LMFDB - Embedded newform 336.2.bo.a.101.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			101.54
Character	$\chi$	$=$	336.101
Dual form			336.2.bo.a.173.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32786 + 0.486611i) q^{2} +(-0.388759 + 1.68786i) q^{3} +(1.52642 + 1.29230i) q^{4} +(-0.224285 + 0.837045i) q^{5} +(-1.33755 + 2.05206i) q^{6} +(2.27219 + 1.35541i) q^{7} +(1.39802 + 2.45877i) q^{8} +(-2.69773 - 1.31234i) q^{9} +O(q^{10})$	\(q+(1.32786 + 0.486611i) q^{2} +(-0.388759 + 1.68786i) q^{3} +(1.52642 + 1.29230i) q^{4} +(-0.224285 + 0.837045i) q^{5} +(-1.33755 + 2.05206i) q^{6} +(2.27219 + 1.35541i) q^{7} +(1.39802 + 2.45877i) q^{8} +(-2.69773 - 1.31234i) q^{9} +(-0.705135 + 1.00234i) q^{10} +(-1.49644 - 5.58477i) q^{11} +(-2.77463 + 2.07398i) q^{12} +(-0.124223 - 0.124223i) q^{13} +(2.35759 + 2.90547i) q^{14} +(-1.32562 - 0.703971i) q^{15} +(0.659908 + 3.94519i) q^{16} +(-1.74467 + 3.02186i) q^{17} +(-2.94361 - 3.05535i) q^{18} +(0.346550 - 1.29334i) q^{19} +(-1.42407 + 0.987836i) q^{20} +(-3.17108 + 3.30821i) q^{21} +(0.730559 - 8.14397i) q^{22} +(-1.74815 - 3.02788i) q^{23} +(-4.69355 + 1.40379i) q^{24} +(3.67979 + 2.12453i) q^{25} +(-0.104502 - 0.225398i) q^{26} +(3.26381 - 4.04321i) q^{27} +(1.71672 + 5.00528i) q^{28} +(1.99563 + 1.99563i) q^{29} +(-1.41768 - 1.57984i) q^{30} +(4.42641 + 2.55559i) q^{31} +(-1.04351 + 5.55977i) q^{32} +(10.0081 - 0.354641i) q^{33} +(-3.78715 + 3.16363i) q^{34} +(-1.64416 + 1.59793i) q^{35} +(-2.42193 - 5.48947i) q^{36} +(2.82045 - 10.5261i) q^{37} +(1.08952 - 1.54874i) q^{38} +(0.257963 - 0.161378i) q^{39} +(-2.37165 + 0.618739i) q^{40} +7.85681i q^{41} +(-5.82056 + 2.84976i) q^{42} +(-4.53143 - 4.53143i) q^{43} +(4.93303 - 10.4585i) q^{44} +(1.70355 - 1.96378i) q^{45} +(-0.847893 - 4.87127i) q^{46} +(-5.88144 - 10.1870i) q^{47} +(-6.91547 - 0.419895i) q^{48} +(3.32573 + 6.15951i) q^{49} +(3.85242 + 4.61170i) q^{50} +(-4.42221 - 4.11953i) q^{51} +(-0.0290825 - 0.350149i) q^{52} +(-1.64946 - 6.15586i) q^{53} +(6.30135 - 3.78060i) q^{54} +5.01033 q^{55} +(-0.156068 + 7.48169i) q^{56} +(2.04825 + 1.08772i) q^{57} +(1.67882 + 3.62101i) q^{58} +(7.87208 - 2.10932i) q^{59} +(-1.11371 - 2.78766i) q^{60} +(0.443640 - 1.65569i) q^{61} +(4.63407 + 5.54740i) q^{62} +(-4.35101 - 6.63843i) q^{63} +(-4.09108 + 6.87481i) q^{64} +(0.131841 - 0.0761186i) q^{65} +(13.4619 + 4.39912i) q^{66} +(0.813578 + 3.03632i) q^{67} +(-6.56825 + 2.35798i) q^{68} +(5.79025 - 1.77351i) q^{69} +(-2.96078 + 1.32176i) q^{70} +1.67369 q^{71} +(-0.544744 - 8.46778i) q^{72} +(-5.43870 + 9.42010i) q^{73} +(8.86726 - 12.6047i) q^{74} +(-5.01645 + 5.38503i) q^{75} +(2.20037 - 1.52633i) q^{76} +(4.16947 - 14.7180i) q^{77} +(0.421066 - 0.0887590i) q^{78} +(1.17913 + 2.04231i) q^{79} +(-3.45031 - 0.332476i) q^{80} +(5.55553 + 7.08069i) q^{81} +(-3.82321 + 10.4327i) q^{82} +(-3.05874 + 3.05874i) q^{83} +(-9.11560 + 0.951729i) q^{84} +(-2.13813 - 2.13813i) q^{85} +(-3.81205 - 8.22214i) q^{86} +(-4.14416 + 2.59252i) q^{87} +(11.6396 - 11.4870i) q^{88} +(6.91129 - 3.99023i) q^{89} +(3.21767 - 1.77866i) q^{90} +(-0.113885 - 0.450630i) q^{91} +(1.24453 - 6.88095i) q^{92} +(-6.03428 + 6.47765i) q^{93} +(-2.85264 - 16.3888i) q^{94} +(1.00486 + 0.580155i) q^{95} +(-8.97844 - 3.92271i) q^{96} -5.88553i q^{97} +(1.41881 + 9.79729i) q^{98} +(-3.29214 + 17.0301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.32786	+	0.486611i	0.938938	+	0.344086i
$2$	1.32786	+	0.486611i	0.938938	+	0.344086i
$3$	−0.388759	+	1.68786i	−0.224450	+	0.974486i
$3$	−0.388759	+	1.68786i	−0.224450	+	0.974486i
$4$	1.52642	+	1.29230i	0.763209	+	0.646151i
$5$	−0.224285	+	0.837045i	−0.100304	+	0.374338i	−0.997770	−	0.0667446i	$-0.978739\pi$
$5$	−0.224285	+	0.837045i	−0.100304	+	0.374338i	0.897467	+	0.441082i	$0.145405\pi$
$6$	−1.33755	+	2.05206i	−0.546052	+	0.837751i
$7$	2.27219	+	1.35541i	0.858808	+	0.512297i
$7$	2.27219	+	1.35541i	0.858808	+	0.512297i
$8$	1.39802	+	2.45877i	0.494275	+	0.869306i
$9$	−2.69773	−	1.31234i	−0.899244	−	0.437447i
$10$	−0.705135	+	1.00234i	−0.222983	+	0.316967i
$11$	−1.49644	−	5.58477i	−0.451192	−	1.68387i	−0.699048	−	0.715075i	$-0.746392\pi$
$11$	−1.49644	−	5.58477i	−0.451192	−	1.68387i	0.247855	−	0.968797i	$-0.420274\pi$
$12$	−2.77463	+	2.07398i	−0.800967	+	0.598708i
$13$	−0.124223	−	0.124223i	−0.0344532	−	0.0344532i	0.689670	−	0.724123i	$-0.257755\pi$
$13$	−0.124223	−	0.124223i	−0.0344532	−	0.0344532i	−0.724123	+	0.689670i	$0.757755\pi$
$14$	2.35759	+	2.90547i	0.630094	+	0.776519i
$15$	−1.32562	−	0.703971i	−0.342274	−	0.181764i
$16$	0.659908	+	3.94519i	0.164977	+	0.986297i
$17$	−1.74467	+	3.02186i	−0.423145	+	0.732908i	−0.996245	−	0.0865769i	$-0.972407\pi$
$17$	−1.74467	+	3.02186i	−0.423145	+	0.732908i	0.573100	+	0.819485i	$0.305741\pi$
$18$	−2.94361	−	3.05535i	−0.693815	−	0.720153i
$19$	0.346550	−	1.29334i	0.0795039	−	0.296713i	−0.914713	−	0.404104i	$-0.867583\pi$
$19$	0.346550	−	1.29334i	0.0795039	−	0.296713i	0.994217	+	0.107392i	$0.0342499\pi$
$20$	−1.42407	+	0.987836i	−0.318431	+	0.220887i
$21$	−3.17108	+	3.30821i	−0.691986	+	0.721911i
$22$	0.730559	−	8.14397i	0.155756	−	1.73630i
$23$	−1.74815	−	3.02788i	−0.364514	−	0.631357i	0.624184	−	0.781278i	$-0.285432\pi$
$23$	−1.74815	−	3.02788i	−0.364514	−	0.631357i	−0.988698	+	0.149920i	$0.952098\pi$
$24$	−4.69355	+	1.40379i	−0.958066	+	0.286548i
$25$	3.67979	+	2.12453i	0.735957	+	0.424905i
$26$	−0.104502	−	0.225398i	−0.0204945	−	0.0442042i
$27$	3.26381	−	4.04321i	0.628121	−	0.778116i
$28$	1.71672	+	5.00528i	0.324429	+	0.945910i
$29$	1.99563	+	1.99563i	0.370579	+	0.370579i	0.867688	−	0.497109i	$-0.165605\pi$
$29$	1.99563	+	1.99563i	0.370579	+	0.370579i	−0.497109	+	0.867688i	$0.665605\pi$
$30$	−1.41768	−	1.57984i	−0.258831	−	0.288437i
$31$	4.42641	+	2.55559i	0.795007	+	0.458997i	0.841722	−	0.539911i	$-0.181542\pi$
$31$	4.42641	+	2.55559i	0.795007	+	0.458997i	−0.0467155	+	0.998908i	$0.514875\pi$
$32$	−1.04351	+	5.55977i	−0.184468	+	0.982839i
$33$	10.0081	−	0.354641i	1.74218	−	0.0617351i
$34$	−3.78715	+	3.16363i	−0.649490	+	0.542557i
$35$	−1.64416	+	1.59793i	−0.277914	+	0.270099i
$36$	−2.42193	−	5.48947i	−0.403655	−	0.914911i
$37$	2.82045	−	10.5261i	0.463679	−	1.73047i	−0.197553	−	0.980292i	$-0.563299\pi$
$37$	2.82045	−	10.5261i	0.463679	−	1.73047i	0.661232	−	0.750181i	$-0.270034\pi$
$38$	1.08952	−	1.54874i	0.176744	−	0.251239i
$39$	0.257963	−	0.161378i	0.0413071	−	0.0258411i
$40$	−2.37165	+	0.618739i	−0.374992	+	0.0978313i
$41$			7.85681i			1.22703i	0.789684	+	0.613513i	$0.210244\pi$
$41$			7.85681i			1.22703i	−0.789684	+	0.613513i	$0.789756\pi$
$42$	−5.82056	+	2.84976i	−0.898131	+	0.439727i
$43$	−4.53143	−	4.53143i	−0.691037	−	0.691037i	0.271423	−	0.962460i	$-0.412506\pi$
$43$	−4.53143	−	4.53143i	−0.691037	−	0.691037i	−0.962460	+	0.271423i	$0.912506\pi$
$44$	4.93303	−	10.4585i	0.743682	−	1.57669i
$45$	1.70355	−	1.96378i	0.253950	−	0.292744i
$46$	−0.847893	−	4.87127i	−0.125015	−	0.718230i
$47$	−5.88144	−	10.1870i	−0.857897	−	1.48592i	−0.873932	−	0.486049i	$-0.838438\pi$
$47$	−5.88144	−	10.1870i	−0.857897	−	1.48592i	0.0160351	−	0.999871i	$-0.494896\pi$
$48$	−6.91547	−	0.419895i	−0.998162	−	0.0606067i
$49$	3.32573	+	6.15951i	0.475104	+	0.879930i
$50$	3.85242	+	4.61170i	0.544814	+	0.652192i
$51$	−4.42221	−	4.11953i	−0.619234	−	0.576850i
$52$	−0.0290825	−	0.350149i	−0.00403302	−	0.0485569i
$53$	−1.64946	−	6.15586i	−0.226571	−	0.845573i	−0.981769	−	0.190077i	$-0.939126\pi$
$53$	−1.64946	−	6.15586i	−0.226571	−	0.845573i	0.755199	−	0.655496i	$-0.227540\pi$
$54$	6.30135	−	3.78060i	0.857506	−	0.514475i
$55$	5.01033			0.675593
$56$	−0.156068	+	7.48169i	−0.0208555	+	0.999783i
$57$	2.04825	+	1.08772i	0.271298	+	0.144073i
$58$	1.67882	+	3.62101i	0.220440	+	0.475462i
$59$	7.87208	−	2.10932i	1.02486	−	0.274610i	0.293033	−	0.956102i	$-0.405336\pi$
$59$	7.87208	−	2.10932i	1.02486	−	0.274610i	0.731825	+	0.681493i	$0.238669\pi$
$60$	−1.11371	−	2.78766i	−0.143779	−	0.359885i
$61$	0.443640	−	1.65569i	0.0568022	−	0.211989i	−0.931692	−	0.363250i	$-0.881667\pi$
$61$	0.443640	−	1.65569i	0.0568022	−	0.211989i	0.988494	+	0.151262i	$0.0483336\pi$
$62$	4.63407	+	5.54740i	0.588527	+	0.704521i
$63$	−4.35101	−	6.63843i	−0.548176	−	0.836363i
$64$	−4.09108	+	6.87481i	−0.511385	+	0.859352i
$65$	0.131841	−	0.0761186i	0.0163529	−	0.00944135i
$66$	13.4619	+	4.39912i	1.65704	+	0.541494i
$67$	0.813578	+	3.03632i	0.0993944	+	0.370945i	0.997649	−	0.0685304i	$-0.0218310\pi$
$67$	0.813578	+	3.03632i	0.0993944	+	0.370945i	−0.898255	+	0.439475i	$0.855164\pi$
$68$	−6.56825	+	2.35798i	−0.796518	+	0.285947i
$69$	5.79025	−	1.77351i	0.697064	−	0.213506i
$70$	−2.96078	+	1.32176i	−0.353881	+	0.157980i
$71$	1.67369			0.198631			0.0993154	−	0.995056i	$-0.468335\pi$
$71$	1.67369			0.198631			0.0993154	+	0.995056i	$0.468335\pi$
$72$	−0.544744	−	8.46778i	−0.0641987	−	0.997937i
$73$	−5.43870	+	9.42010i	−0.636551	+	1.10254i	0.349633	+	0.936887i	$0.386306\pi$
$73$	−5.43870	+	9.42010i	−0.636551	+	1.10254i	−0.986184	+	0.165652i	$0.947027\pi$
$74$	8.86726	−	12.6047i	1.03080	−	1.46526i
$75$	−5.01645	+	5.38503i	−0.579250	+	0.621810i
$76$	2.20037	−	1.52633i	0.252399	−	0.175082i
$77$	4.16947	−	14.7180i	0.475155	−	1.67727i
$78$	0.421066	−	0.0887590i	0.0476764	−	0.0100500i
