LMFDB - Embedded newform 56.6.i.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,6,Mod(9,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("56.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	56.i (of order $3$, degree $2$, 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:	$8.98149390953$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3 x^{9} - 119 x^{8} - 521 x^{7} - 898 x^{6} + 27806 x^{5} + 657990 x^{4} + 3648839 x^{3} + \cdots + 92895579 $ x^10 - 3x^9 - 119x^8 - 521x^7 - 898x^6 + 27806x^5 + 657990x^4 + 3648839x^3 + 1863790x^2 - 25332057*x + 92895579
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$-5.12305 - 3.65205i$ of defining polynomial
Character	$\chi$	$=$	56.9
Dual form			56.6.i.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.5967 - 21.8182i) q^{3} +(-40.3290 + 69.8518i) q^{5} +(-8.39664 - 129.370i) q^{7} +(-195.855 + 339.231i) q^{9} +(253.362 + 438.837i) q^{11} +391.283 q^{13} +2032.05 q^{15} +(449.706 + 778.913i) q^{17} +(-168.157 + 291.256i) q^{19} +(-2716.84 + 1812.83i) q^{21} +(-2436.06 + 4219.37i) q^{23} +(-1690.35 - 2927.78i) q^{25} +3746.51 q^{27} +546.591 q^{29} +(-3049.51 - 5281.91i) q^{31} +(6383.07 - 11055.8i) q^{33} +(9375.33 + 4630.82i) q^{35} +(-7404.84 + 12825.6i) q^{37} +(-4928.89 - 8537.08i) q^{39} -9837.31 q^{41} +18661.0 q^{43} +(-15797.3 - 27361.6i) q^{45} +(-699.243 + 1211.12i) q^{47} +(-16666.0 + 2172.54i) q^{49} +(11329.6 - 19623.5i) q^{51} +(9880.41 + 17113.4i) q^{53} -40871.4 q^{55} +8472.89 q^{57} +(-13585.4 - 23530.6i) q^{59} +(-7083.72 + 12269.4i) q^{61} +(45530.6 + 22489.3i) q^{63} +(-15780.1 + 27331.9i) q^{65} +(25223.0 + 43687.6i) q^{67} +122745. q^{69} -45279.2 q^{71} +(3783.41 + 6553.06i) q^{73} +(-42585.8 + 73760.8i) q^{75} +(54644.7 - 36462.2i) q^{77} +(-2414.96 + 4182.83i) q^{79} +(398.990 + 691.071i) q^{81} -14067.3 q^{83} -72544.7 q^{85} +(-6885.25 - 11925.6i) q^{87} +(44776.9 - 77555.9i) q^{89} +(-3285.47 - 50620.2i) q^{91} +(-76827.7 + 133070. i) q^{93} +(-13563.2 - 23492.1i) q^{95} +7209.53 q^{97} -198489. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 13 q^{3} - 31 q^{5} - 92 q^{7} - 230 q^{9} + 351 q^{11} - 108 q^{13} + 1214 q^{15} - 111 q^{17} - 1035 q^{19} - 1365 q^{21} - 3639 q^{23} - 1540 q^{25} + 7214 q^{27} - 1468 q^{29} - 7677 q^{31} + 7439 q^{33}+ \cdots - 600308 q^{99}+O(q^{100}) $ 10 * q - 13 * q^3 - 31 * q^5 - 92 * q^7 - 230 * q^9 + 351 * q^11 - 108 * q^13 + 1214 * q^15 - 111 * q^17 - 1035 * q^19 - 1365 * q^21 - 3639 * q^23 - 1540 * q^25 + 7214 * q^27 - 1468 * q^29 - 7677 * q^31 + 7439 * q^33 + 19899 * q^35 - 13595 * q^37 + 1406 * q^39 + 10620 * q^41 + 1528 * q^43 - 38978 * q^45 - 6675 * q^47 + 30122 * q^49 - 20975 * q^51 + 30753 * q^53 + 56534 * q^55 - 28778 * q^57 - 87989 * q^59 - 19899 * q^61 + 147318 * q^63 - 119470 * q^65 + 33067 * q^67 + 200798 * q^69 - 217440 * q^71 - 141659 * q^73 - 108788 * q^75 + 271471 * q^77 - 118919 * q^79 + 143851 * q^81 + 422008 * q^83 - 286758 * q^85 - 302154 * q^87 + 55861 * q^89 + 403912 * q^91 - 410381 * q^93 + 26279 * q^95 + 270940 * q^97 - 600308 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−12.5967	−	21.8182i	−0.808080	−	1.39964i	−0.914192	−	0.405282i	$-0.867173\pi$
$3$	−12.5967	−	21.8182i	−0.808080	−	1.39964i	0.106112	−	0.994354i	$-0.466160\pi$
$4$		0			0
$5$	−40.3290	+	69.8518i	−0.721427	+	1.24955i	0.239001	+	0.971019i	$0.423180\pi$
$5$	−40.3290	+	69.8518i	−0.721427	+	1.24955i	−0.960428	+	0.278528i	$0.910153\pi$
$6$		0			0
$7$	−8.39664	−	129.370i	−0.0647680	−	0.997900i
$7$	−8.39664	−	129.370i	−0.0647680	−	0.997900i
$8$		0			0
$9$	−195.855	+	339.231i	−0.805987	+	1.39601i
$10$		0			0
$11$	253.362	+	438.837i	0.631336	+	1.09351i	0.987279	+	0.158998i	$0.0508264\pi$
$11$	253.362	+	438.837i	0.631336	+	1.09351i	−0.355943	+	0.934508i	$0.615840\pi$
$12$		0			0
$13$	391.283			0.642145			0.321072	−	0.947055i	$-0.395957\pi$
$13$	391.283			0.642145			0.321072	+	0.947055i	$0.395957\pi$
$14$		0			0
$15$	2032.05			2.33188
$16$		0			0
$17$	449.706	+	778.913i	0.377404	+	0.653682i	0.990684	−	0.136183i	$-0.0434836\pi$
$17$	449.706	+	778.913i	0.377404	+	0.653682i	−0.613280	+	0.789866i	$0.710150\pi$
$18$		0			0
$19$	−168.157	+	291.256i	−0.106864	+	0.185093i	−0.914498	−	0.404590i	$-0.867414\pi$
$19$	−168.157	+	291.256i	−0.106864	+	0.185093i	0.807634	+	0.589684i	$0.200748\pi$
$20$		0			0
$21$	−2716.84	+	1812.83i	−1.34436	+	0.897035i
$22$		0			0
$23$	−2436.06	+	4219.37i	−0.960213	+	1.66314i	−0.238252	+	0.971203i	$0.576575\pi$
$23$	−2436.06	+	4219.37i	−0.960213	+	1.66314i	−0.721960	+	0.691934i	$0.756759\pi$
$24$		0			0
$25$	−1690.35	−	2927.78i	−0.540913	−	0.936889i
$26$		0			0
$27$	3746.51			0.989048
$28$		0			0
$29$	546.591			0.120689			0.0603444	−	0.998178i	$-0.480780\pi$
$29$	546.591			0.120689			0.0603444	+	0.998178i	$0.480780\pi$
$30$		0			0
$31$	−3049.51	−	5281.91i	−0.569936	−	0.987158i	−0.996572	−	0.0827346i	$-0.973635\pi$
$31$	−3049.51	−	5281.91i	−0.569936	−	0.987158i	0.426636	−	0.904424i	$-0.359699\pi$
$32$		0			0
$33$	6383.07	−	11055.8i	1.02034	−	1.76728i
$34$		0			0
$35$	9375.33	+	4630.82i	1.29365	+	0.638981i
$36$		0			0
$37$	−7404.84	+	12825.6i	−0.889224	+	1.54018i	−0.0484303	+	0.998827i	$0.515422\pi$
$37$	−7404.84	+	12825.6i	−0.889224	+	1.54018i	−0.840794	+	0.541355i	$0.817911\pi$
$38$		0			0
$39$	−4928.89	−	8537.08i	−0.518904	−	0.898769i
$40$		0			0
$41$	−9837.31			−0.913938			−0.456969	−	0.889483i	$-0.651065\pi$
$41$	−9837.31			−0.913938			−0.456969	+	0.889483i	$0.651065\pi$
$42$		0			0
$43$	18661.0			1.53909			0.769546	−	0.638591i	$-0.220482\pi$
$43$	18661.0			1.53909			0.769546	+	0.638591i	$0.220482\pi$
$44$		0			0
$45$	−15797.3	−	27361.6i	−1.16292	−	2.01424i
$46$		0			0
$47$	−699.243	+	1211.12i	−0.0461725	+	0.0799731i	−0.888188	−	0.459480i	$-0.848036\pi$
$47$	−699.243	+	1211.12i	−0.0461725	+	0.0799731i	0.842016	+	0.539453i	$0.181369\pi$
$48$		0			0
$49$	−16666.0	+	2172.54i	−0.991610	+	0.129264i
$50$		0			0
$51$	11329.6	−	19623.5i	0.609945	−	1.05646i
$52$		0			0
$53$	9880.41	+	17113.4i	0.483154	+	0.836847i	0.999813	−	0.0193444i	$-0.00615789\pi$
$53$	9880.41	+	17113.4i	0.483154	+	0.836847i	−0.516659	+	0.856191i	$0.672825\pi$
$54$		0			0
$55$	−40871.4			−1.82185
$56$		0			0
$57$	8472.89			0.345418
$58$		0			0
$59$	−13585.4	−	23530.6i	−0.508092	−	0.880041i	−0.999956	−	0.00936932i	$-0.997018\pi$
$59$	−13585.4	−	23530.6i	−0.508092	−	0.880041i	0.491864	−	0.870672i	$-0.336316\pi$
$60$		0			0
$61$	−7083.72	+	12269.4i	−0.243746	+	0.422180i	−0.961778	−	0.273830i	$-0.911710\pi$
$61$	−7083.72	+	12269.4i	−0.243746	+	0.422180i	0.718033	+	0.696009i	$0.245043\pi$
$62$		0			0
$63$	45530.6	+	22489.3i	1.44528	+	0.713878i
$64$		0			0
$65$	−15780.1	+	27331.9i	−0.463260	+	0.802391i
$66$		0			0
