LMFDB - Embedded newform 165.6.c.b.34.5

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			34.5
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.81495i q^{2} -9.00000i q^{3} -29.0734 q^{4} +(48.1851 - 28.3407i) q^{5} -70.3345 q^{6} +11.0326i q^{7} -22.8710i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q-7.81495i q^{2} -9.00000i q^{3} -29.0734 q^{4} +(48.1851 - 28.3407i) q^{5} -70.3345 q^{6} +11.0326i q^{7} -22.8710i q^{8} -81.0000 q^{9} +(-221.481 - 376.564i) q^{10} +121.000 q^{11} +261.661i q^{12} -248.951i q^{13} +86.2194 q^{14} +(-255.067 - 433.666i) q^{15} -1109.09 q^{16} -669.264i q^{17} +633.011i q^{18} -2327.66 q^{19} +(-1400.91 + 823.963i) q^{20} +99.2936 q^{21} -945.609i q^{22} -867.792i q^{23} -205.839 q^{24} +(1518.60 - 2731.20i) q^{25} -1945.54 q^{26} +729.000i q^{27} -320.756i q^{28} -2640.61 q^{29} +(-3389.08 + 1993.33i) q^{30} -3381.17 q^{31} +7935.57i q^{32} -1089.00i q^{33} -5230.26 q^{34} +(312.673 + 531.608i) q^{35} +2354.95 q^{36} -434.439i q^{37} +18190.5i q^{38} -2240.56 q^{39} +(-648.181 - 1102.04i) q^{40} +6114.13 q^{41} -775.975i q^{42} -6682.47i q^{43} -3517.89 q^{44} +(-3902.99 + 2295.60i) q^{45} -6781.75 q^{46} +20195.8i q^{47} +9981.77i q^{48} +16685.3 q^{49} +(-21344.2 - 11867.8i) q^{50} -6023.37 q^{51} +7237.87i q^{52} -3335.16i q^{53} +5697.10 q^{54} +(5830.39 - 3429.23i) q^{55} +252.327 q^{56} +20948.9i q^{57} +20636.2i q^{58} +35671.0 q^{59} +(7415.66 + 12608.2i) q^{60} +16705.5 q^{61} +26423.7i q^{62} -893.642i q^{63} +26525.4 q^{64} +(-7055.46 - 11995.7i) q^{65} -8510.48 q^{66} +15071.1i q^{67} +19457.8i q^{68} -7810.13 q^{69} +(4154.49 - 2443.52i) q^{70} -21017.5 q^{71} +1852.55i q^{72} -5360.83i q^{73} -3395.12 q^{74} +(-24580.8 - 13667.4i) q^{75} +67673.1 q^{76} +1334.95i q^{77} +17509.9i q^{78} -11717.1 q^{79} +(-53441.4 + 31432.3i) q^{80} +6561.00 q^{81} -47781.6i q^{82} -51987.1i q^{83} -2886.81 q^{84} +(-18967.4 - 32248.5i) q^{85} -52223.2 q^{86} +23765.5i q^{87} -2767.39i q^{88} -89693.5 q^{89} +(17940.0 + 30501.7i) q^{90} +2746.58 q^{91} +25229.7i q^{92} +30430.5i q^{93} +157829. q^{94} +(-112158. + 65967.6i) q^{95} +71420.2 q^{96} +19443.4i q^{97} -130395. i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	7.81495i		−	1.38150i	−0.723093	−	0.690750i	$-0.757280\pi$
$2$		−	7.81495i		−	1.38150i	0.723093	−	0.690750i	$-0.242720\pi$
$3$		−	9.00000i		−	0.577350i
$3$		−	9.00000i		−	0.577350i
$4$	−29.0734			−0.908545
$5$	48.1851	−	28.3407i	0.861961	−	0.506975i
$5$	48.1851	−	28.3407i	0.861961	−	0.506975i
$6$	−70.3345			−0.797610
$7$			11.0326i			0.0851008i	0.999094	+	0.0425504i	$0.0135483\pi$
$7$			11.0326i			0.0851008i	−0.999094	+	0.0425504i	$0.986452\pi$
$8$		−	22.8710i		−	0.126346i
$9$	−81.0000			−0.333333
$10$	−221.481	−	376.564i	−0.700386	−	1.19080i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$			261.661i			0.524549i
$13$		−	248.951i		−	0.408560i	−0.978913	−	0.204280i	$-0.934515\pi$
$13$		−	248.951i		−	0.408560i	0.978913	−	0.204280i	$-0.0654853\pi$
$14$	86.2194			0.117567
$15$	−255.067	−	433.666i	−0.292702	−	0.497653i
$16$	−1109.09			−1.08309
$17$		−	669.264i		−	0.561662i	−0.959757	−	0.280831i	$-0.909390\pi$
$17$		−	669.264i		−	0.561662i	0.959757	−	0.280831i	$-0.0906100\pi$
$18$			633.011i			0.460500i
$19$	−2327.66			−1.47923			−0.739615	−	0.673030i	$-0.764992\pi$
$19$	−2327.66			−1.47923			−0.739615	+	0.673030i	$0.764992\pi$
$20$	−1400.91	+	823.963i	−0.783130	+	0.460609i
$21$	99.2936			0.0491330
$22$		−	945.609i		−	0.416538i
$23$		−	867.792i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$23$		−	867.792i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$24$	−205.839			−0.0729456
$25$	1518.60	−	2731.20i	0.485953	−	0.873985i
$26$	−1945.54			−0.564426
$27$			729.000i			0.192450i
$28$		−	320.756i		−	0.0773179i
$29$	−2640.61			−0.583055			−0.291527	−	0.956562i	$-0.594163\pi$
$29$	−2640.61			−0.583055			−0.291527	+	0.956562i	$0.594163\pi$
$30$	−3389.08	+	1993.33i	−0.687509	+	0.404368i
$31$	−3381.17			−0.631921			−0.315961	−	0.948772i	$-0.602327\pi$
$31$	−3381.17			−0.631921			−0.315961	+	0.948772i	$0.602327\pi$
$32$			7935.57i			1.36995i
$33$		−	1089.00i		−	0.174078i
$34$	−5230.26			−0.775937
$35$	312.673	+	531.608i	0.0431440	+	0.0733536i
$36$	2354.95			0.302848
$37$		−	434.439i		−	0.0521705i	−0.999660	−	0.0260852i	$-0.991696\pi$
$37$		−	434.439i		−	0.0521705i	0.999660	−	0.0260852i	$-0.00830413\pi$
$38$			18190.5i			2.04356i
$39$	−2240.56			−0.235882
$40$	−648.181	−	1102.04i	−0.0640540	−	0.108905i
$41$	6114.13			0.568035			0.284018	−	0.958819i	$-0.408333\pi$
$41$	6114.13			0.568035			0.284018	+	0.958819i	$0.408333\pi$
$42$		−	775.975i		−	0.0678772i
$43$		−	6682.47i		−	0.551145i	−0.961280	−	0.275573i	$-0.911133\pi$
$43$		−	6682.47i		−	0.551145i	0.961280	−	0.275573i	$-0.0888674\pi$
$44$	−3517.89			−0.273937
$45$	−3902.99	+	2295.60i	−0.287320	+	0.168992i
$46$	−6781.75			−0.472550
$47$			20195.8i			1.33357i	0.745249	+	0.666787i	$0.232331\pi$
$47$			20195.8i			1.33357i	−0.745249	+	0.666787i	$0.767669\pi$
$48$			9981.77i			0.625323i
$49$	16685.3			0.992758
$50$	−21344.2	−	11867.8i	−1.20741	−	0.671345i
$51$	−6023.37			−0.324276
$52$			7237.87i			0.371195i
$53$		−	3335.16i		−	0.163090i	−0.996670	−	0.0815450i	$-0.974015\pi$
$53$		−	3335.16i		−	0.163090i	0.996670	−	0.0815450i	$-0.0259854\pi$
$54$	5697.10			0.265870
$55$	5830.39	−	3429.23i	0.259891	−	0.152859i
$56$	252.327			0.0107521
$57$			20948.9i			0.854034i
$58$			20636.2i			0.805491i
$59$	35671.0			1.33409			0.667045	−	0.745017i	$-0.267559\pi$
$59$	35671.0			1.33409			0.667045	+	0.745017i	$0.267559\pi$
$60$	7415.66	+	12608.2i	0.265933	+	0.452140i
$61$	16705.5			0.574825			0.287412	−	0.957807i	$-0.407205\pi$
$61$	16705.5			0.574825			0.287412	+	0.957807i	$0.407205\pi$
$62$			26423.7i			0.873000i
$63$		−	893.642i		−	0.0283669i
$64$	26525.4			0.809490
$65$	−7055.46	−	11995.7i	−0.207130	−	0.352163i
$66$	−8510.48			−0.240488
$67$			15071.1i			0.410164i	0.978745	+	0.205082i	$0.0657462\pi$
$67$			15071.1i			0.410164i	−0.978745	+	0.205082i	$0.934254\pi$
$68$			19457.8i			0.510295i
$69$	−7810.13			−0.197486
$70$	4154.49	−	2443.52i	0.101338	−	0.0596034i
$71$	−21017.5			−0.494806			−0.247403	−	0.968913i	$-0.579577\pi$
$71$	−21017.5			−0.494806			−0.247403	+	0.968913i	$0.579577\pi$
$72$			1852.55i			0.0421152i
$73$		−	5360.83i		−	0.117740i	−0.998266	−	0.0588701i	$-0.981250\pi$
$73$		−	5360.83i		−	0.117740i	0.998266	−	0.0588701i	$-0.0187498\pi$
$74$	−3395.12			−0.0720735
$75$	−24580.8	−	13667.4i	−0.504595	−	0.280565i
$76$	67673.1			1.34395
$77$			1334.95i			0.0256589i
$78$			17509.9i			0.325871i
$79$	−11717.1			−0.211228			−0.105614	−	0.994407i	$-0.533681\pi$
$79$	−11717.1			−0.211228			−0.105614	+	0.994407i	$0.533681\pi$
$80$	−53441.4	+	31432.3i	−0.933582	+	0.549100i
$81$	6561.00			0.111111
$82$		−	47781.6i		−	0.784741i
$83$		−	51987.1i		−	0.828325i	−0.910203	−	0.414162i	$-0.864075\pi$
$83$		−	51987.1i		−	0.828325i	0.910203	−	0.414162i	$-0.135925\pi$
