LMFDB - Embedded newform 336.6.q.h.193.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{505})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 127x^{2} + 126x + 15876 $ x^4 - x^3 + 127x^2 + 126x + 15876
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 7 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.2
Root			$5.86805 - 10.1638i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.6.q.h.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50000 - 7.79423i) q^{3} +(35.0764 + 60.7540i) q^{5} +(90.7639 + 92.5684i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(4.50000 - 7.79423i) q^{3} +(35.0764 + 60.7540i) q^{5} +(90.7639 + 92.5684i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(311.535 - 539.594i) q^{11} -278.847 q^{13} +631.374 q^{15} +(443.527 - 768.212i) q^{17} +(-791.562 - 1371.03i) q^{19} +(1129.94 - 290.877i) q^{21} +(-969.695 - 1679.56i) q^{23} +(-898.202 + 1555.73i) q^{25} -729.000 q^{27} +8573.01 q^{29} +(1653.43 - 2863.83i) q^{31} +(-2803.81 - 4856.34i) q^{33} +(-2440.24 + 8761.24i) q^{35} +(6828.69 + 11827.6i) q^{37} +(-1254.81 + 2173.40i) q^{39} -1516.08 q^{41} -1994.62 q^{43} +(2841.19 - 4921.08i) q^{45} +(12617.7 + 21854.6i) q^{47} +(-330.830 + 16803.7i) q^{49} +(-3991.74 - 6913.90i) q^{51} +(-584.564 + 1012.49i) q^{53} +43710.0 q^{55} -14248.1 q^{57} +(13556.8 - 23481.0i) q^{59} +(-6973.97 - 12079.3i) q^{61} +(2817.56 - 10115.9i) q^{63} +(-9780.95 - 16941.1i) q^{65} +(20091.7 - 34799.9i) q^{67} -17454.5 q^{69} -63175.6 q^{71} +(41276.1 - 71492.2i) q^{73} +(8083.82 + 14001.6i) q^{75} +(78225.4 - 20137.4i) q^{77} +(50718.0 + 87846.2i) q^{79} +(-3280.50 + 5681.99i) q^{81} -19358.7 q^{83} +62229.3 q^{85} +(38578.5 - 66820.0i) q^{87} +(-46.7136 - 80.9103i) q^{89} +(-25309.3 - 25812.5i) q^{91} +(-14880.9 - 25774.4i) q^{93} +(55530.2 - 96181.1i) q^{95} +44541.8 q^{97} -50468.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9}+O(q^{10}) $ 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9	$ 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9} + 145 q^{11} - 1430 q^{13} - 306 q^{15} - 1372 q^{17} + 1081 q^{19} + 2295 q^{21} - 4508 q^{23} - 6267 q^{25} - 2916 q^{27} + 15730 q^{29} + 8816 q^{31} - 1305 q^{33} - 24278 q^{35} + 14573 q^{37} - 6435 q^{39} + 14700 q^{41} + 11842 q^{43} - 1377 q^{45} + 44808 q^{47} + 17014 q^{49} + 12348 q^{51} - 9417 q^{53} + 170750 q^{55} + 19458 q^{57} - 5077 q^{59} - 42368 q^{61} - 12393 q^{63} + 18450 q^{65} + 30501 q^{67} - 81144 q^{69} - 183488 q^{71} + 85665 q^{73} + 56403 q^{75} + 154585 q^{77} + 94646 q^{79} - 13122 q^{81} - 67682 q^{83} + 518224 q^{85} + 70785 q^{87} - 27558 q^{89} - 149395 q^{91} - 79344 q^{93} + 343246 q^{95} - 93342 q^{97} - 23490 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9 + 145 * q^11 - 1430 * q^13 - 306 * q^15 - 1372 * q^17 + 1081 * q^19 + 2295 * q^21 - 4508 * q^23 - 6267 * q^25 - 2916 * q^27 + 15730 * q^29 + 8816 * q^31 - 1305 * q^33 - 24278 * q^35 + 14573 * q^37 - 6435 * q^39 + 14700 * q^41 + 11842 * q^43 - 1377 * q^45 + 44808 * q^47 + 17014 * q^49 + 12348 * q^51 - 9417 * q^53 + 170750 * q^55 + 19458 * q^57 - 5077 * q^59 - 42368 * q^61 - 12393 * q^63 + 18450 * q^65 + 30501 * q^67 - 81144 * q^69 - 183488 * q^71 + 85665 * q^73 + 56403 * q^75 + 154585 * q^77 + 94646 * q^79 - 13122 * q^81 - 67682 * q^83 + 518224 * q^85 + 70785 * q^87 - 27558 * q^89 - 149395 * q^91 - 79344 * q^93 + 343246 * q^95 - 93342 * q^97 - 23490 * 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
$5$	35.0764	+	60.7540i	0.627465	+	1.08680i	0.988059	+	0.154078i	$0.0492408\pi$
$5$	35.0764	+	60.7540i	0.627465	+	1.08680i	−0.360594	+	0.932723i	$0.617426\pi$
$6$		0			0
$7$	90.7639	+	92.5684i	0.700113	+	0.714032i
$7$	90.7639	+	92.5684i	0.700113	+	0.714032i
$8$		0			0
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$		0			0
$11$	311.535	−	539.594i	0.776291	−	1.34458i	−0.157775	−	0.987475i	$-0.550432\pi$
$11$	311.535	−	539.594i	0.776291	−	1.34458i	0.934066	−	0.357100i	$-0.116235\pi$
$12$		0			0
$13$	−278.847			−0.457623			−0.228812	−	0.973471i	$-0.573484\pi$
$13$	−278.847			−0.457623			−0.228812	+	0.973471i	$0.573484\pi$
$14$		0			0
$15$	631.374			0.724534
$16$		0			0
$17$	443.527	−	768.212i	0.372218	−	0.644701i	−0.617688	−	0.786423i	$-0.711931\pi$
$17$	443.527	−	768.212i	0.372218	−	0.644701i	0.989907	+	0.141722i	$0.0452639\pi$
$18$		0			0
$19$	−791.562	−	1371.03i	−0.503038	−	0.871287i	−0.999994	−	0.00351150i	$-0.998882\pi$
$19$	−791.562	−	1371.03i	−0.503038	−	0.871287i	0.496956	−	0.867776i	$-0.334451\pi$
$20$		0			0
$21$	1129.94	−	290.877i	0.559121	−	0.143933i
$22$		0			0
$23$	−969.695	−	1679.56i	−0.382222	−	0.662027i	0.609158	−	0.793049i	$-0.291508\pi$
$23$	−969.695	−	1679.56i	−0.382222	−	0.662027i	−0.991380	+	0.131022i	$0.958174\pi$
$24$		0			0
$25$	−898.202	+	1555.73i	−0.287425	+	0.497834i
$26$		0			0
$27$	−729.000			−0.192450
$28$		0			0
$29$	8573.01			1.89295			0.946473	−	0.322782i	$-0.104618\pi$
$29$	8573.01			1.89295			0.946473	+	0.322782i	$0.104618\pi$
$30$		0			0
$31$	1653.43	−	2863.83i	0.309017	−	0.535232i	−0.669131	−	0.743145i	$-0.733333\pi$
$31$	1653.43	−	2863.83i	0.309017	−	0.535232i	0.978148	+	0.207912i	$0.0666668\pi$
$32$		0			0
$33$	−2803.81	−	4856.34i	−0.448192	−	0.776291i
$34$		0			0
$35$	−2440.24	+	8761.24i	−0.336715	+	1.20891i
$36$		0			0
$37$	6828.69	+	11827.6i	0.820036	+	1.42034i	0.905655	+	0.424016i	$0.139380\pi$
$37$	6828.69	+	11827.6i	0.820036	+	1.42034i	−0.0856192	+	0.996328i	$0.527287\pi$
$38$		0			0
$39$	−1254.81	+	2173.40i	−0.132104	+	0.228812i
$40$		0			0
$41$	−1516.08			−0.140852			−0.0704259	−	0.997517i	$-0.522436\pi$
$41$	−1516.08			−0.140852			−0.0704259	+	0.997517i	$0.522436\pi$
$42$		0			0
$43$	−1994.62			−0.164509			−0.0822544	−	0.996611i	$-0.526212\pi$
$43$	−1994.62			−0.164509			−0.0822544	+	0.996611i	$0.526212\pi$
$44$		0			0
$45$	2841.19	−	4921.08i	0.209155	−	0.362267i
$46$		0			0
$47$	12617.7	+	21854.6i	0.833177	+	1.44310i	0.895506	+	0.445049i	$0.146814\pi$
$47$	12617.7	+	21854.6i	0.833177	+	1.44310i	−0.0623292	+	0.998056i	$0.519853\pi$
$48$		0			0
$49$	−330.830	+	16803.7i	−0.0196841	+	0.999806i
$50$		0			0
$51$	−3991.74	−	6913.90i	−0.214900	−	0.372218i
$52$		0			0
$53$	−584.564	+	1012.49i	−0.0285853	+	0.0495111i	−0.879964	−	0.475040i	$-0.842434\pi$
$53$	−584.564	+	1012.49i	−0.0285853	+	0.0495111i	0.851379	+	0.524551i	$0.175767\pi$
$54$		0			0
$55$	43710.0			1.94838
$56$		0			0
$57$	−14248.1			−0.580858
$58$		0			0
$59$	13556.8	−	23481.0i	0.507022	−	0.878188i	−0.492945	−	0.870060i	$-0.664080\pi$
$59$	13556.8	−	23481.0i	0.507022	−	0.878188i	0.999967	−	0.00812731i	$-0.00258703\pi$
$60$		0			0
$61$	−6973.97	−	12079.3i	−0.239969	−	0.415639i	0.720736	−	0.693210i	$-0.243804\pi$
$61$	−6973.97	−	12079.3i	−0.239969	−	0.415639i	−0.960705	+	0.277571i	$0.910471\pi$
$62$		0			0
$63$	2817.56	−	10115.9i	0.0894379	−	0.321111i
$64$		0			0