$79$	1.17913	+	2.04231i	0.132662	+	0.229778i	0.924702	−	0.380692i	$-0.124314\pi$
$79$	1.17913	+	2.04231i	0.132662	+	0.229778i	−0.792040	+	0.610470i	$0.790981\pi$
$80$	−3.45031	−	0.332476i	−0.385756	−	0.0371719i
$81$	5.55553	+	7.08069i	0.617281	+	0.786743i
$82$	−3.82321	+	10.4327i	−0.422203	+	1.15210i
$83$	−3.05874	+	3.05874i	−0.335740	+	0.335740i	−0.854761	−	0.519021i	$-0.826297\pi$
$83$	−3.05874	+	3.05874i	−0.335740	+	0.335740i	0.519021	+	0.854761i	$0.326297\pi$
$84$	−9.11560	+	0.951729i	−0.994594	+	0.103842i
$85$	−2.13813	−	2.13813i	−0.231912	−	0.231912i
$86$	−3.81205	−	8.22214i	−0.411064	−	0.886617i
$87$	−4.14416	+	2.59252i	−0.444301	+	0.277948i
$88$	11.6396	−	11.4870i	1.24079	−	1.22452i
$89$	6.91129	−	3.99023i	0.732595	−	0.422964i	−0.0867758	−	0.996228i	$-0.527656\pi$
$89$	6.91129	−	3.99023i	0.732595	−	0.422964i	0.819371	+	0.573264i	$0.194323\pi$
$90$	3.21767	−	1.77866i	0.339173	−	0.187487i
$91$	−0.113885	−	0.450630i	−0.0119384	−	0.0472389i
$92$	1.24453	−	6.88095i	0.129752	−	0.717389i
$93$	−6.03428	+	6.47765i	−0.625726	+	0.671701i
$94$	−2.85264	−	16.3888i	−0.294227	−	1.69038i
$95$	1.00486	+	0.580155i	0.103096	+	0.0595227i
$96$	−8.97844	−	3.92271i	−0.916358	−	0.400360i
$97$		−	5.88553i		−	0.597585i	−0.954318	−	0.298793i	$-0.903416\pi$
$97$		−	5.88553i		−	0.597585i	0.954318	−	0.298793i	$-0.0965839\pi$
$98$	1.41881	+	9.79729i	0.143321	+	0.989676i
$99$	−3.29214	+	17.0301i	−0.330872	+	1.71158i
$100$	2.87137	+	7.99831i	0.287137	+	0.799831i
$101$	−16.7380	+	4.48492i	−1.66549	+	0.446267i	−0.963889	−	0.266304i	$-0.914197\pi$
$101$	−16.7380	+	4.48492i	−1.66549	+	0.446267i	−0.701600	+	0.712571i	$0.747531\pi$
$102$	−3.86746	−	7.62206i	−0.382936	−	0.754696i
$103$	−8.51730	−	14.7524i	−0.839234	−	1.45360i	−0.890536	−	0.454913i	$-0.849670\pi$
$103$	−8.51730	−	14.7524i	−0.839234	−	1.45360i	0.0513016	−	0.998683i	$-0.483663\pi$
$104$	0.131769	−	0.479100i	0.0129210	−	0.0469796i
$105$	−2.05790	−	3.39632i	−0.200830	−	0.331447i
$106$	0.805265	−	8.97676i	0.0782142	−	0.871900i
$107$	0.245411	+	0.0657577i	0.0237248	+	0.00635704i	0.270662	−	0.962674i	$-0.412757\pi$
$107$	0.245411	+	0.0657577i	0.0237248	+	0.00635704i	−0.246937	+	0.969032i	$0.579424\pi$
$108$	10.2070	−	1.95380i	0.982168	−	0.188004i
$109$	2.61921	+	9.77503i	0.250875	+	0.936278i	0.970339	+	0.241748i	$0.0777209\pi$
$109$	2.61921	+	9.77503i	0.250875	+	0.936278i	−0.719464	+	0.694530i	$0.755612\pi$
$110$	6.65302	+	2.43809i	0.634340	+	0.232462i
$111$	16.6700	+	8.85262i	1.58225	+	0.840253i
$112$	−3.84791	+	9.85868i	−0.363593	+	0.931558i
$113$		−	2.44101i		−	0.229631i	−0.993387	−	0.114816i	$-0.963372\pi$
$113$		−	2.44101i		−	0.229631i	0.993387	−	0.114816i	$-0.0366277\pi$
$114$	2.19049	+	2.44105i	0.205158	+	0.228625i
$115$	2.92656	−	0.784169i	0.272903	−	0.0731241i
$116$	0.467210	+	5.62513i	0.0433793	+	0.522280i
$117$	0.172097	+	0.498142i	0.0159104	+	0.0460532i
$118$	11.4794	+	1.02977i	1.05677	+	0.0947978i
$119$	−8.06009	+	4.50150i	−0.738867	+	0.412652i
$120$	−0.122342	−	4.24356i	−0.0111683	−	0.387382i
$121$	−19.4241	+	11.2145i	−1.76583	+	1.01950i
$122$	1.39477	−	1.98264i	0.126276	−	0.179500i
$123$	−13.2612	−	3.05440i	−1.19572	−	0.275406i
$124$	3.45396	+	9.62116i	0.310175	+	0.864006i
$125$	−5.66744	+	5.66744i	−0.506912	+	0.506912i
$126$	−2.54720	−	10.9321i	−0.226922	−	0.973913i
$127$	10.2896			0.913058			0.456529	−	0.889708i	$-0.349092\pi$
$127$	10.2896			0.913058			0.456529	+	0.889708i	$0.349092\pi$
$128$	−8.77774	+	7.13801i	−0.775850	+	0.630917i
$129$	9.41005	−	5.88678i	0.828508	−	0.518302i
$130$	0.212107	−	0.0369193i	0.0186030	−	0.00323804i
$131$	−11.0289	−	2.95518i	−0.963597	−	0.258195i	−0.257475	−	0.966285i	$-0.582890\pi$
$131$	−11.0289	−	2.95518i	−0.963597	−	0.258195i	−0.706122	+	0.708090i	$0.749557\pi$
$132$	15.7348	+	12.3921i	1.36954	+	1.07859i
$133$	2.54043	−	2.46900i	0.220284	−	0.214090i
$134$	−0.397188	+	4.42769i	−0.0343119	+	0.382495i
$135$	2.65232	+	3.63879i	0.228275	+	0.313177i
$136$	−9.86913	−	0.0651232i	−0.846271	−	0.00558427i
$137$	−5.13667	+	8.89697i	−0.438855	+	0.760119i	−0.997601	−	0.0692192i	$-0.977949\pi$
$137$	−5.13667	+	8.89697i	−0.438855	+	0.760119i	0.558746	+	0.829339i	$0.311283\pi$
$138$	8.55164	+	0.462626i	0.727964	+	0.0393814i
$139$	−4.79178	+	4.79178i	−0.406434	+	0.406434i	−0.880493	−	0.474059i	$-0.842788\pi$
$139$	−4.79178	+	4.79178i	−0.406434	+	0.406434i	0.474059	+	0.880493i	$0.342788\pi$
$140$	−4.57468	+	0.314358i	−0.386631	+	0.0265681i
$141$	19.4806	−	5.96677i	1.64056	−	0.502493i
$142$	2.22243	+	0.814438i	0.186502	+	0.0683461i
$143$	−0.507864	+	0.879646i	−0.0424697	+	0.0735597i
$144$	3.39717	−	11.5091i	0.283098	−	0.959091i
$145$	−2.11802	+	1.22284i	−0.175892	+	0.101551i
$146$	−11.8057	+	9.86203i	−0.977050	+	0.816187i
$147$	−11.6893	+	3.21879i	−0.964116	+	0.265481i
$148$	17.9080	−	12.4223i	1.47203	−	1.02111i
$149$	1.58785	+	0.425463i	0.130082	+	0.0348553i	0.323272	−	0.946306i	$-0.395217\pi$
$149$	1.58785	+	0.425463i	0.130082	+	0.0348553i	−0.193191	+	0.981161i	$0.561884\pi$
$150$	−9.28155	+	4.70950i	−0.757836	+	0.384529i
$151$	−3.54744	−	2.04811i	−0.288686	−	0.166673i	0.348663	−	0.937248i	$-0.386636\pi$
$151$	−3.54744	−	2.04811i	−0.288686	−	0.166673i	−0.637349	+	0.770575i	$0.719969\pi$
$152$	3.66451	−	0.956031i	0.297231	−	0.0775443i
$153$	8.67236	−	5.86257i	0.701119	−	0.473960i
$154$	12.6984	−	17.5145i	1.02327	−	1.41136i
$155$	−3.13192	+	3.13192i	−0.251562	+	0.251562i
$156$	0.602308	+	0.0870363i	0.0482232	+	0.00696848i
$157$	−2.18986	+	0.586771i	−0.174770	+	0.0468295i	−0.345143	−	0.938550i	$-0.612169\pi$
$157$	−2.18986	+	0.586771i	−0.174770	+	0.0468295i	0.170373	+	0.985380i	$0.445503\pi$
$158$	0.571905	+	3.28568i	0.0454983	+	0.261395i
$159$	11.0315	−	0.390906i	0.874852	−	0.0310009i
$160$	−4.41974	−	2.12044i	−0.349411	−	0.167636i
$161$	0.131891	−	9.24939i	0.0103945	−	0.728954i
$162$	3.93141	+	12.1055i	0.308881	+	0.951101i
$163$	−19.3957	−	5.19707i	−1.51919	−	0.407066i	−0.599714	−	0.800214i	$-0.704719\pi$
$163$	−19.3957	−	5.19707i	−1.51919	−	0.407066i	−0.919475	+	0.393149i	$0.871386\pi$
$164$	−10.1534	+	11.9928i	−0.792845	+	0.936478i
$165$	−1.94781	+	8.45673i	−0.151637	+	0.658356i
$166$	−5.54999	+	2.57316i	−0.430763	+	0.199716i
$167$		−	7.00150i		−	0.541792i	−0.962609	−	0.270896i	$-0.912680\pi$
$167$		−	7.00150i		−	0.541792i	0.962609	−	0.270896i	$-0.0873200\pi$
$168$	−12.5674	−	3.17199i	−0.969593	−	0.244725i
$169$		−	12.9691i		−	0.997626i
$170$	−1.79869	−	3.87957i	−0.137954	−	0.297549i
$171$	−2.63220	+	3.03430i	−0.201289	+	0.232038i
$172$	−1.06088	−	12.7728i	−0.0808914	−	0.973920i
$173$	−0.119913	−	0.0321306i	−0.00911682	−	0.00244285i	0.254258	−	0.967136i	$-0.418169\pi$
$173$	−0.119913	−	0.0321306i	−0.00911682	−	0.00244285i	−0.263375	+	0.964694i	$0.584836\pi$
$174$	−6.76441	+	1.42591i	−0.512809	+	0.108098i
$175$	5.48158	+	9.81495i	0.414369	+	0.741941i
$176$	21.0455	−	9.58916i	1.58636	−	0.722810i
$177$	0.499888	+	14.1070i	0.0375739	+	1.06034i
$178$	11.1189	−	1.93536i	0.833397	−	0.145061i
$179$	16.9948	−	4.55374i	1.27025	−	0.340362i	0.440123	−	0.897937i	$-0.354935\pi$
$179$	16.9948	−	4.55374i	1.27025	−	0.340362i	0.830127	+	0.557575i	$0.188268\pi$
$180$	5.13813	−	0.796056i	0.382974	−	0.0593345i
$181$	−9.08621	+	9.08621i	−0.675372	+	0.675372i	−0.958949	−	0.283577i	$-0.908479\pi$
$181$	−9.08621	+	9.08621i	−0.675372	+	0.675372i	0.283577	+	0.958949i	$0.408479\pi$
$182$	0.0680584	−	0.653791i	0.00504482	−	0.0484622i
$183$	2.62210	+	1.39246i	0.193831	+	0.102934i
$184$	5.00092	−	8.53133i	0.368672	−	0.628938i
$185$	8.17820	+	4.72169i	0.601273	+	0.347145i
$186$	−11.1648	+	5.66505i	−0.818640	+	0.415382i
$187$	19.4872	+	5.22157i	1.42504	+	0.381839i
$188$	4.18709	−	23.1502i	0.305375	−	1.68840i
$189$	12.8962	−	4.76315i	0.938062	−	0.346468i
$190$	1.05200	+	1.25934i	0.0763201	+	0.0913621i
$191$	−12.6628	+	7.31086i	−0.916247	+	0.528996i	−0.882436	−	0.470433i	$-0.844098\pi$
$191$	−12.6628	+	7.31086i	−0.916247	+	0.528996i	−0.0338112	+	0.999428i	$0.510765\pi$
$192$	−10.0133	−	9.57781i	−0.722645	−	0.691219i
$193$	−4.14094	+	7.17232i	−0.298071	+	0.516275i	−0.975695	−	0.219135i	$-0.929677\pi$
$193$	−4.14094	+	7.17232i	−0.298071	+	0.516275i	0.677623	+	0.735409i	$0.263010\pi$
$194$	2.86397	−	7.81516i	0.205621	−	0.561095i
$195$	0.0772229	+	0.252121i	0.00553005	+	0.0180548i
$196$	−2.88350	+	13.6998i	−0.205964	+	0.978560i
$197$	0.174426	−	0.174426i	0.0124273	−	0.0124273i	−0.700866	−	0.713293i	$-0.747203\pi$
$197$	0.174426	−	0.174426i	0.0124273	−	0.0124273i	0.713293	+	0.700866i	$0.247203\pi$
$198$	−12.6585	+	21.0115i	−0.899601	+	1.49322i
$199$	7.78849	−	13.4901i	0.552111	−	0.956285i	−0.446011	−	0.895028i	$-0.647156\pi$
$199$	7.78849	−	13.4901i	0.552111	−	0.956285i	0.998122	−	0.0612574i	$-0.0195111\pi$
$200$	−0.0793021	+	12.0179i	−0.00560750	+	0.849792i
$201$	−5.44116	+	0.192810i	−0.383790	+	0.0135998i
$202$	−24.4081	−	2.18954i	−1.71735	−	0.154055i
$203$	1.82956	+	7.23936i	0.128410	+	0.508103i
$204$	−1.42647	−	12.0030i	−0.0998727	−	0.840376i
$205$	−6.57650	−	1.76217i	−0.459323	−	0.123075i
$206$	−4.13109	−	23.7337i	−0.287827	−	1.65361i
$207$	0.742427	+	10.4626i	0.0516023	+	0.727200i
$208$	0.408106	−	0.572057i	0.0282971	−	0.0396650i
$209$	−7.74160			−0.535498
$210$	−1.07991	−	5.51123i	−0.0745209	−	0.380311i
$211$	−10.3013	+	10.3013i	−0.709167	+	0.709167i	−0.966360	−	0.257193i	$-0.917202\pi$
