LMFDB - Embedded newform 572.2.bg.a.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	572.9
Dual form			572.2.bg.a.445.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.153632 - 1.46171i) q^{3} +(0.347814 + 1.07046i) q^{5} +(0.456258 - 4.34101i) q^{7} +(0.821453 - 0.174605i) q^{9} +O(q^{10})$	\(q+(-0.153632 - 1.46171i) q^{3} +(0.347814 + 1.07046i) q^{5} +(0.456258 - 4.34101i) q^{7} +(0.821453 - 0.174605i) q^{9} +(3.16285 + 0.998183i) q^{11} +(-2.63415 + 2.46196i) q^{13} +(1.51127 - 0.672859i) q^{15} +(1.08014 - 1.19961i) q^{17} +(-5.01372 - 2.23225i) q^{19} -6.41538 q^{21} +(2.77148 - 4.80034i) q^{23} +(3.02017 - 2.19429i) q^{25} +(-1.74397 - 5.36738i) q^{27} +(-3.32186 + 1.47899i) q^{29} +(-0.402046 + 1.23737i) q^{31} +(0.973139 - 4.77652i) q^{33} +(4.80557 - 1.02145i) q^{35} +(-0.408641 + 0.181939i) q^{37} +(4.00336 + 3.47212i) q^{39} +(-0.595870 - 5.66932i) q^{41} +(2.24746 + 3.89272i) q^{43} +(0.472620 + 0.818602i) q^{45} +(7.41355 - 5.38626i) q^{47} +(-11.7891 - 2.50586i) q^{49} +(-1.91943 - 1.39455i) q^{51} +(-2.67804 + 8.24215i) q^{53} +(0.0315674 + 3.73289i) q^{55} +(-2.49263 + 7.67154i) q^{57} +(0.716387 - 6.81597i) q^{59} +(3.68983 - 4.09798i) q^{61} +(-0.383168 - 3.64560i) q^{63} +(-3.55163 - 1.96345i) q^{65} +(-2.41714 + 4.18661i) q^{67} +(-7.44249 - 3.31361i) q^{69} +(-4.17462 + 4.63639i) q^{71} +(4.92480 + 3.57808i) q^{73} +(-3.67140 - 4.07750i) q^{75} +(5.77620 - 13.2745i) q^{77} +(-5.12771 + 15.7815i) q^{79} +(-5.27601 + 2.34903i) q^{81} +(1.60256 + 4.93218i) q^{83} +(1.65982 + 0.739002i) q^{85} +(2.67219 + 4.62837i) q^{87} +(-2.05255 + 3.55512i) q^{89} +(9.48554 + 12.5581i) q^{91} +(1.87044 + 0.397575i) q^{93} +(0.645696 - 6.14339i) q^{95} +(6.39482 - 1.35926i) q^{97} +(2.77242 + 0.267710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.153632	−	1.46171i	−0.0886994	−	0.843918i	−0.944919	−	0.327305i	$-0.893859\pi$
$3$	−0.153632	−	1.46171i	−0.0886994	−	0.843918i	0.856219	−	0.516613i	$-0.172807\pi$
$4$		0			0
$5$	0.347814	+	1.07046i	0.155547	+	0.478724i	0.998216	−	0.0597077i	$-0.0190169\pi$
$5$	0.347814	+	1.07046i	0.155547	+	0.478724i	−0.842669	+	0.538432i	$0.819017\pi$
$6$		0			0
$7$	0.456258	−	4.34101i	0.172449	−	1.64075i	−0.475969	−	0.879462i	$-0.657903\pi$
$7$	0.456258	−	4.34101i	0.172449	−	1.64075i	0.648418	−	0.761284i	$-0.275431\pi$
$8$		0			0
$9$	0.821453	−	0.174605i	0.273818	−	0.0582017i
$10$		0			0
$11$	3.16285	+	0.998183i	0.953636	+	0.300964i
$11$	3.16285	+	0.998183i	0.953636	+	0.300964i
$12$		0			0
$13$	−2.63415	+	2.46196i	−0.730582	+	0.682825i
$13$	−2.63415	+	2.46196i	−0.730582	+	0.682825i
$14$		0			0
$15$	1.51127	−	0.672859i	0.390207	−	0.173731i
$16$		0			0
$17$	1.08014	−	1.19961i	0.261972	−	0.290949i	−0.597781	−	0.801659i	$-0.703951\pi$
$17$	1.08014	−	1.19961i	0.261972	−	0.290949i	0.859753	+	0.510710i	$0.170618\pi$
$18$		0			0
$19$	−5.01372	−	2.23225i	−1.15023	−	0.512113i	−0.259091	−	0.965853i	$-0.583423\pi$
$19$	−5.01372	−	2.23225i	−1.15023	−	0.512113i	−0.891134	+	0.453740i	$0.850090\pi$
$20$		0			0
$21$	−6.41538			−1.39995
$22$		0			0
$23$	2.77148	−	4.80034i	0.577893	−	1.00094i	−0.417828	−	0.908526i	$-0.637208\pi$
$23$	2.77148	−	4.80034i	0.577893	−	1.00094i	0.995721	−	0.0924138i	$-0.0294583\pi$
$24$		0			0
$25$	3.02017	−	2.19429i	0.604035	−	0.438857i
$26$		0			0
$27$	−1.74397	−	5.36738i	−0.335626	−	1.03295i
$28$		0			0
$29$	−3.32186	+	1.47899i	−0.616854	+	0.274641i	−0.691282	−	0.722585i	$-0.742954\pi$
$29$	−3.32186	+	1.47899i	−0.616854	+	0.274641i	0.0744278	+	0.997226i	$0.476287\pi$
$30$		0			0
$31$	−0.402046	+	1.23737i	−0.0722096	+	0.222238i	−0.980648	−	0.195781i	$-0.937276\pi$
$31$	−0.402046	+	1.23737i	−0.0722096	+	0.222238i	0.908438	+	0.418020i	$0.137276\pi$
$32$		0			0
$33$	0.973139	−	4.77652i	0.169402	−	0.831486i
$34$		0			0
$35$	4.80557	−	1.02145i	0.812289	−	0.172657i
$36$		0			0
$37$	−0.408641	+	0.181939i	−0.0671802	+	0.0299106i	−0.440052	−	0.897972i	$-0.645040\pi$
$37$	−0.408641	+	0.181939i	−0.0671802	+	0.0299106i	0.372872	+	0.927883i	$0.378373\pi$
$38$		0			0
$39$	4.00336	+	3.47212i	0.641051	+	0.555985i
$40$		0			0
$41$	−0.595870	−	5.66932i	−0.0930592	−	0.885399i	−0.937086	−	0.349098i	$-0.886488\pi$
$41$	−0.595870	−	5.66932i	−0.0930592	−	0.885399i	0.844027	−	0.536301i	$-0.180179\pi$
$42$		0			0
$43$	2.24746	+	3.89272i	0.342735	+	0.593634i	0.984940	−	0.172899i	$-0.0553135\pi$
$43$	2.24746	+	3.89272i	0.342735	+	0.593634i	−0.642205	+	0.766533i	$0.721980\pi$
$44$		0			0
$45$	0.472620	+	0.818602i	0.0704541	+	0.122030i
$46$		0			0
$47$	7.41355	−	5.38626i	1.08138	−	0.785667i	0.103455	−	0.994634i	$-0.467010\pi$
$47$	7.41355	−	5.38626i	1.08138	−	0.785667i	0.977923	+	0.208967i	$0.0670102\pi$
$48$		0			0
$49$	−11.7891	−	2.50586i	−1.68416	−	0.357980i
$50$		0			0
$51$	−1.91943	−	1.39455i	−0.268774	−	0.195276i
$52$		0			0
$53$	−2.67804	+	8.24215i	−0.367857	+	1.13215i	0.580316	+	0.814391i	$0.302929\pi$
$53$	−2.67804	+	8.24215i	−0.367857	+	1.13215i	−0.948173	+	0.317755i	$0.897071\pi$
$54$		0			0
$55$	0.0315674	+	3.73289i	0.00425655	+	0.503343i
$56$		0			0
$57$	−2.49263	+	7.67154i	−0.330157	+	1.01612i
$58$		0			0
$59$	0.716387	−	6.81597i	0.0932657	−	0.887364i	−0.843435	−	0.537232i	$-0.819470\pi$
$59$	0.716387	−	6.81597i	0.0932657	−	0.887364i	0.936700	−	0.350132i	$-0.113863\pi$
$60$		0			0
$61$	3.68983	−	4.09798i	0.472435	−	0.524692i	−0.459080	−	0.888395i	$-0.651821\pi$
$61$	3.68983	−	4.09798i	0.472435	−	0.524692i	0.931515	+	0.363703i	$0.118488\pi$
$62$		0			0
$63$	−0.383168	−	3.64560i	−0.0482746	−	0.459302i
$64$		0			0
$65$	−3.55163	−	1.96345i	−0.440525	−	0.243536i
$66$		0			0
$67$	−2.41714	+	4.18661i	−0.295301	+	0.511476i	−0.975055	−	0.221964i	$-0.928753\pi$
$67$	−2.41714	+	4.18661i	−0.295301	+	0.511476i	0.679754	+	0.733440i	$0.262087\pi$
$68$		0			0
$69$	−7.44249	−	3.31361i	−0.895970	−	0.398912i
$70$		0			0
$71$	−4.17462	+	4.63639i	−0.495437	+	0.550238i	−0.938062	−	0.346469i	$-0.887381\pi$
$71$	−4.17462	+	4.63639i	−0.495437	+	0.550238i	0.442625	+	0.896707i	$0.354047\pi$
$72$		0			0
$73$	4.92480	+	3.57808i	0.576405	+	0.418783i	0.837426	−	0.546550i	$-0.184059\pi$
$73$	4.92480	+	3.57808i	0.576405	+	0.418783i	−0.261021	+	0.965333i	$0.584059\pi$
$74$		0			0
$75$	−3.67140	−	4.07750i	−0.423937	−	0.470830i
$76$		0			0
$77$	5.77620	−	13.2745i	0.658259	−	1.51277i
$78$		0			0
$79$	−5.12771	+	15.7815i	−0.576912	+	1.77555i	0.0526622	+	0.998612i	$0.483229\pi$
$79$	−5.12771	+	15.7815i	−0.576912	+	1.77555i	−0.629574	+	0.776940i	$0.716771\pi$
$80$		0			0
$81$	−5.27601	+	2.34903i	−0.586224	+	0.261004i
$82$		0			0
$83$	1.60256	+	4.93218i	0.175904	+	0.541377i	0.999674	−	0.0255477i	$-0.00813297\pi$
$83$	1.60256	+	4.93218i	0.175904	+	0.541377i	−0.823769	+	0.566925i	$0.808133\pi$
