LMFDB - Embedded newform 140.6.i.d.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,6,Mod(81,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("140.81");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	140.i (of order $3$, degree $2$, 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:	$22.4537347738$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 955 x^{12} + 2982 x^{11} + 679713 x^{10} + 1284921 x^{9} + 189493777 x^{8} + \cdots + 29\!\cdots\!00 $ x^14 - x^13 + 955x^12 + 2982x^11 + 679713x^10 + 1284921x^9 + 189493777x^8 - 432995194x^7 + 37948415515x^6 - 114490218225x^5 + 3541871074053x^4 - 22604917736772x^3 + 236082781322836x^2 - 815077229722000x + 2907851700250000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{5}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.4
Root			$2.48906 + 4.31118i$ of defining polynomial
Character	$\chi$	$=$	140.121
Dual form			140.6.i.d.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.489062 - 0.847081i) q^{3} +(12.5000 - 21.6506i) q^{5} +(124.053 + 37.6545i) q^{7} +(121.022 - 209.616i) q^{9} +O(q^{10})$	\(q+(-0.489062 - 0.847081i) q^{3} +(12.5000 - 21.6506i) q^{5} +(124.053 + 37.6545i) q^{7} +(121.022 - 209.616i) q^{9} +(110.552 + 191.482i) q^{11} -1064.81 q^{13} -24.4531 q^{15} +(863.965 + 1496.43i) q^{17} +(1119.86 - 1939.66i) q^{19} +(-28.7732 - 123.498i) q^{21} +(1828.68 - 3167.37i) q^{23} +(-312.500 - 541.266i) q^{25} -474.433 q^{27} +1946.84 q^{29} +(-44.0257 - 76.2548i) q^{31} +(108.134 - 187.294i) q^{33} +(2365.91 - 2215.14i) q^{35} +(6706.02 - 11615.2i) q^{37} +(520.756 + 901.976i) q^{39} +12293.0 q^{41} +3861.54 q^{43} +(-3025.54 - 5240.39i) q^{45} +(701.213 - 1214.54i) q^{47} +(13971.3 + 9342.30i) q^{49} +(845.065 - 1463.70i) q^{51} +(-9246.92 - 16016.1i) q^{53} +5527.62 q^{55} -2190.73 q^{57} +(-17703.1 - 30662.7i) q^{59} +(19165.0 - 33194.8i) q^{61} +(22906.1 - 21446.4i) q^{63} +(-13310.1 + 23053.7i) q^{65} +(15628.5 + 27069.4i) q^{67} -3577.36 q^{69} -24787.2 q^{71} +(37168.3 + 64377.3i) q^{73} +(-305.664 + 529.425i) q^{75} +(6504.19 + 27916.8i) q^{77} +(-33775.2 + 58500.4i) q^{79} +(-29176.2 - 50534.7i) q^{81} -16697.0 q^{83} +43198.2 q^{85} +(-952.124 - 1649.13i) q^{87} +(9344.38 - 16184.9i) q^{89} +(-132092. - 40094.7i) q^{91} +(-43.0626 + 74.5867i) q^{93} +(-27996.6 - 48491.5i) q^{95} -48997.0 q^{97} +53517.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 27 q^{3} + 175 q^{5} - 225 q^{7} - 312 q^{9}+O(q^{10}) $ 14 * q + 27 * q^3 + 175 * q^5 - 225 * q^7 - 312 * q^9	$ 14 q + 27 q^{3} + 175 q^{5} - 225 q^{7} - 312 q^{9} - 590 q^{11} - 1708 q^{13} + 1350 q^{15} + 1328 q^{17} + 2990 q^{19} + 993 q^{21} - 4089 q^{23} - 4375 q^{25} - 8562 q^{27} - 6126 q^{29} + 5740 q^{31} - 1470 q^{33} - 3000 q^{35} - 12218 q^{37} + 1560 q^{39} - 16954 q^{41} - 18390 q^{43} + 7800 q^{45} + 28652 q^{47} + 20435 q^{49} - 41244 q^{51} - 24932 q^{53} - 29500 q^{55} - 125868 q^{57} + 38242 q^{59} + 61299 q^{61} + 145548 q^{63} - 21350 q^{65} - 24913 q^{67} - 172302 q^{69} - 72340 q^{71} + 94780 q^{73} + 16875 q^{75} + 198344 q^{77} + 594 q^{79} + 53265 q^{81} - 227170 q^{83} + 66400 q^{85} + 43875 q^{87} + 36823 q^{89} + 138176 q^{91} + 21828 q^{93} - 74750 q^{95} - 515900 q^{97} + 756864 q^{99}+O(q^{100}) $ 14 * q + 27 * q^3 + 175 * q^5 - 225 * q^7 - 312 * q^9 - 590 * q^11 - 1708 * q^13 + 1350 * q^15 + 1328 * q^17 + 2990 * q^19 + 993 * q^21 - 4089 * q^23 - 4375 * q^25 - 8562 * q^27 - 6126 * q^29 + 5740 * q^31 - 1470 * q^33 - 3000 * q^35 - 12218 * q^37 + 1560 * q^39 - 16954 * q^41 - 18390 * q^43 + 7800 * q^45 + 28652 * q^47 + 20435 * q^49 - 41244 * q^51 - 24932 * q^53 - 29500 * q^55 - 125868 * q^57 + 38242 * q^59 + 61299 * q^61 + 145548 * q^63 - 21350 * q^65 - 24913 * q^67 - 172302 * q^69 - 72340 * q^71 + 94780 * q^73 + 16875 * q^75 + 198344 * q^77 + 594 * q^79 + 53265 * q^81 - 227170 * q^83 + 66400 * q^85 + 43875 * q^87 + 36823 * q^89 + 138176 * q^91 + 21828 * q^93 - 74750 * q^95 - 515900 * q^97 + 756864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.489062	−	0.847081i	−0.0313734	−	0.0543403i	0.849912	−	0.526924i	$-0.176655\pi$
$3$	−0.489062	−	0.847081i	−0.0313734	−	0.0543403i	−0.881286	+	0.472584i	$0.843321\pi$
$4$		0			0
$5$	12.5000	−	21.6506i	0.223607	−	0.387298i
$5$	12.5000	−	21.6506i	0.223607	−	0.387298i
$6$		0			0
$7$	124.053	+	37.6545i	0.956890	+	0.290450i
$7$	124.053	+	37.6545i	0.956890	+	0.290450i
$8$		0			0
$9$	121.022	−	209.616i	0.498031	−	0.862616i
$10$		0			0
$11$	110.552	+	191.482i	0.275478	+	0.477142i	0.970256	−	0.242083i	$-0.0778306\pi$
$11$	110.552	+	191.482i	0.275478	+	0.477142i	−0.694778	+	0.719225i	$0.744497\pi$
$12$		0			0
$13$	−1064.81			−1.74748			−0.873739	−	0.486395i	$-0.838312\pi$
$13$	−1064.81			−1.74748			−0.873739	+	0.486395i	$0.838312\pi$
$14$		0			0
$15$	−24.4531			−0.0280612
$16$		0			0
$17$	863.965	+	1496.43i	0.725059	+	1.25584i	0.958950	+	0.283577i	$0.0915211\pi$
$17$	863.965	+	1496.43i	0.725059	+	1.25584i	−0.233890	+	0.972263i	$0.575146\pi$
$18$		0			0
$19$	1119.86	−	1939.66i	0.711674	−	1.23266i	−0.252554	−	0.967583i	$-0.581271\pi$
$19$	1119.86	−	1939.66i	0.711674	−	1.23266i	0.964228	−	0.265073i	$-0.0853960\pi$
$20$		0			0
$21$	−28.7732	−	123.498i	−0.0142377	−	0.0611100i
$22$		0			0
$23$	1828.68	−	3167.37i	0.720807	−	1.24847i	−0.239870	−	0.970805i	$-0.577105\pi$
$23$	1828.68	−	3167.37i	0.720807	−	1.24847i	0.960677	−	0.277669i	$-0.0895619\pi$
$24$		0			0
$25$	−312.500	−	541.266i	−0.100000	−	0.173205i
$26$		0			0
$27$	−474.433			−0.125246
$28$		0			0
$29$	1946.84			0.429867			0.214934	−	0.976629i	$-0.431047\pi$
$29$	1946.84			0.429867			0.214934	+	0.976629i	$0.431047\pi$
$30$		0			0
$31$	−44.0257	−	76.2548i	−0.00822815	−	0.0142516i	0.861882	−	0.507109i	$-0.169286\pi$
$31$	−44.0257	−	76.2548i	−0.00822815	−	0.0142516i	−0.870110	+	0.492857i	$0.835952\pi$
$32$		0			0
$33$	108.134	−	187.294i	0.0172853	−	0.0299391i
$34$		0			0
$35$	2365.91	−	2215.14i	0.326458	−	0.305655i
$36$		0			0
$37$	6706.02	−	11615.2i	0.805305	−	1.39483i	−0.110779	−	0.993845i	$-0.535335\pi$
$37$	6706.02	−	11615.2i	0.805305	−	1.39483i	0.916085	−	0.400985i	$-0.131332\pi$
$38$		0			0
$39$	520.756	+	901.976i	0.0548243	+	0.0949584i
$40$		0			0
$41$	12293.0			1.14208			0.571042	−	0.820921i	$-0.306539\pi$
$41$	12293.0			1.14208			0.571042	+	0.820921i	$0.306539\pi$
$42$		0			0
$43$	3861.54			0.318485			0.159242	−	0.987240i	$-0.449095\pi$
$43$	3861.54			0.318485			0.159242	+	0.987240i	$0.449095\pi$
$44$		0			0
$45$	−3025.54	−	5240.39i	−0.222726	−	0.385773i
$46$		0			0
$47$	701.213	−	1214.54i	0.0463026	−	0.0801985i	−0.841945	−	0.539563i	$-0.818589\pi$
$47$	701.213	−	1214.54i	0.0463026	−	0.0801985i	0.888248	+	0.459364i	$0.151923\pi$
$48$		0			0
$49$	13971.3	+	9342.30i	0.831277	+	0.555858i
$50$		0			0
$51$	845.065	−	1463.70i	0.0454951	−	0.0787998i
$52$		0			0
$53$	−9246.92	−	16016.1i	−0.452176	−	0.783191i	0.546345	−	0.837560i	$-0.316019\pi$
