LMFDB - Embedded newform 15.7.d.c.14.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,7,Mod(14,15)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("15.14");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	15.d (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:	$3.45081125430$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 60x^{6} + 7774x^{4} + 206220x^{2} + 5736025 $ x^8 + 60x^6 + 7774x^4 + 206220*x^2 + 5736025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.3
Root			$5.55992 - 6.77589i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.7.d.c.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12691 q^{2} +(19.8701 - 18.2805i) q^{3} -59.4763 q^{4} +(72.7643 - 101.638i) q^{5} +(-42.2619 + 38.8810i) q^{6} -435.542i q^{7} +262.622 q^{8} +(60.6432 - 726.473i) q^{9} +O(q^{10})$	\(q-2.12691 q^{2} +(19.8701 - 18.2805i) q^{3} -59.4763 q^{4} +(72.7643 - 101.638i) q^{5} +(-42.2619 + 38.8810i) q^{6} -435.542i q^{7} +262.622 q^{8} +(60.6432 - 726.473i) q^{9} +(-154.763 + 216.175i) q^{10} +1656.22i q^{11} +(-1181.80 + 1087.26i) q^{12} +1642.06i q^{13} +926.356i q^{14} +(-412.170 - 3349.74i) q^{15} +3247.91 q^{16} +2050.83 q^{17} +(-128.982 + 1545.14i) q^{18} -3633.48 q^{19} +(-4327.75 + 6045.07i) q^{20} +(-7961.94 - 8654.27i) q^{21} -3522.63i q^{22} +21270.9 q^{23} +(5218.34 - 4800.88i) q^{24} +(-5035.72 - 14791.3i) q^{25} -3492.50i q^{26} +(-12075.3 - 15543.7i) q^{27} +25904.4i q^{28} +11487.1i q^{29} +(876.647 + 7124.57i) q^{30} +13405.1 q^{31} -23715.8 q^{32} +(30276.7 + 32909.4i) q^{33} -4361.93 q^{34} +(-44267.8 - 31691.9i) q^{35} +(-3606.83 + 43207.9i) q^{36} +1778.45i q^{37} +7728.06 q^{38} +(30017.7 + 32627.9i) q^{39} +(19109.5 - 26692.5i) q^{40} +2293.20i q^{41} +(16934.3 + 18406.8i) q^{42} +14419.6i q^{43} -98506.0i q^{44} +(-69424.9 - 59025.0i) q^{45} -45241.3 q^{46} +49600.2 q^{47} +(64536.3 - 59373.5i) q^{48} -72047.6 q^{49} +(10710.5 + 31459.7i) q^{50} +(40750.3 - 37490.3i) q^{51} -97663.5i q^{52} -81759.3 q^{53} +(25683.1 + 33060.0i) q^{54} +(168336. + 120514. i) q^{55} -114383. i q^{56} +(-72197.6 + 66421.9i) q^{57} -24432.0i q^{58} +200972. i q^{59} +(24514.4 + 199230. i) q^{60} +63762.1 q^{61} -28511.4 q^{62} +(-316409. - 26412.7i) q^{63} -157425. q^{64} +(166896. + 119483. i) q^{65} +(-64395.6 - 69995.1i) q^{66} +351519. i q^{67} -121976. q^{68} +(422656. - 388844. i) q^{69} +(94153.3 + 67405.6i) q^{70} +404271. i q^{71} +(15926.3 - 190788. i) q^{72} -666493. i q^{73} -3782.59i q^{74} +(-370453. - 201849. i) q^{75} +216106. q^{76} +721354. q^{77} +(-63844.8 - 69396.4i) q^{78} -758661. q^{79} +(236332. - 330112. i) q^{80} +(-524086. - 88111.4i) q^{81} -4877.43i q^{82} -261108. q^{83} +(473547. + 514724. i) q^{84} +(149227. - 208443. i) q^{85} -30669.1i q^{86} +(209990. + 228250. i) q^{87} +434961. i q^{88} -316622. i q^{89} +(147660. + 125541. i) q^{90} +715185. q^{91} -1.26512e6 q^{92} +(266361. - 245053. i) q^{93} -105495. q^{94} +(-264387. + 369301. i) q^{95} +(-471236. + 433538. i) q^{96} -320890. i q^{97} +153239. q^{98} +(1.20320e6 + 100439. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9}+O(q^{10}) $ 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9	$ 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9} + 4240 q^{10} + 1980 q^{15} + 784 q^{16} - 28520 q^{19} + 24228 q^{21} + 14904 q^{24} + 800 q^{25} - 71100 q^{30} + 5896 q^{31} + 105344 q^{34} - 186624 q^{36} + 233568 q^{39} + 141920 q^{40} - 159300 q^{45} + 59336 q^{46} - 1041472 q^{49} + 66888 q^{51} + 917892 q^{54} + 442800 q^{55} - 638640 q^{60} + 1493416 q^{61} - 2063584 q^{64} - 1221840 q^{66} + 1502532 q^{69} + 2273400 q^{70} - 2574000 q^{75} - 219168 q^{76} - 1286360 q^{79} - 1752192 q^{81} + 6238728 q^{84} + 1651240 q^{85} - 2737440 q^{90} + 383616 q^{91} - 7641736 q^{94} - 151056 q^{96} + 6322320 q^{99}+O(q^{100}) $ 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9 + 4240 * q^10 + 1980 * q^15 + 784 * q^16 - 28520 * q^19 + 24228 * q^21 + 14904 * q^24 + 800 * q^25 - 71100 * q^30 + 5896 * q^31 + 105344 * q^34 - 186624 * q^36 + 233568 * q^39 + 141920 * q^40 - 159300 * q^45 + 59336 * q^46 - 1041472 * q^49 + 66888 * q^51 + 917892 * q^54 + 442800 * q^55 - 638640 * q^60 + 1493416 * q^61 - 2063584 * q^64 - 1221840 * q^66 + 1502532 * q^69 + 2273400 * q^70 - 2574000 * q^75 - 219168 * q^76 - 1286360 * q^79 - 1752192 * q^81 + 6238728 * q^84 + 1651240 * q^85 - 2737440 * q^90 + 383616 * q^91 - 7641736 * q^94 - 151056 * q^96 + 6322320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.12691			−0.265863			−0.132932	−	0.991125i	$-0.542439\pi$
$2$	−2.12691			−0.265863			−0.132932	+	0.991125i	$0.542439\pi$
$3$	19.8701	−	18.2805i	0.735930	−	0.677057i
$3$	19.8701	−	18.2805i	0.735930	−	0.677057i
$4$	−59.4763			−0.929317
$5$	72.7643	−	101.638i	0.582114	−	0.813107i
$5$	72.7643	−	101.638i	0.582114	−	0.813107i
$6$	−42.2619	+	38.8810i	−0.195657	+	0.180005i
$7$		−	435.542i		−	1.26980i	−0.772594	−	0.634901i	$-0.781041\pi$
$7$		−	435.542i		−	1.26980i	0.772594	−	0.634901i	$-0.218959\pi$
$8$	262.622			0.512934
$9$	60.6432	−	726.473i	0.0831869	−	0.996534i
$10$	−154.763	+	216.175i	−0.154763	+	0.216175i
$11$			1656.22i			1.24435i	0.782880	+	0.622173i	$0.213750\pi$
$11$			1656.22i			1.24435i	−0.782880	+	0.622173i	$0.786250\pi$
$12$	−1181.80	+	1087.26i	−0.683912	+	0.629201i
$13$			1642.06i			0.747409i	0.927548	+	0.373705i	$0.121913\pi$
$13$			1642.06i			0.747409i	−0.927548	+	0.373705i	$0.878087\pi$
$14$			926.356i			0.337593i
$15$	−412.170	−	3349.74i	−0.122125	−	0.992515i
$16$	3247.91			0.792946
$17$	2050.83			0.417430			0.208715	−	0.977977i	$-0.433072\pi$
$17$	2050.83			0.417430			0.208715	+	0.977977i	$0.433072\pi$
$18$	−128.982	+	1545.14i	−0.0221163	+	0.264942i
$19$	−3633.48			−0.529738			−0.264869	−	0.964284i	$-0.585329\pi$
$19$	−3633.48			−0.529738			−0.264869	+	0.964284i	$0.585329\pi$
$20$	−4327.75	+	6045.07i	−0.540968	+	0.755634i
$21$	−7961.94	−	8654.27i	−0.859728	−	0.934485i
$22$		−	3522.63i		−	0.330826i
$23$	21270.9			1.74825			0.874124	−	0.485703i	$-0.161436\pi$
$23$	21270.9			1.74825			0.874124	+	0.485703i	$0.161436\pi$
$24$	5218.34	−	4800.88i	0.377484	−	0.347286i
$25$	−5035.72	−	14791.3i	−0.322286	−	0.946642i
$26$		−	3492.50i		−	0.198709i
$27$	−12075.3	−	15543.7i	−0.613491	−	0.789702i
$28$			25904.4i			1.18005i
$29$			11487.1i			0.470995i	0.971875	+	0.235498i	$0.0756720\pi$
$29$			11487.1i			0.470995i	−0.971875	+	0.235498i	$0.924328\pi$
$30$	876.647	+	7124.57i	0.0324684	+	0.263873i
$31$	13405.1			0.449972			0.224986	−	0.974362i	$-0.427766\pi$
$31$	13405.1			0.449972			0.224986	+	0.974362i	$0.427766\pi$
$32$	−23715.8			−0.723750
$33$	30276.7	+	32909.4i	0.842493	+	0.915751i
$34$	−4361.93			−0.110979
$35$	−44267.8	−	31691.9i	−1.03248	−	0.739169i
$36$	−3606.83	+	43207.9i	−0.0773070	+	0.926096i
$37$			1778.45i			0.0351105i	0.999846	+	0.0175552i	$0.00558829\pi$
$37$			1778.45i			0.0351105i	−0.999846	+	0.0175552i	$0.994412\pi$
$38$	7728.06			0.140838
$39$	30017.7	+	32627.9i	0.506039	+	0.550041i
$40$	19109.5	−	26692.5i	0.298586	−	0.417070i
$41$			2293.20i			0.0332729i	0.999862	+	0.0166365i	$0.00529580\pi$
$41$			2293.20i			0.0332729i	−0.999862	+	0.0166365i	$0.994704\pi$
$42$	16934.3	+	18406.8i	0.228570	+	0.248445i
$43$			14419.6i			0.181362i	0.995880	+	0.0906811i	$0.0289044\pi$
$43$			14419.6i			0.181362i	−0.995880	+	0.0906811i	$0.971096\pi$
$44$		−	98506.0i		−	1.15639i
$45$	−69424.9	−	59025.0i	−0.761865	−	0.647736i
$46$	−45241.3			−0.464795
$47$	49600.2			0.477738			0.238869	−	0.971052i	$-0.423223\pi$
$47$	49600.2			0.477738			0.238869	+	0.971052i	$0.423223\pi$
$48$	64536.3	−	59373.5i	0.583553	−	0.536870i
$49$	−72047.6			−0.612395
$50$	10710.5	+	31459.7i	0.0856840	+	0.251677i
$51$	40750.3	−	37490.3i	0.307199	−	0.282624i
$52$		−	97663.5i		−	0.694580i
$53$	−81759.3			−0.549174			−0.274587	−	0.961562i	$-0.588541\pi$
$53$	−81759.3			−0.549174			−0.274587	+	0.961562i	$0.588541\pi$
$54$	25683.1	+	33060.0i	0.163105	+	0.209953i
$55$	168336.	+	120514.i	1.01179	+	0.724351i
$56$		−	114383.i		−	0.651325i
$57$	−72197.6	+	66421.9i	−0.389851	+	0.358663i
$58$		−	24432.0i		−	0.125220i
$59$			200972.i			0.978541i	0.872132	+	0.489270i	$0.162737\pi$
$59$			200972.i			0.978541i	−0.872132	+	0.489270i	$0.837263\pi$
$60$	24514.4	+	199230.i	0.113492	+	0.922361i
$61$	63762.1			0.280914			0.140457	−	0.990087i	$-0.455143\pi$
