LMFDB - Embedded newform 588.6.i.p.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,6,Mod(361,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("588.361");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	588.i (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:	$94.3056860500$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 91x^{6} - 2x^{5} + 5907x^{4} - 304x^{3} + 167650x^{2} + 161744x + 3378244 $ x^8 - 2x^7 + 91x^6 - 2x^5 + 5907x^4 - 304x^3 + 167650x^2 + 161744*x + 3378244
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-2.68047 + 4.64270i$ of defining polynomial
Character	$\chi$	$=$	588.361
Dual form			588.6.i.p.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.50000 + 7.79423i) q^{3} +(-17.6925 - 30.6443i) q^{5} +(-40.5000 - 70.1481i) q^{9} +(-21.7786 + 37.7216i) q^{11} -648.252 q^{13} +318.465 q^{15} +(299.319 - 518.436i) q^{17} +(-320.493 - 555.111i) q^{19} +(135.824 + 235.254i) q^{23} +(936.453 - 1621.98i) q^{25} +729.000 q^{27} -5289.56 q^{29} +(-221.551 + 383.737i) q^{31} +(-196.007 - 339.495i) q^{33} +(4443.81 + 7696.91i) q^{37} +(2917.13 - 5052.62i) q^{39} -7487.34 q^{41} +3604.32 q^{43} +(-1433.09 + 2482.19i) q^{45} +(-1507.67 - 2611.35i) q^{47} +(2693.87 + 4665.93i) q^{51} +(3556.73 - 6160.44i) q^{53} +1541.27 q^{55} +5768.88 q^{57} +(16401.4 - 28408.1i) q^{59} +(-9581.63 - 16595.9i) q^{61} +(11469.2 + 19865.2i) q^{65} +(-7495.96 + 12983.4i) q^{67} -2444.83 q^{69} +25088.7 q^{71} +(5744.11 - 9949.10i) q^{73} +(8428.07 + 14597.9i) q^{75} +(27018.7 + 46797.8i) q^{79} +(-3280.50 + 5681.99i) q^{81} +12148.2 q^{83} -21182.8 q^{85} +(23803.0 - 41228.0i) q^{87} +(44522.5 + 77115.2i) q^{89} +(-1993.96 - 3453.63i) q^{93} +(-11340.6 + 19642.6i) q^{95} -35813.0 q^{97} +3528.13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{3} - 324 q^{9} + 1872 q^{17} + 1728 q^{19} + 3648 q^{23} + 3996 q^{25} + 5832 q^{27} - 2496 q^{29} + 3888 q^{31} + 12032 q^{37} + 18144 q^{41} - 4256 q^{43} + 19872 q^{47} + 16848 q^{51} + 22248 q^{53}+ \cdots - 641088 q^{97}+O(q^{100}) $ 8 * q - 36 * q^3 - 324 * q^9 + 1872 * q^17 + 1728 * q^19 + 3648 * q^23 + 3996 * q^25 + 5832 * q^27 - 2496 * q^29 + 3888 * q^31 + 12032 * q^37 + 18144 * q^41 - 4256 * q^43 + 19872 * q^47 + 16848 * q^51 + 22248 * q^53 - 42336 * q^55 - 31104 * q^57 - 5040 * q^59 + 8640 * q^61 + 83880 * q^65 + 86160 * q^67 - 65664 * q^69 - 13440 * q^71 + 18144 * q^73 + 35964 * q^75 + 19648 * q^79 - 26244 * q^81 - 525024 * q^83 + 40336 * q^85 + 11232 * q^87 + 49680 * q^89 + 34992 * q^93 - 112032 * q^95 - 641088 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−17.6925	−	30.6443i	−0.316493	−	0.548181i	0.663261	−	0.748388i	$-0.269172\pi$
$5$	−17.6925	−	30.6443i	−0.316493	−	0.548181i	−0.979754	+	0.200207i	$0.935839\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$		0			0
$11$	−21.7786	+	37.7216i	−0.0542685	+	0.0939959i	−0.891883	−	0.452265i	$-0.850616\pi$
$11$	−21.7786	+	37.7216i	−0.0542685	+	0.0939959i	0.837615	+	0.546261i	$0.183949\pi$
$12$		0			0
$13$	−648.252			−1.06386			−0.531931	−	0.846788i	$-0.678534\pi$
$13$	−648.252			−1.06386			−0.531931	+	0.846788i	$0.678534\pi$
$14$		0			0
$15$	318.465			0.365454
$16$		0			0
$17$	299.319	−	518.436i	0.251196	−	0.435084i	−0.712660	−	0.701510i	$-0.752510\pi$
$17$	299.319	−	518.436i	0.251196	−	0.435084i	0.963855	+	0.266426i	$0.0858429\pi$
$18$		0			0
$19$	−320.493	−	555.111i	−0.203674	−	0.352773i	0.746036	−	0.665906i	$-0.231955\pi$
$19$	−320.493	−	555.111i	−0.203674	−	0.352773i	−0.949709	+	0.313133i	$0.898622\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	135.824	+	235.254i	0.0535373	+	0.0927293i	0.891552	−	0.452918i	$-0.149617\pi$
$23$	135.824	+	235.254i	0.0535373	+	0.0927293i	−0.838015	+	0.545648i	$0.816284\pi$
$24$		0			0
$25$	936.453	−	1621.98i	0.299665	−	0.519035i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	−5289.56			−1.16795			−0.583975	−	0.811772i	$-0.698503\pi$
$29$	−5289.56			−1.16795			−0.583975	+	0.811772i	$0.698503\pi$
$30$		0			0
$31$	−221.551	+	383.737i	−0.0414065	+	0.0717182i	−0.885986	−	0.463712i	$-0.846517\pi$
$31$	−221.551	+	383.737i	−0.0414065	+	0.0717182i	0.844579	+	0.535430i	$0.179851\pi$
$32$		0			0
$33$	−196.007	−	339.495i	−0.0313320	−	0.0542685i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4443.81	+	7696.91i	0.533644	+	0.924298i	0.999228	+	0.0392943i	$0.0125110\pi$
$37$	4443.81	+	7696.91i	0.533644	+	0.924298i	−0.465584	+	0.885004i	$0.654156\pi$
$38$		0			0
$39$	2917.13	−	5052.62i	0.307111	−	0.531931i
$40$		0			0
$41$	−7487.34			−0.695614			−0.347807	−	0.937566i	$-0.613073\pi$
$41$	−7487.34			−0.695614			−0.347807	+	0.937566i	$0.613073\pi$
$42$		0			0
$43$	3604.32			0.297270			0.148635	−	0.988892i	$-0.452512\pi$
$43$	3604.32			0.297270			0.148635	+	0.988892i	$0.452512\pi$
$44$		0			0
$45$	−1433.09	+	2482.19i	−0.105498	+	0.182727i
$46$		0			0
$47$	−1507.67	−	2611.35i	−0.0995543	−	0.172433i	0.811946	−	0.583733i	$-0.198408\pi$
$47$	−1507.67	−	2611.35i	−0.0995543	−	0.172433i	−0.911500	+	0.411299i	$0.865075\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2693.87	+	4665.93i	0.145028	+	0.251196i
$52$		0			0
$53$	3556.73	−	6160.44i	0.173925	−	0.301247i	−0.765864	−	0.643003i	$-0.777688\pi$
$53$	3556.73	−	6160.44i	0.173925	−	0.301247i	0.939789	+	0.341756i	$0.111022\pi$
$54$		0			0
$55$	1541.27			0.0687024
$56$		0			0
$57$	5768.88			0.235182
$58$		0			0
$59$	16401.4	−	28408.1i	0.613412	−	1.06246i	−0.377249	−	0.926112i	$-0.623130\pi$
$59$	16401.4	−	28408.1i	0.613412	−	1.06246i	0.990661	−	0.136348i	$-0.0435367\pi$
$60$		0			0
$61$	−9581.63	−	16595.9i	−0.329697	−	0.571052i	0.652755	−	0.757569i	$-0.273613\pi$
$61$	−9581.63	−	16595.9i	−0.329697	−	0.571052i	−0.982452	+	0.186517i	$0.940280\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11469.2	+	19865.2i	0.336705	+	0.583189i
$66$		0			0
$67$	−7495.96	+	12983.4i	−0.204005	+	0.353347i	−0.949815	−	0.312812i	$-0.898729\pi$
$67$	−7495.96	+	12983.4i	−0.204005	+	0.353347i	0.745810	+	0.666158i	$0.232063\pi$
$68$		0			0
$69$	−2444.83			−0.0618195
$70$		0			0
$71$	25088.7			0.590653			0.295327	−	0.955396i	$-0.404572\pi$
$71$	25088.7			0.590653			0.295327	+	0.955396i	$0.404572\pi$
$72$		0			0
$73$	5744.11	−	9949.10i	0.126158	−	0.218513i	−0.796027	−	0.605261i	$-0.793069\pi$
