LMFDB - Embedded newform 416.4.i.d.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,4,Mod(289,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("416.289");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	416.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5447945624$
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} + 74x^{6} + 5367x^{4} + 8066x^{2} + 11881 $ x^8 + 74x^6 + 5367x^4 + 8066*x^2 + 11881
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			321.2
Root			$-0.613091 - 1.06190i$ of defining polynomial
Character	$\chi$	$=$	416.321
Dual form			416.4.i.d.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.613091 + 1.06190i) q^{3} +13.8322 q^{5} +(12.7720 + 22.1218i) q^{7} +(12.7482 + 22.0806i) q^{9} +(31.0618 - 53.8007i) q^{11} +(-13.0000 + 45.0333i) q^{13} +(-8.48037 + 14.6884i) q^{15} +(28.4161 + 49.2181i) q^{17} +(-13.9982 - 24.2456i) q^{19} -31.3216 q^{21} +(28.7124 - 49.7313i) q^{23} +66.3286 q^{25} -64.3702 q^{27} +(12.3322 - 21.3599i) q^{29} -297.130 q^{31} +(38.0874 + 65.9694i) q^{33} +(176.664 + 305.992i) q^{35} +(-19.4161 + 33.6296i) q^{37} +(-39.8509 - 41.4143i) q^{39} +(58.4020 - 101.155i) q^{41} +(-40.6655 - 70.4347i) q^{43} +(176.336 + 305.422i) q^{45} +462.450 q^{47} +(-154.748 + 268.032i) q^{49} -69.6865 q^{51} +412.182 q^{53} +(429.652 - 744.179i) q^{55} +34.3286 q^{57} +(-4.18873 - 7.25510i) q^{59} +(403.800 + 699.403i) q^{61} +(-325.641 + 564.027i) q^{63} +(-179.818 + 622.908i) q^{65} +(-0.921795 + 1.59660i) q^{67} +(35.2066 + 60.9796i) q^{69} +(329.212 + 570.213i) q^{71} -487.090 q^{73} +(-40.6655 + 70.4347i) q^{75} +1586.89 q^{77} -1240.62 q^{79} +(-304.738 + 527.821i) q^{81} -438.544 q^{83} +(393.056 + 680.793i) q^{85} +(15.1215 + 26.1911i) q^{87} +(-423.011 + 732.676i) q^{89} +(-1162.25 + 287.583i) q^{91} +(182.168 - 315.524i) q^{93} +(-193.625 - 335.369i) q^{95} +(359.129 + 622.030i) q^{97} +1583.93 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{5} - 40 q^{9} - 104 q^{13} + 180 q^{17} + 696 q^{21} + 152 q^{25} + 4 q^{29} + 636 q^{33} - 108 q^{37} - 716 q^{41} + 1600 q^{45} - 1096 q^{49} + 4528 q^{53} - 104 q^{57} + 580 q^{61} - 208 q^{65}+ \cdots - 156 q^{97}+O(q^{100}) $ 8 * q + 16 * q^5 - 40 * q^9 - 104 * q^13 + 180 * q^17 + 696 * q^21 + 152 * q^25 + 4 * q^29 + 636 * q^33 - 108 * q^37 - 716 * q^41 + 1600 * q^45 - 1096 * q^49 + 4528 * q^53 - 104 * q^57 + 580 * q^61 - 208 * q^65 + 3500 * q^69 + 2256 * q^73 + 3608 * q^77 - 1444 * q^81 + 920 * q^85 - 4236 * q^89 + 1552 * q^93 - 156 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.613091	+	1.06190i	−0.117989	+	0.204364i	−0.918971	−	0.394326i	$-0.870978\pi$
$3$	−0.613091	+	1.06190i	−0.117989	+	0.204364i	0.800981	+	0.598689i	$0.204312\pi$
$4$		0			0
$5$	13.8322			1.23719			0.618593	−	0.785712i	$-0.287703\pi$
$5$	13.8322			1.23719			0.618593	+	0.785712i	$0.287703\pi$
$6$		0			0
$7$	12.7720	+	22.1218i	0.689623	+	1.19446i	0.971960	+	0.235147i	$0.0755573\pi$
$7$	12.7720	+	22.1218i	0.689623	+	1.19446i	−0.282336	+	0.959316i	$0.591109\pi$
$8$		0			0
$9$	12.7482	+	22.0806i	0.472157	+	0.817800i
$10$		0			0
$11$	31.0618	−	53.8007i	0.851408	−	1.47468i	−0.0285288	−	0.999593i	$-0.509082\pi$
$11$	31.0618	−	53.8007i	0.851408	−	1.47468i	0.879937	−	0.475090i	$-0.157584\pi$
$12$		0			0
$13$	−13.0000	+	45.0333i	−0.277350	+	0.960769i
$13$	−13.0000	+	45.0333i	−0.277350	+	0.960769i
$14$		0			0
$15$	−8.48037	+	14.6884i	−0.145975	+	0.252836i
$16$		0			0
$17$	28.4161	+	49.2181i	0.405407	+	0.702185i	0.994369	−	0.105976i	$-0.0337966\pi$
$17$	28.4161	+	49.2181i	0.405407	+	0.702185i	−0.588962	+	0.808161i	$0.700463\pi$
$18$		0			0
$19$	−13.9982	−	24.2456i	−0.169021	−	0.292753i	0.769055	−	0.639183i	$-0.220727\pi$
$19$	−13.9982	−	24.2456i	−0.169021	−	0.292753i	−0.938076	+	0.346429i	$0.887394\pi$
$20$		0			0
$21$	−31.3216			−0.325473
$22$		0			0
$23$	28.7124	−	49.7313i	0.260302	−	0.450856i	−0.706020	−	0.708192i	$-0.749511\pi$
$23$	28.7124	−	49.7313i	0.260302	−	0.450856i	0.966322	+	0.257336i	$0.0828446\pi$
$24$		0			0
$25$	66.3286			0.530629
$26$		0			0
$27$	−64.3702			−0.458817
$28$		0			0
$29$	12.3322	−	21.3599i	0.0789664	−	0.136774i	−0.823838	−	0.566826i	$-0.808171\pi$
$29$	12.3322	−	21.3599i	0.0789664	−	0.136774i	0.902804	+	0.430052i	$0.141505\pi$
$30$		0			0
$31$	−297.130			−1.72149			−0.860745	−	0.509037i	$-0.830002\pi$
$31$	−297.130			−1.72149			−0.860745	+	0.509037i	$0.830002\pi$
$32$		0			0
$33$	38.0874	+	65.9694i	0.200914	+	0.347994i
$34$		0			0
$35$	176.664	+	305.992i	0.853192	+	1.47777i
$36$		0			0
$37$	−19.4161	+	33.6296i	−0.0862698	+	0.149424i	−0.905932	−	0.423424i	$-0.860828\pi$
$37$	−19.4161	+	33.6296i	−0.0862698	+	0.149424i	0.819662	+	0.572848i	$0.194161\pi$
$38$		0			0
$39$	−39.8509	−	41.4143i	−0.163622	−	0.170041i
$40$		0			0
$41$	58.4020	−	101.155i	0.222460	−	0.385312i	−0.733094	−	0.680127i	$-0.761925\pi$
$41$	58.4020	−	101.155i	0.222460	−	0.385312i	0.955554	+	0.294815i	$0.0952580\pi$
$42$		0			0
$43$	−40.6655	−	70.4347i	−0.144219	−	0.249795i	0.784862	−	0.619670i	$-0.212734\pi$
$43$	−40.6655	−	70.4347i	−0.144219	−	0.249795i	−0.929081	+	0.369875i	$0.879400\pi$
$44$		0			0
$45$	176.336	+	305.422i	0.584146	+	1.01177i
$46$		0			0
$47$	462.450			1.43522			0.717610	−	0.696445i	$-0.245236\pi$
$47$	462.450			1.43522			0.717610	+	0.696445i	$0.245236\pi$
$48$		0			0
$49$	−154.748	+	268.032i	−0.451161	+	0.781434i
$50$		0			0
$51$	−69.6865			−0.191335
$52$		0			0
$53$	412.182			1.06826			0.534128	−	0.845404i	$-0.320640\pi$
$53$	412.182			1.06826			0.534128	+	0.845404i	$0.320640\pi$
$54$		0			0
$55$	429.652	−	744.179i	1.05335	−	1.82446i
$56$		0			0
$57$	34.3286			0.0797709
$58$		0			0
$59$	−4.18873	−	7.25510i	−0.00924283	−	0.0160090i	0.861367	−	0.507983i	$-0.169609\pi$
$59$	−4.18873	−	7.25510i	−0.00924283	−	0.0160090i	−0.870610	+	0.491974i	$0.836275\pi$
$60$		0			0
$61$	403.800	+	699.403i	0.847563	+	1.46802i	0.883377	+	0.468664i	$0.155264\pi$
$61$	403.800	+	699.403i	0.847563	+	1.46802i	−0.0358134	+	0.999358i	$0.511402\pi$
$62$		0			0
$63$	−325.641	+	564.027i	−0.651221	+	1.12795i
$64$		0			0
$65$	−179.818	+	622.908i	−0.343134	+	1.18865i
$66$		0			0
$67$	−0.921795	+	1.59660i	−0.00168082	+	0.00291127i	−0.866865	−	0.498544i	$-0.833868\pi$
$67$	−0.921795	+	1.59660i	−0.00168082	+	0.00291127i	0.865184	+	0.501455i	$0.167202\pi$
$68$		0			0
$69$	35.2066	+	60.9796i	0.0614257	+	0.106392i
$70$		0			0