$61$	63762.1			0.280914			0.140457	+	0.990087i	$0.455143\pi$
$62$	−28511.4			−0.119631
$63$	−316409.	−	26412.7i	−1.26540	−	0.105631i
$64$	−157425.			−0.600528
$65$	166896.	+	119483.i	0.607724	+	0.435077i
$66$	−64395.6	−	69995.1i	−0.223988	−	0.243465i
$67$			351519.i			1.16876i	0.811481	+	0.584378i	$0.198662\pi$
$67$			351519.i			1.16876i	−0.811481	+	0.584378i	$0.801338\pi$
$68$	−121976.			−0.387924
$69$	422656.	−	388844.i	1.28659	−	1.18366i
$70$	94153.3	+	67405.6i	0.274500	+	0.196518i
$71$			404271.i			1.12953i	0.825252	+	0.564765i	$0.191033\pi$
$71$			404271.i			1.12953i	−0.825252	+	0.564765i	$0.808967\pi$
$72$	15926.3	−	190788.i	0.0426694	−	0.511156i
$73$		−	666493.i		−	1.71328i	−0.515918	−	0.856638i	$-0.672549\pi$
$73$		−	666493.i		−	1.71328i	0.515918	−	0.856638i	$-0.327451\pi$
$74$		−	3782.59i		−	0.00933458i
$75$	−370453.	−	201849.i	−0.878111	−	0.478457i
$76$	216106.			0.492295
$77$	721354.			1.58007
$78$	−63844.8	−	69396.4i	−0.134537	−	0.146236i
$79$	−758661.			−1.53875			−0.769373	−	0.638800i	$-0.779431\pi$
$79$	−758661.			−1.53875			−0.769373	+	0.638800i	$0.779431\pi$
$80$	236332.	−	330112.i	0.461585	−	0.644750i
$81$	−524086.	−	88111.4i	−0.986160	−	0.165797i
$82$		−	4877.43i		−	0.00884605i
$83$	−261108.			−0.456652			−0.228326	−	0.973585i	$-0.573325\pi$
$83$	−261108.			−0.456652			−0.228326	+	0.973585i	$0.573325\pi$
$84$	473547.	+	514724.i	0.798960	+	0.868433i
$85$	149227.	−	208443.i	0.242992	−	0.339415i
$86$		−	30669.1i		−	0.0482176i
$87$	209990.	+	228250.i	0.318891	+	0.346620i
$88$			434961.i			0.638267i
$89$		−	316622.i		−	0.449128i	−0.974459	−	0.224564i	$-0.927904\pi$
$89$		−	316622.i		−	0.449128i	0.974459	−	0.224564i	$-0.0720958\pi$
$90$	147660.	+	125541.i	0.202552	+	0.172209i
$91$	715185.			0.949061
$92$	−1.26512e6			−1.62468
$93$	266361.	−	245053.i	0.331148	−	0.304657i
$94$	−105495.			−0.127013
$95$	−264387.	+	369301.i	−0.308368	+	0.430734i
$96$	−471236.	+	433538.i	−0.532629	+	0.490020i
$97$		−	320890.i		−	0.351594i	−0.984426	−	0.175797i	$-0.943750\pi$
$97$		−	320890.i		−	0.351594i	0.984426	−	0.175797i	$-0.0562502\pi$
$98$	153239.			0.162813
$99$	1.20320e6	+	100439.i	1.24003	+	0.103513i
$100$	299506.	+	879731.i	0.299506	+	0.879731i
$101$		−	1.04037e6i		−	1.00977i	−0.863187	−	0.504885i	$-0.831535\pi$
$101$		−	1.04037e6i		−	1.00977i	0.863187	−	0.504885i	$-0.168465\pi$
$102$	−86672.0	+	79738.4i	−0.0816729	+	0.0751393i
$103$			1.11001e6i			1.01582i	0.861411	+	0.507908i	$0.169581\pi$
$103$			1.11001e6i			1.01582i	−0.861411	+	0.507908i	$0.830419\pi$
$104$			431241.i			0.383372i
$105$	−1.45895e6	+	179517.i	−1.26030	+	0.155074i
$106$	173894.			0.146005
$107$	−324497.			−0.264886			−0.132443	−	0.991191i	$-0.542282\pi$
$107$	−324497.			−0.264886			−0.132443	+	0.991191i	$0.542282\pi$
$108$	718196.	+	924481.i	0.570127	+	0.733883i
$109$	−1.66575e6			−1.28626			−0.643131	−	0.765756i	$-0.722365\pi$
$109$	−1.66575e6			−1.28626			−0.643131	+	0.765756i	$0.722365\pi$
$110$	−358034.	−	256322.i	−0.268997	−	0.192578i
$111$	32511.0	+	35338.0i	0.0237718	+	0.0258388i
$112$		−	1.41460e6i		−	1.00688i
$113$	1.42795e6			0.989644			0.494822	−	0.868994i	$-0.335233\pi$
$113$	1.42795e6			0.989644			0.494822	+	0.868994i	$0.335233\pi$
$114$	153557.	−	141273.i	0.103647	−	0.0953554i
$115$	1.54776e6	−	2.16194e6i	1.01768	−	1.42151i
$116$		−	683210.i		−	0.437704i
$117$	1.19291e6	+	99579.7i	0.744819	+	0.0621746i
$118$		−	427448.i		−	0.260158i
$119$		−	893223.i		−	0.530053i
$120$	−108245.	−	879716.i	−0.0626419	−	0.509095i
$121$	−971515.			−0.548395
$122$	−135616.			−0.0746846
$123$	41921.0	+	45566.2i	0.0225277	+	0.0244866i
$124$	−797286.			−0.418166
$125$	−1.86978e6	−	564455.i	−0.957329	−	0.289001i
$126$	672973.	+	56177.2i	0.336423	+	0.0280833i
$127$			2.38770e6i			1.16565i	0.812598	+	0.582825i	$0.198053\pi$
$127$			2.38770e6i			1.16565i	−0.812598	+	0.582825i	$0.801947\pi$
$128$	1.85264e6			0.883408
$129$	263598.	+	286519.i	0.122793	+	0.133470i
$130$	−354972.	−	254129.i	−0.161571	−	0.115671i
$131$			3.72507e6i			1.65699i	0.559995	+	0.828496i	$0.310803\pi$
$131$			3.72507e6i			1.65699i	−0.559995	+	0.828496i	$0.689197\pi$
$132$	−1.80074e6	−	1.95733e6i	−0.782943	−	0.851023i
$133$			1.58253e6i			0.672663i
$134$		−	747647.i		−	0.310729i
$135$	−2.45849e6	+	96291.9i	−0.999234	+	0.0391371i
$136$	538594.			0.214114
$137$	847766.			0.329696			0.164848	−	0.986319i	$-0.447287\pi$
$137$	847766.			0.329696			0.164848	+	0.986319i	$0.447287\pi$
$138$	−898949.	+	827035.i	−0.342056	+	0.314693i
$139$	2.46214e6			0.916788			0.458394	−	0.888749i	$-0.348425\pi$
$139$	2.46214e6			0.916788			0.458394	+	0.888749i	$0.348425\pi$
$140$	2.63288e6	+	1.88492e6i	0.959505	+	0.686922i
$141$	985562.	−	906719.i	0.351582	−	0.323456i
$142$		−	859847.i		−	0.300301i
$143$	−2.71961e6			−0.930035
$144$	196964.	−	2.35952e6i	0.0659627	−	0.790198i
$145$	1.16753e6	+	835851.i	0.382969	+	0.274173i
$146$			1.41757e6i			0.455497i
$147$	−1.43160e6	+	1.31707e6i	−0.450680	+	0.414626i
$148$		−	105776.i		−	0.0326287i
$149$			4.72080e6i			1.42711i	0.700600	+	0.713554i	$0.252916\pi$
$149$			4.72080e6i			1.42711i	−0.700600	+	0.713554i	$0.747084\pi$
$150$	787919.	+	429313.i	0.233457	+	0.127204i
$151$	−887165.			−0.257676			−0.128838	−	0.991666i	$-0.541125\pi$
$151$	−887165.			−0.257676			−0.128838	+	0.991666i	$0.541125\pi$
$152$	−954232.			−0.271721
$153$	124369.	−	1.48987e6i	0.0347247	−	0.415983i
$154$	−1.53425e6			−0.420083
$155$	975413.	−	1.36247e6i	0.261935	−	0.365875i
$156$	−1.78534e6	−	1.94058e6i	−0.470270	−	0.511162i
$157$		−	194223.i		−	0.0501883i	−0.999685	−	0.0250941i	$-0.992011\pi$
$157$		−	194223.i		−	0.0501883i	0.999685	−	0.0250941i	$-0.00798855\pi$
$158$	1.61360e6			0.409096
$159$	−1.62457e6	+	1.49460e6i	−0.404153	+	0.371822i
$160$	−1.72566e6	+	2.41044e6i	−0.421305	+	0.588486i
$161$		−	9.26438e6i		−	2.21993i
$162$	1.11468e6	+	187405.i	0.262184	+	0.0440793i
$163$		−	6.47309e6i		−	1.49468i	−0.664440	−	0.747342i	$-0.731330\pi$
$163$		−	6.47309e6i		−	1.49468i	0.664440	−	0.747342i	$-0.268670\pi$
$164$		−	136391.i		−	0.0309211i
$165$	5.54791e6	−	682646.i	1.23503	−	0.151965i
$166$	555351.			0.121407
$167$	6.50498e6			1.39668			0.698339	−	0.715767i	$-0.253923\pi$
$167$	6.50498e6			1.39668			0.698339	+	0.715767i	$0.253923\pi$
$168$	−2.09098e6	−	2.27280e6i	−0.440984	−	0.479329i
$169$	2.13045e6			0.441380
$170$	−317392.	+	443339.i	−0.0646026	+	0.0902380i
$171$	−220346.	+	2.63962e6i	−0.0440673	+	0.527902i
$172$		−	857622.i		−	0.168543i
$173$	−8.85981e6			−1.71114			−0.855571	−	0.517686i	$-0.826794\pi$
$173$	−8.85981e6			−1.71114			−0.855571	+	0.517686i	$0.826794\pi$
$174$	−446630.	−	485466.i	−0.0847813	−	0.0921534i
$175$	−6.44222e6	+	2.19327e6i	−1.20205	+	0.409239i
$176$			5.37926e6i			0.986699i
$177$	3.67387e6	+	3.99333e6i	0.662528	+	0.720138i
$178$			673424.i			0.119407i
$179$		−	6.68287e6i		−	1.16521i	−0.812755	−	0.582605i	$-0.802033\pi$
$179$		−	6.68287e6i		−	1.16521i	0.812755	−	0.582605i	$-0.197967\pi$
$180$	4.12913e6	+	3.51059e6i	0.708013	+	0.601952i
$181$	−189580.			−0.0319710			−0.0159855	−	0.999872i	$-0.505089\pi$
$181$	−189580.			−0.0319710			−0.0159855	+	0.999872i	$0.505089\pi$
$182$	−1.52113e6			−0.252320
$183$	1.26696e6	−	1.16561e6i	0.206733	−	0.190195i
$184$	5.58622e6			0.896736
$185$	180759.	+	129408.i	0.0285486	+	0.0204383i
$186$	−566525.	+	521204.i	−0.0880400	+	0.0809970i
$187$			3.39664e6i			0.519427i
$188$	−2.95003e6			−0.443970
$189$	−6.76993e6	+	5.25932e6i	−1.00276	+	0.779011i
$190$	562327.	−	785468.i	0.0819838	−	0.114516i
$191$			1.66754e6i			0.239319i	0.992815	+	0.119659i	$0.0381803\pi$
$191$			1.66754e6i			0.239319i	−0.992815	+	0.119659i	$0.961820\pi$
$192$	−3.12805e6	+	2.87781e6i	−0.441947	+	0.406592i
$193$		−	1.72259e6i		−	0.239612i	−0.992797	−	0.119806i	$-0.961773\pi$
$193$		−	1.72259e6i		−	0.239612i	0.992797	−	0.119806i	$-0.0382273\pi$
$194$			682503.i			0.0934758i
$195$	5.50046e6	−	676808.i	0.741815	−	0.0912770i
$196$	4.28513e6			0.569109
$197$	−7.69080e6			−1.00594			−0.502971	−	0.864304i	$-0.667760\pi$
$197$	−7.69080e6			−1.00594			−0.502971	+	0.864304i	$0.667760\pi$
$198$	−2.55910e6	−	213624.i	−0.329679	−	0.0275203i
$199$	1.88774e6			0.239542			0.119771	−	0.992802i	$-0.461784\pi$
$199$	1.88774e6			0.239542			0.119771	+	0.992802i	$0.461784\pi$
$200$	−1.32249e6	−	3.88452e6i	−0.165312	−	0.485565i