$67$	25223.0	+	43687.6i	0.686453	+	1.18897i	0.972978	+	0.230898i	$0.0741664\pi$
$67$	25223.0	+	43687.6i	0.686453	+	1.18897i	−0.286525	+	0.958073i	$0.592500\pi$
$68$		0			0
$69$	122745.			3.10372
$70$		0			0
$71$	−45279.2			−1.06599			−0.532995	−	0.846118i	$-0.678934\pi$
$71$	−45279.2			−1.06599			−0.532995	+	0.846118i	$0.678934\pi$
$72$		0			0
$73$	3783.41	+	6553.06i	0.0830953	+	0.143925i	0.904578	−	0.426308i	$-0.140186\pi$
$73$	3783.41	+	6553.06i	0.0830953	+	0.143925i	−0.821483	+	0.570233i	$0.806853\pi$
$74$		0			0
$75$	−42585.8	+	73760.8i	−0.874202	+	1.51416i
$76$		0			0
$77$	54644.7	−	36462.2i	1.05032	−	0.700834i
$78$		0			0
$79$	−2414.96	+	4182.83i	−0.0435353	+	0.0754054i	−0.886972	−	0.461823i	$-0.847195\pi$
$79$	−2414.96	+	4182.83i	−0.0435353	+	0.0754054i	0.843437	+	0.537229i	$0.180529\pi$
$80$		0			0
$81$	398.990	+	691.071i	0.00675693	+	0.0117033i
$82$		0			0
$83$	−14067.3			−0.224138			−0.112069	−	0.993700i	$-0.535748\pi$
$83$	−14067.3			−0.224138			−0.112069	+	0.993700i	$0.535748\pi$
$84$		0			0
$85$	−72544.7			−1.08908
$86$		0			0
$87$	−6885.25	−	11925.6i	−0.0975262	−	0.168920i
$88$		0			0
$89$	44776.9	−	77555.9i	0.599210	−	1.03786i	−0.393727	−	0.919227i	$-0.628815\pi$
$89$	44776.9	−	77555.9i	0.599210	−	1.03786i	0.992938	−	0.118636i	$-0.0378520\pi$
$90$		0			0
$91$	−3285.47	−	50620.2i	−0.0415904	−	0.640797i
$92$		0			0
$93$	−76827.7	+	133070.i	−0.921108	+	1.59541i
$94$		0			0
$95$	−13563.2	−	23492.1i	−0.154189	−	0.267063i
$96$		0			0
$97$	7209.53			0.0777997			0.0388998	−	0.999243i	$-0.487615\pi$
$97$	7209.53			0.0777997			0.0388998	+	0.999243i	$0.487615\pi$
$98$		0			0
$99$	−198489.			−2.03539
$100$		0			0
$101$	97609.2	+	169064.i	0.952110	+	1.64910i	0.740847	+	0.671674i	$0.234424\pi$
$101$	97609.2	+	169064.i	0.952110	+	1.64910i	0.211263	+	0.977429i	$0.432242\pi$
$102$		0			0
$103$	11816.8	−	20467.2i	0.109750	−	0.190093i	−0.805919	−	0.592026i	$-0.798328\pi$
$103$	11816.8	−	20467.2i	0.109750	−	0.190093i	0.915669	+	0.401933i	$0.131662\pi$
$104$		0			0
$105$	−17062.4	−	262886.i	−0.151031	−	2.32699i
$106$		0			0
$107$	53546.1	−	92744.5i	0.452135	−	0.783121i	−0.546383	−	0.837535i	$-0.683996\pi$
$107$	53546.1	−	92744.5i	0.452135	−	0.783121i	0.998518	+	0.0544144i	$0.0173292\pi$
$108$		0			0
$109$	−23110.7	−	40029.0i	−0.186315	−	0.322707i	0.757704	−	0.652598i	$-0.226321\pi$
$109$	−23110.7	−	40029.0i	−0.186315	−	0.322707i	−0.944019	+	0.329892i	$0.892988\pi$
$110$		0			0
$111$	373107.			2.87426
$112$		0			0
$113$	55520.3			0.409030			0.204515	−	0.978863i	$-0.434438\pi$
$113$	55520.3			0.409030			0.204515	+	0.978863i	$0.434438\pi$
$114$		0			0
$115$	−196487.	−	340326.i	−1.38545	−	2.39966i
$116$		0			0
$117$	−76634.7	+	132735.i	−0.517560	+	0.896441i
$118$		0			0
$119$	96991.7	−	64718.5i	0.627866	−	0.418949i
$120$		0			0
$121$	−47859.5	+	82895.1i	−0.297170	+	0.514713i
$122$		0			0
$123$	123918.	+	214632.i	0.738535	+	1.27918i
$124$		0			0
$125$	20624.8			0.118063
$126$		0			0
$127$	−230185.			−1.26639			−0.633195	−	0.773992i	$-0.718257\pi$
$127$	−230185.			−1.26639			−0.633195	+	0.773992i	$0.718257\pi$
$128$		0			0
$129$	−235068.	−	407150.i	−1.24371	−	2.15417i
$130$		0			0
$131$	−99500.5	+	172340.i	−0.506579	+	0.877420i	0.493392	+	0.869807i	$0.335757\pi$
$131$	−99500.5	+	172340.i	−0.506579	+	0.877420i	−0.999971	+	0.00761308i	$0.997577\pi$
$132$		0			0
$133$	39091.6	+	19308.8i	0.191626	+	0.0946512i
$134$		0			0
$135$	−151093.	+	261701.i	−0.713526	+	1.23586i
$136$		0			0
$137$	−63765.5	−	110445.i	−0.290258	−	0.502741i	0.683613	−	0.729845i	$-0.260408\pi$
$137$	−63765.5	−	110445.i	−0.290258	−	0.502741i	−0.973871	+	0.227104i	$0.927074\pi$
$138$		0			0
$139$	17259.8			0.0757703			0.0378851	−	0.999282i	$-0.487938\pi$
$139$	17259.8			0.0757703			0.0378851	+	0.999282i	$0.487938\pi$
$140$		0			0
$141$	35232.7			0.149244
$142$		0			0
$143$	99136.5	+	171709.i	0.405409	+	0.702189i
$144$		0			0
$145$	−22043.4	+	38180.4i	−0.0870682	+	0.150806i
$146$		0			0
$147$	257338.	+	336254.i	0.982223	+	1.28344i
$148$		0			0
$149$	417.263	−	722.720i	0.00153973	−	0.00266689i	−0.865255	−	0.501333i	$-0.832843\pi$
$149$	417.263	−	722.720i	0.00153973	−	0.00266689i	0.866794	+	0.498666i	$0.166177\pi$
$150$		0			0
$151$	−20469.3	−	35453.9i	−0.0730569	−	0.126538i	0.827183	−	0.561933i	$-0.189942\pi$
$151$	−20469.3	−	35453.9i	−0.0730569	−	0.126538i	−0.900240	+	0.435395i	$0.856609\pi$
$152$		0			0
$153$	−352308.			−1.21673
$154$		0			0
$155$	491935.			1.64467
$156$		0			0
$157$	−16444.1	−	28482.0i	−0.0532428	−	0.0922193i	0.838176	−	0.545400i	$-0.183622\pi$
$157$	−16444.1	−	28482.0i	−0.0532428	−	0.0922193i	−0.891418	+	0.453181i	$0.850289\pi$
$158$		0			0
$159$	248922.	−	431145.i	0.780854	−	1.35248i
$160$		0			0
$161$	566313.	+	279723.i	1.72184	+	0.850479i
$162$		0			0
$163$	35149.3	−	60880.4i	0.103621	−	0.179477i	−0.809553	−	0.587047i	$-0.800290\pi$
$163$	35149.3	−	60880.4i	0.103621	−	0.179477i	0.913174	+	0.407570i	$0.133624\pi$
$164$		0			0
$165$	514846.	+	891739.i	1.47220	+	2.54993i
$166$		0			0
$167$	227937.			0.632447			0.316224	−	0.948685i	$-0.397585\pi$
$167$	227937.			0.632447			0.316224	+	0.948685i	$0.397585\pi$
$168$		0			0
$169$	−218190.			−0.587650
$170$		0			0
$171$	−65868.6	−	114088.i	−0.172262	−	0.298366i
$172$		0			0
$173$	16895.1	−	29263.2i	0.0429186	−	0.0743372i	−0.843768	−	0.536708i	$-0.819668\pi$
$173$	16895.1	−	29263.2i	0.0429186	−	0.0743372i	0.886687	+	0.462371i	$0.153001\pi$
$174$		0			0
$175$	−364572.	+	243264.i	−0.899888	+	0.600458i
$176$		0			0
$177$	−342263.	+	592817.i	−0.821158	+	1.42229i
$178$		0			0
$179$	−307606.	−	532789.i	−0.717567	−	1.24286i	−0.961961	−	0.273186i	$-0.911922\pi$
$179$	−307606.	−	532789.i	−0.717567	−	1.24286i	0.244394	−	0.969676i	$-0.421411\pi$
$180$		0			0
$181$	−678787.			−1.54006			−0.770029	−	0.638008i	$-0.779758\pi$
$181$	−678787.			−1.54006			−0.770029	+	0.638008i	$0.779758\pi$
$182$		0			0
$183$	356927.			0.787864
$184$		0			0
$185$	−597259.	−	1.03448e6i	−1.28302	−	2.22226i
$186$		0			0
$187$	−227877.	+	394695.i	−0.476537	+	0.825386i
$188$		0			0
$189$	−31458.1	−	484684.i	−0.0640587	−	0.986971i
$190$		0			0
$191$	−327588.	+	567398.i	−0.649747	+	1.12539i	0.333436	+	0.942773i	$0.391792\pi$
$191$	−327588.	+	567398.i	−0.649747	+	1.12539i	−0.983183	+	0.182622i	$0.941542\pi$
$192$		0			0
$193$	160230.	+	277526.i	0.309635	+	0.536303i	0.978282	−	0.207276i	$-0.0664598\pi$
$193$	160230.	+	277526.i	0.309635	+	0.536303i	−0.668648	+	0.743579i	$0.733126\pi$
$194$		0			0
$195$	795108.			1.49741
$196$		0			0
$197$	202103.			0.371029			0.185514	−	0.982642i	$-0.440605\pi$
$197$	202103.			0.371029			0.185514	+	0.982642i	$0.440605\pi$
$198$		0			0
$199$	−319170.	−	552819.i	−0.571333	−	0.989578i	−0.996429	−	0.0844301i	$-0.973093\pi$
$199$	−319170.	−	552819.i	−0.571333	−	0.989578i	0.425096	−	0.905148i	$-0.360240\pi$