$84$	−2886.81			−0.0446395
$85$	−18967.4	−	32248.5i	−0.284748	−	0.484131i
$86$	−52223.2			−0.761408
$87$			23765.5i			0.336627i
$88$		−	2767.39i		−	0.0380946i
$89$	−89693.5			−1.20029			−0.600145	−	0.799892i	$-0.704890\pi$
$89$	−89693.5			−1.20029			−0.600145	+	0.799892i	$0.704890\pi$
$90$	17940.0	+	30501.7i	0.233462	+	0.396933i
$91$	2746.58			0.0347688
$92$			25229.7i			0.310772i
$93$			30430.5i			0.364840i
$94$	157829.			1.84233
$95$	−112158.	+	65967.6i	−1.27504	+	0.749932i
$96$	71420.2			0.790939
$97$			19443.4i			0.209819i	0.994482	+	0.104909i	$0.0334552\pi$
$97$			19443.4i			0.209819i	−0.994482	+	0.104909i	$0.966545\pi$
$98$		−	130395.i		−	1.37150i
$99$	−9801.00			−0.100504
$100$	−44151.0	+	79405.4i	−0.441510	+	0.794054i
$101$	−144534.			−1.40983			−0.704917	−	0.709290i	$-0.749016\pi$
$101$	−144534.			−1.40983			−0.704917	+	0.709290i	$0.749016\pi$
$102$			47072.4i			0.447987i
$103$		−	156184.i		−	1.45059i	−0.688441	−	0.725293i	$-0.741704\pi$
$103$		−	156184.i		−	1.45059i	0.688441	−	0.725293i	$-0.258296\pi$
$104$	−5693.76			−0.0516197
$105$	4784.47	−	2814.06i	0.0423507	−	0.0249092i
$106$	−26064.1			−0.225309
$107$		−	53993.7i		−	0.455915i	−0.973671	−	0.227957i	$-0.926795\pi$
$107$		−	53993.7i		−	0.455915i	0.973671	−	0.227957i	$-0.0732047\pi$
$108$		−	21194.5i		−	0.174850i
$109$	119467.			0.963120			0.481560	−	0.876413i	$-0.340070\pi$
$109$	119467.			0.963120			0.481560	+	0.876413i	$0.340070\pi$
$110$	−26799.3	−	45564.2i	−0.211174	−	0.359040i
$111$	−3909.95			−0.0301206
$112$		−	12236.1i		−	0.0921719i
$113$		−	143349.i		−	1.05609i	−0.849217	−	0.528043i	$-0.822926\pi$
$113$		−	143349.i		−	1.05609i	0.849217	−	0.528043i	$-0.177074\pi$
$114$	163715.			1.17985
$115$	−24593.9	−	41814.6i	−0.173413	−	0.294838i
$116$	76771.6			0.529731
$117$			20165.0i			0.136187i
$118$		−	278767.i		−	1.84305i
$119$	7383.74			0.0477979
$120$	−9918.36	+	5833.63i	−0.0628763	+	0.0369816i
$121$	14641.0			0.0909091
$122$		−	130553.i		−	0.794121i
$123$		−	55027.2i		−	0.327955i
$124$	98302.3			0.574129
$125$	−4230.25	−	174642.i	−0.0242154	−	0.999707i
$126$	−6983.77			−0.0391889
$127$		−	160600.i		−	0.883562i	−0.897123	−	0.441781i	$-0.854347\pi$
$127$		−	160600.i		−	0.883562i	0.897123	−	0.441781i	$-0.145653\pi$
$128$			46643.9i			0.251634i
$129$	−60142.2			−0.318204
$130$	−93746.0	+	55138.1i	−0.486513	+	0.286150i
$131$	−6734.56			−0.0342871			−0.0171436	−	0.999853i	$-0.505457\pi$
$131$	−6734.56			−0.0342871			−0.0171436	+	0.999853i	$0.505457\pi$
$132$			31661.0i			0.158157i
$133$		−	25680.2i		−	0.125884i
$134$	117780.			0.566642
$135$	20660.4	+	35126.9i	0.0975673	+	0.165884i
$136$	−15306.7			−0.0709635
$137$		−	117299.i		−	0.533942i	−0.963705	−	0.266971i	$-0.913977\pi$
$137$		−	117299.i		−	0.533942i	0.963705	−	0.266971i	$-0.0860228\pi$
$138$			61035.8i			0.272827i
$139$	364129.			1.59852			0.799261	−	0.600985i	$-0.205225\pi$
$139$	364129.			1.59852			0.799261	+	0.600985i	$0.205225\pi$
$140$	−9090.47	−	15455.7i	−0.0391982	−	0.0666450i
$141$	181762.			0.769939
$142$			164251.i			0.683575i
$143$		−	30123.1i		−	0.123185i
$144$	89835.9			0.361030
$145$	−127238.	+	74836.9i	−0.502570	+	0.295594i
$146$	−41894.6			−0.162658
$147$		−	150168.i		−	0.573169i
$148$			12630.6i			0.0473992i
$149$	296786.			1.09516			0.547580	−	0.836753i	$-0.315549\pi$
$149$	296786.			1.09516			0.547580	+	0.836753i	$0.315549\pi$
$150$	−106810.	+	192098.i	−0.387601	+	0.697099i
$151$	−464852.			−1.65910			−0.829549	−	0.558433i	$-0.811403\pi$
$151$	−464852.			−1.65910			−0.829549	+	0.558433i	$0.811403\pi$
$152$			53235.9i			0.186894i
$153$			54210.4i			0.187221i
$154$	10432.5			0.0354477
$155$	−162922.	+	95824.9i	−0.544692	+	0.320368i
$156$	65140.8			0.214310
$157$		−	188905.i		−	0.611639i	−0.952089	−	0.305820i	$-0.901070\pi$
$157$		−	188905.i		−	0.611639i	0.952089	−	0.305820i	$-0.0989305\pi$
$158$			91568.4i			0.291812i
$159$	−30016.5			−0.0941601
$160$	224900.	+	382376.i	0.694528	+	1.18084i
$161$	9574.02			0.0291092
$162$		−	51273.9i		−	0.153500i
$163$			547363.i			1.61364i	0.590797	+	0.806820i	$0.298813\pi$
$163$			547363.i			1.61364i	−0.590797	+	0.806820i	$0.701187\pi$
$164$	−177759.			−0.516085
$165$	−30863.1	−	52473.6i	−0.0882530	−	0.150048i
$166$	−406277.			−1.14433
$167$			146681.i			0.406990i	0.979076	+	0.203495i	$0.0652300\pi$
$167$			146681.i			0.406990i	−0.979076	+	0.203495i	$0.934770\pi$
$168$		−	2270.94i		−	0.00620773i
$169$	309316.			0.833079
$170$	−252021.	+	148230.i	−0.668827	+	0.393380i
$171$	188540.			0.493076
$172$			194282.i			0.500740i
$173$		−	625665.i		−	1.58937i	−0.607019	−	0.794687i	$-0.707635\pi$
$173$		−	625665.i		−	1.58937i	0.607019	−	0.794687i	$-0.292365\pi$
$174$	185726.			0.465050
$175$	30132.3	+	16754.2i	0.0743768	+	0.0413550i
$176$	−134199.			−0.326564
$177$		−	321039.i		−	0.770238i
$178$			700950.i			1.65820i
$179$	−233383.			−0.544422			−0.272211	−	0.962238i	$-0.587755\pi$
$179$	−233383.			−0.544422			−0.272211	+	0.962238i	$0.587755\pi$
$180$	113473.	−	66741.0i	0.261043	−	0.153536i
$181$	503730.			1.14288			0.571441	−	0.820643i	$-0.306385\pi$
$181$	503730.			1.14288			0.571441	+	0.820643i	$0.306385\pi$
$182$		−	21464.4i		−	0.0480331i
$183$		−	150350.i		−	0.331875i
$184$	−19847.3			−0.0432171
$185$	−12312.3	−	20933.5i	−0.0264491	−	0.0449689i
$186$	237813.			0.504027
$187$		−	80980.9i		−	0.169347i
$188$		−	587162.i		−	1.21161i
$189$	−8042.78			−0.0163777
$190$	515534.	+	876513.i	1.03603	+	1.76147i
$191$	953992.			1.89217			0.946087	−	0.323912i	$-0.104998\pi$
$191$	953992.			1.89217			0.946087	+	0.323912i	$0.104998\pi$
$192$		−	238728.i		−	0.467359i
$193$		−	862260.i		−	1.66627i	−0.553070	−	0.833135i	$-0.686544\pi$
$193$		−	862260.i		−	1.66627i	0.553070	−	0.833135i	$-0.313456\pi$
$194$	151950.			0.289865
$195$	−107962.	+	63499.2i	−0.203321	+	0.119586i
$196$	−485098.			−0.901965
$197$			497679.i			0.913658i	0.889554	+	0.456829i	$0.151015\pi$
$197$			497679.i			0.913658i	−0.889554	+	0.456829i	$0.848985\pi$
$198$			76594.3i			0.138846i
$199$	387099.			0.692930			0.346465	−	0.938063i	$-0.387382\pi$
$199$	387099.			0.692930			0.346465	+	0.938063i	$0.387382\pi$
$200$	−62465.3	−	34732.0i	−0.110424	−	0.0613980i
$201$	135640.			0.236808
$202$			1.12953e6i			1.94769i
$203$		−	29132.9i		−	0.0496184i
$204$	175120.			0.294619
$205$	294610.	−	173279.i	0.489624	−	0.287979i
$206$	−1.22057e6			−2.00399
$207$			70291.2i			0.114018i
$208$			276108.i			0.442508i
$209$	−281647.			−0.446004
$210$	−21991.7	−	37390.4i	−0.0344120	−	0.0585075i
$211$	−717688.			−1.10976			−0.554880	−	0.831930i	$-0.687236\pi$
$211$	−717688.			−1.10976			−0.554880	+	0.831930i	$0.687236\pi$
$212$			96964.6i			0.148175i
$213$			189158.i			0.285677i
$214$	−421958.			−0.629846
$215$	−189386.	−	321995.i	−0.279417	−	0.475066i
$216$	16672.9			0.0243152
$217$		−	37303.2i		−	0.0537770i
$218$		−	933626.i		−	1.33055i
$219$	−48247.5			−0.0679773
$220$	−169510.	+	99699.5i	−0.236123	+	0.138879i