$84$		0			0
$85$	1.65982	+	0.739002i	0.180033	+	0.0801560i
$86$		0			0
$87$	2.67219	+	4.62837i	0.286489	+	0.496214i
$88$		0			0
$89$	−2.05255	+	3.55512i	−0.217570	+	0.376842i	−0.954065	−	0.299601i	$-0.903146\pi$
$89$	−2.05255	+	3.55512i	−0.217570	+	0.376842i	0.736494	+	0.676444i	$0.236480\pi$
$90$		0			0
$91$	9.48554	+	12.5581i	0.994355	+	1.31645i
$92$		0			0
$93$	1.87044	+	0.397575i	0.193956	+	0.0412266i
$94$		0			0
$95$	0.645696	−	6.14339i	0.0662470	−	0.630299i
$96$		0			0
$97$	6.39482	−	1.35926i	0.649296	−	0.138012i	0.128522	−	0.991707i	$-0.458977\pi$
$97$	6.39482	−	1.35926i	0.649296	−	0.138012i	0.520774	+	0.853695i	$0.325643\pi$
$98$		0			0
$99$	2.77242	+	0.267710i	0.278639	+	0.0269059i
$100$		0			0
$101$	−1.69079	−	1.87782i	−0.168240	−	0.186850i	0.653129	−	0.757247i	$-0.273456\pi$
$101$	−1.69079	−	1.87782i	−0.168240	−	0.186850i	−0.821369	+	0.570397i	$0.806789\pi$
$102$		0			0
$103$	13.7065	+	9.95833i	1.35054	+	0.981223i	0.998984	+	0.0450553i	$0.0143464\pi$
$103$	13.7065	+	9.95833i	1.35054	+	0.981223i	0.351553	+	0.936168i	$0.385654\pi$
$104$		0			0
$105$	−2.23136	−	6.86741i	−0.217758	−	0.670191i
$106$		0			0
$107$	0.260352	+	2.47708i	0.0251691	+	0.239468i	0.999873	+	0.0159661i	$0.00508237\pi$
$107$	0.260352	+	2.47708i	0.0251691	+	0.239468i	−0.974703	+	0.223502i	$0.928251\pi$
$108$		0			0
$109$	−2.52483			−0.241835			−0.120917	−	0.992663i	$-0.538584\pi$
$109$	−2.52483			−0.241835			−0.120917	+	0.992663i	$0.538584\pi$
$110$		0			0
$111$	0.328722	+	0.569363i	0.0312009	+	0.0540415i
$112$		0			0
$113$	13.4982	+	6.00979i	1.26981	+	0.565354i	0.927355	−	0.374182i	$-0.122076\pi$
$113$	13.4982	+	6.00979i	1.26981	+	0.565354i	0.342450	+	0.939536i	$0.388743\pi$
$114$		0			0
$115$	6.10253	+	1.29713i	0.569064	+	0.120958i
$116$		0			0
$117$	−1.73396	+	2.48232i	−0.160304	+	0.229491i
$118$		0			0
$119$	−4.71471	−	5.23621i	−0.432197	−	0.480003i
$120$		0			0
$121$	9.00726	+	6.31421i	0.818842	+	0.574019i
$122$		0			0
$123$	−8.19535	+	1.74198i	−0.738950	+	0.157069i
$124$		0			0
$125$	7.95229	+	5.77768i	0.711275	+	0.516771i
$126$		0			0
$127$	6.90507	+	1.46772i	0.612726	+	0.130239i	0.503813	−	0.863813i	$-0.331930\pi$
$127$	6.90507	+	1.46772i	0.612726	+	0.130239i	0.108912	+	0.994051i	$0.465263\pi$
$128$		0			0
$129$	5.34474	−	3.88318i	0.470578	−	0.341895i
$130$		0			0
$131$	11.9539			1.04442			0.522209	−	0.852817i	$-0.325108\pi$
$131$	11.9539			1.04442			0.522209	+	0.852817i	$0.325108\pi$
$132$		0			0
$133$	−11.9778	+	20.7461i	−1.03860	+	1.79891i
$134$		0			0
$135$	5.13899	−	3.73369i	0.442294	−	0.321345i
$136$		0			0
$137$	−12.0612	+	13.3953i	−1.03046	+	1.14444i	−0.0410659	+	0.999156i	$0.513075\pi$
$137$	−12.0612	+	13.3953i	−1.03046	+	1.14444i	−0.989390	+	0.145281i	$0.953591\pi$
$138$		0			0
$139$	0.580785	−	5.52580i	0.0492615	−	0.468692i	−0.941887	−	0.335931i	$-0.890949\pi$
$139$	0.580785	−	5.52580i	0.0492615	−	0.468692i	0.991148	−	0.132761i	$-0.0423843\pi$
$140$		0			0
$141$	−9.01210	−	10.0090i	−0.758956	−	0.842906i
$142$		0			0
$143$	−10.7889	+	5.15746i	−0.902214	+	0.431288i
$144$		0			0
$145$	−2.73859	−	3.04151i	−0.227427	−	0.252583i
$146$		0			0
$147$	−1.85165	+	17.6173i	−0.152721	+	1.45305i
$148$		0			0
$149$	−9.32068	+	10.3517i	−0.763580	+	0.848042i	−0.992094	−	0.125499i	$-0.959947\pi$
$149$	−9.32068	+	10.3517i	−0.763580	+	0.848042i	0.228514	+	0.973541i	$0.426613\pi$
$150$		0			0
$151$	−19.1547	+	13.9167i	−1.55879	+	1.13253i	−0.621798	+	0.783177i	$0.713598\pi$
$151$	−19.1547	+	13.9167i	−1.55879	+	1.13253i	−0.936992	+	0.349350i	$0.886402\pi$
$152$		0			0
$153$	0.677823	−	1.17402i	0.0547987	−	0.0949141i
$154$		0			0
$155$	−1.46439			−0.117623
$156$		0			0
$157$	9.40260	−	6.83139i	0.750409	−	0.545204i	−0.145544	−	0.989352i	$-0.546493\pi$
$157$	9.40260	−	6.83139i	0.750409	−	0.545204i	0.895954	+	0.444147i	$0.146493\pi$
$158$		0			0
$159$	12.4591	+	2.64826i	0.988068	+	0.210020i
$160$		0			0
$161$	−19.5738	−	14.2212i	−1.54263	−	1.12079i
$162$		0			0
$163$	19.6573	−	4.17828i	1.53968	−	0.327269i	0.641577	−	0.767059i	$-0.278281\pi$
$163$	19.6573	−	4.17828i	1.53968	−	0.327269i	0.898101	+	0.439790i	$0.144947\pi$
$164$		0			0
$165$	5.45155	−	0.619633i	0.424402	−	0.0482383i
$166$		0			0
$167$	−11.0159	−	12.2344i	−0.852438	−	0.946729i	0.146660	−	0.989187i	$-0.453148\pi$
$167$	−11.0159	−	12.2344i	−0.852438	−	0.946729i	−0.999098	+	0.0424582i	$0.986481\pi$
$168$		0			0
$169$	0.877486	−	12.9704i	0.0674990	−	0.997719i
$170$		0			0
$171$	−4.50829	−	0.958267i	−0.344758	−	0.0732805i
$172$		0			0
$173$	1.12671	+	0.501644i	0.0856622	+	0.0381393i	0.449120	−	0.893471i	$-0.351737\pi$
$173$	1.12671	+	0.501644i	0.0856622	+	0.0381393i	−0.363458	+	0.931610i	$0.618404\pi$
$174$		0			0
$175$	−8.14743	−	14.1118i	−0.615888	−	1.06675i
$176$		0			0
$177$	−10.0730			−0.757135
$178$		0			0
$179$	−0.661863	−	6.29720i	−0.0494699	−	0.470675i	−0.991011	−	0.133778i	$-0.957289\pi$
$179$	−0.661863	−	6.29720i	−0.0494699	−	0.470675i	0.941541	−	0.336897i	$-0.109377\pi$
$180$		0			0
$181$	1.18812	+	3.65666i	0.0883123	+	0.271797i	0.985453	−	0.169947i	$-0.0543597\pi$
$181$	1.18812	+	3.65666i	0.0883123	+	0.271797i	−0.897141	+	0.441745i	$0.854360\pi$
$182$		0			0
$183$	−6.55692	−	4.76388i	−0.484702	−	0.352156i
$184$		0			0
$185$	−0.336889	−	0.374153i	−0.0247686	−	0.0275083i
$186$		0			0
$187$	4.61375	−	2.71602i	0.337391	−	0.198615i
$188$		0			0
$189$	−24.0955	+	5.12166i	−1.75269	+	0.372546i
$190$		0			0
$191$	−0.936949	+	8.91447i	−0.0677952	+	0.645029i	0.906878	+	0.421394i	$0.138459\pi$
$191$	−0.936949	+	8.91447i	−0.0677952	+	0.645029i	−0.974673	+	0.223635i	$0.928208\pi$
$192$		0			0
$193$	−5.92740	−	1.25991i	−0.426664	−	0.0906902i	−0.0104253	−	0.999946i	$-0.503319\pi$
$193$	−5.92740	−	1.25991i	−0.426664	−	0.0906902i	−0.416238	+	0.909255i	$0.636652\pi$
$194$		0			0
$195$	−2.32435	+	5.49309i	−0.166450	+	0.393368i
$196$		0			0
$197$	−8.57775	+	14.8571i	−0.611140	+	1.05853i	0.379909	+	0.925024i	$0.375955\pi$
$197$	−8.57775	+	14.8571i	−0.611140	+	1.05853i	−0.991049	+	0.133501i	$0.957378\pi$
$198$		0			0
$199$	−2.09251	−	3.62434i	−0.148334	−	0.256923i	0.782278	−	0.622930i	$-0.214058\pi$
$199$	−2.09251	−	3.62434i	−0.148334	−	0.256923i	−0.930612	+	0.366007i	$0.880725\pi$
$200$		0			0
$201$	6.49096	+	2.88996i	0.457837	+	0.203842i
$202$		0			0
$203$	4.90467	+	15.0950i	0.344240	+	1.05946i
$204$		0			0
$205$	5.86153	−	2.60972i	0.409387	−	0.182271i
$206$		0			0
$207$	1.43847	−	4.42717i	0.0999808	−	0.307709i
$208$		0			0
$209$	−13.6294	−	12.0649i	−0.942768	−	0.834545i
$210$		0			0
$211$	16.9996	+	18.8799i	1.17030	+	1.29975i	0.945605	+	0.325318i	$0.105471\pi$
$211$	16.9996	+	18.8799i	1.17030	+	1.29975i	0.224693	+	0.974430i	$0.427862\pi$
$212$		0			0