$65$	−9780.95	−	16941.1i	−0.287143	−	0.497345i
$66$		0			0
$67$	20091.7	−	34799.9i	0.546802	−	0.947088i	−0.451690	−	0.892175i	$-0.649179\pi$
$67$	20091.7	−	34799.9i	0.546802	−	0.947088i	0.998491	−	0.0549130i	$-0.0174882\pi$
$68$		0			0
$69$	−17454.5			−0.441352
$70$		0			0
$71$	−63175.6			−1.48732			−0.743658	−	0.668560i	$-0.766911\pi$
$71$	−63175.6			−1.48732			−0.743658	+	0.668560i	$0.766911\pi$
$72$		0			0
$73$	41276.1	−	71492.2i	0.906549	−	1.57019i	0.0877237	−	0.996145i	$-0.472041\pi$
$73$	41276.1	−	71492.2i	0.906549	−	1.57019i	0.818825	−	0.574043i	$-0.194626\pi$
$74$		0			0
$75$	8083.82	+	14001.6i	0.165945	+	0.287425i
$76$		0			0
$77$	78225.4	−	20137.4i	1.50356	−	0.387058i
$78$		0			0
$79$	50718.0	+	87846.2i	0.914313	+	1.58364i	0.807905	+	0.589313i	$0.200602\pi$
$79$	50718.0	+	87846.2i	0.914313	+	1.58364i	0.106408	+	0.994323i	$0.466065\pi$
$80$		0			0
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−19358.7			−0.308448			−0.154224	−	0.988036i	$-0.549288\pi$
$83$	−19358.7			−0.308448			−0.154224	+	0.988036i	$0.549288\pi$
$84$		0			0
$85$	62229.3			0.934216
$86$		0			0
$87$	38578.5	−	66820.0i	0.546447	−	0.946473i
$88$		0			0
$89$	−46.7136	−	80.9103i	−0.000625127	−	0.00108275i	0.865713	−	0.500541i	$-0.166866\pi$
$89$	−46.7136	−	80.9103i	−0.000625127	−	0.00108275i	−0.866338	+	0.499459i	$0.833532\pi$
$90$		0			0
$91$	−25309.3	−	25812.5i	−0.320388	−	0.326758i
$92$		0			0
$93$	−14880.9	−	25774.4i	−0.178411	−	0.309017i
$94$		0			0
$95$	55530.2	−	96181.1i	0.631277	−	1.09340i
$96$		0			0
$97$	44541.8			0.480660			0.240330	−	0.970691i	$-0.422744\pi$
$97$	44541.8			0.480660			0.240330	+	0.970691i	$0.422744\pi$
$98$		0			0
$99$	−50468.6			−0.517527
$100$		0			0
$101$	4976.12	−	8618.89i	0.0485386	−	0.0840713i	−0.840735	−	0.541446i	$-0.817877\pi$
$101$	4976.12	−	8618.89i	0.0485386	−	0.0840713i	0.889274	+	0.457375i	$0.151210\pi$
$102$		0			0
$103$	21011.2	+	36392.4i	0.195145	+	0.338001i	0.946948	−	0.321387i	$-0.104149\pi$
$103$	21011.2	+	36392.4i	0.195145	+	0.338001i	−0.751803	+	0.659388i	$0.770816\pi$
$104$		0			0
$105$	57306.0	+	58445.3i	0.507256	+	0.517341i
$106$		0			0
$107$	−41782.4	−	72369.2i	−0.352804	−	0.611075i	0.633935	−	0.773386i	$-0.281439\pi$
$107$	−41782.4	−	72369.2i	−0.352804	−	0.611075i	−0.986740	+	0.162311i	$0.948105\pi$
$108$		0			0
$109$	−63445.4	+	109891.i	−0.511486	+	0.885920i	0.488425	+	0.872606i	$0.337572\pi$
$109$	−63445.4	+	109891.i	−0.511486	+	0.885920i	−0.999911	+	0.0133145i	$0.995762\pi$
$110$		0			0
$111$	122916.			0.946896
$112$		0			0
$113$	100340.			0.739228			0.369614	−	0.929185i	$-0.379490\pi$
$113$	100340.			0.739228			0.369614	+	0.929185i	$0.379490\pi$
$114$		0			0
$115$	68026.7	−	117826.i	0.479661	−	0.830798i
$116$		0			0
$117$	11293.3	+	19560.6i	0.0762705	+	0.132104i
$118$		0			0
$119$	111368.	−	28669.3i	0.720932	−	0.185588i
$120$		0			0
$121$	−113582.	−	196730.i	−0.705255	−	1.22154i
$122$		0			0
$123$	−6822.36	+	11816.7i	−0.0406604	+	0.0704259i
$124$		0			0
$125$	93204.6			0.533534
$126$		0			0
$127$	−111986.			−0.616103			−0.308052	−	0.951370i	$-0.599677\pi$
$127$	−111986.			−0.616103			−0.308052	+	0.951370i	$0.599677\pi$
$128$		0			0
$129$	−8975.80	+	15546.5i	−0.0474896	+	0.0822544i
$130$		0			0
$131$	173687.	+	300834.i	0.884277	+	1.53161i	0.846540	+	0.532325i	$0.178682\pi$
$131$	173687.	+	300834.i	0.884277	+	1.53161i	0.0377368	+	0.999288i	$0.487985\pi$
$132$		0			0
$133$	55068.4	−	197713.i	0.269944	−	0.969185i
$134$		0			0
$135$	−25570.7	−	44289.7i	−0.120756	−	0.209155i
$136$		0			0
$137$	−102444.	+	177438.i	−0.466319	+	0.807689i	−0.999260	−	0.0384637i	$-0.987754\pi$
$137$	−102444.	+	177438.i	−0.466319	+	0.807689i	0.532941	+	0.846153i	$0.321087\pi$
$138$		0			0
$139$	−18263.3			−0.0801754			−0.0400877	−	0.999196i	$-0.512764\pi$
$139$	−18263.3			−0.0801754			−0.0400877	+	0.999196i	$0.512764\pi$
$140$		0			0
$141$	227119.			0.962070
$142$		0			0
$143$	−86870.6	+	150464.i	−0.355249	+	0.615309i
$144$		0			0
$145$	300710.	+	520845.i	1.18776	+	2.05726i
$146$		0			0
$147$	129483.	+	78195.4i	0.494221	+	0.298461i
$148$		0			0
$149$	28404.1	+	49197.4i	0.104813	+	0.181542i	0.913662	−	0.406475i	$-0.133242\pi$
$149$	28404.1	+	49197.4i	0.104813	+	0.181542i	−0.808849	+	0.588017i	$0.799909\pi$
$150$		0			0
$151$	163471.	−	283139.i	0.583441	−	1.01055i	−0.411627	−	0.911353i	$-0.635039\pi$
$151$	163471.	−	283139.i	0.583441	−	1.01055i	0.995068	−	0.0991972i	$-0.0316275\pi$
$152$		0			0
$153$	−71851.4			−0.248146
$154$		0			0
$155$	231985.			0.775588
$156$		0			0
$157$	191192.	−	331155.i	0.619043	−	1.07221i	−0.370617	−	0.928786i	$-0.620854\pi$
$157$	191192.	−	331155.i	0.619043	−	1.07221i	0.989661	−	0.143429i	$-0.0458128\pi$
$158$		0			0
$159$	5261.07	+	9112.45i	0.0165037	+	0.0285853i
$160$		0			0
$161$	67461.0	−	242207.i	0.205111	−	0.736413i
$162$		0			0
$163$	66399.8	+	115008.i	0.195748	+	0.339046i	0.947146	−	0.320804i	$-0.103953\pi$
$163$	66399.8	+	115008.i	0.195748	+	0.339046i	−0.751397	+	0.659850i	$0.770620\pi$
$164$		0			0
$165$	196695.	−	340686.i	0.562449	−	0.974191i
$166$		0			0
$167$	−26878.3			−0.0745780			−0.0372890	−	0.999305i	$-0.511872\pi$
$167$	−26878.3			−0.0745780			−0.0372890	+	0.999305i	$0.511872\pi$
$168$		0			0
$169$	−293537.			−0.790581
$170$		0			0
$171$	−64116.5	+	111053.i	−0.167679	+	0.290429i
$172$		0			0
$173$	70987.7	+	122954.i	0.180330	+	0.312341i	0.941993	−	0.335633i	$-0.108950\pi$
$173$	70987.7	+	122954.i	0.180330	+	0.312341i	−0.761663	+	0.647973i	$0.775617\pi$
$174$		0			0
$175$	−225536.	+	58059.1i	−0.556699	+	0.143310i
$176$		0			0
$177$	−122011.	−	211329.i	−0.292729	−	0.507022i
$178$		0			0
$179$	−240656.	+	416829.i	−0.561390	+	0.972356i	0.435985	+	0.899954i	$0.356400\pi$
$179$	−240656.	+	416829.i	−0.561390	+	0.972356i	−0.997375	+	0.0724026i	$0.976933\pi$
$180$		0			0
$181$	−772210.			−1.75202			−0.876010	−	0.482293i	$-0.839804\pi$
$181$	−772210.			−1.75202			−0.876010	+	0.482293i	$0.839804\pi$
$182$		0			0
$183$	−125532.			−0.277093
$184$		0			0
$185$	−479051.	+	829740.i	−1.02909	+	1.78243i
$186$		0			0
$187$	−276348.	−	478649.i	−0.577900	−	1.00095i
$188$		0			0
$189$	−66166.9	−	67482.4i	−0.134737	−	0.137416i
$190$		0			0
$191$	−72643.3	−	125822.i	−0.144083	−	0.249559i	0.784948	−	0.619562i	$-0.212690\pi$
$191$	−72643.3	−	125822.i	−0.144083	−	0.249559i	−0.929030	+	0.370003i	$0.879357\pi$
$192$		0			0
$193$	281241.	−	487124.i	0.543483	−	0.941340i	−0.455218	−	0.890380i	$-0.650439\pi$
$193$	281241.	−	487124.i	0.543483	−	0.941340i	0.998701	−	0.0509599i	$-0.0162281\pi$
$194$		0			0
$195$	−176057.			−0.331564
$196$		0			0
$197$	368578.			0.676650			0.338325	−	0.941029i	$-0.390140\pi$
$197$	368578.			0.676650			0.338325	+	0.941029i	$0.390140\pi$
$198$		0			0
$199$	518272.	−	897674.i	0.927738	−	1.60689i	0.140641	−	0.990061i	$-0.455084\pi$
$199$	518272.	−	897674.i	0.927738	−	1.60689i	0.787097	−	0.616829i	$-0.211583\pi$