$211$	−10.3013	+	10.3013i	−0.709167	+	0.709167i	0.257193	+	0.966360i	$0.417202\pi$
$212$	5.43747	−	11.5280i	0.373447	−	0.791748i
$213$	−0.650663	+	2.82496i	−0.0445827	+	0.193563i
$214$	0.293873	+	0.206737i	0.0200887	+	0.0141322i
$215$	4.80934	−	2.77668i	0.327995	−	0.189368i
$216$	14.5042	+	2.37247i	0.986885	+	0.161426i
$217$	6.59379	+	11.8064i	0.447616	+	0.801470i
$218$	−1.27870	+	14.2544i	−0.0866043	+	0.965430i
$219$	−13.7854	−	12.8419i	−0.931534	−	0.867775i
$220$	7.64787	+	6.47487i	0.515619	+	0.436535i
$221$	0.592111	−	0.158656i	0.0398297	−	0.0106723i
$222$	17.8277	+	19.8669i	1.19651	+	1.33338i
$223$			13.9846i			0.936476i	0.883602	+	0.468238i	$0.155111\pi$
$223$			13.9846i			0.936476i	−0.883602	+	0.468238i	$0.844889\pi$
$224$	−9.90683	+	11.2185i	−0.661928	+	0.749568i
$225$	−7.13898	−	10.5605i	−0.475932	−	0.704036i
$226$	1.18782	−	3.24132i	0.0790129	−	0.215609i
$227$	4.86517	+	18.1571i	0.322913	+	1.20513i	0.916393	+	0.400279i	$0.131087\pi$
$227$	4.86517	+	18.1571i	0.322913	+	1.20513i	−0.593480	+	0.804849i	$0.702246\pi$
$228$	1.72082	+	4.30728i	0.113964	+	0.285257i
$229$	−16.9205	−	4.53383i	−1.11814	−	0.299604i	−0.348008	−	0.937492i	$-0.613142\pi$
$229$	−16.9205	−	4.53383i	−1.11814	−	0.299604i	−0.770130	+	0.637888i	$0.779808\pi$
$230$	4.26764	+	0.382831i	0.281400	+	0.0252431i
$231$	23.2209	+	12.7592i	1.52782	+	0.839494i
$232$	−2.11686	+	7.69673i	−0.138979	+	0.505315i
$233$	11.9486	+	20.6956i	0.782780	+	1.35581i	0.930317	+	0.366757i	$0.119532\pi$
$233$	11.9486	+	20.6956i	0.782780	+	1.35581i	−0.147537	+	0.989057i	$0.547135\pi$
$234$	−0.0138807	+	0.745206i	−0.000907412	+	0.0487157i
$235$	9.84606	−	2.63824i	0.642286	−	0.172100i
$236$	14.7420	+	6.95341i	0.959620	+	0.452628i
$237$	−3.90553	+	1.19624i	−0.253691	+	0.0777039i
$238$	−12.8931	+	2.05523i	−0.835738	+	0.133221i
$239$		−	4.58228i		−	0.296403i	−0.988957	−	0.148202i	$-0.952652\pi$
$239$		−	4.58228i		−	0.296403i	0.988957	−	0.148202i	$-0.0473484\pi$
$240$	1.90251	−	5.69438i	0.122807	−	0.367571i
$241$	−25.5960	−	14.7779i	−1.64879	−	0.951927i	−0.977555	−	0.210678i	$-0.932433\pi$
$241$	−25.5960	−	14.7779i	−1.64879	−	0.951927i	−0.671230	−	0.741249i	$-0.734234\pi$
$242$	−31.2495	+	5.43929i	−2.00880	+	0.349651i
$243$	−14.1110	+	6.62426i	−0.905218	+	0.424947i
$244$	2.81683	−	1.95395i	0.180329	−	0.125089i
$245$	−5.90170	+	1.40229i	−0.377046	+	0.0895892i
$246$	−16.1227	−	10.5089i	−1.02794	−	0.670020i
$247$	−0.203711	+	0.117613i	−0.0129618	+	0.00748353i
$248$	−0.0953924	+	14.4563i	−0.00605742	+	0.917975i
$249$	−3.97361	−	6.35183i	−0.251817	−	0.402531i
$250$	−10.2834	+	4.76772i	−0.650380	+	0.301537i
$251$	14.9573	+	14.9573i	0.944098	+	0.944098i	0.998518	−	0.0544206i	$-0.0173312\pi$
$251$	14.9573	+	14.9573i	0.944098	+	0.944098i	−0.0544206	+	0.998518i	$0.517331\pi$
$252$	1.93739	−	15.7558i	0.122044	−	0.992525i
$253$	−14.2940	+	14.2940i	−0.898659	+	0.898659i
$254$	13.6632	+	5.00706i	0.857305	+	0.314171i
$255$	4.44007	−	2.77764i	0.278048	−	0.173943i
$256$	−15.1290	+	5.20693i	−0.945565	+	0.325433i
$257$	−0.412351	−	0.714213i	−0.0257218	−	0.0445514i	0.852878	−	0.522110i	$-0.174855\pi$
$257$	−0.412351	−	0.714213i	−0.0257218	−	0.0445514i	−0.878600	+	0.477559i	$0.841522\pi$
$258$	15.3598	−	3.23778i	0.956259	−	0.201575i
$259$	20.6757	−	20.0944i	1.28473	−	1.24860i
$260$	0.299613	+	0.0541899i	0.0185812	+	0.00336072i
$261$	−2.76473	−	8.00263i	−0.171133	−	0.495350i
$262$	−13.2068	−	9.29083i	−0.815917	−	0.573990i
$263$	8.55527	−	14.8182i	0.527540	−	0.913727i	−0.471944	−	0.881628i	$-0.656448\pi$
$263$	8.55527	−	14.8182i	0.527540	−	0.913727i	0.999485	−	0.0320983i	$-0.0102190\pi$
$264$	14.8634	+	24.1117i	0.914782	+	1.48397i
$265$	5.52268			0.339256
$266$	4.57478	−	2.04228i	0.280498	−	0.125220i
$267$	4.04813	+	13.2165i	0.247741	+	0.808838i
$268$	−2.68198	+	5.68608i	−0.163828	+	0.347332i
$269$	−5.04909	−	18.8435i	−0.307848	−	1.14891i	−0.930466	−	0.366379i	$-0.880597\pi$
$269$	−5.04909	−	18.8435i	−0.307848	−	1.14891i	0.622617	−	0.782526i	$-0.286069\pi$
$270$	1.75123	+	6.12245i	0.106577	+	0.372600i
$271$	23.2129	−	13.4020i	1.41008	−	0.814111i	0.414687	−	0.909964i	$-0.363891\pi$
$271$	23.2129	−	13.4020i	1.41008	−	0.814111i	0.995395	+	0.0958531i	$0.0305579\pi$
$272$	−13.0731	−	4.88891i	−0.792675	−	0.296434i
$273$	0.804874	−	0.0170355i	0.0487132	−	0.00103104i
$274$	−11.1501	+	9.31436i	−0.673604	+	0.562701i
$275$	6.35843	−	23.7300i	0.383428	−	1.43097i
$276$	11.1303	+	4.77563i	0.669963	+	0.287459i
$277$	14.8501	−	3.97908i	0.892259	−	0.239080i	0.216570	−	0.976267i	$-0.430513\pi$
$277$	14.8501	−	3.97908i	0.892259	−	0.239080i	0.675689	+	0.737187i	$0.263846\pi$
$278$	−8.69455	+	4.03108i	−0.521464	+	0.241768i
$279$	−8.58747	−	12.7033i	−0.514118	−	0.760524i
$280$	−6.22750	−	1.80867i	−0.372165	−	0.108089i
$281$	9.55555			0.570036			0.285018	−	0.958522i	$-0.408000\pi$
$281$	9.55555			0.570036			0.285018	+	0.958522i	$0.408000\pi$
$282$	28.7710	+	1.55645i	1.71329	+	0.0926854i
$283$	−6.16214	−	22.9974i	−0.366301	−	1.36705i	−0.865648	−	0.500652i	$-0.833094\pi$
$283$	−6.16214	−	22.9974i	−0.366301	−	1.36705i	0.499347	−	0.866402i	$-0.333573\pi$
$284$	2.55476	+	2.16292i	0.151597	+	0.128346i
$285$	−1.36987	+	1.47052i	−0.0811439	+	0.0871060i
$286$	−1.10242	+	0.920914i	−0.0651873	+	0.0544548i
$287$	−10.6492	+	17.8522i	−0.628602	+	1.05378i
$288$	10.1114	−	13.6293i	0.595821	−	0.803117i
$289$	2.41225	+	4.17814i	0.141897	+	0.245773i
$290$	−3.40749	+	0.593107i	−0.200094	+	0.0348284i
$291$	9.93394	+	2.28805i	0.582338	+	0.134128i
$292$	−20.4753	+	7.35057i	−1.19823	+	0.430160i
$293$	3.12364	+	3.12364i	0.182485	+	0.182485i	0.792438	−	0.609953i	$-0.208812\pi$
$293$	3.12364	+	3.12364i	0.182485	+	0.182485i	−0.609953	+	0.792438i	$0.708812\pi$
$294$	−17.0880	−	1.41404i	−0.996594	−	0.0824684i
$295$			7.06237i			0.411187i
$296$	29.8242	−	7.78081i	1.73350	−	0.452250i
$297$	−27.4645	−	12.1772i	−1.59365	−	0.706596i
$298$	1.90140	+	1.33762i	0.110145	+	0.0774862i
$299$	−0.158972	+	0.593291i	−0.00919358	+	0.0343109i
$300$	−14.6163	+	1.73704i	−0.843872	+	0.100288i
$301$	−4.15434	−	16.4382i	−0.239452	−	0.947484i
$302$	−3.71386	−	4.44583i	−0.213709	−	0.255829i
$303$	−1.06288	−	29.9949i	−0.0610611	−	1.72316i
$304$	5.33116	+	0.513717i	0.305763	+	0.0294637i
$305$	1.28638	+	0.742693i	0.0736580	+	0.0425265i
$306$	14.3685	−	3.56459i	0.821390	−	0.203774i
$307$	−4.51853	−	4.51853i	−0.257886	−	0.257886i	0.566308	−	0.824194i	$-0.308371\pi$
$307$	−4.51853	−	4.51853i	−0.257886	−	0.257886i	−0.824194	+	0.566308i	$0.808371\pi$
$308$	25.3844	−	17.0776i	1.44641	−	0.973085i
$309$	28.2111	−	8.64087i	1.60487	−	0.491562i
$310$	−5.68278	+	2.63472i	−0.322760	+	0.149642i
$311$	11.9241	+	6.88436i	0.676152	+	0.390377i	0.798404	−	0.602123i	$-0.205678\pi$
$311$	11.9241	+	6.88436i	0.676152	+	0.390377i	−0.122252	+	0.992499i	$0.539012\pi$
$312$	0.757427	+	0.408662i	0.0428809	+	0.0231359i
$313$	−4.80811	−	8.32789i	−0.271770	−	0.470720i	0.697545	−	0.716541i	$-0.254276\pi$
$313$	−4.80811	−	8.32789i	−0.271770	−	0.470720i	−0.969315	+	0.245821i	$0.920942\pi$
$314$	−3.19336	−	0.286461i	−0.180212	−	0.0161660i
$315$	6.53253	−	2.15309i	0.368066	−	0.121313i
$316$	−0.839439	+	4.64121i	−0.0472222	+	0.261089i
$317$	3.68996	−	13.7711i	0.207249	−	0.773464i	−0.781503	−	0.623901i	$-0.785547\pi$
$317$	3.68996	−	13.7711i	0.207249	−	0.773464i	0.988752	−	0.149563i	$-0.0477866\pi$
$318$	14.8385	+	4.84897i	0.832099	+	0.271917i
$319$	8.15881	−	14.1315i	0.456806	−	0.791211i
$320$	−4.83696	−	4.96634i	−0.270394	−	0.277627i
$321$	−0.206395	+	0.388655i	−0.0115199	+	0.0216926i
$322$	4.67599	−	12.2177i	0.260583	−	0.680866i
$323$	3.30368	+	3.30368i	0.183822	+	0.183822i
$324$	−0.670328	+	17.9875i	−0.0372405	+	0.999306i
$325$	−0.193199	−	0.721027i	−0.0107167	−	0.0399954i
$326$	−23.2258	−	16.3391i	−1.28636	−	0.904941i
$327$	−17.5171	+	0.620728i	−0.968698	+	0.0343264i
$328$	−19.3181	+	10.9840i	−1.06666	+	0.606488i
$329$	0.443731	−	31.1185i	0.0244637	−	1.71562i
$330$	−6.70156	+	10.2815i	−0.368909	+	0.565979i
$331$	−9.31527	+	34.7651i	−0.512014	+	1.91086i	−0.114002	+	0.993480i	$0.536367\pi$
$331$	−9.31527	+	34.7651i	−0.512014	+	1.91086i	−0.398011	+	0.917380i	$0.630300\pi$
$332$	−8.62173	+	0.716101i	−0.473179	+	0.0393011i
$333$	−21.4226	+	24.6951i	−1.17395	+	1.35328i
$334$	3.40701	−	9.29700i	0.186423	−	0.508709i
$335$	−2.72401			−0.148828
$336$	−15.1441	−	10.3274i	−0.826181	−	0.563405i
$337$	−7.79829			−0.424800			−0.212400	−	0.977183i	$-0.568128\pi$
$337$	−7.79829			−0.424800			−0.212400	+	0.977183i	$0.568128\pi$
$338$	6.31093	−	17.2212i	0.343269	−	0.936709i
$339$	4.12008	+	0.948965i	0.223772	+	0.0515407i
$340$	−0.500570	−	6.02678i	−0.0271472	−	0.326848i
$341$	7.64855	−	28.5448i	0.414192	−	1.54579i
$342$	−4.97171	+	2.74826i	−0.268840	+	0.148609i
$343$	−0.791968	+	18.5033i	−0.0427622	+	0.999085i
$344$	4.80671	−	17.4768i	0.259160	−	0.942284i
$345$	0.185841	+	5.24447i	0.0100053	+	0.282353i
$346$	−0.143593	−	0.101016i	−0.00771958	−	0.00543065i
$347$	4.08389	+	15.2413i	0.219235	+	0.818196i	0.984633	+	0.174638i	$0.0558756\pi$
$347$	4.08389	+	15.2413i	0.219235	+	0.818196i	−0.765398	+	0.643557i	$0.777458\pi$
$348$	−9.67605	−	1.39823i	−0.518691	−	0.0749532i
$349$	7.97573	+	7.97573i	0.426931	+	0.426931i	0.887582	−	0.460651i	$-0.152384\pi$
$349$	7.97573	+	7.97573i	0.426931	+	0.426931i	−0.460651	+	0.887582i	$0.652384\pi$
