LMFDB - Embedded newform 304.6.i.d.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,6,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, 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("304.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	304.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:	$48.7566812231$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 3057 x^{16} + 14564 x^{15} + 3829838 x^{14} - 15907074 x^{13} + \cdots + 66\!\cdots\!83 $ x^18 - 5x^17 - 3057x^16 + 14564x^15 + 3829838x^14 - 15907074x^13 - 2546775754x^12 + 7879525640x^11 + 976140188391x^10 - 1502012839499x^9 - 219575028272723x^8 - 104014033904304x^7 + 28115925509664606x^6 + 76771209356887914x^5 - 1810997176122162810x^4 - 9301294316540690604x^3 + 37701980111568799233x^2 + 354684213311311368351*x + 668276771042404734183
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.7
Root			$-12.0901 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	304.49
Dual form			304.6.i.d.273.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.79505 - 11.7694i) q^{3} +(-47.4871 + 82.2500i) q^{5} -189.860 q^{7} +(29.1546 + 50.4972i) q^{9} +O(q^{10})$	\(q+(6.79505 - 11.7694i) q^{3} +(-47.4871 + 82.2500i) q^{5} -189.860 q^{7} +(29.1546 + 50.4972i) q^{9} +530.005 q^{11} +(-353.895 - 612.964i) q^{13} +(645.354 + 1117.79i) q^{15} +(-764.589 + 1324.31i) q^{17} +(-654.031 + 1431.20i) q^{19} +(-1290.11 + 2234.53i) q^{21} +(-497.425 - 861.565i) q^{23} +(-2947.54 - 5105.29i) q^{25} +4094.82 q^{27} +(-1290.66 - 2235.49i) q^{29} +2790.81 q^{31} +(3601.41 - 6237.82i) q^{33} +(9015.88 - 15616.0i) q^{35} +7238.14 q^{37} -9618.94 q^{39} +(2181.63 - 3778.69i) q^{41} +(3121.70 - 5406.94i) q^{43} -5537.86 q^{45} +(-12320.9 - 21340.4i) q^{47} +19239.7 q^{49} +(10390.8 + 17997.5i) q^{51} +(-15497.6 - 26842.6i) q^{53} +(-25168.4 + 43592.9i) q^{55} +(12400.2 + 17422.6i) q^{57} +(18177.7 - 31484.8i) q^{59} +(2886.93 + 5000.30i) q^{61} +(-5535.27 - 9587.38i) q^{63} +67221.7 q^{65} +(-30388.4 - 52634.2i) q^{67} -13520.1 q^{69} +(-14829.0 + 25684.5i) q^{71} +(-39002.3 + 67553.9i) q^{73} -80114.7 q^{75} -100627. q^{77} +(33427.5 - 57898.2i) q^{79} +(20740.0 - 35922.7i) q^{81} +21919.5 q^{83} +(-72616.2 - 125775. i) q^{85} -35080.4 q^{87} +(-45374.8 - 78591.5i) q^{89} +(67190.4 + 116377. i) q^{91} +(18963.7 - 32846.0i) q^{93} +(-86658.4 - 121758. i) q^{95} +(-30757.3 + 53273.1i) q^{97} +(15452.1 + 26763.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 11 q^{3} + 11 q^{5} - 336 q^{7} - 902 q^{9}+O(q^{10}) $ 18 * q + 11 * q^3 + 11 * q^5 - 336 * q^7 - 902 * q^9	$ 18 q + 11 q^{3} + 11 q^{5} - 336 q^{7} - 902 q^{9} + 320 q^{11} + 227 q^{13} + 101 q^{15} + 179 q^{17} + 868 q^{19} - 5700 q^{21} + 3425 q^{23} - 7054 q^{25} - 14722 q^{27} - 7349 q^{29} + 9960 q^{31} - 2998 q^{33} - 15888 q^{35} + 26444 q^{37} + 30246 q^{39} - 7311 q^{41} + 8283 q^{43} - 62164 q^{45} - 37603 q^{47} + 124738 q^{49} - 47227 q^{51} - 20337 q^{53} - 716 q^{55} - 57555 q^{57} + 74455 q^{59} - 7569 q^{61} + 52544 q^{63} + 188998 q^{65} + 26177 q^{67} + 116282 q^{69} + 53463 q^{71} - 14103 q^{73} - 120912 q^{75} - 31960 q^{77} - 31825 q^{79} - 21137 q^{81} - 82600 q^{83} - 50787 q^{85} + 339766 q^{87} - 155197 q^{89} + 2800 q^{91} - 46460 q^{93} - 49315 q^{95} + 111241 q^{97} + 193544 q^{99}+O(q^{100}) $ 18 * q + 11 * q^3 + 11 * q^5 - 336 * q^7 - 902 * q^9 + 320 * q^11 + 227 * q^13 + 101 * q^15 + 179 * q^17 + 868 * q^19 - 5700 * q^21 + 3425 * q^23 - 7054 * q^25 - 14722 * q^27 - 7349 * q^29 + 9960 * q^31 - 2998 * q^33 - 15888 * q^35 + 26444 * q^37 + 30246 * q^39 - 7311 * q^41 + 8283 * q^43 - 62164 * q^45 - 37603 * q^47 + 124738 * q^49 - 47227 * q^51 - 20337 * q^53 - 716 * q^55 - 57555 * q^57 + 74455 * q^59 - 7569 * q^61 + 52544 * q^63 + 188998 * q^65 + 26177 * q^67 + 116282 * q^69 + 53463 * q^71 - 14103 * q^73 - 120912 * q^75 - 31960 * q^77 - 31825 * q^79 - 21137 * q^81 - 82600 * q^83 - 50787 * q^85 + 339766 * q^87 - 155197 * q^89 + 2800 * q^91 - 46460 * q^93 - 49315 * q^95 + 111241 * q^97 + 193544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	6.79505	−	11.7694i	0.435903	−	0.755006i	−0.561466	−	0.827500i	$-0.689762\pi$
$3$	6.79505	−	11.7694i	0.435903	−	0.755006i	0.997369	+	0.0724940i	$0.0230958\pi$
$4$		0			0
$5$	−47.4871	+	82.2500i	−0.849474	+	1.47133i	0.0322040	+	0.999481i	$0.489747\pi$
$5$	−47.4871	+	82.2500i	−0.849474	+	1.47133i	−0.881678	+	0.471851i	$0.843586\pi$
$6$		0			0
$7$	−189.860			−1.46449			−0.732247	−	0.681039i	$-0.761528\pi$
$7$	−189.860			−1.46449			−0.732247	+	0.681039i	$0.761528\pi$
$8$		0			0
$9$	29.1546	+	50.4972i	0.119978	+	0.207807i
$10$		0			0
$11$	530.005			1.32068			0.660341	−	0.750966i	$-0.270412\pi$
$11$	530.005			1.32068			0.660341	+	0.750966i	$0.270412\pi$
$12$		0			0
$13$	−353.895	−	612.964i	−0.580786	−	1.00595i	−0.995386	−	0.0959473i	$-0.969412\pi$
$13$	−353.895	−	612.964i	−0.580786	−	1.00595i	0.414600	−	0.910004i	$-0.363921\pi$
$14$		0			0
$15$	645.354	+	1117.79i	0.740576	+	1.28272i
$16$		0			0
$17$	−764.589	+	1324.31i	−0.641661	+	1.11139i	0.343401	+	0.939189i	$0.388421\pi$
$17$	−764.589	+	1324.31i	−0.641661	+	1.11139i	−0.985062	+	0.172201i	$0.944912\pi$
$18$		0			0
$19$	−654.031	+	1431.20i	−0.415637	+	0.909530i
$19$	−654.031	+	1431.20i	−0.415637	+	0.909530i
$20$		0			0
$21$	−1290.11	+	2234.53i	−0.638377	+	1.10570i
$22$		0			0
$23$	−497.425	−	861.565i	−0.196068	−	0.339600i	0.751182	−	0.660095i	$-0.229484\pi$
$23$	−497.425	−	861.565i	−0.196068	−	0.339600i	−0.947250	+	0.320495i	$0.896151\pi$
$24$		0			0
$25$	−2947.54	−	5105.29i	−0.943213	−	1.63369i
$26$		0			0
$27$	4094.82			1.08100
$28$		0			0
$29$	−1290.66	−	2235.49i	−0.284982	−	0.493603i	0.687623	−	0.726068i	$-0.258654\pi$
$29$	−1290.66	−	2235.49i	−0.284982	−	0.493603i	−0.972605	+	0.232465i	$0.925321\pi$
$30$		0			0
$31$	2790.81			0.521585			0.260793	−	0.965395i	$-0.416016\pi$
$31$	2790.81			0.521585			0.260793	+	0.965395i	$0.416016\pi$
$32$		0			0
$33$	3601.41	−	6237.82i	0.575689	−	0.997122i
$34$		0			0
$35$	9015.88	−	15616.0i	1.24405	−	2.15476i
$36$		0			0
$37$	7238.14			0.869206			0.434603	−	0.900622i	$-0.356889\pi$
$37$	7238.14			0.869206			0.434603	+	0.900622i	$0.356889\pi$
$38$		0			0
$39$	−9618.94			−1.01266
$40$		0			0
$41$	2181.63	−	3778.69i	0.202685	−	0.351060i	−0.746708	−	0.665152i	$-0.768367\pi$
$41$	2181.63	−	3778.69i	0.202685	−	0.351060i	0.949393	+	0.314092i	$0.101700\pi$
$42$		0			0
$43$	3121.70	−	5406.94i	0.257466	−	0.445944i	−0.708096	−	0.706116i	$-0.750446\pi$
$43$	3121.70	−	5406.94i	0.257466	−	0.445944i	0.965562	+	0.260172i	$0.0837791\pi$
$44$		0			0
$45$	−5537.86			−0.407671
$46$		0			0
$47$	−12320.9	−	21340.4i	−0.813576	−	1.40915i	−0.910346	−	0.413848i	$-0.864185\pi$
$47$	−12320.9	−	21340.4i	−0.813576	−	1.40915i	0.0967705	−	0.995307i	$-0.469149\pi$
$48$		0			0
$49$	19239.7			1.14474
$50$		0			0
$51$	10390.8	+	17997.5i	0.559404	+	0.968916i