$71$	329.212	+	570.213i	0.550286	+	0.953124i	0.998254	+	0.0590740i	$0.0188148\pi$
$71$	329.212	+	570.213i	0.550286	+	0.953124i	−0.447967	+	0.894050i	$0.647852\pi$
$72$		0			0
$73$	−487.090			−0.780954			−0.390477	−	0.920613i	$-0.627690\pi$
$73$	−487.090			−0.780954			−0.390477	+	0.920613i	$0.627690\pi$
$74$		0			0
$75$	−40.6655	+	70.4347i	−0.0626086	+	0.108441i
$76$		0			0
$77$	1586.89			2.34861
$78$		0			0
$79$	−1240.62			−1.76684			−0.883422	−	0.468577i	$-0.844767\pi$
$79$	−1240.62			−1.76684			−0.883422	+	0.468577i	$0.844767\pi$
$80$		0			0
$81$	−304.738	+	527.821i	−0.418022	+	0.724034i
$82$		0			0
$83$	−438.544			−0.579957			−0.289979	−	0.957033i	$-0.593648\pi$
$83$	−438.544			−0.579957			−0.289979	+	0.957033i	$0.593648\pi$
$84$		0			0
$85$	393.056	+	680.793i	0.501563	+	0.868733i
$86$		0			0
$87$	15.1215	+	26.1911i	0.0186344	+	0.0322757i
$88$		0			0
$89$	−423.011	+	732.676i	−0.503809	+	0.872623i	0.496181	+	0.868219i	$0.334735\pi$
$89$	−423.011	+	732.676i	−0.503809	+	0.872623i	−0.999990	+	0.00440423i	$0.998598\pi$
$90$		0			0
$91$	−1162.25	+	287.583i	−1.33887	+	0.331284i
$92$		0			0
$93$	182.168	−	315.524i	0.203117	−	0.351810i
$94$		0			0
$95$	−193.625	−	335.369i	−0.209111	−	0.362190i
$96$		0			0
$97$	359.129	+	622.030i	0.375918	+	0.651109i	0.990464	−	0.137772i	$-0.0439941\pi$
$97$	359.129	+	622.030i	0.375918	+	0.651109i	−0.614546	+	0.788881i	$0.710661\pi$
$98$		0			0
$99$	1583.93			1.60799
$100$		0			0
$101$	612.192	−	1060.35i	0.603122	−	1.04464i	−0.389223	−	0.921144i	$-0.627256\pi$
$101$	612.192	−	1060.35i	0.603122	−	1.04464i	0.992345	−	0.123495i	$-0.0394103\pi$
$102$		0			0
$103$	838.674			0.802301			0.401150	−	0.916012i	$-0.368610\pi$
$103$	838.674			0.802301			0.401150	+	0.916012i	$0.368610\pi$
$104$		0			0
$105$	−433.245			−0.402671
$106$		0			0
$107$	840.307	−	1455.45i	0.759211	−	1.31499i	−0.184043	−	0.982918i	$-0.558918\pi$
$107$	840.307	−	1455.45i	0.759211	−	1.31499i	0.943254	−	0.332073i	$-0.107748\pi$
$108$		0			0
$109$	923.874			0.811845			0.405923	−	0.913907i	$-0.366950\pi$
$109$	923.874			0.811845			0.405923	+	0.913907i	$0.366950\pi$
$110$		0			0
$111$	−23.8076	−	41.2360i	−0.0203578	−	0.0352608i
$112$		0			0
$113$	−573.024	−	992.507i	−0.477040	−	0.826258i	0.522613	−	0.852570i	$-0.324957\pi$
$113$	−573.024	−	992.507i	−0.477040	−	0.826258i	−0.999654	+	0.0263115i	$0.991624\pi$
$114$		0			0
$115$	397.154	−	687.891i	0.322042	−	0.557793i
$116$		0			0
$117$	−1160.09	+	287.048i	−0.916670	+	0.226817i
$118$		0			0
$119$	−725.861	+	1257.23i	−0.559156	+	0.968486i
$120$		0			0
$121$	−1264.17	−	2189.61i	−0.949793	−	1.64509i
$122$		0			0
$123$	71.6115	+	124.035i	0.0524958	+	0.0909254i
$124$		0			0
$125$	−811.552			−0.580699
$126$		0			0
$127$	1246.97	−	2159.82i	0.871266	−	1.50908i	0.0105775	−	0.999944i	$-0.496633\pi$
$127$	1246.97	−	2159.82i	0.871266	−	1.50908i	0.860688	−	0.509132i	$-0.170034\pi$
$128$		0			0
$129$	99.7265			0.0680654
$130$		0			0
$131$	−396.837			−0.264670			−0.132335	−	0.991205i	$-0.542247\pi$
$131$	−396.837			−0.264670			−0.132335	+	0.991205i	$0.542247\pi$
$132$		0			0
$133$	357.570	−	619.329i	0.233122	−	0.403779i
$134$		0			0
$135$	−890.379			−0.567642
$136$		0			0
$137$	−796.661	−	1379.86i	−0.496813	−	0.860505i	0.503181	−	0.864181i	$-0.332163\pi$
$137$	−796.661	−	1379.86i	−0.496813	−	0.860505i	−0.999993	+	0.00367660i	$0.998830\pi$
$138$		0			0
$139$	1418.11	+	2456.24i	0.865344	+	1.49882i	0.866706	+	0.498820i	$0.166233\pi$
$139$	1418.11	+	2456.24i	0.865344	+	1.49882i	−0.00136200	+	0.999999i	$0.500434\pi$
$140$		0			0
$141$	−283.524	+	491.078i	−0.169341	+	0.293307i
$142$		0			0
$143$	2019.02	+	2098.23i	1.18069	+	1.22701i
$144$		0			0
$145$	170.580	−	295.454i	0.0976961	−	0.169215i
$146$		0			0
$147$	−189.749	−	328.656i	−0.106464	−	0.184402i
$148$		0			0
$149$	−9.66784	−	16.7452i	−0.00531557	−	0.00920684i	0.863355	−	0.504596i	$-0.168359\pi$
$149$	−9.66784	−	16.7452i	−0.00531557	−	0.00920684i	−0.868671	+	0.495390i	$0.835025\pi$
$150$		0			0
$151$	−1268.20			−0.683473			−0.341736	−	0.939796i	$-0.611015\pi$
$151$	−1268.20			−0.683473			−0.341736	+	0.939796i	$0.611015\pi$
$152$		0			0
$153$	−724.510	+	1254.89i	−0.382831	+	0.663083i
$154$		0			0
$155$	−4109.95			−2.12980
$156$		0			0
$157$	−290.839			−0.147844			−0.0739220	−	0.997264i	$-0.523552\pi$
$157$	−290.839			−0.147844			−0.0739220	+	0.997264i	$0.523552\pi$
$158$		0			0
$159$	−252.705	+	437.698i	−0.126043	+	0.218313i
$160$		0			0
$161$	1466.86			0.718041
$162$		0			0
$163$	−1157.26	−	2004.44i	−0.556097	−	0.963188i	−0.997817	−	0.0660351i	$-0.978965\pi$
$163$	−1157.26	−	2004.44i	−0.556097	−	0.963188i	0.441721	−	0.897153i	$-0.354368\pi$
$164$		0			0
$165$	526.832	+	912.499i	0.248568	+	0.430533i
$166$		0			0
$167$	1101.77	−	1908.32i	0.510523	−	0.884251i	−0.489403	−	0.872058i	$-0.662785\pi$
$167$	1101.77	−	1908.32i	0.510523	−	0.884251i	0.999926	−	0.0121933i	$-0.00388134\pi$
$168$		0			0
$169$	−1859.00	−	1170.87i	−0.846154	−	0.532939i
$170$		0			0
$171$	356.904	−	618.177i	0.159609	−	0.276451i
$172$		0			0
$173$	−1826.74	−	3164.01i	−0.802802	−	1.39049i	−0.917765	−	0.397124i	$-0.870008\pi$
$173$	−1826.74	−	3164.01i	−0.802802	−	1.39049i	0.114963	−	0.993370i	$-0.463325\pi$
$174$		0			0
$175$	847.150	+	1467.31i	0.365934	+	0.633817i
$176$		0			0
$177$	10.2723			0.00436222
$178$		0			0
$179$	−1148.47	+	1989.21i	−0.479558	+	0.830619i	−0.999725	−	0.0234455i	$-0.992536\pi$
$179$	−1148.47	+	1989.21i	−0.479558	+	0.830619i	0.520167	+	0.854065i	$0.325870\pi$
$180$		0			0
$181$	3694.28			1.51709			0.758546	−	0.651620i	$-0.225910\pi$
$181$	3694.28			1.51709			0.758546	+	0.651620i	$0.225910\pi$
$182$		0			0
$183$	−990.265			−0.400014
$184$		0			0
$185$	−268.566	+	465.171i	−0.106732	+	0.184865i
$186$		0			0
$187$	3530.62			1.38067
$188$		0			0
$189$	−822.137	−	1423.98i	−0.316411	−	0.548040i
$190$		0			0
$191$	−2326.87	−	4030.25i	−0.881499	−	1.52680i	−0.849675	−	0.527307i	$-0.823202\pi$
$191$	−2326.87	−	4030.25i	−0.881499	−	1.52680i	−0.0318235	−	0.999494i	$-0.510131\pi$
$192$		0			0
$193$	−1168.60	+	2024.08i	−0.435844	+	0.754904i	−0.997364	−	0.0725588i	$-0.976883\pi$
$193$	−1168.60	+	2024.08i	−0.435844	+	0.754904i	0.561520	+	0.827463i	$0.310217\pi$
$194$		0			0
$195$	−551.224	−	572.849i	−0.202431	−	0.210372i
$196$		0			0
$197$	1759.00	−	3046.68i	0.636161	−	1.10186i	−0.350107	−	0.936710i	$-0.613855\pi$
$197$	1759.00	−	3046.68i	0.636161	−	1.10186i	0.986268	−	0.165153i	$-0.0528119\pi$
$198$		0			0
