LMFDB - Embedded newform 460.2.s.a.449.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			449.3
Character	$\chi$	$=$	460.449
Dual form			460.2.s.a.209.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25585 - 0.324343i) q^{3} +(-0.690439 - 2.12680i) q^{5} +(-3.55862 + 3.08356i) q^{7} +(2.10519 + 0.618140i) q^{9} +O(q^{10})$	\(q+(-2.25585 - 0.324343i) q^{3} +(-0.690439 - 2.12680i) q^{5} +(-3.55862 + 3.08356i) q^{7} +(2.10519 + 0.618140i) q^{9} +(1.12817 + 0.725030i) q^{11} +(3.67148 + 3.18136i) q^{13} +(0.867716 + 5.02169i) q^{15} +(5.55976 - 2.53906i) q^{17} +(1.84811 - 4.04680i) q^{19} +(9.02784 - 5.80184i) q^{21} +(-0.167809 - 4.79289i) q^{23} +(-4.04659 + 2.93686i) q^{25} +(1.67078 + 0.763020i) q^{27} +(1.39007 + 3.04382i) q^{29} +(1.02296 + 7.11486i) q^{31} +(-2.30982 - 2.00147i) q^{33} +(9.01513 + 5.43947i) q^{35} +(-0.942245 + 3.20899i) q^{37} +(-7.25047 - 8.36749i) q^{39} +(1.71129 - 0.502481i) q^{41} +(5.67503 + 0.815947i) q^{43} +(-0.138845 - 4.90411i) q^{45} +11.3505i q^{47} +(2.15921 - 15.0176i) q^{49} +(-13.3655 + 3.92447i) q^{51} +(5.72249 - 4.95857i) q^{53} +(0.763064 - 2.89998i) q^{55} +(-5.48161 + 8.52955i) q^{57} +(-2.17149 + 2.50603i) q^{59} +(1.79164 + 12.4611i) q^{61} +(-9.39763 + 4.29175i) q^{63} +(4.23119 - 10.0051i) q^{65} +(2.75086 + 4.28041i) q^{67} +(-1.17599 + 10.8665i) q^{69} +(-1.25133 + 0.804182i) q^{71} +(-12.6343 - 5.76989i) q^{73} +(10.0810 - 5.31264i) q^{75} +(-6.25039 + 0.898671i) q^{77} +(3.76577 - 4.34593i) q^{79} +(-9.05885 - 5.82177i) q^{81} +(-0.233623 + 0.795647i) q^{83} +(-9.23875 - 10.0715i) q^{85} +(-2.14854 - 7.31726i) q^{87} +(0.786701 - 5.47163i) q^{89} -22.8753 q^{91} -16.3819i q^{93} +(-9.88275 - 1.13650i) q^{95} +(2.67603 + 9.11374i) q^{97} +(1.92684 + 2.22369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.25585	−	0.324343i	−1.30242	−	0.187259i	−0.544031	−	0.839065i	$-0.683103\pi$
$3$	−2.25585	−	0.324343i	−1.30242	−	0.187259i	−0.758386	+	0.651806i	$0.774012\pi$
$4$		0			0
$5$	−0.690439	−	2.12680i	−0.308774	−	0.951135i
$5$	−0.690439	−	2.12680i	−0.308774	−	0.951135i
$6$		0			0
$7$	−3.55862	+	3.08356i	−1.34503	+	1.16548i	−0.373752	+	0.927529i	$0.621929\pi$
$7$	−3.55862	+	3.08356i	−1.34503	+	1.16548i	−0.971278	+	0.237947i	$0.923526\pi$
$8$		0			0
$9$	2.10519	+	0.618140i	0.701730	+	0.206047i
$10$		0			0
$11$	1.12817	+	0.725030i	0.340156	+	0.218605i	0.699554	−	0.714579i	$-0.253382\pi$
$11$	1.12817	+	0.725030i	0.340156	+	0.218605i	−0.359399	+	0.933184i	$0.617018\pi$
$12$		0			0
$13$	3.67148	+	3.18136i	1.01829	+	0.882350i	0.993093	−	0.117333i	$-0.0374345\pi$
$13$	3.67148	+	3.18136i	1.01829	+	0.882350i	0.0251932	+	0.999683i	$0.491980\pi$
$14$		0			0
$15$	0.867716	+	5.02169i	0.224043	+	1.29660i
$16$		0			0
$17$	5.55976	−	2.53906i	1.34844	−	0.615812i	0.395359	−	0.918527i	$-0.370620\pi$
$17$	5.55976	−	2.53906i	1.34844	−	0.615812i	0.953081	+	0.302715i	$0.0978930\pi$
$18$		0			0
$19$	1.84811	−	4.04680i	0.423986	−	0.928399i	−0.570279	−	0.821451i	$-0.693165\pi$
$19$	1.84811	−	4.04680i	0.423986	−	0.928399i	0.994265	−	0.106948i	$-0.0341078\pi$
$20$		0			0
$21$	9.02784	−	5.80184i	1.97004	−	1.26607i
$22$		0			0
$23$	−0.167809	−	4.79289i	−0.0349906	−	0.999388i
$23$	−0.167809	−	4.79289i	−0.0349906	−	0.999388i
$24$		0			0
$25$	−4.04659	+	2.93686i	−0.809317	+	0.587372i
$26$		0			0
$27$	1.67078	+	0.763020i	0.321542	+	0.146843i
$28$		0			0
$29$	1.39007	+	3.04382i	0.258129	+	0.565223i	0.993681	−	0.112245i	$-0.0358043\pi$
$29$	1.39007	+	3.04382i	0.258129	+	0.565223i	−0.735552	+	0.677469i	$0.763077\pi$
$30$		0			0
$31$	1.02296	+	7.11486i	0.183729	+	1.27787i	0.847848	+	0.530239i	$0.177898\pi$
$31$	1.02296	+	7.11486i	0.183729	+	1.27787i	−0.664119	+	0.747627i	$0.731193\pi$
$32$		0			0
$33$	−2.30982	−	2.00147i	−0.402089	−	0.348412i
$34$		0			0
$35$	9.01513	+	5.43947i	1.52384	+	0.919438i
$36$		0			0
$37$	−0.942245	+	3.20899i	−0.154904	+	0.527555i	−0.999975	−	0.00709947i	$-0.997740\pi$
$37$	−0.942245	+	3.20899i	−0.154904	+	0.527555i	0.845071	+	0.534655i	$0.179558\pi$
$38$		0			0
$39$	−7.25047	−	8.36749i	−1.16100	−	1.33987i
$40$		0			0
$41$	1.71129	−	0.502481i	0.267259	−	0.0784744i	−0.145357	−	0.989379i	$-0.546433\pi$
$41$	1.71129	−	0.502481i	0.267259	−	0.0784744i	0.412616	+	0.910905i	$0.364615\pi$
$42$		0			0
$43$	5.67503	+	0.815947i	0.865435	+	0.124431i	0.560712	−	0.828011i	$-0.310527\pi$
$43$	5.67503	+	0.815947i	0.865435	+	0.124431i	0.304722	+	0.952441i	$0.401436\pi$
$44$		0			0
$45$	−0.138845	−	4.90411i	−0.0206978	−	0.731062i
$46$		0			0
$47$			11.3505i			1.65563i	0.560999	+	0.827817i	$0.310417\pi$
$47$			11.3505i			1.65563i	−0.560999	+	0.827817i	$0.689583\pi$
$48$		0			0
$49$	2.15921	−	15.0176i	0.308459	−	2.14538i
$50$		0			0
$51$	−13.3655	+	3.92447i	−1.87155	+	0.549536i
$52$		0			0
$53$	5.72249	−	4.95857i	0.786045	−	0.681112i	−0.166320	−	0.986072i	$-0.553189\pi$
$53$	5.72249	−	4.95857i	0.786045	−	0.681112i	0.952365	+	0.304960i	$0.0986431\pi$
$54$		0			0
$55$	0.763064	−	2.89998i	0.102892	−	0.391034i
$56$		0			0
$57$	−5.48161	+	8.52955i	−0.726057	+	1.12977i
$58$		0			0
$59$	−2.17149	+	2.50603i	−0.282704	+	0.326257i	−0.879286	−	0.476295i	$-0.841980\pi$
$59$	−2.17149	+	2.50603i	−0.282704	+	0.326257i	0.596582	+	0.802552i	$0.296525\pi$
$60$		0			0
$61$	1.79164	+	12.4611i	0.229395	+	1.59548i	0.700664	+	0.713491i	$0.252887\pi$
$61$	1.79164	+	12.4611i	0.229395	+	1.59548i	−0.471269	+	0.881990i	$0.656204\pi$
$62$		0			0
$63$	−9.39763	+	4.29175i	−1.18399	+	0.540710i
$64$		0			0
$65$	4.23119	−	10.0051i	0.524814	−	1.24097i
$66$		0			0
$67$	2.75086	+	4.28041i	0.336070	+	0.522936i	0.967624	−	0.252396i	$-0.0812187\pi$
$67$	2.75086	+	4.28041i	0.336070	+	0.522936i	−0.631553	+	0.775332i	$0.717582\pi$
$68$		0			0
$69$	−1.17599	+	10.8665i	−0.141572	+	1.30817i
$70$		0			0
$71$	−1.25133	+	0.804182i	−0.148506	+	0.0954389i	−0.612784	−	0.790251i	$-0.709950\pi$
$71$	−1.25133	+	0.804182i	−0.148506	+	0.0954389i	0.464278	+	0.885690i	$0.346314\pi$
$72$		0			0
$73$	−12.6343	−	5.76989i	−1.47873	−	0.675315i	−0.497381	−	0.867532i	$-0.665705\pi$
$73$	−12.6343	−	5.76989i	−1.47873	−	0.675315i	−0.981352	+	0.192218i	$0.938432\pi$
$74$		0			0
$75$	10.0810	−	5.31264i	1.16406	−	0.613450i
$76$		0			0
$77$	−6.25039	+	0.898671i	−0.712298	+	0.102413i
$78$		0			0
$79$	3.76577	−	4.34593i	0.423682	−	0.488955i	−0.503273	−	0.864127i	$-0.667871\pi$
$79$	3.76577	−	4.34593i	0.423682	−	0.488955i	0.926955	+	0.375172i	$0.122416\pi$
$80$		0			0
$81$	−9.05885	−	5.82177i	−1.00654	−	0.646863i
$82$		0			0
$83$	−0.233623	+	0.795647i	−0.0256435	+	0.0873336i	−0.971321	−	0.237774i	$-0.923582\pi$
$83$	−0.233623	+	0.795647i	−0.0256435	+	0.0873336i	0.945677	+	0.325107i	$0.105400\pi$
$84$		0			0
