LMFDB - Embedded newform 1512.2.j.c.323.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.8
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16953 + 0.795104i) q^{2} +(0.735620 - 1.85980i) q^{4} +2.09311 q^{5} +1.00000i q^{7} +(0.618402 + 2.76000i) q^{8} +O(q^{10})$	\(q+(-1.16953 + 0.795104i) q^{2} +(0.735620 - 1.85980i) q^{4} +2.09311 q^{5} +1.00000i q^{7} +(0.618402 + 2.76000i) q^{8} +(-2.44797 + 1.66424i) q^{10} -0.961211i q^{11} -4.60210i q^{13} +(-0.795104 - 1.16953i) q^{14} +(-2.91773 - 2.73622i) q^{16} +3.28066i q^{17} +3.66977 q^{19} +(1.53974 - 3.89278i) q^{20} +(0.764262 + 1.12417i) q^{22} +2.40322 q^{23} -0.618872 q^{25} +(3.65914 + 5.38231i) q^{26} +(1.85980 + 0.735620i) q^{28} +9.31771 q^{29} -1.84927i q^{31} +(5.58795 + 0.880204i) q^{32} +(-2.60847 - 3.83684i) q^{34} +2.09311i q^{35} -2.29364i q^{37} +(-4.29193 + 2.91785i) q^{38} +(1.29439 + 5.77699i) q^{40} -0.314406i q^{41} -8.64261 q^{43} +(-1.78766 - 0.707086i) q^{44} +(-2.81064 + 1.91081i) q^{46} +2.34305 q^{47} -1.00000 q^{49} +(0.723792 - 0.492067i) q^{50} +(-8.55899 - 3.38540i) q^{52} +7.73354 q^{53} -2.01192i q^{55} +(-2.76000 + 0.618402i) q^{56} +(-10.8974 + 7.40855i) q^{58} +7.99530i q^{59} -10.6321i q^{61} +(1.47036 + 2.16278i) q^{62} +(-7.23516 + 3.41357i) q^{64} -9.63272i q^{65} +4.12203 q^{67} +(6.10138 + 2.41332i) q^{68} +(-1.66424 - 2.44797i) q^{70} -6.79440 q^{71} +16.0267 q^{73} +(1.82368 + 2.68249i) q^{74} +(2.69956 - 6.82505i) q^{76} +0.961211 q^{77} -1.26231i q^{79} +(-6.10713 - 5.72721i) q^{80} +(0.249985 + 0.367709i) q^{82} -2.99495i q^{83} +6.86680i q^{85} +(10.1078 - 6.87177i) q^{86} +(2.65294 - 0.594415i) q^{88} -12.8990i q^{89} +4.60210 q^{91} +(1.76785 - 4.46950i) q^{92} +(-2.74028 + 1.86297i) q^{94} +7.68126 q^{95} +4.98346 q^{97} +(1.16953 - 0.795104i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.16953	+	0.795104i	−0.826986	+	0.562223i
$2$	−1.16953	+	0.795104i	−0.826986	+	0.562223i
$3$		0			0
$3$		0			0
$4$	0.735620	−	1.85980i	0.367810	−	0.929901i
$5$	2.09311			0.936069			0.468035	−	0.883710i	$-0.344962\pi$
$5$	2.09311			0.936069			0.468035	+	0.883710i	$0.344962\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.618402	+	2.76000i	0.218638	+	0.975806i
$9$		0			0
$10$	−2.44797	+	1.66424i	−0.774116	+	0.526280i
$11$		−	0.961211i		−	0.289816i	−0.989445	−	0.144908i	$-0.953711\pi$
$11$		−	0.961211i		−	0.289816i	0.989445	−	0.144908i	$-0.0462886\pi$
$12$		0			0
$13$		−	4.60210i		−	1.27639i	−0.769874	−	0.638196i	$-0.779681\pi$
$13$		−	4.60210i		−	1.27639i	0.769874	−	0.638196i	$-0.220319\pi$
$14$	−0.795104	−	1.16953i	−0.212500	−	0.312571i
$15$		0			0
$16$	−2.91773	−	2.73622i	−0.729431	−	0.684054i
$17$			3.28066i			0.795677i	0.917455	+	0.397839i	$0.130240\pi$
$17$			3.28066i			0.795677i	−0.917455	+	0.397839i	$0.869760\pi$
$18$		0			0
$19$	3.66977			0.841904			0.420952	−	0.907083i	$-0.361696\pi$
$19$	3.66977			0.841904			0.420952	+	0.907083i	$0.361696\pi$
$20$	1.53974	−	3.89278i	0.344296	−	0.870452i
$21$		0			0
$22$	0.764262	+	1.12417i	0.162941	+	0.239674i
$23$	2.40322			0.501105			0.250553	−	0.968103i	$-0.419388\pi$
$23$	2.40322			0.501105			0.250553	+	0.968103i	$0.419388\pi$
$24$		0			0
$25$	−0.618872			−0.123774
$26$	3.65914	+	5.38231i	0.717617	+	1.05556i
$27$		0			0
$28$	1.85980	+	0.735620i	0.351470	+	0.139019i
$29$	9.31771			1.73026			0.865128	−	0.501552i	$-0.167237\pi$
$29$	9.31771			1.73026			0.865128	+	0.501552i	$0.167237\pi$
$30$		0			0
$31$		−	1.84927i		−	0.332138i	−0.986114	−	0.166069i	$-0.946892\pi$
$31$		−	1.84927i		−	0.332138i	0.986114	−	0.166069i	$-0.0531075\pi$
$32$	5.58795	+	0.880204i	0.987820	+	0.155600i
$33$		0			0
$34$	−2.60847	−	3.83684i	−0.447348	−	0.658013i
$35$			2.09311i			0.353801i
$36$		0			0
$37$		−	2.29364i		−	0.377072i	−0.982066	−	0.188536i	$-0.939626\pi$
$37$		−	2.29364i		−	0.377072i	0.982066	−	0.188536i	$-0.0603742\pi$
$38$	−4.29193	+	2.91785i	−0.696242	+	0.473338i
$39$		0			0
$40$	1.29439	+	5.77699i	0.204660	+	0.913422i
$41$		−	0.314406i		−	0.0491020i	−0.999699	−	0.0245510i	$-0.992184\pi$
$41$		−	0.314406i		−	0.0491020i	0.999699	−	0.0245510i	$-0.00781561\pi$
$42$		0			0
$43$	−8.64261			−1.31799			−0.658993	−	0.752149i	$-0.729017\pi$
$43$	−8.64261			−1.31799			−0.658993	+	0.752149i	$0.729017\pi$
$44$	−1.78766	−	0.707086i	−0.269500	−	0.106597i
$45$		0			0
$46$	−2.81064	+	1.91081i	−0.414407	+	0.281733i
$47$	2.34305			0.341769			0.170884	−	0.985291i	$-0.445338\pi$
$47$	2.34305			0.341769			0.170884	+	0.985291i	$0.445338\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.723792	−	0.492067i	0.102360	−	0.0695888i
$51$		0			0
$52$	−8.55899	−	3.38540i	−1.18692	−	0.469470i
$53$	7.73354			1.06228			0.531142	−	0.847283i	$-0.321763\pi$
$53$	7.73354			1.06228			0.531142	+	0.847283i	$0.321763\pi$
$54$		0			0
$55$		−	2.01192i		−	0.271288i
$56$	−2.76000	+	0.618402i	−0.368820	+	0.0826374i
$57$		0			0
$58$	−10.8974	+	7.40855i	−1.43090	+	0.972790i
$59$			7.99530i			1.04090i	0.853892	+	0.520450i	$0.174236\pi$
$59$			7.99530i			1.04090i	−0.853892	+	0.520450i	$0.825764\pi$
$60$		0			0
$61$		−	10.6321i		−	1.36130i	−0.732610	−	0.680649i	$-0.761698\pi$
$61$		−	10.6321i		−	1.36130i	0.732610	−	0.680649i	$-0.238302\pi$
$62$	1.47036	+	2.16278i	0.186736	+	0.274674i
$63$		0			0
$64$	−7.23516	+	3.41357i	−0.904395	+	0.426697i
$65$		−	9.63272i		−	1.19479i
$66$		0			0
$67$	4.12203			0.503586			0.251793	−	0.967781i	$-0.418980\pi$
$67$	4.12203			0.503586			0.251793	+	0.967781i	$0.418980\pi$
$68$	6.10138	+	2.41332i	0.739901	+	0.292658i
$69$		0			0
$70$	−1.66424	−	2.44797i	−0.198915	−	0.292588i
$71$	−6.79440			−0.806347			−0.403174	−	0.915124i	$-0.632093\pi$
$71$	−6.79440			−0.806347			−0.403174	+	0.915124i	$0.632093\pi$
$72$		0			0
$73$	16.0267			1.87579			0.937894	−	0.346922i	$-0.112773\pi$
$73$	16.0267			1.87579			0.937894	+	0.346922i	$0.112773\pi$
$74$	1.82368	+	2.68249i	0.211999	+	0.311833i
$75$		0			0
$76$	2.69956	−	6.82505i	0.309661	−	0.782887i
$77$	0.961211			0.109540
$78$		0			0
$79$		−	1.26231i		−	0.142021i	−0.997476	−	0.0710106i	$-0.977378\pi$
$79$		−	1.26231i		−	0.142021i	0.997476	−	0.0710106i	$-0.0226224\pi$
$80$	−6.10713	−	5.72721i	−0.682798	−	0.640322i
$81$		0			0
$82$	0.249985	+	0.367709i	0.0276063	+	0.0406066i
$83$		−	2.99495i		−	0.328738i	−0.986399	−	0.164369i	$-0.947441\pi$
$83$		−	2.99495i		−	0.328738i	0.986399	−	0.164369i	$-0.0525589\pi$
$84$		0			0
$85$			6.86680i			0.744809i