$200$		0			0
$201$	−180825.	−	313199.i	−0.315696	−	0.546802i
$202$		0			0
$203$	778120.	+	793590.i	1.32528	+	1.35162i
$204$		0			0
$205$	−53178.5	−	92107.9i	−0.0883796	−	0.153078i
$206$		0			0
$207$	−78545.3	+	136044.i	−0.127407	+	0.220676i
$208$		0			0
$209$	−986395.			−1.56202
$210$		0			0
$211$	253980.			0.392730			0.196365	−	0.980531i	$-0.437086\pi$
$211$	253980.			0.392730			0.196365	+	0.980531i	$0.437086\pi$
$212$		0			0
$213$	−284290.	+	492405.i	−0.429351	+	0.743658i
$214$		0			0
$215$	−69964.0	−	121181.i	−0.103224	−	0.178788i
$216$		0			0
$217$	415172.	−	106877.i	0.598520	−	0.154075i
$218$		0			0
$219$	−371485.	−	643430.i	−0.523396	−	0.906549i
$220$		0			0
$221$	−123676.	+	214214.i	−0.170336	+	0.295030i
$222$		0			0
$223$	−959995.			−1.29273			−0.646363	−	0.763030i	$-0.723711\pi$
$223$	−959995.			−1.29273			−0.646363	+	0.763030i	$0.723711\pi$
$224$		0			0
$225$	145509.			0.191616
$226$		0			0
$227$	234150.	−	405559.i	0.301598	−	0.522383i	−0.674900	−	0.737909i	$-0.735813\pi$
$227$	234150.	−	405559.i	0.301598	−	0.522383i	0.976498	+	0.215526i	$0.0691465\pi$
$228$		0			0
$229$	392208.	+	679323.i	0.494228	+	0.856028i	0.999978	−	0.00665222i	$-0.00211748\pi$
$229$	392208.	+	679323.i	0.494228	+	0.856028i	−0.505750	+	0.862680i	$0.668784\pi$
$230$		0			0
$231$	195059.	−	700325.i	0.240512	−	0.863514i
$232$		0			0
$233$	65058.2	+	112684.i	0.0785077	+	0.135979i	0.902606	−	0.430467i	$-0.141651\pi$
$233$	65058.2	+	112684.i	0.0785077	+	0.135979i	−0.824099	+	0.566446i	$0.808318\pi$
$234$		0			0
$235$	−885169.	+	1.53316e6i	−1.04558	+	1.81100i
$236$		0			0
$237$	912925.			1.05576
$238$		0			0
$239$	−1.52937e6			−1.73188			−0.865942	−	0.500145i	$-0.833280\pi$
$239$	−1.52937e6			−1.73188			−0.865942	+	0.500145i	$0.833280\pi$
$240$		0			0
$241$	596184.	−	1.03262e6i	0.661208	−	1.14525i	−0.319091	−	0.947724i	$-0.603378\pi$
$241$	596184.	−	1.03262e6i	0.661208	−	1.14525i	0.980299	−	0.197521i	$-0.0632891\pi$
$242$		0			0
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−1.03250e6	+	569315.i	−1.09894	+	0.605951i
$246$		0			0
$247$	220725.	+	382307.i	0.230202	+	0.398721i
$248$		0			0
$249$	−87114.3	+	150886.i	−0.0890412	+	0.154224i
$250$		0			0
$251$	−1.60850e6			−1.61152			−0.805761	−	0.592241i	$-0.798243\pi$
$251$	−1.60850e6			−1.61152			−0.805761	+	0.592241i	$0.798243\pi$
$252$		0			0
$253$	−1.20837e6			−1.18686
$254$		0			0
$255$	280032.	−	485029.i	0.269685	−	0.467108i
$256$		0			0
$257$	374165.	+	648072.i	0.353370	+	0.612055i	0.986838	−	0.161714i	$-0.0517023\pi$
$257$	374165.	+	648072.i	0.353370	+	0.612055i	−0.633467	+	0.773769i	$0.718369\pi$
$258$		0			0
$259$	−475067.	+	1.70564e6i	−0.440054	+	1.57993i
$260$		0			0
$261$	−347207.	−	601380.i	−0.315491	−	0.546447i
$262$		0			0
$263$	−107321.	+	185886.i	−0.0956745	+	0.165713i	−0.909890	−	0.414850i	$-0.863834\pi$
$263$	−107321.	+	185886.i	−0.0956745	+	0.165713i	0.814215	+	0.580563i	$0.197167\pi$
$264$		0			0
$265$	−82017.5			−0.0717450
$266$		0			0
$267$	−840.844			−0.000721834
$268$		0			0
$269$	−504366.	+	873587.i	−0.424976	+	0.736081i	−0.996418	−	0.0845618i	$-0.973051\pi$
$269$	−504366.	+	873587.i	−0.424976	+	0.736081i	0.571442	+	0.820643i	$0.306384\pi$
$270$		0			0
$271$	−679701.	−	1.17728e6i	−0.562205	−	0.973768i	−0.997304	−	0.0733853i	$-0.976620\pi$
$271$	−679701.	−	1.17728e6i	−0.562205	−	0.973768i	0.435098	−	0.900383i	$-0.356714\pi$
$272$		0			0
$273$	−315080.	+	81110.2i	−0.255867	+	0.0658671i
$274$		0			0
$275$	559642.	+	969328.i	0.446250	+	0.772928i
$276$		0			0
$277$	−702583.	+	1.21691e6i	−0.550172	+	0.952926i	0.448090	+	0.893989i	$0.352105\pi$
$277$	−702583.	+	1.21691e6i	−0.550172	+	0.952926i	−0.998262	+	0.0589373i	$0.981229\pi$
$278$		0			0
$279$	−267856.			−0.206011
$280$		0			0
$281$	−677663.			−0.511974			−0.255987	−	0.966680i	$-0.582400\pi$
$281$	−677663.			−0.511974			−0.255987	+	0.966680i	$0.582400\pi$
$282$		0			0
$283$	−380189.	+	658507.i	−0.282185	+	0.488758i	−0.971923	−	0.235301i	$-0.924392\pi$
$283$	−380189.	+	658507.i	−0.282185	+	0.488758i	0.689738	+	0.724059i	$0.257726\pi$
$284$		0			0
$285$	−499772.	−	865630.i	−0.364468	−	0.631277i
$286$		0			0
$287$	−137605.	−	140341.i	−0.0986121	−	0.100573i
$288$		0			0
$289$	316496.	+	548187.i	0.222907	+	0.386086i
$290$		0			0
$291$	200438.	−	347169.i	0.138755	−	0.240330i
$292$		0			0
$293$	264378.			0.179910			0.0899552	−	0.995946i	$-0.471328\pi$
$293$	264378.			0.179910			0.0899552	+	0.995946i	$0.471328\pi$
$294$		0			0
$295$	1.90209e6			1.27255
$296$		0			0
$297$	−227109.	+	393364.i	−0.149397	+	0.258764i
$298$		0			0
$299$	270397.	+	468341.i	0.174914	+	0.302959i
$300$		0			0
$301$	−181040.	−	184639.i	−0.115175	−	0.117465i
$302$		0			0
$303$	−44785.0	−	77570.0i	−0.0280238	−	0.0485386i
$304$		0			0
$305$	489243.	−	847394.i	0.301145	−	0.521598i
$306$		0			0
$307$	1.46108e6			0.884765			0.442383	−	0.896826i	$-0.354133\pi$
$307$	1.46108e6			0.884765			0.442383	+	0.896826i	$0.354133\pi$
$308$		0			0
$309$	378201.			0.225334
$310$		0			0
$311$	−1.35810e6	+	2.35230e6i	−0.796216	+	1.37909i	0.125848	+	0.992050i	$0.459835\pi$
$311$	−1.35810e6	+	2.35230e6i	−0.796216	+	1.37909i	−0.922064	+	0.387038i	$0.873498\pi$
$312$		0			0
$313$	−1.01125e6	−	1.75154e6i	−0.583442	−	1.01055i	−0.995068	−	0.0991986i	$-0.968372\pi$
$313$	−1.01125e6	−	1.75154e6i	−0.583442	−	1.01055i	0.411625	−	0.911353i	$-0.364961\pi$
$314$		0			0
$315$	713413.	−	183652.i	0.405102	−	0.104284i
$316$		0			0
$317$	315814.	+	547006.i	0.176516	+	0.305734i	0.940685	−	0.339282i	$-0.110184\pi$
$317$	315814.	+	547006.i	0.176516	+	0.305734i	−0.764169	+	0.645016i	$0.776851\pi$
$318$		0			0
$319$	2.67079e6	−	4.62594e6i	1.46948	−	2.54521i
$320$		0			0
$321$	−752083.			−0.407383
$322$		0			0
$323$	−1.40432e6			−0.748960
$324$		0			0
$325$	250461.	−	433811.i	0.131532	−	0.227820i
$326$		0			0
$327$	571009.	+	989016.i	0.295307	+	0.511486i
$328$		0			0
$329$	−877808.	+	3.15161e6i	−0.447105	+	1.60525i
$330$		0			0
$331$	455510.	+	788966.i	0.228522	+	0.395811i	0.957370	−	0.288864i	$-0.0932774\pi$
$331$	455510.	+	788966.i	0.228522	+	0.395811i	−0.728848	+	0.684675i	$0.759944\pi$
$332$		0			0
$333$	553123.	−	958038.i	0.273345	−	0.473448i
$334$		0			0
$335$	2.81898e6			1.37240
$336$		0			0
$337$	1.39984e6			0.671434			0.335717	−	0.941963i	$-0.391021\pi$
$337$	1.39984e6			0.671434			0.335717	+	0.941963i	$0.391021\pi$
$338$		0			0
$339$	451531.	−	782074.i	0.213397	−	0.369614i
$340$		0			0
$341$	−1.03020e6	−	1.78436e6i	−0.479774	−	0.830992i
$342$		0			0
$343$	−1.58552e6	+	1.49455e6i	−0.727675	+	0.685922i
$344$		0			0
$345$	−612240.	−	1.06043e6i	−0.276933	−	0.479661i
$346$		0			0
$347$	−1.83723e6	+	3.18218e6i	−0.819107	+	1.41873i	0.0872340	+	0.996188i	$0.472197\pi$
$347$	−1.83723e6	+	3.18218e6i	−0.819107	+	1.41873i	−0.906341	+	0.422547i	$0.861136\pi$
$348$		0			0
$349$	89227.3			0.0392134			0.0196067	−	0.999808i	$-0.493759\pi$