$52$		0			0
$53$	−15497.6	−	26842.6i	−0.757833	−	1.31261i	−0.943953	−	0.330079i	$-0.892925\pi$
$53$	−15497.6	−	26842.6i	−0.757833	−	1.31261i	0.186120	−	0.982527i	$-0.440409\pi$
$54$		0			0
$55$	−25168.4	+	43592.9i	−1.12188	+	1.94316i
$56$		0			0
$57$	12400.2	+	17422.6i	0.505523	+	0.710275i
$58$		0			0
$59$	18177.7	−	31484.8i	0.679845	−	1.17753i	−0.295182	−	0.955441i	$-0.595380\pi$
$59$	18177.7	−	31484.8i	0.679845	−	1.17753i	0.975027	−	0.222085i	$-0.0712863\pi$
$60$		0			0
$61$	2886.93	+	5000.30i	0.0993370	+	0.172057i	0.911410	−	0.411499i	$-0.134994\pi$
$61$	2886.93	+	5000.30i	0.0993370	+	0.172057i	−0.812073	+	0.583555i	$0.801661\pi$
$62$		0			0
$63$	−5535.27	−	9587.38i	−0.175706	−	0.304333i
$64$		0			0
$65$	67221.7			1.97345
$66$		0			0
$67$	−30388.4	−	52634.2i	−0.827029	−	1.43246i	−0.900359	−	0.435148i	$-0.856696\pi$
$67$	−30388.4	−	52634.2i	−0.827029	−	1.43246i	0.0733301	−	0.997308i	$-0.476637\pi$
$68$		0			0
$69$	−13520.1			−0.341867
$70$		0			0
$71$	−14829.0	+	25684.5i	−0.349112	+	0.604680i	−0.986092	−	0.166201i	$-0.946850\pi$
$71$	−14829.0	+	25684.5i	−0.349112	+	0.604680i	0.636980	+	0.770880i	$0.280183\pi$
$72$		0			0
$73$	−39002.3	+	67553.9i	−0.856609	+	1.48369i	0.0185353	+	0.999828i	$0.494100\pi$
$73$	−39002.3	+	67553.9i	−0.856609	+	1.48369i	−0.875144	+	0.483862i	$0.839234\pi$
$74$		0			0
$75$	−80114.7			−1.64460
$76$		0			0
$77$	−100627.			−1.93413
$78$		0			0
$79$	33427.5	−	57898.2i	0.602611	−	1.04375i	−0.389814	−	0.920894i	$-0.627461\pi$
$79$	33427.5	−	57898.2i	0.602611	−	1.04375i	0.992424	−	0.122858i	$-0.0392061\pi$
$80$		0			0
$81$	20740.0	−	35922.7i	0.351233	−	0.608354i
$82$		0			0
$83$	21919.5			0.349250			0.174625	−	0.984635i	$-0.444129\pi$
$83$	21919.5			0.349250			0.174625	+	0.984635i	$0.444129\pi$
$84$		0			0
$85$	−72616.2	−	125775.i	−1.09015	−	1.88819i
$86$		0			0
$87$	−35080.4			−0.496898
$88$		0			0
$89$	−45374.8	−	78591.5i	−0.607211	−	1.05172i	−0.991698	−	0.128590i	$-0.958955\pi$
$89$	−45374.8	−	78591.5i	−0.607211	−	1.05172i	0.384487	−	0.923131i	$-0.374378\pi$
$90$		0			0
$91$	67190.4	+	116377.i	0.850558	+	1.47321i
$92$		0			0
$93$	18963.7	−	32846.0i	0.227360	−	0.393800i
$94$		0			0
$95$	−86658.4	−	121758.i	−0.985149	−	1.38416i
$96$		0			0
$97$	−30757.3	+	53273.1i	−0.331908	+	0.574882i	−0.982886	−	0.184215i	$-0.941026\pi$
$97$	−30757.3	+	53273.1i	−0.331908	+	0.574882i	0.650978	+	0.759097i	$0.274359\pi$
$98$		0			0
$99$	15452.1	+	26763.7i	0.158452	+	0.274447i
$100$		0			0
$101$	5882.91	+	10189.5i	0.0573837	+	0.0993915i	0.893290	−	0.449480i	$-0.148391\pi$
$101$	5882.91	+	10189.5i	0.0573837	+	0.0993915i	−0.835906	+	0.548872i	$0.815057\pi$
$102$		0			0
$103$	57682.4			0.535735			0.267868	−	0.963456i	$-0.413681\pi$
$103$	57682.4			0.535735			0.267868	+	0.963456i	$0.413681\pi$
$104$		0			0
$105$	−122527.	−	212222.i	−1.08457	−	1.87853i
$106$		0			0
$107$	79892.9			0.674604			0.337302	−	0.941397i	$-0.390486\pi$
$107$	79892.9			0.674604			0.337302	+	0.941397i	$0.390486\pi$
$108$		0			0
$109$	−98323.4	+	170301.i	−0.792667	+	1.37294i	0.131643	+	0.991297i	$0.457975\pi$
$109$	−98323.4	+	170301.i	−0.792667	+	1.37294i	−0.924310	+	0.381642i	$0.875359\pi$
$110$		0			0
$111$	49183.5	−	85188.4i	0.378889	−	0.656255i
$112$		0			0
$113$	205714.			1.51554			0.757770	−	0.652521i	$-0.226289\pi$
$113$	205714.			1.51554			0.757770	+	0.652521i	$0.226289\pi$
$114$		0			0
$115$	94484.9			0.666220
$116$		0			0
$117$	20635.3	−	35741.4i	0.139363	−	0.241383i
$118$		0			0
$119$	145165.	−	251433.i	0.939709	−	1.62762i
$120$		0			0
$121$	119854.			0.744199
$122$		0			0
$123$	−29648.6	−	51352.8i	−0.176702	−	0.306056i
$124$		0			0
$125$	263086.			1.50599
$126$		0			0
$127$	143.620	+	248.756i	0.000790141	+	0.00136856i	0.866420	−	0.499316i	$-0.166415\pi$
$127$	143.620	+	248.756i	0.000790141	+	0.00136856i	−0.865630	+	0.500684i	$0.833082\pi$
$128$		0			0
$129$	−42424.2	−	73480.9i	−0.224460	−	0.388777i
$130$		0			0
$131$	21086.6	−	36523.1i	0.107357	−	0.185947i	−0.807342	−	0.590084i	$-0.799095\pi$
$131$	21086.6	−	36523.1i	0.107357	−	0.185947i	0.914699	+	0.404137i	$0.132428\pi$
$132$		0			0
$133$	124174.	−	271728.i	0.608698	−	1.33200i
$134$		0			0
$135$	−194451.	+	336799.i	−0.918281	+	1.59051i
$136$		0			0
$137$	−52318.5	−	90618.2i	−0.238152	−	0.412491i	0.722032	−	0.691859i	$-0.243208\pi$
$137$	−52318.5	−	90618.2i	−0.238152	−	0.412491i	−0.960184	+	0.279369i	$0.909875\pi$
$138$		0			0
$139$	−64404.7	−	111552.i	−0.282736	−	0.489713i	0.689322	−	0.724455i	$-0.257909\pi$
$139$	−64404.7	−	111552.i	−0.282736	−	0.489713i	−0.972058	+	0.234743i	$0.924575\pi$
$140$		0			0
$141$	−334885.			−1.41856
$142$		0			0
$143$	−187566.	−	324874.i	−0.767033	−	1.32854i
$144$		0			0
$145$	245159.			0.968339
$146$		0			0
$147$	130735.	−	226439.i	0.498997	−	0.864288i
$148$		0			0
$149$	−136506.	+	236435.i	−0.503716	+	0.872462i	0.496275	+	0.868165i	$0.334701\pi$
$149$	−136506.	+	236435.i	−0.503716	+	0.872462i	−0.999991	+	0.00429614i	$0.998632\pi$
$150$		0			0
$151$	−68761.9			−0.245418			−0.122709	−	0.992443i	$-0.539158\pi$
$151$	−68761.9			−0.245418			−0.122709	+	0.992443i	$0.539158\pi$
$152$		0			0
$153$	−89165.0			−0.307940
$154$		0			0
$155$	−132527.	+	229544.i	−0.443073	+	0.767425i
$156$		0			0
$157$	275998.	−	478042.i	0.893628	−	1.54781i	0.0581337	−	0.998309i	$-0.481485\pi$
$157$	275998.	−	478042.i	0.893628	−	1.54781i	0.835494	−	0.549500i	$-0.185182\pi$
$158$		0			0
$159$	−421227.			−1.32137
$160$		0			0
$161$	94440.9	+	163576.i	0.287141	+	0.497343i
$162$		0			0
$163$	153395.			0.452211			0.226106	−	0.974103i	$-0.427401\pi$
$163$	153395.			0.452211			0.226106	+	0.974103i	$0.427401\pi$
$164$		0			0
$165$	342041.	+	592432.i	0.978065	+	1.69406i
$166$		0			0
$167$	−146626.	−	253963.i	−0.406836	−	0.704660i	0.587697	−	0.809081i	$-0.300035\pi$
$167$	−146626.	−	253963.i	−0.406836	−	0.704660i	−0.994533	+	0.104421i	$0.966701\pi$
$168$		0			0
$169$	−64836.9	+	112301.i	−0.174625	+	0.302459i
$170$		0			0
$171$	−91339.7	+	8699.36i	−0.238874	+	0.0227508i
$172$		0			0
$173$	−114249.	+	197885.i	−0.290227	+	0.502688i	−0.973863	−	0.227135i	$-0.927064\pi$
$173$	−114249.	+	197885.i	−0.290227	+	0.502688i	0.683636	+	0.729823i	$0.260398\pi$
$174$		0			0
$175$	559619.	+	969289.i	1.38133	+	2.39253i
$176$		0			0
$177$	−247037.	−	427881.i	−0.592693	−	1.02657i
$178$		0			0
$179$	−247143.			−0.576521			−0.288261	−	0.957552i	$-0.593077\pi$
$179$	−247143.			−0.576521			−0.288261	+	0.957552i	$0.593077\pi$
$180$		0			0
$181$	353864.	+	612910.i	0.802859	+	1.39059i	0.917727	+	0.397213i	$0.130022\pi$
$181$	353864.	+	612910.i	0.802859	+	1.39059i	−0.114867	+	0.993381i	$0.536644\pi$
$182$		0			0
$183$	78467.2			0.173205
$184$		0			0
$185$	−343718.	+	595337.i	−0.738368	+	1.27889i
$186$		0			0
$187$	−405236.	+	701889.i	−0.847430	+	1.46779i
$188$		0			0
$189$	−777442.			−1.58312
$190$		0			0
$191$	−10502.1			−0.0208301			−0.0104151	−	0.999946i	$-0.503315\pi$
