LMFDB - Embedded newform 294.6.d.a.293.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(293,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("294.293");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.9
Character	$\chi$	$=$	294.293
Dual form			294.6.d.a.293.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000i q^{2} +(9.81768 - 12.1084i) q^{3} -16.0000 q^{4} -51.7855 q^{5} +(-48.4336 - 39.2707i) q^{6} +64.0000i q^{8} +(-50.2262 - 237.753i) q^{9} +207.142i q^{10} +453.242i q^{11} +(-157.083 + 193.734i) q^{12} -645.676i q^{13} +(-508.414 + 627.039i) q^{15} +256.000 q^{16} -834.812 q^{17} +(-951.011 + 200.905i) q^{18} +2066.63i q^{19} +828.569 q^{20} +1812.97 q^{22} +754.622i q^{23} +(774.937 + 628.332i) q^{24} -443.258 q^{25} -2582.70 q^{26} +(-3371.91 - 1726.02i) q^{27} +1454.53i q^{29} +(2508.16 + 2033.66i) q^{30} +3988.18i q^{31} -1024.00i q^{32} +(5488.03 + 4449.79i) q^{33} +3339.25i q^{34} +(803.619 + 3804.04i) q^{36} +15483.8 q^{37} +8266.53 q^{38} +(-7818.10 - 6339.04i) q^{39} -3314.27i q^{40} +19408.4 q^{41} -6770.34 q^{43} -7251.87i q^{44} +(2600.99 + 12312.2i) q^{45} +3018.49 q^{46} +5360.97 q^{47} +(2513.33 - 3099.75i) q^{48} +1773.03i q^{50} +(-8195.92 + 10108.2i) q^{51} +10330.8i q^{52} +34824.1i q^{53} +(-6904.09 + 13487.6i) q^{54} -23471.4i q^{55} +(25023.6 + 20289.5i) q^{57} +5818.10 q^{58} +4908.90 q^{59} +(8134.62 - 10032.6i) q^{60} -33592.3i q^{61} +15952.7 q^{62} -4096.00 q^{64} +33436.7i q^{65} +(17799.1 - 21952.1i) q^{66} -27503.9 q^{67} +13357.0 q^{68} +(9137.26 + 7408.64i) q^{69} +44855.5i q^{71} +(15216.2 - 3214.47i) q^{72} -81855.7i q^{73} -61935.0i q^{74} +(-4351.77 + 5367.14i) q^{75} -33066.1i q^{76} +(-25356.2 + 31272.4i) q^{78} -33844.3 q^{79} -13257.1 q^{80} +(-54003.7 + 23882.8i) q^{81} -77633.5i q^{82} -9450.81 q^{83} +43231.2 q^{85} +27081.3i q^{86} +(17612.0 + 14280.1i) q^{87} -29007.5 q^{88} +88428.0 q^{89} +(49248.6 - 10404.0i) q^{90} -12074.0i q^{92} +(48290.4 + 39154.7i) q^{93} -21443.9i q^{94} -107022. i q^{95} +(-12399.0 - 10053.3i) q^{96} +10166.3i q^{97} +(107759. - 22764.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 448 q^{4} + 60 q^{9} - 516 q^{15} + 7168 q^{16} - 3264 q^{18} + 3312 q^{22} + 26416 q^{25} - 4896 q^{30} - 960 q^{36} - 10976 q^{37} - 43776 q^{39} - 40352 q^{43} + 23136 q^{46} + 69144 q^{51} + 57168 q^{57}+ \cdots + 153216 q^{99}+O(q^{100}) $ 28 * q - 448 * q^4 + 60 * q^9 - 516 * q^15 + 7168 * q^16 - 3264 * q^18 + 3312 * q^22 + 26416 * q^25 - 4896 * q^30 - 960 * q^36 - 10976 * q^37 - 43776 * q^39 - 40352 * q^43 + 23136 * q^46 + 69144 * q^51 + 57168 * q^57 - 85104 * q^58 + 8256 * q^60 - 114688 * q^64 - 110296 * q^67 + 52224 * q^72 + 87840 * q^78 - 943588 * q^79 + 491076 * q^81 - 562056 * q^85 - 52992 * q^88 + 1120896 * q^93 + 153216 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$	9.81768	−	12.1084i	0.629805	−	0.776754i
$3$	9.81768	−	12.1084i	0.629805	−	0.776754i
$4$	−16.0000			−0.500000
$5$	−51.7855			−0.926368			−0.463184	−	0.886262i	$-0.653293\pi$
$5$	−51.7855			−0.926368			−0.463184	+	0.886262i	$0.653293\pi$
$6$	−48.4336	−	39.2707i	−0.549248	−	0.445339i
$7$		0			0
$7$		0			0
$8$			64.0000i			0.353553i
$9$	−50.2262	−	237.753i	−0.206692	−	0.978406i
$10$			207.142i			0.655041i
$11$			453.242i			1.12940i	0.825296	+	0.564701i	$0.191008\pi$
$11$			453.242i			1.12940i	−0.825296	+	0.564701i	$0.808992\pi$
$12$	−157.083	+	193.734i	−0.314902	+	0.388377i
$13$		−	645.676i		−	1.05964i	−0.848112	−	0.529818i	$-0.822260\pi$
$13$		−	645.676i		−	1.05964i	0.848112	−	0.529818i	$-0.177740\pi$
$14$		0			0
$15$	−508.414	+	627.039i	−0.583431	+	0.719560i
$16$	256.000			0.250000
$17$	−834.812			−0.700594			−0.350297	−	0.936639i	$-0.613919\pi$
$17$	−834.812			−0.700594			−0.350297	+	0.936639i	$0.613919\pi$
$18$	−951.011	+	200.905i	−0.691838	+	0.146153i
$19$			2066.63i			1.31335i	0.754175	+	0.656673i	$0.228037\pi$
$19$			2066.63i			1.31335i	−0.754175	+	0.656673i	$0.771963\pi$
$20$	828.569			0.463184
$21$		0			0
$22$	1812.97			0.798608
$23$			754.622i			0.297447i	0.988879	+	0.148724i	$0.0475165\pi$
$23$			754.622i			0.297447i	−0.988879	+	0.148724i	$0.952484\pi$
$24$	774.937	+	628.332i	0.274624	+	0.222670i
$25$	−443.258			−0.141843
$26$	−2582.70			−0.749275
$27$	−3371.91	−	1726.02i	−0.890156	−	0.455656i
$28$		0			0
$29$			1454.53i			0.321164i	0.987023	+	0.160582i	$0.0513370\pi$
$29$			1454.53i			0.321164i	−0.987023	+	0.160582i	$0.948663\pi$
$30$	2508.16	+	2033.66i	0.508805	+	0.412548i
$31$			3988.18i			0.745367i	0.927959	+	0.372684i	$0.121562\pi$
$31$			3988.18i			0.745367i	−0.927959	+	0.372684i	$0.878438\pi$
$32$		−	1024.00i		−	0.176777i
$33$	5488.03	+	4449.79i	0.877267	+	0.711302i
$34$			3339.25i			0.495394i
$35$		0			0
$36$	803.619	+	3804.04i	0.103346	+	0.489203i
$37$	15483.8			1.85940			0.929698	−	0.368323i	$-0.120068\pi$
$37$	15483.8			1.85940			0.929698	+	0.368323i	$0.120068\pi$
$38$	8266.53			0.928676
$39$	−7818.10	−	6339.04i	−0.823075	−	0.667363i
$40$		−	3314.27i		−	0.327521i
$41$	19408.4			1.80314			0.901570	−	0.432633i	$-0.142415\pi$
$41$	19408.4			1.80314			0.901570	+	0.432633i	$0.142415\pi$
$42$		0			0
$43$	−6770.34			−0.558392			−0.279196	−	0.960234i	$-0.590068\pi$
$43$	−6770.34			−0.558392			−0.279196	+	0.960234i	$0.590068\pi$
$44$		−	7251.87i		−	0.564701i
$45$	2600.99	+	12312.2i	0.191473	+	0.906364i
$46$	3018.49			0.210327
$47$	5360.97			0.353996			0.176998	−	0.984211i	$-0.443361\pi$
$47$	5360.97			0.353996			0.176998	+	0.984211i	$0.443361\pi$
$48$	2513.33	−	3099.75i	0.157451	−	0.194188i
$49$		0			0
$50$			1773.03i			0.100298i
$51$	−8195.92	+	10108.2i	−0.441237	+	0.544189i
$52$			10330.8i			0.529818i
$53$			34824.1i			1.70290i	0.524433	+	0.851452i	$0.324277\pi$
$53$			34824.1i			1.70290i	−0.524433	+	0.851452i	$0.675723\pi$
$54$	−6904.09	+	13487.6i	−0.322197	+	0.629435i
$55$		−	23471.4i		−	1.04624i
$56$		0			0
$57$	25023.6	+	20289.5i	1.02015	+	0.827151i
$58$	5818.10			0.227097
$59$	4908.90			0.183592			0.0917961	−	0.995778i	$-0.470739\pi$
$59$	4908.90			0.183592			0.0917961	+	0.995778i	$0.470739\pi$
$60$	8134.62	−	10032.6i	0.291715	−	0.359780i
$61$		−	33592.3i		−	1.15589i	−0.816077	−	0.577944i	$-0.803855\pi$
$61$		−	33592.3i		−	1.15589i	0.816077	−	0.577944i	$-0.196145\pi$
$62$	15952.7			0.527054
$63$		0			0
$64$	−4096.00			−0.125000
$65$			33436.7i			0.981612i
$66$	17799.1	−	21952.1i	0.502967	−	0.620321i
$67$	−27503.9			−0.748527			−0.374264	−	0.927322i	$-0.622104\pi$
$67$	−27503.9			−0.748527			−0.374264	+	0.927322i	$0.622104\pi$
$68$	13357.0			0.350297
$69$	9137.26	+	7408.64i	0.231043	+	0.187334i
$70$		0			0
$71$			44855.5i			1.05601i	0.849240	+	0.528007i	$0.177061\pi$
$71$			44855.5i			1.05601i	−0.849240	+	0.528007i	$0.822939\pi$
$72$	15216.2	−	3214.47i	0.345919	−	0.0730767i
$73$		−	81855.7i		−	1.79780i	−0.438153	−	0.898900i	$-0.644367\pi$
$73$		−	81855.7i		−	1.79780i	0.438153	−	0.898900i	$-0.355633\pi$
$74$		−	61935.0i		−	1.31479i
$75$	−4351.77	+	5367.14i	−0.0893331	+	0.110177i
$76$		−	33066.1i		−	0.656673i
$77$		0			0
