LMFDB - Embedded newform 336.6.q.l.289.1

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 564x^{8} + 117814x^{6} + 11067780x^{4} + 427918225x^{2} + 3489248448 $ x^10 + 564x^8 + 117814x^6 + 11067780x^4 + 427918225x^2 + 3489248448
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$10.6668i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.6.q.l.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 - 7.79423i) q^{3} +(-50.8171 + 88.0179i) q^{5} +(119.572 - 50.0952i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.50000 - 7.79423i) q^{3} +(-50.8171 + 88.0179i) q^{5} +(119.572 - 50.0952i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-235.597 - 408.067i) q^{11} -255.165 q^{13} +914.708 q^{15} +(-350.839 - 607.671i) q^{17} +(-436.405 + 755.876i) q^{19} +(-928.527 - 706.544i) q^{21} +(-305.616 + 529.342i) q^{23} +(-3602.26 - 6239.30i) q^{25} +729.000 q^{27} +7796.57 q^{29} +(-1781.41 - 3085.49i) q^{31} +(-2120.38 + 3672.60i) q^{33} +(-1667.04 + 13070.2i) q^{35} +(-3476.02 + 6020.64i) q^{37} +(1148.24 + 1988.81i) q^{39} -13514.5 q^{41} +14342.6 q^{43} +(-4116.19 - 7129.45i) q^{45} +(-5419.18 + 9386.30i) q^{47} +(11788.0 - 11980.0i) q^{49} +(-3157.55 + 5469.04i) q^{51} +(15284.1 + 26472.8i) q^{53} +47889.5 q^{55} +7855.30 q^{57} +(23014.5 + 39862.2i) q^{59} +(19787.6 - 34273.2i) q^{61} +(-1328.59 + 10416.6i) q^{63} +(12966.7 - 22459.0i) q^{65} +(-11495.2 - 19910.2i) q^{67} +5501.08 q^{69} +57595.4 q^{71} +(-8211.83 - 14223.3i) q^{73} +(-32420.4 + 56153.7i) q^{75} +(-48613.0 - 36991.1i) q^{77} +(48378.7 - 83794.4i) q^{79} +(-3280.50 - 5681.99i) q^{81} +46981.2 q^{83} +71314.5 q^{85} +(-35084.6 - 60768.3i) q^{87} +(-2330.73 + 4036.94i) q^{89} +(-30510.5 + 12782.5i) q^{91} +(-16032.7 + 27769.4i) q^{93} +(-44353.7 - 76822.9i) q^{95} -27688.8 q^{97} +38166.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−50.8171	+	88.0179i	−0.909045	+	1.57451i	−0.0936503	+	0.995605i	$0.529854\pi$
$5$	−50.8171	+	88.0179i	−0.909045	+	1.57451i	−0.815394	+	0.578906i	$0.803480\pi$
$6$		0			0
$7$	119.572	−	50.0952i	0.922326	−	0.386412i
$7$	119.572	−	50.0952i	0.922326	−	0.386412i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	−235.597	−	408.067i	−0.587068	−	1.01683i	−0.994614	−	0.103648i	$-0.966949\pi$
$11$	−235.597	−	408.067i	−0.587068	−	1.01683i	0.407546	−	0.913185i	$-0.366385\pi$
$12$		0			0
$13$	−255.165			−0.418757			−0.209378	−	0.977835i	$-0.567144\pi$
$13$	−255.165			−0.418757			−0.209378	+	0.977835i	$0.567144\pi$
$14$		0			0
$15$	914.708			1.04967
$16$		0			0
$17$	−350.839	−	607.671i	−0.294432	−	0.509972i	0.680420	−	0.732822i	$-0.261797\pi$
$17$	−350.839	−	607.671i	−0.294432	−	0.509972i	−0.974853	+	0.222850i	$0.928464\pi$
$18$		0			0
$19$	−436.405	+	755.876i	−0.277336	+	0.480360i	−0.970722	−	0.240207i	$-0.922785\pi$
$19$	−436.405	+	755.876i	−0.277336	+	0.480360i	0.693386	+	0.720566i	$0.256118\pi$
$20$		0			0
$21$	−928.527	−	706.544i	−0.459459	−	0.349616i
$22$		0			0
$23$	−305.616	+	529.342i	−0.120464	+	0.208649i	−0.919951	−	0.392034i	$-0.871771\pi$
$23$	−305.616	+	529.342i	−0.120464	+	0.208649i	0.799487	+	0.600683i	$0.205105\pi$
$24$		0			0
$25$	−3602.26	−	6239.30i	−1.15272	−	1.99658i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	7796.57			1.72151			0.860754	−	0.509022i	$-0.169993\pi$
$29$	7796.57			1.72151			0.860754	+	0.509022i	$0.169993\pi$
$30$		0			0
$31$	−1781.41	−	3085.49i	−0.332935	−	0.576660i	0.650151	−	0.759805i	$-0.274706\pi$
$31$	−1781.41	−	3085.49i	−0.332935	−	0.576660i	−0.983086	+	0.183145i	$0.941372\pi$
$32$		0			0
$33$	−2120.38	+	3672.60i	−0.338944	+	0.587068i
$34$		0			0
$35$	−1667.04	+	13070.2i	−0.230026	+	1.80348i
$36$		0			0
$37$	−3476.02	+	6020.64i	−0.417424	+	0.723000i	−0.995680	−	0.0928558i	$-0.970400\pi$
$37$	−3476.02	+	6020.64i	−0.417424	+	0.723000i	0.578255	+	0.815856i	$0.303734\pi$
$38$		0			0
$39$	1148.24	+	1988.81i	0.120885	+	0.209378i
$40$		0			0
$41$	−13514.5			−1.25557			−0.627784	−	0.778387i	$-0.716038\pi$
$41$	−13514.5			−1.25557			−0.627784	+	0.778387i	$0.716038\pi$
$42$		0			0
$43$	14342.6			1.18292			0.591460	−	0.806334i	$-0.298552\pi$
$43$	14342.6			1.18292			0.591460	+	0.806334i	$0.298552\pi$
$44$		0			0
$45$	−4116.19	−	7129.45i	−0.303015	−	0.524837i
$46$		0			0
$47$	−5419.18	+	9386.30i	−0.357840	+	0.619797i	−0.987600	−	0.156993i	$-0.949820\pi$
$47$	−5419.18	+	9386.30i	−0.357840	+	0.619797i	0.629760	+	0.776790i	$0.283153\pi$
$48$		0			0
$49$	11788.0	−	11980.0i	0.701371	−	0.712796i
$50$		0			0
$51$	−3157.55	+	5469.04i	−0.169991	+	0.294432i
$52$		0			0
$53$	15284.1	+	26472.8i	0.747395	+	1.29453i	0.949067	+	0.315073i	$0.102029\pi$
$53$	15284.1	+	26472.8i	0.747395	+	1.29453i	−0.201672	+	0.979453i	$0.564638\pi$
$54$		0			0
$55$	47889.5			2.13469
$56$		0			0
$57$	7855.30			0.320240
$58$		0			0
$59$	23014.5	+	39862.2i	0.860738	+	1.49084i	0.871218	+	0.490897i	$0.163331\pi$
$59$	23014.5	+	39862.2i	0.860738	+	1.49084i	−0.0104799	+	0.999945i	$0.503336\pi$
$60$		0			0
$61$	19787.6	−	34273.2i	0.680878	−	1.17931i	−0.293836	−	0.955856i	$-0.594932\pi$
$61$	19787.6	−	34273.2i	0.680878	−	1.17931i	0.974713	−	0.223459i	$-0.0717348\pi$
$62$		0			0
$63$	−1328.59	+	10416.6i	−0.0421735	+	0.330655i
$64$		0			0
$65$	12966.7	−	22459.0i	0.380669	−	0.659337i
$66$		0			0
$67$	−11495.2	−	19910.2i	−0.312844	−	0.541862i	0.666133	−	0.745833i	$-0.267948\pi$
$67$	−11495.2	−	19910.2i	−0.312844	−	0.541862i	−0.978977	+	0.203971i	$0.934615\pi$
$68$		0			0
$69$	5501.08			0.139099
$70$		0			0
$71$	57595.4			1.35594			0.677972	−	0.735087i	$-0.262859\pi$
$71$	57595.4			1.35594			0.677972	+	0.735087i	$0.262859\pi$
$72$		0			0
$73$	−8211.83	−	14223.3i	−0.180357	−	0.312387i	0.761645	−	0.647994i	$-0.224392\pi$
$73$	−8211.83	−	14223.3i	−0.180357	−	0.312387i	−0.942002	+	0.335607i	$0.891059\pi$
$74$		0			0
$75$	−32420.4	+	56153.7i	−0.665525	+	1.15272i
$76$		0			0
$77$	−48613.0	−	36991.1i	−0.934385	−	0.711001i
$78$		0			0
$79$	48378.7	−	83794.4i	0.872141	−	1.51059i	0.0123641	−	0.999924i	$-0.496064\pi$
$79$	48378.7	−	83794.4i	0.872141	−	1.51059i	0.859777	−	0.510669i	$-0.170602\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	46981.2			0.748564			0.374282	−	0.927315i	$-0.377889\pi$
$83$	46981.2			0.748564			0.374282	+	0.927315i	$0.377889\pi$
$84$		0			0
$85$	71314.5			1.07061
$86$		0			0
$87$	−35084.6	−	60768.3i	−0.496956	−	0.860754i
$88$		0			0
$89$	−2330.73	+	4036.94i	−0.0311901	+	0.0540228i	−0.881199	−	0.472745i	$-0.843263\pi$