$73$	5744.11	−	9949.10i	0.126158	−	0.218513i	0.922185	+	0.386749i	$0.126402\pi$
$74$		0			0
$75$	8428.07	+	14597.9i	0.173012	+	0.299665i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	27018.7	+	46797.8i	0.487076	+	0.843641i	0.999890	−	0.0148591i	$-0.00472996\pi$
$79$	27018.7	+	46797.8i	0.487076	+	0.843641i	−0.512813	+	0.858500i	$0.671397\pi$
$80$		0			0
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12148.2			0.193561			0.0967804	−	0.995306i	$-0.469146\pi$
$83$	12148.2			0.193561			0.0967804	+	0.995306i	$0.469146\pi$
$84$		0			0
$85$	−21182.8			−0.318006
$86$		0			0
$87$	23803.0	−	41228.0i	0.337158	−	0.583975i
$88$		0			0
$89$	44522.5	+	77115.2i	0.595806	+	1.03197i	0.993433	+	0.114418i	$0.0365005\pi$
$89$	44522.5	+	77115.2i	0.595806	+	1.03197i	−0.397627	+	0.917547i	$0.630166\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1993.96	−	3453.63i	−0.0239061	−	0.0414065i
$94$		0			0
$95$	−11340.6	+	19642.6i	−0.128922	+	0.223300i
$96$		0			0
$97$	−35813.0			−0.386466			−0.193233	−	0.981153i	$-0.561897\pi$
$97$	−35813.0			−0.386466			−0.193233	+	0.981153i	$0.561897\pi$
$98$		0			0
$99$	3528.13			0.0361790
$100$		0			0
$101$	−15438.2	+	26739.8i	−0.150589	+	0.260828i	−0.931444	−	0.363884i	$-0.881450\pi$
$101$	−15438.2	+	26739.8i	−0.150589	+	0.260828i	0.780855	+	0.624712i	$0.214784\pi$
$102$		0			0
$103$	10390.1	+	17996.1i	0.0964994	+	0.167142i	0.910233	−	0.414096i	$-0.135902\pi$
$103$	10390.1	+	17996.1i	0.0964994	+	0.167142i	−0.813734	+	0.581237i	$0.802569\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	54798.1	+	94913.0i	0.462707	+	0.801431i	0.999095	−	0.0425401i	$-0.0135450\pi$
$107$	54798.1	+	94913.0i	0.462707	+	0.801431i	−0.536388	+	0.843971i	$0.680212\pi$
$108$		0			0
$109$	−95423.2	+	165278.i	−0.769286	+	1.33244i	0.168665	+	0.985673i	$0.446054\pi$
$109$	−95423.2	+	165278.i	−0.769286	+	1.33244i	−0.937951	+	0.346768i	$0.887279\pi$
$110$		0			0
$111$	−79988.6			−0.616199
$112$		0			0
$113$	193044.			1.42220			0.711099	−	0.703092i	$-0.248198\pi$
$113$	193044.			1.42220			0.711099	+	0.703092i	$0.248198\pi$
$114$		0			0
$115$	4806.12	−	8324.44i	0.0338883	−	0.0586963i
$116$		0			0
$117$	26254.2	+	45473.6i	0.177310	+	0.307111i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	79576.9	+	137831.i	0.494110	+	0.855823i
$122$		0			0
$123$	33693.0	−	58358.1i	0.200806	−	0.347807i
$124$		0			0
$125$	−176851.			−1.01235
$126$		0			0
$127$	124379.			0.684286			0.342143	−	0.939648i	$-0.388847\pi$
$127$	124379.			0.684286			0.342143	+	0.939648i	$0.388847\pi$
$128$		0			0
$129$	−16219.4	+	28092.9i	−0.0858146	+	0.148635i
$130$		0			0
$131$	9690.58	+	16784.6i	0.0493368	+	0.0854539i	0.889639	−	0.456664i	$-0.150956\pi$
$131$	9690.58	+	16784.6i	0.0493368	+	0.0854539i	−0.840302	+	0.542118i	$0.817623\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−12897.8	−	22339.7i	−0.0609090	−	0.105498i
$136$		0			0
$137$	−30976.2	+	53652.3i	−0.141002	+	0.244223i	−0.927874	−	0.372893i	$-0.878366\pi$
$137$	−30976.2	+	53652.3i	−0.141002	+	0.244223i	0.786872	+	0.617116i	$0.211699\pi$
$138$		0			0
$139$	−381525.			−1.67489			−0.837444	−	0.546523i	$-0.815951\pi$
$139$	−381525.			−1.67489			−0.837444	+	0.546523i	$0.815951\pi$
$140$		0			0
$141$	27138.0			0.114955
$142$		0			0
$143$	14118.0	−	24453.1i	0.0577343	−	0.0999987i
$144$		0			0
$145$	93585.4	+	162095.i	0.369648	+	0.640248i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	42012.9	+	72768.4i	0.155030	+	0.268520i	0.933070	−	0.359695i	$-0.117119\pi$
$149$	42012.9	+	72768.4i	0.155030	+	0.268520i	−0.778040	+	0.628215i	$0.783786\pi$
$150$		0			0
$151$	−26755.2	+	46341.3i	−0.0954916	+	0.165396i	−0.909814	−	0.415017i	$-0.863776\pi$
$151$	−26755.2	+	46341.3i	−0.0954916	+	0.165396i	0.814322	+	0.580413i	$0.197109\pi$
$152$		0			0
$153$	−48489.7			−0.167464
$154$		0			0
$155$	15679.1			0.0524195
$156$		0			0
$157$	−203424.	+	352340.i	−0.658646	+	1.14081i	0.322320	+	0.946631i	$0.395537\pi$
$157$	−203424.	+	352340.i	−0.658646	+	1.14081i	−0.980966	+	0.194178i	$0.937796\pi$
$158$		0			0
$159$	32010.6	+	55444.0i	0.100416	+	0.173925i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	228934.	+	396525.i	0.674902	+	1.16896i	0.976497	+	0.215529i	$0.0691475\pi$
$163$	228934.	+	396525.i	0.674902	+	1.16896i	−0.301595	+	0.953436i	$0.597519\pi$
$164$		0			0
$165$	−6935.71	+	12013.0i	−0.0198327	+	0.0343512i
$166$		0			0
$167$	−492535.			−1.36661			−0.683307	−	0.730132i	$-0.739459\pi$
$167$	−492535.			−1.36661			−0.683307	+	0.730132i	$0.739459\pi$
$168$		0			0
$169$	48937.6			0.131803
$170$		0			0
$171$	−25960.0	+	44964.0i	−0.0678913	+	0.117591i
$172$		0			0
$173$	378270.	+	655182.i	0.960918	+	1.66436i	0.720204	+	0.693763i	$0.244048\pi$
$173$	378270.	+	655182.i	0.960918	+	1.66436i	0.240714	+	0.970596i	$0.422618\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	147613.	+	255673.i	0.354153	+	0.613412i
$178$		0			0
$179$	−302928.	+	524687.i	−0.706654	+	1.22396i	0.259437	+	0.965760i	$0.416463\pi$
$179$	−302928.	+	524687.i	−0.706654	+	1.22396i	−0.966091	+	0.258201i	$0.916870\pi$
$180$		0			0
$181$	−491062.			−1.11414			−0.557070	−	0.830465i	$-0.688075\pi$
$181$	−491062.			−1.11414			−0.557070	+	0.830465i	$0.688075\pi$
$182$		0			0
$183$	172469.			0.380701
$184$		0			0
$185$	157244.	−	272355.i	0.337789	−	0.585067i
$186$		0			0
$187$	13037.5	+	22581.6i	0.0272641	+	0.0472227i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	215198.	+	372734.i	0.426830	+	0.739292i	0.996589	−	0.0825200i	$-0.0262968\pi$
$191$	215198.	+	372734.i	0.426830	+	0.739292i	−0.569759	+	0.821812i	$0.692964\pi$
$192$		0			0
$193$	−16025.6	+	27757.1i	−0.0309685	+	0.0536391i	−0.881094	−	0.472941i	$-0.843192\pi$
$193$	−16025.6	+	27757.1i	−0.0309685	+	0.0536391i	0.850126	+	0.526580i	$0.176526\pi$
$194$		0			0
$195$	−206445.			−0.388793
$196$		0			0
$197$	283226.			0.519957			0.259978	−	0.965614i	$-0.416285\pi$
$197$	283226.			0.519957			0.259978	+	0.965614i	$0.416285\pi$
$198$		0			0
$199$	264275.	−	457737.i	0.473067	−	0.819376i	−0.526458	−	0.850201i	$-0.676480\pi$
$199$	264275.	−	457737.i	0.473067	−	0.819376i	0.999525	+	0.0308250i	$0.00981345\pi$
$200$		0			0
$201$	−67463.7	−	116851.i	−0.117782	−	0.204005i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	132470.	+	229444.i	0.220157	+	0.381322i
