LMFDB - Embedded newform 336.6.q.j.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$8$
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			289.1
Root			$-0.874091 - 1.51397i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.6.q.j.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.50000 + 7.79423i) q^{3} +(-29.1836 + 50.5475i) q^{5} +(21.4366 - 127.857i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(8.71205 + 15.0897i) q^{11} +889.933 q^{13} -525.305 q^{15} +(-513.318 - 889.092i) q^{17} +(-869.702 + 1506.37i) q^{19} +(1093.01 - 408.276i) q^{21} +(1968.11 - 3408.87i) q^{23} +(-140.869 - 243.993i) q^{25} -729.000 q^{27} +5633.53 q^{29} +(-1548.27 - 2681.68i) q^{31} +(-78.4084 + 135.807i) q^{33} +(5837.27 + 4814.91i) q^{35} +(-2513.43 + 4353.39i) q^{37} +(4004.70 + 6936.34i) q^{39} +18367.0 q^{41} +1630.91 q^{43} +(-2363.87 - 4094.35i) q^{45} +(-4802.62 + 8318.38i) q^{47} +(-15887.9 - 5481.65i) q^{49} +(4619.86 - 8001.83i) q^{51} +(11628.3 + 20140.7i) q^{53} -1017.00 q^{55} -15654.6 q^{57} +(-1801.62 - 3120.50i) q^{59} +(-11438.3 + 19811.7i) q^{61} +(8100.75 + 6681.95i) q^{63} +(-25971.5 + 44983.9i) q^{65} +(23506.4 + 40714.2i) q^{67} +35426.0 q^{69} +1599.63 q^{71} +(-2965.67 - 5136.70i) q^{73} +(1267.82 - 2195.93i) q^{75} +(2116.09 - 790.427i) q^{77} +(-44234.4 + 76616.3i) q^{79} +(-3280.50 - 5681.99i) q^{81} +95823.9 q^{83} +59921.9 q^{85} +(25350.9 + 43909.0i) q^{87} +(23253.9 - 40277.0i) q^{89} +(19077.1 - 113784. i) q^{91} +(13934.4 - 24135.1i) q^{93} +(-50762.1 - 87922.5i) q^{95} -75981.8 q^{97} -1411.35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$		0			0
$5$	−29.1836	+	50.5475i	−0.522053	+	0.904222i	0.477618	+	0.878568i	$0.341500\pi$
$5$	−29.1836	+	50.5475i	−0.522053	+	0.904222i	−0.999671	+	0.0256544i	$0.991833\pi$
$6$		0			0
$7$	21.4366	−	127.857i	0.165352	−	0.986235i
$7$	21.4366	−	127.857i	0.165352	−	0.986235i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	8.71205	+	15.0897i	0.0217089	+	0.0376010i	0.876676	−	0.481082i	$-0.159756\pi$
$11$	8.71205	+	15.0897i	0.0217089	+	0.0376010i	−0.854967	+	0.518683i	$0.826423\pi$
$12$		0			0
$13$	889.933			1.46049			0.730246	−	0.683185i	$-0.239406\pi$
$13$	889.933			1.46049			0.730246	+	0.683185i	$0.239406\pi$
$14$		0			0
$15$	−525.305			−0.602815
$16$		0			0
$17$	−513.318	−	889.092i	−0.430788	−	0.746147i	0.566153	−	0.824300i	$-0.308431\pi$
$17$	−513.318	−	889.092i	−0.430788	−	0.746147i	−0.996941	+	0.0781529i	$0.975098\pi$
$18$		0			0
$19$	−869.702	+	1506.37i	−0.552696	+	0.957297i	0.445383	+	0.895340i	$0.353068\pi$
$19$	−869.702	+	1506.37i	−0.552696	+	0.957297i	−0.998079	+	0.0619572i	$0.980266\pi$
$20$		0			0
$21$	1093.01	−	408.276i	0.540850	−	0.202025i
$22$		0			0
$23$	1968.11	−	3408.87i	0.775764	−	1.34366i	−0.158599	−	0.987343i	$-0.550698\pi$
$23$	1968.11	−	3408.87i	0.775764	−	1.34366i	0.934364	−	0.356320i	$-0.115969\pi$
$24$		0			0
$25$	−140.869	−	243.993i	−0.0450782	−	0.0780777i
$26$		0			0
$27$	−729.000			−0.192450
$28$		0			0
$29$	5633.53			1.24390			0.621950	−	0.783057i	$-0.286341\pi$
$29$	5633.53			1.24390			0.621950	+	0.783057i	$0.286341\pi$
$30$		0			0
$31$	−1548.27	−	2681.68i	−0.289362	−	0.501190i	0.684296	−	0.729205i	$-0.260110\pi$
$31$	−1548.27	−	2681.68i	−0.289362	−	0.501190i	−0.973658	+	0.228015i	$0.926776\pi$
$32$		0			0
$33$	−78.4084	+	135.807i	−0.0125337	+	0.0217089i
$34$		0			0
$35$	5837.27	+	4814.91i	0.805452	+	0.664382i
$36$		0			0
$37$	−2513.43	+	4353.39i	−0.301830	+	0.522785i	−0.976551	−	0.215288i	$-0.930931\pi$
$37$	−2513.43	+	4353.39i	−0.301830	+	0.522785i	0.674720	+	0.738073i	$0.264264\pi$
$38$		0			0
$39$	4004.70	+	6936.34i	0.421608	+	0.730246i
$40$		0			0
$41$	18367.0			1.70639			0.853195	−	0.521592i	$-0.174662\pi$
$41$	18367.0			1.70639			0.853195	+	0.521592i	$0.174662\pi$
$42$		0			0
$43$	1630.91			0.134511			0.0672557	−	0.997736i	$-0.478576\pi$
$43$	1630.91			0.134511			0.0672557	+	0.997736i	$0.478576\pi$
$44$		0			0
$45$	−2363.87	−	4094.35i	−0.174018	−	0.301407i
$46$		0			0
$47$	−4802.62	+	8318.38i	−0.317127	+	0.549280i	−0.979887	−	0.199551i	$-0.936051\pi$
$47$	−4802.62	+	8318.38i	−0.317127	+	0.549280i	0.662760	+	0.748832i	$0.269385\pi$
$48$		0			0
$49$	−15887.9	−	5481.65i	−0.945317	−	0.326153i
$50$		0			0
$51$	4619.86	−	8001.83i	0.248716	−	0.430788i
$52$		0			0
$53$	11628.3	+	20140.7i	0.568624	+	0.984886i	0.996702	+	0.0811440i	$0.0258574\pi$
$53$	11628.3	+	20140.7i	0.568624	+	0.984886i	−0.428078	+	0.903742i	$0.640809\pi$
$54$		0			0
$55$	−1017.00			−0.0453328
$56$		0			0
$57$	−15654.6			−0.638198
$58$		0			0
$59$	−1801.62	−	3120.50i	−0.0673803	−	0.116706i	0.830367	−	0.557217i	$-0.188131\pi$
$59$	−1801.62	−	3120.50i	−0.0673803	−	0.116706i	−0.897747	+	0.440511i	$0.854797\pi$
$60$		0			0
$61$	−11438.3	+	19811.7i	−0.393584	+	0.681707i	−0.992919	−	0.118791i	$-0.962098\pi$
$61$	−11438.3	+	19811.7i	−0.393584	+	0.681707i	0.599336	+	0.800498i	$0.295431\pi$
$62$		0			0
$63$	8100.75	+	6681.95i	0.257143	+	0.212106i
$64$		0			0
$65$	−25971.5	+	44983.9i	−0.762454	+	1.32061i
$66$		0			0
$67$	23506.4	+	40714.2i	0.639733	+	1.10805i	0.985491	+	0.169726i	$0.0542884\pi$
$67$	23506.4	+	40714.2i	0.639733	+	1.10805i	−0.345758	+	0.938324i	$0.612378\pi$
$68$		0			0
$69$	35426.0			0.895776
$70$		0			0
$71$	1599.63			0.0376595			0.0188298	−	0.999823i	$-0.494006\pi$
$71$	1599.63			0.0376595			0.0188298	+	0.999823i	$0.494006\pi$
$72$		0			0
$73$	−2965.67	−	5136.70i	−0.0651353	−	0.112818i	0.831619	−	0.555347i	$-0.187415\pi$
$73$	−2965.67	−	5136.70i	−0.0651353	−	0.112818i	−0.896754	+	0.442529i	$0.854081\pi$
$74$		0			0
$75$	1267.82	−	2195.93i	0.0260259	−	0.0450782i
$76$		0			0
$77$	2116.09	−	790.427i	0.0406730	−	0.0151927i
$78$		0			0
$79$	−44234.4	+	76616.3i	−0.797431	+	1.38119i	0.123854	+	0.992300i	$0.460475\pi$
$79$	−44234.4	+	76616.3i	−0.797431	+	1.38119i	−0.921284	+	0.388890i	$0.872859\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	95823.9			1.52679			0.763394	−	0.645933i	$-0.223531\pi$
$83$	95823.9			1.52679			0.763394	+	0.645933i	$0.223531\pi$
$84$		0			0
$85$	59921.9			0.899577
$86$		0			0
$87$	25350.9	+	43909.0i	0.359083	+	0.621950i
$88$		0			0
$89$	23253.9	−	40277.0i	0.311187	−	0.538992i	−0.667433	−	0.744670i	$-0.732607\pi$
$89$	23253.9	−	40277.0i	0.311187	−	0.538992i	0.978620	+	0.205679i	$0.0659401\pi$
$90$		0			0
$91$	19077.1	−	113784.i	0.241496	−	1.44039i
$92$		0			0
$93$	13934.4	−	24135.1i	0.167063	−	0.289362i
$94$		0			0
$95$	−50762.1	−	87922.5i	−0.577073	−	0.999519i