$221$	−166614.			−0.229473
$222$			30556.1i			0.0416117i
$223$			113180.i			0.152409i	0.997092	+	0.0762043i	$0.0242801\pi$
$223$			113180.i			0.152409i	−0.997092	+	0.0762043i	$0.975720\pi$
$224$	−87550.2			−0.116584
$225$	−123007.	+	221227.i	−0.161984	+	0.291328i
$226$	−1.12027e6			−1.45898
$227$			616694.i			0.794337i	0.917746	+	0.397169i	$0.130007\pi$
$227$			616694.i			0.794337i	−0.917746	+	0.397169i	$0.869993\pi$
$228$		−	609058.i		−	0.775928i
$229$	−502825.			−0.633620			−0.316810	−	0.948489i	$-0.602612\pi$
$229$	−502825.			−0.633620			−0.316810	+	0.948489i	$0.602612\pi$
$230$	−326779.	+	192200.i	−0.407319	+	0.239571i
$231$	12014.5			0.0148141
$232$			60393.4i			0.0736664i
$233$		−	141935.i		−	0.171277i	−0.996326	−	0.0856383i	$-0.972707\pi$
$233$		−	141935.i		−	0.171277i	0.996326	−	0.0856383i	$-0.0272930\pi$
$234$	157589.			0.188142
$235$	572365.	+	973137.i	0.676088	+	1.14949i
$236$	−1.03708e6			−1.21208
$237$			105454.i			0.121953i
$238$		−	57703.5i		−	0.0660328i
$239$	−733743.			−0.830901			−0.415450	−	0.909616i	$-0.636376\pi$
$239$	−733743.			−0.830901			−0.415450	+	0.909616i	$0.636376\pi$
$240$	282891.	+	480972.i	0.317023	+	0.539004i
$241$	−327132.			−0.362811			−0.181406	−	0.983408i	$-0.558065\pi$
$241$	−327132.			−0.362811			−0.181406	+	0.983408i	$0.558065\pi$
$242$		−	114419.i		−	0.125591i
$243$		−	59049.0i		−	0.0641500i
$244$	−485687.			−0.522254
$245$	803982.	−	472873.i	0.855718	−	0.503303i
$246$	−430035.			−0.453071
$247$			579474.i			0.604354i
$248$			77330.7i			0.0798404i
$249$	−467884.			−0.478233
$250$	−1.36482e6	+	33059.2i	−1.38110	+	0.0334535i
$251$	36093.3			0.0361612			0.0180806	−	0.999837i	$-0.494244\pi$
$251$	36093.3			0.0361612			0.0180806	+	0.999837i	$0.494244\pi$
$252$			25981.3i			0.0257726i
$253$		−	105003.i		−	0.103134i
$254$	−1.25508e6			−1.22064
$255$	−290237.	+	170707.i	−0.279513	+	0.164400i
$256$	1.21333e6			1.15712
$257$			1.70289e6i			1.60825i	0.594459	+	0.804126i	$0.297366\pi$
$257$			1.70289e6i			1.60825i	−0.594459	+	0.804126i	$0.702634\pi$
$258$			470009.i			0.439599i
$259$	4793.00			0.00443975
$260$	205127.	+	348757.i	0.188186	+	0.319956i
$261$	213889.			0.194352
$262$			52630.3i			0.0473677i
$263$		−	411013.i		−	0.366409i	−0.983075	−	0.183205i	$-0.941353\pi$
$263$		−	411013.i		−	0.366409i	0.983075	−	0.183205i	$-0.0586471\pi$
$264$	−24906.5			−0.0219939
$265$	−94521.0	−	160705.i	−0.0826825	−	0.140577i
$266$	−200689.			−0.173908
$267$			807241.i			0.692987i
$268$		−	438169.i		−	0.372653i
$269$	100472.			0.0846571			0.0423286	−	0.999104i	$-0.486522\pi$
$269$	100472.			0.0846571			0.0423286	+	0.999104i	$0.486522\pi$
$270$	274515.	−	161460.i	0.229170	−	0.134789i
$271$	1.74029e6			1.43945			0.719727	−	0.694257i	$-0.244267\pi$
$271$	1.74029e6			1.43945			0.719727	+	0.694257i	$0.244267\pi$
$272$			742271.i			0.608331i
$273$		−	24719.3i		−	0.0200738i
$274$	−916689.			−0.737642
$275$	183751.	−	330475.i	0.146520	−	0.263516i
$276$	227067.			0.179425
$277$		−	1.99970e6i		−	1.56590i	−0.622083	−	0.782951i	$-0.713714\pi$
$277$		−	1.99970e6i		−	1.56590i	0.622083	−	0.782951i	$-0.286286\pi$
$278$		−	2.84565e6i		−	2.20836i
$279$	273875.			0.210640
$280$	12158.4	−	7151.13i	0.00926790	−	0.00545105i
$281$	1.76621e6			1.33437			0.667184	−	0.744893i	$-0.267499\pi$
$281$	1.76621e6			1.33437			0.667184	+	0.744893i	$0.267499\pi$
$282$		−	1.42046e6i		−	1.06367i
$283$		−	2.31041e6i		−	1.71484i	−0.514619	−	0.857419i	$-0.672067\pi$
$283$		−	2.31041e6i		−	1.71484i	0.514619	−	0.857419i	$-0.327933\pi$
$284$	611051.			0.449554
$285$	593709.	+	1.00943e6i	0.432973	+	0.736144i
$286$	−235410.			−0.170181
$287$			67454.9i			0.0483403i
$288$		−	642782.i		−	0.456649i
$289$	971943.			0.684536
$290$	584846.	+	994359.i	0.408363	+	0.694301i
$291$	174991.			0.121139
$292$			155858.i			0.106972i
$293$		−	480796.i		−	0.327183i	−0.986528	−	0.163592i	$-0.947692\pi$
$293$		−	480796.i		−	0.327183i	0.986528	−	0.163592i	$-0.0523080\pi$
$294$	−1.17355e6			−0.791834
$295$	1.71881e6	−	1.01094e6i	1.14993	−	0.676350i
$296$	−9936.05			−0.00659150
$297$			88209.0i			0.0580259i
$298$		−	2.31937e6i		−	1.51296i
$299$	−216038.			−0.139750
$300$	714649.	+	397359.i	0.458447	+	0.254906i
$301$	73725.2			0.0469029
$302$			3.63279e6i			2.29205i
$303$			1.30081e6i			0.813968i
$304$	2.58157e6			1.60214
$305$	804957.	−	473447.i	0.495477	−	0.291422i
$306$	423651.			0.258646
$307$		−	1.27658e6i		−	0.773043i	−0.922280	−	0.386521i	$-0.873677\pi$
$307$		−	1.27658e6i		−	0.773043i	0.922280	−	0.386521i	$-0.126323\pi$
$308$		−	38811.5i		−	0.0233122i
$309$	−1.40566e6			−0.837496
$310$	748867.	+	1.27323e6i	0.442589	+	0.752492i
$311$	2.50885e6			1.47087			0.735434	−	0.677596i	$-0.236978\pi$
$311$	2.50885e6			1.47087			0.735434	+	0.677596i	$0.236978\pi$
$312$			51243.8i			0.0298027i
$313$		−	1.85827e6i		−	1.07213i	−0.844177	−	0.536065i	$-0.819910\pi$
$313$		−	1.85827e6i		−	1.07213i	0.844177	−	0.536065i	$-0.180090\pi$
$314$	−1.47629e6			−0.844980
$315$	−25326.5	−	43060.2i	−0.0143813	−	0.0244512i
$316$	340656.			0.191910
$317$			2.48818e6i			1.39070i	0.718670	+	0.695352i	$0.244751\pi$
$317$			2.48818e6i			1.39070i	−0.718670	+	0.695352i	$0.755249\pi$
$318$			234577.i			0.130082i
$319$	−319514.			−0.175798
$320$	1.27813e6	−	751749.i	0.697749	−	0.410391i
$321$	−485943.			−0.263222
$322$		−	74820.5i		−	0.0402143i
$323$			1.55782e6i			0.830827i
$324$	−190751.			−0.100949
$325$	−679936.	−	378058.i	−0.357075	−	0.198541i
$326$	4.27762e6			2.22924
$327$		−	1.07520e6i		−	0.556058i
$328$		−	139836.i		−	0.0717687i
$329$	−222813.			−0.113488
$330$	−410078.	+	241193.i	−0.207292	+	0.121922i
$331$	2.19276e6			1.10007			0.550037	−	0.835141i	$-0.314614\pi$
$331$	2.19276e6			1.10007			0.550037	+	0.835141i	$0.314614\pi$
$332$			1.51144e6i			0.752570i
$333$			35189.6i			0.0173902i
$334$	1.14631e6			0.562257
$335$	427126.	+	726202.i	0.207943	+	0.353546i
$336$	−110125.			−0.0532155
$337$		−	1.08814e6i		−	0.521926i	−0.965349	−	0.260963i	$-0.915960\pi$
$337$		−	1.08814e6i		−	0.521926i	0.965349	−	0.260963i	$-0.0840400\pi$
$338$		−	2.41729e6i		−	1.15090i
$339$	−1.29014e6			−0.609732
$340$	551448.	+	937576.i	0.258707	+	0.439854i
$341$	−409122.			−0.190531
$342$		−	1.47343e6i		−	0.681186i
$343$			369508.i			0.169585i
$344$	−152835.			−0.0696347
$345$	−376332.	+	221345.i	−0.170225	+	0.100120i
$346$	−4.88954e6			−2.19572
$347$			1.48961e6i			0.664123i	0.943258	+	0.332061i	$0.107744\pi$
$347$			1.48961e6i			0.664123i	−0.943258	+	0.332061i	$0.892256\pi$
$348$		−	690944.i		−	0.305841i
$349$	−3.61825e6			−1.59014			−0.795070	−	0.606518i	$-0.792566\pi$
$349$	−3.61825e6			−1.59014			−0.795070	+	0.606518i	$0.792566\pi$
$350$	130933.	−	235483.i	0.0571320	−	0.102752i
$351$	181485.			0.0786274
$352$			960205.i			0.413054i
$353$			346438.i			0.147975i	0.997259	+	0.0739875i	$0.0235725\pi$
$353$			346438.i			0.147975i	−0.997259	+	0.0739875i	$0.976428\pi$
$354$	−2.50890e6			−1.06408
$355$	−1.01273e6	+	595652.i	−0.426504	+	0.250854i
