LMFDB - Embedded newform 165.6.c.b.34.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(34,165)]

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([0, 1, 0]))

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.20
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.72893i q^{2} -9.00000i q^{3} -0.820586 q^{4} +(-32.0393 - 45.8092i) q^{5} +51.5603 q^{6} -158.171i q^{7} +178.625i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q+5.72893i q^{2} -9.00000i q^{3} -0.820586 q^{4} +(-32.0393 - 45.8092i) q^{5} +51.5603 q^{6} -158.171i q^{7} +178.625i q^{8} -81.0000 q^{9} +(262.437 - 183.551i) q^{10} +121.000 q^{11} +7.38528i q^{12} +78.2418i q^{13} +906.152 q^{14} +(-412.283 + 288.354i) q^{15} -1049.59 q^{16} +88.2340i q^{17} -464.043i q^{18} -1865.42 q^{19} +(26.2910 + 37.5904i) q^{20} -1423.54 q^{21} +693.200i q^{22} +503.122i q^{23} +1607.62 q^{24} +(-1071.96 + 2935.39i) q^{25} -448.241 q^{26} +729.000i q^{27} +129.793i q^{28} -1050.22 q^{29} +(-1651.96 - 2361.94i) q^{30} -9057.51 q^{31} -297.011i q^{32} -1089.00i q^{33} -505.486 q^{34} +(-7245.70 + 5067.70i) q^{35} +66.4675 q^{36} +3899.39i q^{37} -10686.9i q^{38} +704.176 q^{39} +(8182.64 - 5723.01i) q^{40} -9454.73 q^{41} -8155.37i q^{42} -8918.80i q^{43} -99.2910 q^{44} +(2595.19 + 3710.54i) q^{45} -2882.35 q^{46} +9431.40i q^{47} +9446.27i q^{48} -8211.19 q^{49} +(-16816.6 - 6141.20i) q^{50} +794.106 q^{51} -64.2042i q^{52} -25507.5i q^{53} -4176.39 q^{54} +(-3876.76 - 5542.91i) q^{55} +28253.3 q^{56} +16788.8i q^{57} -6016.65i q^{58} -9907.66 q^{59} +(338.314 - 236.619i) q^{60} -15614.3 q^{61} -51889.8i q^{62} +12811.9i q^{63} -31885.2 q^{64} +(3584.19 - 2506.81i) q^{65} +6238.80 q^{66} -16879.9i q^{67} -72.4036i q^{68} +4528.10 q^{69} +(-29032.5 - 41510.1i) q^{70} +71467.7 q^{71} -14468.6i q^{72} -65733.0i q^{73} -22339.3 q^{74} +(26418.5 + 9647.67i) q^{75} +1530.74 q^{76} -19138.7i q^{77} +4034.17i q^{78} -104481. q^{79} +(33628.0 + 48080.7i) q^{80} +6561.00 q^{81} -54165.4i q^{82} +15457.9i q^{83} +1168.14 q^{84} +(4041.93 - 2826.96i) q^{85} +51095.2 q^{86} +9452.01i q^{87} +21613.6i q^{88} -2774.62 q^{89} +(-21257.4 + 14867.6i) q^{90} +12375.6 q^{91} -412.855i q^{92} +81517.6i q^{93} -54031.8 q^{94} +(59766.8 + 85453.4i) q^{95} -2673.10 q^{96} +125401. i q^{97} -47041.3i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * 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 $

$2$			5.72893i			1.01274i	0.862316	+	0.506370i	$0.169013\pi$
$2$			5.72893i			1.01274i	−0.862316	+	0.506370i	$0.830987\pi$
$3$		−	9.00000i		−	0.577350i
$3$		−	9.00000i		−	0.577350i
$4$	−0.820586			−0.0256433
$5$	−32.0393	−	45.8092i	−0.573137	−	0.819460i
$5$	−32.0393	−	45.8092i	−0.573137	−	0.819460i
$6$	51.5603			0.584706
$7$		−	158.171i		−	1.22006i	−0.792377	−	0.610032i	$-0.791156\pi$
$7$		−	158.171i		−	1.22006i	0.792377	−	0.610032i	$-0.208844\pi$
$8$			178.625i			0.986770i
$9$	−81.0000			−0.333333
$10$	262.437	−	183.551i	0.829900	−	0.580439i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$			7.38528i			0.0148052i
$13$			78.2418i			0.128405i	0.997937	+	0.0642023i	$0.0204503\pi$
$13$			78.2418i			0.128405i	−0.997937	+	0.0642023i	$0.979550\pi$
$14$	906.152			1.23561
$15$	−412.283	+	288.354i	−0.473115	+	0.330901i
$16$	−1049.59			−1.02499
$17$			88.2340i			0.0740480i	0.999314	+	0.0370240i	$0.0117878\pi$
$17$			88.2340i			0.0740480i	−0.999314	+	0.0370240i	$0.988212\pi$
$18$		−	464.043i		−	0.337580i
$19$	−1865.42			−1.18548			−0.592738	−	0.805395i	$-0.701953\pi$
$19$	−1865.42			−1.18548			−0.592738	+	0.805395i	$0.701953\pi$
$20$	26.2910	+	37.5904i	0.0146971	+	0.0210137i
$21$	−1423.54			−0.704405
$22$			693.200i			0.305353i
$23$			503.122i			0.198314i	0.995072	+	0.0991571i	$0.0316146\pi$
$23$			503.122i			0.198314i	−0.995072	+	0.0991571i	$0.968385\pi$
$24$	1607.62			0.569712
$25$	−1071.96	+	2935.39i	−0.343028	+	0.939325i
$26$	−448.241			−0.130040
$27$			729.000i			0.192450i
$28$			129.793i			0.0312865i
$29$	−1050.22			−0.231892			−0.115946	−	0.993255i	$-0.536990\pi$
$29$	−1050.22			−0.231892			−0.115946	+	0.993255i	$0.536990\pi$
$30$	−1651.96	−	2361.94i	−0.335117	−	0.479143i
$31$	−9057.51			−1.69280			−0.846398	−	0.532550i	$-0.821234\pi$
$31$	−9057.51			−1.69280			−0.846398	+	0.532550i	$0.821234\pi$
$32$		−	297.011i		−	0.0512741i
$33$		−	1089.00i		−	0.174078i
$34$	−505.486			−0.0749914
$35$	−7245.70	+	5067.70i	−0.999794	+	0.699264i
$36$	66.4675			0.00854778
$37$			3899.39i			0.468266i	0.972205	+	0.234133i	$0.0752251\pi$
$37$			3899.39i			0.468266i	−0.972205	+	0.234133i	$0.924775\pi$
$38$		−	10686.9i		−	1.20058i
$39$	704.176			0.0741344
$40$	8182.64	−	5723.01i	0.808619	−	0.565555i
$41$	−9454.73			−0.878394			−0.439197	−	0.898391i	$-0.644737\pi$
$41$	−9454.73			−0.878394			−0.439197	+	0.898391i	$0.644737\pi$
$42$		−	8155.37i		−	0.713379i
$43$		−	8918.80i		−	0.735589i	−0.929907	−	0.367795i	$-0.880113\pi$
$43$		−	8918.80i		−	0.735589i	0.929907	−	0.367795i	$-0.119887\pi$
$44$	−99.2910			−0.00773175
$45$	2595.19	+	3710.54i	0.191046	+	0.273153i
$46$	−2882.35			−0.200841
$47$			9431.40i			0.622776i	0.950283	+	0.311388i	$0.100794\pi$
$47$			9431.40i			0.622776i	−0.950283	+	0.311388i	$0.899206\pi$
$48$			9446.27i			0.591776i
$49$	−8211.19			−0.488558
$50$	−16816.6	−	6141.20i	−0.951293	−	0.347399i
$51$	794.106			0.0427516
$52$		−	64.2042i		−	0.00329272i
$53$		−	25507.5i		−	1.24732i	−0.781695	−	0.623661i	$-0.785645\pi$
$53$		−	25507.5i		−	1.24732i	0.781695	−	0.623661i	$-0.214355\pi$
$54$	−4176.39			−0.194902
$55$	−3876.76	−	5542.91i	−0.172807	−	0.247076i
$56$	28253.3			1.20392
$57$			16788.8i			0.684435i
$58$		−	6016.65i		−	0.234847i
$59$	−9907.66			−0.370545			−0.185273	−	0.982687i	$-0.559317\pi$
$59$	−9907.66			−0.370545			−0.185273	+	0.982687i	$0.559317\pi$
$60$	338.314	−	236.619i	0.0121322	−	0.00848540i
$61$	−15614.3			−0.537278			−0.268639	−	0.963241i	$-0.586574\pi$
$61$	−15614.3			−0.537278			−0.268639	+	0.963241i	$0.586574\pi$
$62$		−	51889.8i		−	1.71436i
$63$			12811.9i			0.406688i
$64$	−31885.2			−0.973058
$65$	3584.19	−	2506.81i	0.105222	−	0.0735934i
$66$	6238.80			0.176295
$67$		−	16879.9i		−	0.459392i	−0.973262	−	0.229696i	$-0.926227\pi$
$67$		−	16879.9i		−	0.459392i	0.973262	−	0.229696i	$-0.0737732\pi$
$68$		−	72.4036i		−	0.00189884i
$69$	4528.10			0.114497
$70$	−29032.5	−	41510.1i	−0.708173	−	1.01253i
$71$	71467.7			1.68253			0.841267	−	0.540620i	$-0.181810\pi$
$71$	71467.7			1.68253			0.841267	+	0.540620i	$0.181810\pi$
$72$		−	14468.6i		−	0.328923i
$73$		−	65733.0i		−	1.44370i	−0.692050	−	0.721849i	$-0.743292\pi$
$73$		−	65733.0i		−	1.44370i	0.692050	−	0.721849i	$-0.256708\pi$
$74$	−22339.3			−0.474232
$75$	26418.5	+	9647.67i	0.542320	+	0.198047i
$76$	1530.74			0.0303995
$77$		−	19138.7i		−	0.367863i
$78$			4034.17i			0.0750789i
$79$	−104481.			−1.88352			−0.941762	−	0.336281i	$-0.890831\pi$
$79$	−104481.			−1.88352			−0.941762	+	0.336281i	$0.890831\pi$
$80$	33628.0	+	48080.7i	0.587457	+	0.839934i