$53$	−9246.92	−	16016.1i	−0.452176	−	0.783191i	−0.998521	+	0.0543688i	$0.982685\pi$
$54$		0			0
$55$	5527.62			0.246395
$56$		0			0
$57$	−2190.73			−0.0893104
$58$		0			0
$59$	−17703.1	−	30662.7i	−0.662095	−	1.14678i	−0.980064	−	0.198681i	$-0.936334\pi$
$59$	−17703.1	−	30662.7i	−0.662095	−	1.14678i	0.317969	−	0.948101i	$-0.396999\pi$
$60$		0			0
$61$	19165.0	−	33194.8i	0.659455	−	1.14221i	−0.321302	−	0.946977i	$-0.604120\pi$
$61$	19165.0	−	33194.8i	0.659455	−	1.14221i	0.980757	−	0.195233i	$-0.0625462\pi$
$62$		0			0
$63$	22906.1	−	21446.4i	0.727108	−	0.680775i
$64$		0			0
$65$	−13310.1	+	23053.7i	−0.390748	+	0.676796i
$66$		0			0
$67$	15628.5	+	27069.4i	0.425336	+	0.736703i	0.996452	−	0.0841665i	$-0.0268228\pi$
$67$	15628.5	+	27069.4i	0.425336	+	0.736703i	−0.571116	+	0.820869i	$0.693489\pi$
$68$		0			0
$69$	−3577.36			−0.0904565
$70$		0			0
$71$	−24787.2			−0.583555			−0.291778	−	0.956486i	$-0.594247\pi$
$71$	−24787.2			−0.583555			−0.291778	+	0.956486i	$0.594247\pi$
$72$		0			0
$73$	37168.3	+	64377.3i	0.816329	+	1.41392i	0.908370	+	0.418168i	$0.137328\pi$
$73$	37168.3	+	64377.3i	0.816329	+	1.41392i	−0.0920407	+	0.995755i	$0.529339\pi$
$74$		0			0
$75$	−305.664	+	529.425i	−0.00627467	+	0.0108681i
$76$		0			0
$77$	6504.19	+	27916.8i	0.125016	+	0.536585i
$78$		0			0
$79$	−33775.2	+	58500.4i	−0.608878	+	1.05461i	0.382547	+	0.923936i	$0.375047\pi$
$79$	−33775.2	+	58500.4i	−0.608878	+	1.05461i	−0.991426	+	0.130672i	$0.958286\pi$
$80$		0			0
$81$	−29176.2	−	50534.7i	−0.494102	−	0.855810i
$82$		0			0
$83$	−16697.0			−0.266037			−0.133019	−	0.991114i	$-0.542467\pi$
$83$	−16697.0			−0.266037			−0.133019	+	0.991114i	$0.542467\pi$
$84$		0			0
$85$	43198.2			0.648513
$86$		0			0
$87$	−952.124	−	1649.13i	−0.0134864	−	0.0233591i
$88$		0			0
$89$	9344.38	−	16184.9i	0.125048	−	0.216589i	−0.796704	−	0.604370i	$-0.793425\pi$
$89$	9344.38	−	16184.9i	0.125048	−	0.216589i	0.921752	+	0.387781i	$0.126758\pi$
$90$		0			0
$91$	−132092.	−	40094.7i	−1.67214	−	0.507556i
$92$		0			0
$93$	−43.0626	+	74.5867i	−0.000516290	+	0.000894240i
$94$		0			0
$95$	−27996.6	−	48491.5i	−0.318270	−	0.551260i
$96$		0			0
$97$	−48997.0			−0.528738			−0.264369	−	0.964422i	$-0.585164\pi$
$97$	−48997.0			−0.528738			−0.264369	+	0.964422i	$0.585164\pi$
$98$		0			0
$99$	53517.0			0.548787
$100$		0			0
$101$	66210.7	+	114680.i	0.645840	+	1.11863i	0.984107	+	0.177577i	$0.0568260\pi$
$101$	66210.7	+	114680.i	0.645840	+	1.11863i	−0.338267	+	0.941050i	$0.609841\pi$
$102$		0			0
$103$	−91370.1	+	158258.i	−0.848615	+	1.46985i	0.0338285	+	0.999428i	$0.489230\pi$
$103$	−91370.1	+	158258.i	−0.848615	+	1.46985i	−0.882444	+	0.470417i	$0.844103\pi$
$104$		0			0
$105$	−3033.48	−	920.770i	−0.0268515	−	0.00815038i
$106$		0			0
$107$	1455.95	−	2521.78i	0.0122938	−	0.0212935i	−0.859813	−	0.510609i	$-0.829420\pi$
$107$	1455.95	−	2521.78i	0.0122938	−	0.0212935i	0.872107	+	0.489315i	$0.162753\pi$
$108$		0			0
$109$	−2905.92	−	5033.20i	−0.0234270	−	0.0405768i	0.854074	−	0.520151i	$-0.174124\pi$
$109$	−2905.92	−	5033.20i	−0.0234270	−	0.0405768i	−0.877501	+	0.479574i	$0.840791\pi$
$110$		0			0
$111$	−13118.6			−0.101061
$112$		0			0
$113$	−200359.			−1.47609			−0.738047	−	0.674750i	$-0.764252\pi$
$113$	−200359.			−1.47609			−0.738047	+	0.674750i	$0.764252\pi$
$114$		0			0
$115$	−45717.1	−	79184.3i	−0.322355	−	0.558335i
$116$		0			0
$117$	−128864.	+	223200.i	−0.870299	+	1.50740i
$118$		0			0
$119$	50830.0	+	218169.i	0.329043	+	1.41229i
$120$		0			0
$121$	56081.8	−	97136.5i	0.348224	−	0.603141i
$122$		0			0
$123$	−6012.04	−	10413.2i	−0.0358310	−	0.0620611i
$124$		0			0
$125$	−15625.0			−0.0894427
$126$		0			0
$127$	90848.6			0.499815			0.249907	−	0.968270i	$-0.419600\pi$
$127$	90848.6			0.499815			0.249907	+	0.968270i	$0.419600\pi$
$128$		0			0
$129$	−1888.53	−	3271.03i	−0.00999194	−	0.0173066i
$130$		0			0
$131$	11877.4	−	20572.3i	0.0604706	−	0.104738i	−0.834205	−	0.551454i	$-0.814073\pi$
$131$	11877.4	−	20572.3i	0.0604706	−	0.104738i	0.894676	+	0.446716i	$0.147407\pi$
$132$		0			0
$133$	211959.	−	198453.i	1.03902	−	0.972810i
$134$		0			0
$135$	−5930.41	+	10271.8i	−0.0280059	+	0.0485077i
$136$		0			0
$137$	115472.	+	200004.i	0.525625	+	0.910409i	0.999554	+	0.0298465i	$0.00950186\pi$
$137$	115472.	+	200004.i	0.525625	+	0.910409i	−0.473929	+	0.880563i	$0.657165\pi$
$138$		0			0
$139$	−312412.			−1.37148			−0.685742	−	0.727844i	$-0.740522\pi$
$139$	−312412.			−1.37148			−0.685742	+	0.727844i	$0.740522\pi$
$140$		0			0
$141$	−1371.75			−0.00581067
$142$		0			0
$143$	−117717.	−	203892.i	−0.481392	−	0.833795i
$144$		0			0
$145$	24335.4	−	42150.2i	0.0961212	−	0.166487i
$146$		0			0
$147$	1080.86	−	16403.8i	0.00412549	−	0.0626109i
$148$		0			0
$149$	−56947.8	+	98636.6i	−0.210141	+	0.363976i	−0.951759	−	0.306848i	$-0.900726\pi$
$149$	−56947.8	+	98636.6i	−0.210141	+	0.363976i	0.741617	+	0.670823i	$0.234059\pi$
$150$		0			0
$151$	−197675.	−	342383.i	−0.705520	−	1.22200i	−0.966504	−	0.256653i	$-0.917380\pi$
$151$	−197675.	−	342383.i	−0.705520	−	1.22200i	0.260983	−	0.965343i	$-0.415953\pi$
$152$		0			0
$153$	418234.			1.44441
$154$		0			0
$155$	−2201.29			−0.00735948
$156$		0			0
$157$	212294.	+	367704.i	0.687367	+	1.19056i	0.972687	+	0.232123i	$0.0745671\pi$
$157$	212294.	+	367704.i	0.687367	+	1.19056i	−0.285319	+	0.958433i	$0.592100\pi$
$158$		0			0
$159$	−9044.63	+	15665.8i	−0.0283725	+	0.0491427i
$160$		0			0
$161$	346119.	−	324064.i	1.05235	−	0.985294i
$162$		0			0
$163$	−111330.	+	192830.i	−0.328204	+	0.568466i	−0.982156	−	0.188070i	$-0.939777\pi$
$163$	−111330.	+	192830.i	−0.328204	+	0.568466i	0.653951	+	0.756537i	$0.273110\pi$
$164$		0			0
$165$	−2703.35	−	4682.34i	−0.00773024	−	0.0133892i
$166$		0			0
$167$	32195.9			0.0893326			0.0446663	−	0.999002i	$-0.485778\pi$
$167$	32195.9			0.0893326			0.0446663	+	0.999002i	$0.485778\pi$
$168$		0			0
$169$	762517.			2.05368
$170$		0			0
$171$	−271055.	−	469482.i	−0.708872	−	1.22780i
$172$		0			0
$173$	37685.1	−	65272.5i	0.0957314	−	0.165812i	−0.814182	−	0.580609i	$-0.802814\pi$
$173$	37685.1	−	65272.5i	0.0957314	−	0.165812i	0.909914	+	0.414798i	$0.136148\pi$
$174$		0			0
$175$	−18385.5	−	78912.7i	−0.0453816	−	0.194783i
$176$		0			0
$177$	−17315.9	+	29992.0i	−0.0415443	+	0.0719568i
$178$		0			0
$179$	−199568.	−	345662.i	−0.465542	−	0.806342i	0.533684	−	0.845684i	$-0.320807\pi$
$179$	−199568.	−	345662.i	−0.465542	−	0.806342i	−0.999226	+	0.0393420i	$0.987474\pi$
$180$		0			0
$181$	−500148.			−1.13476			−0.567378	−	0.823458i	$-0.692042\pi$
$181$	−500148.			−1.13476			−0.567378	+	0.823458i	$0.692042\pi$
$182$		0			0
$183$	−37491.6			−0.0827573
$184$		0			0
$185$	−167651.	−	290379.i	−0.360143	−	0.623787i
$186$		0			0
$187$	−191027.	+	330868.i	−0.399476	+	0.691912i
$188$		0			0
$189$	−58854.8	−	17864.5i	−0.119847	−	0.0363778i
$190$		0			0
$191$	466977.	−	808828.i	0.926215	−	1.60425i	0.136621	−	0.990623i	$-0.456376\pi$