$200$		0			0
$201$	635455.	−	1.10064e6i	1.10942	−	1.92157i
$202$		0			0
$203$	−4589.53	−	70712.2i	−0.00781678	−	0.120435i
$204$		0			0
$205$	396729.	−	687154.i	0.659339	−	1.14201i
$206$		0			0
$207$	−954226.	−	1.65277e6i	−1.54784	−	2.68093i
$208$		0			0
$209$	−170418.			−0.269868
$210$		0			0
$211$	−517370.			−0.800010			−0.400005	−	0.916513i	$-0.630992\pi$
$211$	−517370.			−0.800010			−0.400005	+	0.916513i	$0.630992\pi$
$212$		0			0
$213$	570370.	+	987909.i	0.861405	+	1.49200i
$214$		0			0
$215$	−752581.	+	1.30351e6i	−1.11034	+	1.92317i
$216$		0			0
$217$	−657713.	+	438865.i	−0.948172	+	0.632676i
$218$		0			0
$219$	95317.2	−	165094.i	0.134295	−	0.232606i
$220$		0			0
$221$	175962.	+	304776.i	0.242348	+	0.419759i
$222$		0			0
$223$	755836.			1.01781			0.508904	−	0.860824i	$-0.330051\pi$
$223$	755836.			1.01781			0.508904	+	0.860824i	$0.330051\pi$
$224$		0			0
$225$	1.32426e6			1.74388
$226$		0			0
$227$	440624.	+	763184.i	0.567550	+	0.983025i	0.996807	+	0.0798426i	$0.0254418\pi$
$227$	440624.	+	763184.i	0.567550	+	0.983025i	−0.429258	+	0.903182i	$0.641225\pi$
$228$		0			0
$229$	139756.	−	242065.i	0.176109	−	0.305031i	−0.764435	−	0.644701i	$-0.776982\pi$
$229$	139756.	−	242065.i	0.176109	−	0.305031i	0.940545	+	0.339670i	$0.110315\pi$
$230$		0			0
$231$	−1.48388e6	−	732944.i	−1.82966	−	0.903734i
$232$		0			0
$233$	533391.	−	923860.i	0.643659	−	1.11485i	−0.340950	−	0.940081i	$-0.610749\pi$
$233$	533391.	−	923860.i	0.643659	−	1.11485i	0.984609	−	0.174769i	$-0.0559179\pi$
$234$		0			0
$235$	−56399.5	−	97686.8i	−0.0666201	−	0.115389i
$236$		0			0
$237$	121682.			0.140720
$238$		0			0
$239$	−270341.			−0.306138			−0.153069	−	0.988215i	$-0.548916\pi$
$239$	−270341.			−0.306138			−0.153069	+	0.988215i	$0.548916\pi$
$240$		0			0
$241$	657034.	+	1.13802e6i	0.728694	+	1.26214i	0.957435	+	0.288648i	$0.0932058\pi$
$241$	657034.	+	1.13802e6i	0.728694	+	1.26214i	−0.228741	+	0.973487i	$0.573461\pi$
$242$		0			0
$243$	465253.	−	805841.i	0.505444	−	0.875455i
$244$		0			0
$245$	520367.	−	1.25177e6i	0.553853	−	1.33232i
$246$		0			0
$247$	−65796.9	+	113964.i	−0.0686220	+	0.118857i
$248$		0			0
$249$	177202.	+	306923.i	0.181122	+	0.313712i
$250$		0			0
$251$	−1.31291e6			−1.31538			−0.657690	−	0.753289i	$-0.728466\pi$
$251$	−1.31291e6			−1.31538			−0.657690	+	0.753289i	$0.728466\pi$
$252$		0			0
$253$	−2.46882e6			−2.42487
$254$		0			0
$255$	913825.	+	1.58279e6i	0.880061	+	1.52431i
$256$		0			0
$257$	−353720.	+	612661.i	−0.334062	+	0.578612i	−0.983304	−	0.181970i	$-0.941753\pi$
$257$	−353720.	+	612661.i	−0.334062	+	0.578612i	0.649242	+	0.760582i	$0.275086\pi$
$258$		0			0
$259$	1.72141e6	+	850270.i	1.59454	+	0.787603i
$260$		0			0
$261$	−107052.	+	185420.i	−0.0972736	+	0.168483i
$262$		0			0
$263$	369721.	+	640376.i	0.329598	+	0.570881i	0.982432	−	0.186620i	$-0.0597534\pi$
$263$	369721.	+	640376.i	0.329598	+	0.570881i	−0.652834	+	0.757501i	$0.726420\pi$
$264$		0			0
$265$	−1.59387e6			−1.39424
$266$		0			0
$267$	−2.25617e6			−1.93684
$268$		0			0
$269$	619595.	+	1.07317e6i	0.522068	+	0.904249i	0.999670	+	0.0256724i	$0.00817269\pi$
$269$	619595.	+	1.07317e6i	0.522068	+	0.904249i	−0.477602	+	0.878576i	$0.658494\pi$
$270$		0			0
$271$	257391.	−	445815.i	0.212898	−	0.368749i	−0.739723	−	0.672912i	$-0.765043\pi$
$271$	257391.	−	445815.i	0.212898	−	0.368749i	0.952620	+	0.304163i	$0.0983766\pi$
$272$		0			0
$273$	−1.06305e6	+	709331.i	−0.863273	+	0.576026i
$274$		0			0
$275$	856544.	−	1.48358e6i	0.682996	−	1.18298i
$276$		0			0
$277$	648520.	+	1.12327e6i	0.507837	+	0.879599i	0.999959	+	0.00907261i	$0.00288794\pi$
$277$	648520.	+	1.12327e6i	0.507837	+	0.879599i	−0.492122	+	0.870526i	$0.663779\pi$
$278$		0			0
$279$	2.38905e6			1.83744
$280$		0			0
$281$	2.61884e6			1.97853			0.989265	−	0.146133i	$-0.0466828\pi$
$281$	2.61884e6			1.97853			0.989265	+	0.146133i	$0.0466828\pi$
$282$		0			0
$283$	−20922.9	−	36239.4i	−0.0155294	−	0.0268977i	0.858156	−	0.513389i	$-0.171610\pi$
$283$	−20922.9	−	36239.4i	−0.0155294	−	0.0268977i	−0.873686	+	0.486491i	$0.838277\pi$
$284$		0			0
$285$	−341703.	+	591847.i	−0.249194	+	0.431616i
$286$		0			0
$287$	82600.4	+	1.27265e6i	0.0591940	+	0.912019i
$288$		0			0
$289$	305458.	−	529069.i	0.215133	−	0.372621i
$290$		0			0
$291$	−90816.5	−	157299.i	−0.0628684	−	0.108891i
$292$		0			0
$293$	−1.94837e6			−1.32588			−0.662938	−	0.748674i	$-0.730691\pi$
$293$	−1.94837e6			−1.32588			−0.662938	+	0.748674i	$0.730691\pi$
$294$		0			0
$295$	2.19154e6			1.46620
$296$		0			0
$297$	949225.	+	1.64411e6i	0.624422	+	1.08153i
$298$		0			0
$299$	−953188.	+	1.65097e6i	−0.616596	+	1.06798i
$300$		0			0
$301$	−156690.	−	2.41417e6i	−0.0996840	−	1.53586i
$302$		0			0
$303$	2.45911e6	−	4.25931e6i	1.53876	−	2.66521i
$304$		0			0
$305$	−571358.	−	989622.i	−0.351689	−	0.609143i
$306$		0			0
$307$	−209113.			−0.126630			−0.0633149	−	0.997994i	$-0.520167\pi$
$307$	−209113.			−0.126630			−0.0633149	+	0.997994i	$0.520167\pi$
$308$		0			0
$309$	−595410.			−0.354748
$310$		0			0
$311$	46862.0	+	81167.3i	0.0274739	+	0.0475861i	0.879435	−	0.476018i	$-0.157920\pi$
$311$	46862.0	+	81167.3i	0.0274739	+	0.0475861i	−0.851962	+	0.523604i	$0.824587\pi$
$312$		0			0
$313$	250057.	−	433112.i	0.144271	−	0.249884i	−0.784830	−	0.619711i	$-0.787250\pi$
$313$	250057.	−	433112.i	0.144271	−	0.249884i	0.929101	+	0.369827i	$0.120583\pi$
$314$		0			0
$315$	−3.40712e6	+	2.27343e6i	−1.93469	+	1.29094i
$316$		0			0
$317$	737146.	−	1.27677e6i	0.412007	−	0.713618i	−0.583102	−	0.812399i	$-0.698161\pi$
$317$	737146.	−	1.27677e6i	0.412007	−	0.713618i	0.995109	+	0.0987813i	$0.0314944\pi$
$318$		0			0
$319$	138485.	+	239864.i	0.0761952	+	0.131974i
$320$		0			0
$321$	−2.69802e6			−1.46145
$322$		0			0
$323$	−302484.			−0.161323
$324$		0			0
$325$	−661407.	−	1.14559e6i	−0.347345	−	0.601618i
$326$		0			0
$327$	−582239.	+	1.00847e6i	−0.301115	+	0.521546i
$328$		0			0
$329$	162554.	+	80291.4i	0.0827957	+	0.0408958i
$330$		0			0
$331$	1.18818e6	−	2.05800e6i	0.596093	−	1.03246i	−0.397299	−	0.917689i	$-0.630052\pi$
$331$	1.18818e6	−	2.05800e6i	0.596093	−	1.03246i	0.993392	−	0.114774i	$-0.0366143\pi$
$332$		0			0
$333$	−2.90055e6	−	5.02390e6i	−1.43341	−	2.48273i
$334$		0			0
$335$	−4.06888e6			−1.98090
$336$		0			0
$337$	2.56857e6			1.23202			0.616008	−	0.787740i	$-0.288749\pi$
$337$	2.56857e6			1.23202			0.616008	+	0.787740i	$0.288749\pi$
$338$		0			0
$339$	−699374.	−	1.21135e6i	−0.330529	−	0.572494i
$340$		0			0
$341$	1.54526e6	−	2.67647e6i	0.719642	−	1.24646i
$342$		0			0
$343$	420999.	+	2.13783e6i	0.193217	+	0.981156i
$344$		0			0
$345$	−4.95019e6	+	8.57398e6i	−2.23910	+	3.87824i
$346$		0			0
$347$	306273.	+	530480.i	0.136548	+	0.236508i	0.926188	−	0.377063i	$-0.123066\pi$
