LMFDB - Embedded newform 33.5.b.a.23.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,5,Mod(23,33)]

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([1, 0]))

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

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	33.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.41120878177$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 162x^{12} + 10041x^{10} + 298396x^{8} + 4418856x^{6} + 32113344x^{4} + 102865552x^{2} + 102193344 $ x^14 + 162x^12 + 10041x^10 + 298396x^8 + 4418856x^6 + 32113344x^4 + 102865552x^2 + 102193344
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{9}\cdot 11^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.13
Root			$6.53421i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.5.b.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.53421i q^{2} +(-8.21241 - 3.68190i) q^{3} -26.6960 q^{4} -12.2301i q^{5} +(24.0583 - 53.6616i) q^{6} -55.6823 q^{7} -69.8897i q^{8} +(53.8873 + 60.4745i) q^{9} +O(q^{10})$	\(q+6.53421i q^{2} +(-8.21241 - 3.68190i) q^{3} -26.6960 q^{4} -12.2301i q^{5} +(24.0583 - 53.6616i) q^{6} -55.6823 q^{7} -69.8897i q^{8} +(53.8873 + 60.4745i) q^{9} +79.9138 q^{10} -36.4829i q^{11} +(219.238 + 98.2918i) q^{12} -240.766 q^{13} -363.840i q^{14} +(-45.0298 + 100.438i) q^{15} +29.5391 q^{16} +364.488i q^{17} +(-395.153 + 352.111i) q^{18} -230.441 q^{19} +326.493i q^{20} +(457.286 + 205.016i) q^{21} +238.387 q^{22} -193.129i q^{23} +(-257.327 + 573.963i) q^{24} +475.426 q^{25} -1573.21i q^{26} +(-219.884 - 695.048i) q^{27} +1486.49 q^{28} +1409.35i q^{29} +(-656.285 - 294.234i) q^{30} +1055.18 q^{31} -925.221i q^{32} +(-134.326 + 299.612i) q^{33} -2381.64 q^{34} +680.998i q^{35} +(-1438.57 - 1614.42i) q^{36} +166.677 q^{37} -1505.75i q^{38} +(1977.27 + 886.474i) q^{39} -854.756 q^{40} -2132.83i q^{41} +(-1339.62 + 2988.00i) q^{42} -3380.68 q^{43} +973.945i q^{44} +(739.606 - 659.045i) q^{45} +1261.95 q^{46} -98.7035i q^{47} +(-242.587 - 108.760i) q^{48} +699.520 q^{49} +3106.53i q^{50} +(1342.01 - 2993.33i) q^{51} +6427.47 q^{52} +2134.50i q^{53} +(4541.60 - 1436.77i) q^{54} -446.188 q^{55} +3891.62i q^{56} +(1892.47 + 848.459i) q^{57} -9209.02 q^{58} -646.367i q^{59} +(1202.11 - 2681.30i) q^{60} +646.151 q^{61} +6894.76i q^{62} +(-3000.57 - 3367.36i) q^{63} +6518.22 q^{64} +2944.58i q^{65} +(-1957.73 - 877.716i) q^{66} -6267.27 q^{67} -9730.37i q^{68} +(-711.080 + 1586.05i) q^{69} -4449.79 q^{70} +2443.23i q^{71} +(4226.54 - 3766.17i) q^{72} -565.074 q^{73} +1089.10i q^{74} +(-3904.39 - 1750.47i) q^{75} +6151.84 q^{76} +2031.45i q^{77} +(-5792.41 + 12919.9i) q^{78} -5754.20 q^{79} -361.265i q^{80} +(-753.321 + 6517.61i) q^{81} +13936.4 q^{82} -4764.61i q^{83} +(-12207.7 - 5473.11i) q^{84} +4457.71 q^{85} -22090.1i q^{86} +(5189.09 - 11574.2i) q^{87} -2549.78 q^{88} -11493.5i q^{89} +(4306.34 + 4832.75i) q^{90} +13406.4 q^{91} +5155.76i q^{92} +(-8665.55 - 3885.05i) q^{93} +644.950 q^{94} +2818.31i q^{95} +(-3406.57 + 7598.29i) q^{96} -3561.20 q^{97} +4570.81i q^{98} +(2206.28 - 1965.96i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9}+O(q^{10}) $ 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9	$ 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9} - 156 q^{10} - 100 q^{12} - 104 q^{13} + 151 q^{15} + 356 q^{16} - 34 q^{18} + 1072 q^{19} + 718 q^{21} + 1200 q^{24} - 1060 q^{25} - 1154 q^{27} - 1808 q^{28} - 3026 q^{30} + 3310 q^{31} - 605 q^{33} - 2304 q^{34} + 2644 q^{36} - 362 q^{37} + 4264 q^{39} + 1896 q^{40} - 7364 q^{42} - 6740 q^{43} + 3611 q^{45} - 4068 q^{46} - 2956 q^{48} + 7074 q^{49} - 7046 q^{51} + 13072 q^{52} + 20512 q^{54} + 726 q^{55} + 3876 q^{57} - 7848 q^{58} - 8416 q^{60} - 3560 q^{61} - 17662 q^{63} + 12020 q^{64} + 1210 q^{66} - 16514 q^{67} + 9833 q^{69} + 13320 q^{70} + 8160 q^{72} + 12664 q^{73} - 5386 q^{75} - 43736 q^{76} + 19096 q^{78} + 3052 q^{79} - 11611 q^{81} + 10200 q^{82} - 39184 q^{84} + 34884 q^{85} + 37068 q^{87} - 7260 q^{88} - 26686 q^{90} - 45856 q^{91} + 2719 q^{93} + 6120 q^{94} - 38368 q^{96} - 27854 q^{97} + 4235 q^{99}+O(q^{100}) $ 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9 - 156 * q^10 - 100 * q^12 - 104 * q^13 + 151 * q^15 + 356 * q^16 - 34 * q^18 + 1072 * q^19 + 718 * q^21 + 1200 * q^24 - 1060 * q^25 - 1154 * q^27 - 1808 * q^28 - 3026 * q^30 + 3310 * q^31 - 605 * q^33 - 2304 * q^34 + 2644 * q^36 - 362 * q^37 + 4264 * q^39 + 1896 * q^40 - 7364 * q^42 - 6740 * q^43 + 3611 * q^45 - 4068 * q^46 - 2956 * q^48 + 7074 * q^49 - 7046 * q^51 + 13072 * q^52 + 20512 * q^54 + 726 * q^55 + 3876 * q^57 - 7848 * q^58 - 8416 * q^60 - 3560 * q^61 - 17662 * q^63 + 12020 * q^64 + 1210 * q^66 - 16514 * q^67 + 9833 * q^69 + 13320 * q^70 + 8160 * q^72 + 12664 * q^73 - 5386 * q^75 - 43736 * q^76 + 19096 * q^78 + 3052 * q^79 - 11611 * q^81 + 10200 * q^82 - 39184 * q^84 + 34884 * q^85 + 37068 * q^87 - 7260 * q^88 - 26686 * q^90 - 45856 * q^91 + 2719 * q^93 + 6120 * q^94 - 38368 * q^96 - 27854 * q^97 + 4235 * 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 $

$2$			6.53421i			1.63355i	0.576954	+	0.816777i	$0.304241\pi$
$2$			6.53421i			1.63355i	−0.576954	+	0.816777i	$0.695759\pi$
$3$	−8.21241	−	3.68190i	−0.912490	−	0.409100i
$3$	−8.21241	−	3.68190i	−0.912490	−	0.409100i
$4$	−26.6960			−1.66850
$5$		−	12.2301i		−	0.489202i	−0.969624	−	0.244601i	$-0.921343\pi$
$5$		−	12.2301i		−	0.489202i	0.969624	−	0.244601i	$-0.0786570\pi$
$6$	24.0583	−	53.6616i	0.668286	−	1.49060i
$7$	−55.6823			−1.13637			−0.568187	−	0.822900i	$-0.692355\pi$
$7$	−55.6823			−1.13637			−0.568187	+	0.822900i	$0.692355\pi$
$8$		−	69.8897i		−	1.09203i
$9$	53.8873	+	60.4745i	0.665275	+	0.746598i
$10$	79.9138			0.799138
$11$		−	36.4829i		−	0.301511i
$11$		−	36.4829i		−	0.301511i
$12$	219.238	+	98.2918i	1.52249	+	0.682582i
$13$	−240.766			−1.42465			−0.712324	−	0.701850i	$-0.752357\pi$
$13$	−240.766			−1.42465			−0.712324	+	0.701850i	$0.752357\pi$
$14$		−	363.840i		−	1.85633i
$15$	−45.0298	+	100.438i	−0.200132	+	0.446392i
$16$	29.5391			0.115387
$17$			364.488i			1.26121i	0.776106	+	0.630603i	$0.217192\pi$
$17$			364.488i			1.26121i	−0.776106	+	0.630603i	$0.782808\pi$
$18$	−395.153	+	352.111i	−1.21961	+	1.08676i
$19$	−230.441			−0.638340			−0.319170	−	0.947697i	$-0.603404\pi$
$19$	−230.441			−0.638340			−0.319170	+	0.947697i	$0.603404\pi$
$20$			326.493i			0.816233i
$21$	457.286	+	205.016i	1.03693	+	0.464890i
$22$	238.387			0.492535
$23$		−	193.129i		−	0.365083i	−0.983198	−	0.182541i	$-0.941568\pi$
$23$		−	193.129i		−	0.365083i	0.983198	−	0.182541i	$-0.0584324\pi$
$24$	−257.327	+	573.963i	−0.446748	+	0.996464i
$25$	475.426			0.760681
$26$		−	1573.21i		−	2.32724i
$27$	−219.884	−	695.048i	−0.301624	−	0.953427i
$28$	1486.49			1.89604
$29$			1409.35i			1.67581i	0.545818	+	0.837904i	$0.316219\pi$
$29$			1409.35i			1.67581i	−0.545818	+	0.837904i	$0.683781\pi$
$30$	−656.285	−	294.234i	−0.729206	−	0.326927i
$31$	1055.18			1.09800			0.549000	−	0.835822i	$-0.315009\pi$
$31$	1055.18			1.09800			0.549000	+	0.835822i	$0.315009\pi$
$32$		−	925.221i		−	0.903536i
$33$	−134.326	+	299.612i	−0.123348	+	0.275126i
$34$	−2381.64			−2.06025
$35$			680.998i			0.555917i
$36$	−1438.57	−	1614.42i	−1.11001	−	1.24570i
$37$	166.677			0.121751			0.0608753	−	0.998145i	$-0.480611\pi$
$37$	166.677			0.121751			0.0608753	+	0.998145i	$0.480611\pi$
$38$		−	1505.75i		−	1.04276i
$39$	1977.27	+	886.474i	1.29998	+	0.582823i
$40$	−854.756			−0.534222
$41$		−	2132.83i		−	1.26879i	−0.773010	−	0.634394i	$-0.781250\pi$
$41$		−	2132.83i		−	1.26879i	0.773010	−	0.634394i	$-0.218750\pi$
$42$	−1339.62	+	2988.00i	−0.759423	+	1.69388i
$43$	−3380.68			−1.82838			−0.914192	−	0.405282i	$-0.867173\pi$
