889i
$957$	−1.26897e9			−1.44782
$958$	2.87563e7	−	2.43393e8i	0.0327066	−	0.276830i
$959$		−	2.73603e8i		−	0.310217i
$960$	−4.82577e8	+	5.66452e8i	−0.545447	+	0.640250i
$961$	2.13850e8			0.240957
$962$	5.27361e7	+	6.23062e6i	0.0592356	+	0.00699851i
$963$		−	3.05406e8i		−	0.341978i
$964$	1.44895e9	+	3.47227e8i	1.61742	+	0.387598i
$965$	5.61087e8			0.624379
$966$	6.98398e7	−	5.91125e8i	0.0774768	−	0.655765i
$967$			1.01984e9i			1.12786i	0.825823	+	0.563929i	$0.190711\pi$
$967$			1.01984e9i			1.12786i	−0.825823	+	0.563929i	$0.809289\pi$
$968$	−8.29692e7	−	3.05502e7i	−0.0914725	−	0.0336813i
$969$	1.69243e9			1.86012
$970$	−2.39892e8	−	2.83425e7i	−0.262845	−	0.0310544i
$971$		−	1.05811e9i		−	1.15578i	−0.816116	−	0.577889i	$-0.803877\pi$
$971$		−	1.05811e9i		−	1.15578i	0.816116	−	0.577889i	$-0.196123\pi$
$972$	5.48549e8	−	2.28906e9i	0.597333	−	2.49263i
$973$	3.01431e8			0.327227
$974$	−3.70036e7	+	3.13199e8i	−0.0400468	+	0.338957i
$975$		−	1.27414e8i		−	0.137468i
$976$	5.25164e8	+	2.67035e8i	0.564866	+	0.287223i
$977$	−1.09291e8			−0.117192			−0.0585961	−	0.998282i	$-0.518662\pi$
$977$	−1.09291e8			−0.117192			−0.0585961	+	0.998282i	$0.518662\pi$
$978$	−6.12550e8	−	7.23711e7i	−0.654825	−	0.0773657i
$979$			1.14014e9i			1.21510i
$980$	−3.80023e8	−	9.10684e7i	−0.403767	−	0.0967586i
$981$	2.17830e9			2.30733
$982$	6.43960e7	−	5.45049e8i	0.0680025	−	0.575574i
$983$			1.80844e9i			1.90390i	0.306255	+	0.951950i	$0.400924\pi$
$983$			1.80844e9i			1.90390i	−0.306255	+	0.951950i	$0.599076\pi$
$984$	−1.39723e7	+	3.79463e7i	−0.0146650	+	0.0398276i
$985$	−3.65572e7			−0.0382529
$986$	−5.55139e8	−	6.55882e7i	−0.579124	−	0.0684218i
$987$			5.38358e8i			0.559912i
$988$	1.12885e8	−	4.71063e8i	0.117049	−	0.488436i
$989$	−9.16193e7			−0.0947105
$990$	1.22719e8	−	1.03870e9i	0.126475	−	1.07049i
$991$		−	4.67836e8i		−	0.480698i	−0.970687	−	0.240349i	$-0.922738\pi$
$991$		−	4.67836e8i		−	0.480698i	0.970687	−	0.240349i	$-0.0772619\pi$
$992$	−4.71771e8	+	7.07645e8i	−0.483277	+	0.724904i
$993$	−7.78470e8			−0.795049
$994$	3.44224e8	+	4.06691e7i	0.350495	+	0.0414100i
$995$			3.17600e8i			0.322413i
$996$	−3.13597e8	−	7.51503e7i	−0.317391	−	0.0760594i
$997$	1.52490e9			1.53871			0.769356	−	0.638820i	$-0.220577\pi$
$997$	1.52490e9			1.53871			0.769356	+	0.638820i	$0.220577\pi$
$998$	9.02683e7	−	7.64033e8i	0.0908121	−	0.768635i
$999$		−	4.70427e8i		−	0.471841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.7.b.a.11.1	✓	12
3.2	odd	2		180.7.c.a.91.12		12
4.3	odd	2	inner	20.7.b.a.11.2	yes	12
5.2	odd	4		100.7.d.b.99.13		24
5.3	odd	4		100.7.d.b.99.12		24
5.4	even	2		100.7.b.h.51.12		12
8.3	odd	2		320.7.b.d.191.1		12
8.5	even	2		320.7.b.d.191.12		12
12.11	even	2		180.7.c.a.91.11		12