$86$	10.1078	−	6.87177i	1.08995	−	0.741002i
$87$		0			0
$88$	2.65294	−	0.594415i	0.282804	−	0.0633648i
$89$		−	12.8990i		−	1.36729i	−0.729815	−	0.683645i	$-0.760394\pi$
$89$		−	12.8990i		−	1.36729i	0.729815	−	0.683645i	$-0.239606\pi$
$90$		0			0
$91$	4.60210			0.482431
$92$	1.76785	−	4.46950i	0.184312	−	0.465978i
$93$		0			0
$94$	−2.74028	+	1.86297i	−0.282638	+	0.192150i
$95$	7.68126			0.788080
$96$		0			0
$97$	4.98346			0.505994			0.252997	−	0.967467i	$-0.418584\pi$
$97$	4.98346			0.505994			0.252997	+	0.967467i	$0.418584\pi$
$98$	1.16953	−	0.795104i	0.118141	−	0.0803176i
$99$		0			0
$100$	−0.455255	+	1.15098i	−0.0455255	+	0.115098i
$101$	−3.18764			−0.317182			−0.158591	−	0.987344i	$-0.550695\pi$
$101$	−3.18764			−0.317182			−0.158591	+	0.987344i	$0.550695\pi$
$102$		0			0
$103$			0.535425i			0.0527570i	0.999652	+	0.0263785i	$0.00839750\pi$
$103$			0.535425i			0.0527570i	−0.999652	+	0.0263785i	$0.991602\pi$
$104$	12.7018	−	2.84595i	1.24551	−	0.279068i
$105$		0			0
$106$	−9.04464	+	6.14897i	−0.878493	+	0.597240i
$107$			9.70673i			0.938385i	0.883096	+	0.469193i	$0.155455\pi$
$107$			9.70673i			0.938385i	−0.883096	+	0.469193i	$0.844545\pi$
$108$		0			0
$109$		−	8.03576i		−	0.769686i	−0.922982	−	0.384843i	$-0.874256\pi$
$109$		−	8.03576i		−	0.769686i	0.922982	−	0.384843i	$-0.125744\pi$
$110$	1.59969	+	2.35301i	0.152524	+	0.224351i
$111$		0			0
$112$	2.73622	−	2.91773i	0.258548	−	0.275699i
$113$		−	12.7809i		−	1.20233i	−0.799126	−	0.601163i	$-0.794704\pi$
$113$		−	12.7809i		−	1.20233i	0.799126	−	0.601163i	$-0.205296\pi$
$114$		0			0
$115$	5.03021			0.469069
$116$	6.85430	−	17.3291i	0.636406	−	1.60897i
$117$		0			0
$118$	−6.35709	−	9.35078i	−0.585218	−	0.860809i
$119$	−3.28066			−0.300738
$120$		0			0
$121$	10.0761			0.916007
$122$	8.45360	+	12.4346i	0.765353	+	1.12577i
$123$		0			0
$124$	−3.43927	−	1.36036i	−0.308856	−	0.122164i
$125$	−11.7609			−1.05193
$126$		0			0
$127$			16.6260i			1.47532i	0.675175	+	0.737658i	$0.264068\pi$
$127$			16.6260i			1.47532i	−0.675175	+	0.737658i	$0.735932\pi$
$128$	5.74762	−	9.74499i	0.508023	−	0.861344i
$129$		0			0
$130$	7.65901	+	11.2658i	0.671739	+	0.988075i
$131$			14.5603i			1.27214i	0.771632	+	0.636069i	$0.219440\pi$
$131$			14.5603i			1.27214i	−0.771632	+	0.636069i	$0.780560\pi$
$132$		0			0
$133$			3.66977i			0.318210i
$134$	−4.82086	+	3.27744i	−0.416459	+	0.283128i
$135$		0			0
$136$	−9.05461	+	2.02877i	−0.776426	+	0.173965i
$137$			17.2672i			1.47524i	0.675216	+	0.737620i	$0.264050\pi$
$137$			17.2672i			1.47524i	−0.675216	+	0.737620i	$0.735950\pi$
$138$		0			0
$139$	14.5580			1.23480			0.617398	−	0.786651i	$-0.288187\pi$
$139$	14.5580			1.23480			0.617398	+	0.786651i	$0.288187\pi$
$140$	3.89278	+	1.53974i	0.329000	+	0.130132i
$141$		0			0
$142$	7.94629	−	5.40225i	0.666837	−	0.453347i
$143$	−4.42358			−0.369919
$144$		0			0
$145$	19.5030			1.61964
$146$	−18.7438	+	12.7429i	−1.55125	+	1.05461i
$147$		0			0
$148$	−4.26571	−	1.68725i	−0.350640	−	0.138691i
$149$	20.1739			1.65271			0.826356	−	0.563148i	$-0.190410\pi$
$149$	20.1739			1.65271			0.826356	+	0.563148i	$0.190410\pi$
$150$		0			0
$151$		−	11.9560i		−	0.972966i	−0.873690	−	0.486483i	$-0.838280\pi$
$151$		−	11.9560i		−	0.972966i	0.873690	−	0.486483i	$-0.161720\pi$
$152$	2.26940	+	10.1286i	0.184072	+	0.821535i
$153$		0			0
$154$	−1.12417	+	0.764262i	−0.0905881	+	0.0615860i
$155$		−	3.87073i		−	0.310905i
$156$		0			0
$157$			22.1011i			1.76386i	0.471381	+	0.881930i	$0.343756\pi$
$157$			22.1011i			1.76386i	−0.471381	+	0.881930i	$0.656244\pi$
$158$	1.00367	+	1.47632i	0.0798476	+	0.117450i
$159$		0			0
$160$	11.6962	+	1.84237i	0.924668	+	0.145652i
$161$			2.40322i			0.189400i
$162$		0			0
$163$	11.2054			0.877674			0.438837	−	0.898567i	$-0.355391\pi$
$163$	11.2054			0.877674			0.438837	+	0.898567i	$0.355391\pi$
$164$	−0.584733	−	0.231284i	−0.0456600	−	0.0180602i
$165$		0			0
$166$	2.38130	+	3.50270i	0.184824	+	0.271862i
$167$	−1.76628			−0.136679			−0.0683395	−	0.997662i	$-0.521770\pi$
$167$	−1.76628			−0.136679			−0.0683395	+	0.997662i	$0.521770\pi$
$168$		0			0
$169$	−8.17930			−0.629177
$170$	−5.45982	−	8.03095i	−0.418749	−	0.615946i
$171$		0			0
$172$	−6.35768	+	16.0735i	−0.484768	+	1.22560i
$173$	−4.37240			−0.332428			−0.166214	−	0.986090i	$-0.553154\pi$
$173$	−4.37240			−0.332428			−0.166214	+	0.986090i	$0.553154\pi$
$174$		0			0
$175$		−	0.618872i		−	0.0467823i
$176$	−2.63008	+	2.80455i	−0.198250	+	0.211401i
$177$		0			0
$178$	10.2560	+	15.0858i	0.768722	+	1.13073i
$179$			17.0068i			1.27115i	0.772041	+	0.635573i	$0.219236\pi$
$179$			17.0068i			1.27115i	−0.772041	+	0.635573i	$0.780764\pi$
$180$		0			0
$181$		−	8.50624i		−	0.632264i	−0.948715	−	0.316132i	$-0.897616\pi$
$181$		−	8.50624i		−	0.632264i	0.948715	−	0.316132i	$-0.102384\pi$
$182$	−5.38231	+	3.65914i	−0.398963	+	0.271234i
$183$		0			0
$184$	1.48615	+	6.63287i	0.109561	+	0.488981i
$185$		−	4.80085i		−	0.352965i
$186$		0			0
$187$	3.15341			0.230600
$188$	1.72359	−	4.35761i	0.125706	−	0.317811i
$189$		0			0
$190$	−8.98349	+	6.10739i	−0.651731	+	0.443077i
$191$	0.725194			0.0524732			0.0262366	−	0.999656i	$-0.491648\pi$
$191$	0.725194			0.0524732			0.0262366	+	0.999656i	$0.491648\pi$
$192$		0			0
$193$	−15.7648			−1.13478			−0.567388	−	0.823450i	$-0.692046\pi$
$193$	−15.7648			−1.13478			−0.567388	+	0.823450i	$0.692046\pi$
$194$	−5.82833	+	3.96237i	−0.418450	+	0.284481i
$195$		0			0
$196$	−0.735620	+	1.85980i	−0.0525443	+	0.132843i
$197$	−5.76032			−0.410406			−0.205203	−	0.978719i	$-0.565785\pi$
$197$	−5.76032			−0.410406			−0.205203	+	0.978719i	$0.565785\pi$
$198$		0			0
$199$		−	11.7773i		−	0.834872i	−0.908706	−	0.417436i	$-0.862929\pi$
$199$		−	11.7773i		−	0.834872i	0.908706	−	0.417436i	$-0.137071\pi$
$200$	−0.382712	−	1.70808i	−0.0270618	−	0.120780i
$201$		0			0
$202$	3.72805	−	2.53450i	0.262305	−	0.178327i
$203$			9.31771i			0.653975i
$204$		0			0
$205$		−	0.658088i		−	0.0459629i
$206$	−0.425718	−	0.626197i	−0.0296612	−	0.0436292i
$207$		0			0
$208$	−12.5923	+	13.4277i	−0.873121	+	0.931040i
$209$		−	3.52742i		−	0.243997i
$210$		0			0
$211$	19.9971			1.37666			0.688328	−	0.725399i	$-0.258345\pi$
$211$	19.9971			1.37666			0.688328	+	0.725399i	$0.258345\pi$
$212$	5.68895	−	14.3829i	0.390719	−	0.987818i
$213$		0			0
$214$	−7.71786	−	11.3524i	−0.527582	−	0.776031i
$215$	−18.0900			−1.23373
$216$		0			0
