LMFDB - Embedded newform 165.6.c.b.34.16

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			34.16
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.33747i q^{2} +9.00000i q^{3} +20.8613 q^{4} +(21.4823 - 51.6092i) q^{5} -30.0373 q^{6} -103.473i q^{7} +176.423i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q+3.33747i q^{2} +9.00000i q^{3} +20.8613 q^{4} +(21.4823 - 51.6092i) q^{5} -30.0373 q^{6} -103.473i q^{7} +176.423i q^{8} -81.0000 q^{9} +(172.244 + 71.6967i) q^{10} +121.000 q^{11} +187.751i q^{12} -357.925i q^{13} +345.339 q^{14} +(464.483 + 193.341i) q^{15} +78.7535 q^{16} -2067.63i q^{17} -270.335i q^{18} -1320.17 q^{19} +(448.149 - 1076.63i) q^{20} +931.258 q^{21} +403.834i q^{22} -2498.44i q^{23} -1587.81 q^{24} +(-2202.02 - 2217.37i) q^{25} +1194.57 q^{26} -729.000i q^{27} -2158.58i q^{28} -1657.60 q^{29} +(-645.271 + 1550.20i) q^{30} +4690.57 q^{31} +5908.38i q^{32} +1089.00i q^{33} +6900.67 q^{34} +(-5340.16 - 2222.84i) q^{35} -1689.76 q^{36} -5214.75i q^{37} -4406.02i q^{38} +3221.33 q^{39} +(9105.05 + 3789.98i) q^{40} +13577.0 q^{41} +3108.05i q^{42} +10764.0i q^{43} +2524.21 q^{44} +(-1740.07 + 4180.34i) q^{45} +8338.46 q^{46} +2926.95i q^{47} +708.782i q^{48} +6100.32 q^{49} +(7400.42 - 7349.18i) q^{50} +18608.7 q^{51} -7466.78i q^{52} -21529.9i q^{53} +2433.02 q^{54} +(2599.36 - 6244.71i) q^{55} +18255.0 q^{56} -11881.5i q^{57} -5532.19i q^{58} +4541.09 q^{59} +(9689.70 + 4033.34i) q^{60} +3649.55 q^{61} +15654.6i q^{62} +8381.32i q^{63} -17198.9 q^{64} +(-18472.2 - 7689.07i) q^{65} -3634.51 q^{66} +55473.7i q^{67} -43133.4i q^{68} +22485.9 q^{69} +(7418.68 - 17822.6i) q^{70} +4491.83 q^{71} -14290.3i q^{72} +33559.8i q^{73} +17404.1 q^{74} +(19956.4 - 19818.2i) q^{75} -27540.4 q^{76} -12520.2i q^{77} +10751.1i q^{78} +7912.05 q^{79} +(1691.81 - 4064.41i) q^{80} +6561.00 q^{81} +45312.9i q^{82} -20569.6i q^{83} +19427.2 q^{84} +(-106709. - 44417.6i) q^{85} -35924.5 q^{86} -14918.4i q^{87} +21347.2i q^{88} +111119. q^{89} +(-13951.8 - 5807.43i) q^{90} -37035.6 q^{91} -52120.6i q^{92} +42215.1i q^{93} -9768.61 q^{94} +(-28360.3 + 68132.8i) q^{95} -53175.4 q^{96} +58271.1i q^{97} +20359.7i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			3.33747i			0.589987i	0.955499	+	0.294994i	$0.0953176\pi$
$2$			3.33747i			0.589987i	−0.955499	+	0.294994i	$0.904682\pi$
$3$			9.00000i			0.577350i
$3$			9.00000i			0.577350i
$4$	20.8613			0.651915
$5$	21.4823	−	51.6092i	0.384288	−	0.923213i
$5$	21.4823	−	51.6092i	0.384288	−	0.923213i
$6$	−30.0373			−0.340629
$7$		−	103.473i		−	0.798146i	−0.916919	−	0.399073i	$-0.869332\pi$
$7$		−	103.473i		−	0.798146i	0.916919	−	0.399073i	$-0.130668\pi$
$8$			176.423i			0.974609i
$9$	−81.0000			−0.333333
$10$	172.244	+	71.6967i	0.544684	+	0.226725i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$			187.751i			0.376383i
$13$		−	357.925i		−	0.587400i	−0.955898	−	0.293700i	$-0.905113\pi$
$13$		−	357.925i		−	0.587400i	0.955898	−	0.293700i	$-0.0948867\pi$
$14$	345.339			0.470896
$15$	464.483	+	193.341i	0.533017	+	0.221869i
$16$	78.7535			0.0769078
$17$		−	2067.63i		−	1.73521i	−0.497258	−	0.867603i	$-0.665660\pi$
$17$		−	2067.63i		−	1.73521i	0.497258	−	0.867603i	$-0.334340\pi$
$18$		−	270.335i		−	0.196662i
$19$	−1320.17			−0.838967			−0.419484	−	0.907763i	$-0.637789\pi$
$19$	−1320.17			−0.838967			−0.419484	+	0.907763i	$0.637789\pi$
$20$	448.149	−	1076.63i	0.250523	−	0.601856i
$21$	931.258			0.460810
$22$			403.834i			0.177888i
$23$		−	2498.44i		−	0.984802i	−0.870369	−	0.492401i	$-0.836119\pi$
$23$		−	2498.44i		−	0.984802i	0.870369	−	0.492401i	$-0.163881\pi$
$24$	−1587.81			−0.562691
$25$	−2202.02	−	2217.37i	−0.704646	−	0.709559i
$26$	1194.57			0.346559
$27$		−	729.000i		−	0.192450i
$28$		−	2158.58i		−	0.520323i
$29$	−1657.60			−0.366003			−0.183002	−	0.983113i	$-0.558581\pi$
$29$	−1657.60			−0.366003			−0.183002	+	0.983113i	$0.558581\pi$
$30$	−645.271	+	1550.20i	−0.130900	+	0.314474i
$31$	4690.57			0.876640			0.438320	−	0.898819i	$-0.355574\pi$
$31$	4690.57			0.876640			0.438320	+	0.898819i	$0.355574\pi$
$32$			5908.38i			1.01998i
$33$			1089.00i			0.174078i
$34$	6900.67			1.02375
$35$	−5340.16	−	2222.84i	−0.736859	−	0.306718i
$36$	−1689.76			−0.217305
$37$		−	5214.75i		−	0.626223i	−0.949716	−	0.313112i	$-0.898629\pi$
$37$		−	5214.75i		−	0.626223i	0.949716	−	0.313112i	$-0.101371\pi$
$38$		−	4406.02i		−	0.494980i
$39$	3221.33			0.339136
$40$	9105.05	+	3789.98i	0.899772	+	0.374530i
$41$	13577.0			1.26138			0.630688	−	0.776037i	$-0.282773\pi$
$41$	13577.0			1.26138			0.630688	+	0.776037i	$0.282773\pi$
$42$			3108.05i			0.271872i
$43$			10764.0i			0.887774i	0.896083	+	0.443887i	$0.146401\pi$
$43$			10764.0i			0.887774i	−0.896083	+	0.443887i	$0.853599\pi$
$44$	2524.21			0.196560
$45$	−1740.07	+	4180.34i	−0.128096	+	0.307738i
$46$	8338.46			0.581021
$47$			2926.95i			0.193273i	0.995320	+	0.0966363i	$0.0308084\pi$
$47$			2926.95i			0.193273i	−0.995320	+	0.0966363i	$0.969192\pi$
$48$			708.782i			0.0444027i
$49$	6100.32			0.362963
$50$	7400.42	−	7349.18i	0.418631	−	0.415732i
$51$	18608.7			1.00182
$52$		−	7466.78i		−	0.382935i
$53$		−	21529.9i		−	1.05282i	−0.850232	−	0.526408i	$-0.823538\pi$
$53$		−	21529.9i		−	1.05282i	0.850232	−	0.526408i	$-0.176462\pi$
$54$	2433.02			0.113543
$55$	2599.36	−	6244.71i	0.115867	−	0.278359i
$56$	18255.0			0.777880
$57$		−	11881.5i		−	0.484378i
$58$		−	5532.19i		−	0.215937i
$59$	4541.09			0.169836			0.0849181	−	0.996388i	$-0.472937\pi$
$59$	4541.09			0.169836			0.0849181	+	0.996388i	$0.472937\pi$
$60$	9689.70	+	4033.34i	0.347482	+	0.144639i
$61$	3649.55			0.125578			0.0627892	−	0.998027i	$-0.480000\pi$
$61$	3649.55			0.125578			0.0627892	+	0.998027i	$0.480000\pi$
$62$			15654.6i			0.517207i
$63$			8381.32i			0.266049i
$64$	−17198.9			−0.524870
$65$	−18472.2	−	7689.07i	−0.542296	−	0.225731i
$66$	−3634.51			−0.102704
$67$			55473.7i			1.50973i	0.655878	+	0.754867i	$0.272299\pi$
$67$			55473.7i			1.50973i	−0.655878	+	0.754867i	$0.727701\pi$
$68$		−	43133.4i		−	1.13121i
$69$	22485.9			0.568575
$70$	7418.68	−	17822.6i	0.180960	−	0.434738i
$71$	4491.83			0.105749			0.0528746	−	0.998601i	$-0.483162\pi$
$71$	4491.83			0.105749			0.0528746	+	0.998601i	$0.483162\pi$
$72$		−	14290.3i		−	0.324870i
$73$			33559.8i			0.737076i	0.929613	+	0.368538i	$0.120141\pi$
$73$			33559.8i			0.737076i	−0.929613	+	0.368538i	$0.879859\pi$
$74$	17404.1			0.369464
$75$	19956.4	−	19818.2i	0.409664	−	0.406827i
$76$	−27540.4			−0.546935
$77$		−	12520.2i		−	0.240650i
$78$			10751.1i			0.200086i
$79$	7912.05			0.142634			0.0713168	−	0.997454i	$-0.477280\pi$
$79$	7912.05			0.142634			0.0713168	+	0.997454i	$0.477280\pi$
$80$	1691.81	−	4064.41i	0.0295547	−	0.0710023i
$81$	6561.00			0.111111
$82$			45312.9i			0.744196i
$83$		−	20569.6i		−	0.327741i	−0.986482	−	0.163870i	$-0.947602\pi$
$83$		−	20569.6i		−	0.327741i	0.986482	−	0.163870i	$-0.0523978\pi$
$84$	19427.2			0.300409
