LMFDB - Embedded newform 252.9.bg.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(29,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("252.29");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.bg (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$102.659409735$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	252.29
Dual form			252.9.bg.a.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-80.9976 - 0.623037i) q^{3} +(25.8029 - 14.8973i) q^{5} +(453.746 - 785.912i) q^{7} +(6560.22 + 100.929i) q^{9} +O(q^{10})$	\(q+(-80.9976 - 0.623037i) q^{3} +(25.8029 - 14.8973i) q^{5} +(453.746 - 785.912i) q^{7} +(6560.22 + 100.929i) q^{9} +(18470.7 + 10664.0i) q^{11} +(20811.8 + 36047.1i) q^{13} +(-2099.26 + 1190.57i) q^{15} -50217.1i q^{17} +137508. q^{19} +(-37242.0 + 63374.3i) q^{21} +(22174.3 - 12802.3i) q^{23} +(-194869. + 337522. i) q^{25} +(-531300. - 12262.3i) q^{27} +(-216652. - 125084. i) q^{29} +(19183.8 + 33227.3i) q^{31} +(-1.48943e6 - 875269. i) q^{33} -27038.4i q^{35} +811314. q^{37} +(-1.66325e6 - 2.93270e6i) q^{39} +(788767. - 455395. i) q^{41} +(1.66430e6 - 2.88266e6i) q^{43} +(170777. - 95125.6i) q^{45} +(2.95902e6 + 1.70839e6i) q^{47} +(-411772. - 713209. i) q^{49} +(-31287.1 + 4.06747e6i) q^{51} -3.88980e6i q^{53} +635463. q^{55} +(-1.11378e7 - 85672.6i) q^{57} +(-1.43031e7 + 8.25793e6i) q^{59} +(4.05153e6 - 7.01746e6i) q^{61} +(3.05600e6 - 5.10996e6i) q^{63} +(1.07401e6 + 620081. i) q^{65} +(-1.14683e7 - 1.98637e7i) q^{67} +(-1.80404e6 + 1.02314e6i) q^{69} +1.36266e7i q^{71} -1.57599e7 q^{73} +(1.59942e7 - 2.72171e7i) q^{75} +(1.67620e7 - 9.67753e6i) q^{77} +(-2.82863e7 + 4.89933e7i) q^{79} +(4.30263e7 + 1.32423e6i) q^{81} +(1.95807e7 + 1.13049e7i) q^{83} +(-748101. - 1.29575e6i) q^{85} +(1.74703e7 + 1.02665e7i) q^{87} -6.11097e6i q^{89} +3.77731e7 q^{91} +(-1.53314e6 - 2.70329e6i) q^{93} +(3.54811e6 - 2.04850e6i) q^{95} +(-7.12972e7 + 1.23490e8i) q^{97} +(1.20095e8 + 7.18227e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9}+O(q^{10}) $ 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9	$ 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9} - 6102 q^{11} - 63218 q^{15} - 354144 q^{19} + 81634 q^{21} - 689760 q^{23} + 4088394 q^{25} - 2939076 q^{27} - 1902474 q^{29} + 613830 q^{31} - 3732526 q^{33} + 4437300 q^{37} - 2690876 q^{39} + 8275176 q^{41} - 2941680 q^{43} + 7299362 q^{45} - 7663950 q^{47} - 39530064 q^{49} - 23625052 q^{51} + 8608908 q^{55} + 28697652 q^{57} + 38291778 q^{59} + 7577556 q^{63} + 42391494 q^{65} + 47903562 q^{67} - 52586968 q^{69} - 32396448 q^{73} + 245976220 q^{75} + 11461314 q^{79} - 16224230 q^{81} - 104964174 q^{83} + 108387294 q^{85} - 213493700 q^{87} - 12590844 q^{91} - 88124258 q^{93} + 293841792 q^{95} + 9277590 q^{97} - 77959808 q^{99}+O(q^{100}) $ 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9 - 6102 * q^11 - 63218 * q^15 - 354144 * q^19 + 81634 * q^21 - 689760 * q^23 + 4088394 * q^25 - 2939076 * q^27 - 1902474 * q^29 + 613830 * q^31 - 3732526 * q^33 + 4437300 * q^37 - 2690876 * q^39 + 8275176 * q^41 - 2941680 * q^43 + 7299362 * q^45 - 7663950 * q^47 - 39530064 * q^49 - 23625052 * q^51 + 8608908 * q^55 + 28697652 * q^57 + 38291778 * q^59 + 7577556 * q^63 + 42391494 * q^65 + 47903562 * q^67 - 52586968 * q^69 - 32396448 * q^73 + 245976220 * q^75 + 11461314 * q^79 - 16224230 * q^81 - 104964174 * q^83 + 108387294 * q^85 - 213493700 * q^87 - 12590844 * q^91 - 88124258 * q^93 + 293841792 * q^95 + 9277590 * q^97 - 77959808 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−80.9976	−	0.623037i	−0.999970	−	0.00769182i
$3$	−80.9976	−	0.623037i	−0.999970	−	0.00769182i
$4$		0			0
$5$	25.8029	−	14.8973i	0.0412847	−	0.0238357i	−0.479216	−	0.877697i	$-0.659079\pi$
$5$	25.8029	−	14.8973i	0.0412847	−	0.0238357i	0.520500	+	0.853861i	$0.325745\pi$
$6$		0			0
$7$	453.746	−	785.912i	0.188982	−	0.327327i
$7$	453.746	−	785.912i	0.188982	−	0.327327i
$8$		0			0
$9$	6560.22	+	100.929i	0.999882	+	0.0153832i
$10$		0			0
$11$	18470.7	+	10664.0i	1.26157	+	0.728368i	0.973378	−	0.229205i	$-0.0736125\pi$
$11$	18470.7	+	10664.0i	1.26157	+	0.728368i	0.288192	+	0.957573i	$0.406946\pi$
$12$		0			0
$13$	20811.8	+	36047.1i	0.728679	+	1.26211i	0.957442	+	0.288627i	$0.0931988\pi$
$13$	20811.8	+	36047.1i	0.728679	+	1.26211i	−0.228762	+	0.973482i	$0.573468\pi$
$14$		0			0
$15$	−2099.26	+	1190.57i	−0.0414668	+	0.0235175i
$16$		0			0
$17$		−	50217.1i		−	0.601251i	−0.953742	−	0.300626i	$-0.902805\pi$
$17$		−	50217.1i		−	0.601251i	0.953742	−	0.300626i	$-0.0971955\pi$
$18$		0			0
$19$	137508.			1.05515			0.527574	−	0.849509i	$-0.323102\pi$
$19$	137508.			1.05515			0.527574	+	0.849509i	$0.323102\pi$
$20$		0			0
$21$	−37242.0	+	63374.3i	−0.191494	+	0.325864i
$22$		0			0
$23$	22174.3	−	12802.3i	0.0792390	−	0.0457487i	−0.459857	−	0.887993i	$-0.652099\pi$
$23$	22174.3	−	12802.3i	0.0792390	−	0.0457487i	0.539096	+	0.842244i	$0.318766\pi$
$24$		0			0
$25$	−194869.	+	337522.i	−0.498864	+	0.864057i
$26$		0			0
$27$	−531300.	−	12262.3i	−0.999734	−	0.0230736i
$28$		0			0
$29$	−216652.	−	125084.i	−0.306316	−	0.176852i	0.338961	−	0.940801i	$-0.389925\pi$
$29$	−216652.	−	125084.i	−0.306316	−	0.176852i	−0.645277	+	0.763949i	$0.723258\pi$
$30$		0			0
$31$	19183.8	+	33227.3i	0.0207725	+	0.0359790i	0.876225	−	0.481903i	$-0.160054\pi$
$31$	19183.8	+	33227.3i	0.0207725	+	0.0359790i	−0.855452	+	0.517882i	$0.826721\pi$
$32$		0			0
$33$	−1.48943e6	−	875269.i	−1.25593	−	0.738050i
$34$		0			0
$35$		−	27038.4i		−	0.0180181i
$36$		0			0
$37$	811314.			0.432894			0.216447	−	0.976294i	$-0.430553\pi$
$37$	811314.			0.432894			0.216447	+	0.976294i	$0.430553\pi$
$38$		0			0
$39$	−1.66325e6	−	2.93270e6i	−0.718950	−	1.26768i
$40$		0			0
$41$	788767.	−	455395.i	0.279134	−	0.161158i	−0.353897	−	0.935284i	$-0.615144\pi$
$41$	788767.	−	455395.i	0.279134	−	0.161158i	0.633031	+	0.774126i	$0.281810\pi$
$42$		0			0
$43$	1.66430e6	−	2.88266e6i	0.486809	−	0.843179i	−0.513076	−	0.858343i	$-0.671494\pi$
$43$	1.66430e6	−	2.88266e6i	0.486809	−	0.843179i	0.999885	+	0.0151649i	$0.00482731\pi$
$44$		0			0
$45$	170777.	−	95125.6i	0.0416465	−	0.0231978i
$46$		0			0
$47$	2.95902e6	+	1.70839e6i	0.606396	+	0.350103i	0.771554	−	0.636164i	$-0.219480\pi$
$47$	2.95902e6	+	1.70839e6i	0.606396	+	0.350103i	−0.165158	+	0.986267i	$0.552813\pi$
$48$		0			0
$49$	−411772.	−	713209.i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−31287.1	+	4.06747e6i	−0.00462472	+	0.601234i
$52$		0			0
$53$		−	3.88980e6i		−	0.492974i	−0.969146	−	0.246487i	$-0.920724\pi$
$53$		−	3.88980e6i		−	0.492974i	0.969146	−	0.246487i	$-0.0792762\pi$
$54$		0			0
$55$	635463.			0.0694448
$56$		0			0
$57$	−1.11378e7	−	85672.6i	−1.05512	−	0.00811601i
$58$		0			0
$59$	−1.43031e7	+	8.25793e6i	−1.18038	+	0.681495i	−0.956104	−	0.293029i	$-0.905337\pi$
$59$	−1.43031e7	+	8.25793e6i	−1.18038	+	0.681495i	−0.224281	+	0.974524i	$0.572003\pi$
$60$		0			0
$61$	4.05153e6	−	7.01746e6i	0.292617	−	0.506828i	−0.681810	−	0.731529i	$-0.738807\pi$
$61$	4.05153e6	−	7.01746e6i	0.292617	−	0.506828i	0.974428	+	0.224701i	$0.0721404\pi$
$62$		0			0
$63$	3.05600e6	−	5.10996e6i	0.193995	−	0.324381i