$78$	−25356.2	+	31272.4i	−0.471897	+	0.582002i
$79$	−33844.3			−0.610124			−0.305062	−	0.952333i	$-0.598677\pi$
$79$	−33844.3			−0.610124			−0.305062	+	0.952333i	$0.598677\pi$
$80$	−13257.1			−0.231592
$81$	−54003.7	+	23882.8i	−0.914557	+	0.404457i
$82$		−	77633.5i		−	1.27501i
$83$	−9450.81			−0.150582			−0.0752911	−	0.997162i	$-0.523989\pi$
$83$	−9450.81			−0.150582			−0.0752911	+	0.997162i	$0.523989\pi$
$84$		0			0
$85$	43231.2			0.649007
$86$			27081.3i			0.394843i
$87$	17612.0	+	14280.1i	0.249465	+	0.202270i
$88$	−29007.5			−0.399304
$89$	88428.0			1.18335			0.591677	−	0.806175i	$-0.298466\pi$
$89$	88428.0			1.18335			0.591677	+	0.806175i	$0.298466\pi$
$90$	49248.6	−	10404.0i	0.640896	−	0.135392i
$91$		0			0
$92$		−	12074.0i		−	0.148724i
$93$	48290.4	+	39154.7i	0.578966	+	0.469436i
$94$		−	21443.9i		−	0.250313i
$95$		−	107022.i		−	1.21664i
$96$	−12399.0	−	10053.3i	−0.137312	−	0.111335i
$97$			10166.3i			0.109707i	0.998494	+	0.0548534i	$0.0174691\pi$
$97$			10166.3i			0.109707i	−0.998494	+	0.0548534i	$0.982531\pi$
$98$		0			0
$99$	107759.	−	22764.6i	1.10501	−	0.233438i
$100$	7092.13			0.0709213
$101$	−33793.4			−0.329631			−0.164816	−	0.986324i	$-0.552703\pi$
$101$	−33793.4			−0.329631			−0.164816	+	0.986324i	$0.552703\pi$
$102$	40432.9	+	32783.7i	0.384799	+	0.312002i
$103$			124679.i			1.15798i	0.815334	+	0.578991i	$0.196553\pi$
$103$			124679.i			1.15798i	−0.815334	+	0.578991i	$0.803447\pi$
$104$	41323.3			0.374638
$105$		0			0
$106$	139296.			1.20413
$107$			118610.i			1.00153i	0.865584	+	0.500764i	$0.166948\pi$
$107$			118610.i			1.00153i	−0.865584	+	0.500764i	$0.833052\pi$
$108$	53950.5	+	27616.4i	0.445078	+	0.227828i
$109$	38236.1			0.308253			0.154127	−	0.988051i	$-0.450744\pi$
$109$	38236.1			0.308253			0.154127	+	0.988051i	$0.450744\pi$
$110$	−93885.5			−0.739804
$111$	152015.	−	187483.i	1.17106	−	1.44429i
$112$		0			0
$113$			144560.i			1.06500i	0.846429	+	0.532502i	$0.178748\pi$
$113$			144560.i			1.06500i	−0.846429	+	0.532502i	$0.821252\pi$
$114$	81158.2	−	100094.i	0.584884	−	0.721352i
$115$		−	39078.5i		−	0.275546i
$116$		−	23272.4i		−	0.160582i
$117$	−153511.	+	32429.8i	−1.03675	+	0.219018i
$118$		−	19635.6i		−	0.129819i
$119$		0			0
$120$	−40130.5	−	32538.5i	−0.254403	−	0.206274i
$121$	−44377.3			−0.275548
$122$	−134369.			−0.817336
$123$	190545.	−	235004.i	1.13563	−	1.40060i
$124$		−	63810.8i		−	0.372684i
$125$	184784.			1.05777
$126$		0			0
$127$	107284.			0.590237			0.295118	−	0.955461i	$-0.404641\pi$
$127$	107284.			0.590237			0.295118	+	0.955461i	$0.404641\pi$
$128$			16384.0i			0.0883883i
$129$	−66469.0	+	81977.9i	−0.351678	+	0.433733i
$130$	133747.			0.694105
$131$	147808.			0.752522			0.376261	−	0.926514i	$-0.377210\pi$
$131$	147808.			0.752522			0.376261	+	0.926514i	$0.377210\pi$
$132$	−87808.5	−	71196.6i	−0.438633	−	0.355651i
$133$		0			0
$134$			110016.i			0.529289i
$135$	174616.	+	89383.0i	0.824612	+	0.422105i
$136$		−	53427.9i		−	0.247697i
$137$			287912.i			1.31057i	0.755383	+	0.655283i	$0.227451\pi$
$137$			287912.i			1.31057i	−0.755383	+	0.655283i	$0.772549\pi$
$138$	29634.6	−	36549.0i	0.132465	−	0.163372i
$139$		−	34769.7i		−	0.152638i	−0.997083	−	0.0763192i	$-0.975683\pi$
$139$		−	34769.7i		−	0.152638i	0.997083	−	0.0763192i	$-0.0243168\pi$
$140$		0			0
$141$	52632.3	−	64912.7i	0.222948	−	0.274968i
$142$	179422.			0.746715
$143$	292648.			1.19675
$144$	−12857.9	−	60864.7i	−0.0516730	−	0.244602i
$145$		−	75323.4i		−	0.297516i
$146$	−327423.			−1.27124
$147$		0			0
$148$	−247740.			−0.929698
$149$			167696.i			0.618810i	0.950930	+	0.309405i	$0.100130\pi$
$149$			167696.i			0.618810i	−0.950930	+	0.309405i	$0.899870\pi$
$150$	21468.6	+	17407.1i	0.0779067	+	0.0631680i
$151$	−456147.			−1.62803			−0.814015	−	0.580843i	$-0.802723\pi$
$151$	−456147.			−1.62803			−0.814015	+	0.580843i	$0.802723\pi$
$152$	−132264.			−0.464338
$153$	41929.4	+	198479.i	0.144807	+	0.685465i
$154$		0			0
$155$		−	206530.i		−	0.690484i
$156$	125090.	+	101425.i	0.411538	+	0.333682i
$157$			182676.i			0.591471i	0.955270	+	0.295736i	$0.0955647\pi$
$157$			182676.i			0.591471i	−0.955270	+	0.295736i	$0.904435\pi$
$158$			135377.i			0.431422i
$159$	421664.	+	341892.i	1.32274	+	1.07250i
$160$			53028.4i			0.163760i
$161$		0			0
$162$	95531.2	+	216015.i	0.285995	+	0.646689i
$163$	−505273.			−1.48956			−0.744778	−	0.667312i	$-0.767445\pi$
$163$	−505273.			−1.48956			−0.744778	+	0.667312i	$0.767445\pi$
$164$	−310534.			−0.901570
$165$	−284201.	−	230435.i	−0.812672	−	0.658928i
$166$			37803.2i			0.106478i
$167$	−219889.			−0.610116			−0.305058	−	0.952334i	$-0.598676\pi$
$167$	−219889.			−0.610116			−0.305058	+	0.952334i	$0.598676\pi$
$168$		0			0
$169$	−45604.7			−0.122827
$170$		−	172925.i		−	0.458918i
$171$	491347.	−	103799.i	1.28499	−	0.271458i
$172$	108325.			0.279196
$173$	−143085.			−0.363480			−0.181740	−	0.983347i	$-0.558173\pi$
$173$	−143085.			−0.363480			−0.181740	+	0.983347i	$0.558173\pi$
$174$	57120.3	−	70447.8i	0.143027	−	0.176398i
$175$		0			0
$176$			116030.i			0.282350i
$177$	48194.0	−	59438.9i	0.115627	−	0.142606i
$178$		−	353712.i		−	0.836758i
$179$			764119.i			1.78250i	0.453516	+	0.891248i	$0.350169\pi$
$179$			764119.i			1.78250i	−0.453516	+	0.891248i	$0.649831\pi$
$180$	−41615.8	−	196994.i	−0.0957364	−	0.453182i
$181$			186403.i			0.422918i	0.977387	+	0.211459i	$0.0678215\pi$
$181$			186403.i			0.422918i	−0.977387	+	0.211459i	$0.932179\pi$
$182$		0			0
$183$	−406749.	−	329799.i	−0.897840	−	0.727983i
$184$	−48295.8			−0.105163
$185$	−801834.			−1.72248
$186$	156619.	−	193162.i	0.331941	−	0.409391i
$187$		−	378372.i		−	0.791252i
$188$	−85775.4			−0.176998
$189$		0			0
$190$	−428087.			−0.860295
$191$		−	659693.i		−	1.30845i	−0.756298	−	0.654227i	$-0.772994\pi$
$191$		−	659693.i		−	1.30845i	0.756298	−	0.654227i	$-0.227006\pi$
$192$	−40213.2	+	49596.0i	−0.0787256	+	0.0970942i
$193$	20527.9			0.0396691			0.0198345	−	0.999803i	$-0.493686\pi$
$193$	20527.9			0.0396691			0.0198345	+	0.999803i	$0.493686\pi$
$194$	40665.2			0.0775744
$195$	404864.	+	328271.i	0.762471	+	0.618224i
$196$		0			0
$197$		−	558536.i		−	1.02538i	−0.858573	−	0.512691i	$-0.828649\pi$
$197$		−	558536.i		−	1.02538i	0.858573	−	0.512691i	$-0.171351\pi$
$198$	−91058.4	−	431038.i	−0.165066	−	0.781362i
$199$			245715.i			0.439844i	0.975517	+	0.219922i	$0.0705803\pi$
$199$			245715.i			0.439844i	−0.975517	+	0.219922i	$0.929420\pi$
$200$		−	28368.5i		−	0.0501489i
$201$	−270025.	+	333028.i	−0.471426	+	0.581421i
$202$			135174.i			0.233084i
$203$		0			0
$204$	131135.	−	161732.i	0.220619	−	0.272094i
$205$	−1.00507e6			−1.67037
$206$	498718.			0.818817
$207$	179413.	−	37901.8i	0.291024	−	0.0614800i
$208$		−	165293.i		−	0.264909i
$209$	−936684.			−1.48330
$210$		0			0
$211$	−475438.			−0.735170			−0.367585	−	0.929990i	$-0.619815\pi$
$211$	−475438.			−0.735170			−0.367585	+	0.929990i	$0.619815\pi$
$212$		−	557186.i		−	0.851452i
$213$	543128.	+	440377.i	0.820263	+	0.665083i
$214$	474442.			0.708188
$215$	350605.			0.517276
$216$	110465.	−	215802.i	0.161099	−	0.314718i