$85$	−106709.	−	44417.6i	−1.60197	−	0.666818i
$86$	−35924.5			−0.523775
$87$		−	14918.4i		−	0.211312i
$88$			21347.2i			0.293856i
$89$	111119.			1.48701			0.743504	−	0.668732i	$-0.233163\pi$
$89$	111119.			1.48701			0.743504	+	0.668732i	$0.233163\pi$
$90$	−13951.8	−	5807.43i	−0.181561	−	0.0755750i
$91$	−37035.6			−0.468831
$92$		−	52120.6i		−	0.642007i
$93$			42215.1i			0.506128i
$94$	−9768.61			−0.114028
$95$	−28360.3	+	68132.8i	−0.322405	+	0.774546i
$96$	−53175.4			−0.588888
$97$			58271.1i			0.628816i	0.949288	+	0.314408i	$0.101806\pi$
$97$			58271.1i			0.628816i	−0.949288	+	0.314408i	$0.898194\pi$
$98$			20359.7i			0.214144i
$99$	−9801.00			−0.100504
$100$	−45936.9	−	46257.2i	−0.459369	−	0.462572i
$101$	−56503.6			−0.551153			−0.275577	−	0.961279i	$-0.588869\pi$
$101$	−56503.6			−0.551153			−0.275577	+	0.961279i	$0.588869\pi$
$102$			62106.0i			0.591062i
$103$			95588.6i			0.887796i	0.896077	+	0.443898i	$0.146405\pi$
$103$			95588.6i			0.887796i	−0.896077	+	0.443898i	$0.853595\pi$
$104$	63146.3			0.572486
$105$	20005.6	−	48061.5i	0.177084	−	0.425426i
$106$	71855.5			0.621148
$107$		−	211645.i		−	1.78710i	−0.448964	−	0.893550i	$-0.648207\pi$
$107$		−	211645.i		−	1.78710i	0.448964	−	0.893550i	$-0.351793\pi$
$108$		−	15207.9i		−	0.125461i
$109$	−370.739			−0.00298884			−0.00149442	−	0.999999i	$-0.500476\pi$
$109$	−370.739			−0.00298884			−0.00149442	+	0.999999i	$0.500476\pi$
$110$	20841.6	+	8675.30i	0.164228	+	0.0683601i
$111$	46932.8			0.361550
$112$		−	8148.87i		−	0.0613836i
$113$		−	14124.9i		−	0.104061i	−0.998645	−	0.0520307i	$-0.983431\pi$
$113$		−	14124.9i		−	0.104061i	0.998645	−	0.0520307i	$-0.0165694\pi$
$114$	39654.2			0.285777
$115$	−128942.	−	53672.3i	−0.909182	−	0.378447i
$116$	−34579.6			−0.238603
$117$			28992.0i			0.195800i
$118$			15155.8i			0.100201i
$119$	−213944.			−1.38495
$120$	−34109.8	+	81945.5i	−0.216235	+	0.519484i
$121$	14641.0			0.0909091
$122$			12180.3i			0.0740897i
$123$			122193.i			0.728255i
$124$	97851.3			0.571495
$125$	−161741.	+	66010.0i	−0.925861	+	0.377864i
$126$	−27972.4			−0.156965
$127$		−	39049.1i		−	0.214834i	−0.994214	−	0.107417i	$-0.965742\pi$
$127$		−	39049.1i		−	0.214834i	0.994214	−	0.107417i	$-0.0342579\pi$
$128$			131667.i			0.710317i
$129$	−96876.0			−0.512556
$130$	25662.1	−	61650.6i	0.133178	−	0.319948i
$131$	−152838.			−0.778131			−0.389066	−	0.921210i	$-0.627202\pi$
$131$	−152838.			−0.778131			−0.389066	+	0.921210i	$0.627202\pi$
$132$			22717.9i			0.113484i
$133$			136602.i			0.669618i
$134$	−185142.			−0.890724
$135$	−37623.1	−	15660.6i	−0.177672	−	0.0739562i
$136$	364778.			1.69115
$137$		−	323866.i		−	1.47422i	−0.675771	−	0.737112i	$-0.736189\pi$
$137$		−	323866.i		−	1.47422i	0.675771	−	0.737112i	$-0.263811\pi$
$138$			75046.2i			0.335452i
$139$	−195925.			−0.860108			−0.430054	−	0.902803i	$-0.641506\pi$
$139$	−195925.			−0.860108			−0.430054	+	0.902803i	$0.641506\pi$
$140$	−111403.	−	46371.4i	−0.480369	−	0.199954i
$141$	−26342.5			−0.111586
$142$			14991.4i			0.0623907i
$143$		−	43309.0i		−	0.177108i
$144$	−6379.04			−0.0256359
$145$	−35609.1	+	85547.4i	−0.140650	+	0.337899i
$146$	−112005.			−0.434865
$147$			54902.9i			0.209557i
$148$		−	108786.i		−	0.408244i
$149$	−435048.			−1.60536			−0.802679	−	0.596411i	$-0.796593\pi$
$149$	−435048.			−1.60536			−0.802679	+	0.596411i	$0.796593\pi$
$150$	66142.6	+	66603.8i	0.240023	+	0.241697i
$151$	−94062.6			−0.335718			−0.167859	−	0.985811i	$-0.553685\pi$
$151$	−94062.6			−0.335718			−0.167859	+	0.985811i	$0.553685\pi$
$152$		−	232908.i		−	0.817665i
$153$			167478.i			0.578402i
$154$	41786.0			0.141981
$155$	100764.	−	242077.i	0.336882	−	0.809326i
$156$	67201.0			0.221088
$157$			194996.i			0.631360i	0.948866	+	0.315680i	$0.102233\pi$
$157$			194996.i			0.631360i	−0.948866	+	0.315680i	$0.897767\pi$
$158$			26406.3i			0.0841520i
$159$	193769.			0.607844
$160$	304927.	+	126926.i	0.941662	+	0.391967i
$161$	−258521.			−0.786015
$162$			21897.2i			0.0655542i
$163$			154239.i			0.454701i	0.973813	+	0.227350i	$0.0730063\pi$
$163$			154239.i			0.454701i	−0.973813	+	0.227350i	$0.926994\pi$
$164$	283234.			0.822309
$165$	56202.4	+	23394.3i	0.160711	+	0.0668959i
$166$	68650.4			0.193363
$167$			297517.i			0.825506i	0.910843	+	0.412753i	$0.135433\pi$
$167$			297517.i			0.825506i	−0.910843	+	0.412753i	$0.864567\pi$
$168$			164295.i			0.449109i
$169$	243182.			0.654961
$170$	148242.	−	356138.i	0.393414	−	0.945139i
$171$	106934.			0.279656
$172$			224551.i			0.578753i
$173$		−	49837.8i		−	0.126603i	−0.997994	−	0.0633014i	$-0.979837\pi$
$173$		−	49837.8i		−	0.126603i	0.997994	−	0.0633014i	$-0.0201629\pi$
$174$	49789.8			0.124671
$175$	−229438.	+	227850.i	−0.566332	+	0.562410i
$176$	9529.18			0.0231886
$177$			40869.8i			0.0980550i
$178$			370856.i			0.877316i
$179$	825399.			1.92545			0.962724	−	0.270487i	$-0.0871848\pi$
$179$	825399.			1.92545			0.962724	+	0.270487i	$0.0871848\pi$
$180$	−36300.1	+	87207.3i	−0.0835076	+	0.200619i
$181$	−631320.			−1.43236			−0.716182	−	0.697914i	$-0.754112\pi$
$181$	−631320.			−1.43236			−0.716182	+	0.697914i	$0.754112\pi$
$182$		−	123605.i		−	0.276604i
$183$			32846.0i			0.0725027i
$184$	440782.			0.959797
$185$	−269129.	−	112025.i	−0.578138	−	0.240650i
$186$	−140892.			−0.298609
$187$		−	250184.i		−	0.523184i
$188$			61059.9i			0.125997i
$189$	−75431.9			−0.153603
$190$	−227391.	−	94651.7i	−0.456972	−	0.190215i
$191$	367056.			0.728030			0.364015	−	0.931393i	$-0.381406\pi$
$191$	367056.			0.728030			0.364015	+	0.931393i	$0.381406\pi$
$192$		−	154790.i		−	0.303034i
$193$			239853.i			0.463501i	0.972775	+	0.231751i	$0.0744453\pi$
$193$			239853.i			0.463501i	−0.972775	+	0.231751i	$0.925555\pi$
$194$	−194478.			−0.370994
$195$	69201.7	−	166250.i	0.130326	−	0.313095i
$196$	127260.			0.236621
$197$		−	889966.i		−	1.63383i	−0.576755	−	0.816917i	$-0.695681\pi$
$197$		−	889966.i		−	1.63383i	0.576755	−	0.816917i	$-0.304319\pi$
$198$		−	32710.6i		−	0.0592960i
$199$	−2447.34			−0.00438089			−0.00219045	−	0.999998i	$-0.500697\pi$
$199$	−2447.34			−0.00438089			−0.00219045	+	0.999998i	$0.500697\pi$
$200$	391196.	−	388487.i	0.691543	−	0.686754i
$201$	−499264.			−0.871645
$202$		−	188579.i		−	0.325174i
$203$			171517.i			0.292124i
$204$	388201.			0.653102
$205$	291666.	−	700698.i	0.484731	−	1.16452i
$206$	−319024.			−0.523788
$207$			202373.i			0.328267i
$208$		−	28187.9i		−	0.0451756i
$209$	−159740.			−0.252958
$210$	160404.	+	66768.1i	0.250996	+	0.104477i
$211$	779165.			1.20482			0.602411	−	0.798186i	$-0.294207\pi$
$211$	779165.			1.20482			0.602411	+	0.798186i	$0.294207\pi$
$212$		−	449141.i		−	0.686347i
$213$			40426.4i			0.0610543i
$214$	706360.			1.05437
$215$	555521.	+	231236.i	0.819605	+	0.341161i
$216$	128612.			0.187564
$217$		−	485348.i		−	0.699687i
$218$		−	1237.33i		−	0.00176338i
$219$	−302038.			−0.425551
$220$	54226.0	−	130273.i	0.0755355	−	0.181467i
$221$	−740058.			−1.01926
$222$			156637.i			0.213310i