$64$		0			0
$65$	1.07401e6	+	620081.i	0.0601666	+	0.0347372i
$66$		0			0
$67$	−1.14683e7	−	1.98637e7i	−0.569116	−	0.985737i	−0.996654	−	0.0817400i	$-0.973952\pi$
$67$	−1.14683e7	−	1.98637e7i	−0.569116	−	0.985737i	0.427538	−	0.903997i	$-0.359381\pi$
$68$		0			0
$69$	−1.80404e6	+	1.02314e6i	−0.0795885	+	0.0451378i
$70$		0			0
$71$			1.36266e7i			0.536234i	0.963386	+	0.268117i	$0.0864013\pi$
$71$			1.36266e7i			0.536234i	−0.963386	+	0.268117i	$0.913599\pi$
$72$		0			0
$73$	−1.57599e7			−0.554962			−0.277481	−	0.960731i	$-0.589500\pi$
$73$	−1.57599e7			−0.554962			−0.277481	+	0.960731i	$0.589500\pi$
$74$		0			0
$75$	1.59942e7	−	2.72171e7i	0.505495	−	0.860195i
$76$		0			0
$77$	1.67620e7	−	9.67753e6i	0.476829	−	0.275297i
$78$		0			0
$79$	−2.82863e7	+	4.89933e7i	−0.726219	+	1.25785i	0.232251	+	0.972656i	$0.425391\pi$
$79$	−2.82863e7	+	4.89933e7i	−0.726219	+	1.25785i	−0.958470	+	0.285192i	$0.907942\pi$
$80$		0			0
$81$	4.30263e7	+	1.32423e6i	0.999527	+	0.0307627i
$82$		0			0
$83$	1.95807e7	+	1.13049e7i	0.412588	+	0.238208i	0.691901	−	0.721992i	$-0.256773\pi$
$83$	1.95807e7	+	1.13049e7i	0.412588	+	0.238208i	−0.279313	+	0.960200i	$0.590107\pi$
$84$		0			0
$85$	−748101.	−	1.29575e6i	−0.0143313	−	0.0248225i
$86$		0			0
$87$	1.74703e7	+	1.02665e7i	0.304947	+	0.179203i
$88$		0			0
$89$		−	6.11097e6i		−	0.0973981i	−0.998813	−	0.0486990i	$-0.984492\pi$
$89$		−	6.11097e6i		−	0.0973981i	0.998813	−	0.0486990i	$-0.0155075\pi$
$90$		0			0
$91$	3.77731e7			0.550830
$92$		0			0
$93$	−1.53314e6	−	2.70329e6i	−0.0204951	−	0.0361377i
$94$		0			0
$95$	3.54811e6	−	2.04850e6i	0.0435615	−	0.0251502i
$96$		0			0
$97$	−7.12972e7	+	1.23490e8i	−0.805352	+	1.39491i	0.110702	+	0.993854i	$0.464690\pi$
$97$	−7.12972e7	+	1.23490e8i	−0.805352	+	1.39491i	−0.916053	+	0.401056i	$0.868643\pi$
$98$		0			0
$99$	1.20095e8	+	7.18227e7i	1.25022	+	0.747689i
$100$		0			0
$101$	−3.39062e7	−	1.95757e7i	−0.325832	−	0.188119i	0.328157	−	0.944623i	$-0.393572\pi$
$101$	−3.39062e7	−	1.95757e7i	−0.325832	−	0.188119i	−0.653989	+	0.756504i	$0.726906\pi$
$102$		0			0
$103$	5.49602e6	+	9.51939e6i	0.0488314	+	0.0845785i	0.889408	−	0.457114i	$-0.151117\pi$
$103$	5.49602e6	+	9.51939e6i	0.0488314	+	0.0845785i	−0.840577	+	0.541693i	$0.817784\pi$
$104$		0			0
$105$	−16846.0	+	2.19005e6i	−0.000138592	+	0.0180176i
$106$		0			0
$107$			1.72417e8i			1.31536i	0.753297	+	0.657680i	$0.228462\pi$
$107$			1.72417e8i			1.31536i	−0.753297	+	0.657680i	$0.771538\pi$
$108$		0			0
$109$	1.56212e8			1.10665			0.553323	−	0.832967i	$-0.313359\pi$
$109$	1.56212e8			1.10665			0.553323	+	0.832967i	$0.313359\pi$
$110$		0			0
$111$	−6.57145e7	−	505479.i	−0.432882	−	0.00332974i
$112$		0			0
$113$	2.24138e8	−	1.29406e8i	1.37468	−	0.793673i	0.383168	−	0.923679i	$-0.374833\pi$
$113$	2.24138e8	−	1.29406e8i	1.37468	−	0.793673i	0.991513	+	0.130006i	$0.0414997\pi$
$114$		0			0
$115$	381442.	−	660677.i	0.00218091	−	0.00377744i
$116$		0			0
$117$	1.32892e8	+	2.38578e8i	0.709178	+	1.27317i
$118$		0			0
$119$	−3.94662e7	−	2.27858e7i	−0.196806	−	0.113626i
$120$		0			0
$121$	1.20264e8	+	2.08303e8i	0.561040	+	0.971750i
$122$		0			0
$123$	−6.41719e7	+	3.63944e7i	−0.280366	+	0.159006i
$124$		0			0
$125$			2.32506e7i			0.0952346i
$126$		0			0
$127$	4.36594e8			1.67827			0.839137	−	0.543920i	$-0.183060\pi$
$127$	4.36594e8			1.67827			0.839137	+	0.543920i	$0.183060\pi$
$128$		0			0
$129$	−1.36601e8	+	2.32452e8i	−0.493281	+	0.839409i
$130$		0			0
$131$	5.45826e6	−	3.15133e6i	0.0185340	−	0.0107006i	−0.490704	−	0.871326i	$-0.663260\pi$
$131$	5.45826e6	−	3.15133e6i	0.0185340	−	0.0107006i	0.509238	+	0.860626i	$0.329927\pi$
$132$		0			0
$133$	6.23938e7	−	1.08069e8i	0.199404	−	0.345378i
$134$		0			0
$135$	−1.38918e7	+	7.59855e6i	−0.0418237	+	0.0228768i
$136$		0			0
$137$	1.86783e8	+	1.07839e8i	0.530218	+	0.306121i	0.741105	−	0.671389i	$-0.234302\pi$
$137$	1.86783e8	+	1.07839e8i	0.530218	+	0.306121i	−0.210887	+	0.977510i	$0.567635\pi$
$138$		0			0
$139$	6.59746e7	+	1.14271e8i	0.176733	+	0.306110i	0.940760	−	0.339074i	$-0.110114\pi$
$139$	6.59746e7	+	1.14271e8i	0.176733	+	0.306110i	−0.764027	+	0.645185i	$0.776780\pi$
$140$		0			0
$141$	−2.38609e8	−	1.40219e8i	−0.603685	−	0.354757i
$142$		0			0
$143$			8.87752e8i			2.12299i
$144$		0			0
$145$	−7.45366e6			−0.0168616
$146$		0			0
$147$	3.29081e7	+	5.80248e7i	0.0704748	+	0.124264i
$148$		0			0
$149$	3.82796e8	−	2.21007e8i	0.776644	−	0.448395i	−0.0585958	−	0.998282i	$-0.518662\pi$
$149$	3.82796e8	−	2.21007e8i	0.776644	−	0.448395i	0.835240	+	0.549886i	$0.185329\pi$
$150$		0			0
$151$	−1.48552e8	+	2.57299e8i	−0.285739	+	0.494914i	−0.972788	−	0.231697i	$-0.925572\pi$
$151$	−1.48552e8	+	2.57299e8i	−0.285739	+	0.494914i	0.687049	+	0.726611i	$0.258906\pi$
$152$		0			0
$153$	5.06837e6	−	3.29436e8i	0.00924916	−	0.601180i
$154$		0			0
$155$	989997.	+	571575.i	0.00171517	+	0.000990254i
$156$		0			0
$157$	−2.80102e8	−	4.85151e8i	−0.461018	−	0.798506i	0.537994	−	0.842949i	$-0.319182\pi$
$157$	−2.80102e8	−	4.85151e8i	−0.461018	−	0.798506i	−0.999012	+	0.0444424i	$0.985849\pi$
$158$		0			0
$159$	−2.42349e6	+	3.15065e8i	−0.00379186	+	0.492959i
$160$		0			0
$161$		−	2.32361e7i		−	0.0345827i
$162$		0			0
$163$	6.91142e8			0.979077			0.489539	−	0.871982i	$-0.337165\pi$
$163$	6.91142e8			0.979077			0.489539	+	0.871982i	$0.337165\pi$
$164$		0			0
$165$	−5.14710e7	−	395917.i	−0.0694427	−	0.000534156i
$166$		0			0
$167$	−2.11775e8	+	1.22268e8i	−0.272275	+	0.157198i	−0.629921	−	0.776659i	$-0.716913\pi$
$167$	−2.11775e8	+	1.22268e8i	−0.272275	+	0.157198i	0.357646	+	0.933857i	$0.383579\pi$
$168$		0			0
$169$	−4.58398e8	+	7.93968e8i	−0.561947	+	0.973321i
$170$		0			0
$171$	9.02083e8	+	1.38785e7i	1.05502	+	0.0162315i
$172$		0			0
$173$	6.30212e8	+	3.63853e8i	0.703561	+	0.406201i	0.808672	−	0.588259i	$-0.200186\pi$
$173$	6.30212e8	+	3.63853e8i	0.703561	+	0.406201i	−0.105111	+	0.994460i	$0.533520\pi$
$174$		0			0
$175$	1.76842e8	+	3.06299e8i	0.188553	+	0.326583i
$176$		0			0
$177$	1.16367e9	−	6.59961e8i	1.18559	−	0.672396i
$178$		0			0
$179$			4.89107e8i			0.476422i	0.971213	+	0.238211i	$0.0765610\pi$
$179$			4.89107e8i			0.476422i	−0.971213	+	0.238211i	$0.923439\pi$
$180$		0			0
$181$	−7.48400e8			−0.697300			−0.348650	−	0.937253i	$-0.613360\pi$
$181$	−7.48400e8			−0.697300			−0.348650	+	0.937253i	$0.613360\pi$
$182$		0			0
$183$	−3.32537e8	+	5.65873e8i	−0.296507	+	0.504563i
$184$		0			0
$185$	2.09343e7	−	1.20864e7i	0.0178719	−	0.0103184i
$186$		0			0
$187$	5.35517e8	−	9.27543e8i	0.437932	−	0.758521i
$188$		0			0
$189$	−2.50712e8	+	4.11991e8i	−0.196485	+	0.322879i
$190$		0			0
$191$	−1.52294e9	−	8.79269e8i	−1.14432	−	0.660676i	−0.196826	−	0.980438i	$-0.563064\pi$
$191$	−1.52294e9	−	8.79269e8i	−1.14432	−	0.660676i	−0.947498	+	0.319762i	$0.896397\pi$
$192$		0			0
$193$	5.49654e8	+	9.52028e8i	0.396150	+	0.686152i	0.993247	−	0.116017i	$-0.0370126\pi$
$193$	5.49654e8	+	9.52028e8i	0.396150	+	0.686152i	−0.597097	+	0.802169i	$0.703679\pi$
$194$		0			0
$195$	−8.66061e7	−	5.08942e7i	−0.0598977	−	0.0351990i
$196$		0			0
$197$		−	1.27000e9i		−	0.843215i	−0.906779	−	0.421607i	$-0.861466\pi$
$197$		−	1.27000e9i		−	0.843215i	0.906779	−	0.421607i	$-0.138534\pi$
