LMFDB - Embedded newform 63.6.p.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(17,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.p (of order $6$, 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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	63.17
Dual form			63.6.p.a.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 + 1.41421i) q^{2} +(-12.0000 + 20.7846i) q^{4} +(25.7196 + 44.5477i) q^{5} +(122.500 + 42.4352i) q^{7} -158.392i q^{8} +O(q^{10})$	\(q+(-2.44949 + 1.41421i) q^{2} +(-12.0000 + 20.7846i) q^{4} +(25.7196 + 44.5477i) q^{5} +(122.500 + 42.4352i) q^{7} -158.392i q^{8} +(-126.000 - 72.7461i) q^{10} +(-500.921 - 289.207i) q^{11} +1151.81i q^{13} +(-360.075 + 69.2965i) q^{14} +(-160.000 - 277.128i) q^{16} +(188.611 - 326.683i) q^{17} +(-1501.50 + 866.891i) q^{19} -1234.54 q^{20} +1636.00 q^{22} +(-3992.67 + 2305.17i) q^{23} +(239.500 - 414.826i) q^{25} +(-1628.91 - 2821.36i) q^{26} +(-2352.00 + 2036.89i) q^{28} -4601.85i q^{29} +(-1963.50 - 1133.63i) q^{31} +(5173.32 + 2986.82i) q^{32} +1066.94i q^{34} +(1260.26 + 6548.52i) q^{35} +(-101.500 - 175.803i) q^{37} +(2451.94 - 4246.88i) q^{38} +(7056.00 - 4073.78i) q^{40} +85.7321 q^{41} +4697.00 q^{43} +(12022.1 - 6940.96i) q^{44} +(6520.00 - 11293.0i) q^{46} +(11993.9 + 20774.1i) q^{47} +(13205.5 + 10396.6i) q^{49} +1354.82i q^{50} +(-23940.0 - 13821.8i) q^{52} +(6425.01 + 3709.48i) q^{53} -29753.2i q^{55} +(6721.40 - 19403.0i) q^{56} +(6508.00 + 11272.2i) q^{58} +(2486.23 - 4306.28i) q^{59} +(-15099.0 + 8717.41i) q^{61} +6412.76 q^{62} -6656.00 q^{64} +(-51310.7 + 29624.2i) q^{65} +(-15098.5 + 26151.4i) q^{67} +(4526.66 + 7840.40i) q^{68} +(-12348.0 - 14258.2i) q^{70} -3961.21i q^{71} +(46189.5 + 26667.5i) q^{73} +(497.246 + 287.085i) q^{74} -41610.8i q^{76} +(-49090.2 - 56684.5i) q^{77} +(19692.5 + 34108.4i) q^{79} +(8230.29 - 14255.3i) q^{80} +(-210.000 + 121.244i) q^{82} -63561.8 q^{83} +19404.0 q^{85} +(-11505.3 + 6642.56i) q^{86} +(-45808.0 + 79341.8i) q^{88} +(52691.0 + 91263.4i) q^{89} +(-48877.5 + 141097. i) q^{91} -110648. i q^{92} +(-58758.0 - 33923.9i) q^{94} +(-77236.1 - 44592.3i) q^{95} -2061.14i q^{97} +(-47049.8 - 6791.05i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 48 q^{4} + 490 q^{7}+O(q^{10}) $ 4 * q - 48 * q^4 + 490 * q^7	$ 4 q - 48 q^{4} + 490 q^{7} - 504 q^{10} - 640 q^{16} - 6006 q^{19} + 6544 q^{22} + 958 q^{25} - 9408 q^{28} - 7854 q^{31} - 406 q^{37} + 28224 q^{40} + 18788 q^{43} + 26080 q^{46} + 52822 q^{49} - 95760 q^{52} + 26032 q^{58} - 60396 q^{61} - 26624 q^{64} - 60394 q^{67} - 49392 q^{70} + 184758 q^{73} + 78770 q^{79} - 840 q^{82} + 77616 q^{85} - 183232 q^{88} - 195510 q^{91} - 235032 q^{94}+O(q^{100}) $ 4 * q - 48 * q^4 + 490 * q^7 - 504 * q^10 - 640 * q^16 - 6006 * q^19 + 6544 * q^22 + 958 * q^25 - 9408 * q^28 - 7854 * q^31 - 406 * q^37 + 28224 * q^40 + 18788 * q^43 + 26080 * q^46 + 52822 * q^49 - 95760 * q^52 + 26032 * q^58 - 60396 * q^61 - 26624 * q^64 - 60394 * q^67 - 49392 * q^70 + 184758 * q^73 + 78770 * q^79 - 840 * q^82 + 77616 * q^85 - 183232 * q^88 - 195510 * q^91 - 235032 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.44949	+	1.41421i	−0.433013	+	0.250000i	−0.700629	−	0.713525i	$-0.747097\pi$
$2$	−2.44949	+	1.41421i	−0.433013	+	0.250000i	0.267617	+	0.963525i	$0.413764\pi$
$3$		0			0
$3$		0			0
$4$	−12.0000	+	20.7846i	−0.375000	+	0.649519i
$5$	25.7196	+	44.5477i	0.460087	+	0.796894i	0.998965	−	0.0454899i	$-0.0144849\pi$
$5$	25.7196	+	44.5477i	0.460087	+	0.796894i	−0.538878	+	0.842384i	$0.681152\pi$
$6$		0			0
$7$	122.500	+	42.4352i	0.944911	+	0.327327i
$7$	122.500	+	42.4352i	0.944911	+	0.327327i
$8$		−	158.392i		−	0.875000i
$9$		0			0
$10$	−126.000	−	72.7461i	−0.398447	−	0.230043i
$11$	−500.921	−	289.207i	−1.24821	−	0.720654i	−0.277457	−	0.960738i	$-0.589492\pi$
$11$	−500.921	−	289.207i	−1.24821	−	0.720654i	−0.970752	+	0.240084i	$0.922825\pi$
$12$		0			0
$13$			1151.81i			1.89027i	0.326680	+	0.945135i	$0.394070\pi$
$13$			1151.81i			1.89027i	−0.326680	+	0.945135i	$0.605930\pi$
$14$	−360.075	+	69.2965i	−0.490990	+	0.0944911i
$15$		0			0
$16$	−160.000	−	277.128i	−0.156250	−	0.270633i
$17$	188.611	−	326.683i	0.158287	−	0.274160i	−0.775964	−	0.630777i	$-0.782736\pi$
$17$	188.611	−	326.683i	0.158287	−	0.274160i	0.934251	+	0.356616i	$0.116070\pi$
$18$		0			0
$19$	−1501.50	+	866.891i	−0.954204	+	0.550910i	−0.894384	−	0.447299i	$-0.852386\pi$
$19$	−1501.50	+	866.891i	−0.954204	+	0.550910i	−0.0598198	+	0.998209i	$0.519053\pi$
$20$	−1234.54			−0.690130
$21$		0			0
$22$	1636.00			0.720654
$23$	−3992.67	+	2305.17i	−1.57378	+	0.908622i	−0.578079	+	0.815981i	$0.696197\pi$
$23$	−3992.67	+	2305.17i	−1.57378	+	0.908622i	−0.995700	+	0.0926407i	$0.970469\pi$
$24$		0			0
$25$	239.500	−	414.826i	0.0766400	−	0.132744i
$26$	−1628.91	−	2821.36i	−0.472568	−	0.818511i
$27$		0			0
$28$	−2352.00	+	2036.89i	−0.566947	+	0.490990i
$29$		−	4601.85i		−	1.01610i	−0.861327	−	0.508051i	$-0.830366\pi$
$29$		−	4601.85i		−	1.01610i	0.861327	−	0.508051i	$-0.169634\pi$
$30$		0			0
$31$	−1963.50	−	1133.63i	−0.366967	−	0.211868i	0.305166	−	0.952299i	$-0.401288\pi$
$31$	−1963.50	−	1133.63i	−0.366967	−	0.211868i	−0.672132	+	0.740431i	$0.734621\pi$
$32$	5173.32	+	2986.82i	0.893089	+	0.515625i
$33$		0			0
$34$			1066.94i			0.158287i
$35$	1260.26	+	6548.52i	0.173897	+	0.903593i
$36$		0			0
$37$	−101.500	−	175.803i	−0.0121888	−	0.0211117i	0.859867	−	0.510519i	$-0.170547\pi$
$37$	−101.500	−	175.803i	−0.0121888	−	0.0211117i	−0.872055	+	0.489407i	$0.837213\pi$
$38$	2451.94	−	4246.88i	0.275455	−	0.477102i
$39$		0			0
$40$	7056.00	−	4073.78i	0.697282	−	0.402576i
$41$	85.7321			0.00796497			0.00398248	−	0.999992i	$-0.498732\pi$
$41$	85.7321			0.00796497			0.00398248	+	0.999992i	$0.498732\pi$
$42$		0			0
$43$	4697.00			0.387391			0.193695	−	0.981062i	$-0.437953\pi$
$43$	4697.00			0.387391			0.193695	+	0.981062i	$0.437953\pi$
$44$	12022.1	−	6940.96i	0.936157	−	0.540490i
$45$		0			0
$46$	6520.00	−	11293.0i	0.454311	−	0.786889i
$47$	11993.9	+	20774.1i	0.791985	+	1.37176i	0.924736	+	0.380608i	$0.124285\pi$
$47$	11993.9	+	20774.1i	0.791985	+	1.37176i	−0.132752	+	0.991149i	$0.542381\pi$
$48$		0			0
$49$	13205.5	+	10396.6i	0.785714	+	0.618590i
$50$			1354.82i			0.0766400i
$51$		0			0
$52$	−23940.0	−	13821.8i	−1.22777	−	0.708851i
$53$	6425.01	+	3709.48i	0.314184	+	0.181394i	0.648797	−	0.760961i	$-0.275272\pi$
$53$	6425.01	+	3709.48i	0.314184	+	0.181394i	−0.334613	+	0.942356i	$0.608606\pi$
$54$		0			0
$55$		−	29753.2i		−	1.32625i
$56$	6721.40	−	19403.0i	0.286411	−	0.826797i
$57$		0			0
$58$	6508.00	+	11272.2i	0.254026	+	0.439985i
$59$	2486.23	−	4306.28i	0.0929847	−	0.161054i	−0.815781	−	0.578361i	$-0.803693\pi$
$59$	2486.23	−	4306.28i	0.0929847	−	0.161054i	0.908766	+	0.417307i	$0.137026\pi$
$60$		0			0
$61$	−15099.0	+	8717.41i	−0.519546	+	0.299960i	−0.736749	−	0.676167i	$-0.763640\pi$
$61$	−15099.0	+	8717.41i	−0.519546	+	0.299960i	0.217203	+	0.976126i	$0.430307\pi$
$62$	6412.76			0.211868
$63$		0			0
$64$	−6656.00			−0.203125
$65$	−51310.7	+	29624.2i	−1.50634	+	0.869689i
$66$		0			0
$67$	−15098.5	+	26151.4i	−0.410910	+	0.711717i	−0.994990	−	0.0999794i	$-0.968122\pi$
$67$	−15098.5	+	26151.4i	−0.410910	+	0.711717i	0.584079	+	0.811697i	$0.301456\pi$
$68$	4526.66	+	7840.40i	0.118715	+	0.205620i
$69$		0			0
$70$	−12348.0	−	14258.2i	−0.301198	−	0.347793i
$71$		−	3961.21i		−	0.0932572i	−0.998912	−	0.0466286i	$-0.985152\pi$
$71$		−	3961.21i		−	0.0932572i	0.998912	−	0.0466286i	$-0.0148477\pi$