$356$	2.60770e6			1.09052
$357$		−	66453.6i		−	0.0275961i
$358$			1.82387e6i			0.752120i
$359$	1.75327e6			0.717981			0.358991	−	0.933341i	$-0.383121\pi$
$359$	1.75327e6			0.717981			0.358991	+	0.933341i	$0.383121\pi$
$360$	52502.6	+	89265.3i	0.0213513	+	0.0363016i
$361$	2.94190e6			1.18812
$362$		−	3.93663e6i		−	1.57889i
$363$		−	131769.i		−	0.0524864i
$364$	−79852.6			−0.0315890
$365$	−151930.	−	258312.i	−0.0596913	−	0.101487i
$366$	−1.17498e6			−0.458486
$367$		−	2.68865e6i		−	1.04200i	−0.853556	−	0.521001i	$-0.825559\pi$
$367$		−	2.68865e6i		−	1.04200i	0.853556	−	0.521001i	$-0.174441\pi$
$368$			962456.i			0.370477i
$369$	−495245.			−0.189345
$370$	−163594.	+	96220.3i	−0.0621246	+	0.0365395i
$371$	36795.6			0.0138791
$372$		−	884720.i		−	0.331473i
$373$		−	2.73768e6i		−	1.01885i	−0.860515	−	0.509426i	$-0.829858\pi$
$373$		−	2.73768e6i		−	1.01885i	0.860515	−	0.509426i	$-0.170142\pi$
$374$	−632862.			−0.233954
$375$	−1.57177e6	+	38072.2i	−0.577181	+	0.0139807i
$376$	461898.			0.168491
$377$			657383.i			0.238213i
$378$			62853.9i			0.0226257i
$379$	−1.99354e6			−0.712898			−0.356449	−	0.934315i	$-0.616013\pi$
$379$	−1.99354e6			−0.712898			−0.356449	+	0.934315i	$0.616013\pi$
$380$	3.26083e6	−	1.91791e6i	1.15843	−	0.681347i
$381$	−1.44540e6			−0.510125
$382$		−	7.45540e6i		−	2.61404i
$383$			3.32117e6i			1.15690i	0.815720	+	0.578448i	$0.196341\pi$
$383$			3.32117e6i			1.15690i	−0.815720	+	0.578448i	$0.803659\pi$
$384$	419795.			0.145281
$385$	37833.4	+	64324.6i	0.0130084	+	0.0221169i
$386$	−6.73852e6			−2.30195
$387$			541280.i			0.183715i
$388$		−	565288.i		−	0.190630i
$389$	−640065.			−0.214462			−0.107231	−	0.994234i	$-0.534198\pi$
$389$	−640065.			−0.214462			−0.107231	+	0.994234i	$0.534198\pi$
$390$	496243.	+	843714.i	0.165209	+	0.280888i
$391$	−580782.			−0.192119
$392$		−	381609.i		−	0.125431i
$393$			60611.1i			0.0197957i
$394$	3.88934e6			1.26222
$395$	−564589.	+	332071.i	−0.182070	+	0.107087i
$396$	284949.			0.0913122
$397$		−	806457.i		−	0.256806i	−0.991722	−	0.128403i	$-0.959015\pi$
$397$		−	806457.i		−	0.256806i	0.991722	−	0.128403i	$-0.0409851\pi$
$398$		−	3.02516e6i		−	0.957284i
$399$	−231122.			−0.0726789
$400$	−1.68426e6	+	3.02914e6i	−0.526332	+	0.946605i
$401$	2.17447e6			0.675292			0.337646	−	0.941273i	$-0.390369\pi$
$401$	2.17447e6			0.675292			0.337646	+	0.941273i	$0.390369\pi$
$402$		−	1.06002e6i		−	0.327151i
$403$			841747.i			0.258178i
$404$	4.20211e6			1.28090
$405$	316142.	−	185944.i	0.0957734	−	0.0563305i
$406$	−227672.			−0.0685479
$407$		−	52567.1i		−	0.0157300i
$408$			137760.i			0.0409708i
$409$	−4.98556e6			−1.47369			−0.736844	−	0.676063i	$-0.763685\pi$
$409$	−4.98556e6			−1.47369			−0.736844	+	0.676063i	$0.763685\pi$
$410$	−1.35417e6	−	2.30236e6i	−0.397844	−	0.676416i
$411$	−1.05569e6			−0.308272
$412$			4.54080e6i			1.31792i
$413$			393545.i			0.113532i
$414$	549322.			0.157517
$415$	−1.47335e6	−	2.50500e6i	−0.419940	−	0.713984i
$416$	1.97557e6			0.559705
$417$		−	3.27716e6i		−	0.922907i
$418$			2.20106e6i			0.616156i
$419$	−5.22690e6			−1.45448			−0.727242	−	0.686382i	$-0.759198\pi$
$419$	−5.22690e6			−1.45448			−0.727242	+	0.686382i	$0.759198\pi$
$420$	−139101.	+	81814.2i	−0.0384775	+	0.0226311i
$421$	1.48521e6			0.408398			0.204199	−	0.978929i	$-0.434541\pi$
$421$	1.48521e6			0.408398			0.204199	+	0.978929i	$0.434541\pi$
$422$			5.60869e6i			1.53314i
$423$		−	1.63586e6i		−	0.444524i
$424$	−76278.5			−0.0206057
$425$	−1.82790e6	−	1.01635e6i	−0.490884	−	0.272942i
$426$	1.47826e6			0.394662
$427$			184306.i			0.0489181i
$428$			1.56978e6i			0.414219i
$429$	−271108.			−0.0711212
$430$	−2.51638e6	+	1.48004e6i	−0.656304	+	0.386014i
$431$	−301670.			−0.0782238			−0.0391119	−	0.999235i	$-0.512453\pi$
$431$	−301670.			−0.0782238			−0.0391119	+	0.999235i	$0.512453\pi$
$432$		−	808523.i		−	0.208441i
$433$			1.78448e6i			0.457396i	0.973497	+	0.228698i	$0.0734468\pi$
$433$			1.78448e6i			0.457396i	−0.973497	+	0.228698i	$0.926553\pi$
$434$	−291523.			−0.0742930
$435$	673532.	+	1.14514e6i	0.170661	+	0.290159i
$436$	−3.47331e6			−0.875038
$437$			2.01993e6i			0.505978i
$438$			377051.i			0.0939108i
$439$	499339.			0.123661			0.0618307	−	0.998087i	$-0.480306\pi$
$439$	499339.			0.123661			0.0618307	+	0.998087i	$0.480306\pi$
$440$	−78429.9	−	133347.i	−0.0193130	−	0.0328361i
$441$	−1.35151e6			−0.330919
$442$			1.30208e6i			0.317017i
$443$		−	4.62775e6i		−	1.12037i	−0.828369	−	0.560184i	$-0.810731\pi$
$443$		−	4.62775e6i		−	1.12037i	0.828369	−	0.560184i	$-0.189269\pi$
$444$	113676.			0.0273659
$445$	−4.32189e6	+	2.54198e6i	−1.03460	+	0.608516i
$446$	884500.			0.210553
$447$		−	2.67107e6i		−	0.632291i
$448$			292645.i			0.0688883i
$449$	−3.31281e6			−0.775499			−0.387749	−	0.921765i	$-0.626747\pi$
$449$	−3.31281e6			−0.775499			−0.387749	+	0.921765i	$0.626747\pi$
$450$	1.72888e6	+	961293.i	0.402470	+	0.223782i
$451$	739810.			0.171269
$452$			4.16766e6i			0.959502i
$453$			4.18367e6i			0.957881i
$454$	4.81943e6			1.09738
$455$	132344.	−	77840.3i	0.0299693	−	0.0176269i
$456$	479123.			0.107903
$457$		−	7.09134e6i		−	1.58832i	−0.607709	−	0.794160i	$-0.707911\pi$
$457$		−	7.09134e6i		−	1.58832i	0.607709	−	0.794160i	$-0.292089\pi$
$458$			3.92956e6i			0.875346i
$459$	487893.			0.108092
$460$	715028.	+	1.21569e6i	0.157554	+	0.267874i
$461$	−3.68457e6			−0.807485			−0.403742	−	0.914873i	$-0.632291\pi$
$461$	−3.68457e6			−0.807485			−0.403742	+	0.914873i	$0.632291\pi$
$462$		−	93892.9i		−	0.0204658i
$463$			5.32110e6i			1.15358i	0.816892	+	0.576791i	$0.195695\pi$
$463$			5.32110e6i			1.15358i	−0.816892	+	0.576791i	$0.804305\pi$
$464$	2.92866e6			0.631501
$465$	862424.	+	1.46630e6i	0.184965	+	0.314478i
$466$	−1.10921e6			−0.236619
$467$			9.27946e6i			1.96893i	0.175581	+	0.984465i	$0.443820\pi$
$467$			9.27946e6i			1.96893i	−0.175581	+	0.984465i	$0.556180\pi$
$468$		−	586267.i		−	0.123732i
$469$	−166274.			−0.0349053
$470$	7.60502e6	−	4.47300e6i	1.58802	−	0.934016i
$471$	−1.70015e6			−0.353130
$472$		−	815831.i		−	0.168556i
$473$		−	808579.i		−	0.166177i
$474$	824116.			0.168478
$475$	−3.53479e6	+	6.35731e6i	−0.718837	+	1.29282i
$476$	−214671.			−0.0434265
$477$			270148.i			0.0543633i
$478$			5.73416e6i			1.14789i
$479$	4.22915e6			0.842199			0.421100	−	0.907014i	$-0.361644\pi$
$479$	4.22915e6			0.842199			0.421100	+	0.907014i	$0.361644\pi$
$480$	3.44139e6	−	2.02410e6i	0.681758	−	0.400986i
$481$	−108154.			−0.0213148
$482$			2.55652e6i			0.501224i
$483$		−	86166.2i		−	0.0168062i
$484$	−425664.			−0.0825950
$485$	551042.	+	936884.i	0.106373	+	0.180855i
$486$	−461465.			−0.0886233
$487$			8.16043e6i			1.55916i	0.626302	+	0.779580i	$0.284568\pi$
$487$			8.16043e6i			1.55916i	−0.626302	+	0.779580i	$0.715432\pi$
$488$		−	382072.i		−	0.0726265i
$489$	4.92627e6			0.931635
$490$	−3.69548e6	−	6.28308e6i	−0.695314	−	1.18218i
$491$	−1.72620e6			−0.323138			−0.161569	−	0.986861i	$-0.551655\pi$
$491$	−1.72620e6			−0.323138			−0.161569	+	0.986861i	$0.551655\pi$