$201$	6.42596e6	+	6.98472e6i	0.791315	+	0.860124i
$202$			2.21276e6i			0.268460i
$203$	5.00311e6			0.598070
$204$	−2.42367e6	+	2.22979e6i	−0.285485	+	0.262647i
$205$	233078.	+	166863.i	0.0270545	+	0.0193687i
$206$		−	2.36089e6i		−	0.270068i
$207$	1.28994e6	−	1.54528e7i	0.145431	−	1.74219i
$208$			5.33325e6i			0.592655i
$209$		−	6.01785e6i		−	0.659177i
$210$	3.10305e6	−	381817.i	0.335066	−	0.0412284i
$211$	−1.09494e7			−1.16558			−0.582792	−	0.812621i	$-0.698040\pi$
$211$	−1.09494e7			−1.16558			−0.582792	+	0.812621i	$0.698040\pi$
$212$	4.86274e6			0.510356
$213$	7.39030e6	+	8.03292e6i	0.764757	+	0.831256i
$214$	690175.			0.0704235
$215$	1.46558e6	+	1.04923e6i	0.147467	+	0.105574i
$216$	−3.17125e6	−	4.08212e6i	−0.314680	−	0.405065i
$217$		−	5.83849e6i		−	0.571375i
$218$	3.54289e6			0.341970
$219$	−1.21839e7	−	1.32433e7i	−1.15999	−	1.26085i
$220$	−1.00120e7	−	7.16772e6i	−0.940269	−	0.673151i
$221$			3.36758e6i			0.311991i
$222$	−69147.9	−	75160.6i	−0.00632004	−	0.00686960i
$223$		−	759092.i		−	0.0684510i	−0.999414	−	0.0342255i	$-0.989104\pi$
$223$		−	759092.i		−	0.0684510i	0.999414	−	0.0342255i	$-0.0108964\pi$
$224$			1.03292e7i			0.919018i
$225$	−1.10509e7	+	2.76132e6i	−0.970171	+	0.242421i
$226$	−3.03712e6			−0.263110
$227$	2.00289e6			0.171230			0.0856150	−	0.996328i	$-0.472714\pi$
$227$	2.00289e6			0.171230			0.0856150	+	0.996328i	$0.472714\pi$
$228$	4.29404e6	−	3.95053e6i	0.362295	−	0.333312i
$229$	2.31530e7			1.92797			0.963985	−	0.265958i	$-0.0856882\pi$
$229$	2.31530e7			1.92797			0.963985	+	0.265958i	$0.0856882\pi$
$230$	−3.29195e6	+	4.59825e6i	−0.270564	+	0.377928i
$231$	1.43334e7	−	1.31868e7i	1.16282	−	1.06980i
$232$			3.01677e6i			0.241590i
$233$	1.49781e7			1.18411			0.592053	−	0.805899i	$-0.298318\pi$
$233$	1.49781e7			1.18411			0.592053	+	0.805899i	$0.298318\pi$
$234$	−2.53721e6	−	211797.i	−0.198020	−	0.0165299i
$235$	3.60912e6	−	5.04128e6i	0.278098	−	0.388452i
$236$		−	1.19531e7i		−	0.909375i
$237$	−1.50747e7	+	1.38687e7i	−1.13241	+	1.04182i
$238$			1.89980e6i			0.140921i
$239$			1.59997e7i			1.17197i	0.810320	+	0.585987i	$0.199293\pi$
$239$			1.59997e7i			1.17197i	−0.810320	+	0.585987i	$0.800707\pi$
$240$	−1.33869e6	−	1.08796e7i	−0.0968382	−	0.787011i
$241$	−1.18471e7			−0.846374			−0.423187	−	0.906042i	$-0.639089\pi$
$241$	−1.18471e7			−0.846374			−0.423187	+	0.906042i	$0.639089\pi$
$242$	2.06632e6			0.145798
$243$	−1.20244e7	+	7.82979e6i	−0.837999	+	0.545672i
$244$	−3.79233e6			−0.261058
$245$	−5.24249e6	+	7.32281e6i	−0.356484	+	0.497943i
$246$	−89162.1	−	96915.1i	−0.00598928	−	0.00651008i
$247$		−	5.96638e6i		−	0.395931i
$248$	3.52048e6			0.230806
$249$	−5.18824e6	+	4.77319e6i	−0.336064	+	0.309179i
$250$	3.97685e6	+	1.20054e6i	0.254518	+	0.0768347i
$251$			1.97249e7i			1.24737i	0.781677	+	0.623684i	$0.214365\pi$
$251$			1.97249e7i			1.24737i	−0.781677	+	0.623684i	$0.785635\pi$
$252$	1.88189e7	+	1.57093e6i	1.17596	+	0.0981645i
$253$			3.52294e7i			2.17542i
$254$		−	5.07840e6i		−	0.309903i
$255$	−845292.	−	6.86975e6i	−0.0509784	−	0.414305i
$256$	6.13480e6			0.365662
$257$	−2.17655e7			−1.28224			−0.641121	−	0.767440i	$-0.721530\pi$
$257$	−2.17655e7			−1.28224			−0.641121	+	0.767440i	$0.721530\pi$
$258$	−560647.	−	609398.i	−0.0326460	−	0.0354848i
$259$	774589.			0.0445833
$260$	−9.92636e6	−	7.10641e6i	−0.564768	−	0.404325i
$261$	8.34507e6	+	696615.i	0.469363	+	0.0391806i
$262$		−	7.92287e6i		−	0.440533i
$263$	6.41978e6			0.352901			0.176451	−	0.984309i	$-0.443538\pi$
$263$	6.41978e6			0.352901			0.176451	+	0.984309i	$0.443538\pi$
$264$	7.95133e6	+	8.64273e6i	0.432143	+	0.469720i
$265$	−5.94916e6	+	8.30988e6i	−0.319682	+	0.446537i
$266$		−	3.36589e6i		−	0.178836i
$267$	−5.78802e6	−	6.29131e6i	−0.304086	−	0.330527i
$268$		−	2.09070e7i		−	1.08615i
$269$		−	1.81275e7i		−	0.931279i	−0.884974	−	0.465640i	$-0.845824\pi$
$269$		−	1.81275e7i		−	0.931279i	0.884974	−	0.465640i	$-0.154176\pi$
$270$	5.22898e6	−	204804.i	0.265659	−	0.0104051i
$271$	6.59587e6			0.331409			0.165705	−	0.986175i	$-0.447010\pi$
$271$	6.59587e6			0.331409			0.165705	+	0.986175i	$0.447010\pi$
$272$	6.66092e6			0.330999
$273$	1.42108e7	−	1.30740e7i	0.698443	−	0.642569i
$274$	−1.80312e6			−0.0876541
$275$	2.44977e7	−	8.34028e6i	1.17795	−	0.401035i
$276$	−2.51380e7	+	2.31270e7i	−1.19565	+	1.10000i
$277$		−	1.53762e7i		−	0.723452i	−0.932284	−	0.361726i	$-0.882188\pi$
$277$		−	1.53762e7i		−	0.723452i	0.932284	−	0.361726i	$-0.117812\pi$
$278$	−5.23675e6			−0.243740
$279$	812929.	−	9.73845e6i	0.0374317	−	0.448412i
$280$	−1.16257e7	−	8.32300e6i	−0.529597	−	0.379145i
$281$		−	2.59304e6i		−	0.116866i	−0.998291	−	0.0584332i	$-0.981390\pi$
$281$		−	2.59304e6i		−	0.116866i	0.998291	−	0.0584332i	$-0.0186105\pi$
$282$	−2.09620e6	+	1.92850e6i	−0.0934727	+	0.0859950i
$283$		−	2.10258e7i		−	0.927671i	−0.885921	−	0.463836i	$-0.846473\pi$
$283$		−	2.10258e7i		−	0.927671i	0.885921	−	0.463836i	$-0.153527\pi$
$284$		−	2.40446e7i		−	1.04969i
$285$	1.49761e6	+	1.21712e7i	0.0646941	+	0.525773i
$286$	5.78436e6			0.247262
$287$	998786.			0.0422500
$288$	−1.43820e6	+	1.72289e7i	−0.0602065	+	0.721241i
$289$	−1.99317e7			−0.825752
$290$	−2.48323e6	−	1.77778e6i	−0.101817	−	0.0728925i
$291$	−5.86605e6	−	6.37612e6i	−0.238049	−	0.258748i
$292$			3.96405e7i			1.59218i
$293$	−2.09599e7			−0.833269			−0.416635	−	0.909074i	$-0.636791\pi$
$293$	−2.09599e7			−0.833269			−0.416635	+	0.909074i	$0.636791\pi$
$294$	3.04487e6	−	2.80128e6i	0.119819	−	0.110234i
$295$	2.04264e7	+	1.46236e7i	0.795659	+	0.569623i
$296$			467061.i			0.0180094i
$297$	2.57438e7	−	1.99995e7i	0.982662	−	0.763394i
$298$		−	1.00407e7i		−	0.379415i
$299$			3.49281e7i			1.30666i
$300$	2.20332e7	+	1.20052e7i	0.816043	+	0.444638i
$301$	6.28033e6			0.230294
$302$	1.88692e6			0.0685065
$303$	−1.90185e7	−	2.06722e7i	−0.683672	−	0.743120i
$304$	−1.18012e7			−0.420054
$305$	4.63960e6	−	6.48068e6i	0.163524	−	0.228413i
$306$	−264521.	+	3.16882e6i	−0.00923201	+	0.110595i
$307$			1.65687e7i			0.572628i	0.958136	+	0.286314i	$0.0924301\pi$
$307$			1.65687e7i			0.572628i	−0.958136	+	0.286314i	$0.907570\pi$
$308$	−4.29035e7			−1.46839
$309$	2.02916e7	+	2.20560e7i	0.687766	+	0.747570i
$310$	−2.07461e6	+	2.89785e6i	−0.0696389	+	0.0972728i
$311$		−	3.99698e7i		−	1.32877i	−0.747389	−	0.664386i	$-0.768693\pi$
$311$		−	3.99698e7i		−	1.32877i	0.747389	−	0.664386i	$-0.231307\pi$
$312$	7.88332e6	+	8.56881e6i	0.259565	+	0.282135i
$313$		−	9.30508e6i		−	0.303450i	−0.988423	−	0.151725i	$-0.951517\pi$
$313$		−	9.30508e6i		−	0.303450i	0.988423	−	0.151725i	$-0.0484828\pi$
$314$			413095.i			0.0133432i
$315$	−2.57078e7	+	3.02374e7i	−0.822496	+	0.967416i
$316$	4.51223e7			1.42998
$317$	8.66108e6			0.271891			0.135945	−	0.990716i	$-0.456593\pi$
$317$	8.66108e6			0.271891			0.135945	+	0.990716i	$0.456593\pi$
$318$	3.45530e6	−	3.17888e6i	0.107450	−	0.0988538i
$319$	−1.90252e7			−0.586081
$320$	−1.14549e7	+	1.60004e7i	−0.349576	+	0.488294i
$321$	−6.44780e6	+	5.93199e6i	−0.194938	+	0.179343i
$322$			1.97045e7i			0.590197i
$323$	−7.45165e6			−0.221129
$324$	3.11707e7	+	5.24054e6i	0.916455	+	0.154078i
$325$	2.42881e7	−	8.26894e6i	0.707529	−	0.240880i
$326$			1.37677e7i			0.397381i
$327$	−3.30986e7	+	3.04508e7i	−0.946600	+	0.870873i
$328$			602247.i			0.0170668i
$329$		−	2.16030e7i		−	0.606632i
$330$	−1.17999e7	+	1.45192e6i	−0.328349	+	0.0404019i
$331$	−4.31746e7			−1.19054			−0.595270	−	0.803526i	$-0.702955\pi$
$331$	−4.31746e7			−1.19054			−0.595270	+	0.803526i	$0.702955\pi$
$332$	1.55297e7			0.424374
$333$	1.29200e6	+	107851.i	0.0349888	+	0.00292073i
$334$	−1.38355e7			−0.371325
$335$	3.57278e7	+	2.55780e7i	0.950324	+	0.680350i
$336$	−2.58597e7	−	2.81083e7i	−0.681718	−	0.740997i
$337$		−	4.99446e7i		−	1.30497i	−0.757804	−	0.652483i	$-0.773728\pi$
$337$		−	4.99446e7i		−	1.30497i	0.757804	−	0.652483i	$-0.226272\pi$
$338$	−4.53128e6			−0.117347
$339$	2.83736e7	−	2.61038e7i	0.728309	−	0.670045i
$340$	−8.87548e6	+	1.23974e7i	−0.225816	+	0.315424i
$341$			2.22019e7i			0.559920i
$342$	468655.	−	5.61423e6i	0.0117159	−	0.140350i
$343$		−	1.98613e7i		−	0.492181i
$344$			3.78690e6i			0.0930269i
$345$	−8.76725e6	−	7.12520e7i	−0.213504	−	1.73516i
$346$	1.88440e7			0.454930
$347$	1.43523e7			0.343506			0.171753	−	0.985140i	$-0.445057\pi$
$347$	1.43523e7			0.343506			0.171753	+	0.985140i	$0.445057\pi$