$206$		0			0
$207$	11001.7	−	19055.5i	0.0178458	−	0.0309098i
$208$		0			0
$209$	27919.6			0.0442123
$210$		0			0
$211$	701155.			1.08420			0.542098	−	0.840315i	$-0.317630\pi$
$211$	701155.			1.08420			0.542098	+	0.840315i	$0.317630\pi$
$212$		0			0
$213$	−112899.	+	195547.i	−0.170507	+	0.295327i
$214$		0			0
$215$	−63769.3	−	110452.i	−0.0940839	−	0.162958i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	51697.0	+	89541.9i	0.0728375	+	0.126158i
$220$		0			0
$221$	−194034.	+	336077.i	−0.267238	+	0.462869i
$222$		0			0
$223$	−222810.			−0.300036			−0.150018	−	0.988683i	$-0.547933\pi$
$223$	−222810.			−0.300036			−0.150018	+	0.988683i	$0.547933\pi$
$224$		0			0
$225$	−151705.			−0.199777
$226$		0			0
$227$	284442.	−	492668.i	0.366377	−	0.634584i	−0.622619	−	0.782525i	$-0.713931\pi$
$227$	284442.	−	492668.i	0.366377	−	0.634584i	0.988996	+	0.147941i	$0.0472646\pi$
$228$		0			0
$229$	284674.	+	493071.i	0.358724	+	0.621327i	0.987748	−	0.156058i	$-0.0498788\pi$
$229$	284674.	+	493071.i	0.358724	+	0.621327i	−0.629024	+	0.777386i	$0.716545\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	571174.	+	989303.i	0.689254	+	1.19382i	0.972080	+	0.234651i	$0.0753947\pi$
$233$	571174.	+	989303.i	0.689254	+	1.19382i	−0.282826	+	0.959171i	$0.591272\pi$
$234$		0			0
$235$	−53348.7	+	92402.6i	−0.0630164	+	0.109148i
$236$		0			0
$237$	−486337.			−0.562427
$238$		0			0
$239$	955201.			1.08168			0.540842	−	0.841124i	$-0.318106\pi$
$239$	955201.			1.08168			0.540842	+	0.841124i	$0.318106\pi$
$240$		0			0
$241$	185835.	−	321876.i	0.206103	−	0.356981i	−0.744380	−	0.667756i	$-0.767255\pi$
$241$	185835.	−	321876.i	0.206103	−	0.356981i	0.950484	+	0.310774i	$0.100588\pi$
$242$		0			0
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	207760.	+	359852.i	0.216681	+	0.375302i
$248$		0			0
$249$	−54667.0	+	94686.0i	−0.0558762	+	0.0967804i
$250$		0			0
$251$	791754.			0.793242			0.396621	−	0.917982i	$-0.370183\pi$
$251$	791754.			0.793242			0.396621	+	0.917982i	$0.370183\pi$
$252$		0			0
$253$	−11832.2			−0.0116216
$254$		0			0
$255$	95322.6	−	165104.i	0.0918006	−	0.159003i
$256$		0			0
$257$	146814.	+	254290.i	0.138655	+	0.240157i	0.926988	−	0.375092i	$-0.122389\pi$
$257$	146814.	+	254290.i	0.138655	+	0.240157i	−0.788333	+	0.615249i	$0.789055\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	214227.	+	371052.i	0.194658	+	0.337158i
$262$		0			0
$263$	−499792.	+	865666.i	−0.445554	+	0.771722i	−0.998091	−	0.0617666i	$-0.980327\pi$
$263$	−499792.	+	865666.i	−0.445554	+	0.771722i	0.552537	+	0.833489i	$0.313660\pi$
$264$		0			0
$265$	−251710.			−0.220184
$266$		0			0
$267$	−801405.			−0.687977
$268$		0			0
$269$	−163695.	+	283529.i	−0.137929	+	0.238900i	−0.926713	−	0.375771i	$-0.877378\pi$
$269$	−163695.	+	283529.i	−0.137929	+	0.238900i	0.788783	+	0.614671i	$0.210711\pi$
$270$		0			0
$271$	377418.	+	653708.i	0.312176	+	0.540705i	0.978833	−	0.204660i	$-0.0656087\pi$
$271$	377418.	+	653708.i	0.312176	+	0.540705i	−0.666657	+	0.745365i	$0.732275\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	40789.3	+	70649.1i	0.0325248	+	0.0563345i
$276$		0			0
$277$	916726.	−	1.58782e6i	0.717861	−	1.24337i	−0.243985	−	0.969779i	$-0.578455\pi$
$277$	916726.	−	1.58782e6i	0.717861	−	1.24337i	0.961846	−	0.273592i	$-0.0882119\pi$
$278$		0			0
$279$	35891.2			0.0276044
$280$		0			0
$281$	826428.			0.624366			0.312183	−	0.950022i	$-0.398940\pi$
$281$	826428.			0.624366			0.312183	+	0.950022i	$0.398940\pi$
$282$		0			0
$283$	348118.	−	602959.i	0.258381	−	0.447529i	−0.707427	−	0.706786i	$-0.750144\pi$
$283$	348118.	−	602959.i	0.258381	−	0.447529i	0.965808	+	0.259257i	$0.0834776\pi$
$284$		0			0
$285$	−102066.	−	176783.i	−0.0744334	−	0.128922i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	530744.	+	919276.i	0.373801	+	0.647443i
$290$		0			0
$291$	161158.	−	279135.i	0.111563	−	0.193233i
$292$		0			0
$293$	1.74281e6			1.18599			0.592994	−	0.805207i	$-0.297946\pi$
$293$	1.74281e6			1.18599			0.592994	+	0.805207i	$0.297946\pi$
$294$		0			0
$295$	−1.16073e6			−0.776561
$296$		0			0
$297$	−15876.6	+	27499.1i	−0.0104440	+	0.0180895i
$298$		0			0
$299$	−88048.0	−	152504.i	−0.0569563	−	0.0986512i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−138944.	−	240658.i	−0.0869427	−	0.150589i
$304$		0			0
$305$	−339046.	+	587244.i	−0.208693	+	0.361467i
$306$		0			0
$307$	−3.25919e6			−1.97362			−0.986810	−	0.161881i	$-0.948244\pi$
$307$	−3.25919e6			−1.97362			−0.986810	+	0.161881i	$0.948244\pi$
$308$		0			0
$309$	−187021.			−0.111428
$310$		0			0
$311$	521355.	−	903013.i	0.305656	−	0.529411i	−0.671752	−	0.740777i	$-0.734458\pi$
$311$	521355.	−	903013.i	0.305656	−	0.529411i	0.977407	+	0.211366i	$0.0677911\pi$
$312$		0			0
$313$	−665471.	−	1.15263e6i	−0.383945	−	0.665012i	0.607678	−	0.794184i	$-0.292101\pi$
$313$	−665471.	−	1.15263e6i	−0.383945	−	0.665012i	−0.991622	+	0.129172i	$0.958768\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−155988.	−	270180.i	−0.0871855	−	0.151010i	0.819135	−	0.573601i	$-0.194454\pi$
$317$	−155988.	−	270180.i	−0.0871855	−	0.151010i	−0.906320	+	0.422591i	$0.861121\pi$
$318$		0			0
$319$	115199.	−	199531.i	0.0633830	−	0.109783i
$320$		0			0
$321$	−986365.			−0.534288
$322$		0			0
$323$	−383719.			−0.204648
$324$		0			0
$325$	−607057.	+	1.05145e6i	−0.318802	+	0.552182i
$326$		0			0
$327$	−858809.	−	1.48750e6i	−0.444147	−	0.769286i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.28844e6	−	2.23164e6i	−0.646387	−	1.11958i	−0.983979	−	0.178283i	$-0.942946\pi$
$331$	−1.28844e6	−	2.23164e6i	−0.646387	−	1.11958i	0.337592	−	0.941293i	$-0.390388\pi$
$332$		0			0
$333$	359949.	−	623450.i	0.177881	−	0.308099i
$334$		0			0
$335$	530489.			0.258264
$336$		0			0
$337$	−47287.5			−0.0226815			−0.0113408	−	0.999936i	$-0.503610\pi$
$337$	−47287.5			−0.0226815			−0.0113408	+	0.999936i	$0.503610\pi$
$338$		0			0
$339$	−868697.	+	1.50463e6i	−0.410553	+	0.711099i
$340$		0			0
$341$	−9650.13	−	16714.5i	−0.00449415	−	0.00778409i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	43255.1	+	74920.0i	0.0195654	+	0.0338883i
$346$		0			0
$347$	−164977.	+	285748.i	−0.0735529	+	0.127397i	−0.900456	−	0.434947i	$-0.856767\pi$
$347$	−164977.	+	285748.i	−0.0735529	+	0.127397i	0.826903	+	0.562344i	$0.190100\pi$
$348$		0			0