$199$	543.974	+	942.191i	0.193775	+	0.335629i	0.946498	−	0.322709i	$-0.104593\pi$
$199$	543.974	+	942.191i	0.193775	+	0.335629i	−0.752723	+	0.658337i	$0.771260\pi$
$200$		0			0
$201$	−1.13029	−	1.95772i	−0.000396639	−	0.000686998i
$202$		0			0
$203$	630.026			0.217828
$204$		0			0
$205$	807.826	−	1399.20i	0.275224	−	0.476703i
$206$		0			0
$207$	1464.13			0.491613
$208$		0			0
$209$	−1739.24			−0.575625
$210$		0			0
$211$	−2037.62	+	3529.26i	−0.664812	+	1.15149i	0.314524	+	0.949249i	$0.398155\pi$
$211$	−2037.62	+	3529.26i	−0.664812	+	1.15149i	−0.979336	+	0.202239i	$0.935178\pi$
$212$		0			0
$213$	−807.349			−0.259712
$214$		0			0
$215$	−562.491	−	974.264i	−0.178426	−	0.309043i
$216$		0			0
$217$	−3794.95	−	6573.05i	−1.18718	−	2.05626i
$218$		0			0
$219$	298.631	−	517.243i	0.0921442	−	0.159598i
$220$		0			0
$221$	−2585.86	+	639.835i	−0.787077	+	0.194751i
$222$		0			0
$223$	−1012.07	+	1752.95i	−0.303915	+	0.526396i	−0.977019	−	0.213152i	$-0.931627\pi$
$223$	−1012.07	+	1752.95i	−0.303915	+	0.526396i	0.673104	+	0.739548i	$0.264960\pi$
$224$		0			0
$225$	845.573	+	1464.58i	0.250540	+	0.433948i
$226$		0			0
$227$	2264.35	+	3921.97i	0.662071	+	1.14674i	0.980071	+	0.198650i	$0.0636557\pi$
$227$	2264.35	+	3921.97i	0.662071	+	1.14674i	−0.317999	+	0.948091i	$0.603011\pi$
$228$		0			0
$229$	−24.4613			−0.00705872			−0.00352936	−	0.999994i	$-0.501123\pi$
$229$	−24.4613			−0.00705872			−0.00352936	+	0.999994i	$0.501123\pi$
$230$		0			0
$231$	−972.906	+	1685.12i	−0.277110	+	0.479969i
$232$		0			0
$233$	−2991.73			−0.841180			−0.420590	−	0.907251i	$-0.638177\pi$
$233$	−2991.73			−0.841180			−0.420590	+	0.907251i	$0.638177\pi$
$234$		0			0
$235$	6396.69			1.77563
$236$		0			0
$237$	760.613	−	1317.42i	0.208469	−	0.361079i
$238$		0			0
$239$	2113.39			0.571982			0.285991	−	0.958232i	$-0.407677\pi$
$239$	2113.39			0.571982			0.285991	+	0.958232i	$0.407677\pi$
$240$		0			0
$241$	−3485.44	−	6036.96i	−0.931606	−	1.61359i	−0.780577	−	0.625060i	$-0.785075\pi$
$241$	−3485.44	−	6036.96i	−0.931606	−	1.61359i	−0.151029	−	0.988529i	$-0.548259\pi$
$242$		0			0
$243$	−1242.66	−	2152.35i	−0.328053	−	0.568204i
$244$		0			0
$245$	−2140.50	+	3707.46i	−0.558170	+	0.966779i
$246$		0			0
$247$	1273.84	−	315.192i	0.328146	−	0.0811952i
$248$		0			0
$249$	268.867	−	465.692i	0.0684288	−	0.118522i
$250$		0			0
$251$	−2853.18	−	4941.86i	−0.717495	−	1.24274i	−0.961989	−	0.273087i	$-0.911955\pi$
$251$	−2853.18	−	4941.86i	−0.717495	−	1.24274i	0.244494	−	0.969651i	$-0.421378\pi$
$252$		0			0
$253$	−1783.72	−	3089.49i	−0.443246	−	0.767725i
$254$		0			0
$255$	−963.915			−0.236717
$256$		0			0
$257$	−1002.07	+	1735.64i	−0.243220	+	0.421269i	−0.961630	−	0.274351i	$-0.911537\pi$
$257$	−1002.07	+	1735.64i	−0.243220	+	0.421269i	0.718410	+	0.695620i	$0.244870\pi$
$258$		0			0
$259$	−991.929			−0.237975
$260$		0			0
$261$	628.853			0.149138
$262$		0			0
$263$	−270.030	+	467.705i	−0.0633108	+	0.109658i	−0.895943	−	0.444168i	$-0.853499\pi$
$263$	−270.030	+	467.705i	−0.0633108	+	0.109658i	0.832633	+	0.553826i	$0.186833\pi$
$264$		0			0
$265$	5701.37			1.32163
$266$		0			0
$267$	−518.688	−	898.394i	−0.118888	−	0.205921i
$268$		0			0
$269$	−79.2764	−	137.311i	−0.0179687	−	0.0311226i	0.856901	−	0.515481i	$-0.172387\pi$
$269$	−79.2764	−	137.311i	−0.0179687	−	0.0311226i	−0.874870	+	0.484358i	$0.839053\pi$
$270$		0			0
$271$	−3466.13	+	6003.51i	−0.776945	+	1.34571i	0.156749	+	0.987638i	$0.449899\pi$
$271$	−3466.13	+	6003.51i	−0.776945	+	1.34571i	−0.933695	+	0.358070i	$0.883435\pi$
$272$		0			0
$273$	407.181	−	1410.52i	0.0902700	−	0.312704i
$274$		0			0
$275$	2060.29	−	3568.52i	0.451782	−	0.782510i
$276$		0			0
$277$	2241.25	+	3881.97i	0.486151	+	0.842039i	0.999873	−	0.0159180i	$-0.00506706\pi$
$277$	2241.25	+	3881.97i	0.486151	+	0.842039i	−0.513722	+	0.857957i	$0.671734\pi$
$278$		0			0
$279$	−3787.89	−	6560.81i	−0.812813	−	1.40783i
$280$		0			0
$281$	7631.00			1.62003			0.810013	−	0.586411i	$-0.199460\pi$
$281$	7631.00			1.62003			0.810013	+	0.586411i	$0.199460\pi$
$282$		0			0
$283$	1201.42	−	2080.92i	0.252357	−	0.437096i	−0.711817	−	0.702365i	$-0.752127\pi$
$283$	1201.42	−	2080.92i	0.252357	−	0.437096i	0.964174	+	0.265269i	$0.0854608\pi$
$284$		0			0
$285$	474.839			0.0986914
$286$		0			0
$287$	2983.64			0.613654
$288$		0			0
$289$	841.553	−	1457.61i	0.171291	−	0.296685i
$290$		0			0
$291$	−880.715			−0.177417
$292$		0			0
$293$	1416.14	+	2452.82i	0.282360	+	0.489062i	0.971966	−	0.235123i	$-0.0755493\pi$
$293$	1416.14	+	2452.82i	0.282360	+	0.489062i	−0.689605	+	0.724185i	$0.742216\pi$
$294$		0			0
$295$	−57.9392	−	100.354i	−0.0114351	−	0.0198062i
$296$		0			0
$297$	−1999.46	+	3463.16i	−0.390641	+	0.676609i
$298$		0			0
$299$	1866.30	+	1939.52i	0.360974	+	0.375135i
$300$		0			0
$301$	1038.76	−	1799.18i	0.198914	−	0.344529i
$302$		0			0
$303$	750.658	+	1300.18i	0.142324	+	0.246513i
$304$		0			0
$305$	5585.43	+	9674.25i	1.04859	+	1.81622i
$306$		0			0
$307$	−7397.22			−1.37518			−0.687592	−	0.726097i	$-0.741332\pi$
$307$	−7397.22			−1.37518			−0.687592	+	0.726097i	$0.741332\pi$
$308$		0			0
$309$	−514.183	+	890.591i	−0.0946630	+	0.163961i
$310$		0			0
$311$	5160.32			0.940884			0.470442	−	0.882431i	$-0.344095\pi$
$311$	5160.32			0.940884			0.470442	+	0.882431i	$0.344095\pi$
$312$		0			0
$313$	3804.66			0.687067			0.343533	−	0.939140i	$-0.388376\pi$
$313$	3804.66			0.687067			0.343533	+	0.939140i	$0.388376\pi$
$314$		0			0
$315$	−4504.32	+	7801.71i	−0.805682	+	1.39548i
$316$		0			0
$317$	−7727.00			−1.36906			−0.684530	−	0.728985i	$-0.739992\pi$
$317$	−7727.00			−1.36906			−0.684530	+	0.728985i	$0.739992\pi$
$318$		0			0
$319$	−766.119	−	1326.96i	−0.134465	−	0.232901i
$320$		0			0
$321$	1030.37	+	1784.65i	0.179158	+	0.310310i
$322$		0			0
$323$	795.547	−	1377.93i	0.137045	−	0.237368i
$324$		0			0
$325$	−862.272	+	2987.00i	−0.147170	+	0.509812i
$326$		0			0
$327$	−566.419	+	981.066i	−0.0957891	+	0.165912i
$328$		0			0
$329$	5906.42	+	10230.2i	0.989761	+	1.71432i
$330$		0			0
$331$	−3767.67	−	6525.80i	−0.625650	−	1.08366i	−0.988415	−	0.151776i	$-0.951501\pi$
$331$	−3767.67	−	6525.80i	−0.625650	−	1.08366i	0.362765	−	0.931881i	$-0.381833\pi$
$332$		0			0
$333$	−990.083			−0.162932
$334$		0			0
$335$	−12.7504	+	22.0844i	−0.00207949	+	0.00360179i
$336$		0			0
$337$	4662.39			0.753640			0.376820	−	0.926286i	$-0.377017\pi$
$337$	4662.39			0.753640			0.376820	+	0.926286i	$0.377017\pi$