$191$	−10502.1			−0.0208301			−0.0104151	+	0.999946i	$0.503315\pi$
$192$		0			0
$193$	496794.	−	860472.i	0.960025	−	1.66281i	0.237601	−	0.971363i	$-0.423639\pi$
$193$	496794.	−	860472.i	0.960025	−	1.66281i	0.722424	−	0.691450i	$-0.243028\pi$
$194$		0			0
$195$	456775.	−	791158.i	0.860233	−	1.48997i
$196$		0			0
$197$	−185300.			−0.340182			−0.170091	−	0.985428i	$-0.554406\pi$
$197$	−185300.			−0.340182			−0.170091	+	0.985428i	$0.554406\pi$
$198$		0			0
$199$	−43149.9	−	74737.8i	−0.0772408	−	0.133785i	0.824818	−	0.565399i	$-0.191278\pi$
$199$	−43149.9	−	74737.8i	−0.0772408	−	0.133785i	−0.902059	+	0.431614i	$0.857944\pi$
$200$		0			0
$201$	−825963.			−1.44202
$202$		0			0
$203$	245045.	+	424430.i	0.417354	+	0.722879i
$204$		0			0
$205$	207198.	+	358878.i	0.344351	+	0.596433i
$206$		0			0
$207$	29004.4	−	50237.1i	0.0470476	−	0.0814889i
$208$		0			0
$209$	−346640.	+	758544.i	−0.548924	+	1.20120i
$210$		0			0
$211$	−151234.	+	261945.i	−0.233853	+	0.405045i	−0.958939	−	0.283613i	$-0.908467\pi$
$211$	−151234.	+	261945.i	−0.233853	+	0.405045i	0.725086	+	0.688659i	$0.241800\pi$
$212$		0			0
$213$	201527.	+	349055.i	0.304358	+	0.527163i
$214$		0			0
$215$	296481.	+	513519.i	0.437422	+	0.757636i
$216$		0			0
$217$	−529861.			−0.763858
$218$		0			0
$219$	530045.	+	918064.i	0.746796	+	1.29349i
$220$		0			0
$221$	1.08234e6			1.49067
$222$		0			0
$223$	339486.	−	588007.i	0.457151	−	0.791809i	−0.541658	−	0.840599i	$-0.682203\pi$
$223$	339486.	−	588007.i	0.457151	−	0.791809i	0.998809	+	0.0487901i	$0.0155365\pi$
$224$		0			0
$225$	171868.	−	297685.i	0.226329	−	0.392013i
$226$		0			0
$227$	−231581.			−0.298289			−0.149145	−	0.988815i	$-0.547652\pi$
$227$	−231581.			−0.298289			−0.149145	+	0.988815i	$0.547652\pi$
$228$		0			0
$229$	33377.9			0.0420601			0.0210300	−	0.999779i	$-0.493305\pi$
$229$	33377.9			0.0420601			0.0210300	+	0.999779i	$0.493305\pi$
$230$		0			0
$231$	−683762.	+	1.18431e6i	−0.843093	+	1.46028i
$232$		0			0
$233$	542190.	−	939100.i	0.654277	−	1.13324i	−0.327798	−	0.944748i	$-0.606306\pi$
$233$	542190.	−	939100.i	0.654277	−	1.13324i	0.982075	−	0.188493i	$-0.0603602\pi$
$234$		0			0
$235$	2.34033e6			2.76445
$236$		0			0
$237$	−454284.	−	786843.i	−0.525359	−	0.909949i
$238$		0			0
$239$	284041.			0.321652			0.160826	−	0.986983i	$-0.448584\pi$
$239$	284041.			0.321652			0.160826	+	0.986983i	$0.448584\pi$
$240$		0			0
$241$	306804.	+	531400.i	0.340266	+	0.589357i	0.984482	−	0.175486i	$-0.0561497\pi$
$241$	306804.	+	531400.i	0.340266	+	0.589357i	−0.644216	+	0.764843i	$0.722816\pi$
$242$		0			0
$243$	215663.	+	373539.i	0.234293	+	0.405807i
$244$		0			0
$245$	−913637.	+	1.58246e6i	−0.972430	+	1.68430i
$246$		0			0
$247$	1.10873e6	−	105598.i	1.15634	−	0.110132i
$248$		0			0
$249$	148944.	−	257979.i	0.152239	−	0.263685i
$250$		0			0
$251$	−369089.	−	639282.i	−0.369783	−	0.640484i	0.619748	−	0.784801i	$-0.287235\pi$
$251$	−369089.	−	639282.i	−0.369783	−	0.640484i	−0.989531	+	0.144317i	$0.953901\pi$
$252$		0			0
$253$	−263637.	−	456633.i	−0.258944	−	0.448504i
$254$		0			0
$255$	−1.97372e6			−1.90080
$256$		0			0
$257$	686359.	+	1.18881e6i	0.648214	+	1.12274i	0.983549	+	0.180641i	$0.0578172\pi$
$257$	686359.	+	1.18881e6i	0.648214	+	1.12274i	−0.335335	+	0.942099i	$0.608849\pi$
$258$		0			0
$259$	−1.37423e6			−1.27295
$260$		0			0
$261$	75257.3	−	130349.i	0.0683829	−	0.118443i
$262$		0			0
$263$	146329.	−	253449.i	0.130449	−	0.225944i	−0.793401	−	0.608699i	$-0.791692\pi$
$263$	146329.	−	253449.i	0.130449	−	0.225944i	0.923850	+	0.382756i	$0.125025\pi$
$264$		0			0
$265$	2.94373e6			2.57504
$266$		0			0
$267$	−1.23330e6			−1.05874
$268$		0			0
$269$	−977718.	+	1.69346e6i	−0.823821	+	1.42690i	0.0789962	+	0.996875i	$0.474828\pi$
$269$	−977718.	+	1.69346e6i	−0.823821	+	1.42690i	−0.902817	+	0.430025i	$0.858505\pi$
$270$		0			0
$271$	713502.	−	1.23582e6i	0.590163	−	1.02219i	−0.404047	−	0.914738i	$-0.632397\pi$
$271$	713502.	−	1.23582e6i	0.590163	−	1.02219i	0.994210	−	0.107454i	$-0.0342698\pi$
$272$		0			0
$273$	1.82625e6			1.48304
$274$		0			0
$275$	−1.56221e6	−	2.70583e6i	−1.24568	−	2.15759i
$276$		0			0
$277$	−1.20887e6			−0.946629			−0.473315	−	0.880893i	$-0.656943\pi$
$277$	−1.20887e6			−0.946629			−0.473315	+	0.880893i	$0.656943\pi$
$278$		0			0
$279$	81364.7	+	140928.i	0.0625785	+	0.108389i
$280$		0			0
$281$	−996432.	−	1.72587e6i	−0.752804	−	1.30389i	−0.946459	−	0.322825i	$-0.895367\pi$
$281$	−996432.	−	1.72587e6i	−0.752804	−	1.30389i	0.193655	−	0.981070i	$-0.437966\pi$
$282$		0			0
$283$	−33435.3	+	57911.6i	−0.0248164	+	0.0429832i	−0.878167	−	0.478354i	$-0.841233\pi$
$283$	−33435.3	+	57911.6i	−0.0248164	+	0.0429832i	0.853350	+	0.521338i	$0.174567\pi$
$284$		0			0
$285$	−2.02186e6	+	192566.i	−1.47448	+	0.140432i
$286$		0			0
$287$	−414203.	+	717421.i	−0.296831	+	0.514126i
$288$		0			0
$289$	−459264.	−	795469.i	−0.323458	−	0.560246i
$290$		0			0
$291$	417994.	+	723987.i	0.289360	+	0.501185i
$292$		0			0
$293$	1.98637e6			1.35173			0.675866	−	0.737025i	$-0.263770\pi$
$293$	1.98637e6			1.35173			0.675866	+	0.737025i	$0.263770\pi$
$294$		0			0
$295$	1.72641e6	+	2.99024e6i	1.15502	+	2.00056i
$296$		0			0
$297$	2.17027e6			1.42766
$298$		0			0
$299$	−352072.	+	609807.i	−0.227748	+	0.394470i
$300$		0			0
$301$	−592685.	+	1.02656e6i	−0.377058	+	0.653083i
$302$		0			0
$303$	159899.			0.100055
$304$		0			0
$305$	−548366.			−0.337537
$306$		0			0
$307$	−932152.	+	1.61454e6i	−0.564470	+	0.977691i	0.432629	+	0.901572i	$0.357586\pi$
$307$	−932152.	+	1.61454e6i	−0.564470	+	0.977691i	−0.997099	+	0.0761187i	$0.975747\pi$
$308$		0			0
$309$	391955.	−	678886.i	0.233528	−	0.404483i
$310$		0			0
$311$	−1.73570e6			−1.01759			−0.508796	−	0.860887i	$-0.669909\pi$
$311$	−1.73570e6			−1.01759			−0.508796	+	0.860887i	$0.669909\pi$
$312$		0			0
$313$	26566.2	+	46014.0i	0.0153274	+	0.0265478i	0.873587	−	0.486667i	$-0.161788\pi$
$313$	26566.2	+	46014.0i	0.0153274	+	0.0265478i	−0.858260	+	0.513215i	$0.828454\pi$
$314$		0			0
$315$	1.05142e6			0.597032
$316$		0			0
$317$	−690554.	−	1.19607e6i	−0.385966	−	0.668514i	0.605936	−	0.795513i	$-0.292799\pi$
$317$	−690554.	−	1.19607e6i	−0.385966	−	0.668514i	−0.991903	+	0.127000i	$0.959465\pi$
$318$		0			0
$319$	−684056.	−	1.18482e6i	−0.376370	−	0.651892i
$320$		0			0
$321$	542876.	−	940289.i	0.294062	−	0.509330i
$322$		0			0
$323$	−1.39529e6	−	1.96042e6i	−0.744144	−	1.04555i
$324$		0			0
$325$	−2.08624e6	+	3.61347e6i	−1.09561	+	1.89765i
$326$		0			0
$327$	1.33623e6	+	2.31441e6i	0.691051	+	1.19694i
$328$		0			0
$329$	2.33924e6	+	4.05169e6i	1.19148	+	2.06370i
$330$		0			0
$331$	79218.6			0.0397427			0.0198713	−	0.999803i	$-0.493674\pi$
$331$	79218.6			0.0397427			0.0198713	+	0.999803i	$0.493674\pi$
$332$		0			0
$333$	211025.	+	365506.i	0.104285	+	0.180627i
$334$		0			0
$335$	5.77222e6			2.81016
$336$		0			0
