LMFDB - Embedded newform 33.5.c.a.10.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,5,Mod(10,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("33.10");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	33.c (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:	$3.41120878177$
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} + 102x^{6} + 2913x^{4} + 23292x^{2} + 41364 $ x^8 + 102x^6 + 2913x^4 + 23292*x^2 + 41364
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.6
Root			$3.00247i$ of defining polynomial
Character	$\chi$	$=$	33.10
Dual form			33.5.c.a.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} +15.6013i q^{6} +1.45810i q^{7} +69.0123i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} +15.6013i q^{6} +1.45810i q^{7} +69.0123i q^{8} +27.0000 q^{9} +26.1989i q^{10} +(-62.2476 + 103.760i) q^{11} +36.2960 q^{12} -162.221i q^{13} -4.37791 q^{14} +45.3405 q^{15} -95.4447 q^{16} -189.734i q^{17} +81.0667i q^{18} -590.443i q^{19} +60.9511 q^{20} +7.57652i q^{21} +(-311.538 - 186.897i) q^{22} -12.8557 q^{23} +358.598i q^{24} -548.861 q^{25} +487.064 q^{26} +140.296 q^{27} +10.1851i q^{28} +282.359i q^{29} +136.134i q^{30} -304.206 q^{31} +817.627i q^{32} +(-323.448 + 539.155i) q^{33} +569.671 q^{34} +12.7231i q^{35} +188.600 q^{36} +464.276 q^{37} +1772.79 q^{38} -842.925i q^{39} +602.186i q^{40} -1193.81i q^{41} -22.7483 q^{42} +1591.11i q^{43} +(-434.810 + 724.784i) q^{44} +235.596 q^{45} -38.5989i q^{46} -1825.87 q^{47} -495.945 q^{48} +2398.87 q^{49} -1647.94i q^{50} -985.887i q^{51} -1133.14i q^{52} -4023.28 q^{53} +421.235i q^{54} +(-543.159 + 905.391i) q^{55} -100.627 q^{56} -3068.03i q^{57} -847.774 q^{58} -1489.12 q^{59} +316.711 q^{60} +356.601i q^{61} -913.368i q^{62} +39.3688i q^{63} -3982.02 q^{64} -1415.51i q^{65} +(-1618.80 - 971.143i) q^{66} +8259.07 q^{67} -1325.32i q^{68} -66.8002 q^{69} -38.2007 q^{70} +7971.63 q^{71} +1863.33i q^{72} +5780.93i q^{73} +1393.98i q^{74} -2851.96 q^{75} -4124.34i q^{76} +(-151.293 - 90.7633i) q^{77} +2530.86 q^{78} +11304.5i q^{79} -832.830 q^{80} +729.000 q^{81} +3584.37 q^{82} +5449.44i q^{83} +52.9233i q^{84} -1655.58i q^{85} -4777.26 q^{86} +1467.18i q^{87} +(-7160.75 - 4295.85i) q^{88} +7332.12 q^{89} +707.371i q^{90} +236.535 q^{91} -89.7992 q^{92} -1580.70 q^{93} -5482.13i q^{94} -5152.08i q^{95} +4248.51i q^{96} -11228.1 q^{97} +7202.55i q^{98} +(-1680.69 + 2801.53i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9}+O(q^{10}) $ 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9	$ 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9} + 36 q^{11} - 360 q^{12} - 1140 q^{14} + 108 q^{15} + 1412 q^{16} + 2532 q^{20} - 780 q^{22} + 516 q^{23} - 2280 q^{25} - 1524 q^{26} + 2752 q^{31} + 1008 q^{33} - 4920 q^{34} - 2052 q^{36} + 5296 q^{37} + 696 q^{38} - 4356 q^{42} - 6540 q^{44} - 972 q^{45} + 420 q^{47} + 9936 q^{48} - 6832 q^{49} + 3540 q^{53} + 3784 q^{55} + 17964 q^{56} + 21624 q^{58} - 16632 q^{59} - 612 q^{60} - 27508 q^{64} + 360 q^{66} - 3656 q^{67} + 9036 q^{69} + 3312 q^{70} - 13212 q^{71} - 9288 q^{75} + 23268 q^{77} - 13140 q^{78} - 4476 q^{80} + 5832 q^{81} + 17088 q^{82} + 19896 q^{86} - 12516 q^{88} + 15528 q^{89} - 19752 q^{91} - 81180 q^{92} - 21384 q^{93} + 7624 q^{97} + 972 q^{99}+O(q^{100}) $ 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9 + 36 * q^11 - 360 * q^12 - 1140 * q^14 + 108 * q^15 + 1412 * q^16 + 2532 * q^20 - 780 * q^22 + 516 * q^23 - 2280 * q^25 - 1524 * q^26 + 2752 * q^31 + 1008 * q^33 - 4920 * q^34 - 2052 * q^36 + 5296 * q^37 + 696 * q^38 - 4356 * q^42 - 6540 * q^44 - 972 * q^45 + 420 * q^47 + 9936 * q^48 - 6832 * q^49 + 3540 * q^53 + 3784 * q^55 + 17964 * q^56 + 21624 * q^58 - 16632 * q^59 - 612 * q^60 - 27508 * q^64 + 360 * q^66 - 3656 * q^67 + 9036 * q^69 + 3312 * q^70 - 13212 * q^71 - 9288 * q^75 + 23268 * q^77 - 13140 * q^78 - 4476 * q^80 + 5832 * q^81 + 17088 * q^82 + 19896 * q^86 - 12516 * q^88 + 15528 * q^89 - 19752 * q^91 - 81180 * q^92 - 21384 * q^93 + 7624 * q^97 + 972 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$1$

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 $

$2$			3.00247i			0.750618i	0.926900	+	0.375309i	$0.122463\pi$
$2$			3.00247i			0.750618i	−0.926900	+	0.375309i	$0.877537\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	6.98517			0.436573
$5$	8.72578			0.349031			0.174516	−	0.984654i	$-0.444164\pi$
$5$	8.72578			0.349031			0.174516	+	0.984654i	$0.444164\pi$
$6$			15.6013i			0.433369i
$7$			1.45810i			0.0297572i	0.999889	+	0.0148786i	$0.00473618\pi$
$7$			1.45810i			0.0297572i	−0.999889	+	0.0148786i	$0.995264\pi$
$8$			69.0123i			1.07832i
$9$	27.0000			0.333333
$10$			26.1989i			0.261989i
$11$	−62.2476	+	103.760i	−0.514443	+	0.857525i
$11$	−62.2476	+	103.760i	−0.514443	+	0.857525i
$12$	36.2960			0.252056
$13$		−	162.221i		−	0.959888i	−0.877299	−	0.479944i	$-0.840657\pi$
$13$		−	162.221i		−	0.959888i	0.877299	−	0.479944i	$-0.159343\pi$
$14$	−4.37791			−0.0223363
$15$	45.3405			0.201513
$16$	−95.4447			−0.372831
$17$		−	189.734i		−	0.656519i	−0.944588	−	0.328259i	$-0.893538\pi$
$17$		−	189.734i		−	0.656519i	0.944588	−	0.328259i	$-0.106462\pi$
$18$			81.0667i			0.250206i
$19$		−	590.443i		−	1.63558i	−0.575520	−	0.817788i	$-0.695200\pi$
$19$		−	590.443i		−	1.63558i	0.575520	−	0.817788i	$-0.304800\pi$
$20$	60.9511			0.152378
$21$			7.57652i			0.0171803i
$22$	−311.538	−	186.897i	−0.643673	−	0.386150i
$23$	−12.8557			−0.0243019			−0.0121509	−	0.999926i	$-0.503868\pi$
$23$	−12.8557			−0.0243019			−0.0121509	+	0.999926i	$0.503868\pi$
$24$			358.598i			0.622567i
$25$	−548.861			−0.878177
$26$	487.064			0.720509
$27$	140.296			0.192450
$28$			10.1851i			0.0129912i
$29$			282.359i			0.335742i	0.985809	+	0.167871i	$0.0536892\pi$
$29$			282.359i			0.335742i	−0.985809	+	0.167871i	$0.946311\pi$
$30$			136.134i			0.151259i
$31$	−304.206			−0.316551			−0.158275	−	0.987395i	$-0.550593\pi$
$31$	−304.206			−0.316551			−0.158275	+	0.987395i	$0.550593\pi$
$32$			817.627i			0.798464i
$33$	−323.448	+	539.155i	−0.297014	+	0.495092i
$34$	569.671			0.492795
$35$			12.7231i			0.0103862i
$36$	188.600			0.145524
$37$	464.276			0.339135			0.169568	−	0.985519i	$-0.445763\pi$
$37$	464.276			0.339135			0.169568	+	0.985519i	$0.445763\pi$
$38$	1772.79			1.22769
$39$		−	842.925i		−	0.554191i
$40$			602.186i			0.376366i
$41$		−	1193.81i		−	0.710177i	−0.934833	−	0.355089i	$-0.884451\pi$
$41$		−	1193.81i		−	0.710177i	0.934833	−	0.355089i	$-0.115549\pi$
$42$	−22.7483			−0.0128959
$43$			1591.11i			0.860525i	0.902704	+	0.430263i	$0.141579\pi$
$43$			1591.11i			0.860525i	−0.902704	+	0.430263i	$0.858421\pi$
$44$	−434.810	+	724.784i	−0.224592	+	0.374372i
$45$	235.596			0.116344
$46$		−	38.5989i		−	0.0182414i
$47$	−1825.87			−0.826561			−0.413281	−	0.910604i	$-0.635617\pi$
$47$	−1825.87			−0.826561			−0.413281	+	0.910604i	$0.635617\pi$
$48$	−495.945			−0.215254
$49$	2398.87			0.999115