$349$	3.37497e6			1.48322			0.741612	−	0.670830i	$-0.234062\pi$
$349$	3.37497e6			1.48322			0.741612	+	0.670830i	$0.234062\pi$
$350$		0			0
$351$	−472576.			−0.204740
$352$		0			0
$353$	248157.	−	429821.i	0.105996	−	0.183591i	−0.808149	−	0.588979i	$-0.799530\pi$
$353$	248157.	−	429821.i	0.105996	−	0.183591i	0.914145	+	0.405388i	$0.132864\pi$
$354$		0			0
$355$	−443882.	−	768825.i	−0.186937	−	0.323785i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.96667e6	−	3.40636e6i	−0.805368	−	1.39494i	−0.916042	−	0.401082i	$-0.868634\pi$
$359$	−1.96667e6	−	3.40636e6i	−0.805368	−	1.39494i	0.110674	−	0.993857i	$-0.464699\pi$
$360$		0			0
$361$	1.03262e6	−	1.78855e6i	0.417034	−	0.722324i
$362$		0			0
$363$	−1.43238e6			−0.570549
$364$		0			0
$365$	−406510.			−0.159713
$366$		0			0
$367$	−1.40772e6	+	2.43824e6i	−0.545571	+	0.944957i	0.453000	+	0.891511i	$0.350354\pi$
$367$	−1.40772e6	+	2.43824e6i	−0.545571	+	0.944957i	−0.998571	+	0.0534461i	$0.982979\pi$
$368$		0			0
$369$	303237.	+	525223.i	0.115936	+	0.200806i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−744213.	−	1.28901e6i	−0.276965	−	0.479718i	0.693664	−	0.720299i	$-0.255995\pi$
$373$	−744213.	−	1.28901e6i	−0.276965	−	0.479718i	−0.970629	+	0.240581i	$0.922662\pi$
$374$		0			0
$375$	795828.	−	1.37841e6i	0.292241	−	0.506176i
$376$		0			0
$377$	3.42897e6			1.24254
$378$		0			0
$379$	−1.54843e6			−0.553724			−0.276862	−	0.960910i	$-0.589294\pi$
$379$	−1.54843e6			−0.553724			−0.276862	+	0.960910i	$0.589294\pi$
$380$		0			0
$381$	−559705.	+	969438.i	−0.197536	+	0.342143i
$382$		0			0
$383$	1.59370e6	+	2.76037e6i	0.555150	+	0.961548i	0.997892	+	0.0648991i	$0.0206726\pi$
$383$	1.59370e6	+	2.76037e6i	0.555150	+	0.961548i	−0.442742	+	0.896649i	$0.645994\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−145975.	−	252836.i	−0.0495451	−	0.0858146i
$388$		0			0
$389$	−1.70810e6	+	2.95851e6i	−0.572319	+	0.991286i	0.424008	+	0.905658i	$0.360623\pi$
$389$	−1.70810e6	+	2.95851e6i	−0.572319	+	0.991286i	−0.996327	+	0.0856275i	$0.972711\pi$
$390$		0			0
$391$	162619.			0.0537934
$392$		0			0
$393$	−174430.			−0.0569693
$394$		0			0
$395$	956056.	−	1.65594e6i	0.308312	−	0.534012i
$396$		0			0
$397$	−906989.	−	1.57095e6i	−0.288819	−	0.500249i	0.684709	−	0.728816i	$-0.259929\pi$
$397$	−906989.	−	1.57095e6i	−0.288819	−	0.500249i	−0.973528	+	0.228567i	$0.926596\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.14325e6	−	1.98016e6i	−0.355042	−	0.614951i	0.632083	−	0.774900i	$-0.282200\pi$
$401$	−1.14325e6	−	1.98016e6i	−0.355042	−	0.614951i	−0.987125	+	0.159950i	$0.948867\pi$
$402$		0			0
$403$	143621.	−	248758.i	0.0440509	−	0.0762983i
$404$		0			0
$405$	232161.			0.0703317
$406$		0			0
$407$	−387120.			−0.115840
$408$		0			0
$409$	−1.50491e6	+	2.60658e6i	−0.444838	+	0.770482i	−0.998041	−	0.0625644i	$-0.980072\pi$
$409$	−1.50491e6	+	2.60658e6i	−0.444838	+	0.770482i	0.553203	+	0.833047i	$0.313405\pi$
$410$		0			0
$411$	−278786.	−	482871.i	−0.0814078	−	0.141002i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−214932.	−	372273.i	−0.0612605	−	0.106106i
$416$		0			0
$417$	1.71686e6	−	2.97369e6i	0.483499	−	0.837444i
$418$		0			0
$419$	6.78379e6			1.88772			0.943860	−	0.330347i	$-0.107166\pi$
$419$	6.78379e6			1.88772			0.943860	+	0.330347i	$0.107166\pi$
$420$		0			0
$421$	−2.60696e6			−0.716852			−0.358426	−	0.933558i	$-0.616686\pi$
$421$	−2.60696e6			−0.716852			−0.358426	+	0.933558i	$0.616686\pi$
$422$		0			0
$423$	−122121.	+	211520.i	−0.0331848	+	0.0574777i
$424$		0			0
$425$	−560597.	−	970982.i	−0.150549	−	0.260759i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	127062.	+	220078.i	0.0333329	+	0.0577343i
$430$		0			0
$431$	−1.86270e6	+	3.22629e6i	−0.483003	+	0.836586i	−0.999810	−	0.0195166i	$-0.993787\pi$
$431$	−1.86270e6	+	3.22629e6i	−0.483003	+	0.836586i	0.516807	+	0.856102i	$0.327121\pi$
$432$		0			0
$433$	846651.			0.217013			0.108506	−	0.994096i	$-0.465393\pi$
$433$	846651.			0.217013			0.108506	+	0.994096i	$0.465393\pi$
$434$		0			0
$435$	−1.68454e6			−0.426832
$436$		0			0
$437$	87061.3	−	150795.i	0.0218083	−	0.0377730i
$438$		0			0
$439$	−1.88962e6	−	3.27292e6i	−0.467965	−	0.810539i	0.531365	−	0.847143i	$-0.321679\pi$
$439$	−1.88962e6	−	3.27292e6i	−0.467965	−	0.810539i	−0.999330	+	0.0366039i	$0.988346\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.99864e6	−	6.92584e6i	−0.968061	−	1.67673i	−0.701155	−	0.713008i	$-0.747332\pi$
$443$	−3.99864e6	−	6.92584e6i	−0.968061	−	1.67673i	−0.266906	−	0.963723i	$-0.586001\pi$
$444$		0			0
$445$	1.57543e6	−	2.72872e6i	0.377136	−	0.653219i
$446$		0			0
$447$	−756232.			−0.179014
$448$		0			0
$449$	6.53115e6			1.52888			0.764441	−	0.644694i	$-0.223015\pi$
$449$	6.53115e6			1.52888			0.764441	+	0.644694i	$0.223015\pi$
$450$		0			0
$451$	163064.	−	282435.i	0.0377499	−	0.0653848i
$452$		0			0
$453$	−240796.	−	417072.i	−0.0551321	−	0.0954916i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.48083e6	−	6.02898e6i	−0.779638	−	1.35037i	−0.932151	−	0.362070i	$-0.882070\pi$
$457$	−3.48083e6	−	6.02898e6i	−0.779638	−	1.35037i	0.152513	−	0.988301i	$-0.451263\pi$
$458$		0			0
$459$	218204.	−	377940.i	0.0483427	−	0.0837319i
$460$		0			0
$461$	8.54527e6			1.87272			0.936362	−	0.351037i	$-0.114171\pi$
$461$	8.54527e6			1.87272			0.936362	+	0.351037i	$0.114171\pi$
$462$		0			0
$463$	−5.93376e6			−1.28640			−0.643202	−	0.765696i	$-0.722394\pi$
$463$	−5.93376e6			−1.28640			−0.643202	+	0.765696i	$0.722394\pi$
$464$		0			0
$465$	−70556.1	+	122207.i	−0.0151322	+	0.0262097i
$466$		0			0
$467$	125369.	+	217145.i	0.0266010	+	0.0460742i	0.879019	−	0.476786i	$-0.158198\pi$
$467$	125369.	+	217145.i	0.0266010	+	0.0460742i	−0.852418	+	0.522860i	$0.824865\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.83081e6	−	3.17106e6i	−0.380270	−	0.658646i
$472$		0			0
$473$	−78496.9	+	135961.i	−0.0161324	+	0.0279422i
$474$		0			0
$475$	−1.20051e6			−0.244135
$476$		0			0
$477$	−576191.			−0.115950
$478$		0			0
$479$	3.27627e6	−	5.67466e6i	0.652440	−	1.13006i	−0.330089	−	0.943950i	$-0.607079\pi$
$479$	3.27627e6	−	5.67466e6i	0.652440	−	1.13006i	0.982529	−	0.186109i	$-0.0595878\pi$
$480$		0			0
$481$	−2.88071e6	−	4.98954e6i	−0.567723	−	0.983326i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	633620.	+	1.09746e6i	0.122314	+	0.211853i