$337$	1.06653e6	−	1.84729e6i	0.511563	−	0.886053i	−0.488347	−	0.872649i	$-0.662400\pi$
$337$	1.06653e6	−	1.84729e6i	0.511563	−	0.886053i	0.999910	−	0.0134034i	$-0.00426657\pi$
$338$		0			0
$339$	1.39784e6	−	2.42112e6i	0.660628	−	1.14424i
$340$		0			0
$341$	1.47914e6			0.688848
$342$		0			0
$343$	−461871.			−0.211976
$344$		0			0
$345$	642030.	−	1.11203e6i	0.290407	−	0.503000i
$346$		0			0
$347$	−988867.	+	1.71277e6i	−0.440874	+	0.763616i	−0.997755	−	0.0669767i	$-0.978665\pi$
$347$	−988867.	+	1.71277e6i	−0.440874	+	0.763616i	0.556881	+	0.830592i	$0.311998\pi$
$348$		0			0
$349$	−2.01158e6			−0.884043			−0.442022	−	0.897004i	$-0.645739\pi$
$349$	−2.01158e6			−0.884043			−0.442022	+	0.897004i	$0.645739\pi$
$350$		0			0
$351$	−1.44914e6	−	2.50998e6i	−0.627829	−	1.08743i
$352$		0			0
$353$	−2.89132e6			−1.23498			−0.617490	−	0.786579i	$-0.711850\pi$
$353$	−2.89132e6			−1.23498			−0.617490	+	0.786579i	$0.711850\pi$
$354$		0			0
$355$	−1.40837e6	−	2.43936e6i	−0.593123	−	1.02732i
$356$		0			0
$357$	−1.97280e6	−	3.41699e6i	−0.819243	−	1.41897i
$358$		0			0
$359$	371558.	−	643557.i	0.152156	−	0.263543i	−0.779864	−	0.625950i	$-0.784712\pi$
$359$	371558.	−	643557.i	0.152156	−	0.263543i	0.932020	+	0.362407i	$0.118045\pi$
$360$		0			0
$361$	−1.62059e6	−	1.87210e6i	−0.654491	−	0.756070i
$362$		0			0
$363$	814414.	−	1.41061e6i	0.324398	−	0.561875i
$364$		0			0
$365$	−3.70420e6	−	6.41587e6i	−1.45533	−	2.52071i
$366$		0			0
$367$	−2.21010e6	−	3.82801e6i	−0.856540	−	1.48357i	−0.875209	−	0.483745i	$-0.839276\pi$
$367$	−2.21010e6	−	3.82801e6i	−0.856540	−	1.48357i	0.0186695	−	0.999826i	$-0.494057\pi$
$368$		0			0
$369$	254418.			0.0972705
$370$		0			0
$371$	2.94236e6	+	5.09632e6i	1.10984	+	1.92230i
$372$		0			0
$373$	−2.07890e6			−0.773680			−0.386840	−	0.922147i	$-0.626433\pi$
$373$	−2.07890e6			−0.773680			−0.386840	+	0.922147i	$0.626433\pi$
$374$		0			0
$375$	1.78768e6	−	3.09636e6i	0.656466	−	1.13703i
$376$		0			0
$377$	−913517.	+	1.58226e6i	−0.331027	+	0.573355i
$378$		0			0
$379$	−3.87208e6			−1.38467			−0.692335	−	0.721576i	$-0.743418\pi$
$379$	−3.87208e6			−1.38467			−0.692335	+	0.721576i	$0.743418\pi$
$380$		0			0
$381$	3903.61			0.00137770
$382$		0			0
$383$	72504.1	−	125581.i	0.0252560	−	0.0437448i	−0.853121	−	0.521713i	$-0.825293\pi$
$383$	72504.1	−	125581.i	0.0252560	−	0.0437448i	0.878377	+	0.477968i	$0.158627\pi$
$384$		0			0
$385$	4.77846e6	−	8.27653e6i	1.64299	−	2.84575i
$386$		0			0
$387$	364047.			0.123561
$388$		0			0
$389$	670618.	+	1.16154e6i	0.224699	+	0.389190i	0.956229	−	0.292619i	$-0.0945268\pi$
$389$	670618.	+	1.16154e6i	0.224699	+	0.389190i	−0.731530	+	0.681809i	$0.761193\pi$
$390$		0			0
$391$	1.52130e6			0.503238
$392$		0			0
$393$	−286570.	−	496353.i	−0.0935942	−	0.162110i
$394$		0			0
$395$	3.17475e6	+	5.49883e6i	1.02380	+	1.77328i
$396$		0			0
$397$	−635788.	+	1.10122e6i	−0.202458	+	0.350668i	−0.949320	−	0.314311i	$-0.898226\pi$
$397$	−635788.	+	1.10122e6i	−0.202458	+	0.350668i	0.746862	+	0.664980i	$0.231560\pi$
$398$		0			0
$399$	−2.35430e6	−	3.30786e6i	−0.740336	−	1.04019i
$400$		0			0
$401$	722427.	−	1.25128e6i	0.224354	−	0.388592i	−0.731772	−	0.681550i	$-0.761306\pi$
$401$	722427.	−	1.25128e6i	0.224354	−	0.388592i	0.956125	+	0.292958i	$0.0946396\pi$
$402$		0			0
$403$	−987652.	−	1.71066e6i	−0.302929	−	0.524689i
$404$		0			0
$405$	1.96976e6	+	3.41172e6i	0.596727	+	1.03356i
$406$		0			0
$407$	3.83625e6			1.14794
$408$		0			0
$409$	306511.	+	530893.i	0.0906020	+	0.156927i	0.907765	−	0.419480i	$-0.137788\pi$
$409$	306511.	+	530893.i	0.0906020	+	0.156927i	−0.817163	+	0.576407i	$0.804454\pi$
$410$		0			0
$411$	−1.42203e6			−0.415244
$412$		0			0
$413$	−3.45122e6	+	5.97769e6i	−0.995629	+	1.72448i
$414$		0			0
$415$	−1.04089e6	+	1.80288e6i	−0.296679	+	0.513862i
$416$		0			0
$417$	−1.75053e6			−0.492981
$418$		0			0
$419$	−6.30914e6			−1.75564			−0.877820	−	0.478991i	$-0.841003\pi$
$419$	−6.30914e6			−1.75564			−0.877820	+	0.478991i	$0.841003\pi$
$420$		0			0
$421$	−1.28732e6	+	2.22970e6i	−0.353981	+	0.613113i	−0.986943	−	0.161070i	$-0.948506\pi$
$421$	−1.28732e6	+	2.22970e6i	−0.353981	+	0.613113i	0.632962	+	0.774183i	$0.281839\pi$
$422$		0			0
$423$	718421.	−	1.24434e6i	0.195222	−	0.338134i
$424$		0			0
$425$	9.01463e6			2.42089
$426$		0			0
$427$	−548111.	−	949356.i	−0.145478	−	0.251976i
$428$		0			0
$429$	−5.09808e6			−1.33741
$430$		0			0
$431$	921074.	+	1.59535e6i	0.238837	+	0.413678i	0.960381	−	0.278691i	$-0.0899005\pi$
$431$	921074.	+	1.59535e6i	0.238837	+	0.413678i	−0.721544	+	0.692369i	$0.756567\pi$
$432$		0			0
$433$	−2.48716e6	−	4.30788e6i	−0.637505	−	1.10419i	−0.985979	−	0.166872i	$-0.946633\pi$
$433$	−2.48716e6	−	4.30788e6i	−0.637505	−	1.10419i	0.348474	−	0.937318i	$-0.386700\pi$
$434$		0			0
$435$	1.66587e6	−	2.88537e6i	0.422102	−	0.731101i
$436$		0			0
$437$	1.55841e6	−	148425.i	0.390370	−	0.0371796i
$438$		0			0
$439$	−1.97430e6	+	3.41959e6i	−0.488936	+	0.846863i	−0.999919	−	0.0127283i	$-0.995948\pi$
$439$	−1.97430e6	+	3.41959e6i	−0.488936	+	0.846863i	0.510983	+	0.859591i	$0.329282\pi$
$440$		0			0
$441$	560925.	+	971550.i	0.137344	+	0.237886i
$442$		0			0
$443$	−3.42436e6	−	5.93117e6i	−0.829031	−	1.43592i	−0.898799	−	0.438360i	$-0.855560\pi$
$443$	−3.42436e6	−	5.93117e6i	−0.829031	−	1.43592i	0.0697689	−	0.997563i	$-0.477774\pi$
$444$		0			0
$445$	8.61886e6			2.06324
$446$		0			0
$447$	1.85513e6	+	3.21318e6i	0.439142	+	0.760617i
$448$		0			0
$449$	−3.05530e6			−0.715216			−0.357608	−	0.933872i	$-0.616408\pi$
$449$	−3.05530e6			−0.715216			−0.357608	+	0.933872i	$0.616408\pi$
$450$		0			0
$451$	1.15627e6	−	2.00272e6i	0.267682	−	0.463639i
$452$		0			0
$453$	−467241.	+	809285.i	−0.106978	+	0.185292i
$454$		0			0
$455$	−1.27627e7			−2.89011
$456$		0			0
$457$	−5.86875e6			−1.31448			−0.657242	−	0.753680i	$-0.728277\pi$
$457$	−5.86875e6			−1.31448			−0.657242	+	0.753680i	$0.728277\pi$
$458$		0			0
$459$	−3.13086e6	+	5.42280e6i	−0.693636	+	1.20141i
$460$		0			0
$461$	970738.	−	1.68137e6i	0.212740	−	0.368477i	−0.739831	−	0.672793i	$-0.765095\pi$
$461$	970738.	−	1.68137e6i	0.212740	−	0.368477i	0.952571	+	0.304316i	$0.0984279\pi$
$462$		0			0
$463$	−2.37394e6			−0.514656			−0.257328	−	0.966324i	$-0.582842\pi$
$463$	−2.37394e6			−0.514656			−0.257328	+	0.966324i	$0.582842\pi$
$464$		0			0
$465$	1.80106e6	+	3.11952e6i	0.386274	+	0.669046i
$466$		0			0
$467$	2.72608e6			0.578425			0.289212	−	0.957265i	$-0.406607\pi$
$467$	2.72608e6			0.578425			0.289212	+	0.957265i	$0.406607\pi$
$468$		0			0
$469$	5.76953e6	+	9.99312e6i	1.21118	+	2.09782i
$470$		0			0
$471$	−3.75084e6	−	6.49664e6i	−0.779069	−	1.34939i
$472$		0			0
$473$	1.65452e6	−	2.86570e6i	0.340031	−	0.588950i
$474$		0			0
$475$	9.23449e6	−	879510.i	1.87793	−	0.178857i
$476$		0			0
$477$	903649.	−	1.56517e6i	0.181846	−	0.314967i
$478$		0			0
$479$	2.64917e6	+	4.58849e6i	0.527558	+	0.913757i	0.999484	+	0.0321192i	$0.0102256\pi$
