LMFDB - Embedded newform 21.7.d.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(13,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("21.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.d (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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 1123x^{5} + 44168x^{4} - 138697x^{3} + 660109x^{2} + 680340x + 1040400 $ x^8 - x^7 + 212x^6 - 1123x^5 + 44168x^4 - 138697x^3 + 660109x^2 + 680340x + 1040400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{7}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.8
Root			$6.44130 - 11.1567i$ of defining polynomial
Character	$\chi$	$=$	21.13
Dual form			21.7.d.a.13.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+13.8826 q^{2} +15.5885i q^{3} +128.727 q^{4} -109.244i q^{5} +216.408i q^{6} +(86.6767 + 331.868i) q^{7} +898.572 q^{8} -243.000 q^{9} +O(q^{10})$	\(q+13.8826 q^{2} +15.5885i q^{3} +128.727 q^{4} -109.244i q^{5} +216.408i q^{6} +(86.6767 + 331.868i) q^{7} +898.572 q^{8} -243.000 q^{9} -1516.59i q^{10} -1737.67 q^{11} +2006.65i q^{12} -3262.69i q^{13} +(1203.30 + 4607.19i) q^{14} +1702.94 q^{15} +4236.02 q^{16} -1697.67i q^{17} -3373.47 q^{18} +5844.00i q^{19} -14062.6i q^{20} +(-5173.30 + 1351.16i) q^{21} -24123.4 q^{22} -9183.59 q^{23} +14007.4i q^{24} +3690.76 q^{25} -45294.6i q^{26} -3788.00i q^{27} +(11157.6 + 42720.2i) q^{28} +39201.5 q^{29} +23641.3 q^{30} +52622.3i q^{31} +1298.31 q^{32} -27087.6i q^{33} -23568.0i q^{34} +(36254.5 - 9468.91i) q^{35} -31280.5 q^{36} +31886.0 q^{37} +81129.9i q^{38} +50860.3 q^{39} -98163.6i q^{40} -30379.8i q^{41} +(-71818.9 + 18757.6i) q^{42} +49382.5 q^{43} -223684. q^{44} +26546.3i q^{45} -127492. q^{46} -5725.77i q^{47} +66033.0i q^{48} +(-102623. + 57530.4i) q^{49} +51237.3 q^{50} +26464.0 q^{51} -419995. i q^{52} +95850.1 q^{53} -52587.2i q^{54} +189830. i q^{55} +(77885.3 + 298207. i) q^{56} -91098.9 q^{57} +544218. q^{58} -267076. i q^{59} +219214. q^{60} -83516.6i q^{61} +730534. i q^{62} +(-21062.4 - 80643.8i) q^{63} -253081. q^{64} -356429. q^{65} -376046. i q^{66} -452018. q^{67} -218535. i q^{68} -143158. i q^{69} +(503307. - 131453. i) q^{70} +55293.2 q^{71} -218353. q^{72} +575111. i q^{73} +442661. q^{74} +57533.3i q^{75} +752277. i q^{76} +(-150616. - 576677. i) q^{77} +706074. q^{78} -54794.0 q^{79} -462759. i q^{80} +59049.0 q^{81} -421750. i q^{82} +204708. i q^{83} +(-665941. + 173930. i) q^{84} -185460. q^{85} +685557. q^{86} +611090. i q^{87} -1.56142e6 q^{88} -748708. i q^{89} +368531. i q^{90} +(1.08278e6 - 282799. i) q^{91} -1.18217e6 q^{92} -820300. q^{93} -79488.5i q^{94} +638421. q^{95} +20238.7i q^{96} -424248. i q^{97} +(-1.42468e6 + 798671. i) q^{98} +422254. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9	$ 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9} - 6848 q^{11} + 12082 q^{14} - 4536 q^{15} + 28466 q^{16} - 2430 q^{18} + 6804 q^{21} - 7764 q^{22} - 24320 q^{23} - 77056 q^{25} - 30142 q^{28} + 60496 q^{29} + 89424 q^{30} + 5082 q^{32} + 103656 q^{35} - 84078 q^{36} - 39112 q^{37} + 108864 q^{39} - 267624 q^{42} - 29272 q^{43} - 577884 q^{44} + 564972 q^{46} - 94864 q^{49} + 240154 q^{50} + 103032 q^{51} + 232288 q^{53} + 225722 q^{56} + 180792 q^{57} + 987684 q^{58} - 375192 q^{60} - 6804 q^{63} - 690734 q^{64} - 836304 q^{65} - 2163848 q^{67} - 366744 q^{70} - 506288 q^{71} + 355266 q^{72} + 512324 q^{74} + 1536304 q^{77} + 1272024 q^{78} - 93272 q^{79} + 472392 q^{81} - 653184 q^{84} + 3740760 q^{85} + 3846452 q^{86} - 2077548 q^{88} + 1890336 q^{91} - 9701580 q^{92} - 2153952 q^{93} + 4154832 q^{95} - 507542 q^{98} + 1664064 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9 - 6848 * q^11 + 12082 * q^14 - 4536 * q^15 + 28466 * q^16 - 2430 * q^18 + 6804 * q^21 - 7764 * q^22 - 24320 * q^23 - 77056 * q^25 - 30142 * q^28 + 60496 * q^29 + 89424 * q^30 + 5082 * q^32 + 103656 * q^35 - 84078 * q^36 - 39112 * q^37 + 108864 * q^39 - 267624 * q^42 - 29272 * q^43 - 577884 * q^44 + 564972 * q^46 - 94864 * q^49 + 240154 * q^50 + 103032 * q^51 + 232288 * q^53 + 225722 * q^56 + 180792 * q^57 + 987684 * q^58 - 375192 * q^60 - 6804 * q^63 - 690734 * q^64 - 836304 * q^65 - 2163848 * q^67 - 366744 * q^70 - 506288 * q^71 + 355266 * q^72 + 512324 * q^74 + 1536304 * q^77 + 1272024 * q^78 - 93272 * q^79 + 472392 * q^81 - 653184 * q^84 + 3740760 * q^85 + 3846452 * q^86 - 2077548 * q^88 + 1890336 * q^91 - 9701580 * q^92 - 2153952 * q^93 + 4154832 * q^95 - 507542 * q^98 + 1664064 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$-1$

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 $

$2$	13.8826			1.73532			0.867662	−	0.497154i	$-0.165622\pi$
$2$	13.8826			1.73532			0.867662	+	0.497154i	$0.165622\pi$
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	128.727			2.01135
$5$		−	109.244i		−	0.873952i	−0.899473	−	0.436976i	$-0.856050\pi$
$5$		−	109.244i		−	0.873952i	0.899473	−	0.436976i	$-0.143950\pi$
$6$			216.408i			1.00189i
$7$	86.6767	+	331.868i	0.252702	+	0.967544i
$7$	86.6767	+	331.868i	0.252702	+	0.967544i
$8$	898.572			1.75502
$9$	−243.000			−0.333333
$10$		−	1516.59i		−	1.51659i
$11$	−1737.67			−1.30554			−0.652769	−	0.757557i	$-0.726393\pi$
$11$	−1737.67			−1.30554			−0.652769	+	0.757557i	$0.726393\pi$
$12$			2006.65i			1.16125i
$13$		−	3262.69i		−	1.48507i	−0.669809	−	0.742534i	$-0.733624\pi$
$13$		−	3262.69i		−	1.48507i	0.669809	−	0.742534i	$-0.266376\pi$
$14$	1203.30	+	4607.19i	0.438520	+	1.67900i
$15$	1702.94			0.504576
$16$	4236.02			1.03418
$17$		−	1697.67i		−	0.345546i	−0.984962	−	0.172773i	$-0.944727\pi$
$17$		−	1697.67i		−	0.345546i	0.984962	−	0.172773i	$-0.0552726\pi$
$18$	−3373.47			−0.578442
$19$			5844.00i			0.852019i	0.904719	+	0.426009i	$0.140081\pi$
$19$			5844.00i			0.852019i	−0.904719	+	0.426009i	$0.859919\pi$
$20$		−	14062.6i		−	1.75782i
$21$	−5173.30	+	1351.16i	−0.558612	+	0.145897i
$22$	−24123.4			−2.26553
$23$	−9183.59			−0.754795			−0.377398	−	0.926051i	$-0.623181\pi$
$23$	−9183.59			−0.754795			−0.377398	+	0.926051i	$0.623181\pi$
$24$			14007.4i			1.01326i
$25$	3690.76			0.236209
$26$		−	45294.6i		−	2.57707i
$27$		−	3788.00i		−	0.192450i
$28$	11157.6	+	42720.2i	0.508272	+	1.94607i
$29$	39201.5			1.60734			0.803671	−	0.595074i	$-0.202877\pi$
$29$	39201.5			1.60734			0.803671	+	0.595074i	$0.202877\pi$
$30$	23641.3			0.875603
$31$			52622.3i			1.76638i	0.469014	+	0.883191i	$0.344609\pi$
$31$			52622.3i			1.76638i	−0.469014	+	0.883191i	$0.655391\pi$
$32$	1298.31			0.0396213
$33$		−	27087.6i		−	0.753752i
$34$		−	23568.0i		−	0.599634i
$35$	36254.5	−	9468.91i	0.845587	−	0.220849i
$36$	−31280.5			−0.670451
$37$	31886.0			0.629499			0.314749	−	0.949175i	$-0.398080\pi$
$37$	31886.0			0.629499			0.314749	+	0.949175i	$0.398080\pi$
$38$			81129.9i			1.47853i
$39$	50860.3			0.857404
$40$		−	98163.6i		−	1.53381i
$41$		−	30379.8i		−	0.440791i	−0.975411	−	0.220395i	$-0.929265\pi$
$41$		−	30379.8i		−	0.440791i	0.975411	−	0.220395i	$-0.0707348\pi$
$42$	−71818.9	+	18757.6i	−0.969373	+	0.253179i
$43$	49382.5			0.621109			0.310554	−	0.950556i	$-0.399485\pi$
$43$	49382.5			0.621109			0.310554	+	0.950556i	$0.399485\pi$
$44$	−223684.			−2.62590
$45$			26546.3i			0.291317i
$46$	−127492.			−1.30981
$47$		−	5725.77i		−	0.0551493i	−0.999620	−	0.0275746i	$-0.991222\pi$
$47$		−	5725.77i		−	0.0551493i	0.999620	−	0.0275746i	$-0.00877840\pi$
$48$			66033.0i			0.597086i
$49$	−102623.	+	57530.4i	−0.872284	+	0.489000i
