LMFDB - Embedded newform 165.6.f.a.131.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(131,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.131");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.f (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:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.57
Character	$\chi$	$=$	165.131
Dual form			165.6.f.a.131.58

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.10019 q^{2} +(-8.98370 + 12.7394i) q^{3} +5.21231 q^{4} +25.0000i q^{5} +(-54.8023 + 77.7129i) q^{6} +135.027i q^{7} -163.410 q^{8} +(-81.5861 - 228.895i) q^{9} +O(q^{10})$	\(q+6.10019 q^{2} +(-8.98370 + 12.7394i) q^{3} +5.21231 q^{4} +25.0000i q^{5} +(-54.8023 + 77.7129i) q^{6} +135.027i q^{7} -163.410 q^{8} +(-81.5861 - 228.895i) q^{9} +152.505i q^{10} +(-8.52928 + 401.221i) q^{11} +(-46.8258 + 66.4018i) q^{12} -924.545i q^{13} +823.688i q^{14} +(-318.486 - 224.593i) q^{15} -1163.63 q^{16} +526.034 q^{17} +(-497.691 - 1396.30i) q^{18} -1792.55i q^{19} +130.308i q^{20} +(-1720.16 - 1213.04i) q^{21} +(-52.0302 + 2447.52i) q^{22} +752.129i q^{23} +(1468.03 - 2081.75i) q^{24} -625.000 q^{25} -5639.90i q^{26} +(3648.93 + 1016.96i) q^{27} +703.800i q^{28} -4638.26 q^{29} +(-1942.82 - 1370.06i) q^{30} -126.504 q^{31} -1869.22 q^{32} +(-5034.70 - 3713.11i) q^{33} +3208.91 q^{34} -3375.67 q^{35} +(-425.252 - 1193.07i) q^{36} -14307.0 q^{37} -10934.9i q^{38} +(11778.2 + 8305.84i) q^{39} -4085.25i q^{40} -5898.93 q^{41} +(-10493.3 - 7399.77i) q^{42} -12896.4i q^{43} +(-44.4572 + 2091.29i) q^{44} +(5722.36 - 2039.65i) q^{45} +4588.13i q^{46} -21380.5i q^{47} +(10453.7 - 14823.9i) q^{48} -1425.19 q^{49} -3812.62 q^{50} +(-4725.73 + 6701.37i) q^{51} -4819.02i q^{52} +24141.4i q^{53} +(22259.2 + 6203.65i) q^{54} +(-10030.5 - 213.232i) q^{55} -22064.7i q^{56} +(22836.1 + 16103.8i) q^{57} -28294.3 q^{58} -35668.0i q^{59} +(-1660.05 - 1170.65i) q^{60} +31568.0i q^{61} -771.700 q^{62} +(30906.9 - 11016.3i) q^{63} +25833.4 q^{64} +23113.6 q^{65} +(-30712.6 - 22650.7i) q^{66} -51032.9 q^{67} +2741.85 q^{68} +(-9581.69 - 6756.90i) q^{69} -20592.2 q^{70} +58996.3i q^{71} +(13332.0 + 37403.7i) q^{72} +56680.6i q^{73} -87275.3 q^{74} +(5614.81 - 7962.14i) q^{75} -9343.34i q^{76} +(-54175.5 - 1151.68i) q^{77} +(71849.1 + 50667.2i) q^{78} +48573.2i q^{79} -29090.6i q^{80} +(-45736.4 + 37349.2i) q^{81} -35984.6 q^{82} +86938.3 q^{83} +(-8966.02 - 6322.73i) q^{84} +13150.8i q^{85} -78670.3i q^{86} +(41668.8 - 59088.8i) q^{87} +(1393.77 - 65563.5i) q^{88} +30949.9i q^{89} +(34907.5 - 12442.3i) q^{90} +124838. q^{91} +3920.33i q^{92} +(1136.48 - 1611.59i) q^{93} -130425. i q^{94} +44813.8 q^{95} +(16792.5 - 23812.8i) q^{96} -75401.2 q^{97} -8693.90 q^{98} +(92533.1 - 30781.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	6.10019			1.07837			0.539186	−	0.842187i	$-0.318732\pi$
$2$	6.10019			1.07837			0.539186	+	0.842187i	$0.318732\pi$
$3$	−8.98370	+	12.7394i	−0.576305	+	0.817235i
$3$	−8.98370	+	12.7394i	−0.576305	+	0.817235i
$4$	5.21231			0.162885
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	−54.8023	+	77.7129i	−0.621471	+	0.881283i
$7$			135.027i			1.04154i	0.853698	+	0.520768i	$0.174354\pi$
$7$			135.027i			1.04154i	−0.853698	+	0.520768i	$0.825646\pi$
$8$	−163.410			−0.902721
$9$	−81.5861	−	228.895i	−0.335745	−	0.941953i
$10$			152.505i			0.482262i
$11$	−8.52928	+	401.221i	−0.0212535	+	0.999774i
$11$	−8.52928	+	401.221i	−0.0212535	+	0.999774i
$12$	−46.8258	+	66.4018i	−0.0938712	+	0.133115i
$13$		−	924.545i		−	1.51729i	−0.651502	−	0.758647i	$-0.725861\pi$
$13$		−	924.545i		−	1.51729i	0.651502	−	0.758647i	$-0.274139\pi$
$14$			823.688i			1.12316i
$15$	−318.486	−	224.593i	−0.365479	−	0.257731i
$16$	−1163.63			−1.13635
$17$	526.034			0.441460			0.220730	−	0.975335i	$-0.429156\pi$
$17$	526.034			0.441460			0.220730	+	0.975335i	$0.429156\pi$
$18$	−497.691	−	1396.30i	−0.362058	−	1.01577i
$19$		−	1792.55i		−	1.13917i	−0.821933	−	0.569584i	$-0.807104\pi$
$19$		−	1792.55i		−	1.13917i	0.821933	−	0.569584i	$-0.192896\pi$
$20$			130.308i			0.0728442i
$21$	−1720.16	−	1213.04i	−0.851179	−	0.600242i
$22$	−52.0302	+	2447.52i	−0.0229192	+	1.07813i
$23$			752.129i			0.296464i	0.988953	+	0.148232i	$0.0473583\pi$
$23$			752.129i			0.296464i	−0.988953	+	0.148232i	$0.952642\pi$
$24$	1468.03	−	2081.75i	0.520243	−	0.737735i
$25$	−625.000			−0.200000
$26$		−	5639.90i		−	1.63621i
$27$	3648.93	+	1016.96i	0.963288	+	0.268469i
$28$			703.800i			0.169650i
$29$	−4638.26			−1.02414			−0.512071	−	0.858943i	$-0.671122\pi$
$29$	−4638.26			−1.02414			−0.512071	+	0.858943i	$0.671122\pi$
$30$	−1942.82	−	1370.06i	−0.394122	−	0.277930i
$31$	−126.504			−0.0236429			−0.0118214	−	0.999930i	$-0.503763\pi$
$31$	−126.504			−0.0236429			−0.0118214	+	0.999930i	$0.503763\pi$
$32$	−1869.22			−0.322690
$33$	−5034.70	−	3713.11i	−0.804802	−	0.593544i
$34$	3208.91			0.476058
$35$	−3375.67			−0.465789
$36$	−425.252	−	1193.07i	−0.0546878	−	0.153430i
$37$	−14307.0			−1.71808			−0.859040	−	0.511908i	$-0.828939\pi$
$37$	−14307.0			−1.71808			−0.859040	+	0.511908i	$0.828939\pi$
$38$		−	10934.9i		−	1.22845i
$39$	11778.2	+	8305.84i	1.23999	+	0.874424i
$40$		−	4085.25i		−	0.403709i
$41$	−5898.93			−0.548041			−0.274021	−	0.961724i	$-0.588354\pi$
$41$	−5898.93			−0.548041			−0.274021	+	0.961724i	$0.588354\pi$
$42$	−10493.3	−	7399.77i	−0.917887	−	0.647284i
$43$		−	12896.4i		−	1.06364i	−0.846856	−	0.531822i	$-0.821508\pi$
$43$		−	12896.4i		−	1.06364i	0.846856	−	0.531822i	$-0.178492\pi$
$44$	−44.4572	+	2091.29i	−0.00346187	+	0.162848i
$45$	5722.36	−	2039.65i	0.421254	−	0.150150i
$46$			4588.13i			0.319699i
$47$		−	21380.5i		−	1.41180i	−0.708313	−	0.705899i	$-0.750543\pi$
$47$		−	21380.5i		−	1.41180i	0.708313	−	0.705899i	$-0.249457\pi$
$48$	10453.7	−	14823.9i	0.654886	−	0.928667i
$49$	−1425.19			−0.0847971
$50$	−3812.62			−0.215674
$51$	−4725.73	+	6701.37i	−0.254416	+	0.360777i
$52$		−	4819.02i		−	0.247144i
$53$			24141.4i			1.18052i	0.807213	+	0.590260i	$0.200975\pi$
$53$			24141.4i			1.18052i	−0.807213	+	0.590260i	$0.799025\pi$
$54$	22259.2	+	6203.65i	1.03878	+	0.289509i
$55$	−10030.5	−	213.232i	−0.447113	−	0.00950486i
$56$		−	22064.7i		−	0.940217i
$57$	22836.1	+	16103.8i	0.930969	+	0.656509i
$58$	−28294.3			−1.10441
$59$		−	35668.0i		−	1.33398i	−0.745067	−	0.666989i	$-0.767583\pi$
$59$		−	35668.0i		−	1.33398i	0.745067	−	0.666989i	$-0.232417\pi$
$60$	−1660.05	−	1170.65i	−0.0595308	−	0.0419805i
$61$			31568.0i			1.08623i	0.839658	+	0.543116i	$0.182756\pi$
$61$			31568.0i			1.08623i	−0.839658	+	0.543116i	$0.817244\pi$
$62$	−771.700			−0.0254958
$63$	30906.9	−	11016.3i	0.981078	−	0.349691i
$64$	25833.4			0.788374
$65$	23113.6			0.678555
$66$	−30712.6	−	22650.7i	−0.867875	−	0.640061i
$67$	−51032.9			−1.38888			−0.694438	−	0.719553i	$-0.744347\pi$
$67$	−51032.9			−1.38888			−0.694438	+	0.719553i	$0.744347\pi$
$68$	2741.85			0.0719071
$69$	−9581.69	−	6756.90i	−0.242281	−	0.170854i
$70$	−20592.2			−0.502294
$71$			58996.3i			1.38893i	0.719528	+	0.694463i	$0.244358\pi$
$71$			58996.3i			1.38893i	−0.719528	+	0.694463i	$0.755642\pi$
$72$	13332.0	+	37403.7i	0.303084	+	0.850321i
$73$			56680.6i			1.24488i	0.782667	+	0.622440i	$0.213859\pi$
$73$			56680.6i			1.24488i	−0.782667	+	0.622440i	$0.786141\pi$
$74$	−87275.3			−1.85273
$75$	5614.81	−	7962.14i	0.115261	−	0.163447i
$76$		−	9343.34i		−	0.185553i
$77$	−54175.5	−	1151.68i	−1.04130	−	0.0221363i
$78$	71849.1	+	50667.2i	1.33716	+	0.942954i
$79$			48573.2i			0.875647i	0.899061	+	0.437824i	$0.144251\pi$