$96$		0			0
$97$	−75981.8			−0.819937			−0.409968	−	0.912100i	$-0.634460\pi$
$97$	−75981.8			−0.819937			−0.409968	+	0.912100i	$0.634460\pi$
$98$		0			0
$99$	−1411.35			−0.0144726
$100$		0			0
$101$	23078.7	+	39973.5i	0.225117	+	0.389914i	0.956355	−	0.292209i	$-0.0943903\pi$
$101$	23078.7	+	39973.5i	0.225117	+	0.389914i	−0.731238	+	0.682123i	$0.761057\pi$
$102$		0			0
$103$	−40986.8	+	70991.2i	−0.380672	+	0.659343i	−0.991158	−	0.132683i	$-0.957641\pi$
$103$	−40986.8	+	70991.2i	−0.380672	+	0.659343i	0.610487	+	0.792027i	$0.290974\pi$
$104$		0			0
$105$	−11260.8	+	67164.1i	−0.0996769	+	0.594517i
$106$		0			0
$107$	−1426.84	+	2471.35i	−0.0120480	+	0.0208677i	−0.871987	−	0.489530i	$-0.837168\pi$
$107$	−1426.84	+	2471.35i	−0.0120480	+	0.0208677i	0.859939	+	0.510398i	$0.170502\pi$
$108$		0			0
$109$	83139.2	+	144001.i	0.670254	+	1.16091i	0.977832	+	0.209391i	$0.0671483\pi$
$109$	83139.2	+	144001.i	0.670254	+	1.16091i	−0.307578	+	0.951523i	$0.599518\pi$
$110$		0			0
$111$	−45241.7			−0.348523
$112$		0			0
$113$	260304.			1.91772			0.958858	−	0.283886i	$-0.0916237\pi$
$113$	260304.			1.91772			0.958858	+	0.283886i	$0.0916237\pi$
$114$		0			0
$115$	114873.	+	198966.i	0.809980	+	1.40293i
$116$		0			0
$117$	−36042.3	+	62427.1i	−0.243415	+	0.421608i
$118$		0			0
$119$	−124681.	+	46572.3i	−0.807108	+	0.301481i
$120$		0			0
$121$	80373.7	−	139211.i	0.499057	−	0.864393i
$122$		0			0
$123$	82651.5	+	143157.i	0.492592	+	0.853195i
$124$		0			0
$125$	−165953.			−0.949973
$126$		0			0
$127$	233743.			1.28596			0.642982	−	0.765882i	$-0.277697\pi$
$127$	233743.			1.28596			0.642982	+	0.765882i	$0.277697\pi$
$128$		0			0
$129$	7339.10	+	12711.7i	0.0388301	+	0.0672557i
$130$		0			0
$131$	−78644.9	+	136217.i	−0.400398	+	0.693510i	−0.993774	−	0.111415i	$-0.964462\pi$
$131$	−78644.9	+	136217.i	−0.400398	+	0.693510i	0.593376	+	0.804926i	$0.297795\pi$
$132$		0			0
$133$	173957.	+	143489.i	0.852730	+	0.703379i
$134$		0			0
$135$	21274.9	−	36849.2i	0.100469	−	0.174018i
$136$		0			0
$137$	85773.8	+	148564.i	0.390439	+	0.676260i	0.992507	−	0.122185i	$-0.0389900\pi$
$137$	85773.8	+	148564.i	0.390439	+	0.676260i	−0.602069	+	0.798444i	$0.705657\pi$
$138$		0			0
$139$	−210625.			−0.924642			−0.462321	−	0.886713i	$-0.652983\pi$
$139$	−210625.			−0.924642			−0.462321	+	0.886713i	$0.652983\pi$
$140$		0			0
$141$	−86447.1			−0.366187
$142$		0			0
$143$	7753.14	+	13428.8i	0.0317057	+	0.0549159i
$144$		0			0
$145$	−164407.	+	284761.i	−0.649381	+	1.12476i
$146$		0			0
$147$	−28770.6	−	148502.i	−0.109813	−	0.566811i
$148$		0			0
$149$	−119706.	+	207338.i	−0.441725	+	0.765090i	−0.997818	−	0.0660304i	$-0.978967\pi$
$149$	−119706.	+	207338.i	−0.441725	+	0.765090i	0.556093	+	0.831120i	$0.312300\pi$
$150$		0			0
$151$	108520.	+	187962.i	0.387317	+	0.670852i	0.992088	−	0.125547i	$-0.0400686\pi$
$151$	108520.	+	187962.i	0.387317	+	0.670852i	−0.604771	+	0.796400i	$0.706735\pi$
$152$		0			0
$153$	83157.5			0.287192
$154$		0			0
$155$	180736.			0.604249
$156$		0			0
$157$	−83452.2	−	144543.i	−0.270202	−	0.468004i	0.698711	−	0.715404i	$-0.253757\pi$
$157$	−83452.2	−	144543.i	−0.270202	−	0.468004i	−0.968913	+	0.247400i	$0.920424\pi$
$158$		0			0
$159$	−104654.	+	181267.i	−0.328295	+	0.568624i
$160$		0			0
$161$	−393659.	−	324712.i	−1.19689	−	0.987264i
$162$		0			0
$163$	253086.	−	438358.i	0.746104	−	1.29229i	−0.203574	−	0.979060i	$-0.565256\pi$
$163$	253086.	−	438358.i	0.746104	−	1.29229i	0.949677	−	0.313230i	$-0.101411\pi$
$164$		0			0
$165$	−4576.49	−	7926.71i	−0.0130865	−	0.0226664i
$166$		0			0
$167$	565560.			1.56923			0.784616	−	0.619982i	$-0.212860\pi$
$167$	565560.			1.56923			0.784616	+	0.619982i	$0.212860\pi$
$168$		0			0
$169$	420688.			1.13304
$170$		0			0
$171$	−70445.8	−	122016.i	−0.184232	−	0.319099i
$172$		0			0
$173$	329718.	−	571088.i	0.837581	−	1.45073i	−0.0543304	−	0.998523i	$-0.517302\pi$
$173$	329718.	−	571088.i	0.837581	−	1.45073i	0.891911	−	0.452210i	$-0.149364\pi$
$174$		0			0
$175$	−34216.0	+	12780.8i	−0.0844567	+	0.0315473i
$176$		0			0
$177$	16214.6	−	28084.5i	0.0389020	−	0.0673803i
$178$		0			0
$179$	82645.0	+	143145.i	0.192790	+	0.333922i	0.946174	−	0.323659i	$-0.104913\pi$
$179$	82645.0	+	143145.i	0.192790	+	0.333922i	−0.753384	+	0.657581i	$0.771580\pi$
$180$		0			0
$181$	148492.			0.336904			0.168452	−	0.985710i	$-0.446123\pi$
$181$	148492.			0.336904			0.168452	+	0.985710i	$0.446123\pi$
$182$		0			0
$183$	−205889.			−0.454471
$184$		0			0
$185$	−146702.	−	254095.i	−0.315142	−	0.545843i
$186$		0			0
$187$	8944.10	−	15491.6i	0.0187039	−	0.0323961i
$188$		0			0
$189$	−15627.3	+	93207.9i	−0.0318221	+	0.189801i
$190$		0			0
$191$	192955.	−	334208.i	0.382713	−	0.662879i	−0.608736	−	0.793373i	$-0.708323\pi$
$191$	192955.	−	334208.i	0.382713	−	0.662879i	0.991449	+	0.130494i	$0.0416564\pi$
$192$		0			0
$193$	−248148.	−	429805.i	−0.479531	−	0.830573i	0.520193	−	0.854049i	$-0.325860\pi$
$193$	−248148.	−	429805.i	−0.479531	−	0.830573i	−0.999724	+	0.0234760i	$0.992527\pi$
$194$		0			0
$195$	−467487.			−0.880406
$196$		0			0
$197$	441439.			0.810411			0.405206	−	0.914226i	$-0.367200\pi$
$197$	441439.			0.810411			0.405206	+	0.914226i	$0.367200\pi$
$198$		0			0
$199$	−37919.4	−	65678.3i	−0.0678779	−	0.117568i	0.830089	−	0.557631i	$-0.188290\pi$
$199$	−37919.4	−	65678.3i	−0.0678779	−	0.117568i	−0.897967	+	0.440063i	$0.854956\pi$
$200$		0			0
$201$	−211557.	+	366428.i	−0.369350	+	0.639733i
$202$		0			0
$203$	120764.	−	720287.i	0.205682	−	1.22678i
$204$		0			0
$205$	−536016.	+	928406.i	−0.890826	+	1.54296i
$206$		0			0
$207$	159417.	+	276118.i	0.258588	+	0.447888i
$208$		0			0
$209$	−30307.5			−0.0479938
$210$		0			0
$211$	−778704.			−1.20411			−0.602055	−	0.798454i	$-0.705651\pi$
$211$	−778704.			−1.20411			−0.602055	+	0.798454i	$0.705651\pi$
$212$		0			0
$213$	7198.35	+	12467.9i	0.0108714	+	0.0188298i
$214$		0			0
$215$	−47595.9	+	82438.6i	−0.0702221	+	0.121628i
$216$		0			0
$217$	−376061.	+	140471.i	−0.542137	+	0.202506i
$218$		0			0
$219$	26691.1	−	46230.3i	0.0376059	−	0.0651353i
$220$		0			0
$221$	−456818.	−	791233.i	−0.629163	−	1.08974i
$222$		0			0
$223$	−738085.			−0.993903			−0.496951	−	0.867778i	$-0.665547\pi$
$223$	−738085.			−0.993903			−0.496951	+	0.867778i	$0.665547\pi$
$224$		0			0
$225$	22820.8			0.0300521
$226$		0			0
$227$	−272058.	−	471218.i	−0.350426	−	0.606956i	0.635898	−	0.771773i	$-0.280630\pi$
$227$	−272058.	−	471218.i	−0.350426	−	0.606956i	−0.986324	+	0.164817i	$0.947297\pi$