$347$	306273.	+	530480.i	0.136548	+	0.236508i	−0.789640	+	0.613571i	$0.789733\pi$
$348$		0			0
$349$	3.83323e6			1.68462			0.842310	−	0.538994i	$-0.181195\pi$
$349$	3.83323e6			1.68462			0.842310	+	0.538994i	$0.181195\pi$
$350$		0			0
$351$	1.46595e6			0.635112
$352$		0			0
$353$	−1.42925e6	−	2.47554e6i	−0.610481	−	1.05738i	−0.991159	−	0.132676i	$-0.957643\pi$
$353$	−1.42925e6	−	2.47554e6i	−0.610481	−	1.05738i	0.380679	−	0.924707i	$-0.375690\pi$
$354$		0			0
$355$	1.82606e6	−	3.16284e6i	0.769034	−	1.33201i
$356$		0			0
$357$	−2.63382e6	−	1.30094e6i	−1.09374	−	0.540239i
$358$		0			0
$359$	−193874.	+	335800.i	−0.0793933	+	0.137513i	−0.902988	−	0.429665i	$-0.858632\pi$
$359$	−193874.	+	335800.i	−0.0793933	+	0.137513i	0.823595	+	0.567178i	$0.191965\pi$
$360$		0			0
$361$	1.18150e6	+	2.04641e6i	0.477160	+	0.826466i
$362$		0			0
$363$	2.41149e6			0.960549
$364$		0			0
$365$	−610325.			−0.239789
$366$		0			0
$367$	−96154.9	−	166545.i	−0.0372654	−	0.0645456i	0.846791	−	0.531926i	$-0.178531\pi$
$367$	−96154.9	−	166545.i	−0.0372654	−	0.0645456i	−0.884057	+	0.467380i	$0.845198\pi$
$368$		0			0
$369$	1.92669e6	−	3.33712e6i	0.736622	−	1.27587i
$370$		0			0
$371$	2.13099e6	−	1.42192e6i	0.803797	−	0.536340i
$372$		0			0
$373$	1.13262e6	−	1.96175e6i	0.421514	−	0.730083i	−0.574574	−	0.818453i	$-0.694832\pi$
$373$	1.13262e6	−	1.96175e6i	0.421514	−	0.730083i	0.996088	+	0.0883694i	$0.0281656\pi$
$374$		0			0
$375$	−259805.	−	449995.i	−0.0954044	−	0.165245i
$376$		0			0
$377$	213872.			0.0774997
$378$		0			0
$379$	4.46258e6			1.59583			0.797917	−	0.602767i	$-0.205935\pi$
$379$	4.46258e6			1.59583			0.797917	+	0.602767i	$0.205935\pi$
$380$		0			0
$381$	2.89957e6	+	5.02221e6i	1.02334	+	1.77248i
$382$		0			0
$383$	902218.	−	1.56269e6i	0.314279	−	0.544346i	−0.665005	−	0.746839i	$-0.731571\pi$
$383$	902218.	−	1.56269e6i	0.314279	−	0.544346i	0.979284	+	0.202492i	$0.0649041\pi$
$384$		0			0
$385$	343182.	+	5.28752e6i	0.117998	+	1.81803i
$386$		0			0
$387$	−3.65486e6	+	6.33040e6i	−1.24049	+	2.14859i
$388$		0			0
$389$	−55455.6	−	96051.9i	−0.0185811	−	0.0321834i	0.856585	−	0.516005i	$-0.172582\pi$
$389$	−55455.6	−	96051.9i	−0.0185811	−	0.0321834i	−0.875166	+	0.483822i	$0.839248\pi$
$390$		0			0
$391$	−4.38203e6			−1.44955
$392$		0			0
$393$	5.01352e6			1.63742
$394$		0			0
$395$	−194786.	−	337379.i	−0.0628151	−	0.108799i
$396$		0			0
$397$	−2.74389e6	+	4.75256e6i	−0.873758	+	1.51339i	−0.0156779	+	0.999877i	$0.504991\pi$
$397$	−2.74389e6	+	4.75256e6i	−0.873758	+	1.51339i	−0.858080	+	0.513516i	$0.828343\pi$
$398$		0			0
$399$	−71143.9	−	1.09614e6i	−0.0223720	−	0.344692i
$400$		0			0
$401$	−467219.	+	809247.i	−0.145097	+	0.251316i	−0.929409	−	0.369051i	$-0.879683\pi$
$401$	−467219.	+	809247.i	−0.145097	+	0.251316i	0.784312	+	0.620367i	$0.213016\pi$
$402$		0			0
$403$	−1.19322e6	−	2.06672e6i	−0.365982	−	0.633899i
$404$		0			0
$405$	−64363.4			−0.0194985
$406$		0			0
$407$	−7.50443e6			−2.24560
$408$		0			0
$409$	738463.	+	1.27905e6i	0.218283	+	0.378078i	0.954283	−	0.298904i	$-0.0966210\pi$
$409$	738463.	+	1.27905e6i	0.218283	+	0.378078i	−0.736000	+	0.676981i	$0.763288\pi$
$410$		0			0
$411$	−1.60647e6	+	2.78249e6i	−0.469103	+	0.812511i
$412$		0			0
$413$	−2.93007e6	+	1.95512e6i	−0.845285	+	0.564024i
$414$		0			0
$415$	567320.	−	982627.i	0.161699	−	0.280071i
$416$		0			0
$417$	−217417.	−	376577.i	−0.0612285	−	0.106051i
$418$		0			0
$419$	2.66235e6			0.740849			0.370424	−	0.928863i	$-0.379212\pi$
$419$	2.66235e6			0.740849			0.370424	+	0.928863i	$0.379212\pi$
$420$		0			0
$421$	−1.02032e6			−0.280563			−0.140282	−	0.990112i	$-0.544801\pi$
$421$	−1.02032e6			−0.280563			−0.140282	+	0.990112i	$0.544801\pi$
$422$		0			0
$423$	−273900.	−	474409.i	−0.0744288	−	0.128915i
$424$		0			0
$425$	1.52032e6	−	2.63328e6i	0.408285	−	0.707170i
$426$		0			0
$427$	1.64676e6	+	813396.i	0.437080	+	0.215890i
$428$		0			0
$429$	2.49759e6	−	4.32595e6i	0.655206	−	1.13485i
$430$		0			0
$431$	100134.	+	173436.i	0.0259649	+	0.0449725i	0.878716	−	0.477345i	$-0.158401\pi$
$431$	100134.	+	173436.i	0.0259649	+	0.0449725i	−0.852751	+	0.522318i	$0.825068\pi$
$432$		0			0
$433$	5.84752e6			1.49883			0.749415	−	0.662101i	$-0.230335\pi$
$433$	5.84752e6			1.49883			0.749415	+	0.662101i	$0.230335\pi$
$434$		0			0
$435$	1.11070e6			0.281432
$436$		0			0
$437$	−819278.	−	1.41903e6i	−0.205224	−	0.355458i
$438$		0			0
$439$	−3.16278e6	+	5.47809e6i	−0.783262	+	1.35665i	0.146769	+	0.989171i	$0.453112\pi$
$439$	−3.16278e6	+	5.47809e6i	−0.783262	+	1.35665i	−0.930032	+	0.367479i	$0.880221\pi$
$440$		0			0
$441$	2.52712e6	−	6.07912e6i	0.618771	−	1.48848i
$442$		0			0
$443$	−1.10193e6	+	1.90859e6i	−0.266774	+	0.462066i	−0.968027	−	0.250846i	$-0.919291\pi$
$443$	−1.10193e6	+	1.90859e6i	−0.266774	+	0.462066i	0.701253	+	0.712913i	$0.252624\pi$
$444$		0			0
$445$	3.61162e6	+	6.25550e6i	0.864573	+	1.49748i
$446$		0			0
$447$	−21024.6			−0.00497689
$448$		0			0
$449$	−2.66634e6			−0.624166			−0.312083	−	0.950055i	$-0.601027\pi$
$449$	−2.66634e6			−0.624166			−0.312083	+	0.950055i	$0.601027\pi$
$450$		0			0
$451$	−2.49241e6	−	4.31697e6i	−0.577002	−	0.999397i
$452$		0			0
$453$	−515693.	+	893206.i	−0.118072	+	0.204506i
$454$		0			0
$455$	3.66841e6	+	1.81196e6i	0.830710	+	0.410319i
$456$		0			0
$457$	3.04406e6	−	5.27247e6i	0.681809	−	1.18093i	−0.292619	−	0.956229i	$-0.594527\pi$
$457$	3.04406e6	−	5.27247e6i	0.681809	−	1.18093i	0.974428	−	0.224699i	$-0.0721400\pi$
$458$		0			0
$459$	1.68483e6	+	2.91820e6i	0.373270	+	0.646523i
$460$		0			0
$461$	381317.			0.0835668			0.0417834	−	0.999127i	$-0.486696\pi$
$461$	381317.			0.0835668			0.0417834	+	0.999127i	$0.486696\pi$
$462$		0			0
$463$	−99697.8			−0.0216139			−0.0108069	−	0.999942i	$-0.503440\pi$
$463$	−99697.8			−0.0216139			−0.0108069	+	0.999942i	$0.503440\pi$
$464$		0			0
$465$	−6.19677e6	−	1.07331e7i	−1.32902	−	2.30194i
$466$		0			0
$467$	−2.81889e6	+	4.88246e6i	−0.598116	+	1.03597i	0.394983	+	0.918689i	$0.370751\pi$
$467$	−2.81889e6	+	4.88246e6i	−0.598116	+	1.03597i	−0.993099	+	0.117279i	$0.962583\pi$
$468$		0			0
$469$	5.44006e6	−	3.62993e6i	1.14201	−	0.762019i
$470$		0			0
$471$	−414284.	+	717561.i	−0.0860490	+	0.149041i
$472$		0			0
$473$	4.72801e6	+	8.18915e6i	0.971685	+	1.68301i
$474$		0			0
$475$	1.13698e6			0.231216
$476$		0			0
$477$	−7.74051e6			−1.55766
$478$		0			0
$479$	870394.	+	1.50757e6i	0.173331	+	0.300219i	0.939583	−	0.342322i	$-0.111213\pi$
$479$	870394.	+	1.50757e6i	0.173331	+	0.300219i	−0.766251	+	0.642541i	$0.777880\pi$
$480$		0			0
$481$	−2.89739e6	+	5.01843e6i	−0.571011	+	0.989020i
$482$		0			0
$483$	−1.03065e6	−	1.58795e7i	−0.201022	−	3.09720i
$484$		0			0
$485$	−290753.	+	503599.i	−0.0561268	+	0.0972144i
$486$		0			0
$487$	−2.41235e6	−	4.17832e6i	−0.460913	−	0.798324i	0.538094	−	0.842885i	$-0.319145\pi$
