LMFDB - Embedded newform 49.6.c.h.18.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not 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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.54095201243136.19
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 102x^{6} + 320x^{5} + 4283x^{4} - 9104x^{3} - 85298x^{2} + 89904x + 714364 $ x^8 - 4x^7 - 102x^6 + 320x^5 + 4283x^4 - 9104x^3 - 85298x^2 + 89904*x + 714364
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.4
Root			$6.52218 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.6.c.h.30.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.90754 + 6.76805i) q^{2} +(11.7593 - 20.3677i) q^{3} +(-14.5377 + 25.1800i) q^{4} +(-37.1377 - 64.3243i) q^{5} +183.799 q^{6} +22.8562 q^{8} +(-155.062 - 268.575i) q^{9} +O(q^{10})$	\(q+(3.90754 + 6.76805i) q^{2} +(11.7593 - 20.3677i) q^{3} +(-14.5377 + 25.1800i) q^{4} +(-37.1377 - 64.3243i) q^{5} +183.799 q^{6} +22.8562 q^{8} +(-155.062 - 268.575i) q^{9} +(290.234 - 502.699i) q^{10} +(212.110 - 367.385i) q^{11} +(341.906 + 592.198i) q^{12} +252.233 q^{13} -1746.85 q^{15} +(554.517 + 960.452i) q^{16} +(-552.173 + 956.392i) q^{17} +(1211.82 - 2098.93i) q^{18} +(-3.23550 - 5.60405i) q^{19} +2159.58 q^{20} +3315.30 q^{22} +(1806.19 + 3128.42i) q^{23} +(268.773 - 465.529i) q^{24} +(-1195.91 + 2071.38i) q^{25} +(985.611 + 1707.13i) q^{26} -1578.65 q^{27} -5005.02 q^{29} +(-6825.88 - 11822.8i) q^{30} +(1410.85 - 2443.66i) q^{31} +(-3967.89 + 6872.59i) q^{32} +(-4988.52 - 8640.36i) q^{33} -8630.55 q^{34} +9016.95 q^{36} +(1023.44 + 1772.65i) q^{37} +(25.2857 - 43.7961i) q^{38} +(2966.08 - 5137.41i) q^{39} +(-848.827 - 1470.21i) q^{40} -9393.81 q^{41} +10320.8 q^{43} +(6167.16 + 10681.8i) q^{44} +(-11517.3 + 19948.5i) q^{45} +(-14115.5 + 24448.8i) q^{46} +(8517.79 + 14753.3i) q^{47} +26082.9 q^{48} -18692.3 q^{50} +(12986.3 + 22493.0i) q^{51} +(-3666.89 + 6351.24i) q^{52} +(19753.3 - 34213.8i) q^{53} +(-6168.63 - 10684.4i) q^{54} -31509.0 q^{55} -152.189 q^{57} +(-19557.3 - 33874.2i) q^{58} +(16974.9 - 29401.4i) q^{59} +(25395.1 - 43985.7i) q^{60} +(14147.6 + 24504.4i) q^{61} +22051.7 q^{62} -26529.7 q^{64} +(-9367.36 - 16224.7i) q^{65} +(38985.6 - 67525.1i) q^{66} +(-28050.5 + 48584.8i) q^{67} +(-16054.6 - 27807.5i) q^{68} +84958.2 q^{69} -15537.4 q^{71} +(-3544.13 - 6138.61i) q^{72} +(-39109.8 + 67740.1i) q^{73} +(-7998.24 + 13853.4i) q^{74} +(28126.1 + 48715.9i) q^{75} +188.147 q^{76} +46360.3 q^{78} +(22667.7 + 39261.7i) q^{79} +(41187.0 - 71337.9i) q^{80} +(19116.2 - 33110.3i) q^{81} +(-36706.6 - 63577.8i) q^{82} -1381.82 q^{83} +82025.7 q^{85} +(40328.8 + 69851.5i) q^{86} +(-58855.4 + 101941. i) q^{87} +(4848.03 - 8397.03i) q^{88} +(-34439.7 - 59651.3i) q^{89} -180016. q^{90} -105031. q^{92} +(-33181.1 - 57471.3i) q^{93} +(-66567.2 + 115298. i) q^{94} +(-240.318 + 416.243i) q^{95} +(93319.2 + 161634. i) q^{96} -108857. q^{97} -131560. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9	$ 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9} + 1952 q^{11} - 8192 q^{15} + 1566 q^{16} + 5974 q^{18} + 7048 q^{22} + 7136 q^{23} - 2764 q^{25} - 6704 q^{29} - 25608 q^{30} - 27810 q^{32} + 55340 q^{36} + 9208 q^{37} - 2464 q^{39} + 40896 q^{43} - 1900 q^{44} - 56712 q^{46} - 86140 q^{50} + 67408 q^{51} + 102920 q^{53} - 31152 q^{57} - 96972 q^{58} + 87080 q^{60} - 80636 q^{64} + 63168 q^{65} + 22896 q^{67} - 307648 q^{71} - 77358 q^{72} - 17596 q^{74} + 266112 q^{78} + 90688 q^{79} + 17204 q^{81} + 545312 q^{85} + 161860 q^{86} - 154812 q^{88} - 424400 q^{92} - 247760 q^{93} - 108224 q^{95} - 84544 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9 + 1952 * q^11 - 8192 * q^15 + 1566 * q^16 + 5974 * q^18 + 7048 * q^22 + 7136 * q^23 - 2764 * q^25 - 6704 * q^29 - 25608 * q^30 - 27810 * q^32 + 55340 * q^36 + 9208 * q^37 - 2464 * q^39 + 40896 * q^43 - 1900 * q^44 - 56712 * q^46 - 86140 * q^50 + 67408 * q^51 + 102920 * q^53 - 31152 * q^57 - 96972 * q^58 + 87080 * q^60 - 80636 * q^64 + 63168 * q^65 + 22896 * q^67 - 307648 * q^71 - 77358 * q^72 - 17596 * q^74 + 266112 * q^78 + 90688 * q^79 + 17204 * q^81 + 545312 * q^85 + 161860 * q^86 - 154812 * q^88 - 424400 * q^92 - 247760 * q^93 - 108224 * q^95 - 84544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	3.90754	+	6.76805i	0.690761	+	1.19643i	0.971589	+	0.236676i	$0.0760578\pi$
$2$	3.90754	+	6.76805i	0.690761	+	1.19643i	−0.280827	+	0.959758i	$0.590609\pi$
$3$	11.7593	−	20.3677i	0.754359	−	1.30659i	−0.191334	−	0.981525i	$-0.561281\pi$
$3$	11.7593	−	20.3677i	0.754359	−	1.30659i	0.945692	−	0.325063i	$-0.105385\pi$
$4$	−14.5377	+	25.1800i	−0.454303	+	0.786875i
$5$	−37.1377	−	64.3243i	−0.664339	−	1.15067i	−0.979464	−	0.201618i	$-0.935380\pi$
$5$	−37.1377	−	64.3243i	−0.664339	−	1.15067i	0.315125	−	0.949050i	$-0.397953\pi$
$6$	183.799			2.08433
$7$		0			0
$7$		0			0
$8$	22.8562			0.126264
$9$	−155.062	−	268.575i	−0.638114	−	1.10525i
$10$	290.234	−	502.699i	0.917799	−	1.58967i
$11$	212.110	−	367.385i	0.528541	−	0.915460i	−0.470905	−	0.882184i	$-0.656073\pi$
$11$	212.110	−	367.385i	0.528541	−	0.915460i	0.999446	−	0.0332758i	$-0.0105940\pi$
$12$	341.906	+	592.198i	0.685414	+	1.18717i
$13$	252.233			0.413946			0.206973	−	0.978347i	$-0.433639\pi$
$13$	252.233			0.413946			0.206973	+	0.978347i	$0.433639\pi$
$14$		0			0
$15$	−1746.85			−2.00460
$16$	554.517	+	960.452i	0.541521	+	0.937942i
$17$	−552.173	+	956.392i	−0.463397	+	0.802627i	−0.999128	−	0.0417619i	$-0.986703\pi$
$17$	−552.173	+	956.392i	−0.463397	+	0.802627i	0.535731	+	0.844389i	$0.320036\pi$
$18$	1211.82	−	2098.93i	0.881569	−	1.52692i
$19$	−3.23550	−	5.60405i	−0.00205616	−	0.00356138i	0.864995	−	0.501780i	$-0.167321\pi$
$19$	−3.23550	−	5.60405i	−0.00205616	−	0.00356138i	−0.867052	+	0.498218i	$0.833988\pi$
$20$	2159.58			1.20724
$21$		0			0
$22$	3315.30			1.46038
$23$	1806.19	+	3128.42i	0.711942	+	1.23312i	0.964127	+	0.265440i	$0.0855173\pi$
$23$	1806.19	+	3128.42i	0.711942	+	1.23312i	−0.252186	+	0.967679i	$0.581149\pi$
$24$	268.773	−	465.529i	0.0952484	−	0.164975i
$25$	−1195.91	+	2071.38i	−0.382692	+	0.662842i
$26$	985.611	+	1707.13i	0.285938	+	0.495260i
$27$	−1578.65			−0.416751
$28$		0			0
$29$	−5005.02			−1.10512			−0.552561	−	0.833472i	$-0.686350\pi$
$29$	−5005.02			−1.10512			−0.552561	+	0.833472i	$0.686350\pi$
$30$	−6825.88	−	11822.8i	−1.38470	−	2.39837i
$31$	1410.85	−	2443.66i	0.263679	−	0.456705i	−0.703538	−	0.710658i	$-0.748397\pi$
$31$	1410.85	−	2443.66i	0.263679	−	0.456705i	0.967217	+	0.253953i	$0.0817308\pi$
$32$	−3967.89	+	6872.59i	−0.684991	+	1.18644i
$33$	−4988.52	−	8640.36i	−0.797419	−	1.38117i
$34$	−8630.55			−1.28039
$35$		0			0
$36$	9016.95			1.15959
$37$	1023.44	+	1772.65i	0.122902	+	0.212872i	0.920911	−	0.389774i	$-0.127447\pi$
$37$	1023.44	+	1772.65i	0.122902	+	0.212872i	−0.798009	+	0.602645i	$0.794113\pi$
$38$	25.2857	−	43.7961i	0.00284063	−	0.00492012i
$39$	2966.08	−	5137.41i	0.312264	−	0.540857i
$40$	−848.827	−	1470.21i	−0.0838821	−	0.145288i
$41$	−9393.81			−0.872734			−0.436367	−	0.899769i	$-0.643735\pi$
$41$	−9393.81			−0.872734			−0.436367	+	0.899769i	$0.643735\pi$
$42$		0			0
$43$	10320.8			0.851218			0.425609	−	0.904907i	$-0.360060\pi$
$43$	10320.8			0.851218			0.425609	+	0.904907i	$0.360060\pi$
$44$	6167.16	+	10681.8i	0.480235	+	0.831791i
$45$	−11517.3	+	19948.5i	−0.847848	+	1.46852i
$46$	−14115.5	+	24448.8i	−0.983564	+	1.70358i
$47$	8517.79	+	14753.3i	0.562448	+	0.974189i	0.997282	+	0.0736781i	$0.0234737\pi$
$47$	8517.79	+	14753.3i	0.562448	+	0.974189i	−0.434834	+	0.900511i	$0.643193\pi$
$48$	26082.9			1.63400
$49$		0			0
$50$	−18692.3			−1.05739
$51$	12986.3	+	22493.0i	0.699135	+	1.21094i
$52$	−3666.89	+	6351.24i	−0.188057	+	0.325724i
$53$	19753.3	−	34213.8i	0.965941	−	1.67306i	0.258877	−	0.965910i	$-0.416648\pi$
$53$	19753.3	−	34213.8i	0.965941	−	1.67306i	0.707064	−	0.707149i	$-0.250019\pi$
$54$	−6168.63	−	10684.4i	−0.287875	−	0.498615i
$55$	−31509.0			−1.40452
$56$		0			0
$57$	−152.189			−0.00620433
$58$	−19557.3	−	33874.2i	−0.763376	−	1.32221i
$59$	16974.9	−	29401.4i	0.634859	−	1.09961i	−0.351687	−	0.936118i	$-0.614392\pi$
$59$	16974.9	−	29401.4i	0.634859	−	1.09961i	0.986545	−	0.163489i	$-0.0522750\pi$
$60$	25395.1	−	43985.7i	0.910694	−	1.57737i
$61$	14147.6	+	24504.4i	0.486809	+	0.843178i	0.999885	−	0.0151652i	$-0.00482741\pi$
