LMFDB - Embedded newform 165.6.c.b.34.19

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			34.19
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.09558i q^{2} -9.00000i q^{3} +6.03505 q^{4} +(54.3767 - 12.9683i) q^{5} +45.8602 q^{6} +170.277i q^{7} +193.811i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q+5.09558i q^{2} -9.00000i q^{3} +6.03505 q^{4} +(54.3767 - 12.9683i) q^{5} +45.8602 q^{6} +170.277i q^{7} +193.811i q^{8} -81.0000 q^{9} +(66.0813 + 277.081i) q^{10} +121.000 q^{11} -54.3155i q^{12} -364.335i q^{13} -867.659 q^{14} +(-116.715 - 489.390i) q^{15} -794.456 q^{16} +1307.63i q^{17} -412.742i q^{18} -619.655 q^{19} +(328.166 - 78.2647i) q^{20} +1532.49 q^{21} +616.565i q^{22} +922.189i q^{23} +1744.30 q^{24} +(2788.64 - 1410.35i) q^{25} +1856.50 q^{26} +729.000i q^{27} +1027.63i q^{28} +3433.99 q^{29} +(2493.73 - 594.731i) q^{30} +1479.05 q^{31} +2153.73i q^{32} -1089.00i q^{33} -6663.11 q^{34} +(2208.21 + 9259.08i) q^{35} -488.839 q^{36} +5289.91i q^{37} -3157.50i q^{38} -3279.02 q^{39} +(2513.40 + 10538.8i) q^{40} -7669.49 q^{41} +7808.93i q^{42} +17366.5i q^{43} +730.242 q^{44} +(-4404.51 + 1050.44i) q^{45} -4699.09 q^{46} -6946.36i q^{47} +7150.11i q^{48} -12187.2 q^{49} +(7186.56 + 14209.8i) q^{50} +11768.6 q^{51} -2198.78i q^{52} -17379.4i q^{53} -3714.68 q^{54} +(6579.58 - 1569.17i) q^{55} -33001.5 q^{56} +5576.90i q^{57} +17498.2i q^{58} -34047.9 q^{59} +(-704.382 - 2953.50i) q^{60} +48554.5 q^{61} +7536.59i q^{62} -13792.4i q^{63} -36397.1 q^{64} +(-4724.83 - 19811.3i) q^{65} +5549.09 q^{66} +34368.8i q^{67} +7891.59i q^{68} +8299.70 q^{69} +(-47180.4 + 11252.1i) q^{70} +48448.3 q^{71} -15698.7i q^{72} +59439.7i q^{73} -26955.1 q^{74} +(-12693.2 - 25097.8i) q^{75} -3739.65 q^{76} +20603.5i q^{77} -16708.5i q^{78} -3591.22 q^{79} +(-43199.9 + 10302.8i) q^{80} +6561.00 q^{81} -39080.5i q^{82} -64310.2i q^{83} +9248.67 q^{84} +(16957.7 + 71104.3i) q^{85} -88492.6 q^{86} -30905.9i q^{87} +23451.1i q^{88} -26956.3 q^{89} +(-5352.58 - 22443.5i) q^{90} +62037.9 q^{91} +5565.46i q^{92} -13311.4i q^{93} +35395.8 q^{94} +(-33694.8 + 8035.91i) q^{95} +19383.5 q^{96} +16545.8i q^{97} -62100.8i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			5.09558i			0.900780i	0.892832	+	0.450390i	$0.148715\pi$
$2$			5.09558i			0.900780i	−0.892832	+	0.450390i	$0.851285\pi$
$3$		−	9.00000i		−	0.577350i
$3$		−	9.00000i		−	0.577350i
$4$	6.03505			0.188595
$5$	54.3767	−	12.9683i	0.972719	−	0.231985i
$5$	54.3767	−	12.9683i	0.972719	−	0.231985i
$6$	45.8602			0.520066
$7$			170.277i			1.31344i	0.754134	+	0.656720i	$0.228057\pi$
$7$			170.277i			1.31344i	−0.754134	+	0.656720i	$0.771943\pi$
$8$			193.811i			1.07066i
$9$	−81.0000			−0.333333
$10$	66.0813	+	277.081i	0.208967	+	0.876206i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$		−	54.3155i		−	0.108886i
$13$		−	364.335i		−	0.597920i	−0.954266	−	0.298960i	$-0.903360\pi$
$13$		−	364.335i		−	0.597920i	0.954266	−	0.298960i	$-0.0966397\pi$
$14$	−867.659			−1.18312
$15$	−116.715	−	489.390i	−0.133937	−	0.561600i
$16$	−794.456			−0.775836
$17$			1307.63i			1.09739i	0.836023	+	0.548695i	$0.184875\pi$
$17$			1307.63i			1.09739i	−0.836023	+	0.548695i	$0.815125\pi$
$18$		−	412.742i		−	0.300260i
$19$	−619.655			−0.393791			−0.196896	−	0.980424i	$-0.563086\pi$
$19$	−619.655			−0.393791			−0.196896	+	0.980424i	$0.563086\pi$
$20$	328.166	−	78.2647i	0.183450	−	0.0437513i
$21$	1532.49			0.758315
$22$			616.565i			0.271595i
$23$			922.189i			0.363497i	0.983345	+	0.181748i	$0.0581756\pi$
$23$			922.189i			0.363497i	−0.983345	+	0.181748i	$0.941824\pi$
$24$	1744.30			0.618148
$25$	2788.64	−	1410.35i	0.892366	−	0.451312i
$26$	1856.50			0.538594
$27$			729.000i			0.192450i
$28$			1027.63i			0.247709i
$29$	3433.99			0.758235			0.379118	−	0.925349i	$-0.376228\pi$
$29$	3433.99			0.758235			0.379118	+	0.925349i	$0.376228\pi$
$30$	2493.73	−	594.731i	0.505878	−	0.120647i
$31$	1479.05			0.276425			0.138212	−	0.990403i	$-0.455864\pi$
$31$	1479.05			0.276425			0.138212	+	0.990403i	$0.455864\pi$
$32$			2153.73i			0.371805i
$33$		−	1089.00i		−	0.174078i
$34$	−6663.11			−0.988507
$35$	2208.21	+	9259.08i	0.304698	+	1.27761i
$36$	−488.839			−0.0628651
$37$			5289.91i			0.635249i	0.948217	+	0.317624i	$0.102885\pi$
$37$			5289.91i			0.635249i	−0.948217	+	0.317624i	$0.897115\pi$
$38$		−	3157.50i		−	0.354719i
$39$	−3279.02			−0.345209
$40$	2513.40	+	10538.8i	0.248378	+	1.04145i
$41$	−7669.49			−0.712536			−0.356268	−	0.934384i	$-0.615951\pi$
$41$	−7669.49			−0.712536			−0.356268	+	0.934384i	$0.615951\pi$
$42$			7808.93i			0.683075i
$43$			17366.5i			1.43233i	0.697933	+	0.716164i	$0.254104\pi$
$43$			17366.5i			1.43233i	−0.697933	+	0.716164i	$0.745896\pi$
$44$	730.242			0.0568637
$45$	−4404.51	+	1050.44i	−0.324240	+	0.0773283i
$46$	−4699.09			−0.327430
$47$		−	6946.36i		−	0.458683i	−0.973346	−	0.229342i	$-0.926343\pi$
$47$		−	6946.36i		−	0.458683i	0.973346	−	0.229342i	$-0.0736573\pi$
$48$			7150.11i			0.447929i
$49$	−12187.2			−0.725126
$50$	7186.56	+	14209.8i	0.406533	+	0.803825i
$51$	11768.6			0.633578
$52$		−	2198.78i		−	0.112765i
$53$		−	17379.4i		−	0.849857i	−0.905227	−	0.424929i	$-0.860299\pi$
$53$		−	17379.4i		−	0.849857i	0.905227	−	0.424929i	$-0.139701\pi$
$54$	−3714.68			−0.173355
$55$	6579.58	−	1569.17i	0.293286	−	0.0699461i
$56$	−33001.5			−1.40625
$57$			5576.90i			0.227356i
$58$			17498.2i			0.683003i
$59$	−34047.9			−1.27339			−0.636693	−	0.771117i	$-0.719698\pi$
$59$	−34047.9			−1.27339			−0.636693	+	0.771117i	$0.719698\pi$
$60$	−704.382	−	2953.50i	−0.0252598	−	0.105915i
$61$	48554.5			1.67073			0.835363	−	0.549699i	$-0.185258\pi$
$61$	48554.5			1.67073			0.835363	+	0.549699i	$0.185258\pi$
$62$			7536.59i			0.248998i
$63$		−	13792.4i		−	0.437813i
$64$	−36397.1			−1.11075
$65$	−4724.83	−	19811.3i	−0.138708	−	0.581608i
$66$	5549.09			0.156806
$67$			34368.8i			0.935358i	0.883898	+	0.467679i	$0.154910\pi$
$67$			34368.8i			0.935358i	−0.883898	+	0.467679i	$0.845090\pi$
$68$			7891.59i			0.206963i
$69$	8299.70			0.209865
$70$	−47180.4	+	11252.1i	−1.15084	+	0.274466i
$71$	48448.3			1.14060			0.570299	−	0.821437i	$-0.306827\pi$
$71$	48448.3			1.14060			0.570299	+	0.821437i	$0.306827\pi$
$72$		−	15698.7i		−	0.356888i
$73$			59439.7i			1.30548i	0.757583	+	0.652739i	$0.226380\pi$
$73$			59439.7i			1.30548i	−0.757583	+	0.652739i	$0.773620\pi$
$74$	−26955.1			−0.572219
$75$	−12693.2	−	25097.8i	−0.260565	−	0.515208i
$76$	−3739.65			−0.0742673
$77$			20603.5i			0.396017i
$78$		−	16708.5i		−	0.310957i
$79$	−3591.22			−0.0647402			−0.0323701	−	0.999476i	$-0.510306\pi$
$79$	−3591.22			−0.0647402			−0.0323701	+	0.999476i	$0.510306\pi$
$80$	−43199.9	+	10302.8i	−0.754671	+	0.179982i
$81$	6561.00			0.111111
$82$		−	39080.5i		−	0.641838i
$83$		−	64310.2i		−	1.02467i	−0.858785	−	0.512336i	$-0.828780\pi$
$83$		−	64310.2i		−	1.02467i	0.858785	−	0.512336i	$-0.171220\pi$
$84$	9248.67			0.143015