$79$			48573.2i			0.875647i	−0.899061	+	0.437824i	$0.855749\pi$
$80$		−	29090.6i		−	0.508193i
$81$	−45736.4	+	37349.2i	−0.774550	+	0.632513i
$82$	−35984.6			−0.590992
$83$	86938.3			1.38521			0.692606	−	0.721317i	$-0.256463\pi$
$83$	86938.3			1.38521			0.692606	+	0.721317i	$0.256463\pi$
$84$	−8966.02	−	6322.73i	−0.138644	−	0.0977703i
$85$			13150.8i			0.197427i
$86$		−	78670.3i		−	1.14700i
$87$	41668.8	−	59088.8i	0.590218	−	0.836965i
$88$	1393.77	−	65563.5i	0.0191860	−	0.902517i
$89$			30949.9i			0.414175i	0.978322	+	0.207087i	$0.0663985\pi$
$89$			30949.9i			0.414175i	−0.978322	+	0.207087i	$0.933602\pi$
$90$	34907.5	−	12442.3i	0.454268	−	0.161917i
$91$	124838.			1.58032
$92$			3920.33i			0.0482895i
$93$	1136.48	−	1611.59i	0.0136255	−	0.0193218i
$94$		−	130425.i		−	1.52244i
$95$	44813.8			0.509452
$96$	16792.5	−	23812.8i	0.185968	−	0.263713i
$97$	−75401.2			−0.813671			−0.406836	−	0.913501i	$-0.633368\pi$
$97$	−75401.2			−0.813671			−0.406836	+	0.913501i	$0.633368\pi$
$98$	−8693.90			−0.0914428
$99$	92533.1	−	30781.8i	0.948876	−	0.315650i
$100$	−3257.69			−0.0325769
$101$	−97555.7			−0.951589			−0.475794	−	0.879557i	$-0.657839\pi$
$101$	−97555.7			−0.951589			−0.475794	+	0.879557i	$0.657839\pi$
$102$	−28827.9	+	40879.6i	−0.274354	+	0.389051i
$103$	−55954.7			−0.519689			−0.259845	−	0.965650i	$-0.583671\pi$
$103$	−55954.7			−0.519689			−0.259845	+	0.965650i	$0.583671\pi$
$104$			151080.i			1.36969i
$105$	30326.0	−	43004.0i	0.268436	−	0.380659i
$106$			147267.i			1.27304i
$107$	−169982.			−1.43531			−0.717653	−	0.696401i	$-0.754783\pi$
$107$	−169982.			−1.43531			−0.717653	+	0.696401i	$0.754783\pi$
$108$	19019.4	+	5300.71i	0.156905	+	0.0437295i
$109$			28235.8i			0.227633i	0.993502	+	0.113816i	$0.0363075\pi$
$109$			28235.8i			0.227633i	−0.993502	+	0.113816i	$0.963692\pi$
$110$	−61188.1	−	1300.76i	−0.482153	−	0.0102498i
$111$	128530.	−	182263.i	0.990138	−	1.40408i
$112$		−	157120.i		−	1.18355i
$113$		−	59707.3i		−	0.439877i	−0.975514	−	0.219939i	$-0.929414\pi$
$113$		−	59707.3i		−	0.439877i	0.975514	−	0.219939i	$-0.0705857\pi$
$114$	139305.	+	98236.1i	1.00393	+	0.707960i
$115$	−18803.2			−0.132583
$116$	−24176.1			−0.166817
$117$	−211623.	+	75430.1i	−1.42922	+	0.509425i
$118$		−	217582.i		−	1.43852i
$119$			71028.6i			0.459797i
$120$	52043.7	+	36700.7i	0.329925	+	0.232660i
$121$	−160906.	−	6844.25i	−0.999097	−	0.0424974i
$122$			192571.i			1.17136i
$123$	52994.2	−	75148.9i	0.315839	−	0.447878i
$124$	−659.379			−0.00385107
$125$		−	15625.0i		−	0.0894427i
$126$	188538.	−	67201.5i	1.05797	−	0.377097i
$127$			28219.9i			0.155255i	0.996982	+	0.0776277i	$0.0247346\pi$
$127$			28219.9i			0.155255i	−0.996982	+	0.0776277i	$0.975265\pi$
$128$	217404.			1.17285
$129$	164292.	+	115857.i	0.869247	+	0.612983i
$130$	140998.			0.731734
$131$	−94069.5			−0.478929			−0.239464	−	0.970905i	$-0.576972\pi$
$131$	−94069.5			−0.478929			−0.239464	+	0.970905i	$0.576972\pi$
$132$	−26242.4	−	19353.9i	−0.131090	−	0.0966792i
$133$	242042.			1.18649
$134$	−311310.			−1.49772
$135$	−25424.0	+	91223.3i	−0.120063	+	0.430796i
$136$	−85959.2			−0.398515
$137$		−	138598.i		−	0.630891i	−0.948944	−	0.315446i	$-0.897846\pi$
$137$		−	138598.i		−	0.630891i	0.948944	−	0.315446i	$-0.102154\pi$
$138$	−58450.1	−	41218.4i	−0.261269	−	0.184244i
$139$		−	30604.3i		−	0.134352i	−0.997741	−	0.0671762i	$-0.978601\pi$
$139$		−	30604.3i		−	0.134352i	0.997741	−	0.0671762i	$-0.0213990\pi$
$140$	−17595.0			−0.0758699
$141$	272375.	+	192076.i	1.15377	+	0.813626i
$142$			359889.i			1.49778i
$143$	370947.	+	7885.70i	1.51695	+	0.0322478i
$144$	94935.7	+	266348.i	0.381525	+	1.07039i
$145$		−	115957.i		−	0.458010i
$146$			345763.i			1.34244i
$147$	12803.4	−	18156.0i	0.0488690	−	0.0692992i
$148$	−74572.4			−0.279849
$149$	439630.			1.62227			0.811133	−	0.584862i	$-0.198851\pi$
$149$	439630.			1.62227			0.811133	+	0.584862i	$0.198851\pi$
$150$	34251.4	−	48570.6i	0.124294	−	0.176257i
$151$			355772.i			1.26978i	0.772601	+	0.634892i	$0.218955\pi$
$151$			355772.i			1.26978i	−0.772601	+	0.634892i	$0.781045\pi$
$152$			292921.i			1.02835i
$153$	−42917.1	−	120406.i	−0.148218	−	0.415835i
$154$	−330481.	−	7025.46i	−1.12291	−	0.0238711i
$155$		−	3162.60i		−	0.0105734i
$156$	61391.5	+	43292.6i	0.201975	+	0.142430i
$157$	−383079.			−1.24033			−0.620167	−	0.784470i	$-0.712935\pi$
$157$	−383079.			−1.24033			−0.620167	+	0.784470i	$0.712935\pi$
$158$			296306.i			0.944273i
$159$	−307548.	−	216879.i	−0.964762	−	0.680339i
$160$		−	46730.4i		−	0.144311i
$161$	−101557.			−0.308778
$162$	−279001.	+	227837.i	−0.835253	+	0.682083i
$163$	−472937.			−1.39423			−0.697115	−	0.716959i	$-0.745533\pi$
$163$	−472937.			−1.39423			−0.697115	+	0.716959i	$0.745533\pi$
$164$	−30747.0			−0.0892675
$165$	92827.7	−	125868.i	0.265441	−	0.359918i
$166$	530340.			1.49377
$167$	504262.			1.39915			0.699577	−	0.714558i	$-0.253372\pi$
$167$	504262.			1.39915			0.699577	+	0.714558i	$0.253372\pi$
$168$	281092.	+	198223.i	0.768378	+	0.541851i
$169$	−483491.			−1.30218
$170$			80222.7i			0.212900i
$171$	−410306.	+	146248.i	−1.07304	+	0.382471i
$172$		−	67219.8i		−	0.173251i
$173$	24295.6			0.0617182			0.0308591	−	0.999524i	$-0.490176\pi$
$173$	24295.6			0.0617182			0.0308591	+	0.999524i	$0.490176\pi$
$174$	254187.	−	360453.i	0.636474	−	0.902559i
$175$		−	84391.6i		−	0.208307i
$176$	9924.89	−	466871.i	0.0241515	−	1.13610i
$177$	454390.	+	320431.i	1.09017	+	0.768778i
$178$			188800.i			0.446634i
$179$		−	134851.i		−	0.314574i	−0.987553	−	0.157287i	$-0.949725\pi$
$179$		−	134851.i		−	0.314574i	0.987553	−	0.157287i	$-0.0502748\pi$
$180$	29826.7	−	10631.3i	0.0686158	−	0.0244571i
$181$	47011.8			0.106662			0.0533311	−	0.998577i	$-0.483016\pi$
$181$	47011.8			0.106662			0.0533311	+	0.998577i	$0.483016\pi$
$182$	761537.			1.70417
$183$	−402158.	−	283598.i	−0.887706	−	0.626001i
$184$		−	122905.i		−	0.267625i
$185$		−	357674.i		−	0.768349i
$186$	6932.72	−	9831.01i	0.0146934	−	0.0208361i
$187$	−4486.69	+	211056.i	−0.00938258	+	0.441360i
$188$		−	111442.i		−	0.229960i
$189$	−137317.	+	492703.i	−0.279620	+	1.00330i
$190$	273373.			0.549378
$191$		−	926791.i		−	1.83822i	−0.393996	−	0.919112i	$-0.628907\pi$
$191$		−	926791.i		−	1.83822i	0.393996	−	0.919112i	$-0.371093\pi$
$192$	−232080.	+	329103.i	−0.454344	+	0.644287i
$193$		−	504233.i		−	0.974401i	−0.873290	−	0.487201i	$-0.838018\pi$
$193$		−	504233.i		−	0.974401i	0.873290	−	0.487201i	$-0.161982\pi$
$194$	−459962.			−0.877440
$195$	−207646.	+	294454.i	−0.391054	+	0.554538i
$196$	−7428.51			−0.0138122
$197$	−133610.			−0.245287			−0.122644	−	0.992451i	$-0.539137\pi$
$197$	−133610.			−0.245287			−0.122644	+	0.992451i	$0.539137\pi$
$198$	564470.	−	187775.i	1.02324	−	0.340388i
$199$	−507883.			−0.909141			−0.454570	−	0.890711i	$-0.650207\pi$
$199$	−507883.			−0.909141			−0.454570	+	0.890711i	$0.650207\pi$
$200$	102131.			0.180544
$201$	458464.	−	650130.i	0.800415	−	1.13504i
$202$	−595108.			−1.02617
$203$		−	626289.i		−	1.06668i
$204$	−24632.0	+	34929.6i	−0.0414404	+	0.0587650i
$205$		−	147473.i		−	0.245091i
$206$	−341335.			−0.560418
$207$	172158.	−	61363.3i	0.279256	−	0.0995366i
$208$			1.07582e6i			1.72418i
$209$	719210.	+	15289.2i	1.13891	+	0.0242113i
$210$	184994.	−	262333.i	0.289474	−	0.410492i
$211$		−	106875.i		−	0.165261i	−0.996580	−	0.0826305i	$-0.973668\pi$
$211$		−	106875.i		−	0.165261i	0.996580	−	0.0826305i	$-0.0263321\pi$
$212$			125833.i			0.192289i
$213$	−751580.	−	530006.i	−1.13508	−	0.800445i
$214$	−1.03692e6			−1.54779
$215$	322409.			0.475676
$216$	−596272.	−	166181.i	−0.869581	−	0.242353i