$191$	466977.	−	808828.i	0.926215	−	1.60425i	0.789595	−	0.613629i	$-0.210291\pi$
$192$		0			0
$193$	208764.	+	361590.i	0.403425	+	0.698752i	0.994137	−	0.108130i	$-0.0344863\pi$
$193$	208764.	+	361590.i	0.403425	+	0.698752i	−0.590712	+	0.806883i	$0.701153\pi$
$194$		0			0
$195$	26037.8			0.0490363
$196$		0			0
$197$	870857.			1.59875			0.799376	−	0.600831i	$-0.205163\pi$
$197$	870857.			1.59875			0.799376	+	0.600831i	$0.205163\pi$
$198$		0			0
$199$	470475.	+	814886.i	0.842178	+	1.45869i	0.888050	+	0.459747i	$0.152060\pi$
$199$	470475.	+	814886.i	0.842178	+	1.45869i	−0.0458719	+	0.998947i	$0.514607\pi$
$200$		0			0
$201$	15286.7	−	26477.3i	0.0266884	−	0.0462257i
$202$		0			0
$203$	241511.	+	73307.1i	0.411336	+	0.124855i
$204$		0			0
$205$	153662.	−	266151.i	0.255378	−	0.442327i
$206$		0			0
$207$	−442621.	−	766641.i	−0.717969	−	1.24356i
$208$		0			0
$209$	495215.			0.784202
$210$		0			0
$211$	529745.			0.819145			0.409573	−	0.912278i	$-0.365678\pi$
$211$	529745.			0.819145			0.409573	+	0.912278i	$0.365678\pi$
$212$		0			0
$213$	12122.5	+	20996.8i	0.0183081	+	0.0317105i
$214$		0			0
$215$	48269.2	−	83604.7i	0.0712154	−	0.123349i
$216$		0			0
$217$	−2590.19	−	11117.4i	−0.00373406	−	0.0160271i
$218$		0			0
$219$	36355.2	−	62969.1i	0.0512220	−	0.0887190i
$220$		0			0
$221$	−919954.	−	1.59341e6i	−1.26703	−	2.19455i
$222$		0			0
$223$	−137809.			−0.185573			−0.0927867	−	0.995686i	$-0.529577\pi$
$223$	−137809.			−0.185573			−0.0927867	+	0.995686i	$0.529577\pi$
$224$		0			0
$225$	−151277.			−0.199213
$226$		0			0
$227$	620589.	+	1.07489e6i	0.799355	+	1.38452i	0.920037	+	0.391832i	$0.128159\pi$
$227$	620589.	+	1.07489e6i	0.799355	+	1.38452i	−0.120682	+	0.992691i	$0.538508\pi$
$228$		0			0
$229$	−317968.	+	550736.i	−0.400677	+	0.693992i	−0.993808	−	0.111114i	$-0.964558\pi$
$229$	−317968.	+	550736.i	−0.400677	+	0.693992i	0.593131	+	0.805106i	$0.297892\pi$
$230$		0			0
$231$	20466.8	−	19162.6i	0.0252360	−	0.0236279i
$232$		0			0
$233$	−423100.	+	732831.i	−0.510568	+	0.884330i	0.489357	+	0.872084i	$0.337232\pi$
$233$	−423100.	+	732831.i	−0.510568	+	0.884330i	−0.999925	+	0.0122463i	$0.996102\pi$
$234$		0			0
$235$	−17530.3	−	30363.4i	−0.0207072	−	0.0358659i
$236$		0			0
$237$	66072.7			0.0764102
$238$		0			0
$239$	−1.44232e6			−1.63330			−0.816651	−	0.577132i	$-0.804172\pi$
$239$	−1.44232e6			−1.63330			−0.816651	+	0.577132i	$0.804172\pi$
$240$		0			0
$241$	144280.	+	249900.i	0.160016	+	0.277156i	0.934874	−	0.354979i	$-0.115512\pi$
$241$	144280.	+	249900.i	0.160016	+	0.277156i	−0.774858	+	0.632135i	$0.782179\pi$
$242$		0			0
$243$	−86181.6	+	149271.i	−0.0936265	+	0.162166i
$244$		0			0
$245$	376908.	−	185708.i	0.401162	−	0.197659i
$246$		0			0
$247$	−1.19244e6	+	2.06536e6i	−1.24364	+	2.15404i
$248$		0			0
$249$	8165.86	+	14143.7i	0.00834648	+	0.0144565i
$250$		0			0
$251$	−1.45550e6			−1.45824			−0.729121	−	0.684385i	$-0.760071\pi$
$251$	−1.45550e6			−1.45824			−0.729121	+	0.684385i	$0.760071\pi$
$252$		0			0
$253$	808662.			0.794265
$254$		0			0
$255$	−21126.6	−	36592.4i	−0.0203460	−	0.0352404i
$256$		0			0
$257$	−499305.	+	864821.i	−0.471556	+	0.816759i	−0.999470	−	0.0325389i	$-0.989641\pi$
$257$	−499305.	+	864821.i	−0.471556	+	0.816759i	0.527915	+	0.849297i	$0.322974\pi$
$258$		0			0
$259$	1.26926e6	−	1.18838e6i	1.17572	−	1.10080i
$260$		0			0
$261$	235609.	−	408087.i	0.214087	−	0.370810i
$262$		0			0
$263$	−764286.	−	1.32378e6i	−0.681344	−	1.18012i	−0.974571	−	0.224080i	$-0.928062\pi$
$263$	−764286.	−	1.32378e6i	−0.681344	−	1.18012i	0.293227	−	0.956043i	$-0.405271\pi$
$264$		0			0
$265$	−462346.			−0.404438
$266$		0			0
$267$	−18279.9			−0.0156927
$268$		0			0
$269$	202430.	+	350619.i	0.170566	+	0.295430i	0.938618	−	0.344958i	$-0.112107\pi$
$269$	202430.	+	350619.i	0.170566	+	0.295430i	−0.768052	+	0.640388i	$0.778774\pi$
$270$		0			0
$271$	43030.8	−	74531.5i	0.0355923	−	0.0616476i	−0.847681	−	0.530507i	$-0.822002\pi$
$271$	43030.8	−	74531.5i	0.0355923	−	0.0616476i	0.883273	+	0.468859i	$0.155335\pi$
$272$		0			0
$273$	30637.9	+	131502.i	0.0248801	+	0.106788i
$274$		0			0
$275$	69095.3	−	119677.i	0.0550956	−	0.0954283i
$276$		0			0
$277$	732623.	+	1.26894e6i	0.573695	+	0.993669i	0.996182	+	0.0873002i	$0.0278239\pi$
$277$	732623.	+	1.26894e6i	0.573695	+	0.993669i	−0.422487	+	0.906369i	$0.638843\pi$
$278$		0			0
$279$	−21312.3			−0.0163915
$280$		0			0
$281$	375945.			0.284026			0.142013	−	0.989865i	$-0.454642\pi$
$281$	375945.			0.284026			0.142013	+	0.989865i	$0.454642\pi$
$282$		0			0
$283$	−134680.	−	233273.i	−0.0999627	−	0.173140i	0.811706	−	0.584066i	$-0.198539\pi$
$283$	−134680.	−	233273.i	−0.0999627	−	0.173140i	−0.911669	+	0.410925i	$0.865206\pi$
$284$		0			0
$285$	−27384.2	+	47430.7i	−0.0199704	+	0.0345898i
$286$		0			0
$287$	1.52498e6	+	462886.i	1.09285	+	0.331718i
$288$		0			0
$289$	−782941.	+	1.35609e6i	−0.551422	+	0.955092i
$290$		0			0
$291$	23962.6	+	41504.4i	0.0165883	+	0.0287317i
$292$		0			0
$293$	−2.17033e6			−1.47692			−0.738459	−	0.674298i	$-0.764446\pi$
$293$	−2.17033e6			−1.47692			−0.738459	+	0.674298i	$0.764446\pi$
$294$		0			0
$295$	−885157.			−0.592196
$296$		0			0
$297$	−52449.7	−	90845.6i	−0.0345026	−	0.0597603i
$298$		0			0
$299$	−1.94719e6	+	3.37264e6i	−1.25959	+	2.18168i
$300$		0			0
$301$	479035.	+	145404.i	0.304755	+	0.0925040i
$302$		0			0
$303$	64762.3	−	112172.i	0.0405243	−	0.0701902i
$304$		0			0
$305$	−479126.	−	829871.i	−0.294917	−	0.510812i
$306$		0			0
$307$	−1.01798e6			−0.616441			−0.308221	−	0.951315i	$-0.599734\pi$
$307$	−1.01798e6			−0.616441			−0.308221	+	0.951315i	$0.599734\pi$
$308$		0			0
$309$	178743.			0.106496
$310$		0			0
$311$	−881052.	−	1.52603e6i	−0.516536	−	0.894667i	−0.999816	−	0.0192007i	$-0.993888\pi$
$311$	−881052.	−	1.52603e6i	−0.516536	−	0.894667i	0.483280	−	0.875466i	$-0.339445\pi$
$312$		0			0
$313$	−966574.	+	1.67415e6i	−0.557666	+	0.965906i	0.440025	+	0.897986i	$0.354970\pi$
$313$	−966574.	+	1.67415e6i	−0.557666	+	0.965906i	−0.997691	+	0.0679201i	$0.978364\pi$
$314$		0			0
$315$	−178003.	−	764011.i	−0.101077	−	0.433834i
$316$		0			0
$317$	767292.	−	1.32899e6i	0.428857	−	0.742802i	−0.567915	−	0.823087i	$-0.692250\pi$
$317$	767292.	−	1.32899e6i	0.428857	−	0.742802i	0.996772	+	0.0802854i	$0.0255832\pi$
$318$		0			0
$319$	215227.	+	372785.i	0.118419	+	0.205107i
$320$		0			0
$321$	−2848.20			−0.00154279
$322$		0			0
$323$	3.87009e6			2.06402
$324$		0			0
$325$	332752.	+	576343.i	0.174748	+	0.302672i
$326$		0			0
$327$	−2842.35	+	4923.09i	−0.00146997	+	0.00254606i
$328$		0			0
$329$	132720.	−	124263.i	0.0676002	−	0.0632925i
$330$		0			0
$331$	−627418.	+	1.08672e6i	−0.314765	+	0.545189i	−0.979388	−	0.201990i	$-0.935259\pi$
$331$	−627418.	+	1.08672e6i	−0.314765	+	0.545189i	0.664622	+	0.747179i	$0.268592\pi$
$332$		0			0
$333$	−1.62315e6	−	2.81137e6i	−0.802135	−	1.38934i
$334$		0			0
$335$	781427.			0.380432
$336$		0			0