$349$	89227.3			0.0392134			0.0196067	+	0.999808i	$0.493759\pi$
$350$		0			0
$351$	203280.			0.0880696
$352$		0			0
$353$	1.35541e6	−	2.34764e6i	0.578940	−	1.00275i	−0.416661	−	0.909062i	$-0.636800\pi$
$353$	1.35541e6	−	2.34764e6i	0.578940	−	1.00275i	0.995601	−	0.0936917i	$-0.0298668\pi$
$354$		0			0
$355$	−2.21597e6	−	3.83817e6i	−0.933239	−	1.61642i
$356$		0			0
$357$	277703.	−	997042.i	0.115321	−	0.414041i
$358$		0			0
$359$	−1.38711e6	−	2.40254e6i	−0.568034	−	0.983863i	−0.996760	−	0.0804289i	$-0.974371\pi$
$359$	−1.38711e6	−	2.40254e6i	−0.568034	−	0.983863i	0.428727	−	0.903434i	$-0.358962\pi$
$360$		0			0
$361$	−15090.3	+	26137.2i	−0.00609439	+	0.0105558i
$362$		0			0
$363$	−2.04448e6			−0.814358
$364$		0			0
$365$	5.79126e6			2.27531
$366$		0			0
$367$	1.08959e6	−	1.88723e6i	0.422277	−	0.731406i	−0.573884	−	0.818936i	$-0.694564\pi$
$367$	1.08959e6	−	1.88723e6i	0.422277	−	0.731406i	0.996162	+	0.0875303i	$0.0278975\pi$
$368$		0			0
$369$	61401.2	+	106350.i	0.0234753	+	0.0406604i
$370$		0			0
$371$	−146782.	+	37785.8i	−0.0553655	+	0.0142526i
$372$		0			0
$373$	−368827.	−	638827.i	−0.137262	−	0.237745i	0.789197	−	0.614140i	$-0.210497\pi$
$373$	−368827.	−	638827.i	−0.137262	−	0.237745i	−0.926459	+	0.376395i	$0.877164\pi$
$374$		0			0
$375$	419421.	−	726458.i	0.154018	−	0.266767i
$376$		0			0
$377$	−2.39056e6			−0.866256
$378$		0			0
$379$	1.43040e6			0.511517			0.255758	−	0.966741i	$-0.417675\pi$
$379$	1.43040e6			0.511517			0.255758	+	0.966741i	$0.417675\pi$
$380$		0			0
$381$	−503936.	+	872843.i	−0.177854	+	0.308052i
$382$		0			0
$383$	785201.	+	1.36001e6i	0.273517	+	0.473745i	0.969760	−	0.244061i	$-0.0784797\pi$
$383$	785201.	+	1.36001e6i	0.273517	+	0.473745i	−0.696243	+	0.717806i	$0.745146\pi$
$384$		0			0
$385$	3.96729e6	+	4.04616e6i	1.36409	+	1.39121i
$386$		0			0
$387$	80782.2	+	139919.i	0.0274181	+	0.0474896i
$388$		0			0
$389$	−2.79379e6	+	4.83899e6i	−0.936096	+	1.62137i	−0.163427	+	0.986555i	$0.552255\pi$
$389$	−2.79379e6	+	4.83899e6i	−0.936096	+	1.62137i	−0.772669	+	0.634810i	$0.781079\pi$
$390$		0			0
$391$	−1.72034e6			−0.569080
$392$		0			0
$393$	3.12636e6			1.02108
$394$		0			0
$395$	−3.55801e6	+	6.16265e6i	−1.14740	+	1.98735i
$396$		0			0
$397$	−2.18419e6	−	3.78314e6i	−0.695529	−	1.20469i	−0.970002	−	0.243096i	$-0.921837\pi$
$397$	−2.18419e6	−	3.78314e6i	−0.695529	−	1.20469i	0.274473	−	0.961595i	$-0.411496\pi$
$398$		0			0
$399$	−1.29321e6	−	1.31893e6i	−0.406666	−	0.414751i
$400$		0			0
$401$	1.25489e6	+	2.17354e6i	0.389714	+	0.675004i	0.992411	−	0.122966i	$-0.0392406\pi$
$401$	1.25489e6	+	2.17354e6i	0.389714	+	0.675004i	−0.602697	+	0.797970i	$0.705907\pi$
$402$		0			0
$403$	−461055.	+	798570.i	−0.141413	+	0.244935i
$404$		0			0
$405$	−460272.			−0.139437
$406$		0			0
$407$	8.50948e6			2.54634
$408$		0			0
$409$	970989.	−	1.68180e6i	0.287016	−	0.497126i	−0.686080	−	0.727526i	$-0.740670\pi$
$409$	970989.	−	1.68180e6i	0.287016	−	0.497126i	0.973096	+	0.230400i	$0.0740034\pi$
$410$		0			0
$411$	921993.	+	1.59694e6i	0.269230	+	0.466319i
$412$		0			0
$413$	3.40407e6	−	876301.i	0.982027	−	0.252801i
$414$		0			0
$415$	−679034.	−	1.17612e6i	−0.193540	−	0.335221i
$416$		0			0
$417$	−82184.7	+	142348.i	−0.0231447	+	0.0400877i
$418$		0			0
$419$	1.00437e6			0.279484			0.139742	−	0.990188i	$-0.455373\pi$
$419$	1.00437e6			0.279484			0.139742	+	0.990188i	$0.455373\pi$
$420$		0			0
$421$	−6.22615e6			−1.71204			−0.856021	−	0.516940i	$-0.827071\pi$
$421$	−6.22615e6			−1.71204			−0.856021	+	0.516940i	$0.827071\pi$
$422$		0			0
$423$	1.02204e6	−	1.77022e6i	0.277726	−	0.481035i
$424$		0			0
$425$	796754.	+	1.38002e6i	0.213970	+	0.370606i
$426$		0			0
$427$	485175.	−	1.74193e6i	0.128774	−	0.462340i
$428$		0			0
$429$	781835.	+	1.35418e6i	0.205103	+	0.355249i
$430$		0			0
$431$	1.11271e6	−	1.92727e6i	0.288529	−	0.499747i	−0.684930	−	0.728609i	$-0.740167\pi$
$431$	1.11271e6	−	1.92727e6i	0.288529	−	0.499747i	0.973459	+	0.228862i	$0.0735004\pi$
$432$		0			0
$433$	1.33678e6			0.342642			0.171321	−	0.985215i	$-0.445197\pi$
$433$	1.33678e6			0.342642			0.171321	+	0.985215i	$0.445197\pi$
$434$		0			0
$435$	5.41278e6			1.37150
$436$		0			0
$437$	−1.53515e6	+	2.65895e6i	−0.384544	+	0.666050i
$438$		0			0
$439$	−805992.	−	1.39602e6i	−0.199604	−	0.345724i	0.748796	−	0.662800i	$-0.230632\pi$
$439$	−805992.	−	1.39602e6i	−0.199604	−	0.345724i	−0.948400	+	0.317076i	$0.897299\pi$
$440$		0			0
$441$	1.19215e6	−	657345.i	0.291900	−	0.160952i
$442$		0			0
$443$	−621897.	−	1.07716e6i	−0.150560	−	0.260777i	0.780874	−	0.624689i	$-0.214774\pi$
$443$	−621897.	−	1.07716e6i	−0.150560	−	0.260777i	−0.931433	+	0.363912i	$0.881441\pi$
$444$		0			0
$445$	3277.08	−	5676.07i	0.000784490	−	0.00135878i
$446$		0			0
$447$	511274.			0.121028
$448$		0			0
$449$	4.83017e6			1.13070			0.565349	−	0.824852i	$-0.308742\pi$
$449$	4.83017e6			1.13070			0.565349	+	0.824852i	$0.308742\pi$
$450$		0			0
$451$	−472311.	+	818067.i	−0.109342	+	0.189386i
$452$		0			0
$453$	−1.47123e6	−	2.54825e6i	−0.336850	−	0.583441i
$454$		0			0
$455$	680454.	−	2.44305e6i	0.154089	−	0.553227i
$456$		0			0
$457$	−2.73513e6	−	4.73739e6i	−0.612615	−	1.06108i	−0.990798	−	0.135350i	$-0.956784\pi$
$457$	−2.73513e6	−	4.73739e6i	−0.612615	−	1.06108i	0.378183	−	0.925731i	$-0.376549\pi$
$458$		0			0
$459$	−323331.	+	560026.i	−0.0716335	+	0.124073i
$460$		0			0
$461$	−1.05068e6			−0.230260			−0.115130	−	0.993350i	$-0.536729\pi$
$461$	−1.05068e6			−0.230260			−0.115130	+	0.993350i	$0.536729\pi$
$462$		0			0
$463$	−2.85654e6			−0.619281			−0.309640	−	0.950854i	$-0.600209\pi$
$463$	−2.85654e6			−0.619281			−0.309640	+	0.950854i	$0.600209\pi$
$464$		0			0
$465$	1.04393e6	−	1.80815e6i	0.223893	−	0.387794i
$466$		0			0
$467$	621271.	+	1.07607e6i	0.131822	+	0.228323i	0.924379	−	0.381475i	$-0.124584\pi$
$467$	621271.	+	1.07607e6i	0.131822	+	0.228323i	−0.792557	+	0.609798i	$0.791250\pi$
$468$		0			0
$469$	5.04497e6	−	1.29871e6i	1.05907	−	0.272635i
$470$		0			0
$471$	−1.72073e6	−	2.98039e6i	−0.357405	−	0.619043i
$472$		0			0
$473$	−621393.	+	1.07628e6i	−0.127707	+	0.221195i
$474$		0			0
$475$	2.84393e6			0.578342
$476$		0			0
$477$	94699.3			0.0190568
$478$		0			0
$479$	3.85580e6	−	6.67845e6i	0.767849	−	1.32995i	−0.170877	−	0.985292i	$-0.554660\pi$
$479$	3.85580e6	−	6.67845e6i	0.767849	−	1.32995i	0.938727	−	0.344662i	$-0.112006\pi$
$480$		0			0
$481$	−1.90416e6	−	3.29810e6i	−0.375267	−	0.649982i
$482$		0			0
$483$	−1.58424e6	−	1.61574e6i	−0.308996	−	0.315139i
$484$		0			0
$485$	1.56236e6	+	2.70609e6i	0.301598	+	0.522382i
$486$		0			0
$487$	−3.17105e6	+	5.49242e6i	−0.605871	+	1.04940i	0.386042	+	0.922481i	$0.373842\pi$
$487$	−3.17105e6	+	5.49242e6i	−0.605871	+	1.04940i	−0.991913	+	0.126919i	$0.959491\pi$
$488$		0			0
$489$	1.19520e6			0.226030
$490$		0			0
$491$	4.00002e6			0.748788			0.374394	−	0.927270i	$-0.377851\pi$