$217$		0			0
$218$		−	152945.i		−	0.217968i
$219$	−991140.	−	803633.i	−1.39645	−	1.13226i
$220$			375542.i			0.523121i
$221$			539018.i			0.742374i
$222$	−749933.	−	608058.i	−1.02127	−	0.828062i
$223$			1.17495e6i			1.58219i	0.611695	+	0.791094i	$0.290488\pi$
$223$			1.17495e6i			1.58219i	−0.611695	+	0.791094i	$0.709512\pi$
$224$		0			0
$225$	22263.1	+	105386.i	0.0293177	+	0.138780i
$226$	578238.			0.753071
$227$	−226179.			−0.291331			−0.145666	−	0.989334i	$-0.546532\pi$
$227$	−226179.			−0.291331			−0.145666	+	0.989334i	$0.546532\pi$
$228$	−400377.	−	324633.i	−0.510073	−	0.413576i
$229$			781225.i			0.984436i	0.870472	+	0.492218i	$0.163814\pi$
$229$			781225.i			0.984436i	−0.870472	+	0.492218i	$0.836186\pi$
$230$	−156314.			−0.194840
$231$		0			0
$232$	−93089.6			−0.113548
$233$			1.57982e6i			1.90642i	0.302306	+	0.953211i	$0.402244\pi$
$233$			1.57982e6i			1.90642i	−0.302306	+	0.953211i	$0.597756\pi$
$234$	129719.	+	614045.i	0.154869	+	0.733095i
$235$	−277620.			−0.327931
$236$	−78542.4			−0.0917961
$237$	−332273.	+	409800.i	−0.384259	+	0.473916i
$238$		0			0
$239$			1.06612e6i			1.20729i	0.797254	+	0.603644i	$0.206285\pi$
$239$			1.06612e6i			1.20729i	−0.797254	+	0.603644i	$0.793715\pi$
$240$	−130154.	+	160522.i	−0.145858	+	0.179890i
$241$		−	288887.i		−	0.320395i	−0.987085	−	0.160197i	$-0.948787\pi$
$241$		−	288887.i		−	0.320395i	0.987085	−	0.160197i	$-0.0512131\pi$
$242$			177509.i			0.194842i
$243$	−241009.	+	888371.i	−0.261828	+	0.965114i
$244$			537477.i			0.577944i
$245$		0			0
$246$	−940017.	−	762181.i	−0.990371	−	0.803009i
$247$	1.33437e6			1.39167
$248$	−255243.			−0.263527
$249$	−92785.0	+	114434.i	−0.0948374	+	0.116965i
$250$		−	739137.i		−	0.747954i
$251$	−1.78066e6			−1.78401			−0.892003	−	0.452030i	$-0.850700\pi$
$251$	−1.78066e6			−1.78401			−0.892003	+	0.452030i	$0.850700\pi$
$252$		0			0
$253$	−342026.			−0.335937
$254$		−	429136.i		−	0.417360i
$255$	424430.	−	523460.i	0.408748	−	0.504119i
$256$	65536.0			0.0625000
$257$	1.37352e6			1.29718			0.648591	−	0.761137i	$-0.275359\pi$
$257$	1.37352e6			1.29718			0.648591	+	0.761137i	$0.275359\pi$
$258$	327911.	+	265876.i	0.306695	+	0.248674i
$259$		0			0
$260$		−	534987.i		−	0.490806i
$261$	345817.	−	73055.2i	0.314228	−	0.0663820i
$262$		−	591231.i		−	0.532113i
$263$			468938.i			0.418048i	0.977910	+	0.209024i	$0.0670287\pi$
$263$			468938.i			0.418048i	−0.977910	+	0.209024i	$0.932971\pi$
$264$	−284786.	+	351234.i	−0.251483	+	0.310161i
$265$		−	1.80338e6i		−	1.57752i
$266$		0			0
$267$	868158.	−	1.07072e6i	0.745282	−	0.919175i
$268$	440063.			0.374264
$269$	−2.22292e6			−1.87302			−0.936511	−	0.350638i	$-0.885965\pi$
$269$	−2.22292e6			−1.87302			−0.936511	+	0.350638i	$0.885965\pi$
$270$	357532.	−	698464.i	0.298473	−	0.583089i
$271$			259965.i			0.215026i	0.994204	+	0.107513i	$0.0342888\pi$
$271$			259965.i			0.215026i	−0.994204	+	0.107513i	$0.965711\pi$
$272$	−213712.			−0.175148
$273$		0			0
$274$	1.15165e6			0.926710
$275$		−	200903.i		−	0.160197i
$276$	−146196.	−	118538.i	−0.115522	−	0.0936668i
$277$	1.39166e6			1.08977			0.544885	−	0.838511i	$-0.316573\pi$
$277$	1.39166e6			1.08977			0.544885	+	0.838511i	$0.316573\pi$
$278$	−139079.			−0.107932
$279$	948200.	−	200311.i	0.729272	−	0.154061i
$280$		0			0
$281$		−	1.81463e6i		−	1.37095i	−0.728096	−	0.685475i	$-0.759594\pi$
$281$		−	1.81463e6i		−	1.37095i	0.728096	−	0.685475i	$-0.240406\pi$
$282$	−259651.	−	210529.i	−0.194431	−	0.157648i
$283$			1.14413e6i			0.849200i	0.905381	+	0.424600i	$0.139585\pi$
$283$			1.14413e6i			0.849200i	−0.905381	+	0.424600i	$0.860415\pi$
$284$		−	717688.i		−	0.528007i
$285$	−1.29586e6	−	1.05070e6i	−0.945031	−	0.766247i
$286$		−	1.17059e6i		−	0.846233i
$287$		0			0
$288$	−243459.	+	51431.6i	−0.172959	+	0.0365383i
$289$	−722947.			−0.509169
$290$	−301293.			−0.210375
$291$	123097.	+	99809.4i	0.0852151	+	0.0690938i
$292$			1.30969e6i			0.898900i
$293$	29080.6			0.0197895			0.00989475	−	0.999951i	$-0.496850\pi$
$293$	29080.6			0.0197895			0.00989475	+	0.999951i	$0.496850\pi$
$294$		0			0
$295$	−254210.			−0.170074
$296$			990960.i			0.657396i
$297$	782306.	−	1.52829e6i	0.514619	−	1.00534i
$298$	670784.			0.437565
$299$	487241.			0.315186
$300$	69628.3	−	85874.2i	0.0446665	−	0.0550883i
$301$		0			0
$302$			1.82459e6i			1.15119i
$303$	−331773.	+	409183.i	−0.207603	+	0.256042i
$304$			529058.i			0.328336i
$305$			1.73960e6i			1.07078i
$306$	793915.	−	167718.i	0.484697	−	0.102394i
$307$			193469.i			0.117156i	0.998283	+	0.0585780i	$0.0186566\pi$
$307$			193469.i			0.117156i	−0.998283	+	0.0585780i	$0.981343\pi$
$308$		0			0
$309$	1.50967e6	+	1.22406e6i	0.899466	+	0.729302i
$310$	−826120.			−0.488246
$311$	−2.55667e6			−1.49890			−0.749451	−	0.662060i	$-0.769683\pi$
$311$	−2.55667e6			−1.49890			−0.749451	+	0.662060i	$0.769683\pi$
$312$	405699.	−	500358.i	0.235949	−	0.291001i
$313$			423190.i			0.244160i	0.992520	+	0.122080i	$0.0389564\pi$
$313$			423190.i			0.244160i	−0.992520	+	0.122080i	$0.961044\pi$
$314$	730706.			0.418233
$315$		0			0
$316$	541509.			0.305062
$317$		−	36170.8i		−	0.0202167i	−0.999949	−	0.0101083i	$-0.996782\pi$
$317$		−	36170.8i		−	0.0202167i	0.999949	−	0.0101083i	$-0.00321764\pi$
$318$	1.36757e6	−	1.68665e6i	0.758370	−	0.935316i
$319$	−659252.			−0.362723
$320$	212114.			0.115796
$321$	1.43618e6	+	1.16448e6i	0.777941	+	0.630767i
$322$		0			0
$323$		−	1.72525e6i		−	0.920122i
$324$	864059.	−	382125.i	0.457278	−	0.202229i
$325$			286201.i			0.150301i
$326$			2.02109e6i			1.05328i
$327$	375390.	−	462978.i	0.194139	−	0.239437i
$328$			1.24214e6i			0.637506i
$329$		0			0
$330$	−921738.	+	1.13680e6i	−0.465932	+	0.574646i
$331$	219141.			0.109939			0.0549697	−	0.998488i	$-0.482494\pi$
$331$	219141.			0.109939			0.0549697	+	0.998488i	$0.482494\pi$
$332$	151213.			0.0752911
$333$	−777689.	−	3.68130e6i	−0.384322	−	1.81924i
$334$			879557.i			0.431417i
$335$	1.42431e6			0.693411
$336$		0			0
$337$	−279137.			−0.133889			−0.0669443	−	0.997757i	$-0.521325\pi$
$337$	−279137.			−0.133889			−0.0669443	+	0.997757i	$0.521325\pi$
$338$			182419.i			0.0868516i
$339$	1.75038e6	+	1.41924e6i	0.827245	+	0.670744i
$340$	−691699.			−0.324504
$341$	−1.80761e6			−0.841819
$342$	−415196.	−	1.96539e6i	−0.191950	−	0.908622i
$343$		0			0
$344$		−	433301.i		−	0.197421i
$345$	−473178.	−	383660.i	−0.214031	−	0.173540i
$346$			572341.i			0.257019i
$347$		−	2.22153e6i		−	0.990441i	−0.868767	−	0.495220i	$-0.835087\pi$
$347$		−	2.22153e6i		−	0.990441i	0.868767	−	0.495220i	$-0.164913\pi$
$348$	−281791.	−	228481.i	−0.124732	−	0.101135i
$349$		−	2.77164e6i		−	1.21807i	−0.793142	−	0.609037i	$-0.791556\pi$
$349$		−	2.77164e6i		−	1.21807i	0.793142	−	0.609037i	$-0.208444\pi$
$350$		0			0
$351$	−1.11445e6	+	2.17716e6i	−0.482829	+	0.943241i
$352$	464120.			0.199652
$353$	3.40150e6			1.45289			0.726447	−	0.687222i	$-0.241170\pi$
$353$	3.40150e6			1.45289			0.726447	+	0.687222i	$0.241170\pi$
$354$	−237756.	−	192776.i	−0.100838	−	0.0817608i
$355$		−	2.32287e6i		−	0.978258i