$81$	6561.00			0.111111
$82$		−	54165.4i		−	0.889585i
$83$			15457.9i			0.246294i	0.992388	+	0.123147i	$0.0392987\pi$
$83$			15457.9i			0.246294i	−0.992388	+	0.123147i	$0.960701\pi$
$84$	1168.14			0.0180633
$85$	4041.93	−	2826.96i	0.0606794	−	0.0424397i
$86$	51095.2			0.744961
$87$			9452.01i			0.133883i
$88$			21613.6i			0.297522i
$89$	−2774.62			−0.0371303			−0.0185651	−	0.999828i	$-0.505910\pi$
$89$	−2774.62			−0.0371303			−0.0185651	+	0.999828i	$0.505910\pi$
$90$	−21257.4	+	14867.6i	−0.276633	+	0.193480i
$91$	12375.6			0.156662
$92$		−	412.855i		−	0.00508544i
$93$			81517.6i			0.977336i
$94$	−54031.8			−0.630710
$95$	59766.8	+	85453.4i	0.679440	+	0.971450i
$96$	−2673.10			−0.0296031
$97$			125401.i			1.35323i	0.736338	+	0.676614i	$0.236553\pi$
$97$			125401.i			1.35323i	−0.736338	+	0.676614i	$0.763447\pi$
$98$		−	47041.3i		−	0.494782i
$99$	−9801.00			−0.100504
$100$	879.638	−	2408.74i	0.00879638	−	0.0240874i
$101$	50984.8			0.497322			0.248661	−	0.968591i	$-0.420010\pi$
$101$	50984.8			0.497322			0.248661	+	0.968591i	$0.420010\pi$
$102$			4549.37i			0.0432963i
$103$			51464.8i			0.477989i	0.971021	+	0.238994i	$0.0768177\pi$
$103$			51464.8i			0.477989i	−0.971021	+	0.238994i	$0.923182\pi$
$104$	−13975.9			−0.126706
$105$	45609.3	+	65211.3i	0.403720	+	0.577231i
$106$	146131.			1.26321
$107$			139655.i			1.17923i	0.807686	+	0.589613i	$0.200720\pi$
$107$			139655.i			1.17923i	−0.807686	+	0.589613i	$0.799280\pi$
$108$		−	598.208i		−	0.00493506i
$109$	−144034.			−1.16118			−0.580591	−	0.814195i	$-0.697178\pi$
$109$	−144034.			−1.16118			−0.580591	+	0.814195i	$0.697178\pi$
$110$	31754.9	−	22209.7i	0.250224	−	0.175009i
$111$	35094.5			0.270353
$112$			166014.i			1.25055i
$113$		−	62064.4i		−	0.457242i	−0.973515	−	0.228621i	$-0.926578\pi$
$113$		−	62064.4i		−	0.457242i	0.973515	−	0.228621i	$-0.0734217\pi$
$114$	−96181.7			−0.693155
$115$	23047.6	−	16119.7i	0.162510	−	0.113661i
$116$	861.799			0.00594649
$117$		−	6337.59i		−	0.0428015i
$118$		−	56760.3i		−	0.375266i
$119$	13956.1			0.0903434
$120$	−51507.1	−	73643.8i	−0.326523	−	0.466856i
$121$	14641.0			0.0909091
$122$		−	89453.4i		−	0.544124i
$123$			85092.5i			0.507141i
$124$	7432.47			0.0434089
$125$	168813.	−	44942.2i	0.966341	−	0.257264i
$126$	−73398.3			−0.411870
$127$			285166.i			1.56888i	0.620207	+	0.784438i	$0.287049\pi$
$127$			285166.i			1.56888i	−0.620207	+	0.784438i	$0.712951\pi$
$128$		−	192172.i		−	1.03673i
$129$	−80269.2			−0.424693
$130$	14361.4	+	20533.6i	0.0745310	+	0.106563i
$131$	−198363.			−1.00991			−0.504954	−	0.863146i	$-0.668491\pi$
$131$	−198363.			−1.00991			−0.504954	+	0.863146i	$0.668491\pi$
$132$			893.619i			0.00446393i
$133$			295056.i			1.44636i
$134$	96703.8			0.465245
$135$	33394.9	−	23356.7i	0.157705	−	0.110300i
$136$	−15760.7			−0.0730684
$137$		−	166328.i		−	0.757120i	−0.925577	−	0.378560i	$-0.876419\pi$
$137$		−	166328.i		−	0.757120i	0.925577	−	0.378560i	$-0.123581\pi$
$138$			25941.1i			0.115955i
$139$	301037.			1.32155			0.660774	−	0.750585i	$-0.270228\pi$
$139$	301037.			1.32155			0.660774	+	0.750585i	$0.270228\pi$
$140$	5945.73	−	4158.49i	0.0256380	−	0.0179315i
$141$	84882.6			0.359560
$142$			409433.i			1.70397i
$143$			9467.26i			0.0387154i
$144$	85016.4			0.341662
$145$	33648.4	+	48109.9i	0.132906	+	0.190027i
$146$	376580.			1.46209
$147$			73900.7i			0.282069i
$148$		−	3199.79i		−	0.0120079i
$149$	−107457.			−0.396525			−0.198263	−	0.980149i	$-0.563530\pi$
$149$	−107457.			−0.396525			−0.198263	+	0.980149i	$0.563530\pi$
$150$	−55270.8	+	151350.i	−0.200571	+	0.549229i
$151$	24082.4			0.0859522			0.0429761	−	0.999076i	$-0.486316\pi$
$151$	24082.4			0.0859522			0.0429761	+	0.999076i	$0.486316\pi$
$152$		−	333210.i		−	1.16979i
$153$		−	7146.95i		−	0.0246827i
$154$	109644.			0.372550
$155$	290197.	+	414917.i	0.970204	+	1.38718i
$156$	−577.837			−0.00190105
$157$		−	479707.i		−	1.55320i	−0.629994	−	0.776600i	$-0.716943\pi$
$157$		−	479707.i		−	1.55320i	0.629994	−	0.776600i	$-0.283057\pi$
$158$		−	598566.i		−	1.90752i
$159$	−229568.			−0.720142
$160$	−13605.9	+	9516.05i	−0.0420171	+	0.0293871i
$161$	79579.5			0.241956
$162$			37587.5i			0.112527i
$163$		−	437032.i		−	1.28838i	−0.764866	−	0.644190i	$-0.777195\pi$
$163$		−	437032.i		−	1.28838i	0.764866	−	0.644190i	$-0.222805\pi$
$164$	7758.42			0.0225249
$165$	−49886.2	+	34890.8i	−0.142650	+	0.0997703i
$166$	−88557.0			−0.249432
$167$		−	592592.i		−	1.64424i	−0.569316	−	0.822119i	$-0.692792\pi$
$167$		−	592592.i		−	1.64424i	0.569316	−	0.822119i	$-0.307208\pi$
$168$		−	254280.i		−	0.695086i
$169$	365171.			0.983512
$170$	16195.4	+	23155.9i	0.0429804	+	0.0614524i
$171$	151099.			0.395159
$172$			7318.65i			0.0188630i
$173$		−	193454.i		−	0.491432i	−0.969342	−	0.245716i	$-0.920977\pi$
$173$		−	193454.i		−	0.491432i	0.969342	−	0.245716i	$-0.0790231\pi$
$174$	−54149.9			−0.135589
$175$	464295.	+	169554.i	1.14604	+	0.418517i
$176$	−127000.			−0.309045
$177$			89169.0i			0.213934i
$178$		−	15895.6i		−	0.0376033i
$179$	373735.			0.871828			0.435914	−	0.899988i	$-0.356425\pi$
$179$	373735.			0.871828			0.435914	+	0.899988i	$0.356425\pi$
$180$	−2129.57	−	3044.82i	−0.00489905	−	0.00700456i
$181$	−234887.			−0.532921			−0.266461	−	0.963846i	$-0.585854\pi$
$181$	−234887.			−0.532921			−0.266461	+	0.963846i	$0.585854\pi$
$182$			70899.0i			0.158658i
$183$			140529.i			0.310198i
$184$	−89869.9			−0.195691
$185$	178628.	−	124934.i	0.383725	−	0.268380i
$186$	−467008.			−0.989788
$187$			10676.3i			0.0223263i
$188$		−	7739.28i		−	0.0159700i
$189$	115307.			0.234802
$190$	−489556.	+	342400.i	−0.983826	+	0.688096i
$191$	261514.			0.518695			0.259348	−	0.965784i	$-0.416492\pi$
$191$	261514.			0.518695			0.259348	+	0.965784i	$0.416492\pi$
$192$			286967.i			0.561796i
$193$		−	688977.i		−	1.33141i	−0.746215	−	0.665705i	$-0.768131\pi$
$193$		−	688977.i		−	1.33141i	0.746215	−	0.665705i	$-0.231869\pi$
$194$	−718412.			−1.37047
$195$	−22561.3	−	32257.7i	−0.0424892	−	0.0607502i
$196$	6737.99			0.0125282
$197$			625063.i			1.14752i	0.819025	+	0.573758i	$0.194515\pi$
$197$			625063.i			1.14752i	−0.819025	+	0.573758i	$0.805485\pi$
$198$		−	56149.2i		−	0.101784i
$199$	−1.02019e6			−1.82619			−0.913097	−	0.407742i	$-0.866316\pi$
$199$	−1.02019e6			−1.82619			−0.913097	+	0.407742i	$0.866316\pi$
$200$	−524333.	−	191479.i	−0.926898	−	0.338490i
$201$	−151919.			−0.265230
$202$			292088.i			0.503658i
$203$			166115.i			0.282924i
$204$	−651.632			−0.00109629
$205$	302923.	+	433113.i	0.503440	+	0.719808i
$206$	−294838.			−0.484079
$207$		−	40752.9i		−	0.0661047i
$208$		−	82121.4i		−	0.131613i
$209$	−225716.			−0.357434
$210$	−373591.	+	261293.i	−0.584585	+	0.408864i
$211$	−544322.			−0.841685			−0.420843	−	0.907134i	$-0.638266\pi$
$211$	−544322.			−0.841685			−0.420843	+	0.907134i	$0.638266\pi$
$212$			20931.1i			0.0319855i
$213$		−	643209.i		−	0.971412i
$214$	−800073.			−1.19425
$215$	−408563.	+	285752.i	−0.602786	+	0.421593i