$198$		0			0
$199$	−6.13813e8			−0.391403			−0.195701	−	0.980664i	$-0.562698\pi$
$199$	−6.13813e8			−0.391403			−0.195701	+	0.980664i	$0.562698\pi$
$200$		0			0
$201$	9.16531e8	+	1.61606e9i	0.561517	+	0.990086i
$202$		0			0
$203$	−1.96610e8	+	1.13513e8i	−0.115777	+	0.0668436i
$204$		0			0
$205$	1.35683e7	−	2.35010e7i	0.00768265	−	0.0133067i
$206$		0			0
$207$	1.46761e8	−	8.17482e7i	0.0799334	−	0.0445243i
$208$		0			0
$209$	2.53986e9	+	1.46639e9i	1.33114	+	0.768536i
$210$		0			0
$211$	4.96837e8	+	8.60547e8i	0.250659	+	0.434155i	0.963708	−	0.266960i	$-0.0860192\pi$
$211$	4.96837e8	+	8.60547e8i	0.250659	+	0.434155i	−0.713048	+	0.701115i	$0.752686\pi$
$212$		0			0
$213$	8.48988e6	−	1.10372e9i	0.00412461	−	0.536218i
$214$		0			0
$215$		−	9.91748e7i		−	0.0464138i
$216$		0			0
$217$	3.48183e7			0.0157025
$218$		0			0
$219$	1.27652e9	+	9.81903e6i	0.554946	+	0.00426867i
$220$		0			0
$221$	1.81018e9	−	1.04511e9i	0.758845	−	0.438120i
$222$		0			0
$223$	−2.12100e9	+	3.67369e9i	−0.857674	+	1.48553i	0.0164685	+	0.999864i	$0.494758\pi$
$223$	−2.12100e9	+	3.67369e9i	−0.857674	+	1.48553i	−0.874142	+	0.485670i	$0.838576\pi$
$224$		0			0
$225$	−1.31245e9	+	2.19455e9i	−0.512097	+	0.856281i
$226$		0			0
$227$	2.38403e9	+	1.37642e9i	0.897860	+	0.518380i	0.876505	−	0.481392i	$-0.159869\pi$
$227$	2.38403e9	+	1.37642e9i	0.897860	+	0.518380i	0.0213546	+	0.999772i	$0.493202\pi$
$228$		0			0
$229$	1.60345e8	+	2.77727e8i	0.0583062	+	0.100989i	0.893705	−	0.448655i	$-0.148097\pi$
$229$	1.60345e8	+	2.77727e8i	0.0583062	+	0.100989i	−0.835399	+	0.549644i	$0.814763\pi$
$230$		0			0
$231$	−1.36371e9	+	7.73414e8i	−0.478932	+	0.271621i
$232$		0			0
$233$		−	1.10293e9i		−	0.374216i	−0.982339	−	0.187108i	$-0.940089\pi$
$233$		−	1.10293e9i		−	0.374216i	0.982339	−	0.187108i	$-0.0599114\pi$
$234$		0			0
$235$	1.01802e8			0.0333798
$236$		0			0
$237$	2.32165e9	−	3.95072e9i	0.735873	−	1.25223i
$238$		0			0
$239$	−2.17860e9	+	1.25781e9i	−0.667706	+	0.385500i	−0.795207	−	0.606338i	$-0.792638\pi$
$239$	−2.17860e9	+	1.25781e9i	−0.667706	+	0.385500i	0.127501	+	0.991838i	$0.459304\pi$
$240$		0			0
$241$	3.83697e8	−	6.64583e8i	0.113742	−	0.197007i	−0.803534	−	0.595259i	$-0.797050\pi$
$241$	3.83697e8	−	6.64583e8i	0.113742	−	0.197007i	0.917276	+	0.398252i	$0.130383\pi$
$242$		0			0
$243$	−3.48421e9	−	1.34067e8i	−0.999261	−	0.0384500i
$244$		0			0
$245$	−2.12498e7	−	1.22686e7i	−0.00589782	−	0.00340511i
$246$		0			0
$247$	2.86179e9	+	4.95677e9i	0.768865	+	1.33171i
$248$		0			0
$249$	−1.57895e9	−	9.27873e8i	−0.410744	−	0.241374i
$250$		0			0
$251$			5.40586e8i			0.136198i	0.997679	+	0.0680989i	$0.0216933\pi$
$251$			5.40586e8i			0.136198i	−0.997679	+	0.0680989i	$0.978307\pi$
$252$		0			0
$253$	5.46099e8			0.133287
$254$		0			0
$255$	5.97871e7	+	1.05419e8i	0.0141399	+	0.0249320i
$256$		0			0
$257$	6.64552e9	−	3.83679e9i	1.52334	−	0.879500i	0.523720	−	0.851890i	$-0.324544\pi$
$257$	6.64552e9	−	3.83679e9i	1.52334	−	0.879500i	0.999619	−	0.0276101i	$-0.00878969\pi$
$258$		0			0
$259$	3.68131e8	−	6.37621e8i	0.0818094	−	0.141698i
$260$		0			0
$261$	−1.40866e9	−	8.42444e8i	−0.303559	−	0.181543i
$262$		0			0
$263$	8.06162e9	+	4.65438e9i	1.68500	+	0.972834i	0.958251	+	0.285927i	$0.0923015\pi$
$263$	8.06162e9	+	4.65438e9i	1.68500	+	0.972834i	0.726746	+	0.686907i	$0.241032\pi$
$264$		0			0
$265$	−5.79477e7	−	1.00368e8i	−0.0117504	−	0.0203523i
$266$		0			0
$267$	−3.80736e6	+	4.94974e8i	−0.000749168	+	0.0973952i
$268$		0			0
$269$			1.59296e9i			0.304225i	0.988363	+	0.152113i	$0.0486076\pi$
$269$			1.59296e9i			0.304225i	−0.988363	+	0.152113i	$0.951392\pi$
$270$		0			0
$271$	−3.12322e9			−0.579063			−0.289531	−	0.957169i	$-0.593499\pi$
$271$	−3.12322e9			−0.579063			−0.289531	+	0.957169i	$0.593499\pi$
$272$		0			0
$273$	−3.05953e9	−	2.35341e7i	−0.550814	−	0.00423688i
$274$		0			0
$275$	−7.19870e9	+	4.15617e9i	−1.25870	+	0.726713i
$276$		0			0
$277$	1.79591e9	−	3.11061e9i	0.305047	−	0.528356i	−0.672225	−	0.740347i	$-0.734661\pi$
$277$	1.79591e9	−	3.11061e9i	0.305047	−	0.528356i	0.977272	+	0.211991i	$0.0679946\pi$
$278$		0			0
$279$	1.22496e8	+	2.19915e8i	0.0202165	+	0.0362942i
$280$		0			0
$281$	−6.27711e9	−	3.62409e9i	−1.00678	−	0.581265i	−0.0965326	−	0.995330i	$-0.530775\pi$
$281$	−6.27711e9	−	3.62409e9i	−1.00678	−	0.581265i	−0.910247	+	0.414065i	$0.864109\pi$
$282$		0			0
$283$	−1.19705e9	−	2.07335e9i	−0.186623	−	0.323241i	0.757499	−	0.652836i	$-0.226421\pi$
$283$	−1.19705e9	−	2.07335e9i	−0.186623	−	0.323241i	−0.944122	+	0.329595i	$0.893088\pi$
$284$		0			0
$285$	−2.88665e8	+	1.63713e8i	−0.0437537	+	0.0248144i
$286$		0			0
$287$		−	8.26534e8i		−	0.121824i
$288$		0			0
$289$	4.45400e9			0.638497
$290$		0			0
$291$	5.85184e9	−	9.95801e9i	0.816057	−	1.38867i
$292$		0			0
$293$	−3.68906e9	+	2.12988e9i	−0.500548	+	0.288991i	−0.728940	−	0.684578i	$-0.759987\pi$
$293$	−3.68906e9	+	2.12988e9i	−0.500548	+	0.288991i	0.228392	+	0.973569i	$0.426653\pi$
$294$		0			0
$295$	−2.46042e8	+	4.26158e8i	−0.0324879	+	0.0562707i
$296$		0			0
$297$	−9.68268e9	−	5.89229e9i	−1.24443	−	0.757283i
$298$		0			0
$299$	9.22975e8	+	5.32880e8i	0.115480	+	0.0666722i
$300$		0			0
$301$	−1.51034e9	−	2.61599e9i	−0.183997	−	0.318692i
$302$		0			0
$303$	2.73412e9	+	1.60671e9i	0.324375	+	0.190620i
$304$		0			0
$305$		−	2.41428e8i		−	0.0278990i
$306$		0			0
$307$	−1.20281e10			−1.35408			−0.677038	−	0.735948i	$-0.736737\pi$
$307$	−1.20281e10			−1.35408			−0.677038	+	0.735948i	$0.736737\pi$
$308$		0			0
$309$	−4.39234e8	−	7.74472e8i	−0.0481794	−	0.0849516i
$310$		0			0
$311$	1.00721e10	−	5.81516e9i	1.07666	−	0.621613i	0.146670	−	0.989186i	$-0.453145\pi$
$311$	1.00721e10	−	5.81516e9i	1.07666	−	0.621613i	0.929995	+	0.367573i	$0.119811\pi$
$312$		0			0
$313$	3.89683e9	−	6.74950e9i	0.406007	−	0.703225i	−0.588431	−	0.808548i	$-0.700254\pi$
$313$	3.89683e9	−	6.74950e9i	0.406007	−	0.703225i	0.994438	+	0.105322i	$0.0335874\pi$
$314$		0			0
$315$	2.72896e6	−	1.77378e8i	0.000277176	−	0.0180160i
$316$		0			0
$317$	−1.55684e10	−	8.98845e9i	−1.54173	−	0.890118i	−0.998730	−	0.0503855i	$-0.983955\pi$
$317$	−1.55684e10	−	8.98845e9i	−1.54173	−	0.890118i	−0.543000	−	0.839733i	$-0.682712\pi$
$318$		0			0
$319$	−2.66780e9	−	4.62076e9i	−0.257626	−	0.446222i
$320$		0			0
$321$	1.07422e8	−	1.39654e10i	0.0101175	−	1.31532i
$322$		0			0
$323$		−	6.90526e9i		−	0.634410i
$324$		0			0
$325$	−1.62223e10			−1.45405
$326$		0			0
$327$	−1.26528e10	−	9.73260e7i	−1.10661	−	0.00851212i
$328$		0			0
$329$	2.68529e9	−	1.55035e9i	0.229196	−	0.132326i
$330$		0			0
$331$	−5.04175e9	+	8.73257e9i	−0.420019	+	0.727495i	−0.995941	−	0.0900100i	$-0.971310\pi$
$331$	−5.04175e9	+	8.73257e9i	−0.420019	+	0.727495i	0.575921	+	0.817505i	$0.304643\pi$
$332$		0			0
$333$	5.32240e9	+	8.18851e7i	0.432843	+	0.00665929i
$334$		0			0
$335$	−5.91833e8	−	3.41695e8i	−0.0469916	−	0.0271306i
$336$		0			0
$337$	9.77247e8	+	1.69264e9i	0.0757678	+	0.131234i	0.901420	−	0.432946i	$-0.142526\pi$
$337$	9.77247e8	+	1.69264e9i	0.0757678	+	0.131234i	−0.825652	+	0.564180i	$0.809193\pi$
$338$		0			0
$339$	−1.82353e10	+	1.03419e10i	−1.38075	+	0.783075i
$340$		0			0
$341$			8.18307e8i			0.0605200i