$72$		0			0
$73$	46189.5	+	26667.5i	1.01446	+	0.585700i	0.912495	−	0.409087i	$-0.134153\pi$
$73$	46189.5	+	26667.5i	1.01446	+	0.585700i	0.101968	+	0.994788i	$0.467486\pi$
$74$	497.246	+	287.085i	0.0105558	+	0.00609441i
$75$		0			0
$76$		−	41610.8i		−	0.826365i
$77$	−49090.2	−	56684.5i	−0.943557	−	1.08953i
$78$		0			0
$79$	19692.5	+	34108.4i	0.355004	+	0.614885i	0.987119	−	0.159990i	$-0.0511462\pi$
$79$	19692.5	+	34108.4i	0.355004	+	0.614885i	−0.632115	+	0.774875i	$0.717813\pi$
$80$	8230.29	−	14255.3i	0.143777	−	0.249029i
$81$		0			0
$82$	−210.000	+	121.244i	−0.00344893	+	0.00199124i
$83$	−63561.8			−1.01275			−0.506374	−	0.862314i	$-0.669014\pi$
$83$	−63561.8			−1.01275			−0.506374	+	0.862314i	$0.669014\pi$
$84$		0			0
$85$	19404.0			0.291302
$86$	−11505.3	+	6642.56i	−0.167745	+	0.0968477i
$87$		0			0
$88$	−45808.0	+	79341.8i	−0.630572	+	1.09218i
$89$	52691.0	+	91263.4i	0.705117	+	1.22130i	0.966649	+	0.256104i	$0.0824389\pi$
$89$	52691.0	+	91263.4i	0.705117	+	1.22130i	−0.261532	+	0.965195i	$0.584228\pi$
$90$		0			0
$91$	−48877.5	+	141097.i	−0.618736	+	1.78614i
$92$		−	110648.i		−	1.36293i
$93$		0			0
$94$	−58758.0	−	33923.9i	−0.685879	−	0.395992i
$95$	−77236.1	−	44592.3i	−0.878034	−	0.506933i
$96$		0			0
$97$		−	2061.14i		−	0.0222422i	−0.999938	−	0.0111211i	$-0.996460\pi$
$97$		−	2061.14i		−	0.0222422i	0.999938	−	0.0111211i	$-0.00354003\pi$
$98$	−47049.8	−	6791.05i	−0.494872	−	0.0714286i
$99$		0			0
$100$	5748.00	+	9955.83i	0.0574800	+	0.0995583i
$101$	15869.0	−	27485.9i	0.154791	−	0.268106i	−0.778192	−	0.628027i	$-0.783863\pi$
$101$	15869.0	−	27485.9i	0.154791	−	0.268106i	0.932983	+	0.359920i	$0.117196\pi$
$102$		0			0
$103$	146318.	−	84476.4i	1.35895	−	0.784590i	0.369467	−	0.929244i	$-0.379540\pi$
$103$	146318.	−	84476.4i	1.35895	−	0.784590i	0.989482	+	0.144654i	$0.0462070\pi$
$104$	182438.			1.65399
$105$		0			0
$106$	−20984.0			−0.181394
$107$	−118724.	+	68545.5i	−1.00249	+	0.578788i	−0.908984	−	0.416831i	$-0.863141\pi$
$107$	−118724.	+	68545.5i	−1.00249	+	0.578788i	−0.0935062	+	0.995619i	$0.529808\pi$
$108$		0			0
$109$	103302.	−	178925.i	0.832807	−	1.44246i	−0.0629958	−	0.998014i	$-0.520065\pi$
$109$	103302.	−	178925.i	0.832807	−	1.44246i	0.895803	−	0.444451i	$-0.146601\pi$
$110$	42077.3	+	72880.1i	0.331563	+	0.574285i
$111$		0			0
$112$	−7840.00	−	40737.8i	−0.0590569	−	0.306869i
$113$			70505.6i			0.519431i	0.965685	+	0.259715i	$0.0836287\pi$
$113$			70505.6i			0.519431i	−0.965685	+	0.259715i	$0.916371\pi$
$114$		0			0
$115$	−205380.	−	118576.i	−1.44815	−	0.836090i
$116$	95647.7	+	55222.2i	0.659978	+	0.381038i
$117$		0			0
$118$			14064.3i			0.0929847i
$119$	36967.7	−	32015.0i	0.239307	−	0.207246i
$120$		0			0
$121$	86755.5	+	150265.i	0.538683	+	0.933027i
$122$	24656.6	−	42706.4i	0.149980	−	0.259773i
$123$		0			0
$124$	47124.0	−	27207.1i	0.275225	−	0.158901i
$125$	185387.			1.06122
$126$		0			0
$127$	25289.0			0.139131			0.0695653	−	0.997577i	$-0.477839\pi$
$127$	25289.0			0.139131			0.0695653	+	0.997577i	$0.477839\pi$
$128$	−149243.	+	86165.2i	−0.805133	+	0.464844i
$129$		0			0
$130$	83790.0	−	145129.i	0.434844	−	0.753172i
$131$	72709.4	+	125936.i	0.370180	+	0.641170i	0.989593	−	0.143895i	$-0.0459628\pi$
$131$	72709.4	+	125936.i	0.370180	+	0.641170i	−0.619413	+	0.785065i	$0.712629\pi$
$132$		0			0
$133$	−220720.	+	42477.7i	−1.08197	+	0.208224i
$134$		−	85410.0i		−	0.410910i
$135$		0			0
$136$	−51744.0	−	29874.4i	−0.239890	−	0.138501i
$137$	291039.	+	168031.i	1.32480	+	0.764872i	0.984490	−	0.175443i	$-0.0561357\pi$
$137$	291039.	+	168031.i	1.32480	+	0.764872i	0.340307	+	0.940314i	$0.389469\pi$
$138$		0			0
$139$		−	108768.i		−	0.477488i	−0.971083	−	0.238744i	$-0.923264\pi$
$139$		−	108768.i		−	0.477488i	0.971083	−	0.238744i	$-0.0767357\pi$
$140$	−151231.	−	52388.1i	−0.652112	−	0.225898i
$141$		0			0
$142$	5602.00	+	9702.95i	0.0233143	+	0.0403815i
$143$	333112.	−	576967.i	1.36223	−	2.35945i
$144$		0			0
$145$	205002.	−	118358.i	0.809726	−	0.467496i
$146$	−150854.			−0.585700
$147$		0			0
$148$	4872.00			0.0182832
$149$	−254370.	+	146860.i	−0.938641	+	0.541925i	−0.889534	−	0.456869i	$-0.848971\pi$
$149$	−254370.	+	146860.i	−0.938641	+	0.541925i	−0.0491073	+	0.998794i	$0.515638\pi$
$150$		0			0
$151$	−95347.0	+	165146.i	−0.340302	+	0.589421i	−0.984489	−	0.175448i	$-0.943863\pi$
$151$	−95347.0	+	165146.i	−0.340302	+	0.589421i	0.644187	+	0.764868i	$0.277196\pi$
$152$	137309.	+	237825.i	0.482046	+	0.834929i
$153$		0			0
$154$	200410.	+	69424.1i	0.680954	+	0.235889i
$155$		−	116626.i		−	0.389911i
$156$		0			0
$157$	236271.	+	136411.i	0.765000	+	0.441673i	0.831088	−	0.556141i	$-0.187719\pi$
$157$	236271.	+	136411.i	0.765000	+	0.441673i	−0.0660882	+	0.997814i	$0.521052\pi$
$158$	−96473.2	−	55698.8i	−0.307442	−	0.177502i
$159$		0			0
$160$			307280.i			0.948929i
$161$	−586922.	+	112953.i	−1.78450	+	0.343427i
$162$		0			0
$163$	93683.0	+	162264.i	0.276180	+	0.478357i	0.970432	−	0.241374i	$-0.0775982\pi$
$163$	93683.0	+	162264.i	0.276180	+	0.478357i	−0.694252	+	0.719732i	$0.744265\pi$
$164$	−1028.79	+	1781.91i	−0.00298686	+	0.00517340i
$165$		0			0
$166$	155694.	−	89890.0i	0.438532	−	0.253187i
$167$	218908.			0.607395			0.303698	−	0.952768i	$-0.401779\pi$
$167$	218908.			0.607395			0.303698	+	0.952768i	$0.401779\pi$
$168$		0			0
$169$	−955382.			−2.57312
$170$	−47529.9	+	27441.4i	−0.126138	+	0.0728256i
$171$		0			0
$172$	−56364.0	+	97625.3i	−0.145272	+	0.251618i
$173$	−49141.7	−	85115.9i	−0.124834	−	0.216220i	0.796834	−	0.604199i	$-0.206507\pi$
$173$	−49141.7	−	85115.9i	−0.124834	−	0.216220i	−0.921668	+	0.387979i	$0.873173\pi$
$174$		0			0
$175$	46942.0	−	40653.0i	0.115869	−	0.100345i
$176$			185092.i			0.450409i
$177$		0			0
$178$	−258132.	−	149033.i	−0.610649	−	0.352559i
$179$	−301061.	−	173817.i	−0.702298	−	0.405472i	0.105905	−	0.994376i	$-0.466226\pi$
$179$	−301061.	−	173817.i	−0.702298	−	0.405472i	−0.808203	+	0.588904i	$0.799559\pi$
$180$		0			0
$181$		−	275526.i		−	0.625124i	−0.949897	−	0.312562i	$-0.898813\pi$
$181$		−	275526.i		−	0.625124i	0.949897	−	0.312562i	$-0.101187\pi$
$182$	−79816.6	−	414739.i	−0.178614	−	0.928104i
$183$		0			0
$184$	365120.	+	632406.i	0.795044	+	1.37706i
$185$	5221.09	−	9043.19i	0.0112158	−	0.0194264i
$186$		0			0
$187$	−188958.	+	109095.i	−0.395149	+	0.228140i
$188$	−575708.			−1.18798
$189$		0			0
$190$	252252.			0.506933
$191$	−240485.	+	138844.i	−0.476984	+	0.275387i	−0.719159	−	0.694846i	$-0.755473\pi$
$191$	−240485.	+	138844.i	−0.476984	+	0.275387i	0.242175	+	0.970233i	$0.422139\pi$
$192$		0			0
$193$	114810.	−	198858.i	0.221865	−	0.384281i	−0.733509	−	0.679679i	$-0.762119\pi$
$193$	114810.	−	198858.i	0.221865	−	0.384281i	0.955374	+	0.295398i	$0.0954523\pi$
$194$	2914.89	+	5048.74i	0.00556056	+	0.00963117i
$195$		0			0
$196$	−374556.	+	149712.i	−0.696429	+	0.278365i
$197$			21074.6i			0.0386896i	0.999813	+	0.0193448i	$0.00615802\pi$
$197$			21074.6i			0.0386896i	−0.999813	+	0.0193448i	$0.993842\pi$
$198$		0			0
$199$	−444360.	−	256551.i	−0.795431	−	0.459242i	0.0464403	−	0.998921i	$-0.485212\pi$
$199$	−444360.	−	256551.i	−0.795431	−	0.459242i	−0.841871	+	0.539679i	$0.818546\pi$
$200$	−65705.1	−	37934.9i	−0.116151	−	0.0670600i
$201$		0			0
$202$			89768.7i			0.154791i
$203$	195281.	−	563727.i	0.332598	−	0.960127i
$204$		0			0
$205$	2205.00	+	3819.17i	0.00366458	+	0.00634723i
$206$	−238935.	+	413848.i	−0.392295	+	0.679475i
$207$		0			0
$208$	319200.	−	184290.i	0.511569	−	0.295355i