$492$			1.59983e6i			0.297962i
$493$			1.76727e6i			0.327480i
$494$	4.52856e6			0.834916
$495$	−472262.	+	277768.i	−0.0866303	+	0.0509529i
$496$	3.75001e6			0.684428
$497$		−	231878.i		−	0.0421084i
$498$			3.65649e6i			0.660680i
$499$	−568851.			−0.102270			−0.0511349	−	0.998692i	$-0.516284\pi$
$499$	−568851.			−0.102270			−0.0511349	+	0.998692i	$0.516284\pi$
$500$	122988.	+	5.07743e6i	0.0220007	+	0.908278i
$501$	1.32013e6			0.234976
$502$		−	282068.i		−	0.0499567i
$503$		−	2.06495e6i		−	0.363906i	−0.983307	−	0.181953i	$-0.941758\pi$
$503$		−	2.06495e6i		−	0.363906i	0.983307	−	0.181953i	$-0.0582419\pi$
$504$	−20438.5			−0.00358404
$505$	−6.96440e6	+	4.09621e6i	−1.21522	+	0.714750i
$506$	−820592.			−0.142479
$507$		−	2.78385e6i		−	0.480978i
$508$			4.66920e6i			0.802755i
$509$	4.03961e6			0.691107			0.345554	−	0.938399i	$-0.387691\pi$
$509$	4.03961e6			0.691107			0.345554	+	0.938399i	$0.387691\pi$
$510$	1.33407e6	+	2.26819e6i	0.227118	+	0.386147i
$511$	59144.0			0.0100198
$512$		−	7.98952e6i		−	1.34693i
$513$		−	1.69686e6i		−	0.284678i
$514$	1.33080e7			2.22180
$515$	−4.42637e6	−	7.52574e6i	−0.735410	−	1.25035i
$516$	1.74854e6			0.289102
$517$			2.44369e6i			0.402087i
$518$		−	37457.1i		−	0.00613352i
$519$	−5.63098e6			−0.917626
$520$	−274354.	+	161365.i	−0.0444942	+	0.0261699i
$521$	2.55223e6			0.411932			0.205966	−	0.978559i	$-0.433966\pi$
$521$	2.55223e6			0.411932			0.205966	+	0.978559i	$0.433966\pi$
$522$		−	1.67154e6i		−	0.268497i
$523$			1.54874e6i			0.247586i	0.992308	+	0.123793i	$0.0395058\pi$
$523$			1.54874e6i			0.247586i	−0.992308	+	0.123793i	$0.960494\pi$
$524$	195797.			0.0311514
$525$	150788.	−	271191.i	0.0238763	−	0.0429415i
$526$	−3.21205e6			−0.506195
$527$			2.26290e6i			0.354926i
$528$			1.20779e6i			0.188542i
$529$	5.68328e6			0.882998
$530$	−1.25590e6	+	738677.i	−0.194208	+	0.114226i
$531$	−2.88935e6			−0.444697
$532$			746611.i			0.114371i
$533$		−	1.52212e6i		−	0.232076i
$534$	6.30855e6			0.957362
$535$	−1.53022e6	−	2.60169e6i	−0.231137	−	0.392981i
$536$	344691.			0.0518224
$537$			2.10044e6i			0.314322i
$538$		−	785182.i		−	0.116954i
$539$	2.01892e6			0.299328
$540$	−600669.	−	1.02126e6i	−0.0886443	−	0.150713i
$541$	171030.			0.0251235			0.0125617	−	0.999921i	$-0.496001\pi$
$541$	171030.			0.0251235			0.0125617	+	0.999921i	$0.496001\pi$
$542$		−	1.36003e7i		−	1.98861i
$543$		−	4.53357e6i		−	0.659843i
$544$	5.31099e6			0.769447
$545$	5.75651e6	−	3.38577e6i	0.830172	−	0.488277i
$546$	−193180.			−0.0277319
$547$			1.12874e7i			1.61297i	0.591252	+	0.806487i	$0.298634\pi$
$547$			1.12874e7i			1.61297i	−0.591252	+	0.806487i	$0.701366\pi$
$548$			3.41029e6i			0.485110i
$549$	−1.35315e6			−0.191608
$550$	−2.58265e6	−	1.43601e6i	−0.364048	−	0.202418i
$551$	6.14644e6			0.862472
$552$			178625.i			0.0249514i
$553$		−	129270.i		−	0.0179757i
$554$	−1.56275e7			−2.16329
$555$	−188401.	+	110811.i	−0.0259628	+	0.0152704i
$556$	−1.05865e7			−1.45233
$557$		−	164004.i		−	0.0223984i	−0.999937	−	0.0111992i	$-0.996435\pi$
$557$		−	164004.i		−	0.0223984i	0.999937	−	0.0111992i	$-0.00356489\pi$
$558$		−	2.14032e6i		−	0.291000i
$559$	−1.66361e6			−0.225176
$560$	−346781.	−	589598.i	−0.0467288	−	0.0794486i
$561$	−728828.			−0.0977728
$562$		−	1.38028e7i		−	1.84343i
$563$			9.26696e6i			1.23216i	0.787685	+	0.616079i	$0.211280\pi$
$563$			9.26696e6i			1.23216i	−0.787685	+	0.616079i	$0.788720\pi$
$564$	−5.28446e6			−0.699524
$565$	−4.06263e6	−	6.90730e6i	−0.535409	−	0.910305i
$566$	−1.80557e7			−2.36905
$567$			72385.0i			0.00945565i
$568$			480691.i			0.0625166i
$569$	8.70558e6			1.12724			0.563621	−	0.826034i	$-0.309408\pi$
$569$	8.70558e6			1.12724			0.563621	+	0.826034i	$0.309408\pi$
$570$	7.88862e6	−	4.63980e6i	1.01698	−	0.598153i
$571$	−3.36751e6			−0.432233			−0.216117	−	0.976368i	$-0.569339\pi$
$571$	−3.36751e6			−0.432233			−0.216117	+	0.976368i	$0.569339\pi$
$572$			875782.i			0.111920i
$573$		−	8.58593e6i		−	1.09245i
$574$	527157.			0.0667821
$575$	−2.37012e6	−	1.31783e6i	−0.298951	−	0.166223i
$576$	−2.14856e6			−0.269830
$577$		−	702817.i		−	0.0878826i	−0.999034	−	0.0439413i	$-0.986009\pi$
$577$		−	702817.i		−	0.0878826i	0.999034	−	0.0439413i	$-0.0139914\pi$
$578$		−	7.59568e6i		−	0.945687i
$579$	−7.76034e6			−0.962021
$580$	3.69925e6	−	2.17576e6i	0.456608	−	0.268560i
$581$	573554.			0.0704911
$582$		−	1.36755e6i		−	0.167353i
$583$		−	403555.i		−	0.0491735i
$584$	−122607.			−0.0148759
$585$	571492.	+	971654.i	0.0690432	+	0.117388i
$586$	−3.75739e6			−0.452004
$587$		−	3.09026e6i		−	0.370168i	−0.982723	−	0.185084i	$-0.940744\pi$
$587$		−	3.09026e6i		−	0.370168i	0.982723	−	0.185084i	$-0.0592558\pi$
$588$			4.36589e6i			0.520750i
$589$	7.87022e6			0.934757
$590$	−7.90047e6	−	1.34324e7i	−0.934379	−	1.58864i
$591$	4.47911e6			0.527501
$592$			481830.i			0.0565054i
$593$			1.16268e7i			1.35777i	0.734246	+	0.678883i	$0.237536\pi$
$593$			1.16268e7i			1.35777i	−0.734246	+	0.678883i	$0.762464\pi$
$594$	689349.			0.0801628
$595$	355786.	−	209261.i	0.0411999	−	0.0242323i
$596$	−8.62859e6			−0.995002
$597$		−	3.48389e6i		−	0.400063i
$598$			1.68833e6i			0.193065i
$599$	2.09163e6			0.238187			0.119093	−	0.992883i	$-0.462001\pi$
$599$	2.09163e6			0.238187			0.119093	+	0.992883i	$0.462001\pi$
$600$	−312588.	+	562188.i	−0.0354482	+	0.0637534i
$601$	2.26126e6			0.255367			0.127683	−	0.991815i	$-0.459246\pi$
$601$	2.26126e6			0.255367			0.127683	+	0.991815i	$0.459246\pi$
$602$		−	576159.i		−	0.0647964i
$603$		−	1.22076e6i		−	0.136721i
$604$	1.35148e7			1.50737
$605$	705478.	−	414937.i	0.0783601	−	0.0460886i
$606$	1.01658e7			1.12450
$607$			1.26470e7i			1.39321i	0.717457	+	0.696603i	$0.245306\pi$
$607$			1.26470e7i			1.39321i	−0.717457	+	0.696603i	$0.754694\pi$
$608$		−	1.84713e7i		−	2.02646i
$609$	−262196.			−0.0286472
$610$	−3.69996e6	−	6.29070e6i	−0.402599	−	0.684501i
$611$	5.02777e6			0.544845
$612$		−	1.57608e6i		−	0.170098i
$613$		−	9.20580e6i		−	0.989488i	−0.869039	−	0.494744i	$-0.835262\pi$
$613$		−	9.20580e6i		−	0.989488i	0.869039	−	0.494744i	$-0.164738\pi$
$614$	−9.97644e6			−1.06796
$615$	−1.55951e6	−	2.65149e6i	−0.166265	−	0.282685i
$616$	30531.6			0.00324188
$617$			1.90063e6i			0.200995i	0.994937	+	0.100497i	$0.0320434\pi$
$617$			1.90063e6i			0.200995i	−0.994937	+	0.100497i	$0.967957\pi$
$618$			1.09851e7i			1.15700i
$619$	3.94913e6			0.414261			0.207131	−	0.978313i	$-0.433587\pi$
$619$	3.94913e6			0.414261			0.207131	+	0.978313i	$0.433587\pi$
$620$	4.73670e6	−	2.78596e6i	0.494877	−	0.291069i
$621$	632620.			0.0658285
$622$		−	1.96065e7i		−	2.03201i
$623$		−	989554.i		−	0.102146i
$624$	2.48497e6			0.255482
$625$	−5.15331e6	−	8.29523e6i	−0.527699	−	0.849432i
$626$	−1.45223e7			−1.48115
$627$			2.53482e6i			0.257501i
$628$			5.49213e6i			0.555702i
$629$	−290754.			−0.0293022
$630$	−336514.	+	197925.i	−0.0337793	+	0.0198678i
$631$	−1.50561e7			−1.50536			−0.752680	−	0.658387i	$-0.771239\pi$