$50$		−	1647.94i		−	0.659175i
$51$		−	985.887i		−	0.379041i
$52$		−	1133.14i		−	0.419061i
$53$	−4023.28			−1.43228			−0.716141	−	0.697955i	$-0.754093\pi$
$53$	−4023.28			−1.43228			−0.716141	+	0.697955i	$0.754093\pi$
$54$			421.235i			0.144456i
$55$	−543.159	+	905.391i	−0.179557	+	0.299303i
$56$	−100.627			−0.0320877
$57$		−	3068.03i		−	0.944300i
$58$	−847.774			−0.252014
$59$	−1489.12			−0.427785			−0.213893	−	0.976857i	$-0.568614\pi$
$59$	−1489.12			−0.427785			−0.213893	+	0.976857i	$0.568614\pi$
$60$	316.711			0.0879753
$61$			356.601i			0.0958346i	0.998851	+	0.0479173i	$0.0152584\pi$
$61$			356.601i			0.0958346i	−0.998851	+	0.0479173i	$0.984742\pi$
$62$		−	913.368i		−	0.237609i
$63$			39.3688i			0.00991906i
$64$	−3982.02			−0.972172
$65$		−	1415.51i		−	0.335031i
$66$	−1618.80	−	971.143i	−0.371625	−	0.222944i
$67$	8259.07			1.83985			0.919923	−	0.392098i	$-0.128251\pi$
$67$	8259.07			1.83985			0.919923	+	0.392098i	$0.128251\pi$
$68$		−	1325.32i		−	0.286618i
$69$	−66.8002			−0.0140307
$70$	−38.2007			−0.00779606
$71$	7971.63			1.58136			0.790680	−	0.612230i	$-0.209727\pi$
$71$	7971.63			1.58136			0.790680	+	0.612230i	$0.209727\pi$
$72$			1863.33i			0.359439i
$73$			5780.93i			1.08481i	0.840118	+	0.542403i	$0.182485\pi$
$73$			5780.93i			1.08481i	−0.840118	+	0.542403i	$0.817515\pi$
$74$			1393.98i			0.254561i
$75$	−2851.96			−0.507016
$76$		−	4124.34i		−	0.714048i
$77$	−151.293	−	90.7633i	−0.0255175	−	0.0153084i
$78$	2530.86			0.415986
$79$			11304.5i			1.81133i	0.423998	+	0.905663i	$0.360626\pi$
$79$			11304.5i			1.81133i	−0.423998	+	0.905663i	$0.639374\pi$
$80$	−832.830			−0.130130
$81$	729.000			0.111111
$82$	3584.37			0.533071
$83$			5449.44i			0.791036i	0.918458	+	0.395518i	$0.129435\pi$
$83$			5449.44i			0.791036i	−0.918458	+	0.395518i	$0.870565\pi$
$84$			52.9233i			0.00750046i
$85$		−	1655.58i		−	0.229146i
$86$	−4777.26			−0.645925
$87$			1467.18i			0.193841i
$88$	−7160.75	−	4295.85i	−0.924684	−	0.554733i
$89$	7332.12			0.925656			0.462828	−	0.886448i	$-0.346835\pi$
$89$	7332.12			0.925656			0.462828	+	0.886448i	$0.346835\pi$
$90$			707.371i			0.0873297i
$91$	236.535			0.0285636
$92$	−89.7992			−0.0106096
$93$	−1580.70			−0.182761
$94$		−	5482.13i		−	0.620432i
$95$		−	5152.08i		−	0.570867i
$96$			4248.51i			0.460993i
$97$	−11228.1			−1.19334			−0.596669	−	0.802487i	$-0.703509\pi$
$97$	−11228.1			−1.19334			−0.596669	+	0.802487i	$0.703509\pi$
$98$			7202.55i			0.749953i
$99$	−1680.69	+	2801.53i	−0.171481	+	0.285842i
$100$	−3833.88			−0.383388
$101$		−	12735.1i		−	1.24842i	−0.781258	−	0.624209i	$-0.785422\pi$
$101$		−	12735.1i		−	1.24842i	0.781258	−	0.624209i	$-0.214578\pi$
$102$	2960.10			0.284515
$103$	4637.37			0.437117			0.218558	−	0.975824i	$-0.429865\pi$
$103$	4637.37			0.437117			0.218558	+	0.975824i	$0.429865\pi$
$104$	11195.2			1.03506
$105$			66.1111i			0.00599647i
$106$		−	12079.8i		−	1.07510i
$107$			15858.6i			1.38515i	0.721347	+	0.692574i	$0.243524\pi$
$107$			15858.6i			1.38515i	−0.721347	+	0.692574i	$0.756476\pi$
$108$	979.992			0.0840185
$109$		−	19516.7i		−	1.64268i	−0.570438	−	0.821341i	$-0.693226\pi$
$109$		−	19516.7i		−	1.64268i	0.570438	−	0.821341i	$-0.306774\pi$
$110$	−2718.41	−	1630.82i	−0.224662	−	0.134778i
$111$	2412.45			0.195800
$112$		−	139.168i		−	0.0110944i
$113$	−15343.5			−1.20162			−0.600811	−	0.799391i	$-0.705156\pi$
$113$	−15343.5			−1.20162			−0.600811	+	0.799391i	$0.705156\pi$
$114$	9211.67			0.708808
$115$	−112.176			−0.00848212
$116$			1972.32i			0.146576i
$117$		−	4379.97i		−	0.319963i
$118$		−	4471.04i		−	0.321103i
$119$	276.652			0.0195362
$120$			3129.05i			0.217295i
$121$	−6891.47	−	12917.7i	−0.470697	−	0.882295i
$122$	−1070.68			−0.0719351
$123$		−	6203.21i		−	0.410021i
$124$	−2124.93			−0.138198
$125$	−10242.9			−0.655543
$126$	−118.204			−0.00744542
$127$			19359.4i			1.20028i	0.799893	+	0.600142i	$0.204889\pi$
$127$			19359.4i			1.20028i	−0.799893	+	0.600142i	$0.795111\pi$
$128$			1126.14i			0.0687341i
$129$			8267.66i			0.496824i
$130$	4250.01			0.251480
$131$		−	13966.3i		−	0.813842i	−0.913463	−	0.406921i	$-0.866602\pi$
$131$		−	13966.3i		−	0.813842i	0.913463	−	0.406921i	$-0.133398\pi$
$132$	−2259.34	+	3766.09i	−0.129668	+	0.216144i
$133$	860.926			0.0486701
$134$			24797.6i			1.38102i
$135$	1224.19			0.0671711
$136$	13094.0			0.707936
$137$	10923.8			0.582010			0.291005	−	0.956721i	$-0.406010\pi$
$137$	10923.8			0.582010			0.291005	+	0.956721i	$0.406010\pi$
$138$		−	200.566i		−	0.0105317i
$139$			27425.4i			1.41946i	0.704474	+	0.709730i	$0.251183\pi$
$139$			27425.4i			1.41946i	−0.704474	+	0.709730i	$0.748817\pi$
$140$			88.8729i			0.00453433i
$141$	−9487.52			−0.477215
$142$			23934.6i			1.18700i
$143$	16832.1	+	10097.9i	0.823127	+	0.493807i
$144$	−2577.01			−0.124277
$145$			2463.80i			0.117184i
$146$	−17357.1			−0.814275
$147$	12464.9			0.576839
$148$	3243.05			0.148057
$149$		−	17646.6i		−	0.794856i	−0.917633	−	0.397428i	$-0.869903\pi$
$149$		−	17646.6i		−	0.794856i	0.917633	−	0.397428i	$-0.130097\pi$
$150$		−	8562.94i		−	0.380575i
$151$		−	19482.1i		−	0.854441i	−0.904147	−	0.427221i	$-0.859493\pi$
$151$		−	19482.1i		−	0.854441i	0.904147	−	0.427221i	$-0.140507\pi$
$152$	40747.8			1.76367
$153$		−	5122.82i		−	0.218840i
$154$	272.514	−	454.254i	0.0114907	−	0.0191539i
$155$	−2654.43			−0.110486
$156$		−	5887.97i		−	0.241945i
$157$	20642.6			0.837462			0.418731	−	0.908110i	$-0.362475\pi$
$157$	20642.6			0.837462			0.418731	+	0.908110i	$0.362475\pi$
$158$	−33941.4			−1.35961
$159$	−20905.6			−0.826929
$160$			7134.43i			0.278689i
$161$		−	18.7449i		−	0.000723156i
$162$			2188.80i			0.0834020i
$163$	5888.63			0.221635			0.110818	−	0.993841i	$-0.464653\pi$
$163$	5888.63			0.221635			0.110818	+	0.993841i	$0.464653\pi$
$164$		−	8338.95i		−	0.310044i
$165$	−2822.34	+	4704.55i	−0.103667	+	0.172803i
$166$	−16361.8			−0.593765
$167$		−	25996.3i		−	0.932135i	−0.884749	−	0.466067i	$-0.845670\pi$
$167$		−	25996.3i		−	0.932135i	0.884749	−	0.466067i	$-0.154330\pi$
$168$	−522.873			−0.0185258
$169$	2245.35			0.0786159
$170$	4970.82			0.172001
$171$		−	15942.0i		−	0.545192i
$172$			11114.2i			0.375682i
$173$		−	22355.9i		−	0.746964i	−0.927637	−	0.373482i	$-0.878164\pi$
$173$		−	22355.9i		−	0.746964i	0.927637	−	0.373482i	$-0.121836\pi$
$174$	−4405.16			−0.145500
$175$		−	800.295i		−	0.0261321i
$176$	5941.21	−	9903.39i	0.191800	−	0.319712i
$177$	−7737.70			−0.246982
$178$			22014.5i			0.694814i
$179$	9227.98			0.288005			0.144003	−	0.989577i	$-0.454003\pi$
$179$	9227.98			0.288005			0.144003	+	0.989577i	$0.454003\pi$
$180$	1645.68			0.0507925
$181$	−52256.0			−1.59507			−0.797534	−	0.603274i	$-0.793862\pi$
$181$	−52256.0			−1.59507			−0.797534	+	0.603274i	$0.793862\pi$
$182$			710.189i			0.0214403i
$183$			1852.95i			0.0553301i
$184$		−	887.202i		−	0.0262052i
$185$	4051.17			0.118369
$186$		−	4746.00i		−	0.137184i
$187$	19686.9	+	11810.5i	0.562981	+	0.337742i
$188$	−12754.0			−0.360854