$85$	16957.7	+	71104.3i	0.254578	+	1.06745i
$86$	−88492.6			−1.29021
$87$		−	30905.9i		−	0.437767i
$88$			23451.1i			0.322817i
$89$	−26956.3			−0.360732			−0.180366	−	0.983600i	$-0.557728\pi$
$89$	−26956.3			−0.360732			−0.180366	+	0.983600i	$0.557728\pi$
$90$	−5352.58	−	22443.5i	−0.0696558	−	0.292069i
$91$	62037.9			0.785332
$92$			5565.46i			0.0685538i
$93$		−	13311.4i		−	0.159594i
$94$	35395.8			0.413173
$95$	−33694.8	+	8035.91i	−0.383049	+	0.0913536i
$96$	19383.5			0.214662
$97$			16545.8i			0.178549i	0.996007	+	0.0892745i	$0.0284548\pi$
$97$			16545.8i			0.178549i	−0.996007	+	0.0892745i	$0.971545\pi$
$98$		−	62100.8i		−	0.653179i
$99$	−9801.00			−0.100504
$100$	16829.6	−	8511.55i	0.168296	−	0.0851155i
$101$	137886.			1.34498			0.672492	−	0.740104i	$-0.265224\pi$
$101$	137886.			1.34498			0.672492	+	0.740104i	$0.265224\pi$
$102$			59968.0i			0.570715i
$103$			63842.9i			0.592952i	0.955040	+	0.296476i	$0.0958116\pi$
$103$			63842.9i			0.592952i	−0.955040	+	0.296476i	$0.904188\pi$
$104$	70612.1			0.640171
$105$	83331.8	−	19873.9i	0.737628	−	0.175918i
$106$	88558.3			0.765534
$107$		−	37586.9i		−	0.317378i	−0.987329	−	0.158689i	$-0.949273\pi$
$107$		−	37586.9i		−	0.317378i	0.987329	−	0.158689i	$-0.0507267\pi$
$108$			4399.55i			0.0362952i
$109$	148487.			1.19708			0.598538	−	0.801095i	$-0.295749\pi$
$109$	148487.			1.19708			0.598538	+	0.801095i	$0.295749\pi$
$110$	7995.83	+	33526.8i	0.0630060	+	0.264186i
$111$	47609.2			0.366761
$112$		−	135277.i		−	1.01901i
$113$		−	189126.i		−	1.39333i	−0.717395	−	0.696666i	$-0.754666\pi$
$113$		−	189126.i		−	1.39333i	0.717395	−	0.696666i	$-0.245334\pi$
$114$	−28417.5			−0.204797
$115$	11959.3	+	50145.6i	0.0843257	+	0.353580i
$116$	20724.3			0.143000
$117$			29511.2i			0.199307i
$118$		−	173494.i		−	1.14704i
$119$	−222658.			−1.44136
$120$	94849.0	−	22620.6i	0.601284	−	0.143401i
$121$	14641.0			0.0909091
$122$			247413.i			1.50496i
$123$			69025.4i			0.411383i
$124$	8926.12			0.0521325
$125$	133347.	−	112854.i	0.763324	−	0.646016i
$126$	70280.4			0.394374
$127$		−	308080.i		−	1.69494i	−0.530846	−	0.847469i	$-0.678126\pi$
$127$		−	308080.i		−	1.69494i	0.530846	−	0.847469i	$-0.321874\pi$
$128$		−	116545.i		−	0.628737i
$129$	156299.			0.826954
$130$	100950.	−	24075.7i	0.523901	−	0.124946i
$131$	64949.6			0.330673			0.165336	−	0.986237i	$-0.447129\pi$
$131$	64949.6			0.330673			0.165336	+	0.986237i	$0.447129\pi$
$132$		−	6572.17i		−	0.0328303i
$133$		−	105513.i		−	0.517222i
$134$	−175129.			−0.842552
$135$	9453.93	+	39640.6i	0.0446455	+	0.187200i
$136$	−253432.			−1.17493
$137$		−	306828.i		−	1.39667i	−0.715772	−	0.698334i	$-0.753925\pi$
$137$		−	306828.i		−	1.39667i	0.715772	−	0.698334i	$-0.246075\pi$
$138$			42291.8i			0.189042i
$139$	−416315.			−1.82762			−0.913808	−	0.406147i	$-0.866872\pi$
$139$	−416315.			−1.82762			−0.913808	+	0.406147i	$0.866872\pi$
$140$	13326.7	+	55879.1i	0.0574647	+	0.240951i
$141$	−62517.3			−0.264821
$142$			246872.i			1.02743i
$143$		−	44084.6i		−	0.180280i
$144$	64351.0			0.258612
$145$	186729.	−	44533.2i	0.737550	−	0.175899i
$146$	−302880.			−1.17595
$147$			109685.i			0.418651i
$148$			31924.9i			0.119805i
$149$	−478891.			−1.76714			−0.883570	−	0.468300i	$-0.844867\pi$
$149$	−478891.			−1.76714			−0.883570	+	0.468300i	$0.844867\pi$
$150$	127888.	−	64679.0i	0.464089	−	0.234712i
$151$	251861.			0.898914			0.449457	−	0.893302i	$-0.351618\pi$
$151$	251861.			0.898914			0.449457	+	0.893302i	$0.351618\pi$
$152$		−	120096.i		−	0.421618i
$153$		−	105918.i		−	0.365797i
$154$	−104987.			−0.356724
$155$	80425.5	−	19180.8i	0.268884	−	0.0641264i
$156$	−19789.1			−0.0651049
$157$		−	35343.5i		−	0.114435i	−0.998362	−	0.0572177i	$-0.981777\pi$
$157$		−	35343.5i		−	0.114435i	0.998362	−	0.0572177i	$-0.0182229\pi$
$158$		−	18299.3i		−	0.0583167i
$159$	−156415.			−0.490665
$160$	27930.3	+	117112.i	0.0862532	+	0.361662i
$161$	−157027.			−0.477431
$162$			33432.1i			0.100087i
$163$		−	482364.i		−	1.42202i	−0.703182	−	0.711010i	$-0.748238\pi$
$163$		−	482364.i		−	1.42202i	0.703182	−	0.711010i	$-0.251762\pi$
$164$	−46285.8			−0.134381
$165$	−14122.5	−	59216.2i	−0.0403834	−	0.169329i
$166$	327698.			0.923003
$167$			285420.i			0.791941i	0.918263	+	0.395970i	$0.129592\pi$
$167$			285420.i			0.791941i	−0.918263	+	0.395970i	$0.870408\pi$
$168$			297013.i			0.811900i
$169$	238553.			0.642492
$170$	−362318.	+	86409.5i	−0.961540	+	0.229319i
$171$	50192.1			0.131264
$172$			104808.i			0.270130i
$173$		−	473489.i		−	1.20280i	−0.798947	−	0.601402i	$-0.794609\pi$
$173$		−	473489.i		−	1.20280i	0.798947	−	0.601402i	$-0.205391\pi$
$174$	157484.			0.394332
$175$	240150.	+	474841.i	0.592772	+	1.17207i
$176$	−96129.2			−0.233923
$177$			306431.i			0.735190i
$178$		−	137358.i		−	0.324940i
$179$	−487786.			−1.13788			−0.568940	−	0.822379i	$-0.692646\pi$
$179$	−487786.			−1.13788			−0.568940	+	0.822379i	$0.692646\pi$
$180$	−26581.5	+	6339.44i	−0.0611501	+	0.0145838i
$181$	−129180.			−0.293088			−0.146544	−	0.989204i	$-0.546815\pi$
$181$	−129180.			−0.293088			−0.146544	+	0.989204i	$0.546815\pi$
$182$			316119.i			0.707411i
$183$		−	436991.i		−	0.964594i
$184$	−178730.			−0.389182
$185$	68601.3	+	287647.i	0.147368	+	0.617919i
$186$	67829.3			0.143759
$187$			158223.i			0.330876i
$188$		−	41921.7i		−	0.0865056i
$189$	−124132.			−0.252772
$190$	−40947.6	−	171695.i	−0.0822895	−	0.345042i
$191$	−386800.			−0.767191			−0.383595	−	0.923501i	$-0.625314\pi$
$191$	−386800.			−0.767191			−0.383595	+	0.923501i	$0.625314\pi$
$192$			327574.i			0.641292i
$193$		−	618444.i		−	1.19511i	−0.801828	−	0.597554i	$-0.796139\pi$
$193$		−	618444.i		−	1.19511i	0.801828	−	0.597554i	$-0.203861\pi$
$194$	−84310.3			−0.160833
$195$	−178302.	+	42523.4i	−0.335792	+	0.0800833i
$196$	−73550.3			−0.136755
$197$		−	870016.i		−	1.59721i	−0.601856	−	0.798605i	$-0.705572\pi$
$197$		−	870016.i		−	1.59721i	0.601856	−	0.798605i	$-0.294428\pi$
$198$		−	49941.8i		−	0.0905318i
$199$	903963.			1.61815			0.809074	−	0.587707i	$-0.199969\pi$
$199$	903963.			1.61815			0.809074	+	0.587707i	$0.199969\pi$
$200$	273341.	+	540469.i	0.483203	+	0.955423i
$201$	309320.			0.540029
$202$			702610.i			1.21153i
$203$			584729.i			0.995897i
$204$	71024.3			0.119490
$205$	−417041.	+	99460.6i	−0.693097	+	0.165298i
$206$	−325317.			−0.534120
$207$		−	74697.3i		−	0.121166i
$208$			289449.i			0.463888i
$209$	−74978.3			−0.118733
$210$	101269.	+	424624.i	0.158463	+	0.664440i
$211$	414396.			0.640780			0.320390	−	0.947286i	$-0.396186\pi$
$211$	414396.			0.640780			0.320390	+	0.947286i	$0.396186\pi$
$212$		−	104886.i		−	0.160279i
$213$		−	436034.i		−	0.658524i
$214$	191527.			0.285888
$215$	225215.	+	944335.i	0.332278	+	1.39325i
$216$	−141288.			−0.206049
$217$			251847.i			0.363068i
$218$			756626.i			1.07830i
$219$	534957.			0.753718
$220$	39708.1	−	9470.03i	0.0553124	−	0.0131915i
$221$	476414.			0.656151
$222$			242596.i			0.330371i
$223$		−	526103.i		−	0.708449i	−0.935160	−	0.354224i	$-0.884745\pi$
