LMFDB - Embedded newform 336.6.q.b.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.6.q.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 + 7.79423i) q^{3} +(-5.50000 - 9.52628i) q^{5} +(-129.500 + 6.06218i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.50000 + 7.79423i) q^{3} +(-5.50000 - 9.52628i) q^{5} +(-129.500 + 6.06218i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(134.500 - 232.961i) q^{11} -308.000 q^{13} +99.0000 q^{15} +(-948.000 + 1641.98i) q^{17} +(-82.0000 - 142.028i) q^{19} +(535.500 - 1036.63i) q^{21} +(-1632.00 - 2826.71i) q^{23} +(1502.00 - 2601.54i) q^{25} +729.000 q^{27} +2417.00 q^{29} +(1420.50 - 2460.38i) q^{31} +(1210.50 + 2096.65i) q^{33} +(770.000 + 1200.31i) q^{35} +(5664.00 + 9810.34i) q^{37} +(1386.00 - 2400.62i) q^{39} -16856.0 q^{41} +7894.00 q^{43} +(-445.500 + 771.629i) q^{45} +(10551.0 + 18274.9i) q^{47} +(16733.5 - 1570.10i) q^{49} +(-8532.00 - 14777.9i) q^{51} +(14845.5 - 25713.2i) q^{53} -2959.00 q^{55} +1476.00 q^{57} +(-4081.50 + 7069.37i) q^{59} +(-7583.00 - 13134.1i) q^{61} +(5670.00 + 8838.66i) q^{63} +(1694.00 + 2934.09i) q^{65} +(-16039.0 + 27780.4i) q^{67} +29376.0 q^{69} +38274.0 q^{71} +(-17433.0 + 30194.8i) q^{73} +(13518.0 + 23413.9i) q^{75} +(-16005.5 + 30983.8i) q^{77} +(6764.50 + 11716.5i) q^{79} +(-3280.50 + 5681.99i) q^{81} +68103.0 q^{83} +20856.0 q^{85} +(-10876.5 + 18838.7i) q^{87} +(57461.0 + 99525.4i) q^{89} +(39886.0 - 1867.15i) q^{91} +(12784.5 + 22143.4i) q^{93} +(-902.000 + 1562.31i) q^{95} +154959. q^{97} -21789.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 9 q^{3} - 11 q^{5} - 259 q^{7} - 81 q^{9}+O(q^{10}) $ 2 * q - 9 * q^3 - 11 * q^5 - 259 * q^7 - 81 * q^9	$ 2 q - 9 q^{3} - 11 q^{5} - 259 q^{7} - 81 q^{9} + 269 q^{11} - 616 q^{13} + 198 q^{15} - 1896 q^{17} - 164 q^{19} + 1071 q^{21} - 3264 q^{23} + 3004 q^{25} + 1458 q^{27} + 4834 q^{29} + 2841 q^{31} + 2421 q^{33} + 1540 q^{35} + 11328 q^{37} + 2772 q^{39} - 33712 q^{41} + 15788 q^{43} - 891 q^{45} + 21102 q^{47} + 33467 q^{49} - 17064 q^{51} + 29691 q^{53} - 5918 q^{55} + 2952 q^{57} - 8163 q^{59} - 15166 q^{61} + 11340 q^{63} + 3388 q^{65} - 32078 q^{67} + 58752 q^{69} + 76548 q^{71} - 34866 q^{73} + 27036 q^{75} - 32011 q^{77} + 13529 q^{79} - 6561 q^{81} + 136206 q^{83} + 41712 q^{85} - 21753 q^{87} + 114922 q^{89} + 79772 q^{91} + 25569 q^{93} - 1804 q^{95} + 309918 q^{97} - 43578 q^{99}+O(q^{100}) $ 2 * q - 9 * q^3 - 11 * q^5 - 259 * q^7 - 81 * q^9 + 269 * q^11 - 616 * q^13 + 198 * q^15 - 1896 * q^17 - 164 * q^19 + 1071 * q^21 - 3264 * q^23 + 3004 * q^25 + 1458 * q^27 + 4834 * q^29 + 2841 * q^31 + 2421 * q^33 + 1540 * q^35 + 11328 * q^37 + 2772 * q^39 - 33712 * q^41 + 15788 * q^43 - 891 * q^45 + 21102 * q^47 + 33467 * q^49 - 17064 * q^51 + 29691 * q^53 - 5918 * q^55 + 2952 * q^57 - 8163 * q^59 - 15166 * q^61 + 11340 * q^63 + 3388 * q^65 - 32078 * q^67 + 58752 * q^69 + 76548 * q^71 - 34866 * q^73 + 27036 * q^75 - 32011 * q^77 + 13529 * q^79 - 6561 * q^81 + 136206 * q^83 + 41712 * q^85 - 21753 * q^87 + 114922 * q^89 + 79772 * q^91 + 25569 * q^93 - 1804 * q^95 + 309918 * q^97 - 43578 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$		0			0
$5$	−5.50000	−	9.52628i	−0.0983870	−	0.170411i	0.812630	−	0.582780i	$-0.198035\pi$
$5$	−5.50000	−	9.52628i	−0.0983870	−	0.170411i	−0.911017	+	0.412368i	$0.864702\pi$
$6$		0			0
$7$	−129.500	+	6.06218i	−0.998906	+	0.0467610i
$7$	−129.500	+	6.06218i	−0.998906	+	0.0467610i
$8$		0			0
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$		0			0
$11$	134.500	−	232.961i	0.335151	−	0.580499i	−0.648363	−	0.761332i	$-0.724546\pi$
$11$	134.500	−	232.961i	0.335151	−	0.580499i	0.983514	+	0.180833i	$0.0578793\pi$
$12$		0			0
$13$	−308.000			−0.505466			−0.252733	−	0.967536i	$-0.581329\pi$
$13$	−308.000			−0.505466			−0.252733	+	0.967536i	$0.581329\pi$
$14$		0			0
$15$	99.0000			0.113608
$16$		0			0
$17$	−948.000	+	1641.98i	−0.795584	+	1.37799i	0.126884	+	0.991918i	$0.459502\pi$
$17$	−948.000	+	1641.98i	−0.795584	+	1.37799i	−0.922468	+	0.386074i	$0.873831\pi$
$18$		0			0
$19$	−82.0000	−	142.028i	−0.0521111	−	0.0902590i	0.838793	−	0.544450i	$-0.183262\pi$
$19$	−82.0000	−	142.028i	−0.0521111	−	0.0902590i	−0.890904	+	0.454191i	$0.849928\pi$
$20$		0			0
$21$	535.500	−	1036.63i	0.264979	−	0.512952i
$22$		0			0
$23$	−1632.00	−	2826.71i	−0.643281	−	1.11419i	−0.984696	−	0.174282i	$-0.944239\pi$
$23$	−1632.00	−	2826.71i	−0.643281	−	1.11419i	0.341415	−	0.939913i	$-0.389094\pi$
$24$		0			0
$25$	1502.00	−	2601.54i	0.480640	−	0.832493i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	2417.00			0.533681			0.266840	−	0.963741i	$-0.414020\pi$
$29$	2417.00			0.533681			0.266840	+	0.963741i	$0.414020\pi$
$30$		0			0
$31$	1420.50	−	2460.38i	0.265483	−	0.459830i	−0.702207	−	0.711973i	$-0.747802\pi$
$31$	1420.50	−	2460.38i	0.265483	−	0.459830i	0.967690	+	0.252143i	$0.0811352\pi$
$32$		0			0
$33$	1210.50	+	2096.65i	0.193500	+	0.335151i
$34$		0			0
$35$	770.000	+	1200.31i	0.106248	+	0.165624i
$36$		0			0
$37$	5664.00	+	9810.34i	0.680172	+	1.17809i	0.974928	+	0.222520i	$0.0714284\pi$
$37$	5664.00	+	9810.34i	0.680172	+	1.17809i	−0.294756	+	0.955573i	$0.595238\pi$
$38$		0			0
$39$	1386.00	−	2400.62i	0.145916	−	0.252733i
$40$		0			0
$41$	−16856.0			−1.56601			−0.783006	−	0.622015i	$-0.786314\pi$
$41$	−16856.0			−1.56601			−0.783006	+	0.622015i	$0.786314\pi$
$42$		0			0
$43$	7894.00			0.651067			0.325534	−	0.945530i	$-0.394456\pi$
$43$	7894.00			0.651067			0.325534	+	0.945530i	$0.394456\pi$
$44$		0			0
$45$	−445.500	+	771.629i	−0.0327957	+	0.0568038i
$46$		0			0
$47$	10551.0	+	18274.9i	0.696705	+	1.20673i	0.969603	+	0.244685i	$0.0786847\pi$
$47$	10551.0	+	18274.9i	0.696705	+	1.20673i	−0.272897	+	0.962043i	$0.587982\pi$
$48$		0			0
$49$	16733.5	−	1570.10i	0.995627	−	0.0934196i
$50$		0			0
$51$	−8532.00	−	14777.9i	−0.459331	−	0.795584i
$52$		0			0
$53$	14845.5	−	25713.2i	0.725947	−	1.25738i	−0.232635	−	0.972564i	$-0.574735\pi$
$53$	14845.5	−	25713.2i	0.725947	−	1.25738i	0.958583	−	0.284814i	$-0.0919318\pi$
$54$		0			0
$55$	−2959.00			−0.131898
$56$		0			0
$57$	1476.00			0.0601727
$58$		0			0
$59$	−4081.50	+	7069.37i	−0.152648	+	0.264393i	−0.932200	−	0.361944i	$-0.882113\pi$
$59$	−4081.50	+	7069.37i	−0.152648	+	0.264393i	0.779552	+	0.626337i	$0.215447\pi$
$60$		0			0
$61$	−7583.00	−	13134.1i	−0.260925	−	0.451936i	0.705563	−	0.708648i	$-0.250694\pi$
$61$	−7583.00	−	13134.1i	−0.260925	−	0.451936i	−0.966488	+	0.256711i	$0.917361\pi$
$62$		0			0
$63$	5670.00	+	8838.66i	0.179983	+	0.280566i
$64$		0			0
$65$	1694.00	+	2934.09i	0.0497313	+	0.0861372i
$66$		0			0
$67$	−16039.0	+	27780.4i	−0.436506	+	0.756051i	−0.997417	−	0.0718253i	$-0.977118\pi$
$67$	−16039.0	+	27780.4i	−0.436506	+	0.756051i	0.560911	+	0.827876i	$0.310451\pi$
$68$		0			0
$69$	29376.0			0.742797