$189$			204.566i			0.00572677i
$190$	15469.0			0.428503
$191$	−70655.7			−1.93678			−0.968390	−	0.249442i	$-0.919753\pi$
$191$	−70655.7			−1.93678			−0.968390	+	0.249442i	$0.919753\pi$
$192$	−20691.2			−0.561284
$193$		−	21752.7i		−	0.583981i	−0.956421	−	0.291991i	$-0.905682\pi$
$193$		−	21752.7i		−	0.583981i	0.956421	−	0.291991i	$-0.0943176\pi$
$194$		−	33712.1i		−	0.895741i
$195$		−	7355.18i		−	0.193430i
$196$	16756.5			0.436186
$197$			67346.7i			1.73534i	0.497144	+	0.867668i	$0.334382\pi$
$197$			67346.7i			1.73534i	−0.497144	+	0.867668i	$0.665618\pi$
$198$	−8411.52	−	5046.21i	−0.214558	−	0.128717i
$199$	4956.39			0.125158			0.0625791	−	0.998040i	$-0.480067\pi$
$199$	4956.39			0.125158			0.0625791	+	0.998040i	$0.480067\pi$
$200$		−	37878.1i		−	0.946954i
$201$	42915.4			1.06224
$202$	38236.8			0.937084
$203$	−411.708			−0.00999073
$204$		−	6886.58i		−	0.165479i
$205$		−	10416.9i		−	0.247874i
$206$			13923.6i			0.328108i
$207$	−347.104			−0.00810063
$208$			15483.1i			0.357876i
$209$	61264.6	+	36753.6i	1.40255	+	0.841410i
$210$	−198.497			−0.00450106
$211$		−	5230.33i		−	0.117480i	−0.998273	−	0.0587400i	$-0.981292\pi$
$211$		−	5230.33i		−	0.117480i	0.998273	−	0.0587400i	$-0.0187083\pi$
$212$	−28103.3			−0.625296
$213$	41421.8			0.912998
$214$	−47614.9			−1.03972
$215$			13883.7i			0.300350i
$216$			9682.16i			0.207522i
$217$		−	443.563i		−	0.00941967i
$218$	58598.3			1.23303
$219$			30038.6i			0.626313i
$220$	−3794.06	+	6324.31i	−0.0783896	+	0.130668i
$221$	−30778.8			−0.630184
$222$			7243.31i			0.146971i
$223$	70116.0			1.40996			0.704981	−	0.709226i	$-0.250956\pi$
$223$	70116.0			1.40996			0.704981	+	0.709226i	$0.250956\pi$
$224$	−1192.18			−0.0237600
$225$	−14819.2			−0.292726
$226$		−	46068.5i		−	0.901960i
$227$			69181.4i			1.34257i	0.741198	+	0.671287i	$0.234258\pi$
$227$			69181.4i			1.34257i	−0.741198	+	0.671287i	$0.765742\pi$
$228$		−	21430.7i		−	0.412256i
$229$	−27970.4			−0.533369			−0.266685	−	0.963784i	$-0.585928\pi$
$229$	−27970.4			−0.533369			−0.266685	+	0.963784i	$0.585928\pi$
$230$		−	336.805i		−	0.00636683i
$231$	−786.143	−	471.620i	−0.0147325	−	0.00883829i
$232$	−19486.2			−0.362036
$233$			67591.9i			1.24504i	0.782604	+	0.622519i	$0.213891\pi$
$233$			67591.9i			1.24504i	−0.782604	+	0.622519i	$0.786109\pi$
$234$	13150.7			0.240170
$235$	−15932.2			−0.288496
$236$	−10401.8			−0.186759
$237$			58739.8i			1.04577i
$238$			830.638i			0.0146642i
$239$		−	31589.5i		−	0.553028i	−0.961010	−	0.276514i	$-0.910821\pi$
$239$		−	31589.5i		−	0.553028i	0.961010	−	0.276514i	$-0.0891792\pi$
$240$	−4327.51			−0.0751304
$241$		−	64415.3i		−	1.10906i	−0.832164	−	0.554530i	$-0.812898\pi$
$241$		−	64415.3i		−	1.10906i	0.832164	−	0.554530i	$-0.187102\pi$
$242$	38785.0	−	20691.4i	0.662266	−	0.353313i
$243$	3788.00			0.0641500
$244$			2490.91i			0.0418388i
$245$	20932.1			0.348722
$246$	18624.9			0.307769
$247$	−95782.2			−1.56997
$248$		−	20993.9i		−	0.341342i
$249$			28316.1i			0.456705i
$250$		−	30753.9i		−	0.492062i
$251$	34822.1			0.552722			0.276361	−	0.961054i	$-0.410871\pi$
$251$	34822.1			0.552722			0.276361	+	0.961054i	$0.410871\pi$
$252$			274.997i			0.00433039i
$253$	800.237	−	1333.91i	0.0125019	−	0.0208395i
$254$	−58126.0			−0.900955
$255$		−	8602.63i		−	0.132297i
$256$	−67093.5			−1.02376
$257$	−73746.1			−1.11654			−0.558268	−	0.829661i	$-0.688534\pi$
$257$	−73746.1			−1.11654			−0.558268	+	0.829661i	$0.688534\pi$
$258$	−24823.4			−0.372925
$259$			676.962i			0.0100917i
$260$		−	9887.54i		−	0.146265i
$261$			7623.69i			0.111914i
$262$	41933.5			0.610884
$263$		−	103570.i		−	1.49734i	−0.662942	−	0.748671i	$-0.730692\pi$
$263$		−	103570.i		−	1.49734i	0.662942	−	0.748671i	$-0.269308\pi$
$264$	−37208.3	−	22321.9i	−0.533866	−	0.320275i
$265$	−35106.3			−0.499911
$266$			2584.91i			0.0365327i
$267$	38098.8			0.534428
$268$	57691.0			0.803227
$269$	118870.			1.64274			0.821371	−	0.570395i	$-0.193210\pi$
$269$	118870.			1.64274			0.821371	+	0.570395i	$0.193210\pi$
$270$			3675.60i			0.0504198i
$271$		−	102742.i		−	1.39897i	−0.714646	−	0.699486i	$-0.753412\pi$
$271$		−	102742.i		−	1.39897i	0.714646	−	0.699486i	$-0.246588\pi$
$272$			18109.1i			0.244771i
$273$	1229.07			0.0164912
$274$			32798.3i			0.436867i
$275$	34165.3	−	56950.1i	0.451772	−	0.753059i
$276$	−466.611			−0.00612543
$277$		−	103336.i		−	1.34677i	−0.739292	−	0.673385i	$-0.764839\pi$
$277$		−	103336.i		−	1.34677i	0.739292	−	0.673385i	$-0.235161\pi$
$278$	−82343.9			−1.06547
$279$	−8213.55			−0.105517
$280$	−878.049			−0.0111996
$281$			37257.8i			0.471850i	0.971771	+	0.235925i	$0.0758120\pi$
$281$			37257.8i			0.471850i	−0.971771	+	0.235925i	$0.924188\pi$
$282$		−	28486.0i		−	0.358206i
$283$			126640.i			1.58124i	0.612310	+	0.790618i	$0.290241\pi$
$283$			126640.i			1.58124i	−0.612310	+	0.790618i	$0.709759\pi$
$284$	55683.2			0.690379
$285$		−	26771.0i		−	0.329590i
$286$	−30318.6	+	50538.0i	−0.370661	+	0.617854i
$287$	1740.69			0.0211329
$288$			22075.9i			0.266155i
$289$	47522.0			0.568983
$290$	−7397.49			−0.0879607
$291$	−58343.0			−0.688974
$292$			40380.8i			0.473597i
$293$		−	1337.08i		−	0.0155748i	−0.999970	−	0.00778741i	$-0.997521\pi$
$293$		−	1337.08i		−	0.0155748i	0.999970	−	0.00778741i	$-0.00247883\pi$
$294$			37425.5i			0.432986i
$295$	−12993.7			−0.149310
$296$			32040.8i			0.365695i
$297$	−8733.10	+	14557.2i	−0.0990046	+	0.165031i
$298$	52983.4			0.596633
$299$			2085.46i			0.0233271i
$300$	−19921.4			−0.221349
$301$	−2320.00			−0.0256068
$302$	58494.5			0.641359
$303$		−	66173.5i		−	0.720774i
$304$			56354.7i			0.609793i
$305$			3111.62i			0.0334493i
$306$	15381.1			0.164265
$307$			70825.1i			0.751468i	0.926728	+	0.375734i	$0.122609\pi$
$307$			70825.1i			0.751468i	−0.926728	+	0.375734i	$0.877391\pi$
$308$	−1056.81	−	633.997i	−0.0111403	−	0.00668322i
$309$	24096.5			0.252369
$310$		−	7969.85i		−	0.0829329i
$311$	−79979.1			−0.826905			−0.413453	−	0.910526i	$-0.635677\pi$
$311$	−79979.1			−0.826905			−0.413453	+	0.910526i	$0.635677\pi$
$312$	58172.2			0.597594
$313$	45118.3			0.460537			0.230268	−	0.973127i	$-0.426040\pi$
$313$	45118.3			0.460537			0.230268	+	0.973127i	$0.426040\pi$
$314$			61978.8i			0.628614i
$315$			343.523i			0.00346206i
$316$			78963.7i			0.790776i
$317$	−53392.1			−0.531322			−0.265661	−	0.964066i	$-0.585590\pi$
$317$	−53392.1			−0.531322			−0.265661	+	0.964066i	$0.585590\pi$
$318$		−	62768.4i		−	0.620707i
$319$	−29297.7	−	17576.2i	−0.287907	−	0.172720i
$320$	−34746.2			−0.339318
$321$			82403.5i			0.799716i
$322$	56.2811			0.000542814
$323$	−112027.			−1.07379
$324$	5092.19			0.0485081
$325$			89036.7i			0.842951i
$326$			17680.4i			0.166363i
$327$		−	101412.i		−	0.948403i
$328$	82387.4			0.765796
$329$		−	2662.31i		−	0.0245961i
$330$	−14125.3	−	8473.98i	−0.129709	−	0.0778144i
$331$	97744.9			0.892151			0.446075	−	0.894995i	$-0.352821\pi$
$331$	97744.9			0.892151			0.446075	+	0.894995i	$0.352821\pi$
$332$			38065.3i			0.345345i