$223$		−	526103.i		−	0.708449i	0.935160	−	0.354224i	$-0.115255\pi$
$224$	−366729.			−0.488344
$225$	−225880.	+	114238.i	−0.297455	+	0.150437i
$226$	963706.			1.25509
$227$			582127.i			0.749813i	0.927063	+	0.374907i	$0.122325\pi$
$227$			582127.i			0.749813i	−0.927063	+	0.374907i	$0.877675\pi$
$228$			33656.9i			0.0428782i
$229$	59916.3			0.0755016			0.0377508	−	0.999287i	$-0.487981\pi$
$229$	59916.3			0.0755016			0.0377508	+	0.999287i	$0.487981\pi$
$230$	−255521.	+	60939.4i	−0.318498	+	0.0759589i
$231$	185431.			0.228641
$232$			665544.i			0.811814i
$233$			282811.i			0.341276i	0.985334	+	0.170638i	$0.0545829\pi$
$233$			282811.i			0.341276i	−0.985334	+	0.170638i	$0.945417\pi$
$234$	−150377.			−0.179531
$235$	−90082.9	−	377720.i	−0.106408	−	0.446170i
$236$	−205481.			−0.240155
$237$			32321.0i			0.0373778i
$238$		−	1.13457e6i		−	1.29834i
$239$	1.69607e6			1.92065			0.960327	−	0.278875i	$-0.0899615\pi$
$239$	1.69607e6			1.92065			0.960327	+	0.278875i	$0.0899615\pi$
$240$	92725.1	+	388799.i	0.103913	+	0.435710i
$241$	−1.04493e6			−1.15890			−0.579449	−	0.815008i	$-0.696732\pi$
$241$	−1.04493e6			−1.15890			−0.579449	+	0.815008i	$0.696732\pi$
$242$			74604.4i			0.0818891i
$243$		−	59049.0i		−	0.0641500i
$244$	293029.			0.315091
$245$	−662699.	+	158048.i	−0.705344	+	0.168218i
$246$	−351724.			−0.370565
$247$			225762.i			0.235456i
$248$			286655.i			0.295958i
$249$	−578792.			−0.591594
$250$	575058.	+	679482.i	0.581918	+	0.687587i
$251$	−1.92822e6			−1.93184			−0.965921	−	0.258837i	$-0.916661\pi$
$251$	−1.92822e6			−1.93184			−0.965921	+	0.258837i	$0.916661\pi$
$252$		−	83238.0i		−	0.0825696i
$253$			111585.i			0.109598i
$254$	1.56984e6			1.52677
$255$	639939.	−	152620.i	0.616294	−	0.146981i
$256$	−570842.			−0.544397
$257$		−	686476.i		−	0.648324i	−0.946002	−	0.324162i	$-0.894918\pi$
$257$		−	686476.i		−	0.648324i	0.946002	−	0.324162i	$-0.105082\pi$
$258$			796434.i			0.744904i
$259$	−900748.			−0.834361
$260$	−28514.6	−	119563.i	−0.0261598	−	0.109689i
$261$	−278153.			−0.252745
$262$			330956.i			0.297863i
$263$		−	507368.i		−	0.452307i	−0.974092	−	0.226154i	$-0.927385\pi$
$263$		−	507368.i		−	0.452307i	0.974092	−	0.226154i	$-0.0726151\pi$
$264$	211060.			0.186378
$265$	−225383.	−	945036.i	−0.197154	−	0.826673i
$266$	537650.			0.465903
$267$			242606.i			0.208269i
$268$			207418.i			0.176404i
$269$	−717068.			−0.604198			−0.302099	−	0.953277i	$-0.597687\pi$
$269$	−717068.			−0.604198			−0.302099	+	0.953277i	$0.597687\pi$
$270$	−201992.	+	48173.2i	−0.168626	+	0.0402158i
$271$	−315074.			−0.260609			−0.130304	−	0.991474i	$-0.541595\pi$
$271$	−315074.			−0.260609			−0.130304	+	0.991474i	$0.541595\pi$
$272$		−	1.03885e6i		−	0.851395i
$273$		−	558341.i		−	0.453412i
$274$	1.56347e6			1.25809
$275$	337426.	−	170652.i	0.269058	−	0.136076i
$276$	50089.1			0.0395795
$277$			1.42881e6i			1.11885i	0.828879	+	0.559427i	$0.188979\pi$
$277$			1.42881e6i			1.11885i	−0.828879	+	0.559427i	$0.811021\pi$
$278$		−	2.12137e6i		−	1.64628i
$279$	−119803.			−0.0921416
$280$	−1.79451e6	+	427974.i	−1.36789	+	0.326229i
$281$	432306.			0.326607			0.163303	−	0.986576i	$-0.447785\pi$
$281$	432306.			0.326607			0.163303	+	0.986576i	$0.447785\pi$
$282$		−	318562.i		−	0.238545i
$283$			257624.i			0.191214i	0.995419	+	0.0956071i	$0.0304793\pi$
$283$			257624.i			0.191214i	−0.995419	+	0.0956071i	$0.969521\pi$
$284$	292388.			0.215112
$285$	72323.2	+	303253.i	0.0527431	+	0.221153i
$286$	224637.			0.162392
$287$		−	1.30594e6i		−	0.935873i
$288$		−	174452.i		−	0.123935i
$289$	−290027.			−0.204265
$290$	226922.	+	951492.i	0.158446	+	0.664370i
$291$	148912.			0.103085
$292$			358722.i			0.246207i
$293$		−	993168.i		−	0.675855i	−0.941172	−	0.337928i	$-0.890274\pi$
$293$		−	993168.i		−	0.675855i	0.941172	−	0.337928i	$-0.109726\pi$
$294$	−558907.			−0.377113
$295$	−1.85141e6	+	441545.i	−1.23865	+	0.295406i
$296$	−1.02524e6			−0.680137
$297$			88209.0i			0.0580259i
$298$		−	2.44023e6i		−	1.59180i
$299$	335986.			0.217342
$300$	−76603.9	−	151467.i	−0.0491414	−	0.0971658i
$301$	−2.95712e6			−1.88128
$302$			1.28338e6i			0.809723i
$303$		−	1.24098e6i		−	0.776527i
$304$	492289.			0.305518
$305$	2.64023e6	−	629672.i	1.62515	−	0.387583i
$306$	539712.			0.329502
$307$			1.93257e6i			1.17028i	0.810933	+	0.585139i	$0.198960\pi$
$307$			1.93257e6i			1.17028i	−0.810933	+	0.585139i	$0.801040\pi$
$308$			124343.i			0.0746870i
$309$	574587.			0.342341
$310$	97737.2	+	409815.i	0.0577638	+	0.242205i
$311$	2.35905e6			1.38305			0.691523	−	0.722354i	$-0.256940\pi$
$311$	2.35905e6			1.38305			0.691523	+	0.722354i	$0.256940\pi$
$312$		−	635509.i		−	0.369603i
$313$			133954.i			0.0772849i	0.999253	+	0.0386425i	$0.0123033\pi$
$313$			133954.i			0.0772849i	−0.999253	+	0.0386425i	$0.987697\pi$
$314$	180096.			0.103081
$315$	−178865.	−	749986.i	−0.101566	−	0.425870i
$316$	−21673.2			−0.0122097
$317$		−	1.69094e6i		−	0.945102i	−0.881303	−	0.472551i	$-0.843333\pi$
$317$		−	1.69094e6i		−	0.945102i	0.881303	−	0.472551i	$-0.156667\pi$
$318$		−	797025.i		−	0.441981i
$319$	415513.			0.228616
$320$	−1.97915e6	+	472010.i	−1.08045	+	0.257677i
$321$	−338282.			−0.183238
$322$		−	800146.i		−	0.430060i
$323$		−	810277.i		−	0.432143i
$324$	39596.0			0.0209550
$325$	−513841.	−	1.01600e6i	−0.269849	−	0.533563i
$326$	2.45792e6			1.28093
$327$		−	1.33638e6i		−	0.691132i
$328$		−	1.48643e6i		−	0.762886i
$329$	1.18280e6			0.602453
$330$	301741.	−	71962.5i	0.152528	−	0.0363765i
$331$	313289.			0.157172			0.0785860	−	0.996907i	$-0.474959\pi$
$331$	313289.			0.157172			0.0785860	+	0.996907i	$0.474959\pi$
$332$		−	388115.i		−	0.193248i
$333$		−	428482.i		−	0.211750i
$334$	−1.45438e6			−0.713364
$335$	445707.	+	1.86886e6i	0.216989	+	0.909841i
$336$	−1.21750e6			−0.588328
$337$		−	1.93465e6i		−	0.927957i	−0.885846	−	0.463979i	$-0.846421\pi$
$337$		−	1.93465e6i		−	0.927957i	0.885846	−	0.463979i	$-0.153579\pi$
$338$			1.21556e6i			0.578744i
$339$	−1.70213e6			−0.804441
$340$	102341.	+	429118.i	0.0480122	+	0.201317i
$341$	178964.			0.0833452
$342$			255758.i			0.118240i
$343$			786647.i			0.361031i
$344$	−3.36582e6			−1.53354
$345$	451310.	−	107633.i	0.204140	−	0.0486855i
$346$	2.41270e6			1.08346
$347$		−	360768.i		−	0.160844i	−0.996761	−	0.0804218i	$-0.974373\pi$
$347$		−	360768.i		−	0.160844i	0.996761	−	0.0804218i	$-0.0256267\pi$
$348$		−	186519.i		−	0.0825609i
$349$	1.67266e6			0.735095			0.367547	−	0.930005i	$-0.380198\pi$
$349$	1.67266e6			0.735095			0.367547	+	0.930005i	$0.380198\pi$
$350$	−2.41959e6	+	1.22370e6i	−1.05578	+	0.533957i
$351$	265600.			0.115070
$352$			260601.i			0.112103i
$353$		−	268287.i		−	0.114594i	−0.998357	−	0.0572971i	$-0.981752\pi$
$353$		−	268287.i		−	0.114594i	0.998357	−	0.0572971i	$-0.0182482\pi$
$354$	−1.56144e6			−0.662245
$355$	2.63446e6	−	628294.i	1.10948	−	0.264601i
$356$	−162682.			−0.0680324
$357$			2.00392e6i			0.832167i
$358$		−	2.48555e6i		−	1.02498i