$356$	−1.41485e6			−0.591677
$357$		0			0
$358$	3.05648e6			1.26041
$359$			197860.i			0.0810257i	0.999179	+	0.0405128i	$0.0128992\pi$
$359$			197860.i			0.0810257i	−0.999179	+	0.0405128i	$0.987101\pi$
$360$	−787978.	+	166463.i	−0.320448	+	0.0676959i
$361$	−1.79487e6			−0.724877
$362$	745611.			0.299048
$363$	−435682.	+	537338.i	−0.173542	+	0.214033i
$364$		0			0
$365$			4.23894e6i			1.66543i
$366$	−1.31920e6	+	1.62700e6i	−0.514762	+	0.634869i
$367$		−	2.34797e6i		−	0.909970i	−0.890499	−	0.454985i	$-0.849645\pi$
$367$		−	2.34797e6i		−	0.909970i	0.890499	−	0.454985i	$-0.150355\pi$
$368$			193183.i			0.0743618i
$369$	−974808.	−	4.61439e6i	−0.372695	−	1.76420i
$370$			3.20734e6i			1.21798i
$371$		0			0
$372$	−772646.	−	626475.i	−0.289483	−	0.234718i
$373$	4.18523e6			1.55757			0.778785	−	0.627292i	$-0.215837\pi$
$373$	4.18523e6			1.55757			0.778785	+	0.627292i	$0.215837\pi$
$374$	−1.51349e6			−0.559499
$375$	1.81415e6	−	2.23744e6i	0.666186	−	0.821624i
$376$			343102.i			0.125156i
$377$	939152.			0.340316
$378$		0			0
$379$	1.16220e6			0.415606			0.207803	−	0.978171i	$-0.433369\pi$
$379$	1.16220e6			0.415606			0.207803	+	0.978171i	$0.433369\pi$
$380$			1.71235e6i			0.608321i
$381$	1.05328e6	−	1.29904e6i	0.371734	−	0.458468i
$382$	−2.63877e6			−0.925217
$383$	501080.			0.174546			0.0872730	−	0.996184i	$-0.472185\pi$
$383$	501080.			0.174546			0.0872730	+	0.996184i	$0.472185\pi$
$384$	198384.	+	160853.i	0.0686560	+	0.0556674i
$385$		0			0
$386$		−	82111.8i		−	0.0280503i
$387$	340048.	+	1.60967e6i	0.115415	+	0.546334i
$388$		−	162661.i		−	0.0548534i
$389$			689216.i			0.230930i	0.993312	+	0.115465i	$0.0368359\pi$
$389$			689216.i			0.230930i	−0.993312	+	0.115465i	$0.963164\pi$
$390$	1.31308e6	−	1.61946e6i	0.437150	−	0.539148i
$391$		−	629967.i		−	0.208390i
$392$		0			0
$393$	1.45113e6	−	1.78971e6i	0.473942	−	0.584524i
$394$	−2.23414e6			−0.725055
$395$	1.75265e6			0.565199
$396$	−1.72415e6	+	364234.i	−0.552507	+	0.116719i
$397$			1.81071e6i			0.576598i	0.957540	+	0.288299i	$0.0930896\pi$
$397$			1.81071e6i			0.576598i	−0.957540	+	0.288299i	$0.906910\pi$
$398$	982860.			0.311017
$399$		0			0
$400$	−113474.			−0.0354606
$401$		−	1.36292e6i		−	0.423261i	−0.977350	−	0.211631i	$-0.932123\pi$
$401$		−	1.36292e6i		−	0.423261i	0.977350	−	0.211631i	$-0.0678774\pi$
$402$	1.33211e6	+	1.08010e6i	0.411127	+	0.333348i
$403$	2.57507e6			0.789817
$404$	540694.			0.164816
$405$	2.79661e6	−	1.23678e6i	0.847216	−	0.374676i
$406$		0			0
$407$			7.01789e6i			2.10000i
$408$	−646926.	−	524539.i	−0.192400	−	0.156001i
$409$		−	314547.i		−	0.0929773i	−0.998919	−	0.0464887i	$-0.985197\pi$
$409$		−	314547.i		−	0.0929773i	0.998919	−	0.0464887i	$-0.0148031\pi$
$410$			4.02029e6i			1.18113i
$411$	3.48616e6	+	2.82663e6i	1.01799	+	0.825401i
$412$		−	1.99487e6i		−	0.578991i
$413$		0			0
$414$	−151607.	−	717654.i	−0.0434729	−	0.205785i
$415$	489415.			0.139495
$416$	−661172.			−0.187319
$417$	−421005.	−	341358.i	−0.118562	−	0.0961324i
$418$			3.74674e6i			1.04885i
$419$	2.75221e6			0.765856			0.382928	−	0.923778i	$-0.374916\pi$
$419$	2.75221e6			0.765856			0.382928	+	0.923778i	$0.374916\pi$
$420$		0			0
$421$	−759489.			−0.208841			−0.104421	−	0.994533i	$-0.533299\pi$
$421$	−759489.			−0.208841			−0.104421	+	0.994533i	$0.533299\pi$
$422$			1.90175e6i			0.519844i
$423$	−269261.	−	1.27458e6i	−0.0731682	−	0.346352i
$424$	−2.22874e6			−0.602067
$425$	370037.			0.0993740
$426$	1.76151e6	−	2.17251e6i	0.470285	−	0.580014i
$427$		0			0
$428$		−	1.89777e6i		−	0.500764i
$429$	2.87312e6	−	3.54349e6i	0.753721	−	0.929583i
$430$		−	1.40242e6i		−	0.365770i
$431$			1.12460e6i			0.291611i	0.989313	+	0.145805i	$0.0465773\pi$
$431$			1.12460e6i			0.291611i	−0.989313	+	0.145805i	$0.953423\pi$
$432$	−863208.	−	441862.i	−0.222539	−	0.113914i
$433$		−	5.88187e6i		−	1.50763i	−0.657085	−	0.753816i	$-0.728211\pi$
$433$		−	5.88187e6i		−	1.50763i	0.657085	−	0.753816i	$-0.271789\pi$
$434$		0			0
$435$	−912045.	−	739501.i	−0.231096	−	0.187377i
$436$	−611778.			−0.154127
$437$	−1.55953e6			−0.390651
$438$	−3.21453e6	+	3.96456e6i	−0.800631	+	0.987438i
$439$		−	1.95736e6i		−	0.484741i	−0.970184	−	0.242371i	$-0.922075\pi$
$439$		−	1.95736e6i		−	0.484741i	0.970184	−	0.242371i	$-0.0779250\pi$
$440$	1.50217e6			0.369902
$441$		0			0
$442$	2.15607e6			0.524937
$443$			3.38550e6i			0.819622i	0.912171	+	0.409811i	$0.134405\pi$
$443$			3.38550e6i			0.819622i	−0.912171	+	0.409811i	$0.865595\pi$
$444$	−2.43223e6	+	2.99973e6i	−0.585528	+	0.722146i
$445$	−4.57929e6			−1.09622
$446$	4.69981e6			1.11878
$447$	2.03053e6	+	1.64639e6i	0.480663	+	0.389729i
$448$		0			0
$449$			274544.i			0.0642681i	0.999484	+	0.0321340i	$0.0102303\pi$
$449$			274544.i			0.0642681i	−0.999484	+	0.0321340i	$0.989770\pi$
$450$	421543.	−	89052.6i	0.0981320	−	0.0207308i
$451$			8.79669e6i			2.03647i
$452$		−	2.31295e6i		−	0.532502i
$453$	−4.47831e6	+	5.52321e6i	−1.02534	+	1.26458i
$454$			904714.i			0.206002i
$455$		0			0
$456$	−1.29853e6	+	1.60151e6i	−0.292442	+	0.360676i
$457$	5.44191e6			1.21888			0.609440	−	0.792832i	$-0.291394\pi$
$457$	5.44191e6			1.21888			0.609440	+	0.792832i	$0.291394\pi$
$458$	3.12490e6			0.696102
$459$	2.81491e6	+	1.44090e6i	0.623638	+	0.319230i
$460$			625256.i			0.137773i
$461$	−3.82312e6			−0.837848			−0.418924	−	0.908021i	$-0.637593\pi$
$461$	−3.82312e6			−0.837848			−0.418924	+	0.908021i	$0.637593\pi$
$462$		0			0
$463$	−6.74062e6			−1.46133			−0.730664	−	0.682738i	$-0.760789\pi$
$463$	−6.74062e6			−1.46133			−0.730664	+	0.682738i	$0.760789\pi$
$464$			372358.i			0.0802909i
$465$	−2.50074e6	−	2.02765e6i	−0.536336	−	0.434870i
$466$	6.31930e6			1.34804
$467$	−4.06885e6			−0.863335			−0.431667	−	0.902033i	$-0.642075\pi$
$467$	−4.06885e6			−0.863335			−0.431667	+	0.902033i	$0.642075\pi$
$468$	2.45618e6	−	518877.i	0.518377	−	0.109509i
$469$		0			0
$470$			1.11048e6i			0.231882i
$471$	2.21192e6	+	1.79346e6i	0.459427	+	0.372511i
$472$			314170.i			0.0649097i
$473$		−	3.06860e6i		−	0.630649i
$474$	1.63920e6	+	1.32909e6i	0.335109	+	0.271712i
$475$		−	916051.i		−	0.186288i
$476$		0			0
$477$	8.27952e6	−	1.74908e6i	1.66613	−	0.351977i
$478$	4.26448e6			0.853681
$479$	2.34505e6			0.466997			0.233498	−	0.972357i	$-0.424983\pi$
$479$	2.34505e6			0.466997			0.233498	+	0.972357i	$0.424983\pi$
$480$	642088.	+	520616.i	0.127201	+	0.103137i
$481$		−	9.99749e6i		−	1.97028i
$482$	−1.15555e6			−0.226553
$483$		0			0
$484$	710037.			0.137774
$485$		−	526467.i		−	0.101629i
$486$	3.55349e6	+	964034.i	0.682439	+	0.185141i
$487$	4.27665e6			0.817111			0.408556	−	0.912733i	$-0.366033\pi$
$487$	4.27665e6			0.817111			0.408556	+	0.912733i	$0.366033\pi$
$488$	2.14991e6			0.408668
$489$	−4.96061e6	+	6.11804e6i	−0.938130	+	1.15702i
$490$		0			0
$491$			596779.i			0.111715i	0.998439	+	0.0558573i	$0.0177892\pi$
$491$			596779.i			0.111715i	−0.998439	+	0.0558573i	$0.982211\pi$
$492$	−3.04872e6	+	3.76007e6i	−0.567813	+	0.700298i
$493$		−	1.21425e6i		−	0.225005i
$494$		−	5.33750e6i		−	0.984058i
$495$	−5.58038e6	+	1.17888e6i	−1.02365	+	0.216250i