$50$	51237.3			0.409899
$51$	26464.0			0.199501
$52$		−	419995.i		−	2.98699i
$53$	95850.1			0.643821			0.321910	−	0.946770i	$-0.395675\pi$
$53$	95850.1			0.643821			0.321910	+	0.946770i	$0.395675\pi$
$54$		−	52587.2i		−	0.333963i
$55$			189830.i			1.14098i
$56$	77885.3	+	298207.i	0.443498	+	1.69806i
$57$	−91098.9			−0.491913
$58$	544218.			2.78926
$59$		−	267076.i		−	1.30040i	−0.759761	−	0.650202i	$-0.774684\pi$
$59$		−	267076.i		−	1.30040i	0.759761	−	0.650202i	$-0.225316\pi$
$60$	219214.			1.01488
$61$		−	83516.6i		−	0.367945i	−0.982931	−	0.183973i	$-0.941104\pi$
$61$		−	83516.6i		−	0.367945i	0.982931	−	0.183973i	$-0.0588958\pi$
$62$			730534.i			3.06524i
$63$	−21062.4	−	80643.8i	−0.0842339	−	0.322515i
$64$	−253081.			−0.965428
$65$	−356429.			−1.29788
$66$		−	376046.i		−	1.30801i
$67$	−452018.			−1.50290			−0.751452	−	0.659788i	$-0.770646\pi$
$67$	−452018.			−1.50290			−0.751452	+	0.659788i	$0.770646\pi$
$68$		−	218535.i		−	0.695014i
$69$		−	143158.i		−	0.435781i
$70$	503307.	−	131453.i	1.46737	−	0.383245i
$71$	55293.2			0.154489			0.0772443	−	0.997012i	$-0.475388\pi$
$71$	55293.2			0.154489			0.0772443	+	0.997012i	$0.475388\pi$
$72$	−218353.			−0.585008
$73$			575111.i			1.47837i	0.673502	+	0.739185i	$0.264789\pi$
$73$			575111.i			1.47837i	−0.673502	+	0.739185i	$0.735211\pi$
$74$	442661.			1.09238
$75$			57533.3i			0.136375i
$76$			752277.i			1.71371i
$77$	−150616.	−	576677.i	−0.329912	−	1.26317i
$78$	706074.			1.48787
$79$	−54794.0			−0.111135			−0.0555676	−	0.998455i	$-0.517697\pi$
$79$	−54794.0			−0.111135			−0.0555676	+	0.998455i	$0.517697\pi$
$80$		−	462759.i		−	0.903827i
$81$	59049.0			0.111111
$82$		−	421750.i		−	0.764915i
$83$			204708.i			0.358014i	0.983848	+	0.179007i	$0.0572884\pi$
$83$			204708.i			0.358014i	−0.983848	+	0.179007i	$0.942712\pi$
$84$	−665941.	+	173930.i	−1.12357	+	0.293451i
$85$	−185460.			−0.301990
$86$	685557.			1.07783
$87$			611090.i			0.927999i
$88$	−1.56142e6			−2.29125
$89$		−	748708.i		−	1.06204i	−0.847358	−	0.531022i	$-0.821808\pi$
$89$		−	748708.i		−	1.06204i	0.847358	−	0.531022i	$-0.178192\pi$
$90$			368531.i			0.505530i
$91$	1.08278e6	−	282799.i	1.43687	−	0.375279i
$92$	−1.18217e6			−1.51816
$93$	−820300.			−1.01982
$94$		−	79488.5i		−	0.0957019i
$95$	638421.			0.744623
$96$			20238.7i			0.0228754i
$97$		−	424248.i		−	0.464841i	−0.972615	−	0.232420i	$-0.925336\pi$
$97$		−	424248.i		−	0.464841i	0.972615	−	0.232420i	$-0.0746645\pi$
$98$	−1.42468e6	+	798671.i	−1.51370	+	0.848574i
$99$	422254.			0.435179
$100$	475099.			0.475099
$101$			1.23918e6i			1.20274i	0.798972	+	0.601368i	$0.205377\pi$
$101$			1.23918e6i			1.20274i	−0.798972	+	0.601368i	$0.794623\pi$
$102$	367389.			0.346199
$103$		−	1.07972e6i		−	0.988097i	−0.869434	−	0.494048i	$-0.835517\pi$
$103$		−	1.07972e6i		−	0.988097i	0.869434	−	0.494048i	$-0.164483\pi$
$104$		−	2.93176e6i		−	2.60633i
$105$	147606.	+	565152.i	0.127507	+	0.488200i
$106$	1.33065e6			1.11724
$107$	992100.			0.809849			0.404925	−	0.914350i	$-0.367298\pi$
$107$	992100.			0.809849			0.404925	+	0.914350i	$0.367298\pi$
$108$		−	487615.i		−	0.387085i
$109$	−797352.			−0.615702			−0.307851	−	0.951435i	$-0.599610\pi$
$109$	−797352.			−0.615702			−0.307851	+	0.951435i	$0.599610\pi$
$110$			2.63533e6i			1.97996i
$111$			497054.i			0.363441i
$112$	367164.	+	1.40580e6i	0.261340	+	1.00062i
$113$	−846487.			−0.586658			−0.293329	−	0.956012i	$-0.594763\pi$
$113$	−846487.			−0.586658			−0.293329	+	0.956012i	$0.594763\pi$
$114$	−1.26469e6			−0.853629
$115$			1.00325e6i			0.659654i
$116$	5.04627e6			3.23293
$117$			792834.i			0.495022i
$118$		−	3.70771e6i		−	2.25662i
$119$	563400.	−	147148.i	0.334331	−	0.0873200i
$120$	1.53022e6			0.885543
$121$	1.24794e6			0.704428
$122$		−	1.15943e6i		−	0.638505i
$123$	473573.			0.254491
$124$			6.77388e6i			3.55281i
$125$		−	2.11013e6i		−	1.08039i
$126$	−292401.	−	1.11955e6i	−0.146173	−	0.559668i
$127$	318048.			0.155268			0.0776339	−	0.996982i	$-0.475263\pi$
$127$	318048.			0.155268			0.0776339	+	0.996982i	$0.475263\pi$
$128$	−3.59652e6			−1.71495
$129$			769797.i			0.358597i
$130$	−4.94817e6			−2.25224
$131$		−	2.41304e6i		−	1.07337i	−0.843781	−	0.536687i	$-0.819676\pi$
$131$		−	2.41304e6i		−	1.07337i	0.843781	−	0.536687i	$-0.180324\pi$
$132$		−	3.48689e6i		−	1.51606i
$133$	−1.93943e6	+	506538.i	−0.824366	+	0.215307i
$134$	−6.27518e6			−2.60802
$135$	−413816.			−0.168192
$136$		−	1.52548e6i		−	0.606441i
$137$	−2.26455e6			−0.880683			−0.440341	−	0.897830i	$-0.645143\pi$
$137$	−2.26455e6			−0.880683			−0.440341	+	0.897830i	$0.645143\pi$
$138$		−	1.98741e6i		−	0.756222i
$139$			741349.i			0.276044i	0.990429	+	0.138022i	$0.0440745\pi$
$139$			741349.i			0.276044i	−0.990429	+	0.138022i	$0.955926\pi$
$140$	4.66692e6	−	1.21890e6i	1.70077	−	0.444205i
$141$	89255.8			0.0318405
$142$	767613.			0.268088
$143$			5.66948e6i			1.93881i
$144$	−1.02935e6			−0.344728
$145$		−	4.28252e6i		−	1.40474i
$146$			7.98404e6i			2.56545i
$147$	−896810.	−	1.59974e6i	−0.282324	−	0.503613i
$148$	4.10457e6			1.26614
$149$	204962.			0.0619603			0.0309802	−	0.999520i	$-0.490137\pi$
$149$	204962.			0.0619603			0.0309802	+	0.999520i	$0.490137\pi$
$150$			798711.i			0.236655i
$151$	3.82185e6			1.11005			0.555025	−	0.831834i	$-0.312709\pi$
$151$	3.82185e6			1.11005			0.555025	+	0.831834i	$0.312709\pi$
$152$			5.25125e6i			1.49531i
$153$			412533.i			0.115182i
$154$	−2.09094e6	−	8.00577e6i	−0.572504	−	2.19200i
$155$	5.74866e6			1.54373
$156$	6.54707e6			1.72454
$157$			1.89152e6i			0.488778i	0.969677	+	0.244389i	$0.0785874\pi$
$157$			1.89152e6i			0.488778i	−0.969677	+	0.244389i	$0.921413\pi$
$158$	−760683.			−0.192856
$159$			1.49416e6i			0.371710i
$160$		−	141833.i		−	0.0346271i
$161$	−796004.	−	3.04774e6i	−0.190738	−	0.730298i
$162$	819753.			0.192814
$163$	2.21036e6			0.510388			0.255194	−	0.966890i	$-0.417861\pi$
$163$	2.21036e6			0.510388			0.255194	+	0.966890i	$0.417861\pi$
$164$		−	3.91068e6i		−	0.886586i
$165$	−2.95916e6			−0.658743
$166$			2.84187e6i			0.621270i
$167$		−	2.60126e6i		−	0.558515i	−0.960216	−	0.279258i	$-0.909912\pi$
$167$		−	2.60126e6i		−	0.558515i	0.960216	−	0.279258i	$-0.0900883\pi$
$168$	−4.64859e6	+	1.21411e6i	−0.980377	+	0.256053i
$169$	−5.81835e6			−1.20542
$170$	−2.57466e6			−0.524051
$171$		−	1.42009e6i		−	0.284006i
$172$	6.35684e6			1.24927
$173$			3.27646e6i			0.632801i	0.948626	+	0.316400i	$0.102474\pi$
$173$			3.27646e6i			0.632801i	−0.948626	+	0.316400i	$0.897526\pi$
$174$			8.48352e6i			1.61038i
$175$	319903.	+	1.22484e6i	0.0596903	+	0.228542i
$176$	−7.36080e6			−1.35017
$177$	4.16330e6			0.750789
$178$		−	1.03940e7i		−	1.84299i
$179$	1.70201e6			0.296758			0.148379	−	0.988931i	$-0.452594\pi$
$179$	1.70201e6			0.296758			0.148379	+	0.988931i	$0.452594\pi$
$180$			3.41721e6i			0.585941i
$181$			4.11903e6i			0.694639i	0.937747	+	0.347319i	$0.112908\pi$
$181$			4.11903e6i			0.694639i	−0.937747	+	0.347319i	$0.887092\pi$
$182$	1.50318e7	−	3.92599e6i	2.49343	−	0.651231i
$183$	1.30190e6			0.212433
$184$	−8.25212e6			−1.32468
$185$		−	3.48335e6i		−	0.550152i
$186$	−1.13879e7			−1.76972
$187$			2.94998e6i			0.451123i
$188$		−	737058.i		−	0.110925i
$189$	1.25711e6	−	328331.i	0.186204	−	0.0486325i
$190$	8.86295e6			1.29216
$191$	−1.22139e7			−1.75289			−0.876445	−	0.481501i	$-0.840092\pi$
$191$	−1.22139e7			−1.75289			−0.876445	+	0.481501i	$0.840092\pi$
$192$		−	3.94515e6i		−	0.557390i