$217$		−	17081.4i		−	0.0246249i
$218$			172244.i			0.245472i
$219$	−722079.	−	509202.i	−1.01736	−	0.717431i
$220$	−52282.2	−	1111.43i	−0.0728278	−	0.00154820i
$221$		−	486342.i		−	0.669825i
$222$	784055.	−	1.11184e6i	1.06774	−	1.51411i
$223$	−621918.			−0.837473			−0.418737	−	0.908108i	$-0.637527\pi$
$223$	−621918.			−0.837473			−0.418737	+	0.908108i	$0.637527\pi$
$224$		−	252394.i		−	0.336093i
$225$	50991.3	+	143059.i	0.0671491	+	0.188391i
$226$		−	364226.i		−	0.474351i
$227$	−877327.			−1.13005			−0.565024	−	0.825075i	$-0.691133\pi$
$227$	−877327.			−1.13005			−0.565024	+	0.825075i	$0.691133\pi$
$228$	119029.	+	83937.8i	0.151640	+	0.106935i
$229$	1.08480e6			1.36697			0.683487	−	0.729963i	$-0.260463\pi$
$229$	1.08480e6			1.36697			0.683487	+	0.729963i	$0.260463\pi$
$230$	−114703.			−0.142974
$231$	501368.	−	679819.i	0.618197	−	0.838230i
$232$	757938.			0.924515
$233$	−516714.			−0.623535			−0.311767	−	0.950158i	$-0.600921\pi$
$233$	−516714.			−0.623535			−0.311767	+	0.950158i	$0.600921\pi$
$234$	−1.29094e6	+	460138.i	−1.54123	+	0.549349i
$235$	534511.			0.631375
$236$		−	185913.i		−	0.217285i
$237$	−618795.	−	436368.i	−0.715609	−	0.504640i
$238$			433288.i			0.495831i
$239$	484109.			0.548212			0.274106	−	0.961700i	$-0.411618\pi$
$239$	484109.			0.548212			0.274106	+	0.961700i	$0.411618\pi$
$240$	370598.	+	261342.i	0.415313	+	0.292874i
$241$		−	1.12720e6i		−	1.25014i	−0.780568	−	0.625071i	$-0.785070\pi$
$241$		−	1.12720e6i		−	1.25014i	0.780568	−	0.625071i	$-0.214930\pi$
$242$	−981554.	−	41751.2i	−1.07740	−	0.0458280i
$243$	−64925.6	−	918190.i	−0.0705343	−	0.997509i
$244$			164542.i			0.176930i
$245$		−	35629.6i		−	0.0379224i
$246$	323275.	−	458423.i	0.340592	−	0.482979i
$247$	−1.65730e6			−1.72845
$248$	20672.0			0.0213429
$249$	−781028.	+	1.10754e6i	−0.798304	+	1.13204i
$250$		−	95315.5i		−	0.0964525i
$251$			186589.i			0.186940i	0.995622	+	0.0934701i	$0.0297960\pi$
$251$			186589.i			0.186940i	−0.995622	+	0.0934701i	$0.970204\pi$
$252$	161096.	−	57420.4i	0.159803	−	0.0569593i
$253$	−301770.	−	6415.12i	−0.296398	−	0.00630091i
$254$			172147.i			0.167423i
$255$	−167534.	−	118143.i	−0.161344	−	0.113778i
$256$	499534.			0.476393
$257$			1.50895e6i			1.42509i	0.701628	+	0.712543i	$0.252457\pi$
$257$			1.50895e6i			1.42509i	−0.701628	+	0.712543i	$0.747543\pi$
$258$	1.00221e6	+	706750.i	0.937371	+	0.661023i
$259$		−	1.93182e6i		−	1.78944i
$260$	120475.			0.110526
$261$	378418.	+	1.06167e6i	0.343851	+	0.964694i
$262$	−573842.			−0.516463
$263$	−1.05599e6			−0.941394			−0.470697	−	0.882295i	$-0.655997\pi$
$263$	−1.05599e6			−0.941394			−0.470697	+	0.882295i	$0.655997\pi$
$264$	822720.	+	606759.i	0.726512	+	0.535805i
$265$	−603536.			−0.527945
$266$	1.47650e6			1.27947
$267$	−394284.	−	278044.i	−0.338478	−	0.238691i
$268$	−265999.			−0.226226
$269$			833544.i			0.702341i	0.936312	+	0.351170i	$0.114216\pi$
$269$			833544.i			0.702341i	−0.936312	+	0.351170i	$0.885784\pi$
$270$	−155091.	+	556479.i	−0.129473	+	0.464558i
$271$			762378.i			0.630590i	0.948994	+	0.315295i	$0.102103\pi$
$271$			762378.i			0.630590i	−0.948994	+	0.315295i	$0.897897\pi$
$272$	−612107.			−0.501655
$273$	−1.12151e6	+	1.59037e6i	−0.910744	+	1.29149i
$274$		−	845472.i		−	0.680335i
$275$	5330.80	−	250763.i	0.00425070	−	0.199955i
$276$	−49942.7	−	35219.1i	−0.0394639	−	0.0278295i
$277$		−	1.43181e6i		−	1.12120i	−0.828085	−	0.560602i	$-0.810570\pi$
$277$		−	1.43181e6i		−	1.12120i	0.828085	−	0.560602i	$-0.189430\pi$
$278$		−	186692.i		−	0.144882i
$279$	10321.0	+	28956.1i	0.00793799	+	0.0222705i
$280$	551617.			0.420478
$281$	1.09894e6			0.830247			0.415123	−	0.909765i	$-0.363738\pi$
$281$	1.09894e6			0.830247			0.415123	+	0.909765i	$0.363738\pi$
$282$	1.66154e6	+	1.17170e6i	1.24419	+	0.877391i
$283$			2.15126e6i			1.59671i	0.602185	+	0.798356i	$0.294297\pi$
$283$			2.15126e6i			1.59671i	−0.602185	+	0.798356i	$0.705703\pi$
$284$			307507.i			0.226235i
$285$	−402594.	+	570903.i	−0.293600	+	0.416342i
$286$	2.26285e6	+	48104.3i	1.63584	+	0.0347751i
$287$		−	796512.i		−	0.570805i
$288$	152502.	+	427854.i	0.108342	+	0.303958i
$289$	−1.14315e6			−0.805113
$290$		−	707357.i		−	0.493905i
$291$	677382.	−	960568.i	0.468923	−	0.664960i
$292$			295437.i			0.202772i
$293$	−1.31609e6			−0.895603			−0.447802	−	0.894133i	$-0.647793\pi$
$293$	−1.31609e6			−0.895603			−0.447802	+	0.894133i	$0.647793\pi$
$294$	78103.4	−	110755.i	0.0526989	−	0.0747302i
$295$	891700.			0.596573
$296$	2.33790e6			1.55095
$297$	−439148.	+	1.45535e6i	−0.288882	+	0.957365i
$298$	2.68183e6			1.74940
$299$	695377.			0.449824
$300$	29266.2	−	41501.2i	0.0187742	−	0.0266230i
$301$	1.74135e6			1.10782
$302$			2.17028e6i			1.36930i
$303$	876412.	−	1.24280e6i	0.548405	−	0.777672i
$304$			2.08586e6i			1.29450i
$305$	−789200.			−0.485778
$306$	−261802.	−	734501.i	−0.159834	−	0.448424i
$307$			2.49068e6i			1.50825i	0.656733	+	0.754123i	$0.271938\pi$
$307$			2.49068e6i			1.50825i	−0.656733	+	0.754123i	$0.728062\pi$
$308$	−282379.	−	6002.91i	−0.169612	−	0.00360566i
$309$	502681.	−	712832.i	0.299500	−	0.424708i
$310$		−	19292.5i		−	0.0114021i
$311$			1.08753e6i			0.637588i	0.947824	+	0.318794i	$0.103278\pi$
$311$			1.08753e6i			0.637588i	−0.947824	+	0.318794i	$0.896722\pi$
$312$	−1.92467e6	−	1.35726e6i	−1.11936	−	0.789361i
$313$	−1.89168e6			−1.09141			−0.545703	−	0.837978i	$-0.683737\pi$
$313$	−1.89168e6			−1.09141			−0.545703	+	0.837978i	$0.683737\pi$
$314$	−2.33685e6			−1.33754
$315$	275407.	+	772671.i	0.156387	+	0.438751i
$316$			253179.i			0.142630i
$317$			56871.9i			0.0317870i	0.999874	+	0.0158935i	$0.00505927\pi$
$317$			56871.9i			0.0317870i	−0.999874	+	0.0158935i	$0.994941\pi$
$318$	−1.87610e6	−	1.32301e6i	−1.04037	−	0.733658i
$319$	39561.0	−	1.86097e6i	0.0217666	−	1.02391i
$320$			645836.i			0.352572i
$321$	1.52707e6	−	2.16548e6i	0.827173	−	1.17298i
$322$	−619519.			−0.332978
$323$		−	942944.i		−	0.502898i
$324$	−238392.	+	194676.i	−0.126162	+	0.103027i
$325$			577841.i			0.303459i
$326$	−2.88501e6			−1.50350
$327$	−359708.	−	253662.i	−0.186029	−	0.131186i
$328$	963943.			0.494728
$329$	2.88693e6			1.47044
$330$	566267.	−	767816.i	0.286244	−	0.388126i
$331$	3.32227e6			1.66673			0.833364	−	0.552725i	$-0.186412\pi$
$331$	3.32227e6			1.66673			0.833364	+	0.552725i	$0.186412\pi$
$332$	453149.			0.225630
$333$	1.16725e6	+	3.27479e6i	0.576838	+	1.61835i
$334$	3.07610e6			1.50881
$335$		−	1.27582e6i		−	0.621124i
$336$	2.00162e6	+	1.41152e6i	0.967240	+	0.682087i
$337$			806645.i			0.386908i	0.981109	+	0.193454i	$0.0619690\pi$
$337$			806645.i			0.386908i	−0.981109	+	0.193454i	$0.938031\pi$
$338$	−2.94939e6			−1.40424
$339$	760637.	+	536393.i	0.359483	+	0.253503i
$340$			68546.3i			0.0321578i
$341$	1078.99	−	50756.1i	0.000502495	−	0.0236376i
$342$	−2.50294e6	+	892138.i	−1.15714	+	0.412445i
$343$			2.07695e6i			0.953217i
$344$			2.10739e6i			0.960174i
$345$	168923.	−	239542.i	0.0764082	−	0.108351i
$346$	148208.			0.0665551
$347$	3.91407e6			1.74504			0.872519	−	0.488580i	$-0.162485\pi$
$347$	3.91407e6			1.74504			0.872519	+	0.488580i	$0.162485\pi$
$348$	217191.	−	307989.i	0.0961375	−	0.136329i
$349$		−	1.99021e6i		−	0.874652i	−0.899303	−	0.437326i	$-0.855926\pi$
$349$		−	1.99021e6i		−	0.874652i	0.899303	−	0.437326i	$-0.144074\pi$
$350$		−	514805.i		−	0.224632i
$351$	940225.	−	3.37360e6i	0.407347	−	1.46159i
$352$	15943.1	−	749969.i	0.00685829	−	0.322617i
$353$			1.34083e6i			0.572714i	0.958123	+	0.286357i	$0.0924443\pi$
$353$			1.34083e6i			0.572714i	−0.958123	+	0.286357i	$0.907556\pi$