$496$			1.02097e6i			0.186342i
$497$		0			0
$498$	457736.	+	371140.i	0.0827069	+	0.0670602i
$499$	−4.28430e6			−0.770245			−0.385122	−	0.922865i	$-0.625841\pi$
$499$	−4.28430e6			−0.770245			−0.385122	+	0.922865i	$0.625841\pi$
$500$	−2.95655e6			−0.528883
$501$	−2.15880e6	+	2.66250e6i	−0.384254	+	0.473910i
$502$			7.12263e6i			1.26148i
$503$	−4.95292e6			−0.872854			−0.436427	−	0.899740i	$-0.643756\pi$
$503$	−4.95292e6			−0.872854			−0.436427	+	0.899740i	$0.643756\pi$
$504$		0			0
$505$	1.75001e6			0.305360
$506$			1.36811e6i			0.237544i
$507$	−447733.	+	552200.i	−0.0773569	+	0.0954061i
$508$	−1.71655e6			−0.295118
$509$	−366780.			−0.0627496			−0.0313748	−	0.999508i	$-0.509989\pi$
$509$	−366780.			−0.0627496			−0.0313748	+	0.999508i	$0.509989\pi$
$510$	−2.09384e6	−	1.69772e6i	−0.356466	−	0.289028i
$511$		0			0
$512$		−	262144.i		−	0.0441942i
$513$	3.56705e6	−	6.96849e6i	0.598434	−	1.16908i
$514$		−	5.49407e6i		−	0.917246i
$515$		−	6.45659e6i		−	1.07272i
$516$	1.06350e6	−	1.31165e6i	0.175839	−	0.216866i
$517$			2.42981e6i			0.399804i
$518$		0			0
$519$	−1.40477e6	+	1.73253e6i	−0.228921	+	0.282334i
$520$	−2.13995e6			−0.347052
$521$	−235391.			−0.0379923			−0.0189961	−	0.999820i	$-0.506047\pi$
$521$	−235391.			−0.0379923			−0.0189961	+	0.999820i	$0.506047\pi$
$522$	−292221.	−	1.38327e6i	−0.0469391	−	0.222193i
$523$		−	5.89434e6i		−	0.942283i	−0.882058	−	0.471141i	$-0.843842\pi$
$523$		−	5.89434e6i		−	0.942283i	0.882058	−	0.471141i	$-0.156158\pi$
$524$	−2.36493e6			−0.376261
$525$		0			0
$526$	1.87575e6			0.295605
$527$		−	3.32938e6i		−	0.522199i
$528$	1.40494e6	+	1.13915e6i	0.219317	+	0.177826i
$529$	5.86689e6			0.911525
$530$	−7.21354e6			−1.11547
$531$	−246555.	−	1.16710e6i	−0.0379471	−	0.179628i
$532$		0			0
$533$		−	1.25315e7i		−	1.91067i
$534$	−4.28288e6	−	3.47263e6i	−0.649955	−	0.526994i
$535$		−	6.14230e6i		−	0.927784i
$536$		−	1.76025e6i		−	0.264644i
$537$	9.25225e6	+	7.50188e6i	1.38456	+	1.12262i
$538$			8.89167e6i			1.32443i
$539$		0			0
$540$	−2.79386e6	−	1.43013e6i	−0.412306	−	0.211053i
$541$	−3.02975e6			−0.445054			−0.222527	−	0.974926i	$-0.571431\pi$
$541$	−3.02975e6			−0.445054			−0.222527	+	0.974926i	$0.571431\pi$
$542$	1.03986e6			0.152046
$543$	2.25704e6	+	1.83004e6i	0.328503	+	0.266356i
$544$			854847.i			0.123849i
$545$	−1.98008e6			−0.285556
$546$		0			0
$547$	−1.95647e6			−0.279579			−0.139789	−	0.990181i	$-0.544643\pi$
$547$	−1.95647e6			−0.279579			−0.139789	+	0.990181i	$0.544643\pi$
$548$		−	4.60660e6i		−	0.655283i
$549$	−7.98667e6	+	1.68721e6i	−1.13093	+	0.238913i
$550$	−803612.			−0.113277
$551$	−3.00597e6			−0.421799
$552$	−474153.	+	584784.i	−0.0662325	+	0.0816861i
$553$		0			0
$554$		−	5.56666e6i		−	0.770584i
$555$	−7.87216e6	+	9.70892e6i	−1.08483	+	1.33795i
$556$			556315.i			0.0763192i
$557$			8.87892e6i			1.21261i	0.795231	+	0.606307i	$0.207350\pi$
$557$			8.87892e6i			1.21261i	−0.795231	+	0.606307i	$0.792650\pi$
$558$	−801243.	−	3.79280e6i	−0.108938	−	0.515673i
$559$			4.37144e6i			0.591692i
$560$		0			0
$561$	−4.58147e6	−	3.71473e6i	−0.614607	−	0.498334i
$562$	−7.25851e6			−0.969408
$563$	−4.64860e6			−0.618090			−0.309045	−	0.951047i	$-0.600009\pi$
$563$	−4.64860e6			−0.618090			−0.309045	+	0.951047i	$0.600009\pi$
$564$	−842116.	+	1.03860e6i	−0.111474	+	0.137484i
$565$		−	7.48610e6i		−	0.986585i
$566$	4.57653e6			0.600475
$567$		0			0
$568$	−2.87075e6			−0.373358
$569$		−	1.52111e7i		−	1.96961i	−0.173655	−	0.984807i	$-0.555558\pi$
$569$		−	1.52111e7i		−	1.96961i	0.173655	−	0.984807i	$-0.444442\pi$
$570$	−4.20282e6	+	5.18344e6i	−0.541818	+	0.668237i
$571$	−3.07924e6			−0.395233			−0.197616	−	0.980279i	$-0.563320\pi$
$571$	−3.07924e6			−0.395233			−0.197616	+	0.980279i	$0.563320\pi$
$572$	−4.68236e6			−0.598377
$573$	−7.98782e6	−	6.47666e6i	−1.01635	−	0.824071i
$574$		0			0
$575$		−	334492.i		−	0.0421907i
$576$	205726.	+	973835.i	0.0258365	+	0.122301i
$577$			387655.i			0.0484736i	0.999706	+	0.0242368i	$0.00771557\pi$
$577$			387655.i			0.0484736i	−0.999706	+	0.0242368i	$0.992284\pi$
$578$			2.89179e6i			0.360037i
$579$	201537.	−	248560.i	0.0249838	−	0.0308131i
$580$			1.20517e6i			0.148758i
$581$		0			0
$582$	399238.	−	492390.i	0.0488567	−	0.0602562i
$583$	−1.57837e7			−1.92326
$584$	5.23876e6			0.635619
$585$	7.94966e6	−	1.67940e6i	0.960415	−	0.202891i
$586$		−	116323.i		−	0.0139933i
$587$	1.46128e7			1.75040			0.875200	−	0.483762i	$-0.160730\pi$
$587$	1.46128e7			1.75040			0.875200	+	0.483762i	$0.160730\pi$
$588$		0			0
$589$	−8.24209e6			−0.978925
$590$			1.01684e6i			0.120260i
$591$	−6.76297e6	−	5.48353e6i	−0.796469	−	0.645790i
$592$	3.96384e6			0.464849
$593$	4.47738e6			0.522862			0.261431	−	0.965222i	$-0.415806\pi$
$593$	4.47738e6			0.522862			0.261431	+	0.965222i	$0.415806\pi$
$594$	−6.11316e6	−	3.12922e6i	−0.710885	−	0.363890i
$595$		0			0
$596$		−	2.68314e6i		−	0.309405i
$597$	2.97521e6	+	2.41235e6i	0.341651	+	0.277016i
$598$		−	1.94897e6i		−	0.222870i
$599$		−	1.87106e6i		−	0.213069i	−0.994309	−	0.106535i	$-0.966024\pi$
$599$		−	1.87106e6i		−	0.213069i	0.994309	−	0.106535i	$-0.0339755\pi$
$600$	−343497.	−	278513.i	−0.0389533	−	0.0315840i
$601$		−	4.17439e6i		−	0.471419i	−0.971824	−	0.235709i	$-0.924259\pi$
$601$		−	4.17439e6i		−	0.471419i	0.971824	−	0.235709i	$-0.0757413\pi$
$602$		0			0
$603$	1.38142e6	+	6.53913e6i	0.154715	+	0.732363i
$604$	7.29835e6			0.814015
$605$	2.29810e6			0.255259
$606$	1.63673e6	+	1.32709e6i	0.181049	+	0.146798i
$607$			7.37398e6i			0.812326i	0.913801	+	0.406163i	$0.133133\pi$
$607$			7.37398e6i			0.812326i	−0.913801	+	0.406163i	$0.866867\pi$
$608$	2.11623e6			0.232169
$609$		0			0
$610$	6.95839e6			0.757154
$611$		−	3.46145e6i		−	0.375107i
$612$	−670870.	−	3.17566e6i	−0.0724036	−	0.342732i
$613$	−800852.			−0.0860797			−0.0430399	−	0.999073i	$-0.513704\pi$
$613$	−800852.			−0.0860797			−0.0430399	+	0.999073i	$0.513704\pi$
$614$	773874.			0.0828418
$615$	−9.86749e6	+	1.21698e7i	−1.05201	+	1.29747i
$616$		0			0
$617$		−	9.07689e6i		−	0.959896i	−0.877297	−	0.479948i	$-0.840655\pi$
$617$		−	9.07689e6i		−	0.959896i	0.877297	−	0.479948i	$-0.159345\pi$
$618$	4.89625e6	−	6.03867e6i	0.515695	−	0.636019i
$619$		−	9.43127e6i		−	0.989335i	−0.869082	−	0.494668i	$-0.835290\pi$
$619$		−	9.43127e6i		−	0.989335i	0.869082	−	0.494668i	$-0.164710\pi$
$620$			3.30448e6i			0.345242i
$621$	1.30249e6	−	2.54451e6i	0.135534	−	0.264774i
$622$			1.02267e7i			1.05988i
$623$		0			0
$624$	−2.00143e6	−	1.62280e6i	−0.205769	−	0.166841i
$625$	−8.18397e6			−0.838038
$626$	1.69276e6			0.172647
$627$	−9.19607e6	+	1.13417e7i	−0.934186	+	1.15215i
$628$		−	2.92282e6i		−	0.295736i
$629$	−1.29260e7			−1.30268
$630$		0			0
$631$	−1.86977e7			−1.86945			−0.934726	−	0.355369i	$-0.884355\pi$
$631$	−1.86977e7			−1.86945			−0.934726	+	0.355369i	$0.884355\pi$
$632$		−	2.16603e6i		−	0.215711i
$633$	−4.66770e6	+	5.75679e6i	−0.463013	+	0.571046i
$634$	−144683.			−0.0142953
$635$	−5.55577e6			−0.546776
$636$	−6.74662e6	−	5.47027e6i	−0.661368	−	0.536248i
$637$		0			0