$85$	−9.23875	−	10.0715i	−1.00208	−	1.09240i
$86$		0			0
$87$	−2.14854	−	7.31726i	−0.230348	−	0.784493i
$88$		0			0
$89$	0.786701	−	5.47163i	0.0833902	−	0.579991i	−0.904692	−	0.426066i	$-0.859899\pi$
$89$	0.786701	−	5.47163i	0.0833902	−	0.579991i	0.988082	−	0.153926i	$-0.0491916\pi$
$90$		0			0
$91$	−22.8753			−2.39798
$92$		0			0
$93$		−	16.3819i		−	1.69872i
$94$		0			0
$95$	−9.88275	−	1.13650i	−1.01395	−	0.116602i
$96$		0			0
$97$	2.67603	+	9.11374i	0.271710	+	0.925360i	0.976423	+	0.215867i	$0.0692577\pi$
$97$	2.67603	+	9.11374i	0.271710	+	0.925360i	−0.704713	+	0.709493i	$0.748924\pi$
$98$		0			0
$99$	1.92684	+	2.22369i	0.193655	+	0.223489i
$100$		0			0
$101$	7.62485	+	2.23886i	0.758701	+	0.222775i	0.638128	−	0.769930i	$-0.279709\pi$
$101$	7.62485	+	2.23886i	0.758701	+	0.222775i	0.120572	+	0.992705i	$0.461527\pi$
$102$		0			0
$103$	6.38444	−	9.93438i	0.629077	−	0.978863i	−0.369687	−	0.929156i	$-0.620535\pi$
$103$	6.38444	−	9.93438i	0.629077	−	0.978863i	0.998764	−	0.0497067i	$-0.0158287\pi$
$104$		0			0
$105$	−18.5725	−	15.1946i	−1.81250	−	1.48284i
$106$		0			0
$107$	4.04044	−	0.580927i	0.390604	−	0.0561604i	0.0557849	−	0.998443i	$-0.482234\pi$
$107$	4.04044	−	0.580927i	0.390604	−	0.0561604i	0.334819	+	0.942282i	$0.391325\pi$
$108$		0			0
$109$	−0.144587	−	0.316602i	−0.0138490	−	0.0303250i	0.902581	−	0.430520i	$-0.141670\pi$
$109$	−0.144587	−	0.316602i	−0.0138490	−	0.0303250i	−0.916430	+	0.400195i	$0.868942\pi$
$110$		0			0
$111$	3.16638	−	6.93340i	0.300539	−	0.658089i
$112$		0			0
$113$	8.63071	+	13.4296i	0.811909	+	1.26335i	0.961554	+	0.274615i	$0.0885504\pi$
$113$	8.63071	+	13.4296i	0.811909	+	1.26335i	−0.149646	+	0.988740i	$0.547813\pi$
$114$		0			0
$115$	−10.0777	+	3.66610i	−0.939749	+	0.341866i
$116$		0			0
$117$	5.76264	+	8.96685i	0.532757	+	0.828985i
$118$		0			0
$119$	−11.9557	+	26.1794i	−1.09598	+	2.39986i
$120$		0			0
$121$	−3.82247	−	8.37004i	−0.347497	−	0.760913i
$122$		0			0
$123$	−4.02340	+	0.578478i	−0.362778	+	0.0521596i
$124$		0			0
$125$	9.04004	+	6.57857i	0.808566	+	0.588405i
$126$		0			0
$127$	8.34425	−	12.9839i	0.740432	−	1.15213i	−0.242853	−	0.970063i	$-0.578083\pi$
$127$	8.34425	−	12.9839i	0.740432	−	1.15213i	0.983285	−	0.182072i	$-0.0582803\pi$
$128$		0			0
$129$	−12.5374	−	3.68131i	−1.10386	−	0.324121i
$130$		0			0
$131$	1.94752	+	2.24756i	0.170156	+	0.196370i	0.834422	−	0.551125i	$-0.185801\pi$
$131$	1.94752	+	2.24756i	0.170156	+	0.196370i	−0.664266	+	0.747496i	$0.731256\pi$
$132$		0			0
$133$	5.90182	+	20.0998i	0.511753	+	1.74287i
$134$		0			0
$135$	0.469221	−	4.08024i	0.0403841	−	0.351171i
$136$		0			0
$137$			11.8874i			1.01561i	0.861473	+	0.507804i	$0.169543\pi$
$137$			11.8874i			1.01561i	−0.861473	+	0.507804i	$0.830457\pi$
$138$		0			0
$139$	4.93129			0.418267			0.209133	−	0.977887i	$-0.432936\pi$
$139$	4.93129			0.418267			0.209133	+	0.977887i	$0.432936\pi$
$140$		0			0
$141$	3.68143	−	25.6049i	0.310033	−	2.15632i
$142$		0			0
$143$	1.83547	+	6.25104i	0.153490	+	0.522739i
$144$		0			0
$145$	5.51385	−	5.05797i	0.457900	−	0.420042i
$146$		0			0
$147$	−9.74172	+	33.1773i	−0.803484	+	2.73641i
$148$		0			0
$149$	5.56661	+	3.57745i	0.456035	+	0.293076i	0.748420	−	0.663225i	$-0.230813\pi$
$149$	5.56661	+	3.57745i	0.456035	+	0.293076i	−0.292385	+	0.956301i	$0.594449\pi$
$150$		0			0
$151$	9.41222	−	10.8623i	0.765955	−	0.883960i	−0.230057	−	0.973177i	$-0.573891\pi$
$151$	9.41222	−	10.8623i	0.765955	−	0.883960i	0.996012	+	0.0892176i	$0.0284367\pi$
$152$		0			0
$153$	13.2738	−	1.90849i	1.07313	−	0.154292i
$154$		0			0
$155$	14.4256	−	7.08802i	1.15869	−	0.569323i
$156$		0			0
$157$	−0.0167346	−	0.00764244i	−0.00133557	−	0.000609933i	0.414747	−	0.909937i	$-0.363870\pi$
$157$	−0.0167346	−	0.00764244i	−0.00133557	−	0.000609933i	−0.416083	+	0.909327i	$0.636597\pi$
$158$		0			0
$159$	−14.5174	+	9.32975i	−1.15130	+	0.739897i
$160$		0			0
$161$	15.3763	+	16.5386i	1.21183	+	1.30343i
$162$		0			0
$163$	−9.40494	−	14.6344i	−0.736651	−	1.14625i	−0.984146	−	0.177363i	$-0.943243\pi$
$163$	−9.40494	−	14.6344i	−0.736651	−	1.14625i	0.247494	−	0.968889i	$-0.420393\pi$
$164$		0			0
$165$	−2.66195	+	6.29444i	−0.207232	+	0.490021i
$166$		0			0
$167$	−8.00728	+	3.65680i	−0.619622	+	0.282972i	−0.700389	−	0.713761i	$-0.746990\pi$
$167$	−8.00728	+	3.65680i	−0.619622	+	0.282972i	0.0807672	+	0.996733i	$0.474263\pi$
$168$		0			0
$169$	1.50865	+	10.4929i	0.116050	+	0.807147i
$170$		0			0
$171$	6.39211	−	7.37689i	0.488817	−	0.564125i
$172$		0			0
$173$	1.77676	−	2.76469i	0.135085	−	0.210196i	−0.767121	−	0.641503i	$-0.778311\pi$
$173$	1.77676	−	2.76469i	0.135085	−	0.210196i	0.902205	+	0.431307i	$0.141948\pi$
$174$		0			0
$175$	5.34427	−	22.9290i	0.403989	−	1.73327i
$176$		0			0
$177$	5.71136	−	4.94893i	0.429292	−	0.371984i
$178$		0			0
$179$	15.1624	−	4.45209i	1.13329	−	0.332765i	0.339292	−	0.940681i	$-0.389813\pi$
$179$	15.1624	−	4.45209i	1.13329	−	0.332765i	0.794001	+	0.607917i	$0.207994\pi$
$180$		0			0
$181$	−1.86026	+	12.9384i	−0.138272	+	0.961703i	0.796039	+	0.605245i	$0.206925\pi$
$181$	−1.86026	+	12.9384i	−0.138272	+	0.961703i	−0.934311	+	0.356458i	$0.883984\pi$
$182$		0			0
$183$		−	28.6915i		−	2.12094i
$184$		0			0
$185$	7.47546	−	0.211645i	0.549607	−	0.0155604i
$186$		0			0
$187$	8.11324	+	1.16651i	0.593299	+	0.0853035i
$188$		0			0
$189$	−8.29848	+	2.43665i	−0.603626	+	0.177241i
$190$		0			0
$191$	−7.76748	−	8.96415i	−0.562035	−	0.648623i	0.401609	−	0.915811i	$-0.368451\pi$
$191$	−7.76748	−	8.96415i	−0.562035	−	0.648623i	−0.963644	+	0.267188i	$0.913906\pi$
$192$		0			0
$193$	−3.80345	+	12.9533i	−0.273778	+	0.932402i	0.701731	+	0.712442i	$0.252411\pi$
$193$	−3.80345	+	12.9533i	−0.273778	+	0.932402i	−0.975509	+	0.219960i	$0.929407\pi$
$194$		0			0
$195$	−12.7900	+	21.1976i	−0.915910	+	1.51799i
$196$		0			0
$197$	−5.40341	−	4.68208i	−0.384977	−	0.333585i	0.440775	−	0.897618i	$-0.354704\pi$
$197$	−5.40341	−	4.68208i	−0.384977	−	0.333585i	−0.825752	+	0.564033i	$0.809249\pi$
$198$		0			0
$199$	0.579733	+	4.03213i	0.0410962	+	0.285830i	0.999998	+	0.00209146i	$0.000665734\pi$
$199$	0.579733	+	4.03213i	0.0410962	+	0.285830i	−0.958902	+	0.283739i	$0.908425\pi$
$200$		0			0
$201$	−4.81720	−	10.5482i	−0.339779	−	0.744013i
$202$		0			0
$203$	−14.3325	−	6.54544i	−1.00594	−	0.459400i
$204$		0			0
$205$	−2.25022	−	3.29265i	−0.157162	−	0.229969i
$206$		0			0
$207$	2.60941	−	10.1937i	0.181366	−	0.708510i
$208$		0			0
$209$	5.01903	−	3.22554i	0.347174	−	0.223115i
$210$		0			0
$211$	−0.890575	+	1.95009i	−0.0613097	+	0.134250i	−0.937807	−	0.347158i	$-0.887147\pi$
$211$	−0.890575	+	1.95009i	−0.0613097	+	0.134250i	0.876497	+	0.481407i	$0.159874\pi$
$212$		0			0