$228$		0			0
$229$	116781.	−	202271.i	0.147158	−	0.254885i	−0.783018	−	0.621999i	$-0.786321\pi$
$229$	116781.	−	202271.i	0.147158	−	0.254885i	0.930176	+	0.367114i	$0.119654\pi$
$230$		0			0
$231$	15683.2	+	12936.3i	0.0193376	+	0.0159508i
$232$		0			0
$233$	309050.	−	535290.i	0.372940	−	0.645951i	−0.617077	−	0.786903i	$-0.711683\pi$
$233$	309050.	−	535290.i	0.372940	−	0.645951i	0.990016	+	0.140952i	$0.0450164\pi$
$234$		0			0
$235$	−280316.	−	485521.i	−0.331114	−	0.573506i
$236$		0			0
$237$	−796220.			−0.920794
$238$		0			0
$239$	−937500.			−1.06164			−0.530819	−	0.847485i	$-0.678116\pi$
$239$	−937500.			−1.06164			−0.530819	+	0.847485i	$0.678116\pi$
$240$		0			0
$241$	−466018.	−	807167.i	−0.516845	−	0.895202i	−0.999809	−	0.0195613i	$-0.993773\pi$
$241$	−466018.	−	807167.i	−0.516845	−	0.895202i	0.482964	−	0.875640i	$-0.339560\pi$
$242$		0			0
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$		0			0
$245$	740752.	−	643122.i	0.788420	−	0.684508i
$246$		0			0
$247$	−773976.	+	1.34057e6i	−0.807208	+	1.39812i
$248$		0			0
$249$	431208.	+	746874.i	0.440746	+	0.763394i
$250$		0			0
$251$	−214975.			−0.215379			−0.107690	−	0.994185i	$-0.534345\pi$
$251$	−214975.			−0.215379			−0.107690	+	0.994185i	$0.534345\pi$
$252$		0			0
$253$	68585.1			0.0673641
$254$		0			0
$255$	269649.	+	467045.i	0.259685	+	0.449788i
$256$		0			0
$257$	−39593.5	+	68578.0i	−0.0373931	+	0.0647667i	−0.884116	−	0.467267i	$-0.845239\pi$
$257$	−39593.5	+	68578.0i	−0.0373931	+	0.0647667i	0.846723	+	0.532034i	$0.178572\pi$
$258$		0			0
$259$	502733.	+	414682.i	0.465680	+	0.384119i
$260$		0			0
$261$	−228158.	+	395181.i	−0.207317	+	0.359083i
$262$		0			0
$263$	−216414.	−	374840.i	−0.192928	−	0.334162i	0.753291	−	0.657687i	$-0.228465\pi$
$263$	−216414.	−	374840.i	−0.192928	−	0.334162i	−0.946219	+	0.323526i	$0.895132\pi$
$264$		0			0
$265$	−1.35742e6			−1.18741
$266$		0			0
$267$	418571.			0.359328
$268$		0			0
$269$	2345.93	+	4063.27i	0.00197667	+	0.00342369i	0.867012	−	0.498287i	$-0.166037\pi$
$269$	2345.93	+	4063.27i	0.00197667	+	0.00342369i	−0.865035	+	0.501711i	$0.832704\pi$
$270$		0			0
$271$	52632.1	−	91161.5i	0.0435339	−	0.0754029i	−0.843437	−	0.537227i	$-0.819472\pi$
$271$	52632.1	−	91161.5i	0.0435339	−	0.0754029i	0.886971	+	0.461825i	$0.152805\pi$
$272$		0			0
$273$	972709.	−	363338.i	0.789907	−	0.295056i
$274$		0			0
$275$	2454.52	−	4251.35i	0.00195720	−	0.00338997i
$276$		0			0
$277$	381558.	+	660879.i	0.298787	+	0.517514i	0.975859	−	0.218403i	$-0.0700847\pi$
$277$	381558.	+	660879.i	0.298787	+	0.517514i	−0.677072	+	0.735917i	$0.736751\pi$
$278$		0			0
$279$	250819.			0.192908
$280$		0			0
$281$	−729540.			−0.551167			−0.275584	−	0.961277i	$-0.588871\pi$
$281$	−729540.			−0.551167			−0.275584	+	0.961277i	$0.588871\pi$
$282$		0			0
$283$	−595214.	−	1.03094e6i	−0.441781	−	0.765188i	0.556040	−	0.831155i	$-0.312320\pi$
$283$	−595214.	−	1.03094e6i	−0.441781	−	0.765188i	−0.997822	+	0.0659675i	$0.978987\pi$
$284$		0			0
$285$	456859.	−	791303.i	0.333173	−	0.577073i
$286$		0			0
$287$	393726.	−	2.34835e6i	0.282156	−	1.68290i
$288$		0			0
$289$	182938.	−	316859.i	0.128843	−	0.223162i
$290$		0			0
$291$	−341918.	−	592220.i	−0.236695	−	0.409968i
$292$		0			0
$293$	−1.02503e6			−0.697537			−0.348769	−	0.937209i	$-0.613400\pi$
$293$	−1.02503e6			−0.697537			−0.348769	+	0.937209i	$0.613400\pi$
$294$		0			0
$295$	210311.			0.140704
$296$		0			0
$297$	−6351.08	−	11000.4i	−0.00417789	−	0.00723631i
$298$		0			0
$299$	1.75149e6	−	3.03366e6i	1.13300	−	1.96241i
$300$		0			0
$301$	34961.2	−	208524.i	0.0222418	−	0.132660i
$302$		0			0
$303$	−207708.	+	359762.i	−0.129971	+	0.225117i
$304$		0			0
$305$	−667623.	−	1.15636e6i	−0.410943	−	0.711774i
$306$		0			0
$307$	709845.			0.429850			0.214925	−	0.976631i	$-0.431049\pi$
$307$	709845.			0.429850			0.214925	+	0.976631i	$0.431049\pi$
$308$		0			0
$309$	−737762.			−0.439562
$310$		0			0
$311$	783816.	+	1.35761e6i	0.459529	+	0.795928i	0.998936	−	0.0461175i	$-0.0146849\pi$
$311$	783816.	+	1.35761e6i	0.459529	+	0.795928i	−0.539407	+	0.842045i	$0.681352\pi$
$312$		0			0
$313$	−186476.	+	322986.i	−0.107588	+	0.186347i	−0.914792	−	0.403924i	$-0.867646\pi$
$313$	−186476.	+	322986.i	−0.107588	+	0.186347i	0.807205	+	0.590271i	$0.200979\pi$
$314$		0			0
$315$	−574166.	+	214470.i	−0.326033	+	0.121784i
$316$		0			0
$317$	1.51408e6	−	2.62246e6i	0.846253	−	1.46575i	−0.0382747	−	0.999267i	$-0.512186\pi$
$317$	1.51408e6	−	2.62246e6i	0.846253	−	1.46575i	0.884528	−	0.466487i	$-0.154480\pi$
$318$		0			0
$319$	49079.6	+	85008.3i	0.0270037	+	0.0467719i
$320$		0			0
$321$	−25683.1			−0.0139118
$322$		0			0
$323$	1.78573e6			0.952380
$324$		0			0
$325$	−125364.	−	217137.i	−0.0658363	−	0.114032i
$326$		0			0
$327$	−748253.	+	1.29601e6i	−0.386971	+	0.670254i
$328$		0			0
$329$	960613.	+	792367.i	0.489281	+	0.403586i
$330$		0			0
$331$	533448.	−	923959.i	0.267622	−	0.463535i	−0.700625	−	0.713529i	$-0.747095\pi$
$331$	533448.	−	923959.i	0.267622	−	0.463535i	0.968247	+	0.249995i	$0.0804288\pi$
$332$		0			0
$333$	−203588.	−	352624.i	−0.100610	−	0.174262i
$334$		0			0
$335$	−2.74401e6			−1.33590
$336$		0			0
$337$	1.55734e6			0.746981			0.373490	−	0.927634i	$-0.378161\pi$
$337$	1.55734e6			0.746981			0.373490	+	0.927634i	$0.378161\pi$
$338$		0			0
$339$	1.17137e6	+	2.02887e6i	0.553597	+	0.958858i
$340$		0			0
$341$	26977.1	−	46725.8i	0.0125635	−	0.0217606i
$342$		0			0
$343$	−1.04145e6	+	1.91388e6i	−0.477973	+	0.878374i
$344$		0			0
$345$	−1.03386e6	+	1.79070e6i	−0.467642	+	0.809980i
$346$		0			0
$347$	−1.11748e6	−	1.93553e6i	−0.498214	−	0.862932i	0.501784	−	0.864993i	$-0.332677\pi$
$347$	−1.11748e6	−	1.93553e6i	−0.498214	−	0.862932i	−0.999998	+	0.00206105i	$0.999344\pi$
$348$		0			0
$349$	−1.72982e6			−0.760218			−0.380109	−	0.924942i	$-0.624114\pi$
$349$	−1.72982e6			−0.760218			−0.380109	+	0.924942i	$0.624114\pi$
$350$		0			0
$351$	−648761.			−0.281072
$352$		0			0
$353$	1.18287e6	+	2.04879e6i	0.505242	+	0.875105i	0.999982	+	0.00606386i	$0.00193020\pi$
$353$	1.18287e6	+	2.04879e6i	0.505242	+	0.875105i	−0.494739	+	0.869041i	$0.664736\pi$
$354$		0			0
$355$	−46683.1	+	80857.6i	−0.0196603	+	0.0340526i
$356$		0			0
$357$	−924058.	−	762214.i	−0.383733	−	0.316524i
$358$		0			0
$359$	25514.3	−	44192.1i	0.0104484	−	0.0180971i	−0.860754	−	0.509021i	$-0.830007\pi$
$359$	25514.3	−	44192.1i	0.0104484	−	0.0180971i	0.871202	+	0.490924i	$0.163341\pi$
$360$		0			0