$348$	−1.24895e7	−	1.35755e7i	−0.296350	−	0.322119i
$349$	−9.38031e6			−0.220669			−0.110334	−	0.993895i	$-0.535192\pi$
$349$	−9.38031e6			−0.220669			−0.110334	+	0.993895i	$0.535192\pi$
$350$	1.37020e7	−	4.66487e6i	0.319580	−	0.108802i
$351$	2.55237e7	−	1.98284e7i	0.590230	−	0.458529i
$352$		−	3.92787e7i		−	0.900594i
$353$	6.20079e7			1.40969			0.704844	−	0.709362i	$-0.251017\pi$
$353$	6.20079e7			1.40969			0.704844	+	0.709362i	$0.251017\pi$
$354$	−7.81398e6	−	8.49344e6i	−0.176142	−	0.191458i
$355$	4.10895e7	+	2.94165e7i	0.918429	+	0.657516i
$356$			1.88315e7i			0.417383i
$357$	−1.63286e7	−	1.77484e7i	−0.358876	−	0.390082i
$358$			1.42138e7i			0.309786i
$359$			5.05945e7i			1.09350i	0.837295	+	0.546751i	$0.184136\pi$
$359$			5.05945e7i			1.09350i	−0.837295	+	0.546751i	$0.815864\pi$
$360$	−1.82325e7	−	1.55013e7i	−0.390786	−	0.332246i
$361$	−3.38437e7			−0.719377
$362$	403218.			0.00849991
$363$	−1.93041e7	+	1.77598e7i	−0.403580	+	0.371295i
$364$	−4.25365e7			−0.881978
$365$	−6.77413e7	−	4.84969e7i	−1.39308	−	0.997322i
$366$	−2.69470e6	+	2.47913e6i	−0.0549627	+	0.0505658i
$367$			2.24355e7i			0.453876i	0.973909	+	0.226938i	$0.0728714\pi$
$367$			2.24355e7i			0.453876i	−0.973909	+	0.226938i	$0.927129\pi$
$368$	6.90860e7			1.38627
$369$	1.66595e6	+	139067.i	0.0331576	+	0.00276787i
$370$	−384457.	−	275238.i	−0.00759001	−	0.00543379i
$371$			3.56096e7i			0.697341i
$372$	−1.58422e7	+	1.45748e7i	−0.307741	+	0.283123i
$373$			5.65242e7i			1.08920i	0.838696	+	0.544600i	$0.183319\pi$
$373$			5.65242e7i			1.08920i	−0.838696	+	0.544600i	$0.816681\pi$
$374$		−	7.22432e6i		−	0.138096i
$375$	−4.74713e7	+	2.29649e7i	−0.900197	+	0.435482i
$376$	1.30261e7			0.245048
$377$	−1.88625e7			−0.352026
$378$	1.43990e7	−	1.11861e7i	0.266598	−	0.207110i
$379$	2.11040e7			0.387657			0.193829	−	0.981035i	$-0.437909\pi$
$379$	2.11040e7			0.387657			0.193829	+	0.981035i	$0.437909\pi$
$380$	1.57248e7	−	2.19646e7i	0.286572	−	0.400288i
$381$	4.36484e7	+	4.74438e7i	0.789211	+	0.857837i
$382$		−	3.54670e6i		−	0.0636261i
$383$	−7.65355e7			−1.36228			−0.681141	−	0.732153i	$-0.738516\pi$
$383$	−7.65355e7			−1.36228			−0.681141	+	0.732153i	$0.738516\pi$
$384$	3.68122e7	−	3.38673e7i	0.650127	−	0.598118i
$385$	5.24888e7	−	7.33173e7i	0.919782	−	1.28477i
$386$			3.66378e6i			0.0637041i
$387$	1.04754e7	+	874449.i	0.180734	+	0.0150870i
$388$			1.90853e7i			0.326742i
$389$		−	3.71640e7i		−	0.631355i	−0.948867	−	0.315678i	$-0.897768\pi$
$389$		−	3.71640e7i		−	0.631355i	0.948867	−	0.315678i	$-0.102232\pi$
$390$	−1.16990e7	+	1.43951e6i	−0.197221	+	0.0242672i
$391$	4.36231e7			0.729770
$392$	−1.89213e7			−0.314118
$393$	6.80963e7	+	7.40176e7i	1.12188	+	1.21943i
$394$	1.63576e7			0.267443
$395$	−5.52034e7	+	7.71091e7i	−0.895725	+	1.25116i
$396$	−7.15620e7	−	5.97372e6i	−1.15238	−	0.0961965i
$397$			8.06527e7i			1.28898i	0.764611	+	0.644492i	$0.222931\pi$
$397$			8.06527e7i			1.28898i	−0.764611	+	0.644492i	$0.777069\pi$
$398$	−4.01504e6			−0.0636855
$399$	2.89295e7	+	3.14451e7i	0.455431	+	0.495033i
$400$	−1.63556e7	−	4.80407e7i	−0.255556	−	0.750637i
$401$		−	7.88088e7i		−	1.22220i	−0.791554	−	0.611099i	$-0.790728\pi$
$401$		−	7.88088e7i		−	1.22220i	0.791554	−	0.611099i	$-0.209272\pi$
$402$	−1.36674e7	−	1.48558e7i	−0.210382	−	0.228675i
$403$			2.20120e7i			0.336313i
$404$			6.18771e7i			0.938395i
$405$	−4.70902e7	+	4.68559e7i	−0.708868	+	0.705341i
$406$	−1.06411e7			−0.159005
$407$	−2.94551e6			−0.0436895
$408$	1.07019e7	−	9.84580e6i	0.157573	−	0.144967i
$409$	−8.05292e7			−1.17702			−0.588509	−	0.808490i	$-0.700285\pi$
$409$	−8.05292e7			−1.17702			−0.588509	+	0.808490i	$0.700285\pi$
$410$	−495734.	−	354903.i	−0.00719279	−	0.00514941i
$411$	1.68452e7	−	1.54976e7i	0.242634	−	0.223223i
$412$		−	6.60192e7i		−	0.944015i
$413$	8.75316e7			1.24255
$414$	−2.74358e6	+	3.28666e7i	−0.0386648	+	0.463184i
$415$	−1.89993e7	+	2.65385e7i	−0.265823	+	0.371307i
$416$		−	3.89428e7i		−	0.540937i
$417$	4.89231e7	−	4.50093e7i	0.674692	−	0.620718i
$418$			1.27994e7i			0.175251i
$419$		−	1.20097e8i		−	1.63264i	−0.577598	−	0.816322i	$-0.696010\pi$
$419$		−	1.20097e8i		−	1.63264i	0.577598	−	0.816322i	$-0.303990\pi$
$420$	8.67729e7	−	1.06770e7i	1.17121	−	0.144113i
$421$	−5.38191e7			−0.721258			−0.360629	−	0.932709i	$-0.617438\pi$
$421$	−5.38191e7			−0.721258			−0.360629	+	0.932709i	$0.617438\pi$
$422$	2.32884e7			0.309886
$423$	3.00792e6	−	3.60332e7i	0.0397415	−	0.476082i
$424$	−2.14718e7			−0.281690
$425$	−1.03274e7	−	3.03344e7i	−0.134532	−	0.395157i
$426$	−1.57185e7	−	1.70853e7i	−0.203321	−	0.221000i
$427$		−	2.77711e7i		−	0.356705i
$428$	1.92999e7			0.246163
$429$	−5.40391e7	+	4.97160e7i	−0.684441	+	0.629687i
$430$	−3.11715e6	−	2.23161e6i	−0.0392060	−	0.0280681i
$431$		−	2.73801e7i		−	0.341982i	−0.985273	−	0.170991i	$-0.945303\pi$
$431$		−	2.73801e7i		−	0.341982i	0.985273	−	0.170991i	$-0.0546969\pi$
$432$	−3.92196e7	−	5.04845e7i	−0.486465	−	0.626191i
$433$		−	9.01003e7i		−	1.10985i	−0.831902	−	0.554923i	$-0.812748\pi$
$433$		−	9.01003e7i		−	1.10985i	0.831902	−	0.554923i	$-0.187252\pi$
$434$			1.24179e7i			0.151908i
$435$	3.84788e7	−	4.73464e6i	0.467470	−	0.0575201i
$436$	9.90724e7			1.19535
$437$	−7.72874e7			−0.926114
$438$	2.59139e7	+	2.81673e7i	0.308398	+	0.335214i
$439$	6.12364e7			0.723796			0.361898	−	0.932218i	$-0.382129\pi$
$439$	6.12364e7			0.723796			0.361898	+	0.932218i	$0.382129\pi$
$440$	4.42088e7	+	3.16496e7i	0.518980	+	0.371544i
$441$	−4.36920e6	+	5.23407e7i	−0.0509432	+	0.610272i
$442$		−	7.16253e6i		−	0.0829469i
$443$	−7.59607e7			−0.873731			−0.436866	−	0.899527i	$-0.643912\pi$
$443$	−7.59607e7			−0.873731			−0.436866	+	0.899527i	$0.643912\pi$
$444$	−1.93364e6	−	2.10177e6i	−0.0220915	−	0.0240125i
$445$	−3.21809e7	−	2.30387e7i	−0.365189	−	0.261444i
$446$			1.61452e6i			0.0181986i
$447$	8.62988e7	+	9.38028e7i	0.966234	+	1.05025i
$448$			6.85651e7i			0.762551i
$449$		−	2.63688e7i		−	0.291308i	−0.989336	−	0.145654i	$-0.953471\pi$
$449$		−	2.63688e7i		−	0.291308i	0.989336	−	0.145654i	$-0.0465286\pi$
$450$	2.35041e7	−	5.87308e6i	0.257933	−	0.0644508i
$451$	−3.79806e6			−0.0414030
$452$	−8.49294e7			−0.919692
$453$	−1.76281e7	+	1.62179e7i	−0.189631	+	0.174461i
$454$	−4.25996e6			−0.0455238
$455$	5.20399e7	−	7.26902e7i	0.552462	−	0.771688i
$456$	−1.89607e7	+	1.74439e7i	−0.199968	+	0.183971i
$457$			1.03214e7i			0.108141i	0.998537	+	0.0540704i	$0.0172195\pi$
$457$			1.03214e7i			0.108141i	−0.998537	+	0.0540704i	$0.982780\pi$
$458$	−4.92442e7			−0.512576
$459$	−2.47645e7	−	3.18775e7i	−0.256089	−	0.329645i
$460$	−9.20552e7	+	1.28584e8i	−0.945747	+	1.32104i
$461$			1.30665e8i			1.33369i	0.745195	+	0.666847i	$0.232356\pi$
$461$			1.30665e8i			1.33369i	−0.745195	+	0.666847i	$0.767644\pi$
$462$	−3.04858e7	+	2.80470e7i	−0.309152	+	0.284420i
$463$		−	5.27156e7i		−	0.531125i	−0.964094	−	0.265562i	$-0.914442\pi$
$463$		−	5.27156e7i		−	0.531125i	0.964094	−	0.265562i	$-0.0855576\pi$
$464$			3.73091e7i			0.373474i
$465$	−5.52519e6	−	4.49036e7i	−0.0549526	−	0.446604i
$466$	−3.18571e7			−0.314810
$467$	1.26681e8			1.24383			0.621915	−	0.783084i	$-0.286355\pi$
$467$	1.26681e8			1.24383			0.621915	+	0.783084i	$0.286355\pi$
$468$	−7.09499e7	−	5.92263e6i	−0.692172	−	0.0577799i
$469$	1.53101e8			1.48409
$470$	−7.67626e6	+	1.07223e7i	−0.0739360	+	0.103275i
$471$	−3.55051e6	−	3.85924e6i	−0.0339804	−	0.0369351i
$472$			5.27797e7i			0.501927i
$473$	−2.38820e7			−0.225677
$474$	3.20624e7	−	2.94975e7i	0.301066	−	0.276981i
$475$	1.82972e7	+	5.37438e7i	0.170727	+	0.501473i
$476$			5.31256e7i			0.492587i
$477$	−4.95815e6	+	5.93959e7i	−0.0456840	+	0.547270i
$478$		−	3.40298e7i		−	0.311585i
$479$			9.80146e7i			0.891834i	0.895074	+	0.445917i	$0.147122\pi$
$479$			9.80146e7i			0.891834i	−0.895074	+	0.445917i	$0.852878\pi$
$480$	9.77496e6	+	7.94418e7i	0.0883876	+	0.718332i
$481$	−2.92032e6			−0.0262419
$482$	2.51977e7			0.225020
$483$	−1.69358e8	−	1.84084e8i	−1.50302	−	1.63371i
$484$	5.77821e7			0.509632
$485$	−3.26147e7	−	2.33493e7i	−0.285883	−	0.204668i
$486$	2.55747e7	−	1.66532e7i	0.222793	−	0.145074i
$487$			1.76499e7i			0.152811i	0.997077	+	0.0764056i	$0.0243444\pi$
$487$			1.76499e7i			0.152811i	−0.997077	+	0.0764056i	$0.975656\pi$
$488$	1.67454e7			0.144090
$489$	−1.18332e8	−	1.28621e8i	−1.01199	−	1.09998i
$490$	1.11503e7	−	1.55749e7i	0.0947759	−	0.132385i