$213$	3.08365	−	1.40826i	0.211288	−	0.0964921i
$214$		0			0
$215$	−2.18291	−	12.6330i	−0.148873	−	0.861566i
$216$		0			0
$217$	−25.5794	−	22.1647i	−1.73644	−	1.50464i
$218$		0			0
$219$	26.6297	+	17.1139i	1.79947	+	1.15645i
$220$		0			0
$221$	28.4902	+	8.36548i	1.91646	+	0.562723i
$222$		0			0
$223$	−18.9457	+	16.4166i	−1.26870	+	1.09933i	−0.278389	+	0.960468i	$0.589800\pi$
$223$	−18.9457	+	16.4166i	−1.26870	+	1.09933i	−0.990311	+	0.138867i	$0.955654\pi$
$224$		0			0
$225$	−10.3342	+	3.68129i	−0.688948	+	0.245419i
$226$		0			0
$227$	18.4075	+	2.64660i	1.22175	+	0.175661i	0.722853	−	0.691002i	$-0.242830\pi$
$227$	18.4075	+	2.64660i	1.22175	+	0.175661i	0.498895	+	0.866663i	$0.333739\pi$
$228$		0			0
$229$	0.541213			0.0357644			0.0178822	−	0.999840i	$-0.494308\pi$
$229$	0.541213			0.0357644			0.0178822	+	0.999840i	$0.494308\pi$
$230$		0			0
$231$	14.3914			0.946887
$232$		0			0
$233$	−6.80874	−	0.978949i	−0.446055	−	0.0641331i	−0.0843726	−	0.996434i	$-0.526889\pi$
$233$	−6.80874	−	0.978949i	−0.446055	−	0.0641331i	−0.361683	+	0.932301i	$0.617798\pi$
$234$		0			0
$235$	24.1402	−	7.83680i	1.57473	−	0.511216i
$236$		0			0
$237$	−9.90458	+	8.58237i	−0.643372	+	0.557485i
$238$		0			0
$239$	14.0287	+	4.11920i	0.907442	+	0.266449i	0.701964	−	0.712213i	$-0.252307\pi$
$239$	14.0287	+	4.11920i	0.907442	+	0.266449i	0.205478	+	0.978662i	$0.434125\pi$
$240$		0			0
$241$	−0.449448	−	0.288843i	−0.0289515	−	0.0186060i	0.526085	−	0.850432i	$-0.323659\pi$
$241$	−0.449448	−	0.288843i	−0.0289515	−	0.0186060i	−0.555037	+	0.831826i	$0.687296\pi$
$242$		0			0
$243$	14.3828	+	12.4627i	0.922655	+	0.799485i
$244$		0			0
$245$	−33.4304	+	5.77656i	−2.13579	+	0.369051i
$246$		0			0
$247$	19.6596	−	8.97824i	1.25091	−	0.571272i
$248$		0			0
$249$	0.785081	−	1.71909i	0.0497525	−	0.108943i
$250$		0			0
$251$	−25.2178	+	16.2065i	−1.59174	+	1.02295i	−0.620688	+	0.784058i	$0.713147\pi$
$251$	−25.2178	+	16.2065i	−1.59174	+	1.02295i	−0.971047	+	0.238888i	$0.923217\pi$
$252$		0			0
$253$	3.28568	−	5.52886i	0.206569	−	0.347597i
$254$		0			0
$255$	17.5747	+	25.7162i	1.10057	+	1.61041i
$256$		0			0
$257$	−8.34877	−	3.81275i	−0.520782	−	0.237833i	0.137640	−	0.990482i	$-0.456048\pi$
$257$	−8.34877	−	3.81275i	−0.520782	−	0.237833i	−0.658422	+	0.752649i	$0.728776\pi$
$258$		0			0
$259$	−6.54203	−	14.3250i	−0.406502	−	0.890115i
$260$		0			0
$261$	1.04485	+	7.26707i	0.0646744	+	0.449821i
$262$		0			0
$263$	−17.8045	−	15.4277i	−1.09787	−	0.951314i	−0.0988340	−	0.995104i	$-0.531511\pi$
$263$	−17.8045	−	15.4277i	−1.09787	−	0.951314i	−0.999041	+	0.0437900i	$0.986057\pi$
$264$		0			0
$265$	−14.4969	−	8.74703i	−0.890540	−	0.537326i
$266$		0			0
$267$	−3.54936	+	12.0880i	−0.217217	+	0.739775i
$268$		0			0
$269$	15.0702	+	17.3919i	0.918844	+	1.06040i	0.997979	+	0.0635382i	$0.0202385\pi$
$269$	15.0702	+	17.3919i	0.918844	+	1.06040i	−0.0791358	+	0.996864i	$0.525216\pi$
$270$		0			0
$271$	2.14425	−	0.629609i	0.130254	−	0.0382460i	−0.215956	−	0.976403i	$-0.569287\pi$
$271$	2.14425	−	0.629609i	0.130254	−	0.0382460i	0.346210	+	0.938157i	$0.387469\pi$
$272$		0			0
$273$	51.6033	+	7.41943i	3.12317	+	0.449044i
$274$		0			0
$275$	−6.69455	+	0.379375i	−0.403696	+	0.0228772i
$276$		0			0
$277$			19.0768i			1.14622i	0.819480	+	0.573108i	$0.194263\pi$
$277$			19.0768i			1.14622i	−0.819480	+	0.573108i	$0.805737\pi$
$278$		0			0
$279$	−2.24445	+	15.6105i	−0.134371	+	0.934574i
$280$		0			0
$281$	9.15148	−	2.68712i	0.545932	−	0.160300i	0.00287480	−	0.999996i	$-0.499085\pi$
$281$	9.15148	−	2.68712i	0.545932	−	0.160300i	0.543057	+	0.839696i	$0.317267\pi$
$282$		0			0
$283$	−13.3414	+	11.5604i	−0.793062	+	0.687192i	−0.954011	−	0.299771i	$-0.903090\pi$
$283$	−13.3414	+	11.5604i	−0.793062	+	0.687192i	0.160949	+	0.986963i	$0.448544\pi$
$284$		0			0
$285$	21.9254	+	5.76917i	1.29875	+	0.341736i
$286$		0			0
$287$	−4.54041	+	7.06501i	−0.268012	+	0.417034i
$288$		0			0
$289$	13.3315	−	15.3854i	0.784205	−	0.905021i
$290$		0			0
$291$	−3.08076	−	21.4272i	−0.180598	−	1.25608i
$292$		0			0
$293$	−5.42133	+	2.47584i	−0.316717	+	0.144640i	−0.567430	−	0.823422i	$-0.692062\pi$
$293$	−5.42133	+	2.47584i	−0.316717	+	0.144640i	0.250713	+	0.968062i	$0.419335\pi$
$294$		0			0
$295$	6.82911	+	2.88806i	0.397606	+	0.168150i
$296$		0			0
$297$	1.33171	+	2.07218i	0.0772737	+	0.120240i
$298$		0			0
$299$	14.6318	−	18.1309i	0.846179	−	1.04854i
$300$		0			0
$301$	−22.7113	+	14.5957i	−1.30906	+	0.841280i
$302$		0			0
$303$	−16.4744	−	7.52359i	−0.946428	−	0.432219i
$304$		0			0
$305$	25.2653	−	12.4141i	1.44669	−	0.710829i
$306$		0			0
$307$	−1.25750	+	0.180801i	−0.0717691	+	0.0103188i	−0.178106	−	0.984011i	$-0.556997\pi$
$307$	−1.25750	+	0.180801i	−0.0717691	+	0.0103188i	0.106337	+	0.994330i	$0.466088\pi$
$308$		0			0
$309$	−17.6245	+	20.3397i	−1.00262	+	1.15709i
$310$		0			0
$311$	20.9895	+	13.4892i	1.19021	+	0.764900i	0.977235	−	0.212159i	$-0.0680494\pi$
$311$	20.9895	+	13.4892i	1.19021	+	0.764900i	0.212972	+	0.977058i	$0.431686\pi$
$312$		0			0
$313$	3.29293	−	11.2147i	0.186127	−	0.633891i	−0.812570	−	0.582864i	$-0.801932\pi$
$313$	3.29293	−	11.2147i	0.186127	−	0.633891i	0.998697	−	0.0510276i	$-0.0162496\pi$
$314$		0			0
$315$	15.6162	+	17.0237i	0.879874	+	0.959178i
$316$		0			0
$317$	−7.78120	−	26.5003i	−0.437036	−	1.48841i	−0.824148	−	0.566375i	$-0.808346\pi$
$317$	−7.78120	−	26.5003i	−0.437036	−	1.48841i	0.387112	−	0.922033i	$-0.373473\pi$
$318$		0			0
$319$	−0.638632	+	4.44178i	−0.0357565	+	0.248692i
$320$		0			0
$321$	−9.30305			−0.519246
$322$		0			0
$323$		−	27.1917i		−	1.51299i
$324$		0			0
$325$	−24.2002	−	2.09102i	−1.34238	−	0.115989i
$326$		0			0
$327$	0.223480	+	0.761103i	0.0123585	+	0.0420891i
$328$		0			0
$329$	−34.9998	−	40.3919i	−1.92960	−	2.22688i
$330$		0			0
$331$	−7.11727	−	2.08982i	−0.391201	−	0.114867i	0.0802160	−	0.996778i	$-0.474439\pi$
$331$	−7.11727	−	2.08982i	−0.391201	−	0.114867i	−0.471417	+	0.881911i	$0.656257\pi$
$332$		0			0
$333$	−3.96721	+	6.17310i	−0.217402	+	0.338284i
$334$		0			0
$335$	7.20430	−	8.80590i	0.393613	−	0.481118i
$336$		0			0
$337$	12.0424	−	1.73144i	0.655991	−	0.0943173i	0.193721	−	0.981057i	$-0.437944\pi$
$337$	12.0424	−	1.73144i	0.655991	−	0.0943173i	0.462270	+	0.886739i	$0.347035\pi$
$338$		0			0
$339$	−15.1138	−	33.0946i	−0.820869	−	1.79745i
$340$		0			0
$341$	−4.00441	+	8.76844i	−0.216851	+	0.474838i
$342$		0			0
$343$	20.8039	+	32.3715i	1.12330	+	1.74790i
$344$		0			0
$345$	23.9228	−	5.00156i	1.28796	−	0.269275i
$346$		0			0
$347$	−8.60801	−	13.3943i	−0.462102	−	0.719045i	0.529508	−	0.848305i	$-0.322376\pi$
$347$	−8.60801	−	13.3943i	−0.462102	−	0.719045i	−0.991611	+	0.129259i	$0.958740\pi$
$348$		0			0