$491$	4.00002e6			0.748788			0.374394	+	0.927270i	$0.377851\pi$
$492$		0			0
$493$	3.80236e6	−	6.58589e6i	0.704590	−	1.22039i
$494$		0			0
$495$	−1.77025e6	−	3.06617e6i	−0.324730	−	0.562449i
$496$		0			0
$497$	−5.73406e6	−	5.84807e6i	−1.04129	−	1.06199i
$498$		0			0
$499$	2.31833e6	+	4.01547e6i	0.416797	+	0.721913i	0.995615	−	0.0935435i	$-0.0298194\pi$
$499$	2.31833e6	+	4.01547e6i	0.416797	+	0.721913i	−0.578819	+	0.815456i	$0.696486\pi$
$500$		0			0
$501$	−120952.	+	209496.i	−0.0215288	+	0.0372890i
$502$		0			0
$503$	−3.74567e6			−0.660099			−0.330050	−	0.943964i	$-0.607065\pi$
$503$	−3.74567e6			−0.660099			−0.330050	+	0.943964i	$0.607065\pi$
$504$		0			0
$505$	698176.			0.121825
$506$		0			0
$507$	−1.32092e6	+	2.28790e6i	−0.228221	+	0.395291i
$508$		0			0
$509$	−2.51298e6	−	4.35261e6i	−0.429927	−	0.744655i	0.566939	−	0.823759i	$-0.308127\pi$
$509$	−2.51298e6	−	4.35261e6i	−0.429927	−	0.744655i	−0.996866	+	0.0791042i	$0.974794\pi$
$510$		0			0
$511$	1.03643e7	−	2.66805e6i	1.75585	−	0.452004i
$512$		0			0
$513$	577048.	+	999477.i	0.0968097	+	0.167679i
$514$		0			0
$515$	−1.47399e6	+	2.55303e6i	−0.244893	+	0.424167i
$516$		0			0
$517$	1.57235e7			2.58715
$518$		0			0
$519$	1.27778e6			0.208227
$520$		0			0
$521$	3.02210e6	−	5.23443e6i	0.487769	−	0.844841i	−0.512132	−	0.858907i	$-0.671144\pi$
$521$	3.02210e6	−	5.23443e6i	0.487769	−	0.844841i	0.999901	+	0.0140661i	$0.00447751\pi$
$522$		0			0
$523$	4.62823e6	+	8.01633e6i	0.739879	+	1.28151i	0.952550	+	0.304384i	$0.0984505\pi$
$523$	4.62823e6	+	8.01633e6i	0.739879	+	1.28151i	−0.212671	+	0.977124i	$0.568216\pi$
$524$		0			0
$525$	−562386.	+	2.01914e6i	−0.0890504	+	0.319720i
$526$		0			0
$527$	−1.46668e6	−	2.54037e6i	−0.230043	−	0.398447i
$528$		0			0
$529$	1.33756e6	−	2.31672e6i	0.207813	−	0.359943i
$530$		0			0
$531$	−2.19620e6			−0.338015
$532$		0			0
$533$	422755.			0.0644570
$534$		0			0
$535$	2.93115e6	−	5.07690e6i	0.442745	−	0.766856i
$536$		0			0
$537$	2.16591e6	+	3.75146e6i	0.324119	+	0.561390i
$538$		0			0
$539$	8.96413e6	+	5.41346e6i	1.32903	+	0.802607i
$540$		0			0
$541$	3.29622e6	+	5.70922e6i	0.484198	+	0.838656i	0.999835	−	0.0181511i	$-0.00577801\pi$
$541$	3.29622e6	+	5.70922e6i	0.484198	+	0.838656i	−0.515637	+	0.856807i	$0.672445\pi$
$542$		0			0
$543$	−3.47495e6	+	6.01878e6i	−0.505765	+	0.876010i
$544$		0			0
$545$	−8.90174e6			−1.28376
$546$		0			0
$547$	−6.00764e6			−0.858491			−0.429245	−	0.903188i	$-0.641220\pi$
$547$	−6.00764e6			−0.858491			−0.429245	+	0.903188i	$0.641220\pi$
$548$		0			0
$549$	−564892.	+	978422.i	−0.0799898	+	0.138546i
$550$		0			0
$551$	−6.78607e6	−	1.17538e7i	−0.952224	−	1.64930i
$552$		0			0
$553$	−3.52842e6	+	1.26682e7i	−0.490645	+	1.76157i
$554$		0			0
$555$	4.31146e6	+	7.46766e6i	0.594144	+	1.02909i
$556$		0			0
$557$	−5.61296e6	+	9.72192e6i	−0.766573	+	1.32774i	0.172838	+	0.984950i	$0.444706\pi$
$557$	−5.61296e6	+	9.72192e6i	−0.766573	+	1.32774i	−0.939411	+	0.342793i	$0.888627\pi$
$558$		0			0
$559$	556195.			0.0752831
$560$		0			0
$561$	−4.97426e6			−0.667301
$562$		0			0
$563$	−2.91075e6	+	5.04157e6i	−0.387021	+	0.670340i	−0.992047	−	0.125866i	$-0.959829\pi$
$563$	−2.91075e6	+	5.04157e6i	−0.387021	+	0.670340i	0.605027	+	0.796205i	$0.293162\pi$
$564$		0			0
$565$	3.51957e6	+	6.09607e6i	0.463840	+	0.803394i
$566$		0			0
$567$	−823724.	+	212049.i	−0.107603	+	0.0276999i
$568$		0			0
$569$	−1.45476e6	−	2.51972e6i	−0.188370	−	0.326266i	0.756337	−	0.654182i	$-0.226987\pi$
$569$	−1.45476e6	−	2.51972e6i	−0.188370	−	0.326266i	−0.944707	+	0.327916i	$0.893654\pi$
$570$		0			0
$571$	−1.50123e6	+	2.60020e6i	−0.192689	+	0.333747i	−0.946140	−	0.323757i	$-0.895054\pi$
$571$	−1.50123e6	+	2.60020e6i	−0.192689	+	0.333747i	0.753452	+	0.657503i	$0.228387\pi$
$572$		0			0
$573$	−1.30758e6			−0.166373
$574$		0			0
$575$	3.48393e6			0.439440
$576$		0			0
$577$	−7.30311e6	+	1.26494e7i	−0.913205	+	1.58172i	−0.103696	+	0.994609i	$0.533067\pi$
$577$	−7.30311e6	+	1.26494e7i	−0.913205	+	1.58172i	−0.809509	+	0.587108i	$0.800266\pi$
$578$		0			0
$579$	−2.53117e6	−	4.38412e6i	−0.313780	−	0.543483i
$580$		0			0
$581$	−1.75707e6	−	1.79201e6i	−0.215948	−	0.220242i
$582$		0			0
$583$	364224.	+	630854.i	0.0443810	+	0.0768701i
$584$		0			0
$585$	−792257.	+	1.37223e6i	−0.0957142	+	0.165782i
$586$		0			0
$587$	−2.20529e6			−0.264162			−0.132081	−	0.991239i	$-0.542166\pi$
$587$	−2.20529e6			−0.264162			−0.132081	+	0.991239i	$0.542166\pi$
$588$		0			0
$589$	−5.23517e6			−0.621788
$590$		0			0
$591$	1.65860e6	−	2.87278e6i	0.195332	−	0.338325i
$592$		0			0
$593$	1.00011e6	+	1.73224e6i	0.116792	+	0.202289i	0.918494	−	0.395434i	$-0.129406\pi$
$593$	1.00011e6	+	1.73224e6i	0.116792	+	0.202289i	−0.801703	+	0.597723i	$0.796072\pi$
$594$		0			0
$595$	5.64817e6	+	5.76047e6i	0.654057	+	0.667061i
$596$		0			0
$597$	−4.66445e6	−	8.07907e6i	−0.535630	−	0.927738i
$598$		0			0
$599$	−5.57277e6	+	9.65231e6i	−0.634605	+	1.09917i	0.351993	+	0.936003i	$0.385504\pi$
$599$	−5.57277e6	+	9.65231e6i	−0.634605	+	1.09917i	−0.986599	+	0.163166i	$0.947829\pi$
$600$		0			0
$601$	−9.97261e6			−1.12622			−0.563109	−	0.826382i	$-0.690395\pi$
$601$	−9.97261e6			−1.12622			−0.563109	+	0.826382i	$0.690395\pi$
$602$		0			0
$603$	−3.25486e6			−0.364534
$604$		0			0
$605$	7.96809e6	−	1.38011e7i	0.885045	−	1.53294i
$606$		0			0
$607$	−7.83501e6	−	1.35706e7i	−0.863113	−	1.49496i	−0.868909	−	0.494973i	$-0.835178\pi$
$607$	−7.83501e6	−	1.35706e7i	−0.863113	−	1.49496i	0.00579535	−	0.999983i	$-0.498155\pi$
$608$		0			0
$609$	9.68696e6	−	2.49369e6i	1.05839	−	0.272458i
$610$		0			0
$611$	−3.51842e6	−	6.09409e6i	−0.381281	−	0.660398i
$612$		0			0
$613$	−2.16282e6	+	3.74612e6i	−0.232472	+	0.402653i	−0.958535	−	0.284975i	$-0.908015\pi$
$613$	−2.16282e6	+	3.74612e6i	−0.232472	+	0.402653i	0.726063	+	0.687628i	$0.241348\pi$
$614$		0			0
$615$	−957214.			−0.102052
$616$		0			0
$617$	−1.04397e7			−1.10402			−0.552010	−	0.833837i	$-0.686139\pi$
$617$	−1.04397e7			−1.10402			−0.552010	+	0.833837i	$0.686139\pi$
$618$		0			0
$619$	2.82947e6	−	4.90079e6i	0.296810	−	0.514091i	−0.678594	−	0.734514i	$-0.737410\pi$
$619$	2.82947e6	−	4.90079e6i	0.296810	−	0.514091i	0.975404	+	0.220423i	$0.0707437\pi$
$620$		0			0
$621$	706907.	+	1.22440e6i	0.0735586	+	0.127407i
$622$		0			0
$623$	3249.83	−	11667.9i	0.000335460	−	0.00120441i
$624$		0			0
$625$	6.07616e6	+	1.05242e7i	0.622199	+	1.07768i
$626$		0			0
$627$	−4.43878e6	+	7.68819e6i	−0.450915	+	0.781008i
$628$		0			0
$629$	1.21148e7			1.22093
$630$		0			0
$631$	−5.16299e6			−0.516212			−0.258106	−	0.966117i	$-0.583098\pi$
$631$	−5.16299e6			−0.516212			−0.258106	+	0.966117i	$0.583098\pi$
$632$		0			0
$633$	1.14291e6	−	1.97958e6i	0.113371	−	0.196365i
$634$		0			0
$635$	−3.92805e6	−	6.80359e6i	−0.386583	−	0.669582i
$636$		0			0
$637$	92251.0	−	4.68568e6i	0.00900788	−	0.457535i
$638$		0			0
$639$	2.55861e6	+	4.43165e6i	0.247886	+	0.429351i