$209$	1.00284e6			1.58806
$210$		0			0
$211$	444710.			0.687655			0.343828	−	0.939033i	$-0.388276\pi$
$211$	444710.			0.687655			0.343828	+	0.939033i	$0.388276\pi$
$212$	−154200.	+	89027.6i	−0.235638	+	0.136046i
$213$		0			0
$214$	193876.	−	335803.i	0.289394	−	0.501245i
$215$	120805.	+	209241.i	0.178233	+	0.308709i
$216$		0			0
$217$	−192423.	−	222191.i	−0.277401	−	0.320315i
$218$			584367.i			0.832807i
$219$		0			0
$220$	618408.	+	357038.i	0.861427	+	0.497345i
$221$	376278.	+	217244.i	0.518237	+	0.299204i
$222$		0			0
$223$		−	286280.i		−	0.385504i	−0.981247	−	0.192752i	$-0.938259\pi$
$223$		−	286280.i		−	0.385504i	0.981247	−	0.192752i	$-0.0617413\pi$
$224$	506986.	+	585417.i	0.675112	+	0.779552i
$225$		0			0
$226$	−99710.0	−	172703.i	−0.129858	−	0.224920i
$227$	245288.	−	424852.i	0.315945	−	0.547234i	−0.663693	−	0.748005i	$-0.731012\pi$
$227$	245288.	−	424852.i	0.315945	−	0.547234i	0.979638	+	0.200772i	$0.0643450\pi$
$228$		0			0
$229$	797233.	−	460283.i	1.00461	−	0.580011i	0.0949999	−	0.995477i	$-0.469715\pi$
$229$	797233.	−	460283.i	1.00461	−	0.580011i	0.909609	+	0.415466i	$0.136382\pi$
$230$	670768.			0.836090
$231$		0			0
$232$	−728896.			−0.889090
$233$	1.09357e6	−	631374.i	1.31965	−	0.761898i	0.335974	−	0.941871i	$-0.390935\pi$
$233$	1.09357e6	−	631374.i	1.31965	−	0.761898i	0.983671	+	0.179974i	$0.0576013\pi$
$234$		0			0
$235$	−616959.	+	1.06860e6i	−0.728764	+	1.26226i
$236$	59669.6	+	103351.i	0.0697385	+	0.120791i
$237$		0			0
$238$	−45276.0	+	130701.i	−0.0518114	+	0.149567i
$239$		−	723615.i		−	0.819432i	−0.912213	−	0.409716i	$-0.865628\pi$
$239$		−	723615.i		−	0.819432i	0.912213	−	0.409716i	$-0.134372\pi$
$240$		0			0
$241$	491652.	+	283855.i	0.545275	+	0.314814i	0.747214	−	0.664584i	$-0.231391\pi$
$241$	491652.	+	283855.i	0.545275	+	0.314814i	−0.201939	+	0.979398i	$0.564724\pi$
$242$	−425013.	−	245382.i	−0.466514	−	0.269342i
$243$		0			0
$244$		−	418436.i		−	0.449940i
$245$	−123506.	+	855673.i	−0.131453	+	0.910736i
$246$		0			0
$247$	−998498.	−	1.72945e6i	−1.04137	−	1.80370i
$248$	−179557.	+	311003.i	−0.185385	+	0.321096i
$249$		0			0
$250$	−454104.	+	262177.i	−0.459521	+	0.265305i
$251$	−621798.			−0.622967			−0.311484	−	0.950252i	$-0.600826\pi$
$251$	−621798.			−0.622967			−0.311484	+	0.950252i	$0.600826\pi$
$252$		0			0
$253$	2.66668e6			2.61921
$254$	−61945.1	+	35764.0i	−0.0602453	+	0.0347826i
$255$		0			0
$256$	350208.	−	606578.i	0.333984	−	0.578478i
$257$	120497.	+	208706.i	0.113800	+	0.197107i	0.917299	−	0.398198i	$-0.130364\pi$
$257$	120497.	+	208706.i	0.113800	+	0.197107i	−0.803500	+	0.595305i	$0.797031\pi$
$258$		0			0
$259$	−4973.50	−	25843.1i	−0.00460694	−	0.0239384i
$260$		−	1.42196e6i		−	1.30453i
$261$		0			0
$262$	−356202.	−	205653.i	−0.320585	−	0.185090i
$263$	339957.	+	196274.i	0.303064	+	0.174974i	0.643819	−	0.765178i	$-0.277349\pi$
$263$	339957.	+	196274.i	0.303064	+	0.174974i	−0.340754	+	0.940152i	$0.610682\pi$
$264$		0			0
$265$			381626.i			0.333829i
$266$	480580.	−	416195.i	0.416449	−	0.360655i
$267$		0			0
$268$	−362364.	−	627633.i	−0.308183	−	0.533788i
$269$	−520197.	+	901007.i	−0.438316	+	0.759185i	−0.997560	−	0.0698180i	$-0.977758\pi$
$269$	−520197.	+	901007.i	−0.438316	+	0.759185i	0.559244	+	0.829003i	$0.311091\pi$
$270$		0			0
$271$	−1.91604e6	+	1.10623e6i	−1.58483	+	0.914999i	−0.590685	+	0.806902i	$0.701142\pi$
$271$	−1.91604e6	+	1.10623e6i	−1.58483	+	0.914999i	−0.994140	+	0.108097i	$0.965524\pi$
$272$	−120711.			−0.0989291
$273$		0			0
$274$	−950528.			−0.764872
$275$	−239941.	+	138530.i	−0.191325	+	0.110462i
$276$		0			0
$277$	86358.5	−	149577.i	0.0676247	−	0.117130i	−0.830231	−	0.557420i	$-0.811791\pi$
$277$	86358.5	−	149577.i	0.0676247	−	0.117130i	0.897855	+	0.440291i	$0.145125\pi$
$278$	153821.	+	266425.i	0.119372	+	0.206758i
$279$		0			0
$280$	1.03723e6	−	199615.i	0.790644	−	0.152159i
$281$			1.93894e6i			1.46487i	0.680837	+	0.732435i	$0.261616\pi$
$281$			1.93894e6i			1.46487i	−0.680837	+	0.732435i	$0.738384\pi$
$282$		0			0
$283$	−324650.	−	187436.i	−0.240962	−	0.139120i	0.374657	−	0.927164i	$-0.377761\pi$
$283$	−324650.	−	187436.i	−0.240962	−	0.139120i	−0.615619	+	0.788044i	$0.711094\pi$
$284$	82332.2	+	47534.5i	0.0605723	+	0.0349714i
$285$		0			0
$286$			1.88437e6i			1.36223i
$287$	10502.2	+	3638.06i	0.00752619	+	0.00260715i
$288$		0			0
$289$	638780.	+	1.10640e6i	0.449891	+	0.779234i
$290$	−334767.	+	579833.i	−0.233748	+	0.404863i
$291$		0			0
$292$	−1.10855e6	+	640020.i	−0.760847	+	0.439275i
$293$	−2.75403e6			−1.87413			−0.937063	−	0.349160i	$-0.886467\pi$
$293$	−2.75403e6			−1.87413			−0.937063	+	0.349160i	$0.886467\pi$
$294$		0			0
$295$	255780.			0.171124
$296$	−27845.8	+	16076.8i	−0.0184727	+	0.0106652i
$297$		0			0
$298$	415384.	−	719466.i	0.270962	−	0.469321i
$299$	−2.65512e6	−	4.59881e6i	−1.71754	−	2.97487i
$300$		0			0
$301$	575382.	+	199318.i	0.366050	+	0.126803i
$302$		−	539364.i		−	0.340302i
$303$		0			0
$304$	480480.	+	277405.i	0.298189	+	0.172159i
$305$	−776682.	−	448417.i	−0.478072	−	0.276015i
$306$		0			0
$307$		−	1.10731e6i		−	0.670535i	−0.942123	−	0.335267i	$-0.891173\pi$
$307$		−	1.10731e6i		−	0.670535i	0.942123	−	0.335267i	$-0.108827\pi$
$308$	1.76725e6	−	340107.i	1.06150	−	0.204286i
$309$		0			0
$310$	164934.	+	285674.i	0.0974779	+	0.168837i
$311$	−451800.	+	782540.i	−0.264878	+	0.458781i	−0.967532	−	0.252750i	$-0.918665\pi$
$311$	−451800.	+	782540.i	−0.264878	+	0.458781i	0.702654	+	0.711532i	$0.251998\pi$
$312$		0			0
$313$	−825878.	+	476821.i	−0.476491	+	0.275102i	−0.718953	−	0.695059i	$-0.755378\pi$
$313$	−825878.	+	476821.i	−0.476491	+	0.275102i	0.242462	+	0.970161i	$0.422045\pi$
$314$	−771658.			−0.441673
$315$		0			0
$316$	−945240.			−0.532506
$317$	1.62936e6	−	940711.i	0.910686	−	0.525785i	0.0300341	−	0.999549i	$-0.490438\pi$
$317$	1.62936e6	−	940711.i	0.910686	−	0.525785i	0.880652	+	0.473764i	$0.157105\pi$
$318$		0			0
$319$	−1.33089e6	+	2.30516e6i	−0.732258	+	1.26831i
$320$	−171190.	−	296510.i	−0.0934552	−	0.161869i
$321$		0			0
$322$	1.27792e6	−	1.10671e6i	0.686853	−	0.594832i
$323$			654020.i			0.348807i
$324$		0			0
$325$	477802.	+	275859.i	0.250923	+	0.144870i
$326$	−458951.	−	264976.i	−0.239179	−	0.138090i
$327$		0			0
$328$		−	13579.3i		−	0.00696935i
$329$	587702.	+	3.05379e6i	0.299342	+	1.55543i
$330$		0			0
$331$	216912.	+	375703.i	0.108821	+	0.188484i	0.915293	−	0.402788i	$-0.131959\pi$
$331$	216912.	+	375703.i	0.108821	+	0.188484i	−0.806472	+	0.591273i	$0.798626\pi$
$332$	762742.	−	1.32111e6i	0.379780	−	0.657799i
$333$		0			0
$334$	−536214.	+	309583.i	−0.263010	+	0.151849i
$335$	−1.55331e6			−0.756217
$336$		0			0
$337$	1.18200e6			0.566947			0.283473	−	0.958980i	$-0.408513\pi$
$337$	1.18200e6			0.566947			0.283473	+	0.958980i	$0.408513\pi$
$338$	2.34020e6	−	1.35111e6i	1.11419	−	0.643280i
$339$		0			0
$340$	−232848.	+	403305.i	−0.109238	+	0.189206i
$341$	655705.	+	1.13571e6i	0.305367	+	0.528912i
$342$		0			0
$343$	1.17649e6	+	1.83397e6i	0.539949	+	0.841698i
$344$		−	743967.i		−	0.338967i
$345$		0			0
$346$	240744.	+	138994.i	0.108110	+	0.0624172i
$347$	1.43566e6	+	828878.i	0.640070	+	0.369544i	0.784641	−	0.619950i	$-0.212847\pi$
$347$	1.43566e6	+	828878.i	0.640070	+	0.369544i	−0.144572	+	0.989494i	$0.546180\pi$
$348$		0			0
$349$		−	1.90976e6i		−	0.839294i	−0.907687	−	0.419647i	$-0.862154\pi$
$349$		−	1.90976e6i		−	0.839294i	0.907687	−	0.419647i	$-0.137846\pi$
$350$	−57492.0	+	165965.i	−0.0250863	+	0.0724180i
$351$		0			0