$638$			2.63701e6i			0.256484i
$639$	1.06645e7	−	2.25292e6i	1.03321	−	0.218270i
$640$		−	848454.i		−	0.0818801i
$641$		−	5.48980e6i		−	0.527729i	−0.964560	−	0.263865i	$-0.915003\pi$
$641$		−	5.48980e6i		−	0.527729i	0.964560	−	0.263865i	$-0.0849972\pi$
$642$	4.65792e6	−	5.74472e6i	0.446020	−	0.550087i
$643$			7.07744e6i			0.675070i	0.941313	+	0.337535i	$0.109593\pi$
$643$			7.07744e6i			0.675070i	−0.941313	+	0.337535i	$0.890407\pi$
$644$		0			0
$645$	3.44213e6	−	4.24527e6i	0.325783	−	0.401796i
$646$	−6.90099e6			−0.650624
$647$	4.27271e6			0.401276			0.200638	−	0.979665i	$-0.435699\pi$
$647$	4.27271e6			0.401276			0.200638	+	0.979665i	$0.435699\pi$
$648$	−1.52850e6	−	3.45623e6i	−0.142997	−	0.323345i
$649$			2.22492e6i			0.207349i
$650$	1.14480e6			0.106279
$651$		0			0
$652$	8.08437e6			0.744778
$653$			1.16466e7i			1.06885i	0.845216	+	0.534424i	$0.179472\pi$
$653$			1.16466e7i			1.06885i	−0.845216	+	0.534424i	$0.820528\pi$
$654$	−1.85191e6	−	1.50156e6i	−0.169307	−	0.137277i
$655$	−7.65431e6			−0.697112
$656$	4.96854e6			0.450785
$657$	−1.94614e7	+	4.11130e6i	−1.75898	+	0.371591i
$658$		0			0
$659$		−	8.49340e6i		−	0.761847i	−0.924607	−	0.380924i	$-0.875606\pi$
$659$		−	8.49340e6i		−	0.761847i	0.924607	−	0.380924i	$-0.124394\pi$
$660$	4.54721e6	+	3.68695e6i	0.406336	+	0.329464i
$661$			5.04077e6i			0.448738i	0.974504	+	0.224369i	$0.0720321\pi$
$661$			5.04077e6i			0.448738i	−0.974504	+	0.224369i	$0.927968\pi$
$662$		−	876564.i		−	0.0777389i
$663$	6.52664e6	+	5.29191e6i	0.576641	+	0.467550i
$664$		−	604852.i		−	0.0532389i
$665$		0			0
$666$	−1.47252e7	+	3.11076e6i	−1.28640	+	0.271757i
$667$	−1.09762e6			−0.0955292
$668$	3.51823e6			0.305058
$669$	1.42268e7	+	1.15353e7i	1.22897	+	0.996470i
$670$		−	5.69722e6i		−	0.490316i
$671$	1.52255e7			1.30546
$672$		0			0
$673$	1.55507e7			1.32346			0.661730	−	0.749742i	$-0.269822\pi$
$673$	1.55507e7			1.32346			0.661730	+	0.749742i	$0.269822\pi$
$674$			1.11655e6i			0.0946735i
$675$	1.49462e6	+	765073.i	0.126262	+	0.0646314i
$676$	729675.			0.0614134
$677$	8.38455e6			0.703086			0.351543	−	0.936172i	$-0.385657\pi$
$677$	8.38455e6			0.703086			0.351543	+	0.936172i	$0.385657\pi$
$678$	5.67696e6	−	7.00154e6i	0.474288	−	0.584951i
$679$		0			0
$680$			2.76679e6i			0.229459i
$681$	−2.22055e6	+	2.73866e6i	−0.183482	+	0.226292i
$682$			7.23044e6i			0.595256i
$683$		−	1.66025e7i		−	1.36183i	−0.732363	−	0.680914i	$-0.761583\pi$
$683$		−	1.66025e7i		−	1.36183i	0.732363	−	0.680914i	$-0.238417\pi$
$684$	−7.86156e6	+	1.66078e6i	−0.642493	+	0.135729i
$685$		−	1.49097e7i		−	1.21407i
$686$		0			0
$687$	9.45938e6	+	7.66982e6i	0.764664	+	0.620003i
$688$	−1.73321e6			−0.139598
$689$	2.24851e7			1.80446
$690$	−1.53464e6	+	1.89271e6i	−0.122711	+	0.151343i
$691$			4.25259e6i			0.338811i	0.985546	+	0.169406i	$0.0541848\pi$
$691$			4.25259e6i			0.338811i	−0.985546	+	0.169406i	$0.945815\pi$
$692$	2.28937e6			0.181740
$693$		0			0
$694$	−8.88612e6			−0.700348
$695$			1.80057e6i			0.141399i
$696$	−913924.	+	1.12717e6i	−0.0715134	+	0.0881992i
$697$	−1.62023e7			−1.26327
$698$	−1.10866e7			−0.861308
$699$	1.91291e7	+	1.55102e7i	1.48082	+	1.20067i
$700$		0			0
$701$			6.21609e6i			0.477773i	0.971047	+	0.238887i	$0.0767825\pi$
$701$			6.21609e6i			0.477773i	−0.971047	+	0.238887i	$0.923218\pi$
$702$	8.70864e6	+	4.45781e6i	0.666972	+	0.341412i
$703$			3.19992e7i			2.44203i
$704$		−	1.85648e6i		−	0.141175i
$705$	−2.72559e6	+	3.36154e6i	−0.206532	+	0.254721i
$706$		−	1.36060e7i		−	1.02735i
$707$		0			0
$708$	−771105.	+	951022.i	−0.0578136	+	0.0713030i
$709$	2.53893e7			1.89686			0.948430	−	0.316985i	$-0.102671\pi$
$709$	2.53893e7			1.89686			0.948430	+	0.316985i	$0.102671\pi$
$710$	−9.29147e6			−0.691733
$711$	1.69987e6	+	8.04657e6i	0.126108	+	0.596949i
$712$			5.65939e6i			0.418379i
$713$	−3.00957e6			−0.221707
$714$		0			0
$715$	−1.51549e7			−1.10863
$716$		−	1.22259e7i		−	0.891248i
$717$	1.29090e7	+	1.04668e7i	0.937765	+	0.760356i
$718$	791441.			0.0572938
$719$	−1.96525e7			−1.41774			−0.708870	−	0.705339i	$-0.750795\pi$
$719$	−1.96525e7			−1.41774			−0.708870	+	0.705339i	$0.750795\pi$
$720$	665853.	+	3.15191e6i	0.0478682	+	0.226591i
$721$		0			0
$722$			7.17947e6i			0.512566i
$723$	−3.49796e6	−	2.83620e6i	−0.248868	−	0.201786i
$724$		−	2.98244e6i		−	0.211459i
$725$		−	644730.i		−	0.0455547i
$726$	2.14935e6	+	1.74273e6i	0.151344	+	0.122712i
$727$			1.40321e7i			0.984660i	0.870409	+	0.492330i	$0.163855\pi$
$727$			1.40321e7i			0.984660i	−0.870409	+	0.492330i	$0.836145\pi$
$728$		0			0
$729$	8.39060e6	+	1.16400e7i	0.584755	+	0.811210i
$730$	1.69558e7			1.17763
$731$	5.65195e6			0.391206
$732$	6.50799e6	+	5.27678e6i	0.448920	+	0.363992i
$733$			1.93215e7i			1.32825i	0.747621	+	0.664125i	$0.231196\pi$
$733$			1.93215e7i			1.32825i	−0.747621	+	0.664125i	$0.768804\pi$
$734$	−9.39187e6			−0.643446
$735$		0			0
$736$	772733.			0.0525817
$737$		−	1.24659e7i		−	0.845388i
$738$	−1.84576e7	+	3.89923e6i	−1.24748	+	0.263535i
$739$	1.64831e7			1.11027			0.555133	−	0.831762i	$-0.312668\pi$
$739$	1.64831e7			1.11027			0.555133	+	0.831762i	$0.312668\pi$
$740$	1.28293e7			0.861242
$741$	1.31005e7	−	1.61571e7i	0.876479	−	1.08098i
$742$		0			0
$743$			1.51394e7i			1.00609i	0.864261	+	0.503043i	$0.167786\pi$
$743$			1.51394e7i			1.00609i	−0.864261	+	0.503043i	$0.832214\pi$
$744$	−2.50590e6	+	3.09059e6i	−0.165971	+	0.204696i
$745$		−	8.68423e6i		−	0.573246i
$746$		−	1.67409e7i		−	1.10137i
$747$	474678.	+	2.24695e6i	0.0311241	+	0.147331i
$748$			6.05395e6i			0.395626i
$749$		0			0
$750$	−8.94975e6	−	7.25661e6i	−0.580976	−	0.471065i
$751$	−1.71437e6			−0.110919			−0.0554593	−	0.998461i	$-0.517662\pi$
$751$	−1.71437e6			−0.110919			−0.0554593	+	0.998461i	$0.517662\pi$
$752$	1.37241e6			0.0884990
$753$	−1.74819e7	+	2.15609e7i	−1.12357	+	1.38573i
$754$		−	3.75661e6i		−	0.240640i
$755$	2.36218e7			1.50816
$756$		0			0
$757$	2.16978e7			1.37618			0.688092	−	0.725624i	$-0.258449\pi$
$757$	2.16978e7			1.37618			0.688092	+	0.725624i	$0.258449\pi$
$758$		−	4.64879e6i		−	0.293878i
$759$	−3.35791e6	+	4.14139e6i	−0.211575	+	0.260941i
$760$	6.84939e6			0.430148
$761$	−4.45762e6			−0.279024			−0.139512	−	0.990220i	$-0.544553\pi$
$761$	−4.45762e6			−0.279024			−0.139512	+	0.990220i	$0.544553\pi$
$762$	−5.19615e6	−	4.21313e6i	−0.324186	−	0.262855i
$763$		0			0
$764$			1.05551e7i			0.654227i
$765$	−2.17134e6	−	1.02783e7i	−0.134145	−	0.634993i
$766$		−	2.00432e6i		−	0.123423i
$767$		−	3.16956e6i		−	0.194541i
$768$	643412.	−	793535.i	0.0393628	−	0.0485471i
$769$		−	1.64855e7i		−	1.00528i	−0.864497	−	0.502638i	$-0.832363\pi$
$769$		−	1.64855e7i		−	1.00528i	0.864497	−	0.502638i	$-0.167637\pi$
$770$		0			0
$771$	1.34847e7	−	1.66311e7i	0.816972	−	1.00759i
$772$	−328447.			−0.0198345
$773$	−1.16889e7			−0.703601			−0.351800	−	0.936075i	$-0.614430\pi$
$773$	−1.16889e7			−0.703601			−0.351800	+	0.936075i	$0.614430\pi$
$774$	6.43866e6	−	1.36019e6i	0.386316	−	0.0816108i
$775$		−	1.76779e6i		−	0.105725i
$776$	−650643.			−0.0387872
$777$		0			0
$778$	2.75686e6			0.163292