$333$	12535.5			0.113045
$334$	78053.2			0.699677
$335$	72066.9			0.642164
$336$		−	723.139i		−	0.00640536i
$337$		−	75385.5i		−	0.663786i	−0.943317	−	0.331893i	$-0.892313\pi$
$337$		−	75385.5i		−	0.663786i	0.943317	−	0.331893i	$-0.107687\pi$
$338$			6741.59i			0.0590105i
$339$	−79727.3			−0.693757
$340$		−	11564.5i		−	0.100039i
$341$	18936.1	−	31564.5i	0.162847	−	0.271450i
$342$	47865.3			0.409231
$343$			6998.71i			0.0594880i
$344$	−109806.			−0.927919
$345$	−582.884			−0.00489716
$346$	67122.9			0.560684
$347$		−	95151.0i		−	0.790232i	−0.918631	−	0.395116i	$-0.870704\pi$
$347$		−	95151.0i		−	0.790232i	0.918631	−	0.395116i	$-0.129296\pi$
$348$			10248.5i			0.0846256i
$349$			106717.i			0.876156i	0.898937	+	0.438078i	$0.144341\pi$
$349$			106717.i			0.876156i	−0.898937	+	0.438078i	$0.855659\pi$
$350$	2402.86			0.0196152
$351$		−	22759.0i		−	0.184730i
$352$	−84837.3	−	50895.3i	−0.684702	−	0.410764i
$353$	62919.0			0.504932			0.252466	−	0.967606i	$-0.418758\pi$
$353$	62919.0			0.504932			0.252466	+	0.967606i	$0.418758\pi$
$354$		−	23232.2i		−	0.185389i
$355$	69558.7			0.551944
$356$	51216.1			0.404116
$357$	1437.52			0.0112792
$358$			27706.7i			0.216182i
$359$		−	147077.i		−	1.14119i	−0.821232	−	0.570594i	$-0.806713\pi$
$359$		−	147077.i		−	1.14119i	0.821232	−	0.570594i	$-0.193287\pi$
$360$			16259.0i			0.125455i
$361$	−218302.			−1.67511
$362$		−	156897.i		−	1.19729i
$363$	−35809.1	−	67122.2i	−0.271757	−	0.509393i
$364$	1652.24			0.0124701
$365$			50443.2i			0.378631i
$366$	−5563.43			−0.0415318
$367$	−50293.7			−0.373406			−0.186703	−	0.982416i	$-0.559780\pi$
$367$	−50293.7			−0.373406			−0.186703	+	0.982416i	$0.559780\pi$
$368$	1227.01			0.00906050
$369$		−	32232.8i		−	0.236726i
$370$			12163.5i			0.0888497i
$371$		−	5866.36i		−	0.0426207i
$372$	−11041.4			−0.0797884
$373$			29786.2i			0.214090i	0.994254	+	0.107045i	$0.0341389\pi$
$373$			29786.2i			0.214090i	−0.994254	+	0.107045i	$0.965861\pi$
$374$	−35460.6	+	59109.3i	−0.253515	+	0.422584i
$375$	−53223.4			−0.378478
$376$		−	126008.i		−	0.891295i
$377$	45804.5			0.322274
$378$	−614.204			−0.00429862
$379$	80930.7			0.563423			0.281712	−	0.959499i	$-0.409098\pi$
$379$	80930.7			0.563423			0.281712	+	0.959499i	$0.409098\pi$
$380$		−	35988.1i		−	0.249225i
$381$			100594.i			0.692985i
$382$		−	212142.i		−	1.45378i
$383$	−266517.			−1.81688			−0.908441	−	0.418012i	$-0.862727\pi$
$383$	−266517.			−1.81688			−0.908441	+	0.418012i	$0.862727\pi$
$384$			5851.59i			0.0396836i
$385$	−1320.15	−	791.981i	−0.00890641	−	0.00534310i
$386$	65311.9			0.438347
$387$			42960.0i			0.286842i
$388$	−78430.3			−0.520979
$389$	4358.49			0.0288029			0.0144015	−	0.999896i	$-0.495416\pi$
$389$	4358.49			0.0288029			0.0144015	+	0.999896i	$0.495416\pi$
$390$	22083.7			0.145192
$391$			2439.16i			0.0159547i
$392$			165552.i			1.07736i
$393$		−	72571.2i		−	0.469872i
$394$	−202206.			−1.30257
$395$			98640.5i			0.632209i
$396$	−11739.9	+	19569.2i	−0.0748640	+	0.124791i
$397$	−11014.6			−0.0698859			−0.0349429	−	0.999389i	$-0.511125\pi$
$397$	−11014.6			−0.0698859			−0.0349429	+	0.999389i	$0.511125\pi$
$398$			14881.4i			0.0939459i
$399$	4473.50			0.0280997
$400$	52385.9			0.327412
$401$	244214.			1.51873			0.759366	−	0.650664i	$-0.225509\pi$
$401$	244214.			1.51873			0.759366	+	0.650664i	$0.225509\pi$
$402$			128852.i			0.797333i
$403$			49348.5i			0.303853i
$404$		−	88956.8i		−	0.545025i
$405$	6361.10			0.0387813
$406$		−	1236.14i		−	0.00749922i
$407$	−28900.1	+	48173.5i	−0.174466	+	0.290817i
$408$	68038.3			0.408727
$409$		−	9069.88i		−	0.0542194i	−0.999632	−	0.0271097i	$-0.991370\pi$
$409$		−	9069.88i		−	0.0542194i	0.999632	−	0.0271097i	$-0.00863035\pi$
$410$	31276.5			0.186059
$411$	56761.5			0.336024
$412$	32392.8			0.190833
$413$		−	2171.29i		−	0.0127297i
$414$		−	1042.17i		−	0.00608048i
$415$			47550.7i			0.276096i
$416$	132636.			0.766435
$417$			142506.i			0.819525i
$418$	−110352.	+	183945.i	−0.631578	+	1.05278i
$419$	317776.			1.81006			0.905029	−	0.425350i	$-0.139849\pi$
$419$	317776.			1.81006			0.905029	+	0.425350i	$0.139849\pi$
$420$			461.797i			0.00261790i
$421$	89267.7			0.503651			0.251826	−	0.967773i	$-0.418969\pi$
$421$	89267.7			0.503651			0.251826	+	0.967773i	$0.418969\pi$
$422$	15703.9			0.0881826
$423$	−49298.6			−0.275520
$424$		−	277656.i		−	1.54445i
$425$			104138.i			0.576540i
$426$			124368.i			0.685313i
$427$	−519.960			−0.00285177
$428$			110775.i			0.604718i
$429$	87462.3	+	52470.1i	0.475233	+	0.285100i
$430$	−41685.4			−0.225448
$431$		−	80855.4i		−	0.435266i	−0.976031	−	0.217633i	$-0.930166\pi$
$431$		−	80855.4i		−	0.435266i	0.976031	−	0.217633i	$-0.0698335\pi$
$432$	−13390.5			−0.0717514
$433$	17118.8			0.0913057			0.0456529	−	0.998957i	$-0.485463\pi$
$433$	17118.8			0.0913057			0.0456529	+	0.998957i	$0.485463\pi$
$434$	1331.78			0.00707057
$435$			12802.3i			0.0676564i
$436$		−	136327.i		−	0.717150i
$437$			7590.56i			0.0397476i
$438$	−90190.1			−0.470122
$439$			32476.8i			0.168517i	0.996444	+	0.0842585i	$0.0268522\pi$
$439$			32476.8i			0.168517i	−0.996444	+	0.0842585i	$0.973148\pi$
$440$	−62483.1	−	37484.6i	−0.322743	−	0.193619i
$441$	64769.6			0.333038
$442$		−	92412.6i		−	0.473028i
$443$	4735.01			0.0241276			0.0120638	−	0.999927i	$-0.496160\pi$
$443$	4735.01			0.0241276			0.0120638	+	0.999927i	$0.496160\pi$
$444$	16851.4			0.0854809
$445$	63978.5			0.323083
$446$			210521.i			1.05834i
$447$		−	91694.4i		−	0.458910i
$448$		−	5806.19i		−	0.0289291i
$449$	−217096.			−1.07686			−0.538430	−	0.842670i	$-0.680982\pi$
$449$	−217096.			−1.07686			−0.538430	+	0.842670i	$0.680982\pi$
$450$		−	44494.3i		−	0.219725i
$451$	123870.	+	74311.7i	0.608994	+	0.365346i
$452$	−107177.			−0.524596
$453$		−	101232.i		−	0.493312i
$454$	−207715.			−1.00776
$455$	2063.95			0.00996957
$456$	211732.			1.01826
$457$		−	226266.i		−	1.08340i	−0.840573	−	0.541698i	$-0.817782\pi$
$457$		−	226266.i		−	1.08340i	0.840573	−	0.541698i	$-0.182218\pi$
$458$		−	83980.4i		−	0.400356i
$459$		−	26618.9i		−	0.126347i
$460$	−783.569			−0.00370307
$461$			280319.i			1.31902i	0.751697	+	0.659509i	$0.229236\pi$
$461$			280319.i			1.31902i	−0.751697	+	0.659509i	$0.770764\pi$
$462$	1416.03	−	2360.37i	0.00663418	−	0.0110585i
$463$	176739.			0.824463			0.412231	−	0.911079i	$-0.364750\pi$
$463$	176739.			0.824463			0.412231	+	0.911079i	$0.364750\pi$
$464$		−	26949.7i		−	0.125175i
$465$	−13792.8			−0.0637892
$466$	−202943.			−0.934548
$467$	−211683.			−0.970625			−0.485312	−	0.874341i	$-0.661294\pi$
$467$	−211683.			−0.970625			−0.485312	+	0.874341i	$0.661294\pi$
$468$		−	30594.8i		−	0.139687i
$469$			12042.6i			0.0547487i
$470$		−	47835.9i		−	0.216550i
$471$	107262.			0.483509
$472$		−	102768.i		−	0.461288i
$473$	−165094.	−	99042.8i	−0.737921	−	0.442691i
$474$	−176365.			−0.784973
$475$			324071.i			1.43633i
$476$	1932.46			0.00852896
$477$	−108629.			−0.477428
$478$	94846.5			0.415112
$479$		−	80152.2i		−	0.349337i	−0.984627	−	0.174668i	$-0.944115\pi$