$61$	14147.6	+	24504.4i	0.486809	+	0.843178i	−0.513076	+	0.858343i	$0.671494\pi$
$62$	22051.7			0.728556
$63$		0			0
$64$	−26529.7			−0.809621
$65$	−9367.36	−	16224.7i	−0.275001	−	0.476315i
$66$	38985.6	−	67525.1i	1.10165	−	1.90812i
$67$	−28050.5	+	48584.8i	−0.763402	+	1.32225i	0.177686	+	0.984087i	$0.443139\pi$
$67$	−28050.5	+	48584.8i	−0.763402	+	1.32225i	−0.941088	+	0.338163i	$0.890194\pi$
$68$	−16054.6	−	27807.5i	−0.421045	−	0.729271i
$69$	84958.2			2.14824
$70$		0			0
$71$	−15537.4			−0.365791			−0.182895	−	0.983132i	$-0.558547\pi$
$71$	−15537.4			−0.365791			−0.182895	+	0.983132i	$0.558547\pi$
$72$	−3544.13	−	6138.61i	−0.0805709	−	0.139553i
$73$	−39109.8	+	67740.1i	−0.858970	+	1.48778i	0.0139419	+	0.999903i	$0.495562\pi$
$73$	−39109.8	+	67740.1i	−0.858970	+	1.48778i	−0.872912	+	0.487877i	$0.837771\pi$
$74$	−7998.24	+	13853.4i	−0.169791	+	0.294087i
$75$	28126.1	+	48715.9i	0.577374	+	1.00004i
$76$	188.147			0.00373648
$77$		0			0
$78$	46360.3			0.862800
$79$	22667.7	+	39261.7i	0.408640	+	0.707784i	0.994738	−	0.102456i	$-0.0326700\pi$
$79$	22667.7	+	39261.7i	0.408640	+	0.707784i	−0.586098	+	0.810240i	$0.699337\pi$
$80$	41187.0	−	71337.9i	0.719507	−	1.24622i
$81$	19116.2	−	33110.3i	0.323735	−	0.560725i
$82$	−36706.6	−	63577.8i	−0.602851	−	1.04417i
$83$	−1381.82			−0.0220169			−0.0110085	−	0.999939i	$-0.503504\pi$
$83$	−1381.82			−0.0220169			−0.0110085	+	0.999939i	$0.503504\pi$
$84$		0			0
$85$	82025.7			1.23141
$86$	40328.8	+	69851.5i	0.587989	+	1.01843i
$87$	−58855.4	+	101941.i	−0.833659	+	1.44394i
$88$	4848.03	−	8397.03i	0.0667357	−	0.115590i
$89$	−34439.7	−	59651.3i	−0.460876	−	0.798261i	0.538128	−	0.842863i	$-0.319132\pi$
$89$	−34439.7	−	59651.3i	−0.460876	−	0.798261i	−0.999005	+	0.0446014i	$0.985798\pi$
$90$	−180016.			−2.34264
$91$		0			0
$92$	−105031.			−1.29375
$93$	−33181.1	−	57471.3i	−0.397817	−	0.689039i
$94$	−66567.2	+	115298.i	−0.777035	+	1.34586i
$95$	−240.318	+	416.243i	−0.00273198	+	0.00473192i
$96$	93319.2	+	161634.i	1.03346	+	1.79000i
$97$	−108857.			−1.17470			−0.587351	−	0.809332i	$-0.699829\pi$
$97$	−108857.			−1.17470			−0.587351	+	0.809332i	$0.699829\pi$
$98$		0			0
$99$	−131560.			−1.34908
$100$	−34771.6	−	60226.1i	−0.347716	−	0.602261i
$101$	8986.13	−	15564.4i	0.0876535	−	0.151820i	−0.818865	−	0.573986i	$-0.805396\pi$
$101$	8986.13	−	15564.4i	0.0876535	−	0.151820i	0.906519	+	0.422165i	$0.138730\pi$
$102$	−101489.	+	175784.i	−0.965871	+	1.67294i
$103$	15886.8	+	27516.8i	0.147552	+	0.255567i	0.930322	−	0.366744i	$-0.119527\pi$
$103$	15886.8	+	27516.8i	0.147552	+	0.255567i	−0.782770	+	0.622311i	$0.786194\pi$
$104$	5765.11			0.0522666
$105$		0			0
$106$	308747.			2.66894
$107$	−4114.68	−	7126.84i	−0.0347438	−	0.0601780i	0.848131	−	0.529787i	$-0.177728\pi$
$107$	−4114.68	−	7126.84i	−0.0347438	−	0.0601780i	−0.882874	+	0.469609i	$0.844395\pi$
$108$	22949.9	−	39750.4i	0.189331	−	0.327931i
$109$	5534.34	−	9585.75i	0.0446169	−	0.0772787i	−0.842855	−	0.538141i	$-0.819127\pi$
$109$	5534.34	−	9585.75i	0.0446169	−	0.0772787i	0.887471	+	0.460863i	$0.152460\pi$
$110$	−123123.	−	213255.i	−0.970188	−	1.68042i
$111$	48139.6			0.370847
$112$		0			0
$113$	65184.3			0.480228			0.240114	−	0.970745i	$-0.422815\pi$
$113$	65184.3			0.480228			0.240114	+	0.970745i	$0.422815\pi$
$114$	−594.683	−	1030.02i	−0.00428571	−	0.00742308i
$115$	134156.	−	232364.i	0.945941	−	1.63842i
$116$	72761.3	−	126026.i	0.502060	−	0.869594i
$117$	−39111.7	−	67743.5i	−0.264145	−	0.457513i
$118$	265320.			1.75414
$119$		0			0
$120$	−39926.4			−0.253109
$121$	−9455.43	−	16377.3i	−0.0587108	−	0.101690i
$122$	−110565.	+	191504.i	−0.672538	+	1.16487i
$123$	−110464.	+	191330.i	−0.658355	+	1.14030i
$124$	41020.8	+	71050.2i	0.239580	+	0.414964i
$125$	−54456.9			−0.311730
$126$		0			0
$127$	−194777.			−1.07159			−0.535796	−	0.844348i	$-0.679988\pi$
$127$	−194777.			−1.07159			−0.535796	+	0.844348i	$0.679988\pi$
$128$	23307.0	+	40369.0i	0.125737	+	0.217782i
$129$	121365.	−	210210.i	0.642124	−	1.11219i
$130$	73206.6	−	126798.i	0.379920	−	0.658040i
$131$	−118252.	−	204818.i	−0.602046	−	1.04277i	−0.992511	−	0.122156i	$-0.961019\pi$
$131$	−118252.	−	204818.i	−0.602046	−	1.04277i	0.390465	−	0.920618i	$-0.372314\pi$
$132$	290086.			1.44908
$133$		0			0
$134$	−438433.			−2.10931
$135$	58627.3	+	101546.i	0.276864	+	0.479542i
$136$	−12620.6	+	21859.5i	−0.0585104	+	0.101343i
$137$	100452.	−	173987.i	0.457252	−	0.791983i	−0.541563	−	0.840660i	$-0.682167\pi$
$137$	100452.	−	173987.i	0.457252	−	0.791983i	0.998815	+	0.0486772i	$0.0155005\pi$
$138$	331977.	+	575001.i	1.48392	+	2.57022i
$139$	−52985.2			−0.232604			−0.116302	−	0.993214i	$-0.537104\pi$
$139$	−52985.2			−0.232604			−0.116302	+	0.993214i	$0.537104\pi$
$140$		0			0
$141$	400653.			1.69715
$142$	−60713.0	−	105158.i	−0.252674	−	0.437644i
$143$	53501.1	−	92666.6i	0.218788	−	0.378951i
$144$	171969.	−	297859.i	0.691104	−	1.19703i
$145$	185875.	+	321944.i	0.734176	+	1.27163i
$146$	−611291.			−2.37337
$147$		0			0
$148$	−59513.7			−0.223338
$149$	50385.2	+	87269.7i	0.185925	+	0.322031i	0.943888	−	0.330266i	$-0.107139\pi$
$149$	50385.2	+	87269.7i	0.185925	+	0.322031i	−0.757963	+	0.652298i	$0.773805\pi$
$150$	−219808.	+	380718.i	−0.797655	+	1.38158i
$151$	228952.	−	396556.i	0.817150	−	1.41535i	−0.0906234	−	0.995885i	$-0.528886\pi$
$151$	228952.	−	396556.i	0.817150	−	1.41535i	0.907774	−	0.419460i	$-0.137781\pi$
$152$	−73.9513	−	128.087i	−0.000259619	−	0.000449674i
$153$	342484.			1.18280
$154$		0			0
$155$	−209582.			−0.700688
$156$	86240.0	+	149372.i	0.283725	+	0.491426i
$157$	−89518.6	+	155051.i	−0.289844	+	0.502024i	−0.973772	−	0.227525i	$-0.926937\pi$
$157$	−89518.6	+	155051.i	−0.289844	+	0.502024i	0.683928	+	0.729549i	$0.260270\pi$
$158$	−177150.	+	306833.i	−0.564545	+	0.977820i
$159$	−464570.	−	804659.i	−1.45733	−	2.52417i
$160$	589433.			1.82027
$161$		0			0
$162$	298789.			0.894494
$163$	−121805.	−	210972.i	−0.359084	−	0.621952i	0.628724	−	0.777629i	$-0.283578\pi$
$163$	−121805.	−	210972.i	−0.359084	−	0.621952i	−0.987808	+	0.155677i	$0.950244\pi$
$164$	136564.	−	236536.i	0.396485	−	0.686733i
$165$	−370524.	+	641766.i	−1.05951	+	1.83513i
$166$	−5399.52	−	9352.24i	−0.0152085	−	0.0263418i
$167$	−117033.			−0.324725			−0.162362	−	0.986731i	$-0.551911\pi$
$167$	−117033.			−0.324725			−0.162362	+	0.986731i	$0.551911\pi$
$168$		0			0
$169$	−307671.			−0.828648
$170$	320518.	+	555154.i	0.850610	+	1.47330i
$171$	−1003.40	+	1737.95i	−0.00262413	+	0.00454513i
$172$	−150040.	+	259877.i	−0.386711	+	0.669803i
$173$	134867.	+	233596.i	0.342602	+	0.593403i	0.984915	−	0.173039i	$-0.0553586\pi$
$173$	134867.	+	233596.i	0.342602	+	0.593403i	−0.642313	+	0.766442i	$0.722025\pi$
$174$	−919919.			−2.30344
$175$		0			0
$176$	470474.			1.14486
$177$	−399225.	−	691479.i	−0.957822	−	1.65900i
$178$	269149.	−	466180.i	0.636711	−	1.10282i
$179$	−188262.	+	326080.i	−0.439168	+	0.760661i	−0.997626	−	0.0688718i	$-0.978060\pi$
$179$	−188262.	+	326080.i	−0.439168	+	0.760661i	0.558457	+	0.829533i	$0.311393\pi$
$180$	−334869.	−	580009.i	−0.770359	−	1.33430i
$181$	434641.			0.986131			0.493065	−	0.869992i	$-0.335876\pi$
$181$	434641.			0.986131			0.493065	+	0.869992i	$0.335876\pi$
$182$		0			0
$183$	665464.			1.46891
$184$	41282.8	+	71503.9i	0.0898927	+	0.155699i
$185$	76016.2	−	131664.i	0.163296	−	0.282838i
$186$	259312.	−	449142.i	0.549593	−	0.951923i
$187$	234243.	+	405720.i	0.489848	+	0.848442i
$188$	−495316.			−1.02209
$189$		0			0
$190$	−3756.20			−0.00754857
$191$	−282970.	−	490118.i	−0.561250	−	0.972114i	−0.997388	−	0.0722342i	$-0.976987\pi$
$191$	−282970.	−	490118.i	−0.561250	−	0.972114i	0.436137	−	0.899880i	$-0.356346\pi$
$192$	−311970.	+	540348.i	−0.610744	+	1.05784i
$193$	−257231.	+	445537.i	−0.497084	+	0.860974i	−0.999994	−	0.00336433i	$-0.998929\pi$
$193$	−257231.	+	445537.i	−0.497084	+	0.860974i	0.502911	+	0.864338i	$0.332262\pi$
$194$	−425363.	−	736751.i	−0.811439	−	1.40545i
$195$	−440614.			−0.829796
$196$		0			0
$197$	−298541.			−0.548073			−0.274037	−	0.961719i	$-0.588359\pi$
$197$	−298541.			−0.548073			−0.274037	+	0.961719i	$0.588359\pi$
$198$	−514077.	−	890407.i	−0.931891	−	1.61408i
$199$	−295959.	+	512617.i	−0.529785	+	0.917614i	0.469612	+	0.882873i	$0.344394\pi$
$199$	−295959.	+	512617.i	−0.529785	+	0.917614i	−0.999396	+	0.0347408i	$0.988939\pi$