$349$	4.83637	−	10.5902i	0.258885	−	0.566878i	−0.734903	−	0.678172i	$-0.762772\pi$
$349$	4.83637	−	10.5902i	0.258885	−	0.566878i	0.993788	+	0.111294i	$0.0354995\pi$
$350$		0			0
$351$	3.70680	+	8.11676i	0.197854	+	0.433241i
$352$		0			0
$353$	1.69087	−	0.243110i	0.0899958	−	0.0129394i	−0.0971698	−	0.995268i	$-0.530979\pi$
$353$	1.69087	−	0.243110i	0.0899958	−	0.0129394i	0.187166	+	0.982328i	$0.440070\pi$
$354$		0			0
$355$	2.57431	+	2.10610i	0.136630	+	0.111780i
$356$		0			0
$357$	35.4614	−	55.1790i	1.87682	−	2.92038i
$358$		0			0
$359$	5.32329	+	1.56306i	0.280953	+	0.0824952i	0.419173	−	0.907906i	$-0.362320\pi$
$359$	5.32329	+	1.56306i	0.280953	+	0.0824952i	−0.138220	+	0.990401i	$0.544138\pi$
$360$		0			0
$361$	−0.518701	−	0.598613i	−0.0273001	−	0.0315060i
$362$		0			0
$363$	5.90816	+	20.1214i	0.310098	+	1.05610i
$364$		0			0
$365$	−3.54821	+	30.8544i	−0.185722	+	1.61500i
$366$		0			0
$367$			11.0965i			0.579230i	0.957143	+	0.289615i	$0.0935273\pi$
$367$			11.0965i			0.579230i	−0.957143	+	0.289615i	$0.906473\pi$
$368$		0			0
$369$	3.91320			0.203713
$370$		0			0
$371$	−5.07412	+	35.2913i	−0.263435	+	1.83223i
$372$		0			0
$373$	2.55340	+	8.69608i	0.132210	+	0.450266i	0.998812	−	0.0487343i	$-0.0155188\pi$
$373$	2.55340	+	8.69608i	0.132210	+	0.450266i	−0.866602	+	0.499001i	$0.833701\pi$
$374$		0			0
$375$	−18.2593	−	17.7724i	−0.942906	−	0.917760i
$376$		0			0
$377$	−4.57988	+	15.5976i	−0.235876	+	0.803319i
$378$		0			0
$379$	1.48414	+	0.953802i	0.0762354	+	0.0489935i	0.578203	−	0.815893i	$-0.303754\pi$
$379$	1.48414	+	0.953802i	0.0762354	+	0.0489935i	−0.501968	+	0.864886i	$0.667390\pi$
$380$		0			0
$381$	−23.0346	+	26.5834i	−1.18010	+	1.36191i
$382$		0			0
$383$	16.9270	−	2.43374i	0.864930	−	0.124358i	0.304452	−	0.952528i	$-0.401527\pi$
$383$	16.9270	−	2.43374i	0.864930	−	0.124358i	0.560478	+	0.828169i	$0.310617\pi$
$384$		0			0
$385$	6.22681	+	12.6729i	0.317348	+	0.645870i
$386$		0			0
$387$	11.4427	+	5.22569i	0.581663	+	0.265637i
$388$		0			0
$389$	15.8900	−	10.2119i	0.805657	−	0.517764i	−0.0718003	−	0.997419i	$-0.522874\pi$
$389$	15.8900	−	10.2119i	0.805657	−	0.517764i	0.877457	+	0.479655i	$0.159238\pi$
$390$		0			0
$391$	−13.1024	−	26.2213i	−0.662618	−	1.32607i
$392$		0			0
$393$	−3.66434	−	5.70183i	−0.184842	−	0.287619i
$394$		0			0
$395$	−11.8430	−	5.00845i	−0.595885	−	0.252002i
$396$		0			0
$397$	31.2367	−	14.2653i	1.56772	−	0.715955i	0.573097	−	0.819487i	$-0.305742\pi$
$397$	31.2367	−	14.2653i	1.56772	−	0.715955i	0.994626	+	0.103532i	$0.0330144\pi$
$398$		0			0
$399$	−6.79443	−	47.2563i	−0.340147	−	2.36577i
$400$		0			0
$401$	−6.45621	+	7.45087i	−0.322408	+	0.372079i	−0.893698	−	0.448670i	$-0.851898\pi$
$401$	−6.45621	+	7.45087i	−0.322408	+	0.372079i	0.571290	+	0.820749i	$0.306443\pi$
$402$		0			0
$403$	−18.8791	+	29.3765i	−0.940436	+	1.46335i
$404$		0			0
$405$	−6.12717	+	23.2860i	−0.304462	+	1.15709i
$406$		0			0
$407$	−3.38963	+	2.93713i	−0.168018	+	0.145588i
$408$		0			0
$409$	−31.1285	+	9.14015i	−1.53920	+	0.451951i	−0.937853	−	0.347033i	$-0.887189\pi$
$409$	−31.1285	+	9.14015i	−1.53920	+	0.451951i	−0.601352	+	0.798984i	$0.705371\pi$
$410$		0			0
$411$	3.85558	−	26.8162i	0.190182	−	1.32274i
$412$		0			0
$413$		−	15.6139i		−	0.768310i
$414$		0			0
$415$	1.85349	−	0.0524758i	0.0909841	−	0.00257594i
$416$		0			0
$417$	−11.1243	−	1.59943i	−0.544757	−	0.0783243i
$418$		0			0
$419$	−6.95647	+	2.04260i	−0.339846	+	0.0997878i	−0.447202	−	0.894433i	$-0.647580\pi$
$419$	−6.95647	+	2.04260i	−0.339846	+	0.0997878i	0.107356	+	0.994221i	$0.465761\pi$
$420$		0			0
$421$	13.4418	+	15.5126i	0.655112	+	0.756039i	0.981971	−	0.189034i	$-0.0605357\pi$
$421$	13.4418	+	15.5126i	0.655112	+	0.756039i	−0.326859	+	0.945073i	$0.605990\pi$
$422$		0			0
$423$	−7.01616	+	23.8949i	−0.341137	+	1.16181i
$424$		0			0
$425$	−15.0412	+	26.6027i	−0.729605	+	1.29042i
$426$		0			0
$427$	−44.8003	−	38.8197i	−2.16804	−	1.87862i
$428$		0			0
$429$	−2.11307	−	14.6968i	−0.102020	−	0.709566i
$430$		0			0
$431$	−1.22193	−	2.67566i	−0.0588585	−	0.128882i	0.877917	−	0.478812i	$-0.158933\pi$
$431$	−1.22193	−	2.67566i	−0.0588585	−	0.128882i	−0.936776	+	0.349930i	$0.886205\pi$
$432$		0			0
$433$	0.425302	+	0.194229i	0.0204387	+	0.00933404i	0.425608	−	0.904908i	$-0.360060\pi$
$433$	0.425302	+	0.194229i	0.0204387	+	0.00933404i	−0.405169	+	0.914242i	$0.632787\pi$
$434$		0			0
$435$	−14.0789	+	9.62166i	−0.675034	+	0.461323i
$436$		0			0
$437$	−19.7060	−	8.17871i	−0.942666	−	0.391241i
$438$		0			0
$439$	−16.4997	+	10.6037i	−0.787489	+	0.506088i	−0.871511	−	0.490376i	$-0.836860\pi$
$439$	−16.4997	+	10.6037i	−0.787489	+	0.506088i	0.0840225	+	0.996464i	$0.473223\pi$
$440$		0			0
$441$	13.8286	−	30.2803i	0.658502	−	1.44192i
$442$		0			0
$443$	14.2761	−	6.51968i	0.678279	−	0.309759i	−0.0463239	−	0.998926i	$-0.514751\pi$
$443$	14.2761	−	6.51968i	0.678279	−	0.309759i	0.724603	+	0.689167i	$0.242023\pi$
$444$		0			0
$445$	−12.1802	+	2.10467i	−0.577399	+	0.0997709i
$446$		0			0
$447$	−11.3971	−	9.87568i	−0.539066	−	0.467103i
$448$		0			0
$449$	−24.5198	−	15.7579i	−1.15716	−	0.743662i	−0.186109	−	0.982529i	$-0.559588\pi$
$449$	−24.5198	−	15.7579i	−1.15716	−	0.743662i	−0.971052	+	0.238867i	$0.923224\pi$
$450$		0			0
$451$	2.29494	+	0.673856i	0.108065	+	0.0317306i
$452$		0			0
$453$	−24.7557	+	21.4509i	−1.16312	+	1.00785i
$454$		0			0
$455$	15.7940	+	48.6513i	0.740434	+	2.28081i
$456$		0			0
$457$	−30.0514	−	4.32073i	−1.40574	−	0.202115i	−0.602668	−	0.797992i	$-0.705895\pi$
$457$	−30.0514	−	4.32073i	−1.40574	−	0.202115i	−0.803076	+	0.595877i	$0.796805\pi$
$458$		0			0
$459$	11.2265			0.524008
$460$		0			0
$461$	−27.9537			−1.30193			−0.650967	−	0.759106i	$-0.725636\pi$
$461$	−27.9537			−1.30193			−0.650967	+	0.759106i	$0.725636\pi$
$462$		0			0
$463$	−22.0676	−	3.17284i	−1.02557	−	0.147454i	−0.391055	−	0.920367i	$-0.627890\pi$
$463$	−22.0676	−	3.17284i	−1.02557	−	0.147454i	−0.634512	+	0.772913i	$0.718799\pi$
$464$		0			0
$465$	−34.8410	+	11.3107i	−1.61571	+	0.524520i
$466$		0			0
$467$	32.0769	−	27.7948i	1.48434	−	1.28619i	0.618594	−	0.785711i	$-0.287703\pi$
$467$	32.0769	−	27.7948i	1.48434	−	1.28619i	0.865748	−	0.500480i	$-0.166843\pi$
$468$		0			0
$469$	−22.9881	−	6.74993i	−1.06149	−	0.311683i
$470$		0			0
$471$	0.0352720	+	0.0226680i	0.00162525	+	0.00104448i
$472$		0			0
$473$	5.81081	+	5.03510i	0.267181	+	0.231514i
$474$		0			0
$475$	4.40633	+	21.8034i	0.202176	+	1.00041i
$476$		0			0
$477$	15.1120	−	6.90143i	0.691932	−	0.315995i
$478$		0			0
$479$	−5.52393	+	12.0957i	−0.252395	+	0.552667i	−0.992840	−	0.119449i	$-0.961887\pi$
$479$	−5.52393	+	12.0957i	−0.252395	+	0.552667i	0.740446	+	0.672116i	$0.234614\pi$
$480$		0			0