$217$	1.84927			0.125537
$218$	6.38926	+	9.39810i	0.432735	+	0.636519i
$219$		0			0
$220$	−3.74178	−	1.48001i	−0.252271	−	0.0997824i
$221$	15.0979			1.01560
$222$		0			0
$223$			6.84047i			0.458071i	0.973418	+	0.229036i	$0.0735573\pi$
$223$			6.84047i			0.458071i	−0.973418	+	0.229036i	$0.926443\pi$
$224$	−0.880204	+	5.58795i	−0.0588111	+	0.373361i
$225$		0			0
$226$	10.1621	+	14.9477i	0.675976	+	0.994307i
$227$			13.9061i			0.922981i	0.887145	+	0.461490i	$0.152685\pi$
$227$			13.9061i			0.922981i	−0.887145	+	0.461490i	$0.847315\pi$
$228$		0			0
$229$			3.87934i			0.256354i	0.991751	+	0.128177i	$0.0409126\pi$
$229$			3.87934i			0.256354i	−0.991751	+	0.128177i	$0.959087\pi$
$230$	−5.88300	+	3.99953i	−0.387913	+	0.263722i
$231$		0			0
$232$	5.76209	+	25.7168i	0.378300	+	1.68839i
$233$		−	21.8307i		−	1.43017i	−0.699035	−	0.715087i	$-0.746387\pi$
$233$		−	21.8307i		−	1.43017i	0.699035	−	0.715087i	$-0.253613\pi$
$234$		0			0
$235$	4.90427			0.319919
$236$	14.8697	+	5.88151i	0.967933	+	0.382853i
$237$		0			0
$238$	3.83684	−	2.60847i	0.248706	−	0.169082i
$239$	−27.8956			−1.80441			−0.902207	−	0.431303i	$-0.858054\pi$
$239$	−27.8956			−1.80441			−0.902207	+	0.431303i	$0.858054\pi$
$240$		0			0
$241$	−6.17606			−0.397835			−0.198918	−	0.980016i	$-0.563743\pi$
$241$	−6.17606			−0.397835			−0.198918	+	0.980016i	$0.563743\pi$
$242$	−11.7843	+	8.01152i	−0.757524	+	0.515000i
$243$		0			0
$244$	−19.7736	−	7.82117i	−1.26587	−	0.500699i
$245$	−2.09311			−0.133724
$246$		0			0
$247$		−	16.8887i		−	1.07460i
$248$	5.10397	−	1.14359i	0.324103	−	0.0726181i
$249$		0			0
$250$	13.7548	−	9.35117i	0.869931	−	0.591420i
$251$		−	18.6366i		−	1.17633i	−0.808740	−	0.588167i	$-0.799850\pi$
$251$		−	18.6366i		−	1.17633i	0.808740	−	0.588167i	$-0.200150\pi$
$252$		0			0
$253$		−	2.31000i		−	0.145228i
$254$	−13.2194	−	19.4446i	−0.829456	−	1.22006i
$255$		0			0
$256$	1.02624	+	15.9671i	0.0641402	+	0.997941i
$257$		−	8.25845i		−	0.515148i	−0.966259	−	0.257574i	$-0.917077\pi$
$257$		−	8.25845i		−	0.515148i	0.966259	−	0.257574i	$-0.0829231\pi$
$258$		0			0
$259$	2.29364			0.142520
$260$	−17.9149	−	7.08602i	−1.11104	−	0.439456i
$261$		0			0
$262$	−11.5769	−	17.0287i	−0.715225	−	1.05204i
$263$	−9.34158			−0.576027			−0.288013	−	0.957626i	$-0.592995\pi$
$263$	−9.34158			−0.576027			−0.288013	+	0.957626i	$0.592995\pi$
$264$		0			0
$265$	16.1872			0.994371
$266$	−2.91785	−	4.29193i	−0.178905	−	0.263155i
$267$		0			0
$268$	3.03225	−	7.66616i	0.185224	−	0.468286i
$269$	11.9972			0.731484			0.365742	−	0.930716i	$-0.380815\pi$
$269$	11.9972			0.731484			0.365742	+	0.930716i	$0.380815\pi$
$270$		0			0
$271$		−	23.7030i		−	1.43986i	−0.694049	−	0.719928i	$-0.744175\pi$
$271$		−	23.7030i		−	1.43986i	0.694049	−	0.719928i	$-0.255825\pi$
$272$	8.97660	−	9.57207i	0.544286	−	0.580392i
$273$		0			0
$274$	−13.7292	−	20.1946i	−0.829414	−	1.22000i
$275$			0.594866i			0.0358718i
$276$		0			0
$277$		−	13.7688i		−	0.827284i	−0.910440	−	0.413642i	$-0.864256\pi$
$277$		−	13.7688i		−	0.827284i	0.910440	−	0.413642i	$-0.135744\pi$
$278$	−17.0261	+	11.5751i	−1.02116	+	0.694230i
$279$		0			0
$280$	−5.77699	+	1.29439i	−0.345241	+	0.0773544i
$281$		−	8.69078i		−	0.518448i	−0.965817	−	0.259224i	$-0.916533\pi$
$281$		−	8.69078i		−	0.518448i	0.965817	−	0.259224i	$-0.0834669\pi$
$282$		0			0
$283$	−32.7518			−1.94689			−0.973447	−	0.228913i	$-0.926483\pi$
$283$	−32.7518			−1.94689			−0.973447	+	0.228913i	$0.926483\pi$
$284$	−4.99810	+	12.6362i	−0.296583	+	0.749823i
$285$		0			0
$286$	5.17353	−	3.51721i	0.305917	−	0.207977i
$287$	0.314406			0.0185588
$288$		0			0
$289$	6.23727			0.366898
$290$	−22.8095	+	15.5069i	−1.33942	+	0.910599i
$291$		0			0
$292$	11.7896	−	29.8066i	0.689934	−	1.74430i
$293$	12.3629			0.722249			0.361124	−	0.932518i	$-0.382393\pi$
$293$	12.3629			0.722249			0.361124	+	0.932518i	$0.382393\pi$
$294$		0			0
$295$			16.7351i			0.974354i
$296$	6.33044	−	1.41839i	0.367949	−	0.0824423i
$297$		0			0
$298$	−23.5941	+	16.0404i	−1.36677	+	0.929193i
$299$		−	11.0598i		−	0.639607i
$300$		0			0
$301$		−	8.64261i		−	0.498152i
$302$	9.50627	+	13.9830i	0.547024	+	0.804629i
$303$		0			0
$304$	−10.7074	−	10.0413i	−0.614111	−	0.575908i
$305$		−	22.2542i		−	1.27427i
$306$		0			0
$307$	15.2600			0.870935			0.435468	−	0.900204i	$-0.356583\pi$
$307$	15.2600			0.870935			0.435468	+	0.900204i	$0.356583\pi$
$308$	0.707086	−	1.78766i	0.0402900	−	0.101861i
$309$		0			0
$310$	3.07763	+	4.52695i	0.174798	+	0.257114i
$311$	−5.12076			−0.290372			−0.145186	−	0.989404i	$-0.546378\pi$
$311$	−5.12076			−0.290372			−0.145186	+	0.989404i	$0.546378\pi$
$312$		0			0
$313$	−11.7058			−0.661649			−0.330825	−	0.943692i	$-0.607327\pi$
$313$	−11.7058			−0.661649			−0.330825	+	0.943692i	$0.607327\pi$
$314$	−17.5727	−	25.8480i	−0.991683	−	1.45869i
$315$		0			0
$316$	−2.34765	−	0.928583i	−0.132066	−	0.0522369i
$317$	−18.5302			−1.04076			−0.520379	−	0.853935i	$-0.674209\pi$
$317$	−18.5302			−1.04076			−0.520379	+	0.853935i	$0.674209\pi$
$318$		0			0
$319$		−	8.95628i		−	0.501456i
$320$	−15.1440	+	7.14500i	−0.846576	+	0.399418i
$321$		0			0
$322$	−1.91081	−	2.81064i	−0.106485	−	0.156631i
$323$			12.0393i			0.669883i
$324$		0			0
$325$			2.84811i			0.157985i
$326$	−13.1051	+	8.90945i	−0.725824	+	0.493449i
$327$		0			0
$328$	0.867760	−	0.194429i	0.0479140	−	0.0107356i
$329$			2.34305i			0.129176i
$330$		0			0
$331$	−20.4688			−1.12507			−0.562534	−	0.826774i	$-0.690174\pi$
$331$	−20.4688			−1.12507			−0.562534	+	0.826774i	$0.690174\pi$
$332$	−5.57001	−	2.20315i	−0.305694	−	0.120913i
$333$		0			0
$334$	2.06573	−	1.40438i	0.113032	−	0.0768442i
$335$	8.62789			0.471392
$336$		0			0
$337$	−19.9419			−1.08631			−0.543153	−	0.839634i	$-0.682769\pi$
$337$	−19.9419			−1.08631			−0.543153	+	0.839634i	$0.682769\pi$
$338$	9.56597	−	6.50339i	0.520320	−	0.353738i
$339$		0			0
$340$	12.7709	+	5.05136i	0.692598	+	0.273948i
$341$	−1.77754			−0.0962590
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−5.34461	−	23.8536i	−0.288162	−	1.28610i
$345$		0			0
$346$	5.11367	−	3.47651i	0.274913	−	0.186898i
$347$			10.1743i			0.546187i	0.961987	+	0.273094i	$0.0880469\pi$
$347$			10.1743i			0.546187i	−0.961987	+	0.273094i	$0.911953\pi$
$348$		0			0
$349$			31.9386i			1.70963i	0.518930	+	0.854817i	$0.326331\pi$
$349$			31.9386i			1.70963i	−0.518930	+	0.854817i	$0.673669\pi$
$350$	0.492067	+	0.723792i	0.0263021	+	0.0386883i