$89$	−2330.73	+	4036.94i	−0.0311901	+	0.0540228i	0.850009	+	0.526768i	$0.176596\pi$
$90$		0			0
$91$	−30510.5	+	12782.5i	−0.386230	+	0.161813i
$92$		0			0
$93$	−16032.7	+	27769.4i	−0.192220	+	0.332935i
$94$		0			0
$95$	−44353.7	−	76822.9i	−0.504221	−	0.873337i
$96$		0			0
$97$	−27688.8			−0.298796			−0.149398	−	0.988777i	$-0.547734\pi$
$97$	−27688.8			−0.298796			−0.149398	+	0.988777i	$0.547734\pi$
$98$		0			0
$99$	38166.8			0.391379
$100$		0			0
$101$	−26174.9	−	45336.3i	−0.255318	−	0.442225i	0.709663	−	0.704541i	$-0.248847\pi$
$101$	−26174.9	−	45336.3i	−0.255318	−	0.442225i	−0.964982	+	0.262316i	$0.915514\pi$
$102$		0			0
$103$	54841.6	−	94988.4i	0.509350	−	0.882221i	−0.490591	−	0.871390i	$-0.663219\pi$
$103$	54841.6	−	94988.4i	0.509350	−	0.882221i	0.999941	−	0.0108308i	$-0.00344762\pi$
$104$		0			0
$105$	109374.	−	45822.5i	0.968142	−	0.405607i
$106$		0			0
$107$	18294.2	−	31686.6i	0.154474	−	0.267557i	−0.778393	−	0.627777i	$-0.783965\pi$
$107$	18294.2	−	31686.6i	0.154474	−	0.267557i	0.932867	+	0.360220i	$0.117298\pi$
$108$		0			0
$109$	100213.	+	173574.i	0.807902	+	1.39933i	0.914314	+	0.405005i	$0.132730\pi$
$109$	100213.	+	173574.i	0.807902	+	1.39933i	−0.106413	+	0.994322i	$0.533936\pi$
$110$		0			0
$111$	62568.3			0.482000
$112$		0			0
$113$	214592.			1.58095			0.790474	−	0.612495i	$-0.209834\pi$
$113$	214592.			1.58095			0.790474	+	0.612495i	$0.209834\pi$
$114$		0			0
$115$	−31061.0	−	53799.3i	−0.219014	−	0.379343i
$116$		0			0
$117$	10334.2	−	17899.3i	0.0697928	−	0.120885i
$118$		0			0
$119$	−72391.9	−	55085.1i	−0.468622	−	0.356588i
$120$		0			0
$121$	−30486.8	+	52804.6i	−0.189299	+	0.327875i
$122$		0			0
$123$	60815.3	+	105335.i	0.362451	+	0.627784i
$124$		0			0
$125$	414619.			2.37342
$126$		0			0
$127$	115653.			0.636277			0.318138	−	0.948044i	$-0.396942\pi$
$127$	115653.			0.636277			0.318138	+	0.948044i	$0.396942\pi$
$128$		0			0
$129$	−64541.5	−	111789.i	−0.341479	−	0.591460i
$130$		0			0
$131$	−130099.	+	225339.i	−0.662365	+	1.14725i	0.317628	+	0.948215i	$0.397114\pi$
$131$	−130099.	+	225339.i	−0.662365	+	1.14725i	−0.979993	+	0.199034i	$0.936220\pi$
$132$		0			0
$133$	−14316.1	+	112243.i	−0.0701774	+	0.550214i
$134$		0			0
$135$	−37045.7	+	64165.0i	−0.174946	+	0.303015i
$136$		0			0
$137$	165251.	+	286224.i	0.752217	+	1.30288i	0.946746	+	0.321982i	$0.104349\pi$
$137$	165251.	+	286224.i	0.752217	+	1.30288i	−0.194529	+	0.980897i	$0.562318\pi$
$138$		0			0
$139$	97382.1			0.427506			0.213753	−	0.976888i	$-0.431431\pi$
$139$	97382.1			0.427506			0.213753	+	0.976888i	$0.431431\pi$
$140$		0			0
$141$	97545.3			0.413198
$142$		0			0
$143$	60116.1	+	104124.i	0.245839	+	0.425806i
$144$		0			0
$145$	−396200.	+	686238.i	−1.56493	+	2.71053i
$146$		0			0
$147$	−146420.	−	37968.2i	−0.558866	−	0.144919i
$148$		0			0
$149$	162195.	−	280930.i	0.598511	−	1.03665i	−0.394531	−	0.918883i	$-0.629093\pi$
$149$	162195.	−	280930.i	0.598511	−	1.03665i	0.993041	−	0.117768i	$-0.0375739\pi$
$150$		0			0
$151$	98072.8	+	169867.i	0.350031	+	0.606271i	0.986254	−	0.165233i	$-0.0528378\pi$
$151$	98072.8	+	169867.i	0.350031	+	0.606271i	−0.636224	+	0.771505i	$0.719504\pi$
$152$		0			0
$153$	56835.9			0.196288
$154$		0			0
$155$	362105.			1.21061
$156$		0			0
$157$	95894.8	+	166095.i	0.310489	+	0.537782i	0.978468	−	0.206397i	$-0.0661740\pi$
$157$	95894.8	+	166095.i	0.310489	+	0.537782i	−0.667980	+	0.744180i	$0.732841\pi$
$158$		0			0
$159$	137557.	−	238256.i	0.431509	−	0.747395i
$160$		0			0
$161$	−10025.6	+	78604.4i	−0.0304822	+	0.238991i
$162$		0			0
$163$	260716.	−	451573.i	0.768597	−	1.33125i	−0.169727	−	0.985491i	$-0.554288\pi$
$163$	260716.	−	451573.i	0.768597	−	1.33125i	0.938324	−	0.345758i	$-0.112378\pi$
$164$		0			0
$165$	−215503.	−	373262.i	−0.616231	−	1.06734i
$166$		0			0
$167$	7272.16			0.0201777			0.0100889	−	0.999949i	$-0.496789\pi$
$167$	7272.16			0.0201777			0.0100889	+	0.999949i	$0.496789\pi$
$168$		0			0
$169$	−306184.			−0.824643
$170$		0			0
$171$	−35348.8	−	61226.0i	−0.0924453	−	0.160120i
$172$		0			0
$173$	−159029.	+	275447.i	−0.403982	+	0.699717i	−0.994202	−	0.107525i	$-0.965707\pi$
$173$	−159029.	+	275447.i	−0.403982	+	0.699717i	0.590221	+	0.807242i	$0.299041\pi$
$174$		0			0
$175$	−743289.	−	565590.i	−1.83469	−	1.39607i
$176$		0			0
$177$	207130.	−	358760.i	0.496947	−	0.860738i
$178$		0			0
$179$	−44521.4	−	77113.4i	−0.103857	−	0.179886i	0.809414	−	0.587239i	$-0.199785\pi$
$179$	−44521.4	−	77113.4i	−0.103857	−	0.179886i	−0.913271	+	0.407353i	$0.866452\pi$
$180$		0			0
$181$	12898.0			0.0292635			0.0146318	−	0.999893i	$-0.495342\pi$
$181$	12898.0			0.0292635			0.0146318	+	0.999893i	$0.495342\pi$
$182$		0			0
$183$	−356177.			−0.786210
$184$		0			0
$185$	−353283.	−	611903.i	−0.758915	−	1.31448i
$186$		0			0
$187$	−165314.	+	286331.i	−0.345704	+	0.598777i
$188$		0			0
$189$	87168.0	−	36519.4i	0.177502	−	0.0743650i
$190$		0			0
$191$	−446964.	+	774164.i	−0.886521	+	1.53550i	−0.0425600	+	0.999094i	$0.513551\pi$
$191$	−446964.	+	774164.i	−0.886521	+	1.53550i	−0.843961	+	0.536405i	$0.819782\pi$
$192$		0			0
$193$	−273850.	−	474323.i	−0.529200	−	0.916602i	−0.999420	−	0.0340524i	$-0.989159\pi$
$193$	−273850.	−	474323.i	−0.529200	−	0.916602i	0.470220	−	0.882549i	$-0.344175\pi$
$194$		0			0
$195$	−233401.			−0.439558
$196$		0			0
$197$	−861346.			−1.58129			−0.790646	−	0.612274i	$-0.790255\pi$
$197$	−861346.			−1.58129			−0.790646	+	0.612274i	$0.790255\pi$
$198$		0			0
$199$	60232.8	+	104326.i	0.107820	+	0.186750i	0.914887	−	0.403710i	$-0.132280\pi$
$199$	60232.8	+	104326.i	0.107820	+	0.186750i	−0.807067	+	0.590460i	$0.798946\pi$
$200$		0			0
$201$	−103456.	+	179192.i	−0.180621	+	0.312844i
$202$		0			0
$203$	932252.	−	390571.i	1.58779	−	0.665211i
$204$		0			0
$205$	686768.	−	1.18952e6i	1.14137	−	1.97691i
$206$		0			0
$207$	−24754.9	−	42876.7i	−0.0401546	−	0.0695497i
$208$		0			0
$209$	411264.			0.651261
$210$		0			0
$211$	208799.			0.322866			0.161433	−	0.986884i	$-0.448389\pi$
$211$	208799.			0.322866			0.161433	+	0.986884i	$0.448389\pi$
$212$		0			0
$213$	−259179.	−	448912.i	−0.391428	−	0.677972i
$214$		0			0
$215$	−728847.	+	1.26240e6i	−1.07533	+	1.86252i
$216$		0			0
$217$	−367575.	−	279699.i	−0.529903	−	0.403219i
$218$		0			0
$219$	−73906.4	+	128010.i	−0.104129	+	0.180357i
$220$		0			0
$221$	89521.7	+	155056.i	0.123296	+	0.213554i
$222$		0			0
$223$	287964.			0.387772			0.193886	−	0.981024i	$-0.437891\pi$