$640$		0			0
$641$	2.01202e6	−	3.48492e6i	0.193413	−	0.335002i	−0.752966	−	0.658060i	$-0.771377\pi$
$641$	2.01202e6	−	3.48492e6i	0.193413	−	0.335002i	0.946379	+	0.323058i	$0.104711\pi$
$642$		0			0
$643$	−1.00121e7			−0.954990			−0.477495	−	0.878635i	$-0.658455\pi$
$643$	−1.00121e7			−0.954990			−0.477495	+	0.878635i	$0.658455\pi$
$644$		0			0
$645$	−1.25935e6			−0.119192
$646$		0			0
$647$	569445.	−	986307.i	0.0534799	−	0.0926300i	−0.838046	−	0.545599i	$-0.816302\pi$
$647$	569445.	−	986307.i	0.0534799	−	0.0926300i	0.891526	+	0.452969i	$0.149635\pi$
$648$		0			0
$649$	−8.44681e6	−	1.46303e7i	−0.787193	−	1.36346i
$650$		0			0
$651$	1.03525e6	−	3.71689e6i	0.0957401	−	0.343738i
$652$		0			0
$653$	3.84828e6	+	6.66541e6i	0.353170	+	0.611708i	0.986803	−	0.161926i	$-0.0517705\pi$
$653$	3.84828e6	+	6.66541e6i	0.353170	+	0.611708i	−0.633633	+	0.773634i	$0.718437\pi$
$654$		0			0
$655$	−1.21846e7	+	2.11043e7i	−1.10971	+	1.92207i
$656$		0			0
$657$	−6.68672e6			−0.604366
$658$		0			0
$659$	−7.43906e6			−0.667275			−0.333637	−	0.942702i	$-0.608276\pi$
$659$	−7.43906e6			−0.667275			−0.333637	+	0.942702i	$0.608276\pi$
$660$		0			0
$661$	−3.01487e6	+	5.22190e6i	−0.268389	+	0.464863i	−0.968446	−	0.249224i	$-0.919825\pi$
$661$	−3.01487e6	+	5.22190e6i	−0.268389	+	0.464863i	0.700057	+	0.714087i	$0.253158\pi$
$662$		0			0
$663$	1.11309e6	+	1.92792e6i	0.0983434	+	0.170336i
$664$		0			0
$665$	1.39435e7	−	3.58943e6i	1.22269	−	0.314754i
$666$		0			0
$667$	−8.31320e6	−	1.43989e7i	−0.723525	−	1.25318i
$668$		0			0
$669$	−4.31998e6	+	7.48242e6i	−0.373178	+	0.646363i
$670$		0			0
$671$	−8.69054e6			−0.745144
$672$		0			0
$673$	5.04651e6			0.429490			0.214745	−	0.976670i	$-0.431108\pi$
$673$	5.04651e6			0.429490			0.214745	+	0.976670i	$0.431108\pi$
$674$		0			0
$675$	654789.	−	1.13413e6i	0.0553149	−	0.0958082i
$676$		0			0
$677$	−2.27126e6	−	3.93394e6i	−0.190456	−	0.329880i	0.754945	−	0.655788i	$-0.227663\pi$
$677$	−2.27126e6	−	3.93394e6i	−0.190456	−	0.329880i	−0.945402	+	0.325908i	$0.894330\pi$
$678$		0			0
$679$	4.04279e6	+	4.12316e6i	0.336517	+	0.343207i
$680$		0			0
$681$	−2.10735e6	−	3.65003e6i	−0.174128	−	0.301598i
$682$		0			0
$683$	5.11519e6	−	8.85977e6i	0.419576	−	0.726726i	−0.576321	−	0.817223i	$-0.695512\pi$
$683$	5.11519e6	−	8.85977e6i	0.419576	−	0.726726i	0.995897	+	0.0904970i	$0.0288456\pi$
$684$		0			0
$685$	−1.43734e7			−1.17040
$686$		0			0
$687$	7.05974e6			0.570685
$688$		0			0
$689$	163004.	−	282331.i	0.0130813	−	0.0226574i
$690$		0			0
$691$	8.00543e6	+	1.38658e7i	0.637807	+	1.10471i	0.985913	+	0.167259i	$0.0534917\pi$
$691$	8.00543e6	+	1.38658e7i	0.637807	+	1.10471i	−0.348106	+	0.937455i	$0.613175\pi$
$692$		0			0
$693$	−4.58073e6	−	4.67180e6i	−0.362327	−	0.369531i
$694$		0			0
$695$	−640609.	−	1.10957e6i	−0.0503073	−	0.0871348i
$696$		0			0
$697$	−672422.	+	1.16467e6i	−0.0524276	+	0.0908073i
$698$		0			0
$699$	1.17105e6			0.0906529
$700$		0			0
$701$	−2.94129e6			−0.226070			−0.113035	−	0.993591i	$-0.536057\pi$
$701$	−2.94129e6			−0.226070			−0.113035	+	0.993591i	$0.536057\pi$
$702$		0			0
$703$	1.08107e7	−	1.87246e7i	0.825018	−	1.42897i
$704$		0			0
$705$	7.96652e6	+	1.37984e7i	0.603665	+	1.04558i
$706$		0			0
$707$	1.24949e6	−	321652.i	0.0940121	−	0.0242013i
$708$		0			0
$709$	−1.25922e7	−	2.18103e7i	−0.940774	−	1.62947i	−0.763999	−	0.645218i	$-0.776767\pi$
$709$	−1.25922e7	−	2.18103e7i	−0.940774	−	1.62947i	−0.176776	−	0.984251i	$-0.556567\pi$
$710$		0			0
$711$	4.10816e6	−	7.11554e6i	0.304771	−	0.527879i
$712$		0			0
$713$	−6.41329e6			−0.472451
$714$		0			0
$715$	−1.21884e7			−0.891624
$716$		0			0
$717$	−6.88218e6	+	1.19203e7i	−0.499952	+	0.865942i
$718$		0			0
$719$	−277636.	−	480880.i	−0.0200288	−	0.0346908i	0.855837	−	0.517245i	$-0.173042\pi$
$719$	−277636.	−	480880.i	−0.0200288	−	0.0346908i	−0.875866	+	0.482554i	$0.839709\pi$
$720$		0			0
$721$	−1.46173e6	+	5.24809e6i	−0.104720	+	0.375978i
$722$		0			0
$723$	−5.36566e6	−	9.29359e6i	−0.381748	−	0.661208i
$724$		0			0
$725$	−7.70029e6	+	1.33373e7i	−0.544079	+	0.942373i
$726$		0			0
$727$	−2.33527e6			−0.163871			−0.0819353	−	0.996638i	$-0.526110\pi$
$727$	−2.33527e6			−0.163871			−0.0819353	+	0.996638i	$0.526110\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−884669.	+	1.53229e6i	−0.0612332	+	0.106059i
$732$		0			0
$733$	−9.40828e6	−	1.62956e7i	−0.646771	−	1.12024i	−0.983889	−	0.178778i	$-0.942786\pi$
$733$	−9.40828e6	−	1.62956e7i	−0.646771	−	1.12024i	0.337119	−	0.941462i	$-0.390548\pi$
$734$		0			0
$735$	−208878.	+	1.06095e7i	−0.0142618	+	0.724394i
$736$		0			0
$737$	−1.25185e7	−	2.16827e7i	−0.848954	−	1.47043i
$738$		0			0
$739$	−6.79448e6	+	1.17684e7i	−0.457663	+	0.792695i	−0.998837	−	0.0482156i	$-0.984647\pi$
$739$	−6.79448e6	+	1.17684e7i	−0.457663	+	0.792695i	0.541174	+	0.840910i	$0.317980\pi$
$740$		0			0
$741$	3.97305e6			0.265814
$742$		0			0
$743$	3.43819e6			0.228485			0.114242	−	0.993453i	$-0.463556\pi$
$743$	3.43819e6			0.228485			0.114242	+	0.993453i	$0.463556\pi$
$744$		0			0
$745$	−1.99263e6	+	3.45133e6i	−0.131533	+	0.227822i
$746$		0			0
$747$	784029.	+	1.35798e6i	0.0514080	+	0.0890412i
$748$		0			0
$749$	2.90677e6	−	1.04362e7i	0.189324	−	0.679735i
$750$		0			0
$751$	7.97370e6	+	1.38109e7i	0.515894	+	0.893554i	0.999830	+	0.0184506i	$0.00587334\pi$
$751$	7.97370e6	+	1.38109e7i	0.515894	+	0.893554i	−0.483936	+	0.875103i	$0.660793\pi$
$752$		0			0
$753$	−7.23824e6	+	1.25370e7i	−0.465206	+	0.805761i
$754$		0			0
$755$	2.29358e7			1.46436
$756$		0			0
$757$	1.95867e7			1.24229			0.621144	−	0.783697i	$-0.286668\pi$
$757$	1.95867e7			1.24229			0.621144	+	0.783697i	$0.286668\pi$
$758$		0			0
$759$	−5.43768e6	+	9.41834e6i	−0.342617	+	0.593430i
$760$		0			0
$761$	−3.24407e6	−	5.61890e6i	−0.203062	−	0.351714i	0.746451	−	0.665440i	$-0.231756\pi$
$761$	−3.24407e6	−	5.61890e6i	−0.203062	−	0.351714i	−0.949514	+	0.313726i	$0.898423\pi$
$762$		0			0
$763$	−1.59310e7	+	4.10106e6i	−0.990674	+	0.255026i
$764$		0			0
$765$	−2.52029e6	−	4.36526e6i	−0.155703	−	0.269685i
$766$		0			0
$767$	−3.78027e6	+	6.54763e6i	−0.232025	+	0.401879i
$768$		0			0
$769$	−1.38085e7			−0.842036			−0.421018	−	0.907052i	$-0.638327\pi$
$769$	−1.38085e7			−0.842036			−0.421018	+	0.907052i	$0.638327\pi$
$770$		0			0
$771$	6.73496e6			0.408037
$772$		0			0
$773$	−502649.	+	870613.i	−0.0302563	+	0.0524054i	−0.880757	−	0.473568i	$-0.842966\pi$
$773$	−502649.	+	870613.i	−0.0302563	+	0.0524054i	0.850501	+	0.525974i	$0.176299\pi$
$774$		0			0
$775$	2.97023e6	+	5.14459e6i	0.177638	+	0.307678i
$776$		0			0
$777$	1.11564e7	+	1.13782e7i	0.662934	+	0.676114i
$778$		0			0
$779$	1.20007e6	+	2.07858e6i	0.0708538	+	0.122722i
$780$		0			0
$781$	−1.96814e7	+	3.40891e7i	−1.15459	+	1.99981i
$782$		0			0
$783$	−6.24972e6			−0.364298
$784$		0			0
$785$	2.68253e7			1.55371
$786$		0			0
$787$	791725.	−	1.37131e6i	0.0455656	−	0.0789220i	−0.842343	−	0.538942i	$-0.818824\pi$