$486$		0			0
$487$	−1.39404e6	+	2.41456e6i	−0.266351	+	0.461333i	−0.967917	−	0.251271i	$-0.919151\pi$
$487$	−1.39404e6	+	2.41456e6i	−0.266351	+	0.461333i	0.701566	+	0.712605i	$0.252485\pi$
$488$		0			0
$489$	−4.12081e6			−0.779310
$490$		0			0
$491$	−2.79773e6			−0.523724			−0.261862	−	0.965105i	$-0.584337\pi$
$491$	−2.79773e6			−0.523724			−0.261862	+	0.965105i	$0.584337\pi$
$492$		0			0
$493$	−1.58327e6	+	2.74230e6i	−0.293384	+	0.508156i
$494$		0			0
$495$	−62421.4	−	108117.i	−0.0114504	−	0.0198327i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.72384e6	+	2.98577e6i	0.309917	+	0.536791i	0.978344	−	0.206986i	$-0.0663656\pi$
$499$	1.72384e6	+	2.98577e6i	0.309917	+	0.536791i	−0.668427	+	0.743777i	$0.733032\pi$
$500$		0			0
$501$	2.21641e6	−	3.83893e6i	0.394507	−	0.683307i
$502$		0			0
$503$	9.58331e6			1.68887			0.844434	−	0.535660i	$-0.179937\pi$
$503$	9.58331e6			1.68887			0.844434	+	0.535660i	$0.179937\pi$
$504$		0			0
$505$	1.09256e6			0.190641
$506$		0			0
$507$	−220219.	+	381431.i	−0.0380483	+	0.0659016i
$508$		0			0
$509$	387716.	+	671544.i	0.0663314	+	0.114889i	0.897284	−	0.441454i	$-0.145537\pi$
$509$	387716.	+	671544.i	0.0663314	+	0.114889i	−0.830952	+	0.556343i	$0.812204\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−233640.	−	404676.i	−0.0391970	−	0.0678913i
$514$		0			0
$515$	367651.	−	636791.i	0.0610827	−	0.105798i
$516$		0			0
$517$	131339.			0.0216107
$518$		0			0
$519$	−6.80886e6			−1.10957
$520$		0			0
$521$	−1.69232e6	+	2.93119e6i	−0.273142	+	0.473096i	−0.969665	−	0.244439i	$-0.921396\pi$
$521$	−1.69232e6	+	2.93119e6i	−0.273142	+	0.473096i	0.696523	+	0.717535i	$0.254730\pi$
$522$		0			0
$523$	95363.3	+	165174.i	0.0152450	+	0.0264051i	0.873547	−	0.486739i	$-0.161814\pi$
$523$	95363.3	+	165174.i	0.0152450	+	0.0264051i	−0.858302	+	0.513144i	$0.828481\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	132629.	+	229720.i	0.0208023	+	0.0360306i
$528$		0			0
$529$	3.18128e6	−	5.51013e6i	0.494268	−	0.856096i
$530$		0			0
$531$	−2.65703e6			−0.408941
$532$		0			0
$533$	4.85368e6			0.740037
$534$		0			0
$535$	1.93903e6	−	3.35849e6i	0.292886	−	0.507294i
$536$		0			0
$537$	−2.72635e6	−	4.72218e6i	−0.407987	−	0.706654i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.65675e6	+	2.86958e6i	0.243369	+	0.421527i	0.961672	−	0.274203i	$-0.0884142\pi$
$541$	1.65675e6	+	2.86958e6i	0.243369	+	0.421527i	−0.718303	+	0.695730i	$0.755081\pi$
$542$		0			0
$543$	2.20978e6	−	3.82745e6i	0.321625	−	0.557070i
$544$		0			0
$545$	6.75309e6			0.973893
$546$		0			0
$547$	−9.56473e6			−1.36680			−0.683399	−	0.730045i	$-0.739499\pi$
$547$	−9.56473e6			−1.36680			−0.683399	+	0.730045i	$0.739499\pi$
$548$		0			0
$549$	−776112.	+	1.34427e6i	−0.109899	+	0.190351i
$550$		0			0
$551$	1.69527e6	+	2.93629e6i	0.237881	+	0.412022i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.41520e6	+	2.45119e6i	0.195022	+	0.337789i
$556$		0			0
$557$	551612.	−	955419.i	0.0753348	−	0.130484i	−0.825897	−	0.563821i	$-0.809331\pi$
$557$	551612.	−	955419.i	0.0753348	−	0.130484i	0.901232	+	0.433337i	$0.142664\pi$
$558$		0			0
$559$	−2.33650e6			−0.316255
$560$		0			0
$561$	−234675.			−0.0314818
$562$		0			0
$563$	3.34291e6	−	5.79008e6i	0.444481	−	0.769864i	−0.553535	−	0.832826i	$-0.686721\pi$
$563$	3.34291e6	−	5.79008e6i	0.444481	−	0.769864i	0.998016	+	0.0629623i	$0.0200548\pi$
$564$		0			0
$565$	−3.41542e6	−	5.91569e6i	−0.450115	−	0.779622i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.79528e6	−	3.10951e6i	−0.232461	−	0.402635i	0.726070	−	0.687620i	$-0.241345\pi$
$569$	−1.79528e6	−	3.10951e6i	−0.232461	−	0.402635i	−0.958532	+	0.284985i	$0.908011\pi$
$570$		0			0
$571$	3.43553e6	−	5.95051e6i	0.440964	−	0.763773i	−0.556797	−	0.830649i	$-0.687970\pi$
$571$	3.43553e6	−	5.95051e6i	0.440964	−	0.763773i	0.997761	+	0.0668760i	$0.0213032\pi$
$572$		0			0
$573$	−3.87357e6			−0.492861
$574$		0			0
$575$	508770.			0.0641730
$576$		0			0
$577$	−3.18091e6	+	5.50950e6i	−0.397752	+	0.688926i	−0.993448	−	0.114284i	$-0.963543\pi$
$577$	−3.18091e6	+	5.50950e6i	−0.397752	+	0.688926i	0.595697	+	0.803210i	$0.296876\pi$
$578$		0			0
$579$	−144230.	−	249814.i	−0.0178797	−	0.0309685i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	154921.	+	268332.i	0.0188773	+	0.0326964i
$584$		0			0
$585$	929004.	−	1.60908e6i	0.112235	−	0.194396i
$586$		0			0
$587$	604781.			0.0724441			0.0362220	−	0.999344i	$-0.488468\pi$
$587$	604781.			0.0724441			0.0362220	+	0.999344i	$0.488468\pi$
$588$		0			0
$589$	284022.			0.0337337
$590$		0			0
$591$	−1.27452e6	+	2.20753e6i	−0.150099	+	0.259978i
$592$		0			0
$593$	1.42291e6	+	2.46454e6i	0.166165	+	0.287806i	0.937068	−	0.349146i	$-0.113528\pi$
$593$	1.42291e6	+	2.46454e6i	0.166165	+	0.287806i	−0.770903	+	0.636952i	$0.780195\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.37847e6	+	4.11963e6i	0.273125	+	0.473067i
$598$		0			0
$599$	−7.12692e6	+	1.23442e7i	−0.811587	+	1.40571i	0.100166	+	0.994971i	$0.468062\pi$
$599$	−7.12692e6	+	1.23442e7i	−0.811587	+	1.40571i	−0.911753	+	0.410739i	$0.865271\pi$
$600$		0			0
$601$	−3.70613e6			−0.418538			−0.209269	−	0.977858i	$-0.567108\pi$
$601$	−3.70613e6			−0.418538			−0.209269	+	0.977858i	$0.567108\pi$
$602$		0			0
$603$	1.21435e6			0.136003
$604$		0			0
$605$	2.81582e6	−	4.87715e6i	0.312764	−	0.541724i
$606$		0			0
$607$	589577.	+	1.02118e6i	0.0649485	+	0.112494i	0.896671	−	0.442697i	$-0.145978\pi$
$607$	589577.	+	1.02118e6i	0.0649485	+	0.112494i	−0.831723	+	0.555191i	$0.812645\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	977347.	+	1.69281e6i	0.105912	+	0.183445i
$612$		0			0
$613$	4.21653e6	−	7.30324e6i	0.453214	−	0.784990i	−0.545369	−	0.838196i	$-0.683611\pi$
$613$	4.21653e6	−	7.30324e6i	0.453214	−	0.784990i	0.998584	+	0.0532055i	$0.0169438\pi$
$614$		0			0
$615$	−2.38445e6			−0.254215
$616$		0			0
$617$	1.68786e7			1.78494			0.892471	−	0.451105i	$-0.148970\pi$
$617$	1.68786e7			1.78494			0.892471	+	0.451105i	$0.148970\pi$
$618$		0			0
$619$	358059.	−	620176.i	0.0375602	−	0.0650561i	−0.846634	−	0.532175i	$-0.821375\pi$
$619$	358059.	−	620176.i	0.0375602	−	0.0650561i	0.884194	+	0.467119i	$0.154708\pi$
$620$		0			0
$621$	99015.5	+	171500.i	0.0103033	+	0.0178458i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	202510.	+	350758.i	0.0207370	+	0.0359176i