$481$	−13.6684	+	8.78414i	−0.623225	+	0.400522i
$482$		0			0
$483$	−29.3226	−	42.2959i	−1.33422	−	1.92453i
$484$		0			0
$485$	17.5355	−	11.9839i	0.796245	−	0.544160i
$486$		0			0
$487$	−17.7049	−	8.08558i	−0.802288	−	0.366392i	−0.0283050	−	0.999599i	$-0.509011\pi$
$487$	−17.7049	−	8.08558i	−0.802288	−	0.366392i	−0.773983	+	0.633207i	$0.781738\pi$
$488$		0			0
$489$	16.4696	+	36.0634i	0.744781	+	1.63084i
$490$		0			0
$491$	−2.69420	−	18.7386i	−0.121588	−	0.845660i	−0.955758	−	0.294153i	$-0.904962\pi$
$491$	−2.69420	−	18.7386i	−0.121588	−	0.845660i	0.834171	−	0.551506i	$-0.185947\pi$
$492$		0			0
$493$	15.4569	+	13.3935i	0.696142	+	0.603211i
$494$		0			0
$495$	3.39899	−	5.63334i	0.152773	−	0.253200i
$496$		0			0
$497$	1.97327	−	6.72033i	0.0885131	−	0.301448i
$498$		0			0
$499$	2.39282	+	2.76146i	0.107117	+	0.123620i	0.806776	−	0.590857i	$-0.201210\pi$
$499$	2.39282	+	2.76146i	0.107117	+	0.123620i	−0.699659	+	0.714477i	$0.746665\pi$
$500$		0			0
$501$	19.2493	−	5.65210i	0.859995	−	0.252517i
$502$		0			0
$503$	4.61681	+	0.663797i	0.205853	+	0.0295973i	0.244470	−	0.969657i	$-0.421386\pi$
$503$	4.61681	+	0.663797i	0.205853	+	0.0295973i	−0.0386166	+	0.999254i	$0.512295\pi$
$504$		0			0
$505$	−0.502886	−	17.7623i	−0.0223781	−	0.790414i
$506$		0			0
$507$		−	24.1598i		−	1.07297i
$508$		0			0
$509$	2.93248	−	20.3959i	0.129980	−	0.904031i	−0.815594	−	0.578624i	$-0.803590\pi$
$509$	2.93248	−	20.3959i	0.129980	−	0.904031i	0.945574	−	0.325406i	$-0.105501\pi$
$510$		0			0
$511$	62.7524	−	18.4258i	2.77600	−	0.815108i
$512$		0			0
$513$	6.17557	−	5.35117i	0.272658	−	0.236260i
$514$		0			0
$515$	−25.5365	−	6.71936i	−1.12527	−	0.296090i
$516$		0			0
$517$	−8.22942	+	12.8052i	−0.361930	+	0.563173i
$518$		0			0
$519$	−4.90481	+	5.66046i	−0.215297	+	0.248466i
$520$		0			0
$521$	−4.65964	−	32.4085i	−0.204143	−	1.41984i	−0.791824	−	0.610750i	$-0.790868\pi$
$521$	−4.65964	−	32.4085i	−0.204143	−	1.41984i	0.587681	−	0.809093i	$-0.300041\pi$
$522$		0			0
$523$	0.933532	−	0.426330i	0.0408205	−	0.0186421i	−0.394900	−	0.918724i	$-0.629221\pi$
$523$	0.933532	−	0.426330i	0.0408205	−	0.0186421i	0.435721	+	0.900082i	$0.356494\pi$
$524$		0			0
$525$	−19.4927	+	49.9911i	−0.850733	+	2.18179i
$526$		0			0
$527$	23.7525	+	36.9595i	1.03467	+	1.60998i
$528$		0			0
$529$	−22.9437	+	1.60858i	−0.997551	+	0.0699384i
$530$		0			0
$531$	−6.12047	+	3.93339i	−0.265606	+	0.170694i
$532$		0			0
$533$	7.88156	+	3.59939i	0.341388	+	0.155907i
$534$		0			0
$535$	−4.02520	−	8.19212i	−0.174024	−	0.354176i
$536$		0			0
$537$	−35.6482	+	5.12543i	−1.53833	+	0.221179i
$538$		0			0
$539$	13.3242	−	15.3770i	0.573914	−	0.662332i
$540$		0			0
$541$	−10.1324	−	6.51169i	−0.435625	−	0.279959i	0.304393	−	0.952547i	$-0.401547\pi$
$541$	−10.1324	−	6.51169i	−0.435625	−	0.279959i	−0.740018	+	0.672587i	$0.765183\pi$
$542$		0			0
$543$	8.39294	−	28.5837i	0.360175	−	1.22664i
$544$		0			0
$545$	−0.573522	+	0.526103i	−0.0245670	+	0.0225358i
$546$		0			0
$547$	−12.1446	−	41.3607i	−0.519266	−	1.76846i	−0.632146	−	0.774849i	$-0.717826\pi$
$547$	−12.1446	−	41.3607i	−0.519266	−	1.76846i	0.112880	−	0.993609i	$-0.463992\pi$
$548$		0			0
$549$	−3.93097	+	27.3405i	−0.167770	+	1.16686i
$550$		0			0
$551$	14.8867			0.634195
$552$		0			0
$553$			27.0775i			1.15145i
$554$		0			0
$555$	−16.9322	−	1.94717i	−0.718731	−	0.0826528i
$556$		0			0
$557$	13.1609	+	44.8220i	0.557646	+	1.89917i	0.416358	+	0.909201i	$0.363306\pi$
$557$	13.1609	+	44.8220i	0.557646	+	1.89917i	0.141288	+	0.989968i	$0.454876\pi$
$558$		0			0
$559$	18.2400	+	21.0500i	0.771468	+	0.890322i
$560$		0			0
$561$	−17.9239	−	5.26294i	−0.756749	−	0.222201i
$562$		0			0
$563$	13.2846	−	20.6712i	0.559878	−	0.871187i	−0.439760	−	0.898116i	$-0.644936\pi$
$563$	13.2846	−	20.6712i	0.559878	−	0.871187i	0.999637	+	0.0269288i	$0.00857273\pi$
$564$		0			0
$565$	22.6032	−	27.6282i	0.950925	−	1.16233i
$566$		0			0
$567$	50.1887	−	7.21605i	2.10773	−	0.303046i
$568$		0			0
$569$	19.2848	+	42.2278i	0.808460	+	1.77028i	0.613889	+	0.789392i	$0.289604\pi$
$569$	19.2848	+	42.2278i	0.808460	+	1.77028i	0.194571	+	0.980888i	$0.437668\pi$
$570$		0			0
$571$	13.6717	−	29.9368i	0.572142	−	1.25282i	−0.373507	−	0.927628i	$-0.621845\pi$
$571$	13.6717	−	29.9368i	0.572142	−	1.25282i	0.945649	−	0.325189i	$-0.105428\pi$
$572$		0			0
$573$	14.6148	+	22.7411i	0.610543	+	0.950024i
$574$		0			0
$575$	14.7551	+	18.9020i	0.615331	+	0.788269i
$576$		0			0
$577$	13.1992	+	20.5383i	0.549490	+	0.855023i	0.999273	−	0.0381149i	$-0.0121353\pi$
$577$	13.1992	+	20.5383i	0.549490	+	0.855023i	−0.449784	+	0.893138i	$0.648499\pi$
$578$		0			0
$579$	12.7813	−	27.9872i	0.531174	−	1.16311i
$580$		0			0
$581$	−1.62205	−	3.55179i	−0.0672939	−	0.147353i
$582$		0			0
$583$	10.0511	−	1.44512i	0.416272	−	0.0598509i
$584$		0			0
$585$	15.0920	−	18.4471i	0.623976	−	0.762693i
$586$		0			0
$587$	18.2177	−	28.3473i	0.751924	−	1.17002i	−0.228581	−	0.973525i	$-0.573409\pi$
$587$	18.2177	−	28.3473i	0.751924	−	1.17002i	0.980505	−	0.196492i	$-0.0629551\pi$
$588$		0			0
$589$	30.6829	+	9.00932i	1.26427	+	0.371223i
$590$		0			0
$591$	10.6707	+	12.3146i	0.438934	+	0.506557i
$592$		0			0
$593$	−1.99268	−	6.78643i	−0.0818294	−	0.278685i	0.908406	−	0.418088i	$-0.137300\pi$
$593$	−1.99268	−	6.78643i	−0.0818294	−	0.278685i	−0.990236	+	0.139403i	$0.955482\pi$
$594$		0			0
$595$	63.9331	+	7.35219i	2.62100	+	0.301411i
$596$		0			0
$597$		−	9.28392i		−	0.379966i
$598$		0			0
$599$	−40.7686			−1.66576			−0.832881	−	0.553453i	$-0.813310\pi$
$599$	−40.7686			−1.66576			−0.832881	+	0.553453i	$0.813310\pi$
$600$		0			0
$601$	−3.08511	+	21.4574i	−0.125844	+	0.875266i	0.824898	+	0.565282i	$0.191233\pi$
$601$	−3.08511	+	21.4574i	−0.125844	+	0.875266i	−0.950742	+	0.309984i	$0.899676\pi$
$602$		0			0
$603$	3.14518	+	10.7115i	0.128082	+	0.436206i
$604$		0			0
$605$	−15.1622	+	13.9086i	−0.616433	+	0.565467i
$606$		0			0
$607$	−4.11641	+	14.0192i	−0.167080	+	0.569021i	0.832801	+	0.553573i	$0.186736\pi$
$607$	−4.11641	+	14.0192i	−0.167080	+	0.569021i	−0.999881	+	0.0154488i	$0.995082\pi$
$608$		0			0
$609$	30.2090	+	19.4142i	1.22413	+	0.786702i
$610$		0			0
$611$	−36.1098	+	41.6730i	−1.46085	+	1.68591i
$612$		0			0
$613$	2.27379	−	0.326922i	0.0918377	−	0.0132043i	−0.0962428	−	0.995358i	$-0.530683\pi$
$613$	2.27379	−	0.326922i	0.0918377	−	0.0132043i	0.188080	+	0.982154i	$0.439773\pi$
$614$		0			0
$615$	4.00822	+	8.15758i	0.161627	+	0.328945i
$616$		0			0
$617$	−9.25976	−	4.22879i	−0.372784	−	0.170245i	0.220208	−	0.975453i	$-0.429326\pi$
$617$	−9.25976	−	4.22879i	−0.372784	−	0.170245i	−0.592992	+	0.805208i	$0.702054\pi$
$618$		0			0
$619$	10.6764	−	6.86129i	0.429120	−	0.275779i	−0.308201	−	0.951321i	$-0.599727\pi$