$354$	2.77187e6	+	1.95469e6i	1.17561	+	0.829029i
$355$	−1.47491e6			−0.621147
$356$			161320.i			0.0674627i
$357$	−904864.	−	638100.i	−0.375762	−	0.264983i
$358$		−	822620.i		−	0.339228i
$359$	−2.67052e6			−1.09360			−0.546801	−	0.837262i	$-0.684155\pi$
$359$	−2.67052e6			−1.09360			−0.546801	+	0.837262i	$0.684155\pi$
$360$	−935091.	+	333300.i	−0.380275	+	0.135543i
$361$	−737150.			−0.297706
$362$	286781.			0.115022
$363$	1.53272e6	−	1.98836e6i	0.610515	−	0.792005i
$364$	650695.			0.257409
$365$	−1.41702e6			−0.556727
$366$	−2.45324e6	−	1.73000e6i	−0.957277	−	0.675061i
$367$	2.58831e6			1.00312			0.501558	−	0.865124i	$-0.332761\pi$
$367$	2.58831e6			1.00312			0.501558	+	0.865124i	$0.332761\pi$
$368$		−	875197.i		−	0.336888i
$369$	481270.	+	1.35023e6i	0.184002	+	0.516229i
$370$		−	2.18188e6i		−	0.828566i
$371$	−3.25974e6			−1.22955
$372$	5923.67	−	8400.11i	0.00221939	−	0.00314722i
$373$			2.99168e6i			1.11338i	0.830720	+	0.556690i	$0.187929\pi$
$373$			2.99168e6i			1.11338i	−0.830720	+	0.556690i	$0.812071\pi$
$374$	−27369.7	+	1.28748e6i	−0.0101179	+	0.475950i
$375$	199054.	+	140370.i	0.0730957	+	0.0515463i
$376$			3.49378e6i			1.27446i
$377$			4.28828e6i			1.55393i
$378$	−837658.	+	3.00558e6i	−0.301534	+	1.08193i
$379$	2.18258e6			0.780499			0.390250	−	0.920709i	$-0.372389\pi$
$379$	2.18258e6			0.780499			0.390250	+	0.920709i	$0.372389\pi$
$380$	233584.			0.0829819
$381$	−359506.	−	253520.i	−0.126880	−	0.0894745i
$382$		−	5.65360e6i		−	1.98229i
$383$			97107.5i			0.0338264i	0.999857	+	0.0169132i	$0.00538390\pi$
$383$			97107.5i			0.0338264i	−0.999857	+	0.0169132i	$0.994616\pi$
$384$	−1.95309e6	+	2.76960e6i	−0.675919	+	0.958493i
$385$	28792.0	−	1.35439e6i	0.00989965	−	0.465684i
$386$		−	3.07592e6i		−	1.05077i
$387$	−2.95191e6	+	1.05216e6i	−1.00190	+	0.357113i
$388$	−393014.			−0.132535
$389$			328105.i			0.109936i	0.998488	+	0.0549679i	$0.0175056\pi$
$389$			328105.i			0.109936i	−0.998488	+	0.0549679i	$0.982494\pi$
$390$	−1.26668e6	+	1.79623e6i	−0.421702	+	0.597998i
$391$			395645.i			0.130877i
$392$	232890.			0.0765482
$393$	845093.	−	1.19839e6i	0.276009	−	0.391397i
$394$	−815049.			−0.264511
$395$	−1.21433e6			−0.391601
$396$	482311.	−	160444.i	0.154557	−	0.0514145i
$397$	−1.81741e6			−0.578730			−0.289365	−	0.957219i	$-0.593444\pi$
$397$	−1.81741e6			−0.578730			−0.289365	+	0.957219i	$0.593444\pi$
$398$	−3.09818e6			−0.980391
$399$	−2.17444e6	+	3.08348e6i	−0.683777	+	0.969637i
$400$	727266.			0.227271
$401$			2.92041e6i			0.906948i	0.891270	+	0.453474i	$0.149815\pi$
$401$			2.92041e6i			0.906948i	−0.891270	+	0.453474i	$0.850185\pi$
$402$	2.79672e6	−	3.96592e6i	0.863145	−	1.22399i
$403$			116959.i			0.0358732i
$404$	−508491.			−0.154999
$405$	−933731.	−	1.14341e6i	−0.282868	−	0.346389i
$406$		−	3.82048e6i		−	1.15028i
$407$	122028.	−	5.74026e6i	0.0365152	−	1.71769i
$408$	772232.	−	1.09507e6i	0.229666	−	0.325681i
$409$		−	3.54633e6i		−	1.04826i	−0.851637	−	0.524132i	$-0.824390\pi$
$409$		−	3.54633e6i		−	1.04826i	0.851637	−	0.524132i	$-0.175610\pi$
$410$		−	899614.i		−	0.264300i
$411$	1.76566e6	+	1.24512e6i	0.515586	+	0.363586i
$412$	−291653.			−0.0846494
$413$	4.81613e6			1.38939
$414$	1.05020e6	−	374328.i	0.301141	−	0.107337i
$415$			2.17346e6i			0.619485i
$416$			1.72818e6i			0.489615i
$417$	389881.	+	274940.i	0.109797	+	0.0774279i
$418$	4.38732e6	+	93267.0i	1.22817	+	0.0261088i
$419$		−	4.97613e6i		−	1.38470i	−0.721560	−	0.692352i	$-0.756574\pi$
$419$		−	4.97613e6i		−	1.38470i	0.721560	−	0.692352i	$-0.243426\pi$
$420$	158068.	−	224150.i	0.0437242	−	0.0620035i
$421$	164736.			0.0452984			0.0226492	−	0.999743i	$-0.492790\pi$
$421$	164736.			0.0452984			0.0226492	+	0.999743i	$0.492790\pi$
$422$		−	651958.i		−	0.178213i
$423$	−4.89387e6	+	1.74435e6i	−1.32985	+	0.474004i
$424$		−	3.94495e6i		−	1.06568i
$425$	−328771.			−0.0882920
$426$	−4.58478e6	−	3.23314e6i	−1.22404	−	0.863177i
$427$	−4.26252e6			−1.13135
$428$	−886000.			−0.233789
$429$	−3.43294e6	+	4.65481e6i	−0.900581	+	1.22112i
$430$	1.96676e6			0.512955
$431$	−141176.			−0.0366073			−0.0183036	−	0.999832i	$-0.505827\pi$
$431$	−141176.			−0.0366073			−0.0183036	+	0.999832i	$0.505827\pi$
$432$	−4.24599e6	−	1.18336e6i	−1.09464	−	0.305076i
$433$	4.93145e6			1.26402			0.632012	−	0.774959i	$-0.282229\pi$
$433$	4.93145e6			1.26402			0.632012	+	0.774959i	$0.282229\pi$
$434$		−	104200.i		−	0.0265548i
$435$	1.47722e6	+	1.04172e6i	0.374302	+	0.263954i
$436$			147174.i			0.0370778i
$437$	1.34823e6			0.337723
$438$	−4.40482e6	−	3.10623e6i	−1.09709	−	0.773657i
$439$			1.26826e6i			0.314084i	0.987592	+	0.157042i	$0.0501958\pi$
$439$			1.26826e6i			0.314084i	−0.987592	+	0.157042i	$0.949804\pi$
$440$	1.63909e6	+	34844.2i	0.403618	+	0.00858024i
$441$	116275.	+	326217.i	0.0284702	+	0.0798749i
$442$		−	2.96678e6i		−	0.722320i
$443$		−	6.64110e6i		−	1.60779i	−0.594768	−	0.803897i	$-0.702756\pi$
$443$		−	6.64110e6i		−	1.60779i	0.594768	−	0.803897i	$-0.297244\pi$
$444$	669936.	−	950010.i	0.161278	−	0.228702i
$445$	−773747.			−0.185225
$446$	−3.79382e6			−0.903107
$447$	−3.94951e6	+	5.60064e6i	−0.934920	+	1.32577i
$448$			3.48820e6i			0.821120i
$449$			713555.i			0.167037i	0.996506	+	0.0835183i	$0.0266157\pi$
$449$			713555.i			0.167037i	−0.996506	+	0.0835183i	$0.973384\pi$
$450$	311057.	+	872687.i	0.0724116	+	0.203155i
$451$	50313.6	−	2.36677e6i	0.0116478	−	0.547917i
$452$		−	311213.i		−	0.0716492i
$453$	−4.53234e6	−	3.19615e6i	−1.03771	−	0.731783i
$454$	−5.35186e6			−1.21861
$455$			3.12096e6i			0.706739i
$456$	−3.73165e6	−	2.63152e6i	−0.840405	−	0.592644i
$457$			6.45174e6i			1.44506i	0.691339	+	0.722531i	$0.257021\pi$
$457$			6.45174e6i			1.44506i	−0.691339	+	0.722531i	$0.742979\pi$
$458$	6.61747e6			1.47411
$459$	1.91946e6	+	534955.i	0.425253	+	0.118518i
$460$	−98008.2			−0.0215957
$461$	3.86213e6			0.846397			0.423199	−	0.906037i	$-0.360907\pi$
$461$	3.86213e6			0.846397			0.423199	+	0.906037i	$0.360907\pi$
$462$	3.05844e6	−	4.14702e6i	0.666646	−	0.903923i
$463$	−4.65118e6			−1.00835			−0.504174	−	0.863602i	$-0.668203\pi$
$463$	−4.65118e6			−1.00835			−0.504174	+	0.863602i	$0.668203\pi$
$464$	5.39720e6			1.16379
$465$	40289.8	+	28411.9i	0.00864097	+	0.00609352i
$466$	−3.15206e6			−0.672402
$467$			6.67245e6i			1.41577i	0.706327	+	0.707886i	$0.250351\pi$
$467$			6.67245e6i			1.41577i	−0.706327	+	0.707886i	$0.749649\pi$
$468$	−1.10305e6	+	393165.i	−0.232798	+	0.0829774i
$469$		−	6.89080e6i		−	1.44656i
$470$	3.26062e6			0.680857
$471$	3.44146e6	−	4.88020e6i	0.714811	−	1.01364i
$472$			5.82851e6i			1.20421i
$473$	5.17429e6	+	109997.i	1.06340	+	0.0226062i
$474$	−3.77477e6	−	2.66192e6i	−0.771693	−	0.544189i
$475$			1.12035e6i			0.227834i
$476$			370223.i			0.0748938i
$477$	5.52584e6	−	1.96961e6i	1.11199	−	0.396354i
$478$	2.95316e6			0.591176
$479$	2.94369e6			0.586210			0.293105	−	0.956080i	$-0.405311\pi$
$479$	2.94369e6			0.586210			0.293105	+	0.956080i	$0.405311\pi$
$480$	595319.	+	419812.i	0.117936	+	0.0831672i
$481$			1.32274e7i			2.60683i
$482$		−	6.87615e6i		−	1.34812i
$483$	912362.	−	1.29378e6i	0.177951	−	0.252344i
$484$	−838689.	−	35674.4i	−0.162738	−	0.00692218i
$485$		−	1.88503e6i		−	0.363885i
$486$	−396059.	−	5.60113e6i	−0.0760622	−	1.07569i
$487$	2.51735e6			0.480974			0.240487	−	0.970652i	$-0.422693\pi$
$487$	2.51735e6			0.480974			0.240487	+	0.970652i	$0.422693\pi$
$488$		−	5.15853e6i		−	0.980564i
$489$	4.24873e6	−	6.02495e6i	0.803502	−	1.13941i
$490$		−	217348.i		−	0.0408945i
$491$	7.51649e6			1.40706			0.703528	−	0.710668i	$-0.251607\pi$
$491$	7.51649e6			1.40706			0.703528	+	0.710668i	$0.251607\pi$