$787$	791725.	−	1.37131e6i	0.0455656	−	0.0789220i	0.887909	+	0.460020i	$0.152158\pi$
$788$		0			0
$789$	965891.	+	1.67297e6i	0.0552377	+	0.0956745i
$790$		0			0
$791$	9.10726e6	+	9.28833e6i	0.517543	+	0.527833i
$792$		0			0
$793$	1.94467e6	+	3.36827e6i	0.109816	+	0.190206i
$794$		0			0
$795$	−369079.	+	639263.i	−0.0207110	+	0.0358725i
$796$		0			0
$797$	−7.91759e6			−0.441517			−0.220758	−	0.975329i	$-0.570853\pi$
$797$	−7.91759e6			−0.441517			−0.220758	+	0.975329i	$0.570853\pi$
$798$		0			0
$799$	2.23853e7			1.24050
$800$		0			0
$801$	−3783.80	+	6553.73i	−0.000208376	+	0.000360917i
$802$		0			0
$803$	−2.57178e7	−	4.45446e7i	−1.40749	−	2.43785i
$804$		0			0
$805$	1.70813e7	−	4.39720e6i	0.929034	−	0.239159i
$806$		0			0
$807$	4.53929e6	+	7.86228e6i	0.245360	+	0.424976i
$808$		0			0
$809$	−6.87535e6	+	1.19085e7i	−0.369338	+	0.639711i	−0.989462	−	0.144792i	$-0.953749\pi$
$809$	−6.87535e6	+	1.19085e7i	−0.369338	+	0.639711i	0.620125	+	0.784503i	$0.287082\pi$
$810$		0			0
$811$	−227123.			−0.0121257			−0.00606287	−	0.999982i	$-0.501930\pi$
$811$	−227123.			−0.0121257			−0.00606287	+	0.999982i	$0.501930\pi$
$812$		0			0
$813$	−1.22346e7			−0.649179
$814$		0			0
$815$	−4.65812e6	+	8.06811e6i	−0.245650	+	0.425479i
$816$		0			0
$817$	1.57887e6	+	2.73468e6i	0.0827542	+	0.143334i
$818$		0			0
$819$	−785668.	+	2.82080e6i	−0.0409288	+	0.146948i
$820$		0			0
$821$	9.63220e6	+	1.66835e7i	0.498733	+	0.863830i	0.999999	−	0.00146278i	$-0.000465616\pi$
$821$	9.63220e6	+	1.66835e7i	0.498733	+	0.863830i	−0.501266	+	0.865293i	$0.667132\pi$
$822$		0			0
$823$	−1.14901e7	+	1.99014e7i	−0.591321	+	1.02420i	0.402733	+	0.915317i	$0.368060\pi$
$823$	−1.14901e7	+	1.99014e7i	−0.591321	+	1.02420i	−0.994055	+	0.108881i	$0.965273\pi$
$824$		0			0
$825$	1.00736e7			0.515285
$826$		0			0
$827$	−6.11402e6			−0.310859			−0.155429	−	0.987847i	$-0.549676\pi$
$827$	−6.11402e6			−0.310859			−0.155429	+	0.987847i	$0.549676\pi$
$828$		0			0
$829$	5.99463e6	−	1.03830e7i	0.302954	−	0.524731i	−0.673850	−	0.738868i	$-0.735361\pi$
$829$	5.99463e6	−	1.03830e7i	0.302954	−	0.524731i	0.976804	+	0.214137i	$0.0686939\pi$
$830$		0			0
$831$	6.32325e6	+	1.09522e7i	0.317642	+	0.550172i
$832$		0			0
$833$	1.27621e7	+	7.70706e6i	0.637250	+	0.384837i
$834$		0			0
$835$	−942793.	−	1.63297e6i	−0.0467951	−	0.0810515i
$836$		0			0
$837$	−1.20535e6	+	2.08773e6i	−0.0594703	+	0.103006i
$838$		0			0
$839$	3.32286e6			0.162970			0.0814850	−	0.996675i	$-0.474034\pi$
$839$	3.32286e6			0.162970			0.0814850	+	0.996675i	$0.474034\pi$
$840$		0			0
$841$	5.29854e7			2.58325
$842$		0			0
$843$	−3.04948e6	+	5.28186e6i	−0.147794	+	0.255987i
$844$		0			0
$845$	−1.02962e7	−	1.78336e7i	−0.496062	−	0.859204i
$846$		0			0
$847$	7.90182e6	−	2.83701e7i	0.378459	−	1.35879i
$848$		0			0
$849$	3.42170e6	+	5.92656e6i	0.162919	+	0.282185i
$850$		0			0
$851$	1.32435e7	−	2.29384e7i	0.626871	−	1.08577i
$852$		0			0
$853$	356407.			0.0167716			0.00838579	−	0.999965i	$-0.497331\pi$
$853$	356407.			0.0167716			0.00838579	+	0.999965i	$0.497331\pi$
$854$		0			0
$855$	−8.99589e6			−0.420852
$856$		0			0
$857$	1.21137e7	−	2.09816e7i	0.563411	−	0.975857i	−0.433784	−	0.901017i	$-0.642822\pi$
$857$	1.21137e7	−	2.09816e7i	0.563411	−	0.975857i	0.997196	−	0.0748401i	$-0.0238446\pi$
$858$		0			0
$859$	608564.	+	1.05406e6i	0.0281400	+	0.0487399i	0.879752	−	0.475432i	$-0.157708\pi$
$859$	608564.	+	1.05406e6i	0.0281400	+	0.0487399i	−0.851612	+	0.524172i	$0.824375\pi$
$860$		0			0
$861$	−1.71307e6	+	440992.i	−0.0787532	+	0.0202732i
$862$		0			0
$863$	−1.41648e6	−	2.45341e6i	−0.0647414	−	0.112135i	0.831838	−	0.555019i	$-0.187289\pi$
$863$	−1.41648e6	−	2.45341e6i	−0.0647414	−	0.112135i	−0.896579	+	0.442883i	$0.853956\pi$
$864$		0			0
$865$	−4.97998e6	+	8.62558e6i	−0.226302	+	0.391966i
$866$		0			0
$867$	5.69692e6			0.257391
$868$		0			0
$869$	6.32017e7			2.83909
$870$		0			0
$871$	−5.60252e6	+	9.70385e6i	−0.250229	+	0.433410i
$872$		0			0
$873$	−1.80394e6	−	3.12452e6i	−0.0801101	−	0.138755i
$874$		0			0
$875$	8.45962e6	+	8.62781e6i	0.373534	+	0.380961i
$876$		0			0
$877$	8.03404e6	+	1.39154e7i	0.352724	+	0.610936i	0.986726	−	0.162396i	$-0.0519222\pi$
$877$	8.03404e6	+	1.39154e7i	0.352724	+	0.610936i	−0.634002	+	0.773332i	$0.718589\pi$
$878$		0			0
$879$	1.18970e6	−	2.06062e6i	0.0519357	−	0.0899552i
$880$		0			0
$881$	−3.99391e7			−1.73364			−0.866819	−	0.498624i	$-0.833839\pi$
$881$	−3.99391e7			−1.73364			−0.866819	+	0.498624i	$0.833839\pi$
$882$		0			0
$883$	1.95253e7			0.842744			0.421372	−	0.906888i	$-0.361549\pi$
$883$	1.95253e7			0.842744			0.421372	+	0.906888i	$0.361549\pi$
$884$		0			0
$885$	8.55941e6	−	1.48253e7i	0.367355	−	0.636277i
$886$		0			0
$887$	−4.51559e6	−	7.82122e6i	−0.192710	−	0.333784i	0.753437	−	0.657520i	$-0.228394\pi$
$887$	−4.51559e6	−	7.82122e6i	−0.192710	−	0.333784i	−0.946148	+	0.323736i	$0.895061\pi$
$888$		0			0
$889$	−1.01643e7	−	1.03663e7i	−0.431342	−	0.439918i
$890$		0			0
$891$	2.04398e6	+	3.54027e6i	0.0862545	+	0.149397i
$892$		0			0
$893$	1.99755e7	−	3.45985e7i	0.838239	−	1.45187i
$894$		0			0
$895$	−3.37654e7			−1.40901
$896$		0			0
$897$	4.86714e6			0.201973
$898$		0			0
$899$	1.41749e7	−	2.45516e7i	0.584952	−	1.01317i
$900$		0			0
$901$	518540.	+	898137.i	0.0212799	+	0.0368579i
$902$		0			0
$903$	−2.25380e6	+	580189.i	−0.0919804	+	0.0236783i
$904$		0			0
$905$	−2.70863e7	−	4.69149e7i	−1.09933	−	1.90410i
$906$		0			0
$907$	2.10298e7	−	3.64247e7i	0.848822	−	1.47020i	−0.0334385	−	0.999441i	$-0.510646\pi$
$907$	2.10298e7	−	3.64247e7i	0.848822	−	1.47020i	0.882260	−	0.470762i	$-0.156021\pi$
$908$		0			0
$909$	−806131.			−0.0323591
$910$		0			0
$911$	3.79082e6			0.151334			0.0756670	−	0.997133i	$-0.475891\pi$
$911$	3.79082e6			0.151334			0.0756670	+	0.997133i	$0.475891\pi$
$912$		0			0
$913$	−6.03091e6	+	1.04458e7i	−0.239445	+	0.414731i
$914$		0			0
$915$	−4.40319e6	−	7.62655e6i	−0.173866	−	0.301145i
$916$		0			0
$917$	−1.20833e7	+	4.33828e7i	−0.474527	+	1.70370i
$918$		0			0
$919$	1.26550e7	+	2.19190e7i	0.494279	+	0.856116i	0.999978	−	0.00659344i	$-0.00209877\pi$
$919$	1.26550e7	+	2.19190e7i	0.494279	+	0.856116i	−0.505699	+	0.862710i	$0.668765\pi$
$920$		0			0
$921$	6.57486e6	−	1.13880e7i	0.255410	−	0.442383i
$922$		0			0
$923$	1.76163e7			0.680631
$924$		0			0
$925$	−2.45342e7			−0.942794
$926$		0			0
$927$	1.70190e6	−	2.94779e6i	0.0650483	−	0.112667i
$928$		0			0
$929$	−2.13009e7	−	3.68943e7i	−0.809765	−	1.40255i	−0.913026	−	0.407900i	$-0.866261\pi$
$929$	−2.13009e7	−	3.68943e7i	−0.809765	−	1.40255i	0.103261	−	0.994654i	$-0.467072\pi$
$930$		0			0
$931$	2.33002e7	−	1.28476e7i	0.881020	−	0.485790i
$932$		0			0
$933$	1.22229e7	+	2.11707e7i	0.459696	+	0.796216i
$934$		0			0
$935$	1.93866e7	−	3.35785e7i	0.725224	−	1.25612i
$936$		0			0
$937$	3.24902e7			1.20893			0.604467	−	0.796630i	$-0.293386\pi$