$631$	−1.50561e7			−1.50536			−0.752680	+	0.658387i	$0.771239\pi$
$632$			267981.i			0.0266877i
$633$			6.45919e6i			0.640721i
$634$	1.94450e7			1.92126
$635$	−4.55153e6	−	7.73853e6i	−0.447943	−	0.761596i
$636$	872682.			0.0855486
$637$		−	4.15382e6i		−	0.405601i
$638$			2.49698e6i			0.242865i
$639$	1.70242e6			0.164935
$640$	1.32192e6	+	2.24754e6i	0.127572	+	0.216899i
$641$	1.51936e7			1.46055			0.730276	−	0.683153i	$-0.239392\pi$
$641$	1.51936e7			1.46055			0.730276	+	0.683153i	$0.239392\pi$
$642$			3.79762e6i			0.363642i
$643$			1.61149e6i			0.153709i	0.997042	+	0.0768547i	$0.0244878\pi$
$643$			1.61149e6i			0.153709i	−0.997042	+	0.0768547i	$0.975512\pi$
$644$	−278350.			−0.0264470
$645$	−2.89796e6	+	1.70448e6i	−0.274279	+	0.161321i
$646$	1.21743e7			1.14779
$647$			2.05398e7i			1.92902i	0.264055	+	0.964508i	$0.414940\pi$
$647$			2.05398e7i			1.92902i	−0.264055	+	0.964508i	$0.585060\pi$
$648$		−	150057.i		−	0.0140384i
$649$	4.31619e6			0.402244
$650$	−2.95451e6	+	5.31367e6i	−0.274285	+	0.493300i
$651$	−335729.			−0.0310482
$652$		−	1.59137e7i		−	1.46606i
$653$		−	7.96056e6i		−	0.730568i	−0.930896	−	0.365284i	$-0.880972\pi$
$653$		−	7.96056e6i		−	0.730568i	0.930896	−	0.365284i	$-0.119028\pi$
$654$	−8.40263e6			−0.768194
$655$	−324506.	+	190863.i	−0.0295542	+	0.0173827i
$656$	−6.78110e6			−0.615234
$657$			434227.i			0.0392467i
$658$			1.74127e6i			0.156784i
$659$	−2.91266e6			−0.261262			−0.130631	−	0.991431i	$-0.541700\pi$
$659$	−2.91266e6			−0.261262			−0.130631	+	0.991431i	$0.541700\pi$
$660$	897295.	+	1.52559e6i	0.0801818	+	0.136325i
$661$	1.89585e7			1.68772			0.843860	−	0.536564i	$-0.180278\pi$
$661$	1.89585e7			1.68772			0.843860	+	0.536564i	$0.180278\pi$
$662$		−	1.71363e7i		−	1.51975i
$663$			1.49953e6i			0.132486i
$664$	−1.18900e6			−0.104655
$665$	−727796.	−	1.23740e6i	−0.0638198	−	0.108507i
$666$	275005.			0.0240245
$667$			2.29150e6i			0.199437i
$668$		−	4.26453e6i		−	0.369768i
$669$	1.01862e6			0.0879931
$670$	5.67523e6	−	3.33797e6i	0.488424	−	0.287273i
$671$	2.02137e6			0.173316
$672$			787952.i			0.0673095i
$673$			2.14478e7i			1.82535i	0.408688	+	0.912674i	$0.365986\pi$
$673$			2.14478e7i			1.82535i	−0.408688	+	0.912674i	$0.634014\pi$
$674$	−8.50374e6			−0.721041
$675$	1.99105e6	+	1.10706e6i	0.168198	+	0.0935218i
$676$	−8.99289e6			−0.756889
$677$		−	1.84040e7i		−	1.54326i	−0.636071	−	0.771631i	$-0.719441\pi$
$677$		−	1.84040e7i		−	1.54326i	0.636071	−	0.771631i	$-0.280559\pi$
$678$			1.00824e7i			0.842345i
$679$	−214512.			−0.0178557
$680$	−737556.	+	433804.i	−0.0611677	+	0.0359767i
$681$	5.55024e6			0.458611
$682$			3.19727e6i			0.263219i
$683$			2.04252e7i			1.67538i	0.546143	+	0.837692i	$0.316095\pi$
$683$			2.04252e7i			1.67538i	−0.546143	+	0.837692i	$0.683905\pi$
$684$	−5.48152e6			−0.447982
$685$	−3.32435e6	−	5.65208e6i	−0.270695	−	0.460237i
$686$	2.88768e6			0.234282
$687$			4.52543e6i			0.365820i
$688$			7.41143e6i			0.596940i
$689$	−830293.			−0.0666321
$690$	1.72980e6	+	2.94101e6i	0.138316	+	0.235166i
$691$	1.16275e6			0.0926388			0.0463194	−	0.998927i	$-0.485251\pi$
$691$	1.16275e6			0.0926388			0.0463194	+	0.998927i	$0.485251\pi$
$692$			1.81902e7i			1.44402i
$693$		−	108131.i		−	0.00855295i
$694$	1.16412e7			0.917486
$695$	1.75456e7	−	1.03197e7i	1.37786	−	0.810410i
$696$	543540.			0.0425313
$697$		−	4.09197e6i		−	0.319044i
$698$			2.82765e7i			2.19678i
$699$	−1.27741e6			−0.0988866
$700$	−876050.	−	487102.i	−0.0675747	−	0.0375729i
$701$	1.80087e7			1.38416			0.692082	−	0.721818i	$-0.256693\pi$
$701$	1.80087e7			1.38416			0.692082	+	0.721818i	$0.256693\pi$
$702$		−	1.41830e6i		−	0.108624i
$703$			1.01123e6i			0.0771721i
$704$	3.20957e6			0.244071
$705$	8.75824e6	−	5.15128e6i	0.663657	−	0.390340i
$706$	2.70739e6			0.204428
$707$		−	1.59459e6i		−	0.119978i
$708$			9.33371e6i			0.699795i
$709$	1.64523e7			1.22917			0.614583	−	0.788852i	$-0.289324\pi$
$709$	1.64523e7			1.22917			0.614583	+	0.788852i	$0.289324\pi$
$710$	4.65499e6	+	7.91444e6i	0.346555	+	0.589215i
$711$	949084.			0.0704094
$712$			2.05138e6i			0.151651i
$713$			2.93415e6i			0.216152i
$714$	−519332.			−0.0381241
$715$	−853711.	−	1.45148e6i	−0.0624519	−	0.106181i
$716$	6.78523e6			0.494632
$717$			6.60369e6i			0.479721i
$718$		−	1.37017e7i		−	0.991892i
$719$	−2.09659e7			−1.51249			−0.756243	−	0.654290i	$-0.772967\pi$
$719$	−2.09659e7			−1.51249			−0.756243	+	0.654290i	$0.772967\pi$
$720$	4.32875e6	−	2.54602e6i	0.311194	−	0.183033i
$721$	1.72312e6			0.123446
$722$		−	2.29908e7i		−	1.64139i
$723$			2.94419e6i			0.209469i
$724$	−1.46452e7			−1.03836
$725$	−4.01004e6	+	7.21204e6i	−0.283337	+	0.509581i
$726$	−1.02977e6			−0.0725100
$727$		−	1.23702e7i		−	0.868040i	−0.900903	−	0.434020i	$-0.857095\pi$
$727$		−	1.23702e7i		−	0.868040i	0.900903	−	0.434020i	$-0.142905\pi$
$728$		−	62817.1i		−	0.00439288i
$729$	−531441.			−0.0370370
$730$	−2.01870e6	+	1.18732e6i	−0.140205	+	0.0824636i
$731$	−4.47234e6			−0.309557
$732$			4.37118e6i			0.301524i
$733$		−	1.78981e7i		−	1.23040i	−0.788371	−	0.615200i	$-0.789075\pi$
$733$		−	1.78981e7i		−	1.23040i	0.788371	−	0.615200i	$-0.210925\pi$
$734$	−2.10116e7			−1.43953
$735$	−4.25586e6	−	7.23583e6i	−0.290582	−	0.494049i
$736$	6.88643e6			0.468597
$737$			1.82360e6i			0.123669i
$738$			3.87031e6i			0.261580i
$739$	2.08324e6			0.140323			0.0701615	−	0.997536i	$-0.477649\pi$
$739$	2.08324e6			0.140323			0.0701615	+	0.997536i	$0.477649\pi$
$740$	357962.	+	608608.i	0.0240302	+	0.0408563i
$741$	5.21526e6			0.348924
$742$		−	287556.i		−	0.0191740i
$743$			7.09623e6i			0.471580i	0.971804	+	0.235790i	$0.0757678\pi$
$743$			7.09623e6i			0.471580i	−0.971804	+	0.235790i	$0.924232\pi$
$744$	695977.			0.0460959
$745$	1.43007e7	−	8.41114e6i	0.943985	−	0.555219i
$746$	−2.13948e7			−1.40754
$747$			4.21096e6i			0.276108i
$748$			2.35439e6i			0.153860i
$749$	595692.			0.0387987
$750$	297533.	+	1.22833e7i	0.0193144	+	0.797376i
$751$	−1.82817e7			−1.18282			−0.591408	−	0.806373i	$-0.701428\pi$
$751$	−1.82817e7			−1.18282			−0.591408	+	0.806373i	$0.701428\pi$
$752$		−	2.23989e7i		−	1.44438i
$753$		−	324840.i		−	0.0208777i
$754$	5.13742e6			0.329091
$755$	−2.23989e7	+	1.31743e7i	−1.43008	+	0.841121i
$756$	233831.			0.0148798
$757$		−	1.02358e6i		−	0.0649206i	−0.999473	−	0.0324603i	$-0.989666\pi$
$757$		−	1.02358e6i		−	0.0649206i	0.999473	−	0.0324603i	$-0.0103342\pi$
$758$			1.55794e7i			0.984869i
$759$	−945026.			−0.0595442
$760$	1.50874e6	+	2.56517e6i	0.0947505	+	0.161095i
$761$	9.52820e6			0.596416			0.298208	−	0.954501i	$-0.403611\pi$
$761$	9.52820e6			0.596416			0.298208	+	0.954501i	$0.403611\pi$
$762$			1.12957e7i			0.704738i
$763$			1.31803e6i			0.0819623i
$764$	−2.77358e7			−1.71913
$765$	1.53636e6	+	2.61213e6i	0.0949161	+	0.161377i
$766$	2.59548e7			1.59825
$767$		−	8.88034e6i		−	0.545056i
$768$		−	1.09200e7i		−	0.668065i
$769$	1.07522e6			0.0655666			0.0327833	−	0.999462i	$-0.489563\pi$
$769$	1.07522e6			0.0655666			0.0327833	+	0.999462i	$0.489563\pi$