$223$			1.27044e6i			1.71077i	0.517990	+	0.855387i	$0.326680\pi$
$223$			1.27044e6i			1.71077i	−0.517990	+	0.855387i	$0.673320\pi$
$224$	611358.			0.814096
$225$	178363.	+	179607.i	0.234882	+	0.236520i
$226$	47141.5			0.0613949
$227$		−	1755.97i		−	0.00226179i	−0.999999	−	0.00113089i	$-0.999640\pi$
$227$		−	1755.97i		−	0.00226179i	0.999999	−	0.00113089i	$-0.000359974\pi$
$228$		−	247863.i		−	0.315773i
$229$	185101.			0.233249			0.116624	−	0.993176i	$-0.462793\pi$
$229$	185101.			0.233249			0.116624	+	0.993176i	$0.462793\pi$
$230$	179130.	−	430341.i	0.223279	−	0.536406i
$231$	112682.			0.138939
$232$		−	292439.i		−	0.356710i
$233$			172318.i			0.207941i	0.994580	+	0.103971i	$0.0331548\pi$
$233$			172318.i			0.207941i	−0.994580	+	0.103971i	$0.966845\pi$
$234$	−96759.9			−0.115520
$235$	151057.	+	62877.7i	0.178432	+	0.0742723i
$236$	94733.0			0.110719
$237$			71208.5i			0.0823495i
$238$		−	714033.i		−	0.817102i
$239$	−1.58068e6			−1.78999			−0.894994	−	0.446078i	$-0.852820\pi$
$239$	−1.58068e6			−1.78999			−0.894994	+	0.446078i	$0.852820\pi$
$240$	36579.7	+	15226.3i	0.0409932	+	0.0170634i
$241$	1.44227e6			1.59957			0.799785	−	0.600287i	$-0.204947\pi$
$241$	1.44227e6			1.59957			0.799785	+	0.600287i	$0.204947\pi$
$242$			48863.9i			0.0536352i
$243$			59049.0i			0.0641500i
$244$	76134.3			0.0818664
$245$	131049.	−	314833.i	0.139482	−	0.335092i
$246$	−407816.			−0.429662
$247$			472521.i			0.492810i
$248$			827525.i			0.854381i
$249$	185126.			0.189221
$250$	−220307.	−	539807.i	−0.222935	−	0.546247i
$251$	1.18482e6			1.18705			0.593524	−	0.804816i	$-0.297736\pi$
$251$	1.18482e6			1.18705			0.593524	+	0.804816i	$0.297736\pi$
$252$			174845.i			0.173441i
$253$		−	302311.i		−	0.296929i
$254$	130325.			0.126749
$255$	399758.	−	960380.i	0.384988	−	0.924895i
$256$	−989801.			−0.943948
$257$			307999.i			0.290882i	0.989367	+	0.145441i	$0.0464601\pi$
$257$			307999.i			0.290882i	−0.989367	+	0.145441i	$0.953540\pi$
$258$		−	323321.i		−	0.302402i
$259$	−539586.			−0.499818
$260$	−385354.	−	160404.i	−0.353531	−	0.147157i
$261$	134266.			0.122001
$262$		−	510093.i		−	0.459088i
$263$			1.92302e6i			1.71433i	0.515045	+	0.857163i	$0.327775\pi$
$263$			1.92302e6i			1.71433i	−0.515045	+	0.857163i	$0.672225\pi$
$264$	−192125.			−0.169658
$265$	−1.11114e6	−	462513.i	−0.971974	−	0.404584i
$266$	−455905.			−0.395066
$267$			1.00007e6i			0.858524i
$268$			1.15725e6i			0.984218i
$269$	1.14532e6			0.965040			0.482520	−	0.875885i	$-0.339722\pi$
$269$	1.14532e6			0.965040			0.482520	+	0.875885i	$0.339722\pi$
$270$	52266.9	−	125566.i	0.0436332	−	0.104825i
$271$	−737503.			−0.610015			−0.305008	−	0.952350i	$-0.598659\pi$
$271$	−737503.			−0.610015			−0.305008	+	0.952350i	$0.598659\pi$
$272$		−	162833.i		−	0.133451i
$273$		−	333321.i		−	0.270680i
$274$	1.08089e6			0.869774
$275$	−266444.	−	268302.i	−0.212459	−	0.213940i
$276$	469085.			0.370663
$277$		−	1.91454e6i		−	1.49922i	−0.661878	−	0.749611i	$-0.730240\pi$
$277$		−	1.91454e6i		−	1.49922i	0.661878	−	0.749611i	$-0.269760\pi$
$278$		−	653895.i		−	0.507453i
$279$	−379936.			−0.292213
$280$	392161.	−	942128.i	0.298930	−	0.718149i
$281$	−1.09912e6			−0.830387			−0.415193	−	0.909733i	$-0.636286\pi$
$281$	−1.09912e6			−0.830387			−0.415193	+	0.909733i	$0.636286\pi$
$282$		−	87917.5i		−	0.0658343i
$283$			371541.i			0.275766i	0.990449	+	0.137883i	$0.0440298\pi$
$283$			371541.i			0.275766i	−0.990449	+	0.137883i	$0.955970\pi$
$284$	93705.2			0.0689395
$285$	−613195.	−	255243.i	−0.447184	−	0.186141i
$286$	144543.			0.104491
$287$		−	1.40485e6i		−	1.00676i
$288$		−	478578.i		−	0.339995i
$289$	−2.85525e6			−2.01094
$290$	−285512.	−	118844.i	−0.199356	−	0.0829820i
$291$	−524440.			−0.363047
$292$			700100.i			0.480511i
$293$			2.86231e6i			1.94781i	0.226948	+	0.973907i	$0.427125\pi$
$293$			2.86231e6i			1.94781i	−0.226948	+	0.973907i	$0.572875\pi$
$294$	−183237.			−0.123636
$295$	97553.3	−	234362.i	0.0652660	−	0.156795i
$296$	920003.			0.610323
$297$		−	88209.0i		−	0.0580259i
$298$		−	1.45196e6i		−	0.947141i
$299$	−894254.			−0.578473
$300$	416315.	−	413432.i	0.267066	−	0.265217i
$301$	1.11378e6			0.708573
$302$		−	313931.i		−	0.198069i
$303$		−	508532.i		−	0.318209i
$304$	−103968.			−0.0645231
$305$	78400.9	−	188350.i	0.0482582	−	0.115936i
$306$	−558954.			−0.341250
$307$			2.67276e6i			1.61851i	0.587460	+	0.809253i	$0.300128\pi$
$307$			2.67276e6i			1.61851i	−0.587460	+	0.809253i	$0.699872\pi$
$308$		−	261188.i		−	0.156883i
$309$	−860298.			−0.512569
$310$	807924.	+	336298.i	0.477492	+	0.198756i
$311$	1.84386e6			1.08100			0.540500	−	0.841344i	$-0.318235\pi$
$311$	1.84386e6			1.08100			0.540500	+	0.841344i	$0.318235\pi$
$312$			568317.i			0.330525i
$313$			1.87741e6i			1.08318i	0.840644	+	0.541588i	$0.182177\pi$
$313$			1.87741e6i			1.08318i	−0.840644	+	0.541588i	$0.817823\pi$
$314$	−650794.			−0.372494
$315$	432553.	+	180050.i	0.245620	+	0.102239i
$316$	165056.			0.0929849
$317$			2.04246e6i			1.14158i	0.821097	+	0.570789i	$0.193362\pi$
$317$			2.04246e6i			1.14158i	−0.821097	+	0.570789i	$0.806638\pi$
$318$			646699.i			0.358620i
$319$	−200570.			−0.110354
$320$	−369473.	+	887623.i	−0.201701	+	0.484567i
$321$	1.90481e6			1.03178
$322$		−	862807.i		−	0.463739i
$323$			2.72962e6i			1.45578i
$324$	136871.			0.0724350
$325$	−793654.	+	788158.i	−0.416795	+	0.413909i
$326$	−514769.			−0.268268
$327$		−	3336.65i		−	0.00172561i
$328$			2.39530e6i			1.22935i
$329$	302860.			0.154260
$330$	−78077.7	+	187574.i	−0.0394677	+	0.0948174i
$331$	−2.48973e6			−1.24906			−0.624528	−	0.781002i	$-0.714709\pi$
$331$	−2.48973e6			−1.24906			−0.624528	+	0.781002i	$0.714709\pi$
$332$		−	429108.i		−	0.213659i
$333$			422395.i			0.208741i
$334$	−992954.			−0.487038
$335$	2.86295e6	+	1.19171e6i	1.39381	+	0.580172i
$336$	73339.8			0.0354398
$337$			2.26543e6i			1.08662i	0.839534	+	0.543308i	$0.182828\pi$
$337$			2.26543e6i			1.08662i	−0.839534	+	0.543308i	$0.817172\pi$
$338$			811615.i			0.386419i
$339$	127124.			0.0600799
$340$	−2.22608e6	−	926607.i	−1.04434	−	0.434709i
$341$	567559.			0.264317
$342$			356888.i			0.164993i
$343$		−	2.37029e6i		−	1.08784i
$344$	−1.89902e6			−0.865232
$345$	483050.	−	1.16048e6i	0.218497	−	0.524916i
$346$	166332.			0.0746941
$347$		−	887458.i		−	0.395662i	−0.980236	−	0.197831i	$-0.936610\pi$
$347$		−	887458.i		−	0.395662i	0.980236	−	0.197831i	$-0.0633897\pi$
$348$		−	311217.i		−	0.137757i
$349$	−3.37834e6			−1.48470			−0.742351	−	0.670011i	$-0.766289\pi$
$349$	−3.37834e6			−1.48470			−0.742351	+	0.670011i	$0.766289\pi$
$350$	−760442.	−	765744.i	−0.331815	−	0.334129i
$351$	−260928.			−0.113045
$352$			714914.i			0.307537i
$353$			1.23199e6i			0.526222i	0.964766	+	0.263111i	$0.0847485\pi$
$353$			1.23199e6i			0.526222i	−0.964766	+	0.263111i	$0.915251\pi$
$354$	−136402.			−0.0578512
$355$	96495.0	−	231820.i	0.0406381	−	0.0976291i
$356$	2.31808e6			0.969402
$357$		−	1.92550e6i		−	0.799600i
$358$			2.75475e6i			1.13599i