$487$	−2.41235e6	−	4.17832e6i	−0.460913	−	0.798324i	−0.999007	+	0.0445607i	$0.985811\pi$
$488$		0			0
$489$	−1.77106e6			−0.334936
$490$		0			0
$491$	−4.46085e6			−0.835053			−0.417527	−	0.908665i	$-0.637103\pi$
$491$	−4.46085e6			−0.835053			−0.417527	+	0.908665i	$0.637103\pi$
$492$		0			0
$493$	245805.	+	425746.i	0.0455484	+	0.0788921i
$494$		0			0
$495$	8.00486e6	−	1.38648e7i	1.46839	−	2.54332i
$496$		0			0
$497$	380193.	+	5.85775e6i	0.0690420	+	1.06375i
$498$		0			0
$499$	370378.	−	641513.i	0.0665876	−	0.115333i	−0.830810	−	0.556557i	$-0.812122\pi$
$499$	370378.	−	641513.i	0.0665876	−	0.115333i	0.897397	+	0.441224i	$0.145455\pi$
$500$		0			0
$501$	−2.87126e6	−	4.97317e6i	−0.511068	−	0.885196i
$502$		0			0
$503$	−3.74899e6			−0.660686			−0.330343	−	0.943861i	$-0.607164\pi$
$503$	−3.74899e6			−0.660686			−0.330343	+	0.943861i	$0.607164\pi$
$504$		0			0
$505$	−1.57459e7			−2.74751
$506$		0			0
$507$	2.74848e6	+	4.76051e6i	0.474868	+	0.822496i
$508$		0			0
$509$	1.33228e6	−	2.30757e6i	0.227929	−	0.394785i	−0.729265	−	0.684231i	$-0.760138\pi$
$509$	1.33228e6	−	2.30757e6i	0.227929	−	0.394785i	0.957194	+	0.289446i	$0.0934711\pi$
$510$		0			0
$511$	815999.	−	544482.i	0.138241	−	0.0922426i
$512$		0			0
$513$	−630001.	+	1.09119e6i	−0.105693	+	0.183066i
$514$		0			0
$515$	953116.	+	1.65085e6i	0.158353	+	0.274276i
$516$		0			0
$517$	−708647.			−0.116601
$518$		0			0
$519$	−851292.			−0.138727
$520$		0			0
$521$	−416312.	−	721073.i	−0.0671930	−	0.116382i	0.830472	−	0.557061i	$-0.188071\pi$
$521$	−416312.	−	721073.i	−0.0671930	−	0.116382i	−0.897665	+	0.440679i	$0.854738\pi$
$522$		0			0
$523$	936507.	−	1.62208e6i	0.149712	−	0.259309i	−0.781409	−	0.624019i	$-0.785499\pi$
$523$	936507.	−	1.62208e6i	0.149712	−	0.259309i	0.931121	+	0.364710i	$0.118832\pi$
$524$		0			0
$525$	9.89999e6	+	4.88997e6i	1.56760	+	0.774297i
$526$		0			0
$527$	2.74277e6	−	4.75061e6i	0.430192	−	0.745114i
$528$		0			0
$529$	−8.65056e6	−	1.49832e7i	−1.34402	−	2.32791i
$530$		0			0
$531$	1.06431e7			1.63806
$532$		0			0
$533$	−3.84918e6			−0.586881
$534$		0			0
$535$	4.31892e6	+	7.48058e6i	0.652364	+	1.12993i
$536$		0			0
$537$	−7.74966e6	+	1.34228e7i	−1.15970	+	2.00866i
$538$		0			0
$539$	−5.17593e6	−	6.76321e6i	−0.767390	−	1.00272i
$540$		0			0
$541$	−2.23793e6	+	3.87621e6i	−0.328741	+	0.569395i	−0.982262	−	0.187512i	$-0.939958\pi$
$541$	−2.23793e6	+	3.87621e6i	−0.328741	+	0.569395i	0.653522	+	0.756908i	$0.273291\pi$
$542$		0			0
$543$	8.55050e6	+	1.48099e7i	1.24449	+	2.15552i
$544$		0			0
$545$	3.72813e6			0.537650
$546$		0			0
$547$	6.12226e6			0.874869			0.437435	−	0.899250i	$-0.355887\pi$
$547$	6.12226e6			0.874869			0.437435	+	0.899250i	$0.355887\pi$
$548$		0			0
$549$	−2.77476e6	−	4.80603e6i	−0.392911	−	0.680543i
$550$		0			0
$551$	−91912.9	+	159198.i	−0.0128973	+	0.0223387i
$552$		0			0
$553$	561409.	+	277300.i	0.0780668	+	0.0385601i
$554$		0			0
$555$	−1.50470e7	+	2.60622e7i	−2.07357	+	3.59152i
$556$		0			0
$557$	4.76272e6	+	8.24927e6i	0.650454	+	1.12662i	0.983013	+	0.183537i	$0.0587547\pi$
$557$	4.76272e6	+	8.24927e6i	0.650454	+	1.12662i	−0.332559	+	0.943083i	$0.607912\pi$
$558$		0			0
$559$	7.30176e6			0.988321
$560$		0			0
$561$	1.14820e7			1.54032
$562$		0			0
$563$	−4.04958e6	−	7.01408e6i	−0.538442	−	0.932609i	−0.998988	−	0.0449731i	$-0.985680\pi$
$563$	−4.04958e6	−	7.01408e6i	−0.538442	−	0.932609i	0.460546	−	0.887636i	$-0.347654\pi$
$564$		0			0
$565$	−2.23908e6	+	3.87819e6i	−0.295085	+	0.511103i
$566$		0			0
$567$	86053.4	−	57419.8i	0.0112411	−	0.00750074i
$568$		0			0
$569$	3.69587e6	−	6.40144e6i	0.478560	−	0.828890i	−0.521138	−	0.853472i	$-0.674492\pi$
$569$	3.69587e6	−	6.40144e6i	0.478560	−	0.828890i	0.999698	+	0.0245827i	$0.00782570\pi$
$570$		0			0
$571$	−1.73172e6	−	2.99943e6i	−0.222273	−	0.384989i	0.733225	−	0.679986i	$-0.238014\pi$
$571$	−1.73172e6	−	2.99943e6i	−0.222273	−	0.384989i	−0.955498	+	0.294998i	$0.904681\pi$
$572$		0			0
$573$	1.65061e7			2.10019
$574$		0			0
$575$	1.64712e7			2.07757
$576$		0			0
$577$	−2.58289e6	−	4.47369e6i	−0.322973	−	0.559405i	0.658127	−	0.752907i	$-0.271349\pi$
$577$	−2.58289e6	−	4.47369e6i	−0.322973	−	0.559405i	−0.981100	+	0.193502i	$0.938015\pi$
$578$		0			0
$579$	4.03674e6	−	6.99184e6i	0.500420	−	0.866752i
$580$		0			0
$581$	118118.	+	1.81988e6i	0.0145170	+	0.223667i
$582$		0			0
$583$	−5.00665e6	+	8.67177e6i	−0.610065	+	1.05666i
$584$		0			0
$585$	−6.18120e6	−	1.07062e7i	−0.746764	−	1.29343i
$586$		0			0
$587$	4.08305e6			0.489090			0.244545	−	0.969638i	$-0.421361\pi$
$587$	4.08305e6			0.489090			0.244545	+	0.969638i	$0.421361\pi$
$588$		0			0
$589$	2.05118e6			0.243622
$590$		0			0
$591$	−2.54584e6	−	4.40952e6i	−0.299821	−	0.519305i
$592$		0			0
$593$	3.91092e6	−	6.77391e6i	0.456712	−	0.791048i	−0.542073	−	0.840331i	$-0.682360\pi$
$593$	3.91092e6	−	6.77391e6i	0.456712	−	0.791048i	0.998785	+	0.0492833i	$0.0156937\pi$
$594$		0			0
$595$	609132.	+	9.38508e6i	0.0705373	+	1.08679i
$596$		0			0
$597$	−8.04100e6	+	1.39274e7i	−0.923366	+	1.59932i
$598$		0			0
$599$	3.15891e6	+	5.47139e6i	0.359725	+	0.623061i	0.987915	−	0.154999i	$-0.0495373\pi$
$599$	3.15891e6	+	5.47139e6i	0.359725	+	0.623061i	−0.628190	+	0.778060i	$0.716204\pi$
$600$		0			0
$601$	−1.68407e6			−0.190184			−0.0950919	−	0.995468i	$-0.530315\pi$
$601$	−1.68407e6			−0.190184			−0.0950919	+	0.995468i	$0.530315\pi$
$602$		0			0
$603$	−1.97602e7			−2.21309
$604$		0			0
$605$	−3.86025e6	−	6.68615e6i	−0.428773	−	0.742656i
$606$		0			0
$607$	−2.72757e6	+	4.72429e6i	−0.300472	+	0.520432i	−0.976243	−	0.216679i	$-0.930477\pi$
$607$	−2.72757e6	+	4.72429e6i	−0.300472	+	0.520432i	0.675771	+	0.737112i	$0.263811\pi$
$608$		0			0
$609$	−1.48500e6	+	990877.i	−0.162249	+	0.108262i
$610$		0			0
$611$	−273602.	+	473893.i	−0.0296494	+	0.0513543i
$612$		0			0
$613$	4.06685e6	+	7.04399e6i	0.437127	+	0.757125i	0.997467	−	0.0711373i	$-0.0226629\pi$
$613$	4.06685e6	+	7.04399e6i	0.437127	+	0.757125i	−0.560340	+	0.828263i	$0.689330\pi$
$614$		0			0
$615$	−1.99899e7			−2.13120
$616$		0			0
$617$	2.83775e6			0.300097			0.150048	−	0.988679i	$-0.452057\pi$
$617$	2.83775e6			0.300097			0.150048	+	0.988679i	$0.452057\pi$
$618$		0			0
$619$	−6.19545e6	−	1.07308e7i	−0.649900	−	1.12566i	−0.983146	−	0.182820i	$-0.941478\pi$
$619$	−6.19545e6	−	1.07308e7i	−0.649900	−	1.12566i	0.333247	−	0.942840i	$-0.391856\pi$
$620$		0			0
$621$	−9.12670e6	+	1.58079e7i	−0.949697	+	1.64492i
$622$		0			0
$623$	−1.04094e7	−	5.14157e6i	−1.07449	−	0.530732i
$624$		0			0
$625$	4.45058e6	−	7.70863e6i	0.455739	−	0.789363i
$626$		0			0
$627$	2.14671e6	+	3.71822e6i	0.218075	+	0.377716i
$628$		0			0
$629$	−1.33200e7			−1.34239
$630$		0			0
$631$	3.25659e6			0.325604			0.162802	−	0.986659i	$-0.447947\pi$