$491$			4.95972e6i			0.0418999i	0.999781	+	0.0209500i	$0.00666907\pi$
$491$			4.95972e6i			0.0418999i	−0.999781	+	0.0209500i	$0.993331\pi$
$492$	−2.49331e6	−	2.71011e6i	−0.0209354	−	0.0227558i
$493$			2.35581e7i			0.196607i
$494$			1.26899e7i			0.105264i
$495$	9.77585e7	−	1.14983e8i	0.806008	−	0.948022i
$496$	4.35386e7			0.356804
$497$	1.76077e8			1.43428
$498$	1.10349e7	−	1.01521e7i	0.0893470	−	0.0821994i
$499$	−6.60496e7			−0.531580			−0.265790	−	0.964031i	$-0.585633\pi$
$499$	−6.60496e7			−0.531580			−0.265790	+	0.964031i	$0.585633\pi$
$500$	1.11208e8	+	3.35717e7i	0.889662	+	0.268573i
$501$	1.29255e8	−	1.18915e8i	1.02786	−	0.945631i
$502$		−	4.19531e7i		−	0.331629i
$503$	−4.81772e7			−0.378562			−0.189281	−	0.981923i	$-0.560616\pi$
$503$	−4.81772e7			−0.378562			−0.189281	+	0.981923i	$0.560616\pi$
$504$	−8.30962e7	−	6.93656e6i	−0.649067	−	0.0541817i
$505$	−1.05741e8	−	7.57015e7i	−0.821050	−	0.587801i
$506$		−	7.49296e7i		−	0.578365i
$507$	4.23324e7	−	3.89459e7i	0.324825	−	0.298839i
$508$		−	1.42011e8i		−	1.08326i
$509$			1.50656e8i			1.14244i	0.820796	+	0.571221i	$0.193530\pi$
$509$			1.50656e8i			1.14244i	−0.820796	+	0.571221i	$0.806470\pi$
$510$	1.79786e6	+	1.46113e7i	0.0135533	+	0.110148i
$511$	−2.90286e8			−2.17552
$512$	−1.31617e8			−0.980624
$513$	4.38755e7	+	5.64777e7i	0.324990	+	0.418335i
$514$	4.62932e7			0.340901
$515$	1.12820e8	+	8.07691e7i	0.825967	+	0.591321i
$516$	−1.56778e7	−	1.70411e7i	−0.114113	−	0.124036i
$517$			8.21490e7i			0.594471i
$518$	−1.64748e6			−0.0118531
$519$	−1.76045e8	+	1.61962e8i	−1.25928	+	1.15854i
$520$	4.38306e7	+	3.13789e7i	0.311722	+	0.223166i
$521$		−	1.18571e8i		−	0.838427i	−0.907888	−	0.419213i	$-0.862306\pi$
$521$		−	1.18571e8i		−	0.838427i	0.907888	−	0.419213i	$-0.137694\pi$
$522$	−1.77492e7	−	1.48163e6i	−0.124786	−	0.0104167i
$523$		−	1.41962e8i		−	0.992354i	−0.868221	−	0.496177i	$-0.834737\pi$
$523$		−	1.41962e8i		−	0.992354i	0.868221	−	0.496177i	$-0.165263\pi$
$524$		−	2.21553e8i		−	1.53987i
$525$	−8.79136e7	+	1.61348e8i	−0.607545	+	1.11503i
$526$	−1.36543e7			−0.0938234
$527$	2.74916e7			0.187832
$528$	9.83358e7	+	1.06887e8i	0.668052	+	0.726142i
$529$	3.04417e8			2.05637
$530$	1.26533e7	−	1.76743e7i	0.0849916	−	0.118718i
$531$	1.46001e8	+	1.21876e7i	0.975149	+	0.0814018i
$532$		−	9.41230e7i		−	0.625117i
$533$	−3.76557e6			−0.0248685
$534$	1.23106e7	+	1.33810e7i	0.0808452	+	0.0878750i
$535$	−2.36118e7	+	3.29814e7i	−0.154194	+	0.215381i
$536$			9.23167e7i			0.599495i
$537$	−1.22167e8	−	1.32789e8i	−0.788914	−	0.857513i
$538$			3.85554e7i			0.247593i
$539$		−	1.19327e8i		−	0.762031i
$540$	1.46222e8	−	5.72708e6i	0.928605	−	0.0363707i
$541$	5.66633e7			0.357857			0.178929	−	0.983862i	$-0.442737\pi$
$541$	5.66633e7			0.357857			0.178929	+	0.983862i	$0.442737\pi$
$542$	−1.40288e7			−0.0881095
$543$	−3.76697e6	+	3.46562e6i	−0.0235284	+	0.0216462i
$544$	−4.86372e7			−0.302115
$545$	−1.21207e8	+	1.69304e8i	−0.748752	+	1.04587i
$546$	−3.02250e7	+	2.78071e7i	−0.185690	+	0.170835i
$547$			1.19120e8i			0.727818i	0.931434	+	0.363909i	$0.118558\pi$
$547$			1.19120e8i			0.727818i	−0.931434	+	0.363909i	$0.881442\pi$
$548$	−5.04219e7			−0.306392
$549$	3.86674e6	−	4.63215e7i	0.0233683	−	0.279940i
$550$	−5.21042e7	+	1.77390e7i	−0.313173	+	0.106620i
$551$		−	4.17381e7i		−	0.249504i
$552$	1.10999e8	−	1.02119e8i	0.659935	−	0.607142i
$553$			3.30429e8i			1.95390i
$554$			3.27037e7i			0.192339i
$555$	5.95734e6	−	733024.i	0.0348476	−	0.00428785i
$556$	−1.46439e8			−0.851986
$557$	−2.53351e8			−1.46608			−0.733039	−	0.680187i	$-0.761899\pi$
$557$	−2.53351e8			−1.46608			−0.733039	+	0.680187i	$0.761899\pi$
$558$	−1.72902e6	+	2.07128e7i	−0.00995172	+	0.119216i
$559$	−2.36778e7			−0.135552
$560$	−1.43778e8	−	1.02932e8i	−0.818705	−	0.586122i
$561$	6.20924e7	+	6.74916e7i	0.351682	+	0.382262i
$562$			5.51514e6i			0.0310705i
$563$	7.90742e7			0.443108			0.221554	−	0.975148i	$-0.428887\pi$
$563$	7.90742e7			0.443108			0.221554	+	0.975148i	$0.428887\pi$
$564$	−5.86175e7	+	5.39282e7i	−0.326731	+	0.300593i
$565$	1.03904e8	−	1.45135e8i	0.576086	−	0.804686i
$566$			4.47200e7i			0.246634i
$567$	−3.83762e7	+	2.28261e8i	−0.210529	+	1.25223i
$568$			1.06171e8i			0.579375i
$569$			2.08101e8i			1.12963i	0.825216	+	0.564817i	$0.191053\pi$
$569$			2.08101e8i			1.12963i	−0.825216	+	0.564817i	$0.808947\pi$
$570$	−3.18528e6	−	2.58870e7i	−0.0171998	−	0.139784i
$571$	2.63959e8			1.41784			0.708922	−	0.705287i	$-0.249182\pi$
$571$	2.63959e8			1.41784			0.708922	+	0.705287i	$0.249182\pi$
$572$	1.61753e8			0.864297
$573$	3.04836e7	+	3.31343e7i	0.162033	+	0.176122i
$574$	−2.12432e6			−0.0112327
$575$	−1.07114e8	−	3.14624e8i	−0.563436	−	1.65497i
$576$	−9.54675e6	+	1.14365e8i	−0.0499561	+	0.598447i
$577$		−	6.12849e7i		−	0.319026i	−0.987196	−	0.159513i	$-0.949008\pi$
$577$		−	6.12849e7i		−	0.319026i	0.987196	−	0.159513i	$-0.0509924\pi$
$578$	4.23927e7			0.219537
$579$	−3.14898e7	−	3.42280e7i	−0.162231	−	0.176338i
$580$	−6.94404e7	−	4.97133e7i	−0.355900	−	0.254794i
$581$			1.13723e8i			0.579857i
$582$	1.24765e7	+	1.35614e7i	0.0632885	+	0.0687917i
$583$		−	1.35412e8i		−	0.683361i
$584$		−	1.75036e8i		−	0.878798i
$585$	9.69224e7	−	1.14000e8i	0.484124	−	0.569424i
$586$	4.45796e7			0.221536
$587$	31678.0			0.000156619			7.83094e−5	−	1.00000i	$-0.499975\pi$
$587$	31678.0			0.000156619			7.83094e−5		1.00000i	$0.499975\pi$
$588$	8.51459e7	−	7.83344e7i	0.418824	−	0.385319i
$589$	−4.87072e7			−0.238367
$590$	−4.34451e7	−	3.11029e7i	−0.211536	−	0.151442i
$591$	−1.52817e8	+	1.40592e8i	−0.740303	+	0.681080i
$592$			5.77624e6i			0.0278407i
$593$	2.05099e8			0.983558			0.491779	−	0.870720i	$-0.336347\pi$
$593$	2.05099e8			0.983558			0.491779	+	0.870720i	$0.336347\pi$
$594$	−5.47547e7	+	4.25370e7i	−0.261254	+	0.202958i
$595$	−9.07857e7	−	6.49947e7i	−0.430990	−	0.308551i
$596$		−	2.80776e8i		−	1.32623i
$597$	3.75096e7	−	3.45089e7i	0.176286	−	0.162184i
$598$		−	7.42888e7i		−	0.347392i
$599$		−	1.19102e8i		−	0.554166i	−0.960846	−	0.277083i	$-0.910632\pi$
$599$		−	1.19102e8i		−	0.554166i	0.960846	−	0.277083i	$-0.0893677\pi$
$600$	−9.72893e7	−	5.30100e7i	−0.450413	−	0.245417i
$601$	−2.82454e8			−1.30114			−0.650571	−	0.759445i	$-0.725470\pi$
$601$	−2.82454e8			−1.30114			−0.650571	+	0.759445i	$0.725470\pi$
$602$	−1.33577e7			−0.0612267
$603$	2.55369e8	+	2.13172e7i	1.16471	+	0.0972252i
$604$	5.27653e7			0.239462
$605$	−7.06916e7	+	9.87432e7i	−0.319228	+	0.445904i
$606$	4.04505e7	+	4.39678e7i	0.181763	+	0.197568i
$607$		−	3.99029e8i		−	1.78418i	−0.451861	−	0.892089i	$-0.649240\pi$
$607$		−	3.99029e8i		−	1.78418i	0.451861	−	0.892089i	$-0.350760\pi$
$608$	8.61709e7			0.383398
$609$	9.94124e7	−	9.14596e7i	0.440138	−	0.404928i
$610$	−9.86800e6	+	1.37838e7i	−0.0434750	+	0.0607266i
$611$			8.14464e7i			0.357066i
$612$	−7.39701e6	+	8.86122e7i	−0.0322702	+	0.386580i
$613$			4.41908e8i			1.91845i	0.282645	+	0.959225i	$0.408788\pi$
$613$			4.41908e8i			1.91845i	−0.282645	+	0.959225i	$0.591212\pi$
$614$		−	3.52400e7i		−	0.152241i
$615$	7.68163e6	−	945191.i	0.0330239	−	0.00406344i
$616$	1.89444e8			0.810472
$617$	9.43666e7			0.401757			0.200878	−	0.979616i	$-0.435620\pi$
$617$	9.43666e7			0.401757			0.200878	+	0.979616i	$0.435620\pi$
$618$	−4.31583e7	−	4.69111e7i	−0.182852	−	0.198751i
$619$	−1.32184e7			−0.0557322			−0.0278661	−	0.999612i	$-0.508871\pi$
$619$	−1.32184e7			−0.0557322			−0.0278661	+	0.999612i	$0.508871\pi$
$620$	−5.80139e7	+	8.10349e7i	−0.243421	+	0.340014i
$621$	−2.56854e8	−	3.30629e8i	−1.07253	−	1.38059i
$622$			8.50120e7i			0.353272i
$623$	−1.37902e8			−0.570304
$624$	9.74948e7	+	1.05972e8i	0.401262	+	0.436153i
$625$	−1.93424e8	+	1.48970e8i	−0.792263	+	0.610179i
$626$			1.97910e7i			0.0806762i
$627$	−1.10010e8	−	1.19575e8i	−0.446301	−	0.485109i
$628$			1.15517e7i			0.0466408i
$629$			3.64730e6i			0.0146561i
$630$	5.46782e7	−	6.43122e7i	0.218672	−	0.257200i
$631$	1.42588e8			0.567537			0.283768	−	0.958893i	$-0.408415\pi$
$631$	1.42588e8			0.567537			0.283768	+	0.958893i	$0.408415\pi$
$632$	−1.99241e8			−0.789275
$633$	−2.17566e8	+	2.00161e8i	−0.857789	+	0.789168i
$634$	−1.84213e7			−0.0722857
$635$	2.42682e8	+	1.73739e8i	0.947798	+	0.678541i
$636$	9.66232e7	−	8.88935e7i	0.375587	−	0.345540i
$637$		−	1.18306e8i		−	0.457710i
$638$	4.04648e7			0.155817
$639$	2.93692e8	+	2.45163e7i	1.12562	+	0.0939621i