$216$	−130217.			−0.189904
$217$			1.43264e6i			2.06532i
$218$		−	825163.i		−	1.17598i
$219$	−591597.			−0.833520
$220$	3181.22	+	4548.44i	0.00443135	+	0.00633586i
$221$	−6903.58			−0.00950810
$222$			201054.i			0.273798i
$223$		−	852497.i		−	1.14797i	−0.818866	−	0.573985i	$-0.805397\pi$
$223$		−	852497.i		−	1.14797i	0.818866	−	0.573985i	$-0.194603\pi$
$224$	−46978.7			−0.0625577
$225$	86829.0	−	237767.i	0.114343	−	0.313108i
$226$	355562.			0.463068
$227$		−	909729.i		−	1.17178i	−0.810390	−	0.585891i	$-0.800744\pi$
$227$		−	909729.i		−	1.17178i	0.810390	−	0.585891i	$-0.199256\pi$
$228$		−	13776.6i		−	0.0175512i
$229$	561762.			0.707886			0.353943	−	0.935267i	$-0.384841\pi$
$229$	561762.			0.707886			0.353943	+	0.935267i	$0.384841\pi$
$230$	92348.5	+	132038.i	0.115109	+	0.164581i
$231$	−172249.			−0.212386
$232$		−	187596.i		−	0.228825i
$233$			604654.i			0.729654i	0.931075	+	0.364827i	$0.118872\pi$
$233$			604654.i			0.729654i	−0.931075	+	0.364827i	$0.881128\pi$
$234$	36307.6			0.0433468
$235$	432045.	−	302176.i	0.510340	−	0.356936i
$236$	8130.10			0.00950201
$237$			940332.i			1.08745i
$238$			79953.4i			0.0914944i
$239$	1.13697e6			1.28752			0.643760	−	0.765227i	$-0.277373\pi$
$239$	1.13697e6			1.28752			0.643760	+	0.765227i	$0.277373\pi$
$240$	432726.	−	302652.i	0.484936	−	0.339169i
$241$	261399.			0.289909			0.144954	−	0.989438i	$-0.453696\pi$
$241$	261399.			0.289909			0.144954	+	0.989438i	$0.453696\pi$
$242$			83877.2i			0.0920673i
$243$		−	59049.0i		−	0.0641500i
$244$	12812.9			0.0137776
$245$	263081.	+	376148.i	0.280010	+	0.400353i
$246$	−487489.			−0.513602
$247$		−	145954.i		−	0.152220i
$248$		−	1.61789e6i		−	1.67040i
$249$	139121.			0.142198
$250$	257471.	+	967116.i	0.260542	+	0.978653i
$251$	565375.			0.566438			0.283219	−	0.959055i	$-0.408598\pi$
$251$	565375.			0.566438			0.283219	+	0.959055i	$0.408598\pi$
$252$		−	10513.3i		−	0.0104288i
$253$			60877.8i			0.0597940i
$254$	−1.63370e6			−1.58886
$255$	−25442.6	−	36377.3i	−0.0245025	−	0.0350332i
$256$	80614.3			0.0768798
$257$		−	1.51946e6i		−	1.43501i	−0.696551	−	0.717507i	$-0.745283\pi$
$257$		−	1.51946e6i		−	1.43501i	0.696551	−	0.717507i	$-0.254717\pi$
$258$		−	459856.i		−	0.430103i
$259$	616772.			0.571315
$260$	−2941.14	+	2057.06i	−0.00269825	+	0.00188718i
$261$	85068.1			0.0772975
$262$		−	1.13641e6i		−	1.02278i
$263$			730370.i			0.651109i	0.945523	+	0.325554i	$0.105551\pi$
$263$			730370.i			0.651109i	−0.945523	+	0.325554i	$0.894449\pi$
$264$	194522.			0.171775
$265$	−1.16848e6	+	817244.i	−1.02213	+	0.714886i
$266$	−1.69035e6			−1.46478
$267$			24971.6i			0.0214372i
$268$			13851.4i			0.0117803i
$269$	475262.			0.400453			0.200227	−	0.979750i	$-0.435832\pi$
$269$	475262.			0.400453			0.200227	+	0.979750i	$0.435832\pi$
$270$	133809.	+	191317.i	0.111706	+	0.159714i
$271$	−961313.			−0.795136			−0.397568	−	0.917573i	$-0.630146\pi$
$271$	−961313.			−0.795136			−0.397568	+	0.917573i	$0.630146\pi$
$272$		−	92609.1i		−	0.0758982i
$273$		−	111381.i		−	0.0904488i
$274$	952883.			0.766766
$275$	−129708.	+	355182.i	−0.103427	+	0.283217i
$276$	−3715.70			−0.00293608
$277$			428260.i			0.335358i	0.985842	+	0.167679i	$0.0536272\pi$
$277$			428260.i			0.335358i	−0.985842	+	0.167679i	$0.946373\pi$
$278$			1.72462e6i			1.33839i
$279$	733659.			0.564265
$280$	−905216.	−	1.29426e6i	−0.690013	−	0.986567i
$281$	−212752.			−0.160734			−0.0803670	−	0.996765i	$-0.525609\pi$
$281$	−212752.			−0.160734			−0.0803670	+	0.996765i	$0.525609\pi$
$282$			486286.i			0.364141i
$283$			563864.i			0.418512i	0.977861	+	0.209256i	$0.0671043\pi$
$283$			563864.i			0.418512i	−0.977861	+	0.209256i	$0.932896\pi$
$284$	−58645.4			−0.0431458
$285$	769080.	−	537901.i	0.560867	−	0.392275i
$286$	−54237.2			−0.0392087
$287$			1.49547e6i			1.07170i
$288$			24057.9i			0.0170914i
$289$	1.41207e6			0.994517
$290$	−275618.	+	192769.i	−0.192448	+	0.134599i
$291$	1.12861e6			0.781287
$292$			53939.6i			0.0370212i
$293$		−	1.80961e6i		−	1.23145i	−0.787963	−	0.615723i	$-0.788864\pi$
$293$		−	1.80961e6i		−	1.23145i	0.787963	−	0.615723i	$-0.211136\pi$
$294$	−423371.			−0.285663
$295$	317435.	+	453862.i	0.212373	+	0.303647i
$296$	−696527.			−0.462071
$297$			88209.0i			0.0580259i
$298$		−	615616.i		−	0.401577i
$299$	−39365.2			−0.0254644
$300$	−21678.7	−	7916.75i	−0.0139069	−	0.00507859i
$301$	−1.41070e6			−0.897466
$302$			137966.i			0.0870473i
$303$		−	458863.i		−	0.287129i
$304$	1.95792e6			1.21510
$305$	500273.	+	715281.i	0.307934	+	0.440278i
$306$	40944.3			0.0249971
$307$		−	774049.i		−	0.468730i	−0.972149	−	0.234365i	$-0.924699\pi$
$307$		−	774049.i		−	0.468730i	0.972149	−	0.234365i	$-0.0753011\pi$
$308$			15705.0i			0.00943324i
$309$	463184.			0.275967
$310$	−2.37703e6	+	1.66251e6i	−1.40485	+	0.982565i
$311$	1.35808e6			0.796205			0.398102	−	0.917341i	$-0.369669\pi$
$311$	1.35808e6			0.796205			0.398102	+	0.917341i	$0.369669\pi$
$312$			125783.i			0.0731536i
$313$		−	3.38315e6i		−	1.95191i	−0.217968	−	0.975956i	$-0.569943\pi$
$313$		−	3.38315e6i		−	1.95191i	0.217968	−	0.975956i	$-0.430057\pi$
$314$	2.74821e6			1.57299
$315$	586902.	−	410484.i	0.333265	−	0.233088i
$316$	85736.0			0.0482998
$317$			668139.i			0.373438i	0.982413	+	0.186719i	$0.0597854\pi$
$317$			668139.i			0.373438i	−0.982413	+	0.186719i	$0.940215\pi$
$318$		−	1.31518e6i		−	0.729317i
$319$	−127077.			−0.0699182
$320$	1.02158e6	+	1.46063e6i	0.557696	+	0.797382i
$321$	1.25689e6			0.680826
$322$			455905.i			0.245039i
$323$		−	164593.i		−	0.0877821i
$324$	−5383.87			−0.00284926
$325$	−229670.	−	83872.3i	−0.120614	−	0.0440464i
$326$	2.50372e6			1.30479
$327$			1.29631e6i			0.670409i
$328$		−	1.68885e6i		−	0.866773i
$329$	1.49178e6			0.759827
$330$	−199887.	−	285794.i	−0.101041	−	0.144467i
$331$	94884.0			0.0476018			0.0238009	−	0.999717i	$-0.492423\pi$
$331$	94884.0			0.0476018			0.0238009	+	0.999717i	$0.492423\pi$
$332$		−	12684.5i		−	0.00631581i
$333$		−	315851.i		−	0.156089i
$334$	3.39491e6			1.66519
$335$	−773256.	+	540822.i	−0.376453	+	0.263295i
$336$	1.49413e6			0.722005
$337$			507319.i			0.243336i	0.992571	+	0.121668i	$0.0388243\pi$
$337$			507319.i			0.243336i	−0.992571	+	0.121668i	$0.961176\pi$
$338$			2.09204e6i			0.996043i
$339$	−558580.			−0.263989
$340$	−3316.75	+	2319.76i	−0.00155602	+	0.00108829i
$341$	−1.09596e6			−0.510397
$342$			865635.i			0.400193i
$343$		−	1.35961e6i		−	0.623993i
$344$	1.59312e6			0.725858
$345$	−145077.	−	207429.i	−0.0656223	−	0.0938255i
$346$	1.10829e6			0.497693
$347$			2.91869e6i			1.30126i	0.759394	+	0.650631i	$0.225495\pi$
$347$			2.91869e6i			1.30126i	−0.759394	+	0.650631i	$0.774505\pi$
$348$		−	7756.19i		−	0.00343321i
$349$	1.69598e6			0.745346			0.372673	−	0.927963i	$-0.378441\pi$
$349$	1.69598e6			0.745346			0.372673	+	0.927963i	$0.378441\pi$
$350$	−971361.	+	2.65991e6i	−0.423849	+	1.16064i
$351$	−57038.3			−0.0247115
$352$		−	35938.4i		−	0.0154597i
$353$			2.54669e6i			1.08777i	0.839159	+	0.543887i	$0.183048\pi$