$361$	−274712.	−	475815.i	−0.110945	−	0.192163i
$362$		0			0
$363$	1.44673e6			0.576262
$364$		0			0
$365$	346197.			0.136016
$366$		0			0
$367$	1.88411e6	+	3.26338e6i	0.730200	+	1.26474i	0.956797	+	0.290755i	$0.0939065\pi$
$367$	1.88411e6	+	3.26338e6i	0.730200	+	1.26474i	−0.226597	+	0.973989i	$0.572760\pi$
$368$		0			0
$369$	−743863.	+	1.28841e6i	−0.284398	+	0.492592i
$370$		0			0
$371$	2.82441e6	−	1.05501e6i	1.06535	−	0.397943i
$372$		0			0
$373$	−2.31720e6	+	4.01351e6i	−0.862366	+	1.49366i	0.00727258	+	0.999974i	$0.497685\pi$
$373$	−2.31720e6	+	4.01351e6i	−0.862366	+	1.49366i	−0.869639	+	0.493689i	$0.835648\pi$
$374$		0			0
$375$	−746790.	−	1.29348e6i	−0.274234	−	0.474986i
$376$		0			0
$377$	5.01346e6			1.81670
$378$		0			0
$379$	4.17169e6			1.49181			0.745905	−	0.666052i	$-0.232017\pi$
$379$	4.17169e6			1.49181			0.745905	+	0.666052i	$0.232017\pi$
$380$		0			0
$381$	1.05184e6	+	1.82184e6i	0.371226	+	0.642982i
$382$		0			0
$383$	−2.08586e6	+	3.61281e6i	−0.726588	+	1.25849i	0.231730	+	0.972780i	$0.425562\pi$
$383$	−2.08586e6	+	3.61281e6i	−0.726588	+	1.25849i	−0.958317	+	0.285706i	$0.907772\pi$
$384$		0			0
$385$	−21800.9	+	130030.i	−0.00749590	+	0.0447088i
$386$		0			0
$387$	−66051.9	+	114405.i	−0.0224186	+	0.0388301i
$388$		0			0
$389$	−1.37697e6	−	2.38498e6i	−0.461371	−	0.799119i	0.537658	−	0.843163i	$-0.319309\pi$
$389$	−1.37697e6	−	2.38498e6i	−0.461371	−	0.799119i	−0.999030	+	0.0440442i	$0.985976\pi$
$390$		0			0
$391$	−4.04106e6			−1.33676
$392$		0			0
$393$	−1.41561e6			−0.462340
$394$		0			0
$395$	−2.58184e6	−	4.47189e6i	−0.832602	−	1.44211i
$396$		0			0
$397$	1.26602e6	−	2.19281e6i	0.403148	−	0.698274i	−0.590956	−	0.806704i	$-0.701249\pi$
$397$	1.26602e6	−	2.19281e6i	0.403148	−	0.698274i	0.994104	+	0.108430i	$0.0345825\pi$
$398$		0			0
$399$	−335582.	+	2.00156e6i	−0.105528	+	0.629413i
$400$		0			0
$401$	1.07873e6	−	1.86842e6i	0.335007	−	0.580249i	−0.648479	−	0.761232i	$-0.724595\pi$
$401$	1.07873e6	−	1.86842e6i	0.335007	−	0.580249i	0.983486	+	0.180983i	$0.0579280\pi$
$402$		0			0
$403$	−1.37785e6	−	2.38651e6i	−0.422611	−	0.731983i
$404$		0			0
$405$	382948.			0.116012
$406$		0			0
$407$	−87588.5			−0.0262096
$408$		0			0
$409$	2.16402e6	+	3.74819e6i	0.639665	+	1.10793i	0.985506	+	0.169640i	$0.0542604\pi$
$409$	2.16402e6	+	3.74819e6i	0.639665	+	1.10793i	−0.345841	+	0.938293i	$0.612406\pi$
$410$		0			0
$411$	−771964.	+	1.33708e6i	−0.225420	+	0.390439i
$412$		0			0
$413$	−437599.	+	163457.i	−0.126241	+	0.0471552i
$414$		0			0
$415$	−2.79649e6	+	4.84366e6i	−0.797064	+	1.38056i
$416$		0			0
$417$	−947814.	−	1.64166e6i	−0.266921	−	0.462321i
$418$		0			0
$419$	1.51129e6			0.420544			0.210272	−	0.977643i	$-0.432565\pi$
$419$	1.51129e6			0.420544			0.210272	+	0.977643i	$0.432565\pi$
$420$		0			0
$421$	1.11586e6			0.306835			0.153418	−	0.988161i	$-0.450972\pi$
$421$	1.11586e6			0.306835			0.153418	+	0.988161i	$0.450972\pi$
$422$		0			0
$423$	−389012.	−	673788.i	−0.105709	−	0.183093i
$424$		0			0
$425$	−144621.	+	250492.i	−0.0388383	+	0.0672699i
$426$		0			0
$427$	2.28787e6	+	1.88717e6i	0.607243	+	0.500888i
$428$		0			0
$429$	−69778.3	+	120860.i	−0.0183053	+	0.0317057i
$430$		0			0
$431$	3.10672e6	+	5.38100e6i	0.805581	+	1.39531i	0.915898	+	0.401411i	$0.131480\pi$
$431$	3.10672e6	+	5.38100e6i	0.805581	+	1.39531i	−0.110317	+	0.993896i	$0.535187\pi$
$432$		0			0
$433$	3.24118e6			0.830775			0.415388	−	0.909644i	$-0.363646\pi$
$433$	3.24118e6			0.830775			0.415388	+	0.909644i	$0.363646\pi$
$434$		0			0
$435$	−2.95932e6			−0.749841
$436$		0			0
$437$	3.42334e6	+	5.92939e6i	0.857524	+	1.48527i
$438$		0			0
$439$	1.15248e6	−	1.99616e6i	0.285413	−	0.494349i	−0.687297	−	0.726377i	$-0.741203\pi$
$439$	1.15248e6	−	1.99616e6i	0.285413	−	0.494349i	0.972709	+	0.232028i	$0.0745360\pi$
$440$		0			0
$441$	1.02799e6	−	892502.i	0.251705	−	0.218531i
$442$		0			0
$443$	766328.	−	1.32732e6i	0.185526	−	0.321341i	−0.758228	−	0.651990i	$-0.773934\pi$
$443$	766328.	−	1.32732e6i	0.185526	−	0.321341i	0.943754	+	0.330649i	$0.107268\pi$
$444$		0			0
$445$	1.35727e6	+	2.35086e6i	0.324912	+	0.562764i
$446$		0			0
$447$	−2.15472e6			−0.510060
$448$		0			0
$449$	−3.55718e6			−0.832702			−0.416351	−	0.909204i	$-0.636691\pi$
$449$	−3.55718e6			−0.832702			−0.416351	+	0.909204i	$0.636691\pi$
$450$		0			0
$451$	160014.	+	277153.i	0.0370439	+	0.0641620i
$452$		0			0
$453$	−976678.	+	1.69166e6i	−0.223617	+	0.387317i
$454$		0			0
$455$	5.19478e6	+	4.28494e6i	1.17636	+	0.970324i
$456$		0			0
$457$	−1.25941e6	+	2.18137e6i	−0.282083	+	0.488583i	−0.971898	−	0.235403i	$-0.924359\pi$
$457$	−1.25941e6	+	2.18137e6i	−0.282083	+	0.488583i	0.689814	+	0.723986i	$0.257692\pi$
$458$		0			0
$459$	374209.	+	648148.i	0.0829053	+	0.143596i
$460$		0			0
$461$	−6.63271e6			−1.45358			−0.726789	−	0.686861i	$-0.758988\pi$
$461$	−6.63271e6			−1.45358			−0.726789	+	0.686861i	$0.758988\pi$
$462$		0			0
$463$	4.40432e6			0.954830			0.477415	−	0.878678i	$-0.341574\pi$
$463$	4.40432e6			0.954830			0.477415	+	0.878678i	$0.341574\pi$
$464$		0			0
$465$	813313.	+	1.40870e6i	0.174432	+	0.302124i
$466$		0			0
$467$	122922.	−	212908.i	0.0260819	−	0.0451751i	−0.852690	−	0.522417i	$-0.825030\pi$
$467$	122922.	−	212908.i	0.0260819	−	0.0451751i	0.878772	+	0.477242i	$0.158364\pi$
$468$		0			0
$469$	5.70951e6	−	2.13269e6i	1.19858	−	0.447708i
$470$		0			0
$471$	751070.	−	1.30089e6i	0.156001	−	0.270202i
$472$		0			0
$473$	14208.6	+	24610.0i	0.00292010	+	0.00505776i
$474$		0			0
$475$	490057.			0.0996581
$476$		0			0
$477$	−1.88378e6			−0.379083
$478$		0			0
$479$	−20175.6	−	34945.1i	−0.00401779	−	0.00695901i	0.864010	−	0.503475i	$-0.167946\pi$
$479$	−20175.6	−	34945.1i	−0.00401779	−	0.00695901i	−0.868027	+	0.496516i	$0.834612\pi$
$480$		0			0
$481$	−2.23678e6	+	3.87422e6i	−0.440820	+	0.763523i
$482$		0			0
$483$	759412.	−	4.52947e6i	0.148119	−	0.883445i
$484$		0			0
$485$	2.21743e6	−	3.84069e6i	0.428050	−	0.741405i
$486$		0			0
$487$	−1.65484e6	−	2.86627e6i	−0.316180	−	0.547639i	0.663508	−	0.748169i	$-0.269067\pi$
$487$	−1.65484e6	−	2.86627e6i	−0.316180	−	0.547639i	−0.979688	+	0.200530i	$0.935734\pi$
$488$		0			0
$489$	4.55555e6			0.861526
$490$		0			0
$491$	1.97959e6			0.370570			0.185285	−	0.982685i	$-0.440679\pi$
$491$	1.97959e6			0.370570			0.185285	+	0.982685i	$0.440679\pi$
$492$		0			0
$493$	−2.89179e6	−	5.00872e6i	−0.535857	−	0.928132i
$494$		0			0
$495$	41188.4	−	71340.4i	0.00755547	−	0.0130865i
$496$		0			0