$359$	−1.03637e6			−0.424405			−0.212202	−	0.977226i	$-0.568064\pi$
$359$	−1.03637e6			−0.424405			−0.212202	+	0.977226i	$0.568064\pi$
$360$	−737509.	−	306988.i	−0.299924	−	0.124843i
$361$	−733257.			−0.296134
$362$		−	2.10701e6i		−	0.845076i
$363$			131769.i			0.0524864i
$364$	−772611.			−0.305638
$365$	1.73199e6	+	720943.i	0.680478	+	0.283249i
$366$	−109623.			−0.0427757
$367$		−	4.31603e6i		−	1.67270i	−0.548192	−	0.836352i	$-0.684684\pi$
$367$		−	4.31603e6i		−	1.67270i	0.548192	−	0.836352i	$-0.315316\pi$
$368$		−	196761.i		−	0.0757389i
$369$	−1.09974e6			−0.420458
$370$	373881.	−	898211.i	0.141980	−	0.341094i
$371$	−2.22777e6			−0.840301
$372$			880661.i			0.329953i
$373$		−	2.03599e6i		−	0.757712i	−0.925456	−	0.378856i	$-0.876318\pi$
$373$		−	2.03599e6i		−	0.757712i	0.925456	−	0.378856i	$-0.123682\pi$
$374$	834981.			0.308672
$375$	−594090.	−	1.45567e6i	−0.218160	−	0.534546i
$376$	−516381.			−0.188365
$377$			593297.i			0.214990i
$378$		−	251752.i		−	0.0906240i
$379$	3.67933e6			1.31574			0.657872	−	0.753130i	$-0.271457\pi$
$379$	3.67933e6			1.31574			0.657872	+	0.753130i	$0.271457\pi$
$380$	−591632.	+	1.42134e6i	−0.210180	+	0.504938i
$381$	351442.			0.124034
$382$			1.22504e6i			0.429528i
$383$		−	3.35614e6i		−	1.16908i	−0.811366	−	0.584539i	$-0.801275\pi$
$383$		−	3.35614e6i		−	1.16908i	0.811366	−	0.584539i	$-0.198725\pi$
$384$	−1.18500e6			−0.410102
$385$	−646160.	−	268964.i	−0.222171	−	0.0924789i
$386$	−800501.			−0.273460
$387$		−	871884.i		−	0.295925i
$388$			1.21561e6i			0.409935i
$389$	−5.94481e6			−1.99188			−0.995942	−	0.0900021i	$-0.971313\pi$
$389$	−5.94481e6			−1.99188			−0.995942	+	0.0900021i	$0.971313\pi$
$390$	554855.	+	230959.i	0.184722	+	0.0768905i
$391$	−5.16585e6			−1.70883
$392$			1.07624e6i			0.353747i
$393$		−	1.37554e6i		−	0.449254i
$394$	2.97024e6			0.963941
$395$	169969.	−	408335.i	0.0548123	−	0.131681i
$396$	−204461.			−0.0655199
$397$		−	4.07424e6i		−	1.29739i	−0.761048	−	0.648695i	$-0.775315\pi$
$397$		−	4.07424e6i		−	1.29739i	0.761048	−	0.648695i	$-0.224685\pi$
$398$		−	8167.95i		−	0.00258467i
$399$	−1.22942e6			−0.386604
$400$	−173417.	−	174626.i	−0.0541927	−	0.0545706i
$401$	1.76526e6			0.548209			0.274105	−	0.961700i	$-0.411619\pi$
$401$	1.76526e6			0.548209			0.274105	+	0.961700i	$0.411619\pi$
$402$		−	1.66628e6i		−	0.514260i
$403$		−	1.67887e6i		−	0.514939i
$404$	−1.17874e6			−0.359305
$405$	140946.	−	338608.i	0.0426986	−	0.102579i
$406$	−572433.			−0.172349
$407$		−	630985.i		−	0.188813i
$408$			3.28300e6i			0.976384i
$409$	3.05109e6			0.901877			0.450938	−	0.892555i	$-0.351089\pi$
$409$	3.05109e6			0.901877			0.450938	+	0.892555i	$0.351089\pi$
$410$	2.33856e6	+	973427.i	0.687051	+	0.285985i
$411$	2.91479e6			0.851144
$412$			1.99410e6i			0.578767i
$413$		−	469881.i		−	0.135554i
$414$	−675416.			−0.193674
$415$	−1.06158e6	−	441883.i	−0.302574	−	0.125947i
$416$	2.11476e6			0.599139
$417$		−	1.76333e6i		−	0.496584i
$418$		−	533129.i		−	0.149242i
$419$	6.61264e6			1.84009			0.920046	−	0.391810i	$-0.128151\pi$
$419$	6.61264e6			1.84009			0.920046	+	0.391810i	$0.128151\pi$
$420$	417342.	−	1.00262e6i	0.115443	−	0.277341i
$421$	2.29303e6			0.630527			0.315263	−	0.949004i	$-0.397907\pi$
$421$	2.29303e6			0.630527			0.315263	+	0.949004i	$0.397907\pi$
$422$			2.60044e6i			0.710830i
$423$		−	237083.i		−	0.0644242i
$424$	3.79837e6			1.02608
$425$	−4.58471e6	+	4.55296e6i	−1.23123	+	1.22271i
$426$	−134922.			−0.0360213
$427$		−	377630.i		−	0.100230i
$428$		−	4.41519e6i		−	1.16504i
$429$	389781.			0.102253
$430$	−771743.	+	1.85404e6i	−0.201280	+	0.483556i
$431$	5.53759e6			1.43591			0.717956	−	0.696089i	$-0.245078\pi$
$431$	5.53759e6			1.43591			0.717956	+	0.696089i	$0.245078\pi$
$432$		−	57411.3i		−	0.0148009i
$433$		−	2.55617e6i		−	0.655195i	−0.944817	−	0.327598i	$-0.893761\pi$
$433$		−	2.55617e6i		−	0.655195i	0.944817	−	0.327598i	$-0.106239\pi$
$434$	1.61983e6			0.412806
$435$	−769927.	−	320482.i	−0.195086	−	0.0812046i
$436$	−7734.09			−0.00194847
$437$			3.29835e6i			0.826216i
$438$		−	1.00804e6i		−	0.251070i
$439$	696199.			0.172414			0.0862070	−	0.996277i	$-0.472525\pi$
$439$	696199.			0.172414			0.0862070	+	0.996277i	$0.472525\pi$
$440$	1.10171e6	+	458588.i	0.271291	+	0.112925i
$441$	−494126.			−0.120988
$442$		−	2.46992e6i		−	0.601351i
$443$			6.82989e6i			1.65350i	0.562570	+	0.826750i	$0.309813\pi$
$443$			6.82989e6i			1.65350i	−0.562570	+	0.826750i	$0.690187\pi$
$444$	979077.			0.235700
$445$	2.38709e6	−	5.73476e6i	0.571439	−	1.37282i
$446$	−4.24006e6			−1.00933
$447$		−	3.91544e6i		−	0.926854i
$448$			1.77963e6i			0.418923i
$449$	6.68298e6			1.56442			0.782212	−	0.623013i	$-0.214091\pi$
$449$	6.68298e6			1.56442			0.782212	+	0.623013i	$0.214091\pi$
$450$	−599434.	+	595283.i	−0.139544	+	0.138577i
$451$	1.64282e6			0.380319
$452$		−	294664.i		−	0.0678392i
$453$		−	846564.i		−	0.193827i
$454$	5860.49			0.00133443
$455$	−795612.	+	1.91138e6i	−0.180166	+	0.432831i
$456$	2.09617e6			0.472079
$457$		−	616838.i		−	0.138159i	−0.997611	−	0.0690797i	$-0.977994\pi$
$457$		−	616838.i		−	0.138159i	0.997611	−	0.0690797i	$-0.0220063\pi$
$458$			617769.i			0.137614i
$459$	−1.50730e6			−0.333941
$460$	−2.68990e6	−	1.11967e6i	−0.592709	−	0.246715i
$461$	3.55459e6			0.779001			0.389500	−	0.921026i	$-0.372648\pi$
$461$	3.55459e6			0.779001			0.389500	+	0.921026i	$0.372648\pi$
$462$			376074.i			0.0819725i
$463$		−	3.23948e6i		−	0.702299i	−0.936319	−	0.351150i	$-0.885791\pi$
$463$		−	3.23948e6i		−	0.702299i	0.936319	−	0.351150i	$-0.114209\pi$
$464$	−130542.			−0.0281485
$465$	2.17869e6	+	906880.i	0.467265	+	0.194499i
$466$	−575106.			−0.122683
$467$		−	7.20656e6i		−	1.52910i	−0.644564	−	0.764550i	$-0.722961\pi$
$467$		−	7.20656e6i		−	1.52910i	0.644564	−	0.764550i	$-0.277039\pi$
$468$			604809.i			0.127645i
$469$	5.74004e6			1.20499
$470$	−209853.	+	504150.i	−0.0438197	+	0.105273i
$471$	−1.75497e6			−0.364516
$472$			801154.i			0.165524i
$473$			1.30244e6i			0.267674i
$474$	−237656.			−0.0485852
$475$	2.90703e6	+	2.92730e6i	0.591175	+	0.595297i
$476$	−4.46315e6			−0.902868
$477$			1.74392e6i			0.350939i
$478$		−	5.27549e6i		−	1.05607i
$479$	−772579.			−0.153852			−0.0769261	−	0.997037i	$-0.524511\pi$
$479$	−772579.			−0.153852			−0.0769261	+	0.997037i	$0.524511\pi$
$480$	−1.14233e6	+	2.74434e6i	−0.226302	+	0.543669i
$481$	−1.86649e6			−0.367844
$482$			4.81353e6i			0.943726i
$483$		−	2.32669e6i		−	0.453806i
$484$	305430.			0.0592650
$485$	3.00732e6	+	1.25180e6i	0.580532	+	0.241646i
$486$	−197074.			−0.0378477
$487$			3.08873e6i			0.590143i	0.955475	+	0.295072i	$0.0953435\pi$
$487$			3.08873e6i			0.590143i	−0.955475	+	0.295072i	$0.904656\pi$
$488$			643865.i			0.122390i
$489$	−1.38815e6			−0.262522
$490$	1.05075e6	+	437373.i	0.197700	+	0.0822928i
$491$	4.82049e6			0.902375			0.451187	−	0.892429i	$-0.351001\pi$
$491$	4.82049e6			0.902375			0.451187	+	0.892429i	$0.351001\pi$
$492$			2.54910e6i			0.474761i
$493$			3.42731e6i			0.635091i