$338$		0			0
$339$	1405.26			0.225143
$340$		0			0
$341$	−9229.41	+	15985.8i	−1.46569	+	2.53865i
$342$		0			0
$343$	855.814			0.134722
$344$		0			0
$345$	486.983	+	843.479i	0.0759950	+	0.131627i
$346$		0			0
$347$	3601.76	+	6238.43i	0.557212	+	0.965120i	0.997728	+	0.0673751i	$0.0214624\pi$
$347$	3601.76	+	6238.43i	0.557212	+	0.965120i	−0.440515	+	0.897745i	$0.645204\pi$
$348$		0			0
$349$	3523.18	−	6102.33i	0.540377	−	0.935961i	−0.458505	−	0.888692i	$-0.651615\pi$
$349$	3523.18	−	6102.33i	0.540377	−	0.935961i	0.998882	−	0.0472689i	$-0.0150518\pi$
$350$		0			0
$351$	836.813	−	2898.80i	0.127253	−	0.440817i
$352$		0			0
$353$	−1851.90	+	3207.59i	−0.279226	+	0.483634i	−0.971193	−	0.238295i	$-0.923411\pi$
$353$	−1851.90	+	3207.59i	−0.279226	+	0.483634i	0.691966	+	0.721930i	$0.256745\pi$
$354$		0			0
$355$	4553.72	+	7887.27i	0.680807	+	1.17919i
$356$		0			0
$357$	−890.037	−	1541.59i	−0.131949	−	0.228542i
$358$		0			0
$359$	1444.39			0.212345			0.106173	−	0.994348i	$-0.466140\pi$
$359$	1444.39			0.212345			0.106173	+	0.994348i	$0.466140\pi$
$360$		0			0
$361$	3037.60	−	5261.28i	0.442864	−	0.767062i
$362$		0			0
$363$	3100.21			0.448262
$364$		0			0
$365$	−6737.51			−0.966185
$366$		0			0
$367$	1549.30	−	2683.46i	0.220361	−	0.381677i	−0.734556	−	0.678548i	$-0.762610\pi$
$367$	1549.30	−	2683.46i	0.220361	−	0.381677i	0.954918	+	0.296871i	$0.0959430\pi$
$368$		0			0
$369$	2978.09			0.420144
$370$		0			0
$371$	5264.39	+	9118.19i	0.736694	+	1.27599i
$372$		0			0
$373$	2289.51	+	3965.54i	0.317818	+	0.550477i	0.980033	−	0.198837i	$-0.0637165\pi$
$373$	2289.51	+	3965.54i	0.317818	+	0.550477i	−0.662214	+	0.749315i	$0.730383\pi$
$374$		0			0
$375$	497.555	−	861.790i	0.0685163	−	0.118674i
$376$		0			0
$377$	801.590	+	833.037i	0.109507	+	0.113803i
$378$		0			0
$379$	3386.92	−	5866.32i	0.459036	−	0.795073i	−0.539875	−	0.841745i	$-0.681528\pi$
$379$	3386.92	−	5866.32i	0.459036	−	0.795073i	0.998910	+	0.0466724i	$0.0148617\pi$
$380$		0			0
$381$	1529.01	+	2648.33i	0.205600	+	0.356110i
$382$		0			0
$383$	−4722.07	−	8178.87i	−0.629991	−	1.09118i	−0.987553	−	0.157287i	$-0.949725\pi$
$383$	−4722.07	−	8178.87i	−0.629991	−	1.09118i	0.357562	−	0.933889i	$-0.383608\pi$
$384$		0			0
$385$	21950.1			2.90566
$386$		0			0
$387$	1036.83	−	1795.84i	0.136188	−	0.235885i
$388$		0			0
$389$	5899.20			0.768898			0.384449	−	0.923146i	$-0.374391\pi$
$389$	5899.20			0.768898			0.384449	+	0.923146i	$0.374391\pi$
$390$		0			0
$391$	3263.57			0.422112
$392$		0			0
$393$	243.297	−	421.403i	0.0312283	−	0.0540889i
$394$		0			0
$395$	−17160.5			−2.18592
$396$		0			0
$397$	−5915.29	−	10245.6i	−0.747808	−	1.29524i	−0.948871	−	0.315664i	$-0.897773\pi$
$397$	−5915.29	−	10245.6i	−0.747808	−	1.29524i	0.201063	−	0.979578i	$-0.435560\pi$
$398$		0			0
$399$	438.446	+	759.410i	0.0550119	+	0.0952833i
$400$		0			0
$401$	−700.942	+	1214.07i	−0.0872902	+	0.151191i	−0.906365	−	0.422496i	$-0.861154\pi$
$401$	−700.942	+	1214.07i	−0.0872902	+	0.151191i	0.819075	+	0.573687i	$0.194487\pi$
$402$		0			0
$403$	3862.69	−	13380.8i	0.477455	−	1.65395i
$404$		0			0
$405$	−4215.18	+	7300.91i	−0.517170	+	0.895765i
$406$		0			0
$407$	1206.20	+	2089.20i	0.146902	+	0.254441i
$408$		0			0
$409$	−6640.14	−	11501.1i	−0.802772	−	1.39044i	−0.917785	−	0.397078i	$-0.870024\pi$
$409$	−6640.14	−	11501.1i	−0.802772	−	1.39044i	0.115013	−	0.993364i	$-0.463309\pi$
$410$		0			0
$411$	1953.70			0.234474
$412$		0			0
$413$	106.997	−	185.324i	0.0127481	−	0.0220804i
$414$		0			0
$415$	−6066.01			−0.717515
$416$		0			0
$417$	−3477.73			−0.408405
$418$		0			0
$419$	6089.01	−	10546.5i	0.709947	−	1.22966i	−0.254929	−	0.966960i	$-0.582052\pi$
$419$	6089.01	−	10546.5i	0.709947	−	1.22966i	0.964876	−	0.262705i	$-0.0846145\pi$
$420$		0			0
$421$	6141.75			0.710998			0.355499	−	0.934677i	$-0.384311\pi$
$421$	6141.75			0.710998			0.355499	+	0.934677i	$0.384311\pi$
$422$		0			0
$423$	5895.43	+	10211.2i	0.677649	+	1.17372i
$424$		0			0
$425$	1884.80	+	3264.57i	0.215121	+	0.372600i
$426$		0			0
$427$	−10314.7	+	17865.6i	−1.16900	+	2.02477i
$428$		0			0
$429$	−3465.96	+	857.602i	−0.390065	+	0.0965161i
$430$		0			0
$431$	−4269.15	+	7394.38i	−0.477117	+	0.826391i	−0.999656	−	0.0262241i	$-0.991652\pi$
$431$	−4269.15	+	7394.38i	−0.477117	+	0.826391i	0.522539	+	0.852616i	$0.324985\pi$
$432$		0			0
$433$	7470.26	+	12938.9i	0.829094	+	1.43603i	0.898750	+	0.438462i	$0.144477\pi$
$433$	7470.26	+	12938.9i	0.829094	+	1.43603i	−0.0696557	+	0.997571i	$0.522190\pi$
$434$		0			0
$435$	209.163	+	362.280i	0.0230542	+	0.0399310i
$436$		0			0
$437$	−1607.68			−0.175986
$438$		0			0
$439$	−2266.51	+	3925.71i	−0.246411	+	0.426797i	−0.962528	−	0.271184i	$-0.912585\pi$
$439$	−2266.51	+	3925.71i	−0.246411	+	0.426797i	0.716116	+	0.697981i	$0.245918\pi$
$440$		0			0
$441$	−7891.07			−0.852075
$442$		0			0
$443$	−4626.67			−0.496207			−0.248103	−	0.968734i	$-0.579807\pi$
$443$	−4626.67			−0.496207			−0.248103	+	0.968734i	$0.579807\pi$
$444$		0			0
$445$	−5851.15	+	10134.5i	−0.623306	+	1.07960i
$446$		0			0
$447$	23.7091			0.00250872
$448$		0			0
$449$	836.152	+	1448.26i	0.0878852	+	0.152222i	0.906617	−	0.421954i	$-0.138656\pi$
$449$	836.152	+	1448.26i	0.0878852	+	0.152222i	−0.818732	+	0.574176i	$0.805322\pi$
$450$		0			0
$451$	−3628.15	−	6284.13i	−0.378809	−	0.656116i
$452$		0			0
$453$	777.520	−	1346.70i	0.0806425	−	0.139677i
$454$		0			0
$455$	−16076.5	+	3977.89i	−1.65643	+	0.409860i
$456$		0			0
$457$	2887.88	−	5001.96i	0.295601	−	0.511996i	−0.679524	−	0.733654i	$-0.737814\pi$
$457$	2887.88	−	5001.96i	0.295601	−	0.511996i	0.975124	+	0.221658i	$0.0711469\pi$
$458$		0			0
$459$	−1829.15	−	3168.18i	−0.186007	−	0.322174i
$460$		0			0
$461$	−8876.18	−	15374.0i	−0.896757	−	1.55323i	−0.831615	−	0.555353i	$-0.812583\pi$
$461$	−8876.18	−	15374.0i	−0.896757	−	1.55323i	−0.0651426	−	0.997876i	$-0.520750\pi$
$462$		0			0
$463$	3060.93			0.307243			0.153621	−	0.988130i	$-0.450906\pi$
$463$	3060.93			0.307243			0.153621	+	0.988130i	$0.450906\pi$
$464$		0			0
$465$	2519.77	−	4364.38i	0.251294	−	0.435254i
$466$		0			0
$467$	−1019.98			−0.101068			−0.0505342	−	0.998722i	$-0.516092\pi$
$467$	−1019.98			−0.101068			−0.0505342	+	0.998722i	$0.516092\pi$
$468$		0			0
$469$	−47.0927			−0.00463654
$470$		0			0
$471$	178.311	−	308.843i	0.0174440	−	0.0302139i
$472$		0			0
$473$	−5052.58			−0.491158
$474$		0			0
$475$	−928.481	−	1608.18i	−0.0896876	−	0.155343i