$70$		0			0
$71$	38274.0			0.901069			0.450534	−	0.892759i	$-0.351233\pi$
$71$	38274.0			0.901069			0.450534	+	0.892759i	$0.351233\pi$
$72$		0			0
$73$	−17433.0	+	30194.8i	−0.382882	+	0.663171i	−0.991473	−	0.130313i	$-0.958402\pi$
$73$	−17433.0	+	30194.8i	−0.382882	+	0.663171i	0.608591	+	0.793484i	$0.291735\pi$
$74$		0			0
$75$	13518.0	+	23413.9i	0.277498	+	0.480640i
$76$		0			0
$77$	−16005.5	+	30983.8i	−0.307640	+	0.595536i
$78$		0			0
$79$	6764.50	+	11716.5i	0.121946	+	0.211217i	0.920535	−	0.390660i	$-0.127753\pi$
$79$	6764.50	+	11716.5i	0.121946	+	0.211217i	−0.798589	+	0.601877i	$0.794420\pi$
$80$		0			0
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	68103.0			1.08510			0.542552	−	0.840023i	$-0.317458\pi$
$83$	68103.0			1.08510			0.542552	+	0.840023i	$0.317458\pi$
$84$		0			0
$85$	20856.0			0.313100
$86$		0			0
$87$	−10876.5	+	18838.7i	−0.154060	+	0.266840i
$88$		0			0
$89$	57461.0	+	99525.4i	0.768950	+	1.33186i	0.938133	+	0.346276i	$0.112554\pi$
$89$	57461.0	+	99525.4i	0.768950	+	1.33186i	−0.169183	+	0.985585i	$0.554113\pi$
$90$		0			0
$91$	39886.0	−	1867.15i	0.504914	−	0.0236361i
$92$		0			0
$93$	12784.5	+	22143.4i	0.153277	+	0.265483i
$94$		0			0
$95$	−902.000	+	1562.31i	−0.0102541	+	0.0177606i
$96$		0			0
$97$	154959.			1.67220			0.836099	−	0.548579i	$-0.184831\pi$
$97$	154959.			1.67220			0.836099	+	0.548579i	$0.184831\pi$
$98$		0			0
$99$	−21789.0			−0.223434
$100$		0			0
$101$	53785.0	−	93158.4i	0.524636	−	0.908695i	−0.474953	−	0.880011i	$-0.657535\pi$
$101$	53785.0	−	93158.4i	0.524636	−	0.908695i	0.999589	−	0.0286843i	$-0.00913174\pi$
$102$		0			0
$103$	4468.00	+	7738.80i	0.0414973	+	0.0718755i	0.886028	−	0.463632i	$-0.153454\pi$
$103$	4468.00	+	7738.80i	0.0414973	+	0.0718755i	−0.844531	+	0.535507i	$0.820121\pi$
$104$		0			0
$105$	−12820.5	+	600.156i	−0.113483	+	0.00531240i
$106$		0			0
$107$	96833.5	+	167721.i	0.817648	+	1.41621i	0.907411	+	0.420244i	$0.138056\pi$
$107$	96833.5	+	167721.i	0.817648	+	1.41621i	−0.0897634	+	0.995963i	$0.528611\pi$
$108$		0			0
$109$	−102555.	+	177630.i	−0.826781	+	1.43203i	0.0737692	+	0.997275i	$0.476497\pi$
$109$	−102555.	+	177630.i	−0.826781	+	1.43203i	−0.900550	+	0.434752i	$0.856836\pi$
$110$		0			0
$111$	−101952.			−0.785395
$112$		0			0
$113$	46664.0			0.343784			0.171892	−	0.985116i	$-0.445012\pi$
$113$	46664.0			0.343784			0.171892	+	0.985116i	$0.445012\pi$
$114$		0			0
$115$	−17952.0	+	31093.8i	−0.126581	+	0.219245i
$116$		0			0
$117$	12474.0	+	21605.6i	0.0842444	+	0.145916i
$118$		0			0
$119$	112812.	−	218384.i	0.730277	−	1.41369i
$120$		0			0
$121$	44345.0	+	76807.8i	0.275348	+	0.476916i
$122$		0			0
$123$	75852.0	−	131380.i	0.452069	−	0.783006i
$124$		0			0
$125$	−67419.0			−0.385929
$126$		0			0
$127$	304365.			1.67450			0.837250	−	0.546820i	$-0.184162\pi$
$127$	304365.			1.67450			0.837250	+	0.546820i	$0.184162\pi$
$128$		0			0
$129$	−35523.0	+	61527.6i	−0.187947	+	0.325534i
$130$		0			0
$131$	−6651.50	−	11520.7i	−0.0338642	−	0.0586546i	0.848597	−	0.529041i	$-0.177448\pi$
$131$	−6651.50	−	11520.7i	−0.0338642	−	0.0586546i	−0.882461	+	0.470386i	$0.844115\pi$
$132$		0			0
$133$	11480.0	+	17895.5i	0.0562746	+	0.0877235i
$134$		0			0
$135$	−4009.50	−	6944.66i	−0.0189346	−	0.0327957i
$136$		0			0
$137$	199131.	−	344905.i	0.906437	−	1.56999i	0.0874596	−	0.996168i	$-0.472125\pi$
$137$	199131.	−	344905.i	0.906437	−	1.56999i	0.818977	−	0.573826i	$-0.194542\pi$
$138$		0			0
$139$	−230286.			−1.01095			−0.505476	−	0.862841i	$-0.668683\pi$
$139$	−230286.			−1.01095			−0.505476	+	0.862841i	$0.668683\pi$
$140$		0			0
$141$	−189918.			−0.804486
$142$		0			0
$143$	−41426.0	+	71751.9i	−0.169408	+	0.293423i
$144$		0			0
$145$	−13293.5	−	23025.0i	−0.0525073	−	0.0909452i
$146$		0			0
$147$	−63063.0	+	137490.i	−0.240703	+	0.524781i
$148$		0			0
$149$	48567.0	+	84120.5i	0.179216	+	0.310410i	0.941612	−	0.336700i	$-0.109311\pi$
$149$	48567.0	+	84120.5i	0.179216	+	0.310410i	−0.762397	+	0.647110i	$0.775977\pi$
$150$		0			0
$151$	−14523.5	+	25155.4i	−0.0518357	+	0.0897821i	−0.890779	−	0.454437i	$-0.849841\pi$
$151$	−14523.5	+	25155.4i	−0.0518357	+	0.0897821i	0.838943	+	0.544219i	$0.183174\pi$
$152$		0			0
$153$	153576.			0.530389
$154$		0			0
$155$	−31251.0			−0.104480
$156$		0			0
$157$	288250.	−	499264.i	0.933298	−	1.61652i	0.155656	−	0.987811i	$-0.450251\pi$
$157$	288250.	−	499264.i	0.933298	−	1.61652i	0.777642	−	0.628708i	$-0.216416\pi$
$158$		0			0
$159$	133610.	+	231418.i	0.419126	+	0.725947i
$160$		0			0
$161$	228480.	+	356165.i	0.694678	+	1.08290i
$162$		0			0
$163$	−132616.	−	229698.i	−0.390955	−	0.677154i	0.601621	−	0.798782i	$-0.294522\pi$
$163$	−132616.	−	229698.i	−0.390955	−	0.677154i	−0.992576	+	0.121628i	$0.961189\pi$
$164$		0			0
$165$	13315.5	−	23063.1i	0.0380757	−	0.0659490i
$166$		0			0
$167$	363790.			1.00939			0.504696	−	0.863297i	$-0.331605\pi$
$167$	363790.			1.00939			0.504696	+	0.863297i	$0.331605\pi$
$168$		0			0
$169$	−276429.			−0.744504
$170$		0			0
$171$	−6642.00	+	11504.3i	−0.0173704	+	0.0300863i
$172$		0			0
$173$	82423.0	+	142761.i	0.209379	+	0.362655i	0.951519	−	0.307590i	$-0.0995224\pi$
$173$	82423.0	+	142761.i	0.209379	+	0.362655i	−0.742140	+	0.670245i	$0.766189\pi$
$174$		0			0
$175$	−178738.	+	346005.i	−0.441186	+	0.854057i
$176$		0			0
$177$	−36733.5	−	63624.3i	−0.0881311	−	0.152648i
$178$		0			0
$179$	15314.0	−	26524.6i	0.0357237	−	0.0618752i	−0.847611	−	0.530618i	$-0.821960\pi$
$179$	15314.0	−	26524.6i	0.0357237	−	0.0618752i	0.883334	+	0.468743i	$0.155293\pi$
$180$		0			0
$181$	−651392.			−1.47790			−0.738952	−	0.673759i	$-0.764679\pi$
$181$	−651392.			−1.47790			−0.738952	+	0.673759i	$0.764679\pi$
$182$		0			0
$183$	136494.			0.301291
$184$		0			0
$185$	62304.0	−	107914.i	0.133840	−	0.231818i
$186$		0			0
$187$	255012.	+	441694.i	0.533282	+	0.923671i
$188$		0			0
$189$	−94405.5	+	4419.33i	−0.192240	+	0.00899915i
$190$		0			0
$191$	−378680.	−	655893.i	−0.751085	−	1.30092i	−0.947297	−	0.320356i	$-0.896198\pi$
$191$	−378680.	−	655893.i	−0.751085	−	1.30092i	0.196213	−	0.980561i	$-0.437136\pi$
$192$		0			0
$193$	80169.5	−	138858.i	0.154923	−	0.268335i	−0.778108	−	0.628131i	$-0.783820\pi$
$193$	80169.5	−	138858.i	0.154923	−	0.268335i	0.933031	+	0.359796i	$0.117154\pi$
$194$		0			0
$195$	−30492.0			−0.0574248
$196$		0			0
$197$	−61738.0			−0.113341			−0.0566705	−	0.998393i	$-0.518048\pi$
$197$	−61738.0			−0.113341			−0.0566705	+	0.998393i	$0.518048\pi$
$198$		0			0
$199$	185454.	−	321216.i	0.331974	−	0.574995i	−0.650925	−	0.759142i	$-0.725619\pi$
$199$	185454.	−	321216.i	0.331974	−	0.574995i	0.982899	+	0.184147i	$0.0589522\pi$
$200$		0			0
$201$	−144351.	−	250023.i	−0.252017	−	0.436506i
$202$		0			0
$203$	−313001.	+	14652.3i	−0.533097	+	0.0249554i
$204$		0			0
$205$	92708.0	+	160575.i	0.154075	+	0.266866i
$206$		0			0