$492$	276222.	−	391700.i	0.0514453	−	0.0729525i
$493$	−2.43988e6			−0.452118
$494$	−1.01098e7			−1.86392
$495$	769544.	+	2.31333e6i	0.141163	+	0.424350i
$496$	147204.			0.0268667
$497$	−7.96608e6			−1.44662
$498$	−4.76442e6	+	6.75623e6i	−0.860868	+	1.22076i
$499$	6.97956e6			1.25481			0.627403	−	0.778695i	$-0.284118\pi$
$499$	6.97956e6			1.25481			0.627403	+	0.778695i	$0.284118\pi$
$500$		−	81442.3i		−	0.0145688i
$501$	−4.53014e6	+	6.42401e6i	−0.806339	+	1.14344i
$502$			1.13823e6i			0.201591i
$503$	6.49235e6			1.14415			0.572073	−	0.820202i	$-0.306139\pi$
$503$	6.49235e6			1.14415			0.572073	+	0.820202i	$0.306139\pi$
$504$	−5.05049e6	+	1.80017e6i	−0.885640	+	0.315673i
$505$		−	2.43889e6i		−	0.425563i
$506$	−1.84085e6	−	39133.4i	−0.319627	−	0.00679472i
$507$	4.34354e6	−	6.15940e6i	0.750454	−	1.06419i
$508$			147091.i			0.0252887i
$509$			2.12745e6i			0.363970i	0.983301	+	0.181985i	$0.0582522\pi$
$509$			2.12745e6i			0.363970i	−0.983301	+	0.181985i	$0.941748\pi$
$510$	−1.02199e6	−	720697.i	−0.173989	−	0.122695i
$511$	−7.65339e6			−1.29659
$512$	−3.90967e6			−0.659121
$513$	1.82296e6	−	6.54091e6i	0.305832	−	1.09735i
$514$			9.20486e6i			1.53677i
$515$		−	1.39887e6i		−	0.232412i
$516$	856342.	+	603883.i	0.141587	+	0.0998455i
$517$	8.57829e6	+	182360.i	1.41148	+	0.0300056i
$518$		−	1.17845e7i		−	1.92968i
$519$	−218265.	+	309513.i	−0.0355685	+	0.0504383i
$520$	−3.77700e6			−0.612546
$521$			2.08059e6i			0.335808i	0.985803	+	0.167904i	$0.0536999\pi$
$521$			2.08059e6i			0.335808i	−0.985803	+	0.167904i	$0.946300\pi$
$522$	2.30842e6	+	6.47640e6i	0.370799	+	1.04030i
$523$		−	6.58450e6i		−	1.05261i	−0.850295	−	0.526307i	$-0.823576\pi$
$523$		−	6.58450e6i		−	1.05261i	0.850295	−	0.526307i	$-0.176424\pi$
$524$	−490319.			−0.0780101
$525$	1.07510e6	+	758149.i	0.170236	+	0.120048i
$526$	−6.44175e6			−1.01517
$527$	−66545.5			−0.0104374
$528$	5.85851e6	+	4.32067e6i	0.914539	+	0.674475i
$529$	5.87065e6			0.912109
$530$	−3.68168e6			−0.569320
$531$	−8.16421e6	+	2.91002e6i	−1.25655	+	0.447877i
$532$	1.26160e6			0.193260
$533$			5.45382e6i			0.831540i
$534$	−2.40521e6	−	1.69612e6i	−0.365005	−	0.257398i
$535$		−	4.24956e6i		−	0.641888i
$536$	8.33928e6			1.25377
$537$	1.71793e6	+	1.21147e6i	0.257081	+	0.181291i
$538$			5.08478e6i			0.757384i
$539$	12155.8	−	571814.i	0.00180224	−	0.0847780i
$540$	−132518.	+	475484.i	−0.0195564	+	0.0701700i
$541$			1.05096e7i			1.54381i	0.635741	+	0.771903i	$0.280695\pi$
$541$			1.05096e7i			1.54381i	−0.635741	+	0.771903i	$0.719305\pi$
$542$			4.65065e6i			0.680010i
$543$	−422340.	+	598904.i	−0.0614700	+	0.0871681i
$544$	−983272.			−0.142455
$545$	−705896.			−0.101800
$546$	−6.84142e6	+	9.70154e6i	−0.982120	+	1.39271i
$547$		−	1.17665e7i		−	1.68142i	−0.541482	−	0.840712i	$-0.682137\pi$
$547$		−	1.17665e7i		−	1.68142i	0.541482	−	0.840712i	$-0.317863\pi$
$548$		−	722414.i		−	0.102763i
$549$	7.22574e6	−	2.57551e6i	1.02318	−	0.364697i
$550$	32518.9	−	1.52970e6i	0.00458383	−	0.215626i
$551$			8.31433e6i			1.16667i
$552$	1.56574e6	+	1.10415e6i	0.218712	+	0.154233i
$553$	−6.55868e6			−0.912018
$554$		−	8.73429e6i		−	1.20908i
$555$	4.55657e6	+	3.21324e6i	0.627922	+	0.442803i
$556$		−	159519.i		−	0.0218839i
$557$	−7.53101e6			−1.02853			−0.514263	−	0.857633i	$-0.671934\pi$
$557$	−7.53101e6			−1.02853			−0.514263	+	0.857633i	$0.671934\pi$
$558$	62960.0	+	176638.i	0.00856010	+	0.0240159i
$559$	−1.19233e7			−1.61386
$560$	3.92801e6			0.529301
$561$	−2.64842e6	−	1.95322e6i	−0.355288	−	0.262026i
$562$	6.70372e6			0.895314
$563$	1.14486e7			1.52223			0.761114	−	0.648618i	$-0.224653\pi$
$563$	1.14486e7			1.52223			0.761114	+	0.648618i	$0.224653\pi$
$564$	1.41970e6	+	1.00116e6i	0.187931	+	0.132527i
$565$	1.49268e6			0.196719
$566$			1.31231e7i			1.72185i
$567$	−5.04314e6	−	6.17563e6i	−0.658785	−	0.806722i
$568$		−	9.64059e6i		−	1.25381i
$569$	−2.12583e6			−0.275263			−0.137631	−	0.990484i	$-0.543949\pi$
$569$	−2.12583e6			−0.275263			−0.137631	+	0.990484i	$0.543949\pi$
$570$	−2.45590e6	+	3.48261e6i	−0.316609	+	0.448971i
$571$		−	5.69606e6i		−	0.731113i	−0.930789	−	0.365557i	$-0.880879\pi$
$571$		−	5.69606e6i		−	0.731113i	0.930789	−	0.365557i	$-0.119121\pi$
$572$	1.93349e6	+	41102.7i	0.247088	+	0.00525268i
$573$	1.18068e7	+	8.32602e6i	1.50226	+	1.05938i
$574$		−	4.85887e6i		−	0.615539i
$575$		−	470081.i		−	0.0592929i
$576$	−2.10765e6	−	5.91313e6i	−0.264693	−	0.742611i
$577$	−1.68644e6			−0.210878			−0.105439	−	0.994426i	$-0.533625\pi$
$577$	−1.68644e6			−0.210878			−0.105439	+	0.994426i	$0.533625\pi$
$578$	−6.97340e6			−0.868211
$579$	6.42364e6	+	4.52988e6i	0.796315	+	0.561552i
$580$		−	604401.i		−	0.0746029i
$581$			1.17390e7i			1.44275i
$582$	4.13216e6	−	5.85965e6i	0.505673	−	0.717074i
$583$	−9.68605e6	−	205909.i	−1.18025	−	0.0250902i
$584$		−	9.26218e6i		−	1.12378i
$585$	−1.88575e6	−	5.29058e6i	−0.227822	−	0.639166i
$586$	−8.02838e6			−0.965793
$587$			7.18810e6i			0.861031i	0.902583	+	0.430515i	$0.141668\pi$
$587$			7.18810e6i			0.861031i	−0.902583	+	0.430515i	$0.858332\pi$
$588$	66735.5	−	94634.9i	0.00796001	−	0.0112878i
$589$			226766.i			0.0269333i
$590$	5.43954e6			0.643328
$591$	1.20032e6	−	1.70212e6i	0.141360	−	0.200457i
$592$	1.66480e7			1.95235
$593$	−1.03114e7			−1.20415			−0.602075	−	0.798439i	$-0.705659\pi$
$593$	−1.03114e7			−1.20415			−0.602075	+	0.798439i	$0.705659\pi$
$594$	−2.67889e6	+	8.87793e6i	−0.311522	+	1.03239i
$595$	−1.77571e6			−0.205627
$596$	2.29149e6			0.264242
$597$	4.56267e6	−	6.47014e6i	0.523942	−	0.742981i
$598$	4.24193e6			0.485077
$599$		−	1.39087e6i		−	0.158387i	−0.996859	−	0.0791937i	$-0.974765\pi$
$599$		−	1.39087e6i		−	0.158387i	0.996859	−	0.0791937i	$-0.0252346\pi$
$600$	−917517.	+	1.30109e6i	−0.104049	+	0.147547i
$601$		−	1.09083e7i		−	1.23189i	−0.787790	−	0.615944i	$-0.788775\pi$
$601$		−	1.09083e7i		−	1.23189i	0.787790	−	0.615944i	$-0.211225\pi$
$602$	1.06226e7			1.19464
$603$	4.16358e6	+	1.16812e7i	0.466308	+	1.30825i
$604$			1.85440e6i			0.206828i
$605$	171106.	−	4.02264e6i	0.0190054	−	0.446810i
$606$	5.34628e6	−	7.58134e6i	0.591385	−	0.838619i
$607$			1.31075e7i			1.44393i	0.691928	+	0.721967i	$0.256762\pi$
$607$			1.31075e7i			1.44393i	−0.691928	+	0.721967i	$0.743238\pi$
$608$			3.35067e6i			0.367598i
$609$	7.97856e6	+	5.62639e6i	0.871729	+	0.614733i
$610$	−4.81427e6			−0.523849
$611$	−1.97672e7			−2.14211
$612$	−223697.	−	627595.i	−0.0241425	−	0.0677331i
$613$		−	6.01788e6i		−	0.646833i	−0.946257	−	0.323417i	$-0.895169\pi$
$613$		−	6.01788e6i		−	0.646833i	0.946257	−	0.323417i	$-0.104831\pi$
$614$			1.51936e7i			1.62645i
$615$	1.87872e6	+	1.32485e6i	0.200297	+	0.141247i
$616$	8.85282e6	+	188196.i	0.940004	+	0.0199829i
$617$			9.69026e6i			1.02476i	0.858759	+	0.512380i	$0.171236\pi$
$617$			9.69026e6i			1.02476i	−0.858759	+	0.512380i	$0.828764\pi$
$618$	3.06645e6	−	4.34841e6i	0.322972	−	0.457993i
$619$	−5.74045e6			−0.602170			−0.301085	−	0.953597i	$-0.597349\pi$
$619$	−5.74045e6			−0.602170			−0.301085	+	0.953597i	$0.597349\pi$
$620$		−	16484.5i		−	0.00172225i
$621$	−764885.	+	2.74447e6i	−0.0795916	+	0.285581i
$622$			6.63413e6i			0.687556i
$623$	−4.17906e6			−0.431378
$624$	−1.37054e7	−	9.66489e6i	−1.40906	−	0.993655i
$625$	390625.			0.0400000
$626$	−1.15396e7			−1.17694
$627$	−6.65595e6	+	9.02497e6i	−0.676147	+	0.916805i
$628$	−1.99672e6			−0.202031
$629$	−7.52596e6			−0.758464
$630$	1.68004e6	+	4.71344e6i	0.168643	+	0.473137i
$631$	−3.95883e6			−0.395816			−0.197908	−	0.980221i	$-0.563415\pi$
$631$	−3.95883e6			−0.395816			−0.197908	+	0.980221i	$0.563415\pi$