$223$	287964.			0.387772			0.193886	+	0.981024i	$0.437891\pi$
$224$		0			0
$225$	583566.			0.768483
$226$		0			0
$227$	327821.	+	567803.i	0.422253	+	0.731364i	0.996159	−	0.0875573i	$-0.0279061\pi$
$227$	327821.	+	567803.i	0.422253	+	0.731364i	−0.573907	+	0.818921i	$0.694573\pi$
$228$		0			0
$229$	−547729.	+	948695.i	−0.690204	+	1.19547i	0.281567	+	0.959542i	$0.409146\pi$
$229$	−547729.	+	948695.i	−0.690204	+	1.19547i	−0.971771	+	0.235926i	$0.924188\pi$
$230$		0			0
$231$	−69558.3	+	545361.i	−0.0857668	+	0.672441i
$232$		0			0
$233$	−326138.	+	564888.i	−0.393561	+	0.681667i	−0.992916	−	0.118816i	$-0.962090\pi$
$233$	−326138.	+	564888.i	−0.393561	+	0.681667i	0.599356	+	0.800483i	$0.295424\pi$
$234$		0			0
$235$	−550775.	−	953969.i	−0.650585	−	1.12685i
$236$		0			0
$237$	−870817.			−1.00706
$238$		0			0
$239$	1.14839e6			1.30046			0.650229	−	0.759738i	$-0.274673\pi$
$239$	1.14839e6			1.30046			0.650229	+	0.759738i	$0.274673\pi$
$240$		0			0
$241$	22190.5	+	38435.1i	0.0246107	+	0.0426270i	0.878068	−	0.478535i	$-0.158832\pi$
$241$	22190.5	+	38435.1i	0.0246107	+	0.0426270i	−0.853458	+	0.521162i	$0.825499\pi$
$242$		0			0
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	455421.	+	1.64634e6i	0.484727	+	1.75228i
$246$		0			0
$247$	111355.	−	192873.i	0.116136	−	0.201154i
$248$		0			0
$249$	−211415.	−	366182.i	−0.216092	−	0.374282i
$250$		0			0
$251$	480478.			0.481381			0.240691	−	0.970602i	$-0.422626\pi$
$251$	480478.			0.481381			0.240691	+	0.970602i	$0.422626\pi$
$252$		0			0
$253$	288009.			0.282882
$254$		0			0
$255$	−320915.	−	555842.i	−0.309058	−	0.535304i
$256$		0			0
$257$	750170.	−	1.29933e6i	0.708479	−	1.22712i	−0.256942	−	0.966427i	$-0.582715\pi$
$257$	750170.	−	1.29933e6i	0.708479	−	1.22712i	0.965421	−	0.260695i	$-0.0839516\pi$
$258$		0			0
$259$	−114030.	+	894032.i	−0.105625	+	0.828140i
$260$		0			0
$261$	−315761.	+	546915.i	−0.286918	+	0.496956i
$262$		0			0
$263$	−623499.	−	1.07993e6i	−0.555836	−	0.962736i	−0.997838	−	0.0657220i	$-0.979065\pi$
$263$	−623499.	−	1.07993e6i	−0.555836	−	0.962736i	0.442002	−	0.897014i	$-0.354268\pi$
$264$		0			0
$265$	−3.10678e6			−2.71766
$266$		0			0
$267$	41953.1			0.0360152
$268$		0			0
$269$	−110309.	−	191061.i	−0.0929460	−	0.160987i	0.815804	−	0.578329i	$-0.196295\pi$
$269$	−110309.	−	191061.i	−0.0929460	−	0.160987i	−0.908750	+	0.417342i	$0.862962\pi$
$270$		0			0
$271$	1.05936e6	−	1.83487e6i	0.876238	−	1.51769i	0.0208009	−	0.999784i	$-0.493378\pi$
$271$	1.05936e6	−	1.83487e6i	0.876238	−	1.51769i	0.855438	−	0.517906i	$-0.173288\pi$
$272$		0			0
$273$	236927.	+	180285.i	0.192401	+	0.146404i
$274$		0			0
$275$	−1.69737e6	+	2.93993e6i	−1.35346	+	2.34425i
$276$		0			0
$277$	−735579.	−	1.27406e6i	−0.576010	−	0.997678i	−0.995931	−	0.0901174i	$-0.971276\pi$
$277$	−735579.	−	1.27406e6i	−0.576010	−	0.997678i	0.419922	−	0.907560i	$-0.362058\pi$
$278$		0			0
$279$	288588.			0.221957
$280$		0			0
$281$	435646.			0.329131			0.164565	−	0.986366i	$-0.447378\pi$
$281$	435646.			0.329131			0.164565	+	0.986366i	$0.447378\pi$
$282$		0			0
$283$	561436.	+	972436.i	0.416710	+	0.721764i	0.995606	−	0.0936378i	$-0.0298496\pi$
$283$	561436.	+	972436.i	0.416710	+	0.721764i	−0.578896	+	0.815401i	$0.696516\pi$
$284$		0			0
$285$	−399184.	+	691406.i	−0.291112	+	0.504221i
$286$		0			0
$287$	−1.61596e6	+	677011.i	−1.15804	+	0.485167i
$288$		0			0
$289$	463752.	−	803243.i	0.326619	−	0.565721i
$290$		0			0
$291$	124600.	+	215813.i	0.0862551	+	0.149398i
$292$		0			0
$293$	−2.13890e6			−1.45553			−0.727767	−	0.685825i	$-0.759442\pi$
$293$	−2.13890e6			−1.45553			−0.727767	+	0.685825i	$0.759442\pi$
$294$		0			0
$295$	−4.67812e6			−3.12980
$296$		0			0
$297$	−171750.	−	297481.i	−0.112981	−	0.195689i
$298$		0			0
$299$	77982.3	−	135069.i	0.0504450	−	0.0873733i
$300$		0			0
$301$	1.71497e6	−	718492.i	1.09104	−	0.457094i
$302$		0			0
$303$	−235574.	+	408027.i	−0.147408	+	0.255318i
$304$		0			0
$305$	2.01110e6	+	3.48333e6i	1.23790	+	2.14410i
$306$		0			0
$307$	2.24001e6			1.35645			0.678226	−	0.734853i	$-0.262749\pi$
$307$	2.24001e6			1.35645			0.678226	+	0.734853i	$0.262749\pi$
$308$		0			0
$309$	−987148.			−0.588147
$310$		0			0
$311$	−1.00830e6	−	1.74642e6i	−0.591136	−	1.02388i	−0.994080	−	0.108652i	$-0.965346\pi$
$311$	−1.00830e6	−	1.74642e6i	−0.591136	−	1.02388i	0.402944	−	0.915225i	$-0.367987\pi$
$312$		0			0
$313$	918901.	−	1.59158e6i	0.530161	−	0.918266i	−0.469220	−	0.883081i	$-0.655465\pi$
$313$	918901.	−	1.59158e6i	0.530161	−	0.918266i	0.999381	−	0.0351842i	$-0.0112018\pi$
$314$		0			0
$315$	−849332.	−	646281.i	−0.482282	−	0.366982i
$316$		0			0
$317$	212225.	−	367584.i	0.118617	−	0.205451i	−0.800603	−	0.599196i	$-0.795487\pi$
$317$	212225.	−	367584.i	0.118617	−	0.205451i	0.919220	+	0.393744i	$0.128820\pi$
$318$		0			0
$319$	−1.83685e6	−	3.18152e6i	−1.01064	−	1.75048i
$320$		0			0
$321$	−329296.			−0.178371
$322$		0			0
$323$	612432.			0.326627
$324$		0			0
$325$	919170.	+	1.59205e6i	0.482711	+	0.836080i
$326$		0			0
$327$	901919.	−	1.56217e6i	0.466442	−	0.807902i
$328$		0			0
$329$	−177775.	+	1.39381e6i	−0.0905482	+	0.709929i
$330$		0			0
$331$	−949650.	+	1.64484e6i	−0.476424	+	0.825191i	−0.999635	−	0.0270125i	$-0.991401\pi$
$331$	−949650.	+	1.64484e6i	−0.476424	+	0.825191i	0.523211	+	0.852203i	$0.324734\pi$
$332$		0			0
$333$	−281558.	−	487672.i	−0.139141	−	0.241000i
$334$		0			0
$335$	2.33660e6			1.13756
$336$		0			0
$337$	−2.44999e6			−1.17514			−0.587571	−	0.809173i	$-0.699916\pi$
$337$	−2.44999e6			−1.17514			−0.587571	+	0.809173i	$0.699916\pi$
$338$		0			0
$339$	−965665.	−	1.67258e6i	−0.456381	−	0.790474i
$340$		0			0
$341$	−839391.	+	1.45387e6i	−0.390911	+	0.677078i
$342$		0			0
$343$	809371.	−	2.02299e6i	0.371460	−	0.928449i
$344$		0			0
$345$	−279549.	+	484194.i	−0.126448	+	0.219014i
$346$		0			0
$347$	−1.35322e6	−	2.34385e6i	−0.603316	−	1.04497i	−0.992315	−	0.123736i	$-0.960512\pi$
$347$	−1.35322e6	−	2.34385e6i	−0.603316	−	1.04497i	0.388999	−	0.921238i	$-0.372821\pi$
$348$		0			0
$349$	1.94710e6			0.855705			0.427852	−	0.903849i	$-0.359270\pi$
$349$	1.94710e6			0.855705			0.427852	+	0.903849i	$0.359270\pi$
$350$		0			0
$351$	−186015.			−0.0805898
$352$		0			0
$353$	1.88688e6	+	3.26818e6i	0.805950	+	1.39595i	0.915648	+	0.401982i	$0.131679\pi$
$353$	1.88688e6	+	3.26818e6i	0.805950	+	1.39595i	−0.109697	+	0.993965i	$0.534988\pi$
$354$		0			0
$355$	−2.92683e6	+	5.06942e6i	−1.23261	+	2.13495i
$356$		0			0
