LMFDB - Embedded newform 336.6.q.j.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.4
Root			$0.895402 - 1.55088i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.6.q.j.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50000 - 7.79423i) q^{3} +(52.0958 + 90.2327i) q^{5} +(7.12980 - 129.446i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(4.50000 - 7.79423i) q^{3} +(52.0958 + 90.2327i) q^{5} +(7.12980 - 129.446i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(-248.830 + 430.986i) q^{11} -206.551 q^{13} +937.725 q^{15} +(-31.5793 + 54.6969i) q^{17} +(661.977 + 1146.58i) q^{19} +(-976.845 - 638.077i) q^{21} +(-97.2187 - 168.388i) q^{23} +(-3865.45 + 6695.16i) q^{25} -729.000 q^{27} +4323.14 q^{29} +(-3762.66 + 6517.11i) q^{31} +(2239.47 + 3878.87i) q^{33} +(12051.7 - 6100.24i) q^{35} +(-5177.82 - 8968.25i) q^{37} +(-929.481 + 1609.91i) q^{39} -4180.92 q^{41} -5960.87 q^{43} +(4219.76 - 7308.85i) q^{45} +(-2194.87 - 3801.62i) q^{47} +(-16705.3 - 1845.84i) q^{49} +(284.214 + 492.273i) q^{51} +(-8892.39 + 15402.1i) q^{53} -51852.0 q^{55} +11915.6 q^{57} +(1750.23 - 3031.49i) q^{59} +(5316.23 + 9207.98i) q^{61} +(-9369.11 + 4742.41i) q^{63} +(-10760.5 - 18637.7i) q^{65} +(-6637.37 + 11496.3i) q^{67} -1749.94 q^{69} -38811.1 q^{71} +(-15687.8 + 27172.1i) q^{73} +(34789.1 + 60256.5i) q^{75} +(54015.1 + 35282.8i) q^{77} +(19745.7 + 34200.6i) q^{79} +(-3280.50 + 5681.99i) q^{81} +102372. q^{83} -6580.60 q^{85} +(19454.1 - 33695.5i) q^{87} +(56410.5 + 97705.8i) q^{89} +(-1472.67 + 26737.2i) q^{91} +(33863.9 + 58654.0i) q^{93} +(-68972.6 + 119464. i) q^{95} +30334.3 q^{97} +40310.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 36 q^{3} - 258 q^{7} - 324 q^{9}+O(q^{10}) $ 8 * q + 36 * q^3 - 258 * q^7 - 324 * q^9	$ 8 q + 36 q^{3} - 258 q^{7} - 324 q^{9} + 402 q^{11} + 924 q^{13} - 276 q^{17} + 510 q^{19} - 3564 q^{21} + 6900 q^{23} - 2814 q^{25} - 5832 q^{27} + 1080 q^{29} - 6410 q^{31} - 3618 q^{33} + 33108 q^{35} - 15250 q^{37} + 4158 q^{39} + 8616 q^{41} - 58396 q^{43} - 15060 q^{47} - 64252 q^{49} + 2484 q^{51} - 13692 q^{53} - 146248 q^{55} + 9180 q^{57} + 34830 q^{59} + 5364 q^{61} - 11178 q^{63} - 66864 q^{65} - 5994 q^{67} + 124200 q^{69} - 178536 q^{71} - 59638 q^{73} + 25326 q^{75} - 75660 q^{77} - 44062 q^{79} - 26244 q^{81} + 416892 q^{83} + 72648 q^{85} + 4860 q^{87} + 77520 q^{89} - 104722 q^{91} + 57690 q^{93} - 221376 q^{95} - 377260 q^{97} - 65124 q^{99}+O(q^{100}) $ 8 * q + 36 * q^3 - 258 * q^7 - 324 * q^9 + 402 * q^11 + 924 * q^13 - 276 * q^17 + 510 * q^19 - 3564 * q^21 + 6900 * q^23 - 2814 * q^25 - 5832 * q^27 + 1080 * q^29 - 6410 * q^31 - 3618 * q^33 + 33108 * q^35 - 15250 * q^37 + 4158 * q^39 + 8616 * q^41 - 58396 * q^43 - 15060 * q^47 - 64252 * q^49 + 2484 * q^51 - 13692 * q^53 - 146248 * q^55 + 9180 * q^57 + 34830 * q^59 + 5364 * q^61 - 11178 * q^63 - 66864 * q^65 - 5994 * q^67 + 124200 * q^69 - 178536 * q^71 - 59638 * q^73 + 25326 * q^75 - 75660 * q^77 - 44062 * q^79 - 26244 * q^81 + 416892 * q^83 + 72648 * q^85 + 4860 * q^87 + 77520 * q^89 - 104722 * q^91 + 57690 * q^93 - 221376 * q^95 - 377260 * q^97 - 65124 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$4$		0			0
$5$	52.0958	+	90.2327i	0.931919	+	1.61413i	0.780038	+	0.625732i	$0.215200\pi$
$5$	52.0958	+	90.2327i	0.931919	+	1.61413i	0.151881	+	0.988399i	$0.451467\pi$
$6$		0			0
$7$	7.12980	−	129.446i	0.0549961	−	0.998487i
$7$	7.12980	−	129.446i	0.0549961	−	0.998487i
$8$		0			0
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$		0			0
$11$	−248.830	+	430.986i	−0.620041	+	1.07394i	0.369436	+	0.929256i	$0.379551\pi$
$11$	−248.830	+	430.986i	−0.620041	+	1.07394i	−0.989477	+	0.144687i	$0.953782\pi$
$12$		0			0
$13$	−206.551			−0.338977			−0.169488	−	0.985532i	$-0.554211\pi$
$13$	−206.551			−0.338977			−0.169488	+	0.985532i	$0.554211\pi$
$14$		0			0
$15$	937.725			1.07609
$16$		0			0
$17$	−31.5793	+	54.6969i	−0.0265021	+	0.0459030i	−0.878972	−	0.476873i	$-0.841770\pi$
$17$	−31.5793	+	54.6969i	−0.0265021	+	0.0459030i	0.852470	+	0.522776i	$0.175104\pi$
$18$		0			0
$19$	661.977	+	1146.58i	0.420687	+	0.728651i	0.996007	−	0.0892772i	$-0.0284557\pi$
$19$	661.977	+	1146.58i	0.420687	+	0.728651i	−0.575320	+	0.817929i	$0.695122\pi$
$20$		0			0
$21$	−976.845	−	638.077i	−0.483367	−	0.315736i
$22$		0			0
$23$	−97.2187	−	168.388i	−0.0383204	−	0.0663729i	0.846229	−	0.532819i	$-0.178867\pi$
$23$	−97.2187	−	168.388i	−0.0383204	−	0.0663729i	−0.884550	+	0.466446i	$0.845534\pi$
$24$		0			0
$25$	−3865.45	+	6695.16i	−1.23695	+	2.14245i
$26$		0			0
$27$	−729.000			−0.192450
$28$		0			0
$29$	4323.14			0.954562			0.477281	−	0.878751i	$-0.341622\pi$
$29$	4323.14			0.954562			0.477281	+	0.878751i	$0.341622\pi$
$30$		0			0
$31$	−3762.66	+	6517.11i	−0.703219	+	1.21801i	0.264112	+	0.964492i	$0.414921\pi$
$31$	−3762.66	+	6517.11i	−0.703219	+	1.21801i	−0.967331	+	0.253518i	$0.918412\pi$
$32$		0			0
$33$	2239.47	+	3878.87i	0.357981	+	0.620041i
$34$		0			0
$35$	12051.7	−	6100.24i	1.66294	−	0.841738i
$36$		0			0
$37$	−5177.82	−	8968.25i	−0.621789	−	1.07697i	−0.989152	−	0.146892i	$-0.953073\pi$
$37$	−5177.82	−	8968.25i	−0.621789	−	1.07697i	0.367364	−	0.930077i	$-0.380260\pi$
$38$		0			0
$39$	−929.481	+	1609.91i	−0.0978541	+	0.169488i
$40$		0			0
$41$	−4180.92			−0.388429			−0.194215	−	0.980959i	$-0.562216\pi$
$41$	−4180.92			−0.388429			−0.194215	+	0.980959i	$0.562216\pi$
$42$		0			0
$43$	−5960.87			−0.491630			−0.245815	−	0.969317i	$-0.579056\pi$
$43$	−5960.87			−0.491630			−0.245815	+	0.969317i	$0.579056\pi$
$44$		0			0
$45$	4219.76	−	7308.85i	0.310640	−	0.538044i
$46$		0			0
$47$	−2194.87	−	3801.62i	−0.144932	−	0.251029i	0.784416	−	0.620236i	$-0.212963\pi$
$47$	−2194.87	−	3801.62i	−0.144932	−	0.251029i	−0.929348	+	0.369206i	$0.879630\pi$
$48$		0			0
$49$	−16705.3	−	1845.84i	−0.993951	−	0.109826i
$50$		0			0
$51$	284.214	+	492.273i	0.0153010	+	0.0265021i
$52$		0			0
$53$	−8892.39	+	15402.1i	−0.434839	+	0.753164i	−0.997283	−	0.0736720i	$-0.976528\pi$
$53$	−8892.39	+	15402.1i	−0.434839	+	0.753164i	0.562443	+	0.826836i	$0.309862\pi$
$54$		0			0
$55$	−51852.0			−2.31131
$56$		0			0
$57$	11915.6			0.485768
$58$		0			0
$59$	1750.23	−	3031.49i	0.0654585	−	0.113377i	−0.831439	−	0.555616i	$-0.812482\pi$
$59$	1750.23	−	3031.49i	0.0654585	−	0.113377i	0.896897	+	0.442239i	$0.145816\pi$
$60$		0			0
$61$	5316.23	+	9207.98i	0.182928	+	0.316840i	0.942876	−	0.333143i	$-0.108109\pi$
$61$	5316.23	+	9207.98i	0.182928	+	0.316840i	−0.759949	+	0.649983i	$0.774776\pi$
$62$		0			0
$63$	−9369.11	+	4742.41i	−0.297404	+	0.150538i
$64$		0			0
$65$	−10760.5	−	18637.7i	−0.315899	−	0.547153i
$66$		0			0
$67$	−6637.37	+	11496.3i	−0.180638	+	0.312874i	−0.942098	−	0.335338i	$-0.891150\pi$
$67$	−6637.37	+	11496.3i	−0.180638	+	0.312874i	0.761460	+	0.648212i	$0.224483\pi$