$479$	2.64917e6	+	4.58849e6i	0.527558	+	0.913757i	−0.471926	+	0.881638i	$0.656441\pi$
$480$		0			0
$481$	−2.56154e6	−	4.43672e6i	−0.504823	−	0.874378i
$482$		0			0
$483$	2.56692e6			0.500662
$484$		0			0
$485$	−2.92114e6	−	5.05957e6i	−0.563895	−	0.976695i
$486$		0			0
$487$	−5.45937e6			−1.04309			−0.521543	−	0.853225i	$-0.674644\pi$
$487$	−5.45937e6			−1.04309			−0.521543	+	0.853225i	$0.674644\pi$
$488$		0			0
$489$	1.04233e6	−	1.80536e6i	0.197120	−	0.341422i
$490$		0			0
$491$	3.95495e6	−	6.85017e6i	0.740350	−	1.28232i	−0.211986	−	0.977273i	$-0.567993\pi$
$491$	3.95495e6	−	6.85017e6i	0.740350	−	1.28232i	0.952336	−	0.305051i	$-0.0986735\pi$
$492$		0			0
$493$	3.94730e6			0.731447
$494$		0			0
$495$	−2.93509e6			−0.538404
$496$		0			0
$497$	2.81542e6	−	4.87645e6i	0.511272	−	0.885550i
$498$		0			0
$499$	4.75343e6	−	8.23318e6i	0.854586	−	1.48019i	−0.0224433	−	0.999748i	$-0.507145\pi$
$499$	4.75343e6	−	8.23318e6i	0.854586	−	1.48019i	0.877029	−	0.480438i	$-0.159522\pi$
$500$		0			0
$501$	−3.98532e6			−0.709363
$502$		0			0
$503$	3.72038e6	+	6.44389e6i	0.655643	+	1.13561i	0.981732	+	0.190268i	$0.0609356\pi$
$503$	3.72038e6	+	6.44389e6i	0.655643	+	1.13561i	−0.326090	+	0.945339i	$0.605731\pi$
$504$		0			0
$505$	−1.11745e6			−0.194984
$506$		0			0
$507$	881141.	+	1.52618e6i	0.152239	+	0.263685i
$508$		0			0
$509$	513257.	+	888987.i	0.0878092	+	0.152090i	0.906585	−	0.422024i	$-0.138680\pi$
$509$	513257.	+	888987.i	0.0878092	+	0.152090i	−0.818776	+	0.574114i	$0.805347\pi$
$510$		0			0
$511$	7.40496e6	−	1.28258e7i	1.25450	−	2.17286i
$512$		0			0
$513$	−2.67814e6	+	5.86052e6i	−0.449304	+	0.983202i
$514$		0			0
$515$	−2.73917e6	+	4.74438e6i	−0.455093	+	0.788245i
$516$		0			0
$517$	−6.53014e6	−	1.13105e7i	−1.07447	−	1.86104i
$518$		0			0
$519$	1.55266e6	+	2.68928e6i	0.253022	+	0.438246i
$520$		0			0
$521$	5.83600e6			0.941936			0.470968	−	0.882150i	$-0.343905\pi$
$521$	5.83600e6			0.941936			0.470968	+	0.882150i	$0.343905\pi$
$522$		0			0
$523$	−1.68243e6	−	2.91406e6i	−0.268958	−	0.465848i	0.699635	−	0.714500i	$-0.253346\pi$
$523$	−1.68243e6	−	2.91406e6i	−0.268958	−	0.465848i	−0.968593	+	0.248652i	$0.920012\pi$
$524$		0			0
$525$	1.52106e7			2.40850
$526$		0			0
$527$	−2.13382e6	+	3.69588e6i	−0.334681	+	0.579684i
$528$		0			0
$529$	2.72331e6	−	4.71691e6i	0.423114	−	0.732856i
$530$		0			0
$531$	2.11986e6			0.326265
$532$		0			0
$533$	−3.08827e6			−0.470866
$534$		0			0
$535$	−3.79388e6	+	6.57119e6i	−0.573058	+	0.992566i
$536$		0			0
$537$	−1.67935e6	+	2.90872e6i	−0.251307	+	0.435277i
$538$		0			0
$539$	1.01971e7			1.51184
$540$		0			0
$541$	4.79104e6	+	8.29833e6i	0.703780	+	1.21898i	0.967130	+	0.254282i	$0.0818393\pi$
$541$	4.79104e6	+	8.29833e6i	0.703780	+	1.21898i	−0.263350	+	0.964700i	$0.584827\pi$
$542$		0			0
$543$	9.61809e6			1.39987
$544$		0			0
$545$	−9.33818e6	−	1.61742e7i	−1.34670	−	2.33255i
$546$		0			0
$547$	2.53036e6	+	4.38271e6i	0.361588	+	0.626289i	0.988222	−	0.153024i	$-0.0489013\pi$
$547$	2.53036e6	+	4.38271e6i	0.361588	+	0.626289i	−0.626634	+	0.779314i	$0.715568\pi$
$548$		0			0
$549$	−168334.	+	291563.i	−0.0238364	+	0.0412859i
$550$		0			0
$551$	4.04357e6	−	385117.i	0.567396	−	0.0540398i
$552$		0			0
$553$	−6.34654e6	+	1.09925e7i	−0.882520	+	1.52857i
$554$		0			0
$555$	4.67116e6	+	8.09069e6i	0.643713	+	1.11494i
$556$		0			0
$557$	−3.89885e6	−	6.75300e6i	−0.532474	−	0.922271i	−0.999281	−	0.0379124i	$-0.987929\pi$
$557$	−3.89885e6	−	6.75300e6i	−0.532474	−	0.922271i	0.466807	−	0.884359i	$-0.345404\pi$
$558$		0			0
$559$	−4.41902e6			−0.598131
$560$		0			0
$561$	5.50720e6	+	9.53874e6i	0.738794	+	1.27963i
$562$		0			0
$563$	−4.30439e6			−0.572323			−0.286161	−	0.958181i	$-0.592379\pi$
$563$	−4.30439e6			−0.572323			−0.286161	+	0.958181i	$0.592379\pi$
$564$		0			0
$565$	−9.76875e6	+	1.69200e7i	−1.28741	+	2.22986i
$566$		0			0
$567$	−3.93768e6	+	6.82027e6i	−0.514379	+	0.890930i
$568$		0			0
$569$	−9.79289e6			−1.26803			−0.634016	−	0.773320i	$-0.718595\pi$
$569$	−9.79289e6			−1.26803			−0.634016	+	0.773320i	$0.718595\pi$
$570$		0			0
$571$	6.14671e6			0.788955			0.394477	−	0.918906i	$-0.370926\pi$
$571$	6.14671e6			0.788955			0.394477	+	0.918906i	$0.370926\pi$
$572$		0			0
$573$	−71362.1	+	123603.i	−0.00907990	+	0.0157269i
$574$		0			0
$575$	−2.93236e6	+	5.07899e6i	−0.369869	+	0.640631i
$576$		0			0
$577$	−704051.			−0.0880369			−0.0440185	−	0.999031i	$-0.514016\pi$
$577$	−704051.			−0.0880369			−0.0440185	+	0.999031i	$0.514016\pi$
$578$		0			0
$579$	−6.75148e6	−	1.16939e7i	−0.836955	−	1.44965i
$580$		0			0
$581$	−4.16163e6			−0.511474
$582$		0			0
$583$	−8.21378e6	−	1.42267e7i	−1.00086	−	1.73353i
$584$		0			0
$585$	1.95982e6	+	3.39451e6i	0.236770	+	0.410097i
$586$		0			0
$587$	−4.80763e6	+	8.32707e6i	−0.575885	+	0.997463i	0.420059	+	0.907497i	$0.362009\pi$
$587$	−4.80763e6	+	8.32707e6i	−0.575885	+	0.997463i	−0.995945	+	0.0899662i	$0.971324\pi$
$588$		0			0
$589$	−1.82527e6	+	3.99421e6i	−0.216790	+	0.474398i
$590$		0			0
$591$	−1.25913e6	+	2.18087e6i	−0.148286	+	0.256839i
$592$		0			0
$593$	5.57887e6	+	9.66289e6i	0.651493	+	1.12842i	0.982761	+	0.184882i	$0.0591903\pi$
$593$	5.57887e6	+	9.66289e6i	0.651493	+	1.12842i	−0.331268	+	0.943537i	$0.607476\pi$
$594$		0			0
$595$	1.37869e7	+	2.38796e7i	1.59652	+	2.76525i
$596$		0			0
$597$	−1.17282e6			−0.134678
$598$		0			0
$599$	−4.00898e6	−	6.94376e6i	−0.456528	−	0.790729i	0.542247	−	0.840219i	$-0.317574\pi$
$599$	−4.00898e6	−	6.94376e6i	−0.456528	−	0.790729i	−0.998775	+	0.0494902i	$0.984240\pi$
$600$		0			0
$601$	1.34115e7			1.51458			0.757290	−	0.653079i	$-0.226523\pi$
$601$	1.34115e7			1.51458			0.757290	+	0.653079i	$0.226523\pi$
$602$		0			0
$603$	1.77192e6	−	3.06905e6i	0.198450	−	0.343725i
$604$		0			0
$605$	−5.69151e6	+	9.85799e6i	−0.632178	+	1.09496i
$606$		0			0
$607$	−3.14504e6			−0.346461			−0.173231	−	0.984881i	$-0.555421\pi$
$607$	−3.14504e6			−0.346461			−0.173231	+	0.984881i	$0.555421\pi$
$608$		0			0
$609$	6.66036e6			0.727704
$610$		0			0
$611$	−8.72061e6	+	1.51045e7i	−0.945027	+	1.63683i
$612$		0			0
$613$	1.86161e6	−	3.22440e6i	0.200095	−	0.346575i	−0.748464	−	0.663176i	$-0.769208\pi$
$613$	1.86161e6	−	3.22440e6i	0.200095	−	0.346575i	0.948559	+	0.316601i	$0.102542\pi$
$614$		0			0
$615$	5.63169e6			0.600414
$616$		0			0
$617$	−650699.	−	1.12704e6i	−0.0688125	−	0.119187i	0.829566	−	0.558408i	$-0.188588\pi$
$617$	−650699.	−	1.12704e6i	−0.0688125	−	0.119187i	−0.898379	+	0.439221i	$0.855254\pi$
$618$		0			0
$619$	−1.44161e7			−1.51224			−0.756118	−	0.654435i	$-0.772907\pi$
$619$	−1.44161e7			−1.51224			−0.756118	+	0.654435i	$0.772907\pi$
$620$		0			0
$621$	−2.03687e6	−	3.52795e6i	−0.211950	−	0.367108i
$622$		0			0
$623$	8.61485e6	+	1.49214e7i	0.889257	+	1.54024i
$624$		0			0
$625$	−3.28211e6	+	5.68478e6i	−0.336088	+	0.582122i
$626$		0			0
$627$	6.57216e6	+	9.23408e6i	0.667635	+	0.938047i
$628$		0			0