$353$			2.54669e6i			1.08777i	−0.839159	+	0.543887i	$0.816952\pi$
$354$	−510842.			−0.216660
$355$	−2.28978e6	−	3.27388e6i	−0.964322	−	1.37877i
$356$	2276.81			0.000952144
$357$		−	125605.i		−	0.0521598i
$358$			2.14110e6i			0.882936i
$359$	425376.			0.174196			0.0870978	−	0.996200i	$-0.472241\pi$
$359$	425376.			0.174196			0.0870978	+	0.996200i	$0.472241\pi$
$360$	−662794.	+	463564.i	−0.269540	+	0.188518i
$361$	1.00369e6			0.405353
$362$		−	1.34565e6i		−	0.539711i
$363$		−	131769.i		−	0.0524864i
$364$	−10155.3			−0.00401733
$365$	−3.01118e6	+	2.10604e6i	−1.18305	+	0.827437i
$366$	−805081.			−0.314150
$367$		−	1.88623e6i		−	0.731019i	−0.930808	−	0.365509i	$-0.880895\pi$
$367$		−	1.88623e6i		−	0.731019i	0.930808	−	0.365509i	$-0.119105\pi$
$368$		−	528070.i		−	0.203269i
$369$	765833.			0.292798
$370$	715737.	+	1.02335e6i	0.271800	+	0.388614i
$371$	−4.03456e6			−1.52181
$372$		−	66892.3i		−	0.0250622i
$373$		−	903282.i		−	0.336164i	−0.985773	−	0.168082i	$-0.946243\pi$
$373$		−	903282.i		−	0.336164i	0.985773	−	0.168082i	$-0.0537574\pi$
$374$	−61163.8			−0.0226108
$375$	−404480.	−	1.51932e6i	−0.148532	−	0.557917i
$376$	−1.68468e6			−0.614537
$377$		−	82171.3i		−	0.0297760i
$378$			660585.i			0.237793i
$379$	−4.94830e6			−1.76953			−0.884766	−	0.466036i	$-0.845682\pi$
$379$	−4.94830e6			−1.76953			−0.884766	+	0.466036i	$0.845682\pi$
$380$	−49043.8	−	70121.9i	−0.0174231	−	0.0249112i
$381$	2.56650e6			0.905791
$382$			1.49820e6i			0.525304i
$383$			1.62974e6i			0.567703i	0.958868	+	0.283851i	$0.0916123\pi$
$383$			1.62974e6i			0.567703i	−0.958868	+	0.283851i	$0.908388\pi$
$384$	−1.72955e6			−0.598556
$385$	−876730.	+	613192.i	−0.301449	+	0.210836i
$386$	3.94710e6			1.34837
$387$			722423.i			0.245196i
$388$		−	102902.i		−	0.0347013i
$389$	−5.33558e6			−1.78775			−0.893877	−	0.448311i	$-0.852026\pi$
$389$	−5.33558e6			−1.78775			−0.893877	+	0.448311i	$0.852026\pi$
$390$	184802.	−	129252.i	0.0615241	−	0.0430305i
$391$	−44392.4			−0.0146848
$392$		−	1.46672e6i		−	0.482094i
$393$			1.78527e6i			0.583071i
$394$	−3.58094e6			−1.16214
$395$	3.34751e6	+	4.78620e6i	1.07952	+	1.54347i
$396$	8042.57			0.00257725
$397$			3.89341e6i			1.23981i	0.784678	+	0.619903i	$0.212828\pi$
$397$			3.89341e6i			1.23981i	−0.784678	+	0.619903i	$0.787172\pi$
$398$		−	5.84457e6i		−	1.84946i
$399$	2.65550e6			0.835055
$400$	1.12512e6	−	3.08094e6i	0.351599	−	0.962795i
$401$	401457.			0.124675			0.0623374	−	0.998055i	$-0.480145\pi$
$401$	401457.			0.124675			0.0623374	+	0.998055i	$0.480145\pi$
$402$		−	870335.i		−	0.268609i
$403$		−	708676.i		−	0.217363i
$404$	−41837.5			−0.0127530
$405$	−210210.	−	300554.i	−0.0636819	−	0.0910511i
$406$	−951662.			−0.286528
$407$			471826.i			0.141187i
$408$			141847.i			0.0421861i
$409$	5.92484e6			1.75133			0.875666	−	0.482918i	$-0.160423\pi$
$409$	5.92484e6			1.75133			0.875666	+	0.482918i	$0.160423\pi$
$410$	−2.48127e6	+	1.73542e6i	−0.728979	+	0.509854i
$411$	−1.49695e6			−0.437124
$412$		−	42231.4i		−	0.0122572i
$413$			1.56711e6i			0.452089i
$414$	233470.			0.0669469
$415$	708113.	−	495260.i	0.201828	−	0.141160i
$416$	23238.7			0.00658383
$417$		−	2.70933e6i		−	0.762996i
$418$		−	1.29311e6i		−	0.361988i
$419$	−4.23888e6			−1.17955			−0.589774	−	0.807568i	$-0.700783\pi$
$419$	−4.23888e6			−1.17955			−0.589774	+	0.807568i	$0.700783\pi$
$420$	−37426.4	−	53511.5i	−0.0103527	−	0.0148021i
$421$	5.04583e6			1.38748			0.693740	−	0.720225i	$-0.255962\pi$
$421$	5.04583e6			1.38748			0.693740	+	0.720225i	$0.255962\pi$
$422$		−	3.11838e6i		−	0.852409i
$423$		−	763944.i		−	0.207592i
$424$	4.55627e6			1.23082
$425$	−259001.	−	94583.5i	−0.0695552	−	0.0254006i
$426$	3.68490e6			0.983788
$427$			2.46974e6i			0.655514i
$428$		−	114599.i		−	0.0302393i
$429$	85205.3			0.0223524
$430$	−1.63705e6	−	2.34063e6i	−0.426965	−	0.610466i
$431$	−7.38745e6			−1.91558			−0.957792	−	0.287461i	$-0.907189\pi$
$431$	−7.38745e6			−1.91558			−0.957792	+	0.287461i	$0.907189\pi$
$432$		−	765148.i		−	0.197259i
$433$		−	1.66687e6i		−	0.427249i	−0.976916	−	0.213625i	$-0.931473\pi$
$433$		−	1.66687e6i		−	0.427249i	0.976916	−	0.213625i	$-0.0685270\pi$
$434$	−8.20748e6			−2.09163
$435$	432989.	−	302836.i	0.109712	−	0.0767334i
$436$	118193.			0.0297766
$437$		−	938534.i		−	0.235097i
$438$		−	3.38922e6i		−	0.844139i
$439$	−7.00345e6			−1.73441			−0.867203	−	0.497956i	$-0.834084\pi$
$439$	−7.00345e6			−1.73441			−0.867203	+	0.497956i	$0.834084\pi$
$440$	990100.	−	692484.i	0.243808	−	0.170521i
$441$	665106.			0.162853
$442$		−	39550.1i		−	0.00962924i
$443$			1.09721e6i			0.265633i	0.991141	+	0.132816i	$0.0424020\pi$
$443$			1.09721e6i			0.265633i	−0.991141	+	0.132816i	$0.957598\pi$
$444$	−28798.1			−0.00693276
$445$	88896.9	+	127103.i	0.0212807	+	0.0304268i
$446$	4.88389e6			1.16260
$447$			967117.i			0.228934i
$448$			5.04332e6i			1.18719i
$449$	1.62691e6			0.380844			0.190422	−	0.981702i	$-0.439014\pi$
$449$	1.62691e6			0.380844			0.190422	+	0.981702i	$0.439014\pi$
$450$	1.36215e6	+	497437.i	0.317098	+	0.115800i
$451$	−1.14402e6			−0.264846
$452$			50929.2i			0.0117252i
$453$		−	216741.i		−	0.0496245i
$454$	5.21177e6			1.18671
$455$	−396506.	−	566917.i	−0.0897887	−	0.128378i
$456$	−2.99889e6			−0.675380
$457$		−	857428.i		−	0.192047i	−0.995379	−	0.0960235i	$-0.969388\pi$
$457$		−	857428.i		−	0.192047i	0.995379	−	0.0960235i	$-0.0306124\pi$
$458$			3.21829e6i			0.716905i
$459$	−64322.6			−0.0142505
$460$	−18912.6	+	13227.6i	−0.00416731	+	0.00291465i
$461$	−5.70696e6			−1.25070			−0.625349	−	0.780345i	$-0.715043\pi$
$461$	−5.70696e6			−1.25070			−0.625349	+	0.780345i	$0.715043\pi$
$462$		−	986800.i		−	0.215092i
$463$		−	5.95157e6i		−	1.29027i	−0.764070	−	0.645133i	$-0.776802\pi$
$463$		−	5.95157e6i		−	1.29027i	0.764070	−	0.645133i	$-0.223198\pi$
$464$	1.10230e6			0.237686
$465$	3.73426e6	−	2.61177e6i	0.800888	−	0.560148i
$466$	−3.46402e6			−0.738950
$467$		−	5.25283e6i		−	1.11455i	−0.830326	−	0.557277i	$-0.811846\pi$
$467$		−	5.25283e6i		−	1.11455i	0.830326	−	0.557277i	$-0.188154\pi$
$468$			5200.54i			0.00109757i
$469$	−2.66992e6			−0.560488
$470$	1.73114e6	+	2.47515e6i	0.361483	+	0.516841i
$471$	−4.31737e6			−0.896740
$472$		−	1.76975e6i		−	0.365643i
$473$		−	1.07918e6i		−	0.221789i
$474$	−5.38709e6			−1.10131
$475$	1.99966e6	−	5.47574e6i	0.406652	−	1.11355i
$476$	−11452.2			−0.00231670
$477$			2.06611e6i			0.415774i
$478$			6.51361e6i			1.30392i
$479$	−8.82420e6			−1.75726			−0.878631	−	0.477502i	$-0.841542\pi$
$479$	−8.82420e6			−1.75726			−0.878631	+	0.477502i	$0.841542\pi$
$480$	85644.4	+	122453.i	0.0169666	+	0.0242586i
$481$	−305095.			−0.0601275
$482$			1.49754e6i			0.293602i
$483$		−	716216.i		−	0.139693i
$484$	−12014.2			−0.00233121
$485$	5.74451e6	−	4.01776e6i	1.10892	−	0.775585i
$486$	338287.			0.0649673
$487$			5.99283e6i			1.14501i	0.819901	+	0.572506i	$0.194029\pi$
$487$			5.99283e6i			1.14501i	−0.819901	+	0.572506i	$0.805971\pi$
$488$		−	2.78911e6i		−	0.530170i
$489$	−3.93328e6			−0.743846