$351$		0			0
$352$	0.846062	−	5.37120i	0.0450952	−	0.286286i
$353$			24.3932i			1.29832i	0.760653	+	0.649159i	$0.224879\pi$
$353$			24.3932i			1.29832i	−0.760653	+	0.649159i	$0.775121\pi$
$354$		0			0
$355$	−14.2215			−0.754797
$356$	−23.9895	−	9.48875i	−1.27144	−	0.502903i
$357$		0			0
$358$	−13.5222	−	19.8900i	−0.714668	−	1.05122i
$359$	−8.59571			−0.453664			−0.226832	−	0.973934i	$-0.572837\pi$
$359$	−8.59571			−0.453664			−0.226832	+	0.973934i	$0.572837\pi$
$360$		0			0
$361$	−5.53276			−0.291198
$362$	6.76335	+	9.94834i	0.355474	+	0.522873i
$363$		0			0
$364$	3.38540	−	8.55899i	0.177443	−	0.448613i
$365$	33.5458			1.75587
$366$		0			0
$367$			29.1285i			1.52050i	0.649632	+	0.760249i	$0.274923\pi$
$367$			29.1285i			1.52050i	−0.649632	+	0.760249i	$0.725077\pi$
$368$	−7.01192	−	6.57572i	−0.365522	−	0.342783i
$369$		0			0
$370$	3.81717	+	5.61476i	0.198445	+	0.291897i
$371$			7.73354i			0.401505i
$372$		0			0
$373$			4.56533i			0.236384i	0.992991	+	0.118192i	$0.0377098\pi$
$373$			4.56533i			0.236384i	−0.992991	+	0.118192i	$0.962290\pi$
$374$	−3.68802	+	2.50728i	−0.190703	+	0.129649i
$375$		0			0
$376$	1.44895	+	6.46680i	0.0747237	+	0.333500i
$377$		−	42.8810i		−	2.20848i
$378$		0			0
$379$	15.5673			0.799641			0.399820	−	0.916593i	$-0.369072\pi$
$379$	15.5673			0.799641			0.399820	+	0.916593i	$0.369072\pi$
$380$	5.65049	−	14.2856i	0.289864	−	0.732836i
$381$		0			0
$382$	−0.848139	+	0.576604i	−0.0433946	+	0.0295016i
$383$	3.08947			0.157865			0.0789323	−	0.996880i	$-0.474849\pi$
$383$	3.08947			0.157865			0.0789323	+	0.996880i	$0.474849\pi$
$384$		0			0
$385$	2.01192			0.102537
$386$	18.4375	−	12.5347i	0.938444	−	0.637998i
$387$		0			0
$388$	3.66594	−	9.26825i	0.186110	−	0.470524i
$389$	−30.6022			−1.55160			−0.775798	−	0.630982i	$-0.782652\pi$
$389$	−30.6022			−1.55160			−0.775798	+	0.630982i	$0.782652\pi$
$390$		0			0
$391$			7.88413i			0.398718i
$392$	−0.618402	−	2.76000i	−0.0312340	−	0.139401i
$393$		0			0
$394$	6.73689	−	4.58005i	0.339400	−	0.230740i
$395$		−	2.64216i		−	0.132942i
$396$		0			0
$397$		−	0.403742i		−	0.0202632i	−0.999949	−	0.0101316i	$-0.996775\pi$
$397$		−	0.403742i		−	0.0202632i	0.999949	−	0.0101316i	$-0.00322505\pi$
$398$	9.36419	+	13.7740i	0.469385	+	0.690427i
$399$		0			0
$400$	1.80570	+	1.69337i	0.0902849	+	0.0846684i
$401$		−	30.3779i		−	1.51700i	−0.651672	−	0.758501i	$-0.725932\pi$
$401$		−	30.3779i		−	1.51700i	0.651672	−	0.758501i	$-0.274068\pi$
$402$		0			0
$403$	−8.51051			−0.423939
$404$	−2.34489	+	5.92838i	−0.116663	+	0.294948i
$405$		0			0
$406$	−7.40855	−	10.8974i	−0.367680	−	0.540828i
$407$	−2.20467			−0.109281
$408$		0			0
$409$	−17.8549			−0.882869			−0.441434	−	0.897293i	$-0.645530\pi$
$409$	−17.8549			−0.882869			−0.441434	+	0.897293i	$0.645530\pi$
$410$	0.523248	+	0.769656i	0.0258414	+	0.0380106i
$411$		0			0
$412$	0.995784	+	0.393869i	0.0490587	+	0.0194045i
$413$	−7.99530			−0.393423
$414$		0			0
$415$		−	6.26877i		−	0.307722i
$416$	4.05079	−	25.7163i	0.198606	−	1.26085i
$417$		0			0
$418$	2.80467	+	4.12544i	0.137181	+	0.201782i
$419$			31.1609i			1.52231i	0.648569	+	0.761156i	$0.275368\pi$
$419$			31.1609i			1.52231i	−0.648569	+	0.761156i	$0.724632\pi$
$420$		0			0
$421$			7.19292i			0.350562i	0.984518	+	0.175281i	$0.0560833\pi$
$421$			7.19292i			0.350562i	−0.984518	+	0.175281i	$0.943917\pi$
$422$	−23.3873	+	15.8998i	−1.13848	+	0.773988i
$423$		0			0
$424$	4.78244	+	21.3445i	0.232256	+	1.03658i
$425$		−	2.03031i		−	0.0984844i
$426$		0			0
$427$	10.6321			0.514522
$428$	18.0526	+	7.14047i	0.872605	+	0.345148i
$429$		0			0
$430$	21.1568	−	14.3834i	1.02027	−	0.693629i
$431$	−25.7598			−1.24081			−0.620404	−	0.784283i	$-0.713031\pi$
$431$	−25.7598			−1.24081			−0.620404	+	0.784283i	$0.713031\pi$
$432$		0			0
$433$	−3.66449			−0.176104			−0.0880521	−	0.996116i	$-0.528064\pi$
$433$	−3.66449			−0.176104			−0.0880521	+	0.996116i	$0.528064\pi$
$434$	−2.16278	+	1.47036i	−0.103817	+	0.0705796i
$435$		0			0
$436$	−14.9449	−	5.91127i	−0.715732	−	0.283098i
$437$	8.81926			0.421882
$438$		0			0
$439$		−	39.4350i		−	1.88213i	−0.338227	−	0.941064i	$-0.609827\pi$
$439$		−	39.4350i		−	1.88213i	0.338227	−	0.941064i	$-0.390173\pi$
$440$	5.55290	−	1.24418i	0.264724	−	0.0593138i
$441$		0			0
$442$	−17.6575	+	12.0044i	−0.839883	+	0.570992i
$443$		−	36.1437i		−	1.71724i	−0.512612	−	0.858620i	$-0.671322\pi$
$443$		−	36.1437i		−	1.71724i	0.512612	−	0.858620i	$-0.328678\pi$
$444$		0			0
$445$		−	26.9990i		−	1.27988i
$446$	−5.43888	−	8.00016i	−0.257538	−	0.378819i
$447$		0			0
$448$	−3.41357	−	7.23516i	−0.161276	−	0.341829i
$449$			24.9465i			1.17730i	0.808389	+	0.588649i	$0.200340\pi$
$449$			24.9465i			1.17730i	−0.808389	+	0.588649i	$0.799660\pi$
$450$		0			0
$451$	−0.302210			−0.0142305
$452$	−23.7700	−	9.40190i	−1.11804	−	0.442228i
$453$		0			0
$454$	−11.0568	−	16.2637i	−0.518921	−	0.763292i
$455$	9.63272			0.451589
$456$		0			0
$457$	15.1856			0.710354			0.355177	−	0.934799i	$-0.384421\pi$
$457$	15.1856			0.710354			0.355177	+	0.934799i	$0.384421\pi$
$458$	−3.08448	−	4.53702i	−0.144128	−	0.212001i
$459$		0			0
$460$	3.70032	−	9.35518i	0.172528	−	0.436188i
$461$	−9.29479			−0.432902			−0.216451	−	0.976294i	$-0.569448\pi$
$461$	−9.29479			−0.432902			−0.216451	+	0.976294i	$0.569448\pi$
$462$		0			0
$463$			2.13438i			0.0991930i	0.998769	+	0.0495965i	$0.0157935\pi$
$463$			2.13438i			0.0991930i	−0.998769	+	0.0495965i	$0.984206\pi$
$464$	−27.1865	−	25.4953i	−1.26210	−	1.18359i
$465$		0			0
$466$	17.3576	+	25.5317i	0.804077	+	1.18273i
$467$			41.6077i			1.92538i	0.270612	+	0.962688i	$0.412774\pi$
$467$			41.6077i			1.92538i	−0.270612	+	0.962688i	$0.587226\pi$
$468$		0			0
$469$			4.12203i			0.190338i
$470$	−5.73571	+	3.89940i	−0.264569	+	0.179866i
$471$		0			0
$472$	−22.0670	+	4.94431i	−1.01572	+	0.227580i
$473$			8.30736i			0.381973i
$474$		0			0
$475$	−2.27112			−0.104206
$476$	−2.41332	+	6.10138i	−0.110614	+	0.279656i
$477$		0			0
$478$	32.6248	−	22.1799i	1.49222	−	1.01448i
$479$	−40.9442			−1.87079			−0.935394	−	0.353608i	$-0.884955\pi$
$479$	−40.9442			−1.87079			−0.935394	+	0.353608i	$0.884955\pi$
$480$		0			0
$481$	−10.5556			−0.481292
$482$	7.22312	−	4.91061i	0.329004	−	0.223672i
$483$		0			0
$484$	7.41217	−	18.7395i	0.336917	−	0.851795i
$485$	10.4310			0.473645
$486$		0			0
$487$		−	14.2039i		−	0.643639i	−0.946801	−	0.321820i	$-0.895706\pi$