$629$	−5.53420e6	+	9.58552e6i	−0.557736	+	0.966026i
$630$		0			0
$631$	−1.56517e6	−	2.71095e6i	−0.156490	−	0.271049i	0.777110	−	0.629364i	$-0.216685\pi$
$631$	−1.56517e6	−	2.71095e6i	−0.156490	−	0.271049i	−0.933601	+	0.358315i	$0.883351\pi$
$632$		0			0
$633$	2.05528e6	+	3.55986e6i	0.203874	+	0.353121i
$634$		0			0
$635$	−27280.3			−0.00268482
$636$		0			0
$637$	−6.80883e6	−	1.17932e7i	−0.664851	−	1.15156i
$638$		0			0
$639$	−1.72933e6			−0.167542
$640$		0			0
$641$	−2.12325e6	+	3.67757e6i	−0.204106	+	0.353522i	−0.949848	−	0.312713i	$-0.898762\pi$
$641$	−2.12325e6	+	3.67757e6i	−0.204106	+	0.353522i	0.745742	+	0.666235i	$0.232095\pi$
$642$		0			0
$643$	−5.08032e6	+	8.79938e6i	−0.484578	+	0.839314i	−0.999843	−	0.0177168i	$-0.994360\pi$
$643$	−5.08032e6	+	8.79938e6i	−0.484578	+	0.839314i	0.515265	+	0.857031i	$0.327694\pi$
$644$		0			0
$645$	8.05840e6			0.762693
$646$		0			0
$647$	−3.33300e6			−0.313022			−0.156511	−	0.987676i	$-0.550025\pi$
$647$	−3.33300e6			−0.313022			−0.156511	+	0.987676i	$0.550025\pi$
$648$		0			0
$649$	9.63429e6	−	1.66871e7i	0.897859	−	1.55514i
$650$		0			0
$651$	−3.60044e6	+	6.23614e6i	−0.332968	+	0.576718i
$652$		0			0
$653$	−3.56244e6			−0.326938			−0.163469	−	0.986549i	$-0.552268\pi$
$653$	−3.56244e6			−0.326938			−0.163469	+	0.986549i	$0.552268\pi$
$654$		0			0
$655$	2.00269e6	+	3.46875e6i	0.182394	+	0.315915i
$656$		0			0
$657$	−4.54837e6			−0.411096
$658$		0			0
$659$	−9.65732e6	−	1.67270e7i	−0.866249	−	1.50039i	−0.865801	−	0.500388i	$-0.833191\pi$
$659$	−9.65732e6	−	1.67270e7i	−0.866249	−	1.50039i	−0.000448081	−	1.00000i	$-0.500143\pi$
$660$		0			0
$661$	5.55793e6	+	9.62662e6i	0.494777	+	0.856979i	0.999982	−	0.00602036i	$-0.00191635\pi$
$661$	5.55793e6	+	9.62662e6i	0.494777	+	0.856979i	−0.505205	+	0.863000i	$0.668583\pi$
$662$		0			0
$663$	7.35454e6	−	1.27384e7i	0.649788	−	1.12547i
$664$		0			0
$665$	1.64529e7	+	2.31169e7i	1.44274	+	2.02710i
$666$		0			0
$667$	−1.28401e6	+	2.22398e6i	−0.111752	+	0.193560i
$668$		0			0
$669$	−4.61365e6	−	7.99108e6i	−0.398547	−	0.690303i
$670$		0			0
$671$	1.53008e6	+	2.65018e6i	0.131193	+	0.227232i
$672$		0			0
$673$	4.82842e6			0.410929			0.205465	−	0.978665i	$-0.434129\pi$
$673$	4.82842e6			0.410929			0.205465	+	0.978665i	$0.434129\pi$
$674$		0			0
$675$	−1.20697e7	−	2.09052e7i	−1.01961	−	1.76602i
$676$		0			0
$677$	−3.20527e6			−0.268777			−0.134389	−	0.990929i	$-0.542907\pi$
$677$	−3.20527e6			−0.268777			−0.134389	+	0.990929i	$0.542907\pi$
$678$		0			0
$679$	5.83956e6	−	1.01144e7i	0.486078	−	0.841912i
$680$		0			0
$681$	−1.57360e6	+	2.72556e6i	−0.130025	+	0.225210i
$682$		0			0
$683$	−2.29678e7			−1.88395			−0.941973	−	0.335688i	$-0.891031\pi$
$683$	−2.29678e7			−1.88395			−0.941973	+	0.335688i	$0.891031\pi$
$684$		0			0
$685$	9.93780e6			0.809215
$686$		0			0
$687$	226804.	−	392837.i	0.0183341	−	0.0317556i
$688$		0			0
$689$	−1.09690e7	+	1.89989e7i	−0.880278	+	1.52469i
$690$		0			0
$691$	−7.10876e6			−0.566368			−0.283184	−	0.959066i	$-0.591391\pi$
$691$	−7.10876e6			−0.566368			−0.283184	+	0.959066i	$0.591391\pi$
$692$		0			0
$693$	−2.93372e6	−	5.08135e6i	−0.232052	−	0.401926i
$694$		0			0
$695$	1.22336e7			0.960707
$696$		0			0
$697$	3.33610e6	+	5.77829e6i	0.260110	+	0.450523i
$698$		0			0
$699$	−7.36841e6	−	1.27625e7i	−0.570402	−	0.987965i
$700$		0			0
$701$	7.73351e6	−	1.33948e7i	0.594403	−	1.02954i	−0.399227	−	0.916852i	$-0.630722\pi$
$701$	7.73351e6	−	1.33948e7i	0.594403	−	1.02954i	0.993631	−	0.112685i	$-0.0359451\pi$
$702$		0			0
$703$	−4.73397e6	+	1.03592e7i	−0.361274	+	0.790569i
$704$		0			0
$705$	1.59027e7	−	2.75443e7i	1.20503	−	2.08717i
$706$		0			0
$707$	−1.11693e6	−	1.93458e6i	−0.0840381	−	0.145558i
$708$		0			0
$709$	6.30537e6	+	1.09212e7i	0.471081	+	0.815936i	0.999453	−	0.0330772i	$-0.0105307\pi$
$709$	6.30537e6	+	1.09212e7i	0.471081	+	0.815936i	−0.528372	+	0.849013i	$0.677197\pi$
$710$		0			0
$711$	3.89826e6			0.289199
$712$		0			0
$713$	−1.38822e6	−	2.40446e6i	−0.102266	−	0.177131i
$714$		0			0
$715$	3.56278e7			2.60630
$716$		0			0
$717$	1.93007e6	−	3.34298e6i	0.140209	−	0.242849i
$718$		0			0
$719$	1.02749e7	−	1.77967e7i	0.741234	−	1.28386i	−0.210699	−	0.977551i	$-0.567574\pi$
$719$	1.02749e7	−	1.77967e7i	0.741234	−	1.28386i	0.951934	−	0.306304i	$-0.0990926\pi$
$720$		0			0
$721$	−1.09516e7			−0.784581
$722$		0			0
$723$	8.33899e6			0.593291
$724$		0			0
$725$	−7.60855e6	+	1.31784e7i	−0.537597	+	0.931146i
$726$		0			0
$727$	8.28557e6	−	1.43510e7i	0.581415	−	1.00704i	−0.413897	−	0.910324i	$-0.635833\pi$
$727$	8.28557e6	−	1.43510e7i	0.581415	−	1.00704i	0.995312	−	0.0967169i	$-0.0308342\pi$
$728$		0			0
$729$	1.59414e7			1.11098
$730$		0			0
$731$	4.77363e6	+	8.26818e6i	0.330412	+	0.572290i
$732$		0			0
$733$	2.52568e7			1.73628			0.868139	−	0.496321i	$-0.165316\pi$
$733$	2.52568e7			1.73628			0.868139	+	0.496321i	$0.165316\pi$
$734$		0			0
$735$	1.24164e7	+	2.15059e7i	0.847770	+	1.46838i
$736$		0			0
$737$	−1.61060e7	−	2.78964e7i	−1.09224	−	1.89182i
$738$		0			0
$739$	−6.54248e6	+	1.13319e7i	−0.440688	+	0.763294i	−0.997741	−	0.0671833i	$-0.978599\pi$
$739$	−6.54248e6	+	1.13319e7i	−0.440688	+	0.763294i	0.557053	+	0.830477i	$0.311932\pi$
$740$		0			0
$741$	6.29109e6	−	1.37667e7i	0.420901	−	0.921049i
$742$		0			0
$743$	−1.18603e6	+	2.05426e6i	−0.0788177	+	0.136516i	−0.902740	−	0.430186i	$-0.858448\pi$
$743$	−1.18603e6	+	2.05426e6i	−0.0788177	+	0.136516i	0.823922	+	0.566703i	$0.191781\pi$
$744$		0			0
$745$	−1.29645e7	−	2.24552e7i	−0.855787	−	1.48227i
$746$		0			0
$747$	639054.	+	1.10687e6i	0.0419021	+	0.0725766i
$748$		0			0
$749$	−1.51684e7			−0.987953
$750$		0			0
$751$	1.34919e7	+	2.33686e7i	0.872916	+	1.51193i	0.858966	+	0.512032i	$0.171107\pi$
$751$	1.34919e7	+	2.33686e7i	0.872916	+	1.51193i	0.0139493	+	0.999903i	$0.495560\pi$
$752$		0			0
$753$	−1.00319e7			−0.644758
$754$		0			0
$755$	3.26530e6	−	5.65567e6i	0.208476	−	0.361091i
$756$		0			0
$757$	1.46311e7	−	2.53419e7i	0.927980	−	1.60731i	0.141284	−	0.989969i	$-0.454877\pi$
$757$	1.46311e7	−	2.53419e7i	0.927980	−	1.60731i	0.786697	−	0.617340i	$-0.211790\pi$
$758$		0			0
$759$	−7.16572e6			−0.451497
$760$		0			0
$761$	−2.62075e7			−1.64045			−0.820226	−	0.572040i	$-0.806152\pi$
$761$	−2.62075e7			−1.64045			−0.820226	+	0.572040i	$0.806152\pi$
$762$		0			0
$763$	1.86677e7	−	3.23333e7i	1.16086	−	2.01066i
$764$		0			0
$765$	4.23418e6	−	7.33382e6i	0.261587	−	0.453082i
$766$		0			0
$767$	−2.57321e7			−1.57938
$768$		0			0
$769$	2.54995e6	+	4.41664e6i	0.155495	+	0.269325i	0.933239	−	0.359256i	$-0.116969\pi$
$769$	2.54995e6	+	4.41664e6i	0.155495	+	0.269325i	−0.777744	+	0.628581i	$0.783636\pi$
$770$		0			0
$771$	1.86554e7			1.13023
$772$		0			0
$773$	−8.67472e6	−	1.50250e7i	−0.522164	−	0.904414i	−0.999668	−	0.0257842i	$-0.991792\pi$
$773$	−8.67472e6	−	1.50250e7i	−0.522164	−	0.904414i	0.477504	−	0.878630i	$-0.341542\pi$
$774$		0			0