$207$	−132192.	+	228963.i	−0.214427	+	0.371398i
$208$		0			0
$209$	−44116.0			−0.0698603
$210$		0			0
$211$	−217450.			−0.336243			−0.168122	−	0.985766i	$-0.553770\pi$
$211$	−217450.			−0.336243			−0.168122	+	0.985766i	$0.553770\pi$
$212$		0			0
$213$	−172233.	+	298316.i	−0.260116	+	0.450534i
$214$		0			0
$215$	−43417.0	−	75200.4i	−0.0640566	−	0.110949i
$216$		0			0
$217$	−169040.	+	327230.i	−0.243691	+	0.471742i
$218$		0			0
$219$	−156897.	−	271754.i	−0.221057	−	0.382882i
$220$		0			0
$221$	291984.	−	505731.i	0.402141	−	0.696529i
$222$		0			0
$223$	−589771.			−0.794184			−0.397092	−	0.917779i	$-0.629981\pi$
$223$	−589771.			−0.794184			−0.397092	+	0.917779i	$0.629981\pi$
$224$		0			0
$225$	−243324.			−0.320427
$226$		0			0
$227$	−193522.	+	335191.i	−0.249268	+	0.431745i	−0.963323	−	0.268345i	$-0.913523\pi$
$227$	−193522.	+	335191.i	−0.249268	+	0.431745i	0.714055	+	0.700090i	$0.246857\pi$
$228$		0			0
$229$	116366.	+	201552.i	0.146635	+	0.253979i	0.929982	−	0.367606i	$-0.119822\pi$
$229$	116366.	+	201552.i	0.146635	+	0.253979i	−0.783347	+	0.621585i	$0.786489\pi$
$230$		0			0
$231$	−169470.	−	264178.i	−0.208960	−	0.325736i
$232$		0			0
$233$	−21048.0	−	36456.2i	−0.0253993	−	0.0439928i	0.853046	−	0.521835i	$-0.174752\pi$
$233$	−21048.0	−	36456.2i	−0.0253993	−	0.0439928i	−0.878446	+	0.477842i	$0.841419\pi$
$234$		0			0
$235$	116061.	−	201024.i	0.137093	−	0.237453i
$236$		0			0
$237$	−121761.			−0.140811
$238$		0			0
$239$	313416.			0.354917			0.177458	−	0.984128i	$-0.443212\pi$
$239$	313416.			0.354917			0.177458	+	0.984128i	$0.443212\pi$
$240$		0			0
$241$	−428904.	+	742883.i	−0.475682	+	0.823906i	−0.999612	−	0.0278556i	$-0.991132\pi$
$241$	−428904.	+	742883.i	−0.475682	+	0.823906i	0.523930	+	0.851762i	$0.324465\pi$
$242$		0			0
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−106992.	−	150772.i	−0.113876	−	0.160475i
$246$		0			0
$247$	25256.0	+	43744.7i	0.0263404	+	0.0456229i
$248$		0			0
$249$	−306464.	+	530810.i	−0.313242	+	0.542552i
$250$		0			0
$251$	−454517.			−0.455371			−0.227686	−	0.973735i	$-0.573116\pi$
$251$	−454517.			−0.455371			−0.227686	+	0.973735i	$0.573116\pi$
$252$		0			0
$253$	−878016.			−0.862385
$254$		0			0
$255$	−93852.0	+	162556.i	−0.0903843	+	0.156550i
$256$		0			0
$257$	−439091.	−	760528.i	−0.414688	−	0.718261i	0.580707	−	0.814112i	$-0.302776\pi$
$257$	−439091.	−	760528.i	−0.414688	−	0.718261i	−0.995396	+	0.0958512i	$0.969443\pi$
$258$		0			0
$259$	−792960.	−	1.23610e6i	−0.734517	−	1.14500i
$260$		0			0
$261$	−97888.5	−	169548.i	−0.0889468	−	0.154060i
$262$		0			0
$263$	980467.	−	1.69822e6i	0.874065	−	1.51392i	0.0163091	−	0.999867i	$-0.494808\pi$
$263$	980467.	−	1.69822e6i	0.874065	−	1.51392i	0.857756	−	0.514058i	$-0.171858\pi$
$264$		0			0
$265$	−326601.			−0.285695
$266$		0			0
$267$	−1.03430e6			−0.887907
$268$		0			0
$269$	526898.	−	912613.i	0.443962	−	0.768964i	−0.554018	−	0.832505i	$-0.686906\pi$
$269$	526898.	−	912613.i	0.443962	−	0.768964i	0.997979	+	0.0635408i	$0.0202393\pi$
$270$		0			0
$271$	−52529.5	−	90983.8i	−0.0434490	−	0.0752559i	0.843483	−	0.537156i	$-0.180501\pi$
$271$	−52529.5	−	90983.8i	−0.0434490	−	0.0752559i	−0.886932	+	0.461900i	$0.847168\pi$
$272$		0			0
$273$	−164934.	+	319283.i	−0.133938	+	0.259280i
$274$		0			0
$275$	−404038.	−	699814.i	−0.322174	−	0.558022i
$276$		0			0
$277$	213796.	−	370306.i	0.167417	−	0.289975i	−0.770094	−	0.637931i	$-0.779791\pi$
$277$	213796.	−	370306.i	0.167417	−	0.289975i	0.937511	+	0.347955i	$0.113124\pi$
$278$		0			0
$279$	−230121.			−0.176989
$280$		0			0
$281$	638878.			0.482672			0.241336	−	0.970442i	$-0.422414\pi$
$281$	638878.			0.482672			0.241336	+	0.970442i	$0.422414\pi$
$282$		0			0
$283$	−1.22571e6	+	2.12299e6i	−0.909750	+	1.57573i	−0.0953386	+	0.995445i	$0.530393\pi$
$283$	−1.22571e6	+	2.12299e6i	−0.909750	+	1.57573i	−0.814411	+	0.580288i	$0.802940\pi$
$284$		0			0
$285$	−8118.00	−	14060.8i	−0.00592021	−	0.0102541i
$286$		0			0
$287$	2.18285e6	−	102184.i	1.56430	−	0.0732282i
$288$		0			0
$289$	−1.08748e6	−	1.88357e6i	−0.765908	−	1.32659i
$290$		0			0
$291$	−697316.	+	1.20779e6i	−0.482722	+	0.836099i
$292$		0			0
$293$	1.71617e6			1.16786			0.583930	−	0.811804i	$-0.301514\pi$
$293$	1.71617e6			1.16786			0.583930	+	0.811804i	$0.301514\pi$
$294$		0			0
$295$	89793.0			0.0600741
$296$		0			0
$297$	98050.5	−	169828.i	0.0644998	−	0.111717i
$298$		0			0
$299$	502656.	+	870626.i	0.325157	+	0.563188i
$300$		0			0
$301$	−1.02227e6	+	47854.8i	−0.650355	+	0.0304445i
$302$		0			0
$303$	484065.	+	838425.i	0.302898	+	0.524636i
$304$		0			0
$305$	−83413.0	+	144476.i	−0.0513433	+	0.0889293i
$306$		0			0
$307$	−1.80897e6			−1.09543			−0.547715	−	0.836665i	$-0.684502\pi$
$307$	−1.80897e6			−1.09543			−0.547715	+	0.836665i	$0.684502\pi$
$308$		0			0
$309$	−80424.0			−0.0479170
$310$		0			0
$311$	760728.	−	1.31762e6i	0.445993	−	0.772483i	−0.552127	−	0.833760i	$-0.686184\pi$
$311$	760728.	−	1.31762e6i	0.445993	−	0.772483i	0.998121	+	0.0612765i	$0.0195171\pi$
$312$		0			0
$313$	674200.	+	1.16775e6i	0.388980	+	0.673734i	0.992313	−	0.123756i	$-0.0394941\pi$
$313$	674200.	+	1.16775e6i	0.388980	+	0.673734i	−0.603332	+	0.797490i	$0.706161\pi$
$314$		0			0
$315$	53014.5	−	102627.i	0.0301036	−	0.0582752i
$316$		0			0
$317$	24847.5	+	43037.1i	0.0138878	+	0.0240544i	0.872886	−	0.487925i	$-0.162246\pi$
$317$	24847.5	+	43037.1i	0.0138878	+	0.0240544i	−0.858998	+	0.511979i	$0.828913\pi$
$318$		0			0
$319$	325086.	−	563066.i	0.178864	−	0.309801i
$320$		0			0
$321$	−1.74300e6			−0.944138
$322$		0			0
$323$	310944.			0.165835
$324$		0			0
$325$	−462616.	+	801274.i	−0.242947	+	0.420797i
$326$		0			0
$327$	−922995.	−	1.59867e6i	−0.477342	−	0.826781i
$328$		0			0
$329$	−1.47714e6	−	2.30263e6i	−0.752371	−	1.17283i
$330$		0			0
$331$	793918.	+	1.37511e6i	0.398296	+	0.689868i	0.993516	−	0.113694i	$-0.0362684\pi$
$331$	793918.	+	1.37511e6i	0.398296	+	0.689868i	−0.595220	+	0.803563i	$0.702935\pi$
$332$		0			0
$333$	458784.	−	794637.i	0.226724	−	0.392698i
$334$		0			0
$335$	352858.			0.171786
$336$		0			0
$337$	214825.			0.103041			0.0515205	−	0.998672i	$-0.483593\pi$
$337$	214825.			0.103041			0.0515205	+	0.998672i	$0.483593\pi$
$338$		0			0
$339$	−209988.	+	363710.i	−0.0992419	+	0.171892i
$340$		0			0
$341$	−382114.	−	661842.i	−0.177954	−	0.308225i
$342$		0			0
$343$	−2.15747e6	+	304770.i	−0.990169	+	0.139874i
$344$		0			0
$345$	−161568.	−	279844.i	−0.0730815	−	0.126581i
$346$		0			0
$347$	1.29430e6	−	2.24179e6i	0.577046	−	0.999473i	−0.418770	−	0.908092i	$-0.637539\pi$
$347$	1.29430e6	−	2.24179e6i	0.577046	−	0.999473i	0.995816	−	0.0913809i	$-0.0291281\pi$
$348$		0			0
$349$	−24878.0			−0.0109333			−0.00546666	−	0.999985i	$-0.501740\pi$
$349$	−24878.0			−0.0109333			−0.00546666	+	0.999985i	$0.501740\pi$
$350$		0			0
$351$	−224532.			−0.0972771