$497$	34290.7	−	204525.i	0.00622709	−	0.0371411i
$498$		0			0
$499$	−1.58498e6	+	2.74526e6i	−0.284952	+	0.493551i	−0.972597	−	0.232495i	$-0.925311\pi$
$499$	−1.58498e6	+	2.74526e6i	−0.284952	+	0.493551i	0.687646	+	0.726046i	$0.258644\pi$
$500$		0			0
$501$	2.54502e6	+	4.40810e6i	0.452998	+	0.784616i
$502$		0			0
$503$	4.01273e6			0.707164			0.353582	−	0.935403i	$-0.384963\pi$
$503$	4.01273e6			0.707164			0.353582	+	0.935403i	$0.384963\pi$
$504$		0			0
$505$	−2.69408e6			−0.470092
$506$		0			0
$507$	1.89310e6	+	3.27894e6i	0.327079	+	0.566518i
$508$		0			0
$509$	−2.05629e6	+	3.56159e6i	−0.351795	+	0.609326i	−0.986564	−	0.163375i	$-0.947762\pi$
$509$	−2.05629e6	+	3.56159e6i	−0.351795	+	0.609326i	0.634769	+	0.772702i	$0.281095\pi$
$510$		0			0
$511$	−720338.	+	269070.i	−0.122035	+	0.0455840i
$512$		0			0
$513$	634012.	−	1.09814e6i	0.106366	−	0.184232i
$514$		0			0
$515$	−2.39229e6	−	4.14356e6i	−0.397462	−	0.688424i
$516$		0			0
$517$	−167363.			−0.0275380
$518$		0			0
$519$	5.93492e6			0.967155
$520$		0			0
$521$	−4.27758e6	−	7.40898e6i	−0.690404	−	1.19582i	−0.971705	−	0.236196i	$-0.924099\pi$
$521$	−4.27758e6	−	7.40898e6i	−0.690404	−	1.19582i	0.281301	−	0.959620i	$-0.409234\pi$
$522$		0			0
$523$	−896820.	+	1.55334e6i	−0.143368	+	0.248320i	−0.928763	−	0.370675i	$-0.879126\pi$
$523$	−896820.	+	1.55334e6i	−0.143368	+	0.248320i	0.785395	+	0.618995i	$0.212460\pi$
$524$		0			0
$525$	−253588.	−	209174.i	−0.0401542	−	0.0331214i
$526$		0			0
$527$	−1.58950e6	+	2.75310e6i	−0.249307	+	0.431813i
$528$		0			0
$529$	−4.52875e6	−	7.84402e6i	−0.703621	−	1.21871i
$530$		0			0
$531$	291862.			0.0449202
$532$		0			0
$533$	1.63454e7			2.49217
$534$		0			0
$535$	−83280.6	−	144246.i	−0.0125794	−	0.0217881i
$536$		0			0
$537$	−743805.	+	1.28831e6i	−0.111307	+	0.192790i
$538$		0			0
$539$	−55700.1	−	287501.i	−0.00825818	−	0.0426253i
$540$		0			0
$541$	178780.	−	309657.i	0.0262619	−	0.0454870i	−0.852596	−	0.522571i	$-0.824973\pi$
$541$	178780.	−	309657.i	0.0262619	−	0.0454870i	0.878858	+	0.477084i	$0.158306\pi$
$542$		0			0
$543$	668213.	+	1.15738e6i	0.0972558	+	0.168452i
$544$		0			0
$545$	−9.70522e6			−1.39963
$546$		0			0
$547$	3.79404e6			0.542167			0.271084	−	0.962556i	$-0.412618\pi$
$547$	3.79404e6			0.542167			0.271084	+	0.962556i	$0.412618\pi$
$548$		0			0
$549$	−926502.	−	1.60475e6i	−0.131195	−	0.227236i
$550$		0			0
$551$	−4.89949e6	+	8.48616e6i	−0.687498	+	1.19078i
$552$		0			0
$553$	8.84771e6	+	7.29809e6i	1.23032	+	1.01484i
$554$		0			0
$555$	1.32032e6	−	2.28686e6i	0.181948	−	0.315142i
$556$		0			0
$557$	2.44799e6	+	4.24005e6i	0.334328	+	0.579072i	0.983355	−	0.181692i	$-0.0581575\pi$
$557$	2.44799e6	+	4.24005e6i	0.334328	+	0.579072i	−0.649028	+	0.760765i	$0.724824\pi$
$558$		0			0
$559$	1.45140e6			0.196453
$560$		0			0
$561$	160994.			0.0215974
$562$		0			0
$563$	−2.16583e6	−	3.75133e6i	−0.287974	−	0.498786i	0.685352	−	0.728212i	$-0.259648\pi$
$563$	−2.16583e6	−	3.75133e6i	−0.287974	−	0.498786i	−0.973326	+	0.229426i	$0.926315\pi$
$564$		0			0
$565$	−7.59661e6	+	1.31577e7i	−1.00115	+	1.73404i
$566$		0			0
$567$	−796807.	+	297633.i	−0.104087	+	0.0388798i
$568$		0			0
$569$	1.09848e6	−	1.90262e6i	0.142236	−	0.246361i	−0.786102	−	0.618097i	$-0.787904\pi$
$569$	1.09848e6	−	1.90262e6i	0.142236	−	0.246361i	0.928338	+	0.371736i	$0.121237\pi$
$570$		0			0
$571$	−3.73846e6	−	6.47520e6i	−0.479846	−	0.831118i	0.519886	−	0.854235i	$-0.325974\pi$
$571$	−3.73846e6	−	6.47520e6i	−0.479846	−	0.831118i	−0.999733	+	0.0231172i	$0.992641\pi$
$572$		0			0
$573$	3.47320e6			0.441919
$574$		0			0
$575$	−1.10899e6			−0.139880
$576$		0			0
$577$	683110.	+	1.18318e6i	0.0854183	+	0.147949i	0.905569	−	0.424198i	$-0.139444\pi$
$577$	683110.	+	1.18318e6i	0.0854183	+	0.147949i	−0.820151	+	0.572147i	$0.806111\pi$
$578$		0			0
$579$	2.23333e6	−	3.86824e6i	0.276858	−	0.479531i
$580$		0			0
$581$	2.05414e6	−	1.22518e7i	0.252458	−	1.50577i
$582$		0			0
$583$	−202612.	+	350934.i	−0.0246884	+	0.0427616i
$584$		0			0
$585$	−2.10369e6	−	3.64370e6i	−0.254151	−	0.440203i
$586$		0			0
$587$	9.27217e6			1.11067			0.555336	−	0.831626i	$-0.312590\pi$
$587$	9.27217e6			1.11067			0.555336	+	0.831626i	$0.312590\pi$
$588$		0			0
$589$	5.38612e6			0.639717
$590$		0			0
$591$	1.98648e6	+	3.44068e6i	0.233946	+	0.405206i
$592$		0			0
$593$	−4.60523e6	+	7.97649e6i	−0.537792	+	0.931483i	0.461231	+	0.887280i	$0.347408\pi$
$593$	−4.60523e6	+	7.97649e6i	−0.537792	+	0.931483i	−0.999023	+	0.0442028i	$0.985925\pi$
$594$		0			0
$595$	1.28452e6	−	7.66145e6i	0.148747	−	0.887194i
$596$		0			0
$597$	341275.	−	591105.i	0.0391894	−	0.0678779i
$598$		0			0
$599$	−6.84581e6	−	1.18573e7i	−0.779575	−	1.35026i	−0.932187	−	0.361977i	$-0.882102\pi$
$599$	−6.84581e6	−	1.18573e7i	−0.779575	−	1.35026i	0.152612	−	0.988286i	$-0.451231\pi$
$600$		0			0
$601$	1.61113e6			0.181946			0.0909732	−	0.995853i	$-0.471002\pi$
$601$	1.61113e6			0.181946			0.0909732	+	0.995853i	$0.471002\pi$
$602$		0			0
$603$	−3.80803e6			−0.426489
$604$		0			0
$605$	4.69119e6	+	8.12539e6i	0.521069	+	0.902517i
$606$		0			0
$607$	−7.03281e6	+	1.21812e7i	−0.774742	+	1.34189i	0.160198	+	0.987085i	$0.448787\pi$
$607$	−7.03281e6	+	1.21812e7i	−0.774742	+	1.34189i	−0.934940	+	0.354807i	$0.884547\pi$
$608$		0			0
$609$	6.15752e6	−	2.30003e6i	0.672764	−	0.251299i
$610$		0			0
$611$	−4.27401e6	+	7.40280e6i	−0.463161	+	0.802219i
$612$		0			0
$613$	−6.79842e6	−	1.17752e7i	−0.730729	−	1.26566i	−0.956572	−	0.291497i	$-0.905847\pi$
$613$	−6.79842e6	−	1.17752e7i	−0.730729	−	1.26566i	0.225842	−	0.974164i	$-0.427487\pi$
$614$		0			0
$615$	−9.64828e6			−1.02864
$616$		0			0
$617$	−5.74287e6			−0.607318			−0.303659	−	0.952781i	$-0.598208\pi$
$617$	−5.74287e6			−0.607318			−0.303659	+	0.952781i	$0.598208\pi$
$618$		0			0
$619$	−3.01299e6	−	5.21865e6i	−0.316061	−	0.547434i	0.663602	−	0.748086i	$-0.269027\pi$
$619$	−3.01299e6	−	5.21865e6i	−0.316061	−	0.547434i	−0.979662	+	0.200653i	$0.935694\pi$
$620$		0			0
$621$	−1.43475e6	+	2.48506e6i	−0.149296	+	0.258588i
$622$		0			0
$623$	−4.65122e6	−	3.83658e6i	−0.480117	−	0.396027i
$624$		0			0
$625$	5.28334e6	−	9.15101e6i	0.541014	−	0.937064i
$626$		0			0
$627$	−136384.	−	236224.i	−0.0138546	−	0.0239969i
$628$		0			0
$629$	5.16075e6			0.520099
$630$		0			0
$631$	6.90670e6			0.690554			0.345277	−	0.938501i	$-0.387785\pi$
$631$	6.90670e6			0.690554			0.345277	+	0.938501i	$0.387785\pi$
$632$		0			0
$633$	−3.50417e6	−	6.06940e6i	−0.347597	−	0.602055i
$634$		0			0