$350$	2.50270	+	15.7003i	0.133775	+	0.839215i
$351$	−0.907697	+	0.0968186i	−0.0484493	+	0.00516779i
$352$	32.6116	−	2.49208i	1.73820	−	0.132828i
$353$	8.92287	−	15.4549i	0.474917	−	0.822580i	−0.524671	−	0.851305i	$-0.675812\pi$
$353$	8.92287	−	15.4549i	0.474917	−	0.822580i	0.999587	+	0.0287256i	$0.00914491\pi$
$354$	−6.20083	+	18.9753i	−0.329571	+	1.00853i
$355$	−0.375385	+	1.40096i	−0.0199234	+	0.0743550i
$356$	15.7061	+	2.84071i	0.832422	+	0.150557i
$357$	−4.46447	−	15.3543i	−0.236285	−	0.812635i
$358$	24.7826	+	2.22313i	1.30980	+	0.117496i
$359$	8.36824	+	14.4942i	0.441659	+	0.764976i	0.997813	−	0.0661035i	$-0.0210568\pi$
$359$	8.36824	+	14.4942i	0.441659	+	0.764976i	−0.556154	+	0.831079i	$0.687723\pi$
$360$	7.21009	+	1.44322i	0.380005	+	0.0760646i
$361$	14.9018	+	8.60359i	0.784308	+	0.452820i
$362$	−16.4867	+	7.64375i	−0.866519	+	0.401747i
$363$	−11.3772	−	37.1448i	−0.597148	−	1.94960i
$364$	0.408514	−	0.835025i	0.0214120	−	0.0437672i
$365$	−6.66522	−	6.66522i	−0.348874	−	0.348874i
$366$	2.80418	+	3.12494i	0.146577	+	0.163343i
$367$	−26.4671	−	15.2808i	−1.38157	−	0.797651i	−0.389226	−	0.921142i	$-0.627257\pi$
$367$	−26.4671	−	15.2808i	−1.38157	−	0.797651i	−0.992346	+	0.123492i	$0.960591\pi$
$368$	10.7920	−	8.89491i	0.562569	−	0.463679i
$369$	10.3108	−	21.1956i	0.536759	−	1.10340i
$370$	8.56187	+	10.2493i	0.445110	+	0.532838i
$371$	4.59583	−	16.2230i	0.238604	−	0.842256i
$372$	−17.5819	+	2.08949i	−0.911580	+	0.108335i
$373$	8.51467	−	31.7772i	0.440873	−	1.64536i	−0.285736	−	0.958308i	$-0.592238\pi$
$373$	8.51467	−	31.7772i	0.440873	−	1.64536i	0.726609	−	0.687051i	$-0.241095\pi$
$374$	23.3353	+	16.4162i	1.20664	+	0.848861i
$375$	−7.36257	−	11.7691i	−0.380202	−	0.607754i
$376$	16.8250	−	28.7027i	0.867683	−	1.48023i
$377$		−	0.495805i		−	0.0255353i
$378$	19.4422	−	0.0493396i	0.999997	−	0.00253776i
$379$	−5.96162	−	5.96162i	−0.306228	−	0.306228i	0.537217	−	0.843444i	$-0.319476\pi$
$379$	−5.96162	−	5.96162i	−0.306228	−	0.306228i	−0.843444	+	0.537217i	$0.819476\pi$
$380$	0.784098	+	2.18414i	0.0402234	+	0.112044i
$381$	−4.00019	+	17.3675i	−0.204936	+	0.889762i
$382$	−20.3719	+	3.54594i	−1.04232	+	0.181426i
$383$	10.9394	+	18.9475i	0.558975	+	0.968173i	0.997582	+	0.0694940i	$0.0221385\pi$
$383$	10.9394	+	18.9475i	0.558975	+	0.968173i	−0.438608	+	0.898679i	$0.644528\pi$
$384$	−8.63553	−	17.5906i	−0.440680	−	0.897664i
$385$	11.3844	+	6.79106i	0.580205	+	0.346104i
$386$	−8.98871	+	7.50880i	−0.457513	+	0.382188i
$387$	6.27781	+	18.1714i	0.319119	+	0.923702i
$388$	7.60589	−	8.98379i	0.386130	−	0.456083i
$389$	1.03982	+	3.88066i	0.0527210	+	0.196757i	0.987263	−	0.159094i	$-0.0508574\pi$
$389$	1.03982	+	3.88066i	0.0527210	+	0.196757i	−0.934542	+	0.355852i	$0.884191\pi$
$390$	−0.0201438	+	0.372359i	−0.00102002	+	0.0188551i
$391$	12.1998			0.616969
$392$	−10.4954	+	16.7883i	−0.530096	+	0.847937i
$393$	9.27549	−	17.4663i	0.467887	−	0.881059i
$394$	0.316491	−	0.146735i	0.0159446	−	0.00739243i
$395$	−1.97397	+	0.528923i	−0.0993211	+	0.0266130i
$396$	−27.0332	+	21.7406i	−1.35847	+	1.09250i
$397$	2.77995	−	10.3749i	0.139522	−	0.520702i	−0.860417	−	0.509591i	$-0.829797\pi$
$397$	2.77995	−	10.3749i	0.139522	−	0.520702i	0.999938	−	0.0111107i	$-0.00353672\pi$
$398$	16.9064	−	14.1229i	0.847443	−	0.707919i
$399$	3.17971	+	5.24774i	0.159185	+	0.262716i
$400$	−5.95334	+	15.9194i	−0.297667	+	0.795972i
$401$	−18.5751	+	10.7243i	−0.927596	+	0.535548i	−0.886051	−	0.463589i	$-0.846562\pi$
$401$	−18.5751	+	10.7243i	−0.927596	+	0.535548i	−0.0415458	+	0.999137i	$0.513228\pi$
$402$	−7.31891	−	2.39170i	−0.365034	−	0.119287i
$403$	−0.232398	−	0.867322i	−0.0115766	−	0.0432044i
$404$	−31.3450	−	14.7846i	−1.55947	−	0.735563i
$405$	−7.17288	+	3.06213i	−0.356423	+	0.152158i
$406$	−1.09336	+	10.5031i	−0.0542623	+	0.521262i
$407$	−63.0063			−3.12310
$408$	3.94663	−	16.6324i	0.195387	−	0.823426i
$409$	−2.15950	+	3.74037i	−0.106780	+	0.184949i	−0.914464	−	0.404667i	$-0.867388\pi$
$409$	−2.15950	+	3.74037i	−0.106780	+	0.184949i	0.807684	+	0.589616i	$0.200721\pi$
$410$	−7.87517	−	5.54011i	−0.388927	−	0.273606i
$411$	−13.0199	−	12.1287i	−0.642224	−	0.598267i
$412$	6.06359	−	33.5253i	0.298732	−	1.65167i
$413$	20.7459	+	5.87712i	1.02084	+	0.289194i
$414$	−4.10537	+	14.2541i	−0.201768	+	0.700551i
$415$	−1.87427	−	3.24633i	−0.0920043	−	0.159356i
$416$	0.820277	−	0.561022i	0.0402174	−	0.0275064i
$417$	−6.22500	−	9.95070i	−0.304840	−	0.487288i
$418$	−10.2798	−	3.76715i	−0.502799	−	0.184257i
$419$	−1.00684	+	1.00684i	−0.0491873	+	0.0491873i	−0.731273	−	0.682085i	$-0.761073\pi$
$419$	−1.00684	+	1.00684i	−0.0491873	+	0.0491873i	0.682085	+	0.731273i	$0.261073\pi$
$420$	1.24786	−	7.84363i	0.0608892	−	0.382730i
$421$	20.5242	+	20.5242i	1.00029	+	1.00029i	1.00000		0.000289208i	$9.20576e-5\pi$
$421$	20.5242	+	20.5242i	1.00029	+	1.00029i	0.000289208		1.00000i	$0.499908\pi$
$422$	−18.6913	+	8.66590i	−0.909879	+	0.421850i
$423$	2.49781	+	35.2001i	0.121448	+	1.71149i
$424$	12.8299	−	12.6617i	0.623073	−	0.614904i
$425$	−12.8400	+	7.41320i	−0.622833	+	0.359593i
$426$	−2.23864	+	3.43452i	−0.108463	+	0.166403i
$427$	3.25217	−	3.16073i	0.157383	−	0.152958i
$428$	0.289621	+	0.417519i	0.0139994	+	0.0201815i
$429$	−1.28728	−	1.19917i	−0.0621505	−	0.0578966i
$430$	7.73729	−	1.34675i	0.373125	−	0.0649462i
$431$	−0.524890	−	0.303045i	−0.0252830	−	0.0145972i	0.487305	−	0.873232i	$-0.337980\pi$
$431$	−0.524890	−	0.303045i	−0.0252830	−	0.0145972i	−0.512588	+	0.858635i	$0.671313\pi$
$432$	18.1050	+	10.2082i	0.871079	+	0.491143i
$433$		−	7.72438i		−	0.371210i	−0.982624	−	0.185605i	$-0.940576\pi$
$433$		−	7.72438i		−	0.371210i	0.982624	−	0.185605i	$-0.0594245\pi$
$434$	3.01050	+	18.8858i	0.144508	+	0.906549i
$435$	−1.24058	−	4.05032i	−0.0594814	−	0.194198i
$436$	−8.63428	+	18.3056i	−0.413507	+	0.876679i
$437$	−4.52190	+	1.21164i	−0.216312	+	0.0579606i
$438$	−12.0561	−	23.7604i	−0.576064	−	1.13531i
$439$	5.76099	+	9.97833i	0.274957	+	0.476240i	0.970124	−	0.242608i	$-0.0780030\pi$
$439$	5.76099	+	9.97833i	0.274957	+	0.476240i	−0.695167	+	0.718848i	$0.744670\pi$
$440$	7.00454	+	12.3192i	0.333929	+	0.587297i
$441$	−0.888551	−	20.9812i	−0.0423120	−	0.999104i
$442$	0.863443	+	0.0774556i	0.0410698	+	0.00368419i
$443$	16.7142	+	4.47856i	0.794117	+	0.212783i	0.632999	−	0.774152i	$-0.281824\pi$
$443$	16.7142	+	4.47856i	0.794117	+	0.212783i	0.161118	+	0.986935i	$0.448490\pi$
$444$	14.0052	+	35.0555i	0.664656	+	1.66366i
$445$	1.78990	+	6.68001i	0.0848495	+	0.316663i
$446$	−6.80505	+	18.5695i	−0.322229	+	0.879293i
$447$	−1.33541	+	2.51466i	−0.0631628	+	0.118939i
$448$	−18.6139	+	10.0758i	−0.879425	+	0.476037i
$449$			26.5522i			1.25308i	0.779391	+	0.626538i	$0.215529\pi$
$449$			26.5522i			1.25308i	−0.779391	+	0.626538i	$0.784471\pi$
$450$	−4.34068	−	17.4968i	−0.204622	−	0.824808i
$451$	43.8785	−	11.7572i	2.06616	−	0.553625i
$452$	3.15453	−	3.72601i	0.148376	−	0.175257i
$453$	4.83602	−	5.19135i	0.227216	−	0.243911i
$454$	−2.37518	+	26.4775i	−0.111473	+	1.24265i
$455$	0.402741	+	0.00574284i	0.0188808	+	0.000269228i
$456$	0.189034	+	6.55684i	0.00885235	+	0.307052i
$457$	25.4158	−	14.6738i	1.18890	−	0.686412i	0.230844	−	0.972991i	$-0.425851\pi$
$457$	25.4158	−	14.6738i	1.18890	−	0.686412i	0.958057	+	0.286578i	$0.0925179\pi$
$458$	−20.2618	−	14.2540i	−0.946772	−	0.666045i
$459$	6.52372	+	16.9168i	0.304501	+	0.789611i
$460$	5.48054	+	2.58503i	0.255531	+	0.120528i
$461$	−3.69072	+	3.69072i	−0.171894	+	0.171894i	−0.787811	−	0.615917i	$-0.788786\pi$
$461$	−3.69072	+	3.69072i	−0.171894	+	0.171894i	0.615917	+	0.787811i	$0.288786\pi$
$462$	24.6253	+	28.2420i	1.14567	+	1.31394i
$463$	−2.26837			−0.105420			−0.0527101	−	0.998610i	$-0.516786\pi$
$463$	−2.26837			−0.105420			−0.0527101	+	0.998610i	$0.516786\pi$
$464$	−6.55621	+	9.19008i	−0.304364	+	0.426639i
$465$	−4.06868	−	6.50380i	−0.188680	−	0.301607i
$466$	5.79536	+	33.2952i	0.268465	+	1.54237i
$467$	3.20011	+	0.857468i	0.148084	+	0.0396789i	0.332099	−	0.943244i	$-0.392243\pi$
$467$	3.20011	+	0.857468i	0.148084	+	0.0396789i	−0.184016	+	0.982923i	$0.558910\pi$
$468$	−0.381058	+	0.982774i	−0.0176144	+	0.0454288i
$469$	−2.26685	+	8.00183i	−0.104673	+	0.369490i
$470$	14.3580	+	1.28799i	0.662284	+	0.0594105i
$471$	−0.139059	−	3.92429i	−0.00640751	−	0.180822i
$472$	16.1916	+	16.4068i	0.745281	+	0.755182i
$473$	−18.5260	+	32.0880i	−0.851827	+	1.47541i
$474$	−5.76809	−	0.312042i	−0.264937	−	0.0143326i
$475$	4.02296	−	4.02296i	0.184586	−	0.184586i
$476$	−18.1204	−	3.54489i	−0.830546	−	0.162480i
$477$	−3.62879	+	18.7715i	−0.166151	+	0.859489i
$478$	2.22979	−	6.08462i	0.101988	−	0.278304i
$479$	−10.9507	+	18.9672i	−0.500352	+	0.866635i	0.499648	+	0.866229i	$0.333463\pi$
$479$	−10.9507	+	18.9672i	−0.500352	+	0.866635i	−1.00000		0.000406431i	$0.999871\pi$
$480$	5.29722	−	6.63555i	0.241784	−	0.302870i
$481$	−1.65794	+	0.957211i	−0.0755955	+	0.0436451i
$482$	−26.7968	−	32.0783i	−1.22056	−	1.46112i
$483$	15.5604	+	3.81840i	0.708023	+	0.173743i
$484$	−44.1418	−	7.98377i	−2.00645	−	0.362899i
$485$	4.92645	+	1.32004i	0.223699	+	0.0599399i
$486$	−21.9608	+	1.92954i	−0.996162	+	0.0875255i
$487$	−1.78081	−	1.02815i	−0.0806960	−	0.0465899i	0.459109	−	0.888380i	$-0.348169\pi$
$487$	−1.78081	−	1.02815i	−0.0806960	−	0.0465899i	−0.539805	+	0.841790i	$0.681502\pi$
