LMFDB - Embedded newform 165.6.c.b.34.10

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			34.10
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.62206i q^{2} -9.00000i q^{3} +18.8807 q^{4} +(5.26063 - 55.6536i) q^{5} -32.5985 q^{6} -168.040i q^{7} -184.293i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q-3.62206i q^{2} -9.00000i q^{3} +18.8807 q^{4} +(5.26063 - 55.6536i) q^{5} -32.5985 q^{6} -168.040i q^{7} -184.293i q^{8} -81.0000 q^{9} +(-201.581 - 19.0543i) q^{10} +121.000 q^{11} -169.926i q^{12} -155.005i q^{13} -608.652 q^{14} +(-500.883 - 47.3457i) q^{15} -63.3377 q^{16} +426.797i q^{17} +293.387i q^{18} +1674.14 q^{19} +(99.3244 - 1050.78i) q^{20} -1512.36 q^{21} -438.269i q^{22} -11.2327i q^{23} -1658.64 q^{24} +(-3069.65 - 585.547i) q^{25} -561.437 q^{26} +729.000i q^{27} -3172.72i q^{28} +1107.81 q^{29} +(-171.489 + 1814.23i) q^{30} +7186.50 q^{31} -5667.96i q^{32} -1089.00i q^{33} +1545.88 q^{34} +(-9352.05 - 883.999i) q^{35} -1529.34 q^{36} +4576.30i q^{37} -6063.84i q^{38} -1395.05 q^{39} +(-10256.6 - 969.497i) q^{40} -14041.6 q^{41} +5477.87i q^{42} +20306.0i q^{43} +2284.56 q^{44} +(-426.111 + 4507.94i) q^{45} -40.6856 q^{46} -10551.8i q^{47} +570.039i q^{48} -11430.6 q^{49} +(-2120.88 + 11118.5i) q^{50} +3841.17 q^{51} -2926.60i q^{52} +27069.4i q^{53} +2640.48 q^{54} +(636.537 - 6734.09i) q^{55} -30968.6 q^{56} -15067.3i q^{57} -4012.57i q^{58} -22773.1 q^{59} +(-9457.01 - 893.919i) q^{60} -916.341 q^{61} -26029.9i q^{62} +13611.3i q^{63} -22556.5 q^{64} +(-8626.59 - 815.425i) q^{65} -3944.42 q^{66} +25328.4i q^{67} +8058.22i q^{68} -101.095 q^{69} +(-3201.90 + 33873.7i) q^{70} -16788.6 q^{71} +14927.7i q^{72} -55976.9i q^{73} +16575.6 q^{74} +(-5269.92 + 27626.9i) q^{75} +31608.9 q^{76} -20332.9i q^{77} +5052.94i q^{78} +47517.8 q^{79} +(-333.196 + 3524.97i) q^{80} +6561.00 q^{81} +50859.4i q^{82} -24415.3i q^{83} -28554.5 q^{84} +(23752.8 + 2245.22i) q^{85} +73549.4 q^{86} -9970.33i q^{87} -22299.4i q^{88} +22081.6 q^{89} +(16328.0 + 1543.40i) q^{90} -26047.1 q^{91} -212.082i q^{92} -64678.5i q^{93} -38219.1 q^{94} +(8807.05 - 93172.1i) q^{95} -51011.6 q^{96} +15706.3i q^{97} +41402.1i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.62206i		−	0.640296i	−0.947368	−	0.320148i	$-0.896267\pi$
$2$		−	3.62206i		−	0.640296i	0.947368	−	0.320148i	$-0.103733\pi$
$3$		−	9.00000i		−	0.577350i
$3$		−	9.00000i		−	0.577350i
$4$	18.8807			0.590021
$5$	5.26063	−	55.6536i	0.0941051	−	0.995562i
$5$	5.26063	−	55.6536i	0.0941051	−	0.995562i
$6$	−32.5985			−0.369675
$7$		−	168.040i		−	1.29619i	−0.761560	−	0.648095i	$-0.775566\pi$
$7$		−	168.040i		−	1.29619i	0.761560	−	0.648095i	$-0.224434\pi$
$8$		−	184.293i		−	1.01808i
$9$	−81.0000			−0.333333
$10$	−201.581	−	19.0543i	−0.637454	−	0.0602551i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$		−	169.926i		−	0.340649i
$13$		−	155.005i		−	0.254383i	−0.991878	−	0.127191i	$-0.959404\pi$
$13$		−	155.005i		−	0.254383i	0.991878	−	0.127191i	$-0.0405962\pi$
$14$	−608.652			−0.829944
$15$	−500.883	−	47.3457i	−0.574788	−	0.0543316i
$16$	−63.3377			−0.0618532
$17$			426.797i			0.358178i	0.983833	+	0.179089i	$0.0573150\pi$
$17$			426.797i			0.358178i	−0.983833	+	0.179089i	$0.942685\pi$
$18$			293.387i			0.213432i
$19$	1674.14			1.06392			0.531959	−	0.846770i	$-0.321456\pi$
$19$	1674.14			1.06392			0.531959	+	0.846770i	$0.321456\pi$
$20$	99.3244	−	1050.78i	0.0555240	−	0.587403i
$21$	−1512.36			−0.748355
$22$		−	438.269i		−	0.193056i
$23$		−	11.2327i		−	0.00442757i	−0.999998	−	0.00221379i	$-0.999295\pi$
$23$		−	11.2327i		−	0.00442757i	0.999998	−	0.00221379i	$-0.000704670\pi$
$24$	−1658.64			−0.587791
$25$	−3069.65	−	585.547i	−0.982288	−	0.187375i
$26$	−561.437			−0.162880
$27$			729.000i			0.192450i
$28$		−	3172.72i		−	0.764780i
$29$	1107.81			0.244609			0.122304	−	0.992493i	$-0.460972\pi$
$29$	1107.81			0.244609			0.122304	+	0.992493i	$0.460972\pi$
$30$	−171.489	+	1814.23i	−0.0347883	+	0.368034i
$31$	7186.50			1.34312			0.671558	−	0.740952i	$-0.265625\pi$
$31$	7186.50			1.34312			0.671558	+	0.740952i	$0.265625\pi$
$32$		−	5667.96i		−	0.978480i
$33$		−	1089.00i		−	0.174078i
$34$	1545.88			0.229340
$35$	−9352.05	−	883.999i	−1.29044	−	0.121978i
$36$	−1529.34			−0.196674
$37$			4576.30i			0.549554i	0.961508	+	0.274777i	$0.0886040\pi$
$37$			4576.30i			0.549554i	−0.961508	+	0.274777i	$0.911396\pi$
$38$		−	6063.84i		−	0.681222i
$39$	−1395.05			−0.146868
$40$	−10256.6	−	969.497i	−1.01357	−	0.0958069i
$41$	−14041.6			−1.30454			−0.652268	−	0.757988i	$-0.726182\pi$
$41$	−14041.6			−1.30454			−0.652268	+	0.757988i	$0.726182\pi$
$42$			5477.87i			0.479169i
$43$			20306.0i			1.67476i	0.546621	+	0.837380i	$0.315914\pi$
$43$			20306.0i			1.67476i	−0.546621	+	0.837380i	$0.684086\pi$
$44$	2284.56			0.177898
$45$	−426.111	+	4507.94i	−0.0313684	+	0.331854i
$46$	−40.6856			−0.00283495
$47$		−	10551.8i		−	0.696756i	−0.937354	−	0.348378i	$-0.886733\pi$
$47$		−	10551.8i		−	0.696756i	0.937354	−	0.348378i	$-0.113267\pi$
$48$			570.039i			0.0357110i
$49$	−11430.6			−0.680107
$50$	−2120.88	+	11118.5i	−0.119975	+	0.628955i
$51$	3841.17			0.206794
$52$		−	2926.60i		−	0.150091i
$53$			27069.4i			1.32370i	0.749637	+	0.661849i	$0.230228\pi$
$53$			27069.4i			1.32370i	−0.749637	+	0.661849i	$0.769772\pi$
$54$	2640.48			0.123225
$55$	636.537	−	6734.09i	0.0283737	−	0.300173i
$56$	−30968.6			−1.31963
$57$		−	15067.3i		−	0.614253i
$58$		−	4012.57i		−	0.156622i
$59$	−22773.1			−0.851709			−0.425854	−	0.904792i	$-0.640026\pi$
$59$	−22773.1			−0.851709			−0.425854	+	0.904792i	$0.640026\pi$
$60$	−9457.01	−	893.919i	−0.339137	−	0.0320568i
$61$	−916.341			−0.0315306			−0.0157653	−	0.999876i	$-0.505018\pi$
$61$	−916.341			−0.0315306			−0.0157653	+	0.999876i	$0.505018\pi$
$62$		−	26029.9i		−	0.859991i
$63$			13611.3i			0.432063i
$64$	−22556.5			−0.688369
$65$	−8626.59	−	815.425i	−0.253254	−	0.0239387i
$66$	−3944.42			−0.111461
$67$			25328.4i			0.689321i	0.938727	+	0.344660i	$0.112006\pi$
$67$			25328.4i			0.689321i	−0.938727	+	0.344660i	$0.887994\pi$
$68$			8058.22i			0.211333i
$69$	−101.095			−0.00255626
$70$	−3201.90	+	33873.7i	−0.0781020	+	0.826261i
$71$	−16788.6			−0.395248			−0.197624	−	0.980278i	$-0.563323\pi$
$71$	−16788.6			−0.395248			−0.197624	+	0.980278i	$0.563323\pi$
$72$			14927.7i			0.339361i
$73$		−	55976.9i		−	1.22942i	−0.788752	−	0.614712i	$-0.789272\pi$
$73$		−	55976.9i		−	1.22942i	0.788752	−	0.614712i	$-0.210728\pi$
$74$	16575.6			0.351877
$75$	−5269.92	+	27626.9i	−0.108181	+	0.567125i
$76$	31608.9			0.627735
$77$		−	20332.9i		−	0.390816i
$78$			5052.94i			0.0940389i
$79$	47517.8			0.856621			0.428310	−	0.903632i	$-0.359109\pi$
$79$	47517.8			0.856621			0.428310	+	0.903632i	$0.359109\pi$
$80$	−333.196	+	3524.97i	−0.00582070	+	0.0615787i
$81$	6561.00			0.111111
$82$			50859.4i			0.835289i
$83$		−	24415.3i		−	0.389016i	−0.980901	−	0.194508i	$-0.937689\pi$
$83$		−	24415.3i		−	0.389016i	0.980901	−	0.194508i	$-0.0623110\pi$