$640$	1.34806e8	−	1.88299e8i	0.514244	−	0.718305i
$641$			6.54188e7i			0.248387i	0.992258	+	0.124193i	$0.0396343\pi$
$641$			6.54188e7i			0.248387i	−0.992258	+	0.124193i	$0.960366\pi$
$642$	1.37139e7	−	1.26168e7i	0.0518268	−	0.0476808i
$643$		−	2.37935e8i		−	0.895003i	−0.894283	−	0.447502i	$-0.852314\pi$
$643$		−	2.37935e8i		−	0.895003i	0.894283	−	0.447502i	$-0.147686\pi$
$644$			5.51011e8i			2.06302i
$645$	4.83018e7	−	5.94332e6i	0.180005	−	0.0221488i
$646$	1.58490e7			0.0587899
$647$	1.09113e7			0.0402870			0.0201435	−	0.999797i	$-0.493588\pi$
$647$	1.09113e7			0.0402870			0.0201435	+	0.999797i	$0.493588\pi$
$648$	−1.37637e8	−	2.31400e7i	−0.505835	−	0.0850430i
$649$	−3.32854e8			−1.21764
$650$	−5.16586e7	+	1.75873e7i	−0.188106	+	0.0640410i
$651$	−1.06731e8	−	1.16011e8i	−0.386853	−	0.420492i
$652$			3.84996e8i			1.38903i
$653$	3.43719e8			1.23442			0.617212	−	0.786797i	$-0.288262\pi$
$653$	3.43719e8			1.23442			0.617212	+	0.786797i	$0.288262\pi$
$654$	7.03976e7	−	6.47659e7i	0.251666	−	0.231533i
$655$	3.78610e8	+	2.71052e8i	1.34731	+	0.964559i
$656$			7.44812e6i			0.0263837i
$657$	−4.84190e8	−	4.04183e7i	−1.70734	−	0.142522i
$658$			4.59474e7i			0.161281i
$659$		−	1.28225e8i		−	0.448039i	−0.974585	−	0.224020i	$-0.928082\pi$
$659$		−	1.28225e8i		−	0.448039i	0.974585	−	0.224020i	$-0.0719180\pi$
$660$	−3.29969e8	+	4.06012e7i	−1.14773	+	0.141224i
$661$	2.84082e8			0.983646			0.491823	−	0.870695i	$-0.336331\pi$
$661$	2.84082e8			0.983646			0.491823	+	0.870695i	$0.336331\pi$
$662$	9.18282e7			0.316521
$663$	6.15613e7	+	6.69143e7i	0.211236	+	0.229603i
$664$	−6.85727e7			−0.234232
$665$	1.60846e8	+	1.15152e8i	0.546947	+	0.391566i
$666$	−2.74795e6	−	229389.i	−0.00930222	−	0.000776514i
$667$			2.44341e8i			0.823416i
$668$	−3.86892e8			−1.29796
$669$	−1.38766e7	−	1.50833e7i	−0.0463453	−	0.0503752i
$670$	−7.59897e7	−	5.44020e7i	−0.252656	−	0.180880i
$671$			1.05604e8i			0.349554i
$672$	1.88824e8	+	2.05243e8i	0.622228	+	0.676333i
$673$		−	5.16601e8i		−	1.69477i	−0.530981	−	0.847384i	$-0.678177\pi$
$673$		−	5.16601e8i		−	1.69477i	0.530981	−	0.847384i	$-0.321823\pi$
$674$			1.06227e8i			0.346942i
$675$	−1.69103e8	+	2.56884e8i	−0.549846	+	0.835266i
$676$	−1.26712e8			−0.410181
$677$	1.88030e8			0.605985			0.302992	−	0.952993i	$-0.402014\pi$
$677$	1.88030e8			0.605985			0.302992	+	0.952993i	$0.402014\pi$
$678$	−6.03480e7	+	5.55203e7i	−0.193630	+	0.178140i
$679$	−1.39761e8			−0.446454
$680$	3.91904e7	−	5.47419e7i	0.124639	−	0.174098i
$681$	3.97977e7	−	3.66140e7i	0.126013	−	0.115933i
$682$		−	4.72212e7i		−	0.148862i
$683$	−5.67497e8			−1.78115			−0.890577	−	0.454833i	$-0.849699\pi$
$683$	−5.67497e8			−1.78115			−0.890577	+	0.454833i	$0.849699\pi$
$684$	1.31053e7	−	1.56995e8i	0.0409525	−	0.490589i
$685$	6.16871e7	−	8.61655e7i	0.191921	−	0.268078i
$686$			4.22431e7i			0.130853i
$687$	4.60052e8	−	4.23249e8i	1.41885	−	1.30535i
$688$			4.68334e7i			0.143811i
$689$		−	1.34254e8i		−	0.410457i
$690$	1.86471e7	+	1.51546e8i	0.0567628	+	0.461316i
$691$	−2.80301e8			−0.849552			−0.424776	−	0.905298i	$-0.639647\pi$
$691$	−2.80301e8			−0.849552			−0.424776	+	0.905298i	$0.639647\pi$
$692$	5.26948e8			1.59019
$693$	4.37453e7	−	5.24045e8i	0.131441	−	1.57459i
$694$	−3.05261e7			−0.0913256
$695$	1.79156e8	−	2.50248e8i	0.533675	−	0.745447i
$696$	5.51482e7	+	5.99436e7i	0.163570	+	0.177793i
$697$			4.70298e6i			0.0138891i
$698$	1.99510e7			0.0586677
$699$	2.97618e8	−	2.73809e8i	0.871419	−	0.801707i
$700$	3.83159e8	−	1.30447e8i	1.11708	−	0.380313i
$701$		−	3.08070e8i		−	0.894325i	−0.894453	−	0.447162i	$-0.852435\pi$
$701$		−	3.08070e8i		−	0.894325i	0.894453	−	0.447162i	$-0.147565\pi$
$702$	−5.42864e7	+	4.21731e7i	−0.156921	+	0.121906i
$703$		−	6.46195e6i		−	0.0185994i
$704$		−	2.60731e8i		−	0.747264i
$705$	−2.04437e7	−	1.66148e8i	−0.0583435	−	0.474162i
$706$	−1.31885e8			−0.374784
$707$	−4.53123e8			−1.28221
$708$	−2.18508e8	−	2.37509e8i	−0.615699	−	0.669236i
$709$	−1.79955e8			−0.504924			−0.252462	−	0.967607i	$-0.581240\pi$
$709$	−1.79955e8			−0.504924			−0.252462	+	0.967607i	$0.581240\pi$
$710$	−8.73935e7	−	6.25661e7i	−0.244177	−	0.174809i
$711$	−4.60077e7	+	5.51147e8i	−0.128003	+	1.53341i
$712$		−	8.31519e7i		−	0.230373i
$713$	2.85139e8			0.786662
$714$	3.47294e7	+	3.77493e7i	0.0954119	+	0.103708i
$715$	−1.97891e8	+	2.76417e8i	−0.541387	+	0.756218i
$716$			3.97472e8i			1.08285i
$717$	2.92483e8	+	3.17916e8i	0.793494	+	0.862492i
$718$		−	1.07610e8i		−	0.290722i
$719$		−	1.12572e8i		−	0.302861i	−0.988468	−	0.151431i	$-0.951612\pi$
$719$		−	1.12572e8i		−	0.302861i	0.988468	−	0.151431i	$-0.0483880\pi$
$720$	−2.25486e8	−	1.91708e8i	−0.604118	−	0.513620i
$721$	4.83456e8			1.28988
$722$	7.19824e7			0.191256
$723$	−2.35404e8	+	2.16572e8i	−0.622872	+	0.573044i
$724$	1.12755e7			0.0297112
$725$	1.69909e8	−	5.78458e7i	0.445864	−	0.151795i
$726$	4.10580e7	−	3.77735e7i	0.107297	−	0.0987136i
$727$			2.62827e8i			0.684016i	0.939697	+	0.342008i	$0.111107\pi$
$727$			2.62827e8i			0.684016i	−0.939697	+	0.342008i	$0.888893\pi$
$728$	1.87824e8			0.486806
$729$	−9.57928e7	+	3.75391e8i	−0.247258	+	0.968950i
$730$	1.44079e8	+	1.03148e8i	0.370368	+	0.265151i
$731$			2.95721e7i			0.0757060i
$732$	−7.53541e7	+	6.93259e7i	−0.192120	+	0.176751i
$733$		−	1.65920e8i		−	0.421296i	−0.977562	−	0.210648i	$-0.932443\pi$
$733$		−	1.65920e8i		−	0.421296i	0.977562	−	0.210648i	$-0.0675574\pi$
$734$		−	4.77181e7i		−	0.120669i
$735$	2.96959e7	+	2.41341e8i	0.0747884	+	0.607811i
$736$	−5.04458e8			−1.26529
$737$	−5.82194e8			−1.45434
$738$	−3.54332e6	−	295783.i	−0.00881539	−	0.000735875i
$739$	−5.11768e8			−1.26806			−0.634030	−	0.773309i	$-0.718600\pi$
$739$	−5.11768e8			−1.26806			−0.634030	+	0.773309i	$0.718600\pi$
$740$	−1.07509e7	−	7.69668e6i	−0.0265307	−	0.0189936i
$741$	−1.09069e8	−	1.18553e8i	−0.268068	−	0.291378i
$742$		−	7.57382e7i		−	0.185397i
$743$	−6.05204e8			−1.47549			−0.737743	−	0.675081i	$-0.764109\pi$
$743$	−6.05204e8			−1.47549			−0.737743	+	0.675081i	$0.764109\pi$
$744$	6.99524e7	−	6.43563e7i	0.169857	−	0.156269i
$745$	4.79814e8	+	3.43506e8i	1.16039	+	0.830740i
$746$		−	1.20222e8i		−	0.289578i
$747$	−1.58344e7	+	1.89688e8i	−0.0379874	+	0.455069i
$748$		−	2.02019e8i		−	0.482712i
$749$			1.41332e8i			0.336353i
$750$	1.00967e8	−	4.88441e7i	0.239329	−	0.115779i
$751$	6.21581e8			1.46750			0.733750	−	0.679420i	$-0.237768\pi$
$751$	6.21581e8			1.46750			0.733750	+	0.679420i	$0.237768\pi$
$752$	1.61097e8			0.378821
$753$	3.60583e8	+	3.91937e8i	0.844539	+	0.917976i
$754$	4.01187e7			0.0935908
$755$	−6.45539e7	+	9.01700e7i	−0.149997	+	0.209518i
$756$	4.02650e8	−	3.12804e8i	0.931886	−	0.723948i
$757$		−	7.60813e8i		−	1.75384i	−0.480634	−	0.876921i	$-0.659594\pi$
$757$		−	7.60813e8i		−	1.75384i	0.480634	−	0.876921i	$-0.340406\pi$
$758$	−4.48863e7			−0.103064
$759$	6.44013e8	+	7.00013e8i	1.47289	+	1.60096i
$760$	−6.94340e7	+	9.69866e7i	−0.158173	+	0.220938i
$761$		−	3.10324e8i		−	0.704145i	−0.935973	−	0.352072i	$-0.885477\pi$
$761$		−	3.10324e8i		−	0.704145i	0.935973	−	0.352072i	$-0.114523\pi$
$762$	−9.28360e7	−	1.00908e8i	−0.209822	−	0.228067i
$763$			7.25503e8i			1.63330i
$764$		−	9.91792e7i		−	0.222403i
$765$	−1.42379e8	−	1.21050e8i	−0.318025	−	0.270384i
$766$	1.62784e8			0.362180
$767$	−3.30007e8			−0.731370
$768$	1.21899e8	−	1.12147e8i	0.269102	−	0.247574i
$769$	2.84071e8			0.624667			0.312333	−	0.949973i	$-0.398889\pi$
$769$	2.84071e8			0.624667			0.312333	+	0.949973i	$0.398889\pi$
$770$	−1.11639e8	+	1.55939e8i	−0.244536	+	0.341572i
$771$	−4.32483e8	+	3.97886e8i	−0.943640	+	0.868151i
$772$			1.02453e8i			0.222676i
$773$	−3.25761e8			−0.705279			−0.352640	−	0.935759i	$-0.614716\pi$
$773$	−3.25761e8			−0.705279			−0.352640	+	0.935759i	$0.614716\pi$
$774$	−2.22803e7	−	1.85987e6i	−0.0480504	−	0.00401107i
$775$	−6.75044e7	−	1.98279e8i	−0.145020	−	0.425962i
$776$		−	8.42729e7i		−	0.180344i
$777$	1.53912e7	−	1.41599e7i	0.0328102	−	0.0301854i
$778$			7.90443e7i			0.167854i
$779$		−	8.33230e6i		−	0.0176260i
$780$	−3.27147e8	+	4.02540e7i	−0.689381	+	0.0848253i
$781$	−6.69564e8			−1.40553
$782$	−9.27822e7			−0.194019
$783$	1.78552e8	−	1.38711e8i	0.371946	−	0.288951i
$784$	−2.34004e8			−0.485596
$785$	−1.97405e7	−	1.41325e7i	−0.0408085	−	0.0292153i
$786$	−1.44834e8	−	1.57428e8i	−0.298266	−	0.324202i
$787$			2.49839e8i			0.512550i	0.966604	+	0.256275i	$0.0824953\pi$