$635$	−6.82146e6	+	1.18151e7i	−0.671341	+	1.16280i
$636$		0			0
$637$	−1.41392e7	−	4.87830e6i	−1.38063	−	0.476343i
$638$		0			0
$639$	−64785.2	+	112211.i	−0.00627659	+	0.0108714i
$640$		0			0
$641$	−8.24828e6	−	1.42864e7i	−0.792900	−	1.37334i	−0.924164	−	0.381995i	$-0.875237\pi$
$641$	−8.24828e6	−	1.42864e7i	−0.792900	−	1.37334i	0.131265	−	0.991347i	$-0.458096\pi$
$642$		0			0
$643$	−1.70171e7			−1.62315			−0.811576	−	0.584247i	$-0.801390\pi$
$643$	−1.70171e7			−1.62315			−0.811576	+	0.584247i	$0.801390\pi$
$644$		0			0
$645$	−856727.			−0.0810855
$646$		0			0
$647$	1.74287e6	+	3.01873e6i	0.163683	+	0.283507i	0.936187	−	0.351503i	$-0.114329\pi$
$647$	1.74287e6	+	3.01873e6i	0.163683	+	0.283507i	−0.772504	+	0.635010i	$0.780996\pi$
$648$		0			0
$649$	31391.6	−	54371.8i	0.00292551	−	0.00506713i
$650$		0			0
$651$	−2.78714e6	−	2.29899e6i	−0.257754	−	0.212610i
$652$		0			0
$653$	−7.72245e6	+	1.33757e7i	−0.708716	+	1.22753i	0.256618	+	0.966513i	$0.417392\pi$
$653$	−7.72245e6	+	1.33757e7i	−0.708716	+	1.22753i	−0.965334	+	0.261019i	$0.915941\pi$
$654$		0			0
$655$	−4.59029e6	−	7.95061e6i	−0.418058	−	0.724098i
$656$		0			0
$657$	480439.			0.0434235
$658$		0			0
$659$	3.11193e6			0.279136			0.139568	−	0.990212i	$-0.455429\pi$
$659$	3.11193e6			0.279136			0.139568	+	0.990212i	$0.455429\pi$
$660$		0			0
$661$	−4.08610e6	−	7.07733e6i	−0.363752	−	0.630037i	0.624823	−	0.780766i	$-0.285171\pi$
$661$	−4.08610e6	−	7.07733e6i	−0.363752	−	0.630037i	−0.988575	+	0.150729i	$0.951838\pi$
$662$		0			0
$663$	4.11137e6	−	7.12110e6i	0.363247	−	0.629163i
$664$		0			0
$665$	−1.23297e7	+	4.60554e6i	−1.08118	+	0.403856i
$666$		0			0
$667$	1.10874e7	−	1.92039e7i	0.964973	−	1.67138i
$668$		0			0
$669$	−3.32138e6	−	5.75280e6i	−0.286915	−	0.496951i
$670$		0			0
$671$	−398604.			−0.0341771
$672$		0			0
$673$	1.60182e7			1.36325			0.681627	−	0.731700i	$-0.261273\pi$
$673$	1.60182e7			1.36325			0.681627	+	0.731700i	$0.261273\pi$
$674$		0			0
$675$	102694.	+	177871.i	0.00867530	+	0.0150261i
$676$		0			0
$677$	−512185.	+	887131.i	−0.0429492	+	0.0743902i	−0.886701	−	0.462344i	$-0.847009\pi$
$677$	−512185.	+	887131.i	−0.0429492	+	0.0743902i	0.843752	+	0.536734i	$0.180342\pi$
$678$		0			0
$679$	−1.62879e6	+	9.71483e6i	−0.135579	+	0.808650i
$680$		0			0
$681$	2.44852e6	−	4.24096e6i	0.202319	−	0.350426i
$682$		0			0
$683$	−2.69688e6	−	4.67114e6i	−0.221213	−	0.383152i	0.733964	−	0.679189i	$-0.237668\pi$
$683$	−2.69688e6	−	4.67114e6i	−0.221213	−	0.383152i	−0.955177	+	0.296037i	$0.904335\pi$
$684$		0			0
$685$	−1.00128e7			−0.815319
$686$		0			0
$687$	2.10206e6			0.169924
$688$		0			0
$689$	1.03484e7	+	1.79239e7i	0.830470	+	1.43842i
$690$		0			0
$691$	−452826.	+	784318.i	−0.0360775	+	0.0624881i	−0.883500	−	0.468430i	$-0.844820\pi$
$691$	−452826.	+	784318.i	−0.0360775	+	0.0624881i	0.847423	+	0.530919i	$0.178153\pi$
$692$		0			0
$693$	−30254.6	+	180452.i	−0.00239308	+	0.0142734i
$694$		0			0
$695$	6.14682e6	−	1.06466e7i	0.482712	−	0.836082i
$696$		0			0
$697$	−9.42810e6	−	1.63300e7i	−0.735093	−	1.27322i
$698$		0			0
$699$	5.56290e6			0.430634
$700$		0			0
$701$	1.12573e7			0.865246			0.432623	−	0.901575i	$-0.357588\pi$
$701$	1.12573e7			0.865246			0.432623	+	0.901575i	$0.357588\pi$
$702$		0			0
$703$	−4.37187e6	−	7.57230e6i	−0.333640	−	0.577882i
$704$		0			0
$705$	2.52284e6	−	4.36969e6i	0.191169	−	0.331114i
$706$		0			0
$707$	5.60563e6	−	2.09388e6i	0.421770	−	0.157545i
$708$		0			0
$709$	−2.17755e6	+	3.77162e6i	−0.162687	+	0.281781i	−0.935831	−	0.352448i	$-0.885349\pi$
$709$	−2.17755e6	+	3.77162e6i	−0.162687	+	0.281781i	0.773145	+	0.634230i	$0.218683\pi$
$710$		0			0
$711$	−3.58299e6	−	6.20592e6i	−0.265810	−	0.460397i
$712$		0			0
$713$	−1.21886e7			−0.897907
$714$		0			0
$715$	−905060.			−0.0662082
$716$		0			0
$717$	−4.21875e6	−	7.30709e6i	−0.306469	−	0.530819i
$718$		0			0
$719$	−7.07221e6	+	1.22494e7i	−0.510191	+	0.883676i	0.489739	+	0.871869i	$0.337092\pi$
$719$	−7.07221e6	+	1.22494e7i	−0.510191	+	0.883676i	−0.999930	+	0.0118076i	$0.996241\pi$
$720$		0			0
$721$	8.19812e6	+	6.76227e6i	0.587322	+	0.484456i
$722$		0			0
$723$	4.19416e6	−	7.26450e6i	0.298401	−	0.516845i
$724$		0			0
$725$	−793591.	−	1.37454e6i	−0.0560727	−	0.0971208i
$726$		0			0
$727$	6.26406e6			0.439561			0.219781	−	0.975549i	$-0.429466\pi$
$727$	6.26406e6			0.439561			0.219781	+	0.975549i	$0.429466\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−837176.	−	1.45003e6i	−0.0579460	−	0.100365i
$732$		0			0
$733$	1.02089e7	−	1.76823e7i	0.701806	−	1.21556i	−0.266025	−	0.963966i	$-0.585710\pi$
$733$	1.02089e7	−	1.76823e7i	0.701806	−	1.21556i	0.967832	−	0.251598i	$-0.0809562\pi$
$734$		0			0
$735$	8.34602e6	+	2.87954e6i	0.569851	+	0.196610i
$736$		0			0
$737$	−409577.	+	709409.i	−0.0277758	+	0.0481092i
$738$		0			0
$739$	7.42256e6	+	1.28563e7i	0.499969	+	0.865971i	1.00000		3.61537e-5i	$-1.15081e-5\pi$
$739$	7.42256e6	+	1.28563e7i	0.499969	+	0.865971i	−0.500031	+	0.866007i	$0.666678\pi$
$740$		0			0
$741$	−1.39316e7			−0.932083
$742$		0			0
$743$	−2.36601e7			−1.57234			−0.786168	−	0.618013i	$-0.787938\pi$
$743$	−2.36601e7			−1.57234			−0.786168	+	0.618013i	$0.787938\pi$
$744$		0			0
$745$	−6.98694e6	−	1.21017e7i	−0.461207	−	0.798834i
$746$		0			0
$747$	−3.88087e6	+	6.72186e6i	−0.254465	+	0.440746i
$748$		0			0
$749$	285394.	+	235409.i	0.0185883	+	0.0153327i
$750$		0			0
$751$	1.03287e7	−	1.78898e7i	0.668258	−	1.15746i	−0.310133	−	0.950693i	$-0.600373\pi$
$751$	1.03287e7	−	1.78898e7i	0.668258	−	1.15746i	0.978391	−	0.206764i	$-0.0662932\pi$
$752$		0			0
$753$	−967389.	−	1.67557e6i	−0.0621747	−	0.107690i
$754$		0			0
$755$	−1.26680e7			−0.808799
$756$		0			0
$757$	−1.26697e7			−0.803573			−0.401787	−	0.915733i	$-0.631611\pi$
$757$	−1.26697e7			−0.803573			−0.401787	+	0.915733i	$0.631611\pi$
$758$		0			0
$759$	308633.	+	534568.i	0.0194463	+	0.0336820i
$760$		0			0
$761$	−8.13761e6	+	1.40948e7i	−0.509372	+	0.882259i	0.490569	+	0.871402i	$0.336789\pi$
$761$	−8.13761e6	+	1.40948e7i	−0.509372	+	0.882259i	−0.999941	+	0.0108563i	$0.996544\pi$
$762$		0			0
$763$	2.01938e7	−	7.54305e6i	1.25576	−	0.469068i
$764$		0			0
$765$	−2.42684e6	+	4.20341e6i	−0.149929	+	0.259685i
$766$		0			0
$767$	−1.60332e6	−	2.77703e6i	−0.0984084	−	0.170448i
$768$		0			0
$769$	1.60471e7			0.978547			0.489273	−	0.872130i	$-0.337262\pi$
$769$	1.60471e7			0.978547			0.489273	+	0.872130i	$0.337262\pi$
$770$		0			0
$771$	−712683.			−0.0431778
$772$		0			0