$68$		0			0
$69$	−1749.94			−0.0442486
$70$		0			0
$71$	−38811.1			−0.913713			−0.456857	−	0.889540i	$-0.651025\pi$
$71$	−38811.1			−0.913713			−0.456857	+	0.889540i	$0.651025\pi$
$72$		0			0
$73$	−15687.8	+	27172.1i	−0.344552	+	0.596782i	−0.985272	−	0.170992i	$-0.945303\pi$
$73$	−15687.8	+	27172.1i	−0.344552	+	0.596782i	0.640720	+	0.767775i	$0.278636\pi$
$74$		0			0
$75$	34789.1	+	60256.5i	0.714151	+	1.23695i
$76$		0			0
$77$	54015.1	+	35282.8i	1.03822	+	0.678166i
$78$		0			0
$79$	19745.7	+	34200.6i	0.355964	+	0.616547i	0.987282	−	0.158976i	$-0.0508194\pi$
$79$	19745.7	+	34200.6i	0.355964	+	0.616547i	−0.631319	+	0.775523i	$0.717486\pi$
$80$		0			0
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	102372.			1.63112			0.815559	−	0.578675i	$-0.196430\pi$
$83$	102372.			1.63112			0.815559	+	0.578675i	$0.196430\pi$
$84$		0			0
$85$	−6580.60			−0.0987912
$86$		0			0
$87$	19454.1	−	33695.5i	0.275558	−	0.477281i
$88$		0			0
$89$	56410.5	+	97705.8i	0.754892	+	1.30751i	0.945428	+	0.325831i	$0.105644\pi$
$89$	56410.5	+	97705.8i	0.754892	+	1.30751i	−0.190536	+	0.981680i	$0.561023\pi$
$90$		0			0
$91$	−1472.67	+	26737.2i	−0.0186424	+	0.338464i
$92$		0			0
$93$	33863.9	+	58654.0i	0.406004	+	0.703219i
$94$		0			0
$95$	−68972.6	+	119464.i	−0.784092	+	1.35809i
$96$		0			0
$97$	30334.3			0.327345			0.163672	−	0.986515i	$-0.447666\pi$
$97$	30334.3			0.327345			0.163672	+	0.986515i	$0.447666\pi$
$98$		0			0
$99$	40310.4			0.413361
$100$		0			0
$101$	−53398.2	+	92488.4i	−0.520862	+	0.902160i	0.478843	+	0.877900i	$0.341056\pi$
$101$	−53398.2	+	92488.4i	−0.520862	+	0.902160i	−0.999706	+	0.0242599i	$0.992277\pi$
$102$		0			0
$103$	78767.8	+	136430.i	0.731570	+	1.26712i	0.956212	+	0.292674i	$0.0945452\pi$
$103$	78767.8	+	136430.i	0.731570	+	1.26712i	−0.224643	+	0.974441i	$0.572121\pi$
$104$		0			0
$105$	6685.79	−	121384.i	0.0591806	−	1.07446i
$106$		0			0
$107$	−44662.2	−	77357.1i	−0.377121	−	0.653192i	0.613521	−	0.789678i	$-0.289752\pi$
$107$	−44662.2	−	77357.1i	−0.377121	−	0.653192i	−0.990642	+	0.136486i	$0.956419\pi$
$108$		0			0
$109$	−83802.3	+	145150.i	−0.675600	+	1.17017i	0.300693	+	0.953721i	$0.402782\pi$
$109$	−83802.3	+	145150.i	−0.675600	+	1.17017i	−0.976293	+	0.216452i	$0.930551\pi$
$110$		0			0
$111$	−93200.8			−0.717980
$112$		0			0
$113$	−115794.			−0.853079			−0.426539	−	0.904469i	$-0.640267\pi$
$113$	−115794.			−0.853079			−0.426539	+	0.904469i	$0.640267\pi$
$114$		0			0
$115$	10129.4	−	17544.6i	0.0714230	−	0.123708i
$116$		0			0
$117$	8365.33	+	14489.2i	0.0564961	+	0.0978541i
$118$		0			0
$119$	6855.13	+	4477.78i	0.0443760	+	0.0289865i
$120$		0			0
$121$	−43307.1	−	75010.0i	−0.268903	−	0.465753i
$122$		0			0
$123$	−18814.1	+	32587.0i	−0.112130	+	0.194215i
$124$		0			0
$125$	−479898.			−2.74709
$126$		0			0
$127$	−201513.			−1.10865			−0.554325	−	0.832300i	$-0.687023\pi$
$127$	−201513.			−1.10865			−0.554325	+	0.832300i	$0.687023\pi$
$128$		0			0
$129$	−26823.9	+	46460.4i	−0.141921	+	0.245815i
$130$		0			0
$131$	19234.8	+	33315.6i	0.0979285	+	0.169617i	0.910827	−	0.412788i	$-0.135445\pi$
$131$	19234.8	+	33315.6i	0.0979285	+	0.169617i	−0.812899	+	0.582405i	$0.802112\pi$
$132$		0			0
$133$	153139.	−	77515.2i	0.750685	−	0.379977i
$134$		0			0
$135$	−37977.9	−	65779.6i	−0.179348	−	0.310640i
$136$		0			0
$137$	120861.	−	209337.i	0.550155	−	0.952896i	−0.448108	−	0.893979i	$-0.647902\pi$
$137$	120861.	−	209337.i	0.550155	−	0.952896i	0.998263	−	0.0589167i	$-0.0187646\pi$
$138$		0			0
$139$	53112.2			0.233162			0.116581	−	0.993181i	$-0.462807\pi$
$139$	53112.2			0.233162			0.116581	+	0.993181i	$0.462807\pi$
$140$		0			0
$141$	−39507.6			−0.167353
$142$		0			0
$143$	51396.1	−	89020.7i	0.210180	−	0.364042i
$144$		0			0
$145$	225218.	+	390088.i	0.889574	+	1.54079i
$146$		0			0
$147$	−89560.9	+	121899.i	−0.341842	+	0.465271i
$148$		0			0
$149$	−64531.0	−	111771.i	−0.238124	−	0.412443i	0.722052	−	0.691839i	$-0.243199\pi$
$149$	−64531.0	−	111771.i	−0.238124	−	0.412443i	−0.960176	+	0.279396i	$0.909866\pi$
$150$		0			0
$151$	76603.2	−	132681.i	0.273404	−	0.473549i	−0.696327	−	0.717724i	$-0.745184\pi$
$151$	76603.2	−	132681.i	0.273404	−	0.473549i	0.969731	+	0.244175i	$0.0785172\pi$
$152$		0			0
$153$	5115.85			0.0176681
$154$		0			0
$155$	−784075.			−2.62137
$156$		0			0
$157$	75593.9	−	130932.i	0.244758	−	0.423934i	−0.717305	−	0.696759i	$-0.754625\pi$
$157$	75593.9	−	130932.i	0.244758	−	0.423934i	0.962064	+	0.272825i	$0.0879581\pi$
$158$		0			0
$159$	80031.5	+	138619.i	0.251055	+	0.434839i
$160$		0			0
$161$	−22490.2	+	11384.0i	−0.0683799	+	0.0346122i
$162$		0			0
$163$	−16458.3	−	28506.7i	−0.0485196	−	0.0840384i	0.840746	−	0.541430i	$-0.182117\pi$
$163$	−16458.3	−	28506.7i	−0.0485196	−	0.0840384i	−0.889265	+	0.457392i	$0.848784\pi$
$164$		0			0
$165$	−233334.	+	404146.i	−0.667219	+	1.15566i
$166$		0			0
$167$	−217586.			−0.603725			−0.301862	−	0.953352i	$-0.597608\pi$
$167$	−217586.			−0.603725			−0.301862	+	0.953352i	$0.597608\pi$
$168$		0			0
$169$	−328630.			−0.885095
$170$		0			0
$171$	53620.2	−	92872.9i	0.140229	−	0.242884i
$172$		0			0
$173$	210621.	+	364807.i	0.535041	+	0.926718i	0.999161	+	0.0409458i	$0.0130371\pi$
$173$	210621.	+	364807.i	0.535041	+	0.926718i	−0.464121	+	0.885772i	$0.653630\pi$
$174$		0			0
$175$	839100.	+	548101.i	2.07118	+	1.35290i
$176$		0			0
$177$	−15752.1	−	27283.4i	−0.0377925	−	0.0654585i
$178$		0			0
$179$	1747.03	−	3025.94i	0.00407538	−	0.00705876i	−0.863981	−	0.503525i	$-0.832036\pi$
$179$	1747.03	−	3025.94i	0.00407538	−	0.00705876i	0.868056	+	0.496466i	$0.165369\pi$
$180$		0			0
$181$	594611.			1.34908			0.674538	−	0.738240i	$-0.264343\pi$
$181$	594611.			1.34908			0.674538	+	0.738240i	$0.264343\pi$
$182$		0			0
$183$	95692.2			0.211227
$184$		0			0
$185$	539486.	−	934418.i	1.15891	−	2.00730i
$186$		0			0
$187$	−15715.7	−	27220.5i	−0.0328648	−	0.0569235i
$188$		0			0
$189$	−5197.62	+	94365.8i	−0.0105840	+	0.192159i
$190$		0			0
$191$	414322.	+	717627.i	0.821778	+	1.42336i	0.904357	+	0.426777i	$0.140351\pi$
$191$	414322.	+	717627.i	0.821778	+	1.42336i	−0.0825782	+	0.996585i	$0.526315\pi$
$192$		0			0
$193$	−109869.	+	190299.i	−0.212316	+	0.367743i	−0.952439	−	0.304729i	$-0.901434\pi$
$193$	−109869.	+	190299.i	−0.212316	+	0.367743i	0.740123	+	0.672472i	$0.234767\pi$
$194$		0			0
$195$	−193688.			−0.364768
$196$		0			0
$197$	475612.			0.873146			0.436573	−	0.899669i	$-0.356192\pi$
$197$	475612.			0.873146			0.436573	+	0.899669i	$0.356192\pi$
$198$		0			0
$199$	313778.	−	543479.i	0.561681	−	0.972859i	−0.435669	−	0.900107i	$-0.643488\pi$
$199$	313778.	−	543479.i	0.561681	−	0.972859i	0.997350	−	0.0727525i	$-0.0231783\pi$
$200$		0			0
$201$	59736.4	+	103466.i	0.104291	+	0.180638i
$202$		0			0
$203$	30823.1	−	559611.i	0.0524972	−	0.953117i
$204$		0			0
$205$	−217808.	−	377255.i	−0.361984	−	0.626975i