$631$	3.25659e6			0.325604			0.162802	+	0.986659i	$0.447947\pi$
$632$		0			0
$633$	6.51717e6	+	1.12881e7i	0.646472	+	1.11972i
$634$		0			0
$635$	9.28312e6	−	1.60788e7i	0.913608	−	1.58241i
$636$		0			0
$637$	−6.52113e6	+	850079.i	−0.636757	+	0.0830062i
$638$		0			0
$639$	8.86815e6	−	1.53601e7i	0.859174	−	1.48813i
$640$		0			0
$641$	−1.15075e6	−	1.99316e6i	−0.110621	−	0.191601i	0.805400	−	0.592732i	$-0.201951\pi$
$641$	−1.15075e6	−	1.99316e6i	−0.110621	−	0.191601i	−0.916021	+	0.401131i	$0.868617\pi$
$642$		0			0
$643$	−8.68991e6			−0.828872			−0.414436	−	0.910078i	$-0.636021\pi$
$643$	−8.68991e6			−0.828872			−0.414436	+	0.910078i	$0.636021\pi$
$644$		0			0
$645$	3.79202e7			3.58898
$646$		0			0
$647$	1.14216e6	+	1.97828e6i	0.107267	+	0.185792i	0.914662	−	0.404219i	$-0.132457\pi$
$647$	1.14216e6	+	1.97828e6i	0.107267	+	0.185792i	−0.807395	+	0.590011i	$0.799123\pi$
$648$		0			0
$649$	6.88406e6	−	1.19235e7i	0.641554	−	1.11120i
$650$		0			0
$651$	1.78602e7	+	8.82184e6i	1.65171	+	0.815843i
$652$		0			0
$653$	−1.08384e6	+	1.87726e6i	−0.0994674	+	0.172283i	−0.911464	−	0.411379i	$-0.865047\pi$
$653$	−1.08384e6	+	1.87726e6i	−0.0994674	+	0.172283i	0.811997	+	0.583662i	$0.198381\pi$
$654$		0			0
$655$	−8.02550e6	−	1.39006e7i	−0.730919	−	1.26599i
$656$		0			0
$657$	−2.96400e6			−0.267895
$658$		0			0
$659$	1.18596e7			1.06380			0.531898	−	0.846809i	$-0.321479\pi$
$659$	1.18596e7			1.06380			0.531898	+	0.846809i	$0.321479\pi$
$660$		0			0
$661$	−713359.	−	1.23557e6i	−0.0635045	−	0.109993i	0.832525	−	0.553987i	$-0.186894\pi$
$661$	−713359.	−	1.23557e6i	−0.0635045	−	0.109993i	−0.896030	+	0.443994i	$0.853561\pi$
$662$		0			0
$663$	4.43310e6	−	7.67835e6i	0.391673	−	0.678397i
$664$		0			0
$665$	−2.92528e6	+	1.95192e6i	−0.256515	+	0.171162i
$666$		0			0
$667$	−1.33152e6	+	2.30627e6i	−0.115887	+	0.200722i
$668$		0			0
$669$	−9.52106e6	−	1.64910e7i	−0.822470	−	1.42456i
$670$		0			0
$671$	−7.17899e6			−0.615541
$672$		0			0
$673$	−2.07459e7			−1.76561			−0.882806	−	0.469738i	$-0.844348\pi$
$673$	−2.07459e7			−1.76561			−0.882806	+	0.469738i	$0.844348\pi$
$674$		0			0
$675$	−6.33292e6	−	1.09689e7i	−0.534989	−	0.926628i
$676$		0			0
$677$	6.42895e6	−	1.11353e7i	0.539098	−	0.933746i	−0.459854	−	0.887994i	$-0.652098\pi$
$677$	6.42895e6	−	1.11353e7i	0.539098	−	0.933746i	0.998953	−	0.0457516i	$-0.0145683\pi$
$678$		0			0
$679$	−60535.9	−	932695.i	−0.00503893	−	0.0776363i
$680$		0			0
$681$	1.11008e7	−	1.92272e7i	0.917251	−	1.58873i
$682$		0			0
$683$	9.64820e6	+	1.67112e7i	0.791397	+	1.37074i	0.925102	+	0.379719i	$0.123979\pi$
$683$	9.64820e6	+	1.67112e7i	0.791397	+	1.37074i	−0.133705	+	0.991021i	$0.542687\pi$
$684$		0			0
$685$	1.02864e7			0.837599
$686$		0			0
$687$	−7.04189e6			−0.569242
$688$		0			0
$689$	3.86604e6	+	6.69618e6i	0.310255	+	0.537377i
$690$		0			0
$691$	−9.14995e6	+	1.58482e7i	−0.728993	+	1.26265i	0.228316	+	0.973587i	$0.426678\pi$
$691$	−9.14995e6	+	1.58482e7i	−0.728993	+	1.26265i	−0.957309	+	0.289066i	$0.906655\pi$
$692$		0			0
$693$	1.66664e6	+	2.56784e7i	0.131828	+	2.03112i
$694$		0			0
$695$	−696070.	+	1.20563e6i	−0.0546627	+	0.0946786i
$696$		0			0
$697$	−4.42389e6	−	7.66241e6i	−0.344924	−	0.597425i
$698$		0			0
$699$	−2.68759e7			−2.08051
$700$		0			0
$701$	−1.61515e7			−1.24142			−0.620710	−	0.784040i	$-0.713156\pi$
$701$	−1.61515e7			−1.24142			−0.620710	+	0.784040i	$0.713156\pi$
$702$		0			0
$703$	−2.49035e6	−	4.31341e6i	−0.190052	−	0.329179i
$704$		0			0
$705$	−1.42090e6	+	2.46107e6i	−0.107669	+	0.186488i
$706$		0			0
$707$	2.10522e7	−	1.40472e7i	1.58397	−	1.05692i
$708$		0			0
$709$	−749950.	+	1.29895e6i	−0.0560295	+	0.0970459i	−0.892680	−	0.450692i	$-0.851177\pi$
$709$	−749950.	+	1.29895e6i	−0.0560295	+	0.0970459i	0.836650	+	0.547738i	$0.184511\pi$
$710$		0			0
$711$	−945963.	−	1.63846e6i	−0.0701778	−	0.121552i
$712$		0			0
$713$	2.97151e7			2.18904
$714$		0			0
$715$	−1.59923e7			−1.16989
$716$		0			0
$717$	3.40541e6	+	5.89835e6i	0.247384	+	0.428482i
$718$		0			0
$719$	−8.78693e6	+	1.52194e7i	−0.633892	+	1.09793i	0.352857	+	0.935677i	$0.385210\pi$
$719$	−8.78693e6	+	1.52194e7i	−0.633892	+	1.09793i	−0.986749	+	0.162255i	$0.948123\pi$
$720$		0			0
$721$	−2.74706e6	−	1.35687e6i	−0.196802	−	0.0972078i
$722$		0			0
$723$	1.65530e7	−	2.86706e7i	1.17769	−	2.03981i
$724$		0			0
$725$	−923931.	−	1.60030e6i	−0.0652822	−	0.113072i
$726$		0			0
$727$	−2.16304e7			−1.51785			−0.758923	−	0.651180i	$-0.774274\pi$
$727$	−2.16304e7			−1.51785			−0.758923	+	0.651180i	$0.774274\pi$
$728$		0			0
$729$	−2.32487e7			−1.62024
$730$		0			0
$731$	8.39198e6	+	1.45353e7i	0.580859	+	1.00608i
$732$		0			0
$733$	6.27682e6	−	1.08718e7i	0.431499	−	0.747378i	−0.565504	−	0.824746i	$-0.691318\pi$
$733$	6.27682e6	−	1.08718e7i	0.431499	−	0.747378i	0.997003	+	0.0773678i	$0.0246516\pi$
$734$		0			0
$735$	−3.38662e7	+	4.41472e6i	−2.31232	+	0.301429i
$736$		0			0
$737$	−1.27811e7	+	2.21376e7i	−0.866764	+	1.50128i
$738$		0			0
$739$	378866.	+	656215.i	0.0255196	+	0.0442013i	0.878503	−	0.477737i	$-0.158543\pi$
$739$	378866.	+	656215.i	0.0255196	+	0.0442013i	−0.852984	+	0.521938i	$0.825209\pi$
$740$		0			0
$741$	3.31530e6			0.221808
$742$		0			0
$743$	2.40878e7			1.60075			0.800377	−	0.599497i	$-0.204633\pi$
$743$	2.40878e7			1.60075			0.800377	+	0.599497i	$0.204633\pi$
$744$		0			0
$745$	33655.6	+	58293.2i	0.00222160	+	0.00384793i
$746$		0			0
$747$	2.75515e6	−	4.77206e6i	0.180652	−	0.312899i
$748$		0			0
$749$	−1.24479e7	−	6.14849e6i	−0.810760	−	0.400464i
$750$		0			0
$751$	6.88436e6	−	1.19241e7i	0.445414	−	0.771480i	−0.552667	−	0.833402i	$-0.686390\pi$
$751$	6.88436e6	−	1.19241e7i	0.445414	−	0.771480i	0.998081	+	0.0619225i	$0.0197232\pi$
$752$		0			0
$753$	1.65384e7	+	2.86453e7i	1.06293	+	1.84105i
$754$		0			0
$755$	3.30203e6			0.210821
$756$		0			0
$757$	2.43930e7			1.54713			0.773564	−	0.633718i	$-0.218472\pi$
$757$	2.43930e7			1.54713			0.773564	+	0.633718i	$0.218472\pi$
$758$		0			0
$759$	3.10990e7	+	5.38651e7i	1.95949	+	3.39393i
$760$		0			0
$761$	−1.28001e7	+	2.21704e7i	−0.801220	+	1.38775i	0.117594	+	0.993062i	$0.462482\pi$
$761$	−1.28001e7	+	2.21704e7i	−0.801220	+	1.38775i	−0.918814	+	0.394692i	$0.870851\pi$
$762$		0			0
$763$	−4.98448e6	+	3.32594e6i	−0.309962	+	0.206825i
$764$		0			0
$765$	1.42082e7	−	2.46094e7i	0.877781	−	1.52036i
$766$		0			0
$767$	−5.31574e6	−	9.20713e6i	−0.326269	−	0.565114i
$768$		0			0
$769$	2.09807e7			1.27939			0.639697	−	0.768627i	$-0.279060\pi$
$769$	2.09807e7			1.27939			0.639697	+	0.768627i	$0.279060\pi$
$770$		0			0
$771$	1.78229e7			1.07979
$772$		0			0
$773$	5.64645e6	+	9.77993e6i	0.339881	+	0.588691i	0.984410	−	0.175889i	$-0.0562800\pi$
$773$	5.64645e6	+	9.77993e6i	0.339881	+	0.588691i	−0.644529	+	0.764580i	$0.722947\pi$
$774$		0			0