$773$	−1.07839e6	−	1.86782e6i	−0.0649121	−	0.112431i	0.831743	−	0.555161i	$-0.187343\pi$
$773$	−1.07839e6	−	1.86782e6i	−0.0649121	−	0.112431i	−0.896655	+	0.442730i	$0.854010\pi$
$774$		0			0
$775$	−436206.	+	755531.i	−0.0260878	+	0.0451854i
$776$		0			0
$777$	−969828.	+	5.78448e6i	−0.0576292	+	0.343726i
$778$		0			0
$779$	−1.59738e7	+	2.76674e7i	−0.943115	+	1.63352i
$780$		0			0
$781$	13936.1	+	24138.0i	0.000817548	+	0.00141603i
$782$		0			0
$783$	−4.10684e6			−0.239389
$784$		0			0
$785$	9.74175e6			0.564239
$786$		0			0
$787$	7.00503e6	+	1.21331e7i	0.403156	+	0.698286i	0.994105	−	0.108423i	$-0.0345799\pi$
$787$	7.00503e6	+	1.21331e7i	0.403156	+	0.698286i	−0.590949	+	0.806709i	$0.701247\pi$
$788$		0			0
$789$	1.94773e6	−	3.37356e6i	0.111387	−	0.192928i
$790$		0			0
$791$	5.58002e6	−	3.32817e7i	0.317099	−	1.89132i
$792$		0			0
$793$	−1.01793e7	+	1.76311e7i	−0.574825	+	0.995627i
$794$		0			0
$795$	−6.10839e6	−	1.05800e7i	−0.342775	−	0.593703i
$796$		0			0
$797$	4.73289e6			0.263925			0.131963	−	0.991255i	$-0.457872\pi$
$797$	4.73289e6			0.263925			0.131963	+	0.991255i	$0.457872\pi$
$798$		0			0
$799$	9.86107e6			0.546459
$800$		0			0
$801$	1.88357e6	+	3.26244e6i	0.103729	+	0.179664i
$802$		0			0
$803$	51674.2	−	89502.3i	0.00282804	−	0.00489830i
$804$		0			0
$805$	2.79018e7	−	1.04222e7i	1.51755	−	0.566853i
$806$		0			0
$807$	−21113.4	+	36569.4i	−0.00114123	+	0.00197667i
$808$		0			0
$809$	−4.05446e6	−	7.02253e6i	−0.217802	−	0.377244i	0.736334	−	0.676618i	$-0.236555\pi$
$809$	−4.05446e6	−	7.02253e6i	−0.217802	−	0.377244i	−0.954136	+	0.299375i	$0.903222\pi$
$810$		0			0
$811$	9.13444e6			0.487674			0.243837	−	0.969816i	$-0.421594\pi$
$811$	9.13444e6			0.487674			0.243837	+	0.969816i	$0.421594\pi$
$812$		0			0
$813$	947378.			0.0502686
$814$		0			0
$815$	1.47719e7	+	2.55858e7i	0.779011	+	1.34929i
$816$		0			0
$817$	−1.41841e6	+	2.45675e6i	−0.0743439	+	0.128767i
$818$		0			0
$819$	7.20913e6	+	5.94649e6i	0.375555	+	0.309778i
$820$		0			0
$821$	−850776.	+	1.47359e6i	−0.0440511	+	0.0762988i	−0.887210	−	0.461365i	$-0.847360\pi$
$821$	−850776.	+	1.47359e6i	−0.0440511	+	0.0762988i	0.843159	+	0.537664i	$0.180693\pi$
$822$		0			0
$823$	−1.24604e7	−	2.15820e7i	−0.641256	−	1.11069i	−0.985153	−	0.171680i	$-0.945080\pi$
$823$	−1.24604e7	−	2.15820e7i	−0.641256	−	1.11069i	0.343897	−	0.939007i	$-0.388253\pi$
$824$		0			0
$825$	44181.4			0.00225998
$826$		0			0
$827$	1.91232e7			0.972292			0.486146	−	0.873878i	$-0.338402\pi$
$827$	1.91232e7			0.972292			0.486146	+	0.873878i	$0.338402\pi$
$828$		0			0
$829$	1.10134e7	+	1.90757e7i	0.556588	+	0.964038i	0.997778	+	0.0666248i	$0.0212231\pi$
$829$	1.10134e7	+	1.90757e7i	0.556588	+	0.964038i	−0.441190	+	0.897414i	$0.645444\pi$
$830$		0			0
$831$	−3.43403e6	+	5.94791e6i	−0.172505	+	0.298787i
$832$		0			0
$833$	3.28187e6	+	1.69397e7i	0.163874	+	0.845849i
$834$		0			0
$835$	−1.65051e7	+	2.85877e7i	−0.819222	+	1.41893i
$836$		0			0
$837$	1.12869e6	+	1.95494e6i	0.0556877	+	0.0964540i
$838$		0			0
$839$	−4.28039e6			−0.209932			−0.104966	−	0.994476i	$-0.533473\pi$
$839$	−4.28039e6			−0.209932			−0.104966	+	0.994476i	$0.533473\pi$
$840$		0			0
$841$	1.12255e7			0.547286
$842$		0			0
$843$	−3.28293e6	−	5.68620e6i	−0.159108	−	0.275584i
$844$		0			0
$845$	−1.22772e7	+	2.12648e7i	−0.591504	+	1.02452i
$846$		0			0
$847$	−1.60762e7	−	1.32606e7i	−0.769974	−	0.635117i
$848$		0			0
$849$	5.35693e6	−	9.27848e6i	0.255063	−	0.441781i
$850$		0			0
$851$	9.89342e6	+	1.71359e7i	0.468298	+	0.811116i
$852$		0			0
$853$	−1.72415e7			−0.811341			−0.405670	−	0.914019i	$-0.632962\pi$
$853$	−1.72415e7			−0.811341			−0.405670	+	0.914019i	$0.632962\pi$
$854$		0			0
$855$	8.22346e6			0.384715
$856$		0			0
$857$	−1.04170e7	−	1.80427e7i	−0.484495	−	0.839171i	0.515346	−	0.856982i	$-0.327663\pi$
$857$	−1.04170e7	−	1.80427e7i	−0.484495	−	0.839171i	−0.999841	+	0.0178115i	$0.994330\pi$
$858$		0			0
$859$	−7.91782e6	+	1.37141e7i	−0.366119	+	0.634137i	−0.988955	−	0.148215i	$-0.952647\pi$
$859$	−7.91782e6	+	1.37141e7i	−0.366119	+	0.634137i	0.622836	+	0.782353i	$0.285980\pi$
$860$		0			0
$861$	2.00754e7	−	7.49880e6i	0.922902	−	0.344734i
$862$		0			0
$863$	−7.96408e6	+	1.37942e7i	−0.364006	+	0.630477i	−0.988616	−	0.150460i	$-0.951925\pi$
$863$	−7.96408e6	+	1.37942e7i	−0.364006	+	0.630477i	0.624610	+	0.780937i	$0.285258\pi$
$864$		0			0
$865$	1.92447e7	+	3.33328e7i	0.874523	+	1.51472i
$866$		0			0
$867$	3.29289e6			0.148775
$868$		0			0
$869$	−1.54149e6			−0.0692455
$870$		0			0
$871$	2.09191e7	+	3.62330e7i	0.934325	+	1.61830i
$872$		0			0
$873$	3.07726e6	−	5.32998e6i	0.136656	−	0.236695i
$874$		0			0
$875$	−3.55747e6	+	2.12183e7i	−0.157080	+	0.936896i
$876$		0			0
$877$	−2.60367e6	+	4.50969e6i	−0.114311	+	0.197992i	−0.917504	−	0.397727i	$-0.869799\pi$
$877$	−2.60367e6	+	4.50969e6i	−0.114311	+	0.197992i	0.803193	+	0.595718i	$0.203133\pi$
$878$		0			0
$879$	−4.61263e6	−	7.98931e6i	−0.201362	−	0.348769i
$880$		0			0
$881$	−932829.			−0.0404913			−0.0202457	−	0.999795i	$-0.506445\pi$
$881$	−932829.			−0.0404913			−0.0202457	+	0.999795i	$0.506445\pi$
$882$		0			0
$883$	−1.33789e7			−0.577457			−0.288728	−	0.957411i	$-0.593232\pi$
$883$	−1.33789e7			−0.577457			−0.288728	+	0.957411i	$0.593232\pi$
$884$		0			0
$885$	946401.	+	1.63921e6i	0.0406178	+	0.0703522i
$886$		0			0
$887$	−3.48450e6	+	6.03533e6i	−0.148707	+	0.257568i	−0.930750	−	0.365657i	$-0.880844\pi$
$887$	−3.48450e6	+	6.03533e6i	−0.148707	+	0.257568i	0.782043	+	0.623225i	$0.214178\pi$
$888$		0			0
$889$	5.01064e6	−	2.98857e7i	0.212637	−	1.26826i
$890$		0			0
$891$	57159.8	−	99003.6i	0.00241210	−	0.00417789i
$892$		0			0
$893$	−8.35369e6	−	1.44690e7i	−0.350550	−	0.607170i
$894$		0			0
$895$	−9.64753e6			−0.402586
$896$		0			0
$897$	3.15268e7			1.30827
$898$		0			0
$899$	−8.72220e6	−	1.51073e7i	−0.359937	−	0.623429i
$900$		0			0
$901$	1.19380e7	−	2.06772e7i	0.489913	−	0.848554i
$902$		0			0
$903$	1.78261e6	−	665862.i	0.0727506	−	0.0271747i
$904$		0			0
$905$	−4.33353e6	+	7.50590e6i	−0.175882	+	0.304636i
$906$		0			0
$907$	−1.88282e7	−	3.26113e7i	−0.759959	−	1.31629i	−0.942871	−	0.333158i	$-0.891886\pi$
$907$	−1.88282e7	−	3.26113e7i	−0.759959	−	1.31629i	0.182913	−	0.983129i	$-0.441447\pi$
$908$		0			0
$909$	−3.73875e6			−0.150078
$910$		0			0
$911$	3.09942e7			1.23733			0.618663	−	0.785657i	$-0.287675\pi$
$911$	3.09942e7			1.23733			0.618663	+	0.785657i	$0.287675\pi$
$912$		0			0
$913$	834823.	+	1.44596e6i	0.0331450	+	0.0574087i
$914$		0			0