$490$	−2.15492e6	+	1.50717e6i	−0.405454	+	0.283578i
$491$	6.17263e6			1.15549			0.577745	−	0.816217i	$-0.303933\pi$
$491$	6.17263e6			1.15549			0.577745	+	0.816217i	$0.303933\pi$
$492$		−	69825.8i		−	0.0130048i
$493$		−	92665.3i		−	0.0171712i
$494$	836159.			0.154160
$495$	314017.	+	448976.i	0.0576024	+	0.0823588i
$496$	9.50663e6			1.73509
$497$		−	1.13041e7i		−	2.05280i
$498$			797013.i			0.144010i
$499$	2.47210e6			0.444441			0.222221	−	0.974996i	$-0.428669\pi$
$499$	2.47210e6			0.444441			0.222221	+	0.974996i	$0.428669\pi$
$500$	−138526.	+	36879.0i	−0.0247802	+	0.00659711i
$501$	−5.33333e6			−0.949301
$502$			3.23899e6i			0.573655i
$503$			8.18126e6i			1.44178i	0.693047	+	0.720892i	$0.256268\pi$
$503$			8.18126e6i			1.44178i	−0.693047	+	0.720892i	$0.743732\pi$
$504$	−2.28852e6			−0.401308
$505$	−1.63352e6	−	2.33557e6i	−0.285034	−	0.407535i
$506$	−348764.			−0.0605558
$507$		−	3.28654e6i		−	0.567831i
$508$		−	234003.i		−	0.0402312i
$509$	−1.19487e6			−0.204421			−0.102211	−	0.994763i	$-0.532592\pi$
$509$	−1.19487e6			−0.204421			−0.102211	+	0.994763i	$0.532592\pi$
$510$	208403.	−	145759.i	0.0354796	−	0.0248147i
$511$	−1.03971e7			−1.76141
$512$		−	5.68768e6i		−	0.958870i
$513$		−	1.35989e6i		−	0.228145i
$514$	8.70486e6			1.45330
$515$	2.35756e6	−	1.64890e6i	0.391692	−	0.273953i
$516$	65867.8			0.0108905
$517$			1.14120e6i			0.187774i
$518$			3.53344e6i			0.578593i
$519$	−1.74109e6			−0.283728
$520$	447779.	+	640225.i	0.0726198	+	0.103830i
$521$	1.09929e6			0.177426			0.0887128	−	0.996057i	$-0.471725\pi$
$521$	1.09929e6			0.177426			0.0887128	+	0.996057i	$0.471725\pi$
$522$			487349.i			0.0782823i
$523$		−	7.07488e6i		−	1.13101i	−0.824746	−	0.565503i	$-0.808682\pi$
$523$		−	7.07488e6i		−	1.13101i	0.824746	−	0.565503i	$-0.191318\pi$
$524$	162774.			0.0258974
$525$	1.52598e6	−	4.17865e6i	0.241631	−	0.661665i
$526$	−4.18424e6			−0.659404
$527$		−	799180.i		−	0.125348i
$528$			1.14300e6i			0.178427i
$529$	6.18321e6			0.960671
$530$	−4.68193e6	−	6.69413e6i	−0.723994	−	1.03515i
$531$	802521.			0.123515
$532$		−	242119.i		−	0.0370894i
$533$		−	739755.i		−	0.112790i
$534$	−143060.			−0.0217103
$535$	6.39748e6	−	4.47445e6i	0.966327	−	0.675857i
$536$	3.01517e6			0.453315
$537$		−	3.36361e6i		−	0.503350i
$538$			2.72274e6i			0.405555i
$539$	−993554.			−0.147306
$540$	−27403.4	+	19166.2i	−0.00404408	+	0.00282847i
$541$	−3.53440e6			−0.519186			−0.259593	−	0.965718i	$-0.583588\pi$
$541$	−3.53440e6			−0.519186			−0.259593	+	0.965718i	$0.583588\pi$
$542$		−	5.50729e6i		−	0.805267i
$543$			2.11398e6i			0.307682i
$544$	26206.5			0.00379675
$545$	4.61477e6	+	6.59810e6i	0.665516	+	0.951542i
$546$	638091.			0.0916011
$547$			1.37763e6i			0.196863i	0.995144	+	0.0984316i	$0.0313826\pi$
$547$			1.37763e6i			0.196863i	−0.995144	+	0.0984316i	$0.968617\pi$
$548$			136487.i			0.0194151i
$549$	1.26476e6			0.179093
$550$	−2.03481e6	−	743085.i	−0.286826	−	0.104745i
$551$	1.95911e6			0.274903
$552$			808829.i			0.112982i
$553$			1.65260e7i			2.29802i
$554$	−2.45347e6			−0.339630
$555$	−1.12440e6	−	1.60765e6i	−0.154950	−	0.221544i
$556$	−247027.			−0.0338889
$557$			9.57607e6i			1.30782i	0.756571	+	0.653912i	$0.226873\pi$
$557$			9.57607e6i			1.30782i	−0.756571	+	0.653912i	$0.773127\pi$
$558$			4.20308e6i			0.571455i
$559$	697823.			0.0944530
$560$	7.60498e6	−	5.31899e6i	1.02477	−	0.716736i
$561$	96086.8			0.0128901
$562$		−	1.21884e6i		−	0.162782i
$563$		−	4.58027e6i		−	0.609003i	−0.952512	−	0.304502i	$-0.901510\pi$
$563$		−	4.58027e6i		−	0.609003i	0.952512	−	0.304502i	$-0.0984899\pi$
$564$	−69653.5			−0.00922031
$565$	−2.84312e6	+	1.98850e6i	−0.374692	+	0.262062i
$566$	−3.23033e6			−0.423844
$567$		−	1.03776e6i		−	0.135563i
$568$			1.27659e7i			1.66027i
$569$	943189.			0.122129			0.0610644	−	0.998134i	$-0.480550\pi$
$569$	943189.			0.122129			0.0610644	+	0.998134i	$0.480550\pi$
$570$	3.08160e6	+	4.40600e6i	0.397273	+	0.568012i
$571$	−581249.			−0.0746057			−0.0373029	−	0.999304i	$-0.511877\pi$
$571$	−581249.			−0.0746057			−0.0373029	+	0.999304i	$0.511877\pi$
$572$		−	7768.70i		−	0.000992792i
$573$		−	2.35363e6i		−	0.299469i
$574$	−8.56742e6			−1.08535
$575$	−1.47686e6	−	539328.i	−0.186281	−	0.0680273i
$576$	2.58270e6			0.324353
$577$		−	3.08163e6i		−	0.385338i	−0.981264	−	0.192669i	$-0.938286\pi$
$577$		−	3.08163e6i		−	0.385338i	0.981264	−	0.192669i	$-0.0617143\pi$
$578$			8.08965e6i			1.00719i
$579$	−6.20079e6			−0.768689
$580$	−27611.5	−	39478.3i	−0.00340816	−	0.00487291i
$581$	2.44499e6			0.300495
$582$			6.46571e6i			0.791241i
$583$		−	3.08641e6i		−	0.376082i
$584$	1.17415e7			1.42460
$585$	−290320.	+	203052.i	−0.0350741	+	0.0245311i
$586$	1.03671e7			1.24713
$587$			5.79374e6i			0.694007i	0.937864	+	0.347004i	$0.112801\pi$
$587$			5.79374e6i			0.694007i	−0.937864	+	0.347004i	$0.887199\pi$
$588$		−	60641.9i		−	0.00723318i
$589$	1.68961e7			2.00677
$590$	−2.60014e6	+	1.81856e6i	−0.307515	+	0.215079i
$591$	5.62557e6			0.662518
$592$		−	4.09274e6i		−	0.479966i
$593$			1.14174e7i			1.33331i	0.745366	+	0.666656i	$0.232275\pi$
$593$			1.14174e7i			1.33331i	−0.745366	+	0.666656i	$0.767725\pi$
$594$	−505343.			−0.0587652
$595$	−447144.	−	639317.i	−0.0517791	−	0.0740327i
$596$	88178.1			0.0101682
$597$			9.18168e6i			1.05435i
$598$		−	225520.i		−	0.0257889i
$599$	−1.33518e7			−1.52045			−0.760224	−	0.649661i	$-0.774911\pi$
$599$	−1.33518e7			−1.52045			−0.760224	+	0.649661i	$0.774911\pi$
$600$	−1.72331e6	+	4.71900e6i	−0.195427	+	0.535145i
$601$	1774.23			0.000200366			0.000100183	−	1.00000i	$-0.499968\pi$
$601$	1774.23			0.000200366			0.000100183		1.00000i	$0.499968\pi$
$602$		−	8.08179e6i		−	0.908901i
$603$			1.36727e6i			0.153131i
$604$	−19761.7			−0.00220410
$605$	−469088.	−	670692.i	−0.0521034	−	0.0744963i
$606$	2.62879e6			0.290787
$607$		−	2.48398e6i		−	0.273638i	−0.990596	−	0.136819i	$-0.956312\pi$
$607$		−	2.48398e6i		−	0.273638i	0.990596	−	0.136819i	$-0.0436879\pi$
$608$			554051.i			0.0607842i
$609$	1.49504e6			0.163346
$610$	−4.09779e6	+	2.86603e6i	−0.445887	+	0.311857i
$611$	−737930.			−0.0799672
$612$			5864.69i			0.000632946i
$613$		−	3.19717e6i		−	0.343649i	−0.985128	−	0.171824i	$-0.945034\pi$
$613$		−	3.19717e6i		−	0.343649i	0.985128	−	0.171824i	$-0.0549662\pi$
$614$	4.43447e6			0.474702
$615$	3.89802e6	−	2.72631e6i	0.415582	−	0.290661i
$616$	3.41865e6			0.362997
$617$		−	3.43973e6i		−	0.363757i	−0.983321	−	0.181878i	$-0.941782\pi$
$617$		−	3.43973e6i		−	0.363757i	0.983321	−	0.181878i	$-0.0582177\pi$
$618$			2.65354e6i			0.279483i
$619$	580297.			0.0608729			0.0304364	−	0.999537i	$-0.490310\pi$
$619$	580297.			0.0608729			0.0304364	+	0.999537i	$0.490310\pi$
$620$	−238131.	−	340476.i	−0.0248793	−	0.0355719i
$621$	−366776.			−0.0381656
$622$			7.78035e6i			0.806349i
$623$			438865.i			0.0453013i
$624$	−739093.			−0.0759867
$625$	−7.46742e6	−	6.29326e6i	−0.764663	−	0.644430i
$626$	1.93818e7			1.97678
$627$			2.03144e6i			0.206365i
$628$			393641.i			0.0398292i