$619$	10.6764	−	6.86129i	0.429120	−	0.275779i	0.737321	+	0.675543i	$0.236091\pi$
$620$		0			0
$621$	3.37670	−	8.13592i	0.135502	−	0.326483i
$622$		0			0
$623$	14.0725	+	21.8973i	0.563803	+	0.877295i
$624$		0			0
$625$	7.74973	−	23.7685i	0.309989	−	0.950740i
$626$		0			0
$627$	−12.3684	+	5.64844i	−0.493945	+	0.225577i
$628$		0			0
$629$	2.90916	+	20.2337i	0.115996	+	0.806768i
$630$		0			0
$631$	−23.1703	+	26.7399i	−0.922394	+	1.06450i	0.0753365	+	0.997158i	$0.475997\pi$
$631$	−23.1703	+	26.7399i	−0.922394	+	1.06450i	−0.997730	+	0.0673407i	$0.978549\pi$
$632$		0			0
$633$	2.64150	−	4.11026i	0.104990	−	0.163368i
$634$		0			0
$635$	−33.3754	−	8.78197i	−1.32446	−	0.348502i
$636$		0			0
$637$	55.7040	−	48.2678i	2.20707	−	1.91244i
$638$		0			0
$639$	−3.13139	+	0.919458i	−0.123876	+	0.0363732i
$640$		0			0
$641$	6.72404	−	46.7668i	0.265584	−	1.84718i	−0.223202	−	0.974772i	$-0.571651\pi$
$641$	6.72404	−	46.7668i	0.265584	−	1.84718i	0.488786	−	0.872404i	$-0.337440\pi$
$642$		0			0
$643$		−	19.7575i		−	0.779162i	−0.920992	−	0.389581i	$-0.872620\pi$
$643$		−	19.7575i		−	0.779162i	0.920992	−	0.389581i	$-0.127380\pi$
$644$		0			0
$645$	0.826886	+	29.2063i	0.0325586	+	1.15000i
$646$		0			0
$647$	10.2710	+	1.47675i	0.403794	+	0.0580569i	0.341220	−	0.939983i	$-0.389160\pi$
$647$	10.2710	+	1.47675i	0.403794	+	0.0580569i	0.0625744	+	0.998040i	$0.480069\pi$
$648$		0			0
$649$	−4.26675	+	1.25283i	−0.167485	+	0.0491779i
$650$		0			0
$651$	50.5144	+	58.2967i	1.97982	+	2.28483i
$652$		0			0
$653$	−12.7518	+	43.4286i	−0.499016	+	1.69949i	0.196091	+	0.980586i	$0.437175\pi$
$653$	−12.7518	+	43.4286i	−0.499016	+	1.69949i	−0.695107	+	0.718906i	$0.744643\pi$
$654$		0			0
$655$	3.43547	−	5.69380i	0.134235	−	0.222475i
$656$		0			0
$657$	−23.0310	−	19.9565i	−0.898525	−	0.778576i
$658$		0			0
$659$	−0.426805	−	2.96849i	−0.0166260	−	0.115636i	0.979818	−	0.199890i	$-0.0640585\pi$
$659$	−0.426805	−	2.96849i	−0.0166260	−	0.115636i	−0.996444	+	0.0842538i	$0.973149\pi$
$660$		0			0
$661$	7.53374	+	16.4966i	0.293028	+	0.641643i	0.997692	−	0.0678986i	$-0.0216294\pi$
$661$	7.53374	+	16.4966i	0.293028	+	0.641643i	−0.704664	+	0.709541i	$0.748902\pi$
$662$		0			0
$663$	−61.5564	−	28.1119i	−2.39065	−	1.09177i
$664$		0			0
$665$	38.6734	−	26.4297i	1.49969	−	1.02490i
$666$		0			0
$667$	14.3554	−	7.17322i	0.555845	−	0.277748i
$668$		0			0
$669$	48.0634	−	30.8884i	1.85824	−	1.19422i
$670$		0			0
$671$	−7.01341	+	15.3572i	−0.270750	+	0.592859i
$672$		0			0
$673$	−23.2561	+	10.6207i	−0.896456	+	0.409398i	−0.809708	−	0.586832i	$-0.800375\pi$
$673$	−23.2561	+	10.6207i	−0.896456	+	0.409398i	−0.0867479	+	0.996230i	$0.527647\pi$
$674$		0			0
$675$	−9.00184	+	1.81922i	−0.346481	+	0.0700218i
$676$		0			0
$677$	−29.8513	−	25.8663i	−1.14728	−	0.994121i	−0.999987	−	0.00502797i	$-0.998400\pi$
$677$	−29.8513	−	25.8663i	−1.14728	−	0.994121i	−0.147290	−	0.989093i	$-0.547055\pi$
$678$		0			0
$679$	−37.6257	−	24.1806i	−1.44394	−	0.927965i
$680$		0			0
$681$	−40.6662	−	11.9407i	−1.55833	−	0.457567i
$682$		0			0
$683$	−10.9645	+	9.50081i	−0.419546	+	0.363538i	−0.838901	−	0.544284i	$-0.816801\pi$
$683$	−10.9645	+	9.50081i	−0.419546	+	0.363538i	0.419356	+	0.907822i	$0.362256\pi$
$684$		0			0
$685$	25.2821	−	8.20752i	0.965981	−	0.313593i
$686$		0			0
$687$	−1.22090	−	0.175538i	−0.0465801	−	0.00669721i
$688$		0			0
$689$	36.7850			1.40140
$690$		0			0
$691$	43.9802			1.67309			0.836543	−	0.547901i	$-0.184573\pi$
$691$	43.9802			1.67309			0.836543	+	0.547901i	$0.184573\pi$
$692$		0			0
$693$	−13.7138	−	1.97174i	−0.520943	−	0.0749003i
$694$		0			0
$695$	−3.40476	−	10.4879i	−0.129150	−	0.397828i
$696$		0			0
$697$	8.23855	−	7.13875i	0.312058	−	0.270399i
$698$		0			0
$699$	15.0420	+	4.41673i	0.568941	+	0.167056i
$700$		0			0
$701$	−14.6277	−	9.40068i	−0.552482	−	0.355059i	0.234421	−	0.972135i	$-0.424681\pi$
$701$	−14.6277	−	9.40068i	−0.552482	−	0.355059i	−0.786903	+	0.617076i	$0.788317\pi$
$702$		0			0
$703$	11.2448	+	9.74365i	0.424105	+	0.367489i
$704$		0			0
$705$	−56.9985	+	9.84897i	−2.14669	+	0.370934i
$706$		0			0
$707$	−34.0375	+	15.5444i	−1.28011	+	0.584608i
$708$		0			0
$709$	−12.3836	+	27.1163i	−0.465076	+	1.01837i	0.521226	+	0.853419i	$0.325475\pi$
$709$	−12.3836	+	27.1163i	−0.465076	+	1.01837i	−0.986301	+	0.164954i	$0.947252\pi$
$710$		0			0
$711$	10.6140	−	6.82123i	0.398058	−	0.255816i
$712$		0			0
$713$	33.9291	−	6.09689i	1.27065	−	0.228330i
$714$		0			0
$715$	12.0275	−	8.21966i	0.449802	−	0.307398i
$716$		0			0
$717$	−30.3107	−	13.8424i	−1.13197	−	0.516954i
$718$		0			0
$719$	8.94893	+	19.5954i	0.333739	+	0.730786i	0.999887	−	0.0150334i	$-0.00478545\pi$
$719$	8.94893	+	19.5954i	0.333739	+	0.730786i	−0.666148	+	0.745819i	$0.732058\pi$
$720$		0			0
$721$	7.91347	+	55.0394i	0.294713	+	2.04977i
$722$		0			0
$723$	0.920205	+	0.797362i	0.0342228	+	0.0296542i
$724$		0			0
$725$	−14.5643	−	8.23465i	−0.540904	−	0.305827i
$726$		0			0
$727$	−10.6060	+	36.1208i	−0.393355	+	1.33964i	0.490319	+	0.871543i	$0.336880\pi$
$727$	−10.6060	+	36.1208i	−0.393355	+	1.33964i	−0.883675	+	0.468102i	$0.844938\pi$
$728$		0			0
$729$	−7.24803	−	8.36468i	−0.268446	−	0.309803i
$730$		0			0
$731$	33.6236	−	9.87277i	1.24361	−	0.365158i
$732$		0			0
$733$	27.5689	+	3.96380i	1.01828	+	0.146406i	0.631184	−	0.775633i	$-0.282569\pi$
$733$	27.5689	+	3.96380i	1.01828	+	0.146406i	0.387095	+	0.922040i	$0.373478\pi$
$734$		0			0
$735$	77.2876	−	2.18816i	2.85080	−	0.0807115i
$736$		0			0
$737$			6.82349i			0.251346i
$738$		0			0
$739$	−2.57695	+	17.9231i	−0.0947945	+	0.659310i	0.885916	+	0.463845i	$0.153531\pi$
$739$	−2.57695	+	17.9231i	−0.0947945	+	0.659310i	−0.980711	+	0.195465i	$0.937378\pi$
$740$		0			0
$741$	−47.2612	+	13.8771i	−1.73618	+	0.509789i
$742$		0			0
$743$	−29.5900	+	25.6399i	−1.08555	+	0.940636i	−0.998455	−	0.0555639i	$-0.982304\pi$
$743$	−29.5900	+	25.6399i	−1.08555	+	0.940636i	−0.0870966	+	0.996200i	$0.527759\pi$
$744$		0			0
$745$	3.76511	−	14.3091i	0.137943	−	0.524245i
$746$		0			0
$747$	−0.983642	+	1.53058i	−0.0359896	+	0.0560009i
$748$		0			0
$749$	−12.5870	+	14.5262i	−0.459921	+	0.530777i
$750$		0			0
$751$	−3.66044	−	25.4589i	−0.133571	−	0.929009i	−0.940846	−	0.338833i	$-0.889968\pi$
$751$	−3.66044	−	25.4589i	−0.133571	−	0.929009i	0.807275	−	0.590175i	$-0.200941\pi$
$752$		0			0
$753$	62.1441	−	28.3803i	2.26466	−	1.03423i
$754$		0			0
$755$	−29.6005	−	12.5182i	−1.07727	−	0.455584i
$756$		0			0
$757$	−8.74409	−	13.6061i	−0.317809	−	0.494521i	0.645191	−	0.764021i	$-0.276778\pi$
$757$	−8.74409	−	13.6061i	−0.317809	−	0.494521i	−0.963000	+	0.269501i	$0.913141\pi$
$758$		0			0
$759$	−9.20524	+	11.4066i	−0.334129	+	0.414034i