$487$		−	14.2039i		−	0.643639i	0.946801	−	0.321820i	$-0.104294\pi$
$488$	29.3445	−	6.57490i	1.32836	−	0.297632i
$489$		0			0
$490$	2.44797	−	1.66424i	0.110588	−	0.0751828i
$491$		−	39.3013i		−	1.77364i	−0.462113	−	0.886821i	$-0.652909\pi$
$491$		−	39.3013i		−	1.77364i	0.462113	−	0.886821i	$-0.347091\pi$
$492$		0			0
$493$			30.5682i			1.37672i
$494$	13.4282	+	19.7519i	0.604165	+	0.888678i
$495$		0			0
$496$	−5.06000	+	5.39566i	−0.227201	+	0.242272i
$497$		−	6.79440i		−	0.304771i
$498$		0			0
$499$	−32.3257			−1.44710			−0.723548	−	0.690274i	$-0.757490\pi$
$499$	−32.3257			−1.44710			−0.723548	+	0.690274i	$0.757490\pi$
$500$	−8.65159	+	21.8730i	−0.386911	+	0.978191i
$501$		0			0
$502$	14.8180	+	21.7962i	0.661362	+	0.972810i
$503$	19.7861			0.882217			0.441108	−	0.897454i	$-0.354585\pi$
$503$	19.7861			0.882217			0.441108	+	0.897454i	$0.354585\pi$
$504$		0			0
$505$	−6.67210			−0.296904
$506$	1.83669	+	2.70162i	0.0816507	+	0.120102i
$507$		0			0
$508$	30.9210	+	12.2304i	1.37190	+	0.542636i
$509$	−33.7174			−1.49450			−0.747248	−	0.664545i	$-0.768625\pi$
$509$	−33.7174			−1.49450			−0.747248	+	0.664545i	$0.768625\pi$
$510$		0			0
$511$			16.0267i			0.708981i
$512$	−13.8957	−	17.8580i	−0.614109	−	0.789222i
$513$		0			0
$514$	6.56632	+	9.65854i	0.289628	+	0.426020i
$515$			1.12070i			0.0493842i
$516$		0			0
$517$		−	2.25216i		−	0.0990500i
$518$	−2.68249	+	1.82368i	−0.117862	+	0.0801279i
$519$		0			0
$520$	26.5863	−	5.95689i	1.16588	−	0.261227i
$521$			28.4958i			1.24842i	0.781255	+	0.624212i	$0.214580\pi$
$521$			28.4958i			1.24842i	−0.781255	+	0.624212i	$0.785420\pi$
$522$		0			0
$523$	−4.42637			−0.193552			−0.0967758	−	0.995306i	$-0.530853\pi$
$523$	−4.42637			−0.193552			−0.0967758	+	0.995306i	$0.530853\pi$
$524$	27.0792	+	10.7108i	1.18296	+	0.467905i
$525$		0			0
$526$	10.9253	−	7.42753i	0.476366	−	0.323855i
$527$	6.06682			0.264275
$528$		0			0
$529$	−17.2246			−0.748894
$530$	−18.9315	+	12.8705i	−0.822330	+	0.559058i
$531$		0			0
$532$	6.82505	+	2.69956i	0.295903	+	0.117041i
$533$	−1.44693			−0.0626734
$534$		0			0
$535$			20.3173i			0.878394i
$536$	2.54907	+	11.3768i	0.110103	+	0.491403i
$537$		0			0
$538$	−14.0312	+	9.53905i	−0.604927	+	0.411258i
$539$			0.961211i			0.0414023i
$540$		0			0
$541$		−	33.7548i		−	1.45123i	−0.688101	−	0.725615i	$-0.741555\pi$
$541$		−	33.7548i		−	1.45123i	0.688101	−	0.725615i	$-0.258445\pi$
$542$	18.8464	+	27.7215i	0.809520	+	1.19074i
$543$		0			0
$544$	−2.88765	+	18.3322i	−0.123807	+	0.785986i
$545$		−	16.8198i		−	0.720480i
$546$		0			0
$547$	−14.6641			−0.626992			−0.313496	−	0.949589i	$-0.601500\pi$
$547$	−14.6641			−0.626992			−0.313496	+	0.949589i	$0.601500\pi$
$548$	32.1136	+	12.7021i	1.37183	+	0.542608i
$549$		0			0
$550$	−0.472980	−	0.695716i	−0.0201680	−	0.0296654i
$551$	34.1939			1.45671
$552$		0			0
$553$	1.26231			0.0536790
$554$	10.9476	+	16.1030i	0.465118	+	0.684152i
$555$		0			0
$556$	10.7092	−	27.0750i	0.454170	−	1.14824i
$557$	15.4373			0.654099			0.327050	−	0.945007i	$-0.393946\pi$
$557$	15.4373			0.654099			0.327050	+	0.945007i	$0.393946\pi$
$558$		0			0
$559$			39.7741i			1.68227i
$560$	5.72721	−	6.10713i	0.242019	−	0.258073i
$561$		0			0
$562$	6.91007	+	10.1642i	0.291484	+	0.428749i
$563$			26.9472i			1.13569i	0.823135	+	0.567845i	$0.192223\pi$
$563$			26.9472i			1.13569i	−0.823135	+	0.567845i	$0.807777\pi$
$564$		0			0
$565$		−	26.7519i		−	1.12546i
$566$	38.3044	−	26.0411i	1.61005	−	1.09459i
$567$		0			0
$568$	−4.20167	−	18.7525i	−0.176298	−	0.786838i
$569$			3.63013i			0.152183i	0.997101	+	0.0760915i	$0.0242441\pi$
$569$			3.63013i			0.152183i	−0.997101	+	0.0760915i	$0.975756\pi$
$570$		0			0
$571$	−16.2293			−0.679174			−0.339587	−	0.940575i	$-0.610287\pi$
$571$	−16.2293			−0.679174			−0.339587	+	0.940575i	$0.610287\pi$
$572$	−3.25408	+	8.22699i	−0.136060	+	0.343988i
$573$		0			0
$574$	−0.367709	+	0.249985i	−0.0153479	+	0.0104342i
$575$	−1.48728			−0.0620240
$576$		0			0
$577$	42.1511			1.75477			0.877386	−	0.479786i	$-0.159286\pi$
$577$	42.1511			1.75477			0.877386	+	0.479786i	$0.159286\pi$
$578$	−7.29470	+	4.95927i	−0.303419	+	0.206279i
$579$		0			0
$580$	14.3468	−	36.2718i	0.595720	−	1.50610i
$581$	2.99495			0.124251
$582$		0			0
$583$		−	7.43356i		−	0.307867i
$584$	9.91097	+	44.2337i	0.410119	+	1.83040i
$585$		0			0
$586$	−14.4588	+	9.82979i	−0.597289	+	0.406065i
$587$			22.7097i			0.937328i	0.883377	+	0.468664i	$0.155264\pi$
$587$			22.7097i			0.937328i	−0.883377	+	0.468664i	$0.844736\pi$
$588$		0			0
$589$		−	6.78640i		−	0.279629i
$590$	−13.3061	−	19.5722i	−0.547804	−	0.805777i
$591$		0			0
$592$	−6.27589	+	6.69221i	−0.257938	+	0.275048i
$593$			22.8921i			0.940068i	0.882648	+	0.470034i	$0.155758\pi$
$593$			22.8921i			0.940068i	−0.882648	+	0.470034i	$0.844242\pi$
$594$		0			0
$595$	−6.86680			−0.281511
$596$	14.8404	−	37.5195i	0.607885	−	1.53686i
$597$		0			0
$598$	8.79371	+	12.9349i	0.359602	+	0.528945i
$599$	−31.0216			−1.26751			−0.633755	−	0.773534i	$-0.718487\pi$
$599$	−31.0216			−1.26751			−0.633755	+	0.773534i	$0.718487\pi$
$600$		0			0
$601$	−36.3657			−1.48339			−0.741693	−	0.670739i	$-0.765977\pi$
$601$	−36.3657			−1.48339			−0.741693	+	0.670739i	$0.765977\pi$
$602$	6.87177	+	10.1078i	0.280072	+	0.411964i
$603$		0			0
$604$	−22.2358	−	8.79508i	−0.904762	−	0.357867i
$605$	21.0904			0.857446
$606$		0			0
$607$			27.1019i			1.10003i	0.835154	+	0.550016i	$0.185378\pi$
$607$			27.1019i			1.10003i	−0.835154	+	0.550016i	$0.814622\pi$
$608$	20.5065	+	3.23015i	0.831649	+	0.131000i
$609$		0			0
$610$	17.6944	+	26.0270i	0.716424	+	1.05380i
$611$		−	10.7829i		−	0.436231i
$612$		0			0
$613$		−	21.7164i		−	0.877118i	−0.898702	−	0.438559i	$-0.855489\pi$
$613$		−	21.7164i		−	0.877118i	0.898702	−	0.438559i	$-0.144511\pi$
$614$	−17.8471	+	12.1333i	−0.720251	+	0.489660i
$615$		0			0
$616$	0.594415	+	2.65294i	0.0239496	+	0.106890i
$617$		−	15.0335i		−	0.605224i	−0.953114	−	0.302612i	$-0.902141\pi$
$617$		−	15.0335i		−	0.605224i	0.953114	−	0.302612i	$-0.0978587\pi$
$618$		0			0
$619$	−12.2249			−0.491359			−0.245680	−	0.969351i	$-0.579011\pi$
$619$	−12.2249			−0.491359			−0.245680	+	0.969351i	$0.579011\pi$
$620$	−7.19879	−	2.84739i	−0.289110	−	0.114354i
$621$		0			0
$622$	5.98891	−	4.07154i	0.240133	−	0.163254i
$623$	12.8990			0.516787
$624$		0			0
$625$	−21.5226			−0.860906
$626$	13.6903	−	9.30730i	0.547174	−	0.371995i
$627$		0			0