$213$	7.41841	+	5.38979i	0.508301	+	0.369302i
$214$		0			0
$215$	−3.38530	+	3.75976i	−0.230876	+	0.256413i
$216$		0			0
$217$	5.18799	+	2.30984i	0.352184	+	0.156802i
$218$		0			0
$219$	4.47350	−	7.74834i	0.302291	−	0.523584i
$220$		0			0
$221$	0.108161	+	5.81922i	0.00727569	+	0.391443i
$222$		0			0
$223$	−1.02691	−	9.77041i	−0.0687671	−	0.654275i	−0.973561	−	0.228426i	$-0.926642\pi$
$223$	−1.02691	−	9.77041i	−0.0687671	−	0.654275i	0.904794	−	0.425849i	$-0.140025\pi$
$224$		0			0
$225$	2.09780	−	2.32984i	0.139853	−	0.155323i
$226$		0			0
$227$	0.873227	−	8.30820i	0.0579581	−	0.551434i	−0.926559	−	0.376148i	$-0.877248\pi$
$227$	0.873227	−	8.30820i	0.0579581	−	0.551434i	0.984518	−	0.175286i	$-0.0560850\pi$
$228$		0			0
$229$	−7.21751	+	22.2132i	−0.476946	+	1.46789i	0.366369	+	0.930470i	$0.380601\pi$
$229$	−7.21751	+	22.2132i	−0.476946	+	1.46789i	−0.843315	+	0.537420i	$0.819399\pi$
$230$		0			0
$231$	−20.2909	−	6.40373i	−1.33504	−	0.421334i
$232$		0			0
$233$	9.40418	−	28.9431i	0.616088	−	1.89612i	0.232631	−	0.972565i	$-0.425266\pi$
$233$	9.40418	−	28.9431i	0.616088	−	1.89612i	0.383457	−	0.923559i	$-0.374734\pi$
$234$		0			0
$235$	8.34431	+	6.06250i	0.544323	+	0.395474i
$236$		0			0
$237$	23.8557	+	5.07068i	1.54959	+	0.329376i
$238$		0			0
$239$	19.5122	−	14.1764i	1.26214	−	0.916996i	0.263276	−	0.964721i	$-0.415197\pi$
$239$	19.5122	−	14.1764i	1.26214	−	0.916996i	0.998861	+	0.0477251i	$0.0151972\pi$
$240$		0			0
$241$	0.756559	+	1.31040i	0.0487342	+	0.0844101i	0.889363	−	0.457201i	$-0.151148\pi$
$241$	0.756559	+	1.31040i	0.0487342	+	0.0844101i	−0.840629	+	0.541611i	$0.817815\pi$
$242$		0			0
$243$	−4.22122	−	7.31137i	−0.270792	−	0.469025i
$244$		0			0
$245$	−1.41800	−	13.4914i	−0.0905927	−	0.861932i
$246$		0			0
$247$	18.7026	−	6.46350i	1.19002	−	0.411263i
$248$		0			0
$249$	6.96321	−	3.10022i	0.441275	−	0.196468i
$250$		0			0
$251$	−17.0911	+	3.63283i	−1.07878	+	0.229302i	−0.712833	−	0.701333i	$-0.752588\pi$
$251$	−17.0911	+	3.63283i	−1.07878	+	0.229302i	−0.365948	+	0.930635i	$0.619255\pi$
$252$		0			0
$253$	13.5574	−	12.4163i	0.852346	−	0.780607i
$254$		0			0
$255$	0.825203	−	2.53971i	0.0516762	−	0.159043i
$256$		0			0
$257$	16.6481	−	7.41223i	1.03848	−	0.462362i	0.184592	−	0.982815i	$-0.440904\pi$
$257$	16.6481	−	7.41223i	1.03848	−	0.462362i	0.853890	+	0.520453i	$0.174237\pi$
$258$		0			0
$259$	0.603352	+	1.85693i	0.0374904	+	0.115384i
$260$		0			0
$261$	−2.47051	+	1.79493i	−0.152921	+	0.111104i
$262$		0			0
$263$	15.1065	−	26.1653i	0.931510	−	1.61342i	0.150767	−	0.988569i	$-0.451826\pi$
$263$	15.1065	−	26.1653i	0.931510	−	1.61342i	0.780742	−	0.624853i	$-0.214841\pi$
$264$		0			0
$265$	−9.75435			−0.599205
$266$		0			0
$267$	5.51189	+	2.45405i	0.337322	+	0.150186i
$268$		0			0
$269$	4.59269	−	5.10070i	0.280021	−	0.310995i	−0.586684	−	0.809816i	$-0.699567\pi$
$269$	4.59269	−	5.10070i	0.280021	−	0.310995i	0.866705	+	0.498821i	$0.166234\pi$
$270$		0			0
$271$	−21.0960	+	9.39255i	−1.28149	+	0.570557i	−0.930661	−	0.365883i	$-0.880767\pi$
$271$	−21.0960	+	9.39255i	−1.28149	+	0.570557i	−0.350830	+	0.936439i	$0.614101\pi$
$272$		0			0
$273$	16.8991	−	15.7944i	1.02278	−	0.955922i
$274$		0			0
$275$	11.7427	−	3.92551i	0.708109	−	0.236717i
$276$		0			0
$277$	−16.1880	+	3.44086i	−0.972642	+	0.206741i	−0.666714	−	0.745313i	$-0.732300\pi$
$277$	−16.1880	+	3.44086i	−0.972642	+	0.206741i	−0.305928	+	0.952055i	$0.598967\pi$
$278$		0			0
$279$	−0.114210	+	1.08664i	−0.00683760	+	0.0650554i
$280$		0			0
$281$	5.14762	+	15.8427i	0.307081	+	0.945099i	0.978892	+	0.204376i	$0.0655167\pi$
$281$	5.14762	+	15.8427i	0.307081	+	0.945099i	−0.671811	+	0.740722i	$0.734483\pi$
$282$		0			0
$283$	−0.526769	−	5.01187i	−0.0313131	−	0.297925i	−0.998959	−	0.0456131i	$-0.985476\pi$
$283$	−0.526769	−	5.01187i	−0.0313131	−	0.297925i	0.967646	−	0.252312i	$-0.0811908\pi$
$284$		0			0
$285$	−9.07905			−0.537796
$286$		0			0
$287$	−24.8824			−1.46876
$288$		0			0
$289$	1.50461	+	14.3154i	0.0885063	+	0.842081i
$290$		0			0
$291$	−2.96929	−	9.13854i	−0.174063	−	0.535711i
$292$		0			0
$293$	1.63067	−	15.5148i	0.0952645	−	0.906382i	−0.837631	−	0.546236i	$-0.816060\pi$
$293$	1.63067	−	15.5148i	0.0952645	−	0.906382i	0.932896	−	0.360146i	$-0.117273\pi$
$294$		0			0
$295$	7.54539	−	1.60382i	0.439310	−	0.0933782i
$296$		0			0
$297$	−0.158282	−	18.7170i	−0.00918444	−	1.08607i
$298$		0			0
$299$	4.51777	+	19.4681i	0.261269	+	1.12587i
$300$		0			0
$301$	17.9237	−	7.98016i	1.03311	−	0.459969i
$302$		0			0
$303$	−2.48506	+	2.75994i	−0.142763	+	0.158554i
$304$		0			0
$305$	5.67009	+	2.52449i	0.324669	+	0.144552i
$306$		0			0
$307$	−22.1919			−1.26656			−0.633279	−	0.773924i	$-0.718291\pi$
$307$	−22.1919			−1.26656			−0.633279	+	0.773924i	$0.718291\pi$
$308$		0			0
$309$	12.4504	−	21.5648i	0.708280	−	1.22678i
$310$		0			0
$311$	3.66690	−	2.66416i	0.207931	−	0.151071i	−0.478946	−	0.877844i	$-0.658981\pi$
$311$	3.66690	−	2.66416i	0.207931	−	0.151071i	0.686877	+	0.726774i	$0.258981\pi$
$312$		0			0
$313$	6.52326	+	20.0765i	0.368717	+	1.13479i	0.947621	+	0.319397i	$0.103481\pi$
$313$	6.52326	+	20.0765i	0.368717	+	1.13479i	−0.578904	+	0.815396i	$0.696519\pi$
$314$		0			0
$315$	3.76919	−	1.67815i	0.212370	−	0.0945532i
$316$		0			0
$317$	−9.60741	+	29.5686i	−0.539606	+	1.66074i	0.193875	+	0.981026i	$0.437894\pi$
$317$	−9.60741	+	29.5686i	−0.539606	+	1.66074i	−0.733481	+	0.679710i	$0.762106\pi$
$318$		0			0
$319$	−11.9829	+	1.36199i	−0.670911	+	0.0762570i
$320$		0			0
$321$	3.58077	−	0.761117i	0.199859	−	0.0424814i
$322$		0			0
$323$	−8.09334	+	3.60339i	−0.450325	+	0.200498i
$324$		0			0
$325$	−2.55334	+	13.2156i	−0.141634	+	0.733071i
$326$		0			0
$327$	0.387894	+	3.69056i	0.0214506	+	0.204089i
$328$		0			0
$329$	−19.9993	−	34.6398i	−1.10260	−	1.90975i
$330$		0			0
$331$	−11.5831	−	20.0626i	−0.636667	−	1.10274i	−0.986159	−	0.165800i	$-0.946979\pi$
$331$	−11.5831	−	20.0626i	−0.636667	−	1.10274i	0.349493	−	0.936939i	$-0.386354\pi$
$332$		0			0
$333$	−0.303912	+	0.220805i	−0.0166543	+	0.0121000i
$334$		0			0
$335$	−5.32232	−	1.13129i	−0.290789	−	0.0618092i
$336$		0			0
$337$	−13.0298	−	9.46673i	−0.709781	−	0.515686i	0.173322	−	0.984865i	$-0.444550\pi$
$337$	−13.0298	−	9.46673i	−0.709781	−	0.515686i	−0.883103	+	0.469179i	$0.844550\pi$
$338$		0			0
$339$	6.71081	−	20.6538i	0.364481	−	1.12176i
$340$		0			0
$341$	−2.50673	+	3.51230i	−0.135747	+	0.190202i
$342$		0			0
$343$	−6.81499	+	20.9744i	−0.367975	+	1.13251i
$344$		0			0
$345$	0.958488	−	9.11940i	0.0516033	−	0.490972i
$346$		0			0
$347$	−1.48686	+	1.65133i	−0.0798190	+	0.0886479i	−0.781731	−	0.623615i	$-0.785663\pi$
$347$	−1.48686	+	1.65133i	−0.0798190	+	0.0886479i	0.701912	+	0.712263i	$0.252330\pi$
$348$		0			0