$629$	−344059.			−0.0346742
$630$	2.35163e6	+	3.36232e6i	0.236058	+	0.337511i
$631$	−1.94969e7			−1.94936			−0.974680	−	0.223604i	$-0.928218\pi$
$631$	−1.94969e7			−1.94936			−0.974680	+	0.223604i	$0.928218\pi$
$632$		−	1.86629e7i		−	1.85861i
$633$			4.89890e6i			0.485947i
$634$	−3.82772e6			−0.378196
$635$	1.30632e7	−	9.13653e6i	1.28563	−	0.899181i
$636$	188380.			0.0184668
$637$		−	642458.i		−	0.0627330i
$638$		−	728015.i		−	0.0708090i
$639$	−5.78888e6			−0.560845
$640$	−8.80325e6	+	6.15707e6i	−0.849558	+	0.594188i
$641$	−1.50533e7			−1.44706			−0.723530	−	0.690293i	$-0.757482\pi$
$641$	−1.50533e7			−1.44706			−0.723530	+	0.690293i	$0.757482\pi$
$642$			7.20065e6i			0.689500i
$643$		−	1.34527e7i		−	1.28316i	−0.767056	−	0.641580i	$-0.778279\pi$
$643$		−	1.34527e7i		−	1.28316i	0.767056	−	0.641580i	$-0.221721\pi$
$644$	−65301.9			−0.00620456
$645$	2.57177e6	+	3.67707e6i	0.243407	+	0.348019i
$646$	942943.			0.0889005
$647$			1.15666e7i			1.08629i	0.839638	+	0.543146i	$0.182767\pi$
$647$			1.15666e7i			1.08629i	−0.839638	+	0.543146i	$0.817233\pi$
$648$			1.17196e6i			0.109641i
$649$	−1.19883e6			−0.111724
$650$	480498.	−	1.31576e6i	0.0446076	−	0.122150i
$651$	1.28938e7			1.19241
$652$			358622.i			0.0330383i
$653$			8.60996e6i			0.790165i	0.918646	+	0.395083i	$0.129284\pi$
$653$			8.60996e6i			0.790165i	−0.918646	+	0.395083i	$0.870716\pi$
$654$	−7.42646e6			−0.678950
$655$	6.35541e6	+	9.08684e6i	0.578816	+	0.827580i
$656$	9.92354e6			0.900341
$657$			5.32438e6i			0.481233i
$658$			8.54628e6i			0.769507i
$659$	3.14337e6			0.281957			0.140978	−	0.990013i	$-0.454975\pi$
$659$	3.14337e6			0.281957			0.140978	+	0.990013i	$0.454975\pi$
$660$	40935.9	−	28630.9i	0.00365801	−	0.00255844i
$661$	−2.75239e6			−0.245023			−0.122511	−	0.992467i	$-0.539095\pi$
$661$	−2.75239e6			−0.245023			−0.122511	+	0.992467i	$0.539095\pi$
$662$			543584.i			0.0482083i
$663$			62132.2i			0.00548951i
$664$	−2.76116e6			−0.243036
$665$	1.35163e7	−	9.45340e6i	1.18523	−	0.828961i
$666$	1.80948e6			0.158077
$667$		−	528390.i		−	0.0459876i
$668$			486273.i			0.0421637i
$669$	−7.67247e6			−0.662781
$670$	−3.09833e6	−	4.42992e6i	−0.266649	−	0.381250i
$671$	−1.88934e6			−0.161996
$672$			422808.i			0.0361177i
$673$			1.66398e7i			1.41615i	0.706136	+	0.708076i	$0.250437\pi$
$673$			1.66398e7i			1.41615i	−0.706136	+	0.708076i	$0.749563\pi$
$674$	−2.90639e6			−0.246436
$675$	−2.13990e6	−	781461.i	−0.180773	−	0.0660158i
$676$	−299655.			−0.0252205
$677$			1.05991e7i			0.888789i	0.895831	+	0.444395i	$0.146581\pi$
$677$			1.05991e7i			0.888789i	−0.895831	+	0.444395i	$0.853419\pi$
$678$		−	3.20006e6i		−	0.267352i
$679$	1.98348e7			1.65103
$680$	504964.	+	721987.i	0.0418782	+	0.0598766i
$681$	−8.18756e6			−0.676529
$682$		−	6.27867e6i		−	0.516900i
$683$		−	544094.i		−	0.0446296i	−0.999751	−	0.0223148i	$-0.992896\pi$
$683$		−	544094.i		−	0.0446296i	0.999751	−	0.0223148i	$-0.00710360\pi$
$684$	−123990.			−0.0101332
$685$	−7.61937e6	+	5.32905e6i	−0.620429	+	0.433933i
$686$	7.78911e6			0.631943
$687$		−	5.05586e6i		−	0.408698i
$688$			9.36104e6i			0.753969i
$689$	1.99575e6			0.160162
$690$	1.18834e6	−	831137.i	0.0950208	−	0.0664584i
$691$	−7.88699e6			−0.628371			−0.314185	−	0.949362i	$-0.601731\pi$
$691$	−7.88699e6			−0.628371			−0.314185	+	0.949362i	$0.601731\pi$
$692$			158746.i			0.0126020i
$693$			1.55024e6i			0.122621i
$694$	−1.67210e7			−1.31784
$695$	−9.64502e6	−	1.37903e7i	−0.757428	−	1.08296i
$696$	−1.68836e6			−0.132112
$697$		−	834228.i		−	0.0650433i
$698$			9.71616e6i			0.754842i
$699$	5.44188e6			0.421266
$700$	−380994.	−	139134.i	−0.0293882	−	0.0107322i
$701$	2.22952e7			1.71363			0.856814	−	0.515625i	$-0.172440\pi$
$701$	2.22952e7			1.71363			0.856814	+	0.515625i	$0.172440\pi$
$702$		−	326768.i		−	0.0250263i
$703$		−	7.27400e6i		−	0.555118i
$704$	−3.85811e6			−0.293388
$705$	−2.71958e6	−	3.88840e6i	−0.206077	−	0.294645i
$706$	−1.45898e7			−1.10163
$707$		−	8.06434e6i		−	0.606765i
$708$		−	73170.9i		−	0.00548599i
$709$	8.40301e6			0.627797			0.313899	−	0.949457i	$-0.398365\pi$
$709$	8.40301e6			0.627797			0.313899	+	0.949457i	$0.398365\pi$
$710$	1.87558e7	−	1.31180e7i	1.39633	−	0.976608i
$711$	8.46299e6			0.627841
$712$		−	495615.i		−	0.0366390i
$713$		−	4.55703e6i		−	0.335706i
$714$	719580.			0.0528243
$715$	433687.	−	303325.i	0.0317257	−	0.0221892i
$716$	−306682.			−0.0223566
$717$		−	1.02327e7i		−	0.743350i
$718$			2.43695e6i			0.176415i
$719$	−1.39897e7			−1.00922			−0.504612	−	0.863346i	$-0.668364\pi$
$719$	−1.39897e7			−1.00922			−0.504612	+	0.863346i	$0.668364\pi$
$720$	−2.72387e6	−	3.89453e6i	−0.195819	−	0.279978i
$721$	8.14027e6			0.583177
$722$			5.75009e6i			0.410517i
$723$		−	2.35259e6i		−	0.167379i
$724$	192745.			0.0136659
$725$	1.12580e6	−	3.08282e6i	0.0795456	−	0.217822i
$726$	754895.			0.0531551
$727$		−	1.69990e7i		−	1.19286i	−0.802666	−	0.596428i	$-0.796586\pi$
$727$		−	1.69990e7i		−	1.19286i	0.802666	−	0.596428i	$-0.203414\pi$
$728$			2.21059e6i			0.154589i
$729$	−531441.			−0.0370370
$730$	−1.20654e7	−	1.72508e7i	−0.837979	−	1.19813i
$731$	786941.			0.0544689
$732$		−	115316.i		−	0.00795450i
$733$			9.14170e6i			0.628445i	0.949349	+	0.314222i	$0.101744\pi$
$733$			9.14170e6i			0.628445i	−0.949349	+	0.314222i	$0.898256\pi$
$734$	1.08060e7			0.740332
$735$	3.38533e6	−	2.36773e6i	0.231144	−	0.161664i
$736$	149433.			0.0101684
$737$		−	2.04247e6i		−	0.138512i
$738$			4.38740e6i			0.296528i
$739$	1.54222e7			1.03881			0.519405	−	0.854528i	$-0.326154\pi$
$739$	1.54222e7			1.03881			0.519405	+	0.854528i	$0.326154\pi$
$740$	−146580.	+	102519.i	−0.00983998	+	0.00688217i
$741$	−1.31358e6			−0.0878845
$742$		−	2.31137e7i		−	1.54120i
$743$		−	2.34940e7i		−	1.56129i	−0.624973	−	0.780646i	$-0.714890\pi$
$743$		−	2.34940e7i		−	1.56129i	0.624973	−	0.780646i	$-0.285110\pi$
$744$	−1.45610e7			−0.964407
$745$	3.44286e6	+	4.92254e6i	0.227263	+	0.324936i
$746$	5.17484e6			0.340447
$747$		−	1.25209e6i		−	0.0820981i
$748$		−	8760.83i		−	0.000572521i
$749$	2.20894e7			1.43873
$750$	8.70405e6	−	2.31723e6i	0.565025	−	0.150424i
$751$	9.67937e6			0.626250			0.313125	−	0.949712i	$-0.398624\pi$
$751$	9.67937e6			0.626250			0.313125	+	0.949712i	$0.398624\pi$
$752$		−	9.89906e6i		−	0.638336i
$753$		−	5.08838e6i		−	0.327033i
$754$	470754.			0.0301554
$755$	−771583.	−	1.10319e6i	−0.0492624	−	0.0704343i
$756$	−94619.3			−0.00602109
$757$			6.06490e6i			0.384666i	0.981330	+	0.192333i	$0.0616054\pi$
$757$			6.06490e6i			0.384666i	−0.981330	+	0.192333i	$0.938395\pi$
$758$		−	2.83485e7i		−	1.79208i
$759$	547900.			0.0345221
$760$	−1.52641e7	+	1.06758e7i	−0.958598	+	0.670451i
$761$	−2.42020e7			−1.51492			−0.757461	−	0.652880i	$-0.773561\pi$
$761$	−2.42020e7			−1.51492			−0.757461	+	0.652880i	$0.773561\pi$
$762$			1.47033e7i			0.917331i
$763$			2.27821e7i			1.41672i
$764$	−214595.			−0.0133011
$765$	−327396.	+	228983.i	−0.0202265	+	0.0141466i
$766$	−9.33665e6			−0.574936