$628$	41.1037	+	16.2580i	1.64021	+	0.648765i
$629$	7.52465			0.300028
$630$		0			0
$631$			0.290118i			0.0115494i	0.999983	+	0.00577472i	$0.00183816\pi$
$631$			0.290118i			0.0115494i	−0.999983	+	0.00577472i	$0.998162\pi$
$632$	3.48398	−	0.780617i	0.138585	−	0.0310513i
$633$		0			0
$634$	21.6717	−	14.7334i	0.860692	−	0.585138i
$635$			34.8000i			1.38100i
$636$		0			0
$637$			4.60210i			0.182342i
$638$	7.12117	+	10.4747i	0.281930	+	0.414696i
$639$		0			0
$640$	12.0304	−	20.3974i	0.475544	−	0.806277i
$641$			32.2612i			1.27424i	0.770764	+	0.637120i	$0.219875\pi$
$641$			32.2612i			1.27424i	−0.770764	+	0.637120i	$0.780125\pi$
$642$		0			0
$643$	−25.2641			−0.996317			−0.498159	−	0.867086i	$-0.665990\pi$
$643$	−25.2641			−0.996317			−0.498159	+	0.867086i	$0.665990\pi$
$644$	4.46950	+	1.76785i	0.176123	+	0.0696632i
$645$		0			0
$646$	−9.57248	−	14.0803i	−0.376624	−	0.553984i
$647$	−15.6735			−0.616188			−0.308094	−	0.951356i	$-0.599691\pi$
$647$	−15.6735			−0.616188			−0.308094	+	0.951356i	$0.599691\pi$
$648$		0			0
$649$	7.68517			0.301669
$650$	−2.26454	−	3.33096i	−0.0888226	−	0.130651i
$651$		0			0
$652$	8.24291	−	20.8398i	0.322817	−	0.816150i
$653$	−17.4580			−0.683183			−0.341591	−	0.939849i	$-0.610966\pi$
$653$	−17.4580			−0.683183			−0.341591	+	0.939849i	$0.610966\pi$
$654$		0			0
$655$			30.4763i			1.19081i
$656$	−0.860283	+	0.917351i	−0.0335884	+	0.0358165i
$657$		0			0
$658$	−1.86297	−	2.74028i	−0.0726260	−	0.106827i
$659$		−	34.8692i		−	1.35831i	−0.733995	−	0.679155i	$-0.762347\pi$
$659$		−	34.8692i		−	1.35831i	0.733995	−	0.679155i	$-0.237653\pi$
$660$		0			0
$661$			13.7607i			0.535230i	0.963526	+	0.267615i	$0.0862355\pi$
$661$			13.7607i			0.535230i	−0.963526	+	0.267615i	$0.913765\pi$
$662$	23.9390	−	16.2748i	0.930415	−	0.632540i
$663$		0			0
$664$	8.26605	−	1.85208i	0.320785	−	0.0718748i
$665$			7.68126i			0.297866i
$666$		0			0
$667$	22.3925			0.867040
$668$	−1.29931	+	3.28494i	−0.0502720	+	0.127098i
$669$		0			0
$670$	−10.0906	+	6.86006i	−0.389834	+	0.265027i
$671$	−10.2197			−0.394526
$672$		0			0
$673$	−8.50938			−0.328013			−0.164006	−	0.986459i	$-0.552442\pi$
$673$	−8.50938			−0.328013			−0.164006	+	0.986459i	$0.552442\pi$
$674$	23.3227	−	15.8559i	0.898359	−	0.610746i
$675$		0			0
$676$	−6.01686	+	15.2119i	−0.231418	+	0.585072i
$677$	3.14515			0.120878			0.0604390	−	0.998172i	$-0.480750\pi$
$677$	3.14515			0.120878			0.0604390	+	0.998172i	$0.480750\pi$
$678$		0			0
$679$			4.98346i			0.191248i
$680$	−18.9523	+	4.24644i	−0.726789	+	0.162844i
$681$		0			0
$682$	2.07889	−	1.41333i	0.0796048	−	0.0541190i
$683$			9.12590i			0.349193i	0.984640	+	0.174596i	$0.0558621\pi$
$683$			9.12590i			0.349193i	−0.984640	+	0.174596i	$0.944138\pi$
$684$		0			0
$685$			36.1423i			1.38093i
$686$	0.795104	+	1.16953i	0.0303572	+	0.0446530i
$687$		0			0
$688$	25.2168	+	23.6480i	0.961380	+	0.901573i
$689$		−	35.5905i		−	1.35589i
$690$		0			0
$691$	−15.6298			−0.594586			−0.297293	−	0.954786i	$-0.596084\pi$
$691$	−15.6298			−0.594586			−0.297293	+	0.954786i	$0.596084\pi$
$692$	−3.21643	+	8.13180i	−0.122270	+	0.309125i
$693$		0			0
$694$	−8.08965	−	11.8992i	−0.307079	−	0.451689i
$695$	30.4716			1.15585
$696$		0			0
$697$	1.03146			0.0390693
$698$	−25.3945	−	37.3533i	−0.961196	−	1.41384i
$699$		0			0
$700$	−1.15098	−	0.455255i	−0.0435029	−	0.0172070i
$701$	50.4853			1.90680			0.953402	−	0.301701i	$-0.0975546\pi$
$701$	50.4853			1.90680			0.953402	+	0.301701i	$0.0975546\pi$
$702$		0			0
$703$		−	8.41714i		−	0.317458i
$704$	3.28116	+	6.95451i	0.123664	+	0.262108i
$705$		0			0
$706$	−19.3951	−	28.5286i	−0.729944	−	1.07369i
$707$		−	3.18764i		−	0.119884i
$708$		0			0
$709$			28.7706i			1.08050i	0.841504	+	0.540251i	$0.181671\pi$
$709$			28.7706i			1.08050i	−0.841504	+	0.540251i	$0.818329\pi$
$710$	16.6325	−	11.3075i	0.624206	−	0.424364i
$711$		0			0
$712$	35.6011	−	7.97676i	1.33421	−	0.298942i
$713$		−	4.44419i		−	0.166436i
$714$		0			0
$715$	−9.25907			−0.346270
$716$	31.6292	+	12.5105i	1.18204	+	0.467541i
$717$		0			0
$718$	10.0530	−	6.83448i	0.375174	−	0.255061i
$719$	−0.582170			−0.0217113			−0.0108556	−	0.999941i	$-0.503456\pi$
$719$	−0.582170			−0.0217113			−0.0108556	+	0.999941i	$0.503456\pi$
$720$		0			0
$721$	−0.535425			−0.0199403
$722$	6.47076	−	4.39912i	0.240817	−	0.163718i
$723$		0			0
$724$	−15.8199	−	6.25737i	−0.587943	−	0.232553i
$725$	−5.76647			−0.214161
$726$		0			0
$727$			6.92907i			0.256985i	0.991710	+	0.128492i	$0.0410138\pi$
$727$			6.92907i			0.256985i	−0.991710	+	0.128492i	$0.958986\pi$
$728$	2.84595	+	12.7018i	0.105478	+	0.470759i
$729$		0			0
$730$	−39.2330	+	26.6724i	−1.45208	+	0.987189i
$731$		−	28.3535i		−	1.04869i
$732$		0			0
$733$		−	1.86770i		−	0.0689850i	−0.999405	−	0.0344925i	$-0.989019\pi$
$733$		−	1.86770i		−	0.0689850i	0.999405	−	0.0344925i	$-0.0109815\pi$
$734$	−23.1602	−	34.0668i	−0.854859	−	1.25743i
$735$		0			0
$736$	13.4291	+	2.11532i	0.495002	+	0.0779717i
$737$		−	3.96214i		−	0.145947i
$738$		0			0
$739$	−38.7036			−1.42373			−0.711867	−	0.702314i	$-0.752150\pi$
$739$	−38.7036			−1.42373			−0.711867	+	0.702314i	$0.752150\pi$
$740$	−8.92863	−	3.53160i	−0.328223	−	0.129824i
$741$		0			0
$742$	−6.14897	−	9.04464i	−0.225736	−	0.332039i
$743$	−23.3088			−0.855118			−0.427559	−	0.903987i	$-0.640626\pi$
$743$	−23.3088			−0.855118			−0.427559	+	0.903987i	$0.640626\pi$
$744$		0			0
$745$	42.2263			1.54705
$746$	−3.62991	−	5.33931i	−0.132900	−	0.195486i
$747$		0			0
$748$	2.31971	−	5.86471i	0.0848170	−	0.214435i
$749$	−9.70673			−0.354676
$750$		0			0
$751$			26.6345i			0.971908i	0.873984	+	0.485954i	$0.161528\pi$
$751$			26.6345i			0.971908i	−0.873984	+	0.485954i	$0.838472\pi$
$752$	−6.83637	−	6.41109i	−0.249297	−	0.233788i
$753$		0			0
$754$	34.0948	+	50.1508i	1.24166	+	1.82638i
$755$		−	25.0253i		−	0.910764i
$756$		0			0
$757$			26.4285i			0.960562i	0.877115	+	0.480281i	$0.159465\pi$
$757$			26.4285i			0.960562i	−0.877115	+	0.480281i	$0.840535\pi$
$758$	−18.2065	+	12.3777i	−0.661292	+	0.449577i
$759$		0			0
$760$	4.75010	+	21.2002i	0.172304	+	0.769013i
$761$			13.2617i			0.480736i	0.970682	+	0.240368i	$0.0772681\pi$
$761$			13.2617i			0.480736i	−0.970682	+	0.240368i	$0.922732\pi$
$762$		0			0
$763$	8.03576			0.290914
$764$	0.533467	−	1.34872i	0.0193002	−	0.0487949i
$765$		0			0
$766$	−3.61324	+	2.45645i	−0.130552	+	0.0887552i
$767$	36.7951			1.32860
$768$		0			0