$770$	502693.	−	295666.i	0.0305546	−	0.0179711i
$771$	1.53260e7			0.928524
$772$			2.50689e7i			1.51388i
$773$		−	6.01805e6i		−	0.362249i	−0.983460	−	0.181124i	$-0.942026\pi$
$773$		−	6.01805e6i		−	0.362249i	0.983460	−	0.181124i	$-0.0579737\pi$
$774$	4.23008e6			0.253803
$775$	−5.13466e6	+	9.23466e6i	−0.307084	+	0.552290i
$776$	444691.			0.0265096
$777$		−	43137.0i		−	0.00256329i
$778$			5.00207e6i			0.296279i
$779$	−1.42316e7			−0.840254
$780$	3.13881e6	−	1.84614e6i	0.184726	−	0.108650i
$781$	−2.54312e6			−0.149190
$782$			4.53878e6i			0.265413i
$783$		−	1.92500e6i		−	0.112209i
$784$	−1.85054e7			−1.07525
$785$	−5.35372e6	−	9.10242e6i	−0.310086	−	0.527209i
$786$	473673.			0.0273478
$787$			2.82761e7i			1.62736i	0.581314	+	0.813679i	$0.302539\pi$
$787$			2.82761e7i			1.62736i	−0.581314	+	0.813679i	$0.697461\pi$
$788$		−	1.44692e7i		−	0.830100i
$789$	−3.69912e6			−0.211547
$790$	2.59512e6	+	4.41223e6i	0.147941	+	0.251530i
$791$	1.58152e6			0.0898738
$792$			224158.i			0.0126982i
$793$		−	4.15886e6i		−	0.234850i
$794$	−6.30242e6			−0.354777
$795$	−1.44635e6	+	850689.i	−0.0811623	+	0.0477368i
$796$	−1.12543e7			−0.629558
$797$			2.70959e7i			1.51098i	0.655161	+	0.755490i	$0.272601\pi$
$797$			2.70959e7i			1.51098i	−0.655161	+	0.755490i	$0.727399\pi$
$798$			1.80620e6i			0.100406i
$799$	1.35163e7			0.749017
$800$	2.16737e7	+	1.20510e7i	1.19731	+	0.665730i
$801$	7.26517e6			0.400096
$802$		−	1.69933e7i		−	0.932917i
$803$		−	648660.i		−	0.0355000i
$804$	−3.94352e6			−0.215151
$805$	461325.	−	271335.i	0.0250910	−	0.0147576i
$806$	6.57821e6			0.356673
$807$		−	904246.i		−	0.0488768i
$808$			3.30564e6i			0.178126i
$809$	−1.78310e7			−0.957868			−0.478934	−	0.877851i	$-0.658977\pi$
$809$	−1.78310e7			−0.957868			−0.478934	+	0.877851i	$0.658977\pi$
$810$	−1.45314e6	−	2.47064e6i	−0.0778207	−	0.132311i
$811$	−2.28534e7			−1.22011			−0.610055	−	0.792359i	$-0.708853\pi$
$811$	−2.28534e7			−1.22011			−0.610055	+	0.792359i	$0.708853\pi$
$812$			846992.i			0.0450806i
$813$		−	1.56626e7i		−	0.831070i
$814$	−410810.			−0.0217310
$815$	1.55127e7	+	2.63747e7i	0.818075	+	1.39089i
$816$	6.68044e6			0.351220
$817$			1.55545e7i			0.815270i
$818$			3.89619e7i			2.03590i
$819$	−222473.			−0.0115896
$820$	−8.56532e6	+	5.03782e6i	−0.444845	+	0.261642i
$821$	−3.84556e6			−0.199114			−0.0995570	−	0.995032i	$-0.531743\pi$
$821$	−3.84556e6			−0.199114			−0.0995570	+	0.995032i	$0.531743\pi$
$822$			8.25020e6i			0.425878i
$823$		−	2.40452e7i		−	1.23746i	−0.785605	−	0.618728i	$-0.787648\pi$
$823$		−	2.40452e7i		−	1.23746i	0.785605	−	0.618728i	$-0.212352\pi$
$824$	−3.57208e6			−0.183275
$825$	−2.97428e6	−	1.65376e6i	−0.152141	−	0.0845936i
$826$	3.07553e6			0.156845
$827$		−	3.67928e7i		−	1.87068i	−0.353754	−	0.935339i	$-0.615095\pi$
$827$		−	3.67928e7i		−	1.87068i	0.353754	−	0.935339i	$-0.384905\pi$
$828$		−	2.04361e6i		−	0.103591i
$829$	−3.38058e7			−1.70846			−0.854231	−	0.519894i	$-0.825971\pi$
$829$	−3.38058e7			−1.70846			−0.854231	+	0.519894i	$0.825971\pi$
$830$	−1.95765e7	+	1.15142e7i	−0.986369	+	0.580147i
$831$	−1.79973e7			−0.904074
$832$		−	6.60352e6i		−	0.330725i
$833$		−	1.11669e7i		−	0.557594i
$834$	−2.56109e7			−1.27500
$835$	4.15706e6	+	7.06785e6i	0.206333	+	0.350809i
$836$	8.18844e6			0.405215
$837$		−	2.46487e6i		−	0.121613i
$838$			4.08479e7i			2.00937i
$839$	2.59170e7			1.27110			0.635550	−	0.772060i	$-0.280773\pi$
$839$	2.59170e7			1.27110			0.635550	+	0.772060i	$0.280773\pi$
$840$	−64360.2	−	109426.i	−0.00314716	−	0.00535082i
$841$	−1.35383e7			−0.660047
$842$		−	1.16069e7i		−	0.564202i
$843$		−	1.58959e7i		−	0.770398i
$844$	2.08656e7			1.00827
$845$	1.49044e7	−	8.76626e6i	0.718081	−	0.422350i
$846$	−1.27842e7			−0.614111
$847$			161529.i			0.00773644i
$848$			3.69898e6i			0.176641i
$849$	−2.07937e7			−0.990062
$850$	−7.94270e6	+	1.42849e7i	−0.377069	+	0.678157i
$851$	−377003.			−0.0178452
$852$		−	5.49946e6i		−	0.259550i
$853$		−	1.25062e7i		−	0.588510i	−0.955727	−	0.294255i	$-0.904929\pi$
$853$		−	1.25062e7i		−	0.588510i	0.955727	−	0.294255i	$-0.0950714\pi$
$854$	1.44034e6			0.0675803
$855$	9.08484e6	−	5.34338e6i	0.425013	−	0.249977i
$856$	−1.23489e6			−0.0576028
$857$		−	3.10464e7i		−	1.44398i	−0.691906	−	0.721988i	$-0.743229\pi$
$857$		−	3.10464e7i		−	1.44398i	0.691906	−	0.721988i	$-0.256771\pi$
$858$			2.11869e6i			0.0982539i
$859$	−3.06277e7			−1.41622			−0.708111	−	0.706102i	$-0.750452\pi$
$859$	−3.06277e7			−1.41622			−0.708111	+	0.706102i	$0.750452\pi$
$860$	5.50611e6	+	9.36151e6i	0.253863	+	0.431618i
$861$	607094.			0.0279093
$862$			2.35754e6i			0.108066i
$863$			5.27975e6i			0.241316i	0.992694	+	0.120658i	$0.0385005\pi$
$863$			5.27975e6i			0.241316i	−0.992694	+	0.120658i	$0.961500\pi$
$864$	−5.78503e6			−0.263646
$865$	−1.77318e7	−	3.01477e7i	−0.805773	−	1.36998i
$866$	1.39456e7			0.631893
$867$		−	8.74749e6i		−	0.395217i
$868$			1.08453e6i			0.0488588i
$869$	−1.41777e6			−0.0636877
$870$	8.94923e6	−	5.26362e6i	0.400855	−	0.235769i
$871$	3.75197e6			0.167577
$872$		−	2.73232e6i		−	0.121686i
$873$		−	1.57492e6i		−	0.0699395i
$874$	1.57856e7			0.699009
$875$	1.92675e6	−	46670.7i	0.0850759	−	0.00206075i
$876$	1.40272e6			0.0617605
$877$			2.47729e7i			1.08762i	0.839207	+	0.543811i	$0.183019\pi$
$877$			2.47729e7i			1.08762i	−0.839207	+	0.543811i	$0.816981\pi$
$878$		−	3.90231e6i		−	0.170838i
$879$	−4.32716e6			−0.188899
$880$	−6.46641e6	+	3.80331e6i	−0.281486	+	0.165560i
$881$	3.14613e7			1.36564			0.682822	−	0.730585i	$-0.260753\pi$
$881$	3.14613e7			1.36564			0.682822	+	0.730585i	$0.260753\pi$
$882$			1.05620e7i			0.457165i
$883$			5.34805e6i			0.230831i	0.993317	+	0.115415i	$0.0368199\pi$
$883$			5.34805e6i			0.230831i	−0.993317	+	0.115415i	$0.963180\pi$
$884$	4.84404e6			0.208486
$885$	−9.09849e6	−	1.54693e7i	−0.390491	−	0.663915i
$886$	−3.61656e7			−1.54779
$887$		−	5.37540e6i		−	0.229404i	−0.993400	−	0.114702i	$-0.963409\pi$
$887$		−	5.37540e6i		−	0.229404i	0.993400	−	0.114702i	$-0.0365913\pi$
$888$			89424.5i			0.00380561i
$889$	1.77184e6			0.0751918
$890$	1.98654e7	+	3.37753e7i	0.840666	+	1.42930i
$891$	793881.			0.0335013
$892$		−	3.29054e6i		−	0.138470i
$893$		−	4.70090e7i		−	1.97266i
$894$	−2.08743e7			−0.873511
$895$	−1.12456e7	+	6.61424e6i	−0.469271	+	0.276008i
$896$	−514604.			−0.0214143
$897$			1.94434e6i			0.0806847i
$898$			2.58895e7i			1.07135i
$899$	8.92836e6			0.368445
$900$	3.57623e6	−	6.43184e6i	0.147170	−	0.264685i
$901$	−2.23210e6			−0.0916015
$902$		−	5.78158e6i		−	0.236608i
$903$		−	663527.i		−	0.0270794i
$904$	−3.27854e6			−0.133432
$905$	2.42723e7	−	1.42761e7i	0.985120	−	0.579412i
$906$	3.26951e7			1.32331
$907$			1.34668e7i			0.543558i	0.962360	+	0.271779i	$0.0876120\pi$
$907$			1.34668e7i			0.543558i	−0.962360	+	0.271779i	$0.912388\pi$
$908$		−	1.79294e7i		−	0.721691i
$909$	1.17073e7			0.469944
$910$	−608318.	−	1.03426e6i	−0.0243516	−	0.0414027i
$911$	5.76380e6			0.230098			0.115049	−	0.993360i	$-0.463297\pi$