$84$	−28554.5			−0.441546
$85$	23752.8	+	2245.22i	0.356589	+	0.0337064i
$86$	73549.4			1.07234
$87$		−	9970.33i		−	0.141225i
$88$		−	22299.4i		−	0.306964i
$89$	22081.6			0.295499			0.147749	−	0.989025i	$-0.452797\pi$
$89$	22081.6			0.295499			0.147749	+	0.989025i	$0.452797\pi$
$90$	16328.0	+	1543.40i	0.212485	+	0.0200850i
$91$	−26047.1			−0.329728
$92$		−	212.082i		−	0.00261236i
$93$		−	64678.5i		−	0.775448i
$94$	−38219.1			−0.446130
$95$	8807.05	−	93172.1i	0.100120	−	1.05920i
$96$	−51011.6			−0.564925
$97$			15706.3i			0.169490i	0.996403	+	0.0847449i	$0.0270075\pi$
$97$			15706.3i			0.169490i	−0.996403	+	0.0847449i	$0.972992\pi$
$98$			41402.1i			0.435469i
$99$	−9801.00			−0.100504
$100$	−57957.1	−	11055.5i	−0.579571	−	0.110555i
$101$	10765.2			0.105007			0.0525033	−	0.998621i	$-0.483280\pi$
$101$	10765.2			0.105007			0.0525033	+	0.998621i	$0.483280\pi$
$102$		−	13913.0i		−	0.132409i
$103$		−	28684.5i		−	0.266412i	−0.991088	−	0.133206i	$-0.957473\pi$
$103$		−	28684.5i		−	0.266412i	0.991088	−	0.133206i	$-0.0425272\pi$
$104$	−28566.3			−0.258983
$105$	−7955.99	+	84168.5i	−0.0704240	+	0.745034i
$106$	98046.9			0.847558
$107$		−	121918.i		−	1.02946i	−0.857354	−	0.514728i	$-0.827893\pi$
$107$		−	121918.i		−	1.02946i	0.857354	−	0.514728i	$-0.172107\pi$
$108$			13764.0i			0.113550i
$109$	169782.			1.36876			0.684378	−	0.729128i	$-0.260074\pi$
$109$	169782.			1.36876			0.684378	+	0.729128i	$0.260074\pi$
$110$	−24391.3	−	2305.57i	−0.192200	−	0.0181676i
$111$	41186.7			0.317285
$112$			10643.3i			0.0801735i
$113$		−	220268.i		−	1.62276i	−0.584519	−	0.811380i	$-0.698717\pi$
$113$		−	220268.i		−	1.62276i	0.584519	−	0.811380i	$-0.301283\pi$
$114$	−54574.6			−0.393304
$115$	−625.142	−	59.0912i	−0.00440792	−	0.000416657i
$116$	20916.3			0.144324
$117$			12555.4i			0.0847942i
$118$			82485.3i			0.545346i
$119$	71719.1			0.464267
$120$	−8725.47	+	92309.1i	−0.0553141	+	0.585183i
$121$	14641.0			0.0909091
$122$			3319.04i			0.0201889i
$123$			126374.i			0.753174i
$124$	135686.			0.792467
$125$	−48736.1	+	167757.i	−0.278982	+	0.960296i
$126$	49300.8			0.276648
$127$			230988.i			1.27081i	0.772180	+	0.635404i	$0.219166\pi$
$127$			230988.i			1.27081i	−0.772180	+	0.635404i	$0.780834\pi$
$128$		−	99673.7i		−	0.537720i
$129$	182754.			0.966923
$130$	−2953.52	+	31246.0i	−0.0153278	+	0.162157i
$131$	175894.			0.895513			0.447757	−	0.894155i	$-0.352223\pi$
$131$	175894.			0.895513			0.447757	+	0.894155i	$0.352223\pi$
$132$		−	20561.1i		−	0.102710i
$133$		−	281323.i		−	1.37904i
$134$	91741.1			0.441369
$135$	40571.5	+	3835.00i	0.191596	+	0.0181105i
$136$	78655.7			0.364655
$137$			8437.54i			0.0384073i	0.999816	+	0.0192037i	$0.00611309\pi$
$137$			8437.54i			0.0384073i	−0.999816	+	0.0192037i	$0.993887\pi$
$138$			366.170i			0.00163676i
$139$	75054.6			0.329489			0.164744	−	0.986336i	$-0.447320\pi$
$139$	75054.6			0.329489			0.164744	+	0.986336i	$0.447320\pi$
$140$	−176573.	−	16690.5i	−0.761386	−	0.0719696i
$141$	−94965.9			−0.402272
$142$			60809.5i			0.253076i
$143$		−	18755.6i		−	0.0766992i
$144$	5130.35			0.0206177
$145$	5827.80	−	61653.9i	0.0230189	−	0.243523i
$146$	−202752.			−0.787194
$147$			102875.i			0.392660i
$148$			86403.7i			0.324248i
$149$	119523.			0.441049			0.220524	−	0.975381i	$-0.429223\pi$
$149$	119523.			0.441049			0.220524	+	0.975381i	$0.429223\pi$
$150$	100066.	+	19088.0i	0.363127	+	0.0692678i
$151$	372713.			1.33025			0.665124	−	0.746733i	$-0.268379\pi$
$151$	372713.			1.33025			0.665124	+	0.746733i	$0.268379\pi$
$152$		−	308532.i		−	1.08316i
$153$		−	34570.6i		−	0.119393i
$154$	−73646.9			−0.250238
$155$	37805.6	−	399955.i	0.126394	−	1.33716i
$156$	−26339.4			−0.0866552
$157$			407799.i			1.32038i	0.751101	+	0.660188i	$0.229523\pi$
$157$			407799.i			1.32038i	−0.751101	+	0.660188i	$0.770477\pi$
$158$		−	172112.i		−	0.548491i
$159$	243624.			0.764237
$160$	−315442.	−	29817.1i	−0.974137	−	0.0920799i
$161$	−1887.55			−0.00573897
$162$		−	23764.3i		−	0.0711440i
$163$		−	360328.i		−	1.06225i	−0.847292	−	0.531127i	$-0.821769\pi$
$163$		−	360328.i		−	1.06225i	0.847292	−	0.531127i	$-0.178231\pi$
$164$	−265115.			−0.769704
$165$	−60606.8	−	5728.83i	−0.173305	−	0.0163816i
$166$	−88433.8			−0.249085
$167$			69666.3i			0.193300i	0.995318	+	0.0966500i	$0.0308127\pi$
$167$			69666.3i			0.193300i	−0.995318	+	0.0966500i	$0.969187\pi$
$168$			278718.i			0.761888i
$169$	347266.			0.935289
$170$	8132.33	−	86034.1i	0.0215821	−	0.228322i
$171$	−135605.			−0.354639
$172$			383391.i			0.988144i
$173$		−	627131.i		−	1.59310i	−0.604572	−	0.796550i	$-0.706656\pi$
$173$		−	627131.i		−	1.59310i	0.604572	−	0.796550i	$-0.293344\pi$
$174$	−36113.1			−0.0904257
$175$	−98395.5	+	515825.i	−0.242873	+	1.27323i
$176$	−7663.86			−0.0186494
$177$			204957.i			0.491734i
$178$		−	79980.8i		−	0.189206i
$179$	662582.			1.54564			0.772818	−	0.634628i	$-0.218846\pi$
$179$	662582.			1.54564			0.772818	+	0.634628i	$0.218846\pi$
$180$	−8045.27	+	85113.1i	−0.0185080	+	0.195801i
$181$	−525680.			−1.19268			−0.596341	−	0.802731i	$-0.703379\pi$
$181$	−525680.			−1.19268			−0.596341	+	0.802731i	$0.703379\pi$
$182$			94344.1i			0.211123i
$183$			8247.07i			0.0182042i
$184$	−2070.11			−0.00450764
$185$	254688.	+	24074.2i	0.547115	+	0.0517158i
$186$	−234269.			−0.496516
$187$			51642.5i			0.107995i
$188$		−	199225.i		−	0.411101i
$189$	122501.			0.249452
$190$	−337475.	−	31899.6i	−0.678199	−	0.0641065i
$191$	−824338.			−1.63502			−0.817508	−	0.575918i	$-0.804645\pi$
$191$	−824338.			−1.63502			−0.817508	+	0.575918i	$0.804645\pi$
$192$			203008.i			0.397430i
$193$			783372.i			1.51382i	0.653518	+	0.756911i	$0.273293\pi$
$193$			783372.i			1.51382i	−0.653518	+	0.756911i	$0.726707\pi$
$194$	56889.0			0.108524
$195$	−7338.82	+	77639.3i	−0.0138210	+	0.146216i
$196$	−215817.			−0.401278
$197$		−	272361.i		−	0.500010i	−0.968245	−	0.250005i	$-0.919568\pi$
$197$		−	272361.i		−	0.500010i	0.968245	−	0.250005i	$-0.0804323\pi$
$198$			35499.8i			0.0643521i
$199$	−982522.			−1.75877			−0.879386	−	0.476109i	$-0.842047\pi$
$199$	−982522.			−1.75877			−0.879386	+	0.476109i	$0.842047\pi$
$200$	−107912.	+	565715.i	−0.190763	+	1.00005i
$201$	227956.			0.397979
$202$		−	38992.0i		−	0.0672353i
$203$		−	186157.i		−	0.317059i
$204$	72524.0			0.122013
$205$	−73867.6	+	781465.i	−0.122763	+	1.29875i
$206$	−103897.			−0.170583
$207$			909.851i			0.00147586i
$208$			9817.66i			0.0157344i
$209$	202571.			0.320783
$210$	304863.	+	28817.1i	0.477042	+	0.0450922i
$211$	−430400.			−0.665527			−0.332764	−	0.943010i	$-0.607981\pi$
$211$	−430400.			−0.665527			−0.332764	+	0.943010i	$0.607981\pi$
$212$			511089.i			0.781010i
$213$			151098.i			0.228197i
$214$	−441593.			−0.659156
$215$	1.13010e6	+	106822.i	1.66733	+	0.157603i
$216$	134349.			0.195930
$217$		−	1.20762e6i		−	1.74093i
$218$		−	614961.i		−	0.876408i
$219$	−503792.			−0.709808
$220$	12018.2	−	127144.i	0.0167411	−	0.177109i
$221$	66155.7			0.0911143