$488$	4.69117	−	1.22387i	0.212359	−	0.0554022i
$489$	16.3122	−	30.7168i	0.737662	−	1.38906i
$490$	−8.51899	−	1.00978i	−0.384849	−	0.0456174i
$491$	−12.7157	+	12.7157i	−0.573852	+	0.573852i	−0.933203	−	0.359351i	$-0.882998\pi$
$491$	−12.7157	+	12.7157i	−0.573852	+	0.573852i	0.359351	+	0.933203i	$0.382998\pi$
$492$	−16.2949	−	21.7998i	−0.734631	−	0.982809i
$493$	−9.51223	+	2.54880i	−0.428409	+	0.114792i
$494$	−0.327732	+	0.0570450i	−0.0147454	+	0.00256657i
$495$	−13.5165	−	6.57526i	−0.607523	−	0.295536i
$496$	−7.16126	+	19.1495i	−0.321550	+	0.859837i
$497$	3.80295	+	2.26854i	0.170586	+	0.101758i
$498$	−2.18552	−	10.3679i	−0.0979353	−	0.464598i
$499$	33.5091	+	8.97874i	1.50007	+	0.401944i	0.913125	−	0.407680i	$-0.133662\pi$
$499$	33.5091	+	8.97874i	1.50007	+	0.401944i	0.586949	+	0.809624i	$0.300329\pi$
$500$	−15.9749	+	1.32684i	−0.714421	+	0.0593381i
$501$	11.8175	+	2.72190i	0.527969	+	0.121605i
$502$	12.5828	+	27.1396i	0.561598	+	1.21130i
$503$		−	12.9532i		−	0.577555i	−0.957396	−	0.288778i	$-0.906751\pi$
$503$		−	12.9532i		−	0.577555i	0.957396	−	0.288778i	$-0.0932488\pi$
$504$	10.2395	−	19.9788i	0.456106	−	0.889926i
$505$		−	15.0163i		−	0.668218i
$506$	−25.9361	+	12.0248i	−1.15300	+	0.534569i
$507$	21.8901	+	5.04187i	0.972172	+	0.223917i
$508$	15.7063	+	13.2973i	0.696855	+	0.589974i
$509$	8.29819	+	2.22349i	0.367811	+	0.0985546i	0.437990	−	0.898980i	$-0.355691\pi$
$509$	8.29819	+	2.22349i	0.367811	+	0.0985546i	−0.0701794	+	0.997534i	$0.522357\pi$
$510$	7.24742	−	1.52772i	0.320921	−	0.0676488i
$511$	−25.1259	+	14.0326i	−1.11150	+	0.620766i
$512$	−22.6230	−	0.447897i	−0.999804	−	0.0197945i
$513$	−4.09817	−	5.62239i	−0.180939	−	0.248235i
$514$	−0.200000	−	1.14903i	−0.00882162	−	0.0506815i
$515$	14.2587	−	3.82061i	0.628314	−	0.168356i
$516$	21.9712	+	3.17494i	0.967227	+	0.139769i
$517$	−48.0906	+	48.0906i	−2.11502	+	2.11502i
$518$	37.2326	−	16.6215i	1.63591	−	0.730305i
$519$	0.100849	−	0.189905i	0.00442679	−	0.00833592i
$520$	0.371475	+	0.217752i	0.0162902	+	0.00954905i
$521$	10.6856	+	6.16932i	0.468143	+	0.270283i	0.715462	−	0.698652i	$-0.246216\pi$
$521$	10.6856	+	6.16932i	0.468143	+	0.270283i	−0.247319	+	0.968934i	$0.579550\pi$
$522$	0.222993	−	11.9717i	0.00976015	−	0.523987i
$523$	−2.98859	−	0.800789i	−0.130682	−	0.0350161i	0.192885	−	0.981221i	$-0.438215\pi$
$523$	−2.98859	−	0.800789i	−0.130682	−	0.0350161i	−0.323567	+	0.946205i	$0.604882\pi$
$524$	−13.0157	−	18.7635i	−0.568593	−	0.819686i
$525$	−18.6973	+	5.43649i	−0.816016	+	0.237268i
$526$	18.5709	−	15.5133i	0.809728	−	0.676413i
$527$	−15.4453	+	8.91732i	−0.672806	+	0.388445i
$528$	8.00353	+	39.2497i	0.348309	+	1.70812i
$529$	5.38795	−	9.33220i	0.234259	−	0.405748i
$530$	7.33334	+	2.68740i	0.318540	+	0.116733i
$531$	−24.0049	−	4.64047i	−1.04172	−	0.201379i
$532$	7.06847	−	0.485723i	0.306457	−	0.0210587i
$533$	0.975993	−	0.975993i	0.0422749	−	0.0422749i
$534$	−1.05597	+	19.5195i	−0.0456961	+	0.844693i
$535$	−0.110084	+	0.190672i	−0.00475936	+	0.00824345i
$536$	−6.32820	+	6.24523i	−0.273336	+	0.269753i
$537$	1.07919	+	30.4551i	0.0465706	+	1.31423i
$538$	2.46496	−	27.4784i	0.106272	−	1.18468i
$539$	29.4227	−	27.7907i	1.26733	−	1.19703i
$540$	−0.653866	+	8.98192i	−0.0281379	+	0.386520i
$541$	10.0929	+	2.70437i	0.433926	+	0.116270i	0.469168	−	0.883109i	$-0.344554\pi$
$541$	10.0929	+	2.70437i	0.433926	+	0.116270i	−0.0352425	+	0.999379i	$0.511220\pi$
$542$	37.3450	−	6.50026i	1.60410	−	0.279210i
$543$	−11.8039	−	18.8686i	−0.506553	−	0.809728i
$544$	−14.9803	−	12.8533i	−0.642274	−	0.551081i
$545$	−8.76959			−0.375648
$546$	1.07705	+	0.369040i	0.0460934	+	0.0157935i
$547$	−5.68276	+	5.68276i	−0.242977	+	0.242977i	−0.818081	−	0.575103i	$-0.804962\pi$
$547$	−5.68276	+	5.68276i	−0.242977	+	0.242977i	0.575103	+	0.818081i	$0.304962\pi$
$548$	−19.3383	+	6.94237i	−0.826090	+	0.296563i
$549$	−3.36964	+	3.88439i	−0.143813	+	0.165782i
$550$	19.9904	−	28.4160i	0.852393	−	1.21166i
$551$	3.27262	−	1.88945i	0.139418	−	0.0804931i
$552$	12.4555	+	11.7575i	0.530143	+	0.500431i
$553$	−0.0889605	+	6.23873i	−0.00378299	+	0.265298i
$554$	21.6552	+	1.94259i	0.920040	+	0.0825326i
$555$	−11.1489	+	11.9680i	−0.473244	+	0.508015i
$556$	−13.5067	+	1.12183i	−0.572812	+	0.0475764i
$557$	24.7033	−	6.61922i	1.04671	−	0.280466i	0.305819	−	0.952090i	$-0.401070\pi$
$557$	24.7033	−	6.61922i	1.04671	−	0.280466i	0.740892	+	0.671624i	$0.234403\pi$
$558$	−5.22140	−	21.0469i	−0.221040	−	0.890986i
$559$			1.12581i			0.0476168i
$560$	−7.38913	−	5.43203i	−0.312248	−	0.229545i
$561$	−16.3891	+	30.8617i	−0.691948	+	1.30298i
$562$	12.6884	+	4.64984i	0.535229	+	0.196142i
$563$	0.131523	+	0.490851i	0.00554304	+	0.0206869i	0.968642	−	0.248461i	$-0.0799247\pi$
$563$	0.131523	+	0.490851i	0.00554304	+	0.0206869i	−0.963099	+	0.269148i	$0.913258\pi$
$564$	37.4464	+	16.0670i	1.57678	+	0.676544i
$565$	2.04324	+	0.547484i	0.0859596	+	0.0230328i
$566$	3.00835	−	33.5359i	0.126450	−	1.40962i
$567$	3.02600	+	23.6187i	0.127080	+	0.991892i
$568$	2.33986	+	4.11522i	0.0981781	+	0.172671i
$569$	8.57445	+	14.8514i	0.359460	+	0.622603i	0.987871	−	0.155279i	$-0.0496277\pi$
$569$	8.57445	+	14.8514i	0.359460	+	0.622603i	−0.628411	+	0.777882i	$0.716294\pi$
$570$	−2.53456	+	1.28605i	−0.106161	+	0.0538666i
$571$	−9.93395	+	2.66179i	−0.415723	+	0.111393i	−0.460617	−	0.887599i	$-0.652372\pi$
$571$	−9.93395	+	2.66179i	−0.415723	+	0.111393i	0.0448939	+	0.998992i	$0.485705\pi$
$572$	−1.91198	+	0.686394i	−0.0799440	+	0.0286996i
$573$	−7.41693	−	24.2152i	−0.309847	−	1.01160i
$574$	−22.8277	+	18.5232i	−0.952810	+	0.773142i
$575$		−	14.8560i		−	0.619536i
$576$	20.0587	−	13.1775i	0.835781	−	0.549063i
$577$	31.7254	+	18.3166i	1.32074	+	0.762532i	0.983847	−	0.179010i	$-0.0572893\pi$
$577$	31.7254	+	18.3166i	1.32074	+	0.762532i	0.336897	+	0.941542i	$0.390623\pi$
$578$	1.17000	+	6.72180i	0.0486654	+	0.279590i
$579$	−10.4960	−	9.77762i	−0.436200	−	0.406344i
$580$	−4.81327	−	0.870559i	−0.199860	−	0.0361480i
$581$	−11.0959	+	2.80420i	−0.460335	+	0.116338i
$582$	12.0775	+	7.87218i	0.500628	+	0.326312i
$583$	−31.9108	+	18.4237i	−1.32161	+	0.763032i
$584$	−30.7652	−	0.203010i	−1.27307	−	0.00840061i
$585$	−0.455566	+	0.0323270i	−0.0188353	+	0.00133656i
$586$	2.62775	+	5.66774i	0.108551	+	0.234132i
$587$	8.32984	+	8.32984i	0.343809	+	0.343809i	0.857797	−	0.513988i	$-0.171832\pi$
$587$	8.32984	+	8.32984i	0.343809	+	0.343809i	−0.513988	+	0.857797i	$0.671832\pi$
$588$	−22.0024	−	10.1929i	−0.907364	−	0.420347i
$589$	4.83922	−	4.83922i	0.199396	−	0.199396i
$590$	−3.43663	+	9.37784i	−0.141484	+	0.386079i
$591$	0.226597	+	0.362216i	0.00932095	+	0.0148996i
$592$	43.3885	+	4.18097i	1.78326	+	0.171837i
$593$	18.2653	+	31.6364i	0.750065	+	1.29915i	0.947790	+	0.318894i	$0.103311\pi$
$593$	18.2653	+	31.6364i	0.750065	+	1.29915i	−0.197725	+	0.980258i	$0.563355\pi$
$594$	−30.5434	−	29.5342i	−1.25321	−	1.21180i
$595$	−1.96020	−	7.75628i	−0.0803603	−	0.317976i
$596$	1.87390	+	2.70142i	0.0767578	+	0.110654i
$597$	19.7415	+	18.3903i	0.807965	+	0.752663i
$598$	−0.499794	+	0.710449i	−0.0204381	+	0.0290524i
$599$	9.07955	−	15.7262i	0.370980	−	0.642557i	−0.618736	−	0.785599i	$-0.712355\pi$
$599$	9.07955	−	15.7262i	0.370980	−	0.642557i	0.989717	+	0.143042i	$0.0456884\pi$
$600$	−20.2536	−	4.80591i	−0.826851	−	0.196200i
$601$	20.9059			0.852769			0.426384	−	0.904542i	$-0.359787\pi$
$601$	20.9059			0.852769			0.426384	+	0.904542i	$0.359787\pi$
$602$	2.48265	−	23.8492i	0.101185	−	0.972021i
$603$	1.78986	−	9.25886i	0.0728888	−	0.377050i
$604$	−2.76809	−	7.71064i	−0.112632	−	0.313741i
$605$	−5.03050	−	18.7741i	−0.204519	−	0.763275i
$606$	13.1845	−	40.3462i	0.535583	−	1.63895i
$607$	−39.6809	+	22.9098i	−1.61060	+	0.929879i	−0.621366	+	0.783520i	$0.713422\pi$
$607$	−39.6809	+	22.9098i	−1.61060	+	0.929879i	−0.989232	+	0.146359i	$0.953245\pi$
$608$	6.82905	+	3.27635i	0.276955	+	0.132874i
$609$	−12.9303	+	0.273675i	−0.523961	+	0.0110899i
$610$	1.34673	+	1.61216i	0.0545275	+	0.0652744i
$611$	−0.534842	+	1.99606i	−0.0216374	+	0.0807519i
$612$	20.8139	+	2.25858i	0.841351	+	0.0912979i
$613$	0.614291	−	0.164599i	0.0248110	−	0.00664808i	−0.246392	−	0.969170i	$-0.579245\pi$
$613$	0.614291	−	0.164599i	0.0248110	−	0.00664808i	0.271203	+	0.962522i	$0.412578\pi$
$614$	−3.80121	−	8.19875i	−0.153404	−	0.330874i
$615$	5.53096	−	10.4151i	0.223030	−	0.419979i
$616$	42.0171	−	10.3243i	1.69292	−	0.415976i
$617$	−33.6131			−1.35321			−0.676606	−	0.736345i	$-0.736550\pi$
$617$	−33.6131			−1.35321			−0.676606	+	0.736345i	$0.736550\pi$
$618$	41.6651	+	2.25400i	1.67602	+	0.0906691i
$619$	1.59927	+	5.96857i	0.0642803	+	0.239897i	0.990589	−	0.136867i	$-0.0437033\pi$
$619$	1.59927	+	5.96857i	0.0642803	+	0.239897i	−0.926309	+	0.376764i	$0.877037\pi$
$620$	−8.82802	+	0.733234i	−0.354542	+	0.0294474i
$621$	−17.9480	−	2.81431i	−0.720228	−	0.112934i
$622$	12.4835	+	14.9439i	0.500542	+	0.599194i
$623$	21.1122	+	0.301047i	0.845842	+	0.0120612i
$624$	0.806897	+	0.911218i	0.0323017	+	0.0364779i
$625$	7.14985	+	12.3839i	0.285994	+	0.495356i
$626$	−2.33204	−	13.3979i	−0.0932073	−	0.535489i
$627$	3.00962	−	13.0667i	0.120193	−	0.521835i
$628$	−4.10093	−	1.93430i	−0.163645	−	0.0771871i
$629$	26.8875	+	26.8875i	1.07208	+	1.07208i
$630$	9.72199	+	0.319803i	0.387334	+	0.0127413i