$357$	−103583.	+	812122.i	−0.0430146	+	0.337249i
$358$		0			0
$359$	1.43537e6	−	2.48613e6i	0.587796	−	1.01809i	−0.406725	−	0.913551i	$-0.633329\pi$
$359$	1.43537e6	−	2.48613e6i	0.587796	−	1.01809i	0.994521	−	0.104541i	$-0.0333375\pi$
$360$		0			0
$361$	857150.	+	1.48463e6i	0.346170	+	0.599583i
$362$		0			0
$363$	548762.			0.218583
$364$		0			0
$365$	1.66921e6			0.655809
$366$		0			0
$367$	1.06983e6	+	1.85301e6i	0.414621	+	0.718145i	0.995389	−	0.0959248i	$-0.0305808\pi$
$367$	1.06983e6	+	1.85301e6i	0.414621	+	0.718145i	−0.580768	+	0.814069i	$0.697248\pi$
$368$		0			0
$369$	547337.	−	948016.i	0.209261	−	0.362451i
$370$		0			0
$371$	3.15371e6	+	2.39975e6i	1.18956	+	0.905173i
$372$		0			0
$373$	1.27174e6	−	2.20271e6i	0.473287	−	0.819758i	−0.526245	−	0.850333i	$-0.676401\pi$
$373$	1.27174e6	−	2.20271e6i	0.473287	−	0.819758i	0.999532	+	0.0305751i	$0.00973388\pi$
$374$		0			0
$375$	−1.86579e6	−	3.23164e6i	−0.685147	−	1.18671i
$376$		0			0
$377$	−1.98941e6			−0.720893
$378$		0			0
$379$	−832054.			−0.297546			−0.148773	−	0.988871i	$-0.547532\pi$
$379$	−832054.			−0.297546			−0.148773	+	0.988871i	$0.547532\pi$
$380$		0			0
$381$	−520437.	−	901423.i	−0.183677	−	0.318138i
$382$		0			0
$383$	2.04659e6	−	3.54480e6i	0.712909	−	1.23480i	−0.250851	−	0.968026i	$-0.580710\pi$
$383$	2.04659e6	−	3.54480e6i	0.712909	−	1.23480i	0.963760	−	0.266770i	$-0.0859563\pi$
$384$		0			0
$385$	5.72625e6	−	2.39903e6i	1.96888	−	0.824868i
$386$		0			0
$387$	−580873.	+	1.00610e6i	−0.197153	+	0.341479i
$388$		0			0
$389$	−1.75926e6	−	3.04713e6i	−0.589462	−	1.02098i	−0.994303	−	0.106591i	$-0.966006\pi$
$389$	−1.75926e6	−	3.04713e6i	−0.589462	−	1.02098i	0.404841	−	0.914387i	$-0.367327\pi$
$390$		0			0
$391$	428888.			0.141874
$392$		0			0
$393$	2.34179e6			0.764833
$394$		0			0
$395$	4.91694e6	+	8.51639e6i	1.58563	+	2.74639i
$396$		0			0
$397$	−202327.	+	350441.i	−0.0644284	+	0.111593i	−0.896440	−	0.443164i	$-0.853856\pi$
$397$	−202327.	+	350441.i	−0.0644284	+	0.111593i	0.832012	+	0.554758i	$0.187189\pi$
$398$		0			0
$399$	939274.	−	393512.i	0.295366	−	0.123745i
$400$		0			0
$401$	1.13865e6	−	1.97221e6i	0.353615	−	0.612479i	−0.633265	−	0.773935i	$-0.718286\pi$
$401$	1.13865e6	−	1.97221e6i	0.353615	−	0.612479i	0.986880	+	0.161456i	$0.0516189\pi$
$402$		0			0
$403$	454553.	+	787308.i	0.139419	+	0.241481i
$404$		0			0
$405$	666822.			0.202010
$406$		0			0
$407$	3.27576e6			0.980227
$408$		0			0
$409$	134968.	+	233771.i	0.0398952	+	0.0691006i	0.885284	−	0.465052i	$-0.153964\pi$
$409$	134968.	+	233771.i	0.0398952	+	0.0691006i	−0.845388	+	0.534152i	$0.820631\pi$
$410$		0			0
$411$	1.48726e6	−	2.57601e6i	0.434293	−	0.752217i
$412$		0			0
$413$	4.74879e6	+	3.61350e6i	1.36996	+	1.04244i
$414$		0			0
$415$	−2.38745e6	+	4.13518e6i	−0.680478	+	1.17862i
$416$		0			0
$417$	−438219.	−	759018.i	−0.123410	−	0.213753i
$418$		0			0
$419$	−410729.			−0.114293			−0.0571467	−	0.998366i	$-0.518200\pi$
$419$	−410729.			−0.114293			−0.0571467	+	0.998366i	$0.518200\pi$
$420$		0			0
$421$	−6.33710e6			−1.74255			−0.871275	−	0.490796i	$-0.836706\pi$
$421$	−6.33710e6			−1.74255			−0.871275	+	0.490796i	$0.836706\pi$
$422$		0			0
$423$	−438954.	−	760290.i	−0.119280	−	0.206599i
$424$		0			0
$425$	−2.52763e6	+	4.37798e6i	−0.678799	+	1.17571i
$426$		0			0
$427$	649127.	−	5.08938e6i	0.172290	−	1.35081i
$428$		0			0
$429$	541045.	−	937117.i	0.141935	−	0.245839i
$430$		0			0
$431$	−222445.	−	385286.i	−0.0576806	−	0.0999056i	0.835743	−	0.549120i	$-0.185037\pi$
$431$	−222445.	−	385286.i	−0.0576806	−	0.0999056i	−0.893424	+	0.449215i	$0.851704\pi$
$432$		0			0
$433$	−3.02927e6			−0.776460			−0.388230	−	0.921563i	$-0.626913\pi$
$433$	−3.02927e6			−0.776460			−0.388230	+	0.921563i	$0.626913\pi$
$434$		0			0
$435$	7.13159e6			1.80702
$436$		0			0
$437$	−266745.	−	462015.i	−0.0668178	−	0.115732i
$438$		0			0
$439$	−708949.	+	1.22794e6i	−0.175571	+	0.304099i	−0.940359	−	0.340184i	$-0.889511\pi$
$439$	−708949.	+	1.22794e6i	−0.175571	+	0.304099i	0.764787	+	0.644283i	$0.222844\pi$
$440$		0			0
$441$	362959.	+	1.31209e6i	0.0888712	+	0.321268i
$442$		0			0
$443$	−3.16232e6	+	5.47730e6i	−0.765591	+	1.32604i	0.174342	+	0.984685i	$0.444220\pi$
$443$	−3.16232e6	+	5.47730e6i	−0.765591	+	1.32604i	−0.939933	+	0.341358i	$0.889113\pi$
$444$		0			0
$445$	−236882.	−	410291.i	−0.0567063	−	0.0982182i
$446$		0			0
$447$	−2.91951e6			−0.691100
$448$		0			0
$449$	4.95953e6			1.16098			0.580490	−	0.814267i	$-0.302861\pi$
$449$	4.95953e6			1.16098			0.580490	+	0.814267i	$0.302861\pi$
$450$		0			0
$451$	3.18398e6	+	5.51482e6i	0.737105	+	1.27670i
$452$		0			0
$453$	882655.	−	1.52880e6i	0.202090	−	0.350031i
$454$		0			0
$455$	425370.	−	3.33504e6i	0.0963248	−	0.755219i
$456$		0			0
$457$	1.86189e6	−	3.22489e6i	0.417027	−	0.722311i	−0.578612	−	0.815603i	$-0.696406\pi$
$457$	1.86189e6	−	3.22489e6i	0.417027	−	0.722311i	0.995639	+	0.0932916i	$0.0297389\pi$
$458$		0			0
$459$	−255762.	−	442992.i	−0.0566635	−	0.0981441i
$460$		0			0
$461$	5.75815e6			1.26192			0.630958	−	0.775817i	$-0.282662\pi$
$461$	5.75815e6			1.26192			0.630958	+	0.775817i	$0.282662\pi$
$462$		0			0
$463$	1.04695e6			0.226972			0.113486	−	0.993540i	$-0.463798\pi$
$463$	1.04695e6			0.226972			0.113486	+	0.993540i	$0.463798\pi$
$464$		0			0
$465$	−1.62947e6	−	2.82233e6i	−0.349473	−	0.605306i
$466$		0			0
$467$	4.45735e6	−	7.72036e6i	0.945768	−	1.63812i	0.191563	−	0.981480i	$-0.438644\pi$
$467$	4.45735e6	−	7.72036e6i	0.945768	−	1.63812i	0.754206	−	0.656638i	$-0.228022\pi$
$468$		0			0
$469$	−2.37191e6	−	1.80485e6i	−0.497926	−	0.378887i
$470$		0			0
$471$	863053.	−	1.49485e6i	0.179261	−	0.310489i
$472$		0			0
$473$	−3.37907e6	−	5.85272e6i	−0.694455	−	1.20283i
$474$		0			0
$475$	6.28819e6			1.27877
$476$		0			0
$477$	−2.47602e6			−0.498263
$478$		0			0
$479$	165550.	+	286742.i	0.0329679	+	0.0571021i	0.882039	−	0.471177i	$-0.156171\pi$
$479$	165550.	+	286742.i	0.0329679	+	0.0571021i	−0.849071	+	0.528279i	$0.822837\pi$
$480$		0			0
$481$	886957.	−	1.53625e6i	0.174799	−	0.302761i
$482$		0			0
$483$	657776.	−	275578.i	0.128295	−	0.0537497i
$484$		0			0
$485$	1.40707e6	−	2.43711e6i	0.271619	−	0.470458i
$486$		0			0
$487$	−830665.	−	1.43875e6i	−0.158710	−	0.274893i	0.775694	−	0.631109i	$-0.217400\pi$
$487$	−830665.	−	1.43875e6i	−0.158710	−	0.274893i	−0.934404	+	0.356216i	$0.884067\pi$
$488$		0			0
$489$	−4.69289e6			−0.887499
$490$		0			0
$491$	1.52601e6			0.285663			0.142832	−	0.989747i	$-0.454379\pi$