$222$		−	149181.i		−	0.203156i
$223$		−	532033.i		−	0.716434i	−0.933638	−	0.358217i	$-0.883385\pi$
$223$		−	532033.i		−	0.716434i	0.933638	−	0.358217i	$-0.116615\pi$
$224$	−952446.			−1.26829
$225$	248642.	+	47429.3i	0.327429	+	0.0624583i
$226$	−797822.			−1.03905
$227$			792684.i			1.02102i	0.859871	+	0.510512i	$0.170544\pi$
$227$			792684.i			1.02102i	−0.859871	+	0.510512i	$0.829456\pi$
$228$		−	284481.i		−	0.362423i
$229$	−286558.			−0.361097			−0.180549	−	0.983566i	$-0.557787\pi$
$229$	−286558.			−0.361097			−0.180549	+	0.983566i	$0.557787\pi$
$230$	−214.032	+	2264.30i	−0.000266784	+	0.00282237i
$231$	−182996.			−0.225638
$232$		−	204162.i		−	0.249032i
$233$		−	1.41434e6i		−	1.70673i	−0.521312	−	0.853366i	$-0.674557\pi$
$233$		−	1.41434e6i		−	1.70673i	0.521312	−	0.853366i	$-0.325443\pi$
$234$	45476.4			0.0542934
$235$	−587244.	−	55509.0i	−0.693664	−	0.0655682i
$236$	−429971.			−0.502527
$237$		−	427660.i		−	0.494570i
$238$		−	259771.i		−	0.297268i
$239$	−1.00694e6			−1.14028			−0.570138	−	0.821549i	$-0.693110\pi$
$239$	−1.00694e6			−1.14028			−0.570138	+	0.821549i	$0.693110\pi$
$240$	31724.7	+	2998.77i	0.0355525	+	0.00336058i
$241$	1.08716e6			1.20573			0.602866	−	0.797843i	$-0.294025\pi$
$241$	1.08716e6			1.20573			0.602866	+	0.797843i	$0.294025\pi$
$242$		−	53030.6i		−	0.0582087i
$243$		−	59049.0i		−	0.0641500i
$244$	−17301.1			−0.0186037
$245$	−60132.0	+	636152.i	−0.0640015	+	0.677089i
$246$	457735.			0.482254
$247$		−	259500.i		−	0.270642i
$248$		−	1.32442e6i		−	1.36740i
$249$	−219738.			−0.224598
$250$	607625.	+	176525.i	0.614874	+	0.178631i
$251$	312788.			0.313376			0.156688	−	0.987648i	$-0.449918\pi$
$251$	312788.			0.313376			0.156688	+	0.987648i	$0.449918\pi$
$252$			256990.i			0.254927i
$253$		−	1359.16i		−	0.00133496i
$254$	836652.			0.813693
$255$	20207.0	−	213775.i	0.0194604	−	0.205877i
$256$	−1.08283e6			−1.03267
$257$			1.50645e6i			1.42273i	0.702822	+	0.711366i	$0.251923\pi$
$257$			1.50645e6i			1.42273i	−0.702822	+	0.711366i	$0.748077\pi$
$258$		−	661945.i		−	0.619117i
$259$	769003.			0.712326
$260$	−162876.	−	15395.8i	−0.149425	−	0.0141243i
$261$	−89732.9			−0.0815362
$262$		−	637097.i		−	0.573393i
$263$		−	189662.i		−	0.169079i	−0.996420	−	0.0845397i	$-0.973058\pi$
$263$		−	189662.i		−	0.169079i	0.996420	−	0.0845397i	$-0.0269420\pi$
$264$	−200695.			−0.177226
$265$	1.50651e6	+	142402.i	1.31782	+	0.124567i
$266$	−1.01897e6			−0.882993
$267$		−	198734.i		−	0.170606i
$268$			478218.i			0.406714i
$269$	−1.60463e6			−1.35206			−0.676029	−	0.736875i	$-0.736301\pi$
$269$	−1.60463e6			−1.35206			−0.676029	+	0.736875i	$0.736301\pi$
$270$	13890.6	−	146952.i	0.0115961	−	0.122678i
$271$	1.71899e6			1.42184			0.710921	−	0.703272i	$-0.248278\pi$
$271$	1.71899e6			1.42184			0.710921	+	0.703272i	$0.248278\pi$
$272$		−	27032.3i		−	0.0221545i
$273$			234424.i			0.190369i
$274$	30561.3			0.0245921
$275$	−371428.	−	70851.1i	−0.296171	−	0.0564957i
$276$	−1908.73			−0.00150825
$277$			756133.i			0.592105i	0.955172	+	0.296053i	$0.0956704\pi$
$277$			756133.i			0.592105i	−0.955172	+	0.296053i	$0.904330\pi$
$278$		−	271852.i		−	0.210970i
$279$	−582107.			−0.447705
$280$	−162915.	+	1.72352e6i	−0.124184	+	1.31377i
$281$	772332.			0.583497			0.291748	−	0.956495i	$-0.405763\pi$
$281$	772332.			0.583497			0.291748	+	0.956495i	$0.405763\pi$
$282$			343972.i			0.257573i
$283$		−	1.93103e6i		−	1.43325i	−0.697458	−	0.716625i	$-0.745686\pi$
$283$		−	1.93103e6i		−	1.43325i	0.697458	−	0.716625i	$-0.254314\pi$
$284$	−316981.			−0.233205
$285$	−838548.	−	79263.4i	−0.611528	−	0.0578044i
$286$	−67933.9			−0.0491102
$287$			2.35955e6i			1.69093i
$288$			459105.i			0.326160i
$289$	1.23770e6			0.871708
$290$	−223314.	−	21108.6i	−0.155927	−	0.0147389i
$291$	141356.			0.0978550
$292$		−	1.05688e6i		−	0.725386i
$293$			1.70779e6i			1.16216i	0.813847	+	0.581080i	$0.197370\pi$
$293$			1.70779e6i			1.16216i	−0.813847	+	0.581080i	$0.802630\pi$
$294$	372619.			0.251418
$295$	−119801.	+	1.26740e6i	−0.0801501	+	0.847929i
$296$	843379.			0.559492
$297$			88209.0i			0.0580259i
$298$		−	432920.i		−	0.282402i
$299$	−1741.13			−0.00112630
$300$	−99499.7	+	521614.i	−0.0638291	+	0.334616i
$301$	3.41222e6			2.17081
$302$		−	1.34999e6i		−	0.851752i
$303$		−	96886.4i		−	0.0606256i
$304$	−106036.			−0.0658068
$305$	−4820.53	+	50997.7i	−0.00296719	+	0.0313907i
$306$	−125217.			−0.0764467
$307$		−	256601.i		−	0.155386i	−0.996977	−	0.0776931i	$-0.975245\pi$
$307$		−	256601.i		−	0.155386i	0.996977	−	0.0776931i	$-0.0247554\pi$
$308$		−	383899.i		−	0.230590i
$309$	−258160.			−0.153813
$310$	−1.44866e6	−	136934.i	−0.856175	−	0.0809295i
$311$	2.08034e6			1.21964			0.609822	−	0.792539i	$-0.291241\pi$
$311$	2.08034e6			1.21964			0.609822	+	0.792539i	$0.291241\pi$
$312$			257097.i			0.149524i
$313$		−	1.05439e6i		−	0.608331i	−0.952619	−	0.304166i	$-0.901622\pi$
$313$		−	1.05439e6i		−	0.608331i	0.952619	−	0.304166i	$-0.0983776\pi$
$314$	1.47707e6			0.845431
$315$	757516.	+	71603.9i	0.430146	+	0.0406593i
$316$	897169.			0.505425
$317$			2.35341e6i			1.31538i	0.753291	+	0.657688i	$0.228465\pi$
$317$			2.35341e6i			1.31538i	−0.753291	+	0.657688i	$0.771535\pi$
$318$		−	882422.i		−	0.489338i
$319$	134045.			0.0737523
$320$	−118661.	+	1.25535e6i	−0.0647791	+	0.685315i
$321$	−1.09726e6			−0.594356
$322$			6836.82i			0.00367464i
$323$			714519.i			0.381072i
$324$	123876.			0.0655579
$325$	−90762.7	+	475811.i	−0.0476649	+	0.249877i
$326$	−1.30513e6			−0.680157
$327$		−	1.52804e6i		−	0.790251i
$328$			2.58776e6i			1.32813i
$329$	−1.77312e6			−0.903127
$330$	−20750.2	+	219521.i	−0.0104891	+	0.110967i
$331$	−376896.			−0.189083			−0.0945414	−	0.995521i	$-0.530138\pi$
$331$	−376896.			−0.189083			−0.0945414	+	0.995521i	$0.530138\pi$
$332$		−	460978.i		−	0.229528i
$333$		−	370680.i		−	0.183185i
$334$	252336.			0.123769
$335$	1.40962e6	+	133244.i	0.686262	+	0.0648686i
$336$	95789.6			0.0462882
$337$		−	3.13928e6i		−	1.50576i	−0.658159	−	0.752879i	$-0.728665\pi$
$337$		−	3.13928e6i		−	1.50576i	0.658159	−	0.752879i	$-0.271335\pi$
$338$		−	1.25782e6i		−	0.598862i
$339$	−1.98241e6			−0.936901
$340$	448469.	+	42391.4i	0.210395	+	0.0198875i
$341$	869567.			0.404965
$342$			491171.i			0.227074i
$343$		−	903460.i		−	0.414642i
$344$	3.74225e6			1.70505
$345$	−531.821	+	5626.28i	−0.000240557	+	0.00254491i
$346$	−2.27151e6			−1.02006
$347$			1.74141e6i			0.776384i	0.921579	+	0.388192i	$0.126900\pi$
$347$			1.74141e6i			0.776384i	−0.921579	+	0.388192i	$0.873100\pi$
$348$		−	188247.i		−	0.0833257i
$349$	4.40916e6			1.93772			0.968862	−	0.247602i	$-0.0796425\pi$
$349$	4.40916e6			1.93772			0.968862	+	0.247602i	$0.0796425\pi$
$350$	1.86835e6	+	356394.i	0.815245	+	0.155511i
$351$	112999.			0.0489560
$352$		−	685823.i		−	0.295023i
$353$		−	1.97624e6i		−	0.844116i	−0.906569	−	0.422058i	$-0.861308\pi$
$353$		−	1.97624e6i		−	0.844116i	0.906569	−	0.422058i	$-0.138692\pi$
$354$	742368.			0.314855
$355$	−88318.9	+	934349.i	−0.0371948	+	0.393494i