$352$	−1.72762e6	−	2.99232e6i	−0.743174	−	1.28722i
$353$	−1.41960e6	+	2.45881e6i	−0.606356	+	1.05024i	0.385479	+	0.922717i	$0.374036\pi$
$353$	−1.41960e6	+	2.45881e6i	−0.606356	+	1.05024i	−0.991836	+	0.127523i	$0.959297\pi$
$354$		0			0
$355$	176463.	−	101881.i	0.0743161	−	0.0429064i
$356$	−2.52917e6			−1.05768
$357$		0			0
$358$	983260.			0.405472
$359$	2.36983e6	−	1.36822e6i	0.970467	−	0.560299i	0.0710882	−	0.997470i	$-0.477353\pi$
$359$	2.36983e6	−	1.36822e6i	0.970467	−	0.560299i	0.899378	+	0.437171i	$0.144020\pi$
$360$		0			0
$361$	264952.	−	458910.i	0.107004	−	0.185336i
$362$	389653.	+	674898.i	0.156281	+	0.270687i
$363$		0			0
$364$	−2.34612e6	−	2.70907e6i	−0.928104	−	1.07168i
$365$			2.74352e6i			1.07789i
$366$		0			0
$367$	2.02504e6	+	1.16916e6i	0.784817	+	0.453114i	0.838135	−	0.545463i	$-0.183646\pi$
$367$	2.02504e6	+	1.16916e6i	0.784817	+	0.453114i	−0.0533175	+	0.998578i	$0.516980\pi$
$368$	1.27765e6	+	737654.i	0.491806	+	0.283944i
$369$		0			0
$370$			29534.9i			0.0112158i
$371$	629651.	+	727059.i	0.237501	+	0.274242i
$372$		0			0
$373$	−1.15375e6	−	1.99835e6i	−0.429377	−	0.743703i	0.567441	−	0.823414i	$-0.307934\pi$
$373$	−1.15375e6	−	1.99835e6i	−0.429377	−	0.743703i	−0.996818	+	0.0797110i	$0.974600\pi$
$374$	308567.	−	534454.i	0.114070	−	0.197575i
$375$		0			0
$376$	3.29045e6	−	1.89974e6i	1.20029	−	0.692987i
$377$	5.30048e6			1.92071
$378$		0			0
$379$	−2.36146e6			−0.844466			−0.422233	−	0.906487i	$-0.638754\pi$
$379$	−2.36146e6			−0.844466			−0.422233	+	0.906487i	$0.638754\pi$
$380$	1.85367e6	−	1.07021e6i	0.658525	−	0.380200i
$381$		0			0
$382$	392710.	−	680194.i	0.137694	−	0.238492i
$383$	−2.09296e6	−	3.62512e6i	−0.729062	−	1.26277i	−0.957280	−	0.289162i	$-0.906623\pi$
$383$	−2.09296e6	−	3.62512e6i	−0.729062	−	1.26277i	0.228218	−	0.973610i	$-0.426710\pi$
$384$		0			0
$385$	1.26258e6	−	3.64476e6i	0.434118	−	1.25319i
$386$			649466.i			0.221865i
$387$		0			0
$388$	42840.0	+	24733.7i	0.0144467	+	0.00834083i
$389$	−1.73709e6	−	1.00291e6i	−0.582034	−	0.336038i	0.179907	−	0.983684i	$-0.442420\pi$
$389$	−1.73709e6	−	1.00291e6i	−0.582034	−	0.336038i	−0.761941	+	0.647646i	$0.775754\pi$
$390$		0			0
$391$			1.73912e6i			0.575290i
$392$	1.64674e6	−	2.09164e6i	0.541266	−	0.687500i
$393$		0			0
$394$	−29804.0	−	51622.0i	−0.00967239	−	0.0167531i
$395$	−1.01297e6	+	1.75451e6i	−0.326665	+	0.565801i
$396$		0			0
$397$	−5.05996e6	+	2.92137e6i	−1.61128	+	0.930273i	−0.622205	+	0.782854i	$0.713763\pi$
$397$	−5.05996e6	+	2.92137e6i	−1.61128	+	0.930273i	−0.989074	+	0.147418i	$0.952904\pi$
$398$	1.45127e6			0.459242
$399$		0			0
$400$	−153280.			−0.0479000
$401$	−3.61786e6	+	2.08877e6i	−1.12355	+	0.648679i	−0.942304	−	0.334759i	$-0.891345\pi$
$401$	−3.61786e6	+	2.08877e6i	−1.12355	+	0.648679i	−0.181242	+	0.983439i	$0.558012\pi$
$402$		0			0
$403$	1.30573e6	−	2.26159e6i	0.400488	−	0.693666i
$404$	380856.	+	659663.i	0.116094	+	0.201080i
$405$		0			0
$406$	318892.	+	1.65701e6i	0.0960127	+	0.498896i
$407$			117418.i			0.0351357i
$408$		0			0
$409$	1.81118e6	+	1.04568e6i	0.535368	+	0.309095i	0.743200	−	0.669070i	$-0.233307\pi$
$409$	1.81118e6	+	1.04568e6i	0.535368	+	0.309095i	−0.207832	+	0.978165i	$0.566641\pi$
$410$	−10802.2	−	6236.68i	−0.00317362	−	0.00183229i
$411$		0			0
$412$			4.05487e6i			1.17688i
$413$	487301.	−	422015.i	0.140580	−	0.121746i
$414$		0			0
$415$	−1.63479e6	−	2.83153e6i	−0.465952	−	0.807052i
$416$	−3.44026e6	+	5.95870e6i	−0.974671	+	1.68818i
$417$		0			0
$418$	−2.45645e6	+	1.41823e6i	−0.687651	+	0.397015i
$419$	6.55448e6			1.82391			0.911954	−	0.410291i	$-0.134573\pi$
$419$	6.55448e6			1.82391			0.911954	+	0.410291i	$0.134573\pi$
$420$		0			0
$421$	5.99908e6			1.64960			0.824801	−	0.565423i	$-0.191287\pi$
$421$	5.99908e6			1.64960			0.824801	+	0.565423i	$0.191287\pi$
$422$	−1.08931e6	+	628915.i	−0.297763	+	0.171914i
$423$		0			0
$424$	587552.	−	1.01767e6i	0.158720	−	0.274911i
$425$	−90344.5	−	156481.i	−0.0242622	−	0.0420233i
$426$		0			0
$427$	−2.21955e6	+	427153.i	−0.589109	+	0.113374i
$428$		−	3.29018e6i		−	0.868182i
$429$		0			0
$430$	−591822.	−	341689.i	−0.154355	−	0.0891167i
$431$	−4.56105e6	−	2.63332e6i	−1.18269	−	0.682827i	−0.226056	−	0.974114i	$-0.572583\pi$
$431$	−4.56105e6	−	2.63332e6i	−1.18269	−	0.682827i	−0.956636	+	0.291287i	$0.905917\pi$
$432$		0			0
$433$			809992.i			0.207616i	0.994597	+	0.103808i	$0.0331028\pi$
$433$			809992.i			0.207616i	−0.994597	+	0.103808i	$0.966897\pi$
$434$	785564.	+	272127.i	0.200197	+	0.0693502i
$435$		0			0
$436$	2.47926e6	+	4.29420e6i	0.624606	+	1.08185i
$437$	3.99666e6	−	6.92242e6i	1.00114	−	1.73402i
$438$		0			0
$439$	4.69333e6	−	2.70970e6i	1.16230	−	0.671057i	0.210449	−	0.977605i	$-0.432507\pi$
$439$	4.69333e6	−	2.70970e6i	1.16230	−	0.671057i	0.951855	+	0.306548i	$0.0991739\pi$
$440$	−4.71266e6			−1.16047
$441$		0			0
$442$	−1.22892e6			−0.299204
$443$	2.44784e6	−	1.41326e6i	0.592616	−	0.342147i	−0.173515	−	0.984831i	$-0.555513\pi$
$443$	2.44784e6	−	1.41326e6i	0.592616	−	0.342147i	0.766131	+	0.642684i	$0.222179\pi$
$444$		0			0
$445$	−2.71039e6	+	4.69453e6i	−0.648830	+	1.12381i
$446$	404861.	+	701241.i	0.0963761	+	0.166928i
$447$		0			0
$448$	−815360.	−	282449.i	−0.191935	−	0.0664883i
$449$			3.89941e6i			0.912816i	0.889771	+	0.456408i	$0.150864\pi$
$449$			3.89941e6i			0.912816i	−0.889771	+	0.456408i	$0.849136\pi$
$450$		0			0
$451$	−42945.0	−	24794.3i	−0.00994194	−	0.00573998i
$452$	−1.46543e6	−	846067.i	−0.337380	−	0.194787i
$453$		0			0
$454$			1.38756e6i			0.315945i
$455$	−7.54267e6	+	1.45159e6i	−1.70803	+	0.328711i
$456$		0			0
$457$	323362.	+	560079.i	0.0724266	+	0.125446i	0.899964	−	0.435964i	$-0.143592\pi$
$457$	323362.	+	560079.i	0.0724266	+	0.125446i	−0.827538	+	0.561410i	$0.810259\pi$
$458$	−1.30188e6	+	2.25492e6i	−0.290005	+	0.502304i
$459$		0			0
$460$	4.92912e6	−	2.84583e6i	1.08611	−	0.627067i
$461$	−4.99109e6			−1.09381			−0.546906	−	0.837194i	$-0.684194\pi$
$461$	−4.99109e6			−1.09381			−0.546906	+	0.837194i	$0.684194\pi$
$462$		0			0
$463$	−6.41938e6			−1.39168			−0.695842	−	0.718195i	$-0.744969\pi$
$463$	−6.41938e6			−1.39168			−0.695842	+	0.718195i	$0.744969\pi$
$464$	−1.27530e6	+	736296.i	−0.274991	+	0.158766i
$465$		0			0
$466$	−1.78579e6	+	3.09309e6i	−0.380949	+	0.659823i
$467$	−2.33242e6	−	4.03987e6i	−0.494897	−	0.857186i	0.505086	−	0.863069i	$-0.331461\pi$
$467$	−2.33242e6	−	4.03987e6i	−0.494897	−	0.857186i	−0.999983	+	0.00588278i	$0.998127\pi$
$468$		0			0
$469$	−2.95931e6	+	2.56283e6i	−0.621238	+	0.538008i
$470$		−	3.49005e6i		−	0.728764i
$471$		0			0
$472$	−682080.	−	393799.i	−0.140922	−	0.0813616i
$473$	−2.35282e6	−	1.35840e6i	−0.483545	−	0.279175i
$474$		0			0
$475$			830482.i			0.168887i
$476$	221806.	+	1.15254e6i	0.0448700	+	0.233151i
$477$		0			0
$478$	1.02335e6	+	1.77249e6i	0.204858	+	0.354824i
$479$	3.90892e6	−	6.77045e6i	0.778428	−	1.34828i	−0.154420	−	0.988005i	$-0.549351\pi$
$479$	3.90892e6	−	6.77045e6i	0.778428	−	1.34828i	0.932848	−	0.360271i	$-0.117316\pi$
$480$		0			0
$481$	202492.	−	116909.i	0.0399067	−	0.0230402i
$482$	−1.60573e6			−0.314814
$483$		0			0
$484$	−4.16426e6			−0.808025
$485$	91819.1	−	53011.8i	0.0177247	−	0.0102334i
$486$		0			0
$487$	1.03108e6	−	1.78589e6i	0.197002	−	0.341218i	−0.750553	−	0.660810i	$-0.770213\pi$
$487$	1.03108e6	−	1.78589e6i	0.197002	−	0.341218i	0.947555	+	0.319593i	$0.103546\pi$
$488$	1.38077e6	+	2.39156e6i	0.262465	+	0.454602i
$489$		0			0
$490$	−907578.	−	2.27063e6i	−0.170763	−	0.427224i