$491$	1.52601e6			0.285663			0.142832	+	0.989747i	$0.454379\pi$
$492$		0			0
$493$	−2.73534e6	−	4.73775e6i	−0.506868	−	0.877920i
$494$		0			0
$495$	−1.93953e6	+	3.35936e6i	−0.355781	+	0.616231i
$496$		0			0
$497$	6.88680e6	−	2.88525e6i	1.25062	−	0.523953i
$498$		0			0
$499$	1.65254e6	−	2.86228e6i	0.297098	−	0.514589i	−0.678373	−	0.734718i	$-0.737315\pi$
$499$	1.65254e6	−	2.86228e6i	0.297098	−	0.514589i	0.975471	+	0.220129i	$0.0706479\pi$
$500$		0			0
$501$	−32724.7	−	56680.8i	−0.00582480	−	0.0100889i
$502$		0			0
$503$	−8.10716e6			−1.42873			−0.714363	−	0.699776i	$-0.753283\pi$
$503$	−8.10716e6			−1.42873			−0.714363	+	0.699776i	$0.753283\pi$
$504$		0			0
$505$	5.32054e6			0.928384
$506$		0			0
$507$	1.37783e6	+	2.38647e6i	0.238054	+	0.412321i
$508$		0			0
$509$	−2.28293e6	+	3.95414e6i	−0.390569	+	0.676485i	−0.992525	−	0.122045i	$-0.961055\pi$
$509$	−2.28293e6	+	3.95414e6i	−0.390569	+	0.676485i	0.601956	+	0.798529i	$0.294388\pi$
$510$		0			0
$511$	−1.69442e6	−	1.28934e6i	−0.287058	−	0.218431i
$512$		0			0
$513$	−318140.	+	551034.i	−0.0533733	+	0.0924453i
$514$		0			0
$515$	5.57378e6	+	9.65407e6i	0.926044	+	1.60396i
$516$		0			0
$517$	5.10698e6			0.840307
$518$		0			0
$519$	2.86253e6			0.466478
$520$		0			0
$521$	−969034.	−	1.67842e6i	−0.156403	−	0.270898i	0.777166	−	0.629295i	$-0.216656\pi$
$521$	−969034.	−	1.67842e6i	−0.156403	−	0.270898i	−0.933569	+	0.358398i	$0.883323\pi$
$522$		0			0
$523$	−1.84914e6	+	3.20281e6i	−0.295608	+	0.512008i	−0.975126	−	0.221651i	$-0.928855\pi$
$523$	−1.84914e6	+	3.20281e6i	−0.295608	+	0.512008i	0.679518	+	0.733659i	$0.262189\pi$
$524$		0			0
$525$	−1.06354e6	+	8.33852e6i	−0.168405	+	1.32035i
$526$		0			0
$527$	−1.24998e6	+	2.16502e6i	−0.196054	+	0.339575i
$528$		0			0
$529$	3.03137e6	+	5.25049e6i	0.470977	+	0.815756i
$530$		0			0
$531$	−3.72834e6			−0.573825
$532$		0			0
$533$	3.44842e6			0.525778
$534$		0			0
$535$	1.85932e6	+	3.22044e6i	0.280847	+	0.486442i
$536$		0			0
$537$	−400693.	+	694020.i	−0.0599620	+	0.103857i
$538$		0			0
$539$	−7.66583e6	−	1.98782e6i	−1.13655	−	0.294717i
$540$		0			0
$541$	3.09539e6	−	5.36137e6i	0.454697	−	0.787558i	−0.543974	−	0.839102i	$-0.683081\pi$
$541$	3.09539e6	−	5.36137e6i	0.454697	−	0.787558i	0.998671	+	0.0515443i	$0.0164143\pi$
$542$		0			0
$543$	−58041.1	−	100530.i	−0.00844766	−	0.0146318i
$544$		0			0
$545$	−2.03702e7			−2.93768
$546$		0			0
$547$	5.33568e6			0.762468			0.381234	−	0.924479i	$-0.375499\pi$
$547$	5.33568e6			0.762468			0.381234	+	0.924479i	$0.375499\pi$
$548$		0			0
$549$	1.60280e6	+	2.77613e6i	0.226959	+	0.393105i
$550$		0			0
$551$	−3.40247e6	+	5.89325e6i	−0.477436	+	0.826943i
$552$		0			0
$553$	1.58705e6	−	1.24430e7i	0.220687	−	1.73027i
$554$		0			0
$555$	−3.17954e6	+	5.50713e6i	−0.438160	+	0.758915i
$556$		0			0
$557$	−3.39678e6	−	5.88339e6i	−0.463905	−	0.803507i	0.535247	−	0.844696i	$-0.320219\pi$
$557$	−3.39678e6	−	5.88339e6i	−0.463905	−	0.803507i	−0.999151	+	0.0411892i	$0.986885\pi$
$558$		0			0
$559$	−3.65971e6			−0.495356
$560$		0			0
$561$	2.97564e6			0.399185
$562$		0			0
$563$	−4.83409e6	−	8.37289e6i	−0.642752	−	1.11328i	−0.984816	−	0.173603i	$-0.944459\pi$
$563$	−4.83409e6	−	8.37289e6i	−0.642752	−	1.11328i	0.342063	−	0.939677i	$-0.388874\pi$
$564$		0			0
$565$	−1.09050e7	+	1.88879e7i	−1.43715	+	2.48922i
$566$		0			0
$567$	−676896.	−	515070.i	−0.0884229	−	0.0672836i
$568$		0			0
$569$	−7.01186e6	+	1.21449e7i	−0.907931	+	1.57258i	−0.0909968	+	0.995851i	$0.529005\pi$
$569$	−7.01186e6	+	1.21449e7i	−0.907931	+	1.57258i	−0.816934	+	0.576731i	$0.804328\pi$
$570$		0			0
$571$	−3.98153e6	−	6.89621e6i	−0.511045	−	0.885157i	−0.999918	−	0.0128014i	$-0.995925\pi$
$571$	−3.98153e6	−	6.89621e6i	−0.511045	−	0.885157i	0.488873	−	0.872355i	$-0.337408\pi$
$572$		0			0
$573$	8.04535e6			1.02367
$574$		0			0
$575$	4.40363e6			0.555445
$576$		0			0
$577$	4.83735e6	+	8.37853e6i	0.604878	+	1.04768i	0.992071	+	0.125680i	$0.0401114\pi$
$577$	4.83735e6	+	8.37853e6i	0.604878	+	1.04768i	−0.387193	+	0.921999i	$0.626555\pi$
$578$		0			0
$579$	−2.46465e6	+	4.26890e6i	−0.305534	+	0.529200i
$580$		0			0
$581$	5.61764e6	−	2.35353e6i	0.690420	−	0.289254i
$582$		0			0
$583$	7.20179e6	−	1.24739e7i	0.877544	−	1.51995i
$584$		0			0
$585$	1.05031e6	+	1.81918e6i	0.126890	+	0.219779i
$586$		0			0
$587$	8.70633e6			1.04289			0.521447	−	0.853284i	$-0.325392\pi$
$587$	8.70633e6			1.04289			0.521447	+	0.853284i	$0.325392\pi$
$588$		0			0
$589$	3.10967e6			0.369339
$590$		0			0
$591$	3.87606e6	+	6.71353e6i	0.456480	+	0.790646i
$592$		0			0
$593$	−2.74937e6	+	4.76205e6i	−0.321068	+	0.556106i	−0.980709	−	0.195475i	$-0.937375\pi$
$593$	−2.74937e6	+	4.76205e6i	−0.321068	+	0.556106i	0.659641	+	0.751581i	$0.270708\pi$
$594$		0			0
$595$	8.52723e6	−	3.57251e6i	0.987451	−	0.413696i
$596$		0			0
$597$	542095.	−	938936.i	0.0622500	−	0.107820i
$598$		0			0
$599$	−3.92126e6	−	6.79183e6i	−0.446539	−	0.773428i	0.551619	−	0.834096i	$-0.314010\pi$
$599$	−3.92126e6	−	6.79183e6i	−0.446539	−	0.773428i	−0.998158	+	0.0606683i	$0.980677\pi$
$600$		0			0
$601$	−5.36830e6			−0.606248			−0.303124	−	0.952951i	$-0.598030\pi$
$601$	−5.36830e6			−0.606248			−0.303124	+	0.952951i	$0.598030\pi$
$602$		0			0
$603$	1.86222e6			0.208563
$604$		0			0
$605$	−3.09850e6	−	5.36676e6i	−0.344162	−	0.596106i
$606$		0			0
$607$	−4.40674e6	+	7.63269e6i	−0.485451	+	0.840826i	−0.999860	−	0.0167191i	$-0.994678\pi$
$607$	−4.40674e6	+	7.63269e6i	−0.485451	+	0.840826i	0.514409	+	0.857545i	$0.328011\pi$
$608$		0			0
$609$	−7.23933e6	−	5.50862e6i	−0.790961	−	0.601866i
$610$		0			0
$611$	1.38278e6	−	2.39505e6i	0.149848	−	0.259544i
$612$		0			0
$613$	6.53071e6	+	1.13115e7i	0.701955	+	1.21582i	0.967779	+	0.251800i	$0.0810226\pi$
$613$	6.53071e6	+	1.13115e7i	0.701955	+	1.21582i	−0.265824	+	0.964022i	$0.585644\pi$
$614$		0			0
$615$	−1.23618e7			−1.31794
$616$		0			0
$617$	5.39942e6			0.570997			0.285499	−	0.958379i	$-0.407841\pi$
$617$	5.39942e6			0.570997			0.285499	+	0.958379i	$0.407841\pi$
$618$		0			0
$619$	−6.85666e6	−	1.18761e7i	−0.719260	−	1.24579i	−0.961293	−	0.275527i	$-0.911148\pi$
$619$	−6.85666e6	−	1.18761e7i	−0.719260	−	1.24579i	0.242033	−	0.970268i	$-0.422186\pi$
$620$		0			0
$621$	−222794.	+	385890.i	−0.0231832	+	0.0401546i
$622$		0			0
$623$	−76458.8	+	599463.i	−0.00789237	+	0.0618789i
$624$		0			0
$625$	−9.81270e6	+	1.69961e7i	−1.00482	+	1.74040i
$626$		0			0
$627$	−1.85069e6	−	3.20548e6i	−0.188003	−	0.325630i