$767$		−	775193.i		−	0.0475797i
$768$		−	725529.i		−	0.0443866i
$769$	−3.47840e6			−0.212111			−0.106055	−	0.994360i	$-0.533822\pi$
$769$	−3.47840e6			−0.212111			−0.106055	+	0.994360i	$0.533822\pi$
$770$	−3.51293e6	−	5.02272e6i	−0.213522	−	0.305290i
$771$	−1.36751e7			−0.828506
$772$			565365.i			0.0341418i
$773$		−	1.02630e7i		−	0.617769i	−0.951100	−	0.308884i	$-0.900044\pi$
$773$		−	1.02630e7i		−	0.617769i	0.951100	−	0.308884i	$-0.0999556\pi$
$774$	−4.13871e6			−0.248320
$775$	9.70932e6	−	2.65873e7i	0.580677	−	1.59009i
$776$	−2.23997e7			−1.33533
$777$		−	5.55095e6i		−	0.329849i
$778$		−	3.05672e7i		−	1.81053i
$779$	1.76370e7			1.04131
$780$	18513.5	+	26470.3i	0.00108956	+	0.00155784i
$781$	8.64759e6			0.507303
$782$		−	254321.i		−	0.0148719i
$783$		−	765613.i		−	0.0446277i
$784$	8.61834e6			0.500764
$785$	−2.19750e7	+	1.53695e7i	−1.27278	+	0.890196i
$786$	−1.02277e7			−0.590500
$787$		−	2.49651e7i		−	1.43680i	−0.695629	−	0.718401i	$-0.744874\pi$
$787$		−	2.49651e7i		−	1.43680i	0.695629	−	0.718401i	$-0.255126\pi$
$788$		−	512919.i		−	0.0294261i
$789$	6.57333e6			0.375918
$790$	−2.74198e7	+	1.91776e7i	−1.56314	+	1.09327i
$791$	−9.81681e6			−0.557865
$792$		−	1.75070e6i		−	0.0991742i
$793$		−	1.22169e6i		−	0.0689890i
$794$	−2.23050e7			−1.25560
$795$	7.35519e6	+	1.05163e7i	0.412740	+	0.590127i
$796$	837151.			0.0468297
$797$			2.85688e7i			1.59311i	0.604564	+	0.796557i	$0.293347\pi$
$797$			2.85688e7i			1.59311i	−0.604564	+	0.796557i	$0.706653\pi$
$798$			1.52132e7i			0.845694i
$799$	−832170.			−0.0461153
$800$	871845.	+	318385.i	0.0481631	+	0.0175885i
$801$	224744.			0.0123768
$802$			2.29992e6i			0.126263i
$803$		−	7.95370e6i		−	0.435292i
$804$	124663.			0.00680138
$805$	−2.54967e6	−	3.64547e6i	−0.138674	−	0.198273i
$806$	4.05995e6			0.220132
$807$		−	4.27735e6i		−	0.231202i
$808$			9.10714e6i			0.490743i
$809$	−1.00028e7			−0.537340			−0.268670	−	0.963232i	$-0.586584\pi$
$809$	−1.00028e7			−0.537340			−0.268670	+	0.963232i	$0.586584\pi$
$810$	1.72185e6	−	1.20428e6i	0.0922111	−	0.0644932i
$811$	−7.88288e6			−0.420855			−0.210428	−	0.977609i	$-0.567486\pi$
$811$	−7.88288e6			−0.420855			−0.210428	+	0.977609i	$0.567486\pi$
$812$		−	136312.i		−	0.00725511i
$813$			8.65181e6i			0.459072i
$814$	−2.70306e6			−0.142986
$815$	−2.00201e7	+	1.40022e7i	−1.05578	+	0.738418i
$816$	−833482.			−0.0438198
$817$			1.66373e7i			0.872023i
$818$			3.39430e7i			1.77364i
$819$	−1.00242e6			−0.0522206
$820$	−248575.	−	355407.i	−0.0129099	−	0.0184583i
$821$	1.84331e7			0.954423			0.477211	−	0.878789i	$-0.341648\pi$
$821$	1.84331e7			0.954423			0.477211	+	0.878789i	$0.341648\pi$
$822$		−	8.57594e6i		−	0.442693i
$823$			1.93527e7i			0.995961i	0.867188	+	0.497981i	$0.165925\pi$
$823$			1.93527e7i			0.995961i	−0.867188	+	0.497981i	$0.834075\pi$
$824$	−9.19288e6			−0.471665
$825$	3.19664e6	+	1.16737e6i	0.163516	+	0.0597135i
$826$	−8.97785e6			−0.457849
$827$		−	1.33049e7i		−	0.676471i	−0.941062	−	0.338235i	$-0.890170\pi$
$827$		−	1.33049e7i		−	0.676471i	0.941062	−	0.338235i	$-0.109830\pi$
$828$			33441.3i			0.00169515i
$829$	1.61482e7			0.816090			0.408045	−	0.912962i	$-0.366211\pi$
$829$	1.61482e7			0.816090			0.408045	+	0.912962i	$0.366211\pi$
$830$	2.83731e6	+	4.05672e6i	0.142959	+	0.204400i
$831$	3.85434e6			0.193619
$832$		−	2.49475e6i		−	0.124945i
$833$		−	724505.i		−	0.0361767i
$834$	1.55216e7			0.772717
$835$	−2.71461e7	+	1.89862e7i	−1.34739	+	0.942373i
$836$	185219.			0.00916581
$837$		−	6.60293e6i		−	0.325779i
$838$		−	2.42842e7i		−	1.19458i
$839$	−2.17566e7			−1.06705			−0.533527	−	0.845783i	$-0.679134\pi$
$839$	−2.17566e7			−1.06705			−0.533527	+	0.845783i	$0.679134\pi$
$840$	−1.16483e7	+	8.14695e6i	−0.569595	+	0.398379i
$841$	−1.94082e7			−0.946226
$842$			2.89072e7i			1.40516i
$843$			1.91477e6i			0.0927998i
$844$	446663.			0.0215836
$845$	−1.16998e7	−	1.67282e7i	−0.563687	−	0.805949i
$846$	4.37658e6			0.210237
$847$		−	2.31579e6i		−	0.110915i
$848$			2.67723e7i			1.27849i
$849$	5.07478e6			0.241628
$850$	541862.	−	1.48380e6i	0.0257242	−	0.0704413i
$851$	−1.96187e6			−0.0928638
$852$			527809.i			0.0249102i
$853$			1.29447e7i			0.609142i	0.952490	+	0.304571i	$0.0985130\pi$
$853$			1.29447e7i			0.609142i	−0.952490	+	0.304571i	$0.901487\pi$
$854$	−1.41490e7			−0.663866
$855$	−4.84111e6	−	6.92172e6i	−0.226480	−	0.323817i
$856$	−2.49458e7			−1.16362
$857$			3.34203e7i			1.55438i	0.629264	+	0.777192i	$0.283356\pi$
$857$			3.34203e7i			1.55438i	−0.629264	+	0.777192i	$0.716644\pi$
$858$			488135.i			0.0226371i
$859$	4.22247e7			1.95247			0.976234	−	0.216719i	$-0.0695356\pi$
$859$	4.22247e7			1.95247			0.976234	+	0.216719i	$0.0695356\pi$
$860$	335261.	−	234485.i	0.0154574	−	0.0108111i
$861$	1.34592e7			0.618745
$862$		−	4.23221e7i		−	1.93999i
$863$			9.62825e6i			0.440069i	0.975492	+	0.220034i	$0.0706169\pi$
$863$			9.62825e6i			0.440069i	−0.975492	+	0.220034i	$0.929383\pi$
$864$	216521.			0.00986771
$865$	−8.86199e6	+	6.19815e6i	−0.402709	+	0.281658i
$866$	9.54936e6			0.432693
$867$		−	1.27086e7i		−	0.574185i
$868$		−	1.17560e6i		−	0.0529617i
$869$	−1.26422e7			−0.567904
$870$	1.73492e6	+	2.48056e6i	0.0777110	+	0.111110i
$871$	1.32072e6			0.0589880
$872$		−	2.57281e7i		−	1.14582i
$873$		−	1.01575e7i		−	0.451076i
$874$	5.37679e6			0.238092
$875$	−7.10857e6	−	2.67014e7i	−0.313879	−	1.17900i
$876$	485457.			0.0213742
$877$			1.37201e7i			0.602362i	0.953567	+	0.301181i	$0.0973808\pi$
$877$			1.37201e7i			0.602362i	−0.953567	+	0.301181i	$0.902619\pi$
$878$		−	4.01222e7i		−	1.75650i
$879$	−1.62865e7			−0.710976
$880$	4.06899e6	+	5.81776e6i	0.177125	+	0.253250i
$881$	2.99671e7			1.30078			0.650392	−	0.759599i	$-0.274605\pi$
$881$	2.99671e7			1.30078			0.650392	+	0.759599i	$0.274605\pi$
$882$			3.81034e6i			0.164927i
$883$			6.57264e6i			0.283686i	0.989889	+	0.141843i	$0.0453028\pi$
$883$			6.57264e6i			0.283686i	−0.989889	+	0.141843i	$0.954697\pi$
$884$	5664.99			0.000243819
$885$	4.08476e6	−	2.85691e6i	0.175311	−	0.122614i
$886$	−6.28585e6			−0.269017
$887$			1.99178e7i			0.850028i	0.905187	+	0.425014i	$0.139731\pi$
$887$			1.99178e7i			0.850028i	−0.905187	+	0.425014i	$0.860269\pi$
$888$			6.26874e6i			0.266777i
$889$	4.51051e7			1.91413
$890$	−728163.	+	509284.i	−0.0308144	+	0.0215519i
$891$	793881.			0.0335013
$892$			699548.i			0.0294378i
$893$		−	1.75935e7i		−	0.738285i
$894$	−5.54054e6			−0.231851
$895$	−1.19742e7	−	1.71205e7i	−0.499677	−	0.714428i
$896$	−3.03961e7			−1.26488
$897$			354287.i			0.0147019i
$898$			9.32044e6i			0.385696i
$899$	9.51241e6			0.392547
$900$	−71250.7	+	195108.i	−0.00293213	+	0.00802914i
$901$	2.25063e6			0.0923617
$902$		−	6.55402e6i		−	0.268220i
$903$			1.26963e7i			0.518152i
$904$	1.10862e7			0.451193
$905$	7.52563e6	+	1.07600e7i	0.305437	+	0.436707i
$906$	1.24170e6			0.0502568
$907$			4.17948e7i			1.68696i	0.537163	+	0.843478i	$0.319496\pi$
$907$			4.17948e7i			1.68696i	−0.537163	+	0.843478i	$0.680504\pi$
$908$			746511.i			0.0300484i