$760$		0			0
$761$	13.3472	−	8.57772i	0.483835	−	0.310942i	−0.275887	−	0.961190i	$-0.588971\pi$
$761$	13.3472	−	8.57772i	0.483835	−	0.310942i	0.759722	+	0.650248i	$0.225335\pi$
$762$		0			0
$763$	1.49079	+	0.680822i	0.0539703	+	0.0246474i
$764$		0			0
$765$	−13.2238	−	26.9132i	−0.478106	−	0.973047i
$766$		0			0
$767$	−15.9452	+	2.29257i	−0.575746	+	0.0827798i
$768$		0			0
$769$	12.2351	−	14.1200i	0.441208	−	0.509181i	−0.490973	−	0.871175i	$-0.663359\pi$
$769$	12.2351	−	14.1200i	0.441208	−	0.509181i	0.932180	+	0.361994i	$0.117904\pi$
$770$		0			0
$771$	17.5969	+	11.3089i	0.633739	+	0.407279i
$772$		0			0
$773$	7.81677	−	26.6215i	0.281150	−	0.957508i	−0.690943	−	0.722910i	$-0.742804\pi$
$773$	7.81677	−	26.6215i	0.281150	−	0.957508i	0.972092	−	0.234598i	$-0.0753775\pi$
$774$		0			0
$775$	−25.0348	−	25.7866i	−0.899278	−	0.926282i
$776$		0			0
$777$	10.1116	+	34.4370i	0.362753	+	1.23542i
$778$		0			0
$779$	1.12922	−	7.85390i	0.0404585	−	0.281395i
$780$		0			0
$781$	−1.99477			−0.0713785
$782$		0			0
$783$			6.14620i			0.219647i
$784$		0			0
$785$	−0.00469974	+	0.0408679i	−0.000167741	+	0.00145864i
$786$		0			0
$787$	9.54581	+	32.5101i	0.340272	+	1.15886i	0.934916	+	0.354870i	$0.115475\pi$
$787$	9.54581	+	32.5101i	0.340272	+	1.15886i	−0.594644	+	0.803989i	$0.702707\pi$
$788$		0			0
$789$	35.1605	+	40.5774i	1.25175	+	1.44459i
$790$		0			0
$791$	−72.1245	−	21.1777i	−2.56445	−	0.752991i
$792$		0			0
$793$	−33.0653	+	51.4505i	−1.17418	+	1.82706i
$794$		0			0
$795$	29.8659	+	24.4340i	1.05923	+	0.866584i
$796$		0			0
$797$	29.2041	−	4.19891i	1.03446	−	0.148733i	0.395891	−	0.918297i	$-0.370436\pi$
$797$	29.2041	−	4.19891i	1.03446	−	0.148733i	0.638569	+	0.769564i	$0.279527\pi$
$798$		0			0
$799$	28.8194	+	63.1058i	1.01956	+	2.23252i
$800$		0			0
$801$	5.03838	−	11.0325i	0.178023	−	0.389815i
$802$		0			0
$803$	−10.0703	−	15.6697i	−0.355373	−	0.552970i
$804$		0			0
$805$	24.5580	−	44.1214i	0.865555	−	1.55507i
$806$		0			0
$807$	−28.3551	−	44.1214i	−0.998147	−	1.55315i
$808$		0			0
$809$	4.92832	−	10.7915i	0.173271	−	0.379410i	−0.802995	−	0.595985i	$-0.796762\pi$
$809$	4.92832	−	10.7915i	0.173271	−	0.379410i	0.976266	+	0.216576i	$0.0694889\pi$
$810$		0			0
$811$	11.2274	+	24.5846i	0.394248	+	0.863282i	0.997821	+	0.0659748i	$0.0210157\pi$
$811$	11.2274	+	24.5846i	0.394248	+	0.863282i	−0.603574	+	0.797307i	$0.706257\pi$
$812$		0			0
$813$	−5.04132	+	0.724833i	−0.176807	+	0.0254210i
$814$		0			0
$815$	−24.6309	+	30.1066i	−0.862782	+	1.05459i
$816$		0			0
$817$	13.7901	−	21.4578i	0.482453	−	0.750712i
$818$		0			0
$819$	−48.1568	−	14.1401i	−1.68274	−	0.494096i
$820$		0			0
$821$	−12.8060	−	14.7789i	−0.446932	−	0.515787i	0.486920	−	0.873446i	$-0.338120\pi$
$821$	−12.8060	−	14.7789i	−0.446932	−	0.515787i	−0.933852	+	0.357660i	$0.883575\pi$
$822$		0			0
$823$	9.33624	+	31.7963i	0.325441	+	1.10835i	0.945994	+	0.324185i	$0.105090\pi$
$823$	9.33624	+	31.7963i	0.325441	+	1.10835i	−0.620553	+	0.784165i	$0.713092\pi$
$824$		0			0
$825$	15.2249	+	1.31551i	0.530065	+	0.0458002i
$826$		0			0
$827$			0.258574i			0.00899151i	0.999990	+	0.00449576i	$0.00143105\pi$
$827$			0.258574i			0.00899151i	−0.999990	+	0.00449576i	$0.998569\pi$
$828$		0			0
$829$	−7.49798			−0.260416			−0.130208	−	0.991487i	$-0.541564\pi$
$829$	−7.49798			−0.260416			−0.130208	+	0.991487i	$0.541564\pi$
$830$		0			0
$831$	6.18743	−	43.0345i	0.214640	−	1.49285i
$832$		0			0
$833$	−26.1260	−	88.9769i	−0.905211	−	3.08287i
$834$		0			0
$835$	13.3058	+	14.5051i	0.460468	+	0.501970i
$836$		0			0
$837$	−3.71963	+	12.6679i	−0.128569	+	0.437867i
$838$		0			0
$839$	−29.9903	−	19.2736i	−1.03538	−	0.665398i	−0.0915396	−	0.995801i	$-0.529179\pi$
$839$	−29.9903	−	19.2736i	−1.03538	−	0.665398i	−0.943840	+	0.330404i	$0.892815\pi$
$840$		0			0
$841$	11.6584	−	13.4545i	0.402014	−	0.463949i
$842$		0			0
$843$	−21.5159	+	3.09353i	−0.741048	+	0.106547i
$844$		0			0
$845$	21.2747	−	10.4533i	0.731873	−	0.359605i
$846$		0			0
$847$	39.4122	+	17.9989i	1.35422	+	0.618451i
$848$		0			0
$849$	33.8457	−	21.7513i	1.16158	−	0.746502i
$850$		0			0
$851$	15.5385	+	3.97758i	0.532652	+	0.136350i
$852$		0			0
$853$	−3.82226	−	5.94756i	−0.130872	−	0.203640i	0.769633	−	0.638486i	$-0.220439\pi$
$853$	−3.82226	−	5.94756i	−0.130872	−	0.203640i	−0.900505	+	0.434846i	$0.856803\pi$
$854$		0			0
$855$	−20.1026	−	8.50147i	−0.687493	−	0.290744i
$856$		0			0
$857$	1.38121	−	0.630775i	0.0471811	−	0.0215469i	−0.391685	−	0.920099i	$-0.628108\pi$
$857$	1.38121	−	0.630775i	0.0471811	−	0.0215469i	0.438866	+	0.898553i	$0.355380\pi$
$858$		0			0
$859$	−1.16284	−	8.08775i	−0.0396757	−	0.275950i	0.960320	−	0.278901i	$-0.0899700\pi$
$859$	−1.16284	−	8.08775i	−0.0396757	−	0.275950i	−0.999996	+	0.00295024i	$0.999061\pi$
$860$		0			0
$861$	12.5340	−	14.4650i	0.427156	−	0.492965i
$862$		0			0
$863$	5.24292	−	8.15814i	0.178471	−	0.277706i	−0.740480	−	0.672079i	$-0.765402\pi$
$863$	5.24292	−	8.15814i	0.178471	−	0.277706i	0.918951	+	0.394373i	$0.129038\pi$
$864$		0			0
$865$	−7.10670	−	1.86997i	−0.241635	−	0.0635808i
$866$		0			0
$867$	−35.0640	+	30.3831i	−1.19084	+	1.03186i
$868$		0			0
$869$	7.39935	−	2.17265i	0.251006	−	0.0737020i
$870$		0			0
$871$	−3.51781	+	24.4669i	−0.119197	+	0.829030i
$872$		0			0
$873$			20.8403i			0.705338i
$874$		0			0
$875$	−52.4554	+	4.46489i	−1.77332	+	0.150941i
$876$		0			0
$877$	4.07695	+	0.586177i	0.137669	+	0.0197938i	0.210805	−	0.977528i	$-0.432392\pi$
$877$	4.07695	+	0.586177i	0.137669	+	0.0197938i	−0.0731359	+	0.997322i	$0.523301\pi$
$878$		0			0
$879$	13.0327	−	3.82676i	0.439583	−	0.129073i
$880$		0			0
$881$	−1.38461	−	1.59792i	−0.0466486	−	0.0538354i	0.731946	−	0.681363i	$-0.238612\pi$
$881$	−1.38461	−	1.59792i	−0.0466486	−	0.0538354i	−0.778594	+	0.627528i	$0.784067\pi$
$882$		0			0
$883$	−4.19903	+	14.3006i	−0.141309	+	0.481253i	−0.999485	−	0.0321027i	$-0.989780\pi$
$883$	−4.19903	+	14.3006i	−0.141309	+	0.481253i	0.858176	+	0.513356i	$0.171598\pi$
$884$		0			0
$885$	−14.4687	−	8.73002i	−0.486362	−	0.293456i
$886$		0			0
$887$	14.6911	+	12.7299i	0.493280	+	0.427430i	0.865646	−	0.500656i	$-0.166908\pi$
$887$	14.6911	+	12.7299i	0.493280	+	0.427430i	−0.372366	+	0.928086i	$0.621453\pi$
$888$		0			0
$889$	10.3426	+	71.9347i	0.346881	+	2.41261i
$890$		0			0
$891$	−5.99895	−	13.1359i	−0.200973	−	0.440069i
$892$		0			0
$893$	45.9330	+	20.9769i	1.53709	+	0.701965i
$894$		0			0
$895$	−19.9375	−	29.1736i	−0.666436	−	0.975166i
$896$		0			0
$897$	−38.8878	+	36.1549i	−1.29843	+	1.20718i
$898$		0			0
$899$	−20.2344	+	13.0038i	−0.674854	+	0.433702i
$900$		0			0
$901$	19.2256	−	42.0982i	0.640498	−	1.40249i
$902$		0			0
$903$	55.9673	−	25.5594i	1.86247	−	0.850564i