$43$	−3380.68			−1.82838			−0.914192	+	0.405282i	$0.867173\pi$
$44$			973.945i			0.503071i
$45$	739.606	−	659.045i	0.365238	−	0.325454i
$46$	1261.95			0.596383
$47$		−	98.7035i		−	0.0446824i	−0.999750	−	0.0223412i	$-0.992888\pi$
$47$		−	98.7035i		−	0.0446824i	0.999750	−	0.0223412i	$-0.00711202\pi$
$48$	−242.587	−	108.760i	−0.105290	−	0.0472048i
$49$	699.520			0.291345
$50$			3106.53i			1.24261i
$51$	1342.01	−	2993.33i	0.515958	−	1.15084i
$52$	6427.47			2.37702
$53$			2134.50i			0.759878i	0.925011	+	0.379939i	$0.124055\pi$
$53$			2134.50i			0.759878i	−0.925011	+	0.379939i	$0.875945\pi$
$54$	4541.60	−	1436.77i	1.55747	−	0.492719i
$55$	−446.188			−0.147500
$56$			3891.62i			1.24095i
$57$	1892.47	+	848.459i	0.582479	+	0.261145i
$58$	−9209.02			−2.73752
$59$		−	646.367i		−	0.185684i	−0.995681	−	0.0928421i	$-0.970405\pi$
$59$		−	646.367i		−	0.185684i	0.995681	−	0.0928421i	$-0.0295952\pi$
$60$	1202.11	−	2681.30i	0.333921	−	0.744804i
$61$	646.151			0.173650			0.0868249	−	0.996224i	$-0.472328\pi$
$61$	646.151			0.173650			0.0868249	+	0.996224i	$0.472328\pi$
$62$			6894.76i			1.79364i
$63$	−3000.57	−	3367.36i	−0.756001	−	0.848415i
$64$	6518.22			1.59136
$65$			2944.58i			0.696942i
$66$	−1957.73	−	877.716i	−0.449433	−	0.201496i
$67$	−6267.27			−1.39614			−0.698070	−	0.716030i	$-0.745958\pi$
$67$	−6267.27			−1.39614			−0.698070	+	0.716030i	$0.745958\pi$
$68$		−	9730.37i		−	2.10432i
$69$	−711.080	+	1586.05i	−0.149355	+	0.333134i
$70$	−4449.79			−0.908120
$71$			2443.23i			0.484671i	0.970193	+	0.242335i	$0.0779134\pi$
$71$			2443.23i			0.484671i	−0.970193	+	0.242335i	$0.922087\pi$
$72$	4226.54	−	3766.17i	0.815306	−	0.726498i
$73$	−565.074			−0.106038			−0.0530188	−	0.998594i	$-0.516884\pi$
$73$	−565.074			−0.106038			−0.0530188	+	0.998594i	$0.516884\pi$
$74$			1089.10i			0.198886i
$75$	−3904.39	−	1750.47i	−0.694114	−	0.311194i
$76$	6151.84			1.06507
$77$			2031.45i			0.342630i
$78$	−5792.41	+	12919.9i	−0.952073	+	2.12358i
$79$	−5754.20			−0.922000			−0.461000	−	0.887400i	$-0.652509\pi$
$79$	−5754.20			−0.922000			−0.461000	+	0.887400i	$0.652509\pi$
$80$		−	361.265i		−	0.0564476i
$81$	−753.321	+	6517.61i	−0.114818	+	0.993387i
$82$	13936.4			2.07263
$83$		−	4764.61i		−	0.691626i	−0.938303	−	0.345813i	$-0.887603\pi$
$83$		−	4764.61i		−	0.691626i	0.938303	−	0.345813i	$-0.112397\pi$
$84$	−12207.7	−	5473.11i	−1.73011	−	0.775668i
$85$	4457.71			0.616985
$86$		−	22090.1i		−	2.98676i
$87$	5189.09	−	11574.2i	0.685572	−	1.52916i
$88$	−2549.78			−0.329259
$89$		−	11493.5i		−	1.45101i	−0.688214	−	0.725507i	$-0.741605\pi$
$89$		−	11493.5i		−	1.45101i	0.688214	−	0.725507i	$-0.258395\pi$
$90$	4306.34	+	4832.75i	0.531647	+	0.596635i
$91$	13406.4			1.61893
$92$			5155.76i			0.609140i
$93$	−8665.55	−	3885.05i	−1.00191	−	0.449191i
$94$	644.950			0.0729911
$95$			2818.31i			0.312278i
$96$	−3406.57	+	7598.29i	−0.369636	+	0.824467i
$97$	−3561.20			−0.378489			−0.189244	−	0.981930i	$-0.560604\pi$
$97$	−3561.20			−0.378489			−0.189244	+	0.981930i	$0.560604\pi$
$98$			4570.81i			0.475928i
$99$	2206.28	−	1965.96i	0.225108	−	0.200588i
$100$	−12691.9			−1.26919
$101$			10890.9i			1.06763i	0.845602	+	0.533815i	$0.179242\pi$
$101$			10890.9i			1.06763i	−0.845602	+	0.533815i	$0.820758\pi$
$102$	19559.0	+	8768.97i	1.87995	+	0.842846i
$103$	4377.08			0.412581			0.206291	−	0.978491i	$-0.433861\pi$
$103$	4377.08			0.412581			0.206291	+	0.978491i	$0.433861\pi$
$104$			16827.0i			1.55575i
$105$	2507.36	−	5592.63i	0.227425	−	0.507268i
$106$	−13947.3			−1.24130
$107$			6407.09i			0.559620i	0.960055	+	0.279810i	$0.0902715\pi$
$107$			6407.09i			0.559620i	−0.960055	+	0.279810i	$0.909729\pi$
$108$	5870.01	+	18555.0i	0.503259	+	1.59079i
$109$	3082.46			0.259444			0.129722	−	0.991550i	$-0.458591\pi$
$109$	3082.46			0.259444			0.129722	+	0.991550i	$0.458591\pi$
$110$		−	2915.49i		−	0.240949i
$111$	−1368.82	−	613.686i	−0.111096	−	0.0498081i
$112$	−1644.81			−0.131123
$113$			21553.0i			1.68791i	0.536411	+	0.843957i	$0.319780\pi$
$113$			21553.0i			1.68791i	−0.536411	+	0.843957i	$0.680220\pi$
$114$	−5544.02	+	12365.8i	−0.426594	+	0.951511i
$115$	−2361.98			−0.178599
$116$		−	37624.1i		−	2.79608i
$117$	−12974.2	−	14560.2i	−0.947783	−	1.06364i
$118$	4223.50			0.303325
$119$		−	20295.6i		−	1.43320i
$120$	7019.60	+	3147.12i	0.487472	+	0.218550i
$121$	−1331.00			−0.0909091
$122$			4222.09i			0.283666i
$123$	−7852.87	+	17515.7i	−0.519061	+	1.15776i
$124$	−28169.0			−1.83201
$125$		−	13458.3i		−	0.861329i
$126$	22003.0	−	19606.4i	1.38593	−	1.23497i
$127$	10542.1			0.653614			0.326807	−	0.945091i	$-0.394027\pi$
$127$	10542.1			0.653614			0.326807	+	0.945091i	$0.394027\pi$
$128$			27787.9i			1.69604i
$129$	27763.5	+	12447.3i	1.66838	+	0.747991i
$130$	−19240.5			−1.13849
$131$		−	11247.1i		−	0.655386i	−0.944784	−	0.327693i	$-0.893729\pi$
$131$		−	11247.1i		−	0.655386i	0.944784	−	0.327693i	$-0.106271\pi$
$132$	3585.97	−	7998.44i	0.205806	−	0.459047i
$133$	12831.5			0.725393
$134$		−	40951.7i		−	2.28067i
$135$	−8500.48	+	2689.19i	−0.466419	+	0.147555i
$136$	25474.0			1.37727
$137$			20313.8i			1.08231i	0.840924	+	0.541153i	$0.182012\pi$
$137$			20313.8i			1.08231i	−0.840924	+	0.541153i	$0.817988\pi$
$138$	−10363.6	−	4646.35i	−0.544193	−	0.243980i
$139$	9769.63			0.505648			0.252824	−	0.967512i	$-0.418641\pi$
$139$	9769.63			0.505648			0.252824	+	0.967512i	$0.418641\pi$
$140$		−	18179.9i		−	0.927546i
$141$	−363.416	+	810.593i	−0.0182796	+	0.0407722i
$142$	−15964.6			−0.791736
$143$			8783.82i			0.429548i
$144$	1591.78	+	1786.36i	0.0767642	+	0.0861478i
$145$	17236.5			0.819809
$146$		−	3692.31i		−	0.173218i
$147$	−5744.74	−	2575.56i	−0.265850	−	0.119189i
$148$	−4449.59			−0.203141
$149$			25209.0i			1.13549i	0.823204	+	0.567746i	$0.192184\pi$
$149$			25209.0i			1.13549i	−0.823204	+	0.567746i	$0.807816\pi$
$150$	11437.9	−	25512.1i	0.508353	−	1.13387i
$151$	−1442.16			−0.0632499			−0.0316249	−	0.999500i	$-0.510068\pi$
$151$	−1442.16			−0.0632499			−0.0316249	+	0.999500i	$0.510068\pi$
$152$			16105.5i			0.697085i
$153$	−22042.2	+	19641.3i	−0.941614	+	0.839048i
$154$	−13273.9			−0.559704
$155$		−	12904.9i		−	0.537144i
$156$	−52785.0	−	23665.3i	−2.16901	−	0.972439i
$157$	−18621.1			−0.755452			−0.377726	−	0.925917i	$-0.623294\pi$
$157$	−18621.1			−0.755452			−0.377726	+	0.925917i	$0.623294\pi$
$158$		−	37599.2i		−	1.50614i
$159$	7859.00	−	17529.4i	0.310866	−	0.693381i
$160$	−11315.5			−0.442012
$161$			10753.9i			0.414871i
$162$	−42587.5	−	4922.36i	−1.62275	−	0.187561i
$163$	−35946.8			−1.35296			−0.676480	−	0.736461i	$-0.736496\pi$
$163$	−35946.8			−1.35296			−0.676480	+	0.736461i	$0.736496\pi$
$164$			56938.1i			2.11697i
$165$	3664.28	+	1642.82i	0.134592	+	0.0603422i
$166$	31133.0			1.12981
$167$			49205.5i			1.76433i	0.470937	+	0.882167i	$0.343916\pi$
$167$			49205.5i			1.76433i	−0.470937	+	0.882167i	$0.656084\pi$
$168$	14328.5	−	31959.6i	0.507672	−	1.13235i
$169$	29407.1			1.02962
$170$			29127.7i			1.00788i
$171$	−12417.8	−	13935.8i	−0.424672	−	0.476584i
$172$	90250.5			3.05065
$173$		−	14368.5i		−	0.480085i	−0.970762	−	0.240043i	$-0.922839\pi$
$173$		−	14368.5i		−	0.480085i	0.970762	−	0.240043i	$-0.0771614\pi$
$174$	75628.2	+	33906.7i	2.49796	+	1.11992i
$175$	−26472.8			−0.864418
$176$		−	1077.67i		−	0.0347905i
$177$	−2379.86	+	5308.23i	−0.0759633	+	0.169435i
$178$	75100.9			2.37031
$179$		−	31364.5i		−	0.978887i	−0.872035	−	0.489444i	$-0.837200\pi$
$179$		−	31364.5i		−	0.978887i	0.872035	−	0.489444i	$-0.162800\pi$
$180$	−19744.5	+	17593.8i	−0.609398	+	0.543020i
$181$	−39689.8			−1.21150			−0.605748	−	0.795657i	$-0.707126\pi$
$181$	−39689.8			−1.21150			−0.605748	+	0.795657i	$0.707126\pi$