$206$		0			0
$207$	−7874.71	+	13639.4i	−0.0127735	+	0.0221243i
$208$		0			0
$209$	−658879.			−1.04337
$210$		0			0
$211$	−570989.			−0.882920			−0.441460	−	0.897281i	$-0.645539\pi$
$211$	−570989.			−0.882920			−0.441460	+	0.897281i	$0.645539\pi$
$212$		0			0
$213$	−174650.	+	302502.i	−0.263766	+	0.456857i
$214$		0			0
$215$	−310536.	−	537865.i	−0.458159	−	0.793555i
$216$		0			0
$217$	816785.	+	533525.i	1.17749	+	0.769140i
$218$		0			0
$219$	141190.	+	244549.i	0.198927	+	0.344552i
$220$		0			0
$221$	6522.75	−	11297.7i	0.00898359	−	0.0155600i
$222$		0			0
$223$	−4233.11			−0.00570029			−0.00285015	−	0.999996i	$-0.500907\pi$
$223$	−4233.11			−0.00570029			−0.00285015	+	0.999996i	$0.500907\pi$
$224$		0			0
$225$	626204.			0.824630
$226$		0			0
$227$	564931.	−	978490.i	0.727664	−	1.26035i	−0.230204	−	0.973142i	$-0.573939\pi$
$227$	564931.	−	978490.i	0.727664	−	1.26035i	0.957868	−	0.287209i	$-0.0927274\pi$
$228$		0			0
$229$	−402322.	−	696842.i	−0.506973	−	0.878103i	−0.999967	−	0.00807048i	$-0.997431\pi$
$229$	−402322.	−	696842.i	−0.506973	−	0.878103i	0.492994	−	0.870032i	$-0.335902\pi$
$230$		0			0
$231$	518070.	−	262234.i	0.638791	−	0.323339i
$232$		0			0
$233$	−584636.	−	1.01262e6i	−0.705498	−	1.22196i	−0.966511	−	0.256624i	$-0.917390\pi$
$233$	−584636.	−	1.01262e6i	−0.705498	−	1.22196i	0.261013	−	0.965335i	$-0.415943\pi$
$234$		0			0
$235$	228687.	−	396098.i	0.270130	−	0.467878i
$236$		0			0
$237$	355423.			0.411031
$238$		0			0
$239$	1.70554e6			1.93138			0.965689	−	0.259700i	$-0.0836238\pi$
$239$	1.70554e6			1.93138			0.965689	+	0.259700i	$0.0836238\pi$
$240$		0			0
$241$	−475598.	+	823760.i	−0.527470	+	0.913604i	0.472018	+	0.881589i	$0.343526\pi$
$241$	−475598.	+	823760.i	−0.527470	+	0.913604i	−0.999487	+	0.0320153i	$0.989807\pi$
$242$		0			0
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−703723.	−	1.60353e6i	−0.749008	−	1.70672i
$246$		0			0
$247$	−136732.	−	236827.i	−0.142603	−	0.246996i
$248$		0			0
$249$	460673.	−	797909.i	0.470863	−	0.815559i
$250$		0			0
$251$	−1.14498e6			−1.14713			−0.573566	−	0.819159i	$-0.694440\pi$
$251$	−1.14498e6			−1.14713			−0.573566	+	0.819159i	$0.694440\pi$
$252$		0			0
$253$	96763.6			0.0950409
$254$		0			0
$255$	−29612.7	+	51290.7i	−0.0285186	+	0.0493956i
$256$		0			0
$257$	−591869.	−	1.02515e6i	−0.558976	−	0.968175i	−0.997582	−	0.0694955i	$-0.977861\pi$
$257$	−591869.	−	1.02515e6i	−0.558976	−	0.968175i	0.438606	−	0.898679i	$-0.355472\pi$
$258$		0			0
$259$	−1.19782e6	+	606305.i	−1.10954	+	0.561619i
$260$		0			0
$261$	−175087.	−	303260.i	−0.159094	−	0.275558i
$262$		0			0
$263$	224158.	−	388253.i	0.199832	−	0.346119i	−0.748642	−	0.662975i	$-0.769294\pi$
$263$	224158.	−	388253.i	0.199832	−	0.346119i	0.948474	+	0.316856i	$0.102627\pi$
$264$		0			0
$265$	−1.85303e6			−1.62094
$266$		0			0
$267$	1.01539e6			0.871674
$268$		0			0
$269$	−373737.	+	647332.i	−0.314909	+	0.545439i	−0.979418	−	0.201841i	$-0.935307\pi$
$269$	−373737.	+	647332.i	−0.314909	+	0.545439i	0.664509	+	0.747280i	$0.268641\pi$
$270$		0			0
$271$	−116319.	−	201470.i	−0.0962114	−	0.166643i	0.813902	−	0.581002i	$-0.197339\pi$
$271$	−116319.	−	201470.i	−0.0962114	−	0.166643i	−0.910114	+	0.414359i	$0.864006\pi$
$272$		0			0
$273$	201769.	+	131796.i	0.163850	+	0.107027i
$274$		0			0
$275$	−1.92368e6	−	3.33191e6i	−1.53391	−	2.65682i
$276$		0			0
$277$	1.21462e6	−	2.10379e6i	0.951134	−	1.64741i	0.208157	−	0.978095i	$-0.433253\pi$
$277$	1.21462e6	−	2.10379e6i	0.951134	−	1.64741i	0.742977	−	0.669317i	$-0.233413\pi$
$278$		0			0
$279$	609550.			0.468812
$280$		0			0
$281$	2.51704e6			1.90163			0.950813	−	0.309766i	$-0.100251\pi$
$281$	2.51704e6			1.90163			0.950813	+	0.309766i	$0.100251\pi$
$282$		0			0
$283$	130497.	−	226028.i	0.0968579	−	0.167763i	−0.813525	−	0.581530i	$-0.802454\pi$
$283$	130497.	−	226028.i	0.0968579	−	0.167763i	0.910382	+	0.413768i	$0.135787\pi$
$284$		0			0
$285$	620753.	+	1.07518e6i	0.452696	+	0.784092i
$286$		0			0
$287$	−29809.1	+	541201.i	−0.0213621	+	0.387841i
$288$		0			0
$289$	707934.	+	1.22618e6i	0.498595	+	0.863592i
$290$		0			0
$291$	136505.	−	236433.i	0.0944963	−	0.163672i
$292$		0			0
$293$	65011.7			0.0442408			0.0221204	−	0.999755i	$-0.492958\pi$
$293$	65011.7			0.0442408			0.0221204	+	0.999755i	$0.492958\pi$
$294$		0			0
$295$	364720.			0.244008
$296$		0			0
$297$	181397.	−	314189.i	0.119327	−	0.206680i
$298$		0			0
$299$	20080.6	+	34780.7i	0.0129897	+	0.0224989i
$300$		0			0
$301$	−42499.8	+	771608.i	−0.0270377	+	0.490886i
$302$		0			0
$303$	480584.	+	832395.i	0.300720	+	0.520862i
$304$		0			0
$305$	−553907.	+	959395.i	−0.340947	+	0.590538i
$306$		0			0
$307$	2.35599e6			1.42668			0.713342	−	0.700816i	$-0.247181\pi$
$307$	2.35599e6			1.42668			0.713342	+	0.700816i	$0.247181\pi$
$308$		0			0
$309$	1.41782e6			0.844744
$310$		0			0
$311$	−1.05903e6	+	1.83429e6i	−0.620878	+	1.07539i	0.368445	+	0.929650i	$0.379890\pi$
$311$	−1.05903e6	+	1.83429e6i	−0.620878	+	1.07539i	−0.989323	+	0.145742i	$0.953443\pi$
$312$		0			0
$313$	93756.8	+	162392.i	0.0540931	+	0.0936920i	0.891804	−	0.452422i	$-0.149440\pi$
$313$	93756.8	+	162392.i	0.0540931	+	0.0936920i	−0.837711	+	0.546114i	$0.816107\pi$
$314$		0			0
$315$	−916012.	−	598340.i	−0.520145	−	0.339760i
$316$		0			0
$317$	502705.	+	870711.i	0.280974	+	0.486661i	0.971625	−	0.236527i	$-0.0760093\pi$
$317$	502705.	+	870711.i	0.280974	+	0.486661i	−0.690651	+	0.723188i	$0.742676\pi$
$318$		0			0
$319$	−1.07573e6	+	1.86321e6i	−0.591868	+	1.02515i
$320$		0			0
$321$	−803919.			−0.435461
$322$		0			0
$323$	−83619.1			−0.0445964
$324$		0			0
$325$	798415.	−	1.38290e6i	0.419296	−	0.726241i
$326$		0			0
$327$	754220.	+	1.30635e6i	0.390058	+	0.675600i
$328$		0			0
$329$	−507753.	+	257011.i	−0.258620	+	0.130907i
$330$		0			0
$331$	839920.	+	1.45478e6i	0.421374	+	0.729841i	0.996074	−	0.0885229i	$-0.0282146\pi$
$331$	839920.	+	1.45478e6i	0.421374	+	0.729841i	−0.574700	+	0.818364i	$0.694881\pi$
$332$		0			0
$333$	−419404.	+	726429.i	−0.207263	+	0.358990i
$334$		0			0
$335$	−1.38312e6			−0.673360
$336$		0			0
$337$	−995036.			−0.477270			−0.238635	−	0.971109i	$-0.576700\pi$
$337$	−995036.			−0.477270			−0.238635	+	0.971109i	$0.576700\pi$
$338$		0			0
$339$	−521072.	+	902523.i	−0.246263	+	0.426539i
$340$		0			0
$341$	−1.87252e6	−	3.24330e6i	−0.872049	−	1.51043i
$342$		0			0
$343$	−358042.	+	2.14927e6i	−0.164323	+	0.986407i
$344$		0			0
$345$	−91164.4	−	157901.i	−0.0412361	−	0.0714230i
$346$		0			0
$347$	2.02833e6	−	3.51317e6i	0.904304	−	1.56630i	0.0824546	−	0.996595i	$-0.473724\pi$
$347$	2.02833e6	−	3.51317e6i	0.904304	−	1.56630i	0.821849	−	0.569705i	$-0.192943\pi$
$348$		0			0
$349$	2.86202e6			1.25779			0.628897	−	0.777488i	$-0.283507\pi$
$349$	2.86202e6			1.25779			0.628897	+	0.777488i	$0.283507\pi$
$350$		0			0
$351$	150576.			0.0652361