$193$	3.31020e6			0.460450			0.230225	−	0.973137i	$-0.426054\pi$
$193$	3.31020e6			0.460450			0.230225	+	0.973137i	$0.426054\pi$
$194$		−	5.88966e6i		−	0.806649i
$195$		−	5.55618e6i		−	0.749329i
$196$	−1.32103e7	+	7.40569e6i	−1.75447	+	0.983552i
$197$	−3.18294e6			−0.416322			−0.208161	−	0.978095i	$-0.566748\pi$
$197$	−3.18294e6			−0.416322			−0.208161	+	0.978095i	$0.566748\pi$
$198$	5.86198e6			0.755177
$199$			5.15755e6i			0.654462i	0.944944	+	0.327231i	$0.106115\pi$
$199$			5.15755e6i			0.654462i	−0.944944	+	0.327231i	$0.893885\pi$
$200$	3.31641e6			0.414552
$201$		−	7.04626e6i		−	0.867702i
$202$			1.72030e7i			2.08714i
$203$	3.39785e6	+	1.30097e7i	0.406178	+	1.55517i
$204$	3.40662e6			0.401266
$205$	−3.31880e6			−0.385230
$206$		−	1.49893e7i		−	1.71467i
$207$	2.23161e6			0.251598
$208$		−	1.38208e7i		−	1.53583i
$209$		−	1.01549e7i		−	1.11234i
$210$	2.04915e6	+	7.84578e6i	0.221267	+	0.847185i
$211$	−4.48851e6			−0.477809			−0.238905	−	0.971043i	$-0.576788\pi$
$211$	−4.48851e6			−0.477809			−0.238905	+	0.971043i	$0.576788\pi$
$212$	1.23385e7			1.29495
$213$			861935.i			0.0891940i
$214$	1.37729e7			1.40535
$215$		−	5.39474e6i		−	0.542819i
$216$		−	3.40379e6i		−	0.337754i
$217$	−1.74636e7	+	4.56112e6i	−1.70905	+	0.446368i
$218$	−1.10693e7			−1.06844
$219$	−8.96509e6			−0.853537
$220$			2.44361e7i			2.29491i
$221$	−5.53896e6			−0.513158
$222$			6.90040e6i			0.630689i
$223$		−	2.12917e7i		−	1.91998i	−0.280037	−	0.959989i	$-0.590347\pi$
$223$		−	2.12917e7i		−	1.91998i	0.280037	−	0.959989i	$-0.409653\pi$
$224$	112533.	+	430868.i	0.0100124	+	0.0383354i
$225$	−896855.			−0.0787362
$226$	−1.17514e7			−1.01804
$227$			5.73444e6i			0.490245i	0.969492	+	0.245123i	$0.0788282\pi$
$227$			5.73444e6i			0.490245i	−0.969492	+	0.245123i	$0.921172\pi$
$228$	−1.17268e7			−0.989411
$229$		−	57165.2i		−	0.00476020i	−0.999997	−	0.00238010i	$-0.999242\pi$
$229$		−	57165.2i		−	0.00476020i	0.999997	−	0.00238010i	$-0.000757610\pi$
$230$			1.39277e7i			1.14471i
$231$	8.98950e6	−	2.34786e6i	0.729289	−	0.190475i
$232$	3.52253e7			2.82092
$233$	2.16255e7			1.70962			0.854808	−	0.518945i	$-0.173675\pi$
$233$	2.16255e7			1.70962			0.854808	+	0.518945i	$0.173675\pi$
$234$			1.10066e7i			0.859024i
$235$	−625505.			−0.0481978
$236$		−	3.43797e7i		−	2.61557i
$237$		−	854154.i		−	0.0641640i
$238$	7.82146e6	−	2.04280e6i	0.580172	−	0.151529i
$239$	−1.61219e7			−1.18092			−0.590461	−	0.807066i	$-0.701054\pi$
$239$	−1.61219e7			−1.18092			−0.590461	+	0.807066i	$0.701054\pi$
$240$	7.21370e6			0.521825
$241$		−	829677.i		−	0.0592731i	−0.999561	−	0.0296366i	$-0.990565\pi$
$241$		−	829677.i		−	0.0592731i	0.999561	−	0.0296366i	$-0.00943499\pi$
$242$	1.73246e7			1.22241
$243$			920483.i			0.0641500i
$244$		−	1.07508e7i		−	0.740068i
$245$	6.28485e6	+	1.12110e7i	0.427363	+	0.762334i
$246$	6.57443e6			0.441624
$247$	1.90672e7			1.26530
$248$			4.72849e7i			3.10004i
$249$	−3.19108e6			−0.206699
$250$		−	2.92941e7i		−	1.87482i
$251$			1.15419e7i			0.729890i	0.931029	+	0.364945i	$0.118912\pi$
$251$			1.15419e7i			0.729890i	−0.931029	+	0.364945i	$0.881088\pi$
$252$	−2.71129e6	−	1.03810e7i	−0.169424	−	0.648691i
$253$	1.59581e7			0.985413
$254$	4.41533e6			0.269440
$255$		−	2.89103e6i		−	0.174354i
$256$	−3.37318e7			−2.01057
$257$			2.28862e7i			1.34826i	0.738611	+	0.674132i	$0.235482\pi$
$257$			2.28862e7i			1.34826i	−0.738611	+	0.674132i	$0.764518\pi$
$258$			1.06868e7i			0.622283i
$259$	2.76377e6	+	1.05819e7i	0.159075	+	0.609068i
$260$	−4.58819e7			−2.61049
$261$	−9.52596e6			−0.535781
$262$		−	3.34993e7i		−	1.86265i
$263$	−8.94339e6			−0.491626			−0.245813	−	0.969317i	$-0.579055\pi$
$263$	−8.94339e6			−0.491626			−0.245813	+	0.969317i	$0.579055\pi$
$264$		−	2.43402e7i		−	1.32285i
$265$		−	1.04710e7i		−	0.562668i
$266$	−2.69244e7	+	7.03207e6i	−1.43054	+	0.373627i
$267$	1.16712e7			0.613171
$268$	−5.81867e7			−3.02287
$269$		−	5.75740e6i		−	0.295781i	−0.989004	−	0.147890i	$-0.952752\pi$
$269$		−	5.75740e6i		−	0.295781i	0.989004	−	0.147890i	$-0.0472483\pi$
$270$	−5.74483e6			−0.291868
$271$		−	2.95208e6i		−	0.148327i	−0.997246	−	0.0741635i	$-0.976371\pi$
$271$		−	2.95208e6i		−	0.148327i	0.997246	−	0.0741635i	$-0.0236287\pi$
$272$		−	7.19134e6i		−	0.357358i
$273$	4.40841e6	+	1.68789e7i	0.216667	+	0.829576i
$274$	−3.14378e7			−1.52827
$275$	−6.41332e6			−0.308379
$276$		−	1.84282e7i		−	0.876509i
$277$	3.28942e7			1.54768			0.773838	−	0.633384i	$-0.218334\pi$
$277$	3.28942e7			1.54768			0.773838	+	0.633384i	$0.218334\pi$
$278$			1.02919e7i			0.479026i
$279$		−	1.27872e7i		−	0.588794i
$280$	3.25773e7	−	8.50849e6i	1.48402	−	0.387595i
$281$	2.82035e7			1.27111			0.635556	−	0.772055i	$-0.280771\pi$
$281$	2.82035e7			1.27111			0.635556	+	0.772055i	$0.280771\pi$
$282$	1.23910e6			0.0552535
$283$		−	2.86963e7i		−	1.26610i	−0.774113	−	0.633048i	$-0.781804\pi$
$283$		−	2.86963e7i		−	1.26610i	0.774113	−	0.633048i	$-0.218196\pi$
$284$	7.11769e6			0.310731
$285$			9.95200e6i			0.429908i
$286$			7.87072e7i			3.36447i
$287$	1.00821e7	−	2.63322e6i	0.426485	−	0.111389i
$288$	−315490.			−0.0132071
$289$	2.12555e7			0.880598
$290$		−	5.94525e7i		−	2.43768i
$291$	6.61336e6			0.268376
$292$			7.40320e7i			2.97352i
$293$		−	1.88493e7i		−	0.749365i	−0.927153	−	0.374682i	$-0.877752\pi$
$293$		−	1.88493e7i		−	0.749365i	0.927153	−	0.374682i	$-0.122248\pi$
$294$	−1.24501e7	−	2.22085e7i	−0.489925	−	0.873932i
$295$	−2.91764e7			−1.13649
$296$	2.86519e7			1.10479
$297$			6.58229e6i			0.251251i
$298$	2.84540e6			0.107521
$299$			2.99632e7i			1.12092i
$300$			7.40605e6i			0.274298i
$301$	4.28031e6	+	1.63885e7i	0.156955	+	0.600950i
$302$	5.30572e7			1.92630
$303$	−1.93169e7			−0.694400
$304$			2.47553e7i			0.881144i
$305$	−9.12368e6			−0.321566
$306$			5.72703e6i			0.199878i
$307$		−	3.69805e7i		−	1.27808i	−0.769174	−	0.639039i	$-0.779332\pi$
$307$		−	3.69805e7i		−	1.27808i	0.769174	−	0.639039i	$-0.220668\pi$
$308$	−1.93882e7	−	7.42336e7i	−0.663568	−	2.54067i
$309$	1.68312e7			0.570478
$310$	7.98064e7			2.67888
$311$		−	8.07734e6i		−	0.268526i	−0.990946	−	0.134263i	$-0.957133\pi$
$311$		−	8.07734e6i		−	0.268526i	0.990946	−	0.134263i	$-0.0428668\pi$
$312$	4.57017e7			1.50476
$313$			2.28788e7i			0.746105i	0.927810	+	0.373052i	$0.121689\pi$
$313$			2.28788e7i			0.746105i	−0.927810	+	0.373052i	$0.878311\pi$
$314$			2.62592e7i			0.848189i
$315$	−8.80985e6	+	2.30094e6i	−0.281862	+	0.0736164i
$316$	−7.05344e6			−0.223532
$317$	−4.69587e7			−1.47414			−0.737069	−	0.675818i	$-0.763791\pi$
$317$	−4.69587e7			−1.47414			−0.737069	+	0.675818i	$0.763791\pi$
$318$			2.07428e7i			0.645038i
$319$	−6.81192e7			−2.09845
$320$			2.76476e7i			0.843737i
$321$			1.54653e7i			0.467567i
$322$	−1.10506e7	−	4.23105e7i	−0.330992	−	1.26730i
$323$	9.92115e6			0.294411
$324$	7.60117e6			0.223484
$325$		−	1.20418e7i		−	0.350786i
$326$	3.06856e7			0.885689
$327$		−	1.24295e7i		−	0.355476i
$328$		−	2.72984e7i		−	0.773598i
$329$	1.90020e6	−	496291.i	0.0533594	−	0.0139363i
$330$	−4.10808e7			−1.14313
$331$	1.92488e7			0.530785			0.265393	−	0.964140i	$-0.414498\pi$
$331$	1.92488e7			0.530785			0.265393	+	0.964140i	$0.414498\pi$
$332$			2.63513e7i			0.720092i
$333$	−7.74830e6			−0.209833
$334$		−	3.61123e7i		−	0.969205i
$335$			4.93802e7i			1.31346i
$336$	−2.19142e7	+	5.72352e6i	−0.577707	+	0.150885i
$337$	−2.46720e7			−0.644637			−0.322319	−	0.946631i	$-0.604462\pi$
$337$	−2.46720e7			−0.644637			−0.322319	+	0.946631i	$0.604462\pi$