$182$			87600.2i			2.64461i
$183$	−5306.45	−	2379.06i	−0.158454	−	0.0710401i
$184$	−13497.7			−0.398680
$185$		−	2038.46i		−	0.0595607i
$186$	25385.8	−	56622.6i	0.733778	−	1.63668i
$187$	13297.6			0.380268
$188$			2634.98i			0.0745525i
$189$	12243.6	+	38701.9i	0.342757	+	1.08345i
$190$	−18415.4			−0.510122
$191$			9677.22i			0.265267i	0.991165	+	0.132634i	$0.0423434\pi$
$191$			9677.22i			0.265267i	−0.991165	+	0.132634i	$0.957657\pi$
$192$	−53530.3	−	23999.4i	−1.45210	−	0.651025i
$193$	50560.2			1.35736			0.678678	−	0.734436i	$-0.262553\pi$
$193$	50560.2			1.35736			0.678678	+	0.734436i	$0.262553\pi$
$194$		−	23269.6i		−	0.618282i
$195$	10841.6	−	24182.1i	0.285118	−	0.635952i
$196$	−18674.4			−0.486109
$197$		−	45640.9i		−	1.17604i	−0.808847	−	0.588019i	$-0.799908\pi$
$197$		−	45640.9i		−	1.17604i	0.808847	−	0.588019i	$-0.200092\pi$
$198$	12846.0	+	14416.3i	0.327671	+	0.367726i
$199$	−22348.8			−0.564350			−0.282175	−	0.959363i	$-0.591056\pi$
$199$	−22348.8			−0.564350			−0.282175	+	0.959363i	$0.591056\pi$
$200$		−	33227.4i		−	0.830684i
$201$	51469.4	+	23075.4i	1.27396	+	0.571160i
$202$	−71163.4			−1.74403
$203$		−	78476.1i		−	1.90434i
$204$	−35826.2	+	79909.7i	−0.860876	+	1.92017i
$205$	−26084.7			−0.620695
$206$			28600.7i			0.673974i
$207$	11679.4	−	10407.2i	0.272570	−	0.242881i
$208$	−7112.00			−0.164386
$209$			8407.15i			0.192467i
$210$	36543.5	+	16383.7i	0.828650	+	0.371511i
$211$	−13894.7			−0.312092			−0.156046	−	0.987750i	$-0.549875\pi$
$211$	−13894.7			−0.312092			−0.156046	+	0.987750i	$0.549875\pi$
$212$		−	56982.5i		−	1.26786i
$213$	8995.70	−	20064.8i	0.198279	−	0.442257i
$214$	−41865.3			−0.914169
$215$			41345.9i			0.894449i
$216$	−48576.7	+	15367.6i	−1.04117	+	0.329381i
$217$	−58754.7			−1.24774
$218$			20141.4i			0.423816i
$219$	4640.62	+	2080.54i	0.0967581	+	0.0433799i
$220$	11911.4			0.246104
$221$		−	87756.3i		−	1.79677i
$222$	4009.95	−	8944.14i	0.0813642	−	0.181482i
$223$	19370.4			0.389519			0.194759	−	0.980851i	$-0.437607\pi$
$223$	19370.4			0.389519			0.194759	+	0.980851i	$0.437607\pi$
$224$			51518.4i			1.02675i
$225$	25619.4	+	28751.1i	0.506062	+	0.567923i
$226$	−140832.			−2.75730
$227$			26993.2i			0.523845i	0.965089	+	0.261923i	$0.0843566\pi$
$227$			26993.2i			0.523845i	−0.965089	+	0.261923i	$0.915643\pi$
$228$	−50521.4	−	22650.4i	−0.971865	−	0.435719i
$229$	20752.0			0.395722			0.197861	−	0.980230i	$-0.436601\pi$
$229$	20752.0			0.395722			0.197861	+	0.980230i	$0.436601\pi$
$230$		−	15433.7i		−	0.291752i
$231$	7479.59	−	16683.1i	0.140170	−	0.312646i
$232$	98499.4			1.83003
$233$		−	51931.6i		−	0.956576i	−0.878203	−	0.478288i	$-0.841257\pi$
$233$		−	51931.6i		−	0.956576i	0.878203	−	0.478288i	$-0.158743\pi$
$234$	95139.3	−	84776.3i	1.73751	−	1.54826i
$235$	−1207.15			−0.0218587
$236$			17255.4i			0.309814i
$237$	47255.9	+	21186.4i	0.841316	+	0.377190i
$238$	132615.			2.34121
$239$			13344.0i			0.233609i	0.993155	+	0.116805i	$0.0372651\pi$
$239$			13344.0i			0.233609i	−0.993155	+	0.116805i	$0.962735\pi$
$240$	−1330.14	+	2966.85i	−0.0230927	+	0.0515079i
$241$	−36663.9			−0.631254			−0.315627	−	0.948883i	$-0.602215\pi$
$241$	−36663.9			−0.631254			−0.315627	+	0.948883i	$0.602215\pi$
$242$		−	8697.04i		−	0.148505i
$243$	30183.7	−	50751.6i	0.511164	−	0.859483i
$244$	−17249.6			−0.289734
$245$		−	8555.17i		−	0.142527i
$246$	−114451.	−	51312.4i	−1.89126	−	0.847914i
$247$	55482.2			0.909411
$248$		−	73746.1i		−	1.19905i
$249$	−17542.8	+	39128.9i	−0.282944	+	0.631102i
$250$	87939.2			1.40703
$251$			56339.7i			0.894267i	0.894467	+	0.447133i	$0.147555\pi$
$251$			56339.7i			0.894267i	−0.894467	+	0.447133i	$0.852445\pi$
$252$	80103.1	+	89894.9i	1.26139	+	1.41558i
$253$	−7045.90			−0.110077
$254$			68884.7i			1.06771i
$255$	−36608.6	−	16412.8i	−0.562992	−	0.252408i
$256$	−77280.6			−1.17921
$257$		−	56793.0i		−	0.859861i	−0.902862	−	0.429931i	$-0.858538\pi$
$257$		−	56793.0i		−	0.859861i	0.902862	−	0.429931i	$-0.141462\pi$
$258$	−81333.4	+	181413.i	−1.22188	+	2.72539i
$259$	−9280.93			−0.138354
$260$		−	78608.4i		−	1.16285i
$261$	−85229.9	+	75946.3i	−1.25115	+	1.11487i
$262$	73490.8			1.07061
$263$			42310.2i			0.611694i	0.952081	+	0.305847i	$0.0989396\pi$
$263$			42310.2i			0.611694i	−0.952081	+	0.305847i	$0.901060\pi$
$264$	20939.8	+	9388.02i	0.300445	+	0.134700i
$265$	26105.0			0.371734
$266$			83843.7i			1.18497i
$267$	−42317.8	+	94389.2i	−0.593609	+	1.32404i
$268$	167311.			2.32946
$269$		−	69091.8i		−	0.954821i	−0.878680	−	0.477410i	$-0.841576\pi$
$269$		−	69091.8i		−	0.954821i	0.878680	−	0.477410i	$-0.158424\pi$
$270$	−17571.8	−	55544.0i	−0.241039	−	0.761920i
$271$	24065.7			0.327688			0.163844	−	0.986486i	$-0.447611\pi$
$271$	24065.7			0.327688			0.163844	+	0.986486i	$0.447611\pi$
$272$			10766.7i			0.145527i
$273$	−110099.	−	49360.9i	−1.47726	−	0.662305i
$274$	−132735.			−1.76801
$275$		−	17344.9i		−	0.229354i
$276$	18983.0	−	42341.2i	0.249199	−	0.555834i
$277$	−105023.			−1.36876			−0.684379	−	0.729126i	$-0.739927\pi$
$277$	−105023.			−1.36876			−0.684379	+	0.729126i	$0.739927\pi$
$278$			63836.9i			0.826004i
$279$	56860.7	+	63811.3i	0.730472	+	0.819765i
$280$	47594.8			0.607076
$281$		−	79708.2i		−	1.00946i	−0.863277	−	0.504731i	$-0.831592\pi$
$281$		−	79708.2i		−	1.00946i	0.863277	−	0.504731i	$-0.168408\pi$
$282$	−5296.59	−	2374.64i	−0.0666037	−	0.0298606i
$283$	47921.7			0.598355			0.299178	−	0.954197i	$-0.403288\pi$
$283$	47921.7			0.598355			0.299178	+	0.954197i	$0.403288\pi$
$284$		−	65224.3i		−	0.808672i
$285$	10376.7	−	23145.1i	0.127753	−	0.284950i
$286$	−57395.4			−0.701689
$287$			118761.i			1.44182i
$288$	55952.2	−	49857.6i	0.674578	−	0.601100i
$289$	−49330.7			−0.590638
$290$			112627.i			1.33920i
$291$	29246.0	+	13112.0i	0.345367	+	0.154840i
$292$	15085.2			0.176923
$293$		−	77785.9i		−	0.906078i	−0.891491	−	0.453039i	$-0.850340\pi$
$293$		−	77785.9i		−	0.906078i	0.891491	−	0.453039i	$-0.149660\pi$
$294$	16829.3	−	37537.4i	0.194702	−	0.434280i
$295$	−7905.11			−0.0908372
$296$		−	11649.0i		−	0.132955i
$297$	−25357.4	+	8021.99i	−0.287469	+	0.0909430i
$298$	−164721.			−1.85489
$299$			46498.8i			0.520115i
$300$	104231.	+	46730.4i	1.15813	+	0.519227i
$301$	188244.			2.07773
$302$		−	9423.39i		−	0.103322i
$303$	40099.1	−	89440.4i	0.436767	−	0.974201i
$304$	−6807.01			−0.0736562
$305$		−	7902.46i		−	0.0849499i
$306$	−128340.	−	144029.i	−1.37063	−	1.53818i
$307$	−102393.			−1.08641			−0.543206	−	0.839600i	$-0.682790\pi$
$307$	−102393.			−1.08641			−0.543206	+	0.839600i	$0.682790\pi$
$308$		−	54231.5i		−	0.571677i
$309$	−35946.3	−	16115.9i	−0.376476	−	0.168787i
$310$	84323.3			0.877454
$311$			129420.i			1.33808i	0.743227	+	0.669040i	$0.233294\pi$
$311$			129420.i			1.33808i	−0.743227	+	0.669040i	$0.766706\pi$
$312$	61955.4	−	138191.i	0.636459	−	1.41961i
$313$	15168.1			0.154825			0.0774127	−	0.996999i	$-0.475334\pi$
$313$	15168.1			0.154825			0.0774127	+	0.996999i	$0.475334\pi$
$314$		−	121674.i		−	1.23407i
$315$	−41183.0	+	36697.1i	−0.415047	+	0.369838i
$316$	153614.			1.53836
$317$			183996.i			1.83101i	0.402308	+	0.915504i	$0.368208\pi$
$317$			183996.i			1.83101i	−0.402308	+	0.915504i	$0.631792\pi$
$318$	114541.	+	51352.4i	1.13268	+	0.507816i
$319$	51417.3			0.505275
$320$		−	79718.2i		−	0.778498i
$321$	23590.2	−	52617.6i	0.228940	−	0.510648i
$322$	−70268.1			−0.677714
$323$		−	83993.0i		−	0.805078i
$324$	20110.6	−	173994.i	0.191574	−	1.65746i
$325$	−114466.			−1.08370
$326$		−	234884.i		−	2.21013i
$327$	−25314.4	−	11349.3i	−0.236740	−	0.106139i
$328$	−149063.			−1.38555
$329$			5496.04i			0.0507759i
$330$	−10734.5	+	23943.2i	−0.0985722	+	0.219864i
$331$	56678.8			0.517326			0.258663	−	0.965968i	$-0.416718\pi$