$476$		0			0
$477$	5254.59	+	9101.22i	0.504384	+	0.873619i
$478$		0			0
$479$	−2854.97	+	4944.96i	−0.272332	+	0.471693i	−0.969459	−	0.245255i	$-0.921128\pi$
$479$	−2854.97	+	4944.96i	−0.272332	+	0.471693i	0.697126	+	0.716948i	$0.254462\pi$
$480$		0			0
$481$	−1262.05	−	1311.56i	−0.119635	−	0.124328i
$482$		0			0
$483$	−899.317	+	1557.66i	−0.0847212	+	0.146741i
$484$		0			0
$485$	4967.53	+	8604.02i	0.465080	+	0.805543i
$486$		0			0
$487$	313.040	+	542.202i	0.0291278	+	0.0504507i	0.880222	−	0.474562i	$-0.157394\pi$
$487$	313.040	+	542.202i	0.0291278	+	0.0504507i	−0.851094	+	0.525013i	$0.824060\pi$
$488$		0			0
$489$	2838.03			0.262454
$490$		0			0
$491$	8004.57	−	13864.3i	0.735725	−	1.27431i	−0.218679	−	0.975797i	$-0.570175\pi$
$491$	8004.57	−	13864.3i	0.735725	−	1.27431i	0.954404	−	0.298516i	$-0.0964918\pi$
$492$		0			0
$493$	1401.73			0.128054
$494$		0			0
$495$	21909.2			1.98939
$496$		0			0
$497$	−8409.41	+	14565.5i	−0.758981	+	1.31459i
$498$		0			0
$499$	8716.04			0.781931			0.390965	−	0.920405i	$-0.372141\pi$
$499$	8716.04			0.781931			0.390965	+	0.920405i	$0.372141\pi$
$500$		0			0
$501$	1350.97	+	2339.94i	0.120472	+	0.208664i
$502$		0			0
$503$	6079.76	+	10530.5i	0.538933	+	0.933459i	0.998962	+	0.0455551i	$0.0145056\pi$
$503$	6079.76	+	10530.5i	0.538933	+	0.933459i	−0.460029	+	0.887904i	$0.652161\pi$
$504$		0			0
$505$	8467.94	−	14666.9i	0.746175	−	1.29241i
$506$		0			0
$507$	2383.08	−	1256.23i	0.208750	−	0.110042i
$508$		0			0
$509$	1267.48	−	2195.34i	0.110373	−	0.191172i	−0.805547	−	0.592531i	$-0.798129\pi$
$509$	1267.48	−	2195.34i	0.110373	−	0.191172i	0.915921	+	0.401359i	$0.131462\pi$
$510$		0			0
$511$	−6221.12	−	10775.3i	−0.538564	−	0.932820i
$512$		0			0
$513$	901.066	+	1560.69i	0.0775498	+	0.134320i
$514$		0			0
$515$	11600.7			0.992595
$516$		0			0
$517$	14364.6	−	24880.1i	1.22196	−	2.11649i
$518$		0			0
$519$	4479.84			0.378889
$520$		0			0
$521$	−19884.2			−1.67206			−0.836030	−	0.548684i	$-0.815129\pi$
$521$	−19884.2			−1.67206			−0.836030	+	0.548684i	$0.815129\pi$
$522$		0			0
$523$	179.507	−	310.915i	0.0150082	−	0.0259950i	−0.858424	−	0.512941i	$-0.828556\pi$
$523$	179.507	−	310.915i	0.0150082	−	0.0259950i	0.873432	+	0.486946i	$0.161889\pi$
$524$		0			0
$525$	−2077.52			−0.172705
$526$		0			0
$527$	−8443.28	−	14624.2i	−0.697903	−	1.20880i
$528$		0			0
$529$	4434.70	+	7681.13i	0.364486	+	0.631308i
$530$		0			0
$531$	106.798	−	184.980i	0.00872813	−	0.0151176i
$532$		0			0
$533$	3796.13	+	3945.05i	0.308496	+	0.320599i
$534$		0			0
$535$	11623.3	−	20132.1i	0.939285	−	1.62689i
$536$		0			0
$537$	−1408.24	−	2439.14i	−0.113166	−	0.196008i
$538$		0			0
$539$	9613.53	+	16651.1i	0.768245	+	1.33064i
$540$		0			0
$541$	−6607.14			−0.525070			−0.262535	−	0.964922i	$-0.584559\pi$
$541$	−6607.14			−0.525070			−0.262535	+	0.964922i	$0.584559\pi$
$542$		0			0
$543$	−2264.93	+	3922.97i	−0.179001	+	0.310038i
$544$		0			0
$545$	12779.2			1.00440
$546$		0			0
$547$	−23607.2			−1.84529			−0.922644	−	0.385654i	$-0.873976\pi$
$547$	−23607.2			−1.84529			−0.922644	+	0.385654i	$0.873976\pi$
$548$		0			0
$549$	−10295.5	+	17832.3i	−0.800366	+	1.38627i
$550$		0			0
$551$	−690.511			−0.0533880
$552$		0			0
$553$	−15845.2	−	27444.7i	−1.21846	−	2.11043i
$554$		0			0
$555$	−329.311	−	570.384i	−0.0251864	−	0.0436242i
$556$		0			0
$557$	6312.86	−	10934.2i	0.480223	−	0.831771i	−0.519519	−	0.854459i	$-0.673889\pi$
$557$	6312.86	−	10934.2i	0.480223	−	0.831771i	0.999743	+	0.0226876i	$0.00722230\pi$
$558$		0			0
$559$	3700.56	−	915.651i	0.279995	−	0.0692807i
$560$		0			0
$561$	−2164.59	+	3749.18i	−0.162904	+	0.282158i
$562$		0			0
$563$	4243.47	+	7349.91i	0.317657	+	0.550199i	0.979999	−	0.199003i	$-0.0637705\pi$
$563$	4243.47	+	7349.91i	0.317657	+	0.550199i	−0.662341	+	0.749202i	$0.730437\pi$
$564$		0			0
$565$	−7926.16	−	13728.5i	−0.590188	−	1.02224i
$566$		0			0
$567$	−15568.4			−1.15311
$568$		0			0
$569$	2504.88	−	4338.57i	0.184552	−	0.319653i	−0.758874	−	0.651238i	$-0.774250\pi$
$569$	2504.88	−	4338.57i	0.184552	−	0.319653i	0.943425	+	0.331585i	$0.107583\pi$
$570$		0			0
$571$	16275.6			1.19284			0.596419	−	0.802673i	$-0.296590\pi$
$571$	16275.6			1.19284			0.596419	+	0.802673i	$0.296590\pi$
$572$		0			0
$573$	5706.32			0.416030
$574$		0			0
$575$	1904.45	−	3298.61i	0.138124	−	0.239237i
$576$		0			0
$577$	−20850.8			−1.50438			−0.752191	−	0.658945i	$-0.771003\pi$
$577$	−20850.8			−1.50438			−0.752191	+	0.658945i	$0.771003\pi$
$578$		0			0
$579$	−1432.92	−	2481.89i	−0.102850	−	0.178141i
$580$		0			0
$581$	−5601.09	−	9701.37i	−0.399952	−	0.692738i
$582$		0			0
$583$	12803.1	−	22175.7i	0.909522	−	1.57534i
$584$		0			0
$585$	−16046.5	+	3970.49i	−1.13409	+	0.280615i
$586$		0			0
$587$	−8392.84	+	14536.8i	−0.590135	+	1.02214i	0.404078	+	0.914724i	$0.367592\pi$
$587$	−8392.84	+	14536.8i	−0.590135	+	1.02214i	−0.994214	+	0.107420i	$0.965741\pi$
$588$		0			0
$589$	4159.29	+	7204.09i	0.290968	+	0.503972i
$590$		0			0
$591$	2156.86	+	3735.78i	0.150120	+	0.260016i
$592$		0			0
$593$	22582.3			1.56382			0.781909	−	0.623393i	$-0.214246\pi$
$593$	22582.3			1.56382			0.781909	+	0.623393i	$0.214246\pi$
$594$		0			0
$595$	−10040.2	+	17390.2i	−0.691780	+	1.19820i
$596$		0			0
$597$	−1334.02			−0.0914538
$598$		0			0
$599$	−27736.8			−1.89198			−0.945990	−	0.324195i	$-0.894907\pi$
$599$	−27736.8			−1.89198			−0.945990	+	0.324195i	$0.894907\pi$
$600$		0			0
$601$	3514.04	−	6086.49i	0.238504	−	0.413100i	−0.721782	−	0.692121i	$-0.756676\pi$
$601$	3514.04	−	6086.49i	0.238504	−	0.413100i	0.960285	+	0.279021i	$0.0900098\pi$
$602$		0			0
$603$	−47.0051			−0.00317445
$604$		0			0
$605$	−17486.3	−	30287.1i	−1.17507	−	2.03528i
$606$		0			0
$607$	7180.51	+	12437.0i	0.480145	+	0.831635i	0.999741	−	0.0227768i	$-0.00725072\pi$
$607$	7180.51	+	12437.0i	0.480145	+	0.831635i	−0.519596	+	0.854412i	$0.673917\pi$
$608$		0			0
$609$	−386.263	+	669.027i	−0.0257014	+	0.0445162i
$610$		0			0
$611$	−6011.85	+	20825.7i	−0.398058	+	1.37891i
$612$		0			0
$613$	12038.9	−	20852.0i	0.793224	−	1.37390i	−0.130737	−	0.991417i	$-0.541734\pi$
$613$	12038.9	−	20852.0i	0.793224	−	1.37390i	0.923961	−	0.382487i	$-0.124932\pi$
$614$		0			0
$615$	990.541	+	1715.67i	0.0649471	+	0.112492i
$616$		0			0
$617$	−13044.7	−	22594.1i	−0.851152	−	1.47424i	−0.880169	−	0.474660i	$-0.842571\pi$
$617$	−13044.7	−	22594.1i	−0.851152	−	1.47424i	0.0290175	−	0.999579i	$-0.490762\pi$
$618$		0			0