$352$		0			0
$353$	−416343.	+	721126.i	−0.177834	+	0.308017i	−0.941138	−	0.338022i	$-0.890242\pi$
$353$	−416343.	+	721126.i	−0.177834	+	0.308017i	0.763305	+	0.646039i	$0.223576\pi$
$354$		0			0
$355$	−2.02190e6	−	3.50203e6i	−0.851507	−	1.47485i
$356$		0			0
$357$	65748.9	−	33280.4i	0.0273035	−	0.0138203i
$358$		0			0
$359$	−1.34875e6	−	2.33611e6i	−0.552327	−	0.956659i	−0.998106	−	0.0615157i	$-0.980407\pi$
$359$	−1.34875e6	−	2.33611e6i	−0.552327	−	0.956659i	0.445779	−	0.895143i	$-0.352927\pi$
$360$		0			0
$361$	361621.	−	626346.i	0.146045	−	0.252957i
$362$		0			0
$363$	−779527.			−0.310502
$364$		0			0
$365$	−3.26908e6			−1.28438
$366$		0			0
$367$	727411.	−	1.25991e6i	0.281913	−	0.488287i	−0.689943	−	0.723864i	$-0.742364\pi$
$367$	727411.	−	1.25991e6i	0.281913	−	0.488287i	0.971856	+	0.235576i	$0.0756978\pi$
$368$		0			0
$369$	169327.	+	293283.i	0.0647382	+	0.112130i
$370$		0			0
$371$	1.93033e6	+	1.26089e6i	0.728110	+	0.475602i
$372$		0			0
$373$	1.02344e6	+	1.77265e6i	0.380883	+	0.659708i	0.991189	−	0.132457i	$-0.0422868\pi$
$373$	1.02344e6	+	1.77265e6i	0.380883	+	0.659708i	−0.610306	+	0.792166i	$0.708953\pi$
$374$		0			0
$375$	−2.15954e6	+	3.74043e6i	−0.793018	+	1.37355i
$376$		0			0
$377$	−892950.			−0.323574
$378$		0			0
$379$	416898.			0.149084			0.0745421	−	0.997218i	$-0.476250\pi$
$379$	416898.			0.149084			0.0745421	+	0.997218i	$0.476250\pi$
$380$		0			0
$381$	−906810.	+	1.57064e6i	−0.320040	+	0.554325i
$382$		0			0
$383$	−1.93813e6	−	3.35694e6i	−0.675127	−	1.16935i	−0.976432	−	0.215827i	$-0.930755\pi$
$383$	−1.93813e6	−	3.35694e6i	−0.675127	−	1.16935i	0.301305	−	0.953528i	$-0.402578\pi$
$384$		0			0
$385$	−369694.	+	6.71201e6i	−0.127113	+	2.30782i
$386$		0			0
$387$	241415.	+	418143.i	0.0819383	+	0.141921i
$388$		0			0
$389$	−1.41901e6	+	2.45780e6i	−0.475458	+	0.823517i	−0.999605	−	0.0281111i	$-0.991051\pi$
$389$	−1.41901e6	+	2.45780e6i	−0.475458	+	0.823517i	0.524147	+	0.851628i	$0.324384\pi$
$390$		0			0
$391$	12280.4			0.00406228
$392$		0			0
$393$	346226.			0.113078
$394$		0			0
$395$	−2.05734e6	+	3.56342e6i	−0.663458	+	1.14914i
$396$		0			0
$397$	−2.17133e6	−	3.76085e6i	−0.691432	−	1.19760i	−0.971369	−	0.237577i	$-0.923647\pi$
$397$	−2.17133e6	−	3.76085e6i	−0.691432	−	1.19760i	0.279937	−	0.960018i	$-0.409686\pi$
$398$		0			0
$399$	84955.8	−	1.54242e6i	0.0267153	−	0.485032i
$400$		0			0
$401$	−1.70152e6	−	2.94712e6i	−0.528417	−	0.915244i	−0.999451	−	0.0331296i	$-0.989453\pi$
$401$	−1.70152e6	−	2.94712e6i	−0.528417	−	0.915244i	0.471034	−	0.882115i	$-0.343881\pi$
$402$		0			0
$403$	777182.	−	1.34612e6i	0.238375	−	0.412877i
$404$		0			0
$405$	−683602.			−0.207093
$406$		0			0
$407$	5.15359e6			1.54214
$408$		0			0
$409$	2.64716e6	−	4.58501e6i	0.782477	−	1.35529i	−0.148018	−	0.988985i	$-0.547289\pi$
$409$	2.64716e6	−	4.58501e6i	0.782477	−	1.35529i	0.930495	−	0.366305i	$-0.119377\pi$
$410$		0			0
$411$	−1.08775e6	−	1.88404e6i	−0.317632	−	0.550155i
$412$		0			0
$413$	−379935.	−	248174.i	−0.109606	−	0.0715947i
$414$		0			0
$415$	5.33315e6	+	9.23728e6i	1.52007	+	2.63284i
$416$		0			0
$417$	239005.	−	413969.i	0.0673080	−	0.116581i
$418$		0			0
$419$	−2.87267e6			−0.799376			−0.399688	−	0.916651i	$-0.630881\pi$
$419$	−2.87267e6			−0.799376			−0.399688	+	0.916651i	$0.630881\pi$
$420$		0			0
$421$	2.08688e6			0.573843			0.286921	−	0.957954i	$-0.407368\pi$
$421$	2.08688e6			0.573843			0.286921	+	0.957954i	$0.407368\pi$
$422$		0			0
$423$	−177784.	+	307932.i	−0.0483106	+	0.0836765i
$424$		0			0
$425$	−244137.	−	422857.i	−0.0655633	−	0.113559i
$426$		0			0
$427$	1.22984e6	−	622512.i	0.326421	−	0.165226i
$428$		0			0
$429$	−462565.	−	801187.i	−0.121347	−	0.210180i
$430$		0			0
$431$	−1.21432e6	+	2.10326e6i	−0.314876	+	0.545380i	−0.979411	−	0.201876i	$-0.935296\pi$
$431$	−1.21432e6	+	2.10326e6i	−0.314876	+	0.545380i	0.664535	+	0.747257i	$0.268629\pi$
$432$		0			0
$433$	956219.			0.245097			0.122548	−	0.992463i	$-0.460893\pi$
$433$	956219.			0.245097			0.122548	+	0.992463i	$0.460893\pi$
$434$		0			0
$435$	4.05392e6			1.02719
$436$		0			0
$437$	128713.	−	222938.i	0.0322418	−	0.0558444i
$438$		0			0
$439$	1.32102e6	+	2.28808e6i	0.327152	+	0.566644i	0.981946	−	0.189164i	$-0.0605778\pi$
$439$	1.32102e6	+	2.28808e6i	0.327152	+	0.566644i	−0.654794	+	0.755808i	$0.727244\pi$
$440$		0			0
$441$	547084.	+	1.24660e6i	0.133955	+	0.305233i
$442$		0			0
$443$	−1.71983e6	−	2.97883e6i	−0.416366	−	0.721168i	0.579205	−	0.815182i	$-0.303363\pi$
$443$	−1.71983e6	−	2.97883e6i	−0.416366	−	0.721168i	−0.995571	+	0.0940147i	$0.970030\pi$
$444$		0			0
$445$	−5.87750e6	+	1.01801e7i	−1.40700	+	2.43699i
$446$		0			0
$447$	−1.16156e6			−0.274962
$448$		0			0
$449$	4.39903e6			1.02977			0.514886	−	0.857259i	$-0.327834\pi$
$449$	4.39903e6			1.02977			0.514886	+	0.857259i	$0.327834\pi$
$450$		0			0
$451$	1.04034e6	−	1.80192e6i	0.240842	−	0.417151i
$452$		0			0
$453$	−689429.	−	1.19413e6i	−0.157850	−	0.273404i
$454$		0			0
$455$	−2.48929e6	+	1.26001e6i	−0.563698	+	0.285329i
$456$		0			0
$457$	1.12555e6	+	1.94951e6i	0.252101	+	0.436652i	0.964104	−	0.265524i	$-0.0855451\pi$
$457$	1.12555e6	+	1.94951e6i	0.252101	+	0.436652i	−0.712003	+	0.702176i	$0.752212\pi$
$458$		0			0
$459$	23021.3	−	39874.1i	0.00510033	−	0.00883403i
$460$		0			0
$461$	1.85307e6			0.406107			0.203053	−	0.979168i	$-0.434913\pi$
$461$	1.85307e6			0.406107			0.203053	+	0.979168i	$0.434913\pi$
$462$		0			0
$463$	3.01089e6			0.652744			0.326372	−	0.945241i	$-0.394174\pi$
$463$	3.01089e6			0.652744			0.326372	+	0.945241i	$0.394174\pi$
$464$		0			0
$465$	−3.52834e6	+	6.11126e6i	−0.756725	+	1.31069i
$466$		0			0
$467$	−533627.	−	924270.i	−0.113226	−	0.196113i	0.803843	−	0.594841i	$-0.202785\pi$
$467$	−533627.	−	924270.i	−0.113226	−	0.196113i	−0.917069	+	0.398728i	$0.869452\pi$
$468$		0			0
$469$	1.44082e6	+	941145.i	0.302466	+	0.197572i
$470$		0			0
$471$	−680345.	−	1.17839e6i	−0.141311	−	0.244758i
$472$		0			0
$473$	1.48324e6	−	2.56905e6i	0.304831	−	0.527983i
$474$		0			0
$475$	−1.02354e7			−2.08147
$476$		0			0
$477$	1.44057e6			0.289893
$478$		0			0
$479$	−2.84394e6	+	4.92585e6i	−0.566346	+	0.980939i	0.430577	+	0.902554i	$0.358310\pi$
$479$	−2.84394e6	+	4.92585e6i	−0.566346	+	0.980939i	−0.996923	+	0.0783858i	$0.975023\pi$
$480$		0			0
$481$	1.06949e6	+	1.85240e6i	0.210772	+	0.365068i
$482$		0			0
$483$	−12476.7	+	226522.i	−0.00243350	+	0.0441816i
$484$		0			0
$485$	1.58029e6	+	2.73715e6i	0.305059	+	0.528377i
$486$		0			0
$487$	−3.42239e6	+	5.92775e6i	−0.653893	+	1.13258i	0.328277	+	0.944582i	$0.393532\pi$
$487$	−3.42239e6	+	5.92775e6i	−0.653893	+	1.13258i	−0.982170	+	0.187995i	$0.939801\pi$
$488$		0			0
$489$	−296250.			−0.0560256
$490$		0			0
$491$	−5.60132e6			−1.04854			−0.524272	−	0.851551i	$-0.675662\pi$
$491$	−5.60132e6			−1.04854			−0.524272	+	0.851551i	$0.675662\pi$