$491$			3.97446e6i			0.744003i	0.928232	+	0.372001i	$0.121328\pi$
$491$			3.97446e6i			0.744003i	−0.928232	+	0.372001i	$0.878672\pi$
$492$		0			0
$493$	−1.50335e6	−	867958.i	−0.278575	−	0.160835i
$494$	4.89162e6	+	2.82418e6i	0.901852	+	0.520684i
$495$		0			0
$496$			725521.i			0.132418i
$497$	168095.	−	485248.i	0.0305256	−	0.0881197i
$498$		0			0
$499$	−1.37827e6	−	2.38723e6i	−0.247789	−	0.429184i	0.715123	−	0.698999i	$-0.246371\pi$
$499$	−1.37827e6	−	2.38723e6i	−0.247789	−	0.429184i	−0.962912	+	0.269815i	$0.913037\pi$
$500$	−2.22465e6	+	3.85320e6i	−0.397957	+	0.689281i
$501$		0			0
$502$	1.52309e6	−	879355.i	0.269753	−	0.155742i
$503$	4.61230e6			0.812827			0.406413	−	0.913689i	$-0.366779\pi$
$503$	4.61230e6			0.812827			0.406413	+	0.913689i	$0.366779\pi$
$504$		0			0
$505$	1.63258e6			0.284870
$506$	−6.53201e6	+	3.77126e6i	−1.13415	+	0.654801i
$507$		0			0
$508$	−303468.	+	525622.i	−0.0521739	+	0.0903679i
$509$	2.74524e6	+	4.75489e6i	0.469662	+	0.813479i	0.999398	−	0.0346839i	$-0.0110424\pi$
$509$	2.74524e6	+	4.75489e6i	0.469662	+	0.813479i	−0.529736	+	0.848162i	$0.677709\pi$
$510$		0			0
$511$	4.52657e6	+	5.22683e6i	0.766862	+	0.885496i
$512$		−	3.53350e6i		−	0.595703i
$513$		0			0
$514$	−590310.	−	340816.i	−0.0985536	−	0.0568999i
$515$	7.52647e6	+	4.34541e6i	1.25047	+	0.721959i
$516$		0			0
$517$		−	1.38749e7i		−	2.28299i
$518$	48730.1	+	56268.7i	0.00797946	+	0.00921388i
$519$		0			0
$520$	4.69224e6	+	8.12720e6i	0.760978	+	1.31805i
$521$	2.97605e6	−	5.15468e6i	0.480338	−	0.831969i	−0.519408	−	0.854526i	$-0.673848\pi$
$521$	2.97605e6	−	5.15468e6i	0.480338	−	0.831969i	0.999746	+	0.0225574i	$0.00718084\pi$
$522$		0			0
$523$	−3.13588e6	+	1.81050e6i	−0.501308	+	0.289430i	−0.729254	−	0.684243i	$-0.760133\pi$
$523$	−3.13588e6	+	1.81050e6i	−0.501308	+	0.289430i	0.227945	+	0.973674i	$0.426799\pi$
$524$	−3.49005e6			−0.555269
$525$		0			0
$526$	−1.11030e6			−0.174974
$527$	−740674.	+	427628.i	−0.116172	+	0.0670718i
$528$		0			0
$529$	7.40943e6	−	1.28335e7i	1.15119	−	1.99391i
$530$	−539701.	−	934790.i	−0.0834571	−	0.144552i
$531$		0			0
$532$	1.76576e6	−	5.09732e6i	0.270491	−	0.780842i
$533$			98747.5i			0.0150559i
$534$		0			0
$535$	−6.10709e6	−	3.52593e6i	−0.922466	−	0.532586i
$536$	4.14217e6	+	2.39148e6i	0.622752	+	0.359546i
$537$		0			0
$538$		−	2.94268e6i		−	0.438316i
$539$	−3.60813e6	−	9.02701e6i	−0.534947	−	1.33836i
$540$		0			0
$541$	5.40403e6	+	9.36005e6i	0.793825	+	1.37494i	0.923583	+	0.383399i	$0.125247\pi$
$541$	5.40403e6	+	9.36005e6i	0.793825	+	1.37494i	−0.129758	+	0.991546i	$0.541420\pi$
$542$	3.12888e6	−	5.41938e6i	0.457500	−	0.792413i
$543$		0			0
$544$	1.95149e6	−	1.12669e6i	0.282728	−	0.163233i
$545$	1.06276e7			1.53266
$546$		0			0
$547$	−87526.0			−0.0125074			−0.00625372	−	0.999980i	$-0.501991\pi$
$547$	−87526.0			−0.0125074			−0.00625372	+	0.999980i	$0.501991\pi$
$548$	−6.98493e6	+	4.03275e6i	−0.993597	+	0.573654i
$549$		0			0
$550$	391822.	−	678656.i	0.0552309	−	0.0956627i
$551$	3.98931e6	+	6.90968e6i	0.559781	+	0.969569i
$552$		0			0
$553$	964932.	+	5.01394e6i	0.134179	+	0.697214i
$554$			488517.i			0.0676247i
$555$		0			0
$556$	2.26069e6	+	1.30521e6i	0.310138	+	0.179058i
$557$	4.72497e6	+	2.72796e6i	0.645299	+	0.372564i	0.786653	−	0.617396i	$-0.211812\pi$
$557$	4.72497e6	+	2.72796e6i	0.645299	+	0.372564i	−0.141354	+	0.989959i	$0.545146\pi$
$558$		0			0
$559$			5.41007e6i			0.732273i
$560$	1.61314e6	−	1.39702e6i	0.217371	−	0.188249i
$561$		0			0
$562$	−2.74208e6	−	4.74942e6i	−0.366218	−	0.634308i
$563$	2.22906e6	−	3.86085e6i	0.296381	−	0.513348i	−0.678924	−	0.734209i	$-0.737553\pi$
$563$	2.22906e6	−	3.86085e6i	0.296381	−	0.513348i	0.975305	+	0.220861i	$0.0708867\pi$
$564$		0			0
$565$	−3.14086e6	+	1.81338e6i	−0.413931	+	0.238983i
$566$	1.06030e6			0.139120
$567$		0			0
$568$	−627424.			−0.0816000
$569$	7.40162e6	−	4.27333e6i	0.958399	−	0.553332i	0.0627189	−	0.998031i	$-0.480023\pi$
$569$	7.40162e6	−	4.27333e6i	0.958399	−	0.553332i	0.895680	+	0.444699i	$0.146690\pi$
$570$		0			0
$571$	−1.65024e6	+	2.85830e6i	−0.211815	+	0.366875i	−0.952283	−	0.305217i	$-0.901271\pi$
$571$	−1.65024e6	+	2.85830e6i	−0.211815	+	0.366875i	0.740467	+	0.672092i	$0.234604\pi$
$572$	7.99469e6	+	1.38472e7i	1.02167	+	1.76959i
$573$		0			0
$574$	−30870.0	+	5940.93i	−0.00391072	+	0.000752619i
$575$			2.20835e6i			0.278547i
$576$		0			0
$577$	−1.36571e7	−	7.88491e6i	−1.70772	−	0.985955i	−0.937367	−	0.348344i	$-0.886744\pi$
$577$	−1.36571e7	−	7.88491e6i	−1.70772	−	0.985955i	−0.770358	−	0.637612i	$-0.779922\pi$
$578$	−3.12937e6	−	1.80674e6i	−0.389617	−	0.224945i
$579$		0			0
$580$			5.68118e6i			0.701243i
$581$	−7.78632e6	−	2.69726e6i	−0.956956	−	0.331499i
$582$		0			0
$583$	−2.14561e6	−	3.71631e6i	−0.261445	−	0.452836i
$584$	4.22392e6	−	7.31604e6i	0.512488	−	0.887655i
$585$		0			0
$586$	6.74596e6	−	3.89478e6i	0.811520	−	0.468532i
$587$	3.36204e6			0.402724			0.201362	−	0.979517i	$-0.435463\pi$
$587$	3.36204e6			0.402724			0.201362	+	0.979517i	$0.435463\pi$
$588$		0			0
$589$	3.93093e6			0.466882
$590$	−626530.	+	361728.i	−0.0740990	+	0.0427811i
$591$		0			0
$592$	−32480.0	+	56257.0i	−0.00380901	+	0.00659739i
$593$	481412.	+	833830.i	0.0562186	+	0.0973734i	0.892765	−	0.450523i	$-0.148762\pi$
$593$	481412.	+	833830.i	0.0562186	+	0.0973734i	−0.836546	+	0.547896i	$0.815429\pi$
$594$		0			0
$595$	2.37699e6	+	823413.i	0.275255	+	0.0953511i
$596$		−	7.04930e6i		−	0.812887i
$597$		0			0
$598$	1.30074e7	+	7.50983e6i	1.48743	+	0.858770i
$599$	−6.08692e6	−	3.51428e6i	−0.693155	−	0.400193i	0.111638	−	0.993749i	$-0.464390\pi$
$599$	−6.08692e6	−	3.51428e6i	−0.693155	−	0.400193i	−0.804793	+	0.593556i	$0.797724\pi$
$600$		0			0
$601$		−	9.08125e6i		−	1.02556i	−0.858521	−	0.512778i	$-0.828616\pi$
$601$		−	9.08125e6i		−	1.02556i	0.858521	−	0.512778i	$-0.171384\pi$
$602$	−1.69127e6	+	325485.i	−0.190205	+	0.0366050i
$603$		0			0
$604$	−2.28833e6	−	3.96350e6i	−0.255227	−	0.442065i
$605$	−4.46264e6	+	7.72952e6i	−0.495682	+	0.858547i
$606$		0			0
$607$	1.07185e7	−	6.18835e6i	1.18077	−	0.681715i	0.224574	−	0.974457i	$-0.427901\pi$
$607$	1.07185e7	−	6.18835e6i	1.18077	−	0.681715i	0.956192	+	0.292742i	$0.0945676\pi$
$608$	−1.03570e7			−1.13625
$609$		0			0
$610$	2.53663e6			0.276015
$611$	−2.39279e7	+	1.38148e7i	−2.59299	+	1.49706i
$612$		0			0
$613$	−5.73078e6	+	9.92601e6i	−0.615975	+	1.06690i	0.374238	+	0.927333i	$0.377904\pi$
$613$	−5.73078e6	+	9.92601e6i	−0.615975	+	1.06690i	−0.990213	+	0.139567i	$0.955429\pi$
$614$	1.56597e6	+	2.71233e6i	0.167634	+	0.290350i
$615$		0			0
$616$	−8.97837e6	+	7.77549e6i	−0.953335	+	0.825612i
$617$		−	1.38242e7i		−	1.46193i	−0.682417	−	0.730963i	$-0.739071\pi$
$617$		−	1.38242e7i		−	1.46193i	0.682417	−	0.730963i	$-0.260929\pi$
$618$		0			0
$619$	−7.38168e6	−	4.26181e6i	−0.774334	−	0.447062i	0.0600843	−	0.998193i	$-0.480863\pi$
$619$	−7.38168e6	−	4.26181e6i	−0.774334	−	0.447062i	−0.834419	+	0.551131i	$0.814196\pi$
$620$	2.42402e6	+	1.39951e6i	0.253255	+	0.146217i
$621$		0			0
$622$		−	2.55577e6i		−	0.264878i
$623$	2.58186e6	+	1.34157e7i	0.266509	+	1.38482i
$624$		0			0
$625$	4.01965e6	+	6.96225e6i	0.411613	+	0.712934i
$626$	1.34865e6	−	2.33593e6i	0.137551	−	0.238246i
$627$		0			0
$628$	−5.67050e6	+	3.27387e6i	−0.573750	+	0.331255i
$629$	−76575.9			−0.00771731
$630$		0			0
$631$	8.57038e6			0.856893			0.428446	−	0.903567i	$-0.359061\pi$
$631$	8.57038e6			0.856893			0.428446	+	0.903567i	$0.359061\pi$
$632$	5.40250e6	−	3.11913e6i	0.538024	−	0.310628i
$633$		0			0