$352$		0			0
$353$	868004.	−	1.50343e6i	0.370753	−	0.642163i	−0.618928	−	0.785447i	$-0.712433\pi$
$353$	868004.	−	1.50343e6i	0.370753	−	0.642163i	0.989682	+	0.143284i	$0.0457662\pi$
$354$		0			0
$355$	−210507.	−	364609.i	−0.0886535	−	0.153552i
$356$		0			0
$357$	1.19448e6	+	1.86201e6i	0.496030	+	0.773235i
$358$		0			0
$359$	431213.	+	746883.i	0.176586	+	0.305856i	0.940709	−	0.339215i	$-0.110161\pi$
$359$	431213.	+	746883.i	0.176586	+	0.305856i	−0.764123	+	0.645070i	$0.776828\pi$
$360$		0			0
$361$	1.22460e6	−	2.12107e6i	0.494569	−	0.856618i
$362$		0			0
$363$	−798210.			−0.317944
$364$		0			0
$365$	383526.			0.150682
$366$		0			0
$367$	1.55771e6	−	2.69803e6i	0.603700	−	1.04564i	−0.388555	−	0.921425i	$-0.627026\pi$
$367$	1.55771e6	−	2.69803e6i	0.603700	−	1.04564i	0.992255	−	0.124214i	$-0.0396409\pi$
$368$		0			0
$369$	682668.	+	1.18242e6i	0.261002	+	0.452069i
$370$		0			0
$371$	−1.76661e6	+	3.41985e6i	−0.666357	+	1.28995i
$372$		0			0
$373$	898472.	+	1.55620e6i	0.334374	+	0.579153i	0.983364	−	0.181644i	$-0.0581418\pi$
$373$	898472.	+	1.55620e6i	0.334374	+	0.579153i	−0.648990	+	0.760797i	$0.724808\pi$
$374$		0			0
$375$	303386.	−	525479.i	0.111408	−	0.192964i
$376$		0			0
$377$	−744436.			−0.269758
$378$		0			0
$379$	−3.45466e6			−1.23540			−0.617699	−	0.786415i	$-0.711935\pi$
$379$	−3.45466e6			−1.23540			−0.617699	+	0.786415i	$0.711935\pi$
$380$		0			0
$381$	−1.36964e6	+	2.37229e6i	−0.483387	+	0.837250i
$382$		0			0
$383$	1.07752e6	+	1.86632e6i	0.375343	+	0.650113i	0.990378	−	0.138387i	$-0.0441917\pi$
$383$	1.07752e6	+	1.86632e6i	0.375343	+	0.650113i	−0.615036	+	0.788499i	$0.710858\pi$
$384$		0			0
$385$	383191.	−	17938.0i	0.131754	−	0.00616768i
$386$		0			0
$387$	−319707.	−	553749.i	−0.108511	−	0.187947i
$388$		0			0
$389$	231387.	−	400774.i	0.0775291	−	0.134284i	−0.824654	−	0.565637i	$-0.808630\pi$
$389$	231387.	−	400774.i	0.0775291	−	0.134284i	0.902183	+	0.431353i	$0.141964\pi$
$390$		0			0
$391$	6.18854e6			2.04714
$392$		0			0
$393$	119727.			0.0391031
$394$		0			0
$395$	74409.5	−	128881.i	0.0239958	−	0.0415620i
$396$		0			0
$397$	2.03311e6	+	3.52144e6i	0.647416	+	1.12136i	0.983738	+	0.179611i	$0.0574839\pi$
$397$	2.03311e6	+	3.52144e6i	0.647416	+	1.12136i	−0.336321	+	0.941747i	$0.609183\pi$
$398$		0			0
$399$	−191142.	+	8947.77i	−0.0601068	+	0.00281373i
$400$		0			0
$401$	2.53432e6	+	4.38956e6i	0.787045	+	1.36320i	0.927769	+	0.373154i	$0.121724\pi$
$401$	2.53432e6	+	4.38956e6i	0.787045	+	1.36320i	−0.140724	+	0.990049i	$0.544943\pi$
$402$		0			0
$403$	−437514.	+	757796.i	−0.134193	+	0.232429i
$404$		0			0
$405$	72171.0			0.0218638
$406$		0			0
$407$	3.04723e6			0.911842
$408$		0			0
$409$	−1.43867e6	+	2.49185e6i	−0.425258	+	0.736568i	−0.996444	−	0.0842522i	$-0.973150\pi$
$409$	−1.43867e6	+	2.49185e6i	−0.425258	+	0.736568i	0.571187	+	0.820820i	$0.306483\pi$
$410$		0			0
$411$	1.79218e6	+	3.10415e6i	0.523331	+	0.906437i
$412$		0			0
$413$	485698.	−	940226.i	0.140117	−	0.271242i
$414$		0			0
$415$	−374567.	−	648768.i	−0.106760	−	0.184914i
$416$		0			0
$417$	1.03629e6	−	1.79490e6i	0.291837	−	0.505476i
$418$		0			0
$419$	3.41342e6			0.949850			0.474925	−	0.880026i	$-0.342475\pi$
$419$	3.41342e6			0.949850			0.474925	+	0.880026i	$0.342475\pi$
$420$		0			0
$421$	−1.30737e6			−0.359496			−0.179748	−	0.983713i	$-0.557528\pi$
$421$	−1.30737e6			−0.359496			−0.179748	+	0.983713i	$0.557528\pi$
$422$		0			0
$423$	854631.	−	1.48026e6i	0.232235	−	0.402243i
$424$		0			0
$425$	2.84779e6	+	4.93252e6i	0.764779	+	1.32464i
$426$		0			0
$427$	1.06162e6	+	1.65490e6i	0.281773	+	0.439241i
$428$		0			0
$429$	−372834.	−	645767.i	−0.0978075	−	0.169408i
$430$		0			0
$431$	967734.	−	1.67616e6i	0.250936	−	0.434634i	−0.712848	−	0.701319i	$-0.752595\pi$
$431$	967734.	−	1.67616e6i	0.250936	−	0.434634i	0.963784	+	0.266685i	$0.0859283\pi$
$432$		0			0
$433$	516670.			0.132432			0.0662161	−	0.997805i	$-0.478907\pi$
$433$	516670.			0.132432			0.0662161	+	0.997805i	$0.478907\pi$
$434$		0			0
$435$	239283.			0.0606302
$436$		0			0
$437$	−267648.	+	463580.i	−0.0670441	+	0.116124i
$438$		0			0
$439$	1.45765e6	+	2.52472e6i	0.360987	+	0.625249i	0.988124	−	0.153661i	$-0.0491064\pi$
$439$	1.45765e6	+	2.52472e6i	0.360987	+	0.625249i	−0.627136	+	0.778910i	$0.715773\pi$
$440$		0			0
$441$	−787846.	−	1.11023e6i	−0.192906	−	0.271843i
$442$		0			0
$443$	−891896.	−	1.54481e6i	−0.215926	−	0.373995i	0.737633	−	0.675202i	$-0.235944\pi$
$443$	−891896.	−	1.54481e6i	−0.215926	−	0.373995i	−0.953559	+	0.301208i	$0.902610\pi$
$444$		0			0
$445$	632071.	−	1.09478e6i	0.151309	−	0.262076i
$446$		0			0
$447$	−874206.			−0.206940
$448$		0			0
$449$	4.00158e6			0.936733			0.468366	−	0.883534i	$-0.344843\pi$
$449$	4.00158e6			0.936733			0.468366	+	0.883534i	$0.344843\pi$
$450$		0			0
$451$	−2.26713e6	+	3.92679e6i	−0.524850	+	0.909067i
$452$		0			0
$453$	−130712.	−	226399.i	−0.0299274	−	0.0518357i
$454$		0			0
$455$	−237160.	−	369696.i	−0.0537048	−	0.0837175i
$456$		0			0
$457$	583832.	+	1.01123e6i	0.130767	+	0.226495i	0.923972	−	0.382459i	$-0.124923\pi$
$457$	583832.	+	1.01123e6i	0.130767	+	0.226495i	−0.793206	+	0.608954i	$0.791589\pi$
$458$		0			0
$459$	−691092.	+	1.19701e6i	−0.153110	+	0.265195i
$460$		0			0
$461$	3.61358e6			0.791928			0.395964	−	0.918266i	$-0.370411\pi$
$461$	3.61358e6			0.791928			0.395964	+	0.918266i	$0.370411\pi$
$462$		0			0
$463$	1.80111e6			0.390471			0.195235	−	0.980756i	$-0.437453\pi$
$463$	1.80111e6			0.390471			0.195235	+	0.980756i	$0.437453\pi$
$464$		0			0
$465$	140630.	−	243577.i	0.0301609	−	0.0522402i
$466$		0			0
$467$	−1.18487e6	−	2.05226e6i	−0.251409	−	0.435452i	0.712505	−	0.701667i	$-0.247560\pi$
$467$	−1.18487e6	−	2.05226e6i	−0.251409	−	0.435452i	−0.963914	+	0.266214i	$0.914227\pi$
$468$		0			0
$469$	1.90864e6	−	3.69479e6i	0.400675	−	0.775635i
$470$		0			0
$471$	2.59425e6	+	4.49337e6i	0.538840	+	0.933298i
$472$		0			0
$473$	1.06174e6	−	1.83899e6i	0.218206	−	0.377944i
$474$		0			0
$475$	−492656.			−0.100187
$476$		0			0
$477$	−2.40497e6			−0.483965
$478$		0			0
$479$	259073.	−	448728.i	0.0515921	−	0.0893602i	−0.839076	−	0.544014i	$-0.816904\pi$
$479$	259073.	−	448728.i	0.0515921	−	0.0893602i	0.890668	+	0.454654i	$0.150237\pi$
$480$		0			0
$481$	−1.74451e6	−	3.02158e6i	−0.343804	−	0.595486i
$482$		0			0
$483$	−3.80419e6	+	178083.i	−0.741984	+	0.0347339i
$484$		0			0
$485$	−852274.	−	1.47618e6i	−0.164522	−	0.284961i
$486$		0			0
$487$	1.41306e6	−	2.44750e6i	0.269985	−	0.467627i	−0.698873	−	0.715246i	$-0.746315\pi$
$487$	1.41306e6	−	2.44750e6i	0.269985	−	0.467627i	0.968858	+	0.247619i	$0.0796480\pi$
$488$		0			0
$489$	2.38709e6			0.451436
$490$		0			0
$491$	−9.34747e6			−1.74981			−0.874904	−	0.484296i	$-0.839076\pi$
$491$	−9.34747e6			−1.74981			−0.874904	+	0.484296i	$0.839076\pi$
$492$		0			0
$493$	−2.29132e6	+	3.96868e6i	−0.424588	+	0.735408i