$494$	−1.57703e6			−0.290751
$495$	−210548.	+	505822.i	−0.0386224	+	0.0927864i
$496$	369399.			0.0674204
$497$		−	464783.i		−	0.0844033i
$498$			617854.i			0.111638i
$499$	9.37761e6			1.68594			0.842968	−	0.537964i	$-0.180806\pi$
$499$	9.37761e6			1.68594			0.842968	+	0.537964i	$0.180806\pi$
$500$	−3.37413e6	+	1.37705e6i	−0.603583	+	0.246335i
$501$	−2.67765e6			−0.476606
$502$			3.95430e6i			0.700343i
$503$			4.35545e6i			0.767562i	0.923424	+	0.383781i	$0.125378\pi$
$503$			4.35545e6i			0.767562i	−0.923424	+	0.383781i	$0.874622\pi$
$504$	−1.47866e6			−0.259293
$505$	−1.21383e6	+	2.91610e6i	−0.211802	+	0.508832i
$506$	1.00895e6			0.175184
$507$			2.18864e6i			0.378142i
$508$		−	814615.i		−	0.140053i
$509$	−1.05979e7			−1.81311			−0.906556	−	0.422086i	$-0.861298\pi$
$509$	−1.05979e7			−1.81311			−0.906556	+	0.422086i	$0.861298\pi$
$510$	3.20524e6	+	1.33418e6i	0.545676	+	0.227138i
$511$	3.47253e6			0.588294
$512$			909912.i			0.153400i
$513$			962402.i			0.161459i
$514$	−1.02794e6			−0.171617
$515$	4.93325e6	+	2.05347e6i	0.819625	+	0.341169i
$516$	−2.02096e6			−0.334143
$517$			354161.i			0.0582739i
$518$		−	1.80086e6i		−	0.294886i
$519$	448540.			0.0730942
$520$	1.35653e6	−	3.25893e6i	0.219999	−	0.528526i
$521$	6.52699e6			1.05346			0.526731	−	0.850032i	$-0.323418\pi$
$521$	6.52699e6			1.05346			0.526731	+	0.850032i	$0.323418\pi$
$522$			448108.i			0.0719791i
$523$		−	9.35815e6i		−	1.49601i	−0.663690	−	0.748007i	$-0.731011\pi$
$523$		−	9.35815e6i		−	1.49601i	0.663690	−	0.748007i	$-0.268989\pi$
$524$	−3.18839e6			−0.507275
$525$	−2.05065e6	−	2.06495e6i	−0.324708	−	0.326972i
$526$	−6.41801e6			−1.01143
$527$		−	9.69837e6i		−	1.52115i
$528$			85762.6i			0.0133879i
$529$	194157.			0.0301657
$530$	1.54362e6	−	3.70840e6i	0.238700	−	0.573452i
$531$	−367829.			−0.0566121
$532$			2.84969e6i			0.436534i
$533$		−	4.85955e6i		−	0.740932i
$534$	−3.33771e6			−0.506518
$535$	−1.09228e7	−	4.54663e6i	−1.64987	−	0.686761i
$536$	−9.78685e6			−1.47140
$537$			7.42860e6i			1.11166i
$538$			3.82247e6i			0.569361i
$539$	738139.			0.109438
$540$	−784866.	−	326701.i	−0.115827	−	0.0482132i
$541$	9.93079e6			1.45878			0.729392	−	0.684096i	$-0.239803\pi$
$541$	9.93079e6			1.45878			0.729392	+	0.684096i	$0.239803\pi$
$542$		−	2.46140e6i		−	0.359901i
$543$		−	5.68188e6i		−	0.826975i
$544$	1.22163e7			1.76988
$545$	−7964.34	+	19133.5i	−0.00114857	+	0.00275933i
$546$	1.11245e6			0.159698
$547$			8.79495e6i			1.25680i	0.777891	+	0.628399i	$0.216289\pi$
$547$			8.79495e6i			1.25680i	−0.777891	+	0.628399i	$0.783711\pi$
$548$		−	6.75625e6i		−	0.961068i
$549$	−295614.			−0.0418595
$550$	895451.	−	889250.i	0.126222	−	0.125348i
$551$	2.18831e6			0.307065
$552$			3.96704e6i			0.554139i
$553$		−	818685.i		−	0.113842i
$554$	6.38974e6			0.884522
$555$	1.00823e6	−	2.42216e6i	0.138939	−	0.333788i
$556$	−4.08725e6			−0.560717
$557$		−	2.78134e6i		−	0.379853i	−0.981798	−	0.189927i	$-0.939175\pi$
$557$		−	2.78134e6i		−	0.379853i	0.981798	−	0.189927i	$-0.0608250\pi$
$558$		−	1.26803e6i		−	0.172402i
$559$	3.85271e6			0.521479
$560$	−420557.	−	175057.i	−0.0566702	−	0.0235890i
$561$	2.25165e6			0.302061
$562$		−	3.66829e6i		−	0.489918i
$563$		−	460410.i		−	0.0612172i	−0.999531	−	0.0306086i	$-0.990255\pi$
$563$		−	460410.i		−	0.0612172i	0.999531	−	0.0306086i	$-0.00974455\pi$
$564$	−549539.			−0.0727446
$565$	−728975.	−	303436.i	−0.0960709	−	0.0399895i
$566$	−1.24001e6			−0.162698
$567$		−	678887.i		−	0.0886829i
$568$			792462.i			0.103064i
$569$	−8.74980e6			−1.13297			−0.566484	−	0.824073i	$-0.691697\pi$
$569$	−8.74980e6			−1.13297			−0.566484	+	0.824073i	$0.691697\pi$
$570$	851865.	−	2.04652e6i	0.109821	−	0.263833i
$571$	−8.95646e6			−1.14960			−0.574799	−	0.818295i	$-0.694920\pi$
$571$	−8.95646e6			−1.14960			−0.574799	+	0.818295i	$0.694920\pi$
$572$		−	903480.i		−	0.115459i
$573$			3.30351e6i			0.420328i
$574$	4.68866e6			0.593977
$575$	−5.53996e6	+	5.50160e6i	−0.698775	+	0.693936i
$576$	1.39311e6			0.174957
$577$			1.14055e7i			1.42618i	0.701071	+	0.713091i	$0.252706\pi$
$577$			1.14055e7i			1.42618i	−0.701071	+	0.713091i	$0.747294\pi$
$578$		−	9.52931e6i		−	1.18643i
$579$	−2.15867e6			−0.267603
$580$	−742852.	+	1.78463e6i	−0.0916921	+	0.220281i
$581$	−2.12840e6			−0.261585
$582$		−	1.75030e6i		−	0.214193i
$583$		−	2.60512e6i		−	0.317436i
$584$	−5.92072e6			−0.718361
$585$	1.49625e6	+	622815.i	0.180765	+	0.0752436i
$586$	−9.55288e6			−1.14919
$587$		−	1.05278e7i		−	1.26108i	−0.776157	−	0.630539i	$-0.782834\pi$
$587$		−	1.05278e7i		−	1.26108i	0.776157	−	0.630539i	$-0.217166\pi$
$588$			1.14534e6i			0.136613i
$589$	−6.19234e6			−0.735472
$590$	782177.	+	325582.i	0.0925071	+	0.0385061i
$591$	8.00969e6			0.943294
$592$		−	410680.i		−	0.0481614i
$593$			7.64531e6i			0.892809i	0.894831	+	0.446404i	$0.147296\pi$
$593$			7.64531e6i			0.892809i	−0.894831	+	0.446404i	$0.852704\pi$
$594$	294395.			0.0342345
$595$	−4.59602e6	+	1.10415e7i	−0.532218	+	1.27860i
$596$	−9.07566e6			−1.04656
$597$		−	22026.1i		−	0.00252931i
$598$		−	2.98455e6i		−	0.341292i
$599$	1.28357e7			1.46168			0.730838	−	0.682550i	$-0.239129\pi$
$599$	1.28357e7			1.46168			0.730838	+	0.682550i	$0.239129\pi$
$600$	3.49638e6	+	3.52076e6i	0.396498	+	0.399262i
$601$	−1.49774e7			−1.69142			−0.845710	−	0.533643i	$-0.820823\pi$
$601$	−1.49774e7			−1.69142			−0.845710	+	0.533643i	$0.820823\pi$
$602$			3.71722e6i			0.418049i
$603$		−	4.49337e6i		−	0.503245i
$604$	−1.96227e6			−0.218860
$605$	314523.	−	755610.i	0.0349353	−	0.0839285i
$606$	1.69721e6			0.187739
$607$			273921.i			0.0301754i	0.999886	+	0.0150877i	$0.00480274\pi$
$607$			273921.i			0.0301754i	−0.999886	+	0.0150877i	$0.995197\pi$
$608$		−	7.80005e6i		−	0.855733i
$609$	−1.54365e6			−0.168658
$610$	628614.	+	261661.i	0.0684006	+	0.0284718i
$611$	1.04763e6			0.113528
$612$			3.49381e6i			0.377069i
$613$		−	3.61183e6i		−	0.388219i	−0.980980	−	0.194109i	$-0.937818\pi$
$613$		−	3.61183e6i		−	0.388219i	0.980980	−	0.194109i	$-0.0621816\pi$
$614$	−8.92027e6			−0.954898
$615$	6.30629e6	+	2.62499e6i	0.672335	+	0.279860i
$616$	2.20886e6			0.234540
$617$			1.11537e7i			1.17952i	0.807579	+	0.589759i	$0.200777\pi$
$617$			1.11537e7i			1.17952i	−0.807579	+	0.589759i	$0.799223\pi$
$618$		−	2.87122e6i		−	0.302409i
$619$	8.08693e6			0.848314			0.424157	−	0.905589i	$-0.360570\pi$
$619$	8.08693e6			0.848314			0.424157	+	0.905589i	$0.360570\pi$
$620$	2.10207e6	−	5.05002e6i	0.219618	−	0.527612i
$621$	−1.82136e6			−0.189525
$622$			6.15382e6i			0.637777i
$623$		−	1.14978e7i		−	1.18685i
$624$	253691.			0.0260822
$625$	−67856.7	+	9.76539e6i	−0.00694852	+	0.999976i
$626$	−6.26582e6			−0.639060
$627$		−	1.43766e6i		−	0.146045i
$628$			4.06787e6i			0.411593i
$629$	−1.07822e7			−1.08663
$630$	−600913.	+	1.44363e6i	−0.0603199	+	0.144913i
$631$	−1.09030e7			−1.09012			−0.545060	−	0.838397i	$-0.683493\pi$
$631$	−1.09030e7			−1.09012			−0.545060	+	0.838397i	$0.683493\pi$
$632$			1.39587e6i			0.139012i