$349$	−1.54874	−	14.7353i	−0.0829020	−	0.788760i	−0.954434	−	0.298422i	$-0.903540\pi$
$349$	−1.54874	−	14.7353i	−0.0829020	−	0.788760i	0.871532	−	0.490338i	$-0.163127\pi$
$350$		0			0
$351$	17.8081	+	9.84489i	0.950528	+	0.525481i
$352$		0			0
$353$	6.39829	−	11.0822i	0.340547	−	0.589844i	−0.643988	−	0.765036i	$-0.722721\pi$
$353$	6.39829	−	11.0822i	0.340547	−	0.589844i	0.984534	+	0.175192i	$0.0560546\pi$
$354$		0			0
$355$	−6.41506	−	2.85617i	−0.340476	−	0.151590i
$356$		0			0
$357$	−6.92949	+	7.69598i	−0.366748	+	0.407314i
$358$		0			0
$359$	−26.5165	−	19.2654i	−1.39949	−	1.01679i	−0.994748	−	0.102356i	$-0.967362\pi$
$359$	−26.5165	−	19.2654i	−1.39949	−	1.01679i	−0.404740	−	0.914432i	$-0.632638\pi$
$360$		0			0
$361$	7.44093	+	8.26399i	0.391628	+	0.434947i
$362$		0			0
$363$	7.84574	−	14.1361i	0.411794	−	0.741951i
$364$		0			0
$365$	−2.11728	+	6.51631i	−0.110823	+	0.341079i
$366$		0			0
$367$	−33.7359	+	15.0202i	−1.76100	+	0.784047i	−0.772091	+	0.635512i	$0.780789\pi$
$367$	−33.7359	+	15.0202i	−1.76100	+	0.784047i	−0.988907	+	0.148535i	$0.952544\pi$
$368$		0			0
$369$	−1.47937	−	4.55304i	−0.0770130	−	0.237022i
$370$		0			0
$371$	34.5574	+	15.3859i	1.79413	+	0.798798i
$372$		0			0
$373$	9.67905	+	16.7646i	0.501162	+	0.868038i	0.999999	+	0.00134244i	$0.000427311\pi$
$373$	9.67905	+	16.7646i	0.501162	+	0.868038i	−0.498837	+	0.866696i	$0.666239\pi$
$374$		0			0
$375$	7.22356	−	12.5116i	0.373023	−	0.646095i
$376$		0			0
$377$	5.10907	−	12.0742i	0.263130	−	0.621851i
$378$		0			0
$379$	−8.47955	−	1.80238i	−0.435565	−	0.0925823i	−0.0150898	−	0.999886i	$-0.504803\pi$
$379$	−8.47955	−	1.80238i	−0.435565	−	0.0925823i	−0.420476	+	0.907304i	$0.638137\pi$
$380$		0			0
$381$	1.08454	−	10.3187i	0.0555625	−	0.528642i
$382$		0			0
$383$	9.00692	−	1.91448i	0.460232	−	0.0978253i	0.0280397	−	0.999607i	$-0.491074\pi$
$383$	9.00692	−	1.91448i	0.460232	−	0.0978253i	0.432192	+	0.901781i	$0.357740\pi$
$384$		0			0
$385$	16.2189	+	1.56613i	0.826591	+	0.0798172i
$386$		0			0
$387$	2.52587	+	2.80527i	0.128397	+	0.142600i
$388$		0			0
$389$	10.5633	+	7.67472i	0.535583	+	0.389124i	0.822442	−	0.568849i	$-0.192611\pi$
$389$	10.5633	+	7.67472i	0.535583	+	0.389124i	−0.286859	+	0.957973i	$0.592611\pi$
$390$		0			0
$391$	−2.76498	−	8.50973i	−0.139831	−	0.430355i
$392$		0			0
$393$	−1.83650	−	17.4732i	−0.0926393	−	0.881404i
$394$		0			0
$395$	−18.6769			−0.939737
$396$		0			0
$397$	4.70279	+	8.14547i	0.236026	+	0.408809i	0.959570	−	0.281469i	$-0.0908216\pi$
$397$	4.70279	+	8.14547i	0.236026	+	0.408809i	−0.723544	+	0.690278i	$0.757488\pi$
$398$		0			0
$399$	32.1649	+	14.3207i	1.61026	+	0.716934i
$400$		0			0
$401$	−8.02528	−	1.70583i	−0.400763	−	0.0851849i	0.00312062	−	0.999995i	$-0.499007\pi$
$401$	−8.02528	−	1.70583i	−0.400763	−	0.0851849i	−0.403884	+	0.914810i	$0.632340\pi$
$402$		0			0
$403$	−1.98731	−	4.24924i	−0.0989949	−	0.211670i
$404$		0			0
$405$	−4.34961	−	4.83074i	−0.216134	−	0.240041i
$406$		0			0
$407$	−1.47408	+	0.167547i	−0.0730674	+	0.00830498i
$408$		0			0
$409$	−11.8485	+	2.51848i	−0.585871	+	0.124531i	−0.491305	−	0.870988i	$-0.663480\pi$
$409$	−11.8485	+	2.51848i	−0.585871	+	0.124531i	−0.0945665	+	0.995519i	$0.530147\pi$
$410$		0			0
$411$	21.4330	+	15.5720i	1.05721	+	0.768110i
$412$		0			0
$413$	−29.2613	−	6.21968i	−1.43985	−	0.306051i
$414$		0			0
$415$	−4.72231	+	3.43096i	−0.231809	+	0.168419i
$416$		0			0
$417$	−8.16634			−0.399907
$418$		0			0
$419$	15.4573	−	26.7729i	0.755139	−	1.30794i	−0.190166	−	0.981752i	$-0.560903\pi$
$419$	15.4573	−	26.7729i	0.755139	−	1.30794i	0.945305	−	0.326188i	$-0.105764\pi$
$420$		0			0
$421$	2.06986	−	1.50384i	0.100879	−	0.0732926i	−0.536202	−	0.844089i	$-0.680142\pi$
$421$	2.06986	−	1.50384i	0.100879	−	0.0732926i	0.637081	+	0.770797i	$0.280142\pi$
$422$		0			0
$423$	5.14941	−	5.71900i	0.250373	−	0.278067i
$424$		0			0
$425$	0.629908	−	5.99317i	0.0305550	−	0.290711i
$426$		0			0
$427$	−16.1058	−	17.8873i	−0.779415	−	0.865629i
$428$		0			0
$429$	9.19622	+	14.9779i	0.443998	+	0.723140i
$430$		0			0
$431$	8.95896	+	9.94994i	0.431538	+	0.479272i	0.919217	−	0.393751i	$-0.128823\pi$
$431$	8.95896	+	9.94994i	0.431538	+	0.479272i	−0.487679	+	0.873023i	$0.662156\pi$
$432$		0			0
$433$	−3.50899	+	33.3858i	−0.168631	+	1.60442i	0.503505	+	0.863993i	$0.332044\pi$
$433$	−3.50899	+	33.3858i	−0.168631	+	1.60442i	−0.672136	+	0.740428i	$0.734623\pi$
$434$		0			0
$435$	−4.02506	+	4.47029i	−0.192987	+	0.214334i
$436$		0			0
$437$	−24.6110	+	17.8809i	−1.17730	+	0.855360i
$438$		0			0
$439$	−15.8182	+	27.3979i	−0.754961	+	1.30763i	0.190432	+	0.981700i	$0.439011\pi$
$439$	−15.8182	+	27.3979i	−0.754961	+	1.30763i	−0.945394	+	0.325931i	$0.894322\pi$
$440$		0			0
$441$	−10.1217			−0.481988
$442$		0			0
$443$	13.0301	−	9.46694i	0.619080	−	0.449788i	−0.233520	−	0.972352i	$-0.575024\pi$
$443$	13.0301	−	9.46694i	0.619080	−	0.449788i	0.852600	+	0.522564i	$0.175024\pi$
$444$		0			0
$445$	−4.51952	−	0.960654i	−0.214246	−	0.0455394i
$446$		0			0
$447$	16.5631	+	12.0338i	0.783407	+	0.569178i
$448$		0			0
$449$	31.5317	−	6.70227i	1.48807	−	0.316300i	0.609070	−	0.793117i	$-0.291543\pi$
$449$	31.5317	−	6.70227i	1.48807	−	0.316300i	0.879002	+	0.476817i	$0.158210\pi$
$450$		0			0
$451$	3.77437	−	18.5260i	0.177728	−	0.872355i
$452$		0			0
$453$	23.2850	+	25.8606i	1.09402	+	1.21504i
$454$		0			0
$455$	−10.1438	+	14.5218i	−0.475549	+	0.680792i
$456$		0			0
$457$	14.8191	+	3.14989i	0.693207	+	0.147346i	0.541025	−	0.841007i	$-0.318037\pi$
$457$	14.8191	+	3.14989i	0.693207	+	0.147346i	0.152182	+	0.988352i	$0.451370\pi$
$458$		0			0
$459$	−8.32250	−	3.70541i	−0.388461	−	0.172954i
$460$		0			0
$461$	13.5474	+	23.4648i	0.630965	+	1.09286i	0.987355	+	0.158526i	$0.0506742\pi$
$461$	13.5474	+	23.4648i	0.630965	+	1.09286i	−0.356390	+	0.934337i	$0.615992\pi$
$462$		0			0
$463$	−25.0322			−1.16335			−0.581674	−	0.813422i	$-0.697602\pi$
$463$	−25.0322			−1.16335			−0.581674	+	0.813422i	$0.697602\pi$
$464$		0			0
$465$	0.224977	+	2.14051i	0.0104331	+	0.0992640i
$466$		0			0
$467$	−9.52064	−	29.3015i	−0.440563	−	1.35591i	−0.887277	−	0.461236i	$-0.847406\pi$
$467$	−9.52064	−	29.3015i	−0.440563	−	1.35591i	0.446715	−	0.894676i	$-0.352594\pi$
$468$		0			0
$469$	17.0713	+	12.4030i	0.788278	+	0.572718i
$470$		0			0
$471$	−11.4300	−	12.6943i	−0.526669	−	0.584925i
$472$		0			0
$473$	3.22274	+	14.5555i	0.148182	+	0.669261i
$474$		0			0
$475$	−20.0405	+	4.25974i	−0.919521	+	0.195450i
$476$		0			0
$477$	−0.760759	+	7.23814i	−0.0348328	+	0.331412i
$478$		0			0
$479$	−7.06867	−	1.50249i	−0.322976	−	0.0686507i	0.0435707	−	0.999050i	$-0.486127\pi$
$479$	−7.06867	−	1.50249i	−0.322976	−	0.0686507i	−0.366547	+	0.930400i	$0.619460\pi$