$779$			4.01100e7i			2.36815i
$780$	−6.47783e6	−	5.25233e6i	−0.381235	−	0.309112i
$781$	−2.03304e7			−1.19266
$782$	−2.51987e6			−0.147354
$783$	2.51054e6	−	4.90452e6i	0.146340	−	0.285886i
$784$		0			0
$785$		−	9.46000e6i		−	0.547920i
$786$	−7.15886e6	−	5.80452e6i	−0.413321	−	0.335128i
$787$		−	1.36544e7i		−	0.785842i	−0.919572	−	0.392921i	$-0.871465\pi$
$787$		−	1.36544e7i		−	0.785842i	0.919572	−	0.392921i	$-0.128535\pi$
$788$			8.93658e6i			0.512691i
$789$	5.67809e6	+	4.60389e6i	0.324721	+	0.263289i
$790$		−	7.01058e6i		−	0.399656i
$791$		0			0
$792$	1.45693e6	+	6.89661e6i	0.0825329	+	0.390681i
$793$	−2.16898e7			−1.22482
$794$	7.24284e6			0.407716
$795$	−2.18361e7	−	1.77051e7i	−1.22534	−	0.993527i
$796$		−	3.93144e6i		−	0.219922i
$797$	1.88724e7			1.05240			0.526200	−	0.850361i	$-0.323616\pi$
$797$	1.88724e7			1.05240			0.526200	+	0.850361i	$0.323616\pi$
$798$		0			0
$799$	−4.47540e6			−0.248007
$800$			453896.i			0.0250745i
$801$	−4.44140e6	−	2.10240e7i	−0.244590	−	1.15780i
$802$	−5.45167e6			−0.299291
$803$	3.71004e7			2.03044
$804$	4.32040e6	−	5.32845e6i	0.235713	−	0.290711i
$805$		0			0
$806$		−	1.03003e7i		−	0.558485i
$807$	−2.18239e7	+	2.69160e7i	−1.17964	+	1.45488i
$808$		−	2.16278e6i		−	0.116542i
$809$		−	2.22245e7i		−	1.19388i	−0.802285	−	0.596941i	$-0.796383\pi$
$809$		−	2.22245e7i		−	1.19388i	0.802285	−	0.596941i	$-0.203617\pi$
$810$	−4.94714e6	−	1.11864e7i	−0.264936	−	0.599072i
$811$		−	9.63993e6i		−	0.514661i	−0.966323	−	0.257331i	$-0.917157\pi$
$811$		−	9.63993e6i		−	0.514661i	0.966323	−	0.257331i	$-0.0828430\pi$
$812$		0			0
$813$	3.14776e6	+	2.55225e6i	0.167022	+	0.135425i
$814$	2.80715e7			1.48493
$815$	2.61658e7			1.37988
$816$	−2.09815e6	+	2.58771e6i	−0.110309	+	0.136047i
$817$		−	1.39918e7i		−	0.733362i
$818$	−1.25819e6			−0.0657449
$819$		0			0
$820$	1.60812e7			0.835186
$821$		−	2.73858e6i		−	0.141797i	−0.997484	−	0.0708986i	$-0.977413\pi$
$821$		−	2.73858e6i		−	0.141797i	0.997484	−	0.0708986i	$-0.0225867\pi$
$822$	1.13065e7	−	1.39446e7i	0.583647	−	0.719826i
$823$	3.29152e6			0.169394			0.0846968	−	0.996407i	$-0.473008\pi$
$823$	3.29152e6			0.169394			0.0846968	+	0.996407i	$0.473008\pi$
$824$	−7.97948e6			−0.409408
$825$	−2.43261e6	−	1.97240e6i	−0.124434	−	0.100893i
$826$		0			0
$827$			2.80950e7i			1.42845i	0.699916	+	0.714225i	$0.253221\pi$
$827$			2.80950e7i			1.42845i	−0.699916	+	0.714225i	$0.746779\pi$
$828$	−2.87061e6	+	606428.i	−0.145512	+	0.0307400i
$829$		−	1.76526e7i		−	0.892119i	−0.895003	−	0.446059i	$-0.852827\pi$
$829$		−	1.76526e7i		−	0.892119i	0.895003	−	0.446059i	$-0.147173\pi$
$830$		−	1.95766e6i		−	0.0986375i
$831$	1.36629e7	−	1.68508e7i	0.686343	−	0.846483i
$832$			2.64469e6i			0.132454i
$833$		0			0
$834$	−1.36543e6	+	1.68402e6i	−0.0679759	+	0.0838363i
$835$	1.13871e7			0.565192
$836$	1.49869e7			0.741648
$837$	6.88368e6	−	1.34478e7i	0.339631	−	0.663493i
$838$		−	1.10089e7i		−	0.541542i
$839$	−2.52447e7			−1.23813			−0.619065	−	0.785340i	$-0.712488\pi$
$839$	−2.52447e7			−1.23813			−0.619065	+	0.785340i	$0.712488\pi$
$840$		0			0
$841$	1.83955e7			0.896854
$842$			3.03796e6i			0.147673i
$843$	−2.19722e7	−	1.78154e7i	−1.06489	−	0.863431i
$844$	7.60701e6			0.367585
$845$	2.36166e6			0.113783
$846$	−5.09834e6	+	1.07704e6i	−0.244908	+	0.0517377i
$847$		0			0
$848$			8.91497e6i			0.425726i
$849$	1.38536e7	+	1.12327e7i	0.659619	+	0.534830i
$850$		−	1.48015e6i		−	0.0702680i
$851$			1.16844e7i			0.553072i
$852$	−8.69005e6	−	7.04603e6i	−0.410131	−	0.332541i
$853$			1.05962e7i			0.498630i	0.968422	+	0.249315i	$0.0802054\pi$
$853$			1.05962e7i			0.498630i	−0.968422	+	0.249315i	$0.919795\pi$
$854$		0			0
$855$	−2.54447e7	+	5.37529e6i	−1.19037	+	0.251470i
$856$	−7.59106e6			−0.354094
$857$	−1.46215e7			−0.680048			−0.340024	−	0.940417i	$-0.610435\pi$
$857$	−1.46215e7			−0.680048			−0.340024	+	0.940417i	$0.610435\pi$
$858$	−1.41740e7	−	1.14925e7i	−0.657314	−	0.532961i
$859$			9.57574e6i			0.442781i	0.975185	+	0.221391i	$0.0710596\pi$
$859$			9.57574e6i			0.442781i	−0.975185	+	0.221391i	$0.928940\pi$
$860$	−5.60969e6			−0.258638
$861$		0			0
$862$	4.49838e6			0.206200
$863$			2.31365e7i			1.05747i	0.848786	+	0.528737i	$0.177334\pi$
$863$			2.31365e7i			1.05747i	−0.848786	+	0.528737i	$0.822666\pi$
$864$	−1.76745e6	+	3.45283e6i	−0.0805494	+	0.157359i
$865$	7.40975e6			0.336716
$866$	−2.35275e7			−1.06606
$867$	−7.09766e6	+	8.75372e6i	−0.320677	+	0.395499i
$868$		0			0
$869$		−	1.53397e7i		−	0.689075i
$870$	−2.95800e6	+	3.64818e6i	−0.132495	+	0.163410i
$871$			1.77586e7i			0.793166i
$872$			2.44711e6i			0.108984i
$873$	2.41706e6	−	510614.i	0.107338	−	0.0226755i
$874$			6.23810e6i			0.276232i
$875$		0			0
$876$	1.58582e7	+	1.28581e7i	0.698224	+	0.566132i
$877$	2.38822e7			1.04852			0.524258	−	0.851560i	$-0.324343\pi$
$877$	2.38822e7			1.04852			0.524258	+	0.851560i	$0.324343\pi$
$878$	−7.82945e6			−0.342764
$879$	285505.	−	352120.i	0.0124635	−	0.0153716i
$880$		−	6.00867e6i		−	0.261560i
$881$	9.62250e6			0.417684			0.208842	−	0.977949i	$-0.433030\pi$
$881$	9.62250e6			0.417684			0.208842	+	0.977949i	$0.433030\pi$
$882$		0			0
$883$	−692985.			−0.0299104			−0.0149552	−	0.999888i	$-0.504761\pi$
$883$	−692985.			−0.0299104			−0.0149552	+	0.999888i	$0.504761\pi$
$884$		−	8.62429e6i		−	0.371187i
$885$	−2.49575e6	+	3.07807e6i	−0.107113	+	0.132106i
$886$	1.35420e7			0.579560
$887$	−8.07328e6			−0.344541			−0.172270	−	0.985050i	$-0.555110\pi$
$887$	−8.07328e6			−0.344541			−0.172270	+	0.985050i	$0.555110\pi$
$888$	1.19989e7	+	9.72893e6i	0.510634	+	0.414031i
$889$		0			0
$890$			1.83172e7i			0.775146i
$891$	−1.08247e7	−	2.44767e7i	−0.456795	−	1.03290i
$892$		−	1.87992e7i		−	0.791094i
$893$			1.10791e7i			0.464919i
$894$	6.58555e6	−	8.12212e6i	0.275580	−	0.339880i
$895$		−	3.95703e7i		−	1.65125i
$896$		0			0
$897$	4.78358e6	−	5.89971e6i	0.198505	−	0.244821i
$898$	1.09817e6			0.0454444
$899$	−5.80090e6			−0.239385
$900$	−356210.	−	1.68617e6i	−0.0146589	−	0.0693898i
$901$		−	2.90716e7i		−	1.19304i
$902$	3.51868e7			1.44000
$903$		0			0
$904$	−9.25182e6			−0.376535
$905$		−	9.65297e6i		−	0.391777i
$906$	2.20928e7	+	1.79132e7i	0.894192	+	0.725026i
$907$	3.87958e7			1.56591			0.782954	−	0.622080i	$-0.213712\pi$
$907$	3.87958e7			1.56591			0.782954	+	0.622080i	$0.213712\pi$
$908$	3.61886e6			0.145666
$909$	1.69731e6	+	8.03447e6i	0.0681321	+	0.322513i
$910$		0			0
$911$			1.13804e7i			0.454321i	0.973857	+	0.227160i	$0.0729442\pi$
$911$			1.13804e7i			0.454321i	−0.973857	+	0.227160i	$0.927056\pi$
$912$	6.40604e6	+	5.19412e6i	0.255037	+	0.206788i
$913$		−	4.28350e6i		−	0.170068i
$914$		−	2.17677e7i		−	0.861879i
$915$	2.10637e7	+	1.70788e7i	0.831730	+	0.674381i
$916$		−	1.24996e7i		−	0.492218i
$917$		0			0
$918$	5.76361e6	−	1.12596e7i	0.225729	−	0.440978i
$919$	−2.18961e7			−0.855221			−0.427611	−	0.903963i	$-0.640645\pi$
$919$	−2.18961e7			−0.855221			−0.427611	+	0.903963i	$0.640645\pi$
$920$	2.50102e6			0.0974201
$921$	2.34259e6	+	1.89941e6i	0.0910013	+	0.0737854i
$922$			1.52925e7i			0.592448i