$769$	−4.34986			−0.156860			−0.0784300	−	0.996920i	$-0.524991\pi$
$769$	−4.34986			−0.156860			−0.0784300	+	0.996920i	$0.524991\pi$
$770$	−2.35301	+	1.59969i	−0.0847967	+	0.0576488i
$771$		0			0
$772$	−11.5969	+	29.3194i	−0.417382	+	1.05523i
$773$	34.8861			1.25477			0.627383	−	0.778711i	$-0.284126\pi$
$773$	34.8861			1.25477			0.627383	+	0.778711i	$0.284126\pi$
$774$		0			0
$775$			1.14446i			0.0411102i
$776$	3.08178	+	13.7543i	0.110630	+	0.493752i
$777$		0			0
$778$	35.7904	−	24.3320i	1.28315	−	0.872343i
$779$		−	1.15380i		−	0.0413391i
$780$		0			0
$781$			6.53085i			0.233692i
$782$	−6.26870	−	9.22076i	−0.224168	−	0.329734i
$783$		0			0
$784$	2.91773	+	2.73622i	0.104204	+	0.0977220i
$785$			46.2601i			1.65109i
$786$		0			0
$787$	12.9317			0.460964			0.230482	−	0.973077i	$-0.425970\pi$
$787$	12.9317			0.460964			0.230482	+	0.973077i	$0.425970\pi$
$788$	−4.23741	+	10.7131i	−0.150951	+	0.381637i
$789$		0			0
$790$	2.10079	+	3.09010i	0.0747429	+	0.109941i
$791$	12.7809			0.454437
$792$		0			0
$793$	−48.9299			−1.73755
$794$	0.321017	+	0.472190i	0.0113925	+	0.0167574i
$795$		0			0
$796$	−21.9035	−	8.66364i	−0.776349	−	0.307075i
$797$	11.1981			0.396656			0.198328	−	0.980136i	$-0.436449\pi$
$797$	11.1981			0.396656			0.198328	+	0.980136i	$0.436449\pi$
$798$		0			0
$799$			7.68675i			0.271938i
$800$	−3.45823	−	0.544734i	−0.122267	−	0.0192592i
$801$		0			0
$802$	24.1536	+	35.5280i	0.852894	+	1.25454i
$803$		−	15.4051i		−	0.543633i
$804$		0			0
$805$			5.03021i			0.177291i
$806$	9.95334	−	6.76674i	0.350591	−	0.238348i
$807$		0			0
$808$	−1.97124	−	8.79788i	−0.0693481	−	0.309508i
$809$		−	23.6434i		−	0.831258i	−0.909534	−	0.415629i	$-0.863561\pi$
$809$		−	23.6434i		−	0.831258i	0.909534	−	0.415629i	$-0.136439\pi$
$810$		0			0
$811$	34.8213			1.22274			0.611371	−	0.791344i	$-0.290618\pi$
$811$	34.8213			1.22274			0.611371	+	0.791344i	$0.290618\pi$
$812$	17.3291	+	6.85430i	0.608132	+	0.240539i
$813$		0			0
$814$	2.57844	−	1.75294i	0.0903742	−	0.0614406i
$815$	23.4542			0.821564
$816$		0			0
$817$	−31.7164			−1.10962
$818$	20.8819	−	14.1965i	0.730120	−	0.496369i
$819$		0			0
$820$	−1.22391	−	0.484103i	−0.0427409	−	0.0169056i
$821$	−0.361884			−0.0126298			−0.00631491	−	0.999980i	$-0.502010\pi$
$821$	−0.361884			−0.0126298			−0.00631491	+	0.999980i	$0.502010\pi$
$822$		0			0
$823$		−	49.2033i		−	1.71512i	−0.514386	−	0.857559i	$-0.671980\pi$
$823$		−	49.2033i		−	1.71512i	0.514386	−	0.857559i	$-0.328020\pi$
$824$	−1.47777	+	0.331108i	−0.0514806	+	0.0115347i
$825$		0			0
$826$	9.35078	−	6.35709i	0.325355	−	0.221192i
$827$			16.2920i			0.566529i	0.959042	+	0.283264i	$0.0914174\pi$
$827$			16.2920i			0.566529i	−0.959042	+	0.283264i	$0.908583\pi$
$828$		0			0
$829$			6.40526i			0.222464i	0.993794	+	0.111232i	$0.0354796\pi$
$829$			6.40526i			0.222464i	−0.993794	+	0.111232i	$0.964520\pi$
$830$	4.98432	+	7.33154i	0.173008	+	0.254482i
$831$		0			0
$832$	15.7096	+	33.2969i	0.544632	+	1.15436i
$833$		−	3.28066i		−	0.113668i
$834$		0			0
$835$	−3.69703			−0.127941
$836$	−6.56031	−	2.59485i	−0.226893	−	0.0897446i
$837$		0			0
$838$	−24.7762	−	36.4438i	−0.855879	−	1.25893i
$839$	23.3877			0.807432			0.403716	−	0.914884i	$-0.367718\pi$
$839$	23.3877			0.807432			0.403716	+	0.914884i	$0.367718\pi$
$840$		0			0
$841$	57.8197			1.99378
$842$	−5.71912	−	8.41237i	−0.197094	−	0.289909i
$843$		0			0
$844$	14.7103	−	37.1906i	0.506348	−	1.28015i
$845$	−17.1202			−0.588953
$846$		0			0
$847$			10.0761i			0.346218i
$848$	−22.5643	−	21.1606i	−0.774863	−	0.726659i
$849$		0			0
$850$	1.61431	+	2.37452i	0.0553702	+	0.0814452i
$851$		−	5.51211i		−	0.188953i
$852$		0			0
$853$		−	22.3667i		−	0.765821i	−0.923786	−	0.382910i	$-0.874922\pi$
$853$		−	22.3667i		−	0.765821i	0.923786	−	0.382910i	$-0.125078\pi$
$854$	−12.4346	+	8.45360i	−0.425502	+	0.289276i
$855$		0			0
$856$	−26.7906	+	6.00266i	−0.915682	+	0.205167i
$857$			34.7703i			1.18773i	0.804564	+	0.593866i	$0.202399\pi$
$857$			34.7703i			1.18773i	−0.804564	+	0.593866i	$0.797601\pi$
$858$		0			0
$859$	16.1287			0.550305			0.275152	−	0.961401i	$-0.411272\pi$
$859$	16.1287			0.550305			0.275152	+	0.961401i	$0.411272\pi$
$860$	−13.3073	+	33.6437i	−0.453777	+	1.14724i
$861$		0			0
$862$	30.1270	−	20.4817i	1.02613	−	0.697611i
$863$	34.3951			1.17082			0.585412	−	0.810736i	$-0.300933\pi$
$863$	34.3951			1.17082			0.585412	+	0.810736i	$0.300933\pi$
$864$		0			0
$865$	−9.15194			−0.311175
$866$	4.28575	−	2.91365i	0.145636	−	0.0990099i
$867$		0			0
$868$	1.36036	−	3.43927i	0.0461736	−	0.116737i
$869$	−1.21335			−0.0411600
$870$		0			0
$871$		−	18.9700i		−	0.642774i
$872$	22.1787	−	4.96933i	0.751064	−	0.168283i
$873$		0			0
$874$	−10.3144	+	7.01222i	−0.348891	+	0.237192i
$875$		−	11.7609i		−	0.397592i
$876$		0			0
$877$		−	14.0555i		−	0.474620i	−0.971434	−	0.237310i	$-0.923734\pi$
$877$		−	14.0555i		−	0.474620i	0.971434	−	0.237310i	$-0.0762658\pi$
$878$	31.3549	+	46.1206i	1.05818	+	1.55649i
$879$		0			0
$880$	−5.50506	+	5.87024i	−0.185575	+	0.197886i
$881$		−	41.1209i		−	1.38540i	−0.721226	−	0.692700i	$-0.756421\pi$
$881$		−	41.1209i		−	1.38540i	0.721226	−	0.692700i	$-0.243579\pi$
$882$		0			0
$883$	−18.8276			−0.633598			−0.316799	−	0.948493i	$-0.602608\pi$
$883$	−18.8276			−0.633598			−0.316799	+	0.948493i	$0.602608\pi$
$884$	11.1063	−	28.0791i	0.373547	−	0.944404i
$885$		0			0
$886$	28.7380	+	42.2713i	0.965473	+	1.42013i
$887$	10.8728			0.365071			0.182536	−	0.983199i	$-0.441570\pi$
$887$	10.8728			0.365071			0.182536	+	0.983199i	$0.441570\pi$
$888$		0			0
$889$	−16.6260			−0.557617
$890$	21.4670	+	31.5763i	0.719577	+	1.05844i
$891$		0			0
$892$	12.7219	+	5.03199i	0.425961	+	0.168483i
$893$	8.59846			0.287736
$894$		0			0
$895$			35.5971i			1.18988i
$896$	9.74499	+	5.74762i	0.325557	+	0.192014i
$897$		0			0
$898$	−19.8350	−	29.1758i	−0.661904	−	0.973608i
$899$		−	17.2310i		−	0.574684i
$900$		0			0
$901$			25.3711i			0.845235i
$902$	0.353446	−	0.240289i	0.0117684	−	0.00800074i
$903$		0			0
$904$	35.2753	−	7.90374i	1.17324	−	0.262874i
$905$		−	17.8045i		−	0.591843i
$906$		0			0
$907$	15.4589			0.513304			0.256652	−	0.966504i	$-0.417381\pi$
$907$	15.4589			0.513304			0.256652	+	0.966504i	$0.417381\pi$
$908$	25.8626	+	10.2296i	0.858281	+	0.339482i
$909$		0			0
$910$	−11.2658	+	7.65901i	−0.373457	+	0.253894i
$911$	23.9492			0.793473			0.396737	−	0.917933i	$-0.370143\pi$