$337$	−345146.			−0.165549			−0.0827747	−	0.996568i	$-0.526378\pi$
$337$	−345146.			−0.165549			−0.0827747	+	0.996568i	$0.526378\pi$
$338$		0			0
$339$	97988.3	+	169721.i	0.0463100	+	0.0802113i
$340$		0			0
$341$	9734.31	−	16860.3i	0.00453335	−	0.00785199i
$342$		0			0
$343$	1.38140e6	+	1.68502e6i	0.633992	+	0.773340i
$344$		0			0
$345$	−44717.0	+	77452.1i	−0.0202267	+	0.0350337i
$346$		0			0
$347$	−1.12146e6	−	1.94242e6i	−0.499988	−	0.866004i	0.500012	−	0.866018i	$-0.333329\pi$
$347$	−1.12146e6	−	1.94242e6i	−0.499988	−	0.866004i	−1.00000		1.42627e-5i	$0.999995\pi$
$348$		0			0
$349$	−326684.			−0.143570			−0.0717850	−	0.997420i	$-0.522870\pi$
$349$	−326684.			−0.143570			−0.0717850	+	0.997420i	$0.522870\pi$
$350$		0			0
$351$	505178.			0.218865
$352$		0			0
$353$	1.28606e6	+	2.22752e6i	0.549318	+	0.951446i	0.998321	+	0.0579165i	$0.0184457\pi$
$353$	1.28606e6	+	2.22752e6i	0.549318	+	0.951446i	−0.449004	+	0.893530i	$0.648221\pi$
$354$		0			0
$355$	−309840.	+	536659.i	−0.130487	+	0.226010i
$356$		0			0
$357$	159948.	−	149755.i	0.0664212	−	0.0621887i
$358$		0			0
$359$	2.38758e6	−	4.13541e6i	0.977736	−	1.69349i	0.307142	−	0.951664i	$-0.400627\pi$
$359$	2.38758e6	−	4.13541e6i	0.977736	−	1.69349i	0.670594	−	0.741825i	$-0.266039\pi$
$360$		0			0
$361$	−1.27014e6	−	2.19995e6i	−0.512960	−	0.888473i
$362$		0			0
$363$	−109710.			−0.0436998
$364$		0			0
$365$	1.85841e6			0.730147
$366$		0			0
$367$	1.11459e6	+	1.93053e6i	0.431968	+	0.748191i	0.997043	−	0.0768491i	$-0.0244860\pi$
$367$	1.11459e6	+	1.93053e6i	0.431968	+	0.748191i	−0.565075	+	0.825040i	$0.691153\pi$
$368$		0			0
$369$	1.48772e6	−	2.57680e6i	0.568794	−	0.985180i
$370$		0			0
$371$	−544028.	−	2.33504e6i	−0.205204	−	0.880763i
$372$		0			0
$373$	62803.9	−	108780.i	0.0233730	−	0.0404832i	−0.854102	−	0.520105i	$-0.825893\pi$
$373$	62803.9	−	108780.i	0.0233730	−	0.0404832i	0.877475	+	0.479622i	$0.159226\pi$
$374$		0			0
$375$	7641.60	+	13235.6i	0.00280612	+	0.00486034i
$376$		0			0
$377$	−2.07300e6			−0.751183
$378$		0			0
$379$	3.05381e6			1.09205			0.546027	−	0.837767i	$-0.316140\pi$
$379$	3.05381e6			1.09205			0.546027	+	0.837767i	$0.316140\pi$
$380$		0			0
$381$	−44430.6	−	76956.1i	−0.0156809	−	0.0271600i
$382$		0			0
$383$	−577281.	+	999880.i	−0.201090	+	0.348298i	−0.948880	−	0.315637i	$-0.897782\pi$
$383$	−577281.	+	999880.i	−0.201090	+	0.348298i	0.747790	+	0.663935i	$0.231115\pi$
$384$		0			0
$385$	685718.	+	208140.i	0.235773	+	0.0715655i
$386$		0			0
$387$	467329.	−	809438.i	0.158616	−	0.274730i
$388$		0			0
$389$	−1.87997e6	−	3.25620e6i	−0.629907	−	1.09103i	−0.987570	−	0.157181i	$-0.949759\pi$
$389$	−1.87997e6	−	3.25620e6i	−0.629907	−	1.09103i	0.357662	−	0.933851i	$-0.383574\pi$
$390$		0			0
$391$	6.31967e6			2.09051
$392$		0			0
$393$	−23235.2			−0.00758867
$394$		0			0
$395$	844381.	+	1.46251e6i	0.272299	+	0.471635i
$396$		0			0
$397$	315474.	−	546417.i	0.100459	−	0.174000i	−0.811415	−	0.584470i	$-0.801302\pi$
$397$	315474.	−	546417.i	0.100459	−	0.174000i	0.911874	+	0.410471i	$0.134636\pi$
$398$		0			0
$399$	−271767.	−	82490.9i	−0.0854603	−	0.0259402i
$400$		0			0
$401$	−2.95463e6	+	5.11757e6i	−0.917576	+	1.58929i	−0.114490	+	0.993424i	$0.536523\pi$
$401$	−2.95463e6	+	5.11757e6i	−0.917576	+	1.58929i	−0.803086	+	0.595863i	$0.796810\pi$
$402$		0			0
$403$	46878.8	+	81196.5i	0.0143785	+	0.0249043i
$404$		0			0
$405$	−1.45881e6			−0.441938
$406$		0			0
$407$	2.96547e6			0.887375
$408$		0			0
$409$	−316134.	−	547560.i	−0.0934465	−	0.161854i	0.815513	−	0.578739i	$-0.196455\pi$
$409$	−316134.	−	547560.i	−0.0934465	−	0.161854i	−0.908959	+	0.416885i	$0.863122\pi$
$410$		0			0
$411$	112946.	−	195629.i	0.0329812	−	0.0571252i
$412$		0			0
$413$	−1.04154e6	−	4.47041e6i	−0.300469	−	1.28965i
$414$		0			0
$415$	−208712.	+	361500.i	−0.0594877	+	0.103036i
$416$		0			0
$417$	152789.	+	264638.i	0.0430281	+	0.0745268i
$418$		0			0
$419$	−1.24571e6			−0.346643			−0.173321	−	0.984865i	$-0.555450\pi$
$419$	−1.24571e6			−0.346643			−0.173321	+	0.984865i	$0.555450\pi$
$420$		0			0
$421$	−145810.			−0.0400943			−0.0200471	−	0.999799i	$-0.506382\pi$
$421$	−145810.			−0.0400943			−0.0200471	+	0.999799i	$0.506382\pi$
$422$		0			0
$423$	−169724.	−	293971.i	−0.0461203	−	0.0798827i
$424$		0			0
$425$	539978.	−	935269.i	0.145012	−	0.251168i
$426$		0			0
$427$	3.62741e6	−	3.39627e6i	0.962781	−	0.901430i
$428$		0			0
$429$	−115142.	+	199431.i	−0.0302057	+	0.0523179i
$430$		0			0
$431$	1.97817e6	+	3.42630e6i	0.512945	+	0.888447i	0.999887	+	0.0150130i	$0.00477897\pi$
$431$	1.97817e6	+	3.42630e6i	0.512945	+	0.888447i	−0.486942	+	0.873434i	$0.661888\pi$
$432$		0			0
$433$	1.52292e6			0.390353			0.195177	−	0.980768i	$-0.437472\pi$
$433$	1.52292e6			0.390353			0.195177	+	0.980768i	$0.437472\pi$
$434$		0			0
$435$	−47606.2			−0.0120626
$436$		0			0
$437$	−4.09575e6	−	7.09405e6i	−1.02596	−	1.77701i
$438$		0			0
$439$	−2.66626e6	+	4.61809e6i	−0.660299	+	1.14367i	0.320238	+	0.947337i	$0.396237\pi$
$439$	−2.66626e6	+	4.61809e6i	−0.660299	+	1.14367i	−0.980537	+	0.196334i	$0.937096\pi$
$440$		0			0
$441$	3.64912e6	−	1.79798e6i	0.893494	−	0.440238i
$442$		0			0
$443$	2.45687e6	−	4.25543e6i	0.594804	−	1.03023i	−0.398771	−	0.917051i	$-0.630563\pi$
$443$	2.45687e6	−	4.25543e6i	0.594804	−	1.03023i	0.993575	−	0.113179i	$-0.0361035\pi$
$444$		0			0
$445$	−233609.	−	404623.i	−0.0559230	−	0.0968615i
$446$		0			0
$447$	111404.			0.0263714
$448$		0			0
$449$	1.22232e6			0.286134			0.143067	−	0.989713i	$-0.454304\pi$
$449$	1.22232e6			0.286134			0.143067	+	0.989713i	$0.454304\pi$
$450$		0			0
$451$	1.35902e6	+	2.35389e6i	0.314619	+	0.544936i
$452$		0			0
$453$	−193351.	+	334893.i	−0.0442691	+	0.0766763i
$454$		0			0
$455$	−2.51923e6	+	2.35870e6i	−0.570478	+	0.534126i
$456$		0			0
$457$	−612416.	+	1.06073e6i	−0.137169	+	0.237584i	−0.926424	−	0.376482i	$-0.877134\pi$
$457$	−612416.	+	1.06073e6i	−0.137169	+	0.237584i	0.789255	+	0.614066i	$0.210467\pi$
$458$		0			0
$459$	−409893.	−	709956.i	−0.0908111	−	0.157289i
$460$		0			0
$461$	−463384.			−0.101552			−0.0507760	−	0.998710i	$-0.516169\pi$
$461$	−463384.			−0.101552			−0.0507760	+	0.998710i	$0.516169\pi$
$462$		0			0
$463$	−3.09945e6			−0.671943			−0.335972	−	0.941872i	$-0.609065\pi$
$463$	−3.09945e6			−0.671943			−0.335972	+	0.941872i	$0.609065\pi$
$464$		0			0
$465$	1076.57	+	1864.67i	0.000230892	+	0.000399916i
$466$		0			0
$467$	632320.	−	1.09521e6i	0.134167	−	0.232384i	−0.791112	−	0.611671i	$-0.790498\pi$
$467$	632320.	−	1.09521e6i	0.134167	−	0.232384i	0.925279	+	0.379288i	$0.123831\pi$
$468$		0			0
$469$	919482.	+	3.94653e6i	0.193024	+	0.828482i
$470$		0			0
$471$	207650.	−	359661.i	0.0431300	−	0.0747034i
$472$		0			0
$473$	426902.	+	739417.i	0.0877356	+	0.151962i
$474$		0			0
$475$	−1.39983e6			−0.284670
$476$		0			0
$477$	−4.47631e6			−0.900791
$478$		0			0
$479$	−1.26554e6	−	2.19198e6i	−0.252021	−	0.436513i	0.712061	−	0.702118i	$-0.247762\pi$