$633$			7.01248e6i			0.695605i
$634$	−6.81665e6			−0.673516
$635$	−2.01529e6	−	838867.i	−0.198337	−	0.0825579i
$636$	4.04227e6			0.396262
$637$		−	2.18346e6i		−	0.213205i
$638$		−	669396.i		−	0.0651075i
$639$	−363838.			−0.0352497
$640$	6.79523e6	+	2.82852e6i	0.655774	+	0.272966i
$641$	−1.28118e7			−1.23159			−0.615794	−	0.787907i	$-0.711165\pi$
$641$	−1.28118e7			−1.23159			−0.615794	+	0.787907i	$0.711165\pi$
$642$			6.35724e6i			0.608739i
$643$		−	4.42120e6i		−	0.421709i	−0.977517	−	0.210854i	$-0.932375\pi$
$643$		−	4.42120e6i		−	0.421709i	0.977517	−	0.210854i	$-0.0676246\pi$
$644$	−5.39308e6			−0.512415
$645$	−2.08112e6	+	4.99969e6i	−0.196969	+	0.473199i
$646$	−9.11003e6			−0.858892
$647$			2.82953e6i			0.265738i	0.991134	+	0.132869i	$0.0424189\pi$
$647$			2.82953e6i			0.265738i	−0.991134	+	0.132869i	$0.957581\pi$
$648$			1.15751e6i			0.108290i
$649$	549472.			0.0512076
$650$	−2.63046e6	−	2.64880e6i	−0.244201	−	0.245904i
$651$	4.36813e6			0.403964
$652$			3.21763e6i			0.296426i
$653$		−	1.51923e7i		−	1.39425i	−0.716948	−	0.697127i	$-0.754461\pi$
$653$		−	1.51923e7i		−	1.39425i	0.716948	−	0.697127i	$-0.245539\pi$
$654$	11136.0			0.00101809
$655$	−3.28332e6	+	7.88784e6i	−0.299026	+	0.718381i
$656$	1.06924e6			0.0970096
$657$		−	2.71834e6i		−	0.245692i
$658$			1.01079e6i			0.0910113i
$659$	1.45583e7			1.30587			0.652933	−	0.757416i	$-0.273538\pi$
$659$	1.45583e7			1.30587			0.652933	+	0.757416i	$0.273538\pi$
$660$	1.17245e6	+	488034.i	0.104770	+	0.0436104i
$661$	5.60047e6			0.498564			0.249282	−	0.968431i	$-0.419805\pi$
$661$	5.60047e6			0.498564			0.249282	+	0.968431i	$0.419805\pi$
$662$		−	8.30941e6i		−	0.736928i
$663$		−	6.66052e6i		−	0.588470i
$664$	3.62895e6			0.319419
$665$	7.04991e6	+	2.93453e6i	0.618200	+	0.257326i
$666$	−1.40973e6			−0.123155
$667$			4.14141e6i			0.360440i
$668$			6.20658e6i			0.538159i
$669$	−1.14340e7			−0.987715
$670$	−3.97729e6	+	9.55503e6i	−0.342294	+	0.822328i
$671$	441596.			0.0378633
$672$			5.50222e6i			0.470018i
$673$		−	2.22862e6i		−	0.189670i	−0.995493	−	0.0948351i	$-0.969768\pi$
$673$		−	2.22862e6i		−	0.189670i	0.995493	−	0.0948351i	$-0.0302324\pi$
$674$	−7.56081e6			−0.641089
$675$	−1.61646e6	+	1.60527e6i	−0.136555	+	0.135609i
$676$	5.07310e6			0.426979
$677$			1.47850e7i			1.23980i	0.784683	+	0.619898i	$0.212826\pi$
$677$			1.47850e7i			1.23980i	−0.784683	+	0.619898i	$0.787174\pi$
$678$			424274.i			0.0354464i
$679$	6.02949e6			0.501887
$680$	7.83629e6	−	1.88259e7i	0.649887	−	1.56129i
$681$	15803.7			0.00130584
$682$			1.89421e6i			0.155944i
$683$			415268.i			0.0340625i	0.999855	+	0.0170313i	$0.00542148\pi$
$683$			415268.i			0.0340625i	−0.999855	+	0.0170313i	$0.994579\pi$
$684$	2.23077e6			0.182312
$685$	−1.67144e7	−	6.95739e6i	−1.36102	−	0.566526i
$686$	7.91078e6			0.641814
$687$			1.66591e6i			0.134666i
$688$			847703.i			0.0682767i
$689$	−7.70610e6			−0.618424
$690$	3.87307e6	+	1.61217e6i	0.309694	+	0.128910i
$691$	8.64233e6			0.688550			0.344275	−	0.938869i	$-0.388125\pi$
$691$	8.64233e6			0.688550			0.344275	+	0.938869i	$0.388125\pi$
$692$		−	1.03968e6i		−	0.0825342i
$693$			1.01414e6i			0.0802167i
$694$	2.96187e6			0.233436
$695$	−4.20893e6	+	1.01115e7i	−0.330529	+	0.794063i
$696$	2.63195e6			0.205947
$697$		−	2.80723e7i		−	2.18875i
$698$		−	1.12751e7i		−	0.875956i
$699$	−1.55086e6			−0.120055
$700$	−4.78638e6	+	4.75323e6i	−0.369200	+	0.366644i
$701$	−1.30512e7			−1.00313			−0.501564	−	0.865121i	$-0.667242\pi$
$701$	−1.30512e7			−1.00313			−0.501564	+	0.865121i	$0.667242\pi$
$702$		−	870839.i		−	0.0666953i
$703$			6.88434e6i			0.525381i
$704$	−2.08107e6			−0.158254
$705$	−565899.	+	1.35952e6i	−0.0428811	+	0.103018i
$706$	−4.11172e6			−0.310464
$707$			5.84660e6i			0.439901i
$708$			852597.i			0.0639235i
$709$	1.56007e7			1.16555			0.582773	−	0.812635i	$-0.301968\pi$
$709$	1.56007e7			1.16555			0.582773	+	0.812635i	$0.301968\pi$
$710$	773692.	+	322049.i	0.0575999	+	0.0239760i
$711$	−640876.			−0.0475445
$712$			1.96039e7i			1.44925i
$713$		−	1.17191e7i		−	0.863317i
$714$	6.42630e6			0.471754
$715$	−2.23514e6	−	930378.i	−0.163508	−	0.0680604i
$716$	1.72189e7			1.25523
$717$		−	1.42262e7i		−	1.03345i
$718$		−	3.45887e6i		−	0.250394i
$719$	6.44874e6			0.465214			0.232607	−	0.972571i	$-0.425274\pi$
$719$	6.44874e6			0.465214			0.232607	+	0.972571i	$0.425274\pi$
$720$	−137037.	+	329217.i	−0.00985157	+	0.0236674i
$721$	9.89085e6			0.708591
$722$		−	2.44723e6i		−	0.174715i
$723$			1.29804e7i			0.923512i
$724$	−1.31701e7			−0.933779
$725$	3.65006e6	+	3.67552e6i	0.257903	+	0.259701i
$726$	−439775.			−0.0309663
$727$		−	8.36468e6i		−	0.586967i	−0.955964	−	0.293483i	$-0.905185\pi$
$727$		−	8.36468e6i		−	0.586967i	0.955964	−	0.293483i	$-0.0948145\pi$
$728$		−	6.53394e6i		−	0.456927i
$729$	−531441.			−0.0370370
$730$	−2.40613e6	+	5.78048e6i	−0.167113	+	0.401473i
$731$	2.22560e7			1.54047
$732$			685209.i			0.0472656i
$733$			3.08435e6i			0.212033i	0.994364	+	0.106017i	$0.0338097\pi$
$733$			3.08435e6i			0.212033i	−0.994364	+	0.106017i	$0.966190\pi$
$734$	1.44046e7			0.986875
$735$	2.83349e6	+	1.17944e6i	0.193466	+	0.0805301i
$736$	1.47617e7			1.00448
$737$			6.71232e6i			0.455202i
$738$		−	3.67034e6i		−	0.248065i
$739$	2.28100e7			1.53644			0.768218	−	0.640189i	$-0.221144\pi$
$739$	2.28100e7			1.53644			0.768218	+	0.640189i	$0.221144\pi$
$740$	−5.61438e6	−	2.33699e6i	−0.376897	−	0.156883i
$741$	−4.25269e6			−0.284524
$742$		−	7.43511e6i		−	0.495767i
$743$			1.21470e7i			0.807232i	0.914929	+	0.403616i	$0.132247\pi$
$743$			1.21470e7i			0.807232i	−0.914929	+	0.403616i	$0.867753\pi$
$744$	−7.44772e6			−0.493277
$745$	−9.34586e6	+	2.24525e7i	−0.616919	+	1.48209i
$746$	6.79507e6			0.447040
$747$			1.66614e6i			0.109247i
$748$		−	5.21915e6i		−	0.341072i
$749$	−2.18996e7			−1.42637
$750$	4.85827e6	−	1.98276e6i	0.315376	−	0.128711i
$751$	2.29619e7			1.48562			0.742809	−	0.669503i	$-0.233493\pi$
$751$	2.29619e7			1.48562			0.742809	+	0.669503i	$0.233493\pi$
$752$			230508.i			0.0148642i
$753$			1.06634e7i			0.685342i
$754$	−1.98011e6			−0.126842
$755$	−2.02069e6	+	4.85450e6i	−0.129012	+	0.309939i
$756$	−1.57361e6			−0.100136
$757$		−	8.97752e6i		−	0.569399i	−0.958617	−	0.284699i	$-0.908106\pi$
$757$		−	8.97752e6i		−	0.569399i	0.958617	−	0.284699i	$-0.0918938\pi$
$758$			1.22797e7i			0.776272i
$759$	2.72080e6			0.171432
$760$	−1.20202e7	−	5.00341e6i	−0.754879	−	0.314219i
$761$	1.81766e7			1.13776			0.568880	−	0.822421i	$-0.307377\pi$
$761$	1.81766e7			1.13776			0.568880	+	0.822421i	$0.307377\pi$
$762$			1.17293e6i			0.0731786i
$763$			38361.5i			0.00238553i
$764$	7.65726e6			0.474613
$765$	8.64342e6	+	3.59782e6i	0.533988	+	0.222273i
$766$	1.12010e7			0.689741
$767$		−	1.62537e6i		−	0.0997618i
$768$		−	8.90821e6i		−	0.544989i
$769$	1.53679e7			0.937127			0.468564	−	0.883430i	$-0.344772\pi$
$769$	1.53679e7			0.937127			0.468564	+	0.883430i	$0.344772\pi$
$770$	897660.	−	2.15654e6i	0.0545614	−	0.131078i