$480$		0			0
$481$	0.628496	−	1.48531i	0.0286569	−	0.0677244i
$482$		0			0
$483$	−17.7801	+	30.7960i	−0.809022	+	1.40127i
$484$		0			0
$485$	3.67924	+	6.37263i	0.167066	+	0.289366i
$486$		0			0
$487$	−23.4604	−	10.4452i	−1.06309	−	0.473319i	−0.200749	−	0.979643i	$-0.564338\pi$
$487$	−23.4604	−	10.4452i	−1.06309	−	0.473319i	−0.862344	+	0.506323i	$0.831004\pi$
$488$		0			0
$489$	−9.12742	−	28.0913i	−0.412756	−	1.27033i
$490$		0			0
$491$	−19.9354	+	8.87583i	−0.899674	+	0.400561i	−0.803846	−	0.594837i	$-0.797216\pi$
$491$	−19.9354	+	8.87583i	−0.899674	+	0.400561i	−0.0958276	+	0.995398i	$0.530550\pi$
$492$		0			0
$493$	−1.81385	+	5.58246i	−0.0816917	+	0.251421i
$494$		0			0
$495$	0.677713	+	3.06088i	0.0304609	+	0.137576i
$496$		0			0
$497$	18.2219	+	20.2375i	0.817363	+	0.907774i
$498$		0			0
$499$	3.07900	+	2.23703i	0.137835	+	0.100143i	0.654566	−	0.756005i	$-0.272851\pi$
$499$	3.07900	+	2.23703i	0.137835	+	0.100143i	−0.516731	+	0.856148i	$0.672851\pi$
$500$		0			0
$501$	−16.1908	+	17.9817i	−0.723351	+	0.803362i
$502$		0			0
$503$	33.3824	+	14.8628i	1.48845	+	0.662699i	0.980109	−	0.198458i	$-0.0635935\pi$
$503$	33.3824	+	14.8628i	1.48845	+	0.662699i	0.508338	+	0.861158i	$0.330260\pi$
$504$		0			0
$505$	1.42205	−	2.46306i	0.0632802	−	0.109605i
$506$		0			0
$507$	−19.0937	+	0.710029i	−0.847980	+	0.0315335i
$508$		0			0
$509$	−2.87368	−	27.3413i	−0.127374	−	1.21188i	−0.852300	−	0.523053i	$-0.824793\pi$
$509$	−2.87368	−	27.3413i	−0.127374	−	1.21188i	0.724926	−	0.688827i	$-0.241874\pi$
$510$		0			0
$511$	17.7794	−	19.7461i	0.786516	−	0.873515i
$512$		0			0
$513$	−3.23757	+	30.8035i	−0.142942	+	1.36001i
$514$		0			0
$515$	−5.89270	+	18.1359i	−0.259663	+	0.799162i
$516$		0			0
$517$	28.8244	−	9.63586i	1.26770	−	0.423785i
$518$		0			0
$519$	0.560158	−	1.72399i	0.0245882	−	0.0756748i
$520$		0			0
$521$	−2.71813	−	1.97484i	−0.119083	−	0.0865192i	0.526649	−	0.850083i	$-0.323448\pi$
$521$	−2.71813	−	1.97484i	−0.119083	−	0.0865192i	−0.645733	+	0.763563i	$0.723448\pi$
$522$		0			0
$523$	−19.5493	−	4.15534i	−0.854832	−	0.181700i	−0.240404	−	0.970673i	$-0.577280\pi$
$523$	−19.5493	−	4.15534i	−0.854832	−	0.181700i	−0.614428	+	0.788973i	$0.710613\pi$
$524$		0			0
$525$	−19.3756	+	14.0772i	−0.845620	+	0.614379i
$526$		0			0
$527$	1.05010	+	1.81883i	0.0457431	+	0.0792294i
$528$		0			0
$529$	−3.86218	−	6.68948i	−0.167921	−	0.290847i
$530$		0			0
$531$	−0.601625	−	5.72408i	−0.0261083	−	0.248404i
$532$		0			0
$533$	15.5273	+	13.4668i	0.672560	+	0.583313i
$534$		0			0
$535$	−2.56106	+	1.14026i	−0.110724	+	0.0492977i
$536$		0			0
$537$	−9.10299	+	1.93490i	−0.392823	+	0.0834971i
$538$		0			0
$539$	−34.7860	−	19.6934i	−1.49834	−	0.848253i
$540$		0			0
$541$	−4.70154	+	14.4698i	−0.202135	+	0.622107i	0.797684	+	0.603076i	$0.206058\pi$
$541$	−4.70154	+	14.4698i	−0.202135	+	0.622107i	−0.999819	+	0.0190314i	$0.993942\pi$
$542$		0			0
$543$	5.16244	−	2.29847i	0.221541	−	0.0986366i
$544$		0			0
$545$	−0.878170	−	2.70273i	−0.0376167	−	0.115772i
$546$		0			0
$547$	19.4611	−	14.1393i	0.832095	−	0.604553i	−0.0880559	−	0.996116i	$-0.528065\pi$
$547$	19.4611	−	14.1393i	0.832095	−	0.604553i	0.920151	+	0.391563i	$0.128065\pi$
$548$		0			0
$549$	2.31550	−	4.01056i	0.0988230	−	0.171166i
$550$		0			0
$551$	19.9563			0.850168
$552$		0			0
$553$	66.1679	+	29.4598i	2.81374	+	1.25276i
$554$		0			0
$555$	−0.495146	+	0.549916i	−0.0210178	+	0.0233426i
$556$		0			0
$557$	18.1700	−	8.08981i	0.769888	−	0.342776i	0.0160799	−	0.999871i	$-0.494881\pi$
$557$	18.1700	−	8.08981i	0.769888	−	0.342776i	0.753808	+	0.657094i	$0.228215\pi$
$558$		0			0
$559$	−15.5039	−	4.72084i	−0.655744	−	0.199670i
$560$		0			0
$561$	−4.67886	−	6.32669i	−0.197541	−	0.267113i
$562$		0			0
$563$	4.12326	−	0.876427i	0.173775	−	0.0369370i	−0.120202	−	0.992749i	$-0.538354\pi$
$563$	4.12326	−	0.876427i	0.173775	−	0.0369370i	0.293977	+	0.955812i	$0.405021\pi$
$564$		0			0
$565$	−1.73838	+	16.5396i	−0.0731343	+	0.695826i
$566$		0			0
$567$	7.78994	+	23.9750i	0.327147	+	1.00685i
$568$		0			0
$569$	−3.04881	−	29.0075i	−0.127813	−	1.21606i	−0.850910	−	0.525312i	$-0.823949\pi$
$569$	−3.04881	−	29.0075i	−0.127813	−	1.21606i	0.723097	−	0.690747i	$-0.242718\pi$
$570$		0			0
$571$	26.5144			1.10959			0.554797	−	0.831986i	$-0.312796\pi$
$571$	26.5144			1.10959			0.554797	+	0.831986i	$0.312796\pi$
$572$		0			0
$573$	13.1743			0.550365
$574$		0			0
$575$	−2.16297	−	20.5793i	−0.0902020	−	0.858215i
$576$		0			0
$577$	1.70546	+	5.24886i	0.0709992	+	0.218513i	0.980260	−	0.197715i	$-0.0633519\pi$
$577$	1.70546	+	5.24886i	0.0709992	+	0.218513i	−0.909260	+	0.416228i	$0.863352\pi$
$578$		0			0
$579$	−0.930982	+	8.85770i	−0.0386903	+	0.368113i
$580$		0			0
$581$	22.1418	−	4.70639i	0.918597	−	0.195254i
$582$		0			0
$583$	−16.6974	+	23.3955i	−0.691536	+	0.968944i
$584$		0			0
$585$	−3.26032	−	0.992748i	−0.134798	−	0.0410451i
$586$		0			0
$587$	−42.5283	+	18.9348i	−1.75533	+	0.781523i	−0.764793	+	0.644276i	$0.777159\pi$
$587$	−42.5283	+	18.9348i	−1.75533	+	0.781523i	−0.990537	+	0.137247i	$0.956175\pi$
$588$		0			0
$589$	4.77786	−	5.30635i	0.196868	−	0.218644i
$590$		0			0
$591$	23.0346	+	10.2557i	0.947516	+	0.421861i
$592$		0			0
$593$	−25.0067			−1.02690			−0.513451	−	0.858119i	$-0.671633\pi$
$593$	−25.0067			−1.02690			−0.513451	+	0.858119i	$0.671633\pi$
$594$		0			0
$595$	3.96532	−	6.86813i	0.162562	−	0.281566i
$596$		0			0
$597$	−4.97626	+	3.61546i	−0.203665	+	0.147971i
$598$		0			0
$599$	9.74869	+	30.0034i	0.398321	+	1.22590i	0.926345	+	0.376676i	$0.122933\pi$
$599$	9.74869	+	30.0034i	0.398321	+	1.22590i	−0.528025	+	0.849229i	$0.677067\pi$
$600$		0			0
$601$	−20.7599	+	9.24290i	−0.846814	+	0.377026i	−0.783820	−	0.620988i	$-0.786732\pi$
$601$	−20.7599	+	9.24290i	−0.846814	+	0.377026i	−0.0629938	+	0.998014i	$0.520065\pi$
$602$		0			0
$603$	−1.25456	+	3.86115i	−0.0510898	+	0.157238i
$604$		0			0
$605$	−3.62626	+	11.8381i	−0.147429	+	0.481286i
$606$		0			0
$607$	31.1126	−	6.61318i	1.26282	−	0.268421i	0.472618	−	0.881267i	$-0.343309\pi$
$607$	31.1126	−	6.61318i	1.26282	−	0.268421i	0.790202	+	0.612847i	$0.209976\pi$
$608$		0			0
$609$	21.3110	−	9.48827i	0.863566	−	0.384484i
$610$		0			0
$611$	−6.26763	+	32.4401i	−0.253561	+	1.31239i
$612$		0			0
$613$	2.61196	+	24.8512i	0.105496	+	1.00373i	0.911355	+	0.411621i	$0.135037\pi$
$613$	2.61196	+	24.8512i	0.105496	+	1.00373i	−0.805859	+	0.592108i	$0.798296\pi$
$614$		0			0
$615$	−4.71517	−	8.16691i	−0.190134	−	0.329322i
$616$		0			0
$617$	10.5787	+	18.3229i	0.425884	+	0.737652i	0.996503	−	0.0835628i	$-0.0266299\pi$
$617$	10.5787	+	18.3229i	0.425884	+	0.737652i	−0.570619	+	0.821215i	$0.693297\pi$
$618$		0			0
$619$	−6.11769	+	4.44476i	−0.245891	+	0.178650i	−0.703904	−	0.710295i	$-0.748561\pi$