$356$	416916.			0.174350
$357$		−	645472.i		−	0.268045i
$358$		−	2.39991e6i		−	0.989664i
$359$	−340087.			−0.139269			−0.0696343	−	0.997573i	$-0.522183\pi$
$359$	−340087.			−0.139269			−0.0696343	+	0.997573i	$0.522183\pi$
$360$	830782.	+	78529.3i	0.337855	+	0.0319356i
$361$	326652.			0.131922
$362$			1.90404e6i			0.763669i
$363$		−	131769.i		−	0.0524864i
$364$	−491787.			−0.194547
$365$	−3.11532e6	−	294474.i	−1.22397	−	0.115695i
$366$	29871.4			0.0116561
$367$			3.60337e6i			1.39651i	0.715850	+	0.698254i	$0.246039\pi$
$367$			3.60337e6i			1.39651i	−0.715850	+	0.698254i	$0.753961\pi$
$368$			711.455i			0.000273859i
$369$	1.13737e6			0.434845
$370$	87198.3	−	922494.i	0.0331134	−	0.350315i
$371$	4.54875e6			1.71576
$372$		−	1.22118e6i		−	0.457531i
$373$		−	1.94994e6i		−	0.725687i	−0.931850	−	0.362844i	$-0.881806\pi$
$373$		−	1.94994e6i		−	0.725687i	0.931850	−	0.362844i	$-0.118194\pi$
$374$	187052.			0.0691486
$375$	1.50981e6	+	438625.i	0.554427	+	0.161070i
$376$	−1.94462e6			−0.709356
$377$		−	171717.i		−	0.0622242i
$378$		−	443707.i		−	0.159723i
$379$	−2.15699e6			−0.771349			−0.385674	−	0.922635i	$-0.626031\pi$
$379$	−2.15699e6			−0.771349			−0.385674	+	0.922635i	$0.626031\pi$
$380$	166283.	−	1.75915e6i	0.0590730	−	0.624949i
$381$	2.07889e6			0.733701
$382$			2.98580e6i			1.04689i
$383$			1.66805e6i			0.581049i	0.956868	+	0.290525i	$0.0938298\pi$
$383$			1.66805e6i			0.581049i	−0.956868	+	0.290525i	$0.906170\pi$
$384$	−897064.			−0.310453
$385$	−1.13160e6	−	106964.i	−0.389081	−	0.0367777i
$386$	2.83742e6			0.969294
$387$		−	1.64478e6i		−	0.558253i
$388$			296545.i			0.100003i
$389$	−1.58917e6			−0.532473			−0.266236	−	0.963908i	$-0.585780\pi$
$389$	−1.58917e6			−0.532473			−0.266236	+	0.963908i	$0.585780\pi$
$390$	281214.	+	26581.6i	0.0936215	+	0.00884953i
$391$	4794.09			0.00158586
$392$			2.10657e6i			0.692406i
$393$		−	1.58304e6i		−	0.517025i
$394$	−986506.			−0.320154
$395$	249974.	−	2.64454e6i	0.0806124	−	0.852819i
$396$	−185050.			−0.0592994
$397$		−	4.07780e6i		−	1.29852i	−0.760566	−	0.649261i	$-0.775078\pi$
$397$		−	4.07780e6i		−	1.29852i	0.760566	−	0.649261i	$-0.224922\pi$
$398$			3.55875e6i			1.12613i
$399$	−2.53191e6			−0.796189
$400$	194425.	+	37087.2i	0.0607577	+	0.0115897i
$401$	−4.89367e6			−1.51976			−0.759878	−	0.650066i	$-0.774741\pi$
$401$	−4.89367e6			−1.51976			−0.759878	+	0.650066i	$0.774741\pi$
$402$		−	825670.i		−	0.254824i
$403$		−	1.11394e6i		−	0.341665i
$404$	203254.			0.0619562
$405$	34515.0	−	365143.i	0.0104561	−	0.110618i
$406$	−674273.			−0.203012
$407$			553732.i			0.165697i
$408$		−	707901.i		−	0.210534i
$409$	−508943.			−0.150439			−0.0752196	−	0.997167i	$-0.523966\pi$
$409$	−508943.			−0.150439			−0.0752196	+	0.997167i	$0.523966\pi$
$410$	2.83051e6	+	267553.i	0.831582	+	0.0786049i
$411$	75937.8			0.0221745
$412$		−	541583.i		−	0.157189i
$413$			3.82679e6i			1.10398i
$414$	3295.53			0.000944985
$415$	−1.35880e6	−	128440.i	−0.387290	−	0.0366084i
$416$	−878562.			−0.248908
$417$		−	675492.i		−	0.190230i
$418$		−	733725.i		−	0.205396i
$419$	−6.78930e6			−1.88925			−0.944626	−	0.328148i	$-0.893575\pi$
$419$	−6.78930e6			−1.88925			−0.944626	+	0.328148i	$0.893575\pi$
$420$	−150215.	+	1.58916e6i	−0.0415517	+	0.439586i
$421$	−3.93204e6			−1.08122			−0.540608	−	0.841275i	$-0.681806\pi$
$421$	−3.93204e6			−1.08122			−0.540608	+	0.841275i	$0.681806\pi$
$422$			1.55893e6i			0.426134i
$423$			854693.i			0.232252i
$424$	4.98869e6			1.34764
$425$	249910.	−	1.31012e6i	0.0671136	−	0.351834i
$426$	547285.			0.146113
$427$			153982.i			0.0408697i
$428$		−	2.30189e6i		−	0.607401i
$429$	−168800.			−0.0442823
$430$	386917.	−	4.09329e6i	0.100913	−	1.06758i
$431$	−3.24173e6			−0.840589			−0.420295	−	0.907388i	$-0.638073\pi$
$431$	−3.24173e6			−0.840589			−0.420295	+	0.907388i	$0.638073\pi$
$432$		−	46173.2i		−	0.0119037i
$433$		−	5.96730e6i		−	1.52953i	−0.644309	−	0.764765i	$-0.722855\pi$
$433$		−	5.96730e6i		−	1.52953i	0.644309	−	0.764765i	$-0.277145\pi$
$434$	−4.37408e6			−1.11471
$435$	−554885.	−	52450.2i	−0.140598	−	0.0132900i
$436$	3.20560e6			0.807595
$437$		−	18805.2i		−	0.00471057i
$438$			1.82476e6i			0.454487i
$439$	−2.85969e6			−0.708203			−0.354101	−	0.935207i	$-0.615213\pi$
$439$	−2.85969e6			−0.708203			−0.354101	+	0.935207i	$0.615213\pi$
$440$	−1.24104e6	−	117309.i	−0.305602	−	0.0288869i
$441$	925875.			0.226702
$442$		−	239620.i		−	0.0583401i
$443$			2.52822e6i			0.612077i	0.952019	+	0.306038i	$0.0990036\pi$
$443$			2.52822e6i			0.612077i	−0.952019	+	0.306038i	$0.900996\pi$
$444$	777633.			0.187205
$445$	116163.	−	1.22892e6i	0.0278079	−	0.294187i
$446$	−1.92705e6			−0.458730
$447$		−	1.07571e6i		−	0.254640i
$448$			3.79040e6i			0.892257i
$449$	−5.72753e6			−1.34076			−0.670380	−	0.742018i	$-0.733869\pi$
$449$	−5.72753e6			−1.34076			−0.670380	+	0.742018i	$0.733869\pi$
$450$	171792.	−	900595.i	0.0399918	−	0.209652i
$451$	−1.69903e6			−0.393333
$452$		−	4.15880e6i		−	0.957464i
$453$		−	3.35442e6i		−	0.768019i
$454$	2.87115e6			0.653757
$455$	−137024.	+	1.44962e6i	−0.0310291	+	0.328265i
$456$	−2.77679e6			−0.625362
$457$			4.94045e6i			1.10656i	0.832994	+	0.553281i	$0.186625\pi$
$457$			4.94045e6i			1.10656i	−0.832994	+	0.553281i	$0.813375\pi$
$458$			1.03793e6i			0.231209i
$459$	−311135.			−0.0689314
$460$	−11803.1	−	1115.68i	−0.00260077	−	0.000245836i
$461$	6.18580e6			1.35564			0.677818	−	0.735229i	$-0.262926\pi$
$461$	6.18580e6			1.35564			0.677818	+	0.735229i	$0.262926\pi$
$462$			662822.i			0.144475i
$463$		−	1.23230e6i		−	0.267155i	−0.991038	−	0.133577i	$-0.957354\pi$
$463$		−	1.23230e6i		−	0.267155i	0.991038	−	0.133577i	$-0.0426465\pi$
$464$	−70166.4			−0.0151298
$465$	−3.59959e6	−	340250.i	−0.772007	−	0.0729736i
$466$	−5.12284e6			−1.09281
$467$			7.74380e6i			1.64309i	0.570142	+	0.821546i	$0.306888\pi$
$467$			7.74380e6i			1.64309i	−0.570142	+	0.821546i	$0.693112\pi$
$468$			237055.i			0.0500304i
$469$	4.25620e6			0.893490
$470$	−201057.	+	2.12703e6i	−0.0419831	+	0.444150i
$471$	3.67019e6			0.762319
$472$			4.19691e6i			0.867111i
$473$			2.45702e6i			0.504959i
$474$	−1.54901e6			−0.316671
$475$	−5.13903e6	−	980288.i	−1.04507	−	0.199352i
$476$	1.35411e6			0.273927
$477$		−	2.19262e6i		−	0.441233i
$478$			3.64721e6i			0.730114i
$479$	3.36135e6			0.669384			0.334692	−	0.942328i	$-0.391368\pi$
$479$	3.36135e6			0.669384			0.334692	+	0.942328i	$0.391368\pi$
$480$	−268353.	+	2.83898e6i	−0.0531623	+	0.562418i
$481$	709349.			0.139797
$482$		−	3.93776e6i		−	0.772025i
$483$			16988.0i			0.00331340i
$484$	276432.			0.0536383
$485$	874111.	+	82624.9i	0.168738	+	0.0159499i
$486$	−213879.			−0.0410750
$487$		−	397760.i		−	0.0759973i	−0.999278	−	0.0379987i	$-0.987902\pi$
$487$		−	397760.i		−	0.0759973i	0.999278	−	0.0379987i	$-0.0120983\pi$
$488$			168875.i			0.0321008i
$489$	−3.24295e6			−0.613293
$490$	2.30418e6	+	217802.i	0.433537	+	0.0409799i
$491$	−585823.			−0.109664			−0.0548318	−	0.998496i	$-0.517462\pi$