$200$	−27334.0	+	47344.0i	−0.0483202	+	0.0836931i
$201$	659707.	+	1.14265e6i	1.15176	+	1.99490i
$202$	140455.			0.242191
$203$		0			0
$204$	−755165.			−1.27048
$205$	348864.	+	604250.i	0.579791	+	1.00423i
$206$	−124157.	+	215046.i	−0.203846	+	0.353072i
$207$	560143.	−	970196.i	0.908600	−	1.57374i
$208$	139868.	+	242258.i	0.224161	+	0.388258i
$209$	−2745.12			−0.00434706
$210$		0			0
$211$	−140535.			−0.217309			−0.108655	−	0.994080i	$-0.534654\pi$
$211$	−140535.			−0.217309			−0.108655	+	0.994080i	$0.534654\pi$
$212$	574335.	+	994778.i	0.877659	+	1.52015i
$213$	−182709.	+	316461.i	−0.275937	+	0.477938i
$214$	32156.5	−	55696.8i	0.0479993	−	0.0831372i
$215$	−383289.	−	663877.i	−0.565497	−	0.979470i
$216$	−36082.0			−0.0526206
$217$		0			0
$218$	86502.5			0.123278
$219$	919806.	+	1.59315e6i	1.29594	+	2.24464i
$220$	458068.	−	793397.i	0.638077	−	1.10518i
$221$	−139277.	+	241234.i	−0.191822	+	0.332245i
$222$	188107.	+	325811.i	0.256167	+	0.443694i
$223$	−490.526			−0.000660541			−0.000330271	−	1.00000i	$-0.500105\pi$
$223$	−490.526			−0.000660541			−0.000330271		1.00000i	$0.500105\pi$
$224$		0			0
$225$	741761.			0.976804
$226$	254710.	+	441171.i	0.331723	+	0.574561i
$227$	296949.	−	514331.i	0.382488	−	0.662488i	−0.608930	−	0.793224i	$-0.708401\pi$
$227$	296949.	−	514331.i	0.382488	−	0.662488i	0.991417	+	0.130736i	$0.0417342\pi$
$228$	2212.47	−	3832.11i	0.00281865	−	0.00488204i
$229$	−17940.2	−	31073.3i	−0.0226067	−	0.0391560i	0.854501	−	0.519450i	$-0.173863\pi$
$229$	−17940.2	−	31073.3i	−0.0226067	−	0.0391560i	−0.877107	+	0.480294i	$0.840530\pi$
$230$	2.09687e6			2.61368
$231$		0			0
$232$	−114396.			−0.139537
$233$	−624109.	−	1.08099e6i	−0.753131	−	1.30446i	−0.946298	−	0.323295i	$-0.895209\pi$
$233$	−624109.	−	1.08099e6i	−0.753131	−	1.30446i	0.193167	−	0.981166i	$-0.438124\pi$
$234$	305661.	−	529421.i	0.364922	−	0.632064i
$235$	632662.	−	1.09580e6i	0.747312	−	1.29438i
$236$	493551.	+	854856.i	0.576836	+	0.999109i
$237$	1.06623e6			1.23304
$238$		0			0
$239$	−576943.			−0.653339			−0.326669	−	0.945139i	$-0.605926\pi$
$239$	−576943.			−0.653339			−0.326669	+	0.945139i	$0.605926\pi$
$240$	−968659.	−	1.67777e6i	−1.08553	−	1.88020i
$241$	−691205.	+	1.19720e6i	−0.766592	+	1.32778i	0.172809	+	0.984955i	$0.444716\pi$
$241$	−691205.	+	1.19720e6i	−0.766592	+	1.32778i	−0.939401	+	0.342820i	$0.888618\pi$
$242$	73894.9	−	127990.i	0.0811103	−	0.140487i
$243$	−641392.	−	1.11092e6i	−0.696800	−	1.20689i
$244$	−822694.			−0.884634
$245$		0			0
$246$	−1.72658e6			−1.81906
$247$	−816.101	−	1413.53i	−0.000851141	−	0.00147422i
$248$	32246.6	−	55852.8i	0.0332932	−	0.0576654i
$249$	−16249.2	+	28144.5i	−0.0166087	+	0.0287671i
$250$	−212792.	−	368567.i	−0.215331	−	0.372964i
$251$	−323217.			−0.323824			−0.161912	−	0.986805i	$-0.551766\pi$
$251$	−323217.			−0.323824			−0.161912	+	0.986805i	$0.551766\pi$
$252$		0			0
$253$	1.53244e6			1.50516
$254$	−761100.	−	1.31826e6i	−0.740214	−	1.28209i
$255$	964564.	−	1.67067e6i	0.928925	−	1.60895i
$256$	−606621.	+	1.05070e6i	−0.578519	+	1.00202i
$257$	923007.	+	1.59870e6i	0.871711	+	1.50985i	0.860226	+	0.509913i	$0.170322\pi$
$257$	923007.	+	1.59870e6i	0.871711	+	1.50985i	0.0114847	+	0.999934i	$0.496344\pi$
$258$	1.89695e6			1.77422
$259$		0			0
$260$	544719.			0.499734
$261$	776087.	+	1.34422e6i	0.705195	+	1.22143i
$262$	924146.	−	1.60067e6i	0.831740	−	1.44062i
$263$	229111.	−	396832.i	0.204248	−	0.353767i	−0.745645	−	0.666343i	$-0.767859\pi$
$263$	229111.	−	396832.i	0.204248	−	0.353767i	0.949893	+	0.312576i	$0.101192\pi$
$264$	−114019.	−	197486.i	−0.100685	−	0.174392i
$265$	−2.93437e6			−2.56685
$266$		0			0
$267$	−1.61995e6			−1.39066
$268$	−815577.	−	1.41262e6i	−0.693631	−	1.20140i
$269$	208479.	−	361096.i	0.175663	−	0.304258i	−0.764727	−	0.644354i	$-0.777126\pi$
$269$	208479.	−	361096.i	0.175663	−	0.304258i	0.940391	+	0.340096i	$0.110460\pi$
$270$	−458177.	+	793586.i	−0.382493	+	0.662498i
$271$	−450189.	−	779751.i	−0.372368	−	0.644960i	0.617562	−	0.786523i	$-0.288121\pi$
$271$	−450189.	−	779751.i	−0.372368	−	0.644960i	−0.989929	+	0.141563i	$0.954787\pi$
$272$	−1.22476e6			−1.00376
$273$		0			0
$274$	1.57007e6			1.26341
$275$	507329.	+	878719.i	0.404536	+	0.700678i
$276$	−1.23509e6	+	2.13925e6i	−0.975950	+	1.69039i
$277$	223821.	−	387669.i	0.175267	−	0.303572i	−0.764986	−	0.644046i	$-0.777254\pi$
$277$	223821.	−	387669.i	0.175267	−	0.303572i	0.940254	+	0.340475i	$0.110588\pi$
$278$	−207042.	−	358607.i	−0.160674	−	0.278295i
$279$	−875072.			−0.673029
$280$		0			0
$281$	−768521.			−0.580617			−0.290309	−	0.956933i	$-0.593758\pi$
$281$	−768521.			−0.580617			−0.290309	+	0.956933i	$0.593758\pi$
$282$	1.56557e6	+	2.71164e6i	1.17233	+	2.03053i
$283$	−1.06610e6	+	1.84654e6i	−0.791282	+	1.37054i	0.133892	+	0.990996i	$0.457253\pi$
$283$	−1.06610e6	+	1.84654e6i	−0.791282	+	1.37054i	−0.925173	+	0.379544i	$0.876081\pi$
$284$	225878.	−	391232.i	0.166180	−	0.287832i
$285$	5651.93	+	9789.43i	0.00412178	+	0.00713913i
$286$	836230.			0.604520
$287$		0			0
$288$	2.46107e6			1.74841
$289$	100138.	+	173443.i	0.0705266	+	0.122156i
$290$	−1.45262e6	+	2.51602e6i	−1.01428	+	1.75679i
$291$	−1.28008e6	+	2.21717e6i	−0.886147	+	1.53485i
$292$	−1.13713e6	−	1.96957e6i	−0.780465	−	1.35180i
$293$	2.42669e6			1.65138			0.825688	−	0.564128i	$-0.190787\pi$
$293$	2.42669e6			1.65138			0.825688	+	0.564128i	$0.190787\pi$
$294$		0			0
$295$	−2.52163e6			−1.68704
$296$	23391.9	+	40516.0i	0.0155180	+	0.0268781i
$297$	−334847.	+	579971.i	−0.220270	+	0.381518i
$298$	−393764.	+	682019.i	−0.256859	+	0.444893i
$299$	455582.	+	789091.i	0.294706	+	0.510445i
$300$	−1.63556e6			−1.04921
$301$		0			0
$302$	3.57855e6			2.25782
$303$	−211341.	−	366054.i	−0.132244	−	0.229054i
$304$	3588.28	−	6215.09i	0.00222691	−	0.00385712i
$305$	1.05082e6	−	1.82007e6i	0.646812	−	1.12031i
$306$	1.33827e6	+	2.31795e6i	0.817033	+	1.41514i
$307$	−2.44328e6			−1.47954			−0.739772	−	0.672857i	$-0.765067\pi$
$307$	−2.44328e6			−1.47954			−0.739772	+	0.672857i	$0.765067\pi$
$308$		0			0
$309$	747271.			0.445228
$310$	−818949.	−	1.41846e6i	−0.484008	−	0.838327i
$311$	−577324.	+	999955.i	−0.338469	+	0.586245i	−0.984145	−	0.177366i	$-0.943242\pi$
$311$	−577324.	+	999955.i	−0.338469	+	0.586245i	0.645676	+	0.763611i	$0.276576\pi$
$312$	67793.5	−	117422.i	0.0394277	−	0.0682908i
$313$	−828531.	−	1.43506e6i	−0.478022	−	0.827959i	0.521660	−	0.853153i	$-0.325313\pi$
$313$	−828531.	−	1.43506e6i	−0.478022	−	0.827959i	−0.999683	+	0.0251945i	$0.991980\pi$
$314$	−1.39919e6			−0.800852
$315$		0			0
$316$	−1.31815e6			−0.742584
$317$	−410680.	−	711319.i	−0.229539	−	0.397573i	0.728133	−	0.685436i	$-0.240388\pi$
$317$	−410680.	−	711319.i	−0.229539	−	0.397573i	−0.957671	+	0.287863i	$0.907055\pi$
$318$	3.63065e6	−	6.28847e6i	2.01334	−	3.48720i
$319$	−1.06161e6	+	1.83877e6i	−0.584103	+	1.01170i
$320$	985249.	+	1.70650e6i	0.537862	+	0.931605i
$321$	−193543.			−0.104837
$322$		0			0
$323$	7146.23			0.00381128
$324$	555811.	+	962693.i	0.294147	+	0.509478i
$325$	−301649.	+	522471.i	−0.158414	+	0.274381i
$326$	951915.	−	1.64877e6i	0.496083	−	0.859241i
$327$	−130160.	−	225443.i	−0.0673143	−	0.116592i
$328$	−214707.			−0.110195
$329$		0			0
$330$	−5.79134e6			−2.92748
$331$	47835.3	+	82853.2i	0.0239982	+	0.0415661i	0.877775	−	0.479073i	$-0.159027\pi$
$331$	47835.3	+	82853.2i	0.0239982	+	0.0415661i	−0.853777	+	0.520639i	$0.825694\pi$
$332$	20088.5	−	34794.3i	0.0100024	−	0.0173246i
$333$	317392.	−	549740.i	0.156850	−	0.271673i
$334$	−457309.	−	792082.i	−0.224307	−	0.388512i
$335$	4.16691e6			2.02863
$336$		0			0
$337$	2.37020e6			1.13687			0.568435	−	0.822728i	$-0.307549\pi$
$337$	2.37020e6			1.13687			0.568435	+	0.822728i	$0.307549\pi$
$338$	−1.20224e6	−	2.08234e6i	−0.572398	−	0.991423i
$339$	766522.	−	1.32765e6i	0.362264	−	0.627460i
$340$	−1.19246e6	+	2.06541e6i	−0.559433	+	0.968966i
$341$	−598507.	−	1.03665e6i	−0.278730	−	0.482774i
$342$	−15683.4			−0.00725060
$343$		0			0
$344$	235894.			0.107478
$345$	−3.15515e6	−	5.46488e6i	−1.42716	−	2.47191i
$346$	−1.05399e6	+	1.82557e6i	−0.473312	+	0.819800i
$347$	−245286.	+	424847.i	−0.109358	+	0.189413i	−0.915510	−	0.402295i	$-0.868213\pi$
$347$	−245286.	+	424847.i	−0.109358	+	0.189413i	0.806153	+	0.591708i	$0.201546\pi$
$348$	−1.71124e6	−	2.96396e6i	−0.757467	−	1.31197i