$775$	−1.03095e7	+	1.78566e7i	−0.616572	+	1.06793i
$776$		0			0
$777$	−3.13284e6	−	4.82687e7i	−0.186160	−	2.86822i
$778$		0			0
$779$	1.65421e6	−	2.86518e6i	0.0976668	−	0.169164i
$780$		0			0
$781$	−1.14721e7	−	1.98702e7i	−0.672998	−	1.16567i
$782$		0			0
$783$	2.04781e6			0.119367
$784$		0			0
$785$	2.65270e6			0.153643
$786$		0			0
$787$	1.18585e7	+	2.05395e7i	0.682482	+	1.18209i	0.974221	+	0.225596i	$0.0724329\pi$
$787$	1.18585e7	+	2.05395e7i	0.682482	+	1.18209i	−0.291739	+	0.956498i	$0.594234\pi$
$788$		0			0
$789$	9.31455e6	−	1.61333e7i	0.532683	−	0.922635i
$790$		0			0
$791$	−466184.	−	7.18264e6i	−0.0264921	−	0.408172i
$792$		0			0
$793$	−2.77174e6	+	4.80080e6i	−0.156520	+	0.271101i
$794$		0			0
$795$	2.00775e7	+	3.47753e7i	1.12666	+	1.95143i
$796$		0			0
$797$	−2.73492e7			−1.52510			−0.762550	−	0.646929i	$-0.776053\pi$
$797$	−2.73492e7			−1.52510			−0.762550	+	0.646929i	$0.776053\pi$
$798$		0			0
$799$	−1.25781e6			−0.0697026
$800$		0			0
$801$	1.75396e7	+	3.03794e7i	0.965912	+	1.67301i
$802$		0			0
$803$	−1.91715e6	+	3.32060e6i	−0.104922	+	0.181730i
$804$		0			0
$805$	−4.23780e7	+	2.82771e7i	−2.30489	+	1.53796i
$806$		0			0
$807$	1.56097e7	−	2.70369e7i	0.843746	−	1.46141i
$808$		0			0
$809$	5.46781e6	+	9.47052e6i	0.293726	+	0.508748i	0.974688	−	0.223571i	$-0.0717714\pi$
$809$	5.46781e6	+	9.47052e6i	0.293726	+	0.508748i	−0.680962	+	0.732319i	$0.738438\pi$
$810$		0			0
$811$	3.14053e7			1.67668			0.838342	−	0.545144i	$-0.183525\pi$
$811$	3.14053e7			1.67668			0.838342	+	0.545144i	$0.183525\pi$
$812$		0			0
$813$	−1.29691e7			−0.688153
$814$		0			0
$815$	2.83507e6	+	4.91049e6i	0.149510	+	0.258959i
$816$		0			0
$817$	−3.13798e6	+	5.43514e6i	−0.164473	+	0.284876i
$818$		0			0
$819$	1.78154e7	+	8.79968e6i	0.928080	+	0.458413i
$820$		0			0
$821$	−1.56250e7	+	2.70634e7i	−0.809028	+	1.40128i	0.104510	+	0.994524i	$0.466673\pi$
$821$	−1.56250e7	+	2.70634e7i	−0.809028	+	1.40128i	−0.913538	+	0.406754i	$0.866661\pi$
$822$		0			0
$823$	−1.83382e7	−	3.17627e7i	−0.943749	−	1.63462i	−0.758236	−	0.651980i	$-0.773939\pi$
$823$	−1.83382e7	−	3.17627e7i	−0.943749	−	1.63462i	−0.185513	−	0.982642i	$-0.559395\pi$
$824$		0			0
$825$	−4.31586e7			−2.20766
$826$		0			0
$827$	−1.67620e7			−0.852242			−0.426121	−	0.904666i	$-0.640120\pi$
$827$	−1.67620e7			−0.852242			−0.426121	+	0.904666i	$0.640120\pi$
$828$		0			0
$829$	595242.	+	1.03099e6i	0.0300820	+	0.0521036i	0.880674	−	0.473722i	$-0.157090\pi$
$829$	595242.	+	1.03099e6i	0.0300820	+	0.0521036i	−0.850592	+	0.525826i	$0.823756\pi$
$830$		0			0
$831$	1.63385e7	−	2.82990e7i	0.820745	−	1.42157i
$832$		0			0
$833$	−9.18701e6	−	1.20044e7i	−0.458735	−	0.599413i
$834$		0			0
$835$	−9.19248e6	+	1.59218e7i	−0.456264	+	0.790273i
$836$		0			0
$837$	−1.14250e7	−	1.97887e7i	−0.563694	−	0.976347i
$838$		0			0
$839$	8.21562e6			0.402935			0.201468	−	0.979495i	$-0.435429\pi$
$839$	8.21562e6			0.402935			0.201468	+	0.979495i	$0.435429\pi$
$840$		0			0
$841$	−2.02124e7			−0.985434
$842$		0			0
$843$	−3.29888e7	−	5.71382e7i	−1.59881	−	2.76922i
$844$		0			0
$845$	8.79939e6	−	1.52410e7i	0.423946	−	0.734297i
$846$		0			0
$847$	1.11260e7	+	5.49553e6i	0.532880	+	0.263209i
$848$		0			0
$849$	−527119.	+	912996.i	−0.0250980	+	0.0434710i
$850$		0			0
$851$	−3.60772e7	−	6.24875e7i	−1.70769	−	2.95780i
$852$		0			0
$853$	2.55133e7			1.20059			0.600295	−	0.799779i	$-0.295050\pi$
$853$	2.55133e7			1.20059			0.600295	+	0.799779i	$0.295050\pi$
$854$		0			0
$855$	1.06257e7			0.497096
$856$		0			0
$857$	1.43863e7	+	2.49178e7i	0.669109	+	1.15893i	0.978154	+	0.207884i	$0.0666576\pi$
$857$	1.43863e7	+	2.49178e7i	0.669109	+	1.15893i	−0.309044	+	0.951048i	$0.600009\pi$
$858$		0			0
$859$	−5.17972e6	+	8.97154e6i	−0.239510	+	0.414843i	−0.960574	−	0.278025i	$-0.910320\pi$
$859$	−5.17972e6	+	8.97154e6i	−0.239510	+	0.414843i	0.721064	+	0.692869i	$0.243653\pi$
$860$		0			0
$861$	2.67264e7	−	1.78334e7i	1.22866	−	0.819835i
$862$		0			0
$863$	−2.87161e6	+	4.97377e6i	−0.131250	+	0.227331i	−0.924159	−	0.382009i	$-0.875232\pi$
$863$	−2.87161e6	+	4.97377e6i	−0.131250	+	0.227331i	0.792909	+	0.609340i	$0.208566\pi$
$864$		0			0
$865$	1.36272e6	+	2.36031e6i	0.0619253	+	0.107258i
$866$		0			0
$867$	−1.53911e7			−0.695379
$868$		0			0
$869$	−2.44744e6			−0.109942
$870$		0			0
$871$	9.86936e6	+	1.70942e7i	0.440802	+	0.763491i
$872$		0			0
$873$	−1.41202e6	+	2.44569e6i	−0.0627055	+	0.108609i
$874$		0			0
$875$	−173179.	−	2.66822e6i	−0.00764671	−	0.117815i
$876$		0			0
$877$	1.80935e7	−	3.13389e7i	0.794372	−	1.37589i	−0.128866	−	0.991662i	$-0.541134\pi$
$877$	1.80935e7	−	3.13389e7i	0.794372	−	1.37589i	0.923237	−	0.384230i	$-0.125533\pi$
$878$		0			0
$879$	2.45431e7	+	4.25099e7i	1.07141	+	1.85574i
$880$		0			0
$881$	−2.20285e7			−0.956192			−0.478096	−	0.878308i	$-0.658673\pi$
$881$	−2.20285e7			−0.956192			−0.478096	+	0.878308i	$0.658673\pi$
$882$		0			0
$883$	−3.82050e7			−1.64899			−0.824497	−	0.565867i	$-0.808542\pi$
$883$	−3.82050e7			−1.64899			−0.824497	+	0.565867i	$0.808542\pi$
$884$		0			0
$885$	−2.76062e7	−	4.78154e7i	−1.18481	−	2.05215i
$886$		0			0
$887$	1.87196e7	−	3.24233e7i	0.798890	−	1.38372i	−0.121449	−	0.992598i	$-0.538754\pi$
$887$	1.87196e7	−	3.24233e7i	0.798890	−	1.38372i	0.920339	−	0.391121i	$-0.127913\pi$
$888$		0			0
$889$	1.93278e6	+	2.97789e7i	0.0820216	+	1.26373i
$890$		0			0
$891$	−202178.	+	350183.i	−0.00853178	+	0.0147775i
$892$		0			0
$893$	−235165.	−	407317.i	−0.00986832	−	0.0170924i
$894$		0			0
$895$	4.96218e7			2.07069
$896$		0			0
$897$	4.80282e7			1.99304
$898$		0			0
$899$	−1.66683e6	−	2.88704e6i	−0.0687849	−	0.119139i
$900$		0			0
$901$	−8.88655e6	+	1.53920e7i	−0.364688	+	0.631658i
$902$		0			0
$903$	−5.06990e7	+	3.38294e7i	−2.06909	+	1.38062i
$904$		0			0
$905$	2.73748e7	−	4.74145e7i	1.11104	−	1.92438i
$906$		0			0
$907$	1.19207e7	+	2.06473e7i	0.481154	+	0.833383i	0.999766	−	0.0216263i	$-0.00688439\pi$
$907$	1.19207e7	+	2.06473e7i	0.481154	+	0.833383i	−0.518612	+	0.855010i	$0.673551\pi$
$908$		0			0
$909$	−7.64689e7			−3.06955
$910$		0			0
$911$	1.78434e7			0.712332			0.356166	−	0.934423i	$-0.384084\pi$
$911$	1.78434e7			0.712332			0.356166	+	0.934423i	$0.384084\pi$
$912$		0			0
$913$	−3.56413e6	−	6.17325e6i	−0.141506	−	0.245096i
$914$		0			0
$915$	−1.43945e7	+	2.49320e7i	−0.568386	+	0.984473i
$916$		0			0
$917$	2.31310e7	+	1.14253e7i	0.908388	+	0.448686i
$918$		0			0
$919$	−8.21451e6	+	1.42280e7i	−0.320843	+	0.555717i	−0.980662	−	0.195708i	$-0.937300\pi$
$919$	−8.21451e6	+	1.42280e7i	−0.320843	+	0.555717i	0.659819	+	0.751425i	$0.270633\pi$
$920$		0			0
$921$	2.63414e6	+	4.56247e6i	0.102327	+	0.177236i
$922$		0			0
$923$	−1.77170e7			−0.684520
$924$		0			0
$925$	5.00672e7			1.92397
$926$		0			0
$927$	4.62874e6	+	8.01721e6i	0.176915	+	0.306425i