$787$			2.49839e8i			0.512550i	−0.966604	+	0.256275i	$0.917505\pi$
$788$	4.57420e8			0.934838
$789$	1.27562e8	−	1.17357e8i	0.259711	−	0.238934i
$790$	1.17413e8	−	1.64004e8i	0.238140	−	0.332639i
$791$		−	6.21934e8i		−	1.25665i
$792$	3.15988e8	+	2.63775e7i	0.636055	+	0.0530955i
$793$			1.04701e8i			0.209958i
$794$		−	1.71541e8i		−	0.342693i
$795$	3.36988e7	+	2.73872e8i	0.0670676	+	0.545063i
$796$	−1.12276e8			−0.222611
$797$	5.86697e8			1.15888			0.579441	−	0.815014i	$-0.303271\pi$
$797$	5.86697e8			1.15888			0.579441	+	0.815014i	$0.303271\pi$
$798$	−6.15304e7	−	6.68807e7i	−0.121082	−	0.131611i
$799$	1.01722e8			0.199422
$800$	1.19426e8	+	3.50788e8i	0.233254	+	0.685132i
$801$	−2.30017e8	−	1.92010e7i	−0.447572	−	0.0373616i
$802$			1.67619e8i			0.324938i
$803$	1.10386e9			2.13191
$804$	−3.82192e8	−	4.15425e8i	−0.735383	−	0.799327i
$805$	−9.41616e8	−	6.74116e8i	−1.80504	−	1.29225i
$806$		−	4.68174e7i		−	0.0894133i
$807$	−3.31380e8	−	3.60195e8i	−0.630530	−	0.685357i
$808$		−	2.73223e8i		−	0.517945i
$809$			2.77810e8i			0.524690i	0.964974	+	0.262345i	$0.0844958\pi$
$809$			2.77810e8i			0.524690i	−0.964974	+	0.262345i	$0.915504\pi$
$810$	1.00156e8	−	9.96580e7i	0.188462	−	0.187524i
$811$	8.34478e8			1.56442			0.782208	−	0.623017i	$-0.214093\pi$
$811$	8.34478e8			1.56442			0.782208	+	0.623017i	$0.214093\pi$
$812$	−2.97566e8			−0.555797
$813$	1.31061e8	−	1.20576e8i	0.243894	−	0.224383i
$814$	6.26482e6			0.0116154
$815$	−6.57915e8	−	4.71010e8i	−1.21534	−	0.870076i
$816$	1.32353e8	−	1.21765e8i	0.243592	−	0.224106i
$817$		−	5.23932e7i		−	0.0960746i
$818$	1.71278e8			0.312926
$819$	4.33711e7	−	5.19563e8i	0.0789494	−	0.945771i
$820$	−1.38626e7	−	9.92441e6i	−0.0251422	−	0.0179996i
$821$			9.66638e8i			1.74676i	0.487035	+	0.873382i	$0.338078\pi$
$821$			9.66638e8i			1.74676i	−0.487035	+	0.873382i	$0.661922\pi$
$822$	−3.58282e7	+	3.29620e7i	−0.0645073	+	0.0593469i
$823$			1.87029e8i			0.335513i	0.985828	+	0.167757i	$0.0536523\pi$
$823$			1.87029e8i			0.335513i	−0.985828	+	0.167757i	$0.946348\pi$
$824$			2.91513e8i			0.521047i
$825$	3.34307e8	−	6.13553e8i	0.595365	−	1.09267i
$826$	−1.86171e8			−0.330349
$827$	4.27582e8			0.755967			0.377983	−	0.925812i	$-0.376618\pi$
$827$	4.27582e8			0.755967			0.377983	+	0.925812i	$0.376618\pi$
$828$	−7.67207e7	+	9.19073e8i	−0.135152	+	1.61904i
$829$	−3.32937e8			−0.584383			−0.292192	−	0.956360i	$-0.594385\pi$
$829$	−3.32937e8			−0.584383			−0.292192	+	0.956360i	$0.594385\pi$
$830$	4.04097e7	−	5.64450e7i	0.0706727	−	0.0987168i
$831$	−2.81085e8	−	3.05527e8i	−0.489818	−	0.532410i
$832$		−	2.58501e8i		−	0.448840i
$833$	−1.47758e8			−0.255632
$834$	−1.04055e8	+	9.57306e7i	−0.179376	+	0.165026i
$835$	4.73330e8	−	6.61156e8i	0.813026	−	1.13565i
$836$			3.57919e8i			0.612585i
$837$	−1.61871e8	−	2.08365e8i	−0.276054	−	0.355344i
$838$			2.55436e8i			0.434060i
$839$			7.38219e8i			1.24997i	0.780637	+	0.624984i	$0.214895\pi$
$839$			7.38219e8i			1.24997i	−0.780637	+	0.624984i	$0.785105\pi$
$840$	−3.83153e8	+	4.71453e7i	−0.646449	+	0.0795427i
$841$	4.62870e8			0.778164
$842$	1.14468e8			0.191756
$843$	−4.74021e7	−	5.15239e7i	−0.0791252	−	0.0860055i
$844$	6.51231e8			1.08320
$845$	1.55021e8	−	2.16536e8i	0.256933	−	0.358889i
$846$	−6.39755e6	+	7.66392e7i	−0.0105658	+	0.126573i
$847$			4.23135e8i			0.696352i
$848$	−2.65547e8			−0.435465
$849$	−3.84364e8	−	4.17786e8i	−0.628087	−	0.682702i
$850$	2.19654e7	+	6.45185e7i	0.0357671	+	0.105058i
$851$			3.78293e7i			0.0613818i
$852$	−4.39548e8	−	4.77768e8i	−0.710701	−	0.772500i
$853$			5.75317e8i			0.926958i	0.886108	+	0.463479i	$0.153399\pi$
$853$			5.75317e8i			0.926958i	−0.886108	+	0.463479i	$0.846601\pi$
$854$			5.90664e7i			0.0948346i
$855$	2.52254e8	+	2.14466e8i	0.403589	+	0.343131i
$856$	−8.52202e7			−0.135869
$857$	−6.26425e7			−0.0995236			−0.0497618	−	0.998761i	$-0.515846\pi$
$857$	−6.26425e7			−0.0995236			−0.0497618	+	0.998761i	$0.515846\pi$
$858$	1.14936e8	−	1.05741e8i	0.181968	−	0.167411i
$859$	−2.99365e8			−0.472304			−0.236152	−	0.971716i	$-0.575886\pi$
$859$	−2.99365e8			−0.472304			−0.236152	+	0.971716i	$0.575886\pi$
$860$	−8.71673e7	−	6.24043e7i	−0.137044	−	0.0981113i
$861$	1.98460e7	−	1.82584e7i	0.0310931	−	0.0286057i
$862$			5.82349e7i			0.0909204i
$863$	7.30432e8			1.13644			0.568221	−	0.822876i	$-0.307632\pi$
$863$	7.30432e8			1.13644			0.568221	+	0.822876i	$0.307632\pi$
$864$	2.86377e8	+	3.68632e8i	0.444014	+	0.571546i
$865$	−6.44677e8	+	9.00497e8i	−0.996080	+	1.39134i
$866$			1.91635e8i			0.295067i
$867$	−3.96044e8	+	3.64362e8i	−0.607696	+	0.559082i
$868$			3.47251e8i			0.530988i
$869$		−	1.25651e9i		−	1.91473i
$870$	−8.18407e7	+	1.00701e7i	−0.124283	+	0.0152925i
$871$	−5.77214e8			−0.873540
$872$	−4.37462e8			−0.659768
$873$	−2.33118e8	−	1.94598e7i	−0.350375	−	0.0292480i
$874$	1.64383e8			0.246220
$875$	−2.45844e8	+	8.14369e8i	−0.366974	+	1.21562i
$876$	7.24651e8	+	7.87662e8i	1.07799	+	1.17173i
$877$		−	1.05004e8i		−	0.155670i	−0.996966	−	0.0778352i	$-0.975199\pi$
$877$		−	1.05004e8i		−	0.155670i	0.996966	−	0.0778352i	$-0.0248008\pi$
$878$	−1.30244e8			−0.192431
$879$	−4.16475e8	+	3.83158e8i	−0.613228	+	0.564171i
$880$	5.46739e8	+	3.91418e8i	0.802292	+	0.574371i
$881$			8.93750e8i			1.30704i	0.756910	+	0.653519i	$0.226708\pi$
$881$			8.93750e8i			1.30704i	−0.756910	+	0.653519i	$0.773292\pi$
$882$	9.29288e6	−	1.11324e8i	0.0135439	−	0.162249i
$883$		−	8.90249e8i		−	1.29309i	−0.762875	−	0.646546i	$-0.776213\pi$
$883$		−	8.90249e8i		−	1.29309i	0.762875	−	0.646546i	$-0.223787\pi$
$884$		−	2.00291e8i		−	0.289938i
$885$	6.73203e8	−	8.28346e7i	0.971216	−	0.119504i
$886$	1.61561e8			0.232293
$887$	−5.07023e8			−0.726535			−0.363267	−	0.931685i	$-0.618339\pi$
$887$	−5.07023e8			−0.726535			−0.363267	+	0.931685i	$0.618339\pi$
$888$	8.53812e6	+	9.28055e6i	0.0121934	+	0.0132536i
$889$	1.03994e9			1.48014
$890$	6.84457e7	+	4.90012e7i	0.0970904	+	0.0695083i
$891$	1.45932e8	−	8.68003e8i	0.206309	−	1.22712i
$892$			4.51480e7i			0.0636127i
$893$	−1.80221e8			−0.253076
$894$	−1.83549e8	−	1.99510e8i	−0.256886	−	0.279223i
$895$	−6.79236e8	−	4.86274e8i	−0.947440	−	0.678285i
$896$		−	8.06902e8i		−	1.12175i
$897$	6.38505e8	+	6.94025e8i	0.884681	+	0.961608i
$898$			5.60840e7i			0.0774480i
$899$			1.53986e8i			0.211935i
$900$	6.57264e8	−	1.64233e8i	0.901596	−	0.225286i
$901$	−1.67675e8			−0.229241
$902$	8.07811e6			0.0110075
$903$	1.24791e8	−	1.14808e8i	0.169480	−	0.155922i
$904$	3.75013e8			0.507622
$905$	−1.37946e7	+	1.92686e7i	−0.0186108	+	0.0259958i
$906$	3.74933e7	−	3.44939e7i	0.0504160	−	0.0463828i
$907$		−	1.12026e9i		−	1.50140i	−0.660643	−	0.750700i	$-0.729716\pi$
$907$		−	1.12026e9i		−	1.50140i	0.660643	−	0.750700i	$-0.270284\pi$
$908$	−1.19125e8			−0.159127
$909$	−7.55798e8	−	6.30912e7i	−1.00627	−	0.0839995i
$910$	−1.10684e8	+	1.54605e8i	−0.146879	+	0.205163i
$911$		−	1.11807e9i		−	1.47881i	−0.673261	−	0.739405i	$-0.735107\pi$
$911$		−	1.11807e9i		−	1.47881i	0.673261	−	0.739405i	$-0.264893\pi$
$912$	−2.34491e8	+	2.15732e8i	−0.309131	+	0.284401i
$913$		−	4.32452e8i		−	0.568232i
$914$		−	2.19526e7i		−	0.0287507i
$915$	−2.62808e7	−	2.13586e8i	−0.0343065	−	0.278811i
$916$	−1.37705e9			−1.79169
$917$	1.62242e9			2.10405
$918$	5.26717e7	+	6.78005e7i	0.0680847	+	0.0876405i
$919$	−1.35382e8			−0.174427			−0.0872137	−	0.996190i	$-0.527796\pi$
$919$	−1.35382e8			−0.174427			−0.0872137	+	0.996190i	$0.527796\pi$
$920$	4.06477e8	−	5.67774e8i	0.522003	−	0.729142i
$921$	3.02885e8	+	3.29222e8i	0.387702	+	0.421415i
$922$		−	2.77912e8i		−	0.354580i
$923$	−6.63837e8			−0.844221
$924$	−8.52497e8	+	7.84299e8i	−1.08063	+	0.994182i
$925$	2.63056e7	−	8.95578e6i	0.0332370	−	0.0113156i
$926$			1.12121e8i			0.141206i
$927$	8.06392e8	+	6.73146e7i	1.01230	+	0.0845026i
$928$		−	2.72426e8i		−	0.340883i
$929$			7.76001e7i			0.0967866i	0.998828	+	0.0483933i	$0.0154101\pi$
$929$			7.76001e7i			0.0967866i	−0.998828	+	0.0483933i	$0.984590\pi$
$930$	1.17516e7	+	9.55057e7i	0.0146099	+	0.118735i
$931$	2.61783e8			0.324409
$932$	−8.90845e8			−1.10041
$933$	−7.30670e8	−	7.94205e8i	−0.899655	−	0.977884i
$934$	−2.69439e8			−0.330689
$935$	3.45229e8	+	2.47154e8i	0.422349	+	0.302366i
$936$	3.13285e8	+	2.61519e7i	0.382043	+	0.0318915i
$937$			9.07338e8i			1.10294i	0.834196	+	0.551468i	$0.185932\pi$
$937$			9.07338e8i			1.10294i	−0.834196	+	0.551468i	$0.814068\pi$