$619$	−20791.1			−1.35003			−0.675013	−	0.737806i	$-0.735862\pi$
$619$	−20791.1			−1.35003			−0.675013	+	0.737806i	$0.735862\pi$
$620$		0			0
$621$	−1848.22	+	3201.21i	−0.119431	+	0.206860i
$622$		0			0
$623$	−21610.8			−1.38975
$624$		0			0
$625$	−19516.6			−1.24906
$626$		0			0
$627$	1066.31	−	1846.90i	0.0679176	−	0.117637i
$628$		0			0
$629$	−2206.92			−0.139897
$630$		0			0
$631$	5930.20	+	10271.4i	0.374133	+	0.648017i	0.990197	−	0.139679i	$-0.0446072\pi$
$631$	5930.20	+	10271.4i	0.374133	+	0.648017i	−0.616064	+	0.787696i	$0.711274\pi$
$632$		0			0
$633$	−2498.49	−	4327.51i	−0.156882	−	0.271727i
$634$		0			0
$635$	17248.3	−	29874.9i	1.07792	−	1.86701i
$636$		0			0
$637$	−10058.6	−	10453.2i	−0.625648	−	0.650192i
$638$		0			0
$639$	−8393.76	+	14538.4i	−0.519643	+	0.900048i
$640$		0			0
$641$	2421.50	+	4194.16i	0.149210	+	0.258439i	0.930936	−	0.365183i	$-0.118994\pi$
$641$	2421.50	+	4194.16i	0.149210	+	0.258439i	−0.781726	+	0.623622i	$0.785660\pi$
$642$		0			0
$643$	−4804.75	−	8322.07i	−0.294682	−	0.510405i	0.680229	−	0.733000i	$-0.261881\pi$
$643$	−4804.75	−	8322.07i	−0.294682	−	0.510405i	−0.974911	+	0.222595i	$0.928547\pi$
$644$		0			0
$645$	1379.43			0.0842095
$646$		0			0
$647$	8923.09	−	15455.2i	0.542199	−	0.939116i	−0.456578	−	0.889683i	$-0.650925\pi$
$647$	8923.09	−	15455.2i	0.542199	−	0.939116i	0.998777	−	0.0494331i	$-0.0157415\pi$
$648$		0			0
$649$	−520.439			−0.0314777
$650$		0			0
$651$	9306.59			0.560298
$652$		0			0
$653$	−9391.52	+	16266.6i	−0.562816	+	0.974826i	0.434433	+	0.900704i	$0.356949\pi$
$653$	−9391.52	+	16266.6i	−0.562816	+	0.974826i	−0.997249	+	0.0741216i	$0.976385\pi$
$654$		0			0
$655$	−5489.11			−0.327446
$656$		0			0
$657$	−6209.54	−	10755.2i	−0.368733	−	0.638664i
$658$		0			0
$659$	−10374.1	−	17968.5i	−0.613229	−	1.06214i	−0.990692	−	0.136120i	$-0.956537\pi$
$659$	−10374.1	−	17968.5i	−0.613229	−	1.06214i	0.377463	−	0.926025i	$-0.376796\pi$
$660$		0			0
$661$	−2460.41	+	4261.55i	−0.144779	+	0.250764i	−0.929290	−	0.369350i	$-0.879580\pi$
$661$	−2460.41	+	4261.55i	−0.144779	+	0.250764i	0.784512	+	0.620114i	$0.212914\pi$
$662$		0			0
$663$	905.925	−	3138.22i	0.0530667	−	0.183828i
$664$		0			0
$665$	4945.96	−	8566.66i	0.288415	−	0.499550i
$666$		0			0
$667$	−708.171	−	1226.59i	−0.0411102	−	0.0712049i
$668$		0			0
$669$	−1240.98	−	2149.44i	−0.0717174	−	0.124218i
$670$		0			0
$671$	50171.1			2.88649
$672$		0			0
$673$	9886.94	−	17124.7i	0.566291	−	0.980844i	−0.430638	−	0.902525i	$-0.641711\pi$
$673$	9886.94	−	17124.7i	0.566291	−	0.980844i	0.996928	−	0.0783195i	$-0.0249554\pi$
$674$		0			0
$675$	−4269.59			−0.243462
$676$		0			0
$677$	−5214.00			−0.295997			−0.147999	−	0.988988i	$-0.547283\pi$
$677$	−5214.00			−0.295997			−0.147999	+	0.988988i	$0.547283\pi$
$678$		0			0
$679$	−9173.60	+	15889.1i	−0.518484	+	0.898040i
$680$		0			0
$681$	−5553.01			−0.312469
$682$		0			0
$683$	−14970.7	−	25930.0i	−0.838707	−	1.45268i	−0.890977	−	0.454049i	$-0.849979\pi$
$683$	−14970.7	−	25930.0i	−0.838707	−	1.45268i	0.0522700	−	0.998633i	$-0.483354\pi$
$684$		0			0
$685$	−11019.5	−	19086.4i	−0.614650	−	1.06460i
$686$		0			0
$687$	14.9970	−	25.9755i	0.000832854	−	0.00144254i
$688$		0			0
$689$	−5358.37	+	18561.9i	−0.296281	+	1.02635i
$690$		0			0
$691$	−610.634	+	1057.65i	−0.0336174	+	0.0582270i	−0.882345	−	0.470604i	$-0.844036\pi$
$691$	−610.634	+	1057.65i	−0.0336174	+	0.0582270i	0.848727	+	0.528831i	$0.177369\pi$
$692$		0			0
$693$	20230.0	+	35039.4i	1.10891	+	1.92069i
$694$		0			0
$695$	19615.6	+	33975.2i	1.07059	+	1.85432i
$696$		0			0
$697$	6638.22			0.360747
$698$		0			0
$699$	1834.20	−	3176.93i	0.0992502	−	0.171906i
$700$		0			0
$701$	22838.2			1.23051			0.615253	−	0.788329i	$-0.289054\pi$
$701$	22838.2			1.23051			0.615253	+	0.788329i	$0.289054\pi$
$702$		0			0
$703$	1087.16			0.0583258
$704$		0			0
$705$	−3921.75	+	6792.67i	−0.209506	+	0.362875i
$706$		0			0
$707$	31275.7			1.66371
$708$		0			0
$709$	4386.16	+	7597.05i	0.232335	+	0.402417i	0.958495	−	0.285110i	$-0.0920300\pi$
$709$	4386.16	+	7597.05i	0.232335	+	0.402417i	−0.726160	+	0.687526i	$0.758697\pi$
$710$		0			0
$711$	−15815.7	−	27393.7i	−0.834228	−	1.44493i
$712$		0			0
$713$	−8531.31	+	14776.7i	−0.448107	+	0.776144i
$714$		0			0
$715$	27927.4	+	29023.0i	1.46073	+	1.51804i
$716$		0			0
$717$	−1295.70	+	2244.22i	−0.0674878	+	0.116892i
$718$		0			0
$719$	−2370.08	−	4105.10i	−0.122933	−	0.212927i	0.797990	−	0.602671i	$-0.205897\pi$
$719$	−2370.08	−	4105.10i	−0.122933	−	0.212927i	−0.920923	+	0.389744i	$0.872564\pi$
$720$		0			0
$721$	10711.5	+	18552.9i	0.553285	+	0.958318i
$722$		0			0
$723$	8547.57			0.439678
$724$		0			0
$725$	817.975	−	1416.77i	0.0419019	−	0.0725761i
$726$		0			0
$727$	−16666.9			−0.850265			−0.425132	−	0.905131i	$-0.639772\pi$
$727$	−16666.9			−0.850265			−0.425132	+	0.905131i	$0.639772\pi$
$728$		0			0
$729$	−13408.4			−0.681216
$730$		0			0
$731$	2311.11	−	4002.95i	0.116935	−	0.202537i
$732$		0			0
$733$	31724.7			1.59861			0.799304	−	0.600927i	$-0.205202\pi$
$733$	31724.7			1.59861			0.799304	+	0.600927i	$0.205202\pi$
$734$		0			0
$735$	−2624.64	−	4546.02i	−0.131716	−	0.228139i
$736$		0			0
$737$	57.2653	+	99.1864i	0.00286214	+	0.00495736i
$738$		0			0
$739$	−2672.71	+	4629.27i	−0.133041	+	0.230434i	−0.924847	−	0.380338i	$-0.875807\pi$
$739$	−2672.71	+	4629.27i	−0.133041	+	0.230434i	0.791806	+	0.610772i	$0.209141\pi$
$740$		0			0
$741$	−446.272	+	1545.93i	−0.0221245	+	0.0766414i
$742$		0			0
$743$	−7782.47	+	13479.6i	−0.384268	+	0.665572i	−0.991667	−	0.128825i	$-0.958880\pi$
$743$	−7782.47	+	13479.6i	−0.384268	+	0.665572i	0.607399	+	0.794397i	$0.292213\pi$
$744$		0			0
$745$	−133.727	−	231.622i	−0.00657635	−	0.0113906i
$746$		0			0
$747$	−5590.67	−	9683.32i	−0.273831	−	0.474289i
$748$		0			0
$749$	42929.6			2.09428
$750$		0			0
$751$	−9995.88	+	17313.4i	−0.485692	+	0.841243i	−0.999865	−	0.0164434i	$-0.994766\pi$
$751$	−9995.88	+	17313.4i	−0.485692	+	0.841243i	0.514173	+	0.857687i	$0.328099\pi$
$752$		0			0
$753$	6997.04			0.338627
$754$		0			0
$755$	−17541.9			−0.845583
$756$		0			0
$757$	−5269.15	+	9126.44i	−0.252986	+	0.438185i	−0.964347	−	0.264642i	$-0.914746\pi$
$757$	−5269.15	+	9126.44i	−0.252986	+	0.438185i	0.711360	+	0.702827i	$0.248079\pi$
$758$		0			0
$759$	4374.32			0.209193
$760$		0			0
$761$	−4418.07	−	7652.33i	−0.210453	−	0.364516i	0.741403	−	0.671060i	$-0.234161\pi$
$761$	−4418.07	−	7652.33i	−0.210453	−	0.364516i	−0.951857	+	0.306544i	$0.900827\pi$