$349$	4.21208e6			1.85111			0.925557	−	0.378607i	$-0.123597\pi$
$349$	4.21208e6			1.85111			0.925557	+	0.378607i	$0.123597\pi$
$350$		0			0
$351$	−398188.			−0.172512
$352$	1.68326e6	+	2.91549e6i	0.724092	+	1.25416i
$353$	1.58689e6	−	2.74858e6i	0.677814	−	1.17401i	−0.297824	−	0.954621i	$-0.596261\pi$
$353$	1.58689e6	−	2.74858e6i	0.677814	−	1.17401i	0.975638	−	0.219387i	$-0.0704058\pi$
$354$	3.11997e6	−	5.40396e6i	1.32325	−	2.29194i
$355$	577023.	+	999433.i	0.243009	+	0.420904i
$356$	2.00269e6			0.837509
$357$		0			0
$358$	−2.94257e6			−1.21344
$359$	1.70049e6	+	2.94533e6i	0.696366	+	1.20614i	0.969718	+	0.244227i	$0.0785343\pi$
$359$	1.70049e6	+	2.94533e6i	0.696366	+	1.20614i	−0.273352	+	0.961914i	$0.588132\pi$
$360$	−263241.	+	455947.i	−0.107053	+	0.185421i
$361$	1.23803e6	−	2.14433e6i	0.499992	−	0.866011i
$362$	1.69838e6	+	2.94167e6i	0.681181	+	1.17984i
$363$	−444757.			−0.177156
$364$		0			0
$365$	5.80978e6			2.28259
$366$	2.60032e6	+	4.50389e6i	1.01467	+	1.75746i
$367$	984358.	−	1.70496e6i	0.381494	−	0.660767i	−0.609782	−	0.792569i	$-0.708743\pi$
$367$	984358.	−	1.70496e6i	0.381494	−	0.660767i	0.991276	+	0.131802i	$0.0420763\pi$
$368$	−2.00313e6	+	3.46952e6i	−0.771063	+	1.33552i
$369$	1.45662e6	+	2.52294e6i	0.556904	+	0.964586i
$370$	1.18814e6			0.451196
$371$		0			0
$372$	1.92950e6			0.722917
$373$	1.73944e6	+	3.01280e6i	0.647349	+	1.12124i	0.983754	+	0.179523i	$0.0574556\pi$
$373$	1.73944e6	+	3.01280e6i	0.647349	+	1.12124i	−0.336405	+	0.941717i	$0.609211\pi$
$374$	−1.83062e6	+	3.17073e6i	−0.676737	+	1.17214i
$375$	−640375.	+	1.10916e6i	−0.235156	+	0.407302i
$376$	194685.	+	337204.i	0.0710170	+	0.123005i
$377$	−1.26243e6			−0.457462
$378$		0			0
$379$	−421294.			−0.150656			−0.0753281	−	0.997159i	$-0.524000\pi$
$379$	−421294.			−0.150656			−0.0753281	+	0.997159i	$0.524000\pi$
$380$	−6987.33	−	12102.4i	−0.00248229	−	0.00429945i
$381$	−2.29044e6	+	3.96716e6i	−0.808364	+	1.40013i
$382$	2.21143e6	−	3.83031e6i	0.775380	−	1.34300i
$383$	1.33455e6	+	2.31151e6i	0.464877	+	0.805190i	0.999196	−	0.0400925i	$-0.0127653\pi$
$383$	1.33455e6	+	2.31151e6i	0.464877	+	0.805190i	−0.534319	+	0.845283i	$0.679432\pi$
$384$	1.09630e6			0.379402
$385$		0			0
$386$	−4.02055e6			−1.37346
$387$	−1.60036e6	−	2.77190e6i	−0.543175	−	0.940806i
$388$	1.58253e6	−	2.74102e6i	0.533670	−	0.924344i
$389$	−1.55089e6	+	2.68622e6i	−0.519645	+	0.900051i	0.480095	+	0.877217i	$0.340602\pi$
$389$	−1.55089e6	+	2.68622e6i	−0.519645	+	0.900051i	−0.999739	+	0.0228343i	$0.992731\pi$
$390$	−1.72171e6	−	2.98210e6i	−0.573191	−	0.992797i
$391$	−3.98933e6			−1.31965
$392$		0			0
$393$	−5.56223e6			−1.81663
$394$	−1.16656e6	−	2.02054e6i	−0.378588	−	0.655733i
$395$	1.68365e6	−	2.91617e6i	0.542950	−	0.940417i
$396$	1.91258e6	−	3.31269e6i	0.612889	−	1.06156i
$397$	306629.	+	531096.i	0.0976419	+	0.169121i	0.910708	−	0.413050i	$-0.135537\pi$
$397$	306629.	+	531096.i	0.0976419	+	0.169121i	−0.813066	+	0.582171i	$0.802203\pi$
$398$	−4.62589e6			−1.46382
$399$		0			0
$400$	−2.65262e6			−0.828942
$401$	−1.41111e6	−	2.44412e6i	−0.438229	−	0.759035i	0.559324	−	0.828949i	$-0.311061\pi$
$401$	−1.41111e6	−	2.44412e6i	−0.438229	−	0.759035i	−0.997553	+	0.0699139i	$0.977728\pi$
$402$	−5.15566e6	+	8.92986e6i	−1.59118	+	2.75600i
$403$	355862.	−	616371.i	0.109149	−	0.189051i
$404$	261275.	+	452542.i	0.0796425	+	0.137945i
$405$	−2.83973e6			−0.860278
$406$		0			0
$407$	868324.			0.259834
$408$	296819.	+	514105.i	0.0882756	+	0.152898i
$409$	1.14175e6	−	1.97757e6i	0.337492	−	0.584553i	−0.646469	−	0.762941i	$-0.723755\pi$
$409$	1.14175e6	−	1.97757e6i	0.337492	−	0.584553i	0.983960	+	0.178388i	$0.0570882\pi$
$410$	−2.72640e6	+	4.72226e6i	−0.800994	+	1.38736i
$411$	−2.36248e6	−	4.09193e6i	−0.689864	−	1.19488i
$412$	−923831.			−0.268132
$413$		0			0
$414$	8.75511e6			2.51050
$415$	51317.6	+	88884.8i	0.0146267	+	0.0253342i
$416$	−1.00084e6	+	1.73350e6i	−0.283550	+	0.491123i
$417$	−623068.	+	1.07919e6i	−0.175467	+	0.303918i
$418$	−10726.7	−	18579.1i	−0.00300278	−	0.00520097i
$419$	2.65270e6			0.738163			0.369082	−	0.929397i	$-0.379672\pi$
$419$	2.65270e6			0.738163			0.369082	+	0.929397i	$0.379672\pi$
$420$		0			0
$421$	2.93674e6			0.807532			0.403766	−	0.914862i	$-0.367701\pi$
$421$	2.93674e6			0.807532			0.403766	+	0.914862i	$0.367701\pi$
$422$	−549146.	−	951148.i	−0.150109	−	0.259996i
$423$	2.64157e6	−	4.57533e6i	0.717812	−	1.24329i
$424$	451487.	−	781998.i	0.121964	−	0.211247i
$425$	−1.32070e6	−	2.28752e6i	−0.354676	−	0.614317i
$426$	−2.85577e6			−0.762428
$427$		0			0
$428$	239272.			0.0631367
$429$	−1.25827e6	−	2.17939e6i	−0.330089	−	0.571730i
$430$	2.99543e6	−	5.18824e6i	0.781247	−	1.35316i
$431$	1.22283e6	−	2.11800e6i	0.317082	−	0.549202i	−0.662796	−	0.748800i	$-0.730630\pi$
$431$	1.22283e6	−	2.11800e6i	0.317082	−	0.549202i	0.979878	+	0.199598i	$0.0639636\pi$
$432$	−875389.	−	1.51622e6i	−0.225679	−	0.390888i
$433$	2.11718e6			0.542673			0.271336	−	0.962485i	$-0.412534\pi$
$433$	2.11718e6			0.542673			0.271336	+	0.962485i	$0.412534\pi$
$434$		0			0
$435$	8.74301e6			2.21533
$436$	160913.	+	278709.i	0.0405391	+	0.0702158i
$437$	11687.9	−	20244.0i	0.00292773	−	0.00507099i
$438$	−7.18835e6	+	1.24506e7i	−1.79038	+	3.10102i
$439$	2.32382e6	+	4.02498e6i	0.575495	+	0.996786i	0.995988	+	0.0894902i	$0.0285238\pi$
$439$	2.32382e6	+	4.02498e6i	0.575495	+	0.996786i	−0.420493	+	0.907296i	$0.638143\pi$
$440$	−720178.			−0.177340
$441$		0			0
$442$	−2.17691e6			−0.530012
$443$	−2.21462e6	−	3.83584e6i	−0.536155	−	0.928648i	−0.999106	−	0.0422645i	$-0.986543\pi$
$443$	−2.21462e6	−	3.83584e6i	−0.536155	−	0.928648i	0.462951	−	0.886384i	$-0.346791\pi$
$444$	−699839.	+	1.21216e6i	−0.168477	+	0.291811i
$445$	−2.55802e6	+	4.43062e6i	−0.612356	+	1.06063i
$446$	−1916.75	−	3319.91i	−0.000456276	−	0.000790294i
$447$	2.36998e6			0.561016
$448$		0			0
$449$	−6.70171e6			−1.56881			−0.784404	−	0.620250i	$-0.787031\pi$
$449$	−6.70171e6			−1.56881			−0.784404	+	0.620250i	$0.787031\pi$
$450$	2.89846e6	+	5.02027e6i	0.674739	+	1.16868i
$451$	−1.99252e6	+	3.45114e6i	−0.461276	+	0.798953i
$452$	−947629.	+	1.64134e6i	−0.218169	+	0.377879i
$453$	−5.38462e6	−	9.32644e6i	−1.23285	−	2.13536i
$454$	4.64136e6			1.05683
$455$		0			0
$456$	−3478.46			−0.000783385
$457$	2.94172e6	+	5.09521e6i	0.658887	+	1.14123i	0.980904	+	0.194491i	$0.0623057\pi$
$457$	2.94172e6	+	5.09521e6i	0.658887	+	1.14123i	−0.322018	+	0.946734i	$0.604361\pi$
$458$	140204.	−	242840.i	0.0312317	−	0.0540949i
$459$	871688.	−	1.50981e6i	0.193121	−	0.334495i
$460$	3.90062e6	+	6.75607e6i	0.859487	+	1.48867i
$461$	−1.54764e6			−0.339171			−0.169585	−	0.985515i	$-0.554243\pi$
$461$	−1.54764e6			−0.339171			−0.169585	+	0.985515i	$0.554243\pi$
$462$		0			0
$463$	−3.93764e6			−0.853656			−0.426828	−	0.904333i	$-0.640369\pi$
$463$	−3.93764e6			−0.853656			−0.426828	+	0.904333i	$0.640369\pi$
$464$	−2.77537e6	−	4.80708e6i	−0.598447	−	1.03654i
$465$	−2.46453e6	+	4.26870e6i	−0.528570	+	0.915510i
$466$	4.87746e6	−	8.44800e6i	1.04047	−	1.80214i
$467$	−3.40793e6	−	5.90271e6i	−0.723100	−	1.25245i	−0.959751	−	0.280852i	$-0.909383\pi$
$467$	−3.40793e6	−	5.90271e6i	−0.723100	−	1.25245i	0.236651	−	0.971595i	$-0.423950\pi$
$468$	2.27438e6			0.480007
$469$		0			0
$470$	9.88860e6			2.06486
$471$	2.10535e6	+	3.64657e6i	0.437293	+	0.757413i
$472$	387982.	−	672005.i	0.0801598	−	0.138841i
$473$	2.18913e6	−	3.79169e6i	0.449904	−	0.779256i
$474$	4.16632e6	+	7.21627e6i	0.851739	+	1.47525i
$475$	15477.5			0.00314750
$476$		0			0
$477$	−1.22519e7			−2.46552
$478$	−2.25443e6	−	3.90478e6i	−0.451301	−	0.781677i
$479$	−2.60203e6	+	4.50685e6i	−0.518171	+	0.897499i	0.481606	+	0.876388i	$0.340054\pi$
$479$	−2.60203e6	+	4.50685e6i	−0.518171	+	0.897499i	−0.999777	+	0.0211112i	$0.993280\pi$
$480$	6.93132e6	−	1.20054e7i	1.37313	−	2.37834i
$481$	258145.	+	447121.i	0.0508747	+	0.0881175i
$482$	−1.08036e7			−2.11813
$483$		0			0
$484$	549840.			0.106690
$485$	4.04270e6	+	7.00216e6i	0.780400	+	1.35169i
$486$	5.01253e6	−	8.68195e6i	0.962644	−	1.66735i
$487$	77499.2	−	134233.i	0.0148073	−	0.0256469i	−0.858527	−	0.512769i	$-0.828620\pi$
$487$	77499.2	−	134233.i	0.0148073	−	0.0256469i	0.873334	+	0.487122i	$0.161953\pi$
$488$	323361.	+	560078.i	0.0614665	+	0.106463i
$489$	−5.72936e6			−1.08351
$490$		0			0
$491$	−1.61951e6			−0.303165			−0.151583	−	0.988445i	$-0.548437\pi$