$628$		0			0
$629$	4.87809e6			0.491613
$630$		0			0
$631$	3.71529e6			0.371466			0.185733	−	0.982600i	$-0.440534\pi$
$631$	3.71529e6			0.371466			0.185733	+	0.982600i	$0.440534\pi$
$632$		0			0
$633$	−939594.	−	1.62742e6i	−0.0932032	−	0.161433i
$634$		0			0
$635$	−5.87713e6	+	1.01795e7i	−0.578404	+	1.00183i
$636$		0			0
$637$	−3.00787e6	+	3.05686e6i	−0.293704	+	0.298488i
$638$		0			0
$639$	−2.33261e6	+	4.04021e6i	−0.225991	+	0.391428i
$640$		0			0
$641$	3.24111e6	+	5.61376e6i	0.311565	+	0.539646i	0.978701	−	0.205289i	$-0.0658136\pi$
$641$	3.24111e6	+	5.61376e6i	0.311565	+	0.539646i	−0.667136	+	0.744936i	$0.732480\pi$
$642$		0			0
$643$	−509372.			−0.0485856			−0.0242928	−	0.999705i	$-0.507733\pi$
$643$	−509372.			−0.0485856			−0.0242928	+	0.999705i	$0.507733\pi$
$644$		0			0
$645$	1.31193e7			1.24168
$646$		0			0
$647$	−6.17516e6	−	1.06957e7i	−0.579946	−	1.00450i	−0.995485	−	0.0949207i	$-0.969740\pi$
$647$	−6.17516e6	−	1.06957e7i	−0.579946	−	1.00450i	0.415539	−	0.909576i	$-0.363593\pi$
$648$		0			0
$649$	1.08443e7	−	1.87829e7i	1.01062	−	1.75045i
$650$		0			0
$651$	−525947.	+	4.12361e6i	−0.0486396	+	0.381351i
$652$		0			0
$653$	4.20890e6	−	7.29003e6i	0.386265	−	0.669031i	−0.605679	−	0.795709i	$-0.707098\pi$
$653$	4.20890e6	−	7.29003e6i	0.386265	−	0.669031i	0.991944	+	0.126678i	$0.0404316\pi$
$654$		0			0
$655$	−1.32226e7	−	2.29021e7i	−1.20424	−	2.08580i
$656$		0			0
$657$	1.33032e6			0.120238
$658$		0			0
$659$	−1.93659e6			−0.173709			−0.0868547	−	0.996221i	$-0.527682\pi$
$659$	−1.93659e6			−0.173709			−0.0868547	+	0.996221i	$0.527682\pi$
$660$		0			0
$661$	−1.45747e6	−	2.52441e6i	−0.129747	−	0.224728i	0.793832	−	0.608137i	$-0.208083\pi$
$661$	−1.45747e6	−	2.52441e6i	−0.129747	−	0.224728i	−0.923578	+	0.383410i	$0.874750\pi$
$662$		0			0
$663$	805695.	−	1.39551e6i	0.0711847	−	0.123296i
$664$		0			0
$665$	−9.15193e6	−	6.96397e6i	−0.802525	−	0.610665i
$666$		0			0
$667$	−2.38276e6	+	4.12705e6i	−0.207379	+	0.359191i
$668$		0			0
$669$	−1.29584e6	−	2.24446e6i	−0.111940	−	0.193886i
$670$		0			0
$671$	−1.86477e7			−1.59889
$672$		0			0
$673$	−1.76154e6			−0.149918			−0.0749590	−	0.997187i	$-0.523883\pi$
$673$	−1.76154e6			−0.149918			−0.0749590	+	0.997187i	$0.523883\pi$
$674$		0			0
$675$	−2.62605e6	−	4.54845e6i	−0.221842	−	0.384241i
$676$		0			0
$677$	−1.36374e6	+	2.36207e6i	−0.114356	+	0.198071i	−0.917522	−	0.397684i	$-0.869814\pi$
$677$	−1.36374e6	+	2.36207e6i	−0.114356	+	0.198071i	0.803166	+	0.595755i	$0.203147\pi$
$678$		0			0
$679$	−3.31081e6	+	1.38708e6i	−0.275588	+	0.115458i
$680$		0			0
$681$	2.95039e6	−	5.11023e6i	0.243788	−	0.422253i
$682$		0			0
$683$	−3.15780e6	−	5.46947e6i	−0.259020	−	0.448635i	0.706960	−	0.707254i	$-0.250066\pi$
$683$	−3.15780e6	−	5.46947e6i	−0.259020	−	0.448635i	−0.965980	+	0.258618i	$0.916733\pi$
$684$		0			0
$685$	−3.35904e7			−2.73520
$686$		0			0
$687$	9.85913e6			0.796979
$688$		0			0
$689$	−3.89996e6	−	6.75493e6i	−0.312977	−	0.542092i
$690$		0			0
$691$	−7.79484e6	+	1.35011e7i	−0.621029	+	1.07565i	0.368265	+	0.929721i	$0.379952\pi$
$691$	−7.79484e6	+	1.35011e7i	−0.621029	+	1.07565i	−0.989294	+	0.145933i	$0.953381\pi$
$692$		0			0
$693$	4.56368e6	−	1.91197e6i	0.360979	−	0.151234i
$694$		0			0
$695$	−4.94868e6	+	8.57136e6i	−0.388622	+	0.673113i
$696$		0			0
$697$	4.74142e6	+	8.21237e6i	0.369680	+	0.640305i
$698$		0			0
$699$	5.87049e6			0.454445
$700$		0			0
$701$	1.36349e7			1.04799			0.523994	−	0.851722i	$-0.324442\pi$
$701$	1.36349e7			1.04799			0.523994	+	0.851722i	$0.324442\pi$
$702$		0			0
$703$	−3.03391e6	−	5.25488e6i	−0.231534	−	0.401028i
$704$		0			0
$705$	−4.95697e6	+	8.58572e6i	−0.375616	+	0.650585i
$706$		0			0
$707$	−5.40092e6	−	4.10972e6i	−0.406368	−	0.309217i
$708$		0			0
$709$	−7.76317e6	+	1.34462e7i	−0.579994	+	1.00458i	0.415486	+	0.909600i	$0.363612\pi$
$709$	−7.76317e6	+	1.34462e7i	−0.579994	+	1.00458i	−0.995479	+	0.0949789i	$0.969722\pi$
$710$		0			0
$711$	3.91868e6	+	6.78735e6i	0.290714	+	0.503531i
$712$		0			0
$713$	2.17771e6			0.160426
$714$		0			0
$715$	−1.22197e7			−0.893914
$716$		0			0
$717$	−5.16778e6	−	8.95085e6i	−0.375410	−	0.650229i
$718$		0			0
$719$	756604.	−	1.31048e6i	0.0545816	−	0.0945381i	−0.837444	−	0.546524i	$-0.815951\pi$
$719$	756604.	−	1.31048e6i	0.0545816	−	0.0945381i	0.892025	+	0.451986i	$0.149284\pi$
$720$		0			0
$721$	1.79906e6	−	1.41052e7i	0.128887	−	1.01051i
$722$		0			0
$723$	199714.	−	345916.i	0.0142090	−	0.0246107i
$724$		0			0
$725$	−2.80853e7	−	4.86452e7i	−1.98442	−	3.43712i
$726$		0			0
$727$	2.52924e7			1.77482			0.887408	−	0.460984i	$-0.152504\pi$
$727$	2.52924e7			1.77482			0.887408	+	0.460984i	$0.152504\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−5.03193e6	−	8.71555e6i	−0.348290	−	0.603256i
$732$		0			0
$733$	−1.21301e7	+	2.10099e7i	−0.833882	+	1.44433i	0.0610562	+	0.998134i	$0.480553\pi$
$733$	−1.21301e7	+	2.10099e7i	−0.833882	+	1.44433i	−0.894938	+	0.446191i	$0.852780\pi$
$734$		0			0
$735$	1.07825e7	−	1.09582e7i	0.736212	−	0.748203i
$736$		0			0
$737$	−5.41646e6	+	9.38158e6i	−0.367322	+	0.636220i
$738$		0			0
$739$	3.59676e6	+	6.22978e6i	0.242271	+	0.419625i	0.961361	−	0.275292i	$-0.0887745\pi$
$739$	3.59676e6	+	6.22978e6i	0.242271	+	0.419625i	−0.719090	+	0.694917i	$0.755441\pi$
$740$		0			0
$741$	−2.00439e6			−0.134103
$742$		0			0
$743$	3.64218e6			0.242041			0.121021	−	0.992650i	$-0.461383\pi$
$743$	3.64218e6			0.242041			0.121021	+	0.992650i	$0.461383\pi$
$744$		0			0
$745$	1.64846e7	+	2.85521e7i	1.08815	+	1.88472i
$746$		0			0
$747$	−1.90274e6	+	3.29564e6i	−0.124761	+	0.216092i
$748$		0			0
$749$	600137.	−	4.70528e6i	0.0390882	−	0.306465i
$750$		0			0
$751$	8.17834e6	−	1.41653e7i	0.529134	−	0.916486i	−0.470289	−	0.882512i	$-0.655850\pi$
$751$	8.17834e6	−	1.41653e7i	0.529134	−	0.916486i	0.999423	−	0.0339739i	$-0.0108163\pi$
$752$		0			0
$753$	−2.16215e6	−	3.74495e6i	−0.138963	−	0.240691i
$754$		0			0
$755$	−1.99351e7			−1.27277
$756$		0			0
$757$	1.10742e7			0.702378			0.351189	−	0.936305i	$-0.385777\pi$
$757$	1.10742e7			0.702378			0.351189	+	0.936305i	$0.385777\pi$
$758$		0			0
$759$	−1.29604e6	−	2.24481e6i	−0.0816609	−	0.141441i
$760$		0			0
$761$	3.89306e6	−	6.74298e6i	0.243685	−	0.422076i	−0.718076	−	0.695965i	$-0.754977\pi$
$761$	3.89306e6	−	6.74298e6i	0.243685	−	0.422076i	0.961761	+	0.273889i	$0.0883102\pi$
$762$		0			0
$763$	2.06779e7	+	1.57344e7i	1.28587	+	0.978453i
$764$		0			0
$765$	−2.88824e6	+	5.00258e6i	−0.178435	+	0.309058i