$632$		−	7.93735e6i		−	0.790465i
$633$	1.36153e6	+	960134.i	0.135057	+	0.0952407i
$634$			346929.i			0.0342782i
$635$	−705499.			−0.0694324
$636$	−1.60304e6	−	1.13044e6i	−0.157145	−	0.110817i
$637$			1.31765e6i			0.128662i
$638$	241330.	−	1.13523e7i	0.0234725	−	1.10416i
$639$	1.35039e7	−	4.81328e6i	1.30830	−	0.466326i
$640$			5.43510e6i			0.524514i
$641$			1.25261e7i			1.20412i	0.798451	+	0.602059i	$0.205653\pi$
$641$			1.25261e7i			1.20412i	−0.798451	+	0.602059i	$0.794347\pi$
$642$	9.31542e6	−	1.32098e7i	0.892000	−	1.26491i
$643$	−1.07611e7			−1.02643			−0.513213	−	0.858261i	$-0.671545\pi$
$643$	−1.07611e7			−1.02643			−0.513213	+	0.858261i	$0.671545\pi$
$644$	−529349.			−0.0502953
$645$	−2.89643e6	+	4.10731e6i	−0.274134	+	0.388739i
$646$		−	5.75214e6i		−	0.542310i
$647$		−	8.70118e6i		−	0.817179i	−0.912718	−	0.408590i	$-0.866021\pi$
$647$		−	8.70118e6i		−	0.817179i	0.912718	−	0.408590i	$-0.133979\pi$
$648$	7.47379e6	−	6.10324e6i	0.699203	−	0.570983i
$649$	1.43108e7	+	304222.i	1.33368	+	0.0283517i
$650$			3.52494e6i			0.327241i
$651$	217608.	+	153455.i	0.0201243	+	0.0141915i
$652$	−2.46509e6			−0.227099
$653$		−	9.62589e6i		−	0.883401i	−0.897163	−	0.441700i	$-0.854375\pi$
$653$		−	9.62589e6i		−	0.883401i	0.897163	−	0.441700i	$-0.145625\pi$
$654$	−2.19429e6	−	1.54739e6i	−0.200609	−	0.141467i
$655$		−	2.35174e6i		−	0.214183i
$656$	6.86414e6			0.622768
$657$	1.29739e7	−	4.62435e6i	1.17262	−	0.417963i
$658$	1.76108e7			1.58568
$659$	1.11106e6			0.0996611			0.0498306	−	0.998758i	$-0.484132\pi$
$659$	1.11106e6			0.0996611			0.0498306	+	0.998758i	$0.484132\pi$
$660$	483847.	−	656060.i	0.0432362	−	0.0586252i
$661$	−1.00663e7			−0.896123			−0.448061	−	0.894003i	$-0.647885\pi$
$661$	−1.00663e7			−0.896123			−0.448061	+	0.894003i	$0.647885\pi$
$662$	2.02665e7			1.79735
$663$	6.19572e6	+	4.36915e6i	0.547404	+	0.386023i
$664$	−1.42066e7			−1.25046
$665$			6.05106e6i			0.530612i
$666$	7.12045e6	+	1.99768e7i	0.622045	+	1.74518i
$667$		−	3.48857e6i		−	0.303622i
$668$	2.62837e6			0.227901
$669$	5.58713e6	−	7.92288e6i	0.482640	−	0.684412i
$670$		−	7.78276e6i		−	0.669802i
$671$	−1.26657e7	−	269252.i	−1.08599	−	0.0230862i
$672$	3.21536e6	+	2.26743e6i	0.274667	+	0.193692i
$673$		−	6.18838e6i		−	0.526671i	−0.964704	−	0.263335i	$-0.915177\pi$
$673$		−	6.18838e6i		−	0.526671i	0.964704	−	0.263335i	$-0.0848226\pi$
$674$			4.92069e6i			0.417231i
$675$	−2.28058e6	−	635600.i	−0.192658	−	0.0536938i
$676$	−2.52010e6			−0.212105
$677$	−6.96335e6			−0.583911			−0.291956	−	0.956432i	$-0.594306\pi$
$677$	−6.96335e6			−0.583911			−0.291956	+	0.956432i	$0.594306\pi$
$678$	4.64003e6	+	3.27210e6i	0.387656	+	0.273371i
$679$		−	1.01812e7i		−	0.847468i
$680$		−	2.14898e6i		−	0.178221i
$681$	7.88164e6	−	1.11766e7i	0.651252	−	0.923514i
$682$	6582.04	−	309622.i	0.000541876	−	0.0254901i
$683$		−	1.20449e7i		−	0.987990i	−0.869465	−	0.493995i	$-0.835536\pi$
$683$		−	1.20449e7i		−	0.987990i	0.869465	−	0.493995i	$-0.164464\pi$
$684$	−2.13864e6	+	762287.i	−0.174782	+	0.0622986i
$685$	3.46494e6			0.282143
$686$			1.26698e7i			1.02792i
$687$	−9.74550e6	+	1.38197e7i	−0.787794	+	1.11714i
$688$			1.50065e7i			1.20867i
$689$	2.23198e7			1.79120
$690$	1.03046e6	−	1.46125e6i	0.0823964	−	0.116843i
$691$	−1.23021e7			−0.980130			−0.490065	−	0.871686i	$-0.663027\pi$
$691$	−1.23021e7			−0.980130			−0.490065	+	0.871686i	$0.663027\pi$
$692$	126636.			0.0100529
$693$	4.15636e6	+	1.24944e7i	0.328761	+	0.988288i
$694$	2.38766e7			1.88180
$695$	765107.			0.0600842
$696$	−6.80909e6	+	9.65570e6i	−0.532802	+	0.755546i
$697$	−3.10303e6			−0.241938
$698$		−	1.21407e7i		−	0.943200i
$699$	4.64201e6	−	6.58265e6i	0.359346	−	0.509574i
$700$		−	439875.i		−	0.0339300i
$701$	−1.53226e7			−1.17770			−0.588852	−	0.808241i	$-0.700420\pi$
$701$	−1.53226e7			−1.17770			−0.588852	+	0.808241i	$0.700420\pi$
$702$	5.73555e6	−	2.05796e7i	0.439271	−	1.57614i
$703$			2.56460e7i			1.95718i
$704$	−220341.	+	1.03649e7i	−0.0167557	+	0.788196i
$705$	−4.80189e6	+	6.80937e6i	−0.363864	+	0.515982i
$706$			8.17933e6i			0.617598i
$707$		−	1.31726e7i		−	0.991114i
$708$	2.36842e6	+	1.67018e6i	0.177573	+	0.125222i
$709$	−9.56725e6			−0.714779			−0.357389	−	0.933955i	$-0.616333\pi$
$709$	−9.56725e6			−0.714779			−0.357389	+	0.933955i	$0.616333\pi$
$710$	−8.99722e6			−0.669827
$711$	1.11181e7	−	3.96290e6i	0.824818	−	0.293995i
$712$		−	5.05752e6i		−	0.373884i
$713$		−	95147.5i		−	0.00700928i
$714$	−5.51984e6	−	3.89253e6i	−0.405211	−	0.285750i
$715$	−197143.	+	9.27367e6i	−0.0144217	+	0.678401i
$716$		−	702888.i		−	0.0512393i
$717$	−4.34909e6	+	6.16727e6i	−0.315937	+	0.448018i
$718$	−1.62907e7			−1.17931
$719$			4.67253e6i			0.337077i	0.985695	+	0.168539i	$0.0539048\pi$
$719$			4.67253e6i			0.337077i	−0.985695	+	0.168539i	$0.946095\pi$
$720$	−6.65869e6	+	2.37339e6i	−0.478693	+	0.170623i
$721$		−	7.55538e6i		−	0.541275i
$722$	−4.49675e6			−0.321038
$723$	1.43599e7	+	1.01265e7i	1.02166	+	0.720463i
$724$	245040.			0.0173736
$725$	2.89891e6			0.204828
$726$	9.34988e6	−	1.21294e7i	0.658361	−	0.854075i
$727$	1.71797e7			1.20553			0.602767	−	0.797917i	$-0.294065\pi$
$727$	1.71797e7			1.20553			0.602767	+	0.797917i	$0.294065\pi$
$728$	−2.03998e7			−1.42659
$729$	1.22805e7	+	7.42163e6i	0.855849	+	0.517226i
$730$	−8.64407e6			−0.600359
$731$		−	6.78393e6i		−	0.469556i
$732$	−2.09617e6	−	1.47820e6i	−0.144594	−	0.101966i
$733$		−	1.19522e7i		−	0.821652i	−0.911714	−	0.410826i	$-0.865240\pi$
$733$		−	1.19522e7i		−	0.821652i	0.911714	−	0.410826i	$-0.134760\pi$
$734$	1.57892e7			1.08173
$735$	453901.	+	320086.i	0.0309915	+	0.0218549i
$736$		−	1.40589e6i		−	0.0956660i
$737$	435274.	−	2.04755e7i	0.0295185	−	1.38856i
$738$	2.93584e6	+	8.23667e6i	0.198423	+	0.556687i
$739$			2.50610e7i			1.68806i	0.536297	+	0.844029i	$0.319823\pi$
$739$			2.50610e7i			1.68806i	−0.536297	+	0.844029i	$0.680177\pi$
$740$		−	1.86431e6i		−	0.125152i
$741$	1.48887e7	−	2.11130e7i	0.996117	−	1.41255i
$742$	−1.98850e7			−1.32592
$743$	−9.76597e6			−0.648998			−0.324499	−	0.945886i	$-0.605196\pi$
$743$	−9.76597e6			−0.648998			−0.324499	+	0.945886i	$0.605196\pi$
$744$	−185712.	+	263350.i	−0.0123000	+	0.0174422i
$745$			1.09908e7i			0.725499i
$746$			1.82498e7i			1.20064i
$747$	−7.09296e6	−	1.98997e7i	−0.465078	−	1.30480i
$748$	−23386.0	+	1.10009e6i	−0.00152828	+	0.0718908i
$749$		−	2.29521e7i		−	1.49492i
$750$	1.21426e6	+	856286.i	0.0788243	+	0.0555860i
$751$	−1.43799e7			−0.930372			−0.465186	−	0.885213i	$-0.654013\pi$
$751$	−1.43799e7			−0.930372			−0.465186	+	0.885213i	$0.654013\pi$
$752$			2.48789e7i			1.60430i
$753$	−2.37704e6	−	1.67626e6i	−0.152774	−	0.107735i
$754$			2.61593e7i			1.67571i
$755$	−8.89431e6			−0.567865
$756$	−715737.	+	2.56812e6i	−0.0455459	+	0.163422i
$757$	−1.30558e7			−0.828065			−0.414032	−	0.910262i	$-0.635880\pi$
$757$	−1.30558e7			−0.828065			−0.414032	+	0.910262i	$0.635880\pi$
$758$	1.33142e7			0.841668
$759$	2.79274e6	−	3.78674e6i	0.175965	−	0.238595i
$760$	−7.32303e6			−0.459893
$761$	1.22599e7			0.767407			0.383704	−	0.923456i	$-0.374648\pi$
$761$	1.22599e7			0.767407			0.383704	+	0.923456i	$0.374648\pi$
$762$	−2.19305e6	−	1.54652e6i	−0.136824	−	0.0964867i
$763$	−3.81259e6			−0.237087
$764$		−	4.83072e6i		−	0.299419i
$765$	3.01016e6	−	1.07293e6i	0.185967	−	0.0662852i
$766$			592374.i			0.0364774i
$767$	−3.29767e7			−2.02404
$768$	−4.48767e6	+	6.36378e6i	−0.274548	+	0.389325i
$769$			6.41394e6i			0.391119i	0.980692	+	0.195560i	$0.0626523\pi$
$769$			6.41394e6i			0.391119i	−0.980692	+	0.195560i	$0.937348\pi$