$359$	2.33979e6			0.958165			0.479083	−	0.877770i	$-0.340969\pi$
$359$	2.33979e6			0.958165			0.479083	+	0.877770i	$0.340969\pi$
$360$	−203586.	−	853641.i	−0.0827925	−	0.347152i
$361$	−2.09213e6			−0.844928
$362$		−	658247.i		−	0.264008i
$363$		−	131769.i		−	0.0524864i
$364$	374402.			0.148110
$365$	770835.	+	3.23213e6i	0.302851	+	1.26986i
$366$	2.22672e6			0.868887
$367$			1.87216e6i			0.725569i	0.931873	+	0.362785i	$0.118174\pi$
$367$			1.87216e6i			0.725569i	−0.931873	+	0.362785i	$0.881826\pi$
$368$		−	732639.i		−	0.282014i
$369$	621229.			0.237512
$370$	−1.46573e6	+	349564.i	−0.556609	+	0.132746i
$371$	2.95931e6			1.11624
$372$		−	80335.1i		−	0.0300987i
$373$			1.51377e6i			0.563363i	0.959508	+	0.281681i	$0.0908921\pi$
$373$			1.51377e6i			0.563363i	−0.959508	+	0.281681i	$0.909108\pi$
$374$	−806236.			−0.298046
$375$	−1.01569e6	−	1.20013e6i	−0.372977	−	0.440705i
$376$	1.34628e6			0.491095
$377$		−	1.25112e6i		−	0.453364i
$378$		−	632524.i		−	0.227692i
$379$	2.85481e6			1.02089			0.510446	−	0.859910i	$-0.329480\pi$
$379$	2.85481e6			1.02089			0.510446	+	0.859910i	$0.329480\pi$
$380$	−203350.	+	48497.1i	−0.0722412	+	0.0172289i
$381$	−2.77272e6			−0.978572
$382$		−	1.97097e6i		−	0.691070i
$383$		−	3.23968e6i		−	1.12851i	−0.825601	−	0.564254i	$-0.809164\pi$
$383$		−	3.23968e6i		−	1.12851i	0.825601	−	0.564254i	$-0.190836\pi$
$384$	−1.04891e6			−0.363002
$385$	267193.	+	1.12035e6i	0.0918700	+	0.385214i
$386$	3.15133e6			1.07653
$387$		−	1.40669e6i		−	0.477442i
$388$			99854.6i			0.0336735i
$389$	558246.			0.187047			0.0935237	−	0.995617i	$-0.470187\pi$
$389$	558246.			0.187047			0.0935237	+	0.995617i	$0.470187\pi$
$390$	−216682.	−	908553.i	−0.0721374	−	0.302474i
$391$	−1.20588e6			−0.398897
$392$		−	2.36201e6i		−	0.776365i
$393$		−	584547.i		−	0.190914i
$394$	4.43324e6			1.43873
$395$	−195278.	+	46572.2i	−0.0629740	+	0.0150187i
$396$	−59149.6			−0.0189546
$397$			1.57535e6i			0.501651i	0.968032	+	0.250826i	$0.0807021\pi$
$397$			1.57535e6i			0.501651i	−0.968032	+	0.250826i	$0.919298\pi$
$398$			4.60622e6i			1.45760i
$399$	−949616.			−0.298618
$400$	−2.21546e6	+	1.12046e6i	−0.692330	+	0.350145i
$401$	2.98866e6			0.928145			0.464073	−	0.885797i	$-0.346388\pi$
$401$	2.98866e6			0.928145			0.464073	+	0.885797i	$0.346388\pi$
$402$			1.57616e6i			0.486448i
$403$		−	538868.i		−	0.165280i
$404$	832150.			0.253658
$405$	356765.	−	85085.3i	0.108080	−	0.0257761i
$406$	−2.97953e6			−0.897084
$407$			640079.i			0.191535i
$408$			2.28089e6i			0.678349i
$409$	−6.60301e6			−1.95179			−0.975897	−	0.218232i	$-0.929971\pi$
$409$	−6.60301e6			−1.95179			−0.975897	+	0.218232i	$0.929971\pi$
$410$	−506809.	−	2.12507e6i	−0.148897	−	0.624328i
$411$	−2.76145e6			−0.806367
$412$			385296.i			0.111828i
$413$		−	5.79757e6i		−	1.67252i
$414$	380626.			0.109143
$415$	−833997.	−	3.49697e6i	−0.237708	−	0.996717i
$416$	784678.			0.222310
$417$			3.74683e6i			1.05517i
$418$		−	382058.i		−	0.106952i
$419$	2.41796e6			0.672842			0.336421	−	0.941712i	$-0.390783\pi$
$419$	2.41796e6			0.672842			0.336421	+	0.941712i	$0.390783\pi$
$420$	502912.	−	119940.i	0.139113	−	0.0331773i
$421$	−315653.			−0.0867971			−0.0433986	−	0.999058i	$-0.513819\pi$
$421$	−315653.			−0.0867971			−0.0433986	+	0.999058i	$0.513819\pi$
$422$			2.11159e6i			0.577202i
$423$			562656.i			0.152894i
$424$	3.36832e6			0.909911
$425$	1.84421e6	+	3.64650e6i	0.495266	+	0.979274i
$426$	2.22185e6			0.593186
$427$			8.26771e6i			2.19440i
$428$		−	226839.i		−	0.0598561i
$429$	−396761.			−0.104084
$430$	−4.81193e6	+	1.14760e6i	−1.25501	+	0.299310i
$431$	−1.62617e6			−0.421669			−0.210835	−	0.977522i	$-0.567618\pi$
$431$	−1.62617e6			−0.421669			−0.210835	+	0.977522i	$0.567618\pi$
$432$		−	579159.i		−	0.149310i
$433$			756561.i			0.193921i	0.995288	+	0.0969603i	$0.0309120\pi$
$433$			756561.i			0.193921i	−0.995288	+	0.0969603i	$0.969088\pi$
$434$	−1.28331e6			−0.327044
$435$	−400798.	−	1.68056e6i	−0.101555	−	0.425825i
$436$	896126.			0.225763
$437$		−	571439.i		−	0.143142i
$438$			2.72592e6i			0.678934i
$439$	3.70064e6			0.916463			0.458232	−	0.888833i	$-0.348483\pi$
$439$	3.70064e6			0.916463			0.458232	+	0.888833i	$0.348483\pi$
$440$	304122.	+	1.27519e6i	0.0748887	+	0.314010i
$441$	987162.			0.241709
$442$			2.42761e6i			0.591048i
$443$			6.39510e6i			1.54824i	0.633039	+	0.774120i	$0.281807\pi$
$443$			6.39510e6i			1.54824i	−0.633039	+	0.774120i	$0.718193\pi$
$444$	287324.			0.0691694
$445$	−1.46579e6	+	349578.i	−0.350891	+	0.0836843i
$446$	2.68080e6			0.638157
$447$			4.31002e6i			1.02026i
$448$		−	6.19758e6i		−	1.45891i
$449$	7.10566e6			1.66337			0.831684	−	0.555249i	$-0.187377\pi$
$449$	7.10566e6			1.66337			0.831684	+	0.555249i	$0.187377\pi$
$450$	−582111.	−	1.15099e6i	−0.135511	−	0.267942i
$451$	−928008.			−0.214838
$452$		−	1.14138e6i		−	0.262776i
$453$		−	2.26675e6i		−	0.518988i
$454$	−2.96628e6			−0.675417
$455$	3.37341e6	−	804528.i	0.763908	−	0.182185i
$456$	−1.08086e6			−0.243421
$457$		−	2.49947e6i		−	0.559832i	−0.960025	−	0.279916i	$-0.909693\pi$
$457$		−	2.49947e6i		−	0.559832i	0.960025	−	0.279916i	$-0.0903066\pi$
$458$			305308.i			0.0680103i
$459$	−953259.			−0.211193
$460$	72174.8	+	302631.i	0.0159034	+	0.0666836i
$461$	−5.72233e6			−1.25407			−0.627033	−	0.778993i	$-0.715731\pi$
$461$	−5.72233e6			−1.25407			−0.627033	+	0.778993i	$0.715731\pi$
$462$			944881.i			0.205955i
$463$			5.64981e6i			1.22485i	0.790530	+	0.612423i	$0.209805\pi$
$463$			5.64981e6i			1.22485i	−0.790530	+	0.612423i	$0.790195\pi$
$464$	−2.72815e6			−0.588266
$465$	−172627.	−	723830.i	−0.0370234	−	0.155240i
$466$	−1.44108e6			−0.307415
$467$			8.10977e6i			1.72074i	0.509666	+	0.860372i	$0.329769\pi$
$467$			8.10977e6i			1.72074i	−0.509666	+	0.860372i	$0.670231\pi$
$468$			178101.i			0.0375883i
$469$	−5.85222e6			−1.22854
$470$	1.92470e6	−	459025.i	0.401901	−	0.0958498i
$471$	−318092.			−0.0660693
$472$		−	6.59885e6i		−	1.36337i
$473$			2.10135e6i			0.431863i
$474$	−164694.			−0.0336691
$475$	−1.72800e6	+	873932.i	−0.351406	+	0.177723i
$476$	−1.34375e6			−0.271833
$477$			1.40773e6i			0.283286i
$478$			8.64247e6i			1.73009i
$479$	−5.82406e6			−1.15981			−0.579905	−	0.814684i	$-0.696910\pi$
$479$	−5.82406e6			−1.15981			−0.579905	+	0.814684i	$0.696910\pi$
$480$	1.05401e6	−	251372.i	0.208806	−	0.0497983i
$481$	1.92730e6			0.379828
$482$		−	5.32454e6i		−	1.04391i
$483$			1.41325e6i			0.275645i
$484$	88359.2			0.0171450
$485$	214571.	+	899704.i	0.0414207	+	0.173678i
$486$	300889.			0.0577851
$487$		−	7.82723e6i		−	1.49550i	−0.663981	−	0.747749i	$-0.731135\pi$
$487$		−	7.82723e6i		−	1.49550i	0.663981	−	0.747749i	$-0.268865\pi$
$488$			9.41039e6i			1.78878i
$489$	−4.34127e6			−0.821004
$490$	−805345.	−	3.37683e6i	−0.151528	−	0.635359i
$491$	−5.95082e6			−1.11397			−0.556985	−	0.830523i	$-0.688042\pi$
$491$	−5.95082e6			−1.11397			−0.556985	+	0.830523i	$0.688042\pi$
$492$			416572.i			0.0775849i
$493$			4.49037e6i			0.832080i