$491$	−1.61951e6			−0.303165			−0.151583	+	0.988445i	$0.548437\pi$
$492$	−3.21179e6	−	5.56299e6i	−0.598184	−	1.03609i
$493$	2.76364e6	−	4.78676e6i	0.512111	−	0.887002i
$494$	6377.89	−	11046.8i	0.00117587	−	0.00203667i
$495$	4.88584e6	+	8.46253e6i	0.896244	+	1.55234i
$496$	3.12935e6			0.571150
$497$		0			0
$498$	−253978.			−0.0458905
$499$	−2.05337e6	−	3.55654e6i	−0.369161	−	0.639405i	0.620274	−	0.784385i	$-0.287022\pi$
$499$	−2.05337e6	−	3.55654e6i	−0.369161	−	0.639405i	−0.989435	+	0.144980i	$0.953688\pi$
$500$	791678.	−	1.37123e6i	0.141620	−	0.245292i
$501$	−1.37622e6	+	2.38368e6i	−0.244959	+	0.424281i
$502$	−1.26298e6	−	2.18755e6i	−0.223685	−	0.387435i
$503$	3.40748e6			0.600501			0.300250	−	0.953860i	$-0.402930\pi$
$503$	3.40748e6			0.600501			0.300250	+	0.953860i	$0.402930\pi$
$504$		0			0
$505$	−1.33490e6			−0.232927
$506$	5.98808e6	+	1.03717e7i	1.03971	+	1.80083i
$507$	−3.61800e6	+	6.26655e6i	−0.625098	+	1.08270i
$508$	2.83161e6	−	4.90450e6i	0.486827	−	0.843209i
$509$	5.35453e6	+	9.27432e6i	0.916067	+	1.58667i	0.805332	+	0.592825i	$0.201987\pi$
$509$	5.35453e6	+	9.27432e6i	0.916067	+	1.58667i	0.110735	+	0.993850i	$0.464679\pi$
$510$	1.50763e7			2.56666
$511$		0			0
$512$	−7.98992e6			−1.34700
$513$	5107.72	+	8846.83i	0.000856907	+	0.00148421i
$514$	−7.21337e6	+	1.24939e7i	−1.20429	+	2.08589i
$515$	1.18000e6	−	2.04382e6i	0.196049	−	0.339566i
$516$	3.52873e6	+	6.11194e6i	0.583437	+	1.01054i
$517$	7.22682e6			1.18911
$518$		0			0
$519$	6.34374e6			1.03378
$520$	−214103.	−	370836.i	−0.0347227	−	0.0601415i
$521$	3.96000e6	−	6.85893e6i	0.639148	−	1.10704i	−0.346472	−	0.938060i	$-0.612621\pi$
$521$	3.96000e6	−	6.85893e6i	0.639148	−	1.10704i	0.985620	−	0.168976i	$-0.0540461\pi$
$522$	−6.06517e6	+	1.05052e7i	−0.974242	+	1.68744i
$523$	−4.16373e6	−	7.21179e6i	−0.665623	−	1.15289i	−0.979116	−	0.203303i	$-0.934832\pi$
$523$	−4.16373e6	−	7.21179e6i	−0.665623	−	1.15289i	0.313493	−	0.949591i	$-0.398501\pi$
$524$	6.87643e6			1.09404
$525$		0			0
$526$	3.58104e6			0.564345
$527$	1.55806e6	+	2.69864e6i	0.244376	+	0.423271i
$528$	5.53244e6	−	9.58246e6i	0.863638	−	1.49586i
$529$	−3.30649e6	+	5.72701e6i	−0.513722	+	0.889793i
$530$	−1.14662e7	−	1.98600e7i	−1.77308	−	3.07106i
$531$	−1.05286e7			−1.62045
$532$		0			0
$533$	−2.36943e6			−0.361265
$534$	−6.33000e6	−	1.09639e7i	−0.960618	−	1.66384i
$535$	−305619.	+	529348.i	−0.0461632	+	0.0799571i
$536$	−641128.	+	1.11047e6i	−0.0963902	+	0.166953i
$537$	4.42766e6	+	7.66893e6i	0.662581	+	1.14762i
$538$	3.25856e6			0.485366
$539$		0			0
$540$	−3.40922e6			−0.503119
$541$	−311631.	−	539760.i	−0.0457770	−	0.0792880i	0.842229	−	0.539120i	$-0.181243\pi$
$541$	−311631.	−	539760.i	−0.0457770	−	0.0792880i	−0.888006	+	0.459832i	$0.847910\pi$
$542$	3.51826e6	−	6.09381e6i	0.514434	−	0.891027i
$543$	5.11107e6	−	8.85264e6i	0.743896	−	1.28847i
$544$	−4.38193e6	−	7.58973e6i	−0.634846	−	1.09959i
$545$	−822129.			−0.118563
$546$		0			0
$547$	1.05691e7			1.51032			0.755159	−	0.655541i	$-0.227559\pi$
$547$	1.05691e7			1.51032			0.755159	+	0.655541i	$0.227559\pi$
$548$	2.92067e6	+	5.05874e6i	0.415461	+	0.719600i
$549$	4.38751e6	−	7.59939e6i	0.621280	−	1.07609i
$550$	−3.96481e6	+	6.86725e6i	−0.558876	+	0.968002i
$551$	16193.7	+	28048.4i	0.00227231	+	0.00393576i
$552$	1.94182e6			0.271245
$553$		0			0
$554$	3.49835e6			0.484272
$555$	−1.78779e6	−	3.09655e6i	−0.246368	−	0.426722i
$556$	770282.	−	1.33417e6i	0.105673	−	0.183030i
$557$	6.76989e6	−	1.17258e7i	0.924579	−	1.60142i	0.132341	−	0.991204i	$-0.457751\pi$
$557$	6.76989e6	−	1.17258e7i	0.924579	−	1.60142i	0.792237	−	0.610213i	$-0.208916\pi$
$558$	−3.41938e6	−	5.92254e6i	−0.464902	−	0.805234i
$559$	2.60324e6			0.352359
$560$		0			0
$561$	1.10181e7			1.47809
$562$	−3.00302e6	−	5.20139e6i	−0.401068	−	0.694670i
$563$	−6.98785e6	+	1.21033e7i	−0.929122	+	1.60929i	−0.144327	+	0.989530i	$0.546102\pi$
$563$	−6.98785e6	+	1.21033e7i	−0.929122	+	1.60929i	−0.784795	+	0.619756i	$0.787232\pi$
$564$	−5.82456e6	+	1.00884e7i	−0.771020	+	1.33545i
$565$	−2.42079e6	−	4.19294e6i	−0.319034	−	0.552583i
$566$	−1.66633e7			−2.18635
$567$		0			0
$568$	−355127.			−0.0461862
$569$	2.80997e6	+	4.86701e6i	0.363848	+	0.630204i	0.988591	−	0.150627i	$-0.0481293\pi$
$569$	2.80997e6	+	4.86701e6i	0.363848	+	0.630204i	−0.624742	+	0.780831i	$0.714796\pi$
$570$	−44170.3	+	76505.1i	−0.00569433	+	0.00986287i
$571$	−4.35395e6	+	7.54126e6i	−0.558847	+	0.967951i	0.438746	+	0.898611i	$0.355423\pi$
$571$	−4.35395e6	+	7.54126e6i	−0.558847	+	0.967951i	−0.997593	+	0.0693403i	$0.977911\pi$
$572$	1.55556e6	+	2.69432e6i	0.198792	+	0.344317i
$573$	−1.33101e7			−1.69354
$574$		0			0
$575$	−8.64019e6			−1.08982
$576$	4.11373e6	+	7.12520e6i	0.516630	+	0.894830i
$577$	−3.31996e6	+	5.75034e6i	−0.415139	+	0.719042i	−0.995443	−	0.0953580i	$-0.969600\pi$
$577$	−3.31996e6	+	5.75034e6i	−0.415139	+	0.719042i	0.580304	+	0.814400i	$0.302934\pi$
$578$	−782583.	+	1.35547e6i	−0.0974340	+	0.168761i
$579$	6.04970e6	+	1.04784e7i	0.749959	+	1.29897i
$580$	−1.08087e7			−1.33415
$581$		0			0
$582$	−2.00079e7			−2.44846
$583$	−8.37974e6	−	1.45141e7i	−1.02108	−	1.76856i
$584$	−893902.	+	1.54828e6i	−0.108457	+	0.187853i
$585$	−2.90504e6	+	5.03167e6i	−0.350964	+	0.607887i
$586$	9.48239e6	+	1.64240e7i	1.14071	+	1.97576i
$587$	1.36652e7			1.63689			0.818446	−	0.574583i	$-0.194836\pi$
$587$	1.36652e7			1.63689			0.818446	+	0.574583i	$0.194836\pi$
$588$		0			0
$589$	−18259.2			−0.00216866
$590$	−9.85337e6	−	1.70665e7i	−1.16535	−	2.01844i
$591$	−3.51063e6	+	6.08059e6i	−0.413444	+	0.716106i
$592$	−1.13503e6	+	1.96593e6i	−0.133108	+	0.230549i
$593$	−3.51295e6	−	6.08460e6i	−0.410237	−	0.710551i	0.584678	−	0.811265i	$-0.301221\pi$
$593$	−3.51295e6	−	6.08460e6i	−0.410237	−	0.710551i	−0.994915	+	0.100714i	$0.967887\pi$
$594$	−5.23370e6			−0.608615
$595$		0			0
$596$	−2.92994e6			−0.337864
$597$	6.96054e6	+	1.20560e7i	0.799295	+	1.38442i
$598$	−3.56041e6	+	6.16681e6i	−0.407143	+	0.705192i
$599$	1.79331e6	−	3.10611e6i	0.204216	−	0.353712i	−0.745667	−	0.666319i	$-0.767869\pi$
$599$	1.79331e6	−	3.10611e6i	0.204216	−	0.353712i	0.949883	+	0.312607i	$0.101202\pi$
$600$	642858.	+	1.11346e6i	0.0729016	+	0.126269i
$601$	−1.58600e7			−1.79108			−0.895542	−	0.444977i	$-0.853212\pi$
$601$	−1.58600e7			−1.79108			−0.895542	+	0.444977i	$0.853212\pi$
$602$		0			0
$603$	1.73982e7			1.94855
$604$	6.65686e6	+	1.15300e7i	0.742467	+	1.28599i
$605$	−702305.	+	1.21643e6i	−0.0780077	+	0.135113i
$606$	1.65165e6	−	2.86073e6i	0.182699	−	0.316443i
$607$	3.22085e6	+	5.57867e6i	0.354812	+	0.614553i	0.987086	−	0.160192i	$-0.0512114\pi$
$607$	3.22085e6	+	5.57867e6i	0.354812	+	0.614553i	−0.632274	+	0.774745i	$0.717878\pi$
$608$	51352.5			0.00563381
$609$		0			0
$610$	1.64244e7			1.78717
$611$	2.14847e6	+	3.72126e6i	0.232823	+	0.403262i
$612$	−4.97892e6	+	8.62375e6i	−0.537349	+	0.930716i
$613$	2.29433e6	−	3.97389e6i	0.246606	−	0.427134i	−0.715976	−	0.698125i	$-0.754018\pi$
$613$	2.29433e6	−	3.97389e6i	0.246606	−	0.427134i	0.962582	+	0.270991i	$0.0873513\pi$
$614$	−9.54722e6	−	1.65363e7i	−1.02201	−	1.77018i
$615$	1.64096e7			1.74948
$616$		0			0
$617$	1.47104e6			0.155565			0.0777825	−	0.996970i	$-0.475216\pi$
$617$	1.47104e6			0.155565			0.0777825	+	0.996970i	$0.475216\pi$
$618$	2.91999e6	+	5.05757e6i	0.307546	+	0.532685i
$619$	−1.56784e6	+	2.71558e6i	−0.164466	+	0.284863i	−0.936465	−	0.350760i	$-0.885923\pi$
$619$	−1.56784e6	+	2.71558e6i	−0.164466	+	0.284863i	0.772000	+	0.635623i	$0.219257\pi$
$620$	3.04684e6	−	5.27727e6i	0.318324	−	0.551354i
$621$	−2.85134e6	−	4.93867e6i	−0.296702	−	0.513903i
$622$	−9.02366e6			−0.935205
$623$		0			0
$624$	6.57898e6			0.676390
$625$	5.75963e6	+	9.97597e6i	0.589786	+	1.02154i
$626$	6.47503e6	−	1.12151e7i	0.660399	−	1.14384i
$627$	−32280.7	+	55911.8i	−0.00327924	+	0.00567982i
$628$	−2.60279e6	−	4.50816e6i	−0.263354	−	0.456142i
$629$	−2.26046e6			−0.227809
$630$		0			0
$631$	484547.			0.0484465			0.0242233	−	0.999707i	$-0.492289\pi$
$631$	484547.			0.0484465			0.0242233	+	0.999707i	$0.492289\pi$
$632$	518099.	+	897374.i	0.0515965	+	0.0893678i
$633$	−1.65259e6	+	2.86237e6i	−0.163929	+	0.283934i
$634$	3.20950e6	−	5.55901e6i	0.317113	−	0.549256i
$635$	7.23358e6	+	1.25289e7i	0.711900	+	1.23305i
$636$	2.70151e7			2.64828
$637$		0			0
$638$	−1.65932e7			−1.61390