$491$	−585823.			−0.109664			−0.0548318	+	0.998496i	$0.517462\pi$
$492$			2.38603e6i			0.444389i
$493$			472812.i			0.0876135i
$494$	−939926.			−0.173291
$495$	−51559.5	+	545461.i	−0.00945792	+	0.100058i
$496$	−455177.			−0.0830760
$497$			2.82117e6i			0.512316i
$498$			795904.i			0.143809i
$499$	−7.82230e6			−1.40632			−0.703158	−	0.711034i	$-0.748227\pi$
$499$	−7.82230e6			−1.40632			−0.703158	+	0.711034i	$0.748227\pi$
$500$	−920171.	+	3.16737e6i	−0.164605	+	0.566595i
$501$	626997.			0.111602
$502$		−	1.13294e6i		−	0.200653i
$503$			4.04320e6i			0.712534i	0.934384	+	0.356267i	$0.115951\pi$
$503$			4.04320e6i			0.712534i	−0.934384	+	0.356267i	$0.884049\pi$
$504$	2.50846e6			0.439876
$505$	56631.5	−	599120.i	0.00988166	−	0.104541i
$506$	−4922.96			−0.000854771
$507$		−	3.12540e6i		−	0.539990i
$508$			4.36121e6i			0.749804i
$509$	1.07585e7			1.84060			0.920299	−	0.391216i	$-0.127946\pi$
$509$	1.07585e7			1.84060			0.920299	+	0.391216i	$0.127946\pi$
$510$	−774307.	−	73191.0i	−0.131822	−	0.0124604i
$511$	−9.40637e6			−1.59357
$512$			732521.i			0.123494i
$513$			1.22045e6i			0.204751i
$514$	5.45646e6			0.910969
$515$	−1.59640e6	−	150899.i	−0.265230	−	0.0250707i
$516$	3.45052e6			0.570505
$517$		−	1.27676e6i		−	0.210080i
$518$		−	2.78537e6i		−	0.456099i
$519$	−5.64418e6			−0.919777
$520$	−150277.	+	1.58982e6i	−0.0243716	+	0.257834i
$521$	−3.48830e6			−0.563014			−0.281507	−	0.959559i	$-0.590834\pi$
$521$	−3.48830e6			−0.563014			−0.281507	+	0.959559i	$0.590834\pi$
$522$			325018.i			0.0522073i
$523$			5.47692e6i			0.875552i	0.899084	+	0.437776i	$0.144234\pi$
$523$			5.47692e6i			0.875552i	−0.899084	+	0.437776i	$0.855766\pi$
$524$	3.32099e6			0.528372
$525$	4.64243e6	+	885559.i	0.735101	+	0.140223i
$526$	−686967.			−0.108261
$527$			3.06718e6i			0.481075i
$528$			68974.7i			0.0107673i
$529$	6.43622e6			0.999980
$530$	515789.	−	5.45667e6i	0.0797595	−	0.843797i
$531$	1.84462e6			0.283903
$532$		−	5.31158e6i		−	0.813663i
$533$			2.17651e6i			0.331851i
$534$	−719828.			−0.109238
$535$	−6.78517e6	−	641365.i	−1.02489	−	0.0968770i
$536$	4.66785e6			0.701786
$537$		−	5.96324e6i		−	0.892374i
$538$			5.81208e6i			0.865717i
$539$	−1.38310e6			−0.205060
$540$	766018.	+	72407.5i	0.113046	+	0.0106856i
$541$	−7.78523e6			−1.14361			−0.571806	−	0.820389i	$-0.693757\pi$
$541$	−7.78523e6			−1.14361			−0.571806	+	0.820389i	$0.693757\pi$
$542$		−	6.22630e6i		−	0.910399i
$543$			4.73112e6i			0.688596i
$544$	2.41907e6			0.350470
$545$	893162.	−	9.44899e6i	0.128807	−	1.36268i
$546$	849097.			0.121892
$547$		−	3.92034e6i		−	0.560215i	−0.959969	−	0.280108i	$-0.909630\pi$
$547$		−	3.92034e6i		−	0.560215i	0.959969	−	0.280108i	$-0.0903702\pi$
$548$			159307.i			0.0226612i
$549$	74223.6			0.0105102
$550$	−256627.	+	1.34533e6i	−0.0361739	+	0.189637i
$551$	1.85464e6			0.260244
$552$			18631.0i			0.00260249i
$553$		−	7.98491e6i		−	1.11034i
$554$	2.73876e6			0.379122
$555$	216668.	−	2.29219e6i	0.0298581	−	0.315877i
$556$	1.41708e6			0.194405
$557$		−	5.56520e6i		−	0.760051i	−0.924976	−	0.380026i	$-0.875915\pi$
$557$		−	5.56520e6i		−	0.760051i	0.924976	−	0.380026i	$-0.124085\pi$
$558$			2.10843e6i			0.286664i
$559$	3.14753e6			0.426030
$560$	592337.	+	55990.4i	0.0798177	+	0.00754473i
$561$	464782.			0.0623508
$562$		−	2.79743e6i		−	0.373610i
$563$		−	6.49216e6i		−	0.863213i	−0.902062	−	0.431607i	$-0.857947\pi$
$563$		−	6.49216e6i		−	0.863213i	0.902062	−	0.431607i	$-0.142053\pi$
$564$	−1.79302e6			−0.237349
$565$	−1.22587e7	−	1.15875e6i	−1.61556	−	0.152710i
$566$	−6.99429e6			−0.917704
$567$		−	1.10251e6i		−	0.144021i
$568$			3.09403e6i			0.402396i
$569$	1.02437e7			1.32641			0.663204	−	0.748439i	$-0.269196\pi$
$569$	1.02437e7			1.32641			0.663204	+	0.748439i	$0.269196\pi$
$570$	−287097.	+	3.03727e6i	−0.0370119	+	0.391558i
$571$	−1.42962e7			−1.83498			−0.917488	−	0.397764i	$-0.869786\pi$
$571$	−1.42962e7			−1.83498			−0.917488	+	0.397764i	$0.869786\pi$
$572$		−	354119.i		−	0.0452542i
$573$			7.41904e6i			0.943976i
$574$	8.54643e6			1.08269
$575$	−6577.28	+	34480.5i	−0.000829616	+	0.00434915i
$576$	1.82708e6			0.229456
$577$			5.37436e6i			0.672027i	0.941857	+	0.336014i	$0.109079\pi$
$577$			5.37436e6i			0.672027i	−0.941857	+	0.336014i	$0.890921\pi$
$578$		−	4.48303e6i		−	0.558151i
$579$	7.05035e6			0.874006
$580$	110033.	−	1.16407e6i	0.0135817	−	0.143684i
$581$	−4.10276e6			−0.504238
$582$		−	512001.i		−	0.0626561i
$583$			3.27540e6i			0.399110i
$584$	−1.03161e7			−1.25166
$585$	698754.	+	66049.4i	0.0844179	+	0.00797956i
$586$	6.18572e6			0.744126
$587$		−	1.17715e7i		−	1.41006i	−0.709178	−	0.705030i	$-0.750934\pi$
$587$		−	1.17715e7i		−	1.41006i	0.709178	−	0.705030i	$-0.249066\pi$
$588$			1.94235e6i			0.231678i
$589$	1.20312e7			1.42897
$590$	4.59061e6	+	433925.i	0.542925	+	0.0513198i
$591$	−2.45125e6			−0.288681
$592$		−	289852.i		−	0.0339917i
$593$		−	3.16466e6i		−	0.369564i	−0.982780	−	0.184782i	$-0.940842\pi$
$593$		−	3.16466e6i		−	0.369564i	0.982780	−	0.184782i	$-0.0591579\pi$
$594$	319498.			0.0371537
$595$	377288.	−	3.99143e6i	0.0436899	−	0.462207i
$596$	2.25668e6			0.260228
$597$			8.84270e6i			1.01543i
$598$			6306.47i			0.000721163i
$599$	−4.34303e6			−0.494567			−0.247284	−	0.968943i	$-0.579538\pi$
$599$	−4.34303e6			−0.494567			−0.247284	+	0.968943i	$0.579538\pi$
$600$	5.09143e6	+	971209.i	0.577380	+	0.110137i
$601$	8.05946e6			0.910165			0.455082	−	0.890449i	$-0.349610\pi$
$601$	8.05946e6			0.910165			0.455082	+	0.890449i	$0.349610\pi$
$602$		−	1.23593e7i		−	1.38996i
$603$		−	2.05160e6i		−	0.229774i
$604$	7.03708e6			0.784874
$605$	77020.9	−	814825.i	0.00855501	−	0.0905057i
$606$	−350928.			−0.0388183
$607$			284560.i			0.0313475i	0.999877	+	0.0156737i	$0.00498931\pi$
$607$			284560.i			0.0313475i	−0.999877	+	0.0156737i	$0.995011\pi$
$608$		−	9.48897e6i		−	1.04102i
$609$	−1.67542e6			−0.183054
$610$	184717.	+	17460.3i	0.0200993	+	0.00189988i
$611$	−1.63558e6			−0.177243
$612$		−	652716.i		−	0.0704443i
$613$			1.43183e7i			1.53901i	0.638644	+	0.769503i	$0.279496\pi$
$613$			1.43183e7i			1.53901i	−0.638644	+	0.769503i	$0.720504\pi$
$614$	−929424.			−0.0994931
$615$	7.03318e6	+	664808.i	0.749832	+	0.0708775i
$616$	−3.74720e6			−0.397883
$617$			1.35489e7i			1.43282i	0.697679	+	0.716411i	$0.254216\pi$
$617$			1.35489e7i			1.43282i	−0.697679	+	0.716411i	$0.745784\pi$
$618$			935072.i			0.0984859i
$619$	1.25027e7			1.31152			0.655762	−	0.754968i	$-0.272348\pi$
$619$	1.25027e7			1.31152			0.655762	+	0.754968i	$0.272348\pi$
$620$	713795.	−	7.55142e6i	0.0745752	−	0.788950i
$621$	8188.65			0.000852086
$622$		−	7.53511e6i		−	0.780932i
$623$		−	3.71060e6i		−	0.383022i
$624$	88358.9			0.00908425
$625$	9.07990e6	+	3.59485e6i	0.929781	+	0.368112i
$626$	−3.81906e6			−0.389512
$627$		−	1.82314e6i		−	0.185204i
$628$			7.69953e6i			0.779050i
$629$	−1.95315e6			−0.196838
$630$	259354.	−	2.74377e6i	0.0260340	−	0.275420i
$631$	272233.			0.0272187			0.0136093	−	0.999907i	$-0.495668\pi$