$492$		0			0
$493$	−136522.	+	236462.i	−0.0252979	+	0.0438172i
$494$		0			0
$495$	2.10001e6	+	3.63732e6i	0.385219	+	0.667219i
$496$		0			0
$497$	−276715.	+	5.02392e6i	−0.0502507	+	0.912330i
$498$		0			0
$499$	−1.16764e6	−	2.02242e6i	−0.209923	−	0.363596i	0.741767	−	0.670657i	$-0.233988\pi$
$499$	−1.16764e6	−	2.02242e6i	−0.209923	−	0.363596i	−0.951690	+	0.307061i	$0.900655\pi$
$500$		0			0
$501$	−979135.	+	1.69591e6i	−0.174280	+	0.301862i
$502$		0			0
$503$	1.08278e7			1.90819			0.954093	−	0.299510i	$-0.0968233\pi$
$503$	1.08278e7			1.90819			0.954093	+	0.299510i	$0.0968233\pi$
$504$		0			0
$505$	−1.11273e7			−1.94161
$506$		0			0
$507$	−1.47883e6	+	2.56141e6i	−0.255505	+	0.442547i
$508$		0			0
$509$	−1.58924e6	−	2.75264e6i	−0.271890	−	0.470928i	0.697455	−	0.716628i	$-0.254316\pi$
$509$	−1.58924e6	−	2.75264e6i	−0.271890	−	0.470928i	−0.969346	+	0.245700i	$0.920982\pi$
$510$		0			0
$511$	3.40546e6	+	2.22445e6i	0.576930	+	0.376852i
$512$		0			0
$513$	−482582.	−	835856.i	−0.0809613	−	0.140229i
$514$		0			0
$515$	−8.20695e6	+	1.42149e7i	−1.36353	+	2.36170i
$516$		0			0
$517$	2.18460e6			0.359455
$518$		0			0
$519$	3.79118e6			0.617812
$520$		0			0
$521$	3.17918e6	−	5.50651e6i	0.513123	−	0.888755i	−0.486761	−	0.873535i	$-0.661822\pi$
$521$	3.17918e6	−	5.50651e6i	0.513123	−	0.888755i	0.999884	−	0.0152197i	$-0.00484477\pi$
$522$		0			0
$523$	−3.61094e6	−	6.25433e6i	−0.577252	−	0.999830i	−0.995793	−	0.0916321i	$-0.970792\pi$
$523$	−3.61094e6	−	6.25433e6i	−0.577252	−	0.999830i	0.418541	−	0.908198i	$-0.362542\pi$
$524$		0			0
$525$	8.04798e6	−	4.07368e6i	1.27435	−	0.645043i
$526$		0			0
$527$	−237644.	−	411612.i	−0.0372735	−	0.0645597i
$528$		0			0
$529$	3.19927e6	−	5.54130e6i	0.497063	−	0.860939i
$530$		0			0
$531$	−283538.			−0.0436390
$532$		0			0
$533$	863574.			0.131668
$534$		0			0
$535$	4.65343e6	−	8.05997e6i	0.702892	−	1.21744i
$536$		0			0
$537$	−15723.3	−	27233.5i	−0.00235292	−	0.00407538i
$538$		0			0
$539$	4.95232e6	−	6.74046e6i	0.734237	−	0.999350i
$540$		0			0
$541$	4.71583e6	+	8.16805e6i	0.692731	+	1.19985i	0.970940	+	0.239325i	$0.0769260\pi$
$541$	4.71583e6	+	8.16805e6i	0.692731	+	1.19985i	−0.278209	+	0.960521i	$0.589741\pi$
$542$		0			0
$543$	2.67575e6	−	4.63453e6i	0.389444	−	0.674538i
$544$		0			0
$545$	−1.74630e7			−2.51842
$546$		0			0
$547$	−9.91568e6			−1.41695			−0.708474	−	0.705737i	$-0.750616\pi$
$547$	−9.91568e6			−1.41695			−0.708474	+	0.705737i	$0.750616\pi$
$548$		0			0
$549$	430615.	−	745847.i	0.0609759	−	0.105613i
$550$		0			0
$551$	2.86182e6	+	4.95682e6i	0.401572	+	0.695543i
$552$		0			0
$553$	4.56790e6	−	2.31216e6i	0.635191	−	0.321517i
$554$		0			0
$555$	−4.85538e6	−	8.40976e6i	−0.669099	−	1.15891i
$556$		0			0
$557$	−4.82306e6	+	8.35379e6i	−0.658696	+	1.14089i	0.322258	+	0.946652i	$0.395558\pi$
$557$	−4.82306e6	+	8.35379e6i	−0.658696	+	1.14089i	−0.980953	+	0.194243i	$0.937775\pi$
$558$		0			0
$559$	1.23123e6			0.166651
$560$		0			0
$561$	−282883.			−0.0379490
$562$		0			0
$563$	1.54752e6	−	2.68038e6i	0.205762	−	0.356390i	−0.744613	−	0.667496i	$-0.767366\pi$
$563$	1.54752e6	−	2.68038e6i	0.205762	−	0.356390i	0.950375	+	0.311106i	$0.100699\pi$
$564$		0			0
$565$	−6.03238e6	−	1.04484e7i	−0.795000	−	1.37698i
$566$		0			0
$567$	712120.	+	465158.i	0.0930241	+	0.0607635i
$568$		0			0
$569$	6.15927e6	+	1.06682e7i	0.797533	+	1.38137i	0.921218	+	0.389046i	$0.127195\pi$
$569$	6.15927e6	+	1.06682e7i	0.797533	+	1.38137i	−0.123685	+	0.992322i	$0.539471\pi$
$570$		0			0
$571$	−1.61755e6	+	2.80168e6i	−0.207619	+	0.359607i	−0.950964	−	0.309302i	$-0.899905\pi$
$571$	−1.61755e6	+	2.80168e6i	−0.207619	+	0.359607i	0.743345	+	0.668908i	$0.233238\pi$
$572$		0			0
$573$	7.45780e6			0.948908
$574$		0			0
$575$	1.50318e6			0.189601
$576$		0			0
$577$	4.52525e6	−	7.83796e6i	0.565852	−	0.980084i	−0.431118	−	0.902296i	$-0.641881\pi$
$577$	4.52525e6	−	7.83796e6i	0.565852	−	0.980084i	0.996970	−	0.0777887i	$-0.0247859\pi$
$578$		0			0
$579$	988825.	+	1.71269e6i	0.122581	+	0.212316i
$580$		0			0
$581$	729890.	−	1.32516e7i	0.0897051	−	1.62865i
$582$		0			0
$583$	−4.42538e6	−	7.66499e6i	−0.539237	−	0.933986i
$584$		0			0
$585$	−871598.	+	1.50965e6i	−0.105300	+	0.182384i
$586$		0			0
$587$	2.13170e6			0.255347			0.127673	−	0.991816i	$-0.459249\pi$
$587$	2.13170e6			0.255347			0.127673	+	0.991816i	$0.459249\pi$
$588$		0			0
$589$	−9.96318e6			−1.18334
$590$		0			0
$591$	2.14025e6	−	3.70703e6i	0.252056	−	0.436573i
$592$		0			0
$593$	3.63467e6	+	6.29543e6i	0.424451	+	0.735171i	0.996369	−	0.0851397i	$-0.0271337\pi$
$593$	3.63467e6	+	6.29543e6i	0.424451	+	0.735171i	−0.571918	+	0.820311i	$0.693800\pi$
$594$		0			0
$595$	−46918.4	+	851830.i	−0.00543313	+	0.0986417i
$596$		0			0
$597$	−2.82400e6	−	4.89131e6i	−0.324286	−	0.561681i
$598$		0			0
$599$	−1.10282e6	+	1.91015e6i	−0.125585	+	0.217520i	−0.921962	−	0.387281i	$-0.873414\pi$
$599$	−1.10282e6	+	1.91015e6i	−0.125585	+	0.217520i	0.796376	+	0.604802i	$0.206748\pi$
$600$		0			0
$601$	−1.00121e7			−1.13067			−0.565336	−	0.824860i	$-0.691254\pi$
$601$	−1.00121e7			−1.13067			−0.565336	+	0.824860i	$0.691254\pi$
$602$		0			0
$603$	1.07525e6			0.120425
$604$		0			0
$605$	4.51224e6	−	7.81542e6i	0.501191	−	0.868088i
$606$		0			0
$607$	3.16069e6	+	5.47448e6i	0.348185	+	0.603075i	0.985927	−	0.167175i	$-0.0534646\pi$
$607$	3.16069e6	+	5.47448e6i	0.348185	+	0.603075i	−0.637742	+	0.770250i	$0.720131\pi$
$608$		0			0
$609$	−4.22303e6	−	2.75849e6i	−0.461404	−	0.301390i
$610$		0			0
$611$	453353.	+	785231.i	0.0491285	+	0.0850931i
$612$		0			0
$613$	−7.15392e6	+	1.23910e7i	−0.768941	+	1.33185i	0.169196	+	0.985582i	$0.445883\pi$
$613$	−7.15392e6	+	1.23910e7i	−0.768941	+	1.33185i	−0.938138	+	0.346263i	$0.887451\pi$
$614$		0			0
$615$	−3.92055e6			−0.417984
$616$		0			0
$617$	1.73991e7			1.83999			0.919993	−	0.391936i	$-0.128194\pi$
$617$	1.73991e7			1.83999			0.919993	+	0.391936i	$0.128194\pi$
$618$		0			0
$619$	4.13368e6	−	7.15975e6i	0.433621	−	0.751054i	−0.563561	−	0.826074i	$-0.690569\pi$
$619$	4.13368e6	−	7.15975e6i	0.433621	−	0.751054i	0.997182	+	0.0750208i	$0.0239023\pi$
$620$		0			0
$621$	70872.4	+	122755.i	0.00737476	+	0.0127735i
$622$		0			0
$623$	1.30498e7	−	6.60547e6i	1.34705	−	0.681841i
$624$		0			0
$625$	−1.29211e7	−	2.23800e7i	−1.32312	−	2.29172i
$626$		0			0
$627$	−2.96495e6	+	5.13545e6i	−0.301196	+	0.521687i
$628$		0			0
$629$	654048.			0.0659148
$630$		0			0
$631$	−2.83238e6			−0.283190			−0.141595	−	0.989925i	$-0.545223\pi$
$631$	−2.83238e6			−0.283190			−0.141595	+	0.989925i	$0.545223\pi$
$632$		0			0
$633$	−2.56945e6	+	4.45041e6i	−0.254877	+	0.441460i
$634$		0			0
$635$	−1.04980e7	−	1.81831e7i	−1.03317	−	1.78951i
$636$		0			0
$637$	3.45051e6	+	381261.i	0.336926	+	0.0372284i
$638$		0			0
$639$	1.57185e6	+	2.72252e6i	0.152286	+	0.263766i
$640$		0			0