$338$	−8.07738e7			−2.09180
$339$		−	1.31954e7i		−	0.338707i
$340$	−2.38736e7			−0.607408
$341$		−	9.14401e7i		−	2.30608i
$342$		−	1.97146e7i		−	0.492843i
$343$	−2.79875e7	−	2.90708e7i	−0.693557	−	0.720402i
$344$	4.43737e7			1.09006
$345$	−1.56391e7			−0.380852
$346$			4.54858e7i			1.09811i
$347$	5.94599e6			0.142310			0.0711550	−	0.997465i	$-0.477331\pi$
$347$	5.94599e6			0.142310			0.0711550	+	0.997465i	$0.477331\pi$
$348$			7.86635e7i			1.86653i
$349$			7.77341e6i			0.182867i	0.995811	+	0.0914335i	$0.0291449\pi$
$349$			7.77341e6i			0.182867i	−0.995811	+	0.0914335i	$0.970855\pi$
$350$	4.44108e6	+	1.70040e7i	0.103582	+	0.396595i
$351$	−1.23591e7			−0.285801
$352$	−2.25604e6			−0.0517271
$353$			7.92420e6i			0.180149i	0.995935	+	0.0900744i	$0.0287105\pi$
$353$			7.92420e6i			0.180149i	−0.995935	+	0.0900744i	$0.971290\pi$
$354$	5.77974e7			1.30286
$355$		−	6.04044e6i		−	0.135016i
$356$		−	9.63785e7i		−	2.13614i
$357$	2.29381e6	+	8.78254e6i	0.0504142	+	0.193026i
$358$	2.36283e7			0.514971
$359$	−6.87826e7			−1.48660			−0.743302	−	0.668956i	$-0.766741\pi$
$359$	−6.87826e7			−1.48660			−0.743302	+	0.668956i	$0.766741\pi$
$360$			2.38537e7i			0.511269i
$361$	1.28936e7			0.274064
$362$			5.71828e7i			1.20542i
$363$			1.94534e7i			0.406702i
$364$	1.39383e8	−	3.64038e7i	2.89005	−	0.754818i
$365$	6.28274e7			1.29202
$366$	1.80737e7			0.368641
$367$			8.68506e7i			1.75701i	0.477732	+	0.878506i	$0.341459\pi$
$367$			8.68506e7i			1.75701i	−0.477732	+	0.878506i	$0.658541\pi$
$368$	−3.89019e7			−0.780597
$369$			7.38228e6i			0.146930i
$370$		−	4.83580e7i		−	0.954691i
$371$	8.30797e6	+	3.18096e7i	0.162695	+	0.622925i
$372$	−1.05594e8			−2.05122
$373$	8.00272e7			1.54210			0.771048	−	0.636777i	$-0.219733\pi$
$373$	8.00272e7			1.54210			0.771048	+	0.636777i	$0.219733\pi$
$374$			4.09534e7i			0.782845i
$375$	3.28937e7			0.623761
$376$		−	5.14501e6i		−	0.0967883i
$377$		−	1.27902e8i		−	2.38701i
$378$	1.74520e7	−	4.55809e6i	0.323124	−	0.0843931i
$379$	−7.50679e7			−1.37891			−0.689456	−	0.724327i	$-0.742151\pi$
$379$	−7.50679e7			−1.37891			−0.689456	+	0.724327i	$0.742151\pi$
$380$	8.21817e7			1.49770
$381$			4.95788e6i			0.0896439i
$382$	−1.69561e8			−3.04183
$383$		−	1.72348e7i		−	0.306768i	−0.988167	−	0.153384i	$-0.950983\pi$
$383$		−	1.72348e7i		−	0.306768i	0.988167	−	0.153384i	$-0.0490172\pi$
$384$		−	5.60641e7i		−	0.990128i
$385$	−6.29984e7	+	1.64538e7i	−1.10395	+	0.288327i
$386$	4.59542e7			0.799031
$387$	−1.19999e7			−0.207036
$388$		−	5.46119e7i		−	0.934958i
$389$	−2.16482e7			−0.367767			−0.183884	−	0.982948i	$-0.558867\pi$
$389$	−2.16482e7			−0.367767			−0.183884	+	0.982948i	$0.558867\pi$
$390$		−	7.71343e7i		−	1.30033i
$391$			1.55907e7i			0.260816i
$392$	−9.22144e7	+	5.16952e7i	−1.53088	+	0.858207i
$393$	3.76156e7			0.619713
$394$	−4.41875e7			−0.722454
$395$			5.98592e6i			0.0971268i
$396$	5.43553e7			0.875298
$397$			1.11131e8i			1.77608i	0.459763	+	0.888042i	$0.347934\pi$
$397$			1.11131e8i			1.77608i	−0.459763	+	0.888042i	$0.652066\pi$
$398$			7.16002e7i			1.13570i
$399$	−7.89615e6	−	3.02328e7i	−0.124307	−	0.475948i
$400$	1.56341e7			0.244283
$401$	7.55623e7			1.17185			0.585925	−	0.810365i	$-0.300731\pi$
$401$	7.55623e7			1.17185			0.585925	+	0.810365i	$0.300731\pi$
$402$		−	9.78204e7i		−	1.50574i
$403$	1.71690e8			2.62319
$404$			1.59515e8i			2.41912i
$405$		−	6.45075e6i		−	0.0971057i
$406$	4.71710e7	+	1.80608e8i	0.704851	+	2.69873i
$407$	−5.54074e7			−0.821834
$408$	2.37798e7			0.350129
$409$			1.17041e7i			0.171067i	0.996335	+	0.0855336i	$0.0272595\pi$
$409$			1.17041e7i			0.171067i	−0.996335	+	0.0855336i	$0.972741\pi$
$410$	−4.60736e7			−0.668499
$411$		−	3.53008e7i		−	0.508462i
$412$		−	1.38989e8i		−	1.98741i
$413$	8.86338e7	−	2.31493e7i	1.25820	−	0.328615i
$414$	3.09806e7			0.436605
$415$	2.23631e7			0.312887
$416$		−	4.23599e6i		−	0.0588403i
$417$	−1.15565e7			−0.159374
$418$		−	1.40977e8i		−	1.93028i
$419$		−	1.79735e7i		−	0.244337i	−0.992509	−	0.122169i	$-0.961015\pi$
$419$		−	1.79735e7i		−	0.244337i	0.992509	−	0.122169i	$-0.0389849\pi$
$420$	1.90008e7	+	7.27501e7i	0.256462	+	0.981941i
$421$	−4.94461e7			−0.662653			−0.331326	−	0.943516i	$-0.607496\pi$
$421$	−4.94461e7			−0.662653			−0.331326	+	0.943516i	$0.607496\pi$
$422$	−6.23122e7			−0.829154
$423$			1.39136e6i			0.0183831i
$424$	8.61283e7			1.12992
$425$		−	6.26568e6i		−	0.0816209i
$426$			1.19659e7i			0.154781i
$427$	2.77165e7	−	7.23895e6i	0.356003	−	0.0929805i
$428$	1.27710e8			1.62889
$429$	−8.83785e7			−1.11937
$430$		−	7.48930e7i		−	0.941967i
$431$	−2.49969e7			−0.312216			−0.156108	−	0.987740i	$-0.549895\pi$
$431$	−2.49969e7			−0.312216			−0.156108	+	0.987740i	$0.549895\pi$
$432$		−	1.60460e7i		−	0.199029i
$433$			1.48394e8i			1.82791i	0.405821	+	0.913953i	$0.366986\pi$
$433$			1.48394e8i			1.82791i	−0.405821	+	0.913953i	$0.633014\pi$
$434$	−2.42440e8	+	6.33203e7i	−2.96576	+	0.774593i
$435$	6.67579e7			0.811027
$436$	−1.02640e8			−1.23839
$437$		−	5.36689e7i		−	0.643100i
$438$	−1.24459e8			−1.48116
$439$		−	1.44121e8i		−	1.70346i	−0.523978	−	0.851732i	$-0.675553\pi$
$439$		−	1.44121e8i		−	1.70346i	0.523978	−	0.851732i	$-0.324447\pi$
$440$			1.70576e8i			2.00244i
$441$	2.49375e7	−	1.39799e7i	0.290761	−	0.163000i
$442$	−7.68952e7			−0.890497
$443$	1.25475e8			1.44327			0.721634	−	0.692275i	$-0.243392\pi$
$443$	1.25475e8			1.44327			0.721634	+	0.692275i	$0.243392\pi$
$444$			6.39840e7i			0.731008i
$445$	−8.17918e7			−0.928174
$446$		−	2.95585e8i		−	3.33179i
$447$			3.19504e6i			0.0357728i
$448$	−2.19362e7	−	8.39895e7i	−0.243965	−	0.934094i
$449$	−1.89962e7			−0.209860			−0.104930	−	0.994480i	$-0.533462\pi$
$449$	−1.89962e7			−0.209860			−0.104930	+	0.994480i	$0.533462\pi$
$450$	−1.24507e7			−0.136633
$451$			5.27900e7i			0.575469i
$452$	−1.08965e8			−1.17998
$453$			5.95767e7i			0.640888i
$454$			7.96089e7i			0.850734i
$455$	−3.08941e7	−	1.18287e8i	−0.327976	−	1.25575i
$456$	−8.18589e7			−0.863319
$457$	−1.01696e8			−1.06550			−0.532752	−	0.846271i	$-0.678842\pi$
$457$	−1.01696e8			−1.06550			−0.532752	+	0.846271i	$0.678842\pi$
$458$		−	793601.i		−	0.00826049i
$459$	−6.43075e6			−0.0665003
$460$			1.29145e8i			1.32680i
$461$			1.20646e8i			1.23144i	0.787967	+	0.615718i	$0.211134\pi$
$461$			1.20646e8i			1.23144i	−0.787967	+	0.615718i	$0.788866\pi$
$462$	1.24798e8	−	3.25945e7i	1.26555	−	0.330535i
$463$	1.78238e7			0.179580			0.0897901	−	0.995961i	$-0.471380\pi$
$463$	1.78238e7			0.179580			0.0897901	+	0.995961i	$0.471380\pi$
$464$	1.66058e8			1.66229
$465$			8.96128e7i			0.891274i
$466$	3.00218e8			2.96674
$467$			3.91277e7i			0.384179i	0.981377	+	0.192090i	$0.0615264\pi$
$467$			3.91277e7i			0.384179i	−0.981377	+	0.192090i	$0.938474\pi$
$468$			1.02059e8i			0.995664i
$469$	−3.91794e7	−	1.50010e8i	−0.379786	−	1.45413i
$470$	−8.68364e6			−0.0836389
$471$	−2.94859e7			−0.282196
$472$		−	2.39987e8i		−	2.28224i
$473$	−8.58105e7			−0.810881
$474$		−	1.18579e7i		−	0.111345i
$475$			2.15688e7i			0.201254i
$476$	7.25246e7	−	1.89419e7i	0.672457	−	0.175631i
$477$	−2.32916e7			−0.214607
$478$	−2.23813e8			−2.04928
$479$			1.81487e8i			1.65135i	0.564146	+	0.825675i	$0.309206\pi$
$479$			1.81487e8i			1.65135i	−0.564146	+	0.825675i	$0.690794\pi$
$480$	2.21095e6			0.0199920
$481$		−	1.04034e8i		−	0.934848i
$482$		−	1.15181e7i		−	0.102858i
$483$	4.75095e7	−	1.24085e7i	0.421638	−	0.110123i
$484$	1.60643e8			1.41685
$485$	−4.63465e7			−0.406248