$762$		0			0
$763$	11799.7	+	20437.7i	0.559867	+	0.969719i
$764$		0			0
$765$	−10021.5	+	17357.8i	−0.473633	+	0.820357i
$766$		0			0
$767$	381.175	−	94.3163i	0.0179445	−	0.00444011i
$768$		0			0
$769$	−3299.23	+	5714.43i	−0.154711	+	0.267968i	−0.932954	−	0.359996i	$-0.882778\pi$
$769$	−3299.23	+	5714.43i	−0.154711	+	0.267968i	0.778242	+	0.627964i	$0.216111\pi$
$770$		0			0
$771$	−1228.72	−	2128.21i	−0.0573948	−	0.0994106i
$772$		0			0
$773$	3278.11	+	5677.84i	0.152529	+	0.264189i	0.932157	−	0.362055i	$-0.117925\pi$
$773$	3278.11	+	5677.84i	0.152529	+	0.264189i	−0.779627	+	0.626244i	$0.784591\pi$
$774$		0			0
$775$	−19708.2			−0.913472
$776$		0			0
$777$	608.143	−	1053.33i	0.0280785	−	0.0486334i
$778$		0			0
$779$	−3270.09			−0.150402
$780$		0			0
$781$	40903.8			1.87407
$782$		0			0
$783$	−793.824	+	1374.94i	−0.0362311	+	0.0627541i
$784$		0			0
$785$	−4022.93			−0.182910
$786$		0			0
$787$	−5240.67	−	9077.10i	−0.237369	−	0.411136i	0.722589	−	0.691278i	$-0.242952\pi$
$787$	−5240.67	−	9077.10i	−0.237369	−	0.411136i	−0.959959	+	0.280142i	$0.909618\pi$
$788$		0			0
$789$	−331.106	−	573.492i	−0.0149400	−	0.0258769i
$790$		0			0
$791$	14637.3	−	25352.6i	0.657957	−	1.13961i
$792$		0			0
$793$	−36745.8	+	9092.24i	−1.64550	+	0.407156i
$794$		0			0
$795$	−3495.46	+	6054.31i	−0.155938	+	0.270093i
$796$		0			0
$797$	1047.41	+	1814.16i	0.0465508	+	0.0806284i	0.888362	−	0.459144i	$-0.151844\pi$
$797$	1047.41	+	1814.16i	0.0465508	+	0.0806284i	−0.841811	+	0.539772i	$0.818510\pi$
$798$		0			0
$799$	13141.0	+	22760.9i	0.581847	+	1.00779i
$800$		0			0
$801$	−21570.6			−0.951508
$802$		0			0
$803$	−15129.9	+	26205.8i	−0.664911	+	1.15166i
$804$		0			0
$805$	20289.8			0.888350
$806$		0			0
$807$	194.415			0.00848044
$808$		0			0
$809$	−14326.1	+	24813.5i	−0.622594	+	1.07837i	0.366406	+	0.930455i	$0.380588\pi$
$809$	−14326.1	+	24813.5i	−0.622594	+	1.07837i	−0.989001	+	0.147910i	$0.952745\pi$
$810$		0			0
$811$	13299.6			0.575845			0.287923	−	0.957654i	$-0.407035\pi$
$811$	13299.6			0.575845			0.287923	+	0.957654i	$0.407035\pi$
$812$		0			0
$813$	−4250.10	−	7361.39i	−0.183343	−	0.317559i
$814$		0			0
$815$	−16007.4	−	27725.7i	−0.687995	−	1.19164i
$816$		0			0
$817$	−1138.49	+	1971.92i	−0.0487522	+	0.0844414i
$818$		0			0
$819$	−21166.7	−	21997.1i	−0.903081	−	0.938510i
$820$		0			0
$821$	16726.6	−	28971.3i	0.711038	−	1.23155i	−0.253430	−	0.967354i	$-0.581559\pi$
$821$	16726.6	−	28971.3i	0.711038	−	1.23155i	0.964468	−	0.264200i	$-0.0851078\pi$
$822$		0			0
$823$	−4275.00	−	7404.52i	−0.181066	−	0.313615i	0.761178	−	0.648543i	$-0.224621\pi$
$823$	−4275.00	−	7404.52i	−0.181066	−	0.313615i	−0.942244	+	0.334928i	$0.891288\pi$
$824$		0			0
$825$	2526.29	+	4375.66i	0.106611	+	0.184656i
$826$		0			0
$827$	−11423.5			−0.480333			−0.240167	−	0.970732i	$-0.577202\pi$
$827$	−11423.5			−0.480333			−0.240167	+	0.970732i	$0.577202\pi$
$828$		0			0
$829$	−7274.46	+	12599.7i	−0.304768	+	0.527873i	−0.977210	−	0.212277i	$-0.931912\pi$
$829$	−7274.46	+	12599.7i	−0.304768	+	0.527873i	0.672442	+	0.740150i	$0.265245\pi$
$830$		0			0
$831$	−5496.37			−0.229443
$832$		0			0
$833$	−17589.4			−0.731615
$834$		0			0
$835$	15239.8	−	26396.1i	0.631611	−	1.09398i
$836$		0			0
$837$	19126.3			0.789848
$838$		0			0
$839$	9473.23	+	16408.1i	0.389812	+	0.675174i	0.992424	−	0.122860i	$-0.0392067\pi$
$839$	9473.23	+	16408.1i	0.389812	+	0.675174i	−0.602612	+	0.798034i	$0.705873\pi$
$840$		0			0
$841$	11890.3	+	20594.7i	0.487529	+	0.844424i
$842$		0			0
$843$	−4678.50	+	8103.40i	−0.191146	+	0.331074i
$844$		0			0
$845$	−25714.0	−	16195.6i	−1.04685	−	0.659344i
$846$		0			0
$847$	32292.1	−	55931.5i	1.31000	−	2.26898i
$848$		0			0
$849$	1473.16	+	2551.59i	0.0595510	+	0.103145i
$850$		0			0
$851$	1114.96	+	1931.17i	0.0449124	+	0.0777905i
$852$		0			0
$853$	44528.2			1.78736			0.893679	−	0.448707i	$-0.148115\pi$
$853$	44528.2			1.78736			0.893679	+	0.448707i	$0.148115\pi$
$854$		0			0
$855$	4936.76	−	8550.72i	0.197466	−	0.342022i
$856$		0			0
$857$	3613.56			0.144034			0.0720169	−	0.997403i	$-0.477056\pi$
$857$	3613.56			0.144034			0.0720169	+	0.997403i	$0.477056\pi$
$858$		0			0
$859$	−13773.8			−0.547095			−0.273548	−	0.961858i	$-0.588197\pi$
$859$	−13773.8			−0.547095			−0.273548	+	0.961858i	$0.588197\pi$
$860$		0			0
$861$	−1829.24	+	3168.34i	−0.0724047	+	0.125409i
$862$		0			0
$863$	1110.05			0.0437849			0.0218925	−	0.999760i	$-0.493031\pi$
$863$	1110.05			0.0437849			0.0218925	+	0.999760i	$0.493031\pi$
$864$		0			0
$865$	−25267.8	−	43765.1i	−0.993216	−	1.72030i
$866$		0			0
$867$	1031.90	+	1787.30i	0.0404210	+	0.0700113i
$868$		0			0
$869$	−38536.0	+	66746.2i	−1.50431	+	2.60554i
$870$		0			0
$871$	−59.9167	−	62.2672i	−0.00233088	−	0.00242232i
$872$		0			0
$873$	−9156.53	+	15859.6i	−0.354985	+	0.614851i
$874$		0			0
$875$	−10365.1	−	17953.0i	−0.400464	−	0.693623i
$876$		0			0
$877$	−8606.62	−	14907.1i	−0.331385	−	0.573976i	0.651398	−	0.758736i	$-0.274183\pi$
$877$	−8606.62	−	14907.1i	−0.331385	−	0.573976i	−0.982784	+	0.184760i	$0.940849\pi$
$878$		0			0
$879$	−3472.88			−0.133262
$880$		0			0
$881$	−7567.74	+	13107.7i	−0.289403	+	0.501260i	−0.973667	−	0.227974i	$-0.926790\pi$
$881$	−7567.74	+	13107.7i	−0.289403	+	0.501260i	0.684265	+	0.729234i	$0.260123\pi$
$882$		0			0
$883$	23884.1			0.910266			0.455133	−	0.890424i	$-0.349592\pi$
$883$	23884.1			0.910266			0.455133	+	0.890424i	$0.349592\pi$
$884$		0			0
$885$	142.088			0.00539688
$886$		0			0
$887$	−4591.78	+	7953.19i	−0.173818	+	0.301062i	−0.939752	−	0.341858i	$-0.888944\pi$
$887$	−4591.78	+	7953.19i	−0.173818	+	0.301062i	0.765933	+	0.642920i	$0.222277\pi$
$888$		0			0
$889$	63705.3			2.40338
$890$		0			0
$891$	18931.4	+	32790.2i	0.711814	+	1.23290i
$892$		0			0
$893$	−6473.47	−	11212.4i	−0.242583	−	0.420165i
$894$		0			0
$895$	−15885.9	+	27515.1i	−0.593303	+	1.02763i
$896$		0			0
$897$	−3203.80	+	792.734i	−0.119255	+	0.0295080i
$898$		0			0
$899$	−3664.26	+	6346.68i	−0.135940	+	0.235455i
$900$		0			0
$901$	11712.6	+	20286.8i	0.433078	+	0.750113i
$902$		0			0
$903$	1273.71	+	2206.13i	0.0469395	+	0.0813015i
$904$		0			0
$905$	51099.8			1.87692
$906$		0			0
$907$	6376.01	−	11043.6i	0.233420	−	0.404295i	−0.725392	−	0.688336i	$-0.758342\pi$
$907$	6376.01	−	11043.6i	0.233420	−	0.404295i	0.958812	+	0.284040i	$0.0916750\pi$
$908$		0			0
$909$	31217.5			1.13907
$910$		0			0