$923$	2.89621e7			1.11899
$924$		0			0
$925$	−6.86330e6			−0.263741
$926$			2.69625e7i			1.03331i
$927$	2.96429e7	−	6.26217e6i	1.13298	−	0.239346i
$928$	1.48943e6			0.0567742
$929$	−3.17704e7			−1.20777			−0.603885	−	0.797072i	$-0.706381\pi$
$929$	−3.17704e7			−1.20777			−0.603885	+	0.797072i	$0.706381\pi$
$930$	−8.11058e6	+	1.00030e7i	−0.307500	+	0.379247i
$931$		0			0
$932$		−	2.52772e7i		−	0.953211i
$933$	−2.51006e7	+	3.09571e7i	−0.944016	+	1.16428i
$934$			1.62754e7i			0.610470i
$935$			1.95942e7i			0.732990i
$936$	−2.07551e6	−	9.82472e6i	−0.0774346	−	0.366548i
$937$		−	9.04032e6i		−	0.336384i	−0.985754	−	0.168192i	$-0.946207\pi$
$937$		−	9.04032e6i		−	0.336384i	0.985754	−	0.168192i	$-0.0537928\pi$
$938$		0			0
$939$	5.12415e6	+	4.15474e6i	0.189652	+	0.153773i
$940$	4.44193e6			0.163965
$941$	−6.45640e6			−0.237693			−0.118847	−	0.992913i	$-0.537920\pi$
$941$	−6.45640e6			−0.237693			−0.118847	+	0.992913i	$0.537920\pi$
$942$	7.17384e6	−	8.84767e6i	0.263405	−	0.324864i
$943$			1.46460e7i			0.536339i
$944$	1.25668e6			0.0458981
$945$		0			0
$946$	−1.22744e7			−0.445936
$947$		−	3.57334e7i		−	1.29479i	−0.762154	−	0.647396i	$-0.775858\pi$
$947$		−	3.57334e7i		−	1.29479i	0.762154	−	0.647396i	$-0.224142\pi$
$948$	5.31636e6	−	6.55680e6i	0.192129	−	0.236958i
$949$	−5.28523e7			−1.90501
$950$	−3.66420e6			−0.131726
$951$	−437970.	−	355113.i	−0.0157034	−	0.0127326i
$952$		0			0
$953$		−	1.85895e7i		−	0.663033i	−0.943449	−	0.331516i	$-0.892440\pi$
$953$		−	1.85895e7i		−	0.663033i	0.943449	−	0.331516i	$-0.107560\pi$
$954$	−6.99632e6	−	3.31181e7i	−0.248885	−	1.17813i
$955$			3.41626e7i			1.21211i
$956$		−	1.70579e7i		−	0.603644i
$957$	−6.47233e6	+	7.98248e6i	−0.228444	+	0.281746i
$958$		−	9.38022e6i		−	0.330217i
$959$		0			0
$960$	2.08246e6	−	2.56835e6i	0.0729289	−	0.0899449i
$961$	1.27236e7			0.444428
$962$	−3.99900e7			−1.39320
$963$	2.81999e7	−	5.95734e6i	0.979901	−	0.207008i
$964$			4.62219e6i			0.160197i
$965$	−1.06305e6			−0.0367482
$966$		0			0
$967$	4.34595e7			1.49458			0.747288	−	0.664500i	$-0.231355\pi$
$967$	4.34595e7			1.49458			0.747288	+	0.664500i	$0.231355\pi$
$968$		−	2.84015e6i		−	0.0974210i
$969$	−2.08900e7	−	1.69379e7i	−0.714708	−	0.579497i
$970$	−2.10587e6			−0.0718624
$971$	4.52687e7			1.54081			0.770407	−	0.637553i	$-0.220053\pi$
$971$	4.52687e7			1.54081			0.770407	+	0.637553i	$0.220053\pi$
$972$	3.85614e6	−	1.42139e7i	0.130914	−	0.482557i
$973$		0			0
$974$		−	1.71066e7i		−	0.577785i
$975$	3.46543e6	+	2.80983e6i	0.116747	+	0.0946605i
$976$		−	8.59964e6i		−	0.288972i
$977$			1.79054e7i			0.600133i	0.953918	+	0.300067i	$0.0970089\pi$
$977$			1.79054e7i			0.600133i	−0.953918	+	0.300067i	$0.902991\pi$
$978$	2.44722e7	+	1.98424e7i	0.818136	+	0.663358i
$979$			4.00793e7i			1.33648i
$980$		0			0
$981$	−1.92045e6	−	9.09074e6i	−0.0637135	−	0.301597i
$982$	2.38712e6			0.0789942
$983$	−1.12555e7			−0.371519			−0.185760	−	0.982595i	$-0.559475\pi$
$983$	−1.12555e7			−0.371519			−0.185760	+	0.982595i	$0.559475\pi$
$984$	1.50403e7	+	1.21949e7i	0.495185	+	0.401505i
$985$			2.89241e7i			0.949881i
$986$	−4.85702e6			−0.159103
$987$		0			0
$988$	−2.13500e7			−0.695834
$989$		−	5.10904e6i		−	0.166092i
$990$	4.71551e6	+	2.23215e7i	0.152912	+	0.723829i
$991$	3.85163e6			0.124583			0.0622917	−	0.998058i	$-0.480159\pi$
$991$	3.85163e6			0.124583			0.0622917	+	0.998058i	$0.480159\pi$
$992$	4.08389e6			0.131764
$993$	2.15146e6	−	2.65344e6i	0.0692404	−	0.0853959i
$994$		0			0
$995$		−	1.27245e7i		−	0.407458i
$996$	1.48456e6	−	1.83094e6i	0.0474187	−	0.0584826i
$997$			5.88461e6i			0.187491i	0.995596	+	0.0937454i	$0.0298840\pi$
$997$			5.88461e6i			0.187491i	−0.995596	+	0.0937454i	$0.970116\pi$
$998$			1.71372e7i			0.544645i
$999$	−5.22098e7	−	2.67253e7i	−1.65515	−	0.847245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.d.a.293.9		28
3.2	odd	2	inner	294.6.d.a.293.20		28
7.4	even	3		42.6.f.a.5.8	yes	28
7.5	odd	6		42.6.f.a.17.3	yes	28
7.6	odd	2	inner	294.6.d.a.293.19		28
21.5	even	6		42.6.f.a.17.8	yes	28
21.11	odd	6		42.6.f.a.5.3	✓	28
21.20	even	2	inner	294.6.d.a.293.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.f.a.5.3	✓	28	21.11	odd	6
42.6.f.a.5.8	yes	28	7.4	even	3
42.6.f.a.17.3	yes	28	7.5	odd	6
42.6.f.a.17.8	yes	28	21.5	even	6
294.6.d.a.293.9		28	1.1	even	1	trivial
294.6.d.a.293.10		28	21.20	even	2	inner
294.6.d.a.293.19		28	7.6	odd	2	inner
294.6.d.a.293.20		28	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} +(9.81768 - 12.1084i) q^{3} -16.0000 q^{4} -51.7855 q^{5} +(-48.4336 - 39.2707i) q^{6} +64.0000i q^{8} +(-50.2262 - 237.753i) q^{9} +207.142i q^{10} +453.242i q^{11} +(-157.083 + 193.734i) q^{12} -645.676i q^{13} +(-508.414 + 627.039i) q^{15} +256.000 q^{16} -834.812 q^{17} +(-951.011 + 200.905i) q^{18} +2066.63i q^{19} +828.569 q^{20} +1812.97 q^{22} +754.622i q^{23} +(774.937 + 628.332i) q^{24} -443.258 q^{25} -2582.70 q^{26} +(-3371.91 - 1726.02i) q^{27} +1454.53i q^{29} +(2508.16 + 2033.66i) q^{30} +3988.18i q^{31} -1024.00i q^{32} +(5488.03 + 4449.79i) q^{33} +3339.25i q^{34} +(803.619 + 3804.04i) q^{36} +15483.8 q^{37} +8266.53 q^{38} +(-7818.10 - 6339.04i) q^{39} -3314.27i q^{40} +19408.4 q^{41} -6770.34 q^{43} -7251.87i q^{44} +(2600.99 + 12312.2i) q^{45} +3018.49 q^{46} +5360.97 q^{47} +(2513.33 - 3099.75i) q^{48} +1773.03i q^{50} +(-8195.92 + 10108.2i) q^{51} +10330.8i q^{52} +34824.1i q^{53} +(-6904.09 + 13487.6i) q^{54} -23471.4i q^{55} +(25023.6 + 20289.5i) q^{57} +5818.10 q^{58} +4908.90 q^{59} +(8134.62 - 10032.6i) q^{60} -33592.3i q^{61} +15952.7 q^{62} -4096.00 q^{64} +33436.7i q^{65} +(17799.1 - 21952.1i) q^{66} -27503.9 q^{67} +13357.0 q^{68} +(9137.26 + 7408.64i) q^{69} +44855.5i q^{71} +(15216.2 - 3214.47i) q^{72} -81855.7i q^{73} -61935.0i q^{74} +(-4351.77 + 5367.14i) q^{75} -33066.1i q^{76} +(-25356.2 + 31272.4i) q^{78} -33844.3 q^{79} -13257.1 q^{80} +(-54003.7 + 23882.8i) q^{81} -77633.5i q^{82} -9450.81 q^{83} +43231.2 q^{85} +27081.3i q^{86} +(17612.0 + 14280.1i) q^{87} -29007.5 q^{88} +88428.0 q^{89} +(49248.6 - 10404.0i) q^{90} -12074.0i q^{92} +(48290.4 + 39154.7i) q^{93} -21443.9i q^{94} -107022. i q^{95} +(-12399.0 - 10053.3i) q^{96} +10166.3i q^{97} +(107759. - 22764.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 448 q^{4} + 60 q^{9} - 516 q^{15} + 7168 q^{16} - 3264 q^{18} + 3312 q^{22} + 26416 q^{25} - 4896 q^{30} - 960 q^{36} - 10976 q^{37} - 43776 q^{39} - 40352 q^{43} + 23136 q^{46} + 69144 q^{51} + 57168 q^{57}+ \cdots + 153216 q^{99}+O(q^{100}) \) 28 * q - 448 * q^4 + 60 * q^9 - 516 * q^15 + 7168 * q^16 - 3264 * q^18 + 3312 * q^22 + 26416 * q^25 - 4896 * q^30 - 960 * q^36 - 10976 * q^37 - 43776 * q^39 - 40352 * q^43 + 23136 * q^46 + 69144 * q^51 + 57168 * q^57 - 85104 * q^58 + 8256 * q^60 - 114688 * q^64 - 110296 * q^67 + 52224 * q^72 + 87840 * q^78 - 943588 * q^79 + 491076 * q^81 - 562056 * q^85 - 52992 * q^88 + 1120896 * q^93 + 153216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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