$938$	−3.25632e8			−0.394565
$939$	−1.70102e8	−	1.84893e8i	−0.205453	−	0.223318i
$940$	−2.14657e8	+	2.99837e8i	−0.258441	+	0.360995i
$941$		−	9.68700e8i		−	1.16257i	−0.813699	−	0.581287i	$-0.802549\pi$
$941$		−	9.68700e8i		−	1.16257i	0.813699	−	0.581287i	$-0.197451\pi$
$942$	7.55160e6	+	8.20824e6i	0.00903412	+	0.00981968i
$943$			4.87786e7i			0.0581693i
$944$			6.52738e8i			0.775931i
$945$	4.19391e7	+	1.07078e9i	0.0496963	+	1.26883i
$946$	5.07948e7			0.0599993
$947$	1.34579e9			1.58463			0.792316	−	0.610111i	$-0.208875\pi$
$947$	1.34579e9			1.58463			0.792316	+	0.610111i	$0.208875\pi$
$948$	8.96586e8	−	8.24861e8i	1.05237	−	0.968179i
$949$	1.09442e9			1.28052
$950$	−3.89164e7	−	1.14308e8i	−0.0453901	−	0.133323i
$951$	1.72097e8	−	1.58329e8i	0.200092	−	0.184085i
$952$		−	2.34580e8i		−	0.271882i
$953$	−1.43926e9			−1.66288			−0.831438	−	0.555618i	$-0.812482\pi$
$953$	−1.43926e9			−1.66288			−0.831438	+	0.555618i	$0.812482\pi$
$954$	1.05455e7	−	1.26330e8i	0.0121457	−	0.145499i
$955$	1.69486e8	+	1.21338e8i	0.194592	+	0.139311i
$956$		−	9.51603e8i		−	1.08914i
$957$	−3.78033e8	+	3.47791e8i	−0.431314	+	0.396810i
$958$		−	2.08468e8i		−	0.237106i
$959$		−	3.69237e8i		−	0.418649i
$960$	6.48858e7	+	5.27332e8i	0.0733392	+	0.596033i
$961$	−7.07807e8			−0.797525
$962$	6.21124e6			0.00697675
$963$	−1.96786e7	+	2.35739e8i	−0.0220351	+	0.263968i
$964$	7.04623e8			0.786549
$965$	−1.75081e8	−	1.25343e8i	−0.194830	−	0.139482i
$966$	3.60208e8	+	3.91530e8i	0.399597	+	0.434344i
$967$			1.43947e9i			1.59192i	0.605348	+	0.795961i	$0.293034\pi$
$967$			1.43947e9i			1.59192i	−0.605348	+	0.795961i	$0.706966\pi$
$968$	−2.55141e8			−0.281290
$969$	−1.48065e8	+	1.36220e8i	−0.162735	+	0.149717i
$970$	6.93685e7	+	4.96618e7i	0.0760058	+	0.0544136i
$971$			1.68414e9i			1.83959i	0.392404	+	0.919793i	$0.371644\pi$
$971$			1.68414e9i			1.83959i	−0.392404	+	0.919793i	$0.628356\pi$
$972$	7.15165e8	−	4.65687e8i	0.778767	−	0.507102i
$973$		−	1.07237e9i		−	1.16414i
$974$		−	3.75396e7i		−	0.0406268i
$975$	3.31448e8	−	6.08306e8i	0.357603	−	0.656308i
$976$	2.07093e8			0.222750
$977$	−1.63598e9			−1.75426			−0.877132	−	0.480249i	$-0.840546\pi$
$977$	−1.63598e9			−1.75426			−0.877132	+	0.480249i	$0.840546\pi$
$978$	2.51680e8	+	2.73565e8i	0.269050	+	0.292445i
$979$	5.24396e8			0.558871
$980$	3.11804e8	−	4.35533e8i	0.331286	−	0.462746i
$981$	−1.01016e8	+	1.21012e9i	−0.107000	+	1.28180i
$982$		−	1.05489e7i		−	0.0111396i
$983$	−2.95943e8			−0.311564			−0.155782	−	0.987791i	$-0.549790\pi$
$983$	−2.95943e8			−0.311564			−0.155782	+	0.987791i	$0.549790\pi$
$984$	1.10094e7	+	1.19667e7i	0.0115552	+	0.0125600i
$985$	−5.59615e8	+	7.81680e8i	−0.585573	+	0.817938i
$986$		−	5.01059e7i		−	0.0522707i
$987$	−3.94914e8	−	4.29253e8i	−0.410725	−	0.446439i
$988$			3.54858e8i			0.367946i
$989$			3.06718e8i			0.317066i
$990$	−2.07923e8	+	2.44558e8i	−0.214288	+	0.252044i
$991$	−3.86120e7			−0.0396735			−0.0198368	−	0.999803i	$-0.506315\pi$
$991$	−3.86120e7			−0.0396735			−0.0198368	+	0.999803i	$0.506315\pi$
$992$	−3.17913e8			−0.325667
$993$	−8.57884e8	+	7.89255e8i	−0.876155	+	0.806064i
$994$	−3.74499e8			−0.381322
$995$	1.37360e8	−	1.91867e8i	0.139441	−	0.194774i
$996$	3.08577e8	−	2.83891e8i	0.312310	−	0.287326i
$997$			1.82082e9i			1.83731i	0.395064	+	0.918654i	$0.370722\pi$
$997$			1.82082e9i			1.83731i	−0.395064	+	0.918654i	$0.629278\pi$
$998$	1.40481e8			0.141328
$999$	2.76437e7	−	2.14754e7i	0.0277268	−	0.0215399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.7.d.c.14.3	✓	8
3.2	odd	2	inner	15.7.d.c.14.5	yes	8
4.3	odd	2		240.7.c.c.209.2		8
5.2	odd	4		75.7.c.e.26.3		8
5.3	odd	4		75.7.c.e.26.6		8
5.4	even	2	inner	15.7.d.c.14.6	yes	8
12.11	even	2		240.7.c.c.209.8		8
15.2	even	4		75.7.c.e.26.5		8
15.8	even	4		75.7.c.e.26.4		8
15.14	odd	2	inner	15.7.d.c.14.4	yes	8
20.19	odd	2		240.7.c.c.209.7		8
60.59	even	2		240.7.c.c.209.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.7.d.c.14.3	✓	8	1.1	even	1	trivial
15.7.d.c.14.4	yes	8	15.14	odd	2	inner
15.7.d.c.14.5	yes	8	3.2	odd	2	inner
15.7.d.c.14.6	yes	8	5.4	even	2	inner
75.7.c.e.26.3		8	5.2	odd	4
75.7.c.e.26.4		8	15.8	even	4
75.7.c.e.26.5		8	15.2	even	4
75.7.c.e.26.6		8	5.3	odd	4
240.7.c.c.209.1		8	60.59	even	2
240.7.c.c.209.2		8	4.3	odd	2
240.7.c.c.209.7		8	20.19	odd	2
240.7.c.c.209.8		8	12.11	even	2

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.12691 q^{2} +(19.8701 - 18.2805i) q^{3} -59.4763 q^{4} +(72.7643 - 101.638i) q^{5} +(-42.2619 + 38.8810i) q^{6} -435.542i q^{7} +262.622 q^{8} +(60.6432 - 726.473i) q^{9} +O(q^{10})\)	\(q-2.12691 q^{2} +(19.8701 - 18.2805i) q^{3} -59.4763 q^{4} +(72.7643 - 101.638i) q^{5} +(-42.2619 + 38.8810i) q^{6} -435.542i q^{7} +262.622 q^{8} +(60.6432 - 726.473i) q^{9} +(-154.763 + 216.175i) q^{10} +1656.22i q^{11} +(-1181.80 + 1087.26i) q^{12} +1642.06i q^{13} +926.356i q^{14} +(-412.170 - 3349.74i) q^{15} +3247.91 q^{16} +2050.83 q^{17} +(-128.982 + 1545.14i) q^{18} -3633.48 q^{19} +(-4327.75 + 6045.07i) q^{20} +(-7961.94 - 8654.27i) q^{21} -3522.63i q^{22} +21270.9 q^{23} +(5218.34 - 4800.88i) q^{24} +(-5035.72 - 14791.3i) q^{25} -3492.50i q^{26} +(-12075.3 - 15543.7i) q^{27} +25904.4i q^{28} +11487.1i q^{29} +(876.647 + 7124.57i) q^{30} +13405.1 q^{31} -23715.8 q^{32} +(30276.7 + 32909.4i) q^{33} -4361.93 q^{34} +(-44267.8 - 31691.9i) q^{35} +(-3606.83 + 43207.9i) q^{36} +1778.45i q^{37} +7728.06 q^{38} +(30017.7 + 32627.9i) q^{39} +(19109.5 - 26692.5i) q^{40} +2293.20i q^{41} +(16934.3 + 18406.8i) q^{42} +14419.6i q^{43} -98506.0i q^{44} +(-69424.9 - 59025.0i) q^{45} -45241.3 q^{46} +49600.2 q^{47} +(64536.3 - 59373.5i) q^{48} -72047.6 q^{49} +(10710.5 + 31459.7i) q^{50} +(40750.3 - 37490.3i) q^{51} -97663.5i q^{52} -81759.3 q^{53} +(25683.1 + 33060.0i) q^{54} +(168336. + 120514. i) q^{55} -114383. i q^{56} +(-72197.6 + 66421.9i) q^{57} -24432.0i q^{58} +200972. i q^{59} +(24514.4 + 199230. i) q^{60} +63762.1 q^{61} -28511.4 q^{62} +(-316409. - 26412.7i) q^{63} -157425. q^{64} +(166896. + 119483. i) q^{65} +(-64395.6 - 69995.1i) q^{66} +351519. i q^{67} -121976. q^{68} +(422656. - 388844. i) q^{69} +(94153.3 + 67405.6i) q^{70} +404271. i q^{71} +(15926.3 - 190788. i) q^{72} -666493. i q^{73} -3782.59i q^{74} +(-370453. - 201849. i) q^{75} +216106. q^{76} +721354. q^{77} +(-63844.8 - 69396.4i) q^{78} -758661. q^{79} +(236332. - 330112. i) q^{80} +(-524086. - 88111.4i) q^{81} -4877.43i q^{82} -261108. q^{83} +(473547. + 514724. i) q^{84} +(149227. - 208443. i) q^{85} -30669.1i q^{86} +(209990. + 228250. i) q^{87} +434961. i q^{88} -316622. i q^{89} +(147660. + 125541. i) q^{90} +715185. q^{91} -1.26512e6 q^{92} +(266361. - 245053. i) q^{93} -105495. q^{94} +(-264387. + 369301. i) q^{95} +(-471236. + 433538. i) q^{96} -320890. i q^{97} +153239. q^{98} +(1.20320e6 + 100439. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9}+O(q^{10}) \) 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9	\( 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9} + 4240 q^{10} + 1980 q^{15} + 784 q^{16} - 28520 q^{19} + 24228 q^{21} + 14904 q^{24} + 800 q^{25} - 71100 q^{30} + 5896 q^{31} + 105344 q^{34} - 186624 q^{36} + 233568 q^{39} + 141920 q^{40} - 159300 q^{45} + 59336 q^{46} - 1041472 q^{49} + 66888 q^{51} + 917892 q^{54} + 442800 q^{55} - 638640 q^{60} + 1493416 q^{61} - 2063584 q^{64} - 1221840 q^{66} + 1502532 q^{69} + 2273400 q^{70} - 2574000 q^{75} - 219168 q^{76} - 1286360 q^{79} - 1752192 q^{81} + 6238728 q^{84} + 1651240 q^{85} - 2737440 q^{90} + 383616 q^{91} - 7641736 q^{94} - 151056 q^{96} + 6322320 q^{99}+O(q^{100}) \) 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9 + 4240 * q^10 + 1980 * q^15 + 784 * q^16 - 28520 * q^19 + 24228 * q^21 + 14904 * q^24 + 800 * q^25 - 71100 * q^30 + 5896 * q^31 + 105344 * q^34 - 186624 * q^36 + 233568 * q^39 + 141920 * q^40 - 159300 * q^45 + 59336 * q^46 - 1041472 * q^49 + 66888 * q^51 + 917892 * q^54 + 442800 * q^55 - 638640 * q^60 + 1493416 * q^61 - 2063584 * q^64 - 1221840 * q^66 + 1502532 * q^69 + 2273400 * q^70 - 2574000 * q^75 - 219168 * q^76 - 1286360 * q^79 - 1752192 * q^81 + 6238728 * q^84 + 1651240 * q^85 - 2737440 * q^90 + 383616 * q^91 - 7641736 * q^94 - 151056 * q^96 + 6322320 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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