$486$			1.27787e7i			0.111321i
$487$	5.76690e7			0.499293			0.249647	−	0.968337i	$-0.419686\pi$
$487$	5.76690e7			0.499293			0.249647	+	0.968337i	$0.419686\pi$
$488$		−	7.50457e7i		−	0.645753i
$489$			3.44561e7i			0.294673i
$490$	8.72500e7	+	1.55637e8i	0.741613	+	1.32290i
$491$	2.71509e7			0.229372			0.114686	−	0.993402i	$-0.463414\pi$
$491$	2.71509e7			0.229372			0.114686	+	0.993402i	$0.463414\pi$
$492$	6.09615e7			0.511870
$493$		−	6.65510e7i		−	0.555410i
$494$	2.64702e8			2.19571
$495$		−	4.61287e7i		−	0.380326i
$496$			2.22909e8i			1.82676i
$497$	4.79263e6	+	1.83500e7i	0.0390395	+	0.149475i
$498$	−4.43004e7			−0.358691
$499$	1.83523e8			1.47703			0.738513	−	0.674240i	$-0.235528\pi$
$499$	1.83523e8			1.47703			0.738513	+	0.674240i	$0.235528\pi$
$500$		−	2.71630e8i		−	2.17304i
$501$	4.05497e7			0.322459
$502$			1.60232e8i			1.26660i
$503$			1.41739e8i			1.11374i	0.830598	+	0.556872i	$0.187999\pi$
$503$			1.41739e8i			1.11374i	−0.830598	+	0.556872i	$0.812001\pi$
$504$	−1.89261e7	−	7.24643e7i	−0.147833	−	0.566021i
$505$	1.35373e8			1.05113
$506$	2.21539e8			1.71001
$507$		−	9.06991e7i		−	0.695952i
$508$	4.09412e7			0.312298
$509$		−	7.87062e7i		−	0.596837i	−0.954435	−	0.298418i	$-0.903541\pi$
$509$		−	7.87062e7i		−	0.596837i	0.954435	−	0.298418i	$-0.0964591\pi$
$510$		−	4.01350e7i		−	0.302561i
$511$	−1.90861e8	+	4.98487e7i	−1.43039	+	0.373587i
$512$	−2.38108e8			−1.77404
$513$	2.21370e7			0.163971
$514$			3.17720e8i			2.33968i
$515$	−1.17953e8			−0.863549
$516$			9.90933e7i			0.721265i
$517$			9.94949e6i			0.0719995i
$518$	3.83684e7	+	1.46905e8i	0.276048	+	1.05693i
$519$	−5.10750e7			−0.365348
$520$	−3.20277e8			−2.27780
$521$		−	2.28675e8i		−	1.61698i	−0.588509	−	0.808491i	$-0.700285\pi$
$521$		−	2.28675e8i		−	1.61698i	0.588509	−	0.808491i	$-0.299715\pi$
$522$	−1.32245e8			−0.929753
$523$		−	1.28753e7i		−	0.0900023i	−0.998987	−	0.0450011i	$-0.985671\pi$
$523$		−	1.28753e7i		−	0.0900023i	0.998987	−	0.0450011i	$-0.0143291\pi$
$524$		−	3.10623e8i		−	2.15893i
$525$	−1.90934e7	+	4.98679e6i	−0.131949	+	0.0344622i
$526$	−1.24158e8			−0.853131
$527$	8.93350e7			0.610365
$528$		−	1.14744e8i		−	0.779519i
$529$	−6.36975e7			−0.430284
$530$		−	1.45365e8i		−	0.976412i
$531$			6.48994e7i			0.433468i
$532$	−2.49657e8	+	6.52049e7i	−1.65809	+	0.433057i
$533$	−9.91198e7			−0.654604
$534$	1.62027e8			1.06405
$535$		−	1.08381e8i		−	0.707769i
$536$	−4.06170e8			−2.63763
$537$			2.65317e7i			0.171333i
$538$		−	7.99277e7i		−	0.513276i
$539$	1.78325e8	−	9.99689e7i	1.13880	−	0.638408i
$540$	−5.32690e7			−0.338293
$541$	−1.75664e7			−0.110941			−0.0554703	−	0.998460i	$-0.517666\pi$
$541$	−1.75664e7			−0.110941			−0.0554703	+	0.998460i	$0.517666\pi$
$542$		−	4.09825e7i		−	0.257395i
$543$	−6.42093e7			−0.401050
$544$		−	2.20410e6i		−	0.0136910i
$545$			8.71059e7i			0.538094i
$546$	6.12001e7	+	2.34323e8i	0.375988	+	1.43958i
$547$	1.12464e8			0.687149			0.343575	−	0.939125i	$-0.388362\pi$
$547$	1.12464e8			0.687149			0.343575	+	0.939125i	$0.388362\pi$
$548$	−2.91507e8			−1.77136
$549$			2.02945e7i			0.122648i
$550$	−8.90336e7			−0.535138
$551$			2.29093e8i			1.36949i
$552$		−	1.28638e8i		−	0.764806i
$553$	−4.74937e6	−	1.81844e7i	−0.0280841	−	0.107528i
$554$	4.56657e8			2.68572
$555$	5.43001e7			0.317630
$556$			9.54313e7i			0.555222i
$557$	1.65969e7			0.0960422			0.0480211	−	0.998846i	$-0.484709\pi$
$557$	1.65969e7			0.0960422			0.0480211	+	0.998846i	$0.484709\pi$
$558$		−	1.77520e8i		−	1.02175i
$559$		−	1.61120e8i		−	0.922388i
$560$	1.53575e8	−	4.01104e7i	0.874492	−	0.228399i
$561$	−4.59857e7			−0.260456
$562$	3.91538e8			2.20579
$563$			3.10595e8i			1.74048i	0.492627	+	0.870241i	$0.336037\pi$
$563$			3.10595e8i			1.74048i	−0.492627	+	0.870241i	$0.663963\pi$
$564$	1.14896e7			0.0640424
$565$			9.24736e7i			0.512711i
$566$		−	3.98379e8i		−	2.19709i
$567$	5.11817e6	+	1.95965e7i	0.0280780	+	0.107505i
$568$	4.96849e7			0.271131
$569$	−1.98512e8			−1.07758			−0.538790	−	0.842440i	$-0.681118\pi$
$569$	−1.98512e8			−1.07758			−0.538790	+	0.842440i	$0.681118\pi$
$570$			1.38160e8i			0.746031i
$571$	2.57131e8			1.38116			0.690582	−	0.723254i	$-0.257354\pi$
$571$	2.57131e8			1.38116			0.690582	+	0.723254i	$0.257354\pi$
$572$			7.29813e8i			3.89963i
$573$		−	1.90396e8i		−	1.01203i
$574$	1.39965e8	−	3.65559e7i	0.740089	−	0.193295i
$575$	−3.38944e7			−0.178289
$576$	6.14987e7			0.321809
$577$		−	1.69816e8i		−	0.883997i	−0.897016	−	0.441998i	$-0.854270\pi$
$577$		−	1.69816e8i		−	0.883997i	0.897016	−	0.441998i	$-0.145730\pi$
$578$	2.95082e8			1.52812
$579$			5.16010e7i			0.265841i
$580$		−	5.51274e8i		−	2.82542i
$581$	−6.79359e7	+	1.77434e7i	−0.346394	+	0.0904707i
$582$	9.18107e7			0.465719
$583$	−1.66556e8			−0.840532
$584$			5.16779e8i			2.59457i
$585$	8.66123e7			0.432626
$586$		−	2.61678e8i		−	1.30039i
$587$			1.41210e8i			0.698155i	0.937094	+	0.349078i	$0.113505\pi$
$587$			1.41210e8i			0.698155i	−0.937094	+	0.349078i	$0.886495\pi$
$588$	−1.15443e8	−	2.05929e8i	−0.567854	−	1.01294i
$589$	−3.07524e8			−1.50499
$590$	−4.05045e8			−1.97218
$591$		−	4.96171e7i		−	0.240364i
$592$	1.35070e8			0.651018
$593$			3.03054e7i			0.145330i	0.997356	+	0.0726651i	$0.0231504\pi$
$593$			3.03054e7i			0.145330i	−0.997356	+	0.0726651i	$0.976850\pi$
$594$			9.13792e7i			0.436002i
$595$	−1.60750e7	−	6.15481e7i	−0.0763135	−	0.292189i
$596$	2.63840e7			0.124624
$597$	−8.03982e7			−0.377854
$598$			4.15967e8i			1.94516i
$599$	−3.56035e8			−1.65658			−0.828289	−	0.560300i	$-0.810686\pi$
$599$	−3.56035e8			−1.65658			−0.828289	+	0.560300i	$0.810686\pi$
$600$			5.16978e7i			0.239342i
$601$			6.01567e7i			0.277116i	0.990354	+	0.138558i	$0.0442467\pi$
$601$			6.01567e7i			0.277116i	−0.990354	+	0.138558i	$0.955753\pi$
$602$	5.94219e7	+	2.27514e8i	0.272368	+	1.04284i
$603$	1.09840e8			0.500968
$604$	4.91973e8			2.23270
$605$		−	1.36330e8i		−	0.615636i
$606$	−2.68169e8			−1.20501
$607$		−	2.79993e8i		−	1.25193i	−0.779850	−	0.625967i	$-0.784705\pi$
$607$		−	2.79993e8i		−	1.25193i	0.779850	−	0.625967i	$-0.215295\pi$
$608$			7.58733e6i			0.0337581i
$609$	−2.02801e8	+	5.29673e7i	−0.897880	+	0.234507i
$610$	−1.26660e8			−0.558022
$611$	−1.86814e7			−0.0819004
$612$			5.31039e7i			0.231671i
$613$	2.39624e8			1.04028			0.520139	−	0.854082i	$-0.325880\pi$
$613$	2.39624e8			1.04028			0.520139	+	0.854082i	$0.325880\pi$
$614$		−	5.13385e8i		−	2.21788i
$615$		−	5.17350e7i		−	0.222413i
$616$	−1.35339e8	−	5.18185e8i	−0.579003	−	2.21688i
$617$	1.13428e8			0.482910			0.241455	−	0.970412i	$-0.422375\pi$
$617$	1.13428e8			0.482910			0.241455	+	0.970412i	$0.422375\pi$
$618$	2.33660e8			0.989964
$619$			1.42242e8i			0.599730i	0.953982	+	0.299865i	$0.0969416\pi$
$619$			1.42242e8i			0.599730i	−0.953982	+	0.299865i	$0.903058\pi$
$620$	7.40005e8			3.10499
$621$			3.47874e7i			0.145260i
$622$		−	1.12134e8i		−	0.465981i
$623$	2.48472e8	−	6.48955e7i	1.02757	−	0.268380i
$624$	2.15445e8			0.886713
$625$	−1.72851e8			−0.707997
$626$			3.17617e8i			1.29473i
$627$	1.58300e8			0.642211
$628$			2.43489e8i			0.983105i
$629$		−	5.41318e7i		−	0.217521i
$630$	−1.22304e8	+	3.19431e7i	−0.489123	+	0.127748i
$631$	−7.72931e7			−0.307647			−0.153824	−	0.988098i	$-0.549159\pi$
$631$	−7.72931e7			−0.307647			−0.153824	+	0.988098i	$0.549159\pi$
$632$	−4.92364e7			−0.195045
$633$		−	6.99689e7i		−	0.275863i
$634$	−6.51908e8			−2.55811
$635$		−	3.47448e7i		−	0.135697i
$636$			1.92337e8i			0.747640i