$631$		−	1.42992i		−	0.0569242i	−0.999595	−	0.0284621i	$-0.990939\pi$
$631$		−	1.42992i		−	0.0569242i	0.999595	−	0.0284621i	$-0.00906099\pi$
$632$	−3.37312	+	5.75440i	−0.134176	+	0.228898i
$633$	−13.3824	−	21.3918i	−0.531901	−	0.850246i
$634$	11.6009	−	16.4905i	0.460732	−	0.654923i
$635$	−2.30782	+	8.61290i	−0.0915830	+	0.341792i
$636$	17.3438	+	13.6593i	0.687727	+	0.541627i
$637$	0.352020	−	1.17828i	0.0139475	−	0.0466852i
$638$	17.7103	−	14.7944i	0.701157	−	0.585717i
$639$	−4.51518	−	2.19645i	−0.178618	−	0.0868904i
$640$	−4.00612	−	8.94832i	−0.158356	−	0.353713i
$641$	5.17909	+	2.99015i	0.204562	+	0.118104i	0.598782	−	0.800912i	$-0.295652\pi$
$641$	5.17909	+	2.99015i	0.204562	+	0.118104i	−0.394220	+	0.919016i	$0.628985\pi$
$642$	−0.463188	+	0.415645i	−0.0182806	+	0.0164042i
$643$	−19.0080	−	19.0080i	−0.749603	−	0.749603i	0.224801	−	0.974405i	$-0.427827\pi$
$643$	−19.0080	−	19.0080i	−0.749603	−	0.749603i	−0.974405	+	0.224801i	$0.927827\pi$
$644$	12.1543	−	13.9480i	0.478948	−	0.549628i
$645$	2.81696	+	9.19695i	0.110918	+	0.362130i
$646$	2.77921	+	5.99442i	0.109347	+	0.235847i
$647$	38.2823	+	22.1023i	1.50503	+	0.868932i	0.999983	+	0.00584236i	$0.00185969\pi$
$647$	38.2823	+	22.1023i	1.50503	+	0.868932i	0.505051	+	0.863089i	$0.331474\pi$
$648$	−9.64303	+	23.5587i	−0.378814	+	0.925473i
$649$	−23.5601	−	40.8073i	−0.924815	−	1.60183i
$650$	0.0943194	−	1.05143i	0.00369951	−	0.0412407i
$651$	−22.4909	+	6.53954i	−0.881489	+	0.256305i
$652$	−22.8898	−	32.9980i	−0.896434	−	1.29230i
$653$	−4.49506	+	16.7758i	−0.175905	+	0.656487i	0.820490	+	0.571660i	$0.193700\pi$
$653$	−4.49506	+	16.7758i	−0.175905	+	0.656487i	−0.996396	+	0.0848271i	$0.972966\pi$
$654$	−23.5623	−	7.69979i	−0.921359	−	0.301085i
$655$	4.94723	−	8.56886i	0.193304	−	0.334813i
$656$	−30.9966	+	5.18477i	−1.21021	+	0.202431i
$657$	27.0345	−	18.2755i	1.05472	−	0.712995i
$658$	15.7318	−	41.1051i	0.613291	−	1.60244i
$659$	−35.1349	−	35.1349i	−1.36866	−	1.36866i	−0.862351	−	0.506310i	$-0.831009\pi$
$659$	−35.1349	−	35.1349i	−1.36866	−	1.36866i	−0.506310	−	0.862351i	$-0.668991\pi$
$660$	−13.9018	+	10.3914i	−0.541128	+	0.404483i
$661$	11.1353	+	41.5576i	0.433114	+	1.61640i	0.745540	+	0.666461i	$0.232192\pi$
$661$	11.1353	+	41.5576i	0.433114	+	1.61640i	−0.312427	+	0.949942i	$0.601142\pi$
$662$	−29.2864	+	41.6302i	−1.13825	+	1.61800i
$663$	0.0375999	+	1.06108i	0.00146026	+	0.0412089i
$664$	−11.7969	−	3.24455i	−0.457809	−	0.125913i
$665$	1.49688	+	2.68022i	0.0580467	+	0.103934i
$666$	−40.4631	+	22.3671i	−1.56791	+	0.866709i
$667$	2.55388	−	9.53120i	0.0988865	−	0.369049i
$668$	9.04805	−	10.6872i	0.350080	−	0.413501i
$669$	−23.6040	−	5.43663i	−0.912583	−	0.210192i
$670$	−3.61710	−	1.32553i	−0.139741	−	0.0512098i
$671$	−9.91051			−0.382591
$672$	−15.0839	−	21.0826i	−0.581873	−	0.813280i
$673$	−16.3864			−0.631649			−0.315824	−	0.948818i	$-0.602281\pi$
$673$	−16.3864			−0.631649			−0.315824	+	0.948818i	$0.602281\pi$
$674$	−10.3550	−	3.79474i	−0.398861	−	0.146168i
$675$	20.6000	−	7.94409i	0.792896	−	0.305768i
$676$	16.7600	−	19.7963i	0.644617	−	0.761397i
$677$	−3.20755	+	11.9707i	−0.123276	+	0.460073i	−0.999772	−	0.0213360i	$-0.993208\pi$
$677$	−3.20755	+	11.9707i	−0.123276	+	0.460073i	0.876496	+	0.481409i	$0.159875\pi$
$678$	5.00911	+	3.26497i	0.192374	+	0.125390i
$679$	7.97731	−	13.3731i	0.306141	−	0.513211i
$680$	2.26801	−	8.24630i	0.0869744	−	0.316231i
$681$	−32.5380	+	1.15300i	−1.24686	+	0.0441831i
$682$	24.0464	−	34.1815i	0.920784	−	1.30888i
$683$	−13.4378	−	50.1506i	−0.514183	−	1.91896i	−0.368501	−	0.929628i	$-0.620129\pi$
$683$	−13.4378	−	50.1506i	−0.514183	−	1.91896i	−0.145683	−	0.989331i	$-0.546538\pi$
$684$	−7.93907	+	1.23001i	−0.303558	+	0.0470305i
$685$	−6.29508	−	6.29508i	−0.240523	−	0.240523i
$686$	−10.0555	+	24.1844i	−0.383923	+	0.923365i
$687$	14.2305	−	26.7968i	0.542926	−	1.02236i
$688$	14.8870	−	20.8677i	0.567562	−	0.795573i
$689$	−0.559797	+	0.969597i	−0.0213266	+	0.0369387i
$690$	−2.30525	+	7.05435i	−0.0877593	+	0.268554i
$691$	−9.42763	+	35.1844i	−0.358644	+	1.33848i	0.517192	+	0.855869i	$0.326977\pi$
$691$	−9.42763	+	35.1844i	−0.358644	+	1.33848i	−0.875836	+	0.482608i	$0.839690\pi$
$692$	−0.141515	−	0.204009i	−0.00537960	−	0.00775525i
$693$	−30.5631	+	34.2334i	−1.16100	+	1.30042i
$694$	−1.99375	+	22.2256i	−0.0756819	+	0.843671i
$695$	−2.93621	−	5.08566i	−0.111377	−	0.192910i
$696$	−12.1680	−	6.56514i	−0.461228	−	0.248851i
$697$	−23.7422	−	13.7075i	−0.899298	−	0.519210i
$698$	6.70956	+	14.4717i	0.253961	+	0.547763i
$699$	−39.5764	+	12.1220i	−1.49692	+	0.458495i
$700$	−4.31670	+	22.0656i	−0.163156	+	0.834001i
$701$	9.18394	+	9.18394i	0.346873	+	0.346873i	0.858943	−	0.512071i	$-0.171121\pi$
$701$	9.18394	+	9.18394i	0.346873	+	0.346873i	−0.512071	+	0.858943i	$0.671121\pi$
$702$	−1.25241	−	0.313134i	−0.0472690	−	0.0118185i
$703$	−12.6364	−	7.29560i	−0.476589	−	0.275159i
$704$	44.5163	+	12.5600i	1.67777	+	0.473375i
$705$	0.625239	+	17.6444i	0.0235479	+	0.664527i
$706$	19.3688	−	16.1799i	0.728956	−	0.608939i
$707$	−44.1108	−	12.4962i	−1.65896	−	0.469968i
$708$	−17.4674	+	22.1792i	−0.656466	+	0.833544i
$709$	4.34186	−	16.2040i	0.163062	−	0.608555i	−0.835218	−	0.549920i	$-0.814658\pi$
$709$	4.34186	−	16.2040i	0.163062	−	0.608555i	0.998279	−	0.0586356i	$-0.0186750\pi$
$710$	−1.18018	+	1.67760i	−0.0442913	+	0.0629594i
$711$	−0.500768	−	7.05703i	−0.0187803	−	0.264659i
$712$	19.4732	+	11.4148i	0.729788	+	0.427789i
$713$		−	17.8702i		−	0.669244i
$714$	1.54339	−	22.5608i	0.0577598	−	0.844316i
$715$	−0.622397	−	0.622397i	−0.0232763	−	0.0232763i
$716$	31.8260	+	15.0115i	1.18939	+	0.561006i
$717$	7.73424	+	1.78140i	0.288840	+	0.0665277i
$718$	4.05879	+	23.3184i	0.151473	+	0.870234i
$719$	−10.7446	−	18.6102i	−0.400706	−	0.694042i	0.593106	−	0.805125i	$-0.297902\pi$
$719$	−10.7446	−	18.6102i	−0.400706	−	0.694042i	−0.993811	+	0.111082i	$0.964568\pi$
$720$	8.87169	+	5.42491i	0.330628	+	0.202174i
$721$	0.642596	−	45.0647i	0.0239315	−	1.67830i
$722$	15.6010	+	18.6758i	0.580607	+	0.695040i
$723$	34.8937	−	37.4575i	1.29771	−	1.39306i
$724$	−25.6115	+	2.12723i	−0.951843	+	0.0790578i
$725$	3.10373	+	11.5833i	0.115270	+	0.430192i
$726$	2.96778	−	54.8594i	0.110145	−	2.03602i
$727$	−27.2660			−1.01124			−0.505619	−	0.862757i	$-0.668736\pi$
$727$	−27.2660			−1.01124			−0.505619	+	0.862757i	$0.668736\pi$
$728$	0.948782	−	0.910007i	0.0351642	−	0.0337271i
$729$	−5.69506	−	26.3925i	−0.210928	−	0.977502i
$730$	−5.60710	−	12.0938i	−0.207528	−	0.447613i
$731$	21.5992	−	5.78749i	0.798875	−	0.214058i
$732$	2.20293	+	5.51402i	0.0814227	+	0.203804i
$733$	−1.83153	+	6.83537i	−0.0676491	+	0.252470i	−0.991466	−	0.130364i	$-0.958385\pi$
$733$	−1.83153	+	6.83537i	−0.0676491	+	0.252470i	0.923817	+	0.382834i	$0.125052\pi$
$734$	−27.7088	−	33.1699i	−1.02275	−	1.22432i
$735$	−0.0725358	−	10.5064i	−0.00267552	−	0.387534i
$736$	18.6586	−	6.55969i	0.687763	−	0.241793i
$737$	15.7397	−	9.08730i	0.579778	−	0.334735i
$738$	24.0053	−	23.1274i	0.883647	−	0.851330i
$739$	10.3916	+	38.7821i	0.382262	+	1.42662i	0.842438	+	0.538794i	$0.181120\pi$
$739$	10.3916	+	38.7821i	0.382262	+	1.42662i	−0.460175	+	0.887828i	$0.652213\pi$
$740$	6.38151	+	17.7760i	0.234589	+	0.653458i
$741$	−0.119319	−	0.389559i	−0.00438330	−	0.0143108i
$742$	13.9969	−	19.3055i	0.513843	−	0.708726i
$743$	11.6648			0.427942			0.213971	−	0.976840i	$-0.431360\pi$
$743$	11.6648			0.427942			0.213971	+	0.976840i	$0.431360\pi$
$744$	−24.3631	−	5.78102i	−0.893193	−	0.211942i
$745$	−0.712263	+	1.23368i	−0.0260953	+	0.0451984i
$746$	26.7694	−	38.0523i	0.980098	−	1.39319i
$747$	12.2658	−	4.23756i	0.448781	−	0.155044i
$748$	22.9977	+	33.1536i	0.840881	+	1.21222i
$749$	0.468493	+	0.482047i	0.0171184	+	0.0176136i
$750$	−4.04948	−	19.2104i	−0.147866	−	0.701466i
$751$	−19.0586	−	33.0104i	−0.695456	−	1.20457i	−0.970027	−	0.242999i	$-0.921869\pi$
$751$	−19.0586	−	33.0104i	−0.695456	−	1.20457i	0.274570	−	0.961567i	$-0.411464\pi$
$752$	36.3083	−	29.9259i	1.32403	−	1.09128i
$753$	−31.0606	+	19.4310i	−1.13191	+	0.708107i
$754$	0.241264	−	0.658359i	0.00878633	−	0.0239760i
$755$	2.51000	−	2.51000i	0.0913483	−	0.0913483i
$756$	25.8405	+	9.39526i	0.939808	+	0.341702i
$757$	15.5465	+	15.5465i	0.565049	+	0.565049i	0.930737	−	0.365688i	$-0.119166\pi$
$757$	15.5465	+	15.5465i	0.565049	+	0.565049i	−0.365688	+	0.930737i	$0.619166\pi$
$758$	−5.01520	−	10.8172i	−0.182160	−	0.392898i
$759$	−18.5694	−	29.6833i	−0.674026	−	1.07743i
$760$	−0.0216554	+	3.28178i	−0.000785525	+	0.119043i
$761$	30.5621	−	17.6450i	1.10787	−	0.639631i	0.169596	−	0.985514i	$-0.445754\pi$
$761$	30.5621	−	17.6450i	1.10787	−	0.639631i	0.938278	+	0.345883i	$0.112420\pi$
$762$	−13.7629	+	21.1150i	−0.498577	+	0.764916i
$763$	−7.29782	+	25.7609i	−0.264199	+	0.932606i
$764$	−28.7766	−	5.20471i	−1.04110	−	0.188300i
$765$	2.96215	+	8.57404i	0.107097	+	0.309995i
$766$	5.30584	+	30.4828i	0.191708	+	1.10139i
$767$	−1.23992	−	0.715865i	−0.0447707	−	0.0258484i
$768$	−2.90701	−	27.5599i	−0.104898	−	0.994483i
$769$		−	6.22612i		−	0.224520i	−0.993679	−	0.112260i	$-0.964191\pi$
$769$		−	6.22612i		−	0.224520i	0.993679	−	0.112260i	$-0.0358089\pi$
$770$	11.8123	+	14.5574i	0.425687	+	0.524611i
$771$	1.36580	−	0.418334i	0.0491879	−	0.0150659i
$772$	−15.5896	+	5.59661i	−0.561082	+	0.201426i