$766$		0			0
$767$	−5.87248e6	−	1.01714e7i	−0.360440	−	0.624300i
$768$		0			0
$769$	−1.17681e7			−0.717615			−0.358807	−	0.933412i	$-0.616817\pi$
$769$	−1.17681e7			−0.717615			−0.358807	+	0.933412i	$0.616817\pi$
$770$		0			0
$771$	−1.35031e7			−0.818081
$772$		0			0
$773$	1.30185e7	+	2.25487e7i	0.783631	+	1.35729i	0.929814	+	0.368031i	$0.119968\pi$
$773$	1.30185e7	+	2.25487e7i	0.783631	+	1.35729i	−0.146183	+	0.989258i	$0.546699\pi$
$774$		0			0
$775$	−1.28342e7	+	2.22295e7i	−0.767564	+	1.32946i
$776$		0			0
$777$	7.48142e6	−	3.13437e6i	0.444561	−	0.186251i
$778$		0			0
$779$	5.89780e6	−	1.02153e7i	0.348214	−	0.603125i
$780$		0			0
$781$	−1.35693e7	−	2.35028e7i	−0.796032	−	1.37877i
$782$		0			0
$783$	5.68370e6			0.331304
$784$		0			0
$785$	−1.94924e7			−1.12899
$786$		0			0
$787$	1.65392e7	+	2.86468e7i	0.951871	+	1.64869i	0.741372	+	0.671094i	$0.234175\pi$
$787$	1.65392e7	+	2.86468e7i	0.951871	+	1.64869i	0.210499	+	0.977594i	$0.432491\pi$
$788$		0			0
$789$	−5.61149e6	+	9.71939e6i	−0.320912	+	0.555836i
$790$		0			0
$791$	2.56592e7	−	1.07500e7i	1.45815	−	0.610898i
$792$		0			0
$793$	−5.04910e6	+	8.74530e6i	−0.285122	+	0.493846i
$794$		0			0
$795$	1.39805e7	+	2.42149e7i	0.784521	+	1.35883i
$796$		0			0
$797$	8.83350e6			0.492591			0.246296	−	0.969195i	$-0.420787\pi$
$797$	8.83350e6			0.492591			0.246296	+	0.969195i	$0.420787\pi$
$798$		0			0
$799$	7.60504e6			0.421439
$800$		0			0
$801$	−188789.	−	326992.i	−0.0103967	−	0.0180076i
$802$		0			0
$803$	−3.86937e6	+	6.70194e6i	−0.211764	+	0.366785i
$804$		0			0
$805$	−6.40911e6	−	4.87688e6i	−0.348585	−	0.265248i
$806$		0			0
$807$	−992782.	+	1.71955e6i	−0.0536624	+	0.0929460i
$808$		0			0
$809$	−7.17774e6	−	1.24322e7i	−0.385581	−	0.667847i	0.606268	−	0.795260i	$-0.292666\pi$
$809$	−7.17774e6	−	1.24322e7i	−0.385581	−	0.667847i	−0.991850	+	0.127414i	$0.959332\pi$
$810$		0			0
$811$	−2.93449e7			−1.56668			−0.783341	−	0.621592i	$-0.786486\pi$
$811$	−2.93449e7			−1.56668			−0.783341	+	0.621592i	$0.786486\pi$
$812$		0			0
$813$	−1.90686e7			−1.01179
$814$		0			0
$815$	2.64977e7	+	4.58953e7i	1.39738	+	2.42033i
$816$		0			0
$817$	−6.25917e6	+	1.08412e7i	−0.328066	+	0.568227i
$818$		0			0
$819$	339009.	−	2.65795e6i	0.0176604	−	0.138464i
$820$		0			0
$821$	7.71305e6	−	1.33594e7i	0.399363	−	0.691717i	−0.594284	−	0.804255i	$-0.702565\pi$
$821$	7.71305e6	−	1.33594e7i	0.399363	−	0.691717i	0.993647	+	0.112538i	$0.0358979\pi$
$822$		0			0
$823$	1.18703e7	+	2.05600e7i	0.610890	+	1.05809i	0.991091	+	0.133189i	$0.0425216\pi$
$823$	1.18703e7	+	2.05600e7i	0.610890	+	1.05809i	−0.380201	+	0.924904i	$0.624145\pi$
$824$		0			0
$825$	3.05526e7			1.56284
$826$		0			0
$827$	−4.44932e6			−0.226219			−0.113110	−	0.993583i	$-0.536081\pi$
$827$	−4.44932e6			−0.226219			−0.113110	+	0.993583i	$0.536081\pi$
$828$		0			0
$829$	7.88950e6	+	1.36650e7i	0.398716	+	0.690596i	0.993568	−	0.113239i	$-0.0361227\pi$
$829$	7.88950e6	+	1.36650e7i	0.398716	+	0.690596i	−0.594852	+	0.803835i	$0.702789\pi$
$830$		0			0
$831$	−6.62021e6	+	1.14665e7i	−0.332559	+	0.576010i
$832$		0			0
$833$	−1.14155e7	−	2.96016e6i	−0.570012	−	0.147810i
$834$		0			0
$835$	−369550.	+	640080.i	−0.0183424	+	0.0317700i
$836$		0			0
$837$	−1.29865e6	−	2.24932e6i	−0.0640734	−	0.110978i
$838$		0			0
$839$	−2.78553e7			−1.36616			−0.683081	−	0.730342i	$-0.739361\pi$
$839$	−2.78553e7			−1.36616			−0.683081	+	0.730342i	$0.739361\pi$
$840$		0			0
$841$	4.02754e7			1.96359
$842$		0			0
$843$	−1.96041e6	−	3.39553e6i	−0.0950118	−	0.164565i
$844$		0			0
$845$	1.55594e7	−	2.69497e7i	0.749637	−	1.29841i
$846$		0			0
$847$	−1.00011e6	+	7.84119e6i	−0.0479003	+	0.375555i
$848$		0			0
$849$	5.05293e6	−	8.75193e6i	0.240588	−	0.416710i
$850$		0			0
$851$	−2.12465e6	−	3.68000e6i	−0.100569	−	0.174191i
$852$		0			0
$853$	3.12919e7			1.47251			0.736257	−	0.676703i	$-0.236592\pi$
$853$	3.12919e7			1.47251			0.736257	+	0.676703i	$0.236592\pi$
$854$		0			0
$855$	7.18531e6			0.336148
$856$		0			0
$857$	3.15712e6	+	5.46829e6i	0.146838	+	0.254331i	0.930057	−	0.367415i	$-0.119757\pi$
$857$	3.15712e6	+	5.46829e6i	0.146838	+	0.254331i	−0.783219	+	0.621746i	$0.786424\pi$
$858$		0			0
$859$	3.23498e6	−	5.60316e6i	0.149585	−	0.259089i	−0.781489	−	0.623919i	$-0.785539\pi$
$859$	3.23498e6	−	5.60316e6i	0.149585	−	0.259089i	0.931074	+	0.364830i	$0.118873\pi$
$860$		0			0
$861$	1.25486e7	+	9.54859e6i	0.576882	+	0.438966i
$862$		0			0
$863$	−403541.	+	698953.i	−0.0184442	+	0.0319463i	−0.875100	−	0.483942i	$-0.839205\pi$
$863$	−403541.	+	698953.i	−0.0184442	+	0.0319463i	0.856656	+	0.515888i	$0.172538\pi$
$864$		0			0
$865$	−1.61628e7	−	2.79948e7i	−0.734475	−	1.27215i
$866$		0			0
$867$	−8.34754e6			−0.377147
$868$		0			0
$869$	−4.55916e7			−2.04803
$870$		0			0
$871$	2.93316e6	+	5.08038e6i	0.131006	+	0.226908i
$872$		0			0
$873$	1.12140e6	−	1.94232e6i	0.0497994	−	0.0862551i
$874$		0			0
$875$	4.95769e7	−	2.07704e7i	2.18907	−	0.917118i
$876$		0			0
$877$	−6.82168e6	+	1.18155e7i	−0.299497	+	0.518744i	−0.976021	−	0.217677i	$-0.930152\pi$
$877$	−6.82168e6	+	1.18155e7i	−0.299497	+	0.518744i	0.676524	+	0.736420i	$0.263485\pi$
$878$		0			0
$879$	9.62507e6	+	1.66711e7i	0.420176	+	0.727767i
$880$		0			0
$881$	9.07073e6			0.393733			0.196867	−	0.980430i	$-0.436923\pi$
$881$	9.07073e6			0.393733			0.196867	+	0.980430i	$0.436923\pi$
$882$		0			0
$883$	2.43984e7			1.05308			0.526539	−	0.850151i	$-0.323489\pi$
$883$	2.43984e7			1.05308			0.526539	+	0.850151i	$0.323489\pi$
$884$		0			0
$885$	2.10515e7	+	3.64623e7i	0.903494	+	1.56490i
$886$		0			0
$887$	1.50175e7	−	2.60111e7i	0.640898	−	1.11007i	−0.344335	−	0.938847i	$-0.611896\pi$
$887$	1.50175e7	−	2.60111e7i	0.640898	−	1.11007i	0.985233	−	0.171221i	$-0.0547712\pi$
$888$		0			0
$889$	1.38288e7	−	5.79364e6i	0.586855	−	0.245865i
$890$		0			0
$891$	−1.54575e6	+	2.67733e6i	−0.0652298	+	0.112981i
$892$		0			0
$893$	−4.72992e6	−	8.19246e6i	−0.198484	−	0.343784i
$894$		0			0
$895$	9.04980e6			0.377643
$896$		0			0
$897$	−1.40368e6			−0.0582489
$898$		0			0
$899$	−1.38889e7	−	2.40563e7i	−0.573150	−	0.992725i
$900$		0			0
$901$	1.07245e7	−	1.85754e7i	0.440115	−	0.762301i
$902$		0			0
$903$	−1.33174e7	−	1.01336e7i	−0.543503	−	0.413567i
$904$		0			0
$905$	−655441.	+	1.13526e6i	−0.0266019	+	0.0460758i
$906$		0			0
$907$	−1.99243e7	−	3.45099e7i	−0.804201	−	1.39292i	−0.916829	−	0.399279i	$-0.869260\pi$
$907$	−1.99243e7	−	3.45099e7i	−0.804201	−	1.39292i	0.112629	−	0.993637i	$-0.464073\pi$