$639$	2.40926e6	+	4.17296e6i	0.233416	+	0.404289i
$640$	1.73114e6	−	2.99842e6i	0.167064	−	0.289363i
$641$	−1.52042e6	+	2.63345e6i	−0.146157	+	0.253151i	−0.929804	−	0.368055i	$-0.880024\pi$
$641$	−1.52042e6	+	2.63345e6i	−0.146157	+	0.253151i	0.783647	+	0.621206i	$0.213357\pi$
$642$	−756276.	−	1.30991e6i	−0.0724174	−	0.125431i
$643$	−5.25888e6			−0.501609			−0.250805	−	0.968038i	$-0.580695\pi$
$643$	−5.25888e6			−0.501609			−0.250805	+	0.968038i	$0.580695\pi$
$644$		0			0
$645$	−1.80288e7			−1.70635
$646$	27924.1	+	48366.0i	0.00263268	+	0.00455994i
$647$	1.05985e7	−	1.83571e7i	0.995368	−	1.72403i	0.414425	−	0.910083i	$-0.363983\pi$
$647$	1.05985e7	−	1.83571e7i	0.995368	−	1.72403i	0.580942	−	0.813945i	$-0.302684\pi$
$648$	436925.	−	756776.i	0.0408761	−	0.0707994i
$649$	−7.20107e6	−	1.24726e7i	−0.671097	−	1.16237i
$650$	−4.71481e6			−0.437705
$651$		0			0
$652$	7.08305e6			0.652531
$653$	−6.50529e6	−	1.12675e7i	−0.597013	−	1.03406i	−0.993259	−	0.115912i	$-0.963021\pi$
$653$	−6.50529e6	−	1.12675e7i	−0.597013	−	1.03406i	0.396247	−	0.918144i	$-0.370313\pi$
$654$	1.01721e6	−	1.76186e6i	0.0929962	−	0.161074i
$655$	−8.78319e6	+	1.52129e7i	−0.799924	+	1.38551i
$656$	−5.20903e6	−	9.02230e6i	−0.472604	−	0.818574i
$657$	2.42577e7			2.19248
$658$		0			0
$659$	−1.59874e7			−1.43405			−0.717024	−	0.697049i	$-0.754496\pi$
$659$	−1.59874e7			−1.43405			−0.717024	+	0.697049i	$0.754496\pi$
$660$	−1.07731e7	−	1.86596e7i	−0.962678	−	1.66741i
$661$	2.01571e6	−	3.49131e6i	0.179442	−	0.310803i	−0.762248	−	0.647286i	$-0.775904\pi$
$661$	2.01571e6	−	3.49131e6i	0.179442	−	0.310803i	0.941690	+	0.336483i	$0.109237\pi$
$662$	−373837.	+	647504.i	−0.0331541	+	0.0574245i
$663$	3.27559e6	+	5.67348e6i	0.289404	+	0.501263i
$664$	−31583.3			−0.00277995
$665$		0			0
$666$	4.96089e6			0.433385
$667$	−9.04002e6	−	1.56578e7i	−0.786783	−	1.36275i
$668$	1.70138e6	−	2.94688e6i	0.147523	−	0.255518i
$669$	−5768.24	+	9990.88i	−0.000498285	+	0.000863055i
$670$	1.62824e7	+	2.82019e7i	1.40130	+	2.42712i
$671$	1.20034e7			1.02919
$672$		0			0
$673$	2.98234e6			0.253816			0.126908	−	0.991914i	$-0.459495\pi$
$673$	2.98234e6			0.253816			0.126908	+	0.991914i	$0.459495\pi$
$674$	9.26165e6	+	1.60416e7i	0.785305	+	1.36019i
$675$	1.88793e6	−	3.26998e6i	0.159487	−	0.276240i
$676$	4.47283e6	−	7.74717e6i	0.376457	−	0.652043i
$677$	973478.	+	1.68611e6i	0.0816309	+	0.141389i	0.903951	−	0.427637i	$-0.140654\pi$
$677$	973478.	+	1.68611e6i	0.0816309	+	0.141389i	−0.822320	+	0.569026i	$0.807320\pi$
$678$	1.19808e7			1.00095
$679$		0			0
$680$	1.87480e6			0.155483
$681$	−6.98382e6	−	1.20963e7i	−0.577066	−	0.999507i
$682$	4.67738e6	−	8.10146e6i	0.385072	−	0.666964i
$683$	−5.99700e6	+	1.03871e7i	−0.491906	+	0.852006i	−0.999957	−	0.00932092i	$-0.997033\pi$
$683$	−5.99700e6	+	1.03871e7i	−0.491906	+	0.852006i	0.508050	+	0.861327i	$0.330366\pi$
$684$	−29174.3	−	50531.4i	−0.00238430	−	0.00412973i
$685$	−1.49221e7			−1.21508
$686$		0			0
$687$	−843854.			−0.0682143
$688$	5.72305e6	+	9.91261e6i	0.460953	+	0.798393i
$689$	4.98245e6	−	8.62986e6i	0.399848	−	0.692557i
$690$	2.46577e7	−	4.27084e7i	1.97165	−	3.41500i
$691$	−4.33152e6	−	7.50242e6i	−0.345100	−	0.597731i	0.640272	−	0.768149i	$-0.278822\pi$
$691$	−4.33152e6	−	7.50242e6i	−0.345100	−	0.597731i	−0.985372	+	0.170417i	$0.945488\pi$
$692$	−7.84260e6			−0.622579
$693$		0			0
$694$	−3.83385e6			−0.302160
$695$	1.96775e6	+	3.40824e6i	0.154528	+	0.267650i
$696$	−1.34521e6	+	2.32998e6i	−0.105261	+	0.182318i
$697$	5.18701e6	−	8.98416e6i	0.404422	−	0.700480i
$698$	1.64589e7	+	2.85076e7i	1.27868	+	2.21474i
$699$	−2.93563e7			−2.27252
$700$		0			0
$701$	−8.13382e6			−0.625172			−0.312586	−	0.949889i	$-0.601195\pi$
$701$	−8.13382e6			−0.625172			−0.312586	+	0.949889i	$0.601195\pi$
$702$	−1.55593e6	−	2.69496e6i	−0.119165	−	0.206400i
$703$	6622.67	−	11470.8i	0.000505411	−	0.000875397i
$704$	−5.62719e6	+	9.74658e6i	−0.427918	+	0.741175i
$705$	−1.48793e7	−	2.57717e7i	−1.12748	−	1.95286i
$706$	2.48033e7			1.87283
$707$		0			0
$708$	2.32152e7			1.74056
$709$	−1.10663e7	−	1.91674e7i	−0.826773	−	1.43201i	−0.900556	−	0.434739i	$-0.856841\pi$
$709$	−1.10663e7	−	1.91674e7i	−0.826773	−	1.43201i	0.0737829	−	0.997274i	$-0.476493\pi$
$710$	−4.50948e6	+	7.81064e6i	−0.335722	+	0.581488i
$711$	7.02980e6	−	1.21760e7i	0.521517	−	0.903295i
$712$	−787162.	−	1.36341e6i	−0.0581921	−	0.100792i
$713$	1.01930e7			0.750896
$714$		0			0
$715$	−7.94762e6			−0.581396
$716$	−5.47379e6	−	9.48089e6i	−0.399030	−	0.691141i
$717$	−6.78444e6	+	1.17510e7i	−0.492852	+	0.853644i
$718$	−1.32894e7	+	2.30180e7i	−0.962046	+	1.66631i
$719$	−3.61598e6	−	6.26306e6i	−0.260858	−	0.451819i	0.705612	−	0.708598i	$-0.250672\pi$
$719$	−3.61598e6	−	6.26306e6i	−0.260858	−	0.451819i	−0.966470	+	0.256779i	$0.917339\pi$
$720$	−2.55461e7			−1.83651
$721$		0			0
$722$	1.93506e7			1.38150
$723$	1.62562e7	+	2.81565e7i	1.15657	+	2.00324i
$724$	−6.31868e6	+	1.09443e7i	−0.448002	+	0.775962i
$725$	5.98556e6	−	1.03673e7i	0.422921	−	0.732521i
$726$	−1.73790e6	−	3.01014e6i	−0.122373	−	0.211955i
$727$	1.70200e7			1.19433			0.597163	−	0.802120i	$-0.296295\pi$
$727$	1.70200e7			1.19433			0.597163	+	0.802120i	$0.296295\pi$
$728$		0			0
$729$	−2.08788e7			−1.45508
$730$	2.27019e7	+	3.93209e7i	1.57672	+	2.73097i
$731$	−5.69886e6	+	9.87071e6i	−0.394452	+	0.683211i
$732$	−9.67430e6	+	1.67564e7i	−0.667332	+	1.15585i
$733$	500056.	+	866123.i	0.0343763	+	0.0595415i	0.882702	−	0.469934i	$-0.155722\pi$
$733$	500056.	+	866123.i	0.0343763	+	0.0595415i	−0.848325	+	0.529475i	$0.822389\pi$
$734$	1.53857e7			1.05409
$735$		0			0
$736$	−2.86671e7			−1.95070
$737$	1.18995e7	+	2.06106e7i	0.806978	+	1.39773i
$738$	−1.13836e7	+	1.97170e7i	−0.769376	+	1.33260i
$739$	−1.62989e6	+	2.82306e6i	−0.109786	+	0.190155i	−0.915684	−	0.401900i	$-0.868350\pi$
$739$	−1.62989e6	+	2.82306e6i	−0.109786	+	0.190155i	0.805897	+	0.592055i	$0.201683\pi$
$740$	2.21020e6	+	3.82818e6i	0.148372	+	0.256988i
$741$	−38387.1			−0.00256826
$742$		0			0
$743$	1.36125e7			0.904617			0.452309	−	0.891861i	$-0.350601\pi$
$743$	1.36125e7			0.904617			0.452309	+	0.891861i	$0.350601\pi$
$744$	−758394.	−	1.31358e6i	−0.0502300	−	0.0870008i
$745$	3.74238e6	−	6.48199e6i	0.247034	−	0.427875i
$746$	−1.35939e7	+	2.35453e7i	−0.894327	+	1.54902i
$747$	214268.	+	371123.i	0.0140493	+	0.0243341i
$748$	−1.36214e7			−0.890158
$749$		0			0
$750$	−1.00092e7			−0.649747
$751$	−3.28272e6	−	5.68584e6i	−0.212390	−	0.367870i	0.740072	−	0.672528i	$-0.234791\pi$
$751$	−3.28272e6	−	5.68584e6i	−0.212390	−	0.367870i	−0.952462	+	0.304657i	$0.901458\pi$
$752$	−9.44653e6	+	1.63619e7i	−0.609155	+	1.05509i
$753$	−3.80080e6	+	6.58318e6i	−0.244280	+	0.423105i
$754$	−4.93300e6	−	8.54421e6i	−0.315997	−	0.547323i
$755$	−3.40110e7			−2.17146
$756$		0			0
$757$	2.62531e7			1.66510			0.832551	−	0.553948i	$-0.186879\pi$
$757$	2.62531e7			1.66510			0.832551	+	0.553948i	$0.186879\pi$
$758$	−1.64622e6	−	2.85134e6i	−0.104068	−	0.180250i
$759$	1.80204e7	−	3.12123e7i	1.13543	−	1.96662i
$760$	−5492.76	+	9513.74i	−0.000344950	+	0.000597472i
$761$	−2.62555e6	−	4.54759e6i	−0.164346	−	0.284656i	0.772077	−	0.635529i	$-0.219218\pi$
$761$	−2.62555e6	−	4.54759e6i	−0.164346	−	0.284656i	−0.936423	+	0.350874i	$0.885885\pi$
$762$	−3.58000e7			−2.23355
$763$		0			0
$764$	1.64549e7			1.01991
$765$	−1.27191e7	−	2.20300e7i	−0.785780	−	1.36101i
$766$	−1.04296e7	+	1.80646e7i	−0.642238	+	1.11239i
$767$	4.28163e6	−	7.41601e6i	0.262797	−	0.455179i
$768$	1.42669e7	+	2.47109e7i	0.872821	+	1.51177i
$769$	1.77307e7			1.08121			0.540605	−	0.841277i	$-0.318195\pi$
$769$	1.77307e7			1.08121			0.540605	+	0.841277i	$0.318195\pi$
$770$		0			0
$771$	4.34156e7			2.63033
$772$	−7.47907e6	−	1.29541e7i	−0.451653	−	0.782285i
$773$	1.91296e6	−	3.31334e6i	0.115148	−	0.199442i	−0.802691	−	0.596395i	$-0.796599\pi$
$773$	1.91296e6	−	3.31334e6i	0.115148	−	0.199442i	0.917839	+	0.396953i	$0.129932\pi$
$774$	1.25069e7	−	2.16626e7i	0.750408	−	1.29974i
$775$	3.37449e6	+	5.84479e6i	0.201815	+	0.349554i
$776$	−2.48807e6			−0.148323
$777$		0			0
$778$	−2.42406e7			−1.43580
$779$	30393.6	+	52643.3i	0.00179448	+	0.00310813i
$780$	6.40550e6	−	1.10947e7i	0.376979	−	0.652946i
$781$	−3.29563e6	+	5.70820e6i	−0.193335	+	0.334867i
$782$	−1.55884e7	−	2.70000e7i	−0.911561	−	1.57887i
$783$	7.90117e6			0.460561