$626$		0			0
$627$	−125638.	+	217612.i	−0.0127630	+	0.0221062i
$628$		0			0
$629$	5.32048e6			0.536196
$630$		0			0
$631$	−564276.			−0.0564181			−0.0282090	−	0.999602i	$-0.508980\pi$
$631$	−564276.			−0.0564181			−0.0282090	+	0.999602i	$0.508980\pi$
$632$		0			0
$633$	−3.15520e6	+	5.46497e6i	−0.312981	+	0.542098i
$634$		0			0
$635$	−2.20057e6	−	3.81150e6i	−0.216571	−	0.375113i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.01609e6	−	1.75993e6i	−0.0984422	−	0.170507i
$640$		0			0
$641$	−8.86193e6	+	1.53493e7i	−0.851889	+	1.47552i	0.0276117	+	0.999619i	$0.491210\pi$
$641$	−8.86193e6	+	1.53493e7i	−0.851889	+	1.47552i	−0.879501	+	0.475897i	$0.842124\pi$
$642$		0			0
$643$	−1.52159e7			−1.45134			−0.725671	−	0.688042i	$-0.758470\pi$
$643$	−1.52159e7			−1.45134			−0.725671	+	0.688042i	$0.758470\pi$
$644$		0			0
$645$	1.14785e6			0.108639
$646$		0			0
$647$	7.82800e6	−	1.35585e7i	0.735174	−	1.27336i	−0.219473	−	0.975618i	$-0.570434\pi$
$647$	7.82800e6	−	1.35585e7i	0.735174	−	1.27336i	0.954647	−	0.297740i	$-0.0962327\pi$
$648$		0			0
$649$	714401.	+	1.23738e6i	0.0665779	+	0.115316i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	282189.	+	488765.i	0.0258974	+	0.0448557i	0.878684	−	0.477404i	$-0.158422\pi$
$653$	282189.	+	488765.i	0.0258974	+	0.0448557i	−0.852786	+	0.522260i	$0.825089\pi$
$654$		0			0
$655$	342901.	−	593921.i	0.0312295	−	0.0540911i
$656$		0			0
$657$	−930546.			−0.0841055
$658$		0			0
$659$	−1.79285e7			−1.60816			−0.804082	−	0.594518i	$-0.797343\pi$
$659$	−1.79285e7			−1.60816			−0.804082	+	0.594518i	$0.797343\pi$
$660$		0			0
$661$	−3.23606e6	+	5.60501e6i	−0.288079	+	0.498968i	−0.973351	−	0.229319i	$-0.926350\pi$
$661$	−3.23606e6	+	5.60501e6i	−0.288079	+	0.498968i	0.685272	+	0.728287i	$0.259683\pi$
$662$		0			0
$663$	−1.74631e6	−	3.02470e6i	−0.154290	−	0.267238i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−718448.	−	1.24439e6i	−0.0625289	−	0.108303i
$668$		0			0
$669$	1.00265e6	−	1.73663e6i	0.0866128	−	0.150018i
$670$		0			0
$671$	834698.			0.0715687
$672$		0			0
$673$	1.60916e7			1.36950			0.684751	−	0.728778i	$-0.259911\pi$
$673$	1.60916e7			1.36950			0.684751	+	0.728778i	$0.259911\pi$
$674$		0			0
$675$	682674.	−	1.18243e6i	0.0576705	−	0.0998883i
$676$		0			0
$677$	7.72406e6	+	1.33785e7i	0.647700	+	1.12185i	0.983671	+	0.179977i	$0.0576022\pi$
$677$	7.72406e6	+	1.33785e7i	0.647700	+	1.12185i	−0.335971	+	0.941872i	$0.609064\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.55998e6	+	4.43401e6i	0.211528	+	0.366377i
$682$		0			0
$683$	−6.36336e6	+	1.10217e7i	−0.521957	+	0.904056i	0.477717	+	0.878514i	$0.341464\pi$
$683$	−6.36336e6	+	1.10217e7i	−0.521957	+	0.904056i	−0.999674	+	0.0255418i	$0.991869\pi$
$684$		0			0
$685$	2.19218e6			0.178505
$686$		0			0
$687$	−5.12414e6			−0.414218
$688$		0			0
$689$	−2.30566e6	+	3.99352e6i	−0.185032	+	0.320485i
$690$		0			0
$691$	1.01252e7	+	1.75373e7i	0.806692	+	1.39723i	0.915143	+	0.403130i	$0.132078\pi$
$691$	1.01252e7	+	1.75373e7i	0.806692	+	1.39723i	−0.108450	+	0.994102i	$0.534589\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.75012e6	+	1.16915e7i	0.530090	+	0.918142i
$696$		0			0
$697$	−2.24111e6	+	3.88171e6i	−0.174735	+	0.302650i
$698$		0			0
$699$	−1.02811e7			−0.795881
$700$		0			0
$701$	1.86857e7			1.43619			0.718097	−	0.695943i	$-0.245013\pi$
$701$	1.86857e7			1.43619			0.718097	+	0.695943i	$0.245013\pi$
$702$		0			0
$703$	2.84843e6	−	4.93362e6i	0.217378	−	0.376511i
$704$		0			0
$705$	−480138.	−	831623.i	−0.0363826	−	0.0630164i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	9.31412e6	+	1.61325e7i	0.695867	+	1.20528i	0.969888	+	0.243553i	$0.0783131\pi$
$709$	9.31412e6	+	1.61325e7i	0.695867	+	1.20528i	−0.274020	+	0.961724i	$0.588354\pi$
$710$		0			0
$711$	2.18852e6	−	3.79062e6i	0.162359	−	0.281214i
$712$		0			0
$713$	−120367.			−0.00886717
$714$		0			0
$715$	−999131.			−0.0730899
$716$		0			0
$717$	−4.29841e6	+	7.44506e6i	−0.312255	+	0.540842i
$718$		0			0
$719$	9.46227e6	+	1.63891e7i	0.682611	+	1.18232i	0.974181	+	0.225767i	$0.0724889\pi$
$719$	9.46227e6	+	1.63891e7i	0.682611	+	1.18232i	−0.291570	+	0.956549i	$0.594178\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.67251e6	+	2.89688e6i	0.118994	+	0.206103i
$724$		0			0
$725$	−4.95342e6	+	8.57958e6i	−0.349994	+	0.606207i
$726$		0			0
$727$	−1.55979e7			−1.09454			−0.547270	−	0.836956i	$-0.684333\pi$
$727$	−1.55979e7			−1.09454			−0.547270	+	0.836956i	$0.684333\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	1.07884e6	−	1.86861e6i	0.0746731	−	0.129338i
$732$		0			0
$733$	4.27960e6	+	7.41248e6i	0.294200	+	0.509569i	0.974798	−	0.223087i	$-0.0716135\pi$
$733$	4.27960e6	+	7.41248e6i	0.294200	+	0.509569i	−0.680598	+	0.732657i	$0.738280\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−326503.	−	565520.i	−0.0221421	−	0.0383512i
$738$		0			0
$739$	−1.41686e6	+	2.45407e6i	−0.0954367	+	0.165301i	−0.909791	−	0.415067i	$-0.863758\pi$
$739$	−1.41686e6	+	2.45407e6i	−0.0954367	+	0.165301i	0.814354	+	0.580368i	$0.197091\pi$
$740$		0			0
$741$	−3.73969e6			−0.250201
$742$		0			0
$743$	1.04924e7			0.697274			0.348637	−	0.937258i	$-0.386645\pi$
$743$	1.04924e7			0.697274			0.348637	+	0.937258i	$0.386645\pi$
$744$		0			0
$745$	1.48662e6	−	2.57491e6i	0.0981319	−	0.169969i
$746$		0			0
$747$	−492003.	−	852174.i	−0.0322601	−	0.0558762i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−4.33439e6	−	7.50738e6i	−0.280432	−	0.485723i	0.691059	−	0.722798i	$-0.257144\pi$
$751$	−4.33439e6	−	7.50738e6i	−0.280432	−	0.485723i	−0.971491	+	0.237076i	$0.923811\pi$
$752$		0			0
$753$	−3.56289e6	+	6.17111e6i	−0.228989	+	0.396621i
$754$		0			0
$755$	1.89346e6			0.120890
$756$		0			0
$757$	1.08369e7			0.687332			0.343666	−	0.939092i	$-0.388331\pi$
$757$	1.08369e7			0.687332			0.343666	+	0.939092i	$0.388331\pi$
$758$		0			0
$759$	53244.9	−	92222.9i	0.00335486	−	0.00581078i
$760$		0			0
$761$	−199347.	−	345279.i	−0.0124781	−	0.0216127i	0.859719	−	0.510767i	$-0.170639\pi$
$761$	−199347.	−	345279.i	−0.0124781	−	0.0216127i	−0.872197	+	0.489155i	$0.837305\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	857903.	+	1.48593e6i	0.0530011	+	0.0918006i
$766$		0			0
$767$	−1.06323e7	+	1.84156e7i	−0.652586	+	1.13031i
$768$		0			0