$771$	−2.77199e6			−0.167941
$772$			5.00363e6i			0.302163i
$773$			732946.i			0.0441188i	0.999757	+	0.0220594i	$0.00702229\pi$
$773$			732946.i			0.0441188i	−0.999757	+	0.0220594i	$0.992978\pi$
$774$	2.90989e6			0.174592
$775$	−1.03287e7	−	1.04007e7i	−0.617721	−	0.622028i
$776$	−1.02804e7			−0.612850
$777$		−	4.85628e6i		−	0.288570i
$778$		−	1.98406e7i		−	1.17519i
$779$	−1.79239e7			−1.05825
$780$	1.44363e6	−	3.46819e6i	0.0849612	−	0.204111i
$781$	543511.			0.0318846
$782$		−	1.72409e7i		−	1.00819i
$783$			1.20839e6i			0.0704373i
$784$	480422.			0.0279147
$785$	1.00636e7	+	4.18897e6i	0.582880	+	0.242624i
$786$	4.59083e6			0.265054
$787$		−	2.25077e7i		−	1.29537i	−0.761908	−	0.647685i	$-0.775737\pi$
$787$		−	2.25077e7i		−	1.29537i	0.761908	−	0.647685i	$-0.224263\pi$
$788$		−	1.85658e7i		−	1.06512i
$789$	−1.73071e7			−0.989767
$790$	1.36281e6	+	567268.i	0.0776902	+	0.0323386i
$791$	−1.46155e6			−0.0830562
$792$		−	1.72912e6i		−	0.0979519i
$793$		−	1.30627e6i		−	0.0737648i
$794$	1.35977e7			0.765444
$795$	4.16262e6	−	1.00003e7i	0.233587	−	0.561169i
$796$	−51054.7			−0.00285597
$797$			5.07705e6i			0.283117i	0.989930	+	0.141558i	$0.0452113\pi$
$797$			5.07705e6i			0.283117i	−0.989930	+	0.141558i	$0.954789\pi$
$798$		−	4.10314e6i		−	0.228092i
$799$	6.05185e6			0.335368
$800$	1.31011e7	−	1.30104e7i	0.723739	−	0.718727i
$801$	−9.00063e6			−0.495669
$802$			5.89149e6i			0.323437i
$803$			4.06073e6i			0.222237i
$804$	−1.04153e7			−0.568238
$805$	−5.55363e6	+	1.33421e7i	−0.302056	+	0.725660i
$806$	5.60320e6			0.303807
$807$			1.03079e7i			0.557166i
$808$		−	9.96853e6i		−	0.537159i
$809$	−1.15468e7			−0.620282			−0.310141	−	0.950691i	$-0.600376\pi$
$809$	−1.15468e7			−0.620282			−0.310141	+	0.950691i	$0.600376\pi$
$810$	1.13009e6	+	470402.i	0.0605205	+	0.0251917i
$811$	−2.62543e7			−1.40168			−0.700838	−	0.713320i	$-0.747190\pi$
$811$	−2.62543e7			−1.40168			−0.700838	+	0.713320i	$0.747190\pi$
$812$			3.57806e6i			0.190440i
$813$		−	6.63753e6i		−	0.352192i
$814$	2.10590e6			0.111398
$815$	7.96016e6	+	3.31342e6i	0.419786	+	0.174736i
$816$	1.46550e6			0.0770479
$817$		−	1.42103e7i		−	0.744813i
$818$			1.01829e7i			0.532096i
$819$	2.99989e6			0.156277
$820$	6.08452e6	−	1.46175e7i	0.316003	−	0.759167i
$821$	−3.96273e6			−0.205180			−0.102590	−	0.994724i	$-0.532713\pi$
$821$	−3.96273e6			−0.205180			−0.102590	+	0.994724i	$0.532713\pi$
$822$			9.72803e6i			0.502164i
$823$		−	9.86765e6i		−	0.507825i	−0.967227	−	0.253913i	$-0.918282\pi$
$823$		−	9.86765e6i		−	0.507825i	0.967227	−	0.253913i	$-0.0817176\pi$
$824$	−1.68640e7			−0.865254
$825$	2.41472e6	−	2.39800e6i	0.123518	−	0.122663i
$826$	1.56821e6			0.0799752
$827$		−	5.90399e6i		−	0.300180i	−0.988672	−	0.150090i	$-0.952044\pi$
$827$		−	5.90399e6i		−	0.300180i	0.988672	−	0.150090i	$-0.0479564\pi$
$828$			4.22177e6i			0.214002i
$829$	−2.38090e7			−1.20325			−0.601624	−	0.798779i	$-0.705480\pi$
$829$	−2.38090e7			−1.20325			−0.601624	+	0.798779i	$0.705480\pi$
$830$	1.47477e6	−	3.54299e6i	0.0743070	−	0.178515i
$831$	1.72309e7			0.865576
$832$			6.15593e6i			0.308309i
$833$		−	1.26132e7i		−	0.629816i
$834$	5.88505e6			0.292978
$835$	1.53546e7	+	6.39135e6i	0.762118	+	0.317232i
$836$	−3.33239e6			−0.164907
$837$		−	3.41943e6i		−	0.168709i
$838$			2.20695e7i			1.08563i
$839$	−1.88904e7			−0.926479			−0.463240	−	0.886233i	$-0.653313\pi$
$839$	−1.88904e7			−0.926479			−0.463240	+	0.886233i	$0.653313\pi$
$840$	8.47915e6	+	3.52945e6i	0.414624	+	0.172587i
$841$	−1.77635e7			−0.866042
$842$			7.65291e6i			0.372003i
$843$		−	9.89210e6i		−	0.479424i
$844$	1.62544e7			0.785442
$845$	5.22413e6	−	1.25504e7i	0.251693	−	0.604669i
$846$	791257.			0.0380095
$847$		−	1.51495e6i		−	0.0725587i
$848$		−	1.69556e6i		−	0.0809697i
$849$	−3.34387e6			−0.159214
$850$	−1.51954e7	−	1.53013e7i	−0.721381	−	0.726411i
$851$	−1.30287e7			−0.616706
$852$			843347.i			0.0398022i
$853$			2.79626e7i			1.31585i	0.753085	+	0.657924i	$0.228565\pi$
$853$			2.79626e7i			1.31585i	−0.753085	+	0.657924i	$0.771435\pi$
$854$	1.26033e6			0.0591344
$855$	2.29718e6	−	5.51875e6i	0.107468	−	0.258182i
$856$	3.73391e7			1.74172
$857$		−	2.82523e6i		−	0.131402i	−0.997839	−	0.0657009i	$-0.979072\pi$
$857$		−	2.82523e6i		−	0.131402i	0.997839	−	0.0657009i	$-0.0209283\pi$
$858$			1.30088e6i			0.0603281i
$859$	−5.68353e6			−0.262806			−0.131403	−	0.991329i	$-0.541948\pi$
$859$	−5.68353e6			−0.262806			−0.131403	+	0.991329i	$0.541948\pi$
$860$	1.15889e7	+	4.82387e6i	0.534312	+	0.222408i
$861$	1.26437e7			0.581254
$862$			1.84816e7i			0.847170i
$863$		−	2.23836e6i		−	0.102306i	−0.998691	−	0.0511532i	$-0.983710\pi$
$863$		−	2.23836e6i		−	0.102306i	0.998691	−	0.0511532i	$-0.0162897\pi$
$864$	4.30721e6			0.196296
$865$	−2.57209e6	−	1.07063e6i	−0.116881	−	0.0486519i
$866$	8.53116e6			0.386557
$867$		−	2.56972e7i		−	1.16102i
$868$		−	1.01250e7i		−	0.456136i
$869$	957359.			0.0430056
$870$	1.06960e6	−	2.56961e6i	0.0479097	−	0.115098i
$871$	1.98555e7			0.886818
$872$		−	65406.9i		−	0.00291295i
$873$		−	4.71996e6i		−	0.209605i
$874$	−1.10082e7			−0.487457
$875$	6.83026e6	+	1.67359e7i	0.301590	+	0.738972i
$876$	−6.30090e6			−0.277423
$877$		−	6.04256e6i		−	0.265291i	−0.991164	−	0.132645i	$-0.957653\pi$
$877$		−	6.04256e6i		−	0.265291i	0.991164	−	0.132645i	$-0.0423471\pi$
$878$			2.32355e6i			0.101722i
$879$	−2.57608e7			−1.12457
$880$	204709.	−	491793.i	0.00891108	−	0.0214080i
$881$	3.77877e7			1.64025			0.820126	−	0.572183i	$-0.193903\pi$
$881$	3.77877e7			1.64025			0.820126	+	0.572183i	$0.193903\pi$
$882$		−	1.64913e6i		−	0.0713812i
$883$			4.27448e7i			1.84494i	0.386070	+	0.922469i	$0.373832\pi$
$883$			4.27448e7i			1.84494i	−0.386070	+	0.922469i	$0.626168\pi$
$884$	−1.54386e7			−0.664471
$885$	2.10926e6	+	877980.i	0.0905257	+	0.0376813i
$886$	−2.27946e7			−0.975544
$887$			971018.i			0.0414398i	0.999785	+	0.0207199i	$0.00659583\pi$
$887$			971018.i			0.0414398i	−0.999785	+	0.0207199i	$0.993404\pi$
$888$			8.28002e6i			0.352370i
$889$	−4.04053e6			−0.171468
$890$	1.91396e7	+	7.96686e6i	0.809949	+	0.337142i
$891$	793881.			0.0335013
$892$			2.65030e7i			1.11528i
$893$		−	3.86406e6i		−	0.162149i
$894$	1.30677e7			0.546832
$895$	1.77315e7	−	4.25982e7i	0.739926	−	1.77760i
$896$	1.36240e7			0.566937
$897$		−	8.04828e6i		−	0.333981i
$898$			2.23043e7i			0.922990i
$899$	−7.77509e6			−0.320853
$900$	3.72089e6	+	3.74683e6i	0.153123	+	0.154191i
$901$	−4.45159e7			−1.82685
$902$			5.48286e6i			0.224383i
$903$			1.00241e7i			0.409095i
$904$	2.49196e6			0.101419
$905$	−1.35622e7	+	3.25819e7i	−0.550440	+	1.32238i
$906$	2.82538e6			0.114355
$907$		−	1.74008e7i		−	0.702348i	−0.936310	−	0.351174i	$-0.885783\pi$
$907$		−	1.74008e7i		−	0.702348i	0.936310	−	0.351174i	$-0.114217\pi$
$908$		−	36631.7i		−	0.00147449i
$909$	4.57679e6			0.183718
$910$	−6.37918e6	−	2.65533e6i	−0.255365	−	0.106296i
$911$	−1.56534e7			−0.624903			−0.312451	−	0.949934i	$-0.601150\pi$