20.3	even	4		100.7.d.b.99.14		24
20.7	even	4		100.7.d.b.99.11		24
20.19	odd	2		100.7.b.h.51.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.b.a.11.1	✓	12	1.1	even	1	trivial
20.7.b.a.11.2	yes	12	4.3	odd	2	inner
100.7.b.h.51.11		12	20.19	odd	2
100.7.b.h.51.12		12	5.4	even	2
100.7.d.b.99.11		24	20.7	even	4
100.7.d.b.99.12		24	5.3	odd	4
100.7.d.b.99.13		24	5.2	odd	4
100.7.d.b.99.14		24	20.3	even	4
180.7.c.a.91.11		12	12.11	even	2
180.7.c.a.91.12		12	3.2	odd	2
320.7.b.d.191.1		12	8.3	odd	2
320.7.b.d.191.12		12	8.5	even	2

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.94474 - 0.938649i) q^{2} -50.7798i q^{3} +(62.2379 + 14.9147i) q^{4} -55.9017 q^{5} +(-47.6645 + 403.433i) q^{6} -91.7717i q^{7} +(-480.464 - 176.913i) q^{8} -1849.59 q^{9} +O(q^{10})\)	\(q+(-7.94474 - 0.938649i) q^{2} -50.7798i q^{3} +(62.2379 + 14.9147i) q^{4} -55.9017 q^{5} +(-47.6645 + 403.433i) q^{6} -91.7717i q^{7} +(-480.464 - 176.913i) q^{8} -1849.59 q^{9} +(444.125 + 52.4721i) q^{10} +1264.47i q^{11} +(757.364 - 3160.43i) q^{12} +802.924 q^{13} +(-86.1415 + 729.103i) q^{14} +2838.68i q^{15} +(3651.11 + 1856.51i) q^{16} -3535.66 q^{17} +(14694.5 + 1736.12i) q^{18} -9426.47i q^{19} +(-3479.20 - 833.754i) q^{20} -4660.16 q^{21} +(1186.89 - 10045.9i) q^{22} -15966.1i q^{23} +(-8983.59 + 24397.9i) q^{24} +3125.00 q^{25} +(-6379.03 - 753.664i) q^{26} +56903.5i q^{27} +(1368.74 - 5711.68i) q^{28} -19762.9 q^{29} +(2664.52 - 22552.6i) q^{30} -25954.8i q^{31} +(-27264.5 - 18176.6i) q^{32} +64209.4 q^{33} +(28089.9 + 3318.75i) q^{34} +5130.20i q^{35} +(-115115. - 27586.0i) q^{36} -8267.10 q^{37} +(-8848.15 + 74890.9i) q^{38} -40772.4i q^{39} +(26858.8 + 9889.71i) q^{40} +1555.31 q^{41} +(37023.7 + 4374.25i) q^{42} -5738.36i q^{43} +(-18859.1 + 78697.7i) q^{44} +103395. q^{45} +(-14986.6 + 126847. i) q^{46} -115524. i q^{47} +(94273.4 - 185403. i) q^{48} +109227. q^{49} +(-24827.3 - 2933.28i) q^{50} +179540. i q^{51} +(49972.3 + 11975.3i) q^{52} -76765.7 q^{53} +(53412.5 - 452084. i) q^{54} -70685.8i q^{55} +(-16235.6 + 44093.0i) q^{56} -478675. q^{57} +(157011. + 18550.5i) q^{58} +277315. i q^{59} +(-42337.9 + 176673. i) q^{60} +143837. q^{61} +(-24362.5 + 206205. i) q^{62} +169740. i q^{63} +(199548. + 170000. i) q^{64} -44884.8 q^{65} +(-510127. - 60270.1i) q^{66} -332157. i q^{67} +(-220052. - 52733.2i) q^{68} -810757. q^{69} +(4815.45 - 40758.1i) q^{70} -472120. i q^{71} +(888663. + 327216. i) q^{72} +168409. q^{73} +(65680.0 + 7759.91i) q^{74} -158687. i q^{75} +(140593. - 586684. i) q^{76} +116042. q^{77} +(-38271.0 + 323926. i) q^{78} +439200. i q^{79} +(-204103. - 103782. i) q^{80} +1.54120e6 q^{81} +(-12356.5 - 1459.89i) q^{82} -99226.2i q^{83} +(-290038. - 