$331$	56678.8			0.517326			0.258663	+	0.965968i	$0.416718\pi$
$332$			127196.i			1.15398i
$333$	8981.75	+	10079.7i	0.0809976	+	0.0908988i
$334$	−321519.			−2.88213
$335$			76649.1i			0.682995i
$336$	13507.8	+	6056.00i	0.119648	+	0.0536423i
$337$	−49203.1			−0.433244			−0.216622	−	0.976256i	$-0.569504\pi$
$337$	−49203.1			−0.433244			−0.216622	+	0.976256i	$0.569504\pi$
$338$			192152.i			1.68195i
$339$	79355.8	−	177002.i	0.690525	−	1.54020i
$340$	−119003.			−1.02944
$341$		−	38495.9i		−	0.331059i
$342$	91059.4	−	81140.8i	0.778525	−	0.693725i
$343$	94742.3			0.805297
$344$			236275.i			1.99664i
$345$	19397.5	+	8696.56i	0.162970	+	0.0730650i
$346$	93886.7			0.784245
$347$			72696.7i			0.603748i	0.953348	+	0.301874i	$0.0976122\pi$
$347$			72696.7i			0.603748i	−0.953348	+	0.301874i	$0.902388\pi$
$348$	−138528.	+	308984.i	−1.14388	+	2.55140i
$349$	126043.			1.03483			0.517415	−	0.855734i	$-0.326894\pi$
$349$	126043.			1.03483			0.517415	+	0.855734i	$0.326894\pi$
$350$		−	172979.i		−	1.41207i
$351$	52940.4	+	167344.i	0.429708	+	1.35830i
$352$	−33754.7			−0.272426
$353$		−	28911.6i		−	0.232018i	−0.993248	−	0.116009i	$-0.962990\pi$
$353$		−	28911.6i		−	0.232018i	0.993248	−	0.116009i	$-0.0370102\pi$
$354$	−34685.1	−	15550.5i	−0.276781	−	0.124090i
$355$	29880.8			0.237102
$356$			306830.i			2.42101i
$357$	−74726.1	+	166675.i	−0.586322	+	1.30778i
$358$	204943.			1.59906
$359$			101384.i			0.786651i	0.919399	+	0.393325i	$0.128675\pi$
$359$			101384.i			0.786651i	−0.919399	+	0.393325i	$0.871325\pi$
$360$	−46060.5	−	51690.9i	−0.355405	−	0.398849i
$361$	−77218.0			−0.592522
$362$		−	259342.i		−	1.97904i
$363$	10930.7	+	4900.60i	0.0829536	+	0.0371909i
$364$	−357896.			−2.70119
$365$			6910.89i			0.0518738i
$366$	15545.3	−	34673.5i	0.116048	−	0.258843i
$367$	70918.5			0.526536			0.263268	−	0.964723i	$-0.415200\pi$
$367$	70918.5			0.526536			0.263268	+	0.964723i	$0.415200\pi$
$368$		−	5704.85i		−	0.0421259i
$369$	128982.	−	114933.i	0.947275	−	0.844094i
$370$	13319.8			0.0972956
$371$		−	118854.i		−	0.863506i
$372$	231335.	+	103715.i	1.67169	+	0.749475i
$373$	260123.			1.86966			0.934828	−	0.355102i	$-0.115554\pi$
$373$	260123.			1.86966			0.934828	+	0.355102i	$0.115554\pi$
$374$			86889.2i			0.621188i
$375$	−49552.0	+	110525.i	−0.352369	+	0.785954i
$376$	−6898.36			−0.0487944
$377$		−	339324.i		−	2.38744i
$378$	−252887.	+	80002.5i	−1.76987	+	0.559913i
$379$	92357.3			0.642973			0.321487	−	0.946914i	$-0.395818\pi$
$379$	92357.3			0.642973			0.321487	+	0.946914i	$0.395818\pi$
$380$		−	75237.4i		−	0.521035i
$381$	−86576.4	−	38815.1i	−0.596416	−	0.267393i
$382$	−63233.1			−0.433329
$383$			98348.8i			0.670458i	0.942137	+	0.335229i	$0.108814\pi$
$383$			98348.8i			0.670458i	−0.942137	+	0.335229i	$0.891186\pi$
$384$	102312.	−	228206.i	0.693849	−	1.54762i
$385$	24844.8			0.167615
$386$			330371.i			2.21731i
$387$	−182176.	−	204445.i	−1.21638	−	1.36507i
$388$	95069.7			0.631508
$389$		−	15966.2i		−	0.105512i	−0.998607	−	0.0527560i	$-0.983199\pi$
$389$		−	15966.2i		−	0.105512i	0.998607	−	0.0527560i	$-0.0168006\pi$
$390$	158011.	+	70841.5i	1.03886	+	0.465756i
$391$	70393.2			0.460444
$392$		−	48889.3i		−	0.318157i
$393$	−41410.5	+	92365.5i	−0.268118	+	0.598033i
$394$	298227.			1.92112
$395$			70374.3i			0.451045i
$396$	−58898.8	+	52483.3i	−0.375592	+	0.334681i
$397$	159710.			1.01333			0.506667	−	0.862142i	$-0.330877\pi$
$397$	159710.			1.01333			0.506667	+	0.862142i	$0.330877\pi$
$398$		−	146032.i		−	0.921897i
$399$	−105377.	−	47244.2i	−0.661914	−	0.296758i
$400$	14043.6			0.0877728
$401$		−	148056.i		−	0.920738i	−0.887728	−	0.460369i	$-0.847717\pi$
$401$		−	148056.i		−	0.920738i	0.887728	−	0.460369i	$-0.152283\pi$
$402$	−150780.	+	336312.i	−0.933021	+	2.08109i
$403$	−254051.			−1.56426
$404$		−	290743.i		−	1.78134i
$405$	79710.8	+	9213.16i	0.485967	+	0.0561692i
$406$	512780.			3.11085
$407$		−	6080.84i		−	0.0367092i
$408$	−209203.	−	93792.6i	−1.25674	−	0.563441i
$409$	−228118.			−1.36368			−0.681840	−	0.731501i	$-0.738820\pi$
$409$	−228118.			−1.36368			−0.681840	+	0.731501i	$0.738820\pi$
$410$		−	170443.i		−	1.01394i
$411$	74793.3	−	166825.i	0.442771	−	0.987593i
$412$	−116850.			−0.688391
$413$			35991.2i			0.211007i
$414$	68002.8	+	76315.5i	0.396759	+	0.445258i
$415$	−58271.5			−0.338345
$416$			222761.i			1.28722i
$417$	−80232.2	−	35970.8i	−0.461399	−	0.206861i
$418$	−54934.1			−0.314405
$419$			293966.i			1.67444i	0.546869	+	0.837218i	$0.315820\pi$
$419$			293966.i			1.67444i	−0.546869	+	0.837218i	$0.684180\pi$
$420$	−66936.5	+	149301.i	−0.379459	+	0.846376i
$421$	−113830.			−0.642234			−0.321117	−	0.947040i	$-0.604058\pi$
$421$	−113830.			−0.642234			−0.321117	+	0.947040i	$0.604058\pi$
$422$		−	90790.6i		−	0.509819i
$423$	5969.04	−	5318.86i	0.0333598	−	0.0297261i
$424$	149180.			0.829808
$425$			173287.i			0.959375i
$426$	131107.	+	58779.9i	0.722451	+	0.323899i
$427$	−35979.2			−0.197331
$428$		−	171043.i		−	0.933725i
$429$	32341.1	−	72136.3i	0.175728	−	0.391958i
$430$	−270163.			−1.46113
$431$			75254.8i			0.405116i	0.979270	+	0.202558i	$0.0649255\pi$
$431$			75254.8i			0.405116i	−0.979270	+	0.202558i	$0.935075\pi$
$432$	−6495.17	−	20531.1i	−0.0348035	−	0.110013i
$433$	−346783.			−1.84962			−0.924808	−	0.380434i	$-0.875775\pi$
$433$	−346783.			−1.84962			−0.924808	+	0.380434i	$0.875775\pi$
$434$		−	383916.i		−	2.03825i
$435$	−141553.	−	63462.9i	−0.748067	−	0.335383i
$436$	−82289.2			−0.432882
$437$			44504.8i			0.233047i
$438$	−13594.7	+	30322.8i	−0.0708634	+	0.158060i
$439$	−339864.			−1.76350			−0.881751	−	0.471716i	$-0.843635\pi$
$439$	−339864.			−1.76350			−0.881751	+	0.471716i	$0.843635\pi$
$440$			31183.9i			0.161074i
$441$	37695.2	+	42303.1i	0.193825	+	0.217518i
$442$	573418.			2.93513
$443$		−	351959.i		−	1.79343i	−0.442608	−	0.896715i	$-0.645947\pi$
$443$		−	351959.i		−	1.79343i	0.442608	−	0.896715i	$-0.354053\pi$
$444$	36541.9	+	16382.9i	0.185364	+	0.0831047i
$445$	−140566.			−0.709840
$446$			126570.i			0.636300i
$447$	92817.1	−	207027.i	0.464529	−	1.03612i
$448$	−362949.			−1.80838
$449$			166371.i			0.825249i	0.910901	+	0.412625i	$0.135388\pi$
$449$			166371.i			0.825249i	−0.910901	+	0.412625i	$0.864612\pi$
$450$	−187866.	+	167403.i	−0.927733	+	0.826680i
$451$	−77811.9			−0.382554
$452$		−	575377.i		−	2.81628i
$453$	11843.6	+	5309.89i	0.0577149	+	0.0258755i
$454$	−176380.			−0.855730
$455$		−	163961.i		−	0.791986i
$456$	59298.6	−	132265.i	0.285177	−	0.636083i
$457$	290818.			1.39248			0.696240	−	0.717809i	$-0.254855\pi$
$457$	290818.			1.39248			0.696240	+	0.717809i	$0.254855\pi$
$458$			135598.i			0.646433i
$459$	253337.	−	80145.0i	1.20247	−	0.380409i
$460$	63055.3			0.297993
$461$			10869.0i			0.0511430i	0.999673	+	0.0255715i	$0.00814055\pi$
$461$			10869.0i			0.0511430i	−0.999673	+	0.0255715i	$0.991859\pi$
$462$	109011.	+	48873.2i	0.510724	+	0.228975i
$463$	258579.			1.20623			0.603115	−	0.797654i	$-0.293926\pi$
$463$	258579.			1.20623			0.603115	+	0.797654i	$0.293926\pi$
$464$			41631.0i			0.193367i
$465$	−47514.5	+	105980.i	−0.219745	+	0.490139i
$466$	339332.			1.56262
$467$		−	157973.i		−	0.724349i	−0.932110	−	0.362175i	$-0.882034\pi$
$467$		−	157973.i		−	0.724349i	0.932110	−	0.362175i	$-0.117966\pi$
$468$	346359.	+	388698.i	1.58137	+	1.77468i
$469$	348976.			1.58654
$470$		−	7887.77i		−	0.0357074i
$471$	152924.	+	68561.1i	0.689342	+	0.309055i
$472$	−45174.4			−0.202772
$473$			123337.i			0.551278i
$474$	−138436.	+	308780.i	−0.616160	+	1.37433i
$475$	−109557.			−0.485573
$476$			541809.i			2.39129i
$477$	−129083.	+	115022.i	−0.567324	+	0.505528i
$478$	−87192.5			−0.381613
$479$			253169.i			1.10342i	0.834037	+	0.551709i	$0.186024\pi$