$342$		0			0
$343$	−7.47359e8			−0.0539949
$344$		0			0
$345$	−3.13075e7	+	5.32756e7i	−0.00220990	+	0.00376055i
$346$		0			0
$347$	2.33051e10	−	1.34552e10i	1.60744	−	0.928054i	0.617495	−	0.786575i	$-0.288148\pi$
$347$	2.33051e10	−	1.34552e10i	1.60744	−	0.928054i	0.989941	−	0.141479i	$-0.0451858\pi$
$348$		0			0
$349$	−8.95933e9	+	1.55180e10i	−0.603912	+	1.04601i	0.388310	+	0.921529i	$0.373059\pi$
$349$	−8.95933e9	+	1.55180e10i	−0.603912	+	1.04601i	−0.992222	+	0.124478i	$0.960274\pi$
$350$		0			0
$351$	−1.06153e10	−	1.94070e10i	−0.699364	−	1.27859i
$352$		0			0
$353$	−3.01256e9	−	1.73930e9i	−0.194016	−	0.112015i	0.399845	−	0.916583i	$-0.369064\pi$
$353$	−3.01256e9	−	1.73930e9i	−0.194016	−	0.112015i	−0.593861	+	0.804568i	$0.702397\pi$
$354$		0			0
$355$	2.03000e8	+	3.51606e8i	0.0127815	+	0.0221383i
$356$		0			0
$357$	3.18247e9	+	1.87019e9i	0.195926	+	0.115136i
$358$		0			0
$359$		−	2.30326e10i		−	1.38665i	−0.720627	−	0.693323i	$-0.756146\pi$
$359$		−	2.30326e10i		−	1.38665i	0.720627	−	0.693323i	$-0.243854\pi$
$360$		0			0
$361$	1.92489e9			0.113339
$362$		0			0
$363$	−9.61131e9	−	1.69470e10i	−0.553549	−	0.976036i
$364$		0			0
$365$	−4.06653e8	+	2.34781e8i	−0.0229114	+	0.0132279i
$366$		0			0
$367$	−8.16145e9	+	1.41360e10i	−0.449887	+	0.779227i	−0.998378	−	0.0569295i	$-0.981869\pi$
$367$	−8.16145e9	+	1.41360e10i	−0.449887	+	0.779227i	0.548492	+	0.836156i	$0.315202\pi$
$368$		0			0
$369$	5.22045e9	−	2.90788e9i	0.281580	−	0.156845i
$370$		0			0
$371$	−3.05704e9	−	1.76498e9i	−0.161364	−	0.0931633i
$372$		0			0
$373$	1.09498e10	+	1.89656e10i	0.565678	+	0.979784i	0.996986	+	0.0775789i	$0.0247190\pi$
$373$	1.09498e10	+	1.89656e10i	0.565678	+	0.979784i	−0.431308	+	0.902205i	$0.641948\pi$
$374$		0			0
$375$	1.44860e7	−	1.88325e9i	0.000732527	−	0.0952318i
$376$		0			0
$377$		−	1.04129e10i		−	0.515473i
$378$		0			0
$379$	−1.42429e10			−0.690306			−0.345153	−	0.938546i	$-0.612173\pi$
$379$	−1.42429e10			−0.690306			−0.345153	+	0.938546i	$0.612173\pi$
$380$		0			0
$381$	−3.53631e10	−	2.72014e8i	−1.67822	−	0.0129090i
$382$		0			0
$383$	1.08013e10	−	6.23611e9i	0.501972	−	0.289814i	−0.227556	−	0.973765i	$-0.573073\pi$
$383$	1.08013e10	−	6.23611e9i	0.501972	−	0.289814i	0.729528	+	0.683951i	$0.239740\pi$
$384$		0			0
$385$	2.88339e8	−	4.99418e8i	0.0131238	−	0.0227311i
$386$		0			0
$387$	1.12092e10	−	1.87429e10i	0.499723	−	0.835590i
$388$		0			0
$389$	1.28379e10	+	7.41199e9i	0.560657	+	0.323695i	0.753409	−	0.657552i	$-0.228408\pi$
$389$	1.28379e10	+	7.41199e9i	0.560657	+	0.323695i	−0.192752	+	0.981247i	$0.561741\pi$
$390$		0			0
$391$	−6.42897e8	−	1.11353e9i	−0.0275064	−	0.0476426i
$392$		0			0
$393$	−4.44069e8	+	2.51849e8i	−0.0186158	+	0.0105577i
$394$		0			0
$395$			1.68556e9i			0.0692399i
$396$		0			0
$397$	2.15583e10			0.867866			0.433933	−	0.900945i	$-0.357125\pi$
$397$	2.15583e10			0.867866			0.433933	+	0.900945i	$0.357125\pi$
$398$		0			0
$399$	−5.12108e9	+	8.71447e9i	−0.202055	+	0.343834i
$400$		0			0
$401$	3.62066e10	−	2.09039e10i	1.40026	−	0.808443i	0.405845	−	0.913942i	$-0.366977\pi$
$401$	3.62066e10	−	2.09039e10i	1.40026	−	0.808443i	0.994419	+	0.105499i	$0.0336439\pi$
$402$		0			0
$403$	−7.98499e8	+	1.38304e9i	−0.0302729	+	0.0524342i
$404$		0			0
$405$	1.12993e9	−	6.06809e8i	0.0419984	−	0.0225544i
$406$		0			0
$407$	1.49855e10	+	8.65188e9i	0.546127	+	0.315306i
$408$		0			0
$409$	1.63856e9	+	2.83807e9i	0.0585557	+	0.101421i	0.893817	−	0.448431i	$-0.148017\pi$
$409$	1.63856e9	+	2.83807e9i	0.0585557	+	0.101421i	−0.835262	+	0.549853i	$0.814684\pi$
$410$		0			0
$411$	−1.50618e10	−	8.85108e9i	−0.527848	−	0.310191i
$412$		0			0
$413$			1.49880e10i			0.515162i
$414$		0			0
$415$	6.73654e8			0.0227114
$416$		0			0
$417$	−5.27259e9	−	9.29681e9i	−0.174373	−	0.307461i
$418$		0			0
$419$	−4.18462e10	+	2.41599e10i	−1.35769	+	0.783861i	−0.989312	−	0.145816i	$-0.953419\pi$
$419$	−4.18462e10	+	2.41599e10i	−1.35769	+	0.783861i	−0.368375	+	0.929677i	$0.620086\pi$
$420$		0			0
$421$	−1.30068e10	+	2.25284e10i	−0.414039	+	0.717137i	−0.995327	−	0.0965612i	$-0.969216\pi$
$421$	−1.30068e10	+	2.25284e10i	−0.414039	+	0.717137i	0.581288	+	0.813698i	$0.302549\pi$
$422$		0			0
$423$	1.92394e10	+	1.15061e10i	0.600939	+	0.359390i
$424$		0			0
$425$	1.69494e10	+	9.78574e9i	0.519516	+	0.299943i
$426$		0			0
$427$	−3.67674e9	−	6.36830e9i	−0.110599	−	0.191563i
$428$		0			0
$429$	5.53102e8	−	7.19057e10i	0.0163296	−	2.12292i
$430$		0			0
$431$			1.95435e10i			0.566360i	0.959067	+	0.283180i	$0.0913895\pi$
$431$			1.95435e10i			0.566360i	−0.959067	+	0.283180i	$0.908611\pi$
$432$		0			0
$433$	−1.65790e10			−0.471637			−0.235819	−	0.971797i	$-0.575777\pi$
$433$	−1.65790e10			−0.471637			−0.235819	+	0.971797i	$0.575777\pi$
$434$		0			0
$435$	6.03729e8	+	4.64391e6i	0.0168611	+	0.000129696i
$436$		0			0
$437$	3.04915e9	−	1.76043e9i	0.0836089	−	0.0482716i
$438$		0			0
$439$	−1.75798e10	+	3.04491e10i	−0.473321	+	0.819817i	−0.999534	−	0.0305365i	$-0.990278\pi$
$439$	−1.75798e10	+	3.04491e10i	−0.473321	+	0.819817i	0.526212	+	0.850353i	$0.323612\pi$
$440$		0			0
$441$	−2.62933e9	−	4.72037e9i	−0.0695169	−	0.124802i
$442$		0			0
$443$	5.98749e10	+	3.45688e10i	1.55464	+	0.897572i	0.997754	+	0.0669831i	$0.0213373\pi$
$443$	5.98749e10	+	3.45688e10i	1.55464	+	0.897572i	0.556886	+	0.830589i	$0.311996\pi$
$444$		0			0
$445$	−9.10372e7	−	1.57681e8i	−0.00232156	−	0.00402105i
$446$		0			0
$447$	−3.11432e10	+	1.76626e10i	−0.780070	+	0.442408i
$448$		0			0
$449$			2.87299e10i			0.706886i	0.935456	+	0.353443i	$0.114989\pi$
$449$			2.87299e10i			0.706886i	−0.935456	+	0.353443i	$0.885011\pi$
$450$		0			0
$451$	1.94254e10			0.469530
$452$		0			0
$453$	1.21926e10	−	2.07480e10i	0.289537	−	0.492702i
$454$		0			0
$455$	9.74658e8	−	5.62719e8i	0.0227408	−	0.0131294i
$456$		0			0
$457$	−1.26954e10	+	2.19890e10i	−0.291058	+	0.504128i	−0.974060	−	0.226289i	$-0.927341\pi$
$457$	−1.26954e10	+	2.19890e10i	−0.291058	+	0.504128i	0.683002	+	0.730416i	$0.260674\pi$
$458$		0			0
$459$	−6.15776e8	+	2.66803e10i	−0.0138731	+	0.601091i
$460$		0			0
$461$	3.71520e10	+	2.14497e10i	0.822580	+	0.474917i	0.851305	−	0.524671i	$-0.175812\pi$
$461$	3.71520e10	+	2.14497e10i	0.822580	+	0.474917i	−0.0287256	+	0.999587i	$0.509145\pi$
$462$		0			0
$463$	4.08461e9	+	7.07475e9i	0.0888846	+	0.153953i	0.907040	−	0.421045i	$-0.138336\pi$
$463$	4.08461e9	+	7.07475e9i	0.0888846	+	0.153953i	−0.818155	+	0.574997i	$0.805003\pi$
$464$		0			0
$465$	−7.98313e7	−	4.69130e7i	−0.00170750	−	0.00100342i
$466$		0			0
$467$			2.11691e10i			0.445077i	0.974924	+	0.222539i	$0.0714343\pi$
$467$			2.11691e10i			0.445077i	−0.974924	+	0.222539i	$0.928566\pi$
$468$		0			0
$469$	−2.08148e10			−0.430211
$470$		0			0
$471$	2.23853e10	+	3.94706e10i	0.454862	+	0.802029i
$472$		0			0
$473$	6.14816e10	−	3.54964e10i	1.22829	−	0.709153i
$474$		0			0
$475$	−2.67960e10	+	4.64120e10i	−0.526375	+	0.911709i
$476$		0			0
$477$	3.92594e8	−	2.55180e10i	0.00758350	−	0.492916i
$478$		0			0
$479$	5.49311e10	+	3.17145e10i	1.04346	+	0.602443i	0.920812	−	0.390007i	$-0.127527\pi$
$479$	5.49311e10	+	3.17145e10i	1.04346	+	0.602443i	0.122650	+	0.992450i	$0.460861\pi$
$480$		0			0