$928$		0			0
$929$	6.82722e6	−	1.18251e7i	0.259540	−	0.449537i	−0.706579	−	0.707635i	$-0.749762\pi$
$929$	6.82722e6	−	1.18251e7i	0.259540	−	0.449537i	0.966119	+	0.258098i	$0.0830957\pi$
$930$		0			0
$931$	2.16973e6	−	5.21940e6i	0.0820412	−	0.197354i
$932$		0			0
$933$	1.18061e6	−	2.04489e6i	0.0444022	−	0.0769068i
$934$		0			0
$935$	−1.83801e7	−	3.18353e7i	−0.687573	−	1.19091i
$936$		0			0
$937$	3.81848e7			1.42083			0.710414	−	0.703784i	$-0.248508\pi$
$937$	3.81848e7			1.42083			0.710414	+	0.703784i	$0.248508\pi$
$938$		0			0
$939$	−1.25996e7			−0.466330
$940$		0			0
$941$	−3.51554e6	−	6.08909e6i	−0.129425	−	0.224170i	0.794029	−	0.607880i	$-0.207980\pi$
$941$	−3.51554e6	−	6.08909e6i	−0.129425	−	0.224170i	−0.923454	+	0.383709i	$0.874646\pi$
$942$		0			0
$943$	2.39642e7	−	4.15073e7i	0.877575	−	1.52000i
$944$		0			0
$945$	3.51248e7	+	1.73494e7i	1.27948	+	0.631983i
$946$		0			0
$947$	−1.10099e7	+	1.90698e7i	−0.398942	+	0.690988i	−0.993596	−	0.112994i	$-0.963956\pi$
$947$	−1.10099e7	+	1.90698e7i	−0.398942	+	0.690988i	0.594653	+	0.803982i	$0.297289\pi$
$948$		0			0
$949$	1.48039e6	+	2.56410e6i	0.0533592	+	0.0924209i
$950$		0			0
$951$	−3.71425e7			−1.33174
$952$		0			0
$953$	578419.			0.0206305			0.0103153	−	0.999947i	$-0.496716\pi$
$953$	578419.			0.0206305			0.0103153	+	0.999947i	$0.496716\pi$
$954$		0			0
$955$	−2.64226e7	−	4.57652e7i	−0.937489	−	1.62378i
$956$		0			0
$957$	3.48893e6	−	6.04300e6i	0.123144	−	0.213291i
$958$		0			0
$959$	−1.37528e7	+	9.17668e6i	−0.482886	+	0.322210i
$960$		0			0
$961$	−4.28447e6	+	7.42093e6i	−0.149654	+	0.259209i
$962$		0			0
$963$	2.09745e7	+	3.63289e7i	0.728830	+	1.26237i
$964$		0			0
$965$	−2.58476e7			−0.893516
$966$		0			0
$967$	2.00036e7			0.687925			0.343963	−	0.938983i	$-0.388231\pi$
$967$	2.00036e7			0.687925			0.343963	+	0.938983i	$0.388231\pi$
$968$		0			0
$969$	3.81031e6	+	6.59965e6i	0.130362	+	0.225793i
$970$		0			0
$971$	−2.54560e7	+	4.40910e7i	−0.866446	+	1.50073i	−0.000840840		1.00000i	$0.500268\pi$
$971$	−2.54560e7	+	4.40910e7i	−0.866446	+	1.50073i	−0.865605	+	0.500728i	$0.833066\pi$
$972$		0			0
$973$	−144924.	−	2.23289e6i	−0.00490749	−	0.0756112i
$974$		0			0
$975$	−1.66631e7	+	2.88614e7i	−0.561364	+	0.972312i
$976$		0			0
$977$	8.69359e6	+	1.50577e7i	0.291382	+	0.504688i	0.974137	−	0.225959i	$-0.0725516\pi$
$977$	8.69359e6	+	1.50577e7i	0.291382	+	0.504688i	−0.682755	+	0.730648i	$0.739218\pi$
$978$		0			0
$979$	4.53792e7			1.51321
$980$		0			0
$981$	1.81054e7			0.600670
$982$		0			0
$983$	−5.54285e6	−	9.60050e6i	−0.182957	−	0.316891i	0.759929	−	0.650006i	$-0.225234\pi$
$983$	−5.54285e6	−	9.60050e6i	−0.182957	−	0.316891i	−0.942886	+	0.333115i	$0.891900\pi$
$984$		0			0
$985$	−8.15062e6	+	1.41173e7i	−0.267670	+	0.463618i
$986$		0			0
$987$	−295836.	−	4.55804e6i	−0.00966625	−	0.148931i
$988$		0			0
$989$	−4.54593e7	+	7.87379e7i	−1.47786	+	2.55972i
$990$		0			0
$991$	−1.91462e7	−	3.31622e7i	−0.619297	−	1.07265i	−0.989614	−	0.143749i	$-0.954084\pi$
$991$	−1.91462e7	−	3.31622e7i	−0.619297	−	1.07265i	0.370317	−	0.928905i	$-0.379249\pi$
$992$		0			0
$993$	−5.98689e7			−1.92676
$994$		0			0
$995$	5.14872e7			1.64870
$996$		0			0
$997$	−2.63586e7	−	4.56545e7i	−0.839818	−	1.45461i	−0.890047	−	0.455869i	$-0.849329\pi$
$997$	−2.63586e7	−	4.56545e7i	−0.839818	−	1.45461i	0.0502293	−	0.998738i	$-0.484005\pi$
$998$		0			0
$999$	−2.77423e7	+	4.80511e7i	−0.879486	+	1.52331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.6.i.a.9.1	✓	10
3.2	odd	2		504.6.s.d.289.5		10
4.3	odd	2		112.6.i.g.65.5		10
7.2	even	3		392.6.a.l.1.5		5
7.3	odd	6		392.6.i.p.361.5		10
7.4	even	3	inner	56.6.i.a.25.1	yes	10
7.5	odd	6		392.6.a.i.1.1		5
7.6	odd	2		392.6.i.p.177.5		10
21.11	odd	6		504.6.s.d.361.5		10
28.11	odd	6		112.6.i.g.81.5		10
28.19	even	6		784.6.a.bm.1.5		5
28.23	odd	6		784.6.a.bj.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.6.i.a.9.1	✓	10	1.1	even	1	trivial
56.6.i.a.25.1	yes	10	7.4	even	3	inner
112.6.i.g.65.5		10	4.3	odd	2
112.6.i.g.81.5		10	28.11	odd	6
392.6.a.i.1.1		5	7.5	odd	6
392.6.a.l.1.5		5	7.2	even	3
392.6.i.p.177.5		10	7.6	odd	2
392.6.i.p.361.5		10	7.3	odd	6
504.6.s.d.289.5		10	3.2	odd	2
504.6.s.d.361.5		10	21.11	odd	6
784.6.a.bj.1.1		5	28.23	odd	6
784.6.a.bm.1.5		5	28.19	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	56.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.5967 - 21.8182i) q^{3} +(-40.3290 + 69.8518i) q^{5} +(-8.39664 - 129.370i) q^{7} +(-195.855 + 339.231i) q^{9} +(253.362 + 438.837i) q^{11} +391.283 q^{13} +2032.05 q^{15} +(449.706 + 778.913i) q^{17} +(-168.157 + 291.256i) q^{19} +(-2716.84 + 1812.83i) q^{21} +(-2436.06 + 4219.37i) q^{23} +(-1690.35 - 2927.78i) q^{25} +3746.51 q^{27} +546.591 q^{29} +(-3049.51 - 5281.91i) q^{31} +(6383.07 - 11055.8i) q^{33} +(9375.33 + 4630.82i) q^{35} +(-7404.84 + 12825.6i) q^{37} +(-4928.89 - 8537.08i) q^{39} -9837.31 q^{41} +18661.0 q^{43} +(-15797.3 - 27361.6i) q^{45} +(-699.243 + 1211.12i) q^{47} +(-16666.0 + 2172.54i) q^{49} +(11329.6 - 19623.5i) q^{51} +(9880.41 + 17113.4i) q^{53} -40871.4 q^{55} +8472.89 q^{57} +(-13585.4 - 23530.6i) q^{59} +(-7083.72 + 12269.4i) q^{61} +(45530.6 + 22489.3i) q^{63} +(-15780.1 + 27331.9i) q^{65} +(25223.0 + 43687.6i) q^{67} +122745. q^{69} -45279.2 q^{71} +(3783.41 + 6553.06i) q^{73} +(-42585.8 + 73760.8i) q^{75} +(54644.7 - 36462.2i) q^{77} +(-2414.96 + 4182.83i) q^{79} +(398.990 + 691.071i) q^{81} -14067.3 q^{83} -72544.7 q^{85} +(-6885.25 - 11925.6i) q^{87} +(44776.9 - 77555.9i) q^{89} +(-3285.47 - 50620.2i) q^{91} +(-76827.7 + 133070. i) q^{93} +(-13563.2 - 23492.1i) q^{95} +7209.53 q^{97} -198489. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 13 q^{3} - 31 q^{5} - 92 q^{7} - 230 q^{9} + 351 q^{11} - 108 q^{13} + 1214 q^{15} - 111 q^{17} - 1035 q^{19} - 1365 q^{21} - 3639 q^{23} - 1540 q^{25} + 7214 q^{27} - 1468 q^{29} - 7677 q^{31} + 7439 q^{33}+ \cdots - 600308 q^{99}+O(q^{100}) \) 10 * q - 13 * q^3 - 31 * q^5 - 92 * q^7 - 230 * q^9 + 351 * q^11 - 108 * q^13 + 1214 * q^15 - 111 * q^17 - 1035 * q^19 - 1365 * q^21 - 3639 * q^23 - 1540 * q^25 + 7214 * q^27 - 1468 * q^29 - 7677 * q^31 + 7439 * q^33 + 19899 * q^35 - 13595 * q^37 + 1406 * q^39 + 10620 * q^41 + 1528 * q^43 - 38978 * q^45 - 6675 * q^47 + 30122 * q^49 - 20975 * q^51 + 30753 * q^53 + 56534 * q^55 - 28778 * q^57 - 87989 * q^59 - 19899 * q^61 + 147318 * q^63 - 119470 * q^65 + 33067 * q^67 + 200798 * q^69 - 217440 * q^71 - 141659 * q^73 - 108788 * q^75 + 271471 * q^77 - 118919 * q^79 + 143851 * q^81 + 422008 * q^83 - 286758 * q^85 - 302154 * q^87 + 55861 * q^89 + 403912 * q^91 - 410381 * q^93 + 26279 * q^95 + 270940 * q^97 - 600308 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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