$494$		0			0
$495$	119840.	+	207568.i	0.0219830	+	0.0380757i
$496$		0			0
$497$	−4.95648e6	+	232024.i	−0.900083	+	0.0421349i
$498$		0			0
$499$	4.08593e6	+	7.07703e6i	0.734580	+	1.27233i	0.954907	+	0.296904i	$0.0959542\pi$
$499$	4.08593e6	+	7.07703e6i	0.734580	+	1.27233i	−0.220327	+	0.975426i	$0.570712\pi$
$500$		0			0
$501$	−1.63706e6	+	2.83546e6i	−0.291386	+	0.504696i
$502$		0			0
$503$	7.37713e6			1.30007			0.650036	−	0.759903i	$-0.274754\pi$
$503$	7.37713e6			1.30007			0.650036	+	0.759903i	$0.274754\pi$
$504$		0			0
$505$	−1.18327e6			−0.206469
$506$		0			0
$507$	1.24393e6	−	2.15455e6i	0.214920	−	0.372252i
$508$		0			0
$509$	163158.	+	282597.i	0.0279134	+	0.0483474i	0.879645	−	0.475631i	$-0.157780\pi$
$509$	163158.	+	282597.i	0.0279134	+	0.0483474i	−0.851731	+	0.523979i	$0.824447\pi$
$510$		0			0
$511$	2.07453e6	−	4.01591e6i	0.351453	−	0.680350i
$512$		0			0
$513$	−59778.0	−	103539.i	−0.0100288	−	0.0173704i
$514$		0			0
$515$	49148.0	−	85126.8i	0.00816559	−	0.0141432i
$516$		0			0
$517$	5.67644e6			0.934006
$518$		0			0
$519$	−1.48361e6			−0.241770
$520$		0			0
$521$	1.08351e6	−	1.87670e6i	0.174880	−	0.302901i	−0.765240	−	0.643745i	$-0.777380\pi$
$521$	1.08351e6	−	1.87670e6i	0.174880	−	0.302901i	0.940120	+	0.340844i	$0.110713\pi$
$522$		0			0
$523$	−361702.	−	626486.i	−0.0578225	−	0.100151i	0.835665	−	0.549239i	$-0.185082\pi$
$523$	−361702.	−	626486.i	−0.0578225	−	0.100151i	−0.893488	+	0.449088i	$0.851749\pi$
$524$		0			0
$525$	−1.89252e6	−	2.95015e6i	−0.299669	−	0.467138i
$526$		0			0
$527$	2.69327e6	+	4.66488e6i	0.422428	+	0.731667i
$528$		0			0
$529$	−2.10868e6	+	3.65233e6i	−0.327620	+	0.567455i
$530$		0			0
$531$	661203.			0.101765
$532$		0			0
$533$	5.19165e6			0.791566
$534$		0			0
$535$	1.06517e6	−	1.84493e6i	0.160892	−	0.278673i
$536$		0			0
$537$	137826.	+	238722.i	0.0206251	+	0.0357237i
$538$		0			0
$539$	1.88488e6	−	4.10943e6i	0.279455	−	0.609270i
$540$		0			0
$541$	−2.99982e6	−	5.19584e6i	−0.440659	−	0.763243i	0.557080	−	0.830459i	$-0.311922\pi$
$541$	−2.99982e6	−	5.19584e6i	−0.440659	−	0.763243i	−0.997738	+	0.0672159i	$0.978588\pi$
$542$		0			0
$543$	2.93126e6	−	5.07710e6i	0.426634	−	0.738952i
$544$		0			0
$545$	2.25621e6			0.325378
$546$		0			0
$547$	−7.01570e6			−1.00254			−0.501271	−	0.865290i	$-0.667134\pi$
$547$	−7.01570e6			−1.00254			−0.501271	+	0.865290i	$0.667134\pi$
$548$		0			0
$549$	−614223.	+	1.06387e6i	−0.0869752	+	0.150645i
$550$		0			0
$551$	−198194.	−	343282.i	−0.0278107	−	0.0481695i
$552$		0			0
$553$	−947030.	−	1.47627e6i	−0.131689	−	0.205284i
$554$		0			0
$555$	560736.	+	971223.i	0.0772727	+	0.133840i
$556$		0			0
$557$	4.45936e6	−	7.72384e6i	0.609025	−	1.05486i	−0.382377	−	0.924006i	$-0.624894\pi$
$557$	4.45936e6	−	7.72384e6i	0.609025	−	1.05486i	0.991402	−	0.130855i	$-0.0417722\pi$
$558$		0			0
$559$	−2.43135e6			−0.329093
$560$		0			0
$561$	−4.59022e6			−0.615781
$562$		0			0
$563$	−6.67412e6	+	1.15599e7i	−0.887407	+	1.53703i	−0.0444767	+	0.999010i	$0.514162\pi$
$563$	−6.67412e6	+	1.15599e7i	−0.887407	+	1.53703i	−0.842930	+	0.538023i	$0.819171\pi$
$564$		0			0
$565$	−256652.	−	444534.i	−0.0338239	−	0.0585847i
$566$		0			0
$567$	390380.	−	755705.i	0.0509952	−	0.0987176i
$568$		0			0
$569$	−551074.	−	954488.i	−0.0713558	−	0.123592i	0.828140	−	0.560521i	$-0.189399\pi$
$569$	−551074.	−	954488.i	−0.0713558	−	0.123592i	−0.899496	+	0.436930i	$0.856066\pi$
$570$		0			0
$571$	946741.	−	1.63980e6i	0.121518	−	0.210475i	−0.798848	−	0.601532i	$-0.794557\pi$
$571$	946741.	−	1.63980e6i	0.121518	−	0.210475i	0.920367	+	0.391057i	$0.127890\pi$
$572$		0			0
$573$	6.81624e6			0.867278
$574$		0			0
$575$	−9.80506e6			−1.23675
$576$		0			0
$577$	−1.41476e6	+	2.45043e6i	−0.176906	+	0.306410i	−0.940819	−	0.338909i	$-0.889942\pi$
$577$	−1.41476e6	+	2.45043e6i	−0.176906	+	0.306410i	0.763913	+	0.645319i	$0.223275\pi$
$578$		0			0
$579$	721526.	+	1.24972e6i	0.0894448	+	0.154923i
$580$		0			0
$581$	−8.81934e6	+	412852.i	−1.08392	+	0.0507405i
$582$		0			0
$583$	−3.99344e6	−	6.91684e6i	−0.486604	−	0.842823i
$584$		0			0
$585$	137214.	−	237662.i	0.0165771	−	0.0287124i
$586$		0			0
$587$	1.06799e7			1.27930			0.639649	−	0.768667i	$-0.279080\pi$
$587$	1.06799e7			1.27930			0.639649	+	0.768667i	$0.279080\pi$
$588$		0			0
$589$	−465924.			−0.0553384
$590$		0			0
$591$	277821.	−	481200.i	0.0327187	−	0.0566705i
$592$		0			0
$593$	7.34984e6	+	1.27303e7i	0.858304	+	1.48663i	0.873545	+	0.486743i	$0.161815\pi$
$593$	7.34984e6	+	1.27303e7i	0.858304	+	1.48663i	−0.0152406	+	0.999884i	$0.504851\pi$
$594$		0			0
$595$	−2.70085e6	+	126433.i	−0.312758	+	0.0146409i
$596$		0			0
$597$	1.66909e6	+	2.89094e6i	0.191665	+	0.331974i
$598$		0			0
$599$	4.24581e6	−	7.35396e6i	0.483497	−	0.837441i	−0.516323	−	0.856394i	$-0.672700\pi$
$599$	4.24581e6	−	7.35396e6i	0.483497	−	0.837441i	0.999820	+	0.0189523i	$0.00603306\pi$
$600$		0			0
$601$	8.62947e6			0.974536			0.487268	−	0.873253i	$-0.337994\pi$
$601$	8.62947e6			0.974536			0.487268	+	0.873253i	$0.337994\pi$
$602$		0			0
$603$	2.59832e6			0.291004
$604$		0			0
$605$	487795.	−	844886.i	0.0541812	−	0.0938447i
$606$		0			0
$607$	5.29037e6	+	9.16319e6i	0.582793	+	1.00943i	0.995147	+	0.0984029i	$0.0313734\pi$
$607$	5.29037e6	+	9.16319e6i	0.582793	+	1.00943i	−0.412354	+	0.911024i	$0.635293\pi$
$608$		0			0
$609$	1.29430e6	−	2.50554e6i	0.141414	−	0.273753i
$610$		0			0
$611$	−3.24971e6	−	5.62866e6i	−0.352161	−	0.609961i
$612$		0			0
$613$	−1.92392e6	+	3.33233e6i	−0.206793	+	0.358176i	−0.950703	−	0.310104i	$-0.899636\pi$
$613$	−1.92392e6	+	3.33233e6i	−0.206793	+	0.358176i	0.743910	+	0.668280i	$0.232969\pi$
$614$		0			0
$615$	−1.66874e6			−0.177911
$616$		0			0
$617$	−1.51001e7			−1.59686			−0.798428	−	0.602090i	$-0.794335\pi$
$617$	−1.51001e7			−1.59686			−0.798428	+	0.602090i	$0.794335\pi$
$618$		0			0
$619$	4.96551e6	−	8.60051e6i	0.520879	−	0.902190i	−0.478826	−	0.877910i	$-0.658937\pi$
$619$	4.96551e6	−	8.60051e6i	0.520879	−	0.902190i	0.999705	−	0.0242796i	$-0.00772920\pi$
$620$		0			0
$621$	−1.18973e6	−	2.06067e6i	−0.123799	−	0.214427i
$622$		0			0
$623$	−8.04454e6	−	1.25402e7i	−0.830388	−	1.29445i
$624$		0			0
$625$	−4.32295e6	−	7.48756e6i	−0.442670	−	0.766726i
$626$		0			0
$627$	198522.	−	343850.i	0.0201669	−	0.0349301i
$628$		0			0
$629$	−2.14779e7			−2.16454
$630$		0			0
$631$	9.25224e6			0.925068			0.462534	−	0.886602i	$-0.346940\pi$
$631$	9.25224e6			0.925068			0.462534	+	0.886602i	$0.346940\pi$
$632$		0			0
$633$	978525.	−	1.69486e6i	0.0970650	−	0.168122i
$634$		0			0
$635$	−1.67401e6	−	2.89947e6i	−0.164749	−	0.285354i
$636$		0			0
$637$	−5.15392e6	+	483592.i	−0.503256	+	0.0472205i
$638$		0			0
$639$	−1.55010e6	−	2.68485e6i	−0.150178	−	0.260116i
$640$		0			0
$641$	−2.50214e6	+	4.33384e6i	−0.240529	+	0.416608i	−0.960865	−	0.277017i	$-0.910654\pi$