69504.6i) q^{84} +197650. q^{85} +(-5386.31 + 45589.8i) q^{86} +1.00356e6i q^{87} +(223700. - 607531. i) q^{88} +901678. q^{89} +(-821450. - 97052.0i) q^{90} -73685.8i q^{91} +(238129. - 993697. i) q^{92} -1.31798e6 q^{93} +(-108436. + 917806. i) q^{94} +526956. i q^{95} +(-923006. + 1.38449e6i) q^{96} -540145. q^{97} +(-867780. - 102526. i) q^{98} -2.33875e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9}+O(q^{10}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9} + 750 q^{10} - 440 q^{12} - 5040 q^{13} + 6248 q^{14} + 3312 q^{16} + 6840 q^{17} + 15790 q^{18} - 3500 q^{20} - 27464 q^{21} - 26160 q^{22} + 28528 q^{24} + 37500 q^{25} - 18684 q^{26} + 19320 q^{28} - 74968 q^{29} - 13000 q^{30} - 60800 q^{32} + 112880 q^{33} + 48204 q^{34} - 128580 q^{36} + 62640 q^{37} + 74800 q^{38} + 57000 q^{40} - 16976 q^{41} - 138360 q^{42} - 222160 q^{44} + 77000 q^{45} - 144792 q^{46} + 297600 q^{48} + 72564 q^{49} - 31250 q^{50} + 548280 q^{52} + 322160 q^{53} + 150416 q^{54} - 246512 q^{56} - 1213440 q^{57} + 350700 q^{58} + 157000 q^{60} + 46464 q^{61} - 7120 q^{62} - 542784 q^{64} - 133000 q^{65} - 65200 q^{66} - 1678280 q^{68} + 41256 q^{69} - 360000 q^{70} + 2317560 q^{72} - 415080 q^{73} + 1581924 q^{74} + 208320 q^{76} + 75600 q^{77} + 473200 q^{78} + 734000 q^{80} + 2287428 q^{81} - 3169500 q^{82} - 2256224 q^{84} + 372000 q^{85} - 62512 q^{86} - 278880 q^{88} + 278392 q^{89} - 2162250 q^{90} + 4095720 q^{92} - 3646000 q^{93} + 4706568 q^{94} - 2641152 q^{96} + 2344680 q^{97} + 1050270 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9 + 750 * q^10 - 440 * q^12 - 5040 * q^13 + 6248 * q^14 + 3312 * q^16 + 6840 * q^17 + 15790 * q^18 - 3500 * q^20 - 27464 * q^21 - 26160 * q^22 + 28528 * q^24 + 37500 * q^25 - 18684 * q^26 + 19320 * q^28 - 74968 * q^29 - 13000 * q^30 - 60800 * q^32 + 112880 * q^33 + 48204 * q^34 - 128580 * q^36 + 62640 * q^37 + 74800 * q^38 + 57000 * q^40 - 16976 * q^41 - 138360 * q^42 - 222160 * q^44 + 77000 * q^45 - 144792 * q^46 + 297600 * q^48 + 72564 * q^49 - 31250 * q^50 + 548280 * q^52 + 322160 * q^53 + 150416 * q^54 - 246512 * q^56 - 1213440 * q^57 + 350700 * q^58 + 157000 * q^60 + 46464 * q^61 - 7120 * q^62 - 542784 * q^64 - 133000 * q^65 - 65200 * q^66 - 1678280 * q^68 + 41256 * q^69 - 360000 * q^70 + 2317560 * q^72 - 415080 * q^73 + 1581924 * q^74 + 208320 * q^76 + 75600 * q^77 + 473200 * q^78 + 734000 * q^80 + 2287428 * q^81 - 3169500 * q^82 - 2256224 * q^84 + 372000 * q^85 - 62512 * q^86 - 278880 * q^88 + 278392 * q^89 - 2162250 * q^90 + 4095720 * q^92 - 3646000 * q^93 + 4706568 * q^94 - 2641152 * q^96 + 2344680 * q^97 + 1050270 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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