$641$	1.78588e6	−	3.09324e6i	0.171675	−	0.297350i	−0.767330	−	0.641252i	$-0.778415\pi$
$641$	1.78588e6	−	3.09324e6i	0.171675	−	0.297350i	0.939006	+	0.343902i	$0.111749\pi$
$642$		0			0
$643$	5.96911e6			0.569354			0.284677	−	0.958624i	$-0.408114\pi$
$643$	5.96911e6			0.569354			0.284677	+	0.958624i	$0.408114\pi$
$644$		0			0
$645$	−5.58966e6			−0.529037
$646$		0			0
$647$	−841379.	+	1.45731e6i	−0.0790189	+	0.136865i	−0.902827	−	0.430004i	$-0.858512\pi$
$647$	−841379.	+	1.45731e6i	−0.0790189	+	0.136865i	0.823808	+	0.566869i	$0.191845\pi$
$648$		0			0
$649$	871021.	+	1.50865e6i	0.0811739	+	0.140597i
$650$		0			0
$651$	7.83395e6	−	3.96534e6i	0.724483	−	0.366715i
$652$		0			0
$653$	−8.51526e6	−	1.47489e7i	−0.781475	−	1.35355i	−0.931082	−	0.364809i	$-0.881134\pi$
$653$	−8.51526e6	−	1.47489e7i	−0.781475	−	1.35355i	0.149608	−	0.988745i	$-0.452199\pi$
$654$		0			0
$655$	−2.00411e6	+	3.47121e6i	−0.182523	+	0.316139i
$656$		0			0
$657$	2.54143e6			0.229702
$658$		0			0
$659$	1.99303e7			1.78772			0.893862	−	0.448342i	$-0.147985\pi$
$659$	1.99303e7			1.78772			0.893862	+	0.448342i	$0.147985\pi$
$660$		0			0
$661$	−4.77867e6	+	8.27691e6i	−0.425406	+	0.736825i	−0.996458	−	0.0840888i	$-0.973202\pi$
$661$	−4.77867e6	+	8.27691e6i	−0.425406	+	0.736825i	0.571052	+	0.820914i	$0.306535\pi$
$662$		0			0
$663$	−58704.7	−	101680.i	−0.00518668	−	0.00898359i
$664$		0			0
$665$	1.49723e7	+	9.77995e6i	1.31291	+	0.857595i
$666$		0			0
$667$	−420290.	−	727963.i	−0.0365792	−	0.0633570i
$668$		0			0
$669$	−19049.0	+	32993.8i	−0.00164553	+	0.00285015i
$670$		0			0
$671$	−5.29135e6			−0.453691
$672$		0			0
$673$	1.80397e7			1.53530			0.767648	−	0.640872i	$-0.221427\pi$
$673$	1.80397e7			1.53530			0.767648	+	0.640872i	$0.221427\pi$
$674$		0			0
$675$	2.81792e6	−	4.88077e6i	0.238050	−	0.412315i
$676$		0			0
$677$	7.23704e6	+	1.25349e7i	0.606861	+	1.05111i	0.991754	+	0.128153i	$0.0409048\pi$
$677$	7.23704e6	+	1.25349e7i	0.606861	+	1.05111i	−0.384894	+	0.922961i	$0.625762\pi$
$678$		0			0
$679$	216278.	−	3.92665e6i	0.0180027	−	0.326849i
$680$		0			0
$681$	−5.08438e6	−	8.80641e6i	−0.420117	−	0.727664i
$682$		0			0
$683$	1.34392e6	−	2.32774e6i	0.110236	−	0.190934i	−0.805629	−	0.592420i	$-0.798173\pi$
$683$	1.34392e6	−	2.32774e6i	0.110236	−	0.190934i	0.915865	+	0.401486i	$0.131506\pi$
$684$		0			0
$685$	2.51854e7			2.05080
$686$		0			0
$687$	−7.24179e6			−0.585402
$688$		0			0
$689$	1.83674e6	−	3.18132e6i	0.147400	−	0.255305i
$690$		0			0
$691$	2.33814e6	+	4.04977e6i	0.186284	+	0.322653i	0.944008	−	0.329922i	$-0.107022\pi$
$691$	2.33814e6	+	4.04977e6i	0.186284	+	0.322653i	−0.757725	+	0.652574i	$0.773689\pi$
$692$		0			0
$693$	287405.	−	5.21801e6i	0.0227333	−	0.412735i
$694$		0			0
$695$	2.76693e6	+	4.79246e6i	0.217288	+	0.376354i
$696$		0			0
$697$	132030.	−	228683.i	0.0102942	−	0.0178301i
$698$		0			0
$699$	−1.05235e7			−0.814639
$700$		0			0
$701$	6.34801e6			0.487913			0.243957	−	0.969786i	$-0.421555\pi$
$701$	6.34801e6			0.487913			0.243957	+	0.969786i	$0.421555\pi$
$702$		0			0
$703$	6.85520e6	−	1.18736e7i	0.523157	−	0.906135i
$704$		0			0
$705$	−2.05818e6	−	3.56488e6i	−0.155959	−	0.270130i
$706$		0			0
$707$	1.15915e7	+	7.57158e6i	0.872150	+	0.569690i
$708$		0			0
$709$	3.20526e6	+	5.55168e6i	0.239468	+	0.414771i	0.960562	−	0.278067i	$-0.0896936\pi$
$709$	3.20526e6	+	5.55168e6i	0.239468	+	0.414771i	−0.721094	+	0.692838i	$0.756360\pi$
$710$		0			0
$711$	1.59940e6	−	2.77025e6i	0.118655	−	0.205516i
$712$		0			0
$713$	1.46320e6			0.107790
$714$		0			0
$715$	1.07101e7			0.783481
$716$		0			0
$717$	7.67493e6	−	1.32934e7i	0.557541	−	0.965689i
$718$		0			0
$719$	3.67253e6	+	6.36100e6i	0.264937	+	0.458885i	0.967547	−	0.252691i	$-0.0813155\pi$
$719$	3.67253e6	+	6.36100e6i	0.264937	+	0.458885i	−0.702610	+	0.711575i	$0.747982\pi$
$720$		0			0
$721$	1.82218e7	−	9.22343e6i	1.30543	−	0.660776i
$722$		0			0
$723$	4.28038e6	+	7.41384e6i	0.304535	+	0.527470i
$724$		0			0
$725$	−1.67109e7	+	2.89441e7i	−1.18074	+	2.04510i
$726$		0			0
$727$	−1.57839e7			−1.10759			−0.553793	−	0.832655i	$-0.686820\pi$
$727$	−1.57839e7			−1.10759			−0.553793	+	0.832655i	$0.686820\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	188240.	−	326041.i	0.0130292	−	0.0225673i
$732$		0			0
$733$	−6.76835e6	−	1.17231e7i	−0.465289	−	0.805905i	0.533925	−	0.845532i	$-0.320716\pi$
$733$	−6.76835e6	−	1.17231e7i	−0.465289	−	0.805905i	−0.999215	+	0.0396269i	$0.987383\pi$
$734$		0			0
$735$	−1.56650e7	−	1.73089e6i	−1.06958	−	0.118182i
$736$		0			0
$737$	−3.30315e6	−	5.72123e6i	−0.224006	−	0.387990i
$738$		0			0
$739$	−3.66851e6	+	6.35405e6i	−0.247103	+	0.427996i	−0.962721	−	0.270497i	$-0.912812\pi$
$739$	−3.66851e6	+	6.35405e6i	−0.247103	+	0.427996i	0.715617	+	0.698492i	$0.246145\pi$
$740$		0			0
$741$	−2.46118e6			−0.164664
$742$		0			0
$743$	−1.20844e7			−0.803068			−0.401534	−	0.915844i	$-0.631523\pi$
$743$	−1.20844e7			−0.803068			−0.401534	+	0.915844i	$0.631523\pi$
$744$		0			0
$745$	6.72360e6	−	1.16456e7i	0.443824	−	0.768726i
$746$		0			0
$747$	−4.14606e6	−	7.18118e6i	−0.271853	−	0.470863i
$748$		0			0
$749$	−1.03320e7	+	5.22978e6i	−0.672944	+	0.340627i
$750$		0			0
$751$	4.39088e6	+	7.60523e6i	0.284087	+	0.492054i	0.972387	−	0.233372i	$-0.0749761\pi$
$751$	4.39088e6	+	7.60523e6i	0.284087	+	0.492054i	−0.688300	+	0.725426i	$0.741643\pi$
$752$		0			0
$753$	−5.15241e6	+	8.92423e6i	−0.331148	+	0.573566i
$754$		0			0
$755$	1.59628e7			1.01916
$756$		0			0
$757$	465874.			0.0295480			0.0147740	−	0.999891i	$-0.495297\pi$
$757$	465874.			0.0295480			0.0147740	+	0.999891i	$0.495297\pi$
$758$		0			0
$759$	435436.	−	754198.i	0.0274360	−	0.0475205i
$760$		0			0
$761$	−7.49891e6	−	1.29885e7i	−0.469393	−	0.813013i	0.529995	−	0.848001i	$-0.322194\pi$
$761$	−7.49891e6	−	1.29885e7i	−0.469393	−	0.813013i	−0.999388	+	0.0349882i	$0.988861\pi$
$762$		0			0
$763$	1.81915e7	+	1.18827e7i	1.13125	+	0.738932i
$764$		0			0
$765$	266514.	+	461616.i	0.0164652	+	0.0285186i
$766$		0			0
$767$	−361513.	+	626159.i	−0.0221889	+	0.0384323i
$768$		0			0
$769$	−1.85606e7			−1.13181			−0.565907	−	0.824469i	$-0.691474\pi$
$769$	−1.85606e7			−1.13181			−0.565907	+	0.824469i	$0.691474\pi$
$770$		0			0
$771$	−1.06537e7			−0.645450
$772$		0			0
$773$	−6.13802e6	+	1.06314e7i	−0.369470	+	0.639941i	−0.989483	−	0.144651i	$-0.953794\pi$
$773$	−6.13802e6	+	1.06314e7i	−0.369470	+	0.639941i	0.620013	+	0.784592i	$0.287128\pi$
$774$		0			0
$775$	−2.90888e7	−	5.03832e7i	−1.73969	−	3.01323i
$776$		0			0
$777$	−664503.	+	1.20644e7i	−0.0394861	+	0.716893i
$778$		0			0
$779$	−2.76767e6	−	4.79375e6i	−0.163407	−	0.283029i
$780$		0			0
$781$	9.65736e6	−	1.67270e7i	0.566540	−	0.981276i
$782$		0			0
$783$	−3.15157e6			−0.183706
$784$		0			0
$785$	1.57525e7			0.912380
$786$		0			0
$787$	2.63496e6	−	4.56388e6i	0.151648	−	0.262662i	−0.780185	−	0.625548i	$-0.784875\pi$