$631$	272233.			0.0272187			0.0136093	+	0.999907i	$0.495668\pi$
$632$		−	8.75719e6i		−	0.872112i
$633$			3.87360e6i			0.384242i
$634$	8.52419e6			0.842229
$635$	1.28553e7	+	1.21514e6i	1.26517	+	0.119590i
$636$	4.59980e6			0.450916
$637$			1.77179e6i			0.173007i
$638$		−	485521.i		−	0.0472233i
$639$	1.35988e6			0.131749
$640$	−5.54720e6	−	524347.i	−0.535333	−	0.0506021i
$641$	1.57242e7			1.51156			0.755779	−	0.654827i	$-0.227258\pi$
$641$	1.57242e7			1.51156			0.755779	+	0.654827i	$0.227258\pi$
$642$			3.97434e6i			0.380564i
$643$			5.47692e6i			0.522407i	0.965284	+	0.261203i	$0.0841193\pi$
$643$			5.47692e6i			0.522407i	−0.965284	+	0.261203i	$0.915881\pi$
$644$	−35638.2			−0.00338611
$645$	961400.	−	1.01709e7i	0.0909924	−	0.962632i
$646$	2.58803e6			0.243999
$647$		−	3.91671e6i		−	0.367841i	−0.982941	−	0.183921i	$-0.941121\pi$
$647$		−	3.91671e6i		−	0.367841i	0.982941	−	0.183921i	$-0.0588789\pi$
$648$		−	1.20915e6i		−	0.113120i
$649$	−2.75554e6			−0.256800
$650$	1.72342e6	+	328748.i	0.159995	+	0.0305196i
$651$	−1.08686e7			−1.00513
$652$		−	6.80323e6i		−	0.626753i
$653$			1.51457e7i			1.38997i	0.719024	+	0.694985i	$0.244589\pi$
$653$			1.51457e7i			1.38997i	−0.719024	+	0.694985i	$0.755411\pi$
$654$	−5.53465e6			−0.505995
$655$	925312.	−	9.78912e6i	0.0842723	−	0.891539i
$656$	889361.			0.0806898
$657$			4.53413e6i			0.409808i
$658$			6.42235e6i			0.578269i
$659$	−1.56274e6			−0.140176			−0.0700880	−	0.997541i	$-0.522328\pi$
$659$	−1.56274e6			−0.140176			−0.0700880	+	0.997541i	$0.522328\pi$
$660$	−1.14430e6	−	108164.i	−0.102254	−	0.00966549i
$661$	1.33712e7			1.19033			0.595163	−	0.803605i	$-0.297088\pi$
$661$	1.33712e7			1.19033			0.595163	+	0.803605i	$0.297088\pi$
$662$			1.36514e6i			0.121069i
$663$		−	595401.i		−	0.0526049i
$664$	−4.49957e6			−0.396051
$665$	−1.56567e7	−	1.47994e6i	−1.37292	−	0.129775i
$666$	−1.34263e6			−0.117292
$667$		−	12443.8i		−	0.00108302i
$668$			1.31535e6i			0.114051i
$669$	−4.78829e6			−0.413633
$670$	482616.	−	5.10572e6i	0.0415351	−	0.439410i
$671$	−110877.			−0.00950684
$672$			8.57201e6i			0.732250i
$673$			1.30303e7i			1.10896i	0.832196	+	0.554481i	$0.187083\pi$
$673$			1.30303e7i			1.10896i	−0.832196	+	0.554481i	$0.812917\pi$
$674$	−1.13707e7			−0.964130
$675$	426863.	−	2.23778e6i	0.0360603	−	0.189042i
$676$	6.55663e6			0.551841
$677$			1.20799e7i			1.01296i	0.862253	+	0.506478i	$0.169053\pi$
$677$			1.20799e7i			1.01296i	−0.862253	+	0.506478i	$0.830947\pi$
$678$			7.18040e6i			0.599894i
$679$	2.63929e6			0.219691
$680$	413779.	−	4.37747e6i	0.0343159	−	0.363037i
$681$	7.13416e6			0.589488
$682$		−	3.14962e6i		−	0.259297i
$683$			1.84029e7i			1.50950i	0.656011	+	0.754752i	$0.272243\pi$
$683$			1.84029e7i			1.50950i	−0.656011	+	0.754752i	$0.727757\pi$
$684$	−2.56032e6			−0.209245
$685$	469580.	+	44386.8i	0.0382369	+	0.00361433i
$686$	−3.27238e6			−0.265494
$687$			2.57903e6i			0.208480i
$688$		−	1.28613e6i		−	0.103589i
$689$	4.19589e6			0.336726
$690$	20378.7	+	1926.29i	0.00162950	+	0.000154028i
$691$	5.23001e6			0.416684			0.208342	−	0.978056i	$-0.433193\pi$
$691$	5.23001e6			0.416684			0.208342	+	0.978056i	$0.433193\pi$
$692$		−	1.18407e7i		−	0.939963i
$693$			1.64696e6i			0.130272i
$694$	6.30748e6			0.497115
$695$	394835.	−	4.17706e6i	0.0310065	−	0.328026i
$696$	−1.83746e6			−0.143779
$697$		−	5.99290e6i		−	0.467257i
$698$		−	1.59702e7i		−	1.24072i
$699$	−1.27291e7			−0.985382
$700$	−1.85777e6	+	9.73914e6i	−0.143301	+	0.751234i
$701$	4.83055e6			0.371280			0.185640	−	0.982618i	$-0.440564\pi$
$701$	4.83055e6			0.371280			0.185640	+	0.982618i	$0.440564\pi$
$702$		−	409288.i		−	0.0313463i
$703$			7.66137e6i			0.584680i
$704$	−2.72934e6			−0.207551
$705$	−499581.	+	5.28520e6i	−0.0378558	+	0.400487i
$706$	−7.15804e6			−0.540484
$707$		−	1.80898e6i		−	0.136109i
$708$			3.86974e6i			0.290134i
$709$	6.13980e6			0.458711			0.229355	−	0.973343i	$-0.426338\pi$
$709$	6.13980e6			0.458711			0.229355	+	0.973343i	$0.426338\pi$
$710$	3.38427e6	+	319896.i	0.251953	+	0.0238157i
$711$	−3.84894e6			−0.285540
$712$		−	4.06948e6i		−	0.300842i
$713$		−	80724.0i		−	0.00594674i
$714$	−2.33794e6			−0.171628
$715$	−1.04382e6	−	98666.4i	−0.0763589	−	0.00721779i
$716$	1.25100e7			0.911959
$717$			9.06249e6i			0.658339i
$718$			1.23181e6i			0.0891731i
$719$	−1.31130e7			−0.945974			−0.472987	−	0.881069i	$-0.656824\pi$
$719$	−1.31130e7			−0.945974			−0.472987	+	0.881069i	$0.656824\pi$
$720$	26988.9	−	285523.i	0.00194023	−	0.0205262i
$721$	−4.82015e6			−0.345321
$722$		−	1.18315e6i		−	0.0844690i
$723$		−	9.78444e6i		−	0.696130i
$724$	−9.92520e6			−0.703708
$725$	−3.40060e6	−	648677.i	−0.240276	−	0.0458335i
$726$	−477275.			−0.0336068
$727$			2.62296e7i			1.84059i	0.391229	+	0.920293i	$0.372050\pi$
$727$			2.62296e7i			1.84059i	−0.391229	+	0.920293i	$0.627950\pi$
$728$			4.80029e6i			0.335691i
$729$	−531441.			−0.0370370
$730$	−1.06660e6	+	1.12839e7i	−0.0740790	+	0.783701i
$731$	−8.66653e6			−0.599863
$732$			155710.i			0.0107409i
$733$			261993.i			0.0180106i	0.999959	+	0.00900532i	$0.00286652\pi$
$733$			261993.i			0.0180106i	−0.999959	+	0.00900532i	$0.997133\pi$
$734$	1.30516e7			0.894178
$735$	5.72537e6	+	541188.i	0.390917	+	0.0369513i
$736$	−63666.6			−0.00433229
$737$			3.06474e6i			0.207838i
$738$		−	4.11961e6i		−	0.278430i
$739$	−2.14527e7			−1.44501			−0.722506	−	0.691365i	$-0.757010\pi$
$739$	−2.14527e7			−1.44501			−0.722506	+	0.691365i	$0.757010\pi$
$740$	4.80868e6	+	454538.i	0.322809	+	0.0305134i
$741$	−2.33550e6			−0.156255
$742$		−	1.64758e7i		−	1.09860i
$743$		−	1.11848e7i		−	0.743283i	−0.928376	−	0.371642i	$-0.878795\pi$
$743$		−	1.11848e7i		−	0.743283i	0.928376	−	0.371642i	$-0.121205\pi$
$744$	−1.19198e7			−0.789471
$745$	628768.	−	6.65190e6i	0.0415049	−	0.439092i
$746$	−7.06280e6			−0.464654
$747$			1.97764e6i			0.129672i
$748$			975045.i			0.0637192i
$749$	−2.04871e7			−1.33437
$750$	1.58873e6	−	5.46863e6i	0.103133	−	0.354997i
$751$	5.63342e6			0.364479			0.182239	−	0.983254i	$-0.441665\pi$
$751$	5.63342e6			0.364479			0.182239	+	0.983254i	$0.441665\pi$
$752$			668325.i			0.0430966i
$753$		−	2.81509e6i		−	0.180928i
$754$	−621968.			−0.0398419
$755$	1.96071e6	−	2.07428e7i	0.125183	−	1.32434i
$756$	2.31291e6			0.147182
$757$		−	7.69867e6i		−	0.488288i	−0.969739	−	0.244144i	$-0.921493\pi$
$757$		−	7.69867e6i		−	0.488288i	0.969739	−	0.244144i	$-0.0785069\pi$
$758$			7.81276e6i			0.493891i
$759$	−12232.4			−0.000770741
$760$	−1.71709e7	−	1.62308e6i	−1.07835	−	0.101931i
$761$	2.39899e7			1.50164			0.750822	−	0.660505i	$-0.229658\pi$
$761$	2.39899e7			1.50164			0.750822	+	0.660505i	$0.229658\pi$
$762$		−	7.52987e6i		−	0.469786i
$763$		−	2.85303e7i		−	1.77417i
$764$	−1.55641e7			−0.964694
$765$	−1.92398e6	−	181863.i	−0.118863	−	0.0112355i
$766$	6.04179e6			0.372043
$767$			3.52994e6i			0.216660i
$768$			9.74549e6i			0.596212i
$769$	2.03436e7			1.24054			0.620272	−	0.784387i	$-0.287022\pi$