$634$	−2.66073e6	+	4.60852e6i	−0.262892	+	0.455343i
$635$	650424.	+	1.12657e6i	0.0640121	+	0.110872i
$636$		0			0
$637$	−1.19750e7	+	1.52103e7i	−1.16930	+	1.48521i
$638$		−	7.52863e6i		−	0.732258i
$639$		0			0
$640$	−7.67693e6	−	4.43228e6i	−0.740862	−	0.427737i
$641$	−1.33147e7	−	7.68722e6i	−1.27993	−	0.738966i	−0.303092	−	0.952961i	$-0.598019\pi$
$641$	−1.33147e7	−	7.68722e6i	−1.27993	−	0.738966i	−0.976835	+	0.213996i	$0.931352\pi$
$642$		0			0
$643$		−	1.52086e7i		−	1.45065i	−0.688408	−	0.725324i	$-0.741690\pi$
$643$		−	1.52086e7i		−	1.45065i	0.688408	−	0.725324i	$-0.258310\pi$
$644$	4.69538e6	−	1.35544e7i	0.446124	−	1.28785i
$645$		0			0
$646$	−924924.	−	1.60202e6i	−0.0872017	−	0.151038i
$647$	−309553.	+	536162.i	−0.0290720	+	0.0503541i	−0.880195	−	0.474612i	$-0.842589\pi$
$647$	−309553.	+	536162.i	−0.0290720	+	0.0503541i	0.851123	+	0.524966i	$0.175922\pi$
$648$		0			0
$649$	−2.49081e6	+	1.43807e6i	−0.232129	+	0.134020i
$650$	−1.56050e6			−0.144870
$651$		0			0
$652$	−4.49678e6			−0.414270
$653$	−7.99640e6	+	4.61672e6i	−0.733857	+	0.423693i	−0.819832	−	0.572605i	$-0.805933\pi$
$653$	−7.99640e6	+	4.61672e6i	−0.733857	+	0.423693i	0.0859746	+	0.996297i	$0.472600\pi$
$654$		0			0
$655$	−3.74012e6	+	6.47808e6i	−0.340630	+	0.589988i
$656$	−13717.1	−	23758.8i	−0.00124453	−	0.00215558i
$657$		0			0
$658$	−5.75828e6	−	6.64909e6i	−0.518476	−	0.598684i
$659$			1.34210e7i			1.20384i	0.798555	+	0.601922i	$0.205598\pi$
$659$			1.34210e7i			1.20384i	−0.798555	+	0.601922i	$0.794402\pi$
$660$		0			0
$661$	8.68876e6	+	5.01646e6i	0.773489	+	0.446574i	0.834118	−	0.551586i	$-0.185977\pi$
$661$	8.68876e6	+	5.01646e6i	0.773489	+	0.446574i	−0.0606288	+	0.998160i	$0.519311\pi$
$662$	−1.06265e6	−	613521.i	−0.0942422	−	0.0544107i
$663$		0			0
$664$			1.00677e7i			0.886154i
$665$	−7.56914e6	−	8.74009e6i	−0.663731	−	0.766411i
$666$		0			0
$667$	1.06080e7	+	1.83737e7i	0.923253	+	1.59912i
$668$	−2.62690e6	+	4.54993e6i	−0.227773	+	0.394515i
$669$		0			0
$670$	3.80482e6	−	2.19672e6i	0.327452	−	0.189054i
$671$	1.00845e7			0.864668
$672$		0			0
$673$	−2.68578e6			−0.228577			−0.114289	−	0.993448i	$-0.536459\pi$
$673$	−2.68578e6			−0.228577			−0.114289	+	0.993448i	$0.536459\pi$
$674$	−2.89529e6	+	1.67160e6i	−0.245495	+	0.141737i
$675$		0			0
$676$	1.14646e7	−	1.98572e7i	0.964921	−	1.67129i
$677$	−9.98207e6	−	1.72894e7i	−0.837045	−	1.44980i	−0.892354	−	0.451335i	$-0.850948\pi$
$677$	−9.98207e6	−	1.72894e7i	−0.837045	−	1.44980i	0.0553094	−	0.998469i	$-0.482385\pi$
$678$		0			0
$679$	87465.0	−	252490.i	0.00728048	−	0.0210169i
$680$		−	3.07344e6i		−	0.254890i
$681$		0			0
$682$	−3.21229e6	−	1.85461e6i	−0.264456	−	0.152684i
$683$	5.55076e6	+	3.20473e6i	0.455303	+	0.262869i	0.710067	−	0.704134i	$-0.248665\pi$
$683$	5.55076e6	+	3.20473e6i	0.455303	+	0.262869i	−0.254764	+	0.967003i	$0.581998\pi$
$684$		0			0
$685$			1.72868e7i			1.40763i
$686$	−5.47542e6	−	2.82847e6i	−0.444229	−	0.229478i
$687$		0			0
$688$	−751520.	−	1.30167e6i	−0.0605298	−	0.104841i
$689$	−4.27263e6	+	7.40042e6i	−0.342884	+	0.593893i
$690$		0			0
$691$	−1.04702e7	+	6.04496e6i	−0.834178	+	0.481613i	−0.855281	−	0.518165i	$-0.826615\pi$
$691$	−1.04702e7	+	6.04496e6i	−0.834178	+	0.481613i	0.0211032	+	0.999777i	$0.493282\pi$
$692$	2.35880e6			0.187252
$693$		0			0
$694$	−4.68884e6			−0.369544
$695$	4.84535e6	−	2.79746e6i	0.380507	−	0.219686i
$696$		0			0
$697$	16170.0	−	28007.3i	0.00126075	−	0.00218368i
$698$	2.70080e6	+	4.67793e6i	0.209824	+	0.363425i
$699$		0			0
$700$	281652.	+	1.46351e6i	0.0217254	+	0.112888i
$701$			1.17104e6i			0.0900073i	0.998987	+	0.0450036i	$0.0143299\pi$
$701$			1.17104e6i			0.0900073i	−0.998987	+	0.0450036i	$0.985670\pi$
$702$		0			0
$703$	304804.	+	175979.i	0.0232613	+	0.0134299i
$704$	3.33413e6	+	1.92496e6i	0.253542	+	0.146383i
$705$		0			0
$706$		−	8.03045e6i		−	0.606356i
$707$	3.11033e6	−	2.69362e6i	0.234023	−	0.202669i
$708$		0			0
$709$	−6.70482e6	−	1.16131e7i	−0.500924	−	0.867626i	−0.999999	−	0.00106721i	$-0.999660\pi$
$709$	−6.70482e6	−	1.16131e7i	−0.500924	−	0.867626i	0.499075	−	0.866559i	$-0.333673\pi$
$710$	−288163.	+	499113.i	−0.0214532	+	0.0371580i
$711$		0			0
$712$	1.44554e7	−	8.34582e6i	1.06864	−	0.616977i
$713$	1.04528e7			0.770032
$714$		0			0
$715$	3.42701e7			2.50698
$716$	7.22546e6	−	4.17162e6i	0.526724	−	0.304104i
$717$		0			0
$718$	−3.86991e6	+	6.70288e6i	−0.280150	+	0.485233i
$719$	8.87713e6	+	1.53756e7i	0.640398	+	1.10920i	0.985344	+	0.170580i	$0.0545640\pi$
$719$	8.87713e6	+	1.53756e7i	0.640398	+	1.10920i	−0.344946	+	0.938623i	$0.612103\pi$
$720$		0			0
$721$	2.15087e7	−	4.13935e6i	1.54090	−	0.296547i
$722$			1.49879e6i			0.107004i
$723$		0			0
$724$	5.72670e6	+	3.30631e6i	0.406030	+	0.234421i
$725$	−1.90897e6	−	1.10214e6i	−0.134882	−	0.0778741i
$726$		0			0
$727$		−	5.19333e6i		−	0.364427i	−0.983259	−	0.182213i	$-0.941674\pi$
$727$		−	5.19333e6i		−	0.364427i	0.983259	−	0.182213i	$-0.0583262\pi$
$728$	2.23487e7	+	7.74180e6i	1.56287	+	0.541394i
$729$		0			0
$730$	−3.87992e6	−	6.72022e6i	−0.269473	−	0.466741i
$731$	885905.	−	1.53443e6i	0.0613188	−	0.106207i
$732$		0			0
$733$	−1.11633e6	+	644513.i	−0.0767418	+	0.0443069i	−0.537880	−	0.843021i	$-0.680775\pi$
$733$	−1.11633e6	+	644513.i	−0.0767418	+	0.0443069i	0.461138	+	0.887328i	$0.347441\pi$
$734$	−6.61375e6			−0.453114
$735$		0			0
$736$	−2.75405e7			−1.87403
$737$	1.51263e7	−	8.73317e6i	1.02580	−	0.592248i
$738$		0			0
$739$	6.45618e6	−	1.11824e7i	0.434875	−	0.753226i	−0.562410	−	0.826858i	$-0.690126\pi$
$739$	6.45618e6	−	1.11824e7i	0.434875	−	0.753226i	0.997285	+	0.0736323i	$0.0234591\pi$
$740$	125306.	+	217037.i	0.00841188	+	0.0145698i
$741$		0			0
$742$	−2.57054e6	−	890461.i	−0.171401	−	0.0593752i
$743$			8.96758e6i			0.595941i	0.954575	+	0.297970i	$0.0963097\pi$
$743$			8.96758e6i			0.595941i	−0.954575	+	0.297970i	$0.903690\pi$
$744$		0			0
$745$	−1.30846e7	−	7.55440e6i	−0.863713	−	0.498665i
$746$	5.65219e6	+	3.26329e6i	0.371852	+	0.214689i
$747$		0			0
$748$		−	5.23656e6i		−	0.342209i
$749$	−1.74525e7	+	3.35873e6i	−1.13672	+	0.218761i
$750$		0			0
$751$	−1.85293e6	−	3.20937e6i	−0.119884	−	0.207644i	0.799838	−	0.600216i	$-0.204919\pi$
$751$	−1.85293e6	−	3.20937e6i	−0.119884	−	0.207644i	−0.919721	+	0.392572i	$0.871585\pi$
$752$	3.83806e6	−	6.64771e6i	0.247495	−	0.428674i
$753$		0			0
$754$	−1.29835e7	+	7.49600e6i	−0.831691	+	0.480177i
$755$	−9.80916e6			−0.626274
$756$		0			0
$757$	−2.81893e7			−1.78791			−0.893953	−	0.448161i	$-0.852079\pi$
$757$	−2.81893e7			−1.78791			−0.893953	+	0.448161i	$0.852079\pi$
$758$	5.78436e6	−	3.33960e6i	0.365664	−	0.211116i
$759$		0			0
$760$	−7.06306e6	+	1.22336e7i	−0.443566	+	0.768280i
$761$	4.93658e6	+	8.55040e6i	0.309004	+	0.535211i	0.978145	−	0.207925i	$-0.0666710\pi$
$761$	4.93658e6	+	8.55040e6i	0.309004	+	0.535211i	−0.669141	+	0.743136i	$0.733338\pi$
$762$		0			0
$763$	2.02473e7	−	1.75347e7i	1.25909	−	1.09040i
$764$		−	6.66451e6i		−	0.413081i
$765$		0			0
$766$	1.02534e7	+	5.91979e6i	0.631386	+	0.364531i
$767$	4.96003e6	+	2.86368e6i	0.304436	+	0.175766i
$768$		0			0
$769$		−	2.61429e6i		−	0.159418i	−0.996818	−	0.0797091i	$-0.974601\pi$
$769$		−	2.61429e6i		−	0.159418i	0.996818	−	0.0797091i	$-0.0253991\pi$
$770$	2.06179e6	+	1.07134e7i	0.125319	+	0.651177i
$771$		0			0
$772$	2.75545e6	+	4.77258e6i	0.166399	+	0.288211i
$773$	4.27050e6	−	7.39672e6i	0.257057	−	0.445236i	−0.708395	−	0.705816i	$-0.750580\pi$
$773$	4.27050e6	−	7.39672e6i	0.257057	−	0.445236i	0.965452	+	0.260580i	$0.0839138\pi$