$479$	−1.26554e6	−	2.19198e6i	−0.252021	−	0.436513i	−0.964082	+	0.265604i	$0.914429\pi$
$480$		0			0
$481$	−7.14061e6	+	1.23679e7i	−1.40725	+	2.43743i
$482$		0			0
$483$	−443782.	−	134704.i	−0.0865570	−	0.0262731i
$484$		0			0
$485$	−612463.	+	1.06082e6i	−0.118229	+	0.204779i
$486$		0			0
$487$	−1.49777e6	−	2.59422e6i	−0.286170	−	0.495661i	0.686722	−	0.726920i	$-0.259049\pi$
$487$	−1.49777e6	−	2.59422e6i	−0.286170	−	0.495661i	−0.972892	+	0.231259i	$0.925716\pi$
$488$		0			0
$489$	217790.			0.0411875
$490$		0			0
$491$	−143990.			−0.0269543			−0.0134772	−	0.999909i	$-0.504290\pi$
$491$	−143990.			−0.0269543			−0.0134772	+	0.999909i	$0.504290\pi$
$492$		0			0
$493$	1.68200e6	+	2.91330e6i	0.311679	+	0.539844i
$494$		0			0
$495$	668962.	−	1.15868e6i	0.122712	−	0.212544i
$496$		0			0
$497$	−3.07493e6	−	933350.i	−0.558398	−	0.169494i
$498$		0			0
$499$	−3.47915e6	+	6.02607e6i	−0.625493	+	1.08338i	0.362953	+	0.931808i	$0.381769\pi$
$499$	−3.47915e6	+	6.02607e6i	−0.625493	+	1.08338i	−0.988445	+	0.151577i	$0.951565\pi$
$500$		0			0
$501$	−15745.8	−	27272.6i	−0.00280266	−	0.00485436i
$502$		0			0
$503$	551360.			0.0971662			0.0485831	−	0.998819i	$-0.484529\pi$
$503$	551360.			0.0971662			0.0485831	+	0.998819i	$0.484529\pi$
$504$		0			0
$505$	3.31054e6			0.577657
$506$		0			0
$507$	−372919.	−	645914.i	−0.0644309	−	0.111598i
$508$		0			0
$509$	4.48595e6	−	7.76989e6i	0.767467	−	1.32929i	−0.171465	−	0.985190i	$-0.554850\pi$
$509$	4.48595e6	−	7.76989e6i	0.767467	−	1.32929i	0.938932	−	0.344102i	$-0.111817\pi$
$510$		0			0
$511$	2.18674e6	+	9.38575e6i	0.370463	+	1.59007i
$512$		0			0
$513$	−531300.	+	920239.i	−0.0891346	+	0.154386i
$514$		0			0
$515$	2.28425e6	+	3.95644e6i	0.379512	+	0.657335i
$516$		0			0
$517$	310083.			0.0510214
$518$		0			0
$519$	−73721.5			−0.0120137
$520$		0			0
$521$	5.53705e6	+	9.59045e6i	0.893684	+	1.54791i	0.835425	+	0.549604i	$0.185221\pi$
$521$	5.53705e6	+	9.59045e6i	0.893684	+	1.54791i	0.0582585	+	0.998302i	$0.481445\pi$
$522$		0			0
$523$	2.03496e6	−	3.52465e6i	0.325313	−	0.563458i	−0.656263	−	0.754532i	$-0.727864\pi$
$523$	2.03496e6	−	3.52465e6i	0.325313	−	0.563458i	0.981576	+	0.191074i	$0.0611971\pi$
$524$		0			0
$525$	−57853.8	+	54167.2i	−0.00916080	+	0.00857705i
$526$		0			0
$527$	76073.3	−	131763.i	0.0119318	−	0.0206665i
$528$		0			0
$529$	−3.47000e6	−	6.01021e6i	−0.539125	−	0.933792i
$530$		0			0
$531$	−8.56985e6			−1.31898
$532$		0			0
$533$	−1.30896e7			−1.99577
$534$		0			0
$535$	−36398.7	−	63044.5i	−0.00549796	−	0.00952275i
$536$		0			0
$537$	−195202.	+	338101.i	−0.0292112	+	0.0505953i
$538$		0			0
$539$	−244328.	+	3.70807e6i	−0.0362244	+	0.549764i
$540$		0			0
$541$	1.13978e6	−	1.97416e6i	0.167428	−	0.289994i	−0.770087	−	0.637939i	$-0.779787\pi$
$541$	1.13978e6	−	1.97416e6i	0.167428	−	0.289994i	0.937515	+	0.347945i	$0.113121\pi$
$542$		0			0
$543$	244604.	+	423666.i	0.0356011	+	0.0616629i
$544$		0			0
$545$	−145296.			−0.0209538
$546$		0			0
$547$	140199.			0.0200344			0.0100172	−	0.999950i	$-0.496811\pi$
$547$	140199.			0.0200344			0.0100172	+	0.999950i	$0.496811\pi$
$548$		0			0
$549$	−4.63877e6	−	8.03458e6i	−0.656859	−	1.13771i
$550$		0			0
$551$	2.18019e6	−	3.77620e6i	0.305925	−	0.529878i
$552$		0			0
$553$	−6.39272e6	+	5.98536e6i	−0.888941	+	0.832295i
$554$		0			0
$555$	−163983.	+	284027.i	−0.0225978	+	0.0391406i
$556$		0			0
$557$	−832245.	−	1.44149e6i	−0.113661	−	0.196867i	0.803582	−	0.595193i	$-0.202925\pi$
$557$	−832245.	−	1.44149e6i	−0.113661	−	0.196867i	−0.917244	+	0.398326i	$0.869591\pi$
$558$		0			0
$559$	−4.11178e6			−0.556546
$560$		0			0
$561$	373696.			0.0501316
$562$		0			0
$563$	1.26036e6	+	2.18300e6i	0.167580	+	0.290257i	0.937569	−	0.347801i	$-0.113071\pi$
$563$	1.26036e6	+	2.18300e6i	0.167580	+	0.290257i	−0.769988	+	0.638058i	$0.779738\pi$
$564$		0			0
$565$	−2.50449e6	+	4.33791e6i	−0.330064	+	0.571688i
$566$		0			0
$567$	−1.71654e6	−	7.36760e6i	−0.224231	−	0.962428i
$568$		0			0
$569$	2.51584e6	−	4.35756e6i	0.325763	−	0.564239i	−0.655903	−	0.754845i	$-0.727712\pi$
$569$	2.51584e6	−	4.35756e6i	0.325763	−	0.564239i	0.981667	+	0.190606i	$0.0610454\pi$
$570$		0			0
$571$	6.29594e6	+	1.09049e7i	0.808110	+	1.39969i	0.914172	+	0.405328i	$0.132843\pi$
$571$	6.29594e6	+	1.09049e7i	0.808110	+	1.39969i	−0.106062	+	0.994360i	$0.533824\pi$
$572$		0			0
$573$	−913523.			−0.116234
$574$		0			0
$575$	−2.28585e6			−0.288323
$576$		0			0
$577$	3.02816e6	+	5.24492e6i	0.378651	+	0.655843i	0.990866	−	0.134848i	$-0.0430547\pi$
$577$	3.02816e6	+	5.24492e6i	0.378651	+	0.655843i	−0.612215	+	0.790691i	$0.709721\pi$
$578$		0			0
$579$	204197.	−	353680.i	0.0253136	−	0.0438444i
$580$		0			0
$581$	−2.07131e6	−	628716.i	−0.254568	−	0.0772706i
$582$		0			0
$583$	2.04454e6	−	3.54125e6i	0.249129	−	0.431504i
$584$		0			0
$585$	3.22161e6	+	5.58000e6i	0.389210	+	0.674131i
$586$		0			0
$587$	−1.17428e7			−1.40662			−0.703312	−	0.710881i	$-0.748296\pi$
$587$	−1.17428e7			−1.40662			−0.703312	+	0.710881i	$0.748296\pi$
$588$		0			0
$589$	−197211.			−0.0234231
$590$		0			0
$591$	−425903.	−	737686.i	−0.0501582	−	0.0868766i
$592$		0			0
$593$	1.09575e6	−	1.89789e6i	0.127960	−	0.221633i	−0.794926	−	0.606706i	$-0.792490\pi$
$593$	1.09575e6	−	1.89789e6i	0.127960	−	0.221633i	0.922886	+	0.385073i	$0.125824\pi$
$594$		0			0
$595$	5.35887e6	+	1.62661e6i	0.620556	+	0.188361i
$596$		0			0
$597$	460183.	−	797060.i	0.0528439	−	0.0915283i
$598$		0			0
$599$	2.20958e6	+	3.82710e6i	0.251618	+	0.435816i	0.963972	−	0.266006i	$-0.0857039\pi$
$599$	2.20958e6	+	3.82710e6i	0.251618	+	0.435816i	−0.712353	+	0.701821i	$0.752371\pi$
$600$		0			0
$601$	4.11214e6			0.464389			0.232194	−	0.972669i	$-0.425409\pi$
$601$	4.11214e6			0.464389			0.232194	+	0.972669i	$0.425409\pi$
$602$		0			0
$603$	7.56557e6			0.847322
$604$		0			0
$605$	−1.40205e6	−	2.42841e6i	−0.155730	−	0.269733i
$606$		0			0
$607$	6.51713e6	−	1.12880e7i	0.717935	−	1.24350i	−0.243882	−	0.969805i	$-0.578421\pi$
$607$	6.51713e6	−	1.12880e7i	0.717935	−	1.24350i	0.961817	−	0.273694i	$-0.0882456\pi$
$608$		0			0
$609$	−56016.7	−	240431.i	−0.00612033	−	0.0262692i
$610$		0			0
$611$	−746656.	+	1.29325e6i	−0.0809128	+	0.140145i
$612$		0			0
$613$	3.52136e6	+	6.09917e6i	0.378494	+	0.655571i	0.990843	−	0.135016i	$-0.0431086\pi$
$613$	3.52136e6	+	6.09917e6i	0.378494	+	0.655571i	−0.612349	+	0.790587i	$0.709775\pi$
$614$		0			0
$615$	−300602.			−0.0320482
$616$		0			0
$617$	5.80501e6			0.613889			0.306945	−	0.951727i	$-0.400693\pi$
$617$	5.80501e6			0.613889			0.306945	+	0.951727i	$0.400693\pi$
$618$		0			0
$619$	−2.67824e6	−	4.63885e6i	−0.280946	−	0.486613i	0.690672	−	0.723168i	$-0.257315\pi$
$619$	−2.67824e6	−	4.63885e6i	−0.280946	−	0.486613i	−0.971618	+	0.236555i	$0.923982\pi$
$620$		0			0
$621$	−867587.	+	1.50271e6i	−0.0902785	+	0.156367i
$622$		0			0
$623$	1.76863e6	−	1.65593e6i	0.182565	−	0.170932i
$624$		0			0