$494$	−1.15039e6			−0.212094
$495$	−532946.	+	127103.i	−0.0977620	+	0.0233154i
$496$	−1.17504e6			−0.214460
$497$			8.24962e6i			1.49811i
$498$		−	2.94928e6i		−	0.532896i
$499$	1.80923e6			0.325269			0.162634	−	0.986686i	$-0.448001\pi$
$499$	1.80923e6			0.325269			0.162634	+	0.986686i	$0.448001\pi$
$500$	804758.	−	681082.i	0.143959	−	0.121836i
$501$	2.56878e6			0.457227
$502$		−	9.82539e6i		−	1.74016i
$503$			2.53156e6i			0.446137i	0.974803	+	0.223068i	$0.0716073\pi$
$503$			2.53156e6i			0.446137i	−0.974803	+	0.223068i	$0.928393\pi$
$504$	2.67312e6			0.468751
$505$	7.49779e6	−	1.78816e6i	1.30829	−	0.312016i
$506$	−568590.			−0.0987240
$507$		−	2.14697e6i		−	0.370943i
$508$		−	1.85928e6i		−	0.319657i
$509$	−8.24104e6			−1.40990			−0.704948	−	0.709259i	$-0.749030\pi$
$509$	−8.24104e6			−1.40990			−0.704948	+	0.709259i	$0.749030\pi$
$510$	777686.	+	3.26086e6i	0.132397	+	0.555145i
$511$	−1.01212e7			−1.71467
$512$		−	6.63821e6i		−	1.11912i
$513$		−	451729.i		−	0.0757852i
$514$	3.49799e6			0.583998
$515$	827938.	+	3.47157e6i	0.137556	+	0.576776i
$516$	943272.			0.155960
$517$		−	840510.i		−	0.138298i
$518$		−	4.58984e6i		−	0.751576i
$519$	−4.26140e6			−0.694439
$520$	3.83965e6	−	915722.i	0.622706	−	0.148510i
$521$	5.59646e6			0.903273			0.451637	−	0.892202i	$-0.350840\pi$
$521$	5.59646e6			0.903273			0.451637	+	0.892202i	$0.350840\pi$
$522$		−	1.41735e6i		−	0.227668i
$523$			1.34040e6i			0.214279i	0.994244	+	0.107140i	$0.0341692\pi$
$523$			1.34040e6i			0.214279i	−0.994244	+	0.107140i	$0.965831\pi$
$524$	391974.			0.0623634
$525$	4.27357e6	−	2.16135e6i	0.676695	−	0.342237i
$526$	2.58533e6			0.407429
$527$			1.93404e6i			0.303346i
$528$			865163.i			0.135056i
$529$	5.58591e6			0.867870
$530$	4.81551e6	−	1.14846e6i	0.744650	−	0.177592i
$531$	2.75788e6			0.424462
$532$		−	636776.i		−	0.0975456i
$533$			2.79427e6i			0.426039i
$534$	−1.23622e6			−0.187604
$535$	−487440.	−	2.04385e6i	−0.0736269	−	0.308720i
$536$	−6.66105e6			−1.00145
$537$			4.39007e6i			0.656955i
$538$		−	3.65388e6i		−	0.544250i
$539$	−1.47465e6			−0.218634
$540$	57055.0	+	239233.i	0.00841994	+	0.0353051i
$541$	2.97220e6			0.436602			0.218301	−	0.975882i	$-0.429949\pi$
$541$	2.97220e6			0.436602			0.218301	+	0.975882i	$0.429949\pi$
$542$		−	1.60548e6i		−	0.234751i
$543$			1.16262e6i			0.169215i
$544$	−2.81627e6			−0.408015
$545$	8.07422e6	−	1.92563e6i	1.16442	−	0.277703i
$546$	2.84507e6			0.408424
$547$		−	4.70253e6i		−	0.671991i	−0.941864	−	0.335995i	$-0.890927\pi$
$547$		−	4.70253e6i		−	0.671991i	0.941864	−	0.335995i	$-0.109073\pi$
$548$		−	1.85172e6i		−	0.263405i
$549$	−3.93292e6			−0.556908
$550$	869574.	+	1.71938e6i	0.122574	+	0.242362i
$551$	−2.12789e6			−0.298586
$552$			1.60857e6i			0.224694i
$553$		−	611501.i		−	0.0850324i
$554$	−7.28059e6			−1.00784
$555$	2.58883e6	−	617412.i	0.356755	−	0.0850830i
$556$	−2.51248e6			−0.344680
$557$		−	5.61923e6i		−	0.767431i	−0.923451	−	0.383715i	$-0.874644\pi$
$557$		−	5.61923e6i		−	0.767431i	0.923451	−	0.383715i	$-0.125356\pi$
$558$		−	610464.i		−	0.0829993i
$559$	6.32724e6			0.856417
$560$	−1.75433e6	−	7.35594e6i	−0.236396	−	0.991215i
$561$	1.42400e6			0.191031
$562$			2.20285e6i			0.294201i
$563$			1.12518e7i			1.49607i	0.663658	+	0.748036i	$0.269003\pi$
$563$			1.12518e7i			1.49607i	−0.663658	+	0.748036i	$0.730997\pi$
$564$	−377295.			−0.0499440
$565$	−2.45265e6	−	1.02840e7i	−0.323232	−	1.35532i
$566$	−1.31274e6			−0.172242
$567$			1.11719e6i			0.145938i
$568$			9.38979e6i			1.22120i
$569$	−3.62036e6			−0.468782			−0.234391	−	0.972142i	$-0.575310\pi$
$569$	−3.62036e6			−0.468782			−0.234391	+	0.972142i	$0.575310\pi$
$570$	−1.54525e6	+	368529.i	−0.199210	+	0.0475099i
$571$	−6.01771e6			−0.772397			−0.386199	−	0.922416i	$-0.626212\pi$
$571$	−6.01771e6			−0.772397			−0.386199	+	0.922416i	$0.626212\pi$
$572$		−	266053.i		−	0.0339999i
$573$			3.48120e6i			0.442938i
$574$	6.65450e6			0.843016
$575$	1.30061e6	+	2.57166e6i	0.164050	+	0.324372i
$576$	2.94816e6			0.370250
$577$			3.81655e6i			0.477233i	0.971114	+	0.238617i	$0.0766940\pi$
$577$			3.81655e6i			0.477233i	−0.971114	+	0.238617i	$0.923306\pi$
$578$		−	1.47785e6i		−	0.183998i
$579$	−5.56600e6			−0.689996
$580$	1.12692e6	−	268760.i	0.139099	−	0.0331738i
$581$	1.09505e7			1.34584
$582$			758793.i			0.0928572i
$583$		−	2.10291e6i		−	0.256242i
$584$	−1.15200e7			−1.39773
$585$	382711.	+	1.60472e6i	0.0462361	+	0.193869i
$586$	5.06077e6			0.608797
$587$			4.77208e6i			0.571627i	0.958285	+	0.285813i	$0.0922638\pi$
$587$			4.77208e6i			0.571627i	−0.958285	+	0.285813i	$0.907736\pi$
$588$			661953.i			0.0789558i
$589$	−916498.			−0.108854
$590$	−2.24993e6	−	9.43402e6i	−0.266096	−	1.11575i
$591$	−7.83015e6			−0.922149
$592$		−	4.20260e6i		−	0.492849i
$593$		−	1.97557e6i		−	0.230704i	−0.993325	−	0.115352i	$-0.963200\pi$
$593$		−	1.97557e6i		−	0.230704i	0.993325	−	0.115352i	$-0.0367996\pi$
$594$	−449476.			−0.0522686
$595$	−1.21074e7	+	2.88751e6i	−1.40204	+	0.334373i
$596$	−2.89013e6			−0.333274
$597$		−	8.13567e6i		−	0.934238i
$598$			1.71204e6i			0.195777i
$599$	7989.43			0.000909806			0.000454903	−	1.00000i	$-0.499855\pi$
$599$	7989.43			0.000909806			0.000454903		1.00000i	$0.499855\pi$
$600$	4.86422e6	−	2.46007e6i	0.551614	−	0.278978i
$601$	1.62885e7			1.83948			0.919741	−	0.392526i	$-0.128399\pi$
$601$	1.62885e7			1.83948			0.919741	+	0.392526i	$0.128399\pi$
$602$		−	1.50682e7i		−	1.69462i
$603$		−	2.78388e6i		−	0.311786i
$604$	1.51999e6			0.169531
$605$	796129.	−	189870.i	0.0884290	−	0.0210895i
$606$	6.32349e6			0.699480
$607$			1.05514e7i			1.16235i	0.813778	+	0.581176i	$0.197407\pi$
$607$			1.05514e7i			1.16235i	−0.813778	+	0.581176i	$0.802593\pi$
$608$		−	1.33457e6i		−	0.146414i
$609$	5.26256e6			0.574981
$610$	3.20854e6	+	1.34535e7i	0.349127	+	1.46390i
$611$	−2.53081e6			−0.274256
$612$		−	639219.i		−	0.0689876i
$613$		−	1.45442e7i		−	1.56329i	−0.623723	−	0.781645i	$-0.714381\pi$
$613$		−	1.45442e7i		−	1.56329i	0.623723	−	0.781645i	$-0.285619\pi$
$614$	−9.84757e6			−1.05416
$615$	895145.	+	3.75337e6i	0.0954346	+	0.400160i
$616$	−3.99318e6			−0.424001
$617$		−	1.74916e7i		−	1.84977i	−0.380246	−	0.924885i	$-0.624161\pi$
$617$		−	1.74916e7i		−	1.84977i	0.380246	−	0.924885i	$-0.375839\pi$
$618$			2.92785e6i			0.308374i
$619$	1.56180e7			1.63832			0.819160	−	0.573565i	$-0.194440\pi$
$619$	1.56180e7			1.63832			0.819160	+	0.573565i	$0.194440\pi$
$620$	485372.	−	115757.i	0.0507103	−	0.0120939i
$621$	−672276.			−0.0699549
$622$			1.20208e7i			1.24582i
$623$		−	4.59003e6i		−	0.473800i
$624$	2.60504e6			0.267826
$625$	5.78744e6	−	7.86593e6i	0.592634	−	0.805472i
$626$	−682573.			−0.0696167
$627$			674805.i			0.0685503i
$628$		−	213300.i		−	0.0215820i
$629$	−6.91722e6			−0.697115
$630$	3.82161e6	−	911421.i	0.383615	−	0.0914887i
$631$	9.11463e6			0.911309			0.455655	−	0.890157i	$-0.349405\pi$
$631$	9.11463e6			0.911309			0.455655	+	0.890157i	$0.349405\pi$
$632$		−	696016.i		−	0.0693149i