$773$	9.25469	−	2.47979i	0.332868	−	0.0891917i	−0.0885140	−	0.996075i	$-0.528212\pi$
$773$	9.25469	−	2.47979i	0.332868	−	0.0891917i	0.421382	+	0.906883i	$0.361545\pi$
$774$	−0.506345	+	27.1839i	−0.0182002	+	0.977104i
$775$	10.8588	+	18.8080i	0.390061	+	0.675605i
$776$	14.4712	−	8.22809i	0.519484	−	0.295371i
$777$	25.8786	+	42.7096i	0.928389	+	1.53220i
$778$	−0.507640	+	5.65896i	−0.0181998	+	0.202884i
$779$	10.1615	+	2.72277i	0.364074	+	0.0975535i
$780$	−0.207942	+	0.484638i	−0.00744553	+	0.0173528i
$781$	−2.50457	−	9.34719i	−0.0896206	−	0.334469i
$782$	16.1996	+	5.93655i	0.579296	+	0.212291i
$783$	14.5821	−	1.55539i	0.521122	−	0.0555850i
$784$	−22.1058	+	17.1853i	−0.789491	+	0.613762i
$785$		−	1.96462i		−	0.0701202i
$786$	20.8159	−	18.6793i	0.742477	−	0.666267i
$787$	−20.5741	+	5.51281i	−0.733387	+	0.196510i	−0.606137	−	0.795360i	$-0.707282\pi$
$787$	−20.5741	+	5.51281i	−0.733387	+	0.196510i	−0.127250	+	0.991871i	$0.540615\pi$
$788$	0.491658	−	0.0408360i	0.0175146	−	0.00145472i
$789$	21.6850	+	20.2008i	0.772007	+	0.719166i
$790$	−2.87853	−	0.258220i	−0.102414	−	0.00918705i
$791$	3.30857	−	5.54645i	0.117639	−	0.197209i
$792$	−46.4754	+	15.7138i	−1.65143	+	0.558364i
$793$	−0.260784	+	0.150564i	−0.00926070	+	0.00534667i
$794$	8.73993	−	12.4237i	0.310169	−	0.440899i
$795$	−2.14699	+	9.32151i	−0.0761460	+	0.330600i
$796$	29.3217	−	10.5264i	1.03928	−	0.373098i
$797$	9.21921	−	9.21921i	0.326561	−	0.326561i	−0.524716	−	0.851277i	$-0.675829\pi$
$797$	9.21921	−	9.21921i	0.326561	−	0.326561i	0.851277	+	0.524716i	$0.175829\pi$
$798$	1.66860	+	8.51554i	0.0590677	+	0.301447i
$799$	41.0447			1.45206
$800$	−15.6518	+	18.2418i	−0.553374	+	0.644946i
$801$	−23.8814	+	1.69463i	−0.843806	+	0.0598766i
$802$	−29.8837	+	5.20156i	−1.05523	+	0.183673i
$803$	60.7477	+	16.2773i	2.14374	+	0.574414i
$804$	−8.55465	−	6.73731i	−0.301699	−	0.237607i
$805$	7.71258	+	2.18490i	0.271833	+	0.0770077i
$806$	0.113457	−	1.26477i	0.00399634	−	0.0445496i
$807$	33.7680	−	1.19659i	1.18869	−	0.0421218i
$808$	−34.4274	−	34.8848i	−1.21115	−	1.22724i
$809$	−13.8920	+	24.0616i	−0.488415	+	0.845960i	−0.999911	−	0.0133254i	$-0.995758\pi$
$809$	−13.8920	+	24.0616i	−0.488415	+	0.845960i	0.511496	+	0.859286i	$0.329092\pi$
$810$	−11.0146	+	0.575674i	−0.387015	+	0.0202271i
$811$	15.6738	−	15.6738i	0.550381	−	0.550381i	−0.376170	−	0.926551i	$-0.622759\pi$
$811$	15.6738	−	15.6738i	0.550381	−	0.550381i	0.926551	+	0.376170i	$0.122759\pi$
$812$	−6.56276	+	13.4146i	−0.230308	+	0.470762i
$813$	13.5964	+	44.3902i	0.476847	+	1.55683i
$814$	−83.6634	−	30.6596i	−2.93240	−	1.07462i
$815$	8.70035	−	15.0695i	0.304760	−	0.527860i
$816$	13.3341	−	20.1650i	0.466786	−	0.705916i
$817$	−7.43105	+	4.29032i	−0.259979	+	0.150099i
$818$	−4.68762	+	3.91584i	−0.163899	+	0.136914i
$819$	−0.284148	+	1.36514i	−0.00992895	+	0.0477017i
$820$	−7.76124	−	11.1886i	−0.271034	−	0.390724i
$821$	−25.2310	−	6.76061i	−0.880567	−	0.235947i	−0.209915	−	0.977720i	$-0.567319\pi$
$821$	−25.2310	−	6.76061i	−0.880567	−	0.235947i	−0.670652	+	0.741773i	$0.733985\pi$
$822$	−11.3866	−	22.4409i	−0.397154	−	0.782716i
$823$	−14.6550	−	8.46106i	−0.510840	−	0.294934i	0.222339	−	0.974970i	$-0.428631\pi$
$823$	−14.6550	−	8.46106i	−0.510840	−	0.294934i	−0.733179	+	0.680036i	$0.761964\pi$
$824$	24.3654	−	41.5662i	0.848808	−	1.44803i
$825$	37.5810	+	19.9574i	1.30840	+	0.694827i
$826$	24.6877	+	17.8992i	0.858996	+	0.622792i
$827$	6.91465	−	6.91465i	0.240446	−	0.240446i	−0.576589	−	0.817035i	$-0.695616\pi$
$827$	6.91465	−	6.91465i	0.240446	−	0.240446i	0.817035	+	0.576589i	$0.195616\pi$
$828$	−12.3876	+	16.9297i	−0.430498	+	0.588349i
$829$	23.1308	−	6.19787i	0.803365	−	0.215261i	0.166304	−	0.986075i	$-0.446817\pi$
$829$	23.1308	−	6.19787i	0.803365	−	0.215261i	0.637061	+	0.770813i	$0.280150\pi$
$830$	−0.909065	−	5.22271i	−0.0315541	−	0.181283i
$831$	0.943005	+	26.6118i	0.0327125	+	0.923155i
$832$	1.36221	−	0.345802i	0.0472262	−	0.0119885i
$833$	−24.4155	−	0.696441i	−0.845946	−	0.0241303i
$834$	−3.42380	−	16.2423i	−0.118557	−	0.562424i
$835$	5.86057	+	1.57033i	0.202813	+	0.0543437i
$836$	−11.8169	−	10.0045i	−0.408697	−	0.346013i
$837$	24.7797	−	9.55593i	0.856513	−	0.330301i
$838$	−1.82688	+	0.847000i	−0.0631085	+	0.0292591i
$839$			53.1082i			1.83350i	0.399462	+	0.916750i	$0.369197\pi$
$839$			53.1082i			1.83350i	−0.399462	+	0.916750i	$0.630803\pi$
$840$	5.47378	−	9.80801i	0.188863	−	0.338408i
$841$		−	21.0349i		−	0.725342i
$842$	17.2659	+	37.2406i	0.595024	+	1.28340i
$843$	−3.71480	+	16.1284i	−0.127945	+	0.555492i
$844$	−29.0364	+	2.41169i	−0.999473	+	0.0830138i
$845$	10.8558	+	2.90879i	0.373449	+	0.100065i
$846$	−13.8121	+	47.9563i	−0.474868	+	1.64877i
$847$	−59.3355	−	0.846089i	−2.03879	−	0.0290720i
$848$	23.1976	−	10.5697i	0.796607	−	0.362966i
$849$	41.2120	−	1.46037i	1.41439	−	0.0501197i
$850$	−20.6571	+	3.59557i	−0.708533	+	0.123327i
$851$	−36.8022	+	9.86113i	−1.26156	+	0.338035i
$852$	−4.64388	+	3.47121i	−0.159097	+	0.118922i
$853$	25.5060	−	25.5060i	0.873310	−	0.873310i	−0.119522	−	0.992832i	$-0.538136\pi$
$853$	25.5060	−	25.5060i	0.873310	−	0.873310i	0.992832	+	0.119522i	$0.0381361\pi$
$854$	5.85647	−	2.61445i	0.200404	−	0.0894648i
$855$	−1.94948	−	2.88382i	−0.0666707	−	0.0986245i
$856$	0.181407	+	0.695339i	0.00620035	+	0.0237662i
$857$	−21.1037	−	12.1842i	−0.720887	−	0.416205i	0.0941918	−	0.995554i	$-0.469973\pi$
$857$	−21.1037	−	12.1842i	−0.720887	−	0.416205i	−0.815079	+	0.579350i	$0.803307\pi$
$858$	−1.12580	−	2.21874i	−0.0384341	−	0.0757465i
$859$	6.52316	+	1.74788i	0.222567	+	0.0596368i	0.368379	−	0.929676i	$-0.379913\pi$
$859$	6.52316	+	1.74788i	0.222567	+	0.0596368i	−0.145812	+	0.989312i	$0.546579\pi$
$860$	10.9294	+	1.97676i	0.372689	+	0.0674069i
$861$	−25.9920	−	24.9145i	−0.885805	−	0.849085i
$862$	−0.549514	−	0.657818i	−0.0187165	−	0.0224054i
$863$	−35.3090	+	20.3856i	−1.20193	+	0.693935i	−0.960984	−	0.276603i	$-0.910791\pi$
$863$	−35.3090	+	20.3856i	−1.20193	+	0.693935i	−0.240947	+	0.970538i	$0.577458\pi$
$864$	19.0735	+	22.3652i	0.648894	+	0.760879i
$865$	0.0537895	−	0.0931662i	0.00182890	−	0.00316775i
$866$	3.75877	−	10.2569i	0.127728	−	0.348543i
$867$	−7.98988	+	2.44725i	−0.271351	+	0.0831128i
$868$	−5.19255	+	26.5427i	−0.176247	+	0.900917i
$869$	9.64135	−	9.64135i	0.327061	−	0.327061i
$870$	0.323610	−	5.98193i	0.0109714	−	0.202806i
$871$	0.276114	−	0.478244i	0.00935577	−	0.0162047i
$872$	−20.3728	+	20.1057i	−0.689911	+	0.680866i
$873$	−7.72382	+	15.8776i	−0.261412	+	0.537375i
$874$	−6.59405	−	0.591522i	−0.223047	−	0.0200085i
$875$	−20.5592	+	5.19582i	−0.695029	+	0.175651i
$876$	−4.44676	−	37.4171i	−0.150242	−	1.26421i
$877$	30.2968	+	8.11801i	1.02305	+	0.274126i	0.731073	−	0.682299i	$-0.239020\pi$
$877$	30.2968	+	8.11801i	1.02305	+	0.274126i	0.291978	+	0.956425i	$0.405687\pi$
$878$	2.79422	+	16.0532i	0.0943002	+	0.541768i
$879$	−6.48660	+	4.05791i	−0.218787	+	0.136870i
$880$	3.30636	+	19.7667i	0.111457	+	0.666336i
$881$	14.3252			0.482627			0.241313	−	0.970447i	$-0.422422\pi$
$881$	14.3252			0.482627			0.241313	+	0.970447i	$0.422422\pi$
$882$	9.02982	−	28.2924i	0.304050	−	0.952656i
$883$	−26.2056	+	26.2056i	−0.881888	+	0.881888i	−0.993726	−	0.111838i	$-0.964326\pi$
$883$	−26.2056	+	26.2056i	−0.881888	+	0.881888i	0.111838	+	0.993726i	$0.464326\pi$
$884$	1.10884	+	0.523011i	0.0372943	+	0.0175908i
$885$	−11.9203	−	2.74556i	−0.400696	−	0.0922910i
$886$	20.0148	+	14.0802i	0.672411	+	0.473035i
$887$	20.7034	−	11.9531i	0.695151	−	0.401345i	−0.110388	−	0.993889i	$-0.535209\pi$
$887$	20.7034	−	11.9531i	0.695151	−	0.401345i	0.805539	+	0.592543i	$0.201876\pi$
$888$	1.53849	+	53.3639i	0.0516282	+	1.79077i
$889$	23.3801	+	13.9467i	0.784142	+	0.467757i
$890$	−0.873830	+	9.74110i	−0.0292908	+	0.326522i
$891$	31.2305	−	41.6221i	1.04626	−	1.39439i
$892$	−18.0723	+	21.3463i	−0.605105	+	0.714727i
$893$	−15.2134	+	4.07642i	−0.509098	+	0.136412i
$894$	−2.99690	+	2.68929i	−0.100231	+	0.0899433i
$895$			15.2467i			0.509642i
$896$	−29.6197	+	4.32151i	−0.989524	+	0.144372i
$897$	−0.939590	−	0.498969i	−0.0313720	−	0.0166601i
$898$	−12.9206	+	35.2576i	−0.431166	+	1.17656i
$899$	3.73347	+	13.9335i	0.124518	+	0.464708i
$900$	2.75033	−	25.3455i	0.0916777	−	0.844851i
$901$	21.4799	+	5.75552i	0.715599	+	0.191744i
$902$	63.9856	+	5.73986i	2.13049	+	0.191116i
$903$	29.3604	−	0.621427i	0.977054	−	0.0206798i
$904$	6.00188	−	3.41258i	0.199620	−	0.113501i
$905$	−5.56766	−	9.64347i	−0.185075	−	0.320560i
$906$	8.94773	−	4.54011i	0.297268	−	0.150835i
$907$	−18.2981	+	4.90297i	−0.607580	+	0.162801i	−0.549475	−	0.835510i	$-0.685172\pi$
$907$	−18.2981	+	4.90297i	−0.607580	+	0.162801i	−0.0581047	+	0.998310i	$0.518506\pi$
$908$	−16.0381	+	34.0026i	−0.532245	+	1.12842i
$909$	51.0403	+	9.86677i	1.69290	+	0.327260i
$910$	0.531988	+	0.203604i	0.0176352	+	0.00674940i
$911$		−	20.0171i		−	0.663197i	−0.943421	−	0.331598i	$-0.892412\pi$
$911$		−	20.0171i		−	0.663197i	0.943421	−	0.331598i	$-0.107588\pi$
$912$	−2.93962	+	8.79854i	−0.0973405	+	0.291349i
$913$	21.6596	+	12.5052i	0.716827	+	0.413860i
$914$	40.8891	−	7.11715i	1.35249	−	0.235414i
$915$	−1.75365	+	1.88250i	−0.0579740	+	0.0622336i
$916$	−19.9687	−	28.7869i	−0.659784	−	0.951147i
$917$	−21.0543	−	21.6634i	−0.695273	−	0.715388i
$918$	0.430656	+	25.6377i	0.0142138	+	0.846170i