$641$	−2.50214e6	+	4.33384e6i	−0.240529	+	0.416608i	0.720336	+	0.693625i	$0.243987\pi$
$642$		0			0
$643$	−1.26137e7			−1.20314			−0.601569	−	0.798821i	$-0.705457\pi$
$643$	−1.26137e7			−1.20314			−0.601569	+	0.798821i	$0.705457\pi$
$644$		0			0
$645$	781506.			0.0739662
$646$		0			0
$647$	−6.26916e6	+	1.08585e7i	−0.588774	+	1.01979i	0.405620	+	0.914042i	$0.367056\pi$
$647$	−6.26916e6	+	1.08585e7i	−0.588774	+	1.01979i	−0.994393	+	0.105744i	$0.966278\pi$
$648$		0			0
$649$	1.09792e6	+	1.90166e6i	0.102320	+	0.177223i
$650$		0			0
$651$	−1.78983e6	−	2.79007e6i	−0.165523	−	0.258025i
$652$		0			0
$653$	4.33033e6	+	7.50035e6i	0.397409	+	0.688333i	0.993405	−	0.114654i	$-0.0365760\pi$
$653$	4.33033e6	+	7.50035e6i	0.397409	+	0.688333i	−0.595996	+	0.802987i	$0.703243\pi$
$654$		0			0
$655$	−73166.5	+	126728.i	−0.00666360	+	0.0115417i
$656$		0			0
$657$	2.82415e6			0.255255
$658$		0			0
$659$	−7.94177e6			−0.712367			−0.356183	−	0.934416i	$-0.615922\pi$
$659$	−7.94177e6			−0.712367			−0.356183	+	0.934416i	$0.615922\pi$
$660$		0			0
$661$	1.05708e6	−	1.83092e6i	0.0941032	−	0.162992i	−0.815131	−	0.579277i	$-0.803335\pi$
$661$	1.05708e6	−	1.83092e6i	0.0941032	−	0.162992i	0.909234	+	0.416285i	$0.136668\pi$
$662$		0			0
$663$	2.62786e6	+	4.55158e6i	0.232176	+	0.402141i
$664$		0			0
$665$	107338.	−	207787.i	0.00941238	−	0.0182207i
$666$		0			0
$667$	−3.94454e6	−	6.83215e6i	−0.343307	−	0.594625i
$668$		0			0
$669$	2.65397e6	−	4.59681e6i	0.229261	−	0.397092i
$670$		0			0
$671$	−4.07965e6			−0.349798
$672$		0			0
$673$	−442307.			−0.0376432			−0.0188216	−	0.999823i	$-0.505991\pi$
$673$	−442307.			−0.0376432			−0.0188216	+	0.999823i	$0.505991\pi$
$674$		0			0
$675$	1.09496e6	−	1.89652e6i	0.0924992	−	0.160213i
$676$		0			0
$677$	−5.37804e6	−	9.31503e6i	−0.450975	−	0.781111i	0.547472	−	0.836824i	$-0.315590\pi$
$677$	−5.37804e6	−	9.31503e6i	−0.450975	−	0.781111i	−0.998447	+	0.0557130i	$0.982257\pi$
$678$		0			0
$679$	−2.00672e7	+	939389.i	−1.67037	+	0.0781936i
$680$		0			0
$681$	−1.74170e6	−	3.01672e6i	−0.143915	−	0.249268i
$682$		0			0
$683$	−5.74430e6	+	9.94941e6i	−0.471178	+	0.816104i	−0.999456	−	0.0329669i	$-0.989504\pi$
$683$	−5.74430e6	+	9.94941e6i	−0.471178	+	0.816104i	0.528278	+	0.849071i	$0.322838\pi$
$684$		0			0
$685$	−4.38088e6			−0.356726
$686$		0			0
$687$	−2.09459e6			−0.169319
$688$		0			0
$689$	−4.57241e6	+	7.91965e6i	−0.366942	+	0.635562i
$690$		0			0
$691$	5.06942e6	+	8.78049e6i	0.403890	+	0.699558i	0.994192	−	0.107625i	$-0.0343246\pi$
$691$	5.06942e6	+	8.78049e6i	0.403890	+	0.699558i	−0.590302	+	0.807183i	$0.700991\pi$
$692$		0			0
$693$	2.82168e6	−	132089.i	0.223190	−	0.0104480i
$694$		0			0
$695$	1.26657e6	+	2.19377e6i	0.0994645	+	0.172278i
$696$		0			0
$697$	1.59795e7	−	2.76773e7i	1.24589	−	2.15795i
$698$		0			0
$699$	378864.			0.0293285
$700$		0			0
$701$	−1.96839e7			−1.51292			−0.756459	−	0.654041i	$-0.773073\pi$
$701$	−1.96839e7			−1.51292			−0.756459	+	0.654041i	$0.773073\pi$
$702$		0			0
$703$	928896.	−	1.60890e6i	0.0708890	−	0.122783i
$704$		0			0
$705$	1.04455e6	+	1.80921e6i	0.0791509	+	0.137093i
$706$		0			0
$707$	−6.40042e6	+	1.23901e7i	−0.481570	+	0.932234i
$708$		0			0
$709$	1.00859e7	+	1.74692e7i	0.753524	+	1.30514i	0.946105	+	0.323861i	$0.104981\pi$
$709$	1.00859e7	+	1.74692e7i	0.753524	+	1.30514i	−0.192581	+	0.981281i	$0.561686\pi$
$710$		0			0
$711$	547924.	−	949033.i	0.0406487	−	0.0704056i
$712$		0			0
$713$	−9.27302e6			−0.683121
$714$		0			0
$715$	911372.			0.0666700
$716$		0			0
$717$	−1.41037e6	+	2.44284e6i	−0.102456	+	0.177458i
$718$		0			0
$719$	2.07867e6	+	3.60037e6i	0.149956	+	0.259731i	0.931211	−	0.364481i	$-0.118753\pi$
$719$	2.07867e6	+	3.60037e6i	0.149956	+	0.259731i	−0.781255	+	0.624212i	$0.785420\pi$
$720$		0			0
$721$	−625520.	−	975089.i	−0.0448129	−	0.0698564i
$722$		0			0
$723$	−3.86013e6	−	6.68594e6i	−0.274635	−	0.475682i
$724$		0			0
$725$	3.63033e6	−	6.28792e6i	0.256508	−	0.444286i
$726$		0			0
$727$	1.54433e7			1.08369			0.541845	−	0.840479i	$-0.317726\pi$
$727$	1.54433e7			1.08369			0.541845	+	0.840479i	$0.317726\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−7.48351e6	+	1.29618e7i	−0.517979	+	0.897166i
$732$		0			0
$733$	3.10207e6	+	5.37294e6i	0.213251	+	0.369362i	0.952730	−	0.303818i	$-0.0982614\pi$
$733$	3.10207e6	+	5.37294e6i	0.213251	+	0.369362i	−0.739479	+	0.673180i	$0.764928\pi$
$734$		0			0
$735$	1.65662e6	−	155440.i	0.113111	−	0.0106132i
$736$		0			0
$737$	4.31449e6	+	7.47292e6i	0.292591	+	0.506782i
$738$		0			0
$739$	1.09492e7	−	1.89646e7i	0.737517	−	1.27742i	−0.216093	−	0.976373i	$-0.569331\pi$
$739$	1.09492e7	−	1.89646e7i	0.737517	−	1.27742i	0.953610	−	0.301045i	$-0.0973353\pi$
$740$		0			0
$741$	−454608.			−0.0304153
$742$		0			0
$743$	2.75483e6			0.183073			0.0915363	−	0.995802i	$-0.470822\pi$
$743$	2.75483e6			0.183073			0.0915363	+	0.995802i	$0.470822\pi$
$744$		0			0
$745$	534237.	−	925326.i	0.0352650	−	0.0610807i
$746$		0			0
$747$	−2.75817e6	−	4.77729e6i	−0.180851	−	0.313242i
$748$		0			0
$749$	−1.35567e7	−	2.11328e7i	−0.882976	−	1.37642i
$750$		0			0
$751$	6.45604e6	+	1.11822e7i	0.417702	+	0.723481i	0.995708	−	0.0925517i	$-0.0295024\pi$
$751$	6.45604e6	+	1.11822e7i	0.417702	+	0.723481i	−0.578006	+	0.816032i	$0.696169\pi$
$752$		0			0
$753$	2.04533e6	−	3.54261e6i	0.131454	−	0.227686i
$754$		0			0
$755$	319517.			0.0203998
$756$		0			0
$757$	−2.64315e7			−1.67642			−0.838209	−	0.545349i	$-0.816397\pi$
$757$	−2.64315e7			−1.67642			−0.838209	+	0.545349i	$0.816397\pi$
$758$		0			0
$759$	3.95107e6	−	6.84346e6i	0.248949	−	0.431192i
$760$		0			0
$761$	−6.11069e6	−	1.05840e7i	−0.382498	−	0.662506i	0.608921	−	0.793231i	$-0.291603\pi$
$761$	−6.11069e6	−	1.05840e7i	−0.382498	−	0.662506i	−0.991419	+	0.130725i	$0.958269\pi$
$762$		0			0
$763$	1.22040e7	−	2.36249e7i	0.758914	−	1.46912i
$764$		0			0
$765$	−844668.	−	1.46301e6i	−0.0521834	−	0.0903843i
$766$		0			0
$767$	1.25710e6	−	2.17736e6i	0.0771582	−	0.133642i
$768$		0			0
$769$	6.10654e6			0.372374			0.186187	−	0.982514i	$-0.440387\pi$
$769$	6.10654e6			0.372374			0.186187	+	0.982514i	$0.440387\pi$
$770$		0			0
$771$	7.90364e6			0.478841
$772$		0			0
$773$	1.51110e6	−	2.61730e6i	0.0909588	−	0.157545i	−0.816956	−	0.576700i	$-0.804340\pi$
$773$	1.51110e6	−	2.61730e6i	0.0909588	−	0.157545i	0.907915	+	0.419155i	$0.137674\pi$
$774$		0			0
$775$	−4.26718e6	−	7.39098e6i	−0.255204	−	0.442026i
$776$		0			0
$777$	1.32028e7	−	618051.i	0.784536	−	0.0367259i
$778$		0			0
$779$	1.38219e6	+	2.39403e6i	0.0816065	+	0.141347i
$780$		0			0
$781$	5.14785e6	−	8.91634e6i	0.301994	−	0.523069i
$782$		0			0
$783$	1.76199e6			0.102707
$784$		0			0
$785$	−6.34150e6			−0.367297
$786$		0			0
$787$	−1.04143e7	+	1.80380e7i	−0.599365	+	1.03813i	0.393550	+	0.919303i	$0.371247\pi$
$787$	−1.04143e7	+	1.80380e7i	−0.599365	+	1.03813i	−0.992915	+	0.118828i	$0.962086\pi$