$481$	1.68849e10	+	2.92455e10i	0.315441	+	0.546360i
$482$		0			0
$483$	−1.44769e7	+	1.88207e9i	−0.000266004	+	0.0345817i
$484$		0			0
$485$			4.24855e9i			0.0767846i
$486$		0			0
$487$	8.23063e10			1.46325			0.731623	−	0.681709i	$-0.238763\pi$
$487$	8.23063e10			1.46325			0.731623	+	0.681709i	$0.238763\pi$
$488$		0			0
$489$	−5.59809e10	−	4.30607e8i	−0.979048	−	0.00753088i
$490$		0			0
$491$	1.15415e10	−	6.66350e9i	0.198581	−	0.114651i	−0.397413	−	0.917640i	$-0.630092\pi$
$491$	1.15415e10	−	6.66350e9i	0.198581	−	0.114651i	0.595993	+	0.802989i	$0.296758\pi$
$492$		0			0
$493$	−6.28135e9	+	1.08796e10i	−0.106332	+	0.184173i
$494$		0			0
$495$	4.16878e9	+	6.41367e7i	0.0694365	+	0.00106828i
$496$		0			0
$497$	1.07093e10	+	6.18302e9i	0.175524	+	0.101339i
$498$		0			0
$499$	2.89749e10	+	5.01860e10i	0.467326	+	0.809432i	0.999303	−	0.0373263i	$-0.0118841\pi$
$499$	2.89749e10	+	5.01860e10i	0.467326	+	0.809432i	−0.531977	+	0.846759i	$0.678551\pi$
$500$		0			0
$501$	1.72294e10	−	9.77148e9i	0.273476	−	0.155099i
$502$		0			0
$503$		−	1.14304e11i		−	1.78563i	−0.450427	−	0.892813i	$-0.648728\pi$
$503$		−	1.14304e11i		−	1.78563i	0.450427	−	0.892813i	$-0.351272\pi$
$504$		0			0
$505$	−1.16650e9			−0.0179358
$506$		0			0
$507$	3.76238e10	−	6.40239e10i	0.569417	−	0.968970i
$508$		0			0
$509$	5.96751e10	−	3.44534e10i	0.889041	−	0.513288i	0.0154126	−	0.999881i	$-0.495094\pi$
$509$	5.96751e10	−	3.44534e10i	0.889041	−	0.513288i	0.873629	+	0.486593i	$0.161760\pi$
$510$		0			0
$511$	−7.15102e9	+	1.23859e10i	−0.104878	+	0.181654i
$512$		0			0
$513$	−7.30579e10	−	1.68616e9i	−1.05487	−	0.0243461i
$514$		0			0
$515$	2.83627e8	+	1.63752e8i	0.00403198	+	0.00232787i
$516$		0			0
$517$	3.64367e10	+	6.31102e10i	0.510008	+	0.883359i
$518$		0			0
$519$	−5.08189e10	−	2.98639e10i	−0.700416	−	0.411601i
$520$		0			0
$521$		−	1.14590e11i		−	1.55523i	−0.628740	−	0.777615i	$-0.716429\pi$
$521$		−	1.14590e11i		−	1.55523i	0.628740	−	0.777615i	$-0.283571\pi$
$522$		0			0
$523$	−9.31461e10			−1.24497			−0.622483	−	0.782633i	$-0.713876\pi$
$523$	−9.31461e10			−1.24497			−0.622483	+	0.782633i	$0.713876\pi$
$524$		0			0
$525$	−1.41329e10	−	2.49197e10i	−0.186035	−	0.328024i
$526$		0			0
$527$	1.66858e9	−	9.63355e8i	0.0216324	−	0.0124895i
$528$		0			0
$529$	−3.88277e10	+	6.72515e10i	−0.495814	+	0.858775i
$530$		0			0
$531$	−9.46653e10	+	5.27302e10i	−1.19073	+	0.663257i
$532$		0			0
$533$	3.28313e10	+	1.89552e10i	0.406799	+	0.234865i
$534$		0			0
$535$	2.56855e9	+	4.44886e9i	0.0313526	+	0.0543043i
$536$		0			0
$537$	3.04732e8	−	3.96165e10i	0.00366455	−	0.476408i
$538$		0			0
$539$		−	1.75646e10i		−	0.208105i
$540$		0			0
$541$	−1.29961e11			−1.51714			−0.758570	−	0.651592i	$-0.774102\pi$
$541$	−1.29961e11			−1.51714			−0.758570	+	0.651592i	$0.774102\pi$
$542$		0			0
$543$	6.06186e10	+	4.66281e8i	0.697279	+	0.00536350i
$544$		0			0
$545$	4.03073e9	−	2.32715e9i	0.0456876	−	0.0263777i
$546$		0			0
$547$	−8.30098e10	+	1.43777e11i	−0.927214	+	1.60598i	−0.139253	+	0.990257i	$0.544470\pi$
$547$	−8.30098e10	+	1.43777e11i	−0.927214	+	1.60598i	−0.787961	+	0.615725i	$0.788863\pi$
$548$		0			0
$549$	2.72872e10	−	4.56272e10i	0.300379	−	0.502267i
$550$		0			0
$551$	−2.97913e10	−	1.72000e10i	−0.323209	−	0.186605i
$552$		0			0
$553$	2.56696e10	+	4.44611e10i	0.274485	+	0.475422i
$554$		0			0
$555$	−1.70316e9	+	9.65928e8i	−0.0179508	+	0.0101806i
$556$		0			0
$557$		−	6.41134e10i		−	0.666083i	−0.942912	−	0.333041i	$-0.891925\pi$
$557$		−	6.41134e10i		−	0.666083i	0.942912	−	0.333041i	$-0.108075\pi$
$558$		0			0
$559$	1.38549e11			1.41891
$560$		0			0
$561$	−4.39535e10	+	7.47951e10i	−0.443754	+	0.755130i
$562$		0			0
$563$	−6.03352e10	+	3.48345e10i	−0.600533	+	0.346718i	−0.769251	−	0.638946i	$-0.779371\pi$
$563$	−6.03352e10	+	3.48345e10i	−0.600533	+	0.346718i	0.168718	+	0.985664i	$0.446037\pi$
$564$		0			0
$565$	3.85562e9	−	6.67812e9i	0.0378355	−	0.0655331i
$566$		0			0
$567$	2.05638e10	−	3.32140e10i	0.198962	−	0.321358i
$568$		0			0
$569$	1.80139e11	+	1.04003e11i	1.71854	+	0.992199i	0.921602	+	0.388137i	$0.126881\pi$
$569$	1.80139e11	+	1.04003e11i	1.71854	+	0.992199i	0.796937	+	0.604062i	$0.206452\pi$
$570$		0			0
$571$	6.25037e10	+	1.08260e11i	0.587978	+	1.01841i	0.994497	+	0.104766i	$0.0334093\pi$
$571$	6.25037e10	+	1.08260e11i	0.587978	+	1.01841i	−0.406519	+	0.913643i	$0.633257\pi$
$572$		0			0
$573$	1.22807e11	+	7.21676e10i	1.13921	+	0.669458i
$574$		0			0
$575$			9.97911e9i			0.0912894i
$576$		0			0
$577$	2.21184e10			0.199550			0.0997748	−	0.995010i	$-0.468188\pi$
$577$	2.21184e10			0.199550			0.0997748	+	0.995010i	$0.468188\pi$
$578$		0			0
$579$	−4.39275e10	−	7.74545e10i	−0.390861	−	0.689179i
$580$		0			0
$581$	1.77694e10	−	1.02592e10i	0.155944	−	0.0900341i
$582$		0			0
$583$	4.14810e10	−	7.18472e10i	0.359066	−	0.621921i
$584$		0			0
$585$	6.98317e9	+	4.17627e9i	0.0596251	+	0.0356587i
$586$		0			0
$587$	8.65107e10	+	4.99470e10i	0.728647	+	0.420685i	0.817927	−	0.575322i	$-0.195123\pi$
$587$	8.65107e10	+	4.99470e10i	0.728647	+	0.420685i	−0.0892799	+	0.996007i	$0.528457\pi$
$588$		0			0
$589$	2.63793e9	+	4.56902e9i	0.0219180	+	0.0379631i
$590$		0			0
$591$	−7.91256e8	+	1.02867e11i	−0.00648585	+	0.843190i
$592$		0			0
$593$			1.45584e11i			1.17732i	0.808380	+	0.588661i	$0.200345\pi$
$593$			1.45584e11i			1.17732i	−0.808380	+	0.588661i	$0.799655\pi$
$594$		0			0
$595$	−1.35779e9			−0.0108334
$596$		0			0
$597$	4.97174e10	+	3.82428e8i	0.391391	+	0.00301060i
$598$		0			0
$599$	7.98073e10	−	4.60768e10i	0.619920	−	0.357911i	−0.156918	−	0.987612i	$-0.550156\pi$
$599$	7.98073e10	−	4.60768e10i	0.619920	−	0.357911i	0.776838	+	0.629701i	$0.216823\pi$
$600$		0			0
$601$	7.53661e10	−	1.30538e11i	0.577667	−	1.00055i	−0.418079	−	0.908411i	$-0.637296\pi$
$601$	7.53661e10	−	1.30538e11i	0.577667	−	1.00055i	0.995746	−	0.0921386i	$-0.0293703\pi$
$602$		0			0
$603$	−7.32299e10	−	1.31468e11i	−0.553885	−	0.994376i
$604$		0			0
$605$	6.20632e9	+	3.58322e9i	0.0463247	+	0.0267456i
$606$		0			0
$607$	8.26384e10	+	1.43134e11i	0.608733	+	1.05436i	0.991449	+	0.130491i	$0.0416554\pi$
$607$	8.26384e10	+	1.43134e11i	0.608733	+	1.05436i	−0.382716	+	0.923866i	$0.625011\pi$
$608$		0			0
$609$	1.59956e10	−	9.07176e9i	0.116287	−	0.0659511i
$610$		0			0
$611$			1.42219e11i			1.02045i
$612$		0			0
$613$	1.23120e11			0.871937			0.435969	−	0.899962i	$-0.356406\pi$
$613$	1.23120e11			0.871937			0.435969	+	0.899962i	$0.356406\pi$
$614$		0			0
$615$	−1.11364e9	+	1.89507e9i	−0.00778478	+	0.0132473i
$616$		0			0
$617$	7.98773e10	−	4.61172e10i	0.551166	−	0.318216i	−0.198426	−	0.980116i	$-0.563583\pi$
$617$	7.98773e10	−	4.61172e10i	0.551166	−	0.318216i	0.749592	+	0.661900i	$0.230250\pi$
$618$		0			0
$619$	−1.05942e11	+	1.83497e11i	−0.721617	+	1.24988i	0.238735	+	0.971085i	$0.423267\pi$
$619$	−1.05942e11	+	1.83497e11i	−0.721617	+	1.24988i	−0.960352	+	0.278792i	$0.910066\pi$
$620$		0			0
$621$	−1.19382e10	+	6.52997e9i	−0.0802735	+	0.0439081i
$622$		0			0
$623$	−4.80269e9	−	2.77283e9i	−0.0318810	−	0.0184065i
$624$		0			0
$625$	−7.57742e10	−	1.31245e11i	−0.496594	−	0.860126i
$626$		0			0
$627$	−2.04809e11	−	1.20357e11i	−1.32519	−	0.778753i