$769$	2.03436e7			1.24054			0.620272	+	0.784387i	$0.287022\pi$
$770$	−387429.	+	4.09872e6i	−0.0235486	+	0.249127i
$771$	1.35581e7			0.821415
$772$			1.47906e7i			0.893188i
$773$			1.86605e7i			1.12324i	0.827394	+	0.561622i	$0.189822\pi$
$773$			1.86605e7i			1.12324i	−0.827394	+	0.561622i	$0.810178\pi$
$774$	−5.95750e6			−0.357447
$775$	−2.20601e7	−	4.20803e6i	−1.31933	−	0.251666i
$776$	2.89455e6			0.172555
$777$		−	6.92102e6i		−	0.411261i
$778$			5.75608e6i			0.340940i
$779$	−2.35076e7			−1.38792
$780$	−138562.	+	1.46588e6i	−0.00815469	+	0.0862706i
$781$	−2.03143e6			−0.119172
$782$		−	17364.5i		−	0.00101542i
$783$			807596.i			0.0470750i
$784$	723985.			0.0420668
$785$	2.26955e7	+	2.14528e6i	1.31452	+	0.124254i
$786$	−5.73388e6			−0.331049
$787$		−	2.98644e7i		−	1.71877i	−0.511333	−	0.859383i	$-0.670848\pi$
$787$		−	2.98644e7i		−	1.71877i	0.511333	−	0.859383i	$-0.329152\pi$
$788$		−	5.14235e6i		−	0.295017i
$789$	−1.70696e6			−0.0976180
$790$	−9.57867e6	−	905420.i	−0.546057	−	0.0516157i
$791$	−3.70138e7			−2.10341
$792$			1.80625e6i			0.102321i
$793$			142037.i			0.00802084i
$794$	−1.47700e7			−0.831438
$795$	1.28162e6	−	1.35586e7i	0.0719186	−	0.760846i
$796$	−1.85507e7			−1.03771
$797$		−	2.60350e7i		−	1.45182i	−0.687791	−	0.725909i	$-0.741419\pi$
$797$		−	2.60350e7i		−	1.45182i	0.687791	−	0.725909i	$-0.258581\pi$
$798$			9.17073e6i			0.509796i
$799$	4.50346e6			0.249563
$800$	−3.31885e6	+	1.73987e7i	−0.183343	+	0.961149i
$801$	−1.78861e6			−0.0984995
$802$			1.77252e7i			0.973093i
$803$		−	6.77320e6i		−	0.370685i
$804$	4.30396e6			0.234816
$805$	−9929.71	+	105049.i	−0.000540066	+	0.00571350i
$806$	−4.03477e6			−0.218767
$807$			1.44417e7i			0.780611i
$808$		−	1.98394e6i		−	0.106906i
$809$	1.97670e7			1.06186			0.530932	−	0.847414i	$-0.321842\pi$
$809$	1.97670e7			1.06186			0.530932	+	0.847414i	$0.321842\pi$
$810$	−1.32257e6	−	125015.i	−0.0708282	−	0.00669501i
$811$	7.26108e6			0.387658			0.193829	−	0.981035i	$-0.437909\pi$
$811$	7.26108e6			0.387658			0.193829	+	0.981035i	$0.437909\pi$
$812$		−	3.51478e6i		−	0.187072i
$813$		−	1.54710e7i		−	0.820901i
$814$	2.00565e6			0.106095
$815$	−2.00535e7	−	1.89555e6i	−1.05754	−	0.0999635i
$816$	−243291.			−0.0127909
$817$			3.39951e7i			1.78181i
$818$			1.84342e6i			0.0963256i
$819$	2.10981e6			0.109909
$820$	−1.39467e6	+	1.47546e7i	−0.0724331	+	0.766289i
$821$	3.10030e7			1.60526			0.802631	−	0.596476i	$-0.203433\pi$
$821$	3.10030e7			1.60526			0.802631	+	0.596476i	$0.203433\pi$
$822$		−	275051.i		−	0.0141982i
$823$		−	2.56767e7i		−	1.32142i	−0.750643	−	0.660709i	$-0.770256\pi$
$823$		−	2.56767e7i		−	1.32142i	0.750643	−	0.660709i	$-0.229744\pi$
$824$	−5.28635e6			−0.271230
$825$	−637660.	+	3.34285e6i	−0.0326178	+	0.170994i
$826$	1.38609e7			0.706871
$827$			1.60345e7i			0.815254i	0.913149	+	0.407627i	$0.133644\pi$
$827$			1.60345e7i			0.815254i	−0.913149	+	0.407627i	$0.866356\pi$
$828$			17178.6i			0.000870787i
$829$	1.90352e7			0.961992			0.480996	−	0.876723i	$-0.340275\pi$
$829$	1.90352e7			0.961992			0.480996	+	0.876723i	$0.340275\pi$
$830$	−465218.	+	4.92166e6i	−0.0234402	+	0.247980i
$831$	6.80520e6			0.341852
$832$			3.49637e6i			0.175109i
$833$		−	4.87853e6i		−	0.243599i
$834$	−2.44667e6			−0.121804
$835$	3.87718e6	+	366489.i	0.192442	+	0.0181905i
$836$	3.82468e6			0.189269
$837$			5.23896e6i			0.258483i
$838$			2.45912e7i			1.20968i
$839$	−2.86604e7			−1.40565			−0.702826	−	0.711362i	$-0.748079\pi$
$839$	−2.86604e7			−1.40565			−0.702826	+	0.711362i	$0.748079\pi$
$840$	1.55117e7	+	1.46623e6i	0.758507	+	0.0716976i
$841$	−1.92839e7			−0.940167
$842$			1.42421e7i			0.692297i
$843$		−	6.95099e6i		−	0.336882i
$844$	−8.12625e6			−0.392676
$845$	1.82684e6	−	1.93266e7i	0.0880155	−	0.931139i
$846$	3.09575e6			0.148710
$847$		−	2.46028e6i		−	0.117835i
$848$		−	1.71451e6i		−	0.0818749i
$849$	−1.73792e7			−0.827488
$850$	−4.74533e6	−	905187.i	−0.225278	−	0.0429726i
$851$	51404.3			0.00243319
$852$			2.85283e6i			0.134641i
$853$		−	5.22750e6i		−	0.245992i	−0.992407	−	0.122996i	$-0.960750\pi$
$853$		−	5.22750e6i		−	0.245992i	0.992407	−	0.122996i	$-0.0392503\pi$
$854$	557733.			0.0261687
$855$	−713371.	+	7.54694e6i	−0.0333734	+	0.353066i
$856$	−2.24686e7			−1.04807
$857$			9.88397e6i			0.459705i	0.973225	+	0.229853i	$0.0738244\pi$
$857$			9.88397e6i			0.459705i	−0.973225	+	0.229853i	$0.926176\pi$
$858$			611405.i			0.0283538i
$859$	1.37127e7			0.634076			0.317038	−	0.948413i	$-0.397312\pi$
$859$	1.37127e7			0.634076			0.317038	+	0.948413i	$0.397312\pi$
$860$	2.13371e7	+	2.01688e6i	0.983759	+	0.0929894i
$861$	2.12360e7			0.976257
$862$			1.17417e7i			0.538226i
$863$			3.39850e7i			1.55332i	0.629921	+	0.776659i	$0.283087\pi$
$863$			3.39850e7i			1.55332i	−0.629921	+	0.776659i	$0.716913\pi$
$864$	4.13194e6			0.188308
$865$	−3.49021e7	−	3.29911e6i	−1.58603	−	0.149919i
$866$	−2.16139e7			−0.979352
$867$		−	1.11393e7i		−	0.503281i
$868$		−	2.28007e7i		−	1.02719i
$869$	5.74965e6			0.258281
$870$	−189978.	+	2.00983e6i	−0.00850952	+	0.0900244i
$871$	3.92603e6			0.175351
$872$		−	3.12896e7i		−	1.39351i
$873$		−	1.27221e6i		−	0.0564966i
$874$	−68113.4			−0.00301616
$875$	2.81899e7	+	8.18963e6i	1.24473	+	0.361613i
$876$	−9.51193e6			−0.418802
$877$		−	1.66649e7i		−	0.731653i	−0.930683	−	0.365826i	$-0.880786\pi$
$877$		−	1.66649e7i		−	0.731653i	0.930683	−	0.365826i	$-0.119214\pi$
$878$			1.03580e7i			0.453459i
$879$	1.53701e7			0.670973
$880$	−40316.8	+	426522.i	−0.00175501	+	0.0185667i
$881$	−1.85938e7			−0.807103			−0.403551	−	0.914957i	$-0.632224\pi$
$881$	−1.85938e7			−0.807103			−0.403551	+	0.914957i	$0.632224\pi$
$882$		−	3.35357e6i		−	0.145156i
$883$		−	1.41760e7i		−	0.611859i	−0.952054	−	0.305929i	$-0.901033\pi$
$883$		−	1.41760e7i		−	0.611859i	0.952054	−	0.305929i	$-0.0989672\pi$
$884$	1.24907e6			0.0537594
$885$	1.14066e7	+	1.07821e6i	0.489552	+	0.0462747i
$886$	9.15737e6			0.391910
$887$			1.10264e7i			0.470570i	0.971926	+	0.235285i	$0.0756023\pi$
$887$			1.10264e7i			0.470570i	−0.971926	+	0.235285i	$0.924398\pi$
$888$		−	7.59041e6i		−	0.323023i
$889$	3.88153e7			1.64721
$890$	−4.45122e6	−	420750.i	−0.188367	−	0.0178053i
$891$	793881.			0.0335013
$892$		−	1.00451e7i		−	0.422711i
$893$		−	1.76652e7i		−	0.741291i
$894$	−3.89628e6			−0.163045
$895$	3.48560e6	−	3.68751e7i	0.145452	−	1.53878i
$896$	−1.67492e7			−0.696986
$897$			15670.2i			0.000650268i
$898$			2.07454e7i			0.858483i
$899$	7.96131e6			0.328538
$900$	4.69453e6	+	895497.i	0.193190	+	0.0368517i
$901$	−1.15531e7			−0.474120
$902$			6.15399e6i			0.251849i
$903$		−	3.07100e7i		−	1.25332i
$904$	−4.05937e7			−1.65211
$905$	−2.76541e6	+	2.92560e7i	−0.112237	+	1.18739i
$906$	−1.21499e7			−0.491759
$907$			1.14062e7i			0.460388i	0.973145	+	0.230194i	$0.0739360\pi$
$907$			1.14062e7i			0.460388i	−0.973145	+	0.230194i	$0.926064\pi$
$908$			1.49664e7i			0.602426i
$909$	−871978.			−0.0350022
$910$	5.25059e6	+	496310.i	0.210187	+	0.0198678i
$911$	2.17910e7			0.869922			0.434961	−	0.900449i	$-0.356762\pi$