$479$			253169.i			1.10342i	−0.834037	+	0.551709i	$0.813976\pi$
$480$	92927.6	+	41662.5i	0.403331	+	0.180827i
$481$	−40130.0			−0.173452
$482$		−	239570.i		−	1.03119i
$483$	39594.6	−	88315.1i	0.169723	−	0.378565i
$484$	35532.3			0.151682
$485$			43553.7i			0.185158i
$486$	331622.	+	197227.i	1.40401	+	0.835014i
$487$	−185191.			−0.780841			−0.390421	−	0.920637i	$-0.627670\pi$
$487$	−185191.			−0.780841			−0.390421	+	0.920637i	$0.627670\pi$
$488$		−	45159.3i		−	0.189630i
$489$	295210.	+	132352.i	1.23456	+	0.553496i
$490$	55901.3			0.232825
$491$			15476.5i			0.0641963i	0.999485	+	0.0320981i	$0.0102189\pi$
$491$			15476.5i			0.0641963i	−0.999485	+	0.0320981i	$0.989781\pi$
$492$	209640.	−	467599.i	0.866052	−	1.93171i
$493$	−513693.			−2.11354
$494$			362533.i			1.48557i
$495$	−24043.8	−	26983.0i	−0.0981281	−	0.110123i
$496$	31169.0			0.126695
$497$		−	136044.i		−	0.550767i
$498$	−255677.	−	114628.i	−1.03094	−	0.462204i
$499$	210607.			0.845808			0.422904	−	0.906174i	$-0.361011\pi$
$499$	210607.			0.845808			0.422904	+	0.906174i	$0.361011\pi$
$500$			359282.i			1.43713i
$501$	181169.	−	404096.i	0.721788	−	1.60994i
$502$	−368136.			−1.46083
$503$		−	148025.i		−	0.585057i	−0.956257	−	0.292528i	$-0.905503\pi$
$503$		−	148025.i		−	0.585057i	0.956257	−	0.292528i	$-0.0944966\pi$
$504$	−235344.	+	209709.i	−0.926492	+	0.825574i
$505$	133196.			0.522287
$506$		−	46039.4i		−	0.179816i
$507$	−241503.	−	108274.i	−0.939521	−	0.421219i
$508$	−281433.			−1.09055
$509$		−	60096.5i		−	0.231960i	−0.993252	−	0.115980i	$-0.962999\pi$
$509$		−	60096.5i		−	0.231960i	0.993252	−	0.115980i	$-0.0370009\pi$
$510$	107245.	−	239208.i	0.412322	−	0.919678i
$511$	31464.6			0.120498
$512$		−	60361.9i		−	0.230262i
$513$	50670.2	+	160168.i	0.192539	+	0.608611i
$514$	371097.			1.40463
$515$		−	53531.9i		−	0.201836i
$516$	−741174.	−	332293.i	−2.78369	−	1.24802i
$517$	−3600.99			−0.0134723
$518$		−	60643.6i		−	0.226009i
$519$	−52903.2	+	118000.i	−0.196403	+	0.438073i
$520$	205796.			0.761079
$521$		−	341.536i		−	0.00125823i	−1.00000		0.000629116i	$-0.999800\pi$
$521$		−	341.536i		−	0.00125823i	1.00000		0.000629116i	$-0.000200254\pi$
$522$	−496249.	−	556911.i	−1.82120	−	2.04383i
$523$	−207296.			−0.757858			−0.378929	−	0.925426i	$-0.623708\pi$
$523$	−207296.			−0.757858			−0.378929	+	0.925426i	$0.623708\pi$
$524$			300251.i			1.09351i
$525$	217405.	+	97470.1i	0.788772	+	0.353633i
$526$	−276464.			−0.999235
$527$			384600.i			1.38480i
$528$	−3967.87	+	8850.27i	−0.0142328	+	0.0317460i
$529$	242542.			0.866714
$530$			170576.i			0.607248i
$531$	39088.7	−	34831.0i	0.138632	−	0.123531i
$532$	−342549.			−1.21032
$533$			513513.i			1.80758i
$534$	−616759.	−	276514.i	−2.16288	−	0.969693i
$535$	78359.1			0.273767
$536$			438018.i			1.52462i
$537$	−115481.	+	257578.i	−0.400462	+	0.893224i
$538$	451461.			1.55975
$539$		−	25520.5i		−	0.0878439i
$540$	226929.	−	71790.6i	0.778219	−	0.246195i
$541$	17837.9			0.0609466			0.0304733	−	0.999536i	$-0.490299\pi$
$541$	17837.9			0.0609466			0.0304733	+	0.999536i	$0.490299\pi$
$542$			157251.i			0.535296i
$543$	325949.	+	146134.i	1.10548	+	0.495622i
$544$	337232.			1.13954
$545$		−	37698.6i		−	0.126921i
$546$	322535.	−	719409.i	1.08191	−	2.41318i
$547$	−392402.			−1.31147			−0.655733	−	0.754993i	$-0.727640\pi$
$547$	−392402.			−1.31147			−0.655733	+	0.754993i	$0.727640\pi$
$548$		−	542297.i		−	1.80583i
$549$	34819.3	+	39075.6i	0.115525	+	0.129647i
$550$	113335.			0.374662
$551$		−	324773.i		−	1.06974i
$552$	110849.	+	49697.2i	0.363792	+	0.163100i
$553$	320407.			1.04774
$554$		−	686246.i		−	2.23594i
$555$	−7505.41	+	16740.7i	−0.0243662	+	0.0543485i
$556$	−260810.			−0.843673
$557$		−	94804.3i		−	0.305575i	−0.988259	−	0.152787i	$-0.951175\pi$
$557$		−	94804.3i		−	0.305575i	0.988259	−	0.152787i	$-0.0488250\pi$
$558$	−416957.	+	371540.i	−1.33913	+	1.19327i
$559$	813952.			2.60480
$560$			20116.1i			0.0641456i
$561$	−109205.	−	48960.3i	−0.346990	−	0.155567i
$562$	520830.			1.64901
$563$		−	251403.i		−	0.793148i	−0.918003	−	0.396574i	$-0.870199\pi$
$563$		−	251403.i		−	0.793148i	0.918003	−	0.396574i	$-0.129801\pi$
$564$	9701.74	−	21639.6i	0.0304994	−	0.0680284i
$565$	263594.			0.825731
$566$			313130.i			0.977445i
$567$	41946.6	−	362916.i	0.130476	−	1.12886i
$568$	170756.			0.529274
$569$		−	416380.i		−	1.28607i	−0.765836	−	0.643036i	$-0.777674\pi$
$569$		−	416380.i		−	1.28607i	0.765836	−	0.643036i	$-0.222326\pi$
$570$	151235.	+	67803.6i	0.465481	+	0.208691i
$571$	−125300.			−0.384306			−0.192153	−	0.981365i	$-0.561547\pi$
$571$	−125300.			−0.384306			−0.192153	+	0.981365i	$0.561547\pi$
$572$		−	234493.i		−	0.716699i
$573$	35630.5	−	79473.3i	0.108521	−	0.242054i
$574$	−776011.			−2.35529
$575$		−	91818.4i		−	0.277712i
$576$	351249.	+	394186.i	1.05869	+	1.18811i
$577$	−404941.			−1.21630			−0.608149	−	0.793823i	$-0.708088\pi$
$577$	−404941.			−1.21630			−0.608149	+	0.793823i	$0.708088\pi$
$578$		−	322337.i		−	0.964840i
$579$	−415221.	−	186157.i	−1.23857	−	0.555294i
$580$	−460145.			−1.36785
$581$			265305.i			0.785946i
$582$	−85676.4	+	191100.i	−0.252939	+	0.564176i
$583$	77872.6			0.229112
$584$			39492.9i			0.115796i
$585$	−178072.	+	158675.i	−0.520335	+	0.463658i
$586$	508270.			1.48013
$587$			462984.i			1.34366i	0.740705	+	0.671830i	$0.234491\pi$
$587$			462984.i			1.34366i	−0.740705	+	0.671830i	$0.765509\pi$
$588$	153361.	+	68757.1i	0.443569	+	0.198867i
$589$	−243156.			−0.700898
$590$		−	51653.7i		−	0.148387i
$591$	−168045.	+	374822.i	−0.481117	+	1.07312i
$592$	4923.47			0.0140484
$593$		−	441032.i		−	1.25418i	−0.778945	−	0.627092i	$-0.784245\pi$
$593$		−	441032.i		−	1.25418i	0.778945	−	0.627092i	$-0.215755\pi$
$594$	−52417.4	−	165690.i	−0.148560	−	0.469596i
$595$	−248216.			−0.701125
$596$		−	672980.i		−	1.89456i
$597$	183538.	+	82286.1i	0.514964	+	0.230875i
$598$	−303833.			−0.849636
$599$			208142.i			0.580105i	0.957011	+	0.290053i	$0.0936728\pi$
$599$			208142.i			0.580105i	−0.957011	+	0.290053i	$0.906327\pi$
$600$	−122340.	+	272877.i	−0.339833	+	0.757991i
$601$	85200.2			0.235880			0.117940	−	0.993021i	$-0.462371\pi$
$601$	85200.2			0.235880			0.117940	+	0.993021i	$0.462371\pi$
$602$			1.23003e6i			3.39408i
$603$	−337726.	−	379010.i	−0.928817	−	1.04236i
$604$	38499.9			0.105532
$605$			16278.2i			0.0444729i
$606$	584423.	+	262016.i	1.59141	+	0.713482i
$607$	30451.9			0.0826489			0.0413245	−	0.999146i	$-0.486842\pi$
$607$	30451.9			0.0826489			0.0413245	+	0.999146i	$0.486842\pi$
$608$			213209.i			0.576764i
$609$	−288941.	+	644478.i	−0.779066	+	1.73769i
$610$	51636.4			0.138770
$611$			23764.4i			0.0636567i
$612$	588439.	−	524343.i	1.57108	−	1.39995i
$613$	−12887.7			−0.0342969			−0.0171485	−	0.999853i	$-0.505459\pi$
$613$	−12887.7			−0.0342969			−0.0171485	+	0.999853i	$0.505459\pi$
$614$		−	669059.i		−	1.77471i
$615$	214218.	+	96041.1i	0.566377	+	0.253926i
$616$	141978.			0.374161
$617$			377411.i			0.991389i	0.868497	+	0.495695i	$0.165086\pi$
$617$			377411.i			0.991389i	−0.868497	+	0.495695i	$0.834914\pi$
$618$	105305.	−	234881.i	0.275722	−	0.614994i
$619$	562183.			1.46722			0.733612	−	0.679568i	$-0.237833\pi$
$619$	562183.			1.46722			0.733612	+	0.679568i	$0.237833\pi$
$620$			344508.i			0.896224i
$621$	−134234.	+	42465.9i	−0.348080	+	0.110118i
$622$	−845660.			−2.18582
$623$			639984.i			1.64889i
$624$	58406.6	+	26185.6i	0.150001	+	0.0672503i
$625$	132546.			0.339317
$626$			99111.6i			0.252916i
$627$	30954.2	−	69042.9i	0.0787381	−	0.175624i
$628$	497109.			1.26047
$629$			60751.6i			0.153552i
$630$	−239787.	−	269099.i	−0.604150	−	0.678001i
$631$	−615464.			−1.54577			−0.772884	−	0.634548i	$-0.781186\pi$
$631$	−615464.			−1.54577			−0.772884	+	0.634548i	$0.781186\pi$