$770$	175637.	−	8.26202e6i	0.0106755	−	0.502180i
$771$	−1.92231e7	−	1.35559e7i	−1.16463	−	0.821284i
$772$		−	2.62822e6i		−	0.158715i
$773$			2.68851e7i			1.61832i	0.587591	+	0.809158i	$0.300077\pi$
$773$			2.68851e7i			1.61832i	−0.587591	+	0.809158i	$0.699923\pi$
$774$	−1.80072e7	+	6.41840e6i	−1.08042	+	0.385101i
$775$	79065.1			0.00472858
$776$	1.23213e7			0.734518
$777$	2.46103e7	+	1.73549e7i	1.46240	+	1.03126i
$778$			2.00150e6i			0.118552i
$779$			1.05741e7i			0.624312i
$780$	−1.08232e6	+	1.53479e6i	−0.0636967	+	0.0903258i
$781$	−2.36706e7	−	503196.i	−1.38861	−	0.0295196i
$782$			2.41351e6i			0.141134i
$783$	−1.69247e7	−	4.71693e6i	−0.986544	−	0.274951i
$784$	1.65838e6			0.0963595
$785$		−	9.57696e6i		−	0.554694i
$786$	5.15523e6	−	7.31042e6i	0.297640	−	0.422071i
$787$		−	1.74800e7i		−	1.00602i	−0.864282	−	0.503008i	$-0.832227\pi$
$787$		−	1.74800e7i		−	1.00602i	0.864282	−	0.503008i	$-0.167773\pi$
$788$	−696419.			−0.0399535
$789$	9.48672e6	−	1.34527e7i	0.542530	−	0.769340i
$790$	−7.40765e6			−0.422292
$791$	8.06207e6			0.458148
$792$	−1.51208e7	+	5.03005e6i	−0.856570	+	0.284944i
$793$	2.91860e7			1.64813
$794$	−1.10865e7			−0.624086
$795$	5.42199e6	−	7.68870e6i	0.304257	−	0.431455i
$796$	−2.64724e6			−0.148085
$797$			1.86660e6i			0.104089i	0.998645	+	0.0520445i	$0.0165738\pi$
$797$			1.86660e6i			0.104089i	−0.998645	+	0.0520445i	$0.983426\pi$
$798$	−1.32645e7	+	1.88098e7i	−0.737366	+	1.04563i
$799$		−	1.12468e7i		−	0.623252i
$800$	1.16826e6			0.0645379
$801$	7.08426e6	−	2.52508e6i	0.390133	−	0.139057i
$802$			1.78150e7i			0.978026i
$803$	−2.27415e7	−	483445.i	−1.24460	−	0.0264581i
$804$	2.38966e6	−	3.38868e6i	0.130375	−	0.184880i
$805$		−	2.53894e6i		−	0.138090i
$806$			713471.i			0.0386847i
$807$	−1.06189e7	−	7.48831e6i	−0.573977	−	0.404762i
$808$	1.59416e7			0.859019
$809$	1.85740e6			0.0997778			0.0498889	−	0.998755i	$-0.484113\pi$
$809$	1.85740e6			0.0997778			0.0498889	+	0.998755i	$0.484113\pi$
$810$	−5.69594e6	−	6.97502e6i	−0.305037	−	0.373536i
$811$		−	2.58157e7i		−	1.37826i	−0.724637	−	0.689130i	$-0.757993\pi$
$811$		−	2.58157e7i		−	1.37826i	0.724637	−	0.689130i	$-0.242007\pi$
$812$		−	3.26441e6i		−	0.173746i
$813$	−9.71225e6	−	6.84897e6i	−0.515340	−	0.363412i
$814$	744395.	−	3.50167e7i	0.0393770	−	1.85231i
$815$		−	1.18234e7i		−	0.623519i
$816$	5.49898e6	−	7.79789e6i	0.289106	−	0.409970i
$817$	−2.31174e7			−1.21167
$818$		−	2.16333e7i		−	1.13042i
$819$	−1.01851e7	−	2.85748e7i	−0.530584	−	1.48858i
$820$		−	768676.i		−	0.0399216i
$821$	3.43690e7			1.77955			0.889774	−	0.456402i	$-0.150862\pi$
$821$	3.43690e7			1.77955			0.889774	+	0.456402i	$0.150862\pi$
$822$	1.07708e7	+	7.59547e6i	0.555993	+	0.392080i
$823$	−242002.			−0.0124543			−0.00622715	−	0.999981i	$-0.501982\pi$
$823$	−242002.			−0.0124543			−0.00622715	+	0.999981i	$0.501982\pi$
$824$	9.14356e6			0.469135
$825$	3.14669e6	+	2.32069e6i	0.160960	+	0.118709i
$826$	2.93793e7			1.49827
$827$	9.63544e6			0.489900			0.244950	−	0.969536i	$-0.421228\pi$
$827$	9.63544e6			0.489900			0.244950	+	0.969536i	$0.421228\pi$
$828$	897342.	−	319844.i	0.0454864	−	0.0162130i
$829$	1.79915e7			0.909243			0.454621	−	0.890685i	$-0.349775\pi$
$829$	1.79915e7			0.909243			0.454621	+	0.890685i	$0.349775\pi$
$830$			1.32585e7i			0.668035i
$831$	1.82404e7	+	1.28629e7i	0.916288	+	0.646156i
$832$		−	2.38842e7i		−	1.19620i
$833$	−749696.			−0.0374345
$834$	2.37835e6	+	1.67719e6i	0.118402	+	0.0834961i
$835$			1.26066e7i			0.625720i
$836$	3.74875e6	+	79692.0i	0.185511	+	0.00394366i
$837$	−461605.	−	128650.i	−0.0227749	−	0.00634739i
$838$		−	3.03554e7i		−	1.49323i
$839$		−	2.31511e7i		−	1.13545i	−0.823219	−	0.567724i	$-0.807824\pi$
$839$		−	2.31511e7i		−	1.13545i	0.823219	−	0.567724i	$-0.192176\pi$
$840$	−4.95557e6	+	7.02729e6i	−0.242323	+	0.343629i
$841$	1.00233e6			0.0488673
$842$	1.00492e6			0.0488485
$843$	−9.87253e6	+	1.39998e7i	−0.478475	+	0.678506i
$844$		−	557066.i		−	0.0269185i
$845$		−	1.20873e7i		−	0.582353i
$846$	−2.98535e7	+	1.06409e7i	−1.43407	+	0.511153i
$847$	924156.	−	2.17265e7i	0.0442626	−	1.04060i
$848$		−	2.80916e7i		−	1.34149i
$849$	−2.74058e7	−	1.93263e7i	−1.30489	−	0.920193i
$850$	−2.00557e6			−0.0952116
$851$		−	1.07607e7i		−	0.509350i
$852$	−3.91747e6	−	2.76255e6i	−0.184887	−	0.130380i
$853$		−	3.79666e7i		−	1.78661i	−0.449454	−	0.893304i	$-0.648381\pi$
$853$		−	3.79666e7i		−	1.78661i	0.449454	−	0.893304i	$-0.351619\pi$
$854$	−2.60022e7			−1.22001
$855$	−3.65619e6	−	1.02576e7i	−0.171046	−	0.479880i
$856$	2.77768e7			1.29568
$857$	3.01704e6			0.140323			0.0701614	−	0.997536i	$-0.477649\pi$
$857$	3.01704e6			0.140323			0.0701614	+	0.997536i	$0.477649\pi$
$858$	−2.09416e7	+	2.83952e7i	−0.971160	+	1.31682i
$859$	−1.62097e7			−0.749537			−0.374768	−	0.927119i	$-0.622278\pi$
$859$	−1.62097e7			−0.749537			−0.374768	+	0.927119i	$0.622278\pi$
$860$	1.68050e6			0.0774803
$861$	1.01471e7	+	7.15563e6i	0.466481	+	0.328958i
$862$	−861200.			−0.0394763
$863$		−	3.39239e7i		−	1.55053i	−0.631639	−	0.775263i	$-0.717617\pi$
$863$		−	3.39239e7i		−	1.55053i	0.631639	−	0.775263i	$-0.282383\pi$
$864$	−6.82065e6	−	1.90092e6i	−0.310843	−	0.0866322i
$865$			607391.i			0.0276012i
$866$	3.00828e7			1.36309
$867$	1.02697e7	−	1.45630e7i	0.463991	−	0.657966i
$868$		−	89033.7i		−	0.00401102i
$869$	−1.94886e7	−	414295.i	−0.875450	−	0.0186106i
$870$	9.01132e6	+	6.35468e6i	0.403637	+	0.284640i
$871$			4.71822e7i			2.10733i
$872$		−	4.61402e6i		−	0.205489i
$873$	6.15169e6	+	1.72589e7i	0.273186	+	0.766440i
$874$	8.22447e6			0.364191
$875$	2.10979e6			0.0931578
$876$	−3.76370e6	−	2.65412e6i	−0.165712	−	0.116858i
$877$			1.91460e7i			0.840578i	0.907390	+	0.420289i	$0.138071\pi$
$877$			1.91460e7i			0.840578i	−0.907390	+	0.420289i	$0.861929\pi$
$878$			7.73660e6i			0.338699i
$879$	1.18233e7	−	1.67662e7i	0.516140	−	0.731918i
$880$	1.16718e7	+	248122.i	0.508078	+	0.0108009i
$881$			1.33987e7i			0.581596i	0.956784	+	0.290798i	$0.0939208\pi$
$881$			1.33987e7i			0.581596i	−0.956784	+	0.290798i	$0.906079\pi$
$882$	709302.	+	1.98999e6i	0.0307015	+	0.0861348i
$883$	−2.08452e7			−0.899716			−0.449858	−	0.893100i	$-0.648525\pi$
$883$	−2.08452e7			−0.899716			−0.449858	+	0.893100i	$0.648525\pi$
$884$		−	2.53497e6i		−	0.109104i
$885$	−8.01077e6	+	1.13598e7i	−0.343808	+	0.487541i
$886$		−	4.05120e7i		−	1.73380i
$887$	4.53293e7			1.93450			0.967252	−	0.253817i	$-0.0816862\pi$
$887$	4.53293e7			1.93450			0.967252	+	0.253817i	$0.0816862\pi$
$888$	−2.10030e7	+	2.97836e7i	−0.893819	+	1.26749i
$889$	−3.81044e6			−0.161704
$890$	−4.72000e6			−0.199741
$891$	−1.45952e7	−	1.86690e7i	−0.615908	−	0.787818i
$892$	−3.24163e6			−0.136412
$893$	−3.83256e7			−1.60828
$894$	−2.40928e7	+	3.41650e7i	−1.00819	+	1.42967i
$895$	3.37129e6			0.140682
$896$			2.93553e7i			1.22156i
$897$	−6.24706e6	+	8.85871e6i	−0.259236	+	0.367612i
$898$			4.35282e6i			0.180127i
$899$	586760.			0.0242137
$900$	265783.	+	745668.i	0.0109376	+	0.0306859i
$901$			1.26992e7i			0.521152i
$902$	306922.	−	1.44378e7i	0.0125607	−	0.590858i
$903$	−1.56438e7	+	2.21838e7i	−0.638444	+	0.905352i
$904$			9.75677e6i			0.397086i
$905$			1.17530e6i			0.0477008i
$906$	−2.76481e7	−	1.94971e7i	−1.11904	−	0.789134i
$907$	−2.39225e7			−0.965582			−0.482791	−	0.875736i	$-0.660377\pi$
$907$	−2.39225e7			−0.965582			−0.482791	+	0.875736i	$0.660377\pi$
$908$	−4.57290e6			−0.184067
$909$	7.95919e6	+	2.23300e7i	0.319492	+	0.896352i
$910$			1.90384e7i			0.762127i
$911$			1.06474e6i			0.0425057i	0.999774	+	0.0212528i	$0.00676550\pi$
$911$			1.06474e6i			0.0425057i	−0.999774	+	0.0212528i	$0.993234\pi$