$625$	−195312.	+	338291.i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−242191.	−	419487.i	−0.0246030	−	0.0426137i
$628$		0			0
$629$	2.31751e7			2.33558
$630$		0			0
$631$	−8.17906e6			−0.817768			−0.408884	−	0.912586i	$-0.634082\pi$
$631$	−8.17906e6			−0.817768			−0.408884	+	0.912586i	$0.634082\pi$
$632$		0			0
$633$	−259078.	−	448737.i	−0.0256993	−	0.0445126i
$634$		0			0
$635$	1.13561e6	−	1.96693e6i	0.111762	−	0.193577i
$636$		0			0
$637$	−1.48767e7	−	9.94773e6i	−1.45264	−	0.971350i
$638$		0			0
$639$	−2.99979e6	+	5.19579e6i	−0.290629	+	0.503384i
$640$		0			0
$641$	−66819.9	−	115735.i	−0.00642334	−	0.0111255i	0.862796	−	0.505552i	$-0.168711\pi$
$641$	−66819.9	−	115735.i	−0.00642334	−	0.0111255i	−0.869219	+	0.494427i	$0.835378\pi$
$642$		0			0
$643$	1.57783e7			1.50498			0.752491	−	0.658602i	$-0.228852\pi$
$643$	1.57783e7			1.50498			0.752491	+	0.658602i	$0.228852\pi$
$644$		0			0
$645$	−94426.6			−0.00893707
$646$		0			0
$647$	−5.20267e6	−	9.01129e6i	−0.488614	−	0.846304i	0.511300	−	0.859402i	$-0.329164\pi$
$647$	−5.20267e6	−	9.01129e6i	−0.488614	−	0.846304i	−0.999914	+	0.0130981i	$0.995831\pi$
$648$		0			0
$649$	3.91425e6	−	6.77968e6i	0.364785	−	0.631826i
$650$		0			0
$651$	−8150.57	+	7631.20i	−0.000753764	+	0.000705733i
$652$		0			0
$653$	−2.50783e6	+	4.34368e6i	−0.230152	+	0.398635i	−0.957853	−	0.287260i	$-0.907256\pi$
$653$	−2.50783e6	+	4.34368e6i	−0.230152	+	0.398635i	0.727701	+	0.685895i	$0.240589\pi$
$654$		0			0
$655$	−296936.	−	514308.i	−0.0270433	−	0.0468403i
$656$		0			0
$657$	1.79927e7			1.62623
$658$		0			0
$659$	−1.87344e7			−1.68045			−0.840226	−	0.542236i	$-0.817578\pi$
$659$	−1.87344e7			−1.68045			−0.840226	+	0.542236i	$0.817578\pi$
$660$		0			0
$661$	−3.67702e6	−	6.36878e6i	−0.327335	−	0.566961i	0.654647	−	0.755934i	$-0.272817\pi$
$661$	−3.67702e6	−	6.36878e6i	−0.327335	−	0.566961i	−0.981982	+	0.188974i	$0.939484\pi$
$662$		0			0
$663$	−899830.	+	1.55855e6i	−0.0795017	+	0.137701i
$664$		0			0
$665$	−1.64714e6	−	7.06971e6i	−0.144436	−	0.619937i
$666$		0			0
$667$	3.56015e6	−	6.16635e6i	0.309851	−	0.536678i
$668$		0			0
$669$	67397.2	+	116735.i	0.00582206	+	0.0100841i
$670$		0			0
$671$	8.47497e6			0.726661
$672$		0			0
$673$	2.42769e6			0.206612			0.103306	−	0.994650i	$-0.467058\pi$
$673$	2.42769e6			0.206612			0.103306	+	0.994650i	$0.467058\pi$
$674$		0			0
$675$	148260.	+	256794.i	0.0125246	+	0.0216933i
$676$		0			0
$677$	8.37058e6	−	1.44983e7i	0.701914	−	1.21575i	−0.265880	−	0.964006i	$-0.585663\pi$
$677$	8.37058e6	−	1.44983e7i	0.701914	−	1.21575i	0.967794	−	0.251744i	$-0.0810041\pi$
$678$		0			0
$679$	−6.07822e6	−	1.84496e6i	−0.505944	−	0.153572i
$680$		0			0
$681$	607014.	−	1.05138e6i	0.0501569	−	0.0868743i
$682$		0			0
$683$	−6.56200e6	−	1.13657e7i	−0.538251	−	0.932277i	−0.998998	−	0.0447462i	$-0.985752\pi$
$683$	−6.56200e6	−	1.13657e7i	−0.538251	−	0.932277i	0.460748	−	0.887531i	$-0.347581\pi$
$684$		0			0
$685$	5.77361e6			0.470133
$686$		0			0
$687$	622024.			0.0502823
$688$		0			0
$689$	9.84617e6	+	1.70541e7i	0.790167	+	1.36861i
$690$		0			0
$691$	9.24637e6	−	1.60152e7i	0.736675	−	1.27596i	−0.217310	−	0.976103i	$-0.569728\pi$
$691$	9.24637e6	−	1.60152e7i	0.736675	−	1.27596i	0.953985	−	0.299856i	$-0.0969386\pi$
$692$		0			0
$693$	6.63894e6	+	2.01515e6i	0.525128	+	0.159395i
$694$		0			0
$695$	−3.90515e6	+	6.76392e6i	−0.306673	+	0.531174i
$696$		0			0
$697$	1.06207e7	+	1.83956e7i	0.828079	+	1.43427i
$698$		0			0
$699$	827690.			0.0640729
$700$		0			0
$701$	9.59372e6			0.737381			0.368691	−	0.929552i	$-0.379806\pi$
$701$	9.59372e6			0.737381			0.368691	+	0.929552i	$0.379806\pi$
$702$		0			0
$703$	−1.50197e7	−	2.60148e7i	−1.14623	−	1.98533i
$704$		0			0
$705$	−17146.8	+	29699.2i	−0.00129931	+	0.00225046i
$706$		0			0
$707$	3.89541e6	+	1.67196e7i	0.293092	+	1.25799i
$708$		0			0
$709$	1.18712e7	−	2.05615e7i	0.886907	−	1.53617i	0.0433953	−	0.999058i	$-0.486183\pi$
$709$	1.18712e7	−	2.05615e7i	0.886907	−	1.53617i	0.843512	−	0.537110i	$-0.180484\pi$
$710$		0			0
$711$	8.17507e6	+	1.41596e7i	0.606481	+	1.05046i
$712$		0			0
$713$	−322037.			−0.0237236
$714$		0			0
$715$	−5.88584e6			−0.430570
$716$		0			0
$717$	705383.	+	1.22176e6i	0.0512422	+	0.0887540i
$718$		0			0
$719$	−6.86325e6	+	1.18875e7i	−0.495117	+	0.857568i	−0.999984	−	0.00562936i	$-0.998208\pi$
$719$	−6.86325e6	+	1.18875e7i	−0.495117	+	0.857568i	0.504867	+	0.863197i	$0.331541\pi$
$720$		0			0
$721$	−1.72938e7	+	1.61918e7i	−1.23895	+	1.16000i
$722$		0			0
$723$	141124.	−	244434.i	0.0100405	−	0.0173906i
$724$		0			0
$725$	−608386.	−	1.05376e6i	−0.0429867	−	0.0744552i
$726$		0			0
$727$	−2.21306e7			−1.55295			−0.776474	−	0.630150i	$-0.782993\pi$
$727$	−2.21306e7			−1.55295			−0.776474	+	0.630150i	$0.782993\pi$
$728$		0			0
$729$	−1.40111e7			−0.976455
$730$		0			0
$731$	3.33623e6	+	5.77852e6i	0.230921	+	0.399966i
$732$		0			0
$733$	5.96376e6	−	1.03295e7i	0.409978	−	0.710102i	−0.584909	−	0.811099i	$-0.698870\pi$
$733$	5.96376e6	−	1.03295e7i	0.409978	−	0.710102i	0.994887	+	0.100997i	$0.0322032\pi$
$734$		0			0
$735$	−341641.	−	228448.i	−0.0233266	−	0.0155980i
$736$		0			0
$737$	−3.45555e6	+	5.98519e6i	−0.234341	+	0.405891i
$738$		0			0
$739$	−2.38639e6	−	4.13335e6i	−0.160742	−	0.278414i	0.774393	−	0.632705i	$-0.218056\pi$
$739$	−2.38639e6	−	4.13335e6i	−0.160742	−	0.278414i	−0.935135	+	0.354291i	$0.884722\pi$
$740$		0			0
$741$	2.33270e6			0.156068
$742$		0			0
$743$	−2.20892e6			−0.146794			−0.0733968	−	0.997303i	$-0.523384\pi$
$743$	−2.20892e6			−0.146794			−0.0733968	+	0.997303i	$0.523384\pi$
$744$		0			0
$745$	1.42370e6	+	2.46591e6i	0.0939781	+	0.162775i
$746$		0			0
$747$	−2.02069e6	+	3.49995e6i	−0.132495	+	0.229488i
$748$		0			0
$749$	275571.	−	258011.i	0.0179485	−	0.0168048i
$750$		0			0
$751$	1.21318e7	−	2.10128e7i	0.784917	−	1.35952i	−0.144131	−	0.989559i	$-0.546039\pi$
$751$	1.21318e7	−	2.10128e7i	0.784917	−	1.35952i	0.929048	−	0.369958i	$-0.120628\pi$
$752$		0			0
$753$	711833.	+	1.23293e6i	0.0457499	+	0.0792412i
$754$		0			0
$755$	−9.88375e6			−0.631036
$756$		0			0
$757$	4.49576e6			0.285143			0.142572	−	0.989784i	$-0.454463\pi$
$757$	4.49576e6			0.285143			0.142572	+	0.989784i	$0.454463\pi$
$758$		0			0
$759$	−395486.	−	685002.i	−0.0249188	−	0.0431606i
$760$		0			0
$761$	5.79579e6	−	1.00386e7i	0.362787	−	0.628365i	−0.625632	−	0.780119i	$-0.715159\pi$
$761$	5.79579e6	−	1.00386e7i	0.362787	−	0.628365i	0.988418	+	0.151754i	$0.0484920\pi$
$762$		0			0
$763$	−170965.	−	733804.i	−0.0106315	−	0.0456319i
$764$		0			0
$765$	5.22792e6	−	9.05502e6i	0.322980	−	0.559417i
$766$		0			0
$767$	1.88504e7	+	3.26498e7i	1.15700	+	2.00398i
$768$		0			0
$769$	5.13304e6			0.313011			0.156505	−	0.987677i	$-0.449977\pi$
$769$	5.13304e6			0.313011			0.156505	+	0.987677i	$0.449977\pi$
$770$		0			0
$771$	976765.			0.0591771
$772$		0			0
$773$	−5.82125e6	−	1.00827e7i	−0.350403	−	0.606915i	0.635917	−	0.771757i	$-0.280622\pi$
$773$	−5.82125e6	−	1.00827e7i	−0.350403	−	0.606915i	−0.986320	+	0.164842i	$0.947289\pi$