$632$			402160.i			1.00685i
$633$	114109.	+	51158.7i	0.284781	+	0.127677i
$634$	−1.20227e6			−2.99105
$635$		−	128931.i		−	0.319750i
$636$	−209804.	+	467963.i	−0.518679	+	1.15691i
$637$	−168420.			−0.415065
$638$			335972.i			0.825394i
$639$	−147753.	+	131659.i	−0.361854	+	0.322439i
$640$	339848.			0.829706
$641$			455836.i			1.10941i	0.832047	+	0.554705i	$0.187169\pi$
$641$			455836.i			1.10941i	−0.832047	+	0.554705i	$0.812831\pi$
$642$	343815.	+	154144.i	0.834170	+	0.373986i
$643$	225848.			0.546254			0.273127	−	0.961978i	$-0.411942\pi$
$643$	225848.			0.546254			0.273127	+	0.961978i	$0.411942\pi$
$644$		−	287085.i		−	0.692211i
$645$	152231.	−	339550.i	0.365919	−	0.816176i
$646$	548828.			1.31514
$647$		−	630061.i		−	1.50513i	−0.658517	−	0.752566i	$-0.728816\pi$
$647$		−	630061.i		−	1.50513i	0.658517	−	0.752566i	$-0.271184\pi$
$648$	455514.	+	52649.4i	1.08480	+	0.125384i
$649$	−23581.3			−0.0559859
$650$		−	747946.i		−	1.77029i
$651$	482518.	+	216329.i	1.13855	+	0.510449i
$652$	959635.			2.25741
$653$		−	638162.i		−	1.49660i	−0.663363	−	0.748298i	$-0.730871\pi$
$653$		−	638162.i		−	1.49660i	0.663363	−	0.748298i	$-0.269129\pi$
$654$	74158.7	−	165410.i	0.173383	−	0.386728i
$655$	−137552.			−0.320616
$656$		−	63002.0i		−	0.146402i
$657$	−30450.3	−	34172.5i	−0.0705441	−	0.0791674i
$658$	−35912.3			−0.0829452
$659$		−	146902.i		−	0.338266i	−0.985593	−	0.169133i	$-0.945903\pi$
$659$		−	146902.i		−	0.338266i	0.985593	−	0.169133i	$-0.0540967\pi$
$660$	−97821.4	−	43856.6i	−0.224567	−	0.100681i
$661$	−329362.			−0.753824			−0.376912	−	0.926249i	$-0.623014\pi$
$661$	−329362.			−0.753824			−0.376912	+	0.926249i	$0.623014\pi$
$662$			370351.i			0.845081i
$663$	−323109.	+	720690.i	−0.735060	+	1.63954i
$664$	−332997.			−0.755274
$665$		−	156930.i		−	0.354864i
$666$	−65862.8	+	58688.7i	−0.148488	+	0.132314i
$667$	272187.			0.611809
$668$		−	1.31359e6i		−	2.94379i
$669$	−159077.	−	71319.7i	−0.355432	−	0.159352i
$670$	−500842.			−1.11571
$671$		−	23573.4i		−	0.0523574i
$672$	189686.	−	423090.i	0.420045	−	0.936903i
$673$	83654.5			0.184697			0.0923483	−	0.995727i	$-0.470563\pi$
$673$	83654.5			0.184697			0.0923483	+	0.995727i	$0.470563\pi$
$674$		−	321504.i		−	0.707728i
$675$	−104538.	−	330444.i	−0.229439	−	0.725254i
$676$	−785051.			−1.71793
$677$			505261.i			1.10240i	0.834374	+	0.551199i	$0.185829\pi$
$677$			505261.i			1.10240i	−0.834374	+	0.551199i	$0.814171\pi$
$678$	1.15657e6	+	518528.i	2.51601	+	1.12801i
$679$	198296.			0.430105
$680$		−	311548.i		−	0.673764i
$681$	99386.3	−	221679.i	0.214305	−	0.478004i
$682$	251541.			0.540803
$683$		−	775320.i		−	1.66203i	−0.556247	−	0.831017i	$-0.687759\pi$
$683$		−	775320.i		−	1.66203i	0.556247	−	0.831017i	$-0.312241\pi$
$684$	331506.	+	372029.i	0.708564	+	0.795179i
$685$	248439.			0.529467
$686$			619067.i			1.31550i
$687$	−170424.	−	76406.9i	−0.361092	−	0.161890i
$688$	−99862.2			−0.210972
$689$		−	513914.i		−	1.08256i
$690$	−56825.2	+	126748.i	−0.119356	+	0.266221i
$691$	−70726.3			−0.148124			−0.0740619	−	0.997254i	$-0.523596\pi$
$691$	−70726.3			−0.148124			−0.0740619	+	0.997254i	$0.523596\pi$
$692$			383580.i			0.801021i
$693$	−122851.	+	109469.i	−0.255807	+	0.227943i
$694$	−475016.			−0.986255
$695$		−	119483.i		−	0.247364i
$696$	−808917.	−	362664.i	−1.66988	−	0.748663i
$697$	777393.			1.60020
$698$			823595.i			1.69045i
$699$	−191207.	+	426483.i	−0.391335	+	0.872866i
$700$	706717.			1.44228
$701$			97279.2i			0.197963i	0.995089	+	0.0989815i	$0.0315585\pi$
$701$			97279.2i			0.197963i	−0.995089	+	0.0989815i	$0.968442\pi$
$702$	−1.09346e6	+	345924.i	−2.21885	+	0.701951i
$703$	−38409.1			−0.0777183
$704$		−	237803.i		−	0.479814i
$705$	9913.60	+	4444.60i	0.0199459	+	0.00894240i
$706$	188914.			0.379015
$707$		−	606430.i		−	1.21323i
$708$	63532.5	−	141708.i	0.126745	−	0.282702i
$709$	−517960.			−1.03039			−0.515197	−	0.857072i	$-0.672281\pi$
$709$	−517960.			−1.03039			−0.515197	+	0.857072i	$0.672281\pi$
$710$			195248.i			0.387319i
$711$	−310078.	−	347982.i	−0.613384	−	0.688364i
$712$	−803277.			−1.58455
$713$		−	203785.i		−	0.400861i
$714$	−1.08909e6	−	488276.i	−2.13633	−	0.957788i
$715$	107427.			0.210136
$716$			837306.i			1.63327i
$717$	49131.2	−	109586.i	0.0955694	−	0.213166i
$718$	−662467.			−1.28504
$719$		−	359186.i		−	0.694803i	−0.937716	−	0.347401i	$-0.887064\pi$
$719$		−	359186.i		−	0.694803i	0.937716	−	0.347401i	$-0.112936\pi$
$720$	21847.3	−	19467.6i	0.0421437	−	0.0375532i
$721$	−243726.			−0.468847
$722$		−	504559.i		−	0.967916i
$723$	301099.	+	134993.i	0.576013	+	0.258246i
$724$	1.05956e6			2.02138
$725$			670043.i			1.27475i
$726$	−32021.6	+	71423.6i	−0.0607533	+	0.135509i
$727$	62474.1			0.118204			0.0591019	−	0.998252i	$-0.481176\pi$
$727$	62474.1			0.118204			0.0591019	+	0.998252i	$0.481176\pi$
$728$		−	936969.i		−	1.76792i
$729$	−434743.	+	305660.i	−0.818046	+	0.575152i
$730$	−45157.2			−0.0847386
$731$		−	1.23222e6i		−	2.30597i
$732$	141661.	+	63511.3i	0.264380	+	0.118530i
$733$	505895.			0.941570			0.470785	−	0.882248i	$-0.343971\pi$
$733$	505895.			0.941570			0.470785	+	0.882248i	$0.343971\pi$
$734$			463397.i			0.860124i
$735$	−31499.3	+	70258.6i	−0.0583077	+	0.130054i
$736$	−178687.			−0.329866
$737$			228648.i			0.420952i
$738$	750995.	+	842796.i	1.37887	+	1.54743i
$739$	251495.			0.460512			0.230256	−	0.973130i	$-0.426044\pi$
$739$	251495.			0.460512			0.230256	+	0.973130i	$0.426044\pi$
$740$			54418.8i			0.0993769i
$741$	−455643.	−	204280.i	−0.829828	−	0.372040i
$742$	776616.			1.41058
$743$			428180.i			0.775620i	0.921739	+	0.387810i	$0.126768\pi$
$743$			428180.i			0.775620i	−0.921739	+	0.387810i	$0.873232\pi$
$744$	−271525.	+	605633.i	−0.490529	+	1.09412i
$745$	308308.			0.555485
$746$			1.69970e6i			3.05418i
$747$	288137.	−	256752.i	0.516367	−	0.460122i
$748$	−354992.			−0.634476
$749$		−	356762.i		−	0.635937i
$750$	−722193.	−	323783.i	−1.28390	−	0.575614i
$751$	−882284.			−1.56433			−0.782165	−	0.623071i	$-0.785885\pi$
$751$	−882284.			−1.56433			−0.782165	+	0.623071i	$0.785885\pi$
$752$		−	2915.61i		−	0.00515577i
$753$	207437.	−	462685.i	0.365844	−	0.816009i
$754$	2.21722e6			3.90001
$755$			17637.7i			0.0309420i
$756$	−326856.	−	1.03318e6i	−0.571890	−	1.80773i
$757$	494040.			0.862125			0.431063	−	0.902322i	$-0.358139\pi$
$757$	494040.			0.862125			0.431063	+	0.902322i	$0.358139\pi$
$758$			603482.i			1.05033i
$759$	57863.8	+	25942.3i	0.100444	+	0.0450323i
$760$	196971.			0.341016
$761$			712584.i			1.23046i	0.788348	+	0.615229i	$0.210936\pi$
$761$			712584.i			1.23046i	−0.788348	+	0.615229i	$0.789064\pi$
$762$	253626.	−	565709.i	0.436801	−	0.974278i
$763$	−171638.			−0.294826
$764$		−	258343.i		−	0.442598i
$765$	240214.	+	269578.i	0.410465	+	0.460640i
$766$	−642632.			−1.09523
$767$			155623.i			0.264535i
$768$	634660.	+	284539.i	1.07602	+	0.482414i
$769$	159565.			0.269826			0.134913	−	0.990857i	$-0.456924\pi$
$769$	159565.			0.269826			0.134913	+	0.990857i	$0.456924\pi$
$770$			162341.i			0.273808i
$771$	−209106.	+	466407.i	−0.351769	+	0.784614i
$772$	−1.34975e6			−2.26475
$773$		−	23188.7i		−	0.0388077i	−0.999812	−	0.0194038i	$-0.993823\pi$
$773$		−	23188.7i		−	0.0388077i	0.999812	−	0.0194038i	$-0.00617682\pi$
$774$	1.33589e6	−	1.19038e6i	2.22991	−	1.98702i
$775$	501659.			0.835228
$776$			248891.i			0.413320i
$777$	76218.8	+	34171.4i	0.126247	+	0.0566006i
$778$	104327.			0.172360
$779$			491492.i			0.809919i
$780$	−289428.	+	645564.i	−0.475720	+	1.06108i
$781$	89135.9			0.146134
$782$			459964.i			0.752161i
$783$	979569.	−	309894.i	1.59776	−	0.505463i
$784$	20663.2			0.0336175
$785$			227738.i			0.369569i
$786$	−603536.	−	270585.i	−0.976918	−	0.437985i
$787$	−1.10276e6			−1.78045			−0.890226	−	0.455519i	$-0.849454\pi$