$628$		0			0
$629$		−	4.07419e10i		−	0.260278i
$630$		0			0
$631$	−1.18627e11			−0.748285			−0.374142	−	0.927371i	$-0.622063\pi$
$631$	−1.18627e11			−0.748285			−0.374142	+	0.927371i	$0.622063\pi$
$632$		0			0
$633$	−3.97065e10	−	7.00118e10i	−0.247313	−	0.436070i
$634$		0			0
$635$	1.12654e10	−	6.50409e9i	0.0692871	−	0.0400029i
$636$		0			0
$637$	1.71394e10	−	2.96863e10i	0.104097	−	0.180301i
$638$		0			0
$639$	−1.37532e9	+	8.93935e10i	−0.00824898	+	0.536170i
$640$		0			0
$641$	−5.98456e10	−	3.45519e10i	−0.354487	−	0.204663i	0.312173	−	0.950025i	$-0.398943\pi$
$641$	−5.98456e10	−	3.45519e10i	−0.354487	−	0.204663i	−0.666660	+	0.745362i	$0.732277\pi$
$642$		0			0
$643$	−5.81290e10	−	1.00682e11i	−0.340055	−	0.588992i	0.644388	−	0.764699i	$-0.277112\pi$
$643$	−5.81290e10	−	1.00682e11i	−0.340055	−	0.588992i	−0.984443	+	0.175707i	$0.943779\pi$
$644$		0			0
$645$	−6.17896e7	+	8.03292e9i	−0.000357007	+	0.0464125i
$646$		0			0
$647$			2.51751e11i			1.43666i	0.695701	+	0.718331i	$0.255094\pi$
$647$			2.51751e11i			1.43666i	−0.695701	+	0.718331i	$0.744906\pi$
$648$		0			0
$649$	−3.52251e11			−1.98552
$650$		0			0
$651$	−2.82020e9	−	2.16931e7i	−0.0157020	−	0.000120781i
$652$		0			0
$653$	5.64648e10	−	3.25999e10i	0.310545	−	0.179293i	−0.336625	−	0.941639i	$-0.609286\pi$
$653$	5.64648e10	−	3.25999e10i	0.310545	−	0.179293i	0.647170	+	0.762345i	$0.275952\pi$
$654$		0			0
$655$	9.38928e7	−	1.62627e8i	0.000510114	−	0.000883543i
$656$		0			0
$657$	−1.03389e11	−	1.59064e9i	−0.554896	−	0.00853708i
$658$		0			0
$659$	1.86632e11	+	1.07752e11i	0.989564	+	0.571325i	0.905144	−	0.425105i	$-0.139763\pi$
$659$	1.86632e11	+	1.07752e11i	0.989564	+	0.571325i	0.0844198	+	0.996430i	$0.473096\pi$
$660$		0			0
$661$	9.87126e10	+	1.70975e11i	0.517091	+	0.895627i	0.999803	+	0.0198482i	$0.00631828\pi$
$661$	9.87126e10	+	1.70975e11i	0.517091	+	0.895627i	−0.482712	+	0.875779i	$0.660348\pi$
$662$		0			0
$663$	−1.47272e11	+	8.35235e10i	−0.762193	+	0.432270i
$664$		0			0
$665$		−	3.71800e9i		−	0.0190118i
$666$		0			0
$667$	−6.40547e9			−0.0323629
$668$		0			0
$669$	1.74085e11	−	2.96238e11i	0.869075	−	1.47889i
$670$		0			0
$671$	1.49669e11	−	8.64114e10i	0.738315	−	0.426266i
$672$		0			0
$673$	1.38112e11	−	2.39217e11i	0.673241	−	1.16609i	−0.303739	−	0.952755i	$-0.598235\pi$
$673$	1.38112e11	−	2.39217e11i	0.673241	−	1.16609i	0.976980	−	0.213332i	$-0.0684316\pi$
$674$		0			0
$675$	1.07672e11	−	1.76936e11i	0.518668	−	0.852317i
$676$		0			0
$677$	−2.90594e11	−	1.67775e11i	−1.38335	−	0.798677i	−0.390795	−	0.920478i	$-0.627800\pi$
$677$	−2.90594e11	−	1.67775e11i	−1.38335	−	0.798677i	−0.992555	+	0.121800i	$0.961133\pi$
$678$		0			0
$679$	6.47017e10	+	1.12067e11i	0.304394	+	0.527226i
$680$		0			0
$681$	−1.92243e11	−	1.12972e11i	−0.893846	−	0.525270i
$682$		0			0
$683$			2.06542e11i			0.949130i	0.880220	+	0.474565i	$0.157395\pi$
$683$			2.06542e11i			0.949130i	−0.880220	+	0.474565i	$0.842605\pi$
$684$		0			0
$685$	6.42606e9			0.0291865
$686$		0			0
$687$	−1.28146e10	−	2.25951e10i	−0.0575277	−	0.101435i
$688$		0			0
$689$	1.40216e11	−	8.09538e10i	0.622187	−	0.359220i
$690$		0			0
$691$	−1.86326e11	+	3.22726e11i	−0.817262	+	1.41554i	0.0904310	+	0.995903i	$0.471176\pi$
$691$	−1.86326e11	+	3.22726e11i	−0.817262	+	1.41554i	−0.907693	+	0.419636i	$0.862158\pi$
$692$		0			0
$693$	1.10939e11	−	6.17950e10i	0.481007	−	0.267930i
$694$		0			0
$695$	3.40468e9	+	1.96569e9i	0.0145927	+	0.00842512i
$696$		0			0
$697$	−2.28686e10	−	3.96096e10i	−0.0968966	−	0.167830i
$698$		0			0
$699$	−6.87163e8	+	8.93343e10i	−0.00287840	+	0.374205i
$700$		0			0
$701$		−	3.23542e11i		−	1.33986i	−0.742425	−	0.669929i	$-0.766324\pi$
$701$		−	3.23542e11i		−	1.33986i	0.742425	−	0.669929i	$-0.233676\pi$
$702$		0			0
$703$	1.11562e11			0.456768
$704$		0			0
$705$	−8.24571e9	−	6.34263e7i	−0.0333789	−	0.000256752i
$706$		0			0
$707$	−3.07696e10	+	1.77648e10i	−0.123153	+	0.0711023i
$708$		0			0
$709$	1.51845e11	−	2.63003e11i	0.600919	−	1.04082i	−0.391763	−	0.920066i	$-0.628135\pi$
$709$	1.51845e11	−	2.63003e11i	0.600919	−	1.04082i	0.992682	−	0.120756i	$-0.0385318\pi$
$710$		0			0
$711$	−1.90509e11	+	3.18552e11i	−0.745483	+	1.24653i
$712$		0			0
$713$	8.50775e8	+	4.91195e8i	0.00329198	+	0.00190062i
$714$		0			0
$715$	1.32251e10	+	2.29066e10i	0.0506030	+	0.0876469i
$716$		0			0
$717$	1.77245e11	−	1.00523e11i	0.670651	−	0.380353i
$718$		0			0
$719$		−	1.75821e11i		−	0.657892i	−0.944349	−	0.328946i	$-0.893307\pi$
$719$		−	1.75821e11i		−	0.657892i	0.944349	−	0.328946i	$-0.106693\pi$
$720$		0			0
$721$	9.97520e9			0.0369131
$722$		0			0
$723$	−3.14926e10	+	5.35906e10i	−0.115254	+	0.196126i
$724$		0			0
$725$	8.44372e10	−	4.87498e10i	0.305620	−	0.176450i
$726$		0			0
$727$	−1.82762e11	+	3.16552e11i	−0.654255	+	1.13320i	0.327825	+	0.944739i	$0.393684\pi$
$727$	−1.82762e11	+	3.16552e11i	−0.654255	+	1.13320i	−0.982080	+	0.188465i	$0.939649\pi$
$728$		0			0
$729$	2.82129e11	+	1.30299e10i	0.998935	+	0.0461350i
$730$		0			0
$731$	−1.44759e11	−	8.35766e10i	−0.506962	−	0.292695i
$732$		0			0
$733$	−6.67553e10	−	1.15624e11i	−0.231244	−	0.400526i	0.726931	−	0.686711i	$-0.240946\pi$
$733$	−6.67553e10	−	1.15624e11i	−0.231244	−	0.400526i	−0.958174	+	0.286185i	$0.907613\pi$
$734$		0			0
$735$	1.71354e9	+	1.00697e9i	0.00587145	+	0.00345037i
$736$		0			0
$737$		−	4.89194e11i		−	1.65810i
$738$		0			0
$739$	−2.92712e11			−0.981439			−0.490720	−	0.871318i	$-0.663266\pi$
$739$	−2.92712e11			−0.981439			−0.490720	+	0.871318i	$0.663266\pi$
$740$		0			0
$741$	−2.28710e11	−	4.03269e11i	−0.758599	−	1.33759i
$742$		0			0
$743$	−3.10312e11	+	1.79159e11i	−1.01822	+	0.587871i	−0.913589	−	0.406639i	$-0.866701\pi$
$743$	−3.10312e11	+	1.79159e11i	−1.01822	+	0.587871i	−0.104634	+	0.994511i	$0.533367\pi$
$744$		0			0
$745$	6.58484e9	−	1.14053e10i	0.0213757	−	0.0370238i
$746$		0			0
$747$	1.27313e11	+	7.61392e10i	0.408875	+	0.244527i
$748$		0			0
$749$	1.35504e11	+	7.82335e10i	0.430553	+	0.248580i
$750$		0			0
$751$	3.55353e10	+	6.15489e10i	0.111712	+	0.193491i	0.916461	−	0.400125i	$-0.131033\pi$
$751$	3.55353e10	+	6.15489e10i	0.111712	+	0.193491i	−0.804749	+	0.593616i	$0.797700\pi$
$752$		0			0
$753$	3.36805e8	−	4.37862e10i	0.00104761	−	0.136194i
$754$		0			0
$755$			8.85209e9i			0.0272432i
$756$		0			0
$757$	−1.85074e11			−0.563590			−0.281795	−	0.959475i	$-0.590930\pi$
$757$	−1.85074e11			−0.563590			−0.281795	+	0.959475i	$0.590930\pi$
$758$		0			0
$759$	−4.42327e10	−	3.40240e8i	−0.133283	−	0.00102522i
$760$		0			0
$761$	−3.12732e11	+	1.80556e11i	−0.932467	+	0.538360i	−0.887591	−	0.460632i	$-0.847623\pi$
$761$	−3.12732e11	+	1.80556e11i	−0.932467	+	0.538360i	−0.0448762	+	0.998993i	$0.514289\pi$
$762$		0			0
$763$	7.08807e10	−	1.22769e11i	0.209137	−	0.362235i
$764$		0			0
$765$	−4.77693e9	−	8.57591e9i	−0.0139477	−	0.0250400i
$766$		0			0
$767$	−5.95349e11	−	3.43725e11i	−1.72024	−	0.993183i
$768$		0			0
$769$	−3.09106e11	−	5.35388e11i	−0.883899	−	1.53096i	−0.846970	−	0.531641i	$-0.821576\pi$
$769$	−3.09106e11	−	5.35388e11i	−0.883899	−	1.53096i	−0.0369292	−	0.999318i	$-0.511758\pi$
$770$		0			0
$771$	−5.40662e11	+	3.06631e11i	−1.53006	+	0.867757i
$772$		0			0