$904$		0			0
$905$	28.8018	−	4.97677i	0.957404	−	0.165433i
$906$		0			0
$907$	−0.828312	−	0.717737i	−0.0275037	−	0.0238321i	0.641000	−	0.767540i	$-0.278520\pi$
$907$	−0.828312	−	0.717737i	−0.0275037	−	0.0238321i	−0.668504	+	0.743708i	$0.733065\pi$
$908$		0			0
$909$	14.6678	+	9.42644i	0.486501	+	0.312655i
$910$		0			0
$911$	15.0170	+	4.40939i	0.497535	+	0.146090i	0.520866	−	0.853638i	$-0.325609\pi$
$911$	15.0170	+	4.40939i	0.497535	+	0.146090i	−0.0233310	+	0.999728i	$0.507427\pi$
$912$		0			0
$913$	−0.840434	+	0.728241i	−0.0278143	+	0.0241012i
$914$		0			0
$915$	−61.0212	+	19.8097i	−2.01730	+	0.654890i
$916$		0			0
$917$	−13.8610	−	1.99291i	−0.457730	−	0.0658116i
$918$		0			0
$919$	16.7573			0.552771			0.276385	−	0.961047i	$-0.410863\pi$
$919$	16.7573			0.552771			0.276385	+	0.961047i	$0.410863\pi$
$920$		0			0
$921$	2.89537			0.0954056
$922$		0			0
$923$	−7.15263	−	1.02839i	−0.235432	−	0.0338500i
$924$		0			0
$925$	−5.61148	−	15.7527i	−0.184504	−	0.517946i
$926$		0			0
$927$	19.5813	−	16.9673i	0.643134	−	0.557278i
$928$		0			0
$929$	−37.0805	−	10.8878i	−1.21657	−	0.357217i	−0.390404	−	0.920644i	$-0.627665\pi$
$929$	−37.0805	−	10.8878i	−1.21657	−	0.357217i	−0.826166	+	0.563426i	$0.809483\pi$
$930$		0			0
$931$	−56.7829	−	36.4922i	−1.86098	−	1.19598i
$932$		0			0
$933$	−42.9742	−	37.2373i	−1.40691	−	1.21910i
$934$		0			0
$935$	−3.12077	−	18.0607i	−0.102060	−	0.590647i
$936$		0			0
$937$	−0.141984	+	0.0648418i	−0.00463840	+	0.00211829i	−0.417733	−	0.908570i	$-0.637175\pi$
$937$	−0.141984	+	0.0648418i	−0.00463840	+	0.00211829i	0.413094	+	0.910688i	$0.364448\pi$
$938$		0			0
$939$	−11.0658	+	24.2306i	−0.361117	+	0.790736i
$940$		0			0
$941$	32.9485	−	21.1747i	1.07409	−	0.690276i	0.120906	−	0.992664i	$-0.461420\pi$
$941$	32.9485	−	21.1747i	1.07409	−	0.690276i	0.953185	+	0.302388i	$0.0977838\pi$
$942$		0			0
$943$	−2.69551	−	8.11773i	−0.0877779	−	0.264350i
$944$		0			0
$945$	10.9119	+	15.9669i	0.354964	+	0.519403i
$946$		0			0
$947$	8.12899	+	3.71239i	0.264157	+	0.120636i	0.543091	−	0.839674i	$-0.317254\pi$
$947$	8.12899	+	3.71239i	0.264157	+	0.120636i	−0.278934	+	0.960310i	$0.589981\pi$
$948$		0			0
$949$	−28.0305	−	61.3783i	−0.909909	−	1.99242i
$950$		0			0
$951$	8.95805	+	62.3046i	0.290485	+	2.02037i
$952$		0			0
$953$	18.2130	+	15.7816i	0.589976	+	0.511217i	0.897903	−	0.440193i	$-0.145090\pi$
$953$	18.2130	+	15.7816i	0.589976	+	0.511217i	−0.307927	+	0.951410i	$0.599635\pi$
$954$		0			0
$955$	−13.7020	+	22.7091i	−0.443387	+	0.734850i
$956$		0			0
$957$	2.88132	−	9.81287i	0.0931398	−	0.317205i
$958$		0			0
$959$	−36.6554	−	42.3026i	−1.18367	−	1.36602i
$960$		0			0
$961$	−19.8305	+	5.82275i	−0.639693	+	0.187831i
$962$		0			0
$963$	8.86498	+	1.27459i	0.285670	+	0.0410732i
$964$		0			0
$965$	30.1753	−	0.854320i	0.971376	−	0.0275015i
$966$		0			0
$967$		−	52.7009i		−	1.69475i	−0.530998	−	0.847373i	$-0.678183\pi$
$967$		−	52.7009i		−	1.69475i	0.530998	−	0.847373i	$-0.321817\pi$
$968$		0			0
$969$	−8.81942	+	61.3404i	−0.283321	+	1.97054i
$970$		0			0
$971$	−26.9282	+	7.90684i	−0.864167	+	0.253742i	−0.683633	−	0.729826i	$-0.739601\pi$
$971$	−26.9282	+	7.90684i	−0.864167	+	0.253742i	−0.180535	+	0.983569i	$0.557783\pi$
$972$		0			0
$973$	−17.5486	+	15.2059i	−0.562581	+	0.487479i
$974$		0			0
$975$	53.9138	+	12.5662i	1.72662	+	0.402439i
$976$		0			0
$977$	11.4855	−	17.8718i	0.367454	−	0.571770i	−0.607460	−	0.794350i	$-0.707811\pi$
$977$	11.4855	−	17.8718i	0.367454	−	0.571770i	0.974914	+	0.222580i	$0.0714479\pi$
$978$		0			0
$979$	4.85463	−	5.60254i	0.155155	−	0.179058i
$980$		0			0
$981$	−0.108679	−	0.755882i	−0.00346987	−	0.0241335i
$982$		0			0
$983$	−7.15020	+	3.26539i	−0.228056	+	0.104150i	−0.526166	−	0.850382i	$-0.676371\pi$
$983$	−7.15020	+	3.26539i	−0.228056	+	0.104150i	0.298110	+	0.954531i	$0.403644\pi$
$984$		0			0
$985$	−6.22714	+	14.7247i	−0.198413	+	0.469168i
$986$		0			0
$987$	65.8535	+	102.470i	2.09614	+	3.26166i
$988$		0			0
$989$	2.95842	−	27.3368i	0.0940724	−	0.869259i
$990$		0			0
$991$	9.99819	−	6.42544i	0.317603	−	0.204111i	−0.372120	−	0.928185i	$-0.621369\pi$
$991$	9.99819	−	6.42544i	0.317603	−	0.204111i	0.689722	+	0.724074i	$0.257733\pi$
$992$		0			0
$993$	15.3777	+	7.02276i	0.487996	+	0.222860i
$994$		0			0
$995$	8.17528	−	4.01692i	0.259174	−	0.127345i
$996$		0			0
$997$	15.6689	−	2.25284i	0.496238	−	0.0713482i	0.110348	−	0.993893i	$-0.464804\pi$
$997$	15.6689	−	2.25284i	0.496238	−	0.0713482i	0.385890	+	0.922545i	$0.373894\pi$
$998$		0			0
$999$	−4.02281	+	4.64257i	−0.127276	+	0.146885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.449.3	yes	120
5.4	even	2	inner	460.2.s.a.449.10	yes	120
23.2	even	11	inner	460.2.s.a.209.10	yes	120
115.94	even	22	inner	460.2.s.a.209.3	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.209.3	✓	120	115.94	even	22	inner
460.2.s.a.209.10	yes	120	23.2	even	11	inner
460.2.s.a.449.3	yes	120	1.1	even	1	trivial
460.2.s.a.449.10	yes	120	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25585 - 0.324343i) q^{3} +(-0.690439 - 2.12680i) q^{5} +(-3.55862 + 3.08356i) q^{7} +(2.10519 + 0.618140i) q^{9} +O(q^{10})\)	\(q+(-2.25585 - 0.324343i) q^{3} +(-0.690439 - 2.12680i) q^{5} +(-3.55862 + 3.08356i) q^{7} +(2.10519 + 0.618140i) q^{9} +(1.12817 + 0.725030i) q^{11} +(3.67148 + 3.18136i) q^{13} +(0.867716 + 5.02169i) q^{15} +(5.55976 - 2.53906i) q^{17} +(1.84811 - 4.04680i) q^{19} +(9.02784 - 5.80184i) q^{21} +(-0.167809 - 4.79289i) q^{23} +(-4.04659 + 2.93686i) q^{25} +(1.67078 + 0.763020i) q^{27} +(1.39007 + 3.04382i) q^{29} +(1.02296 + 7.11486i) q^{31} +(-2.30982 - 2.00147i) q^{33} +(9.01513 + 5.43947i) q^{35} +(-0.942245 + 3.20899i) q^{37} +(-7.25047 - 8.36749i) q^{39} +(1.71129 - 0.502481i) q^{41} +(5.67503 + 0.815947i) q^{43} +(-0.138845 - 4.90411i) q^{45} +11.3505i q^{47} +(2.15921 - 15.0176i) q^{49} +(-13.3655 + 3.92447i) q^{51} +(5.72249 - 4.95857i) q^{53} +(0.763064 - 2.89998i) q^{55} +(-5.48161 + 8.52955i) q^{57} +(-2.17149 + 2.50603i) q^{59} +(1.79164 + 12.4611i) q^{61} +(-9.39763 + 4.29175i) q^{63} +(4.23119 - 10.0051i) q^{65} +(2.75086 + 4.28041i) q^{67} +(-1.17599 + 10.8665i) q^{69} +(-1.25133 + 0.804182i) q^{71} +(-12.6343 - 5.76989i) q^{73} +(10.0810 - 5.31264i) q^{75} +(-6.25039 + 0.898671i) q^{77} +(3.76577 - 4.34593i) q^{79} +(-9.05885 - 5.82177i) q^{81} +(-0.233623 + 0.795647i) q^{83} +(-9.23875 - 10.0715i) q^{85} +(-2.14854 - 7.31726i) q^{87} +(0.786701 - 5.47163i) q^{89} -22.8753 q^{91} -16.3819i q^{93} +(-9.88275 - 1.13650i) q^{95} +(2.67603 + 9.11374i) q^{97} +(1.92684 + 2.22369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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