$787$	−1.10276e6			−1.78045			−0.890226	+	0.455519i	$0.849454\pi$
$788$			1.21843e6i			1.96222i
$789$	155782.	−	347469.i	0.250244	−	0.558164i
$790$	−459841.			−0.736806
$791$		−	1.20012e6i		−	1.91810i
$792$	−137401.	−	154196.i	−0.219048	−	0.245824i
$793$	−155571.			−0.247390
$794$			1.04358e6i			1.65533i
$795$	−214385.	−	96116.1i	−0.339204	−	0.152076i
$796$	596624.			0.941617
$797$		−	341644.i		−	0.537845i	−0.963162	−	0.268923i	$-0.913332\pi$
$797$		−	341644.i		−	0.537845i	0.963162	−	0.268923i	$-0.0866676\pi$
$798$	308704.	−	688558.i	0.484770	−	1.08127i
$799$	35976.3			0.0563537
$800$		−	439874.i		−	0.687303i
$801$	695062.	−	619353.i	1.08332	−	0.965324i
$802$	967427.			1.50408
$803$			20615.5i			0.0319715i
$804$	−1.37402e6	−	616021.i	−2.12560	−	0.952979i
$805$	131520.			0.202956
$806$		−	1.66002e6i		−	2.55531i
$807$	−254389.	+	567410.i	−0.390617	+	0.871264i
$808$	761161.			1.16588
$809$		−	265521.i		−	0.405696i	−0.979210	−	0.202848i	$-0.934980\pi$
$809$		−	265521.i		−	0.405696i	0.979210	−	0.202848i	$-0.0650198\pi$
$810$	−60200.7	+	520847.i	−0.0917554	+	0.793853i
$811$	−1.11340e6			−1.69282			−0.846411	−	0.532530i	$-0.821241\pi$
$811$	−1.11340e6			−1.69282			−0.846411	+	0.532530i	$0.821241\pi$
$812$			2.09499e6i			3.17739i
$813$	−197638.	−	88607.5i	−0.299012	−	0.134057i
$814$	39733.5			0.0599664
$815$			439632.i			0.661872i
$816$	39641.7	−	88420.2i	0.0595349	−	0.132792i
$817$	779047.			1.16713
$818$		−	1.49057e6i		−	2.22765i
$819$	722434.	+	810744.i	1.07704	+	1.20869i
$820$	696356.			1.03563
$821$			510010.i			0.756645i	0.925674	+	0.378323i	$0.123499\pi$
$821$			510010.i			0.756645i	−0.925674	+	0.378323i	$0.876501\pi$
$822$	1.09007e6	+	488716.i	1.61329	+	0.723290i
$823$	−945709.			−1.39623			−0.698117	−	0.715984i	$-0.745978\pi$
$823$	−945709.			−1.39623			−0.698117	+	0.715984i	$0.745978\pi$
$824$		−	305913.i		−	0.450550i
$825$	−63862.1	+	142443.i	−0.0938286	+	0.209283i
$826$	−235174.			−0.344691
$827$			950428.i			1.38966i	0.719174	+	0.694830i	$0.244520\pi$
$827$			950428.i			1.38966i	−0.719174	+	0.694830i	$0.755480\pi$
$828$	−311792.	+	277830.i	−0.454783	+	0.405246i
$829$	−1.29593e6			−1.88569			−0.942847	−	0.333227i	$-0.891863\pi$
$829$	−1.29593e6			−1.88569			−0.942847	+	0.333227i	$0.891863\pi$
$830$		−	380758.i		−	0.552705i
$831$	862496.	+	386686.i	1.24898	+	0.559959i
$832$	−1.56936e6			−2.26713
$833$			254967.i			0.367446i
$834$	235041.	−	524254.i	0.337918	−	0.753720i
$835$	601786.			0.863116
$836$		−	224437.i		−	0.321131i
$837$	−232016.	−	733400.i	−0.331183	−	1.04686i
$838$	−1.92084e6			−2.73528
$839$			1.10661e6i			1.57206i	0.618186	+	0.786032i	$0.287868\pi$
$839$			1.10661e6i			1.57206i	−0.618186	+	0.786032i	$0.712132\pi$
$840$	−390868.	−	175239.i	−0.553951	−	0.248355i
$841$	−1.27900e6			−1.80833
$842$		−	743791.i		−	1.04912i
$843$	−293477.	+	654596.i	−0.412971	+	0.921124i
$844$	370931.			0.520725
$845$		−	359650.i		−	0.503694i
$846$	34754.6	+	39003.0i	0.0485592	+	0.0544951i
$847$	74113.2			0.103307
$848$			63051.1i			0.0876802i
$849$	−393552.	−	176443.i	−0.545993	−	0.244787i
$850$	−1.13229e6			−1.56719
$851$		−	32190.1i		−	0.0444491i
$852$	−240149.	+	535648.i	−0.330827	+	0.737905i
$853$	−119139.			−0.163740			−0.0818699	−	0.996643i	$-0.526089\pi$
$853$	−119139.			−0.163740			−0.0818699	+	0.996643i	$0.526089\pi$
$854$		−	235096.i		−	0.322351i
$855$	−170436.	+	151871.i	−0.233146	+	0.207751i
$856$	447790.			0.611120
$857$		−	371725.i		−	0.506128i	−0.967450	−	0.253064i	$-0.918562\pi$
$857$		−	371725.i		−	0.506128i	0.967450	−	0.253064i	$-0.0814383\pi$
$858$	471354.	+	211324.i	0.640284	+	0.287061i
$859$	696088.			0.943361			0.471680	−	0.881770i	$-0.343648\pi$
$859$	696088.			0.943361			0.471680	+	0.881770i	$0.343648\pi$
$860$		−	1.10377e6i		−	1.49239i
$861$	437266.	−	975315.i	0.589847	−	1.31564i
$862$	−491731.			−0.661779
$863$			204621.i			0.274744i	0.990520	+	0.137372i	$0.0438656\pi$
$863$			204621.i			0.274744i	−0.990520	+	0.137372i	$0.956134\pi$
$864$	−643073.	+	203441.i	−0.861456	+	0.272528i
$865$	−175727.			−0.234859
$866$		−	2.26595e6i		−	3.02145i
$867$	405124.	+	181631.i	0.538952	+	0.241630i
$868$	1.56851e6			2.08185
$869$			209930.i			0.277994i
$870$	414680.	−	924938.i	0.547867	−	1.22201i
$871$	1.50894e6			1.98901
$872$		−	215432.i		−	0.283320i
$873$	−191903.	−	215362.i	−0.251799	−	0.282579i
$874$	−290804.			−0.380695
$875$			749388.i			0.978792i
$876$	−123886.	−	55542.1i	−0.161441	−	0.0723793i
$877$	−219352.			−0.285195			−0.142598	−	0.989781i	$-0.545546\pi$
$877$	−219352.			−0.285195			−0.142598	+	0.989781i	$0.545546\pi$
$878$		−	2.22074e6i		−	2.88077i
$879$	−286400.	+	638809.i	−0.370676	+	0.826787i
$880$	−13180.0			−0.0170196
$881$			222752.i			0.286992i	0.989651	+	0.143496i	$0.0458344\pi$
$881$			222752.i			0.286992i	−0.989651	+	0.143496i	$0.954166\pi$
$882$	−276418.	+	246309.i	−0.355327	+	0.316623i
$883$	696113.			0.892808			0.446404	−	0.894831i	$-0.352704\pi$
$883$	696113.			0.892808			0.446404	+	0.894831i	$0.352704\pi$
$884$			2.34274e6i			2.99791i
$885$	64920.0	+	29105.8i	0.0828880	+	0.0371615i
$886$	2.29978e6			2.92967
$887$		−	1.33561e6i		−	1.69759i	−0.528725	−	0.848793i	$-0.677330\pi$
$887$		−	1.33561e6i		−	1.69759i	0.528725	−	0.848793i	$-0.322670\pi$
$888$	−42890.3	+	95666.2i	−0.0543918	+	0.121320i
$889$	−587011.			−0.742750
$890$		−	918489.i		−	1.15956i
$891$	237781.	+	27483.3i	0.299517	+	0.0346189i
$892$	−517111.			−0.649911
$893$			22745.3i			0.0285226i
$894$	1.35276e6	+	606487.i	1.69256	+	0.758833i
$895$	−383590.			−0.478874
$896$		−	1.54729e6i		−	1.92733i
$897$	171204.	−	381867.i	0.212779	−	0.474600i
$898$	−1.08710e6			−1.34809
$899$			1.48712e6i			1.84004i
$900$	−683935.	−	767539.i	−0.844364	−	0.947578i
$901$	−778000.			−0.958363
$902$		−	508440.i		−	0.624923i
$903$	−1.54594e6	−	693095.i	−1.89590	−	0.849997i
$904$	1.50633e6			1.84325
$905$			485409.i			0.592667i
$906$	−34695.9	+	77388.7i	−0.0422690	+	0.0942804i
$907$	1.13627e6			1.38124			0.690618	−	0.723220i	$-0.257339\pi$
$907$	1.13627e6			1.38124			0.690618	+	0.723220i	$0.257339\pi$
$908$		−	720610.i		−	0.874035i
$909$	−658620.	+	586880.i	−0.797090	+	0.710267i
$910$	1.07136e6			1.29375
$911$			704097.i			0.848390i	0.905571	+	0.424195i	$0.139443\pi$
$911$			704097.i			0.848390i	−0.905571	+	0.424195i	$0.860557\pi$
$912$	55902.0	+	25062.7i	0.0672106	+	0.0301327i
$913$	−173827.			−0.208533
$914$			1.90027e6i			2.27469i
$915$	−29096.1	+	64898.3i	−0.0347530	+	0.0775159i
$916$	−553996.			−0.660261
$917$			626263.i			0.744763i
$918$	523685.	+	1.65536e6i	0.621419	+	1.96429i
$919$	71450.5			0.0846008			0.0423004	−	0.999105i	$-0.486531\pi$
$919$	71450.5			0.0846008			0.0423004	+	0.999105i	$0.486531\pi$
$920$			165078.i			0.195035i
$921$	840895.	+	377001.i	0.991339	+	0.444450i
$922$	−71020.2			−0.0835449
$923$		−	588245.i		−	0.690486i
$924$	−199675.	+	445372.i	−0.233873	+	0.521649i
$925$	79242.3			0.0926133
$926$			1.68961e6i			1.97044i
$927$	235869.	+	264701.i	0.274480	+	0.308032i
$928$	1.30396e6			1.51415
$929$		−	21830.7i		−	0.0252951i	−0.999920	−	0.0126475i	$-0.995974\pi$
$929$		−	21830.7i		−	0.0252951i	0.999920	−	0.0126475i	$-0.00402594\pi$
$930$	−692497.	−	310470.i	−0.800668	−	0.358966i
$931$	−161198.			−0.185977
$932$			1.38636e6i			1.59605i
$933$	476512.	−	1.06285e6i	0.547408	−	1.22098i
$934$	1.03223e6			1.18326
$935$		−	162630.i		−	0.186028i
$936$	−1.01761e6	+	906764.i	−1.16152	+	1.03501i
$937$	904804.			1.03057			0.515283	−	0.857020i	$-0.327687\pi$
$937$	904804.			1.03057			0.515283	+	0.857020i	$0.327687\pi$
$938$			2.28029e6i			2.59169i
$939$	−124567.	−	55847.3i	−0.141277	−	0.0633390i
$940$	32226.0			0.0364713