$479$		−	80152.2i		−	0.349337i	0.984627	−	0.174668i	$-0.0558854\pi$
$480$			37071.6i			0.160901i
$481$		−	75315.3i		−	0.325532i
$482$	193405.			0.832480
$483$		−	97.4015i		−	0.000417514i
$484$	−48138.1	−	90232.2i	−0.205494	−	0.385186i
$485$	−97974.1			−0.416512
$486$			11373.3i			0.0481522i
$487$	−173605.			−0.731988			−0.365994	−	0.930617i	$-0.619271\pi$
$487$	−173605.			−0.731988			−0.365994	+	0.930617i	$0.619271\pi$
$488$	−24609.8			−0.103340
$489$	30598.2			0.127961
$490$			62847.9i			0.261757i
$491$			152879.i			0.634138i	0.948402	+	0.317069i	$0.102699\pi$
$491$			152879.i			0.634138i	−0.948402	+	0.317069i	$0.897301\pi$
$492$		−	43330.4i		−	0.179004i
$493$	53573.1			0.220421
$494$		−	287583.i		−	1.17845i
$495$	−14665.3	+	24445.6i	−0.0598522	+	0.0997676i
$496$	29034.8			0.118020
$497$			11623.5i			0.0470568i
$498$	−85018.4			−0.342811
$499$	122586.			0.492312			0.246156	−	0.969230i	$-0.420832\pi$
$499$	122586.			0.492312			0.246156	+	0.969230i	$0.420832\pi$
$500$	−71548.0			−0.286192
$501$		−	135081.i		−	0.538168i
$502$			104552.i			0.414883i
$503$		−	355305.i		−	1.40432i	−0.712020	−	0.702159i	$-0.752220\pi$
$503$		−	355305.i		−	1.40432i	0.712020	−	0.702159i	$-0.247780\pi$
$504$	−2716.93			−0.0106959
$505$		−	111124.i		−	0.435737i
$506$	4005.04	+	2402.69i	0.0156425	+	0.00938418i
$507$	11667.2			0.0453889
$508$			135229.i			0.524012i
$509$	34844.7			0.134493			0.0672467	−	0.997736i	$-0.478579\pi$
$509$	34844.7			0.134493			0.0672467	+	0.997736i	$0.478579\pi$
$510$	25829.2			0.0993047
$511$	−8429.19			−0.0322808
$512$		−	183428.i		−	0.699722i
$513$		−	82836.8i		−	0.314767i
$514$		−	221421.i		−	0.838092i
$515$	40464.7			0.152567
$516$			57751.0i			0.216900i
$517$	113656.	−	189454.i	0.425219	−	0.708797i
$518$	−2032.56			−0.00757501
$519$		−	116165.i		−	0.431260i
$520$	97687.3			0.361269
$521$	130516.			0.480825			0.240412	−	0.970671i	$-0.422717\pi$
$521$	130516.			0.480825			0.240412	+	0.970671i	$0.422717\pi$
$522$	−22889.9			−0.0840046
$523$			436331.i			1.59519i	0.603192	+	0.797596i	$0.293895\pi$
$523$			436331.i			1.59519i	−0.603192	+	0.797596i	$0.706105\pi$
$524$		−	97557.3i		−	0.355301i
$525$		−	4158.45i		−	0.0150874i
$526$	310965.			1.12393
$527$			57718.1i			0.207822i
$528$	30871.4	−	51459.5i	0.110736	−	0.184586i
$529$	−279676.			−0.999409
$530$		−	105406.i		−	0.375242i
$531$	−40206.2			−0.142595
$532$	6013.71			0.0212481
$533$	−193661.			−0.681690
$534$			114391.i			0.401151i
$535$			138378.i			0.483460i
$536$			569978.i			1.98394i
$537$	47950.0			0.166280
$538$			356905.i			1.23307i
$539$	−149324.	+	248908.i	−0.513987	+	0.856765i
$540$	8551.20			0.0293251
$541$			80892.7i			0.276385i	0.990405	+	0.138193i	$0.0441293\pi$
$541$			80892.7i			0.276385i	−0.990405	+	0.138193i	$0.955871\pi$
$542$	308480.			1.05009
$543$	−271530.			−0.920913
$544$	155132.			0.524206
$545$		−	170298.i		−	0.573347i
$546$			3690.25i			0.0123786i
$547$			231848.i			0.774870i	0.921897	+	0.387435i	$0.126639\pi$
$547$			231848.i			0.774870i	−0.921897	+	0.387435i	$0.873361\pi$
$548$	76304.2			0.254090
$549$			9628.21i			0.0319449i
$550$	170991.	+	102580.i	0.565259	+	0.339108i
$551$	166717.			0.549131
$552$		−	4610.03i		−	0.0151296i
$553$	−16483.1			−0.0539000
$554$	310264.			1.01091
$555$	21050.5			0.0683402
$556$			191571.i			0.619698i
$557$		−	461600.i		−	1.48784i	−0.668270	−	0.743919i	$-0.732965\pi$
$557$		−	461600.i		−	1.48784i	0.668270	−	0.743919i	$-0.267035\pi$
$558$		−	24660.9i		−	0.0792029i
$559$	258112.			0.826007
$560$		−	1214.35i		−	0.00387229i
$561$	102296.	+	61369.1i	0.325037	+	0.194995i
$562$	−111865.			−0.354179
$563$		−	35282.9i		−	0.111313i	−0.998450	−	0.0556566i	$-0.982275\pi$
$563$		−	35282.9i		−	0.111313i	0.998450	−	0.0556566i	$-0.0177252\pi$
$564$	−66271.9			−0.208339
$565$	−133884.			−0.419404
$566$	−380232.			−1.18690
$567$			1062.96i			0.00330635i
$568$			550141.i			1.70521i
$569$			296349.i			0.915332i	0.889124	+	0.457666i	$0.151314\pi$
$569$			296349.i			0.915332i	−0.889124	+	0.457666i	$0.848686\pi$
$570$	80379.1			0.247396
$571$		−	241258.i		−	0.739963i	−0.929039	−	0.369982i	$-0.879364\pi$
$571$		−	241258.i		−	0.739963i	0.929039	−	0.369982i	$-0.120636\pi$
$572$	117575.	+	70535.3i	0.359355	+	0.215583i
$573$	−367138.			−1.11820
$574$			5226.38i			0.0158627i
$575$	7055.99			0.0213414
$576$	−107514.			−0.324057
$577$	−457944.			−1.37550			−0.687750	−	0.725948i	$-0.741401\pi$
$577$	−457944.			−1.37550			−0.687750	+	0.725948i	$0.741401\pi$
$578$			142683.i			0.427089i
$579$		−	113030.i		−	0.337162i
$580$			17210.1i			0.0511595i
$581$	−7945.85			−0.0235390
$582$		−	175173.i		−	0.517156i
$583$	250440.	−	417458.i	0.736828	−	1.22822i
$584$	−398956.			−1.16977
$585$		−	38218.6i		−	0.111677i
$586$	4014.55			0.0116907
$587$	481837.			1.39838			0.699188	−	0.714938i	$-0.253545\pi$
$587$	481837.			1.39838			0.699188	+	0.714938i	$0.253545\pi$
$588$	87069.5			0.251832
$589$			179616.i			0.517743i
$590$		−	39013.3i		−	0.112075i
$591$			349944.i			1.00190i
$592$	−44312.7			−0.126440
$593$		−	495129.i		−	1.40802i	−0.710190	−	0.704010i	$-0.751391\pi$
$593$		−	495129.i		−	1.40802i	0.710190	−	0.704010i	$-0.248609\pi$
$594$	−43707.5	−	26220.9i	−0.123875	−	0.0743146i
$595$	2414.00			0.00681873
$596$		−	123264.i		−	0.347013i
$597$	25754.1			0.0722601
$598$	−6261.55			−0.0175097
$599$	−341737.			−0.952442			−0.476221	−	0.879326i	$-0.657994\pi$
$599$	−341737.			−0.952442			−0.476221	+	0.879326i	$0.657994\pi$
$600$		−	196821.i		−	0.546724i
$601$		−	404022.i		−	1.11855i	−0.828982	−	0.559275i	$-0.811080\pi$
$601$		−	404022.i		−	1.11855i	0.828982	−	0.559275i	$-0.188920\pi$
$602$		−	6965.74i		−	0.0192209i
$603$	222995.			0.613282
$604$		−	136086.i		−	0.373026i
$605$	−60133.5	−	112717.i	−0.164288	−	0.307949i
$606$	198684.			0.541026
$607$		−	85001.6i		−	0.230701i	−0.993325	−	0.115351i	$-0.963201\pi$
$607$		−	85001.6i		−	0.230701i	0.993325	−	0.115351i	$-0.0367991\pi$
$608$	482762.			1.30595
$609$	−2139.30			−0.00576815
$610$	−9342.54			−0.0251076
$611$			296195.i			0.793406i
$612$		−	35783.7i		−	0.0955395i
$613$		−	296743.i		−	0.789695i	−0.918747	−	0.394847i	$-0.870797\pi$
$613$		−	296743.i		−	0.789695i	0.918747	−	0.394847i	$-0.129203\pi$
$614$	−212650.			−0.564065
$615$		−	54127.8i		−	0.143110i
$616$	6263.79	−	10441.1i	0.0165073	−	0.0275160i
$617$	−205712.			−0.540368			−0.270184	−	0.962809i	$-0.587085\pi$
$617$	−205712.			−0.540368			−0.270184	+	0.962809i	$0.587085\pi$
$618$			72349.0i			0.189433i
$619$	−23798.6			−0.0621112			−0.0310556	−	0.999518i	$-0.509887\pi$
$619$	−23798.6			−0.0621112			−0.0310556	+	0.999518i	$0.509887\pi$
$620$	−18541.6			−0.0482353
$621$	−1803.61			−0.00467690
$622$		−	240135.i		−	0.620690i
$623$			10691.0i			0.0275449i
$624$			80452.8i			0.206620i
$625$	253661.			0.649372
$626$			135466.i			0.345687i
$627$	318340.	+	190978.i	0.809761	+	0.485789i
$628$	144192.			0.365613
$629$		−	88088.9i		−	0.222649i