$774$		0			0
$775$	−940516.	+	543007.i	−0.0562487	+	0.0324752i
$776$	−326468.			−0.0194619
$777$		0			0
$778$	5.67332e6			0.336038
$779$	−128727.	+	74320.5i	−0.00760021	+	0.00438798i
$780$		0			0
$781$	−1.14561e6	+	1.98425e6i	−0.0672061	+	0.116404i
$782$	−2.45948e6	−	4.25995e6i	−0.143823	−	0.249108i
$783$		0			0
$784$	768320.	−	5.32308e6i	0.0446429	−	0.309295i
$785$			1.40338e7i			0.812832i
$786$		0			0
$787$	1.82432e7	+	1.05327e7i	1.04994	+	0.606182i	0.922632	−	0.385681i	$-0.126034\pi$
$787$	1.82432e7	+	1.05327e7i	1.04994	+	0.606182i	0.127306	+	0.991863i	$0.459367\pi$
$788$	−438028.	−	252895.i	−0.0251296	−	0.0145086i
$789$		0			0
$790$		−	5.73021e6i		−	0.326665i
$791$	−2.99192e6	+	8.63694e6i	−0.170024	+	0.490816i
$792$		0			0
$793$	−1.00408e7	−	1.73912e7i	−0.567005	−	0.982081i
$794$	8.26288e6	−	1.43117e7i	0.465136	−	0.805640i
$795$		0			0
$796$	1.06646e7	−	6.15723e6i	0.596573	−	0.344432i
$797$	−3.23910e6			−0.180625			−0.0903126	−	0.995913i	$-0.528787\pi$
$797$	−3.23910e6			−0.180625			−0.0903126	+	0.995913i	$0.528787\pi$
$798$		0			0
$799$	9.04873e6			0.501442
$800$	2.47802e6	−	1.43069e6i	0.136893	−	0.0790350i
$801$		0			0
$802$	5.90794e6	−	1.02329e7i	0.324340	−	0.561773i
$803$	−1.54248e7	−	2.67166e7i	−0.844174	−	1.46215i
$804$		0			0
$805$	−2.01272e7	−	2.32409e7i	−1.09470	−	1.26405i
$806$			7.38631e6i			0.400488i
$807$		0			0
$808$	−4.35355e6	−	2.51352e6i	−0.234593	−	0.135442i
$809$	5.46924e6	+	3.15767e6i	0.293803	+	0.169627i	0.639656	−	0.768662i	$-0.279077\pi$
$809$	5.46924e6	+	3.15767e6i	0.293803	+	0.169627i	−0.345853	+	0.938289i	$0.612410\pi$
$810$		0			0
$811$			2.96115e7i			1.58092i	0.612516	+	0.790458i	$0.290157\pi$
$811$			2.96115e7i			1.58092i	−0.612516	+	0.790458i	$0.709843\pi$
$812$	9.37347e6	+	1.08236e7i	0.498896	+	0.576076i
$813$		0			0
$814$	−166054.	−	287614.i	−0.00878392	−	0.0152142i
$815$	−4.81899e6	+	8.34673e6i	−0.254133	+	0.440172i
$816$		0			0
$817$	−7.05255e6	+	4.07179e6i	−0.369650	+	0.213418i
$818$	−5.91528e6			−0.309095
$819$		0			0
$820$	−105840.			−0.00549687
$821$	1.15659e7	−	6.67757e6i	0.598854	−	0.345749i	−0.169736	−	0.985489i	$-0.554292\pi$
$821$	1.15659e7	−	6.67757e6i	0.598854	−	0.345749i	0.768591	+	0.639741i	$0.220958\pi$
$822$		0			0
$823$	717167.	−	1.24217e6i	0.0369080	−	0.0639266i	−0.846981	−	0.531623i	$-0.821582\pi$
$823$	717167.	−	1.24217e6i	0.0369080	−	0.0639266i	0.883889	+	0.467696i	$0.154916\pi$
$824$	−1.33804e7	−	2.31755e7i	−0.686516	−	1.18908i
$825$		0			0
$826$	−596820.	+	1.72287e6i	−0.0304364	+	0.0878623i
$827$			2.58805e7i			1.31586i	0.753080	+	0.657929i	$0.228567\pi$
$827$			2.58805e7i			1.31586i	−0.753080	+	0.657929i	$0.771433\pi$
$828$		0			0
$829$	1.92235e7	+	1.10987e7i	0.971508	+	0.560901i	0.899696	−	0.436518i	$-0.143788\pi$
$829$	1.92235e7	+	1.10987e7i	0.971508	+	0.560901i	0.0718125	+	0.997418i	$0.477122\pi$
$830$	8.00879e6	+	4.62388e6i	0.403526	+	0.232976i
$831$		0			0
$832$		−	7.66647e6i		−	0.383961i
$833$	5.88711e6	−	2.35310e6i	0.293961	−	0.117497i
$834$		0			0
$835$	5.63025e6	+	9.75187e6i	0.279455	+	0.484030i
$836$	−1.20341e7	+	2.08437e7i	−0.595523	+	1.03148i
$837$		0			0
$838$	−1.60551e7	+	9.26943e6i	−0.789776	+	0.455977i
$839$	−2.56110e7			−1.25609			−0.628047	−	0.778175i	$-0.716146\pi$
$839$	−2.56110e7			−1.25609			−0.628047	+	0.778175i	$0.716146\pi$
$840$		0			0
$841$	−665883.			−0.0324644
$842$	−1.46947e7	+	8.48397e6i	−0.714298	+	0.412400i
$843$		0			0
$844$	−5.33652e6	+	9.24312e6i	−0.257871	+	0.446645i
$845$	−2.45721e7	−	4.25601e7i	−1.18386	−	2.05051i
$846$		0			0
$847$	4.25102e6	+	2.20889e7i	0.203603	+	1.05795i
$848$		−	2.37407e6i		−	0.113371i
$849$		0			0
$850$	442596.	+	255533.i	0.0210117	+	0.0121311i
$851$	810512.	+	467949.i	0.0383650	+	0.0221501i
$852$		0			0
$853$			3.68131e7i			1.73233i	0.499760	+	0.866164i	$0.333421\pi$
$853$			3.68131e7i			1.73233i	−0.499760	+	0.866164i	$0.666579\pi$
$854$	4.83269e6	−	4.18523e6i	0.226748	−	0.196370i
$855$		0			0
$856$	1.08571e7	+	1.88050e7i	0.506440	+	0.877179i
$857$	−9.12615e6	+	1.58070e7i	−0.424459	+	0.735184i	−0.996370	−	0.0851314i	$-0.972869\pi$
$857$	−9.12615e6	+	1.58070e7i	−0.424459	+	0.735184i	0.571911	+	0.820316i	$0.306202\pi$
$858$		0			0
$859$	−9.62482e6	+	5.55690e6i	−0.445051	+	0.256950i	−0.705738	−	0.708473i	$-0.749384\pi$
$859$	−9.62482e6	+	5.55690e6i	−0.445051	+	0.256950i	0.260687	+	0.965423i	$0.416051\pi$
$860$	−5.79865e6			−0.267350
$861$		0			0
$862$	1.48963e7			0.682827
$863$	3.34146e7	−	1.92920e7i	1.52725	−	0.881758i	0.527773	−	0.849385i	$-0.323027\pi$
$863$	3.34146e7	−	1.92920e7i	1.52725	−	0.881758i	0.999476	−	0.0323723i	$-0.0103062\pi$
$864$		0			0
$865$	2.52781e6	−	4.37830e6i	0.114869	−	0.198960i
$866$	−1.14550e6	−	1.98407e6i	−0.0519040	−	0.0899004i
$867$		0			0
$868$	6.92723e6	−	1.33315e6i	0.312076	−	0.0600590i
$869$		−	2.27808e7i		−	1.02334i
$870$		0			0
$871$	−3.01215e7	−	1.73907e7i	−1.34534	−	0.776731i
$872$	−2.83403e7	−	1.63623e7i	−1.26216	−	0.728706i
$873$		0			0
$874$			2.26085e7i			1.00114i
$875$	2.27099e7	+	7.86695e6i	1.00276	+	0.347365i
$876$		0			0
$877$	−1.14475e7	−	1.98276e7i	−0.502587	−	0.870507i	−0.999996	−	0.00299005i	$-0.999048\pi$
$877$	−1.14475e7	−	1.98276e7i	−0.502587	−	0.870507i	0.497408	−	0.867517i	$-0.334285\pi$
$878$	−7.66418e6	+	1.32747e7i	−0.335528	+	0.581152i
$879$		0			0
$880$	−8.24544e6	+	4.76051e6i	−0.358928	+	0.207227i
$881$	2.09177e7			0.907975			0.453987	−	0.891008i	$-0.350001\pi$
$881$	2.09177e7			0.907975			0.453987	+	0.891008i	$0.350001\pi$
$882$		0			0
$883$	−2.26473e7			−0.977497			−0.488748	−	0.872425i	$-0.662546\pi$
$883$	−2.26473e7			−0.977497			−0.488748	+	0.872425i	$0.662546\pi$
$884$	−9.03068e6	+	5.21387e6i	−0.388678	+	0.224403i
$885$		0			0
$886$	−3.99730e6	+	6.92353e6i	−0.171074	+	0.296308i
$887$	−2.41453e6	−	4.18210e6i	−0.103044	−	0.178478i	0.809893	−	0.586577i	$-0.199525\pi$
$887$	−2.41453e6	−	4.18210e6i	−0.103044	−	0.178478i	−0.912938	+	0.408099i	$0.866192\pi$
$888$		0			0
$889$	3.09790e6	+	1.07314e6i	0.131466	+	0.0455411i
$890$		−	1.53323e7i		−	0.648830i
$891$		0			0
$892$	5.95022e6	+	3.43536e6i	0.250392	+	0.144564i
$893$	−3.60178e7	−	2.07949e7i	−1.51143	−	0.872625i
$894$		0			0
$895$		−	1.78821e7i		−	0.746209i
$896$	−2.19386e7	+	4.22209e6i	−0.912935	+	0.175694i
$897$		0			0
$898$	−5.51460e6	−	9.55157e6i	−0.228204	−	0.395261i
$899$	−5.21678e6	+	9.03573e6i	−0.215280	+	0.372876i
$900$		0			0
$901$	2.42365e6	−	1.39930e6i	0.0994623	−	0.0574246i
$902$	140258.			0.00573998
$903$		0			0
$904$	1.11675e7			0.454502
$905$	1.22741e7	−	7.08643e6i	0.498157	−	0.287611i
$906$		0			0
$907$	5.95760e6	−	1.03189e7i	0.240466	−	0.416499i	−0.720381	−	0.693578i	$-0.756033\pi$
$907$	5.95760e6	−	1.03189e7i	0.240466	−	0.416499i	0.960847	+	0.277079i	$0.0893665\pi$
$908$	5.88692e6	+	1.01964e7i	0.236959	+	0.410425i
$909$		0			0
$910$	1.64228e7	−	1.42226e7i	0.657423	−	0.569345i
$911$		−	1.33120e7i		−	0.531432i	−0.964051	−	0.265716i	$-0.914392\pi$
$911$		−	1.33120e7i		−	0.531432i	0.964051	−	0.265716i	$-0.0856083\pi$
$912$		0			0
$913$	3.18394e7	+	1.83825e7i	1.26412	+	0.729840i
$914$	−1.58414e6	−	914604.i	−0.0627232	−	0.0362133i
$915$		0			0
$916$			2.20936e7i			0.870016i
$917$	3.56276e6	+	1.85127e7i	0.139915	+	0.727018i
$918$		0			0
$919$	−1.11617e7	−	1.93326e7i	−0.435954	−	0.755095i	0.561419	−	0.827532i	$-0.310256\pi$
$919$	−1.11617e7	−	1.93326e7i	−0.435954	−	0.755095i	−0.997373	+	0.0724369i	$0.976922\pi$
$920$	−1.87815e7	+	3.25305e7i	−0.731579	+	1.26713i
$921$		0			0