$774$		0			0
$775$	−27516.1	+	47659.3i	−0.00164563	+	0.00285032i
$776$		0			0
$777$	−1.62741e6	−	493976.i	−0.0967038	−	0.0293531i
$778$		0			0
$779$	1.37665e7	−	2.38442e7i	0.812792	−	1.40780i
$780$		0			0
$781$	−2.74029e6	−	4.74632e6i	−0.160757	−	0.278439i
$782$		0			0
$783$	−923642.			−0.0538393
$784$		0			0
$785$	1.06147e7			0.614800
$786$		0			0
$787$	780535.	+	1.35193e6i	0.0449217	+	0.0778066i	0.887612	−	0.460592i	$-0.152363\pi$
$787$	780535.	+	1.35193e6i	0.0449217	+	0.0778066i	−0.842690	+	0.538399i	$0.819030\pi$
$788$		0			0
$789$	−747567.	+	1.29482e6i	−0.0427521	+	0.0740488i
$790$		0			0
$791$	−2.48552e7	−	7.54443e6i	−1.41246	−	0.428732i
$792$		0			0
$793$	−2.04070e7	+	3.53460e7i	−1.15238	+	1.99599i
$794$		0			0
$795$	226116.	+	391644.i	0.0126886	+	0.0219773i
$796$		0			0
$797$	−2.19483e7			−1.22393			−0.611963	−	0.790886i	$-0.709620\pi$
$797$	−2.19483e7			−1.22393			−0.611963	+	0.790886i	$0.709620\pi$
$798$		0			0
$799$	2.42329e6			0.134289
$800$		0			0
$801$	−2.26174e6	−	3.91745e6i	−0.124555	−	0.215736i
$802$		0			0
$803$	−8.21809e6	+	1.42341e7i	−0.449761	+	0.779009i
$804$		0			0
$805$	−2.68970e6	−	1.15445e7i	−0.146290	−	0.627893i
$806$		0			0
$807$	198001.	−	342949.i	0.0107025	−	0.0185372i
$808$		0			0
$809$	1.73642e7	+	3.00757e7i	0.932789	+	1.61564i	0.778529	+	0.627608i	$0.215966\pi$
$809$	1.73642e7	+	3.00757e7i	0.932789	+	1.61564i	0.154260	+	0.988030i	$0.450701\pi$
$810$		0			0
$811$	−1.07921e7			−0.576174			−0.288087	−	0.957604i	$-0.593019\pi$
$811$	−1.07921e7			−0.576174			−0.288087	+	0.957604i	$0.593019\pi$
$812$		0			0
$813$	−84178.9			−0.00446660
$814$		0			0
$815$	2.78326e6	+	4.82074e6i	0.146777	+	0.254226i
$816$		0			0
$817$	4.32439e6	−	7.49007e6i	0.226658	−	0.392582i
$818$		0			0
$819$	−2.43905e7	+	2.28363e7i	−1.27061	+	1.18964i
$820$		0			0
$821$	−1.58599e7	+	2.74701e7i	−0.821188	+	1.42234i	0.0836107	+	0.996498i	$0.473355\pi$
$821$	−1.58599e7	+	2.74701e7i	−0.821188	+	1.42234i	−0.904798	+	0.425840i	$0.859979\pi$
$822$		0			0
$823$	1.65014e7	+	2.85813e7i	0.849223	+	1.47090i	0.881903	+	0.471432i	$0.156263\pi$
$823$	1.65014e7	+	2.85813e7i	0.849223	+	1.47090i	−0.0326796	+	0.999466i	$0.510404\pi$
$824$		0			0
$825$	−135168.			−0.00691413
$826$		0			0
$827$	−2.33424e7			−1.18681			−0.593407	−	0.804903i	$-0.702217\pi$
$827$	−2.33424e7			−1.18681			−0.593407	+	0.804903i	$0.702217\pi$
$828$		0			0
$829$	132382.	+	229293.i	0.00669026	+	0.0115879i	0.869351	−	0.494195i	$-0.164537\pi$
$829$	132382.	+	229293.i	0.00669026	+	0.0115879i	−0.862661	+	0.505783i	$0.831204\pi$
$830$		0			0
$831$	716597.	−	1.24118e6i	0.0359975	−	0.0623495i
$832$		0			0
$833$	−1.90942e6	+	2.89785e7i	−0.0953429	+	1.44698i
$834$		0			0
$835$	402449.	−	697063.i	0.0199754	−	0.0345984i
$836$		0			0
$837$	20887.2	+	36177.8i	0.00103055	+	0.00178496i
$838$		0			0
$839$	6.62082e6			0.324719			0.162359	−	0.986732i	$-0.448090\pi$
$839$	6.62082e6			0.324719			0.162359	+	0.986732i	$0.448090\pi$
$840$		0			0
$841$	−1.67210e7			−0.815214
$842$		0			0
$843$	−183861.	−	318456.i	−0.00891086	−	0.0154341i
$844$		0			0
$845$	9.53147e6	−	1.65090e7i	0.459217	−	0.795387i
$846$		0			0
$847$	1.06147e7	−	9.93834e6i	0.508395	−	0.475998i
$848$		0			0
$849$	−131734.	+	228170.i	−0.00627233	+	0.0108640i
$850$		0			0
$851$	−2.45264e7	−	4.24809e7i	−1.16094	−	2.01081i
$852$		0			0
$853$	1.08548e7			0.510800			0.255400	−	0.966836i	$-0.417793\pi$
$853$	1.08548e7			0.510800			0.255400	+	0.966836i	$0.417793\pi$
$854$		0			0
$855$	−1.35528e7			−0.634035
$856$		0			0
$857$	4.74615e6	+	8.22058e6i	0.220744	+	0.382340i	0.955034	−	0.296496i	$-0.0958180\pi$
$857$	4.74615e6	+	8.22058e6i	0.220744	+	0.382340i	−0.734290	+	0.678836i	$0.762485\pi$
$858$		0			0
$859$	−1.58335e7	+	2.74244e7i	−0.732140	+	1.26810i	0.223827	+	0.974629i	$0.428145\pi$
$859$	−1.58335e7	+	2.74244e7i	−0.732140	+	1.26810i	−0.955967	+	0.293474i	$0.905189\pi$
$860$		0			0
$861$	−353709.	−	1.51816e6i	−0.0162607	−	0.0697928i
$862$		0			0
$863$	1.68524e7	−	2.91893e7i	0.770258	−	1.33413i	−0.167164	−	0.985929i	$-0.553461\pi$
$863$	1.68524e7	−	2.91893e7i	0.770258	−	1.33413i	0.937422	−	0.348196i	$-0.113206\pi$
$864$		0			0
$865$	−942128.	−	1.63181e6i	−0.0428124	−	0.0741532i
$866$		0			0
$867$	1.53163e6			0.0691999
$868$		0			0
$869$	−1.49357e7			−0.670930
$870$		0			0
$871$	−1.66414e7	−	2.88237e7i	−0.743265	−	1.28737i
$872$		0			0
$873$	−5.92970e6	+	1.02705e7i	−0.263328	+	0.456097i
$874$		0			0
$875$	−1.93833e6	−	588351.i	−0.0855869	−	0.0259787i
$876$		0			0
$877$	−1.74452e7	+	3.02159e7i	−0.765908	+	1.32659i	0.173858	+	0.984771i	$0.444377\pi$
$877$	−1.74452e7	+	3.02159e7i	−0.765908	+	1.32659i	−0.939765	+	0.341820i	$0.888957\pi$
$878$		0			0
$879$	1.06143e6	+	1.83844e6i	0.0463359	+	0.0802561i
$880$		0			0
$881$	2.52144e7			1.09448			0.547241	−	0.836975i	$-0.315678\pi$
$881$	2.52144e7			1.09448			0.547241	+	0.836975i	$0.315678\pi$
$882$		0			0
$883$	−1.69692e7			−0.732419			−0.366210	−	0.930532i	$-0.619345\pi$
$883$	−1.69692e7			−0.732419			−0.366210	+	0.930532i	$0.619345\pi$
$884$		0			0
$885$	432897.	+	749799.i	0.0185792	+	0.0321801i
$886$		0			0
$887$	−318849.	+	552263.i	−0.0136074	+	0.0235688i	−0.872749	−	0.488169i	$-0.837665\pi$
$887$	−318849.	+	552263.i	−0.0136074	+	0.0235688i	0.859142	+	0.511738i	$0.170998\pi$
$888$		0			0
$889$	1.12700e7	+	3.42086e6i	0.478268	+	0.145171i
$890$		0			0
$891$	6.45101e6	−	1.11735e7i	0.272228	−	0.471513i
$892$		0			0
$893$	−1.57053e6	−	2.72023e6i	−0.0659047	−	0.114150i
$894$		0			0
$895$	−9.97841e6			−0.416393
$896$		0			0
$897$	3.80919e6			0.158071
$898$		0			0
$899$	−85710.8	−	148456.i	−0.00353701	−	0.00612628i
$900$		0			0
$901$	1.59780e7	−	2.76747e7i	0.655709	−	1.13572i
$902$		0			0
$903$	−111109.	−	476893.i	−0.00453450	−	0.0194626i
$904$		0			0
$905$	−6.25185e6	+	1.08285e7i	−0.253739	+	0.439489i
$906$		0			0
$907$	1.91366e7	+	3.31455e7i	0.772407	+	1.33785i	0.936240	+	0.351360i	$0.114281\pi$
$907$	1.91366e7	+	3.31455e7i	0.772407	+	1.33785i	−0.163833	+	0.986488i	$0.552386\pi$
$908$		0			0
$909$	3.20517e7			1.28659
$910$		0			0
$911$	−1.18499e7			−0.473063			−0.236531	−	0.971624i	$-0.576011\pi$
$911$	−1.18499e7			−0.473063			−0.236531	+	0.971624i	$0.576011\pi$
$912$		0			0
$913$	−1.84589e6	−	3.19718e6i	−0.0732874	−	0.126937i
$914$		0			0
$915$	−468645.	+	811717.i	−0.0185051	+	0.0320517i
$916$		0			0
$917$	2.24807e6	−	2.10482e6i	0.0882850	−	0.0826592i
$918$		0			0
$919$	−2.14860e7	+	3.72148e7i	−0.839201	+	1.45354i	0.0513621	+	0.998680i	$0.483644\pi$
$919$	−2.14860e7	+	3.72148e7i	−0.839201	+	1.45354i	−0.890563	+	0.454859i	$0.849690\pi$
$920$		0			0
$921$	497854.	+	862308.i	0.0193398	+	0.0334976i
$922$		0			0
$923$	2.63936e7			1.01975
$924$		0			0
$925$	−8.38253e6			−0.322122
$926$		0			0
$927$	2.21155e7	+	3.83052e7i	0.845274	+	1.46406i
$928$		0			0
$929$	4.60194e6	−	7.97079e6i	0.174945	−	0.303013i	−0.765197	−	0.643796i	$-0.777359\pi$