$637$	1.87704e8	+	3.34828e8i	0.726198	+	1.29540i
$638$	−9.45672e8			−3.64148
$639$	−1.34362e7			−0.0514962
$640$			3.92898e8i			1.49879i
$641$	−1.45416e8			−0.552124			−0.276062	−	0.961140i	$-0.589030\pi$
$641$	−1.45416e8			−0.552124			−0.276062	+	0.961140i	$0.589030\pi$
$642$			2.14699e8i			0.811380i
$643$			2.88497e8i			1.08520i	0.839992	+	0.542598i	$0.182559\pi$
$643$			2.88497e8i			1.08520i	−0.839992	+	0.542598i	$0.817441\pi$
$644$	−1.02467e8	−	3.92325e8i	−0.383641	−	1.46889i
$645$	8.40957e7			0.313397
$646$	1.37731e8			0.510899
$647$		−	4.41658e8i		−	1.63070i	−0.578971	−	0.815348i	$-0.696545\pi$
$647$		−	4.41658e8i		−	1.63070i	0.578971	−	0.815348i	$-0.303455\pi$
$648$	5.30598e7			0.195003
$649$			4.64090e8i			1.69773i
$650$		−	1.67172e8i		−	0.608727i
$651$	−7.11009e7	−	2.72231e8i	−0.257710	−	0.986721i
$652$	2.84532e8			1.02657
$653$	4.17563e8			1.49962			0.749812	−	0.661651i	$-0.230144\pi$
$653$	4.17563e8			1.49962			0.749812	+	0.661651i	$0.230144\pi$
$654$		−	1.72554e8i		−	0.616866i
$655$	−2.63610e8			−0.938077
$656$		−	1.28689e8i		−	0.455859i
$657$		−	1.39752e8i		−	0.492790i
$658$	2.63797e7	−	6.88980e6i	0.0925959	−	0.0241840i
$659$	2.81904e8			0.985021			0.492510	−	0.870307i	$-0.336079\pi$
$659$	2.81904e8			0.985021			0.492510	+	0.870307i	$0.336079\pi$
$660$	−3.80922e8			−1.32496
$661$		−	4.89236e8i		−	1.69400i	−0.531591	−	0.847001i	$-0.678405\pi$
$661$		−	4.89236e8i		−	1.69400i	0.531591	−	0.847001i	$-0.321595\pi$
$662$	2.67223e8			0.921085
$663$		−	8.63439e7i		−	0.296272i
$664$			1.83945e8i			0.628323i
$665$	5.53363e7	+	2.11871e8i	0.188168	+	0.720456i
$666$	−1.07567e8			−0.364128
$667$	−3.60010e8			−1.21321
$668$		−	3.34852e8i		−	1.12337i
$669$	3.31905e8			1.10850
$670$			6.85525e8i			2.27929i
$671$			1.45124e8i			0.480367i
$672$	−6.71656e6	+	1.75422e6i	−0.0221329	+	0.00578065i
$673$	3.88192e8			1.27351			0.636754	−	0.771067i	$-0.280277\pi$
$673$	3.88192e8			1.27351			0.636754	+	0.771067i	$0.280277\pi$
$674$	−3.42512e8			−1.11865
$675$		−	1.39806e7i		−	0.0454584i
$676$	−7.48976e8			−2.42453
$677$			4.40231e8i			1.41878i	0.704817	+	0.709389i	$0.251029\pi$
$677$			4.40231e8i			1.41878i	−0.704817	+	0.709389i	$0.748971\pi$
$678$		−	1.83187e8i		−	0.587767i
$679$	1.40794e8	−	3.67724e7i	0.449754	−	0.117466i
$680$	−1.66649e8			−0.530000
$681$	−8.93910e7			−0.283043
$682$		−	1.26943e9i		−	4.00179i
$683$	3.70500e8			1.16286			0.581429	−	0.813597i	$-0.302494\pi$
$683$	3.70500e8			1.16286			0.581429	+	0.813597i	$0.302494\pi$
$684$		−	1.82803e8i		−	0.571236i
$685$			2.47388e8i			0.769674i
$686$	−3.88540e8	−	4.03578e8i	−1.20355	−	1.25013i
$687$	891117.			0.00274830
$688$	2.09185e8			0.642341
$689$		−	3.12729e8i		−	0.956117i
$690$	−2.17112e8			−0.660901
$691$			3.01672e8i			0.914325i	0.889383	+	0.457162i	$0.151134\pi$
$691$			3.01672e8i			0.914325i	−0.889383	+	0.457162i	$0.848866\pi$
$692$			4.21768e8i			1.27279i
$693$	3.65996e7	+	1.40132e8i	0.109971	+	0.421055i
$694$	8.25458e7			0.246954
$695$	8.09879e7			0.241249
$696$			5.49109e8i			1.62866i
$697$	−5.15747e7			−0.152313
$698$			1.07915e8i			0.317334i
$699$			3.37108e8i			0.987047i
$700$	4.11800e7	+	1.57670e8i	0.120058	+	0.459679i
$701$	−6.33588e8			−1.83930			−0.919650	−	0.392738i	$-0.871528\pi$
$701$	−6.33588e8			−1.83930			−0.919650	+	0.392738i	$0.871528\pi$
$702$	−1.71576e8			−0.495958
$703$			1.86342e8i			0.536345i
$704$	4.39772e8			1.26040
$705$		−	9.75066e6i		−	0.0278270i
$706$			1.10008e8i			0.312617i
$707$	−4.11244e8	+	1.07408e8i	−1.16370	+	0.303933i
$708$	5.35927e8			1.51010
$709$	3.72631e8			1.04554			0.522769	−	0.852474i	$-0.324899\pi$
$709$	3.72631e8			1.04554			0.522769	+	0.852474i	$0.324899\pi$
$710$		−	8.38570e7i		−	0.234296i
$711$	1.33149e7			0.0370451
$712$		−	6.72768e8i		−	1.86391i
$713$		−	4.83261e8i		−	1.33326i
$714$	3.18441e7	+	1.21925e8i	0.0874851	+	0.334963i
$715$	6.19357e8			1.69443
$716$	2.19093e8			0.596884
$717$		−	2.51315e8i		−	0.681806i
$718$	−9.54881e8			−2.57974
$719$		−	2.77281e8i		−	0.745992i	−0.927833	−	0.372996i	$-0.878331\pi$
$719$		−	2.77281e8i		−	0.745992i	0.927833	−	0.372996i	$-0.121669\pi$
$720$			1.12450e8i			0.301276i
$721$	3.58324e8	−	9.35866e7i	0.956027	−	0.249694i
$722$	1.78996e8			0.475590
$723$	1.29334e7			0.0342214
$724$			5.30228e8i			1.39716i
$725$	1.44683e8			0.379668
$726$			2.70064e8i			0.705760i
$727$		−	6.89903e7i		−	0.179550i	−0.995962	−	0.0897749i	$-0.971385\pi$
$727$		−	6.89903e7i		−	0.179550i	0.995962	−	0.0897749i	$-0.0286148\pi$
$728$	9.72958e8	−	2.54116e8i	2.52174	−	0.658624i
$729$	−1.43489e7			−0.0370370
$730$	8.72208e8			2.24208
$731$		−	8.38350e7i		−	0.214621i
$732$	1.67588e8			0.427278
$733$		−	1.60124e8i		−	0.406579i	−0.979119	−	0.203290i	$-0.934837\pi$
$733$		−	1.60124e8i		−	0.406579i	0.979119	−	0.203290i	$-0.0651633\pi$
$734$			1.20571e9i			3.04899i
$735$	−1.74762e8	+	9.79711e7i	−0.440134	+	0.246738i
$736$	−1.19232e7			−0.0299060
$737$	7.85458e8			1.96210
$738$			1.02485e8i			0.254972i
$739$	−3.01004e8			−0.745828			−0.372914	−	0.927866i	$-0.621641\pi$
$739$	−3.01004e8			−0.745828			−0.372914	+	0.927866i	$0.621641\pi$
$740$		−	4.48400e8i		−	1.10655i
$741$			2.97228e8i			0.730524i
$742$	1.15336e8	+	4.41599e8i	0.282328	+	1.08098i
$743$	−3.62698e8			−0.884257			−0.442128	−	0.896952i	$-0.645776\pi$
$743$	−3.62698e8			−0.884257			−0.442128	+	0.896952i	$0.645776\pi$
$744$	−7.37098e8			−1.78981
$745$		−	2.23908e7i		−	0.0541503i
$746$	1.11099e9			2.67604
$747$		−	4.97440e7i		−	0.119338i
$748$			3.79741e8i			0.907367i
$749$	8.59920e7	+	3.29246e8i	0.204650	+	0.783565i
$750$	4.56650e8			1.08243
$751$	−7.18068e8			−1.69530			−0.847648	−	0.530558i	$-0.821982\pi$
$751$	−7.18068e8			−1.69530			−0.847648	+	0.530558i	$0.821982\pi$
$752$		−	2.42544e7i		−	0.0570345i
$753$	−1.79921e8			−0.421402
$754$		−	1.77562e9i		−	4.14224i
$755$		−	4.17514e8i		−	0.970130i
$756$	1.61824e8	−	4.22649e7i	0.374522	−	0.0978170i
$757$	−5.90320e8			−1.36082			−0.680409	−	0.732833i	$-0.738198\pi$
$757$	−5.90320e8			−1.36082			−0.680409	+	0.732833i	$0.738198\pi$
$758$	−1.04214e9			−2.39286
$759$			2.48761e8i			0.568929i
$760$	5.73667e8			1.30683
$761$			1.26733e8i			0.287565i	0.989609	+	0.143783i	$0.0459266\pi$
$761$			1.26733e8i			0.287565i	−0.989609	+	0.143783i	$0.954073\pi$
$762$			6.88282e7i			0.155561i
$763$	−6.91118e7	−	2.64615e8i	−0.155589	−	0.595719i
$764$	−1.57226e9			−3.52568
$765$	4.50667e7			0.100663
$766$		−	2.39264e8i		−	0.532343i
$767$	−8.71386e8			−1.93119
$768$		−	5.25827e8i		−	1.16080i
$769$		−	4.30753e8i		−	0.947216i	−0.880736	−	0.473608i	$-0.842951\pi$
$769$		−	4.30753e8i		−	0.947216i	0.880736	−	0.473608i	$-0.157049\pi$
$770$	−8.74582e8	+	2.28422e8i	−1.91570	+	0.500341i
$771$	−3.56761e8			−0.778420
$772$	4.26111e8			0.926128
$773$			7.66316e8i			1.65909i	0.558441	+	0.829544i	$0.311400\pi$
$773$			7.66316e8i			1.65909i	−0.558441	+	0.829544i	$0.688600\pi$
$774$	−1.66590e8			−0.359275
$775$			1.94216e8i			0.417234i
$776$		−	3.81217e8i		−	0.815806i
$777$	−1.64956e8	+	4.30830e7i	−0.351646	+	0.0918423i
$778$	−3.00533e8			−0.638196
$779$	1.77539e8			0.375562
$780$		−	7.15228e8i		−	1.50717i
$781$	−9.60813e7			−0.201691
$782$			2.16439e8i			0.452601i
$783$		−	1.48495e8i		−	0.309333i
$784$	−4.34714e8	+	2.43700e8i	−0.902102	+	0.505716i
$785$	2.06637e8			0.427168
$786$	5.22202e8			1.07540
$787$			3.20416e8i			0.657340i	0.944445	+	0.328670i	$0.106600\pi$
$787$			3.20416e8i			0.657340i	−0.944445	+	0.328670i	$0.893400\pi$