$619$	−6.11769	+	4.44476i	−0.245891	+	0.178650i	0.458013	+	0.888946i	$0.348561\pi$
$620$		0			0
$621$	−30.5986	−	6.50393i	−1.22788	−	0.260994i
$622$		0			0
$623$	14.4963	+	10.5322i	0.580783	+	0.421963i
$624$		0			0
$625$	2.34916	−	7.22997i	0.0939664	−	0.289199i
$626$		0			0
$627$	−15.5414	+	21.7758i	−0.620665	+	0.869643i
$628$		0			0
$629$	−0.223132	+	0.686730i	−0.00889686	+	0.0273817i
$630$		0			0
$631$	4.82418	−	45.8990i	0.192048	−	1.82721i	−0.296912	−	0.954905i	$-0.595957\pi$
$631$	4.82418	−	45.8990i	0.192048	−	1.82721i	0.488959	−	0.872307i	$-0.337377\pi$
$632$		0			0
$633$	24.9853	−	27.7490i	0.993076	−	1.10292i
$634$		0			0
$635$	0.830543	+	7.90209i	0.0329591	+	0.313585i
$636$		0			0
$637$	37.2237	−	22.4236i	1.47486	−	0.888455i
$638$		0			0
$639$	−2.61972	+	4.53748i	−0.103634	+	0.179500i
$640$		0			0
$641$	−13.4974	−	6.00942i	−0.533114	−	0.237358i	0.122480	−	0.992471i	$-0.460915\pi$
$641$	−13.4974	−	6.00942i	−0.533114	−	0.237358i	−0.655594	+	0.755113i	$0.727582\pi$
$642$		0			0
$643$	−11.2309	+	12.4731i	−0.442902	+	0.491893i	−0.922718	−	0.385477i	$-0.874037\pi$
$643$	−11.2309	+	12.4731i	−0.442902	+	0.491893i	0.479815	+	0.877369i	$0.340704\pi$
$644$		0			0
$645$	6.01576	+	4.37071i	0.236870	+	0.172096i
$646$		0			0
$647$	12.8636	+	14.2865i	0.505720	+	0.561659i	0.940900	−	0.338685i	$-0.109982\pi$
$647$	12.8636	+	14.2865i	0.505720	+	0.561659i	−0.435180	+	0.900343i	$0.643315\pi$
$648$		0			0
$649$	9.06941	−	20.8428i	0.356006	−	0.818152i
$650$		0			0
$651$	2.57928	−	7.93820i	0.101090	−	0.311123i
$652$		0			0
$653$	4.91789	−	2.18958i	0.192452	−	0.0856850i	−0.308248	−	0.951306i	$-0.599743\pi$
$653$	4.91789	−	2.18958i	0.192452	−	0.0856850i	0.500700	+	0.865621i	$0.333076\pi$
$654$		0			0
$655$	4.15774	+	12.7962i	0.162456	+	0.499989i
$656$		0			0
$657$	4.67024	+	2.07933i	0.182204	+	0.0811223i
$658$		0			0
$659$	−11.1147	−	19.2513i	−0.432969	−	0.749924i	0.564158	−	0.825667i	$-0.309201\pi$
$659$	−11.1147	−	19.2513i	−0.432969	−	0.749924i	−0.997127	+	0.0757423i	$0.975867\pi$
$660$		0			0
$661$	−7.57064	+	13.1127i	−0.294464	+	0.510026i	−0.974860	−	0.222818i	$-0.928474\pi$
$661$	−7.57064	+	13.1127i	−0.294464	+	0.510026i	0.680396	+	0.732844i	$0.261808\pi$
$662$		0			0
$663$	8.48938	−	1.05212i	0.329700	−	0.0408608i
$664$		0			0
$665$	−26.3739	−	5.60594i	−1.02274	−	0.217389i
$666$		0			0
$667$	−2.10682	+	20.0450i	−0.0815763	+	0.776147i
$668$		0			0
$669$	−14.1237	+	3.00209i	−0.546055	+	0.116068i
$670$		0			0
$671$	15.7609	−	9.27816i	0.608444	−	0.358179i
$672$		0			0
$673$	−6.19435	−	6.87952i	−0.238775	−	0.265186i	0.611833	−	0.790987i	$-0.290432\pi$
$673$	−6.19435	−	6.87952i	−0.238775	−	0.265186i	−0.850608	+	0.525801i	$0.823766\pi$
$674$		0			0
$675$	−17.0446	−	12.3837i	−0.656048	−	0.476647i
$676$		0			0
$677$	9.29439	+	28.6052i	0.357212	+	1.09939i	0.954716	+	0.297520i	$0.0961595\pi$
$677$	9.29439	+	28.6052i	0.357212	+	1.09939i	−0.597503	+	0.801867i	$0.703840\pi$
$678$		0			0
$679$	−2.98287	−	28.3801i	−0.114472	−	1.08913i
$680$		0			0
$681$	−12.2783			−0.470506
$682$		0			0
$683$	4.66164	+	8.07420i	0.178373	+	0.308951i	0.941323	−	0.337506i	$-0.109583\pi$
$683$	4.66164	+	8.07420i	0.178373	+	0.308951i	−0.762951	+	0.646457i	$0.776250\pi$
$684$		0			0
$685$	−18.5342	−	8.25195i	−0.708154	−	0.315291i
$686$		0			0
$687$	33.5781	+	7.13724i	1.28108	+	0.272303i
$688$		0			0
$689$	−13.2375	−	28.3043i	−0.504309	−	1.07831i
$690$		0			0
$691$	27.9633	+	31.0564i	1.06377	+	1.18144i	0.982790	+	0.184725i	$0.0591395\pi$
$691$	27.9633	+	31.0564i	1.06377	+	1.18144i	0.0809837	+	0.996715i	$0.474194\pi$
$692$		0			0
$693$	2.42707	−	11.9130i	0.0921968	−	0.452536i
$694$		0			0
$695$	6.11715	−	1.30024i	0.232037	−	0.0493210i
$696$		0			0
$697$	−7.44461	−	5.40883i	−0.281985	−	0.204874i
$698$		0			0
$699$	−43.7511	−	9.29959i	−1.65482	−	0.351743i
$700$		0			0
$701$	−17.2162	+	12.5083i	−0.650248	+	0.472433i	−0.863356	−	0.504596i	$-0.831641\pi$
$701$	−17.2162	+	12.5083i	−0.650248	+	0.472433i	0.213108	+	0.977029i	$0.431641\pi$
$702$		0			0
$703$	2.45494			0.0925900
$704$		0			0
$705$	7.57965	−	13.1283i	0.285466	−	0.494442i
$706$		0			0
$707$	−8.92305	+	6.48297i	−0.335586	+	0.243817i
$708$		0			0
$709$	29.3926	−	32.6438i	1.10386	−	1.22597i	0.131793	−	0.991277i	$-0.457927\pi$
$709$	29.3926	−	32.6438i	1.10386	−	1.22597i	0.972071	−	0.234688i	$-0.0754068\pi$
$710$		0			0
$711$	−1.45664	+	13.8590i	−0.0546284	+	0.519755i
$712$		0			0
$713$	4.82553	+	5.35930i	0.180718	+	0.200707i
$714$		0			0
$715$	−9.27338	−	9.75527i	−0.346805	−	0.364826i
$716$		0			0
$717$	−23.7195	−	26.3431i	−0.885820	−	0.983802i
$718$		0			0
$719$	−2.31255	+	22.0025i	−0.0862437	+	0.820554i	0.862829	+	0.505496i	$0.168690\pi$
$719$	−2.31255	+	22.0025i	−0.0862437	+	0.820554i	−0.949073	+	0.315058i	$0.897976\pi$
$720$		0			0
$721$	49.4828	−	54.9563i	1.84284	−	2.04668i
$722$		0			0
$723$	1.79919	−	1.30719i	0.0669125	−	0.0486148i
$724$		0			0
$725$	−6.78728	+	11.7559i	−0.252073	+	0.436603i
$726$		0			0
$727$	−17.0972			−0.634100			−0.317050	−	0.948409i	$-0.602692\pi$
$727$	−17.0972			−0.634100			−0.317050	+	0.948409i	$0.602692\pi$
$728$		0			0
$729$	−24.0556	+	17.4774i	−0.890947	+	0.647311i
$730$		0			0
$731$	7.09732	+	1.50858i	0.262504	+	0.0557969i
$732$		0			0
$733$	−13.8599	−	10.0698i	−0.511927	−	0.371937i	0.301627	−	0.953426i	$-0.402470\pi$
$733$	−13.8599	−	10.0698i	−0.511927	−	0.371937i	−0.813554	+	0.581489i	$0.802470\pi$
$734$		0			0
$735$	−19.5026	+	4.14541i	−0.719364	+	0.152906i
$736$		0			0
$737$	−11.8241	+	10.8289i	−0.435545	+	0.398887i
$738$		0			0
$739$	−29.0147	−	32.2241i	−1.06732	−	1.18538i	−0.981971	−	0.189030i	$-0.939466\pi$
$739$	−29.0147	−	32.2241i	−1.06732	−	1.18538i	−0.0853508	−	0.996351i	$-0.527201\pi$
$740$		0			0
$741$	−12.3211	−	26.3447i	−0.452626	−	0.967798i
$742$		0			0
$743$	−17.7325	−	3.76915i	−0.650541	−	0.138277i	−0.129191	−	0.991620i	$-0.541238\pi$
$743$	−17.7325	−	3.76915i	−0.650541	−	0.138277i	−0.521350	+	0.853343i	$0.674571\pi$
$744$		0			0
$745$	−14.3229	−	6.37697i	−0.524751	−	0.233634i
$746$		0			0
$747$	2.17761	+	3.77174i	0.0796747	+	0.138001i
$748$		0			0
$749$	10.8718			0.397247
$750$		0			0
$751$	2.00554	+	19.0814i	0.0731831	+	0.696291i	0.968186	+	0.250231i	$0.0805065\pi$
$751$	2.00554	+	19.0814i	0.0731831	+	0.696291i	−0.895003	+	0.446060i	$0.852827\pi$
$752$		0			0
$753$	7.93587	+	24.4241i	0.289199	+	0.890064i
$754$		0			0
$755$	−21.5596	−	15.6640i	−0.784634	−	0.570070i
$756$		0			0
$757$	−25.0426	−	27.8126i	−0.910188	−	1.01087i	−0.999889	−	0.0148978i	$-0.995258\pi$
$757$	−25.0426	−	27.8126i	−0.910188	−	1.01087i	0.0897007	−	0.995969i	$-0.471409\pi$
$758$		0			0
$759$	−20.2319	−	17.9094i	−0.734371	−	0.650071i