$633$		−	3.72956e6i		−	0.369955i
$634$	8.61630e6			0.851329
$635$	−3.99528e6	−	1.67523e7i	−0.393200	−	1.64870i
$636$	−943972.			−0.0925372
$637$			4.44022e6i			0.433567i
$638$			2.11728e6i			0.205933i
$639$	−3.92431e6			−0.380199
$640$	−1.51140e6	−	6.33733e6i	−0.145857	−	0.611585i
$641$	1.47144e7			1.41448			0.707242	−	0.706971i	$-0.249939\pi$
$641$	1.47144e7			1.41448			0.707242	+	0.706971i	$0.249939\pi$
$642$		−	1.72374e6i		−	0.165057i
$643$			1.99364e7i			1.90160i	0.309807	+	0.950799i	$0.399735\pi$
$643$			1.99364e7i			1.90160i	−0.309807	+	0.950799i	$0.600265\pi$
$644$	−947669.			−0.0900413
$645$	8.49901e6	−	2.02694e6i	0.804395	−	0.191841i
$646$	4.12883e6			0.389266
$647$		−	1.17295e7i		−	1.10159i	−0.834641	−	0.550794i	$-0.814325\pi$
$647$		−	1.17295e7i		−	1.10159i	0.834641	−	0.550794i	$-0.185675\pi$
$648$			1.27159e6i			0.118963i
$649$	−4.11980e6			−0.383940
$650$	5.17712e6	−	2.61832e6i	0.480623	−	0.243074i
$651$	2.26662e6			0.209617
$652$		−	2.91109e6i		−	0.268187i
$653$			1.62173e7i			1.48832i	0.668004	+	0.744158i	$0.267149\pi$
$653$			1.62173e7i			1.48832i	−0.668004	+	0.744158i	$0.732851\pi$
$654$	6.80964e6			0.622558
$655$	3.53174e6	−	842289.i	0.321652	−	0.0767111i
$656$	6.09307e6			0.552811
$657$		−	4.81462e6i		−	0.435159i
$658$			6.02708e6i			0.542678i
$659$	806061.			0.0723027			0.0361513	−	0.999346i	$-0.488490\pi$
$659$	806061.			0.0723027			0.0361513	+	0.999346i	$0.488490\pi$
$660$	−85230.2	−	357373.i	−0.00761612	−	0.0319346i
$661$	−1.54634e7			−1.37658			−0.688291	−	0.725435i	$-0.741639\pi$
$661$	−1.54634e7			−1.37658			−0.688291	+	0.725435i	$0.741639\pi$
$662$			1.59639e6i			0.141577i
$663$		−	4.28773e6i		−	0.378829i
$664$	1.24640e7			1.09708
$665$	−1.36833e6	−	5.73744e6i	−0.119988	−	0.503111i
$666$	2.18337e6			0.190740
$667$			3.16679e6i			0.275616i
$668$			1.72252e6i			0.149356i
$669$	−4.73493e6			−0.409023
$670$	−9.52294e6	+	2.27114e6i	−0.819566	+	0.195459i
$671$	5.87510e6			0.503743
$672$			3.30057e6i			0.281945i
$673$			3.23414e6i			0.275246i	0.990485	+	0.137623i	$0.0439462\pi$
$673$			3.23414e6i			0.275246i	−0.990485	+	0.137623i	$0.956054\pi$
$674$	9.85817e6			0.835885
$675$	1.02815e6	+	2.03292e6i	0.0868551	+	0.171736i
$676$	1.43968e6			0.121171
$677$		−	8.24825e6i		−	0.691656i	−0.938298	−	0.345828i	$-0.887598\pi$
$677$		−	8.24825e6i		−	0.691656i	0.938298	−	0.345828i	$-0.112402\pi$
$678$		−	8.67336e6i		−	0.724624i
$679$	−2.81736e6			−0.234514
$680$	−1.37808e7	+	3.28659e6i	−1.14288	+	0.272567i
$681$	5.23914e6			0.432905
$682$			911928.i			0.0750757i
$683$		−	1.23891e7i		−	1.01622i	−0.861291	−	0.508111i	$-0.830344\pi$
$683$		−	1.23891e7i		−	1.01622i	0.861291	−	0.508111i	$-0.169656\pi$
$684$	302912.			0.0247558
$685$	−3.97905e6	−	1.66843e7i	−0.324006	−	1.35857i
$686$	−4.00842e6			−0.325210
$687$		−	539247.i		−	0.0435909i
$688$		−	1.37970e7i		−	1.11125i
$689$	−6.33194e6			−0.508146
$690$	548455.	+	2.29969e6i	0.0438549	+	0.183885i
$691$	−1.75824e7			−1.40082			−0.700410	−	0.713741i	$-0.746999\pi$
$691$	−1.75824e7			−1.40082			−0.700410	+	0.713741i	$0.746999\pi$
$692$		−	2.85753e6i		−	0.226843i
$693$		−	1.66888e6i		−	0.132006i
$694$	1.83832e6			0.144885
$695$	−2.26378e7	+	5.39892e6i	−1.77776	+	0.423979i
$696$	5.98989e6			0.468701
$697$		−	1.00288e7i		−	0.781930i
$698$			8.52316e6i			0.662158i
$699$	2.54530e6			0.197036
$700$	1.44932e6	+	2.86569e6i	0.111794	+	0.221047i
$701$	−1.26176e7			−0.969797			−0.484898	−	0.874571i	$-0.661143\pi$
$701$	−1.26176e7			−0.969797			−0.484898	+	0.874571i	$0.661143\pi$
$702$			1.35339e6i			0.103652i
$703$		−	3.27792e6i		−	0.250155i
$704$	−4.40405e6			−0.334904
$705$	−3.39948e6	+	810746.i	−0.257596	+	0.0614344i
$706$	1.36708e6			0.103224
$707$			2.34788e7i			1.76656i
$708$			1.84933e6i			0.138653i
$709$	−5.87588e6			−0.438993			−0.219496	−	0.975613i	$-0.570441\pi$
$709$	−5.87588e6			−0.438993			−0.219496	+	0.975613i	$0.570441\pi$
$710$	3.20152e6	+	1.34241e7i	0.238348	+	0.999399i
$711$	290889.			0.0215801
$712$		−	5.22441e6i		−	0.386222i
$713$			1.36396e6i			0.100479i
$714$	−1.02112e7			−0.749600
$715$	−571704.	−	2.39717e6i	−0.0418221	−	0.175361i
$716$	−2.94381e6			−0.214599
$717$		−	1.52646e7i		−	1.10889i
$718$			1.19226e7i			0.863096i
$719$	9.06132e6			0.653686			0.326843	−	0.945079i	$-0.394015\pi$
$719$	9.06132e6			0.653686			0.326843	+	0.945079i	$0.394015\pi$
$720$	3.49919e6	−	834526.i	0.251557	−	0.0599941i
$721$	−1.08710e7			−0.778808
$722$		−	1.06606e7i		−	0.761095i
$723$			9.40439e6i			0.669090i
$724$	−779608.			−0.0552752
$725$	9.57617e6	−	4.84313e6i	0.676623	−	0.342201i
$726$	671440.			0.0472787
$727$			8.13363e6i			0.570753i	0.958415	+	0.285376i	$0.0921186\pi$
$727$			8.13363e6i			0.570753i	−0.958415	+	0.285376i	$0.907881\pi$
$728$			1.20236e7i			0.840826i
$729$	−531441.			−0.0370370
$730$	−1.64696e7	+	3.92785e6i	−1.14387	+	0.272802i
$731$	−2.27089e7			−1.57182
$732$		−	2.63726e6i		−	0.181918i
$733$		−	1.02344e7i		−	0.703561i	−0.936083	−	0.351780i	$-0.885576\pi$
$733$		−	1.02344e7i		−	0.703561i	0.936083	−	0.351780i	$-0.114424\pi$
$734$	−9.53976e6			−0.653578
$735$	1.42243e6	+	5.96429e6i	0.0971208	+	0.407230i
$736$	−1.98614e6			−0.135150
$737$			4.15863e6i			0.282021i
$738$			3.16552e6i			0.213946i
$739$	1.70091e7			1.14570			0.572850	−	0.819660i	$-0.305838\pi$
$739$	1.70091e7			1.14570			0.572850	+	0.819660i	$0.305838\pi$
$740$	414013.	+	1.73597e6i	0.0277929	+	0.116537i
$741$	2.03186e6			0.135940
$742$			1.50794e7i			1.00548i
$743$			1.55671e7i			1.03451i	0.855830	+	0.517257i	$0.173047\pi$
$743$			1.55671e7i			1.03451i	−0.855830	+	0.517257i	$0.826953\pi$
$744$	2.57989e6			0.170871
$745$	−2.60405e7	+	6.21042e6i	−1.71893	+	0.409950i
$746$	−7.71354e6			−0.507466
$747$			5.20912e6i			0.341557i
$748$			954882.i			0.0624016i
$749$	6.40018e6			0.416857
$750$	6.11533e6	−	5.17552e6i	0.396979	−	0.335971i
$751$	−2.29900e7			−1.48744			−0.743719	−	0.668493i	$-0.766940\pi$
$751$	−2.29900e7			−1.48744			−0.743719	+	0.668493i	$0.766940\pi$
$752$			5.51858e6i			0.355863i
$753$			1.73540e7i			1.11535i
$754$	6.37520e6			0.408381
$755$	1.36953e7	−	3.26622e6i	0.874391	−	0.208534i
$756$	−749142.			−0.0476716
$757$			1.66179e7i			1.05399i	0.849869	+	0.526994i	$0.176681\pi$
$757$			1.66179e7i			1.05399i	−0.849869	+	0.526994i	$0.823319\pi$
$758$			1.45469e7i			0.919599i
$759$	1.00426e6			0.0632766
$760$	−1.55744e6	−	6.53041e6i	−0.0978090	−	0.410116i
$761$	−2.43312e7			−1.52300			−0.761502	−	0.648162i	$-0.775538\pi$
$761$	−2.43312e7			−1.52300			−0.761502	+	0.648162i	$0.775538\pi$
$762$		−	1.41286e7i		−	0.881478i
$763$			2.52839e7i			1.57229i
$764$	−2.33436e6			−0.144689
$765$	−1.37358e6	−	5.75945e6i	−0.0848593	−	0.355818i
$766$	1.65080e7			1.01654
$767$			1.24049e7i			0.761383i
$768$			5.13758e6i			0.314308i
$769$	1.81242e7			1.10520			0.552602	−	0.833445i	$-0.313635\pi$
$769$	1.81242e7			1.10520			0.552602	+	0.833445i	$0.313635\pi$
$770$	−5.70883e6	+	1.36150e6i	−0.346993	+	0.0827546i