$788$	−4.09729e8			−0.837371
$789$		−	1.39414e8i		−	0.283841i
$790$			8.31000e7i			0.168547i
$791$	−7.33707e7	−	2.80922e8i	−0.148250	−	0.567618i
$792$	3.79426e8			0.763750
$793$	−2.72489e8			−0.546424
$794$			1.54279e9i			3.08208i
$795$	1.63227e8			0.324857
$796$			6.63913e8i			1.31635i
$797$		−	2.32752e8i		−	0.459746i	−0.973221	−	0.229873i	$-0.926169\pi$
$797$		−	2.32752e8i		−	0.459746i	0.973221	−	0.229873i	$-0.0738310\pi$
$798$	−1.09619e8	−	4.19709e8i	−0.215714	−	0.825924i
$799$	−9.72044e6			−0.0190566
$800$	4.79176e6			0.00935890
$801$			1.81936e8i			0.354014i
$802$	1.04900e9			2.03354
$803$		−	9.99354e8i		−	1.93007i
$804$		−	9.07040e8i		−	1.74525i
$805$	−3.32947e8	+	8.69586e7i	−0.638245	+	0.166696i
$806$	2.38351e9			4.55209
$807$	8.97491e7			0.170769
$808$			1.11349e9i			2.11083i
$809$	−1.83306e8			−0.346203			−0.173101	−	0.984904i	$-0.555379\pi$
$809$	−1.83306e8			−0.346203			−0.173101	+	0.984904i	$0.555379\pi$
$810$		−	8.95531e7i		−	0.168510i
$811$		−	7.56850e8i		−	1.41889i	−0.704763	−	0.709443i	$-0.748947\pi$
$811$		−	7.56850e8i		−	1.41889i	0.704763	−	0.709443i	$-0.251053\pi$
$812$	4.37394e8	+	1.67469e9i	0.816967	+	3.12800i
$813$	4.60184e7			0.0856366
$814$	−7.69198e8			−1.42615
$815$		−	2.41469e8i		−	0.446054i
$816$	1.12102e8			0.206321
$817$			2.88591e8i			0.529196i
$818$			1.62483e8i			0.296857i
$819$	−2.63116e8	+	6.87203e7i	−0.478956	+	0.125093i
$820$	−4.27218e8			−0.774833
$821$	−6.47578e7			−0.117021			−0.0585103	−	0.998287i	$-0.518635\pi$
$821$	−6.47578e7			−0.117021			−0.0585103	+	0.998287i	$0.518635\pi$
$822$		−	4.90066e8i		−	0.882347i
$823$	3.15162e8			0.565371			0.282686	−	0.959213i	$-0.408775\pi$
$823$	3.15162e8			0.565371			0.282686	+	0.959213i	$0.408775\pi$
$824$		−	9.70206e8i		−	1.73413i
$825$		−	9.99738e7i		−	0.178043i
$826$	1.23047e9	−	3.21372e8i	2.18338	−	0.570253i
$827$	−2.92523e8			−0.517183			−0.258591	−	0.965987i	$-0.583258\pi$
$827$	−2.92523e8			−0.517183			−0.258591	+	0.965987i	$0.583258\pi$
$828$	2.87268e8			0.506053
$829$		−	5.06899e8i		−	0.889730i	−0.895598	−	0.444865i	$-0.853252\pi$
$829$		−	5.06899e8i		−	0.889730i	0.895598	−	0.444865i	$-0.146748\pi$
$830$	3.10458e8			0.542960
$831$			5.12770e8i			0.893551i
$832$			8.25726e8i			1.43373i
$833$	9.76674e7	+	1.74220e8i	0.168972	+	0.301414i
$834$	−1.60434e8			−0.276566
$835$	−2.84172e8			−0.488115
$836$		−	1.30721e9i		−	2.23731i
$837$	1.99333e8			0.339940
$838$		−	2.49518e8i		−	0.424005i
$839$			2.49136e8i			0.421843i	0.977503	+	0.210921i	$0.0676464\pi$
$839$			2.49136e8i			0.421843i	−0.977503	+	0.210921i	$0.932354\pi$
$840$	1.32634e8	+	5.07830e8i	0.223778	+	0.856802i
$841$	9.41932e8			1.58355
$842$	−6.86441e8			−1.14992
$843$			4.39649e8i			0.733877i
$844$	−5.77790e8			−0.961043
$845$			6.35620e8i			1.05348i
$846$			1.93157e7i			0.0319006i
$847$	1.08167e8	+	4.14150e8i	0.178010	+	0.681565i
$848$	4.06023e8			0.665829
$849$	4.47331e8			0.730981
$850$		−	8.69839e7i		−	0.141639i
$851$	−2.92828e8			−0.475143
$852$			1.10954e8i			0.179401i
$853$		−	4.98327e7i		−	0.0802911i	−0.999194	−	0.0401456i	$-0.987218\pi$
$853$		−	4.98327e7i		−	0.0802911i	0.999194	−	0.0401456i	$-0.0127822\pi$
$854$	3.84777e8	−	1.00495e8i	0.617782	−	0.161351i
$855$	−1.55136e8			−0.248208
$856$	8.91473e8			1.42130
$857$		−	5.86747e8i		−	0.932198i	−0.884733	−	0.466099i	$-0.845659\pi$
$857$		−	5.86747e8i		−	0.932198i	0.884733	−	0.466099i	$-0.154341\pi$
$858$	−1.22692e9			−1.94248
$859$		−	1.12027e9i		−	1.76743i	−0.468021	−	0.883717i	$-0.655033\pi$
$859$		−	1.12027e9i		−	1.76743i	0.468021	−	0.883717i	$-0.344967\pi$
$860$		−	6.94446e8i		−	1.09180i
$861$	4.10478e7	+	1.57164e8i	0.0643103	+	0.246231i
$862$	−3.47022e8			−0.541796
$863$	1.46832e8			0.228449			0.114225	−	0.993455i	$-0.463562\pi$
$863$	1.46832e8			0.228449			0.114225	+	0.993455i	$0.463562\pi$
$864$		−	4.91800e6i		−	0.00762513i
$865$	3.57934e8			0.553037
$866$			2.06010e9i			3.17201i
$867$			3.31340e8i			0.508414i
$868$	−2.24803e9	+	5.87138e8i	−3.43750	+	0.897802i
$869$	9.52139e7			0.145091
$870$	9.26773e8			1.40739
$871$			1.47479e9i			2.23191i
$872$	−7.16478e8			−1.08057
$873$			1.03092e8i			0.154947i
$874$		−	7.45063e8i		−	1.11599i
$875$	7.00284e8	−	1.82899e8i	1.04532	−	0.273016i
$876$	−1.15405e9			−1.71676
$877$	−4.68591e8			−0.694696			−0.347348	−	0.937736i	$-0.612918\pi$
$877$	−4.68591e8			−0.694696			−0.347348	+	0.937736i	$0.612918\pi$
$878$		−	2.00077e9i		−	2.95606i
$879$	2.93832e8			0.432646
$880$			8.04123e8i			1.17998i
$881$			5.14343e8i			0.752186i	0.926582	+	0.376093i	$0.122733\pi$
$881$			5.14343e8i			0.752186i	−0.926582	+	0.376093i	$0.877267\pi$
$882$	3.46197e8	−	1.94077e8i	0.504565	−	0.282858i
$883$	7.42034e8			1.07781			0.538905	−	0.842367i	$-0.318838\pi$
$883$	7.42034e8			1.07781			0.538905	+	0.842367i	$0.318838\pi$
$884$	−7.13011e8			−1.03214
$885$		−	4.54815e8i		−	0.656153i
$886$	1.74192e9			2.50454
$887$		−	8.74959e8i		−	1.25377i	−0.779113	−	0.626883i	$-0.784330\pi$
$887$		−	8.74959e8i		−	1.25377i	0.779113	−	0.626883i	$-0.215670\pi$
$888$			4.46638e8i			0.637848i
$889$	2.75673e7	+	1.05550e8i	0.0392364	+	0.150228i
$890$	−1.13548e9			−1.61068
$891$	−1.02608e8			−0.145060
$892$		−	2.74081e9i		−	3.86175i
$893$	3.34614e7			0.0469882
$894$			4.43554e7i			0.0620774i
$895$		−	1.85934e8i		−	0.259352i
$896$	−3.11734e8	−	1.19357e9i	−0.433372	−	1.65929i
$897$	−4.67081e8			−0.647164
$898$	−2.63717e8			−0.364175
$899$			2.06287e9i			2.83918i
$900$	−1.15449e8			−0.158366
$901$		−	1.62721e8i		−	0.222470i
$902$			7.32862e8i			0.998626i
$903$	−2.55471e8	+	6.67235e7i	−0.346959	+	0.0906182i
$904$	−7.60630e8			−1.02960
$905$	4.49979e8			0.607081
$906$			8.27080e8i			1.11215i
$907$	−1.70978e8			−0.229149			−0.114575	−	0.993415i	$-0.536551\pi$
$907$	−1.70978e8			−0.229149			−0.114575	+	0.993415i	$0.536551\pi$
$908$			7.38174e8i			0.986055i
$909$		−	3.01121e8i		−	0.400912i
$910$	−4.28891e8	−	1.64214e9i	−0.569144	−	2.17914i
$911$	3.41772e8			0.452044			0.226022	−	0.974122i	$-0.427428\pi$
$911$	3.41772e8			0.452044			0.226022	+	0.974122i	$0.427428\pi$
$912$	−3.85896e8			−0.508729
$913$		−	3.55714e8i		−	0.467400i
$914$	−1.41181e9			−1.84900
$915$		−	1.42224e8i		−	0.185656i
$916$		−	7.35868e6i		−	0.00957444i
$917$	8.00811e8	−	2.09155e8i	1.03854	−	0.271244i
$918$	−8.92755e7			−0.115400
$919$	4.10798e8			0.529276			0.264638	−	0.964348i	$-0.414748\pi$
$919$	4.10798e8			0.529276			0.264638	+	0.964348i	$0.414748\pi$
$920$			9.01494e8i			1.15771i
$921$	5.76469e8			0.737899
$922$			1.67489e9i			2.13694i
$923$		−	1.80405e8i		−	0.229426i
$924$	1.15719e9	−	3.02232e8i	1.46686	−	0.383111i
$925$	1.17684e8			0.148693
$926$	2.47441e8			0.311630
$927$			2.62372e8i			0.329366i
$928$	5.08957e7			0.0636850
$929$		−	2.87075e6i		−	0.00358054i	−0.999998	−	0.00179027i	$-0.999430\pi$
$929$		−	2.87075e6i		−	0.00358054i	0.999998	−	0.00179027i	$-0.000569861\pi$
$930$			1.24406e9i			1.54665i
$931$	−3.36207e8	−	5.99730e8i	−0.416637	−	0.743202i
$932$	2.78378e9			3.43864
$933$	1.25913e8			0.155034
$934$			5.43194e8i			0.666676i
$935$	3.22268e8			0.394259
$936$			7.12419e8i			0.868776i
$937$			1.80346e8i			0.219224i	0.993974	+	0.109612i	$0.0349608\pi$
$937$			1.80346e8i			0.219224i	−0.993974	+	0.109612i	$0.965039\pi$
$938$	−5.43912e8	−	2.08253e9i	−0.659053	−	2.52338i
$939$	−3.56645e8			−0.430764
$940$	−8.05191e7			−0.0969428
$941$			4.15983e8i			0.499237i	0.968344	+	0.249619i	$0.0803052\pi$
$941$			4.15983e8i			0.499237i	−0.968344	+	0.249619i	$0.919695\pi$