$760$		0			0
$761$	−15.7375	+	3.34511i	−0.570484	+	0.121260i	−0.484117	−	0.875003i	$-0.660859\pi$
$761$	−15.7375	+	3.34511i	−0.570484	+	0.121260i	−0.0863669	+	0.996263i	$0.527526\pi$
$762$		0			0
$763$	−1.15197	+	10.9603i	−0.0417042	+	0.396789i
$764$		0			0
$765$	1.49250	+	0.317241i	0.0539615	+	0.0114699i
$766$		0			0
$767$	14.8936	+	19.7180i	0.537776	+	0.711976i
$768$		0			0
$769$	8.16469	−	14.1417i	0.294426	−	0.509961i	−0.680425	−	0.732818i	$-0.738205\pi$
$769$	8.16469	−	14.1417i	0.294426	−	0.509961i	0.974851	+	0.222857i	$0.0715382\pi$
$770$		0			0
$771$	−13.3922	−	23.1960i	−0.482308	−	0.835383i
$772$		0			0
$773$	26.6653	+	11.8721i	0.959082	+	0.427011i	0.825735	−	0.564058i	$-0.190761\pi$
$773$	26.6653	+	11.8721i	0.959082	+	0.427011i	0.133347	+	0.991069i	$0.457427\pi$
$774$		0			0
$775$	1.50089	+	4.61928i	0.0539137	+	0.165929i
$776$		0			0
$777$	2.62159	−	1.16721i	0.0940490	−	0.0418733i
$778$		0			0
$779$	−9.66782	+	29.7545i	−0.346386	+	1.06607i
$780$		0			0
$781$	−17.8317	+	10.4972i	−0.638068	+	0.375618i
$782$		0			0
$783$	13.7315	+	15.2504i	0.490723	+	0.545004i
$784$		0			0
$785$	10.5831	+	7.68906i	0.377726	+	0.274434i
$786$		0			0
$787$	−7.39109	+	8.20864i	−0.263464	+	0.292606i	−0.860333	−	0.509732i	$-0.829744\pi$
$787$	−7.39109	+	8.20864i	−0.263464	+	0.292606i	0.596869	+	0.802339i	$0.296411\pi$
$788$		0			0
$789$	−40.5669	−	18.0616i	−1.44422	−	0.643008i
$790$		0			0
$791$	32.2472	−	55.8538i	1.14658	−	1.98593i
$792$		0			0
$793$	0.369487	+	19.8789i	0.0131209	+	0.705921i
$794$		0			0
$795$	1.49858	+	14.2580i	0.0531491	+	0.505680i
$796$		0			0
$797$	11.9734	−	13.2978i	0.424120	−	0.471033i	−0.492778	−	0.870155i	$-0.664018\pi$
$797$	11.9734	−	13.2978i	0.424120	−	0.471033i	0.916898	+	0.399122i	$0.130685\pi$
$798$		0			0
$799$	1.54622	−	14.7113i	0.0547013	−	0.520448i
$800$		0			0
$801$	−1.06533	+	3.27875i	−0.0376416	+	0.115849i
$802$		0			0
$803$	12.0048	+	16.2328i	0.423642	+	0.572843i
$804$		0			0
$805$	8.41519	−	25.8993i	0.296597	−	0.912830i
$806$		0			0
$807$	−8.16132	−	5.92954i	−0.287292	−	0.208730i
$808$		0			0
$809$	4.78663	+	1.01743i	0.168289	+	0.0357709i	0.291285	−	0.956636i	$-0.405917\pi$
$809$	4.78663	+	1.01743i	0.168289	+	0.0357709i	−0.122997	+	0.992407i	$0.539250\pi$
$810$		0			0
$811$	2.57606	−	1.87162i	0.0904577	−	0.0657214i	−0.541637	−	0.840612i	$-0.682195\pi$
$811$	2.57606	−	1.87162i	0.0904577	−	0.0657214i	0.632095	+	0.774891i	$0.282195\pi$
$812$		0			0
$813$	16.9702	+	29.3932i	0.595170	+	1.03087i
$814$		0			0
$815$	11.3098	+	19.5891i	0.396164	+	0.686175i
$816$		0			0
$817$	−2.57861	−	24.5339i	−0.0902143	−	0.858332i
$818$		0			0
$819$	9.98464	+	8.65970i	0.348892	+	0.302594i
$820$		0			0
$821$	26.8859	−	11.9704i	0.938324	−	0.417769i	0.120161	−	0.992754i	$-0.461659\pi$
$821$	26.8859	−	11.9704i	0.938324	−	0.417769i	0.818163	+	0.574986i	$0.194992\pi$
$822$		0			0
$823$	−30.5153	+	6.48623i	−1.06370	+	0.226096i	−0.706340	−	0.707873i	$-0.749655\pi$
$823$	−30.5153	+	6.48623i	−1.06370	+	0.226096i	−0.357356	+	0.933968i	$0.616322\pi$
$824$		0			0
$825$	−7.54200	−	16.5613i	−0.262579	−	0.576589i
$826$		0			0
$827$	13.9160	−	42.8292i	0.483908	−	1.48932i	−0.349647	−	0.936881i	$-0.613699\pi$
$827$	13.9160	−	42.8292i	0.483908	−	1.48932i	0.833556	−	0.552436i	$-0.186301\pi$
$828$		0			0
$829$	41.2416	−	18.3620i	1.43238	−	0.637737i	0.463688	−	0.885999i	$-0.346526\pi$
$829$	41.2416	−	18.3620i	1.43238	−	0.637737i	0.968693	+	0.248262i	$0.0798593\pi$
$830$		0			0
$831$	7.51653	+	23.1335i	0.260746	+	0.802492i
$832$		0			0
$833$	−15.7399	+	11.4357i	−0.545356	+	0.396225i
$834$		0			0
$835$	9.26498	−	16.0474i	0.320628	−	0.555344i
$836$		0			0
$837$	7.34258			0.253797
$838$		0			0
$839$	−31.4340	−	13.9953i	−1.08522	−	0.483172i	−0.215394	−	0.976527i	$-0.569104\pi$
$839$	−31.4340	−	13.9953i	−1.08522	−	0.483172i	−0.869828	+	0.493355i	$0.835770\pi$
$840$		0			0
$841$	−10.5574	+	11.7252i	−0.364050	+	0.404318i
$842$		0			0
$843$	22.3666	−	9.95827i	0.770348	−	0.342981i
$844$		0			0
$845$	14.1894	−	3.57195i	0.488132	−	0.122879i
$846$		0			0
$847$	31.5197	−	36.2197i	1.08303	−	1.24452i
$848$		0			0
$849$	−7.24496	+	1.53996i	−0.248647	+	0.0528515i
$850$		0			0
$851$	−0.259172	+	2.46586i	−0.00888430	+	0.0845284i
$852$		0			0
$853$	−7.22200	−	22.2270i	−0.247277	−	0.761039i	−0.995254	−	0.0973147i	$-0.968975\pi$
$853$	−7.22200	−	22.2270i	−0.247277	−	0.761039i	0.747977	−	0.663725i	$-0.231025\pi$
$854$		0			0
$855$	−0.542259	−	5.15925i	−0.0185449	−	0.176442i
$856$		0			0
$857$	38.0998			1.30146			0.650731	−	0.759308i	$-0.274462\pi$
$857$	38.0998			1.30146			0.650731	+	0.759308i	$0.274462\pi$
$858$		0			0
$859$	8.79738			0.300163			0.150081	−	0.988674i	$-0.452046\pi$
$859$	8.79738			0.300163			0.150081	+	0.988674i	$0.452046\pi$
$860$		0			0
$861$	3.82273	+	36.3709i	0.130278	+	1.23952i
$862$		0			0
$863$	−11.9537	−	36.7896i	−0.406908	−	1.25233i	−0.919291	−	0.393577i	$-0.871237\pi$
$863$	−11.9537	−	36.7896i	−0.406908	−	1.25233i	0.512383	−	0.858757i	$-0.328763\pi$
$864$		0			0
$865$	−0.145104	+	1.38058i	−0.00493370	+	0.0469410i
$866$		0			0
$867$	20.6938	−	4.39859i	0.702797	−	0.149384i
$868$		0			0
$869$	−31.9710	+	44.7960i	−1.08454	+	1.51960i
$870$		0			0
$871$	−3.94017	−	16.9791i	−0.133508	−	0.575314i
$872$		0			0
$873$	5.01571	−	2.23314i	0.169756	−	0.0755803i
$874$		0			0
$875$	28.7092	−	31.8848i	0.970549	−	1.07790i
$876$		0			0
$877$	−13.8786	−	6.17913i	−0.468646	−	0.208654i	0.158806	−	0.987310i	$-0.449235\pi$
$877$	−13.8786	−	6.17913i	−0.468646	−	0.208654i	−0.627452	+	0.778655i	$0.715902\pi$
$878$		0			0
$879$	−22.9286			−0.773362
$880$		0			0
$881$	−5.54452	+	9.60339i	−0.186800	+	0.323546i	−0.944181	−	0.329426i	$-0.893145\pi$
$881$	−5.54452	+	9.60339i	−0.186800	+	0.323546i	0.757382	+	0.652972i	$0.226478\pi$
$882$		0			0
$883$	9.16573	−	6.65929i	0.308451	−	0.224103i	−0.422780	−	0.906232i	$-0.638946\pi$
$883$	9.16573	−	6.65929i	0.308451	−	0.224103i	0.731232	+	0.682129i	$0.238946\pi$
$884$		0			0
$885$	−3.50353	−	10.7828i	−0.117770	−	0.362459i
$886$		0			0
$887$	17.8313	−	7.93900i	0.598716	−	0.266566i	−0.0849211	−	0.996388i	$-0.527064\pi$
$887$	17.8313	−	7.93900i	0.598716	−	0.266566i	0.683637	+	0.729822i	$0.260397\pi$
$888$		0			0
$889$	9.52186	−	29.3053i	0.319353	−	0.982868i
$890$		0			0
$891$	−19.0320	+	2.16321i	−0.637596	+	0.0724704i
$892$		0			0
$893$	−49.1929	+	10.4563i	−1.64618	+	0.349906i
$894$		0			0
$895$	6.51070	−	2.89875i	0.217629	−	0.0968945i
$896$		0			0
$897$	27.7626	−	9.59458i	0.926966	−	0.320354i
$898$		0			0
$899$	−0.494514	−	4.70499i	−0.0164930	−	0.156920i
$900$		0			0
$901$	6.99475	+	12.1153i	0.233029	+	0.403618i
$902$		0			0
$903$	−14.4183	−	24.9733i	−0.479812	−	0.831059i
$904$		0			0