$941$		−	521870.i		−	0.589363i	−0.955595	−	0.294682i	$-0.904786\pi$
$941$		−	521870.i		−	0.589363i	0.955595	−	0.294682i	$-0.0952136\pi$
$942$	−447993.	+	999240.i	−0.504858	+	1.12608i
$943$	−411912.			−0.463213
$944$		−	19093.1i		−	0.0214256i
$945$	473327.	−	149740.i	0.530026	−	0.167678i
$946$	−805910.			−0.900543
$947$		−	204829.i		−	0.228397i	−0.993458	−	0.114199i	$-0.963570\pi$
$947$		−	204829.i		−	0.228397i	0.993458	−	0.114199i	$-0.0364301\pi$
$948$	−1.26154e6	−	565591.i	−1.40373	−	0.629340i
$949$	136050.			0.151066
$950$		−	715872.i		−	0.793210i
$951$	677455.	−	1.51105e6i	0.749065	−	1.67078i
$952$	−1.41845e6			−1.56509
$953$		−	883943.i		−	0.973281i	−0.873602	−	0.486641i	$-0.838222\pi$
$953$		−	883943.i		−	0.973281i	0.873602	−	0.486641i	$-0.161778\pi$
$954$	−751581.	−	843454.i	−0.825807	−	0.926754i
$955$	118353.			0.129769
$956$		−	356231.i		−	0.389776i
$957$	−422260.	−	189313.i	−0.461058	−	0.206708i
$958$	−1.65426e6			−1.80249
$959$		−	1.13112e6i		−	1.22990i
$960$	−293514.	+	654678.i	−0.318483	+	0.710371i
$961$	189879.			0.205604
$962$		−	262218.i		−	0.283343i
$963$	−387465.	+	345261.i	−0.417811	+	0.372301i
$964$	978777.			1.05325
$965$		−	618354.i		−	0.664022i
$966$	577070.	+	258720.i	0.618407	+	0.277252i
$967$	209664.			0.224218			0.112109	−	0.993696i	$-0.464239\pi$
$967$	209664.			0.224218			0.112109	+	0.993696i	$0.464239\pi$
$968$			93023.2i			0.0992752i
$969$	−309253.	+	689785.i	−0.329357	+	0.734626i
$970$	−284589.			−0.302465
$971$			469766.i			0.498246i	0.968472	+	0.249123i	$0.0801423\pi$
$971$			469766.i			0.498246i	−0.968472	+	0.249123i	$0.919858\pi$
$972$	−805784.	+	1.35486e6i	−0.852876	+	1.43405i
$973$	−543996.			−0.574606
$974$		−	1.21008e6i		−	1.27555i
$975$	940043.	+	421452.i	0.988868	+	0.443342i
$976$	19086.7			0.0200369
$977$		−	458939.i		−	0.480801i	−0.970674	−	0.240401i	$-0.922721\pi$
$977$		−	458939.i		−	0.480801i	0.970674	−	0.240401i	$-0.0772789\pi$
$978$	−864819.	+	1.92896e6i	−0.904165	+	2.01672i
$979$	−419315.			−0.437497
$980$			228389.i			0.237806i
$981$	166105.	+	186410.i	0.172602	+	0.193701i
$982$	−101127.			−0.104868
$983$			1.11358e6i			1.15243i	0.817297	+	0.576217i	$0.195472\pi$
$983$			1.11358e6i			1.15243i	−0.817297	+	0.576217i	$0.804528\pi$
$984$	1.22417e6	+	548835.i	1.26430	+	0.566829i
$985$	−558191.			−0.575321
$986$		−	3.35658e6i		−	3.45258i
$987$	20235.8	−	45135.7i	0.0207724	−	0.0463325i
$988$	−1.48115e6			−1.51735
$989$			652907.i			0.667511i
$990$	176312.	−	157108.i	0.179892	−	0.160298i
$991$	690091.			0.702682			0.351341	−	0.936248i	$-0.385726\pi$
$991$	690091.			0.702682			0.351341	+	0.936248i	$0.385726\pi$
$992$		−	976273.i		−	0.992082i
$993$	−465469.	−	208685.i	−0.472055	−	0.211638i
$994$	888944.			0.899708
$995$			273328.i			0.276082i
$996$	468322.	−	1.04458e6i	0.472091	−	1.05299i
$997$	978433.			0.984330			0.492165	−	0.870502i	$-0.336206\pi$
$997$	978433.			0.984330			0.492165	+	0.870502i	$0.336206\pi$
$998$			1.37615e6i			1.38167i
$999$	−36649.5	−	115848.i	−0.0367229	−	0.116080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.5.b.a.23.13	yes	14
3.2	odd	2	inner	33.5.b.a.23.2	✓	14
4.3	odd	2		528.5.i.d.353.14		14
12.11	even	2		528.5.i.d.353.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.b.a.23.2	✓	14	3.2	odd	2	inner
33.5.b.a.23.13	yes	14	1.1	even	1	trivial
528.5.i.d.353.13		14	12.11	even	2
528.5.i.d.353.14		14	4.3	odd	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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.53421i q^{2} +(-8.21241 - 3.68190i) q^{3} -26.6960 q^{4} -12.2301i q^{5} +(24.0583 - 53.6616i) q^{6} -55.6823 q^{7} -69.8897i q^{8} +(53.8873 + 60.4745i) q^{9} +O(q^{10})\)	\(q+6.53421i q^{2} +(-8.21241 - 3.68190i) q^{3} -26.6960 q^{4} -12.2301i q^{5} +(24.0583 - 53.6616i) q^{6} -55.6823 q^{7} -69.8897i q^{8} +(53.8873 + 60.4745i) q^{9} +79.9138 q^{10} -36.4829i q^{11} +(219.238 + 98.2918i) q^{12} -240.766 q^{13} -363.840i q^{14} +(-45.0298 + 100.438i) q^{15} +29.5391 q^{16} +364.488i q^{17} +(-395.153 + 352.111i) q^{18} -230.441 q^{19} +326.493i q^{20} +(457.286 + 205.016i) q^{21} +238.387 q^{22} -193.129i q^{23} +(-257.327 + 573.963i) q^{24} +475.426 q^{25} -1573.21i q^{26} +(-219.884 - 695.048i) q^{27} +1486.49 q^{28} +1409.35i q^{29} +(-656.285 - 294.234i) q^{30} +1055.18 q^{31} -925.221i q^{32} +(-134.326 + 299.612i) q^{33} -2381.64 q^{34} +680.998i q^{35} +(-1438.57 - 1614.42i) q^{36} +166.677 q^{37} -1505.75i q^{38} +(1977.27 + 886.474i) q^{39} -854.756 q^{40} -2132.83i q^{41} +(-1339.62 + 2988.00i) q^{42} -3380.68 q^{43} +973.945i q^{44} +(739.606 - 659.045i) q^{45} +1261.95 q^{46} -98.7035i q^{47} +(-242.587 - 108.760i) q^{48} +699.520 q^{49} +3106.53i q^{50} +(1342.01 - 2993.33i) q^{51} +6427.47 q^{52} +2134.50i q^{53} +(4541.60 - 1436.77i) q^{54} -446.188 q^{55} +3891.62i q^{56} +(1892.47 + 848.459i) q^{57} -9209.02 q^{58} -646.367i q^{59} +(1202.11 - 2681.30i) q^{60} +646.151 q^{61} +6894.76i q^{62} +(-3000.57 - 3367.36i) q^{63} +6518.22 q^{64} +2944.58i q^{65} +(-1957.73 - 877.716i) q^{66} -6267.27 q^{67} -9730.37i q^{68} +(-711.080 + 1586.05i) q^{69} -4449.79 q^{70} +2443.23i q^{71} +(4226.54 - 3766.17i) q^{72} -565.074 q^{73} +1089.10i q^{74} +(-3904.39 - 1750.47i) q^{75} +6151.84 q^{76} +2031.45i q^{77} +(-5792.41 + 12919.9i) q^{78} -5754.20 q^{79} -361.265i q^{80} +(-753.321 + 6517.61i) q^{81} +13936.4 q^{82} -4764.61i q^{83} +(-12207.7 - 5473.11i) q^{84} +4457.71 q^{85} -22090.1i q^{86} +(5189.09 - 11574.2i) q^{87} -2549.78 q^{88} -11493.5i q^{89} +(4306.34 + 4832.75i) q^{90} +13406.4 q^{91} +5155.76i q^{92} +(-8665.55 - 3885.05i) q^{93} +644.950 q^{94} +2818.31i q^{95} +(-3406.57 + 7598.29i) q^{96} -3561.20 q^{97} +4570.81i q^{98} +(2206.28 - 1965.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9}+O(q^{10}) \) 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9	\( 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9} - 156 q^{10} - 100 q^{12} - 104 q^{13} + 151 q^{15} + 356 q^{16} - 34 q^{18} + 1072 q^{19} + 718 q^{21} + 1200 q^{24} - 1060 q^{25} - 1154 q^{27} - 1808 q^{28} - 3026 q^{30} + 3310 q^{31} - 605 q^{33} - 2304 q^{34} + 2644 q^{36} - 362 q^{37} + 4264 q^{39} + 1896 q^{40} - 7364 q^{42} - 6740 q^{43} + 3611 q^{45} - 4068 q^{46} - 2956 q^{48} + 7074 q^{49} - 7046 q^{51} + 13072 q^{52} + 20512 q^{54} + 726 q^{55} + 3876 q^{57} - 7848 q^{58} - 8416 q^{60} - 3560 q^{61} - 17662 q^{63} + 12020 q^{64} + 1210 q^{66} - 16514 q^{67} + 9833 q^{69} + 13320 q^{70} + 8160 q^{72} + 12664 q^{73} - 5386 q^{75} - 43736 q^{76} + 19096 q^{78} + 3052 q^{79} - 11611 q^{81} + 10200 q^{82} - 39184 q^{84} + 34884 q^{85} + 37068 q^{87} - 7260 q^{88} - 26686 q^{90} - 45856 q^{91} + 2719 q^{93} + 6120 q^{94} - 38368 q^{96} - 27854 q^{97} + 4235 q^{99}+O(q^{100}) \) 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9 - 156 * q^10 - 100 * q^12 - 104 * q^13 + 151 * q^15 + 356 * q^16 - 34 * q^18 + 1072 * q^19 + 718 * q^21 + 1200 * q^24 - 1060 * q^25 - 1154 * q^27 - 1808 * q^28 - 3026 * q^30 + 3310 * q^31 - 605 * q^33 - 2304 * q^34 + 2644 * q^36 - 362 * q^37 + 4264 * q^39 + 1896 * q^40 - 7364 * q^42 - 6740 * q^43 + 3611 * q^45 - 4068 * q^46 - 2956 * q^48 + 7074 * q^49 - 7046 * q^51 + 13072 * q^52 + 20512 * q^54 + 726 * q^55 + 3876 * q^57 - 7848 * q^58 - 8416 * q^60 - 3560 * q^61 - 17662 * q^63 + 12020 * q^64 + 1210 * q^66 - 16514 * q^67 + 9833 * q^69 + 13320 * q^70 + 8160 * q^72 + 12664 * q^73 - 5386 * q^75 - 43736 * q^76 + 19096 * q^78 + 3052 * q^79 - 11611 * q^81 + 10200 * q^82 - 39184 * q^84 + 34884 * q^85 + 37068 * q^87 - 7260 * q^88 - 26686 * q^90 - 45856 * q^91 + 2719 * q^93 + 6120 * q^94 - 38368 * q^96 - 27854 * q^97 + 4235 * q^99

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