$787$	2.63496e6	−	4.56388e6i	0.151648	−	0.262662i	0.931833	+	0.362886i	$0.118209\pi$
$788$		0			0
$789$	−2.01742e6	−	3.49428e6i	−0.115373	−	0.199832i
$790$		0			0
$791$	−825586.	+	1.49890e7i	−0.0469160	+	0.851788i
$792$		0			0
$793$	−1.09807e6	−	1.90192e6i	−0.0620082	−	0.107401i
$794$		0			0
$795$	−8.33862e6	+	1.44429e7i	−0.467925	+	0.810470i
$796$		0			0
$797$	1.11889e7			0.623940			0.311970	−	0.950092i	$-0.399011\pi$
$797$	1.11889e7			0.623940			0.311970	+	0.950092i	$0.399011\pi$
$798$		0			0
$799$	277250.			0.0153640
$800$		0			0
$801$	4.56925e6	−	7.91417e6i	0.251631	−	0.435837i
$802$		0			0
$803$	−7.80719e6	−	1.35225e7i	−0.427274	−	0.740059i
$804$		0			0
$805$	−2.19885e6	−	1.43629e6i	−0.119593	−	0.0781184i
$806$		0			0
$807$	3.36363e6	+	5.82599e6i	0.181813	+	0.314909i
$808$		0			0
$809$	−3.52526e6	+	6.10592e6i	−0.189374	+	0.328005i	−0.945042	−	0.326950i	$-0.893979\pi$
$809$	−3.52526e6	+	6.10592e6i	−0.189374	+	0.328005i	0.755668	+	0.654955i	$0.227312\pi$
$810$		0			0
$811$	2.54873e7			1.36073			0.680364	−	0.732875i	$-0.261822\pi$
$811$	2.54873e7			1.36073			0.680364	+	0.732875i	$0.261822\pi$
$812$		0			0
$813$	−2.09374e6			−0.111095
$814$		0			0
$815$	1.71482e6	−	2.97016e6i	0.0904326	−	0.156634i
$816$		0			0
$817$	−3.94596e6	−	6.83460e6i	−0.206822	−	0.358227i
$818$		0			0
$819$	1.93520e6	−	979550.i	0.100813	−	0.0510290i
$820$		0			0
$821$	1.17439e7	+	2.03411e7i	0.608073	+	1.05321i	0.991558	+	0.129666i	$0.0413904\pi$
$821$	1.17439e7	+	2.03411e7i	0.608073	+	1.05321i	−0.383485	+	0.923547i	$0.625276\pi$
$822$		0			0
$823$	−6.04517e6	+	1.04705e7i	−0.311107	+	0.538852i	−0.978602	−	0.205761i	$-0.934033\pi$
$823$	−6.04517e6	+	1.04705e7i	−0.311107	+	0.538852i	0.667496	+	0.744614i	$0.267366\pi$
$824$		0			0
$825$	−3.46263e7			−1.77121
$826$		0			0
$827$	−3.33335e6			−0.169480			−0.0847398	−	0.996403i	$-0.527006\pi$
$827$	−3.33335e6			−0.169480			−0.0847398	+	0.996403i	$0.527006\pi$
$828$		0			0
$829$	3.85267e6	−	6.67302e6i	0.194704	−	0.337238i	−0.752099	−	0.659050i	$-0.770959\pi$
$829$	3.85267e6	−	6.67302e6i	0.194704	−	0.337238i	0.946804	+	0.321812i	$0.104292\pi$
$830$		0			0
$831$	−1.09316e7	−	1.89341e7i	−0.549138	−	0.951134i
$832$		0			0
$833$	628505.	−	855440.i	0.0313831	−	0.0427147i
$834$		0			0
$835$	−1.13353e7	−	1.96333e7i	−0.562622	−	0.974490i
$836$		0			0
$837$	2.74298e6	−	4.75098e6i	0.135335	−	0.234406i
$838$		0			0
$839$	−2.40843e7			−1.18121			−0.590607	−	0.806959i	$-0.701112\pi$
$839$	−2.40843e7			−1.18121			−0.590607	+	0.806959i	$0.701112\pi$
$840$		0			0
$841$	−1.82163e6			−0.0888116
$842$		0			0
$843$	1.13267e7	−	1.96184e7i	0.548952	−	0.950813i
$844$		0			0
$845$	−1.71202e7	−	2.96531e7i	−0.824837	−	1.42866i
$846$		0			0
$847$	−1.00185e7	+	5.07110e6i	−0.479837	+	0.242881i
$848$		0			0
$849$	−1.17447e6	−	2.03425e6i	−0.0559209	−	0.0968579i
$850$		0			0
$851$	−1.00676e6	+	1.74376e6i	−0.0476544	+	0.0825398i
$852$		0			0
$853$	−2.82938e7			−1.33143			−0.665716	−	0.746206i	$-0.731874\pi$
$853$	−2.82938e7			−1.33143			−0.665716	+	0.746206i	$0.731874\pi$
$854$		0			0
$855$	1.11736e7			0.522728
$856$		0			0
$857$	−1.08088e7	+	1.87214e7i	−0.502719	+	0.870734i	0.497276	+	0.867592i	$0.334334\pi$
$857$	−1.08088e7	+	1.87214e7i	−0.502719	+	0.870734i	−0.999995	+	0.00314220i	$0.999000\pi$
$858$		0			0
$859$	1.62691e7	+	2.81789e7i	0.752282	+	1.30299i	0.946714	+	0.322075i	$0.104380\pi$
$859$	1.62691e7	+	2.81789e7i	0.752282	+	1.30299i	−0.194432	+	0.980916i	$0.562286\pi$
$860$		0			0
$861$	4.08411e6	+	2.66774e6i	0.187754	+	0.122641i
$862$		0			0
$863$	4.03192e6	+	6.98349e6i	0.184283	+	0.319187i	0.943335	−	0.331843i	$-0.107670\pi$
$863$	4.03192e6	+	6.98349e6i	0.184283	+	0.319187i	−0.759052	+	0.651030i	$0.774337\pi$
$864$		0			0
$865$	−2.19450e7	+	3.80098e7i	−0.997229	+	1.72725i
$866$		0			0
$867$	1.27428e7			0.575728
$868$		0			0
$869$	−1.96533e7			−0.882849
$870$		0			0
$871$	1.37096e6	−	2.37457e6i	0.0612321	−	0.106057i
$872$		0			0
$873$	−1.22854e6	−	2.12790e6i	−0.0545574	−	0.0944963i
$874$		0			0
$875$	−3.42157e6	+	6.21206e7i	−0.151080	+	2.74294i
$876$		0			0
$877$	−8.51559e6	−	1.47494e7i	−0.373866	−	0.647555i	0.616291	−	0.787519i	$-0.288635\pi$
$877$	−8.51559e6	−	1.47494e7i	−0.373866	−	0.647555i	−0.990157	+	0.139964i	$0.955301\pi$
$878$		0			0
$879$	292553.	−	506716.i	0.0127712	−	0.0221204i
$880$		0			0
$881$	1.24740e7			0.541459			0.270729	−	0.962655i	$-0.412735\pi$
$881$	1.24740e7			0.541459			0.270729	+	0.962655i	$0.412735\pi$
$882$		0			0
$883$	−7.28955e6			−0.314629			−0.157315	−	0.987549i	$-0.550284\pi$
$883$	−7.28955e6			−0.314629			−0.157315	+	0.987549i	$0.550284\pi$
$884$		0			0
$885$	1.64124e6	−	2.84271e6i	0.0704390	−	0.122004i
$886$		0			0
$887$	9.38377e6	+	1.62532e7i	0.400469	+	0.693632i	0.993782	−	0.111339i	$-0.0355140\pi$
$887$	9.38377e6	+	1.62532e7i	0.400469	+	0.693632i	−0.593314	+	0.804971i	$0.702181\pi$
$888$		0			0
$889$	−1.43675e6	+	2.60850e7i	−0.0609714	+	1.10697i
$890$		0			0
$891$	−1.63257e6	−	2.82770e6i	−0.0688935	−	0.119327i
$892$		0			0
$893$	2.90591e6	−	5.03318e6i	0.121942	−	0.211210i
$894$		0			0
$895$	364052.			0.0151917
$896$		0			0
$897$	361452.			0.0149992
$898$		0			0
$899$	−1.62665e7	+	2.81744e7i	−0.671266	+	1.16267i
$900$		0			0
$901$	−561631.	−	972773.i	−0.0230483	−	0.0399208i
$902$		0			0
$903$	5.82284e6	+	3.80349e6i	0.237638	+	0.155225i
$904$		0			0
$905$	3.09767e7	+	5.36533e7i	1.25723	+	2.17758i
$906$		0			0
$907$	631833.	−	1.09437e6i	0.0255026	−	0.0441718i	−0.852992	−	0.521923i	$-0.825215\pi$
$907$	631833.	−	1.09437e6i	0.0255026	−	0.0441718i	0.878495	+	0.477751i	$0.158548\pi$
$908$		0			0
$909$	8.65051e6			0.347242
$910$		0			0
$911$	2.47718e7			0.988921			0.494461	−	0.869200i	$-0.335366\pi$
$911$	2.47718e7			0.988921			0.494461	+	0.869200i	$0.335366\pi$
$912$		0			0
$913$	−2.54732e7	+	4.41208e7i	−1.01136	+	1.75173i
$914$		0			0
$915$	4.98516e6	+	8.63456e6i	0.196846	+	0.340947i
$916$		0			0
$917$	4.44970e6	−	2.25233e6i	0.174746	−	0.0884520i
$918$		0			0
$919$	−4.68338e6	−	8.11185e6i	−0.182924	−	0.316834i	0.759951	−	0.649980i	$-0.225223\pi$
$919$	−4.68338e6	−	8.11185e6i	−0.182924	−	0.316834i	−0.942875	+	0.333147i	$0.891890\pi$
$920$		0			0
$921$	1.06020e7	−	1.83631e7i	0.411848	−	0.713342i
$922$		0			0
$923$	8.01648e6			0.309727
$924$		0			0
$925$	8.00586e7			3.07648
$926$		0			0
$927$	6.38019e6	−	1.10508e7i	0.243857	−	0.422372i
$928$		0			0
$929$	3.43675e6	+	5.95263e6i	0.130650	+	0.226292i	0.923927	−	0.382568i	$-0.124960\pi$
$929$	3.43675e6	+	5.95263e6i	0.130650	+	0.226292i	−0.793277	+	0.608860i	$0.791627\pi$
$930$		0			0
$931$	−8.94215e6	−	2.03759e7i	−0.338118	−	0.770446i
$932$		0			0
$933$	9.53125e6	+	1.65086e7i	0.358464	+	0.620878i
$934$		0			0
$935$	1.63745e6	−	2.83615e6i	0.0612546	−	0.106096i
$936$		0			0
$937$	−4.26197e7			−1.58585			−0.792923	−	0.609322i	$-0.791442\pi$