$909$	−4.12977e6			−0.165774
$910$	3.24782e6	−	2.27156e6i	0.130014	−	0.0909326i
$911$	−2.46957e7			−0.985882			−0.492941	−	0.870063i	$-0.664078\pi$
$911$	−2.46957e7			−0.985882			−0.492941	+	0.870063i	$0.664078\pi$
$912$		−	1.76213e7i		−	0.701536i
$913$			1.87040e6i			0.0742605i
$914$	4.91214e6			0.194494
$915$	6.43753e6	−	4.50246e6i	0.254195	−	0.177786i
$916$	−460974.			−0.0181526
$917$			3.13753e7i			1.23215i
$918$		−	368499.i		−	0.0144321i
$919$	2.76370e7			1.07945			0.539724	−	0.841842i	$-0.318529\pi$
$919$	2.76370e7			1.07945			0.539724	+	0.841842i	$0.318529\pi$
$920$	2.87937e6	+	4.11687e6i	0.112157	+	0.160361i
$921$	−6.96644e6			−0.270621
$922$		−	3.26947e7i		−	1.26663i
$923$			5.59176e6i			0.216045i
$924$	141345.			0.00544628
$925$	−1.14462e7	−	4.18000e6i	−0.439854	−	0.160628i
$926$	3.40961e7			1.30670
$927$		−	4.16865e6i		−	0.159330i
$928$			311928.i			0.0118901i
$929$	2.99531e7			1.13868			0.569340	−	0.822102i	$-0.307199\pi$
$929$	2.99531e7			1.13868			0.569340	+	0.822102i	$0.307199\pi$
$930$	1.49626e7	+	2.13933e7i	0.567284	+	0.811092i
$931$	1.53173e7			0.579173
$932$		−	496171.i		−	0.0187108i
$933$		−	1.22227e7i		−	0.459689i
$934$	3.00931e7			1.12875
$935$	489073.	−	342062.i	0.0182955	−	0.0127960i
$936$	1.13205e6			0.0422353
$937$			3.96082e7i			1.47379i	0.676006	+	0.736896i	$0.263709\pi$
$937$			3.96082e7i			1.47379i	−0.676006	+	0.736896i	$0.736291\pi$
$938$		−	1.52958e7i		−	0.567629i
$939$	−3.04483e7			−1.12694
$940$	−354530.	+	247961.i	−0.0130868	+	0.00915302i
$941$	−3.50065e6			−0.128877			−0.0644383	−	0.997922i	$-0.520526\pi$
$941$	−3.50065e6			−0.128877			−0.0644383	+	0.997922i	$0.520526\pi$
$942$		−	2.47339e7i		−	0.908165i
$943$		−	4.75688e6i		−	0.174198i
$944$	1.03989e7			0.379804
$945$	−3.69436e6	−	5.28212e6i	−0.134573	−	0.192410i
$946$	6.18251e6			0.224614
$947$			2.56533e7i			0.929540i	0.885432	+	0.464770i	$0.153863\pi$
$947$			2.56533e7i			0.929540i	−0.885432	+	0.464770i	$0.846137\pi$
$948$		−	771624.i		−	0.0278859i
$949$	5.14307e6			0.185377
$950$	3.13701e7	+	1.14559e7i	1.12773	+	0.411833i
$951$	6.01325e6			0.215604
$952$			2.49290e6i			0.0891482i
$953$			1.43726e7i			0.512629i	0.966593	+	0.256314i	$0.0825082\pi$
$953$			1.43726e7i			0.512629i	−0.966593	+	0.256314i	$0.917492\pi$
$954$	−1.18366e7			−0.421071
$955$	−8.37875e6	−	1.19798e7i	−0.297283	−	0.425050i
$956$	−932982.			−0.0330163
$957$			1.14369e6i			0.0403673i
$958$		−	5.05532e7i		−	1.77965i
$959$	−2.63084e7			−0.923735
$960$	1.31457e7	−	9.19422e6i	0.460369	−	0.321986i
$961$	5.34094e7			1.86556
$962$		−	1.74787e6i		−	0.0608935i
$963$		−	1.13120e7i		−	0.393075i
$964$	−214501.			−0.00743423
$965$	−3.15615e7	+	2.20744e7i	−1.09104	+	0.763080i
$966$	4.10315e6			0.141473
$967$			3.41494e7i			1.17440i	0.809441	+	0.587201i	$0.199770\pi$
$967$			3.41494e7i			1.17440i	−0.809441	+	0.587201i	$0.800230\pi$
$968$			2.61524e6i			0.0897064i
$969$	−1.48134e6			−0.0506810
$970$	2.30174e7	+	3.29099e7i	0.785466	+	1.12304i
$971$	8.76612e6			0.298373			0.149186	−	0.988809i	$-0.452335\pi$
$971$	8.76612e6			0.298373			0.149186	+	0.988809i	$0.452335\pi$
$972$			48454.8i			0.00164502i
$973$		−	4.76154e7i		−	1.61237i
$974$	−3.43325e7			−1.15960
$975$	−754851.	+	2.06703e6i	−0.0254302	+	0.0696363i
$976$	1.63886e7			0.550703
$977$			4.92659e7i			1.65124i	0.564227	+	0.825620i	$0.309174\pi$
$977$			4.92659e7i			1.65124i	−0.564227	+	0.825620i	$0.690826\pi$
$978$		−	2.25335e7i		−	0.753323i
$979$	−335729.			−0.0111952
$980$	−215881.	−	308662.i	−0.00718040	−	0.0102664i
$981$	1.16668e7			0.387061
$982$			3.53625e7i			1.17021i
$983$		−	5.54306e7i		−	1.82964i	−0.403861	−	0.914820i	$-0.632332\pi$
$983$		−	5.54306e7i		−	1.82964i	0.403861	−	0.914820i	$-0.367668\pi$
$984$	−1.51996e7			−0.500432
$985$	2.86336e7	−	2.00266e7i	0.940342	−	0.657683i
$986$	530873.			0.0173899
$987$		−	1.34260e7i		−	0.438686i
$988$			119768.i			0.00390344i
$989$	4.48725e6			0.145878
$990$	−2.57215e6	+	1.79898e6i	−0.0834081	+	0.0583363i
$991$	−1.51099e7			−0.488739			−0.244370	−	0.969682i	$-0.578581\pi$
$991$	−1.51099e7			−0.488739			−0.244370	+	0.969682i	$0.578581\pi$
$992$			2.69018e6i			0.0867966i
$993$		−	853956.i		−	0.0274829i
$994$	6.47606e7			2.07895
$995$	3.26861e7	+	4.67339e7i	1.04666	+	1.49649i
$996$	−114161.			−0.00364643
$997$		−	3.98499e7i		−	1.26966i	−0.772650	−	0.634832i	$-0.781069\pi$
$997$		−	3.98499e7i		−	1.26966i	0.772650	−	0.634832i	$-0.218931\pi$
$998$			1.41625e7i			0.450104i
$999$	−2.84266e6			−0.0901178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.b.34.20	yes	26
5.2	odd	4		825.6.a.v.1.4		13
5.3	odd	4		825.6.a.y.1.10		13
5.4	even	2	inner	165.6.c.b.34.7	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.b.34.7	✓	26	5.4	even	2	inner
165.6.c.b.34.20	yes	26	1.1	even	1	trivial
825.6.a.v.1.4		13	5.2	odd	4
825.6.a.y.1.10		13	5.3	odd	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.72893i q^{2} -9.00000i q^{3} -0.820586 q^{4} +(-32.0393 - 45.8092i) q^{5} +51.5603 q^{6} -158.171i q^{7} +178.625i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q+5.72893i q^{2} -9.00000i q^{3} -0.820586 q^{4} +(-32.0393 - 45.8092i) q^{5} +51.5603 q^{6} -158.171i q^{7} +178.625i q^{8} -81.0000 q^{9} +(262.437 - 183.551i) q^{10} +121.000 q^{11} +7.38528i q^{12} +78.2418i q^{13} +906.152 q^{14} +(-412.283 + 288.354i) q^{15} -1049.59 q^{16} +88.2340i q^{17} -464.043i q^{18} -1865.42 q^{19} +(26.2910 + 37.5904i) q^{20} -1423.54 q^{21} +693.200i q^{22} +503.122i q^{23} +1607.62 q^{24} +(-1071.96 + 2935.39i) q^{25} -448.241 q^{26} +729.000i q^{27} +129.793i q^{28} -1050.22 q^{29} +(-1651.96 - 2361.94i) q^{30} -9057.51 q^{31} -297.011i q^{32} -1089.00i q^{33} -505.486 q^{34} +(-7245.70 + 5067.70i) q^{35} +66.4675 q^{36} +3899.39i q^{37} -10686.9i q^{38} +704.176 q^{39} +(8182.64 - 5723.01i) q^{40} -9454.73 q^{41} -8155.37i q^{42} -8918.80i q^{43} -99.2910 q^{44} +(2595.19 + 3710.54i) q^{45} -2882.35 q^{46} +9431.40i q^{47} +9446.27i q^{48} -8211.19 q^{49} +(-16816.6 - 6141.20i) q^{50} +794.106 q^{51} -64.2042i q^{52} -25507.5i q^{53} -4176.39 q^{54} +(-3876.76 - 5542.91i) q^{55} +28253.3 q^{56} +16788.8i q^{57} -6016.65i q^{58} -9907.66 q^{59} +(338.314 - 236.619i) q^{60} -15614.3 q^{61} -51889.8i q^{62} +12811.9i q^{63} -31885.2 q^{64} +(3584.19 - 2506.81i) q^{65} +6238.80 q^{66} -16879.9i q^{67} -72.4036i q^{68} +4528.10 q^{69} +(-29032.5 - 41510.1i) q^{70} +71467.7 q^{71} -14468.6i q^{72} -65733.0i q^{73} -22339.3 q^{74} +(26418.5 + 9647.67i) q^{75} +1530.74 q^{76} -19138.7i q^{77} +4034.17i q^{78} -104481. q^{79} +(33628.0 + 48080.7i) q^{80} +6561.00 q^{81} -54165.4i q^{82} +15457.9i q^{83} +1168.14 q^{84} +(4041.93 - 2826.96i) q^{85} +51095.2 q^{86} +9452.01i q^{87} +21613.6i q^{88} -2774.62 q^{89} +(-21257.4 + 14867.6i) q^{90} +12375.6 q^{91} -412.855i q^{92} +81517.6i q^{93} -54031.8 q^{94} +(59766.8 + 85453.4i) q^{95} -2673.10 q^{96} +125401. i q^{97} -47041.3i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more