$915$	6.00860e6	−	1.04072e7i	0.237258	−	0.410943i
$916$		0			0
$917$	1.57304e7	+	1.29753e7i	0.617757	+	0.509560i
$918$		0			0
$919$	358007.	−	620086.i	0.0139831	−	0.0242194i	−0.858949	−	0.512061i	$-0.828882\pi$
$919$	358007.	−	620086.i	0.0139831	−	0.0242194i	0.872932	+	0.487841i	$0.162216\pi$
$920$		0			0
$921$	3.19430e6	+	5.53269e6i	0.124087	+	0.214925i
$922$		0			0
$923$	1.42357e6			0.0550014
$924$		0			0
$925$	1.41626e6			0.0544238
$926$		0			0
$927$	−3.31993e6	−	5.75029e6i	−0.126891	−	0.219781i
$928$		0			0
$929$	−2.08815e7	+	3.61678e7i	−0.793820	+	1.37494i	0.129766	+	0.991545i	$0.458577\pi$
$929$	−2.08815e7	+	3.61678e7i	−0.793820	+	1.37494i	−0.923586	+	0.383392i	$0.874756\pi$
$930$		0			0
$931$	2.20751e7	−	1.91657e7i	0.834698	−	0.724686i
$932$		0			0
$933$	−7.05434e6	+	1.22185e7i	−0.265309	+	0.459529i
$934$		0			0
$935$	522043.	+	904204.i	0.0195289	+	0.0338250i
$936$		0			0
$937$	−2.17917e7			−0.810854			−0.405427	−	0.914127i	$-0.632877\pi$
$937$	−2.17917e7			−0.810854			−0.405427	+	0.914127i	$0.632877\pi$
$938$		0			0
$939$	−3.35657e6			−0.124232
$940$		0			0
$941$	1.07609e6	+	1.86385e6i	0.0396164	+	0.0686177i	0.885154	−	0.465299i	$-0.154053\pi$
$941$	1.07609e6	+	1.86385e6i	0.0396164	+	0.0686177i	−0.845537	+	0.533916i	$0.820720\pi$
$942$		0			0
$943$	3.61483e7	−	6.26106e7i	1.32376	−	2.29281i
$944$		0			0
$945$	−4.25537e6	−	3.51007e6i	−0.155009	−	0.127860i
$946$		0			0
$947$	−1.32125e7	+	2.28847e7i	−0.478750	+	0.829220i	−0.999703	−	0.0243656i	$-0.992243\pi$
$947$	−1.32125e7	+	2.28847e7i	−0.478750	+	0.829220i	0.520953	+	0.853585i	$0.325577\pi$
$948$		0			0
$949$	−2.63925e6	−	4.57132e6i	−0.0951295	−	0.164769i
$950$		0			0
$951$	2.72534e7			0.977169
$952$		0			0
$953$	9.07051e6			0.323519			0.161759	−	0.986830i	$-0.448283\pi$
$953$	9.07051e6			0.323519			0.161759	+	0.986830i	$0.448283\pi$
$954$		0			0
$955$	1.12623e7	+	1.95068e7i	0.399593	+	0.692115i
$956$		0			0
$957$	−441716.	+	765075.i	−0.0155906	+	0.0270037i
$958$		0			0
$959$	2.08337e7	−	7.78208e6i	0.731511	−	0.273243i
$960$		0			0
$961$	9.52032e6	−	1.64897e7i	0.332539	−	0.575975i
$962$		0			0
$963$	−115574.	−	200180.i	−0.00401600	−	0.00695592i
$964$		0			0
$965$	2.89674e7			1.00136
$966$		0			0
$967$	−1.80108e7			−0.619395			−0.309698	−	0.950835i	$-0.600228\pi$
$967$	−1.80108e7			−0.619395			−0.309698	+	0.950835i	$0.600228\pi$
$968$		0			0
$969$	8.03580e6	+	1.39184e7i	0.274928	+	0.476190i
$970$		0			0
$971$	−2.33815e7	+	4.04980e7i	−0.795838	+	1.37843i	0.126467	+	0.991971i	$0.459636\pi$
$971$	−2.33815e7	+	4.04980e7i	−0.795838	+	1.37843i	−0.922305	+	0.386462i	$0.873697\pi$
$972$		0			0
$973$	−4.51509e6	+	2.69300e7i	−0.152892	+	0.911914i
$974$		0			0
$975$	1.12828e6	−	1.95424e6i	0.0380106	−	0.0658363i
$976$		0			0
$977$	−2.16217e6	−	3.74498e6i	−0.0724690	−	0.125520i	0.827514	−	0.561445i	$-0.189755\pi$
$977$	−2.16217e6	−	3.74498e6i	−0.0724690	−	0.125520i	−0.899983	+	0.435925i	$0.856421\pi$
$978$		0			0
$979$	810357.			0.0270221
$980$		0			0
$981$	−1.34685e7			−0.446836
$982$		0			0
$983$	1.04367e7	+	1.80768e7i	0.344491	+	0.596676i	0.985261	−	0.171057i	$-0.0547181\pi$
$983$	1.04367e7	+	1.80768e7i	0.344491	+	0.596676i	−0.640770	+	0.767733i	$0.721385\pi$
$984$		0			0
$985$	−1.28828e7	+	2.23137e7i	−0.423077	+	0.732792i
$986$		0			0
$987$	−1.85313e6	+	1.10529e7i	−0.0605499	+	0.361146i
$988$		0			0
$989$	3.20981e6	−	5.55956e6i	0.104349	−	0.180738i
$990$		0			0
$991$	2.06104e7	+	3.56983e7i	0.666658	+	1.15469i	0.978833	+	0.204661i	$0.0656090\pi$
$991$	2.06104e7	+	3.56983e7i	0.666658	+	1.15469i	−0.312175	+	0.950025i	$0.601058\pi$
$992$		0			0
$993$	9.60206e6			0.309023
$994$		0			0
$995$	4.42650e6			0.141743
$996$		0			0
$997$	2.67307e7	+	4.62990e7i	0.851674	+	1.47514i	0.879697	+	0.475535i	$0.157745\pi$
$997$	2.67307e7	+	4.62990e7i	0.851674	+	1.47514i	−0.0280235	+	0.999607i	$0.508921\pi$
$998$		0			0
$999$	1.83229e6	−	3.17362e6i	0.0580872	−	0.100610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.j.289.1		8
4.3	odd	2		21.6.e.c.16.2	yes	8
7.4	even	3	inner	336.6.q.j.193.1		8
12.11	even	2		63.6.e.e.37.3		8
28.3	even	6		147.6.e.o.67.2		8
28.11	odd	6		21.6.e.c.4.2	✓	8
28.19	even	6		147.6.a.l.1.3		4
28.23	odd	6		147.6.a.m.1.3		4
28.27	even	2		147.6.e.o.79.2		8
84.11	even	6		63.6.e.e.46.3		8
84.23	even	6		441.6.a.w.1.2		4
84.47	odd	6		441.6.a.v.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.2	✓	8	28.11	odd	6
21.6.e.c.16.2	yes	8	4.3	odd	2
63.6.e.e.37.3		8	12.11	even	2
63.6.e.e.46.3		8	84.11	even	6
147.6.a.l.1.3		4	28.19	even	6
147.6.a.m.1.3		4	28.23	odd	6
147.6.e.o.67.2		8	28.3	even	6
147.6.e.o.79.2		8	28.27	even	2
336.6.q.j.193.1		8	7.4	even	3	inner
336.6.q.j.289.1		8	1.1	even	1	trivial
441.6.a.v.1.2		4	84.47	odd	6
441.6.a.w.1.2		4	84.23	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)

\(f(q)\)	\(=\)	\(q+(4.50000 + 7.79423i) q^{3} +(-29.1836 + 50.5475i) q^{5} +(21.4366 - 127.857i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(8.71205 + 15.0897i) q^{11} +889.933 q^{13} -525.305 q^{15} +(-513.318 - 889.092i) q^{17} +(-869.702 + 1506.37i) q^{19} +(1093.01 - 408.276i) q^{21} +(1968.11 - 3408.87i) q^{23} +(-140.869 - 243.993i) q^{25} -729.000 q^{27} +5633.53 q^{29} +(-1548.27 - 2681.68i) q^{31} +(-78.4084 + 135.807i) q^{33} +(5837.27 + 4814.91i) q^{35} +(-2513.43 + 4353.39i) q^{37} +(4004.70 + 6936.34i) q^{39} +18367.0 q^{41} +1630.91 q^{43} +(-2363.87 - 4094.35i) q^{45} +(-4802.62 + 8318.38i) q^{47} +(-15887.9 - 5481.65i) q^{49} +(4619.86 - 8001.83i) q^{51} +(11628.3 + 20140.7i) q^{53} -1017.00 q^{55} -15654.6 q^{57} +(-1801.62 - 3120.50i) q^{59} +(-11438.3 + 19811.7i) q^{61} +(8100.75 + 6681.95i) q^{63} +(-25971.5 + 44983.9i) q^{65} +(23506.4 + 40714.2i) q^{67} +35426.0 q^{69} +1599.63 q^{71} +(-2965.67 - 5136.70i) q^{73} +(1267.82 - 2195.93i) q^{75} +(2116.09 - 790.427i) q^{77} +(-44234.4 + 76616.3i) q^{79} +(-3280.50 - 5681.99i) q^{81} +95823.9 q^{83} +59921.9 q^{85} +(25350.9 + 43909.0i) q^{87} +(23253.9 - 40277.0i) q^{89} +(19077.1 - 113784. i) q^{91} +(13934.4 - 24135.1i) q^{93} +(-50762.1 - 87922.5i) q^{95} -75981.8 q^{97} -1411.35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 36 q^{3} - 258 q^{7} - 324 q^{9} + 402 q^{11} + 924 q^{13} - 276 q^{17} + 510 q^{19} - 3564 q^{21} + 6900 q^{23} - 2814 q^{25} - 5832 q^{27} + 1080 q^{29} - 6410 q^{31} - 3618 q^{33} + 33108 q^{35}+ \cdots - 65124 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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