$911$	23.9492			0.793473			0.396737	+	0.917933i	$0.370143\pi$
$912$		0			0
$913$	−2.87878			−0.0952736
$914$	−17.7601	+	12.0741i	−0.587452	+	0.399377i
$915$		0			0
$916$	7.21480	+	2.85372i	0.238384	+	0.0942896i
$917$	−14.5603			−0.480823
$918$		0			0
$919$		−	24.4853i		−	0.807694i	−0.914826	−	0.403847i	$-0.867673\pi$
$919$		−	24.4853i		−	0.807694i	0.914826	−	0.403847i	$-0.132327\pi$
$920$	3.11069	+	13.8833i	0.102556	+	0.457720i
$921$		0			0
$922$	10.8706	−	7.39032i	0.358003	−	0.243387i
$923$			31.2685i			1.02922i
$924$		0			0
$925$			1.41947i			0.0466719i
$926$	−1.69705	−	2.49623i	−0.0557686	−	0.0820312i
$927$		0			0
$928$	52.0669	+	8.20149i	1.70918	+	0.269227i
$929$			35.7122i			1.17168i	0.810428	+	0.585839i	$0.199235\pi$
$929$			35.7122i			1.17168i	−0.810428	+	0.585839i	$0.800765\pi$
$930$		0			0
$931$	−3.66977			−0.120272
$932$	−40.6007	−	16.0591i	−1.32992	−	0.526033i
$933$		0			0
$934$	−33.0825	−	48.6617i	−1.08249	−	1.59226i
$935$	6.60044			0.215857
$936$		0			0
$937$	0.263959			0.00862315			0.00431157	−	0.999991i	$-0.498628\pi$
$937$	0.263959			0.00862315			0.00431157	+	0.999991i	$0.498628\pi$
$938$	−3.27744	−	4.82086i	−0.107012	−	0.157407i
$939$		0			0
$940$	3.60768	−	9.12097i	0.117670	−	0.297493i
$941$	−40.9124			−1.33371			−0.666853	−	0.745189i	$-0.732359\pi$
$941$	−40.9124			−1.33371			−0.666853	+	0.745189i	$0.732359\pi$
$942$		0			0
$943$		−	0.755586i		−	0.0246053i
$944$	21.8769	−	23.3281i	0.712031	−	0.759265i
$945$		0			0
$946$	−6.60522	−	9.71575i	−0.214754	−	0.315886i
$947$		−	43.3236i		−	1.40783i	−0.710286	−	0.703913i	$-0.751434\pi$
$947$		−	43.3236i		−	1.40783i	0.710286	−	0.703913i	$-0.248566\pi$
$948$		0			0
$949$		−	73.7566i		−	2.39424i
$950$	2.65615	−	1.80578i	0.0861770	−	0.0585871i
$951$		0			0
$952$	−2.02877	−	9.05461i	−0.0657527	−	0.293462i
$953$			52.0756i			1.68690i	0.537211	+	0.843448i	$0.319478\pi$
$953$			52.0756i			1.68690i	−0.537211	+	0.843448i	$0.680522\pi$
$954$		0			0
$955$	1.51791			0.0491185
$956$	−20.5205	+	51.8802i	−0.663682	+	1.67793i
$957$		0			0
$958$	47.8856	−	32.5549i	1.54711	−	1.05180i
$959$	−17.2672			−0.557588
$960$		0			0
$961$	27.5802			0.889684
$962$	12.3451	−	8.39276i	0.398021	−	0.270593i
$963$		0			0
$964$	−4.54324	+	11.4863i	−0.146328	+	0.369947i
$965$	−32.9976			−1.06223
$966$		0			0
$967$		−	17.3116i		−	0.556705i	−0.960479	−	0.278352i	$-0.910212\pi$
$967$		−	17.3116i		−	0.556705i	0.960479	−	0.278352i	$-0.0897883\pi$
$968$	6.23106	+	27.8099i	0.200274	+	0.893845i
$969$		0			0
$970$	−12.1994	+	8.29369i	−0.391698	+	0.266294i
$971$			8.86074i			0.284355i	0.989841	+	0.142177i	$0.0454103\pi$
$971$			8.86074i			0.284355i	−0.989841	+	0.142177i	$0.954590\pi$
$972$		0			0
$973$			14.5580i			0.466709i
$974$	11.2936	+	16.6119i	0.361869	+	0.532280i
$975$		0			0
$976$	−29.0917	+	31.0215i	−0.931201	+	0.992973i
$977$		−	8.48509i		−	0.271462i	−0.990746	−	0.135731i	$-0.956662\pi$
$977$		−	8.48509i		−	0.271462i	0.990746	−	0.135731i	$-0.0433383\pi$
$978$		0			0
$979$	−12.3986			−0.396262
$980$	−1.53974	+	3.89278i	−0.0491851	+	0.124350i
$981$		0			0
$982$	31.2486	+	45.9642i	0.997183	+	1.46678i
$983$	43.6181			1.39120			0.695600	−	0.718429i	$-0.255138\pi$
$983$	43.6181			1.39120			0.695600	+	0.718429i	$0.255138\pi$
$984$		0			0
$985$	−12.0570			−0.384168
$986$	−24.3049	−	35.7506i	−0.774026	−	1.13853i
$987$		0			0
$988$	−31.4095	−	12.4236i	−0.999271	−	0.395249i
$989$	−20.7700			−0.660449
$990$		0			0
$991$		−	51.0937i		−	1.62304i	−0.584322	−	0.811522i	$-0.698639\pi$
$991$		−	51.0937i		−	1.62304i	0.584322	−	0.811522i	$-0.301361\pi$
$992$	1.62773	−	10.3336i	0.0516806	−	0.328093i
$993$		0			0
$994$	5.40225	+	7.94629i	0.171349	+	0.252041i
$995$		−	24.6513i		−	0.781498i
$996$		0			0
$997$			1.59455i			0.0504998i	0.999681	+	0.0252499i	$0.00803815\pi$
$997$			1.59455i			0.0504998i	−0.999681	+	0.0252499i	$0.991962\pi$
$998$	37.8060	−	25.7023i	1.19673	−	0.813591i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.c.323.8	yes	32
3.2	odd	2	inner	1512.2.j.c.323.25	yes	32
4.3	odd	2		6048.2.j.c.5615.25		32
8.3	odd	2	inner	1512.2.j.c.323.26	yes	32
8.5	even	2		6048.2.j.c.5615.7		32
12.11	even	2		6048.2.j.c.5615.8		32
24.5	odd	2		6048.2.j.c.5615.26		32
24.11	even	2	inner	1512.2.j.c.323.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.c.323.7	✓	32	24.11	even	2	inner
1512.2.j.c.323.8	yes	32	1.1	even	1	trivial
1512.2.j.c.323.25	yes	32	3.2	odd	2	inner
1512.2.j.c.323.26	yes	32	8.3	odd	2	inner
6048.2.j.c.5615.7		32	8.5	even	2
6048.2.j.c.5615.8		32	12.11	even	2
6048.2.j.c.5615.25		32	4.3	odd	2
6048.2.j.c.5615.26		32	24.5	odd	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16953 + 0.795104i) q^{2} +(0.735620 - 1.85980i) q^{4} +2.09311 q^{5} +1.00000i q^{7} +(0.618402 + 2.76000i) q^{8} +O(q^{10})\)	\(q+(-1.16953 + 0.795104i) q^{2} +(0.735620 - 1.85980i) q^{4} +2.09311 q^{5} +1.00000i q^{7} +(0.618402 + 2.76000i) q^{8} +(-2.44797 + 1.66424i) q^{10} -0.961211i q^{11} -4.60210i q^{13} +(-0.795104 - 1.16953i) q^{14} +(-2.91773 - 2.73622i) q^{16} +3.28066i q^{17} +3.66977 q^{19} +(1.53974 - 3.89278i) q^{20} +(0.764262 + 1.12417i) q^{22} +2.40322 q^{23} -0.618872 q^{25} +(3.65914 + 5.38231i) q^{26} +(1.85980 + 0.735620i) q^{28} +9.31771 q^{29} -1.84927i q^{31} +(5.58795 + 0.880204i) q^{32} +(-2.60847 - 3.83684i) q^{34} +2.09311i q^{35} -2.29364i q^{37} +(-4.29193 + 2.91785i) q^{38} +(1.29439 + 5.77699i) q^{40} -0.314406i q^{41} -8.64261 q^{43} +(-1.78766 - 0.707086i) q^{44} +(-2.81064 + 1.91081i) q^{46} +2.34305 q^{47} -1.00000 q^{49} +(0.723792 - 0.492067i) q^{50} +(-8.55899 - 3.38540i) q^{52} +7.73354 q^{53} -2.01192i q^{55} +(-2.76000 + 0.618402i) q^{56} +(-10.8974 + 7.40855i) q^{58} +7.99530i q^{59} -10.6321i q^{61} +(1.47036 + 2.16278i) q^{62} +(-7.23516 + 3.41357i) q^{64} -9.63272i q^{65} +4.12203 q^{67} +(6.10138 + 2.41332i) q^{68} +(-1.66424 - 2.44797i) q^{70} -6.79440 q^{71} +16.0267 q^{73} +(1.82368 + 2.68249i) q^{74} +(2.69956 - 6.82505i) q^{76} +0.961211 q^{77} -1.26231i q^{79} +(-6.10713 - 5.72721i) q^{80} +(0.249985 + 0.367709i) q^{82} -2.99495i q^{83} +6.86680i q^{85} +(10.1078 - 6.87177i) q^{86} +(2.65294 - 0.594415i) q^{88} -12.8990i q^{89} +4.60210 q^{91} +(1.76785 - 4.46950i) q^{92} +(-2.74028 + 1.86297i) q^{94} +7.68126 q^{95} +4.98346 q^{97} +(1.16953 - 0.795104i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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