$775$	−8.22601e6	−	1.42479e7i	−0.491966	−	0.852110i
$776$		0			0
$777$	−9.33797e6	+	1.61738e7i	−0.554881	+	0.961082i
$778$		0			0
$779$	3.98122e6	+	5.59373e6i	0.235057	+	0.330262i
$780$		0			0
$781$	−7.85942e6	+	1.36129e7i	−0.461066	+	0.798589i
$782$		0			0
$783$	−5.28503e6	−	9.15394e6i	−0.308065	−	0.533585i
$784$		0			0
$785$	2.62126e7	+	4.54016e7i	1.51823	+	2.62965i
$786$		0			0
$787$	−3.89085e6			−0.223928			−0.111964	−	0.993712i	$-0.535714\pi$
$787$	−3.89085e6			−0.223928			−0.111964	+	0.993712i	$0.535714\pi$
$788$		0			0
$789$	−1.98862e6	−	3.44439e6i	−0.113726	−	0.196979i
$790$		0			0
$791$	−3.90568e7			−2.21950
$792$		0			0
$793$	2.04334e6	−	3.53917e6i	0.115387	−	0.199856i
$794$		0			0
$795$	2.00028e7	−	3.46459e7i	1.12247	−	1.94417i
$796$		0			0
$797$	−2.46516e6			−0.137467			−0.0687336	−	0.997635i	$-0.521896\pi$
$797$	−2.46516e6			−0.137467			−0.0687336	+	0.997635i	$0.521896\pi$
$798$		0			0
$799$	3.76817e7			2.08816
$800$		0			0
$801$	2.64576e6	−	4.58260e6i	0.145703	−	0.252366i
$802$		0			0
$803$	−2.06714e7	+	3.58039e7i	−1.13131	+	1.95948i
$804$		0			0
$805$	−1.79389e7			−0.975676
$806$		0			0
$807$	1.32873e7	+	2.30143e7i	0.718212	+	1.24398i
$808$		0			0
$809$	1.17605e7			0.631762			0.315881	−	0.948799i	$-0.397700\pi$
$809$	1.17605e7			0.631762			0.315881	+	0.948799i	$0.397700\pi$
$810$		0			0
$811$	−4.70469e6	−	8.14875e6i	−0.251176	−	0.435050i	0.712674	−	0.701496i	$-0.247484\pi$
$811$	−4.70469e6	−	8.14875e6i	−0.251176	−	0.435050i	−0.963850	+	0.266446i	$0.914151\pi$
$812$		0			0
$813$	−9.69656e6	−	1.67949e7i	−0.514507	−	0.891153i
$814$		0			0
$815$	−7.28427e6	+	1.26167e7i	−0.384142	+	0.665353i
$816$		0			0
$817$	5.69674e6	+	8.00409e6i	0.298587	+	0.419524i
$818$		0			0
$819$	−3.91781e6	+	6.78585e6i	−0.204096	+	0.353504i
$820$		0			0
$821$	3.22161e6	+	5.57999e6i	0.166807	+	0.288918i	0.937296	−	0.348536i	$-0.113321\pi$
$821$	3.22161e6	+	5.57999e6i	0.166807	+	0.288918i	−0.770488	+	0.637454i	$0.779988\pi$
$822$		0			0
$823$	−5.61870e6	−	9.73187e6i	−0.289158	−	0.500837i	0.684451	−	0.729059i	$-0.260042\pi$
$823$	−5.61870e6	−	9.73187e6i	−0.289158	−	0.500837i	−0.973609	+	0.228222i	$0.926709\pi$
$824$		0			0
$825$	−4.24612e7			−2.17199
$826$		0			0
$827$	−5.80309e6	−	1.00513e7i	−0.295050	−	0.511042i	0.679946	−	0.733262i	$-0.262003\pi$
$827$	−5.80309e6	−	1.00513e7i	−0.295050	−	0.511042i	−0.974997	+	0.222220i	$0.928670\pi$
$828$		0			0
$829$	−2.34279e7			−1.18399			−0.591993	−	0.805943i	$-0.701659\pi$
$829$	−2.34279e7			−1.18399			−0.591993	+	0.805943i	$0.701659\pi$
$830$		0			0
$831$	−8.21433e6	+	1.42276e7i	−0.412638	+	0.714711i
$832$		0			0
$833$	−1.47105e7	+	2.54793e7i	−0.734537	+	1.27226i
$834$		0			0
$835$	2.78513e7			1.38239
$836$		0			0
$837$	1.14278e7			0.563833
$838$		0			0
$839$	1.33046e7	−	2.30442e7i	0.652523	−	1.13020i	−0.329986	−	0.943986i	$-0.607044\pi$
$839$	1.33046e7	−	2.30442e7i	0.652523	−	1.13020i	0.982509	−	0.186217i	$-0.0596227\pi$
$840$		0			0
$841$	6.92396e6	−	1.19927e7i	0.337571	−	0.584690i
$842$		0			0
$843$	−2.70832e7			−1.31260
$844$		0			0
$845$	−6.15783e6	−	1.06657e7i	−0.296678	−	0.513862i
$846$		0			0
$847$	−2.27554e7			−1.08988
$848$		0			0
$849$	454389.	+	787024.i	0.0216351	+	0.0374730i
$850$		0			0
$851$	−3.60043e6	−	6.23613e6i	−0.170424	−	0.295183i
$852$		0			0
$853$	1.75001e7	−	3.03111e7i	0.823510	−	1.42636i	−0.0795426	−	0.996831i	$-0.525346\pi$
$853$	1.75001e7	−	3.03111e7i	0.823510	−	1.42636i	0.903053	−	0.429530i	$-0.141321\pi$
$854$		0			0
$855$	3.62193e6	−	7.92580e6i	0.169443	−	0.370790i
$856$		0			0
$857$	−4.77062e6	+	8.26296e6i	−0.221882	+	0.384312i	−0.955380	−	0.295381i	$-0.904553\pi$
$857$	−4.77062e6	+	8.26296e6i	−0.221882	+	0.384312i	0.733497	+	0.679692i	$0.237887\pi$
$858$		0			0
$859$	−2.79816e6	−	4.84656e6i	−0.129387	−	0.224105i	0.794052	−	0.607849i	$-0.207968\pi$
$859$	−2.79816e6	−	4.84656e6i	−0.129387	−	0.224105i	−0.923439	+	0.383745i	$0.874634\pi$
$860$		0			0
$861$	5.62906e6	+	9.74983e6i	0.258779	+	0.448218i
$862$		0			0
$863$	−6.93765e6			−0.317092			−0.158546	−	0.987352i	$-0.550681\pi$
$863$	−6.93765e6			−0.317092			−0.158546	+	0.987352i	$0.550681\pi$
$864$		0			0
$865$	−1.08507e7	−	1.87940e7i	−0.493081	−	0.854041i
$866$		0			0
$867$	−1.24829e7			−0.563985
$868$		0			0
$869$	1.77168e7	−	3.06863e7i	0.795856	−	1.37846i
$870$		0			0
$871$	−2.15086e7	+	3.72540e7i	−0.960653	+	1.66390i
$872$		0			0
$873$	−3.58686e6			−0.159286
$874$		0			0
$875$	−4.99494e7			−2.20552
$876$		0			0
$877$	−5.50749e6	+	9.53926e6i	−0.241799	+	0.418809i	−0.961227	−	0.275759i	$-0.911071\pi$
$877$	−5.50749e6	+	9.53926e6i	−0.241799	+	0.418809i	0.719428	+	0.694567i	$0.244404\pi$
$878$		0			0
$879$	1.34975e7	−	2.33783e7i	0.589224	−	1.02057i
$880$		0			0
$881$	−3.01700e7			−1.30959			−0.654796	−	0.755806i	$-0.727246\pi$
$881$	−3.01700e7			−1.30959			−0.654796	+	0.755806i	$0.727246\pi$
$882$		0			0
$883$	−1.52557e7	−	2.64237e7i	−0.658464	−	1.14049i	−0.981013	−	0.193940i	$-0.937873\pi$
$883$	−1.52557e7	−	2.64237e7i	−0.658464	−	1.14049i	0.322550	−	0.946552i	$-0.395460\pi$
$884$		0			0
$885$	4.69243e7			2.01391
$886$		0			0
$887$	−3.89963e6	−	6.75436e6i	−0.166423	−	0.288254i	0.770736	−	0.637154i	$-0.219889\pi$
$887$	−3.89963e6	−	6.75436e6i	−0.166423	−	0.288254i	−0.937160	+	0.348900i	$0.886555\pi$
$888$		0			0
$889$	−27267.6	−	47228.8i	−0.00115716	−	0.00200425i
$890$		0			0
$891$	1.09923e7	−	1.90392e7i	0.463867	−	0.803441i
$892$		0			0
$893$	3.86007e7	−	3.67641e6i	1.61982	−	0.154275i
$894$		0			0
$895$	1.17361e7	−	2.03275e7i	0.489740	−	0.848254i
$896$		0			0
$897$	4.78470e6	+	8.28734e6i	0.198552	+	0.343901i
$898$		0			0
$899$	−3.60198e6	−	6.23882e6i	−0.148642	−	0.257456i
$900$		0			0
$901$	4.73971e7			1.94509
$902$		0			0
$903$	8.05465e6	+	1.39511e7i	0.328721	+	0.569361i
$904$		0			0
$905$	−6.72158e7			−2.72803
$906$		0			0
$907$	3.48982e6	−	6.04454e6i	0.140859	−	0.243975i	−0.786961	−	0.617002i	$-0.788347\pi$
$907$	3.48982e6	−	6.04454e6i	0.140859	−	0.243975i	0.927820	+	0.373027i	$0.121680\pi$
$908$		0			0
$909$	−343027.	+	594141.i	−0.0137695	+	0.0238495i
$910$		0			0
$911$	2.39353e7			0.955528			0.477764	−	0.878488i	$-0.341447\pi$
$911$	2.39353e7			0.955528			0.477764	+	0.878488i	$0.341447\pi$
$912$		0			0
$913$	1.16175e7			0.461247
$914$		0			0
$915$	−3.72618e6	+	6.45393e6i	−0.147133	+	0.254842i
$916$		0			0
$917$	−4.00350e6	+	6.93427e6i	−0.157223	+	0.272319i
$918$		0			0
$919$	9.03520e6			0.352898			0.176449	−	0.984310i	$-0.443539\pi$
$919$	9.03520e6			0.352898			0.176449	+	0.984310i	$0.443539\pi$
$920$		0			0
$921$	1.26680e7	+	2.19417e7i	0.492108	+	0.852356i
$922$		0			0
$923$	2.09916e7			0.811037
$924$		0			0
$925$	−2.13347e7	−	3.69528e7i	−0.819846	−	1.42002i
$926$		0			0
$927$	1.68170e6	+	2.91280e6i	0.0642762	+	0.111330i
$928$		0			0
$929$	−1.55430e6	+	2.69212e6i	−0.0590874	+	0.102342i	−0.894056	−	0.447955i	$-0.852152\pi$
$929$	−1.55430e6	+	2.69212e6i	−0.0590874	+	0.102342i	0.834969	+	0.550298i	$0.185486\pi$