$630$	−1031.42			−0.00259869
$631$	−464381.			−1.16631			−0.583157	−	0.812359i	$-0.698183\pi$
$631$	−464381.			−1.16631			−0.583157	+	0.812359i	$0.698183\pi$
$632$	−780149.			−1.95318
$633$		−	27177.6i		−	0.0678271i
$634$		−	160308.i		−	0.398820i
$635$			168926.i			0.418937i
$636$	−146029.			−0.361015
$637$		−	389148.i		−	0.959038i
$638$	52771.9	−	87965.4i	0.129647	−	0.216108i
$639$	215234.			0.527120
$640$			9826.44i			0.0239903i
$641$	433460.			1.05495			0.527476	−	0.849570i	$-0.323138\pi$
$641$	433460.			1.05495			0.527476	+	0.849570i	$0.323138\pi$
$642$	−247414.			−0.600281
$643$	−228934.			−0.553718			−0.276859	−	0.960910i	$-0.589294\pi$
$643$	−228934.			−0.553718			−0.276859	+	0.960910i	$0.589294\pi$
$644$		−	130.936i		−	0.000315710i
$645$			72141.8i			0.173407i
$646$		−	336358.i		−	0.806003i
$647$	−83987.4			−0.200634			−0.100317	−	0.994956i	$-0.531986\pi$
$647$	−83987.4			−0.200634			−0.100317	+	0.994956i	$0.531986\pi$
$648$			50310.0i			0.119813i
$649$	92694.1	−	154512.i	0.220071	−	0.366836i
$650$	−267330.			−0.632734
$651$		−	2304.82i		−	0.00543845i
$652$	41133.1			0.0967600
$653$	337789.			0.792172			0.396086	−	0.918213i	$-0.370368\pi$
$653$	337789.			0.792172			0.396086	+	0.918213i	$0.370368\pi$
$654$	304486.			0.711888
$655$		−	121867.i		−	0.284056i
$656$			113943.i			0.264776i
$657$			156085.i			0.361602i
$658$	7993.51			0.0184623
$659$			586098.i			1.34958i	0.738008	+	0.674791i	$0.235766\pi$
$659$			586098.i			1.34958i	−0.738008	+	0.674791i	$0.764234\pi$
$660$	−19714.5	+	32862.1i	−0.0452583	+	0.0754410i
$661$	−660271.			−1.51119			−0.755596	−	0.655038i	$-0.772652\pi$
$661$	−660271.			−1.51119			−0.755596	+	0.655038i	$0.772652\pi$
$662$			293476.i			0.669664i
$663$	−159932.			−0.363837
$664$	−376079.			−0.852987
$665$	7512.25			0.0169874
$666$			37637.3i			0.0848536i
$667$		−	3629.92i		−	0.00815916i
$668$		−	181589.i		−	0.406945i
$669$	364333.			0.814042
$670$			216379.i			0.482020i
$671$	−37001.0	−	22197.5i	−0.0821805	−	0.0493014i
$672$	−6194.77			−0.0137179
$673$			362391.i			0.800105i	0.916492	+	0.400052i	$0.131008\pi$
$673$			362391.i			0.800105i	−0.916492	+	0.400052i	$0.868992\pi$
$674$	226343.			0.498249
$675$	−77003.0			−0.169005
$676$	15684.1			0.0343216
$677$			92662.7i			0.202175i	0.994878	+	0.101088i	$0.0322322\pi$
$677$			92662.7i			0.202175i	−0.994878	+	0.101088i	$0.967768\pi$
$678$		−	239379.i		−	0.520747i
$679$		−	16371.7i		−	0.0355104i
$680$	114255.			0.247092
$681$			359477.i			0.775135i
$682$	94771.5	+	56855.0i	0.203755	+	0.122236i
$683$	448358.			0.961132			0.480566	−	0.876958i	$-0.340431\pi$
$683$	448358.			0.961132			0.480566	+	0.876958i	$0.340431\pi$
$684$		−	111357.i		−	0.238016i
$685$	95318.3			0.203140
$686$	−21013.4			−0.0446528
$687$	−145339.			−0.307941
$688$		−	151863.i		−	0.320830i
$689$			652661.i			1.37483i
$690$		−	1750.09i		−	0.00367589i
$691$	358700.			0.751234			0.375617	−	0.926775i	$-0.377431\pi$
$691$	358700.			0.751234			0.375617	+	0.926775i	$0.377431\pi$
$692$		−	156160.i		−	0.326104i
$693$	−4084.92	−	2450.61i	−0.00850584	−	0.00510279i
$694$	285688.			0.593162
$695$			239308.i			0.495436i
$696$	−101253.			−0.209022
$697$	−226506.			−0.466245
$698$	−320414.			−0.657659
$699$			351218.i			0.718823i
$700$		−	5590.19i		−	0.0114086i
$701$		−	159779.i		−	0.325150i	−0.986696	−	0.162575i	$-0.948020\pi$
$701$		−	159779.i		−	0.325150i	0.986696	−	0.162575i	$-0.0519799\pi$
$702$	68333.2			0.138662
$703$		−	274128.i		−	0.554681i
$704$	247871.	−	413176.i	0.500127	−	0.833661i
$705$	−82786.0			−0.166563
$706$			188913.i			0.379011i
$707$	18569.1			0.0371494
$708$	−54049.1			−0.107826
$709$	455705.			0.906550			0.453275	−	0.891371i	$-0.350256\pi$
$709$	455705.			0.906550			0.453275	+	0.891371i	$0.350256\pi$
$710$			208848.i			0.414299i
$711$			305221.i			0.603775i
$712$			506006.i			0.998151i
$713$	3910.78			0.00769279
$714$			4316.12i			0.00846637i
$715$	146873.	+	88111.8i	0.287297	+	0.172354i
$716$	64459.0			0.125735
$717$		−	164144.i		−	0.319291i
$718$	441596.			0.856596
$719$	640858.			1.23966			0.619832	−	0.784735i	$-0.287201\pi$
$719$	640858.			1.23966			0.619832	+	0.784735i	$0.287201\pi$
$720$	−22486.4			−0.0433766
$721$			6761.76i			0.0130074i
$722$		−	655445.i		−	1.25737i
$723$		−	334712.i		−	0.640316i
$724$	−365017.			−0.696363
$725$		−	154976.i		−	0.294841i
$726$	201533.	−	107516.i	0.382360	−	0.203986i
$727$	−324283.			−0.613558			−0.306779	−	0.951781i	$-0.599251\pi$
$727$	−324283.			−0.613558			−0.306779	+	0.951781i	$0.599251\pi$
$728$			16323.8i			0.0308006i
$729$	19683.0			0.0370370
$730$	−151454.			−0.284207
$731$	301888.			0.564951
$732$			12943.2i			0.0241556i
$733$			633078.i			1.17828i	0.808030	+	0.589141i	$0.200534\pi$
$733$			633078.i			1.17828i	−0.808030	+	0.589141i	$0.799466\pi$
$734$		−	151005.i		−	0.280285i
$735$	108766.			0.201335
$736$		−	10511.2i		−	0.0194042i
$737$	−514107.	+	856965.i	−0.946496	+	1.57771i
$738$	96778.1			0.177690
$739$		−	218657.i		−	0.400382i	−0.979757	−	0.200191i	$-0.935844\pi$
$739$		−	218657.i		−	0.400382i	0.979757	−	0.200191i	$-0.0641562\pi$
$740$	28298.1			0.0516766
$741$	−497699.			−0.906422
$742$	17613.6			0.0319919
$743$		−	740582.i		−	1.34152i	−0.741677	−	0.670758i	$-0.765969\pi$
$743$		−	740582.i		−	1.34152i	0.741677	−	0.670758i	$-0.234031\pi$
$744$		−	109088.i		−	0.197074i
$745$		−	153980.i		−	0.277430i
$746$	−89432.1			−0.160700
$747$			147135.i			0.263679i
$748$	137516.	+	82498.2i	0.245782	+	0.147449i
$749$	−23123.4			−0.0412181
$750$		−	159802.i		−	0.284092i
$751$	−1.08089e6			−1.91647			−0.958235	−	0.285982i	$-0.907680\pi$
$751$	−1.08089e6			−1.91647			−0.958235	+	0.285982i	$0.907680\pi$
$752$	174270.			0.308168
$753$	180941.			0.319114
$754$			137527.i			0.241905i
$755$		−	169997.i		−	0.298227i
$756$			1428.93i			0.00250015i
$757$	604976.			1.05571			0.527857	−	0.849333i	$-0.322996\pi$
$757$	604976.			1.05571			0.527857	+	0.849333i	$0.322996\pi$
$758$			242992.i			0.422916i
$759$	4158.15	−	6931.22i	0.00721800	−	0.0120317i
$760$	355557.			0.615576
$761$		−	1.06160e6i		−	1.83312i	−0.399901	−	0.916558i	$-0.630955\pi$
$761$		−	1.06160e6i		−	1.83312i	0.399901	−	0.916558i	$-0.369045\pi$
$762$	−302032.			−0.520167
$763$	28457.3			0.0488816
$764$	−493542.			−0.845546
$765$		−	44700.6i		−	0.0763819i
$766$		−	800209.i		−	1.36378i
$767$			241567.i			0.410626i
$768$	−348628.			−0.591071
$769$			405621.i			0.685912i	0.939352	+	0.342956i	$0.111428\pi$
$769$			405621.i			0.685912i	−0.939352	+	0.342956i	$0.888572\pi$
$770$	2377.90	−	3963.72i	0.00401063	−	0.00668531i
$771$	−383196.			−0.644633
$772$		−	151946.i		−	0.254950i
$773$	−279272.			−0.467377			−0.233689	−	0.972311i	$-0.575080\pi$
$773$	−279272.			−0.467377			−0.233689	+	0.972311i	$0.575080\pi$
$774$	−128986.			−0.215308
$775$	166966.			0.277988
$776$		−	774878.i		−	1.28680i
$777$			3517.60i			0.00582645i
$778$			13086.2i			0.0216200i
$779$	−704875.			−1.16155
$780$		−	51377.2i		−	0.0844464i