$905$	−3.50106	+	2.54367i	−0.116379	+	0.0845545i
$906$		0			0
$907$	19.1657	+	4.07380i	0.636388	+	0.135268i	0.514797	−	0.857312i	$-0.327867\pi$
$907$	19.1657	+	4.07380i	0.636388	+	0.135268i	0.121590	+	0.992580i	$0.461201\pi$
$908$		0			0
$909$	−1.71678	−	1.24732i	−0.0569421	−	0.0413708i
$910$		0			0
$911$	10.8409	−	33.3648i	0.359174	−	1.10542i	−0.594375	−	0.804188i	$-0.702601\pi$
$911$	10.8409	−	33.3648i	0.359174	−	1.10542i	0.953549	−	0.301237i	$-0.0973995\pi$
$912$		0			0
$913$	0.145448	+	17.1994i	0.00481363	+	0.569217i
$914$		0			0
$915$	2.81896	−	8.67587i	0.0931920	−	0.286815i
$916$		0			0
$917$	5.45407	−	51.8920i	0.180109	−	1.71363i
$918$		0			0
$919$	−17.3337	+	19.2510i	−0.571785	+	0.635031i	−0.957791	−	0.287465i	$-0.907188\pi$
$919$	−17.3337	+	19.2510i	−0.571785	+	0.635031i	0.386006	+	0.922496i	$0.373854\pi$
$920$		0			0
$921$	3.40938	+	32.4381i	0.112343	+	1.06887i
$922$		0			0
$923$	−0.418032	−	22.4907i	−0.0137597	−	0.740291i
$924$		0			0
$925$	−0.834942	+	1.44616i	−0.0274527	+	0.0475495i
$926$		0			0
$927$	12.9980	+	5.78708i	0.426910	+	0.190073i
$928$		0			0
$929$	−35.8360	+	39.7999i	−1.17574	+	1.30579i	−0.232918	+	0.972496i	$0.574827\pi$
$929$	−35.8360	+	39.7999i	−1.17574	+	1.30579i	−0.942822	+	0.333296i	$0.891839\pi$
$930$		0			0
$931$	53.5137	+	38.8800i	1.75384	+	1.27424i
$932$		0			0
$933$	−4.45758	−	4.95065i	−0.145935	−	0.162077i
$934$		0			0
$935$	4.51212	+	3.99416i	0.147562	+	0.130623i
$936$		0			0
$937$	11.2871	−	34.7382i	0.368734	−	1.13485i	−0.578876	−	0.815416i	$-0.696508\pi$
$937$	11.2871	−	34.7382i	0.368734	−	1.13485i	0.947610	−	0.319430i	$-0.103492\pi$
$938$		0			0
$939$	28.3439	−	12.6195i	0.924967	−	0.411822i
$940$		0			0
$941$	−16.3754	−	50.3982i	−0.533822	−	1.64293i	−0.746181	−	0.665743i	$-0.768115\pi$
$941$	−16.3754	−	50.3982i	−0.533822	−	1.64293i	0.212359	−	0.977192i	$-0.431885\pi$
$942$		0			0
$943$	−28.8661	−	12.8520i	−0.940010	−	0.418519i
$944$		0			0
$945$	−13.8633	−	24.0119i	−0.450972	−	0.781107i
$946$		0			0
$947$	−5.71260	+	9.89451i	−0.185634	+	0.321528i	−0.943790	−	0.330545i	$-0.892767\pi$
$947$	−5.71260	+	9.89451i	−0.185634	+	0.321528i	0.758156	+	0.652074i	$0.226101\pi$
$948$		0			0
$949$	−21.7818	+	2.69948i	−0.707066	+	0.0876290i
$950$		0			0
$951$	44.6966	+	9.50056i	1.44939	+	0.308077i
$952$		0			0
$953$	3.70991	−	35.2974i	0.120176	−	1.14340i	−0.753691	−	0.657229i	$-0.771728\pi$
$953$	3.70991	−	35.2974i	0.120176	−	1.14340i	0.873866	−	0.486166i	$-0.161605\pi$
$954$		0			0
$955$	−9.86847	+	2.09761i	−0.319336	+	0.0678770i
$956$		0			0
$957$	3.83178	+	17.3062i	0.123864	+	0.559430i
$958$		0			0
$959$	52.6461	+	58.4694i	1.70003	+	1.88807i
$960$		0			0
$961$	23.7101	+	17.2264i	0.764841	+	0.555690i
$962$		0			0
$963$	0.646378	+	1.98935i	0.0208292	+	0.0641058i
$964$		0			0
$965$	−0.712949	−	6.78326i	−0.0229507	−	0.218361i
$966$		0			0
$967$	4.78015			0.153719			0.0768596	−	0.997042i	$-0.475511\pi$
$967$	4.78015			0.153719			0.0768596	+	0.997042i	$0.475511\pi$
$968$		0			0
$969$	6.51049	+	11.2765i	0.209147	+	0.362254i
$970$		0			0
$971$	−43.3826	−	19.3152i	−1.39221	−	0.619853i	−0.432705	−	0.901536i	$-0.642441\pi$
$971$	−43.3826	−	19.3152i	−1.39221	−	0.619853i	−0.959508	+	0.281683i	$0.909108\pi$
$972$		0			0
$973$	−23.7225	−	5.04238i	−0.760510	−	0.161651i
$974$		0			0
$975$	19.7097	+	1.70190i	0.631215	+	0.0545046i
$976$		0			0
$977$	−12.5726	−	13.9633i	−0.402234	−	0.446726i	0.507666	−	0.861554i	$-0.330508\pi$
$977$	−12.5726	−	13.9633i	−0.402234	−	0.446726i	−0.909900	+	0.414828i	$0.863842\pi$
$978$		0			0
$979$	−10.0406	+	9.19551i	−0.320898	+	0.293890i
$980$		0			0
$981$	−2.07403	+	0.440848i	−0.0662186	+	0.0140752i
$982$		0			0
$983$	−16.3165	−	11.8546i	−0.520414	−	0.378103i	0.296346	−	0.955081i	$-0.404232\pi$
$983$	−16.3165	−	11.8546i	−0.520414	−	0.378103i	−0.816760	+	0.576978i	$0.804232\pi$
$984$		0			0
$985$	−18.8874	−	4.01464i	−0.601803	−	0.127917i
$986$		0			0
$987$	−47.5608	+	34.5549i	−1.51388	+	1.09990i
$988$		0			0
$989$	24.9152			0.792256
$990$		0			0
$991$	−1.66312	+	2.88061i	−0.0528308	+	0.0915056i	−0.891231	−	0.453549i	$-0.850158\pi$
$991$	−1.66312	+	2.88061i	−0.0528308	+	0.0915056i	0.838401	+	0.545055i	$0.183491\pi$
$992$		0			0
$993$	−27.5461	+	20.0134i	−0.874150	+	0.635107i
$994$		0			0
$995$	3.15191	−	3.50055i	0.0999222	−	0.110975i
$996$		0			0
$997$	−1.55534	+	14.7980i	−0.0492580	+	0.468658i	0.941892	+	0.335915i	$0.109045\pi$
$997$	−1.55534	+	14.7980i	−0.0492580	+	0.468658i	−0.991150	+	0.132744i	$0.957621\pi$
$998$		0			0
$999$	1.68919	+	1.87604i	0.0534436	+	0.0593551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.9.5	✓	112
11.5	even	5	inner	572.2.bg.a.269.10	yes	112
13.3	even	3	inner	572.2.bg.a.185.10	yes	112
143.16	even	15	inner	572.2.bg.a.445.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.9.5	✓	112	1.1	even	1	trivial
572.2.bg.a.185.10	yes	112	13.3	even	3	inner
572.2.bg.a.269.10	yes	112	11.5	even	5	inner
572.2.bg.a.445.5	yes	112	143.16	even	15	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.153632 - 1.46171i) q^{3} +(0.347814 + 1.07046i) q^{5} +(0.456258 - 4.34101i) q^{7} +(0.821453 - 0.174605i) q^{9} +O(q^{10})\)	\(q+(-0.153632 - 1.46171i) q^{3} +(0.347814 + 1.07046i) q^{5} +(0.456258 - 4.34101i) q^{7} +(0.821453 - 0.174605i) q^{9} +(3.16285 + 0.998183i) q^{11} +(-2.63415 + 2.46196i) q^{13} +(1.51127 - 0.672859i) q^{15} +(1.08014 - 1.19961i) q^{17} +(-5.01372 - 2.23225i) q^{19} -6.41538 q^{21} +(2.77148 - 4.80034i) q^{23} +(3.02017 - 2.19429i) q^{25} +(-1.74397 - 5.36738i) q^{27} +(-3.32186 + 1.47899i) q^{29} +(-0.402046 + 1.23737i) q^{31} +(0.973139 - 4.77652i) q^{33} +(4.80557 - 1.02145i) q^{35} +(-0.408641 + 0.181939i) q^{37} +(4.00336 + 3.47212i) q^{39} +(-0.595870 - 5.66932i) q^{41} +(2.24746 + 3.89272i) q^{43} +(0.472620 + 0.818602i) q^{45} +(7.41355 - 5.38626i) q^{47} +(-11.7891 - 2.50586i) q^{49} +(-1.91943 - 1.39455i) q^{51} +(-2.67804 + 8.24215i) q^{53} +(0.0315674 + 3.73289i) q^{55} +(-2.49263 + 7.67154i) q^{57} +(0.716387 - 6.81597i) q^{59} +(3.68983 - 4.09798i) q^{61} +(-0.383168 - 3.64560i) q^{63} +(-3.55163 - 1.96345i) q^{65} +(-2.41714 + 4.18661i) q^{67} +(-7.44249 - 3.31361i) q^{69} +(-4.17462 + 4.63639i) q^{71} +(4.92480 + 3.57808i) q^{73} +(-3.67140 - 4.07750i) q^{75} +(5.77620 - 13.2745i) q^{77} +(-5.12771 + 15.7815i) q^{79} +(-5.27601 + 2.34903i) q^{81} +(1.60256 + 4.93218i) q^{83} +(1.65982 + 0.739002i) q^{85} +(2.67219 + 4.62837i) q^{87} +(-2.05255 + 3.55512i) q^{89} +(9.48554 + 12.5581i) q^{91} +(1.87044 + 0.397575i) q^{93} +(0.645696 - 6.14339i) q^{95} +(6.39482 - 1.35926i) q^{97} +(2.77242 + 0.267710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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