$911$	2.17910e7			0.869922			0.434961	+	0.900449i	$0.356762\pi$
$912$			954326.i			0.0379935i
$913$		−	2.95425e6i		−	0.117293i
$914$	1.78946e7			0.708527
$915$	458979.	+	43384.8i	0.0181234	+	0.00171311i
$916$	−5.41042e6			−0.213055
$917$		−	2.95572e7i		−	1.16075i
$918$			1.12695e6i			0.0441365i
$919$	−3.12982e7			−1.22245			−0.611225	−	0.791457i	$-0.709323\pi$
$919$	−3.12982e7			−1.22245			−0.611225	+	0.791457i	$0.709323\pi$
$920$	−10890.1	+	115209.i	−0.000424192	+	0.00448763i
$921$	−2.30941e6			−0.0897123
$922$		−	2.24053e7i		−	0.868008i
$923$			2.60232e6i			0.100544i
$924$	−3.45509e6			−0.133131
$925$	2.67964e6	−	1.40476e7i	0.102973	−	0.539820i
$926$	−4.46345e6			−0.171058
$927$			2.32344e6i			0.0888040i
$928$		−	6.27904e6i		−	0.239345i
$929$	3.00058e7			1.14069			0.570343	−	0.821407i	$-0.306810\pi$
$929$	3.00058e7			1.14069			0.570343	+	0.821407i	$0.306810\pi$
$930$	−1.23241e6	+	1.30379e7i	−0.0467247	+	0.494313i
$931$	−1.91364e7			−0.723578
$932$		−	2.67038e7i		−	1.00701i
$933$		−	1.87230e7i		−	0.704161i
$934$	2.80485e7			1.05206
$935$	2.87409e6	+	271672.i	0.107516	+	0.0101629i
$936$	2.31387e6			0.0863276
$937$			2.12772e7i			0.791711i	0.918313	+	0.395855i	$0.129552\pi$
$937$			2.12772e7i			0.791711i	−0.918313	+	0.395855i	$0.870448\pi$
$938$		−	1.54162e7i		−	0.572098i
$939$	−9.48950e6			−0.351220
$940$	−1.10876e7	−	1.04805e6i	−0.409276	−	0.0386867i
$941$	4.12864e7			1.51996			0.759982	−	0.649944i	$-0.225208\pi$
$941$	4.12864e7			1.51996			0.759982	+	0.649944i	$0.225208\pi$
$942$		−	1.32937e7i		−	0.488110i
$943$			157725.i			0.00577593i
$944$	1.44239e6			0.0526809
$945$	644435.	−	6.81765e6i	0.0234747	−	0.248345i
$946$	8.89948e6			0.323323
$947$			1.15296e7i			0.417771i	0.977940	+	0.208886i	$0.0669836\pi$
$947$			1.15296e7i			0.417771i	−0.977940	+	0.208886i	$0.933016\pi$
$948$		−	8.07452e6i		−	0.291807i
$949$	−8.67670e6			−0.312744
$950$	−3.55066e6	+	1.86139e7i	−0.127644	+	0.669157i
$951$	2.11807e7			0.759432
$952$		−	1.32173e7i		−	0.472663i
$953$			9.67798e6i			0.345185i	0.984993	+	0.172593i	$0.0552144\pi$
$953$			9.67798e6i			0.345185i	−0.984993	+	0.172593i	$0.944786\pi$
$954$	−7.94180e6			−0.282519
$955$	−4.33654e6	+	4.58774e7i	−0.153863	+	1.62776i
$956$	−1.90118e7			−0.672788
$957$		−	1.20641e6i		−	0.0425809i
$958$		−	1.21750e7i		−	0.428604i
$959$	1.41785e6			0.0497832
$960$	1.12982e7	+	1.06795e6i	0.395667	+	0.0374002i
$961$	2.30167e7			0.803959
$962$		−	2.56931e6i		−	0.0895113i
$963$			9.87534e6i			0.343152i
$964$	2.05263e7			0.711408
$965$	4.35975e7	+	4.12104e6i	1.50710	+	0.142458i
$966$	61531.4			0.00212155
$967$			3.88946e7i			1.33759i	0.743447	+	0.668795i	$0.233189\pi$
$967$			3.88946e7i			1.33759i	−0.743447	+	0.668795i	$0.766811\pi$
$968$		−	2.69823e6i		−	0.0925531i
$969$	6.43067e6			0.220012
$970$	299272.	−	3.16608e6i	0.0102126	−	0.108042i
$971$	2.79477e7			0.951259			0.475629	−	0.879646i	$-0.342220\pi$
$971$	2.79477e7			0.951259			0.475629	+	0.879646i	$0.342220\pi$
$972$		−	1.11489e6i		−	0.0378499i
$973$		−	1.26122e7i		−	0.427080i
$974$	−1.44071e6			−0.0486608
$975$	4.28230e6	+	816864.i	0.144267	+	0.0275194i
$976$	58038.9			0.00195027
$977$			7.01873e6i			0.235246i	0.993058	+	0.117623i	$0.0375274\pi$
$977$			7.01873e6i			0.235246i	−0.993058	+	0.117623i	$0.962473\pi$
$978$			1.17462e7i			0.392689i
$979$	2.67187e6			0.0890962
$980$	−1.13533e6	+	1.20110e7i	−0.0377623	+	0.399497i
$981$	−1.37524e7			−0.456252
$982$			2.12188e6i			0.0702171i
$983$			4.12903e7i			1.36290i	0.731864	+	0.681450i	$0.238650\pi$
$983$			4.12903e7i			1.36290i	−0.731864	+	0.681450i	$0.761350\pi$
$984$	2.32899e7			0.766795
$985$	−1.51579e7	−	1.43279e6i	−0.497791	−	0.0470535i
$986$	1.71255e6			0.0560985
$987$			1.59581e7i			0.521421i
$988$		−	4.89955e6i		−	0.159685i
$989$	228091.			0.00741512
$990$	1.97569e6	+	186751.i	0.0640666	+	0.00605586i
$991$	2.63627e6			0.0852717			0.0426359	−	0.999091i	$-0.486424\pi$
$991$	2.63627e6			0.0852717			0.0426359	+	0.999091i	$0.486424\pi$
$992$		−	4.07328e7i		−	1.31421i
$993$			3.39207e6i			0.109167i
$994$	1.02184e7			0.328034
$995$	−5.16869e6	+	5.46809e7i	−0.165509	+	1.75097i
$996$	−4.14880e6			−0.132518
$997$			4.09967e7i			1.30620i	0.757270	+	0.653102i	$0.226533\pi$
$997$			4.09967e7i			1.30620i	−0.757270	+	0.653102i	$0.773467\pi$
$998$			2.83328e7i			0.900458i
$999$	−3.33612e6			−0.105762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.b.34.10	✓	26
5.2	odd	4		825.6.a.v.1.10		13
5.3	odd	4		825.6.a.y.1.4		13
5.4	even	2	inner	165.6.c.b.34.17	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.b.34.10	✓	26	1.1	even	1	trivial
165.6.c.b.34.17	yes	26	5.4	even	2	inner
825.6.a.v.1.10		13	5.2	odd	4
825.6.a.y.1.4		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)

\(f(q)\)	\(=\)	\(q-3.62206i q^{2} -9.00000i q^{3} +18.8807 q^{4} +(5.26063 - 55.6536i) q^{5} -32.5985 q^{6} -168.040i q^{7} -184.293i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q-3.62206i q^{2} -9.00000i q^{3} +18.8807 q^{4} +(5.26063 - 55.6536i) q^{5} -32.5985 q^{6} -168.040i q^{7} -184.293i q^{8} -81.0000 q^{9} +(-201.581 - 19.0543i) q^{10} +121.000 q^{11} -169.926i q^{12} -155.005i q^{13} -608.652 q^{14} +(-500.883 - 47.3457i) q^{15} -63.3377 q^{16} +426.797i q^{17} +293.387i q^{18} +1674.14 q^{19} +(99.3244 - 1050.78i) q^{20} -1512.36 q^{21} -438.269i q^{22} -11.2327i q^{23} -1658.64 q^{24} +(-3069.65 - 585.547i) q^{25} -561.437 q^{26} +729.000i q^{27} -3172.72i q^{28} +1107.81 q^{29} +(-171.489 + 1814.23i) q^{30} +7186.50 q^{31} -5667.96i q^{32} -1089.00i q^{33} +1545.88 q^{34} +(-9352.05 - 883.999i) q^{35} -1529.34 q^{36} +4576.30i q^{37} -6063.84i q^{38} -1395.05 q^{39} +(-10256.6 - 969.497i) q^{40} -14041.6 q^{41} +5477.87i q^{42} +20306.0i q^{43} +2284.56 q^{44} +(-426.111 + 4507.94i) q^{45} -40.6856 q^{46} -10551.8i q^{47} +570.039i q^{48} -11430.6 q^{49} +(-2120.88 + 11118.5i) q^{50} +3841.17 q^{51} -2926.60i q^{52} +27069.4i q^{53} +2640.48 q^{54} +(636.537 - 6734.09i) q^{55} -30968.6 q^{56} -15067.3i q^{57} -4012.57i q^{58} -22773.1 q^{59} +(-9457.01 - 893.919i) q^{60} -916.341 q^{61} -26029.9i q^{62} +13611.3i q^{63} -22556.5 q^{64} +(-8626.59 - 815.425i) q^{65} -3944.42 q^{66} +25328.4i q^{67} +8058.22i q^{68} -101.095 q^{69} +(-3201.90 + 33873.7i) q^{70} -16788.6 q^{71} +14927.7i q^{72} -55976.9i q^{73} +16575.6 q^{74} +(-5269.92 + 27626.9i) q^{75} +31608.9 q^{76} -20332.9i q^{77} +5052.94i q^{78} +47517.8 q^{79} +(-333.196 + 3524.97i) q^{80} +6561.00 q^{81} +50859.4i q^{82} -24415.3i q^{83} -28554.5 q^{84} +(23752.8 + 2245.22i) q^{85} +73549.4 q^{86} -9970.33i q^{87} -22299.4i q^{88} +22081.6 q^{89} +(16328.0 + 1543.40i) q^{90} -26047.1 q^{91} -212.082i q^{92} -64678.5i q^{93} -38219.1 q^{94} +(8807.05 - 93172.1i) q^{95} -51011.6 q^{96} +15706.3i q^{97} +41402.1i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 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

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