$922$	1.22256e7	−	7.05846e6i	0.473634	−	0.273453i
$923$	4.56258e6			0.176281
$924$		0			0
$925$	−97237.0			−0.00373661
$926$	1.57242e7	−	9.07838e6i	0.602617	−	0.347921i
$927$		0			0
$928$	1.37449e7	−	2.38069e7i	0.523928	−	0.907470i
$929$	4.78391e6	+	8.28598e6i	0.181863	+	0.314996i	0.942515	−	0.334164i	$-0.108454\pi$
$929$	4.78391e6	+	8.28598e6i	0.181863	+	0.314996i	−0.760652	+	0.649160i	$0.775121\pi$
$930$		0			0
$931$	−2.88408e7	−	4.16281e6i	−1.09052	−	0.157403i
$932$			3.03059e7i			1.14285i
$933$		0			0
$934$	1.14265e7	+	6.59708e6i	0.428593	+	0.247448i
$935$	−9.71986e6	−	5.61177e6i	−0.363606	−	0.209928i
$936$		0			0
$937$		−	6.81897e6i		−	0.253729i	−0.991920	−	0.126864i	$-0.959509\pi$
$937$		−	6.81897e6i		−	0.253729i	0.991920	−	0.126864i	$-0.0404913\pi$
$938$	3.62439e6	−	1.04627e7i	0.134502	−	0.388274i
$939$		0			0
$940$	−1.48070e7	−	2.56465e7i	−0.546573	−	0.946692i
$941$	1.28588e7	−	2.22720e7i	0.473396	−	0.819947i	−0.526140	−	0.850398i	$-0.676361\pi$
$941$	1.28588e7	−	2.22720e7i	0.473396	−	0.819947i	0.999536	+	0.0304514i	$0.00969449\pi$
$942$		0			0
$943$	−342300.	+	197627.i	−0.0125351	+	0.00723714i
$944$	−1.59119e6			−0.0581155
$945$		0			0
$946$	7.68429e6			0.279175
$947$	6.78965e6	−	3.92001e6i	0.246021	−	0.142040i	−0.371920	−	0.928265i	$-0.621300\pi$
$947$	6.78965e6	−	3.92001e6i	0.246021	−	0.142040i	0.617941	+	0.786224i	$0.287967\pi$
$948$		0			0
$949$	−3.07160e7	+	5.32017e7i	−1.10713	+	1.91761i
$950$	−1.17448e6	−	2.03426e6i	−0.0422217	−	0.0731302i
$951$		0			0
$952$	−5.07091e6	−	5.85538e6i	−0.181340	−	0.209393i
$953$			2.65199e7i			0.945888i	0.881092	+	0.472944i	$0.156809\pi$
$953$			2.65199e7i			0.945888i	−0.881092	+	0.472944i	$0.843191\pi$
$954$		0			0
$955$	−1.23704e7	−	7.14203e6i	−0.438909	−	0.253404i
$956$	1.50401e7	+	8.68338e6i	0.532236	+	0.307287i
$957$		0			0
$958$			2.21122e7i			0.778428i
$959$	2.85218e7	+	3.29341e7i	1.00145	+	1.15638i
$960$		0			0
$961$	−1.17444e7	−	2.03418e7i	−0.410224	−	0.710528i
$962$	−330669.	+	572735.i	−0.0115201	+	0.0199534i
$963$		0			0
$964$	−1.17996e7	+	6.81253e6i	−0.408956	+	0.236111i
$965$	1.18115e7			0.408308
$966$		0			0
$967$	1.56461e7			0.538070			0.269035	−	0.963130i	$-0.413295\pi$
$967$	1.56461e7			0.538070			0.269035	+	0.963130i	$0.413295\pi$
$968$	2.38008e7	−	1.37414e7i	0.816399	−	0.471348i
$969$		0			0
$970$	−149940.	+	259704.i	−0.00511668	+	0.00886235i
$971$	1.35593e7	+	2.34853e7i	0.461517	+	0.799371i	0.999037	−	0.0438801i	$-0.0139719\pi$
$971$	1.35593e7	+	2.34853e7i	0.461517	+	0.799371i	−0.537520	+	0.843251i	$0.680639\pi$
$972$		0			0
$973$	4.61558e6	−	1.33240e7i	0.156295	−	0.451184i
$974$			5.83268e6i			0.197002i
$975$		0			0
$976$	4.83168e6	+	2.78957e6i	0.162358	+	0.0937374i
$977$	2.10473e7	+	1.21517e7i	0.705441	+	0.407286i	0.809371	−	0.587298i	$-0.199808\pi$
$977$	2.10473e7	+	1.21517e7i	0.705441	+	0.407286i	−0.103930	+	0.994585i	$0.533142\pi$
$978$		0			0
$979$		−	6.09543e7i		−	2.03258i
$980$	−1.63028e7	−	1.28351e7i	−0.542245	−	0.426907i
$981$		0			0
$982$	−5.62074e6	−	9.73540e6i	−0.186001	−	0.322163i
$983$	−6.51412e6	+	1.12828e7i	−0.215016	+	0.372419i	−0.953278	−	0.302095i	$-0.902314\pi$
$983$	−6.51412e6	+	1.12828e7i	−0.215016	+	0.372419i	0.738261	+	0.674515i	$0.235647\pi$
$984$		0			0
$985$	−938826.	+	542031.i	−0.0308315	+	0.0178006i
$986$	4.90991e6			0.160835
$987$		0			0
$988$	4.79279e7			1.56205
$989$	−1.87536e7	+	1.08274e7i	−0.609668	+	0.351992i
$990$		0			0
$991$	1.63738e7	−	2.83602e7i	0.529621	−	0.917330i	−0.469782	−	0.882782i	$-0.655668\pi$
$991$	1.63738e7	−	2.83602e7i	0.529621	−	0.917330i	0.999403	−	0.0345478i	$-0.0109991\pi$
$992$	−6.77188e6	−	1.17292e7i	−0.218489	−	0.378434i
$993$		0			0
$994$	274498.	+	1.42633e6i	0.00881197	+	0.0457884i
$995$		−	2.63936e7i		−	0.845165i
$996$		0			0
$997$	1.87488e7	+	1.08246e7i	0.597358	+	0.344885i	0.768002	−	0.640448i	$-0.221251\pi$
$997$	1.87488e7	+	1.08246e7i	0.597358	+	0.344885i	−0.170643	+	0.985333i	$0.554585\pi$
$998$	6.75211e6	+	3.89833e6i	0.214592	+	0.123895i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.p.a.17.1	✓	4
3.2	odd	2	inner	63.6.p.a.17.2	yes	4
7.3	odd	6		441.6.c.a.440.2		4
7.4	even	3		441.6.c.a.440.1		4
7.5	odd	6	inner	63.6.p.a.26.2	yes	4
21.5	even	6	inner	63.6.p.a.26.1	yes	4
21.11	odd	6		441.6.c.a.440.4		4
21.17	even	6		441.6.c.a.440.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.p.a.17.1	✓	4	1.1	even	1	trivial
63.6.p.a.17.2	yes	4	3.2	odd	2	inner
63.6.p.a.26.1	yes	4	21.5	even	6	inner
63.6.p.a.26.2	yes	4	7.5	odd	6	inner
441.6.c.a.440.1		4	7.4	even	3
441.6.c.a.440.2		4	7.3	odd	6
441.6.c.a.440.3		4	21.17	even	6
441.6.c.a.440.4		4	21.11	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44949 + 1.41421i) q^{2} +(-12.0000 + 20.7846i) q^{4} +(25.7196 + 44.5477i) q^{5} +(122.500 + 42.4352i) q^{7} -158.392i q^{8} +O(q^{10})\)	\(q+(-2.44949 + 1.41421i) q^{2} +(-12.0000 + 20.7846i) q^{4} +(25.7196 + 44.5477i) q^{5} +(122.500 + 42.4352i) q^{7} -158.392i q^{8} +(-126.000 - 72.7461i) q^{10} +(-500.921 - 289.207i) q^{11} +1151.81i q^{13} +(-360.075 + 69.2965i) q^{14} +(-160.000 - 277.128i) q^{16} +(188.611 - 326.683i) q^{17} +(-1501.50 + 866.891i) q^{19} -1234.54 q^{20} +1636.00 q^{22} +(-3992.67 + 2305.17i) q^{23} +(239.500 - 414.826i) q^{25} +(-1628.91 - 2821.36i) q^{26} +(-2352.00 + 2036.89i) q^{28} -4601.85i q^{29} +(-1963.50 - 1133.63i) q^{31} +(5173.32 + 2986.82i) q^{32} +1066.94i q^{34} +(1260.26 + 6548.52i) q^{35} +(-101.500 - 175.803i) q^{37} +(2451.94 - 4246.88i) q^{38} +(7056.00 - 4073.78i) q^{40} +85.7321 q^{41} +4697.00 q^{43} +(12022.1 - 6940.96i) q^{44} +(6520.00 - 11293.0i) q^{46} +(11993.9 + 20774.1i) q^{47} +(13205.5 + 10396.6i) q^{49} +1354.82i q^{50} +(-23940.0 - 13821.8i) q^{52} +(6425.01 + 3709.48i) q^{53} -29753.2i q^{55} +(6721.40 - 19403.0i) q^{56} +(6508.00 + 11272.2i) q^{58} +(2486.23 - 4306.28i) q^{59} +(-15099.0 + 8717.41i) q^{61} +6412.76 q^{62} -6656.00 q^{64} +(-51310.7 + 29624.2i) q^{65} +(-15098.5 + 26151.4i) q^{67} +(4526.66 + 7840.40i) q^{68} +(-12348.0 - 14258.2i) q^{70} -3961.21i q^{71} +(46189.5 + 26667.5i) q^{73} +(497.246 + 287.085i) q^{74} -41610.8i q^{76} +(-49090.2 - 56684.5i) q^{77} +(19692.5 + 34108.4i) q^{79} +(8230.29 - 14255.3i) q^{80} +(-210.000 + 121.244i) q^{82} -63561.8 q^{83} +19404.0 q^{85} +(-11505.3 + 6642.56i) q^{86} +(-45808.0 + 79341.8i) q^{88} +(52691.0 + 91263.4i) q^{89} +(-48877.5 + 141097. i) q^{91} -110648. i q^{92} +(-58758.0 - 33923.9i) q^{94} +(-77236.1 - 44592.3i) q^{95} -2061.14i q^{97} +(-47049.8 - 6791.05i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 48 q^{4} + 490 q^{7}+O(q^{10}) \) 4 * q - 48 * q^4 + 490 * q^7	\( 4 q - 48 q^{4} + 490 q^{7} - 504 q^{10} - 640 q^{16} - 6006 q^{19} + 6544 q^{22} + 958 q^{25} - 9408 q^{28} - 7854 q^{31} - 406 q^{37} + 28224 q^{40} + 18788 q^{43} + 26080 q^{46} + 52822 q^{49} - 95760 q^{52} + 26032 q^{58} - 60396 q^{61} - 26624 q^{64} - 60394 q^{67} - 49392 q^{70} + 184758 q^{73} + 78770 q^{79} - 840 q^{82} + 77616 q^{85} - 183232 q^{88} - 195510 q^{91} - 235032 q^{94}+O(q^{100}) \) 4 * q - 48 * q^4 + 490 * q^7 - 504 * q^10 - 640 * q^16 - 6006 * q^19 + 6544 * q^22 + 958 * q^25 - 9408 * q^28 - 7854 * q^31 - 406 * q^37 + 28224 * q^40 + 18788 * q^43 + 26080 * q^46 + 52822 * q^49 - 95760 * q^52 + 26032 * q^58 - 60396 * q^61 - 26624 * q^64 - 60394 * q^67 - 49392 * q^70 + 184758 * q^73 + 78770 * q^79 - 840 * q^82 + 77616 * q^85 - 183232 * q^88 - 195510 * q^91 - 235032 * q^94

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