$771$	−6.17828e6			−0.374310
$772$		−	3.73235e6i		−	0.225392i
$773$		−	2.02819e7i		−	1.22084i	−0.792077	−	0.610422i	$-0.791000\pi$
$773$		−	2.02819e7i		−	1.22084i	0.792077	−	0.610422i	$-0.209000\pi$
$774$	7.16790e6			0.430071
$775$	4.12453e6	−	2.08597e6i	0.246672	−	0.124754i
$776$	−3.20675e6			−0.191166
$777$			8.10673e6i			0.481719i
$778$			2.84459e6i			0.168489i
$779$	4.75244e6			0.280590
$780$	−1.07606e6	+	256631.i	−0.0633288	+	0.0151033i
$781$	5.86224e6			0.343903
$782$		−	6.14465e6i		−	0.359319i
$783$			2.50338e6i			0.145922i
$784$	9.68219e6			0.562579
$785$	−458347.	−	1.92186e6i	−0.0265473	−	0.111314i
$786$	2.97860e6			0.171971
$787$		−	1.37897e7i		−	0.793630i	−0.917899	−	0.396815i	$-0.870115\pi$
$787$		−	1.37897e7i		−	0.793630i	0.917899	−	0.396815i	$-0.129885\pi$
$788$		−	5.25060e6i		−	0.301226i
$789$	−4.56631e6			−0.261140
$790$	−237312.	−	995057.i	−0.0135286	−	0.0567258i
$791$	3.22037e7			1.83006
$792$		−	1.89954e6i		−	0.107606i
$793$		−	1.76901e7i		−	0.998960i
$794$	−8.02735e6			−0.451878
$795$	−8.50532e6	+	2.02844e6i	−0.477280	+	0.113827i
$796$	5.45547e6			0.305175
$797$			3.04194e6i			0.169631i	0.996397	+	0.0848155i	$0.0270301\pi$
$797$			3.04194e6i			0.169631i	−0.996397	+	0.0848155i	$0.972970\pi$
$798$		−	4.83885e6i		−	0.268989i
$799$	9.08324e6			0.503354
$800$	3.03751e6	+	6.00597e6i	0.167800	+	0.331786i
$801$	2.18346e6			0.120244
$802$			1.52290e7i			0.836055i
$803$			7.19220e6i			0.393616i
$804$	1.86676e6			0.101847
$805$	−8.53862e6	+	2.03639e6i	−0.464406	+	0.110757i
$806$	2.74585e6			0.148881
$807$			6.45361e6i			0.348834i
$808$			2.67238e7i			1.44002i
$809$	6.70668e6			0.360277			0.180138	−	0.983641i	$-0.442345\pi$
$809$	6.70668e6			0.360277			0.180138	+	0.983641i	$0.442345\pi$
$810$	433559.	+	1.81793e6i	0.0232186	+	0.0973562i
$811$	−8.62214e6			−0.460323			−0.230162	−	0.973152i	$-0.573926\pi$
$811$	−8.62214e6			−0.460323			−0.230162	+	0.973152i	$0.573926\pi$
$812$			3.52887e6i			0.187822i
$813$			2.83566e6i			0.150463i
$814$	−3.26157e6			−0.172531
$815$	−6.25546e6	−	2.62293e7i	−0.329887	−	1.38323i
$816$	−9.34966e6			−0.491553
$817$		−	1.07613e7i		−	0.564038i
$818$		−	3.36462e7i		−	1.75814i
$819$	−5.02507e6			−0.261777
$820$	−2.51687e6	+	600250.i	−0.130715	+	0.0311744i
$821$	2.68361e7			1.38951			0.694754	−	0.719247i	$-0.255513\pi$
$821$	2.68361e7			1.38951			0.694754	+	0.719247i	$0.255513\pi$
$822$		−	1.40712e7i		−	0.726359i
$823$		−	1.23875e6i		−	0.0637508i	−0.999492	−	0.0318754i	$-0.989852\pi$
$823$		−	1.23875e6i		−	0.0637508i	0.999492	−	0.0318754i	$-0.0101480\pi$
$824$	−1.23734e7			−0.634852
$825$	−1.53587e6	−	3.03683e6i	−0.0785634	−	0.155341i
$826$	2.95420e7			1.50657
$827$			2.59198e7i			1.31786i	0.752205	+	0.658929i	$0.228990\pi$
$827$			2.59198e7i			1.31786i	−0.752205	+	0.658929i	$0.771010\pi$
$828$		−	450802.i		−	0.0228513i
$829$	6.40573e6			0.323729			0.161865	−	0.986813i	$-0.448249\pi$
$829$	6.40573e6			0.323729			0.161865	+	0.986813i	$0.448249\pi$
$830$	1.78191e7	−	4.24970e6i	0.897823	−	0.214123i
$831$	1.28593e7			0.645971
$832$			1.32607e7i			0.664140i
$833$		−	1.59363e7i		−	0.795746i
$834$	−1.90923e7			−0.950480
$835$	3.70142e6	+	1.55202e7i	0.183718	+	0.770336i
$836$	−452498.			−0.0223924
$837$			1.07822e6i			0.0531980i
$838$			1.23209e7i			0.606083i
$839$	2.24119e7			1.09919			0.549597	−	0.835430i	$-0.314781\pi$
$839$	2.24119e7			1.09919			0.549597	+	0.835430i	$0.314781\pi$
$840$	3.85177e6	+	1.61506e7i	0.188348	+	0.789751i
$841$	−8.71887e6			−0.425080
$842$		−	1.60844e6i		−	0.0781851i
$843$		−	3.89075e6i		−	0.188566i
$844$	2.50090e6			0.120848
$845$	1.29717e7	−	3.09364e6i	0.624964	−	0.149048i
$846$	−2.86706e6			−0.137724
$847$			2.49302e6i			0.119404i
$848$			1.38072e7i			0.659350i
$849$	2.31862e6			0.110398
$850$	−1.85810e7	+	9.39732e6i	−0.882110	+	0.446125i
$851$	−4.87829e6			−0.230911
$852$		−	2.63149e6i		−	0.124195i
$853$			1.15120e7i			0.541725i	0.962618	+	0.270862i	$0.0873088\pi$
$853$			1.15120e7i			0.541725i	−0.962618	+	0.270862i	$0.912691\pi$
$854$	−4.21288e7			−1.97667
$855$	2.72928e6	−	650908.i	0.127683	−	0.0304512i
$856$	7.28474e6			0.339805
$857$			1.03784e7i			0.482701i	0.970438	+	0.241350i	$0.0775903\pi$
$857$			1.03784e7i			0.482701i	−0.970438	+	0.241350i	$0.922410\pi$
$858$		−	2.02173e6i		−	0.0937572i
$859$	−2.03041e7			−0.938860			−0.469430	−	0.882970i	$-0.655541\pi$
$859$	−2.03041e7			−0.938860			−0.469430	+	0.882970i	$0.655541\pi$
$860$	1.35919e6	+	5.69911e6i	0.0626662	+	0.262761i
$861$	−1.17534e7			−0.540327
$862$		−	8.28627e6i		−	0.379831i
$863$		−	3.21077e7i		−	1.46752i	−0.679411	−	0.733758i	$-0.737765\pi$
$863$		−	3.21077e7i		−	1.46752i	0.679411	−	0.733758i	$-0.262235\pi$
$864$	−1.57007e6			−0.0715539
$865$	−6.14037e6	−	2.57468e7i	−0.279032	−	1.16999i
$866$	−3.85512e6			−0.174680
$867$			2.61024e6i			0.117932i
$868$			1.51991e6i			0.0684729i
$869$	−434537.			−0.0195199
$870$	8.56343e6	−	2.04230e6i	0.383574	−	0.0914790i
$871$	1.25218e7			0.559269
$872$			2.87783e7i			1.28166i
$873$		−	1.34021e6i		−	0.0595164i
$874$	2.91182e6			0.128939
$875$	1.92165e7	+	2.27059e7i	0.848503	+	1.00258i
$876$	3.22850e6			0.142148
$877$		−	3.06108e7i		−	1.34393i	−0.740584	−	0.671964i	$-0.765451\pi$
$877$		−	3.06108e7i		−	1.34393i	0.740584	−	0.671964i	$-0.234549\pi$
$878$			1.88569e7i			0.825532i
$879$	−8.93851e6			−0.390205
$880$	−5.22719e6	+	1.24664e6i	−0.227542	+	0.0542667i
$881$	4.04714e7			1.75675			0.878373	−	0.477976i	$-0.158629\pi$
$881$	4.04714e7			1.75675			0.878373	+	0.477976i	$0.158629\pi$
$882$			5.03016e6i			0.217726i
$883$		−	3.01707e7i		−	1.30222i	−0.758985	−	0.651108i	$-0.774304\pi$
$883$		−	3.01707e7i		−	1.30222i	0.758985	−	0.651108i	$-0.225696\pi$
$884$	2.87518e6			0.123747
$885$	3.97390e6	+	1.66627e7i	0.170553	+	0.715134i
$886$	−3.25868e7			−1.39462
$887$			1.68446e7i			0.718874i	0.933169	+	0.359437i	$0.117031\pi$
$887$			1.68446e7i			0.718874i	−0.933169	+	0.359437i	$0.882969\pi$
$888$			9.22716e6i			0.392677i
$889$	5.24588e7			2.22620
$890$	−1.78130e6	−	7.46906e6i	−0.0753812	−	0.316076i
$891$	793881.			0.0335013
$892$		−	3.17506e6i		−	0.133610i
$893$			4.30435e6i			0.180626i
$894$	−2.19620e7			−0.919028
$895$	−2.65242e7	+	6.32578e6i	−1.10684	+	0.263971i
$896$	1.98449e7			0.825809
$897$		−	3.02387e6i		−	0.125482i
$898$			3.62075e7i			1.49833i
$899$	5.07902e6			0.209595
$900$	−1.36320e6	+	689435.i	−0.0560987	+	0.0283718i
$901$	2.27258e7			0.932625
$902$		−	4.72874e6i		−	0.193521i
$903$			2.66141e7i			1.08616i
$904$	3.66546e7			1.49179
$905$	−7.02438e6	+	1.67525e6i	−0.285093	+	0.0679921i
$906$	1.15504e7			0.467494
$907$		−	3.35783e7i		−	1.35532i	−0.735377	−	0.677659i	$-0.762995\pi$
$907$		−	3.35783e7i		−	1.35532i	0.735377	−	0.677659i	$-0.237005\pi$
$908$			3.51317e6i			0.141411i
$909$	−1.11688e7			−0.448328
$910$	4.09954e6	+	1.71895e7i	0.164109	+	0.688113i
$911$	−1.06806e7			−0.426385			−0.213192	−	0.977010i	$-0.568386\pi$
$911$	−1.06806e7			−0.426385			−0.213192	+	0.977010i	$0.568386\pi$