$769$	−1.38915e7			−0.847096			−0.423548	−	0.905874i	$-0.639215\pi$
$769$	−1.38915e7			−0.847096			−0.423548	+	0.905874i	$0.639215\pi$
$770$		0			0
$771$	−2.64266e6			−0.160105
$772$		0			0
$773$	−1.13344e7	+	1.96317e7i	−0.682259	+	1.18171i	0.292031	+	0.956409i	$0.405669\pi$
$773$	−1.13344e7	+	1.96317e7i	−0.682259	+	1.18171i	−0.974290	+	0.225298i	$0.927664\pi$
$774$		0			0
$775$	414944.	+	718703.i	0.0248162	+	0.0429829i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.39964e6	+	4.15630e6i	0.141678	+	0.245394i
$780$		0			0
$781$	−546397.	+	946388.i	−0.0320539	+	0.0555190i
$782$		0			0
$783$	−3.85609e6			−0.224772
$784$		0			0
$785$	1.43963e7			0.833827
$786$		0			0
$787$	3.45674e6	−	5.98725e6i	0.198944	−	0.344581i	−0.749242	−	0.662296i	$-0.769582\pi$
$787$	3.45674e6	−	5.98725e6i	0.198944	−	0.344581i	0.948186	+	0.317715i	$0.102916\pi$
$788$		0			0
$789$	−4.49813e6	−	7.79099e6i	−0.257241	−	0.445554i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.21131e6	+	1.07583e7i	0.350752	+	0.607521i
$794$		0			0
$795$	1.13269e6	−	1.96188e6i	0.0635616	−	0.110092i
$796$		0			0
$797$	−1.94035e6			−0.108202			−0.0541009	−	0.998535i	$-0.517229\pi$
$797$	−1.94035e6			−0.108202			−0.0541009	+	0.998535i	$0.517229\pi$
$798$		0			0
$799$	−1.80509e6			−0.100031
$800$		0			0
$801$	3.60632e6	−	6.24633e6i	0.198602	−	0.343989i
$802$		0			0
$803$	250197.	+	433355.i	0.0136929	+	0.0237167i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.47326e6	−	2.55176e6i	−0.0796334	−	0.137929i
$808$		0			0
$809$	1.14954e7	−	1.99107e7i	0.617524	−	1.06958i	−0.372413	−	0.928067i	$-0.621469\pi$
$809$	1.14954e7	−	1.99107e7i	0.617524	−	1.06958i	0.989936	−	0.141515i	$-0.0451973\pi$
$810$		0			0
$811$	−2.57027e7			−1.37223			−0.686116	−	0.727492i	$-0.740686\pi$
$811$	−2.57027e7			−1.37223			−0.686116	+	0.727492i	$0.740686\pi$
$812$		0			0
$813$	−6.79353e6			−0.360470
$814$		0			0
$815$	8.10081e6	−	1.40310e7i	0.427203	−	0.739937i
$816$		0			0
$817$	−1.15516e6	−	2.00079e6i	−0.0605462	−	0.104869i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.38228e6	+	1.27865e7i	0.382237	+	0.662054i	0.991382	−	0.131005i	$-0.0418205\pi$
$821$	7.38228e6	+	1.27865e7i	0.382237	+	0.662054i	−0.609145	+	0.793059i	$0.708487\pi$
$822$		0			0
$823$	−4.75296e6	+	8.23237e6i	−0.244605	+	0.423668i	−0.962020	−	0.272978i	$-0.911992\pi$
$823$	−4.75296e6	+	8.23237e6i	−0.244605	+	0.423668i	0.717416	+	0.696645i	$0.245325\pi$
$824$		0			0
$825$	−734207.			−0.0375564
$826$		0			0
$827$	2.00621e7			1.02003			0.510014	−	0.860166i	$-0.329640\pi$
$827$	2.00621e7			1.02003			0.510014	+	0.860166i	$0.329640\pi$
$828$		0			0
$829$	−9.61268e6	+	1.66496e7i	−0.485801	+	0.841431i	−0.999867	−	0.0163191i	$-0.994805\pi$
$829$	−9.61268e6	+	1.66496e7i	−0.485801	+	0.841431i	0.514066	+	0.857751i	$0.328139\pi$
$830$		0			0
$831$	8.25054e6	+	1.42903e7i	0.414457	+	0.717861i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.71416e6	+	1.50934e7i	0.432523	+	0.749152i
$836$		0			0
$837$	−161510.	+	279744.i	−0.00796869	+	0.0138022i
$838$		0			0
$839$	−1.80768e7			−0.886577			−0.443289	−	0.896379i	$-0.646188\pi$
$839$	−1.80768e7			−0.886577			−0.443289	+	0.896379i	$0.646188\pi$
$840$		0			0
$841$	7.46827e6			0.364108
$842$		0			0
$843$	−3.71892e6	+	6.44137e6i	−0.180239	+	0.312183i
$844$		0			0
$845$	−865827.	−	1.49966e6i	−0.0417147	−	0.0722520i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	3.13307e6	+	5.42663e6i	0.149176	+	0.258381i
$850$		0			0
$851$	−1.20715e6	+	2.09085e6i	−0.0571397	+	0.0989688i
$852$		0			0
$853$	−1.58070e7			−0.743837			−0.371919	−	0.928265i	$-0.621300\pi$
$853$	−1.58070e7			−0.743837			−0.371919	+	0.928265i	$0.621300\pi$
$854$		0			0
$855$	1.83718e6			0.0859483
$856$		0			0
$857$	8.07474e6	−	1.39859e7i	0.375557	−	0.650484i	−0.614853	−	0.788642i	$-0.710785\pi$
$857$	8.07474e6	−	1.39859e7i	0.375557	−	0.650484i	0.990410	+	0.138157i	$0.0441180\pi$
$858$		0			0
$859$	−725533.	−	1.25666e6i	−0.0335486	−	0.0581079i	0.848764	−	0.528772i	$-0.177348\pi$
$859$	−725533.	−	1.25666e6i	−0.0335486	−	0.0581079i	−0.882312	+	0.470665i	$0.844014\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.36797e6	+	1.44937e7i	0.382466	+	0.662451i	0.991414	−	0.130759i	$-0.0417415\pi$
$863$	8.36797e6	+	1.44937e7i	0.382466	+	0.662451i	−0.608948	+	0.793210i	$0.708408\pi$
$864$		0			0
$865$	1.33851e7	−	2.31836e7i	0.608247	−	1.05351i
$866$		0			0
$867$	−9.55340e6			−0.431629
$868$		0			0
$869$	−2.35372e6			−0.105732
$870$		0			0
$871$	4.85927e6	−	8.41651e6i	0.217033	−	0.375912i
$872$		0			0
$873$	1.45043e6	+	2.51221e6i	0.0644110	+	0.111563i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.87055e6	+	1.53642e7i	0.389450	+	0.674547i	0.992376	−	0.123250i	$-0.0393318\pi$
$877$	8.87055e6	+	1.53642e7i	0.389450	+	0.674547i	−0.602926	+	0.797797i	$0.705998\pi$
$878$		0			0
$879$	−7.84264e6	+	1.35838e7i	−0.342365	+	0.592994i
$880$		0			0
$881$	3.78264e6			0.164193			0.0820967	−	0.996624i	$-0.473838\pi$
$881$	3.78264e6			0.164193			0.0820967	+	0.996624i	$0.473838\pi$
$882$		0			0
$883$	−3.93853e7			−1.69993			−0.849967	−	0.526836i	$-0.823378\pi$
$883$	−3.93853e7			−1.69993			−0.849967	+	0.526836i	$0.823378\pi$
$884$		0			0
$885$	5.22328e6	−	9.04698e6i	0.224174	−	0.388280i
$886$		0			0
$887$	3.58923e6	+	6.21673e6i	0.153177	+	0.265310i	0.932394	−	0.361445i	$-0.117716\pi$
$887$	3.58923e6	+	6.21673e6i	0.153177	+	0.265310i	−0.779217	+	0.626754i	$0.784383\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−142889.	−	247492.i	−0.00602984	−	0.0104440i
$892$		0			0
$893$	−966393.	+	1.67384e6i	−0.0405532	+	0.0702402i
$894$		0			0
$895$	2.14382e7			0.894603
$896$		0			0
$897$	1.58486e6			0.0657675
$898$		0			0
$899$	1.17191e6	−	2.02980e6i	0.0483608	−	0.0837633i
$900$		0			0
$901$	−2.12920e6	−	3.68788e6i	−0.0873784	−	0.151344i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.68810e6	+	1.50482e7i	0.352617	+	0.610751i
$906$		0			0
$907$	−1.09739e7	+	1.90074e7i	−0.442938	+	0.767192i	−0.997906	−	0.0646801i	$-0.979397\pi$
$907$	−1.09739e7	+	1.90074e7i	−0.442938	+	0.767192i	0.554968	+	0.831872i	$0.312731\pi$
$908$		0			0
$909$	2.50099e6			0.100393
$910$		0			0
$911$	−2.60249e7			−1.03895			−0.519474	−	0.854486i	$-0.673872\pi$
$911$	−2.60249e7			−1.03895			−0.519474	+	0.854486i	$0.673872\pi$
$912$		0			0