$937$	3.24902e7			1.20893			0.604467	+	0.796630i	$0.293386\pi$
$938$		0			0
$939$	−1.82025e7			−0.673701
$940$		0			0
$941$	−1.59731e7	+	2.76663e7i	−0.588052	+	1.01854i	0.406435	+	0.913680i	$0.366772\pi$
$941$	−1.59731e7	+	2.76663e7i	−0.588052	+	1.01854i	−0.994487	+	0.104857i	$0.966562\pi$
$942$		0			0
$943$	1.47013e6	+	2.54635e6i	0.0538366	+	0.0932477i
$944$		0			0
$945$	1.77893e6	−	6.38694e6i	0.0648008	−	0.232656i
$946$		0			0
$947$	2.02437e6	+	3.50632e6i	0.0733526	+	0.127050i	0.900369	−	0.435128i	$-0.143297\pi$
$947$	2.02437e6	+	3.50632e6i	0.0733526	+	0.127050i	−0.827016	+	0.562178i	$0.809963\pi$
$948$		0			0
$949$	−1.15097e7	+	1.99354e7i	−0.414858	+	0.718555i
$950$		0			0
$951$	5.68465e6			0.203823
$952$		0			0
$953$	−2.93849e7			−1.04807			−0.524037	−	0.851695i	$-0.675575\pi$
$953$	−2.93849e7			−1.04807			−0.524037	+	0.851695i	$0.675575\pi$
$954$		0			0
$955$	5.09613e6	−	8.82675e6i	0.180814	−	0.313179i
$956$		0			0
$957$	−2.40371e7	−	4.16335e7i	−0.848403	−	1.46948i
$958$		0			0
$959$	−2.57233e7	+	6.62188e6i	−0.903192	+	0.232506i
$960$		0			0
$961$	8.84691e6	+	1.53233e7i	0.309017	+	0.535234i
$962$		0			0
$963$	−3.38437e6	+	5.86191e6i	−0.117601	+	0.203692i
$964$		0			0
$965$	3.94597e7			1.36407
$966$		0			0
$967$	2.00631e7			0.689973			0.344986	−	0.938608i	$-0.387884\pi$
$967$	2.00631e7			0.689973			0.344986	+	0.938608i	$0.387884\pi$
$968$		0			0
$969$	−6.31942e6	+	1.09456e7i	−0.216206	+	0.374480i
$970$		0			0
$971$	−930005.	−	1.61082e6i	−0.0316546	−	0.0548274i	0.849764	−	0.527163i	$-0.176744\pi$
$971$	−930005.	−	1.61082e6i	−0.0316546	−	0.0548274i	−0.881419	+	0.472336i	$0.843411\pi$
$972$		0			0
$973$	−1.65764e6	−	1.69060e6i	−0.0561319	−	0.0572479i
$974$		0			0
$975$	−2.25415e6	−	3.90430e6i	−0.0759401	−	0.131532i
$976$		0			0
$977$	1.85873e7	−	3.21941e7i	0.622987	−	1.07904i	−0.365940	−	0.930639i	$-0.619252\pi$
$977$	1.85873e7	−	3.21941e7i	0.622987	−	1.07904i	0.988926	−	0.148406i	$-0.0474143\pi$
$978$		0			0
$979$	−58211.5			−0.00194112
$980$		0			0
$981$	1.02782e7			0.340991
$982$		0			0
$983$	−969402.	+	1.67905e6i	−0.0319978	+	0.0554218i	−0.881581	−	0.472033i	$-0.843520\pi$
$983$	−969402.	+	1.67905e6i	−0.0319978	+	0.0554218i	0.849583	+	0.527455i	$0.176854\pi$
$984$		0			0
$985$	1.29284e7	+	2.23926e7i	0.424574	+	0.735384i
$986$		0			0
$987$	2.06142e7	+	2.10241e7i	0.673557	+	0.686949i
$988$		0			0
$989$	1.93417e6	+	3.35009e6i	0.0628789	+	0.108909i
$990$		0			0
$991$	−7.46786e6	+	1.29347e7i	−0.241553	+	0.418382i	−0.961157	−	0.276003i	$-0.910990\pi$
$991$	−7.46786e6	+	1.29347e7i	−0.241553	+	0.418382i	0.719604	+	0.694385i	$0.244323\pi$
$992$		0			0
$993$	8.19918e6			0.263874
$994$		0			0
$995$	7.27164e7			2.32849
$996$		0			0
$997$	1.14588e7	−	1.98473e7i	0.365093	−	0.632359i	−0.623698	−	0.781665i	$-0.714371\pi$
$997$	1.14588e7	−	1.98473e7i	0.365093	−	0.632359i	0.988791	+	0.149306i	$0.0477040\pi$
$998$		0			0
$999$	−4.97811e6	−	8.62234e6i	−0.157816	−	0.273345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.h.193.2		4
4.3	odd	2		42.6.e.d.25.2	✓	4
7.2	even	3	inner	336.6.q.h.289.2		4
12.11	even	2		126.6.g.g.109.1		4
28.3	even	6		294.6.a.o.1.2		2
28.11	odd	6		294.6.a.p.1.1		2
28.19	even	6		294.6.e.y.79.1		4
28.23	odd	6		42.6.e.d.37.2	yes	4
28.27	even	2		294.6.e.y.67.1		4
84.11	even	6		882.6.a.bm.1.2		2
84.23	even	6		126.6.g.g.37.1		4
84.59	odd	6		882.6.a.bs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.e.d.25.2	✓	4	4.3	odd	2
42.6.e.d.37.2	yes	4	28.23	odd	6
126.6.g.g.37.1		4	84.23	even	6
126.6.g.g.109.1		4	12.11	even	2
294.6.a.o.1.2		2	28.3	even	6
294.6.a.p.1.1		2	28.11	odd	6
294.6.e.y.67.1		4	28.27	even	2
294.6.e.y.79.1		4	28.19	even	6
336.6.q.h.193.2		4	1.1	even	1	trivial
336.6.q.h.289.2		4	7.2	even	3	inner
882.6.a.bm.1.2		2	84.11	even	6
882.6.a.bs.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(4.50000 - 7.79423i) q^{3} +(35.0764 + 60.7540i) q^{5} +(90.7639 + 92.5684i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.50000 - 7.79423i) q^{3} +(35.0764 + 60.7540i) q^{5} +(90.7639 + 92.5684i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(311.535 - 539.594i) q^{11} -278.847 q^{13} +631.374 q^{15} +(443.527 - 768.212i) q^{17} +(-791.562 - 1371.03i) q^{19} +(1129.94 - 290.877i) q^{21} +(-969.695 - 1679.56i) q^{23} +(-898.202 + 1555.73i) q^{25} -729.000 q^{27} +8573.01 q^{29} +(1653.43 - 2863.83i) q^{31} +(-2803.81 - 4856.34i) q^{33} +(-2440.24 + 8761.24i) q^{35} +(6828.69 + 11827.6i) q^{37} +(-1254.81 + 2173.40i) q^{39} -1516.08 q^{41} -1994.62 q^{43} +(2841.19 - 4921.08i) q^{45} +(12617.7 + 21854.6i) q^{47} +(-330.830 + 16803.7i) q^{49} +(-3991.74 - 6913.90i) q^{51} +(-584.564 + 1012.49i) q^{53} +43710.0 q^{55} -14248.1 q^{57} +(13556.8 - 23481.0i) q^{59} +(-6973.97 - 12079.3i) q^{61} +(2817.56 - 10115.9i) q^{63} +(-9780.95 - 16941.1i) q^{65} +(20091.7 - 34799.9i) q^{67} -17454.5 q^{69} -63175.6 q^{71} +(41276.1 - 71492.2i) q^{73} +(8083.82 + 14001.6i) q^{75} +(78225.4 - 20137.4i) q^{77} +(50718.0 + 87846.2i) q^{79} +(-3280.50 + 5681.99i) q^{81} -19358.7 q^{83} +62229.3 q^{85} +(38578.5 - 66820.0i) q^{87} +(-46.7136 - 80.9103i) q^{89} +(-25309.3 - 25812.5i) q^{91} +(-14880.9 - 25774.4i) q^{93} +(55530.2 - 96181.1i) q^{95} +44541.8 q^{97} -50468.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9}+O(q^{10}) \) 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9	\( 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9} + 145 q^{11} - 1430 q^{13} - 306 q^{15} - 1372 q^{17} + 1081 q^{19} + 2295 q^{21} - 4508 q^{23} - 6267 q^{25} - 2916 q^{27} + 15730 q^{29} + 8816 q^{31} - 1305 q^{33} - 24278 q^{35} + 14573 q^{37} - 6435 q^{39} + 14700 q^{41} + 11842 q^{43} - 1377 q^{45} + 44808 q^{47} + 17014 q^{49} + 12348 q^{51} - 9417 q^{53} + 170750 q^{55} + 19458 q^{57} - 5077 q^{59} - 42368 q^{61} - 12393 q^{63} + 18450 q^{65} + 30501 q^{67} - 81144 q^{69} - 183488 q^{71} + 85665 q^{73} + 56403 q^{75} + 154585 q^{77} + 94646 q^{79} - 13122 q^{81} - 67682 q^{83} + 518224 q^{85} + 70785 q^{87} - 27558 q^{89} - 149395 q^{91} - 79344 q^{93} + 343246 q^{95} - 93342 q^{97} - 23490 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9 + 145 * q^11 - 1430 * q^13 - 306 * q^15 - 1372 * q^17 + 1081 * q^19 + 2295 * q^21 - 4508 * q^23 - 6267 * q^25 - 2916 * q^27 + 15730 * q^29 + 8816 * q^31 - 1305 * q^33 - 24278 * q^35 + 14573 * q^37 - 6435 * q^39 + 14700 * q^41 + 11842 * q^43 - 1377 * q^45 + 44808 * q^47 + 17014 * q^49 + 12348 * q^51 - 9417 * q^53 + 170750 * q^55 + 19458 * q^57 - 5077 * q^59 - 42368 * q^61 - 12393 * q^63 + 18450 * q^65 + 30501 * q^67 - 81144 * q^69 - 183488 * q^71 + 85665 * q^73 + 56403 * q^75 + 154585 * q^77 + 94646 * q^79 - 13122 * q^81 - 67682 * q^83 + 518224 * q^85 + 70785 * q^87 - 27558 * q^89 - 149395 * q^91 - 79344 * q^93 + 343246 * q^95 - 93342 * q^97 - 23490 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more