$912$	−2.65727e7	−	1.87388e7i	−1.05791	−	0.746026i
$913$	−741521.	+	3.48815e7i	−0.0294406	+	1.38490i
$914$			3.93568e7i			1.55831i
$915$	7.08994e6	−	1.00540e7i	0.279956	−	0.396994i
$916$	5.65430e6			0.222659
$917$		−	1.27019e7i		−	0.498821i
$918$	1.17091e7	+	3.26333e6i	0.458581	+	0.127807i
$919$			3.20311e7i			1.25108i	0.780194	+	0.625538i	$0.215120\pi$
$919$			3.20311e7i			1.25108i	−0.780194	+	0.625538i	$0.784880\pi$
$920$	3.07263e6			0.119685
$921$	−3.17299e7	−	2.23755e7i	−1.23259	−	0.869210i
$922$	2.35597e7			0.912730
$923$	5.45448e7			2.10741
$924$	2.61329e6	−	3.54343e6i	0.100695	−	0.136535i
$925$	8.94186e6			0.343616
$926$	−2.83731e7			−1.08737
$927$	4.56513e6	+	1.28077e7i	0.174483	+	0.489523i
$928$	8.66992e6			0.330480
$929$			5.25517e6i			0.199778i	0.994999	+	0.0998889i	$0.0318487\pi$
$929$			5.25517e6i			0.199778i	−0.994999	+	0.0998889i	$0.968151\pi$
$930$	245775.	+	173318.i	0.00931817	+	0.00657107i
$931$			2.55472e6i			0.0965983i
$932$	−2.69328e6			−0.101564
$933$	−1.38545e7	−	9.77004e6i	−0.521059	−	0.367445i
$934$			4.07032e7i			1.52673i
$935$	−5.27640e6	−	112167.i	−0.197382	−	0.00419602i
$936$	3.45814e7	−	1.23260e7i	1.29019	−	0.459868i
$937$			2.65109e6i			0.0986452i	0.998783	+	0.0493226i	$0.0157062\pi$
$937$			2.65109e6i			0.0986452i	−0.998783	+	0.0493226i	$0.984294\pi$
$938$		−	4.20352e7i		−	1.55993i
$939$	1.69943e7	−	2.40989e7i	0.628983	−	0.891936i
$940$	2.78604e6			0.102841
$941$	3.74876e7			1.38011			0.690055	−	0.723757i	$-0.257586\pi$
$941$	3.74876e7			1.38011			0.690055	+	0.723757i	$0.257586\pi$
$942$	2.09936e7	−	2.97702e7i	0.770831	−	1.09308i
$943$		−	4.43675e6i		−	0.162475i
$944$			4.15042e7i			1.51587i
$945$	−1.23176e7	−	3.43292e6i	−0.448689	−	0.125050i
$946$	3.15642e7	+	671001.i	1.14674	+	0.0243778i
$947$			4.66679e7i			1.69100i	0.533975	+	0.845500i	$0.320698\pi$
$947$			4.66679e7i			1.69100i	−0.533975	+	0.845500i	$0.679302\pi$
$948$	−3.22535e6	−	2.27448e6i	−0.116562	−	0.0821981i
$949$	5.24038e7			1.88885
$950$			6.83432e6i			0.245689i
$951$	−724516.	−	510920.i	−0.0259774	−	0.0183190i
$952$		−	1.16068e7i		−	0.415068i
$953$	−4.25883e7			−1.51900			−0.759500	−	0.650508i	$-0.774556\pi$
$953$	−4.25883e7			−1.51900			−0.759500	+	0.650508i	$0.774556\pi$
$954$	3.37087e7	−	1.20150e7i	1.19914	−	0.427417i
$955$	2.31698e7			0.822079
$956$	2.52333e6			0.0892953
$957$	2.33523e7	+	1.72224e7i	0.824231	+	0.607873i
$958$	1.79571e7			0.632152
$959$	1.87144e7			0.657096
$960$	−8.22758e6	−	5.80200e6i	−0.288134	−	0.203189i
$961$	−2.86131e7			−0.999441
$962$			8.06899e7i			2.81114i
$963$	1.38682e7	+	3.89080e7i	0.481897	+	1.35199i
$964$		−	5.87533e6i		−	0.203629i
$965$	1.26058e7			0.435765
$966$	5.56558e6	−	7.89232e6i	0.191897	−	0.272121i
$967$			1.20397e6i			0.0414046i	0.999786	+	0.0207023i	$0.00659022\pi$
$967$			1.20397e6i			0.0414046i	−0.999786	+	0.0207023i	$0.993410\pi$
$968$	2.62936e7	+	1.11842e6i	0.901906	+	0.0383633i
$969$	1.20126e7	+	8.47113e6i	0.410985	+	0.289822i
$970$		−	1.14990e7i		−	0.392403i
$971$		−	1.43455e7i		−	0.488278i	−0.969740	−	0.244139i	$-0.921495\pi$
$971$		−	1.43455e7i		−	0.488278i	0.969740	−	0.244139i	$-0.0785054\pi$
$972$	−338412.	−	4.78589e6i	−0.0114890	−	0.162479i
$973$	4.13239e6			0.139933
$974$	1.53563e7			0.518668
$975$	−7.36136e6	−	5.19115e6i	−0.247997	−	0.174885i
$976$		−	3.67333e7i		−	1.23434i
$977$			1.05338e7i			0.353061i	0.984295	+	0.176531i	$0.0564874\pi$
$977$			1.05338e7i			0.353061i	−0.984295	+	0.176531i	$0.943513\pi$
$978$	2.59180e7	−	3.67533e7i	0.866473	−	1.22871i
$979$	−1.24177e7	−	263980.i	−0.414081	−	0.00880267i
$980$		−	185713.i		−	0.00617698i
$981$	6.46303e6	−	2.30365e6i	0.214419	−	0.0764266i
$982$	4.58520e7			1.51733
$983$			1.50067e7i			0.495337i	0.968845	+	0.247669i	$0.0796644\pi$
$983$			1.50067e7i			0.495337i	−0.968845	+	0.247669i	$0.920336\pi$
$984$	−8.65978e6	+	1.22801e7i	−0.285114	+	0.404309i
$985$		−	3.34026e6i		−	0.109696i
$986$	−1.48837e7			−0.487551
$987$	−2.59353e7	+	3.67779e7i	−0.847420	+	1.20169i
$988$	−8.63834e6			−0.281539
$989$	9.69973e6			0.315333
$990$	4.69436e6	+	1.41117e7i	0.152226	+	0.457607i
$991$	9.48745e6			0.306878			0.153439	−	0.988158i	$-0.450965\pi$
$991$	9.48745e6			0.306878			0.153439	+	0.988158i	$0.450965\pi$
$992$	236464.			0.00762932
$993$	−2.98463e7	+	4.23238e7i	−0.960543	+	1.36211i
$994$	−4.85946e7			−1.55999
$995$		−	1.26971e7i		−	0.406580i
$996$	−4.07096e6	+	5.77286e6i	−0.130031	+	0.184392i
$997$		−	247978.i		−	0.00790088i	−0.999992	−	0.00395044i	$-0.998743\pi$
$997$		−	247978.i		−	0.00790088i	0.999992	−	0.00395044i	$-0.00125747\pi$
$998$	4.25766e7			1.35315
$999$	−5.22052e7	−	1.45496e7i	−1.65501	−	0.461252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.f.a.131.57	yes	80
3.2	odd	2	inner	165.6.f.a.131.23	✓	80
11.10	odd	2	inner	165.6.f.a.131.24	yes	80
33.32	even	2	inner	165.6.f.a.131.58	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.f.a.131.23	✓	80	3.2	odd	2	inner
165.6.f.a.131.24	yes	80	11.10	odd	2	inner
165.6.f.a.131.57	yes	80	1.1	even	1	trivial
165.6.f.a.131.58	yes	80	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.10019 q^{2} +(-8.98370 + 12.7394i) q^{3} +5.21231 q^{4} +25.0000i q^{5} +(-54.8023 + 77.7129i) q^{6} +135.027i q^{7} -163.410 q^{8} +(-81.5861 - 228.895i) q^{9} +O(q^{10})\)	\(q+6.10019 q^{2} +(-8.98370 + 12.7394i) q^{3} +5.21231 q^{4} +25.0000i q^{5} +(-54.8023 + 77.7129i) q^{6} +135.027i q^{7} -163.410 q^{8} +(-81.5861 - 228.895i) q^{9} +152.505i q^{10} +(-8.52928 + 401.221i) q^{11} +(-46.8258 + 66.4018i) q^{12} -924.545i q^{13} +823.688i q^{14} +(-318.486 - 224.593i) q^{15} -1163.63 q^{16} +526.034 q^{17} +(-497.691 - 1396.30i) q^{18} -1792.55i q^{19} +130.308i q^{20} +(-1720.16 - 1213.04i) q^{21} +(-52.0302 + 2447.52i) q^{22} +752.129i q^{23} +(1468.03 - 2081.75i) q^{24} -625.000 q^{25} -5639.90i q^{26} +(3648.93 + 1016.96i) q^{27} +703.800i q^{28} -4638.26 q^{29} +(-1942.82 - 1370.06i) q^{30} -126.504 q^{31} -1869.22 q^{32} +(-5034.70 - 3713.11i) q^{33} +3208.91 q^{34} -3375.67 q^{35} +(-425.252 - 1193.07i) q^{36} -14307.0 q^{37} -10934.9i q^{38} +(11778.2 + 8305.84i) q^{39} -4085.25i q^{40} -5898.93 q^{41} +(-10493.3 - 7399.77i) q^{42} -12896.4i q^{43} +(-44.4572 + 2091.29i) q^{44} +(5722.36 - 2039.65i) q^{45} +4588.13i q^{46} -21380.5i q^{47} +(10453.7 - 14823.9i) q^{48} -1425.19 q^{49} -3812.62 q^{50} +(-4725.73 + 6701.37i) q^{51} -4819.02i q^{52} +24141.4i q^{53} +(22259.2 + 6203.65i) q^{54} +(-10030.5 - 213.232i) q^{55} -22064.7i q^{56} +(22836.1 + 16103.8i) q^{57} -28294.3 q^{58} -35668.0i q^{59} +(-1660.05 - 1170.65i) q^{60} +31568.0i q^{61} -771.700 q^{62} +(30906.9 - 11016.3i) q^{63} +25833.4 q^{64} +23113.6 q^{65} +(-30712.6 - 22650.7i) q^{66} -51032.9 q^{67} +2741.85 q^{68} +(-9581.69 - 6756.90i) q^{69} -20592.2 q^{70} +58996.3i q^{71} +(13332.0 + 37403.7i) q^{72} +56680.6i q^{73} -87275.3 q^{74} +(5614.81 - 7962.14i) q^{75} -9343.34i q^{76} +(-54175.5 - 1151.68i) q^{77} +(71849.1 + 50667.2i) q^{78} +48573.2i q^{79} -29090.6i q^{80} +(-45736.4 + 37349.2i) q^{81} -35984.6 q^{82} +86938.3 q^{83} +(-8966.02 - 6322.73i) q^{84} +13150.8i q^{85} -78670.3i q^{86} +(41668.8 - 59088.8i) q^{87} +(1393.77 - 65563.5i) q^{88} +30949.9i q^{89} +(34907.5 - 12442.3i) q^{90} +124838. q^{91} +3920.33i q^{92} +(1136.48 - 1611.59i) q^{93} -130425. i q^{94} +44813.8 q^{95} +(16792.5 - 23812.8i) q^{96} -75401.2 q^{97} -8693.90 q^{98} +(92533.1 - 30781.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * q^99

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