$913$	−264571.	+	458251.i	−0.0105043	+	0.0181939i
$914$		0			0
$915$	−3.05141e6	−	5.28520e6i	−0.120489	−	0.208693i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.09078e7	−	1.88929e7i	−0.426039	−	0.737922i	0.570478	−	0.821313i	$-0.306758\pi$
$919$	−1.09078e7	−	1.88929e7i	−0.426039	−	0.737922i	−0.996517	+	0.0833915i	$0.973425\pi$
$920$		0			0
$921$	1.46664e7	−	2.54029e7i	0.569735	−	0.986810i
$922$		0			0
$923$	−1.62638e7			−0.628374
$924$		0			0
$925$	1.66457e7			0.639657
$926$		0			0
$927$	841594.	−	1.45768e6i	0.0321665	−	0.0557140i
$928$		0			0
$929$	6.23793e6	+	1.08044e7i	0.237138	+	0.410735i	0.959892	−	0.280370i	$-0.0904573\pi$
$929$	6.23793e6	+	1.08044e7i	0.237138	+	0.410735i	−0.722754	+	0.691106i	$0.757124\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	4.69219e6	+	8.12712e6i	0.176470	+	0.305656i
$934$		0			0
$935$	461332.	−	799050.i	0.0172577	−	0.0298913i
$936$		0			0
$937$	3.37205e7			1.25471			0.627357	−	0.778732i	$-0.284137\pi$
$937$	3.37205e7			1.25471			0.627357	+	0.778732i	$0.284137\pi$
$938$		0			0
$939$	1.19785e7			0.443341
$940$		0			0
$941$	−1.24943e7	+	2.16407e7i	−0.459978	+	0.796706i	−0.998959	−	0.0456123i	$-0.985476\pi$
$941$	−1.24943e7	+	2.16407e7i	−0.459978	+	0.796706i	0.538981	+	0.842318i	$0.318809\pi$
$942$		0			0
$943$	−1.01696e6	−	1.76142e6i	−0.0372413	−	0.0645037i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.59082e7	−	2.75539e7i	−0.576430	−	0.998407i	−0.995885	−	0.0906301i	$-0.971112\pi$
$947$	−1.59082e7	−	2.75539e7i	−0.576430	−	0.998407i	0.419454	−	0.907776i	$-0.362221\pi$
$948$		0			0
$949$	−3.72363e6	+	6.44952e6i	−0.134215	+	0.232467i
$950$		0			0
$951$	2.80779e6			0.100673
$952$		0			0
$953$	−3.79217e6			−0.135256			−0.0676279	−	0.997711i	$-0.521543\pi$
$953$	−3.79217e6			−0.135256			−0.0676279	+	0.997711i	$0.521543\pi$
$954$		0			0
$955$	7.61478e6	−	1.31892e7i	0.270177	−	0.467961i
$956$		0			0
$957$	1.03679e6	+	1.79578e6i	0.0365942	+	0.0633830i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.42164e7	+	2.46235e7i	0.496571	+	0.860086i
$962$		0			0
$963$	4.43864e6	−	7.68795e6i	0.154236	−	0.267144i
$964$		0			0
$965$	1.13413e6			0.0392052
$966$		0			0
$967$	2.32765e7			0.800482			0.400241	−	0.916410i	$-0.368926\pi$
$967$	2.32765e7			0.800482			0.400241	+	0.916410i	$0.368926\pi$
$968$		0			0
$969$	1.72674e6	−	2.99080e6i	0.0590768	−	0.102324i
$970$		0			0
$971$	−1.33082e7	−	2.30505e7i	−0.452973	−	0.784572i	0.545596	−	0.838048i	$-0.316303\pi$
$971$	−1.33082e7	−	2.30505e7i	−0.452973	−	0.784572i	−0.998569	+	0.0534761i	$0.982970\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5.46352e6	−	9.46309e6i	−0.184061	−	0.318802i
$976$		0			0
$977$	7.75064e6	−	1.34245e7i	0.259777	−	0.449948i	−0.706405	−	0.707808i	$-0.749684\pi$
$977$	7.75064e6	−	1.34245e7i	0.259777	−	0.449948i	0.966182	+	0.257860i	$0.0830175\pi$
$978$		0			0
$979$	−3.87855e6			−0.129334
$980$		0			0
$981$	1.54586e7			0.512857
$982$		0			0
$983$	2.30518e7	−	3.99269e7i	0.760889	−	1.31790i	−0.181504	−	0.983390i	$-0.558097\pi$
$983$	2.30518e7	−	3.99269e7i	0.760889	−	1.31790i	0.942393	−	0.334508i	$-0.108570\pi$
$984$		0			0
$985$	−5.01097e6	−	8.67925e6i	−0.164563	−	0.285031i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	489552.	+	847929.i	0.0159150	+	0.0275657i
$990$		0			0
$991$	−9.11404e6	+	1.57860e7i	−0.294799	+	0.510608i	−0.974938	−	0.222476i	$-0.928586\pi$
$991$	−9.11404e6	+	1.57860e7i	−0.294799	+	0.510608i	0.680139	+	0.733083i	$0.261920\pi$
$992$		0			0
$993$	2.31918e7			0.746384
$994$		0			0
$995$	−1.87027e7			−0.598889
$996$		0			0
$997$	4.37420e6	−	7.57634e6i	0.139367	−	0.241391i	−0.787890	−	0.615816i	$-0.788826\pi$
$997$	4.37420e6	−	7.57634e6i	0.139367	−	0.241391i	0.927257	+	0.374425i	$0.122160\pi$
$998$		0			0
$999$	3.23954e6	+	5.61105e6i	0.102700	+	0.177881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.6.i.p.361.1		8
7.2	even	3	inner	588.6.i.p.373.1		8
7.3	odd	6		588.6.a.m.1.1	✓	4
7.4	even	3		588.6.a.o.1.4	yes	4
7.5	odd	6		588.6.i.q.373.4		8
7.6	odd	2		588.6.i.q.361.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.6.a.m.1.1	✓	4	7.3	odd	6
588.6.a.o.1.4	yes	4	7.4	even	3
588.6.i.p.361.1		8	1.1	even	1	trivial
588.6.i.p.373.1		8	7.2	even	3	inner
588.6.i.q.361.4		8	7.6	odd	2
588.6.i.q.373.4		8	7.5	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	588.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 + 7.79423i) q^{3} +(-17.6925 - 30.6443i) q^{5} +(-40.5000 - 70.1481i) q^{9} +(-21.7786 + 37.7216i) q^{11} -648.252 q^{13} +318.465 q^{15} +(299.319 - 518.436i) q^{17} +(-320.493 - 555.111i) q^{19} +(135.824 + 235.254i) q^{23} +(936.453 - 1621.98i) q^{25} +729.000 q^{27} -5289.56 q^{29} +(-221.551 + 383.737i) q^{31} +(-196.007 - 339.495i) q^{33} +(4443.81 + 7696.91i) q^{37} +(2917.13 - 5052.62i) q^{39} -7487.34 q^{41} +3604.32 q^{43} +(-1433.09 + 2482.19i) q^{45} +(-1507.67 - 2611.35i) q^{47} +(2693.87 + 4665.93i) q^{51} +(3556.73 - 6160.44i) q^{53} +1541.27 q^{55} +5768.88 q^{57} +(16401.4 - 28408.1i) q^{59} +(-9581.63 - 16595.9i) q^{61} +(11469.2 + 19865.2i) q^{65} +(-7495.96 + 12983.4i) q^{67} -2444.83 q^{69} +25088.7 q^{71} +(5744.11 - 9949.10i) q^{73} +(8428.07 + 14597.9i) q^{75} +(27018.7 + 46797.8i) q^{79} +(-3280.50 + 5681.99i) q^{81} +12148.2 q^{83} -21182.8 q^{85} +(23803.0 - 41228.0i) q^{87} +(44522.5 + 77115.2i) q^{89} +(-1993.96 - 3453.63i) q^{93} +(-11340.6 + 19642.6i) q^{95} -35813.0 q^{97} +3528.13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{3} - 324 q^{9} + 1872 q^{17} + 1728 q^{19} + 3648 q^{23} + 3996 q^{25} + 5832 q^{27} - 2496 q^{29} + 3888 q^{31} + 12032 q^{37} + 18144 q^{41} - 4256 q^{43} + 19872 q^{47} + 16848 q^{51} + 22248 q^{53}+ \cdots - 641088 q^{97}+O(q^{100}) \) 8 * q - 36 * q^3 - 324 * q^9 + 1872 * q^17 + 1728 * q^19 + 3648 * q^23 + 3996 * q^25 + 5832 * q^27 - 2496 * q^29 + 3888 * q^31 + 12032 * q^37 + 18144 * q^41 - 4256 * q^43 + 19872 * q^47 + 16848 * q^51 + 22248 * q^53 - 42336 * q^55 - 31104 * q^57 - 5040 * q^59 + 8640 * q^61 + 83880 * q^65 + 86160 * q^67 - 65664 * q^69 - 13440 * q^71 + 18144 * q^73 + 35964 * q^75 + 19648 * q^79 - 26244 * q^81 - 525024 * q^83 + 40336 * q^85 + 11232 * q^87 + 49680 * q^89 + 34992 * q^93 - 112032 * q^95 - 641088 * q^97

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