$942$	−4.09340e8			−0.489702
$943$			2.78995e8i			0.332707i
$944$		−	1.13134e9i		−	1.34486i
$945$	−3.58682e7	−	1.37332e8i	−0.0425024	−	0.162733i
$946$	−1.19127e9			−1.40714
$947$	7.57107e8			0.891471			0.445736	−	0.895165i	$-0.352942\pi$
$947$	7.57107e8			0.891471			0.445736	+	0.895165i	$0.352942\pi$
$948$		−	1.09952e8i		−	0.129056i
$949$	1.87641e9			2.19548
$950$			2.99431e8i			0.349241i
$951$		−	7.32013e8i		−	0.851094i
$952$	5.06256e8	−	1.32223e8i	0.586758	−	0.153249i
$953$	−1.67466e9			−1.93485			−0.967425	−	0.253159i	$-0.918530\pi$
$953$	−1.67466e9			−1.93485			−0.967425	+	0.253159i	$0.918530\pi$
$954$	−3.23348e8			−0.372413
$955$			1.33430e9i			1.53194i
$956$	−2.07531e9			−2.37525
$957$		−	1.06187e9i		−	1.21154i
$958$			2.51951e9i			2.86563i
$959$	−1.96283e8	−	7.51530e8i	−0.222550	−	0.852099i
$960$	−4.30983e8			−0.487132
$961$	−1.88160e9			−2.12010
$962$		−	1.44427e9i		−	1.62226i
$963$	−2.41080e8			−0.269950
$964$		−	1.06801e8i		−	0.119219i
$965$		−	3.61620e8i		−	0.402411i
$966$	6.59556e8	−	1.72262e8i	0.731678	−	0.191099i
$967$	−6.89036e8			−0.762013			−0.381007	−	0.924572i	$-0.624422\pi$
$967$	−6.89036e8			−0.762013			−0.381007	+	0.924572i	$0.624422\pi$
$968$	1.12136e9			1.23629
$969$			1.54655e8i			0.169978i
$970$	−6.43409e8			−0.704973
$971$		−	1.45081e9i		−	1.58472i	−0.610051	−	0.792362i	$-0.708851\pi$
$971$		−	1.45081e9i		−	1.58472i	0.610051	−	0.792362i	$-0.291149\pi$
$972$			1.18491e8i			0.129028i
$973$	−2.46030e8	+	6.42577e7i	−0.267085	+	0.0697568i
$974$	8.00596e8			0.866436
$975$	1.87713e8			0.202526
$976$		−	3.53778e8i		−	0.380523i
$977$	−7.38560e8			−0.791958			−0.395979	−	0.918260i	$-0.629595\pi$
$977$	−7.38560e8			−0.791958			−0.395979	+	0.918260i	$0.629595\pi$
$978$			4.78340e8i			0.511353i
$979$			1.30101e9i			1.38654i
$980$	8.09026e8	+	1.44315e9i	0.859576	+	1.53332i
$981$	1.93756e8			0.205234
$982$	3.76925e8			0.398034
$983$		−	4.52694e8i		−	0.476589i	−0.971193	−	0.238294i	$-0.923412\pi$
$983$		−	4.52694e8i		−	0.476589i	0.971193	−	0.238294i	$-0.0765883\pi$
$984$	4.25540e8			0.446637
$985$			3.47717e8i			0.363846i
$986$		−	9.23901e8i		−	0.963817i
$987$	7.73640e6	+	2.96211e7i	0.00804614	+	0.0308071i
$988$	2.45445e9			2.54497
$989$	−4.53509e8			−0.468810
$990$		−	6.40386e8i		−	0.659988i
$991$	−3.20426e8			−0.329236			−0.164618	−	0.986357i	$-0.552639\pi$
$991$	−3.20426e8			−0.329236			−0.164618	+	0.986357i	$0.552639\pi$
$992$			6.83201e7i			0.0699863i
$993$			3.00059e8i			0.306449i
$994$	6.65341e7	+	2.54746e8i	0.0677463	+	0.259387i
$995$	5.63431e8			0.571968
$996$	−4.10776e8			−0.415745
$997$		−	1.31551e7i		−	0.0132742i	−0.999978	−	0.00663710i	$-0.997887\pi$
$997$		−	1.31551e7i		−	0.0132742i	0.999978	−	0.00663710i	$-0.00211267\pi$
$998$	2.54777e9			2.56312
$999$		−	1.20784e8i		−	0.121147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.d.a.13.8	yes	8
3.2	odd	2		63.7.d.f.55.2		8
4.3	odd	2		336.7.f.a.97.2		8
7.2	even	3		147.7.f.b.31.1		8
7.3	odd	6		147.7.f.b.19.1		8
7.4	even	3		147.7.f.c.19.1		8
7.5	odd	6		147.7.f.c.31.1		8
7.6	odd	2	inner	21.7.d.a.13.7	✓	8
21.20	even	2		63.7.d.f.55.1		8
28.27	even	2		336.7.f.a.97.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.d.a.13.7	✓	8	7.6	odd	2	inner
21.7.d.a.13.8	yes	8	1.1	even	1	trivial
63.7.d.f.55.1		8	21.20	even	2
63.7.d.f.55.2		8	3.2	odd	2
147.7.f.b.19.1		8	7.3	odd	6
147.7.f.b.31.1		8	7.2	even	3
147.7.f.c.19.1		8	7.4	even	3
147.7.f.c.31.1		8	7.5	odd	6
336.7.f.a.97.2		8	4.3	odd	2
336.7.f.a.97.7		8	28.27	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+13.8826 q^{2} +15.5885i q^{3} +128.727 q^{4} -109.244i q^{5} +216.408i q^{6} +(86.6767 + 331.868i) q^{7} +898.572 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+13.8826 q^{2} +15.5885i q^{3} +128.727 q^{4} -109.244i q^{5} +216.408i q^{6} +(86.6767 + 331.868i) q^{7} +898.572 q^{8} -243.000 q^{9} -1516.59i q^{10} -1737.67 q^{11} +2006.65i q^{12} -3262.69i q^{13} +(1203.30 + 4607.19i) q^{14} +1702.94 q^{15} +4236.02 q^{16} -1697.67i q^{17} -3373.47 q^{18} +5844.00i q^{19} -14062.6i q^{20} +(-5173.30 + 1351.16i) q^{21} -24123.4 q^{22} -9183.59 q^{23} +14007.4i q^{24} +3690.76 q^{25} -45294.6i q^{26} -3788.00i q^{27} +(11157.6 + 42720.2i) q^{28} +39201.5 q^{29} +23641.3 q^{30} +52622.3i q^{31} +1298.31 q^{32} -27087.6i q^{33} -23568.0i q^{34} +(36254.5 - 9468.91i) q^{35} -31280.5 q^{36} +31886.0 q^{37} +81129.9i q^{38} +50860.3 q^{39} -98163.6i q^{40} -30379.8i q^{41} +(-71818.9 + 18757.6i) q^{42} +49382.5 q^{43} -223684. q^{44} +26546.3i q^{45} -127492. q^{46} -5725.77i q^{47} +66033.0i q^{48} +(-102623. + 57530.4i) q^{49} +51237.3 q^{50} +26464.0 q^{51} -419995. i q^{52} +95850.1 q^{53} -52587.2i q^{54} +189830. i q^{55} +(77885.3 + 298207. i) q^{56} -91098.9 q^{57} +544218. q^{58} -267076. i q^{59} +219214. q^{60} -83516.6i q^{61} +730534. i q^{62} +(-21062.4 - 80643.8i) q^{63} -253081. q^{64} -356429. q^{65} -376046. i q^{66} -452018. q^{67} -218535. i q^{68} -143158. i q^{69} +(503307. - 131453. i) q^{70} +55293.2 q^{71} -218353. q^{72} +575111. i q^{73} +442661. q^{74} +57533.3i q^{75} +752277. i q^{76} +(-150616. - 576677. i) q^{77} +706074. q^{78} -54794.0 q^{79} -462759. i q^{80} +59049.0 q^{81} -421750. i q^{82} +204708. i q^{83} +(-665941. + 173930. i) q^{84} -185460. q^{85} +685557. q^{86} +611090. i q^{87} -1.56142e6 q^{88} -748708. i q^{89} +368531. i q^{90} +(1.08278e6 - 282799. i) q^{91} -1.18217e6 q^{92} -820300. q^{93} -79488.5i q^{94} +638421. q^{95} +20238.7i q^{96} -424248. i q^{97} +(-1.42468e6 + 798671. i) q^{98} +422254. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9	\( 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9} - 6848 q^{11} + 12082 q^{14} - 4536 q^{15} + 28466 q^{16} - 2430 q^{18} + 6804 q^{21} - 7764 q^{22} - 24320 q^{23} - 77056 q^{25} - 30142 q^{28} + 60496 q^{29} + 89424 q^{30} + 5082 q^{32} + 103656 q^{35} - 84078 q^{36} - 39112 q^{37} + 108864 q^{39} - 267624 q^{42} - 29272 q^{43} - 577884 q^{44} + 564972 q^{46} - 94864 q^{49} + 240154 q^{50} + 103032 q^{51} + 232288 q^{53} + 225722 q^{56} + 180792 q^{57} + 987684 q^{58} - 375192 q^{60} - 6804 q^{63} - 690734 q^{64} - 836304 q^{65} - 2163848 q^{67} - 366744 q^{70} - 506288 q^{71} + 355266 q^{72} + 512324 q^{74} + 1536304 q^{77} + 1272024 q^{78} - 93272 q^{79} + 472392 q^{81} - 653184 q^{84} + 3740760 q^{85} + 3846452 q^{86} - 2077548 q^{88} + 1890336 q^{91} - 9701580 q^{92} - 2153952 q^{93} + 4154832 q^{95} - 507542 q^{98} + 1664064 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9 - 6848 * q^11 + 12082 * q^14 - 4536 * q^15 + 28466 * q^16 - 2430 * q^18 + 6804 * q^21 - 7764 * q^22 - 24320 * q^23 - 77056 * q^25 - 30142 * q^28 + 60496 * q^29 + 89424 * q^30 + 5082 * q^32 + 103656 * q^35 - 84078 * q^36 - 39112 * q^37 + 108864 * q^39 - 267624 * q^42 - 29272 * q^43 - 577884 * q^44 + 564972 * q^46 - 94864 * q^49 + 240154 * q^50 + 103032 * q^51 + 232288 * q^53 + 225722 * q^56 + 180792 * q^57 + 987684 * q^58 - 375192 * q^60 - 6804 * q^63 - 690734 * q^64 - 836304 * q^65 - 2163848 * q^67 - 366744 * q^70 - 506288 * q^71 + 355266 * q^72 + 512324 * q^74 + 1536304 * q^77 + 1272024 * q^78 - 93272 * q^79 + 472392 * q^81 - 653184 * q^84 + 3740760 * q^85 + 3846452 * q^86 - 2077548 * q^88 + 1890336 * q^91 - 9701580 * q^92 - 2153952 * q^93 + 4154832 * q^95 - 507542 * q^98 + 1664064 * q^99

Introduction

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