$911$	−15783.7			−0.574027			−0.287014	−	0.957926i	$-0.592663\pi$
$911$	−15783.7			−0.574027			−0.287014	+	0.957926i	$0.592663\pi$
$912$		0			0
$913$	−13622.0	+	23594.0i	−0.493781	+	0.855253i
$914$		0			0
$915$	−13697.5			−0.494891
$916$		0			0
$917$	−5068.40	−	8778.73i	−0.182523	−	0.316139i
$918$		0			0
$919$	26544.7	+	45976.8i	0.952806	+	1.65031i	0.739311	+	0.673364i	$0.235151\pi$
$919$	26544.7	+	45976.8i	0.952806	+	1.65031i	0.213495	+	0.976944i	$0.431515\pi$
$920$		0			0
$921$	4535.17	−	7855.14i	0.162257	−	0.281038i
$922$		0			0
$923$	−29958.3	+	7412.77i	−1.06835	+	0.264349i
$924$		0			0
$925$	−1287.84	+	2230.61i	−0.0457773	+	0.0792886i
$926$		0			0
$927$	10691.6	+	18518.4i	0.378812	+	0.656121i
$928$		0			0
$929$	24382.3	+	42231.4i	0.861096	+	1.49146i	0.870872	+	0.491510i	$0.163555\pi$
$929$	24382.3	+	42231.4i	0.861096	+	1.49146i	−0.00977577	+	0.999952i	$0.503112\pi$
$930$		0			0
$931$	8664.78			0.305023
$932$		0			0
$933$	−3163.74	+	5479.77i	−0.111014	+	0.192282i
$934$		0			0
$935$	48836.1			1.70814
$936$		0			0
$937$	−30351.0			−1.05819			−0.529095	−	0.848562i	$-0.677469\pi$
$937$	−30351.0			−1.05819			−0.529095	+	0.848562i	$0.677469\pi$
$938$		0			0
$939$	−2332.60	+	4040.18i	−0.0810666	+	0.140411i
$940$		0			0
$941$	9796.43			0.339378			0.169689	−	0.985498i	$-0.445724\pi$
$941$	9796.43			0.339378			0.169689	+	0.985498i	$0.445724\pi$
$942$		0			0
$943$	−3353.72	−	5808.81i	−0.115813	−	0.200595i
$944$		0			0
$945$	−11371.9	−	19696.8i	−0.391459	−	0.678027i
$946$		0			0
$947$	−986.513	+	1708.69i	−0.0338515	+	0.0586325i	−0.882455	−	0.470397i	$-0.844111\pi$
$947$	−986.513	+	1708.69i	−0.0338515	+	0.0586325i	0.848603	+	0.529030i	$0.177444\pi$
$948$		0			0
$949$	6332.17	−	21935.3i	0.216598	−	0.750316i
$950$		0			0
$951$	4737.36	−	8205.34i	0.161534	−	0.279786i
$952$		0			0
$953$	2765.13	+	4789.35i	0.0939888	+	0.162793i	0.909186	−	0.416390i	$-0.136705\pi$
$953$	2765.13	+	4789.35i	0.0939888	+	0.162793i	−0.815197	+	0.579183i	$0.803372\pi$
$954$		0			0
$955$	−32185.6	−	55747.1i	−1.09058	−	1.88894i
$956$		0			0
$957$	1878.80			0.0634619
$958$		0			0
$959$	20349.9	−	35247.1i	0.685227	−	1.18685i
$960$		0			0
$961$	58495.4			1.96353
$962$		0			0
$963$	42849.7			1.43387
$964$		0			0
$965$	−16164.3	+	27997.4i	−0.539220	+	0.933957i
$966$		0			0
$967$	−30916.7			−1.02814			−0.514072	−	0.857747i	$-0.671864\pi$
$967$	−30916.7			−1.02814			−0.514072	+	0.857747i	$0.671864\pi$
$968$		0			0
$969$	975.485	+	1689.59i	0.0323396	+	0.0560139i
$970$		0			0
$971$	9462.74	+	16389.9i	0.312743	+	0.541687i	0.978955	−	0.204075i	$-0.0654187\pi$
$971$	9462.74	+	16389.9i	0.312743	+	0.541687i	−0.666212	+	0.745762i	$0.732085\pi$
$972$		0			0
$973$	−36224.3	+	62742.3i	−1.19352	+	2.06724i
$974$		0			0
$975$	−2643.26	−	2746.95i	−0.0868225	−	0.0902286i
$976$		0			0
$977$	12526.0	−	21695.6i	0.410176	−	0.710445i	−0.584733	−	0.811226i	$-0.698801\pi$
$977$	12526.0	−	21695.6i	0.410176	−	0.710445i	0.994909	+	0.100781i	$0.0321340\pi$
$978$		0			0
$979$	26279.0	+	45516.5i	0.857895	+	1.48592i
$980$		0			0
$981$	11777.8	+	20399.7i	0.383318	+	0.663927i
$982$		0			0
$983$	−22680.6			−0.735909			−0.367954	−	0.929844i	$-0.619942\pi$
$983$	−22680.6			−0.735909			−0.367954	+	0.929844i	$0.619942\pi$
$984$		0			0
$985$	24330.8	−	42142.2i	0.787050	−	1.36321i
$986$		0			0
$987$	−14484.7			−0.467125
$988$		0			0
$989$	−4670.41			−0.150162
$990$		0			0
$991$	−10294.5	+	17830.7i	−0.329986	+	0.571553i	−0.982509	−	0.186216i	$-0.940378\pi$
$991$	−10294.5	+	17830.7i	−0.329986	+	0.571553i	0.652522	+	0.757770i	$0.273711\pi$
$992$		0			0
$993$	9239.70			0.295280
$994$		0			0
$995$	7524.34	+	13032.5i	0.239736	+	0.415235i
$996$		0			0
$997$	−15218.4	−	26359.0i	−0.483420	−	0.837309i	0.516398	−	0.856349i	$-0.327272\pi$
$997$	−15218.4	−	26359.0i	−0.483420	−	0.837309i	−0.999819	+	0.0190397i	$0.993939\pi$
$998$		0			0
$999$	1249.82	−	2164.75i	0.0395820	−	0.0685581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.4.i.d.321.2	yes	8
4.3	odd	2	inner	416.4.i.d.321.3	yes	8
13.3	even	3	inner	416.4.i.d.289.2	✓	8
52.3	odd	6	inner	416.4.i.d.289.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.4.i.d.289.2	✓	8	13.3	even	3	inner
416.4.i.d.289.3	yes	8	52.3	odd	6	inner
416.4.i.d.321.2	yes	8	1.1	even	1	trivial
416.4.i.d.321.3	yes	8	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	416.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.613091 + 1.06190i) q^{3} +13.8322 q^{5} +(12.7720 + 22.1218i) q^{7} +(12.7482 + 22.0806i) q^{9} +(31.0618 - 53.8007i) q^{11} +(-13.0000 + 45.0333i) q^{13} +(-8.48037 + 14.6884i) q^{15} +(28.4161 + 49.2181i) q^{17} +(-13.9982 - 24.2456i) q^{19} -31.3216 q^{21} +(28.7124 - 49.7313i) q^{23} +66.3286 q^{25} -64.3702 q^{27} +(12.3322 - 21.3599i) q^{29} -297.130 q^{31} +(38.0874 + 65.9694i) q^{33} +(176.664 + 305.992i) q^{35} +(-19.4161 + 33.6296i) q^{37} +(-39.8509 - 41.4143i) q^{39} +(58.4020 - 101.155i) q^{41} +(-40.6655 - 70.4347i) q^{43} +(176.336 + 305.422i) q^{45} +462.450 q^{47} +(-154.748 + 268.032i) q^{49} -69.6865 q^{51} +412.182 q^{53} +(429.652 - 744.179i) q^{55} +34.3286 q^{57} +(-4.18873 - 7.25510i) q^{59} +(403.800 + 699.403i) q^{61} +(-325.641 + 564.027i) q^{63} +(-179.818 + 622.908i) q^{65} +(-0.921795 + 1.59660i) q^{67} +(35.2066 + 60.9796i) q^{69} +(329.212 + 570.213i) q^{71} -487.090 q^{73} +(-40.6655 + 70.4347i) q^{75} +1586.89 q^{77} -1240.62 q^{79} +(-304.738 + 527.821i) q^{81} -438.544 q^{83} +(393.056 + 680.793i) q^{85} +(15.1215 + 26.1911i) q^{87} +(-423.011 + 732.676i) q^{89} +(-1162.25 + 287.583i) q^{91} +(182.168 - 315.524i) q^{93} +(-193.625 - 335.369i) q^{95} +(359.129 + 622.030i) q^{97} +1583.93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{5} - 40 q^{9} - 104 q^{13} + 180 q^{17} + 696 q^{21} + 152 q^{25} + 4 q^{29} + 636 q^{33} - 108 q^{37} - 716 q^{41} + 1600 q^{45} - 1096 q^{49} + 4528 q^{53} - 104 q^{57} + 580 q^{61} - 208 q^{65}+ \cdots - 156 q^{97}+O(q^{100}) \) 8 * q + 16 * q^5 - 40 * q^9 - 104 * q^13 + 180 * q^17 + 696 * q^21 + 152 * q^25 + 4 * q^29 + 636 * q^33 - 108 * q^37 - 716 * q^41 + 1600 * q^45 - 1096 * q^49 + 4528 * q^53 - 104 * q^57 + 580 * q^61 - 208 * q^65 + 3500 * q^69 + 2256 * q^73 + 3608 * q^77 - 1444 * q^81 + 920 * q^85 - 4236 * q^89 + 1552 * q^93 - 156 * q^97

Introduction

L-functions

Modular forms

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Database

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