$784$		0			0
$785$	1.32980e7			0.770218
$786$	−2.17346e7	−	3.76454e7i	−1.25486	−	2.17348i
$787$	1.47132e7	−	2.54839e7i	0.846777	−	1.46666i	−0.0372915	−	0.999304i	$-0.511873\pi$
$787$	1.47132e7	−	2.54839e7i	0.846777	−	1.46666i	0.884069	−	0.467357i	$-0.154794\pi$
$788$	4.34010e6	−	7.51727e6i	0.248991	−	0.431265i
$789$	−5.38837e6	−	9.33293e6i	−0.308152	−	0.533735i
$790$	2.63157e7			1.50020
$791$		0			0
$792$	−3.00697e6			−0.170340
$793$	3.56850e6	+	6.18082e6i	0.201513	+	0.349031i
$794$	−2.39632e6	+	4.15056e6i	−0.134895	+	0.233644i
$795$	−3.45061e7	+	5.97663e7i	−1.93632	+	3.35381i
$796$	−8.60512e6	−	1.49045e7i	−0.481365	−	0.833749i
$797$	−1.35805e7			−0.757305			−0.378653	−	0.925539i	$-0.623613\pi$
$797$	−1.35805e7			−0.757305			−0.378653	+	0.925539i	$0.623613\pi$
$798$		0			0
$799$	−1.88132e7			−1.04255
$800$	−9.49050e6	−	1.64380e7i	−0.524281	−	0.908082i
$801$	−1.06806e7	+	1.84993e7i	−0.588184	+	1.01876i
$802$	1.10280e7	−	1.91010e7i	0.605424	−	1.04862i
$803$	1.65911e7	+	2.87367e7i	0.908002	+	1.57271i
$804$	−3.83624e7			−2.09299
$805$		0			0
$806$	5.56218e6			0.301583
$807$	−4.90313e6	−	8.49247e6i	−0.265027	−	0.459039i
$808$	205389.	−	355745.i	0.0110675	−	0.0191695i
$809$	5.78569e6	−	1.00211e7i	0.310802	−	0.538325i	−0.667734	−	0.744400i	$-0.732736\pi$
$809$	5.78569e6	−	1.00211e7i	0.310802	−	0.538325i	0.978536	+	0.206075i	$0.0660691\pi$
$810$	−1.10963e7	−	1.92194e7i	−0.594247	−	1.02927i
$811$	3.52530e6			0.188210			0.0941052	−	0.995562i	$-0.470001\pi$
$811$	3.52530e6			0.188210			0.0941052	+	0.995562i	$0.470001\pi$
$812$		0			0
$813$	−2.11756e7			−1.12360
$814$	3.39301e6	+	5.87686e6i	0.179483	+	0.310874i
$815$	−9.04711e6	+	1.56700e7i	−0.477107	+	0.826373i
$816$	−1.44023e7	+	2.49455e7i	−0.757193	+	1.31150i
$817$	−33392.8	−	57838.1i	−0.00175024	−	0.00303151i
$818$	1.78457e7			0.932505
$819$		0			0
$820$	−2.02867e7			−1.05360
$821$	−8.94756e6	−	1.54976e7i	−0.463283	−	0.802430i	0.535839	−	0.844320i	$-0.319995\pi$
$821$	−8.94756e6	−	1.54976e7i	−0.463283	−	0.802430i	−0.999122	+	0.0418900i	$0.986662\pi$
$822$	1.84629e7	−	3.19787e7i	0.953062	−	1.65075i
$823$	1.80710e7	−	3.12999e7i	0.930001	−	1.61081i	0.146686	−	0.989183i	$-0.453139\pi$
$823$	1.80710e7	−	3.12999e7i	0.930001	−	1.61081i	0.783315	−	0.621626i	$-0.213527\pi$
$824$	363113.	+	628931.i	0.0186305	+	0.0322689i
$825$	2.38633e7			1.22066
$826$		0			0
$827$	−1.00605e7			−0.511512			−0.255756	−	0.966741i	$-0.582324\pi$
$827$	−1.00605e7			−0.511512			−0.255756	+	0.966741i	$0.582324\pi$
$828$	1.62864e7	+	2.82088e7i	0.825559	+	1.42991i
$829$	1.01827e7	−	1.76369e7i	0.514607	−	0.891326i	−0.485249	−	0.874376i	$-0.661271\pi$
$829$	1.01827e7	−	1.76369e7i	0.514607	−	0.891326i	0.999856	−	0.0169502i	$-0.00539568\pi$
$830$	−401051.	+	694641.i	−0.0202071	+	0.0349998i
$831$	−5.26395e6	−	9.11742e6i	−0.264429	−	0.458004i
$832$	−6.69166e6			−0.335140
$833$		0			0
$834$	−9.73865e6			−0.484823
$835$	4.34631e6	+	7.52804e6i	0.215727	+	0.373650i
$836$	39907.7	−	69122.2i	0.00197488	−	0.00342059i
$837$	−2.22723e6	+	3.85767e6i	−0.109888	+	0.190332i
$838$	1.03655e7	+	1.79536e7i	0.509895	+	0.883163i
$839$	5.95014e6			0.291825			0.145912	−	0.989298i	$-0.453388\pi$
$839$	5.95014e6			0.291825			0.145912	+	0.989298i	$0.453388\pi$
$840$		0			0
$841$	4.53905e6			0.221297
$842$	1.14754e7	+	1.98760e7i	0.557812	+	0.966159i
$843$	−9.03726e6	+	1.56530e7i	−0.437994	+	0.758627i
$844$	2.04305e6	−	3.53867e6i	0.0987242	−	0.170995i
$845$	1.14262e7	+	1.97907e7i	0.550503	+	0.953499i
$846$	4.12881e7			1.98335
$847$		0			0
$848$	4.38143e7			2.09231
$849$	2.50731e7	+	4.34279e7i	1.19382	+	2.06776i
$850$	1.03214e7	−	1.78771e7i	0.489993	−	0.848694i
$851$	−3.69705e6	+	6.40348e6i	−0.174997	+	0.303105i
$852$	−5.31233e6	−	9.20122e6i	−0.250718	−	0.434257i
$853$	−1.59836e7			−0.752146			−0.376073	−	0.926590i	$-0.622726\pi$
$853$	−1.59836e7			−0.752146			−0.376073	+	0.926590i	$0.622726\pi$
$854$		0			0
$855$	149056.			0.00697325
$856$	−94046.2	−	162893.i	−0.00438689	−	0.00759831i
$857$	−1.17296e6	+	2.03162e6i	−0.0545544	+	0.0944910i	−0.892013	−	0.452010i	$-0.850707\pi$
$857$	−1.17296e6	+	2.03162e6i	−0.0545544	+	0.0944910i	0.837459	+	0.546501i	$0.184041\pi$
$858$	9.83347e6	−	1.70321e7i	0.456025	−	0.789858i
$859$	−6.51117e6	−	1.12777e7i	−0.301076	−	0.521479i	0.675304	−	0.737540i	$-0.264012\pi$
$859$	−6.51117e6	−	1.12777e7i	−0.301076	−	0.521479i	−0.976380	+	0.216061i	$0.930679\pi$
$860$	2.22886e7			1.02763
$861$		0			0
$862$	1.91130e7			0.876112
$863$	−9.83442e6	−	1.70337e7i	−0.449492	−	0.778542i	0.548861	−	0.835913i	$-0.315061\pi$
$863$	−9.83442e6	−	1.70337e7i	−0.449492	−	0.778542i	−0.998353	+	0.0573712i	$0.981728\pi$
$864$	6.26391e6	−	1.08494e7i	0.285471	−	0.494450i
$865$	1.00173e7	−	1.73504e7i	0.455207	−	0.788442i
$866$	8.27296e6	+	1.43292e7i	0.374857	+	0.649272i
$867$	4.71019e6			0.212809
$868$		0			0
$869$	1.92322e7			0.863931
$870$	3.41636e7	+	5.91732e7i	1.53026	+	2.65049i
$871$	−7.07526e6	+	1.22547e7i	−0.316007	+	0.547341i
$872$	126494.	−	219094.i	0.00563351	−	0.00975752i
$873$	1.68796e7	+	2.92363e7i	0.749594	+	1.29834i
$874$	182683.			0.00808946
$875$		0			0
$876$	−5.34874e7			−2.35500
$877$	−1.17291e7	−	2.03153e7i	−0.514950	−	0.891919i	−0.999849	−	0.0173491i	$-0.994477\pi$
$877$	−1.17291e7	−	2.03153e7i	−0.514950	−	0.891919i	0.484900	−	0.874570i	$-0.338856\pi$
$878$	−1.81608e7	+	3.14555e7i	−0.795059	+	1.37708i
$879$	2.85362e7	−	4.94261e7i	1.24573	−	2.15767i
$880$	−1.74723e7	−	3.02629e7i	−0.760577	−	1.31736i
$881$	−4.59257e6			−0.199350			−0.0996750	−	0.995020i	$-0.531780\pi$
$881$	−4.59257e6			−0.199350			−0.0996750	+	0.995020i	$0.531780\pi$
$882$		0			0
$883$	−1.23402e7			−0.532622			−0.266311	−	0.963887i	$-0.585805\pi$
$883$	−1.23402e7			−0.532622			−0.266311	+	0.963887i	$0.585805\pi$
$884$	−4.04952e6	−	7.01397e6i	−0.174290	−	0.301879i
$885$	−2.96526e7	+	5.13598e7i	−1.27264	+	2.20427i
$886$	1.73074e7	−	2.99774e7i	0.740711	−	1.28295i
$887$	6.82772e6	+	1.18259e7i	0.291384	+	0.504693i	0.974137	−	0.225957i	$-0.0725508\pi$
$887$	6.82772e6	+	1.18259e7i	0.291384	+	0.504693i	−0.682753	+	0.730649i	$0.739217\pi$
$888$	1.10029e6			0.0468247
$889$		0			0
$890$	−3.99822e7			−1.69197
$891$	−8.10946e6	−	1.40460e7i	−0.342214	−	0.592732i
$892$	7131.11	−	12351.5i	0.000300086	−	0.000519764i
$893$	55118.6	−	95468.3i	0.00231297	−	0.00400618i
$894$	9.26077e6	+	1.60401e7i	0.387528	+	0.671218i
$895$	2.79665e7			1.16703
$896$		0			0
$897$	2.14293e7			0.889255
$898$	−2.61872e7	−	4.53575e7i	−1.08367	−	1.87698i
$899$	−7.06130e6	+	1.22305e7i	−0.291397	+	0.504715i
$900$	−1.07835e7	+	1.86775e7i	−0.443765	+	0.768623i
$901$	2.18145e7	+	3.77839e7i	0.895229	+	1.55058i
$902$	−3.11433e7			−1.27453
$903$		0			0
$904$	1.48987e6			0.0606355
$905$	−1.61416e7	−	2.79580e7i	−0.655125	−	1.13471i
$906$	4.20812e7	−	7.28868e7i	1.70321	−	2.95004i
$907$	−3.69800e6	+	6.40512e6i	−0.149262	+	0.258529i	−0.930955	−	0.365134i	$-0.881023\pi$
$907$	−3.69800e6	+	6.40512e6i	−0.149262	+	0.258529i	0.781693	+	0.623663i	$0.214356\pi$
$908$	8.63390e6	+	1.49544e7i	0.347530	+	0.601940i
$909$	−5.57362e6			−0.223732
$910$		0			0
$911$	−3.51041e7			−1.40140			−0.700699	−	0.713457i	$-0.747129\pi$
$911$	−3.51041e7			−1.40140			−0.700699	+	0.713457i	$0.747129\pi$
$912$	−84391.3	−	146170.i	−0.00335978	−	0.00581930i
$913$	−293098.	+	507660.i	−0.0116369	+	0.0201556i
$914$	−2.29898e7	+	3.98194e7i	−0.910267	+	1.57663i
$915$	−2.47138e7	−	4.28055e7i	−0.975857	−	1.69023i
$916$	1.04323e6			0.0410812
$917$		0			0
$918$	1.36246e7			0.533602
$919$	2.40668e7	+	4.16850e7i	0.940005	+	1.62814i	0.765455	+	0.643489i	$0.222514\pi$
$919$	2.40668e7	+	4.16850e7i	0.940005	+	1.62814i	0.174550	+	0.984648i	$0.444153\pi$
$920$	3.06629e6	−	5.31097e6i	0.119438	−	0.206873i
$921$	−2.87313e7	+	4.97640e7i	−1.11611	+	1.93315i
$922$	−6.04747e6	−	1.04745e7i	−0.234286	−	0.405795i
$923$	−3.91905e6			−0.151418
$924$		0			0
$925$	−4.89577e6			−0.188134
$926$	−1.53865e7	−	2.66501e7i	−0.589673	−	1.02134i
$927$	4.92688e6	−	8.53361e6i	0.188310	−	0.326162i
$928$	1.98594e7	−	3.43975e7i	0.757000	−	1.31116i
$929$	−9.18009e6	−	1.59004e7i	−0.348986	−	0.604461i	0.637084	−	0.770794i	$-0.280140\pi$
$929$	−9.18009e6	−	1.59004e7i	−0.348986	−	0.604461i	−0.986070	+	0.166334i	$0.946807\pi$
$930$	−3.85210e7			−1.46046
$931$		0			0
$932$	3.62924e7			1.36860
$933$	1.35778e7	+	2.35175e7i	0.510654	+	0.884479i