$929$	4.60194e6	−	7.97079e6i	0.174945	−	0.303013i	0.940142	+	0.340782i	$0.110692\pi$
$930$		0			0
$931$	3.37668e7	−	1.66374e7i	1.27678	−	0.629089i
$932$		0			0
$933$	−861779.	+	1.49264e6i	−0.0324109	+	0.0561374i
$934$		0			0
$935$	4.77567e6	+	8.27170e6i	0.178651	+	0.309433i
$936$		0			0
$937$	−8.46665e6			−0.315038			−0.157519	−	0.987516i	$-0.550350\pi$
$937$	−8.46665e6			−0.315038			−0.157519	+	0.987516i	$0.550350\pi$
$938$		0			0
$939$	1.89086e6			0.0699834
$940$		0			0
$941$	−8.03513e6	−	1.39173e7i	−0.295814	−	0.512365i	0.679360	−	0.733805i	$-0.262258\pi$
$941$	−8.03513e6	−	1.39173e7i	−0.295814	−	0.512365i	−0.975174	+	0.221440i	$0.928924\pi$
$942$		0			0
$943$	2.24800e7	−	3.89365e7i	0.823222	−	1.42586i
$944$		0			0
$945$	−1.12246e6	+	1.05094e6i	−0.0408877	+	0.0382822i
$946$		0			0
$947$	5.00106e6	−	8.66210e6i	0.181212	−	0.313869i	−0.761081	−	0.648656i	$-0.775331\pi$
$947$	5.00106e6	−	8.66210e6i	0.181212	−	0.313869i	0.942294	+	0.334788i	$0.108665\pi$
$948$		0			0
$949$	−3.95770e7	−	6.85493e7i	−1.42652	−	2.47080i
$950$		0			0
$951$	−1.50101e6			−0.0538187
$952$		0			0
$953$	−8.32957e6			−0.297092			−0.148546	−	0.988906i	$-0.547459\pi$
$953$	−8.32957e6			−0.297092			−0.148546	+	0.988906i	$0.547459\pi$
$954$		0			0
$955$	−1.16744e7	−	2.02207e7i	−0.414216	−	0.717443i
$956$		0			0
$957$	210519.	−	364630.i	0.00743039	−	0.0128698i
$958$		0			0
$959$	6.79363e6	+	2.91591e7i	0.238537	+	1.02383i
$960$		0			0
$961$	1.43107e7	−	2.47869e7i	0.499865	−	0.865791i
$962$		0			0
$963$	−352403.	−	610380.i	−0.0122454	−	0.0212097i
$964$		0			0
$965$	1.04382e7			0.360834
$966$		0			0
$967$	1.10680e7			0.380631			0.190316	−	0.981723i	$-0.439049\pi$
$967$	1.10680e7			0.380631			0.190316	+	0.981723i	$0.439049\pi$
$968$		0			0
$969$	−1.89271e6	−	3.27828e6i	−0.0647554	−	0.112160i
$970$		0			0
$971$	−1.43081e7	+	2.47824e7i	−0.487007	+	0.843521i	−0.999888	−	0.0149384i	$-0.995245\pi$
$971$	−1.43081e7	+	2.47824e7i	−0.487007	+	0.843521i	0.512881	+	0.858460i	$0.328578\pi$
$972$		0			0
$973$	−3.87557e7	−	1.17637e7i	−1.31236	−	0.398348i
$974$		0			0
$975$	325473.	−	563735.i	0.0109649	−	0.0189917i
$976$		0			0
$977$	8.24314e6	+	1.42775e7i	0.276284	+	0.478539i	0.970458	−	0.241269i	$-0.0775635\pi$
$977$	8.24314e6	+	1.42775e7i	0.276284	+	0.478539i	−0.694174	+	0.719807i	$0.744230\pi$
$978$		0			0
$979$	4.13218e6			0.137791
$980$		0			0
$981$	−1.40672e6			−0.0466696
$982$		0			0
$983$	1.70878e7	+	2.95970e7i	0.564031	+	0.976930i	0.997139	+	0.0755881i	$0.0240834\pi$
$983$	1.70878e7	+	2.95970e7i	0.564031	+	0.976930i	−0.433108	+	0.901342i	$0.642583\pi$
$984$		0			0
$985$	1.08857e7	−	1.88546e7i	0.357492	−	0.619194i
$986$		0			0
$987$	−170169.	−	51652.5i	−0.00556018	−	0.00168771i
$988$		0			0
$989$	7.06153e6	−	1.22309e7i	0.229566	−	0.397620i
$990$		0			0
$991$	−1.11529e6	−	1.93174e6i	−0.0360747	−	0.0624833i	0.847424	−	0.530916i	$-0.178152\pi$
$991$	−1.11529e6	−	1.93174e6i	−0.0360747	−	0.0624833i	−0.883499	+	0.468433i	$0.844819\pi$
$992$		0			0
$993$	1.22739e6			0.0395010
$994$		0			0
$995$	2.35237e7			0.753267
$996$		0			0
$997$	1.12617e7	+	1.95059e7i	0.358813	+	0.621482i	0.987763	−	0.155964i	$-0.0498484\pi$
$997$	1.12617e7	+	1.95059e7i	0.358813	+	0.621482i	−0.628950	+	0.777446i	$0.716515\pi$
$998$		0			0
$999$	−3.18156e6	+	5.51062e6i	−0.100862	+	0.174697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.6.i.d.121.4	yes	14
7.2	even	3		980.6.a.n.1.4		7
7.4	even	3	inner	140.6.i.d.81.4	✓	14
7.5	odd	6		980.6.a.o.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.6.i.d.81.4	✓	14	7.4	even	3	inner
140.6.i.d.121.4	yes	14	1.1	even	1	trivial
980.6.a.n.1.4		7	7.2	even	3
980.6.a.o.1.4		7	7.5	odd	6

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	140.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.489062 - 0.847081i) q^{3} +(12.5000 - 21.6506i) q^{5} +(124.053 + 37.6545i) q^{7} +(121.022 - 209.616i) q^{9} +O(q^{10})\)	\(q+(-0.489062 - 0.847081i) q^{3} +(12.5000 - 21.6506i) q^{5} +(124.053 + 37.6545i) q^{7} +(121.022 - 209.616i) q^{9} +(110.552 + 191.482i) q^{11} -1064.81 q^{13} -24.4531 q^{15} +(863.965 + 1496.43i) q^{17} +(1119.86 - 1939.66i) q^{19} +(-28.7732 - 123.498i) q^{21} +(1828.68 - 3167.37i) q^{23} +(-312.500 - 541.266i) q^{25} -474.433 q^{27} +1946.84 q^{29} +(-44.0257 - 76.2548i) q^{31} +(108.134 - 187.294i) q^{33} +(2365.91 - 2215.14i) q^{35} +(6706.02 - 11615.2i) q^{37} +(520.756 + 901.976i) q^{39} +12293.0 q^{41} +3861.54 q^{43} +(-3025.54 - 5240.39i) q^{45} +(701.213 - 1214.54i) q^{47} +(13971.3 + 9342.30i) q^{49} +(845.065 - 1463.70i) q^{51} +(-9246.92 - 16016.1i) q^{53} +5527.62 q^{55} -2190.73 q^{57} +(-17703.1 - 30662.7i) q^{59} +(19165.0 - 33194.8i) q^{61} +(22906.1 - 21446.4i) q^{63} +(-13310.1 + 23053.7i) q^{65} +(15628.5 + 27069.4i) q^{67} -3577.36 q^{69} -24787.2 q^{71} +(37168.3 + 64377.3i) q^{73} +(-305.664 + 529.425i) q^{75} +(6504.19 + 27916.8i) q^{77} +(-33775.2 + 58500.4i) q^{79} +(-29176.2 - 50534.7i) q^{81} -16697.0 q^{83} +43198.2 q^{85} +(-952.124 - 1649.13i) q^{87} +(9344.38 - 16184.9i) q^{89} +(-132092. - 40094.7i) q^{91} +(-43.0626 + 74.5867i) q^{93} +(-27996.6 - 48491.5i) q^{95} -48997.0 q^{97} +53517.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{3} + 175 q^{5} - 225 q^{7} - 312 q^{9}+O(q^{10}) \) 14 * q + 27 * q^3 + 175 * q^5 - 225 * q^7 - 312 * q^9	\( 14 q + 27 q^{3} + 175 q^{5} - 225 q^{7} - 312 q^{9} - 590 q^{11} - 1708 q^{13} + 1350 q^{15} + 1328 q^{17} + 2990 q^{19} + 993 q^{21} - 4089 q^{23} - 4375 q^{25} - 8562 q^{27} - 6126 q^{29} + 5740 q^{31} - 1470 q^{33} - 3000 q^{35} - 12218 q^{37} + 1560 q^{39} - 16954 q^{41} - 18390 q^{43} + 7800 q^{45} + 28652 q^{47} + 20435 q^{49} - 41244 q^{51} - 24932 q^{53} - 29500 q^{55} - 125868 q^{57} + 38242 q^{59} + 61299 q^{61} + 145548 q^{63} - 21350 q^{65} - 24913 q^{67} - 172302 q^{69} - 72340 q^{71} + 94780 q^{73} + 16875 q^{75} + 198344 q^{77} + 594 q^{79} + 53265 q^{81} - 227170 q^{83} + 66400 q^{85} + 43875 q^{87} + 36823 q^{89} + 138176 q^{91} + 21828 q^{93} - 74750 q^{95} - 515900 q^{97} + 756864 q^{99}+O(q^{100}) \) 14 * q + 27 * q^3 + 175 * q^5 - 225 * q^7 - 312 * q^9 - 590 * q^11 - 1708 * q^13 + 1350 * q^15 + 1328 * q^17 + 2990 * q^19 + 993 * q^21 - 4089 * q^23 - 4375 * q^25 - 8562 * q^27 - 6126 * q^29 + 5740 * q^31 - 1470 * q^33 - 3000 * q^35 - 12218 * q^37 + 1560 * q^39 - 16954 * q^41 - 18390 * q^43 + 7800 * q^45 + 28652 * q^47 + 20435 * q^49 - 41244 * q^51 - 24932 * q^53 - 29500 * q^55 - 125868 * q^57 + 38242 * q^59 + 61299 * q^61 + 145548 * q^63 - 21350 * q^65 - 24913 * q^67 - 172302 * q^69 - 72340 * q^71 + 94780 * q^73 + 16875 * q^75 + 198344 * q^77 + 594 * q^79 + 53265 * q^81 - 227170 * q^83 + 66400 * q^85 + 43875 * q^87 + 36823 * q^89 + 138176 * q^91 + 21828 * q^93 - 74750 * q^95 - 515900 * q^97 + 756864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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