$773$		−	7.02996e11i		−	1.96895i	−0.175522	−	0.984475i	$-0.556161\pi$
$773$		−	7.02996e11i		−	1.96895i	0.175522	−	0.984475i	$-0.443839\pi$
$774$		0			0
$775$	−1.49533e10			−0.0414505
$776$		0			0
$777$	−3.02150e10	+	5.14164e10i	−0.0828969	+	0.141065i
$778$		0			0
$779$	1.08462e11	−	6.26204e10i	0.294528	−	0.170046i
$780$		0			0
$781$	−1.45315e11	+	2.51692e11i	−0.390575	+	0.676497i
$782$		0			0
$783$	1.13573e11	+	6.91136e10i	0.302154	+	0.183872i
$784$		0			0
$785$	−1.44549e10	−	8.34555e9i	−0.0380660	−	0.0219774i
$786$		0			0
$787$	−2.48650e11	−	4.30675e11i	−0.648172	−	1.12267i	−0.983559	−	0.180586i	$-0.942201\pi$
$787$	−2.48650e11	−	4.30675e11i	−0.648172	−	1.12267i	0.335388	−	0.942080i	$-0.391133\pi$
$788$		0			0
$789$	−6.50072e11	−	3.82016e11i	−1.67746	−	0.985765i
$790$		0			0
$791$		−	2.34870e11i		−	0.599960i
$792$		0			0
$793$	3.37279e11			0.852897
$794$		0			0
$795$	4.63109e9	+	8.16570e9i	0.0115935	+	0.0204421i
$796$		0			0
$797$	−4.48300e11	+	2.58826e11i	−1.11106	+	0.641468i	−0.939103	−	0.343637i	$-0.888341\pi$
$797$	−4.48300e11	+	2.58826e11i	−1.11106	+	0.641468i	−0.171953	+	0.985105i	$0.555008\pi$
$798$		0			0
$799$	8.57905e10	−	1.48593e11i	0.210500	−	0.364597i
$800$		0			0
$801$	6.16775e8	−	4.00894e10i	0.00149829	−	0.0973866i
$802$		0			0
$803$	−2.91096e11	−	1.68065e11i	−0.700124	−	0.404217i
$804$		0			0
$805$	−3.46156e8	−	5.99559e8i	−0.000824305	−	0.00142774i
$806$		0			0
$807$	9.92472e8	−	1.29026e11i	0.00234004	−	0.304216i
$808$		0			0
$809$			6.04421e11i			1.41106i	0.708680	+	0.705530i	$0.249291\pi$
$809$			6.04421e11i			1.41106i	−0.708680	+	0.705530i	$0.750709\pi$
$810$		0			0
$811$	−7.50847e10			−0.173567			−0.0867837	−	0.996227i	$-0.527659\pi$
$811$	−7.50847e10			−0.173567			−0.0867837	+	0.996227i	$0.527659\pi$
$812$		0			0
$813$	2.52974e11	+	1.94588e9i	0.579046	+	0.00445405i
$814$		0			0
$815$	1.78335e10	−	1.02962e10i	0.0404209	−	0.0233370i
$816$		0			0
$817$	2.28855e11	−	3.96389e11i	0.513656	−	0.889679i
$818$		0			0
$819$	2.47800e11	+	3.81241e9i	0.550765	+	0.00847351i
$820$		0			0
$821$	2.21577e11	+	1.27928e11i	0.487700	+	0.281574i	0.723620	−	0.690199i	$-0.242477\pi$
$821$	2.21577e11	+	1.27928e11i	0.487700	+	0.281574i	−0.235920	+	0.971772i	$0.575810\pi$
$822$		0			0
$823$	−2.78252e11	−	4.81947e11i	−0.606512	−	1.05051i	−0.991810	−	0.127718i	$-0.959235\pi$
$823$	−2.78252e11	−	4.81947e11i	−0.606512	−	1.05051i	0.385298	−	0.922792i	$-0.374099\pi$
$824$		0			0
$825$	5.85667e11	−	3.32155e11i	1.26426	−	0.717010i
$826$		0			0
$827$		−	1.66958e10i		−	0.0356932i	−0.999841	−	0.0178466i	$-0.994319\pi$
$827$		−	1.66958e10i		−	0.0356932i	0.999841	−	0.0178466i	$-0.00568104\pi$
$828$		0			0
$829$	6.32590e11			1.33938			0.669690	−	0.742640i	$-0.266427\pi$
$829$	6.32590e11			1.33938			0.669690	+	0.742640i	$0.266427\pi$
$830$		0			0
$831$	−1.47403e11	+	2.50833e11i	−0.309102	+	0.525994i
$832$		0			0
$833$	−3.58153e10	+	2.06780e10i	−0.0743856	+	0.0429465i
$834$		0			0
$835$	−3.64294e9	+	6.30976e9i	−0.00749387	+	0.0129798i
$836$		0			0
$837$	−9.78490e9	−	1.78889e10i	−0.0199368	−	0.0364487i
$838$		0			0
$839$	6.32029e11	+	3.64902e11i	1.27553	+	0.736425i	0.976022	−	0.217670i	$-0.0698456\pi$
$839$	6.32029e11	+	3.64902e11i	1.27553	+	0.736425i	0.299504	+	0.954095i	$0.403179\pi$
$840$		0			0
$841$	−2.18831e11	−	3.79027e11i	−0.437447	−	0.757680i
$842$		0			0
$843$	5.06173e11	+	2.97454e11i	1.00228	+	0.588991i
$844$		0			0
$845$			2.73156e10i			0.0535777i
$846$		0			0
$847$	2.18277e11			0.424106
$848$		0			0
$849$	9.56663e10	+	1.68682e11i	0.184131	+	0.324667i
$850$		0			0
$851$	1.79903e10	−	1.03867e10i	0.0343021	−	0.0198043i
$852$		0			0
$853$	−3.18310e11	+	5.51329e11i	−0.601248	+	1.04139i	0.391384	+	0.920227i	$0.371996\pi$
$853$	−3.18310e11	+	5.51329e11i	−0.601248	+	1.04139i	−0.992632	+	0.121165i	$0.961337\pi$
$854$		0			0
$855$	2.34832e10	−	1.30805e10i	0.0439432	−	0.0244772i
$856$		0			0
$857$	6.55130e11	+	3.78240e11i	1.21452	+	0.701203i	0.963740	−	0.266841i	$-0.0859800\pi$
$857$	6.55130e11	+	3.78240e11i	1.21452	+	0.701203i	0.250779	+	0.968044i	$0.419313\pi$
$858$		0			0
$859$	−1.14705e11	−	1.98674e11i	−0.210673	−	0.364895i	0.741253	−	0.671226i	$-0.234232\pi$
$859$	−1.14705e11	−	1.98674e11i	−0.210673	−	0.364895i	−0.951925	+	0.306331i	$0.900899\pi$
$860$		0			0
$861$	−5.14962e8	+	6.69473e10i	−0.000937049	+	0.121821i
$862$		0			0
$863$			2.73495e10i			0.0493067i	0.999696	+	0.0246534i	$0.00784820\pi$
$863$			2.73495e10i			0.0493067i	−0.999696	+	0.0246534i	$0.992152\pi$
$864$		0			0
$865$	2.16818e10			0.0387284
$866$		0			0
$867$	−3.60763e11	−	2.77501e9i	−0.638478	−	0.00491120i
$868$		0			0
$869$	−1.04493e12	+	6.03292e11i	−1.83235	+	1.05791i
$870$		0			0
$871$	4.77353e11	−	8.26800e11i	0.829406	−	1.43657i
$872$		0			0
$873$	−4.80189e11	+	8.02929e11i	−0.826715	+	1.38236i
$874$		0			0
$875$	1.82730e10	+	1.05499e10i	0.0311728	+	0.0179977i
$876$		0			0
$877$	4.12222e11	+	7.13989e11i	0.696839	+	1.20696i	0.969557	+	0.244867i	$0.0787443\pi$
$877$	4.12222e11	+	7.13989e11i	0.696839	+	1.20696i	−0.272717	+	0.962094i	$0.587922\pi$
$878$		0			0
$879$	3.00132e11	−	1.70217e11i	0.502756	−	0.285133i
$880$		0			0
$881$			8.33298e10i			0.138324i	0.997605	+	0.0691619i	$0.0220325\pi$
$881$			8.33298e10i			0.138324i	−0.997605	+	0.0691619i	$0.977968\pi$
$882$		0			0
$883$	5.16077e11			0.848930			0.424465	−	0.905444i	$-0.360462\pi$
$883$	5.16077e11			0.848930			0.424465	+	0.905444i	$0.360462\pi$
$884$		0			0
$885$	2.01943e10	−	3.43645e10i	0.0329198	−	0.0560191i
$886$		0			0
$887$	−8.42114e11	+	4.86195e11i	−1.36043	+	0.785445i	−0.989681	−	0.143287i	$-0.954233\pi$
$887$	−8.42114e11	+	4.86195e11i	−1.36043	+	0.785445i	−0.370750	+	0.928733i	$0.620899\pi$
$888$		0			0
$889$	1.98103e11	−	3.43124e11i	0.317164	−	0.549344i
$890$		0			0
$891$	7.80603e11	+	4.83294e11i	1.23857	+	0.766833i
$892$		0			0
$893$	4.06889e11	+	2.34917e11i	0.639838	+	0.369411i
$894$		0			0
$895$	7.28639e9	+	1.26204e10i	0.0113559	+	0.0196689i
$896$		0			0
$897$	−7.44268e10	−	4.37371e10i	−0.114963	−	0.0675585i
$898$		0			0
$899$		−	9.59833e9i		−	0.0146946i
$900$		0			0
$901$	−1.95335e11			−0.296401
$902$		0			0
$903$	1.20704e11	+	2.12830e11i	0.181540	+	0.320097i
$904$		0			0
$905$	−1.93109e10	+	1.11492e10i	−0.0287878	+	0.0166207i
$906$		0			0
$907$	1.87671e11	−	3.25056e11i	0.277312	−	0.480318i	−0.693404	−	0.720549i	$-0.743890\pi$
$907$	1.87671e11	−	3.25056e11i	0.277312	−	0.480318i	0.970716	+	0.240231i	$0.0772232\pi$
$908$		0			0
$909$	−2.20456e11	−	1.31843e11i	−0.322899	−	0.193109i
$910$		0			0
$911$	−2.54080e11	−	1.46693e11i	−0.368890	−	0.212979i	0.304083	−	0.952645i	$-0.401650\pi$
$911$	−2.54080e11	−	1.46693e11i	−0.368890	−	0.212979i	−0.672974	+	0.739667i	$0.734983\pi$
$912$		0			0
$913$	2.41113e11	+	4.17619e11i	0.347006	+	0.601032i
$914$		0			0
$915$	−1.50419e8	+	1.95551e10i	−0.000214594	+	0.0278982i
$916$		0			0
$917$		−	5.71961e9i		−	0.00808890i
$918$		0			0
$919$	−5.98813e10			−0.0839517			−0.0419758	−	0.999119i	$-0.513365\pi$
$919$	−5.98813e10			−0.0839517			−0.0419758	+	0.999119i	$0.513365\pi$
$920$		0			0
$921$	9.74246e11	+	7.49394e9i	1.35404	+	0.0104153i
$922$		0			0
$923$	−4.91200e11	+	2.83594e11i	−0.676786	+	0.390742i