$934$	2.66332e7	−	4.61301e7i	0.998980	−	1.73028i
$935$	1.73984e7	−	3.01350e7i	0.650850	−	1.12731i
$936$	−893947.	−	1.54836e6i	−0.0333520	−	0.0577674i
$937$	−2.27081e7			−0.844951			−0.422475	−	0.906374i	$-0.638839\pi$
$937$	−2.27081e7			−0.844951			−0.422475	+	0.906374i	$0.638839\pi$
$938$		0			0
$939$	−3.89718e7			−1.44240
$940$	1.83949e7	+	3.18609e7i	0.679012	+	1.17608i
$941$	2.07901e7	−	3.60095e7i	0.765389	−	1.32569i	−0.174652	−	0.984630i	$-0.555880\pi$
$941$	2.07901e7	−	3.60095e7i	0.765389	−	1.32569i	0.940041	−	0.341062i	$-0.110787\pi$
$942$	−1.64535e7	+	2.84982e7i	−0.604130	+	1.04638i
$943$	−1.69670e7	−	2.93877e7i	−0.621336	−	1.07619i
$944$	3.76515e7			1.37516
$945$		0			0
$946$	3.42165e7			1.24310
$947$	−7.76705e6	−	1.34529e7i	−0.281437	−	0.487463i	0.690302	−	0.723521i	$-0.257478\pi$
$947$	−7.76705e6	−	1.34529e7i	−0.281437	−	0.487463i	−0.971739	+	0.236058i	$0.924144\pi$
$948$	−1.55005e7	+	2.68476e7i	−0.560175	+	0.970251i
$949$	−9.86479e6	+	1.70863e7i	−0.355568	+	0.615861i
$950$	60478.8	+	104752.i	0.00217417	+	0.00376578i
$951$	−1.93172e7			−0.692618
$952$		0			0
$953$	3.94908e7			1.40852			0.704262	−	0.709940i	$-0.251278\pi$
$953$	3.94908e7			1.40852			0.704262	+	0.709940i	$0.251278\pi$
$954$	−4.78749e7	−	8.29218e7i	−1.70309	−	2.94984i
$955$	−2.10177e7	+	3.64037e7i	−0.745721	+	1.29163i
$956$	8.38742e6	−	1.45274e7i	0.296813	−	0.514096i
$957$	2.49676e7	+	4.32452e7i	0.881246	+	1.52636i
$958$	−4.06701e7			−1.43173
$959$		0			0
$960$	4.63433e7			1.62296
$961$	1.03336e7	+	1.78983e7i	0.360947	+	0.625179i
$962$	−2.01742e6	+	3.49428e6i	−0.0702845	+	0.121736i
$963$	−1.27606e6	+	2.21020e6i	−0.0443410	+	0.0768008i
$964$	−2.00970e7	−	3.48091e7i	−0.696529	−	1.20642i
$965$	3.82118e7			1.32093
$966$		0			0
$967$	−1.87472e7			−0.644718			−0.322359	−	0.946617i	$-0.604476\pi$
$967$	−1.87472e7			−0.644718			−0.322359	+	0.946617i	$0.604476\pi$
$968$	−216116.	−	374323.i	−0.00741306	−	0.0128398i
$969$	84034.5	−	145552.i	0.00287507	−	0.00497977i
$970$	−3.15940e7	+	5.47224e7i	−1.07814	+	1.86739i
$971$	−2.67712e7	−	4.63690e7i	−0.911211	−	1.57826i	−0.812356	−	0.583162i	$-0.801815\pi$
$971$	−2.67712e7	−	4.63690e7i	−0.911211	−	1.57826i	−0.0988552	−	0.995102i	$-0.531518\pi$
$972$	3.72974e7			1.26623
$973$		0			0
$974$	1.21132e6			0.0409131
$975$	7.09435e6	+	1.22878e7i	0.239002	+	0.413963i
$976$	−1.56902e7	+	2.71762e7i	−0.527235	+	0.913197i
$977$	−2.23052e7	+	3.86337e7i	−0.747600	+	1.29488i	0.201370	+	0.979515i	$0.435461\pi$
$977$	−2.23052e7	+	3.86337e7i	−0.747600	+	1.29488i	−0.948970	+	0.315366i	$0.897873\pi$
$978$	−2.23877e7	−	3.87766e7i	−0.748449	−	1.29635i
$979$	−2.92200e7			−0.974368
$980$		0			0
$981$	−3.43265e6			−0.113883
$982$	−6.32828e6	−	1.09609e7i	−0.209415	−	0.362717i
$983$	−1.00034e7	+	1.73264e7i	−0.330190	+	0.571906i	−0.982549	−	0.186004i	$-0.940446\pi$
$983$	−1.00034e7	+	1.73264e7i	−0.330190	+	0.571906i	0.652359	+	0.757910i	$0.273779\pi$
$984$	−2.52480e6	+	4.37309e6i	−0.0831265	+	0.143979i
$985$	1.10871e7	+	1.92035e7i	0.364106	+	0.630651i
$986$	4.31961e7			1.41498
$987$		0			0
$988$	47456.9			0.00154670
$989$	1.86413e7	+	3.22877e7i	0.606018	+	1.04965i
$990$	−3.81832e7	+	6.61353e7i	−1.23818	+	2.14459i
$991$	−1.62317e7	+	2.81142e7i	−0.525026	+	0.909371i	0.474550	+	0.880229i	$0.342611\pi$
$991$	−1.62317e7	+	2.81142e7i	−0.525026	+	0.909371i	−0.999575	+	0.0291424i	$0.990722\pi$
$992$	1.11962e7	+	1.93923e7i	0.361235	+	0.625678i
$993$	2.25004e6			0.0724130
$994$		0			0
$995$	4.39649e7			1.40783
$996$	−472453.	−	818312.i	−0.0150907	−	0.0261379i
$997$	1.39470e7	−	2.41569e7i	0.444368	−	0.769668i	−0.553640	−	0.832756i	$-0.686762\pi$
$997$	1.39470e7	−	2.41569e7i	0.444368	−	0.769668i	0.998008	+	0.0630881i	$0.0200949\pi$
$998$	1.60472e7	−	2.77946e7i	0.510004	−	0.883353i
$999$	−1.61565e6	−	2.79839e6i	−0.0512193	−	0.0887144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.h.18.4		8
7.2	even	3	inner	49.6.c.h.30.4		8
7.3	odd	6		49.6.a.g.1.2	yes	4
7.4	even	3		49.6.a.g.1.1	✓	4
7.5	odd	6	inner	49.6.c.h.30.3		8
7.6	odd	2	inner	49.6.c.h.18.3		8
21.11	odd	6		441.6.a.z.1.3		4
21.17	even	6		441.6.a.z.1.4		4
28.3	even	6		784.6.a.bf.1.1		4
28.11	odd	6		784.6.a.bf.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.a.g.1.1	✓	4	7.4	even	3
49.6.a.g.1.2	yes	4	7.3	odd	6
49.6.c.h.18.3		8	7.6	odd	2	inner
49.6.c.h.18.4		8	1.1	even	1	trivial
49.6.c.h.30.3		8	7.5	odd	6	inner
49.6.c.h.30.4		8	7.2	even	3	inner
441.6.a.z.1.3		4	21.11	odd	6
441.6.a.z.1.4		4	21.17	even	6
784.6.a.bf.1.1		4	28.3	even	6
784.6.a.bf.1.4		4	28.11	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.90754 + 6.76805i) q^{2} +(11.7593 - 20.3677i) q^{3} +(-14.5377 + 25.1800i) q^{4} +(-37.1377 - 64.3243i) q^{5} +183.799 q^{6} +22.8562 q^{8} +(-155.062 - 268.575i) q^{9} +O(q^{10})\)	\(q+(3.90754 + 6.76805i) q^{2} +(11.7593 - 20.3677i) q^{3} +(-14.5377 + 25.1800i) q^{4} +(-37.1377 - 64.3243i) q^{5} +183.799 q^{6} +22.8562 q^{8} +(-155.062 - 268.575i) q^{9} +(290.234 - 502.699i) q^{10} +(212.110 - 367.385i) q^{11} +(341.906 + 592.198i) q^{12} +252.233 q^{13} -1746.85 q^{15} +(554.517 + 960.452i) q^{16} +(-552.173 + 956.392i) q^{17} +(1211.82 - 2098.93i) q^{18} +(-3.23550 - 5.60405i) q^{19} +2159.58 q^{20} +3315.30 q^{22} +(1806.19 + 3128.42i) q^{23} +(268.773 - 465.529i) q^{24} +(-1195.91 + 2071.38i) q^{25} +(985.611 + 1707.13i) q^{26} -1578.65 q^{27} -5005.02 q^{29} +(-6825.88 - 11822.8i) q^{30} +(1410.85 - 2443.66i) q^{31} +(-3967.89 + 6872.59i) q^{32} +(-4988.52 - 8640.36i) q^{33} -8630.55 q^{34} +9016.95 q^{36} +(1023.44 + 1772.65i) q^{37} +(25.2857 - 43.7961i) q^{38} +(2966.08 - 5137.41i) q^{39} +(-848.827 - 1470.21i) q^{40} -9393.81 q^{41} +10320.8 q^{43} +(6167.16 + 10681.8i) q^{44} +(-11517.3 + 19948.5i) q^{45} +(-14115.5 + 24448.8i) q^{46} +(8517.79 + 14753.3i) q^{47} +26082.9 q^{48} -18692.3 q^{50} +(12986.3 + 22493.0i) q^{51} +(-3666.89 + 6351.24i) q^{52} +(19753.3 - 34213.8i) q^{53} +(-6168.63 - 10684.4i) q^{54} -31509.0 q^{55} -152.189 q^{57} +(-19557.3 - 33874.2i) q^{58} +(16974.9 - 29401.4i) q^{59} +(25395.1 - 43985.7i) q^{60} +(14147.6 + 24504.4i) q^{61} +22051.7 q^{62} -26529.7 q^{64} +(-9367.36 - 16224.7i) q^{65} +(38985.6 - 67525.1i) q^{66} +(-28050.5 + 48584.8i) q^{67} +(-16054.6 - 27807.5i) q^{68} +84958.2 q^{69} -15537.4 q^{71} +(-3544.13 - 6138.61i) q^{72} +(-39109.8 + 67740.1i) q^{73} +(-7998.24 + 13853.4i) q^{74} +(28126.1 + 48715.9i) q^{75} +188.147 q^{76} +46360.3 q^{78} +(22667.7 + 39261.7i) q^{79} +(41187.0 - 71337.9i) q^{80} +(19116.2 - 33110.3i) q^{81} +(-36706.6 - 63577.8i) q^{82} -1381.82 q^{83} +82025.7 q^{85} +(40328.8 + 69851.5i) q^{86} +(-58855.4 + 101941. i) q^{87} +(4848.03 - 8397.03i) q^{88} +(-34439.7 - 59651.3i) q^{89} -180016. q^{90} -105031. q^{92} +(-33181.1 - 57471.3i) q^{93} +(-66567.2 + 115298. i) q^{94} +(-240.318 + 416.243i) q^{95} +(93319.2 + 161634. i) q^{96} -108857. q^{97} -131560. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9	\( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9} + 1952 q^{11} - 8192 q^{15} + 1566 q^{16} + 5974 q^{18} + 7048 q^{22} + 7136 q^{23} - 2764 q^{25} - 6704 q^{29} - 25608 q^{30} - 27810 q^{32} + 55340 q^{36} + 9208 q^{37} - 2464 q^{39} + 40896 q^{43} - 1900 q^{44} - 56712 q^{46} - 86140 q^{50} + 67408 q^{51} + 102920 q^{53} - 31152 q^{57} - 96972 q^{58} + 87080 q^{60} - 80636 q^{64} + 63168 q^{65} + 22896 q^{67} - 307648 q^{71} - 77358 q^{72} - 17596 q^{74} + 266112 q^{78} + 90688 q^{79} + 17204 q^{81} + 545312 q^{85} + 161860 q^{86} - 154812 q^{88} - 424400 q^{92} - 247760 q^{93} - 108224 q^{95} - 84544 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9 + 1952 * q^11 - 8192 * q^15 + 1566 * q^16 + 5974 * q^18 + 7048 * q^22 + 7136 * q^23 - 2764 * q^25 - 6704 * q^29 - 25608 * q^30 - 27810 * q^32 + 55340 * q^36 + 9208 * q^37 - 2464 * q^39 + 40896 * q^43 - 1900 * q^44 - 56712 * q^46 - 86140 * q^50 + 67408 * q^51 + 102920 * q^53 - 31152 * q^57 - 96972 * q^58 + 87080 * q^60 - 80636 * q^64 + 63168 * q^65 + 22896 * q^67 - 307648 * q^71 - 77358 * q^72 - 17596 * q^74 + 266112 * q^78 + 90688 * q^79 + 17204 * q^81 + 545312 * q^85 + 161860 * q^86 - 154812 * q^88 - 424400 * q^92 - 247760 * q^93 - 108224 * q^95 - 84544 * q^99

Introduction

L-functions

Modular forms

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