$911$	−1.56534e7			−0.624903			−0.312451	+	0.949934i	$0.601150\pi$
$912$		−	935711.i		−	0.0372524i
$913$		−	2.48892e6i		−	0.0988175i
$914$	2.05868e6			0.0815123
$915$	1.69515e6	+	705608.i	0.0669355	+	0.0278619i
$916$	3.86144e6			0.152058
$917$			1.58146e7i			0.621062i
$918$		−	5.03059e6i		−	0.197021i
$919$	3.32140e7			1.29728			0.648639	−	0.761097i	$-0.275339\pi$
$919$	3.32140e7			1.29728			0.648639	+	0.761097i	$0.275339\pi$
$920$	9.46903e6	−	2.27484e7i	0.368838	−	0.886097i
$921$	−2.40549e7			−0.934445
$922$			1.18634e7i			0.459601i
$923$		−	1.60774e6i		−	0.0621171i
$924$	2.35069e6			0.0905766
$925$	−1.15630e7	+	1.14830e7i	−0.444343	+	0.441266i
$926$	1.08117e7			0.414348
$927$		−	7.74268e6i		−	0.295932i
$928$		−	9.79372e6i		−	0.373317i
$929$	7.05863e6			0.268338			0.134169	−	0.990958i	$-0.457164\pi$
$929$	7.05863e6			0.268338			0.134169	+	0.990958i	$0.457164\pi$
$930$	−3.02669e6	+	7.27131e6i	−0.114752	+	0.275680i
$931$	−8.05345e6			−0.304514
$932$			3.59477e6i			0.135560i
$933$			1.65947e7i			0.624116i
$934$	2.40517e7			0.902150
$935$	−1.29118e7	−	5.37453e6i	−0.483011	−	0.201053i
$936$	−5.11485e6			−0.190829
$937$			4.85427e6i			0.180624i	0.995914	+	0.0903120i	$0.0287864\pi$
$937$			4.85427e6i			0.180624i	−0.995914	+	0.0903120i	$0.971214\pi$
$938$			1.91572e7i			0.710928i
$939$	−1.68967e7			−0.625372
$940$	3.15125e6	+	1.31171e6i	0.116322	+	0.0484192i
$941$	−3.79442e7			−1.39692			−0.698460	−	0.715649i	$-0.746131\pi$
$941$	−3.79442e7			−1.39692			−0.698460	+	0.715649i	$0.746131\pi$
$942$		−	5.85715e6i		−	0.215060i
$943$		−	3.39213e7i		−	1.24220i
$944$	357627.			0.0130617
$945$	−1.62045e6	+	3.89298e6i	−0.0590278	+	0.141809i
$946$	−4.34687e6			−0.157924
$947$			1.42196e7i			0.515244i	0.966246	+	0.257622i	$0.0829389\pi$
$947$			1.42196e7i			0.515244i	−0.966246	+	0.257622i	$0.917061\pi$
$948$			1.48550e6i			0.0536849i
$949$	1.20119e7			0.432958
$950$	−9.76979e6	+	9.70214e6i	−0.351218	+	0.348786i
$951$	−1.83821e7			−0.659090
$952$		−	3.77447e7i		−	1.34978i
$953$		−	1.27436e7i		−	0.454529i	−0.973833	−	0.227264i	$-0.927022\pi$
$953$		−	1.27436e7i		−	0.454529i	0.973833	−	0.227264i	$-0.0729782\pi$
$954$	−5.82030e6			−0.207049
$955$	7.88523e6	−	1.89435e7i	0.279773	−	0.672127i
$956$	−3.29751e7			−1.16692
$957$		−	1.80513e6i		−	0.0637130i
$958$		−	2.57846e6i		−	0.0907709i
$959$	−3.35114e7			−1.17665
$960$	−7.98861e6	−	3.32526e6i	−0.279765	−	0.116452i
$961$	−6.62771e6			−0.231502
$962$		−	6.22937e6i		−	0.217023i
$963$			1.71433e7i			0.595700i
$964$	3.00875e7			1.04278
$965$	1.23786e7	+	5.15259e6i	0.427911	+	0.178118i
$966$	7.76526e6			0.267740
$967$		−	4.44841e7i		−	1.52981i	−0.644142	−	0.764906i	$-0.722785\pi$
$967$		−	4.44841e7i		−	1.52981i	0.644142	−	0.764906i	$-0.277215\pi$
$968$			2.58301e6i			0.0886008i
$969$	−2.45666e7			−0.840495
$970$	−4.17785e6	+	1.00369e7i	−0.142568	+	0.342506i
$971$	−1.58495e7			−0.539469			−0.269734	−	0.962935i	$-0.586936\pi$
$971$	−1.58495e7			−0.539469			−0.269734	+	0.962935i	$0.586936\pi$
$972$			1.23184e6i			0.0418204i
$973$			2.02730e7i			0.686492i
$974$	−1.03086e7			−0.348177
$975$	−7.09342e6	−	7.14288e6i	−0.238971	−	0.240637i
$976$	287415.			0.00965795
$977$			3.72698e7i			1.24917i	0.780958	+	0.624584i	$0.214731\pi$
$977$			3.72698e7i			1.24917i	−0.780958	+	0.624584i	$0.785269\pi$
$978$		−	4.63292e6i		−	0.154885i
$979$	1.34454e7			0.448350
$980$	2.73385e6	−	6.56781e6i	0.0909306	−	0.218452i
$981$	30029.9			0.000996279
$982$			1.60882e7i			0.532390i
$983$			1.71461e7i			0.565955i	0.959127	+	0.282978i	$0.0913222\pi$
$983$			1.71461e7i			0.565955i	−0.959127	+	0.282978i	$0.908678\pi$
$984$	−2.15577e7			−0.709764
$985$	−4.59304e7	−	1.91186e7i	−1.50838	−	0.627862i
$986$	−1.14385e7			−0.374695
$987$			2.72574e6i			0.0890619i
$988$			9.85740e6i			0.321270i
$989$	2.68932e7			0.874281
$990$	−1.68817e6	−	702700.i	−0.0547428	−	0.0227867i
$991$	3.65029e7			1.18071			0.590354	−	0.807144i	$-0.298988\pi$
$991$	3.65029e7			1.18071			0.590354	+	0.807144i	$0.298988\pi$
$992$			2.77137e7i			0.894159i
$993$		−	2.24076e7i		−	0.721143i
$994$	1.55120e6			0.0497969
$995$	−52574.7	+	126305.i	−0.00168352	+	0.00404450i
$996$	3.86197e6			0.123356
$997$		−	5.88370e6i		−	0.187462i	−0.995598	−	0.0937309i	$-0.970121\pi$
$997$		−	5.88370e6i		−	0.187462i	0.995598	−	0.0937309i	$-0.0298793\pi$
$998$			3.12975e7i			0.994681i
$999$	−3.80155e6			−0.120517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.b.34.16	yes	26
5.2	odd	4		825.6.a.y.1.5		13
5.3	odd	4		825.6.a.v.1.9		13
5.4	even	2	inner	165.6.c.b.34.11	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.b.34.11	✓	26	5.4	even	2	inner
165.6.c.b.34.16	yes	26	1.1	even	1	trivial
825.6.a.v.1.9		13	5.3	odd	4
825.6.a.y.1.5		13	5.2	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)

\(f(q)\)	\(=\)	\(q+3.33747i q^{2} +9.00000i q^{3} +20.8613 q^{4} +(21.4823 - 51.6092i) q^{5} -30.0373 q^{6} -103.473i q^{7} +176.423i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q+3.33747i q^{2} +9.00000i q^{3} +20.8613 q^{4} +(21.4823 - 51.6092i) q^{5} -30.0373 q^{6} -103.473i q^{7} +176.423i q^{8} -81.0000 q^{9} +(172.244 + 71.6967i) q^{10} +121.000 q^{11} +187.751i q^{12} -357.925i q^{13} +345.339 q^{14} +(464.483 + 193.341i) q^{15} +78.7535 q^{16} -2067.63i q^{17} -270.335i q^{18} -1320.17 q^{19} +(448.149 - 1076.63i) q^{20} +931.258 q^{21} +403.834i q^{22} -2498.44i q^{23} -1587.81 q^{24} +(-2202.02 - 2217.37i) q^{25} +1194.57 q^{26} -729.000i q^{27} -2158.58i q^{28} -1657.60 q^{29} +(-645.271 + 1550.20i) q^{30} +4690.57 q^{31} +5908.38i q^{32} +1089.00i q^{33} +6900.67 q^{34} +(-5340.16 - 2222.84i) q^{35} -1689.76 q^{36} -5214.75i q^{37} -4406.02i q^{38} +3221.33 q^{39} +(9105.05 + 3789.98i) q^{40} +13577.0 q^{41} +3108.05i q^{42} +10764.0i q^{43} +2524.21 q^{44} +(-1740.07 + 4180.34i) q^{45} +8338.46 q^{46} +2926.95i q^{47} +708.782i q^{48} +6100.32 q^{49} +(7400.42 - 7349.18i) q^{50} +18608.7 q^{51} -7466.78i q^{52} -21529.9i q^{53} +2433.02 q^{54} +(2599.36 - 6244.71i) q^{55} +18255.0 q^{56} -11881.5i q^{57} -5532.19i q^{58} +4541.09 q^{59} +(9689.70 + 4033.34i) q^{60} +3649.55 q^{61} +15654.6i q^{62} +8381.32i q^{63} -17198.9 q^{64} +(-18472.2 - 7689.07i) q^{65} -3634.51 q^{66} +55473.7i q^{67} -43133.4i q^{68} +22485.9 q^{69} +(7418.68 - 17822.6i) q^{70} +4491.83 q^{71} -14290.3i q^{72} +33559.8i q^{73} +17404.1 q^{74} +(19956.4 - 19818.2i) q^{75} -27540.4 q^{76} -12520.2i q^{77} +10751.1i q^{78} +7912.05 q^{79} +(1691.81 - 4064.41i) q^{80} +6561.00 q^{81} +45312.9i q^{82} -20569.6i q^{83} +19427.2 q^{84} +(-106709. - 44417.6i) q^{85} -35924.5 q^{86} -14918.4i q^{87} +21347.2i q^{88} +111119. q^{89} +(-13951.8 - 5807.43i) q^{90} -37035.6 q^{91} -52120.6i q^{92} +42215.1i q^{93} -9768.61 q^{94} +(-28360.3 + 68132.8i) q^{95} -53175.4 q^{96} +58271.1i q^{97} +20359.7i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Introduction

L-functions

Modular forms

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