$788$		0			0
$789$	8.82420e6	+	1.52840e7i	0.504642	+	0.874065i
$790$		0			0
$791$	−6.04299e6	+	282885.i	−0.343408	+	0.0160757i
$792$		0			0
$793$	2.33556e6	+	4.04532e6i	0.131889	+	0.228439i
$794$		0			0
$795$	1.46970e6	−	2.54560e6i	0.0824731	−	0.142848i
$796$		0			0
$797$	2.32328e7			1.29556			0.647778	−	0.761829i	$-0.275698\pi$
$797$	2.32328e7			1.29556			0.647778	+	0.761829i	$0.275698\pi$
$798$		0			0
$799$	−4.00094e7			−2.21715
$800$		0			0
$801$	4.65434e6	−	8.06156e6i	0.256317	−	0.443954i
$802$		0			0
$803$	4.68948e6	+	8.12241e6i	0.256647	+	0.444525i
$804$		0			0
$805$	2.13629e6	−	4.13547e6i	0.116190	−	0.224924i
$806$		0			0
$807$	4.74208e6	+	8.21352e6i	0.256321	+	0.443962i
$808$		0			0
$809$	−5.43338e6	+	9.41090e6i	−0.291876	+	0.505545i	−0.974253	−	0.225456i	$-0.927613\pi$
$809$	−5.43338e6	+	9.41090e6i	−0.291876	+	0.505545i	0.682377	+	0.731000i	$0.260946\pi$
$810$		0			0
$811$	2.22632e7			1.18860			0.594299	−	0.804244i	$-0.297430\pi$
$811$	2.22632e7			1.18860			0.594299	+	0.804244i	$0.297430\pi$
$812$		0			0
$813$	945531.			0.0501706
$814$		0			0
$815$	−1.45878e6	+	2.52667e6i	−0.0769298	+	0.133246i
$816$		0			0
$817$	−647308.	−	1.12117e6i	−0.0339278	−	0.0587647i
$818$		0			0
$819$	−1.74636e6	−	2.72231e6i	−0.0909754	−	0.141817i
$820$		0			0
$821$	6.19405e6	+	1.07284e7i	0.320713	+	0.555491i	0.980635	−	0.195843i	$-0.0627442\pi$
$821$	6.19405e6	+	1.07284e7i	0.320713	+	0.555491i	−0.659922	+	0.751334i	$0.729411\pi$
$822$		0			0
$823$	847404.	−	1.46775e6i	0.0436105	−	0.0755356i	−0.843396	−	0.537292i	$-0.819447\pi$
$823$	847404.	−	1.46775e6i	0.0436105	−	0.0755356i	0.887007	+	0.461757i	$0.152781\pi$
$824$		0			0
$825$	7.27268e6			0.372014
$826$		0			0
$827$	378495.			0.0192440			0.00962202	−	0.999954i	$-0.496937\pi$
$827$	378495.			0.0192440			0.00962202	+	0.999954i	$0.496937\pi$
$828$		0			0
$829$	5.21437e6	−	9.03156e6i	0.263521	−	0.456432i	−0.703654	−	0.710543i	$-0.748449\pi$
$829$	5.21437e6	−	9.03156e6i	0.263521	−	0.456432i	0.967175	+	0.254111i	$0.0817827\pi$
$830$		0			0
$831$	1.92416e6	+	3.33275e6i	0.0966584	+	0.167417i
$832$		0			0
$833$	−1.32853e7	+	2.89646e7i	−0.663373	+	1.44629i
$834$		0			0
$835$	−2.00084e6	−	3.46557e6i	−0.0993110	−	0.172012i
$836$		0			0
$837$	1.03554e6	−	1.79362e6i	0.0510923	−	0.0884944i
$838$		0			0
$839$	−3.04082e7			−1.49137			−0.745686	−	0.666297i	$-0.767878\pi$
$839$	−3.04082e7			−1.49137			−0.745686	+	0.666297i	$0.767878\pi$
$840$		0			0
$841$	−1.46693e7			−0.715185
$842$		0			0
$843$	−2.87495e6	+	4.97956e6i	−0.139335	+	0.241336i
$844$		0			0
$845$	1.52036e6	+	2.63334e6i	0.0732495	+	0.126872i
$846$		0			0
$847$	−6.20830e6	−	9.67778e6i	−0.297347	−	0.463519i
$848$		0			0
$849$	−1.10314e7	−	1.91069e7i	−0.525244	−	0.909750i
$850$		0			0
$851$	1.84873e7	−	3.20209e7i	0.875083	−	1.51569i
$852$		0			0
$853$	2.80315e7			1.31909			0.659544	−	0.751666i	$-0.270750\pi$
$853$	2.80315e7			1.31909			0.659544	+	0.751666i	$0.270750\pi$
$854$		0			0
$855$	146124.			0.00683607
$856$		0			0
$857$	−9.40148e6	+	1.62838e7i	−0.437264	+	0.757364i	−0.997477	−	0.0709844i	$-0.977386\pi$
$857$	−9.40148e6	+	1.62838e7i	−0.437264	+	0.757364i	0.560213	+	0.828349i	$0.310719\pi$
$858$		0			0
$859$	3.93162e6	+	6.80976e6i	0.181798	+	0.314883i	0.942493	−	0.334227i	$-0.108475\pi$
$859$	3.93162e6	+	6.80976e6i	0.181798	+	0.314883i	−0.760695	+	0.649109i	$0.775142\pi$
$860$		0			0
$861$	−9.02639e6	+	1.74735e7i	−0.414960	+	0.803288i
$862$		0			0
$863$	−5.64288e6	−	9.77376e6i	−0.257913	−	0.446719i	0.707769	−	0.706444i	$-0.249702\pi$
$863$	−5.64288e6	−	9.77376e6i	−0.257913	−	0.446719i	−0.965683	+	0.259724i	$0.916368\pi$
$864$		0			0
$865$	906653.	−	1.57037e6i	0.0412003	−	0.0713611i
$866$		0			0
$867$	1.95746e7			0.884394
$868$		0			0
$869$	3.63930e6			0.163481
$870$		0			0
$871$	4.94001e6	−	8.55635e6i	0.220639	−	0.382158i
$872$		0			0
$873$	−6.27584e6	−	1.08701e7i	−0.278700	−	0.482722i
$874$		0			0
$875$	8.73076e6	−	408706.i	0.385507	−	0.0180464i
$876$		0			0
$877$	−6.70750e6	−	1.16177e7i	−0.294484	−	0.510062i	0.680381	−	0.732859i	$-0.261814\pi$
$877$	−6.70750e6	−	1.16177e7i	−0.294484	−	0.510062i	−0.974865	+	0.222797i	$0.928481\pi$
$878$		0			0
$879$	−7.72276e6	+	1.33762e7i	−0.337132	+	0.583930i
$880$		0			0
$881$	3.18547e7			1.38272			0.691359	−	0.722511i	$-0.257012\pi$
$881$	3.18547e7			1.38272			0.691359	+	0.722511i	$0.257012\pi$
$882$		0			0
$883$	3.05922e7			1.32041			0.660205	−	0.751086i	$-0.270470\pi$
$883$	3.05922e7			1.32041			0.660205	+	0.751086i	$0.270470\pi$
$884$		0			0
$885$	−404068.	+	699867.i	−0.0173419	+	0.0300371i
$886$		0			0
$887$	−2.31886e6	−	4.01638e6i	−0.0989613	−	0.171406i	0.812294	−	0.583249i	$-0.198219\pi$
$887$	−2.31886e6	−	4.01638e6i	−0.0989613	−	0.171406i	−0.911255	+	0.411843i	$0.864885\pi$
$888$		0			0
$889$	−3.94153e7	+	1.84511e6i	−1.67267	+	0.0783013i
$890$		0			0
$891$	882454.	+	1.52846e6i	0.0372390	+	0.0644998i
$892$		0			0
$893$	1.73036e6	−	2.99708e6i	0.0726121	−	0.125768i
$894$		0			0
$895$	−336908.			−0.0140590
$896$		0			0
$897$	−9.04781e6			−0.375459
$898$		0			0
$899$	3.43335e6	−	5.94673e6i	0.141683	−	0.245403i
$900$		0			0
$901$	2.81471e7	+	4.87522e7i	1.15510	+	2.00070i
$902$		0			0
$903$	4.22724e6	−	8.18318e6i	0.172519	−	0.333966i
$904$		0			0
$905$	3.58266e6	+	6.20534e6i	0.145406	+	0.251851i
$906$		0			0
$907$	302188.	−	523405.i	0.0121972	−	0.0211261i	−0.859862	−	0.510526i	$-0.829451\pi$
$907$	302188.	−	523405.i	0.0121972	−	0.0211261i	0.872060	+	0.489400i	$0.162784\pi$
$908$		0			0
$909$	−8.71317e6			−0.349757
$910$		0			0
$911$	2.44059e7			0.974315			0.487157	−	0.873314i	$-0.338034\pi$
$911$	2.44059e7			0.974315			0.487157	+	0.873314i	$0.338034\pi$
$912$		0			0
$913$	9.15985e6	−	1.58653e7i	0.363673	−	0.629901i
$914$		0			0
$915$	−750717.	−	1.30028e6i	−0.0296431	−	0.0513433i
$916$		0			0
$917$	931210.	+	1.45161e6i	0.0365699	+	0.0570069i
$918$		0			0
$919$	1.83547e7	+	3.17914e7i	0.716902	+	1.24171i	0.962221	+	0.272268i	$0.0877737\pi$
$919$	1.83547e7	+	3.17914e7i	0.716902	+	1.24171i	−0.245320	+	0.969442i	$0.578893\pi$
$920$		0			0
$921$	8.14036e6	−	1.40995e7i	0.316224	−	0.547715i
$922$		0			0
$923$	−1.17884e7			−0.455460
$924$		0			0
$925$	3.40293e7			1.30767
$926$		0			0
$927$	361908.	−	626843.i	0.0138324	−	0.0239585i
$928$		0			0
$929$	1.14544e7	+	1.98396e7i	0.435446	+	0.754214i	0.997332	−	0.0730004i	$-0.0232574\pi$
$929$	1.14544e7	+	1.98396e7i	0.435446	+	0.754214i	−0.561886	+	0.827215i	$0.689924\pi$
$930$		0			0
$931$	−1.59515e6	−	2.24788e6i	−0.0603151	−	0.0849961i
$932$		0			0
$933$	6.84655e6	+	1.18586e7i	0.257494	+	0.445993i
$934$		0			0
$935$	2.80513e6	−	4.85863e6i	0.104936	−	0.181754i
$936$		0			0
$937$	−5.99611e6			−0.223111			−0.111555	−	0.993758i	$-0.535583\pi$
$937$	−5.99611e6			−0.223111			−0.111555	+	0.993758i	$0.535583\pi$