$911$	5.76380e6			0.230098			0.115049	+	0.993360i	$0.463297\pi$
$912$		−	2.32342e7i		−	0.924996i
$913$		−	6.29044e6i		−	0.249749i
$914$	−5.54185e7			−2.19427
$915$	−4.26102e6	−	7.24461e6i	−0.168252	−	0.286064i
$916$	1.46189e7			0.575672
$917$		−	74299.9i		−	0.00291786i
$918$		−	3.81286e6i		−	0.149329i
$919$	9.91711e6			0.387344			0.193672	−	0.981066i	$-0.437960\pi$
$919$	9.91711e6			0.387344			0.193672	+	0.981066i	$0.437960\pi$
$920$	−956342.	+	562486.i	−0.0372515	+	0.0219100i
$921$	−1.14893e7			−0.446316
$922$			2.87947e7i			1.11554i
$923$			5.23233e6i			0.202158i
$924$	−349304.			−0.0134593
$925$	−1.18654e6	−	659741.i	−0.0455962	−	0.0253524i
$926$	4.15841e7			1.59368
$927$			1.26509e7i			0.483529i
$928$		−	2.09548e7i		−	0.798753i
$929$	2.50662e7			0.952905			0.476453	−	0.879200i	$-0.341922\pi$
$929$	2.50662e7			0.952905			0.476453	+	0.879200i	$0.341922\pi$
$930$	1.14590e7	−	6.73980e6i	0.434451	−	0.255529i
$931$	−3.88377e7			−1.46852
$932$			4.12652e6i			0.155613i
$933$		−	2.25796e7i		−	0.849206i
$934$	7.25185e7			2.72008
$935$	−2.29506e6	−	3.90207e6i	−0.0858549	−	0.145971i
$936$	461194.			0.0172066
$937$			782497.i			0.0291161i	0.999894	+	0.0145581i	$0.00463414\pi$
$937$			782497.i			0.0291161i	−0.999894	+	0.0145581i	$0.995366\pi$
$938$			1.29942e6i			0.0482217i
$939$	−1.67244e7			−0.618995
$940$	−1.66406e7	−	2.82924e7i	−0.614256	−	1.04436i
$941$	1.08811e7			0.400589			0.200295	−	0.979736i	$-0.435810\pi$
$941$	1.08811e7			0.400589			0.200295	+	0.979736i	$0.435810\pi$
$942$			1.32866e7i			0.487850i
$943$		−	5.30580e6i		−	0.194299i
$944$	−3.95622e7			−1.44494
$945$	−387542.	+	227938.i	−0.0141169	+	0.00830306i
$946$	−6.31900e6			−0.229573
$947$			3.52427e7i			1.27701i	0.769617	+	0.638505i	$0.220447\pi$
$947$			3.52427e7i			1.27701i	−0.769617	+	0.638505i	$0.779553\pi$
$948$		−	3.06590e6i		−	0.110799i
$949$	−1.33458e6			−0.0481039
$950$	4.96821e7	+	2.76242e7i	1.78604	+	0.993073i
$951$	2.23937e7			0.802923
$952$		−	168873.i		−	0.00603905i
$953$			6.73891e6i			0.240358i	0.992752	+	0.120179i	$0.0383468\pi$
$953$			6.73891e6i			0.240358i	−0.992752	+	0.120179i	$0.961653\pi$
$954$	2.11119e6			0.0751030
$955$	4.59682e7	−	2.70368e7i	1.63098	−	0.959285i
$956$	2.13324e7			0.754911
$957$			2.87562e6i			0.101497i
$958$		−	3.30506e7i		−	1.16350i
$959$	1.29412e6			0.0454389
$960$	−6.76574e6	−	1.15031e7i	−0.236939	−	0.402846i
$961$	−1.71968e7			−0.600675
$962$			845219.i			0.0294464i
$963$			4.37349e6i			0.151972i
$964$	9.51086e6			0.329630
$965$	−2.44371e7	−	4.15481e7i	−0.844756	−	1.43626i
$966$	−673385.			−0.0232178
$967$		−	8.67300e6i		−	0.298266i	−0.988817	−	0.149133i	$-0.952352\pi$
$967$		−	8.67300e6i		−	0.298266i	0.988817	−	0.149133i	$-0.0476482\pi$
$968$		−	334854.i		−	0.0114860i
$969$	1.40204e7			0.479678
$970$	7.32170e6	−	4.30636e6i	0.249852	−	0.146954i
$971$	1.57795e7			0.537089			0.268545	−	0.963267i	$-0.413457\pi$
$971$	1.57795e7			0.537089			0.268545	+	0.963267i	$0.413457\pi$
$972$			1.71676e6i			0.0582832i
$973$			4.01730e6i			0.136035i
$974$	6.37734e7			2.15398
$975$	−3.40252e6	+	6.11942e6i	−0.114628	+	0.206157i
$976$	−1.85279e7			−0.622588
$977$			1.20786e6i			0.0404836i	0.999795	+	0.0202418i	$0.00644361\pi$
$977$			1.20786e6i			0.0404836i	−0.999795	+	0.0202418i	$0.993556\pi$
$978$		−	3.84985e7i		−	1.28706i
$979$	−1.08529e7			−0.361901
$980$	−2.33745e7	+	1.37481e7i	−0.777459	+	0.457273i
$981$	−9.67680e6			−0.321040
$982$			1.34902e7i			0.446416i
$983$			7.42794e6i			0.245180i	0.992457	+	0.122590i	$0.0391200\pi$
$983$			7.42794e6i			0.245180i	−0.992457	+	0.122590i	$0.960880\pi$
$984$	−1.25853e6			−0.0414357
$985$	1.41046e7	+	2.39807e7i	0.463202	+	0.787538i
$986$	1.38111e7			0.452413
$987$			2.00532e6i			0.0655224i
$988$		−	1.68473e7i		−	0.549083i
$989$	−5.79900e6			−0.188522
$990$	2.17074e6	+	3.69070e6i	0.0703914	+	0.119680i
$991$	−4.26703e7			−1.38020			−0.690099	−	0.723715i	$-0.742433\pi$
$991$	−4.26703e7			−1.38020			−0.690099	+	0.723715i	$0.742433\pi$
$992$		−	2.68315e7i		−	0.865698i
$993$		−	1.97349e7i		−	0.635128i
$994$	−1.81212e6			−0.0581728
$995$	1.86524e7	−	1.09707e7i	0.597279	−	0.351298i
$996$	1.36030e7			0.434496
$997$			2.10754e7i			0.671486i	0.941954	+	0.335743i	$0.108987\pi$
$997$			2.10754e7i			0.671486i	−0.941954	+	0.335743i	$0.891013\pi$
$998$			4.44554e6i			0.141286i
$999$	316706.			0.0100402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.b.34.5	✓	26
5.2	odd	4		825.6.a.v.1.12		13
5.3	odd	4		825.6.a.y.1.2		13
5.4	even	2	inner	165.6.c.b.34.22	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.b.34.5	✓	26	1.1	even	1	trivial
165.6.c.b.34.22	yes	26	5.4	even	2	inner
825.6.a.v.1.12		13	5.2	odd	4
825.6.a.y.1.2		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)

\(f(q)\)	\(=\)	\(q-7.81495i q^{2} -9.00000i q^{3} -29.0734 q^{4} +(48.1851 - 28.3407i) q^{5} -70.3345 q^{6} +11.0326i q^{7} -22.8710i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q-7.81495i q^{2} -9.00000i q^{3} -29.0734 q^{4} +(48.1851 - 28.3407i) q^{5} -70.3345 q^{6} +11.0326i q^{7} -22.8710i q^{8} -81.0000 q^{9} +(-221.481 - 376.564i) q^{10} +121.000 q^{11} +261.661i q^{12} -248.951i q^{13} +86.2194 q^{14} +(-255.067 - 433.666i) q^{15} -1109.09 q^{16} -669.264i q^{17} +633.011i q^{18} -2327.66 q^{19} +(-1400.91 + 823.963i) q^{20} +99.2936 q^{21} -945.609i q^{22} -867.792i q^{23} -205.839 q^{24} +(1518.60 - 2731.20i) q^{25} -1945.54 q^{26} +729.000i q^{27} -320.756i q^{28} -2640.61 q^{29} +(-3389.08 + 1993.33i) q^{30} -3381.17 q^{31} +7935.57i q^{32} -1089.00i q^{33} -5230.26 q^{34} +(312.673 + 531.608i) q^{35} +2354.95 q^{36} -434.439i q^{37} +18190.5i q^{38} -2240.56 q^{39} +(-648.181 - 1102.04i) q^{40} +6114.13 q^{41} -775.975i q^{42} -6682.47i q^{43} -3517.89 q^{44} +(-3902.99 + 2295.60i) q^{45} -6781.75 q^{46} +20195.8i q^{47} +9981.77i q^{48} +16685.3 q^{49} +(-21344.2 - 11867.8i) q^{50} -6023.37 q^{51} +7237.87i q^{52} -3335.16i q^{53} +5697.10 q^{54} +(5830.39 - 3429.23i) q^{55} +252.327 q^{56} +20948.9i q^{57} +20636.2i q^{58} +35671.0 q^{59} +(7415.66 + 12608.2i) q^{60} +16705.5 q^{61} +26423.7i q^{62} -893.642i q^{63} +26525.4 q^{64} +(-7055.46 - 11995.7i) q^{65} -8510.48 q^{66} +15071.1i q^{67} +19457.8i q^{68} -7810.13 q^{69} +(4154.49 - 2443.52i) q^{70} -21017.5 q^{71} +1852.55i q^{72} -5360.83i q^{73} -3395.12 q^{74} +(-24580.8 - 13667.4i) q^{75} +67673.1 q^{76} +1334.95i q^{77} +17509.9i q^{78} -11717.1 q^{79} +(-53441.4 + 31432.3i) q^{80} +6561.00 q^{81} -47781.6i q^{82} -51987.1i q^{83} -2886.81 q^{84} +(-18967.4 - 32248.5i) q^{85} -52223.2 q^{86} +23765.5i q^{87} -2767.39i q^{88} -89693.5 q^{89} +(17940.0 + 30501.7i) q^{90} +2746.58 q^{91} +25229.7i q^{92} +30430.5i q^{93} +157829. q^{94} +(-112158. + 65967.6i) q^{95} +71420.2 q^{96} +19443.4i q^{97} -130395. i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 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

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