$912$		−	4.43060e6i		−	0.176391i
$913$		−	7.78153e6i		−	0.308950i
$914$	1.27363e7			0.504285
$915$	−5.66705e6	−	2.37621e7i	−0.223771	−	0.938279i
$916$	361598.			0.0142393
$917$			1.10594e7i			0.434319i
$918$		−	4.85741e6i		−	0.190238i
$919$	2.12108e7			0.828453			0.414226	−	0.910174i	$-0.364052\pi$
$919$	2.12108e7			0.828453			0.414226	+	0.910174i	$0.364052\pi$
$920$	−9.71875e6	+	2.31783e6i	−0.378565	+	0.0902844i
$921$	1.73931e7			0.675661
$922$		−	2.91586e7i		−	1.12964i
$923$		−	1.76514e7i		−	0.681986i
$924$	1.11909e6			0.0431206
$925$	7.46063e6	+	1.47517e7i	0.286696	+	0.566874i
$926$	−2.87891e7			−1.10332
$927$		−	5.17128e6i		−	0.197651i
$928$			7.39587e6i			0.281916i
$929$	−4.20462e7			−1.59841			−0.799203	−	0.601061i	$-0.794745\pi$
$929$	−4.20462e7			−1.59841			−0.799203	+	0.601061i	$0.794745\pi$
$930$	3.68833e6	−	879635.i	0.139837	−	0.0333499i
$931$	7.55186e6			0.285548
$932$			1.70678e6i			0.0643631i
$933$		−	2.12315e7i		−	0.798503i
$934$	−4.13240e7			−1.55001
$935$	2.05189e6	+	8.60362e6i	0.0767581	+	0.321849i
$936$	−5.71958e6			−0.213390
$937$		−	5.84174e6i		−	0.217367i	−0.994076	−	0.108683i	$-0.965337\pi$
$937$		−	5.84174e6i		−	0.217367i	0.994076	−	0.108683i	$-0.0346635\pi$
$938$		−	2.98204e7i		−	1.10664i
$939$	1.20559e6			0.0446205
$940$	−543655.	−	2.27956e6i	−0.0200680	−	0.0841457i
$941$	−1.24009e7			−0.456540			−0.228270	−	0.973598i	$-0.573307\pi$
$941$	−1.24009e7			−0.456540			−0.228270	+	0.973598i	$0.573307\pi$
$942$		−	1.62086e6i		−	0.0595139i
$943$		−	7.07272e6i		−	0.259004i
$944$	2.70496e7			0.987940
$945$	−6.74987e6	+	1.60978e6i	−0.245876	+	0.0586392i
$946$	−1.07076e7			−0.389013
$947$			5.45771e7i			1.97759i	0.149293	+	0.988793i	$0.452300\pi$
$947$			5.45771e7i			1.97759i	−0.149293	+	0.988793i	$0.547700\pi$
$948$			195059.i			0.00704928i
$949$	2.16560e7			0.780571
$950$	−4.45319e6	−	8.80516e6i	−0.160089	−	0.316540i
$951$	−1.52184e7			−0.545655
$952$		−	4.31535e7i		−	1.54321i
$953$		−	1.12765e7i		−	0.402198i	−0.979571	−	0.201099i	$-0.935549\pi$
$953$		−	1.12765e7i		−	0.402198i	0.979571	−	0.201099i	$-0.0644513\pi$
$954$	−7.17322e6			−0.255178
$955$	−2.10329e7	+	5.01616e6i	−0.746262	+	0.177977i
$956$	1.02359e7			0.362227
$957$		−	3.73961e6i		−	0.131992i
$958$		−	2.96770e7i		−	1.04473i
$959$	5.22456e7			1.83444
$960$	4.24809e6	+	1.78124e7i	0.148770	+	0.623798i
$961$	−2.64416e7			−0.923589
$962$			9.82071e6i			0.342141i
$963$			3.04454e6i			0.105793i
$964$	−6.30622e6			−0.218563
$965$	−8.02020e6	−	3.36289e7i	−0.277247	−	1.16251i
$966$	−7.20131e6			−0.248295
$967$		−	2.71697e6i		−	0.0934370i	−0.998908	−	0.0467185i	$-0.985124\pi$
$967$		−	2.71697e6i		−	0.0934370i	0.998908	−	0.0467185i	$-0.0148764\pi$
$968$			2.83758e6i			0.0973330i
$969$	−7.29249e6			−0.249498
$970$	−4.58451e6	+	1.09337e6i	−0.156446	+	0.0373109i
$971$	−3.01426e6			−0.102597			−0.0512983	−	0.998683i	$-0.516336\pi$
$971$	−3.01426e6			−0.102597			−0.0512983	+	0.998683i	$0.516336\pi$
$972$		−	356364.i		−	0.0120984i
$973$		−	7.08888e7i		−	2.40046i
$974$	3.98843e7			1.34711
$975$	−9.14401e6	+	4.62457e6i	−0.308053	+	0.155797i
$976$	−3.85744e7			−1.29621
$977$		−	1.75203e7i		−	0.587227i	−0.955924	−	0.293613i	$-0.905142\pi$
$977$		−	1.75203e7i		−	0.587227i	0.955924	−	0.293613i	$-0.0948578\pi$
$978$		−	2.21213e7i		−	0.739544i
$979$	−3.26171e6			−0.108765
$980$	−3.99942e6	+	953826.i	−0.133025	+	0.0317252i
$981$	−1.20274e7			−0.399025
$982$		−	3.03229e7i		−	1.00344i
$983$		−	2.19475e7i		−	0.724439i	−0.932093	−	0.362219i	$-0.882019\pi$
$983$		−	2.19475e7i		−	0.724439i	0.932093	−	0.362219i	$-0.117981\pi$
$984$	−1.33779e7			−0.440452
$985$	−1.12827e7	−	4.73086e7i	−0.370528	−	1.55364i
$986$	−2.28810e7			−0.749521
$987$		−	1.06452e7i		−	0.347827i
$988$			1.36249e6i			0.0444059i
$989$	−1.60152e7			−0.520646
$990$	−647663.	−	2.71567e6i	−0.0210020	−	0.0880620i
$991$	−4.54381e7			−1.46972			−0.734862	−	0.678216i	$-0.762753\pi$
$991$	−4.54381e7			−1.46972			−0.734862	+	0.678216i	$0.762753\pi$
$992$			3.18546e6i			0.102776i
$993$		−	2.81960e6i		−	0.0907433i
$994$	−4.20366e7			−1.34946
$995$	4.91545e7	−	1.17229e7i	1.57400	−	0.375386i
$996$	−3.49304e6			−0.111572
$997$		−	1.38771e7i		−	0.442141i	−0.975258	−	0.221070i	$-0.929045\pi$
$997$		−	1.38771e7i		−	0.442141i	0.975258	−	0.221070i	$-0.0709550\pi$
$998$			9.21907e6i			0.292995i
$999$	−3.85634e6			−0.122254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.b.34.19	yes	26
5.2	odd	4		825.6.a.v.1.5		13
5.3	odd	4		825.6.a.y.1.9		13
5.4	even	2	inner	165.6.c.b.34.8	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.b.34.8	✓	26	5.4	even	2	inner
165.6.c.b.34.19	yes	26	1.1	even	1	trivial
825.6.a.v.1.5		13	5.2	odd	4
825.6.a.y.1.9		13	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+5.09558i q^{2} -9.00000i q^{3} +6.03505 q^{4} +(54.3767 - 12.9683i) q^{5} +45.8602 q^{6} +170.277i q^{7} +193.811i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q+5.09558i q^{2} -9.00000i q^{3} +6.03505 q^{4} +(54.3767 - 12.9683i) q^{5} +45.8602 q^{6} +170.277i q^{7} +193.811i q^{8} -81.0000 q^{9} +(66.0813 + 277.081i) q^{10} +121.000 q^{11} -54.3155i q^{12} -364.335i q^{13} -867.659 q^{14} +(-116.715 - 489.390i) q^{15} -794.456 q^{16} +1307.63i q^{17} -412.742i q^{18} -619.655 q^{19} +(328.166 - 78.2647i) q^{20} +1532.49 q^{21} +616.565i q^{22} +922.189i q^{23} +1744.30 q^{24} +(2788.64 - 1410.35i) q^{25} +1856.50 q^{26} +729.000i q^{27} +1027.63i q^{28} +3433.99 q^{29} +(2493.73 - 594.731i) q^{30} +1479.05 q^{31} +2153.73i q^{32} -1089.00i q^{33} -6663.11 q^{34} +(2208.21 + 9259.08i) q^{35} -488.839 q^{36} +5289.91i q^{37} -3157.50i q^{38} -3279.02 q^{39} +(2513.40 + 10538.8i) q^{40} -7669.49 q^{41} +7808.93i q^{42} +17366.5i q^{43} +730.242 q^{44} +(-4404.51 + 1050.44i) q^{45} -4699.09 q^{46} -6946.36i q^{47} +7150.11i q^{48} -12187.2 q^{49} +(7186.56 + 14209.8i) q^{50} +11768.6 q^{51} -2198.78i q^{52} -17379.4i q^{53} -3714.68 q^{54} +(6579.58 - 1569.17i) q^{55} -33001.5 q^{56} +5576.90i q^{57} +17498.2i q^{58} -34047.9 q^{59} +(-704.382 - 2953.50i) q^{60} +48554.5 q^{61} +7536.59i q^{62} -13792.4i q^{63} -36397.1 q^{64} +(-4724.83 - 19811.3i) q^{65} +5549.09 q^{66} +34368.8i q^{67} +7891.59i q^{68} +8299.70 q^{69} +(-47180.4 + 11252.1i) q^{70} +48448.3 q^{71} -15698.7i q^{72} +59439.7i q^{73} -26955.1 q^{74} +(-12693.2 - 25097.8i) q^{75} -3739.65 q^{76} +20603.5i q^{77} -16708.5i q^{78} -3591.22 q^{79} +(-43199.9 + 10302.8i) q^{80} +6561.00 q^{81} -39080.5i q^{82} -64310.2i q^{83} +9248.67 q^{84} +(16957.7 + 71104.3i) q^{85} -88492.6 q^{86} -30905.9i q^{87} +23451.1i q^{88} -26956.3 q^{89} +(-5352.58 - 22443.5i) q^{90} +62037.9 q^{91} +5565.46i q^{92} -13311.4i q^{93} +35395.8 q^{94} +(-33694.8 + 8035.91i) q^{95} +19383.5 q^{96} +16545.8i q^{97} -62100.8i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 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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