$924$		0			0
$925$	−1.58100e11	+	2.73837e11i	−0.215955	+	0.374046i
$926$		0			0
$927$	3.50943e10	+	6.30040e10i	0.0475246	+	0.0853197i
$928$		0			0
$929$	−4.30818e11	−	2.48733e11i	−0.578403	−	0.333941i	0.182095	−	0.983281i	$-0.441712\pi$
$929$	−4.30818e11	−	2.48733e11i	−0.578403	−	0.333941i	−0.760498	+	0.649340i	$0.775045\pi$
$930$		0			0
$931$	−5.66219e10	−	9.80720e10i	−0.0753678	−	0.130541i
$932$		0			0
$933$	−8.19443e11	+	4.64738e11i	−1.08141	+	0.613313i
$934$		0			0
$935$		−	3.19111e10i		−	0.0417538i
$936$		0			0
$937$	6.36197e11			0.825340			0.412670	−	0.910881i	$-0.364596\pi$
$937$	6.36197e11			0.825340			0.412670	+	0.910881i	$0.364596\pi$
$938$		0			0
$939$	−3.19839e11	+	5.44266e11i	−0.411404	+	0.700082i
$940$		0			0
$941$	1.77468e11	−	1.02461e11i	0.226340	−	0.130677i	−0.382543	−	0.923938i	$-0.624951\pi$
$941$	1.77468e11	−	1.02461e11i	0.226340	−	0.130677i	0.608882	+	0.793261i	$0.291618\pi$
$942$		0			0
$943$	1.16602e10	−	2.01961e10i	0.0147455	−	0.0255400i
$944$		0			0
$945$	−3.31553e8	+	1.43655e10i	−0.000415744	+	0.0180133i
$946$		0			0
$947$	−1.23127e12	−	7.10872e11i	−1.53092	−	0.883876i	−0.999320	−	0.0368804i	$-0.988258\pi$
$947$	−1.23127e12	−	7.10872e11i	−1.53092	−	0.883876i	−0.531599	−	0.846996i	$-0.678409\pi$
$948$		0			0
$949$	−3.27993e11	−	5.68101e11i	−0.404389	−	0.700423i
$950$		0			0
$951$	1.25541e12	+	7.37742e11i	1.53484	+	0.901951i
$952$		0			0
$953$		−	4.86939e11i		−	0.590341i	−0.955445	−	0.295171i	$-0.904624\pi$
$953$		−	4.86939e11i		−	0.590341i	0.955445	−	0.295171i	$-0.0953765\pi$
$954$		0			0
$955$	−5.23951e10			−0.0629908
$956$		0			0
$957$	2.13206e11	+	3.75933e11i	0.254186	+	0.448190i
$958$		0			0
$959$	1.69504e11	−	9.78631e10i	0.200404	−	0.115703i
$960$		0			0
$961$	4.25709e11	−	7.37350e11i	0.499137	−	0.864531i
$962$		0			0
$963$	−1.74019e10	+	1.13109e12i	−0.0202344	+	1.31520i
$964$		0			0
$965$	2.83654e10	+	1.63768e10i	0.0327099	+	0.0188851i
$966$		0			0
$967$	8.13848e11	+	1.40963e12i	0.930759	+	1.61212i	0.782027	+	0.623245i	$0.214186\pi$
$967$	8.13848e11	+	1.40963e12i	0.930759	+	1.61212i	0.148732	+	0.988877i	$0.452481\pi$
$968$		0			0
$969$	−4.30223e9	+	5.59309e11i	−0.00487976	+	0.634391i
$970$		0			0
$971$			1.88405e11i			0.211942i	0.994369	+	0.105971i	$0.0337950\pi$
$971$			1.88405e11i			0.211942i	−0.994369	+	0.105971i	$0.966205\pi$
$972$		0			0
$973$	1.19743e11			0.133598
$974$		0			0
$975$	1.31397e12	+	1.01071e10i	1.45400	+	0.0111843i
$976$		0			0
$977$	4.07993e11	−	2.35555e11i	0.447790	−	0.258531i	−0.259107	−	0.965849i	$-0.583428\pi$
$977$	4.07993e11	−	2.35555e11i	0.447790	−	0.258531i	0.706896	+	0.707317i	$0.250095\pi$
$978$		0			0
$979$	6.51676e10	−	1.12874e11i	0.0709416	−	0.122875i
$980$		0			0
$981$	1.02479e12	+	1.57663e10i	1.10652	+	0.0170237i
$982$		0			0
$983$	9.99436e11	+	5.77025e11i	1.07039	+	0.617988i	0.928287	−	0.371864i	$-0.121281\pi$
$983$	9.99436e11	+	5.77025e11i	1.07039	+	0.617988i	0.142100	+	0.989852i	$0.454615\pi$
$984$		0			0
$985$	−1.89196e10	−	3.27697e10i	−0.0200986	−	0.0348119i
$986$		0			0
$987$	−2.18468e11	+	1.23902e11i	−0.230207	+	0.130560i
$988$		0			0
$989$		−	8.52280e10i		−	0.0890835i
$990$		0			0
$991$	1.61769e12			1.67726			0.838630	−	0.544701i	$-0.183357\pi$
$991$	1.61769e12			1.67726			0.838630	+	0.544701i	$0.183357\pi$
$992$		0			0
$993$	4.13810e11	−	7.04176e11i	0.425603	−	0.724243i
$994$		0			0
$995$	−1.58382e10	+	9.14418e9i	−0.0161589	+	0.00932937i
$996$		0			0
$997$	−4.86307e11	+	8.42308e11i	−0.492186	+	0.852492i	−0.999960	−	0.00899894i	$-0.997136\pi$
$997$	−4.86307e11	+	8.42308e11i	−0.492186	+	0.852492i	0.507773	+	0.861491i	$0.330469\pi$
$998$		0			0
$999$	−4.31051e11	−	9.94855e9i	−0.432779	−	0.00998845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.bg.a.29.1	✓	96
9.5	odd	6	inner	252.9.bg.a.113.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.9.bg.a.29.1	✓	96	1.1	even	1	trivial
252.9.bg.a.113.1	yes	96	9.5	odd	6	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-80.9976 - 0.623037i) q^{3} +(25.8029 - 14.8973i) q^{5} +(453.746 - 785.912i) q^{7} +(6560.22 + 100.929i) q^{9} +O(q^{10})\)	\(q+(-80.9976 - 0.623037i) q^{3} +(25.8029 - 14.8973i) q^{5} +(453.746 - 785.912i) q^{7} +(6560.22 + 100.929i) q^{9} +(18470.7 + 10664.0i) q^{11} +(20811.8 + 36047.1i) q^{13} +(-2099.26 + 1190.57i) q^{15} -50217.1i q^{17} +137508. q^{19} +(-37242.0 + 63374.3i) q^{21} +(22174.3 - 12802.3i) q^{23} +(-194869. + 337522. i) q^{25} +(-531300. - 12262.3i) q^{27} +(-216652. - 125084. i) q^{29} +(19183.8 + 33227.3i) q^{31} +(-1.48943e6 - 875269. i) q^{33} -27038.4i q^{35} +811314. q^{37} +(-1.66325e6 - 2.93270e6i) q^{39} +(788767. - 455395. i) q^{41} +(1.66430e6 - 2.88266e6i) q^{43} +(170777. - 95125.6i) q^{45} +(2.95902e6 + 1.70839e6i) q^{47} +(-411772. - 713209. i) q^{49} +(-31287.1 + 4.06747e6i) q^{51} -3.88980e6i q^{53} +635463. q^{55} +(-1.11378e7 - 85672.6i) q^{57} +(-1.43031e7 + 8.25793e6i) q^{59} +(4.05153e6 - 7.01746e6i) q^{61} +(3.05600e6 - 5.10996e6i) q^{63} +(1.07401e6 + 620081. i) q^{65} +(-1.14683e7 - 1.98637e7i) q^{67} +(-1.80404e6 + 1.02314e6i) q^{69} +1.36266e7i q^{71} -1.57599e7 q^{73} +(1.59942e7 - 2.72171e7i) q^{75} +(1.67620e7 - 9.67753e6i) q^{77} +(-2.82863e7 + 4.89933e7i) q^{79} +(4.30263e7 + 1.32423e6i) q^{81} +(1.95807e7 + 1.13049e7i) q^{83} +(-748101. - 1.29575e6i) q^{85} +(1.74703e7 + 1.02665e7i) q^{87} -6.11097e6i q^{89} +3.77731e7 q^{91} +(-1.53314e6 - 2.70329e6i) q^{93} +(3.54811e6 - 2.04850e6i) q^{95} +(-7.12972e7 + 1.23490e8i) q^{97} +(1.20095e8 + 7.18227e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9}+O(q^{10}) \) 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9	\( 96 q - 42 q^{3} - 882 q^{5} - 14642 q^{9} - 6102 q^{11} - 63218 q^{15} - 354144 q^{19} + 81634 q^{21} - 689760 q^{23} + 4088394 q^{25} - 2939076 q^{27} - 1902474 q^{29} + 613830 q^{31} - 3732526 q^{33} + 4437300 q^{37} - 2690876 q^{39} + 8275176 q^{41} - 2941680 q^{43} + 7299362 q^{45} - 7663950 q^{47} - 39530064 q^{49} - 23625052 q^{51} + 8608908 q^{55} + 28697652 q^{57} + 38291778 q^{59} + 7577556 q^{63} + 42391494 q^{65} + 47903562 q^{67} - 52586968 q^{69} - 32396448 q^{73} + 245976220 q^{75} + 11461314 q^{79} - 16224230 q^{81} - 104964174 q^{83} + 108387294 q^{85} - 213493700 q^{87} - 12590844 q^{91} - 88124258 q^{93} + 293841792 q^{95} + 9277590 q^{97} - 77959808 q^{99}+O(q^{100}) \) 96 * q - 42 * q^3 - 882 * q^5 - 14642 * q^9 - 6102 * q^11 - 63218 * q^15 - 354144 * q^19 + 81634 * q^21 - 689760 * q^23 + 4088394 * q^25 - 2939076 * q^27 - 1902474 * q^29 + 613830 * q^31 - 3732526 * q^33 + 4437300 * q^37 - 2690876 * q^39 + 8275176 * q^41 - 2941680 * q^43 + 7299362 * q^45 - 7663950 * q^47 - 39530064 * q^49 - 23625052 * q^51 + 8608908 * q^55 + 28697652 * q^57 + 38291778 * q^59 + 7577556 * q^63 + 42391494 * q^65 + 47903562 * q^67 - 52586968 * q^69 - 32396448 * q^73 + 245976220 * q^75 + 11461314 * q^79 - 16224230 * q^81 - 104964174 * q^83 + 108387294 * q^85 - 213493700 * q^87 - 12590844 * q^91 - 88124258 * q^93 + 293841792 * q^95 + 9277590 * q^97 - 77959808 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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