$919$	−6.65546	+	3.84253i	−0.219543	+	0.126753i	−0.605739	−	0.795664i	$-0.707122\pi$
$919$	−6.65546	+	3.84253i	−0.219543	+	0.126753i	0.386195	+	0.922417i	$0.373789\pi$
$920$	6.01948	+	6.09944i	0.198456	+	0.201093i
$921$	9.38327	−	5.87003i	0.309189	−	0.193424i
$922$	−6.69670	+	3.10481i	−0.220544	+	0.102251i
$923$	−0.207910	−	0.207910i	−0.00684346	−	0.00684346i
$924$	18.9561	+	49.4844i	0.623610	+	1.62792i
$925$	32.7415	−	32.7415i	1.07654	−	1.07654i
$926$	−3.01208	−	1.10382i	−0.0989831	−	0.0362736i
$927$	3.61724	+	50.9756i	0.118806	+	1.67426i
$928$	−13.1777	+	9.01280i	−0.432580	+	0.295860i
$929$	−16.0903	−	27.8693i	−0.527906	−	0.914361i	−0.999471	−	0.0325291i	$-0.989644\pi$
$929$	−16.0903	−	27.8693i	−0.527906	−	0.914361i	0.471564	−	0.881832i	$-0.343690\pi$
$930$	−2.23781	−	10.6160i	−0.0733806	−	0.348112i
$931$	9.11887	−	2.16672i	0.298859	−	0.0710114i
$932$	−8.50639	+	47.0314i	−0.278636	+	1.54056i
$933$	−16.2554	+	17.4498i	−0.532179	+	0.571280i
$934$	3.83204	+	2.69581i	0.125388	+	0.0882095i
$935$	−8.74138	+	15.1405i	−0.285874	+	0.495148i
$936$	−0.984220	+	1.11956i	−0.0321702	+	0.0365939i
$937$	18.1655			0.593440			0.296720	−	0.954965i	$-0.404107\pi$
$937$	18.1655			0.593440			0.296720	+	0.954965i	$0.404107\pi$
$938$	−6.90383	+	9.52223i	−0.225418	+	0.310912i
$939$	15.9255	−	4.87787i	0.519709	−	0.159183i
$940$	18.4386	+	8.69702i	0.601402	+	0.283666i
$941$	−6.28017	−	23.4379i	−0.204728	−	0.764055i	−0.989532	−	0.144311i	$-0.953903\pi$
$941$	−6.28017	−	23.4379i	−0.204728	−	0.764055i	0.784805	−	0.619743i	$-0.212763\pi$
$942$	1.72495	−	5.27857i	0.0562020	−	0.171985i
$943$	23.7895	−	13.7349i	0.774692	−	0.447269i
$944$	13.5165	+	29.6649i	0.439925	+	0.965510i
$945$	1.09453	+	11.8630i	0.0356051	+	0.385904i
$946$	−40.2143	+	33.5934i	−1.30748	+	1.09221i
$947$	10.6983	−	39.9267i	0.347649	−	1.29744i	−0.541839	−	0.840483i	$-0.682272\pi$
$947$	10.6983	−	39.9267i	0.347649	−	1.29744i	0.889487	−	0.456960i	$-0.151062\pi$
$948$	−7.50737	−	3.22117i	−0.243828	−	0.104619i
$949$	1.84580	−	0.494580i	0.0599171	−	0.0160547i
$950$	7.29955	−	3.38431i	0.236829	−	0.109801i
$951$	21.8092	+	11.5818i	0.707212	+	0.375565i
$952$	−22.3363	−	13.5247i	−0.723924	−	0.438338i
$953$	8.31415			0.269322			0.134661	−	0.990892i	$-0.457005\pi$
$953$	8.31415			0.269322			0.134661	+	0.990892i	$0.457005\pi$
$954$	−13.9530	+	23.1601i	−0.451744	+	0.749837i
$955$	−3.27944	−	12.2390i	−0.106120	−	0.396046i
$956$	5.92169	−	6.99448i	0.191521	−	0.226218i
$957$	20.6801	+	19.2647i	0.668493	+	0.622738i
$958$	−23.7707	+	19.8571i	−0.767997	+	0.641552i
$959$	−23.7305	+	13.2533i	−0.766299	+	0.427973i
$960$	10.2629	−	6.23339i	0.331233	−	0.201182i
$961$	−2.43793	−	4.22262i	−0.0786429	−	0.136214i
$962$	−2.66730	+	0.464270i	−0.0859971	+	0.0149687i
$963$	−0.575757	−	0.499459i	−0.0185535	−	0.0160949i
$964$	−19.9728	−	55.6351i	−0.643280	−	1.79188i
$965$	−5.07480	−	5.07480i	−0.163364	−	0.163364i
$966$	18.8039	+	12.6422i	0.605007	+	0.406755i
$967$		−	44.0766i		−	1.41741i	−0.705506	−	0.708704i	$-0.749280\pi$
$967$		−	44.0766i		−	1.41741i	0.705506	−	0.708704i	$-0.250720\pi$
$968$	−54.7291	−	32.0812i	−1.75906	−	1.03113i
$969$	−6.86047	+	4.29181i	−0.220390	+	0.137873i
$970$	5.89929	+	4.15009i	0.189415	+	0.133251i
$971$	−7.49863	+	27.9853i	−0.240643	+	0.898091i	0.734881	+	0.678196i	$0.237238\pi$
$971$	−7.49863	+	27.9853i	−0.240643	+	0.898091i	−0.975524	+	0.219895i	$0.929429\pi$
$972$	−30.0998	−	8.12423i	−0.965451	−	0.260585i
$973$	−17.3827	+	4.39303i	−0.557263	+	0.140834i
$974$	−1.86435	−	2.23180i	−0.0597376	−	0.0715114i
$975$	1.29210	−	0.0457862i	0.0413803	−	0.00146633i
$976$	6.82476	+	0.657642i	0.218455	+	0.0210506i
$977$	−41.5372	−	23.9815i	−1.32889	−	0.767237i	−0.343765	−	0.939056i	$-0.611702\pi$
$977$	−41.5372	−	23.9815i	−1.32889	−	0.767237i	−0.985129	+	0.171819i	$0.945036\pi$
$978$	36.6074	−	32.8499i	1.17058	−	1.05042i
$979$	−32.6268	−	32.6268i	−1.04276	−	1.04276i
$980$	−10.8206	−	5.48629i	−0.345653	−	0.175253i
$981$	5.76223	−	29.8077i	0.183974	−	0.951687i
$982$	−23.0723	+	10.6971i	−0.736266	+	0.341357i
$983$	−29.2508	−	16.8879i	−0.932955	−	0.538642i	−0.0452101	−	0.998978i	$-0.514396\pi$
$983$	−29.2508	−	16.8879i	−0.932955	−	0.538642i	−0.887745	+	0.460336i	$0.847729\pi$
$984$	−11.0293	−	36.8763i	−0.351602	−	1.17557i
$985$	0.106881	+	0.185124i	0.00340552	+	0.00589853i
$986$	−13.8712	−	1.24432i	−0.441748	−	0.0396272i
$987$	52.3511	+	12.8466i	1.66635	+	0.408910i
$988$	−0.462940	−	0.0837303i	−0.0147281	−	0.00266382i
$989$	−5.79902	+	21.6423i	−0.184398	+	0.688184i
$990$	−14.7485	−	15.3083i	−0.468737	−	0.486530i
$991$	9.81671	−	17.0030i	0.311838	−	0.540119i	−0.666922	−	0.745127i	$-0.732389\pi$
$991$	9.81671	−	17.0030i	0.311838	−	0.540119i	0.978760	+	0.205008i	$0.0657221\pi$
$992$	−18.8275	+	21.9431i	−0.597774	+	0.696693i
$993$	−55.0571	−	29.2381i	−1.74718	−	0.927843i
$994$	3.94589	+	4.86286i	0.125156	+	0.154241i
$995$	9.54494	+	9.54494i	0.302595	+	0.302595i
$996$	2.14310	−	14.8307i	0.0679067	−	0.469927i
$997$	−10.1300	−	37.8056i	−0.320820	−	1.19732i	−0.918448	−	0.395543i	$-0.870557\pi$
$997$	−10.1300	−	37.8056i	−0.320820	−	1.19732i	0.597628	−	0.801774i	$-0.296110\pi$
$998$	40.1262	+	28.2284i	1.27017	+	0.893555i
$999$	−33.3536	−	45.7587i	−1.05526	−	1.44774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.101.54	yes	240
3.2	odd	2	inner	336.2.bo.a.101.7	yes	240
7.5	odd	6	inner	336.2.bo.a.5.27	✓	240
16.13	even	4	inner	336.2.bo.a.269.34	yes	240
21.5	even	6	inner	336.2.bo.a.5.34	yes	240
48.29	odd	4	inner	336.2.bo.a.269.27	yes	240
112.61	odd	12	inner	336.2.bo.a.173.7	yes	240
336.173	even	12	inner	336.2.bo.a.173.54	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.27	✓	240	7.5	odd	6	inner
336.2.bo.a.5.34	yes	240	21.5	even	6	inner
336.2.bo.a.101.7	yes	240	3.2	odd	2	inner
336.2.bo.a.101.54	yes	240	1.1	even	1	trivial
336.2.bo.a.173.7	yes	240	112.61	odd	12	inner
336.2.bo.a.173.54	yes	240	336.173	even	12	inner
336.2.bo.a.269.27	yes	240	48.29	odd	4	inner
336.2.bo.a.269.34	yes	240	16.13	even	4	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32786 + 0.486611i) q^{2} +(-0.388759 + 1.68786i) q^{3} +(1.52642 + 1.29230i) q^{4} +(-0.224285 + 0.837045i) q^{5} +(-1.33755 + 2.05206i) q^{6} +(2.27219 + 1.35541i) q^{7} +(1.39802 + 2.45877i) q^{8} +(-2.69773 - 1.31234i) q^{9} +O(q^{10})\)	\(q+(1.32786 + 0.486611i) q^{2} +(-0.388759 + 1.68786i) q^{3} +(1.52642 + 1.29230i) q^{4} +(-0.224285 + 0.837045i) q^{5} +(-1.33755 + 2.05206i) q^{6} +(2.27219 + 1.35541i) q^{7} +(1.39802 + 2.45877i) q^{8} +(-2.69773 - 1.31234i) q^{9} +(-0.705135 + 1.00234i) q^{10} +(-1.49644 - 5.58477i) q^{11} +(-2.77463 + 2.07398i) q^{12} +(-0.124223 - 0.124223i) q^{13} +(2.35759 + 2.90547i) q^{14} +(-1.32562 - 0.703971i) q^{15} +(0.659908 + 3.94519i) q^{16} +(-1.74467 + 3.02186i) q^{17} +(-2.94361 - 3.05535i) q^{18} +(0.346550 - 1.29334i) q^{19} +(-1.42407 + 0.987836i) q^{20} +(-3.17108 + 3.30821i) q^{21} +(0.730559 - 8.14397i) q^{22} +(-1.74815 - 3.02788i) q^{23} +(-4.69355 + 1.40379i) q^{24} +(3.67979 + 2.12453i) q^{25} +(-0.104502 - 0.225398i) q^{26} +(3.26381 - 4.04321i) q^{27} +(1.71672 + 5.00528i) q^{28} +(1.99563 + 1.99563i) q^{29} +(-1.41768 - 1.57984i) q^{30} +(4.42641 + 2.55559i) q^{31} +(-1.04351 + 5.55977i) q^{32} +(10.0081 - 0.354641i) q^{33} +(-3.78715 + 3.16363i) q^{34} +(-1.64416 + 1.59793i) q^{35} +(-2.42193 - 5.48947i) q^{36} +(2.82045 - 10.5261i) q^{37} +(1.08952 - 1.54874i) q^{38} +(0.257963 - 0.161378i) q^{39} +(-2.37165 + 0.618739i) q^{40} +7.85681i q^{41} +(-5.82056 + 2.84976i) q^{42} +(-4.53143 - 4.53143i) q^{43} +(4.93303 - 10.4585i) q^{44} +(1.70355 - 1.96378i) q^{45} +(-0.847893 - 4.87127i) q^{46} +(-5.88144 - 10.1870i) q^{47} +(-6.91547 - 0.419895i) q^{48} +(3.32573 + 6.15951i) q^{49} +(3.85242 + 4.61170i) q^{50} +(-4.42221 - 4.11953i) q^{51} +(-0.0290825 - 0.350149i) q^{52} +(-1.64946 - 6.15586i) q^{53} +(6.30135 - 3.78060i) q^{54} +5.01033 q^{55} +(-0.156068 + 7.48169i) q^{56} +(2.04825 + 1.08772i) q^{57} +(1.67882 + 3.62101i) q^{58} +(7.87208 - 2.10932i) q^{59} +(-1.11371 - 2.78766i) q^{60} +(0.443640 - 1.65569i) q^{61} +(4.63407 + 5.54740i) q^{62} +(-4.35101 - 6.63843i) q^{63} +(-4.09108 + 6.87481i) q^{64} +(0.131841 - 0.0761186i) q^{65} +(13.4619 + 4.39912i) q^{66} +(0.813578 + 3.03632i) q^{67} +(-6.56825 + 2.35798i) q^{68} +(5.79025 - 1.77351i) q^{69} +(-2.96078 + 1.32176i) q^{70} +1.67369 q^{71} +(-0.544744 - 8.46778i) q^{72} +(-5.43870 + 9.42010i) q^{73} +(8.86726 - 12.6047i) q^{74} +(-5.01645 + 5.38503i) q^{75} +(2.20037 - 1.52633i) q^{76} +(4.16947 - 14.7180i) q^{77} +(0.421066 - 0.0887590i) q^{78} +(1.17913 + 2.04231i) q^{79} +(-3.45031 - 0.332476i) q^{80} +(5.55553 + 7.08069i) q^{81} +(-3.82321 + 10.4327i) q^{82} +(-3.05874 + 3.05874i) q^{83} +(-9.11560 + 0.951729i) q^{84} +(-2.13813 - 2.13813i) q^{85} +(-3.81205 - 8.22214i) q^{86} +(-4.14416 + 2.59252i) q^{87} +(11.6396 - 11.4870i) q^{88} +(6.91129 - 3.99023i) q^{89} +(3.21767 - 1.77866i) q^{90} +(-0.113885 - 0.450630i) q^{91} +(1.24453 - 6.88095i) q^{92} +(-6.03428 + 6.47765i) q^{93} +(-2.85264 - 16.3888i) q^{94} +(1.00486 + 0.580155i) q^{95} +(-8.97844 - 3.92271i) q^{96} -5.88553i q^{97} +(1.41881 + 9.79729i) q^{98} +(-3.29214 + 17.0301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

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