$938$		0			0
$939$	−1.21356e7			−0.449156
$940$		0			0
$941$	5.82579e6	−	1.00906e7i	0.214477	−	0.371485i	−0.738634	−	0.674107i	$-0.764529\pi$
$941$	5.82579e6	−	1.00906e7i	0.214477	−	0.371485i	0.953111	+	0.302622i	$0.0978619\pi$
$942$		0			0
$943$	2.75090e7	+	4.76470e7i	1.00738	+	1.74484i
$944$		0			0
$945$	561330.	+	875027.i	0.0204474	+	0.0318744i
$946$		0			0
$947$	−554632.	−	960651.i	−0.0200969	−	0.0348089i	0.855802	−	0.517303i	$-0.173064\pi$
$947$	−554632.	−	960651.i	−0.0200969	−	0.0348089i	−0.875899	+	0.482495i	$0.839731\pi$
$948$		0			0
$949$	5.36936e6	−	9.30001e6i	0.193534	−	0.335211i
$950$		0			0
$951$	−447255.			−0.0160363
$952$		0			0
$953$	1.05743e7			0.377155			0.188578	−	0.982058i	$-0.439612\pi$
$953$	1.05743e7			0.377155			0.188578	+	0.982058i	$0.439612\pi$
$954$		0			0
$955$	−4.16548e6	+	7.21482e6i	−0.147794	+	0.255987i
$956$		0			0
$957$	2.92578e6	+	5.06760e6i	0.103267	+	0.178864i
$958$		0			0
$959$	−2.36966e7	+	4.58724e7i	−0.832031	+	1.61066i
$960$		0			0
$961$	1.02789e7	+	1.78036e7i	0.359037	+	0.621871i
$962$		0			0
$963$	7.84351e6	−	1.35854e7i	0.272549	−	0.472069i
$964$		0			0
$965$	−1.76373e6			−0.0609696
$966$		0			0
$967$	−6.32666e6			−0.217575			−0.108787	−	0.994065i	$-0.534697\pi$
$967$	−6.32666e6			−0.217575			−0.108787	+	0.994065i	$0.534697\pi$
$968$		0			0
$969$	−1.39925e6	+	2.42357e6i	−0.0478724	+	0.0829174i
$970$		0			0
$971$	1.96197e7	+	3.39824e7i	0.667798	+	1.15666i	0.978519	+	0.206158i	$0.0660962\pi$
$971$	1.96197e7	+	3.39824e7i	0.667798	+	1.15666i	−0.310721	+	0.950501i	$0.600570\pi$
$972$		0			0
$973$	2.98220e7	−	1.39603e6i	1.00985	−	0.0472731i
$974$		0			0
$975$	−4.16354e6	−	7.21147e6i	−0.140266	−	0.242947i
$976$		0			0
$977$	775371.	−	1.34298e6i	0.0259880	−	0.0450126i	−0.852739	−	0.522337i	$-0.825060\pi$
$977$	775371.	−	1.34298e6i	0.0259880	−	0.0450126i	0.878727	+	0.477325i	$0.158393\pi$
$978$		0			0
$979$	3.09140e7			1.03086
$980$		0			0
$981$	1.66139e7			0.551187
$982$		0			0
$983$	−2.43742e7	+	4.22174e7i	−0.804538	+	1.39350i	0.112064	+	0.993701i	$0.464254\pi$
$983$	−2.43742e7	+	4.22174e7i	−0.804538	+	1.39350i	−0.916602	+	0.399801i	$0.869079\pi$
$984$		0			0
$985$	339559.	+	588133.i	0.0111513	+	0.0193146i
$986$		0			0
$987$	2.45944e7	−	1.15132e6i	0.803606	−	0.0376185i
$988$		0			0
$989$	−1.28830e7	−	2.23140e7i	−0.418819	−	0.725416i
$990$		0			0
$991$	−962758.	+	1.66754e6i	−0.0311410	+	0.0539378i	−0.881176	−	0.472789i	$-0.843247\pi$
$991$	−962758.	+	1.66754e6i	−0.0311410	+	0.0539378i	0.850035	+	0.526726i	$0.176581\pi$
$992$		0			0
$993$	−1.42905e7			−0.459912
$994$		0			0
$995$	−4.07999e6			−0.130648
$996$		0			0
$997$	−2.71282e7	+	4.69874e7i	−0.864337	+	1.49708i	0.00336739	+	0.999994i	$0.498928\pi$
$997$	−2.71282e7	+	4.69874e7i	−0.864337	+	1.49708i	−0.867704	+	0.497081i	$0.834405\pi$
$998$		0			0
$999$	4.12906e6	+	7.15173e6i	0.130899	+	0.226724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.b.193.1		2
4.3	odd	2		21.6.e.a.4.1	✓	2
7.2	even	3	inner	336.6.q.b.289.1		2
12.11	even	2		63.6.e.a.46.1		2
28.3	even	6		147.6.a.d.1.1		1
28.11	odd	6		147.6.a.c.1.1		1
28.19	even	6		147.6.e.g.79.1		2
28.23	odd	6		21.6.e.a.16.1	yes	2
28.27	even	2		147.6.e.g.67.1		2
84.11	even	6		441.6.a.g.1.1		1
84.23	even	6		63.6.e.a.37.1		2
84.59	odd	6		441.6.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.a.4.1	✓	2	4.3	odd	2
21.6.e.a.16.1	yes	2	28.23	odd	6
63.6.e.a.37.1		2	84.23	even	6
63.6.e.a.46.1		2	12.11	even	2
147.6.a.c.1.1		1	28.11	odd	6
147.6.a.d.1.1		1	28.3	even	6
147.6.e.g.67.1		2	28.27	even	2
147.6.e.g.79.1		2	28.19	even	6
336.6.q.b.193.1		2	1.1	even	1	trivial
336.6.q.b.289.1		2	7.2	even	3	inner
441.6.a.g.1.1		1	84.11	even	6
441.6.a.h.1.1		1	84.59	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 + 7.79423i) q^{3} +(-5.50000 - 9.52628i) q^{5} +(-129.500 + 6.06218i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.50000 + 7.79423i) q^{3} +(-5.50000 - 9.52628i) q^{5} +(-129.500 + 6.06218i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(134.500 - 232.961i) q^{11} -308.000 q^{13} +99.0000 q^{15} +(-948.000 + 1641.98i) q^{17} +(-82.0000 - 142.028i) q^{19} +(535.500 - 1036.63i) q^{21} +(-1632.00 - 2826.71i) q^{23} +(1502.00 - 2601.54i) q^{25} +729.000 q^{27} +2417.00 q^{29} +(1420.50 - 2460.38i) q^{31} +(1210.50 + 2096.65i) q^{33} +(770.000 + 1200.31i) q^{35} +(5664.00 + 9810.34i) q^{37} +(1386.00 - 2400.62i) q^{39} -16856.0 q^{41} +7894.00 q^{43} +(-445.500 + 771.629i) q^{45} +(10551.0 + 18274.9i) q^{47} +(16733.5 - 1570.10i) q^{49} +(-8532.00 - 14777.9i) q^{51} +(14845.5 - 25713.2i) q^{53} -2959.00 q^{55} +1476.00 q^{57} +(-4081.50 + 7069.37i) q^{59} +(-7583.00 - 13134.1i) q^{61} +(5670.00 + 8838.66i) q^{63} +(1694.00 + 2934.09i) q^{65} +(-16039.0 + 27780.4i) q^{67} +29376.0 q^{69} +38274.0 q^{71} +(-17433.0 + 30194.8i) q^{73} +(13518.0 + 23413.9i) q^{75} +(-16005.5 + 30983.8i) q^{77} +(6764.50 + 11716.5i) q^{79} +(-3280.50 + 5681.99i) q^{81} +68103.0 q^{83} +20856.0 q^{85} +(-10876.5 + 18838.7i) q^{87} +(57461.0 + 99525.4i) q^{89} +(39886.0 - 1867.15i) q^{91} +(12784.5 + 22143.4i) q^{93} +(-902.000 + 1562.31i) q^{95} +154959. q^{97} -21789.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 9 q^{3} - 11 q^{5} - 259 q^{7} - 81 q^{9}+O(q^{10}) \) 2 * q - 9 * q^3 - 11 * q^5 - 259 * q^7 - 81 * q^9	\( 2 q - 9 q^{3} - 11 q^{5} - 259 q^{7} - 81 q^{9} + 269 q^{11} - 616 q^{13} + 198 q^{15} - 1896 q^{17} - 164 q^{19} + 1071 q^{21} - 3264 q^{23} + 3004 q^{25} + 1458 q^{27} + 4834 q^{29} + 2841 q^{31} + 2421 q^{33} + 1540 q^{35} + 11328 q^{37} + 2772 q^{39} - 33712 q^{41} + 15788 q^{43} - 891 q^{45} + 21102 q^{47} + 33467 q^{49} - 17064 q^{51} + 29691 q^{53} - 5918 q^{55} + 2952 q^{57} - 8163 q^{59} - 15166 q^{61} + 11340 q^{63} + 3388 q^{65} - 32078 q^{67} + 58752 q^{69} + 76548 q^{71} - 34866 q^{73} + 27036 q^{75} - 32011 q^{77} + 13529 q^{79} - 6561 q^{81} + 136206 q^{83} + 41712 q^{85} - 21753 q^{87} + 114922 q^{89} + 79772 q^{91} + 25569 q^{93} - 1804 q^{95} + 309918 q^{97} - 43578 q^{99}+O(q^{100}) \) 2 * q - 9 * q^3 - 11 * q^5 - 259 * q^7 - 81 * q^9 + 269 * q^11 - 616 * q^13 + 198 * q^15 - 1896 * q^17 - 164 * q^19 + 1071 * q^21 - 3264 * q^23 + 3004 * q^25 + 1458 * q^27 + 4834 * q^29 + 2841 * q^31 + 2421 * q^33 + 1540 * q^35 + 11328 * q^37 + 2772 * q^39 - 33712 * q^41 + 15788 * q^43 - 891 * q^45 + 21102 * q^47 + 33467 * q^49 - 17064 * q^51 + 29691 * q^53 - 5918 * q^55 + 2952 * q^57 - 8163 * q^59 - 15166 * q^61 + 11340 * q^63 + 3388 * q^65 - 32078 * q^67 + 58752 * q^69 + 76548 * q^71 - 34866 * q^73 + 27036 * q^75 - 32011 * q^77 + 13529 * q^79 - 6561 * q^81 + 136206 * q^83 + 41712 * q^85 - 21753 * q^87 + 114922 * q^89 + 79772 * q^91 + 25569 * q^93 - 1804 * q^95 + 309918 * q^97 - 43578 * q^99

Introduction

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