$908$		0			0
$909$	4.24034e6			0.170212
$910$		0			0
$911$	−2.18592e6			−0.0872645			−0.0436323	−	0.999048i	$-0.513893\pi$
$911$	−2.18592e6			−0.0872645			−0.0436323	+	0.999048i	$0.513893\pi$
$912$		0			0
$913$	−1.10686e7	−	1.91715e7i	−0.439458	−	0.761164i
$914$		0			0
$915$	1.80999e7	−	3.13500e7i	0.714700	−	1.23790i
$916$		0			0
$917$	−4.26787e6	+	3.34616e7i	−0.167605	+	1.31408i
$918$		0			0
$919$	−1.92470e6	+	3.33368e6i	−0.0751752	+	0.130207i	−0.901162	−	0.433482i	$-0.857285\pi$
$919$	−1.92470e6	+	3.33368e6i	−0.0751752	+	0.130207i	0.825987	+	0.563689i	$0.190618\pi$
$920$		0			0
$921$	−1.00801e7	−	1.74592e7i	−0.391574	−	0.678226i
$922$		0			0
$923$	−1.46963e7			−0.567811
$924$		0			0
$925$	5.00861e7			1.92470
$926$		0			0
$927$	4.44217e6	+	7.69406e6i	0.169783	+	0.294074i
$928$		0			0
$929$	−1.27046e7	+	2.20050e7i	−0.482972	+	0.836532i	−0.999809	−	0.0195517i	$-0.993776\pi$
$929$	−1.27046e7	+	2.20050e7i	−0.482972	+	0.836532i	0.516837	+	0.856084i	$0.327109\pi$
$930$		0			0
$931$	3.91104e6	+	1.41384e7i	0.147883	+	0.534595i
$932$		0			0
$933$	−9.07467e6	+	1.57178e7i	−0.341292	+	0.591136i
$934$		0			0
$935$	−1.68015e7	−	2.91011e7i	−0.628521	−	1.08863i
$936$		0			0
$937$	−2.36510e7			−0.880038			−0.440019	−	0.897989i	$-0.645028\pi$
$937$	−2.36510e7			−0.880038			−0.440019	+	0.897989i	$0.645028\pi$
$938$		0			0
$939$	−1.65402e7			−0.612177
$940$		0			0
$941$	−2.23188e7	−	3.86573e7i	−0.821668	−	1.42317i	−0.904439	−	0.426602i	$-0.859710\pi$
$941$	−2.23188e7	−	3.86573e7i	−0.821668	−	1.42317i	0.0827714	−	0.996569i	$-0.473623\pi$
$942$		0			0
$943$	4.13024e6	−	7.15379e6i	0.151250	−	0.261973i
$944$		0			0
$945$	−1.21527e6	+	9.52815e6i	−0.0442684	+	0.347080i
$946$		0			0
$947$	1.08363e7	−	1.87689e7i	0.392649	−	0.680088i	−0.600149	−	0.799888i	$-0.704892\pi$
$947$	1.08363e7	−	1.87689e7i	0.392649	−	0.680088i	0.992798	+	0.119800i	$0.0382255\pi$
$948$		0			0
$949$	2.09537e6	+	3.62928e6i	0.0755257	+	0.130814i
$950$		0			0
$951$	−3.82005e6			−0.136968
$952$		0			0
$953$	8.43695e6			0.300921			0.150461	−	0.988616i	$-0.451924\pi$
$953$	8.43695e6			0.300921			0.150461	+	0.988616i	$0.451924\pi$
$954$		0			0
$955$	−4.54268e7	−	7.86816e7i	−1.61177	−	2.79167i
$956$		0			0
$957$	−1.65317e7	+	2.86337e7i	−0.583495	+	1.01064i
$958$		0			0
$959$	3.40978e7	+	2.59461e7i	1.19724	+	0.911013i
$960$		0			0
$961$	7.96773e6	−	1.38005e7i	0.278308	−	0.482044i
$962$		0			0
$963$	1.48183e6	+	2.56661e6i	0.0514913	+	0.0891855i
$964$		0			0
$965$	5.56652e7			1.92427
$966$		0			0
$967$	5.25213e6			0.180621			0.0903107	−	0.995914i	$-0.471214\pi$
$967$	5.25213e6			0.180621			0.0903107	+	0.995914i	$0.471214\pi$
$968$		0			0
$969$	−2.75595e6	−	4.77344e6i	−0.0942890	−	0.163313i
$970$		0			0
$971$	2.33994e6	−	4.05289e6i	0.0796446	−	0.137948i	−0.823452	−	0.567386i	$-0.807955\pi$
$971$	2.33994e6	−	4.05289e6i	0.0796446	−	0.137948i	0.903097	+	0.429437i	$0.141288\pi$
$972$		0			0
$973$	1.16442e7	−	4.87837e6i	0.394300	−	0.165193i
$974$		0			0
$975$	8.27253e6	−	1.43284e7i	0.278693	−	0.482711i
$976$		0			0
$977$	1.57282e7	+	2.72421e7i	0.527161	+	0.913070i	0.999499	+	0.0316524i	$0.0100770\pi$
$977$	1.57282e7	+	2.72421e7i	0.527161	+	0.913070i	−0.472338	+	0.881418i	$0.656590\pi$
$978$		0			0
$979$	2.19645e6			0.0732428
$980$		0			0
$981$	−1.62345e7			−0.538601
$982$		0			0
$983$	1.53240e7	+	2.65420e7i	0.505811	+	0.876091i	0.999977	+	0.00672350i	$0.00214017\pi$
$983$	1.53240e7	+	2.65420e7i	0.505811	+	0.876091i	−0.494166	+	0.869368i	$0.664526\pi$
$984$		0			0
$985$	4.37711e7	−	7.58138e7i	1.43746	−	2.48976i
$986$		0			0
$987$	1.16637e7	−	4.88655e6i	0.381104	−	0.159665i
$988$		0			0
$989$	−4.38331e6	+	7.59211e6i	−0.142499	+	0.246815i
$990$		0			0
$991$	1.28763e7	+	2.23024e7i	0.416492	+	0.721386i	0.995584	−	0.0938768i	$-0.0299260\pi$
$991$	1.28763e7	+	2.23024e7i	0.416492	+	0.721386i	−0.579092	+	0.815262i	$0.696593\pi$
$992$		0			0
$993$	1.70937e7			0.550127
$994$		0			0
$995$	−1.22434e7			−0.392053
$996$		0			0
$997$	8.72263e6	+	1.51080e7i	0.277913	+	0.481360i	0.970866	−	0.239623i	$-0.0770238\pi$
$997$	8.72263e6	+	1.51080e7i	0.277913	+	0.481360i	−0.692953	+	0.720983i	$0.743691\pi$
$998$		0			0
$999$	−2.53402e6	+	4.38905e6i	−0.0803334	+	0.139141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.l.289.1		10
4.3	odd	2		168.6.q.c.121.1	yes	10
7.4	even	3	inner	336.6.q.l.193.1		10
12.11	even	2		504.6.s.c.289.5		10
28.11	odd	6		168.6.q.c.25.1	✓	10
84.11	even	6		504.6.s.c.361.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.6.q.c.25.1	✓	10	28.11	odd	6
168.6.q.c.121.1	yes	10	4.3	odd	2
336.6.q.l.193.1		10	7.4	even	3	inner
336.6.q.l.289.1		10	1.1	even	1	trivial
504.6.s.c.289.5		10	12.11	even	2
504.6.s.c.361.5		10	84.11	even	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)

\(f(q)\)	\(=\)	\(q+(-4.50000 - 7.79423i) q^{3} +(-50.8171 + 88.0179i) q^{5} +(119.572 - 50.0952i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.50000 - 7.79423i) q^{3} +(-50.8171 + 88.0179i) q^{5} +(119.572 - 50.0952i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-235.597 - 408.067i) q^{11} -255.165 q^{13} +914.708 q^{15} +(-350.839 - 607.671i) q^{17} +(-436.405 + 755.876i) q^{19} +(-928.527 - 706.544i) q^{21} +(-305.616 + 529.342i) q^{23} +(-3602.26 - 6239.30i) q^{25} +729.000 q^{27} +7796.57 q^{29} +(-1781.41 - 3085.49i) q^{31} +(-2120.38 + 3672.60i) q^{33} +(-1667.04 + 13070.2i) q^{35} +(-3476.02 + 6020.64i) q^{37} +(1148.24 + 1988.81i) q^{39} -13514.5 q^{41} +14342.6 q^{43} +(-4116.19 - 7129.45i) q^{45} +(-5419.18 + 9386.30i) q^{47} +(11788.0 - 11980.0i) q^{49} +(-3157.55 + 5469.04i) q^{51} +(15284.1 + 26472.8i) q^{53} +47889.5 q^{55} +7855.30 q^{57} +(23014.5 + 39862.2i) q^{59} +(19787.6 - 34273.2i) q^{61} +(-1328.59 + 10416.6i) q^{63} +(12966.7 - 22459.0i) q^{65} +(-11495.2 - 19910.2i) q^{67} +5501.08 q^{69} +57595.4 q^{71} +(-8211.83 - 14223.3i) q^{73} +(-32420.4 + 56153.7i) q^{75} +(-48613.0 - 36991.1i) q^{77} +(48378.7 - 83794.4i) q^{79} +(-3280.50 - 5681.99i) q^{81} +46981.2 q^{83} +71314.5 q^{85} +(-35084.6 - 60768.3i) q^{87} +(-2330.73 + 4036.94i) q^{89} +(-30510.5 + 12782.5i) q^{91} +(-16032.7 + 27769.4i) q^{93} +(-44353.7 - 76822.9i) q^{95} -27688.8 q^{97} +38166.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * q^99

Introduction

L-functions

Modular forms

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Database

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