$930$		0			0
$931$	−1.25834e7	+	2.75359e7i	−0.475798	+	1.04118i
$932$		0			0
$933$	−1.17942e7	+	2.04281e7i	−0.443571	+	0.768288i
$934$		0			0
$935$	−3.84869e7	−	6.66613e7i	−1.43974	−	2.49370i
$936$		0			0
$937$	−1.85807e7	−	3.21827e7i	−0.691374	−	1.19750i	−0.971388	−	0.237499i	$-0.923672\pi$
$937$	−1.85807e7	−	3.21827e7i	−0.691374	−	1.19750i	0.280013	−	0.959996i	$-0.409661\pi$
$938$		0			0
$939$	722074.			0.0267250
$940$		0			0
$941$	8.14651e6	+	1.41102e7i	0.299915	+	0.519467i	0.976116	−	0.217249i	$-0.0697085\pi$
$941$	8.14651e6	+	1.41102e7i	0.299915	+	0.519467i	−0.676202	+	0.736717i	$0.736375\pi$
$942$		0			0
$943$	−4.34078e6			−0.158960
$944$		0			0
$945$	3.69184e7	−	6.39446e7i	1.34482	−	2.32929i
$946$		0			0
$947$	−1.90876e7	+	3.30607e7i	−0.691634	+	1.19795i	0.279668	+	0.960097i	$0.409776\pi$
$947$	−1.90876e7	+	3.30607e7i	−0.691634	+	1.19795i	−0.971302	+	0.237849i	$0.923558\pi$
$948$		0			0
$949$	5.52108e7			1.99003
$950$		0			0
$951$	−1.87694e7			−0.672975
$952$		0			0
$953$	−3.93217e6	+	6.81072e6i	−0.140249	+	0.242919i	−0.927590	−	0.373599i	$-0.878124\pi$
$953$	−3.93217e6	+	6.81072e6i	−0.140249	+	0.242919i	0.787341	+	0.616517i	$0.211457\pi$
$954$		0			0
$955$	498713.	−	863795.i	0.0176946	−	0.0306480i
$956$		0			0
$957$	−1.85928e7			−0.656243
$958$		0			0
$959$	9.93317e6	+	1.72047e7i	0.348772	+	0.604090i
$960$		0			0
$961$	−2.08406e7			−0.727949
$962$		0			0
$963$	2.32924e6	+	4.03436e6i	0.0809373	+	0.140188i
$964$		0			0
$965$	4.71825e7	+	8.17225e7i	1.63103	+	2.82503i
$966$		0			0
$967$	−1.96743e6	+	3.40769e6i	−0.0676601	+	0.117191i	−0.897871	−	0.440259i	$-0.854887\pi$
$967$	−1.96743e6	+	3.40769e6i	−0.0676601	+	0.117191i	0.830211	+	0.557450i	$0.188220\pi$
$968$		0			0
$969$	−3.25540e7	+	3.10050e6i	−1.11377	+	0.106077i
$970$		0			0
$971$	2.28377e6	−	3.95561e6i	0.0777329	−	0.134637i	−0.824539	−	0.565806i	$-0.808565\pi$
$971$	2.28377e6	−	3.95561e6i	0.0777329	−	0.134637i	0.902271	+	0.431168i	$0.141899\pi$
$972$		0			0
$973$	1.22279e7	+	2.11793e7i	0.414065	+	0.717181i
$974$		0			0
$975$	2.83522e7	+	4.91075e7i	0.955158	+	1.65438i
$976$		0			0
$977$	−1.77743e7			−0.595739			−0.297870	−	0.954607i	$-0.596276\pi$
$977$	−1.77743e7			−0.595739			−0.297870	+	0.954607i	$0.596276\pi$
$978$		0			0
$979$	−2.40489e7	−	4.16539e7i	−0.801933	−	1.38899i
$980$		0			0
$981$	−1.14663e7			−0.380409
$982$		0			0
$983$	−9.38981e6	+	1.62636e7i	−0.309937	+	0.536826i	−0.978348	−	0.206966i	$-0.933641\pi$
$983$	−9.38981e6	+	1.62636e7i	−0.309937	+	0.536826i	0.668412	+	0.743792i	$0.266975\pi$
$984$		0			0
$985$	8.79937e6	−	1.52410e7i	0.288975	−	0.500520i
$986$		0			0
$987$	6.35811e7			2.07747
$988$		0			0
$989$	−6.21124e6			−0.201924
$990$		0			0
$991$	2.05047e7	−	3.55152e7i	0.663239	−	1.14876i	−0.316521	−	0.948586i	$-0.602515\pi$
$991$	2.05047e7	−	3.55152e7i	0.663239	−	1.14876i	0.979760	−	0.200178i	$-0.0641520\pi$
$992$		0			0
$993$	538295.	−	932354.i	0.0173240	−	0.0300060i
$994$		0			0
$995$	8.19624e6			0.262456
$996$		0			0
$997$	−1.23888e7	−	2.14579e7i	−0.394720	−	0.683676i	0.598345	−	0.801239i	$-0.295825\pi$
$997$	−1.23888e7	−	2.14579e7i	−0.394720	−	0.683676i	−0.993065	+	0.117563i	$0.962492\pi$
$998$		0			0
$999$	2.96389e7			0.939611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.6.i.d.49.7		18
4.3	odd	2		76.6.e.a.49.3	yes	18
12.11	even	2		684.6.k.f.505.9		18
19.7	even	3	inner	304.6.i.d.273.7		18
76.7	odd	6		76.6.e.a.45.3	✓	18
228.83	even	6		684.6.k.f.577.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.e.a.45.3	✓	18	76.7	odd	6
76.6.e.a.49.3	yes	18	4.3	odd	2
304.6.i.d.49.7		18	1.1	even	1	trivial
304.6.i.d.273.7		18	19.7	even	3	inner
684.6.k.f.505.9		18	12.11	even	2
684.6.k.f.577.9		18	228.83	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(6.79505 - 11.7694i) q^{3} +(-47.4871 + 82.2500i) q^{5} -189.860 q^{7} +(29.1546 + 50.4972i) q^{9} +O(q^{10})\)	\(q+(6.79505 - 11.7694i) q^{3} +(-47.4871 + 82.2500i) q^{5} -189.860 q^{7} +(29.1546 + 50.4972i) q^{9} +530.005 q^{11} +(-353.895 - 612.964i) q^{13} +(645.354 + 1117.79i) q^{15} +(-764.589 + 1324.31i) q^{17} +(-654.031 + 1431.20i) q^{19} +(-1290.11 + 2234.53i) q^{21} +(-497.425 - 861.565i) q^{23} +(-2947.54 - 5105.29i) q^{25} +4094.82 q^{27} +(-1290.66 - 2235.49i) q^{29} +2790.81 q^{31} +(3601.41 - 6237.82i) q^{33} +(9015.88 - 15616.0i) q^{35} +7238.14 q^{37} -9618.94 q^{39} +(2181.63 - 3778.69i) q^{41} +(3121.70 - 5406.94i) q^{43} -5537.86 q^{45} +(-12320.9 - 21340.4i) q^{47} +19239.7 q^{49} +(10390.8 + 17997.5i) q^{51} +(-15497.6 - 26842.6i) q^{53} +(-25168.4 + 43592.9i) q^{55} +(12400.2 + 17422.6i) q^{57} +(18177.7 - 31484.8i) q^{59} +(2886.93 + 5000.30i) q^{61} +(-5535.27 - 9587.38i) q^{63} +67221.7 q^{65} +(-30388.4 - 52634.2i) q^{67} -13520.1 q^{69} +(-14829.0 + 25684.5i) q^{71} +(-39002.3 + 67553.9i) q^{73} -80114.7 q^{75} -100627. q^{77} +(33427.5 - 57898.2i) q^{79} +(20740.0 - 35922.7i) q^{81} +21919.5 q^{83} +(-72616.2 - 125775. i) q^{85} -35080.4 q^{87} +(-45374.8 - 78591.5i) q^{89} +(67190.4 + 116377. i) q^{91} +(18963.7 - 32846.0i) q^{93} +(-86658.4 - 121758. i) q^{95} +(-30757.3 + 53273.1i) q^{97} +(15452.1 + 26763.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} + 11 q^{5} - 336 q^{7} - 902 q^{9}+O(q^{10}) \) 18 * q + 11 * q^3 + 11 * q^5 - 336 * q^7 - 902 * q^9	\( 18 q + 11 q^{3} + 11 q^{5} - 336 q^{7} - 902 q^{9} + 320 q^{11} + 227 q^{13} + 101 q^{15} + 179 q^{17} + 868 q^{19} - 5700 q^{21} + 3425 q^{23} - 7054 q^{25} - 14722 q^{27} - 7349 q^{29} + 9960 q^{31} - 2998 q^{33} - 15888 q^{35} + 26444 q^{37} + 30246 q^{39} - 7311 q^{41} + 8283 q^{43} - 62164 q^{45} - 37603 q^{47} + 124738 q^{49} - 47227 q^{51} - 20337 q^{53} - 716 q^{55} - 57555 q^{57} + 74455 q^{59} - 7569 q^{61} + 52544 q^{63} + 188998 q^{65} + 26177 q^{67} + 116282 q^{69} + 53463 q^{71} - 14103 q^{73} - 120912 q^{75} - 31960 q^{77} - 31825 q^{79} - 21137 q^{81} - 82600 q^{83} - 50787 q^{85} + 339766 q^{87} - 155197 q^{89} + 2800 q^{91} - 46460 q^{93} - 49315 q^{95} + 111241 q^{97} + 193544 q^{99}+O(q^{100}) \) 18 * q + 11 * q^3 + 11 * q^5 - 336 * q^7 - 902 * q^9 + 320 * q^11 + 227 * q^13 + 101 * q^15 + 179 * q^17 + 868 * q^19 - 5700 * q^21 + 3425 * q^23 - 7054 * q^25 - 14722 * q^27 - 7349 * q^29 + 9960 * q^31 - 2998 * q^33 - 15888 * q^35 + 26444 * q^37 + 30246 * q^39 - 7311 * q^41 + 8283 * q^43 - 62164 * q^45 - 37603 * q^47 + 124738 * q^49 - 47227 * q^51 - 20337 * q^53 - 716 * q^55 - 57555 * q^57 + 74455 * q^59 - 7569 * q^61 + 52544 * q^63 + 188998 * q^65 + 26177 * q^67 + 116282 * q^69 + 53463 * q^71 - 14103 * q^73 - 120912 * q^75 - 31960 * q^77 - 31825 * q^79 - 21137 * q^81 - 82600 * q^83 - 50787 * q^85 + 339766 * q^87 - 155197 * q^89 + 2800 * q^91 - 46460 * q^93 - 49315 * q^95 + 111241 * q^97 + 193544 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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