$937$	−4.26197e7			−1.58585			−0.792923	+	0.609322i	$0.791442\pi$
$938$		0			0
$939$	1.68762e6			0.0624614
$940$		0			0
$941$	−2.25113e6	+	3.89907e6i	−0.0828755	+	0.143545i	−0.904484	−	0.426508i	$-0.859744\pi$
$941$	−2.25113e6	+	3.89907e6i	−0.0828755	+	0.143545i	0.821608	+	0.570052i	$0.193077\pi$
$942$		0			0
$943$	406463.	+	704015.i	0.0148848	+	0.0257812i
$944$		0			0
$945$	−8.78566e6	+	4.44707e6i	−0.320033	+	0.161992i
$946$		0			0
$947$	1.68863e7	+	2.92479e7i	0.611870	+	1.05979i	0.990925	+	0.134415i	$0.0429156\pi$
$947$	1.68863e7	+	2.92479e7i	0.611870	+	1.05979i	−0.379055	+	0.925374i	$0.623751\pi$
$948$		0			0
$949$	3.24034e6	−	5.61243e6i	0.116795	−	0.202295i
$950$		0			0
$951$	9.04870e6			0.324440
$952$		0			0
$953$	4.81813e7			1.71849			0.859244	−	0.511566i	$-0.170934\pi$
$953$	4.81813e7			1.71849			0.859244	+	0.511566i	$0.170934\pi$
$954$		0			0
$955$	−4.31689e7	+	7.47708e7i	−1.53166	+	2.65292i
$956$		0			0
$957$	9.68153e6	+	1.67689e7i	0.341715	+	0.591868i
$958$		0			0
$959$	−2.62361e7	−	1.71375e7i	−0.921198	−	0.601728i
$960$		0			0
$961$	−1.40006e7	−	2.42498e7i	−0.489033	−	0.847030i
$962$		0			0
$963$	−3.61763e6	+	6.26593e6i	−0.125707	+	0.217731i
$964$		0			0
$965$	−2.28950e7			−0.791446
$966$		0			0
$967$	3.54640e7			1.21961			0.609805	−	0.792551i	$-0.291248\pi$
$967$	3.54640e7			1.21961			0.609805	+	0.792551i	$0.291248\pi$
$968$		0			0
$969$	−376286.	+	651747.i	−0.0128739	+	0.0222982i
$970$		0			0
$971$	−3.92148e6	−	6.79221e6i	−0.133476	−	0.231187i	0.791538	−	0.611119i	$-0.209280\pi$
$971$	−3.92148e6	−	6.79221e6i	−0.133476	−	0.231187i	−0.925014	+	0.379933i	$0.875947\pi$
$972$		0			0
$973$	378679.	−	6.87514e6i	0.0128230	−	0.232809i
$974$		0			0
$975$	−7.18573e6	−	1.24461e7i	−0.242080	−	0.419296i
$976$		0			0
$977$	1.23767e7	−	2.14371e7i	0.414829	−	0.718505i	−0.580582	−	0.814202i	$-0.697175\pi$
$977$	1.23767e7	−	2.14371e7i	0.414829	−	0.718505i	0.995410	+	0.0956975i	$0.0305081\pi$
$978$		0			0
$979$	−5.61464e7			−1.87226
$980$		0			0
$981$	1.35760e7			0.450400
$982$		0			0
$983$	2.26564e7	−	3.92421e7i	0.747838	−	1.29529i	−0.201018	−	0.979587i	$-0.564425\pi$
$983$	2.26564e7	−	3.92421e7i	0.747838	−	1.29529i	0.948857	−	0.315707i	$-0.102242\pi$
$984$		0			0
$985$	2.47774e7	+	4.29157e7i	0.813701	+	1.40937i
$986$		0			0
$987$	−281681.	+	5.11409e6i	−0.00920376	+	0.167100i
$988$		0			0
$989$	579508.	+	1.00374e6i	0.0188395	+	0.0326309i
$990$		0			0
$991$	−1.87071e7	+	3.24017e7i	−0.605095	+	1.04805i	0.386942	+	0.922104i	$0.373531\pi$
$991$	−1.87071e7	+	3.24017e7i	−0.605095	+	1.04805i	−0.992037	+	0.125951i	$0.959802\pi$
$992$		0			0
$993$	1.51186e7			0.486561
$994$		0			0
$995$	6.53861e7			2.09376
$996$		0			0
$997$	−2.32639e7	+	4.02943e7i	−0.741216	+	1.28382i	0.210726	+	0.977545i	$0.432417\pi$
$997$	−2.32639e7	+	4.02943e7i	−0.741216	+	1.28382i	−0.951942	+	0.306279i	$0.900916\pi$
$998$		0			0
$999$	3.77463e6	+	6.53786e6i	0.119663	+	0.207263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.j.193.4		8
4.3	odd	2		21.6.e.c.4.3	✓	8
7.2	even	3	inner	336.6.q.j.289.4		8
12.11	even	2		63.6.e.e.46.2		8
28.3	even	6		147.6.a.l.1.2		4
28.11	odd	6		147.6.a.m.1.2		4
28.19	even	6		147.6.e.o.79.3		8
28.23	odd	6		21.6.e.c.16.3	yes	8
28.27	even	2		147.6.e.o.67.3		8
84.11	even	6		441.6.a.w.1.3		4
84.23	even	6		63.6.e.e.37.2		8
84.59	odd	6		441.6.a.v.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.3	✓	8	4.3	odd	2
21.6.e.c.16.3	yes	8	28.23	odd	6
63.6.e.e.37.2		8	84.23	even	6
63.6.e.e.46.2		8	12.11	even	2
147.6.a.l.1.2		4	28.3	even	6
147.6.a.m.1.2		4	28.11	odd	6
147.6.e.o.67.3		8	28.27	even	2
147.6.e.o.79.3		8	28.19	even	6
336.6.q.j.193.4		8	1.1	even	1	trivial
336.6.q.j.289.4		8	7.2	even	3	inner
441.6.a.v.1.3		4	84.59	odd	6
441.6.a.w.1.3		4	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.50000 - 7.79423i) q^{3} +(52.0958 + 90.2327i) q^{5} +(7.12980 - 129.446i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.50000 - 7.79423i) q^{3} +(52.0958 + 90.2327i) q^{5} +(7.12980 - 129.446i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(-248.830 + 430.986i) q^{11} -206.551 q^{13} +937.725 q^{15} +(-31.5793 + 54.6969i) q^{17} +(661.977 + 1146.58i) q^{19} +(-976.845 - 638.077i) q^{21} +(-97.2187 - 168.388i) q^{23} +(-3865.45 + 6695.16i) q^{25} -729.000 q^{27} +4323.14 q^{29} +(-3762.66 + 6517.11i) q^{31} +(2239.47 + 3878.87i) q^{33} +(12051.7 - 6100.24i) q^{35} +(-5177.82 - 8968.25i) q^{37} +(-929.481 + 1609.91i) q^{39} -4180.92 q^{41} -5960.87 q^{43} +(4219.76 - 7308.85i) q^{45} +(-2194.87 - 3801.62i) q^{47} +(-16705.3 - 1845.84i) q^{49} +(284.214 + 492.273i) q^{51} +(-8892.39 + 15402.1i) q^{53} -51852.0 q^{55} +11915.6 q^{57} +(1750.23 - 3031.49i) q^{59} +(5316.23 + 9207.98i) q^{61} +(-9369.11 + 4742.41i) q^{63} +(-10760.5 - 18637.7i) q^{65} +(-6637.37 + 11496.3i) q^{67} -1749.94 q^{69} -38811.1 q^{71} +(-15687.8 + 27172.1i) q^{73} +(34789.1 + 60256.5i) q^{75} +(54015.1 + 35282.8i) q^{77} +(19745.7 + 34200.6i) q^{79} +(-3280.50 + 5681.99i) q^{81} +102372. q^{83} -6580.60 q^{85} +(19454.1 - 33695.5i) q^{87} +(56410.5 + 97705.8i) q^{89} +(-1472.67 + 26737.2i) q^{91} +(33863.9 + 58654.0i) q^{93} +(-68972.6 + 119464. i) q^{95} +30334.3 q^{97} +40310.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 36 q^{3} - 258 q^{7} - 324 q^{9}+O(q^{10}) \) 8 * q + 36 * q^3 - 258 * q^7 - 324 * q^9	\( 8 q + 36 q^{3} - 258 q^{7} - 324 q^{9} + 402 q^{11} + 924 q^{13} - 276 q^{17} + 510 q^{19} - 3564 q^{21} + 6900 q^{23} - 2814 q^{25} - 5832 q^{27} + 1080 q^{29} - 6410 q^{31} - 3618 q^{33} + 33108 q^{35} - 15250 q^{37} + 4158 q^{39} + 8616 q^{41} - 58396 q^{43} - 15060 q^{47} - 64252 q^{49} + 2484 q^{51} - 13692 q^{53} - 146248 q^{55} + 9180 q^{57} + 34830 q^{59} + 5364 q^{61} - 11178 q^{63} - 66864 q^{65} - 5994 q^{67} + 124200 q^{69} - 178536 q^{71} - 59638 q^{73} + 25326 q^{75} - 75660 q^{77} - 44062 q^{79} - 26244 q^{81} + 416892 q^{83} + 72648 q^{85} + 4860 q^{87} + 77520 q^{89} - 104722 q^{91} + 57690 q^{93} - 221376 q^{95} - 377260 q^{97} - 65124 q^{99}+O(q^{100}) \) 8 * q + 36 * q^3 - 258 * q^7 - 324 * q^9 + 402 * q^11 + 924 * q^13 - 276 * q^17 + 510 * q^19 - 3564 * q^21 + 6900 * q^23 - 2814 * q^25 - 5832 * q^27 + 1080 * q^29 - 6410 * q^31 - 3618 * q^33 + 33108 * q^35 - 15250 * q^37 + 4158 * q^39 + 8616 * q^41 - 58396 * q^43 - 15060 * q^47 - 64252 * q^49 + 2484 * q^51 - 13692 * q^53 - 146248 * q^55 + 9180 * q^57 + 34830 * q^59 + 5364 * q^61 - 11178 * q^63 - 66864 * q^65 - 5994 * q^67 + 124200 * q^69 - 178536 * q^71 - 59638 * q^73 + 25326 * q^75 - 75660 * q^77 - 44062 * q^79 - 26244 * q^81 + 416892 * q^83 + 72648 * q^85 + 4860 * q^87 + 77520 * q^89 - 104722 * q^91 + 57690 * q^93 - 221376 * q^95 - 377260 * q^97 - 65124 * q^99

Introduction

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