$781$	−496215.	+	827141.i	−0.813519	+	1.35605i
$782$	−7323.52			−0.0119758
$783$			39613.8i			0.0646135i
$784$	−228960.			−0.372501
$785$	180123.			0.292301
$786$	217893.			0.352694
$787$		−	637120.i		−	1.02866i	−0.857593	−	0.514330i	$-0.828041\pi$
$787$		−	637120.i		−	1.02866i	0.857593	−	0.514330i	$-0.171959\pi$
$788$			470428.i			0.757601i
$789$		−	538163.i		−	0.864490i
$790$	−296165.			−0.474548
$791$		−	22372.4i		−	0.0357569i
$792$	−193340.	−	115988.i	−0.308228	−	0.184911i
$793$	57848.1			0.0919904
$794$		−	33071.1i		−	0.0524576i
$795$	−182418.			−0.288624
$796$	34621.2			0.0546407
$797$	275712.			0.434049			0.217024	−	0.976166i	$-0.430365\pi$
$797$	275712.			0.434049			0.217024	+	0.976166i	$0.430365\pi$
$798$			13431.6i			0.0210921i
$799$			346430.i			0.542653i
$800$		−	448763.i		−	0.701193i
$801$	197967.			0.308552
$802$			733244.i			1.13999i
$803$	−599832.	−	359849.i	−0.930248	−	0.558071i
$804$	299771.			0.463744
$805$		−	163.564i		−	0.000252404i
$806$	−148168.			−0.228078
$807$	617669.			0.948437
$808$	878879.			1.34619
$809$			974096.i			1.48835i	0.667986	+	0.744174i	$0.267157\pi$
$809$			974096.i			1.48835i	−0.667986	+	0.744174i	$0.732843\pi$
$810$			19099.0i			0.0291099i
$811$		−	379198.i		−	0.576534i	−0.957550	−	0.288267i	$-0.906921\pi$
$811$		−	379198.i		−	0.576534i	0.957550	−	0.288267i	$-0.0930790\pi$
$812$	−2875.85			−0.00436168
$813$		−	533863.i		−	0.807697i
$814$	−144640.	−	86771.6i	−0.218292	−	0.130957i
$815$	51382.9			0.0773576
$816$			94097.7i			0.141318i
$817$	939460.			1.40745
$818$	27232.1			0.0406981
$819$	6386.44			0.00952118
$820$		−	72763.8i		−	0.108215i
$821$			87100.3i			0.129221i	0.997911	+	0.0646106i	$0.0205805\pi$
$821$			87100.3i			0.129221i	−0.997911	+	0.0646106i	$0.979419\pi$
$822$			170425.i			0.252225i
$823$	177783.			0.262477			0.131239	−	0.991351i	$-0.458105\pi$
$823$	177783.			0.262477			0.131239	+	0.991351i	$0.458105\pi$
$824$			320036.i			0.471350i
$825$	177528.	−	295921.i	0.260831	−	0.434779i
$826$	6519.23			0.00955513
$827$			369448.i			0.540185i	0.962834	+	0.270093i	$0.0870543\pi$
$827$			369448.i			0.540185i	−0.962834	+	0.270093i	$0.912946\pi$
$828$	−2424.58			−0.00353652
$829$	805060.			1.17144			0.585718	−	0.810515i	$-0.300812\pi$
$829$	805060.			1.17144			0.585718	+	0.810515i	$0.300812\pi$
$830$	−142769.			−0.207243
$831$		−	536952.i		−	0.777559i
$832$			645967.i			0.933176i
$833$		−	455148.i		−	0.655938i
$834$	−427871.			−0.615150
$835$		−	226838.i		−	0.325344i
$836$	427944.	+	256730.i	0.612314	+	0.367337i
$837$	−42678.9			−0.0609203
$838$			954112.i			1.35866i
$839$	−762552.			−1.08329			−0.541646	−	0.840606i	$-0.682199\pi$
$839$	−762552.			−1.08329			−0.541646	+	0.840606i	$0.682199\pi$
$840$	−4562.48			−0.00646610
$841$	627555.			0.887278
$842$			268024.i			0.378050i
$843$			193597.i			0.272423i
$844$		−	36534.7i		−	0.0512886i
$845$	19592.4			0.0274394
$846$		−	148018.i		−	0.206811i
$847$	18835.3	−	10048.5i	0.0262546	−	0.0140066i
$848$	384001.			0.533999
$849$			658039.i			0.912927i
$850$	−312670.			−0.432761
$851$	−5968.59			−0.00824163
$852$	289338.			0.398590
$853$			602505.i			0.828061i	0.910263	+	0.414031i	$0.135879\pi$
$853$			602505.i			0.828061i	−0.910263	+	0.414031i	$0.864121\pi$
$854$		−	1561.16i		−	0.00214059i
$855$		−	139106.i		−	0.190289i
$856$	−1.09444e6			−1.49363
$857$		−	119350.i		−	0.162502i	−0.996694	−	0.0812512i	$-0.974108\pi$
$857$		−	119350.i		−	0.162502i	0.996694	−	0.0812512i	$-0.0258916\pi$
$858$	−157540.	+	262603.i	−0.214001	+	0.356718i
$859$	437992.			0.593580			0.296790	−	0.954943i	$-0.404084\pi$
$859$	437992.			0.593580			0.296790	+	0.954943i	$0.404084\pi$
$860$			96979.9i			0.131125i
$861$	9044.91			0.0122011
$862$	242766.			0.326718
$863$	776719.			1.04290			0.521450	−	0.853282i	$-0.325391\pi$
$863$	776719.			1.04290			0.521450	+	0.853282i	$0.325391\pi$
$864$			114710.i			0.153664i
$865$		−	195073.i		−	0.260714i
$866$			51398.7i			0.0685357i
$867$	246932.			0.328502
$868$		−	3098.36i		−	0.00411237i
$869$	−1.17296e6	−	703677.i	−1.55326	−	0.931824i
$870$	−38438.5			−0.0507841
$871$		−	1.33979e6i		−	1.76605i
$872$	1.34689e6			1.77133
$873$	−303159.			−0.397779
$874$	−22790.4			−0.0298352
$875$		−	14935.1i		−	0.0195071i
$876$			209825.i			0.273431i
$877$			1.15156e6i			1.49722i	0.663009	+	0.748612i	$0.269279\pi$
$877$			1.15156e6i			1.49722i	−0.663009	+	0.748612i	$0.730721\pi$
$878$	−97510.6			−0.126492
$879$		−	6947.68i		−	0.00899212i
$880$	51841.7	−	86414.8i	0.0669443	−	0.111589i
$881$	228842.			0.294839			0.147419	−	0.989074i	$-0.452903\pi$
$881$	228842.			0.294839			0.147419	+	0.989074i	$0.452903\pi$
$882$			194469.i			0.249984i
$883$	−1.22059e6			−1.56549			−0.782743	−	0.622345i	$-0.786180\pi$
$883$	−1.22059e6			−1.56549			−0.782743	+	0.622345i	$0.786180\pi$
$884$	−214995.			−0.275121
$885$	−67517.4			−0.0862044
$886$			14216.7i			0.0181106i
$887$		−	11201.7i		−	0.0142375i	−0.999975	−	0.00711877i	$-0.997734\pi$
$887$		−	11201.7i		−	0.0142375i	0.999975	−	0.00711877i	$-0.00226599\pi$
$888$			166489.i			0.211134i
$889$	−28228.0			−0.0357171
$890$			192094.i			0.242512i
$891$	−45378.5	+	75641.4i	−0.0571603	+	0.0952805i
$892$	489772.			0.615551
$893$			1.07807e6i			1.35190i
$894$	275310.			0.344466
$895$	80521.3			0.100523
$896$	−1642.03			−0.00204533
$897$			10836.4i			0.0134679i
$898$		−	651825.i		−	0.808310i
$899$		−	85895.1i		−	0.106279i
$900$	−103515.			−0.127796
$901$			763353.i			0.940321i
$902$	−223119.	+	371916.i	−0.274235	+	0.457122i
$903$	−12055.1			−0.0147841
$904$		−	1.05889e6i		−	1.29573i
$905$	−455975.			−0.556729
$906$	303946.			0.370289
$907$	−612933.			−0.745072			−0.372536	−	0.928018i	$-0.621512\pi$
$907$	−612933.			−0.745072			−0.372536	+	0.928018i	$0.621512\pi$
$908$			483244.i			0.586131i
$909$		−	343848.i		−	0.416139i
$910$			6196.95i			0.00748334i
$911$	−606369.			−0.730634			−0.365317	−	0.930883i	$-0.619039\pi$
$911$	−606369.			−0.730634			−0.365317	+	0.930883i	$0.619039\pi$
$912$			292827.i			0.352064i
$913$	−565437.	−	339215.i	−0.678332	−	0.406943i
$914$	679358.			0.813216
$915$			16168.4i			0.0193119i
$916$	−195378.			−0.232855
$917$	20364.4			0.0242176
$918$	79922.6			0.0948384
$919$		−	19670.4i		−	0.0232906i	−0.999932	−	0.0116453i	$-0.996293\pi$
$919$		−	19670.4i		−	0.0232906i	0.999932	−	0.0116453i	$-0.00370690\pi$
$920$		−	7741.53i		−	0.00914642i
$921$			368018.i			0.433860i
$922$	−841649.			−0.990078
$923$		−	1.29317e6i		−	1.51793i
$924$	−5491.34	−	3294.35i	−0.00643183	−	0.00385856i
$925$	−254823.			−0.297821
$926$			530654.i			0.618856i
$927$	125209.			0.145706
$928$	−230864.			−0.268078
$929$	1.51101e6			1.75080			0.875399	−	0.483402i	$-0.160599\pi$
$929$	1.51101e6			1.75080			0.875399	+	0.483402i	$0.160599\pi$
$930$		−	41412.6i		−	0.0478813i
$931$		−	1.41640e6i		−	1.63413i
$932$			472141.i			0.543550i
$933$	−415584.			−0.477414
$934$		−	635571.i		−	0.728568i
$935$	171783.	+	103056.i	0.196498	+	0.117882i
$936$	302272.			0.345021
$937$		−	998435.i		−	1.13721i	−0.822611	−	0.568605i	$-0.807483\pi$
$937$		−	998435.i		−	1.13721i	0.822611	−	0.568605i	$-0.192517\pi$
$938$	−36157.5			−0.0410953
$939$	234442.			0.265891
$940$	−111289.			−0.125949
$941$		−	1.51328e6i		−	1.70900i	−0.519455	−	0.854498i	$-0.673865\pi$
$941$		−	1.51328e6i		−	1.70900i	0.519455	−	0.854498i	$-0.326135\pi$
$942$			322051.i			0.362931i
$943$			15347.2i			0.0172586i
$944$	142129.			0.159492
$945$			1785.00i			0.00199882i
$946$	297373.	−	495691.i	0.332292	−	0.553897i
$947$	873603.			0.974124			0.487062	−	0.873367i	$-0.338069\pi$
$947$	873603.			0.974124			0.487062	+	0.873367i	$0.338069\pi$
$948$			410308.i			0.456555i
$949$	937789.			1.04129
$950$	−973013.			−1.07813
$951$	−277433.			−0.306759
$952$			19092.4i			0.0210662i
$953$			140477.i			0.154675i	0.997005	+	0.0773374i	$0.0246419\pi$
$953$			140477.i			0.154675i	−0.997005	+	0.0773374i	$0.975358\pi$
$954$		−	326154.i		−	0.358366i
$955$	−616526.			−0.675997
$956$		−	220658.i		−	0.241437i
$957$	−152235.	−	91328.4i	−0.166223	−	0.0997199i
$958$	240655.			0.262218
$959$			15927.9i			0.0173190i
$960$	−180547.			−0.195906
$961$	−830980.			−0.899795
$962$	226132.			0.244350
$963$			428181.i			0.461716i
$964$		−	449952.i		−	0.484185i
$965$		−	189809.i		−	0.203828i
$966$	292.445			0.000313394
$967$		−	7957.10i		−	0.00850946i	−0.999991	−	0.00425473i	$-0.998646\pi$
$967$		−	7957.10i		−	0.00850946i	0.999991	−	0.00425473i	$-0.00135433\pi$
$968$	891479.	−	475596.i	0.951394	−	0.507561i
$969$	−582110.			−0.619951
$970$		−	294164.i		−	0.312642i
$971$	−1.09461e6			−1.16097			−0.580487	−	0.814270i	$-0.697138\pi$
$971$	−1.09461e6			−1.16097			−0.580487	+	0.814270i	$0.697138\pi$
$972$	26459.8			0.0280062
$973$	−39989.0			−0.0422391
$974$		−	521244.i		−	0.549443i
$975$			462648.i			0.486678i
$976$		−	34035.6i		−	0.0357301i
$977$	45038.9			0.0471844			0.0235922	−	0.999722i	$-0.492490\pi$
$977$	45038.9			0.0471844			0.0235922	+	0.999722i	$0.492490\pi$
$978$			91870.2i			0.0960499i
$979$	−456407.	+	760784.i	−0.476197	+	0.793773i
$980$	146214.			0.152243
$981$		−	526951.i		−	0.547561i
$982$	−459014.			−0.475995
$983$	113557.			0.117518			0.0587591	−	0.998272i	$-0.481286\pi$
$983$	113557.			0.117518			0.0587591	+	0.998272i	$0.481286\pi$
$984$	428098.			0.442133
$985$			587652.i			0.605687i
$986$			160852.i			0.165452i
$987$		−	13833.8i		−	0.0142006i
$988$	−669055.			−0.685406
$989$		−	20454.8i		−	0.0209124i
$990$	−73397.1	−	44032.1i	−0.0748874	−	0.0449261i
$991$	657037.			0.669025			0.334512	−	0.942391i	$-0.391428\pi$
$991$	657037.			0.669025			0.334512	+	0.942391i	$0.391428\pi$
$992$		−	248727.i		−	0.252754i
$993$	507898.			0.515084
$994$	−34899.1			−0.0353217
$995$	43248.4			0.0436841
$996$			197793.i			0.199385i
$997$			349112.i			0.351216i	0.984460	+	0.175608i	$0.0561892\pi$
$997$			349112.i			0.351216i	−0.984460	+	0.175608i	$0.943811\pi$
$998$			368061.i			0.369538i
$999$	65136.1			0.0652666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.5.c.a.10.6	yes	8
3.2	odd	2		99.5.c.c.10.3		8
4.3	odd	2		528.5.j.a.241.3		8
11.10	odd	2	inner	33.5.c.a.10.3	✓	8
33.32	even	2		99.5.c.c.10.6		8
44.43	even	2		528.5.j.a.241.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.c.a.10.3	✓	8	11.10	odd	2	inner
33.5.c.a.10.6	yes	8	1.1	even	1	trivial
99.5.c.c.10.3		8	3.2	odd	2
99.5.c.c.10.6		8	33.32	even	2
528.5.j.a.241.3		8	4.3	odd	2
528.5.j.a.241.4		8	44.43	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} +15.6013i q^{6} +1.45810i q^{7} +69.0123i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} +15.6013i q^{6} +1.45810i q^{7} +69.0123i q^{8} +27.0000 q^{9} +26.1989i q^{10} +(-62.2476 + 103.760i) q^{11} +36.2960 q^{12} -162.221i q^{13} -4.37791 q^{14} +45.3405 q^{15} -95.4447 q^{16} -189.734i q^{17} +81.0667i q^{18} -590.443i q^{19} +60.9511 q^{20} +7.57652i q^{21} +(-311.538 - 186.897i) q^{22} -12.8557 q^{23} +358.598i q^{24} -548.861 q^{25} +487.064 q^{26} +140.296 q^{27} +10.1851i q^{28} +282.359i q^{29} +136.134i q^{30} -304.206 q^{31} +817.627i q^{32} +(-323.448 + 539.155i) q^{33} +569.671 q^{34} +12.7231i q^{35} +188.600 q^{36} +464.276 q^{37} +1772.79 q^{38} -842.925i q^{39} +602.186i q^{40} -1193.81i q^{41} -22.7483 q^{42} +1591.11i q^{43} +(-434.810 + 724.784i) q^{44} +235.596 q^{45} -38.5989i q^{46} -1825.87 q^{47} -495.945 q^{48} +2398.87 q^{49} -1647.94i q^{50} -985.887i q^{51} -1133.14i q^{52} -4023.28 q^{53} +421.235i q^{54} +(-543.159 + 905.391i) q^{55} -100.627 q^{56} -3068.03i q^{57} -847.774 q^{58} -1489.12 q^{59} +316.711 q^{60} +356.601i q^{61} -913.368i q^{62} +39.3688i q^{63} -3982.02 q^{64} -1415.51i q^{65} +(-1618.80 - 971.143i) q^{66} +8259.07 q^{67} -1325.32i q^{68} -66.8002 q^{69} -38.2007 q^{70} +7971.63 q^{71} +1863.33i q^{72} +5780.93i q^{73} +1393.98i q^{74} -2851.96 q^{75} -4124.34i q^{76} +(-151.293 - 90.7633i) q^{77} +2530.86 q^{78} +11304.5i q^{79} -832.830 q^{80} +729.000 q^{81} +3584.37 q^{82} +5449.44i q^{83} +52.9233i q^{84} -1655.58i q^{85} -4777.26 q^{86} +1467.18i q^{87} +(-7160.75 - 4295.85i) q^{88} +7332.12 q^{89} +707.371i q^{90} +236.535 q^{91} -89.7992 q^{92} -1580.70 q^{93} -5482.13i q^{94} -5152.08i q^{95} +4248.51i q^{96} -11228.1 q^{97} +7202.55i q^{98} +(-1680.69 + 2801.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9}+O(q^{10}) \) 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9	\( 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9} + 36 q^{11} - 360 q^{12} - 1140 q^{14} + 108 q^{15} + 1412 q^{16} + 2532 q^{20} - 780 q^{22} + 516 q^{23} - 2280 q^{25} - 1524 q^{26} + 2752 q^{31} + 1008 q^{33} - 4920 q^{34} - 2052 q^{36} + 5296 q^{37} + 696 q^{38} - 4356 q^{42} - 6540 q^{44} - 972 q^{45} + 420 q^{47} + 9936 q^{48} - 6832 q^{49} + 3540 q^{53} + 3784 q^{55} + 17964 q^{56} + 21624 q^{58} - 16632 q^{59} - 612 q^{60} - 27508 q^{64} + 360 q^{66} - 3656 q^{67} + 9036 q^{69} + 3312 q^{70} - 13212 q^{71} - 9288 q^{75} + 23268 q^{77} - 13140 q^{78} - 4476 q^{80} + 5832 q^{81} + 17088 q^{82} + 19896 q^{86} - 12516 q^{88} + 15528 q^{89} - 19752 q^{91} - 81180 q^{92} - 21384 q^{93} + 7624 q^{97} + 972 q^{99}+O(q^{100}) \) 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9 + 36 * q^11 - 360 * q^12 - 1140 * q^14 + 108 * q^15 + 1412 * q^16 + 2532 * q^20 - 780 * q^22 + 516 * q^23 - 2280 * q^25 - 1524 * q^26 + 2752 * q^31 + 1008 * q^33 - 4920 * q^34 - 2052 * q^36 + 5296 * q^37 + 696 * q^38 - 4356 * q^42 - 6540 * q^44 - 972 * q^45 + 420 * q^47 + 9936 * q^48 - 6832 * q^49 + 3540 * q^53 + 3784 * q^55 + 17964 * q^56 + 21624 * q^58 - 16632 * q^59 - 612 * q^60 - 27508 * q^64 + 360 * q^66 - 3656 * q^67 + 9036 * q^69 + 3312 * q^70 - 13212 * q^71 - 9288 * q^75 + 23268 * q^77 - 13140 * q^78 - 4476 * q^80 + 5832 * q^81 + 17088 * q^82 + 19896 * q^86 - 12516 * q^88 + 15528 * q^89 - 19752 * q^91 - 81180 * q^92 - 21384 * q^93 + 7624 * q^97 + 972 * q^99

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